LMFDB - Embedded newform 570.2.bh.b.13.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(13,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("570.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bh (of order $36$, degree $12$, 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:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			13.9
Character	$\chi$	$=$	570.13
Dual form			570.2.bh.b.307.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.996195 + 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(1.74492 + 1.39830i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(0.637980 + 2.38097i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +O(q^{10})$	\(q+(0.996195 + 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(1.74492 + 1.39830i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(0.637980 + 2.38097i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +(1.61641 + 1.54506i) q^{10} +(-0.937744 - 1.62422i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(-0.546408 + 1.17178i) q^{13} +(0.428037 + 2.42752i) q^{14} +(-2.17238 - 0.529853i) q^{15} +(0.939693 + 0.342020i) q^{16} +(-0.538672 + 6.15705i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-3.32547 - 2.81803i) q^{19} +(1.47560 + 1.68006i) q^{20} +(-1.58445 - 1.88827i) q^{21} +(-0.792616 - 1.69977i) q^{22} +(5.75775 - 4.03162i) q^{23} +(-0.984808 + 0.173648i) q^{24} +(1.08952 + 4.87985i) q^{25} +(-0.646456 + 1.11969i) q^{26} +(-0.258819 + 0.965926i) q^{27} +(0.214836 + 2.45559i) q^{28} +(-1.05098 - 0.881877i) q^{29} +(-2.11794 - 0.717173i) q^{30} +(1.76472 + 1.01886i) q^{31} +(0.906308 + 0.422618i) q^{32} +(1.53631 + 1.07574i) q^{33} +(-1.07324 + 6.08667i) q^{34} +(-2.21609 + 5.04670i) q^{35} +(0.766044 - 0.642788i) q^{36} +(-0.402885 - 0.402885i) q^{37} +(-3.06720 - 3.09714i) q^{38} -1.29291i q^{39} +(1.32356 + 1.80227i) q^{40} +(-3.91035 + 10.7436i) q^{41} +(-1.41385 - 2.01918i) q^{42} +(3.03339 - 4.33212i) q^{43} +(-0.641455 - 1.76238i) q^{44} +(2.19277 - 0.437879i) q^{45} +(6.08722 - 3.51446i) q^{46} +(6.69108 - 0.585394i) q^{47} +(-0.996195 + 0.0871557i) q^{48} +(0.800160 - 0.461973i) q^{49} +(0.660064 + 4.95624i) q^{50} +(-2.11388 - 5.80783i) q^{51} +(-0.741584 + 1.05909i) q^{52} +(-2.17155 - 3.10130i) q^{53} +(-0.342020 + 0.939693i) q^{54} +(0.634855 - 4.14539i) q^{55} +2.46497i q^{56} +(4.20485 + 1.14860i) q^{57} +(-0.970120 - 0.970120i) q^{58} +(4.45848 - 3.74111i) q^{59} +(-2.04737 - 0.899034i) q^{60} +(1.07892 - 6.11887i) q^{61} +(1.66921 + 1.16879i) q^{62} +(2.23402 + 1.04174i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-2.59193 + 1.28062i) q^{65} +(1.43671 + 1.20554i) q^{66} +(-0.367966 - 4.20587i) q^{67} +(-1.59965 + 5.96997i) q^{68} +(-3.51446 + 6.08722i) q^{69} +(-2.64750 + 4.83436i) q^{70} +(1.11437 - 0.196494i) q^{71} +(0.819152 - 0.573576i) q^{72} +(-5.26499 - 11.2908i) q^{73} +(-0.366238 - 0.436466i) q^{74} +(-3.04975 - 3.96220i) q^{75} +(-2.78560 - 3.35268i) q^{76} +(3.26897 - 3.26897i) q^{77} +(0.112685 - 1.28799i) q^{78} +(-14.0174 - 5.10192i) q^{79} +(1.16145 + 1.91077i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(-4.83184 + 10.3619i) q^{82} +(6.42370 - 1.72123i) q^{83} +(-1.23248 - 2.13472i) q^{84} +(-9.54934 + 9.99035i) q^{85} +(3.39941 - 4.05126i) q^{86} +(1.32521 + 0.355089i) q^{87} +(-0.485412 - 1.81158i) q^{88} +(-1.97835 + 0.720059i) q^{89} +(2.22259 - 0.245100i) q^{90} +(-3.13857 - 0.553414i) q^{91} +(6.37036 - 2.97055i) q^{92} +(-2.02997 - 0.177599i) q^{93} +6.71664 q^{94} +(-1.86224 - 9.56724i) q^{95} -1.00000 q^{96} +(6.62135 + 0.579293i) q^{97} +(0.837379 - 0.390476i) q^{98} +(-1.84700 - 0.325675i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{5} + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^5 + 12 * q^7	$ 120 q + 12 q^{5} + 12 q^{7} + 12 q^{10} - 48 q^{13} - 12 q^{17} + 60 q^{21} + 12 q^{22} + 48 q^{23} + 12 q^{25} + 12 q^{26} - 12 q^{30} + 24 q^{33} - 24 q^{38} - 36 q^{41} + 24 q^{43} + 96 q^{47} + 24 q^{52} - 36 q^{55} + 12 q^{57} - 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} - 24 q^{66} + 72 q^{67} + 12 q^{68} + 96 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} - 12 q^{80} - 24 q^{82} - 60 q^{83} - 36 q^{85} - 72 q^{86} + 12 q^{87} - 144 q^{91} - 12 q^{92} + 48 q^{93} + 156 q^{95} - 120 q^{96} - 216 q^{97} - 96 q^{98}+O(q^{100}) $ 120 * q + 12 * q^5 + 12 * q^7 + 12 * q^10 - 48 * q^13 - 12 * q^17 + 60 * q^21 + 12 * q^22 + 48 * q^23 + 12 * q^25 + 12 * q^26 - 12 * q^30 + 24 * q^33 - 24 * q^38 - 36 * q^41 + 24 * q^43 + 96 * q^47 + 24 * q^52 - 36 * q^55 + 12 * q^57 - 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 - 24 * q^66 + 72 * q^67 + 12 * q^68 + 96 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 - 12 * q^80 - 24 * q^82 - 60 * q^83 - 36 * q^85 - 72 * q^86 + 12 * q^87 - 144 * q^91 - 12 * q^92 + 48 * q^93 + 156 * q^95 - 120 * q^96 - 216 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$3$	−0.906308	+	0.422618i	−0.523257	+	0.243999i
$3$	−0.906308	+	0.422618i	−0.523257	+	0.243999i
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	1.74492	+	1.39830i	0.780354	+	0.625339i
$5$	1.74492	+	1.39830i	0.780354	+	0.625339i
$6$	−0.939693	+	0.342020i	−0.383628	+	0.139629i
$7$	0.637980	+	2.38097i	0.241134	+	0.899924i	0.975287	+	0.220940i	$0.0709125\pi$
$7$	0.637980	+	2.38097i	0.241134	+	0.899924i	−0.734154	+	0.678983i	$0.762421\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$	0.642788	−	0.766044i	0.214263	−	0.255348i
$10$	1.61641	+	1.54506i	0.511155	+	0.488590i
$11$	−0.937744	−	1.62422i	−0.282741	−	0.489721i	0.689318	−	0.724459i	$-0.257910\pi$
$11$	−0.937744	−	1.62422i	−0.282741	−	0.489721i	−0.972059	+	0.234738i	$0.924577\pi$
$12$	−0.965926	+	0.258819i	−0.278839	+	0.0747146i
$13$	−0.546408	+	1.17178i	−0.151546	+	0.324992i	−0.967395	−	0.253274i	$-0.918493\pi$
$13$	−0.546408	+	1.17178i	−0.151546	+	0.324992i	0.815848	+	0.578266i	$0.196270\pi$
$14$	0.428037	+	2.42752i	0.114398	+	0.648781i
$15$	−2.17238	−	0.529853i	−0.560907	−	0.136807i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−0.538672	+	6.15705i	−0.130647	+	1.49330i	0.594158	+	0.804349i	$0.297486\pi$
$17$	−0.538672	+	6.15705i	−0.130647	+	1.49330i	−0.724805	+	0.688954i	$0.758070\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	−3.32547	−	2.81803i	−0.762914	−	0.646500i
$19$	−3.32547	−	2.81803i	−0.762914	−	0.646500i
$20$	1.47560	+	1.68006i	0.329955	+	0.375673i
$21$	−1.58445	−	1.88827i	−0.345755	−	0.412055i
$22$	−0.792616	−	1.69977i	−0.168986	−	0.362392i
$23$	5.75775	−	4.03162i	1.20057	−	0.840651i	0.210009	−	0.977699i	$-0.432651\pi$
$23$	5.75775	−	4.03162i	1.20057	−	0.840651i	0.990564	+	0.137049i	$0.0437618\pi$
$24$	−0.984808	+	0.173648i	−0.201023	+	0.0354458i
$25$	1.08952	+	4.87985i	0.217903	+	0.975970i
$26$	−0.646456	+	1.11969i	−0.126780	+	0.219590i
$27$	−0.258819	+	0.965926i	−0.0498097	+	0.185893i
$28$	0.214836	+	2.45559i	0.0406002	+	0.464062i
$29$	−1.05098	−	0.881877i	−0.195162	−	0.163760i	0.539970	−	0.841684i	$-0.318436\pi$
$29$	−1.05098	−	0.881877i	−0.195162	−	0.163760i	−0.735132	+	0.677924i	$0.762880\pi$
$30$	−2.11794	−	0.717173i	−0.386681	−	0.130937i
$31$	1.76472	+	1.01886i	0.316953	+	0.182993i	0.650034	−	0.759905i	$-0.274755\pi$
$31$	1.76472	+	1.01886i	0.316953	+	0.182993i	−0.333080	+	0.942898i	$0.608088\pi$
$32$	0.906308	+	0.422618i	0.160214	+	0.0747091i
$33$	1.53631	+	1.07574i	0.267437	+	0.187262i
$34$	−1.07324	+	6.08667i	−0.184060	+	1.04385i
$35$	−2.21609	+	5.04670i	−0.374587	+	0.853049i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	−0.402885	−	0.402885i	−0.0662339	−	0.0662339i	0.673214	−	0.739448i	$-0.264913\pi$
$37$	−0.402885	−	0.402885i	−0.0662339	−	0.0662339i	−0.739448	+	0.673214i	$0.764913\pi$
$38$	−3.06720	−	3.09714i	−0.497566	−	0.502422i
$39$		−	1.29291i		−	0.207032i
$40$	1.32356	+	1.80227i	0.209273	+	0.284964i
$41$	−3.91035	+	10.7436i	−0.610695	+	1.67787i	0.117985	+	0.993015i	$0.462356\pi$
$41$	−3.91035	+	10.7436i	−0.610695	+	1.67787i	−0.728680	+	0.684854i	$0.759866\pi$
$42$	−1.41385	−	2.01918i	−0.218161	−	0.311566i
$43$	3.03339	−	4.33212i	0.462587	−	0.660643i	−0.518305	−	0.855196i	$-0.673437\pi$
$43$	3.03339	−	4.33212i	0.462587	−	0.660643i	0.980892	+	0.194553i	$0.0623257\pi$
$44$	−0.641455	−	1.76238i	−0.0967030	−	0.265689i
$45$	2.19277	−	0.437879i	0.326880	−	0.0652752i
$46$	6.08722	−	3.51446i	0.897511	−	0.518178i
$47$	6.69108	−	0.585394i	0.975995	−	0.0853885i	0.412015	−	0.911177i	$-0.364825\pi$
$47$	6.69108	−	0.585394i	0.975995	−	0.0853885i	0.563980	+	0.825789i	$0.309270\pi$
$48$	−0.996195	+	0.0871557i	−0.143788	+	0.0125798i
$49$	0.800160	−	0.461973i	0.114309	−	0.0659961i
$50$	0.660064	+	4.95624i	0.0933471	+	0.700918i
$51$	−2.11388	−	5.80783i	−0.296002	−	0.813259i
$52$	−0.741584	+	1.05909i	−0.102839	+	0.146870i
$53$	−2.17155	−	3.10130i	−0.298286	−	0.425996i	0.641832	−	0.766845i	$-0.278174\pi$
$53$	−2.17155	−	3.10130i	−0.298286	−	0.425996i	−0.940118	+	0.340849i	$0.889286\pi$
$54$	−0.342020	+	0.939693i	−0.0465430	+	0.127876i
$55$	0.634855	−	4.14539i	0.0856038	−	0.558964i
$56$			2.46497i			0.329395i
$57$	4.20485	+	1.14860i	0.556945	+	0.152135i
$58$	−0.970120	−	0.970120i	−0.127383	−	0.127383i
$59$	4.45848	−	3.74111i	0.580444	−	0.487051i	−0.304649	−	0.952465i	$-0.598539\pi$
$59$	4.45848	−	3.74111i	0.580444	−	0.487051i	0.885093	+	0.465414i	$0.154095\pi$
$60$	−2.04737	−	0.899034i	−0.264315	−	0.116065i
$61$	1.07892	−	6.11887i	0.138142	−	0.783441i	−0.834479	−	0.551040i	$-0.814231\pi$
$61$	1.07892	−	6.11887i	0.138142	−	0.783441i	0.972620	−	0.232400i	$-0.0746579\pi$
$62$	1.66921	+	1.16879i	0.211989	+	0.148437i
$63$	2.23402	+	1.04174i	0.281460	+	0.131247i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−2.59193	+	1.28062i	−0.321490	+	0.158841i
$66$	1.43671	+	1.20554i	0.176846	+	0.148392i
$67$	−0.367966	−	4.20587i	−0.0449542	−	0.513829i	−0.984973	−	0.172707i	$-0.944749\pi$
$67$	−0.367966	−	4.20587i	−0.0449542	−	0.513829i	0.940019	−	0.341122i	$-0.110807\pi$
$68$	−1.59965	+	5.96997i	−0.193986	+	0.723965i
$69$	−3.51446	+	6.08722i	−0.423091	+	0.732815i
$70$	−2.64750	+	4.83436i	−0.316437	+	0.577816i
$71$	1.11437	−	0.196494i	0.132251	−	0.0233195i	−0.107131	−	0.994245i	$-0.534166\pi$
$71$	1.11437	−	0.196494i	0.132251	−	0.0233195i	0.239382	+	0.970925i	$0.423055\pi$
$72$	0.819152	−	0.573576i	0.0965380	−	0.0675966i
$73$	−5.26499	−	11.2908i	−0.616220	−	1.32149i	−0.928441	−	0.371479i	$-0.878851\pi$
$73$	−5.26499	−	11.2908i	−0.616220	−	1.32149i	0.312221	−	0.950010i	$-0.398927\pi$
$74$	−0.366238	−	0.436466i	−0.0425744	−	0.0507381i
$75$	−3.04975	−	3.96220i	−0.352155	−	0.457515i
$76$	−2.78560	−	3.35268i	−0.319530	−	0.384578i
$77$	3.26897	−	3.26897i	0.372533	−	0.372533i
$78$	0.112685	−	1.28799i	0.0127590	−	0.145836i
$79$	−14.0174	−	5.10192i	−1.57708	−	0.574011i	−0.602515	−	0.798107i	$-0.705835\pi$
$79$	−14.0174	−	5.10192i	−1.57708	−	0.574011i	−0.974567	+	0.224096i	$0.928057\pi$
$80$	1.16145	+	1.91077i	0.129854	+	0.213631i
$81$	−0.173648	−	0.984808i	−0.0192942	−	0.109423i
$82$	−4.83184	+	10.3619i	−0.533588	+	1.14428i
$83$	6.42370	−	1.72123i	0.705093	−	0.188929i	0.111582	−	0.993755i	$-0.464408\pi$
$83$	6.42370	−	1.72123i	0.705093	−	0.188929i	0.593511	+	0.804826i	$0.297741\pi$
$84$	−1.23248	−	2.13472i	−0.134475	−	0.232917i
$85$	−9.54934	+	9.99035i	−1.03577	+	1.08361i
$86$	3.39941	−	4.05126i	0.366568	−	0.436859i
$87$	1.32521	+	0.355089i	0.142077	+	0.0380695i
$88$	−0.485412	−	1.81158i	−0.0517451	−	0.193115i
$89$	−1.97835	+	0.720059i	−0.209704	+	0.0763261i	−0.444736	−	0.895661i	$-0.646703\pi$
$89$	−1.97835	+	0.720059i	−0.209704	+	0.0763261i	0.235032	+	0.971988i	$0.424480\pi$
$90$	2.22259	−	0.245100i	0.234282	−	0.0258358i
$91$	−3.13857	−	0.553414i	−0.329011	−	0.0580135i
$92$	6.37036	−	2.97055i	0.664156	−	0.309701i
$93$	−2.02997	−	0.177599i	−0.210498	−	0.0184162i
$94$	6.71664			0.692769
$95$	−1.86224	−	9.56724i	−0.191062	−	0.981578i
$96$	−1.00000			−0.102062
$97$	6.62135	+	0.579293i	0.672296	+	0.0588183i	0.418192	−	0.908359i	$-0.362664\pi$
$97$	6.62135	+	0.579293i	0.672296	+	0.0588183i	0.254104	+	0.967177i	$0.418219\pi$
$98$	0.837379	−	0.390476i	0.0845880	−	0.0394440i
$99$	−1.84700	−	0.325675i	−0.185630	−	0.0327316i
$100$	0.225587	+	4.99491i	0.0225587	+	0.499491i
$101$	−2.08712	+	0.759650i	−0.207676	+	0.0755880i	−0.443764	−	0.896144i	$-0.646357\pi$
$101$	−2.08712	+	0.759650i	−0.207676	+	0.0755880i	0.236087	+	0.971732i	$0.424135\pi$
$102$	−1.59965	−	5.96997i	−0.158389	−	0.591115i
$103$	−18.4292	−	4.93809i	−1.81588	−	0.486565i	−0.819619	−	0.572908i	$-0.805815\pi$
$103$	−18.4292	−	4.93809i	−1.81588	−	0.486565i	−0.996265	+	0.0863435i	$0.972482\pi$
$104$	−0.831068	+	0.990428i	−0.0814929	+	0.0971194i
$105$	−0.124372	−	5.51043i	−0.0121374	−	0.537763i
$106$	−1.89299	−	3.27876i	−0.183864	−	0.318461i
$107$	12.1049	−	3.24349i	1.17022	−	0.313560i	0.379180	−	0.925323i	$-0.376206\pi$
$107$	12.1049	−	3.24349i	1.17022	−	0.313560i	0.791041	+	0.611763i	$0.209540\pi$
$108$	−0.422618	+	0.906308i	−0.0406665	+	0.0872095i
$109$	−1.07660	−	6.10573i	−0.103120	−	0.584822i	−0.991955	−	0.126594i	$-0.959595\pi$
$109$	−1.07660	−	6.10573i	−0.103120	−	0.584822i	0.888835	−	0.458228i	$-0.151516\pi$
$110$	0.993734	−	4.07428i	0.0947488	−	0.388468i
$111$	0.535405	+	0.194871i	0.0508184	+	0.0184964i
$112$	−0.214836	+	2.45559i	−0.0203001	+	0.232031i
$113$	6.02651	−	6.02651i	0.566926	−	0.566926i	−0.364340	−	0.931266i	$-0.618705\pi$
$113$	6.02651	−	6.02651i	0.566926	−	0.566926i	0.931266	+	0.364340i	$0.118705\pi$
$114$	4.08874	+	1.51070i	0.382945	+	0.141490i
$115$	15.6842	+	1.01619i	1.46256	+	0.0947602i
$116$	−0.881877	−	1.05098i	−0.0818802	−	0.0975811i
$117$	0.546408	+	1.17178i	0.0505155	+	0.108331i
$118$	4.76757	−	3.33829i	0.438891	−	0.307314i
$119$	−15.0034	+	2.64551i	−1.37536	+	0.242513i
$120$	−1.96123	−	1.07405i	−0.179035	−	0.0980472i
$121$	3.74127	−	6.48007i	0.340116	−	0.589097i
$122$	1.60811	−	6.00155i	0.145591	−	0.543355i
$123$	−0.996461	−	11.3896i	−0.0898479	−	1.02697i
$124$	1.56099	+	1.30982i	0.140181	+	0.117626i
$125$	−4.92237	+	10.0384i	−0.440270	+	0.897865i
$126$	2.13472	+	1.23248i	0.190176	+	0.109798i
$127$	−8.81880	−	4.11227i	−0.782542	−	0.364905i	−0.0100659	−	0.999949i	$-0.503204\pi$
$127$	−8.81880	−	4.11227i	−0.782542	−	0.364905i	−0.772476	+	0.635044i	$0.780982\pi$
$128$	0.819152	+	0.573576i	0.0724035	+	0.0506975i
$129$	−0.918346	+	5.20820i	−0.0808559	+	0.458557i
$130$	−2.69368	+	1.04984i	−0.236252	+	0.0920773i
$131$	−9.70206	+	8.14099i	−0.847673	+	0.711282i	−0.959276	−	0.282471i	$-0.908846\pi$
$131$	−9.70206	+	8.14099i	−0.847673	+	0.711282i	0.111603	+	0.993753i	$0.464401\pi$
$132$	1.32617	+	1.32617i	0.115428	+	0.115428i
$133$	4.58807	−	9.71569i	0.397836	−	0.842457i
$134$		−	4.22194i		−	0.364720i
$135$	−1.80227	+	1.32356i	−0.155115	+	0.113914i
$136$	−2.11388	+	5.80783i	−0.181264	+	0.498017i
$137$	6.45813	+	9.22316i	0.551755	+	0.787988i	0.994055	−	0.108879i	$-0.0347262\pi$
$137$	6.45813	+	9.22316i	0.551755	+	0.787988i	−0.442300	+	0.896867i	$0.645837\pi$
$138$	−4.03162	+	5.75775i	−0.343194	+	0.490132i
$139$	−5.58207	−	15.3366i	−0.473465	−	1.30084i	−0.914950	−	0.403567i	$-0.867770\pi$
$139$	−5.58207	−	15.3366i	−0.473465	−	1.30084i	0.441485	−	0.897269i	$-0.354452\pi$
$140$	−3.05877	+	4.58521i	−0.258513	+	0.387521i
$141$	−5.81678	+	3.35832i	−0.489861	+	0.282822i
$142$	1.12726	−	0.0986221i	0.0945972	−	0.00827618i
$143$	2.41561	−	0.211339i	0.202004	−	0.0176730i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$	−0.600752	−	3.00839i	−0.0498897	−	0.249833i
$146$	−4.26090	−	11.7067i	−0.352634	−	0.968855i
$147$	−0.529953	+	0.756852i	−0.0437098	+	0.0624241i
$148$	−0.326804	−	0.466725i	−0.0268631	−	0.0383646i
$149$	6.32346	−	17.3736i	0.518038	−	1.42330i	−0.354641	−	0.935002i	$-0.615397\pi$
$149$	6.32346	−	17.3736i	0.518038	−	1.42330i	0.872679	−	0.488294i	$-0.162381\pi$
$150$	−2.69282	−	4.21292i	−0.219868	−	0.343984i
$151$		−	12.1643i		−	0.989917i	−0.868917	−	0.494959i	$-0.835183\pi$
$151$		−	12.1643i		−	0.989917i	0.868917	−	0.494959i	$-0.164817\pi$
$152$	−2.48279	−	3.58270i	−0.201381	−	0.290595i
$153$	4.37032	+	4.37032i	0.353319	+	0.353319i
$154$	3.54143	−	2.97162i	0.285377	−	0.239460i
$155$	1.65463	+	4.24544i	0.132903	+	0.341002i
$156$	0.224512	−	1.27327i	0.0179753	−	0.101943i
$157$	9.51430	+	6.66198i	0.759324	+	0.531684i	0.887912	−	0.460014i	$-0.152156\pi$
$157$	9.51430	+	6.66198i	0.759324	+	0.531684i	−0.128588	+	0.991698i	$0.541045\pi$
$158$	−13.5194	−	6.30420i	−1.07555	−	0.501536i
$159$	3.27876	+	1.89299i	0.260023	+	0.150124i
$160$	0.990491	+	2.00473i	0.0783052	+	0.158488i
$161$	13.2725	+	11.1370i	1.04602	+	0.877715i
$162$	−0.0871557	−	0.996195i	−0.00684760	−	0.0782684i
$163$	−2.87479	+	10.7289i	−0.225171	+	0.840349i	0.757165	+	0.653223i	$0.226584\pi$
$163$	−2.87479	+	10.7289i	−0.225171	+	0.840349i	−0.982336	+	0.187125i	$0.940083\pi$
$164$	−5.71655	+	9.90136i	−0.446388	+	0.773167i
$165$	1.17654	+	4.02530i	0.0915938	+	0.313369i
$166$	6.54927	−	1.15481i	0.508322	−	0.0896309i
$167$	9.54248	−	6.68172i	0.738419	−	0.517047i	−0.142802	−	0.989751i	$-0.545611\pi$
$167$	9.54248	−	6.68172i	0.738419	−	0.517047i	0.881221	+	0.472705i	$0.156722\pi$
$168$	−1.04174	−	2.23402i	−0.0803719	−	0.172358i
$169$	7.28174	+	8.67804i	0.560134	+	0.667542i
$170$	−10.3837	+	9.12005i	−0.796394	+	0.699476i
$171$	−4.29630	+	0.736063i	−0.328546	+	0.0562881i
$172$	3.73957	−	3.73957i	0.285139	−	0.285139i
$173$	−0.925839	+	10.5824i	−0.0703903	+	0.804564i	0.876163	+	0.482016i	$0.160095\pi$
$173$	−0.925839	+	10.5824i	−0.0703903	+	0.804564i	−0.946553	+	0.322549i	$0.895460\pi$
$174$	1.28922	+	0.469237i	0.0977354	+	0.0355728i
$175$	−10.9237	+	5.70736i	−0.825755	+	0.431436i
$176$	−0.325675	−	1.84700i	−0.0245487	−	0.139223i
$177$	−2.45969	+	5.27483i	−0.184882	+	0.396480i
$178$	−2.03358	+	0.544895i	−0.152423	+	0.0408416i
$179$	11.2192	+	19.4322i	0.838563	+	1.45243i	0.891096	+	0.453815i	$0.149937\pi$
$179$	11.2192	+	19.4322i	0.838563	+	1.45243i	−0.0525331	+	0.998619i	$0.516730\pi$
$180$	2.23550	−	0.0504557i	0.166624	−	0.00376075i
$181$	4.32849	−	5.15850i	0.321734	−	0.383428i	−0.580800	−	0.814046i	$-0.697260\pi$
$181$	4.32849	−	5.15850i	0.321734	−	0.383428i	0.902534	+	0.430618i	$0.141705\pi$
$182$	−3.07839	−	0.824852i	−0.228185	−	0.0611421i
$183$	1.60811	+	6.00155i	0.118875	+	0.443647i
$184$	6.60502	−	2.40403i	0.486928	−	0.177227i
$185$	−0.139650	−	1.26636i	−0.0102673	−	0.0931045i
$186$	−2.00677	−	0.353847i	−0.147143	−	0.0259453i
$187$	10.5055	−	4.89881i	0.768241	−	0.358237i
$188$	6.69108	+	0.585394i	0.487997	+	0.0426942i
$189$	−2.46497			−0.179300
$190$	−1.02131	−	9.69314i	−0.0740939	−	0.703214i
$191$	7.52598			0.544561			0.272280	−	0.962218i	$-0.412222\pi$
$191$	7.52598			0.544561			0.272280	+	0.962218i	$0.412222\pi$
$192$	−0.996195	−	0.0871557i	−0.0718942	−	0.00628992i
$193$	−21.2975	+	9.93117i	−1.53302	+	0.714861i	−0.992011	−	0.126153i	$-0.959737\pi$
$193$	−21.2975	+	9.93117i	−1.53302	+	0.714861i	−0.541014	+	0.841014i	$0.681959\pi$
$194$	6.54566	+	1.15418i	0.469951	+	0.0828651i
$195$	1.80788	−	2.25603i	0.129465	−	0.161558i
$196$	0.868224	−	0.316008i	0.0620160	−	0.0225720i
$197$	3.47427	+	12.9661i	0.247531	+	0.923800i	0.972094	+	0.234591i	$0.0753751\pi$
$197$	3.47427	+	12.9661i	0.247531	+	0.923800i	−0.724563	+	0.689209i	$0.757958\pi$
$198$	−1.81158	−	0.485412i	−0.128744	−	0.0344967i
$199$	−8.83073	+	10.5241i	−0.625994	+	0.746031i	−0.982089	−	0.188419i	$-0.939664\pi$
$199$	−8.83073	+	10.5241i	−0.625994	+	0.746031i	0.356095	+	0.934450i	$0.384108\pi$
$200$	−0.210606	+	4.99556i	−0.0148921	+	0.353240i
$201$	2.11097	+	3.65630i	0.148896	+	0.257896i
$202$	−2.14539	+	0.574855i	−0.150949	+	0.0404466i
$203$	1.42922	−	3.06498i	0.100312	−	0.215119i
$204$	−1.07324	−	6.08667i	−0.0751421	−	0.426152i
$205$	−21.8460	+	13.2789i	−1.52579	+	0.927441i
$206$	−17.9287	−	6.52552i	−1.24915	−	0.454654i
$207$	0.612610	−	7.00216i	0.0425793	−	0.486684i
$208$	−0.914227	+	0.914227i	−0.0633902	+	0.0633902i
$209$	−1.45866	+	8.04388i	−0.100898	+	0.556407i
$210$	0.356367	−	5.50030i	0.0245917	−	0.379557i
$211$	−0.698434	−	0.832361i	−0.0480822	−	0.0573021i	0.741467	−	0.670989i	$-0.234130\pi$
$211$	−0.698434	−	0.832361i	−0.0480822	−	0.0573021i	−0.789550	+	0.613687i	$0.789686\pi$
$212$	−1.60003	−	3.43127i	−0.109890	−	0.235661i
$213$	−0.926921	+	0.649037i	−0.0635116	+	0.0444713i
$214$	12.3415	−	2.17614i	0.843646	−	0.148758i
$215$	11.3506	−	3.31764i	0.774107	−	0.226261i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	−1.30003	+	4.85177i	−0.0882516	+	0.329359i
$218$	−0.540358	−	6.17632i	−0.0365977	−	0.418313i
$219$	9.54340	+	8.00786i	0.644883	+	0.541121i
$220$	1.34505	−	3.97217i	0.0906832	−	0.267804i
$221$	−6.92034	−	3.99546i	−0.465513	−	0.268764i
$222$	0.516383	+	0.240793i	0.0346574	+	0.0161610i
$223$	14.6776	+	10.2774i	0.982886	+	0.688224i	0.950330	−	0.311245i	$-0.100746\pi$
$223$	14.6776	+	10.2774i	0.982886	+	0.688224i	0.0325568	+	0.999470i	$0.489635\pi$
$224$	−0.428037	+	2.42752i	−0.0285994	+	0.162195i
$225$	4.43851	+	2.30209i	0.295901	+	0.153473i
$226$	6.52882	−	5.47833i	0.434291	−	0.364413i
$227$	−18.4252	−	18.4252i	−1.22293	−	1.22293i	−0.966587	−	0.256340i	$-0.917483\pi$
$227$	−18.4252	−	18.4252i	−1.22293	−	1.22293i	−0.256340	−	0.966587i	$-0.582517\pi$
$228$	3.94151	+	1.86131i	0.261033	+	0.123268i
$229$			1.70653i			0.112770i	0.998409	+	0.0563852i	$0.0179575\pi$
$229$			1.70653i			0.112770i	−0.998409	+	0.0563852i	$0.982042\pi$
$230$	15.5360	+	2.37929i	1.02441	+	0.156886i
$231$	−1.58116	+	4.34421i	−0.104033	+	0.285828i
$232$	−0.786922	−	1.12384i	−0.0516640	−	0.0737838i
$233$	6.36818	−	9.09470i	0.417193	−	0.595814i	−0.554464	−	0.832208i	$-0.687077\pi$
$233$	6.36818	−	9.09470i	0.417193	−	0.595814i	0.971657	+	0.236394i	$0.0759656\pi$
$234$	0.442202	+	1.21494i	0.0289076	+	0.0794231i
$235$	12.4940	+	8.33467i	0.815018	+	0.543694i
$236$	5.04038	−	2.91006i	0.328101	−	0.189429i
$237$	14.8603	−	1.30010i	0.965277	−	0.0844508i
$238$	−15.1769	+	1.32781i	−0.983773	+	0.0860690i
$239$	−19.3878	+	11.1935i	−1.25409	+	0.724050i	−0.971919	−	0.235314i	$-0.924388\pi$
$239$	−19.3878	+	11.1935i	−1.25409	+	0.724050i	−0.282172	+	0.959364i	$0.591055\pi$
$240$	−1.86015	−	1.24090i	−0.120072	−	0.0800996i
$241$	−5.41041	−	14.8650i	−0.348515	−	0.957538i	−0.982838	−	0.184470i	$-0.940943\pi$
$241$	−5.41041	−	14.8650i	−0.348515	−	0.957538i	0.634323	−	0.773068i	$-0.281279\pi$
$242$	4.29181	−	6.12934i	0.275888	−	0.394009i
$243$	0.573576	+	0.819152i	0.0367949	+	0.0525486i
$244$	2.12506	−	5.83855i	0.136043	−	0.373775i
$245$	2.04219	+	0.312756i	0.130471	+	0.0199813i
$246$		−	11.4331i		−	0.728948i
$247$	5.11916	−	2.35691i	0.325724	−	0.149967i
$248$	1.44089	+	1.44089i	0.0914965	+	0.0914965i
$249$	−5.09443	+	4.27473i	−0.322846	+	0.270900i
$250$	−5.77855	+	9.57123i	−0.365467	+	0.605338i
$251$	1.24299	−	7.04934i	0.0784568	−	0.444951i	−0.920121	−	0.391635i	$-0.871910\pi$
$251$	1.24299	−	7.04934i	0.0784568	−	0.444951i	0.998578	−	0.0533162i	$-0.0169791\pi$
$252$	2.01918	+	1.41385i	0.127196	+	0.0890639i
$253$	−11.9475	−	5.57123i	−0.751135	−	0.350260i
$254$	−8.42683	−	4.86523i	−0.528746	−	0.305272i
$255$	4.43253	−	13.0901i	0.277576	−	0.819731i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	1.74952	+	19.9972i	0.109132	+	1.24739i	0.831361	+	0.555733i	$0.187562\pi$
$257$	1.74952	+	19.9972i	0.109132	+	1.24739i	−0.722228	+	0.691655i	$0.756882\pi$
$258$	−1.36878	+	5.10834i	−0.0852163	+	0.318032i
$259$	0.702227	−	1.21629i	0.0436342	−	0.0755767i
$260$	−2.77493	+	0.811077i	−0.172094	+	0.0503009i
$261$	−1.35111	+	0.238238i	−0.0836319	+	0.0147466i
$262$	−10.3747	+	7.26442i	−0.640949	+	0.448798i
$263$	8.68925	+	18.6342i	0.535802	+	1.14903i	0.968847	+	0.247659i	$0.0796612\pi$
$263$	8.68925	+	18.6342i	0.535802	+	1.14903i	−0.433045	+	0.901372i	$0.642561\pi$
$264$	1.20554	+	1.43671i	0.0741959	+	0.0884232i
$265$	0.547351	−	8.44801i	0.0336235	−	0.518957i
$266$	5.41739	−	9.27885i	0.332161	−	0.568923i
$267$	1.48868	−	1.48868i	0.0911058	−	0.0911058i
$268$	0.367966	−	4.20587i	0.0224771	−	0.256914i
$269$	−9.49171	−	3.45470i	−0.578720	−	0.210637i	0.0360411	−	0.999350i	$-0.488525\pi$
$269$	−9.49171	−	3.45470i	−0.578720	−	0.210637i	−0.614761	+	0.788713i	$0.710748\pi$
$270$	−1.91077	+	1.16145i	−0.116286	+	0.0706833i
$271$	−0.411748	−	2.33514i	−0.0250119	−	0.141850i	0.969745	−	0.244122i	$-0.0784997\pi$
$271$	−0.411748	−	2.33514i	−0.0250119	−	0.141850i	−0.994756	+	0.102272i	$0.967389\pi$
$272$	−2.61202	+	5.60149i	−0.158377	+	0.339640i
$273$	3.07839	−	0.824852i	0.186313	−	0.0499223i
$274$	5.62970	+	9.75093i	0.340103	+	0.589075i
$275$	6.90427	−	6.34567i	0.416343	−	0.382658i
$276$	−4.51810	+	5.38446i	−0.271958	+	0.324106i
$277$	14.7476	+	3.95161i	0.886098	+	0.237429i	0.673036	−	0.739609i	$-0.264990\pi$
$277$	14.7476	+	3.95161i	0.886098	+	0.237429i	0.213062	+	0.977039i	$0.431656\pi$
$278$	−4.22416	−	15.7648i	−0.253348	−	0.945508i
$279$	1.91483	−	0.696943i	0.114638	−	0.0417249i
$280$	−3.44676	+	4.30118i	−0.205983	+	0.257044i
$281$	−24.5031	−	4.32055i	−1.46173	−	0.257742i	−0.614478	−	0.788934i	$-0.710633\pi$
$281$	−24.5031	−	4.32055i	−1.46173	−	0.257742i	−0.847252	+	0.531191i	$0.821745\pi$
$282$	−6.08734	+	2.83857i	−0.362496	+	0.169035i
$283$	1.27991	+	0.111978i	0.0760830	+	0.00665640i	0.125134	−	0.992140i	$-0.460064\pi$
$283$	1.27991	+	0.111978i	0.0760830	+	0.00665640i	−0.0490507	+	0.998796i	$0.515620\pi$
$284$	1.13156			0.0671458
$285$	5.73105	+	7.88385i	0.339478	+	0.466999i
$286$	2.42484			0.143384
$287$	−28.0750	−	2.45624i	−1.65721	−	0.144987i
$288$	0.906308	−	0.422618i	0.0534047	−	0.0249030i
$289$	−20.8773	−	3.68123i	−1.22808	−	0.216543i
$290$	−0.336267	−	3.04930i	−0.0197463	−	0.179061i
$291$	−6.24580	+	2.27328i	−0.366135	+	0.133262i
$292$	−3.22437	−	12.0335i	−0.188692	−	0.704209i
$293$	21.2311	+	5.68886i	1.24033	+	0.332347i	0.818595	−	0.574371i	$-0.194753\pi$
$293$	21.2311	+	5.68886i	1.24033	+	0.332347i	0.421739	+	0.906717i	$0.361420\pi$
$294$	−0.593901	+	0.707783i	−0.0346370	+	0.0412787i
$295$	13.0109	−	0.293659i	0.757523	−	0.0170975i
$296$	−0.284883	−	0.493432i	−0.0165585	−	0.0286801i
$297$	1.81158	−	0.485412i	0.105119	−	0.0281665i
$298$	7.81360	−	16.7563i	0.452630	−	0.970667i
$299$	1.57807	+	8.94970i	0.0912623	+	0.517574i
$300$	−2.31539	−	4.43159i	−0.133679	−	0.255858i
$301$	12.2499	+	4.45860i	0.706073	+	0.256990i
$302$	1.06019	−	12.1180i	0.0610070	−	0.697314i
$303$	1.57053	−	1.57053i	0.0902248	−	0.0902248i
$304$	−2.16109	−	3.78546i	−0.123947	−	0.217111i
$305$	10.4386	−	9.16830i	0.597715	−	0.524975i
$306$	3.97279	+	4.73459i	0.227109	+	0.270658i
$307$	6.51774	+	13.9773i	0.371987	+	0.797729i	0.999812	+	0.0193745i	$0.00616747\pi$
$307$	6.51774	+	13.9773i	0.371987	+	0.797729i	−0.627825	+	0.778354i	$0.716055\pi$
$308$	3.78695	−	2.65165i	0.215782	−	0.151092i
$309$	18.7895	−	3.31309i	1.06890	−	0.188475i
$310$	1.27832	+	4.37350i	0.0726036	+	0.248398i
$311$	−11.6882	+	20.2446i	−0.662778	+	1.14796i	0.317105	+	0.948390i	$0.397289\pi$
$311$	−11.6882	+	20.2446i	−0.662778	+	1.14796i	−0.979883	+	0.199574i	$0.936044\pi$
$312$	0.334630	−	1.24886i	0.0189447	−	0.0707026i
$313$	−1.48949	−	17.0250i	−0.0841910	−	0.962308i	−0.914388	−	0.404838i	$-0.867328\pi$
$313$	−1.48949	−	17.0250i	−0.0841910	−	0.962308i	0.830197	−	0.557470i	$-0.188228\pi$
$314$	8.89746	+	7.46586i	0.502113	+	0.421323i
$315$	2.44153	+	4.94158i	0.137564	+	0.278427i
$316$	−12.9185	−	7.45851i	−0.726723	−	0.419574i
$317$	−15.6576	−	7.30125i	−0.879417	−	0.410079i	−0.0701616	−	0.997536i	$-0.522351\pi$
$317$	−15.6576	−	7.30125i	−0.879417	−	0.410079i	−0.809256	+	0.587457i	$0.800129\pi$
$318$	3.10130	+	2.17155i	0.173912	+	0.121775i
$319$	−0.446812	+	2.53400i	−0.0250167	+	0.141877i
$320$	0.811998	+	2.08342i	0.0453921	+	0.116467i
$321$	−9.59997	+	8.05533i	−0.535818	+	0.449605i
$322$	12.2513	+	12.2513i	0.682741	+	0.682741i
$323$	19.1421	−	18.9571i	1.06509	−	1.05480i
$324$		−	1.00000i		−	0.0555556i
$325$	−6.31341	−	1.38972i	−0.350205	−	0.0770878i
$326$	−3.79893	+	10.4375i	−0.210403	+	0.578078i
$327$	3.55613	+	5.07867i	0.196654	+	0.280851i
$328$	−6.55776	+	9.36545i	−0.362092	+	0.517121i
$329$	5.66258	+	15.5578i	0.312188	+	0.857730i
$330$	0.821238	+	4.11252i	0.0452077	+	0.226387i
$331$	−6.87127	+	3.96713i	−0.377679	+	0.218053i	−0.676808	−	0.736160i	$-0.736637\pi$
$331$	−6.87127	+	3.96713i	−0.377679	+	0.218053i	0.299129	+	0.954213i	$0.403304\pi$
$332$	6.62500	−	0.579612i	0.363594	−	0.0318104i
$333$	−0.567598	+	0.0496584i	−0.0311042	+	0.00272126i
$334$	10.0885	−	5.82461i	0.552019	−	0.318708i
$335$	5.23899	−	7.85345i	0.286237	−	0.429080i
$336$	−0.843068	−	2.31631i	−0.0459931	−	0.126365i
$337$	−5.42325	+	7.74520i	−0.295423	+	0.421908i	−0.939234	−	0.343276i	$-0.888463\pi$
$337$	−5.42325	+	7.74520i	−0.295423	+	0.421908i	0.643811	+	0.765184i	$0.277352\pi$
$338$	6.49769	+	9.27966i	0.353428	+	0.504747i
$339$	−2.91496	+	8.00879i	−0.158319	+	0.434977i
$340$	−11.1391	+	8.18035i	−0.604101	+	0.443642i
$341$		−	3.82173i		−	0.206958i
$342$	−4.34411	+	0.358814i	−0.234902	+	0.0194024i
$343$	13.8114	+	13.8114i	0.745745	+	0.745745i
$344$	4.05126	−	3.39941i	0.218429	−	0.183284i
$345$	−14.6442	+	5.70747i	−0.788418	+	0.307280i
$346$	−1.84463	+	10.4614i	−0.0991681	+	0.562410i
$347$	−28.4525	−	19.9226i	−1.52741	−	1.06950i	−0.971143	−	0.238499i	$-0.923345\pi$
$347$	−28.4525	−	19.9226i	−1.52741	−	1.06950i	−0.556266	−	0.831004i	$-0.687766\pi$
$348$	1.24342	+	0.579814i	0.0666541	+	0.0310813i
$349$	14.7640	+	8.52401i	0.790300	+	0.456280i	0.840068	−	0.542481i	$-0.182515\pi$
$349$	14.7640	+	8.52401i	0.790300	+	0.456280i	−0.0497684	+	0.998761i	$0.515848\pi$
$350$	−11.3796	+	4.73358i	−0.608264	+	0.253020i
$351$	−0.990428	−	0.831068i	−0.0528651	−	0.0443591i
$352$	−0.163460	−	1.86835i	−0.00871243	−	0.0995835i
$353$	−5.32254	+	19.8640i	−0.283290	+	1.05725i	0.666790	+	0.745246i	$0.267668\pi$
$353$	−5.32254	+	19.8640i	−0.283290	+	1.05725i	−0.950080	+	0.312007i	$0.898999\pi$
$354$	−2.91006	+	5.04038i	−0.154668	+	0.267893i
$355$	2.21925	+	1.21536i	0.117785	+	0.0645045i
$356$	−2.07333	+	0.365584i	−0.109886	+	0.0193759i
$357$	12.4797	−	8.73837i	0.660495	−	0.462483i
$358$	9.48288	+	20.3361i	0.501186	+	1.07480i
$359$	−12.4944	−	14.8902i	−0.659429	−	0.785877i	0.327875	−	0.944721i	$-0.393668\pi$
$359$	−12.4944	−	14.8902i	−0.659429	−	0.785877i	−0.987304	+	0.158845i	$0.949223\pi$
$360$	2.23139	+	0.144573i	0.117605	+	0.00761966i
$361$	3.11745	+	18.7425i	0.164076	+	0.986448i
$362$	4.76161	−	4.76161i	0.250265	−	0.250265i
$363$	−0.652147	+	7.45407i	−0.0342288	+	0.391237i
$364$	−2.99478	−	1.09001i	−0.156969	−	0.0571322i
$365$	6.60092	−	27.0636i	0.345508	−	1.41657i
$366$	1.07892	+	6.11887i	0.0563961	+	0.319838i
$367$	−5.15759	+	11.0605i	−0.269224	+	0.577353i	−0.993716	−	0.111930i	$-0.964297\pi$
$367$	−5.15759	+	11.0605i	−0.269224	+	0.577353i	0.724492	+	0.689283i	$0.242074\pi$
$368$	6.78941	−	1.81922i	0.353922	−	0.0948332i
$369$	5.71655	+	9.90136i	0.297592	+	0.515444i
$370$	−0.0287480	−	1.27371i	−0.00149454	−	0.0662171i
$371$	5.99870	−	7.14898i	0.311437	−	0.371156i
$372$	−1.96829	−	0.527402i	−0.102051	−	0.0273445i
$373$	−3.90155	−	14.5608i	−0.202014	−	0.753928i	−0.990339	−	0.138668i	$-0.955718\pi$
$373$	−3.90155	−	14.5608i	−0.202014	−	0.753928i	0.788325	−	0.615260i	$-0.210949\pi$
$374$	10.8925	−	3.96455i	0.563239	−	0.205002i
$375$	0.218754	−	11.1782i	0.0112964	−	0.577240i
$376$	6.61460	+	1.16633i	0.341122	+	0.0601490i
$377$	1.60763	−	0.749649i	0.0827970	−	0.0386089i
$378$	−2.45559	−	0.214836i	−0.126302	−	0.0110500i
$379$	13.6253			0.699884			0.349942	−	0.936771i	$-0.386201\pi$
$379$	13.6253			0.699884			0.349942	+	0.936771i	$0.386201\pi$
$380$	−0.172615	−	9.74527i	−0.00885495	−	0.499922i
$381$	9.73047			0.498507
$382$	7.49734	+	0.655932i	0.383597	+	0.0335604i
$383$	10.4897	−	4.89144i	0.536000	−	0.249941i	−0.135718	−	0.990747i	$-0.543334\pi$
$383$	10.4897	−	4.89144i	0.536000	−	0.249941i	0.671719	+	0.740806i	$0.265556\pi$
$384$	−0.984808	−	0.173648i	−0.0502558	−	0.00886145i
$385$	10.2751	−	1.13310i	0.523667	−	0.0577482i
$386$	−22.0820	+	8.03718i	−1.12394	+	0.409082i
$387$	−1.36878	−	5.10834i	−0.0695788	−	0.259672i
$388$	6.42016	+	1.72028i	0.325934	+	0.0873338i
$389$	−7.85207	+	9.35774i	−0.398116	+	0.474456i	−0.927445	−	0.373961i	$-0.877999\pi$
$389$	−7.85207	+	9.35774i	−0.398116	+	0.474456i	0.529329	+	0.848417i	$0.322444\pi$
$390$	1.99762	−	2.08988i	0.101154	−	0.105825i
$391$	21.7213	+	37.6224i	1.09849	+	1.90265i
$392$	0.892463	−	0.239135i	0.0450762	−	0.0120781i
$393$	5.35252	−	11.4785i	0.269999	−	0.579014i
$394$	2.33097	+	13.2196i	0.117433	+	0.665994i
$395$	−17.3253	−	28.5030i	−0.871731	−	1.43414i
$396$	−1.76238	−	0.641455i	−0.0885631	−	0.0322343i
$397$	−1.63380	+	18.6744i	−0.0819978	+	0.937239i	0.838091	+	0.545530i	$0.183672\pi$
$397$	−1.63380	+	18.6744i	−0.0819978	+	0.937239i	−0.920089	+	0.391709i	$0.871884\pi$
$398$	−9.71436	+	9.71436i	−0.486937	+	0.486937i
$399$	−0.0521709	+	10.7444i	−0.00261181	+	0.537893i
$400$	−0.645196	+	4.95820i	−0.0322598	+	0.247910i
$401$	22.6712	+	27.0184i	1.13214	+	1.34924i	0.928997	+	0.370088i	$0.120672\pi$
$401$	22.6712	+	27.0184i	1.13214	+	1.34924i	0.203146	+	0.979148i	$0.434883\pi$
$402$	1.78427	+	3.82637i	0.0889912	+	0.190842i
$403$	−2.15814	+	1.51114i	−0.107504	+	0.0752754i
$404$	−2.18733	+	0.385685i	−0.108824	+	0.0191885i
$405$	1.07405	−	1.96123i	0.0533701	−	0.0974541i
$406$	1.69091	−	2.92875i	0.0839186	−	0.145351i
$407$	−0.276571	+	1.03218i	−0.0137091	+	0.0511632i
$408$	−0.538672	−	6.15705i	−0.0266682	−	0.304819i
$409$	−28.3579	−	23.7951i	−1.40221	−	1.17659i	−0.960108	−	0.279629i	$-0.909788\pi$
$409$	−28.3579	−	23.7951i	−1.40221	−	1.17659i	−0.442102	−	0.896965i	$-0.645767\pi$
$410$	−22.9203	+	11.3244i	−1.13195	+	0.559272i
$411$	−9.75093	−	5.62970i	−0.480978	−	0.277693i
$412$	−17.2917	−	8.06327i	−0.851903	−	0.397249i
$413$	11.7519	+	8.22877i	0.578273	+	0.404911i
$414$	1.22056	−	6.92213i	0.0599871	−	0.340204i
$415$	13.6157	+	5.97885i	0.668366	+	0.293490i
$416$	−0.990428	+	0.831068i	−0.0485597	+	0.0407464i
$417$	11.5406	+	11.5406i	0.565146	+	0.565146i
$418$	−2.15418	+	7.88614i	−0.105364	+	0.385724i
$419$			1.41740i			0.0692447i	0.999400	+	0.0346224i	$0.0110228\pi$
$419$			1.41740i			0.0692447i	−0.999400	+	0.0346224i	$0.988977\pi$
$420$	0.834393	−	5.44831i	0.0407142	−	0.265850i
$421$	−1.82957	+	5.02670i	−0.0891677	+	0.244986i	−0.976259	−	0.216609i	$-0.930500\pi$
$421$	−1.82957	+	5.02670i	−0.0891677	+	0.244986i	0.887091	+	0.461595i	$0.152723\pi$
$422$	−0.623231	−	0.890067i	−0.0303384	−	0.0433278i
$423$	3.85251	−	5.50195i	0.187315	−	0.267514i
$424$	−1.29488	−	3.55766i	−0.0628851	−	0.172775i
$425$	−30.6324	+	4.07957i	−1.48589	+	0.197888i
$426$	−0.979961	+	0.565781i	−0.0474793	+	0.0274122i
$427$	15.2572	−	1.33483i	0.738347	−	0.0645970i
$428$	12.4842	−	1.09222i	0.603446	−	0.0527947i
$429$	−2.09997	+	1.21242i	−0.101388	+	0.0585362i
$430$	11.5966	−	2.31575i	0.559237	−	0.111675i
$431$	−8.83843	−	24.2834i	−0.425732	−	1.16969i	−0.948379	−	0.317140i	$-0.897278\pi$
$431$	−8.83843	−	24.2834i	−0.425732	−	1.16969i	0.522647	−	0.852549i	$-0.324945\pi$
$432$	−0.573576	+	0.819152i	−0.0275962	+	0.0394115i
$433$	14.0602	+	20.0801i	0.675691	+	0.964987i	0.999820	+	0.0189744i	$0.00604009\pi$
$433$	14.0602	+	20.0801i	0.675691	+	0.964987i	−0.324128	+	0.946013i	$0.605071\pi$
$434$	−1.71794	+	4.72000i	−0.0824637	+	0.226567i
$435$	1.81587	+	2.47264i	0.0870642	+	0.118554i
$436$		−	6.19992i		−	0.296922i
$437$	−30.5084	−	2.81847i	−1.45941	−	0.134826i
$438$	8.80915	+	8.80915i	0.420918	+	0.420918i
$439$	7.44066	−	6.24346i	0.355123	−	0.297984i	−0.447720	−	0.894174i	$-0.647764\pi$
$439$	7.44066	−	6.24346i	0.355123	−	0.297984i	0.802843	+	0.596190i	$0.203319\pi$
$440$	1.68613	−	3.83983i	0.0803830	−	0.183056i
$441$	0.160441	−	0.909908i	0.00764007	−	0.0433290i
$442$	−6.54578	−	4.58341i	−0.311351	−	0.218010i
$443$	−25.0873	−	11.6984i	−1.19194	−	0.555809i	−0.277573	−	0.960705i	$-0.589530\pi$
$443$	−25.0873	−	11.6984i	−1.19194	−	0.555809i	−0.914363	+	0.404896i	$0.867308\pi$
$444$	0.493432	+	0.284883i	0.0234172	+	0.0135199i
$445$	−4.45892	−	1.50987i	−0.211373	−	0.0715748i
$446$	13.7260	+	11.5175i	0.649947	+	0.545370i
$447$	1.61138	+	18.4182i	0.0762158	+	0.871151i
$448$	−0.637980	+	2.38097i	−0.0301417	+	0.112490i
$449$	16.0927	−	27.8734i	0.759463	−	1.31543i	−0.183662	−	0.982989i	$-0.558795\pi$
$449$	16.0927	−	27.8734i	0.759463	−	1.31543i	0.943125	−	0.332439i	$-0.107871\pi$
$450$	4.22098	+	2.68017i	0.198979	+	0.126344i
$451$	21.1169	−	3.72348i	0.994356	−	0.175332i
$452$	6.98145	−	4.88846i	0.328380	−	0.229934i
$453$	5.14086	+	11.0246i	0.241539	+	0.517981i
$454$	−16.7493	−	19.9610i	−0.786082	−	0.936816i
$455$	−4.70272	−	5.35432i	−0.220467	−	0.251014i
$456$	3.76429	+	2.19775i	0.176279	+	0.102919i
$457$	−2.59305	+	2.59305i	−0.121298	+	0.121298i	−0.765150	−	0.643852i	$-0.777335\pi$
$457$	−2.59305	+	2.59305i	−0.121298	+	0.121298i	0.643852	+	0.765150i	$0.277335\pi$
$458$	−0.148734	+	1.70003i	−0.00694987	+	0.0794373i
$459$	−5.80783	−	2.11388i	−0.271086	−	0.0986674i
$460$	15.2695	+	3.72429i	0.711944	+	0.173646i
$461$	−0.842152	−	4.77608i	−0.0392229	−	0.222444i	0.958896	−	0.283759i	$-0.0915817\pi$
$461$	−0.842152	−	4.77608i	−0.0392229	−	0.222444i	−0.998118	+	0.0613150i	$0.980471\pi$
$462$	−1.95377	+	4.18987i	−0.0908976	+	0.194931i
$463$	−20.5091	+	5.49539i	−0.953137	+	0.255392i	−0.701693	−	0.712479i	$-0.747572\pi$
$463$	−20.5091	+	5.49539i	−0.953137	+	0.255392i	−0.251444	+	0.967872i	$0.580905\pi$
$464$	−0.685979	−	1.18815i	−0.0318458	−	0.0551585i
$465$	−3.29381	−	3.14840i	−0.152747	−	0.146004i
$466$	7.13660	−	8.50507i	0.330597	−	0.393990i
$467$	35.1017	+	9.40547i	1.62431	+	0.435233i	0.952265	−	0.305274i	$-0.0987480\pi$
$467$	35.1017	+	9.40547i	1.62431	+	0.435233i	0.672048	+	0.740507i	$0.265415\pi$
$468$	0.334630	+	1.24886i	0.0154683	+	0.0577284i
$469$	9.77931	−	3.55938i	0.451567	−	0.164357i
$470$	11.7200	+	9.39187i	0.540604	+	0.433215i
$471$	−11.4384	−	2.01689i	−0.527052	−	0.0929334i
$472$	5.27483	−	2.45969i	0.242794	−	0.113217i
$473$	−9.88086	−	0.864464i	−0.454323	−	0.0397481i
$474$	14.9170			0.685161
$475$	10.1284	−	19.2981i	0.464723	−	0.885456i
$476$	−15.2349			−0.698290
$477$	−3.77158	−	0.329970i	−0.172689	−	0.0151083i
$478$	−20.2896	+	9.46119i	−0.928024	+	0.432745i
$479$	−15.4723	−	2.72819i	−0.706948	−	0.124654i	−0.191397	−	0.981513i	$-0.561302\pi$
$479$	−15.4723	−	2.72819i	−0.706948	−	0.124654i	−0.515551	+	0.856859i	$0.672413\pi$
$480$	−1.74492	−	1.39830i	−0.0796445	−	0.0638233i
$481$	0.692231	−	0.251952i	0.0315630	−	0.0114880i
$482$	−4.09425	−	15.2800i	−0.186488	−	0.695983i
$483$	−16.7357	−	4.48431i	−0.761499	−	0.204043i
$484$	4.80969	−	5.73196i	0.218622	−	0.260544i
$485$	10.7437	+	10.2694i	0.487847	+	0.466312i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−6.15310	+	1.64872i	−0.278824	+	0.0747106i	−0.395521	−	0.918457i	$-0.629436\pi$
$487$	−6.15310	+	1.64872i	−0.278824	+	0.0747106i	0.116697	+	0.993168i	$0.462769\pi$
$488$	2.62584	−	5.63113i	0.118866	−	0.254909i
$489$	−1.92877	−	10.9386i	−0.0872219	−	0.494660i
$490$	2.00716	+	0.489555i	0.0906744	+	0.0221159i
$491$	−39.5508	−	14.3953i	−1.78490	−	0.649651i	−0.999531	−	0.0306243i	$-0.990250\pi$
$491$	−39.5508	−	14.3953i	−1.78490	−	0.649651i	−0.785370	−	0.619027i	$-0.787527\pi$
$492$	0.996461	−	11.3896i	0.0449239	−	0.513483i
$493$	5.99589	−	5.99589i	0.270041	−	0.270041i
$494$	5.30510	−	1.90178i	0.238688	−	0.0855650i
$495$	−2.76748	−	3.15093i	−0.124389	−	0.141624i
$496$	1.30982	+	1.56099i	0.0588128	+	0.0700904i
$497$	1.17879	+	2.52793i	0.0528760	+	0.113393i
$498$	−5.44761	+	3.81446i	−0.244113	+	0.170930i
$499$	−34.7216	+	6.12235i	−1.55435	+	0.274074i	−0.883827	−	0.467814i	$-0.845042\pi$
$499$	−34.7216	+	6.12235i	−1.55435	+	0.274074i	−0.670524	+	0.741888i	$0.733931\pi$
$500$	−6.59075	+	9.03117i	−0.294747	+	0.403886i
$501$	−5.82461	+	10.0885i	−0.260224	+	0.450722i
$502$	1.85265	−	6.91419i	0.0826878	−	0.308595i
$503$	2.43397	+	27.8204i	0.108525	+	1.24045i	0.833830	+	0.552021i	$0.186143\pi$
$503$	2.43397	+	27.8204i	0.108525	+	1.24045i	−0.725305	+	0.688427i	$0.758301\pi$
$504$	1.88827	+	1.58445i	0.0841104	+	0.0705770i
$505$	−4.70409	−	1.59289i	−0.209329	−	0.0708827i
$506$	−11.4165	−	6.59132i	−0.507526	−	0.293020i
$507$	−10.2670	−	4.78758i	−0.455973	−	0.212624i
$508$	−7.97073	−	5.58117i	−0.353644	−	0.247624i
$509$	4.40480	−	24.9809i	0.195239	−	1.10726i	−0.716838	−	0.697240i	$-0.754411\pi$
$509$	4.40480	−	24.9809i	0.195239	−	1.10726i	0.912077	−	0.410018i	$-0.134478\pi$
$510$	5.55654	−	12.6539i	0.246048	−	0.560325i
$511$	23.5242	−	19.7391i	1.04065	−	0.873207i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	3.58270	−	2.48279i	0.158180	−	0.109618i
$514$			20.0735i			0.885406i
$515$	−25.2526	−	34.3862i	−1.11276	−	1.51524i
$516$	−1.80879	+	4.96961i	−0.0796275	+	0.218775i
$517$	−7.22533	−	10.3188i	−0.317770	−	0.453822i
$518$	0.805561	−	1.15046i	0.0353943	−	0.0505483i
$519$	−3.63322	−	9.98218i	−0.159481	−	0.438169i
$520$	−2.83506	+	0.566140i	−0.124326	+	0.0248269i
$521$	5.43071	−	3.13542i	0.237924	−	0.137365i	−0.376298	−	0.926499i	$-0.622803\pi$
$521$	5.43071	−	3.13542i	0.237924	−	0.137365i	0.614222	+	0.789133i	$0.289470\pi$
$522$	−1.36674	+	0.119574i	−0.0598204	+	0.00523361i
$523$	−17.4627	+	1.52778i	−0.763589	+	0.0668054i	−0.462295	−	0.886726i	$-0.652974\pi$
$523$	−17.4627	+	1.52778i	−0.763589	+	0.0668054i	−0.301294	+	0.953531i	$0.597418\pi$
$524$	−10.9683	+	6.33257i	−0.479154	+	0.276639i
$525$	7.48821	−	9.78918i	0.326812	−	0.427235i
$526$	7.03211	+	19.3206i	0.306615	+	0.842416i
$527$	−7.22379	+	10.3166i	−0.314673	+	0.449400i
$528$	1.07574	+	1.53631i	0.0468154	+	0.0668593i
$529$	9.03125	−	24.8131i	0.392663	−	1.07883i
$530$	1.28156	−	8.36816i	0.0556674	−	0.363490i
$531$		−	5.82013i		−	0.252572i
$532$	6.20548	−	8.77138i	0.269041	−	0.380288i
$533$	−10.4525	−	10.4525i	−0.452746	−	0.452746i
$534$	1.61276	−	1.35327i	0.0697911	−	0.0585617i
$535$	25.6574	+	11.2666i	1.10927	+	0.487097i
$536$	0.733132	−	4.15780i	0.0316665	−	0.179589i
$537$	−18.3805	−	12.8701i	−0.793176	−	0.555388i
$538$	−9.15450	−	4.26881i	−0.394678	−	0.184042i
$539$	−1.50069	−	0.866424i	−0.0646393	−	0.0373195i
$540$	−2.00473	+	0.990491i	−0.0862697	+	0.0426239i
$541$	16.8311	+	14.1229i	0.723624	+	0.607193i	0.928385	−	0.371619i	$-0.121197\pi$
$541$	16.8311	+	14.1229i	0.723624	+	0.607193i	−0.204761	+	0.978812i	$0.565642\pi$
$542$	−0.206660	−	2.36214i	−0.00887682	−	0.101463i
$543$	−1.74287	+	6.50449i	−0.0747938	+	0.279134i
$544$	−3.09028	+	5.35253i	−0.132495	+	0.229488i
$545$	6.65904	−	12.1594i	0.285242	−	0.520853i
$546$	3.13857	−	0.553414i	0.134318	−	0.0236839i
$547$	−1.36110	+	0.953051i	−0.0581963	+	0.0407495i	−0.602313	−	0.798260i	$-0.705754\pi$
$547$	−1.36110	+	0.953051i	−0.0581963	+	0.0407495i	0.544116	+	0.839010i	$0.316865\pi$
$548$	4.75843	+	10.2045i	0.203270	+	0.435914i
$549$	−3.99381	−	4.75963i	−0.170452	−	0.203136i
$550$	7.43106	−	5.71978i	0.316861	−	0.243892i
$551$	1.00985	+	5.89434i	0.0430209	+	0.251107i
$552$	−4.97019	+	4.97019i	−0.211545	+	0.211545i
$553$	3.20471	−	36.6300i	0.136278	−	1.55767i
$554$	14.3471	+	5.22191i	0.609550	+	0.221858i
$555$	0.661752	+	1.08869i	0.0280898	+	0.0462124i
$556$	−2.83409	−	16.0729i	−0.120192	−	0.681644i
$557$	8.46716	−	18.1579i	0.358765	−	0.769374i	−0.641233	−	0.767346i	$-0.721577\pi$
$557$	8.46716	−	18.1579i	0.358765	−	0.769374i	0.999998	−	0.00202790i	$-0.000645503\pi$
$558$	1.96829	−	0.527402i	0.0833244	−	0.0223267i
$559$	3.41881	+	5.92156i	0.144600	+	0.250455i
$560$	−3.80852	+	3.98440i	−0.160939	+	0.168372i
$561$	−7.45092	+	8.87966i	−0.314578	+	0.374900i
$562$	−24.0333	−	6.43969i	−1.01378	−	0.271642i
$563$	0.970007	+	3.62012i	0.0408809	+	0.152570i	0.983349	−	0.181726i	$-0.0581683\pi$
$563$	0.970007	+	3.62012i	0.0408809	+	0.152570i	−0.942468	+	0.334295i	$0.891502\pi$
$564$	−6.31158	+	2.29723i	−0.265765	+	0.0967307i
$565$	18.9427	−	2.08893i	0.796924	−	0.0878821i
$566$	1.26528	+	0.223104i	0.0531838	+	0.00937775i
$567$	2.23402	−	1.04174i	0.0938199	−	0.0437489i
$568$	1.12726	+	0.0986221i	0.0472986	+	0.00413809i
$569$	−12.1676			−0.510091			−0.255046	−	0.966929i	$-0.582091\pi$
$569$	−12.1676			−0.510091			−0.255046	+	0.966929i	$0.582091\pi$
$570$	5.02212	+	8.35334i	0.210354	+	0.349883i
$571$	7.60384			0.318211			0.159105	−	0.987262i	$-0.449139\pi$
$571$	7.60384			0.318211			0.159105	+	0.987262i	$0.449139\pi$
$572$	2.41561	+	0.211339i	0.101002	+	0.00883652i
$573$	−6.82085	+	3.18061i	−0.284945	+	0.132872i
$574$	−27.7541	−	4.89379i	−1.15843	−	0.204263i
$575$	25.9469	+	23.7044i	1.08206	+	0.988543i
$576$	0.939693	−	0.342020i	0.0391539	−	0.0142508i
$577$	1.61927	+	6.04321i	0.0674112	+	0.251582i	0.991406	−	0.130824i	$-0.0417623\pi$
$577$	1.61927	+	6.04321i	0.0674112	+	0.251582i	−0.923994	+	0.382406i	$0.875096\pi$
$578$	−20.4770	−	5.48680i	−0.851732	−	0.228221i
$579$	15.1050	−	18.0014i	0.627741	−	0.748112i
$580$	−0.0692231	−	3.06701i	−0.00287433	−	0.127351i
$581$	8.19639	+	14.1966i	0.340043	+	0.588973i
$582$	−6.42016	+	1.72028i	−0.266124	+	0.0713078i
$583$	−3.00083	+	6.43531i	−0.124282	+	0.266523i
$584$	−2.16331	−	12.2688i	−0.0895185	−	0.507685i
$585$	−0.685053	+	2.80870i	−0.0283235	+	0.116126i
$586$	20.6545	+	7.51762i	0.853230	+	0.310550i
$587$	1.06178	−	12.1362i	0.0438243	−	0.500914i	−0.942285	−	0.334813i	$-0.891327\pi$
$587$	1.06178	−	12.1362i	0.0438243	−	0.500914i	0.986109	−	0.166101i	$-0.0531177\pi$
$588$	−0.653328	+	0.653328i	−0.0269428	+	0.0269428i
$589$	−2.99734	−	8.36122i	−0.123503	−	0.344518i
$590$	12.9870	+	0.841433i	0.534665	+	0.0346412i
$591$	−8.62849	−	10.2830i	−0.354929	−	0.422987i
$592$	−0.240793	−	0.516383i	−0.00989655	−	0.0212232i
$593$	1.15481	−	0.808604i	0.0474222	−	0.0332054i	−0.549625	−	0.835411i	$-0.685229\pi$
$593$	1.15481	−	0.808604i	0.0474222	−	0.0332054i	0.597047	+	0.802206i	$0.296340\pi$
$594$	1.84700	−	0.325675i	0.0757832	−	0.0133626i
$595$	−29.8790	−	16.3631i	−1.22492	−	0.670821i
$596$	9.24427	−	16.0116i	0.378660	−	0.655859i
$597$	3.55570	−	13.2701i	0.145525	−	0.543107i
$598$	0.792051	+	9.05318i	0.0323894	+	0.370212i
$599$	−8.48508	−	7.11983i	−0.346691	−	0.290908i	0.452769	−	0.891628i	$-0.350436\pi$
$599$	−8.48508	−	7.11983i	−0.346691	−	0.290908i	−0.799460	+	0.600720i	$0.794881\pi$
$600$	−1.92034	−	4.61652i	−0.0783976	−	0.188469i
$601$	34.6501	+	20.0053i	1.41341	+	0.816031i	0.995708	−	0.0925536i	$-0.0295030\pi$
$601$	34.6501	+	20.0053i	1.41341	+	0.816031i	0.417700	+	0.908585i	$0.362836\pi$
$602$	11.8147	+	5.50929i	0.481531	+	0.224542i
$603$	−3.45841	−	2.42160i	−0.140837	−	0.0986153i
$604$	2.11231	−	11.9795i	0.0859487	−	0.487439i
$605$	15.5893	−	6.07581i	0.633796	−	0.247017i
$606$	1.70144	−	1.42768i	0.0691162	−	0.0579954i
$607$	2.38620	+	2.38620i	0.0968530	+	0.0968530i	0.753873	−	0.657020i	$-0.228183\pi$
$607$	2.38620	+	2.38620i	0.0968530	+	0.0968530i	−0.657020	+	0.753873i	$0.728183\pi$
$608$	−1.82295	−	3.95940i	−0.0739302	−	0.160575i
$609$			3.38183i			0.137039i
$610$	11.1980	−	8.22362i	0.453393	−	0.332965i
$611$	−2.97011	+	8.16031i	−0.120158	+	0.330131i
$612$	3.54503	+	5.06282i	0.143299	+	0.204652i
$613$	27.1424	−	38.7634i	1.09627	−	1.56564i	0.306884	−	0.951747i	$-0.400714\pi$
$613$	27.1424	−	38.7634i	1.09627	−	1.56564i	0.789389	−	0.613893i	$-0.210397\pi$
$614$	5.27473	+	14.4922i	0.212871	+	0.584858i
$615$	14.1873	−	21.2673i	0.572088	−	0.857582i
$616$	4.00365	−	2.31151i	0.161312	−	0.0931333i
$617$	−23.3164	+	2.03992i	−0.938683	+	0.0821241i	−0.546218	−	0.837643i	$-0.683933\pi$
$617$	−23.3164	+	2.03992i	−0.938683	+	0.0821241i	−0.392465	+	0.919767i	$0.628378\pi$
$618$	19.0067	−	1.66287i	0.764563	−	0.0668906i
$619$	35.2515	−	20.3525i	1.41688	−	0.818035i	0.420856	−	0.907128i	$-0.361730\pi$
$619$	35.2515	−	20.3525i	1.41688	−	0.818035i	0.996023	+	0.0890921i	$0.0283966\pi$
$620$	0.892278	+	4.46827i	0.0358347	+	0.179450i
$621$	2.40403	+	6.60502i	0.0964704	+	0.265050i
$622$	−13.4082	+	19.1488i	−0.537618	+	0.767799i
$623$	−2.97659	−	4.25101i	−0.119254	−	0.170313i
$624$	0.442202	−	1.21494i	0.0177022	−	0.0486365i
$625$	−22.6259	+	10.6334i	−0.905036	+	0.425335i
$626$		−	17.0900i		−	0.683053i
$627$	−2.07750	−	7.90669i	−0.0829672	−	0.315763i
$628$	8.21291	+	8.21291i	0.327731	+	0.327731i
$629$	2.69761	−	2.26356i	0.107561	−	0.0902541i
$630$	2.00155	+	5.13557i	0.0797436	+	0.204606i
$631$	0.545844	−	3.09563i	0.0217297	−	0.123235i	−0.972013	−	0.234926i	$-0.924515\pi$
$631$	0.545844	−	3.09563i	0.0217297	−	0.123235i	0.993743	+	0.111690i	$0.0356265\pi$
$632$	−12.2193	−	8.55605i	−0.486058	−	0.340341i
$633$	0.984767	+	0.459205i	0.0391410	+	0.0182517i
$634$	−14.9617	−	8.63811i	−0.594203	−	0.343063i
$635$	−9.63794	−	19.5069i	−0.382470	−	0.774109i
$636$	2.90023	+	2.43359i	0.115002	+	0.0964979i
$637$	0.104114	+	1.19003i	0.00412517	+	0.0471509i
$638$	−0.665965	+	2.48541i	−0.0263658	+	0.0983985i
$639$	0.565781	−	0.979961i	0.0223819	−	0.0387666i
$640$	0.627326	+	2.14627i	0.0247972	+	0.0848387i
$641$	43.3599	−	7.64551i	1.71261	−	0.301980i	0.770540	−	0.637391i	$-0.219987\pi$
$641$	43.3599	−	7.64551i	1.71261	−	0.301980i	0.942072	+	0.335412i	$0.108875\pi$
$642$	−10.2655	+	7.18798i	−0.405147	+	0.283687i
$643$	−7.04759	−	15.1136i	−0.277930	−	0.596022i	0.716946	−	0.697129i	$-0.245539\pi$
$643$	−7.04759	−	15.1136i	−0.277930	−	0.596022i	−0.994876	+	0.101107i	$0.967762\pi$
$644$	11.1370	+	13.2725i	0.438857	+	0.523010i
$645$	−8.88507	+	7.80379i	−0.349849	+	0.307274i
$646$	20.7214	−	17.2166i	0.815274	−	0.677377i
$647$	−3.55524	+	3.55524i	−0.139771	+	0.139771i	−0.773530	−	0.633759i	$-0.781511\pi$
$647$	−3.55524	+	3.55524i	−0.139771	+	0.139771i	0.633759	+	0.773530i	$0.281511\pi$
$648$	0.0871557	−	0.996195i	0.00342380	−	0.0391342i
$649$	−10.2573	−	3.73335i	−0.402634	−	0.146547i
$650$	−6.16827	−	1.93468i	−0.241939	−	0.0758845i
$651$	−0.872221	−	4.94661i	−0.0341850	−	0.193873i
$652$	−4.69416	+	10.0667i	−0.183837	+	0.394241i
$653$	−45.3430	+	12.1496i	−1.77441	+	0.475451i	−0.989546	−	0.144219i	$-0.953933\pi$
$653$	−45.3430	+	12.1496i	−1.77441	+	0.475451i	−0.784862	+	0.619671i	$0.787266\pi$
$654$	3.09996	+	5.36928i	0.121218	+	0.209956i
$655$	−28.3129	+	0.639029i	−1.10628	+	0.0249689i
$656$	−7.34906	+	8.75827i	−0.286933	+	0.341953i
$657$	−12.0335	−	3.22437i	−0.469473	−	0.125795i
$658$	4.28508	+	15.9921i	0.167050	+	0.623439i
$659$	25.3435	−	9.22426i	0.987241	−	0.359326i	0.202590	−	0.979264i	$-0.435064\pi$
$659$	25.3435	−	9.22426i	0.987241	−	0.359326i	0.784651	+	0.619937i	$0.212842\pi$
$660$	0.459683	+	4.16845i	0.0178931	+	0.162257i
$661$	−49.5182	−	8.73139i	−1.92603	−	0.339612i	−0.926690	−	0.375827i	$-0.877359\pi$
$661$	−49.5182	−	8.73139i	−1.92603	−	0.339612i	−0.999344	+	0.0362157i	$0.988470\pi$
$662$	−7.19088	+	3.35316i	−0.279481	+	0.130324i
$663$	7.96052	+	0.696455i	0.309161	+	0.0270481i
$664$	6.65031			0.258082
$665$	21.5913	−	10.5377i	0.837274	−	0.408633i
$666$	−0.569766			−0.0220780
$667$	−9.60667	−	0.840475i	−0.371972	−	0.0325433i
$668$	10.5578	−	4.92317i	0.408493	−	0.190483i
$669$	−17.6459	−	3.11144i	−0.682228	−	0.120295i
$670$	5.90353	−	7.36696i	0.228073	−	0.284610i
$671$	−10.9501	+	3.98553i	−0.422726	+	0.153860i
$672$	−0.637980	−	2.38097i	−0.0246106	−	0.0918481i
$673$	−43.7276	−	11.7168i	−1.68558	−	0.451649i	−0.716334	−	0.697758i	$-0.754181\pi$
$673$	−43.7276	−	11.7168i	−1.68558	−	0.451649i	−0.969242	+	0.246109i	$0.920848\pi$
$674$	−6.07765	+	7.24306i	−0.234102	+	0.278992i
$675$	−4.99556	−	0.210606i	−0.192279	−	0.00810623i
$676$	5.66419	+	9.81066i	0.217853	+	0.377333i
$677$	−15.6335	+	4.18899i	−0.600845	+	0.160996i	−0.546405	−	0.837521i	$-0.684004\pi$
$677$	−15.6335	+	4.18899i	−0.600845	+	0.160996i	−0.0544402	+	0.998517i	$0.517337\pi$
$678$	−3.60188	+	7.72425i	−0.138329	+	0.296648i
$679$	2.84501	+	16.1348i	0.109181	+	0.619198i
$680$	−11.8096	+	7.17839i	−0.452879	+	0.275279i
$681$	24.4858	+	8.91210i	0.938298	+	0.341512i
$682$	0.333086	−	3.80719i	0.0127545	−	0.145785i
$683$	−30.2870	+	30.2870i	−1.15890	+	1.15890i	−0.174186	+	0.984713i	$0.555729\pi$
$683$	−30.2870	+	30.2870i	−1.15890	+	1.15890i	−0.984713	+	0.174186i	$0.944271\pi$
$684$	−4.35885	−	0.0211649i	−0.166665	−	0.000809262i
$685$	−1.62780	+	25.1241i	−0.0621952	+	0.959943i
$686$	12.5551	+	14.9626i	0.479356	+	0.571274i
$687$	−0.721209	−	1.54664i	−0.0275159	−	0.0590079i
$688$	4.33212	−	3.03339i	0.165161	−	0.115647i
$689$	4.82058	−	0.849999i	0.183650	−	0.0323824i
$690$	−15.0859	+	4.40942i	−0.574311	+	0.167864i
$691$	−8.11023	+	14.0473i	−0.308528	+	0.534386i	−0.978041	−	0.208415i	$-0.933170\pi$
$691$	−8.11023	+	14.0473i	−0.308528	+	0.534386i	0.669513	+	0.742801i	$0.266503\pi$
$692$	−2.74939	+	10.2609i	−0.104516	+	0.390059i
$693$	−0.402922	−	4.60542i	−0.0153058	−	0.174946i
$694$	−26.6078	−	22.3266i	−1.01002	−	0.847507i
$695$	11.7049	−	34.5666i	0.443992	−	1.31119i
$696$	1.18815	+	0.685979i	0.0450367	+	0.0260020i
$697$	−64.0425	−	29.8635i	−2.42578	−	1.13116i
$698$	13.9649	+	9.77834i	0.528580	+	0.370116i
$699$	−1.92794	+	10.9339i	−0.0729215	+	0.413558i
$700$	−11.7488	+	3.72377i	−0.444064	+	0.140745i
$701$	19.9347	−	16.7272i	0.752925	−	0.631779i	−0.183350	−	0.983048i	$-0.558694\pi$
$701$	19.9347	−	16.7272i	0.752925	−	0.631779i	0.936275	+	0.351269i	$0.114250\pi$
$702$	−0.914227	−	0.914227i	−0.0345053	−	0.0345053i
$703$	0.204440	+	2.47512i	0.00771060	+	0.0933510i
$704$		−	1.87549i		−	0.0706851i
$705$	−14.8458	−	2.27359i	−0.559124	−	0.0856283i
$706$	−7.03354	+	19.3245i	−0.264711	+	0.727287i
$707$	−3.14025	−	4.48474i	−0.118101	−	0.168666i
$708$	−3.33829	+	4.76757i	−0.125461	+	0.179176i
$709$	7.77913	+	21.3730i	0.292151	+	0.802679i	0.995751	+	0.0920829i	$0.0293525\pi$
$709$	7.77913	+	21.3730i	0.292151	+	0.802679i	−0.703600	+	0.710596i	$0.748425\pi$
$710$	2.10488	+	1.40415i	0.0789946	+	0.0526969i
$711$	−12.9185	+	7.45851i	−0.484482	+	0.279716i
$712$	−2.09730	+	0.183490i	−0.0785997	+	0.00687658i
$713$	14.2685	−	1.24833i	0.534359	−	0.0467503i
$714$	13.1938	−	7.61744i	0.493765	−	0.285076i
$715$	4.51058	+	3.00898i	0.168686	+	0.112530i
$716$	7.67439	+	21.0852i	0.286805	+	0.787991i
$717$	12.8407	−	18.3384i	0.479545	−	0.684861i
$718$	−11.1491	−	15.9225i	−0.416080	−	0.594224i
$719$	1.42804	−	3.92352i	0.0532571	−	0.146323i	−0.910212	−	0.414143i	$-0.864081\pi$
$719$	1.42804	−	3.92352i	0.0532571	−	0.146323i	0.963469	+	0.267821i	$0.0863035\pi$
$720$	2.21030	+	0.338501i	0.0823729	+	0.0126152i
$721$		−	47.0299i		−	1.75148i
$722$	1.47207	+	18.9429i	0.0547849	+	0.704981i
$723$	11.1857	+	11.1857i	0.416001	+	0.416001i
$724$	5.15850	−	4.32849i	0.191714	−	0.160867i
$725$	3.15837	−	6.08945i	0.117299	−	0.226156i
$726$	−1.29933	+	7.36887i	−0.0482227	+	0.273484i
$727$	16.6652	+	11.6691i	0.618079	+	0.432783i	0.840231	−	0.542229i	$-0.182419\pi$
$727$	16.6652	+	11.6691i	0.618079	+	0.432783i	−0.222152	+	0.975012i	$0.571308\pi$
$728$	−2.88839	−	1.34688i	−0.107051	−	0.0499186i
$729$	−0.866025	−	0.500000i	−0.0320750	−	0.0185185i
$730$	8.93456	−	26.3853i	0.330683	−	0.976565i
$731$	25.0391	+	21.0103i	0.926104	+	0.777093i
$732$	0.541521	+	6.18962i	0.0200152	+	0.228775i
$733$	−7.83628	+	29.2454i	−0.289440	+	1.08020i	0.656094	+	0.754679i	$0.272207\pi$
$733$	−7.83628	+	29.2454i	−0.289440	+	1.08020i	−0.945534	+	0.325524i	$0.894459\pi$
$734$	−6.10195	+	10.5689i	−0.225227	+	0.390105i
$735$	−1.98303	+	0.579615i	−0.0731453	+	0.0213794i
$736$	6.92213	−	1.22056i	0.255153	−	0.0449904i
$737$	−6.48620	+	4.54169i	−0.238922	+	0.167295i
$738$	4.83184	+	10.3619i	0.177863	+	0.381427i
$739$	−1.53400	−	1.82814i	−0.0564289	−	0.0672494i	0.737092	−	0.675793i	$-0.236199\pi$
$739$	−1.53400	−	1.82814i	−0.0564289	−	0.0672494i	−0.793521	+	0.608543i	$0.791754\pi$
$740$	0.0823727	−	1.27137i	0.00302808	−	0.0467365i
$741$	−3.64346	+	4.29953i	−0.133846	+	0.157947i
$742$	6.59895	−	6.59895i	0.242255	−	0.242255i
$743$	−3.65713	+	41.8012i	−0.134167	+	1.53354i	0.568895	+	0.822410i	$0.307371\pi$
$743$	−3.65713	+	41.8012i	−0.134167	+	1.53354i	−0.703062	+	0.711128i	$0.748184\pi$
$744$	−1.91483	−	0.696943i	−0.0702012	−	0.0255512i
$745$	35.3274	−	21.4734i	1.29429	−	0.786726i
$746$	−2.61764	−	14.8454i	−0.0958388	−	0.543529i
$747$	2.81054	−	6.02722i	0.102832	−	0.220525i
$748$	11.1966	−	3.00012i	0.409388	−	0.109695i
$749$	15.4453	+	26.7521i	0.564359	+	0.977499i
$750$	1.19217	−	11.1166i	0.0435318	−	0.405921i
$751$	−25.5163	+	30.4091i	−0.931102	+	1.10964i	0.0626504	+	0.998036i	$0.480045\pi$
$751$	−25.5163	+	30.4091i	−0.931102	+	1.10964i	−0.993752	+	0.111608i	$0.964400\pi$
$752$	6.48778	+	1.73839i	0.236585	+	0.0633927i
$753$	1.85265	+	6.91419i	0.0675143	+	0.251967i
$754$	1.66685	−	0.606682i	0.0607029	−	0.0220941i
$755$	17.0093	−	21.2258i	0.619033	−	0.772486i
$756$	−2.42752	−	0.428037i	−0.0882879	−	0.0155675i
$757$	−27.0173	+	12.5984i	−0.981960	+	0.457895i	−0.846211	−	0.532848i	$-0.821122\pi$
$757$	−27.0173	+	12.5984i	−0.981960	+	0.457895i	−0.135749	+	0.990743i	$0.543344\pi$
$758$	13.5734	+	1.18752i	0.493009	+	0.0431327i
$759$	13.1826			0.478500
$760$	0.677398	−	9.72323i	0.0245718	−	0.352698i
$761$	35.3642			1.28195			0.640975	−	0.767562i	$-0.278530\pi$
$761$	35.3642			1.28195			0.640975	+	0.767562i	$0.278530\pi$
$762$	9.69344	+	0.848066i	0.351156	+	0.0307222i
$763$	13.8507	−	6.45870i	0.501430	−	0.233821i
$764$	7.41164	+	1.30687i	0.268144	+	0.0472810i
$765$	1.51486	+	13.7369i	0.0547698	+	0.496658i
$766$	10.8761	−	3.95859i	0.392971	−	0.143030i
$767$	1.94759	+	7.26851i	0.0703234	+	0.262451i
$768$	−0.965926	−	0.258819i	−0.0348548	−	0.00933933i
$769$	−18.7195	+	22.3090i	−0.675041	+	0.804483i	−0.989461	−	0.144801i	$-0.953746\pi$
$769$	−18.7195	+	22.3090i	−0.675041	+	0.804483i	0.314420	+	0.949284i	$0.398190\pi$
$770$	10.3347	−	0.233258i	0.372438	−	0.00840602i
$771$	−10.0368	−	17.3842i	−0.361465	−	0.626077i
$772$	−22.6984	+	6.08203i	−0.816934	+	0.218897i
$773$	4.56764	−	9.79534i	0.164287	−	0.352314i	−0.806880	−	0.590715i	$-0.798846\pi$
$773$	4.56764	−	9.79534i	0.164287	−	0.352314i	0.971167	+	0.238401i	$0.0766234\pi$
$774$	−0.918346	−	5.20820i	−0.0330093	−	0.187205i
$775$	−3.04920	+	9.72164i	−0.109531	+	0.349212i
$776$	6.24580	+	2.27328i	0.224211	+	0.0816062i
$777$	−0.122406	+	1.39911i	−0.00439130	+	0.0501928i
$778$	−8.63778	+	8.63778i	−0.309679	+	0.309679i
$779$	43.2795	−	24.7080i	1.55065	−	0.885257i
$780$	2.17217	−	1.90782i	0.0777761	−	0.0683110i
$781$	−1.36414	−	1.62572i	−0.0488129	−	0.0581729i
$782$	18.3597	+	39.3724i	0.656540	+	1.40795i
$783$	1.12384	−	0.786922i	0.0401628	−	0.0281223i
$784$	0.909908	−	0.160441i	0.0324967	−	0.00573005i
$785$	7.28628	+	24.9285i	0.260058	+	0.889736i
$786$	6.33257	−	10.9683i	0.225875	−	0.391227i
$787$	−4.56021	+	17.0189i	−0.162554	+	0.606660i	0.835785	+	0.549056i	$0.185013\pi$
$787$	−4.56021	+	17.0189i	−0.162554	+	0.606660i	−0.998340	+	0.0576039i	$0.981654\pi$
$788$	1.16994	+	13.3725i	0.0416773	+	0.476374i
$789$	−15.7503	−	13.2160i	−0.560724	−	0.470504i
$790$	−14.7752	−	29.9045i	−0.525677	−	1.06396i
$791$	18.1938	+	10.5042i	0.646895	+	0.373485i
$792$	−1.69977	−	0.792616i	−0.0603987	−	0.0281644i
$793$	6.58041	+	4.60765i	0.233677	+	0.163623i
$794$	−3.25516	+	18.4609i	−0.115521	+	0.655153i
$795$	3.07422	+	7.88782i	0.109031	+	0.279752i
$796$	−10.5241	+	8.83073i	−0.373015	+	0.312997i
$797$	17.1106	+	17.1106i	0.606089	+	0.606089i	0.941922	−	0.335833i	$-0.109018\pi$
$797$	17.1106	+	17.1106i	0.606089	+	0.606089i	−0.335833	+	0.941922i	$0.609018\pi$
$798$	−0.988409	+	10.6990i	−0.0349893	+	0.378740i
$799$			41.5126i			1.46861i
$800$	−1.07488	+	4.88310i	−0.0380026	+	0.172644i
$801$	−0.720059	+	1.97835i	−0.0254420	+	0.0699014i
$802$	20.2301	+	28.8915i	0.714349	+	1.02020i
$803$	−13.4015	+	19.1394i	−0.472930	+	0.675415i
$804$	1.44399	+	3.96732i	0.0509255	+	0.139917i
$805$	7.58671	+	37.9921i	0.267396	+	1.33904i
$806$	−2.28163	+	1.31730i	−0.0803669	+	0.0463999i
$807$	10.0624	−	0.880349i	0.354214	−	0.0309897i
$808$	−2.21262	+	0.193579i	−0.0778396	+	0.00681008i
$809$	39.8409	−	23.0022i	1.40073	−	0.808713i	0.406264	−	0.913756i	$-0.366831\pi$
$809$	39.8409	−	23.0022i	1.40073	−	0.808713i	0.994468	+	0.105043i	$0.0334980\pi$
$810$	1.24090	−	1.86015i	0.0436007	−	0.0653591i
$811$	−2.11995	−	5.82451i	−0.0744415	−	0.204526i	0.896891	−	0.442252i	$-0.145820\pi$
$811$	−2.11995	−	5.82451i	−0.0744415	−	0.204526i	−0.971332	+	0.237726i	$0.923598\pi$
$812$	1.93974	−	2.77023i	0.0680714	−	0.0972160i
$813$	1.36004	+	1.94234i	0.0476988	+	0.0681209i
$814$	−0.365479	+	1.00415i	−0.0128100	+	0.0351953i
$815$	−20.0184	+	14.7012i	−0.701215	+	0.514961i
$816$		−	6.18056i		−	0.216363i
$817$	−22.2955	+	5.85817i	−0.780019	+	0.204951i
$818$	−26.1762	−	26.1762i	−0.915228	−	0.915228i
$819$	−2.44137	+	2.04855i	−0.0853084	+	0.0715822i
$820$	−23.8200	+	9.28367i	−0.831831	+	0.324200i
$821$	−3.42531	+	19.4259i	−0.119544	+	0.677969i	0.864855	+	0.502021i	$0.167410\pi$
$821$	−3.42531	+	19.4259i	−0.119544	+	0.677969i	−0.984399	+	0.175948i	$0.943701\pi$
$822$	−9.22316	−	6.45813i	−0.321695	−	0.225253i
$823$	−27.5750	−	12.8584i	−0.961204	−	0.448217i	−0.122298	−	0.992493i	$-0.539026\pi$
$823$	−27.5750	−	12.8584i	−0.961204	−	0.448217i	−0.838906	+	0.544277i	$0.816804\pi$
$824$	−16.5232	−	9.53967i	−0.575612	−	0.332330i
$825$	−3.57560	+	8.66900i	−0.124486	+	0.301816i
$826$	10.9900	+	9.22170i	0.382391	+	0.320864i
$827$	2.72050	+	31.0954i	0.0946010	+	1.08129i	0.884023	+	0.467443i	$0.154825\pi$
$827$	2.72050	+	31.0954i	0.0946010	+	1.08129i	−0.789422	+	0.613851i	$0.789620\pi$
$828$	1.81922	−	6.78941i	0.0632221	−	0.235948i
$829$	16.0947	−	27.8769i	0.558994	−	0.968205i	−0.438587	−	0.898689i	$-0.644521\pi$
$829$	16.0947	−	27.8769i	0.558994	−	0.968205i	0.997581	−	0.0695167i	$-0.0221457\pi$
$830$	13.0428	+	7.14278i	0.452721	+	0.247930i
$831$	−15.0359	+	2.65124i	−0.521590	+	0.0919703i
$832$	−1.05909	+	0.741584i	−0.0367174	+	0.0257098i
$833$	2.41336	+	5.17547i	0.0836181	+	0.179320i
$834$	10.4909	+	12.5025i	0.363269	+	0.432927i
$835$	25.9939	+	1.68416i	0.899557	+	0.0582828i
$836$	−2.83330	+	7.66838i	−0.0979919	+	0.265217i
$837$	−1.44089	+	1.44089i	−0.0498044	+	0.0498044i
$838$	−0.123535	+	1.41201i	−0.00426744	+	0.0487771i
$839$	19.9397	+	7.25745i	0.688394	+	0.250555i	0.662447	−	0.749108i	$-0.269518\pi$
$839$	19.9397	+	7.25745i	0.688394	+	0.250555i	0.0259467	+	0.999663i	$0.491740\pi$
$840$	1.30607	−	5.35485i	0.0450637	−	0.184760i
$841$	−4.70894	−	26.7058i	−0.162377	−	0.920888i
$842$	−2.26071	+	4.84811i	−0.0779093	+	0.167077i
$843$	24.0333	−	6.43969i	0.827749	−	0.221795i
$844$	−0.543285	−	0.940998i	−0.0187007	−	0.0323905i
$845$	0.571582	+	25.3246i	0.0196630	+	0.871192i
$846$	4.31737	−	5.14524i	0.148434	−	0.176897i
$847$	17.8157	+	4.77371i	0.612156	+	0.164027i
$848$	−0.979885	−	3.65698i	−0.0336494	−	0.125581i
$849$	−1.20732	+	0.439428i	−0.0414351	+	0.0150811i
$850$	−30.8714	+	1.39426i	−1.05888	+	0.0478227i
$851$	−3.94399	−	0.695432i	−0.135198	−	0.0238391i
$852$	−1.02554	+	0.478218i	−0.0351345	+	0.0163835i
$853$	23.9170	+	2.09247i	0.818904	+	0.0716448i	0.488905	−	0.872337i	$-0.337396\pi$
$853$	23.9170	+	2.09247i	0.818904	+	0.0716448i	0.329998	+	0.943982i	$0.392952\pi$
$854$	15.3155			0.524085
$855$	−8.52596	−	4.72314i	−0.291582	−	0.161528i
$856$	12.5319			0.428330
$857$	−6.07444	−	0.531445i	−0.207499	−	0.0181538i	−0.0170677	−	0.999854i	$-0.505433\pi$
$857$	−6.07444	−	0.531445i	−0.207499	−	0.0181538i	−0.190431	+	0.981701i	$0.560989\pi$
$858$	−2.19765	+	1.02478i	−0.0750266	+	0.0349855i
$859$	24.9057	+	4.39155i	0.849773	+	0.149838i	0.581542	−	0.813517i	$-0.302450\pi$
$859$	24.9057	+	4.39155i	0.849773	+	0.149838i	0.268231	+	0.963355i	$0.413561\pi$
$860$	11.7543	−	1.29622i	0.400818	−	0.0442009i
$861$	26.4826	−	9.63889i	0.902525	−	0.328492i
$862$	−6.68836	−	24.9613i	−0.227806	−	0.850185i
$863$	40.6692	+	10.8973i	1.38440	+	0.370948i	0.872716	−	0.488229i	$-0.162357\pi$
$863$	40.6692	+	10.8973i	1.38440	+	0.370948i	0.511680	+	0.859176i	$0.329024\pi$
$864$	−0.642788	+	0.766044i	−0.0218681	+	0.0260614i
$865$	−16.4129	+	17.1709i	−0.558054	+	0.583827i
$866$	12.2566	+	21.2291i	0.416497	+	0.721394i
$867$	20.4770	−	5.48680i	0.695436	−	0.186342i
$868$	−2.12278	+	4.55231i	−0.0720518	+	0.154516i
$869$	4.85810	+	27.5517i	0.164800	+	0.934626i
$870$	1.59345	+	2.62150i	0.0540231	+	0.0888770i
$871$	5.12940	+	1.86695i	0.173803	+	0.0632591i
$872$	0.540358	−	6.17632i	0.0182988	−	0.209157i
$873$	4.69988	−	4.69988i	0.159067	−	0.159067i
$874$	−30.1467	−	5.46673i	−1.01973	−	0.184915i
$875$	−27.0416	−	5.31571i	−0.914174	−	0.179704i
$876$	8.00786	+	9.54340i	0.270561	+	0.322442i
$877$	−6.59448	−	14.1419i	−0.222680	−	0.477538i	0.762950	−	0.646457i	$-0.223750\pi$
$877$	−6.59448	−	14.1419i	−0.222680	−	0.477538i	−0.985630	+	0.168919i	$0.945972\pi$
$878$	7.95650	−	5.57120i	0.268519	−	0.188019i
$879$	−21.6461	+	3.81680i	−0.730106	+	0.128737i
$880$	2.01437	−	3.67826i	0.0679046	−	0.123994i
$881$	−9.17542	+	15.8923i	−0.309128	+	0.535425i	−0.978172	−	0.207798i	$-0.933370\pi$
$881$	−9.17542	+	15.8923i	−0.309128	+	0.535425i	0.669044	+	0.743223i	$0.266704\pi$
$882$	0.239135	−	0.892463i	0.00805208	−	0.0300508i
$883$	−3.08247	−	35.2327i	−0.103733	−	1.18568i	−0.852458	−	0.522795i	$-0.824889\pi$
$883$	−3.08247	−	35.2327i	−0.103733	−	1.18568i	0.748725	−	0.662881i	$-0.230666\pi$
$884$	−6.12140	−	5.13647i	−0.205885	−	0.172758i
$885$	−11.6678	+	5.76479i	−0.392208	+	0.193781i
$886$	−23.9723	−	13.8404i	−0.805365	−	0.464978i
$887$	2.63966	+	1.23089i	0.0886311	+	0.0413293i	0.466428	−	0.884559i	$-0.345541\pi$
$887$	2.63966	+	1.23089i	0.0886311	+	0.0413293i	−0.377797	+	0.925888i	$0.623318\pi$
$888$	0.466725	+	0.326804i	0.0156623	+	0.0109668i
$889$	4.16500	−	23.6209i	0.139690	−	0.792219i
$890$	−4.31036	−	1.89275i	−0.144484	−	0.0634450i
$891$	−1.43671	+	1.20554i	−0.0481315	+	0.0403871i
$892$	12.6700	+	12.6700i	0.424223	+	0.424223i
$893$	−23.9006	−	16.9089i	−0.799804	−	0.565836i
$894$			18.4885i			0.618349i
$895$	−7.59543	+	49.5956i	−0.253887	+	1.65780i
$896$	−0.843068	+	2.31631i	−0.0281649	+	0.0773825i
$897$	−5.21253	−	7.44426i	−0.174041	−	0.248557i
$898$	18.4608	−	26.3648i	0.616046	−	0.879804i
$899$	−0.956176	−	2.62707i	−0.0318902	−	0.0876177i
$900$	3.97133	+	3.03786i	0.132378	+	0.101262i
$901$	20.2646	−	11.6998i	0.675111	−	0.389776i
$902$	21.3611	−	1.86885i	0.711246	−	0.0622259i
$903$	−12.9865	+	1.13617i	−0.432163	+	0.0378094i
$904$	7.38094	−	4.26139i	0.245486	−	0.141732i
$905$	14.7660	−	2.94865i	0.490839	−	0.0980166i
$906$	4.16044	+	11.4307i	0.138221	+	0.379760i
$907$	1.06502	−	1.52101i	0.0353634	−	0.0505042i	−0.801081	−	0.598556i	$-0.795741\pi$
$907$	1.06502	−	1.52101i	0.0353634	−	0.0505042i	0.836444	+	0.548052i	$0.184630\pi$
$908$	−14.9458	−	21.3448i	−0.495994	−	0.708353i
$909$	−0.759650	+	2.08712i	−0.0251960	+	0.0692255i
$910$	−4.21816	−	5.74381i	−0.139831	−	0.190406i
$911$			21.4552i			0.710842i	0.934706	+	0.355421i	$0.115663\pi$
$911$			21.4552i			0.710842i	−0.934706	+	0.355421i	$0.884337\pi$
$912$	3.55842	+	2.51747i	0.117831	+	0.0833617i
$913$	−8.81944	−	8.81944i	−0.291881	−	0.291881i
$914$	−2.80919	+	2.35719i	−0.0929196	+	0.0779688i
$915$	−5.58593	+	12.7209i	−0.184665	+	0.420539i
$916$	−0.296335	+	1.68060i	−0.00979119	+	0.0555286i
$917$	−25.5732	−	17.9066i	−0.844502	−	0.591326i
$918$	−5.60149	−	2.61202i	−0.184877	−	0.0862095i
$919$	37.6294	+	21.7254i	1.24128	+	0.716654i	0.969355	−	0.245665i	$-0.0790062\pi$
$919$	37.6294	+	21.7254i	1.24128	+	0.716654i	0.271926	+	0.962318i	$0.412340\pi$
$920$	14.8868	+	5.04094i	0.490803	+	0.166195i
$921$	−11.8142	−	9.91325i	−0.389290	−	0.326653i
$922$	−0.422685	−	4.83131i	−0.0139204	−	0.159111i
$923$	−0.378655	+	1.41316i	−0.0124636	+	0.0465147i
$924$	−2.31151	+	4.00365i	−0.0760430	+	0.131710i
$925$	1.52707	−	2.40497i	0.0502098	−	0.0790750i
$926$	−20.9100	+	3.68699i	−0.687144	+	0.121162i
$927$	−15.6289	+	10.9435i	−0.513320	+	0.359430i
$928$	−0.579814	−	1.24342i	−0.0190333	−	0.0408171i
$929$	21.7321	+	25.8993i	0.713008	+	0.849729i	0.993932	−	0.110001i	$-0.0350853\pi$
$929$	21.7321	+	25.8993i	0.713008	+	0.849729i	−0.280924	+	0.959730i	$0.590641\pi$
$930$	−3.00687	−	3.42350i	−0.0985992	−	0.112261i
$931$	−3.96276	−	0.718598i	−0.129874	−	0.0235511i
$932$	7.85071	−	7.85071i	0.257159	−	0.257159i
$933$	2.03739	−	23.2875i	0.0667011	−	0.762398i
$934$	34.1484	+	12.4290i	1.11737	+	0.406689i
$935$	25.1814	+	6.14183i	0.823519	+	0.200859i
$936$	0.224512	+	1.27327i	0.00733840	+	0.0416181i
$937$	11.5336	−	24.7338i	0.376785	−	0.808017i	−0.622885	−	0.782314i	$-0.714039\pi$
$937$	11.5336	−	24.7338i	0.376785	−	0.808017i	0.999670	−	0.0257040i	$-0.00818272\pi$
$938$	10.0523	−	2.69351i	0.328220	−	0.0879463i
$939$	8.54500	+	14.8004i	0.278855	+	0.482992i
$940$	10.8569	+	10.3776i	0.354112	+	0.338480i
$941$	−4.62732	+	5.51463i	−0.150846	+	0.179772i	−0.836176	−	0.548461i	$-0.815214\pi$
$941$	−4.62732	+	5.51463i	−0.150846	+	0.179772i	0.685329	+	0.728233i	$0.259658\pi$
$942$	−11.2190	−	3.00613i	−0.365536	−	0.0979452i
$943$	20.7993	+	77.6240i	0.677318	+	2.52779i
$944$	5.46913	−	1.99060i	0.178005	−	0.0647886i
$945$	−4.30118	−	3.44676i	−0.139917	−	0.112123i
$946$	−9.76792	−	1.72235i	−0.317583	−	0.0559984i
$947$	10.9059	−	5.08549i	0.354393	−	0.165256i	−0.237266	−	0.971445i	$-0.576251\pi$
$947$	10.9059	−	5.08549i	0.354393	−	0.165256i	0.591659	+	0.806189i	$0.298473\pi$
$948$	14.8603	+	1.30010i	0.482639	+	0.0422254i
$949$	16.1071			0.522860
$950$	11.7718	−	18.3419i	0.381927	−	0.595089i
$951$	17.2762			0.560220
$952$	−15.1769	−	1.32781i	−0.491886	−	0.0430345i
$953$	−20.7271	+	9.66521i	−0.671417	+	0.313087i	−0.728265	−	0.685296i	$-0.759673\pi$
$953$	−20.7271	+	9.66521i	−0.671417	+	0.313087i	0.0568476	+	0.998383i	$0.481895\pi$
$954$	−3.72847	−	0.657430i	−0.120714	−	0.0212851i
$955$	13.1323	+	10.5236i	0.424950	+	0.340535i
$956$	−21.0370	+	7.65683i	−0.680384	+	0.247640i
$957$	−0.665965	−	2.48541i	−0.0215276	−	0.0803420i
$958$	−15.1757	−	4.06630i	−0.490303	−	0.131376i
$959$	−17.8399	+	21.2608i	−0.576082	+	0.686548i
$960$	−1.61641	−	1.54506i	−0.0521695	−	0.0498666i
$961$	−13.4238	−	23.2508i	−0.433027	−	0.750025i
$962$	0.711556	−	0.190661i	0.0229415	−	0.00614715i
$963$	5.29620	−	11.3577i	0.170668	−	0.365998i
$964$	−2.74694	−	15.5787i	−0.0884729	−	0.501755i
$965$	−51.0492	−	12.4511i	−1.64333	−	0.400815i
$966$	−16.2811	−	5.92585i	−0.523837	−	0.190661i
$967$	4.54893	−	51.9945i	0.146284	−	1.67203i	−0.468599	−	0.883411i	$-0.655241\pi$
$967$	4.54893	−	51.9945i	0.146284	−	1.67203i	0.614882	−	0.788619i	$-0.289204\pi$
$968$	5.29096	−	5.29096i	0.170058	−	0.170058i
$969$	−9.33699	+	25.2707i	−0.299947	+	0.811812i
$970$	9.80780	+	11.1667i	0.314909	+	0.358543i
$971$	−18.7719	−	22.3714i	−0.602417	−	0.717933i	0.375524	−	0.926813i	$-0.377463\pi$
$971$	−18.7719	−	22.3714i	−0.602417	−	0.717933i	−0.977941	+	0.208880i	$0.933018\pi$
$972$	0.422618	+	0.906308i	0.0135555	+	0.0290698i
$973$	32.9548	−	23.0752i	1.05648	−	0.739758i
$974$	−6.27338	+	1.10617i	−0.201012	+	0.0354439i
$975$	6.30922	−	1.40865i	0.202057	−	0.0451129i
$976$	3.10663	−	5.38084i	0.0994408	−	0.172237i
$977$	−9.49051	+	35.4191i	−0.303628	+	1.13316i	0.630491	+	0.776196i	$0.282853\pi$
$977$	−9.49051	+	35.4191i	−0.303628	+	1.13316i	−0.934120	+	0.356960i	$0.883813\pi$
$978$	−0.968067	−	11.0651i	−0.0309554	−	0.353822i
$979$	3.02472	+	2.53804i	0.0966704	+	0.0811161i
$980$	1.95686	+	0.662628i	0.0625096	+	0.0211669i
$981$	−5.36928	−	3.09996i	−0.171428	−	0.0989740i
$982$	−38.1456	−	17.7876i	−1.21728	−	0.567625i
$983$	10.2215	+	7.15715i	0.326014	+	0.228278i	0.725112	−	0.688631i	$-0.241788\pi$
$983$	10.2215	+	7.15715i	0.326014	+	0.228278i	−0.399098	+	0.916908i	$0.630677\pi$
$984$	1.98534	−	11.2594i	0.0632903	−	0.358937i
$985$	−12.0682	+	27.4830i	−0.384526	+	0.875681i
$986$	6.49565	−	5.45050i	0.206864	−	0.173579i
$987$	−11.7071	−	11.7071i	−0.372640	−	0.372640i
$988$	5.45066	−	1.43217i	0.173409	−	0.0455634i
$989$		−	37.1727i		−	1.18202i
$990$	−2.48232	−	3.38014i	−0.0788934	−	0.107428i
$991$	−4.14534	+	11.3892i	−0.131681	+	0.361791i	−0.987957	−	0.154728i	$-0.950550\pi$
$991$	−4.14534	+	11.3892i	−0.131681	+	0.361791i	0.856276	+	0.516518i	$0.172772\pi$
$992$	1.16879	+	1.66921i	0.0371091	+	0.0529973i
$993$	4.55090	−	6.49936i	0.144419	−	0.206251i
$994$	0.953983	+	2.62105i	0.0302585	+	0.0831345i
$995$	−30.1247	+	6.01567i	−0.955018	+	0.190709i
$996$	−5.75933	+	3.32515i	−0.182491	+	0.105362i
$997$	−40.2953	+	3.52538i	−1.27616	+	0.111650i	−0.705012	−	0.709195i	$-0.749059\pi$
$997$	−40.2953	+	3.52538i	−1.27616	+	0.111650i	−0.571151	+	0.820845i	$0.693503\pi$
$998$	−35.1230	+	3.07287i	−1.11180	+	0.0972699i
$999$	0.493432	−	0.284883i	0.0156115	−	0.00901330i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bh.b.13.9	✓	120
5.2	odd	4	inner	570.2.bh.b.127.3	yes	120
19.3	odd	18	inner	570.2.bh.b.193.3	yes	120
95.22	even	36	inner	570.2.bh.b.307.9	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.b.13.9	✓	120	1.1	even	1	trivial
570.2.bh.b.127.3	yes	120	5.2	odd	4	inner
570.2.bh.b.193.3	yes	120	19.3	odd	18	inner
570.2.bh.b.307.9	yes	120	95.22	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.996195 + 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(1.74492 + 1.39830i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(0.637980 + 2.38097i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +O(q^{10})\)	\(q+(0.996195 + 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(1.74492 + 1.39830i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(0.637980 + 2.38097i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +(1.61641 + 1.54506i) q^{10} +(-0.937744 - 1.62422i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(-0.546408 + 1.17178i) q^{13} +(0.428037 + 2.42752i) q^{14} +(-2.17238 - 0.529853i) q^{15} +(0.939693 + 0.342020i) q^{16} +(-0.538672 + 6.15705i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-3.32547 - 2.81803i) q^{19} +(1.47560 + 1.68006i) q^{20} +(-1.58445 - 1.88827i) q^{21} +(-0.792616 - 1.69977i) q^{22} +(5.75775 - 4.03162i) q^{23} +(-0.984808 + 0.173648i) q^{24} +(1.08952 + 4.87985i) q^{25} +(-0.646456 + 1.11969i) q^{26} +(-0.258819 + 0.965926i) q^{27} +(0.214836 + 2.45559i) q^{28} +(-1.05098 - 0.881877i) q^{29} +(-2.11794 - 0.717173i) q^{30} +(1.76472 + 1.01886i) q^{31} +(0.906308 + 0.422618i) q^{32} +(1.53631 + 1.07574i) q^{33} +(-1.07324 + 6.08667i) q^{34} +(-2.21609 + 5.04670i) q^{35} +(0.766044 - 0.642788i) q^{36} +(-0.402885 - 0.402885i) q^{37} +(-3.06720 - 3.09714i) q^{38} -1.29291i q^{39} +(1.32356 + 1.80227i) q^{40} +(-3.91035 + 10.7436i) q^{41} +(-1.41385 - 2.01918i) q^{42} +(3.03339 - 4.33212i) q^{43} +(-0.641455 - 1.76238i) q^{44} +(2.19277 - 0.437879i) q^{45} +(6.08722 - 3.51446i) q^{46} +(6.69108 - 0.585394i) q^{47} +(-0.996195 + 0.0871557i) q^{48} +(0.800160 - 0.461973i) q^{49} +(0.660064 + 4.95624i) q^{50} +(-2.11388 - 5.80783i) q^{51} +(-0.741584 + 1.05909i) q^{52} +(-2.17155 - 3.10130i) q^{53} +(-0.342020 + 0.939693i) q^{54} +(0.634855 - 4.14539i) q^{55} +2.46497i q^{56} +(4.20485 + 1.14860i) q^{57} +(-0.970120 - 0.970120i) q^{58} +(4.45848 - 3.74111i) q^{59} +(-2.04737 - 0.899034i) q^{60} +(1.07892 - 6.11887i) q^{61} +(1.66921 + 1.16879i) q^{62} +(2.23402 + 1.04174i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-2.59193 + 1.28062i) q^{65} +(1.43671 + 1.20554i) q^{66} +(-0.367966 - 4.20587i) q^{67} +(-1.59965 + 5.96997i) q^{68} +(-3.51446 + 6.08722i) q^{69} +(-2.64750 + 4.83436i) q^{70} +(1.11437 - 0.196494i) q^{71} +(0.819152 - 0.573576i) q^{72} +(-5.26499 - 11.2908i) q^{73} +(-0.366238 - 0.436466i) q^{74} +(-3.04975 - 3.96220i) q^{75} +(-2.78560 - 3.35268i) q^{76} +(3.26897 - 3.26897i) q^{77} +(0.112685 - 1.28799i) q^{78} +(-14.0174 - 5.10192i) q^{79} +(1.16145 + 1.91077i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(-4.83184 + 10.3619i) q^{82} +(6.42370 - 1.72123i) q^{83} +(-1.23248 - 2.13472i) q^{84} +(-9.54934 + 9.99035i) q^{85} +(3.39941 - 4.05126i) q^{86} +(1.32521 + 0.355089i) q^{87} +(-0.485412 - 1.81158i) q^{88} +(-1.97835 + 0.720059i) q^{89} +(2.22259 - 0.245100i) q^{90} +(-3.13857 - 0.553414i) q^{91} +(6.37036 - 2.97055i) q^{92} +(-2.02997 - 0.177599i) q^{93} +6.71664 q^{94} +(-1.86224 - 9.56724i) q^{95} -1.00000 q^{96} +(6.62135 + 0.579293i) q^{97} +(0.837379 - 0.390476i) q^{98} +(-1.84700 - 0.325675i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{5} + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^5 + 12 * q^7	\( 120 q + 12 q^{5} + 12 q^{7} + 12 q^{10} - 48 q^{13} - 12 q^{17} + 60 q^{21} + 12 q^{22} + 48 q^{23} + 12 q^{25} + 12 q^{26} - 12 q^{30} + 24 q^{33} - 24 q^{38} - 36 q^{41} + 24 q^{43} + 96 q^{47} + 24 q^{52} - 36 q^{55} + 12 q^{57} - 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} - 24 q^{66} + 72 q^{67} + 12 q^{68} + 96 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} - 12 q^{80} - 24 q^{82} - 60 q^{83} - 36 q^{85} - 72 q^{86} + 12 q^{87} - 144 q^{91} - 12 q^{92} + 48 q^{93} + 156 q^{95} - 120 q^{96} - 216 q^{97} - 96 q^{98}+O(q^{100}) \) 120 * q + 12 * q^5 + 12 * q^7 + 12 * q^10 - 48 * q^13 - 12 * q^17 + 60 * q^21 + 12 * q^22 + 48 * q^23 + 12 * q^25 + 12 * q^26 - 12 * q^30 + 24 * q^33 - 24 * q^38 - 36 * q^41 + 24 * q^43 + 96 * q^47 + 24 * q^52 - 36 * q^55 + 12 * q^57 - 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 - 24 * q^66 + 72 * q^67 + 12 * q^68 + 96 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 - 12 * q^80 - 24 * q^82 - 60 * q^83 - 36 * q^85 - 72 * q^86 + 12 * q^87 - 144 * q^91 - 12 * q^92 + 48 * q^93 + 156 * q^95 - 120 * q^96 - 216 * q^97 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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