LMFDB - Embedded newform 570.2.bb.b.431.4

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			431.4
Character	$\chi$	$=$	570.431
Dual form			570.2.bb.b.41.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-1.07847 - 1.35533i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.984808 + 0.173648i) q^{5} +(1.69734 + 0.345017i) q^{6} +(-0.267952 + 0.464106i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.673825 + 2.92335i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.07847 - 1.35533i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.984808 + 0.173648i) q^{5} +(1.69734 + 0.345017i) q^{6} +(-0.267952 + 0.464106i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.673825 + 2.92335i) q^{9} +(0.642788 - 0.766044i) q^{10} +(-0.233354 + 0.134727i) q^{11} +(-1.52201 + 0.826731i) q^{12} +(-0.650596 - 1.78750i) q^{13} +(-0.0930587 - 0.527762i) q^{14} +(1.29743 + 1.14746i) 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} +(0.917993 - 0.137360i) q^{21} +(0.0921587 - 0.253204i) q^{22} +(-0.229565 - 0.0404785i) q^{23} +(0.634515 - 1.61164i) q^{24} +(0.939693 - 0.342020i) q^{25} +(1.64737 + 0.951108i) q^{26} +(4.68879 - 2.23948i) q^{27} +(0.410526 + 0.344472i) q^{28} +(4.10900 + 3.44786i) q^{29} +(-1.73147 - 0.0450352i) q^{30} +(6.10497 + 3.52471i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.434263 + 0.170973i) q^{33} +(-0.502781 - 0.0886538i) q^{34} +(0.183290 - 0.503585i) q^{35} +(2.76193 + 1.17122i) 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} +(-0.614930 + 0.695298i) q^{42} +(-1.13925 - 6.46098i) q^{43} +(0.0921587 + 0.253204i) q^{44} +(0.155954 - 2.99594i) q^{45} +(0.201876 - 0.116553i) q^{46} +(5.83426 - 6.95300i) q^{47} +(0.549877 + 1.64245i) q^{48} +(3.35640 + 5.81346i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.176144 - 0.866555i) q^{51} +(-1.87332 + 0.330316i) q^{52} +(-0.990668 + 5.61836i) q^{53} +(-2.15231 + 4.72943i) q^{54} +(0.206414 - 0.173202i) q^{55} -0.535904 q^{56} +(6.65671 - 3.56204i) q^{57} -5.36392 q^{58} +(-4.93759 + 4.14313i) q^{59} +(1.35533 - 1.07847i) q^{60} +(-1.85625 + 10.5273i) q^{61} +(-6.94232 + 1.22412i) q^{62} +(-1.17619 - 1.09604i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.951108 + 1.64737i) q^{65} +(-0.442564 + 0.148166i) q^{66} +(-3.68533 + 4.39200i) q^{67} +(0.442138 - 0.255268i) q^{68} +(0.192716 + 0.354790i) q^{69} +(0.183290 + 0.503585i) q^{70} +(-1.11428 - 6.31942i) q^{71} +(-2.86861 + 0.878124i) 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} +(-0.487566 - 3.25846i) q^{78} +(2.34946 - 6.45509i) q^{79} +(0.984808 + 0.173648i) q^{80} +(-8.09192 - 3.93965i) q^{81} +(-10.9164 + 3.97326i) q^{82} +(2.54105 + 1.46708i) q^{83} +(0.0241345 - 0.927898i) q^{84} +(-0.391094 - 0.328167i) q^{85} +(5.02575 + 4.21711i) q^{86} +(0.241565 - 9.28744i) q^{87} +(-0.233354 - 0.134727i) q^{88} +(-0.978707 + 0.356220i) q^{89} +(1.80629 + 2.39527i) q^{90} +(1.00392 + 0.177018i) q^{91} +(-0.0797270 + 0.219048i) q^{92} +(-1.80687 - 12.0755i) 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} +(-0.236614 - 0.772957i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{6} + 42 q^{8}+O(q^{10}) $ 84 * q - 6 * q^6 + 42 * q^8	$ 84 q - 6 q^{6} + 42 q^{8} + 24 q^{13} - 24 q^{14} + 12 q^{17} - 12 q^{19} + 36 q^{22} + 24 q^{27} - 12 q^{28} - 12 q^{29} + 36 q^{33} + 12 q^{34} + 6 q^{36} + 18 q^{38} + 12 q^{39} + 6 q^{41} + 24 q^{43} + 36 q^{44} + 12 q^{47} - 12 q^{48} - 54 q^{49} - 42 q^{50} + 96 q^{51} + 12 q^{52} - 60 q^{53} - 18 q^{54} - 96 q^{57} - 24 q^{58} - 18 q^{59} - 48 q^{61} - 12 q^{62} - 114 q^{63} - 42 q^{64} - 24 q^{66} + 6 q^{67} - 54 q^{68} - 48 q^{69} + 48 q^{71} + 84 q^{73} + 24 q^{74} - 12 q^{79} - 36 q^{81} - 6 q^{82} + 36 q^{83} + 18 q^{84} + 12 q^{86} + 6 q^{87} - 12 q^{89} - 24 q^{90} + 24 q^{91} - 6 q^{93} - 12 q^{95} - 42 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) $ 84 * q - 6 * q^6 + 42 * q^8 + 24 * q^13 - 24 * q^14 + 12 * q^17 - 12 * q^19 + 36 * q^22 + 24 * q^27 - 12 * q^28 - 12 * q^29 + 36 * q^33 + 12 * q^34 + 6 * q^36 + 18 * q^38 + 12 * q^39 + 6 * q^41 + 24 * q^43 + 36 * q^44 + 12 * q^47 - 12 * q^48 - 54 * q^49 - 42 * q^50 + 96 * q^51 + 12 * q^52 - 60 * q^53 - 18 * q^54 - 96 * q^57 - 24 * q^58 - 18 * q^59 - 48 * q^61 - 12 * q^62 - 114 * q^63 - 42 * q^64 - 24 * q^66 + 6 * q^67 - 54 * q^68 - 48 * q^69 + 48 * q^71 + 84 * q^73 + 24 * q^74 - 12 * q^79 - 36 * q^81 - 6 * q^82 + 36 * q^83 + 18 * q^84 + 12 * q^86 + 6 * q^87 - 12 * q^89 - 24 * q^90 + 24 * q^91 - 6 * q^93 - 12 * q^95 - 42 * q^97 + 36 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{18}\right)$	$1$

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
$3$	−1.07847	−	1.35533i	−0.622652	−	0.782499i
$3$	−1.07847	−	1.35533i	−0.622652	−	0.782499i
$4$	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
$6$	1.69734	+	0.345017i	0.692936	+	0.140853i
$7$	−0.267952	+	0.464106i	−0.101276	+	0.175416i	−0.912211	−	0.409721i	$-0.865626\pi$
$7$	−0.267952	+	0.464106i	−0.101276	+	0.175416i	0.810934	+	0.585137i	$0.198959\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−0.673825	+	2.92335i	−0.224608	+	0.974449i
$10$	0.642788	−	0.766044i	0.203267	−	0.242245i
$11$	−0.233354	+	0.134727i	−0.0703589	+	0.0406217i	−0.534767	−	0.845000i	$-0.679601\pi$
$11$	−0.233354	+	0.134727i	−0.0703589	+	0.0406217i	0.464408	+	0.885621i	$0.346267\pi$
$12$	−1.52201	+	0.826731i	−0.439367	+	0.238657i
$13$	−0.650596	−	1.78750i	−0.180443	−	0.495763i	0.816187	−	0.577787i	$-0.196084\pi$
$13$	−0.650596	−	1.78750i	−0.180443	−	0.495763i	−0.996630	+	0.0820244i	$0.973861\pi$
$14$	−0.0930587	−	0.527762i	−0.0248710	−	0.141050i
$15$	1.29743	+	1.14746i	0.334995	+	0.296274i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.328167	+	0.391094i	0.0795921	+	0.0948542i	0.804371	−	0.594127i	$-0.202503\pi$
$17$	0.328167	+	0.391094i	0.0795921	+	0.0948542i	−0.724779	+	0.688982i	$0.758058\pi$
$18$	−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
$21$	0.917993	−	0.137360i	0.200322	−	0.0299744i
$22$	0.0921587	−	0.253204i	0.0196483	−	0.0539832i
$23$	−0.229565	−	0.0404785i	−0.0478676	−	0.00844035i	0.149663	−	0.988737i	$-0.452181\pi$
$23$	−0.229565	−	0.0404785i	−0.0478676	−	0.00844035i	−0.197531	+	0.980297i	$0.563292\pi$
$24$	0.634515	−	1.61164i	0.129520	−	0.328975i
$25$	0.939693	−	0.342020i	0.187939	−	0.0684040i
$26$	1.64737	+	0.951108i	0.323075	+	0.186528i
$27$	4.68879	−	2.23948i	0.902358	−	0.430987i
$28$	0.410526	+	0.344472i	0.0775821	+	0.0650991i
$29$	4.10900	+	3.44786i	0.763023	+	0.640252i	0.938912	−	0.344158i	$-0.111836\pi$
$29$	4.10900	+	3.44786i	0.763023	+	0.640252i	−0.175889	+	0.984410i	$0.556280\pi$
$30$	−1.73147	−	0.0450352i	−0.316121	−	0.00822227i
$31$	6.10497	+	3.52471i	1.09649	+	0.633056i	0.935296	−	0.353867i	$-0.115134\pi$
$31$	6.10497	+	3.52471i	1.09649	+	0.633056i	0.161190	+	0.986923i	$0.448467\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	0.434263	+	0.170973i	0.0755955	+	0.0297625i
$34$	−0.502781	−	0.0886538i	−0.0862262	−	0.0152040i
$35$	0.183290	−	0.503585i	0.0309816	−	0.0851213i
$36$	2.76193	+	1.17122i	0.460321	+	0.195204i
$37$			9.16197i			1.50622i	0.657896	+	0.753109i	$0.271447\pi$
$37$			9.16197i			1.50622i	−0.657896	+	0.753109i	$0.728553\pi$
$38$	−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	$-0.0271508\pi$
$41$	10.9164	+	3.97326i	1.70486	+	0.620519i	0.708498	+	0.705713i	$0.249373\pi$
$42$	−0.614930	+	0.695298i	−0.0948857	+	0.107287i
$43$	−1.13925	−	6.46098i	−0.173733	−	0.985291i	−0.939596	−	0.342286i	$-0.888799\pi$
$43$	−1.13925	−	6.46098i	−0.173733	−	0.985291i	0.765862	−	0.643005i	$-0.222312\pi$
$44$	0.0921587	+	0.253204i	0.0138934	+	0.0381719i
$45$	0.155954	−	2.99594i	0.0232482	−	0.446609i
$46$	0.201876	−	0.116553i	0.0297650	−	0.0171848i
$47$	5.83426	−	6.95300i	0.851014	−	1.01420i	−0.148665	−	0.988888i	$-0.547498\pi$
$47$	5.83426	−	6.95300i	0.851014	−	1.01420i	0.999680	−	0.0253119i	$-0.00805789\pi$
$48$	0.549877	+	1.64245i	0.0793679	+	0.237067i
$49$	3.35640	+	5.81346i	0.479486	+	0.830495i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	0.176144	−	0.866555i	0.0246651	−	0.121342i
$52$	−1.87332	+	0.330316i	−0.259782	+	0.0458066i
$53$	−0.990668	+	5.61836i	−0.136079	+	0.771741i	0.838024	+	0.545634i	$0.183711\pi$
$53$	−0.990668	+	5.61836i	−0.136079	+	0.771741i	−0.974102	+	0.226107i	$0.927400\pi$
$54$	−2.15231	+	4.72943i	−0.292893	+	0.643594i
$55$	0.206414	−	0.173202i	0.0278328	−	0.0233545i
$56$	−0.535904			−0.0716131
$57$	6.65671	−	3.56204i	0.881703	−	0.471804i
$58$	−5.36392			−0.704317
$59$	−4.93759	+	4.14313i	−0.642820	+	0.539390i	−0.904883	−	0.425661i	$-0.860042\pi$
$59$	−4.93759	+	4.14313i	−0.642820	+	0.539390i	0.262063	+	0.965051i	$0.415597\pi$
$60$	1.35533	−	1.07847i	0.174972	−	0.139229i
$61$	−1.85625	+	10.5273i	−0.237669	+	1.34789i	0.599252	+	0.800561i	$0.295465\pi$
$61$	−1.85625	+	10.5273i	−0.237669	+	1.34789i	−0.836920	+	0.547325i	$0.815646\pi$
$62$	−6.94232	+	1.22412i	−0.881675	+	0.155463i
$63$	−1.17619	−	1.09604i	−0.148186	−	0.138088i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.951108	+	1.64737i	0.117970	+	0.204331i
$66$	−0.442564	+	0.148166i	−0.0544759	+	0.0182380i
$67$	−3.68533	+	4.39200i	−0.450235	+	0.536569i	−0.942646	−	0.333794i	$-0.891671\pi$
$67$	−3.68533	+	4.39200i	−0.450235	+	0.536569i	0.492412	+	0.870363i	$0.336116\pi$
$68$	0.442138	−	0.255268i	0.0536171	−	0.0309558i
$69$	0.192716	+	0.354790i	0.0232003	+	0.0427117i
$70$	0.183290	+	0.503585i	0.0219073	+	0.0601899i
$71$	−1.11428	−	6.31942i	−0.132241	−	0.749978i	−0.976741	−	0.214422i	$-0.931213\pi$
$71$	−1.11428	−	6.31942i	−0.132241	−	0.749978i	0.844500	−	0.535556i	$-0.179898\pi$
$72$	−2.86861	+	0.878124i	−0.338068	+	0.103488i
$73$	−5.29912	−	1.92872i	−0.620215	−	0.225740i	0.0127519	−	0.999919i	$-0.495941\pi$
$73$	−5.29912	−	1.92872i	−0.620215	−	0.225740i	−0.632967	+	0.774179i	$0.718163\pi$
$74$	−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
$78$	−0.487566	−	3.25846i	−0.0552060	−	0.368948i
$79$	2.34946	−	6.45509i	0.264335	−	0.726254i	−0.734528	−	0.678578i	$-0.762596\pi$
$79$	2.34946	−	6.45509i	0.264335	−	0.726254i	0.998863	−	0.0476758i	$-0.0151814\pi$
$80$	0.984808	+	0.173648i	0.110105	+	0.0194145i
$81$	−8.09192	−	3.93965i	−0.899102	−	0.437739i
$82$	−10.9164	+	3.97326i	−1.20552	+	0.438773i
$83$	2.54105	+	1.46708i	0.278917	+	0.161033i	0.632933	−	0.774207i	$-0.281851\pi$
$83$	2.54105	+	1.46708i	0.278917	+	0.161033i	−0.354016	+	0.935239i	$0.615184\pi$
$84$	0.0241345	−	0.927898i	0.00263329	−	0.101242i
$85$	−0.391094	−	0.328167i	−0.0424201	−	0.0355947i
$86$	5.02575	+	4.21711i	0.541941	+	0.454742i
$87$	0.241565	−	9.28744i	0.0258985	−	0.995719i
$88$	−0.233354	−	0.134727i	−0.0248756	−	0.0143619i
$89$	−0.978707	+	0.356220i	−0.103743	+	0.0377593i	−0.393370	−	0.919380i	$-0.628691\pi$
$89$	−0.978707	+	0.356220i	−0.103743	+	0.0377593i	0.289627	+	0.957140i	$0.406469\pi$
$90$	1.80629	+	2.39527i	0.190399	+	0.252484i
$91$	1.00392	+	0.177018i	0.105239	+	0.0185565i
$92$	−0.0797270	+	0.219048i	−0.00831212	+	0.0228374i
$93$	−1.80687	−	12.0755i	−0.187364	−	1.25217i
$94$			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	0.831467	−	0.555574i	$-0.187502\pi$
$97$	1.37835	+	1.64266i	0.139951	+	0.166787i	−0.691516	+	0.722361i	$0.743057\pi$
$98$	−6.30798	−	2.29592i	−0.637202	−	0.231922i
$99$	−0.236614	−	0.772957i	−0.0237806	−	0.0776851i
$100$	−0.173648	−	0.984808i	−0.0173648	−	0.0984808i
$101$	−0.615693	−	1.69160i	−0.0612637	−	0.168321i	0.905284	−	0.424806i	$-0.139658\pi$
$101$	−0.615693	−	1.69160i	−0.0612637	−	0.168321i	−0.966548	+	0.256485i	$0.917435\pi$
$102$	0.422077	+	0.777043i	0.0417918	+	0.0769387i
$103$	0.441213	−	0.254735i	0.0434740	−	0.0250997i	−0.478105	−	0.878302i	$-0.658676\pi$
$103$	0.441213	−	0.254735i	0.0434740	−	0.0250997i	0.521579	+	0.853203i	$0.325343\pi$
$104$	1.22272	−	1.45718i	0.119898	−	0.142888i
$105$	−0.880194	+	0.294681i	−0.0858981	+	0.0287579i
$106$	−2.85251	−	4.94070i	−0.277061	−	0.479883i
$107$	−3.00447	+	5.20390i	−0.290453	+	0.503080i	−0.973917	−	0.226905i	$-0.927139\pi$
$107$	−3.00447	+	5.20390i	−0.290453	+	0.503080i	0.683464	+	0.729985i	$0.260473\pi$
$108$	−1.39125	−	5.00644i	−0.133873	−	0.481745i
$109$	−8.15550	+	1.43803i	−0.781155	+	0.137739i	−0.549985	−	0.835175i	$-0.685366\pi$
$109$	−8.15550	+	1.43803i	−0.781155	+	0.137739i	−0.231170	+	0.972913i	$0.574255\pi$
$110$	−0.0467902	+	0.265360i	−0.00446127	+	0.0253011i
$111$	12.4175	−	9.88086i	1.17861	−	0.937850i
$112$	0.410526	−	0.344472i	0.0387911	−	0.0325496i
$113$	−3.25482			−0.306187			−0.153094	−	0.988212i	$-0.548924\pi$
$113$	−3.25482			−0.306187			−0.153094	+	0.988212i	$0.548924\pi$
$114$	−2.80970	+	7.00754i	−0.263153	+	0.656316i
$115$	0.233106			0.0217373
$116$	4.10900	−	3.44786i	0.381511	−	0.320126i
$117$	5.66387	−	0.697458i	0.523625	−	0.0644800i
$118$	1.11926	−	6.34765i	0.103036	−	0.584348i
$119$	−0.269442	+	0.0475099i	−0.0246997	+	0.00435522i
$120$	−0.345017	+	1.69734i	−0.0314956	+	0.154945i
$121$	−5.46370	+	9.46340i	−0.496700	+	0.860309i
$122$	−5.34486	−	9.25757i	−0.483901	−	0.838141i
$123$	−6.38794	−	19.0804i	−0.575981	−	1.72042i
$124$	4.53128	−	5.40016i	0.406921	−	0.484949i
$125$	−0.866025	+	0.500000i	−0.0774597	+	0.0447214i
$126$	1.60554	+	0.0835762i	0.143033	+	0.00744556i
$127$	1.72312	+	4.73423i	0.152902	+	0.420095i	0.992367	−	0.123319i	$-0.0393537\pi$
$127$	1.72312	+	4.73423i	0.152902	+	0.420095i	−0.839465	+	0.543414i	$0.817132\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−7.52811	+	8.51200i	−0.662813	+	0.749440i
$130$	−1.78750	−	0.650596i	−0.156774	−	0.0570611i
$131$	−1.36599	−	1.62793i	−0.119347	−	0.142233i	0.703063	−	0.711128i	$-0.251815\pi$
$131$	−1.36599	−	1.62793i	−0.119347	−	0.142233i	−0.822410	+	0.568895i	$0.807371\pi$
$132$	0.243784	−	0.397977i	0.0212187	−	0.0346394i
$133$	−1.78001	−	1.51269i	−0.154346	−	0.131167i
$134$		−	5.73335i		−	0.495286i
$135$	−4.22868	+	3.01965i	−0.363946	+	0.259890i
$136$	−0.174614	+	0.479748i	−0.0149730	+	0.0411380i
$137$	3.53497	+	0.623310i	0.302012	+	0.0532529i	0.322601	−	0.946535i	$-0.395443\pi$
$137$	3.53497	+	0.623310i	0.302012	+	0.0532529i	−0.0205884	+	0.999788i	$0.506554\pi$
$138$	−0.375684	−	0.147909i	−0.0319803	−	0.0125909i
$139$	13.0375	−	4.74526i	1.10582	−	0.402487i	0.276365	−	0.961053i	$-0.410870\pi$
$139$	13.0375	−	4.74526i	1.10582	−	0.402487i	0.829460	+	0.558566i	$0.188648\pi$
$140$	−0.464106	−	0.267952i	−0.0392241	−	0.0226461i
$141$	−15.7156	−	0.408762i	−1.32350	−	0.0344240i
$142$	4.91564	+	4.12471i	0.412511	+	0.346138i
$143$	0.392643	+	0.329467i	0.0328345	+	0.0275514i
$144$	1.63303	−	2.51659i	0.136086	−	0.209716i
$145$	−4.64529	−	2.68196i	−0.385771	−	0.222725i
$146$	5.29912	−	1.92872i	0.438558	−	0.159622i
$147$	4.25938	−	10.8186i	0.351308	−	0.892307i
$148$	9.02277	+	1.59096i	0.741667	+	0.130776i
$149$	6.14443	−	16.8817i	0.503371	−	1.38300i	−0.384592	−	0.923087i	$-0.625658\pi$
$149$	6.14443	−	16.8817i	0.503371	−	1.38300i	0.887963	−	0.459915i	$-0.152120\pi$
$150$	1.71298	−	0.256315i	0.139864	−	0.0209280i
$151$			3.70446i			0.301465i	0.988575	+	0.150732i	$0.0481632\pi$
$151$			3.70446i			0.301465i	−0.988575	+	0.150732i	$0.951837\pi$
$152$	−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
$156$	2.46799	+	2.18272i	0.197598	+	0.174758i
$157$	−0.110660	−	0.627584i	−0.00883162	−	0.0500866i	0.980073	−	0.198635i	$-0.0636509\pi$
$157$	−0.110660	−	0.627584i	−0.00883162	−	0.0500866i	−0.988905	+	0.148549i	$0.952540\pi$
$158$	2.34946	+	6.45509i	0.186913	+	0.513539i
$159$	8.68311	−	4.71652i	0.688616	−	0.374045i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	0.0802986	−	0.0956962i	0.00632842	−	0.00754192i
$162$	8.73113	−	2.18344i	0.685982	−	0.171547i
$163$	−5.80819	−	10.0601i	−0.454932	−	0.787966i	0.543752	−	0.839246i	$-0.317003\pi$
$163$	−5.80819	−	10.0601i	−0.454932	−	0.787966i	−0.998684	+	0.0512800i	$0.983670\pi$
$164$	5.80852	−	10.0607i	0.453569	−	0.785605i
$165$	−0.457355	−	0.0929661i	−0.0356050	−	0.00723740i
$166$	−2.88958	+	0.509510i	−0.224275	+	0.0395457i
$167$	−1.34613	+	7.63430i	−0.104167	+	0.590760i	0.887383	+	0.461033i	$0.152521\pi$
$167$	−1.34613	+	7.63430i	−0.104167	+	0.590760i	−0.991550	+	0.129727i	$0.958590\pi$
$168$	0.577954	+	0.726325i	0.0445901	+	0.0560372i
$169$	7.18670	−	6.03036i	0.552823	−	0.463874i
$170$	0.510537			0.0391564
$171$	−12.0068	−	5.18049i	−0.918181	−	0.396162i
$172$	−6.56066			−0.500245
$173$	−15.1853	+	12.7419i	−1.15451	+	0.968752i	−0.999815	−	0.0192097i	$-0.993885\pi$
$173$	−15.1853	+	12.7419i	−1.15451	+	0.968752i	−0.154698	+	0.987962i	$0.549441\pi$
$174$	5.78480	+	7.26987i	0.438545	+	0.551127i
$175$	−0.0930587	+	0.527762i	−0.00703458	+	0.0398951i
$176$	0.265360	−	0.0467902i	0.0200023	−	0.00352694i
$177$	10.9403	+	2.22383i	0.822325	+	0.167153i
$178$	0.520759	−	0.901982i	0.0390326	−	0.0676064i
$179$	−2.28067	−	3.95024i	−0.170466	−	0.295255i	0.768117	−	0.640309i	$-0.221194\pi$
$179$	−2.28067	−	3.95024i	−0.170466	−	0.295255i	−0.938583	+	0.345054i	$0.887861\pi$
$180$	−2.92335	−	0.673825i	−0.217893	−	0.0502239i
$181$	−14.2151	+	16.9409i	−1.05660	+	1.25921i	−0.0919262	+	0.995766i	$0.529302\pi$
$181$	−14.2151	+	16.9409i	−1.05660	+	1.25921i	−0.964675	+	0.263443i	$0.915142\pi$
$182$	−0.882830	+	0.509702i	−0.0654397	+	0.0377816i
$183$	16.2699	−	8.83753i	1.20270	−	0.653289i
$184$	−0.0797270	−	0.219048i	−0.00587756	−	0.0161485i
$185$	−1.59096	−	9.02277i	−0.116970	−	0.663368i
$186$	9.14613	+	8.08894i	0.670627	+	0.593110i
$187$	−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	$0.948739\pi$
$192$	1.71298	−	0.256315i	0.123624	−	0.0184979i
$193$	6.27088	−	17.2291i	0.451388	−	1.24018i	−0.480360	−	0.877071i	$-0.659494\pi$
$193$	6.27088	−	17.2291i	0.451388	−	1.24018i	0.931748	−	0.363106i	$-0.118284\pi$
$194$	−2.11176	−	0.372360i	−0.151615	−	0.0267339i
$195$	1.20699	−	3.06569i	0.0864340	−	0.219539i
$196$	6.30798	−	2.29592i	0.450570	−	0.163994i
$197$	17.3492	+	10.0166i	1.23608	+	0.713650i	0.968290	−	0.249828i	$-0.0803741\pi$
$197$	17.3492	+	10.0166i	1.23608	+	0.713650i	0.267788	+	0.963478i	$0.413707\pi$
$198$	0.678104	+	0.440027i	0.0481908	+	0.0312713i
$199$	2.55436	+	2.14336i	0.181073	+	0.151939i	0.728819	−	0.684706i	$-0.240069\pi$
$199$	2.55436	+	2.14336i	0.181073	+	0.151939i	−0.547746	+	0.836645i	$0.684514\pi$
$200$	0.766044	+	0.642788i	0.0541675	+	0.0454519i
$201$	9.92710	+	0.258203i	0.700204	+	0.0182122i
$202$	1.55899	+	0.900083i	0.109690	+	0.0633296i
$203$	−2.70119	+	0.983152i	−0.189586	+	0.0690038i
$204$	−0.822803	−	0.323943i	−0.0576077	−	0.0226806i
$205$	−11.4406	−	2.01728i	−0.799043	−	0.140893i
$206$	−0.174249	+	0.478744i	−0.0121405	+	0.0333557i
$207$	0.273019	−	0.643822i	0.0189761	−	0.0447488i
$208$			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	0.491363	−	0.870955i	$-0.336499\pi$
$211$	−6.56110	−	7.81921i	−0.451685	−	0.538297i	−0.943047	+	0.332658i	$0.892054\pi$
$212$	5.36097	+	1.95123i	0.368193	+	0.134011i
$213$	−7.36317	+	8.32550i	−0.504516	+	0.570454i
$214$	−1.04344	−	5.91766i	−0.0713283	−	0.404523i
$215$	2.24388	+	6.16500i	0.153031	+	0.420449i
$216$	4.28384	+	2.94087i	0.291478	+	0.200101i
$217$	−3.27168	+	1.88890i	−0.222096	+	0.128227i
$218$	5.32312	−	6.34385i	0.360527	−	0.429660i
$219$	3.10087	+	9.26210i	0.209537	+	0.625875i
$220$	−0.134727	−	0.233354i	−0.00908329	−	0.0157327i
$221$	0.485576	−	0.841042i	0.0326634	−	0.0565746i
$222$	−3.16103	+	15.5510i	−0.212155	+	1.04371i
$223$	1.46787	−	0.258824i	0.0982955	−	0.0173322i	−0.124284	−	0.992247i	$-0.539663\pi$
$223$	1.46787	−	0.258824i	0.0982955	−	0.0173322i	0.222580	+	0.974915i	$0.428552\pi$
$224$	−0.0930587	+	0.527762i	−0.00621774	+	0.0352626i
$225$	0.366656	+	2.97751i	0.0244437	+	0.198501i
$226$	2.49334	−	2.09216i	0.165854	−	0.139168i
$227$	−1.74710			−0.115959			−0.0579795	−	0.998318i	$-0.518466\pi$
$227$	−1.74710			−0.115959			−0.0579795	+	0.998318i	$0.518466\pi$
$228$	−2.35200	−	7.17413i	−0.155765	−	0.475118i
$229$	−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
$231$	−0.195711	+	0.155732i	−0.0128768	+	0.0102464i
$232$	−0.931435	+	5.28243i	−0.0611517	+	0.346809i
$233$	−18.1764	+	3.20499i	−1.19077	+	0.209966i	−0.733707	−	0.679467i	$-0.762211\pi$
$233$	−18.1764	+	3.20499i	−1.19077	+	0.209966i	−0.457067	+	0.889432i	$0.651100\pi$
$234$	−3.89046	+	4.17495i	−0.254327	+	0.272925i
$235$	−4.53825	+	7.86048i	−0.296043	+	0.512761i
$236$	3.22279	+	5.58203i	0.209785	+	0.363359i
$237$	−11.2826	+	3.77730i	−0.732882	+	0.245362i
$238$	0.175866	−	0.209589i	0.0113997	−	0.0135856i
$239$	1.19701	−	0.691097i	0.0774284	−	0.0447033i	−0.460786	−	0.887511i	$-0.652432\pi$
$239$	1.19701	−	0.691097i	0.0774284	−	0.0447033i	0.538214	+	0.842808i	$0.319099\pi$
$240$	−0.826731	−	1.52201i	−0.0533653	−	0.0982454i
$241$	4.30699	+	11.8333i	0.277437	+	0.762253i	0.997651	+	0.0685006i	$0.0218215\pi$
$241$	4.30699	+	11.8333i	0.277437	+	0.762253i	−0.720214	+	0.693752i	$0.755956\pi$
$242$	−1.89752	−	10.7614i	−0.121977	−	0.691768i
$243$	3.38735	+	15.2160i	0.217298	+	0.976105i
$244$	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
$249$	−0.752067	−	5.02615i	−0.0476603	−	0.318519i
$250$	0.342020	−	0.939693i	0.0216313	−	0.0594314i
$251$	−26.7932	−	4.72436i	−1.69117	−	0.298199i	−0.756574	−	0.653908i	$-0.773128\pi$
$251$	−26.7932	−	4.72436i	−1.69117	−	0.298199i	−0.934597	+	0.355709i	$0.884240\pi$
$252$	−1.28363	+	0.967996i	−0.0808614	+	0.0609780i
$253$	0.0590234	−	0.0214828i	0.00371077	−	0.00135061i
$254$	−4.36309	−	2.51903i	−0.273765	−	0.158058i
$255$	−0.0229921	+	0.883977i	−0.00143982	+	0.0553568i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	23.8566	+	20.0180i	1.48813	+	1.24869i	0.896934	+	0.442165i	$0.145790\pi$
$257$	23.8566	+	20.0180i	1.48813	+	1.24869i	0.591199	+	0.806526i	$0.298655\pi$
$258$	0.295460	−	11.3595i	0.0183946	−	0.707214i
$259$	−4.25212	−	2.45497i	−0.264214	−	0.152544i
$260$	1.78750	−	0.650596i	0.110856	−	0.0403483i
$261$	−12.8480	+	9.68879i	−0.795274	+	0.599721i
$262$	2.09282	+	0.369021i	0.129295	+	0.0227982i
$263$	−8.41522	+	23.1206i	−0.518905	+	1.42568i	0.352824	+	0.935690i	$0.385222\pi$
$263$	−8.41522	+	23.1206i	−0.518905	+	1.42568i	−0.871728	+	0.489989i	$0.837001\pi$
$264$	0.0690650	+	0.461569i	0.00425066	+	0.0284076i
$265$		−	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	$-0.0893914\pi$
$269$	24.9087	+	9.06602i	1.51871	+	0.552765i	0.557883	+	0.829919i	$0.311614\pi$
$270$	1.29836	−	5.03133i	0.0790155	−	0.306197i
$271$	1.67423	+	9.49505i	0.101702	+	0.576783i	0.992486	+	0.122356i	$0.0390449\pi$
$271$	1.67423	+	9.49505i	0.101702	+	0.576783i	−0.890784	+	0.454427i	$0.849844\pi$
$272$	−0.174614	−	0.479748i	−0.0105875	−	0.0290890i
$273$	−0.842773	−	1.55154i	−0.0510070	−	0.0939037i
$274$	−3.10860	+	1.79475i	−0.187797	+	0.108425i
$275$	−0.173202	+	0.206414i	−0.0104445	+	0.0124472i
$276$	0.382865	−	0.128180i	0.0230458	−	0.00771551i
$277$	−4.30168	−	7.45073i	−0.258463	−	0.447671i	0.707367	−	0.706846i	$-0.249883\pi$
$277$	−4.30168	−	7.45073i	−0.258463	−	0.447671i	−0.965830	+	0.259175i	$0.916549\pi$
$278$	−6.93710	+	12.0154i	−0.416060	+	0.720636i
$279$	−14.4176	+	15.4719i	−0.863161	+	0.926280i
$280$	0.527762	−	0.0930587i	0.0315398	−	0.00556132i
$281$	−3.97426	+	22.5391i	−0.237084	+	1.34457i	0.601095	+	0.799177i	$0.294731\pi$
$281$	−3.97426	+	22.5391i	−0.237084	+	1.34457i	−0.838180	+	0.545394i	$0.816380\pi$
$282$	12.3016	−	9.78869i	0.732551	−	0.582908i
$283$	17.2555	−	14.4791i	1.02573	−	0.860692i	0.0353958	−	0.999373i	$-0.488731\pi$
$283$	17.2555	−	14.4791i	1.02573	−	0.860692i	0.990337	+	0.138681i	$0.0442864\pi$
$284$	−6.41691			−0.380774
$285$	−5.93704	+	4.66385i	−0.351680	+	0.276263i
$286$	−0.512560			−0.0303083
$287$	−4.76910	+	4.00175i	−0.281511	+	0.236216i
$288$	0.366656	+	2.97751i	0.0216054	+	0.175451i
$289$	2.90676	−	16.4850i	0.170986	−	0.969708i
$290$	5.28243	−	0.931435i	0.310195	−	0.0546958i
$291$	0.739832	−	3.63967i	0.0433697	−	0.213361i
$292$	−2.81960	+	4.88369i	−0.165005	+	0.285797i
$293$	14.1844	+	24.5681i	0.828663	+	1.43529i	0.899088	+	0.437769i	$0.144231\pi$
$293$	14.1844	+	24.5681i	0.828663	+	1.43529i	−0.0704250	+	0.997517i	$0.522436\pi$
$294$	3.69122	+	11.0254i	0.215276	+	0.643017i
$295$	4.14313	−	4.93759i	0.241223	−	0.287478i
$296$	−7.93449	+	4.58098i	−0.461183	+	0.266264i
$297$	−0.792430	+	1.15430i	−0.0459814	+	0.0669791i
$298$	6.14443	+	16.8817i	0.355937	+	0.977930i
$299$	0.0769988	+	0.436682i	0.00445296	+	0.0252540i
$300$	−1.14746	+	1.29743i	−0.0662488	+	0.0749072i
$301$	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
$306$	0.597952	−	1.41007i	0.0341826	−	0.0806081i
$307$	9.05566	−	24.8802i	0.516834	−	1.41999i	−0.357156	−	0.934045i	$-0.616254\pi$
$307$	9.05566	−	24.8802i	0.516834	−	1.41999i	0.873990	−	0.485944i	$-0.161524\pi$
$308$	−0.142208	−	0.0250750i	−0.00810303	−	0.00142878i
$309$	−0.821082	−	0.323266i	−0.0467097	−	0.0183900i
$310$	6.62428	−	2.41104i	0.376234	−	0.136938i
$311$	4.31145	+	2.48922i	0.244480	+	0.141150i	0.617234	−	0.786780i	$-0.288253\pi$
$311$	4.31145	+	2.48922i	0.244480	+	0.141150i	−0.372754	+	0.927930i	$0.621587\pi$
$312$	−3.29362	−	0.0856667i	−0.186465	−	0.00484992i
$313$	−10.2430	−	8.59492i	−0.578970	−	0.485814i	0.305639	−	0.952148i	$-0.401130\pi$
$313$	−10.2430	−	8.59492i	−0.578970	−	0.485814i	−0.884609	+	0.466334i	$0.845575\pi$
$314$	0.488173	+	0.409626i	0.0275492	+	0.0231165i
$315$	1.34865	+	0.875148i	0.0759877	+	0.0493090i
$316$	−5.94904	−	3.43468i	−0.334660	−	0.193216i
$317$	−12.1126	+	4.40863i	−0.680313	+	0.247614i	−0.658982	−	0.752159i	$-0.729013\pi$
$317$	−12.1126	+	4.40863i	−0.680313	+	0.247614i	−0.0213310	+	0.999772i	$0.506790\pi$
$318$	−3.61993	+	9.19446i	−0.202995	+	0.515600i
$319$	−1.42337	−	0.250979i	−0.0796935	−	0.0140521i
$320$	0.342020	−	0.939693i	0.0191195	−	0.0525304i
$321$	10.2932	−	1.54018i	0.574511	−	0.0859645i
$322$			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
$327$	10.7444	+	9.50250i	0.594168	+	0.525489i
$328$	2.01728	+	11.4406i	0.111386	+	0.631699i
$329$	1.66363	+	4.57079i	0.0917189	+	0.251996i
$330$	0.410112	−	0.222766i	0.0225759	−	0.0122629i
$331$	24.0531	−	13.8871i	1.32208	−	0.763303i	0.338019	−	0.941139i	$-0.390243\pi$
$331$	24.0531	−	13.8871i	1.32208	−	0.763303i	0.984060	+	0.177836i	$0.0569097\pi$
$332$	1.88604	−	2.24769i	0.103510	−	0.123358i
$333$	−26.7836	−	6.17356i	−1.46773	−	0.338309i
$334$	−3.87604	−	6.71349i	−0.212087	−	0.367346i
$335$	2.86668	−	4.96523i	0.156623	−	0.271280i
$336$	−0.909611	−	0.184896i	−0.0496233	−	0.0100869i
$337$	0.774603	−	0.136583i	0.0421953	−	0.00744017i	−0.152511	−	0.988302i	$-0.548736\pi$
$337$	0.774603	−	0.136583i	0.0421953	−	0.00744017i	0.194706	+	0.980862i	$0.437625\pi$
$338$	−1.62909	+	9.23905i	−0.0886110	+	0.502538i
$339$	3.51021	+	4.41134i	0.190648	+	0.239591i
$340$	−0.391094	+	0.328167i	−0.0212100	+	0.0177973i
$341$	−1.89949			−0.102863
$342$	12.5277	−	3.74932i	0.677419	−	0.202740i
$343$	−7.34874			−0.396795
$344$	5.02575	−	4.21711i	0.270970	−	0.227371i
$345$	−0.251397	−	0.315935i	−0.0135348	−	0.0170094i
$346$	3.44222	−	19.5218i	0.185055	−	1.04950i
$347$	−17.8338	+	3.14458i	−0.957368	+	0.168810i	−0.630439	−	0.776239i	$-0.717125\pi$
$347$	−17.8338	+	3.14458i	−0.957368	+	0.168810i	−0.326929	+	0.945049i	$0.606014\pi$
$348$	−9.10440	−	1.85064i	−0.488047	−	0.0992049i
$349$	4.98489	−	8.63408i	0.266835	−	0.462172i	−0.701208	−	0.712957i	$-0.747355\pi$
$349$	4.98489	−	8.63408i	0.266835	−	0.462172i	0.968043	+	0.250785i	$0.0806888\pi$
$350$	−0.267952	−	0.464106i	−0.0143226	−	0.0248075i
$351$	−7.05357	−	6.92421i	−0.376492	−	0.369587i
$352$	−0.173202	+	0.206414i	−0.00923168	+	0.0110019i
$353$	12.3034	−	7.10336i	0.654843	−	0.378074i	−0.135466	−	0.990782i	$-0.543253\pi$
$353$	12.3034	−	7.10336i	0.654843	−	0.378074i	0.790309	+	0.612708i	$0.209920\pi$
$354$	−9.81023	+	5.32875i	−0.521408	+	0.283220i
$355$	2.19471	+	6.02992i	0.116483	+	0.320035i
$356$	0.180858	+	1.02570i	0.00958545	+	0.0543618i
$357$	0.354975	+	0.313944i	0.0187873	+	0.0166157i
$358$	4.28627	+	1.56007i	0.226536	+	0.0824524i
$359$	−14.7475	−	17.5753i	−0.778341	−	0.927591i	0.220516	−	0.975383i	$-0.429226\pi$
$359$	−14.7475	−	17.5753i	−0.778341	−	0.927591i	−0.998857	+	0.0477926i	$0.984781\pi$
$360$	2.67254	−	1.36291i	0.140855	−	0.0718318i
$361$	−17.7714	−	6.72136i	−0.935338	−	0.353756i
$362$		−	22.1148i		−	1.16233i
$363$	18.7184	−	2.80085i	0.982462	−	0.147007i
$364$	0.348657	−	0.957927i	0.0182746	−	0.0502090i
$365$	5.55353	+	0.979238i	0.290685	+	0.0512556i
$366$	−6.78279	+	17.2280i	−0.354542	+	0.900523i
$367$	24.3559	−	8.86481i	1.27137	−	0.462739i	0.383798	−	0.923417i	$-0.374616\pi$
$367$	24.3559	−	8.86481i	1.27137	−	0.462739i	0.887567	+	0.460678i	$0.152394\pi$
$368$	0.201876	+	0.116553i	0.0105235	+	0.00607575i
$369$	−18.9710	+	29.2353i	−0.987591	+	1.52193i
$370$	7.01847	+	5.88920i	0.364873	+	0.306165i
$371$	−2.34206	−	1.96522i	−0.121594	−	0.102029i
$372$	−12.2058	−	0.317472i	−0.632842	−	0.0164601i
$373$	10.4729	+	6.04653i	0.542266	+	0.313078i	0.745997	−	0.665949i	$-0.231973\pi$
$373$	10.4729	+	6.04653i	0.542266	+	0.313078i	−0.203731	+	0.979027i	$0.565307\pi$
$374$	0.129270	−	0.0470504i	0.00668439	−	0.00243292i
$375$	1.61164	+	0.634515i	0.0832248	+	0.0327662i
$376$	8.93861	+	1.57612i	0.460973	+	0.0812821i
$377$	3.48975	−	9.58800i	0.179731	−	0.493807i
$378$	−1.61824	−	2.26616i	−0.0832334	−	0.116559i
$379$			9.41476i			0.483604i	0.970326	+	0.241802i	$0.0777384\pi$
$379$			9.41476i			0.483604i	−0.970326	+	0.241802i	$0.922262\pi$
$380$	−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	$-0.209536\pi$
$383$	19.6447	+	7.15008i	1.00380	+	0.365352i	0.212749	+	0.977107i	$0.431758\pi$
$384$	−1.14746	+	1.29743i	−0.0585562	+	0.0662093i
$385$	0.0250750	+	0.142208i	0.00127794	+	0.00724757i
$386$	6.27088	+	17.2291i	0.319179	+	0.876938i
$387$	19.6554	+	1.02316i	0.999138	+	0.0520101i
$388$	1.85705	−	1.07217i	0.0942774	−	0.0544311i
$389$	16.4586	−	19.6146i	0.834486	−	0.994501i	−0.165480	−	0.986213i	$-0.552917\pi$
$389$	16.4586	−	19.6146i	0.834486	−	0.994501i	0.999966	−	0.00828818i	$-0.00263824\pi$
$390$	1.04598	+	3.12429i	0.0529655	+	0.158205i
$391$	−0.0595047	−	0.103065i	−0.00300928	−	0.00521223i
$392$	−3.35640	+	5.81346i	−0.169524	+	0.293624i
$393$	−0.733198	+	3.60703i	−0.0369850	+	0.181951i
$394$	−19.7288	+	3.47871i	−0.993920	+	0.175255i
$395$	−1.19285	+	6.76500i	−0.0600189	+	0.340384i
$396$	−0.802302	+	0.0987968i	−0.0403172	+	0.00496473i
$397$	−23.8589	+	20.0200i	−1.19744	+	1.00477i	−0.197744	+	0.980254i	$0.563362\pi$
$397$	−23.8589	+	20.0200i	−1.19744	+	1.00477i	−0.999699	+	0.0245208i	$0.992194\pi$
$398$	−3.33447			−0.167142
$399$	−0.130512	+	4.04388i	−0.00653379	+	0.202447i
$400$	−1.00000			−0.0500000
$401$	6.05613	−	5.08169i	0.302429	−	0.253768i	−0.478926	−	0.877855i	$-0.658974\pi$
$401$	6.05613	−	5.08169i	0.302429	−	0.253768i	0.781354	+	0.624088i	$0.214529\pi$
$402$	−7.77057	+	6.18322i	−0.387561	+	0.308391i
$403$	2.32854	−	13.2058i	0.115993	−	0.657827i
$404$	−1.77282	+	0.312595i	−0.0882010	+	0.0155522i
$405$	8.65310	+	2.47465i	0.429976	+	0.122966i
$406$	1.43727	−	2.48943i	0.0713306	−	0.123548i
$407$	−1.23436	−	2.13798i	−0.0611851	−	0.105976i
$408$	0.838530	−	0.280732i	0.0415134	−	0.0138983i
$409$	14.4428	−	17.2123i	0.714151	−	0.851092i	−0.279898	−	0.960030i	$-0.590301\pi$
$409$	14.4428	−	17.2123i	0.714151	−	0.851092i	0.994049	+	0.108938i	$0.0347450\pi$
$410$	10.0607	−	5.80852i	0.496860	−	0.286862i
$411$	−2.96755	−	5.46325i	−0.146378	−	0.269482i
$412$	−0.174249	−	0.478744i	−0.00858462	−	0.0235860i
$413$	−0.599816	−	3.40173i	−0.0295150	−	0.167388i
$414$	0.204696	+	0.668690i	0.0100603	+	0.0328643i
$415$	−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	$-0.147455\pi$
$420$	0.137360	+	0.917993i	0.00670248	+	0.0447934i
$421$	12.7447	−	35.0157i	0.621138	−	1.70656i	−0.0830467	−	0.996546i	$-0.526465\pi$
$421$	12.7447	−	35.0157i	0.621138	−	1.70656i	0.704185	−	0.710017i	$-0.251313\pi$
$422$	10.0522	+	1.77247i	0.489333	+	0.0862826i
$423$	16.3948	+	21.7407i	0.797141	+	1.05707i
$424$	−5.36097	+	1.95123i	−0.260352	+	0.0947603i
$425$	0.442138	+	0.255268i	0.0214468	+	0.0123823i
$426$	0.288987	−	11.1107i	0.0140015	−	0.538313i
$427$	−4.38841	−	3.68231i	−0.212370	−	0.178200i
$428$	4.60312	+	3.86248i	0.222500	+	0.186700i
$429$	0.0230832	−	0.887479i	0.00111447	−	0.0428479i
$430$	−5.68169	−	3.28033i	−0.273996	−	0.158191i
$431$	−17.5447	+	6.38575i	−0.845098	+	0.307591i	−0.728040	−	0.685534i	$-0.759569\pi$
$431$	−17.5447	+	6.38575i	−0.845098	+	0.307591i	−0.117058	+	0.993125i	$0.537346\pi$
$432$	−5.17197	+	0.500759i	−0.248836	+	0.0240928i
$433$	10.8936	+	1.92083i	0.523512	+	0.0923093i	0.429158	−	0.903229i	$-0.358810\pi$
$433$	10.8936	+	1.92083i	0.523512	+	0.0923093i	0.0943539	+	0.995539i	$0.469921\pi$
$434$	1.29209	−	3.54998i	0.0620221	−	0.170404i
$435$	1.37485	+	9.18829i	0.0659191	+	0.440545i
$436$			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	0.928280	+	0.371881i	$0.121287\pi$
$439$	23.7456	+	28.2990i	1.13332	+	1.35064i	0.205037	+	0.978754i	$0.434268\pi$
$440$	0.253204	+	0.0921587i	0.0120710	+	0.00439349i
$441$	−19.2564	+	5.89468i	−0.916971	+	0.280699i
$442$	0.168639	+	0.956397i	0.00802132	+	0.0454912i
$443$	7.07598	+	19.4411i	0.336190	+	0.923675i	0.986464	+	0.163975i	$0.0524317\pi$
$443$	7.07598	+	19.4411i	0.336190	+	0.923675i	−0.650274	+	0.759699i	$0.725346\pi$
$444$	−7.57448	−	13.9446i	−0.359469	−	0.661782i
$445$	0.901982	−	0.520759i	0.0427580	−	0.0246864i
$446$	−0.958081	+	1.14180i	−0.0453664	+	0.0540656i
$447$	−29.5068	+	9.87860i	−1.39562	+	0.467242i
$448$	−0.267952	−	0.464106i	−0.0126595	−	0.0219270i
$449$	19.7374	−	34.1861i	0.931464	−	1.61334i	0.150644	−	0.988588i	$-0.451865\pi$
$449$	19.7374	−	34.1861i	0.931464	−	1.61334i	0.780821	−	0.624755i	$-0.214801\pi$
$450$	−2.19478	−	2.04522i	−0.103463	−	0.0964127i
$451$	−3.08270	+	0.543563i	−0.145159	+	0.0255954i
$452$	−0.565193	+	3.20537i	−0.0265845	+	0.150768i
$453$	5.02076	−	3.99514i	0.235896	−	0.187708i
$454$	1.33835	−	1.12301i	0.0628121	−	0.0527056i
$455$	−1.01940			−0.0477904
$456$	6.41318	+	3.98386i	0.300325	+	0.186561i
$457$	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
$459$	2.41455	+	1.09884i	0.112702	+	0.0512893i
$460$	0.0404785	−	0.229565i	0.00188732	−	0.0107035i
$461$	−17.0136	+	2.99996i	−0.792403	+	0.139722i	−0.555177	−	0.831732i	$-0.687349\pi$
$461$	−17.0136	+	2.99996i	−0.792403	+	0.139722i	−0.237226	+	0.971454i	$0.576238\pi$
$462$	0.0498209	−	0.245098i	0.00231788	−	0.0114030i
$463$	−10.5864	+	18.3361i	−0.491990	+	0.852152i	−0.999957	−	0.00922415i	$-0.997064\pi$
$463$	−10.5864	+	18.3361i	−0.491990	+	0.852152i	0.507967	+	0.861376i	$0.330397\pi$
$464$	−2.68196	−	4.64529i	−0.124507	−	0.215652i
$465$	3.87631	+	11.5783i	0.179760	+	0.536931i
$466$	11.8638	−	14.1387i	0.549579	−	0.654963i
$467$	−2.81741	+	1.62663i	−0.130374	+	0.0752716i	−0.563769	−	0.825933i	$-0.690649\pi$
$467$	−2.81741	+	1.62663i	−0.130374	+	0.0752716i	0.433394	+	0.901204i	$0.357316\pi$
$468$	0.296658	−	5.69893i	0.0137130	−	0.263433i
$469$	−1.05087	−	2.88723i	−0.0485245	−	0.133320i
$470$	−1.57612	−	8.93861i	−0.0727009	−	0.412307i
$471$	−0.731238	+	0.826808i	−0.0336937	+	0.0380973i
$472$	−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
$477$	−15.7569	−	6.68185i	−0.721458	−	0.305941i
$478$	−0.472738	+	1.29884i	−0.0216225	+	0.0594074i
$479$	−11.7497	−	2.07180i	−0.536859	−	0.0946627i	−0.101356	−	0.994850i	$-0.532318\pi$
$479$	−11.7497	−	2.07180i	−0.536859	−	0.0946627i	−0.435503	+	0.900187i	$0.643429\pi$
$480$	1.61164	+	0.634515i	0.0735611	+	0.0289615i
$481$	16.3770	−	5.96074i	0.746727	−	0.271786i
$482$	−10.9057	−	6.29639i	−0.496740	−	0.286793i
$483$	−0.216299	−	0.00562591i	−0.00984194	−	0.000255988i
$484$	8.37087	+	7.02399i	0.380494	+	0.319272i
$485$	−1.64266	−	1.37835i	−0.0745892	−	0.0625878i
$486$	−12.3755	−	9.47877i	−0.561364	−	0.429966i
$487$	6.60985	+	3.81620i	0.299521	+	0.172928i	0.642228	−	0.766514i	$-0.278010\pi$
$487$	6.60985	+	3.81620i	0.299521	+	0.172928i	−0.342707	+	0.939442i	$0.611344\pi$
$488$	−10.0451	+	3.65610i	−0.454718	+	0.165504i
$489$	−7.37077	+	18.7214i	−0.333318	+	0.846613i
$490$	6.61082	+	1.16567i	0.298647	+	0.0526595i
$491$	12.5691	−	34.5334i	0.567238	−	1.55847i	−0.241560	−	0.970386i	$-0.577659\pi$
$491$	12.5691	−	34.5334i	0.567238	−	1.55847i	0.808798	−	0.588087i	$-0.200119\pi$
$492$	−19.8998	+	2.97762i	−0.897151	+	0.134241i
$493$			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
$498$	3.80686	+	3.36683i	0.170590	+	0.150871i
$499$	−5.83153	−	33.0723i	−0.261055	−	1.48052i	−0.780037	−	0.625733i	$-0.784800\pi$
$499$	−5.83153	−	33.0723i	−0.261055	−	1.48052i	0.518982	−	0.854785i	$-0.326311\pi$
$500$	0.342020	+	0.939693i	0.0152956	+	0.0420243i
$501$	11.7987	−	6.40888i	0.527129	−	0.286328i
$502$	23.5615	−	13.6033i	1.05160	−	0.607143i
$503$	19.9507	−	23.7763i	0.889557	−	1.06013i	−0.108262	−	0.994122i	$-0.534529\pi$
$503$	19.9507	−	23.7763i	0.889557	−	1.06013i	0.997819	−	0.0660102i	$-0.0210270\pi$
$504$	0.361105	−	1.56663i	0.0160849	−	0.0697834i
$505$	0.900083	+	1.55899i	0.0400532	+	0.0693741i
$506$	−0.0314057	+	0.0543963i	−0.00139615	+	0.00241821i
$507$	−15.9237	−	3.23680i	−0.707197	−	0.143751i
$508$	4.96152	−	0.874850i	0.220132	−	0.0388152i
$509$	5.30276	−	30.0734i	0.235041	−	1.33298i	−0.607487	−	0.794329i	$-0.707822\pi$
$509$	5.30276	−	30.0734i	0.235041	−	1.33298i	0.842528	−	0.538652i	$-0.181066\pi$
$510$	−0.550596	−	0.691945i	−0.0243808	−	0.0306398i
$511$	2.31504	−	1.94255i	0.102411	−	0.0859333i
$512$	−1.00000			−0.0441942
$513$	5.92763	+	21.8601i	0.261711	+	0.965146i
$514$	−31.1425			−1.37364
$515$	−0.390276	+	0.327480i	−0.0171976	+	0.0144305i
$516$	7.07544	+	8.89184i	0.311479	+	0.391441i
$517$	−0.424691	+	2.40854i	−0.0186779	+	0.105928i
$518$	4.83534	−	0.852600i	0.212453	−	0.0374611i
$519$	33.6463	+	6.83925i	1.47691	+	0.300210i
$520$	−0.951108	+	1.64737i	−0.0417088	+	0.0722418i
$521$	2.91411	+	5.04738i	0.127669	+	0.221130i	0.922773	−	0.385344i	$-0.125917\pi$
$521$	2.91411	+	5.04738i	0.127669	+	0.221130i	−0.795104	+	0.606473i	$0.792584\pi$
$522$	3.61434	−	15.6806i	0.158195	−	0.686322i
$523$	−21.9654	+	26.1773i	−0.960479	+	1.14465i	0.0289420	+	0.999581i	$0.490786\pi$
$523$	−21.9654	+	26.1773i	−0.960479	+	1.14465i	−0.989421	+	0.145073i	$0.953658\pi$
$524$	−1.84040	+	1.06255i	−0.0803982	+	0.0464179i
$525$	0.815651	−	0.443048i	0.0355979	−	0.0193362i
$526$	−8.41522	−	23.1206i	−0.366921	−	1.00811i
$527$	0.624957	+	3.54431i	0.0272236	+	0.154393i
$528$	−0.349598	−	0.309189i	−0.0152143	−	0.0134557i
$529$	−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
$534$	−1.78410	+	0.266957i	−0.0772056	+	0.0115523i
$535$	2.05518	−	5.64656i	0.0888532	−	0.244122i
$536$	−5.64625	−	0.995587i	−0.243881	−	0.0430028i
$537$	−2.89425	+	7.35126i	−0.124896	+	0.317230i
$538$	−24.9087	+	9.06602i	−1.07389	+	0.390864i
$539$	−1.56646	−	0.904396i	−0.0674722	−	0.0389551i
$540$	2.23948	+	4.68879i	0.0963717	+	0.201773i
$541$	16.5317	+	13.8717i	0.710751	+	0.596391i	0.924810	−	0.380430i	$-0.124224\pi$
$541$	16.5317	+	13.8717i	0.710751	+	0.596391i	−0.214059	+	0.976821i	$0.568668\pi$
$542$	−7.38584	−	6.19745i	−0.317249	−	0.266203i
$543$	38.2910	+	0.995944i	1.64322	+	0.0427401i
$544$	0.442138	+	0.255268i	0.0189565	+	0.0109445i
$545$	7.78188	−	2.83237i	0.333339	−	0.121326i
$546$	1.64292	+	0.646828i	0.0703103	+	0.0276817i
$547$	−35.0150	−	6.17409i	−1.49713	−	0.263985i	−0.635732	−	0.771910i	$-0.719302\pi$
$547$	−35.0150	−	6.17409i	−1.49713	−	0.263985i	−0.861402	+	0.507924i	$0.830413\pi$
$548$	1.22768	−	3.37302i	0.0524439	−	0.144088i
$549$	−29.5242	−	12.5200i	−1.26006	−	0.534342i
$550$		−	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
$555$	−10.5130	+	11.8870i	−0.446253	+	0.504576i
$556$	−2.40923	−	13.6634i	−0.102174	−	0.579458i
$557$	−2.09509	−	5.75621i	−0.0887718	−	0.243899i	0.887360	−	0.461077i	$-0.152537\pi$
$557$	−2.09509	−	5.75621i	−0.0887718	−	0.243899i	−0.976132	+	0.217178i	$0.930315\pi$
$558$	1.09938	−	21.1196i	0.0465406	−	0.894066i
$559$	−10.8078	+	6.23989i	−0.457122	+	0.263919i
$560$	−0.344472	+	0.410526i	−0.0145566	+	0.0173479i
$561$	0.0756444	+	0.225945i	0.00319371	+	0.00953942i
$562$	−11.4434	−	19.8206i	−0.482711	−	0.836081i
$563$	8.06195	−	13.9637i	0.339771	−	0.588500i	−0.644619	−	0.764504i	$-0.722984\pi$
$563$	8.06195	−	13.9637i	0.339771	−	0.588500i	0.984389	+	0.176004i	$0.0563172\pi$
$564$	−3.13154	+	15.4059i	−0.131862	+	0.648706i
$565$	3.20537	−	0.565193i	0.134851	−	0.0237779i
$566$	−3.91150	+	22.1832i	−0.164413	+	0.932431i
$567$	3.99666	−	2.69987i	0.167844	−	0.113384i
$568$	4.91564	−	4.12471i	0.206256	−	0.173069i
$569$	−7.45449			−0.312508			−0.156254	−	0.987717i	$-0.549942\pi$
$569$	−7.45449			−0.312508			−0.156254	+	0.987717i	$0.549942\pi$
$570$	1.55017	−	7.38898i	0.0649295	−	0.309490i
$571$	−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
$573$	6.00693	−	4.77985i	0.250943	−	0.199681i
$574$	1.08107	−	6.13103i	0.0451228	−	0.255904i
$575$	−0.229565	+	0.0404785i	−0.00957352	+	0.00168807i
$576$	−2.19478	−	2.04522i	−0.0914492	−	0.0852176i
$577$	−10.1333	+	17.5513i	−0.421853	+	0.730671i	−0.996121	−	0.0879968i	$-0.971953\pi$
$577$	−10.1333	+	17.5513i	−0.421853	+	0.730671i	0.574268	+	0.818667i	$0.305287\pi$
$578$	8.36968	+	14.4967i	0.348133	+	0.602983i
$579$	−30.1140	+	10.0819i	−1.25149	+	0.418989i
$580$	−3.44786	+	4.10900i	−0.143165	+	0.170617i
$581$	−1.36176	+	0.786212i	−0.0564953	+	0.0326176i
$582$	1.77279	+	3.26370i	0.0734845	+	0.135285i
$583$	−0.525768	−	1.44454i	−0.0217751	−	0.0598265i
$584$	−0.979238	−	5.55353i	−0.0405211	−	0.229807i
$585$	−5.45671	+	1.67038i	−0.225607	+	0.0690618i
$586$	−26.6580	−	9.70271i	−1.10123	−	0.400815i
$587$	10.6189	+	12.6551i	0.438287	+	0.522330i	0.939294	−	0.343113i	$-0.111481\pi$
$587$	10.6189	+	12.6551i	0.438287	+	0.522330i	−0.501007	+	0.865443i	$0.667037\pi$
$588$	−9.91465	−	6.07331i	−0.408873	−	0.250459i
$589$	−19.8983	+	23.4147i	−0.819896	+	0.964785i
$590$			6.44557i			0.265360i
$591$	−5.13478	−	34.3163i	−0.211217	−	1.41158i
$592$	3.13358	−	8.60943i	0.128789	−	0.353845i
$593$	−20.7736	−	3.66294i	−0.853068	−	0.150419i	−0.270018	−	0.962855i	$-0.587030\pi$
$593$	−20.7736	−	3.66294i	−0.853068	−	0.150419i	−0.583050	+	0.812436i	$0.698141\pi$
$594$	−0.134931	−	1.39361i	−0.00553630	−	0.0571804i
$595$	0.257099	−	0.0935762i	0.0105400	−	0.00383625i
$596$	−15.5582	−	8.98256i	−0.637291	−	0.367940i
$597$	0.150169	−	5.77353i	0.00614600	−	0.236295i
$598$	−0.339678	−	0.285024i	−0.0138905	−	0.0116555i
$599$	12.3894	+	10.3959i	0.506217	+	0.424766i	0.859795	−	0.510639i	$-0.170591\pi$
$599$	12.3894	+	10.3959i	0.506217	+	0.424766i	−0.353579	+	0.935405i	$0.615035\pi$
$600$	0.0450352	−	1.73147i	0.00183855	−	0.0706868i
$601$	0.702402	+	0.405532i	0.0286516	+	0.0165420i	0.514257	−	0.857636i	$-0.328068\pi$
$601$	0.702402	+	0.405532i	0.0286516	+	0.0165420i	−0.485606	+	0.874178i	$0.661401\pi$
$602$	−3.30385	+	1.20250i	−0.134655	+	0.0490103i
$603$	−10.3561	−	13.7329i	−0.421733	−	0.559248i
$604$	3.64818	+	0.643273i	0.148442	+	0.0261744i
$605$	3.73739	−	10.2684i	0.151946	−	0.417470i
$606$	−0.461409	−	3.08365i	−0.0187435	−	0.125265i
$607$		−	15.6970i		−	0.637123i	−0.947902	−	0.318561i	$-0.896800\pi$
$607$		−	15.6970i		−	0.637123i	0.947902	−	0.318561i	$-0.103200\pi$
$608$	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
$612$	0.448315	+	1.46453i	0.0181221	+	0.0592001i
$613$	5.89200	+	33.4152i	0.237976	+	1.34963i	0.836256	+	0.548340i	$0.184740\pi$
$613$	5.89200	+	33.4152i	0.237976	+	1.34963i	−0.598280	+	0.801287i	$0.704149\pi$
$614$	9.05566	+	24.8802i	0.365457	+	1.00408i
$615$	9.60417	+	17.6813i	0.387277	+	0.712977i
$616$	0.125055	−	0.0722007i	0.00503862	−	0.00290905i
$617$	18.4198	−	21.9518i	0.741552	−	0.883748i	−0.254981	−	0.966946i	$-0.582069\pi$
$617$	18.4198	−	21.9518i	0.741552	−	0.883748i	0.996533	+	0.0831986i	$0.0265136\pi$
$618$	0.836776	−	0.280145i	0.0336601	−	0.0112691i
$619$	12.4597	+	21.5808i	0.500797	+	0.867406i	1.00000		0.000920317i	$0.000292946\pi$
$619$	12.4597	+	21.5808i	0.500797	+	0.867406i	−0.499203	+	0.866485i	$0.666374\pi$
$620$	−3.52471	+	6.10497i	−0.141556	+	0.245182i
$621$	−1.16703	+	0.324310i	−0.0468314	+	0.0130141i
$622$	−4.90280	+	0.864495i	−0.196584	+	0.0346631i
$623$	0.0969224	−	0.549674i	0.00388311	−	0.0220222i
$624$	2.57813	−	2.05147i	0.103208	−	0.0821247i
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	13.3713			0.534426
$627$	−1.07347	+	1.72806i	−0.0428702	+	0.0690119i
$628$	−0.637265			−0.0254296
$629$	−3.58319	+	3.00665i	−0.142871	+	0.119883i
$630$	−1.59566	+	0.196492i	−0.0635725	+	0.00782843i
$631$	−2.54473	+	14.4319i	−0.101304	+	0.574525i	0.891328	+	0.453359i	$0.149774\pi$
$631$	−2.54473	+	14.4319i	−0.101304	+	0.574525i	−0.992632	+	0.121166i	$0.961337\pi$
$632$	6.76500	−	1.19285i	0.269097	−	0.0474491i
$633$	−3.52168	+	17.3252i	−0.139974	+	0.688614i
$634$	6.44499	−	11.1631i	0.255963	−	0.443342i
$635$	−2.51903	−	4.36309i	−0.0999647	−	0.173144i
$636$	−3.13706	−	9.37021i	−0.124393	−	0.371553i
$637$	8.20789	−	9.78178i	0.325208	−	0.387568i
$638$	1.25169	−	0.722665i	0.0495550	−	0.0286106i
$639$	19.2247	+	1.00074i	0.760518	+	0.0395887i
$640$	0.342020	+	0.939693i	0.0135195	+	0.0371446i
$641$	−2.74984	−	15.5951i	−0.108612	−	0.615970i	−0.989716	−	0.143047i	$-0.954310\pi$
$641$	−2.74984	−	15.5951i	−0.108612	−	0.615970i	0.881104	−	0.472923i	$-0.156801\pi$
$642$	−6.89504	+	7.79619i	−0.272126	+	0.307691i
$643$	6.48291	+	2.35959i	0.255661	+	0.0930530i	0.466671	−	0.884431i	$-0.345453\pi$
$643$	6.48291	+	2.35959i	0.255661	+	0.0930530i	−0.211010	+	0.977484i	$0.567675\pi$
$644$	−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	$-0.355251\pi$
$648$	−0.634126	−	8.97763i	−0.0249108	−	0.352675i
$649$	0.594015	−	1.63204i	0.0233171	−	0.0640633i
$650$	1.87332	+	0.330316i	0.0734775	+	0.0129561i
$651$	6.08847	+	2.39708i	0.238626	+	0.0939488i
$652$	−10.9158	+	3.97303i	−0.427497	+	0.155596i
$653$	0.743456	+	0.429234i	0.0290937	+	0.0167972i	0.514476	−	0.857505i	$-0.327986\pi$
$653$	0.743456	+	0.429234i	0.0290937	+	0.0167972i	−0.485383	+	0.874302i	$0.661320\pi$
$654$	−14.3388	−	0.372950i	−0.560691	−	0.0145835i
$655$	1.62793	+	1.36599i	0.0636084	+	0.0533738i
$656$	−8.89917	−	7.46729i	−0.347454	−	0.291549i
$657$	9.20900	−	14.1915i	0.359277	−	0.553665i
$658$	−4.21246	−	2.43206i	−0.164219	−	0.0948117i
$659$	−25.4151	+	9.25036i	−0.990034	+	0.360343i	−0.785733	−	0.618565i	$-0.787714\pi$
$659$	−25.4151	+	9.25036i	−0.990034	+	0.360343i	−0.204300	+	0.978908i	$0.565492\pi$
$660$	−0.170973	+	0.434263i	−0.00665510	+	0.0169037i
$661$	23.3092	+	4.11003i	0.906621	+	0.159862i	0.607469	−	0.794344i	$-0.292185\pi$
$661$	23.3092	+	4.11003i	0.906621	+	0.159862i	0.299152	+	0.954205i	$0.403296\pi$
$662$	−9.49932	+	26.0992i	−0.369202	+	1.01437i
$663$	−1.66356	+	0.248920i	−0.0646075	+	0.00966727i
$664$			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
$669$	−1.93383	−	1.71030i	−0.0747663	−	0.0661242i
$670$	0.995587	+	5.64625i	0.0384629	+	0.218134i
$671$	−0.985151	−	2.70668i	−0.0380313	−	0.104490i
$672$	0.815651	−	0.443048i	0.0314644	−	0.0170910i
$673$	2.45755	−	1.41887i	0.0947315	−	0.0546933i	−0.451886	−	0.892076i	$-0.649249\pi$
$673$	2.45755	−	1.41887i	0.0947315	−	0.0546933i	0.546617	+	0.837383i	$0.315915\pi$
$674$	−0.505586	+	0.602534i	−0.0194744	+	0.0232087i
$675$	3.64007	−	3.70808i	0.140107	−	0.142724i
$676$	−4.69079	−	8.12468i	−0.180415	−	0.312488i
$677$	−17.1962	+	29.7847i	−0.660904	+	1.14472i	0.319475	+	0.947595i	$0.396493\pi$
$677$	−17.1962	+	29.7847i	−0.660904	+	1.14472i	−0.980379	+	0.197124i	$0.936840\pi$
$678$	−5.52453	−	1.12297i	−0.212168	−	0.0431273i
$679$	−1.13170	+	0.199549i	−0.0434306	+	0.00765799i
$680$	0.0886538	−	0.502781i	0.00339972	−	0.0192808i
$681$	1.88418	+	2.36789i	0.0722021	+	0.0907377i
$682$	1.45510	−	1.22097i	0.0557185	−	0.0467534i
$683$	5.84698			0.223729			0.111864	−	0.993723i	$-0.464318\pi$
$683$	5.84698			0.223729			0.111864	+	0.993723i	$0.464318\pi$
$684$	−7.18674	+	10.9248i	−0.274792	+	0.417719i
$685$	−3.58950			−0.137148
$686$	5.62946	−	4.72368i	0.214934	−	0.180351i
$687$	13.0862	+	16.4457i	0.499271	+	0.627443i
$688$	−1.13925	+	6.46098i	−0.0434333	+	0.246323i
$689$	10.6873	−	1.88446i	0.407155	−	0.0717924i
$690$	0.395661	+	0.0804256i	0.0150625	+	0.00306175i
$691$	−1.28333	+	2.22280i	−0.0488203	+	0.0845593i	−0.889403	−	0.457124i	$-0.848880\pi$
$691$	−1.28333	+	2.22280i	−0.0488203	+	0.0845593i	0.840583	+	0.541683i	$0.182213\pi$
$692$	9.91147	+	17.1672i	0.376778	+	0.652598i
$693$	0.422135	+	0.0973012i	0.0160356	+	0.00369617i
$694$	11.6402	−	13.8722i	0.441855	−	0.526583i
$695$	−12.0154	+	6.93710i	−0.455770	+	0.263139i
$696$	8.16395	−	4.43452i	0.309454	−	0.168090i
$697$	2.02850	+	5.57325i	0.0768348	+	0.211102i
$698$	1.73123	+	9.81832i	0.0655282	+	0.371629i
$699$	23.9464	+	21.1785i	0.905736	+	0.801043i
$700$	0.503585	+	0.183290i	0.0190337	+	0.00692770i
$701$	33.6892	+	40.1492i	1.27242	+	1.51641i	0.745512	+	0.666492i	$0.232205\pi$
$701$	33.6892	+	40.1492i	1.27242	+	1.51641i	0.526910	+	0.849921i	$0.323351\pi$
$702$	9.85414	+	0.770305i	0.371921	+	0.0290733i
$703$	−39.2852	−	7.18085i	−1.48167	−	0.270831i
$704$		−	0.269454i		−	0.0101554i
$705$	15.5479	−	2.32644i	0.585567	−	0.0876188i
$706$	−4.85899	+	13.3500i	−0.182870	+	0.502432i
$707$	0.950059	+	0.167521i	0.0357307	+	0.00630028i
$708$	4.08981	−	10.3880i	0.153705	−	0.390403i
$709$	42.3775	−	15.4242i	1.59152	−	0.579266i	0.613853	−	0.789421i	$-0.289619\pi$
$709$	42.3775	−	15.4242i	1.59152	−	0.579266i	0.977668	+	0.210154i	$0.0673966\pi$
$710$	−5.55721	−	3.20846i	−0.208558	−	0.120411i
$711$	17.2873	+	11.2179i	0.648326	+	0.420704i
$712$	−0.797850	−	0.669475i	−0.0299007	−	0.0250896i
$713$	−1.25881	−	1.05627i	−0.0471429	−	0.0395576i
$714$	−0.473726	−	0.0123216i	−0.0177288	−	0.000461123i
$715$	−0.443890	−	0.256280i	−0.0166005	−	0.00958432i
$716$	−4.28627	+	1.56007i	−0.160185	+	0.0583027i
$717$	−2.22760	−	0.877023i	−0.0831913	−	0.0327530i
$718$	22.5944	+	3.98401i	0.843216	+	0.148682i
$719$	−1.71739	+	4.71850i	−0.0640480	+	0.175970i	−0.967588	−	0.252532i	$-0.918737\pi$
$719$	−1.71739	+	4.71850i	−0.0640480	+	0.175970i	0.903540	+	0.428503i	$0.140959\pi$
$720$	−1.17122	+	2.76193i	−0.0436489	+	0.102931i
$721$			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
$726$	−12.5388	+	14.1775i	−0.465358	+	0.526178i
$727$	9.29339	+	52.7054i	0.344673	+	1.95474i	0.293161	+	0.956063i	$0.405293\pi$
$727$	9.29339	+	52.7054i	0.344673	+	1.95474i	0.0515112	+	0.998672i	$0.483596\pi$
$728$	0.348657	+	0.957927i	0.0129221	+	0.0355031i
$729$	16.9695	−	21.0009i	0.628500	−	0.777810i
$730$	−4.88369	+	2.81960i	−0.180754	+	0.104358i
$731$	2.15299	−	2.56583i	0.0796312	−	0.0949007i
$732$	−5.87803	−	17.5573i	−0.217258	−	0.648937i
$733$	6.59099	+	11.4159i	0.243444	+	0.421657i	0.961693	−	0.274129i	$-0.0883896\pi$
$733$	6.59099	+	11.4159i	0.243444	+	0.421657i	−0.718249	+	0.695786i	$0.755056\pi$
$734$	−12.9595	+	22.4465i	−0.478343	+	0.828515i
$735$	−2.31603	+	11.3939i	−0.0854281	+	0.420271i
$736$	−0.229565	+	0.0404785i	−0.00846187	+	0.00149206i
$737$	0.268265	−	1.52140i	0.00988166	−	0.0560417i
$738$	−4.25945	−	34.5899i	−0.156793	−	1.27327i
$739$	−39.8791	+	33.4625i	−1.46698	+	1.23094i	−0.548088	+	0.836420i	$0.684644\pi$
$739$	−39.8791	+	33.4625i	−1.46698	+	1.23094i	−0.918888	+	0.394519i	$0.870911\pi$
$740$	−9.16197			−0.336801
$741$	−10.6980	−	9.58141i	−0.393000	−	0.351982i
$742$	3.05735			0.112239
$743$	11.1192	−	9.33008i	0.407922	−	0.342288i	−0.415624	−	0.909537i	$-0.636437\pi$
$743$	11.1192	−	9.33008i	0.407922	−	0.342288i	0.823546	+	0.567249i	$0.191992\pi$
$744$	9.55426	−	7.60255i	0.350276	−	0.278723i
$745$	−3.11961	+	17.6922i	−0.114294	+	0.648191i
$746$	−11.9093	+	2.09994i	−0.436032	+	0.0768842i
$747$	−6.00100	+	6.43982i	−0.219565	+	0.235621i
$748$	−0.0687831	+	0.119136i	−0.00251496	+	0.00435604i
$749$	−1.61011	−	2.78879i	−0.0588321	−	0.101900i
$750$	−1.64245	+	0.549877i	−0.0599737	+	0.0200787i
$751$	−2.40354	+	2.86443i	−0.0877065	+	0.104524i	−0.808113	−	0.589028i	$-0.799511\pi$
$751$	−2.40354	+	2.86443i	−0.0877065	+	0.104524i	0.720406	+	0.693552i	$0.243955\pi$
$752$	−7.86048	+	4.53825i	−0.286642	+	0.165493i
$753$	22.4925	+	41.4086i	0.819671	+	1.50901i
$754$	3.48975	+	9.58800i	0.127089	+	0.349174i
$755$	−0.643273	−	3.64818i	−0.0234111	−	0.132771i
$756$	2.69631	+	0.695794i	0.0980637	+	0.0253058i
$757$	−29.2090	−	10.6312i	−1.06162	−	0.386398i	−0.248583	−	0.968611i	$-0.579965\pi$
$757$	−29.2090	−	10.6312i	−1.06162	−	0.386398i	−0.813037	+	0.582212i	$0.802187\pi$
$758$	−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	$-0.0105720\pi$
$762$	1.29133	+	8.63010i	0.0467799	+	0.312636i
$763$	1.51788	−	4.17034i	0.0549509	−	0.150976i
$764$	4.36476	+	0.769624i	0.157911	+	0.0278440i
$765$	1.22287	−	0.922177i	0.0442131	−	0.0333414i
$766$	−19.6447	+	7.15008i	−0.709791	+	0.258343i
$767$	10.6182	+	6.13043i	0.383402	+	0.221357i
$768$	0.0450352	−	1.73147i	0.00162507	−	0.0624789i
$769$	26.5280	+	22.2597i	0.956625	+	0.802704i	0.980401	−	0.197014i	$-0.0631243\pi$
$769$	26.5280	+	22.2597i	0.956625	+	0.802704i	−0.0237758	+	0.999717i	$0.507569\pi$
$770$	−0.110618	−	0.0928194i	−0.00398639	−	0.00334498i
$771$	1.40251	−	53.9222i	0.0505102	−	1.94196i
$772$	−15.8784	−	9.16741i	−0.571477	−	0.329942i
$773$	−14.5009	+	5.27790i	−0.521561	+	0.189833i	−0.589366	−	0.807866i	$-0.700623\pi$
$773$	−14.5009	+	5.27790i	−0.521561	+	0.189833i	0.0678053	+	0.997699i	$0.478400\pi$
$774$	−15.7145	+	11.8504i	−0.564848	+	0.425955i
$775$	6.94232	+	1.22412i	0.249375	+	0.0439716i
$776$	−0.733406	+	2.01502i	−0.0263277	+	0.0723349i
$777$	1.25849	+	8.41062i	0.0451480	+	0.301729i
$778$			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
$783$	26.9877	+	6.96429i	0.964460	+	0.248883i
$784$	−1.16567	−	6.61082i	−0.0416310	−	0.236101i
$785$	0.217958	+	0.598833i	0.00777924	+	0.0213733i
$786$	−1.75689	−	3.23444i	−0.0626663	−	0.115369i
$787$	45.4685	−	26.2512i	1.62078	−	0.935755i	0.634063	−	0.773281i	$-0.281386\pi$
$787$	45.4685	−	26.2512i	1.62078	−	0.935755i	0.986713	−	0.162474i	$-0.0519474\pi$
$788$	12.8770	−	15.3462i	0.458725	−	0.546687i
$789$	40.4115	−	13.5294i	1.43869	−	0.481660i
$790$	−3.43468	−	5.94904i	−0.122200	−	0.211657i
$791$	0.872134	−	1.51058i	0.0310095	−	0.0537101i
$792$	0.551093	−	0.591392i	0.0195823	−	0.0210142i
$793$	20.0252	−	3.53099i	0.711117	−	0.125389i
$794$	5.40837	−	30.6724i	0.191936	−	1.08852i
$795$	−7.73218	+	6.15268i	−0.274232	+	0.218213i
$796$	2.55436	−	2.14336i	0.0905367	−	0.0759693i
$797$	−45.9715			−1.62839			−0.814197	−	0.580588i	$-0.802823\pi$
$797$	−45.9715			−1.62839			−0.814197	+	0.580588i	$0.802823\pi$
$798$	−2.49938	−	3.18168i	−0.0884770	−	0.112630i
$799$	4.63389			0.163935
$800$	0.766044	−	0.642788i	0.0270838	−	0.0227260i
$801$	−0.381879	−	3.10113i	−0.0134930	−	0.109573i
$802$	−1.37281	+	7.78561i	−0.0484757	+	0.274919i
$803$	1.49642	−	0.263859i	0.0528076	−	0.00931140i
$804$	1.97810	−	9.73145i	0.0697623	−	0.343202i
$805$	−0.0624612	+	0.108186i	−0.00220147	+	0.00381306i
$806$	6.70475	+	11.6130i	0.236165	+	0.409050i
$807$	−14.5757	−	43.5368i	−0.513090	−	1.53257i
$808$	1.15712	−	1.37901i	0.0407075	−	0.0485133i
$809$	12.2648	−	7.08110i	0.431208	−	0.248958i	−0.268653	−	0.963237i	$-0.586578\pi$
$809$	12.2648	−	7.08110i	0.431208	−	0.248958i	0.699861	+	0.714279i	$0.253245\pi$
$810$	−8.21933	+	3.66641i	−0.288798	+	0.128825i
$811$	−11.7186	−	32.1965i	−0.411494	−	1.13057i	−0.956396	−	0.292072i	$-0.905655\pi$
$811$	−11.7186	−	32.1965i	−0.411494	−	1.13057i	0.544902	−	0.838500i	$-0.316567\pi$
$812$	0.499160	+	2.83087i	0.0175171	+	0.0993442i
$813$	11.0633	−	12.5092i	0.388007	−	0.438717i
$814$	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
$819$	−1.19395	+	2.81552i	−0.0417199	+	0.0983822i
$820$	−3.97326	+	10.9164i	−0.138752	+	0.381219i
$821$	4.02142	+	0.709085i	0.140349	+	0.0247472i	0.243381	−	0.969931i	$-0.421743\pi$
$821$	4.02142	+	0.709085i	0.140349	+	0.0247472i	−0.103032	+	0.994678i	$0.532855\pi$
$822$	5.78499	+	2.27759i	0.201775	+	0.0794401i
$823$	−12.9801	+	4.72436i	−0.452457	+	0.164681i	−0.558189	−	0.829714i	$-0.688504\pi$
$823$	−12.9801	+	4.72436i	−0.452457	+	0.164681i	0.105732	+	0.994395i	$0.466281\pi$
$824$	0.441213	+	0.254735i	0.0153704	+	0.00887410i
$825$	0.466550	+	0.0121349i	0.0162432	+	0.000422483i
$826$	2.64607	+	2.22032i	0.0920687	+	0.0772548i
$827$	6.94845	+	5.83044i	0.241621	+	0.202744i	0.755554	−	0.655086i	$-0.227368\pi$
$827$	6.94845	+	5.83044i	0.241621	+	0.202744i	−0.513933	+	0.857830i	$0.671812\pi$
$828$	−0.586632	−	0.380670i	−0.0203869	−	0.0132292i
$829$	0.0499853	+	0.0288590i	0.00173606	+	0.00100231i	0.500868	−	0.865524i	$-0.333014\pi$
$829$	0.0499853	+	0.0288590i	0.00173606	+	0.00100231i	−0.499132	+	0.866526i	$0.666348\pi$
$830$	2.75720	−	1.00354i	0.0957039	−	0.0348334i
$831$	−5.45897	+	13.8655i	−0.189369	+	0.480990i
$832$	1.87332	+	0.330316i	0.0649456	+	0.0114517i
$833$	−1.17215	+	3.22045i	−0.0406126	+	0.111582i
$834$	23.7662	−	3.55616i	0.822958	−	0.123140i
$835$		−	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	$-0.681208\pi$
$839$	−43.2559	−	15.7439i	−1.49336	−	0.543539i	−0.954332	+	0.298749i	$0.903431\pi$
$840$	−0.695298	−	0.614930i	−0.0239901	−	0.0212171i
$841$	−0.0396507	−	0.224871i	−0.00136727	−	0.00775416i
$842$	12.7447	+	35.0157i	0.439211	+	1.20672i
$843$	34.8340	−	18.9213i	1.19975	−	0.651683i
$844$	−8.83975	+	5.10363i	−0.304277	+	0.175674i
$845$	−6.03036	+	7.18670i	−0.207451	+	0.247230i
$846$	−26.5338	−	6.11597i	−0.912249	−	0.210271i
$847$	−2.92802	−	5.07147i	−0.100608	−	0.174258i
$848$	2.85251	−	4.94070i	0.0979557	−	0.169664i
$849$	−38.2334	−	7.77166i	−1.31217	−	0.266723i
$850$	−0.502781	+	0.0886538i	−0.0172452	+	0.00304080i
$851$	0.370862	−	2.10327i	0.0127130	−	0.0720990i
$852$	6.92042	+	8.69702i	0.237090	+	0.297955i
$853$	4.36087	−	3.65921i	0.149313	−	0.125289i	−0.565071	−	0.825042i	$-0.691151\pi$
$853$	4.36087	−	3.65921i	0.149313	−	0.125289i	0.714384	+	0.699753i	$0.246707\pi$
$854$	5.72866			0.196031
$855$	12.7239	+	3.01683i	0.435150	+	0.103173i
$856$	−6.00895			−0.205382
$857$	3.14858	−	2.64197i	0.107553	−	0.0902481i	−0.587425	−	0.809279i	$-0.699858\pi$
$857$	3.14858	−	2.64197i	0.107553	−	0.0902481i	0.694979	+	0.719031i	$0.255414\pi$
$858$	0.552778	+	0.694686i	0.0188715	+	0.0237162i
$859$	2.80941	−	15.9330i	0.0958560	−	0.543626i	−0.898626	−	0.438716i	$-0.855433\pi$
$859$	2.80941	−	15.9330i	0.0958560	−	0.543626i	0.994482	−	0.104910i	$-0.0334555\pi$
$860$	6.46098	−	1.13925i	0.220318	−	0.0388480i
$861$	10.5670	+	2.14794i	0.360122	+	0.0732016i
$862$	9.33534	−	16.1693i	0.317963	−	0.550728i
$863$	0.0867373	+	0.150233i	0.00295257	+	0.00511400i	0.867498	−	0.497441i	$-0.165727\pi$
$863$	0.0867373	+	0.150233i	0.00295257	+	0.00511400i	−0.864545	+	0.502555i	$0.832393\pi$
$864$	3.64007	−	3.70808i	0.123838	−	0.126151i
$865$	12.7419	−	15.1853i	0.433239	−	0.516314i
$866$	−9.57965	+	5.53081i	−0.325530	+	0.187945i
$867$	−25.4775	+	13.8389i	−0.865260	+	0.469995i
$868$	1.29209	+	3.54998i	0.0438563	+	0.120494i
$869$	0.321419	+	1.82286i	0.0109034	+	0.0618362i
$870$	−6.95932	−	6.15490i	−0.235943	−	0.208671i
$871$	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
$876$	9.65985	−	1.44541i	0.326376	−	0.0488359i
$877$	12.6134	−	34.6551i	0.425925	−	1.17022i	−0.522339	−	0.852738i	$-0.674941\pi$
$877$	12.6134	−	34.6551i	0.425925	−	1.17022i	0.948264	−	0.317482i	$-0.102837\pi$
$878$	−36.3804	−	6.41485i	−1.22778	−	0.216491i
$879$	18.0005	−	45.7204i	0.607140	−	1.54211i
$880$	−0.253204	+	0.0921587i	−0.00853550	+	0.00310667i
$881$	−35.3271	−	20.3961i	−1.19020	−	0.687162i	−0.231848	−	0.972752i	$-0.574477\pi$
$881$	−35.3271	−	20.3961i	−1.19020	−	0.687162i	−0.958352	+	0.285590i	$0.907811\pi$
$882$	10.9622	−	16.8934i	0.369117	−	0.568829i
$883$	−42.6901	−	35.8212i	−1.43664	−	1.20548i	−0.941656	−	0.336576i	$-0.890731\pi$
$883$	−42.6901	−	35.8212i	−1.43664	−	1.20548i	−0.494979	−	0.868905i	$-0.664824\pi$
$884$	−0.743945	−	0.624244i	−0.0250216	−	0.0209956i
$885$	−11.1603	−	0.290278i	−0.375149	−	0.00975757i
$886$	−17.9170	−	10.3444i	−0.601934	−	0.347527i
$887$	−15.7565	+	5.73489i	−0.529051	+	0.192559i	−0.592715	−	0.805413i	$-0.701944\pi$
$887$	−15.7565	+	5.73489i	−0.529051	+	0.192559i	0.0636635	+	0.997971i	$0.479722\pi$
$888$	14.7658	+	5.81341i	0.495508	+	0.195085i
$889$	−2.65890	−	0.468835i	−0.0891766	−	0.0157242i
$890$	−0.356220	+	0.978707i	−0.0119405	+	0.0328063i
$891$	2.41906	−	0.170868i	0.0810415	−	0.00572428i
$892$		−	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
$897$	0.508806	−	0.575305i	0.0169886	−	0.0192089i
$898$	6.85472	+	38.8750i	0.228745	+	1.29728i
$899$	12.9326	+	35.5321i	0.431328	+	1.18506i
$900$	2.99594	+	0.155954i	0.0998648	+	0.00519846i
$901$	−2.52241	+	1.45631i	−0.0840336	+	0.0485168i
$902$	2.01209	−	2.39792i	0.0669953	−	0.0798419i
$903$	−1.93330	−	5.77465i	−0.0643362	−	0.192168i
$904$	−1.62741	−	2.81875i	−0.0541268	−	0.0937504i
$905$	11.0574	−	19.1520i	0.367560	−	0.636633i
$906$	−1.27810	+	6.28773i	−0.0424621	+	0.208896i
$907$	50.4920	−	8.90310i	1.67656	−	0.295623i	0.747145	−	0.664661i	$-0.231424\pi$
$907$	50.4920	−	8.90310i	1.67656	−	0.295623i	0.929414	+	0.369038i	$0.120313\pi$
$908$	−0.303380	+	1.72055i	−0.0100680	+	0.0570986i
$909$	5.36001	−	0.660041i	0.177780	−	0.0218922i
$910$	0.780909	−	0.655261i	0.0258869	−	0.0217217i
$911$	12.0852			0.400402			0.200201	−	0.979755i	$-0.435840\pi$
$911$	12.0852			0.400402			0.200201	+	0.979755i	$0.435840\pi$
$912$	−7.47356	+	1.07050i	−0.247474	+	0.0354476i
$913$	−0.790619			−0.0261657
$914$	−1.48065	+	1.24241i	−0.0489756	+	0.0410954i
$915$	−14.4881	+	11.5285i	−0.478961	+	0.381120i
$916$	−2.10707	+	11.9498i	−0.0696195	+	0.394832i
$917$	1.12155	−	0.197760i	0.0370369	−	0.00653061i
$918$	−2.55597	+	0.710286i	−0.0843596	+	0.0234429i
$919$	−21.6936	+	37.5744i	−0.715606	+	1.23947i	0.247120	+	0.968985i	$0.420516\pi$
$919$	−21.6936	+	37.5744i	−0.715606	+	1.23947i	−0.962725	+	0.270480i	$0.912817\pi$
$920$	0.116553	+	0.201876i	0.00384264	+	0.00665565i
$921$	−43.4871	+	14.5591i	−1.43295	+	0.479738i
$922$	11.1048	−	13.2342i	0.365719	−	0.435846i
$923$	−10.5710	+	6.10318i	−0.347949	+	0.200888i
$924$	0.119381	+	0.219780i	0.00392735	+	0.00723024i
$925$	3.13358	+	8.60943i	0.103031	+	0.283076i
$926$	−3.67661	−	20.8511i	−0.120821	−	0.685209i
$927$	0.447377	+	1.46147i	0.0146938	+	0.0480008i
$928$	5.04044	+	1.83457i	0.165460	+	0.0602227i
$929$	4.89409	+	5.83255i	0.160570	+	0.191360i	0.840331	−	0.542074i	$-0.182361\pi$
$929$	4.89409	+	5.83255i	0.160570	+	0.191360i	−0.679761	+	0.733434i	$0.737916\pi$
$930$	−10.4118	−	6.37785i	−0.341417	−	0.209138i
$931$	−27.5579	+	9.83538i	−0.903175	+	0.322341i
$932$			18.4568i			0.604572i
$933$	−1.27605	−	8.52795i	−0.0417758	−	0.279193i
$934$	1.11268	−	3.05707i	0.0364081	−	0.100030i
$935$	0.135476	+	0.0238881i	0.00443055	+	0.000781225i
$936$	3.43595	+	4.55632i	0.112308	+	0.148928i
$937$	28.7357	−	10.4589i	0.938755	−	0.341679i	0.173081	−	0.984908i	$-0.444628\pi$
$937$	28.7357	−	10.4589i	0.938755	−	0.341679i	0.765674	+	0.643229i	$0.222406\pi$
$938$	2.66088	+	1.53626i	0.0868810	+	0.0501608i
$939$	−0.602180	+	23.1520i	−0.0196514	+	0.755536i
$940$	6.95300	+	5.83426i	0.226782	+	0.190293i
$941$	0.601892	+	0.505047i	0.0196211	+	0.0164641i	0.652545	−	0.757750i	$-0.273701\pi$
$941$	0.601892	+	0.505047i	0.0196211	+	0.0164641i	−0.632924	+	0.774214i	$0.718146\pi$
$942$	0.0286994	−	1.10340i	0.000935076	−	0.0359508i
$943$	−2.34520	−	1.35400i	−0.0763703	−	0.0440924i
$944$	6.05686	−	2.20452i	0.197134	−	0.0717509i
$945$	−0.268358	−	2.77168i	−0.00872970	−	0.0901626i
$946$	−1.74094	−	0.306974i	−0.0566028	−	0.00998059i
$947$	−5.55338	+	15.2578i	−0.180461	+	0.495811i	−0.996633	−	0.0819977i	$-0.973870\pi$
$947$	−5.55338	+	15.2578i	−0.180461	+	0.495811i	0.816172	+	0.577809i	$0.196092\pi$
$948$	1.76072	+	11.7671i	0.0571855	+	0.382177i
$949$			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	$-0.203530\pi$
$953$	31.9078	+	11.6135i	1.03359	+	0.376198i	0.231146	+	0.972919i	$0.425753\pi$
$954$	16.3655	−	5.00972i	0.529852	−	0.162196i
$955$	−0.769624	−	4.36476i	−0.0249045	−	0.141240i
$956$	−0.472738	−	1.29884i	−0.0152894	−	0.0420074i
$957$	1.19490	+	2.19981i	0.0386256	+	0.0711097i
$958$	10.3325	−	5.96550i	0.333829	−	0.192736i
$959$	−1.23648	+	1.47358i	−0.0399281	+	0.0475844i
$960$	−1.64245	+	0.549877i	−0.0530098	+	0.0177472i
$961$	9.34712	+	16.1897i	0.301520	+	0.522248i
$962$	−8.71402	+	15.0931i	−0.280951	+	0.486622i
$963$	−13.1883	−	12.2896i	−0.424988	−	0.396028i
$964$	12.4015	−	2.18671i	0.399424	−	0.0704293i
$965$	−3.18381	+	18.0563i	−0.102490	+	0.581252i
$966$	0.169311	−	0.134725i	0.00544749	−	0.00433469i
$967$	−29.4137	+	24.6810i	−0.945881	+	0.793688i	−0.978599	−	0.205777i	$-0.934028\pi$
$967$	−29.4137	+	24.6810i	−0.945881	+	0.793688i	0.0327184	+	0.999465i	$0.489584\pi$
$968$	−10.9274			−0.351220
$969$	3.57761	+	1.43446i	0.114929	+	0.0460814i
$970$	2.14434			0.0688505
$971$	−40.3116	+	33.8254i	−1.29366	+	1.08551i	−0.302457	+	0.953163i	$0.597807\pi$
$971$	−40.3116	+	33.8254i	−1.29366	+	1.08551i	−0.991203	+	0.132347i	$0.957749\pi$
$972$	15.5730	−	0.693657i	0.499505	−	0.0222491i
$973$	−1.29111	+	7.32228i	−0.0413912	+	0.234741i
$974$	−7.51644	+	1.32535i	−0.240842	+	0.0424670i
$975$	−0.656296	+	3.22871i	−0.0210183	+	0.103401i
$976$	5.34486	−	9.25757i	0.171085	−	0.296328i
$977$	−23.3057	−	40.3667i	−0.745617	−	1.29145i	−0.949906	−	0.312536i	$-0.898822\pi$
$977$	−23.3057	−	40.3667i	−0.745617	−	1.29145i	0.204289	−	0.978911i	$-0.434512\pi$
$978$	−6.38757	−	19.0793i	−0.204252	−	0.610089i
$979$	0.180393	−	0.214984i	0.00576538	−	0.00687091i
$980$	−5.81346	+	3.35640i	−0.185704	+	0.107216i
$981$	1.29150	−	24.8103i	0.0412345	−	0.792133i
$982$	12.5691	+	34.5334i	0.401098	+	1.10201i
$983$	−4.50298	−	25.5377i	−0.143623	−	0.814526i	−0.968463	−	0.249159i	$-0.919846\pi$
$983$	−4.50298	−	25.5377i	−0.143623	−	0.814526i	0.824840	−	0.565367i	$-0.191265\pi$
$984$	13.3301	−	15.0723i	0.424949	−	0.480488i
$985$	−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
$990$	−0.744212	−	0.315590i	−0.0236526	−	0.0100301i
$991$	−4.55250	+	12.5079i	−0.144615	+	0.397327i	−0.990760	−	0.135626i	$-0.956695\pi$
$991$	−4.55250	+	12.5079i	−0.144615	+	0.397327i	0.846145	+	0.532953i	$0.178918\pi$
$992$	6.94232	+	1.22412i	0.220419	+	0.0388658i
$993$	−44.7620	−	17.6231i	−1.42048	−	0.559253i
$994$	−3.23146	+	1.17615i	−0.102496	+	0.0373054i
$995$	−2.88774	−	1.66724i	−0.0915475	−	0.0528550i
$996$	−5.08038	−	0.132140i	−0.160978	−	0.00418702i
$997$	30.5216	+	25.6106i	0.966628	+	0.811097i	0.982019	−	0.188785i	$-0.0604548\pi$
$997$	30.5216	+	25.6106i	0.966628	+	0.811097i	−0.0153909	+	0.999882i	$0.504899\pi$
$998$	25.7257	+	21.5864i	0.814331	+	0.683305i
$999$	20.5180	+	42.9585i	0.649161	+	1.35915i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bb.a.41.14	✓	84	19.3	odd	18
570.2.bb.a.431.14	yes	84	3.2	odd	2
570.2.bb.b.41.4	yes	84	57.41	even	18	inner
570.2.bb.b.431.4	yes	84	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.07847 - 1.35533i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.984808 + 0.173648i) q^{5} +(1.69734 + 0.345017i) q^{6} +(-0.267952 + 0.464106i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.673825 + 2.92335i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.07847 - 1.35533i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.984808 + 0.173648i) q^{5} +(1.69734 + 0.345017i) q^{6} +(-0.267952 + 0.464106i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.673825 + 2.92335i) q^{9} +(0.642788 - 0.766044i) q^{10} +(-0.233354 + 0.134727i) q^{11} +(-1.52201 + 0.826731i) q^{12} +(-0.650596 - 1.78750i) q^{13} +(-0.0930587 - 0.527762i) q^{14} +(1.29743 + 1.14746i) 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} +(0.917993 - 0.137360i) q^{21} +(0.0921587 - 0.253204i) q^{22} +(-0.229565 - 0.0404785i) q^{23} +(0.634515 - 1.61164i) q^{24} +(0.939693 - 0.342020i) q^{25} +(1.64737 + 0.951108i) q^{26} +(4.68879 - 2.23948i) q^{27} +(0.410526 + 0.344472i) q^{28} +(4.10900 + 3.44786i) q^{29} +(-1.73147 - 0.0450352i) q^{30} +(6.10497 + 3.52471i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.434263 + 0.170973i) q^{33} +(-0.502781 - 0.0886538i) q^{34} +(0.183290 - 0.503585i) q^{35} +(2.76193 + 1.17122i) 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} +(-0.614930 + 0.695298i) q^{42} +(-1.13925 - 6.46098i) q^{43} +(0.0921587 + 0.253204i) q^{44} +(0.155954 - 2.99594i) q^{45} +(0.201876 - 0.116553i) q^{46} +(5.83426 - 6.95300i) q^{47} +(0.549877 + 1.64245i) q^{48} +(3.35640 + 5.81346i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.176144 - 0.866555i) q^{51} +(-1.87332 + 0.330316i) q^{52} +(-0.990668 + 5.61836i) q^{53} +(-2.15231 + 4.72943i) q^{54} +(0.206414 - 0.173202i) q^{55} -0.535904 q^{56} +(6.65671 - 3.56204i) q^{57} -5.36392 q^{58} +(-4.93759 + 4.14313i) q^{59} +(1.35533 - 1.07847i) q^{60} +(-1.85625 + 10.5273i) q^{61} +(-6.94232 + 1.22412i) q^{62} +(-1.17619 - 1.09604i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.951108 + 1.64737i) q^{65} +(-0.442564 + 0.148166i) q^{66} +(-3.68533 + 4.39200i) q^{67} +(0.442138 - 0.255268i) q^{68} +(0.192716 + 0.354790i) q^{69} +(0.183290 + 0.503585i) q^{70} +(-1.11428 - 6.31942i) q^{71} +(-2.86861 + 0.878124i) 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} +(-0.487566 - 3.25846i) q^{78} +(2.34946 - 6.45509i) q^{79} +(0.984808 + 0.173648i) q^{80} +(-8.09192 - 3.93965i) q^{81} +(-10.9164 + 3.97326i) q^{82} +(2.54105 + 1.46708i) q^{83} +(0.0241345 - 0.927898i) q^{84} +(-0.391094 - 0.328167i) q^{85} +(5.02575 + 4.21711i) q^{86} +(0.241565 - 9.28744i) q^{87} +(-0.233354 - 0.134727i) q^{88} +(-0.978707 + 0.356220i) q^{89} +(1.80629 + 2.39527i) q^{90} +(1.00392 + 0.177018i) q^{91} +(-0.0797270 + 0.219048i) q^{92} +(-1.80687 - 12.0755i) 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} +(-0.236614 - 0.772957i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{6} + 42 q^{8}+O(q^{10}) \) 84 * q - 6 * q^6 + 42 * q^8	\( 84 q - 6 q^{6} + 42 q^{8} + 24 q^{13} - 24 q^{14} + 12 q^{17} - 12 q^{19} + 36 q^{22} + 24 q^{27} - 12 q^{28} - 12 q^{29} + 36 q^{33} + 12 q^{34} + 6 q^{36} + 18 q^{38} + 12 q^{39} + 6 q^{41} + 24 q^{43} + 36 q^{44} + 12 q^{47} - 12 q^{48} - 54 q^{49} - 42 q^{50} + 96 q^{51} + 12 q^{52} - 60 q^{53} - 18 q^{54} - 96 q^{57} - 24 q^{58} - 18 q^{59} - 48 q^{61} - 12 q^{62} - 114 q^{63} - 42 q^{64} - 24 q^{66} + 6 q^{67} - 54 q^{68} - 48 q^{69} + 48 q^{71} + 84 q^{73} + 24 q^{74} - 12 q^{79} - 36 q^{81} - 6 q^{82} + 36 q^{83} + 18 q^{84} + 12 q^{86} + 6 q^{87} - 12 q^{89} - 24 q^{90} + 24 q^{91} - 6 q^{93} - 12 q^{95} - 42 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) \) 84 * q - 6 * q^6 + 42 * q^8 + 24 * q^13 - 24 * q^14 + 12 * q^17 - 12 * q^19 + 36 * q^22 + 24 * q^27 - 12 * q^28 - 12 * q^29 + 36 * q^33 + 12 * q^34 + 6 * q^36 + 18 * q^38 + 12 * q^39 + 6 * q^41 + 24 * q^43 + 36 * q^44 + 12 * q^47 - 12 * q^48 - 54 * q^49 - 42 * q^50 + 96 * q^51 + 12 * q^52 - 60 * q^53 - 18 * q^54 - 96 * q^57 - 24 * q^58 - 18 * q^59 - 48 * q^61 - 12 * q^62 - 114 * q^63 - 42 * q^64 - 24 * q^66 + 6 * q^67 - 54 * q^68 - 48 * q^69 + 48 * q^71 + 84 * q^73 + 24 * q^74 - 12 * q^79 - 36 * q^81 - 6 * q^82 + 36 * q^83 + 18 * q^84 + 12 * q^86 + 6 * q^87 - 12 * q^89 - 24 * q^90 + 24 * q^91 - 6 * q^93 - 12 * q^95 - 42 * q^97 + 36 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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