LMFDB - Embedded newform 48.8.k.a.11.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,8,Mod(11,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("48.11");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	48.k (of order $4$, degree $2$, 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:	$14.9944812232$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.13
Character	$\chi$	$=$	48.11
Dual form			48.8.k.a.35.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.71273 - 8.27730i) q^{2} +(-22.7540 + 40.8565i) q^{3} +(-9.02745 + 127.681i) q^{4} +(277.521 - 277.521i) q^{5} +(513.677 - 126.773i) q^{6} -1218.23 q^{7} +(1126.48 - 910.049i) q^{8} +(-1151.51 - 1859.30i) q^{9} +O(q^{10})$	\(q+(-7.71273 - 8.27730i) q^{2} +(-22.7540 + 40.8565i) q^{3} +(-9.02745 + 127.681i) q^{4} +(277.521 - 277.521i) q^{5} +(513.677 - 126.773i) q^{6} -1218.23 q^{7} +(1126.48 - 910.049i) q^{8} +(-1151.51 - 1859.30i) q^{9} +(-4437.56 - 156.679i) q^{10} +(2347.10 + 2347.10i) q^{11} +(-5011.20 - 3274.09i) q^{12} +(-1529.99 + 1529.99i) q^{13} +(9395.90 + 10083.7i) q^{14} +(5023.81 + 17653.2i) q^{15} +(-16221.0 - 2305.27i) q^{16} -8646.89i q^{17} +(-6508.73 + 23871.7i) q^{18} +(37924.6 + 37924.6i) q^{19} +(32928.9 + 37939.5i) q^{20} +(27719.7 - 49772.7i) q^{21} +(1325.10 - 37530.3i) q^{22} -36236.1i q^{23} +(11549.4 + 66731.4i) q^{24} -75910.4i q^{25} +(24464.6 + 863.780i) q^{26} +(102166. - 4739.94i) q^{27} +(10997.5 - 155545. i) q^{28} +(155043. + 155043. i) q^{29} +(107374. - 177738. i) q^{30} +272100. i q^{31} +(106027. + 152046. i) q^{32} +(-149301. + 42488.3i) q^{33} +(-71572.9 + 66691.2i) q^{34} +(-338085. + 338085. i) q^{35} +(247793. - 130241. i) q^{36} +(328291. + 328291. i) q^{37} +(21411.0 - 606416. i) q^{38} +(-27696.5 - 97323.3i) q^{39} +(60064.9 - 565179. i) q^{40} -330887. q^{41} +(-625779. + 154439. i) q^{42} +(-208399. + 208399. i) q^{43} +(-320869. + 278493. i) q^{44} +(-835561. - 196427. i) q^{45} +(-299937. + 279480. i) q^{46} +688832. q^{47} +(463279. - 610279. i) q^{48} +660547. q^{49} +(-628333. + 585477. i) q^{50} +(353282. + 196752. i) q^{51} +(-181539. - 209163. i) q^{52} +(205084. - 205084. i) q^{53} +(-827213. - 809101. i) q^{54} +1.30274e6 q^{55} +(-1.37232e6 + 1.10865e6i) q^{56} +(-2.41241e6 + 686529. i) q^{57} +(87532.4 - 2.47915e6i) q^{58} +(-1.17688e6 - 1.17688e6i) q^{59} +(-2.29934e6 + 482082. i) q^{60} +(1.05104e6 - 1.05104e6i) q^{61} +(2.25225e6 - 2.09863e6i) q^{62} +(1.40280e6 + 2.26506e6i) q^{63} +(440774. - 2.05031e6i) q^{64} +849206. i q^{65} +(1.50320e6 + 908104. i) q^{66} +(-754388. - 754388. i) q^{67} +(1.10405e6 + 78059.4i) q^{68} +(1.48048e6 + 824519. i) q^{69} +(5.40599e6 + 190871. i) q^{70} +3.03773e6i q^{71} +(-2.98921e6 - 1.04654e6i) q^{72} +390543. i q^{73} +(185343. - 5.24939e6i) q^{74} +(3.10143e6 + 1.72727e6i) q^{75} +(-5.18463e6 + 4.49990e6i) q^{76} +(-2.85932e6 - 2.85932e6i) q^{77} +(-591958. + 979881. i) q^{78} +523824. i q^{79} +(-5.14143e6 + 3.86190e6i) q^{80} +(-2.13103e6 + 4.28200e6i) q^{81} +(2.55204e6 + 2.73885e6i) q^{82} +(3.62937e6 - 3.62937e6i) q^{83} +(6.10481e6 + 3.98861e6i) q^{84} +(-2.39969e6 - 2.39969e6i) q^{85} +(3.33231e6 + 117655. i) q^{86} +(-9.86239e6 + 2.80667e6i) q^{87} +(4.77995e6 + 507993. i) q^{88} +2.33636e6 q^{89} +(4.81857e6 + 8.43119e6i) q^{90} +(1.86388e6 - 1.86388e6i) q^{91} +(4.62668e6 + 327120. i) q^{92} +(-1.11170e7 - 6.19136e6i) q^{93} +(-5.31278e6 - 5.70167e6i) q^{94} +2.10497e7 q^{95} +(-8.62461e6 + 872224. i) q^{96} +4.76805e6 q^{97} +(-5.09463e6 - 5.46755e6i) q^{98} +(1.66127e6 - 7.06668e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7}+O(q^{10}) $ 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7	$ 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7} - 6504 q^{10} + 12016 q^{12} - 4 q^{13} - 55280 q^{16} + 21172 q^{18} - 60588 q^{19} - 4376 q^{21} - 212744 q^{22} - 317304 q^{24} + 238042 q^{27} + 219736 q^{28} - 503852 q^{30} - 4 q^{33} - 364856 q^{34} + 867620 q^{36} - 4 q^{37} - 283948 q^{39} + 390392 q^{40} - 3022344 q^{42} + 752844 q^{43} - 156252 q^{45} - 1166824 q^{46} + 358320 q^{48} + 9882508 q^{49} + 1121592 q^{51} - 4458688 q^{52} + 203816 q^{54} + 4191000 q^{55} + 4975544 q^{58} - 4390240 q^{60} - 2279892 q^{61} + 4781432 q^{64} + 1457476 q^{66} + 1552540 q^{67} + 4372 q^{69} - 9366152 q^{70} - 1660280 q^{72} - 886066 q^{75} - 6569272 q^{76} - 13616772 q^{78} - 4 q^{81} + 11560256 q^{82} - 10944176 q^{84} + 7846496 q^{85} - 40789116 q^{87} + 24614816 q^{88} + 25746032 q^{90} - 1590680 q^{91} - 14495396 q^{93} - 6995856 q^{94} - 13927736 q^{96} - 8 q^{97} - 4701076 q^{99}+O(q^{100}) $ 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7 - 6504 * q^10 + 12016 * q^12 - 4 * q^13 - 55280 * q^16 + 21172 * q^18 - 60588 * q^19 - 4376 * q^21 - 212744 * q^22 - 317304 * q^24 + 238042 * q^27 + 219736 * q^28 - 503852 * q^30 - 4 * q^33 - 364856 * q^34 + 867620 * q^36 - 4 * q^37 - 283948 * q^39 + 390392 * q^40 - 3022344 * q^42 + 752844 * q^43 - 156252 * q^45 - 1166824 * q^46 + 358320 * q^48 + 9882508 * q^49 + 1121592 * q^51 - 4458688 * q^52 + 203816 * q^54 + 4191000 * q^55 + 4975544 * q^58 - 4390240 * q^60 - 2279892 * q^61 + 4781432 * q^64 + 1457476 * q^66 + 1552540 * q^67 + 4372 * q^69 - 9366152 * q^70 - 1660280 * q^72 - 886066 * q^75 - 6569272 * q^76 - 13616772 * q^78 - 4 * q^81 + 11560256 * q^82 - 10944176 * q^84 + 7846496 * q^85 - 40789116 * q^87 + 24614816 * q^88 + 25746032 * q^90 - 1590680 * q^91 - 14495396 * q^93 - 6995856 * q^94 - 13927736 * q^96 - 8 * q^97 - 4701076 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−7.71273	−	8.27730i	−0.681716	−	0.731617i
$2$	−7.71273	−	8.27730i	−0.681716	−	0.731617i
$3$	−22.7540	+	40.8565i	−0.486557	+	0.873649i
$3$	−22.7540	+	40.8565i	−0.486557	+	0.873649i
$4$	−9.02745	+	127.681i	−0.0705269	+	0.997510i
$5$	277.521	−	277.521i	0.992888	−	0.992888i	−0.00708691	−	0.999975i	$-0.502256\pi$
$5$	277.521	−	277.521i	0.992888	−	0.992888i	0.999975	+	0.00708691i	$0.00225585\pi$
$6$	513.677	−	126.773i	0.970870	−	0.239606i
$7$	−1218.23			−1.34242			−0.671208	−	0.741269i	$-0.734224\pi$
$7$	−1218.23			−1.34242			−0.671208	+	0.741269i	$0.734224\pi$
$8$	1126.48	−	910.049i	0.777875	−	0.628420i
$9$	−1151.51	−	1859.30i	−0.526524	−	0.850161i
$10$	−4437.56	−	156.679i	−1.40328	−	0.0495463i
$11$	2347.10	+	2347.10i	0.531689	+	0.531689i	0.921075	−	0.389386i	$-0.127313\pi$
$11$	2347.10	+	2347.10i	0.531689	+	0.531689i	−0.389386	+	0.921075i	$0.627313\pi$
$12$	−5011.20	−	3274.09i	−0.837158	−	0.546962i
$13$	−1529.99	+	1529.99i	−0.193146	+	0.193146i	−0.797054	−	0.603908i	$-0.793609\pi$
$13$	−1529.99	+	1529.99i	−0.193146	+	0.193146i	0.603908	+	0.797054i	$0.293609\pi$
$14$	9395.90	+	10083.7i	0.915146	+	0.982134i
$15$	5023.81	+	17653.2i	0.384338	+	1.35053i
$16$	−16221.0	−	2305.27i	−0.990052	−	0.140703i
$17$		−	8646.89i		−	0.426863i	−0.976958	−	0.213432i	$-0.931536\pi$
$17$		−	8646.89i		−	0.426863i	0.976958	−	0.213432i	$-0.0684641\pi$
$18$	−6508.73	+	23871.7i	−0.263052	+	0.964782i
$19$	37924.6	+	37924.6i	1.26848	+	1.26848i	0.946873	+	0.321607i	$0.104223\pi$
$19$	37924.6	+	37924.6i	1.26848	+	1.26848i	0.321607	+	0.946873i	$0.395777\pi$
$20$	32928.9	+	37939.5i	0.920390	+	1.06044i
$21$	27719.7	−	49772.7i	0.653162	−	1.17280i
$22$	1325.10	−	37530.3i	0.0265319	−	0.751454i
$23$		−	36236.1i		−	0.621004i	−0.950573	−	0.310502i	$-0.899503\pi$
$23$		−	36236.1i		−	0.621004i	0.950573	−	0.310502i	$-0.100497\pi$
$24$	11549.4	+	66731.4i	0.170537	+	0.985351i
$25$		−	75910.4i		−	0.971653i
$26$	24464.6	+	863.780i	0.272980	+	0.00963821i
$27$	102166.	−	4739.94i	0.998926	−	0.0463446i
$28$	10997.5	−	155545.i	0.0946765	−	1.33907i
$29$	155043.	+	155043.i	1.18048	+	1.18048i	0.979619	+	0.200865i	$0.0643754\pi$
$29$	155043.	+	155043.i	1.18048	+	1.18048i	0.200865	+	0.979619i	$0.435625\pi$
$30$	107374.	−	177738.i	0.726063	−	1.20187i
$31$			272100.i			1.64045i	0.572044	+	0.820223i	$0.306151\pi$
$31$			272100.i			1.64045i	−0.572044	+	0.820223i	$0.693849\pi$
$32$	106027.	+	152046.i	0.571994	+	0.820258i
$33$	−149301.	+	42488.3i	−0.723207	+	0.205812i
$34$	−71572.9	+	66691.2i	−0.312300	+	0.290999i
$35$	−338085.	+	338085.i	−1.33287	+	1.33287i
$36$	247793.	−	130241.i	0.885178	−	0.465253i
$37$	328291.	+	328291.i	1.06550	+	1.06550i	0.997699	+	0.0678014i	$0.0215984\pi$
$37$	328291.	+	328291.i	1.06550	+	1.06550i	0.0678014	+	0.997699i	$0.478402\pi$
$38$	21411.0	−	606416.i	0.0632986	−	1.79278i
$39$	−27696.5	−	97323.3i	−0.0747652	−	0.262719i
$40$	60064.9	−	565179.i	0.148392	−	1.39629i
$41$	−330887.			−0.749784			−0.374892	−	0.927069i	$-0.622320\pi$
$41$	−330887.			−0.749784			−0.374892	+	0.927069i	$0.622320\pi$
$42$	−625779.	+	154439.i	−1.30331	+	0.321651i
$43$	−208399.	+	208399.i	−0.399720	+	0.399720i	−0.878134	−	0.478414i	$-0.841212\pi$
$43$	−208399.	+	208399.i	−0.399720	+	0.399720i	0.478414	+	0.878134i	$0.341212\pi$
$44$	−320869.	+	278493.i	−0.567864	+	0.492867i
$45$	−835561.	−	196427.i	−1.36689	−	0.321335i
$46$	−299937.	+	279480.i	−0.454337	+	0.423348i
$47$	688832.			0.967767			0.483883	−	0.875133i	$-0.339226\pi$
$47$	688832.			0.967767			0.483883	+	0.875133i	$0.339226\pi$
$48$	463279.	−	610279.i	0.604642	−	0.796498i
$49$	660547.			0.802080
$50$	−628333.	+	585477.i	−0.710878	+	0.662391i
$51$	353282.	+	196752.i	0.372928	+	0.207694i
$52$	−181539.	−	209163.i	−0.179043	−	0.206287i
$53$	205084.	−	205084.i	0.189220	−	0.189220i	−0.606139	−	0.795359i	$-0.707283\pi$
$53$	205084.	−	205084.i	0.189220	−	0.189220i	0.795359	+	0.606139i	$0.207283\pi$
$54$	−827213.	−	809101.i	−0.714890	−	0.699237i
$55$	1.30274e6			1.05582
$56$	−1.37232e6	+	1.10865e6i	−1.04423	+	0.843600i
$57$	−2.41241e6	+	686529.i	−1.72539	+	0.491017i
$58$	87532.4	−	2.47915e6i	0.0589075	−	1.66842i
$59$	−1.17688e6	−	1.17688e6i	−0.746019	−	0.746019i	0.227710	−	0.973729i	$-0.426876\pi$
$59$	−1.17688e6	−	1.17688e6i	−0.746019	−	0.746019i	−0.973729	+	0.227710i	$0.926876\pi$
$60$	−2.29934e6	+	482082.i	−1.37428	+	0.288132i
$61$	1.05104e6	−	1.05104e6i	0.592877	−	0.592877i	−0.345531	−	0.938408i	$-0.612301\pi$
$61$	1.05104e6	−	1.05104e6i	0.592877	−	0.592877i	0.938408	+	0.345531i	$0.112301\pi$
$62$	2.25225e6	−	2.09863e6i	1.20018	−	1.11832i
$63$	1.40280e6	+	2.26506e6i	0.706814	+	1.14127i
$64$	440774.	−	2.05031e6i	0.210178	−	0.977663i
$65$			849206.i			0.383545i
$66$	1.50320e6	+	908104.i	0.643597	+	0.388805i
$67$	−754388.	−	754388.i	−0.306431	−	0.306431i	0.537092	−	0.843523i	$-0.319523\pi$
$67$	−754388.	−	754388.i	−0.306431	−	0.306431i	−0.843523	+	0.537092i	$0.819523\pi$
$68$	1.10405e6	+	78059.4i	0.425800	+	0.0301054i
$69$	1.48048e6	+	824519.i	0.542539	+	0.302154i
$70$	5.40599e6	+	190871.i	1.88379	+	0.0665117i
$71$			3.03773e6i			1.00727i	0.863917	+	0.503634i	$0.168004\pi$
$71$			3.03773e6i			1.00727i	−0.863917	+	0.503634i	$0.831996\pi$
$72$	−2.98921e6	−	1.04654e6i	−0.943827	−	0.330440i
$73$			390543.i			0.117500i	0.998273	+	0.0587501i	$0.0187115\pi$
$73$			390543.i			0.117500i	−0.998273	+	0.0587501i	$0.981288\pi$
$74$	185343.	−	5.24939e6i	0.0531697	−	1.50591i
$75$	3.10143e6	+	1.72727e6i	0.848883	+	0.472765i
$76$	−5.18463e6	+	4.49990e6i	−1.35478	+	1.17586i
$77$	−2.85932e6	−	2.85932e6i	−0.713748	−	0.713748i
$78$	−591958.	+	979881.i	−0.141241	+	0.233799i
$79$			523824.i			0.119534i	0.998212	+	0.0597669i	$0.0190357\pi$
$79$			523824.i			0.119534i	−0.998212	+	0.0597669i	$0.980964\pi$
$80$	−5.14143e6	+	3.86190e6i	−1.12271	+	0.843309i
$81$	−2.13103e6	+	4.28200e6i	−0.445546	+	0.895259i
$82$	2.55204e6	+	2.73885e6i	0.511140	+	0.548555i
$83$	3.62937e6	−	3.62937e6i	0.696720	−	0.696720i	−0.266981	−	0.963702i	$-0.586026\pi$
$83$	3.62937e6	−	3.62937e6i	0.696720	−	0.696720i	0.963702	+	0.266981i	$0.0860262\pi$
$84$	6.10481e6	+	3.98861e6i	1.12381	+	0.734250i
$85$	−2.39969e6	−	2.39969e6i	−0.423827	−	0.423827i
$86$	3.33231e6	+	117655.i	0.564938	+	0.0199465i
$87$	−9.86239e6	+	2.80667e6i	−1.60570	+	0.456955i
$88$	4.77995e6	+	507993.i	0.747711	+	0.0794636i
$89$	2.33636e6			0.351297			0.175648	−	0.984453i	$-0.443798\pi$
$89$	2.33636e6			0.351297			0.175648	+	0.984453i	$0.443798\pi$
$90$	4.81857e6	+	8.43119e6i	0.696738	+	1.21910i
$91$	1.86388e6	−	1.86388e6i	0.259282	−	0.259282i
$92$	4.62668e6	+	327120.i	0.619458	+	0.0437975i
$93$	−1.11170e7	−	6.19136e6i	−1.43317	−	0.798171i
$94$	−5.31278e6	−	5.70167e6i	−0.659742	−	0.708035i
$95$	2.10497e7			2.51892
$96$	−8.62461e6	+	872224.i	−0.994925	+	0.100619i
$97$	4.76805e6			0.530444			0.265222	−	0.964187i	$-0.414555\pi$
$97$	4.76805e6			0.530444			0.265222	+	0.964187i	$0.414555\pi$
$98$	−5.09463e6	−	5.46755e6i	−0.546791	−	0.586815i
$99$	1.66127e6	−	7.06668e6i	0.172074	−	0.731968i
$100$	9.69234e6	+	685277.i	0.969234	+	0.0685277i
$101$	−5.84937e6	+	5.84937e6i	−0.564916	+	0.564916i	−0.930700	−	0.365784i	$-0.880801\pi$
$101$	−5.84937e6	+	5.84937e6i	−0.564916	+	0.564916i	0.365784	+	0.930700i	$0.380801\pi$
$102$	−1.09619e6	−	4.44171e6i	−0.102279	−	0.414429i
$103$	7.02521e6			0.633474			0.316737	−	0.948513i	$-0.397413\pi$
$103$	7.02521e6			0.633474			0.316737	+	0.948513i	$0.397413\pi$
$104$	−331141.	+	3.11587e6i	−0.0288666	+	0.271620i
$105$	−6.12016e6	−	2.15057e7i	−0.515941	−	1.81298i
$106$	−3.27930e6	−	115784.i	−0.267430	−	0.00944227i
$107$	1.07383e7	+	1.07383e7i	0.847408	+	0.847408i	0.989809	−	0.142401i	$-0.0454824\pi$
$107$	1.07383e7	+	1.07383e7i	0.847408	+	0.847408i	−0.142401	+	0.989809i	$0.545482\pi$
$108$	−317097.	+	1.30875e7i	−0.0242219	+	0.999707i
$109$	1.70072e6	−	1.70072e6i	0.125789	−	0.125789i	−0.641410	−	0.767198i	$-0.721650\pi$
$109$	1.70072e6	−	1.70072e6i	0.125789	−	0.125789i	0.767198	+	0.641410i	$0.221650\pi$
$110$	−1.00477e7	−	1.07832e7i	−0.719766	−	0.772453i
$111$	−2.08828e7	+	5.94288e6i	−1.44930	+	0.412446i
$112$	1.97610e7	+	2.80836e6i	1.32906	+	0.188881i
$113$		−	1.56001e7i		−	1.01708i	−0.861040	−	0.508538i	$-0.830186\pi$
$113$		−	1.56001e7i		−	1.01708i	0.861040	−	0.508538i	$-0.169814\pi$
$114$	2.42889e7	+	1.46732e7i	1.53547	+	0.927594i
$115$	−1.00563e7	−	1.00563e7i	−0.616588	−	0.616588i
$116$	−2.11958e7	+	1.83965e7i	−1.26080	+	1.09429i
$117$	4.60650e6	+	1.08292e6i	0.265901	+	0.0625092i
$118$	−664427.	+	1.88183e7i	−0.0372272	+	1.05437i
$119$			1.05339e7i			0.573028i
$120$	2.17245e7	+	1.53142e7i	1.14767	+	0.809019i
$121$		−	8.46938e6i		−	0.434613i
$122$	−1.68062e7	−	593382.i	−0.837933	−	0.0295852i
$123$	7.52901e6	−	1.35189e7i	0.364813	−	0.655048i
$124$	−3.47420e7	−	2.45636e6i	−1.63636	−	0.115696i
$125$	614598.	+	614598.i	0.0281453	+	0.0281453i
$126$	7.92914e6	−	2.90812e7i	0.353126	−	1.29514i
$127$			1.31830e7i			0.571087i	0.958366	+	0.285543i	$0.0921741\pi$
$127$			1.31830e7i			0.571087i	−0.958366	+	0.285543i	$0.907826\pi$
$128$	−2.03706e7	+	1.21651e7i	−0.858556	+	0.512719i
$129$	−3.77253e6	−	1.32564e7i	−0.154728	−	0.543702i
$130$	7.02913e6	−	6.54970e6i	0.280608	−	0.261469i
$131$	6.27937e6	−	6.27937e6i	0.244043	−	0.244043i	−0.574477	−	0.818521i	$-0.694795\pi$
$131$	6.27937e6	−	6.27937e6i	0.244043	−	0.244043i	0.818521	+	0.574477i	$0.194795\pi$
$132$	−4.07716e6	−	1.94464e7i	−0.154294	−	0.735921i
$133$	−4.62010e7	−	4.62010e7i	−1.70283	−	1.70283i
$134$	−425902.	+	1.20627e7i	−0.0152913	+	0.433089i
$135$	2.70377e7	−	2.96686e7i	0.945806	−	1.03784i
$136$	−7.86909e6	−	9.74057e6i	−0.268249	−	0.332046i
$137$	−2.74998e7			−0.913709			−0.456855	−	0.889541i	$-0.651024\pi$
$137$	−2.74998e7			−0.913709			−0.456855	+	0.889541i	$0.651024\pi$
$138$	−4.59377e6	−	1.86137e7i	−0.148797	−	0.602914i
$139$	−4.22013e7	+	4.22013e7i	−1.33283	+	1.33283i	−0.429996	+	0.902831i	$0.641485\pi$
$139$	−4.22013e7	+	4.22013e7i	−1.33283	+	1.33283i	−0.902831	+	0.429996i	$0.858515\pi$
$140$	−4.01150e7	−	4.62191e7i	−1.23555	−	1.42355i
$141$	−1.56737e7	+	2.81433e7i	−0.470874	+	0.845488i
$142$	2.51442e7	−	2.34292e7i	0.736934	−	0.686670i
$143$	−7.18208e6			−0.205387
$144$	1.43924e7	+	3.28143e7i	0.401666	+	0.915786i
$145$	8.60555e7			2.34418
$146$	3.23264e6	−	3.01215e6i	0.0859652	−	0.0801018i
$147$	−1.50301e7	+	2.69877e7i	−0.390258	+	0.700736i
$148$	−4.48803e7	+	3.89530e7i	−1.13799	+	0.987701i
$149$	5.97426e6	−	5.97426e6i	0.147956	−	0.147956i	−0.629248	−	0.777204i	$-0.716637\pi$
$149$	5.97426e6	−	5.97426e6i	0.147956	−	0.147956i	0.777204	+	0.629248i	$0.216637\pi$
$150$	−9.62341e6	−	3.89935e7i	−0.232814	−	0.943349i
$151$	1.94550e7			0.459846			0.229923	−	0.973209i	$-0.426153\pi$
$151$	1.94550e7			0.459846			0.229923	+	0.973209i	$0.426153\pi$
$152$	7.72347e7	+	8.20817e6i	1.78386	+	0.189581i
$153$	−1.60772e7	+	9.95696e6i	−0.362902	+	0.224754i
$154$	−1.61428e6	+	4.57206e7i	−0.0356168	+	1.00876i
$155$	7.55132e7	+	7.55132e7i	1.62878	+	1.62878i
$156$	1.26764e7	−	2.65775e6i	0.267337	−	0.0560502i
$157$	−3.87344e7	+	3.87344e7i	−0.798819	+	0.798819i	−0.982909	−	0.184091i	$-0.941066\pi$
$157$	−3.87344e7	+	3.87344e7i	−0.798819	+	0.798819i	0.184091	+	0.982909i	$0.441066\pi$
$158$	4.33585e6	−	4.04011e6i	0.0874529	−	0.0814880i
$159$	3.71252e6	+	1.30455e7i	0.0732452	+	0.257378i
$160$	7.16206e7	+	1.27713e7i	1.38235	+	0.246499i
$161$			4.41440e7i			0.833646i
$162$	5.18795e7	−	1.53867e7i	0.958722	−	0.284344i
$163$	−6.40070e7	−	6.40070e7i	−1.15763	−	1.15763i	−0.984983	−	0.172650i	$-0.944767\pi$
$163$	−6.40070e7	−	6.40070e7i	−1.15763	−	1.15763i	−0.172650	−	0.984983i	$-0.555233\pi$
$164$	2.98706e6	−	4.22481e7i	0.0528800	−	0.747917i
$165$	−2.96426e7	+	5.32254e7i	−0.513715	+	0.922412i
$166$	−5.80338e7	−	2.04903e6i	−0.984698	−	0.0347671i
$167$		−	2.37871e7i		−	0.395216i	−0.980281	−	0.197608i	$-0.936683\pi$
$167$		−	2.37871e7i		−	0.395216i	0.980281	−	0.197608i	$-0.0633173\pi$
$168$	−1.40698e7	−	8.12944e7i	−0.228932	−	1.32275i
$169$			5.80668e7i			0.925389i
$170$	−1.35479e6	+	3.83711e7i	−0.0211495	+	0.599009i
$171$	2.68428e7	−	1.14184e8i	0.410527	−	1.74630i
$172$	−2.47273e7	−	2.84900e7i	−0.370534	−	0.426916i
$173$	2.29993e7	+	2.29993e7i	0.337717	+	0.337717i	0.855508	−	0.517790i	$-0.173245\pi$
$173$	2.29993e7	+	2.29993e7i	0.337717	+	0.337717i	−0.517790	+	0.855508i	$0.673245\pi$
$174$	9.92976e7	+	5.99869e7i	1.42895	+	0.863245i
$175$			9.24765e7i			1.30436i
$176$	−3.26617e7	−	4.34831e7i	−0.451590	−	0.601210i
$177$	7.48619e7	−	2.13044e7i	1.01474	−	0.288777i
$178$	−1.80197e7	−	1.93387e7i	−0.239485	−	0.257015i
$179$	8.58655e7	−	8.58655e7i	1.11901	−	1.11901i	0.127120	−	0.991887i	$-0.459427\pi$
$179$	8.58655e7	−	8.58655e7i	1.11901	−	1.11901i	0.991887	−	0.127120i	$-0.0405735\pi$
$180$	3.26231e7	−	1.04912e8i	0.416938	−	1.34083i
$181$	9.96688e7	+	9.96688e7i	1.24935	+	1.24935i	0.956007	+	0.293343i	$0.0947678\pi$
$181$	9.96688e7	+	9.96688e7i	1.24935	+	1.24935i	0.293343	+	0.956007i	$0.405232\pi$
$182$	−2.98035e7	−	1.05229e6i	−0.366452	−	0.0129385i
$183$	1.90264e7	+	6.68572e7i	0.229497	+	0.806435i
$184$	−3.29767e7	−	4.08194e7i	−0.390251	−	0.483063i
$185$	1.82215e8			2.11584
$186$	3.44949e7	+	1.39771e8i	0.393061	+	1.59266i
$187$	2.02951e7	−	2.02951e7i	0.226959	−	0.226959i
$188$	−6.21839e6	+	8.79509e7i	−0.0682536	+	0.965357i
$189$	−1.24462e8	+	5.77435e6i	−1.34097	+	0.0622138i
$190$	−1.62351e8	−	1.74235e8i	−1.71719	−	1.84288i
$191$	−1.39519e8			−1.44883			−0.724414	−	0.689365i	$-0.757890\pi$
$191$	−1.39519e8			−1.44883			−0.724414	+	0.689365i	$0.757890\pi$
$192$	7.37390e7	+	6.46613e7i	0.751871	+	0.659311i
$193$	3.82483e7			0.382967			0.191484	−	0.981496i	$-0.438670\pi$
$193$	3.82483e7			0.382967			0.191484	+	0.981496i	$0.438670\pi$
$194$	−3.67747e7	−	3.94666e7i	−0.361612	−	0.388082i
$195$	−3.46956e7	−	1.93229e7i	−0.335084	−	0.186617i
$196$	−5.96306e6	+	8.43395e7i	−0.0565682	+	0.800083i
$197$	8.87636e7	−	8.87636e7i	0.827186	−	0.827186i	−0.159941	−	0.987127i	$-0.551130\pi$
$197$	8.87636e7	−	8.87636e7i	0.827186	−	0.827186i	0.987127	+	0.159941i	$0.0511303\pi$
$198$	−7.13059e7	+	4.07526e7i	−0.652826	+	0.373102i
$199$	−8.54053e6			−0.0768244			−0.0384122	−	0.999262i	$-0.512230\pi$
$199$	−8.54053e6			−0.0768244			−0.0384122	+	0.999262i	$0.512230\pi$
$200$	−6.90822e7	−	8.55117e7i	−0.610606	−	0.755824i
$201$	4.79870e7	−	1.36563e7i	0.416809	−	0.118617i
$202$	9.35316e7	+	3.30236e6i	0.798415	+	0.0281900i
$203$	−1.88879e8	−	1.88879e8i	−1.58470	−	1.58470i
$204$	−2.83107e7	+	4.33313e7i	−0.233478	+	0.357352i
$205$	−9.18279e7	+	9.18279e7i	−0.744451	+	0.744451i
$206$	−5.41835e7	−	5.81497e7i	−0.431849	−	0.463460i
$207$	−6.73739e7	+	4.17262e7i	−0.527953	+	0.326973i
$208$	2.83450e7	−	2.12909e7i	0.218401	−	0.164049i
$209$			1.78026e8i			1.34887i
$210$	−1.30806e8	+	2.16527e8i	−0.974678	+	1.61341i
$211$	−1.70799e7	−	1.70799e7i	−0.125169	−	0.125169i	0.641747	−	0.766916i	$-0.278210\pi$
$211$	−1.70799e7	−	1.70799e7i	−0.125169	−	0.125169i	−0.766916	+	0.641747i	$0.778210\pi$
$212$	2.43340e7	+	2.80368e7i	0.175403	+	0.202093i
$213$	−1.24111e8	−	6.91206e7i	−0.879998	−	0.490093i
$214$	6.06249e6	−	1.71706e8i	0.0422866	−	1.19767i
$215$			1.15670e8i			0.793755i
$216$	1.10775e8	−	9.83155e7i	0.747915	−	0.663795i
$217$		−	3.31480e8i		−	2.20216i
$218$	−2.71946e7	−	960173.i	−0.177781	−	0.00627699i
$219$	−1.59562e7	−	8.88643e6i	−0.102654	−	0.0571706i
$220$	−1.17604e7	+	1.66335e8i	−0.0744634	+	1.05319i
$221$	1.32296e7	+	1.32296e7i	0.0824470	+	0.0824470i
$222$	2.10254e8	+	1.27017e8i	1.28976	+	0.779162i
$223$			2.54830e8i			1.53880i	0.638766	+	0.769401i	$0.279445\pi$
$223$			2.54830e8i			1.53880i	−0.638766	+	0.769401i	$0.720555\pi$
$224$	−1.29165e8	−	1.85228e8i	−0.767853	−	1.10113i
$225$	−1.41140e8	+	8.74114e7i	−0.826061	+	0.511598i
$226$	−1.29127e8	+	1.20319e8i	−0.744109	+	0.693356i
$227$	−1.68087e8	+	1.68087e8i	−0.953770	+	0.953770i	−0.998978	−	0.0452075i	$-0.985605\pi$
$227$	−1.68087e8	+	1.68087e8i	−0.953770	+	0.953770i	0.0452075	+	0.998978i	$0.485605\pi$
$228$	−6.58790e7	−	3.14217e8i	−0.368108	−	1.75573i
$229$	−1.48568e8	−	1.48568e8i	−0.817526	−	0.817526i	0.168223	−	0.985749i	$-0.446197\pi$
$229$	−1.48568e8	−	1.48568e8i	−0.817526	−	0.817526i	−0.985749	+	0.168223i	$0.946197\pi$
$230$	−5.67744e6	+	1.60800e8i	−0.0307684	+	0.871443i
$231$	1.81883e8	−	5.17607e7i	0.970844	−	0.276285i
$232$	3.15751e8	+	3.35566e7i	1.66011	+	0.176429i
$233$	1.13316e7			0.0586873			0.0293437	−	0.999569i	$-0.490658\pi$
$233$	1.13316e7			0.0586873			0.0293437	+	0.999569i	$0.490658\pi$
$234$	−2.65651e7	−	4.64816e7i	−0.135536	−	0.237151i
$235$	1.91165e8	−	1.91165e8i	0.960884	−	0.960884i
$236$	1.60890e8	−	1.39641e8i	0.796776	−	0.691547i
$237$	−2.14016e7	−	1.19191e7i	−0.104430	−	0.0581600i
$238$	8.71925e7	−	8.12454e7i	0.419237	−	0.390642i
$239$	−1.04271e8			−0.494051			−0.247025	−	0.969009i	$-0.579453\pi$
$239$	−1.04271e8			−0.494051			−0.247025	+	0.969009i	$0.579453\pi$
$240$	−4.07957e7	−	2.97935e8i	−0.190491	−	1.39117i
$241$	2.49004e8			1.14590			0.572950	−	0.819590i	$-0.305799\pi$
$241$	2.49004e8			1.14590			0.572950	+	0.819590i	$0.305799\pi$
$242$	−7.01036e7	+	6.53221e7i	−0.317970	+	0.296283i
$243$	−1.26458e8	−	1.84499e8i	−0.565358	−	0.824845i
$244$	1.24710e8	+	1.43686e8i	0.549587	+	0.633214i
$245$	1.83316e8	−	1.83316e8i	0.796376	−	0.796376i
$246$	−1.69969e8	+	4.19476e7i	−0.727943	+	0.179653i
$247$	−1.16048e8			−0.490004
$248$	2.47624e8	+	3.06515e8i	1.03089	+	1.27606i
$249$	6.57006e7	+	2.30866e8i	0.269694	+	0.947683i
$250$	346982.	−	9.82745e6i	0.00140448	−	0.0397787i
$251$	2.64707e6	+	2.64707e6i	0.0105659	+	0.0105659i	0.712370	−	0.701804i	$-0.247622\pi$
$251$	2.64707e6	+	2.64707e6i	0.0105659	+	0.0105659i	−0.701804	+	0.712370i	$0.747622\pi$
$252$	−3.01870e8	+	1.58664e8i	−1.18828	+	0.624563i
$253$	8.50500e7	−	8.50500e7i	0.330181	−	0.330181i
$254$	1.09120e8	−	1.01677e8i	0.417817	−	0.389319i
$255$	1.52646e8	−	4.34403e7i	0.576493	−	0.164060i
$256$	2.57807e8	+	7.47877e7i	0.960406	+	0.278606i
$257$		−	2.23477e7i		−	0.0821235i	−0.999157	−	0.0410618i	$-0.986926\pi$
$257$		−	2.23477e7i		−	0.0821235i	0.999157	−	0.0410618i	$-0.0130740\pi$
$258$	−8.06305e7	+	1.33469e8i	−0.292301	+	0.483852i
$259$	−3.99935e8	−	3.99935e8i	−1.43034	−	1.43034i
$260$	−1.08428e8	−	7.66616e6i	−0.382590	−	0.0270503i
$261$	1.09739e8	−	4.66806e8i	0.382048	−	1.62515i
$262$	−1.00407e8	−	3.54513e6i	−0.344914	−	0.0121780i
$263$		−	1.73074e8i		−	0.586659i	−0.956011	−	0.293330i	$-0.905237\pi$
$263$		−	1.73074e8i		−	0.586659i	0.956011	−	0.293330i	$-0.0947633\pi$
$264$	−1.29518e8	+	1.83733e8i	−0.433228	+	0.614573i
$265$		−	1.13830e8i		−	0.375748i
$266$	−2.60836e7	+	7.38756e8i	−0.0849731	+	2.40666i
$267$	−5.31616e7	+	9.54554e7i	−0.170926	+	0.306910i
$268$	1.03131e8	−	8.95110e7i	0.327280	−	0.284056i
$269$	1.80531e8	+	1.80531e8i	0.565481	+	0.565481i	0.930859	−	0.365378i	$-0.119060\pi$
$269$	1.80531e8	+	1.80531e8i	0.565481	+	0.565481i	−0.365378	+	0.930859i	$0.619060\pi$
$270$	−4.54111e8	+	5.02652e6i	−1.40407	+	0.0155416i
$271$		−	8.15682e7i		−	0.248959i	−0.992222	−	0.124480i	$-0.960274\pi$
$271$		−	8.15682e7i		−	0.248959i	0.992222	−	0.124480i	$-0.0397262\pi$
$272$	−1.99334e7	+	1.40261e8i	−0.0600608	+	0.422617i
$273$	3.37408e7	+	1.18562e8i	0.100366	+	0.352678i
$274$	2.12099e8	+	2.27624e8i	0.622890	+	0.668485i
$275$	1.78170e8	−	1.78170e8i	0.516617	−	0.516617i
$276$	−1.18641e8	+	1.81586e8i	−0.339665	+	0.519878i
$277$	3.30113e8	+	3.30113e8i	0.933219	+	0.933219i	0.997906	−	0.0646865i	$-0.0206047\pi$
$277$	3.30113e8	+	3.30113e8i	0.933219	+	0.933219i	−0.0646865	+	0.997906i	$0.520605\pi$
$278$	6.74800e8	+	2.38254e7i	1.88373	+	0.0665096i
$279$	5.05915e8	−	3.13325e8i	1.39464	−	0.863733i
$280$	−7.31730e7	+	6.88520e8i	−0.199204	+	1.87441i
$281$	−4.21551e8			−1.13339			−0.566694	−	0.823929i	$-0.691778\pi$
$281$	−4.21551e8			−1.13339			−0.566694	+	0.823929i	$0.691778\pi$
$282$	3.53837e8	−	8.73255e7i	0.939576	−	0.231883i
$283$	−8.45703e7	+	8.45703e7i	−0.221802	+	0.221802i	−0.809257	−	0.587455i	$-0.800130\pi$
$283$	−8.45703e7	+	8.45703e7i	−0.221802	+	0.221802i	0.587455	+	0.809257i	$0.300130\pi$
$284$	−3.87861e8	−	2.74229e7i	−1.00476	−	0.0710395i
$285$	−4.78966e8	+	8.60018e8i	−1.22560	+	2.20065i
$286$	5.53935e7	+	5.94482e7i	0.140016	+	0.150265i
$287$	4.03097e8			1.00652
$288$	1.60609e8	−	3.72218e8i	0.396183	−	0.918172i
$289$	3.35570e8			0.817788
$290$	−6.63723e8	−	7.12307e8i	−1.59806	−	1.71504i
$291$	−1.08492e8	+	1.94806e8i	−0.258092	+	0.463422i
$292$	−4.98650e7	−	3.52561e6i	−0.117208	−	0.00828693i
$293$	−4.71527e8	+	4.71527e8i	−1.09514	+	1.09514i	−0.100169	+	0.994970i	$0.531938\pi$
$293$	−4.71527e8	+	4.71527e8i	−1.09514	+	1.09514i	−0.994970	+	0.100169i	$0.968062\pi$
$294$	3.39308e8	−	8.37398e7i	0.778716	−	0.192183i
$295$	−6.53216e8			−1.48143
$296$	6.68576e8	+	7.10534e7i	1.49841	+	0.159244i
$297$	2.50919e8	+	2.28669e8i	0.555759	+	0.506477i
$298$	−9.55287e7	−	3.37287e6i	−0.209111	−	0.00738317i
$299$	5.54408e7	+	5.54408e7i	0.119945	+	0.119945i
$300$	−2.48538e8	+	3.80402e8i	−0.531457	+	0.813427i
$301$	2.53878e8	−	2.53878e8i	0.536591	−	0.536591i
$302$	−1.50051e8	−	1.61035e8i	−0.313484	−	0.336431i
$303$	−1.05888e8	−	3.72081e8i	−0.218674	−	0.768403i
$304$	−5.27749e8	−	7.02602e8i	−1.07738	−	1.43434i
$305$		−	5.83370e8i		−	1.17732i
$306$	2.06416e8	+	5.62802e7i	0.411830	+	0.112287i
$307$	2.82920e8	+	2.82920e8i	0.558058	+	0.558058i	0.928754	−	0.370696i	$-0.120881\pi$
$307$	2.82920e8	+	2.82920e8i	0.558058	+	0.558058i	−0.370696	+	0.928754i	$0.620881\pi$
$308$	3.90894e8	−	3.39269e8i	0.762309	−	0.661632i
$309$	−1.59852e8	+	2.87025e8i	−0.308221	+	0.553434i
$310$	4.26323e7	−	1.20746e9i	0.0812779	−	2.30201i
$311$			6.42682e8i			1.21153i	0.795643	+	0.605766i	$0.207133\pi$
$311$			6.42682e8i			1.21153i	−0.795643	+	0.605766i	$0.792867\pi$
$312$	−1.19769e8	−	8.44278e7i	−0.223255	−	0.157378i
$313$		−	6.59402e8i		−	1.21547i	−0.794139	−	0.607736i	$-0.792078\pi$
$313$		−	6.59402e8i		−	1.21547i	0.794139	−	0.607736i	$-0.207922\pi$
$314$	6.19365e8	+	2.18682e7i	1.12900	+	0.0398620i
$315$	1.01791e9	+	2.39294e8i	1.83494	+	0.431365i
$316$	−6.68825e7	−	4.72879e6i	−0.119236	−	0.00843035i
$317$	−6.04967e8	−	6.04967e8i	−1.06666	−	1.06666i	−0.997614	−	0.0690429i	$-0.978005\pi$
$317$	−6.04967e8	−	6.04967e8i	−1.06666	−	1.06666i	−0.0690429	−	0.997614i	$-0.521995\pi$
$318$	7.93478e7	−	1.31346e8i	0.138369	−	0.229046i
$319$			7.27806e8i			1.25530i
$320$	−4.46679e8	−	6.91327e8i	−0.762027	−	1.17939i
$321$	−6.83069e8	+	1.94390e8i	−1.15265	+	0.328024i
$322$	3.65394e8	−	3.40471e8i	0.609909	−	0.568310i
$323$	3.27930e8	−	3.27930e8i	0.541468	−	0.541468i
$324$	−5.27493e8	−	3.10748e8i	−0.861607	−	0.507576i
$325$	1.16142e8	+	1.16142e8i	0.187671	+	0.187671i
$326$	−3.61363e7	+	1.02347e9i	−0.0577672	+	1.63612i
$327$	3.07873e7	+	1.08184e8i	0.0486916	+	0.171098i
$328$	−3.72738e8	+	3.01123e8i	−0.583238	+	0.471179i
$329$	−8.39157e8			−1.29915
$330$	6.69188e8	−	1.65153e8i	1.02506	−	0.252980i
$331$	−6.74009e8	+	6.74009e8i	−1.02157	+	1.02157i	−0.0218073	+	0.999762i	$0.506942\pi$
$331$	−6.74009e8	+	6.74009e8i	−1.02157	+	1.02157i	−0.999762	+	0.0218073i	$0.993058\pi$
$332$	4.30639e8	+	4.96167e8i	0.645848	+	0.744123i
$333$	2.32363e8	−	9.88423e8i	0.344835	−	1.46686i
$334$	−1.96893e8	+	1.83464e8i	−0.289147	+	0.269425i
$335$	−4.18716e8			−0.608503
$336$	−5.64381e8	+	7.43462e8i	−0.811681	+	1.06923i
$337$	5.63005e8			0.801323			0.400662	−	0.916226i	$-0.368780\pi$
$337$	5.63005e8			0.801323			0.400662	+	0.916226i	$0.368780\pi$
$338$	4.80636e8	−	4.47854e8i	0.677030	−	0.630852i
$339$	6.37366e8	+	3.54965e8i	0.888566	+	0.494865i
$340$	3.28059e8	−	2.84732e8i	0.452663	−	0.392881i
$341$	−6.38646e8	+	6.38646e8i	−0.872207	+	0.872207i
$342$	−1.15216e9	+	6.58483e8i	−1.55748	+	0.890129i
$343$	1.98567e8			0.265691
$344$	−4.51046e7	+	4.24411e8i	−0.0597402	+	0.562124i
$345$	6.39685e8	−	1.82043e8i	0.838686	−	0.238676i
$346$	1.29846e7	−	3.67760e8i	0.0168525	−	0.477307i
$347$	−1.74413e8	−	1.74413e8i	−0.224092	−	0.224092i	0.586127	−	0.810219i	$-0.300652\pi$
$347$	−1.74413e8	−	1.74413e8i	−0.224092	−	0.224092i	−0.810219	+	0.586127i	$0.800652\pi$
$348$	−2.69326e8	−	1.28458e9i	−0.342572	−	1.63393i
$349$	1.19152e8	−	1.19152e8i	0.150042	−	0.150042i	−0.628095	−	0.778137i	$-0.716165\pi$
$349$	1.19152e8	−	1.19152e8i	0.150042	−	0.150042i	0.778137	+	0.628095i	$0.216165\pi$
$350$	7.65456e8	−	7.13247e8i	0.954294	−	0.889205i
$351$	−1.49061e8	+	1.63565e8i	−0.183987	+	0.201890i
$352$	−1.08012e8	+	6.05724e8i	−0.131999	+	0.740245i
$353$		−	1.21842e9i		−	1.47429i	−0.675732	−	0.737147i	$-0.736172\pi$
$353$		−	1.21842e9i		−	1.47429i	0.675732	−	0.737147i	$-0.263828\pi$
$354$	−7.53733e8	−	4.55339e8i	−0.903038	−	0.545537i
$355$	8.43032e8	+	8.43032e8i	1.00010	+	1.00010i
$356$	−2.10913e7	+	2.98309e8i	−0.0247759	+	0.350422i
$357$	−4.30379e8	−	2.39689e8i	−0.500625	−	0.278811i
$358$	−1.37299e9	−	4.84768e7i	−1.58153	−	0.0558398i
$359$		−	2.32539e8i		−	0.265256i	−0.991166	−	0.132628i	$-0.957658\pi$
$359$		−	2.32539e8i		−	0.265256i	0.991166	−	0.132628i	$-0.0423416\pi$
$360$	−1.12000e9	+	5.39130e8i	−1.26520	+	0.609024i
$361$			1.98268e9i			2.21808i
$362$	5.62697e7	−	1.59371e9i	0.0623440	−	1.76575i
$363$	3.46029e8	+	1.92713e8i	0.379699	+	0.211464i
$364$	2.21156e8	+	2.54809e8i	0.240350	+	0.276923i
$365$	1.08384e8	+	1.08384e8i	0.116665	+	0.116665i
$366$	4.06652e8	−	6.73139e8i	0.433549	−	0.717664i
$367$		−	7.56975e8i		−	0.799374i	−0.916652	−	0.399687i	$-0.869119\pi$
$367$		−	7.56975e8i		−	0.799374i	0.916652	−	0.399687i	$-0.130881\pi$
$368$	−8.35341e7	+	5.87787e8i	−0.0873769	+	0.614826i
$369$	3.81019e8	+	6.15218e8i	0.394779	+	0.637437i
$370$	−1.40538e9	−	1.50825e9i	−1.44240	−	1.54799i
$371$	−2.49840e8	+	2.49840e8i	−0.254011	+	0.254011i
$372$	8.90880e8	−	1.36354e9i	0.897261	−	1.37331i
$373$	−4.53576e8	−	4.53576e8i	−0.452552	−	0.452552i	0.443649	−	0.896201i	$-0.353684\pi$
$373$	−4.53576e8	−	4.53576e8i	−0.452552	−	0.452552i	−0.896201	+	0.443649i	$0.853684\pi$
$374$	−3.24520e8	−	1.14580e7i	−0.320768	−	0.0113255i
$375$	−3.90949e7	+	1.11257e7i	−0.0382834	+	0.0108948i
$376$	7.75957e8	−	6.26871e8i	0.752801	−	0.608164i
$377$	−4.74429e8			−0.456012
$378$	1.00774e9	+	9.85673e8i	0.959679	+	0.938667i
$379$	−9.53293e8	+	9.53293e8i	−0.899475	+	0.899475i	−0.995390	−	0.0959148i	$-0.969422\pi$
$379$	−9.53293e8	+	9.53293e8i	−0.899475	+	0.899475i	0.0959148	+	0.995390i	$0.469422\pi$
$380$	−1.90025e8	+	2.68766e9i	−0.177652	+	2.51264i
$381$	−5.38612e8	−	2.99967e8i	−0.498929	−	0.277867i
$382$	1.07607e9	+	1.15484e9i	0.987689	+	1.05999i
$383$	−5.68567e8			−0.517114			−0.258557	−	0.965996i	$-0.583247\pi$
$383$	−5.68567e8			−0.517114			−0.258557	+	0.965996i	$0.583247\pi$
$384$	−3.35085e7	−	1.10908e9i	−0.0301992	−	0.999544i
$385$	−1.58704e9			−1.41734
$386$	−2.94999e8	−	3.16593e8i	−0.261075	−	0.280186i
$387$	6.27449e8	+	1.47504e8i	0.550288	+	0.129364i
$388$	−4.30433e7	+	6.08791e8i	−0.0374106	+	0.529123i
$389$	9.25440e8	−	9.25440e8i	0.797121	−	0.797121i	−0.185519	−	0.982641i	$-0.559397\pi$
$389$	9.25440e8	−	9.25440e8i	0.797121	−	0.797121i	0.982641	+	0.185519i	$0.0593967\pi$
$390$	1.07657e8	+	4.36218e8i	0.0918998	+	0.372372i
$391$	−3.13330e8			−0.265084
$392$	7.44095e8	−	6.01130e8i	0.623918	−	0.504043i
$393$	1.13672e8	+	3.99434e8i	0.0944670	+	0.331949i
$394$	−1.41933e9	−	5.01130e7i	−1.16909	−	0.0412775i
$395$	1.45372e8	+	1.45372e8i	0.118684	+	0.118684i
$396$	8.87285e8	+	2.75907e8i	0.718010	+	0.223269i
$397$	1.43951e9	−	1.43951e9i	1.15465	−	1.15465i	0.169038	−	0.985610i	$-0.445934\pi$
$397$	1.43951e9	−	1.43951e9i	1.15465	−	1.15465i	0.985610	−	0.169038i	$-0.0540660\pi$
$398$	6.58708e7	+	7.06926e7i	0.0523724	+	0.0562060i
$399$	2.93887e9	−	8.36352e8i	2.31620	−	0.659149i
$400$	−1.74994e8	+	1.23134e9i	−0.136714	+	0.961987i
$401$			1.20601e9i			0.934001i	0.884257	+	0.467000i	$0.154665\pi$
$401$			1.20601e9i			0.934001i	−0.884257	+	0.467000i	$0.845335\pi$
$402$	−4.83148e8	−	2.91876e8i	−0.370928	−	0.224082i
$403$	−4.16309e8	−	4.16309e8i	−0.316846	−	0.316846i
$404$	−6.94050e8	−	7.99660e8i	−0.523668	−	0.603351i
$405$	5.96937e8	+	1.77975e9i	0.446515	+	1.33127i
$406$	−1.06635e8	+	3.02018e9i	−0.0790784	+	2.23971i
$407$			1.54107e9i			1.13303i
$408$	5.77019e8	−	9.98662e7i	0.420610	−	0.0727961i
$409$		−	1.08898e9i		−	0.787024i	−0.919319	−	0.393512i	$-0.871260\pi$
$409$		−	1.08898e9i		−	0.787024i	0.919319	−	0.393512i	$-0.128740\pi$
$410$	1.46833e9	+	5.18430e7i	1.05216	+	0.0371490i
$411$	6.25732e8	−	1.12355e9i	0.444572	−	0.798261i
$412$	−6.34197e7	+	8.96987e8i	−0.0446770	+	0.631897i
$413$	1.43371e9	+	1.43371e9i	1.00147	+	1.00147i
$414$	8.65017e8	+	2.35851e8i	0.599133	+	0.163357i
$415$		−	2.01445e9i		−	1.38353i
$416$	−3.94848e8	−	7.04088e7i	−0.268908	−	0.0479513i
$417$	−7.63947e8	−	2.68445e9i	−0.515925	−	1.81292i
$418$	1.47358e9	−	1.37307e9i	0.986859	−	0.919549i
$419$	1.18822e9	−	1.18822e9i	0.789129	−	0.789129i	−0.192222	−	0.981351i	$-0.561569\pi$
$419$	1.18822e9	−	1.18822e9i	0.789129	−	0.789129i	0.981351	+	0.192222i	$0.0615695\pi$
$420$	2.80113e9	−	5.87288e8i	1.84485	−	0.386793i
$421$	−1.56602e8	−	1.56602e8i	−0.102285	−	0.102285i	0.654113	−	0.756397i	$-0.273042\pi$
$421$	−1.56602e8	−	1.56602e8i	−0.102285	−	0.102285i	−0.756397	+	0.654113i	$0.773042\pi$
$422$	−9.64275e6	+	2.73108e8i	−0.00624608	+	0.176906i
$423$	−7.93195e8	−	1.28075e9i	−0.509552	−	0.822757i
$424$	4.43871e7	−	4.17660e8i	0.0282798	−	0.266098i
$425$	−6.56389e8			−0.414763
$426$	3.85103e8	+	1.56041e9i	0.241348	+	0.977926i
$427$	−1.28041e9	+	1.28041e9i	−0.795887	+	0.795887i
$428$	−1.46802e9	+	1.27414e9i	−0.905063	+	0.785532i
$429$	1.63421e8	−	2.93435e8i	0.0999328	−	0.179436i
$430$	9.57436e8	−	8.92132e8i	0.580724	−	0.541115i
$431$	1.15527e9			0.695043			0.347522	−	0.937672i	$-0.387023\pi$
$431$	1.15527e9			0.695043			0.347522	+	0.937672i	$0.387023\pi$
$432$	−1.66816e9	−	1.58634e8i	−0.995509	−	0.0946678i
$433$	−7.65693e8			−0.453260			−0.226630	−	0.973981i	$-0.572771\pi$
$433$	−7.65693e8			−0.453260			−0.226630	+	0.973981i	$0.572771\pi$
$434$	−2.74376e9	+	2.55662e9i	−1.61114	+	1.50125i
$435$	−1.95811e9	+	3.51593e9i	−1.14058	+	2.04799i
$436$	2.01797e8	+	2.32504e8i	0.116604	+	0.134347i
$437$	1.37424e9	−	1.37424e9i	0.787731	−	0.787731i
$438$	4.95104e7	+	2.00613e8i	0.0281538	+	0.114077i
$439$	−4.28245e8			−0.241583			−0.120791	−	0.992678i	$-0.538543\pi$
$439$	−4.28245e8			−0.241583			−0.120791	+	0.992678i	$0.538543\pi$
$440$	1.46751e9	−	1.18556e9i	0.821292	−	0.663495i
$441$	−7.60625e8	−	1.22816e9i	−0.422314	−	0.681897i
$442$	7.46901e6	−	2.11542e8i	0.00411420	−	0.116525i
$443$	−3.53754e8	−	3.53754e8i	−0.193325	−	0.193325i	0.603806	−	0.797131i	$-0.293650\pi$
$443$	−3.53754e8	−	3.53754e8i	−0.193325	−	0.193325i	−0.797131	+	0.603806i	$0.793650\pi$
$444$	−5.70276e8	−	2.71999e9i	−0.309204	−	1.47478i
$445$	6.48387e8	−	6.48387e8i	0.348798	−	0.348798i
$446$	2.10930e9	−	1.96543e9i	1.12581	−	1.04903i
$447$	1.08149e8	+	3.80026e8i	0.0572724	+	0.201251i
$448$	−5.36966e8	+	2.49775e9i	−0.282146	+	1.31243i
$449$			1.99457e9i			1.03989i	0.854200	+	0.519945i	$0.174048\pi$
$449$			1.99457e9i			1.03989i	−0.854200	+	0.519945i	$0.825952\pi$
$450$	1.81211e9	+	4.94080e8i	0.937433	+	0.255596i
$451$	−7.76626e8	−	7.76626e8i	−0.398652	−	0.398652i
$452$	1.99184e9	+	1.40829e8i	1.01454	+	0.0717312i
$453$	−4.42680e8	+	7.94864e8i	−0.223741	+	0.401744i
$454$	2.68772e9	+	9.48964e7i	1.34799	+	0.0475942i
$455$		−	1.03453e9i		−	0.514877i
$456$	−2.09276e9	+	2.96877e9i	−1.03358	+	1.46622i
$457$			6.24999e8i			0.306318i	0.988202	+	0.153159i	$0.0489447\pi$
$457$			6.24999e8i			0.306318i	−0.988202	+	0.153159i	$0.951055\pi$
$458$	−8.38767e7	+	2.37561e9i	−0.0407955	+	1.15544i
$459$	−4.09857e7	−	8.83418e8i	−0.0197828	−	0.426405i
$460$	1.37478e9	−	1.19322e9i	0.658538	−	0.571566i
$461$	1.47474e9	+	1.47474e9i	0.701073	+	0.701073i	0.964641	−	0.263568i	$-0.0848992\pi$
$461$	1.47474e9	+	1.47474e9i	0.701073	+	0.701073i	−0.263568	+	0.964641i	$0.584899\pi$
$462$	−1.83125e9	−	1.10628e9i	−0.863975	−	0.521938i
$463$		−	8.31399e8i		−	0.389292i	−0.980874	−	0.194646i	$-0.937644\pi$
$463$		−	8.31399e8i		−	0.389292i	0.980874	−	0.194646i	$-0.0623559\pi$
$464$	−2.15754e9	−	2.87238e9i	−1.00264	−	1.33484i
$465$	−4.80344e9	+	1.36698e9i	−2.21547	+	0.630486i
$466$	−8.73974e7	−	9.37948e7i	−0.0400081	−	0.0429366i
$467$	−1.35758e9	+	1.35758e9i	−0.616817	+	0.616817i	−0.944714	−	0.327896i	$-0.893660\pi$
$467$	−1.35758e9	+	1.35758e9i	−0.616817	+	0.616817i	0.327896	+	0.944714i	$0.393660\pi$
$468$	−1.79853e8	+	5.78388e8i	−0.0811068	+	0.260831i
$469$	9.19019e8	+	9.19019e8i	0.411358	+	0.411358i
$470$	−3.05674e9	−	1.07925e8i	−1.35805	−	0.0479492i
$471$	−7.01188e8	−	2.46392e9i	−0.309216	−	1.08656i
$472$	−2.39675e9	−	2.54716e8i	−1.04912	−	0.111496i
$473$	−9.78268e8			−0.425054
$474$	6.64069e7	+	2.69077e8i	0.0286410	+	0.116052i
$475$	2.87887e9	−	2.87887e9i	1.23252	−	1.23252i
$476$	−1.34498e9	−	9.50944e7i	−0.571601	−	0.0404139i
$477$	−6.17468e8	−	1.45157e8i	−0.260496	−	0.0612384i
$478$	8.04216e8	+	8.63084e8i	0.336802	+	0.361456i
$479$	−1.99595e9			−0.829803			−0.414902	−	0.909866i	$-0.636184\pi$
$479$	−1.99595e9			−0.829803			−0.414902	+	0.909866i	$0.636184\pi$
$480$	−2.15145e9	+	2.63557e9i	−0.887946	+	1.08775i
$481$	−1.00456e9			−0.411595
$482$	−1.92050e9	−	2.06108e9i	−0.781179	−	0.838361i
$483$	−1.80357e9	−	1.00446e9i	−0.728313	−	0.405617i
$484$	1.08138e9	+	7.64569e7i	0.433531	+	0.0306519i
$485$	1.32323e9	−	1.32323e9i	0.526672	−	0.526672i
$486$	−5.51820e8	+	2.46972e9i	−0.218057	+	0.975936i
$487$	−2.44567e9			−0.959505			−0.479752	−	0.877404i	$-0.659273\pi$
$487$	−2.44567e9			−0.959505			−0.479752	+	0.877404i	$0.659273\pi$
$488$	2.27481e8	−	2.14047e9i	0.0886084	−	0.833759i
$489$	4.07152e9	−	1.15868e9i	1.57462	−	0.448110i
$490$	−2.93122e9	−	1.03494e8i	−1.12554	−	0.0397401i
$491$	−2.37985e9	−	2.37985e9i	−0.907329	−	0.907329i	0.0887274	−	0.996056i	$-0.471720\pi$
$491$	−2.37985e9	−	2.37985e9i	−0.907329	−	0.907329i	−0.996056	+	0.0887274i	$0.971720\pi$
$492$	1.65814e9	+	1.08336e9i	0.627687	+	0.410103i
$493$	1.34064e9	−	1.34064e9i	0.503905	−	0.503905i
$494$	8.95050e8	+	9.60567e8i	0.334044	+	0.358495i
$495$	−1.50011e9	−	2.42218e9i	−0.555912	−	0.897613i
$496$	6.27263e8	−	4.41373e9i	0.230815	−	1.62413i
$497$		−	3.70066e9i		−	1.35217i
$498$	1.40422e9	−	2.32444e9i	0.509486	−	0.843364i
$499$	3.72484e9	+	3.72484e9i	1.34201	+	1.34201i	0.894058	+	0.447950i	$0.147846\pi$
$499$	3.72484e9	+	3.72484e9i	1.34201	+	1.34201i	0.447950	+	0.894058i	$0.352154\pi$
$500$	−8.40209e7	+	7.29244e7i	−0.0300602	+	0.0260902i
$501$	9.71860e8	+	5.41254e8i	0.345280	+	0.192295i
$502$	1.49445e6	−	4.23268e7i	0.000527252	−	0.0149332i
$503$		−	6.43804e8i		−	0.225562i	−0.993620	−	0.112781i	$-0.964024\pi$
$503$		−	6.43804e8i		−	0.225562i	0.993620	−	0.112781i	$-0.0359758\pi$
$504$	3.64155e9	+	1.27493e9i	1.26701	+	0.443588i
$505$			3.24664e9i			1.12180i
$506$	−1.35995e9	−	4.80164e7i	−0.466656	−	0.0164764i
$507$	−2.37241e9	−	1.32125e9i	−0.808465	−	0.450255i
$508$	−1.68323e9	−	1.19009e8i	−0.569665	−	0.0402770i
$509$	1.59838e9	+	1.59838e9i	0.537238	+	0.537238i	0.922717	−	0.385479i	$-0.125964\pi$
$509$	1.59838e9	+	1.59838e9i	0.537238	+	0.537238i	−0.385479	+	0.922717i	$0.625964\pi$
$510$	−1.53688e9	−	9.28450e8i	−0.513033	−	0.309930i
$511$		−	4.75772e8i		−	0.157734i
$512$	−1.36936e9	−	2.71076e9i	−0.450891	−	0.892579i
$513$	4.05437e9	+	3.69485e9i	1.32590	+	1.20833i
$514$	−1.84979e8	+	1.72362e8i	−0.0600830	+	0.0559849i
$515$	1.94964e9	−	1.94964e9i	0.628969	−	0.628969i
$516$	1.72665e9	−	3.62011e8i	0.553260	−	0.115997i
$517$	1.61676e9	+	1.61676e9i	0.514551	+	0.514551i
$518$	−2.25790e8	+	6.39498e9i	−0.0713758	+	2.02155i
$519$	−1.46300e9	+	4.16344e8i	−0.459365	+	0.130727i
$520$	7.72819e8	+	9.56616e8i	0.241027	+	0.298350i
$521$	−7.07965e8			−0.219321			−0.109660	−	0.993969i	$-0.534976\pi$
$521$	−7.07965e8			−0.219321			−0.109660	+	0.993969i	$0.534976\pi$
$522$	−4.71028e9	+	2.69201e9i	−1.44944	+	0.828380i
$523$	−7.07191e8	+	7.07191e8i	−0.216163	+	0.216163i	−0.806879	−	0.590717i	$-0.798845\pi$
$523$	−7.07191e8	+	7.07191e8i	−0.216163	+	0.216163i	0.590717	+	0.806879i	$0.298845\pi$
$524$	7.45072e8	+	8.58445e8i	0.226224	+	0.260647i
$525$	−3.77827e9	−	2.10421e9i	−1.13955	−	0.634647i
$526$	−1.43258e9	+	1.33487e9i	−0.429210	+	0.399935i
$527$	2.35281e9			0.700246
$528$	2.51975e9	−	3.45026e8i	0.744971	−	0.102008i
$529$	2.09177e9			0.614354
$530$	−9.42205e8	+	8.77941e8i	−0.274903	+	0.256153i
$531$	−8.32988e8	+	3.54336e9i	−0.241439	+	1.02703i
$532$	6.31608e9	−	5.48193e9i	1.81868	−	1.57849i
$533$	5.06253e8	−	5.06253e8i	0.144818	−	0.144818i
$534$	1.20013e9	−	2.96188e8i	0.341064	−	0.0841730i
$535$	5.96020e9			1.68276
$536$	−1.53633e9	−	1.63275e8i	−0.430932	−	0.0457976i
$537$	1.55438e9	+	5.46195e9i	0.433158	+	1.52208i
$538$	1.01922e8	−	2.88669e9i	0.0282182	−	0.799213i
$539$	1.55037e9	+	1.55037e9i	0.426457	+	0.426457i
$540$	3.54404e9	+	3.72004e9i	0.968547	+	1.01665i
$541$	3.65032e8	−	3.65032e8i	0.0991152	−	0.0991152i	−0.655810	−	0.754926i	$-0.727673\pi$
$541$	3.65032e8	−	3.65032e8i	0.0991152	−	0.0991152i	0.754926	+	0.655810i	$0.227673\pi$
$542$	−6.75165e8	+	6.29114e8i	−0.182143	+	0.169720i
$543$	−6.33999e9	+	1.80425e9i	−1.69937	+	0.483612i
$544$	1.31473e9	−	9.16803e8i	0.350138	−	0.244163i
$545$		−	9.43972e8i		−	0.249788i
$546$	7.21143e8	−	1.19372e9i	0.189604	−	0.313855i
$547$	−1.11740e9	−	1.11740e9i	−0.291913	−	0.291913i	0.545922	−	0.837836i	$-0.316179\pi$
$547$	−1.11740e9	−	1.11740e9i	−0.291913	−	0.291913i	−0.837836	+	0.545922i	$0.816179\pi$
$548$	2.48253e8	−	3.51121e9i	0.0644411	−	0.911434i
$549$	−3.16448e9	−	7.43919e8i	−0.816204	−	0.191877i
$550$	−2.84894e9	−	1.00589e8i	−0.730152	−	0.0257798i
$551$			1.17599e10i			2.99484i
$552$	2.41809e9	−	4.18505e8i	0.611907	−	0.105904i
$553$		−	6.38139e8i		−	0.160464i
$554$	1.86371e8	−	5.27852e9i	0.0465687	−	1.31895i
$555$	−4.14613e9	+	7.44468e9i	−1.02948	+	1.84850i
$556$	−5.00734e9	−	5.76928e9i	−1.23551	−	1.42351i
$557$	5.09723e9	+	5.09723e9i	1.24980	+	1.24980i	0.955807	+	0.293993i	$0.0949844\pi$
$557$	5.09723e9	+	5.09723e9i	1.24980	+	1.24980i	0.293993	+	0.955807i	$0.405016\pi$
$558$	−6.49547e9	−	1.77102e9i	−1.58267	−	0.431523i
$559$		−	6.37696e8i		−	0.154409i
$560$	6.26345e9	−	4.70470e9i	1.50715	−	1.13207i
$561$	3.67392e8	+	1.29099e9i	0.0878536	+	0.308710i
$562$	3.25131e9	+	3.48931e9i	0.772648	+	0.829206i
$563$	5.41089e9	−	5.41089e9i	1.27788	−	1.27788i	0.336025	−	0.941853i	$-0.390917\pi$
$563$	5.41089e9	−	5.41089e9i	1.27788	−	1.27788i	0.941853	−	0.336025i	$-0.109083\pi$
$564$	−3.45187e9	−	2.25530e9i	−0.810173	−	0.529331i
$565$	−4.32935e9	−	4.32935e9i	−1.00984	−	1.00984i
$566$	1.35228e9	+	4.77456e7i	0.313480	+	0.0110682i
$567$	2.59609e9	−	5.21647e9i	0.598108	−	1.20181i
$568$	2.76448e9	+	3.42195e9i	0.632986	+	0.783527i
$569$	6.08077e9			1.38378			0.691888	−	0.722005i	$-0.256779\pi$
$569$	6.08077e9			1.38378			0.691888	+	0.722005i	$0.256779\pi$
$570$	1.08128e10	−	2.66854e9i	2.44554	−	0.603549i
$571$	2.13954e9	−	2.13954e9i	0.480942	−	0.480942i	−0.424490	−	0.905433i	$-0.639547\pi$
$571$	2.13954e9	−	2.13954e9i	0.480942	−	0.480942i	0.905433	+	0.424490i	$0.139547\pi$
$572$	6.48358e7	−	9.17017e8i	0.0144853	−	0.204876i
$573$	3.17462e9	−	5.70026e9i	0.704938	−	1.26577i
$574$	−3.10898e9	−	3.33656e9i	−0.686162	−	0.736388i
$575$	−2.75070e9			−0.603401
$576$	−4.31970e9	+	1.54141e9i	−0.941834	+	0.336078i
$577$	−7.43377e9			−1.61099			−0.805496	−	0.592601i	$-0.798101\pi$
$577$	−7.43377e9			−1.61099			−0.805496	+	0.592601i	$0.798101\pi$
$578$	−2.58816e9	−	2.77761e9i	−0.557499	−	0.598307i
$579$	−8.70304e8	+	1.56269e9i	−0.186336	+	0.334579i
$580$	−7.76861e8	+	1.09877e10i	−0.165328	+	2.33834i
$581$	−4.42142e9	+	4.42142e9i	−0.935288	+	0.935288i
$582$	2.44924e9	−	6.04461e8i	0.514992	−	0.127098i
$583$	9.62706e8			0.201212
$584$	3.55413e8	+	4.39940e8i	0.0738394	+	0.0914004i
$585$	1.57893e9	−	9.77867e8i	0.326075	−	0.201945i
$586$	7.53973e9	+	2.66208e8i	1.54780	+	0.0546487i
$587$	−2.13782e9	−	2.13782e9i	−0.436252	−	0.436252i	0.454496	−	0.890749i	$-0.349819\pi$
$587$	−2.13782e9	−	2.13782e9i	−0.436252	−	0.436252i	−0.890749	+	0.454496i	$0.849819\pi$
$588$	−3.31013e9	−	2.16269e9i	−0.671467	−	0.438707i
$589$	−1.03193e10	+	1.03193e10i	−2.08087	+	2.08087i
$590$	5.03808e9	+	5.40687e9i	1.00991	+	1.08384i
$591$	1.60684e9	+	5.64630e9i	0.320196	+	1.12514i
$592$	−4.56842e9	−	6.08202e9i	−0.904982	−	1.20482i
$593$		−	1.56307e9i		−	0.307813i	−0.988085	−	0.153906i	$-0.950815\pi$
$593$		−	1.56307e9i		−	0.307813i	0.988085	−	0.153906i	$-0.0491854\pi$
$594$	−4.25113e7	−	3.84060e9i	−0.00832246	−	0.751876i
$595$	2.92338e9	+	2.92338e9i	0.568953	+	0.568953i
$596$	7.08869e8	+	8.16734e8i	0.137153	+	0.158022i
$597$	1.94332e8	−	3.48936e8i	0.0373795	−	0.0671175i
$598$	3.13001e7	−	8.86501e8i	0.00598537	−	0.169522i
$599$			1.49123e9i			0.283499i	0.989903	+	0.141749i	$0.0452727\pi$
$599$			1.49123e9i			0.283499i	−0.989903	+	0.141749i	$0.954727\pi$
$600$	5.06561e9	−	8.76718e8i	0.957420	−	0.165703i
$601$		−	3.85284e9i		−	0.723970i	−0.932184	−	0.361985i	$-0.882099\pi$
$601$		−	3.85284e9i		−	0.723970i	0.932184	−	0.361985i	$-0.117901\pi$
$602$	−4.05953e9	−	1.43331e8i	−0.758381	−	0.0267765i
$603$	−5.33951e8	+	2.27132e9i	−0.0991724	+	0.421859i
$604$	−1.75629e8	+	2.48404e9i	−0.0324315	+	0.458701i
$605$	−2.35043e9	−	2.35043e9i	−0.431522	−	0.431522i
$606$	−2.26314e9	+	3.74623e9i	−0.413103	+	0.683818i
$607$			3.35051e9i			0.608066i	0.952661	+	0.304033i	$0.0983334\pi$
$607$			3.35051e9i			0.608066i	−0.952661	+	0.304033i	$0.901667\pi$
$608$	−1.74526e9	+	9.78732e9i	−0.314918	+	1.76604i
$609$	1.20147e10	−	3.41917e9i	2.15552	−	0.613424i
$610$	−4.82873e9	+	4.49938e9i	−0.861348	+	0.802598i
$611$	−1.05390e9	+	1.05390e9i	−0.186920	+	0.186920i
$612$	−1.12618e9	−	2.14264e9i	−0.198600	−	0.377850i
$613$	5.87703e9	+	5.87703e9i	1.03050	+	1.03050i	0.999520	+	0.0309764i	$0.00986168\pi$
$613$	5.87703e9	+	5.87703e9i	1.03050	+	1.03050i	0.0309764	+	0.999520i	$0.490138\pi$
$614$	1.59727e8	−	4.52390e9i	0.0278477	−	0.788722i
$615$	−1.66231e9	−	5.84123e9i	−0.288170	−	1.01261i
$616$	−5.82309e9	−	6.18853e8i	−1.00374	−	0.106673i
$617$	−5.55531e9			−0.952161			−0.476081	−	0.879402i	$-0.657943\pi$
$617$	−5.55531e9			−0.952161			−0.476081	+	0.879402i	$0.657943\pi$
$618$	3.60869e9	−	8.90608e8i	0.615021	−	0.151784i
$619$	2.76399e9	−	2.76399e9i	0.468402	−	0.468402i	−0.432995	−	0.901397i	$-0.642543\pi$
$619$	2.76399e9	−	2.76399e9i	0.468402	−	0.468402i	0.901397	+	0.432995i	$0.142543\pi$
$620$	−1.03233e10	+	8.95993e9i	−1.73960	+	1.50985i
$621$	−1.71757e8	−	3.70210e9i	−0.0287802	−	0.620337i
$622$	5.31967e9	−	4.95684e9i	0.886378	−	0.825921i
$623$	−2.84623e9			−0.471586
$624$	2.24909e8	+	1.64253e9i	0.0370562	+	0.270625i
$625$	6.27163e9			1.02754
$626$	−5.45807e9	+	5.08579e9i	−0.889260	+	0.828607i
$627$	−7.27352e9	−	4.05081e9i	−1.17844	−	0.656305i
$628$	−4.59599e9	−	5.29533e9i	−0.740491	−	0.853168i
$629$	2.83870e9	−	2.83870e9i	0.454823	−	0.454823i
$630$	−5.87014e9	−	1.02711e10i	−0.935313	−	1.63654i
$631$	1.11038e8			0.0175942			0.00879712	−	0.999961i	$-0.497200\pi$
$631$	1.11038e8			0.0175942			0.00879712	+	0.999961i	$0.497200\pi$
$632$	4.76705e8	+	5.90078e8i	0.0751173	+	0.0929822i
$633$	1.08646e9	−	3.09188e8i	0.170256	−	0.0484518i
$634$	−3.41545e8	+	9.67345e9i	−0.0532274	+	1.50754i
$635$	3.65856e9	+	3.65856e9i	0.567025	+	0.567025i
$636$	−1.69918e9	+	3.56252e8i	−0.261902	+	0.0549108i
$637$	−1.01063e9	+	1.01063e9i	−0.154919	+	0.154919i
$638$	6.02427e9	−	5.61337e9i	0.918400	−	0.855759i
$639$	5.64805e9	−	3.49797e9i	0.856339	−	0.530350i
$640$	−2.27721e9	+	9.02932e9i	−0.343378	+	1.36152i
$641$		−	2.11550e9i		−	0.317256i	−0.987338	−	0.158628i	$-0.949293\pi$
$641$		−	2.11550e9i		−	0.317256i	0.987338	−	0.158628i	$-0.0507071\pi$
$642$	6.87735e9	+	4.15469e9i	1.02577	+	0.619679i
$643$	−4.79077e9	−	4.79077e9i	−0.710668	−	0.710668i	0.256007	−	0.966675i	$-0.417593\pi$
$643$	−4.79077e9	−	4.79077e9i	−0.710668	−	0.710668i	−0.966675	+	0.256007i	$0.917593\pi$
$644$	−5.63637e9	−	3.98508e8i	−0.831570	−	0.0587945i
$645$	−4.72587e9	−	2.63196e9i	−0.693463	−	0.386207i
$646$	−5.24361e9	−	1.85139e8i	−0.765274	−	0.0270199i
$647$		−	1.27100e10i		−	1.84494i	−0.386074	−	0.922468i	$-0.626169\pi$
$647$		−	1.27100e10i		−	1.84494i	0.386074	−	0.922468i	$-0.373831\pi$
$648$	1.49626e9	+	6.76294e9i	0.216020	+	0.976389i
$649$		−	5.52451e9i		−	0.793300i
$650$	6.55699e7	−	1.85711e9i	0.00936500	−	0.265242i
$651$	1.35431e10	+	7.54252e9i	1.92391	+	1.07148i
$652$	8.75032e9	−	7.59468e9i	1.23640	−	1.07311i
$653$	2.30203e9	+	2.30203e9i	0.323530	+	0.323530i	0.850120	−	0.526589i	$-0.176529\pi$
$653$	2.30203e9	+	2.30203e9i	0.323530	+	0.323530i	−0.526589	+	0.850120i	$0.676529\pi$
$654$	6.58017e8	−	1.08923e9i	0.0919846	−	0.152264i
$655$		−	3.48531e9i		−	0.484615i
$656$	5.36732e9	+	7.62784e8i	0.742325	+	0.105497i
$657$	7.26137e8	−	4.49713e8i	0.0998940	−	0.0618666i
$658$	6.47220e9	+	6.94596e9i	0.885648	+	0.950477i
$659$	1.63489e9	−	1.63489e9i	0.222530	−	0.222530i	−0.587033	−	0.809563i	$-0.699704\pi$
$659$	1.63489e9	−	1.63489e9i	0.222530	−	0.222530i	0.809563	+	0.587033i	$0.199704\pi$
$660$	−6.52829e9	−	4.26529e9i	−0.883884	−	0.577491i
$661$	−3.18264e9	−	3.18264e9i	−0.428630	−	0.428630i	0.459531	−	0.888162i	$-0.348017\pi$
$661$	−3.18264e9	−	3.18264e9i	−0.428630	−	0.428630i	−0.888162	+	0.459531i	$0.848017\pi$
$662$	1.07774e10	+	3.80523e8i	1.44382	+	0.0509775i
$663$	−8.41544e8	+	2.39489e8i	−0.112145	+	0.0319145i
$664$	7.85519e8	−	7.39134e9i	0.104128	−	0.979794i
$665$	−2.56435e10			−3.38143
$666$	−9.97362e9	+	5.70011e9i	−1.30826	+	0.747693i
$667$	5.61817e9	−	5.61817e9i	0.733086	−	0.733086i
$668$	3.03717e9	+	2.14737e8i	0.394232	+	0.0278734i
$669$	−1.04114e10	−	5.79840e9i	−1.34437	−	0.748716i
$670$	3.22945e9	+	3.46584e9i	0.414826	+	0.445191i
$671$	4.93380e9			0.630453
$672$	1.05068e10	−	1.06257e9i	1.33560	−	0.135072i
$673$	7.78795e8			0.0984851			0.0492425	−	0.998787i	$-0.484319\pi$
$673$	7.78795e8			0.0984851			0.0492425	+	0.998787i	$0.484319\pi$
$674$	−4.34231e9	−	4.66016e9i	−0.546275	−	0.586262i
$675$	−3.59811e8	−	7.75546e9i	−0.0450309	−	0.970609i
$676$	−7.41404e9	−	5.24195e8i	−0.923085	−	0.0652649i
$677$	−2.91823e8	+	2.91823e8i	−0.0361459	+	0.0361459i	−0.724949	−	0.688803i	$-0.758137\pi$
$677$	−2.91823e8	+	2.91823e8i	−0.0361459	+	0.0361459i	0.688803	+	0.724949i	$0.258137\pi$
$678$	−1.97768e9	−	8.01342e9i	−0.243698	−	0.987448i
$679$	−5.80859e9			−0.712077
$680$	−4.88705e9	−	5.19374e8i	−0.596026	−	0.0633431i
$681$	−3.04279e9	−	1.06921e10i	−0.369196	−	1.29732i
$682$	1.02120e10	+	3.60558e8i	1.23272	+	0.0435241i
$683$	−3.74102e9	−	3.74102e9i	−0.449280	−	0.449280i	0.445835	−	0.895115i	$-0.352907\pi$
$683$	−3.74102e9	−	3.74102e9i	−0.449280	−	0.449280i	−0.895115	+	0.445835i	$0.852907\pi$
$684$	1.43368e10	+	4.45811e9i	1.71299	+	0.532666i
$685$	−7.63177e9	+	7.63177e9i	−0.907211	+	0.907211i
$686$	−1.53149e9	−	1.64359e9i	−0.181126	−	0.194384i
$687$	9.45050e9	−	2.68945e9i	1.11200	−	0.316457i
$688$	3.86086e9	−	2.90003e9i	0.451985	−	0.339502i
$689$			6.27551e8i			0.0730941i
$690$	−6.44055e9	−	3.89082e9i	−0.746365	−	0.450888i
$691$	−1.13923e10	−	1.13923e10i	−1.31353	−	1.31353i	−0.918799	−	0.394727i	$-0.870839\pi$
$691$	−1.13923e10	−	1.13923e10i	−1.31353	−	1.31353i	−0.394727	−	0.918799i	$-0.629161\pi$
$692$	−3.14420e9	+	2.72895e9i	−0.360694	+	0.313058i
$693$	−2.02381e9	+	8.60886e9i	−0.230995	+	0.982605i
$694$	−9.84679e7	+	2.78887e9i	−0.0111824	+	0.316716i
$695$			2.34234e10i			2.64670i
$696$	−8.55561e9	+	1.21369e10i	−0.961875	+	1.36451i
$697$			2.86114e9i			0.320055i
$698$	−1.90525e9	−	6.72695e7i	−0.212060	−	0.00748728i
$699$	−2.57839e8	+	4.62968e8i	−0.0285548	+	0.0512721i
$700$	−1.18075e10	−	8.34827e8i	−1.30111	−	0.0919927i
$701$	3.20826e9	+	3.20826e9i	0.351768	+	0.351768i	0.860767	−	0.508999i	$-0.169984\pi$
$701$	3.20826e9	+	3.20826e9i	0.351768	+	0.351768i	−0.508999	+	0.860767i	$0.669984\pi$
$702$	2.50354e9	−	2.77115e7i	0.273133	−	0.00302329i
$703$			2.49007e10i			2.70313i
$704$	5.84683e9	−	3.77774e9i	0.631562	−	0.408064i
$705$	3.46056e9	+	1.21601e10i	0.371950	+	1.30700i
$706$	−1.00852e10	+	9.39732e9i	−1.07862	+	1.00505i
$707$	7.12589e9	−	7.12589e9i	0.758353	−	0.758353i
$708$	2.04436e9	+	9.75079e9i	0.216492	+	1.03258i
$709$	−5.05524e9	−	5.05524e9i	−0.532697	−	0.532697i	0.388677	−	0.921374i	$-0.372932\pi$
$709$	−5.05524e9	−	5.05524e9i	−0.532697	−	0.532697i	−0.921374	+	0.388677i	$0.872932\pi$
$710$	4.75948e8	−	1.34801e10i	0.0499063	−	1.41348i
$711$	9.73946e8	−	6.03187e8i	0.101623	−	0.0629373i
$712$	2.63187e9	−	2.12620e9i	0.273265	−	0.220762i
$713$	9.85984e9			1.01872
$714$	1.33542e9	+	5.41104e9i	0.137301	+	0.556336i
$715$	−1.99317e9	+	1.99317e9i	−0.203927	+	0.203927i
$716$	1.01883e10	+	1.17386e10i	1.03730	+	1.19514i
$717$	2.37259e9	−	4.26015e9i	0.240384	−	0.431627i
$718$	−1.92480e9	+	1.79351e9i	−0.194066	+	0.180830i
$719$	−7.45642e9			−0.748134			−0.374067	−	0.927402i	$-0.622037\pi$
$719$	−7.45642e9			−0.748134			−0.374067	+	0.927402i	$0.622037\pi$
$720$	1.31008e10	+	5.11245e9i	1.30808	+	0.510464i
$721$	−8.55833e9			−0.850385
$722$	1.64113e10	−	1.52919e10i	1.62279	−	1.51210i
$723$	−5.66585e9	+	1.01734e10i	−0.557547	+	1.00111i
$724$	−1.36256e10	+	1.18261e10i	−1.33435	+	1.15813i
$725$	1.17694e10	−	1.17694e10i	1.14702	−	1.14702i
$726$	−1.07369e9	−	4.35053e9i	−0.104136	−	0.421953i
$727$	1.00185e10			0.967013			0.483506	−	0.875341i	$-0.339363\pi$
$727$	1.00185e10			0.967013			0.483506	+	0.875341i	$0.339363\pi$
$728$	4.03407e8	−	3.79585e9i	0.0387510	−	0.364627i
$729$	1.04154e10	−	9.68521e8i	0.995704	−	0.0925897i
$730$	6.11899e7	−	1.73306e9i	0.00582170	−	0.164886i
$731$	1.80200e9	+	1.80200e9i	0.170626	+	0.170626i
$732$	−8.70817e9	+	1.82576e9i	−0.820613	+	0.172051i
$733$	4.05155e9	−	4.05155e9i	0.379977	−	0.379977i	−0.491117	−	0.871094i	$-0.663411\pi$
$733$	4.05155e9	−	4.05155e9i	0.379977	−	0.379977i	0.871094	+	0.491117i	$0.163411\pi$
$734$	−6.26571e9	+	5.83835e9i	−0.584836	+	0.544946i
$735$	3.31846e9	+	1.16608e10i	0.308270	+	1.08323i
$736$	5.50957e9	−	3.84201e9i	0.509384	−	0.355210i
$737$		−	3.54125e9i		−	0.325852i
$738$	2.15365e9	−	7.89882e9i	0.197232	−	0.723378i
$739$	−1.58294e8	−	1.58294e8i	−0.0144281	−	0.0144281i	0.699856	−	0.714284i	$-0.253248\pi$
$739$	−1.58294e8	−	1.58294e8i	−0.0144281	−	0.0144281i	−0.714284	+	0.699856i	$0.753248\pi$
$740$	−1.64494e9	+	2.32655e10i	−0.149224	+	2.11058i
$741$	2.64057e9	−	4.74133e9i	0.238415	−	0.428091i
$742$	3.99495e9	+	1.41051e8i	0.359003	+	0.0126755i
$743$		−	4.99431e9i		−	0.446698i	−0.974738	−	0.223349i	$-0.928301\pi$
$743$		−	4.99431e9i		−	0.446698i	0.974738	−	0.223349i	$-0.0716990\pi$
$744$	−1.81576e10	+	3.14258e9i	−1.61642	+	0.279757i
$745$		−	3.31596e9i		−	0.293807i
$746$	−2.56074e8	+	7.25269e9i	−0.0225829	+	0.639607i
$747$	−1.09274e10	−	2.56885e9i	−0.959164	−	0.225484i
$748$	2.40810e9	+	2.77452e9i	0.210387	+	0.242400i
$749$	−1.30817e10	−	1.30817e10i	−1.13757	−	1.13757i
$750$	3.93620e8	+	2.37791e8i	0.0340693	+	0.0205817i
$751$		−	8.59873e9i		−	0.740789i	−0.928875	−	0.370395i	$-0.879222\pi$
$751$		−	8.59873e9i		−	0.740789i	0.928875	−	0.370395i	$-0.120778\pi$
$752$	−1.11735e10	−	1.58794e9i	−0.958139	−	0.136167i
$753$	−1.68382e8	+	4.79186e7i	−0.0143719	+	0.00408998i
$754$	3.65914e9	+	3.92699e9i	0.310871	+	0.333626i
$755$	5.39917e9	−	5.39917e9i	0.456575	−	0.456575i
$756$	3.86297e8	−	1.59436e10i	0.0325159	−	1.34202i
$757$	−1.41436e10	−	1.41436e10i	−1.18501	−	1.18501i	−0.978429	−	0.206585i	$-0.933765\pi$
$757$	−1.41436e10	−	1.41436e10i	−1.18501	−	1.18501i	−0.206585	−	0.978429i	$-0.566235\pi$
$758$	1.52432e10	+	5.38198e8i	1.27126	+	0.0448848i
$759$	1.53961e9	+	5.41007e9i	0.127810	+	0.449114i
$760$	2.37122e10	−	1.91563e10i	1.95940	−	1.58294i
$761$	1.39613e8			0.0114836			0.00574182	−	0.999984i	$-0.498172\pi$
$761$	1.39613e8			0.0114836			0.00574182	+	0.999984i	$0.498172\pi$
$762$	1.67126e9	+	6.77182e9i	0.136836	+	0.554451i
$763$	−2.07188e9	+	2.07188e9i	−0.168861	+	0.168861i
$764$	1.25950e9	−	1.78140e10i	0.102181	−	1.44522i
$765$	−1.69849e9	+	7.22501e9i	−0.137166	+	0.583476i
$766$	4.38521e9	+	4.70620e9i	0.352525	+	0.378329i
$767$	3.60122e9			0.288181
$768$	−8.92171e9	+	8.83137e9i	−0.710696	+	0.703499i
$769$	2.46932e10			1.95810			0.979052	−	0.203612i	$-0.0652683\pi$
$769$	2.46932e10			1.95810			0.979052	+	0.203612i	$0.0652683\pi$
$770$	1.22404e10	+	1.31364e10i	0.966226	+	1.03695i
$771$	9.13050e8	+	5.08501e8i	0.0717471	+	0.0399578i
$772$	−3.45285e8	+	4.88359e9i	−0.0270095	+	0.382014i
$773$	−1.57995e9	+	1.57995e9i	−0.123031	+	0.123031i	−0.765942	−	0.642910i	$-0.777727\pi$
$773$	−1.57995e9	+	1.57995e9i	−0.123031	+	0.123031i	0.642910	+	0.765942i	$0.277727\pi$
$774$	−3.61842e9	−	6.33124e9i	−0.280495	−	0.490790i
$775$	2.06552e10			1.59394
$776$	5.37113e9	−	4.33916e9i	0.412619	−	0.333342i
$777$	2.54401e10	−	7.23981e9i	1.94556	−	0.553673i
$778$	−1.47978e10	−	5.22473e8i	−1.12660	−	0.0397773i
$779$	−1.25488e10	−	1.25488e10i	−0.951086	−	0.951086i
$780$	2.78038e9	−	4.25554e9i	0.209784	−	0.321088i
$781$	−7.12986e9	+	7.12986e9i	−0.535553	+	0.535553i
$782$	2.41663e9	+	2.59353e9i	0.180712	+	0.193940i
$783$	1.65751e10	+	1.51053e10i	1.23393	+	1.12451i
$784$	−1.07147e10	−	1.52274e9i	−0.794101	−	0.112855i
$785$			2.14992e10i			1.58627i
$786$	2.42952e9	−	4.02163e9i	0.178460	−	0.295409i
$787$	1.34029e10	+	1.34029e10i	0.980136	+	0.980136i	0.999807	−	0.0196708i	$-0.00626181\pi$
$787$	1.34029e10	+	1.34029e10i	0.980136	+	0.980136i	−0.0196708	+	0.999807i	$0.506262\pi$
$788$	1.05321e10	+	1.21348e10i	0.766787	+	0.883465i
$789$	7.07118e9	+	3.93812e9i	0.512534	+	0.285443i
$790$	8.20722e7	−	2.32450e9i	0.00592245	−	0.167739i
$791$			1.90046e10i			1.36534i
$792$	−4.55964e9	−	9.47232e9i	−0.326131	−	0.677514i
$793$			3.21615e9i			0.229024i
$794$	−2.30179e10	−	8.12703e8i	−1.63190	−	0.0576182i
$795$	4.65070e9	+	2.59009e9i	0.328271	+	0.182823i
$796$	7.70992e7	−	1.09047e9i	0.00541819	−	0.0766331i
$797$	−1.03662e10	−	1.03662e10i	−0.725293	−	0.725293i	0.244385	−	0.969678i	$-0.421414\pi$
$797$	−1.03662e10	−	1.03662e10i	−0.725293	−	0.725293i	−0.969678	+	0.244385i	$0.921414\pi$
$798$	−2.95895e10	−	1.78754e10i	−2.06123	−	1.24522i
$799$		−	5.95625e9i		−	0.413104i
$800$	1.15419e10	−	8.04855e9i	0.797006	−	0.555779i
$801$	−2.69033e9	−	4.34399e9i	−0.184966	−	0.298659i
$802$	9.98255e9	−	9.30167e9i	0.683331	−	0.636723i
$803$	−9.16644e8	+	9.16644e8i	−0.0624736	+	0.0624736i
$804$	1.31045e9	+	6.25032e9i	0.0889251	+	0.424137i
$805$	1.22509e10	+	1.22509e10i	0.827717	+	0.827717i
$806$	−2.35034e8	+	6.65679e9i	−0.0158110	+	0.447809i
$807$	−1.14837e10	+	3.26805e9i	−0.769171	+	0.218893i
$808$	−1.26600e9	+	1.19124e10i	−0.0844295	+	0.794438i
$809$	−2.49260e10			−1.65513			−0.827567	−	0.561367i	$-0.810276\pi$
$809$	−2.49260e10			−1.65513			−0.827567	+	0.561367i	$0.810276\pi$
$810$	1.01275e10	−	1.86678e10i	0.669583	−	1.23423i
$811$	7.30049e9	−	7.30049e9i	0.480595	−	0.480595i	−0.424727	−	0.905322i	$-0.639630\pi$
$811$	7.30049e9	−	7.30049e9i	0.480595	−	0.480595i	0.905322	+	0.424727i	$0.139630\pi$
$812$	2.58214e10	−	2.24112e10i	1.69252	−	1.46899i
$813$	3.33259e9	+	1.85601e9i	0.217503	+	0.121133i
$814$	1.27559e10	−	1.18858e10i	0.828944	−	0.772404i
$815$	−3.55265e10			−2.29880
$816$	−5.27702e9	−	4.00592e9i	−0.339996	−	0.258099i
$817$	−1.58069e10			−1.01407
$818$	−9.01381e9	+	8.39901e9i	−0.575800	+	0.536527i
$819$	−5.61179e9	−	1.31924e9i	−0.356950	−	0.0839134i
$820$	−1.08957e10	−	1.25537e10i	−0.690094	−	0.795101i
$821$	−5.28763e9	+	5.28763e9i	−0.333472	+	0.333472i	−0.853904	−	0.520431i	$-0.825771\pi$
$821$	−5.28763e9	+	5.28763e9i	−0.333472	+	0.333472i	0.520431	+	0.853904i	$0.325771\pi$
$822$	−1.41260e10	+	3.48624e9i	−0.887093	+	0.218930i
$823$	−7.46650e9			−0.466893			−0.233447	−	0.972370i	$-0.575000\pi$
$823$	−7.46650e9			−0.466893			−0.233447	+	0.972370i	$0.575000\pi$
$824$	7.91377e9	−	6.39328e9i	0.492763	−	0.398087i
$825$	3.22531e9	+	1.13335e10i	0.199978	+	0.702706i
$826$	8.09427e8	−	2.29251e10i	0.0499744	−	1.41541i
$827$	7.49492e9	+	7.49492e9i	0.460784	+	0.460784i	0.898912	−	0.438128i	$-0.144358\pi$
$827$	7.49492e9	+	7.49492e9i	0.460784	+	0.460784i	−0.438128	+	0.898912i	$0.644358\pi$
$828$	−4.71944e9	−	8.97906e9i	−0.288924	−	0.549699i
$829$	1.32065e10	−	1.32065e10i	0.805093	−	0.805093i	−0.178794	−	0.983887i	$-0.557219\pi$
$829$	1.32065e10	−	1.32065e10i	0.805093	−	0.805093i	0.983887	+	0.178794i	$0.0572194\pi$
$830$	−1.66742e10	+	1.55369e10i	−1.01221	+	0.943175i
$831$	−2.09987e10	+	5.97586e9i	−1.26937	+	0.361241i
$832$	2.46257e9	+	3.81132e9i	0.148237	+	0.229427i
$833$		−	5.71168e9i		−	0.342378i
$834$	−1.63279e10	+	2.70278e10i	−0.974648	+	1.61336i
$835$	−6.60142e9	−	6.60142e9i	−0.392405	−	0.392405i
$836$	−2.27306e10	−	1.60712e9i	−1.34552	−	0.0951320i
$837$	1.28974e9	+	2.77993e10i	0.0760259	+	1.63868i
$838$	−1.89997e10	−	6.70830e8i	−1.11530	−	0.0393784i
$839$		−	1.41148e10i		−	0.825102i	−0.910934	−	0.412551i	$-0.864638\pi$
$839$		−	1.41148e10i		−	0.825102i	0.910934	−	0.412551i	$-0.135362\pi$
$840$	−2.64655e10	−	1.86562e10i	−1.54065	−	1.08604i
$841$			3.08270e10i			1.78709i
$842$	−8.84123e7	+	2.50407e9i	−0.00510412	+	0.144562i
$843$	9.59200e9	−	1.72231e10i	0.551458	−	0.990182i
$844$	2.33497e9	−	2.02660e9i	0.133685	−	0.116030i
$845$	1.61147e10	+	1.61147e10i	0.918808	+	0.918808i
$846$	−4.48342e9	+	1.64436e10i	−0.254573	+	0.933683i
$847$			1.03177e10i			0.583432i
$848$	−3.79944e9	+	2.85389e9i	−0.213961	+	0.160713i
$849$	−1.53093e9	−	5.37956e9i	−0.0858576	−	0.301696i
$850$	5.06255e9	+	5.43313e9i	0.282751	+	0.303448i
$851$	1.18960e10	−	1.18960e10i	0.661680	−	0.661680i
$852$	9.94581e9	−	1.52227e10i	0.550937	−	0.843241i
$853$	6.71555e9	+	6.71555e9i	0.370476	+	0.370476i	0.867651	−	0.497174i	$-0.165629\pi$
$853$	6.71555e9	+	6.71555e9i	0.370476	+	0.370476i	−0.497174	+	0.867651i	$0.665629\pi$
$854$	2.04738e10	+	7.22878e8i	1.12485	+	0.0397157i
$855$	−2.42389e10	−	3.91378e10i	−1.32627	−	2.14148i
$856$	2.18689e10	+	2.32413e9i	1.19170	+	0.126649i
$857$	−1.26443e10			−0.686218			−0.343109	−	0.939296i	$-0.611480\pi$
$857$	−1.26443e10			−0.686218			−0.343109	+	0.939296i	$0.611480\pi$
$858$	−3.68927e9	+	9.10495e8i	−0.199405	+	0.0492121i
$859$	2.86640e9	−	2.86640e9i	0.154298	−	0.154298i	−0.625736	−	0.780035i	$-0.715201\pi$
$859$	2.86640e9	−	2.86640e9i	0.154298	−	0.154298i	0.780035	+	0.625736i	$0.215201\pi$
$860$	−1.47689e10	−	1.04421e9i	−0.791778	−	0.0559811i
$861$	−9.17209e9	+	1.64691e10i	−0.489731	+	0.879346i
$862$	−8.91027e9	−	9.56249e9i	−0.473822	−	0.508506i
$863$	1.22496e10			0.648762			0.324381	−	0.945927i	$-0.394844\pi$
$863$	1.22496e10			0.648762			0.324381	+	0.945927i	$0.394844\pi$
$864$	1.15530e10	+	1.50314e10i	0.609394	+	0.792868i
$865$	1.27656e10			0.670631
$866$	5.90559e9	+	6.33787e9i	0.308994	+	0.331612i
$867$	−7.63557e9	+	1.37102e10i	−0.397901	+	0.714459i
$868$	4.23238e10	+	2.99242e9i	2.19668	+	0.155312i
$869$	−1.22947e9	+	1.22947e9i	−0.0635548	+	0.0635548i
$870$	4.42048e10	−	1.09095e10i	2.27589	−	0.561680i
$871$	2.30841e9			0.118372
$872$	3.68094e8	−	3.46358e9i	0.0187997	−	0.176896i
$873$	−5.49044e9	−	8.86524e9i	−0.279291	−	0.450963i
$874$	−2.19742e10	−	7.75852e8i	−1.11333	−	0.0393087i
$875$	−7.48724e8	−	7.48724e8i	−0.0377827	−	0.0377827i
$876$	1.27867e9	−	1.95709e9i	0.0642681	−	0.0983662i
$877$	−2.10741e10	+	2.10741e10i	−1.05500	+	1.05500i	−0.0565997	+	0.998397i	$0.518026\pi$
$877$	−2.10741e10	+	2.10741e10i	−1.05500	+	1.05500i	−0.998397	+	0.0565997i	$0.981974\pi$
$878$	3.30294e9	+	3.54471e9i	0.164691	+	0.176746i
$879$	−8.53579e9	−	2.99941e10i	−0.423919	−	1.48962i
$880$	−2.11317e10	−	3.00317e9i	−1.04531	−	0.148556i
$881$		−	7.26335e9i		−	0.357867i	−0.983861	−	0.178933i	$-0.942735\pi$
$881$		−	7.26335e9i		−	0.357867i	0.983861	−	0.178933i	$-0.0572646\pi$
$882$	−4.29932e9	+	1.57684e10i	−0.210989	+	0.773832i
$883$	−1.39623e10	−	1.39623e10i	−0.682488	−	0.682488i	0.278072	−	0.960560i	$-0.410305\pi$
$883$	−1.39623e10	−	1.39623e10i	−0.682488	−	0.682488i	−0.960560	+	0.278072i	$0.910305\pi$
$884$	−1.80861e9	+	1.56975e9i	−0.0880564	+	0.0764270i
$885$	1.48633e10	−	2.66881e10i	0.720799	−	1.29425i
$886$	−1.99718e8	+	5.65654e9i	−0.00964714	+	0.273233i
$887$		−	8.62024e9i		−	0.414750i	−0.978261	−	0.207375i	$-0.933508\pi$
$887$		−	8.62024e9i		−	0.414750i	0.978261	−	0.207375i	$-0.0664921\pi$
$888$	−1.81158e10	+	2.56989e10i	−0.868185	+	1.23160i
$889$		−	1.60600e10i		−	0.766636i
$890$	−1.03677e10	−	3.66058e8i	−0.492968	−	0.0174054i
$891$	−1.50520e10	+	5.04854e9i	−0.712891	+	0.239108i
$892$	−3.25370e10	−	2.30046e9i	−1.53497	−	0.108527i
$893$	2.61237e10	+	2.61237e10i	1.22759	+	1.22759i
$894$	2.31147e9	−	3.82622e9i	0.108195	−	0.179097i
$895$		−	4.76589e10i		−	2.22210i
$896$	2.48161e10	−	1.48199e10i	1.15254	−	0.688282i
$897$	−3.52662e9	+	1.00362e9i	−0.163149	+	0.0464295i
$898$	1.65097e10	−	1.53836e10i	0.760802	−	0.708910i
$899$	−4.21872e10	+	4.21872e10i	−1.93652	+	1.93652i
$900$	−9.88666e9	−	1.88101e10i	−0.452065	−	0.860086i
$901$	−1.77334e9	−	1.77334e9i	−0.0807709	−	0.0807709i
$902$	−4.38457e8	+	1.24183e10i	−0.0198932	+	0.563428i
$903$	4.59582e9	+	1.61493e10i	0.207709	+	0.729874i
$904$	−1.41969e10	−	1.75732e10i	−0.639150	−	0.791157i
$905$	5.53203e10			2.48093
$906$	9.99360e9	−	2.46638e9i	0.446450	−	0.110182i
$907$	−1.59200e10	+	1.59200e10i	−0.708464	+	0.708464i	−0.966212	−	0.257748i	$-0.917019\pi$
$907$	−1.59200e10	+	1.59200e10i	−0.708464	+	0.708464i	0.257748	+	0.966212i	$0.417019\pi$
$908$	−1.99442e10	−	2.29790e10i	−0.884129	−	1.01866i
$909$	1.76113e10	+	4.14015e9i	0.777711	+	0.182828i
$910$	−8.56312e9	+	7.97906e9i	−0.376693	+	0.351000i
$911$	−6.62401e9			−0.290273			−0.145136	−	0.989412i	$-0.546362\pi$
$911$	−6.62401e9			−0.290273			−0.145136	+	0.989412i	$0.546362\pi$
$912$	4.07143e10	−	5.57494e9i	1.77732	−	0.243365i
$913$	1.70370e10			0.740877
$914$	5.17331e9	−	4.82045e9i	0.224108	−	0.208822i
$915$	2.38345e10	+	1.32740e10i	1.02856	+	0.572834i
$916$	2.03106e10	−	1.76282e10i	0.873148	−	0.757833i
$917$	−7.64974e9	+	7.64974e9i	−0.327608	+	0.327608i
$918$	−6.99621e9	+	7.15282e9i	−0.298479	+	0.305160i
$919$	1.84648e10			0.784765			0.392382	−	0.919802i	$-0.371651\pi$
$919$	1.84648e10			0.784765			0.392382	+	0.919802i	$0.371651\pi$
$920$	−2.04799e10	−	2.17652e9i	−0.867103	−	0.0921520i
$921$	−1.79967e10	+	5.12155e9i	−0.759074	+	0.216019i
$922$	8.32592e8	−	2.35812e10i	0.0349844	−	0.990850i
$923$	−4.64769e9	−	4.64769e9i	−0.194550	−	0.194550i
$924$	4.96693e9	+	2.36903e10i	0.207127	+	0.987912i
$925$	2.49207e10	−	2.49207e10i	1.03530	−	1.03530i
$926$	−6.88174e9	+	6.41236e9i	−0.284813	+	0.265387i
$927$	−8.08957e9	−	1.30620e10i	−0.333539	−	0.538555i
$928$	−7.13498e9	+	4.00125e10i	−0.293072	+	1.64353i
$929$		−	3.68737e10i		−	1.50890i	−0.656356	−	0.754451i	$-0.727903\pi$
$929$		−	3.68737e10i		−	1.50890i	0.656356	−	0.754451i	$-0.272097\pi$
$930$	4.83625e10	+	2.92164e10i	1.97160	+	1.19107i
$931$	2.50510e10	+	2.50510e10i	1.01742	+	1.01742i
$932$	−1.02295e8	+	1.44683e9i	−0.00413904	+	0.0585412i
$933$	−2.62577e10	−	1.46236e10i	−1.05845	−	0.589480i
$934$	2.17078e10	+	7.66445e8i	0.871768	+	0.0307799i
$935$		−	1.12646e10i		−	0.450689i
$936$	6.17465e9	−	2.97225e9i	0.246120	−	0.118473i
$937$			1.04368e10i			0.414455i	0.978293	+	0.207228i	$0.0664441\pi$
$937$			1.04368e10i			0.414455i	−0.978293	+	0.207228i	$0.933556\pi$
$938$	5.18848e8	−	1.46952e10i	0.0205272	−	0.581386i
$939$	2.69409e10	+	1.50041e10i	1.06190	+	0.591397i
$940$	2.26825e10	+	2.61339e10i	0.890723	+	1.02626i
$941$	1.66179e10	+	1.66179e10i	0.650148	+	0.650148i	0.953029	−	0.302881i	$-0.0979483\pi$
$941$	1.66179e10	+	1.66179e10i	0.650148	+	0.650148i	−0.302881	+	0.953029i	$0.597948\pi$
$942$	−1.49865e10	+	2.48075e10i	−0.584147	+	0.966951i
$943$			1.19901e10i			0.465619i
$944$	1.63771e10	+	2.18032e10i	0.633631	+	0.843564i
$945$	−3.29382e10	+	3.61432e10i	−1.26966	+	1.39321i
$946$	7.54512e9	+	8.09742e9i	0.289766	+	0.310977i
$947$	1.78337e10	−	1.78337e10i	0.682366	−	0.682366i	−0.278166	−	0.960533i	$-0.589727\pi$
$947$	1.78337e10	−	1.78337e10i	0.682366	−	0.682366i	0.960533	+	0.278166i	$0.0897267\pi$
$948$	1.71505e9	−	2.62499e9i	0.0653804	−	0.100069i
$949$	−5.97526e8	−	5.97526e8i	−0.0226947	−	0.0226947i
$950$	−4.60333e10	−	1.62532e9i	−1.74196	−	0.0615043i
$951$	3.84823e10	−	1.09514e10i	1.45087	−	0.412893i
$952$	9.58638e9	+	1.18663e10i	0.360102	+	0.445744i
$953$	1.62944e10			0.609836			0.304918	−	0.952379i	$-0.401371\pi$
$953$	1.62944e10			0.609836			0.304918	+	0.952379i	$0.401371\pi$
$954$	3.56086e9	+	6.23053e9i	0.132781	+	0.232330i
$955$	−3.87194e10	+	3.87194e10i	−1.43852	+	1.43852i
$956$	9.41302e8	−	1.33135e10i	0.0348439	−	0.492820i
$957$	−2.97356e10	−	1.65605e10i	−1.09669	−	0.610776i
$958$	1.53942e10	+	1.65211e10i	0.565690	+	0.607098i
$959$	3.35012e10			1.22658
$960$	3.84089e10	−	2.51926e9i	1.40114	−	0.0919016i
$961$	−4.65255e10			−1.69106
$962$	7.74793e9	+	8.31507e9i	0.280591	+	0.301130i
$963$	7.60050e9	−	3.23310e10i	0.274252	−	1.16661i
$964$	−2.24787e9	+	3.17932e10i	−0.0808169	+	1.14305i
$965$	1.06147e10	−	1.06147e10i	0.380244	−	0.380244i
$966$	5.59628e9	+	2.26758e10i	0.199747	+	0.809362i
$967$	−3.40701e10			−1.21166			−0.605831	−	0.795594i	$-0.707159\pi$
$967$	−3.40701e10			−1.21166			−0.605831	+	0.795594i	$0.707159\pi$
$968$	−7.70755e9	−	9.54061e9i	−0.273119	−	0.338075i
$969$	5.93634e9	+	2.08598e10i	0.209597	+	0.736507i
$970$	−2.11585e10	−	7.47053e8i	−0.744362	−	0.0262815i
$971$	−1.04394e10	−	1.04394e10i	−0.365939	−	0.365939i	0.500055	−	0.865994i	$-0.333313\pi$
$971$	−1.04394e10	−	1.04394e10i	−0.365939	−	0.365939i	−0.865994	+	0.500055i	$0.833313\pi$
$972$	2.46987e10	−	1.44807e10i	0.862664	−	0.505777i
$973$	5.14110e10	−	5.14110e10i	1.78921	−	1.78921i
$974$	1.88628e10	+	2.02436e10i	0.654110	+	0.701990i
$975$	−7.38785e9	+	2.10245e9i	−0.255271	+	0.0726458i
$976$	−1.94719e10	+	1.46260e10i	−0.670398	+	0.503560i
$977$		−	1.63745e10i		−	0.561743i	−0.959745	−	0.280872i	$-0.909376\pi$
$977$		−	1.63745e10i		−	0.561743i	0.959745	−	0.280872i	$-0.0906236\pi$
$978$	−4.09934e10	−	2.47646e10i	−1.40129	−	0.846535i
$979$	5.48367e9	+	5.48367e9i	0.186781	+	0.186781i
$980$	2.17511e10	+	2.50608e10i	0.738227	+	0.850559i
$981$	−5.12055e9	−	1.20376e9i	−0.173171	−	0.0407098i
$982$	−1.34359e9	+	3.80539e10i	−0.0452767	+	1.28236i
$983$		−	8.72672e9i		−	0.293031i	−0.989208	−	0.146516i	$-0.953194\pi$
$983$		−	8.72672e9i		−	0.293031i	0.989208	−	0.146516i	$-0.0468058\pi$
$984$	−3.82154e9	−	2.20806e10i	−0.127866	−	0.738800i
$985$		−	4.92675e10i		−	1.64261i
$986$	−2.14369e10	−	7.56883e8i	−0.712186	−	0.0251455i
$987$	1.90942e10	−	3.42850e10i	0.632109	−	1.13500i
$988$	1.04762e9	−	1.48172e10i	0.0345585	−	0.488784i
$989$	7.55158e9	+	7.55158e9i	0.248228	+	0.248228i
$990$	−8.47917e9	+	3.10986e10i	−0.277735	+	1.01863i
$991$		−	1.25515e10i		−	0.409672i	−0.978796	−	0.204836i	$-0.934334\pi$
$991$		−	1.25515e10i		−	0.409672i	0.978796	−	0.204836i	$-0.0656661\pi$
$992$	−4.13717e10	+	2.88499e10i	−1.34559	+	0.938325i
$993$	−1.22012e10	−	4.28741e10i	−0.395440	−	1.38955i
$994$	−3.06315e10	+	2.85422e10i	−0.989272	+	0.921797i
$995$	−2.37017e9	+	2.37017e9i	−0.0762780	+	0.0762780i
$996$	−3.00704e10	+	6.30460e9i	−0.964344	+	0.202185i
$997$	−1.97841e10	−	1.97841e10i	−0.632243	−	0.632243i	0.316387	−	0.948630i	$-0.397530\pi$
$997$	−1.97841e10	−	1.97841e10i	−0.632243	−	0.632243i	−0.948630	+	0.316387i	$0.897530\pi$
$998$	2.10292e9	−	5.95603e10i	0.0669678	−	1.89671i
$999$	3.50963e10	+	3.19841e10i	1.11374	+	1.01498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.8.k.a.11.13	✓	108
3.2	odd	2	inner	48.8.k.a.11.42	yes	108
16.3	odd	4	inner	48.8.k.a.35.42	yes	108
48.35	even	4	inner	48.8.k.a.35.13	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.8.k.a.11.13	✓	108	1.1	even	1	trivial
48.8.k.a.11.42	yes	108	3.2	odd	2	inner
48.8.k.a.35.13	yes	108	48.35	even	4	inner
48.8.k.a.35.42	yes	108	16.3	odd	4	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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.71273 - 8.27730i) q^{2} +(-22.7540 + 40.8565i) q^{3} +(-9.02745 + 127.681i) q^{4} +(277.521 - 277.521i) q^{5} +(513.677 - 126.773i) q^{6} -1218.23 q^{7} +(1126.48 - 910.049i) q^{8} +(-1151.51 - 1859.30i) q^{9} +O(q^{10})\)	\(q+(-7.71273 - 8.27730i) q^{2} +(-22.7540 + 40.8565i) q^{3} +(-9.02745 + 127.681i) q^{4} +(277.521 - 277.521i) q^{5} +(513.677 - 126.773i) q^{6} -1218.23 q^{7} +(1126.48 - 910.049i) q^{8} +(-1151.51 - 1859.30i) q^{9} +(-4437.56 - 156.679i) q^{10} +(2347.10 + 2347.10i) q^{11} +(-5011.20 - 3274.09i) q^{12} +(-1529.99 + 1529.99i) q^{13} +(9395.90 + 10083.7i) q^{14} +(5023.81 + 17653.2i) q^{15} +(-16221.0 - 2305.27i) q^{16} -8646.89i q^{17} +(-6508.73 + 23871.7i) q^{18} +(37924.6 + 37924.6i) q^{19} +(32928.9 + 37939.5i) q^{20} +(27719.7 - 49772.7i) q^{21} +(1325.10 - 37530.3i) q^{22} -36236.1i q^{23} +(11549.4 + 66731.4i) q^{24} -75910.4i q^{25} +(24464.6 + 863.780i) q^{26} +(102166. - 4739.94i) q^{27} +(10997.5 - 155545. i) q^{28} +(155043. + 155043. i) q^{29} +(107374. - 177738. i) q^{30} +272100. i q^{31} +(106027. + 152046. i) q^{32} +(-149301. + 42488.3i) q^{33} +(-71572.9 + 66691.2i) q^{34} +(-338085. + 338085. i) q^{35} +(247793. - 130241. i) q^{36} +(328291. + 328291. i) q^{37} +(21411.0 - 606416. i) q^{38} +(-27696.5 - 97323.3i) q^{39} +(60064.9 - 565179. i) q^{40} -330887. q^{41} +(-625779. + 154439. i) q^{42} +(-208399. + 208399. i) q^{43} +(-320869. + 278493. i) q^{44} +(-835561. - 196427. i) q^{45} +(-299937. + 279480. i) q^{46} +688832. q^{47} +(463279. - 610279. i) q^{48} +660547. q^{49} +(-628333. + 585477. i) q^{50} +(353282. + 196752. i) q^{51} +(-181539. - 209163. i) q^{52} +(205084. - 205084. i) q^{53} +(-827213. - 809101. i) q^{54} +1.30274e6 q^{55} +(-1.37232e6 + 1.10865e6i) q^{56} +(-2.41241e6 + 686529. i) q^{57} +(87532.4 - 2.47915e6i) q^{58} +(-1.17688e6 - 1.17688e6i) q^{59} +(-2.29934e6 + 482082. i) q^{60} +(1.05104e6 - 1.05104e6i) q^{61} +(2.25225e6 - 2.09863e6i) q^{62} +(1.40280e6 + 2.26506e6i) q^{63} +(440774. - 2.05031e6i) q^{64} +849206. i q^{65} +(1.50320e6 + 908104. i) q^{66} +(-754388. - 754388. i) q^{67} +(1.10405e6 + 78059.4i) q^{68} +(1.48048e6 + 824519. i) q^{69} +(5.40599e6 + 190871. i) q^{70} +3.03773e6i q^{71} +(-2.98921e6 - 1.04654e6i) q^{72} +390543. i q^{73} +(185343. - 5.24939e6i) q^{74} +(3.10143e6 + 1.72727e6i) q^{75} +(-5.18463e6 + 4.49990e6i) q^{76} +(-2.85932e6 - 2.85932e6i) q^{77} +(-591958. + 979881. i) q^{78} +523824. i q^{79} +(-5.14143e6 + 3.86190e6i) q^{80} +(-2.13103e6 + 4.28200e6i) q^{81} +(2.55204e6 + 2.73885e6i) q^{82} +(3.62937e6 - 3.62937e6i) q^{83} +(6.10481e6 + 3.98861e6i) q^{84} +(-2.39969e6 - 2.39969e6i) q^{85} +(3.33231e6 + 117655. i) q^{86} +(-9.86239e6 + 2.80667e6i) q^{87} +(4.77995e6 + 507993. i) q^{88} +2.33636e6 q^{89} +(4.81857e6 + 8.43119e6i) q^{90} +(1.86388e6 - 1.86388e6i) q^{91} +(4.62668e6 + 327120. i) q^{92} +(-1.11170e7 - 6.19136e6i) q^{93} +(-5.31278e6 - 5.70167e6i) q^{94} +2.10497e7 q^{95} +(-8.62461e6 + 872224. i) q^{96} +4.76805e6 q^{97} +(-5.09463e6 - 5.46755e6i) q^{98} +(1.66127e6 - 7.06668e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7}+O(q^{10}) \) 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7	\( 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7} - 6504 q^{10} + 12016 q^{12} - 4 q^{13} - 55280 q^{16} + 21172 q^{18} - 60588 q^{19} - 4376 q^{21} - 212744 q^{22} - 317304 q^{24} + 238042 q^{27} + 219736 q^{28} - 503852 q^{30} - 4 q^{33} - 364856 q^{34} + 867620 q^{36} - 4 q^{37} - 283948 q^{39} + 390392 q^{40} - 3022344 q^{42} + 752844 q^{43} - 156252 q^{45} - 1166824 q^{46} + 358320 q^{48} + 9882508 q^{49} + 1121592 q^{51} - 4458688 q^{52} + 203816 q^{54} + 4191000 q^{55} + 4975544 q^{58} - 4390240 q^{60} - 2279892 q^{61} + 4781432 q^{64} + 1457476 q^{66} + 1552540 q^{67} + 4372 q^{69} - 9366152 q^{70} - 1660280 q^{72} - 886066 q^{75} - 6569272 q^{76} - 13616772 q^{78} - 4 q^{81} + 11560256 q^{82} - 10944176 q^{84} + 7846496 q^{85} - 40789116 q^{87} + 24614816 q^{88} + 25746032 q^{90} - 1590680 q^{91} - 14495396 q^{93} - 6995856 q^{94} - 13927736 q^{96} - 8 q^{97} - 4701076 q^{99}+O(q^{100}) \) 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7 - 6504 * q^10 + 12016 * q^12 - 4 * q^13 - 55280 * q^16 + 21172 * q^18 - 60588 * q^19 - 4376 * q^21 - 212744 * q^22 - 317304 * q^24 + 238042 * q^27 + 219736 * q^28 - 503852 * q^30 - 4 * q^33 - 364856 * q^34 + 867620 * q^36 - 4 * q^37 - 283948 * q^39 + 390392 * q^40 - 3022344 * q^42 + 752844 * q^43 - 156252 * q^45 - 1166824 * q^46 + 358320 * q^48 + 9882508 * q^49 + 1121592 * q^51 - 4458688 * q^52 + 203816 * q^54 + 4191000 * q^55 + 4975544 * q^58 - 4390240 * q^60 - 2279892 * q^61 + 4781432 * q^64 + 1457476 * q^66 + 1552540 * q^67 + 4372 * q^69 - 9366152 * q^70 - 1660280 * q^72 - 886066 * q^75 - 6569272 * q^76 - 13616772 * q^78 - 4 * q^81 + 11560256 * q^82 - 10944176 * q^84 + 7846496 * q^85 - 40789116 * q^87 + 24614816 * q^88 + 25746032 * q^90 - 1590680 * q^91 - 14495396 * q^93 - 6995856 * q^94 - 13927736 * q^96 - 8 * q^97 - 4701076 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more