LMFDB - Embedded newform 75.9.k.a.13.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(13,75)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("75.13");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.k (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$40$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.14
Character	$\chi$	$=$	75.13
Dual form			75.9.k.a.52.14

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.6504 + 1.84524i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(-111.144 + 36.1127i) q^{4} +(-559.413 - 278.715i) q^{5} +(170.462 - 524.628i) q^{6} +(285.116 - 285.116i) q^{7} +(3918.78 - 1996.72i) q^{8} +(-1285.49 - 1769.32i) q^{9} +O(q^{10})$	\(q+(-11.6504 + 1.84524i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(-111.144 + 36.1127i) q^{4} +(-559.413 - 278.715i) q^{5} +(170.462 - 524.628i) q^{6} +(285.116 - 285.116i) q^{7} +(3918.78 - 1996.72i) q^{8} +(-1285.49 - 1769.32i) q^{9} +(7031.68 + 2214.88i) q^{10} +(5947.63 + 4321.20i) q^{11} +(854.938 - 5397.87i) q^{12} +(28462.5 + 4508.02i) q^{13} +(-2795.61 + 3847.82i) q^{14} +(23490.5 - 17392.4i) q^{15} +(-17767.6 + 12908.9i) q^{16} +(63088.2 + 123817. i) q^{17} +(18241.3 + 18241.3i) q^{18} +(-135283. - 43956.1i) q^{19} +(72240.3 + 10775.4i) q^{20} +(5826.98 + 17933.6i) q^{21} +(-77265.9 - 39368.9i) q^{22} +(-55600.3 - 351046. i) q^{23} +205681. i q^{24} +(235261. + 311833. i) q^{25} -339918. q^{26} +(101017. - 15999.5i) q^{27} +(-21392.5 + 41985.1i) q^{28} +(646624. - 210101. i) q^{29} +(-241580. + 245974. i) q^{30} +(388161. - 1.19464e6i) q^{31} +(-612971. + 612971. i) q^{32} +(-306331. + 156084. i) q^{33} +(-963475. - 1.32611e6i) q^{34} +(-238964. + 80031.7i) q^{35} +(206769. + 150226. i) q^{36} +(-4340.75 + 27406.4i) q^{37} +(1.65721e6 + 262476. i) q^{38} +(-792131. + 1.09027e6i) q^{39} +(-2.74874e6 + 24769.7i) q^{40} +(-4.40813e6 + 3.20269e6i) q^{41} +(-100978. - 198181. i) q^{42} +(-1.84485e6 - 1.84485e6i) q^{43} +(-817091. - 265489. i) q^{44} +(225983. + 1.34806e6i) q^{45} +(1.29553e6 + 3.98723e6i) q^{46} +(-3.29098e6 - 1.67684e6i) q^{47} +(-160668. - 1.01442e6i) q^{48} +5.60222e6i q^{49} +(-3.31630e6 - 3.19887e6i) q^{50} -6.49868e6 q^{51} +(-3.32623e6 + 526822. i) q^{52} +(-2.77062e6 + 5.43766e6i) q^{53} +(-1.14736e6 + 372800. i) q^{54} +(-2.12280e6 - 4.07503e6i) q^{55} +(548011. - 1.68660e6i) q^{56} +(4.70377e6 - 4.70377e6i) q^{57} +(-7.14574e6 + 3.64094e6i) q^{58} +(2.34200e6 + 3.22349e6i) q^{59} +(-1.98273e6 + 2.78136e6i) q^{60} +(-8.23867e6 - 5.98574e6i) q^{61} +(-2.31784e6 + 1.46343e7i) q^{62} +(-870974. - 137949. i) q^{63} +(9.31497e6 - 1.28210e7i) q^{64} +(-1.46659e7 - 1.04548e7i) q^{65} +(3.28087e6 - 2.38369e6i) q^{66} +(6.19395e6 + 1.21563e7i) q^{67} +(-1.14832e7 - 1.14832e7i) q^{68} +(1.58079e7 + 5.13631e6i) q^{69} +(2.63634e6 - 1.37335e6i) q^{70} +(1.33236e7 + 4.10057e7i) q^{71} +(-8.57038e6 - 4.36683e6i) q^{72} +(-2.59856e6 - 1.64066e7i) q^{73} -327305. i q^{74} +(-1.79884e7 + 3.18239e6i) q^{75} +1.66232e7 q^{76} +(2.92781e6 - 463719. i) q^{77} +(7.21682e6 - 1.41638e7i) q^{78} +(1.50653e7 - 4.89501e6i) q^{79} +(1.35373e7 - 2.26933e6i) q^{80} +(-1.47802e6 + 4.54887e6i) q^{81} +(4.54467e7 - 4.54467e7i) q^{82} +(-1.41366e7 + 7.20295e6i) q^{83} +(-1.29526e6 - 1.78277e6i) q^{84} +(-782620. - 8.68487e7i) q^{85} +(2.48975e7 + 1.80891e7i) q^{86} +(-4.97396e6 + 3.14043e7i) q^{87} +(3.19357e7 + 5.05812e6i) q^{88} +(-4.12406e7 + 5.67629e7i) q^{89} +(-5.12030e6 - 1.52885e7i) q^{90} +(9.40043e6 - 6.82981e6i) q^{91} +(1.88569e7 + 3.70087e7i) q^{92} +(4.15374e7 + 4.15374e7i) q^{93} +(4.14355e7 + 1.34632e7i) q^{94} +(6.34279e7 + 6.22949e7i) q^{95} +(-1.25274e7 - 3.85555e7i) q^{96} +(-4.80547e7 - 2.44851e7i) q^{97} +(-1.03375e7 - 6.52681e7i) q^{98} -1.60781e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) $ 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8	\( 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8} + 25496 q^{10} - 22680 q^{12} - 133420 q^{13} + 59616 q^{15} + 1310720 q^{16} + 168000 q^{17} - 718900 q^{19} - 641844 q^{20} + 2257100 q^{22} + 1089120 q^{23} - 1459756 q^{25} + 1827840 q^{26} + 3260740 q^{28} + 3913800 q^{29} + 3585384 q^{30} - 641460 q^{32} - 1458000 q^{33} - 4121600 q^{34} + 853140 q^{35} - 22394880 q^{36} - 14553460 q^{37} + 17491260 q^{38} + 3203652 q^{40} + 8749440 q^{41} + 9643860 q^{42} - 23946520 q^{43} + 4277700 q^{44} - 2204496 q^{45} + 26491200 q^{47} - 3661200 q^{48} - 47100924 q^{50} - 169691020 q^{52} - 97028940 q^{53} + 27431764 q^{55} - 4714200 q^{57} + 179119320 q^{58} + 95587200 q^{59} + 38705364 q^{60} + 36738240 q^{61} - 296094660 q^{62} - 9928980 q^{63} - 59695100 q^{64} + 24018972 q^{65} - 88558160 q^{67} + 197811840 q^{68} + 220501420 q^{70} + 38185020 q^{72} + 110964400 q^{73} + 51345576 q^{75} - 97175880 q^{77} - 131709240 q^{78} - 138506200 q^{79} - 339741204 q^{80} + 382637520 q^{81} + 217169400 q^{82} + 862340400 q^{83} + 743029200 q^{84} + 619431268 q^{85} - 335756340 q^{87} - 1380992420 q^{88} - 1141686000 q^{89} - 265834224 q^{90} - 407198400 q^{92} + 402028920 q^{93} + 290042200 q^{94} + 1436174256 q^{95} - 165325860 q^{96} + 1057772920 q^{97} + 1077594720 q^{98}+O(q^{100}) \) 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8 + 25496 * q^10 - 22680 * q^12 - 133420 * q^13 + 59616 * q^15 + 1310720 * q^16 + 168000 * q^17 - 718900 * q^19 - 641844 * q^20 + 2257100 * q^22 + 1089120 * q^23 - 1459756 * q^25 + 1827840 * q^26 + 3260740 * q^28 + 3913800 * q^29 + 3585384 * q^30 - 641460 * q^32 - 1458000 * q^33 - 4121600 * q^34 + 853140 * q^35 - 22394880 * q^36 - 14553460 * q^37 + 17491260 * q^38 + 3203652 * q^40 + 8749440 * q^41 + 9643860 * q^42 - 23946520 * q^43 + 4277700 * q^44 - 2204496 * q^45 + 26491200 * q^47 - 3661200 * q^48 - 47100924 * q^50 - 169691020 * q^52 - 97028940 * q^53 + 27431764 * q^55 - 4714200 * q^57 + 179119320 * q^58 + 95587200 * q^59 + 38705364 * q^60 + 36738240 * q^61 - 296094660 * q^62 - 9928980 * q^63 - 59695100 * q^64 + 24018972 * q^65 - 88558160 * q^67 + 197811840 * q^68 + 220501420 * q^70 + 38185020 * q^72 + 110964400 * q^73 + 51345576 * q^75 - 97175880 * q^77 - 131709240 * q^78 - 138506200 * q^79 - 339741204 * q^80 + 382637520 * q^81 + 217169400 * q^82 + 862340400 * q^83 + 743029200 * q^84 + 619431268 * q^85 - 335756340 * q^87 - 1380992420 * q^88 - 1141686000 * q^89 - 265834224 * q^90 - 407198400 * q^92 + 402028920 * q^93 + 290042200 * q^94 + 1436174256 * q^95 - 165325860 * q^96 + 1057772920 * q^97 + 1077594720 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−11.6504	+	1.84524i	−0.728150	+	0.115328i	−0.509494	−	0.860474i	$-0.670167\pi$
$2$	−11.6504	+	1.84524i	−0.728150	+	0.115328i	−0.218656	+	0.975802i	$0.570167\pi$
$3$	−21.2310	+	41.6683i	−0.262112	+	0.514423i
$3$	−21.2310	+	41.6683i	−0.262112	+	0.514423i
$4$	−111.144	+	36.1127i	−0.434155	+	0.141065i
$5$	−559.413	−	278.715i	−0.895061	−	0.445943i
$5$	−559.413	−	278.715i	−0.895061	−	0.445943i
$6$	170.462	−	524.628i	0.131529	−	0.404806i
$7$	285.116	−	285.116i	0.118749	−	0.118749i	−0.645235	−	0.763984i	$-0.723241\pi$
$7$	285.116	−	285.116i	0.118749	−	0.118749i	0.763984	+	0.645235i	$0.223241\pi$
$8$	3918.78	−	1996.72i	0.956735	−	0.487481i
$9$	−1285.49	−	1769.32i	−0.195928	−	0.269672i
$10$	7031.68	+	2214.88i	0.703168	+	0.221488i
$11$	5947.63	+	4321.20i	0.406231	+	0.295144i	0.772074	−	0.635532i	$-0.219219\pi$
$11$	5947.63	+	4321.20i	0.406231	+	0.295144i	−0.365843	+	0.930676i	$0.619219\pi$
$12$	854.938	−	5397.87i	0.0412297	−	0.260314i
$13$	28462.5	+	4508.02i	0.996553	+	0.157838i	0.633345	−	0.773870i	$-0.281681\pi$
$13$	28462.5	+	4508.02i	0.996553	+	0.157838i	0.363208	+	0.931708i	$0.381681\pi$
$14$	−2795.61	+	3847.82i	−0.0727719	+	0.100162i
$15$	23490.5	−	17392.4i	0.464009	−	0.343553i
$16$	−17767.6	+	12908.9i	−0.271112	+	0.196975i
$17$	63088.2	+	123817.i	0.755357	+	1.48247i	0.872110	+	0.489310i	$0.162751\pi$
$17$	63088.2	+	123817.i	0.755357	+	1.48247i	−0.116753	+	0.993161i	$0.537249\pi$
$18$	18241.3	+	18241.3i	0.173766	+	0.173766i
$19$	−135283.	−	43956.1i	−1.03807	−	0.337291i	−0.260097	−	0.965583i	$-0.583754\pi$
$19$	−135283.	−	43956.1i	−1.03807	−	0.337291i	−0.777978	+	0.628292i	$0.783754\pi$
$20$	72240.3	+	10775.4i	0.451502	+	0.0673462i
$21$	5826.98	+	17933.6i	0.0299617	+	0.0922125i
$22$	−77265.9	−	39368.9i	−0.329835	−	0.168060i
$23$	−55600.3	−	351046.i	−0.198685	−	1.25445i	−0.862309	−	0.506383i	$-0.830982\pi$
$23$	−55600.3	−	351046.i	−0.198685	−	1.25445i	0.663624	−	0.748067i	$-0.269018\pi$
$24$			205681.i			0.619940i
$25$	235261.	+	311833.i	0.602269	+	0.798293i
$26$	−339918.			−0.743843
$27$	101017.	−	15999.5i	0.190081	−	0.0301058i
$28$	−21392.5	+	41985.1i	−0.0348040	+	0.0683067i
$29$	646624.	−	210101.i	0.914239	−	0.297054i	0.186137	−	0.982524i	$-0.440403\pi$
$29$	646624.	−	210101.i	0.914239	−	0.297054i	0.728101	+	0.685470i	$0.240403\pi$
$30$	−241580.	+	245974.i	−0.298247	+	0.303671i
$31$	388161.	−	1.19464e6i	0.420306	−	1.29357i	−0.487112	−	0.873339i	$-0.661950\pi$
$31$	388161.	−	1.19464e6i	0.420306	−	1.29357i	0.907418	−	0.420229i	$-0.138050\pi$
$32$	−612971.	+	612971.i	−0.584575	+	0.584575i
$33$	−306331.	+	156084.i	−0.258307	+	0.131614i
$34$	−963475.	−	1.32611e6i	−0.720983	−	0.992348i
$35$	−238964.	+	80031.7i	−0.159243	+	0.0533322i
$36$	206769.	+	150226.i	0.123105	+	0.0894408i
$37$	−4340.75	+	27406.4i	−0.00231610	+	0.0146233i	−0.988819	−	0.149119i	$-0.952356\pi$
$37$	−4340.75	+	27406.4i	−0.00231610	+	0.0146233i	0.986503	+	0.163742i	$0.0523564\pi$
$38$	1.65721e6	+	262476.i	0.794773	+	0.125880i
$39$	−792131.	+	1.09027e6i	−0.342404	+	0.471278i
$40$	−2.74874e6	+	24769.7i	−1.07372	+	0.00967566i
$41$	−4.40813e6	+	3.20269e6i	−1.55998	+	1.13339i	−0.623953	+	0.781462i	$0.714474\pi$
$41$	−4.40813e6	+	3.20269e6i	−1.55998	+	1.13339i	−0.936027	+	0.351929i	$0.885526\pi$
$42$	−100978.	−	198181.i	−0.0324512	−	0.0636892i
$43$	−1.84485e6	−	1.84485e6i	−0.539620	−	0.539620i	0.383797	−	0.923417i	$-0.374616\pi$
$43$	−1.84485e6	−	1.84485e6i	−0.539620	−	0.539620i	−0.923417	+	0.383797i	$0.874616\pi$
$44$	−817091.	−	265489.i	−0.218002	−	0.0708330i
$45$	225983.	+	1.34806e6i	0.0551094	+	0.328746i
$46$	1.29553e6	+	3.98723e6i	0.289345	+	0.890513i
$47$	−3.29098e6	−	1.67684e6i	−0.674426	−	0.343637i	0.0830080	−	0.996549i	$-0.473547\pi$
$47$	−3.29098e6	−	1.67684e6i	−0.674426	−	0.343637i	−0.757434	+	0.652912i	$0.773547\pi$
$48$	−160668.	−	1.01442e6i	−0.0302666	−	0.191096i
$49$			5.60222e6i			0.971797i
$50$	−3.31630e6	−	3.19887e6i	−0.530608	−	0.511819i
$51$	−6.49868e6			−0.960605
$52$	−3.32623e6	+	526822.i	−0.454923	+	0.0720528i
$53$	−2.77062e6	+	5.43766e6i	−0.351135	+	0.689141i	−0.997251	−	0.0740980i	$-0.976392\pi$
$53$	−2.77062e6	+	5.43766e6i	−0.351135	+	0.689141i	0.646116	+	0.763239i	$0.276392\pi$
$54$	−1.14736e6	+	372800.i	−0.134935	+	0.0438431i
$55$	−2.12280e6	−	4.07503e6i	−0.231984	−	0.445328i
$56$	548011.	−	1.68660e6i	0.0557233	−	0.171499i
$57$	4.70377e6	−	4.70377e6i	0.445602	−	0.445602i
$58$	−7.14574e6	+	3.64094e6i	−0.631444	+	0.321737i
$59$	2.34200e6	+	3.22349e6i	0.193276	+	0.266022i	0.894646	−	0.446776i	$-0.147428\pi$
$59$	2.34200e6	+	3.22349e6i	0.193276	+	0.266022i	−0.701370	+	0.712798i	$0.747428\pi$
$60$	−1.98273e6	+	2.78136e6i	−0.152988	+	0.214611i
$61$	−8.23867e6	−	5.98574e6i	−0.595029	−	0.432314i	0.249082	−	0.968482i	$-0.419871\pi$
$61$	−8.23867e6	−	5.98574e6i	−0.595029	−	0.432314i	−0.844111	+	0.536169i	$0.819871\pi$
$62$	−2.31784e6	+	1.46343e7i	−0.156862	+	0.990385i
$63$	−870974.	−	137949.i	−0.0552895	−	0.00875700i
$64$	9.31497e6	−	1.28210e7i	0.555215	−	0.764188i
$65$	−1.46659e7	−	1.04548e7i	−0.821589	−	0.585681i
$66$	3.28087e6	−	2.38369e6i	0.172907	−	0.125625i
$67$	6.19395e6	+	1.21563e7i	0.307375	+	0.603257i	0.992086	−	0.125557i	$-0.0400718\pi$
$67$	6.19395e6	+	1.21563e7i	0.307375	+	0.603257i	−0.684712	+	0.728814i	$0.740072\pi$
$68$	−1.14832e7	−	1.14832e7i	−0.537067	−	0.537067i
$69$	1.58079e7	+	5.13631e6i	0.697395	+	0.226597i
$70$	2.63634e6	−	1.37335e6i	0.109802	−	0.0571989i
$71$	1.33236e7	+	4.10057e7i	0.524309	+	1.61366i	0.765679	+	0.643223i	$0.222403\pi$
$71$	1.33236e7	+	4.10057e7i	0.524309	+	1.61366i	−0.241370	+	0.970433i	$0.577597\pi$
$72$	−8.57038e6	−	4.36683e6i	−0.318912	−	0.162494i
$73$	−2.59856e6	−	1.64066e7i	−0.0915041	−	0.577734i	−0.990254	−	0.139273i	$-0.955524\pi$
$73$	−2.59856e6	−	1.64066e7i	−0.0915041	−	0.577734i	0.898750	−	0.438461i	$-0.144476\pi$
$74$		−	327305.i		−	0.0109151i
$75$	−1.79884e7	+	3.18239e6i	−0.568522	+	0.100579i
$76$	1.66232e7			0.498265
$77$	2.92781e6	−	463719.i	0.0832875	−	0.0131914i
$78$	7.21682e6	−	1.41638e7i	0.194970	−	0.382650i
$79$	1.50653e7	−	4.89501e6i	0.386785	−	0.125674i	−0.109169	−	0.994023i	$-0.534819\pi$
$79$	1.50653e7	−	4.89501e6i	0.386785	−	0.125674i	0.495953	+	0.868349i	$0.334819\pi$
$80$	1.35373e7	−	2.26933e6i	0.330502	−	0.0554036i
$81$	−1.47802e6	+	4.54887e6i	−0.0343352	+	0.105673i
$82$	4.54467e7	−	4.54467e7i	1.00519	−	1.00519i
$83$	−1.41366e7	+	7.20295e6i	−0.297873	+	0.151774i	−0.596540	−	0.802583i	$-0.703458\pi$
$83$	−1.41366e7	+	7.20295e6i	−0.297873	+	0.151774i	0.298666	+	0.954358i	$0.403458\pi$
$84$	−1.29526e6	−	1.78277e6i	−0.0260160	−	0.0358079i
$85$	−782620.	−	8.68487e7i	−0.0149925	−	1.66375i
$86$	2.48975e7	+	1.80891e7i	0.455157	+	0.330691i
$87$	−4.97396e6	+	3.14043e7i	−0.0868211	+	0.548167i
$88$	3.19357e7	+	5.05812e6i	0.532532	+	0.0843448i
$89$	−4.12406e7	+	5.67629e7i	−0.657303	+	0.904699i	−0.999388	−	0.0349693i	$-0.988867\pi$
$89$	−4.12406e7	+	5.67629e7i	−0.657303	+	0.904699i	0.342086	+	0.939669i	$0.388867\pi$
$90$	−5.12030e6	−	1.52885e7i	−0.0780414	−	0.233021i
$91$	9.40043e6	−	6.82981e6i	0.137083	−	0.0995963i
$92$	1.88569e7	+	3.70087e7i	0.263219	+	0.516597i
$93$	4.15374e7	+	4.15374e7i	0.555274	+	0.555274i
$94$	4.14355e7	+	1.34632e7i	0.530714	+	0.172440i
$95$	6.34279e7	+	6.22949e7i	0.778728	+	0.764818i
$96$	−1.25274e7	−	3.85555e7i	−0.147495	−	0.453943i
$97$	−4.80547e7	−	2.44851e7i	−0.542811	−	0.276576i	0.161011	−	0.986953i	$-0.448525\pi$
$97$	−4.80547e7	−	2.44851e7i	−0.542811	−	0.276576i	−0.703822	+	0.710377i	$0.748525\pi$
$98$	−1.03375e7	−	6.52681e7i	−0.112075	−	0.707614i
$99$		−	1.60781e7i		−	0.167376i
$100$	−3.74089e7	−	2.61623e7i	−0.374089	−	0.261623i
$101$	1.27884e8			1.22894			0.614472	−	0.788939i	$-0.289369\pi$
$101$	1.27884e8			1.22894			0.614472	+	0.788939i	$0.289369\pi$
$102$	7.57123e7	−	1.19916e7i	0.699464	−	0.110784i
$103$	5.62421e7	−	1.10381e8i	0.499704	−	0.980724i	−0.494082	−	0.869415i	$-0.664496\pi$
$103$	5.62421e7	−	1.10381e8i	0.499704	−	0.980724i	0.993786	−	0.111309i	$-0.0355043\pi$
$104$	1.20540e8	−	3.91658e7i	1.03038	−	0.334791i
$105$	1.73866e6	−	1.16563e7i	0.0143040	−	0.0958971i
$106$	2.22451e7	−	6.84633e7i	0.176202	−	0.542294i
$107$	−1.51534e8	+	1.51534e8i	−1.15604	+	1.15604i	−0.170726	+	0.985319i	$0.554611\pi$
$107$	−1.51534e8	+	1.51534e8i	−1.15604	+	1.15604i	−0.985319	+	0.170726i	$0.945389\pi$
$108$	−1.06496e7	+	5.42623e6i	−0.0782775	+	0.0398844i
$109$	4.40462e7	+	6.06244e7i	0.312035	+	0.429479i	0.936014	−	0.351962i	$-0.114485\pi$
$109$	4.40462e7	+	6.06244e7i	0.312035	+	0.429479i	−0.623980	+	0.781440i	$0.714485\pi$
$110$	3.22509e7	+	4.35586e7i	0.220278	+	0.297511i
$111$	−1.04982e6	−	762737.i	−0.00691548	−	0.00502439i
$112$	−1.38529e6	+	8.74637e6i	−0.00880376	+	0.0555848i
$113$	−1.93326e8	−	3.06198e7i	−1.18570	−	0.187797i	−0.467732	−	0.883871i	$-0.654929\pi$
$113$	−1.93326e8	−	3.06198e7i	−1.18570	−	0.187797i	−0.717970	+	0.696074i	$0.754929\pi$
$114$	−4.61212e7	+	6.34804e7i	−0.273075	+	0.375855i
$115$	−6.67382e7	+	2.11877e8i	−0.381578	+	1.21141i
$116$	−6.42807e7	+	4.67027e7i	−0.355017	+	0.257935i
$117$	−2.86121e7	−	5.61543e7i	−0.152688	−	0.299668i
$118$	−3.32334e7	−	3.32334e7i	−0.171414	−	0.171414i
$119$	5.32898e7	+	1.73149e7i	0.265739	+	0.0863440i
$120$	5.73264e7	−	1.15061e8i	0.276458	−	0.554885i
$121$	−4.95391e7	−	1.52466e8i	−0.231103	−	0.711263i
$122$	1.07029e8	+	5.45340e7i	0.483128	+	0.246166i
$123$	−3.98615e7	−	2.51676e8i	−0.174154	−	1.09956i
$124$			1.46794e8i			0.620899i
$125$	−4.46959e7	−	2.40014e8i	−0.183074	−	0.983099i
$126$	1.04017e7			0.0412690
$127$	−2.47277e8	+	3.91649e7i	−0.950538	+	0.150550i	−0.612402	−	0.790547i	$-0.709796\pi$
$127$	−2.47277e8	+	3.91649e7i	−0.950538	+	0.150550i	−0.338136	+	0.941097i	$0.609796\pi$
$128$	1.58839e7	−	3.11740e7i	0.0591723	−	0.116132i
$129$	1.16040e8	−	3.77037e7i	0.419033	−	0.136152i
$130$	1.90155e8	+	9.47402e7i	0.665785	+	0.331712i
$131$	−7.75132e7	+	2.38561e8i	−0.263203	+	0.810055i	0.728899	+	0.684621i	$0.240032\pi$
$131$	−7.75132e7	+	2.38561e8i	−0.263203	+	0.810055i	−0.992102	+	0.125434i	$0.959968\pi$
$132$	2.84101e7	−	2.84101e7i	0.0935789	−	0.0935789i
$133$	−5.11039e7	+	2.60387e7i	−0.163323	+	0.0832173i
$134$	−9.45933e7	−	1.30196e8i	−0.293387	−	0.403813i
$135$	−6.09694e7	−	1.92045e7i	−0.183559	−	0.0578187i
$136$	4.94458e8	+	3.59245e8i	1.44535	+	1.05011i
$137$	−2.10829e7	+	1.33112e8i	−0.0598477	+	0.377864i	0.939526	+	0.342478i	$0.111266\pi$
$137$	−2.10829e7	+	1.33112e8i	−0.0598477	+	0.377864i	−0.999374	+	0.0353860i	$0.988734\pi$
$138$	−1.93647e8	−	3.06706e7i	−0.533941	−	0.0845680i
$139$	2.60488e8	−	3.58532e8i	0.697797	−	0.960435i	−0.302177	−	0.953252i	$-0.597713\pi$
$139$	2.60488e8	−	3.58532e8i	0.697797	−	0.960435i	0.999974	−	0.00718351i	$-0.00228660\pi$
$140$	2.36691e7	−	1.75246e7i	0.0616126	−	0.0456181i
$141$	1.39742e8	−	1.01529e8i	0.353550	−	0.256869i
$142$	−2.30890e8	−	4.53148e8i	−0.567875	−	1.11452i
$143$	1.49804e8	+	1.49804e8i	0.358245	+	0.358245i
$144$	4.56801e7	+	1.48424e7i	0.106237	+	0.0345186i
$145$	−4.20288e8	−	6.26903e7i	−0.950769	−	0.141817i
$146$	6.05484e7	+	1.86349e8i	0.133257	+	0.410124i
$147$	−2.33435e8	−	1.18941e8i	−0.499915	−	0.254719i
$148$	−507274.	−	3.20280e6i	−0.00105729	−	0.00667549i
$149$			6.91390e8i			1.40274i	0.712796	+	0.701372i	$0.247429\pi$
$149$			6.91390e8i			1.40274i	−0.712796	+	0.701372i	$0.752571\pi$
$150$	2.03700e8	−	7.02690e7i	0.402370	−	0.138803i
$151$	−1.41189e7			−0.0271576			−0.0135788	−	0.999908i	$-0.504322\pi$
$151$	−1.41189e7			−0.0271576			−0.0135788	+	0.999908i	$0.504322\pi$
$152$	−6.17913e8	+	9.78678e7i	−1.15758	+	0.183343i
$153$	1.37974e8	−	2.70789e8i	0.251786	−	0.494157i
$154$	−3.32545e7	+	1.08050e7i	−0.0591244	+	0.0192107i
$155$	−5.50106e8	+	5.60110e8i	−0.953058	+	0.970391i
$156$	4.86674e7	−	1.49783e8i	0.0821751	−	0.252909i
$157$	−7.32583e8	+	7.32583e8i	−1.20575	+	1.20575i	−0.233364	+	0.972390i	$0.574973\pi$
$157$	−7.32583e8	+	7.32583e8i	−1.20575	+	1.20575i	−0.972390	+	0.233364i	$0.925027\pi$
$158$	−1.66484e8	+	8.48279e7i	−0.267143	+	0.136116i
$159$	−1.67754e8	−	2.30894e8i	−0.262473	−	0.361264i
$160$	5.13748e8	−	1.72060e8i	0.783918	−	0.262543i
$161$	−1.15941e8	−	8.42364e7i	−0.172558	−	0.125371i
$162$	8.82574e6	−	5.57235e7i	0.0128142	−	0.0809056i
$163$	−7.50845e8	−	1.18922e8i	−1.06365	−	0.168466i	−0.400006	−	0.916513i	$-0.630992\pi$
$163$	−7.50845e8	−	1.18922e8i	−1.06365	−	0.168466i	−0.663646	+	0.748047i	$0.730992\pi$
$164$	3.74277e8	−	5.15148e8i	0.517390	−	0.712126i
$165$	2.14869e8	−	1.93625e6i	0.289893	−	0.00261231i
$166$	1.51406e8	−	1.10003e8i	0.199393	−	0.144867i
$167$	4.80679e8	+	9.43385e8i	0.618001	+	1.21290i	0.961775	+	0.273843i	$0.0882947\pi$
$167$	4.80679e8	+	9.43385e8i	0.618001	+	1.21290i	−0.343774	+	0.939053i	$0.611705\pi$
$168$	5.86430e7	+	5.86430e7i	0.0736172	+	0.0736172i
$169$	1.39879e7	+	4.54495e6i	0.0171477	+	0.00557162i
$170$	1.69375e8	+	1.01038e9i	0.202793	+	1.20973i
$171$	9.61320e7	+	2.95864e8i	0.112430	+	0.346025i
$172$	2.71666e8	+	1.38421e8i	0.310400	+	0.158157i
$173$	−1.41658e8	−	8.94394e8i	−0.158146	−	0.998492i	−0.931295	−	0.364267i	$-0.881320\pi$
$173$	−1.41658e8	−	8.94394e8i	−0.158146	−	0.998492i	0.773149	−	0.634224i	$-0.218680\pi$
$174$		−	3.75051e8i		−	0.409160i
$175$	1.55985e8	+	2.18318e7i	0.166315	+	0.0232776i
$176$	−1.61457e8			−0.168270
$177$	−1.84040e8	+	2.91491e7i	−0.187508	+	0.0296983i
$178$	3.75729e8	−	7.37409e8i	0.374278	−	0.734562i
$179$	−1.11138e9	+	3.61108e8i	−1.08255	+	0.351743i	−0.795364	−	0.606132i	$-0.792720\pi$
$179$	−1.11138e9	+	3.61108e8i	−1.08255	+	0.351743i	−0.287188	+	0.957874i	$0.592720\pi$
$180$	−7.37988e7	−	1.41668e8i	−0.0703007	−	0.134953i
$181$	−2.78766e8	+	8.57953e8i	−0.259732	+	0.799372i	0.733129	+	0.680090i	$0.238059\pi$
$181$	−2.78766e8	+	8.57953e8i	−0.259732	+	0.799372i	−0.992860	+	0.119282i	$0.961941\pi$
$182$	−9.69161e7	+	9.69161e7i	−0.0883305	+	0.0883305i
$183$	4.24331e8	−	2.16207e8i	0.378356	−	0.192782i
$184$	−9.18827e8	−	1.26466e9i	−0.801609	−	1.10332i
$185$	1.00668e7	−	1.41217e7i	0.00859421	−	0.0120559i
$186$	−5.60574e8	−	4.07281e8i	−0.468361	−	0.340285i
$187$	−1.59816e8	+	1.00904e9i	−0.130693	+	0.825165i
$188$	4.26327e8	+	6.75236e7i	0.341280	+	0.0540535i
$189$	2.42398e7	−	3.33632e7i	0.0189968	−	0.0261469i
$190$	−8.53909e8	−	6.08721e8i	−0.655235	−	0.467094i
$191$	−5.52561e7	+	4.01459e7i	−0.0415190	+	0.0301653i	−0.608351	−	0.793668i	$-0.708169\pi$
$191$	−5.52561e7	+	4.01459e7i	−0.0415190	+	0.0301653i	0.566832	+	0.823833i	$0.308169\pi$
$192$	3.36460e8	+	6.60340e8i	0.247588	+	0.485918i
$193$	−1.20261e7	−	1.20261e7i	−0.00866754	−	0.00866754i	0.702760	−	0.711427i	$-0.251951\pi$
$193$	−1.20261e7	−	1.20261e7i	−0.00866754	−	0.00866754i	−0.711427	+	0.702760i	$0.751951\pi$
$194$	6.05037e8	+	1.96588e8i	0.427145	+	0.138788i
$195$	7.47004e8	−	3.89136e8i	0.516636	−	0.269130i
$196$	−2.02311e8	−	6.22651e8i	−0.137087	−	0.421910i
$197$	−1.96684e9	−	1.00215e9i	−1.30588	−	0.665380i	−0.344032	−	0.938958i	$-0.611793\pi$
$197$	−1.96684e9	−	1.00215e9i	−1.30588	−	0.665380i	−0.961850	+	0.273577i	$0.911793\pi$
$198$	2.96680e7	+	1.87316e8i	0.0193031	+	0.121875i
$199$		−	1.62770e9i		−	1.03792i	−0.854799	−	0.518959i	$-0.826320\pi$
$199$		−	1.62770e9i		−	1.03792i	0.854799	−	0.518959i	$-0.173680\pi$
$200$	1.54458e9	+	7.52256e8i	0.965364	+	0.470160i
$201$	−6.38036e8			−0.390896
$202$	−1.48990e9	+	2.35978e8i	−0.894855	+	0.141731i
$203$	1.24460e8	−	2.44266e8i	0.0732899	−	0.143840i
$204$	7.22287e8	−	2.34685e8i	0.417051	−	0.135508i
$205$	3.35860e9	−	5.63019e8i	1.90171	−	0.318792i
$206$	−4.51563e8	+	1.38977e9i	−0.250755	+	0.771744i
$207$	−5.49640e8	+	5.49640e8i	−0.299362	+	0.299362i
$208$	−5.63905e8	+	2.87324e8i	−0.301268	+	0.153504i
$209$	−6.14669e8	−	8.46020e8i	−0.322149	−	0.443400i
$210$	1.25266e6	+	1.39009e8i	0.000644102	+	0.0714771i
$211$	1.39750e9	+	1.01535e9i	0.705056	+	0.512253i	0.881575	−	0.472044i	$-0.156484\pi$
$211$	1.39750e9	+	1.01535e9i	0.705056	+	0.512253i	−0.176519	+	0.984297i	$0.556484\pi$
$212$	1.11568e8	−	7.04415e8i	0.0552329	−	0.348727i
$213$	−1.99151e9	−	3.15424e8i	−0.967529	−	0.153242i
$214$	1.48581e9	−	2.04505e9i	0.708450	−	0.975098i
$215$	5.17848e8	+	1.54622e9i	0.242353	+	0.723633i
$216$	3.63916e8	−	2.64401e8i	0.167181	−	0.121464i
$217$	−2.29939e8	−	4.51281e8i	−0.103699	−	0.203521i
$218$	−6.25023e8	−	6.25023e8i	−0.276739	−	0.276739i
$219$	7.38806e8	+	2.40053e8i	0.321184	+	0.104359i
$220$	3.83096e8	+	3.76253e8i	0.163537	+	0.160616i
$221$	1.23748e9	+	3.80856e9i	0.518762	+	1.59658i
$222$	1.36382e7	+	6.94903e6i	0.00561496	+	0.00286096i
$223$	2.87984e8	+	1.81826e9i	0.116453	+	0.735252i	0.974948	+	0.222432i	$0.0713994\pi$
$223$	2.87984e8	+	1.81826e9i	0.116453	+	0.735252i	−0.858496	+	0.512821i	$0.828601\pi$
$224$			3.49536e8i			0.138835i
$225$	2.49307e8	−	8.17110e8i	0.0972759	−	0.318824i
$226$	2.30882e9			0.885027
$227$	4.08599e9	−	6.47157e8i	1.53884	−	0.243729i	0.671335	−	0.741154i	$-0.265721\pi$
$227$	4.08599e9	−	6.47157e8i	1.53884	−	0.243729i	0.867507	+	0.497426i	$0.165721\pi$
$228$	−3.52928e8	+	6.92660e8i	−0.130601	+	0.256319i
$229$	3.31923e9	−	1.07848e9i	1.20697	−	0.392167i	0.364646	−	0.931146i	$-0.381190\pi$
$229$	3.31923e9	−	1.07848e9i	1.20697	−	0.392167i	0.842319	+	0.538979i	$0.181190\pi$
$230$	3.86563e8	−	2.59160e9i	0.138137	−	0.926096i
$231$	−4.28380e7	+	1.31842e8i	−0.0150446	+	0.0463026i
$232$	2.11447e9	−	2.11447e9i	0.729876	−	0.729876i
$233$	−5.34066e7	+	2.72120e7i	−0.0181205	+	0.00923288i	−0.463027	−	0.886344i	$-0.653237\pi$
$233$	−5.34066e7	+	2.72120e7i	−0.0181205	+	0.00923288i	0.444907	+	0.895577i	$0.353237\pi$
$234$	4.36960e8	+	6.01424e8i	0.145740	+	0.200594i
$235$	1.37366e9	+	1.85529e9i	0.450410	+	0.608332i
$236$	−3.76707e8	−	2.73694e8i	−0.121438	−	0.0882302i
$237$	−1.15885e8	+	7.31670e8i	−0.0367312	+	0.231911i
$238$	−6.52797e8	−	1.03393e8i	−0.203456	−	0.0322243i
$239$	3.11588e9	−	4.28864e9i	0.954969	−	1.31440i	0.00568388	−	0.999984i	$-0.498191\pi$
$239$	3.11588e9	−	4.28864e9i	0.954969	−	1.31440i	0.949285	−	0.314418i	$-0.101809\pi$
$240$	−1.92853e8	+	6.12258e8i	−0.0581274	+	0.184540i
$241$	−4.16541e9	+	3.02635e9i	−1.23478	+	0.897120i	−0.997239	−	0.0742571i	$-0.976341\pi$
$241$	−4.16541e9	+	3.02635e9i	−1.23478	+	0.897120i	−0.237541	+	0.971377i	$0.576341\pi$
$242$	8.58486e8	+	1.68487e9i	0.250306	+	0.491254i
$243$	−1.58164e8	−	1.58164e8i	−0.0453609	−	0.0453609i
$244$	1.13184e9	+	3.67756e8i	0.319319	+	0.103753i
$245$	1.56142e9	−	3.13396e9i	0.433367	−	0.869818i
$246$	9.28804e8	+	2.85857e9i	0.253620	+	0.780563i
$247$	−3.65234e9	−	1.86096e9i	−0.981259	−	0.499976i
$248$	−8.64237e8	−	5.45658e9i	−0.228468	−	1.44249i
$249$		−	7.41972e8i		−	0.193015i
$250$	9.63610e8	+	2.71379e9i	0.246684	+	0.694730i
$251$	−7.34739e8			−0.185114			−0.0925568	−	0.995707i	$-0.529504\pi$
$251$	−7.34739e8			−0.185114			−0.0925568	+	0.995707i	$0.529504\pi$
$252$	1.01785e8	−	1.61211e7i	0.0252395	−	0.00399755i
$253$	1.18625e9	−	2.32815e9i	0.289531	−	0.568237i
$254$	2.80861e9	−	9.12573e8i	0.674771	−	0.219247i
$255$	3.63545e9	+	1.81128e9i	0.859800	+	0.428375i
$256$	−1.38121e9	+	4.25091e9i	−0.321587	+	0.989743i
$257$	−1.63587e9	+	1.63587e9i	−0.374987	+	0.374987i	−0.869290	−	0.494303i	$-0.835423\pi$
$257$	−1.63587e9	+	1.63587e9i	−0.374987	+	0.374987i	0.494303	+	0.869290i	$0.335423\pi$
$258$	−1.28234e9	+	6.53384e8i	−0.289417	+	0.147465i
$259$	6.57638e6	+	9.05162e6i	0.00146146	+	0.00201153i
$260$	2.00757e9	+	6.32356e8i	0.439316	+	0.138378i
$261$	−1.20296e9	−	8.74003e8i	−0.259233	−	0.188344i
$262$	4.62857e8	−	2.92236e9i	0.0982294	−	0.620196i
$263$	−3.25004e9	−	5.14755e8i	−0.679305	−	0.107591i	−0.192759	−	0.981246i	$-0.561744\pi$
$263$	−3.25004e9	−	5.14755e8i	−0.679305	−	0.107591i	−0.486546	+	0.873655i	$0.661744\pi$
$264$	−8.88791e8	+	1.22332e9i	−0.182972	+	0.251839i
$265$	3.06548e9	−	2.26968e9i	0.621605	−	0.460237i
$266$	5.47333e8	−	3.97661e8i	0.109326	−	0.0794303i
$267$	−1.48963e9	−	2.92356e9i	−0.293111	−	0.575264i
$268$	−1.12741e9	−	1.12741e9i	−0.218547	−	0.218547i
$269$	−6.79100e9	−	2.20653e9i	−1.29695	−	0.421406i	−0.422434	−	0.906394i	$-0.638824\pi$
$269$	−6.79100e9	−	2.20653e9i	−1.29695	−	0.421406i	−0.874521	+	0.484988i	$0.838824\pi$
$270$	7.45754e8	+	1.11237e8i	0.140327	+	0.0209312i
$271$	−3.68991e8	−	1.13564e9i	−0.0684130	−	0.210554i	0.911005	−	0.412395i	$-0.135308\pi$
$271$	−3.68991e8	−	1.13564e9i	−0.0684130	−	0.210554i	−0.979418	+	0.201841i	$0.935308\pi$
$272$	−2.71928e9	−	1.38554e9i	−0.496796	−	0.253130i
$273$	8.50055e7	+	5.36704e8i	0.0153037	+	0.0966238i
$274$		−	1.58971e9i		−	0.282043i
$275$	5.17522e7	+	2.87128e9i	0.00904894	+	0.502048i
$276$	−1.94244e9			−0.334742
$277$	−6.14996e9	+	9.74057e8i	−1.04461	+	0.165450i	−0.655075	−	0.755564i	$-0.727363\pi$
$277$	−6.14996e9	+	9.74057e8i	−1.04461	+	0.165450i	−0.389532	+	0.921013i	$0.627363\pi$
$278$	−2.37322e9	+	4.65770e9i	−0.397336	+	0.779816i
$279$	−2.61267e9	+	8.48909e8i	−0.431190	+	0.140102i
$280$	−7.76646e8	+	7.90770e8i	−0.126355	+	0.128653i
$281$	−2.81912e9	+	8.67635e9i	−0.452155	+	1.39159i	0.422287	+	0.906462i	$0.361227\pi$
$281$	−2.81912e9	+	8.67635e9i	−0.452155	+	1.39159i	−0.874442	+	0.485129i	$0.838773\pi$
$282$	−1.44071e9	+	1.44071e9i	−0.227813	+	0.227813i
$283$	−7.73963e9	+	3.94354e9i	−1.20663	+	0.614809i	−0.937396	−	0.348266i	$-0.886771\pi$
$283$	−7.73963e9	+	3.94354e9i	−1.20663	+	0.614809i	−0.269235	+	0.963075i	$0.586771\pi$
$284$	−2.96166e9	−	4.07637e9i	−0.455262	−	0.626614i
$285$	−3.94236e9	+	1.32034e9i	−0.597554	+	0.200128i
$286$	−2.02171e9	−	1.46886e9i	−0.302172	−	0.219541i
$287$	−3.43689e8	+	2.16997e9i	−0.0506568	+	0.319835i
$288$	1.87251e9	+	2.96576e8i	0.272179	+	0.0431088i
$289$	−7.25040e9	+	9.97932e9i	−1.03937	+	1.43057i
$290$	5.01220e9	−	4.51665e7i	0.708658	−	0.00638593i
$291$	2.04050e9	−	1.48251e9i	0.284554	−	0.206741i
$292$	8.81301e8	+	1.72965e9i	0.121225	+	0.237918i
$293$	−6.28605e9	−	6.28605e9i	−0.852919	−	0.852919i	0.137573	−	0.990492i	$-0.456070\pi$
$293$	−6.28605e9	−	6.28605e9i	−0.852919	−	0.852919i	−0.990492	+	0.137573i	$0.956070\pi$
$294$	2.93908e9	+	9.54966e8i	0.393389	+	0.127820i
$295$	−4.11714e8	−	2.45601e9i	−0.0543635	−	0.324297i
$296$	3.77125e7	+	1.16067e8i	0.00491267	+	0.0151197i
$297$	6.69947e8	+	3.41355e8i	0.0861022	+	0.0438713i
$298$	−1.27578e9	−	8.05497e9i	−0.161775	−	1.02141i
$299$		−	1.02423e10i		−	1.28149i
$300$	1.88437e9	−	1.00331e9i	0.232638	−	0.123866i
$301$	−1.05199e9			−0.128158
$302$	1.64490e8	−	2.60527e7i	0.0197748	−	0.00313202i
$303$	−2.71512e9	+	5.32872e9i	−0.322120	+	0.632197i
$304$	2.97108e9	−	9.65363e8i	0.347873	−	0.113031i
$305$	2.94051e9	+	5.64474e9i	0.339800	+	0.652296i
$306$	−1.10778e9	+	3.40939e9i	−0.126348	+	0.388858i
$307$	−5.38965e9	+	5.38965e9i	−0.606746	+	0.606746i	−0.942094	−	0.335348i	$-0.891146\pi$
$307$	−5.38965e9	+	5.38965e9i	−0.606746	+	0.606746i	0.335348	+	0.942094i	$0.391146\pi$
$308$	−3.08661e8	+	1.57271e8i	−0.0342988	+	0.0174761i
$309$	3.40532e9	+	4.68702e9i	0.373529	+	0.514118i
$310$	5.37541e9	−	7.54058e9i	0.582056	−	0.816504i
$311$	4.72432e9	+	3.43242e9i	0.505007	+	0.366909i	0.810926	−	0.585148i	$-0.198964\pi$
$311$	4.72432e9	+	3.43242e9i	0.505007	+	0.366909i	−0.305919	+	0.952057i	$0.598964\pi$
$312$	−9.27216e8	+	5.85421e9i	−0.0978504	+	0.617803i
$313$	7.34863e9	+	1.16391e9i	0.765648	+	0.121267i	0.527030	−	0.849847i	$-0.323306\pi$
$313$	7.34863e9	+	1.16391e9i	0.765648	+	0.121267i	0.238618	+	0.971113i	$0.423306\pi$
$314$	7.18309e9	−	9.88668e9i	0.738912	−	1.01703i
$315$	4.48786e8	+	3.19923e8i	0.0455824	+	0.0324941i
$316$	−1.49764e9	+	1.08810e9i	−0.150196	+	0.109124i
$317$	−3.13966e9	−	6.16193e9i	−0.310918	−	0.610211i	0.681681	−	0.731650i	$-0.261249\pi$
$317$	−3.13966e9	−	6.16193e9i	−0.310918	−	0.610211i	−0.992599	+	0.121439i	$0.961249\pi$
$318$	2.38046e9	+	2.38046e9i	0.232784	+	0.232784i
$319$	4.75377e9	+	1.54459e9i	0.459066	+	0.149160i
$320$	−8.78430e9	+	4.57599e9i	−0.837736	+	0.436401i
$321$	−3.09693e9	−	9.53137e9i	−0.291683	−	0.897708i
$322$	1.50620e9	+	7.67448e8i	0.140107	+	0.0713880i
$323$	−3.09222e9	−	1.95235e10i	−0.284093	−	1.79369i
$324$		−	5.58953e8i		−	0.0507219i
$325$	5.29039e9	+	9.93613e9i	0.474192	+	0.890602i
$326$	8.96708e9			0.793927
$327$	−3.46126e9	+	5.48210e8i	−0.302722	+	0.0479464i
$328$	−1.08796e10	+	2.13525e10i	−0.939980	+	1.84481i
$329$	−1.41641e9	+	4.60218e8i	−0.120894	+	0.0392808i
$330$	−2.49973e9	+	4.19043e8i	−0.210784	+	0.0353348i
$331$	−2.54565e9	+	7.83472e9i	−0.212074	+	0.652697i	0.787274	+	0.616603i	$0.211492\pi$
$331$	−2.54565e9	+	7.83472e9i	−0.212074	+	0.652697i	−0.999348	+	0.0360939i	$0.988508\pi$
$332$	1.31107e9	−	1.31107e9i	0.107913	−	0.107913i
$333$	5.40707e7	−	2.75504e7i	0.00439729	−	0.00224053i
$334$	−7.34087e9	−	1.01038e10i	−0.589878	−	0.811897i
$335$	−7.68371e7	−	8.52674e9i	−0.00610087	−	0.677024i
$336$	−3.35035e8	−	2.43417e8i	−0.0262865	−	0.0190983i
$337$	−2.31094e9	+	1.45907e10i	−0.179172	+	1.13125i	0.720105	+	0.693865i	$0.244094\pi$
$337$	−2.31094e9	+	1.45907e10i	−0.179172	+	1.13125i	−0.899277	+	0.437380i	$0.855906\pi$
$338$	−1.71351e8	−	2.71394e7i	−0.0131287	−	0.00207938i
$339$	5.38037e9	−	7.40545e9i	0.407393	−	0.560728i
$340$	3.22333e9	+	9.62441e9i	0.241206	+	0.720209i
$341$	7.47091e9	−	5.42794e9i	0.552530	−	0.401437i
$342$	−1.66592e9	−	3.26954e9i	−0.121772	−	0.238992i
$343$	3.24092e9	+	3.24092e9i	0.234149	+	0.234149i
$344$	−1.09132e10	−	3.54593e9i	−0.779327	−	0.253219i
$345$	−7.41161e9	−	7.27922e9i	−0.523162	−	0.513817i
$346$	3.30075e9	+	1.01587e10i	0.230307	+	0.708813i
$347$	8.43442e9	+	4.29755e9i	0.581752	+	0.296417i	0.719993	−	0.693981i	$-0.244145\pi$
$347$	8.43442e9	+	4.29755e9i	0.581752	+	0.296417i	−0.138241	+	0.990399i	$0.544145\pi$
$348$	−5.81273e8	−	3.67001e9i	−0.0396336	−	0.250236i
$349$			1.44025e10i			0.970813i	0.874289	+	0.485406i	$0.161328\pi$
$349$			1.44025e10i			0.970813i	−0.874289	+	0.485406i	$0.838672\pi$
$350$	−1.85758e9	+	3.34811e7i	−0.123787	+	0.00223114i
$351$	2.94732e9			0.194177
$352$	−6.29450e9	+	9.96951e8i	−0.410006	+	0.0649386i
$353$	1.03909e10	−	2.03933e10i	0.669196	−	1.31337i	−0.267611	−	0.963527i	$-0.586234\pi$
$353$	1.03909e10	−	2.03933e10i	0.669196	−	1.31337i	0.936808	−	0.349845i	$-0.113766\pi$
$354$	2.09035e9	−	6.79197e8i	0.133109	−	0.0432497i
$355$	3.97551e9	−	2.66526e10i	0.250311	−	1.67813i
$356$	2.53377e9	−	7.79814e9i	0.157749	−	0.485502i
$357$	−1.85288e9	+	1.85288e9i	−0.114071	+	0.114071i
$358$	1.22816e10	−	6.25781e9i	0.747695	−	0.380970i
$359$	1.16192e10	+	1.59924e10i	0.699517	+	0.962802i	0.999959	+	0.00900237i	$0.00286558\pi$
$359$	1.16192e10	+	1.59924e10i	0.699517	+	0.962802i	−0.300443	+	0.953800i	$0.597134\pi$
$360$	3.57729e9	+	4.83155e9i	0.212982	+	0.287658i
$361$	2.62935e9	+	1.91033e9i	0.154817	+	0.112481i
$362$	1.66460e9	−	1.05099e10i	0.0969340	−	0.612017i
$363$	7.40474e9	+	1.17280e9i	0.426465	+	0.0675454i
$364$	−7.98154e8	+	1.09857e9i	−0.0454654	+	0.0625778i
$365$	−3.11910e9	+	9.90234e9i	−0.175735	+	0.557913i
$366$	−4.54467e9	+	3.30190e9i	−0.253267	+	0.184009i
$367$	−3.68684e9	−	7.23582e9i	−0.203231	−	0.398863i	0.766785	−	0.641904i	$-0.221855\pi$
$367$	−3.68684e9	−	7.23582e9i	−0.203231	−	0.398863i	−0.970016	+	0.243041i	$0.921855\pi$
$368$	5.51952e9	+	5.51952e9i	0.300961	+	0.300961i
$369$	1.13332e10	+	3.68237e9i	0.611289	+	0.198620i
$370$	−9.12247e7	+	1.83099e8i	−0.00486750	+	0.00976964i
$371$	7.60413e8	+	2.34031e9i	0.0401378	+	0.123532i
$372$	−6.11664e9	−	3.11659e9i	−0.319405	−	0.162745i
$373$	−3.95119e8	−	2.49469e9i	−0.0204123	−	0.128878i	0.975378	−	0.220540i	$-0.0707821\pi$
$373$	−3.95119e8	−	2.49469e9i	−0.0204123	−	0.128878i	−0.995790	+	0.0916619i	$0.970782\pi$
$374$		−	1.20506e10i		−	0.615916i
$375$	1.09499e10	+	3.23335e9i	0.553715	+	0.163504i
$376$	−1.62448e10			−0.812763
$377$	1.93517e10	−	3.06501e9i	0.957974	−	0.151728i
$378$	−2.20840e8	+	4.33422e8i	−0.0108171	+	0.0212297i
$379$	1.92025e9	−	6.23926e8i	0.0930679	−	0.0302396i	−0.262113	−	0.965037i	$-0.584419\pi$
$379$	1.92025e9	−	6.23926e8i	0.0930679	−	0.0302396i	0.355181	+	0.934798i	$0.384419\pi$
$380$	−9.29924e9	−	4.63313e9i	−0.445978	−	0.222198i
$381$	3.61802e9	−	1.11351e10i	0.171700	−	0.528439i
$382$	5.69676e8	−	5.69676e8i	0.0267531	−	0.0267531i
$383$	1.42960e10	−	7.28417e9i	0.664383	−	0.338520i	−0.0890664	−	0.996026i	$-0.528388\pi$
$383$	1.42960e10	−	7.28417e9i	0.664383	−	0.338520i	0.753450	+	0.657505i	$0.228388\pi$
$384$	9.61732e8	+	1.32371e9i	0.0442313	+	0.0608791i
$385$	−1.76710e9	−	5.56612e8i	−0.0804300	−	0.0253343i
$386$	1.62300e8	+	1.17918e8i	0.00731087	+	0.00531166i
$387$	−8.92602e8	+	5.63567e9i	−0.0397937	+	0.251247i
$388$	6.22519e9	+	9.85973e8i	0.274679	+	0.0435049i
$389$	−5.12127e9	+	7.04882e9i	−0.223655	+	0.307835i	−0.906068	−	0.423132i	$-0.860931\pi$
$389$	−5.12127e9	+	7.04882e9i	−0.223655	+	0.307835i	0.682413	+	0.730967i	$0.260931\pi$
$390$	−7.98484e9	+	5.91199e9i	−0.345150	+	0.255550i
$391$	3.99580e10	−	2.90312e10i	1.70961	−	1.24210i
$392$	1.11861e10	+	2.19539e10i	0.473732	+	0.929752i
$393$	−8.29474e9	−	8.29474e9i	−0.347722	−	0.347722i
$394$	2.47637e10	+	8.04621e9i	1.02762	+	0.333892i
$395$	−9.79203e9	−	1.46058e9i	−0.402239	−	0.0599981i
$396$	5.80624e8	+	1.78698e9i	0.0236110	+	0.0726672i
$397$	−9.02319e9	−	4.59754e9i	−0.363244	−	0.185082i	0.262837	−	0.964840i	$-0.415342\pi$
$397$	−9.02319e9	−	4.59754e9i	−0.363244	−	0.185082i	−0.626080	+	0.779758i	$0.715342\pi$
$398$	3.00351e9	+	1.89634e10i	0.119701	+	0.755759i
$399$		−	2.68224e9i		−	0.105829i
$400$	−8.20547e9	−	2.50356e9i	−0.320526	−	0.0977953i
$401$	1.42528e10			0.551218			0.275609	−	0.961270i	$-0.411120\pi$
$401$	1.42528e10			0.551218			0.275609	+	0.961270i	$0.411120\pi$
$402$	7.43337e9	−	1.17733e9i	0.284631	−	0.0450811i
$403$	1.64335e10	−	3.22526e10i	0.623032	−	1.22277i
$404$	−1.42135e10	+	4.61825e9i	−0.533552	+	0.173361i
$405$	2.09466e9	−	2.13276e9i	0.0778563	−	0.0792722i
$406$	−9.99275e8	+	3.07545e9i	−0.0367774	+	0.113189i
$407$	−1.44246e8	+	1.44246e8i	−0.00525685	+	0.00525685i
$408$	−2.54669e10	+	1.29761e10i	−0.919044	+	0.468276i
$409$	−1.80752e10	−	2.48784e10i	−0.645936	−	0.889054i	0.352979	−	0.935631i	$-0.385169\pi$
$409$	−1.80752e10	−	2.48784e10i	−0.645936	−	0.889054i	−0.998915	+	0.0465769i	$0.985169\pi$
$410$	−3.80902e10	+	1.27568e10i	−1.34796	+	0.451448i
$411$	−5.09893e9	−	3.70459e9i	−0.178695	−	0.129829i
$412$	−2.26478e9	+	1.42992e10i	−0.0786025	+	0.496277i
$413$	1.58681e9	+	2.51326e8i	0.0545412	+	0.00863847i
$414$	5.38931e9	−	7.41775e9i	0.183456	−	0.252505i
$415$	9.91575e9	−	8.93539e7i	0.334298	−	0.00301246i
$416$	−2.02100e10	+	1.46834e10i	−0.674828	+	0.490291i
$417$	9.40894e9	+	1.84661e10i	0.311169	+	0.610704i
$418$	8.72225e9	+	8.72225e9i	0.285709	+	0.285709i
$419$	1.23296e10	+	4.00612e9i	0.400029	+	0.129977i	0.502121	−	0.864798i	$-0.332553\pi$
$419$	1.23296e10	+	4.00612e9i	0.400029	+	0.129977i	−0.102091	+	0.994775i	$0.532553\pi$
$420$	2.27701e8	+	1.35832e9i	0.00731760	+	0.0436520i
$421$	−7.34801e9	−	2.26148e10i	−0.233906	−	0.719888i	−0.997265	−	0.0739135i	$-0.976451\pi$
$421$	−7.34801e9	−	2.26148e10i	−0.233906	−	0.719888i	0.763359	−	0.645975i	$-0.223549\pi$
$422$	−1.81551e10	−	9.25046e9i	−0.572463	−	0.291685i
$423$	1.26365e9	+	7.97836e9i	0.0394698	+	0.249202i
$424$			2.68412e10i			0.830497i
$425$	−2.37682e10	+	4.88025e10i	−0.728518	+	1.49584i
$426$	2.37839e10			0.722179
$427$	−4.05561e9	+	6.42345e8i	−0.121996	+	0.0193222i
$428$	1.13697e10	−	2.23143e10i	0.338824	−	0.664980i
$429$	−9.42260e9	+	3.06159e9i	−0.278190	+	0.0903894i
$430$	−8.88629e9	−	1.70586e10i	−0.259924	−	0.498963i
$431$	5.87815e8	−	1.80911e9i	0.0170346	−	0.0524271i	−0.942178	−	0.335113i	$-0.891225\pi$
$431$	5.87815e8	−	1.80911e9i	0.0170346	−	0.0524271i	0.959212	+	0.282686i	$0.0912255\pi$
$432$	−1.58829e9	+	1.58829e9i	−0.0456031	+	0.0456031i
$433$	5.56200e9	−	2.83398e9i	0.158226	−	0.0806204i	−0.373084	−	0.927798i	$-0.621700\pi$
$433$	5.56200e9	−	2.83398e9i	0.158226	−	0.0806204i	0.531311	+	0.847177i	$0.321700\pi$
$434$	3.51161e9	+	4.83331e9i	0.0989799	+	0.136234i
$435$	1.15353e10	−	1.61817e10i	0.322161	−	0.451925i
$436$	−7.08477e9	−	5.14739e9i	−0.196056	−	0.142443i
$437$	−7.90886e9	+	4.99346e10i	−0.216864	+	1.36923i
$438$	−9.05034e9	−	1.43343e9i	−0.245906	−	0.0389476i
$439$	−1.89092e10	+	2.60262e10i	−0.509113	+	0.700734i	−0.983769	−	0.179437i	$-0.942572\pi$
$439$	−1.89092e10	+	2.60262e10i	−0.509113	+	0.700734i	0.474656	+	0.880171i	$0.342572\pi$
$440$	−1.64555e10	−	1.17305e10i	−0.439036	−	0.312973i
$441$	9.91212e9	−	7.20158e9i	0.262067	−	0.190403i
$442$	−2.14448e10	−	4.20878e10i	−0.561867	−	1.10273i
$443$	3.78985e10	+	3.78985e10i	0.984027	+	0.984027i	0.999874	−	0.0158476i	$-0.00504466\pi$
$443$	3.78985e10	+	3.78985e10i	0.984027	+	0.984027i	−0.0158476	+	0.999874i	$0.505045\pi$
$444$	1.44225e8	+	4.68616e7i	0.00371115	+	0.00120583i
$445$	3.88912e10	−	2.02595e10i	0.991771	−	0.516642i
$446$	−6.71026e9	−	2.06521e10i	−0.169590	−	0.521944i
$447$	−2.88090e10	−	1.46789e10i	−0.721603	−	0.367675i
$448$	−9.99612e8	−	6.31130e9i	−0.0248153	−	0.156678i
$449$			4.44072e10i			1.09262i	0.837584	+	0.546309i	$0.183968\pi$
$449$			4.44072e10i			1.09262i	−0.837584	+	0.546309i	$0.816032\pi$
$450$	−1.39677e9	+	9.97969e9i	−0.0340623	+	0.243370i
$451$	−4.00574e10			−0.968226
$452$	2.25927e10	−	3.57832e9i	0.541269	−	0.0857287i
$453$	2.99758e8	−	5.88308e8i	0.00711832	−	0.0139705i
$454$	−4.64093e10	+	1.50793e10i	−1.09240	+	0.354942i
$455$	−7.16229e9	+	1.20065e9i	−0.167112	+	0.0280138i
$456$	9.04095e9	−	2.78252e10i	0.209100	−	0.643544i
$457$	6.02697e10	−	6.02697e10i	1.38176	−	1.38176i	0.540278	−	0.841486i	$-0.318319\pi$
$457$	6.02697e10	−	6.02697e10i	1.38176	−	1.38176i	0.841486	−	0.540278i	$-0.181681\pi$
$458$	−3.66802e10	+	1.86895e10i	−0.833624	+	0.424753i
$459$	8.35397e9	+	1.14983e10i	0.188210	+	0.259049i
$460$	−2.33923e8	−	2.59588e10i	−0.00522446	−	0.579767i
$461$	9.85315e9	+	7.15873e9i	0.218158	+	0.158501i	0.691497	−	0.722379i	$-0.256951\pi$
$461$	9.85315e9	+	7.15873e9i	0.218158	+	0.158501i	−0.473339	+	0.880880i	$0.656951\pi$
$462$	2.55800e8	−	1.61506e9i	0.00561478	−	0.0354503i
$463$	−3.52811e9	−	5.58797e8i	−0.0767747	−	0.0121599i	0.117929	−	0.993022i	$-0.462374\pi$
$463$	−3.52811e9	−	5.58797e8i	−0.0767747	−	0.0121599i	−0.194704	+	0.980862i	$0.562374\pi$
$464$	−8.77679e9	+	1.20802e10i	−0.189349	+	0.260617i
$465$	−1.16595e10	−	3.48137e10i	−0.249384	−	0.744625i
$466$	5.71995e8	−	4.15579e8i	0.0121297	−	0.00881272i
$467$	6.38969e9	+	1.25405e10i	0.134342	+	0.263661i	0.948371	−	0.317163i	$-0.102730\pi$
$467$	6.38969e9	+	1.25405e10i	0.134342	+	0.263661i	−0.814029	+	0.580824i	$0.802730\pi$
$468$	5.20793e9	+	5.20793e9i	0.108563	+	0.108563i
$469$	5.23195e9	+	1.69996e9i	0.108136	+	0.0351357i
$470$	−1.94272e10	−	1.90802e10i	−0.398123	−	0.391012i
$471$	−1.49720e10	−	4.60790e10i	−0.304225	−	0.936309i
$472$	1.56142e10	+	7.95583e9i	0.314595	+	0.160294i
$473$	−3.00051e9	−	1.89445e10i	−0.0599447	−	0.378476i
$474$		−	8.73809e9i		−	0.173102i
$475$	−1.81199e10	−	5.25269e10i	−0.355943	−	1.03183i
$476$	−6.54810e9			−0.127552
$477$	1.31826e10	−	2.08791e9i	0.254640	−	0.0403310i
$478$	−2.83877e10	+	5.57139e10i	−0.543774	+	1.06722i
$479$	−9.61968e10	+	3.12562e10i	−1.82734	+	0.593737i	−0.827875	+	0.560913i	$0.810450\pi$
$479$	−9.61968e10	+	3.12562e10i	−1.82734	+	0.593737i	−0.999461	+	0.0328246i	$0.989550\pi$
$480$	−3.73796e9	+	2.50600e10i	−0.0704157	+	0.472081i
$481$	−2.47097e8	+	7.60487e8i	−0.00461623	+	0.0142073i
$482$	4.29444e10	−	4.29444e10i	0.795643	−	0.795643i
$483$	5.97154e9	−	3.04265e9i	0.109723	−	0.0559067i
$484$	1.10119e10	+	1.51566e10i	0.200669	+	0.276197i
$485$	2.00581e10	+	2.70908e10i	0.362512	+	0.489615i
$486$	2.13452e9	+	1.55082e9i	0.0382609	+	0.0277982i
$487$	3.48890e9	−	2.20280e10i	0.0620258	−	0.391616i	−0.937072	−	0.349137i	$-0.886475\pi$
$487$	3.48890e9	−	2.20280e10i	0.0620258	−	0.391616i	0.999097	−	0.0424784i	$-0.0135254\pi$
$488$	−4.42374e10	−	7.00652e9i	−0.780029	−	0.123544i
$489$	2.08965e10	−	2.87615e10i	0.365458	−	0.503010i
$490$	−1.24083e10	+	3.93930e10i	−0.215242	+	0.683337i
$491$	1.29752e10	−	9.42700e9i	0.223247	−	0.162199i	−0.470540	−	0.882379i	$-0.655941\pi$
$491$	1.29752e10	−	9.42700e9i	0.223247	−	0.162199i	0.693787	+	0.720180i	$0.255941\pi$
$492$	1.35190e10	+	2.65326e10i	0.230720	+	0.452814i
$493$	6.68084e10	+	6.68084e10i	1.13095	+	1.13095i
$494$	4.59852e10	+	1.49415e10i	0.772165	+	0.250891i
$495$	−4.48120e9	+	8.99431e9i	−0.0746404	+	0.149812i
$496$	8.52479e9	+	2.62366e10i	0.140850	+	0.433492i
$497$	1.54901e10	+	7.89262e9i	0.253881	+	0.129359i
$498$	1.36912e9	+	8.64427e9i	0.0222599	+	0.140544i
$499$			4.38433e10i			0.707133i	0.935409	+	0.353567i	$0.115031\pi$
$499$			4.38433e10i			0.707133i	−0.935409	+	0.353567i	$0.884969\pi$
$500$	1.36352e10	+	2.50620e10i	0.218164	+	0.400991i
$501$	−4.95145e10			−0.785926
$502$	8.56000e9	−	1.35577e9i	0.134790	−	0.0213487i
$503$	−3.07847e10	+	6.04183e10i	−0.480909	+	0.943836i	0.515314	+	0.857001i	$0.327675\pi$
$503$	−3.07847e10	+	6.04183e10i	−0.480909	+	0.943836i	−0.996223	+	0.0868349i	$0.972325\pi$
$504$	−3.68860e9	+	1.19850e9i	−0.0571663	+	0.0185744i
$505$	−7.15402e10	−	3.56432e10i	−1.09998	−	0.548039i
$506$	−9.52432e9	+	2.93128e10i	−0.145289	+	0.447153i
$507$	−4.86358e8	+	4.86358e8i	−0.00736078	+	0.00736078i
$508$	2.60689e10	−	1.32828e10i	0.391443	−	0.199450i
$509$	−5.57303e9	−	7.67062e9i	−0.0830272	−	0.114277i	0.765483	−	0.643456i	$-0.222500\pi$
$509$	−5.57303e9	−	7.67062e9i	−0.0830272	−	0.114277i	−0.848510	+	0.529179i	$0.822500\pi$
$510$	−4.56967e10	−	1.43938e10i	−0.675467	−	0.212763i
$511$	−5.41868e9	−	3.93690e9i	−0.0794712	−	0.0577392i
$512$	6.84649e9	−	4.32270e10i	0.0996295	−	0.629036i
$513$	−1.43691e10	−	2.27584e9i	−0.207472	−	0.0328604i
$514$	1.60399e10	−	2.20771e10i	0.229800	−	0.316293i
$515$	−6.22275e10	+	4.60733e10i	−0.884613	+	0.654969i
$516$	−1.15355e10	+	8.38104e9i	−0.162719	+	0.118222i
$517$	−1.23276e10	−	2.41942e10i	−0.172550	−	0.338649i
$518$	−9.33199e7	−	9.33199e7i	−0.00129615	−	0.00129615i
$519$	4.02754e10	+	1.30863e10i	0.555099	+	0.180362i
$520$	−7.83476e10	−	1.16864e10i	−1.07155	−	0.159833i
$521$	−3.15111e10	−	9.69811e10i	−0.427674	−	1.31624i	−0.900411	−	0.435041i	$-0.856734\pi$
$521$	−3.15111e10	−	9.69811e10i	−0.427674	−	1.31624i	0.472737	−	0.881203i	$-0.343266\pi$
$522$	1.56277e10	+	7.96273e9i	0.210481	+	0.107246i
$523$	4.42337e9	+	2.79281e10i	0.0591216	+	0.373279i	0.999455	+	0.0330236i	$0.0105136\pi$
$523$	4.42337e9	+	2.79281e10i	0.0591216	+	0.373279i	−0.940333	+	0.340256i	$0.889486\pi$
$524$		−	2.93137e10i		−	0.388818i
$525$	−4.22143e9	+	6.03613e9i	−0.0555676	+	0.0794550i
$526$	3.88141e10			0.507045
$527$	1.72405e11	−	2.73063e10i	2.23516	−	0.354014i
$528$	3.42791e9	−	6.72764e9i	0.0441055	−	0.0865620i
$529$	−4.56640e10	+	1.48371e10i	−0.583111	+	0.189464i
$530$	−3.15259e10	+	3.20993e10i	−0.399544	+	0.406810i
$531$	2.69277e9	−	8.28750e9i	0.0338705	−	0.104243i
$532$	4.73954e9	−	4.73954e9i	0.0591684	−	0.0591684i
$533$	−1.39904e11	+	7.12848e10i	−1.73349	+	0.883259i
$534$	2.27494e10	+	3.13119e10i	0.279773	+	0.385074i
$535$	1.27005e11	−	4.25354e10i	1.55026	−	0.519200i
$536$	4.85455e10	+	3.52704e10i	0.588152	+	0.427318i
$537$	8.54892e9	−	5.39758e10i	0.102805	−	0.649085i
$538$	8.31895e10	+	1.31759e10i	0.992977	+	0.157272i
$539$	−2.42083e10	+	3.33199e10i	−0.286820	+	0.394774i
$540$	7.46988e9	−	6.73134e7i	0.0878493	−	0.000791637i
$541$	−4.53754e10	+	3.29672e10i	−0.529702	+	0.384851i	−0.820246	−	0.572011i	$-0.806164\pi$
$541$	−4.53754e10	+	3.29672e10i	−0.529702	+	0.384851i	0.290544	+	0.956862i	$0.406164\pi$
$542$	6.39442e9	+	1.25498e10i	0.0740976	+	0.145425i
$543$	−2.98309e10	−	2.98309e10i	−0.343137	−	0.343137i
$544$	−1.14568e11	−	3.72253e10i	−1.30818	−	0.425053i
$545$	−7.74313e9	−	4.61904e10i	−0.0877669	−	0.523560i
$546$	−1.98070e9	−	6.09596e9i	−0.0222868	−	0.0685916i
$547$	−9.43755e10	−	4.80867e10i	−1.05417	−	0.537126i	−0.161050	−	0.986946i	$-0.551488\pi$
$547$	−9.43755e10	−	4.80867e10i	−1.05417	−	0.537126i	−0.893119	+	0.449821i	$0.851488\pi$
$548$	−2.46381e9	−	1.55559e10i	−0.0273203	−	0.172494i
$549$			2.22714e10i			0.245165i
$550$	−5.90114e9	−	3.33561e10i	−0.0644889	−	0.364522i
$551$	−9.67124e10			−1.04924
$552$	7.22037e10	−	1.14359e10i	0.777684	−	0.123173i
$553$	2.89971e9	−	5.69100e9i	0.0310066	−	0.0608538i
$554$	6.98521e10	−	2.26963e10i	0.741550	−	0.240944i
$555$	3.74696e8	+	7.19285e8i	0.00394918	+	0.00758104i
$556$	−1.60041e10	+	4.92554e10i	−0.167468	+	0.515412i
$557$	−3.09939e10	+	3.09939e10i	−0.322000	+	0.322000i	−0.849534	−	0.527534i	$-0.823117\pi$
$557$	−3.09939e10	+	3.09939e10i	−0.322000	+	0.322000i	0.527534	+	0.849534i	$0.323117\pi$
$558$	2.88722e10	−	1.47111e10i	0.297813	−	0.151743i
$559$	−4.41926e10	−	6.08258e10i	−0.452587	−	0.622932i
$560$	3.21269e9	−	4.50674e9i	0.0326676	−	0.0458258i
$561$	−3.86518e10	−	2.80821e10i	−0.390227	−	0.283517i
$562$	1.68339e10	−	1.06285e11i	0.168748	−	1.06543i
$563$	1.58784e11	+	2.51490e10i	1.58043	+	0.250315i	0.884060	−	0.467373i	$-0.154800\pi$
$563$	1.58784e11	+	2.51490e10i	1.58043	+	0.250315i	0.696365	+	0.717688i	$0.254800\pi$
$564$	−1.18650e10	+	1.63307e10i	−0.117260	+	0.161394i
$565$	9.96147e10	+	7.10117e10i	0.977529	+	0.696845i
$566$	8.28930e10	−	6.02253e10i	0.807704	−	0.586831i
$567$	8.75550e8	+	1.71836e9i	0.00847127	+	0.0166258i
$568$	1.34089e11	+	1.34089e11i	1.28825	+	1.28825i
$569$	8.85319e10	+	2.87658e10i	0.844600	+	0.274427i	0.699182	−	0.714943i	$-0.253548\pi$
$569$	8.85319e10	+	2.87658e10i	0.844600	+	0.274427i	0.145417	+	0.989370i	$0.453548\pi$
$570$	4.34937e10	−	2.26571e10i	0.412028	−	0.214637i
$571$	−1.38681e10	−	4.26816e10i	−0.130459	−	0.401510i	0.864397	−	0.502809i	$-0.167700\pi$
$571$	−1.38681e10	−	4.26816e10i	−0.130459	−	0.401510i	−0.994856	+	0.101299i	$0.967700\pi$
$572$	−2.20597e10	−	1.12400e10i	−0.206070	−	0.104998i
$573$	−4.99665e8	−	3.15476e9i	−0.00463512	−	0.0292650i
$574$		−	2.59152e10i		−	0.238730i
$575$	9.63873e10	−	9.99257e10i	0.881756	−	0.914125i
$576$	−3.46586e10			−0.314863
$577$	3.02068e10	−	4.78428e9i	0.272522	−	0.0431632i	−0.0186778	−	0.999826i	$-0.505946\pi$
$577$	3.02068e10	−	4.78428e9i	0.272522	−	0.0431632i	0.291199	+	0.956662i	$0.405946\pi$
$578$	6.60558e10	−	1.29642e11i	0.591834	−	1.16154i
$579$	7.56433e8	−	2.45780e8i	0.00673064	−	0.00218692i
$580$	4.89762e10	−	8.21013e9i	0.432786	−	0.0725501i
$581$	−1.97689e9	+	6.08424e9i	−0.0173491	+	0.0533951i
$582$	−2.10371e10	+	2.10371e10i	−0.183355	+	0.183355i
$583$	−3.99759e10	+	2.03687e10i	−0.346038	+	0.176315i
$584$	−4.29426e10	−	5.91055e10i	−0.369179	−	0.508132i
$585$	3.54938e8	+	3.93881e10i	0.00303060	+	0.336311i
$586$	8.48343e10	+	6.16358e10i	0.719418	+	0.522688i
$587$	−3.04530e10	+	1.92272e11i	−0.256494	+	1.61944i	0.437334	+	0.899299i	$0.355923\pi$
$587$	−3.04530e10	+	1.92272e11i	−0.256494	+	1.61944i	−0.693828	+	0.720140i	$0.744077\pi$
$588$	3.02400e10	+	4.78955e9i	0.252972	+	0.0400669i
$589$	−1.05023e11	+	1.44552e11i	−0.872618	+	1.20106i
$590$	9.32856e9	+	2.78538e10i	0.0769851	+	0.229867i
$591$	8.35161e10	−	6.06780e10i	0.684574	−	0.497372i
$592$	−2.76663e8	−	5.42981e8i	−0.00225249	−	0.00442077i
$593$	−2.62486e10	−	2.62486e10i	−0.212269	−	0.212269i	0.592962	−	0.805231i	$-0.297959\pi$
$593$	−2.62486e10	−	2.62486e10i	−0.212269	−	0.212269i	−0.805231	+	0.592962i	$0.797959\pi$
$594$	−8.43503e9	−	2.74071e9i	−0.0677549	−	0.0220149i
$595$	−2.49851e10	−	2.45388e10i	−0.199349	−	0.195788i
$596$	−2.49680e10	−	7.68436e10i	−0.197879	−	0.609007i
$597$	6.78235e10	+	3.45578e10i	0.533928	+	0.272050i
$598$	1.88996e10	+	1.19327e11i	0.147791	+	0.933113i
$599$		−	1.40157e11i		−	1.08870i	−0.838858	−	0.544351i	$-0.816776\pi$
$599$		−	1.40157e11i		−	1.08870i	0.838858	−	0.544351i	$-0.183224\pi$
$600$	−6.41383e10	+	4.83889e10i	−0.494894	+	0.373371i
$601$	−1.09579e11			−0.839903			−0.419952	−	0.907546i	$-0.637953\pi$
$601$	−1.09579e11			−0.839903			−0.419952	+	0.907546i	$0.637953\pi$
$602$	1.22561e10	−	1.94118e9i	0.0933186	−	0.0147802i
$603$	1.35462e10	−	2.65858e10i	0.102458	−	0.201086i
$604$	1.56922e9	−	5.09870e8i	0.0117906	−	0.00383100i
$605$	−1.47816e10	+	9.90985e10i	−0.110331	+	0.739683i
$606$	2.17994e10	−	6.70918e10i	0.161642	−	0.497483i
$607$	8.57525e10	−	8.57525e10i	0.631672	−	0.631672i	−0.316815	−	0.948487i	$-0.602613\pi$
$607$	8.57525e10	−	8.57525e10i	0.631672	−	0.631672i	0.948487	+	0.316815i	$0.102613\pi$
$608$	1.09868e11	−	5.59807e10i	0.804004	−	0.409661i
$609$	7.53572e9	+	1.03720e10i	0.0547842	+	0.0754040i
$610$	−4.46740e10	−	6.03376e10i	−0.322653	−	0.435781i
$611$	−8.61105e10	−	6.25630e10i	−0.617862	−	0.448903i
$612$	−5.55597e9	+	3.50790e10i	−0.0396054	+	0.250059i
$613$	1.89985e11	+	3.00907e10i	1.34548	+	0.213103i	0.787277	−	0.616600i	$-0.211490\pi$
$613$	1.89985e11	+	3.00907e10i	1.34548	+	0.213103i	0.558205	+	0.829703i	$0.311490\pi$
$614$	5.28464e10	−	7.27368e10i	0.371828	−	0.511777i
$615$	−4.78466e10	+	1.51901e11i	−0.334465	+	1.06184i
$616$	1.05475e10	−	7.66323e9i	0.0732534	−	0.0532217i
$617$	1.48581e10	+	2.91606e10i	0.102523	+	0.201213i	0.936570	−	0.350481i	$-0.113982\pi$
$617$	1.48581e10	+	2.91606e10i	0.102523	+	0.201213i	−0.834047	+	0.551694i	$0.813982\pi$
$618$	−4.83220e10	−	4.83220e10i	−0.331277	−	0.331277i
$619$	−7.04869e10	−	2.29026e10i	−0.480116	−	0.155999i	0.0589532	−	0.998261i	$-0.481224\pi$
$619$	−7.04869e10	−	2.29026e10i	−0.480116	−	0.155999i	−0.539069	+	0.842262i	$0.681224\pi$
$620$	4.09136e10	−	8.21184e10i	0.276886	−	0.555743i
$621$	−1.12331e10	−	3.45720e10i	−0.0755325	−	0.232465i
$622$	−6.13738e10	−	3.12715e10i	−0.410036	−	0.208924i
$623$	4.42563e9	+	2.79424e10i	0.0293781	+	0.185486i
$624$		−	2.95971e10i		−	0.195214i
$625$	−4.18920e10	+	1.46725e11i	−0.274544	+	0.961575i
$626$	−8.77622e10			−0.571492
$627$	4.83022e10	−	7.65032e9i	0.312534	−	0.0495005i
$628$	5.49663e10	−	1.07877e11i	0.353393	−	0.693573i
$629$	−3.66724e9	+	1.19156e9i	−0.0234281	+	0.00761225i
$630$	−5.81887e9	−	2.89912e9i	−0.0369383	−	0.0184036i
$631$	2.17684e9	−	6.69963e9i	0.0137312	−	0.0422604i	−0.943956	−	0.330071i	$-0.892927\pi$
$631$	2.17684e9	−	6.69963e9i	0.0137312	−	0.0422604i	0.957687	+	0.287811i	$0.0929273\pi$
$632$	4.92637e10	−	4.92637e10i	0.308787	−	0.308787i
$633$	−7.19782e10	+	3.66747e10i	−0.448318	+	0.228429i
$634$	4.79486e10	+	6.59955e10i	0.296769	+	0.408468i
$635$	1.49246e11	+	4.70104e10i	0.917926	+	0.289134i
$636$	2.69830e10	+	1.96043e10i	0.164916	+	0.119818i
$637$	−2.52549e10	+	1.59453e11i	−0.153387	+	0.968447i
$638$	−5.82334e10	−	9.22327e9i	−0.351471	−	0.0556675i
$639$	5.54250e10	−	7.62859e10i	0.332431	−	0.457553i
$640$	−1.75743e10	+	1.30120e10i	−0.104751	+	0.0775579i
$641$	6.54880e10	−	4.75798e10i	0.387909	−	0.281832i	−0.376689	−	0.926340i	$-0.622938\pi$
$641$	6.54880e10	−	4.75798e10i	0.387909	−	0.281832i	0.764598	+	0.644507i	$0.222938\pi$
$642$	5.36682e10	+	1.05330e11i	0.315920	+	0.620027i
$643$	−1.34932e11	−	1.34932e11i	−0.789353	−	0.789353i	0.192035	−	0.981388i	$-0.438491\pi$
$643$	−1.34932e11	−	1.34932e11i	−0.789353	−	0.789353i	−0.981388	+	0.192035i	$0.938491\pi$
$644$	1.59282e10	+	5.17537e9i	0.0926023	+	0.0300883i
$645$	−7.54228e10	−	1.12501e10i	−0.435777	−	0.0650006i
$646$	7.20512e10	+	2.21751e11i	0.413724	+	1.27331i
$647$	−1.09582e11	−	5.58348e10i	−0.625348	−	0.318631i	0.112445	−	0.993658i	$-0.464132\pi$
$647$	−1.09582e11	−	5.58348e10i	−0.625348	−	0.318631i	−0.737793	+	0.675027i	$0.764132\pi$
$648$	3.29079e9	+	2.07772e10i	0.0186638	+	0.117839i
$649$			2.92924e10i			0.165111i
$650$	−7.99697e10	−	1.05998e11i	−0.447994	−	0.593805i
$651$	2.36859e10			0.131876
$652$	8.77461e10	−	1.38976e10i	0.485554	−	0.0769042i
$653$	−1.31127e11	+	2.57351e11i	−0.721173	+	1.41538i	0.180769	+	0.983526i	$0.442141\pi$
$653$	−1.31127e11	+	2.57351e11i	−0.721173	+	1.41538i	−0.901942	+	0.431857i	$0.857859\pi$
$654$	3.93135e10	−	1.27737e10i	0.214897	−	0.0698243i
$655$	1.09852e11	−	1.11850e11i	0.596821	−	0.607675i
$656$	3.69786e10	−	1.13808e11i	0.199680	−	0.614553i
$657$	−2.56882e10	+	2.56882e10i	−0.137871	+	0.137871i
$658$	1.56525e10	−	7.97534e9i	0.0834987	−	0.0425447i
$659$	1.08528e11	+	1.49376e11i	0.575441	+	0.792026i	0.993186	−	0.116538i	$-0.0371797\pi$
$659$	1.08528e11	+	1.49376e11i	0.575441	+	0.792026i	−0.417746	+	0.908564i	$0.637180\pi$
$660$	−2.38113e10	+	7.97469e9i	−0.125490	+	0.0420280i
$661$	1.91049e11	+	1.38805e11i	1.00078	+	0.727108i	0.962255	−	0.272149i	$-0.0877344\pi$
$661$	1.91049e11	+	1.38805e11i	1.00078	+	0.727108i	0.0385239	+	0.999258i	$0.487734\pi$
$662$	1.52009e10	−	9.59750e10i	0.0791477	−	0.499719i
$663$	−1.84969e11	−	2.92962e10i	−0.957293	−	0.151620i
$664$	−4.10159e10	+	5.64536e10i	−0.210999	+	0.290415i
$665$	3.58456e10	−	3.23015e8i	0.183294	−	0.00165172i
$666$	−5.79108e8	+	4.20746e8i	−0.00294349	+	0.00213857i
$667$	−1.09708e11	−	2.15313e11i	−0.554285	−	1.08785i
$668$	−8.74926e10	−	8.74926e10i	−0.439405	−	0.439405i
$669$	−8.18779e10	−	2.66037e10i	−0.408754	−	0.132812i
$670$	1.66291e10	+	9.91982e10i	0.0825219	+	0.492271i
$671$	−2.31349e10	−	7.12020e10i	−0.114124	−	0.351238i
$672$	−1.45645e10	−	7.42101e9i	−0.0714200	−	0.0363903i
$673$	2.67013e10	+	1.68586e11i	0.130159	+	0.821789i	0.963241	+	0.268640i	$0.0865741\pi$
$673$	2.67013e10	+	1.68586e11i	0.130159	+	0.821789i	−0.833082	+	0.553149i	$0.813426\pi$
$674$		−	1.74252e11i		−	0.844380i
$675$	2.87545e10	+	2.77363e10i	0.138513	+	0.133608i
$676$	−1.71880e9			−0.00823071
$677$	−2.78340e11	+	4.40847e10i	−1.32501	+	0.209862i	−0.778530	−	0.627608i	$-0.784034\pi$
$677$	−2.78340e11	+	4.40847e10i	−1.32501	+	0.209862i	−0.546484	+	0.837469i	$0.684034\pi$
$678$	−4.90187e10	+	9.62045e10i	−0.231976	+	0.455278i
$679$	−2.06822e10	+	6.72007e9i	−0.0973013	+	0.0316151i
$680$	−1.76480e11	−	3.38779e11i	−0.825389	−	1.58446i
$681$	−5.97839e10	+	1.83996e11i	−0.277969	+	0.855499i
$682$	−7.70233e10	+	7.70233e10i	−0.356028	+	0.356028i
$683$	4.01829e10	−	2.04742e10i	0.184654	−	0.0940859i	−0.359220	−	0.933253i	$-0.616957\pi$
$683$	4.01829e10	−	2.04742e10i	0.184654	−	0.0940859i	0.543874	+	0.839167i	$0.316957\pi$
$684$	−2.13689e10	−	2.94118e10i	−0.0976243	−	0.134368i
$685$	4.88943e10	−	6.85885e10i	0.222073	−	0.311522i
$686$	−4.37383e10	−	3.17777e10i	−0.197499	−	0.143492i
$687$	−2.55321e10	+	1.61204e11i	−0.114620	+	0.723682i
$688$	5.65937e10	+	8.96356e9i	0.252589	+	0.0400062i
$689$	−1.03372e11	+	1.42279e11i	−0.458697	+	0.631343i
$690$	9.97801e10	+	7.11297e10i	0.440198	+	0.313801i
$691$	−2.53227e11	+	1.83980e11i	−1.11070	+	0.806974i	−0.982774	−	0.184810i	$-0.940833\pi$
$691$	−2.53227e11	+	1.83980e11i	−1.11070	+	0.806974i	−0.127929	+	0.991783i	$0.540833\pi$
$692$	4.80434e10	+	9.42905e10i	0.209512	+	0.411191i
$693$	−4.58412e9	−	4.58412e9i	−0.0198757	−	0.0198757i
$694$	−1.06194e11	−	3.45047e10i	−0.457788	−	0.148744i
$695$	−2.45649e11	+	1.27965e11i	−1.05287	+	0.548470i
$696$	4.32138e10	+	1.32998e11i	0.184156	+	0.566774i
$697$	−6.74650e11	−	3.43751e11i	−2.85856	−	1.45651i
$698$	−2.65761e10	−	1.67795e11i	−0.111962	−	0.706897i
$699$		−	2.80310e9i		−	0.0117417i
$700$	−1.81252e10	+	3.20659e9i	−0.0754901	+	0.0133552i
$701$	1.62166e11			0.671566			0.335783	−	0.941939i	$-0.390999\pi$
$701$	1.62166e11			0.671566			0.335783	+	0.941939i	$0.390999\pi$
$702$	−3.43374e10	+	5.43851e9i	−0.141390	+	0.0223940i
$703$	1.79191e9	−	3.51682e9i	0.00733659	−	0.0143989i
$704$	1.10804e11	−	3.60024e10i	0.451091	−	0.146568i
$705$	−1.06471e11	+	1.78483e10i	−0.430998	+	0.0722503i
$706$	−8.34274e10	+	2.56763e11i	−0.335807	+	1.03351i
$707$	3.64619e10	−	3.64619e10i	0.145936	−	0.145936i
$708$	1.94022e10	−	9.88593e9i	0.0772180	−	0.0393445i
$709$	−2.40767e11	−	3.31387e11i	−0.952821	−	1.31145i	−0.950263	−	0.311449i	$-0.899186\pi$
$709$	−2.40767e11	−	3.31387e11i	−0.952821	−	1.31145i	−0.00255843	−	0.999997i	$-0.500814\pi$
$710$	2.86424e9	+	3.17849e11i	0.0112713	+	1.25080i
$711$	−2.80271e10	−	2.03629e10i	−0.109673	−	0.0796820i
$712$	−4.82736e10	+	3.04787e11i	−0.187841	+	1.18598i
$713$	−4.40955e11	−	6.98404e10i	−1.70623	−	0.270240i
$714$	1.81678e10	−	2.50058e10i	0.0699051	−	0.0962161i
$715$	−4.20499e10	−	1.25555e11i	−0.160894	−	0.480409i
$716$	1.10482e11	−	8.02696e10i	0.420376	−	0.305421i
$717$	1.12547e11	+	2.20886e11i	0.425850	+	0.835777i
$718$	−1.64878e11	−	1.64878e11i	−0.620391	−	0.620391i
$719$	2.76799e11	+	8.99374e10i	1.03574	+	0.336531i	0.777055	−	0.629432i	$-0.216713\pi$
$719$	2.76799e11	+	8.99374e10i	1.03574	+	0.336531i	0.258680	+	0.965963i	$0.416713\pi$
$720$	−2.14173e10	−	2.10347e10i	−0.0796955	−	0.0782720i
$721$	−1.54360e10	−	4.75070e10i	−0.0571206	−	0.175799i
$722$	−3.41579e10	−	1.74043e10i	−0.125702	−	0.0640485i
$723$	−3.76667e10	−	2.37818e11i	−0.137849	−	0.870345i
$724$		−	1.05423e11i		−	0.383690i
$725$	2.17642e11	+	1.52210e11i	0.787754	+	0.550924i
$726$	−8.84323e10			−0.318320
$727$	3.29082e11	−	5.21215e10i	1.17806	−	0.186586i	0.463458	−	0.886119i	$-0.346608\pi$
$727$	3.29082e11	−	5.21215e10i	1.17806	−	0.186586i	0.714601	+	0.699533i	$0.246608\pi$
$728$	2.32010e10	−	4.55346e10i	0.0826004	−	0.162112i
$729$	9.94839e9	−	3.23243e9i	0.0352243	−	0.0114451i
$730$	1.80665e10	−	1.21122e11i	0.0636186	−	0.426511i
$731$	1.12037e11	−	3.44813e11i	0.392365	−	1.20758i
$732$	−3.93538e10	+	3.93538e10i	−0.137070	+	0.137070i
$733$	3.14987e11	−	1.60494e11i	1.09113	−	0.555960i	0.186631	−	0.982430i	$-0.440243\pi$
$733$	3.14987e11	−	1.60494e11i	1.09113	−	0.555960i	0.904501	+	0.426471i	$0.140243\pi$
$734$	5.63050e10	+	7.74971e10i	0.193982	+	0.266994i
$735$	9.74359e10	+	1.31599e11i	0.333864	+	0.450923i
$736$	2.49263e11	+	1.81100e11i	0.849466	+	0.617173i
$737$	−1.56906e10	+	9.90665e10i	−0.0531826	+	0.335782i
$738$	−1.38831e11	−	2.19887e10i	−0.468016	−	0.0741265i
$739$	−1.73044e11	+	2.38174e11i	−0.580200	+	0.798577i	−0.993717	−	0.111919i	$-0.964300\pi$
$739$	−1.73044e11	+	2.38174e11i	−0.580200	+	0.798577i	0.413517	+	0.910496i	$0.364300\pi$
$740$	−6.08891e8	+	1.93307e9i	−0.00203055	+	0.00644646i
$741$	1.55086e11	−	1.12677e11i	0.514398	−	0.373732i
$742$	−1.31776e10	−	2.58624e10i	−0.0434730	−	0.0853205i
$743$	−1.95436e11	−	1.95436e11i	−0.641284	−	0.641284i	0.309587	−	0.950871i	$-0.399809\pi$
$743$	−1.95436e11	−	1.95436e11i	−0.641284	−	0.641284i	−0.950871	+	0.309587i	$0.899809\pi$
$744$	2.45715e11	+	7.98376e10i	0.801936	+	0.260565i
$745$	1.92701e11	−	3.86773e11i	0.625544	−	1.25554i
$746$	9.20660e9	+	2.83350e10i	0.0297265	+	0.0914888i
$747$	3.09167e10	+	1.57528e10i	0.0992912	+	0.0505914i
$748$	−1.86766e10	−	1.17919e11i	−0.0596611	−	0.376685i
$749$			8.64094e10i			0.274558i
$750$	−1.33537e11	−	1.74646e10i	−0.422044	−	0.0551968i
$751$	2.65064e11			0.833280			0.416640	−	0.909071i	$-0.363208\pi$
$751$	2.65064e11			0.833280			0.416640	+	0.909071i	$0.363208\pi$
$752$	8.01192e10	−	1.26896e10i	0.250533	−	0.0396805i
$753$	1.55993e10	−	3.06153e10i	0.0485204	−	0.0952267i
$754$	−2.19799e11	+	7.14171e10i	−0.680050	+	0.220962i
$755$	7.89827e9	+	3.93513e9i	0.0243077	+	0.0121108i
$756$	−1.48926e9	+	4.58347e9i	−0.00455914	+	0.0140316i
$757$	−3.67857e11	+	3.67857e11i	−1.12020	+	1.12020i	−0.128490	+	0.991711i	$0.541013\pi$
$757$	−3.67857e11	+	3.67857e11i	−1.12020	+	1.12020i	−0.991711	+	0.128490i	$0.958987\pi$
$758$	−2.12203e10	+	1.08123e10i	−0.0642799	+	0.0327523i
$759$	7.18247e10	+	9.88582e10i	0.216425	+	0.297883i
$760$	3.72946e11	+	1.17473e11i	1.11787	+	0.352114i
$761$	−5.49904e10	−	3.99529e10i	−0.163964	−	0.119127i	0.502778	−	0.864416i	$-0.332311\pi$
$761$	−5.49904e10	−	3.99529e10i	−0.163964	−	0.119127i	−0.666742	+	0.745289i	$0.732311\pi$
$762$	−2.16044e10	+	1.36405e11i	−0.0640800	+	0.404585i
$763$	2.98433e10	+	4.72671e9i	0.0880538	+	0.0139464i
$764$	4.69158e9	−	6.45740e9i	0.0137704	−	0.0189533i
$765$	−1.52657e11	+	1.13028e11i	−0.445730	+	0.330019i
$766$	−1.53113e11	+	1.11243e11i	−0.444730	+	0.323115i
$767$	5.21277e10	+	1.02306e11i	0.150622	+	0.295612i
$768$	−1.47804e11	−	1.47804e11i	−0.424855	−	0.424855i
$769$	5.55097e11	+	1.80362e11i	1.58732	+	0.515750i	0.963928	−	0.266163i	$-0.0857558\pi$
$769$	5.55097e11	+	1.80362e11i	1.58732	+	0.515750i	0.623388	+	0.781913i	$0.285756\pi$
$770$	2.16145e10	+	3.22402e9i	0.0614869	+	0.00917139i
$771$	−3.34326e10	−	1.02895e11i	−0.0946133	−	0.291190i
$772$	1.77092e9	+	9.02328e8i	0.00498574	+	0.00254036i
$773$	−7.28685e9	−	4.60073e10i	−0.0204090	−	0.128857i	0.975380	−	0.220530i	$-0.0707787\pi$
$773$	−7.28685e9	−	4.60073e10i	−0.0204090	−	0.128857i	−0.995789	+	0.0916726i	$0.970779\pi$
$774$		−	6.73049e10i		−	0.187535i
$775$	4.63847e11	−	1.60011e11i	1.28578	−	0.443549i
$776$	−2.37206e11			−0.654152
$777$	−5.16788e8	+	8.18512e7i	−0.00141784	+	0.000224565i
$778$	4.66580e10	−	9.15715e10i	0.127353	−	0.249944i
$779$	7.37123e11	−	2.39506e11i	2.00166	−	0.650378i
$780$	−6.89719e10	+	7.02263e10i	−0.186335	+	0.189723i
$781$	−9.79505e10	+	3.01461e11i	−0.263271	+	0.810264i
$782$	−4.11957e11	+	4.11957e11i	−1.10160	+	1.10160i
$783$	6.19583e10	−	3.15693e10i	0.164836	−	0.0839882i
$784$	−7.23187e10	−	9.95381e10i	−0.191419	−	0.263466i
$785$	6.13998e11	−	2.05635e11i	1.61692	−	0.541525i
$786$	1.11943e11	+	8.13312e10i	0.293296	+	0.213092i
$787$	1.17497e11	−	7.41844e11i	0.306285	−	1.93381i	−0.0484076	−	0.998828i	$-0.515415\pi$
$787$	1.17497e11	−	7.41844e11i	0.306285	−	1.93381i	0.354693	−	0.934983i	$-0.384585\pi$
$788$	2.54792e11	+	4.03551e10i	0.660817	+	0.104663i
$789$	9.04506e10	−	1.24495e11i	0.233401	−	0.321249i
$790$	1.16776e11	−	1.05231e9i	0.299810	−	0.00270168i
$791$	−6.38504e10	+	4.63900e10i	−0.163101	+	0.118500i
$792$	−3.21035e10	−	6.30066e10i	−0.0815927	−	0.160135i
$793$	−2.07510e11	−	2.07510e11i	−0.524742	−	0.524742i
$794$	1.13607e11	+	3.69133e10i	0.285841	+	0.0928753i
$795$	2.94905e10	+	1.75921e11i	0.0738267	+	0.440401i
$796$	5.87808e10	+	1.80909e11i	0.146414	+	0.450616i
$797$	−3.79612e11	−	1.93422e11i	−0.940819	−	0.479371i	−0.0848476	−	0.996394i	$-0.527040\pi$
$797$	−3.79612e11	−	1.93422e11i	−0.940819	−	0.479371i	−0.855972	+	0.517023i	$0.827040\pi$
$798$	4.94938e9	+	3.12492e10i	0.0122050	+	0.0770596i
$799$		−	5.13270e11i		−	1.25939i
$800$	−3.35353e11	−	4.69363e10i	−0.818734	−	0.114591i
$801$	1.53446e11			0.372757
$802$	−1.66051e11	+	2.62999e10i	−0.401370	+	0.0635707i
$803$	5.54412e10	−	1.08809e11i	0.133343	−	0.261700i
$804$	7.09136e10	−	2.30412e10i	0.169709	−	0.0551418i
$805$	4.13813e10	+	7.94375e10i	0.0985418	+	0.189166i
$806$	−1.31943e11	+	4.06079e11i	−0.312642	+	0.962212i
$807$	2.36122e11	−	2.36122e11i	0.556728	−	0.556728i
$808$	5.01151e11	−	2.55349e11i	1.17577	−	0.599086i
$809$	4.06737e11	+	5.59825e11i	0.949553	+	1.30695i	0.951725	+	0.306951i	$0.0993086\pi$
$809$	4.06737e11	+	5.59825e11i	0.949553	+	1.30695i	−0.00217203	+	0.999998i	$0.500691\pi$
$810$	−2.04682e10	+	2.87126e10i	−0.0475488	+	0.0667010i
$811$	5.95806e11	+	4.32878e11i	1.37728	+	1.00065i	0.997129	+	0.0757252i	$0.0241272\pi$
$811$	5.95806e11	+	4.32878e11i	1.37728	+	1.00065i	0.380149	+	0.924925i	$0.375873\pi$
$812$	−5.01178e9	+	3.16431e10i	−0.0115284	+	0.0727873i
$813$	5.51541e10	+	8.73555e9i	0.126245	+	0.0199953i
$814$	1.41435e9	−	1.94669e9i	0.00322151	−	0.00443403i
$815$	3.86887e11	+	2.75798e11i	0.876908	+	0.625116i
$816$	1.15466e11	−	8.38911e10i	0.260432	−	0.189215i
$817$	1.68485e11	+	3.30670e11i	0.378157	+	0.742175i
$818$	2.56490e11	+	2.56490e11i	0.572871	+	0.572871i
$819$	−2.41683e10	−	7.85274e9i	−0.0537167	−	0.0174536i
$820$	−3.52955e11	+	1.83864e11i	−0.780663	+	0.406670i
$821$	−1.14596e10	−	3.52690e10i	−0.0252230	−	0.0776283i	0.937653	−	0.347574i	$-0.112994\pi$
$821$	−1.14596e10	−	3.52690e10i	−0.0252230	−	0.0776283i	−0.962876	+	0.269945i	$0.912994\pi$
$822$	6.62405e10	+	3.37512e10i	0.145090	+	0.0739268i
$823$	3.33910e10	+	2.10823e11i	0.0727830	+	0.459534i	0.996983	+	0.0776243i	$0.0247335\pi$
$823$	3.33910e10	+	2.10823e11i	0.0727830	+	0.459534i	−0.924200	+	0.381910i	$0.875267\pi$
$824$		−	5.44861e11i		−	1.18189i
$825$	−1.20740e11	−	5.88038e10i	−0.260637	−	0.126937i
$826$	−1.89507e10			−0.0407104
$827$	−2.44352e10	+	3.87015e9i	−0.0522388	+	0.00827382i	−0.182499	−	0.983206i	$-0.558419\pi$
$827$	−2.44352e10	+	3.87015e9i	−0.0522388	+	0.00827382i	0.130260	+	0.991480i	$0.458419\pi$
$828$	4.12399e10	−	8.09380e10i	0.0877398	−	0.172199i
$829$	−8.45745e11	+	2.74799e11i	−1.79069	+	0.581832i	−0.999556	−	0.0298051i	$-0.990511\pi$
$829$	−8.45745e11	+	2.74799e11i	−1.79069	+	0.581832i	−0.791139	+	0.611637i	$0.790511\pi$
$830$	−1.15358e11	+	1.93380e10i	−0.243071	+	0.0407473i
$831$	8.99827e10	−	2.76938e11i	0.188693	−	0.580736i
$832$	3.22925e11	−	3.22925e11i	0.673920	−	0.673920i
$833$	−6.93653e11	+	3.53434e11i	−1.44066	+	0.734054i
$834$	−1.43692e11	−	1.97776e11i	−0.297009	−	0.408798i
$835$	−5.96291e9	−	6.61714e11i	−0.0122663	−	1.36121i
$836$	9.88686e10	+	7.18323e10i	0.202411	+	0.147060i
$837$	2.00972e10	−	1.26889e11i	0.0409481	−	0.258536i
$838$	−1.51037e11	−	2.39219e10i	−0.306271	−	0.0485086i
$839$	4.19586e11	−	5.77511e11i	0.846786	−	1.16550i	−0.137776	−	0.990463i	$-0.543995\pi$
$839$	4.19586e11	−	5.77511e11i	0.846786	−	1.16550i	0.984562	−	0.175037i	$-0.0560046\pi$
$840$	−1.64610e10	−	4.91503e10i	−0.0330628	−	0.0987210i
$841$	−3.07280e10	+	2.23252e10i	−0.0614257	+	0.0446284i
$842$	1.27337e11	+	2.49913e11i	0.253342	+	0.497211i
$843$	−3.01676e11	−	3.01676e11i	−0.597351	−	0.597351i
$844$	−1.91991e11	−	6.23815e10i	−0.378364	−	0.122938i
$845$	−6.55828e9	−	6.44113e9i	−0.0128636	−	0.0126338i
$846$	−2.94440e10	−	9.06193e10i	−0.0574798	−	0.176905i
$847$	−5.75947e10	−	2.93460e10i	−0.111905	−	0.0570184i
$848$	−2.09669e10	−	1.32380e11i	−0.0405463	−	0.255999i
$849$		−	4.06222e11i		−	0.781867i
$850$	1.86857e11	−	6.12426e11i	0.357959	−	1.17322i
$851$	9.86226e9			0.0188043
$852$	2.32734e11	−	3.68615e10i	0.441674	−	0.0699543i
$853$	1.88486e10	−	3.69924e10i	0.0356026	−	0.0698741i	−0.872520	−	0.488578i	$-0.837516\pi$
$853$	1.88486e10	−	3.69924e10i	0.0356026	−	0.0698741i	0.908123	+	0.418704i	$0.137516\pi$
$854$	4.60642e10	−	1.49672e10i	0.0866028	−	0.0281389i
$855$	2.86840e10	−	1.92304e11i	0.0536755	−	0.359851i
$856$	−2.91258e11	+	8.96399e11i	−0.542478	+	1.66958i
$857$	−4.15858e11	+	4.15858e11i	−0.770943	+	0.770943i	−0.978271	−	0.207328i	$-0.933523\pi$
$857$	−4.15858e11	+	4.15858e11i	−0.770943	+	0.770943i	0.207328	+	0.978271i	$0.433523\pi$
$858$	1.04128e11	−	5.30557e10i	0.192140	−	0.0979000i
$859$	5.49974e11	+	7.56974e11i	1.01011	+	1.39030i	0.918910	+	0.394466i	$0.129071\pi$
$859$	5.49974e11	+	7.56974e11i	1.01011	+	1.39030i	0.0912008	+	0.995833i	$0.470929\pi$
$860$	−1.13394e11	−	1.53152e11i	−0.207298	−	0.279981i
$861$	−8.31218e10	−	6.03915e10i	−0.151252	−	0.109891i
$862$	−3.51004e9	+	2.21615e10i	−0.00635744	+	0.0401393i
$863$	−1.03454e12	−	1.63856e11i	−1.86512	−	0.295405i	−0.881025	−	0.473070i	$-0.843146\pi$
$863$	−1.03454e12	−	1.63856e11i	−1.86512	−	0.295405i	−0.984091	+	0.177665i	$0.943146\pi$
$864$	−5.21131e10	+	7.17275e10i	−0.0935173	+	0.128716i
$865$	−1.70035e11	+	5.39818e11i	−0.303721	+	0.964235i
$866$	−5.95701e10	+	4.32802e10i	−0.105915	+	0.0769516i
$867$	−2.61887e11	−	5.13983e11i	−0.463488	−	0.909646i
$868$	4.18533e10	+	4.18533e10i	0.0737311	+	0.0737311i
$869$	1.10755e11	+	3.59865e10i	0.194216	+	0.0631045i
$870$	−1.04532e11	+	2.09809e11i	−0.182462	+	0.366224i
$871$	1.21495e11	+	3.73922e11i	0.211098	+	0.649693i
$872$	2.93658e11	+	1.49626e11i	0.507897	+	0.258786i
$873$	1.84517e10	+	1.16499e11i	0.0317672	+	0.200570i
$874$		−	5.96351e11i		−	1.02201i
$875$	−8.11754e10	−	5.56884e10i	−0.138482	−	0.0950020i
$876$	−9.07824e10			−0.154165
$877$	−1.81857e11	+	2.88033e10i	−0.307420	+	0.0486905i	−0.308238	−	0.951309i	$-0.599739\pi$
$877$	−1.81857e11	+	2.88033e10i	−0.307420	+	0.0486905i	0.000818578		1.00000i	$0.499739\pi$
$878$	1.72275e11	−	3.38108e11i	0.289897	−	0.568954i
$879$	3.95388e11	−	1.28469e11i	0.662321	−	0.215201i
$880$	9.03214e10	+	4.50005e10i	0.150612	+	0.0750389i
$881$	−2.45166e10	+	7.54543e10i	−0.0406965	+	0.125251i	−0.969341	−	0.245721i	$-0.920975\pi$
$881$	−2.45166e10	+	7.54543e10i	−0.0406965	+	0.125251i	0.928644	+	0.370972i	$0.120975\pi$
$882$	−1.02191e11	+	1.02191e11i	−0.168865	+	0.168865i
$883$	2.48993e10	−	1.26868e10i	0.0409585	−	0.0208694i	−0.433391	−	0.901206i	$-0.642683\pi$
$883$	2.48993e10	−	1.26868e10i	0.0409585	−	0.0208694i	0.474350	+	0.880336i	$0.342683\pi$
$884$	−2.75075e11	−	3.78609e11i	−0.450446	−	0.619985i
$885$	1.11079e11	+	3.49883e10i	0.181075	+	0.0570361i
$886$	−5.11464e11	−	3.71601e11i	−0.830005	−	0.603034i
$887$	−1.00040e11	+	6.31625e11i	−0.161613	+	1.02039i	0.764907	+	0.644141i	$0.222785\pi$
$887$	−1.00040e11	+	6.31625e11i	−0.161613	+	1.02039i	−0.926520	+	0.376245i	$0.877215\pi$
$888$	−5.63698e9	−	8.92811e8i	−0.00906557	−	0.00143584i
$889$	−5.93362e10	+	8.16692e10i	−0.0949976	+	0.130753i
$890$	−4.15714e11	+	3.07795e11i	−0.662575	+	0.490571i
$891$	−2.84473e10	+	2.06682e10i	−0.0451368	+	0.0327938i
$892$	−9.76699e10	−	1.91688e11i	−0.154277	−	0.302786i
$893$	3.71507e11	+	3.71507e11i	0.584199	+	0.584199i
$894$	3.62723e11	+	1.17856e11i	0.567839	+	0.184502i
$895$	7.22364e11	+	1.07748e11i	1.12581	+	0.167926i
$896$	−4.35943e9	−	1.34170e10i	−0.00676391	−	0.0208172i
$897$	4.26780e11	+	2.17455e11i	0.659225	+	0.335892i
$898$	−8.19421e10	−	5.17362e11i	−0.126009	−	0.795590i
$899$		−	8.54034e11i		−	1.30748i
$900$	1.79916e9	+	9.98197e10i	0.00274220	+	0.152141i
$901$	−8.48070e11			−1.28686
$902$	4.66685e11	−	7.39156e10i	0.705014	−	0.111663i
$903$	2.23349e10	−	4.38347e10i	0.0335918	−	0.0659276i
$904$	−8.18740e11	+	2.66025e11i	−1.22595	+	0.398335i
$905$	3.95069e11	−	4.02254e11i	0.588951	−	0.599662i
$906$	−2.40673e9	+	7.40715e9i	−0.00357202	+	0.0109936i
$907$	−3.67356e11	+	3.67356e11i	−0.542822	+	0.542822i	−0.924355	−	0.381533i	$-0.875396\pi$
$907$	−3.67356e11	+	3.67356e11i	−0.542822	+	0.542822i	0.381533	+	0.924355i	$0.375396\pi$
$908$	−4.30761e11	+	2.19484e11i	−0.633713	+	0.322893i
$909$	−1.64394e11	−	2.26268e11i	−0.240785	−	0.331412i
$910$	8.12281e10	−	2.72042e10i	0.118452	−	0.0396708i
$911$	3.39471e11	+	2.46640e11i	0.492866	+	0.358088i	0.806286	−	0.591527i	$-0.201475\pi$
$911$	3.39471e11	+	2.46640e11i	0.492866	+	0.358088i	−0.313419	+	0.949615i	$0.601475\pi$
$912$	−2.28542e10	+	1.44295e11i	−0.0330359	+	0.208580i
$913$	−1.15204e11	−	1.82466e10i	−0.165801	−	0.0262602i
$914$	−5.90954e11	+	8.13378e11i	−0.846776	+	1.16549i
$915$	−2.97637e11	+	2.68209e9i	−0.424621	+	0.00382639i
$916$	−3.29964e11	+	2.39733e11i	−0.468688	+	0.340522i
$917$	4.59173e10	+	9.01178e10i	0.0649380	+	0.127448i
$918$	−1.18544e11	−	1.18544e11i	−0.166920	−	0.166920i
$919$	−1.47893e11	−	4.80534e10i	−0.207341	−	0.0673693i	0.203505	−	0.979074i	$-0.434767\pi$
$919$	−1.47893e11	−	4.80534e10i	−0.207341	−	0.0673693i	−0.410846	+	0.911705i	$0.634767\pi$
$920$	1.61526e11	+	9.63556e11i	0.225471	+	1.34501i
$921$	−1.10149e11	−	3.39005e11i	−0.153089	−	0.471160i
$922$	−1.28003e11	−	6.52206e10i	−0.177131	−	0.0902529i
$923$	1.94368e11	+	1.22719e12i	0.267804	+	1.69085i
$924$		−	1.62004e10i		−	0.0222248i
$925$	−9.56743e9	+	5.09408e9i	−0.0130686	+	0.00695823i
$926$	4.21350e10			0.0573058
$927$	−2.67599e11	+	4.23834e10i	−0.362380	+	0.0573954i
$928$	−2.67576e11	+	5.25147e11i	−0.360791	+	0.708092i
$929$	−8.81874e11	+	2.86538e11i	−1.18398	+	0.384698i	−0.833843	−	0.552002i	$-0.813864\pi$
$929$	−8.81874e11	+	2.86538e11i	−1.18398	+	0.384698i	−0.350135	+	0.936699i	$0.613864\pi$
$930$	2.00077e11	+	3.84078e11i	0.267465	+	0.513438i
$931$	2.46252e11	−	7.57885e11i	0.327778	−	1.00880i
$932$	4.95310e9	−	4.95310e9i	0.00656468	−	0.00656468i
$933$	−2.43325e11	+	1.23980e11i	−0.321115	+	0.163616i
$934$	−9.75826e10	−	1.34311e11i	−0.128229	−	0.176492i
$935$	3.70636e11	−	5.19926e11i	0.484955	−	0.680291i
$936$	−2.24249e11	−	1.62926e11i	−0.292164	−	0.212270i
$937$	2.28852e11	−	1.44491e12i	0.296890	−	1.87449i	−0.163164	−	0.986599i	$-0.552170\pi$
$937$	2.28852e11	−	1.44491e12i	0.296890	−	1.87449i	0.460054	−	0.887891i	$-0.347830\pi$
$938$	−6.40911e10	−	1.01510e10i	−0.0827917	−	0.0131129i
$939$	−2.04517e11	+	2.81494e11i	−0.263068	+	0.362081i
$940$	−2.19673e11	−	1.56597e11i	−0.281362	−	0.200573i
$941$	7.39185e11	−	5.37049e11i	0.942746	−	0.684945i	−0.00633430	−	0.999980i	$-0.502016\pi$
$941$	7.39185e11	−	5.37049e11i	0.942746	−	0.684945i	0.949080	+	0.315035i	$0.102016\pi$
$942$	2.59456e11	+	5.09211e11i	0.329504	+	0.646688i
$943$	1.36939e12	+	1.36939e12i	1.73173	+	1.73173i
$944$	−8.32236e10	−	2.70410e10i	−0.104799	−	0.0340514i
$945$	−2.28588e10	+	1.19078e10i	−0.0286634	+	0.0149316i
$946$	6.99143e10	+	2.15174e11i	0.0872975	+	0.268674i
$947$	−1.20138e12	−	6.12135e11i	−1.49376	−	0.761110i	−0.499322	−	0.866416i	$-0.666418\pi$
$947$	−1.20138e12	−	6.12135e11i	−1.49376	−	0.761110i	−0.994440	+	0.105306i	$0.966418\pi$
$948$	−1.35427e10	−	8.55054e10i	−0.0167677	−	0.105867i
$949$		−	4.78689e11i		−	0.590185i
$950$	3.08029e11	+	5.78524e11i	0.378178	+	0.710275i
$951$	3.23415e11			0.395402
$952$	2.43404e11	−	3.85514e10i	0.296333	−	0.0469345i
$953$	1.56153e10	−	3.06468e10i	0.0189313	−	0.0371547i	−0.881347	−	0.472469i	$-0.843363\pi$
$953$	1.56153e10	−	3.06468e10i	0.0189313	−	0.0371547i	0.900278	+	0.435314i	$0.143363\pi$
$954$	−1.49729e11	+	4.86500e10i	−0.180765	+	0.0587340i
$955$	4.21002e10	−	7.05747e9i	0.0506140	−	0.00848468i
$956$	−1.91435e11	+	5.89178e11i	−0.229187	+	0.705366i
$957$	−1.65288e11	+	1.65288e11i	−0.197058	+	0.197058i
$958$	1.06306e12	−	5.41654e11i	1.26210	−	0.643072i
$959$	3.19413e10	+	4.39634e10i	0.0377640	+	0.0519777i
$960$	−4.17385e9	−	4.63180e11i	−0.00491419	−	0.545336i
$961$	−5.86487e11	−	4.26108e11i	−0.687646	−	0.499604i
$962$	1.47550e9	−	9.31594e9i	0.00172282	−	0.0108774i
$963$	4.62907e11	+	7.33172e10i	0.538255	+	0.0852512i
$964$	3.53669e11	−	4.86784e11i	0.409533	−	0.563674i
$965$	3.37571e9	+	1.00794e10i	0.00389275	+	0.0116232i
$966$	−6.39564e10	+	4.64670e10i	−0.0734472	+	0.0533625i
$967$	−3.18708e11	−	6.25501e11i	−0.364492	−	0.715355i	0.633817	−	0.773483i	$-0.281487\pi$
$967$	−3.18708e11	−	6.25501e11i	−0.364492	−	0.715355i	−0.998309	+	0.0581274i	$0.981487\pi$
$968$	−4.98564e11	−	4.98564e11i	−0.567832	−	0.567832i
$969$	8.79161e11	+	2.85657e11i	0.997180	+	0.324003i
$970$	−2.83674e11	−	2.78607e11i	−0.320429	−	0.314706i
$971$	−1.97464e10	−	6.07731e10i	−0.0222132	−	0.0683651i	0.939335	−	0.343000i	$-0.111443\pi$
$971$	−1.97464e10	−	6.07731e10i	−0.0222132	−	0.0683651i	−0.961549	+	0.274635i	$0.911443\pi$
$972$	2.32906e10	+	1.18672e10i	0.0260925	+	0.0132948i
$973$	−2.79537e10	−	1.76492e11i	−0.0311880	−	0.196913i
$974$			2.63073e11i			0.292308i
$975$	−5.26342e11	+	9.48682e9i	−0.582437	+	0.0104979i
$976$	2.23651e11			0.246474
$977$	5.28662e11	−	8.37318e10i	0.580229	−	0.0918993i	0.140581	−	0.990069i	$-0.455103\pi$
$977$	5.28662e11	−	8.37318e10i	0.580229	−	0.0918993i	0.439648	+	0.898170i	$0.355103\pi$
$978$	−1.90380e11	+	3.73643e11i	−0.208097	+	0.408414i
$979$	−4.90568e11	+	1.59395e11i	−0.534033	+	0.173518i
$980$	−6.03661e10	+	4.04706e11i	−0.0654468	+	0.438769i
$981$	5.06432e10	−	1.55864e11i	0.0546821	−	0.168294i
$982$	−1.33771e11	+	1.33771e11i	−0.143852	+	0.143852i
$983$	1.60647e11	−	8.18537e10i	0.172051	−	0.0876646i	−0.365844	−	0.930676i	$-0.619220\pi$
$983$	1.60647e11	−	8.18537e10i	0.172051	−	0.0876646i	0.537895	+	0.843012i	$0.319220\pi$
$984$	−6.58734e11	−	9.06670e11i	−0.702635	−	0.967094i
$985$	8.20961e11	+	1.10881e12i	0.872123	+	1.17791i
$986$	−9.01623e11	−	6.55067e11i	−0.953932	−	0.693072i
$987$	1.08953e10	−	6.87901e10i	0.0114807	−	0.0724865i
$988$	4.73139e11	+	7.49378e10i	0.496547	+	0.0786454i
$989$	−5.45055e11	+	7.50203e11i	−0.569711	+	0.784140i
$990$	3.56111e10	−	1.13056e11i	0.0370719	−	0.117694i
$991$	4.23887e10	−	3.07972e10i	0.0439497	−	0.0319313i	−0.565594	−	0.824684i	$-0.691353\pi$
$991$	4.23887e10	−	3.07972e10i	0.0439497	−	0.0319313i	0.609543	+	0.792753i	$0.291353\pi$
$992$	4.94347e11	+	9.70211e11i	0.510488	+	1.00189i
$993$	−2.72412e11	−	2.72412e11i	−0.280175	−	0.280175i
$994$	−1.95030e11	−	6.33691e10i	−0.199782	−	0.0649131i
$995$	−4.53664e11	+	9.10558e11i	−0.462852	+	0.928999i
$996$	2.67946e10	+	8.24655e10i	0.0272277	+	0.0837982i
$997$	−6.94560e11	−	3.53896e11i	−0.702957	−	0.358175i	0.0656966	−	0.997840i	$-0.479073\pi$
$997$	−6.94560e11	−	3.53896e11i	−0.702957	−	0.358175i	−0.768654	+	0.639665i	$0.779073\pi$
$998$	−8.09016e10	−	5.10792e11i	−0.0815520	−	0.514899i
$999$			2.83795e9i			0.00284933i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.k.a.13.14	✓	320
25.2	odd	20	inner	75.9.k.a.52.14	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.9.k.a.13.14	✓	320	1.1	even	1	trivial
75.9.k.a.52.14	yes	320	25.2	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.6504 + 1.84524i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(-111.144 + 36.1127i) q^{4} +(-559.413 - 278.715i) q^{5} +(170.462 - 524.628i) q^{6} +(285.116 - 285.116i) q^{7} +(3918.78 - 1996.72i) q^{8} +(-1285.49 - 1769.32i) q^{9} +O(q^{10})\)	\(q+(-11.6504 + 1.84524i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(-111.144 + 36.1127i) q^{4} +(-559.413 - 278.715i) q^{5} +(170.462 - 524.628i) q^{6} +(285.116 - 285.116i) q^{7} +(3918.78 - 1996.72i) q^{8} +(-1285.49 - 1769.32i) q^{9} +(7031.68 + 2214.88i) q^{10} +(5947.63 + 4321.20i) q^{11} +(854.938 - 5397.87i) q^{12} +(28462.5 + 4508.02i) q^{13} +(-2795.61 + 3847.82i) q^{14} +(23490.5 - 17392.4i) q^{15} +(-17767.6 + 12908.9i) q^{16} +(63088.2 + 123817. i) q^{17} +(18241.3 + 18241.3i) q^{18} +(-135283. - 43956.1i) q^{19} +(72240.3 + 10775.4i) q^{20} +(5826.98 + 17933.6i) q^{21} +(-77265.9 - 39368.9i) q^{22} +(-55600.3 - 351046. i) q^{23} +205681. i q^{24} +(235261. + 311833. i) q^{25} -339918. q^{26} +(101017. - 15999.5i) q^{27} +(-21392.5 + 41985.1i) q^{28} +(646624. - 210101. i) q^{29} +(-241580. + 245974. i) q^{30} +(388161. - 1.19464e6i) q^{31} +(-612971. + 612971. i) q^{32} +(-306331. + 156084. i) q^{33} +(-963475. - 1.32611e6i) q^{34} +(-238964. + 80031.7i) q^{35} +(206769. + 150226. i) q^{36} +(-4340.75 + 27406.4i) q^{37} +(1.65721e6 + 262476. i) q^{38} +(-792131. + 1.09027e6i) q^{39} +(-2.74874e6 + 24769.7i) q^{40} +(-4.40813e6 + 3.20269e6i) q^{41} +(-100978. - 198181. i) q^{42} +(-1.84485e6 - 1.84485e6i) q^{43} +(-817091. - 265489. i) q^{44} +(225983. + 1.34806e6i) q^{45} +(1.29553e6 + 3.98723e6i) q^{46} +(-3.29098e6 - 1.67684e6i) q^{47} +(-160668. - 1.01442e6i) q^{48} +5.60222e6i q^{49} +(-3.31630e6 - 3.19887e6i) q^{50} -6.49868e6 q^{51} +(-3.32623e6 + 526822. i) q^{52} +(-2.77062e6 + 5.43766e6i) q^{53} +(-1.14736e6 + 372800. i) q^{54} +(-2.12280e6 - 4.07503e6i) q^{55} +(548011. - 1.68660e6i) q^{56} +(4.70377e6 - 4.70377e6i) q^{57} +(-7.14574e6 + 3.64094e6i) q^{58} +(2.34200e6 + 3.22349e6i) q^{59} +(-1.98273e6 + 2.78136e6i) q^{60} +(-8.23867e6 - 5.98574e6i) q^{61} +(-2.31784e6 + 1.46343e7i) q^{62} +(-870974. - 137949. i) q^{63} +(9.31497e6 - 1.28210e7i) q^{64} +(-1.46659e7 - 1.04548e7i) q^{65} +(3.28087e6 - 2.38369e6i) q^{66} +(6.19395e6 + 1.21563e7i) q^{67} +(-1.14832e7 - 1.14832e7i) q^{68} +(1.58079e7 + 5.13631e6i) q^{69} +(2.63634e6 - 1.37335e6i) q^{70} +(1.33236e7 + 4.10057e7i) q^{71} +(-8.57038e6 - 4.36683e6i) q^{72} +(-2.59856e6 - 1.64066e7i) q^{73} -327305. i q^{74} +(-1.79884e7 + 3.18239e6i) q^{75} +1.66232e7 q^{76} +(2.92781e6 - 463719. i) q^{77} +(7.21682e6 - 1.41638e7i) q^{78} +(1.50653e7 - 4.89501e6i) q^{79} +(1.35373e7 - 2.26933e6i) q^{80} +(-1.47802e6 + 4.54887e6i) q^{81} +(4.54467e7 - 4.54467e7i) q^{82} +(-1.41366e7 + 7.20295e6i) q^{83} +(-1.29526e6 - 1.78277e6i) q^{84} +(-782620. - 8.68487e7i) q^{85} +(2.48975e7 + 1.80891e7i) q^{86} +(-4.97396e6 + 3.14043e7i) q^{87} +(3.19357e7 + 5.05812e6i) q^{88} +(-4.12406e7 + 5.67629e7i) q^{89} +(-5.12030e6 - 1.52885e7i) q^{90} +(9.40043e6 - 6.82981e6i) q^{91} +(1.88569e7 + 3.70087e7i) q^{92} +(4.15374e7 + 4.15374e7i) q^{93} +(4.14355e7 + 1.34632e7i) q^{94} +(6.34279e7 + 6.22949e7i) q^{95} +(-1.25274e7 - 3.85555e7i) q^{96} +(-4.80547e7 - 2.44851e7i) q^{97} +(-1.03375e7 - 6.52681e7i) q^{98} -1.60781e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) \) 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8	\( 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8} + 25496 q^{10} - 22680 q^{12} - 133420 q^{13} + 59616 q^{15} + 1310720 q^{16} + 168000 q^{17} - 718900 q^{19} - 641844 q^{20} + 2257100 q^{22} + 1089120 q^{23} - 1459756 q^{25} + 1827840 q^{26} + 3260740 q^{28} + 3913800 q^{29} + 3585384 q^{30} - 641460 q^{32} - 1458000 q^{33} - 4121600 q^{34} + 853140 q^{35} - 22394880 q^{36} - 14553460 q^{37} + 17491260 q^{38} + 3203652 q^{40} + 8749440 q^{41} + 9643860 q^{42} - 23946520 q^{43} + 4277700 q^{44} - 2204496 q^{45} + 26491200 q^{47} - 3661200 q^{48} - 47100924 q^{50} - 169691020 q^{52} - 97028940 q^{53} + 27431764 q^{55} - 4714200 q^{57} + 179119320 q^{58} + 95587200 q^{59} + 38705364 q^{60} + 36738240 q^{61} - 296094660 q^{62} - 9928980 q^{63} - 59695100 q^{64} + 24018972 q^{65} - 88558160 q^{67} + 197811840 q^{68} + 220501420 q^{70} + 38185020 q^{72} + 110964400 q^{73} + 51345576 q^{75} - 97175880 q^{77} - 131709240 q^{78} - 138506200 q^{79} - 339741204 q^{80} + 382637520 q^{81} + 217169400 q^{82} + 862340400 q^{83} + 743029200 q^{84} + 619431268 q^{85} - 335756340 q^{87} - 1380992420 q^{88} - 1141686000 q^{89} - 265834224 q^{90} - 407198400 q^{92} + 402028920 q^{93} + 290042200 q^{94} + 1436174256 q^{95} - 165325860 q^{96} + 1057772920 q^{97} + 1077594720 q^{98}+O(q^{100}) \) 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8 + 25496 * q^10 - 22680 * q^12 - 133420 * q^13 + 59616 * q^15 + 1310720 * q^16 + 168000 * q^17 - 718900 * q^19 - 641844 * q^20 + 2257100 * q^22 + 1089120 * q^23 - 1459756 * q^25 + 1827840 * q^26 + 3260740 * q^28 + 3913800 * q^29 + 3585384 * q^30 - 641460 * q^32 - 1458000 * q^33 - 4121600 * q^34 + 853140 * q^35 - 22394880 * q^36 - 14553460 * q^37 + 17491260 * q^38 + 3203652 * q^40 + 8749440 * q^41 + 9643860 * q^42 - 23946520 * q^43 + 4277700 * q^44 - 2204496 * q^45 + 26491200 * q^47 - 3661200 * q^48 - 47100924 * q^50 - 169691020 * q^52 - 97028940 * q^53 + 27431764 * q^55 - 4714200 * q^57 + 179119320 * q^58 + 95587200 * q^59 + 38705364 * q^60 + 36738240 * q^61 - 296094660 * q^62 - 9928980 * q^63 - 59695100 * q^64 + 24018972 * q^65 - 88558160 * q^67 + 197811840 * q^68 + 220501420 * q^70 + 38185020 * q^72 + 110964400 * q^73 + 51345576 * q^75 - 97175880 * q^77 - 131709240 * q^78 - 138506200 * q^79 - 339741204 * q^80 + 382637520 * q^81 + 217169400 * q^82 + 862340400 * q^83 + 743029200 * q^84 + 619431268 * q^85 - 335756340 * q^87 - 1380992420 * q^88 - 1141686000 * q^89 - 265834224 * q^90 - 407198400 * q^92 + 402028920 * q^93 + 290042200 * q^94 + 1436174256 * q^95 - 165325860 * q^96 + 1057772920 * q^97 + 1077594720 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more