LMFDB - Embedded newform 570.2.bb.a.41.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(41,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 13]))

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

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

chi := DirichletCharacter("570.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.14
Character	$\chi$	$=$	570.41
Dual form			570.2.bb.a.431.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(1.69734 + 0.345017i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(1.07847 + 1.35533i) q^{6} +(-0.267952 - 0.464106i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.76193 + 1.17122i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(1.69734 + 0.345017i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(1.07847 + 1.35533i) q^{6} +(-0.267952 - 0.464106i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.76193 + 1.17122i) q^{9} +(0.642788 + 0.766044i) q^{10} +(0.233354 + 0.134727i) q^{11} +(-0.0450352 + 1.73147i) q^{12} +(-0.650596 + 1.78750i) q^{13} +(0.0930587 - 0.527762i) q^{14} +(1.61164 + 0.634515i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.328167 + 0.391094i) q^{17} +(1.36291 + 2.67254i) q^{18} +(-0.783767 - 4.28786i) q^{19} +1.00000i q^{20} +(-0.294681 - 0.880194i) q^{21} +(0.0921587 + 0.253204i) q^{22} +(0.229565 - 0.0404785i) q^{23} +(-1.14746 + 1.29743i) q^{24} +(0.939693 + 0.342020i) q^{25} +(-1.64737 + 0.951108i) q^{26} +(4.28384 + 2.94087i) q^{27} +(0.410526 - 0.344472i) q^{28} +(-4.10900 + 3.44786i) q^{29} +(0.826731 + 1.52201i) q^{30} +(6.10497 - 3.52471i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.349598 + 0.309189i) q^{33} +(-0.502781 + 0.0886538i) q^{34} +(-0.183290 - 0.503585i) q^{35} +(-0.673825 + 2.92335i) q^{36} -9.16197i q^{37} +(2.15578 - 3.78848i) q^{38} +(-1.72100 + 2.80953i) q^{39} +(-0.642788 + 0.766044i) q^{40} +(-10.9164 + 3.97326i) q^{41} +(0.340039 - 0.863685i) q^{42} +(-1.13925 + 6.46098i) q^{43} +(-0.0921587 + 0.253204i) q^{44} +(2.51659 + 1.63303i) q^{45} +(0.201876 + 0.116553i) q^{46} +(-5.83426 - 6.95300i) q^{47} +(-1.71298 + 0.256315i) q^{48} +(3.35640 - 5.81346i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-0.691945 + 0.550596i) q^{51} +(-1.87332 - 0.330316i) q^{52} +(0.990668 + 5.61836i) q^{53} +(1.39125 + 5.00644i) q^{54} +(0.206414 + 0.173202i) q^{55} +0.535904 q^{56} +(0.149063 - 7.54836i) q^{57} -5.36392 q^{58} +(4.93759 + 4.14313i) q^{59} +(-0.345017 + 1.69734i) q^{60} +(-1.85625 - 10.5273i) q^{61} +(6.94232 + 1.22412i) q^{62} +(-0.196492 - 1.59566i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.951108 + 1.64737i) q^{65} +(0.0690650 + 0.461569i) q^{66} +(-3.68533 - 4.39200i) q^{67} +(-0.442138 - 0.255268i) q^{68} +(0.403615 + 0.0104980i) q^{69} +(0.183290 - 0.503585i) q^{70} +(1.11428 - 6.31942i) q^{71} +(-2.39527 + 1.80629i) q^{72} +(-5.29912 + 1.92872i) q^{73} +(5.88920 - 7.01847i) q^{74} +(1.47698 + 0.904734i) q^{75} +(4.08661 - 1.51644i) q^{76} -0.144401i q^{77} +(-3.12429 + 1.04598i) q^{78} +(2.34946 + 6.45509i) q^{79} +(-0.984808 + 0.173648i) q^{80} +(6.25648 + 6.46966i) q^{81} +(-10.9164 - 3.97326i) q^{82} +(-2.54105 + 1.46708i) q^{83} +(0.815651 - 0.443048i) q^{84} +(-0.391094 + 0.328167i) q^{85} +(-5.02575 + 4.21711i) q^{86} +(-8.16395 + 4.43452i) q^{87} +(-0.233354 + 0.134727i) q^{88} +(0.978707 + 0.356220i) q^{89} +(0.878124 + 2.86861i) q^{90} +(1.00392 - 0.177018i) q^{91} +(0.0797270 + 0.219048i) q^{92} +(11.5783 - 3.87631i) q^{93} -9.07650i q^{94} +(-0.0272815 - 4.35881i) q^{95} +(-1.47698 - 0.904734i) q^{96} +(1.37835 - 1.64266i) q^{97} +(6.30798 - 2.29592i) q^{98} +(0.486711 + 0.645415i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9}+O(q^{10}) $ 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9	$ 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9} + 24 q^{13} + 24 q^{14} - 12 q^{17} - 12 q^{19} + 36 q^{22} - 6 q^{24} - 6 q^{27} - 12 q^{28} + 12 q^{29} - 6 q^{33} + 12 q^{34} - 18 q^{38} + 12 q^{39} - 6 q^{41} + 24 q^{43} - 36 q^{44} - 12 q^{47} - 54 q^{49} + 42 q^{50} - 54 q^{51} + 12 q^{52} + 60 q^{53} - 54 q^{54} - 60 q^{57} - 24 q^{58} + 18 q^{59} - 48 q^{61} + 12 q^{62} + 18 q^{63} - 42 q^{64} + 54 q^{66} + 6 q^{67} + 54 q^{68} - 60 q^{69} - 48 q^{71} - 12 q^{72} + 84 q^{73} - 24 q^{74} + 36 q^{78} - 12 q^{79} + 114 q^{81} - 6 q^{82} - 36 q^{83} - 18 q^{84} - 12 q^{86} + 6 q^{87} + 12 q^{89} + 24 q^{91} + 6 q^{93} + 12 q^{95} - 42 q^{97} - 36 q^{98} + 102 q^{99}+O(q^{100}) $ 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9 + 24 * q^13 + 24 * q^14 - 12 * q^17 - 12 * q^19 + 36 * q^22 - 6 * q^24 - 6 * q^27 - 12 * q^28 + 12 * q^29 - 6 * q^33 + 12 * q^34 - 18 * q^38 + 12 * q^39 - 6 * q^41 + 24 * q^43 - 36 * q^44 - 12 * q^47 - 54 * q^49 + 42 * q^50 - 54 * q^51 + 12 * q^52 + 60 * q^53 - 54 * q^54 - 60 * q^57 - 24 * q^58 + 18 * q^59 - 48 * q^61 + 12 * q^62 + 18 * q^63 - 42 * q^64 + 54 * q^66 + 6 * q^67 + 54 * q^68 - 60 * q^69 - 48 * q^71 - 12 * q^72 + 84 * q^73 - 24 * q^74 + 36 * q^78 - 12 * q^79 + 114 * q^81 - 6 * q^82 - 36 * q^83 - 18 * q^84 - 12 * q^86 + 6 * q^87 + 12 * q^89 + 24 * q^91 + 6 * q^93 + 12 * q^95 - 42 * q^97 - 36 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$	$1$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	1.69734	+	0.345017i	0.979960	+	0.199196i
$3$	1.69734	+	0.345017i	0.979960	+	0.199196i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.984808	+	0.173648i	0.440419	+	0.0776578i
$5$	0.984808	+	0.173648i	0.440419	+	0.0776578i
$6$	1.07847	+	1.35533i	0.440282	+	0.553310i
$7$	−0.267952	−	0.464106i	−0.101276	−	0.175416i	0.810934	−	0.585137i	$-0.198959\pi$
$7$	−0.267952	−	0.464106i	−0.101276	−	0.175416i	−0.912211	+	0.409721i	$0.865626\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	2.76193	+	1.17122i	0.920642	+	0.390407i
$10$	0.642788	+	0.766044i	0.203267	+	0.242245i
$11$	0.233354	+	0.134727i	0.0703589	+	0.0406217i	0.534767	−	0.845000i	$-0.320399\pi$
$11$	0.233354	+	0.134727i	0.0703589	+	0.0406217i	−0.464408	+	0.885621i	$0.653733\pi$
$12$	−0.0450352	+	1.73147i	−0.0130005	+	0.499831i
$13$	−0.650596	+	1.78750i	−0.180443	+	0.495763i	−0.996630	−	0.0820244i	$-0.973861\pi$
$13$	−0.650596	+	1.78750i	−0.180443	+	0.495763i	0.816187	+	0.577787i	$0.196084\pi$
$14$	0.0930587	−	0.527762i	0.0248710	−	0.141050i
$15$	1.61164	+	0.634515i	0.416124	+	0.163831i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−0.328167	+	0.391094i	−0.0795921	+	0.0948542i	−0.804371	−	0.594127i	$-0.797497\pi$
$17$	−0.328167	+	0.391094i	−0.0795921	+	0.0948542i	0.724779	+	0.688982i	$0.241942\pi$
$18$	1.36291	+	2.67254i	0.321241	+	0.629924i
$19$	−0.783767	−	4.28786i	−0.179809	−	0.983702i
$19$	−0.783767	−	4.28786i	−0.179809	−	0.983702i
$20$			1.00000i			0.223607i
$21$	−0.294681	−	0.880194i	−0.0643047	−	0.192074i
$22$	0.0921587	+	0.253204i	0.0196483	+	0.0539832i
$23$	0.229565	−	0.0404785i	0.0478676	−	0.00844035i	−0.149663	−	0.988737i	$-0.547819\pi$
$23$	0.229565	−	0.0404785i	0.0478676	−	0.00844035i	0.197531	+	0.980297i	$0.436708\pi$
$24$	−1.14746	+	1.29743i	−0.234225	+	0.264837i
$25$	0.939693	+	0.342020i	0.187939	+	0.0684040i
$26$	−1.64737	+	0.951108i	−0.323075	+	0.186528i
$27$	4.28384	+	2.94087i	0.824425	+	0.565971i
$28$	0.410526	−	0.344472i	0.0775821	−	0.0650991i
$29$	−4.10900	+	3.44786i	−0.763023	+	0.640252i	−0.938912	−	0.344158i	$-0.888164\pi$
$29$	−4.10900	+	3.44786i	−0.763023	+	0.640252i	0.175889	+	0.984410i	$0.443720\pi$
$30$	0.826731	+	1.52201i	0.150940	+	0.277880i
$31$	6.10497	−	3.52471i	1.09649	−	0.633056i	0.161190	−	0.986923i	$-0.448467\pi$
$31$	6.10497	−	3.52471i	1.09649	−	0.633056i	0.935296	+	0.353867i	$0.115134\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	0.349598	+	0.309189i	0.0608572	+	0.0538228i
$34$	−0.502781	+	0.0886538i	−0.0862262	+	0.0152040i
$35$	−0.183290	−	0.503585i	−0.0309816	−	0.0851213i
$36$	−0.673825	+	2.92335i	−0.112304	+	0.487225i
$37$		−	9.16197i		−	1.50622i	−0.657896	−	0.753109i	$-0.728553\pi$
$37$		−	9.16197i		−	1.50622i	0.657896	−	0.753109i	$-0.271447\pi$
$38$	2.15578	−	3.78848i	0.349714	−	0.614573i
$39$	−1.72100	+	2.80953i	−0.275581	+	0.449884i
$40$	−0.642788	+	0.766044i	−0.101634	+	0.121122i
$41$	−10.9164	+	3.97326i	−1.70486	+	0.620519i	−0.996364	−	0.0851933i	$-0.972849\pi$
$41$	−10.9164	+	3.97326i	−1.70486	+	0.620519i	−0.708498	+	0.705713i	$0.750627\pi$
$42$	0.340039	−	0.863685i	0.0524692	−	0.133269i
$43$	−1.13925	+	6.46098i	−0.173733	+	0.985291i	0.765862	+	0.643005i	$0.222312\pi$
$43$	−1.13925	+	6.46098i	−0.173733	+	0.985291i	−0.939596	+	0.342286i	$0.888799\pi$
$44$	−0.0921587	+	0.253204i	−0.0138934	+	0.0381719i
$45$	2.51659	+	1.63303i	0.375151	+	0.243438i
$46$	0.201876	+	0.116553i	0.0297650	+	0.0171848i
$47$	−5.83426	−	6.95300i	−0.851014	−	1.01420i	−0.999680	−	0.0253119i	$-0.991942\pi$
$47$	−5.83426	−	6.95300i	−0.851014	−	1.01420i	0.148665	−	0.988888i	$-0.452502\pi$
$48$	−1.71298	+	0.256315i	−0.247247	+	0.0369958i
$49$	3.35640	−	5.81346i	0.479486	−	0.830495i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−0.691945	+	0.550596i	−0.0968916	+	0.0770989i
$52$	−1.87332	−	0.330316i	−0.259782	−	0.0458066i
$53$	0.990668	+	5.61836i	0.136079	+	0.771741i	0.974102	+	0.226107i	$0.0725999\pi$
$53$	0.990668	+	5.61836i	0.136079	+	0.771741i	−0.838024	+	0.545634i	$0.816289\pi$
$54$	1.39125	+	5.00644i	0.189326	+	0.681290i
$55$	0.206414	+	0.173202i	0.0278328	+	0.0233545i
$56$	0.535904			0.0716131
$57$	0.149063	−	7.54836i	0.0197439	−	0.999805i
$58$	−5.36392			−0.704317
$59$	4.93759	+	4.14313i	0.642820	+	0.539390i	0.904883	−	0.425661i	$-0.139958\pi$
$59$	4.93759	+	4.14313i	0.642820	+	0.539390i	−0.262063	+	0.965051i	$0.584403\pi$
$60$	−0.345017	+	1.69734i	−0.0445415	+	0.219126i
$61$	−1.85625	−	10.5273i	−0.237669	−	1.34789i	−0.836920	−	0.547325i	$-0.815646\pi$
$61$	−1.85625	−	10.5273i	−0.237669	−	1.34789i	0.599252	−	0.800561i	$-0.295465\pi$
$62$	6.94232	+	1.22412i	0.881675	+	0.155463i
$63$	−0.196492	−	1.59566i	−0.0247557	−	0.201034i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.951108	+	1.64737i	−0.117970	+	0.204331i
$66$	0.0690650	+	0.461569i	0.00850132	+	0.0568153i
$67$	−3.68533	−	4.39200i	−0.450235	−	0.536569i	0.492412	−	0.870363i	$-0.336116\pi$
$67$	−3.68533	−	4.39200i	−0.450235	−	0.536569i	−0.942646	+	0.333794i	$0.891671\pi$
$68$	−0.442138	−	0.255268i	−0.0536171	−	0.0309558i
$69$	0.403615	+	0.0104980i	0.0485896	+	0.00126381i
$70$	0.183290	−	0.503585i	0.0219073	−	0.0601899i
$71$	1.11428	−	6.31942i	0.132241	−	0.749978i	−0.844500	−	0.535556i	$-0.820102\pi$
$71$	1.11428	−	6.31942i	0.132241	−	0.749978i	0.976741	−	0.214422i	$-0.0687867\pi$
$72$	−2.39527	+	1.80629i	−0.282285	+	0.212873i
$73$	−5.29912	+	1.92872i	−0.620215	+	0.225740i	−0.632967	−	0.774179i	$-0.718163\pi$
$73$	−5.29912	+	1.92872i	−0.620215	+	0.225740i	0.0127519	+	0.999919i	$0.495941\pi$
$74$	5.88920	−	7.01847i	0.684605	−	0.815881i
$75$	1.47698	+	0.904734i	0.170546	+	0.104470i
$76$	4.08661	−	1.51644i	0.468767	−	0.173947i
$77$		−	0.144401i		−	0.0164561i
$78$	−3.12429	+	1.04598i	−0.353756	+	0.118434i
$79$	2.34946	+	6.45509i	0.264335	+	0.726254i	0.998863	+	0.0476758i	$0.0151814\pi$
$79$	2.34946	+	6.45509i	0.264335	+	0.726254i	−0.734528	+	0.678578i	$0.762596\pi$
$80$	−0.984808	+	0.173648i	−0.110105	+	0.0194145i
$81$	6.25648	+	6.46966i	0.695164	+	0.718851i
$82$	−10.9164	−	3.97326i	−1.20552	−	0.438773i
$83$	−2.54105	+	1.46708i	−0.278917	+	0.161033i	−0.632933	−	0.774207i	$-0.718149\pi$
$83$	−2.54105	+	1.46708i	−0.278917	+	0.161033i	0.354016	+	0.935239i	$0.384816\pi$
$84$	0.815651	−	0.443048i	0.0889948	−	0.0483405i
$85$	−0.391094	+	0.328167i	−0.0424201	+	0.0355947i
$86$	−5.02575	+	4.21711i	−0.541941	+	0.454742i
$87$	−8.16395	+	4.43452i	−0.875267	+	0.475431i
$88$	−0.233354	+	0.134727i	−0.0248756	+	0.0143619i
$89$	0.978707	+	0.356220i	0.103743	+	0.0377593i	0.393370	−	0.919380i	$-0.371309\pi$
$89$	0.978707	+	0.356220i	0.103743	+	0.0377593i	−0.289627	+	0.957140i	$0.593531\pi$
$90$	0.878124	+	2.86861i	0.0925624	+	0.302378i
$91$	1.00392	−	0.177018i	0.105239	−	0.0185565i
$92$	0.0797270	+	0.219048i	0.00831212	+	0.0228374i
$93$	11.5783	−	3.87631i	1.20061	−	0.401954i
$94$		−	9.07650i		−	0.936169i
$95$	−0.0272815	−	4.35881i	−0.00279903	−	0.447205i
$96$	−1.47698	−	0.904734i	−0.150743	−	0.0923391i
$97$	1.37835	−	1.64266i	0.139951	−	0.166787i	−0.691516	−	0.722361i	$-0.743057\pi$
$97$	1.37835	−	1.64266i	0.139951	−	0.166787i	0.831467	+	0.555574i	$0.187502\pi$
$98$	6.30798	−	2.29592i	0.637202	−	0.231922i
$99$	0.486711	+	0.645415i	0.0489163	+	0.0648667i
$100$	−0.173648	+	0.984808i	−0.0173648	+	0.0984808i
$101$	0.615693	−	1.69160i	0.0612637	−	0.168321i	−0.905284	−	0.424806i	$-0.860342\pi$
$101$	0.615693	−	1.69160i	0.0612637	−	0.168321i	0.966548	+	0.256485i	$0.0825645\pi$
$102$	−0.883977	−	0.0229921i	−0.0875268	−	0.00227656i
$103$	0.441213	+	0.254735i	0.0434740	+	0.0250997i	0.521579	−	0.853203i	$-0.325343\pi$
$103$	0.441213	+	0.254735i	0.0434740	+	0.0250997i	−0.478105	+	0.878302i	$0.658676\pi$
$104$	−1.22272	−	1.45718i	−0.119898	−	0.142888i
$105$	−0.137360	−	0.917993i	−0.0134050	−	0.0895869i
$106$	−2.85251	+	4.94070i	−0.277061	+	0.479883i
$107$	3.00447	+	5.20390i	0.290453	+	0.503080i	0.973917	−	0.226905i	$-0.0728606\pi$
$107$	3.00447	+	5.20390i	0.290453	+	0.503080i	−0.683464	+	0.729985i	$0.739527\pi$
$108$	−2.15231	+	4.72943i	−0.207106	+	0.455090i
$109$	−8.15550	−	1.43803i	−0.781155	−	0.137739i	−0.231170	−	0.972913i	$-0.574255\pi$
$109$	−8.15550	−	1.43803i	−0.781155	−	0.137739i	−0.549985	+	0.835175i	$0.685366\pi$
$110$	0.0467902	+	0.265360i	0.00446127	+	0.0253011i
$111$	3.16103	−	15.5510i	0.300032	−	1.47603i
$112$	0.410526	+	0.344472i	0.0387911	+	0.0325496i
$113$	3.25482			0.306187			0.153094	−	0.988212i	$-0.451076\pi$
$113$	3.25482			0.306187			0.153094	+	0.988212i	$0.451076\pi$
$114$	4.96618	−	5.68657i	0.465126	−	0.532596i
$115$	0.233106			0.0217373
$116$	−4.10900	−	3.44786i	−0.381511	−	0.320126i
$117$	−3.89046	+	4.17495i	−0.359673	+	0.385974i
$118$	1.11926	+	6.34765i	0.103036	+	0.584348i
$119$	0.269442	+	0.0475099i	0.0246997	+	0.00435522i
$120$	−1.35533	+	1.07847i	−0.123724	+	0.0984500i
$121$	−5.46370	−	9.46340i	−0.496700	−	0.860309i
$122$	5.34486	−	9.25757i	0.483901	−	0.838141i
$123$	−19.8998	+	2.97762i	−1.79430	+	0.268483i
$124$	4.53128	+	5.40016i	0.406921	+	0.484949i
$125$	0.866025	+	0.500000i	0.0774597	+	0.0447214i
$126$	0.875148	−	1.34865i	0.0779643	−	0.120147i
$127$	1.72312	−	4.73423i	0.152902	−	0.420095i	−0.839465	−	0.543414i	$-0.817132\pi$
$127$	1.72312	−	4.73423i	0.152902	−	0.420095i	0.992367	+	0.123319i	$0.0393537\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	−4.16284	+	10.5734i	−0.366517	+	0.930938i
$130$	−1.78750	+	0.650596i	−0.156774	+	0.0570611i
$131$	1.36599	−	1.62793i	0.119347	−	0.142233i	−0.703063	−	0.711128i	$-0.748185\pi$
$131$	1.36599	−	1.62793i	0.119347	−	0.142233i	0.822410	+	0.568895i	$0.192629\pi$
$132$	−0.243784	+	0.397977i	−0.0212187	+	0.0346394i
$133$	−1.78001	+	1.51269i	−0.154346	+	0.131167i
$134$		−	5.73335i		−	0.495286i
$135$	3.70808	+	3.64007i	0.319141	+	0.313288i
$136$	−0.174614	−	0.479748i	−0.0149730	−	0.0411380i
$137$	−3.53497	+	0.623310i	−0.302012	+	0.0532529i	−0.322601	−	0.946535i	$-0.604557\pi$
$137$	−3.53497	+	0.623310i	−0.302012	+	0.0532529i	0.0205884	+	0.999788i	$0.493446\pi$
$138$	0.302439	+	0.267481i	0.0257453	+	0.0227695i
$139$	13.0375	+	4.74526i	1.10582	+	0.402487i	0.829460	−	0.558566i	$-0.188648\pi$
$139$	13.0375	+	4.74526i	1.10582	+	0.402487i	0.276365	+	0.961053i	$0.410870\pi$
$140$	0.464106	−	0.267952i	0.0392241	−	0.0226461i
$141$	−7.50382	−	13.8145i	−0.631936	−	1.16339i
$142$	4.91564	−	4.12471i	0.412511	−	0.346138i
$143$	−0.392643	+	0.329467i	−0.0328345	+	0.0275514i
$144$	−2.99594	−	0.155954i	−0.249662	−	0.0129961i
$145$	−4.64529	+	2.68196i	−0.385771	+	0.222725i
$146$	−5.29912	−	1.92872i	−0.438558	−	0.159622i
$147$	7.70270	−	8.70941i	0.635308	−	0.718340i
$148$	9.02277	−	1.59096i	0.741667	−	0.130776i
$149$	−6.14443	−	16.8817i	−0.503371	−	1.38300i	−0.887963	−	0.459915i	$-0.847880\pi$
$149$	−6.14443	−	16.8817i	−0.503371	−	1.38300i	0.384592	−	0.923087i	$-0.374342\pi$
$150$	0.549877	+	1.64245i	0.0448972	+	0.134105i
$151$		−	3.70446i		−	0.301465i	−0.988575	−	0.150732i	$-0.951837\pi$
$151$		−	3.70446i		−	0.301465i	0.988575	−	0.150732i	$-0.0481632\pi$
$152$	4.10528	+	1.46517i	0.332982	+	0.118841i
$153$	−1.36443	+	0.695817i	−0.110308	+	0.0562535i
$154$	0.0928194	−	0.110618i	0.00747960	−	0.00891384i
$155$	6.62428	−	2.41104i	0.532075	−	0.193660i
$156$	−3.06569	−	1.20699i	−0.245452	−	0.0966361i
$157$	−0.110660	+	0.627584i	−0.00883162	+	0.0500866i	−0.988905	−	0.148549i	$-0.952540\pi$
$157$	−0.110660	+	0.627584i	−0.00883162	+	0.0500866i	0.980073	+	0.198635i	$0.0636509\pi$
$158$	−2.34946	+	6.45509i	−0.186913	+	0.513539i
$159$	−0.256927	+	9.87806i	−0.0203756	+	0.783381i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	−0.0802986	−	0.0956962i	−0.00632842	−	0.00754192i
$162$	0.634126	+	8.97763i	0.0498216	+	0.705349i
$163$	−5.80819	+	10.0601i	−0.454932	+	0.787966i	−0.998684	−	0.0512800i	$-0.983670\pi$
$163$	−5.80819	+	10.0601i	−0.454932	+	0.787966i	0.543752	+	0.839246i	$0.317003\pi$
$164$	−5.80852	−	10.0607i	−0.453569	−	0.785605i
$165$	0.290597	+	0.365198i	0.0226229	+	0.0284306i
$166$	−2.88958	−	0.509510i	−0.224275	−	0.0395457i
$167$	1.34613	+	7.63430i	0.104167	+	0.590760i	0.991550	+	0.129727i	$0.0414100\pi$
$167$	1.34613	+	7.63430i	0.104167	+	0.590760i	−0.887383	+	0.461033i	$0.847479\pi$
$168$	0.909611	+	0.184896i	0.0701780	+	0.0142650i
$169$	7.18670	+	6.03036i	0.552823	+	0.463874i
$170$	−0.510537			−0.0391564
$171$	2.85732	−	12.7607i	0.218505	−	0.975836i
$172$	−6.56066			−0.500245
$173$	15.1853	+	12.7419i	1.15451	+	0.968752i	0.999815	−	0.0192097i	$-0.00611502\pi$
$173$	15.1853	+	12.7419i	1.15451	+	0.968752i	0.154698	+	0.987962i	$0.450559\pi$
$174$	−9.10440	−	1.85064i	−0.690203	−	0.140297i
$175$	−0.0930587	−	0.527762i	−0.00703458	−	0.0398951i
$176$	−0.265360	−	0.0467902i	−0.0200023	−	0.00352694i
$177$	6.95133	+	8.73586i	0.522494	+	0.656627i
$178$	0.520759	+	0.901982i	0.0390326	+	0.0676064i
$179$	2.28067	−	3.95024i	0.170466	−	0.295255i	−0.768117	−	0.640309i	$-0.778806\pi$
$179$	2.28067	−	3.95024i	0.170466	−	0.295255i	0.938583	+	0.345054i	$0.112139\pi$
$180$	−1.17122	+	2.76193i	−0.0872977	+	0.205862i
$181$	−14.2151	−	16.9409i	−1.05660	−	1.25921i	−0.964675	−	0.263443i	$-0.915142\pi$
$181$	−14.2151	−	16.9409i	−1.05660	−	1.25921i	−0.0919262	−	0.995766i	$-0.529302\pi$
$182$	0.882830	+	0.509702i	0.0654397	+	0.0377816i
$183$	0.481414	−	18.5089i	0.0355871	−	1.36822i
$184$	−0.0797270	+	0.219048i	−0.00587756	+	0.0161485i
$185$	1.59096	−	9.02277i	0.116970	−	0.663368i
$186$	11.3611	+	4.47296i	0.833039	+	0.327973i
$187$	−0.129270	+	0.0470504i	−0.00945315	+	0.00344067i
$188$	5.83426	−	6.95300i	0.425507	−	0.507100i
$189$	0.217015	−	2.77617i	0.0157855	−	0.201936i
$190$	2.78089	−	3.35658i	0.201747	−	0.243512i
$191$			4.43209i			0.320695i	0.987061	+	0.160347i	$0.0512614\pi$
$191$			4.43209i			0.320695i	−0.987061	+	0.160347i	$0.948739\pi$
$192$	−0.549877	−	1.64245i	−0.0396839	−	0.118533i
$193$	6.27088	+	17.2291i	0.451388	+	1.24018i	0.931748	+	0.363106i	$0.118284\pi$
$193$	6.27088	+	17.2291i	0.451388	+	1.24018i	−0.480360	+	0.877071i	$0.659494\pi$
$194$	2.11176	−	0.372360i	0.151615	−	0.0267339i
$195$	−2.18272	+	2.46799i	−0.156308	+	0.176737i
$196$	6.30798	+	2.29592i	0.450570	+	0.163994i
$197$	−17.3492	+	10.0166i	−1.23608	+	0.713650i	−0.968290	−	0.249828i	$-0.919626\pi$
$197$	−17.3492	+	10.0166i	−1.23608	+	0.713650i	−0.267788	+	0.963478i	$0.586293\pi$
$198$	−0.0420224	+	0.807269i	−0.00298640	+	0.0573701i
$199$	2.55436	−	2.14336i	0.181073	−	0.151939i	−0.547746	−	0.836645i	$-0.684514\pi$
$199$	2.55436	−	2.14336i	0.181073	−	0.151939i	0.728819	+	0.684706i	$0.240069\pi$
$200$	−0.766044	+	0.642788i	−0.0541675	+	0.0454519i
$201$	−4.73994	−	8.72623i	−0.334330	−	0.615500i
$202$	1.55899	−	0.900083i	0.109690	−	0.0633296i
$203$	2.70119	+	0.983152i	0.189586	+	0.0690038i
$204$	−0.662387	−	0.585822i	−0.0463763	−	0.0410158i
$205$	−11.4406	+	2.01728i	−0.799043	+	0.140893i
$206$	0.174249	+	0.478744i	0.0121405	+	0.0333557i
$207$	0.681451	+	0.157073i	0.0473641	+	0.0109173i
$208$		−	1.90222i		−	0.131895i
$209$	0.394795	−	1.10618i	0.0273085	−	0.0765163i
$210$	0.484850	−	0.791516i	0.0334579	−	0.0546198i
$211$	−6.56110	+	7.81921i	−0.451685	+	0.538297i	−0.943047	−	0.332658i	$-0.892054\pi$
$211$	−6.56110	+	7.81921i	−0.451685	+	0.538297i	0.491363	+	0.870955i	$0.336499\pi$
$212$	−5.36097	+	1.95123i	−0.368193	+	0.134011i
$213$	4.07163	−	10.3418i	0.278983	−	0.708606i
$214$	−1.04344	+	5.91766i	−0.0713283	+	0.404523i
$215$	−2.24388	+	6.16500i	−0.153031	+	0.420449i
$216$	−4.68879	+	2.23948i	−0.319032	+	0.152377i
$217$	−3.27168	−	1.88890i	−0.222096	−	0.128227i
$218$	−5.32312	−	6.34385i	−0.360527	−	0.429660i
$219$	−9.65985	+	1.44541i	−0.652752	+	0.0976719i
$220$	−0.134727	+	0.233354i	−0.00908329	+	0.0157327i
$221$	−0.485576	−	0.841042i	−0.0326634	−	0.0565746i
$222$	12.4175	−	9.88086i	0.833405	−	0.663160i
$223$	1.46787	+	0.258824i	0.0982955	+	0.0173322i	0.222580	−	0.974915i	$-0.428552\pi$
$223$	1.46787	+	0.258824i	0.0982955	+	0.0173322i	−0.124284	+	0.992247i	$0.539663\pi$
$224$	0.0930587	+	0.527762i	0.00621774	+	0.0352626i
$225$	2.19478	+	2.04522i	0.146319	+	0.136348i
$226$	2.49334	+	2.09216i	0.165854	+	0.139168i
$227$	1.74710			0.115959			0.0579795	−	0.998318i	$-0.481534\pi$
$227$	1.74710			0.115959			0.0579795	+	0.998318i	$0.481534\pi$
$228$	7.45957	−	1.16396i	0.494022	−	0.0770852i
$229$	−12.1341			−0.801845			−0.400923	−	0.916112i	$-0.631310\pi$
$229$	−12.1341			−0.801845			−0.400923	+	0.916112i	$0.631310\pi$
$230$	0.178570	+	0.149838i	0.0117745	+	0.00988001i
$231$	0.0498209	−	0.245098i	0.00327797	−	0.0161263i
$232$	−0.931435	−	5.28243i	−0.0611517	−	0.346809i
$233$	18.1764	+	3.20499i	1.19077	+	0.209966i	0.733707	−	0.679467i	$-0.237789\pi$
$233$	18.1764	+	3.20499i	1.19077	+	0.209966i	0.457067	+	0.889432i	$0.348900\pi$
$234$	−5.66387	+	0.697458i	−0.370259	+	0.0455943i
$235$	−4.53825	−	7.86048i	−0.296043	−	0.512761i
$236$	−3.22279	+	5.58203i	−0.209785	+	0.363359i
$237$	1.76072	+	11.7671i	0.114371	+	0.764354i
$238$	0.175866	+	0.209589i	0.0113997	+	0.0135856i
$239$	−1.19701	−	0.691097i	−0.0774284	−	0.0447033i	0.460786	−	0.887511i	$-0.347568\pi$
$239$	−1.19701	−	0.691097i	−0.0774284	−	0.0447033i	−0.538214	+	0.842808i	$0.680901\pi$
$240$	−1.73147	−	0.0450352i	−0.111766	−	0.00290701i
$241$	4.30699	−	11.8333i	0.277437	−	0.762253i	−0.720214	−	0.693752i	$-0.755956\pi$
$241$	4.30699	−	11.8333i	0.277437	−	0.762253i	0.997651	−	0.0685006i	$-0.0218215\pi$
$242$	1.89752	−	10.7614i	0.121977	−	0.691768i
$243$	8.38723	+	13.1398i	0.538041	+	0.842919i
$244$	10.0451	−	3.65610i	0.643069	−	0.234058i
$245$	4.31491	−	5.14231i	0.275669	−	0.328530i
$246$	−17.1581	−	10.5103i	−1.09396	−	0.670114i
$247$	8.17445	+	1.38868i	0.520128	+	0.0883596i
$248$			7.04941i			0.447638i
$249$	−4.81919	+	1.61342i	−0.305404	+	0.102247i
$250$	0.342020	+	0.939693i	0.0216313	+	0.0594314i
$251$	26.7932	−	4.72436i	1.69117	−	0.298199i	0.756574	−	0.653908i	$-0.226872\pi$
$251$	26.7932	−	4.72436i	1.69117	−	0.298199i	0.934597	+	0.355709i	$0.115760\pi$
$252$	1.53730	−	0.470590i	0.0968405	−	0.0296444i
$253$	0.0590234	+	0.0214828i	0.00371077	+	0.00135061i
$254$	4.36309	−	2.51903i	0.273765	−	0.158058i
$255$	−0.777043	+	0.422077i	−0.0486603	+	0.0264315i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−23.8566	+	20.0180i	−1.48813	+	1.24869i	−0.591199	+	0.806526i	$0.701345\pi$
$257$	−23.8566	+	20.0180i	−1.48813	+	1.24869i	−0.896934	+	0.442165i	$0.854210\pi$
$258$	−9.98539	+	5.42390i	−0.621663	+	0.337677i
$259$	−4.25212	+	2.45497i	−0.264214	+	0.152544i
$260$	−1.78750	−	0.650596i	−0.110856	−	0.0403483i
$261$	−15.3870	+	4.71019i	−0.952430	+	0.291554i
$262$	2.09282	−	0.369021i	0.129295	−	0.0227982i
$263$	8.41522	+	23.1206i	0.518905	+	1.42568i	0.871728	+	0.489989i	$0.162999\pi$
$263$	8.41522	+	23.1206i	0.518905	+	1.42568i	−0.352824	+	0.935690i	$0.614778\pi$
$264$	−0.442564	+	0.148166i	−0.0272379	+	0.00911901i
$265$			5.70503i			0.350457i
$266$	−2.33590	+	0.0146203i	−0.143223	+	0.000896426i
$267$	1.53830	+	0.942298i	0.0941423	+	0.0576677i
$268$	3.68533	−	4.39200i	0.225117	−	0.268284i
$269$	−24.9087	+	9.06602i	−1.51871	+	0.552765i	−0.960825	−	0.277155i	$-0.910609\pi$
$269$	−24.9087	+	9.06602i	−1.51871	+	0.552765i	−0.557883	+	0.829919i	$0.688386\pi$
$270$	0.500759	+	5.17197i	0.0304752	+	0.314756i
$271$	1.67423	−	9.49505i	0.101702	−	0.576783i	−0.890784	−	0.454427i	$-0.849844\pi$
$271$	1.67423	−	9.49505i	0.101702	−	0.576783i	0.992486	−	0.122356i	$-0.0390449\pi$
$272$	0.174614	−	0.479748i	0.0105875	−	0.0290890i
$273$	1.76506	+	0.0459091i	0.106826	+	0.00277854i
$274$	−3.10860	−	1.79475i	−0.187797	−	0.108425i
$275$	0.173202	+	0.206414i	0.0104445	+	0.0124472i
$276$	0.0597486	+	0.399307i	0.00359644	+	0.0240354i
$277$	−4.30168	+	7.45073i	−0.258463	+	0.447671i	−0.965830	−	0.259175i	$-0.916549\pi$
$277$	−4.30168	+	7.45073i	−0.258463	+	0.447671i	0.707367	+	0.706846i	$0.249883\pi$
$278$	6.93710	+	12.0154i	0.416060	+	0.720636i
$279$	20.9897	−	2.58471i	1.25662	−	0.154742i
$280$	0.527762	+	0.0930587i	0.0315398	+	0.00556132i
$281$	3.97426	+	22.5391i	0.237084	+	1.34457i	0.838180	+	0.545394i	$0.183620\pi$
$281$	3.97426	+	22.5391i	0.237084	+	1.34457i	−0.601095	+	0.799177i	$0.705269\pi$
$282$	3.13154	−	15.4059i	0.186481	−	0.917408i
$283$	17.2555	+	14.4791i	1.02573	+	0.860692i	0.990337	−	0.138681i	$-0.0442864\pi$
$283$	17.2555	+	14.4791i	1.02573	+	0.860692i	0.0353958	+	0.999373i	$0.488731\pi$
$284$	6.41691			0.380774
$285$	1.45756	−	7.40780i	0.0863383	−	0.438800i
$286$	−0.512560			−0.0303083
$287$	4.76910	+	4.00175i	0.281511	+	0.236216i
$288$	−2.19478	−	2.04522i	−0.129329	−	0.120516i
$289$	2.90676	+	16.4850i	0.170986	+	0.969708i
$290$	−5.28243	−	0.931435i	−0.310195	−	0.0546958i
$291$	2.90628	−	2.31259i	0.170369	−	0.135567i
$292$	−2.81960	−	4.88369i	−0.165005	−	0.285797i
$293$	−14.1844	+	24.5681i	−0.828663	+	1.43529i	0.0704250	+	0.997517i	$0.477564\pi$
$293$	−14.1844	+	24.5681i	−0.828663	+	1.43529i	−0.899088	+	0.437769i	$0.855769\pi$
$294$	11.4989	−	1.72059i	0.670630	−	0.100347i
$295$	4.14313	+	4.93759i	0.241223	+	0.287478i
$296$	7.93449	+	4.58098i	0.461183	+	0.266264i
$297$	0.603436	+	1.26341i	0.0350149	+	0.0733106i
$298$	6.14443	−	16.8817i	0.355937	−	0.977930i
$299$	−0.0769988	+	0.436682i	−0.00445296	+	0.0252540i
$300$	−0.634515	+	1.61164i	−0.0366338	+	0.0930482i
$301$	3.30385	−	1.20250i	0.190430	−	0.0693110i
$302$	2.38118	−	2.83778i	0.137022	−	0.163296i
$303$	1.62867	−	2.65880i	0.0935647	−	0.152744i
$304$	2.20303	+	3.76120i	0.126353	+	0.215720i
$305$		−	10.6897i		−	0.612092i
$306$	−1.49248	−	0.344012i	−0.0853192	−	0.0196659i
$307$	9.05566	+	24.8802i	0.516834	+	1.41999i	0.873990	+	0.485944i	$0.161524\pi$
$307$	9.05566	+	24.8802i	0.516834	+	1.41999i	−0.357156	+	0.934045i	$0.616254\pi$
$308$	0.142208	−	0.0250750i	0.00810303	−	0.00142878i
$309$	0.661001	+	0.584597i	0.0376030	+	0.0332566i
$310$	6.62428	+	2.41104i	0.376234	+	0.136938i
$311$	−4.31145	+	2.48922i	−0.244480	+	0.141150i	−0.617234	−	0.786780i	$-0.711747\pi$
$311$	−4.31145	+	2.48922i	−0.244480	+	0.141150i	0.372754	+	0.927930i	$0.378413\pi$
$312$	−1.57262	−	2.89519i	−0.0890321	−	0.163908i
$313$	−10.2430	+	8.59492i	−0.578970	+	0.485814i	−0.884609	−	0.466334i	$-0.845575\pi$
$313$	−10.2430	+	8.59492i	−0.578970	+	0.485814i	0.305639	+	0.952148i	$0.401130\pi$
$314$	−0.488173	+	0.409626i	−0.0275492	+	0.0231165i
$315$	0.0835762	−	1.60554i	0.00470898	−	0.0904618i
$316$	−5.94904	+	3.43468i	−0.334660	+	0.193216i
$317$	12.1126	+	4.40863i	0.680313	+	0.247614i	0.658982	−	0.752159i	$-0.270987\pi$
$317$	12.1126	+	4.40863i	0.680313	+	0.247614i	0.0213310	+	0.999772i	$0.493210\pi$
$318$	−6.54631	+	7.40188i	−0.367099	+	0.415077i
$319$	−1.42337	+	0.250979i	−0.0796935	+	0.0140521i
$320$	−0.342020	−	0.939693i	−0.0191195	−	0.0525304i
$321$	3.30418	+	9.86938i	0.184421	+	0.550855i
$322$		−	0.124922i		−	0.00696166i
$323$	1.93416	+	1.10061i	0.107620	+	0.0612393i
$324$	−5.28494	+	7.28487i	−0.293608	+	0.404715i
$325$	−1.22272	+	1.45718i	−0.0678243	+	0.0808299i
$326$	−10.9158	+	3.97303i	−0.604572	+	0.220046i
$327$	−13.3465	−	5.25462i	−0.738063	−	0.290581i
$328$	2.01728	−	11.4406i	0.111386	−	0.631699i
$329$	−1.66363	+	4.57079i	−0.0917189	+	0.251996i
$330$	−0.0121349	+	0.466550i	−0.000668005	+	0.0256827i
$331$	24.0531	+	13.8871i	1.32208	+	0.763303i	0.984060	−	0.177836i	$-0.0569097\pi$
$331$	24.0531	+	13.8871i	1.32208	+	0.763303i	0.338019	+	0.941139i	$0.390243\pi$
$332$	−1.88604	−	2.24769i	−0.103510	−	0.123358i
$333$	10.7307	−	25.3047i	0.588038	−	1.38669i
$334$	−3.87604	+	6.71349i	−0.212087	+	0.367346i
$335$	−2.86668	−	4.96523i	−0.156623	−	0.271280i
$336$	0.577954	+	0.726325i	0.0315299	+	0.0396243i
$337$	0.774603	+	0.136583i	0.0421953	+	0.00744017i	0.194706	−	0.980862i	$-0.437625\pi$
$337$	0.774603	+	0.136583i	0.0421953	+	0.00744017i	−0.152511	+	0.988302i	$0.548736\pi$
$338$	1.62909	+	9.23905i	0.0886110	+	0.502538i
$339$	5.52453	+	1.12297i	0.300051	+	0.0609912i
$340$	−0.391094	−	0.328167i	−0.0212100	−	0.0177973i
$341$	1.89949			0.102863
$342$	10.3913	−	7.93862i	0.561895	−	0.429271i
$343$	−7.34874			−0.396795
$344$	−5.02575	−	4.21711i	−0.270970	−	0.227371i
$345$	0.395661	+	0.0804256i	0.0213017	+	0.00432997i
$346$	3.44222	+	19.5218i	0.185055	+	1.04950i
$347$	17.8338	+	3.14458i	0.957368	+	0.168810i	0.630439	−	0.776239i	$-0.282875\pi$
$347$	17.8338	+	3.14458i	0.957368	+	0.168810i	0.326929	+	0.945049i	$0.393986\pi$
$348$	−5.78480	−	7.26987i	−0.310098	−	0.389706i
$349$	4.98489	+	8.63408i	0.266835	+	0.462172i	0.968043	−	0.250785i	$-0.0806888\pi$
$349$	4.98489	+	8.63408i	0.266835	+	0.462172i	−0.701208	+	0.712957i	$0.747355\pi$
$350$	0.267952	−	0.464106i	0.0143226	−	0.0248075i
$351$	−8.04385	+	5.74403i	−0.429349	+	0.306594i
$352$	−0.173202	−	0.206414i	−0.00923168	−	0.0110019i
$353$	−12.3034	−	7.10336i	−0.654843	−	0.378074i	0.135466	−	0.990782i	$-0.456747\pi$
$353$	−12.3034	−	7.10336i	−0.654843	−	0.378074i	−0.790309	+	0.612708i	$0.790080\pi$
$354$	−0.290278	+	11.1603i	−0.0154281	+	0.593162i
$355$	2.19471	−	6.02992i	0.116483	−	0.320035i
$356$	−0.180858	+	1.02570i	−0.00958545	+	0.0543618i
$357$	0.440943	+	0.173602i	0.0233372	+	0.00918802i
$358$	4.28627	−	1.56007i	0.226536	−	0.0824524i
$359$	14.7475	−	17.5753i	0.778341	−	0.927591i	−0.220516	−	0.975383i	$-0.570774\pi$
$359$	14.7475	−	17.5753i	0.778341	−	0.927591i	0.998857	+	0.0477926i	$0.0152186\pi$
$360$	−2.67254	+	1.36291i	−0.140855	+	0.0718318i
$361$	−17.7714	+	6.72136i	−0.935338	+	0.353756i
$362$		−	22.1148i		−	1.16233i
$363$	−6.00872	−	17.9477i	−0.315376	−	0.942009i
$364$	0.348657	+	0.957927i	0.0182746	+	0.0502090i
$365$	−5.55353	+	0.979238i	−0.290685	+	0.0512556i
$366$	12.2661	−	13.8692i	0.641158	−	0.724954i
$367$	24.3559	+	8.86481i	1.27137	+	0.462739i	0.887567	−	0.460678i	$-0.152394\pi$
$367$	24.3559	+	8.86481i	1.27137	+	0.462739i	0.383798	+	0.923417i	$0.374616\pi$
$368$	−0.201876	+	0.116553i	−0.0105235	+	0.00607575i
$369$	−34.8040	−	1.81172i	−1.81182	−	0.0943144i
$370$	7.01847	−	5.88920i	0.364873	−	0.306165i
$371$	2.34206	−	1.96522i	0.121594	−	0.102029i
$372$	5.82797	+	10.7293i	0.302166	+	0.556287i
$373$	10.4729	−	6.04653i	0.542266	−	0.313078i	−0.203731	−	0.979027i	$-0.565307\pi$
$373$	10.4729	−	6.04653i	0.542266	−	0.313078i	0.745997	+	0.665949i	$0.231973\pi$
$374$	−0.129270	−	0.0470504i	−0.00668439	−	0.00243292i
$375$	1.29743	+	1.14746i	0.0669991	+	0.0592548i
$376$	8.93861	−	1.57612i	0.460973	−	0.0812821i
$377$	−3.48975	−	9.58800i	−0.179731	−	0.493807i
$378$	1.95073	−	1.98717i	0.100335	−	0.102209i
$379$		−	9.41476i		−	0.483604i	−0.970326	−	0.241802i	$-0.922262\pi$
$379$		−	9.41476i		−	0.483604i	0.970326	−	0.241802i	$-0.0777384\pi$
$380$	4.28786	−	0.783767i	0.219962	−	0.0402064i
$381$	4.55811	−	7.44109i	0.233519	−	0.381219i
$382$	−2.84889	+	3.39518i	−0.145762	+	0.173712i
$383$	−19.6447	+	7.15008i	−1.00380	+	0.365352i	−0.791048	−	0.611755i	$-0.790464\pi$
$383$	−19.6447	+	7.15008i	−1.00380	+	0.365352i	−0.212749	+	0.977107i	$0.568242\pi$
$384$	0.634515	−	1.61164i	0.0323800	−	0.0822438i
$385$	0.0250750	−	0.142208i	0.00127794	−	0.00724757i
$386$	−6.27088	+	17.2291i	−0.319179	+	0.876938i
$387$	−10.7138	+	16.5105i	−0.544611	+	0.839274i
$388$	1.85705	+	1.07217i	0.0942774	+	0.0544311i
$389$	−16.4586	−	19.6146i	−0.834486	−	0.994501i	−0.999966	−	0.00828818i	$-0.997362\pi$
$389$	−16.4586	−	19.6146i	−0.834486	−	0.994501i	0.165480	−	0.986213i	$-0.447083\pi$
$390$	−3.25846	+	0.487566i	−0.164998	+	0.0246889i
$391$	−0.0595047	+	0.103065i	−0.00300928	+	0.00521223i
$392$	3.35640	+	5.81346i	0.169524	+	0.293624i
$393$	2.88022	−	2.29186i	0.145288	−	0.115609i
$394$	−19.7288	−	3.47871i	−0.993920	−	0.175255i
$395$	1.19285	+	6.76500i	0.0600189	+	0.340384i
$396$	−0.551093	+	0.591392i	−0.0276935	+	0.0297186i
$397$	−23.8589	−	20.0200i	−1.19744	−	1.00477i	−0.999699	−	0.0245208i	$-0.992194\pi$
$397$	−23.8589	−	20.0200i	−1.19744	−	1.00477i	−0.197744	−	0.980254i	$-0.563362\pi$
$398$	3.33447			0.167142
$399$	−3.54318	+	1.95342i	−0.177381	+	0.0977931i
$400$	−1.00000			−0.0500000
$401$	−6.05613	−	5.08169i	−0.302429	−	0.253768i	0.478926	−	0.877855i	$-0.341026\pi$
$401$	−6.05613	−	5.08169i	−0.302429	−	0.253768i	−0.781354	+	0.624088i	$0.785471\pi$
$402$	1.97810	−	9.73145i	0.0986588	−	0.485361i
$403$	2.32854	+	13.2058i	0.115993	+	0.657827i
$404$	1.77282	+	0.312595i	0.0882010	+	0.0155522i
$405$	5.03799	+	7.45779i	0.250340	+	0.370581i
$406$	1.43727	+	2.48943i	0.0713306	+	0.123548i
$407$	1.23436	−	2.13798i	0.0611851	−	0.105976i
$408$	−0.130858	−	0.874540i	−0.00647844	−	0.0432962i
$409$	14.4428	+	17.2123i	0.714151	+	0.851092i	0.994049	−	0.108938i	$-0.0347450\pi$
$409$	14.4428	+	17.2123i	0.714151	+	0.851092i	−0.279898	+	0.960030i	$0.590301\pi$
$410$	−10.0607	−	5.80852i	−0.496860	−	0.286862i
$411$	−6.21509	−	0.161654i	−0.306568	−	0.00797379i
$412$	−0.174249	+	0.478744i	−0.00858462	+	0.0235860i
$413$	0.599816	−	3.40173i	0.0295150	−	0.167388i
$414$	0.421057	+	0.558353i	0.0206938	+	0.0274415i
$415$	−2.75720	+	1.00354i	−0.135346	+	0.0492618i
$416$	1.22272	−	1.45718i	0.0599488	−	0.0714442i
$417$	20.4919	+	12.5525i	1.00349	+	0.614697i
$418$	1.01347	−	0.593616i	0.0495705	−	0.0290347i
$419$		−	18.2936i		−	0.893703i	−0.894608	−	0.446851i	$-0.852545\pi$
$419$		−	18.2936i		−	0.893703i	0.894608	−	0.446851i	$-0.147455\pi$
$420$	0.880194	−	0.294681i	0.0429491	−	0.0143790i
$421$	12.7447	+	35.0157i	0.621138	+	1.70656i	0.704185	+	0.710017i	$0.251313\pi$
$421$	12.7447	+	35.0157i	0.621138	+	1.70656i	−0.0830467	+	0.996546i	$0.526465\pi$
$422$	−10.0522	+	1.77247i	−0.489333	+	0.0862826i
$423$	−7.97030	−	26.0369i	−0.387529	−	1.26596i
$424$	−5.36097	−	1.95123i	−0.260352	−	0.0947603i
$425$	−0.442138	+	0.255268i	−0.0214468	+	0.0123823i
$426$	9.76661	−	5.30506i	0.473194	−	0.257031i
$427$	−4.38841	+	3.68231i	−0.212370	+	0.178200i
$428$	−4.60312	+	3.86248i	−0.222500	+	0.186700i
$429$	−0.780121	+	0.423749i	−0.0376646	+	0.0204588i
$430$	−5.68169	+	3.28033i	−0.273996	+	0.158191i
$431$	17.5447	+	6.38575i	0.845098	+	0.307591i	0.728040	−	0.685534i	$-0.240431\pi$
$431$	17.5447	+	6.38575i	0.845098	+	0.307591i	0.117058	+	0.993125i	$0.462654\pi$
$432$	−5.03133	−	1.29836i	−0.242070	−	0.0624673i
$433$	10.8936	−	1.92083i	0.523512	−	0.0923093i	0.0943539	−	0.995539i	$-0.469921\pi$
$433$	10.8936	−	1.92083i	0.523512	−	0.0923093i	0.429158	+	0.903229i	$0.358810\pi$
$434$	−1.29209	−	3.54998i	−0.0620221	−	0.170404i
$435$	−8.80996	+	2.94950i	−0.422405	+	0.141418i
$436$		−	8.28131i		−	0.396603i
$437$	−0.353491	−	0.952615i	−0.0169098	−	0.0455698i
$438$	−8.32897	−	5.10198i	−0.397973	−	0.243782i
$439$	23.7456	−	28.2990i	1.13332	−	1.35064i	0.205037	−	0.978754i	$-0.434268\pi$
$439$	23.7456	−	28.2990i	1.13332	−	1.35064i	0.928280	−	0.371881i	$-0.121287\pi$
$440$	−0.253204	+	0.0921587i	−0.0120710	+	0.00439349i
$441$	16.0790	−	12.1253i	0.765666	−	0.577393i
$442$	0.168639	−	0.956397i	0.00802132	−	0.0454912i
$443$	−7.07598	+	19.4411i	−0.336190	+	0.923675i	0.650274	+	0.759699i	$0.274654\pi$
$443$	−7.07598	+	19.4411i	−0.336190	+	0.923675i	−0.986464	+	0.163975i	$0.947568\pi$
$444$	15.8636	+	0.412611i	0.752854	+	0.0195816i
$445$	0.901982	+	0.520759i	0.0427580	+	0.0246864i
$446$	0.958081	+	1.14180i	0.0453664	+	0.0540656i
$447$	−4.60472	−	30.7739i	−0.217796	−	1.45556i
$448$	−0.267952	+	0.464106i	−0.0126595	+	0.0219270i
$449$	−19.7374	−	34.1861i	−0.931464	−	1.61334i	−0.780821	−	0.624755i	$-0.785199\pi$
$449$	−19.7374	−	34.1861i	−0.931464	−	1.61334i	−0.150644	−	0.988588i	$-0.548135\pi$
$450$	0.366656	+	2.97751i	0.0172843	+	0.140361i
$451$	−3.08270	−	0.543563i	−0.145159	−	0.0255954i
$452$	0.565193	+	3.20537i	0.0265845	+	0.150768i
$453$	1.27810	−	6.28773i	0.0600505	−	0.295423i
$454$	1.33835	+	1.12301i	0.0628121	+	0.0527056i
$455$	1.01940			0.0477904
$456$	6.46254	+	3.90327i	0.302636	+	0.182788i
$457$	1.93285			0.0904151			0.0452075	−	0.998978i	$-0.485605\pi$
$457$	1.93285			0.0904151			0.0452075	+	0.998978i	$0.485605\pi$
$458$	−9.29527	−	7.79966i	−0.434340	−	0.364454i
$459$	−2.55597	+	0.710286i	−0.119303	+	0.0331533i
$460$	0.0404785	+	0.229565i	0.00188732	+	0.0107035i
$461$	17.0136	+	2.99996i	0.792403	+	0.139722i	0.555177	−	0.831732i	$-0.312651\pi$
$461$	17.0136	+	2.99996i	0.792403	+	0.139722i	0.237226	+	0.971454i	$0.423762\pi$
$462$	0.195711	−	0.155732i	0.00910530	−	0.00724530i
$463$	−10.5864	−	18.3361i	−0.491990	−	0.852152i	0.507967	−	0.861376i	$-0.330397\pi$
$463$	−10.5864	−	18.3361i	−0.491990	−	0.852152i	−0.999957	+	0.00922415i	$0.997064\pi$
$464$	2.68196	−	4.64529i	0.124507	−	0.215652i
$465$	12.0755	−	1.80687i	0.559988	−	0.0837915i
$466$	11.8638	+	14.1387i	0.549579	+	0.654963i
$467$	2.81741	+	1.62663i	0.130374	+	0.0752716i	0.563769	−	0.825933i	$-0.309351\pi$
$467$	2.81741	+	1.62663i	0.130374	+	0.0752716i	−0.433394	+	0.901204i	$0.642684\pi$
$468$	−4.78709	−	3.10638i	−0.221283	−	0.143592i
$469$	−1.05087	+	2.88723i	−0.0485245	+	0.133320i
$470$	1.57612	−	8.93861i	0.0727009	−	0.412307i
$471$	−0.404354	+	1.02704i	−0.0186317	+	0.0473237i
$472$	−6.05686	+	2.20452i	−0.278789	+	0.101471i
$473$	−1.13632	+	1.35421i	−0.0522479	+	0.0622666i
$474$	−6.21495	+	10.1459i	−0.285462	+	0.466016i
$475$	0.730033	−	4.29733i	0.0334962	−	0.197175i
$476$			0.273599i			0.0125404i
$477$	−3.84419	+	16.6778i	−0.176013	+	0.763623i
$478$	−0.472738	−	1.29884i	−0.0216225	−	0.0594074i
$479$	11.7497	−	2.07180i	0.536859	−	0.0946627i	0.101356	−	0.994850i	$-0.467682\pi$
$479$	11.7497	−	2.07180i	0.536859	−	0.0946627i	0.435503	+	0.900187i	$0.356571\pi$
$480$	−1.29743	−	1.14746i	−0.0592194	−	0.0523743i
$481$	16.3770	+	5.96074i	0.746727	+	0.271786i
$482$	10.9057	−	6.29639i	0.496740	−	0.286793i
$483$	−0.103277	−	0.190133i	−0.00469928	−	0.00865137i
$484$	8.37087	−	7.02399i	0.380494	−	0.319272i
$485$	1.64266	−	1.37835i	0.0745892	−	0.0625878i
$486$	−2.02111	+	15.4569i	−0.0916793	+	0.701138i
$487$	6.60985	−	3.81620i	0.299521	−	0.172928i	−0.342707	−	0.939442i	$-0.611344\pi$
$487$	6.60985	−	3.81620i	0.299521	−	0.172928i	0.642228	+	0.766514i	$0.278010\pi$
$488$	10.0451	+	3.65610i	0.454718	+	0.165504i
$489$	−13.3294	+	15.0714i	−0.602775	+	0.681554i
$490$	6.61082	−	1.16567i	0.298647	−	0.0526595i
$491$	−12.5691	−	34.5334i	−0.567238	−	1.55847i	−0.808798	−	0.588087i	$-0.799881\pi$
$491$	−12.5691	−	34.5334i	−0.567238	−	1.55847i	0.241560	−	0.970386i	$-0.422341\pi$
$492$	−6.38794	−	19.0804i	−0.287991	−	0.860210i
$493$		−	2.73848i		−	0.123335i
$494$	5.36937	+	6.31823i	0.241579	+	0.284270i
$495$	0.367242	+	0.720126i	0.0165063	+	0.0323673i
$496$	−4.53128	+	5.40016i	−0.203460	+	0.242475i
$497$	−3.23146	+	1.17615i	−0.144951	+	0.0527577i
$498$	−4.72881	−	1.86176i	−0.211903	−	0.0834277i
$499$	−5.83153	+	33.0723i	−0.261055	+	1.48052i	0.518982	+	0.854785i	$0.326311\pi$
$499$	−5.83153	+	33.0723i	−0.261055	+	1.48052i	−0.780037	+	0.625733i	$0.784800\pi$
$500$	−0.342020	+	0.939693i	−0.0152956	+	0.0420243i
$501$	−0.349116	+	13.4224i	−0.0155974	+	0.599671i
$502$	23.5615	+	13.6033i	1.05160	+	0.607143i
$503$	−19.9507	−	23.7763i	−0.889557	−	1.06013i	−0.997819	−	0.0660102i	$-0.978973\pi$
$503$	−19.9507	−	23.7763i	−0.889557	−	1.06013i	0.108262	−	0.994122i	$-0.465471\pi$
$504$	1.48013	+	0.627662i	0.0659301	+	0.0279583i
$505$	0.900083	−	1.55899i	0.0400532	−	0.0693741i
$506$	0.0314057	+	0.0543963i	0.00139615	+	0.00241821i
$507$	10.1177	+	12.7151i	0.449343	+	0.564698i
$508$	4.96152	+	0.874850i	0.220132	+	0.0388152i
$509$	−5.30276	−	30.0734i	−0.235041	−	1.33298i	−0.842528	−	0.538652i	$-0.818934\pi$
$509$	−5.30276	−	30.0734i	−0.235041	−	1.33298i	0.607487	−	0.794329i	$-0.292178\pi$
$510$	−0.866555	−	0.176144i	−0.0383717	−	0.00779978i
$511$	2.31504	+	1.94255i	0.102411	+	0.0859333i
$512$	1.00000			0.0441942
$513$	9.25251	−	20.6734i	0.408508	−	0.912755i
$514$	−31.1425			−1.37364
$515$	0.390276	+	0.327480i	0.0171976	+	0.0144305i
$516$	−11.1357	−	2.26354i	−0.490220	−	0.0996466i
$517$	−0.424691	−	2.40854i	−0.0186779	−	0.105928i
$518$	−4.83534	−	0.852600i	−0.212453	−	0.0374611i
$519$	21.3784	+	26.8666i	0.938406	+	1.17931i
$520$	−0.951108	−	1.64737i	−0.0417088	−	0.0722418i
$521$	−2.91411	+	5.04738i	−0.127669	+	0.221130i	−0.922773	−	0.385344i	$-0.874083\pi$
$521$	−2.91411	+	5.04738i	−0.127669	+	0.221130i	0.795104	+	0.606473i	$0.207416\pi$
$522$	−14.8148	−	6.28234i	−0.648424	−	0.274971i
$523$	−21.9654	−	26.1773i	−0.960479	−	1.14465i	−0.989421	−	0.145073i	$-0.953658\pi$
$523$	−21.9654	−	26.1773i	−0.960479	−	1.14465i	0.0289420	−	0.999581i	$-0.490786\pi$
$524$	1.84040	+	1.06255i	0.0803982	+	0.0464179i
$525$	0.0241345	−	0.927898i	0.00105332	−	0.0404968i
$526$	−8.41522	+	23.1206i	−0.366921	+	1.00811i
$527$	−0.624957	+	3.54431i	−0.0272236	+	0.154393i
$528$	−0.434263	−	0.170973i	−0.0188989	−	0.00744063i
$529$	−21.5619	+	7.84788i	−0.937473	+	0.341212i
$530$	−3.66712	+	4.37031i	−0.159290	+	0.189834i
$531$	8.78475	+	17.2260i	0.381225	+	0.747547i
$532$	−1.79880	−	1.49029i	−0.0779880	−	0.0646123i
$533$		−	22.0981i		−	0.957176i
$534$	0.572707	+	1.71064i	0.0247835	+	0.0740266i
$535$	2.05518	+	5.64656i	0.0888532	+	0.244122i
$536$	5.64625	−	0.995587i	0.243881	−	0.0430028i
$537$	5.23398	−	5.91804i	0.225863	−	0.255382i
$538$	−24.9087	−	9.06602i	−1.07389	−	0.390864i
$539$	1.56646	−	0.904396i	0.0674722	−	0.0389551i
$540$	−2.94087	+	4.28384i	−0.126555	+	0.184347i
$541$	16.5317	−	13.8717i	0.710751	−	0.596391i	−0.214059	−	0.976821i	$-0.568668\pi$
$541$	16.5317	−	13.8717i	0.710751	−	0.596391i	0.924810	+	0.380430i	$0.124224\pi$
$542$	7.38584	−	6.19745i	0.317249	−	0.266203i
$543$	−18.2830	−	33.6589i	−0.784598	−	1.44444i
$544$	0.442138	−	0.255268i	0.0189565	−	0.0109445i
$545$	−7.78188	−	2.83237i	−0.333339	−	0.121326i
$546$	1.32261	+	1.16973i	0.0566024	+	0.0500598i
$547$	−35.0150	+	6.17409i	−1.49713	+	0.263985i	−0.861402	−	0.507924i	$-0.830413\pi$
$547$	−35.0150	+	6.17409i	−1.49713	+	0.263985i	−0.635732	+	0.771910i	$0.719302\pi$
$548$	−1.22768	−	3.37302i	−0.0524439	−	0.144088i
$549$	7.20300	−	31.2498i	0.307417	−	1.33371i
$550$			0.269454i			0.0114896i
$551$	18.0044	+	14.9165i	0.767015	+	0.635464i
$552$	−0.210899	+	0.344292i	−0.00897647	+	0.0146540i
$553$	2.36630	−	2.82005i	0.100626	−	0.119921i
$554$	−8.08452	+	2.94252i	−0.343478	+	0.125016i
$555$	5.81341	−	14.7658i	0.246765	−	0.626774i
$556$	−2.40923	+	13.6634i	−0.102174	+	0.579458i
$557$	2.09509	−	5.75621i	0.0887718	−	0.243899i	−0.887360	−	0.461077i	$-0.847463\pi$
$557$	2.09509	−	5.75621i	0.0887718	−	0.243899i	0.976132	+	0.217178i	$0.0696854\pi$
$558$	17.7405	+	11.5119i	0.751014	+	0.487338i
$559$	−10.8078	−	6.23989i	−0.457122	−	0.263919i
$560$	0.344472	+	0.410526i	0.0145566	+	0.0173479i
$561$	−0.235648	+	0.0352602i	−0.00994907	+	0.00148869i
$562$	−11.4434	+	19.8206i	−0.482711	+	0.836081i
$563$	−8.06195	−	13.9637i	−0.339771	−	0.588500i	0.644619	−	0.764504i	$-0.277016\pi$
$563$	−8.06195	−	13.9637i	−0.339771	−	0.588500i	−0.984389	+	0.176004i	$0.943683\pi$
$564$	12.3016	−	9.78869i	0.517992	−	0.412178i
$565$	3.20537	+	0.565193i	0.134851	+	0.0237779i
$566$	3.91150	+	22.1832i	0.164413	+	0.932431i
$567$	1.32617	−	4.63723i	0.0556940	−	0.194745i
$568$	4.91564	+	4.12471i	0.206256	+	0.173069i
$569$	7.45449			0.312508			0.156254	−	0.987717i	$-0.450058\pi$
$569$	7.45449			0.312508			0.156254	+	0.987717i	$0.450058\pi$
$570$	5.87820	−	4.73781i	0.246211	−	0.198445i
$571$	−28.6140			−1.19746			−0.598730	−	0.800951i	$-0.704328\pi$
$571$	−28.6140			−1.19746			−0.598730	+	0.800951i	$0.704328\pi$
$572$	−0.392643	−	0.329467i	−0.0164172	−	0.0137757i
$573$	−1.52914	+	7.52276i	−0.0638809	+	0.314268i
$574$	1.08107	+	6.13103i	0.0451228	+	0.255904i
$575$	0.229565	+	0.0404785i	0.00957352	+	0.00168807i
$576$	−0.366656	−	2.97751i	−0.0152773	−	0.124063i
$577$	−10.1333	−	17.5513i	−0.421853	−	0.730671i	0.574268	−	0.818667i	$-0.305287\pi$
$577$	−10.1333	−	17.5513i	−0.421853	−	0.730671i	−0.996121	+	0.0879968i	$0.971953\pi$
$578$	−8.36968	+	14.4967i	−0.348133	+	0.602983i
$579$	4.69948	+	31.4072i	0.195304	+	1.30524i
$580$	−3.44786	−	4.10900i	−0.143165	−	0.170617i
$581$	1.36176	+	0.786212i	0.0564953	+	0.0326176i
$582$	3.71284	+	0.0965706i	0.153902	+	0.00400298i
$583$	−0.525768	+	1.44454i	−0.0217751	+	0.0598265i
$584$	0.979238	−	5.55353i	0.0405211	−	0.229807i
$585$	−4.55632	+	3.43595i	−0.188381	+	0.142059i
$586$	−26.6580	+	9.70271i	−1.10123	+	0.400815i
$587$	−10.6189	+	12.6551i	−0.438287	+	0.522330i	−0.939294	−	0.343113i	$-0.888519\pi$
$587$	−10.6189	+	12.6551i	−0.438287	+	0.522330i	0.501007	+	0.865443i	$0.332963\pi$
$588$	9.91465	+	6.07331i	0.408873	+	0.250459i
$589$	−19.8983	−	23.4147i	−0.819896	−	0.964785i
$590$			6.44557i			0.265360i
$591$	−32.9033	+	11.0157i	−1.35346	+	0.453127i
$592$	3.13358	+	8.60943i	0.128789	+	0.353845i
$593$	20.7736	−	3.66294i	0.853068	−	0.150419i	0.270018	−	0.962855i	$-0.412970\pi$
$593$	20.7736	−	3.66294i	0.853068	−	0.150419i	0.583050	+	0.812436i	$0.301859\pi$
$594$	−0.349848	+	1.35571i	−0.0143544	+	0.0556255i
$595$	0.257099	+	0.0935762i	0.0105400	+	0.00383625i
$596$	15.5582	−	8.98256i	0.637291	−	0.367940i
$597$	5.07510	−	2.75671i	0.207710	−	0.112825i
$598$	−0.339678	+	0.285024i	−0.0138905	+	0.0116555i
$599$	−12.3894	+	10.3959i	−0.506217	+	0.424766i	−0.859795	−	0.510639i	$-0.829409\pi$
$599$	−12.3894	+	10.3959i	−0.506217	+	0.424766i	0.353579	+	0.935405i	$0.384965\pi$
$600$	−1.52201	+	0.826731i	−0.0621358	+	0.0337512i
$601$	0.702402	−	0.405532i	0.0286516	−	0.0165420i	−0.485606	−	0.874178i	$-0.661401\pi$
$601$	0.702402	−	0.405532i	0.0286516	−	0.0165420i	0.514257	+	0.857636i	$0.328068\pi$
$602$	3.30385	+	1.20250i	0.134655	+	0.0490103i
$603$	−5.03460	−	16.4467i	−0.205025	−	0.669763i
$604$	3.64818	−	0.643273i	0.148442	−	0.0261744i
$605$	−3.73739	−	10.2684i	−0.151946	−	0.417470i
$606$	2.95668	−	0.989869i	0.120107	−	0.0402107i
$607$			15.6970i			0.637123i	0.947902	+	0.318561i	$0.103200\pi$
$607$			15.6970i			0.637123i	−0.947902	+	0.318561i	$0.896800\pi$
$608$	−0.730033	+	4.29733i	−0.0296067	+	0.174280i
$609$	4.24563	+	2.60070i	0.172042	+	0.105386i
$610$	6.87122	−	8.18880i	0.278208	−	0.331555i
$611$	16.2242	−	5.90514i	0.656362	−	0.238896i
$612$	−0.922177	−	1.22287i	−0.0372768	−	0.0494318i
$613$	5.89200	−	33.4152i	0.237976	−	1.34963i	−0.598280	−	0.801287i	$-0.704149\pi$
$613$	5.89200	−	33.4152i	0.237976	−	1.34963i	0.836256	−	0.548340i	$-0.184740\pi$
$614$	−9.05566	+	24.8802i	−0.365457	+	1.00408i
$615$	−20.1145	−	0.523176i	−0.811095	−	0.0210965i
$616$	0.125055	+	0.0722007i	0.00503862	+	0.00290905i
$617$	−18.4198	−	21.9518i	−0.741552	−	0.883748i	0.254981	−	0.966946i	$-0.417931\pi$
$617$	−18.4198	−	21.9518i	−0.741552	−	0.883748i	−0.996533	+	0.0831986i	$0.973486\pi$
$618$	0.130584	+	0.872711i	0.00525288	+	0.0351056i
$619$	12.4597	−	21.5808i	0.500797	−	0.867406i	−0.499203	−	0.866485i	$-0.666374\pi$
$619$	12.4597	−	21.5808i	0.500797	−	0.867406i	1.00000		0.000920317i	$-0.000292946\pi$
$620$	3.52471	+	6.10497i	0.141556	+	0.245182i
$621$	1.10246	+	0.501718i	0.0442402	+	0.0201332i
$622$	−4.90280	−	0.864495i	−0.196584	−	0.0346631i
$623$	−0.0969224	−	0.549674i	−0.00388311	−	0.0220222i
$624$	0.656296	−	3.22871i	0.0262729	−	0.129252i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	−13.3713			−0.534426
$627$	1.05175	−	1.74136i	0.0420029	−	0.0695431i
$628$	−0.637265			−0.0254296
$629$	3.58319	+	3.00665i	0.142871	+	0.119883i
$630$	1.09604	−	1.17619i	0.0436674	−	0.0468606i
$631$	−2.54473	−	14.4319i	−0.101304	−	0.574525i	−0.992632	−	0.121166i	$-0.961337\pi$
$631$	−2.54473	−	14.4319i	−0.101304	−	0.574525i	0.891328	−	0.453359i	$-0.149774\pi$
$632$	−6.76500	−	1.19285i	−0.269097	−	0.0474491i
$633$	−13.8342	+	11.0082i	−0.549859	+	0.437536i
$634$	6.44499	+	11.1631i	0.255963	+	0.443342i
$635$	2.51903	−	4.36309i	0.0999647	−	0.173144i
$636$	−9.77260	+	1.46228i	−0.387509	+	0.0579833i
$637$	8.20789	+	9.78178i	0.325208	+	0.387568i
$638$	−1.25169	−	0.722665i	−0.0495550	−	0.0286106i
$639$	10.4790	−	16.1487i	0.414544	−	0.638833i
$640$	0.342020	−	0.939693i	0.0135195	−	0.0371446i
$641$	2.74984	−	15.5951i	0.108612	−	0.615970i	−0.881104	−	0.472923i	$-0.843199\pi$
$641$	2.74984	−	15.5951i	0.108612	−	0.615970i	0.989716	−	0.143047i	$-0.0456900\pi$
$642$	−3.81277	+	9.68427i	−0.150478	+	0.382208i
$643$	6.48291	−	2.35959i	0.255661	−	0.0930530i	−0.211010	−	0.977484i	$-0.567675\pi$
$643$	6.48291	−	2.35959i	0.255661	−	0.0930530i	0.466671	+	0.884431i	$0.345453\pi$
$644$	0.0802986	−	0.0956962i	0.00316421	−	0.00377096i
$645$	−5.93565	+	9.68993i	−0.233716	+	0.381540i
$646$	0.774198	+	2.08637i	0.0304604	+	0.0820870i
$647$		−	45.7024i		−	1.79675i	−0.439231	−	0.898374i	$-0.644749\pi$
$647$		−	45.7024i		−	1.79675i	0.439231	−	0.898374i	$-0.355251\pi$
$648$	−8.73113	+	2.18344i	−0.342991	+	0.0857737i
$649$	0.594015	+	1.63204i	0.0233171	+	0.0640633i
$650$	−1.87332	+	0.330316i	−0.0734775	+	0.0129561i
$651$	−4.90144	−	4.33489i	−0.192103	−	0.169898i
$652$	−10.9158	−	3.97303i	−0.427497	−	0.155596i
$653$	−0.743456	+	0.429234i	−0.0290937	+	0.0167972i	−0.514476	−	0.857505i	$-0.672014\pi$
$653$	−0.743456	+	0.429234i	−0.0290937	+	0.0167972i	0.485383	+	0.874302i	$0.338680\pi$
$654$	−6.84641	−	12.6042i	−0.267716	−	0.492865i
$655$	1.62793	−	1.36599i	0.0636084	−	0.0533738i
$656$	8.89917	−	7.46729i	0.347454	−	0.291549i
$657$	−16.8947	−	0.879455i	−0.659127	−	0.0343108i
$658$	−4.21246	+	2.43206i	−0.164219	+	0.0948117i
$659$	25.4151	+	9.25036i	0.990034	+	0.360343i	0.785733	−	0.618565i	$-0.212286\pi$
$659$	25.4151	+	9.25036i	0.990034	+	0.360343i	0.204300	+	0.978908i	$0.434508\pi$
$660$	−0.309189	+	0.349598i	−0.0120351	+	0.0136081i
$661$	23.3092	−	4.11003i	0.906621	−	0.159862i	0.299152	−	0.954205i	$-0.403296\pi$
$661$	23.3092	−	4.11003i	0.906621	−	0.159862i	0.607469	+	0.794344i	$0.292185\pi$
$662$	9.49932	+	26.0992i	0.369202	+	1.01437i
$663$	−0.534014	−	1.59507i	−0.0207394	−	0.0619472i
$664$		−	2.93415i		−	0.113867i
$665$	−2.01564	+	1.18061i	−0.0781632	+	0.0457822i
$666$	24.4857	−	12.4870i	0.948802	−	0.483860i
$667$	−0.803718	+	0.957834i	−0.0311201	+	0.0370875i
$668$	−7.28457	+	2.65137i	−0.281848	+	0.102584i
$669$	2.40217	+	0.945751i	0.0928732	+	0.0365648i
$670$	0.995587	−	5.64625i	0.0384629	−	0.218134i
$671$	0.985151	−	2.70668i	0.0380313	−	0.104490i
$672$	−0.0241345	+	0.927898i	−0.000931010	+	0.0357945i
$673$	2.45755	+	1.41887i	0.0947315	+	0.0546933i	0.546617	−	0.837383i	$-0.315915\pi$
$673$	2.45755	+	1.41887i	0.0947315	+	0.0546933i	−0.451886	+	0.892076i	$0.649249\pi$
$674$	0.505586	+	0.602534i	0.0194744	+	0.0232087i
$675$	3.01965	+	4.22868i	0.116227	+	0.162762i
$676$	−4.69079	+	8.12468i	−0.180415	+	0.312488i
$677$	17.1962	+	29.7847i	0.660904	+	1.14472i	0.980379	+	0.197124i	$0.0631601\pi$
$677$	17.1962	+	29.7847i	0.660904	+	1.14472i	−0.319475	+	0.947595i	$0.603507\pi$
$678$	3.51021	+	4.41134i	0.134809	+	0.169417i
$679$	−1.13170	−	0.199549i	−0.0434306	−	0.00765799i
$680$	−0.0886538	−	0.502781i	−0.00339972	−	0.0192808i
$681$	2.96542	+	0.602778i	0.113635	+	0.0230985i
$682$	1.45510	+	1.22097i	0.0557185	+	0.0467534i
$683$	−5.84698			−0.223729			−0.111864	−	0.993723i	$-0.535682\pi$
$683$	−5.84698			−0.223729			−0.111864	+	0.993723i	$0.535682\pi$
$684$	13.0630	+	0.598040i	0.499477	+	0.0228666i
$685$	−3.58950			−0.137148
$686$	−5.62946	−	4.72368i	−0.214934	−	0.180351i
$687$	−20.5957	−	4.18647i	−0.785776	−	0.159724i
$688$	−1.13925	−	6.46098i	−0.0434333	−	0.246323i
$689$	−10.6873	−	1.88446i	−0.407155	−	0.0717924i
$690$	0.251397	+	0.315935i	0.00957052	+	0.0120275i
$691$	−1.28333	−	2.22280i	−0.0488203	−	0.0845593i	0.840583	−	0.541683i	$-0.182213\pi$
$691$	−1.28333	−	2.22280i	−0.0488203	−	0.0845593i	−0.889403	+	0.457124i	$0.848880\pi$
$692$	−9.91147	+	17.1672i	−0.376778	+	0.652598i
$693$	0.169126	−	0.398826i	0.00642456	−	0.0151501i
$694$	11.6402	+	13.8722i	0.441855	+	0.526583i
$695$	12.0154	+	6.93710i	0.455770	+	0.263139i
$696$	0.241565	−	9.28744i	0.00915651	−	0.352040i
$697$	2.02850	−	5.57325i	0.0768348	−	0.211102i
$698$	−1.73123	+	9.81832i	−0.0655282	+	0.371629i
$699$	29.7457	+	11.7111i	1.12509	+	0.442955i
$700$	0.503585	−	0.183290i	0.0190337	−	0.00692770i
$701$	−33.6892	+	40.1492i	−1.27242	+	1.51641i	−0.526910	+	0.849921i	$0.676649\pi$
$701$	−33.6892	+	40.1492i	−1.27242	+	1.51641i	−0.745512	+	0.666492i	$0.767795\pi$
$702$	−9.85414	−	0.770305i	−0.371921	−	0.0290733i
$703$	−39.2852	+	7.18085i	−1.48167	+	0.270831i
$704$		−	0.269454i		−	0.0101554i
$705$	−4.99096	−	14.9077i	−0.187970	−	0.561456i
$706$	−4.85899	−	13.3500i	−0.182870	−	0.502432i
$707$	−0.950059	+	0.167521i	−0.0357307	+	0.00630028i
$708$	−7.39606	+	8.36269i	−0.277961	+	0.314289i
$709$	42.3775	+	15.4242i	1.59152	+	0.579266i	0.977668	−	0.210154i	$-0.0673966\pi$
$709$	42.3775	+	15.4242i	1.59152	+	0.579266i	0.613853	+	0.789421i	$0.289619\pi$
$710$	5.55721	−	3.20846i	0.208558	−	0.120411i
$711$	−1.07130	+	20.5802i	−0.0401770	+	0.771819i
$712$	−0.797850	+	0.669475i	−0.0299007	+	0.0250896i
$713$	1.25881	−	1.05627i	0.0471429	−	0.0395576i
$714$	0.226192	+	0.416420i	0.00846504	+	0.0155841i
$715$	−0.443890	+	0.256280i	−0.0166005	+	0.00958432i
$716$	4.28627	+	1.56007i	0.160185	+	0.0583027i
$717$	−1.79330	−	1.58602i	−0.0669720	−	0.0592309i
$718$	22.5944	−	3.98401i	0.843216	−	0.148682i
$719$	1.71739	+	4.71850i	0.0640480	+	0.175970i	0.967588	−	0.252532i	$-0.0812634\pi$
$719$	1.71739	+	4.71850i	0.0640480	+	0.175970i	−0.903540	+	0.428503i	$0.859041\pi$
$720$	−2.92335	−	0.673825i	−0.108947	−	0.0251120i
$721$		−	0.273026i		−	0.0101680i
$722$	−17.9341	−	6.27439i	−0.667438	−	0.233508i
$723$	11.3931	−	18.5992i	0.423715	−	0.691713i
$724$	14.2151	−	16.9409i	0.528301	−	0.629604i
$725$	−5.04044	+	1.83457i	−0.187197	+	0.0681342i
$726$	6.93360	−	17.6110i	0.257330	−	0.653607i
$727$	9.29339	−	52.7054i	0.344673	−	1.95474i	0.0515112	−	0.998672i	$-0.483596\pi$
$727$	9.29339	−	52.7054i	0.344673	−	1.95474i	0.293161	−	0.956063i	$-0.405293\pi$
$728$	−0.348657	+	0.957927i	−0.0129221	+	0.0355031i
$729$	9.70254	+	25.1964i	0.359353	+	0.933202i
$730$	−4.88369	−	2.81960i	−0.180754	−	0.104358i
$731$	−2.15299	−	2.56583i	−0.0796312	−	0.0949007i
$732$	18.3113	−	2.73993i	0.676805	−	0.101271i
$733$	6.59099	−	11.4159i	0.243444	−	0.421657i	−0.718249	−	0.695786i	$-0.755056\pi$
$733$	6.59099	−	11.4159i	0.243444	−	0.421657i	0.961693	+	0.274129i	$0.0883896\pi$
$734$	12.9595	+	22.4465i	0.478343	+	0.828515i
$735$	9.09805	−	7.23953i	0.335587	−	0.267034i
$736$	−0.229565	−	0.0404785i	−0.00846187	−	0.00149206i
$737$	−0.268265	−	1.52140i	−0.00988166	−	0.0560417i
$738$	−25.4969	−	23.7594i	−0.938552	−	0.874597i
$739$	−39.8791	−	33.4625i	−1.46698	−	1.23094i	−0.918888	−	0.394519i	$-0.870911\pi$
$739$	−39.8791	−	33.4625i	−1.46698	−	1.23094i	−0.548088	−	0.836420i	$-0.684644\pi$
$740$	9.16197			0.336801
$741$	13.3957	+	5.17739i	0.492104	+	0.190196i
$742$	3.05735			0.112239
$743$	−11.1192	−	9.33008i	−0.407922	−	0.342288i	0.415624	−	0.909537i	$-0.363563\pi$
$743$	−11.1192	−	9.33008i	−0.407922	−	0.342288i	−0.823546	+	0.567249i	$0.808008\pi$
$744$	−2.43217	+	11.9653i	−0.0891675	+	0.438667i
$745$	−3.11961	−	17.6922i	−0.114294	−	0.648191i
$746$	11.9093	+	2.09994i	0.436032	+	0.0768842i
$747$	−8.73647	+	1.07582i	−0.319651	+	0.0393623i
$748$	−0.0687831	−	0.119136i	−0.00251496	−	0.00435604i
$749$	1.61011	−	2.78879i	0.0588321	−	0.101900i
$750$	0.256315	+	1.71298i	0.00935929	+	0.0625492i
$751$	−2.40354	−	2.86443i	−0.0877065	−	0.104524i	0.720406	−	0.693552i	$-0.243955\pi$
$751$	−2.40354	−	2.86443i	−0.0877065	−	0.104524i	−0.808113	+	0.589028i	$0.799511\pi$
$752$	7.86048	+	4.53825i	0.286642	+	0.165493i
$753$	47.1071	+	1.22525i	1.71668	+	0.0446506i
$754$	3.48975	−	9.58800i	0.127089	−	0.349174i
$755$	0.643273	−	3.64818i	0.0234111	−	0.132771i
$756$	2.77168	−	0.268358i	0.100805	−	0.00976010i
$757$	−29.2090	+	10.6312i	−1.06162	+	0.386398i	−0.813037	−	0.582212i	$-0.802187\pi$
$757$	−29.2090	+	10.6312i	−1.06162	+	0.386398i	−0.248583	+	0.968611i	$0.579965\pi$
$758$	6.05169	−	7.21212i	0.219807	−	0.261956i
$759$	0.0927709	+	0.0568276i	0.00336737	+	0.00206271i
$760$	3.78848	+	2.15578i	0.137423	+	0.0781984i
$761$		−	1.83211i		−	0.0664138i	−0.999448	−	0.0332069i	$-0.989428\pi$
$761$		−	1.83211i		−	0.0664138i	0.999448	−	0.0332069i	$-0.0105720\pi$
$762$	8.27476	−	2.77031i	0.299763	−	0.100358i
$763$	1.51788	+	4.17034i	0.0549509	+	0.150976i
$764$	−4.36476	+	0.769624i	−0.157911	+	0.0278440i
$765$	−1.46453	+	0.448315i	−0.0529502	+	0.0162089i
$766$	−19.6447	−	7.15008i	−0.709791	−	0.258343i
$767$	−10.6182	+	6.13043i	−0.383402	+	0.221357i
$768$	1.52201	−	0.826731i	0.0549208	−	0.0298321i
$769$	26.5280	−	22.2597i	0.956625	−	0.802704i	−0.0237758	−	0.999717i	$-0.507569\pi$
$769$	26.5280	−	22.2597i	0.956625	−	0.802704i	0.980401	+	0.197014i	$0.0631243\pi$
$770$	0.110618	−	0.0928194i	0.00398639	−	0.00334498i
$771$	−47.3993	+	25.7465i	−1.70704	+	0.927238i
$772$	−15.8784	+	9.16741i	−0.571477	+	0.329942i
$773$	14.5009	+	5.27790i	0.521561	+	0.189833i	0.589366	−	0.807866i	$-0.299377\pi$
$773$	14.5009	+	5.27790i	0.521561	+	0.189833i	−0.0678053	+	0.997699i	$0.521600\pi$
$774$	−18.8199	+	5.76107i	−0.676468	+	0.207077i
$775$	6.94232	−	1.22412i	0.249375	−	0.0439716i
$776$	0.733406	+	2.01502i	0.0263277	+	0.0723349i
$777$	−8.06431	+	2.69986i	−0.289305	+	0.0968568i
$778$		−	25.6051i		−	0.917987i
$779$	25.5927	+	43.6940i	0.916955	+	1.56550i
$780$	−2.80953	−	1.72100i	−0.100597	−	0.0616217i
$781$	1.11142	−	1.32454i	0.0397697	−	0.0473957i
$782$	−0.111832	+	0.0407036i	−0.00399911	+	0.00145556i
$783$	−27.7420	+	2.68603i	−0.991419	+	0.0959909i
$784$	−1.16567	+	6.61082i	−0.0416310	+	0.236101i
$785$	−0.217958	+	0.598833i	−0.00777924	+	0.0213733i
$786$	3.67955	+	0.0957047i	0.131245	+	0.00341367i
$787$	45.4685	+	26.2512i	1.62078	+	0.935755i	0.986713	+	0.162474i	$0.0519474\pi$
$787$	45.4685	+	26.2512i	1.62078	+	0.935755i	0.634063	+	0.773281i	$0.281386\pi$
$788$	−12.8770	−	15.3462i	−0.458725	−	0.546687i
$789$	6.30649	+	42.1470i	0.224517	+	1.50047i
$790$	−3.43468	+	5.94904i	−0.122200	+	0.211657i
$791$	−0.872134	−	1.51058i	−0.0310095	−	0.0537101i
$792$	−0.802302	+	0.0987968i	−0.0285085	+	0.00351059i
$793$	20.0252	+	3.53099i	0.711117	+	0.125389i
$794$	−5.40837	−	30.6724i	−0.191936	−	1.08852i
$795$	−1.96833	+	9.68337i	−0.0698095	+	0.343434i
$796$	2.55436	+	2.14336i	0.0905367	+	0.0759693i
$797$	45.9715			1.62839			0.814197	−	0.580588i	$-0.197177\pi$
$797$	45.9715			1.62839			0.814197	+	0.580588i	$0.197177\pi$
$798$	−3.96987	−	0.781111i	−0.140532	−	0.0276510i
$799$	4.63389			0.163935
$800$	−0.766044	−	0.642788i	−0.0270838	−	0.0227260i
$801$	2.28591	+	2.13014i	0.0807685	+	0.0752647i
$802$	−1.37281	−	7.78561i	−0.0484757	−	0.274919i
$803$	−1.49642	−	0.263859i	−0.0528076	−	0.00931140i
$804$	7.77057	−	6.18322i	0.274047	−	0.218066i
$805$	−0.0624612	−	0.108186i	−0.00220147	−	0.00381306i
$806$	−6.70475	+	11.6130i	−0.236165	+	0.409050i
$807$	−45.4064	+	6.79420i	−1.59838	+	0.239167i
$808$	1.15712	+	1.37901i	0.0407075	+	0.0485133i
$809$	−12.2648	−	7.08110i	−0.431208	−	0.248958i	0.268653	−	0.963237i	$-0.413422\pi$
$809$	−12.2648	−	7.08110i	−0.431208	−	0.248958i	−0.699861	+	0.714279i	$0.746755\pi$
$810$	−0.934457	+	8.95136i	−0.0328335	+	0.314519i
$811$	−11.7186	+	32.1965i	−0.411494	+	1.13057i	0.544902	+	0.838500i	$0.316567\pi$
$811$	−11.7186	+	32.1965i	−0.411494	+	1.13057i	−0.956396	+	0.292072i	$0.905655\pi$
$812$	−0.499160	+	2.83087i	−0.0175171	+	0.0993442i
$813$	6.11769	−	15.5387i	0.214557	−	0.544965i
$814$	2.31985	−	0.844355i	0.0813105	−	0.0295946i
$815$	−7.46686	+	8.89866i	−0.261553	+	0.311706i
$816$	0.461900	−	0.754050i	0.0161697	−	0.0263970i
$817$	28.5967	−	0.178985i	1.00047	−	0.00626188i
$818$			22.4690i			0.785611i
$819$	2.98007	+	0.686900i	0.104132	+	0.0240022i
$820$	−3.97326	−	10.9164i	−0.138752	−	0.381219i
$821$	−4.02142	+	0.709085i	−0.140349	+	0.0247472i	−0.243381	−	0.969931i	$-0.578257\pi$
$821$	−4.02142	+	0.709085i	−0.140349	+	0.0247472i	0.103032	+	0.994678i	$0.467145\pi$
$822$	−4.65713	−	4.11882i	−0.162436	−	0.143660i
$823$	−12.9801	−	4.72436i	−0.452457	−	0.164681i	0.105732	−	0.994395i	$-0.466281\pi$
$823$	−12.9801	−	4.72436i	−0.452457	−	0.164681i	−0.558189	+	0.829714i	$0.688504\pi$
$824$	−0.441213	+	0.254735i	−0.0153704	+	0.00887410i
$825$	0.222766	+	0.410112i	0.00775571	+	0.0142783i
$826$	2.64607	−	2.22032i	0.0920687	−	0.0772548i
$827$	−6.94845	+	5.83044i	−0.241621	+	0.202744i	−0.755554	−	0.655086i	$-0.772632\pi$
$827$	−6.94845	+	5.83044i	−0.241621	+	0.202744i	0.513933	+	0.857830i	$0.328188\pi$
$828$	−0.0363538	+	0.698373i	−0.00126338	+	0.0242701i
$829$	0.0499853	−	0.0288590i	0.00173606	−	0.00100231i	−0.499132	−	0.866526i	$-0.666348\pi$
$829$	0.0499853	−	0.0288590i	0.00173606	−	0.00100231i	0.500868	+	0.865524i	$0.333014\pi$
$830$	−2.75720	−	1.00354i	−0.0957039	−	0.0348334i
$831$	−9.87204	+	11.1623i	−0.342457	+	0.387215i
$832$	1.87332	−	0.330316i	0.0649456	−	0.0114517i
$833$	1.17215	+	3.22045i	0.0406126	+	0.111582i
$834$	7.62910	+	22.7877i	0.264174	+	0.789072i
$835$			7.75207i			0.268272i
$836$	1.15793	+	0.196710i	0.0400479	+	0.00680337i
$837$	36.5184	+	2.85467i	1.26226	+	0.0986719i
$838$	11.7589	−	14.0137i	0.406205	−	0.484097i
$839$	43.2559	−	15.7439i	1.49336	−	0.543539i	0.539028	−	0.842288i	$-0.318792\pi$
$839$	43.2559	−	15.7439i	1.49336	−	0.543539i	0.954332	+	0.298749i	$0.0965694\pi$
$840$	0.863685	+	0.340039i	0.0298000	+	0.0117325i
$841$	−0.0396507	+	0.224871i	−0.00136727	+	0.00775416i
$842$	−12.7447	+	35.0157i	−0.439211	+	1.20672i
$843$	−1.03071	+	39.6278i	−0.0354996	+	1.36485i
$844$	−8.83975	−	5.10363i	−0.304277	−	0.175674i
$845$	6.03036	+	7.18670i	0.207451	+	0.247230i
$846$	10.6306	−	25.0686i	0.365487	−	0.861877i
$847$	−2.92802	+	5.07147i	−0.100608	+	0.174258i
$848$	−2.85251	−	4.94070i	−0.0979557	−	0.169664i
$849$	24.2929	+	30.5294i	0.833731	+	1.04776i
$850$	−0.502781	−	0.0886538i	−0.0172452	−	0.00304080i
$851$	−0.370862	−	2.10327i	−0.0127130	−	0.0720990i
$852$	10.8917	+	2.21394i	0.373143	+	0.0758484i
$853$	4.36087	+	3.65921i	0.149313	+	0.125289i	0.714384	−	0.699753i	$-0.246707\pi$
$853$	4.36087	+	3.65921i	0.149313	+	0.125289i	−0.565071	+	0.825042i	$0.691151\pi$
$854$	−5.72866			−0.196031
$855$	5.02979	−	12.0707i	0.172015	−	0.412808i
$856$	−6.00895			−0.205382
$857$	−3.14858	−	2.64197i	−0.107553	−	0.0902481i	0.587425	−	0.809279i	$-0.300142\pi$
$857$	−3.14858	−	2.64197i	−0.107553	−	0.0902481i	−0.694979	+	0.719031i	$0.744586\pi$
$858$	−0.869988	−	0.176842i	−0.0297009	−	0.00603727i
$859$	2.80941	+	15.9330i	0.0958560	+	0.543626i	0.994482	+	0.104910i	$0.0334555\pi$
$859$	2.80941	+	15.9330i	0.0958560	+	0.543626i	−0.898626	+	0.438716i	$0.855433\pi$
$860$	−6.46098	−	1.13925i	−0.220318	−	0.0388480i
$861$	6.71411	+	8.43775i	0.228816	+	0.287558i
$862$	9.33534	+	16.1693i	0.317963	+	0.550728i
$863$	−0.0867373	+	0.150233i	−0.00295257	+	0.00511400i	−0.867498	−	0.497441i	$-0.834273\pi$
$863$	−0.0867373	+	0.150233i	−0.00295257	+	0.00511400i	0.864545	+	0.502555i	$0.167607\pi$
$864$	−3.01965	−	4.22868i	−0.102731	−	0.143862i
$865$	12.7419	+	15.1853i	0.433239	+	0.516314i
$866$	9.57965	+	5.53081i	0.325530	+	0.187945i
$867$	−0.753860	+	28.9836i	−0.0256024	+	0.984335i
$868$	1.29209	−	3.54998i	0.0438563	−	0.120494i
$869$	−0.321419	+	1.82286i	−0.0109034	+	0.0618362i
$870$	−8.64472	−	3.40349i	−0.293084	−	0.115389i
$871$	10.2484	−	3.73010i	0.347252	−	0.126390i
$872$	5.32312	−	6.34385i	0.180264	−	0.214830i
$873$	5.73083	−	2.92254i	0.193959	−	0.0989130i
$874$	0.341539	−	0.956966i	0.0115527	−	0.0323698i
$875$		−	0.535904i		−	0.0181168i
$876$	−3.10087	−	9.26210i	−0.104769	−	0.312937i
$877$	12.6134	+	34.6551i	0.425925	+	1.17022i	0.948264	+	0.317482i	$0.102837\pi$
$877$	12.6134	+	34.6551i	0.425925	+	1.17022i	−0.522339	+	0.852738i	$0.674941\pi$
$878$	36.3804	−	6.41485i	1.22778	−	0.216491i
$879$	−32.5522	+	36.8066i	−1.09796	+	1.24146i
$880$	−0.253204	−	0.0921587i	−0.00853550	−	0.00310667i
$881$	35.3271	−	20.3961i	1.19020	−	0.687162i	0.231848	−	0.972752i	$-0.425523\pi$
$881$	35.3271	−	20.3961i	1.19020	−	0.687162i	0.958352	+	0.285590i	$0.0921895\pi$
$882$	20.1112	+	1.04689i	0.677179	+	0.0352505i
$883$	−42.6901	+	35.8212i	−1.43664	+	1.20548i	−0.494979	+	0.868905i	$0.664824\pi$
$883$	−42.6901	+	35.8212i	−1.43664	+	1.20548i	−0.941656	+	0.336576i	$0.890731\pi$
$884$	0.743945	−	0.624244i	0.0250216	−	0.0209956i
$885$	5.32875	+	9.81023i	0.179124	+	0.329767i
$886$	−17.9170	+	10.3444i	−0.601934	+	0.347527i
$887$	15.7565	+	5.73489i	0.529051	+	0.192559i	0.592715	−	0.805413i	$-0.298056\pi$
$887$	15.7565	+	5.73489i	0.529051	+	0.192559i	−0.0636635	+	0.997971i	$0.520278\pi$
$888$	11.8870	+	10.5130i	0.398902	+	0.352794i
$889$	−2.65890	+	0.468835i	−0.0891766	+	0.0157242i
$890$	0.356220	+	0.978707i	0.0119405	+	0.0328063i
$891$	0.588337	+	2.35264i	0.0197100	+	0.0788163i
$892$			1.49051i			0.0499059i
$893$	−25.2408	+	30.4660i	−0.844650	+	1.01951i
$894$	16.2537	−	26.5340i	0.543603	−	0.887431i
$895$	2.93198	−	3.49420i	0.0980052	−	0.116798i
$896$	−0.503585	+	0.183290i	−0.0168236	+	0.00612328i
$897$	−0.281356	+	0.714632i	−0.00939420	+	0.0238609i
$898$	6.85472	−	38.8750i	0.228745	−	1.29728i
$899$	−12.9326	+	35.5321i	−0.431328	+	1.18506i
$900$	−1.63303	+	2.51659i	−0.0544344	+	0.0838862i
$901$	−2.52241	−	1.45631i	−0.0840336	−	0.0485168i
$902$	−2.01209	−	2.39792i	−0.0669953	−	0.0798419i
$903$	6.02263	−	0.901172i	0.200421	−	0.0299891i
$904$	−1.62741	+	2.81875i	−0.0541268	+	0.0937504i
$905$	−11.0574	−	19.1520i	−0.367560	−	0.636633i
$906$	5.02076	−	3.99514i	0.166804	−	0.132729i
$907$	50.4920	+	8.90310i	1.67656	+	0.295623i	0.929414	−	0.369038i	$-0.120313\pi$
$907$	50.4920	+	8.90310i	1.67656	+	0.295623i	0.747145	+	0.664661i	$0.231424\pi$
$908$	0.303380	+	1.72055i	0.0100680	+	0.0570986i
$909$	3.68174	−	3.95097i	0.122116	−	0.131045i
$910$	0.780909	+	0.655261i	0.0258869	+	0.0217217i
$911$	−12.0852			−0.400402			−0.200201	−	0.979755i	$-0.564160\pi$
$911$	−12.0852			−0.400402			−0.200201	+	0.979755i	$0.564160\pi$
$912$	2.44162	+	7.14412i	0.0808501	+	0.236566i
$913$	−0.790619			−0.0261657
$914$	1.48065	+	1.24241i	0.0489756	+	0.0410954i
$915$	3.68813	−	18.1441i	0.121926	−	0.599825i
$916$	−2.10707	−	11.9498i	−0.0696195	−	0.394832i
$917$	−1.12155	−	0.197760i	−0.0370369	−	0.00653061i
$918$	−2.41455	−	1.09884i	−0.0796920	−	0.0362670i
$919$	−21.6936	−	37.5744i	−0.715606	−	1.23947i	−0.962725	−	0.270480i	$-0.912817\pi$
$919$	−21.6936	−	37.5744i	−0.715606	−	1.23947i	0.247120	−	0.968985i	$-0.420516\pi$
$920$	−0.116553	+	0.201876i	−0.00384264	+	0.00665565i
$921$	6.78644	+	45.3546i	0.223621	+	1.49448i
$922$	11.1048	+	13.2342i	0.365719	+	0.435846i
$923$	10.5710	+	6.10318i	0.347949	+	0.200888i
$924$	0.250026	+	0.00650314i	0.00822525	+	0.000213938i
$925$	3.13358	−	8.60943i	0.103031	−	0.283076i
$926$	3.67661	−	20.8511i	0.120821	−	0.685209i
$927$	0.920248	+	1.22032i	0.0302249	+	0.0400805i
$928$	5.04044	−	1.83457i	0.165460	−	0.0602227i
$929$	−4.89409	+	5.83255i	−0.160570	+	0.191360i	−0.840331	−	0.542074i	$-0.817639\pi$
$929$	−4.89409	+	5.83255i	−0.160570	+	0.191360i	0.679761	+	0.733434i	$0.262084\pi$
$930$	10.4118	+	6.37785i	0.341417	+	0.209138i
$931$	−27.5579	−	9.83538i	−0.903175	−	0.322341i
$932$			18.4568i			0.604572i
$933$	−8.17681	+	2.73752i	−0.267697	+	0.0896225i
$934$	1.11268	+	3.05707i	0.0364081	+	0.100030i
$935$	−0.135476	+	0.0238881i	−0.00443055	+	0.000781225i
$936$	−1.67038	−	5.45671i	−0.0545982	−	0.178358i
$937$	28.7357	+	10.4589i	0.938755	+	0.341679i	0.765674	−	0.643229i	$-0.222406\pi$
$937$	28.7357	+	10.4589i	0.938755	+	0.341679i	0.173081	+	0.984908i	$0.444628\pi$
$938$	−2.66088	+	1.53626i	−0.0868810	+	0.0501608i
$939$	−20.3513	+	11.0545i	−0.664139	+	0.360750i
$940$	6.95300	−	5.83426i	0.226782	−	0.190293i
$941$	−0.601892	+	0.505047i	−0.0196211	+	0.0164641i	−0.652545	−	0.757750i	$-0.726299\pi$
$941$	−0.601892	+	0.505047i	−0.0196211	+	0.0164641i	0.632924	+	0.774214i	$0.281854\pi$
$942$	−0.969924	+	0.526847i	−0.0316018	+	0.0171656i
$943$	−2.34520	+	1.35400i	−0.0763703	+	0.0440924i
$944$	−6.05686	−	2.20452i	−0.197134	−	0.0717509i
$945$	0.695794	−	2.69631i	0.0226342	−	0.0877109i
$946$	−1.74094	+	0.306974i	−0.0566028	+	0.00998059i
$947$	5.55338	+	15.2578i	0.180461	+	0.495811i	0.996633	−	0.0819977i	$-0.0261300\pi$
$947$	5.55338	+	15.2578i	0.180461	+	0.495811i	−0.816172	+	0.577809i	$0.803908\pi$
$948$	−11.2826	+	3.77730i	−0.366441	+	0.122681i
$949$		−	10.7270i		−	0.348213i
$950$	3.32151	−	2.82269i	0.107764	−	0.0915802i
$951$	19.0382	+	11.6620i	0.617356	+	0.378167i
$952$	−0.175866	+	0.209589i	−0.00569984	+	0.00679281i
$953$	−31.9078	+	11.6135i	−1.03359	+	0.376198i	−0.802448	−	0.596722i	$-0.796470\pi$
$953$	−31.9078	+	11.6135i	−1.03359	+	0.376198i	−0.231146	+	0.972919i	$0.574247\pi$
$954$	−13.6651	+	10.3049i	−0.442424	+	0.333634i
$955$	−0.769624	+	4.36476i	−0.0249045	+	0.141240i
$956$	0.472738	−	1.29884i	0.0152894	−	0.0420074i
$957$	−2.50254	−	0.0650907i	−0.0808956	−	0.00210408i
$958$	10.3325	+	5.96550i	0.333829	+	0.192736i
$959$	1.23648	+	1.47358i	0.0399281	+	0.0475844i
$960$	−0.256315	−	1.71298i	−0.00827252	−	0.0552862i
$961$	9.34712	−	16.1897i	0.301520	−	0.522248i
$962$	8.71402	+	15.0931i	0.280951	+	0.486622i
$963$	2.20321	+	17.8917i	0.0709976	+	0.576552i
$964$	12.4015	+	2.18671i	0.399424	+	0.0704293i
$965$	3.18381	+	18.0563i	0.102490	+	0.581252i
$966$	0.0431004	−	0.212036i	0.00138673	−	0.00682215i
$967$	−29.4137	−	24.6810i	−0.945881	−	0.793688i	0.0327184	−	0.999465i	$-0.489584\pi$
$967$	−29.4137	−	24.6810i	−0.945881	−	0.793688i	−0.978599	+	0.205777i	$0.934028\pi$
$968$	10.9274			0.351220
$969$	2.90320	+	2.53542i	0.0932643	+	0.0814494i
$970$	2.14434			0.0688505
$971$	40.3116	+	33.8254i	1.29366	+	1.08551i	0.991203	+	0.132347i	$0.0422512\pi$
$971$	40.3116	+	33.8254i	1.29366	+	1.08551i	0.302457	+	0.953163i	$0.402193\pi$
$972$	−11.4837	+	10.5415i	−0.368341	+	0.338119i
$973$	−1.29111	−	7.32228i	−0.0413912	−	0.234741i
$974$	7.51644	+	1.32535i	0.240842	+	0.0424670i
$975$	−2.57813	+	2.05147i	−0.0825661	+	0.0656998i
$976$	5.34486	+	9.25757i	0.171085	+	0.296328i
$977$	23.3057	−	40.3667i	0.745617	−	1.29145i	−0.204289	−	0.978911i	$-0.565488\pi$
$977$	23.3057	−	40.3667i	0.745617	−	1.29145i	0.949906	−	0.312536i	$-0.101178\pi$
$978$	−19.8986	+	2.97745i	−0.636288	+	0.0952083i
$979$	0.180393	+	0.214984i	0.00576538	+	0.00687091i
$980$	5.81346	+	3.35640i	0.185704	+	0.107216i
$981$	−20.8406	−	13.5236i	−0.665390	−	0.431777i
$982$	12.5691	−	34.5334i	0.401098	−	1.10201i
$983$	4.50298	−	25.5377i	0.143623	−	0.814526i	−0.824840	−	0.565367i	$-0.808735\pi$
$983$	4.50298	−	25.5377i	0.143623	−	0.814526i	0.968463	−	0.249159i	$-0.0801542\pi$
$984$	7.37119	−	18.7225i	0.234985	−	0.596852i
$985$	−18.8250	+	6.85173i	−0.599813	+	0.218314i
$986$	1.76026	−	2.09780i	0.0560581	−	0.0668075i
$987$	−4.40074	+	7.18420i	−0.140077	+	0.228676i
$988$	0.0518954	+	8.29140i	0.00165101	+	0.263785i
$989$			1.52933i			0.0486299i
$990$	−0.181565	+	0.787707i	−0.00577050	+	0.0250350i
$991$	−4.55250	−	12.5079i	−0.144615	−	0.397327i	0.846145	−	0.532953i	$-0.178918\pi$
$991$	−4.55250	−	12.5079i	−0.144615	−	0.397327i	−0.990760	+	0.135626i	$0.956695\pi$
$992$	−6.94232	+	1.22412i	−0.220419	+	0.0388658i
$993$	36.0351	+	31.8698i	1.14354	+	1.01136i
$994$	−3.23146	−	1.17615i	−0.102496	−	0.0373054i
$995$	2.88774	−	1.66724i	0.0915475	−	0.0528550i
$996$	−2.42576	−	4.46581i	−0.0768630	−	0.141505i
$997$	30.5216	−	25.6106i	0.966628	−	0.811097i	−0.0153909	−	0.999882i	$-0.504899\pi$
$997$	30.5216	−	25.6106i	0.966628	−	0.811097i	0.982019	+	0.188785i	$0.0604548\pi$
$998$	−25.7257	+	21.5864i	−0.814331	+	0.683305i
$999$	26.9442	−	39.2484i	0.852476	−	1.24176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bb.a.41.14	✓	84
3.2	odd	2		570.2.bb.b.41.4	yes	84
19.13	odd	18		570.2.bb.b.431.4	yes	84
57.32	even	18	inner	570.2.bb.a.431.14	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bb.a.41.14	✓	84	1.1	even	1	trivial
570.2.bb.a.431.14	yes	84	57.32	even	18	inner
570.2.bb.b.41.4	yes	84	3.2	odd	2
570.2.bb.b.431.4	yes	84	19.13	odd	18

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(1.69734 + 0.345017i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(1.07847 + 1.35533i) q^{6} +(-0.267952 - 0.464106i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.76193 + 1.17122i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(1.69734 + 0.345017i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(1.07847 + 1.35533i) q^{6} +(-0.267952 - 0.464106i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.76193 + 1.17122i) q^{9} +(0.642788 + 0.766044i) q^{10} +(0.233354 + 0.134727i) q^{11} +(-0.0450352 + 1.73147i) q^{12} +(-0.650596 + 1.78750i) q^{13} +(0.0930587 - 0.527762i) q^{14} +(1.61164 + 0.634515i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.328167 + 0.391094i) q^{17} +(1.36291 + 2.67254i) q^{18} +(-0.783767 - 4.28786i) q^{19} +1.00000i q^{20} +(-0.294681 - 0.880194i) q^{21} +(0.0921587 + 0.253204i) q^{22} +(0.229565 - 0.0404785i) q^{23} +(-1.14746 + 1.29743i) q^{24} +(0.939693 + 0.342020i) q^{25} +(-1.64737 + 0.951108i) q^{26} +(4.28384 + 2.94087i) q^{27} +(0.410526 - 0.344472i) q^{28} +(-4.10900 + 3.44786i) q^{29} +(0.826731 + 1.52201i) q^{30} +(6.10497 - 3.52471i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.349598 + 0.309189i) q^{33} +(-0.502781 + 0.0886538i) q^{34} +(-0.183290 - 0.503585i) q^{35} +(-0.673825 + 2.92335i) q^{36} -9.16197i q^{37} +(2.15578 - 3.78848i) q^{38} +(-1.72100 + 2.80953i) q^{39} +(-0.642788 + 0.766044i) q^{40} +(-10.9164 + 3.97326i) q^{41} +(0.340039 - 0.863685i) q^{42} +(-1.13925 + 6.46098i) q^{43} +(-0.0921587 + 0.253204i) q^{44} +(2.51659 + 1.63303i) q^{45} +(0.201876 + 0.116553i) q^{46} +(-5.83426 - 6.95300i) q^{47} +(-1.71298 + 0.256315i) q^{48} +(3.35640 - 5.81346i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-0.691945 + 0.550596i) q^{51} +(-1.87332 - 0.330316i) q^{52} +(0.990668 + 5.61836i) q^{53} +(1.39125 + 5.00644i) q^{54} +(0.206414 + 0.173202i) q^{55} +0.535904 q^{56} +(0.149063 - 7.54836i) q^{57} -5.36392 q^{58} +(4.93759 + 4.14313i) q^{59} +(-0.345017 + 1.69734i) q^{60} +(-1.85625 - 10.5273i) q^{61} +(6.94232 + 1.22412i) q^{62} +(-0.196492 - 1.59566i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.951108 + 1.64737i) q^{65} +(0.0690650 + 0.461569i) q^{66} +(-3.68533 - 4.39200i) q^{67} +(-0.442138 - 0.255268i) q^{68} +(0.403615 + 0.0104980i) q^{69} +(0.183290 - 0.503585i) q^{70} +(1.11428 - 6.31942i) q^{71} +(-2.39527 + 1.80629i) q^{72} +(-5.29912 + 1.92872i) q^{73} +(5.88920 - 7.01847i) q^{74} +(1.47698 + 0.904734i) q^{75} +(4.08661 - 1.51644i) q^{76} -0.144401i q^{77} +(-3.12429 + 1.04598i) q^{78} +(2.34946 + 6.45509i) q^{79} +(-0.984808 + 0.173648i) q^{80} +(6.25648 + 6.46966i) q^{81} +(-10.9164 - 3.97326i) q^{82} +(-2.54105 + 1.46708i) q^{83} +(0.815651 - 0.443048i) q^{84} +(-0.391094 + 0.328167i) q^{85} +(-5.02575 + 4.21711i) q^{86} +(-8.16395 + 4.43452i) q^{87} +(-0.233354 + 0.134727i) q^{88} +(0.978707 + 0.356220i) q^{89} +(0.878124 + 2.86861i) q^{90} +(1.00392 - 0.177018i) q^{91} +(0.0797270 + 0.219048i) q^{92} +(11.5783 - 3.87631i) q^{93} -9.07650i q^{94} +(-0.0272815 - 4.35881i) q^{95} +(-1.47698 - 0.904734i) q^{96} +(1.37835 - 1.64266i) q^{97} +(6.30798 - 2.29592i) q^{98} +(0.486711 + 0.645415i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9}+O(q^{10}) \) 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9	\( 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9} + 24 q^{13} + 24 q^{14} - 12 q^{17} - 12 q^{19} + 36 q^{22} - 6 q^{24} - 6 q^{27} - 12 q^{28} + 12 q^{29} - 6 q^{33} + 12 q^{34} - 18 q^{38} + 12 q^{39} - 6 q^{41} + 24 q^{43} - 36 q^{44} - 12 q^{47} - 54 q^{49} + 42 q^{50} - 54 q^{51} + 12 q^{52} + 60 q^{53} - 54 q^{54} - 60 q^{57} - 24 q^{58} + 18 q^{59} - 48 q^{61} + 12 q^{62} + 18 q^{63} - 42 q^{64} + 54 q^{66} + 6 q^{67} + 54 q^{68} - 60 q^{69} - 48 q^{71} - 12 q^{72} + 84 q^{73} - 24 q^{74} + 36 q^{78} - 12 q^{79} + 114 q^{81} - 6 q^{82} - 36 q^{83} - 18 q^{84} - 12 q^{86} + 6 q^{87} + 12 q^{89} + 24 q^{91} + 6 q^{93} + 12 q^{95} - 42 q^{97} - 36 q^{98} + 102 q^{99}+O(q^{100}) \) 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9 + 24 * q^13 + 24 * q^14 - 12 * q^17 - 12 * q^19 + 36 * q^22 - 6 * q^24 - 6 * q^27 - 12 * q^28 + 12 * q^29 - 6 * q^33 + 12 * q^34 - 18 * q^38 + 12 * q^39 - 6 * q^41 + 24 * q^43 - 36 * q^44 - 12 * q^47 - 54 * q^49 + 42 * q^50 - 54 * q^51 + 12 * q^52 + 60 * q^53 - 54 * q^54 - 60 * q^57 - 24 * q^58 + 18 * q^59 - 48 * q^61 + 12 * q^62 + 18 * q^63 - 42 * q^64 + 54 * q^66 + 6 * q^67 + 54 * q^68 - 60 * q^69 - 48 * q^71 - 12 * q^72 + 84 * q^73 - 24 * q^74 + 36 * q^78 - 12 * q^79 + 114 * q^81 - 6 * q^82 - 36 * q^83 - 18 * q^84 - 12 * q^86 + 6 * q^87 + 12 * q^89 + 24 * q^91 + 6 * q^93 + 12 * q^95 - 42 * q^97 - 36 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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