LMFDB - Embedded newform 273.2.bz.a.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(31,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 9]))

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

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

chi := DirichletCharacter("273.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bz (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			31.6
Character	$\chi$	$=$	273.31
Dual form			273.2.bz.a.229.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.905729 + 0.242689i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.970604 - 0.560379i) q^{4} +(-0.812951 + 3.03397i) q^{5} +(-0.663040 - 0.663040i) q^{6} +(-0.856042 + 2.50344i) q^{7} +(-2.06919 - 2.06919i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.905729 + 0.242689i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.970604 - 0.560379i) q^{4} +(-0.812951 + 3.03397i) q^{5} +(-0.663040 - 0.663040i) q^{6} +(-0.856042 + 2.50344i) q^{7} +(-2.06919 - 2.06919i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.47263 + 2.55066i) q^{10} +(-3.76607 + 1.00911i) q^{11} +(0.560379 + 0.970604i) q^{12} +(1.80613 + 3.12056i) q^{13} +(-1.38290 + 2.05968i) q^{14} +(2.22102 - 2.22102i) q^{15} +(-0.251194 - 0.435081i) q^{16} +(2.46817 - 4.27499i) q^{17} +(0.242689 + 0.905729i) q^{18} +(-0.973864 + 3.63451i) q^{19} +(2.48923 - 2.48923i) q^{20} +(1.99307 - 1.74002i) q^{21} -3.65594 q^{22} +(-6.01794 + 3.47446i) q^{23} +(0.757374 + 2.82656i) q^{24} +(-4.21398 - 2.43294i) q^{25} +(0.878534 + 3.26471i) q^{26} -1.00000i q^{27} +(2.23375 - 1.95014i) q^{28} +2.26093 q^{29} +(2.55066 - 1.47263i) q^{30} +(6.50462 - 1.74291i) q^{31} +(1.39282 + 5.19809i) q^{32} +(3.76607 + 1.00911i) q^{33} +(3.27299 - 3.27299i) q^{34} +(-6.89944 - 4.63238i) q^{35} -1.12076i q^{36} +(1.69884 - 6.34014i) q^{37} +(-1.76411 + 3.05553i) q^{38} +(-0.00387011 - 3.60555i) q^{39} +(7.96000 - 4.59571i) q^{40} +(-4.12262 - 4.12262i) q^{41} +(2.22747 - 1.09229i) q^{42} +3.84336i q^{43} +(4.22085 + 1.13097i) q^{44} +(-3.03397 + 0.812951i) q^{45} +(-6.29384 + 1.68643i) q^{46} +(-1.92757 - 0.516490i) q^{47} +0.502389i q^{48} +(-5.53438 - 4.28609i) q^{49} +(-3.22628 - 3.22628i) q^{50} +(-4.27499 + 2.46817i) q^{51} +(-0.00433746 - 4.04095i) q^{52} +(0.345564 - 0.598535i) q^{53} +(0.242689 - 0.905729i) q^{54} -12.2465i q^{55} +(6.95138 - 3.40876i) q^{56} +(2.66065 - 2.66065i) q^{57} +(2.04779 + 0.548704i) q^{58} +(3.53717 + 13.2009i) q^{59} +(-3.40035 + 0.911121i) q^{60} +(8.50811 - 4.91216i) q^{61} +6.31441 q^{62} +(-2.59606 + 0.510364i) q^{63} +6.05086i q^{64} +(-10.9360 + 2.94288i) q^{65} +(3.16614 + 1.82797i) q^{66} +(2.18828 + 8.16676i) q^{67} +(-4.79123 + 2.76622i) q^{68} +6.94892 q^{69} +(-5.12479 - 5.87010i) q^{70} +(-1.76099 + 1.76099i) q^{71} +(0.757374 - 2.82656i) q^{72} +(3.85867 + 14.4008i) q^{73} +(3.07737 - 5.33016i) q^{74} +(2.43294 + 4.21398i) q^{75} +(2.98194 - 2.98194i) q^{76} +(0.697657 - 10.2920i) q^{77} +(0.871523 - 3.26659i) q^{78} +(-2.69505 - 4.66797i) q^{79} +(1.52423 - 0.408417i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.73346 - 4.73449i) q^{82} +(6.16918 + 6.16918i) q^{83} +(-2.90955 + 0.571994i) q^{84} +(10.9637 + 10.9637i) q^{85} +(-0.932741 + 3.48104i) q^{86} +(-1.95803 - 1.13047i) q^{87} +(9.88074 + 5.70465i) q^{88} +(-7.54298 - 2.02113i) q^{89} -2.94525 q^{90} +(-9.35825 + 1.85019i) q^{91} +7.78805 q^{92} +(-6.50462 - 1.74291i) q^{93} +(-1.62051 - 0.935599i) q^{94} +(-10.2353 - 5.90936i) q^{95} +(1.39282 - 5.19809i) q^{96} +(6.07661 + 6.07661i) q^{97} +(-3.97246 - 5.22517i) q^{98} +(-2.75695 - 2.75695i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{7} + 18 q^{9}+O(q^{10}) $ 36 * q - 6 * q^7 + 18 * q^9	$ 36 q - 6 q^{7} + 18 q^{9} + 4 q^{11} - 16 q^{12} - 36 q^{14} + 12 q^{16} + 4 q^{17} - 18 q^{19} + 44 q^{20} + 2 q^{21} - 8 q^{22} - 12 q^{23} - 18 q^{24} - 48 q^{25} - 32 q^{26} + 4 q^{28} - 16 q^{29} - 6 q^{31} + 76 q^{32} - 4 q^{33} - 48 q^{34} + 8 q^{35} - 8 q^{37} + 16 q^{38} + 10 q^{39} + 60 q^{40} - 32 q^{41} + 12 q^{42} + 4 q^{44} + 28 q^{46} + 14 q^{47} + 6 q^{49} - 68 q^{50} - 12 q^{51} - 62 q^{52} - 8 q^{53} - 8 q^{56} - 6 q^{57} + 36 q^{58} + 26 q^{59} - 46 q^{60} + 36 q^{61} + 48 q^{62} - 8 q^{65} - 40 q^{67} + 36 q^{68} - 8 q^{69} - 64 q^{70} - 36 q^{71} - 18 q^{72} - 8 q^{73} + 40 q^{74} + 10 q^{75} - 60 q^{76} + 60 q^{77} + 32 q^{78} + 26 q^{80} - 18 q^{81} + 24 q^{83} - 18 q^{84} + 44 q^{85} + 48 q^{86} + 36 q^{87} + 168 q^{88} + 10 q^{89} + 4 q^{91} - 40 q^{92} + 6 q^{93} + 76 q^{96} + 36 q^{97} + 38 q^{98} + 8 q^{99}+O(q^{100}) $ 36 * q - 6 * q^7 + 18 * q^9 + 4 * q^11 - 16 * q^12 - 36 * q^14 + 12 * q^16 + 4 * q^17 - 18 * q^19 + 44 * q^20 + 2 * q^21 - 8 * q^22 - 12 * q^23 - 18 * q^24 - 48 * q^25 - 32 * q^26 + 4 * q^28 - 16 * q^29 - 6 * q^31 + 76 * q^32 - 4 * q^33 - 48 * q^34 + 8 * q^35 - 8 * q^37 + 16 * q^38 + 10 * q^39 + 60 * q^40 - 32 * q^41 + 12 * q^42 + 4 * q^44 + 28 * q^46 + 14 * q^47 + 6 * q^49 - 68 * q^50 - 12 * q^51 - 62 * q^52 - 8 * q^53 - 8 * q^56 - 6 * q^57 + 36 * q^58 + 26 * q^59 - 46 * q^60 + 36 * q^61 + 48 * q^62 - 8 * q^65 - 40 * q^67 + 36 * q^68 - 8 * q^69 - 64 * q^70 - 36 * q^71 - 18 * q^72 - 8 * q^73 + 40 * q^74 + 10 * q^75 - 60 * q^76 + 60 * q^77 + 32 * q^78 + 26 * q^80 - 18 * q^81 + 24 * q^83 - 18 * q^84 + 44 * q^85 + 48 * q^86 + 36 * q^87 + 168 * q^88 + 10 * q^89 + 4 * q^91 - 40 * q^92 + 6 * q^93 + 76 * q^96 + 36 * q^97 + 38 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.905729	+	0.242689i	0.640447	+	0.171607i	0.564406	−	0.825497i	$-0.309105\pi$
$2$	0.905729	+	0.242689i	0.640447	+	0.171607i	0.0760411	+	0.997105i	$0.475772\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.970604	−	0.560379i	−0.485302	−	0.280189i
$5$	−0.812951	+	3.03397i	−0.363563	+	1.35683i	0.505796	+	0.862653i	$0.331199\pi$
$5$	−0.812951	+	3.03397i	−0.363563	+	1.35683i	−0.869359	+	0.494181i	$0.835468\pi$
$6$	−0.663040	−	0.663040i	−0.270685	−	0.270685i
$7$	−0.856042	+	2.50344i	−0.323553	+	0.946210i
$7$	−0.856042	+	2.50344i	−0.323553	+	0.946210i
$8$	−2.06919	−	2.06919i	−0.731567	−	0.731567i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.47263	+	2.55066i	−0.465685	+	0.806591i
$11$	−3.76607	+	1.00911i	−1.13551	+	0.304260i	−0.777145	−	0.629321i	$-0.783333\pi$
$11$	−3.76607	+	1.00911i	−1.13551	+	0.304260i	−0.358367	+	0.933581i	$0.616666\pi$
$12$	0.560379	+	0.970604i	0.161767	+	0.280189i
$13$	1.80613	+	3.12056i	0.500929	+	0.865488i
$13$	1.80613	+	3.12056i	0.500929	+	0.865488i
$14$	−1.38290	+	2.05968i	−0.369595	+	0.550473i
$15$	2.22102	−	2.22102i	0.573466	−	0.573466i
$16$	−0.251194	−	0.435081i	−0.0627986	−	0.108770i
$17$	2.46817	−	4.27499i	0.598619	−	1.03684i	−0.394406	−	0.918936i	$-0.629050\pi$
$17$	2.46817	−	4.27499i	0.598619	−	1.03684i	0.993025	−	0.117902i	$-0.0376169\pi$
$18$	0.242689	+	0.905729i	0.0572024	+	0.213482i
$19$	−0.973864	+	3.63451i	−0.223420	+	0.833814i	0.759612	+	0.650377i	$0.225389\pi$
$19$	−0.973864	+	3.63451i	−0.223420	+	0.833814i	−0.983031	+	0.183437i	$0.941278\pi$
$20$	2.48923	−	2.48923i	0.556608	−	0.556608i
$21$	1.99307	−	1.74002i	0.434924	−	0.379703i
$22$	−3.65594			−0.779449
$23$	−6.01794	+	3.47446i	−1.25483	+	0.724475i	−0.972064	−	0.234715i	$-0.924584\pi$
$23$	−6.01794	+	3.47446i	−1.25483	+	0.724475i	−0.282763	+	0.959190i	$0.591251\pi$
$24$	0.757374	+	2.82656i	0.154598	+	0.576969i
$25$	−4.21398	−	2.43294i	−0.842797	−	0.486589i
$26$	0.878534	+	3.26471i	0.172295	+	0.640262i
$27$		−	1.00000i		−	0.192450i
$28$	2.23375	−	1.95014i	0.422139	−	0.368541i
$29$	2.26093			0.419845			0.209922	−	0.977718i	$-0.432679\pi$
$29$	2.26093			0.419845			0.209922	+	0.977718i	$0.432679\pi$
$30$	2.55066	−	1.47263i	0.465685	−	0.268864i
$31$	6.50462	−	1.74291i	1.16826	−	0.313036i	0.378003	−	0.925805i	$-0.376611\pi$
$31$	6.50462	−	1.74291i	1.16826	−	0.313036i	0.790262	+	0.612769i	$0.209944\pi$
$32$	1.39282	+	5.19809i	0.246219	+	0.918901i
$33$	3.76607	+	1.00911i	0.655588	+	0.175664i
$34$	3.27299	−	3.27299i	0.561313	−	0.561313i
$35$	−6.89944	−	4.63238i	−1.16622	−	0.783015i
$36$		−	1.12076i		−	0.186793i
$37$	1.69884	−	6.34014i	0.279287	−	1.04231i	−0.673627	−	0.739071i	$-0.735265\pi$
$37$	1.69884	−	6.34014i	0.279287	−	1.04231i	0.952914	−	0.303241i	$-0.0980687\pi$
$38$	−1.76411	+	3.05553i	−0.286177	+	0.495673i
$39$	−0.00387011	−	3.60555i	−0.000619714	−	0.577350i
$40$	7.96000	−	4.59571i	1.25859	−	0.726645i
$41$	−4.12262	−	4.12262i	−0.643845	−	0.643845i	0.307653	−	0.951499i	$-0.400456\pi$
$41$	−4.12262	−	4.12262i	−0.643845	−	0.643845i	−0.951499	+	0.307653i	$0.900456\pi$
$42$	2.22747	−	1.09229i	0.343706	−	0.168544i
$43$			3.84336i			0.586106i	0.956096	+	0.293053i	$0.0946713\pi$
$43$			3.84336i			0.586106i	−0.956096	+	0.293053i	$0.905329\pi$
$44$	4.22085	+	1.13097i	0.636317	+	0.170501i
$45$	−3.03397	+	0.812951i	−0.452278	+	0.121188i
$46$	−6.29384	+	1.68643i	−0.927976	+	0.248650i
$47$	−1.92757	−	0.516490i	−0.281164	−	0.0753378i	0.115481	−	0.993310i	$-0.463159\pi$
$47$	−1.92757	−	0.516490i	−0.281164	−	0.0753378i	−0.396645	+	0.917972i	$0.629826\pi$
$48$			0.502389i			0.0725136i
$49$	−5.53438	−	4.28609i	−0.790626	−	0.612299i
$50$	−3.22628	−	3.22628i	−0.456264	−	0.456264i
$51$	−4.27499	+	2.46817i	−0.598619	+	0.345613i
$52$	−0.00433746	−	4.04095i	−0.000601497	−	0.560378i
$53$	0.345564	−	0.598535i	0.0474669	−	0.0822151i	−0.841316	−	0.540544i	$-0.818218\pi$
$53$	0.345564	−	0.598535i	0.0474669	−	0.0822151i	0.888783	+	0.458329i	$0.151552\pi$
$54$	0.242689	−	0.905729i	0.0330258	−	0.123254i
$55$		−	12.2465i		−	1.65132i
$56$	6.95138	−	3.40876i	0.928918	−	0.455515i
$57$	2.66065	−	2.66065i	0.352411	−	0.352411i
$58$	2.04779	+	0.548704i	0.268888	+	0.0720484i
$59$	3.53717	+	13.2009i	0.460500	+	1.71861i	0.671393	+	0.741101i	$0.265696\pi$
$59$	3.53717	+	13.2009i	0.460500	+	1.71861i	−0.210893	+	0.977509i	$0.567637\pi$
$60$	−3.40035	+	0.911121i	−0.438983	+	0.117625i
$61$	8.50811	−	4.91216i	1.08935	−	0.628938i	0.155948	−	0.987765i	$-0.450157\pi$
$61$	8.50811	−	4.91216i	1.08935	−	0.628938i	0.933404	+	0.358828i	$0.116823\pi$
$62$	6.31441			0.801931
$63$	−2.59606	+	0.510364i	−0.327073	+	0.0642998i
$64$			6.05086i			0.756358i
$65$	−10.9360	+	2.94288i	−1.35644	+	0.365019i
$66$	3.16614	+	1.82797i	0.389724	+	0.225007i
$67$	2.18828	+	8.16676i	0.267341	+	0.997729i	0.960802	+	0.277235i	$0.0894181\pi$
$67$	2.18828	+	8.16676i	0.267341	+	0.997729i	−0.693461	+	0.720494i	$0.743915\pi$
$68$	−4.79123	+	2.76622i	−0.581022	+	0.335453i
$69$	6.94892			0.836552
$70$	−5.12479	−	5.87010i	−0.612530	−	0.701611i
$71$	−1.76099	+	1.76099i	−0.208991	+	0.208991i	−0.803839	−	0.594847i	$-0.797212\pi$
$71$	−1.76099	+	1.76099i	−0.208991	+	0.208991i	0.594847	+	0.803839i	$0.297212\pi$
$72$	0.757374	−	2.82656i	0.0892574	−	0.333113i
$73$	3.85867	+	14.4008i	0.451623	+	1.68548i	0.697829	+	0.716264i	$0.254149\pi$
$73$	3.85867	+	14.4008i	0.451623	+	1.68548i	−0.246206	+	0.969217i	$0.579184\pi$
$74$	3.07737	−	5.33016i	0.357737	−	0.619618i
$75$	2.43294	+	4.21398i	0.280932	+	0.486589i
$76$	2.98194	−	2.98194i	0.342052	−	0.342052i
$77$	0.697657	−	10.2920i	0.0795054	−	1.17288i
$78$	0.871523	−	3.26659i	0.0986805	−	0.369868i
$79$	−2.69505	−	4.66797i	−0.303217	−	0.525187i	0.673646	−	0.739054i	$-0.264727\pi$
$79$	−2.69505	−	4.66797i	−0.303217	−	0.525187i	−0.976863	+	0.213867i	$0.931394\pi$
$80$	1.52423	−	0.408417i	0.170415	−	0.0456625i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.73346	−	4.73449i	−0.301860	−	0.522837i
$83$	6.16918	+	6.16918i	0.677155	+	0.677155i	0.959356	−	0.282200i	$-0.0910643\pi$
$83$	6.16918	+	6.16918i	0.677155	+	0.677155i	−0.282200	+	0.959356i	$0.591064\pi$
$84$	−2.90955	+	0.571994i	−0.317458	+	0.0624097i
$85$	10.9637	+	10.9637i	1.18918	+	1.18918i
$86$	−0.932741	+	3.48104i	−0.100580	+	0.375370i
$87$	−1.95803	−	1.13047i	−0.209922	−	0.121199i
$88$	9.88074	+	5.70465i	1.05329	+	0.608117i
$89$	−7.54298	−	2.02113i	−0.799554	−	0.214240i	−0.164166	−	0.986433i	$-0.552493\pi$
$89$	−7.54298	−	2.02113i	−0.799554	−	0.214240i	−0.635388	+	0.772193i	$0.719160\pi$
$90$	−2.94525			−0.310457
$91$	−9.35825	+	1.85019i	−0.981011	+	0.193953i
$92$	7.78805			0.811961
$93$	−6.50462	−	1.74291i	−0.674498	−	0.180731i
$94$	−1.62051	−	0.935599i	−0.167142	−	0.0964997i
$95$	−10.2353	−	5.90936i	−1.05012	−	0.606287i
$96$	1.39282	−	5.19809i	0.142155	−	0.530528i
$97$	6.07661	+	6.07661i	0.616986	+	0.616986i	0.944757	−	0.327771i	$-0.106298\pi$
$97$	6.07661	+	6.07661i	0.616986	+	0.616986i	−0.327771	+	0.944757i	$0.606298\pi$
$98$	−3.97246	−	5.22517i	−0.401279	−	0.527822i
$99$	−2.75695	−	2.75695i	−0.277084	−	0.277084i
$100$	2.72674	+	4.72285i	0.272674	+	0.472285i
$101$	−5.74102	+	9.94373i	−0.571252	+	0.989438i	0.425185	+	0.905106i	$0.360209\pi$
$101$	−5.74102	+	9.94373i	−0.571252	+	0.989438i	−0.996438	+	0.0843319i	$0.973124\pi$
$102$	−4.47098	+	1.19800i	−0.442693	+	0.118619i
$103$	3.82249	+	6.62075i	0.376641	+	0.652362i	0.990571	−	0.136999i	$-0.0437456\pi$
$103$	3.82249	+	6.62075i	0.376641	+	0.652362i	−0.613930	+	0.789361i	$0.710412\pi$
$104$	2.71981	−	10.1942i	0.266699	−	0.999627i
$105$	3.65890	+	7.46148i	0.357072	+	0.728166i
$106$	0.458245	−	0.458245i	0.0445087	−	0.0445087i
$107$	−1.15874	−	2.00700i	−0.112020	−	0.194024i	0.804565	−	0.593865i	$-0.202399\pi$
$107$	−1.15874	−	2.00700i	−0.112020	−	0.194024i	−0.916585	+	0.399841i	$0.869065\pi$
$108$	−0.560379	+	0.970604i	−0.0539225	+	0.0933964i
$109$	−0.658672	−	2.45820i	−0.0630894	−	0.235453i	0.927180	−	0.374616i	$-0.122225\pi$
$109$	−0.658672	−	2.45820i	−0.0630894	−	0.235453i	−0.990269	+	0.139163i	$0.955559\pi$
$110$	2.97210	−	11.0920i	0.283378	−	1.05758i
$111$	−4.64130	+	4.64130i	−0.440533	+	0.440533i
$112$	1.30423	−	0.256401i	0.123238	−	0.0242276i
$113$	−2.38032			−0.223921			−0.111961	−	0.993713i	$-0.535713\pi$
$113$	−2.38032			−0.223921			−0.111961	+	0.993713i	$0.535713\pi$
$114$	3.05553	−	1.76411i	0.286177	−	0.165224i
$115$	−5.64913	−	21.0828i	−0.526784	−	1.96599i
$116$	−2.19447	−	1.26698i	−0.203752	−	0.117636i
$117$	−1.79942	+	3.12443i	−0.166357	+	0.288854i
$118$			12.8149i			1.17970i
$119$	8.58932	+	9.83848i	0.787382	+	0.901892i
$120$	−9.19142			−0.839058
$121$	3.63868	−	2.10079i	0.330789	−	0.190981i
$122$	8.89817	−	2.38426i	0.805603	−	0.215861i
$123$	1.50898	+	5.63161i	0.136061	+	0.507785i
$124$	−7.29010	−	1.95338i	−0.654671	−	0.175418i
$125$	−0.297866	+	0.297866i	−0.0266420	+	0.0266420i
$126$	−2.47519	−	0.167785i	−0.220507	−	0.0149474i
$127$		−	14.2572i		−	1.26512i	−0.774510	−	0.632562i	$-0.782003\pi$
$127$		−	14.2572i		−	1.26512i	0.774510	−	0.632562i	$-0.217997\pi$
$128$	1.31717	−	4.91574i	0.116422	−	0.434494i
$129$	1.92168	−	3.32844i	0.169194	−	0.293053i
$130$	−10.6193	+	0.0113985i	−0.931370	+	0.000999711i
$131$	−4.52495	+	2.61248i	−0.395347	+	0.228254i	−0.684474	−	0.729037i	$-0.739968\pi$
$131$	−4.52495	+	2.61248i	−0.395347	+	0.228254i	0.289127	+	0.957291i	$0.406635\pi$
$132$	−3.08988	−	3.08988i	−0.268939	−	0.268939i
$133$	−8.26510	−	5.54930i	−0.716675	−	0.481185i
$134$			7.92794i			0.684870i
$135$	3.03397	+	0.812951i	0.261123	+	0.0699677i
$136$	−13.9529	+	3.73866i	−1.19645	+	0.320587i
$137$	16.1716	−	4.33316i	1.38163	−	0.370207i	0.509918	−	0.860223i	$-0.329676\pi$
$137$	16.1716	−	4.33316i	1.38163	−	0.370207i	0.871713	+	0.490016i	$0.163009\pi$
$138$	6.29384	+	1.68643i	0.535767	+	0.143558i
$139$			0.337303i			0.0286097i	0.999898	+	0.0143048i	$0.00455352\pi$
$139$			0.337303i			0.0286097i	−0.999898	+	0.0143048i	$0.995446\pi$
$140$	4.10074	+	8.36251i	0.346576	+	0.706761i
$141$	1.41108	+	1.41108i	0.118834	+	0.118834i
$142$	−2.02235	+	1.16761i	−0.169712	+	0.0979834i
$143$	−9.95100	−	9.92966i	−0.832144	−	0.830360i
$144$	0.251194	−	0.435081i	0.0209329	−	0.0362568i
$145$	−1.83803	+	6.85961i	−0.152640	+	0.569660i
$146$			13.9796i			1.15696i
$147$	2.64987	+	6.47906i	0.218558	+	0.534384i
$148$	−5.20177	+	5.20177i	−0.427583	+	0.427583i
$149$	7.47809	+	2.00375i	0.612629	+	0.164153i	0.551775	−	0.833993i	$-0.313951\pi$
$149$	7.47809	+	2.00375i	0.612629	+	0.164153i	0.0608543	+	0.998147i	$0.480617\pi$
$150$	1.18090	+	4.40717i	0.0964200	+	0.359844i
$151$	−16.0231	+	4.29336i	−1.30394	+	0.349389i	−0.842938	−	0.538011i	$-0.819176\pi$
$151$	−16.0231	+	4.29336i	−1.30394	+	0.349389i	−0.461000	+	0.887400i	$0.652509\pi$
$152$	9.53558	−	5.50537i	0.773438	−	0.446544i
$153$	4.93634			0.399079
$154$	3.12964	−	9.15241i	0.252193	−	0.737522i
$155$			21.1518i			1.69895i
$156$	−2.01672	+	3.50173i	−0.161467	+	0.280363i
$157$	20.9544	+	12.0980i	1.67234	+	0.965527i	0.966323	+	0.257334i	$0.0828439\pi$
$157$	20.9544	+	12.0980i	1.67234	+	0.965527i	0.706019	+	0.708193i	$0.250489\pi$
$158$	−1.30812	−	4.88197i	−0.104068	−	0.388389i
$159$	−0.598535	+	0.345564i	−0.0474669	+	0.0274050i
$160$	−16.9032			−1.33631
$161$	−3.54648	−	18.0398i	−0.279502	−	1.42174i
$162$	−0.663040	+	0.663040i	−0.0520933	+	0.0520933i
$163$	4.59018	−	17.1308i	0.359531	−	1.34179i	−0.515155	−	0.857097i	$-0.672266\pi$
$163$	4.59018	−	17.1308i	0.359531	−	1.34179i	0.874686	−	0.484690i	$-0.161068\pi$
$164$	1.69121	+	6.31166i	0.132061	+	0.492858i
$165$	−6.12326	+	10.6058i	−0.476695	+	0.825660i
$166$	4.09041	+	7.08480i	0.317477	+	0.549887i
$167$	4.91656	−	4.91656i	0.380455	−	0.380455i	−0.490811	−	0.871266i	$-0.663299\pi$
$167$	4.91656	−	4.91656i	0.380455	−	0.380455i	0.871266	+	0.490811i	$0.163299\pi$
$168$	−7.72446	−	0.523615i	−0.595955	−	0.0403978i
$169$	−6.47582	+	11.2723i	−0.498140	+	0.867097i
$170$	7.26938	+	12.5909i	0.557536	+	0.965681i
$171$	−3.63451	+	0.973864i	−0.277938	+	0.0744732i
$172$	2.15373	−	3.73038i	0.164221	−	0.284439i
$173$	−4.51431	−	7.81901i	−0.343217	−	0.594468i	0.641812	−	0.766862i	$-0.278183\pi$
$173$	−4.51431	−	7.81901i	−0.343217	−	0.594468i	−0.985028	+	0.172394i	$0.944850\pi$
$174$	−1.49909	−	1.49909i	−0.113646	−	0.113646i
$175$	9.69806	−	8.46673i	0.733105	−	0.640025i
$176$	1.38506	+	1.38506i	0.104403	+	0.104403i
$177$	3.53717	−	13.2009i	0.265870	−	0.992240i
$178$	−6.34138	−	3.66120i	−0.475307	−	0.274419i
$179$	−9.38548	−	5.41871i	−0.701503	−	0.405013i	0.106404	−	0.994323i	$-0.466066\pi$
$179$	−9.38548	−	5.41871i	−0.701503	−	0.405013i	−0.807907	+	0.589310i	$0.799400\pi$
$180$	3.40035	+	0.911121i	0.253447	+	0.0679109i
$181$	−15.2064			−1.13029			−0.565143	−	0.824993i	$-0.691179\pi$
$181$	−15.2064			−1.13029			−0.565143	+	0.824993i	$0.691179\pi$
$182$	−8.92506	−	0.595376i	−0.661569	−	0.0441322i
$183$	−9.82432			−0.726235
$184$	19.6415	+	5.26293i	1.44799	+	0.387989i
$185$	17.8547	+	10.3084i	1.31271	+	0.757892i
$186$	−5.46844	−	3.15720i	−0.400965	−	0.231497i
$187$	−4.98133	+	18.5906i	−0.364271	+	1.35948i
$188$	1.58147	+	1.58147i	0.115341	+	0.115341i
$189$	2.50344	+	0.856042i	0.182098	+	0.0622679i
$190$	−7.83627	−	7.83627i	−0.568503	−	0.568503i
$191$	1.06302	+	1.84121i	0.0769177	+	0.133225i	0.901919	−	0.431906i	$-0.142159\pi$
$191$	1.06302	+	1.84121i	0.0769177	+	0.133225i	−0.825001	+	0.565131i	$0.808825\pi$
$192$	3.02543	−	5.24020i	0.218342	−	0.378179i
$193$	−10.3901	+	2.78401i	−0.747895	+	0.200398i	−0.612584	−	0.790405i	$-0.709870\pi$
$193$	−10.3901	+	2.78401i	−0.747895	+	0.200398i	−0.135311	+	0.990803i	$0.543203\pi$
$194$	4.02903	+	6.97848i	0.289267	+	0.501026i
$195$	10.9423	+	2.91939i	0.783594	+	0.209062i
$196$	2.96986	+	7.26145i	0.212133	+	0.518675i
$197$	13.7022	−	13.7022i	0.976243	−	0.976243i	−0.0234809	−	0.999724i	$-0.507475\pi$
$197$	13.7022	−	13.7022i	0.976243	−	0.976243i	0.999724	+	0.0234809i	$0.00747490\pi$
$198$	−1.82797	−	3.16614i	−0.129908	−	0.225007i
$199$	−1.07121	+	1.85539i	−0.0759362	+	0.131525i	−0.901493	−	0.432794i	$-0.857528\pi$
$199$	−1.07121	+	1.85539i	−0.0759362	+	0.131525i	0.825557	+	0.564319i	$0.190861\pi$
$200$	3.68530	+	13.7537i	0.260590	+	0.972535i
$201$	2.18828	−	8.16676i	0.154349	−	0.576039i
$202$	−7.61304	+	7.61304i	−0.535652	+	0.535652i
$203$	−1.93545	+	5.66010i	−0.135842	+	0.397261i
$204$	5.53244			0.387348
$205$	15.8594	−	9.15644i	1.10767	−	0.639514i
$206$	1.85536	+	6.92428i	0.129269	+	0.482438i
$207$	−6.01794	−	3.47446i	−0.418276	−	0.241492i
$208$	0.904010	−	1.56968i	0.0626818	−	0.108838i
$209$		−	14.6706i		−	1.01478i
$210$	1.50315	+	7.64605i	0.103727	+	0.527628i
$211$	2.65307			0.182645			0.0913224	−	0.995821i	$-0.470891\pi$
$211$	2.65307			0.182645			0.0913224	+	0.995821i	$0.470891\pi$
$212$	−0.670812	+	0.387294i	−0.0460716	+	0.0265994i
$213$	2.40556	−	0.644568i	0.164826	−	0.0441650i
$214$	−0.562429	−	2.09901i	−0.0384469	−	0.143486i
$215$	−11.6606	−	3.12446i	−0.795249	−	0.213086i
$216$	−2.06919	+	2.06919i	−0.140790	+	0.140790i
$217$	−1.20497	+	17.7759i	−0.0817986	+	1.20671i
$218$		−	2.38631i		−	0.161622i
$219$	3.85867	−	14.4008i	0.260745	−	0.973113i
$220$	−6.86268	+	11.8865i	−0.462682	+	0.801389i
$221$	17.7982	−	0.0191042i	1.19724	−	0.00128509i
$222$	−5.33016	+	3.07737i	−0.357737	+	0.206539i
$223$	−14.3736	−	14.3736i	−0.962529	−	0.962529i	0.0367940	−	0.999323i	$-0.488285\pi$
$223$	−14.3736	−	14.3736i	−0.962529	−	0.962529i	−0.999323	+	0.0367940i	$0.988285\pi$
$224$	−14.2054	−	0.962937i	−0.949139	−	0.0643389i
$225$		−	4.86589i		−	0.324393i
$226$	−2.15592	−	0.577678i	−0.143410	−	0.0384265i
$227$	−2.36952	+	0.634911i	−0.157271	+	0.0421405i	−0.336595	−	0.941649i	$-0.609275\pi$
$227$	−2.36952	+	0.634911i	−0.157271	+	0.0421405i	0.179325	+	0.983790i	$0.442609\pi$
$228$	−4.07340	+	1.09147i	−0.269768	+	0.0722841i
$229$	0.851590	+	0.228183i	0.0562747	+	0.0150787i	0.286847	−	0.957977i	$-0.407393\pi$
$229$	0.851590	+	0.228183i	0.0562747	+	0.0150787i	−0.230572	+	0.973055i	$0.574060\pi$
$230$		−	20.4663i		−	1.34951i
$231$	−5.75017	+	8.56427i	−0.378333	+	0.563487i
$232$	−4.67829	−	4.67829i	−0.307145	−	0.307145i
$233$	−25.0856	+	14.4832i	−1.64341	+	0.948823i	−0.663802	+	0.747909i	$0.731058\pi$
$233$	−25.0856	+	14.4832i	−1.64341	+	0.948823i	−0.979609	+	0.200915i	$0.935609\pi$
$234$	−2.38806	+	2.39319i	−0.156112	+	0.156448i
$235$	3.13403	−	5.42831i	0.204442	−	0.354104i
$236$	3.96431	−	14.7950i	0.258055	−	0.963073i
$237$			5.39010i			0.350125i
$238$	5.39190	+	10.9955i	0.349505	+	0.712734i
$239$	16.4300	−	16.4300i	1.06277	−	1.06277i	0.0648719	−	0.997894i	$-0.479336\pi$
$239$	16.4300	−	16.4300i	1.06277	−	1.06277i	0.997894	−	0.0648719i	$-0.0206639\pi$
$240$	−1.52423	−	0.408417i	−0.0983889	−	0.0263632i
$241$	3.65884	+	13.6550i	0.235686	+	0.879593i	0.977838	+	0.209362i	$0.0671386\pi$
$241$	3.65884	+	13.6550i	0.235686	+	0.879593i	−0.742152	+	0.670232i	$0.766195\pi$
$242$	3.80550	−	1.01968i	0.244627	−	0.0655475i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−11.0107			−0.704886
$245$	17.5031	−	13.3068i	1.11823	−	0.850140i
$246$			5.46692i			0.348558i
$247$	−13.1006	+	3.52538i	−0.833574	+	0.224315i
$248$	−17.0657	−	9.85287i	−1.08367	−	0.625658i
$249$	−2.25808	−	8.42725i	−0.143100	−	0.534056i
$250$	−0.342075	+	0.197497i	−0.0216347	+	0.0124908i
$251$	9.30024			0.587026			0.293513	−	0.955955i	$-0.405176\pi$
$251$	9.30024			0.587026			0.293513	+	0.955955i	$0.405176\pi$
$252$	2.80574	+	0.959415i	0.176745	+	0.0604375i
$253$	19.1578	−	19.1578i	1.20444	−	1.20444i
$254$	3.46007	−	12.9132i	0.217104	−	0.810245i
$255$	−4.01300	−	14.9767i	−0.251304	−	0.937879i
$256$	8.43686	−	14.6131i	0.527304	−	0.913317i
$257$	1.32824	+	2.30057i	0.0828531	+	0.143506i	0.904474	−	0.426528i	$-0.140263\pi$
$257$	1.32824	+	2.30057i	0.0828531	+	0.143506i	−0.821621	+	0.570034i	$0.806930\pi$
$258$	2.54830	−	2.54830i	0.158650	−	0.158650i
$259$	14.4179	+	9.68035i	0.895882	+	0.601508i
$260$	12.2636	+	3.27193i	0.760559	+	0.202917i
$261$	1.13047	+	1.95803i	0.0699741	+	0.121199i
$262$	−4.73240	+	1.26804i	−0.292369	+	0.0783400i
$263$	8.37863	−	14.5122i	0.516648	−	0.894861i	−0.483165	−	0.875530i	$-0.660513\pi$
$263$	8.37863	−	14.5122i	0.516648	−	0.894861i	0.999813	−	0.0193319i	$-0.00615392\pi$
$264$	−5.70465	−	9.88074i	−0.351097	−	0.608117i
$265$	1.53501	+	1.53501i	0.0942951	+	0.0942951i
$266$	−6.13918	−	7.03201i	−0.376417	−	0.431160i
$267$	5.52184	+	5.52184i	0.337931	+	0.337931i
$268$	2.45253	−	9.15296i	0.149812	−	0.559106i
$269$	−10.4636	−	6.04116i	−0.637977	−	0.368336i	0.145858	−	0.989306i	$-0.453406\pi$
$269$	−10.4636	−	6.04116i	−0.637977	−	0.368336i	−0.783835	+	0.620970i	$0.786739\pi$
$270$	2.55066	+	1.47263i	0.155228	+	0.0896212i
$271$	20.0601	+	5.37508i	1.21856	+	0.326513i	0.810116	−	0.586270i	$-0.199404\pi$
$271$	20.0601	+	5.37508i	1.21856	+	0.326513i	0.408446	+	0.912783i	$0.366071\pi$
$272$	−2.47996			−0.150370
$273$	9.02958	+	3.07681i	0.546495	+	0.186217i
$274$	15.6987			0.948392
$275$	18.3253	+	4.91024i	1.10506	+	0.296099i
$276$	−6.74465	−	3.89403i	−0.405980	−	0.234393i
$277$	22.8163	+	13.1730i	1.37090	+	0.791489i	0.991041	−	0.133557i	$-0.0426398\pi$
$277$	22.8163	+	13.1730i	1.37090	+	0.791489i	0.379857	+	0.925045i	$0.375973\pi$
$278$	−0.0818598	+	0.305505i	−0.00490962	+	0.0183230i
$279$	4.76171	+	4.76171i	0.285076	+	0.285076i
$280$	4.69097	+	23.8615i	0.280339	+	1.42600i
$281$	6.43788	+	6.43788i	0.384052	+	0.384052i	0.872560	−	0.488508i	$-0.162459\pi$
$281$	6.43788	+	6.43788i	0.384052	+	0.384052i	−0.488508	+	0.872560i	$0.662459\pi$
$282$	0.935599	+	1.62051i	0.0557141	+	0.0964997i
$283$	8.84685	−	15.3232i	0.525891	−	0.910870i	−0.473654	−	0.880711i	$-0.657065\pi$
$283$	8.84685	−	15.3232i	0.525891	−	0.910870i	0.999545	−	0.0301589i	$-0.00960132\pi$
$284$	2.69605	−	0.722404i	0.159981	−	0.0428668i
$285$	5.90936	+	10.2353i	0.350040	+	0.606287i
$286$	−6.60309	−	11.4086i	−0.390449	−	0.674604i
$287$	13.8499	−	6.79159i	0.817531	−	0.400895i
$288$	−3.80527	+	3.80527i	−0.224228	+	0.224228i
$289$	−3.68372	−	6.38039i	−0.216689	−	0.375317i
$290$	−3.32951	+	5.76688i	−0.195516	+	0.338643i
$291$	−2.22419	−	8.30080i	−0.130384	−	0.486601i
$292$	4.32463	−	16.1398i	0.253080	−	0.944508i
$293$	−0.758303	+	0.758303i	−0.0443006	+	0.0443006i	−0.728910	−	0.684609i	$-0.759973\pi$
$293$	−0.758303	+	0.758303i	−0.0443006	+	0.0443006i	0.684609	+	0.728910i	$0.259973\pi$
$294$	0.827668	+	6.51136i	0.0482706	+	0.379750i
$295$	−42.9267			−2.49929
$296$	−16.6341	+	9.60372i	−0.966839	+	0.558205i
$297$	1.00911	+	3.76607i	0.0585548	+	0.218529i
$298$	6.28683	+	3.62970i	0.364186	+	0.210263i
$299$	−21.7114	−	12.5040i	−1.25560	−	0.723128i
$300$		−	5.45348i		−	0.314857i
$301$	−9.62159	−	3.29007i	−0.554579	−	0.189637i
$302$	−15.5545			−0.895061
$303$	9.94373	−	5.74102i	0.571252	−	0.329813i
$304$	1.82594	−	0.489258i	0.104725	−	0.0280609i
$305$	7.98669	+	29.8067i	0.457317	+	1.70673i
$306$	4.47098	+	1.19800i	0.255589	+	0.0684849i
$307$	21.0609	−	21.0609i	1.20201	−	1.20201i	0.228454	−	0.973555i	$-0.426633\pi$
$307$	21.0609	−	21.0609i	1.20201	−	1.20201i	0.973555	−	0.228454i	$-0.0733669\pi$
$308$	−6.44454	+	9.59846i	−0.367212	+	0.546923i
$309$		−	7.64498i		−	0.434908i
$310$	−5.13330	+	19.1578i	−0.291552	+	1.08809i
$311$	11.7425	−	20.3387i	0.665858	−	1.15330i	−0.313194	−	0.949689i	$-0.601399\pi$
$311$	11.7425	−	20.3387i	0.665858	−	1.15330i	0.979052	−	0.203611i	$-0.0652677\pi$
$312$	−7.45254	+	7.46856i	−0.421917	+	0.422824i
$313$	−3.03233	+	1.75072i	−0.171397	+	0.0989564i	−0.583245	−	0.812297i	$-0.698217\pi$
$313$	−3.03233	+	1.75072i	−0.171397	+	0.0989564i	0.411847	+	0.911253i	$0.364884\pi$
$314$	16.0429	+	16.0429i	0.905355	+	0.905355i
$315$	0.562038	−	8.29128i	0.0316673	−	0.467161i
$316$			6.04100i			0.339833i
$317$	8.70701	+	2.33304i	0.489034	+	0.131036i	0.494906	−	0.868946i	$-0.335202\pi$
$317$	8.70701	+	2.33304i	0.489034	+	0.131036i	−0.00587185	+	0.999983i	$0.501869\pi$
$318$	−0.625975	+	0.167729i	−0.0351029	+	0.00940580i
$319$	−8.51483	+	2.28154i	−0.476739	+	0.127742i
$320$	−18.3582	−	4.91905i	−1.02625	−	0.274983i
$321$			2.31749i			0.129350i
$322$	1.16592	−	17.1999i	0.0649743	−	0.958511i
$323$	13.1338	+	13.1338i	0.730787	+	0.730787i
$324$	0.970604	−	0.560379i	0.0539225	−	0.0311321i
$325$	−0.0188315	−	17.5442i	−0.00104459	−	0.973177i
$326$	8.31492	−	14.4019i	0.460521	−	0.797645i
$327$	−0.658672	+	2.45820i	−0.0364247	+	0.135939i
$328$			17.0609i			0.942033i
$329$	2.94308	−	4.38340i	0.162257	−	0.241665i
$330$	−8.11992	+	8.11992i	−0.446987	+	0.446987i
$331$	−25.9305	−	6.94807i	−1.42527	−	0.381900i	−0.537921	−	0.842995i	$-0.680790\pi$
$331$	−25.9305	−	6.94807i	−1.42527	−	0.381900i	−0.887351	+	0.461095i	$0.847457\pi$
$332$	−2.53075	−	9.44491i	−0.138893	−	0.518357i
$333$	6.34014	−	1.69884i	0.347437	−	0.0930956i
$334$	5.64627	−	3.25988i	0.308950	−	0.178372i
$335$	−26.5567			−1.45095
$336$	−1.25770	−	0.430066i	−0.0686131	−	0.0234620i
$337$		−	26.8916i		−	1.46488i	−0.680833	−	0.732439i	$-0.738382\pi$
$337$		−	26.8916i		−	1.46488i	0.680833	−	0.732439i	$-0.261618\pi$
$338$	−8.60099	+	8.63800i	−0.467832	+	0.469845i
$339$	2.06142	+	1.19016i	0.111961	+	0.0646405i
$340$	−4.49760	−	16.7853i	−0.243917	−	0.910309i
$341$	−22.7381	+	13.1278i	−1.23133	+	0.710911i
$342$	−3.52823			−0.190785
$343$	15.4676	−	10.1859i	0.835173	−	0.549987i
$344$	7.95261	−	7.95261i	0.428776	−	0.428776i
$345$	−5.64913	+	21.0828i	−0.304139	+	1.13506i
$346$	−2.19115	−	8.17748i	−0.117797	−	0.439624i
$347$	−2.05674	+	3.56238i	−0.110412	+	0.191239i	−0.915936	−	0.401324i	$-0.868550\pi$
$347$	−2.05674	+	3.56238i	−0.110412	+	0.191239i	0.805525	+	0.592562i	$0.201884\pi$
$348$	1.26698	+	2.19447i	0.0679172	+	0.117636i
$349$	−13.5784	+	13.5784i	−0.726836	+	0.726836i	−0.969988	−	0.243152i	$-0.921819\pi$
$349$	−13.5784	+	13.5784i	−0.726836	+	0.726836i	0.243152	+	0.969988i	$0.421819\pi$
$350$	10.8386	−	5.31495i	0.579348	−	0.284096i
$351$	3.12056	−	1.80613i	0.166563	−	0.0964039i
$352$	−10.4909	−	18.1708i	−0.559169	−	0.968509i
$353$	−2.08045	+	0.557454i	−0.110731	+	0.0296703i	−0.313759	−	0.949503i	$-0.601588\pi$
$353$	−2.08045	+	0.557454i	−0.110731	+	0.0296703i	0.203028	+	0.979173i	$0.434922\pi$
$354$	6.40743	−	11.0980i	0.340551	−	0.589852i
$355$	−3.91120	−	6.77440i	−0.207585	−	0.359548i
$356$	6.18865	+	6.18865i	0.327998	+	0.327998i
$357$	−2.51933	−	12.8150i	−0.133337	−	0.678243i
$358$	−7.18563	−	7.18563i	−0.379773	−	0.379773i
$359$	−7.43895	+	27.7626i	−0.392613	+	1.46525i	0.433195	+	0.901300i	$0.357386\pi$
$359$	−7.43895	+	27.7626i	−0.392613	+	1.46525i	−0.825808	+	0.563951i	$0.809281\pi$
$360$	7.96000	+	4.59571i	0.419529	+	0.242215i
$361$	4.19323	+	2.42096i	0.220696	+	0.127419i
$362$	−13.7729	−	3.69044i	−0.723888	−	0.193965i
$363$	−4.20158			−0.220526
$364$	10.1200	+	3.44836i	0.530430	+	0.180743i
$365$	−46.8284			−2.45111
$366$	−8.89817	−	2.38426i	−0.465115	−	0.124627i
$367$	−1.58966	−	0.917792i	−0.0829797	−	0.0479084i	0.457936	−	0.888985i	$-0.348589\pi$
$367$	−1.58966	−	0.917792i	−0.0829797	−	0.0479084i	−0.540916	+	0.841077i	$0.681922\pi$
$368$	3.02335	+	1.74553i	0.157603	+	0.0909920i
$369$	1.50898	−	5.63161i	0.0785546	−	0.293170i
$370$	13.6698	+	13.6698i	0.710660	+	0.710660i
$371$	1.20258	+	1.37747i	0.0624346	+	0.0715146i
$372$	5.33673	+	5.33673i	0.276696	+	0.276696i
$373$	12.5022	+	21.6545i	0.647340	+	1.12123i	0.983756	+	0.179512i	$0.0574519\pi$
$373$	12.5022	+	21.6545i	0.647340	+	1.12123i	−0.336416	+	0.941714i	$0.609215\pi$
$374$	−9.02347	+	15.6291i	−0.466593	+	0.808162i
$375$	0.406893	−	0.109027i	0.0210118	−	0.00563011i
$376$	2.91978	+	5.05721i	0.150576	+	0.260805i
$377$	4.08353	+	7.05538i	0.210313	+	0.363371i
$378$	2.05968	+	1.38290i	0.105939	+	0.0711286i
$379$	−15.7347	+	15.7347i	−0.808235	+	0.808235i	−0.984367	−	0.176132i	$-0.943641\pi$
$379$	−15.7347	+	15.7347i	−0.808235	+	0.808235i	0.176132	+	0.984367i	$0.443641\pi$
$380$	6.62295	+	11.4713i	0.339750	+	0.588465i
$381$	−7.12861	+	12.3471i	−0.365210	+	0.632562i
$382$	0.515969	+	1.92562i	0.0263993	+	0.0985235i
$383$	1.33436	−	4.97990i	0.0681826	−	0.254461i	−0.923419	−	0.383794i	$-0.874617\pi$
$383$	1.33436	−	4.97990i	0.0681826	−	0.254461i	0.991601	+	0.129334i	$0.0412838\pi$
$384$	−3.59857	+	3.59857i	−0.183639	+	0.183639i
$385$	30.6584	+	10.4835i	1.56250	+	0.534290i
$386$	−10.0863			−0.513377
$387$	−3.32844	+	1.92168i	−0.169194	+	0.0976844i
$388$	−2.49278	−	9.30318i	−0.126552	−	0.472297i
$389$	15.4083	+	8.89599i	0.781232	+	0.451045i	0.836867	−	0.547407i	$-0.184385\pi$
$389$	15.4083	+	8.89599i	0.781232	+	0.451045i	−0.0556346	+	0.998451i	$0.517718\pi$
$390$	9.20224	+	5.29975i	0.465974	+	0.268364i
$391$			34.3022i			1.73474i
$392$	2.58295	+	20.3204i	0.130459	+	1.02633i
$393$	5.22497			0.263565
$394$	15.7359	−	9.08512i	0.792763	−	0.457702i
$395$	16.3534	−	4.38189i	0.822831	−	0.220477i
$396$	1.13097	+	4.22085i	0.0568335	+	0.212106i
$397$	−7.57049	−	2.02851i	−0.379952	−	0.101808i	0.0637880	−	0.997963i	$-0.479682\pi$
$397$	−7.57049	−	2.02851i	−0.379952	−	0.101808i	−0.443740	+	0.896156i	$0.646349\pi$
$398$	−1.42051	+	1.42051i	−0.0712038	+	0.0712038i
$399$	4.38313	+	8.93838i	0.219431	+	0.447479i
$400$			2.44457i			0.122228i
$401$	−0.620056	+	2.31408i	−0.0309641	+	0.115560i	−0.979678	−	0.200576i	$-0.935719\pi$
$401$	−0.620056	+	2.31408i	−0.0309641	+	0.115560i	0.948714	+	0.316135i	$0.102385\pi$
$402$	3.96397	−	6.86580i	0.197705	−	0.342435i
$403$	17.1870	+	17.1502i	0.856147	+	0.854311i
$404$	11.1445	−	6.43428i	0.554460	−	0.320118i
$405$	−2.22102	−	2.22102i	−0.110364	−	0.110364i
$406$	−3.12664	+	4.65680i	−0.155173	+	0.231113i
$407$			25.5917i			1.26853i
$408$	13.9529	+	3.73866i	0.690769	+	0.185091i
$409$	−18.2165	+	4.88109i	−0.900747	+	0.241354i	−0.679337	−	0.733826i	$-0.737733\pi$
$409$	−18.2165	+	4.88109i	−0.900747	+	0.241354i	−0.221410	+	0.975181i	$0.571066\pi$
$410$	16.5865	−	4.44434i	0.819149	−	0.219490i
$411$	−16.1716	−	4.33316i	−0.797685	−	0.213739i
$412$		−	8.56817i		−	0.422124i
$413$	−36.0756	−	2.44544i	−1.77516	−	0.120332i
$414$	−4.60741	−	4.60741i	−0.226442	−	0.226442i
$415$	−23.7324	+	13.7019i	−1.16498	+	0.672599i
$416$	−13.7054	+	13.7348i	−0.671960	+	0.673404i
$417$	0.168651	−	0.292113i	0.00825890	−	0.0143048i
$418$	3.56039	−	13.2875i	0.174144	−	0.649915i
$419$			9.77138i			0.477363i	0.971098	+	0.238682i	$0.0767152\pi$
$419$			9.77138i			0.477363i	−0.971098	+	0.238682i	$0.923285\pi$
$420$	0.629908	−	9.29251i	0.0307364	−	0.453428i
$421$	8.04069	−	8.04069i	0.391879	−	0.391879i	−0.483477	−	0.875357i	$-0.660626\pi$
$421$	8.04069	−	8.04069i	0.391879	−	0.391879i	0.875357	+	0.483477i	$0.160626\pi$
$422$	2.40296	+	0.643872i	0.116974	+	0.0313432i
$423$	−0.516490	−	1.92757i	−0.0251126	−	0.0937215i
$424$	−1.95352	+	0.523443i	−0.0948711	+	0.0254206i
$425$	−20.8016	+	12.0098i	−1.00903	+	0.582563i
$426$	2.33521			0.113141
$427$	5.01398	+	25.5045i	0.242644	+	1.23425i
$428$			2.59734i			0.125547i
$429$	3.65299	+	13.5748i	0.176368	+	0.655399i
$430$	−9.80311	−	5.65983i	−0.472748	−	0.272941i
$431$	6.11141	+	22.8081i	0.294376	+	1.09863i	0.941711	+	0.336422i	$0.109217\pi$
$431$	6.11141	+	22.8081i	0.294376	+	1.09863i	−0.647335	+	0.762206i	$0.724116\pi$
$432$	−0.435081	+	0.251194i	−0.0209329	+	0.0120856i
$433$	21.2181			1.01968			0.509840	−	0.860270i	$-0.329705\pi$
$433$	21.2181			1.01968			0.509840	+	0.860270i	$0.329705\pi$
$434$	−5.40540	+	15.8077i	−0.259467	+	0.758795i
$435$	5.02159	−	5.02159i	0.240767	−	0.240767i
$436$	−0.738212	+	2.75504i	−0.0353539	+	0.131943i
$437$	−6.76730	−	25.2559i	−0.323724	−	1.20815i
$438$	6.98982	−	12.1067i	0.333987	−	0.578482i
$439$	−3.66625	−	6.35014i	−0.174981	−	0.303076i	0.765174	−	0.643824i	$-0.222653\pi$
$439$	−3.66625	−	6.35014i	−0.174981	−	0.303076i	−0.940155	+	0.340748i	$0.889320\pi$
$440$	−25.3403	+	25.3403i	−1.20805	+	1.20805i
$441$	0.944672	−	6.93596i	0.0449844	−	0.330284i
$442$	16.1250	+	4.30213i	0.766987	+	0.204632i
$443$	4.98843	+	8.64021i	0.237007	+	0.410509i	0.959854	−	0.280499i	$-0.0905001\pi$
$443$	4.98843	+	8.64021i	0.237007	+	0.410509i	−0.722847	+	0.691008i	$0.757167\pi$
$444$	7.10576	−	1.90398i	0.337224	−	0.0903590i
$445$	12.2641	−	21.2421i	0.581376	−	1.00697i
$446$	−9.53028	−	16.5069i	−0.451272	−	0.781626i
$447$	−5.47434	−	5.47434i	−0.258927	−	0.258927i
$448$	−15.1479	−	5.17979i	−0.715673	−	0.244722i
$449$	−26.5870	−	26.5870i	−1.25472	−	1.25472i	−0.953580	−	0.301141i	$-0.902633\pi$
$449$	−26.5870	−	26.5870i	−1.25472	−	1.25472i	−0.301141	−	0.953580i	$-0.597367\pi$
$450$	1.18090	−	4.40717i	0.0556681	−	0.207756i
$451$	19.6863	+	11.3659i	0.926991	+	0.535198i
$452$	2.31035	+	1.33388i	0.108670	+	0.0627404i
$453$	16.0231	+	4.29336i	0.752829	+	0.201720i
$454$	−2.30023			−0.107955
$455$	1.99437	−	29.8968i	0.0934974	−	1.40158i
$456$	−11.0107			−0.515625
$457$	−27.4622	−	7.35848i	−1.28463	−	0.344215i	−0.449011	−	0.893526i	$-0.648223\pi$
$457$	−27.4622	−	7.35848i	−1.28463	−	0.344215i	−0.835618	+	0.549311i	$0.814890\pi$
$458$	0.715932	+	0.413344i	0.0334533	+	0.0193143i
$459$	−4.27499	−	2.46817i	−0.199540	−	0.115204i
$460$	−6.33130	+	23.6287i	−0.295199	+	1.10170i
$461$	−11.0079	−	11.0079i	−0.512689	−	0.512689i	0.402660	−	0.915349i	$-0.368086\pi$
$461$	−11.0079	−	11.0079i	−0.512689	−	0.512689i	−0.915349	+	0.402660i	$0.868086\pi$
$462$	−7.28655	+	6.36140i	−0.339001	+	0.295959i
$463$	23.1538	+	23.1538i	1.07605	+	1.07605i	0.996860	+	0.0791865i	$0.0252323\pi$
$463$	23.1538	+	23.1538i	1.07605	+	1.07605i	0.0791865	+	0.996860i	$0.474768\pi$
$464$	−0.567934	−	0.983690i	−0.0263657	−	0.0456667i
$465$	10.5759	−	18.3180i	0.490445	−	0.849475i
$466$	−26.2356	+	7.02982i	−1.21534	+	0.325650i
$467$	9.27111	+	16.0580i	0.429016	+	0.743077i	0.996786	−	0.0801101i	$-0.0255272\pi$
$467$	9.27111	+	16.0580i	0.429016	+	0.743077i	−0.567770	+	0.823187i	$0.692194\pi$
$468$	3.49739	−	2.02423i	0.161667	−	0.0935700i
$469$	−22.3182	−	1.51288i	−1.03056	−	0.0698582i
$470$	4.15598	−	4.15598i	0.191701	−	0.191701i
$471$	−12.0980	−	20.9544i	−0.557447	−	0.965527i
$472$	19.9960	−	34.6342i	0.920393	−	1.59417i
$473$	−3.87839	−	14.4743i	−0.178328	−	0.665531i
$474$	−1.30812	+	4.88197i	−0.0600840	+	0.224236i
$475$	12.9464	−	12.9464i	0.594022	−	0.594022i
$476$	−2.82356	−	14.3625i	−0.129418	−	0.658306i
$477$	0.691128			0.0316446
$478$	18.8685	−	10.8937i	0.863023	−	0.498267i
$479$	−5.92540	−	22.1139i	−0.270739	−	1.01041i	−0.958644	−	0.284609i	$-0.908136\pi$
$479$	−5.92540	−	22.1139i	−0.270739	−	1.01041i	0.687905	−	0.725801i	$-0.258531\pi$
$480$	14.6386	+	8.45159i	0.668157	+	0.385760i
$481$	22.8531	−	6.14977i	1.04201	−	0.280405i
$482$			13.2556i			0.603778i
$483$	−5.94857	+	17.3962i	−0.270669	+	0.791553i
$484$	−4.70896			−0.214043
$485$	−23.3762	+	13.4963i	−1.06146	+	0.612835i
$486$	0.905729	−	0.242689i	0.0410847	−	0.0110086i
$487$	1.01733	+	3.79673i	0.0460996	+	0.172046i	0.985138	−	0.171768i	$-0.0549478\pi$
$487$	1.01733	+	3.79673i	0.0460996	+	0.172046i	−0.939038	+	0.343814i	$0.888281\pi$
$488$	−27.7690	−	7.44069i	−1.25704	−	0.336824i
$489$	−12.5406	+	12.5406i	−0.567106	+	0.567106i
$490$	19.0825	−	7.80454i	0.862058	−	0.352573i
$491$			22.7591i			1.02710i	0.858058	+	0.513552i	$0.171671\pi$
$491$			22.7591i			1.02710i	−0.858058	+	0.513552i	$0.828329\pi$
$492$	1.69121	−	6.31166i	0.0762454	−	0.284552i
$493$	5.58037	−	9.66548i	0.251327	−	0.435311i
$494$	−12.7212	+	0.0136546i	−0.572354	+	0.000614351i
$495$	10.6058	−	6.12326i	0.476695	−	0.275220i
$496$	−2.39223	−	2.39223i	−0.107414	−	0.107414i
$497$	−2.90105	−	5.91601i	−0.130130	−	0.265369i
$498$		−	8.18082i		−	0.366591i
$499$	−14.7553	−	3.95367i	−0.660538	−	0.176991i	−0.0870494	−	0.996204i	$-0.527744\pi$
$499$	−14.7553	−	3.95367i	−0.660538	−	0.176991i	−0.573489	+	0.819213i	$0.694410\pi$
$500$	0.456028	−	0.122192i	0.0203942	−	0.00546461i
$501$	−6.71615	+	1.79959i	−0.300055	+	0.0803996i
$502$	8.42349	+	2.25707i	0.375959	+	0.100738i
$503$		−	19.8553i		−	0.885303i	−0.896694	−	0.442652i	$-0.854038\pi$
$503$		−	19.8553i		−	0.885303i	0.896694	−	0.442652i	$-0.145962\pi$
$504$	6.42777	+	4.31569i	0.286316	+	0.192236i
$505$	−25.5019	−	25.5019i	−1.13482	−	1.13482i
$506$	22.0012	−	12.7024i	0.978074	−	0.564691i
$507$	11.2444	−	6.52415i	0.499379	−	0.289748i
$508$	−7.98944	+	13.8381i	−0.354474	+	0.613967i
$509$	−7.16987	+	26.7583i	−0.317799	+	1.18604i	0.603556	+	0.797321i	$0.293750\pi$
$509$	−7.16987	+	26.7583i	−0.317799	+	1.18604i	−0.921355	+	0.388722i	$0.872917\pi$
$510$		−	14.5388i		−	0.643787i
$511$	−39.3546	−	2.66771i	−1.74094	−	0.118013i
$512$	3.99079	−	3.99079i	0.176370	−	0.176370i
$513$	3.63451	+	0.973864i	0.160468	+	0.0429972i
$514$	0.644697	+	2.40604i	0.0284364	+	0.106126i
$515$	−23.1947	+	6.21500i	−1.02208	+	0.273865i
$516$	−3.73038	+	2.15373i	−0.164221	+	0.0948129i
$517$	7.78054			0.342188
$518$	10.7094	+	12.2668i	0.470542	+	0.538974i
$519$			9.02862i			0.396312i
$520$	28.7180	+	16.5392i	1.25937	+	0.725294i
$521$	−8.01735	−	4.62882i	−0.351246	−	0.202792i	0.313988	−	0.949427i	$-0.398335\pi$
$521$	−8.01735	−	4.62882i	−0.351246	−	0.202792i	−0.665234	+	0.746635i	$0.731668\pi$
$522$	0.548704	+	2.04779i	0.0240161	+	0.0896295i
$523$	−7.10970	+	4.10478i	−0.310885	+	0.179490i	−0.647323	−	0.762216i	$-0.724111\pi$
$523$	−7.10970	+	4.10478i	−0.310885	+	0.179490i	0.336437	+	0.941706i	$0.390778\pi$
$524$	5.85592			0.255817
$525$	−12.6321	+	2.48337i	−0.551312	+	0.108383i
$526$	11.1107	−	11.1107i	0.484451	−	0.484451i
$527$	8.60358	−	32.1090i	0.374778	−	1.39869i
$528$	−0.506968	−	1.89203i	−0.0220630	−	0.0823401i
$529$	12.6437	−	21.8996i	0.549728	−	0.952157i
$530$	1.01777	+	1.76284i	0.0442093	+	0.0765727i
$531$	−9.66373	+	9.66373i	−0.419370	+	0.419370i
$532$	4.91243	+	10.0178i	0.212981	+	0.434325i
$533$	5.41892	−	20.3109i	0.234720	−	0.879762i
$534$	3.66120	+	6.34138i	0.158436	+	0.274419i
$535$	7.03120	−	1.88400i	0.303985	−	0.0814526i
$536$	12.3706	−	21.4265i	0.534328	−	0.925484i
$537$	5.41871	+	9.38548i	0.233834	+	0.405013i
$538$	−8.01105	−	8.01105i	−0.345381	−	0.345381i
$539$	25.1680	+	10.5569i	1.08406	+	0.454717i
$540$	−2.48923	−	2.48923i	−0.107119	−	0.107119i
$541$	−2.65942	+	9.92508i	−0.114337	+	0.426713i	−0.999236	−	0.0390700i	$-0.987560\pi$
$541$	−2.65942	+	9.92508i	−0.114337	+	0.426713i	0.884899	+	0.465783i	$0.154227\pi$
$542$	16.8645	+	9.73672i	0.724392	+	0.418228i
$543$	13.1692	+	7.60322i	0.565143	+	0.326285i
$544$	25.6595	+	6.87545i	1.10014	+	0.294783i
$545$	7.99358			0.342407
$546$	7.43164	+	4.97814i	0.318045	+	0.213045i
$547$	27.1265			1.15985			0.579923	−	0.814671i	$-0.303083\pi$
$547$	27.1265			1.15985			0.579923	+	0.814671i	$0.303083\pi$
$548$	−18.1244	−	4.85642i	−0.774237	−	0.207456i
$549$	8.50811	+	4.91216i	0.363117	+	0.209646i
$550$	15.4061	+	8.89469i	0.656917	+	0.379271i
$551$	−2.20184	+	8.21739i	−0.0938016	+	0.350072i
$552$	−14.3786	−	14.3786i	−0.611994	−	0.611994i
$553$	13.9930	−	2.75092i	0.595044	−	0.116981i
$554$	17.4684	+	17.4684i	0.742163	+	0.742163i
$555$	−10.3084	−	17.8547i	−0.437569	−	0.757892i
$556$	0.189017	−	0.327388i	0.00801612	−	0.0138843i
$557$	16.3855	−	4.39048i	0.694276	−	0.186031i	0.105610	−	0.994408i	$-0.466320\pi$
$557$	16.3855	−	4.39048i	0.694276	−	0.186031i	0.588665	+	0.808377i	$0.299654\pi$
$558$	3.15720	+	5.46844i	0.133655	+	0.231497i
$559$	−11.9934	+	6.94158i	−0.507268	+	0.293598i
$560$	−0.282362	+	4.16545i	−0.0119320	+	0.176022i
$561$	13.6093	−	13.6093i	0.574583	−	0.574583i
$562$	4.26857	+	7.39338i	0.180059	+	0.311871i
$563$	−3.25552	+	5.63873i	−0.137204	+	0.237644i	−0.926437	−	0.376449i	$-0.877145\pi$
$563$	−3.25552	+	5.63873i	−0.137204	+	0.237644i	0.789233	+	0.614093i	$0.210478\pi$
$564$	−0.578860	−	2.16033i	−0.0243744	−	0.0909665i
$565$	1.93508	−	7.22182i	0.0814095	−	0.303824i
$566$	11.7316	−	11.7316i	0.493117	−	0.493117i
$567$	−1.74002	−	1.99307i	−0.0730739	−	0.0837012i
$568$	7.28763			0.305782
$569$	24.3122	−	14.0366i	1.01922	−	0.588446i	0.105341	−	0.994436i	$-0.466407\pi$
$569$	24.3122	−	14.0366i	1.01922	−	0.588446i	0.913878	+	0.405990i	$0.133073\pi$
$570$	2.86828	+	10.7045i	0.120139	+	0.448364i
$571$	−29.6118	−	17.0964i	−1.23922	−	0.715461i	−0.270282	−	0.962781i	$-0.587117\pi$
$571$	−29.6118	−	17.0964i	−1.23922	−	0.715461i	−0.968934	+	0.247320i	$0.920450\pi$
$572$	4.09411	+	15.2141i	0.171183	+	0.636133i
$573$		−	2.12605i		−	0.0888170i
$574$	14.1925	−	2.79012i	0.592382	−	0.116457i
$575$	33.8127			1.41009
$576$	−5.24020	+	3.02543i	−0.218342	+	0.126060i
$577$	−24.5869	+	6.58803i	−1.02356	+	0.274263i	−0.731287	−	0.682070i	$-0.761080\pi$
$577$	−24.5869	+	6.58803i	−1.02356	+	0.274263i	−0.292278	+	0.956334i	$0.594413\pi$
$578$	−1.78800	−	6.67290i	−0.0743709	−	0.277556i
$579$	10.3901	+	2.78401i	0.431797	+	0.115700i
$580$	5.62798	−	5.62798i	0.233689	−	0.233689i
$581$	−20.7252	+	10.1631i	−0.859827	+	0.421635i
$582$		−	8.05806i		−	0.334017i
$583$	−0.697428	+	2.60284i	−0.0288845	+	0.107798i
$584$	21.8135	−	37.7821i	0.902650	−	1.56344i
$585$	−8.01660	−	7.99941i	−0.331446	−	0.330735i
$586$	−0.870849	+	0.502785i	−0.0359745	+	0.0207699i
$587$	18.0445	+	18.0445i	0.744775	+	0.744775i	0.973493	−	0.228718i	$-0.0734533\pi$
$587$	18.0445	+	18.0445i	0.744775	+	0.744775i	−0.228718	+	0.973493i	$0.573453\pi$
$588$	1.05875	−	7.77353i	0.0436620	−	0.320575i
$589$			25.3385i			1.04405i
$590$	−38.8800	−	10.4179i	−1.60066	−	0.428896i
$591$	−18.7176	+	5.01536i	−0.769939	+	0.206304i
$592$	−3.18521	+	0.853476i	−0.130912	+	0.0350776i
$593$	44.1673	+	11.8346i	1.81373	+	0.485988i	0.995979	−	0.0895825i	$-0.0285533\pi$
$593$	44.1673	+	11.8346i	1.81373	+	0.485988i	0.817752	+	0.575570i	$0.195220\pi$
$594$			3.65594i			0.150005i
$595$	−36.8324	+	18.0616i	−1.50998	+	0.740452i
$596$	−6.13541	−	6.13541i	−0.251316	−	0.251316i
$597$	1.85539	−	1.07121i	0.0759362	−	0.0438418i
$598$	−16.6301	−	16.5944i	−0.680054	−	0.678596i
$599$	0.720416	−	1.24780i	0.0294354	−	0.0509836i	−0.850932	−	0.525275i	$-0.823962\pi$
$599$	0.720416	−	1.24780i	0.0294354	−	0.0509836i	0.880368	+	0.474292i	$0.157296\pi$
$600$	3.68530	−	13.7537i	0.150452	−	0.561493i
$601$			11.7843i			0.480693i	0.970687	+	0.240346i	$0.0772611\pi$
$601$			11.7843i			0.480693i	−0.970687	+	0.240346i	$0.922739\pi$
$602$	−7.91609	−	5.31497i	−0.322636	−	0.216622i
$603$	−5.97849	+	5.97849i	−0.243463	+	0.243463i
$604$	17.9580	+	4.81182i	0.730699	+	0.195790i
$605$	3.41568	+	12.7475i	0.138867	+	0.518259i
$606$	10.3996	−	2.78657i	0.422455	−	0.113197i
$607$	−23.5625	+	13.6038i	−0.956373	+	0.552162i	−0.895055	−	0.445956i	$-0.852864\pi$
$607$	−23.5625	+	13.6038i	−0.956373	+	0.552162i	−0.0613179	+	0.998118i	$0.519530\pi$
$608$	−20.2489			−0.821203
$609$	4.50620	−	3.93407i	0.182601	−	0.159416i
$610$			28.9351i			1.17155i
$611$	−1.86969	−	6.94794i	−0.0756395	−	0.281083i
$612$	−4.79123	−	2.76622i	−0.193674	−	0.111818i
$613$	−4.22632	−	15.7728i	−0.170699	−	0.637059i	−0.997244	−	0.0741881i	$-0.976363\pi$
$613$	−4.22632	−	15.7728i	−0.170699	−	0.637059i	0.826545	−	0.562871i	$-0.190303\pi$
$614$	24.1867	−	13.9642i	0.976096	−	0.563549i
$615$	−18.3129			−0.738447
$616$	−22.7395	+	19.8524i	−0.916202	+	0.799875i
$617$	−3.29857	+	3.29857i	−0.132795	+	0.132795i	−0.770380	−	0.637585i	$-0.779934\pi$
$617$	−3.29857	+	3.29857i	−0.132795	+	0.132795i	0.637585	+	0.770380i	$0.279934\pi$
$618$	1.85536	−	6.92428i	0.0746334	−	0.278536i
$619$	−7.79706	−	29.0990i	−0.313390	−	1.16959i	−0.925479	−	0.378799i	$-0.876337\pi$
$619$	−7.79706	−	29.0990i	−0.313390	−	1.16959i	0.612089	−	0.790789i	$-0.290330\pi$
$620$	11.8530	−	20.5300i	0.476028	−	0.824504i
$621$	3.47446	+	6.01794i	0.139425	+	0.241492i
$622$	15.5715	−	15.5715i	0.624361	−	0.624361i
$623$	11.5169	−	17.1532i	0.461414	−	0.687228i
$624$	−1.56774	+	0.907378i	−0.0627597	+	0.0363242i
$625$	−12.8263	−	22.2158i	−0.513051	−	0.888631i
$626$	−3.17135	+	0.849761i	−0.126753	+	0.0339633i
$627$	−7.33528	+	12.7051i	−0.292943	+	0.507392i
$628$	−13.5589	−	23.4848i	−0.541061	−	0.937144i
$629$	−22.9110	−	22.9110i	−0.913523	−	0.913523i
$630$	2.52126	−	7.37325i	0.100449	−	0.293757i
$631$	−23.2265	−	23.2265i	−0.924632	−	0.924632i	0.0727204	−	0.997352i	$-0.476832\pi$
$631$	−23.2265	−	23.2265i	−0.924632	−	0.924632i	−0.997352	+	0.0727204i	$0.976832\pi$
$632$	−4.08233	+	15.2354i	−0.162386	+	0.606034i
$633$	−2.29763	−	1.32653i	−0.0913224	−	0.0527250i
$634$	7.31999	+	4.22620i	0.290714	+	0.167844i
$635$	43.2560	+	11.5904i	1.71656	+	0.459952i
$636$	0.774587			0.0307144
$637$	3.37922	−	25.0116i	0.133890	−	0.990996i
$638$	−8.26583			−0.327247
$639$	−2.40556	−	0.644568i	−0.0951624	−	0.0254987i
$640$	13.8434	+	7.99251i	0.547210	+	0.315932i
$641$	16.2087	+	9.35810i	0.640206	+	0.369623i	0.784694	−	0.619884i	$-0.212820\pi$
$641$	16.2087	+	9.35810i	0.640206	+	0.369623i	−0.144488	+	0.989507i	$0.546154\pi$
$642$	−0.562429	+	2.09901i	−0.0221973	+	0.0828415i
$643$	16.1086	+	16.1086i	0.635261	+	0.635261i	0.949383	−	0.314122i	$-0.101710\pi$
$643$	16.1086	+	16.1086i	0.635261	+	0.635261i	−0.314122	+	0.949383i	$0.601710\pi$
$644$	−6.66690	+	19.4969i	−0.262713	+	0.768285i
$645$	8.53618	+	8.53618i	0.336112	+	0.336112i
$646$	8.70826	+	15.0832i	0.342622	+	0.593439i
$647$	−6.18133	+	10.7064i	−0.243013	+	0.420911i	−0.961571	−	0.274556i	$-0.911469\pi$
$647$	−6.18133	+	10.7064i	−0.243013	+	0.420911i	0.718558	+	0.695467i	$0.244802\pi$
$648$	2.82656	−	0.757374i	0.111038	−	0.0297525i
$649$	−26.6425	−	46.1461i	−1.04581	−	1.81139i
$650$	4.24073	−	15.8949i	0.166335	−	0.623448i
$651$	9.93149	−	14.7919i	0.389246	−	0.579740i
$652$	−14.0550	+	14.0550i	−0.550435	+	0.550435i
$653$	22.5039	+	38.9780i	0.880648	+	1.52533i	0.850622	+	0.525777i	$0.176225\pi$
$653$	22.5039	+	38.9780i	0.880648	+	1.52533i	0.0300252	+	0.999549i	$0.490441\pi$
$654$	−1.19316	+	2.06661i	−0.0466561	+	0.0808108i
$655$	−4.24764	−	15.8524i	−0.165969	−	0.619405i
$656$	−0.758097	+	2.82926i	−0.0295987	+	0.110464i
$657$	−10.5421	+	10.5421i	−0.411286	+	0.411286i
$658$	3.72943	−	3.25592i	0.145388	−	0.126929i
$659$	−9.90732			−0.385934			−0.192967	−	0.981205i	$-0.561811\pi$
$659$	−9.90732			−0.385934			−0.192967	+	0.981205i	$0.561811\pi$
$660$	11.8865	−	6.86268i	0.462682	−	0.267130i
$661$	6.39147	+	23.8533i	0.248599	+	0.927785i	0.971540	+	0.236875i	$0.0761232\pi$
$661$	6.39147	+	23.8533i	0.248599	+	0.927785i	−0.722941	+	0.690910i	$0.757210\pi$
$662$	−21.7998	−	12.5861i	−0.847274	−	0.489174i
$663$	−15.4233	−	8.88256i	−0.598990	−	0.344970i
$664$		−	25.5303i		−	0.990770i
$665$	23.5555	−	20.5648i	0.913445	−	0.797468i
$666$	6.15474			0.238491
$667$	−13.6062	+	7.85552i	−0.526833	+	0.304167i
$668$	−7.52717	+	2.01690i	−0.291235	+	0.0780362i
$669$	5.26111	+	19.6347i	0.203406	+	0.759123i
$670$	−24.0532	−	6.44503i	−0.929255	−	0.248993i
$671$	−27.0852	+	27.0852i	−1.04561	+	1.04561i
$672$	11.8208	+	7.93663i	0.455996	+	0.306162i
$673$		−	2.24210i		−	0.0864264i	−0.999066	−	0.0432132i	$-0.986241\pi$
$673$		−	2.24210i		−	0.0864264i	0.999066	−	0.0432132i	$-0.0137595\pi$
$674$	6.52630	−	24.3565i	0.251384	−	0.938177i
$675$	−2.43294	+	4.21398i	−0.0936441	+	0.162196i
$676$	12.6022	−	7.31199i	0.484699	−	0.281230i
$677$	16.9090	−	9.76244i	0.649867	−	0.375201i	−0.138538	−	0.990357i	$-0.544240\pi$
$677$	16.9090	−	9.76244i	0.649867	−	0.375201i	0.788405	+	0.615156i	$0.210907\pi$
$678$	1.57824	+	1.57824i	0.0606121	+	0.0606121i
$679$	−20.4142	+	10.0106i	−0.783426	+	0.384170i
$680$		−	45.3719i		−	1.73993i
$681$	2.36952	+	0.634911i	0.0908003	+	0.0243299i
$682$	−23.7805	+	6.37196i	−0.910602	+	0.243995i
$683$	42.3756	−	11.3545i	1.62146	−	0.434468i	0.670028	−	0.742336i	$-0.266282\pi$
$683$	42.3756	−	11.3545i	1.62146	−	0.434468i	0.951429	+	0.307868i	$0.0996154\pi$
$684$	4.07340	+	1.09147i	0.155750	+	0.0417332i
$685$			52.5868i			2.00924i
$686$	16.4815	−	5.47184i	0.629266	−	0.208916i
$687$	−0.623407	−	0.623407i	−0.0237845	−	0.0237845i
$688$	1.67217	−	0.965429i	0.0637510	−	0.0368067i
$689$	2.49190	−	0.00267475i	0.0949337	−	0.000101900i
$690$	−10.2332	+	17.7244i	−0.389570	+	0.674755i
$691$	−5.68005	+	21.1982i	−0.216079	+	0.806419i	0.769704	+	0.638400i	$0.220404\pi$
$691$	−5.68005	+	21.1982i	−0.216079	+	0.806419i	−0.985784	+	0.168019i	$0.946263\pi$
$692$			10.1189i			0.384662i
$693$	9.26192	−	4.54179i	0.351831	−	0.172528i
$694$	−2.72740	+	2.72740i	−0.103531	+	0.103531i
$695$	−1.02337	−	0.274211i	−0.0388186	−	0.0104014i
$696$	1.71237	+	6.39066i	0.0649073	+	0.242237i
$697$	−27.7995	+	7.44886i	−1.05298	+	0.282146i
$698$	−15.5937	+	9.00303i	−0.590230	+	0.340770i
$699$	28.9663			1.09561
$700$	−14.1576	+	2.78326i	−0.535105	+	0.105197i
$701$			4.44352i			0.167829i	0.996473	+	0.0839146i	$0.0267423\pi$
$701$			4.44352i			0.167829i	−0.996473	+	0.0839146i	$0.973258\pi$
$702$	3.26471	−	0.878534i	0.123219	−	0.0331581i
$703$	21.3889	+	12.3489i	0.806696	+	0.465746i
$704$	−6.10602	−	22.7880i	−0.230129	−	0.858854i
$705$	−5.42831	+	3.13403i	−0.204442	+	0.118035i
$706$	−2.01961			−0.0760089
$707$	−19.9789	−	22.8845i	−0.751386	−	0.860661i
$708$	−10.8307	+	10.8307i	−0.407042	+	0.407042i
$709$	−1.61341	+	6.02133i	−0.0605929	+	0.226136i	−0.989582	−	0.143972i	$-0.954013\pi$
$709$	−1.61341	+	6.02133i	−0.0605929	+	0.226136i	0.928989	+	0.370108i	$0.120679\pi$
$710$	−1.89841	−	7.08498i	−0.0712462	−	0.265894i
$711$	2.69505	−	4.66797i	0.101072	−	0.175062i
$712$	11.4257	+	19.7899i	0.428197	+	0.741659i
$713$	−33.0888	+	33.0888i	−1.23918	+	1.23918i
$714$	0.828241	−	12.2184i	0.0309962	−	0.457261i
$715$	38.2160	−	22.1188i	1.42920	−	0.827194i
$716$	6.07306	+	10.5188i	0.226961	+	0.393108i
$717$	−22.4437	+	6.01378i	−0.838177	+	0.224589i
$718$	−13.4753	+	23.3400i	−0.502896	+	0.871041i
$719$	10.6902	+	18.5160i	0.398678	+	0.690531i	0.993563	−	0.113280i	$-0.0361357\pi$
$719$	10.6902	+	18.5160i	0.398678	+	0.690531i	−0.594885	+	0.803811i	$0.702802\pi$
$720$	1.11582	+	1.11582i	0.0415841	+	0.0415841i
$721$	−19.8468	+	3.90173i	−0.739135	+	0.145308i
$722$	3.21039	+	3.21039i	0.119478	+	0.119478i
$723$	3.65884	−	13.6550i	0.136074	−	0.507833i
$724$	14.7594	+	8.52136i	0.548530	+	0.316694i
$725$	−9.52754	−	5.50072i	−0.353844	−	0.204292i
$726$	−3.80550	−	1.01968i	−0.141235	−	0.0378439i
$727$	38.8700			1.44161			0.720805	−	0.693138i	$-0.243772\pi$
$727$	38.8700			1.44161			0.720805	+	0.693138i	$0.243772\pi$
$728$	23.1923	+	15.5356i	0.859565	+	0.575786i
$729$	−1.00000			−0.0370370
$730$	−42.4139	−	11.3648i	−1.56981	−	0.420629i
$731$	16.4303	+	9.48605i	0.607697	+	0.350854i
$732$	9.53553	+	5.50534i	0.352443	+	0.203483i
$733$	2.88314	−	10.7600i	0.106491	−	0.397430i	−0.892019	−	0.451998i	$-0.850711\pi$
$733$	2.88314	−	10.7600i	0.106491	−	0.397430i	0.998510	+	0.0545678i	$0.0173781\pi$
$734$	−1.21706	−	1.21706i	−0.0449227	−	0.0449227i
$735$	−21.8115	+	2.77249i	−0.804530	+	0.102265i
$736$	−26.4425	−	26.4425i	−0.974683	−	0.974683i
$737$	−16.4824	−	28.5484i	−0.607137	−	1.05159i
$738$	2.73346	−	4.73449i	0.100620	−	0.174279i
$739$	31.6580	−	8.48273i	1.16456	−	0.312042i	0.375773	−	0.926712i	$-0.377377\pi$
$739$	31.6580	−	8.48273i	1.16456	−	0.312042i	0.788785	+	0.614670i	$0.210711\pi$
$740$	−11.5533	−	20.0108i	−0.424706	−	0.735613i
$741$	13.1082	+	3.49725i	0.481541	+	0.128475i
$742$	0.754911	+	1.53947i	0.0277137	+	0.0565156i
$743$	18.3140	−	18.3140i	0.671877	−	0.671877i	−0.286271	−	0.958149i	$-0.592416\pi$
$743$	18.3140	−	18.3140i	0.671877	−	0.671877i	0.958149	+	0.286271i	$0.0924159\pi$
$744$	9.85287	+	17.0657i	0.361224	+	0.625658i
$745$	−12.1586	+	21.0594i	−0.445458	+	0.771556i
$746$	6.06831	+	22.6472i	0.222176	+	0.829174i
$747$	−2.25808	+	8.42725i	−0.0826187	+	0.308337i
$748$	15.2527	−	15.2527i	0.557693	−	0.557693i
$749$	6.01634	−	1.18276i	0.219832	−	0.0432172i
$750$	0.394994			0.0144231
$751$	23.9597	−	13.8332i	0.874303	−	0.504779i	0.00552705	−	0.999985i	$-0.498241\pi$
$751$	23.9597	−	13.8332i	0.874303	−	0.504779i	0.868776	+	0.495206i	$0.164907\pi$
$752$	0.259479	+	0.968388i	0.00946222	+	0.0353135i
$753$	−8.05424	−	4.65012i	−0.293513	−	0.169460i
$754$	1.98631	+	7.38129i	0.0723370	+	0.268811i
$755$		−	52.1038i		−	1.89625i
$756$	−1.95014	−	2.23375i	−0.0709258	−	0.0812407i
$757$	29.6437			1.07742			0.538710	−	0.842491i	$-0.318912\pi$
$757$	29.6437			1.07742			0.538710	+	0.842491i	$0.318912\pi$
$758$	−18.0700	+	10.4327i	−0.656330	+	0.378933i
$759$	−26.1701	+	7.01226i	−0.949915	+	0.254529i
$760$	8.95119	+	33.4063i	0.324694	+	1.21177i
$761$	46.0734	+	12.3453i	1.67016	+	0.447518i	0.965154	−	0.261683i	$-0.0842774\pi$
$761$	46.0734	+	12.3453i	1.67016	+	0.447518i	0.705007	+	0.709201i	$0.250944\pi$
$762$	−9.45310	+	9.45310i	−0.342450	+	0.342450i
$763$	6.71779	+	0.455377i	0.243200	+	0.0164857i
$764$		−	2.38278i		−	0.0862061i
$765$	−4.01300	+	14.9767i	−0.145090	+	0.541485i
$766$	2.41714	−	4.18660i	0.0873347	−	0.151268i
$767$	−34.8057	+	34.8804i	−1.25676	+	1.25946i
$768$	−14.6131	+	8.43686i	−0.527304	+	0.304439i
$769$	−27.2194	−	27.2194i	−0.981556	−	0.981556i	0.0182765	−	0.999833i	$-0.494182\pi$
$769$	−27.2194	−	27.2194i	−0.981556	−	0.981556i	−0.999833	+	0.0182765i	$0.994182\pi$
$770$	25.2239	+	16.9357i	0.909007	+	0.610320i
$771$		−	2.65647i		−	0.0956705i
$772$	11.6448	+	3.12020i	0.419104	+	0.112299i
$773$	−19.9752	+	5.35234i	−0.718458	+	0.192510i	−0.599483	−	0.800387i	$-0.704627\pi$
$773$	−19.9752	+	5.35234i	−0.718458	+	0.192510i	−0.118974	+	0.992897i	$0.537961\pi$
$774$	−3.48104	+	0.932741i	−0.125123	+	0.0335267i
$775$	−31.6508	−	8.48080i	−1.13693	−	0.304639i
$776$		−	25.1472i		−	0.902733i
$777$	−7.64606	−	15.5924i	−0.274301	−	0.559373i
$778$	11.7968	+	11.7968i	0.422935	+	0.422935i
$779$	18.9986	−	10.9688i	0.680695	−	0.392999i
$780$	−8.98467	−	8.96540i	−0.321703	−	0.321013i
$781$	4.85497	−	8.40906i	0.173725	−	0.300900i
$782$	−8.32478	+	31.0685i	−0.297694	+	1.11101i
$783$		−	2.26093i		−	0.0807992i
$784$	−0.474593	+	3.48455i	−0.0169497	+	0.124448i
$785$	−53.7399	+	53.7399i	−1.91806	+	1.91806i
$786$	4.73240	+	1.26804i	0.168799	+	0.0452296i
$787$	5.02312	+	18.7465i	0.179055	+	0.668242i	0.995825	+	0.0912790i	$0.0290955\pi$
$787$	5.02312	+	18.7465i	0.179055	+	0.668242i	−0.816771	+	0.576963i	$0.804238\pi$
$788$	−20.9779	+	5.62100i	−0.747306	+	0.200240i
$789$	−14.5122	+	8.37863i	−0.516648	+	0.298287i
$790$	15.8752			0.564815
$791$	2.03765	−	5.95897i	0.0724505	−	0.211877i
$792$			11.4093i			0.405412i
$793$	30.6954	+	17.6781i	1.09003	+	0.627768i
$794$	−6.36451	−	3.67455i	−0.225868	−	0.130405i
$795$	−0.561853	−	2.09687i	−0.0199269	−	0.0743682i
$796$	2.07945	−	1.20057i	0.0737040	−	0.0425530i
$797$	6.52194			0.231019			0.115509	−	0.993306i	$-0.463150\pi$
$797$	6.52194			0.231019			0.115509	+	0.993306i	$0.463150\pi$
$798$	1.80068	+	9.15949i	0.0637434	+	0.324242i
$799$	−6.96555	+	6.96555i	−0.246423	+	0.246423i
$800$	6.77733	−	25.2933i	0.239615	−	0.894254i
$801$	−2.02113	−	7.54298i	−0.0714133	−	0.266518i
$802$	−1.12320	+	1.94545i	−0.0396617	+	0.0686962i
$803$	−29.0640	−	50.3404i	−1.02565	−	1.77647i
$804$	−6.70043	+	6.70043i	−0.236306	+	0.236306i
$805$	57.6154	+	3.90556i	2.03068	+	0.137653i
$806$	11.4046	+	19.7045i	0.401711	+	0.694062i
$807$	6.04116	+	10.4636i	0.212659	+	0.368336i
$808$	32.4546	−	8.69620i	1.14175	−	0.305931i
$809$	−7.01956	+	12.1582i	−0.246794	+	0.427460i	−0.962635	−	0.270804i	$-0.912711\pi$
$809$	−7.01956	+	12.1582i	−0.246794	+	0.427460i	0.715840	+	0.698264i	$0.246044\pi$
$810$	−1.47263	−	2.55066i	−0.0517428	−	0.0896212i
$811$	1.53783	+	1.53783i	0.0540004	+	0.0540004i	0.733591	−	0.679591i	$-0.237843\pi$
$811$	1.53783	+	1.53783i	0.0540004	+	0.0540004i	−0.679591	+	0.733591i	$0.737843\pi$
$812$	5.05036	−	4.40913i	0.177233	−	0.154730i
$813$	−14.6850	−	14.6850i	−0.515025	−	0.515025i
$814$	−6.21084	+	23.1792i	−0.217690	+	0.812429i
$815$	48.2428	+	27.8530i	1.68987	+	0.975647i
$816$	2.14771	+	1.23998i	0.0751849	+	0.0434080i
$817$	−13.9687	−	3.74291i	−0.488703	−	0.130948i
$818$	−17.6838			−0.618299
$819$	−6.28144	−	7.17939i	−0.219491	−	0.250868i
$820$	−20.5243			−0.716739
$821$	−5.01757	−	1.34445i	−0.175114	−	0.0469218i	0.170196	−	0.985410i	$-0.445560\pi$
$821$	−5.01757	−	1.34445i	−0.175114	−	0.0469218i	−0.345311	+	0.938488i	$0.612226\pi$
$822$	−13.5955	−	7.84934i	−0.474196	−	0.273777i
$823$	−13.9084	−	8.03002i	−0.484817	−	0.279909i	0.237605	−	0.971362i	$-0.423638\pi$
$823$	−13.9084	−	8.03002i	−0.484817	−	0.279909i	−0.722422	+	0.691453i	$0.756971\pi$
$824$	5.79012	−	21.6090i	0.201708	−	0.752785i
$825$	−13.4150	−	13.4150i	−0.467051	−	0.467051i
$826$	−32.0812	−	10.9701i	−1.11625	−	0.381697i
$827$	20.7787	+	20.7787i	0.722546	+	0.722546i	0.969123	−	0.246577i	$-0.0793058\pi$
$827$	20.7787	+	20.7787i	0.722546	+	0.722546i	−0.246577	+	0.969123i	$0.579306\pi$
$828$	3.89403	+	6.74465i	0.135327	+	0.234393i
$829$	−6.34108	+	10.9831i	−0.220235	+	0.381458i	−0.954879	−	0.296995i	$-0.904016\pi$
$829$	−6.34108	+	10.9831i	−0.220235	+	0.381458i	0.734644	+	0.678452i	$0.237349\pi$
$830$	−24.8204	+	6.65060i	−0.861528	+	0.230846i
$831$	−13.1730	−	22.8163i	−0.456966	−	0.791489i
$832$	−18.8821	+	10.9286i	−0.654619	+	0.378882i
$833$	−31.9828	+	13.0807i	−1.10814	+	0.453218i
$834$	0.223645	−	0.223645i	0.00774420	−	0.00774420i
$835$	10.9198	+	18.9137i	0.377895	+	0.654534i
$836$	−8.22107	+	14.2393i	−0.284331	+	0.492477i
$837$	−1.74291	−	6.50462i	−0.0602437	−	0.224833i
$838$	−2.37141	+	8.85022i	−0.0819190	+	0.305726i
$839$	12.6699	−	12.6699i	0.437414	−	0.437414i	−0.453727	−	0.891141i	$-0.649906\pi$
$839$	12.6699	−	12.6699i	0.437414	−	0.437414i	0.891141	+	0.453727i	$0.149906\pi$
$840$	7.86824	−	23.0101i	0.271480	−	0.793925i
$841$	−23.8882			−0.823730
$842$	9.23408	−	5.33130i	0.318227	−	0.183729i
$843$	−2.35643	−	8.79431i	−0.0811597	−	0.302892i
$844$	−2.57508	−	1.48672i	−0.0886379	−	0.0511751i
$845$	−28.9352	−	28.8113i	−0.995402	−	0.991137i
$846$		−	1.87120i		−	0.0643331i
$847$	2.14434	+	10.9076i	0.0736803	+	0.374788i
$848$	−0.347215			−0.0119234
$849$	−15.3232	+	8.84685i	−0.525891	+	0.303623i
$850$	−21.7553	+	5.82932i	−0.746201	+	0.199944i
$851$	11.8051	+	44.0571i	0.404673	+	1.51026i
$852$	−2.69605	−	0.722404i	−0.0923651	−	0.0247491i
$853$	0.00600545	−	0.00600545i	0.000205623	−	0.000205623i	−0.707004	−	0.707210i	$-0.749954\pi$
$853$	0.00600545	−	0.00600545i	0.000205623	−	0.000205623i	0.707210	+	0.707004i	$0.249954\pi$
$854$	−1.64837	+	24.3170i	−0.0564060	+	0.832112i
$855$		−	11.8187i		−	0.404191i
$856$	−1.75521	+	6.55052i	−0.0599917	+	0.223892i
$857$	10.1876	−	17.6454i	0.348001	−	0.602756i	−0.637893	−	0.770125i	$-0.720194\pi$
$857$	10.1876	−	17.6454i	0.348001	−	0.602756i	0.985894	+	0.167369i	$0.0535271\pi$
$858$	0.0141489	+	13.1817i	0.000483035	+	0.450015i
$859$	−19.8708	+	11.4724i	−0.677983	+	0.391433i	−0.799095	−	0.601205i	$-0.794687\pi$
$859$	−19.8708	+	11.4724i	−0.677983	+	0.391433i	0.121112	+	0.992639i	$0.461354\pi$
$860$	9.56699	+	9.56699i	0.326232	+	0.326232i
$861$	−15.3901	−	1.04324i	−0.524494	−	0.0355537i
$862$			22.1411i			0.754130i
$863$	34.5180	+	9.24907i	1.17501	+	0.314842i	0.792944	−	0.609294i	$-0.208547\pi$
$863$	34.5180	+	9.24907i	1.17501	+	0.314842i	0.382063	+	0.924136i	$0.375214\pi$
$864$	5.19809	−	1.39282i	0.176843	−	0.0473848i
$865$	27.3926	−	7.33982i	0.931376	−	0.249561i
$866$	19.2179	+	5.14942i	0.653050	+	0.174984i
$867$			7.36744i			0.250211i
$868$	11.1308	−	16.5781i	0.377804	−	0.562698i
$869$	14.8603	+	14.8603i	0.504100	+	0.504100i
$870$	5.76688	−	3.32951i	0.195516	−	0.112881i
$871$	−21.5326	+	21.5789i	−0.729604	+	0.731172i
$872$	−3.72355	+	6.44938i	−0.126095	+	0.218404i
$873$	−2.22419	+	8.30080i	−0.0752775	+	0.280939i
$874$		−	24.5174i		−	0.829312i
$875$	−0.490703	−	1.00067i	−0.0165888	−	0.0338290i
$876$	−11.8151	+	11.8151i	−0.399196	+	0.399196i
$877$	−51.5283	−	13.8070i	−1.73999	−	0.466228i	−0.757543	−	0.652786i	$-0.773600\pi$
$877$	−51.5283	−	13.8070i	−1.73999	−	0.466228i	−0.982444	+	0.186558i	$0.940267\pi$
$878$	−1.77952	−	6.64126i	−0.0600559	−	0.224132i
$879$	1.03586	−	0.277558i	0.0349387	−	0.00936181i
$880$	−5.32823	+	3.07626i	−0.179615	+	0.103701i
$881$	50.6900			1.70779			0.853894	−	0.520447i	$-0.174235\pi$
$881$	50.6900			1.70779			0.853894	+	0.520447i	$0.174235\pi$
$882$	2.53890	−	6.05284i	0.0854892	−	0.203810i
$883$		−	34.3901i		−	1.15732i	−0.815569	−	0.578659i	$-0.803576\pi$
$883$		−	34.3901i		−	1.15732i	0.815569	−	0.578659i	$-0.196424\pi$
$884$	−17.2857	−	9.95519i	−0.581382	−	0.334829i
$885$	37.1756	+	21.4634i	1.24965	+	0.721483i
$886$	2.42128	+	9.03633i	0.0813444	+	0.303581i
$887$	−14.2770	+	8.24283i	−0.479375	+	0.276767i	−0.720156	−	0.693812i	$-0.755930\pi$
$887$	−14.2770	+	8.24283i	−0.479375	+	0.276767i	0.240781	+	0.970579i	$0.422596\pi$
$888$	19.2074			0.644559
$889$	35.6920	+	12.2048i	1.19707	+	0.409335i
$890$	16.2632	−	16.2632i	0.545144	−	0.545144i
$891$	1.00911	−	3.76607i	0.0338066	−	0.126168i
$892$	5.89643	+	22.0058i	0.197427	+	0.736808i
$893$	3.75438	−	6.50277i	0.125635	−	0.217607i
$894$	−3.62970	−	6.28683i	−0.121395	−	0.210263i
$895$	24.0701	−	24.0701i	0.804576	−	0.804576i
$896$	11.1787	+	7.50553i	0.373454	+	0.250742i
$897$	12.5506	+	21.6845i	0.419053	+	0.724026i
$898$	−17.6283	−	30.5330i	−0.588263	−	1.01890i
$899$	14.7065	−	3.94060i	0.490490	−	0.131426i
$900$	−2.72674	+	4.72285i	−0.0908913	+	0.157428i
$901$	−1.70582	−	2.95457i	−0.0568292	−	0.0984310i
$902$	15.0721	+	15.0721i	0.501844	+	0.501844i
$903$	6.68751	+	7.66008i	0.222546	+	0.254912i
$904$	4.92532	+	4.92532i	0.163814	+	0.163814i
$905$	12.3621	−	46.1359i	0.410930	−	1.53361i
$906$	13.4706	+	7.77725i	0.447530	+	0.258382i
$907$	−14.1515	−	8.17037i	−0.469893	−	0.271293i	0.246302	−	0.969193i	$-0.420784\pi$
$907$	−14.1515	−	8.17037i	−0.469893	−	0.271293i	−0.716195	+	0.697900i	$0.754118\pi$
$908$	2.65566	+	0.711581i	0.0881311	+	0.0236147i
$909$	−11.4820			−0.380835
$910$	9.06199	−	26.5944i	0.300402	−	0.881595i
$911$	−20.9813			−0.695142			−0.347571	−	0.937654i	$-0.612994\pi$
$911$	−20.9813			−0.695142			−0.347571	+	0.937654i	$0.612994\pi$
$912$	−1.82594	−	0.489258i	−0.0604628	−	0.0162010i
$913$	−29.4590	−	17.0081i	−0.974949	−	0.562887i
$914$	−23.0875	−	13.3296i	−0.763667	−	0.440903i
$915$	7.98669	−	29.8067i	0.264032	−	0.985380i
$916$	−0.698688	−	0.698688i	−0.0230853	−	0.0230853i
$917$	−2.66664	−	13.5643i	−0.0880601	−	0.447934i
$918$	−3.27299	−	3.27299i	−0.108025	−	0.108025i
$919$	−23.9708	−	41.5187i	−0.790725	−	1.36958i	−0.925519	−	0.378702i	$-0.876370\pi$
$919$	−23.9708	−	41.5187i	−0.790725	−	1.36958i	0.134794	−	0.990874i	$-0.456963\pi$
$920$	−31.9352	+	55.3134i	−1.05287	+	1.82363i
$921$	−28.7697	+	7.70882i	−0.947994	+	0.254014i
$922$	−7.29867	−	12.6417i	−0.240369	−	0.416331i
$923$	−8.67586	−	2.31471i	−0.285569	−	0.0761896i
$924$	10.3804	−	5.09024i	0.341489	−	0.167457i
$925$	−22.5841	+	22.5841i	−0.742559	+	0.742559i
$926$	15.3519	+	26.5902i	0.504493	+	0.873808i
$927$	−3.82249	+	6.62075i	−0.125547	+	0.217454i
$928$	3.14908	+	11.7525i	0.103374	+	0.385796i
$929$	10.2712	−	38.3325i	0.336986	−	1.25765i	−0.564714	−	0.825287i	$-0.691013\pi$
$929$	10.2712	−	38.3325i	0.336986	−	1.25765i	0.901700	−	0.432362i	$-0.142320\pi$
$930$	14.0244	−	14.0244i	0.459880	−	0.459880i
$931$	20.9676	−	15.9407i	0.687185	−	0.522436i
$932$	32.4642			1.06340
$933$	−20.3387	+	11.7425i	−0.665858	+	0.384433i
$934$	4.50000	+	16.7942i	0.147244	+	0.549524i
$935$	−52.3538	−	30.2265i	−1.71215	−	0.988511i
$936$	10.1884	−	2.74169i	0.333017	−	0.0896149i
$937$			20.5205i			0.670376i	0.942151	+	0.335188i	$0.108800\pi$
$937$			20.5205i			0.670376i	−0.942151	+	0.335188i	$0.891200\pi$
$938$	−19.8471	−	6.78665i	−0.648031	−	0.221592i
$939$	3.50143			0.114265
$940$	−6.08381	+	3.51249i	−0.198432	+	0.114565i
$941$	21.7127	−	5.81790i	0.707814	−	0.189658i	0.113086	−	0.993585i	$-0.463926\pi$
$941$	21.7127	−	5.81790i	0.707814	−	0.189658i	0.594728	+	0.803927i	$0.297260\pi$
$942$	−5.87212	−	21.9150i	−0.191324	−	0.714031i
$943$	39.1336	+	10.4858i	1.27436	+	0.341465i
$944$	4.85495	−	4.85495i	0.158015	−	0.158015i
$945$	−4.63238	+	6.89944i	−0.150691	+	0.224439i
$946$		−	14.0511i		−	0.456840i
$947$	−6.86691	+	25.6276i	−0.223144	+	0.832786i	0.759995	+	0.649929i	$0.225201\pi$
$947$	−6.86691	+	25.6276i	−0.223144	+	0.832786i	−0.983139	+	0.182858i	$0.941465\pi$
$948$	3.02050	−	5.23166i	0.0981012	−	0.169916i
$949$	−37.9692	+	38.0508i	−1.23253	+	1.23518i
$950$	14.8679	−	8.58398i	0.482378	−	0.278501i
$951$	−6.37397	−	6.37397i	−0.206690	−	0.206690i
$952$	2.58474	−	38.1305i	0.0837719	−	1.23582i
$953$		−	9.87206i		−	0.319787i	−0.987134	−	0.159894i	$-0.948885\pi$
$953$		−	9.87206i		−	0.319787i	0.987134	−	0.159894i	$-0.0511151\pi$
$954$	0.625975	+	0.167729i	0.0202667	+	0.00543044i
$955$	−6.45038	+	1.72837i	−0.208729	+	0.0559288i
$956$	−25.1540	+	6.73999i	−0.813538	+	0.217987i
$957$	8.51483	+	2.28154i	0.275245	+	0.0737518i
$958$		−	21.4672i		−	0.693575i
$959$	−2.99575	+	44.1939i	−0.0967380	+	1.42709i
$960$	13.4391	+	13.4391i	0.433745	+	0.433745i
$961$	12.4256	−	7.17392i	0.400826	−	0.231417i
$962$	22.1912	−	0.0238195i	0.715473	−	0.000767972i
$963$	1.15874	−	2.00700i	0.0373400	−	0.0646748i
$964$	4.10067	−	15.3039i	0.132074	−	0.492905i
$965$		−	33.7865i		−	1.08763i
$966$	−9.60965	+	14.3126i	−0.309186	+	0.460499i
$967$	25.1198	−	25.1198i	0.807798	−	0.807798i	−0.176502	−	0.984300i	$-0.556478\pi$
$967$	25.1198	−	25.1198i	0.807798	−	0.807798i	0.984300	+	0.176502i	$0.0564783\pi$
$968$	−11.8760	−	3.18217i	−0.381710	−	0.102279i
$969$	−4.80732	−	17.9412i	−0.154433	−	0.576353i
$970$	−24.4479	+	6.55081i	−0.784976	+	0.210334i
$971$	44.3768	−	25.6210i	1.42412	−	0.822216i	0.427472	−	0.904029i	$-0.359404\pi$
$971$	44.3768	−	25.6210i	1.42412	−	0.822216i	0.996648	+	0.0818129i	$0.0260710\pi$
$972$	−1.12076			−0.0359483
$973$	−0.844416	−	0.288745i	−0.0270707	−	0.00925675i
$974$			3.68570i			0.118097i
$975$	−8.75579	+	15.2031i	−0.280410	+	0.486890i
$976$	−4.27438	−	2.46781i	−0.136820	−	0.0789928i
$977$	−9.33312	−	34.8317i	−0.298593	−	1.11436i	−0.938322	−	0.345763i	$-0.887620\pi$
$977$	−9.33312	−	34.8317i	−0.298593	−	1.11436i	0.639729	−	0.768601i	$-0.279047\pi$
$978$	−14.4019	+	8.31492i	−0.460521	+	0.265882i
$979$	30.4469			0.973088
$980$	−24.4454	+	3.10729i	−0.780880	+	0.0992586i
$981$	1.79953	−	1.79953i	0.0574544	−	0.0574544i
$982$	−5.52339	+	20.6136i	−0.176259	+	0.657806i
$983$	4.95918	+	18.5079i	0.158173	+	0.590311i	0.998813	+	0.0487155i	$0.0155128\pi$
$983$	4.95918	+	18.5079i	0.158173	+	0.590311i	−0.840639	+	0.541595i	$0.817821\pi$
$984$	8.53047	−	14.7752i	0.271941	−	0.471016i
$985$	30.4330	+	52.7114i	0.969675	+	1.67953i
$986$	7.40001	−	7.40001i	0.235664	−	0.235664i
$987$	−4.74048	+	2.32460i	−0.150891	+	0.0739928i
$988$	14.6911	+	3.91957i	0.467386	+	0.124698i
$989$	−13.3536	−	23.1291i	−0.424619	−	0.735462i
$990$	11.0920	−	2.97210i	0.352528	−	0.0944595i
$991$	17.0444	−	29.5217i	0.541432	−	0.937788i	−0.457390	−	0.889266i	$-0.651216\pi$
$991$	17.0444	−	29.5217i	0.541432	−	0.937788i	0.998822	−	0.0485220i	$-0.0154511\pi$
$992$	18.1196	+	31.3841i	0.575298	+	0.996445i
$993$	18.9825	+	18.9825i	0.602391	+	0.602391i
$994$	−1.19181	−	6.06236i	−0.0378019	−	0.192286i
$995$	−4.75837	−	4.75837i	−0.150851	−	0.150851i
$996$	−2.53075	+	9.44491i	−0.0801900	+	0.299273i
$997$	39.9883	+	23.0872i	1.26644	+	0.731180i	0.974313	−	0.225199i	$-0.0723032\pi$
$997$	39.9883	+	23.0872i	1.26644	+	0.731180i	0.292128	+	0.956379i	$0.405637\pi$
$998$	−12.4048	−	7.16191i	−0.392667	−	0.226706i
$999$	−6.34014	−	1.69884i	−0.200593	−	0.0537488i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bz.a.31.6	✓	36
3.2	odd	2		819.2.fn.f.577.4		36
7.5	odd	6		273.2.bz.b.187.4	yes	36
13.8	odd	4		273.2.bz.b.73.4	yes	36
21.5	even	6		819.2.fn.g.460.6		36
39.8	even	4		819.2.fn.g.73.6		36
91.47	even	12	inner	273.2.bz.a.229.6	yes	36
273.47	odd	12		819.2.fn.f.775.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bz.a.31.6	✓	36	1.1	even	1	trivial
273.2.bz.a.229.6	yes	36	91.47	even	12	inner
273.2.bz.b.73.4	yes	36	13.8	odd	4
273.2.bz.b.187.4	yes	36	7.5	odd	6
819.2.fn.f.577.4		36	3.2	odd	2
819.2.fn.f.775.4		36	273.47	odd	12
819.2.fn.g.73.6		36	39.8	even	4
819.2.fn.g.460.6		36	21.5	even	6

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.905729 + 0.242689i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.970604 - 0.560379i) q^{4} +(-0.812951 + 3.03397i) q^{5} +(-0.663040 - 0.663040i) q^{6} +(-0.856042 + 2.50344i) q^{7} +(-2.06919 - 2.06919i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.905729 + 0.242689i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.970604 - 0.560379i) q^{4} +(-0.812951 + 3.03397i) q^{5} +(-0.663040 - 0.663040i) q^{6} +(-0.856042 + 2.50344i) q^{7} +(-2.06919 - 2.06919i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.47263 + 2.55066i) q^{10} +(-3.76607 + 1.00911i) q^{11} +(0.560379 + 0.970604i) q^{12} +(1.80613 + 3.12056i) q^{13} +(-1.38290 + 2.05968i) q^{14} +(2.22102 - 2.22102i) q^{15} +(-0.251194 - 0.435081i) q^{16} +(2.46817 - 4.27499i) q^{17} +(0.242689 + 0.905729i) q^{18} +(-0.973864 + 3.63451i) q^{19} +(2.48923 - 2.48923i) q^{20} +(1.99307 - 1.74002i) q^{21} -3.65594 q^{22} +(-6.01794 + 3.47446i) q^{23} +(0.757374 + 2.82656i) q^{24} +(-4.21398 - 2.43294i) q^{25} +(0.878534 + 3.26471i) q^{26} -1.00000i q^{27} +(2.23375 - 1.95014i) q^{28} +2.26093 q^{29} +(2.55066 - 1.47263i) q^{30} +(6.50462 - 1.74291i) q^{31} +(1.39282 + 5.19809i) q^{32} +(3.76607 + 1.00911i) q^{33} +(3.27299 - 3.27299i) q^{34} +(-6.89944 - 4.63238i) q^{35} -1.12076i q^{36} +(1.69884 - 6.34014i) q^{37} +(-1.76411 + 3.05553i) q^{38} +(-0.00387011 - 3.60555i) q^{39} +(7.96000 - 4.59571i) q^{40} +(-4.12262 - 4.12262i) q^{41} +(2.22747 - 1.09229i) q^{42} +3.84336i q^{43} +(4.22085 + 1.13097i) q^{44} +(-3.03397 + 0.812951i) q^{45} +(-6.29384 + 1.68643i) q^{46} +(-1.92757 - 0.516490i) q^{47} +0.502389i q^{48} +(-5.53438 - 4.28609i) q^{49} +(-3.22628 - 3.22628i) q^{50} +(-4.27499 + 2.46817i) q^{51} +(-0.00433746 - 4.04095i) q^{52} +(0.345564 - 0.598535i) q^{53} +(0.242689 - 0.905729i) q^{54} -12.2465i q^{55} +(6.95138 - 3.40876i) q^{56} +(2.66065 - 2.66065i) q^{57} +(2.04779 + 0.548704i) q^{58} +(3.53717 + 13.2009i) q^{59} +(-3.40035 + 0.911121i) q^{60} +(8.50811 - 4.91216i) q^{61} +6.31441 q^{62} +(-2.59606 + 0.510364i) q^{63} +6.05086i q^{64} +(-10.9360 + 2.94288i) q^{65} +(3.16614 + 1.82797i) q^{66} +(2.18828 + 8.16676i) q^{67} +(-4.79123 + 2.76622i) q^{68} +6.94892 q^{69} +(-5.12479 - 5.87010i) q^{70} +(-1.76099 + 1.76099i) q^{71} +(0.757374 - 2.82656i) q^{72} +(3.85867 + 14.4008i) q^{73} +(3.07737 - 5.33016i) q^{74} +(2.43294 + 4.21398i) q^{75} +(2.98194 - 2.98194i) q^{76} +(0.697657 - 10.2920i) q^{77} +(0.871523 - 3.26659i) q^{78} +(-2.69505 - 4.66797i) q^{79} +(1.52423 - 0.408417i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.73346 - 4.73449i) q^{82} +(6.16918 + 6.16918i) q^{83} +(-2.90955 + 0.571994i) q^{84} +(10.9637 + 10.9637i) q^{85} +(-0.932741 + 3.48104i) q^{86} +(-1.95803 - 1.13047i) q^{87} +(9.88074 + 5.70465i) q^{88} +(-7.54298 - 2.02113i) q^{89} -2.94525 q^{90} +(-9.35825 + 1.85019i) q^{91} +7.78805 q^{92} +(-6.50462 - 1.74291i) q^{93} +(-1.62051 - 0.935599i) q^{94} +(-10.2353 - 5.90936i) q^{95} +(1.39282 - 5.19809i) q^{96} +(6.07661 + 6.07661i) q^{97} +(-3.97246 - 5.22517i) q^{98} +(-2.75695 - 2.75695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{7} + 18 q^{9}+O(q^{10}) \) 36 * q - 6 * q^7 + 18 * q^9	\( 36 q - 6 q^{7} + 18 q^{9} + 4 q^{11} - 16 q^{12} - 36 q^{14} + 12 q^{16} + 4 q^{17} - 18 q^{19} + 44 q^{20} + 2 q^{21} - 8 q^{22} - 12 q^{23} - 18 q^{24} - 48 q^{25} - 32 q^{26} + 4 q^{28} - 16 q^{29} - 6 q^{31} + 76 q^{32} - 4 q^{33} - 48 q^{34} + 8 q^{35} - 8 q^{37} + 16 q^{38} + 10 q^{39} + 60 q^{40} - 32 q^{41} + 12 q^{42} + 4 q^{44} + 28 q^{46} + 14 q^{47} + 6 q^{49} - 68 q^{50} - 12 q^{51} - 62 q^{52} - 8 q^{53} - 8 q^{56} - 6 q^{57} + 36 q^{58} + 26 q^{59} - 46 q^{60} + 36 q^{61} + 48 q^{62} - 8 q^{65} - 40 q^{67} + 36 q^{68} - 8 q^{69} - 64 q^{70} - 36 q^{71} - 18 q^{72} - 8 q^{73} + 40 q^{74} + 10 q^{75} - 60 q^{76} + 60 q^{77} + 32 q^{78} + 26 q^{80} - 18 q^{81} + 24 q^{83} - 18 q^{84} + 44 q^{85} + 48 q^{86} + 36 q^{87} + 168 q^{88} + 10 q^{89} + 4 q^{91} - 40 q^{92} + 6 q^{93} + 76 q^{96} + 36 q^{97} + 38 q^{98} + 8 q^{99}+O(q^{100}) \) 36 * q - 6 * q^7 + 18 * q^9 + 4 * q^11 - 16 * q^12 - 36 * q^14 + 12 * q^16 + 4 * q^17 - 18 * q^19 + 44 * q^20 + 2 * q^21 - 8 * q^22 - 12 * q^23 - 18 * q^24 - 48 * q^25 - 32 * q^26 + 4 * q^28 - 16 * q^29 - 6 * q^31 + 76 * q^32 - 4 * q^33 - 48 * q^34 + 8 * q^35 - 8 * q^37 + 16 * q^38 + 10 * q^39 + 60 * q^40 - 32 * q^41 + 12 * q^42 + 4 * q^44 + 28 * q^46 + 14 * q^47 + 6 * q^49 - 68 * q^50 - 12 * q^51 - 62 * q^52 - 8 * q^53 - 8 * q^56 - 6 * q^57 + 36 * q^58 + 26 * q^59 - 46 * q^60 + 36 * q^61 + 48 * q^62 - 8 * q^65 - 40 * q^67 + 36 * q^68 - 8 * q^69 - 64 * q^70 - 36 * q^71 - 18 * q^72 - 8 * q^73 + 40 * q^74 + 10 * q^75 - 60 * q^76 + 60 * q^77 + 32 * q^78 + 26 * q^80 - 18 * q^81 + 24 * q^83 - 18 * q^84 + 44 * q^85 + 48 * q^86 + 36 * q^87 + 168 * q^88 + 10 * q^89 + 4 * q^91 - 40 * q^92 + 6 * q^93 + 76 * q^96 + 36 * q^97 + 38 * q^98 + 8 * q^99

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