LMFDB - Embedded newform 75.9.k.a.13.5

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			13.5
Character	$\chi$	$=$	75.13
Dual form			75.9.k.a.52.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-26.6845 + 4.22641i) q^{2} +(21.2310 - 41.6683i) q^{3} +(450.730 - 146.451i) q^{4} +(365.591 - 506.921i) q^{5} +(-390.433 + 1201.63i) q^{6} +(516.394 - 516.394i) q^{7} +(-5246.00 + 2672.97i) q^{8} +(-1285.49 - 1769.32i) q^{9} +O(q^{10})$	\(q+(-26.6845 + 4.22641i) q^{2} +(21.2310 - 41.6683i) q^{3} +(450.730 - 146.451i) q^{4} +(365.591 - 506.921i) q^{5} +(-390.433 + 1201.63i) q^{6} +(516.394 - 516.394i) q^{7} +(-5246.00 + 2672.97i) q^{8} +(-1285.49 - 1769.32i) q^{9} +(-7613.15 + 15072.1i) q^{10} +(-17439.2 - 12670.3i) q^{11} +(3467.10 - 21890.4i) q^{12} +(-29217.9 - 4627.66i) q^{13} +(-11597.2 + 15962.2i) q^{14} +(-13360.6 - 25996.0i) q^{15} +(30535.9 - 22185.7i) q^{16} +(20801.5 + 40825.2i) q^{17} +(41780.4 + 41780.4i) q^{18} +(84921.4 + 27592.6i) q^{19} +(90543.6 - 282025. i) q^{20} +(-10553.7 - 32480.8i) q^{21} +(518906. + 264396. i) q^{22} +(-62772.2 - 396328. i) q^{23} +275342. i q^{24} +(-123312. - 370651. i) q^{25} +799224. q^{26} +(-101017. + 15999.5i) q^{27} +(157128. - 308381. i) q^{28} +(523617. - 170133. i) q^{29} +(466391. + 637222. i) q^{30} +(-412331. + 1.26902e6i) q^{31} +(344721. - 344721. i) q^{32} +(-898202. + 457657. i) q^{33} +(-727622. - 1.00149e6i) q^{34} +(-72982.0 - 450560. i) q^{35} +(-838526. - 609225. i) q^{36} +(-93416.1 + 589806. i) q^{37} +(-2.38270e6 - 377383. i) q^{38} +(-813153. + 1.11921e6i) q^{39} +(-562905. + 3.63652e6i) q^{40} +(-1.70139e6 + 1.23613e6i) q^{41} +(418897. + 822131. i) q^{42} +(-1.63370e6 - 1.63370e6i) q^{43} +(-9.71595e6 - 3.15690e6i) q^{44} +(-1.36687e6 + 4792.65i) q^{45} +(3.35009e6 + 1.03105e7i) q^{46} +(-3.45033e6 - 1.75803e6i) q^{47} +(-276128. - 1.74340e6i) q^{48} +5.23147e6i q^{49} +(4.85704e6 + 9.36947e6i) q^{50} +2.14275e6 q^{51} +(-1.38471e7 + 2.19317e6i) q^{52} +(4.17543e6 - 8.19475e6i) q^{53} +(2.62796e6 - 853876. i) q^{54} +(-1.27984e7 + 4.20814e6i) q^{55} +(-1.32870e6 + 4.08931e6i) q^{56} +(2.95271e6 - 2.95271e6i) q^{57} +(-1.32534e7 + 6.75295e6i) q^{58} +(-6.04263e6 - 8.31697e6i) q^{59} +(-9.82917e6 - 9.76049e6i) q^{60} +(1.21670e7 + 8.83982e6i) q^{61} +(5.63943e6 - 3.56060e7i) q^{62} +(-1.57748e6 - 249849. i) q^{63} +(-1.34213e7 + 1.84728e7i) q^{64} +(-1.30276e7 + 1.31193e7i) q^{65} +(2.20338e7 - 1.60085e7i) q^{66} +(6.21770e6 + 1.22029e7i) q^{67} +(1.53548e7 + 1.53548e7i) q^{68} +(-1.78470e7 - 5.79884e6i) q^{69} +(3.85174e6 + 1.17145e7i) q^{70} +(8.29281e6 + 2.55226e7i) q^{71} +(1.14730e7 + 5.84579e6i) q^{72} +(509130. + 3.21452e6i) q^{73} -1.61335e7i q^{74} +(-1.80624e7 - 2.73111e6i) q^{75} +4.23176e7 q^{76} +(-1.55484e7 + 2.46262e6i) q^{77} +(1.69683e7 - 3.33023e7i) q^{78} +(-2.66876e7 + 8.67131e6i) q^{79} +(-82714.3 - 2.35902e7i) q^{80} +(-1.47802e6 + 4.54887e6i) q^{81} +(4.01764e7 - 4.01764e7i) q^{82} +(7.42226e7 - 3.78183e7i) q^{83} +(-9.51370e6 - 1.30945e7i) q^{84} +(2.83000e7 + 4.38062e6i) q^{85} +(5.04990e7 + 3.66897e7i) q^{86} +(4.02777e6 - 2.54303e7i) q^{87} +(1.25353e8 + 1.98540e7i) q^{88} +(-5.17975e7 + 7.12931e7i) q^{89} +(3.64539e7 - 5.90483e6i) q^{90} +(-1.74777e7 + 1.26983e7i) q^{91} +(-8.63359e7 - 1.69444e8i) q^{92} +(4.41238e7 + 4.41238e7i) q^{93} +(9.95006e7 + 3.23297e7i) q^{94} +(4.50337e7 - 3.29608e7i) q^{95} +(-7.04514e6 - 2.16827e7i) q^{96} +(-2.10432e7 - 1.07221e7i) q^{97} +(-2.21104e7 - 1.39599e8i) q^{98} +4.71430e7i 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 $

$2$	−26.6845	+	4.22641i	−1.66778	+	0.264151i	−0.917723	−	0.397221i	$-0.869975\pi$
$2$	−26.6845	+	4.22641i	−1.66778	+	0.264151i	−0.750059	+	0.661371i	$0.769975\pi$
$3$	21.2310	−	41.6683i	0.262112	−	0.514423i
$3$	21.2310	−	41.6683i	0.262112	−	0.514423i
$4$	450.730	−	146.451i	1.76066	−	0.572074i
$5$	365.591	−	506.921i	0.584945	−	0.811073i
$5$	365.591	−	506.921i	0.584945	−	0.811073i
$6$	−390.433	+	1201.63i	−0.301260	+	0.927182i
$7$	516.394	−	516.394i	0.215075	−	0.215075i	−0.591344	−	0.806419i	$-0.701403\pi$
$7$	516.394	−	516.394i	0.215075	−	0.215075i	0.806419	+	0.591344i	$0.201403\pi$
$8$	−5246.00	+	2672.97i	−1.28076	+	0.652581i
$9$	−1285.49	−	1769.32i	−0.195928	−	0.269672i
$10$	−7613.15	+	15072.1i	−0.761315	+	1.50721i
$11$	−17439.2	−	12670.3i	−1.19112	−	0.865400i	−0.197738	−	0.980255i	$-0.563360\pi$
$11$	−17439.2	−	12670.3i	−1.19112	−	0.865400i	−0.993382	+	0.114855i	$0.963360\pi$
$12$	3467.10	−	21890.4i	0.167202	−	1.05567i
$13$	−29217.9	−	4627.66i	−1.02300	−	0.162027i	−0.377677	−	0.925937i	$-0.623277\pi$
$13$	−29217.9	−	4627.66i	−1.02300	−	0.162027i	−0.645323	+	0.763910i	$0.723277\pi$
$14$	−11597.2	+	15962.2i	−0.301885	+	0.415510i
$15$	−13360.6	−	25996.0i	−0.263914	−	0.513501i
$16$	30535.9	−	22185.7i	0.465941	−	0.338526i
$17$	20801.5	+	40825.2i	0.249057	+	0.488802i	0.981360	−	0.192177i	$-0.0615547\pi$
$17$	20801.5	+	40825.2i	0.249057	+	0.488802i	−0.732303	+	0.680979i	$0.761555\pi$
$18$	41780.4	+	41780.4i	0.398000	+	0.398000i
$19$	84921.4	+	27592.6i	0.651632	+	0.211728i	0.616134	−	0.787642i	$-0.288698\pi$
$19$	84921.4	+	27592.6i	0.651632	+	0.211728i	0.0354986	+	0.999370i	$0.488698\pi$
$20$	90543.6	−	282025.i	0.565898	−	1.76266i
$21$	−10553.7	−	32480.8i	−0.0542658	−	0.167013i
$22$	518906.	+	264396.i	2.21512	+	1.12866i
$23$	−62772.2	−	396328.i	−0.224314	−	1.41626i	−0.800691	−	0.599077i	$-0.795534\pi$
$23$	−62772.2	−	396328.i	−0.224314	−	1.41626i	0.576378	−	0.817184i	$-0.304466\pi$
$24$			275342.i			0.829902i
$25$	−123312.	−	370651.i	−0.315679	−	0.948866i
$26$	799224.			1.74894
$27$	−101017.	+	15999.5i	−0.190081	+	0.0301058i
$28$	157128.	−	308381.i	0.255635	−	0.501713i
$29$	523617.	−	170133.i	0.740324	−	0.240546i	0.0855114	−	0.996337i	$-0.472748\pi$
$29$	523617.	−	170133.i	0.740324	−	0.240546i	0.654812	+	0.755791i	$0.272748\pi$
$30$	466391.	+	637222.i	0.575792	+	0.786694i
$31$	−412331.	+	1.26902e6i	−0.446477	+	1.37412i	0.434379	+	0.900730i	$0.356968\pi$
$31$	−412331.	+	1.26902e6i	−0.446477	+	1.37412i	−0.880856	+	0.473385i	$0.843032\pi$
$32$	344721.	−	344721.i	0.328752	−	0.328752i
$33$	−898202.	+	457657.i	−0.757388	+	0.385908i
$34$	−727622.	−	1.00149e6i	−0.544490	−	0.749426i
$35$	−72982.0	−	450560.i	−0.0486344	−	0.300248i
$36$	−838526.	−	609225.i	−0.499237	−	0.362717i
$37$	−93416.1	+	589806.i	−0.0498442	+	0.314704i	0.950152	+	0.311789i	$0.100928\pi$
$37$	−93416.1	+	589806.i	−0.0498442	+	0.314704i	−0.999996	+	0.00291559i	$0.999072\pi$
$38$	−2.38270e6	−	377383.i	−1.14271	−	0.180987i
$39$	−813153.	+	1.11921e6i	−0.351491	+	0.483785i
$40$	−562905.	+	3.63652e6i	−0.219885	+	1.42052i
$41$	−1.70139e6	+	1.23613e6i	−0.602100	+	0.437451i	−0.846624	−	0.532192i	$-0.821368\pi$
$41$	−1.70139e6	+	1.23613e6i	−0.602100	+	0.437451i	0.244524	+	0.969643i	$0.421368\pi$
$42$	418897.	+	822131.i	0.134620	+	0.264207i
$43$	−1.63370e6	−	1.63370e6i	−0.477856	−	0.477856i	0.426589	−	0.904446i	$-0.359715\pi$
$43$	−1.63370e6	−	1.63370e6i	−0.477856	−	0.477856i	−0.904446	+	0.426589i	$0.859715\pi$
$44$	−9.71595e6	−	3.15690e6i	−2.59224	−	0.842268i
$45$	−1.36687e6	+	4792.65i	−0.333331	+	0.00116876i
$46$	3.35009e6	+	1.03105e7i	0.748213	+	2.30276i
$47$	−3.45033e6	−	1.75803e6i	−0.707081	−	0.360276i	0.0631819	−	0.998002i	$-0.479875\pi$
$47$	−3.45033e6	−	1.75803e6i	−0.707081	−	0.360276i	−0.770263	+	0.637726i	$0.779875\pi$
$48$	−276128.	−	1.74340e6i	−0.0520170	−	0.328422i
$49$			5.23147e6i			0.907486i
$50$	4.85704e6	+	9.36947e6i	0.777127	+	1.49911i
$51$	2.14275e6			0.316732
$52$	−1.38471e7	+	2.19317e6i	−1.89385	+	0.299957i
$53$	4.17543e6	−	8.19475e6i	0.529173	−	1.03856i	−0.459458	−	0.888200i	$-0.651956\pi$
$53$	4.17543e6	−	8.19475e6i	0.529173	−	1.03856i	0.988631	−	0.150361i	$-0.0480438\pi$
$54$	2.62796e6	−	853876.i	0.309061	−	0.100420i
$55$	−1.27984e7	+	4.20814e6i	−1.39864	+	0.459874i
$56$	−1.32870e6	+	4.08931e6i	−0.135106	+	0.415813i
$57$	2.95271e6	−	2.95271e6i	0.279718	−	0.279718i
$58$	−1.32534e7	+	6.75295e6i	−1.17116	+	0.596735i
$59$	−6.04263e6	−	8.31697e6i	−0.498676	−	0.686368i	0.483283	−	0.875464i	$-0.339444\pi$
$59$	−6.04263e6	−	8.31697e6i	−0.498676	−	0.686368i	−0.981959	+	0.189096i	$0.939444\pi$
$60$	−9.82917e6	−	9.76049e6i	−0.758424	−	0.753124i
$61$	1.21670e7	+	8.83982e6i	0.878745	+	0.638446i	0.932919	−	0.360086i	$-0.117253\pi$
$61$	1.21670e7	+	8.83982e6i	0.878745	+	0.638446i	−0.0541741	+	0.998532i	$0.517253\pi$
$62$	5.63943e6	−	3.56060e7i	0.381653	−	2.40966i
$63$	−1.57748e6	−	249849.i	−0.100139	−	0.0158604i
$64$	−1.34213e7	+	1.84728e7i	−0.799972	+	1.10107i
$65$	−1.30276e7	+	1.31193e7i	−0.729815	+	0.734951i
$66$	2.20338e7	−	1.60085e7i	1.16122	−	0.843675i
$67$	6.21770e6	+	1.22029e7i	0.308554	+	0.605571i	0.992259	−	0.124188i	$-0.0396325\pi$
$67$	6.21770e6	+	1.22029e7i	0.308554	+	0.605571i	−0.683705	+	0.729759i	$0.739632\pi$
$68$	1.53548e7	+	1.53548e7i	0.718137	+	0.718137i
$69$	−1.78470e7	−	5.79884e6i	−0.787352	−	0.255826i
$70$	3.85174e6	+	1.17145e7i	0.160422	+	0.487901i
$71$	8.29281e6	+	2.55226e7i	0.326338	+	1.00437i	0.970833	+	0.239757i	$0.0770678\pi$
$71$	8.29281e6	+	2.55226e7i	0.326338	+	1.00437i	−0.644495	+	0.764609i	$0.722932\pi$
$72$	1.14730e7	+	5.84579e6i	0.426921	+	0.217527i
$73$	509130.	+	3.21452e6i	0.0179282	+	0.113194i	0.995030	−	0.0995802i	$-0.0317500\pi$
$73$	509130.	+	3.21452e6i	0.0179282	+	0.113194i	−0.977101	+	0.212775i	$0.931750\pi$
$74$		−	1.61335e7i		−	0.538024i
$75$	−1.80624e7	−	2.73111e6i	−0.570861	−	0.0863164i
$76$	4.23176e7			1.26843
$77$	−1.55484e7	+	2.46262e6i	−0.442305	+	0.0700543i
$78$	1.69683e7	−	3.33023e7i	0.458417	−	0.899695i
$79$	−2.66876e7	+	8.67131e6i	−0.685173	+	0.222626i	−0.630859	−	0.775898i	$-0.717297\pi$
$79$	−2.66876e7	+	8.67131e6i	−0.685173	+	0.222626i	−0.0543143	+	0.998524i	$0.517297\pi$
$80$	−82714.3	−	2.35902e7i	−0.00201939	−	0.575932i
$81$	−1.47802e6	+	4.54887e6i	−0.0343352	+	0.105673i
$82$	4.01764e7	−	4.01764e7i	0.888618	−	0.888618i
$83$	7.42226e7	−	3.78183e7i	1.56395	−	0.796873i	0.564363	−	0.825527i	$-0.309122\pi$
$83$	7.42226e7	−	3.78183e7i	1.56395	−	0.796873i	0.999589	+	0.0286533i	$0.00912189\pi$
$84$	−9.51370e6	−	1.30945e7i	−0.191088	−	0.263009i
$85$	2.83000e7	+	4.38062e6i	0.542139	+	0.0839188i
$86$	5.04990e7	+	3.66897e7i	0.923186	+	0.670734i
$87$	4.02777e6	−	2.54303e7i	0.0703052	−	0.443889i
$88$	1.25353e8	+	1.98540e7i	2.09028	+	0.331069i
$89$	−5.17975e7	+	7.12931e7i	−0.825560	+	1.13629i	0.163174	+	0.986597i	$0.447827\pi$
$89$	−5.17975e7	+	7.12931e7i	−0.825560	+	1.13629i	−0.988733	+	0.149688i	$0.952173\pi$
$90$	3.64539e7	−	5.90483e6i	0.555615	−	0.0899989i
$91$	−1.74777e7	+	1.26983e7i	−0.254869	+	0.185173i
$92$	−8.63359e7	−	1.69444e8i	−1.20515	−	2.36524i
$93$	4.41238e7	+	4.41238e7i	0.589849	+	0.589849i
$94$	9.95006e7	+	3.23297e7i	1.27442	+	0.414086i
$95$	4.50337e7	−	3.29608e7i	0.552896	−	0.404672i
$96$	−7.04514e6	−	2.16827e7i	−0.0829478	−	0.255287i
$97$	−2.10432e7	−	1.07221e7i	−0.237698	−	0.121113i	0.331085	−	0.943601i	$-0.392585\pi$
$97$	−2.10432e7	−	1.07221e7i	−0.237698	−	0.121113i	−0.568783	+	0.822488i	$0.692585\pi$
$98$	−2.21104e7	−	1.39599e8i	−0.239713	−	1.51349i
$99$			4.71430e7i			0.490769i
$100$	−1.09863e8	−	1.49004e8i	−1.09863	−	1.49004i
$101$	−1.77169e8			−1.70256			−0.851280	−	0.524711i	$-0.824173\pi$
$101$	−1.77169e8			−1.70256			−0.851280	+	0.524711i	$0.824173\pi$
$102$	−5.71783e7	+	9.05616e6i	−0.528239	+	0.0836649i
$103$	−4.40707e7	+	8.64935e7i	−0.391562	+	0.768484i	−0.999678	−	0.0253641i	$-0.991925\pi$
$103$	−4.40707e7	+	8.64935e7i	−0.391562	+	0.768484i	0.608116	+	0.793848i	$0.291925\pi$
$104$	1.65647e8	−	5.38219e7i	1.41596	−	0.460072i
$105$	−2.03235e7	−	6.52482e6i	−0.167202	−	0.0536798i
$106$	−7.67850e7	+	2.36320e8i	−0.608209	+	1.87187i
$107$	−1.30399e8	+	1.30399e8i	−0.994809	+	0.994809i	−0.999987	−	0.00517770i	$-0.998352\pi$
$107$	−1.30399e8	+	1.30399e8i	−0.994809	+	0.994809i	0.00517770	+	0.999987i	$0.498352\pi$
$108$	−4.31881e7	+	2.20054e7i	−0.317445	+	0.161747i
$109$	−4.68562e7	−	6.44921e7i	−0.331941	−	0.456878i	0.610125	−	0.792305i	$-0.291119\pi$
$109$	−4.68562e7	−	6.44921e7i	−0.331941	−	0.456878i	−0.942066	+	0.335427i	$0.891119\pi$
$110$	3.23735e8	−	1.66384e8i	2.21115	−	1.13642i
$111$	2.25929e7	+	1.64147e7i	0.148826	+	0.108129i
$112$	4.31204e6	−	2.72251e7i	0.0274038	−	0.173021i
$113$	−2.84382e7	−	4.50417e6i	−0.174417	−	0.0276249i	0.0686151	−	0.997643i	$-0.478142\pi$
$113$	−2.84382e7	−	4.50417e6i	−0.174417	−	0.0276249i	−0.243032	+	0.970018i	$0.578142\pi$
$114$	−6.63122e7	+	9.12708e7i	−0.392621	+	0.540397i
$115$	−2.23856e8	−	1.13073e8i	−1.27990	−	0.646500i
$116$	2.11094e8	−	1.53369e8i	1.16585	−	0.847041i
$117$	2.93714e7	+	5.76446e7i	0.156740	+	0.307621i
$118$	1.96396e8	+	1.96396e8i	1.01299	+	1.01299i
$119$	3.18237e7	+	1.03401e7i	0.158695	+	0.0515631i
$120$	1.39576e8	+	1.00662e8i	0.673111	+	0.485447i
$121$	7.73480e7	+	2.38053e8i	0.360834	+	1.11053i
$122$	−3.62030e8	−	1.84464e8i	−1.63420	−	0.832667i
$123$	1.53852e7	+	9.71384e7i	0.0672176	+	0.424395i
$124$			6.32374e8i			2.67477i
$125$	−2.32972e8	−	7.29971e7i	−0.954254	−	0.298996i
$126$	4.31504e7			0.171199
$127$	−3.55661e8	+	5.63311e7i	−1.36717	+	0.216538i	−0.796497	−	0.604643i	$-0.793316\pi$
$127$	−3.55661e8	+	5.63311e7i	−1.36717	+	0.216538i	−0.570668	+	0.821181i	$0.693316\pi$
$128$	2.23408e8	−	4.38463e8i	0.832260	−	1.63340i
$129$	−1.02758e8	+	3.33882e7i	−0.371072	+	0.120569i
$130$	2.92189e8	−	4.05143e8i	1.02303	−	1.41852i
$131$	−2.39586e7	+	7.37370e7i	−0.0813535	+	0.250380i	−0.983458	−	0.181138i	$-0.942022\pi$
$131$	−2.39586e7	+	7.37370e7i	−0.0813535	+	0.250380i	0.902104	+	0.431518i	$0.142022\pi$
$132$	−3.37822e8	+	3.37822e8i	−1.11274	+	1.11274i
$133$	5.81016e7	−	2.96042e7i	0.185687	−	0.0946122i
$134$	−2.17491e8	−	2.99351e8i	−0.674562	−	0.928455i
$135$	−2.88203e7	+	5.70567e7i	−0.0867687	+	0.171780i
$136$	−2.18249e8	−	1.58567e8i	−0.637965	−	0.463509i
$137$	−6.04606e6	+	3.81733e7i	−0.0171629	+	0.108362i	−0.994783	−	0.102018i	$-0.967470\pi$
$137$	−6.04606e6	+	3.81733e7i	−0.0171629	+	0.108362i	0.977620	+	0.210380i	$0.0674701\pi$
$138$	5.00747e8	+	7.93105e7i	1.38071	+	0.218683i
$139$	3.02990e8	−	4.17029e8i	0.811650	−	1.11714i	−0.179417	−	0.983773i	$-0.557421\pi$
$139$	3.02990e8	−	4.17029e8i	0.811650	−	1.11714i	0.991067	−	0.133367i	$-0.0425788\pi$
$140$	−9.88801e7	−	1.92393e8i	−0.257393	−	0.500813i
$141$	−1.46508e8	+	1.06444e8i	−0.370668	+	0.269306i
$142$	−3.29159e8	−	6.46010e8i	−0.809565	−	1.58886i
$143$	4.50903e8	+	4.50903e8i	1.07830	+	1.07830i
$144$	−7.85070e7	−	2.55085e7i	−0.182582	−	0.0593246i
$145$	1.05185e8	−	3.27631e8i	0.237949	−	0.741163i
$146$	−2.71718e7	−	8.36261e7i	−0.0598008	−	0.184048i
$147$	2.17986e8	+	1.11070e8i	0.466831	+	0.237862i
$148$	4.42723e7	+	2.79524e8i	0.0922752	+	0.582603i
$149$			6.27198e8i			1.27251i	0.771481	+	0.636253i	$0.219516\pi$
$149$			6.27198e8i			1.27251i	−0.771481	+	0.636253i	$0.780484\pi$
$150$	4.93529e8	−	3.46097e6i	0.974873	−	0.00683649i
$151$	8.99463e8			1.73012			0.865058	−	0.501672i	$-0.167281\pi$
$151$	8.99463e8			1.73012			0.865058	+	0.501672i	$0.167281\pi$
$152$	−5.19252e8	+	8.22414e7i	−0.972756	+	0.154069i
$153$	4.54929e7	−	8.92848e7i	0.0830190	−	0.162934i
$154$	4.04493e8	−	1.31428e8i	0.719164	−	0.233670i
$155$	4.92550e8	+	6.72962e8i	0.853343	+	1.16591i
$156$	−2.02603e8	+	6.23548e8i	−0.342096	+	1.05286i
$157$	5.21447e8	−	5.21447e8i	0.858246	−	0.858246i	−0.132885	−	0.991131i	$-0.542424\pi$
$157$	5.21447e8	−	5.21447e8i	0.858246	−	0.858246i	0.991131	+	0.132885i	$0.0424242\pi$
$158$	6.75496e8	−	3.44182e8i	1.08391	−	0.552281i
$159$	−2.52812e8	−	3.47966e8i	−0.395557	−	0.544438i
$160$	−4.87195e7	−	3.00773e8i	−0.0743400	−	0.458943i
$161$	−2.37077e8	−	1.72246e8i	−0.352846	−	0.256358i
$162$	2.02148e7	−	1.27631e8i	0.0293501	−	0.185309i
$163$	−9.98567e8	−	1.58157e8i	−1.41458	−	0.224047i	−0.598099	−	0.801422i	$-0.704077\pi$
$163$	−9.98567e8	−	1.58157e8i	−1.41458	−	0.224047i	−0.816479	+	0.577375i	$0.804077\pi$
$164$	−5.85835e8	+	8.06333e8i	−0.809841	+	1.11465i
$165$	−9.63786e7	+	6.22632e8i	−0.130030	+	0.840032i
$166$	−1.82076e9	+	1.32286e9i	−2.39784	+	1.74213i
$167$	2.50871e7	+	4.92362e7i	0.0322541	+	0.0633022i	0.906571	−	0.422053i	$-0.138690\pi$
$167$	2.50871e7	+	4.92362e7i	0.0322541	+	0.0633022i	−0.874317	+	0.485355i	$0.838690\pi$
$168$	1.42185e8	+	1.42185e8i	0.178491	+	0.178491i
$169$	5.64646e7	+	1.83464e7i	0.0692196	+	0.0224908i
$170$	−7.73685e8	+	2.71278e6i	−0.926336	+	0.00324802i
$171$	−6.03451e7	−	1.85723e8i	−0.0705761	−	0.217211i
$172$	−9.75612e8	−	4.97099e8i	−1.11471	−	0.567975i
$173$	−1.39063e8	−	8.78012e8i	−0.155249	−	0.980203i	−0.935138	−	0.354285i	$-0.884724\pi$
$173$	−1.39063e8	−	8.78012e8i	−0.155249	−	0.980203i	0.779889	−	0.625918i	$-0.215276\pi$
$174$			6.95618e8i			0.758882i
$175$	−2.55080e8	−	1.27724e8i	−0.271972	−	0.136183i
$176$	−8.13621e8			−0.847952
$177$	−4.74845e8	+	7.52080e7i	−0.483792	+	0.0766251i
$178$	1.08088e9	−	2.12134e9i	1.07670	−	2.11315i
$179$	−1.63892e9	+	5.32516e8i	−1.59641	+	0.518705i	−0.966216	−	0.257732i	$-0.917025\pi$
$179$	−1.63892e9	+	5.32516e8i	−1.59641	+	0.518705i	−0.630194	+	0.776438i	$0.717025\pi$
$180$	−6.15386e8	+	2.02339e8i	−0.586216	+	0.192748i
$181$	−4.94597e8	+	1.52221e9i	−0.460826	+	1.41828i	0.403331	+	0.915054i	$0.367852\pi$
$181$	−4.94597e8	+	1.52221e9i	−0.460826	+	1.41828i	−0.864157	+	0.503223i	$0.832148\pi$
$182$	4.12715e8	−	4.12715e8i	0.376153	−	0.376153i
$183$	6.26657e8	−	3.19298e8i	0.558760	−	0.284703i
$184$	1.38868e9	+	1.91135e9i	1.21152	+	1.66751i
$185$	2.64833e8	+	2.62982e8i	0.226092	+	0.224512i
$186$	−1.36391e9	−	9.90937e8i	−1.13955	−	0.827931i
$187$	1.54507e8	−	9.75520e8i	0.126352	−	0.797756i
$188$	−1.81263e9	−	2.87093e8i	−1.45104	−	0.229822i
$189$	−4.39024e7	+	6.04265e7i	−0.0344065	+	0.0473565i
$190$	−1.06240e9	+	1.06987e9i	−0.815216	+	0.820953i
$191$	1.18823e9	−	8.63298e8i	0.892825	−	0.648675i	−0.0437882	−	0.999041i	$-0.513943\pi$
$191$	1.18823e9	−	8.63298e8i	0.892825	−	0.648675i	0.936613	+	0.350366i	$0.113943\pi$
$192$	4.84783e8	+	9.51440e8i	0.356732	+	0.700127i
$193$	−8.58466e8	−	8.58466e8i	−0.618720	−	0.618720i	0.326483	−	0.945203i	$-0.394136\pi$
$193$	−8.58466e8	−	8.58466e8i	−0.618720	−	0.618720i	−0.945203	+	0.326483i	$0.894136\pi$
$194$	6.06845e8	+	1.97176e8i	0.428421	+	0.139202i
$195$	2.70069e8	+	8.21376e8i	0.186783	+	0.568072i
$196$	7.66155e8	+	2.35798e9i	0.519149	+	1.59778i
$197$	3.04589e8	+	1.55196e8i	0.202232	+	0.103042i	0.552173	−	0.833729i	$-0.313799\pi$
$197$	3.04589e8	+	1.55196e8i	0.202232	+	0.103042i	−0.349942	+	0.936771i	$0.613799\pi$
$198$	−1.99246e8	−	1.25799e9i	−0.129637	−	0.818495i
$199$			9.90337e8i			0.631496i	0.948843	+	0.315748i	$0.102255\pi$
$199$			9.90337e8i			0.631496i	−0.948843	+	0.315748i	$0.897745\pi$
$200$	1.63763e9	+	1.61483e9i	1.02352	+	1.00927i
$201$	6.40483e8			0.392395
$202$	4.72767e9	−	7.48790e8i	2.83950	−	0.449733i
$203$	1.82537e8	−	3.58249e8i	0.107490	−	0.210960i
$204$	9.65803e8	−	3.13808e8i	0.557658	−	0.181194i
$205$	4.60865e6	+	1.31439e9i	0.00260950	+	0.744232i
$206$	8.10447e8	−	2.49430e9i	0.450045	−	1.38509i
$207$	−6.20538e8	+	6.20538e8i	−0.337977	+	0.337977i
$208$	−9.94863e8	+	5.06908e8i	−0.531508	+	0.270817i
$209$	−1.13135e9	−	1.55717e9i	−0.592943	−	0.816116i
$210$	5.69900e8	+	8.82160e7i	0.293036	+	0.0453597i
$211$	−1.63433e9	−	1.18741e9i	−0.824538	−	0.599062i	0.0934705	−	0.995622i	$-0.470204\pi$
$211$	−1.63433e9	−	1.18741e9i	−0.824538	−	0.599062i	−0.918009	+	0.396560i	$0.870204\pi$
$212$	6.81863e8	−	4.30511e9i	0.337562	−	2.13128i
$213$	1.23955e9	+	1.96325e8i	0.602206	+	0.0953800i
$214$	2.92852e9	−	4.03076e9i	1.39634	−	1.92190i
$215$	−1.42542e9	+	2.30890e8i	−0.667096	+	0.108057i
$216$	4.87167e8	−	3.53948e8i	0.223802	−	0.162601i
$217$	4.42391e8	+	8.68242e8i	0.199511	+	0.391563i
$218$	1.52291e9	+	1.52291e9i	0.674290	+	0.674290i
$219$	1.44753e8	+	4.70331e7i	0.0629290	+	0.0204469i
$220$	−5.15236e9	+	3.77108e9i	−2.19946	+	1.60981i
$221$	−4.18851e8	−	1.28909e9i	−0.175586	−	0.540398i
$222$	−6.72255e8	−	3.42531e8i	−0.276772	−	0.141022i
$223$	−8.54915e7	−	5.39772e8i	−0.0345703	−	0.218268i	0.964355	−	0.264611i	$-0.0852435\pi$
$223$	−8.54915e7	−	5.39772e8i	−0.0345703	−	0.218268i	−0.998926	+	0.0463424i	$0.985243\pi$
$224$		−	3.56024e8i		−	0.141412i
$225$	−4.97284e8	+	6.94645e8i	−0.194033	+	0.271040i
$226$	7.77896e8			0.298186
$227$	2.72484e9	−	4.31572e8i	1.02621	−	0.162536i	0.379438	−	0.925217i	$-0.376118\pi$
$227$	2.72484e9	−	4.31572e8i	1.02621	−	0.162536i	0.646774	+	0.762681i	$0.276118\pi$
$228$	8.98446e8	−	1.76330e9i	0.332470	−	0.652509i
$229$	2.55152e9	−	8.29038e8i	0.927804	−	0.301462i	0.194140	−	0.980974i	$-0.437808\pi$
$229$	2.55152e9	−	8.29038e8i	0.927804	−	0.301462i	0.733664	+	0.679512i	$0.237808\pi$
$230$	6.45137e9	+	2.07120e9i	2.30537	+	0.740134i
$231$	−2.27495e8	+	7.00158e8i	−0.0798958	+	0.245894i
$232$	−2.29213e9	+	2.29213e9i	−0.791203	+	0.791203i
$233$	1.02704e9	−	5.23301e8i	0.348468	−	0.177553i	−0.270992	−	0.962582i	$-0.587352\pi$
$233$	1.02704e9	−	5.23301e8i	0.348468	−	0.177553i	0.619460	+	0.785028i	$0.287352\pi$
$234$	−1.02739e9	−	1.41408e9i	−0.342667	−	0.471641i
$235$	−2.15259e9	+	1.10632e9i	−0.705814	+	0.362753i
$236$	−3.94162e9	−	2.86376e9i	−1.27065	−	0.923184i
$237$	−2.05286e8	+	1.29612e9i	−0.0650678	+	0.410822i
$238$	−8.92901e8	−	1.41422e8i	−0.278289	−	0.0440766i
$239$	5.28926e8	−	7.28004e8i	0.162108	−	0.223122i	−0.720234	−	0.693731i	$-0.755966\pi$
$239$	5.28926e8	−	7.28004e8i	0.162108	−	0.223122i	0.882342	+	0.470609i	$0.155966\pi$
$240$	−9.84717e8	−	4.97397e8i	−0.296802	−	0.149919i
$241$	1.44473e9	−	1.04966e9i	0.428271	−	0.311157i	−0.352686	−	0.935742i	$-0.614732\pi$
$241$	1.44473e9	−	1.04966e9i	0.428271	−	0.311157i	0.780957	+	0.624585i	$0.214732\pi$
$242$	−3.07010e9	−	6.02541e9i	−0.895141	−	1.75681i
$243$	1.58164e8	+	1.58164e8i	0.0453609	+	0.0453609i
$244$	6.77862e9	+	2.20251e9i	1.91241	+	0.621381i
$245$	2.65194e9	+	1.91258e9i	0.736037	+	0.530829i
$246$	−8.21093e8	−	2.52707e9i	−0.224208	−	0.690043i
$247$	−2.35354e9	−	1.19919e9i	−0.632314	−	0.322180i
$248$	−1.22898e9	−	7.75945e9i	−0.324890	−	2.05128i
$249$		−	3.89565e9i		−	1.01340i
$250$	6.52527e9	+	9.63255e8i	1.67047	+	0.246593i
$251$	2.56944e9			0.647356			0.323678	−	0.946167i	$-0.395081\pi$
$251$	2.56944e9			0.647356			0.323678	+	0.946167i	$0.395081\pi$
$252$	−7.47610e8	+	1.18410e8i	−0.185384	+	0.0293620i
$253$	−3.92690e9	+	7.70698e9i	−0.958447	+	1.88106i
$254$	9.25255e9	−	3.00634e9i	2.22293	−	0.722275i
$255$	7.83370e8	−	1.08621e9i	0.185271	−	0.256892i
$256$	−2.30207e9	+	7.08506e9i	−0.535993	+	1.64962i
$257$	−4.36061e9	+	4.36061e9i	−0.999572	+	0.999572i	−1.00000		0.000427491i	$-0.999864\pi$
$257$	−4.36061e9	+	4.36061e9i	−0.999572	+	0.999572i	0.000427491		1.00000i	$0.499864\pi$
$258$	2.60094e9	−	1.32525e9i	0.587019	−	0.299101i
$259$	2.56333e8	+	3.52812e8i	0.0569647	+	0.0784051i
$260$	−3.95061e9	+	7.82119e9i	−0.864512	+	1.71151i
$261$	−9.74123e8	−	7.07742e8i	−0.209919	−	0.152515i
$262$	3.27681e8	−	2.06889e9i	0.0695418	−	0.439069i
$263$	−4.65751e9	−	7.37678e8i	−0.973489	−	0.154186i	−0.350625	−	0.936516i	$-0.614031\pi$
$263$	−4.65751e9	−	7.37678e8i	−0.973489	−	0.154186i	−0.622864	+	0.782330i	$0.714031\pi$
$264$	3.48866e9	−	4.80173e9i	0.718197	−	0.988513i
$265$	−2.62759e9	−	5.11254e9i	−0.532812	−	1.03670i
$266$	−1.42529e9	+	1.03554e9i	−0.284693	+	0.206842i
$267$	1.87094e9	+	3.67194e9i	0.368142	+	0.722520i
$268$	4.58964e9	+	4.58964e9i	0.889691	+	0.889691i
$269$	4.42261e9	+	1.43699e9i	0.844635	+	0.274439i	0.699197	−	0.714929i	$-0.253541\pi$
$269$	4.42261e9	+	1.43699e9i	0.844635	+	0.274439i	0.145438	+	0.989367i	$0.453541\pi$
$270$	5.27910e8	−	1.64434e9i	0.0993356	−	0.309411i
$271$	−2.68444e9	−	8.26184e9i	−0.497709	−	1.53179i	−0.812691	−	0.582694i	$-0.801998\pi$
$271$	−2.68444e9	−	8.26184e9i	−0.497709	−	1.53179i	0.314982	−	0.949098i	$-0.398002\pi$
$272$	1.54093e9	+	7.85142e8i	0.281518	+	0.143441i
$273$	1.58046e8	+	9.97860e8i	0.0284532	+	0.179647i
$274$		−	1.04419e9i		−	0.185258i
$275$	−2.54580e9	+	8.02625e9i	−0.445137	+	1.40340i
$276$	−8.89343e9			−1.53261
$277$	6.82280e8	−	1.08062e8i	0.115889	−	0.0183551i	−0.0982204	−	0.995165i	$-0.531315\pi$
$277$	6.82280e8	−	1.08062e8i	0.115889	−	0.0183551i	0.214110	+	0.976810i	$0.431315\pi$
$278$	−6.32259e9	+	1.24088e10i	−1.05856	+	2.07754i
$279$	2.77536e9	−	9.01768e8i	0.458038	−	0.148826i
$280$	1.58720e9	+	2.16856e9i	0.258225	+	0.352808i
$281$	−3.25601e9	+	1.00210e10i	−0.522229	+	1.60725i	0.247504	+	0.968887i	$0.420390\pi$
$281$	−3.25601e9	+	1.00210e10i	−0.522229	+	1.60725i	−0.769732	+	0.638367i	$0.779610\pi$
$282$	3.45962e9	−	3.45962e9i	0.547056	−	0.547056i
$283$	6.39898e9	−	3.26044e9i	0.997619	−	0.508312i	0.122629	−	0.992453i	$-0.460868\pi$
$283$	6.39898e9	−	3.26044e9i	0.997619	−	0.508312i	0.874990	+	0.484140i	$0.160868\pi$
$284$	7.47563e9	+	1.02893e10i	1.14914	+	1.58166i
$285$	−4.17306e8	−	2.57627e9i	−0.0632521	−	0.390492i
$286$	−1.39378e10	−	1.01264e10i	−2.08320	−	1.51353i
$287$	−2.40257e8	+	1.51692e9i	−0.0354118	+	0.223581i
$288$	−1.05306e9	−	1.66788e8i	−0.153067	−	0.0242434i
$289$	2.86625e9	−	3.94505e9i	0.410887	−	0.565538i
$290$	−1.42211e9	+	9.18724e9i	−0.201068	+	1.29895i
$291$	−8.93540e8	+	6.49195e8i	−0.124607	+	0.0905322i
$292$	7.00250e8	+	1.37432e9i	0.0963212	+	0.189041i
$293$	−6.17560e9	−	6.17560e9i	−0.837932	−	0.837932i	0.150655	−	0.988586i	$-0.451862\pi$
$293$	−6.17560e9	−	6.17560e9i	−0.837932	−	0.837932i	−0.988586	+	0.150655i	$0.951862\pi$
$294$	−6.28629e9	−	2.04254e9i	−0.841405	−	0.273389i
$295$	−6.42517e9	+	2.25286e7i	−0.848392	+	0.00297472i
$296$	−1.08647e9	−	3.34382e9i	−0.141531	−	0.435588i
$297$	1.96437e9	+	1.00090e9i	0.252463	+	0.128636i
$298$	−2.65080e9	−	1.67365e10i	−0.336133	−	2.12226i
$299$			1.18704e10i			1.48518i
$300$	−8.54124e9	+	1.41427e9i	−1.05447	+	0.174601i
$301$	−1.68726e9			−0.205550
$302$	−2.40017e10	+	3.80150e9i	−2.88546	+	0.457011i
$303$	−3.76148e9	+	7.38233e9i	−0.446261	+	0.875836i
$304$	3.20531e9	−	1.04147e9i	0.375298	−	0.121942i
$305$	8.92921e9	−	2.93593e9i	1.03184	−	0.339271i
$306$	−8.36601e8	+	2.57479e9i	−0.0954185	+	0.293668i
$307$	−6.60958e9	+	6.60958e9i	−0.744081	+	0.744081i	−0.973361	−	0.229280i	$-0.926363\pi$
$307$	−6.60958e9	+	6.60958e9i	−0.744081	+	0.744081i	0.229280	+	0.973361i	$0.426363\pi$
$308$	−6.64747e9	+	3.38705e9i	−0.738675	+	0.376374i
$309$	2.66837e9	+	3.67269e9i	0.292693	+	0.402857i
$310$	−1.59877e10	−	1.58760e10i	−1.73117	−	1.71907i
$311$	−1.27230e10	−	9.24377e9i	−1.36002	−	0.988115i	−0.998443	−	0.0557740i	$-0.982237\pi$
$311$	−1.27230e10	−	9.24377e9i	−1.36002	−	0.988115i	−0.361580	−	0.932341i	$-0.617763\pi$
$312$	1.27419e9	−	8.04490e9i	0.134467	−	0.848990i
$313$	1.18349e10	+	1.87446e9i	1.23307	+	0.195299i	0.738748	−	0.673981i	$-0.235417\pi$
$313$	1.18349e10	+	1.87446e9i	1.23307	+	0.195299i	0.494320	+	0.869280i	$0.335417\pi$
$314$	−1.17107e10	+	1.61184e10i	−1.20466	+	1.65807i
$315$	−7.03367e8	+	7.08317e8i	−0.0714397	+	0.0719425i
$316$	−1.07590e10	+	7.81684e9i	−1.07900	+	0.783940i
$317$	−1.64492e9	−	3.22834e9i	−0.162895	−	0.319700i	0.795103	−	0.606475i	$-0.207417\pi$
$317$	−1.64492e9	−	3.22834e9i	−0.162895	−	0.319700i	−0.957998	+	0.286775i	$0.907417\pi$
$318$	8.21681e9	+	8.21681e9i	0.803517	+	0.803517i
$319$	−1.12871e10	−	3.66740e9i	−1.08998	−	0.354157i
$320$	4.45756e9	+	1.35570e10i	0.425106	+	1.29290i
$321$	2.66500e9	+	8.20201e9i	0.251002	+	0.772503i
$322$	7.05426e9	+	3.59432e9i	0.656187	+	0.334344i
$323$	6.40016e8	+	4.04090e9i	0.0588005	+	0.371252i
$324$			2.26677e9i			0.205697i
$325$	1.88767e9	+	1.14003e10i	0.169197	+	1.02184i
$326$	2.73147e10			2.41839
$327$	−3.68208e9	+	5.83184e8i	−0.322034	+	0.0510052i
$328$	5.62135e9	−	1.10325e10i	0.485674	−	0.953190i
$329$	−2.68957e9	+	8.73894e8i	−0.229561	+	0.0745891i
$330$	−5.96842e7	−	1.70220e10i	−0.00503273	−	1.43534i
$331$	5.37026e9	−	1.65280e10i	0.447387	−	1.37692i	−0.432457	−	0.901654i	$-0.642353\pi$
$331$	5.37026e9	−	1.65280e10i	0.447387	−	1.37692i	0.879844	−	0.475262i	$-0.157647\pi$
$332$	2.79158e10	−	2.79158e10i	2.29772	−	2.29772i
$333$	1.16364e9	−	5.92905e8i	0.0946329	−	0.0482179i
$334$	−8.77530e8	−	1.20782e9i	−0.0705141	−	0.0970544i
$335$	8.45905e9	+	1.30940e9i	0.671649	+	0.103966i
$336$	−1.04287e9	−	7.57692e8i	−0.0818229	−	0.0594478i
$337$	3.32165e8	−	2.09721e9i	0.0257534	−	0.162601i	−0.971460	−	0.237204i	$-0.923769\pi$
$337$	3.32165e8	−	2.09721e9i	0.0257534	−	0.162601i	0.997213	+	0.0746033i	$0.0237691\pi$
$338$	−1.58427e9	−	2.50923e8i	−0.121384	−	0.0192254i
$339$	−7.91453e8	+	1.08934e9i	−0.0599275	+	0.0824832i
$340$	1.33972e10	−	2.17009e9i	1.00253	−	0.162391i
$341$	2.32697e10	−	1.69064e10i	1.72097	−	1.25036i
$342$	2.39522e9	+	4.70089e9i	0.175082	+	0.343618i
$343$	5.67841e9	+	5.67841e9i	0.410252	+	0.410252i
$344$	1.29372e10	+	4.20355e9i	0.923860	+	0.300180i
$345$	−9.46425e9	+	6.92701e9i	−0.668051	+	0.488956i
$346$	7.42168e9	+	2.28416e10i	0.517843	+	1.59376i
$347$	−2.91600e9	−	1.48578e9i	−0.201127	−	0.102479i	0.350526	−	0.936553i	$-0.386003\pi$
$347$	−2.91600e9	−	1.48578e9i	−0.201127	−	0.102479i	−0.551653	+	0.834074i	$0.686003\pi$
$348$	−1.90886e9	−	1.20521e10i	−0.130154	−	0.821760i
$349$		−	2.74857e10i		−	1.85270i	−0.376666	−	0.926349i	$-0.622929\pi$
$349$		−	2.74857e10i		−	1.85270i	0.376666	−	0.926349i	$-0.377071\pi$
$350$	7.34649e9	+	2.33019e9i	0.489562	+	0.155281i
$351$	3.02554e9			0.199331
$352$	−1.03794e10	+	1.64393e9i	−0.676085	+	0.107081i
$353$	1.68852e9	−	3.31390e9i	0.108744	−	0.213423i	−0.830221	−	0.557434i	$-0.811786\pi$
$353$	1.68852e9	−	3.31390e9i	0.108744	−	0.213423i	0.938966	+	0.344011i	$0.111786\pi$
$354$	1.23531e10	−	4.01378e9i	0.786619	−	0.255588i
$355$	1.59697e10	+	5.12704e9i	1.00550	+	0.322815i
$356$	−1.29057e10	+	3.97197e10i	−0.803493	+	2.47290i
$357$	1.10651e9	−	1.10651e9i	0.0681209	−	0.0681209i
$358$	4.14830e10	−	2.11367e10i	2.52545	−	1.28678i
$359$	−6.96491e9	−	9.58637e9i	−0.419312	−	0.577134i	0.546147	−	0.837690i	$-0.316094\pi$
$359$	−6.96491e9	−	9.58637e9i	−0.419312	−	0.577134i	−0.965459	+	0.260556i	$0.916094\pi$
$360$	7.15777e9	−	3.67874e9i	0.426155	−	0.219022i
$361$	−7.28970e9	−	5.29628e9i	−0.429221	−	0.311847i
$362$	6.76458e9	−	4.27099e10i	0.393919	−	2.48710i
$363$	1.15614e10	+	1.83115e9i	0.665863	+	0.105462i
$364$	−6.01803e9	+	8.28311e9i	−0.342806	+	0.471832i
$365$	1.81564e9	+	9.17111e8i	0.102296	+	0.0516714i
$366$	−1.53726e10	+	1.11688e10i	−0.856686	+	0.622419i
$367$	2.14058e9	+	4.20112e9i	0.117996	+	0.231580i	0.942449	−	0.334351i	$-0.108517\pi$
$367$	2.14058e9	+	4.20112e9i	0.117996	+	0.231580i	−0.824453	+	0.565931i	$0.808517\pi$
$368$	−1.07096e10	−	1.07096e10i	−0.583958	−	0.583958i
$369$	4.37423e9	+	1.42127e9i	0.235937	+	0.0766606i
$370$	−8.17841e9	−	5.89826e9i	−0.436377	−	0.314715i
$371$	−2.07555e9	−	6.38789e9i	−0.109556	−	0.337180i
$372$	2.63499e10	+	1.34259e10i	1.37596	+	0.701089i
$373$	−3.01424e9	−	1.90311e10i	−0.155719	−	0.983172i	−0.934523	−	0.355904i	$-0.884173\pi$
$373$	−3.01424e9	−	1.90311e10i	−0.155719	−	0.983172i	0.778804	−	0.627268i	$-0.215827\pi$
$374$			2.66843e10i			1.36386i
$375$	−7.98790e9	+	8.15774e9i	−0.403931	+	0.412520i
$376$	2.27996e10			1.14071
$377$	−1.60863e10	+	2.54782e9i	−0.796326	+	0.126126i
$378$	9.16127e8	−	1.79800e9i	0.0448733	−	0.0880689i
$379$	−2.97588e10	+	9.66923e9i	−1.44231	+	0.468635i	−0.922617	−	0.385717i	$-0.873954\pi$
$379$	−2.97588e10	+	9.66923e9i	−1.44231	+	0.468635i	−0.519694	+	0.854352i	$0.673954\pi$
$380$	1.54709e10	−	2.14517e10i	0.741962	−	1.02879i
$381$	−5.20383e9	+	1.60157e10i	−0.246958	+	0.760058i
$382$	−2.80586e10	+	2.80586e10i	−1.31769	+	1.31769i
$383$	−6.93073e9	+	3.53138e9i	−0.322095	+	0.164116i	−0.607561	−	0.794273i	$-0.707852\pi$
$383$	−6.93073e9	+	3.53138e9i	−0.322095	+	0.164116i	0.285466	+	0.958389i	$0.407852\pi$
$384$	−1.35268e10	−	1.86181e10i	−0.622115	−	0.856267i
$385$	−4.43599e9	+	8.78210e9i	−0.201905	+	0.399720i
$386$	2.65360e10	+	1.92795e10i	1.19532	+	0.868454i
$387$	−7.90437e8	+	4.99062e9i	−0.0352390	+	0.222490i
$388$	−1.10551e10	−	1.75095e9i	−0.487792	−	0.0772587i
$389$	−1.21023e10	+	1.66574e10i	−0.528530	+	0.727459i	−0.986905	−	0.161300i	$-0.948431\pi$
$389$	−1.21023e10	+	1.66574e10i	−0.528530	+	0.727459i	0.458376	+	0.888759i	$0.348431\pi$
$390$	−1.06781e10	−	2.07766e10i	−0.461569	−	0.898082i
$391$	1.48744e10	−	1.08069e10i	0.636404	−	0.462375i
$392$	−1.39836e10	−	2.74443e10i	−0.592208	−	1.16227i
$393$	2.56383e9	+	2.56383e9i	0.107478	+	0.107478i
$394$	−8.78373e9	−	2.85401e9i	−0.364497	−	0.118432i
$395$	−5.36105e9	+	1.66986e10i	−0.220222	+	0.685950i
$396$	6.90415e9	+	2.12488e10i	0.280756	+	0.864078i
$397$	−1.68878e10	−	8.60475e9i	−0.679846	−	0.346399i	0.0797311	−	0.996816i	$-0.474594\pi$
$397$	−1.68878e10	−	8.60475e9i	−0.679846	−	0.346399i	−0.759577	+	0.650418i	$0.774594\pi$
$398$	−4.18557e9	−	2.64267e10i	−0.166810	−	1.05320i
$399$		−	3.04952e9i		−	0.120321i
$400$	−1.19886e10	−	8.58241e9i	−0.468304	−	0.335250i
$401$	4.19438e10			1.62215			0.811074	−	0.584943i	$-0.198883\pi$
$401$	4.19438e10			1.62215			0.811074	+	0.584943i	$0.198883\pi$
$402$	−1.70910e10	+	2.70695e9i	−0.654429	+	0.103651i
$403$	1.79201e10	−	3.51701e10i	0.679390	−	1.33338i
$404$	−7.98554e10	+	2.59466e10i	−2.99764	+	0.973991i
$405$	1.76557e9	+	2.41226e9i	0.0656243	+	0.0896612i
$406$	−3.35680e9	+	1.03312e10i	−0.123544	+	0.380229i
$407$	9.10213e9	−	9.10213e9i	0.331715	−	0.331715i
$408$	−1.12409e10	+	5.72752e9i	−0.405658	+	0.206693i
$409$	3.86794e9	+	5.32377e9i	0.138225	+	0.190251i	0.872518	−	0.488583i	$-0.162486\pi$
$409$	3.86794e9	+	5.32377e9i	0.138225	+	0.190251i	−0.734293	+	0.678833i	$0.762486\pi$
$410$	−5.67813e9	−	3.50543e10i	−0.200941	−	1.24053i
$411$	1.46225e9	+	1.06239e9i	0.0512454	+	0.0372320i
$412$	−7.19690e9	+	4.54394e10i	−0.249779	+	1.57704i
$413$	−7.41521e9	−	1.17445e9i	−0.254873	−	0.0403679i
$414$	1.39361e10	−	1.91814e10i	0.474395	−	0.652949i
$415$	7.96420e9	−	5.14509e10i	0.268504	−	1.73461i
$416$	−1.16673e10	+	8.47678e9i	−0.389580	+	0.283046i
$417$	−1.09441e10	−	2.14790e10i	−0.361940	−	0.710346i
$418$	3.67709e10	+	3.67709e10i	1.20448	+	1.20448i
$419$	−1.81639e10	−	5.90180e9i	−0.589322	−	0.191482i	−0.000849374	−	1.00000i	$-0.500270\pi$
$419$	−1.81639e10	−	5.90180e9i	−0.589322	−	0.191482i	−0.588472	+	0.808517i	$0.700270\pi$
$420$	−1.01160e10	+	3.54697e7i	−0.325096	+	0.00113988i
$421$	8.80551e9	+	2.71006e10i	0.280302	+	0.862680i	0.987768	+	0.155933i	$0.0498383\pi$
$421$	8.80551e9	+	2.71006e10i	0.280302	+	0.862680i	−0.707466	+	0.706748i	$0.750162\pi$
$422$	4.86299e10	+	2.47782e10i	1.53339	+	0.781303i
$423$	1.32483e9	+	8.36467e9i	0.0413809	+	0.261269i
$424$			5.41505e10i			1.67548i
$425$	1.25668e10	−	1.27443e10i	0.385186	−	0.390626i
$426$	−3.39065e10			−1.02954
$427$	1.08478e10	−	1.71812e9i	0.326309	−	0.0516823i
$428$	−3.96777e10	+	7.78719e10i	−1.18242	+	2.32063i
$429$	2.83615e10	−	9.21520e9i	0.837335	−	0.272067i
$430$	3.70607e10	−	1.21856e10i	1.08403	−	0.356429i
$431$	1.80823e10	−	5.56515e10i	0.524016	−	1.61275i	−0.242239	−	0.970217i	$-0.577882\pi$
$431$	1.80823e10	−	5.56515e10i	0.524016	−	1.61275i	0.766254	−	0.642537i	$-0.222118\pi$
$432$	−2.72968e9	+	2.72968e9i	−0.0783748	+	0.0783748i
$433$	−6.74985e9	+	3.43922e9i	−0.192018	+	0.0978382i	−0.547356	−	0.836900i	$-0.684366\pi$
$433$	−6.74985e9	+	3.43922e9i	−0.192018	+	0.0978382i	0.355338	+	0.934738i	$0.384366\pi$
$434$	−1.54745e10	−	2.12989e10i	−0.436173	−	0.600341i
$435$	−1.14186e10	−	1.13388e10i	−0.318902	−	0.316673i
$436$	−3.05644e10	−	2.22064e10i	−0.845805	−	0.614514i
$437$	5.60503e9	−	3.53888e10i	0.153692	−	0.970375i
$438$	−4.06144e9	−	6.43269e8i	−0.110353	−	0.0174782i
$439$	1.54826e10	−	2.13099e10i	0.416855	−	0.573752i	−0.548019	−	0.836466i	$-0.684618\pi$
$439$	1.54826e10	−	2.13099e10i	0.416855	−	0.573752i	0.964874	+	0.262715i	$0.0846177\pi$
$440$	5.58924e10	−	5.62858e10i	1.49122	−	1.50172i
$441$	9.25615e9	−	6.72499e9i	0.244724	−	0.177802i
$442$	1.66250e10	+	3.26285e10i	0.435586	+	0.854885i
$443$	1.44980e10	+	1.44980e10i	0.376437	+	0.376437i	0.869815	−	0.493378i	$-0.164238\pi$
$443$	1.44980e10	+	1.44980e10i	0.376437	+	0.376437i	−0.493378	+	0.869815i	$0.664238\pi$
$444$	1.25872e10	+	4.08984e9i	0.323891	+	0.105238i
$445$	1.72033e10	+	5.23213e10i	0.438703	+	1.33425i
$446$	4.56260e9	+	1.40422e10i	0.115311	+	0.354892i
$447$	2.61342e10	+	1.33161e10i	0.654606	+	0.333538i
$448$	2.60859e9	+	1.64700e10i	0.0647579	+	0.408866i
$449$			7.37377e9i			0.181428i	0.995877	+	0.0907140i	$0.0289149\pi$
$449$			7.37377e9i			0.181428i	−0.995877	+	0.0907140i	$0.971085\pi$
$450$	1.03339e10	−	2.06380e10i	0.252009	−	0.503289i
$451$	4.53331e10			1.09574
$452$	−1.34776e10	+	2.13464e9i	−0.322893	+	0.0511412i
$453$	1.90965e10	−	3.74790e10i	0.453483	−	0.890011i
$454$	−7.08869e10	+	2.30326e10i	−1.66856	+	0.542149i
$455$	4.73427e7	+	1.35021e10i	0.00110460	+	0.315034i
$456$	−7.59740e9	+	2.33824e10i	−0.175714	+	0.540791i
$457$	−5.34947e10	+	5.34947e10i	−1.22644	+	1.22644i	−0.261139	+	0.965301i	$0.584098\pi$
$457$	−5.34947e10	+	5.34947e10i	−1.22644	+	1.22644i	−0.965301	+	0.261139i	$0.915902\pi$
$458$	−6.45821e10	+	3.29062e10i	−1.46774	+	0.747853i
$459$	−2.75448e9	−	3.79122e9i	−0.0620567	−	0.0854138i
$460$	−1.17458e11	−	1.81816e10i	−2.62332	−	0.406070i
$461$	−3.68132e10	−	2.67464e10i	−0.815080	−	0.592190i	0.100219	−	0.994965i	$-0.468046\pi$
$461$	−3.68132e10	−	2.67464e10i	−0.815080	−	0.592190i	−0.915299	+	0.402775i	$0.868046\pi$
$462$	3.11144e9	−	1.96448e10i	0.0682957	−	0.431202i
$463$	7.01031e10	+	1.11032e10i	1.52550	+	0.241616i	0.862136	−	0.506677i	$-0.169126\pi$
$463$	7.01031e10	+	1.11032e10i	1.52550	+	0.241616i	0.663369	+	0.748293i	$0.269126\pi$
$464$	1.22146e10	−	1.68120e10i	0.263516	−	0.362699i
$465$	3.84985e10	−	6.23602e9i	0.823440	−	0.133381i
$466$	−2.51943e10	+	1.83047e10i	−0.534267	+	0.388168i
$467$	−3.61640e10	−	7.09759e10i	−0.760343	−	1.49226i	−0.867188	−	0.497981i	$-0.834075\pi$
$467$	−3.61640e10	−	7.09759e10i	−0.760343	−	1.49226i	0.106845	−	0.994276i	$-0.465925\pi$
$468$	2.16807e10	+	2.16807e10i	0.451949	+	0.451949i
$469$	9.51231e9	+	3.09074e9i	0.196605	+	0.0638809i
$470$	5.27651e10	−	3.86195e10i	1.08132	−	0.791434i
$471$	−1.06569e10	−	3.27987e10i	−0.216545	−	0.666458i
$472$	5.39307e10	+	2.74790e10i	1.08660	+	0.553648i
$473$	7.79090e9	+	4.91898e10i	0.155648	+	0.982721i
$474$		−	3.54541e10i		−	0.702349i
$475$	−2.44594e8	−	3.48787e10i	−0.00480475	−	0.685150i
$476$	1.58582e10			0.308906
$477$	−1.98666e10	+	3.14656e9i	−0.383751	+	0.0607802i
$478$	−1.10373e10	+	2.16619e10i	−0.211422	+	0.414940i
$479$	4.62562e10	−	1.50295e10i	0.878673	−	0.285498i	0.165267	−	0.986249i	$-0.447151\pi$
$479$	4.62562e10	−	1.50295e10i	0.878673	−	0.285498i	0.713406	+	0.700751i	$0.247151\pi$
$480$	−1.35671e10	−	4.35567e9i	−0.255576	−	0.0820522i
$481$	5.45885e9	−	1.68006e10i	0.101981	−	0.313866i
$482$	−3.41156e10	+	3.41156e10i	−0.632070	+	0.632070i
$483$	−1.22106e10	+	6.22160e9i	−0.224361	+	0.114318i
$484$	6.97261e10	+	9.59698e10i	1.27062	+	1.74885i
$485$	−1.31285e10	+	6.74737e9i	−0.237272	+	0.121946i
$486$	−4.88899e9	−	3.55206e9i	−0.0876342	−	0.0636700i
$487$	−3.60310e9	+	2.27491e10i	−0.0640561	+	0.404434i	0.934738	+	0.355338i	$0.115634\pi$
$487$	−3.60310e9	+	2.27491e10i	−0.0640561	+	0.404434i	−0.998794	+	0.0490963i	$0.984366\pi$
$488$	−8.74565e10	−	1.38517e10i	−1.54210	−	0.244245i
$489$	−2.77908e10	+	3.82507e10i	−0.486032	+	0.668966i
$490$	−7.88491e10	−	3.98280e10i	−1.36777	−	0.690883i
$491$	1.82695e10	−	1.32736e10i	0.314341	−	0.228382i	−0.419416	−	0.907794i	$-0.637765\pi$
$491$	1.82695e10	−	1.32736e10i	0.314341	−	0.228382i	0.733757	+	0.679412i	$0.237765\pi$
$492$	2.11606e10	+	4.15300e10i	0.361133	+	0.708764i
$493$	1.78378e10	+	1.78378e10i	0.301962	+	0.301962i
$494$	6.78712e10	+	2.20527e10i	1.13967	+	0.370300i
$495$	2.38978e10	+	1.72350e10i	0.398049	+	0.287073i
$496$	1.55632e10	+	4.78987e10i	0.257142	+	0.791401i
$497$	1.74621e10	+	8.89738e9i	0.286201	+	0.145827i
$498$	1.64646e10	+	1.03953e11i	0.267691	+	1.69013i
$499$		−	8.01587e10i		−	1.29285i	−0.762977	−	0.646426i	$-0.776263\pi$
$499$		−	8.01587e10i		−	1.29285i	0.762977	−	0.646426i	$-0.223737\pi$
$500$	−1.15698e11	+	1.21706e9i	−1.85117	+	0.0194729i
$501$	2.58421e9			0.0410183
$502$	−6.85641e10	+	1.08595e10i	−1.07965	+	0.170999i
$503$	3.53020e10	−	6.92840e10i	0.551476	−	1.08233i	−0.432097	−	0.901827i	$-0.642226\pi$
$503$	3.53020e10	−	6.92840e10i	0.551476	−	1.08233i	0.983574	−	0.180506i	$-0.0577736\pi$
$504$	8.94332e9	−	2.90586e9i	0.138604	−	0.0450353i
$505$	−6.47714e10	+	8.98107e10i	−0.995904	+	1.38090i
$506$	7.22146e10	−	2.22254e11i	1.10160	−	3.39037i
$507$	1.96327e9	−	1.96327e9i	0.0297130	−	0.0297130i
$508$	−1.52057e11	+	7.74770e10i	−2.28324	+	1.16337i
$509$	−7.86054e10	−	1.08191e11i	−1.17107	−	1.61183i	−0.656293	−	0.754507i	$-0.727876\pi$
$509$	−7.86054e10	−	1.08191e11i	−1.17107	−	1.61183i	−0.514773	−	0.857327i	$-0.672124\pi$
$510$	−1.63131e10	+	3.22957e10i	−0.241133	+	0.477380i
$511$	1.92287e9	+	1.39705e9i	0.0282012	+	0.0204893i
$512$	1.17782e10	−	7.43645e10i	0.171395	−	1.08215i
$513$	−9.01994e9	−	1.42862e9i	−0.130237	−	0.0206275i
$514$	9.79309e10	−	1.34790e11i	1.40303	−	1.93111i
$515$	2.77335e10	+	5.39616e10i	0.394254	+	0.767106i
$516$	−4.14265e10	+	3.00981e10i	−0.584359	+	0.424561i
$517$	3.78962e10	+	7.43754e10i	0.530436	+	1.04104i
$518$	−8.33125e9	−	8.33125e9i	−0.115715	−	0.115715i
$519$	−3.95377e10	−	1.28466e10i	−0.544932	−	0.177059i
$520$	3.32755e10	−	1.03647e11i	0.455104	−	1.41756i
$521$	−2.70025e9	−	8.31052e9i	−0.0366483	−	0.112792i	0.931059	−	0.364869i	$-0.118886\pi$
$521$	−2.70025e9	−	8.31052e9i	−0.0366483	−	0.112792i	−0.967707	+	0.252077i	$0.918886\pi$
$522$	2.89852e10	+	1.47687e10i	0.390386	+	0.198912i
$523$	1.64086e9	+	1.03600e10i	0.0219314	+	0.138469i	0.996224	−	0.0868151i	$-0.0276689\pi$
$523$	1.64086e9	+	1.03600e10i	0.0219314	+	0.138469i	−0.974293	+	0.225284i	$0.927669\pi$
$524$			3.67442e10i			0.487376i
$525$	−1.07377e10	+	7.91700e9i	−0.141342	+	0.104213i
$526$	1.27401e11			1.66430
$527$	−6.03853e10	+	9.56409e9i	−0.782869	+	0.123994i
$528$	−1.72740e10	+	3.39022e10i	−0.222258	+	0.436206i
$529$	−7.86572e10	+	2.55573e10i	−1.00442	+	0.326356i
$530$	9.17235e10	+	1.25320e11i	1.16246	+	1.58825i
$531$	−6.94766e9	+	2.13827e10i	−0.0873897	+	0.268958i
$532$	2.18526e10	−	2.18526e10i	0.272807	−	0.272807i
$533$	5.54315e10	−	2.82437e10i	0.686827	−	0.349956i
$534$	−6.54443e10	−	9.00764e10i	−0.804835	−	1.10776i
$535$	1.84293e10	+	1.13775e11i	0.224954	+	1.38877i
$536$	−6.52362e10	−	4.73968e10i	−0.790368	−	0.574236i
$537$	−1.26069e10	+	7.95966e10i	−0.151604	+	0.957189i
$538$	−1.24088e11	−	1.96537e10i	−1.48116	−	0.234593i
$539$	6.62844e10	−	9.12327e10i	0.785338	−	1.08092i
$540$	−4.63416e9	+	2.99379e10i	−0.0544999	+	0.352084i
$541$	−1.67532e10	+	1.21719e10i	−0.195573	+	0.142092i	−0.681262	−	0.732039i	$-0.738569\pi$
$541$	−1.67532e10	+	1.21719e10i	−0.195573	+	0.142092i	0.485689	+	0.874132i	$0.338569\pi$
$542$	1.06551e11	+	2.09118e11i	1.23469	+	2.42322i
$543$	5.29271e10	+	5.29271e10i	0.608806	+	0.608806i
$544$	2.12440e10	+	6.90261e9i	0.242573	+	0.0788166i
$545$	−4.98226e10	+	1.74693e8i	−0.564729	+	0.00198011i
$546$	−8.43474e9	−	2.59594e10i	−0.0949076	−	0.292096i
$547$	8.50392e10	+	4.33296e10i	0.949882	+	0.483989i	0.859058	−	0.511878i	$-0.171050\pi$
$547$	8.50392e10	+	4.33296e10i	0.949882	+	0.483989i	0.0908239	+	0.995867i	$0.471050\pi$
$548$	2.86538e9	+	1.80913e10i	0.0317732	+	0.200608i
$549$		−	3.28907e10i		−	0.362063i
$550$	3.40112e10	−	2.24936e11i	0.371682	−	2.45815i
$551$	4.91607e10			0.533349
$552$	1.09126e11	−	1.72838e10i	1.17536	−	0.186158i
$553$	−9.30348e9	+	1.82591e10i	−0.0994821	+	0.195245i
$554$	−1.77496e10	+	5.76719e9i	−0.188430	+	0.0612245i
$555$	1.65807e10	−	5.45174e9i	0.174755	−	0.0574597i
$556$	7.54921e10	−	2.32341e11i	0.789955	−	2.43123i
$557$	−9.53569e10	+	9.53569e10i	−0.990675	+	0.990675i	−0.999957	−	0.00928149i	$-0.997046\pi$
$557$	−9.53569e10	+	9.53569e10i	−0.990675	+	0.990675i	0.00928149	+	0.999957i	$0.497046\pi$
$558$	−7.02478e10	+	3.57930e10i	−0.724596	+	0.369200i
$559$	4.01730e10	+	5.52934e10i	0.411421	+	0.566273i
$560$	−1.22245e10	−	1.21391e10i	−0.124303	−	0.123434i
$561$	−3.73679e10	−	2.71494e10i	−0.377265	−	0.274099i
$562$	4.45323e10	−	2.81166e11i	0.446406	−	2.81850i
$563$	−5.23514e10	−	8.29164e9i	−0.521068	−	0.0825291i	−0.109640	−	0.993971i	$-0.534970\pi$
$563$	−5.23514e10	−	8.29164e9i	−0.521068	−	0.0825291i	−0.411428	+	0.911442i	$0.634970\pi$
$564$	−5.04467e10	+	6.94340e10i	−0.498559	+	0.686208i
$565$	−1.26800e10	+	1.27692e10i	−0.124430	+	0.125306i
$566$	−1.56974e11	+	1.14048e11i	−1.52954	+	1.11128i
$567$	1.58577e9	+	3.11225e9i	0.0153429	+	0.0301122i
$568$	−1.11725e11	−	1.11725e11i	−1.07339	−	1.07339i
$569$	−1.86669e11	−	6.06524e10i	−1.78083	−	0.578627i	−0.781838	−	0.623482i	$-0.785717\pi$
$569$	−1.86669e11	−	6.06524e10i	−1.78083	−	0.578627i	−0.998994	+	0.0448549i	$0.985717\pi$
$570$	2.20240e10	+	6.69828e10i	0.208639	+	0.634547i
$571$	2.19697e10	+	6.76158e10i	0.206671	+	0.636068i	0.999641	+	0.0268069i	$0.00853392\pi$
$571$	2.19697e10	+	6.76158e10i	0.206671	+	0.636068i	−0.792970	+	0.609261i	$0.791466\pi$
$572$	2.69271e11	+	1.37200e11i	2.51539	+	1.28165i
$573$	−1.07448e10	−	6.78401e10i	−0.0996737	−	0.629315i
$574$		−	4.14937e10i		−	0.382239i
$575$	−1.39159e11	+	7.21385e10i	−1.27303	+	0.659927i
$576$	4.99373e10			0.453665
$577$	1.33374e10	−	2.11243e9i	0.120328	−	0.0190581i	−0.0959799	−	0.995383i	$-0.530598\pi$
$577$	1.33374e10	−	2.11243e9i	0.120328	−	0.0190581i	0.216308	+	0.976325i	$0.430598\pi$
$578$	−5.98111e10	+	1.17386e11i	−0.535883	+	1.05173i
$579$	−5.39969e10	+	1.75447e10i	−0.480457	+	0.156110i
$580$	−5.71801e8	−	1.63078e11i	−0.00505281	−	1.44106i
$581$	1.87990e10	−	5.78572e10i	0.164979	−	0.507754i
$582$	2.10999e10	−	2.10999e10i	0.183903	−	0.183903i
$583$	−1.76646e11	+	9.00057e10i	−1.52908	+	0.779105i
$584$	−1.12632e10	−	1.55025e10i	−0.0968303	−	0.133275i
$585$	3.99592e10	+	6.18536e9i	0.341187	+	0.0528131i
$586$	1.90893e11	+	1.38692e11i	1.61883	+	1.17615i
$587$	3.47433e10	−	2.19360e11i	0.292630	−	1.84759i	−0.203156	−	0.979146i	$-0.565120\pi$
$587$	3.47433e10	−	2.19360e11i	0.292630	−	1.84759i	0.495785	−	0.868445i	$-0.334880\pi$
$588$	1.14519e11	+	1.81381e10i	0.958008	+	0.151734i
$589$	−7.00314e10	+	9.63900e10i	−0.581878	+	0.800886i
$590$	1.71357e11	−	2.77566e10i	1.41415	−	0.229065i
$591$	1.29335e10	−	9.39672e9i	0.106014	−	0.0770240i
$592$	1.02327e10	+	2.00828e10i	0.0833111	+	0.163507i
$593$	−1.18074e11	−	1.18074e11i	−0.954848	−	0.954848i	0.0441756	−	0.999024i	$-0.485934\pi$
$593$	−1.18074e11	−	1.18074e11i	−0.954848	−	0.954848i	−0.999024	+	0.0441756i	$0.985934\pi$
$594$	−5.66484e10	−	1.84062e10i	−0.455032	−	0.147849i
$595$	1.68761e10	−	1.23518e10i	0.134649	−	0.0985515i
$596$	9.18538e10	+	2.82697e11i	0.727968	+	2.24045i
$597$	4.12656e10	+	2.10259e10i	0.324856	+	0.165522i
$598$	−5.01690e10	−	3.16755e11i	−0.392311	−	2.47696i
$599$			1.21948e11i			0.947254i	0.880725	+	0.473627i	$0.157056\pi$
$599$			1.21948e11i			0.947254i	−0.880725	+	0.473627i	$0.842944\pi$
$600$	1.02056e11	−	3.39529e10i	0.787466	−	0.261982i
$601$	−8.95740e10			−0.686569			−0.343284	−	0.939231i	$-0.611539\pi$
$601$	−8.95740e10			−0.686569			−0.343284	+	0.939231i	$0.611539\pi$
$602$	4.50238e10	−	7.13106e9i	0.342812	−	0.0542961i
$603$	1.35981e10	−	2.66878e10i	0.102851	−	0.201857i
$604$	4.05415e11	−	1.31727e11i	3.04615	−	0.989755i
$605$	1.48952e11	+	4.78205e10i	1.11179	+	0.356938i
$606$	6.91726e10	−	2.12891e11i	0.512913	−	1.57858i
$607$	1.78341e10	−	1.78341e10i	0.131370	−	0.131370i	−0.638364	−	0.769734i	$-0.720389\pi$
$607$	1.78341e10	−	1.78341e10i	0.131370	−	0.131370i	0.769734	+	0.638364i	$0.220389\pi$
$608$	3.87860e10	−	1.97624e10i	0.283831	−	0.144619i
$609$	−1.10522e10	−	1.52120e10i	−0.0803485	−	0.110590i
$610$	−2.25863e11	+	1.16082e11i	−1.63127	+	0.838392i
$611$	9.26759e10	+	6.73330e10i	0.664970	+	0.483129i
$612$	7.42915e9	−	4.69058e10i	0.0529582	−	0.334365i
$613$	1.28556e11	+	2.03613e10i	0.910439	+	0.144199i	0.594048	−	0.804430i	$-0.297529\pi$
$613$	1.28556e11	+	2.03613e10i	0.910439	+	0.144199i	0.316391	+	0.948629i	$0.397529\pi$
$614$	1.48439e11	−	2.04308e11i	1.04442	−	1.43751i
$615$	5.48661e10	+	2.77138e10i	0.383534	+	0.193729i
$616$	7.49843e10	−	5.44793e10i	0.520772	−	0.378363i
$617$	4.70376e10	+	9.23165e10i	0.324567	+	0.636999i	0.994420	−	0.105495i	$-0.0336428\pi$
$617$	4.70376e10	+	9.23165e10i	0.324567	+	0.636999i	−0.669853	+	0.742494i	$0.733643\pi$
$618$	−8.67264e10	−	8.67264e10i	−0.594563	−	0.594563i
$619$	−3.96835e10	−	1.28940e10i	−0.270301	−	0.0878261i	0.170730	−	0.985318i	$-0.445387\pi$
$619$	−3.96835e10	−	1.28940e10i	−0.270301	−	0.0878261i	−0.441031	+	0.897492i	$0.645387\pi$
$620$	3.20563e11	+	2.31190e11i	2.16944	+	1.56460i
$621$	1.26821e10	+	3.90314e10i	0.0852754	+	0.262451i
$622$	3.78574e11	+	1.92893e11i	2.52923	+	1.28871i
$623$	1.00674e10	+	6.35632e10i	0.0668292	+	0.421943i
$624$			5.22164e10i			0.344404i
$625$	−1.22176e11	+	9.14114e10i	−0.800694	+	0.599074i
$626$	−3.23731e11			−2.10808
$627$	−8.89045e10	+	1.40811e10i	−0.575246	+	0.0911100i
$628$	1.58665e11	−	3.11398e11i	1.02010	−	2.00206i
$629$	−2.60222e10	+	8.45512e9i	−0.166242	+	0.0540153i
$630$	1.57754e10	−	2.18738e10i	0.100142	−	0.138855i
$631$	4.83626e10	−	1.48845e11i	0.305065	−	0.938893i	−0.674588	−	0.738194i	$-0.735679\pi$
$631$	4.83626e10	−	1.48845e11i	0.305065	−	0.938893i	0.979653	−	0.200699i	$-0.0643212\pi$
$632$	1.16825e11	−	1.16825e11i	0.732262	−	0.732262i
$633$	−8.41760e10	+	4.28898e10i	−0.524292	+	0.267140i
$634$	5.75382e10	+	7.91945e10i	0.356122	+	0.490160i
$635$	−1.01471e11	+	2.00886e11i	−0.624089	+	1.23553i
$636$	−1.64910e11	−	1.19814e11i	−1.00790	−	0.732284i
$637$	2.42095e10	−	1.52853e11i	0.147037	−	0.928358i
$638$	3.16691e11	+	5.01589e10i	1.91140	+	0.302737i
$639$	3.44974e10	−	4.74816e10i	0.206911	−	0.284788i
$640$	−1.40590e11	−	2.73548e11i	−0.837982	−	1.63047i
$641$	−1.28996e11	+	9.37211e10i	−0.764089	+	0.555143i	−0.900162	−	0.435555i	$-0.856552\pi$
$641$	−1.28996e11	+	9.37211e10i	−0.764089	+	0.555143i	0.136073	+	0.990699i	$0.456552\pi$
$642$	−1.05779e11	−	2.07603e11i	−0.622673	−	1.22206i
$643$	−1.27717e11	−	1.27717e11i	−0.747144	−	0.747144i	0.226798	−	0.973942i	$-0.427174\pi$
$643$	−1.27717e11	−	1.27717e11i	−0.747144	−	0.747144i	−0.973942	+	0.226798i	$0.927174\pi$
$644$	−1.32083e11	−	4.29164e10i	−0.767899	−	0.249505i
$645$	−2.06423e10	+	6.42967e10i	−0.119267	+	0.371492i
$646$	−3.41570e10	−	1.05125e11i	−0.196133	−	0.603634i
$647$	2.09647e10	+	1.06821e10i	0.119639	+	0.0609590i	0.512786	−	0.858517i	$-0.328614\pi$
$647$	2.09647e10	+	1.06821e10i	0.119639	+	0.0609590i	−0.393147	+	0.919476i	$0.628614\pi$
$648$	−4.40532e9	−	2.78141e10i	−0.0249849	−	0.157748i
$649$			2.21603e11i			1.24910i
$650$	−9.85539e10	−	2.96233e11i	−0.552103	−	1.65951i
$651$	4.55706e10			0.253723
$652$	−4.73246e11	+	7.49549e10i	−2.61877	+	0.414772i
$653$	−8.28842e10	+	1.62669e11i	−0.455847	+	0.894650i	0.542656	+	0.839955i	$0.317419\pi$
$653$	−8.28842e10	+	1.62669e11i	−0.455847	+	0.894650i	−0.998503	+	0.0546949i	$0.982581\pi$
$654$	9.57897e10	−	3.11239e10i	0.523610	−	0.170131i
$655$	2.86198e10	+	3.91027e10i	0.155489	+	0.212442i
$656$	−2.45291e10	+	7.54929e10i	−0.132455	+	0.407653i
$657$	5.03304e9	−	5.03304e9i	0.0270127	−	0.0270127i
$658$	6.80764e10	−	3.46866e10i	0.363156	−	0.185037i
$659$	−1.49132e11	−	2.05262e11i	−0.790729	−	1.08835i	−0.994017	−	0.109227i	$-0.965163\pi$
$659$	−1.49132e11	−	2.05262e11i	−0.790729	−	1.08835i	0.203287	−	0.979119i	$-0.434837\pi$
$660$	4.77444e10	+	2.94754e11i	0.251621	+	1.55340i
$661$	3.00627e11	+	2.18419e11i	1.57479	+	1.14415i	0.922379	+	0.386287i	$0.126243\pi$
$661$	3.00627e11	+	2.18419e11i	1.57479	+	1.14415i	0.652412	+	0.757865i	$0.273757\pi$
$662$	−7.34488e10	+	4.63738e11i	−0.382431	+	2.41457i
$663$	−6.26068e10	−	9.91594e9i	−0.324016	−	0.0513192i
$664$	−2.88284e11	+	3.96789e11i	−1.48303	+	2.04121i
$665$	6.23440e9	−	4.02759e10i	0.0318792	−	0.205949i
$666$	−2.85453e10	+	2.07394e10i	−0.145090	+	0.105414i
$667$	−1.00297e11	−	1.96844e11i	−0.506740	−	0.994534i
$668$	1.85182e10	+	1.85182e10i	0.0930022	+	0.0930022i
$669$	−2.43064e10	−	7.89764e9i	−0.121344	−	0.0394269i
$670$	−2.31260e11	+	8.10867e8i	−1.14763	+	0.00402393i
$671$	−1.00179e11	−	3.08319e11i	−0.494180	−	1.52093i
$672$	−1.48349e10	−	7.55876e9i	−0.0727458	−	0.0370658i
$673$	5.55541e10	+	3.50755e11i	0.270804	+	1.70979i	0.630055	+	0.776550i	$0.283032\pi$
$673$	5.55541e10	+	3.50755e11i	0.270804	+	1.70979i	−0.359251	+	0.933241i	$0.616968\pi$
$674$			5.73668e10i			0.277985i
$675$	1.83868e10	+	3.54690e10i	0.0885708	+	0.170857i
$676$	2.81371e10			0.134739
$677$	−1.37244e11	+	2.17374e10i	−0.653341	+	0.103479i	−0.474301	−	0.880363i	$-0.657299\pi$
$677$	−1.37244e11	+	2.17374e10i	−0.653341	+	0.103479i	−0.179040	+	0.983842i	$0.557299\pi$
$678$	1.65155e10	−	3.24136e10i	0.0781581	−	0.153394i
$679$	−1.64034e10	+	5.32980e9i	−0.0771712	+	0.0250745i
$680$	−1.60171e11	+	5.26643e10i	−0.749114	+	0.246309i
$681$	3.98683e10	−	1.22702e11i	0.185370	−	0.570510i
$682$	−5.49486e11	+	5.49486e11i	−2.53991	+	2.53991i
$683$	3.24855e11	−	1.65522e11i	1.49282	−	0.760628i	0.498479	−	0.866902i	$-0.333892\pi$
$683$	3.24855e11	−	1.65522e11i	1.49282	−	0.760628i	0.994337	+	0.106274i	$0.0338919\pi$
$684$	−5.43987e10	−	7.48734e10i	−0.248521	−	0.342060i
$685$	1.71405e10	+	1.70207e10i	0.0778503	+	0.0773063i
$686$	−1.75525e11	−	1.27526e11i	−0.792579	−	0.575842i
$687$	1.96268e10	−	1.23919e11i	0.0881093	−	0.556300i
$688$	−8.61310e10	−	1.36418e10i	−0.384420	−	0.0608861i
$689$	−1.59920e11	+	2.20111e11i	−0.709620	+	0.976707i
$690$	2.23272e11	−	2.24844e11i	0.985006	−	0.991938i
$691$	−2.46781e11	+	1.79297e11i	−1.08243	+	0.786432i	−0.978105	−	0.208112i	$-0.933268\pi$
$691$	−2.46781e11	+	1.79297e11i	−1.08243	+	0.786432i	−0.104325	+	0.994543i	$0.533268\pi$
$692$	−1.91266e11	−	3.75380e11i	−0.834090	−	1.63699i
$693$	2.43444e10	+	2.43444e10i	0.105552	+	0.105552i
$694$	8.40915e10	+	2.73230e10i	0.362505	+	0.117785i
$695$	−1.00631e11	−	3.06054e11i	−0.431312	−	1.31177i
$696$	4.68448e10	+	1.44174e11i	0.199629	+	0.614396i
$697$	−8.58569e10	−	4.37463e10i	−0.363784	−	0.185357i
$698$	1.16166e11	+	7.33442e11i	0.489392	+	3.08990i
$699$		−	5.39051e10i		−	0.225798i
$700$	−1.33677e11	−	2.02125e10i	−0.556757	−	0.0841838i
$701$	8.27322e10			0.342612			0.171306	−	0.985218i	$-0.445201\pi$
$701$	8.27322e10			0.342612			0.171306	+	0.985218i	$0.445201\pi$
$702$	−8.07349e10	+	1.27872e10i	−0.332440	+	0.0526533i
$703$	−2.42073e10	+	4.75096e10i	−0.0991119	+	0.194518i
$704$	4.68114e11	−	1.52099e11i	1.90573	−	0.619208i
$705$	3.96855e8	+	1.13183e11i	0.00160648	+	0.458168i
$706$	−3.10514e10	+	9.55663e10i	−0.124986	+	0.384668i
$707$	−9.14891e10	+	9.14891e10i	−0.366178	+	0.366178i
$708$	−2.03013e11	+	1.03440e11i	−0.807960	+	0.411676i
$709$	1.58766e11	+	2.18522e11i	0.628307	+	0.864790i	0.997925	−	0.0643935i	$-0.0205113\pi$
$709$	1.58766e11	+	2.18522e11i	0.628307	+	0.864790i	−0.369618	+	0.929184i	$0.620511\pi$
$710$	−4.47813e11	−	6.93180e10i	−1.76223	−	0.272780i
$711$	4.96488e10	+	3.60720e10i	0.194281	+	0.141153i
$712$	8.11652e10	−	5.12457e11i	0.315827	−	1.99406i
$713$	5.28833e11	+	8.37588e10i	2.04626	+	0.324095i
$714$	−2.48500e10	+	3.42031e10i	−0.0956167	+	0.131605i
$715$	3.93418e11	−	6.37261e10i	1.50532	−	0.243833i
$716$	−6.60721e11	+	4.80042e11i	−2.51400	+	1.82653i
$717$	−1.91050e10	−	3.74957e10i	−0.0722888	−	0.141875i
$718$	2.26371e11	+	2.26371e11i	0.851772	+	0.851772i
$719$	−7.08407e10	−	2.30175e10i	−0.265074	−	0.0861278i	0.173465	−	0.984840i	$-0.444504\pi$
$719$	−7.08407e10	−	2.30175e10i	−0.265074	−	0.0861278i	−0.438539	+	0.898712i	$0.644504\pi$
$720$	−4.16322e10	+	3.04712e10i	−0.154917	+	0.113386i
$721$	2.19069e10	+	6.74226e10i	0.0810663	+	0.249496i
$722$	2.16906e11	+	1.10519e11i	0.798222	+	0.406714i
$723$	−1.30643e10	−	8.24846e10i	−0.0478115	−	0.301870i
$724$			7.58541e11i			2.76074i
$725$	−1.27628e11	−	1.73100e11i	−0.461950	−	0.626533i
$726$	−3.16250e11			−1.13837
$727$	−4.92001e11	+	7.79253e10i	−1.76128	+	0.278959i	−0.951472	−	0.307736i	$-0.900429\pi$
$727$	−4.92001e11	+	7.79253e10i	−1.76128	+	0.278959i	−0.809808	+	0.586695i	$0.800429\pi$
$728$	5.77457e10	−	1.13332e11i	0.205586	−	0.403486i
$729$	9.94839e9	−	3.23243e9i	0.0352243	−	0.0114451i
$730$	−5.23256e10	−	1.67990e10i	−0.184256	−	0.0591551i
$731$	3.27127e10	−	1.00679e11i	0.114564	−	0.352591i
$732$	2.35692e11	−	2.35692e11i	0.820918	−	0.820918i
$733$	1.68379e11	−	8.57934e10i	0.583273	−	0.297192i	−0.137347	−	0.990523i	$-0.543857\pi$
$733$	1.68379e11	−	8.57934e10i	0.583273	−	0.297192i	0.720620	+	0.693331i	$0.243857\pi$
$734$	−7.48760e10	−	1.03058e11i	−0.257963	−	0.355056i
$735$	1.35997e11	−	6.98958e10i	0.465995	−	0.239498i
$736$	−1.58262e11	−	1.14984e11i	−0.539342	−	0.391855i
$737$	4.61832e10	−	2.91590e11i	0.156536	−	0.988330i
$738$	−1.22731e11	−	1.94387e10i	−0.413741	−	0.0655302i
$739$	4.70886e8	−	6.48119e8i	0.00157884	−	0.00217309i	−0.808227	−	0.588871i	$-0.799572\pi$
$739$	4.70886e8	−	6.48119e8i	0.00157884	−	0.00217309i	0.809806	+	0.586698i	$0.199572\pi$
$740$	1.57882e11	+	7.97489e10i	0.526509	+	0.265949i
$741$	−9.99360e10	+	7.26077e10i	−0.331474	+	0.240830i
$742$	8.23829e10	+	1.61686e11i	0.271782	+	0.533403i
$743$	−3.80086e11	−	3.80086e11i	−1.24717	−	1.24717i	−0.956963	−	0.290211i	$-0.906275\pi$
$743$	−3.80086e11	−	3.80086e11i	−1.24717	−	1.24717i	−0.290211	−	0.956963i	$-0.593725\pi$
$744$	−3.49415e11	−	1.13532e11i	−1.14038	−	0.370532i
$745$	3.17940e11	+	2.29298e11i	1.03209	+	0.744346i
$746$	1.60867e11	+	4.95097e11i	0.519411	+	1.59858i
$747$	−1.62325e11	−	8.27086e10i	−0.521317	−	0.265624i
$748$	−7.32249e10	−	4.62324e11i	−0.233912	−	1.47686i
$749$			1.34675e11i			0.427916i
$750$	1.78675e11	−	2.51446e11i	0.564702	−	0.794692i
$751$	4.00225e11			1.25819			0.629093	−	0.777330i	$-0.283427\pi$
$751$	4.00225e11			1.25819			0.629093	+	0.777330i	$0.283427\pi$
$752$	−1.44362e11	+	2.28647e10i	−0.451421	+	0.0714981i
$753$	5.45518e10	−	1.07064e11i	0.169679	−	0.333015i
$754$	4.18487e11	−	1.35975e11i	1.29478	−	0.420700i
$755$	3.28835e11	−	4.55956e11i	1.01202	−	1.40325i
$756$	−1.09386e10	+	3.36656e10i	−0.0334869	+	0.103062i
$757$	8.23374e10	−	8.23374e10i	0.250734	−	0.250734i	−0.570537	−	0.821272i	$-0.693265\pi$
$757$	8.23374e10	−	8.23374e10i	0.250734	−	0.250734i	0.821272	+	0.570537i	$0.193265\pi$
$758$	7.53234e11	−	3.83792e11i	2.28167	−	1.16257i
$759$	2.37764e11	+	3.27254e11i	0.716439	+	0.986094i
$760$	−1.48144e11	+	2.93286e11i	−0.444047	+	0.879098i
$761$	−1.85432e11	−	1.34725e11i	−0.552901	−	0.401706i	0.275953	−	0.961171i	$-0.411007\pi$
$761$	−1.85432e11	−	1.34725e11i	−0.552901	−	0.401706i	−0.828854	+	0.559465i	$0.811007\pi$
$762$	7.11725e10	−	4.49365e11i	0.211102	−	1.33285i
$763$	−5.74996e10	−	9.10704e9i	−0.169655	−	0.0268707i
$764$	4.09139e11	−	5.63131e11i	1.20087	−	1.65286i
$765$	−2.86285e10	−	5.57029e10i	−0.0835898	−	0.162642i
$766$	1.70018e11	−	1.23525e11i	0.493833	−	0.358791i
$767$	1.38065e11	+	2.70968e11i	0.398935	+	0.782953i
$768$	2.46346e11	+	2.46346e11i	0.708111	+	0.708111i
$769$	−2.69164e10	−	8.74568e9i	−0.0769683	−	0.0250085i	0.270280	−	0.962782i	$-0.412884\pi$
$769$	−2.69164e10	−	8.74568e9i	−0.0769683	−	0.0250085i	−0.347248	+	0.937773i	$0.612884\pi$
$770$	8.12554e10	−	2.53094e11i	0.231147	−	0.719979i
$771$	8.91186e10	+	2.74279e11i	0.252203	+	0.776202i
$772$	−5.12660e11	−	2.61213e11i	−1.44331	−	0.735404i
$773$	7.32720e10	+	4.62621e11i	0.205220	+	1.29571i	0.848138	+	0.529775i	$0.177723\pi$
$773$	7.32720e10	+	4.62621e11i	0.205220	+	1.29571i	−0.642918	+	0.765935i	$0.722277\pi$
$774$		−	1.36513e11i		−	0.380374i
$775$	5.21210e11	−	3.65509e9i	1.44479	−	0.0101319i
$776$	1.39053e11			0.383471
$777$	2.01433e10	−	3.19038e9i	0.0552645	−	0.00875303i
$778$	2.52543e11	−	4.95643e11i	0.689314	−	1.35285i
$779$	−1.78593e11	+	5.80283e10i	−0.484969	+	0.157576i
$780$	2.42020e11	+	3.30667e11i	0.653841	+	0.893331i
$781$	1.78760e11	−	5.50166e11i	0.480470	−	1.47873i
$782$	−3.51242e11	+	3.51242e11i	−0.939247	+	0.939247i
$783$	−5.01720e10	+	2.55639e10i	−0.133479	+	0.0680112i
$784$	1.16064e11	+	1.59748e11i	0.307208	+	0.422835i
$785$	−7.36961e10	−	4.54969e11i	−0.194073	−	1.19813i
$786$	−7.92502e10	−	5.75787e10i	−0.207640	−	0.150859i
$787$	1.95785e10	−	1.23614e11i	0.0510366	−	0.322232i	−0.948940	−	0.315455i	$-0.897843\pi$
$787$	1.95785e10	−	1.23614e11i	0.0510366	−	0.322232i	0.999977	−	0.00677696i	$-0.00215719\pi$
$788$	1.60016e11	+	2.53440e10i	0.415010	+	0.0657311i
$789$	−1.29622e11	+	1.78409e11i	−0.334479	+	0.460371i
$790$	7.24818e10	−	4.68252e11i	0.186089	−	1.20219i
$791$	−1.70112e10	+	1.23594e10i	−0.0434540	+	0.0315712i
$792$	−1.26012e11	−	2.47312e11i	−0.320266	−	0.628558i
$793$	−3.14586e11	−	3.14586e11i	−0.795511	−	0.795511i
$794$	4.87009e11	+	1.58239e11i	1.22534	+	0.398136i
$795$	−2.68817e11	+	9.42554e8i	−0.672958	+	0.00235960i
$796$	1.45036e11	+	4.46375e11i	0.361263	+	1.11185i
$797$	6.45499e10	+	3.28898e10i	0.159979	+	0.0815132i	0.532147	−	0.846652i	$-0.321385\pi$
$797$	6.45499e10	+	3.28898e10i	0.159979	+	0.0815132i	−0.372168	+	0.928165i	$0.621385\pi$
$798$	1.28885e10	+	8.13750e10i	0.0317828	+	0.200668i
$799$		−	1.77430e11i		−	0.435352i
$800$	−1.70279e11	−	8.52630e10i	−0.415721	−	0.208162i
$801$	1.92725e11			0.468175
$802$	−1.11925e12	+	1.77272e11i	−2.70539	+	0.428492i
$803$	3.18502e10	−	6.25095e10i	0.0766037	−	0.150343i
$804$	2.88685e11	−	9.37994e10i	0.690876	−	0.224479i
$805$	−1.73988e11	+	5.72074e10i	−0.414320	+	0.136229i
$806$	−3.29545e11	+	1.01423e12i	−0.780862	+	2.40325i
$807$	1.53773e11	−	1.53773e11i	0.362566	−	0.362566i
$808$	9.29429e11	−	4.73568e11i	2.18057	−	1.11106i
$809$	9.49980e10	+	1.30754e11i	0.221779	+	0.305253i	0.905379	−	0.424604i	$-0.139587\pi$
$809$	9.49980e10	+	1.30754e11i	0.221779	+	0.305253i	−0.683600	+	0.729857i	$0.739587\pi$
$810$	−5.73085e10	−	5.69081e10i	−0.133131	−	0.132201i
$811$	3.62548e11	+	2.63406e11i	0.838072	+	0.608895i	0.921832	−	0.387591i	$-0.126693\pi$
$811$	3.62548e11	+	2.63406e11i	0.838072	+	0.608895i	−0.0837591	+	0.996486i	$0.526693\pi$
$812$	2.98089e10	−	1.88206e11i	0.0685681	−	0.432922i
$813$	−4.01250e11	−	6.35518e10i	−0.918444	−	0.145467i
$814$	−2.04417e11	+	2.81355e11i	−0.465606	+	0.640852i
$815$	−4.45240e11	+	4.48373e11i	−1.00917	+	1.01627i
$816$	6.54310e10	−	4.75384e10i	0.147578	−	0.107222i
$817$	−9.36578e10	−	1.83814e11i	−0.210211	−	0.412562i
$818$	−1.25715e11	−	1.25715e11i	−0.280784	−	0.280784i
$819$	4.49346e10	+	1.46001e10i	0.0998723	+	0.0324505i
$820$	1.94571e11	+	5.91759e11i	0.430351	+	1.30885i
$821$	1.27672e11	+	3.92933e11i	0.281010	+	0.864860i	0.987566	+	0.157203i	$0.0502477\pi$
$821$	1.27672e11	+	3.92933e11i	0.281010	+	0.864860i	−0.706556	+	0.707657i	$0.749752\pi$
$822$	−4.35096e10	−	2.21692e10i	−0.0953010	−	0.0485583i
$823$	−1.28622e11	−	8.12087e11i	−0.280360	−	1.77012i	−0.578580	−	0.815625i	$-0.696393\pi$
$823$	−1.28622e11	−	8.12087e11i	−0.280360	−	1.77012i	0.298220	−	0.954497i	$-0.403607\pi$
$824$		−	5.71545e11i		−	1.23977i
$825$	2.80390e11	+	2.76485e11i	0.605266	+	0.596836i
$826$	2.02835e11			0.435735
$827$	6.49873e11	−	1.02930e11i	1.38933	−	0.220049i	0.583462	−	0.812140i	$-0.301698\pi$
$827$	6.49873e11	−	1.02930e11i	1.38933	−	0.220049i	0.805871	+	0.592092i	$0.201698\pi$
$828$	−1.88817e11	+	3.70574e11i	−0.401716	+	0.788412i
$829$	−1.82925e11	+	5.94358e10i	−0.387306	+	0.125843i	−0.496196	−	0.868211i	$-0.665270\pi$
$829$	−1.82925e11	+	5.94358e10i	−0.387306	+	0.125843i	0.108890	+	0.994054i	$0.465270\pi$
$830$	4.93198e9	+	1.40660e12i	0.0103922	+	2.96387i
$831$	9.98273e9	−	3.07237e10i	0.0209337	−	0.0644272i
$832$	4.77629e11	−	4.77629e11i	0.996775	−	0.996775i
$833$	−2.13576e11	+	1.08822e11i	−0.443581	+	0.226016i
$834$	3.82817e11	+	5.26903e11i	0.791275	+	1.08910i
$835$	3.41305e10	+	5.28313e9i	0.0702096	+	0.0108679i
$836$	−7.37985e11	−	5.36177e11i	−1.51085	−	1.09770i
$837$	2.13486e10	−	1.34790e11i	0.0434978	−	0.274634i
$838$	5.09637e11	+	8.07186e10i	1.03344	+	0.163681i
$839$	4.31244e11	−	5.93556e11i	0.870312	−	1.19788i	−0.108699	−	0.994075i	$-0.534669\pi$
$839$	4.31244e11	−	5.93556e11i	0.870312	−	1.19788i	0.979011	−	0.203807i	$-0.0653315\pi$
$840$	1.24058e11	−	2.00950e10i	0.249176	−	0.0403618i
$841$	−1.59478e11	+	1.15868e11i	−0.318800	+	0.231622i
$842$	−3.49509e11	−	6.85949e11i	−0.695360	−	1.36472i
$843$	3.48428e11	+	3.48428e11i	0.689926	+	0.689926i
$844$	−9.10541e11	−	2.95853e11i	−1.79444	−	0.583050i
$845$	2.99431e10	−	2.19158e10i	0.0587313	−	0.0429863i
$846$	−7.07050e10	−	2.17608e11i	−0.138029	−	0.424808i
$847$	1.62871e11	+	8.29870e10i	0.316454	+	0.161241i
$848$	−5.43051e10	−	3.42869e11i	−0.105016	−	0.663048i
$849$		−	3.35857e11i		−	0.646433i
$850$	−2.81477e11	+	3.93189e11i	−0.539221	+	0.753226i
$851$	2.39621e11			0.456884
$852$	5.87454e11	−	9.30435e10i	1.11485	−	0.176574i
$853$	1.68639e11	−	3.30972e11i	0.318538	−	0.625166i	−0.675108	−	0.737719i	$-0.735903\pi$
$853$	1.68639e11	−	3.30972e11i	0.318538	−	0.625166i	0.993646	+	0.112553i	$0.0359028\pi$
$854$	−2.82206e11	+	9.16944e10i	−0.530561	+	0.172390i
$855$	−1.16208e11	−	3.73084e10i	−0.217457	−	0.0698140i
$856$	3.35521e11	−	1.03263e12i	0.624920	−	1.92331i
$857$	6.42530e11	−	6.42530e11i	1.19116	−	1.19116i	0.214418	−	0.976742i	$-0.431215\pi$
$857$	6.42530e11	−	6.42530e11i	1.19116	−	1.19116i	0.976742	−	0.214418i	$-0.0687853\pi$
$858$	−7.17864e11	+	3.65770e11i	−1.32463	+	0.674931i
$859$	−4.14073e11	−	5.69923e11i	−0.760509	−	1.04675i	−0.997172	−	0.0751588i	$-0.976054\pi$
$859$	−4.14073e11	−	5.69923e11i	−0.760509	−	1.04675i	0.236663	−	0.971592i	$-0.423946\pi$
$860$	−6.08664e11	+	3.12823e11i	−1.11272	+	0.571880i
$861$	5.81065e10	+	4.22169e10i	0.105733	+	0.0768198i
$862$	−2.47311e11	+	1.56146e12i	−0.447934	+	2.82814i
$863$	−1.15157e11	−	1.82391e10i	−0.207610	−	0.0328822i	0.0517630	−	0.998659i	$-0.483516\pi$
$863$	−1.15157e11	−	1.82391e10i	−0.207610	−	0.0328822i	−0.259373	+	0.965777i	$0.583516\pi$
$864$	−2.93072e10	+	4.03380e10i	−0.0525920	+	0.0723867i
$865$	−4.95923e11	−	2.50499e11i	−0.885829	−	0.447447i
$866$	1.65581e11	−	1.20302e11i	0.294401	−	0.213895i
$867$	−1.03530e11	−	2.03189e11i	−0.183227	−	0.359604i
$868$	3.26554e11	+	3.26554e11i	0.575276	+	0.575276i
$869$	5.75278e11	+	1.86919e11i	1.00878	+	0.327774i
$870$	3.52623e11	+	2.54312e11i	0.615508	+	0.443904i
$871$	−1.25197e11	−	3.85318e11i	−0.217532	−	0.669493i
$872$	4.18193e11	+	2.13080e11i	0.723288	+	0.368533i
$873$	8.08003e9	+	5.10153e10i	0.0139109	+	0.0878301i
$874$			9.68021e11i			1.65897i
$875$	−1.58001e11	+	8.26103e10i	−0.269542	+	0.140929i
$876$	7.21325e10			0.122494
$877$	3.42142e11	−	5.41899e10i	0.578373	−	0.0916052i	0.139607	−	0.990207i	$-0.455416\pi$
$877$	3.42142e11	−	5.41899e10i	0.578373	−	0.0916052i	0.438765	+	0.898602i	$0.355416\pi$
$878$	−3.23080e11	+	6.34081e11i	−0.543666	+	1.06700i
$879$	−3.88441e11	+	1.26212e11i	−0.650683	+	0.211420i
$880$	−2.97452e11	+	4.12441e11i	−0.496006	+	0.687751i
$881$	−2.56163e11	+	7.88390e11i	−0.425220	+	1.30869i	0.477564	+	0.878597i	$0.341520\pi$
$881$	−2.56163e11	+	7.88390e11i	−0.425220	+	1.30869i	−0.902784	+	0.430095i	$0.858480\pi$
$882$	−2.18573e11	+	2.18573e11i	−0.361179	+	0.361179i
$883$	−2.73954e10	+	1.39586e10i	−0.0450645	+	0.0229615i	−0.476378	−	0.879241i	$-0.658050\pi$
$883$	−2.73954e10	+	1.39586e10i	−0.0450645	+	0.0229615i	0.431313	+	0.902202i	$0.358050\pi$
$884$	−3.77577e11	−	5.19690e11i	−0.618296	−	0.851012i
$885$	−1.35474e11	+	2.68204e11i	−0.220843	+	0.437212i
$886$	−4.48146e11	−	3.25597e11i	−0.727251	−	0.528379i
$887$	8.35092e10	−	5.27256e11i	0.134909	−	0.851780i	−0.823694	−	0.567034i	$-0.808091\pi$
$887$	8.35092e10	−	5.27256e11i	0.134909	−	0.851780i	0.958603	−	0.284746i	$-0.0919091\pi$
$888$	−1.62398e11	−	2.57213e10i	−0.261174	−	0.0413658i
$889$	−1.54572e11	+	2.12750e11i	−0.247471	+	0.340614i
$890$	−6.80192e11	−	1.32346e12i	−1.08411	−	2.10936i
$891$	8.34111e10	−	6.06017e10i	0.132347	−	0.0961555i
$892$	−1.17584e11	−	2.30771e11i	−0.185732	−	0.364520i
$893$	−2.44498e11	−	2.44498e11i	−0.384477	−	0.384477i
$894$	−7.53659e11	−	2.44879e11i	−1.17984	−	0.383355i
$895$	−3.29229e11	+	1.02548e12i	−0.513105	+	1.59822i
$896$	−1.11053e11	−	3.41786e11i	−0.172305	−	0.530301i
$897$	4.94617e11	+	2.52020e11i	0.764010	+	0.389283i
$898$	−3.11646e10	−	1.96765e11i	−0.0479243	−	0.302582i
$899$			7.34634e11i			1.12469i
$900$	−1.22409e11	+	3.85925e11i	−0.186571	+	0.588211i
$901$	4.21408e11			0.639445
$902$	−1.20969e12	+	1.91596e11i	−1.82746	+	0.289441i
$903$	−3.58223e10	+	7.03053e10i	−0.0538769	+	0.105739i
$904$	1.61226e11	−	5.23856e10i	0.241414	−	0.0784401i
$905$	5.90821e11	+	8.07228e11i	0.880768	+	1.20338i
$906$	−3.51179e11	+	1.08082e12i	−0.521214	+	1.60413i
$907$	9.25147e10	−	9.25147e10i	0.136704	−	0.136704i	−0.635443	−	0.772147i	$-0.719183\pi$
$907$	9.25147e10	−	9.25147e10i	0.136704	−	0.136704i	0.772147	+	0.635443i	$0.219183\pi$
$908$	1.16496e12	−	5.93578e11i	1.71383	−	0.873241i
$909$	2.27749e11	+	3.13469e11i	0.333580	+	0.459133i
$910$	−5.83289e10	−	3.60098e11i	−0.0850587	−	0.525116i
$911$	−2.96141e11	−	2.15159e11i	−0.429957	−	0.312382i	0.351675	−	0.936122i	$-0.385612\pi$
$911$	−2.96141e11	−	2.15159e11i	−0.429957	−	0.312382i	−0.781632	+	0.623740i	$0.785612\pi$
$912$	2.46559e10	−	1.55671e11i	0.0356403	−	0.225024i
$913$	−1.77355e12	−	2.80903e11i	−2.55247	−	0.404271i
$914$	1.20139e12	−	1.65357e12i	1.72147	−	2.36940i
$915$	6.72413e10	−	4.34398e11i	0.0959295	−	0.619731i
$916$	1.02863e12	−	7.47345e11i	1.46109	−	1.06155i
$917$	2.57053e10	+	5.04495e10i	0.0363534	+	0.0713476i
$918$	8.95252e10	+	8.95252e10i	0.126059	+	0.126059i
$919$	−1.95161e11	−	6.34116e10i	−0.273609	−	0.0889010i	0.168999	−	0.985616i	$-0.445947\pi$
$919$	−1.95161e11	−	6.34116e10i	−0.273609	−	0.0889010i	−0.442608	+	0.896715i	$0.645947\pi$
$920$	1.47659e12	−	5.17737e9i	2.06114	−	0.00722700i
$921$	1.35081e11	+	4.15738e11i	0.187740	+	0.577804i
$922$	1.09538e12	+	5.58126e11i	1.51580	+	0.772340i
$923$	−1.24188e11	−	7.84094e11i	−0.171109	−	1.08034i
$924$			3.48899e11i			0.478643i
$925$	2.30132e11	−	3.81054e10i	0.314347	−	0.0520499i
$926$	−1.91759e12			−2.60803
$927$	2.09687e11	−	3.32112e10i	0.283957	−	0.0449744i
$928$	1.21853e11	−	2.39151e11i	0.164303	−	0.322463i
$929$	−7.43811e11	+	2.41679e11i	−0.998619	+	0.324471i	−0.762314	−	0.647208i	$-0.775937\pi$
$929$	−7.43811e11	+	2.41679e11i	−0.998619	+	0.324471i	−0.236306	+	0.971679i	$0.575937\pi$
$930$	−1.00096e12	+	3.29116e11i	−1.33809	+	0.439964i
$931$	−1.44350e11	+	4.44264e11i	−0.192140	+	0.591347i
$932$	3.86278e11	−	3.86278e11i	0.511961	−	0.511961i
$933$	−6.55293e11	+	3.33889e11i	−0.864787	+	0.440631i
$934$	1.26499e12	+	1.74111e12i	1.66227	+	2.28791i
$935$	−4.38025e11	−	4.34964e11i	−0.573129	−	0.569124i
$936$	−3.08165e11	−	2.23895e11i	−0.401494	−	0.291703i
$937$	−5.08802e10	+	3.21245e11i	−0.0660071	+	0.416753i	0.932454	+	0.361290i	$0.117663\pi$
$937$	−5.08802e10	+	3.21245e11i	−0.0660071	+	0.416753i	−0.998461	+	0.0554629i	$0.982337\pi$
$938$	−2.66894e11	−	4.22719e10i	−0.344768	−	0.0546060i
$939$	3.29373e11	−	4.53343e11i	0.423668	−	0.583128i
$940$	−8.08215e11	+	8.13903e11i	−1.03518	+	1.04246i
$941$	−2.21291e11	+	1.60777e11i	−0.282231	+	0.205053i	−0.719890	−	0.694088i	$-0.755808\pi$
$941$	−2.21291e11	+	1.60777e11i	−0.282231	+	0.205053i	0.437659	+	0.899141i	$0.355808\pi$
$942$	4.22996e11	+	8.30176e11i	0.537195	+	1.05431i
$943$	5.96714e11	+	5.96714e11i	0.754604	+	0.754604i
$944$	−3.69035e11	−	1.19907e11i	−0.464707	−	0.150992i
$945$	1.45811e10	+	4.43464e10i	0.0182837	+	0.0556072i
$946$	−4.15792e11	−	1.27968e12i	−0.519173	−	1.59785i
$947$	6.15512e11	+	3.13619e11i	0.765308	+	0.389944i	0.792646	−	0.609682i	$-0.208703\pi$
$947$	6.15512e11	+	3.13619e11i	0.765308	+	0.389944i	−0.0273377	+	0.999626i	$0.508703\pi$
$948$	9.72903e10	+	6.14267e11i	0.120458	+	0.760543i
$949$		−	9.62777e10i		−	0.118703i
$950$	1.53939e11	+	9.29687e11i	0.188996	+	1.14141i
$951$	−1.69443e11			−0.207157
$952$	−1.94586e11	+	3.08194e10i	−0.236899	+	0.0375212i
$953$	−2.59339e11	+	5.08982e11i	−0.314410	+	0.617065i	−0.993088	−	0.117371i	$-0.962553\pi$
$953$	−2.59339e11	+	5.08982e11i	−0.314410	+	0.617065i	0.678678	+	0.734436i	$0.262553\pi$
$954$	5.16832e11	−	1.67929e11i	0.623958	−	0.202736i
$955$	−3.21862e9	−	9.17951e11i	−0.00386951	−	1.10359i
$956$	1.31786e11	−	4.05595e11i	0.157775	−	0.485580i
$957$	−3.92451e11	+	3.92451e11i	−0.467884	+	0.467884i
$958$	−1.17080e12	+	5.96553e11i	−1.39002	+	0.708251i
$959$	1.65903e10	+	2.28346e10i	0.0196147	+	0.0269973i
$960$	6.59537e11	+	1.02091e11i	0.776523	+	0.120200i
$961$	−7.50402e11	−	5.45199e11i	−0.879834	−	0.639237i
$962$	−7.46604e10	+	4.71387e11i	−0.0871746	+	0.550399i
$963$	3.98344e11	+	6.30915e10i	0.463184	+	0.0733611i
$964$	4.97459e11	−	6.84694e11i	0.576036	−	0.792845i
$965$	−7.49021e11	+	1.21327e11i	−0.863744	+	0.139910i
$966$	2.99538e11	−	2.17627e11i	0.343988	−	0.249922i
$967$	−4.08027e11	−	8.00798e11i	−0.466641	−	0.915834i	−0.997653	−	0.0684701i	$-0.978188\pi$
$967$	−4.08027e11	−	8.00798e11i	−0.466641	−	0.915834i	0.531012	−	0.847364i	$-0.321812\pi$
$968$	−1.04208e12	−	1.04208e12i	−1.18686	−	1.18686i
$969$	1.81966e11	+	5.91242e10i	0.206393	+	0.0670610i
$970$	3.21809e11	−	2.35536e11i	0.363506	−	0.266055i
$971$	−1.70578e11	−	5.24986e11i	−0.191888	−	0.590569i	−0.999999	−	0.00153937i	$-0.999510\pi$
$971$	−1.70578e11	−	5.24986e11i	−0.191888	−	0.590569i	0.808111	−	0.589030i	$-0.200490\pi$
$972$	9.44524e10	+	4.81259e10i	0.105815	+	0.0539155i
$973$	−5.88895e10	−	3.71814e11i	−0.0657032	−	0.414834i
$974$		−	6.22276e11i		−	0.691428i
$975$	5.15107e11	+	1.63384e11i	0.570006	+	0.180797i
$976$	5.67647e11			0.625574
$977$	5.78396e11	−	9.16090e10i	0.634815	−	0.100545i	0.169271	−	0.985570i	$-0.445859\pi$
$977$	5.78396e11	−	9.16090e10i	0.634815	−	0.100545i	0.465544	+	0.885025i	$0.345859\pi$
$978$	5.79919e11	−	1.13816e12i	0.633888	−	1.24407i
$979$	1.80661e12	−	5.87004e11i	1.96668	−	0.639014i
$980$	1.47541e12	+	4.73677e11i	1.59959	+	0.513544i
$981$	−5.38741e10	+	1.65807e11i	−0.0581706	+	0.179031i
$982$	−4.31413e11	+	4.31413e11i	−0.463925	+	0.463925i
$983$	−6.49790e11	+	3.31085e11i	−0.695920	+	0.354589i	−0.765900	−	0.642959i	$-0.777706\pi$
$983$	−6.49790e11	+	3.31085e11i	−0.695920	+	0.354589i	0.0699803	+	0.997548i	$0.477706\pi$
$984$	−3.40359e11	−	4.68464e11i	−0.363042	−	0.499684i
$985$	1.90027e11	−	9.76643e10i	0.201869	−	0.103751i
$986$	−5.51381e11	−	4.00602e11i	−0.583370	−	0.423843i
$987$	−2.06887e10	+	1.30623e11i	−0.0218004	+	0.137642i
$988$	−1.23643e12	−	1.95831e11i	−1.29760	−	0.205520i
$989$	−5.44929e11	+	7.50030e11i	−0.569580	+	0.783959i
$990$	−7.10543e11	−	3.58907e11i	−0.739689	−	0.373630i
$991$	−2.51374e11	+	1.82634e11i	−0.260631	+	0.189360i	−0.710425	−	0.703773i	$-0.751497\pi$
$991$	−2.51374e11	+	1.82634e11i	−0.260631	+	0.189360i	0.449794	+	0.893132i	$0.351497\pi$
$992$	2.95320e11	+	5.79599e11i	0.304963	+	0.598523i
$993$	−5.74675e11	−	5.74675e11i	−0.591052	−	0.591052i
$994$	−5.03571e11	−	1.63620e11i	−0.515841	−	0.167607i
$995$	5.02022e11	+	3.62058e11i	0.512190	+	0.369391i
$996$	−5.70521e11	−	1.75588e12i	−0.579742	−	1.78426i
$997$	5.15534e11	+	2.62678e11i	0.521767	+	0.265853i	0.694978	−	0.719031i	$-0.255414\pi$
$997$	5.15534e11	+	2.62678e11i	0.521767	+	0.265853i	−0.173211	+	0.984885i	$0.555414\pi$
$998$	3.38784e11	+	2.13900e12i	0.341508	+	2.15619i
$999$		−	6.10749e10i		−	0.0613198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.k.a.13.5	✓	320
25.2	odd	20	inner	75.9.k.a.52.5	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.9.k.a.13.5	✓	320	1.1	even	1	trivial
75.9.k.a.52.5	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)

\(f(q)\)	\(=\)	\(q+(-26.6845 + 4.22641i) q^{2} +(21.2310 - 41.6683i) q^{3} +(450.730 - 146.451i) q^{4} +(365.591 - 506.921i) q^{5} +(-390.433 + 1201.63i) q^{6} +(516.394 - 516.394i) q^{7} +(-5246.00 + 2672.97i) q^{8} +(-1285.49 - 1769.32i) q^{9} +O(q^{10})\)	\(q+(-26.6845 + 4.22641i) q^{2} +(21.2310 - 41.6683i) q^{3} +(450.730 - 146.451i) q^{4} +(365.591 - 506.921i) q^{5} +(-390.433 + 1201.63i) q^{6} +(516.394 - 516.394i) q^{7} +(-5246.00 + 2672.97i) q^{8} +(-1285.49 - 1769.32i) q^{9} +(-7613.15 + 15072.1i) q^{10} +(-17439.2 - 12670.3i) q^{11} +(3467.10 - 21890.4i) q^{12} +(-29217.9 - 4627.66i) q^{13} +(-11597.2 + 15962.2i) q^{14} +(-13360.6 - 25996.0i) q^{15} +(30535.9 - 22185.7i) q^{16} +(20801.5 + 40825.2i) q^{17} +(41780.4 + 41780.4i) q^{18} +(84921.4 + 27592.6i) q^{19} +(90543.6 - 282025. i) q^{20} +(-10553.7 - 32480.8i) q^{21} +(518906. + 264396. i) q^{22} +(-62772.2 - 396328. i) q^{23} +275342. i q^{24} +(-123312. - 370651. i) q^{25} +799224. q^{26} +(-101017. + 15999.5i) q^{27} +(157128. - 308381. i) q^{28} +(523617. - 170133. i) q^{29} +(466391. + 637222. i) q^{30} +(-412331. + 1.26902e6i) q^{31} +(344721. - 344721. i) q^{32} +(-898202. + 457657. i) q^{33} +(-727622. - 1.00149e6i) q^{34} +(-72982.0 - 450560. i) q^{35} +(-838526. - 609225. i) q^{36} +(-93416.1 + 589806. i) q^{37} +(-2.38270e6 - 377383. i) q^{38} +(-813153. + 1.11921e6i) q^{39} +(-562905. + 3.63652e6i) q^{40} +(-1.70139e6 + 1.23613e6i) q^{41} +(418897. + 822131. i) q^{42} +(-1.63370e6 - 1.63370e6i) q^{43} +(-9.71595e6 - 3.15690e6i) q^{44} +(-1.36687e6 + 4792.65i) q^{45} +(3.35009e6 + 1.03105e7i) q^{46} +(-3.45033e6 - 1.75803e6i) q^{47} +(-276128. - 1.74340e6i) q^{48} +5.23147e6i q^{49} +(4.85704e6 + 9.36947e6i) q^{50} +2.14275e6 q^{51} +(-1.38471e7 + 2.19317e6i) q^{52} +(4.17543e6 - 8.19475e6i) q^{53} +(2.62796e6 - 853876. i) q^{54} +(-1.27984e7 + 4.20814e6i) q^{55} +(-1.32870e6 + 4.08931e6i) q^{56} +(2.95271e6 - 2.95271e6i) q^{57} +(-1.32534e7 + 6.75295e6i) q^{58} +(-6.04263e6 - 8.31697e6i) q^{59} +(-9.82917e6 - 9.76049e6i) q^{60} +(1.21670e7 + 8.83982e6i) q^{61} +(5.63943e6 - 3.56060e7i) q^{62} +(-1.57748e6 - 249849. i) q^{63} +(-1.34213e7 + 1.84728e7i) q^{64} +(-1.30276e7 + 1.31193e7i) q^{65} +(2.20338e7 - 1.60085e7i) q^{66} +(6.21770e6 + 1.22029e7i) q^{67} +(1.53548e7 + 1.53548e7i) q^{68} +(-1.78470e7 - 5.79884e6i) q^{69} +(3.85174e6 + 1.17145e7i) q^{70} +(8.29281e6 + 2.55226e7i) q^{71} +(1.14730e7 + 5.84579e6i) q^{72} +(509130. + 3.21452e6i) q^{73} -1.61335e7i q^{74} +(-1.80624e7 - 2.73111e6i) q^{75} +4.23176e7 q^{76} +(-1.55484e7 + 2.46262e6i) q^{77} +(1.69683e7 - 3.33023e7i) q^{78} +(-2.66876e7 + 8.67131e6i) q^{79} +(-82714.3 - 2.35902e7i) q^{80} +(-1.47802e6 + 4.54887e6i) q^{81} +(4.01764e7 - 4.01764e7i) q^{82} +(7.42226e7 - 3.78183e7i) q^{83} +(-9.51370e6 - 1.30945e7i) q^{84} +(2.83000e7 + 4.38062e6i) q^{85} +(5.04990e7 + 3.66897e7i) q^{86} +(4.02777e6 - 2.54303e7i) q^{87} +(1.25353e8 + 1.98540e7i) q^{88} +(-5.17975e7 + 7.12931e7i) q^{89} +(3.64539e7 - 5.90483e6i) q^{90} +(-1.74777e7 + 1.26983e7i) q^{91} +(-8.63359e7 - 1.69444e8i) q^{92} +(4.41238e7 + 4.41238e7i) q^{93} +(9.95006e7 + 3.23297e7i) q^{94} +(4.50337e7 - 3.29608e7i) q^{95} +(-7.04514e6 - 2.16827e7i) q^{96} +(-2.10432e7 - 1.07221e7i) q^{97} +(-2.21104e7 - 1.39599e8i) q^{98} +4.71430e7i 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