LMFDB - Embedded newform 158.2.g.a.19.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [158,2,Mod(5,158)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("158.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(158, base_ring=CyclotomicField(78)) chi = DirichletCharacter(H, H._module([62])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 158 = 2 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	158.g (of order $39$, degree $24$, minimal)

Newform invariants

comment:select newform

sage:traces = [72,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.26163635194$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$3$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	158.19
Dual form			158.2.g.a.25.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.428693 + 0.903450i) q^{2} +(0.401101 + 1.38476i) q^{3} +(-0.632445 - 0.774605i) q^{4} +(0.137548 + 0.673754i) q^{5} +(-1.42301 - 0.231262i) q^{6} +(-3.29742 + 3.43298i) q^{7} +(0.970942 - 0.239316i) q^{8} +(0.778885 - 0.492537i) q^{9} +(-0.667669 - 0.164566i) q^{10} +(-1.75810 + 0.586939i) q^{11} +(0.818969 - 1.18648i) q^{12} +(5.08299 - 0.826067i) q^{13} +(-1.68795 - 4.45075i) q^{14} +(-0.877819 + 0.460715i) q^{15} +(-0.200026 + 0.979791i) q^{16} +(-2.03725 + 5.37178i) q^{17} +(0.111081 + 0.914831i) q^{18} +(-4.30134 - 1.83263i) q^{19} +(0.434902 - 0.532658i) q^{20} +(-6.07646 - 3.18917i) q^{21} +(0.223413 - 1.83997i) q^{22} +(3.34910 - 5.80080i) q^{23} +(0.720842 + 1.24853i) q^{24} +(4.16487 - 1.77449i) q^{25} +(-1.43273 + 4.94636i) q^{26} +(4.23180 + 3.74905i) q^{27} +(4.74464 + 0.383027i) q^{28} +(-0.155926 + 3.86927i) q^{29} +(-0.0399187 - 0.990571i) q^{30} +(7.87734 - 0.635924i) q^{31} +(-0.799443 - 0.600742i) q^{32} +(-1.51795 - 2.19912i) q^{33} +(-3.97978 - 4.14339i) q^{34} +(-2.76654 - 1.74945i) q^{35} +(-0.874124 - 0.291825i) q^{36} +(7.50680 - 5.64099i) q^{37} +(3.49964 - 3.10041i) q^{38} +(3.18270 + 6.70740i) q^{39} +(0.294791 + 0.621259i) q^{40} +(-1.56725 + 1.38846i) q^{41} +(5.48619 - 4.12261i) q^{42} +(-0.756975 - 0.252715i) q^{43} +(1.56655 + 0.990623i) q^{44} +(0.438983 + 0.457030i) q^{45} +(3.80501 + 5.51250i) q^{46} +(0.273226 + 0.205316i) q^{47} +(-1.43701 + 0.116007i) q^{48} +(-0.630497 - 15.6456i) q^{49} +(-0.182289 + 4.52346i) q^{50} +(-8.25578 - 0.666475i) q^{51} +(-3.85459 - 3.41487i) q^{52} +(-1.07003 + 3.69418i) q^{53} +(-5.20123 + 2.21604i) q^{54} +(-0.637275 - 1.10379i) q^{55} +(-2.38004 + 4.12235i) q^{56} +(0.812483 - 6.69140i) q^{57} +(-3.42885 - 1.79960i) q^{58} +(-1.67470 + 2.05113i) q^{59} +(0.912045 + 0.388586i) q^{60} +(-0.267900 - 2.20636i) q^{61} +(-2.80243 + 7.38940i) q^{62} +(-0.877442 + 4.29800i) q^{63} +(0.885456 - 0.464723i) q^{64} +(1.25572 + 3.31106i) q^{65} +(2.63753 - 0.428641i) q^{66} +(0.864153 - 1.25194i) q^{67} +(5.44945 - 1.81929i) q^{68} +(9.37606 + 2.31099i) q^{69} +(2.76654 - 1.74945i) q^{70} +(-11.0403 + 2.72119i) q^{71} +(0.638380 - 0.664624i) q^{72} +(-10.2653 - 1.66827i) q^{73} +(1.87825 + 9.20027i) q^{74} +(4.12778 + 5.05561i) q^{75} +(1.30080 + 4.49087i) q^{76} +(3.78223 - 7.97089i) q^{77} -7.42420 q^{78} +(-0.591996 - 8.86846i) q^{79} -0.687651 q^{80} +(-2.30898 + 4.86607i) q^{81} +(-0.582540 - 2.01116i) q^{82} +(0.918268 + 1.12467i) q^{83} +(1.37268 + 6.72383i) q^{84} +(-3.89948 - 0.633727i) q^{85} +(0.552825 - 0.575552i) q^{86} +(-5.42057 + 1.33605i) q^{87} +(-1.56655 + 0.990623i) q^{88} +(-12.0934 - 2.98077i) q^{89} +(-0.601092 + 0.200674i) q^{90} +(-13.9249 + 20.1737i) q^{91} +(-6.61145 + 1.07447i) q^{92} +(4.04022 + 10.6532i) q^{93} +(-0.302623 + 0.158829i) q^{94} +(0.643101 - 3.15012i) q^{95} +(0.511228 - 1.34800i) q^{96} +(1.47286 + 12.1301i) q^{97} +(14.4053 + 6.13753i) q^{98} +(-1.08027 + 1.32308i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 3 q^{2} - q^{3} + 3 q^{4} + 14 q^{5} + q^{6} - 4 q^{7} + 6 q^{8} - 2 q^{9} + 2 q^{10} + 7 q^{11} + 2 q^{12} + 23 q^{13} + 5 q^{14} - 16 q^{15} + 3 q^{16} - 58 q^{17} - 4 q^{18} + 20 q^{19} + q^{20}+ \cdots + 10 q^{99}+O(q^{100}) $ 72 * q - 3 * q^2 - q^3 + 3 * q^4 + 14 * q^5 + q^6 - 4 * q^7 + 6 * q^8 - 2 * q^9 + 2 * q^10 + 7 * q^11 + 2 * q^12 + 23 * q^13 + 5 * q^14 - 16 * q^15 + 3 * q^16 - 58 * q^17 - 4 * q^18 + 20 * q^19 + q^20 - 44 * q^21 + q^22 - 5 * q^23 - 12 * q^24 - q^25 - 23 * q^26 - 31 * q^27 - 4 * q^28 + 12 * q^29 + 31 * q^30 - 9 * q^31 - 3 * q^32 - 84 * q^33 - 3 * q^34 - 47 * q^35 - 2 * q^36 - 23 * q^37 - 12 * q^38 - 46 * q^39 - q^40 - 14 * q^41 - 87 * q^42 + 29 * q^43 - 19 * q^44 + 45 * q^45 + 16 * q^46 - 35 * q^47 - q^48 - 27 * q^49 - 38 * q^50 + 53 * q^51 + 6 * q^52 - 46 * q^53 + 43 * q^54 - 4 * q^55 - 22 * q^56 + 24 * q^58 - 34 * q^59 - 83 * q^60 + 93 * q^61 - 31 * q^62 - 51 * q^63 - 6 * q^64 + 100 * q^65 + 88 * q^66 - 14 * q^67 + 29 * q^68 - 36 * q^69 + 47 * q^70 + 26 * q^71 + 2 * q^72 + 37 * q^73 + 49 * q^74 + 123 * q^75 + 33 * q^76 + 28 * q^77 + 12 * q^78 + 142 * q^79 - 2 * q^80 + 229 * q^81 + 84 * q^82 + 4 * q^83 + 113 * q^84 + 49 * q^85 + 49 * q^86 - 161 * q^87 + 19 * q^88 - 2 * q^89 - 19 * q^90 + 117 * q^91 + 21 * q^92 + 64 * q^93 - 44 * q^94 + 80 * q^95 - 2 * q^96 - 38 * q^97 - 64 * q^98 + 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/158\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{16}{39}\right)$

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 $

$2$	−0.428693	+	0.903450i	−0.303131	+	0.638836i
$2$	−0.428693	+	0.903450i	−0.303131	+	0.638836i
$3$	0.401101	+	1.38476i	0.231576	+	0.799493i	0.989171	+	0.146768i	$0.0468871\pi$
$3$	0.401101	+	1.38476i	0.231576	+	0.799493i	−0.757595	+	0.652725i	$0.773626\pi$
$4$	−0.632445	−	0.774605i	−0.316223	−	0.387302i
$5$	0.137548	+	0.673754i	0.0615133	+	0.301312i	0.998895	−	0.0469909i	$-0.0149632\pi$
$5$	0.137548	+	0.673754i	0.0615133	+	0.301312i	−0.937382	+	0.348303i	$0.886758\pi$
$6$	−1.42301	−	0.231262i	−0.580943	−	0.0944124i
$7$	−3.29742	+	3.43298i	−1.24631	+	1.29754i	−0.308149	+	0.951338i	$0.599709\pi$
$7$	−3.29742	+	3.43298i	−1.24631	+	1.29754i	−0.938159	+	0.346205i	$0.887470\pi$
$8$	0.970942	−	0.239316i	0.343280	−	0.0846109i
$9$	0.778885	−	0.492537i	0.259628	−	0.164179i
$10$	−0.667669	−	0.164566i	−0.211136	−	0.0520403i
$11$	−1.75810	+	0.586939i	−0.530086	+	0.176969i	−0.569097	−	0.822270i	$-0.692707\pi$
$11$	−1.75810	+	0.586939i	−0.530086	+	0.176969i	0.0390116	+	0.999239i	$0.487579\pi$
$12$	0.818969	−	1.18648i	0.236416	−	0.342508i
$13$	5.08299	−	0.826067i	1.40977	−	0.229110i	0.592594	−	0.805501i	$-0.298104\pi$
$13$	5.08299	−	0.826067i	1.40977	−	0.229110i	0.817174	+	0.576391i	$0.195540\pi$
$14$	−1.68795	−	4.45075i	−0.451122	−	1.18951i
$15$	−0.877819	+	0.460715i	−0.226652	+	0.118956i
$16$	−0.200026	+	0.979791i	−0.0500064	+	0.244948i
$17$	−2.03725	+	5.37178i	−0.494105	+	1.30285i	0.423696	+	0.905805i	$0.360733\pi$
$17$	−2.03725	+	5.37178i	−0.494105	+	1.30285i	−0.917800	+	0.397042i	$0.870037\pi$
$18$	0.111081	+	0.914831i	0.0261819	+	0.215628i
$19$	−4.30134	−	1.83263i	−0.986794	−	0.420434i	−0.162570	−	0.986697i	$-0.551978\pi$
$19$	−4.30134	−	1.83263i	−0.986794	−	0.420434i	−0.824224	+	0.566263i	$0.808389\pi$
$20$	0.434902	−	0.532658i	0.0972470	−	0.119106i
$21$	−6.07646	−	3.18917i	−1.32599	−	0.695934i
$22$	0.223413	−	1.83997i	0.0476317	−	0.392283i
$23$	3.34910	−	5.80080i	0.698335	−	1.20955i	−0.270709	−	0.962661i	$-0.587258\pi$
$23$	3.34910	−	5.80080i	0.698335	−	1.20955i	0.969044	−	0.246890i	$-0.0794086\pi$
$24$	0.720842	+	1.24853i	0.147141	+	0.254856i
$25$	4.16487	−	1.77449i	0.832974	−	0.354897i
$26$	−1.43273	+	4.94636i	−0.280982	+	0.970061i
$27$	4.23180	+	3.74905i	0.814411	+	0.721505i
$28$	4.74464	+	0.383027i	0.896652	+	0.0723853i
$29$	−0.155926	+	3.86927i	−0.0289548	+	0.718506i	0.917894	+	0.396826i	$0.129888\pi$
$29$	−0.155926	+	3.86927i	−0.0289548	+	0.718506i	−0.946849	+	0.321680i	$0.895753\pi$
$30$	−0.0399187	−	0.990571i	−0.00728812	−	0.180853i
$31$	7.87734	−	0.635924i	1.41481	−	0.114215i	0.650717	−	0.759320i	$-0.274468\pi$
$31$	7.87734	−	0.635924i	1.41481	−	0.114215i	0.764094	+	0.645105i	$0.223186\pi$
$32$	−0.799443	−	0.600742i	−0.141323	−	0.106197i
$33$	−1.51795	−	2.19912i	−0.264240	−	0.382818i
$34$	−3.97978	−	4.14339i	−0.682527	−	0.710586i
$35$	−2.76654	−	1.74945i	−0.467630	−	0.295711i
$36$	−0.874124	−	0.291825i	−0.145687	−	0.0486376i
$37$	7.50680	−	5.64099i	1.23411	−	0.927373i	0.235105	−	0.971970i	$-0.424457\pi$
$37$	7.50680	−	5.64099i	1.23411	−	0.927373i	0.999005	+	0.0445967i	$0.0142003\pi$
$38$	3.49964	−	3.10041i	0.567717	−	0.502953i
$39$	3.18270	+	6.70740i	0.509640	+	1.07404i
$40$	0.294791	+	0.621259i	0.0466106	+	0.0982297i
$41$	−1.56725	+	1.38846i	−0.244764	+	0.216842i	−0.776581	−	0.630017i	$-0.783048\pi$
$41$	−1.56725	+	1.38846i	−0.244764	+	0.216842i	0.531817	+	0.846859i	$0.321509\pi$
$42$	5.48619	−	4.12261i	0.846538	−	0.636132i
$43$	−0.756975	−	0.252715i	−0.115438	−	0.0385387i	0.258362	−	0.966048i	$-0.416817\pi$
$43$	−0.756975	−	0.252715i	−0.115438	−	0.0385387i	−0.373800	+	0.927509i	$0.621945\pi$
$44$	1.56655	+	0.990623i	0.236166	+	0.149342i
$45$	0.438983	+	0.457030i	0.0654397	+	0.0681300i
$46$	3.80501	+	5.51250i	0.561017	+	0.812774i
$47$	0.273226	+	0.205316i	0.0398542	+	0.0299485i	0.620483	−	0.784220i	$-0.286937\pi$
$47$	0.273226	+	0.205316i	0.0398542	+	0.0299485i	−0.580629	+	0.814169i	$0.697193\pi$
$48$	−1.43701	+	0.116007i	−0.207414	+	0.0167442i
$49$	−0.630497	−	15.6456i	−0.0900709	−	2.23509i
$50$	−0.182289	+	4.52346i	−0.0257796	+	0.639714i
$51$	−8.25578	−	0.666475i	−1.15604	−	0.0933252i
$52$	−3.85459	−	3.41487i	−0.534535	−	0.473557i
$53$	−1.07003	+	3.69418i	−0.146980	+	0.507435i	−0.999893	−	0.0146186i	$-0.995347\pi$
$53$	−1.07003	+	3.69418i	−0.146980	+	0.507435i	0.852913	+	0.522053i	$0.174834\pi$
$54$	−5.20123	+	2.21604i	−0.707797	+	0.301564i
$55$	−0.637275	−	1.10379i	−0.0859301	−	0.148835i
$56$	−2.38004	+	4.12235i	−0.318046	+	0.550872i
$57$	0.812483	−	6.69140i	0.107616	−	0.886298i
$58$	−3.42885	−	1.79960i	−0.450230	−	0.236299i
$59$	−1.67470	+	2.05113i	−0.218027	+	0.267035i	−0.872025	−	0.489462i	$-0.837193\pi$
$59$	−1.67470	+	2.05113i	−0.218027	+	0.267035i	0.653998	+	0.756497i	$0.273091\pi$
$60$	0.912045	+	0.388586i	0.117744	+	0.0501662i
$61$	−0.267900	−	2.20636i	−0.0343011	−	0.282495i	−0.999759	−	0.0219373i	$-0.993017\pi$
$61$	−0.267900	−	2.20636i	−0.0343011	−	0.282495i	0.965458	−	0.260558i	$-0.0839065\pi$
$62$	−2.80243	+	7.38940i	−0.355909	+	0.938455i
$63$	−0.877442	+	4.29800i	−0.110547	+	0.541496i
$64$	0.885456	−	0.464723i	0.110682	−	0.0580904i
$65$	1.25572	+	3.31106i	0.155753	+	0.410687i
$66$	2.63753	−	0.428641i	0.324658	−	0.0527620i
$67$	0.864153	−	1.25194i	0.105573	−	0.152949i	−0.766636	−	0.642081i	$-0.778071\pi$
$67$	0.864153	−	1.25194i	0.105573	−	0.152949i	0.872210	+	0.489132i	$0.162686\pi$
$68$	5.44945	−	1.81929i	0.660843	−	0.220622i
$69$	9.37606	+	2.31099i	1.12875	+	0.278211i
$70$	2.76654	−	1.74945i	0.330664	−	0.209099i
$71$	−11.0403	+	2.72119i	−1.31024	+	0.322946i	−0.831753	−	0.555146i	$-0.812662\pi$
$71$	−11.0403	+	2.72119i	−1.31024	+	0.322946i	−0.478491	+	0.878092i	$0.658816\pi$
$72$	0.638380	−	0.664624i	0.0752338	−	0.0783267i
$73$	−10.2653	−	1.66827i	−1.20146	−	0.195256i	−0.473448	−	0.880822i	$-0.656991\pi$
$73$	−10.2653	−	1.66827i	−1.20146	−	0.195256i	−0.728011	+	0.685566i	$0.759555\pi$
$74$	1.87825	+	9.20027i	0.218342	+	1.06951i
$75$	4.12778	+	5.05561i	0.476635	+	0.583772i
$76$	1.30080	+	4.49087i	0.149212	+	0.515139i
$77$	3.78223	−	7.97089i	0.431025	−	0.908367i
$78$	−7.42420			−0.840626
$79$	−0.591996	−	8.86846i	−0.0666048	−	0.997779i
$79$	−0.591996	−	8.86846i	−0.0666048	−	0.997779i
$80$	−0.687651			−0.0768818
$81$	−2.30898	+	4.86607i	−0.256553	+	0.540675i
$82$	−0.582540	−	2.01116i	−0.0643307	−	0.222095i
$83$	0.918268	+	1.12467i	0.100793	+	0.123449i	0.822538	−	0.568710i	$-0.192557\pi$
$83$	0.918268	+	1.12467i	0.100793	+	0.123449i	−0.721745	+	0.692159i	$0.756660\pi$
$84$	1.37268	+	6.72383i	0.149772	+	0.733630i
$85$	−3.89948	−	0.633727i	−0.422958	−	0.0687373i
$86$	0.552825	−	0.575552i	0.0596127	−	0.0620634i
$87$	−5.42057	+	1.33605i	−0.581146	+	0.143240i
$88$	−1.56655	+	0.990623i	−0.166994	+	0.105601i
$89$	−12.0934	−	2.98077i	−1.28190	−	0.315961i	−0.461190	−	0.887302i	$-0.652577\pi$
$89$	−12.0934	−	2.98077i	−1.28190	−	0.315961i	−0.820713	+	0.571341i	$0.806423\pi$
$90$	−0.601092	+	0.200674i	−0.0633607	+	0.0211529i
$91$	−13.9249	+	20.1737i	−1.45972	+	2.11478i
$92$	−6.61145	+	1.07447i	−0.689291	+	0.112021i
$93$	4.04022	+	10.6532i	0.418951	+	1.10468i
$94$	−0.302623	+	0.158829i	−0.0312132	+	0.0163819i
$95$	0.643101	−	3.15012i	0.0659808	−	0.323195i
$96$	0.511228	−	1.34800i	0.0521770	−	0.137579i
$97$	1.47286	+	12.1301i	0.149546	+	1.23162i	0.853393	+	0.521269i	$0.174541\pi$
$97$	1.47286	+	12.1301i	0.149546	+	1.23162i	−0.703847	+	0.710352i	$0.748536\pi$
$98$	14.4053	+	6.13753i	1.45516	+	0.619985i
$99$	−1.08027	+	1.32308i	−0.108571	+	0.132975i
$100$	−4.00858	−	2.10386i	−0.400858	−	0.210386i
$101$	1.84693	−	15.2109i	0.183777	−	1.51354i	−0.550584	−	0.834780i	$-0.685595\pi$
$101$	1.84693	−	15.2109i	0.183777	−	1.51354i	0.734361	−	0.678759i	$-0.237482\pi$
$102$	4.14132	−	7.17297i	0.410052	−	0.710230i
$103$	1.06734	+	1.84868i	0.105168	+	0.182156i	0.913807	−	0.406149i	$-0.133129\pi$
$103$	1.06734	+	1.84868i	0.105168	+	0.182156i	−0.808639	+	0.588305i	$0.799795\pi$
$104$	4.73760	−	2.01850i	0.464560	−	0.197930i
$105$	1.31291	−	4.53270i	0.128127	−	0.442347i
$106$	−2.87879	−	2.55039i	−0.279613	−	0.247716i
$107$	11.5863	+	0.935340i	1.12009	+	0.0904227i	0.626608	−	0.779335i	$-0.284443\pi$
$107$	11.5863	+	0.935340i	1.12009	+	0.0904227i	0.493479	+	0.869758i	$0.335725\pi$
$108$	0.227649	−	5.64905i	0.0219055	−	0.543580i
$109$	−0.152560	−	3.78575i	−0.0146126	−	0.362609i	−0.989909	−	0.141707i	$-0.954741\pi$
$109$	−0.152560	−	3.78575i	−0.0146126	−	0.362609i	0.975296	−	0.220902i	$-0.0709001\pi$
$110$	1.27042	−	0.102559i	0.121129	−	0.00977858i
$111$	10.8224	+	8.13252i	1.02722	+	0.771905i
$112$	−2.70403	−	3.91746i	−0.255507	−	0.370166i
$113$	−3.44697	−	3.58867i	−0.324263	−	0.337594i	0.539039	−	0.842281i	$-0.318787\pi$
$113$	−3.44697	−	3.58867i	−0.324263	−	0.337594i	−0.863302	+	0.504687i	$0.831608\pi$
$114$	5.69704	+	3.60259i	0.533577	+	0.337414i
$115$	4.36898	+	1.45858i	0.407409	+	0.136013i
$116$	3.09577	−	2.32632i	0.287435	−	0.215994i
$117$	3.55220	−	3.14697i	0.328401	−	0.290938i
$118$	−1.13517	−	2.39231i	−0.104500	−	0.220230i
$119$	−11.7235	−	24.7068i	−1.07469	−	2.26487i
$120$	−0.742055	+	0.657403i	−0.0677400	+	0.0600124i
$121$	−6.04747	+	4.54438i	−0.549770	+	0.413125i
$122$	2.10818	+	0.703815i	0.190866	+	0.0637204i
$123$	−2.55132	−	1.61336i	−0.230045	−	0.145472i
$124$	−5.47458	−	5.69964i	−0.491631	−	0.511842i
$125$	3.72159	+	5.39165i	0.332869	+	0.482244i
$126$	−3.50687	−	2.63524i	−0.312417	−	0.234766i
$127$	7.75215	−	0.625818i	0.687892	−	0.0555324i	0.268422	−	0.963301i	$-0.413498\pi$
$127$	7.75215	−	0.625818i	0.687892	−	0.0555324i	0.419470	+	0.907769i	$0.362216\pi$
$128$	0.0402659	+	0.999189i	0.00355904	+	0.0883167i
$129$	0.0463271	−	1.14960i	0.00407887	−	0.101216i
$130$	−3.52970	−	0.284947i	−0.309575	−	0.0249915i
$131$	10.2251	+	9.05864i	0.893370	+	0.791457i	0.978785	−	0.204888i	$-0.0656831\pi$
$131$	10.2251	+	9.05864i	0.893370	+	0.791457i	−0.0854149	+	0.996345i	$0.527222\pi$
$132$	−0.743435	+	2.56663i	−0.0647077	+	0.223397i
$133$	20.4747	−	8.72345i	1.77538	−	0.756419i
$134$	0.760612	+	1.31742i	0.0657068	+	0.113808i
$135$	−1.94386	+	3.36687i	−0.167301	+	0.289774i
$136$	−0.692497	+	5.70323i	−0.0593811	+	0.489048i
$137$	−14.7024	−	7.71639i	−1.25611	−	0.659256i	−0.300467	−	0.953792i	$-0.597142\pi$
$137$	−14.7024	−	7.71639i	−1.25611	−	0.659256i	−0.955640	+	0.294536i	$0.904835\pi$
$138$	−6.10731	+	7.48010i	−0.519889	+	0.636749i
$139$	−1.26636	−	0.539546i	−0.107411	−	0.0457637i	0.337592	−	0.941292i	$-0.390387\pi$
$139$	−1.26636	−	0.539546i	−0.107411	−	0.0457637i	−0.445004	+	0.895529i	$0.646798\pi$
$140$	0.394549	+	3.24941i	0.0333455	+	0.274625i
$141$	−0.174723	+	0.460706i	−0.0147143	+	0.0387985i
$142$	2.27444	−	11.1409i	0.190867	−	0.934926i
$143$	−8.45154	+	4.43571i	−0.706753	+	0.370933i
$144$	0.326786	+	0.861664i	0.0272322	+	0.0718053i
$145$	−2.62839	+	0.427154i	−0.218276	+	0.0354732i
$146$	5.90784	−	8.55899i	0.488937	−	0.708347i
$147$	21.4126	−	7.14856i	1.76608	−	0.589604i
$148$	−9.11718	−	2.24718i	−0.749428	−	0.184717i
$149$	6.65117	−	4.20595i	0.544885	−	0.344565i	−0.233495	−	0.972358i	$-0.575016\pi$
$149$	6.65117	−	4.20595i	0.544885	−	0.344565i	0.778380	+	0.627793i	$0.216042\pi$
$150$	−6.33704	+	1.56194i	−0.517417	+	0.127532i
$151$	6.92417	−	7.20883i	0.563481	−	0.586646i	−0.377118	−	0.926165i	$-0.623085\pi$
$151$	6.92417	−	7.20883i	0.563481	−	0.586646i	0.940599	+	0.339519i	$0.110264\pi$
$152$	−4.61492	−	0.749998i	−0.374320	−	0.0608329i
$153$	1.05902	+	5.18741i	0.0856165	+	0.419378i
$154$	5.57989	+	6.83412i	0.449640	+	0.550709i
$155$	1.51197	+	5.21992i	0.121444	+	0.419274i
$156$	3.18270	−	6.70740i	0.254820	−	0.537022i
$157$	−0.423654			−0.0338113			−0.0169056	−	0.999857i	$-0.505381\pi$
$157$	−0.423654			−0.0338113			−0.0169056	+	0.999857i	$0.505381\pi$
$158$	8.26600	+	3.26700i	0.657607	+	0.259909i
$159$	−5.54475			−0.439728
$160$	0.294791	−	0.621259i	0.0233053	−	0.0491148i
$161$	8.87065	+	30.6250i	0.699105	+	2.41359i
$162$	−3.40641	−	4.17210i	−0.267633	−	0.327791i
$163$	−2.34705	−	11.4966i	−0.183835	−	0.900485i	−0.962131	−	0.272587i	$-0.912121\pi$
$163$	−2.34705	−	11.4966i	−0.183835	−	0.900485i	0.778296	−	0.627898i	$-0.216084\pi$
$164$	2.06671	+	0.335874i	0.161383	+	0.0262273i
$165$	1.27288	−	1.32521i	0.0990935	−	0.103167i
$166$	−1.40974	+	0.347470i	−0.109417	+	0.0269689i
$167$	3.75998	−	2.37766i	0.290956	−	0.183989i	−0.381011	−	0.924570i	$-0.624424\pi$
$167$	3.75998	−	2.37766i	0.290956	−	0.183989i	0.671967	+	0.740581i	$0.265450\pi$
$168$	−6.66311	−	1.64231i	−0.514070	−	0.126707i
$169$	12.8234	−	4.28110i	0.986419	−	0.329315i
$170$	2.24422	−	3.25131i	0.172124	−	0.249364i
$171$	−4.25288	+	0.691161i	−0.325226	+	0.0528544i
$172$	0.282991	+	0.746185i	0.0215778	+	0.0568961i
$173$	−5.69268	+	2.98775i	−0.432807	+	0.227155i	−0.667034	−	0.745027i	$-0.732436\pi$
$173$	−5.69268	+	2.98775i	−0.432807	+	0.227155i	0.234227	+	0.972182i	$0.424744\pi$
$174$	1.11670	−	5.46997i	0.0846569	−	0.414677i
$175$	−7.64156	+	20.1491i	−0.577648	+	1.52313i
$176$	−0.223413	−	1.83997i	−0.0168404	−	0.138693i
$177$	−3.51205	−	1.49635i	−0.263982	−	0.112472i
$178$	7.87734	−	9.64799i	0.590432	−	0.723148i
$179$	18.4877	+	9.70311i	1.38184	+	0.725244i	0.981561	−	0.191150i	$-0.0612217\pi$
$179$	18.4877	+	9.70311i	1.38184	+	0.725244i	0.400277	+	0.916394i	$0.368914\pi$
$180$	0.0763847	−	0.629085i	0.00569338	−	0.0468892i
$181$	−5.29501	+	9.17122i	−0.393575	+	0.681691i	−0.992918	−	0.118801i	$-0.962095\pi$
$181$	−5.29501	+	9.17122i	−0.393575	+	0.681691i	0.599343	+	0.800492i	$0.295428\pi$
$182$	−12.2564	−	21.2288i	−0.908507	−	1.57358i
$183$	2.94783	−	1.25595i	0.217910	−	0.0928426i
$184$	1.86355	−	6.43373i	0.137383	−	0.474301i
$185$	4.83319	+	4.28183i	0.355343	+	0.314806i
$186$	−11.3566	−	0.916801i	−0.832708	−	0.0672231i
$187$	0.428771	−	10.6398i	0.0313548	−	0.778062i
$188$	−0.0137617	−	0.341494i	−0.00100368	−	0.0249060i
$189$	−26.8244	+	2.16549i	−1.95119	+	0.157516i
$190$	2.57028	+	1.93144i	0.186468	+	0.140122i
$191$	−11.6005	−	16.8063i	−0.839386	−	1.21606i	−0.974311	−	0.225205i	$-0.927695\pi$
$191$	−11.6005	−	16.8063i	−0.839386	−	1.21606i	0.134925	−	0.990856i	$-0.456921\pi$
$192$	0.998689	+	1.03975i	0.0720742	+	0.0750372i
$193$	0.0782808	+	0.0495017i	0.00563477	+	0.00356321i	0.537280	−	0.843404i	$-0.319452\pi$
$193$	0.0782808	+	0.0495017i	0.00563477	+	0.00356321i	−0.531645	+	0.846967i	$0.678426\pi$
$194$	−11.5903	−	3.86941i	−0.832136	−	0.277808i
$195$	−4.08137	+	3.06695i	−0.292273	+	0.219629i
$196$	−11.7204	+	10.3834i	−0.837172	+	0.741670i
$197$	−0.704299	−	1.48428i	−0.0501792	−	0.105750i	0.876812	−	0.480833i	$-0.159666\pi$
$197$	−0.704299	−	1.48428i	−0.0501792	−	0.105750i	−0.926991	+	0.375083i	$0.877614\pi$
$198$	−0.732240	−	1.54316i	−0.0520380	−	0.109668i
$199$	12.7906	−	11.3315i	0.906704	−	0.803270i	−0.0743043	−	0.997236i	$-0.523674\pi$
$199$	12.7906	−	11.3315i	0.906704	−	0.803270i	0.981008	+	0.193966i	$0.0621351\pi$
$200$	3.61919	−	2.71964i	0.255915	−	0.192308i
$201$	2.08026	+	0.694492i	0.146730	+	0.0489857i
$202$	12.9505	+	8.18940i	0.911194	+	0.576204i
$203$	−12.7690	−	13.2939i	−0.896206	−	0.933049i
$204$	4.70507	+	6.81647i	0.329421	+	0.477249i
$205$	−1.15106	−	0.864963i	−0.0803933	−	0.0604116i
$206$	−2.12775	+	0.171770i	−0.148248	+	0.0119678i
$207$	−0.248550	−	6.16771i	−0.0172754	−	0.428686i
$208$	−0.207357	+	5.14550i	−0.0143776	+	0.356776i
$209$	8.63780	+	0.697316i	0.597489	+	0.0482343i
$210$	3.53224	+	3.12929i	0.243748	+	0.215941i
$211$	1.01826	−	3.51546i	0.0701002	−	0.242014i	−0.917815	−	0.397008i	$-0.870049\pi$
$211$	1.01826	−	3.51546i	0.0701002	−	0.242014i	0.987915	+	0.154994i	$0.0495358\pi$
$212$	3.53827	−	1.50751i	0.243009	−	0.103537i
$213$	−8.19649	−	14.1967i	−0.561614	−	0.972745i
$214$	−5.81198	+	10.0666i	−0.397299	+	0.688142i
$215$	0.0661477	−	0.544776i	0.00451124	−	0.0371534i
$216$	5.00604	+	2.62737i	0.340618	+	0.178770i
$217$	−23.7918	+	29.1396i	−1.61509	+	1.97813i
$218$	3.48564	+	1.48509i	0.236077	+	0.100583i
$219$	−1.80726	−	14.8841i	−0.122123	−	1.00577i
$220$	−0.451962	+	1.19172i	−0.0304712	+	0.0803461i
$221$	−5.91786	+	28.9876i	−0.398078	+	1.94992i
$222$	−11.9868	+	6.29117i	−0.804503	+	0.422236i
$223$	6.00929	+	15.8452i	0.402412	+	1.06107i	0.971132	+	0.238542i	$0.0766694\pi$
$223$	6.00929	+	15.8452i	0.402412	+	1.06107i	−0.568720	+	0.822531i	$0.692561\pi$
$224$	4.69843	−	0.763570i	0.313927	−	0.0510181i
$225$	2.36996	−	3.43347i	0.157997	−	0.228898i
$226$	4.71988	−	1.57573i	0.313961	−	0.104816i
$227$	−4.93502	−	1.21637i	−0.327549	−	0.0807335i	0.0721122	−	0.997397i	$-0.477026\pi$
$227$	−4.93502	−	1.21637i	−0.327549	−	0.0807335i	−0.399661	+	0.916663i	$0.630872\pi$
$228$	−5.69704	+	3.60259i	−0.377296	+	0.238587i
$229$	9.91588	−	2.44404i	0.655260	−	0.161507i	0.102350	−	0.994748i	$-0.467364\pi$
$229$	9.91588	−	2.44404i	0.655260	−	0.161507i	0.552909	+	0.833241i	$0.313518\pi$
$230$	−3.19070	+	3.32187i	−0.210389	+	0.219038i
$231$	12.5548	+	2.04036i	0.826048	+	0.134246i
$232$	0.774582	+	3.79415i	0.0508538	+	0.249098i
$233$	−7.23513	−	8.86143i	−0.473989	−	0.580531i	0.481169	−	0.876628i	$-0.340212\pi$
$233$	−7.23513	−	8.86143i	−0.473989	−	0.580531i	−0.955158	+	0.296097i	$0.904315\pi$
$234$	1.32033	+	4.55832i	0.0863129	+	0.297987i
$235$	−0.100751	+	0.212328i	−0.00657227	+	0.0138508i
$236$	2.64797			0.172368
$237$	12.0433	−	4.37692i	0.782294	−	0.284312i
$238$	27.3472			1.77265
$239$	−10.2474	+	21.5960i	−0.662851	+	1.39693i	0.241610	+	0.970373i	$0.422324\pi$
$239$	−10.2474	+	21.5960i	−0.662851	+	1.39693i	−0.904461	+	0.426556i	$0.859727\pi$
$240$	−0.275818	−	0.952234i	−0.0178040	−	0.0614664i
$241$	15.2958	+	18.7340i	0.985290	+	1.20676i	0.978387	+	0.206784i	$0.0662999\pi$
$241$	15.2958	+	18.7340i	0.985290	+	1.20676i	0.00690302	+	0.999976i	$0.497803\pi$
$242$	−1.51311	−	7.41173i	−0.0972667	−	0.476444i
$243$	9.07677	+	1.47512i	0.582275	+	0.0946289i
$244$	−1.53962	+	1.60292i	−0.0985643	+	0.102616i
$245$	10.4546	−	2.57682i	0.667918	−	0.164627i
$246$	2.55132	−	1.61336i	0.162666	−	0.102864i
$247$	−23.3775	−	5.76204i	−1.48748	−	0.366630i
$248$	7.49625	−	2.50262i	0.476012	−	0.158916i
$249$	−1.18909	+	1.72269i	−0.0753554	+	0.109171i
$250$	−6.46651	+	1.05091i	−0.408978	+	0.0664654i
$251$	−6.90264	−	18.2008i	−0.435691	−	1.14882i	−0.955617	−	0.294612i	$-0.904810\pi$
$251$	−6.90264	−	18.2008i	−0.435691	−	1.14882i	0.519926	−	0.854211i	$-0.325959\pi$
$252$	3.88418	−	2.03858i	0.244680	−	0.128418i
$253$	−2.48331	+	12.1641i	−0.156125	+	0.764749i
$254$	−2.75789	+	7.27197i	−0.173046	+	0.456284i
$255$	−0.686524	−	5.65404i	−0.0429918	−	0.354070i
$256$	−0.919979	−	0.391967i	−0.0574987	−	0.0244979i
$257$	7.25962	−	8.89142i	0.452843	−	0.554632i	−0.496841	−	0.867841i	$-0.665507\pi$
$257$	7.25962	−	8.89142i	0.452843	−	0.554632i	0.949684	+	0.313210i	$0.101404\pi$
$258$	1.01874	+	0.534677i	0.0634241	+	0.0332875i
$259$	−5.38766	+	44.3714i	−0.334773	+	2.75710i
$260$	1.77059	−	3.06675i	0.109807	−	0.190192i
$261$	1.78431	+	3.09052i	0.110446	+	0.191298i
$262$	−12.5675	+	5.35449i	−0.776420	+	0.330802i
$263$	−1.30846	+	4.51732i	−0.0806829	+	0.278550i	−0.990709	−	0.136002i	$-0.956575\pi$
$263$	−1.30846	+	4.51732i	−0.0806829	+	0.278550i	0.910026	+	0.414552i	$0.136062\pi$
$264$	−2.00012	−	1.77195i	−0.123099	−	0.109056i
$265$	−2.63615	−	0.212812i	−0.161937	−	0.0130729i
$266$	−0.896142	+	22.2375i	−0.0549460	+	1.36347i
$267$	−0.723043	−	17.9421i	−0.0442495	−	1.09804i
$268$	−1.51629	+	0.122408i	−0.0926222	+	0.00747724i
$269$	25.1193	+	18.8760i	1.53155	+	1.15089i	0.938276	+	0.345889i	$0.112423\pi$
$269$	25.1193	+	18.8760i	1.53155	+	1.15089i	0.593277	+	0.804998i	$0.297834\pi$
$270$	−2.20848	−	3.19954i	−0.134404	−	0.194718i
$271$	−17.7631	−	18.4934i	−1.07903	−	1.12339i	−0.991878	−	0.127197i	$-0.959402\pi$
$271$	−17.7631	−	18.4934i	−1.07903	−	1.12339i	−0.0871547	−	0.996195i	$-0.527777\pi$
$272$	−4.85571	−	3.07057i	−0.294421	−	0.186181i
$273$	−33.5211	−	11.1910i	−2.02879	−	0.677309i
$274$	13.2742	−	9.97489i	0.801922	−	0.602605i
$275$	−6.28073	+	5.56424i	−0.378742	+	0.335536i
$276$	−4.13974	−	8.72432i	−0.249183	−	0.525142i
$277$	8.30356	+	17.4994i	0.498912	+	1.05144i	0.984197	+	0.177079i	$0.0566648\pi$
$277$	8.30356	+	17.4994i	0.498912	+	1.05144i	−0.485284	+	0.874356i	$0.661284\pi$
$278$	1.03033	−	0.912796i	0.0617953	−	0.0547459i
$279$	5.82232	−	4.37519i	0.348573	−	0.261936i
$280$	−3.10482	−	1.03654i	−0.185548	−	0.0619451i
$281$	−14.3055	−	9.04625i	−0.853395	−	0.539654i	0.0346562	−	0.999399i	$-0.488966\pi$
$281$	−14.3055	−	9.04625i	−0.853395	−	0.539654i	−0.888051	+	0.459745i	$0.847941\pi$
$282$	−0.341323	−	0.355355i	−0.0203255	−	0.0211611i
$283$	−0.904018	−	1.30970i	−0.0537383	−	0.0778534i	0.795194	−	0.606356i	$-0.207369\pi$
$283$	−0.904018	−	1.30970i	−0.0537383	−	0.0778534i	−0.848932	+	0.528502i	$0.822754\pi$
$284$	9.09025	+	6.83088i	0.539407	+	0.405338i
$285$	4.62012	−	0.372974i	0.273672	−	0.0220931i
$286$	−0.384332	−	9.53710i	−0.0227260	−	0.563941i
$287$	0.401322	−	9.95870i	0.0236893	−	0.587843i
$288$	−0.918562	−	0.0741540i	−0.0541268	−	0.00436956i
$289$	−11.9809	−	10.6142i	−0.704760	−	0.624363i
$290$	0.740857	−	2.55773i	0.0435046	−	0.150195i
$291$	−16.2065	+	6.90494i	−0.950041	+	0.404775i
$292$	5.19997	+	9.00662i	0.304305	+	0.527072i
$293$	7.25629	−	12.5683i	0.423917	−	0.734245i	−0.572402	−	0.819973i	$-0.693988\pi$
$293$	7.25629	−	12.5683i	0.423917	−	0.734245i	0.996319	+	0.0857278i	$0.0273216\pi$
$294$	−2.72103	+	22.4097i	−0.158694	+	1.30696i
$295$	−1.61231	−	0.846206i	−0.0938723	−	0.0492680i
$296$	5.93869	−	7.27357i	0.345179	−	0.422768i
$297$	−9.64038	−	4.10738i	−0.559392	−	0.238335i
$298$	0.948556	+	7.81206i	0.0549484	+	0.452541i
$299$	12.2316	−	32.2520i	0.707370	−	1.86518i
$300$	1.30551	−	6.39479i	0.0753735	−	0.369204i
$301$	3.36363	−	1.76537i	0.193876	−	0.101754i
$302$	3.54448	+	9.34602i	0.203962	+	0.537803i
$303$	21.8043	−	3.54354i	1.25262	−	0.203571i
$304$	2.65597	−	3.84784i	0.152330	−	0.220689i
$305$	1.44969	−	0.483979i	0.0830093	−	0.0277126i
$306$	−5.14056	−	1.26704i	−0.293867	−	0.0724316i
$307$	9.11577	−	5.76446i	0.520264	−	0.328995i	−0.248390	−	0.968660i	$-0.579901\pi$
$307$	9.11577	−	5.76446i	0.520264	−	0.328995i	0.768654	+	0.639665i	$0.220927\pi$
$308$	−8.56634	+	2.11141i	−0.488113	+	0.120309i
$309$	−2.13188	+	2.21952i	−0.121278	+	0.126264i
$310$	−5.36411	−	0.871752i	−0.304661	−	0.0495122i
$311$	−2.82523	−	13.8389i	−0.160204	−	0.784731i	−0.977899	−	0.209079i	$-0.932953\pi$
$311$	−2.82523	−	13.8389i	−0.160204	−	0.784731i	0.817695	−	0.575652i	$-0.195252\pi$
$312$	4.69540	+	5.75083i	0.265825	+	0.325576i
$313$	−4.24827	−	14.6667i	−0.240127	−	0.829013i	−0.986539	−	0.163529i	$-0.947712\pi$
$313$	−4.24827	−	14.6667i	−0.240127	−	0.829013i	0.746412	−	0.665484i	$-0.231775\pi$
$314$	0.181617	−	0.382750i	0.0102493	−	0.0215998i
$315$	−3.01648			−0.169960
$316$	−6.49515	+	6.06738i	−0.365381	+	0.341317i
$317$	13.5801			0.762736			0.381368	−	0.924423i	$-0.375453\pi$
$317$	13.5801			0.762736			0.381368	+	0.924423i	$0.375453\pi$
$318$	2.37699	−	5.00941i	0.133295	−	0.280914i
$319$	−1.99689	−	6.89407i	−0.111804	−	0.385994i
$320$	0.434902	+	0.532658i	0.0243118	+	0.0297765i
$321$	3.35204	+	16.4194i	0.187093	+	0.916441i
$322$	−31.4710	−	5.11453i	−1.75381	−	0.285022i
$323$	18.6073	−	19.3723i	1.03534	−	1.07790i
$324$	5.22959	−	1.28898i	0.290533	−	0.0716098i
$325$	19.7042	−	12.4602i	1.09299	−	0.691165i
$326$	11.3928	+	2.80807i	0.630988	+	0.155525i
$327$	5.18117	−	1.72973i	0.286519	−	0.0956542i
$328$	−1.18943	+	1.72319i	−0.0656753	+	0.0951471i
$329$	−1.60579	+	0.260966i	−0.0885299	+	0.0143875i
$330$	0.651585	+	1.71809i	0.0358686	+	0.0945777i
$331$	−23.9995	+	12.5959i	−1.31913	+	0.692333i	−0.969624	−	0.244600i	$-0.921343\pi$
$331$	−23.9995	+	12.5959i	−1.31913	+	0.692333i	−0.349507	+	0.936934i	$0.613651\pi$
$332$	0.290424	−	1.42259i	0.0159391	−	0.0780748i
$333$	3.06853	−	8.09106i	0.168155	−	0.443387i
$334$	0.536228	+	4.41624i	0.0293411	+	0.241646i
$335$	0.962364	+	0.410025i	0.0525796	+	0.0224021i
$336$	4.34017	−	5.31574i	0.236776	−	0.289997i
$337$	−21.3390	−	11.1996i	−1.16241	−	0.610079i	−0.230607	−	0.973047i	$-0.574071\pi$
$337$	−21.3390	−	11.1996i	−1.16241	−	0.610079i	−0.931802	+	0.362967i	$0.881764\pi$
$338$	−1.62956	+	13.4206i	−0.0886363	+	0.729986i
$339$	3.58688	−	6.21265i	0.194812	−	0.337425i
$340$	1.97532	+	3.42135i	0.107127	+	0.185549i
$341$	−13.4759	+	5.74153i	−0.729759	+	0.310921i
$342$	1.19875	−	4.13856i	0.0648210	−	0.223788i
$343$	30.8493	+	27.3301i	1.66570	+	1.47568i
$344$	−0.795457	−	0.0642160i	−0.0428882	−	0.00346229i
$345$	−0.267383	+	6.63503i	−0.0143954	+	0.357218i
$346$	−0.258874	−	6.42389i	−0.0139171	−	0.345350i
$347$	4.26975	−	0.344690i	0.229212	−	0.0185039i	0.0346731	−	0.999399i	$-0.488961\pi$
$347$	4.26975	−	0.344690i	0.229212	−	0.0185039i	0.194539	+	0.980895i	$0.437679\pi$
$348$	4.46312	+	3.35382i	0.239248	+	0.179784i
$349$	−16.8992	−	24.4827i	−0.904592	−	1.31053i	−0.950223	−	0.311569i	$-0.899145\pi$
$349$	−16.8992	−	24.4827i	−0.904592	−	1.31053i	0.0456315	−	0.998958i	$-0.485470\pi$
$350$	−14.9279	−	15.5416i	−0.797928	−	0.830731i
$351$	24.6072	+	15.5606i	1.31343	+	0.830566i
$352$	1.75810	+	0.586939i	0.0937068	+	0.0312839i
$353$	−14.8720	+	11.1755i	−0.791554	+	0.594814i	−0.917735	−	0.397193i	$-0.869984\pi$
$353$	−14.8720	+	11.1755i	−0.791554	+	0.594814i	0.126181	+	0.992007i	$0.459728\pi$
$354$	2.85747	−	2.53149i	0.151873	−	0.134547i
$355$	−3.35199	−	7.06417i	−0.177905	−	0.374927i
$356$	5.33953	+	11.2528i	0.282994	+	0.596398i
$357$	29.5108	−	26.1442i	1.56187	−	1.38370i
$358$	−16.6918	+	12.5431i	−0.882191	+	0.662923i
$359$	−20.6024	−	6.87810i	−1.08735	−	0.363012i	−0.284189	−	0.958768i	$-0.591724\pi$
$359$	−20.6024	−	6.87810i	−1.08735	−	0.363012i	−0.803165	+	0.595756i	$0.796852\pi$
$360$	0.535601	+	0.338694i	0.0282287	+	0.0178507i
$361$	1.98121	+	2.06266i	0.104274	+	0.108561i
$362$	−6.01581	−	8.71541i	−0.316184	−	0.458072i
$363$	−8.71853	−	6.55155i	−0.457604	−	0.343867i
$364$	24.4334	−	1.97247i	1.28066	−	0.103385i
$365$	−0.287963	−	7.14574i	−0.0150727	−	0.374025i
$366$	−0.129021	+	3.20163i	−0.00674406	+	0.167352i
$367$	20.3954	+	1.64649i	1.06463	+	0.0859460i	0.600347	−	0.799739i	$-0.295029\pi$
$367$	20.3954	+	1.64649i	1.06463	+	0.0859460i	0.464286	+	0.885686i	$0.346311\pi$
$368$	5.01367	+	4.44172i	0.261355	+	0.231541i
$369$	−0.536839	+	1.85338i	−0.0279467	+	0.0964833i
$370$	−5.94037	+	2.53096i	−0.308825	+	0.131578i
$371$	−9.15369	−	15.8547i	−0.475236	−	0.823133i
$372$	5.69678	−	9.86712i	0.295364	−	0.511586i
$373$	−0.742554	+	6.11549i	−0.0384480	+	0.316648i	0.960778	+	0.277318i	$0.0894455\pi$
$373$	−0.742554	+	6.11549i	−0.0384480	+	0.316648i	−0.999226	+	0.0393301i	$0.987478\pi$
$374$	9.42875	+	4.94859i	0.487549	+	0.255886i
$375$	−5.97343	+	7.31612i	−0.308466	+	0.377803i
$376$	0.314422	+	0.133963i	0.0162151	+	0.00690860i
$377$	2.40370	+	19.7963i	0.123797	+	1.01956i
$378$	9.54302	−	25.1629i	0.490840	−	1.29424i
$379$	2.38386	−	11.6769i	0.122451	−	0.599803i	−0.871539	−	0.490327i	$-0.836877\pi$
$379$	2.38386	−	11.6769i	0.122451	−	0.599803i	0.993989	−	0.109477i	$-0.0349175\pi$
$380$	−2.84682	+	1.49413i	−0.146039	+	0.0766472i
$381$	3.97601	+	10.4839i	0.203697	+	0.537105i
$382$	20.1567	−	3.27579i	1.03131	−	0.167604i
$383$	4.87095	−	7.05679i	0.248894	−	0.360585i	−0.678546	−	0.734558i	$-0.737389\pi$
$383$	4.87095	−	7.05679i	0.248894	−	0.360585i	0.927440	+	0.373973i	$0.122005\pi$
$384$	−1.36749	+	0.456535i	−0.0697844	+	0.0232974i
$385$	5.89066	+	1.45192i	0.300216	+	0.0739965i
$386$	−0.0782808	+	0.0495017i	−0.00398439	+	0.00251957i
$387$	−0.714068	+	0.176002i	−0.0362981	+	0.00894668i
$388$	8.46450	−	8.81248i	0.429720	−	0.447386i
$389$	−32.7801	−	5.32728i	−1.66202	−	0.270104i	−0.744448	−	0.667680i	$-0.767287\pi$
$389$	−32.7801	−	5.32728i	−1.66202	−	0.270104i	−0.917569	+	0.397576i	$0.869851\pi$
$390$	−1.02118	−	5.00209i	−0.0517097	−	0.253291i
$391$	24.3377	+	29.8082i	1.23081	+	1.50747i
$392$	−4.35641	−	15.0401i	−0.220032	−	0.759639i
$393$	−8.44277	+	17.7928i	−0.425881	+	0.897526i
$394$	1.64290			0.0827681
$395$	5.89373	−	1.61870i	0.296546	−	0.0814455i
$396$	1.70808			0.0858341
$397$	−5.33750	+	11.2485i	−0.267881	+	0.564548i	−0.992162	−	0.124957i	$-0.960121\pi$
$397$	−5.33750	+	11.2485i	−0.267881	+	0.564548i	0.724281	+	0.689505i	$0.242172\pi$
$398$	4.75421	+	16.4134i	0.238307	+	0.822731i
$399$	20.2923	+	24.8536i	1.01589	+	1.24424i
$400$	0.905543	+	4.43565i	0.0452772	+	0.221782i
$401$	−3.59828	−	0.584778i	−0.179690	−	0.0292024i	0.0699005	−	0.997554i	$-0.477732\pi$
$401$	−3.59828	−	0.584778i	−0.179690	−	0.0292024i	−0.249590	+	0.968352i	$0.580296\pi$
$402$	−1.51923	+	1.58169i	−0.0757723	+	0.0788873i
$403$	39.5151	−	9.73960i	1.96839	−	0.485164i
$404$	−12.9505	+	8.18940i	−0.644312	+	0.407438i
$405$	−3.59613	−	0.886367i	−0.178693	−	0.0440439i
$406$	17.4843	−	5.83713i	0.867734	−	0.289692i
$407$	−9.88675	+	14.3234i	−0.490068	+	0.709986i
$408$	−8.17538	+	1.32863i	−0.404741	+	0.0657769i
$409$	−4.02668	−	10.6175i	−0.199106	−	0.525000i	0.797859	−	0.602844i	$-0.205966\pi$
$409$	−4.02668	−	10.6175i	−0.199106	−	0.525000i	−0.996966	+	0.0778435i	$0.975197\pi$
$410$	1.27490	−	0.669119i	0.0629629	−	0.0330455i
$411$	4.78824	−	23.4543i	0.236186	−	1.15692i
$412$	0.756967	−	1.99596i	0.0372931	−	0.0983338i
$413$	−1.51931	−	12.5126i	−0.0747603	−	0.615707i
$414$	5.67877	+	2.41950i	0.279096	+	0.118912i
$415$	−0.631448	+	0.773384i	−0.0309966	+	0.0379639i
$416$	−4.55981	−	2.39318i	−0.223563	−	0.117335i
$417$	0.239204	−	1.97002i	0.0117139	−	0.0964725i
$418$	−4.33295	+	7.50489i	−0.211932	+	0.367076i
$419$	11.9465	+	20.6919i	0.583623	+	1.01086i	0.995046	+	0.0994202i	$0.0316988\pi$
$419$	11.9465	+	20.6919i	0.583623	+	1.01086i	−0.411422	+	0.911445i	$0.634968\pi$
$420$	−4.34140	+	1.84970i	−0.211839	+	0.0902560i
$421$	−4.15136	+	14.3322i	−0.202325	+	0.698507i	0.793609	+	0.608428i	$0.208199\pi$
$421$	−4.15136	+	14.3322i	−0.202325	+	0.698507i	−0.995935	+	0.0900798i	$0.971288\pi$
$422$	2.73952	+	2.42700i	0.133358	+	0.118145i
$423$	0.313938	+	0.0253437i	0.0152642	+	0.00123225i
$424$	−0.154864	+	3.84291i	−0.00752086	+	0.186628i
$425$	1.04727	+	25.9878i	0.0508002	+	1.26059i
$426$	16.3398	−	1.31909i	0.791667	−	0.0639100i
$427$	8.45776	+	6.35559i	0.409300	+	0.307569i
$428$	−6.60316	−	9.56633i	−0.319176	−	0.462406i
$429$	−9.53233	−	9.92420i	−0.460225	−	0.479145i
$430$	0.463821	+	0.293303i	0.0223674	+	0.0141443i
$431$	0.579269	+	0.193388i	0.0279024	+	0.00931519i	0.330585	−	0.943776i	$-0.392754\pi$
$431$	0.579269	+	0.193388i	0.0279024	+	0.00931519i	−0.302683	+	0.953091i	$0.597882\pi$
$432$	−4.51976	+	3.39638i	−0.217457	+	0.163408i
$433$	−18.4267	+	16.3246i	−0.885532	+	0.784513i	−0.977431	−	0.211256i	$-0.932245\pi$
$433$	−18.4267	+	16.3246i	−0.885532	+	0.784513i	0.0918992	+	0.995768i	$0.470706\pi$
$434$	−16.1269	−	33.9866i	−0.774114	−	1.63141i
$435$	−1.64576	−	3.46836i	−0.0789080	−	0.166295i
$436$	−2.83597	+	2.51245i	−0.135818	+	0.120325i
$437$	−25.0363	+	18.8136i	−1.19765	+	0.899975i
$438$	14.2218	+	4.74794i	0.679544	+	0.226865i
$439$	−19.9326	−	12.6046i	−0.951333	−	0.601586i	−0.0338777	−	0.999426i	$-0.510786\pi$
$439$	−19.9326	−	12.6046i	−0.951333	−	0.601586i	−0.917455	+	0.397840i	$0.869760\pi$
$440$	−0.882912	−	0.919208i	−0.0420912	−	0.0438215i
$441$	−8.19713	−	11.8756i	−0.390339	−	0.565504i
$442$	−23.6519	−	17.7733i	−1.12501	−	0.845388i
$443$	−29.0008	+	2.34119i	−1.37787	+	0.111233i	−0.747086	−	0.664727i	$-0.768548\pi$
$443$	−29.0008	+	2.34119i	−1.37787	+	0.111233i	−0.630782	+	0.775960i	$0.717266\pi$
$444$	−0.545098	−	13.5265i	−0.0258692	−	0.641938i
$445$	0.344876	−	8.55801i	0.0163487	−	0.405688i
$446$	−16.8915	−	1.36362i	−0.799835	−	0.0645694i
$447$	8.49203	+	7.52328i	0.401659	+	0.355839i
$448$	−1.32434	+	4.57214i	−0.0625690	+	0.216013i
$449$	24.7048	−	10.5258i	1.16589	−	0.496741i	0.279714	−	0.960083i	$-0.409760\pi$
$449$	24.7048	−	10.5258i	1.16589	−	0.496741i	0.886179	+	0.463342i	$0.153350\pi$
$450$	2.08599	+	3.61304i	0.0983346	+	0.170320i
$451$	1.94044	−	3.36094i	0.0913716	−	0.158260i
$452$	−0.599785	+	4.93968i	−0.0282115	+	0.232343i
$453$	12.7598	+	6.69687i	0.599508	+	0.314646i
$454$	3.21454	−	3.93710i	0.150866	−	0.184777i
$455$	−15.5074	−	6.60711i	−0.727000	−	0.309746i
$456$	−0.812483	−	6.69140i	−0.0380480	−	0.313354i
$457$	−11.6316	+	30.6701i	−0.544105	+	1.43469i	0.327675	+	0.944791i	$0.393735\pi$
$457$	−11.6316	+	30.6701i	−0.544105	+	1.43469i	−0.871780	+	0.489897i	$0.837034\pi$
$458$	−2.04279	+	10.0062i	−0.0954533	+	0.467561i
$459$	−28.7603	+	15.0946i	−1.34242	+	0.704554i
$460$	−1.63332	−	4.30670i	−0.0761538	−	0.200801i
$461$	34.1599	−	5.55152i	1.59098	−	0.258560i	0.700527	−	0.713626i	$-0.252948\pi$
$461$	34.1599	−	5.55152i	1.59098	−	0.258560i	0.890458	+	0.455066i	$0.150384\pi$
$462$	−7.22553	+	10.4680i	−0.336162	+	0.487015i
$463$	−29.6438	+	9.89654i	−1.37766	+	0.459931i	−0.906534	−	0.422133i	$-0.861282\pi$
$463$	−29.6438	+	9.89654i	−1.37766	+	0.459931i	−0.471129	+	0.882064i	$0.656153\pi$
$464$	−3.75989	−	0.926729i	−0.174548	−	0.0430223i
$465$	−6.62190	+	4.18743i	−0.307083	+	0.194188i
$466$	11.1075	−	2.73775i	0.514545	−	0.126824i
$467$	12.7392	−	13.2630i	0.589502	−	0.613737i	−0.357909	−	0.933757i	$-0.616510\pi$
$467$	12.7392	−	13.2630i	0.589502	−	0.613737i	0.947411	+	0.320020i	$0.103690\pi$
$468$	−4.68423	−	0.761262i	−0.216529	−	0.0351893i
$469$	1.44841	+	7.09480i	0.0668815	+	0.327607i
$470$	−0.148637	−	0.182047i	−0.00685611	−	0.00839720i
$471$	−0.169928	−	0.586660i	−0.00782988	−	0.0270319i
$472$	−1.13517	+	2.39231i	−0.0522502	+	0.110115i
$473$	1.47916			0.0680120
$474$	−1.20852	+	12.7568i	−0.0555092	+	0.585941i
$475$	−21.1665			−0.971185
$476$	−11.7235	+	24.7068i	−0.537347	+	1.13244i
$477$	0.986088	+	3.40437i	0.0451499	+	0.155875i
$478$	−15.1179	−	18.5161i	−0.691477	−	0.846906i
$479$	6.85705	+	33.5881i	0.313307	+	1.53468i	0.765900	+	0.642960i	$0.222294\pi$
$479$	6.85705	+	33.5881i	0.313307	+	1.53468i	−0.452593	+	0.891717i	$0.649501\pi$
$480$	0.978537	+	0.159028i	0.0446639	+	0.00725859i
$481$	33.4972	−	34.8742i	1.52734	−	1.59013i
$482$	−23.4824	+	5.78789i	−1.06959	+	0.263631i
$483$	−38.8504	+	24.5675i	−1.76775	+	1.11786i
$484$	7.34479	+	1.81033i	0.333854	+	0.0822876i
$485$	−7.97009	+	2.66081i	−0.361903	+	0.120821i
$486$	−5.22384	+	7.56804i	−0.236958	+	0.343293i
$487$	−1.78949	+	0.290820i	−0.0810894	+	0.0131783i	−0.200821	−	0.979628i	$-0.564361\pi$
$487$	−1.78949	+	0.290820i	−0.0810894	+	0.0131783i	0.119731	+	0.992806i	$0.461797\pi$
$488$	−0.788132	−	2.07813i	−0.0356771	−	0.0940727i
$489$	14.9787	−	7.86142i	0.677360	−	0.355506i
$490$	−2.15377	+	10.5499i	−0.0972973	+	0.476594i
$491$	9.97597	−	26.3045i	0.450209	−	1.18710i	−0.497357	−	0.867546i	$-0.665696\pi$
$491$	9.97597	−	26.3045i	0.450209	−	1.18710i	0.947567	−	0.319558i	$-0.103535\pi$
$492$	0.363856	+	2.99663i	0.0164039	+	0.135098i
$493$	−20.4672	−	8.72026i	−0.921796	−	0.392741i
$494$	15.2275	−	18.6503i	0.685117	−	0.839116i
$495$	−1.04002	−	0.545846i	−0.0467455	−	0.0245339i
$496$	−0.952597	+	7.84534i	−0.0427729	+	0.352266i
$497$	27.0628	−	46.8741i	1.21393	−	2.10259i
$498$	−1.04661	−	1.81279i	−0.0468999	−	0.0812330i
$499$	−16.4469	+	7.00736i	−0.736264	+	0.313693i	−0.727349	−	0.686268i	$-0.759248\pi$
$499$	−16.4469	+	7.00736i	−0.736264	+	0.313693i	−0.00891451	+	0.999960i	$0.502838\pi$
$500$	1.82270	−	6.29269i	0.0815136	−	0.281418i
$501$	4.80063	+	4.25299i	0.214476	+	0.190010i
$502$	19.4026	+	1.56634i	0.865981	+	0.0699092i
$503$	−1.17718	+	29.2114i	−0.0524878	+	1.30247i	0.731563	+	0.681774i	$0.238791\pi$
$503$	−1.17718	+	29.2114i	−0.0524878	+	1.30247i	−0.784051	+	0.620697i	$0.786850\pi$
$504$	0.176632	+	4.38309i	0.00786783	+	0.195238i
$505$	10.5024	−	0.847844i	0.467352	−	0.0377286i
$506$	−9.92507	−	7.45820i	−0.441223	−	0.331558i
$507$	11.0718	+	16.0403i	0.491716	+	0.712374i
$508$	−5.38757	−	5.60906i	−0.239035	−	0.248862i
$509$	26.0534	+	16.4752i	1.15480	+	0.730249i	0.967703	−	0.252093i	$-0.0811189\pi$
$509$	26.0534	+	16.4752i	1.15480	+	0.730249i	0.187093	+	0.982342i	$0.440093\pi$
$510$	5.40245	+	1.80360i	0.239225	+	0.0798649i
$511$	39.5760	−	29.7395i	1.75074	−	1.31560i
$512$	0.748511	−	0.663123i	0.0330798	−	0.0293062i
$513$	−11.3318	−	23.8813i	−0.500311	−	1.05438i
$514$	4.92081	+	10.3704i	0.217048	+	0.457418i
$515$	−1.09875	+	0.973407i	−0.0484167	+	0.0428934i
$516$	−0.919782	+	0.691171i	−0.0404911	+	0.0304271i
$517$	−0.600866	−	0.200599i	−0.0264261	−	0.00882231i
$518$	−37.7777	−	23.8892i	−1.65986	−	1.04963i
$519$	−6.42067	−	6.68463i	−0.281836	−	0.293423i
$520$	2.01162	+	2.91434i	0.0882154	+	0.127802i
$521$	8.13143	+	6.11037i	0.356244	+	0.267700i	0.763763	−	0.645497i	$-0.223350\pi$
$521$	8.13143	+	6.11037i	0.356244	+	0.267700i	−0.407519	+	0.913197i	$0.633606\pi$
$522$	−3.55705	+	0.287155i	−0.155688	+	0.0125684i
$523$	1.13292	+	28.1131i	0.0495391	+	1.22930i	0.812541	+	0.582904i	$0.198084\pi$
$523$	1.13292	+	28.1131i	0.0495391	+	1.22930i	−0.763002	+	0.646396i	$0.776275\pi$
$524$	0.550056	−	13.6495i	0.0240293	−	0.596281i
$525$	−30.9668	−	2.49990i	−1.35150	−	0.109105i
$526$	−3.52025	−	3.11867i	−0.153490	−	0.135980i
$527$	−12.6320	+	43.6108i	−0.550260	+	1.89972i
$528$	2.45831	−	1.04739i	0.106984	−	0.0455817i
$529$	−10.9329	−	18.9363i	−0.475342	−	0.823317i
$530$	1.32236	−	2.29040i	0.0574398	−	0.0994886i
$531$	−0.294138	+	2.42245i	−0.0127645	+	0.105125i
$532$	−19.7063	−	10.3427i	−0.854378	−	0.448412i
$533$	−6.81937	+	8.35221i	−0.295380	+	0.361774i
$534$	16.5198	+	7.03843i	0.714881	+	0.304582i
$535$	0.963477	+	7.93495i	0.0416548	+	0.343058i
$536$	0.539433	−	1.42237i	0.0233000	−	0.0614370i
$537$	−6.02105	+	29.4930i	−0.259827	+	1.27272i
$538$	−27.8220	+	14.6021i	−1.19949	+	0.629541i
$539$	10.2915	+	27.1364i	0.443286	+	1.16885i
$540$	3.83738	−	0.623635i	0.165135	−	0.0268370i
$541$	0.100790	−	0.146020i	0.00433331	−	0.00627789i	−0.820811	−	0.571200i	$-0.806478\pi$
$541$	0.100790	−	0.146020i	0.00433331	−	0.00627789i	0.825145	+	0.564922i	$0.191094\pi$
$542$	24.3227	−	8.12013i	1.04475	−	0.348789i
$543$	−14.8238	−	3.65374i	−0.636150	−	0.156797i
$544$	4.85571	−	3.07057i	0.208187	−	0.131650i
$545$	2.52968	−	0.623510i	0.108360	−	0.0267082i
$546$	24.4807	−	25.4871i	1.04768	−	1.09075i
$547$	−0.611922	−	0.0994470i	−0.0261639	−	0.00425204i	0.147315	−	0.989090i	$-0.452937\pi$
$547$	−0.611922	−	0.0994470i	−0.0261639	−	0.00425204i	−0.173479	+	0.984838i	$0.555501\pi$
$548$	3.32128	+	16.2687i	0.141878	+	0.694965i
$549$	−1.29538	−	1.58655i	−0.0552853	−	0.0677122i
$550$	−2.33451	−	8.05968i	−0.0995440	−	0.343666i
$551$	7.76163	−	16.3573i	0.330657	−	0.696844i
$552$	9.65667			0.411015
$553$	32.3973	+	27.2107i	1.37767	+	1.15712i
$554$	−19.3695			−0.822931
$555$	−3.99072	+	8.41027i	−0.169397	+	0.356996i
$556$	0.382969	+	1.32216i	0.0162415	+	0.0560722i
$557$	23.9713	+	29.3595i	1.01569	+	1.24400i	0.969506	+	0.245067i	$0.0788100\pi$
$557$	23.9713	+	29.3595i	1.01569	+	1.24400i	0.0461884	+	0.998933i	$0.485293\pi$
$558$	1.45678	+	7.13579i	0.0616705	+	0.302082i
$559$	−4.05646	−	0.659239i	−0.171570	−	0.0278828i
$560$	2.26747	−	2.36069i	0.0958183	−	0.0997574i
$561$	14.9056	−	3.67391i	0.629316	−	0.155112i
$562$	14.3055	−	9.04625i	0.603441	−	0.381593i
$563$	−9.13219	−	2.25088i	−0.384876	−	0.0948634i	0.0421302	−	0.999112i	$-0.486586\pi$
$563$	−9.13219	−	2.25088i	−0.384876	−	0.0948634i	−0.427006	+	0.904249i	$0.640432\pi$
$564$	0.467368	−	0.156030i	0.0196797	−	0.00657006i
$565$	1.94376	−	2.81602i	0.0817746	−	0.118471i
$566$	1.57079	−	0.255279i	0.0660253	−	0.0107302i
$567$	−9.09144	−	23.9721i	−0.381804	−	1.00674i
$568$	−10.0683	+	5.28424i	−0.422456	+	0.221722i
$569$	2.36175	−	11.5686i	0.0990098	−	0.484982i	−0.899804	−	0.436294i	$-0.856291\pi$
$569$	2.36175	−	11.5686i	0.0990098	−	0.484982i	0.998814	−	0.0486883i	$-0.0155041\pi$
$570$	−1.64365	+	4.33394i	−0.0688447	+	0.181529i
$571$	−2.94065	−	24.2184i	−0.123062	−	1.01351i	−0.915153	−	0.403106i	$-0.867930\pi$
$571$	−2.94065	−	24.2184i	−0.123062	−	1.01351i	0.792091	−	0.610403i	$-0.208993\pi$
$572$	8.78106	+	3.74126i	0.367154	+	0.156430i
$573$	18.6197	−	22.8050i	0.777851	−	0.952694i
$574$	8.82514	+	4.63179i	0.368354	+	0.193327i
$575$	3.65511	−	30.1025i	0.152429	−	1.25536i
$576$	0.460775	−	0.798086i	0.0191990	−	0.0332536i
$577$	−1.40092	−	2.42646i	−0.0583209	−	0.101015i	0.835391	−	0.549656i	$-0.185241\pi$
$577$	−1.40092	−	2.42646i	−0.0583209	−	0.101015i	−0.893712	+	0.448642i	$0.851908\pi$
$578$	14.7255	−	6.27395i	0.612500	−	0.260962i
$579$	−0.0371497	+	0.128255i	−0.00154389	+	0.00533012i
$580$	1.99319	+	1.76581i	0.0827626	+	0.0733212i
$581$	−6.88890	−	0.556129i	−0.285800	−	0.0230721i
$582$	0.709330	−	17.6019i	0.0294027	−	0.729620i
$583$	−0.287038	−	7.12277i	−0.0118879	−	0.294995i
$584$	−10.3662	+	0.836848i	−0.428957	+	0.0346290i
$585$	2.60888	+	1.96045i	0.107864	+	0.0810546i
$586$	8.24408	+	11.9436i	0.340560	+	0.493386i
$587$	24.6061	+	25.6177i	1.01560	+	1.05735i	0.998345	+	0.0575032i	$0.0183140\pi$
$587$	24.6061	+	25.6177i	1.01560	+	1.05735i	0.0172573	+	0.999851i	$0.494507\pi$
$588$	−19.0796	−	12.0652i	−0.786829	−	0.497561i
$589$	−35.0485	−	11.7009i	−1.44415	−	0.482127i
$590$	1.45569	−	1.09388i	0.0599298	−	0.0450343i
$591$	1.77288	−	1.57063i	0.0729265	−	0.0646072i
$592$	4.02544	+	8.48343i	0.165445	+	0.348667i
$593$	−6.45640	−	13.6066i	−0.265133	−	0.558755i	0.726602	−	0.687058i	$-0.241098\pi$
$593$	−6.45640	−	13.6066i	−0.265133	−	0.558755i	−0.991735	+	0.128303i	$0.959047\pi$
$594$	7.84358	−	6.94880i	0.321826	−	0.285113i
$595$	15.0338	−	11.2972i	0.616325	−	0.463138i
$596$	−7.46445	−	2.49200i	−0.305756	−	0.102076i
$597$	20.8218	+	13.1669i	0.852179	+	0.538886i
$598$	23.8945	+	24.8768i	0.977119	+	1.01729i
$599$	−20.0011	−	28.9766i	−0.817224	−	1.18395i	−0.980334	−	0.197345i	$-0.936768\pi$
$599$	−20.0011	−	28.9766i	−0.817224	−	1.18395i	0.163111	−	0.986608i	$-0.447847\pi$
$600$	5.21772	+	3.92086i	0.213012	+	0.160068i
$601$	−3.64906	+	0.294583i	−0.148848	+	0.0120163i	−0.154666	−	0.987967i	$-0.549430\pi$
$601$	−3.64906	+	0.294583i	−0.148848	+	0.0120163i	0.00581780	+	0.999983i	$0.498148\pi$
$602$	0.152960	+	3.79567i	0.00623420	+	0.154700i
$603$	0.0564482	−	1.40075i	0.00229875	−	0.0570428i
$604$	−9.96316	−	0.804309i	−0.405395	−	0.0327269i
$605$	−3.89361	−	3.44944i	−0.158298	−	0.140240i
$606$	−6.14591	+	21.2182i	−0.249661	+	0.861929i
$607$	4.51906	−	1.92539i	0.183423	−	0.0781492i	−0.298303	−	0.954471i	$-0.596420\pi$
$607$	4.51906	−	1.92539i	0.183423	−	0.0781492i	0.481726	+	0.876322i	$0.340010\pi$
$608$	2.33774	+	4.04908i	0.0948077	+	0.164212i
$609$	13.2873	−	23.0142i	0.538427	−	0.932582i
$610$	−0.184222	+	1.51721i	−0.00745893	+	0.0614298i
$611$	1.55841	+	0.817918i	0.0630466	+	0.0330894i
$612$	3.34843	−	4.10108i	0.135352	−	0.165776i
$613$	2.19876	+	0.936802i	0.0888069	+	0.0378371i	0.435913	−	0.899989i	$-0.356425\pi$
$613$	2.19876	+	0.936802i	0.0888069	+	0.0378371i	−0.347106	+	0.937826i	$0.612836\pi$
$614$	1.30004	+	10.7068i	0.0524655	+	0.432092i
$615$	0.736078	−	1.94088i	0.0296815	−	0.0782638i
$616$	1.76477	−	8.64441i	0.0711046	−	0.348293i
$617$	25.4256	−	13.3444i	1.02360	−	0.537225i	0.132569	−	0.991174i	$-0.457677\pi$
$617$	25.4256	−	13.3444i	1.02360	−	0.537225i	0.891028	+	0.453948i	$0.149985\pi$
$618$	−1.09131	−	2.87754i	−0.0438988	−	0.115752i
$619$	−6.49784	+	1.05600i	−0.261170	+	0.0424443i	−0.289586	−	0.957152i	$-0.593518\pi$
$619$	−6.49784	+	1.05600i	−0.261170	+	0.0424443i	0.0284162	+	0.999596i	$0.490954\pi$
$620$	3.08714	−	4.47249i	0.123982	−	0.179620i
$621$	35.9202	−	11.9919i	1.44143	−	0.481220i
$622$	13.7139	+	3.38017i	0.549878	+	0.135533i
$623$	50.1101	−	31.6877i	2.00762	−	1.26954i
$624$	−7.20847	+	1.77673i	−0.288570	+	0.0711261i
$625$	12.5595	−	13.0759i	0.502381	−	0.523034i
$626$	15.0719	+	2.44942i	0.602393	+	0.0978984i
$627$	2.49902	+	12.2410i	0.0998012	+	0.488858i
$628$	0.267938	+	0.328164i	0.0106919	+	0.0130952i
$629$	15.0090	+	51.8169i	0.598446	+	2.06608i
$630$	1.29314	−	2.72524i	0.0515201	−	0.108576i
$631$	−22.1689			−0.882530			−0.441265	−	0.897377i	$-0.645470\pi$
$631$	−22.1689			−0.882530			−0.441265	+	0.897377i	$0.645470\pi$
$632$	−2.69715	−	8.46908i	−0.107287	−	0.336882i
$633$	5.27650			0.209722
$634$	−5.82170	+	12.2690i	−0.231209	+	0.487263i
$635$	1.48794	+	5.13696i	0.0590471	+	0.203854i
$636$	3.50675	+	4.29499i	0.139052	+	0.170308i
$637$	−16.1291	−	79.0057i	−0.639059	−	3.13032i
$638$	7.08450	+	1.15134i	0.280478	+	0.0455821i
$639$	−7.25885	+	7.55726i	−0.287156	+	0.298961i
$640$	−0.667669	+	0.164566i	−0.0263920	+	0.00650503i
$641$	−31.8720	+	20.1546i	−1.25887	+	0.796059i	−0.986121	−	0.166027i	$-0.946906\pi$
$641$	−31.8720	+	20.1546i	−1.25887	+	0.796059i	−0.272746	+	0.962086i	$0.587932\pi$
$642$	−16.2711	−	4.01047i	−0.642169	−	0.158281i
$643$	16.5558	−	5.52713i	0.652896	−	0.217969i	0.0291249	−	0.999576i	$-0.490728\pi$
$643$	16.5558	−	5.52713i	0.652896	−	0.217969i	0.623771	+	0.781607i	$0.285600\pi$
$644$	18.1121	−	26.2399i	0.713717	−	1.03400i
$645$	0.780917	−	0.126911i	0.0307486	−	0.00499713i
$646$	9.52508	+	25.1156i	0.374759	+	0.988159i
$647$	−14.3755	+	7.54484i	−0.565159	+	0.296618i	−0.723002	−	0.690846i	$-0.757238\pi$
$647$	−14.3755	+	7.54484i	−0.565159	+	0.296618i	0.157843	+	0.987464i	$0.449546\pi$
$648$	−1.07736	+	5.27725i	−0.0423226	+	0.207310i
$649$	1.74039	−	4.58903i	0.0683163	−	0.180135i
$650$	2.81011	+	23.1433i	0.110221	+	0.907755i
$651$	−49.8944	−	21.2580i	−1.95551	−	0.833167i
$652$	−7.42096	+	9.08902i	−0.290627	+	0.355954i
$653$	−20.1426	−	10.5717i	−0.788242	−	0.413701i	0.0220286	−	0.999757i	$-0.492988\pi$
$653$	−20.1426	−	10.5717i	−0.788242	−	0.413701i	−0.810270	+	0.586056i	$0.800680\pi$
$654$	−0.658405	+	5.42245i	−0.0257457	+	0.212035i
$655$	−4.69686	+	8.13520i	−0.183521	+	0.317868i
$656$	−1.04691	−	1.81331i	−0.0408751	−	0.0707978i
$657$	−8.81715	+	3.75664i	−0.343990	+	0.146560i
$658$	0.452619	−	1.56262i	0.0176449	−	0.0609174i
$659$	−29.7216	−	26.3311i	−1.15779	−	1.02571i	−0.999264	−	0.0383577i	$-0.987787\pi$
$659$	−29.7216	−	26.3311i	−1.15779	−	1.02571i	−0.158526	−	0.987355i	$-0.550674\pi$
$660$	−1.83154	−	0.147857i	−0.0712925	−	0.00575533i
$661$	0.591118	−	14.6684i	0.0229918	−	0.570536i	−0.946106	−	0.323858i	$-0.895020\pi$
$661$	0.591118	−	14.6684i	0.0229918	−	0.570536i	0.969097	−	0.246678i	$-0.0793390\pi$
$662$	−1.09137	−	27.0821i	−0.0424174	−	1.05258i
$663$	−42.5146	+	3.43213i	−1.65113	+	0.133293i
$664$	1.16074	+	0.872238i	0.0450453	+	0.0338494i
$665$	8.69371	+	12.5950i	0.337128	+	0.488414i
$666$	5.99441	+	6.24084i	0.232279	+	0.241828i
$667$	21.9227	+	13.8631i	0.848849	+	0.536780i
$668$	−4.21973	−	1.40875i	−0.163266	−	0.0545063i
$669$	−19.5315	+	14.6770i	−0.755131	+	0.567444i
$670$	−0.782996	+	0.693674i	−0.0302498	+	0.0267989i
$671$	1.76599	+	3.72175i	0.0681753	+	0.143677i
$672$	2.94191	+	6.19995i	0.113487	+	0.239168i
$673$	−1.85568	+	1.64399i	−0.0715313	+	0.0633712i	−0.698131	−	0.715970i	$-0.745985\pi$
$673$	−1.85568	+	1.64399i	−0.0715313	+	0.0633712i	0.626600	+	0.779341i	$0.284446\pi$
$674$	19.2661	−	14.4776i	0.742103	−	0.557655i
$675$	24.2776	+	8.10504i	0.934444	+	0.311963i
$676$	−11.4263	−	7.22555i	−0.439473	−	0.277906i
$677$	−5.99691	−	6.24345i	−0.230480	−	0.239955i	0.595913	−	0.803049i	$-0.296790\pi$
$677$	−5.99691	−	6.24345i	−0.230480	−	0.239955i	−0.826393	+	0.563094i	$0.809611\pi$
$678$	4.07516	+	5.90388i	0.156505	+	0.226737i
$679$	−46.4988	−	34.9416i	−1.78446	−	1.34094i
$680$	−3.93783	+	0.317894i	−0.151009	+	0.0121907i
$681$	−0.295055	−	7.32172i	−0.0113065	−	0.280569i
$682$	0.589816	−	14.6361i	0.0225852	−	0.560446i
$683$	20.7381	+	1.67415i	0.793521	+	0.0640596i	0.470578	−	0.882359i	$-0.344046\pi$
$683$	20.7381	+	1.67415i	0.793521	+	0.0640596i	0.322943	+	0.946418i	$0.395328\pi$
$684$	3.22509	+	2.85718i	0.123315	+	0.109247i
$685$	3.17667	−	10.9672i	0.121374	−	0.419033i
$686$	−37.9162	+	16.1546i	−1.44765	+	0.616785i
$687$	7.36169	+	12.7508i	0.280866	+	0.486474i
$688$	0.399023	−	0.691128i	0.0152126	−	0.0263490i
$689$	−2.38733	+	19.6614i	−0.0909499	+	0.749040i
$690$	−5.87980	−	3.08596i	−0.223840	−	0.117480i
$691$	−14.8535	+	18.1922i	−0.565054	+	0.692065i	−0.975545	−	0.219799i	$-0.929460\pi$
$691$	−14.8535	+	18.1922i	−0.565054	+	0.692065i	0.410491	+	0.911864i	$0.365357\pi$
$692$	5.91464	+	2.51999i	0.224841	+	0.0957957i
$693$	−0.980032	−	8.07129i	−0.0372283	−	0.306603i
$694$	−1.51900	+	4.00527i	−0.0576604	+	0.152038i
$695$	0.189336	−	0.927430i	0.00718193	−	0.0351794i
$696$	−4.94332	+	2.59445i	−0.187376	+	0.0983425i
$697$	−4.26564	−	11.2476i	−0.161573	−	0.426032i
$698$	29.3634	−	4.77202i	1.11142	−	0.180624i
$699$	9.36895	−	13.5733i	0.354366	−	0.513388i
$700$	20.4405	−	6.82404i	0.772578	−	0.257924i
$701$	9.73166	+	2.39864i	0.367560	+	0.0905953i	0.418769	−	0.908093i	$-0.362462\pi$
$701$	9.73166	+	2.39864i	0.367560	+	0.0905953i	−0.0512097	+	0.998688i	$0.516308\pi$
$702$	−24.6072	+	15.5606i	−0.928739	+	0.587299i
$703$	−42.6271	+	10.5066i	−1.60771	+	0.396265i
$704$	−1.28395	+	1.33674i	−0.0483908	+	0.0503801i
$705$	−0.334436	−	0.0543511i	−0.0125956	−	0.00204698i
$706$	−3.72106	−	18.2269i	−0.140044	−	0.685980i
$707$	46.1285	+	56.4971i	1.73484	+	2.12479i
$708$	1.06211	+	3.66681i	0.0399164	+	0.137807i
$709$	11.0935	−	23.3791i	0.416627	−	0.878022i	−0.581302	−	0.813688i	$-0.697456\pi$
$709$	11.0935	−	23.3791i	0.416627	−	0.878022i	0.997928	−	0.0643339i	$-0.0204923\pi$
$710$	7.81910			0.293445
$711$	−4.82914	−	6.61593i	−0.181107	−	0.248117i
$712$	−12.4554			−0.466785
$713$	22.6931	−	47.8246i	0.849862	−	1.79105i
$714$	10.9690	+	37.8693i	0.410504	+	1.41722i
$715$	−4.15107	−	5.08414i	−0.155241	−	0.190136i
$716$	−4.17640	−	20.4574i	−0.156079	−	0.764528i
$717$	−34.0156	−	5.52807i	−1.27034	−	0.206450i
$718$	15.0461	−	15.6647i	0.561516	−	0.584601i
$719$	11.8385	−	2.91793i	0.441502	−	0.108820i	−0.0122974	−	0.999924i	$-0.503914\pi$
$719$	11.8385	−	2.91793i	0.441502	−	0.108820i	0.453799	+	0.891104i	$0.350068\pi$
$720$	−0.535601	+	0.338694i	−0.0199607	+	0.0126224i
$721$	−9.86595	−	2.43174i	−0.367427	−	0.0905627i
$722$	−2.71284	+	0.905678i	−0.100961	+	0.0337059i
$723$	−19.8069	+	28.6953i	−0.736627	+	1.06719i
$724$	10.4529	−	1.69876i	0.388478	−	0.0631338i
$725$	6.21656	+	16.3917i	0.230877	+	0.608773i
$726$	9.65657	−	5.06816i	0.358389	−	0.188097i
$727$	2.07501	−	10.1641i	0.0769580	−	0.376965i	−0.923012	−	0.384772i	$-0.874280\pi$
$727$	2.07501	−	10.1641i	0.0769580	−	0.376965i	0.999970	+	0.00780708i	$0.00248510\pi$
$728$	−8.69238	+	22.9199i	−0.322161	+	0.849469i
$729$	3.54568	+	29.2013i	0.131322	+	1.08153i
$730$	6.57927	+	2.80316i	0.243510	+	0.103750i
$731$	2.89967	−	3.55146i	0.107248	−	0.131355i
$732$	−2.83721	−	1.48908i	−0.104866	−	0.0550380i
$733$	−3.57869	+	29.4732i	−0.132182	+	1.08862i	0.764090	+	0.645110i	$0.223188\pi$
$733$	−3.57869	+	29.4732i	−0.132182	+	1.08862i	−0.896272	+	0.443506i	$0.853735\pi$
$734$	−10.2309	+	17.7204i	−0.377629	+	0.654073i
$735$	7.76163	+	13.4435i	0.286292	+	0.495872i
$736$	−6.16220	+	2.62547i	−0.227142	+	0.0967760i
$737$	−0.784451	+	2.70824i	−0.0288956	+	0.0997593i
$738$	−1.44430	−	1.27954i	−0.0531655	−	0.0471005i
$739$	35.1642	+	2.83875i	1.29354	+	0.104425i	0.707995	−	0.706217i	$-0.249600\pi$
$739$	35.1642	+	2.83875i	1.29354	+	0.104425i	0.585542	+	0.810642i	$0.300882\pi$
$740$	0.260000	−	6.45183i	0.00955779	−	0.237174i
$741$	−1.39770	−	34.6835i	−0.0513457	−	1.27413i
$742$	18.2480	−	1.47313i	0.669906	−	0.0540804i
$743$	−11.9710	−	8.99564i	−0.439174	−	0.330018i	0.358049	−	0.933703i	$-0.383442\pi$
$743$	−11.9710	−	8.99564i	−0.439174	−	0.330018i	−0.797223	+	0.603685i	$0.793699\pi$
$744$	6.47228	+	9.37672i	0.237285	+	0.343767i
$745$	3.74863	+	3.90274i	0.137339	+	0.142985i
$746$	−5.20671	−	3.29252i	−0.190631	−	0.120548i
$747$	1.26917	+	0.423711i	0.0464365	+	0.0155028i
$748$	−8.51284	+	6.39699i	−0.311260	+	0.233897i
$749$	−41.4158	+	36.6912i	−1.51330	+	1.34067i
$750$	−4.04899	−	8.53306i	−0.147848	−	0.311583i
$751$	2.86640	+	6.04081i	0.104596	+	0.220432i	0.949001	−	0.315274i	$-0.102097\pi$
$751$	2.86640	+	6.04081i	0.104596	+	0.220432i	−0.844404	+	0.535707i	$0.820045\pi$
$752$	−0.255819	+	0.226636i	−0.00932877	+	0.00826457i
$753$	22.4351	−	16.8589i	0.817580	−	0.614372i
$754$	−18.9154	−	6.31489i	−0.688859	−	0.229975i
$755$	5.80939	+	3.67363i	0.211425	+	0.133697i
$756$	18.6424	+	19.4088i	0.678017	+	0.705891i
$757$	18.6509	+	27.0205i	0.677878	+	0.982075i	0.999381	+	0.0351669i	$0.0111963\pi$
$757$	18.6509	+	27.0205i	0.677878	+	0.982075i	−0.321504	+	0.946908i	$0.604188\pi$
$758$	9.52758	+	7.15951i	0.346057	+	0.260045i
$759$	−17.8404	+	1.44023i	−0.647566	+	0.0522770i
$760$	−0.129459	−	3.21249i	−0.00469596	−	0.116529i
$761$	0.933734	−	23.1704i	0.0338478	−	0.839925i	−0.889724	−	0.456499i	$-0.849103\pi$
$761$	0.933734	−	23.1704i	0.0338478	−	0.839925i	0.923572	−	0.383426i	$-0.125256\pi$
$762$	−11.1761	−	0.902232i	−0.404869	−	0.0326844i
$763$	13.4994	+	11.9595i	0.488713	+	0.432962i
$764$	−5.68153	+	19.6149i	−0.205550	+	0.709642i
$765$	−3.34938	+	1.42704i	−0.121097	+	0.0515946i
$766$	4.28732	+	7.42586i	0.154907	+	0.268307i
$767$	−6.81810	+	11.8093i	−0.246187	+	0.426409i
$768$	0.173776	−	1.43117i	0.00627059	−	0.0516430i
$769$	−29.8638	−	15.6737i	−1.07692	−	0.565210i	−0.169538	−	0.985524i	$-0.554228\pi$
$769$	−29.8638	−	15.6737i	−1.07692	−	0.565210i	−0.907379	+	0.420314i	$0.861920\pi$
$770$	−3.83702	+	4.69949i	−0.138276	+	0.169358i
$771$	15.2244	+	6.48649i	0.548292	+	0.233605i
$772$	−0.0111640	−	0.0919438i	−0.000401801	−	0.00330913i
$773$	5.01000	−	13.2103i	0.180197	−	0.475141i	−0.814233	−	0.580538i	$-0.802842\pi$
$773$	5.01000	−	13.2103i	0.180197	−	0.475141i	0.994430	+	0.105397i	$0.0336114\pi$
$774$	0.147107	−	0.720576i	0.00528764	−	0.0259006i
$775$	31.6797	−	16.6268i	1.13797	−	0.597251i
$776$	4.33297	+	11.4251i	0.155545	+	0.410137i
$777$	−63.6048	+	10.3368i	−2.28181	+	0.370830i
$778$	18.8655	−	27.3314i	0.676362	−	0.979879i
$779$	9.28582	−	3.10006i	0.332699	−	0.111071i
$780$	4.95691	+	1.22177i	0.177486	+	0.0437464i
$781$	17.8128	−	11.2641i	0.637391	−	0.403061i
$782$	−37.3637	+	9.20931i	−1.33612	+	0.329324i
$783$	−15.1660	+	15.7894i	−0.541987	+	0.564268i
$784$	15.4555	+	2.51177i	0.551983	+	0.0897060i
$785$	−0.0582727	−	0.285439i	−0.00207984	−	0.0101877i
$786$	−12.4555	−	15.2552i	−0.444274	−	0.544137i
$787$	1.14808	+	3.96364i	0.0409247	+	0.141289i	0.978379	−	0.206820i	$-0.0663113\pi$
$787$	1.14808	+	3.96364i	0.0409247	+	0.141289i	−0.937454	+	0.348108i	$0.886824\pi$
$788$	−0.704299	+	1.48428i	−0.0250896	+	0.0528752i
$789$	−6.78024			−0.241383
$790$	−1.06419	+	6.01862i	−0.0378621	+	0.214133i
$791$	23.6859			0.842174
$792$	−0.732240	+	1.54316i	−0.0260190	+	0.0548339i
$793$	−3.18433	−	10.9936i	−0.113079	−	0.390394i
$794$	−7.87435	−	9.64433i	−0.279450	−	0.342264i
$795$	−0.762670	−	3.73580i	−0.0270491	−	0.132495i
$796$	−16.8668	−	2.74113i	−0.597829	−	0.0971566i
$797$	−37.0384	+	38.5611i	−1.31197	+	1.36590i	−0.424229	+	0.905555i	$0.639455\pi$
$797$	−37.0384	+	38.5611i	−1.31197	+	1.36590i	−0.887739	+	0.460348i	$0.847725\pi$
$798$	−31.1532	+	7.67856i	−1.10281	+	0.271818i
$799$	−1.65954	+	1.04943i	−0.0587104	+	0.0371262i
$800$	−4.39559	−	1.08341i	−0.155407	−	0.0383045i
$801$	−10.8875	+	3.63479i	−0.384692	+	0.128429i
$802$	2.07088	−	3.00018i	0.0731252	−	0.105940i
$803$	19.0265	−	3.09211i	0.671431	−	0.109118i
$804$	−0.777692	−	2.05060i	−0.0274271	−	0.0723193i
$805$	−19.4136	+	10.1891i	−0.684240	+	0.359117i
$806$	−8.14059	+	39.8752i	−0.286740	+	1.40455i
$807$	−16.0633	+	42.3555i	−0.565455	+	1.49098i
$808$	−1.84693	−	15.2109i	−0.0649749	−	0.535117i
$809$	12.2088	+	5.20168i	0.429238	+	0.182881i	0.595770	−	0.803155i	$-0.296847\pi$
$809$	12.2088	+	5.20168i	0.429238	+	0.182881i	−0.166533	+	0.986036i	$0.553257\pi$
$810$	2.34242	−	2.86895i	0.0823044	−	0.100805i
$811$	−18.9670	−	9.95467i	−0.666023	−	0.349556i	0.0975933	−	0.995226i	$-0.468886\pi$
$811$	−18.9670	−	9.95467i	−0.666023	−	0.349556i	−0.763616	+	0.645671i	$0.776578\pi$
$812$	−2.22185	+	18.2986i	−0.0779716	+	0.642154i
$813$	18.4841	−	32.0154i	0.648266	−	1.12283i
$814$	−8.70214	−	15.0725i	−0.305010	−	0.528292i
$815$	7.42307	−	3.16267i	0.260019	−	0.110784i
$816$	2.30437	−	7.95562i	0.0806692	−	0.278502i
$817$	2.79287	+	2.47427i	0.0977102	+	0.0865637i
$818$	11.3186	+	0.913729i	0.395744	+	0.0319478i
$819$	−0.909600	+	22.5715i	−0.0317840	+	0.788712i
$820$	0.0579759	+	1.43866i	0.00202460	+	0.0502400i
$821$	−18.7735	+	1.51555i	−0.655200	+	0.0528932i	−0.403596	−	0.914937i	$-0.632240\pi$
$821$	−18.7735	+	1.51555i	−0.655200	+	0.0528932i	−0.251604	+	0.967830i	$0.580958\pi$
$822$	19.1371	+	14.3806i	0.667485	+	0.501582i
$823$	6.89784	+	9.99325i	0.240444	+	0.348343i	0.924564	−	0.381026i	$-0.124429\pi$
$823$	6.89784	+	9.99325i	0.240444	+	0.348343i	−0.684121	+	0.729369i	$0.739814\pi$
$824$	1.47874	+	1.53953i	0.0515144	+	0.0536322i
$825$	−10.2244	−	6.46549i	−0.355967	−	0.225100i
$826$	11.9559	+	3.99145i	0.415998	+	0.138880i
$827$	−40.8672	+	30.7097i	−1.42109	+	1.06788i	−0.435231	+	0.900319i	$0.643333\pi$
$827$	−40.8672	+	30.7097i	−1.42109	+	1.06788i	−0.985861	+	0.167563i	$0.946410\pi$
$828$	−4.62034	+	4.09327i	−0.160568	+	0.142251i
$829$	−2.93931	−	6.19447i	−0.102087	−	0.215143i	0.845980	−	0.533214i	$-0.179016\pi$
$829$	−2.93931	−	6.19447i	−0.102087	−	0.215143i	−0.948067	+	0.318071i	$0.896965\pi$
$830$	−0.428017	−	0.902026i	−0.0148567	−	0.0313098i
$831$	−20.9019	+	18.5175i	−0.725079	+	0.642364i
$832$	4.11687	−	3.09363i	0.142727	−	0.107252i
$833$	85.3292	+	28.4871i	2.95648	+	0.987018i
$834$	1.67727	+	1.06064i	0.0580792	+	0.0367271i
$835$	2.11914	+	2.20626i	0.0733358	+	0.0763507i
$836$	−4.92279	−	7.13190i	−0.170258	−	0.246662i
$837$	35.7195	+	26.8414i	1.23465	+	0.927776i
$838$	−23.8155	+	1.92258i	−0.822691	+	0.0664145i
$839$	−1.54956	−	38.4520i	−0.0534968	−	1.32751i	−0.773614	−	0.633657i	$-0.781553\pi$
$839$	−1.54956	−	38.4520i	−0.0534968	−	1.32751i	0.720118	−	0.693852i	$-0.244088\pi$
$840$	0.190016	−	4.71519i	0.00655617	−	0.162690i
$841$	13.9590	+	1.12689i	0.481345	+	0.0388582i
$842$	−11.1687	−	9.89465i	−0.384900	−	0.340992i
$843$	6.78895	−	23.4382i	0.233824	−	0.807254i
$844$	−3.36709	+	1.43458i	−0.115900	+	0.0493803i
$845$	4.64824	+	8.05100i	0.159904	+	0.276963i
$846$	−0.157479	+	0.272762i	−0.00541426	+	0.00937777i
$847$	4.34029	−	35.7455i	0.149134	−	1.22823i
$848$	−3.40549	−	1.78734i	−0.116945	−	0.0613775i
$849$	1.45102	−	1.77717i	0.0497987	−	0.0609924i
$850$	−23.9277	−	10.1946i	−0.820712	−	0.349673i
$851$	−7.58131	−	62.4377i	−0.259884	−	2.14034i
$852$	−5.81303	+	15.3277i	−0.199151	+	0.525119i
$853$	8.61994	−	42.2233i	0.295141	−	1.44570i	−0.513852	−	0.857879i	$-0.671782\pi$
$853$	8.61994	−	42.2233i	0.295141	−	1.44570i	0.808993	−	0.587818i	$-0.200013\pi$
$854$	−9.36774	+	4.91657i	−0.320558	+	0.168242i
$855$	−1.05065	−	2.77033i	−0.0359314	−	0.0947433i
$856$	11.4734	−	1.86461i	0.392154	−	0.0637312i
$857$	5.55587	−	8.04907i	0.189785	−	0.274951i	−0.716528	−	0.697559i	$-0.754270\pi$
$857$	5.55587	−	8.04907i	0.189785	−	0.274951i	0.906313	+	0.422607i	$0.138885\pi$
$858$	13.0525	−	4.35755i	0.445604	−	0.148764i
$859$	12.1502	+	2.99476i	0.414559	+	0.102180i	0.441078	−	0.897469i	$-0.354596\pi$
$859$	12.1502	+	2.99476i	0.414559	+	0.102180i	−0.0265189	+	0.999648i	$0.508442\pi$
$860$	−0.463821	+	0.293303i	−0.0158162	+	0.0100015i
$861$	13.9514	−	3.43871i	0.475462	−	0.117191i
$862$	−0.423045	+	0.440437i	−0.0144090	+	0.0150013i
$863$	−7.53226	−	1.22411i	−0.256401	−	0.0416692i	0.0308520	−	0.999524i	$-0.490178\pi$
$863$	−7.53226	−	1.22411i	−0.256401	−	0.0416692i	−0.287253	+	0.957855i	$0.592742\pi$
$864$	−1.13087	−	5.53938i	−0.0384730	−	0.188453i
$865$	−2.79603	−	3.42451i	−0.0950678	−	0.116437i
$866$	−6.84911	−	23.6459i	−0.232742	−	0.803520i
$867$	9.89254	−	20.8481i	0.335968	−	0.708038i
$868$	37.6187			1.27686
$869$	6.24603	+	15.2441i	0.211882	+	0.517122i
$870$	3.83901			0.130155
$871$	3.35830	−	7.07746i	0.113792	−	0.239811i
$872$	−1.05412	−	3.63923i	−0.0356969	−	0.123240i
$873$	7.12169	+	8.72248i	0.241033	+	0.295211i
$874$	−6.26424	−	30.6843i	−0.211891	−	1.03791i
$875$	−30.7811	−	5.00241i	−1.04059	−	0.169112i
$876$	−10.3863	+	10.8133i	−0.350921	+	0.365347i
$877$	43.1904	−	10.6455i	1.45843	−	0.359472i	0.571208	−	0.820805i	$-0.306475\pi$
$877$	43.1904	−	10.6455i	1.45843	−	0.359472i	0.887227	+	0.461334i	$0.152629\pi$
$878$	19.9326	−	12.6046i	0.672694	−	0.425386i
$879$	20.3146	+	5.00709i	0.685193	+	0.168885i
$880$	1.20896	−	0.403609i	0.0407539	−	0.0136057i
$881$	−30.3637	+	43.9894i	−1.02298	+	1.48204i	−0.153452	+	0.988156i	$0.549039\pi$
$881$	−30.3637	+	43.9894i	−1.02298	+	1.48204i	−0.869527	+	0.493885i	$0.835576\pi$
$882$	14.2431	−	2.31472i	0.479588	−	0.0779407i
$883$	9.87539	+	26.0393i	0.332333	+	0.876291i	0.992171	+	0.124883i	$0.0398555\pi$
$883$	9.87539	+	26.0393i	0.332333	+	0.876291i	−0.659838	+	0.751408i	$0.729375\pi$
$884$	26.1967	−	13.7491i	0.881089	−	0.462431i
$885$	0.525094	−	2.57208i	0.0176508	−	0.0864596i
$886$	10.3173	−	27.2044i	0.346616	−	0.913950i
$887$	−0.0482950	−	0.397745i	−0.00162159	−	0.0133550i	0.991876	−	0.127211i	$-0.0406027\pi$
$887$	−0.0482950	−	0.397745i	−0.00162159	−	0.0133550i	−0.993497	+	0.113856i	$0.963680\pi$
$888$	12.4542	+	5.30623i	0.417935	+	0.178065i
$889$	−23.4137	+	28.6765i	−0.785269	+	0.961780i
$890$	7.58389	+	3.98033i	0.254213	+	0.133421i
$891$	1.20332	−	9.91025i	0.0403128	−	0.332006i
$892$	8.47322	−	14.6760i	0.283704	−	0.491390i
$893$	−0.798970	−	1.38386i	−0.0267365	−	0.0463090i
$894$	−10.4374	+	4.44695i	−0.349078	+	0.148728i
$895$	−3.99456	+	13.7908i	−0.133523	+	0.460977i
$896$	−3.56297	−	3.15651i	−0.119030	−	0.105452i
$897$	49.5675	+	4.00150i	1.65501	+	0.133606i
$898$	−1.08129	+	26.8319i	−0.0360831	+	0.895393i
$899$	1.23228	+	30.5787i	0.0410988	+	1.01986i
$900$	−4.15845	+	0.335705i	−0.138615	+	0.0111902i
$901$	−17.6644	−	13.2739i	−0.588486	−	0.442219i
$902$	2.20459	+	3.19390i	0.0734047	+	0.106345i
$903$	3.79377	+	3.94974i	0.126249	+	0.131439i
$904$	−4.20563	−	2.65948i	−0.139877	−	0.0884529i
$905$	−6.90747	−	2.30605i	−0.229612	−	0.0766557i
$906$	−11.5203	+	8.65696i	−0.382737	+	0.287608i
$907$	−36.3711	+	32.2220i	−1.20768	+	1.06991i	−0.211983	+	0.977273i	$0.567992\pi$
$907$	−36.3711	+	32.2220i	−1.20768	+	1.06991i	−0.995700	+	0.0926400i	$0.970469\pi$
$908$	2.17892	+	4.59198i	0.0723101	+	0.152390i
$909$	−6.05337	−	12.7572i	−0.200778	−	0.423130i
$910$	12.6171	−	11.1778i	0.418253	−	0.370540i
$911$	32.5196	−	24.4369i	1.07742	−	0.809632i	0.0948477	−	0.995492i	$-0.469764\pi$
$911$	32.5196	−	24.4369i	1.07742	−	0.809632i	0.982576	+	0.185860i	$0.0595072\pi$
$912$	6.39365	+	2.13452i	0.211715	+	0.0706809i
$913$	−2.27452	−	1.43832i	−0.0752756	−	0.0476014i
$914$	−22.7225	−	23.6567i	−0.751595	−	0.782493i
$915$	1.25167	+	1.81336i	0.0413790	+	0.0599478i
$916$	−8.16442	−	6.13516i	−0.269760	−	0.202711i
$917$	−64.8145	+	5.23237i	−2.14036	+	0.172788i
$918$	−1.30787	−	32.4544i	−0.0431661	−	1.07116i
$919$	−1.06095	+	26.3272i	−0.0349975	+	0.868455i	0.882404	+	0.470492i	$0.155924\pi$
$919$	−1.06095	+	26.3272i	−0.0349975	+	0.868455i	−0.917402	+	0.397963i	$0.869717\pi$
$920$	4.59108	+	0.370631i	0.151364	+	0.0122193i
$921$	11.6388	+	10.3110i	0.383510	+	0.339760i
$922$	−9.62856	+	33.2417i	−0.317100	+	1.09476i
$923$	−53.8699	+	22.9518i	−1.77315	+	0.755469i
$924$	−6.35978	−	11.0155i	−0.209221	−	0.362382i
$925$	21.2550	−	36.8147i	0.698860	−	1.21046i
$926$	3.76703	−	31.0243i	0.123792	−	1.01952i
$927$	1.74188	+	0.914209i	0.0572108	+	0.0300266i
$928$	2.44909	−	2.99959i	0.0803953	−	0.0984664i
$929$	1.24930	+	0.532276i	0.0409881	+	0.0174634i	0.412363	−	0.911019i	$-0.364703\pi$
$929$	1.24930	+	0.532276i	0.0409881	+	0.0174634i	−0.371375	+	0.928483i	$0.621114\pi$
$930$	−0.944381	−	7.77768i	−0.0309675	−	0.255040i
$931$	−25.9606	+	68.4525i	−0.850825	+	2.24344i
$932$	−2.28828	+	11.2087i	−0.0749551	+	0.367154i
$933$	18.0304	−	9.46307i	0.590288	−	0.309807i
$934$	6.52121	+	17.1950i	0.213380	+	0.562638i
$935$	7.22761	−	1.17460i	0.236368	−	0.0384136i
$936$	2.69586	−	3.90562i	0.0881168	−	0.127659i
$937$	35.1338	−	11.7294i	1.14777	−	0.383183i	0.321752	−	0.946824i	$-0.395728\pi$
$937$	35.1338	−	11.7294i	1.14777	−	0.383183i	0.826020	+	0.563641i	$0.190600\pi$
$938$	−7.03072	−	1.73292i	−0.229561	−	0.0565818i
$939$	18.6060	−	11.7657i	0.607183	−	0.383959i
$940$	0.228190	−	0.0562438i	0.00744274	−	0.00183447i
$941$	−33.4897	+	34.8665i	−1.09173	+	1.13661i	−0.101839	+	0.994801i	$0.532473\pi$
$941$	−33.4897	+	34.8665i	−1.09173	+	1.13661i	−0.989893	+	0.141813i	$0.954707\pi$
$942$	0.602865	+	0.0979751i	0.0196424	+	0.00319220i
$943$	2.80533	+	13.7414i	0.0913542	+	0.447482i
$944$	−1.67470	−	2.05113i	−0.0545068	−	0.0667587i
$945$	−5.14866	−	17.7752i	−0.167486	−	0.578228i
$946$	−0.634106	+	1.33635i	−0.0206166	+	0.0434485i
$947$	−46.3261			−1.50540			−0.752698	−	0.658366i	$-0.771248\pi$
$947$	−46.3261			−1.50540			−0.752698	+	0.658366i	$0.771248\pi$
$948$	−11.0071	−	6.56060i	−0.357494	−	0.213078i
$949$	−53.5564			−1.73851
$950$	9.07392	−	19.1229i	0.294397	−	0.620428i
$951$	5.44701	+	18.8053i	0.176631	+	0.609802i
$952$	−17.2956	−	21.1833i	−0.560553	−	0.686553i
$953$	−10.4962	−	51.4136i	−0.340004	−	1.66545i	−0.686296	−	0.727322i	$-0.740764\pi$
$953$	−10.4962	−	51.4136i	−0.340004	−	1.66545i	0.346292	−	0.938127i	$-0.387441\pi$
$954$	−3.49841	−	0.568547i	−0.113265	−	0.0184074i
$955$	9.72768	−	10.1276i	0.314780	−	0.327721i
$956$	23.2093	−	5.72058i	0.750643	−	0.185017i
$957$	8.74570	−	5.53044i	0.282708	−	0.178774i
$958$	−33.2847	−	8.20394i	−1.07538	−	0.265057i
$959$	74.9700	−	25.0287i	2.42091	−	0.808218i
$960$	−0.563165	+	0.815886i	−0.0181761	+	0.0263326i
$961$	31.0495	−	5.04603i	1.00160	−	0.162775i
$962$	17.1472	+	45.2133i	0.552847	+	1.45774i
$963$	9.48506	−	4.97814i	0.305652	−	0.160418i
$964$	4.83766	−	23.6964i	0.155810	−	0.763210i
$965$	−0.0225847	+	0.0595509i	−0.000727026	+	0.00191701i
$966$	−5.54064	−	45.6313i	−0.178267	−	1.46816i
$967$	−45.4216	−	19.3523i	−1.46066	−	0.622329i	−0.491972	−	0.870611i	$-0.663724\pi$
$967$	−45.4216	−	19.3523i	−1.46066	−	0.622329i	−0.968688	+	0.248282i	$0.920134\pi$
$968$	−4.78420	+	5.85958i	−0.153770	+	0.188334i
$969$	34.2895	+	17.9965i	1.10154	+	0.578131i
$970$	1.01281	−	8.34125i	0.0325194	−	0.267821i
$971$	2.53257	−	4.38654i	0.0812741	−	0.140771i	−0.822523	−	0.568731i	$-0.807434\pi$
$971$	2.53257	−	4.38654i	0.0812741	−	0.140771i	0.903797	+	0.427960i	$0.140768\pi$
$972$	−4.59793	−	7.96384i	−0.147479	−	0.255440i
$973$	6.02798	−	2.56828i	0.193248	−	0.0823353i
$974$	0.504398	−	1.74139i	0.0161620	−	0.0557976i
$975$	25.1577	+	22.2878i	0.805692	+	0.713781i
$976$	2.21536	+	0.178842i	0.0709118	+	0.00572459i
$977$	0.318650	−	7.90722i	0.0101945	−	0.252974i	−0.986053	−	0.166429i	$-0.946776\pi$
$977$	0.318650	−	7.90722i	0.0101945	−	0.252974i	0.996248	−	0.0865452i	$-0.0275827\pi$
$978$	0.681153	+	16.9026i	0.0217809	+	0.540487i
$979$	23.0110	−	1.85764i	0.735433	−	0.0593703i
$980$	−8.60797	−	6.46847i	−0.274971	−	0.206628i
$981$	−1.98345	−	2.87352i	−0.0633266	−	0.0917444i
$982$	19.4882	+	20.2893i	0.621892	+	0.647458i
$983$	6.13747	+	3.88110i	0.195755	+	0.123788i	0.628747	−	0.777610i	$-0.283568\pi$
$983$	6.13747	+	3.88110i	0.195755	+	0.123788i	−0.432992	+	0.901398i	$0.642542\pi$
$984$	−2.86329	−	0.955906i	−0.0912783	−	0.0304732i
$985$	0.903164	−	0.678684i	0.0287772	−	0.0216247i
$986$	16.6525	−	14.7528i	0.530322	−	0.469825i
$987$	−1.00546	−	2.11896i	−0.0320041	−	0.0674473i
$988$	10.3217	+	21.7525i	0.328377	+	0.692040i
$989$	−4.00113	+	3.54470i	−0.127229	+	0.112715i
$990$	0.938995	−	0.705609i	0.0298432	−	0.0224257i
$991$	−6.28908	−	2.09960i	−0.199779	−	0.0666961i	0.215018	−	0.976610i	$-0.431019\pi$
$991$	−6.28908	−	2.09960i	−0.199779	−	0.0666961i	−0.414797	+	0.909914i	$0.636147\pi$
$992$	−6.67951	−	4.22386i	−0.212075	−	0.134108i
$993$	−27.0686	−	28.1814i	−0.858995	−	0.894308i
$994$	30.7468	+	44.5444i	0.975229	+	1.41286i
$995$	9.39398	+	7.05912i	0.297809	+	0.223789i
$996$	2.08644	−	0.168435i	0.0661114	−	0.00533706i
$997$	1.87921	+	46.6321i	0.0595152	+	1.47685i	0.702888	+	0.711301i	$0.251894\pi$
$997$	1.87921	+	46.6321i	0.0595152	+	1.47685i	−0.643373	+	0.765553i	$0.722465\pi$
$998$	0.719852	−	17.8629i	0.0227865	−	0.565442i
$999$	52.9157	+	4.27179i	1.67418	+	0.135154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	158.2.g.a.19.3	✓	72
79.25	even	39	inner	158.2.g.a.25.3	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
158.2.g.a.19.3	✓	72	1.1	even	1	trivial
158.2.g.a.25.3	yes	72	79.25	even	39	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 158 = 2 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	158.g (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.428693 + 0.903450i) q^{2} +(0.401101 + 1.38476i) q^{3} +(-0.632445 - 0.774605i) q^{4} +(0.137548 + 0.673754i) q^{5} +(-1.42301 - 0.231262i) q^{6} +(-3.29742 + 3.43298i) q^{7} +(0.970942 - 0.239316i) q^{8} +(0.778885 - 0.492537i) q^{9} +(-0.667669 - 0.164566i) q^{10} +(-1.75810 + 0.586939i) q^{11} +(0.818969 - 1.18648i) q^{12} +(5.08299 - 0.826067i) q^{13} +(-1.68795 - 4.45075i) q^{14} +(-0.877819 + 0.460715i) q^{15} +(-0.200026 + 0.979791i) q^{16} +(-2.03725 + 5.37178i) q^{17} +(0.111081 + 0.914831i) q^{18} +(-4.30134 - 1.83263i) q^{19} +(0.434902 - 0.532658i) q^{20} +(-6.07646 - 3.18917i) q^{21} +(0.223413 - 1.83997i) q^{22} +(3.34910 - 5.80080i) q^{23} +(0.720842 + 1.24853i) q^{24} +(4.16487 - 1.77449i) q^{25} +(-1.43273 + 4.94636i) q^{26} +(4.23180 + 3.74905i) q^{27} +(4.74464 + 0.383027i) q^{28} +(-0.155926 + 3.86927i) q^{29} +(-0.0399187 - 0.990571i) q^{30} +(7.87734 - 0.635924i) q^{31} +(-0.799443 - 0.600742i) q^{32} +(-1.51795 - 2.19912i) q^{33} +(-3.97978 - 4.14339i) q^{34} +(-2.76654 - 1.74945i) q^{35} +(-0.874124 - 0.291825i) q^{36} +(7.50680 - 5.64099i) q^{37} +(3.49964 - 3.10041i) q^{38} +(3.18270 + 6.70740i) q^{39} +(0.294791 + 0.621259i) q^{40} +(-1.56725 + 1.38846i) q^{41} +(5.48619 - 4.12261i) q^{42} +(-0.756975 - 0.252715i) q^{43} +(1.56655 + 0.990623i) q^{44} +(0.438983 + 0.457030i) q^{45} +(3.80501 + 5.51250i) q^{46} +(0.273226 + 0.205316i) q^{47} +(-1.43701 + 0.116007i) q^{48} +(-0.630497 - 15.6456i) q^{49} +(-0.182289 + 4.52346i) q^{50} +(-8.25578 - 0.666475i) q^{51} +(-3.85459 - 3.41487i) q^{52} +(-1.07003 + 3.69418i) q^{53} +(-5.20123 + 2.21604i) q^{54} +(-0.637275 - 1.10379i) q^{55} +(-2.38004 + 4.12235i) q^{56} +(0.812483 - 6.69140i) q^{57} +(-3.42885 - 1.79960i) q^{58} +(-1.67470 + 2.05113i) q^{59} +(0.912045 + 0.388586i) q^{60} +(-0.267900 - 2.20636i) q^{61} +(-2.80243 + 7.38940i) q^{62} +(-0.877442 + 4.29800i) q^{63} +(0.885456 - 0.464723i) q^{64} +(1.25572 + 3.31106i) q^{65} +(2.63753 - 0.428641i) q^{66} +(0.864153 - 1.25194i) q^{67} +(5.44945 - 1.81929i) q^{68} +(9.37606 + 2.31099i) q^{69} +(2.76654 - 1.74945i) q^{70} +(-11.0403 + 2.72119i) q^{71} +(0.638380 - 0.664624i) q^{72} +(-10.2653 - 1.66827i) q^{73} +(1.87825 + 9.20027i) q^{74} +(4.12778 + 5.05561i) q^{75} +(1.30080 + 4.49087i) q^{76} +(3.78223 - 7.97089i) q^{77} -7.42420 q^{78} +(-0.591996 - 8.86846i) q^{79} -0.687651 q^{80} +(-2.30898 + 4.86607i) q^{81} +(-0.582540 - 2.01116i) q^{82} +(0.918268 + 1.12467i) q^{83} +(1.37268 + 6.72383i) q^{84} +(-3.89948 - 0.633727i) q^{85} +(0.552825 - 0.575552i) q^{86} +(-5.42057 + 1.33605i) q^{87} +(-1.56655 + 0.990623i) q^{88} +(-12.0934 - 2.98077i) q^{89} +(-0.601092 + 0.200674i) q^{90} +(-13.9249 + 20.1737i) q^{91} +(-6.61145 + 1.07447i) q^{92} +(4.04022 + 10.6532i) q^{93} +(-0.302623 + 0.158829i) q^{94} +(0.643101 - 3.15012i) q^{95} +(0.511228 - 1.34800i) q^{96} +(1.47286 + 12.1301i) q^{97} +(14.4053 + 6.13753i) q^{98} +(-1.08027 + 1.32308i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 3 q^{2} - q^{3} + 3 q^{4} + 14 q^{5} + q^{6} - 4 q^{7} + 6 q^{8} - 2 q^{9} + 2 q^{10} + 7 q^{11} + 2 q^{12} + 23 q^{13} + 5 q^{14} - 16 q^{15} + 3 q^{16} - 58 q^{17} - 4 q^{18} + 20 q^{19} + q^{20}+ \cdots + 10 q^{99}+O(q^{100}) \) 72 * q - 3 * q^2 - q^3 + 3 * q^4 + 14 * q^5 + q^6 - 4 * q^7 + 6 * q^8 - 2 * q^9 + 2 * q^10 + 7 * q^11 + 2 * q^12 + 23 * q^13 + 5 * q^14 - 16 * q^15 + 3 * q^16 - 58 * q^17 - 4 * q^18 + 20 * q^19 + q^20 - 44 * q^21 + q^22 - 5 * q^23 - 12 * q^24 - q^25 - 23 * q^26 - 31 * q^27 - 4 * q^28 + 12 * q^29 + 31 * q^30 - 9 * q^31 - 3 * q^32 - 84 * q^33 - 3 * q^34 - 47 * q^35 - 2 * q^36 - 23 * q^37 - 12 * q^38 - 46 * q^39 - q^40 - 14 * q^41 - 87 * q^42 + 29 * q^43 - 19 * q^44 + 45 * q^45 + 16 * q^46 - 35 * q^47 - q^48 - 27 * q^49 - 38 * q^50 + 53 * q^51 + 6 * q^52 - 46 * q^53 + 43 * q^54 - 4 * q^55 - 22 * q^56 + 24 * q^58 - 34 * q^59 - 83 * q^60 + 93 * q^61 - 31 * q^62 - 51 * q^63 - 6 * q^64 + 100 * q^65 + 88 * q^66 - 14 * q^67 + 29 * q^68 - 36 * q^69 + 47 * q^70 + 26 * q^71 + 2 * q^72 + 37 * q^73 + 49 * q^74 + 123 * q^75 + 33 * q^76 + 28 * q^77 + 12 * q^78 + 142 * q^79 - 2 * q^80 + 229 * q^81 + 84 * q^82 + 4 * q^83 + 113 * q^84 + 49 * q^85 + 49 * q^86 - 161 * q^87 + 19 * q^88 - 2 * q^89 - 19 * q^90 + 117 * q^91 + 21 * q^92 + 64 * q^93 - 44 * q^94 + 80 * q^95 - 2 * q^96 - 38 * q^97 - 64 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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