LMFDB - Embedded newform 54.9.f.a.11.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,9,Mod(5,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("54.5");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	54.f (of order $18$, degree $6$, 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:	$21.9984449433$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.14
Character	$\chi$	$=$	54.11
Dual form			54.9.f.a.5.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.27231 - 8.66680i) q^{2} +(-76.9844 + 25.1872i) q^{3} +(-22.2270 - 126.055i) q^{4} +(421.201 - 1157.24i) q^{5} +(-341.562 + 850.378i) q^{6} +(-165.220 + 937.012i) q^{7} +(-1254.14 - 724.077i) q^{8} +(5292.21 - 3878.04i) q^{9} +O(q^{10})$	\(q+(7.27231 - 8.66680i) q^{2} +(-76.9844 + 25.1872i) q^{3} +(-22.2270 - 126.055i) q^{4} +(421.201 - 1157.24i) q^{5} +(-341.562 + 850.378i) q^{6} +(-165.220 + 937.012i) q^{7} +(-1254.14 - 724.077i) q^{8} +(5292.21 - 3878.04i) q^{9} +(-6966.47 - 12066.3i) q^{10} +(-1207.92 - 3318.74i) q^{11} +(4886.11 + 9144.47i) q^{12} +(24431.3 - 20500.3i) q^{13} +(6919.36 + 8246.17i) q^{14} +(-3278.29 + 99698.4i) q^{15} +(-15395.9 + 5603.66i) q^{16} +(-82073.6 + 47385.2i) q^{17} +(4876.35 - 74068.9i) q^{18} +(49779.7 - 86221.0i) q^{19} +(-155238. - 27372.7i) q^{20} +(-10881.3 - 76296.8i) q^{21} +(-37547.2 - 13666.1i) q^{22} +(-473461. + 83483.9i) q^{23} +(114787. + 24154.5i) q^{24} +(-862560. - 723774. i) q^{25} -360826. i q^{26} +(-309741. + 431845. i) q^{27} +121788. q^{28} +(-247907. + 295444. i) q^{29} +(840226. + 753450. i) q^{30} +(136171. + 772263. i) q^{31} +(-63398.2 + 174185. i) q^{32} +(176581. + 225067. i) q^{33} +(-186187. + 1.05592e6i) q^{34} +(1.01476e6 + 585870. i) q^{35} +(-606478. - 580915. i) q^{36} +(-949984. - 1.64542e6i) q^{37} +(-385247. - 1.05846e6i) q^{38} +(-1.36448e6 + 2.19356e6i) q^{39} +(-1.36618e6 + 1.14636e6i) q^{40} +(960268. + 1.14440e6i) q^{41} +(-740381. - 460548. i) q^{42} +(1.96272e6 - 714370. i) q^{43} +(-391496. + 226030. i) q^{44} +(-2.25875e6 - 7.75780e6i) q^{45} +(-2.71962e6 + 4.71051e6i) q^{46} +(-1.52516e6 - 268926. i) q^{47} +(1.04411e6 - 819175. i) q^{48} +(4.56645e6 + 1.66205e6i) q^{49} +(-1.25456e7 + 2.21213e6i) q^{50} +(5.12489e6 - 5.71513e6i) q^{51} +(-3.12720e6 - 2.62404e6i) q^{52} -5.10302e6i q^{53} +(1.49018e6 + 5.82497e6i) q^{54} -4.34936e6 q^{55} +(885678. - 1.05551e6i) q^{56} +(-1.66060e6 + 7.89148e6i) q^{57} +(757698. + 4.29712e6i) q^{58} +(-6.95884e6 + 1.91193e7i) q^{59} +(1.26404e7 - 1.80275e6i) q^{60} +(4.65089e6 - 2.63765e7i) q^{61} +(7.68333e6 + 4.43597e6i) q^{62} +(2.75939e6 + 5.59960e6i) q^{63} +(1.04858e6 + 1.81619e6i) q^{64} +(-1.34333e7 - 3.69076e7i) q^{65} +(3.23476e6 + 106366. i) q^{66} +(1.26817e7 - 1.06412e7i) q^{67} +(7.79741e6 + 9.29259e6i) q^{68} +(3.43464e7 - 1.83521e7i) q^{69} +(1.24573e7 - 4.53407e6i) q^{70} +(-1.46311e7 + 8.44725e6i) q^{71} +(-9.44517e6 + 1.03164e6i) q^{72} +(-1.24468e7 + 2.15584e7i) q^{73} +(-2.11691e7 - 3.73269e6i) q^{74} +(8.46335e7 + 3.39938e7i) q^{75} +(-1.19751e7 - 4.35857e6i) q^{76} +(3.30927e6 - 583513. i) q^{77} +(9.08818e6 + 2.77780e7i) q^{78} +(2.32815e7 + 1.95355e7i) q^{79} +2.01771e7i q^{80} +(1.29683e7 - 4.10469e7i) q^{81} +1.69017e7 q^{82} +(4.57835e7 - 5.45626e7i) q^{83} +(-9.37576e6 + 3.06749e6i) q^{84} +(2.02666e7 + 1.14938e8i) q^{85} +(8.08217e6 - 2.22056e7i) q^{86} +(1.16436e7 - 2.89887e7i) q^{87} +(-888121. + 5.03678e6i) q^{88} +(-3.94896e7 - 2.27993e7i) q^{89} +(-8.36616e7 - 3.68410e7i) q^{90} +(1.51725e7 + 2.62795e7i) q^{91} +(2.10472e7 + 5.78267e7i) q^{92} +(-2.99342e7 - 5.60225e7i) q^{93} +(-1.34222e7 + 1.12625e7i) q^{94} +(-7.88111e7 - 9.39235e7i) q^{95} +(493441. - 1.50064e7i) q^{96} +(-9.43260e7 + 3.43319e7i) q^{97} +(4.76133e7 - 2.74896e7i) q^{98} +(-1.92628e7 - 1.28791e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) $ 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9 - 45756 * q^11 - 21504 * q^12 + 94464 * q^14 - 70002 * q^15 - 182784 * q^18 - 225792 * q^20 - 2071668 * q^21 + 185472 * q^22 + 552996 * q^23 - 1015182 * q^25 - 4137588 * q^27 - 2856132 * q^29 - 861696 * q^30 - 1841490 * q^31 + 10547334 * q^33 - 661248 * q^34 - 12450834 * q^35 - 5104128 * q^36 + 14063616 * q^38 + 4239102 * q^39 - 15673536 * q^41 - 11028480 * q^42 - 4412520 * q^43 - 12558942 * q^45 + 15173838 * q^47 + 3440640 * q^48 - 11347488 * q^49 - 27744768 * q^50 - 3281850 * q^51 + 16379136 * q^54 + 12091392 * q^56 - 13553658 * q^57 - 86547168 * q^59 - 26125056 * q^60 - 34059456 * q^61 + 108329070 * q^63 + 150994944 * q^64 + 22190346 * q^65 + 152091648 * q^66 + 167100948 * q^67 + 13411584 * q^68 - 40190130 * q^69 - 118080000 * q^70 - 251437608 * q^71 - 60948480 * q^72 + 15265278 * q^73 + 41902848 * q^74 + 138868662 * q^75 + 67995648 * q^76 + 564911586 * q^77 + 201203712 * q^78 + 137535768 * q^79 - 23838948 * q^81 - 482857578 * q^83 - 128300544 * q^84 - 343215000 * q^85 - 46237824 * q^86 + 34353810 * q^87 + 47480832 * q^88 + 375969762 * q^89 + 452712960 * q^90 - 155093598 * q^91 + 97042176 * q^92 + 285095622 * q^93 - 70995456 * q^94 - 966996432 * q^95 - 88080384 * q^96 - 484917300 * q^97 - 234233856 * q^98 + 26756370 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	7.27231	−	8.66680i	0.454519	−	0.541675i
$2$	7.27231	−	8.66680i	0.454519	−	0.541675i
$3$	−76.9844	+	25.1872i	−0.950425	+	0.310953i
$3$	−76.9844	+	25.1872i	−0.950425	+	0.310953i
$4$	−22.2270	−	126.055i	−0.0868241	−	0.492404i
$5$	421.201	−	1157.24i	0.673922	−	1.85159i	0.175932	−	0.984402i	$-0.443706\pi$
$5$	421.201	−	1157.24i	0.673922	−	1.85159i	0.497990	−	0.867183i	$-0.334072\pi$
$6$	−341.562	+	850.378i	−0.263551	+	0.656156i
$7$	−165.220	+	937.012i	−0.0688132	+	0.390259i	0.930876	+	0.365335i	$0.119046\pi$
$7$	−165.220	+	937.012i	−0.0688132	+	0.390259i	−0.999689	+	0.0249241i	$0.992066\pi$
$8$	−1254.14	−	724.077i	−0.306186	−	0.176777i
$9$	5292.21	−	3878.04i	0.806616	−	0.591075i
$10$	−6966.47	−	12066.3i	−0.696647	−	1.20663i
$11$	−1207.92	−	3318.74i	−0.0825027	−	0.226674i	0.891581	−	0.452860i	$-0.149596\pi$
$11$	−1207.92	−	3318.74i	−0.0825027	−	0.226674i	−0.974084	+	0.226186i	$0.927374\pi$
$12$	4886.11	+	9144.47i	0.235634	+	0.440995i
$13$	24431.3	−	20500.3i	0.855407	−	0.717772i	−0.105566	−	0.994412i	$-0.533666\pi$
$13$	24431.3	−	20500.3i	0.855407	−	0.717772i	0.960973	+	0.276640i	$0.0892211\pi$
$14$	6919.36	+	8246.17i	0.180117	+	0.214655i
$15$	−3278.29	+	99698.4i	−0.0647564	+	1.96935i
$16$	−15395.9	+	5603.66i	−0.234923	+	0.0855050i
$17$	−82073.6	+	47385.2i	−0.982671	+	0.567345i	−0.903075	−	0.429482i	$-0.858696\pi$
$17$	−82073.6	+	47385.2i	−0.982671	+	0.567345i	−0.0795953	+	0.996827i	$0.525363\pi$
$18$	4876.35	−	74068.9i	0.0464521	−	0.705579i
$19$	49779.7	−	86221.0i	0.381978	−	0.661605i	−0.609367	−	0.792888i	$-0.708576\pi$
$19$	49779.7	−	86221.0i	0.381978	−	0.661605i	0.991345	+	0.131284i	$0.0419098\pi$
$20$	−155238.	−	27372.7i	−0.970240	−	0.171080i
$21$	−10881.3	−	76296.8i	−0.0559504	−	0.392310i
$22$	−37547.2	−	13666.1i	−0.160283	−	0.0583382i
$23$	−473461.	+	83483.9i	−1.69189	+	0.298326i	−0.934851	−	0.355041i	$-0.884467\pi$
$23$	−473461.	+	83483.9i	−1.69189	+	0.298326i	−0.757041	+	0.653367i	$0.773356\pi$
$24$	114787.	+	24154.5i	0.345976	+	0.0728035i
$25$	−862560.	−	723774.i	−2.20815	−	1.85286i
$26$		−	360826.i		−	0.789594i
$27$	−309741.	+	431845.i	−0.582832	+	0.812593i
$28$	121788.			0.198140
$29$	−247907.	+	295444.i	−0.350507	+	0.417718i	−0.912276	−	0.409576i	$-0.865677\pi$
$29$	−247907.	+	295444.i	−0.350507	+	0.417718i	0.561769	+	0.827294i	$0.310121\pi$
$30$	840226.	+	753450.i	1.03732	+	0.930186i
$31$	136171.	+	772263.i	0.147447	+	0.836216i	0.965369	+	0.260887i	$0.0840150\pi$
$31$	136171.	+	772263.i	0.147447	+	0.836216i	−0.817922	+	0.575329i	$0.804874\pi$
$32$	−63398.2	+	174185.i	−0.0604612	+	0.166116i
$33$	176581.	+	225067.i	0.148898	+	0.189782i
$34$	−186187.	+	1.05592e6i	−0.139326	+	0.790158i
$35$	1.01476e6	+	585870.i	0.676223	+	0.390418i
$36$	−606478.	−	580915.i	−0.361081	−	0.345861i
$37$	−949984.	−	1.64542e6i	−0.506885	−	0.877950i	−0.999968	−	0.00796821i	$-0.997464\pi$
$37$	−949984.	−	1.64542e6i	−0.506885	−	0.877950i	0.493083	−	0.869982i	$-0.335870\pi$
$38$	−385247.	−	1.05846e6i	−0.184759	−	0.507620i
$39$	−1.36448e6	+	2.19356e6i	−0.589807	+	0.948180i
$40$	−1.36618e6	+	1.14636e6i	−0.533663	+	0.447796i
$41$	960268.	+	1.14440e6i	0.339826	+	0.404989i	0.908709	−	0.417429i	$-0.137069\pi$
$41$	960268.	+	1.14440e6i	0.339826	+	0.404989i	−0.568883	+	0.822418i	$0.692624\pi$
$42$	−740381.	−	460548.i	−0.237935	−	0.148005i
$43$	1.96272e6	−	714370.i	0.574095	−	0.208953i	−0.0386249	−	0.999254i	$-0.512298\pi$
$43$	1.96272e6	−	714370.i	0.574095	−	0.208953i	0.612720	+	0.790300i	$0.290076\pi$
$44$	−391496.	+	226030.i	−0.104452	+	0.0603054i
$45$	−2.25875e6	−	7.75780e6i	−0.550830	−	1.89186i
$46$	−2.71962e6	+	4.71051e6i	−0.607402	+	1.05205i
$47$	−1.52516e6	−	268926.i	−0.312553	−	0.0551115i	0.0151715	−	0.999885i	$-0.495171\pi$
$47$	−1.52516e6	−	268926.i	−0.312553	−	0.0551115i	−0.327724	+	0.944773i	$0.606282\pi$
$48$	1.04411e6	−	819175.i	0.196689	−	0.154316i
$49$	4.56645e6	+	1.66205e6i	0.792126	+	0.288310i
$50$	−1.25456e7	+	2.21213e6i	−2.00730	+	0.353941i
$51$	5.12489e6	−	5.71513e6i	0.757537	−	0.844784i
$52$	−3.12720e6	−	2.62404e6i	−0.427704	−	0.358886i
$53$		−	5.10302e6i		−	0.646732i	−0.946274	−	0.323366i	$-0.895186\pi$
$53$		−	5.10302e6i		−	0.646732i	0.946274	−	0.323366i	$-0.104814\pi$
$54$	1.49018e6	+	5.82497e6i	0.175253	+	0.685045i
$55$	−4.34936e6			−0.475307
$56$	885678.	−	1.05551e6i	0.0900583	−	0.107327i
$57$	−1.66060e6	+	7.89148e6i	−0.157313	+	0.747583i
$58$	757698.	+	4.29712e6i	0.0669552	+	0.379722i
$59$	−6.95884e6	+	1.91193e7i	−0.574287	+	1.57784i	0.223373	+	0.974733i	$0.428293\pi$
$59$	−6.95884e6	+	1.91193e7i	−0.574287	+	1.57784i	−0.797660	+	0.603108i	$0.793929\pi$
$60$	1.26404e7	−	1.80275e6i	0.975339	−	0.139101i
$61$	4.65089e6	−	2.63765e7i	0.335905	−	1.90501i	−0.0822014	−	0.996616i	$-0.526195\pi$
$61$	4.65089e6	−	2.63765e7i	0.335905	−	1.90501i	0.418107	−	0.908398i	$-0.362694\pi$
$62$	7.68333e6	+	4.43597e6i	0.519975	+	0.300208i
$63$	2.75939e6	+	5.59960e6i	0.175167	+	0.355463i
$64$	1.04858e6	+	1.81619e6i	0.0625000	+	0.108253i
$65$	−1.34333e7	−	3.69076e7i	−0.752538	−	2.06758i
$66$	3.23476e6	+	106366.i	0.170477	+	0.00560565i
$67$	1.26817e7	−	1.06412e7i	0.629327	−	0.528068i	−0.271392	−	0.962469i	$-0.587484\pi$
$67$	1.26817e7	−	1.06412e7i	0.629327	−	0.528068i	0.900720	+	0.434400i	$0.143040\pi$
$68$	7.79741e6	+	9.29259e6i	0.364682	+	0.434612i
$69$	3.43464e7	−	1.83521e7i	1.51525	−	0.809636i
$70$	1.24573e7	−	4.53407e6i	0.518836	−	0.188841i
$71$	−1.46311e7	+	8.44725e6i	−0.575762	+	0.332416i	−0.759447	−	0.650569i	$-0.774531\pi$
$71$	−1.46311e7	+	8.44725e6i	−0.575762	+	0.332416i	0.183686	+	0.982985i	$0.441197\pi$
$72$	−9.44517e6	+	1.03164e6i	−0.351463	+	0.0383881i
$73$	−1.24468e7	+	2.15584e7i	−0.438293	+	0.759146i	−0.997558	−	0.0698430i	$-0.977750\pi$
$73$	−1.24468e7	+	2.15584e7i	−0.438293	+	0.759146i	0.559265	+	0.828989i	$0.311084\pi$
$74$	−2.11691e7	−	3.73269e6i	−0.705953	−	0.124479i
$75$	8.46335e7	+	3.39938e7i	2.67484	+	1.07437i
$76$	−1.19751e7	−	4.35857e6i	−0.358941	−	0.130644i
$77$	3.30927e6	−	583513.i	0.0941389	−	0.0165992i
$78$	9.08818e6	+	2.77780e7i	0.245527	+	0.750450i
$79$	2.32815e7	+	1.95355e7i	0.597726	+	0.501551i	0.890714	−	0.454565i	$-0.150205\pi$
$79$	2.32815e7	+	1.95355e7i	0.597726	+	0.501551i	−0.292988	+	0.956116i	$0.594650\pi$
$80$			2.01771e7i			0.492604i
$81$	1.29683e7	−	4.10469e7i	0.301260	−	0.953542i
$82$	1.69017e7			0.373830
$83$	4.57835e7	−	5.45626e7i	0.964709	−	1.14970i	−0.0239796	−	0.999712i	$-0.507634\pi$
$83$	4.57835e7	−	5.45626e7i	0.964709	−	1.14970i	0.988689	−	0.149983i	$-0.0479219\pi$
$84$	−9.37576e6	+	3.06749e6i	−0.188317	+	0.0616121i
$85$	2.02666e7	+	1.14938e8i	0.388245	+	2.20184i
$86$	8.08217e6	−	2.22056e7i	0.147752	−	0.405946i
$87$	1.16436e7	−	2.89887e7i	0.203240	−	0.506001i
$88$	−888121.	+	5.03678e6i	−0.0148095	+	0.0839891i
$89$	−3.94896e7	−	2.27993e7i	−0.629394	−	0.363381i	0.151123	−	0.988515i	$-0.451711\pi$
$89$	−3.94896e7	−	2.27993e7i	−0.629394	−	0.363381i	−0.780517	+	0.625134i	$0.785044\pi$
$90$	−8.36616e7	−	3.68410e7i	−1.27514	−	0.561515i
$91$	1.51725e7	+	2.62795e7i	0.221254	+	0.383222i
$92$	2.10472e7	+	5.78267e7i	0.293794	+	0.807192i
$93$	−2.99342e7	−	5.60225e7i	−0.400162	−	0.748912i
$94$	−1.34222e7	+	1.12625e7i	−0.171914	+	0.144253i
$95$	−7.88111e7	−	9.39235e7i	−0.967594	−	1.15313i
$96$	493441.	−	1.50064e7i	0.00580965	−	0.176681i
$97$	−9.43260e7	+	3.43319e7i	−1.06548	+	0.387802i	−0.814484	−	0.580186i	$-0.802980\pi$
$97$	−9.43260e7	+	3.43319e7i	−1.06548	+	0.387802i	−0.250994	+	0.967989i	$0.580757\pi$
$98$	4.76133e7	−	2.74896e7i	0.516207	−	0.298032i
$99$	−1.92628e7	−	1.28791e7i	−0.200529	−	0.134074i
$100$	−7.20635e7	+	1.24818e8i	−0.720635	+	1.24818i
$101$	−3.39731e6	−	599038.i	−0.0326475	−	0.00575664i	0.157301	−	0.987551i	$-0.449721\pi$
$101$	−3.39731e6	−	599038.i	−0.0326475	−	0.00575664i	−0.189948	+	0.981794i	$0.560832\pi$
$102$	−1.22621e7	−	8.59786e7i	−0.113283	−	0.794310i
$103$	−7.09292e7	−	2.58161e7i	−0.630197	−	0.229373i	0.00712010	−	0.999975i	$-0.497734\pi$
$103$	−7.09292e7	−	2.58161e7i	−0.630197	−	0.229373i	−0.637317	+	0.770602i	$0.719956\pi$
$104$	−4.54840e7	+	8.02006e6i	−0.388799	+	0.0685558i
$105$	−9.28769e7	−	1.95440e7i	−0.764101	−	0.160789i
$106$	−4.42269e7	−	3.71108e7i	−0.350318	−	0.293952i
$107$		−	1.79453e8i		−	1.36904i	−0.728995	−	0.684519i	$-0.760012\pi$
$107$		−	1.79453e8i		−	1.36904i	0.728995	−	0.684519i	$-0.239988\pi$
$108$	6.13210e7	+	2.94459e7i	0.450728	+	0.216436i
$109$	6.18096e7			0.437875			0.218937	−	0.975739i	$-0.429741\pi$
$109$	6.18096e7			0.437875			0.218937	+	0.975739i	$0.429741\pi$
$110$	−3.16299e7	+	3.76950e7i	−0.216036	+	0.257462i
$111$	1.14577e8	+	1.02744e8i	0.754757	+	0.676809i
$112$	−2.70697e6	−	1.53520e7i	−0.0172033	−	0.0975647i
$113$	−3.53882e6	+	9.72284e6i	−0.0217043	+	0.0596320i	−0.950072	−	0.312032i	$-0.898990\pi$
$113$	−3.53882e6	+	9.72284e6i	−0.0217043	+	0.0596320i	0.928367	+	0.371664i	$0.121213\pi$
$114$	5.63176e7	+	7.17814e7i	0.333445	+	0.425004i
$115$	−1.02811e8	+	5.83072e8i	−0.587827	+	3.33373i
$116$	4.27525e7	+	2.46832e7i	0.236118	+	0.136323i
$117$	4.97945e7	−	2.03237e8i	0.265728	−	1.08458i
$118$	1.15096e8	+	1.99352e8i	0.593653	+	1.02824i
$119$	−3.08403e7	−	8.47330e7i	−0.153791	−	0.422537i
$120$	7.63008e7	−	1.22662e8i	0.367963	−	0.591541i
$121$	1.54653e8	−	1.29770e8i	0.721470	−	0.605385i
$122$	−1.94777e8	−	2.32127e8i	−0.879223	−	1.04782i
$123$	−1.02750e8	−	6.39147e7i	−0.448912	−	0.279242i
$124$	9.43213e7	−	3.43301e7i	0.398954	−	0.145207i
$125$	−7.84283e8	+	4.52806e8i	−3.21242	+	1.85469i
$126$	6.85977e7	+	1.68069e7i	0.272162	+	0.0666815i
$127$	1.99891e8	−	3.46221e8i	0.768384	−	1.33088i	−0.170054	−	0.985435i	$-0.554394\pi$
$127$	1.99891e8	−	3.46221e8i	0.768384	−	1.33088i	0.938439	−	0.345446i	$-0.112272\pi$
$128$	2.33661e7	+	4.12008e6i	0.0870455	+	0.0153485i
$129$	−1.33106e8	+	1.04431e8i	−0.480659	+	0.377111i
$130$	−4.17562e8	−	1.51980e8i	−1.46200	−	0.532125i
$131$	7.98943e7	−	1.40875e7i	0.271288	−	0.0478354i	−0.0363491	−	0.999339i	$-0.511573\pi$
$131$	7.98943e7	−	1.40875e7i	0.271288	−	0.0478354i	0.307637	+	0.951504i	$0.400462\pi$
$132$	2.44460e7	−	2.72615e7i	0.0805217	−	0.0897955i
$133$	7.25654e7	+	6.08896e7i	0.231912	+	0.194597i
$134$		−	1.87295e8i		−	0.580908i
$135$	3.69285e8	+	5.40338e8i	1.11180	+	1.62679i
$136$	1.37242e8			0.401174
$137$	3.95495e7	−	4.71333e7i	0.112269	−	0.133797i	−0.706983	−	0.707230i	$-0.749944\pi$
$137$	3.95495e7	−	4.71333e7i	0.112269	−	0.133797i	0.819252	+	0.573433i	$0.194389\pi$
$138$	9.07235e7	−	4.31136e8i	0.250152	−	1.18877i
$139$	−6.66192e7	−	3.77816e8i	−0.178460	−	1.01210i	−0.934074	−	0.357079i	$-0.883773\pi$
$139$	−6.66192e7	−	3.77816e8i	−0.178460	−	1.01210i	0.755614	−	0.655017i	$-0.227338\pi$
$140$	5.12971e7	−	1.40938e8i	0.133531	−	0.366872i
$141$	1.24187e8	−	1.77113e7i	0.314195	−	0.0448099i
$142$	−3.31910e7	+	1.88236e8i	−0.0816333	+	0.462965i
$143$	−9.75461e7	−	5.63183e7i	−0.233274	−	0.134681i
$144$	−5.97472e7	+	8.93618e7i	−0.138953	+	0.207827i
$145$	2.37481e8	+	4.11329e8i	0.537226	+	0.930503i
$146$	9.63258e7	+	2.64653e8i	0.211998	+	0.582459i
$147$	−3.93408e8	−	1.29361e7i	−0.842507	−	0.0277034i
$148$	−1.86299e8	+	1.56323e8i	−0.388296	+	0.325819i
$149$	7.29640e7	+	8.69552e7i	0.148035	+	0.176421i	0.834966	−	0.550301i	$-0.185487\pi$
$149$	7.29640e7	+	8.69552e7i	0.148035	+	0.176421i	−0.686931	+	0.726722i	$0.741043\pi$
$150$	9.10099e8	−	4.86288e8i	1.79773	−	0.960569i
$151$	−3.83564e8	+	1.39606e8i	−0.737785	+	0.268532i	−0.683456	−	0.729991i	$-0.739524\pi$
$151$	−3.83564e8	+	1.39606e8i	−0.737785	+	0.268532i	−0.0543287	+	0.998523i	$0.517302\pi$
$152$	−1.24861e8	+	7.20887e7i	−0.233913	+	0.135049i
$153$	−2.50589e8	+	5.69058e8i	−0.457295	+	1.03846i
$154$	1.90088e7	−	3.29243e7i	0.0337966	−	0.0585374i
$155$	9.51050e8	+	1.67696e8i	1.64769	+	0.290533i
$156$	3.06838e8	+	1.23244e8i	0.518097	+	0.208099i
$157$	6.65225e8	+	2.42122e8i	1.09489	+	0.398507i	0.825430	−	0.564505i	$-0.190933\pi$
$157$	6.65225e8	+	2.42122e8i	1.09489	+	0.398507i	0.269459	+	0.963012i	$0.413155\pi$
$158$	3.38620e8	−	5.97078e7i	0.543356	−	0.0958083i
$159$	1.28531e8	+	3.92853e8i	0.201103	+	0.614670i
$160$	1.74871e8	+	1.46734e8i	0.266831	+	0.223898i
$161$		−	4.57431e8i		−	0.680805i
$162$	−2.61436e8	−	4.10899e8i	−0.379581	−	0.596589i
$163$	−4.84478e8			−0.686315			−0.343158	−	0.939278i	$-0.611497\pi$
$163$	−4.84478e8			−0.686315			−0.343158	+	0.939278i	$0.611497\pi$
$164$	1.22914e8	−	1.46484e8i	0.169913	−	0.202495i
$165$	3.34833e8	−	1.09548e8i	0.451744	−	0.147798i
$166$	−1.39932e8	−	7.93593e8i	−0.184282	−	1.04512i
$167$	5.92088e7	−	1.62675e8i	0.0761238	−	0.209149i	−0.895794	−	0.444470i	$-0.853392\pi$
$167$	5.92088e7	−	1.62675e8i	0.0761238	−	0.209149i	0.971918	+	0.235321i	$0.0756143\pi$
$168$	−4.15981e7	+	1.03566e8i	−0.0522200	+	0.130011i
$169$	3.49759e7	−	1.98358e8i	0.0428768	−	0.243167i
$170$	1.14353e9	+	6.60216e8i	1.36915	+	0.790479i
$171$	−7.09241e7	−	6.49347e8i	−0.0829487	−	0.759439i
$172$	−1.33675e8	−	2.31533e8i	−0.152735	−	0.264544i
$173$	−3.28091e8	−	9.01421e8i	−0.366277	−	1.00634i	−0.976765	−	0.214312i	$-0.931249\pi$
$173$	−3.28091e8	−	9.01421e8i	−0.366277	−	1.00634i	0.610489	−	0.792025i	$-0.290973\pi$
$174$	−1.66563e8	−	3.11727e8i	−0.181712	−	0.340077i
$175$	8.20697e8	−	6.88646e8i	0.875045	−	0.734250i
$176$	3.71941e7	+	4.43262e7i	0.0387636	+	0.0461966i
$177$	5.41621e7	−	1.64716e9i	0.0551826	−	1.67820i
$178$	−4.84778e8	+	1.76445e8i	−0.482906	+	0.175764i
$179$	−6.72733e8	+	3.88402e8i	−0.655285	+	0.378329i	−0.790478	−	0.612490i	$-0.790168\pi$
$179$	−6.72733e8	+	3.88402e8i	−0.655285	+	0.378329i	0.135193	+	0.990819i	$0.456835\pi$
$180$	−9.27707e8	+	4.57159e8i	−0.883733	+	0.435489i
$181$	1.61363e8	−	2.79489e8i	0.150345	−	0.260406i	−0.781009	−	0.624520i	$-0.785295\pi$
$181$	1.61363e8	−	2.79489e8i	0.150345	−	0.260406i	0.931354	+	0.364114i	$0.118628\pi$
$182$	3.38098e8	+	5.96158e7i	0.308146	+	0.0543345i
$183$	3.06304e8	+	2.14772e9i	0.273117	+	1.91502i
$184$	6.54234e8	+	2.38122e8i	0.570771	+	0.207744i
$185$	−2.30428e9	+	4.06307e8i	−1.96720	+	0.346871i
$186$	−7.03227e8	−	1.47979e8i	−0.587548	−	0.123637i
$187$	2.56398e8	+	2.15143e8i	0.209675	+	0.175939i
$188$			1.98232e8i			0.158687i
$189$	−3.53468e8	−	3.61580e8i	−0.277015	−	0.283372i
$190$	−1.38716e9			−1.06441
$191$	3.16468e8	−	3.77152e8i	0.237791	−	0.283389i	−0.633930	−	0.773390i	$-0.718559\pi$
$191$	3.16468e8	−	3.77152e8i	0.237791	−	0.283389i	0.871722	+	0.490001i	$0.163004\pi$
$192$	−1.26469e8	−	1.13407e8i	−0.0930632	−	0.0834520i
$193$	−3.01249e8	−	1.70847e9i	−0.217118	−	1.23134i	−0.877193	−	0.480138i	$-0.840587\pi$
$193$	−3.01249e8	−	1.70847e9i	−0.217118	−	1.23134i	0.660075	−	0.751200i	$-0.270524\pi$
$194$	−3.88421e8	+	1.06718e9i	−0.274218	+	0.753407i
$195$	1.96375e9	+	2.50297e9i	1.35815	+	1.73108i
$196$	1.08012e8	−	6.12568e8i	0.0731895	−	0.415078i
$197$	2.13969e9	+	1.23535e9i	1.42065	+	0.820210i	0.996354	−	0.0853152i	$-0.0271897\pi$
$197$	2.13969e9	+	1.23535e9i	1.42065	+	0.820210i	0.424292	+	0.905525i	$0.360523\pi$
$198$	−2.51705e8	+	7.32861e7i	−0.163769	+	0.0476827i
$199$	−6.53271e8	−	1.13150e9i	−0.416564	−	0.721509i	0.579028	−	0.815308i	$-0.303432\pi$
$199$	−6.53271e8	−	1.13150e9i	−0.416564	−	0.721509i	−0.995591	+	0.0937986i	$0.970099\pi$
$200$	5.57702e8	+	1.53227e9i	0.348563	+	0.957670i
$201$	−7.08269e8	+	1.13862e9i	−0.433924	+	0.697581i
$202$	−2.98981e7	+	2.50875e7i	−0.0179572	+	0.0150679i
$203$	−2.35875e8	−	2.81105e8i	−0.138899	−	0.165533i
$204$	−8.34334e8	−	5.18990e8i	−0.481747	−	0.299667i
$205$	1.72882e9	−	6.29237e8i	0.978888	−	0.356286i
$206$	−7.39563e8	+	4.26987e8i	−0.410682	+	0.237108i
$207$	−2.18190e9	+	2.27792e9i	−1.18837	+	1.24067i
$208$	−2.61266e8	+	4.52525e8i	−0.139582	+	0.241763i
$209$	−3.46275e8	−	6.10576e7i	−0.181483	−	0.0320003i
$210$	−8.44814e8	+	6.62816e8i	−0.434394	+	0.340813i
$211$	8.31902e8	+	3.02788e8i	0.419703	+	0.152759i	0.543234	−	0.839581i	$-0.317200\pi$
$211$	8.31902e8	+	3.02788e8i	0.419703	+	0.152759i	−0.123531	+	0.992341i	$0.539422\pi$
$212$	−6.43264e8	+	1.13425e8i	−0.318453	+	0.0561519i
$213$	9.13602e8	−	1.01882e9i	0.443853	−	0.494972i
$214$	−1.55528e9	−	1.30504e9i	−0.741574	−	0.622254i
$215$		−	2.57223e9i		−	1.20380i
$216$	7.01147e8	−	3.17317e8i	0.322103	−	0.145774i
$217$	−7.46118e8			−0.336487
$218$	4.49499e8	−	5.35692e8i	0.199023	−	0.237186i
$219$	4.15211e8	−	1.97316e9i	0.180506	−	0.857800i
$220$	9.66730e7	+	5.48260e8i	0.0412681	+	0.234043i
$221$	−1.03375e9	+	2.84021e9i	−0.433359	+	1.19064i
$222$	1.72371e9	−	2.45832e8i	0.709662	−	0.101211i
$223$	3.88912e8	−	2.20563e9i	0.157265	−	0.891894i	−0.799421	−	0.600772i	$-0.794860\pi$
$223$	3.88912e8	−	2.20563e9i	0.157265	−	0.891894i	0.956686	−	0.291123i	$-0.0940288\pi$
$224$	−1.52739e8	−	8.81837e7i	−0.0606676	−	0.0350265i
$225$	−7.37167e9	−	4.85317e8i	−2.87631	−	0.189363i
$226$	5.85305e7	+	1.01378e8i	0.0224362	+	0.0388606i
$227$	−6.21376e8	−	1.70722e9i	−0.234019	−	0.642962i	−1.00000		9.88992e-5i	$-0.999969\pi$
$227$	−6.21376e8	−	1.70722e9i	−0.234019	−	0.642962i	0.765981	−	0.642863i	$-0.222254\pi$
$228$	1.03167e9	+	3.39236e7i	0.381771	+	0.0125534i
$229$	1.50266e9	−	1.26088e9i	0.546409	−	0.458492i	−0.327314	−	0.944916i	$-0.606143\pi$
$229$	1.50266e9	−	1.26088e9i	0.546409	−	0.458492i	0.873723	+	0.486424i	$0.161699\pi$
$230$	4.30569e9	+	5.13132e9i	1.53862	+	1.83366i
$231$	−2.40065e8	+	1.28273e8i	−0.0843104	+	0.0450491i
$232$	5.24834e8	−	1.91024e8i	0.181163	−	0.0659380i
$233$	−2.05787e9	+	1.18811e9i	−0.698225	+	0.403120i	−0.806686	−	0.590981i	$-0.798741\pi$
$233$	−2.05787e9	+	1.18811e9i	−0.698225	+	0.403120i	0.108461	+	0.994101i	$0.465408\pi$
$234$	−1.39930e9	−	1.90956e9i	−0.466710	−	0.636900i
$235$	−9.53611e8	+	1.65170e9i	−0.312680	+	0.541577i
$236$	2.56476e9	+	4.52236e8i	0.826797	+	0.145787i
$237$	−2.28435e9	−	9.17532e8i	−0.724052	−	0.290822i
$238$	−9.58644e8	−	3.48918e8i	−0.298779	−	0.108747i
$239$	4.41718e9	−	7.78868e8i	1.35380	−	0.238711i	0.550772	−	0.834656i	$-0.314333\pi$
$239$	4.41718e9	−	7.78868e8i	1.35380	−	0.238711i	0.803026	+	0.595945i	$0.203222\pi$
$240$	−5.08204e8	−	1.55332e9i	−0.153177	−	0.468183i
$241$	3.17744e9	+	2.66619e9i	0.941910	+	0.790356i	0.977917	−	0.208995i	$-0.0670193\pi$
$241$	3.17744e9	+	2.66619e9i	0.941910	+	0.790356i	−0.0360066	+	0.999352i	$0.511464\pi$
$242$		−	2.28408e9i		−	0.665962i
$243$	3.55006e7	+	3.48660e9i	0.0101815	+	0.999948i
$244$	−3.42828e9			−0.967201
$245$	3.84679e9	−	4.58442e9i	1.06766	−	1.27239i
$246$	−1.30117e9	+	4.25706e8i	−0.355298	+	0.116244i
$247$	−5.51372e8	−	3.12699e9i	−0.148135	−	0.840114i
$248$	3.88401e8	−	1.06712e9i	0.102677	−	0.282103i
$249$	−2.15034e9	+	5.35363e9i	−0.559383	+	1.39268i
$250$	−1.77917e9	+	1.00902e10i	−0.455467	+	2.58308i
$251$	2.08090e9	+	1.20141e9i	0.524271	+	0.302688i	0.738681	−	0.674056i	$-0.235449\pi$
$251$	2.08090e9	+	1.20141e9i	0.524271	+	0.302688i	−0.214409	+	0.976744i	$0.568783\pi$
$252$	6.44526e8	−	4.72298e8i	0.159823	−	0.117115i
$253$	8.48964e8	+	1.47045e9i	0.207208	+	0.358895i
$254$	−1.54696e9	−	4.25025e9i	−0.371659	−	1.02113i
$255$	−4.45517e9	−	8.33795e9i	−1.05367	−	1.97196i
$256$	2.05633e8	−	1.72547e8i	0.0478778	−	0.0401742i
$257$	−4.22701e8	−	5.03756e8i	−0.0968949	−	0.115475i	0.715418	−	0.698697i	$-0.246236\pi$
$257$	−4.22701e8	−	5.03756e8i	−0.0968949	−	0.115475i	−0.812313	+	0.583222i	$0.801792\pi$
$258$	−6.29052e7	+	1.91305e9i	−0.0141974	+	0.431766i
$259$	1.69873e9	−	6.18289e8i	0.377508	−	0.137402i
$260$	−4.35382e9	+	2.51368e9i	−0.952747	+	0.550069i
$261$	−1.66231e8	+	2.52495e9i	−0.0358220	+	0.544114i
$262$	4.58923e8	−	7.94877e8i	0.0973945	−	0.168692i
$263$	8.20972e9	+	1.44759e9i	1.71595	+	0.302569i	0.943221	−	0.332165i	$-0.107779\pi$
$263$	8.20972e9	+	1.44759e9i	1.71595	+	0.302569i	0.772731	+	0.634734i	$0.218890\pi$
$264$	−5.84910e7	−	4.10123e8i	−0.0120413	−	0.0844304i
$265$	−5.90543e9	−	2.14940e9i	−1.19748	−	0.435847i
$266$	1.05544e9	−	1.86102e8i	0.210817	−	0.0371727i
$267$	3.61434e9	+	7.60562e8i	0.711186	+	0.149654i
$268$	−1.62325e9	−	1.36207e9i	−0.314664	−	0.264034i
$269$		−	9.43068e9i		−	1.80108i	−0.434769	−	0.900542i	$-0.643170\pi$
$269$		−	9.43068e9i		−	1.80108i	0.434769	−	0.900542i	$-0.356830\pi$
$270$	7.36857e9	+	7.28984e8i	1.38653	+	0.137171i
$271$	2.28976e9			0.424535			0.212267	−	0.977212i	$-0.431915\pi$
$271$	2.28976e9			0.424535			0.212267	+	0.977212i	$0.431915\pi$
$272$	9.98069e8	−	1.18945e9i	0.182341	−	0.217306i
$273$	−1.82995e9	−	1.64096e9i	−0.329449	−	0.295425i
$274$	−1.20878e8	−	6.85536e8i	−0.0214460	−	0.121626i
$275$	−1.36011e9	+	3.73687e9i	−0.237817	+	0.653397i
$276$	−3.07680e9	−	3.92164e9i	−0.530228	−	0.675820i
$277$	1.42645e9	−	8.08979e9i	0.242291	−	1.37410i	−0.584411	−	0.811458i	$-0.698674\pi$
$277$	1.42645e9	−	8.08979e9i	0.242291	−	1.37410i	0.826701	−	0.562641i	$-0.190215\pi$
$278$	−3.75894e9	−	2.17022e9i	−0.629340	−	0.363350i
$279$	3.71552e9	+	3.55890e9i	0.613200	+	0.587353i
$280$	−8.48431e8	−	1.46953e9i	−0.138033	−	0.239081i
$281$	3.20271e9	+	8.79938e9i	0.513680	+	1.41132i	0.877375	+	0.479806i	$0.159293\pi$
$281$	3.20271e9	+	8.79938e9i	0.513680	+	1.41132i	−0.363695	+	0.931518i	$0.618485\pi$
$282$	7.49626e8	−	1.20511e9i	0.118535	−	0.190559i
$283$	4.37675e9	−	3.67253e9i	0.682348	−	0.572558i	−0.234343	−	0.972154i	$-0.575294\pi$
$283$	4.37675e9	−	3.67253e9i	0.682348	−	0.572558i	0.916692	+	0.399596i	$0.130849\pi$
$284$	1.39003e9	+	1.65657e9i	0.213673	+	0.254646i
$285$	8.43290e9	+	5.24561e9i	1.27820	+	0.795091i
$286$	−1.19749e9	+	4.35849e8i	−0.178981	+	0.0651436i
$287$	−1.23097e9	+	7.10703e8i	−0.181435	+	0.104752i
$288$	3.39981e8	+	1.16768e9i	0.0494179	+	0.169729i
$289$	1.00284e9	−	1.73697e9i	0.143761	−	0.249001i
$290$	5.29195e9	+	9.33113e8i	0.748210	+	0.131930i
$291$	6.39691e9	−	5.01883e9i	0.892069	−	0.699891i
$292$	2.99421e9	+	1.08980e9i	0.411861	+	0.149905i
$293$	−3.15156e9	+	5.55704e8i	−0.427617	+	0.0754003i	−0.383315	−	0.923618i	$-0.625217\pi$
$293$	−3.15156e9	+	5.55704e8i	−0.427617	+	0.0754003i	−0.0443020	+	0.999018i	$0.514106\pi$
$294$	−2.97310e9	+	3.31551e9i	−0.397942	+	0.443774i
$295$	1.91945e10	+	1.61061e10i	2.53448	+	2.12668i
$296$			2.75145e9i			0.358422i
$297$	1.80732e9	+	5.06313e8i	0.232279	+	0.0650719i
$298$	1.28424e9			0.162848
$299$	−9.85581e9	+	1.17457e10i	−1.23313	+	1.46958i
$300$	2.40396e9	−	1.14241e10i	0.296785	−	1.41038i
$301$	3.45092e8	+	1.95712e9i	0.0420406	+	0.238424i
$302$	−1.57946e9	+	4.33953e9i	−0.189881	+	0.521693i
$303$	2.76628e8	−	3.94522e7i	0.0328191	−	0.00468059i
$304$	−2.83252e8	+	1.60640e9i	−0.0331649	+	0.188087i
$305$	−2.85650e10	−	1.64920e10i	−3.30092	−	1.90579i
$306$	3.10955e9	+	6.31017e9i	0.354660	+	0.719706i
$307$	−1.82399e9	−	3.15925e9i	−0.205338	−	0.355656i	0.744902	−	0.667174i	$-0.232496\pi$
$307$	−1.82399e9	−	3.15925e9i	−0.205338	−	0.355656i	−0.950240	+	0.311517i	$0.899163\pi$
$308$	−1.47110e8	−	4.04181e8i	−0.0163470	−	0.0449131i
$309$	6.11068e9	+	2.00932e8i	0.670279	+	0.0220402i
$310$	8.36972e9	−	7.02303e9i	0.906283	−	0.760462i
$311$	7.11794e8	+	8.48283e8i	0.0760874	+	0.0906774i	0.802745	−	0.596322i	$-0.203372\pi$
$311$	7.11794e8	+	8.48283e8i	0.0760874	+	0.0906774i	−0.726658	+	0.687000i	$0.758927\pi$
$312$	3.29956e9	−	1.76303e9i	0.348207	−	0.186055i
$313$	−1.06323e10	+	3.86986e9i	−1.10778	+	0.403197i	−0.830177	−	0.557500i	$-0.811761\pi$
$313$	−1.06323e10	+	3.86986e9i	−1.10778	+	0.403197i	−0.277599	+	0.960697i	$0.589539\pi$
$314$	6.93615e9	−	4.00459e9i	0.713510	−	0.411945i
$315$	7.64234e9	−	8.34724e8i	0.776219	−	0.0847814i
$316$	1.94507e9	−	3.36897e9i	0.195069	−	0.337869i
$317$	−6.55985e9	−	1.15668e9i	−0.649616	−	0.114545i	−0.160877	−	0.986975i	$-0.551432\pi$
$317$	−6.55985e9	−	1.15668e9i	−0.649616	−	0.114545i	−0.488740	+	0.872430i	$0.662543\pi$
$318$	4.33950e9	+	1.74300e9i	0.424357	+	0.170447i
$319$	1.27995e9	+	4.65865e8i	0.123604	+	0.0449880i
$320$	2.54343e9	−	4.48475e8i	0.242560	−	0.0427699i
$321$	4.51992e9	+	1.38151e10i	0.425707	+	1.30117i
$322$	−3.96447e9	−	3.32658e9i	−0.368775	−	0.309439i
$323$			9.43529e9i			0.866852i
$324$	−5.46242e9	−	7.22372e8i	−0.495684	−	0.0655513i
$325$	−3.59110e10			−3.21880
$326$	−3.52328e9	+	4.19888e9i	−0.311944	+	0.371760i
$327$	−4.75838e9	+	1.55681e9i	−0.416167	+	0.136158i
$328$	−3.75673e8	−	2.13055e9i	−0.0324575	−	0.184075i
$329$	5.03974e8	−	1.38466e9i	0.0430155	−	0.118184i
$330$	1.48558e9	−	3.69860e9i	0.125268	−	0.311876i
$331$	−2.65730e9	+	1.50703e10i	−0.221375	+	1.25548i	0.648120	+	0.761539i	$0.275556\pi$
$331$	−2.65730e9	+	1.50703e10i	−0.221375	+	1.25548i	−0.869495	+	0.493942i	$0.835555\pi$
$332$	−7.89554e9	−	4.55849e9i	−0.649874	−	0.375205i
$333$	−1.14085e10	−	5.02383e9i	−0.927796	−	0.408562i
$334$	−9.79287e8	−	1.69617e9i	−0.0786908	−	0.136296i
$335$	−6.97287e9	−	1.91578e10i	−0.553646	−	1.52113i
$336$	5.95068e8	+	1.11368e9i	0.0466885	+	0.0873786i
$337$	−7.62343e9	+	6.39682e9i	−0.591059	+	0.495958i	−0.888558	−	0.458765i	$-0.848292\pi$
$337$	−7.62343e9	+	6.39682e9i	−0.591059	+	0.495958i	0.297498	+	0.954722i	$0.403848\pi$
$338$	−1.46478e9	−	1.74565e9i	−0.112229	−	0.133749i
$339$	2.75434e7	−	8.37640e8i	0.00208554	−	0.0634248i
$340$	1.40380e10	−	5.10943e9i	1.05049	−	0.382346i
$341$	2.39845e9	−	1.38475e9i	0.177384	−	0.102413i
$342$	−6.14355e9	−	4.10757e9i	−0.449071	−	0.300248i
$343$	−5.05434e9	+	8.75437e9i	−0.365164	+	0.632483i
$344$	−2.97878e9	−	5.25239e8i	−0.212718	−	0.0375079i
$345$	−6.77107e9	−	4.74770e10i	−0.477948	−	3.35125i
$346$	−1.01984e10	−	3.71192e9i	−0.711588	−	0.258997i
$347$	−2.48248e10	+	4.37728e9i	−1.71225	+	0.301916i	−0.941947	−	0.335762i	$-0.891006\pi$
$347$	−2.48248e10	+	4.37728e9i	−1.71225	+	0.301916i	−0.770303	+	0.637678i	$0.779895\pi$
$348$	−3.91298e9	−	8.23405e8i	−0.266803	−	0.0561431i
$349$	3.30959e9	+	2.77708e9i	0.223086	+	0.187192i	0.747480	−	0.664284i	$-0.231264\pi$
$349$	3.30959e9	+	2.77708e9i	0.223086	+	0.187192i	−0.524394	+	0.851476i	$0.675708\pi$
$350$		−	1.21209e10i		−	0.807721i
$351$	1.28558e9	+	1.69003e10i	0.0846974	+	1.11344i
$352$	6.54654e8			0.0426424
$353$	1.95193e10	−	2.32622e10i	1.25709	−	1.49814i	0.468167	−	0.883640i	$-0.344915\pi$
$353$	1.95193e10	−	2.32622e10i	1.25709	−	1.49814i	0.788919	−	0.614497i	$-0.210641\pi$
$354$	−1.38817e10	−	1.24481e10i	−0.883956	−	0.792664i
$355$	3.61288e9	+	2.04897e10i	0.227478	+	1.29009i
$356$	−1.99624e9	+	5.48464e9i	−0.124284	+	0.341466i
$357$	4.50841e9	+	5.74634e9i	0.277556	+	0.353768i
$358$	−1.52611e9	+	8.65503e9i	−0.0929084	+	0.526910i
$359$	4.33420e9	+	2.50235e9i	0.260935	+	0.150651i	0.624761	−	0.780816i	$-0.285196\pi$
$359$	4.33420e9	+	2.50235e9i	0.260935	+	0.150651i	−0.363826	+	0.931467i	$0.618530\pi$
$360$	−2.78447e9	+	1.13649e10i	−0.165780	+	0.676635i
$361$	3.53575e9	+	6.12409e9i	0.208186	+	0.360589i
$362$	−1.24879e9	−	3.43103e9i	−0.0727205	−	0.199798i
$363$	−8.63738e9	+	1.38855e10i	−0.497457	+	0.799717i
$364$	2.97543e9	−	2.49668e9i	0.169490	−	0.142219i
$365$	1.97057e10	+	2.34843e10i	1.11025	+	1.32314i
$366$	2.08414e10	+	1.29642e10i	1.16146	+	0.722475i
$367$	1.18075e10	−	4.29757e9i	0.650868	−	0.236897i	0.00457912	−	0.999990i	$-0.498542\pi$
$367$	1.18075e10	−	4.29757e9i	0.650868	−	0.236897i	0.646289	+	0.763093i	$0.276320\pi$
$368$	6.82155e9	−	3.93842e9i	0.371956	−	0.214749i
$369$	9.51998e9	+	2.33246e9i	0.513488	+	0.125808i
$370$	−1.32361e10	+	2.29255e10i	−0.706240	+	1.22324i
$371$	4.78159e9	+	8.43124e8i	0.252393	+	0.0445037i
$372$	−6.39659e9	+	5.01858e9i	−0.334023	+	0.262065i
$373$	1.16624e10	+	4.24476e9i	0.602493	+	0.219290i	0.625215	−	0.780452i	$-0.285011\pi$
$373$	1.16624e10	+	4.24476e9i	0.602493	+	0.219290i	−0.0227222	+	0.999742i	$0.507233\pi$
$374$	3.72921e9	−	6.57560e8i	0.190603	−	0.0336085i
$375$	4.89727e10	−	5.46129e10i	2.47644	−	2.76166i
$376$	1.71804e9	+	1.44160e9i	0.0859569	+	0.0721264i
$377$			1.23002e10i			0.608903i
$378$	−5.70428e9	+	4.33915e8i	−0.279405	+	0.0212538i
$379$	−3.76163e10			−1.82314			−0.911569	−	0.411148i	$-0.865128\pi$
$379$	−3.76163e10			−1.82314			−0.911569	+	0.411148i	$0.865128\pi$
$380$	−1.00878e10	+	1.20222e10i	−0.483797	+	0.576567i
$381$	−6.66816e9	+	3.16884e10i	−0.316451	+	1.50383i
$382$	−9.67247e8	−	5.48553e9i	−0.0454239	−	0.257611i
$383$	−1.39547e10	+	3.83403e10i	−0.648524	+	1.78181i	−0.0254071	+	0.999677i	$0.508088\pi$
$383$	−1.39547e10	+	3.83403e10i	−0.648524	+	1.78181i	−0.623117	+	0.782129i	$0.714134\pi$
$384$	−1.90260e9	+	2.71345e8i	−0.0875029	+	0.0124795i
$385$	7.18602e8	−	4.07540e9i	0.0327074	−	0.185493i
$386$	−1.69977e10	−	9.81363e9i	−0.765669	−	0.442059i
$387$	7.61674e9	−	1.13921e10i	0.339567	−	0.507878i
$388$	6.42430e9	+	1.11272e10i	0.283464	+	0.490975i
$389$	−1.42692e10	−	3.92044e10i	−0.623163	−	1.71213i	−0.699109	−	0.715015i	$-0.746420\pi$
$389$	−1.42692e10	−	3.92044e10i	−0.623163	−	1.71213i	0.0759455	−	0.997112i	$-0.475803\pi$
$390$	3.59737e10	+	1.18289e9i	1.55499	+	0.0511313i
$391$	3.49027e10	−	2.92869e10i	1.49332	−	1.25304i
$392$	−4.52351e9	−	5.39090e9i	−0.191571	−	0.228306i
$393$	−5.79579e9	+	3.09683e9i	−0.242964	+	0.129822i
$394$	2.62670e10	−	9.56042e9i	1.09000	−	0.396727i
$395$	3.24134e10	−	1.87139e10i	1.33149	−	0.768733i
$396$	−1.19532e9	+	2.71444e9i	−0.0486077	+	0.110382i
$397$	−6.59991e9	+	1.14314e10i	−0.265691	+	0.460190i	−0.967744	−	0.251934i	$-0.918933\pi$
$397$	−6.59991e9	+	1.14314e10i	−0.265691	+	0.460190i	0.702054	+	0.712124i	$0.252267\pi$
$398$	−1.45573e10	−	2.56684e9i	−0.580160	−	0.102298i
$399$	−7.12005e9	−	2.85983e9i	−0.280926	−	0.112836i
$400$	1.73357e10	+	6.30967e9i	0.677175	+	0.246472i
$401$	2.21795e10	−	3.91084e9i	0.857775	−	0.151249i	0.272572	−	0.962135i	$-0.412126\pi$
$401$	2.21795e10	−	3.91084e9i	0.857775	−	0.151249i	0.585203	+	0.810887i	$0.301015\pi$
$402$	4.71744e9	+	1.44188e10i	0.180635	+	0.552110i
$403$	1.91584e10	+	1.60758e10i	0.726340	+	0.609472i
$404$			4.41565e8i			0.0165756i
$405$	−4.20388e10	−	3.22964e10i	−1.56254	−	1.20042i
$406$	−4.15164e9			−0.152797
$407$	−4.31321e9	+	5.14028e9i	−0.157189	+	0.187331i
$408$	−1.05655e10	+	3.45675e9i	−0.381286	+	0.124746i
$409$	−2.64363e9	−	1.49928e10i	−0.0944729	−	0.535782i	−0.994908	−	0.100791i	$-0.967863\pi$
$409$	−2.64363e9	−	1.49928e10i	−0.0944729	−	0.535782i	0.900435	−	0.434991i	$-0.143248\pi$
$410$	7.11901e9	−	1.95593e10i	0.251932	−	0.692179i
$411$	−1.85754e9	+	4.62467e9i	−0.0650986	+	0.162074i
$412$	−1.67772e9	+	9.51482e9i	−0.0582278	+	0.330226i
$413$	−1.67652e10	−	9.67941e9i	−0.576248	−	0.332697i
$414$	3.87480e9	+	3.54758e10i	0.131901	+	1.20762i
$415$	−4.38580e10	−	7.59643e10i	−1.47862	−	2.56105i
$416$	2.02194e9	+	5.55524e9i	0.0675143	+	0.185494i
$417$	1.46448e10	+	2.74080e10i	0.484327	+	0.906429i
$418$	−3.04739e9	+	2.55706e9i	−0.0998213	+	0.0837600i
$419$	−5.20345e9	−	6.20123e9i	−0.168825	−	0.201197i	0.674998	−	0.737820i	$-0.264144\pi$
$419$	−5.20345e9	−	6.20123e9i	−0.168825	−	0.201197i	−0.843823	+	0.536622i	$0.819700\pi$
$420$	−3.99256e8	+	1.21420e10i	−0.0128308	+	0.390207i
$421$	−1.36284e10	+	4.96035e9i	−0.433828	+	0.157901i	−0.549697	−	0.835364i	$-0.685257\pi$
$421$	−1.36284e10	+	4.96035e9i	−0.433828	+	0.157901i	0.115869	+	0.993265i	$0.463035\pi$
$422$	8.67405e9	−	5.00797e9i	0.273509	−	0.157911i
$423$	−9.11436e9	+	4.49141e9i	−0.284685	+	0.140288i
$424$	−3.69498e9	+	6.39990e9i	−0.114327	+	0.198020i
$425$	1.05090e11	+	1.85301e10i	3.22110	+	0.567967i
$426$	−2.18594e9	−	1.53272e10i	−0.0663742	−	0.465398i
$427$	2.39467e10	+	8.71588e9i	0.720334	+	0.262180i
$428$	−2.26210e10	+	3.98870e9i	−0.674120	+	0.118865i
$429$	8.92803e9	+	1.87872e9i	0.263589	+	0.0554667i
$430$	−2.22930e10	−	1.87060e10i	−0.652071	−	0.547152i
$431$			1.85475e10i			0.537498i	0.963210	+	0.268749i	$0.0866102\pi$
$431$			1.85475e10i			0.537498i	−0.963210	+	0.268749i	$0.913390\pi$
$432$	2.34883e9	−	8.38434e9i	0.0674400	−	0.240732i
$433$	6.38463e10			1.81629			0.908143	−	0.418660i	$-0.137500\pi$
$433$	6.38463e10			1.81629			0.908143	+	0.418660i	$0.137500\pi$
$434$	−5.42600e9	+	6.46646e9i	−0.152940	+	0.182267i
$435$	−2.86426e10	−	2.56845e10i	−0.799936	−	0.717321i
$436$	−1.37384e9	−	7.79143e9i	−0.0380181	−	0.215611i
$437$	−1.63707e10	+	4.49780e10i	−0.448891	+	1.23332i
$438$	−1.40815e10	−	1.79480e10i	−0.382606	−	0.487663i
$439$	4.32549e9	−	2.45311e10i	0.116460	−	0.660478i	−0.869557	−	0.493833i	$-0.835595\pi$
$439$	4.32549e9	−	2.45311e10i	0.116460	−	0.660478i	0.986017	−	0.166645i	$-0.0532935\pi$
$440$	5.45470e9	+	3.14927e9i	0.145532	+	0.0840232i
$441$	3.06121e10	−	8.91296e9i	0.809355	−	0.235650i
$442$	1.70978e10	+	2.96143e10i	0.447972	+	0.775911i
$443$	2.96961e9	+	8.15895e9i	0.0771055	+	0.211846i	0.972256	−	0.233918i	$-0.0751546\pi$
$443$	2.96961e9	+	8.15895e9i	0.0771055	+	0.211846i	−0.895151	+	0.445763i	$0.852932\pi$
$444$	1.04048e10	−	1.67268e10i	0.267732	−	0.430409i
$445$	−4.30174e10	+	3.60959e10i	−1.09699	+	0.920487i
$446$	−1.62875e10	−	1.94107e10i	−0.411637	−	0.490570i
$447$	−7.80725e9	−	4.85644e9i	−0.195555	−	0.121643i
$448$	−1.87503e9	+	6.82457e8i	−0.0465476	+	0.0169419i
$449$	−3.59403e9	+	2.07501e9i	−0.0884293	+	0.0510547i	−0.543563	−	0.839369i	$-0.682925\pi$
$449$	−3.59403e9	+	2.07501e9i	−0.0884293	+	0.0510547i	0.455133	+	0.890423i	$0.349592\pi$
$450$	−5.78153e10	+	6.03595e10i	−1.40991	+	1.47196i
$451$	2.63804e9	−	4.56922e9i	0.0637640	−	0.110443i
$452$	1.30427e9	+	2.29979e8i	0.0312475	+	0.00550977i
$453$	2.60122e10	−	2.04084e10i	0.617709	−	0.484636i
$454$	−1.93150e10	−	7.03007e9i	−0.454643	−	0.165477i
$455$	3.68023e10	−	6.48924e9i	0.858677	−	0.151408i
$456$	7.79667e9	−	8.69461e9i	0.180322	−	0.201090i
$457$	1.44812e10	+	1.21511e10i	0.332001	+	0.278582i	0.793514	−	0.608551i	$-0.208249\pi$
$457$	1.44812e10	+	1.21511e10i	0.332001	+	0.278582i	−0.461514	+	0.887133i	$0.652694\pi$
$458$		−	2.21927e10i		−	0.504370i
$459$	4.95848e9	−	5.01202e10i	0.111711	−	1.12918i
$460$	7.57845e10			1.69258
$461$	2.19462e10	−	2.61545e10i	0.485910	−	0.579085i	−0.466263	−	0.884646i	$-0.654400\pi$
$461$	2.19462e10	−	2.61545e10i	0.485910	−	0.579085i	0.952172	+	0.305562i	$0.0988443\pi$
$462$	−6.34115e8	+	3.01344e9i	−0.0139187	+	0.0661445i
$463$	−2.62158e9	−	1.48677e10i	−0.0570478	−	0.323534i	0.942907	−	0.333057i	$-0.108080\pi$
$463$	−2.62158e9	−	1.48677e10i	−0.0570478	−	0.323534i	−0.999955	+	0.00952231i	$0.996969\pi$
$464$	2.16119e9	−	5.93782e9i	0.0466252	−	0.128102i
$465$	−7.74398e10	+	1.10443e10i	−1.65635	+	0.236226i
$466$	−4.66835e9	+	2.64755e10i	−0.0989965	+	0.561437i
$467$	8.41021e8	+	4.85564e8i	0.0176823	+	0.0102089i	0.508815	−	0.860876i	$-0.330084\pi$
$467$	8.41021e8	+	4.85564e8i	0.0176823	+	0.0102089i	−0.491133	+	0.871085i	$0.663417\pi$
$468$	−2.67260e10	−	1.75951e9i	−0.557121	−	0.0366783i
$469$	7.87563e9	+	1.36410e10i	0.162777	+	0.281939i
$470$	7.38003e9	+	2.02765e10i	0.151240	+	0.415528i
$471$	−5.73104e10	−	1.88449e9i	−1.16453	−	0.0382921i
$472$	2.25712e10	−	1.89395e10i	0.454764	−	0.381592i
$473$	−4.74161e9	−	5.65083e9i	−0.0947287	−	0.112893i
$474$	−2.45646e10	+	1.31255e10i	−0.486627	+	0.260017i
$475$	−1.05342e11	+	3.83415e10i	−2.06933	+	0.753173i
$476$	−9.99556e9	+	5.77094e9i	−0.194706	+	0.112414i
$477$	−1.97898e10	−	2.70063e10i	−0.382267	−	0.521664i
$478$	2.53728e10	−	4.39470e10i	0.486024	−	0.841817i
$479$	4.75550e10	+	8.38524e9i	0.903347	+	0.159284i	0.605981	−	0.795479i	$-0.292781\pi$
$479$	4.75550e10	+	8.38524e9i	0.903347	+	0.159284i	0.297366	+	0.954764i	$0.403892\pi$
$480$	−1.71581e10	−	6.89173e9i	−0.323225	−	0.129826i
$481$	−5.69409e10	−	2.07248e10i	−1.06376	−	0.387177i
$482$	4.62147e10	−	8.14890e9i	0.856233	−	0.150977i
$483$	1.15214e10	+	3.52151e10i	0.211698	+	0.647054i
$484$	−1.97956e10	−	1.66105e10i	−0.360735	−	0.302693i
$485$			1.23619e11i			2.23417i
$486$	3.04759e10	+	2.50480e10i	0.546275	+	0.448981i
$487$	−3.24059e10			−0.576114			−0.288057	−	0.957613i	$-0.593009\pi$
$487$	−3.24059e10			−0.576114			−0.288057	+	0.957613i	$0.593009\pi$
$488$	−2.49315e10	+	2.97122e10i	−0.439612	+	0.523909i
$489$	3.72973e10	−	1.22026e10i	0.652291	−	0.213412i
$490$	−1.17573e10	−	6.66787e10i	−0.203949	−	1.15665i
$491$	3.03569e10	−	8.34049e10i	0.522314	−	1.43505i	−0.345624	−	0.938373i	$-0.612333\pi$
$491$	3.03569e10	−	8.34049e10i	0.522314	−	1.43505i	0.867938	−	0.496673i	$-0.165445\pi$
$492$	−5.77298e9	+	1.43728e10i	−0.0985234	+	0.245291i
$493$	6.34694e9	−	3.59953e10i	0.107443	−	0.609338i
$494$	−3.11107e10	−	1.79618e10i	−0.522399	−	0.301607i
$495$	−2.30177e10	+	1.68670e10i	−0.383390	+	0.280942i
$496$	−6.42398e9	−	1.11267e10i	−0.106140	−	0.183839i
$497$	−5.49782e9	−	1.51051e10i	−0.0901084	−	0.247571i
$498$	3.07609e10	+	5.75698e10i	0.500129	+	0.936003i
$499$	2.21791e10	−	1.86105e10i	0.357719	−	0.300162i	−0.446162	−	0.894952i	$-0.647209\pi$
$499$	2.21791e10	−	1.86105e10i	0.357719	−	0.300162i	0.803881	+	0.594790i	$0.202765\pi$
$500$	7.45108e10	+	8.87985e10i	1.19217	+	1.42078i
$501$	−4.60834e8	+	1.40147e10i	−0.00731466	+	0.222451i
$502$	2.55453e10	−	9.29773e9i	0.402250	−	0.146407i
$503$	−5.51505e10	+	3.18412e10i	−0.861545	+	0.497413i	−0.864529	−	0.502583i	$-0.832383\pi$
$503$	−5.51505e10	+	3.18412e10i	−0.861545	+	0.497413i	0.00298469	+	0.999996i	$0.499050\pi$
$504$	5.93880e8	−	9.02068e9i	0.00920400	−	0.139803i
$505$	−2.12418e9	+	3.67920e9i	−0.0326608	+	0.0565702i
$506$	1.89180e10	+	3.33576e9i	0.288585	+	0.0508853i
$507$	2.30349e9	+	1.61515e10i	0.0348622	+	0.244444i
$508$	−4.80861e10	−	1.75019e10i	−0.722045	−	0.262803i
$509$	−5.95246e10	+	1.04958e10i	−0.886799	+	0.156367i	−0.598451	−	0.801159i	$-0.704217\pi$
$509$	−5.95246e10	+	1.04958e10i	−0.886799	+	0.156367i	−0.288348	+	0.957526i	$0.593106\pi$
$510$	−1.04663e11	−	2.20241e10i	−1.54708	−	0.325550i
$511$	−1.81440e10	−	1.52246e10i	−0.266103	−	0.223287i
$512$		−	3.03700e9i		−	0.0441942i
$513$	2.18153e10	+	4.82033e10i	0.314986	+	0.695996i
$514$	−7.43996e9			−0.106590
$515$	−5.97509e10	+	7.12084e10i	−0.849407	+	1.01228i
$516$	1.61226e10	+	1.44575e10i	0.227424	+	0.203936i
$517$	9.49775e8	+	5.38644e9i	0.0132941	+	0.0753945i
$518$	6.99514e9	−	1.92190e10i	0.0971577	−	0.266939i
$519$	4.79621e10	+	6.11317e10i	0.661042	+	0.842553i
$520$	−9.87678e9	+	5.60140e10i	−0.135083	+	0.766096i
$521$	−2.25331e10	−	1.30095e10i	−0.305824	−	0.176567i	0.339232	−	0.940703i	$-0.389833\pi$
$521$	−2.25331e10	−	1.30095e10i	−0.305824	−	0.176567i	−0.645056	+	0.764135i	$0.723166\pi$
$522$	2.06743e10	+	1.98029e10i	0.278451	+	0.266714i
$523$	−1.75711e10	−	3.04341e10i	−0.234851	−	0.406774i	0.724378	−	0.689403i	$-0.242127\pi$
$523$	−1.75711e10	−	3.04341e10i	−0.234851	−	0.406774i	−0.959229	+	0.282629i	$0.908794\pi$
$524$	−3.55162e9	−	9.75799e9i	−0.0471087	−	0.129430i
$525$	−4.58358e10	+	7.36861e10i	−0.603348	+	0.969948i
$526$	7.22496e10	−	6.06246e10i	0.943828	−	0.791965i
$527$	−4.77699e10	−	5.69300e10i	−0.619316	−	0.738072i
$528$	−3.97982e9	−	2.47562e9i	−0.0512069	−	0.0318528i
$529$	1.43607e11	−	5.22687e10i	1.83381	−	0.667451i
$530$	−6.15745e10	+	3.55501e10i	−0.780365	+	0.450544i
$531$	3.73177e10	+	1.28170e11i	0.469393	+	1.61216i
$532$	6.06256e9	−	1.05007e10i	0.0756849	−	0.131090i
$533$	4.69211e10	+	8.27346e9i	0.581380	+	0.102513i
$534$	3.28762e10	−	2.57937e10i	0.404312	−	0.317211i
$535$	−2.07670e11	−	7.55858e10i	−2.53489	−	0.922625i
$536$	−2.36096e10	+	4.16301e9i	−0.286042	+	0.0504368i
$537$	4.20072e10	−	4.68452e10i	0.505157	−	0.563337i
$538$	−8.17339e10	−	6.85828e10i	−0.975602	−	0.818628i
$539$		−	1.71625e10i		−	0.203341i
$540$	5.99045e10	−	5.85605e10i	0.704505	−	0.688700i
$541$	1.38013e11			1.61113			0.805566	−	0.592507i	$-0.201862\pi$
$541$	1.38013e11			1.61113			0.805566	+	0.592507i	$0.201862\pi$
$542$	1.66519e10	−	1.98449e10i	0.192959	−	0.229960i
$543$	−5.38290e9	+	2.55806e10i	−0.0619181	+	0.294247i
$544$	−3.05048e9	−	1.73001e10i	−0.0348315	−	0.197539i
$545$	2.60343e10	−	7.15286e10i	0.295093	−	0.810762i
$546$	−2.75298e10	+	3.92625e9i	−0.309765	+	0.0441781i
$547$	−2.56192e9	+	1.45294e10i	−0.0286165	+	0.162292i	−0.995767	−	0.0919116i	$-0.970702\pi$
$547$	−2.56192e9	+	1.45294e10i	−0.0286165	+	0.162292i	0.967151	+	0.254204i	$0.0818134\pi$
$548$	−6.82047e9	−	3.93780e9i	−0.0756296	−	0.0436648i
$549$	−7.76758e10	−	1.57626e11i	−0.855060	−	1.73516i
$550$	2.24956e10	+	3.89635e10i	0.245837	+	0.425801i
$551$	1.31327e10	+	3.60819e10i	0.142478	+	0.391456i
$552$	−5.63635e10	−	1.85335e9i	−0.607074	−	0.0199619i
$553$	−2.21515e10	+	1.85873e10i	−0.236866	+	0.198754i
$554$	−5.97390e10	−	7.11942e10i	−0.634189	−	0.755798i
$555$	1.67160e11	−	8.93177e10i	1.76182	−	0.941381i
$556$	−4.61450e10	+	1.67954e10i	−0.482865	+	0.175749i
$557$	−5.42333e8	+	3.13116e8i	−0.00563437	+	0.00325300i	−0.502815	−	0.864394i	$-0.667702\pi$
$557$	−5.42333e8	+	3.13116e8i	−0.00563437	+	0.00325300i	0.497180	+	0.867647i	$0.334369\pi$
$558$	5.78647e10	−	6.32020e9i	0.596866	−	0.0651919i
$559$	3.33069e10	−	5.76892e10i	0.341104	−	0.590809i
$560$	−1.89061e10	−	3.33366e9i	−0.192243	−	0.0338976i
$561$	−2.51575e10	−	1.01047e10i	−0.253989	−	0.102017i
$562$	9.95536e10	+	3.62345e10i	0.997957	+	0.363226i
$563$	−1.72031e11	+	3.03337e10i	−1.71227	+	0.301920i	−0.941955	−	0.335739i	$-0.891014\pi$
$563$	−1.72031e11	+	3.03337e10i	−1.71227	+	0.301920i	−0.770319	+	0.637659i	$0.779903\pi$
$564$	−4.99290e9	−	1.52608e10i	−0.0493443	−	0.150820i
$565$	9.76111e9	+	8.19054e9i	0.0957867	+	0.0803746i
$566$		−	6.46402e10i		−	0.629850i
$567$	3.63188e10	+	1.89332e10i	0.351398	+	0.183186i
$568$	2.44659e10			0.235054
$569$	−4.21997e10	+	5.02917e10i	−0.402588	+	0.479786i	−0.928807	−	0.370563i	$-0.879165\pi$
$569$	−4.21997e10	+	5.02917e10i	−0.402588	+	0.479786i	0.526219	+	0.850349i	$0.323609\pi$
$570$	1.06789e11	−	3.49386e10i	1.01165	−	0.330983i
$571$	2.86733e10	+	1.62614e11i	0.269733	+	1.52973i	0.755211	+	0.655481i	$0.227534\pi$
$571$	2.86733e10	+	1.62614e11i	0.269733	+	1.52973i	−0.485479	+	0.874248i	$0.661355\pi$
$572$	−4.93107e9	+	1.35480e10i	−0.0460635	+	0.126558i
$573$	−1.48637e10	+	3.70058e10i	−0.137882	+	0.343282i
$574$	−2.79250e9	+	1.58371e10i	−0.0257244	+	0.145891i
$575$	4.68812e11	+	2.70668e11i	4.28871	+	2.47609i
$576$	1.25925e10	+	5.54522e9i	0.114399	+	0.0503766i
$577$	6.69256e10	+	1.15919e11i	0.603794	+	1.04580i	0.992241	+	0.124331i	$0.0396785\pi$
$577$	6.69256e10	+	1.15919e11i	0.603794	+	1.04580i	−0.388446	+	0.921471i	$0.626988\pi$
$578$	−7.76103e9	−	2.13232e10i	−0.0695357	−	0.191048i
$579$	6.62229e10	+	1.23938e11i	0.589243	+	1.10278i
$580$	4.65718e10	−	3.90784e10i	0.411539	−	0.345322i
$581$	4.35614e10	+	5.19145e10i	0.382294	+	0.455600i
$582$	3.02316e9	−	9.19392e10i	0.0263493	−	0.801326i
$583$	−1.69356e10	+	6.16405e9i	−0.146597	+	0.0533571i
$584$	3.12199e10	−	1.80248e10i	0.268399	−	0.154960i
$585$	−2.14221e11	−	1.43228e11i	−1.82911	−	1.22294i
$586$	−1.81029e10	+	3.13552e10i	−0.153518	+	0.265900i
$587$	−1.85388e11	−	3.26889e10i	−1.56145	−	0.275327i	−0.674886	−	0.737922i	$-0.735807\pi$
$587$	−1.85388e11	−	3.26889e10i	−1.56145	−	0.275327i	−0.886569	+	0.462596i	$0.846918\pi$
$588$	7.11360e9	+	4.98787e10i	0.0595087	+	0.417259i
$589$	7.33638e10	+	2.67023e10i	0.609566	+	0.221864i
$590$	2.79177e11	−	4.92264e10i	2.30394	−	0.406247i
$591$	−1.95838e11	−	4.12100e10i	−1.60526	−	0.337794i
$592$	2.38462e10	+	2.00094e10i	0.194148	+	0.162910i
$593$		−	1.31953e11i		−	1.06709i	−0.845773	−	0.533544i	$-0.820860\pi$
$593$		−	1.31953e11i		−	1.06709i	0.845773	−	0.533544i	$-0.179140\pi$
$594$	1.75315e10	−	1.19816e10i	0.140823	−	0.0962433i
$595$	−1.11046e11			−0.886006
$596$	9.33940e9	−	1.11303e10i	0.0740174	−	0.0882105i
$597$	7.87910e10	+	7.06538e10i	0.620268	+	0.556209i
$598$	3.01231e10	+	1.70837e11i	0.235557	+	1.33591i
$599$	3.38135e10	−	9.29019e10i	0.262653	−	0.721634i	−0.736333	−	0.676619i	$-0.763444\pi$
$599$	3.38135e10	−	9.29019e10i	0.262653	−	0.721634i	0.998986	−	0.0450149i	$-0.0143335\pi$
$600$	−8.15280e10	−	1.03914e11i	−0.629074	−	0.801807i
$601$	3.77021e10	−	2.13819e11i	0.288980	−	1.63888i	−0.401734	−	0.915756i	$-0.631592\pi$
$601$	3.77021e10	−	2.13819e11i	0.288980	−	1.63888i	0.690714	−	0.723128i	$-0.257297\pi$
$602$	1.94716e10	+	1.12419e10i	0.148257	+	0.0855961i
$603$	2.58470e10	−	1.05495e11i	0.195498	−	0.797928i
$604$	2.61235e10	+	4.52473e10i	0.196284	+	0.339973i
$605$	−8.50345e10	−	2.33630e11i	−0.634708	−	1.74385i
$606$	1.66980e9	−	2.68439e9i	0.0123816	−	0.0199047i
$607$	5.79489e10	−	4.86249e10i	0.426865	−	0.358182i	−0.403902	−	0.914802i	$-0.632346\pi$
$607$	5.79489e10	−	4.86249e10i	0.426865	−	0.358182i	0.830767	+	0.556620i	$0.187902\pi$
$608$	1.18625e10	+	1.41371e10i	0.0868081	+	0.103454i
$609$	2.52390e10	+	1.56997e10i	0.183486	+	0.114136i
$610$	−3.50667e11	+	1.27632e11i	−2.53265	+	0.921810i
$611$	−4.27746e10	+	2.46959e10i	−0.306917	+	0.177199i
$612$	7.73026e10	+	1.89397e10i	0.551047	+	0.135010i
$613$	−4.89014e10	+	8.46998e10i	−0.346322	+	0.599847i	−0.985593	−	0.169135i	$-0.945903\pi$
$613$	−4.89014e10	+	8.46998e10i	−0.346322	+	0.599847i	0.639271	+	0.768981i	$0.279236\pi$
$614$	−4.06452e10	−	7.16685e9i	−0.285980	−	0.0504261i
$615$	−1.17243e11	+	9.19855e10i	−0.819572	+	0.643012i
$616$	−4.57279e9	−	1.66436e9i	−0.0317584	−	0.0115591i
$617$	−7.74177e10	+	1.36508e10i	−0.534195	+	0.0941929i	−0.434237	−	0.900799i	$-0.642982\pi$
$617$	−7.74177e10	+	1.36508e10i	−0.534195	+	0.0941929i	−0.0999579	+	0.994992i	$0.531871\pi$
$618$	4.61802e10	−	5.14988e10i	0.316594	−	0.353056i
$619$	9.89604e9	+	8.30377e9i	0.0674061	+	0.0565604i	0.675868	−	0.737022i	$-0.263769\pi$
$619$	9.89604e9	+	8.30377e9i	0.0674061	+	0.0565604i	−0.608462	+	0.793583i	$0.708213\pi$
$620$		−	1.23612e11i		−	0.836556i
$621$	1.10598e11	−	2.30320e11i	0.743671	−	1.54869i
$622$	1.25283e10			0.0837009
$623$	2.78877e10	−	3.32353e10i	0.185123	−	0.220621i
$624$	8.71555e9	−	4.14180e10i	0.0574852	−	0.273181i
$625$	1.17287e11	+	6.65168e11i	0.768652	+	4.35924i
$626$	−4.37824e10	+	1.20291e11i	−0.285104	+	0.783316i
$627$	2.81956e10	−	4.02120e9i	0.182436	−	0.0260187i
$628$	1.57349e10	−	8.92369e10i	0.101164	−	0.573728i
$629$	1.55937e11	+	9.00304e10i	0.996202	+	0.575157i
$630$	4.83431e10	−	7.23050e10i	0.306882	−	0.458993i
$631$	−3.35311e10	−	5.80775e10i	−0.211509	−	0.366345i	0.740678	−	0.671861i	$-0.234505\pi$
$631$	−3.35311e10	−	5.80775e10i	−0.211509	−	0.366345i	−0.952187	+	0.305515i	$0.901171\pi$
$632$	−1.50530e10	−	4.13578e10i	−0.0943527	−	0.259232i
$633$	−7.16699e10	−	2.35666e9i	−0.446398	−	0.0146785i
$634$	−5.77300e10	+	4.84412e10i	−0.357309	+	0.299818i
$635$	−3.16467e11	−	3.77151e11i	−1.94641	−	2.31964i
$636$	4.66644e10	−	2.49339e10i	0.285205	−	0.152392i
$637$	1.45637e11	−	5.30074e10i	0.884531	−	0.321943i
$638$	1.33458e10	−	7.70519e9i	0.0805492	−	0.0465051i
$639$	−4.46719e10	+	1.01445e11i	−0.267936	+	0.608451i
$640$	1.46098e10	−	2.53048e10i	0.0870809	−	0.150829i
$641$	4.61777e10	+	8.14237e9i	0.273527	+	0.0482302i	0.308729	−	0.951150i	$-0.400096\pi$
$641$	4.61777e10	+	8.14237e9i	0.273527	+	0.0482302i	−0.0352021	+	0.999380i	$0.511207\pi$
$642$	1.52603e11	+	6.12944e10i	0.898303	+	0.360812i
$643$	5.22578e9	+	1.90203e9i	0.0305708	+	0.0111269i	0.357260	−	0.934005i	$-0.383711\pi$
$643$	5.22578e9	+	1.90203e9i	0.0305708	+	0.0111269i	−0.326689	+	0.945132i	$0.605933\pi$
$644$	−5.76617e10	+	1.01673e10i	−0.335231	+	0.0591102i
$645$	6.47872e10	+	1.98022e11i	0.374326	+	1.14413i
$646$	8.17738e10	+	6.86164e10i	0.469552	+	0.394001i
$647$		−	8.47891e9i		−	0.0483863i	−0.999707	−	0.0241932i	$-0.992298\pi$
$647$		−	8.47891e9i		−	0.0483863i	0.999707	−	0.0241932i	$-0.00770168\pi$
$648$	−4.59851e10	+	4.20884e10i	−0.260806	+	0.238706i
$649$	7.18575e10			0.405036
$650$	−2.61156e11	+	3.11234e11i	−1.46301	+	1.74354i
$651$	5.74395e10	−	1.87926e10i	0.319806	−	0.104632i
$652$	1.07685e10	+	6.10711e10i	0.0595887	+	0.337944i
$653$	4.02864e9	−	1.10686e10i	0.0221567	−	0.0608752i	−0.928121	−	0.372278i	$-0.878577\pi$
$653$	4.02864e9	−	1.10686e10i	0.0221567	−	0.0608752i	0.950278	+	0.311403i	$0.100799\pi$
$654$	−2.11118e10	+	5.25615e10i	−0.115402	+	0.287314i
$655$	1.73489e10	−	9.83906e10i	0.0942556	−	0.534550i
$656$	−2.11970e10	−	1.22381e10i	−0.114462	−	0.0660845i
$657$	1.77336e10	+	1.62361e11i	0.0951779	+	0.871404i
$658$	−8.33550e9	−	1.44375e10i	−0.0444660	−	0.0770174i
$659$	−2.38467e9	−	6.55183e9i	−0.0126441	−	0.0347393i	0.933210	−	0.359331i	$-0.116995\pi$
$659$	−2.38467e9	−	6.55183e9i	−0.0126441	−	0.0347393i	−0.945854	+	0.324592i	$0.894773\pi$
$660$	−2.12514e10	−	3.97726e10i	−0.111999	−	0.209608i
$661$	−1.08359e11	+	9.09238e10i	−0.567621	+	0.476290i	−0.880855	−	0.473385i	$-0.843032\pi$
$661$	−1.08359e11	+	9.09238e10i	−0.567621	+	0.476290i	0.313235	+	0.949676i	$0.398587\pi$
$662$	1.11287e11	+	1.32626e11i	0.579444	+	0.690554i
$663$	8.04591e9	−	2.44690e11i	0.0416410	−	1.26637i
$664$	−9.69264e10	+	3.52783e10i	−0.498620	+	0.181483i
$665$	1.01029e11	−	5.83289e10i	0.516604	−	0.298261i
$666$	−1.26507e11	+	6.23406e10i	−0.643009	+	0.316865i
$667$	9.27094e10	−	1.60577e11i	0.468404	−	0.811299i
$668$	−2.18221e10	−	3.84782e9i	−0.109595	−	0.0193245i
$669$	2.56135e10	+	1.79595e11i	0.127869	+	0.896581i
$670$	−2.16746e11	−	7.88890e10i	−1.07560	−	0.391487i
$671$	−9.31546e10	+	1.64257e10i	−0.459530	+	0.0810276i
$672$	1.39796e10	+	2.94172e9i	0.0685516	+	0.0144253i
$673$	−1.14548e11	−	9.61170e10i	−0.558376	−	0.468533i	0.319390	−	0.947623i	$-0.396522\pi$
$673$	−1.14548e11	−	9.61170e10i	−0.558376	−	0.468533i	−0.877766	+	0.479090i	$0.840967\pi$
$674$			1.12590e11i			0.545585i
$675$	5.79728e11	−	1.48310e11i	2.79260	−	0.714422i
$676$	−2.57816e10			−0.123459
$677$	−6.46895e10	+	7.70939e10i	−0.307949	+	0.367000i	−0.897716	−	0.440574i	$-0.854775\pi$
$677$	−6.46895e10	+	7.70939e10i	−0.307949	+	0.367000i	0.589767	+	0.807573i	$0.299219\pi$
$678$	−7.05936e9	−	6.33029e9i	−0.0334077	−	0.0299575i
$679$	−1.65848e10	−	9.40569e10i	−0.0780244	−	0.442498i
$680$	5.78066e10	−	1.58822e11i	0.270360	−	0.742807i
$681$	9.08363e10	+	1.15778e11i	0.422349	+	0.538319i
$682$	5.44097e9	−	3.08573e10i	0.0251500	−	0.142633i
$683$	−2.99772e11	−	1.73074e11i	−1.37755	−	0.795331i	−0.385689	−	0.922629i	$-0.626036\pi$
$683$	−2.99772e11	−	1.73074e11i	−1.37755	−	0.795331i	−0.991865	+	0.127298i	$0.959370\pi$
$684$	−8.02773e10	+	2.33734e10i	−0.366749	+	0.106782i
$685$	−3.78863e10	−	6.56209e10i	−0.172076	−	0.298044i
$686$	3.91157e10	+	1.07469e11i	0.176626	+	0.485276i
$687$	−8.39232e10	+	1.34916e11i	−0.376752	+	0.605670i
$688$	−2.62147e10	+	2.19968e10i	−0.117002	+	0.0981760i
$689$	−1.04613e11	−	1.24673e11i	−0.464206	−	0.553219i
$690$	−4.60715e11	−	2.86584e11i	−2.03252	−	1.26431i
$691$	3.08397e11	−	1.12247e11i	1.35269	−	0.492339i	0.438903	−	0.898534i	$-0.355367\pi$
$691$	3.08397e11	−	1.12247e11i	1.35269	−	0.492339i	0.913786	+	0.406196i	$0.133145\pi$
$692$	−1.06337e11	+	6.13934e10i	−0.463723	+	0.267730i
$693$	1.52505e10	−	1.59216e10i	0.0661226	−	0.0690324i
$694$	−1.42596e11	+	2.46984e11i	−0.614711	+	1.06471i
$695$	−4.65285e11	−	8.20422e10i	−1.99425	−	0.351640i
$696$	−3.55927e10	+	2.79250e10i	−0.151678	+	0.119002i
$697$	−1.33040e11	−	4.84228e10i	−0.563706	−	0.205172i
$698$	4.81368e10	−	8.48782e9i	0.202794	−	0.0357581i
$699$	1.28499e11	−	1.43298e11i	0.538259	−	0.600251i
$700$	−1.05049e11	−	8.81467e10i	−0.437523	−	0.367125i
$701$		−	1.31174e11i		−	0.543222i	−0.962407	−	0.271611i	$-0.912444\pi$
$701$		−	1.31174e11i		−	0.543222i	0.962407	−	0.271611i	$-0.0875563\pi$
$702$	1.55821e11	+	1.11762e11i	0.641618	+	0.460201i
$703$	−1.89160e11			−0.774474
$704$	4.76085e9	−	5.67376e9i	0.0193818	−	0.0230983i
$705$	3.18115e10	−	1.51174e11i	0.128774	−	0.611957i
$706$	−5.96584e10	−	3.38340e11i	−0.240134	−	1.36186i
$707$	1.12261e9	−	3.08435e9i	0.00449316	−	0.0123449i
$708$	−2.08837e11	+	2.97839e10i	−0.831141	+	0.118536i
$709$	−6.68245e10	+	3.78981e11i	−0.264454	+	1.49980i	0.506130	+	0.862457i	$0.331076\pi$
$709$	−6.68245e10	+	3.78981e11i	−0.264454	+	1.49980i	−0.770584	+	0.637338i	$0.780035\pi$
$710$	2.03854e11	+	1.17695e11i	0.802206	+	0.463154i
$711$	1.98970e11	+	1.30993e10i	0.778590	+	0.0512588i
$712$	3.30170e10	+	5.71870e10i	0.128475	+	0.222524i
$713$	−1.28943e11	−	3.54268e11i	−0.498930	−	1.37080i
$714$	8.25889e10	+	2.71570e9i	0.317782	+	0.0104493i
$715$	−1.06260e11	+	8.91630e10i	−0.406581	+	0.341162i
$716$	6.39130e10	+	7.61686e10i	0.243185	+	0.289817i
$717$	−3.20437e11	+	1.71217e11i	−1.21246	+	0.647844i
$718$	5.32071e10	−	1.93658e10i	0.200204	−	0.0728681i
$719$	−2.54838e11	+	1.47131e11i	−0.953562	+	0.550539i	−0.894186	−	0.447696i	$-0.852245\pi$
$719$	−2.54838e11	+	1.47131e11i	−0.953562	+	0.550539i	−0.0593765	+	0.998236i	$0.518911\pi$
$720$	7.82475e10	+	1.06781e11i	0.291166	+	0.397342i
$721$	3.59090e10	−	6.21962e10i	0.132881	−	0.230156i
$722$	7.87893e10	+	1.38927e10i	0.289947	+	0.0511255i
$723$	−3.11767e11	−	1.25224e11i	−1.14098	−	0.458285i
$724$	−3.88177e10	−	1.41285e10i	−0.141278	−	0.0514211i
$725$	4.27669e11	−	7.54096e10i	1.54795	−	0.272945i
$726$	5.75295e10	+	1.75838e11i	0.207083	+	0.632947i
$727$	−2.51738e11	−	2.11233e11i	−0.901180	−	0.756179i	0.0692410	−	0.997600i	$-0.477942\pi$
$727$	−2.51738e11	−	2.11233e11i	−0.901180	−	0.756179i	−0.970421	+	0.241420i	$0.922387\pi$
$728$		−	4.39441e10i		−	0.156450i
$729$	−9.05508e10	−	2.67520e11i	−0.320614	−	0.947210i
$730$	3.46840e11			1.22134
$731$	−1.27237e11	+	1.51635e11i	−0.445597	+	0.531042i
$732$	2.63924e11	−	8.63487e10i	0.919252	−	0.300754i
$733$	2.63346e10	+	1.49351e11i	0.0912245	+	0.517360i	0.995839	+	0.0911292i	$0.0290476\pi$
$733$	2.63346e10	+	1.49351e11i	0.0912245	+	0.517360i	−0.904615	+	0.426230i	$0.859841\pi$
$734$	4.86214e10	−	1.33586e11i	0.167511	−	0.460233i
$735$	−1.80674e11	+	4.49819e11i	−0.619079	+	1.54130i
$736$	1.54749e10	−	8.77625e10i	0.0527371	−	0.299087i
$737$	−5.06337e10	−	2.92334e10i	−0.171621	−	0.0990852i
$738$	8.94472e10	−	6.55455e10i	0.301538	−	0.220962i
$739$	1.02390e11	+	1.77344e11i	0.343304	+	0.594620i	0.985044	−	0.172302i	$-0.0551205\pi$
$739$	1.02390e11	+	1.77344e11i	0.343304	+	0.594620i	−0.641740	+	0.766922i	$0.721787\pi$
$740$	1.02434e11	+	2.81436e11i	0.341601	+	0.938540i
$741$	1.21207e11	+	2.26842e11i	0.402027	+	0.752403i
$742$	4.20804e10	−	3.53097e10i	0.138824	−	0.116487i
$743$	2.49587e11	+	2.97446e11i	0.818967	+	0.976006i	0.999972	−	0.00747567i	$-0.00237960\pi$
$743$	2.49587e11	+	2.97446e11i	0.818967	+	0.976006i	−0.181005	+	0.983482i	$0.557935\pi$
$744$	−3.02300e9	+	9.19347e10i	−0.00986614	+	0.300046i
$745$	1.31361e11	−	4.78114e10i	0.426422	−	0.155205i
$746$	1.21601e11	−	7.02064e10i	0.392629	−	0.226684i
$747$	3.06995e10	−	4.66307e11i	0.0985937	−	1.49758i
$748$	2.14210e10	−	3.71023e10i	0.0684280	−	0.118521i
$749$	1.68150e11	+	2.96493e10i	0.534279	+	0.0942079i
$750$	−1.17175e11	−	8.21598e11i	−0.370330	−	2.59666i
$751$	2.17440e11	+	7.91418e10i	0.683566	+	0.248798i	0.660378	−	0.750933i	$-0.270396\pi$
$751$	2.17440e11	+	7.91418e10i	0.683566	+	0.248798i	0.0231881	+	0.999731i	$0.492618\pi$
$752$	2.49882e10	−	4.40609e9i	0.0781382	−	0.0137779i
$753$	−1.90457e11	−	4.00777e10i	−0.592403	−	0.124659i
$754$	1.06604e11	+	8.94511e10i	0.329828	+	0.276758i
$755$			5.02678e11i			1.54704i

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	54.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(7.27231 - 8.66680i) q^{2} +(-76.9844 + 25.1872i) q^{3} +(-22.2270 - 126.055i) q^{4} +(421.201 - 1157.24i) q^{5} +(-341.562 + 850.378i) q^{6} +(-165.220 + 937.012i) q^{7} +(-1254.14 - 724.077i) q^{8} +(5292.21 - 3878.04i) q^{9} +O(q^{10})\)	\(q+(7.27231 - 8.66680i) q^{2} +(-76.9844 + 25.1872i) q^{3} +(-22.2270 - 126.055i) q^{4} +(421.201 - 1157.24i) q^{5} +(-341.562 + 850.378i) q^{6} +(-165.220 + 937.012i) q^{7} +(-1254.14 - 724.077i) q^{8} +(5292.21 - 3878.04i) q^{9} +(-6966.47 - 12066.3i) q^{10} +(-1207.92 - 3318.74i) q^{11} +(4886.11 + 9144.47i) q^{12} +(24431.3 - 20500.3i) q^{13} +(6919.36 + 8246.17i) q^{14} +(-3278.29 + 99698.4i) q^{15} +(-15395.9 + 5603.66i) q^{16} +(-82073.6 + 47385.2i) q^{17} +(4876.35 - 74068.9i) q^{18} +(49779.7 - 86221.0i) q^{19} +(-155238. - 27372.7i) q^{20} +(-10881.3 - 76296.8i) q^{21} +(-37547.2 - 13666.1i) q^{22} +(-473461. + 83483.9i) q^{23} +(114787. + 24154.5i) q^{24} +(-862560. - 723774. i) q^{25} -360826. i q^{26} +(-309741. + 431845. i) q^{27} +121788. q^{28} +(-247907. + 295444. i) q^{29} +(840226. + 753450. i) q^{30} +(136171. + 772263. i) q^{31} +(-63398.2 + 174185. i) q^{32} +(176581. + 225067. i) q^{33} +(-186187. + 1.05592e6i) q^{34} +(1.01476e6 + 585870. i) q^{35} +(-606478. - 580915. i) q^{36} +(-949984. - 1.64542e6i) q^{37} +(-385247. - 1.05846e6i) q^{38} +(-1.36448e6 + 2.19356e6i) q^{39} +(-1.36618e6 + 1.14636e6i) q^{40} +(960268. + 1.14440e6i) q^{41} +(-740381. - 460548. i) q^{42} +(1.96272e6 - 714370. i) q^{43} +(-391496. + 226030. i) q^{44} +(-2.25875e6 - 7.75780e6i) q^{45} +(-2.71962e6 + 4.71051e6i) q^{46} +(-1.52516e6 - 268926. i) q^{47} +(1.04411e6 - 819175. i) q^{48} +(4.56645e6 + 1.66205e6i) q^{49} +(-1.25456e7 + 2.21213e6i) q^{50} +(5.12489e6 - 5.71513e6i) q^{51} +(-3.12720e6 - 2.62404e6i) q^{52} -5.10302e6i q^{53} +(1.49018e6 + 5.82497e6i) q^{54} -4.34936e6 q^{55} +(885678. - 1.05551e6i) q^{56} +(-1.66060e6 + 7.89148e6i) q^{57} +(757698. + 4.29712e6i) q^{58} +(-6.95884e6 + 1.91193e7i) q^{59} +(1.26404e7 - 1.80275e6i) q^{60} +(4.65089e6 - 2.63765e7i) q^{61} +(7.68333e6 + 4.43597e6i) q^{62} +(2.75939e6 + 5.59960e6i) q^{63} +(1.04858e6 + 1.81619e6i) q^{64} +(-1.34333e7 - 3.69076e7i) q^{65} +(3.23476e6 + 106366. i) q^{66} +(1.26817e7 - 1.06412e7i) q^{67} +(7.79741e6 + 9.29259e6i) q^{68} +(3.43464e7 - 1.83521e7i) q^{69} +(1.24573e7 - 4.53407e6i) q^{70} +(-1.46311e7 + 8.44725e6i) q^{71} +(-9.44517e6 + 1.03164e6i) q^{72} +(-1.24468e7 + 2.15584e7i) q^{73} +(-2.11691e7 - 3.73269e6i) q^{74} +(8.46335e7 + 3.39938e7i) q^{75} +(-1.19751e7 - 4.35857e6i) q^{76} +(3.30927e6 - 583513. i) q^{77} +(9.08818e6 + 2.77780e7i) q^{78} +(2.32815e7 + 1.95355e7i) q^{79} +2.01771e7i q^{80} +(1.29683e7 - 4.10469e7i) q^{81} +1.69017e7 q^{82} +(4.57835e7 - 5.45626e7i) q^{83} +(-9.37576e6 + 3.06749e6i) q^{84} +(2.02666e7 + 1.14938e8i) q^{85} +(8.08217e6 - 2.22056e7i) q^{86} +(1.16436e7 - 2.89887e7i) q^{87} +(-888121. + 5.03678e6i) q^{88} +(-3.94896e7 - 2.27993e7i) q^{89} +(-8.36616e7 - 3.68410e7i) q^{90} +(1.51725e7 + 2.62795e7i) q^{91} +(2.10472e7 + 5.78267e7i) q^{92} +(-2.99342e7 - 5.60225e7i) q^{93} +(-1.34222e7 + 1.12625e7i) q^{94} +(-7.88111e7 - 9.39235e7i) q^{95} +(493441. - 1.50064e7i) q^{96} +(-9.43260e7 + 3.43319e7i) q^{97} +(4.76133e7 - 2.74896e7i) q^{98} +(-1.92628e7 - 1.28791e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9 - 45756 * q^11 - 21504 * q^12 + 94464 * q^14 - 70002 * q^15 - 182784 * q^18 - 225792 * q^20 - 2071668 * q^21 + 185472 * q^22 + 552996 * q^23 - 1015182 * q^25 - 4137588 * q^27 - 2856132 * q^29 - 861696 * q^30 - 1841490 * q^31 + 10547334 * q^33 - 661248 * q^34 - 12450834 * q^35 - 5104128 * q^36 + 14063616 * q^38 + 4239102 * q^39 - 15673536 * q^41 - 11028480 * q^42 - 4412520 * q^43 - 12558942 * q^45 + 15173838 * q^47 + 3440640 * q^48 - 11347488 * q^49 - 27744768 * q^50 - 3281850 * q^51 + 16379136 * q^54 + 12091392 * q^56 - 13553658 * q^57 - 86547168 * q^59 - 26125056 * q^60 - 34059456 * q^61 + 108329070 * q^63 + 150994944 * q^64 + 22190346 * q^65 + 152091648 * q^66 + 167100948 * q^67 + 13411584 * q^68 - 40190130 * q^69 - 118080000 * q^70 - 251437608 * q^71 - 60948480 * q^72 + 15265278 * q^73 + 41902848 * q^74 + 138868662 * q^75 + 67995648 * q^76 + 564911586 * q^77 + 201203712 * q^78 + 137535768 * q^79 - 23838948 * q^81 - 482857578 * q^83 - 128300544 * q^84 - 343215000 * q^85 - 46237824 * q^86 + 34353810 * q^87 + 47480832 * q^88 + 375969762 * q^89 + 452712960 * q^90 - 155093598 * q^91 + 97042176 * q^92 + 285095622 * q^93 - 70995456 * q^94 - 966996432 * q^95 - 88080384 * q^96 - 484917300 * q^97 - 234233856 * q^98 + 26756370 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more