LMFDB - Embedded newform 300.2.w.a.223.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 13]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			223.8
Character	$\chi$	$=$	300.223
Dual form			300.2.w.a.187.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.970742 - 1.02843i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(-0.115318 + 1.99667i) q^{4} +(-0.872817 + 2.05869i) q^{5} +(-0.475626 + 1.33183i) q^{6} +(-3.13073 - 3.13073i) q^{7} +(2.16537 - 1.81966i) q^{8} +(-0.587785 + 0.809017i) q^{9} +O(q^{10})$	\(q+(-0.970742 - 1.02843i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(-0.115318 + 1.99667i) q^{4} +(-0.872817 + 2.05869i) q^{5} +(-0.475626 + 1.33183i) q^{6} +(-3.13073 - 3.13073i) q^{7} +(2.16537 - 1.81966i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(2.96449 - 1.10083i) q^{10} +(3.28546 + 4.52205i) q^{11} +(1.83140 - 0.803721i) q^{12} +(0.499696 + 3.15496i) q^{13} +(-0.180590 + 6.25885i) q^{14} +(2.23055 - 0.156939i) q^{15} +(-3.97340 - 0.460505i) q^{16} +(2.24081 + 1.14175i) q^{17} +(1.40260 - 0.180854i) q^{18} +(0.732010 + 2.25289i) q^{19} +(-4.00987 - 1.98013i) q^{20} +(-1.36818 + 4.21082i) q^{21} +(1.46126 - 7.76860i) q^{22} +(-1.33162 + 8.40750i) q^{23} +(-2.60439 - 1.10325i) q^{24} +(-3.47638 - 3.59371i) q^{25} +(2.75956 - 3.57655i) q^{26} +(0.987688 + 0.156434i) q^{27} +(6.61207 - 5.89001i) q^{28} +(3.85116 + 1.25132i) q^{29} +(-2.32669 - 2.14161i) q^{30} +(2.06455 - 0.670814i) q^{31} +(3.38356 + 4.53338i) q^{32} +(2.53761 - 4.98034i) q^{33} +(-1.00105 - 3.41286i) q^{34} +(9.17774 - 3.71264i) q^{35} +(-1.54756 - 1.26691i) q^{36} +(-3.19578 + 0.506162i) q^{37} +(1.60634 - 2.93980i) q^{38} +(2.58423 - 1.87755i) q^{39} +(1.85613 + 6.04605i) q^{40} +(-5.37291 - 3.90365i) q^{41} +(5.65866 - 2.68055i) q^{42} +(1.00326 - 1.00326i) q^{43} +(-9.40793 + 6.03852i) q^{44} +(-1.15248 - 1.91619i) q^{45} +(9.93914 - 6.79205i) q^{46} +(0.610832 - 0.311235i) q^{47} +(1.39357 + 3.74939i) q^{48} +12.6029i q^{49} +(-0.321193 + 7.06377i) q^{50} -2.51493i q^{51} +(-6.35704 + 0.633906i) q^{52} +(-8.35495 + 4.25706i) q^{53} +(-0.797910 - 1.16762i) q^{54} +(-12.1771 + 2.81682i) q^{55} +(-12.4761 - 1.08234i) q^{56} +(1.67502 - 1.67502i) q^{57} +(-2.45160 - 5.17534i) q^{58} +(-3.98846 - 2.89779i) q^{59} +(0.0561323 + 4.47178i) q^{60} +(-2.67411 + 1.94286i) q^{61} +(-2.69403 - 1.47205i) q^{62} +(4.37301 - 0.692617i) q^{63} +(1.37768 - 7.88048i) q^{64} +(-6.93121 - 1.72498i) q^{65} +(-7.58527 + 2.22488i) q^{66} +(-0.883666 + 1.73429i) q^{67} +(-2.53811 + 4.34251i) q^{68} +(8.09568 - 2.63045i) q^{69} +(-12.7274 - 5.83461i) q^{70} +(-7.28443 - 2.36686i) q^{71} +(0.199360 + 2.82139i) q^{72} +(7.69004 + 1.21798i) q^{73} +(3.62283 + 2.79527i) q^{74} +(-1.62378 + 4.72899i) q^{75} +(-4.58271 + 1.20178i) q^{76} +(3.87142 - 24.4432i) q^{77} +(-4.43955 - 0.835068i) q^{78} +(-1.42813 + 4.39533i) q^{79} +(4.41609 - 7.77806i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(1.20110 + 9.31507i) q^{82} +(11.1730 + 5.69295i) q^{83} +(-8.24985 - 3.21739i) q^{84} +(-4.30633 + 3.61660i) q^{85} +(-2.00568 - 0.0578711i) q^{86} +(-0.633458 - 3.99950i) q^{87} +(15.3428 + 3.81351i) q^{88} +(7.91716 + 10.8970i) q^{89} +(-0.851893 + 3.04537i) q^{90} +(8.31290 - 11.4417i) q^{91} +(-16.6335 - 3.62834i) q^{92} +(-1.53499 - 1.53499i) q^{93} +(-0.913043 - 0.326067i) q^{94} +(-5.27691 - 0.459385i) q^{95} +(2.50317 - 5.07288i) q^{96} +(0.0175836 + 0.0345097i) q^{97} +(12.9612 - 12.2342i) q^{98} -5.58956 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8}+O(q^{10}) $ 240 * q + 12 * q^8	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

Coefficient data

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

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

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

$2$	−0.970742	−	1.02843i	−0.686419	−	0.727207i
$2$	−0.970742	−	1.02843i	−0.686419	−	0.727207i
$3$	−0.453990	−	0.891007i	−0.262112	−	0.514423i
$3$	−0.453990	−	0.891007i	−0.262112	−	0.514423i
$4$	−0.115318	+	1.99667i	−0.0576591	+	0.998336i
$5$	−0.872817	+	2.05869i	−0.390335	+	0.920673i
$5$	−0.872817	+	2.05869i	−0.390335	+	0.920673i
$6$	−0.475626	+	1.33183i	−0.194174	+	0.543719i
$7$	−3.13073	−	3.13073i	−1.18330	−	1.18330i	−0.978883	−	0.204421i	$-0.934469\pi$
$7$	−3.13073	−	3.13073i	−1.18330	−	1.18330i	−0.204421	−	0.978883i	$-0.565531\pi$
$8$	2.16537	−	1.81966i	0.765575	−	0.643347i
$9$	−0.587785	+	0.809017i	−0.195928	+	0.269672i
$10$	2.96449	−	1.10083i	0.937453	−	0.348112i
$11$	3.28546	+	4.52205i	0.990605	+	1.36345i	0.930916	+	0.365233i	$0.119011\pi$
$11$	3.28546	+	4.52205i	0.990605	+	1.36345i	0.0596886	+	0.998217i	$0.480989\pi$
$12$	1.83140	−	0.803721i	0.528680	−	0.232014i
$13$	0.499696	+	3.15496i	0.138591	+	0.875028i	0.954795	+	0.297265i	$0.0960743\pi$
$13$	0.499696	+	3.15496i	0.138591	+	0.875028i	−0.816204	+	0.577763i	$0.803926\pi$
$14$	−0.180590	+	6.25885i	−0.0482647	+	1.67275i
$15$	2.23055	−	0.156939i	0.575927	−	0.0405215i
$16$	−3.97340	−	0.460505i	−0.993351	−	0.115126i
$17$	2.24081	+	1.14175i	0.543477	+	0.276916i	0.704101	−	0.710100i	$-0.251350\pi$
$17$	2.24081	+	1.14175i	0.543477	+	0.276916i	−0.160623	+	0.987016i	$0.551350\pi$
$18$	1.40260	−	0.180854i	0.330596	−	0.0426276i
$19$	0.732010	+	2.25289i	0.167935	+	0.516849i	0.999241	−	0.0389657i	$-0.0124063\pi$
$19$	0.732010	+	2.25289i	0.167935	+	0.516849i	−0.831306	+	0.555815i	$0.812406\pi$
$20$	−4.00987	−	1.98013i	−0.896635	−	0.442771i
$21$	−1.36818	+	4.21082i	−0.298561	+	0.918876i
$22$	1.46126	−	7.76860i	0.311541	−	1.65627i
$23$	−1.33162	+	8.40750i	−0.277661	+	1.75308i	0.316364	+	0.948638i	$0.397538\pi$
$23$	−1.33162	+	8.40750i	−0.277661	+	1.75308i	−0.594025	+	0.804447i	$0.702462\pi$
$24$	−2.60439	−	1.10325i	−0.531618	−	0.225201i
$25$	−3.47638	−	3.59371i	−0.695276	−	0.718742i
$26$	2.75956	−	3.57655i	0.541195	−	0.701419i
$27$	0.987688	+	0.156434i	0.190081	+	0.0301058i
$28$	6.61207	−	5.89001i	1.24956	−	1.11311i
$29$	3.85116	+	1.25132i	0.715143	+	0.232364i	0.643916	−	0.765096i	$-0.277309\pi$
$29$	3.85116	+	1.25132i	0.715143	+	0.232364i	0.0712267	+	0.997460i	$0.477309\pi$
$30$	−2.32669	−	2.14161i	−0.424794	−	0.391003i
$31$	2.06455	−	0.670814i	0.370804	−	0.120482i	−0.117686	−	0.993051i	$-0.537548\pi$
$31$	2.06455	−	0.670814i	0.370804	−	0.120482i	0.488491	+	0.872569i	$0.337548\pi$
$32$	3.38356	+	4.53338i	0.598134	+	0.801396i
$33$	2.53761	−	4.98034i	0.441741	−	0.866966i
$34$	−1.00105	−	3.41286i	−0.171678	−	0.585300i
$35$	9.17774	−	3.71264i	1.55132	−	0.627550i
$36$	−1.54756	−	1.26691i	−0.257927	−	0.211152i
$37$	−3.19578	+	0.506162i	−0.525383	+	0.0832126i	−0.413492	−	0.910508i	$-0.635691\pi$
$37$	−3.19578	+	0.506162i	−0.525383	+	0.0832126i	−0.111892	+	0.993720i	$0.535691\pi$
$38$	1.60634	−	2.93980i	0.260583	−	0.476898i
$39$	2.58423	−	1.87755i	0.413808	−	0.300649i
$40$	1.85613	+	6.04605i	0.293480	+	0.955965i
$41$	−5.37291	−	3.90365i	−0.839107	−	0.609647i	0.0830140	−	0.996548i	$-0.473545\pi$
$41$	−5.37291	−	3.90365i	−0.839107	−	0.609647i	−0.922121	+	0.386901i	$0.873545\pi$
$42$	5.65866	−	2.68055i	0.873151	−	0.413618i
$43$	1.00326	−	1.00326i	0.152996	−	0.152996i	−0.626459	−	0.779454i	$-0.715496\pi$
$43$	1.00326	−	1.00326i	0.152996	−	0.152996i	0.779454	+	0.626459i	$0.215496\pi$
$44$	−9.40793	+	6.03852i	−1.41830	+	0.910341i
$45$	−1.15248	−	1.91619i	−0.171802	−	0.285649i
$46$	9.93914	−	6.79205i	1.46545	−	1.00143i
$47$	0.610832	−	0.311235i	0.0890991	−	0.0453982i	−0.408873	−	0.912591i	$-0.634078\pi$
$47$	0.610832	−	0.311235i	0.0890991	−	0.0453982i	0.497972	+	0.867193i	$0.334078\pi$
$48$	1.39357	+	3.74939i	0.201145	+	0.541178i
$49$			12.6029i			1.80042i
$50$	−0.321193	+	7.06377i	−0.0454235	+	0.998968i
$51$		−	2.51493i		−	0.352160i
$52$	−6.35704	+	0.633906i	−0.881563	+	0.0879069i
$53$	−8.35495	+	4.25706i	−1.14764	+	0.584752i	−0.921130	−	0.389256i	$-0.872732\pi$
$53$	−8.35495	+	4.25706i	−1.14764	+	0.584752i	−0.226512	+	0.974008i	$0.572732\pi$
$54$	−0.797910	−	1.16762i	−0.108582	−	0.158893i
$55$	−12.1771	+	2.81682i	−1.64196	+	0.379820i
$56$	−12.4761	−	1.08234i	−1.66718	−	0.144634i
$57$	1.67502	−	1.67502i	0.221862	−	0.221862i
$58$	−2.45160	−	5.17534i	−0.321911	−	0.679555i
$59$	−3.98846	−	2.89779i	−0.519254	−	0.377260i	0.297069	−	0.954856i	$-0.403991\pi$
$59$	−3.98846	−	2.89779i	−0.519254	−	0.377260i	−0.816323	+	0.577596i	$0.803991\pi$
$60$	0.0561323	+	4.47178i	0.00724665	+	0.577305i
$61$	−2.67411	+	1.94286i	−0.342385	+	0.248757i	−0.745667	−	0.666318i	$-0.767869\pi$
$61$	−2.67411	+	1.94286i	−0.342385	+	0.248757i	0.403282	+	0.915076i	$0.367869\pi$
$62$	−2.69403	−	1.47205i	−0.342142	−	0.186951i
$63$	4.37301	−	0.692617i	0.550947	−	0.0872615i
$64$	1.37768	−	7.88048i	0.172211	−	0.985060i
$65$	−6.93121	−	1.72498i	−0.859711	−	0.213958i
$66$	−7.58527	+	2.22488i	−0.933683	+	0.273864i
$67$	−0.883666	+	1.73429i	−0.107957	+	0.211877i	−0.938665	−	0.344831i	$-0.887936\pi$
$67$	−0.883666	+	1.73429i	−0.107957	+	0.211877i	0.830708	+	0.556709i	$0.187936\pi$
$68$	−2.53811	+	4.34251i	−0.307791	+	0.526607i
$69$	8.09568	−	2.63045i	0.974605	−	0.316668i
$70$	−12.7274	−	5.83461i	−1.52121	−	0.697369i
$71$	−7.28443	−	2.36686i	−0.864503	−	0.280894i	−0.156995	−	0.987599i	$-0.550181\pi$
$71$	−7.28443	−	2.36686i	−0.864503	−	0.280894i	−0.707508	+	0.706705i	$0.750181\pi$
$72$	0.199360	+	2.82139i	0.0234948	+	0.332504i
$73$	7.69004	+	1.21798i	0.900051	+	0.142554i	0.589278	−	0.807930i	$-0.299412\pi$
$73$	7.69004	+	1.21798i	0.900051	+	0.142554i	0.310773	+	0.950484i	$0.399412\pi$
$74$	3.62283	+	2.79527i	0.421146	+	0.324944i
$75$	−1.62378	+	4.72899i	−0.187498	+	0.546057i
$76$	−4.58271	+	1.20178i	−0.525672	+	0.137854i
$77$	3.87142	−	24.4432i	0.441190	−	2.78556i
$78$	−4.43955	−	0.835068i	−0.502680	−	0.0945528i
$79$	−1.42813	+	4.39533i	−0.160677	+	0.494513i	−0.998692	−	0.0511346i	$-0.983716\pi$
$79$	−1.42813	+	4.39533i	−0.160677	+	0.494513i	0.838015	+	0.545648i	$0.183716\pi$
$80$	4.41609	−	7.77806i	0.493734	−	0.869613i
$81$	−0.309017	−	0.951057i	−0.0343352	−	0.105673i
$82$	1.20110	+	9.31507i	0.132639	+	1.02868i
$83$	11.1730	+	5.69295i	1.22640	+	0.624882i	0.942575	−	0.333994i	$-0.108396\pi$
$83$	11.1730	+	5.69295i	1.22640	+	0.624882i	0.283825	+	0.958876i	$0.408396\pi$
$84$	−8.24985	−	3.21739i	−0.900133	−	0.351046i
$85$	−4.30633	+	3.61660i	−0.467087	+	0.392275i
$86$	−2.00568	−	0.0578711i	−0.216278	−	0.00624040i
$87$	−0.633458	−	3.99950i	−0.0679138	−	0.428791i
$88$	15.3428	+	3.81351i	1.63555	+	0.406522i
$89$	7.91716	+	10.8970i	0.839218	+	1.15508i	0.986137	+	0.165935i	$0.0530643\pi$
$89$	7.91716	+	10.8970i	0.839218	+	1.15508i	−0.146919	+	0.989149i	$0.546936\pi$
$90$	−0.851893	+	3.04537i	−0.0897974	+	0.321010i
$91$	8.31290	−	11.4417i	0.871429	−	1.19942i
$92$	−16.6335	−	3.62834i	−1.73416	−	0.378281i
$93$	−1.53499	−	1.53499i	−0.159171	−	0.159171i
$94$	−0.913043	−	0.326067i	−0.0941732	−	0.0336312i
$95$	−5.27691	−	0.459385i	−0.541400	−	0.0471319i
$96$	2.50317	−	5.07288i	0.255479	−	0.517749i
$97$	0.0175836	+	0.0345097i	0.00178534	+	0.00350393i	0.891897	−	0.452238i	$-0.149374\pi$
$97$	0.0175836	+	0.0345097i	0.00178534	+	0.00350393i	−0.890112	+	0.455742i	$0.849374\pi$
$98$	12.9612	−	12.2342i	1.30928	−	1.23584i
$99$	−5.58956			−0.561772
$100$	7.57636	−	6.52678i	0.757636	−	0.652678i
$101$	−11.0833			−1.10283			−0.551415	−	0.834231i	$-0.685912\pi$
$101$	−11.0833			−1.10283			−0.551415	+	0.834231i	$0.685912\pi$
$102$	−2.58641	+	2.44134i	−0.256093	+	0.241729i
$103$	−1.29687	−	2.54524i	−0.127784	−	0.250790i	0.818247	−	0.574867i	$-0.194946\pi$
$103$	−1.29687	−	2.54524i	−0.127784	−	0.250790i	−0.946031	+	0.324077i	$0.894946\pi$
$104$	6.82297	+	5.92238i	0.669048	+	0.580738i
$105$	−7.47459	−	6.49192i	−0.729445	−	0.633547i
$106$	12.4886	+	4.45994i	1.21300	+	0.433187i
$107$	−2.43674	−	2.43674i	−0.235568	−	0.235568i	0.579444	−	0.815012i	$-0.303270\pi$
$107$	−2.43674	−	2.43674i	−0.235568	−	0.235568i	−0.815012	+	0.579444i	$0.803270\pi$
$108$	−0.426247	+	1.95405i	−0.0410156	+	0.188029i
$109$	9.69709	−	13.3469i	0.928813	−	1.27840i	−0.0315075	−	0.999504i	$-0.510031\pi$
$109$	9.69709	−	13.3469i	0.928813	−	1.27840i	0.960321	−	0.278898i	$-0.0899692\pi$
$110$	14.7177	+	9.78883i	1.40328	+	0.933329i
$111$	1.90185	+	2.61767i	0.180515	+	0.248458i
$112$	10.9979	+	13.8814i	1.03921	+	1.31167i
$113$	0.925678	+	5.84450i	0.0870805	+	0.549804i	0.992201	+	0.124649i	$0.0397805\pi$
$113$	0.925678	+	5.84450i	0.0870805	+	0.549804i	−0.905120	+	0.425155i	$0.860219\pi$
$114$	−3.34864	−	0.0966202i	−0.313629	−	0.00904931i
$115$	−16.1461	−	10.0796i	−1.50564	−	0.939926i
$116$	−2.94258	+	7.54521i	−0.273212	+	0.700555i
$117$	−2.84613	−	1.45017i	−0.263125	−	0.134069i
$118$	0.891611	+	6.91484i	0.0820795	+	0.636563i
$119$	−3.44087	−	10.5899i	−0.315424	−	0.970775i
$120$	4.54441	−	4.39868i	0.414846	−	0.401543i
$121$	−6.25550	+	19.2525i	−0.568682	+	1.75022i
$122$	4.59396	+	0.864113i	0.415917	+	0.0782331i
$123$	−1.03892	+	6.55951i	−0.0936767	+	0.591451i
$124$	1.10131	+	4.19959i	0.0989010	+	0.377134i
$125$	10.4326	−	4.02013i	0.933118	−	0.359571i
$126$	−4.95737	−	3.82496i	−0.441638	−	0.340755i
$127$	−13.6805	−	2.16678i	−1.21395	−	0.192270i	−0.483565	−	0.875309i	$-0.660658\pi$
$127$	−13.6805	−	2.16678i	−1.21395	−	0.192270i	−0.730383	+	0.683038i	$0.760658\pi$
$128$	−9.44186	+	6.23307i	−0.834551	+	0.550931i
$129$	−1.34938	−	0.438440i	−0.118806	−	0.0386025i
$130$	4.95441	+	8.80275i	0.434530	+	0.772052i
$131$	14.3499	−	4.66256i	1.25376	−	0.407370i	0.394490	−	0.918900i	$-0.370921\pi$
$131$	14.3499	−	4.66256i	1.25376	−	0.407370i	0.859265	+	0.511530i	$0.170921\pi$
$132$	9.65147	+	5.64110i	0.840053	+	0.490995i
$133$	4.76148	−	9.34492i	0.412872	−	0.810307i
$134$	2.64140	−	0.774766i	0.228182	−	0.0669296i
$135$	−1.18412	+	1.89680i	−0.101913	+	0.163251i
$136$	6.92980	−	1.60520i	0.594226	−	0.137645i
$137$	6.63192	−	1.05039i	0.566603	−	0.0897411i	0.133440	−	0.991057i	$-0.457398\pi$
$137$	6.63192	−	1.05039i	0.566603	−	0.0897411i	0.433163	+	0.901316i	$0.357398\pi$
$138$	−10.5640	−	5.77232i	−0.899270	−	0.491372i
$139$	9.86337	−	7.16616i	0.836600	−	0.607826i	−0.0848187	−	0.996396i	$-0.527031\pi$
$139$	9.86337	−	7.16616i	0.836600	−	0.607826i	0.921419	+	0.388571i	$0.127031\pi$
$140$	6.35456	+	18.7531i	0.537058	+	1.58492i
$141$	−0.554624	−	0.402958i	−0.0467078	−	0.0339352i
$142$	4.63717	+	9.78910i	0.389143	+	0.821483i
$143$	−12.6252	+	12.6252i	−1.05577	+	1.05577i
$144$	2.70806	−	2.94387i	0.225672	−	0.245323i
$145$	−5.93743	+	6.83616i	−0.493077	+	0.567712i
$146$	−6.21244	−	9.09098i	−0.514145	−	0.752375i
$147$	11.2293	−	5.72161i	0.926176	−	0.471910i
$148$	−0.642108	−	6.43930i	−0.0527810	−	0.529307i
$149$		−	2.49265i		−	0.204206i	−0.994774	−	0.102103i	$-0.967443\pi$
$149$		−	2.49265i		−	0.204206i	0.994774	−	0.102103i	$-0.0325571\pi$
$150$	6.43968	−	2.92070i	0.525798	−	0.238474i
$151$			10.0136i			0.814898i	0.913228	+	0.407449i	$0.133582\pi$
$151$			10.0136i			0.814898i	−0.913228	+	0.407449i	$0.866418\pi$
$152$	5.68457	+	3.54635i	0.461080	+	0.287647i
$153$	−2.24081	+	1.14175i	−0.181159	+	0.0923052i
$154$	−28.8962	+	19.7466i	−2.32852	+	1.59123i
$155$	−0.420980	+	4.83576i	−0.0338139	+	0.388418i
$156$	3.45085	+	5.37638i	0.276289	+	0.430455i
$157$	16.4345	−	16.4345i	1.31161	−	1.31161i	0.391385	−	0.920227i	$-0.371996\pi$
$157$	16.4345	−	16.4345i	1.31161	−	1.31161i	0.920227	−	0.391385i	$-0.128004\pi$
$158$	5.90661	−	2.79801i	0.469905	−	0.222597i
$159$	7.58614	+	5.51165i	0.601620	+	0.437102i
$160$	−12.2860	+	3.00887i	−0.971296	+	0.237872i
$161$	30.4905	−	22.1527i	2.40299	−	1.74587i
$162$	−0.678115	+	1.24103i	−0.0532777	+	0.0975047i
$163$	−8.56621	+	1.35675i	−0.670957	+	0.106269i	−0.482613	−	0.875834i	$-0.660312\pi$
$163$	−8.56621	+	1.35675i	−0.670957	+	0.106269i	−0.188345	+	0.982103i	$0.560312\pi$
$164$	8.41390	−	10.2778i	0.657015	−	0.802559i
$165$	8.03809	+	9.57107i	0.625764	+	0.745106i
$166$	−4.99137	−	17.0170i	−0.387405	−	1.32078i
$167$	−1.21711	+	2.38872i	−0.0941830	+	0.184845i	−0.933292	−	0.359119i	$-0.883077\pi$
$167$	−1.21711	+	2.38872i	−0.0941830	+	0.184845i	0.839109	+	0.543964i	$0.183077\pi$
$168$	4.69964	+	11.6076i	0.362585	+	0.895547i
$169$	2.65967	−	0.864180i	0.204590	−	0.0664754i
$170$	7.89974	+	0.917957i	0.605882	+	0.0704041i
$171$	−2.25289	−	0.732010i	−0.172283	−	0.0559782i
$172$	1.88749	+	2.11887i	0.143919	+	0.161563i
$173$	−6.20975	−	0.983528i	−0.472118	−	0.0747762i	−0.0841584	−	0.996452i	$-0.526820\pi$
$173$	−6.20975	−	0.983528i	−0.472118	−	0.0747762i	−0.387960	+	0.921676i	$0.626820\pi$
$174$	−3.49826	+	4.53395i	−0.265202	+	0.343717i
$175$	−0.367326	+	22.1345i	−0.0277673	+	1.67321i
$176$	−10.9720	−	19.4809i	−0.827049	−	1.46843i
$177$	−0.771224	+	4.86932i	−0.0579687	+	0.366000i
$178$	3.52127	−	18.7204i	0.263930	−	1.40316i
$179$	5.07285	−	15.6126i	0.379162	−	1.16694i	−0.561465	−	0.827501i	$-0.689762\pi$
$179$	5.07285	−	15.6126i	0.379162	−	1.16694i	0.940627	−	0.339441i	$-0.110238\pi$
$180$	3.95890	−	2.08016i	0.295079	−	0.155046i
$181$	4.84320	+	14.9058i	0.359992	+	1.10794i	0.953058	+	0.302787i	$0.0979172\pi$
$181$	4.84320	+	14.9058i	0.359992	+	1.10794i	−0.593066	+	0.805154i	$0.702083\pi$
$182$	−19.8367	+	2.55777i	−1.47039	+	0.189595i
$183$	2.94512	+	1.50061i	0.217710	+	0.110929i
$184$	12.4153	+	20.6285i	0.915270	+	1.52075i
$185$	1.74730	−	7.02090i	0.128464	−	0.516187i
$186$	−0.0885427	+	3.06869i	−0.00649227	+	0.225008i
$187$	2.19905	+	13.8843i	0.160811	+	1.01532i
$188$	0.550994	+	1.25552i	0.0401853	+	0.0915685i
$189$	−2.60243	−	3.58194i	−0.189299	−	0.260548i
$190$	4.65008	+	5.87286i	0.337352	+	0.426062i
$191$	4.79162	−	6.59510i	0.346709	−	0.477205i	−0.599677	−	0.800242i	$-0.704704\pi$
$191$	4.79162	−	6.59510i	0.346709	−	0.477205i	0.946386	+	0.323038i	$0.104704\pi$
$192$	−7.64702	+	2.35014i	−0.551876	+	0.169607i
$193$	−9.91888	−	9.91888i	−0.713976	−	0.713976i	0.253388	−	0.967365i	$-0.418455\pi$
$193$	−9.91888	−	9.91888i	−0.713976	−	0.713976i	−0.967365	+	0.253388i	$0.918455\pi$
$194$	0.0184216	−	0.0515835i	0.00132259	−	0.00370348i
$195$	1.60974	+	6.95888i	0.115276	+	0.498336i
$196$	−25.1639	−	1.45335i	−1.79742	−	0.103810i
$197$	9.71333	+	19.0635i	0.692046	+	1.35822i	0.922828	+	0.385212i	$0.125872\pi$
$197$	9.71333	+	19.0635i	0.692046	+	1.35822i	−0.230782	+	0.973005i	$0.574128\pi$
$198$	5.42603	+	5.74845i	0.385611	+	0.408525i
$199$	−0.280067			−0.0198535			−0.00992673	−	0.999951i	$-0.503160\pi$
$199$	−0.280067			−0.0198535			−0.00992673	+	0.999951i	$0.503160\pi$
$200$	−14.0670	−	1.45590i	−0.994687	−	0.102948i
$201$	1.94644			0.137291
$202$	10.7590	+	11.3983i	0.757002	+	0.801985i
$203$	−8.13940	−	15.9745i	−0.571274	−	1.12119i
$204$	5.02148	+	0.290017i	0.351574	+	0.0203052i
$205$	12.7259	−	7.65397i	0.888819	−	0.534576i
$206$	−1.35867	+	3.80450i	−0.0946630	+	0.265072i
$207$	−6.01910	−	6.01910i	−0.418357	−	0.418357i
$208$	−0.532620	−	12.7660i	−0.0369305	−	0.885165i
$209$	−7.78271	+	10.7120i	−0.538342	+	0.740964i
$210$	0.579442	+	13.9890i	0.0399853	+	0.965336i
$211$	−1.80054	−	2.47823i	−0.123954	−	0.170609i	0.742530	−	0.669813i	$-0.233626\pi$
$211$	−1.80054	−	2.47823i	−0.123954	−	0.170609i	−0.866484	+	0.499204i	$0.833626\pi$
$212$	−7.53648	−	17.1730i	−0.517608	−	1.17945i
$213$	1.19818	+	7.56501i	0.0820979	+	0.518346i
$214$	−0.140558	+	4.87144i	−0.00960838	+	0.333005i
$215$	1.18974	+	2.94106i	0.0811393	+	0.200578i
$216$	2.42337	−	1.45852i	0.164890	−	0.0992395i
$217$	−8.56369	−	4.36342i	−0.581341	−	0.296208i
$218$	−23.1397	+	2.98367i	−1.56722	+	0.202079i
$219$	−2.40597	−	7.40482i	−0.162581	−	0.500372i
$220$	−4.22002	−	24.6385i	−0.284514	−	1.66113i
$221$	−2.48245	+	7.64021i	−0.166988	+	0.513936i
$222$	0.845874	−	4.49699i	0.0567713	−	0.301818i
$223$	3.84964	−	24.3057i	0.257791	−	1.62763i	−0.430778	−	0.902458i	$-0.641761\pi$
$223$	3.84964	−	24.3057i	0.257791	−	1.62763i	0.688569	−	0.725171i	$-0.258239\pi$
$224$	3.59979	−	24.7858i	0.240521	−	1.65607i
$225$	4.95074	−	0.700122i	0.330049	−	0.0466748i
$226$	5.11204	−	6.62550i	0.340048	−	0.440721i
$227$	3.02165	+	0.478582i	0.200554	+	0.0317646i	0.255903	−	0.966702i	$-0.417627\pi$
$227$	3.02165	+	0.478582i	0.200554	+	0.0317646i	−0.0553493	+	0.998467i	$0.517627\pi$
$228$	3.15130	+	3.53762i	0.208700	+	0.234285i
$229$	2.23135	+	0.725009i	0.147452	+	0.0479099i	0.381813	−	0.924240i	$-0.375300\pi$
$229$	2.23135	+	0.725009i	0.147452	+	0.0479099i	−0.234361	+	0.972150i	$0.575300\pi$
$230$	5.30765	+	26.3898i	0.349976	+	1.74009i
$231$	−23.5367	+	7.64752i	−1.54860	+	0.503170i
$232$	10.6162	−	4.29823i	0.696986	−	0.282192i
$233$	−5.81662	+	11.4158i	−0.381059	+	0.747871i	−0.999272	−	0.0381396i	$-0.987857\pi$
$233$	−5.81662	+	11.4158i	−0.381059	+	0.747871i	0.618213	+	0.786010i	$0.287857\pi$
$234$	1.27146	+	4.33478i	0.0831180	+	0.283373i
$235$	0.107590	+	1.52916i	0.00701840	+	0.0997516i
$236$	6.24588	−	7.62949i	0.406572	−	0.496637i
$237$	4.56462	−	0.722965i	0.296504	−	0.0469616i
$238$	−7.55073	+	13.8187i	−0.489441	+	0.895736i
$239$	10.2098	−	7.41782i	0.660414	−	0.479819i	−0.206389	−	0.978470i	$-0.566171\pi$
$239$	10.2098	−	7.41782i	0.660414	−	0.479819i	0.866803	+	0.498651i	$0.166171\pi$
$240$	−8.93516	−	0.403600i	−0.576762	−	0.0260523i
$241$	−1.54834	−	1.12493i	−0.0997372	−	0.0724633i	0.536799	−	0.843710i	$-0.319633\pi$
$241$	−1.54834	−	1.12493i	−0.0997372	−	0.0724633i	−0.636536	+	0.771247i	$0.719633\pi$
$242$	25.8722	−	12.2559i	1.66313	−	0.787837i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−3.57088	−	5.56338i	−0.228602	−	0.356159i
$245$	−25.9455	−	11.0000i	−1.65760	−	0.702767i
$246$	7.75450	−	5.29914i	0.494409	−	0.337861i
$247$	−6.74200	+	3.43522i	−0.428983	+	0.218578i
$248$	3.24987	−	5.20934i	0.206367	−	0.330793i
$249$		−	12.5398i		−	0.794677i
$250$	−14.2617	−	6.82661i	−0.901992	−	0.431753i
$251$			12.9472i			0.817220i	0.912709	+	0.408610i	$0.133986\pi$
$251$			12.9472i			0.817220i	−0.912709	+	0.408610i	$0.866014\pi$
$252$	0.878641	+	8.81134i	0.0553492	+	0.555062i
$253$	−42.3941	+	21.6009i	−2.66530	+	1.35804i
$254$	11.0519	+	16.1727i	0.693456	+	1.01477i
$255$	5.17744	+	2.19507i	0.324224	+	0.137461i
$256$	15.5759	+	3.65955i	0.973492	+	0.228722i
$257$	−0.485223	+	0.485223i	−0.0302674	+	0.0302674i	−0.722078	−	0.691811i	$-0.756813\pi$
$257$	−0.485223	+	0.485223i	−0.0302674	+	0.0302674i	0.691811	+	0.722078i	$0.256813\pi$
$258$	0.858998	+	1.81335i	0.0534789	+	0.112894i
$259$	11.5898	+	8.42047i	0.720154	+	0.523223i
$260$	4.24352	−	13.6404i	0.263172	−	0.845944i
$261$	−3.27599	+	2.38015i	−0.202779	+	0.147327i
$262$	−18.7251	−	10.2316i	−1.15684	−	0.632113i
$263$	−13.5529	+	2.14656i	−0.835706	+	0.132363i	−0.559598	−	0.828764i	$-0.689045\pi$
$263$	−13.5529	+	2.14656i	−0.835706	+	0.132363i	−0.276107	+	0.961127i	$0.589045\pi$
$264$	−3.56765	−	15.4019i	−0.219573	−	0.947920i
$265$	−1.47161	−	20.9159i	−0.0904005	−	1.28485i
$266$	−14.2327	+	4.17469i	−0.872664	+	0.255967i
$267$	6.11502	−	12.0014i	0.374233	−	0.734474i
$268$	−3.36091	−	1.96439i	−0.205300	−	0.119994i
$269$	−15.8573	+	5.15235i	−0.966837	+	0.314144i	−0.749538	−	0.661961i	$-0.769724\pi$
$269$	−15.8573	+	5.15235i	−0.966837	+	0.314144i	−0.217298	+	0.976105i	$0.569724\pi$
$270$	3.10020	−	0.623527i	0.188672	−	0.0379466i
$271$	21.8755	+	7.10778i	1.32884	+	0.431767i	0.885522	−	0.464597i	$-0.153801\pi$
$271$	21.8755	+	7.10778i	1.32884	+	0.431767i	0.443320	+	0.896364i	$0.353801\pi$
$272$	−8.37788	−	5.56855i	−0.507984	−	0.337643i
$273$	−13.9686	−	2.21241i	−0.845420	−	0.133901i
$274$	−7.51814	−	5.80078i	−0.454187	−	0.350438i
$275$	4.82943	−	27.5274i	0.291225	−	1.65996i
$276$	4.31856	+	16.4678i	0.259947	+	0.991242i
$277$	−1.80843	+	11.4180i	−0.108658	+	0.686039i	0.871882	+	0.489717i	$0.162900\pi$
$277$	−1.80843	+	11.4180i	−0.108658	+	0.686039i	−0.980539	+	0.196322i	$0.937100\pi$
$278$	−16.9447	−	3.18725i	−1.01627	−	0.191158i
$279$	−0.670814	+	2.06455i	−0.0401606	+	0.123601i
$280$	13.1175	−	24.7396i	0.783921	−	1.47847i
$281$	6.71930	+	20.6799i	0.400840	+	1.23366i	0.924319	+	0.381620i	$0.124634\pi$
$281$	6.71930	+	20.6799i	0.400840	+	1.23366i	−0.523479	+	0.852038i	$0.675366\pi$
$282$	0.123985	+	0.961558i	0.00738319	+	0.0572600i
$283$	22.3214	+	11.3733i	1.32687	+	0.676074i	0.966484	−	0.256729i	$-0.0826447\pi$
$283$	22.3214	+	11.3733i	1.32687	+	0.676074i	0.360387	+	0.932803i	$0.382645\pi$
$284$	5.56586	−	14.2717i	0.330273	−	0.846869i
$285$	1.98635	+	4.91032i	0.117661	+	0.290862i
$286$	25.2398	+	0.728258i	1.49246	+	0.0430628i
$287$	4.59986	+	29.0424i	0.271521	+	1.71432i
$288$	−5.65639	+	0.0726993i	−0.333306	+	0.00428385i
$289$	−6.27470	−	8.63638i	−0.369100	−	0.508022i
$290$	12.7942	−	0.529950i	0.751301	−	0.0311197i
$291$	0.0227656	−	0.0313342i	0.00133454	−	0.00183684i
$292$	−3.31871	+	15.2140i	−0.194213	+	0.890334i
$293$	2.94958	+	2.94958i	0.172317	+	0.172317i	0.787996	−	0.615680i	$-0.211119\pi$
$293$	2.94958	+	2.94958i	0.172317	+	0.172317i	−0.615680	+	0.787996i	$0.711119\pi$
$294$	−16.7850	−	5.99428i	−0.978921	−	0.349593i
$295$	9.44684	−	5.68176i	0.550016	−	0.330805i
$296$	−5.99902	+	6.91126i	−0.348686	+	0.401709i
$297$	2.53761	+	4.98034i	0.147247	+	0.288989i
$298$	−2.56351	+	2.41972i	−0.148500	+	0.140171i
$299$	−27.1907			−1.57248
$300$	−9.25500	−	3.78749i	−0.534337	−	0.218671i
$301$	−6.28186			−0.362081
$302$	10.2983	−	9.72066i	0.592599	−	0.559361i
$303$	5.03171	+	9.87529i	0.289064	+	0.567321i
$304$	−1.87110	−	9.28875i	−0.107315	−	0.532746i
$305$	−1.66572	−	7.20092i	−0.0953791	−	0.412323i
$306$	3.34946	+	1.19616i	0.191476	+	0.0683801i
$307$	−5.35419	−	5.35419i	−0.305580	−	0.305580i	0.537612	−	0.843192i	$-0.319326\pi$
$307$	−5.35419	−	5.35419i	−0.305580	−	0.305580i	−0.843192	+	0.537612i	$0.819326\pi$
$308$	48.3587	+	10.5487i	2.75549	+	0.601069i
$309$	−1.67906	+	2.31103i	−0.0955185	+	0.131470i
$310$	5.38188	−	4.26133i	0.305671	−	0.242027i
$311$	−0.584160	−	0.804028i	−0.0331247	−	0.0455922i	0.792133	−	0.610348i	$-0.208970\pi$
$311$	−0.584160	−	0.804028i	−0.0331247	−	0.0455922i	−0.825258	+	0.564756i	$0.808970\pi$
$312$	2.17932	−	8.76802i	0.123380	−	0.496391i
$313$	−3.29954	−	20.8325i	−0.186501	−	1.17752i	−0.886276	−	0.463158i	$-0.846716\pi$
$313$	−3.29954	−	20.8325i	−0.186501	−	1.17752i	0.699775	−	0.714363i	$-0.253284\pi$
$314$	−32.8552	−	0.947990i	−1.85413	−	0.0534982i
$315$	−2.39095	+	9.60718i	−0.134715	+	0.541303i
$316$	−8.61134	−	3.35837i	−0.484426	−	0.188923i
$317$	−5.80146	−	2.95599i	−0.325842	−	0.166025i	0.283415	−	0.958997i	$-0.408532\pi$
$317$	−5.80146	−	2.95599i	−0.325842	−	0.166025i	−0.609258	+	0.792972i	$0.708532\pi$
$318$	−1.69586	−	13.1522i	−0.0950993	−	0.737537i
$319$	6.99432	+	21.5263i	0.391607	+	1.20524i
$320$	15.0210	+	9.71443i	0.839698	+	0.543053i
$321$	−1.06489	+	3.27740i	−0.0594365	+	0.182927i
$322$	−52.3808	−	9.85271i	−2.91907	−	0.549070i
$323$	−0.931949	+	5.88409i	−0.0518550	+	0.327400i
$324$	1.93458	−	0.507332i	0.107477	−	0.0281851i
$325$	9.60087	−	12.7636i	0.532561	−	0.707997i
$326$	9.71091	+	7.49265i	0.537837	+	0.414980i
$327$	−16.2946	−	2.58081i	−0.901092	−	0.142719i
$328$	−18.7377	+	1.32401i	−1.03461	+	0.0731061i
$329$	−2.88674	−	0.937959i	−0.159151	−	0.0517114i
$330$	2.04021	−	17.5576i	0.112310	−	0.966515i
$331$	−11.1372	+	3.61869i	−0.612155	+	0.198901i	−0.598654	−	0.801008i	$-0.704298\pi$
$331$	−11.1372	+	3.61869i	−0.612155	+	0.198901i	−0.0135009	+	0.999909i	$0.504298\pi$
$332$	−12.6554	+	21.6524i	−0.694556	+	1.18833i
$333$	1.46894	−	2.88296i	0.0804974	−	0.157985i
$334$	3.63812	−	1.06712i	0.199069	−	0.0583902i
$335$	−2.79908	−	3.33291i	−0.152930	−	0.182096i
$336$	7.37543	−	16.1012i	0.402363	−	0.878394i
$337$	−23.4066	+	3.70723i	−1.27504	+	0.201946i	−0.757001	−	0.653413i	$-0.773336\pi$
$337$	−23.4066	+	3.70723i	−1.27504	+	0.201946i	−0.518035	+	0.855359i	$0.673336\pi$
$338$	−3.47060	−	1.89638i	−0.188776	−	0.103149i
$339$	4.78724	−	3.47813i	0.260007	−	0.188906i
$340$	−6.72456	−	9.01539i	−0.364690	−	0.488928i
$341$	9.81646	+	7.13208i	0.531591	+	0.386224i
$342$	1.43416	+	3.02753i	0.0775506	+	0.163710i
$343$	17.5412	−	17.5412i	0.947137	−	0.947137i
$344$	0.346841	−	3.99802i	0.0187004	−	0.215559i
$345$	−1.65078	+	18.9624i	−0.0888750	+	1.02090i
$346$	5.01658	+	7.34102i	0.269693	+	0.394655i
$347$	15.6783	−	7.98849i	0.841655	−	0.428844i	0.0206642	−	0.999786i	$-0.493422\pi$
$347$	15.6783	−	7.98849i	0.841655	−	0.428844i	0.820990	+	0.570942i	$0.193422\pi$
$348$	8.05873	−	0.803594i	0.431993	−	0.0430771i
$349$			16.0908i			0.861318i	0.902515	+	0.430659i	$0.141719\pi$
$349$			16.0908i			0.861318i	−0.902515	+	0.430659i	$0.858281\pi$
$350$	23.1203	−	21.1092i	1.23583	−	1.12833i
$351$			3.19428i			0.170498i
$352$	−9.38364	+	30.1949i	−0.500150	+	1.60939i
$353$	27.8753	−	14.2032i	1.48366	−	0.755960i	0.490355	−	0.871523i	$-0.336867\pi$
$353$	27.8753	−	14.2032i	1.48366	−	0.755960i	0.993300	+	0.115563i	$0.0368672\pi$
$354$	5.75639	−	3.93370i	0.305949	−	0.209074i
$355$	11.2306	−	12.9305i	0.596058	−	0.686281i
$356$	−22.6708	+	14.5514i	−1.20155	+	0.771220i
$357$	−7.87355	+	7.87355i	−0.416712	+	0.416712i
$358$	−20.9808	+	9.93879i	−1.10887	+	0.525281i
$359$	−2.17582	−	1.58082i	−0.114835	−	0.0834327i	0.528885	−	0.848693i	$-0.322610\pi$
$359$	−2.17582	−	1.58082i	−0.114835	−	0.0834327i	−0.643721	+	0.765261i	$0.722610\pi$
$360$	−5.98237	−	2.05214i	−0.315298	−	0.108157i
$361$	10.8316	−	7.86964i	0.570086	−	0.414192i
$362$	10.6280	−	19.4506i	0.558597	−	1.02230i
$363$	19.9940	−	3.16674i	1.04941	−	0.166211i
$364$	21.8868	+	17.9176i	1.14718	+	0.939137i
$365$	−9.21943	+	14.7683i	−0.482567	+	0.773008i
$366$	−1.31568	−	4.48555i	−0.0687719	−	0.234463i
$367$	13.0130	−	25.5395i	0.679274	−	1.33315i	−0.251608	−	0.967829i	$-0.580959\pi$
$367$	13.0130	−	25.5395i	0.679274	−	1.33315i	0.930882	−	0.365321i	$-0.119041\pi$
$368$	9.16275	−	32.7932i	0.477641	−	1.70946i
$369$	6.31623	−	2.05227i	0.328810	−	0.106837i
$370$	−8.91666	+	5.01852i	−0.463555	+	0.260900i
$371$	39.4848	+	12.8294i	2.04995	+	0.666069i
$372$	3.24188	−	2.88785i	0.168083	−	0.149728i
$373$	23.2560	+	3.68339i	1.20415	+	0.190719i	0.726084	−	0.687606i	$-0.241338\pi$
$373$	23.2560	+	3.68339i	1.20415	+	0.190719i	0.478065	+	0.878324i	$0.341338\pi$
$374$	12.1442	−	15.7396i	0.627963	−	0.813876i
$375$	−8.31825	−	7.47039i	−0.429553	−	0.385769i
$376$	0.756339	−	1.78545i	0.0390052	−	0.0920773i
$377$	−2.02345	+	12.7755i	−0.104213	+	0.657973i
$378$	−1.15747	+	6.15354i	−0.0595337	+	0.316504i
$379$	−0.771905	+	2.37568i	−0.0396501	+	0.122030i	−0.968922	−	0.247365i	$-0.920435\pi$
$379$	−0.771905	+	2.37568i	−0.0396501	+	0.122030i	0.929272	+	0.369396i	$0.120435\pi$
$380$	1.52576	−	10.4833i	0.0782701	−	0.537782i
$381$	4.28020	+	13.1731i	0.219281	+	0.674878i
$382$	−11.4340	+	1.47432i	−0.585014	+	0.0754327i
$383$	3.36221	+	1.71313i	0.171801	+	0.0875368i	0.537776	−	0.843088i	$-0.319265\pi$
$383$	3.36221	+	1.71313i	0.171801	+	0.0875368i	−0.365975	+	0.930625i	$0.619265\pi$
$384$	9.84022	+	5.58301i	0.502157	+	0.284907i
$385$	46.9419	+	29.3045i	2.39238	+	1.49350i
$386$	−0.572151	+	19.8295i	−0.0291217	+	1.00929i
$387$	0.221953	+	1.40135i	0.0112825	+	0.0712349i
$388$	−0.0709323	+	0.0311291i	−0.00360104	+	0.00158034i
$389$	−14.3077	−	19.6928i	−0.725428	−	0.998466i	−0.999326	−	0.0367073i	$-0.988313\pi$
$389$	−14.3077	−	19.6928i	−0.725428	−	0.998466i	0.273898	−	0.961759i	$-0.411687\pi$
$390$	5.59405	−	8.41077i	0.283266	−	0.425896i
$391$	−12.5832	+	17.3193i	−0.636359	+	0.875873i
$392$	22.9330	+	27.2900i	1.15829	+	1.37835i
$393$	−10.6691	−	10.6691i	−0.538184	−	0.538184i
$394$	10.1762	−	28.4952i	0.512671	−	1.43557i
$395$	−7.80211	−	6.77638i	−0.392567	−	0.340957i
$396$	0.644579	−	11.1605i	0.0323913	−	0.560838i
$397$	7.37656	+	14.4773i	0.370219	+	0.726595i	0.998686	−	0.0512404i	$-0.0163175\pi$
$397$	7.37656	+	14.4773i	0.370219	+	0.726595i	−0.628467	+	0.777836i	$0.716317\pi$
$398$	0.271873	+	0.288029i	0.0136278	+	0.0144376i
$399$	−10.4881			−0.525059
$400$	12.1581	+	15.8802i	0.607907	+	0.794008i
$401$	−22.6082			−1.12900			−0.564500	−	0.825433i	$-0.690931\pi$
$401$	−22.6082			−1.12900			−0.564500	+	0.825433i	$0.690931\pi$
$402$	−1.88949	−	2.00177i	−0.0942393	−	0.0998392i
$403$	3.14804	+	6.17837i	0.156815	+	0.307767i
$404$	1.27811	−	22.1297i	0.0635881	−	1.10099i
$405$	2.22764	+	0.193929i	0.110692	+	0.00963639i
$406$	−8.52730	+	23.8779i	−0.423203	+	1.18504i
$407$	−12.7885	−	12.7885i	−0.633903	−	0.633903i
$408$	−4.57631	−	5.44575i	−0.226561	−	0.269605i
$409$	11.1978	−	15.4124i	0.553695	−	0.762095i	−0.436813	−	0.899552i	$-0.643893\pi$
$409$	11.1978	−	15.4124i	0.553695	−	0.762095i	0.990508	+	0.137457i	$0.0438928\pi$
$410$	−20.2252	−	5.65766i	−0.998849	−	0.279412i
$411$	−3.94674	−	5.43222i	−0.194678	−	0.267951i
$412$	5.23157	−	2.29590i	0.257741	−	0.113111i
$413$	3.41461	+	21.5590i	0.168022	+	1.06085i
$414$	−0.347201	+	12.0332i	−0.0170640	+	0.591400i
$415$	−21.4720	+	18.0329i	−1.05402	+	0.885200i
$416$	−12.6119	+	12.9403i	−0.618348	+	0.634450i
$417$	−10.8630	−	5.53496i	−0.531962	−	0.271048i
$418$	18.5715	−	2.39464i	0.908361	−	0.117126i
$419$	−0.510925	−	1.57246i	−0.0249603	−	0.0768199i	0.937800	−	0.347175i	$-0.112859\pi$
$419$	−0.510925	−	1.57246i	−0.0249603	−	0.0768199i	−0.962761	+	0.270355i	$0.912859\pi$
$420$	13.8242	−	14.1757i	0.674552	−	0.691702i
$421$	11.1243	−	34.2370i	0.542164	−	1.66861i	−0.185475	−	0.982649i	$-0.559382\pi$
$421$	11.1243	−	34.2370i	0.542164	−	1.66861i	0.727639	−	0.685961i	$-0.240618\pi$
$422$	−0.800816	+	4.25745i	−0.0389831	+	0.207249i
$423$	−0.107244	+	0.677113i	−0.00521439	+	0.0329224i
$424$	−10.3452	+	24.4213i	−0.502407	+	1.18600i
$425$	−3.68680	−	12.0220i	−0.178836	−	0.583153i
$426$	6.61692	−	8.57591i	0.320591	−	0.415504i
$427$	14.4545	+	2.28936i	0.699501	+	0.110790i
$428$	5.14636	−	4.58436i	0.248759	−	0.221594i
$429$	16.9808	+	5.51739i	0.819840	+	0.266382i
$430$	1.86973	−	4.07856i	0.0901665	−	0.196686i
$431$	−30.4824	+	9.90433i	−1.46829	+	0.477075i	−0.930590	−	0.366064i	$-0.880705\pi$
$431$	−30.4824	+	9.90433i	−1.46829	+	0.477075i	−0.537696	+	0.843139i	$0.680705\pi$
$432$	−3.85245	−	1.07641i	−0.185351	−	0.0517889i
$433$	−1.92038	+	3.76895i	−0.0922874	+	0.181124i	−0.932536	−	0.361077i	$-0.882409\pi$
$433$	−1.92038	+	3.76895i	−0.0922874	+	0.181124i	0.840249	+	0.542201i	$0.182409\pi$
$434$	3.82568	+	13.0429i	0.183639	+	0.626078i
$435$	8.78660	+	2.18674i	0.421285	+	0.104846i
$436$	25.5311	+	20.9011i	1.22272	+	1.00098i
$437$	−19.9160	+	3.15438i	−0.952709	+	0.150894i
$438$	−5.27973	+	9.66254i	−0.252275	+	0.461694i
$439$	−15.8015	+	11.4805i	−0.754165	+	0.547933i	−0.897115	−	0.441797i	$-0.854341\pi$
$439$	−15.8015	+	11.4805i	−0.754165	+	0.547933i	0.142950	+	0.989730i	$0.454341\pi$
$440$	−21.2423	+	28.2576i	−1.01269	+	1.34713i
$441$	−10.1960	−	7.40781i	−0.485523	−	0.352753i
$442$	10.2672	−	4.86365i	0.488361	−	0.231340i
$443$	−27.1676	+	27.1676i	−1.29077	+	1.29077i	−0.356465	+	0.934309i	$0.616018\pi$
$443$	−27.1676	+	27.1676i	−1.29077	+	1.29077i	−0.934309	+	0.356465i	$0.883982\pi$
$444$	−5.44595	+	3.49550i	−0.258453	+	0.165889i
$445$	−29.3438	+	6.78784i	−1.39103	+	0.321775i
$446$	−28.7336	+	19.6355i	−1.36058	+	0.929767i
$447$	−2.22097	+	1.13164i	−0.105048	+	0.0535248i
$448$	−28.9848	+	20.3585i	−1.36940	+	0.961848i
$449$			2.78749i			0.131550i	0.997834	+	0.0657750i	$0.0209520\pi$
$449$			2.78749i			0.131550i	−0.997834	+	0.0657750i	$0.979048\pi$
$450$	−5.52592	−	4.41183i	−0.260494	−	0.207976i
$451$		−	37.1219i		−	1.74800i
$452$	−11.7763	+	1.17430i	−0.553911	+	0.0552344i
$453$	8.92221	−	4.54609i	0.419202	−	0.213594i
$454$	−2.44106	−	3.57212i	−0.114564	−	0.167648i
$455$	16.2993	+	27.1002i	0.764123	+	1.27048i
$456$	0.579078	−	6.67500i	0.0271178	−	0.312585i
$457$	−3.48269	+	3.48269i	−0.162913	+	0.162913i	−0.783856	−	0.620943i	$-0.786750\pi$
$457$	−3.48269	+	3.48269i	−0.162913	+	0.162913i	0.620943	+	0.783856i	$0.286750\pi$
$458$	−1.42045	−	2.99857i	−0.0663731	−	0.140114i
$459$	2.03462	+	1.47824i	0.0949678	+	0.0689982i
$460$	21.9876	−	31.0762i	1.02518	−	1.44894i
$461$	16.4247	−	11.9333i	0.764977	−	0.555788i	−0.135456	−	0.990783i	$-0.543250\pi$
$461$	16.4247	−	11.9333i	0.764977	−	0.555788i	0.900433	+	0.434995i	$0.143250\pi$
$462$	30.7129	+	16.7819i	1.42890	+	0.780766i
$463$	23.0758	−	3.65484i	1.07242	−	0.169855i	0.404837	−	0.914389i	$-0.367328\pi$
$463$	23.0758	−	3.65484i	1.07242	−	0.169855i	0.667585	+	0.744534i	$0.267328\pi$
$464$	−14.7260	−	6.74547i	−0.683636	−	0.313151i
$465$	4.49982	−	1.82029i	0.208674	−	0.0844141i
$466$	17.3867	−	5.09980i	0.805423	−	0.236244i
$467$	−17.0486	+	33.4598i	−0.788916	+	1.54834i	0.0466277	+	0.998912i	$0.485153\pi$
$467$	−17.0486	+	33.4598i	−0.788916	+	1.54834i	−0.835544	+	0.549423i	$0.814847\pi$
$468$	3.22373	−	5.51556i	0.149017	−	0.254957i
$469$	8.19611	−	2.66308i	0.378461	−	0.122970i
$470$	1.46819	−	1.59507i	0.0677225	−	0.0735752i
$471$	−22.1043	−	7.18212i	−1.01851	−	0.330935i
$472$	−13.9095	+	0.982848i	−0.640237	+	0.0452393i
$473$	7.83296	+	1.24062i	0.360160	+	0.0570437i
$474$	−5.17459	−	3.99256i	−0.237677	−	0.183384i
$475$	5.55151	−	10.4626i	0.254721	−	0.480055i
$476$	21.5414	−	5.64908i	0.987347	−	0.258925i
$477$	1.46688	−	9.26154i	0.0671640	−	0.424057i
$478$	−17.5397	−	3.29918i	−0.802248	−	0.150901i
$479$	3.79867	−	11.6911i	0.173566	−	0.534180i	−0.825999	−	0.563671i	$-0.809389\pi$
$479$	3.79867	−	11.6911i	0.173566	−	0.534180i	0.999565	+	0.0294909i	$0.00938859\pi$
$480$	8.25867	+	9.58094i	0.376955	+	0.437308i
$481$	−3.19384	−	9.82963i	−0.145627	−	0.448193i
$482$	0.346127	+	2.68437i	0.0157657	+	0.122270i
$483$	−33.5806	−	17.1102i	−1.52797	−	0.778539i
$484$	−37.7195	−	14.7104i	−1.71452	−	0.668652i
$485$	−0.0863920	+	0.00607843i	−0.00392286	+	0.000276007i
$486$	1.41363	+	0.0407881i	0.0641233	+	0.00185019i
$487$	0.207837	+	1.31223i	0.00941800	+	0.0594629i	0.991950	−	0.126632i	$-0.0404168\pi$
$487$	0.207837	+	1.31223i	0.00941800	+	0.0594629i	−0.982532	+	0.186095i	$0.940417\pi$
$488$	−2.25512	+	9.07298i	−0.102084	+	0.410715i
$489$	5.09786	+	7.01660i	0.230533	+	0.317301i
$490$	13.8736	+	37.3612i	0.626747	+	1.68781i
$491$	8.08830	−	11.1326i	0.365020	−	0.502407i	−0.586519	−	0.809935i	$-0.699502\pi$
$491$	8.08830	−	11.1326i	0.365020	−	0.502407i	0.951539	+	0.307529i	$0.0995021\pi$
$492$	−12.9774	−	2.83082i	−0.585066	−	0.127623i
$493$	7.20104	+	7.20104i	0.324319	+	0.324319i
$494$	10.0776	+	3.59893i	0.453413	+	0.161924i
$495$	4.87866	−	11.5072i	0.219280	−	0.517209i
$496$	−8.51221	+	1.71468i	−0.382210	+	0.0769912i
$497$	15.3956	+	30.2156i	0.690587	+	1.35535i
$498$	−12.8962	+	12.1729i	−0.577895	+	0.545481i
$499$	31.4768			1.40909			0.704547	−	0.709658i	$-0.251150\pi$
$499$	31.4768			1.40909			0.704547	+	0.709658i	$0.251150\pi$
$500$	6.82382	+	21.2940i	0.305171	+	0.952298i
$501$	2.68092			0.119775
$502$	13.3152	−	12.5684i	0.594288	−	0.560955i
$503$	−2.48046	−	4.86817i	−0.110598	−	0.217061i	0.829073	−	0.559140i	$-0.188869\pi$
$503$	−2.48046	−	4.86817i	−0.110598	−	0.217061i	−0.939671	+	0.342080i	$0.888869\pi$
$504$	8.20887	−	9.45716i	0.365652	−	0.421255i
$505$	9.67368	−	22.8170i	0.430473	−	1.01534i
$506$	63.3687	+	22.6303i	2.81708	+	1.00604i
$507$	−1.97746	−	1.97746i	−0.0878219	−	0.0878219i
$508$	5.90395	−	27.0656i	0.261946	−	1.20084i
$509$	−1.34012	+	1.84452i	−0.0593998	+	0.0817569i	−0.837683	−	0.546156i	$-0.816091\pi$
$509$	−1.34012	+	1.84452i	−0.0593998	+	0.0817569i	0.778284	+	0.627913i	$0.216091\pi$
$510$	−2.76850	−	7.45546i	−0.122591	−	0.330133i
$511$	−20.2622	−	27.8886i	−0.896349	−	1.23372i
$512$	−11.3566	−	19.5711i	−0.501895	−	0.864929i
$513$	0.370567	+	2.33967i	0.0163609	+	0.103299i
$514$	0.970042	+	0.0279891i	0.0427867	+	0.00123455i
$515$	6.37178	−	0.448310i	0.280774	−	0.0197549i
$516$	1.03103	−	2.64371i	0.0453886	−	0.116383i
$517$	3.41429	+	1.73967i	0.150160	+	0.0765104i
$518$	−2.59087	−	20.0933i	−0.113836	−	0.882851i
$519$	1.94284	+	5.97944i	0.0852811	+	0.262468i
$520$	−18.1475	+	8.87721i	−0.795822	+	0.389292i
$521$	−1.68604	+	5.18909i	−0.0738666	+	0.227338i	−0.981173	−	0.193133i	$-0.938135\pi$
$521$	−1.68604	+	5.18909i	−0.0738666	+	0.227338i	0.907306	+	0.420471i	$0.138135\pi$
$522$	5.62795	+	1.05860i	0.246329	+	0.0463338i
$523$	−4.97704	+	31.4238i	−0.217631	+	1.37407i	0.600772	+	0.799421i	$0.294860\pi$
$523$	−4.97704	+	31.4238i	−0.217631	+	1.37407i	−0.818402	+	0.574646i	$0.805140\pi$
$524$	7.65480	+	29.1897i	0.334402	+	1.27516i
$525$	19.8888	−	9.72158i	0.868018	−	0.424285i
$526$	15.3639	+	11.8544i	0.669899	+	0.516874i
$527$	5.39218	+	0.854038i	0.234887	+	0.0372025i
$528$	−12.3764	+	18.6203i	−0.538614	+	0.810345i
$529$	−47.0385	−	15.2837i	−2.04515	−	0.664511i
$530$	−20.0819	+	21.8174i	−0.872300	+	0.947686i
$531$	4.68872	−	1.52346i	0.203473	−	0.0661124i
$532$	18.1097	+	10.5847i	0.785154	+	0.458907i
$533$	9.63101	−	18.9019i	0.417166	−	0.818734i
$534$	−18.2786	+	5.36143i	−0.790994	+	0.232012i
$535$	7.14330	−	2.88965i	0.308832	−	0.124931i
$536$	1.24235	+	5.36336i	0.0536615	+	0.231662i
$537$	−16.2140	+	2.56804i	−0.699684	+	0.110819i
$538$	20.6922	+	11.3064i	0.892103	+	0.487456i
$539$	−56.9911	+	41.4064i	−2.45478	+	1.78350i
$540$	−3.65074	−	2.58304i	−0.157103	−	0.111156i
$541$	33.9936	+	24.6978i	1.46150	+	1.06184i	0.982970	+	0.183767i	$0.0588292\pi$
$541$	33.9936	+	24.6978i	1.46150	+	1.06184i	0.478527	+	0.878073i	$0.341171\pi$
$542$	−13.9257	−	29.3971i	−0.598158	−	1.26272i
$543$	11.0824	−	11.0824i	0.475592	−	0.475592i
$544$	2.40592	+	14.0217i	0.103153	+	0.601173i
$545$	19.0133	+	31.6127i	0.814441	+	1.35414i
$546$	11.2846	+	16.5134i	0.482938	+	0.706708i
$547$	7.64844	−	3.89708i	0.327024	−	0.166627i	−0.282769	−	0.959188i	$-0.591253\pi$
$547$	7.64844	−	3.89708i	0.327024	−	0.166627i	0.609792	+	0.792561i	$0.291253\pi$
$548$	1.33251	+	13.3629i	0.0569220	+	0.570835i
$549$		−	3.30539i		−	0.141070i
$550$	−32.9980	+	21.7553i	−1.40704	+	0.927649i
$551$			9.59223i			0.408643i
$552$	12.7437	−	20.4273i	0.542406	−	0.869442i
$553$	18.2317	−	9.28949i	0.775289	−	0.395029i
$554$	13.4980	−	9.22407i	0.573477	−	0.391893i
$555$	−7.04893	+	1.63056i	−0.299210	+	0.0692136i
$556$	13.1710	+	20.5203i	0.558577	+	0.870255i
$557$	29.0997	−	29.0997i	1.23299	−	1.23299i	0.270186	−	0.962808i	$-0.412915\pi$
$557$	29.0997	−	29.0997i	1.23299	−	1.23299i	0.962808	−	0.270186i	$-0.0870851\pi$
$558$	2.77442	−	1.31427i	0.117451	−	0.0556373i
$559$	3.66656	+	2.66392i	0.155079	+	0.112672i
$560$	−38.1766	+	10.5254i	−1.61325	+	0.444780i
$561$	11.3726	−	8.26270i	0.480153	−	0.348851i
$562$	14.7450	−	26.9851i	0.621981	−	1.13830i
$563$	−3.16605	+	0.501453i	−0.133433	+	0.0211337i	−0.222794	−	0.974866i	$-0.571518\pi$
$563$	−3.16605	+	0.501453i	−0.133433	+	0.0211337i	0.0893606	+	0.995999i	$0.471518\pi$
$564$	0.868534	−	1.06093i	0.0365719	−	0.0446734i
$565$	−12.8399	−	3.19550i	−0.540180	−	0.134436i
$566$	−9.97172	−	33.9965i	−0.419143	−	1.42898i
$567$	−2.01005	+	3.94495i	−0.0844142	+	0.165672i
$568$	−20.0804	+	8.13005i	−0.842554	+	0.341130i
$569$	16.4412	−	5.34207i	0.689250	−	0.223951i	0.0566096	−	0.998396i	$-0.481971\pi$
$569$	16.4412	−	5.34207i	0.689250	−	0.223951i	0.632641	+	0.774445i	$0.281971\pi$
$570$	3.12166	−	6.80947i	0.130752	−	0.285217i
$571$	9.88620	+	3.21222i	0.413724	+	0.134427i	0.508481	−	0.861073i	$-0.330207\pi$
$571$	9.88620	+	3.21222i	0.413724	+	0.134427i	−0.0947565	+	0.995500i	$0.530207\pi$
$572$	−23.7524	−	26.6642i	−0.993137	−	1.11489i
$573$	−8.05163	−	1.27525i	−0.336361	−	0.0532744i
$574$	25.4026	−	32.9233i	1.06029	−	1.37419i
$575$	34.8433	−	24.4422i	1.45307	−	1.01931i
$576$	5.56566	+	5.74660i	0.231903	+	0.239442i
$577$	3.44804	−	21.7701i	0.143544	−	0.906300i	−0.805829	−	0.592148i	$-0.798280\pi$
$577$	3.44804	−	21.7701i	0.143544	−	0.906300i	0.949373	−	0.314152i	$-0.101720\pi$
$578$	−2.79076	+	14.8368i	−0.116080	+	0.617128i
$579$	−4.33471	+	13.3409i	−0.180144	+	0.554427i
$580$	−12.9649	−	12.6434i	−0.538338	−	0.524990i
$581$	−17.1567	−	52.8028i	−0.711779	−	2.19063i
$582$	−0.0543244	+	0.00700468i	−0.00225182	+	0.000290353i
$583$	−46.7006	−	23.7951i	−1.93414	−	0.985493i
$584$	18.8681	−	11.3559i	0.780768	−	0.469909i
$585$	5.46960	−	4.59355i	0.226140	−	0.189920i
$586$	0.170141	−	5.89671i	0.00702847	−	0.243591i
$587$	−1.10642	−	6.98565i	−0.0456668	−	0.288329i	0.954277	−	0.298923i	$-0.0966275\pi$
$587$	−1.10642	−	6.98565i	−0.0456668	−	0.288329i	−0.999944	+	0.0105947i	$0.996628\pi$
$588$	10.1292	+	23.0810i	0.417723	+	0.951845i
$589$	3.02254	+	4.16017i	0.124542	+	0.171417i
$590$	−15.0137	−	4.19984i	−0.618105	−	0.172905i
$591$	12.5759	−	17.3093i	0.517305	−	0.712009i
$592$	12.9312	−	0.539512i	0.531470	−	0.0221738i
$593$	−3.19251	−	3.19251i	−0.131101	−	0.131101i	0.638512	−	0.769612i	$-0.279550\pi$
$593$	−3.19251	−	3.19251i	−0.131101	−	0.131101i	−0.769612	+	0.638512i	$0.779550\pi$
$594$	2.65854	−	7.44437i	0.109081	−	0.305446i
$595$	24.8045	+	2.15937i	1.01689	+	0.0885256i
$596$	4.97701	+	0.287448i	0.203866	+	0.0117743i
$597$	0.127148	+	0.249542i	0.00520382	+	0.0102131i
$598$	26.3952	+	27.9636i	1.07938	+	1.14352i
$599$	21.4369			0.875887			0.437943	−	0.899003i	$-0.355707\pi$
$599$	21.4369			0.875887			0.437943	+	0.899003i	$0.355707\pi$
$600$	5.08907	+	13.1947i	0.207760	+	0.538673i
$601$	−38.5379			−1.57199			−0.785997	−	0.618230i	$-0.787850\pi$
$601$	−38.5379			−1.57199			−0.785997	+	0.618230i	$0.787850\pi$
$602$	6.09807	+	6.46043i	0.248539	+	0.263307i
$603$	−0.883666	−	1.73429i	−0.0359856	−	0.0706258i
$604$	−19.9939	−	1.15475i	−0.813542	−	0.0469863i
$605$	−34.1749	−	29.6820i	−1.38941	−	1.20674i
$606$	5.27150	−	14.7611i	0.214140	−	0.599629i
$607$	−17.6735	−	17.6735i	−0.717346	−	0.717346i	0.250715	−	0.968061i	$-0.419334\pi$
$607$	−17.6735	−	17.6735i	−0.717346	−	0.717346i	−0.968061	+	0.250715i	$0.919334\pi$
$608$	−7.73643	+	10.9413i	−0.313754	+	0.443727i
$609$	−10.5382	+	14.5045i	−0.427027	+	0.587753i
$610$	−5.78862	+	8.70331i	−0.234374	+	0.352387i
$611$	1.28716	+	1.77163i	0.0520730	+	0.0716724i
$612$	−2.02130	−	4.60584i	−0.0817062	−	0.186180i
$613$	−1.08163	−	6.82914i	−0.0436866	−	0.275826i	0.956169	−	0.292815i	$-0.0945921\pi$
$613$	−1.08163	−	6.82914i	−0.0436866	−	0.275826i	−0.999856	+	0.0169887i	$0.994592\pi$
$614$	−0.308846	+	10.7039i	−0.0124640	+	0.431975i
$615$	−12.5972	−	7.86407i	−0.507968	−	0.317110i
$616$	−36.0952	−	59.9734i	−1.45432	−	2.41640i
$617$	41.4816	+	21.1359i	1.66999	+	0.850900i	0.993421	+	0.114516i	$0.0365317\pi$
$617$	41.4816	+	21.1359i	1.66999	+	0.850900i	0.676564	+	0.736384i	$0.263468\pi$
$618$	4.00666	−	0.516625i	0.161171	−	0.0207817i
$619$	−5.89141	−	18.1319i	−0.236796	−	0.728782i	−0.996878	−	0.0789556i	$-0.974841\pi$
$619$	−5.89141	−	18.1319i	−0.236796	−	0.728782i	0.760082	−	0.649827i	$-0.225159\pi$
$620$	−9.60689	−	1.39821i	−0.385822	−	0.0561535i
$621$	−2.63045	+	8.09568i	−0.105556	+	0.324868i
$622$	−0.259813	+	1.38127i	−0.0104176	+	0.0553838i
$623$	9.32919	−	58.9022i	0.373766	−	2.35987i
$624$	−11.1328	+	6.27022i	−0.445669	+	0.251010i
$625$	−0.829530	+	24.9862i	−0.0331812	+	0.999449i
$626$	−18.2216	+	23.6163i	−0.728283	+	0.943897i
$627$	13.0777	+	2.07131i	0.522274	+	0.0827201i
$628$	30.9190	+	34.7094i	1.23380	+	1.38506i
$629$	−7.73907	−	2.51458i	−0.308577	−	0.100263i
$630$	12.2013	−	6.86718i	0.486110	−	0.273595i
$631$	−11.9203	+	3.87314i	−0.474540	+	0.154187i	−0.536516	−	0.843890i	$-0.680260\pi$
$631$	−11.9203	+	3.87314i	−0.474540	+	0.154187i	0.0619760	+	0.998078i	$0.480260\pi$
$632$	4.90556	+	12.1162i	0.195133	+	0.481958i
$633$	−1.39069	+	2.72939i	−0.0552751	+	0.108483i
$634$	2.59170	+	8.83587i	0.102930	+	0.350917i
$635$	16.4013	−	26.2726i	0.650865	−	1.04260i
$636$	−11.8798	+	14.5114i	−0.471064	+	0.575416i
$637$	−39.7617	+	6.29763i	−1.57542	+	0.249521i
$638$	15.3485	−	28.0896i	0.607654	−	1.11208i
$639$	6.19651	−	4.50203i	0.245130	−	0.178097i
$640$	−4.59093	−	24.8782i	−0.181472	−	0.983396i
$641$	−26.8829	−	19.5316i	−1.06181	−	0.771450i	−0.0873879	−	0.996174i	$-0.527852\pi$
$641$	−26.8829	−	19.5316i	−1.06181	−	0.771450i	−0.974422	+	0.224724i	$0.927852\pi$
$642$	4.40430	−	2.08635i	0.173824	−	0.0823417i
$643$	20.5987	−	20.5987i	0.812335	−	0.812335i	−0.172649	−	0.984983i	$-0.555233\pi$
$643$	20.5987	−	20.5987i	0.812335	−	0.812335i	0.984983	+	0.172649i	$0.0552326\pi$
$644$	40.7155	+	63.4342i	1.60442	+	2.49966i
$645$	2.08037	−	2.39527i	0.0819146	−	0.0943138i
$646$	6.95603	−	4.75350i	0.273681	−	0.187024i
$647$	−3.00685	+	1.53207i	−0.118212	+	0.0602318i	−0.512096	−	0.858928i	$-0.671131\pi$
$647$	−3.00685	+	1.53207i	−0.118212	+	0.0602318i	0.393885	+	0.919160i	$0.371131\pi$
$648$	−2.39974	−	1.49709i	−0.0942705	−	0.0588111i
$649$		−	27.5566i		−	1.08169i
$650$	−22.4464	+	2.51639i	−0.880420	+	0.0987009i
$651$			9.61125i			0.376695i
$652$	−1.72115	−	17.2604i	−0.0674056	−	0.675969i
$653$	−14.5287	+	7.40276i	−0.568553	+	0.289692i	−0.714541	−	0.699594i	$-0.753364\pi$
$653$	−14.5287	+	7.40276i	−0.568553	+	0.289692i	0.145987	+	0.989286i	$0.453364\pi$
$654$	13.1637	+	19.2630i	0.514740	+	0.753245i
$655$	−2.92607	+	33.6115i	−0.114331	+	1.31331i
$656$	19.5511	+	17.9850i	0.763341	+	0.702197i
$657$	−5.50546	+	5.50546i	−0.214788	+	0.214788i
$658$	1.83766	+	3.87932i	0.0716395	+	0.151231i
$659$	−28.2601	−	20.5322i	−1.10086	−	0.799819i	−0.119657	−	0.992815i	$-0.538180\pi$
$659$	−28.2601	−	20.5322i	−1.10086	−	0.799819i	−0.981200	+	0.192996i	$0.938180\pi$
$660$	−20.0372	+	14.9457i	−0.779948	+	0.581761i
$661$	15.7161	−	11.4184i	0.611287	−	0.444126i	−0.238580	−	0.971123i	$-0.576682\pi$
$661$	15.7161	−	11.4184i	0.611287	−	0.444126i	0.849867	+	0.526997i	$0.176682\pi$
$662$	14.5329	+	7.94095i	0.564837	+	0.308634i
$663$	7.93448	−	1.25670i	0.308150	−	0.0488061i
$664$	34.5530	−	8.00376i	1.34092	−	0.310606i
$665$	15.0824	+	17.9588i	0.584869	+	0.696412i
$666$	−4.39087	+	1.28791i	−0.170143	+	0.0499056i
$667$	−15.6487	+	30.7124i	−0.605921	+	1.18919i
$668$	−4.62913	−	2.70564i	−0.179107	−	0.104684i
$669$	−23.4042	+	7.60449i	−0.904859	+	0.294007i
$670$	−0.710458	+	6.11405i	−0.0274474	+	0.236206i
$671$	−17.5714	−	5.70930i	−0.678337	−	0.220405i
$672$	−23.7186	+	8.04507i	−0.914964	+	0.310345i
$673$	20.7679	+	3.28931i	0.800544	+	0.126794i	0.543284	−	0.839549i	$-0.317181\pi$
$673$	20.7679	+	3.28931i	0.800544	+	0.126794i	0.257259	+	0.966342i	$0.417181\pi$
$674$	26.5344	+	20.4731i	1.02207	+	0.788596i
$675$	−2.87140	−	4.09329i	−0.110520	−	0.157551i
$676$	1.41878	+	5.41015i	0.0545683	+	0.208083i
$677$	−0.806309	+	5.09083i	−0.0309890	+	0.195657i	−0.998326	−	0.0578369i	$-0.981580\pi$
$677$	−0.806309	+	5.09083i	−0.0309890	+	0.195657i	0.967337	+	0.253494i	$0.0815797\pi$
$678$	−8.22418	−	1.54695i	−0.315848	−	0.0594102i
$679$	0.0529912	−	0.163090i	0.00203361	−	0.00625882i
$680$	−2.74384	+	15.6673i	−0.105222	+	0.600815i
$681$	−0.945379	−	2.90958i	−0.0362270	−	0.111495i
$682$	−2.19445	−	17.0189i	−0.0840297	−	0.651688i
$683$	−28.3296	−	14.4346i	−1.08400	−	0.552327i	−0.181666	−	0.983360i	$-0.558149\pi$
$683$	−28.3296	−	14.4346i	−1.08400	−	0.552327i	−0.902336	+	0.431034i	$0.858149\pi$
$684$	1.72138	−	4.41388i	0.0658187	−	0.168769i
$685$	−3.62602	+	14.5698i	−0.138543	+	0.556685i
$686$	−35.0679	−	1.01183i	−1.33890	−	0.0386319i
$687$	−0.367023	−	2.31729i	−0.0140028	−	0.0884102i
$688$	−4.44836	+	3.52435i	−0.169592	+	0.134364i
$689$	−17.6058	−	24.2323i	−0.670727	−	0.923177i
$690$	21.1039	−	16.7099i	0.803410	−	0.636134i
$691$	−15.5761	+	21.4387i	−0.592545	+	0.815568i	−0.995000	−	0.0998719i	$-0.968157\pi$
$691$	−15.5761	+	21.4387i	−0.592545	+	0.815568i	0.402456	+	0.915439i	$0.368157\pi$
$692$	2.67988	−	12.2854i	0.101874	−	0.467022i
$693$	17.4994	+	17.4994i	0.664748	+	0.664748i
$694$	−23.4351	−	8.36919i	−0.889586	−	0.317690i
$695$	6.14396	+	26.5603i	0.233054	+	1.00749i
$696$	−8.64939	−	7.50773i	−0.327854	−	0.284580i
$697$	−7.58269	−	14.8819i	−0.287215	−	0.563691i
$698$	16.5481	−	15.6200i	0.626357	−	0.591225i
$699$	12.8122			0.484602
$700$	−44.1531	−	3.28595i	−1.66883	−	0.124197i
$701$	−15.0737			−0.569325			−0.284663	−	0.958628i	$-0.591882\pi$
$701$	−15.0737			−0.569325			−0.284663	+	0.958628i	$0.591882\pi$
$702$	3.28508	−	3.10083i	0.123987	−	0.117033i
$703$	−3.47967	−	6.82924i	−0.131238	−	0.257570i
$704$	40.1623	−	19.6611i	1.51367	−	0.741005i
$705$	1.31365	−	0.790089i	0.0494749	−	0.0297565i
$706$	−41.6667	−	14.8801i	−1.56815	−	0.560019i
$707$	34.6988	+	34.6988i	1.30498	+	1.30498i
$708$	−9.63349	−	2.10140i	−0.362049	−	0.0789755i
$709$	−5.26121	+	7.24144i	−0.197589	+	0.271958i	−0.896302	−	0.443444i	$-0.853756\pi$
$709$	−5.26121	+	7.24144i	−0.197589	+	0.271958i	0.698713	+	0.715402i	$0.253756\pi$
$710$	−24.2001	+	1.00240i	−0.908214	+	0.0376192i
$711$	−2.71646	−	3.73889i	−0.101875	−	0.140219i
$712$	36.9725	+	9.18963i	1.38560	+	0.344396i
$713$	2.89067	+	18.2510i	0.108257	+	0.683505i
$714$	15.7405	+	0.454171i	0.589075	+	0.0169969i
$715$	−14.9718	−	37.0107i	−0.559913	−	1.38412i
$716$	30.5883	+	11.9292i	1.14314	+	0.445816i
$717$	−11.2445	−	5.72934i	−0.419932	−	0.213966i
$718$	0.486399	+	3.77224i	0.0181522	+	0.140779i
$719$	10.1858	+	31.3485i	0.379865	+	1.16910i	0.940138	+	0.340795i	$0.110696\pi$
$719$	10.1858	+	31.3485i	0.379865	+	1.16910i	−0.560273	+	0.828308i	$0.689304\pi$
$720$	3.69687	+	8.14452i	0.137774	+	0.303528i
$721$	−3.90833	+	12.0286i	−0.145554	+	0.447968i
$722$	−18.6081	−	3.50013i	−0.692520	−	0.130261i
$723$	−0.299392	+	1.89029i	−0.0111345	+	0.0703005i
$724$	−30.3206	+	7.95136i	−1.12685	+	0.295510i
$725$	−8.89123	−	18.1900i	−0.330212	−	0.675561i
$726$	−22.6658	−	17.4883i	−0.841206	−	0.649050i
$727$	9.78821	+	1.55030i	0.363025	+	0.0574974i	0.335282	−	0.942118i	$-0.391168\pi$
$727$	9.78821	+	1.55030i	0.363025	+	0.0574974i	0.0277421	+	0.999615i	$0.491168\pi$
$728$	−2.81950	−	39.9023i	−0.104498	−	1.47888i
$729$	0.951057	+	0.309017i	0.0352243	+	0.0114451i
$730$	24.1378	−	4.85471i	0.893380	−	0.179681i
$731$	3.39359	−	1.10264i	0.125517	−	0.0407828i
$732$	−3.33586	+	5.70739i	−0.123297	+	0.210951i
$733$	23.8015	−	46.7130i	0.879128	−	1.72539i	0.216733	−	0.976231i	$-0.430460\pi$
$733$	23.8015	−	46.7130i	0.879128	−	1.72539i	0.662395	−	0.749155i	$-0.269540\pi$
$734$	−38.8977	+	11.4093i	−1.43574	+	0.421126i
$735$	1.97789	+	28.1115i	0.0729556	+	1.03691i
$736$	−42.6200	+	22.4105i	−1.57099	+	0.826063i
$737$	−10.7458	+	1.70197i	−0.395827	+	0.0626928i
$738$	−8.24204	−	4.50355i	−0.303394	−	0.165778i
$739$	0.532698	−	0.387028i	0.0195956	−	0.0142370i	−0.577944	−	0.816076i	$-0.696145\pi$
$739$	0.532698	−	0.387028i	0.0195956	−	0.0142370i	0.597540	+	0.801839i	$0.296145\pi$
$740$	13.8169	+	4.29843i	0.507921	+	0.158013i
$741$	6.12161	+	4.44761i	0.224883	+	0.163387i
$742$	−25.1355	−	53.0612i	−0.922753	−	1.94794i
$743$	−3.63738	+	3.63738i	−0.133442	+	0.133442i	−0.770673	−	0.637231i	$-0.780080\pi$
$743$	−3.63738	+	3.63738i	−0.133442	+	0.133442i	0.637231	+	0.770673i	$0.280080\pi$
$744$	−6.11697	−	0.530667i	−0.224259	−	0.0194552i
$745$	5.13159	+	2.17563i	0.188007	+	0.0797089i
$746$	−18.7875	−	27.4927i	−0.687859	−	1.00658i
$747$	−11.1730	+	5.69295i	−0.408800	+	0.208294i
$748$	−27.9759	+	2.78968i	−1.02290	+	0.102001i
$749$			15.2575i			0.557498i
$750$	0.392143	+	15.8065i	0.0143190	+	0.577173i
$751$			32.6192i			1.19029i	0.803618	+	0.595145i	$0.202906\pi$
$751$			32.6192i			1.19029i	−0.803618	+	0.595145i	$0.797094\pi$
$752$	−2.57041	+	0.955369i	−0.0937332	+	0.0348387i
$753$	11.5360	−	5.87790i	0.420397	−	0.214203i
$754$	15.1029	−	10.3208i	0.550016	−	0.375861i
$755$	−20.6149	−	8.74006i	−0.750254	−	0.318083i
$756$	7.45207	−	4.78314i	0.271029	−	0.173961i
$757$	−8.96603	+	8.96603i	−0.325876	+	0.325876i	−0.851016	−	0.525140i	$-0.824013\pi$
$757$	−8.96603	+	8.96603i	−0.325876	+	0.325876i	0.525140	+	0.851016i	$0.324013\pi$
$758$	3.19253	−	1.51233i	0.115958	−	0.0549302i
$759$	38.4931	+	27.9669i	1.39721	+	1.01513i
$760$	−12.2624	+	8.60744i	−0.444804	+	0.312225i
$761$	3.74390	−	2.72010i	0.135716	−	0.0986035i	−0.517856	−	0.855468i	$-0.673270\pi$
$761$	3.74390	−	2.72010i	0.135716	−	0.0986035i	0.653572	+	0.756864i	$0.273270\pi$
$762$	9.39258	−	17.1896i	0.340257	−	0.622712i
$763$	−72.1445	+	11.4266i	−2.61181	+	0.413670i
$764$	12.6157	+	10.3278i	0.456420	+	0.373648i
$765$	−0.394690	−	5.60968i	−0.0142700	−	0.202818i
$766$	−1.50201	−	5.12079i	−0.0542698	−	0.185021i
$767$	7.14938	−	14.0314i	0.258149	−	0.506646i
$768$	−3.81062	−	15.5396i	−0.137504	−	0.560737i
$769$	−15.7087	+	5.10407i	−0.566471	+	0.184058i	−0.578231	−	0.815873i	$-0.696257\pi$
$769$	−15.7087	+	5.10407i	−0.566471	+	0.184058i	0.0117598	+	0.999931i	$0.496257\pi$
$770$	−15.4310	−	76.7233i	−0.556094	−	2.76492i
$771$	0.652623	+	0.212050i	0.0235036	+	0.00763680i
$772$	20.9486	−	18.6609i	0.753956	−	0.671621i
$773$	51.4301	+	8.14573i	1.84981	+	0.292981i	0.979790	−	0.200031i	$-0.0641043\pi$
$773$	51.4301	+	8.14573i	1.84981	+	0.292981i	0.870022	+	0.493012i	$0.164104\pi$
$774$	1.22573	−	1.58862i	0.0440580	−	0.0571016i
$775$	−9.58788	−	5.08740i	−0.344407	−	0.182745i
$776$	0.100871	+	0.0427303i	0.00362106	+	0.00153393i
$777$	2.24104	−	14.1494i	0.0803970	−	0.507606i
$778$	−6.36354	+	33.8310i	−0.228144	+	1.21290i
$779$	4.86148	−	14.9621i	0.174181	−	0.536073i
$780$	−14.0802	+	2.41163i	−0.504153	+	0.0863501i
$781$	−13.2297	−	40.7168i	−0.473396	−	1.45696i
$782$	30.0266	−	3.87168i	1.07375	−	0.138451i
$783$	3.60800	+	1.83837i	0.128939	+	0.0656979i
$784$	5.80371	−	50.0765i	0.207275	−	1.78845i
$785$	19.4891	+	48.1777i	0.695597	+	1.71953i
$786$	−0.615426	+	21.3293i	−0.0219515	+	0.760791i
$787$	4.77301	+	30.1356i	0.170140	+	1.07422i	0.913950	+	0.405828i	$0.133017\pi$
$787$	4.77301	+	30.1356i	0.170140	+	1.07422i	−0.743810	+	0.668391i	$0.766983\pi$
$788$	−39.1837	+	17.1960i	−1.39586	+	0.612581i
$789$	8.06548	+	11.1012i	0.287139	+	0.395212i
$790$	0.604832	+	14.6020i	0.0215189	+	0.519516i
$791$	15.3995	−	21.1956i	0.547543	−	0.753628i
$792$	−12.1035	+	10.1711i	−0.430079	+	0.361414i
$793$	−7.46588	−	7.46588i	−0.265121	−	0.265121i
$794$	7.72810	−	21.6400i	0.274260	−	0.767974i
$795$	−17.9681	+	10.8068i	−0.637262	+	0.383278i
$796$	0.0322969	−	0.559203i	0.00114473	−	0.0198204i
$797$	−0.301409	−	0.591549i	−0.0106765	−	0.0209538i	0.885607	−	0.464436i	$-0.153743\pi$
$797$	−0.301409	−	0.591549i	−0.0106765	−	0.0209538i	−0.896283	+	0.443482i	$0.853743\pi$
$798$	10.1812	+	10.7862i	0.360410	+	0.381827i
$799$	1.72412			0.0609948
$800$	4.52913	−	27.9193i	0.160129	−	0.987096i
$801$	−13.4695			−0.475921
$802$	21.9468	+	23.2509i	0.774967	+	0.821017i
$803$	19.7576	+	38.7764i	0.697229	+	1.36839i
$804$	−0.224460	+	3.88640i	−0.00791609	+	0.137063i
$805$	18.9928	+	82.1057i	0.669407	+	2.89384i
$806$	3.29806	−	9.23513i	0.116169	−	0.325293i
$807$	11.7898	+	11.7898i	0.415022	+	0.415022i
$808$	−23.9995	+	20.1678i	−0.844299	+	0.709501i
$809$	−13.1401	+	18.0858i	−0.461982	+	0.635864i	−0.974918	−	0.222563i	$-0.928558\pi$
$809$	−13.1401	+	18.0858i	−0.461982	+	0.635864i	0.512936	+	0.858427i	$0.328558\pi$
$810$	−1.96303	−	2.47922i	−0.0689737	−	0.0871109i
$811$	−15.2425	−	20.9795i	−0.535237	−	0.736690i	0.452680	−	0.891673i	$-0.350468\pi$
$811$	−15.2425	−	20.9795i	−0.535237	−	0.736690i	−0.987917	+	0.154983i	$0.950468\pi$
$812$	32.8344	−	14.4096i	1.15226	−	0.505677i
$813$	−3.59819	−	22.7181i	−0.126194	−	0.796758i
$814$	−0.737681	+	25.5664i	−0.0258557	+	0.896102i
$815$	4.68360	−	18.8193i	0.164059	−	0.659213i
$816$	−1.15814	+	9.99281i	−0.0405429	+	0.349818i
$817$	2.99463	+	1.52584i	0.104769	+	0.0533824i
$818$	−26.7207	+	3.44541i	−0.934267	+	0.120466i
$819$	4.37035	+	13.4506i	0.152712	+	0.470001i
$820$	13.8149	+	26.2922i	0.482438	+	0.918163i
$821$	−3.64699	+	11.2243i	−0.127281	+	0.391730i	−0.994310	−	0.106528i	$-0.966027\pi$
$821$	−3.64699	+	11.2243i	−0.127281	+	0.391730i	0.867029	+	0.498258i	$0.166027\pi$
$822$	−1.75537	+	9.33221i	−0.0612254	+	0.325498i
$823$	−7.83081	+	49.4418i	−0.272965	+	1.72343i	0.346190	+	0.938164i	$0.387475\pi$
$823$	−7.83081	+	49.4418i	−0.272965	+	1.72343i	−0.619155	+	0.785269i	$0.712525\pi$
$824$	−7.43967	−	3.15155i	−0.259173	−	0.109789i
$825$	−26.7196	+	8.19413i	−0.930257	+	0.285283i
$826$	18.8571	−	24.4399i	0.656123	−	0.850373i
$827$	23.6915	+	3.75236i	0.823833	+	0.130482i	0.554097	−	0.832452i	$-0.313064\pi$
$827$	23.6915	+	3.75236i	0.823833	+	0.130482i	0.269736	+	0.962934i	$0.413064\pi$
$828$	12.7123	−	11.3241i	0.441783	−	0.393539i
$829$	37.4686	+	12.1743i	1.30134	+	0.422830i	0.876047	−	0.482226i	$-0.160172\pi$
$829$	37.4686	+	12.1743i	1.30134	+	0.422830i	0.425291	+	0.905057i	$0.360172\pi$
$830$	39.3893	+	4.57707i	1.36722	+	0.158873i
$831$	10.9945	−	3.57233i	0.381395	−	0.123923i
$832$	25.5510	+	0.408689i	0.885822	+	0.0141687i
$833$	−14.3894	+	28.2408i	−0.498564	+	0.978486i
$834$	4.85285	+	16.5448i	0.168041	+	0.572899i
$835$	−3.85531	−	4.59057i	−0.133418	−	0.158863i
$836$	−20.4908	−	16.7748i	−0.708691	−	0.580169i
$837$	2.14407	−	0.339588i	0.0741100	−	0.0117379i
$838$	−1.12119	+	2.05191i	−0.0387307	+	0.0708819i
$839$	32.2581	−	23.4369i	1.11367	−	0.809132i	0.130436	−	0.991457i	$-0.458362\pi$
$839$	32.2581	−	23.4369i	1.11367	−	0.809132i	0.983238	+	0.182325i	$0.0583622\pi$
$840$	−27.9984	−	0.456236i	−0.966036	−	0.0157416i
$841$	−10.1958	−	7.40772i	−0.351581	−	0.255439i
$842$	−46.0090	+	21.7948i	−1.58558	+	0.751099i
$843$	15.3754	−	15.3754i	0.529557	−	0.529557i
$844$	5.15585	−	3.30931i	0.177472	−	0.113911i
$845$	−0.542331	+	6.22971i	−0.0186567	+	0.214308i
$846$	0.800467	−	0.547010i	0.0275206	−	0.0188066i
$847$	79.8585	−	40.6899i	2.74397	−	1.39812i
$848$	35.1580	−	13.0675i	1.20733	−	0.448740i
$849$		−	25.0519i		−	0.859779i
$850$	−8.78481	+	15.4619i	−0.301316	+	0.530338i
$851$		−	27.5426i		−	0.944147i
$852$	−15.2430	+	1.51999i	−0.522217	+	0.0520740i
$853$	21.2541	−	10.8295i	0.727725	−	0.370795i	−0.0505468	−	0.998722i	$-0.516096\pi$
$853$	21.2541	−	10.8295i	0.727725	−	0.370795i	0.778272	+	0.627927i	$0.216096\pi$
$854$	−11.6771	−	17.0877i	−0.399583	−	0.584730i
$855$	3.47334	−	3.99909i	0.118786	−	0.136766i
$856$	−9.71047	−	0.842416i	−0.331897	−	0.0287932i
$857$	15.1879	−	15.1879i	0.518808	−	0.518808i	−0.398403	−	0.917211i	$-0.630435\pi$
$857$	15.1879	−	15.1879i	0.518808	−	0.518808i	0.917211	+	0.398403i	$0.130435\pi$
$858$	−10.8097	−	22.8194i	−0.369039	−	0.779043i
$859$	−37.4238	−	27.1900i	−1.27688	−	0.927710i	−0.277429	−	0.960746i	$-0.589482\pi$
$859$	−37.4238	−	27.1900i	−1.27688	−	0.927710i	−0.999454	+	0.0330366i	$0.989482\pi$
$860$	−6.00953	+	2.03635i	−0.204923	+	0.0694391i
$861$	23.7886	−	17.2835i	0.810715	−	0.589019i
$862$	39.7764	+	21.7343i	1.35479	+	0.740274i
$863$	7.59376	−	1.20273i	0.258495	−	0.0409415i	−0.0258420	−	0.999666i	$-0.508227\pi$
$863$	7.59376	−	1.20273i	0.258495	−	0.0409415i	0.284337	+	0.958725i	$0.408227\pi$
$864$	2.63272	+	5.00687i	0.0895670	+	0.170337i
$865$	7.44475	−	11.9255i	0.253129	−	0.405479i
$866$	5.74027	−	1.68372i	0.195062	−	0.0572150i
$867$	−4.84642	+	9.51163i	−0.164593	+	0.323032i
$868$	9.69986	−	16.5957i	0.329235	−	0.563295i
$869$	−24.5680	+	7.98262i	−0.833411	+	0.270792i
$870$	−6.28063	−	11.1591i	−0.212933	−	0.378330i
$871$	−5.91318	−	1.92131i	−0.200360	−	0.0651011i
$872$	−3.28898	−	46.5464i	−0.111379	−	1.57626i
$873$	−0.0382543	−	0.00605889i	−0.00129471	−	0.000205062i
$874$	22.5773	+	17.4200i	0.763689	+	0.589240i
$875$	−45.2475	−	20.0756i	−1.52964	−	0.678679i
$876$	15.0625	−	3.95003i	0.508913	−	0.133459i
$877$	−4.08825	+	25.8122i	−0.138051	+	0.871617i	0.817315	+	0.576191i	$0.195462\pi$
$877$	−4.08825	+	25.8122i	−0.138051	+	0.871617i	−0.955366	+	0.295426i	$0.904538\pi$
$878$	27.1460	+	5.10610i	0.916133	+	0.172322i
$879$	1.28902	−	3.96718i	0.0434774	−	0.133810i
$880$	49.6817	−	5.58474i	1.67477	−	0.188261i
$881$	−6.70500	−	20.6359i	−0.225897	−	0.695240i	−0.998199	−	0.0599846i	$-0.980895\pi$
$881$	−6.70500	−	20.6359i	−0.225897	−	0.695240i	0.772302	−	0.635255i	$-0.219105\pi$
$882$	2.27929	+	17.6769i	0.0767476	+	0.595212i
$883$	41.0972	+	20.9401i	1.38303	+	0.704689i	0.977803	−	0.209526i	$-0.0671922\pi$
$883$	41.0972	+	20.9401i	1.38303	+	0.704689i	0.405228	+	0.914216i	$0.367192\pi$
$884$	−14.9687	−	5.83770i	−0.503452	−	0.196343i
$885$	−9.35126	−	5.83773i	−0.314339	−	0.196233i
$886$	54.3127	+	1.56711i	1.82467	+	0.0526482i
$887$	2.23808	+	14.1307i	0.0751474	+	0.474462i	0.996349	+	0.0853759i	$0.0272091\pi$
$887$	2.23808	+	14.1307i	0.0751474	+	0.474462i	−0.921201	+	0.389086i	$0.872791\pi$
$888$	8.88148	+	2.20752i	0.298043	+	0.0740795i
$889$	36.0463	+	49.6135i	1.20895	+	1.66398i
$890$	35.4661	+	23.5887i	1.18883	+	0.790695i
$891$	3.28546	−	4.52205i	0.110067	−	0.151494i
$892$	48.0866	+	10.4894i	1.61006	+	0.351210i
$893$	1.14831	+	1.14831i	0.0384269	+	0.0384269i
$894$	3.31980	+	1.18557i	0.111031	+	0.0396514i
$895$	27.7138	+	24.0704i	0.926371	+	0.804583i
$896$	49.0740	+	10.0459i	1.63945	+	0.335609i
$897$	12.3443	+	24.2271i	0.412165	+	0.808919i
$898$	2.86673	−	2.70594i	0.0956641	−	0.0902984i
$899$	8.79032			0.293174
$900$	0.827003	+	9.96574i	0.0275668	+	0.332191i
$901$	−23.5824			−0.785644
$902$	−38.1771	+	36.0358i	−1.27116	+	1.19986i
$903$	2.85191	+	5.59718i	0.0949055	+	0.186263i
$904$	12.6394	+	10.9711i	0.420381	+	0.364894i
$905$	−34.9136	−	3.03943i	−1.16057	−	0.101034i
$906$	−13.3365	−	4.76274i	−0.443075	−	0.158232i
$907$	−8.28875	−	8.28875i	−0.275223	−	0.275223i	0.555975	−	0.831199i	$-0.312345\pi$
$907$	−8.28875	−	8.28875i	−0.275223	−	0.275223i	−0.831199	+	0.555975i	$0.812345\pi$
$908$	−1.30402	+	5.97805i	−0.0432755	+	0.198389i
$909$	6.51460	−	8.96658i	0.216076	−	0.297403i
$910$	12.0481	−	43.0699i	0.399391	−	1.42775i
$911$	21.3280	+	29.3554i	0.706628	+	0.972589i	0.999863	+	0.0165492i	$0.00526800\pi$
$911$	21.3280	+	29.3554i	0.706628	+	0.972589i	−0.293235	+	0.956040i	$0.594732\pi$
$912$	−7.42688	+	5.88417i	−0.245928	+	0.194844i
$913$	10.9648	+	69.2291i	0.362882	+	2.29115i
$914$	6.96247	+	0.200892i	0.230298	+	0.00664492i
$915$	−5.65984	+	4.75332i	−0.187109	+	0.157140i
$916$	−1.70492	+	4.37166i	−0.0563321	+	0.144444i
$917$	−59.5228	−	30.3284i	−1.96562	−	1.00153i
$918$	−0.454834	−	3.52744i	−0.0150118	−	0.116423i
$919$	−3.80037	−	11.6964i	−0.125363	−	0.385827i	0.868604	−	0.495507i	$-0.165018\pi$
$919$	−3.80037	−	11.6964i	−0.125363	−	0.385827i	−0.993967	+	0.109680i	$0.965018\pi$
$920$	−53.3039	+	7.55441i	−1.75738	+	0.249062i
$921$	−2.33987	+	7.20137i	−0.0771013	+	0.237293i
$922$	−28.2167	−	5.30749i	−0.929267	−	0.174793i
$923$	3.82733	−	24.1648i	0.125978	−	0.795394i
$924$	−12.5554	−	47.8769i	−0.413042	−	1.57503i
$925$	12.9288	+	9.72511i	0.425095	+	0.319760i
$926$	−26.1594	−	20.1838i	−0.859650	−	0.663281i
$927$	2.82142	+	0.446869i	0.0926676	+	0.0146771i
$928$	7.35792	+	21.6927i	0.241535	+	0.712097i
$929$	14.3316	+	4.65661i	0.470204	+	0.152779i	0.534528	−	0.845151i	$-0.320489\pi$
$929$	14.3316	+	4.65661i	0.470204	+	0.152779i	−0.0643245	+	0.997929i	$0.520489\pi$
$930$	−6.24020	−	2.86069i	−0.204624	−	0.0938057i
$931$	−28.3930	+	9.22546i	−0.930544	+	0.302352i
$932$	−22.1228	−	12.9303i	−0.724655	−	0.423547i
$933$	−0.451191	+	0.885511i	−0.0147713	+	0.0289903i
$934$	50.9608	−	14.9476i	1.66749	−	0.489101i
$935$	−30.5027	−	7.59126i	−0.997546	−	0.248261i
$936$	−8.80175	+	2.03881i	−0.287694	+	0.0666407i
$937$	−1.61766	+	0.256212i	−0.0528466	+	0.00837008i	−0.182802	−	0.983150i	$-0.558517\pi$
$937$	−1.61766	+	0.256212i	−0.0528466	+	0.00837008i	0.129955	+	0.991520i	$0.458517\pi$
$938$	−10.6951	−	5.84393i	−0.349207	−	0.190811i
$939$	−17.0639	+	12.3977i	−0.556860	+	0.404582i
$940$	−3.06565	+	0.0384817i	−0.0999903	+	0.00125514i
$941$	3.88602	+	2.82336i	0.126681	+	0.0920388i	0.649321	−	0.760514i	$-0.275053\pi$
$941$	3.88602	+	2.82336i	0.126681	+	0.0920388i	−0.522641	+	0.852553i	$0.675053\pi$
$942$	14.0713	+	29.7046i	0.458468	+	0.967828i
$943$	39.9746	−	39.9746i	1.30175	−	1.30175i
$944$	14.5133	+	13.3508i	0.472369	+	0.434531i
$945$	9.64553	−	2.23121i	0.313769	−	0.0725814i
$946$	−6.32790	−	9.25994i	−0.205738	−	0.301067i
$947$	16.0093	−	8.15712i	0.520231	−	0.265071i	−0.174099	−	0.984728i	$-0.555701\pi$
$947$	16.0093	−	8.15712i	0.520231	−	0.265071i	0.694329	+	0.719657i	$0.255701\pi$
$948$	0.917141	+	9.19743i	0.0297873	+	0.298719i
$949$			24.8704i			0.807326i
$950$	−16.1490	+	4.44713i	−0.523944	+	0.144284i
$951$			6.51113i			0.211138i
$952$	−26.7208	−	16.6699i	−0.866025	−	0.540274i
$953$	31.7955	−	16.2006i	1.02996	−	0.524790i	0.144498	−	0.989505i	$-0.453843\pi$
$953$	31.7955	−	16.2006i	1.02996	−	0.524790i	0.885460	+	0.464715i	$0.153843\pi$
$954$	−10.9488	+	7.48199i	−0.354479	+	0.242238i
$955$	9.39504	+	15.6208i	0.304016	+	0.505476i
$956$	13.6336	+	21.2410i	0.440942	+	0.686981i
$957$	16.0047	−	16.0047i	0.517359	−	0.517359i
$958$	−15.7110	+	7.44240i	−0.507598	+	0.240453i
$959$	−24.0512	−	17.4742i	−0.776655	−	0.564273i
$960$	1.83624	−	17.7940i	0.0592645	−	0.574300i
$961$	−21.2671	+	15.4515i	−0.686037	+	0.498435i
$962$	−7.00865	+	12.8267i	−0.225968	+	0.413548i
$963$	3.40364	−	0.539083i	0.109681	−	0.0173717i
$964$	2.42467	−	2.96180i	0.0780935	−	0.0953931i
$965$	29.0772	−	11.7625i	0.936029	−	0.378648i
$966$	15.0016	+	51.1447i	0.482668	+	1.64555i
$967$	−10.6112	+	20.8256i	−0.341233	+	0.669707i	−0.996307	−	0.0858570i	$-0.972637\pi$
$967$	−10.6112	+	20.8256i	−0.341233	+	0.669707i	0.655075	+	0.755564i	$0.272637\pi$
$968$	21.4874	+	53.0717i	0.690631	+	1.70579i
$969$	5.66586	−	1.84095i	0.182014	−	0.0591398i
$970$	0.0901156	+	0.0829471i	0.00289344	+	0.00266327i
$971$	−6.44259	−	2.09333i	−0.206753	−	0.0671780i	0.203810	−	0.979011i	$-0.434668\pi$
$971$	−6.44259	−	2.09333i	−0.206753	−	0.0671780i	−0.410562	+	0.911833i	$0.634668\pi$
$972$	−1.33032	−	1.49340i	−0.0426700	−	0.0479009i
$973$	−53.3148	−	8.44424i	−1.70920	−	0.270710i
$974$	1.14778	−	1.48758i	0.0367771	−	0.0476653i
$975$	−15.7312	−	2.75989i	−0.503800	−	0.0883871i
$976$	11.5200	−	6.48831i	0.368747	−	0.207686i
$977$	7.66319	−	48.3835i	0.245167	−	1.54792i	−0.491021	−	0.871148i	$-0.663376\pi$
$977$	7.66319	−	48.3835i	0.245167	−	1.54792i	0.736188	−	0.676777i	$-0.236624\pi$
$978$	2.26734	−	12.0541i	0.0725016	−	0.385447i
$979$	−23.2654	+	71.6037i	−0.743567	+	2.28846i
$980$	24.9555	−	50.5361i	0.797173	−	1.61432i
$981$	5.09806	+	15.6902i	0.162769	+	0.500950i
$982$	−19.3007	+	2.48866i	−0.615910	+	0.0794164i
$983$	52.1336	+	26.5634i	1.66280	+	0.847241i	0.994660	+	0.103208i	$0.0329108\pi$
$983$	52.1336	+	26.5634i	1.66280	+	0.847241i	0.668144	+	0.744032i	$0.267089\pi$
$984$	9.68642	+	16.0943i	0.308792	+	0.513067i
$985$	−47.7237	+	3.35778i	−1.52060	+	0.106988i
$986$	0.415379	−	14.3961i	0.0132283	−	0.458465i
$987$	0.474826	+	2.99793i	0.0151139	+	0.0954252i
$988$	−6.08154	−	13.8577i	−0.193479	−	0.440873i
$989$	7.09894	+	9.77086i	0.225733	+	0.310695i
$990$	−16.5702	+	6.15315i	−0.526635	+	0.195560i
$991$	−20.2348	+	27.8508i	−0.642780	+	0.884710i	−0.998760	−	0.0497831i	$-0.984147\pi$
$991$	−20.2348	+	27.8508i	−0.642780	+	0.884710i	0.355980	+	0.934493i	$0.384147\pi$
$992$	10.0266	+	7.08967i	0.318344	+	0.225097i
$993$	8.28045	+	8.28045i	0.262772	+	0.262772i
$994$	16.1293	−	45.1648i	0.511590	−	1.43254i
$995$	0.244448	−	0.576571i	0.00774951	−	0.0182785i
$996$	25.0379	+	1.44607i	0.793355	+	0.0458204i
$997$	19.9099	+	39.0754i	0.630553	+	1.23753i	0.956387	+	0.292103i	$0.0943550\pi$
$997$	19.9099	+	39.0754i	0.630553	+	1.23753i	−0.325834	+	0.945427i	$0.605645\pi$
$998$	−30.5558	−	32.3715i	−0.967228	−	1.02470i
$999$	−3.23562			−0.102370

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.223.8	yes	240
3.2	odd	2		900.2.bj.f.523.23		240
4.3	odd	2	inner	300.2.w.a.223.26	yes	240
12.11	even	2		900.2.bj.f.523.5		240
25.12	odd	20	inner	300.2.w.a.187.26	yes	240
75.62	even	20		900.2.bj.f.487.5		240
100.87	even	20	inner	300.2.w.a.187.8	✓	240
300.287	odd	20		900.2.bj.f.487.23		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.187.8	✓	240	100.87	even	20	inner
300.2.w.a.187.26	yes	240	25.12	odd	20	inner
300.2.w.a.223.8	yes	240	1.1	even	1	trivial
300.2.w.a.223.26	yes	240	4.3	odd	2	inner
900.2.bj.f.487.5		240	75.62	even	20
900.2.bj.f.487.23		240	300.287	odd	20
900.2.bj.f.523.5		240	12.11	even	2
900.2.bj.f.523.23		240	3.2	odd	2

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.970742 - 1.02843i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(-0.115318 + 1.99667i) q^{4} +(-0.872817 + 2.05869i) q^{5} +(-0.475626 + 1.33183i) q^{6} +(-3.13073 - 3.13073i) q^{7} +(2.16537 - 1.81966i) q^{8} +(-0.587785 + 0.809017i) q^{9} +O(q^{10})\)	\(q+(-0.970742 - 1.02843i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(-0.115318 + 1.99667i) q^{4} +(-0.872817 + 2.05869i) q^{5} +(-0.475626 + 1.33183i) q^{6} +(-3.13073 - 3.13073i) q^{7} +(2.16537 - 1.81966i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(2.96449 - 1.10083i) q^{10} +(3.28546 + 4.52205i) q^{11} +(1.83140 - 0.803721i) q^{12} +(0.499696 + 3.15496i) q^{13} +(-0.180590 + 6.25885i) q^{14} +(2.23055 - 0.156939i) q^{15} +(-3.97340 - 0.460505i) q^{16} +(2.24081 + 1.14175i) q^{17} +(1.40260 - 0.180854i) q^{18} +(0.732010 + 2.25289i) q^{19} +(-4.00987 - 1.98013i) q^{20} +(-1.36818 + 4.21082i) q^{21} +(1.46126 - 7.76860i) q^{22} +(-1.33162 + 8.40750i) q^{23} +(-2.60439 - 1.10325i) q^{24} +(-3.47638 - 3.59371i) q^{25} +(2.75956 - 3.57655i) q^{26} +(0.987688 + 0.156434i) q^{27} +(6.61207 - 5.89001i) q^{28} +(3.85116 + 1.25132i) q^{29} +(-2.32669 - 2.14161i) q^{30} +(2.06455 - 0.670814i) q^{31} +(3.38356 + 4.53338i) q^{32} +(2.53761 - 4.98034i) q^{33} +(-1.00105 - 3.41286i) q^{34} +(9.17774 - 3.71264i) q^{35} +(-1.54756 - 1.26691i) q^{36} +(-3.19578 + 0.506162i) q^{37} +(1.60634 - 2.93980i) q^{38} +(2.58423 - 1.87755i) q^{39} +(1.85613 + 6.04605i) q^{40} +(-5.37291 - 3.90365i) q^{41} +(5.65866 - 2.68055i) q^{42} +(1.00326 - 1.00326i) q^{43} +(-9.40793 + 6.03852i) q^{44} +(-1.15248 - 1.91619i) q^{45} +(9.93914 - 6.79205i) q^{46} +(0.610832 - 0.311235i) q^{47} +(1.39357 + 3.74939i) q^{48} +12.6029i q^{49} +(-0.321193 + 7.06377i) q^{50} -2.51493i q^{51} +(-6.35704 + 0.633906i) q^{52} +(-8.35495 + 4.25706i) q^{53} +(-0.797910 - 1.16762i) q^{54} +(-12.1771 + 2.81682i) q^{55} +(-12.4761 - 1.08234i) q^{56} +(1.67502 - 1.67502i) q^{57} +(-2.45160 - 5.17534i) q^{58} +(-3.98846 - 2.89779i) q^{59} +(0.0561323 + 4.47178i) q^{60} +(-2.67411 + 1.94286i) q^{61} +(-2.69403 - 1.47205i) q^{62} +(4.37301 - 0.692617i) q^{63} +(1.37768 - 7.88048i) q^{64} +(-6.93121 - 1.72498i) q^{65} +(-7.58527 + 2.22488i) q^{66} +(-0.883666 + 1.73429i) q^{67} +(-2.53811 + 4.34251i) q^{68} +(8.09568 - 2.63045i) q^{69} +(-12.7274 - 5.83461i) q^{70} +(-7.28443 - 2.36686i) q^{71} +(0.199360 + 2.82139i) q^{72} +(7.69004 + 1.21798i) q^{73} +(3.62283 + 2.79527i) q^{74} +(-1.62378 + 4.72899i) q^{75} +(-4.58271 + 1.20178i) q^{76} +(3.87142 - 24.4432i) q^{77} +(-4.43955 - 0.835068i) q^{78} +(-1.42813 + 4.39533i) q^{79} +(4.41609 - 7.77806i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(1.20110 + 9.31507i) q^{82} +(11.1730 + 5.69295i) q^{83} +(-8.24985 - 3.21739i) q^{84} +(-4.30633 + 3.61660i) q^{85} +(-2.00568 - 0.0578711i) q^{86} +(-0.633458 - 3.99950i) q^{87} +(15.3428 + 3.81351i) q^{88} +(7.91716 + 10.8970i) q^{89} +(-0.851893 + 3.04537i) q^{90} +(8.31290 - 11.4417i) q^{91} +(-16.6335 - 3.62834i) q^{92} +(-1.53499 - 1.53499i) q^{93} +(-0.913043 - 0.326067i) q^{94} +(-5.27691 - 0.459385i) q^{95} +(2.50317 - 5.07288i) q^{96} +(0.0175836 + 0.0345097i) q^{97} +(12.9612 - 12.2342i) q^{98} -5.58956 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8}+O(q^{10}) \) 240 * q + 12 * q^8	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

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