LMFDB - Embedded newform 570.2.bh.a.67.7

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			67.7
Character	$\chi$	$=$	570.67
Dual form			570.2.bh.a.553.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.819152 + 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-1.42376 + 1.72421i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-2.79653 + 0.749327i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +O(q^{10})$	\(q+(0.819152 + 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-1.42376 + 1.72421i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-2.79653 + 0.749327i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +(-2.15524 + 0.595756i) q^{10} +(-2.88592 - 4.99856i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(-0.361148 - 4.12794i) q^{13} +(-2.72058 - 0.990209i) q^{14} +(1.56862 - 1.59356i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(2.24133 - 3.20095i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-2.09658 + 3.82156i) q^{19} +(-2.10718 - 0.748182i) q^{20} +(2.85119 - 0.502742i) q^{21} +(0.503049 - 5.74988i) q^{22} +(-1.92105 + 4.11971i) q^{23} +(0.342020 - 0.939693i) q^{24} +(-0.945812 - 4.90973i) q^{25} +(2.07185 - 3.58856i) q^{26} +(-0.965926 - 0.258819i) q^{27} +(-1.66061 - 2.37159i) q^{28} +(1.40239 - 7.95333i) q^{29} +(2.19897 - 0.405647i) q^{30} +(2.77366 + 1.60137i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(2.43928 + 5.23106i) q^{33} +(3.67198 - 1.33649i) q^{34} +(2.68959 - 5.88867i) q^{35} +(0.173648 + 0.984808i) q^{36} +(-7.02090 + 7.02090i) q^{37} +(-3.90938 + 1.92789i) q^{38} +4.14371i q^{39} +(-1.29696 - 1.82151i) q^{40} +(-0.0737608 - 0.0879047i) q^{41} +(2.62392 + 1.22355i) q^{42} +(-9.55225 + 4.45429i) q^{43} +(3.71007 - 4.42149i) q^{44} +(-1.70154 + 1.45078i) q^{45} +(-3.93660 + 2.27280i) q^{46} +(-8.82560 + 6.17975i) q^{47} +(0.819152 - 0.573576i) q^{48} +(1.19689 - 0.691027i) q^{49} +(2.04134 - 4.56431i) q^{50} +(-2.51178 + 2.99343i) q^{51} +(3.75548 - 1.75121i) q^{52} +(-7.67276 - 3.57787i) q^{53} +(-0.642788 - 0.766044i) q^{54} +(12.7274 + 2.14082i) q^{55} -2.89518i q^{56} +(2.42167 - 3.62429i) q^{57} +(5.71061 - 5.71061i) q^{58} +(0.167014 + 0.947182i) q^{59} +(2.03396 + 0.928988i) q^{60} +(-4.16908 + 1.51742i) q^{61} +(1.35354 + 2.90267i) q^{62} +(-2.88416 + 0.252331i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(7.63163 + 5.25450i) q^{65} +(-1.00227 + 5.68415i) q^{66} +(7.76967 + 11.0962i) q^{67} +(3.77449 + 1.01137i) q^{68} +(2.27280 - 3.93660i) q^{69} +(5.58078 - 3.28103i) q^{70} +(2.27568 - 6.25238i) q^{71} +(-0.422618 + 0.906308i) q^{72} +(0.998934 - 11.4179i) q^{73} +(-9.77821 + 1.72416i) q^{74} +(0.514302 + 4.97348i) q^{75} +(-4.30817 - 0.663089i) q^{76} +(11.8161 + 11.8161i) q^{77} +(-2.37673 + 3.39433i) q^{78} +(1.62835 - 1.36634i) q^{79} +(-0.0176381 - 2.23600i) q^{80} +(0.939693 + 0.342020i) q^{81} +(-0.0100012 - 0.114315i) q^{82} +(-2.74768 - 10.2545i) q^{83} +(1.44759 + 2.50730i) q^{84} +(2.32800 + 8.42192i) q^{85} +(-10.3796 - 1.83021i) q^{86} +(-2.09023 + 7.80084i) q^{87} +(5.57517 - 1.49386i) q^{88} +(-1.22839 - 1.03074i) q^{89} +(-2.22595 + 0.212451i) q^{90} +(4.10314 + 11.2733i) q^{91} +(-4.52829 - 0.396174i) q^{92} +(-2.62353 - 1.83702i) q^{93} -10.7741 q^{94} +(-3.60416 - 9.05594i) q^{95} +1.00000 q^{96} +(7.59355 + 5.31706i) q^{97} +(1.37679 + 0.120454i) q^{98} +(-1.97409 - 5.42376i) 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} + 36 q^{21} - 36 q^{22} - 96 q^{23} + 12 q^{25} + 12 q^{26} + 12 q^{30} + 24 q^{38} + 60 q^{41} + 96 q^{43} - 48 q^{47} - 24 q^{52} - 72 q^{53} + 108 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} - 48 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} + 12 q^{80} - 72 q^{82} + 12 q^{83} - 108 q^{85} - 24 q^{86} + 12 q^{87} - 48 q^{91} - 84 q^{92} - 48 q^{93} - 204 q^{95} + 120 q^{96} + 24 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 + 36 * q^21 - 36 * q^22 - 96 * q^23 + 12 * q^25 + 12 * q^26 + 12 * q^30 + 24 * q^38 + 60 * q^41 + 96 * q^43 - 48 * q^47 - 24 * q^52 - 72 * q^53 + 108 * 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 - 48 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 + 12 * q^80 - 72 * q^82 + 12 * q^83 - 108 * q^85 - 24 * q^86 + 12 * q^87 - 48 * q^91 - 84 * q^92 - 48 * q^93 - 204 * q^95 + 120 * q^96 + 24 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$3$	−0.996195	−	0.0871557i	−0.575153	−	0.0503194i
$3$	−0.996195	−	0.0871557i	−0.575153	−	0.0503194i
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	−1.42376	+	1.72421i	−0.636725	+	0.771091i
$5$	−1.42376	+	1.72421i	−0.636725	+	0.771091i
$6$	−0.766044	−	0.642788i	−0.312736	−	0.262417i
$7$	−2.79653	+	0.749327i	−1.05699	+	0.283219i	−0.745137	−	0.666912i	$-0.767616\pi$
$7$	−2.79653	+	0.749327i	−1.05699	+	0.283219i	−0.311851	+	0.950131i	$0.600949\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$	0.984808	+	0.173648i	0.328269	+	0.0578827i
$10$	−2.15524	+	0.595756i	−0.681548	+	0.188395i
$11$	−2.88592	−	4.99856i	−0.870138	−	1.50712i	−0.861854	−	0.507157i	$-0.830696\pi$
$11$	−2.88592	−	4.99856i	−0.870138	−	1.50712i	−0.00828384	−	0.999966i	$-0.502637\pi$
$12$	−0.258819	−	0.965926i	−0.0747146	−	0.278839i
$13$	−0.361148	−	4.12794i	−0.100164	−	1.14488i	−0.865382	−	0.501113i	$-0.832924\pi$
$13$	−0.361148	−	4.12794i	−0.100164	−	1.14488i	0.765218	−	0.643772i	$-0.222631\pi$
$14$	−2.72058	−	0.990209i	−0.727105	−	0.264645i
$15$	1.56862	−	1.59356i	0.405015	−	0.411456i
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	2.24133	−	3.20095i	0.543603	−	0.776345i	−0.449539	−	0.893261i	$-0.648412\pi$
$17$	2.24133	−	3.20095i	0.543603	−	0.776345i	0.993142	+	0.116916i	$0.0373007\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	−2.09658	+	3.82156i	−0.480988	+	0.876727i
$19$	−2.09658	+	3.82156i	−0.480988	+	0.876727i
$20$	−2.10718	−	0.748182i	−0.471181	−	0.167299i
$21$	2.85119	−	0.502742i	0.622181	−	0.109707i
$22$	0.503049	−	5.74988i	0.107250	−	1.22588i
$23$	−1.92105	+	4.11971i	−0.400567	+	0.859018i	0.597787	+	0.801655i	$0.296047\pi$
$23$	−1.92105	+	4.11971i	−0.400567	+	0.859018i	−0.998353	+	0.0573628i	$0.981731\pi$
$24$	0.342020	−	0.939693i	0.0698146	−	0.191814i
$25$	−0.945812	−	4.90973i	−0.189162	−	0.981946i
$26$	2.07185	−	3.58856i	0.406324	−	0.703774i
$27$	−0.965926	−	0.258819i	−0.185893	−	0.0498097i
$28$	−1.66061	−	2.37159i	−0.313825	−	0.448189i
$29$	1.40239	−	7.95333i	0.260417	−	1.47690i	−0.521360	−	0.853337i	$-0.674575\pi$
$29$	1.40239	−	7.95333i	0.260417	−	1.47690i	0.781776	−	0.623559i	$-0.214314\pi$
$30$	2.19897	−	0.405647i	0.401474	−	0.0740607i
$31$	2.77366	+	1.60137i	0.498163	+	0.287615i	0.727955	−	0.685625i	$-0.240471\pi$
$31$	2.77366	+	1.60137i	0.498163	+	0.287615i	−0.229791	+	0.973240i	$0.573804\pi$
$32$	−0.996195	+	0.0871557i	−0.176104	+	0.0154071i
$33$	2.43928	+	5.23106i	0.424625	+	0.910611i
$34$	3.67198	−	1.33649i	0.629740	−	0.229207i
$35$	2.68959	−	5.88867i	0.454623	−	0.995366i
$36$	0.173648	+	0.984808i	0.0289414	+	0.164135i
$37$	−7.02090	+	7.02090i	−1.15423	+	1.15423i	−0.168533	+	0.985696i	$0.553903\pi$
$37$	−7.02090	+	7.02090i	−1.15423	+	1.15423i	−0.985696	+	0.168533i	$0.946097\pi$
$38$	−3.90938	+	1.92789i	−0.634185	+	0.312746i
$39$			4.14371i			0.663524i
$40$	−1.29696	−	1.82151i	−0.205068	−	0.288005i
$41$	−0.0737608	−	0.0879047i	−0.0115195	−	0.0137284i	0.760254	−	0.649626i	$-0.225075\pi$
$41$	−0.0737608	−	0.0879047i	−0.0115195	−	0.0137284i	−0.771773	+	0.635898i	$0.780630\pi$
$42$	2.62392	+	1.22355i	0.404880	+	0.188799i
$43$	−9.55225	+	4.45429i	−1.45670	+	0.679272i	−0.979855	−	0.199712i	$-0.935999\pi$
$43$	−9.55225	+	4.45429i	−1.45670	+	0.679272i	−0.476850	+	0.878985i	$0.658221\pi$
$44$	3.71007	−	4.42149i	0.559314	−	0.666564i
$45$	−1.70154	+	1.45078i	−0.253650	+	0.216270i
$46$	−3.93660	+	2.27280i	−0.580420	+	0.335105i
$47$	−8.82560	+	6.17975i	−1.28735	+	0.901410i	−0.998434	−	0.0559455i	$-0.982183\pi$
$47$	−8.82560	+	6.17975i	−1.28735	+	0.901410i	−0.288913	+	0.957355i	$0.593294\pi$
$48$	0.819152	−	0.573576i	0.118234	−	0.0827886i
$49$	1.19689	−	0.691027i	0.170985	−	0.0987181i
$50$	2.04134	−	4.56431i	0.288689	−	0.645491i
$51$	−2.51178	+	2.99343i	−0.351720	+	0.419164i
$52$	3.75548	−	1.75121i	0.520791	−	0.242849i
$53$	−7.67276	−	3.57787i	−1.05393	−	0.491458i	−0.183131	−	0.983089i	$-0.558623\pi$
$53$	−7.67276	−	3.57787i	−1.05393	−	0.491458i	−0.870804	+	0.491631i	$0.836401\pi$
$54$	−0.642788	−	0.766044i	−0.0874723	−	0.104245i
$55$	12.7274	+	2.14082i	1.71617	+	0.288668i
$56$		−	2.89518i		−	0.386884i
$57$	2.42167	−	3.62429i	0.320758	−	0.480049i
$58$	5.71061	−	5.71061i	0.749840	−	0.749840i
$59$	0.167014	+	0.947182i	0.0217433	+	0.123313i	0.993747	−	0.111651i	$-0.0356140\pi$
$59$	0.167014	+	0.947182i	0.0217433	+	0.123313i	−0.972004	+	0.234964i	$0.924503\pi$
$60$	2.03396	+	0.928988i	0.262583	+	0.119932i
$61$	−4.16908	+	1.51742i	−0.533796	+	0.194286i	−0.594832	−	0.803850i	$-0.702782\pi$
$61$	−4.16908	+	1.51742i	−0.533796	+	0.194286i	0.0610367	+	0.998136i	$0.480559\pi$
$62$	1.35354	+	2.90267i	0.171899	+	0.368639i
$63$	−2.88416	+	0.252331i	−0.363370	+	0.0317908i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	7.63163	+	5.25450i	0.946587	+	0.651741i
$66$	−1.00227	+	5.68415i	−0.123371	+	0.699671i
$67$	7.76967	+	11.0962i	0.949216	+	1.35562i	0.934590	+	0.355727i	$0.115767\pi$
$67$	7.76967	+	11.0962i	0.949216	+	1.35562i	0.0146259	+	0.999893i	$0.495344\pi$
$68$	3.77449	+	1.01137i	0.457724	+	0.122647i
$69$	2.27280	−	3.93660i	0.273612	−	0.473911i
$70$	5.58078	−	3.28103i	0.667031	−	0.392158i
$71$	2.27568	−	6.25238i	0.270073	−	0.742021i	−0.728314	−	0.685244i	$-0.759696\pi$
$71$	2.27568	−	6.25238i	0.270073	−	0.742021i	0.998387	−	0.0567765i	$-0.0180823\pi$
$72$	−0.422618	+	0.906308i	−0.0498060	+	0.106809i
$73$	0.998934	−	11.4179i	0.116916	−	1.33636i	−0.680419	−	0.732824i	$-0.738202\pi$
$73$	0.998934	−	11.4179i	0.116916	−	1.33636i	0.797335	−	0.603537i	$-0.206242\pi$
$74$	−9.77821	+	1.72416i	−1.13669	+	0.200430i
$75$	0.514302	+	4.97348i	0.0593864	+	0.574288i
$76$	−4.30817	−	0.663089i	−0.494181	−	0.0760615i
$77$	11.8161	+	11.8161i	1.34657	+	1.34657i
$78$	−2.37673	+	3.39433i	−0.269112	+	0.384332i
$79$	1.62835	−	1.36634i	0.183203	−	0.153726i	−0.546574	−	0.837411i	$-0.684068\pi$
$79$	1.62835	−	1.36634i	0.183203	−	0.153726i	0.729777	+	0.683685i	$0.239624\pi$
$80$	−0.0176381	−	2.23600i	−0.00197200	−	0.249992i
$81$	0.939693	+	0.342020i	0.104410	+	0.0380022i
$82$	−0.0100012	−	0.114315i	−0.00110445	−	0.0126240i
$83$	−2.74768	−	10.2545i	−0.301597	−	1.12557i	−0.935835	−	0.352437i	$-0.885353\pi$
$83$	−2.74768	−	10.2545i	−0.301597	−	1.12557i	0.634239	−	0.773137i	$-0.281314\pi$
$84$	1.44759	+	2.50730i	0.157945	+	0.273569i
$85$	2.32800	+	8.42192i	0.252507	+	0.913485i
$86$	−10.3796	−	1.83021i	−1.11926	−	0.197356i
$87$	−2.09023	+	7.80084i	−0.224096	+	0.836338i
$88$	5.57517	−	1.49386i	0.594315	−	0.159246i
$89$	−1.22839	−	1.03074i	−0.130209	−	0.109259i	0.575357	−	0.817902i	$-0.304863\pi$
$89$	−1.22839	−	1.03074i	−0.130209	−	0.109259i	−0.705567	+	0.708644i	$0.749307\pi$
$90$	−2.22595	+	0.212451i	−0.234636	+	0.0223943i
$91$	4.10314	+	11.2733i	0.430126	+	1.18176i
$92$	−4.52829	−	0.396174i	−0.472107	−	0.0413040i
$93$	−2.62353	−	1.83702i	−0.272048	−	0.190490i
$94$	−10.7741			−1.11126
$95$	−3.60416	−	9.05594i	−0.369779	−	0.929120i
$96$	1.00000			0.102062
$97$	7.59355	+	5.31706i	0.771008	+	0.539866i	0.891593	−	0.452837i	$-0.149588\pi$
$97$	7.59355	+	5.31706i	0.771008	+	0.539866i	−0.120585	+	0.992703i	$0.538477\pi$
$98$	1.37679	+	0.120454i	0.139077	+	0.0121677i
$99$	−1.97409	−	5.42376i	−0.198403	−	0.545108i
$100$	4.29015	−	2.56800i	0.429015	−	0.256800i
$101$	11.2686	+	9.45544i	1.12126	+	0.940851i	0.998668	−	0.0516053i	$-0.0164338\pi$
$101$	11.2686	+	9.45544i	1.12126	+	0.940851i	0.122596	+	0.992457i	$0.460878\pi$
$102$	−3.77449	+	1.01137i	−0.373730	+	0.100141i
$103$	−2.71460	+	10.1310i	−0.267477	+	0.998238i	0.693240	+	0.720707i	$0.256183\pi$
$103$	−2.71460	+	10.1310i	−0.267477	+	0.998238i	−0.960717	+	0.277531i	$0.910484\pi$
$104$	4.08076	+	0.719547i	0.400151	+	0.0705574i
$105$	−3.19258	+	5.63185i	−0.311564	+	0.549612i
$106$	−4.23298	−	7.33173i	−0.411143	−	0.712120i
$107$	−1.73372	−	6.47032i	−0.167605	−	0.625509i	−0.997694	−	0.0678782i	$-0.978377\pi$
$107$	−1.73372	−	6.47032i	−0.167605	−	0.625509i	0.830089	−	0.557631i	$-0.188290\pi$
$108$	−0.0871557	−	0.996195i	−0.00838657	−	0.0958589i
$109$	−0.511561	−	0.186193i	−0.0489987	−	0.0178341i	0.317405	−	0.948290i	$-0.397189\pi$
$109$	−0.511561	−	0.186193i	−0.0489987	−	0.0178341i	−0.366403	+	0.930456i	$0.619411\pi$
$110$	9.19778	+	9.05381i	0.876974	+	0.863247i
$111$	7.60610	−	6.38227i	0.721939	−	0.605779i
$112$	1.66061	−	2.37159i	0.156912	−	0.224094i
$113$	1.21043	+	1.21043i	0.113868	+	0.113868i	0.761745	−	0.647877i	$-0.224343\pi$
$113$	1.21043	+	1.21043i	0.113868	+	0.113868i	−0.647877	+	0.761745i	$0.724343\pi$
$114$	4.06253	−	1.57983i	0.380491	−	0.147965i
$115$	−4.36813	−	9.17777i	−0.407330	−	0.855832i
$116$	7.95333	−	1.40239i	0.738448	−	0.130208i
$117$	0.361148	−	4.12794i	0.0333881	−	0.381628i
$118$	−0.406471	+	0.871681i	−0.0374187	+	0.0802447i
$119$	−3.86938	+	10.6310i	−0.354706	+	0.974546i
$120$	1.13327	+	1.92761i	0.103453	+	0.175966i
$121$	−11.1571	+	19.3246i	−1.01428	+	1.75678i
$122$	−4.28546	−	1.14829i	−0.387988	−	0.103961i
$123$	0.0658187	+	0.0939989i	0.00593467	+	0.00847559i
$124$	−0.556150	+	3.15409i	−0.0499438	+	0.283245i
$125$	9.81202	+	5.35950i	0.877614	+	0.479368i
$126$	−2.50730	−	1.44759i	−0.223368	−	0.128961i
$127$	−3.77799	+	0.330531i	−0.335242	+	0.0293299i	−0.253534	−	0.967326i	$-0.581593\pi$
$127$	−3.77799	+	0.330531i	−0.335242	+	0.0293299i	−0.0817080	+	0.996656i	$0.526037\pi$
$128$	−0.422618	−	0.906308i	−0.0373545	−	0.0801070i
$129$	9.90412	−	3.60480i	0.872009	−	0.317385i
$130$	3.23761	+	8.68156i	0.283957	+	0.761423i
$131$	−1.37609	−	7.80419i	−0.120229	−	0.681855i	−0.984027	−	0.178017i	$-0.943032\pi$
$131$	−1.37609	−	7.80419i	−0.120229	−	0.681855i	0.863798	−	0.503838i	$-0.168079\pi$
$132$	−4.08131	+	4.08131i	−0.355232	+	0.355232i
$133$	2.99954	−	12.2581i	0.260093	−	1.06291i
$134$			13.5460i			1.17020i
$135$	1.82151	−	1.29696i	0.156770	−	0.111625i
$136$	2.51178	+	2.99343i	0.215384	+	0.256684i
$137$	−1.68512	−	0.785783i	−0.143969	−	0.0671340i	0.349298	−	0.937012i	$-0.386420\pi$
$137$	−1.68512	−	0.785783i	−0.143969	−	0.0671340i	−0.493268	+	0.869878i	$0.664198\pi$
$138$	4.11971	−	1.92105i	0.350693	−	0.163531i
$139$	12.4651	−	14.8553i	1.05727	−	1.26001i	0.0928414	−	0.995681i	$-0.470405\pi$
$139$	12.4651	−	14.8553i	1.05727	−	1.26001i	0.964433	−	0.264329i	$-0.0851505\pi$
$140$	6.45343	+	0.513342i	0.545414	+	0.0433853i
$141$	9.33062	−	5.38704i	0.785780	−	0.453670i
$142$	5.45034	−	3.81637i	0.457383	−	0.320263i
$143$	−19.5915	+	13.7181i	−1.63832	+	1.14717i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$	11.7166	+	13.7416i	0.973007	+	1.14118i
$146$	7.36730	−	8.78000i	0.609722	−	0.726638i
$147$	−1.25257	+	0.584081i	−0.103310	+	0.0481742i
$148$	−8.99878	−	4.19620i	−0.739695	−	0.344925i
$149$	−7.85170	−	9.35729i	−0.643236	−	0.766579i	0.341641	−	0.939830i	$-0.389017\pi$
$149$	−7.85170	−	9.35729i	−0.643236	−	0.766579i	−0.984878	+	0.173251i	$0.944573\pi$
$150$	−2.43138	+	4.36903i	−0.198521	+	0.356730i
$151$			3.02783i			0.246402i	0.992382	+	0.123201i	$0.0393159\pi$
$151$			3.02783i			0.246402i	−0.992382	+	0.123201i	$0.960684\pi$
$152$	−3.14871	−	3.01423i	−0.255394	−	0.244487i
$153$	2.76312	−	2.76312i	0.223385	−	0.223385i
$154$	2.90175	+	16.4566i	0.233830	+	1.32611i
$155$	−6.71012	+	2.50240i	−0.538970	+	0.200998i
$156$	−3.89381	+	1.41723i	−0.311754	+	0.113469i
$157$	6.69017	+	14.3471i	0.533934	+	1.14503i	0.969550	+	0.244893i	$0.0787527\pi$
$157$	6.69017	+	14.3471i	0.533934	+	1.14503i	−0.435616	+	0.900132i	$0.643470\pi$
$158$	2.11757	−	0.185263i	0.168465	−	0.0147387i
$159$	7.33173	+	4.23298i	0.581444	+	0.335697i
$160$	1.26807	−	1.84174i	0.100250	−	0.145602i
$161$	2.28526	−	12.9604i	0.180104	−	1.02142i
$162$	0.573576	+	0.819152i	0.0450644	+	0.0643587i
$163$	−3.01494	−	0.807851i	−0.236148	−	0.0632758i	0.138804	−	0.990320i	$-0.455674\pi$
$163$	−3.01494	−	0.807851i	−0.236148	−	0.0632758i	−0.374952	+	0.927044i	$0.622341\pi$
$164$	0.0573757	−	0.0993777i	0.00448029	−	0.00776009i
$165$	−12.4924	−	3.24194i	−0.972533	−	0.252385i
$166$	3.63096	−	9.97597i	0.281817	−	0.774286i
$167$	−3.28352	+	7.04154i	−0.254087	+	0.544891i	−0.991432	−	0.130626i	$-0.958301\pi$
$167$	−3.28352	+	7.04154i	−0.254087	+	0.544891i	0.737345	+	0.675516i	$0.236079\pi$
$168$	−0.252331	+	2.88416i	−0.0194678	+	0.222518i
$169$	−4.10696	+	0.724168i	−0.315920	+	0.0557053i
$170$	−2.92363	+	8.23412i	−0.224232	+	0.631528i
$171$	−2.72834	+	3.39944i	−0.208641	+	0.259962i
$172$	−7.45272	−	7.45272i	−0.568265	−	0.568265i
$173$	6.18414	−	8.83187i	0.470172	−	0.671475i	−0.512102	−	0.858924i	$-0.671133\pi$
$173$	6.18414	−	8.83187i	0.470172	−	0.671475i	0.982274	+	0.187450i	$0.0600221\pi$
$174$	−6.18659	+	5.19117i	−0.469004	+	0.393541i
$175$	6.32398	+	13.0215i	0.478048	+	0.984330i
$176$	5.42376	+	1.97409i	0.408831	+	0.148802i
$177$	−0.0838258	−	0.958134i	−0.00630073	−	0.0720177i
$178$	−0.415030	−	1.54891i	−0.0311078	−	0.116096i
$179$	−10.4302	−	18.0657i	−0.779591	−	1.35029i	−0.932178	−	0.362001i	$-0.882094\pi$
$179$	−10.4302	−	18.0657i	−0.779591	−	1.35029i	0.152587	−	0.988290i	$-0.451239\pi$
$180$	−1.94525	−	1.10272i	−0.144990	−	0.0821922i
$181$	−1.11939	−	0.197379i	−0.0832036	−	0.0146710i	0.131891	−	0.991264i	$-0.457895\pi$
$181$	−1.11939	−	0.197379i	−0.0832036	−	0.0146710i	−0.215095	+	0.976593i	$0.569006\pi$
$182$	−3.10499	+	11.5880i	−0.230157	+	0.858959i
$183$	4.28546	−	1.14829i	0.316791	−	0.0848838i
$184$	−3.48213	−	2.92185i	−0.256706	−	0.215402i
$185$	−2.10944	−	22.1016i	−0.155089	−	1.62494i
$186$	−1.09540	−	3.00959i	−0.0803188	−	0.220674i
$187$	−22.4685	−	1.96574i	−1.64306	−	0.143749i
$188$	−8.82560	−	6.17975i	−0.643673	−	0.450705i
$189$	2.89518			0.210593
$190$	2.24192	−	9.48545i	0.162646	−	0.688147i
$191$	−5.34286			−0.386596			−0.193298	−	0.981140i	$-0.561918\pi$
$191$	−5.34286			−0.386596			−0.193298	+	0.981140i	$0.561918\pi$
$192$	0.819152	+	0.573576i	0.0591172	+	0.0413943i
$193$	−17.9926	−	1.57415i	−1.29514	−	0.113310i	−0.581340	−	0.813661i	$-0.697471\pi$
$193$	−17.9926	−	1.57415i	−1.29514	−	0.113310i	−0.713799	+	0.700351i	$0.753027\pi$
$194$	3.17053	+	8.71096i	0.227631	+	0.625411i
$195$	−7.14463	−	5.89965i	−0.511638	−	0.422483i
$196$	1.05871	+	0.888367i	0.0756225	+	0.0634548i
$197$	−16.8984	+	4.52792i	−1.20396	+	0.322601i	−0.804391	−	0.594100i	$-0.797508\pi$
$197$	−16.8984	+	4.52792i	−1.20396	+	0.322601i	−0.399573	+	0.916701i	$0.630842\pi$
$198$	1.49386	−	5.57517i	0.106164	−	0.396210i
$199$	26.3661	+	4.64906i	1.86905	+	0.329563i	0.989302	−	0.145883i	$-0.0466023\pi$
$199$	26.3661	+	4.64906i	1.86905	+	0.329563i	0.879745	+	0.475446i	$0.157713\pi$
$200$	4.98723	+	0.357147i	0.352650	+	0.0252541i
$201$	−6.77300	−	11.7312i	−0.477731	−	0.827454i
$202$	3.80724	+	14.2088i	0.267877	+	0.999729i
$203$	2.03783	+	23.2925i	0.143028	+	1.63482i
$204$	−3.67198	−	1.33649i	−0.257090	−	0.0935732i
$205$	0.256584	−	0.00202399i	0.0179206	−	0.000141362i
$206$	−8.03458	+	6.74181i	−0.559796	+	0.469724i
$207$	−2.60724	+	3.72353i	−0.181216	+	0.258803i
$208$	2.93004	+	2.93004i	0.203162	+	0.203162i
$209$	25.1529	−	0.548846i	1.73986	−	0.0379645i
$210$	−5.84550	+	2.78215i	−0.403378	+	0.191986i
$211$	−10.6560	+	1.87894i	−0.733587	+	0.129351i	−0.527948	−	0.849277i	$-0.677038\pi$
$211$	−10.6560	+	1.87894i	−0.733587	+	0.129351i	−0.205639	+	0.978628i	$0.565927\pi$
$212$	0.737856	−	8.43374i	0.0506762	−	0.579231i
$213$	−2.81195	+	6.03025i	−0.192672	+	0.413186i
$214$	2.29104	−	6.29459i	0.156613	−	0.430290i
$215$	5.91998	−	22.8119i	0.403739	−	1.55576i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	−8.95655	−	2.39990i	−0.608011	−	0.162916i
$218$	−0.312250	−	0.445940i	−0.0211483	−	0.0302029i
$219$	−1.99027	+	11.2874i	−0.134490	+	0.762729i
$220$	2.34133	+	12.6921i	0.157852	+	0.855700i
$221$	−14.0228	−	8.09606i	−0.943275	−	0.544600i
$222$	9.89127	−	0.865374i	0.663859	−	0.0580801i
$223$	3.30198	+	7.08112i	0.221117	+	0.474187i	0.985304	−	0.170807i	$-0.0546376\pi$
$223$	3.30198	+	7.08112i	0.221117	+	0.474187i	−0.764188	+	0.644994i	$0.776860\pi$
$224$	2.72058	−	0.990209i	0.181776	−	0.0661611i
$225$	−0.0788774	−	4.99938i	−0.00525849	−	0.333292i
$226$	0.297252	+	1.68580i	0.0197729	+	0.112138i
$227$	10.6084	−	10.6084i	0.704102	−	0.704102i	−0.261187	−	0.965288i	$-0.584114\pi$
$227$	10.6084	−	10.6084i	0.704102	−	0.704102i	0.965288	+	0.261187i	$0.0841138\pi$
$228$	4.23398	+	1.03605i	0.280402	+	0.0686139i
$229$			1.40594i			0.0929072i	0.998920	+	0.0464536i	$0.0147920\pi$
$229$			1.40594i			0.0929072i	−0.998920	+	0.0464536i	$0.985208\pi$
$230$	1.68599	−	10.0234i	0.111171	−	0.660926i
$231$	−10.7413	−	12.8010i	−0.706726	−	0.842243i
$232$	7.31936	+	3.41307i	0.480540	+	0.224079i
$233$	24.2128	−	11.2906i	1.58623	−	0.739673i	0.588600	−	0.808424i	$-0.299679\pi$
$233$	24.2128	−	11.2906i	1.58623	−	0.739673i	0.997634	+	0.0687515i	$0.0219016\pi$
$234$	2.66352	−	3.17426i	0.174120	−	0.207508i
$235$	1.91034	−	24.0157i	0.124617	−	1.56661i
$236$	−0.832938	+	0.480897i	−0.0542196	+	0.0313037i
$237$	−1.74123	+	1.21923i	−0.113105	+	0.0791972i
$238$	−9.26733	+	6.48905i	−0.600712	+	0.420623i
$239$	−21.2110	+	12.2462i	−1.37202	+	0.792138i	−0.991183	−	0.132502i	$-0.957699\pi$
$239$	−21.2110	+	12.2462i	−1.37202	+	0.792138i	−0.380841	+	0.924640i	$0.624366\pi$
$240$	−0.177309	+	2.22903i	−0.0114453	+	0.143883i
$241$	−1.94599	+	2.31914i	−0.125352	+	0.149389i	−0.825070	−	0.565030i	$-0.808865\pi$
$241$	−1.94599	+	2.31914i	−0.125352	+	0.149389i	0.699718	+	0.714419i	$0.253309\pi$
$242$	−20.2235	+	9.43036i	−1.30001	+	0.606207i
$243$	−0.906308	−	0.422618i	−0.0581397	−	0.0271110i
$244$	−2.85182	−	3.39866i	−0.182569	−	0.217577i
$245$	−0.512613	+	3.04755i	−0.0327497	+	0.194701i
$246$			0.114751i			0.00731628i
$247$	16.5324	+	7.27441i	1.05193	+	0.462860i
$248$	−2.26468	+	2.26468i	−0.143807	+	0.143807i
$249$	1.84349	+	10.4549i	0.116826	+	0.662554i
$250$	4.96346	+	10.0182i	0.313917	+	0.633606i
$251$	−0.226056	+	0.0822775i	−0.0142685	+	0.00519331i	−0.349145	−	0.937069i	$-0.613528\pi$
$251$	−0.226056	+	0.0822775i	−0.0142685	+	0.00519331i	0.334876	+	0.942262i	$0.391306\pi$
$252$	−1.22355	−	2.62392i	−0.0770767	−	0.165292i
$253$	26.1366	−	2.28666i	1.64319	−	0.143761i
$254$	−3.28433	−	1.89621i	−0.206077	−	0.118979i
$255$	−1.58512	−	8.59277i	−0.0992643	−	0.538100i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−0.346065	−	0.494231i	−0.0215869	−	0.0308293i	0.808214	−	0.588890i	$-0.200435\pi$
$257$	−0.346065	−	0.494231i	−0.0215869	−	0.0308293i	−0.829800	+	0.558060i	$0.811546\pi$
$258$	10.1806	+	2.72789i	0.633817	+	0.169831i
$259$	14.3732	−	24.8951i	0.893106	−	1.54691i
$260$	−2.32745	+	8.96853i	−0.144342	+	0.556205i
$261$	2.76216	−	7.58898i	0.170974	−	0.469746i
$262$	3.34907	−	7.18211i	0.206906	−	0.443712i
$263$	−0.156442	+	1.78814i	−0.00964665	+	0.110262i	−0.999491	−	0.0318913i	$-0.989847\pi$
$263$	−0.156442	+	1.78814i	−0.00964665	+	0.110262i	0.989845	+	0.142153i	$0.0454025\pi$
$264$	−5.68415	+	1.00227i	−0.349835	+	0.0616854i
$265$	17.0932	−	8.13543i	1.05002	−	0.499756i
$266$	9.48806	−	8.32081i	0.581750	−	0.510181i
$267$	1.13388	+	1.13388i	0.0693925	+	0.0693925i
$268$	−7.76967	+	11.0962i	−0.474608	+	0.677810i
$269$	4.01695	−	3.37062i	0.244918	−	0.205511i	−0.512062	−	0.858948i	$-0.671118\pi$
$269$	4.01695	−	3.37062i	0.244918	−	0.205511i	0.756980	+	0.653438i	$0.226674\pi$
$270$	2.23600	−	0.0176381i	0.136079	−	0.00107342i
$271$	−2.88698	−	1.05077i	−0.175371	−	0.0638299i	0.252842	−	0.967508i	$-0.418635\pi$
$271$	−2.88698	−	1.05077i	−0.175371	−	0.0638299i	−0.428213	+	0.903678i	$0.640857\pi$
$272$	0.340573	+	3.89277i	0.0206503	+	0.236034i
$273$	−3.10499	−	11.5880i	−0.187923	−	0.701337i
$274$	−0.929661	−	1.61022i	−0.0561629	−	0.0972769i
$275$	−21.8120	+	18.8968i	−1.31532	+	1.13952i
$276$	4.47653	+	0.789334i	0.269456	+	0.0475123i
$277$	5.98760	−	22.3460i	0.359760	−	1.34264i	−0.514628	−	0.857414i	$-0.672070\pi$
$277$	5.98760	−	22.3460i	0.359760	−	1.34264i	0.874388	−	0.485228i	$-0.161263\pi$
$278$	18.7314	−	5.01907i	1.12344	−	0.301024i
$279$	2.45344	+	2.05868i	0.146884	+	0.123250i
$280$	4.99190	+	4.12204i	0.298323	+	0.246339i
$281$	5.54589	+	15.2372i	0.330840	+	0.908976i	0.987894	+	0.155132i	$0.0495803\pi$
$281$	5.54589	+	15.2372i	0.330840	+	0.908976i	−0.657054	+	0.753844i	$0.728198\pi$
$282$	10.7331	+	0.939022i	0.639145	+	0.0559180i
$283$	−22.4428	−	15.7146i	−1.33409	−	0.934137i	−0.334121	−	0.942530i	$-0.608439\pi$
$283$	−22.4428	−	15.7146i	−1.33409	−	0.934137i	−0.999965	+	0.00839310i	$0.997328\pi$
$284$	6.65364			0.394821
$285$	2.80116	+	9.33560i	0.165927	+	0.552993i
$286$	−23.9168			−1.41423
$287$	0.272143	+	0.190557i	0.0160641	+	0.0112482i
$288$	−0.996195	−	0.0871557i	−0.0587013	−	0.00513570i
$289$	0.591810	+	1.62598i	0.0348123	+	0.0956461i
$290$	1.71576	+	17.9768i	0.100753	+	1.05564i
$291$	−7.10124	−	5.95865i	−0.416282	−	0.349302i
$292$	11.0709	−	2.96645i	0.647878	−	0.173598i
$293$	−6.75302	+	25.2026i	−0.394516	+	1.47235i	0.428088	+	0.903737i	$0.359187\pi$
$293$	−6.75302	+	25.2026i	−0.394516	+	1.47235i	−0.822603	+	0.568616i	$0.807479\pi$
$294$	−1.36106	−	0.239991i	−0.0793785	−	0.0139966i
$295$	−1.87093	−	1.06059i	−0.108930	−	0.0617501i
$296$	−4.96453	−	8.59881i	−0.288557	−	0.499796i
$297$	1.49386	+	5.57517i	0.0866827	+	0.323504i
$298$	−1.06461	−	12.1686i	−0.0616714	−	0.704908i
$299$	17.6997	+	6.44216i	1.02360	+	0.372560i
$300$	−4.49764	+	2.18432i	−0.259671	+	0.126112i
$301$	23.3754	−	19.6143i	1.34734	−	1.13055i
$302$	−1.73669	+	2.48026i	−0.0999355	+	0.142723i
$303$	−10.4016	−	10.4016i	−0.597555	−	0.597555i
$304$	−0.850380	−	4.27514i	−0.0487727	−	0.245196i
$305$	3.31941	−	9.34881i	0.190069	−	0.535312i
$306$	3.84828	−	0.678555i	0.219991	−	0.0387904i
$307$	2.92996	−	33.4896i	0.167222	−	1.91135i	−0.197612	−	0.980280i	$-0.563319\pi$
$307$	2.92996	−	33.4896i	0.167222	−	1.91135i	0.364834	−	0.931073i	$-0.381126\pi$
$308$	−7.06216	+	15.1449i	−0.402404	+	0.862958i
$309$	3.58724	−	9.85587i	0.204071	−	0.560681i
$310$	−6.93193	−	1.79892i	−0.393707	−	0.102172i
$311$	−1.27035	+	2.20032i	−0.0720351	+	0.124768i	−0.899793	−	0.436317i	$-0.856283\pi$
$311$	−1.27035	+	2.20032i	−0.0720351	+	0.124768i	0.827758	+	0.561085i	$0.189616\pi$
$312$	−4.00251	−	1.07247i	−0.226598	−	0.0607167i
$313$	−1.16542	−	1.66440i	−0.0658737	−	0.0940774i	0.784864	−	0.619669i	$-0.212733\pi$
$313$	−1.16542	−	1.66440i	−0.0658737	−	0.0940774i	−0.850737	+	0.525591i	$0.823844\pi$
$314$	−2.74890	+	15.5898i	−0.155130	+	0.879783i
$315$	3.67128	−	5.33216i	0.206853	−	0.300433i
$316$	1.84087	+	1.06283i	0.103557	+	0.0597887i
$317$	−0.757816	+	0.0663003i	−0.0425632	+	0.00372380i	−0.108417	−	0.994105i	$-0.534578\pi$
$317$	−0.757816	+	0.0663003i	−0.0425632	+	0.00372380i	0.0658543	+	0.997829i	$0.479023\pi$
$318$	3.57787	+	7.67276i	0.200637	+	0.430267i
$319$	−43.8024	+	15.9428i	−2.45246	+	0.892623i
$320$	2.09512	−	0.781331i	0.117121	−	0.0436777i
$321$	1.16319	+	6.59680i	0.0649231	+	0.368197i
$322$	9.30574	−	9.30574i	0.518588	−	0.518588i
$323$	7.53352	+	15.2764i	0.419176	+	0.850004i
$324$			1.00000i			0.0555556i
$325$	−19.9255	+	5.67739i	−1.10527	+	0.314925i
$326$	−2.00633	−	2.39105i	−0.111120	−	0.132428i
$327$	0.493387	+	0.230070i	0.0272844	+	0.0127229i
$328$	0.104000	−	0.0484961i	0.00574245	−	0.00267775i
$329$	20.0504	−	23.8951i	1.10541	−	1.31738i
$330$	−8.37369	−	9.82100i	−0.460957	−	0.540628i
$331$	−16.9724	+	9.79902i	−0.932887	+	0.538603i	−0.887724	−	0.460377i	$-0.847714\pi$
$331$	−16.9724	+	9.79902i	−0.932887	+	0.538603i	−0.0451636	+	0.998980i	$0.514381\pi$
$332$	8.69629	−	6.08921i	0.477271	−	0.334189i
$333$	−8.13340	+	5.69507i	−0.445708	+	0.312088i
$334$	−6.72857	+	3.88474i	−0.368171	+	0.212563i
$335$	−30.1944	−	2.40183i	−1.64970	−	0.131226i
$336$	−1.86098	+	2.21783i	−0.101525	+	0.120993i
$337$	−18.4176	+	8.58825i	−1.00327	+	0.467832i	−0.853614	−	0.520906i	$-0.825594\pi$
$337$	−18.4176	+	8.58825i	−1.00327	+	0.467832i	−0.149655	+	0.988738i	$0.547816\pi$
$338$	−3.77959	−	1.76245i	−0.205583	−	0.0958648i
$339$	−1.10033	−	1.31132i	−0.0597617	−	0.0712212i
$340$	−7.11779	+	5.06807i	−0.386017	+	0.274855i
$341$		−	18.4857i		−	1.00106i
$342$	−4.18476	+	1.21975i	−0.226286	+	0.0659564i
$343$	11.5011	−	11.5011i	0.620999	−	0.620999i
$344$	−1.83021	−	10.3796i	−0.0986781	−	0.559632i
$345$	3.55161	+	9.52355i	0.191212	+	0.512731i
$346$	10.1315	−	3.68757i	0.544673	−	0.198245i
$347$	3.63483	+	7.79492i	0.195128	+	0.418453i	0.979391	−	0.201976i	$-0.0647362\pi$
$347$	3.63483	+	7.79492i	0.195128	+	0.418453i	−0.784263	+	0.620429i	$0.786958\pi$
$348$	−8.04529	+	0.703872i	−0.431273	+	0.0377315i
$349$	−4.14228	−	2.39155i	−0.221731	−	0.128017i	0.385020	−	0.922908i	$-0.374194\pi$
$349$	−4.14228	−	2.39155i	−0.221731	−	0.128017i	−0.606752	+	0.794892i	$0.707528\pi$
$350$	−2.28850	+	14.2938i	−0.122326	+	0.764038i
$351$	−0.719547	+	4.08076i	−0.0384066	+	0.217815i
$352$	3.31059	+	4.72801i	0.176455	+	0.252004i
$353$	17.6322	+	4.72454i	0.938469	+	0.251462i	0.695462	−	0.718562i	$-0.255200\pi$
$353$	17.6322	+	4.72454i	0.938469	+	0.251462i	0.243007	+	0.970025i	$0.421866\pi$
$354$	0.480897	−	0.832938i	0.0255594	−	0.0442701i
$355$	7.54040	+	12.8256i	0.400203	+	0.680714i
$356$	0.548447	−	1.50685i	0.0290676	−	0.0798627i
$357$	4.78121	−	10.2533i	0.253049	−	0.542665i
$358$	1.81811	−	20.7810i	0.0960899	−	1.09831i
$359$	26.7063	−	4.70904i	1.40950	−	0.248533i	0.583461	−	0.812141i	$-0.301698\pi$
$359$	26.7063	−	4.70904i	1.40950	−	0.248533i	0.826043	+	0.563608i	$0.190587\pi$
$360$	−0.960959	−	2.01905i	−0.0506470	−	0.106413i
$361$	−10.2087	−	16.0244i	−0.537300	−	0.843391i
$362$	−0.803739	−	0.803739i	−0.0422436	−	0.0422436i
$363$	12.7989	−	18.2787i	0.671766	−	0.959381i
$364$	−9.19006	+	7.71138i	−0.481690	+	0.404186i
$365$	18.2646	+	17.9787i	0.956012	+	0.941047i
$366$	4.16908	+	1.51742i	0.217921	+	0.0793168i
$367$	0.0438925	+	0.501694i	0.00229117	+	0.0261882i	0.997254	−	0.0740541i	$-0.0235938\pi$
$367$	0.0438925	+	0.501694i	0.00229117	+	0.0261882i	−0.994963	+	0.100242i	$0.968038\pi$
$368$	−1.17649	−	4.39070i	−0.0613286	−	0.228881i
$369$	−0.0573757	−	0.0993777i	−0.00298686	−	0.00517339i
$370$	10.9490	−	19.3145i	0.569212	−	1.00411i
$371$	24.1381	+	4.25619i	1.25319	+	0.220970i
$372$	0.828931	−	3.09361i	0.0429781	−	0.160396i
$373$	−6.74895	+	1.80838i	−0.349448	+	0.0936342i	−0.429273	−	0.903175i	$-0.641230\pi$
$373$	−6.74895	+	1.80838i	−0.349448	+	0.0936342i	0.0798257	+	0.996809i	$0.474564\pi$
$374$	−17.2776	−	14.4976i	−0.893403	−	0.749654i
$375$	−9.30757	−	6.19428i	−0.480641	−	0.319871i
$376$	−3.68495	−	10.1243i	−0.190037	−	0.522122i
$377$	−33.3373	−	2.91664i	−1.71696	−	0.150215i
$378$	2.37159	+	1.66061i	0.121981	+	0.0854123i
$379$	−28.7824			−1.47845			−0.739227	−	0.673456i	$-0.764809\pi$
$379$	−28.7824			−1.47845			−0.739227	+	0.673456i	$0.764809\pi$
$380$	7.27711	−	6.48411i	0.373308	−	0.332628i
$381$	3.79242			0.194291
$382$	−4.37662	−	3.06454i	−0.223927	−	0.156795i
$383$	3.74631	+	0.327759i	0.191427	+	0.0167477i	0.182466	−	0.983212i	$-0.441592\pi$
$383$	3.74631	+	0.327759i	0.191427	+	0.0167477i	0.00896115	+	0.999960i	$0.497148\pi$
$384$	0.342020	+	0.939693i	0.0174536	+	0.0479535i
$385$	−37.1968	+	3.55016i	−1.89572	+	0.180933i
$386$	−13.8358	−	11.6096i	−0.704224	−	0.590914i
$387$	−10.1806	+	2.72789i	−0.517509	+	0.138666i
$388$	−2.39926	+	8.95415i	−0.121804	+	0.454578i
$389$	26.7177	+	4.71104i	1.35464	+	0.238859i	0.803376	−	0.595472i	$-0.203035\pi$
$389$	26.7177	+	4.71104i	1.35464	+	0.238859i	0.551263	+	0.834331i	$0.314146\pi$
$390$	−2.46864	−	8.93070i	−0.125004	−	0.452224i
$391$	8.88127	+	15.3828i	0.449145	+	0.777942i
$392$	0.357702	+	1.33496i	0.0180667	+	0.0674257i
$393$	0.690673	+	7.89443i	0.0348398	+	0.398221i
$394$	−16.4395	−	5.98349i	−0.828210	−	0.301444i
$395$	0.0374924	+	4.75296i	0.00188645	+	0.239147i
$396$	4.42149	−	3.71007i	0.222188	−	0.186438i
$397$	−11.4797	+	16.3947i	−0.576149	+	0.822826i	−0.996417	−	0.0845739i	$-0.973047\pi$
$397$	−11.4797	+	16.3947i	−0.576149	+	0.822826i	0.420268	+	0.907400i	$0.361936\pi$
$398$	18.9313	+	18.9313i	0.948940	+	0.948940i
$399$	−4.05649	+	11.9501i	−0.203079	+	0.598251i
$400$	3.88045	+	3.15311i	0.194022	+	0.157656i
$401$	−15.7584	+	2.77863i	−0.786937	+	0.138758i	−0.552654	−	0.833411i	$-0.686385\pi$
$401$	−15.7584	+	2.77863i	−0.786937	+	0.138758i	−0.234282	+	0.972169i	$0.575274\pi$
$402$	1.18061	−	13.4945i	0.0588835	−	0.673042i
$403$	5.60866	−	12.0278i	0.279387	−	0.599148i
$404$	−5.03113	+	13.8229i	−0.250308	+	0.687716i
$405$	−1.92761	+	1.13327i	−0.0957838	+	0.0563128i
$406$	−11.6908	+	20.2490i	−0.580203	+	1.00494i
$407$	55.3562	+	14.8326i	2.74390	+	0.735227i
$408$	−2.24133	−	3.20095i	−0.110962	−	0.158471i
$409$	−2.80653	+	15.9166i	−0.138774	+	0.787027i	0.833383	+	0.552696i	$0.186401\pi$
$409$	−2.80653	+	15.9166i	−0.138774	+	0.787027i	−0.972157	+	0.234331i	$0.924710\pi$
$410$	0.211342	+	0.145513i	0.0104375	+	0.00718636i
$411$	1.61022	+	0.929661i	0.0794263	+	0.0458568i
$412$	−10.4485	+	0.914124i	−0.514760	+	0.0450357i
$413$	−1.17681	−	2.52367i	−0.0579069	−	0.124182i
$414$	−4.27146	+	1.55468i	−0.209931	+	0.0764086i
$415$	21.5929	+	9.86233i	1.05995	+	0.484123i
$416$	0.719547	+	4.08076i	0.0352787	+	0.200076i
$417$	−13.7124	+	13.7124i	−0.671498	+	0.671498i
$418$	20.9188	+	13.9775i	1.02317	+	0.683662i
$419$			6.87682i			0.335955i	0.985791	+	0.167977i	$0.0537236\pi$
$419$			6.87682i			0.335955i	−0.985791	+	0.167977i	$0.946276\pi$
$420$	−6.38413	−	1.07384i	−0.311514	−	0.0523981i
$421$	−3.06686	−	3.65494i	−0.149470	−	0.178131i	0.686114	−	0.727494i	$-0.259315\pi$
$421$	−3.06686	−	3.65494i	−0.149470	−	0.178131i	−0.835584	+	0.549363i	$0.814870\pi$
$422$	−9.80657	−	4.57288i	−0.477377	−	0.222604i
$423$	−9.76463	+	4.55332i	−0.474772	+	0.221390i
$424$	5.44181	−	6.48529i	0.264278	−	0.314954i
$425$	−17.8357	−	7.97683i	−0.865158	−	0.386933i
$426$	−5.76222	+	3.32682i	−0.279181	+	0.161185i
$427$	10.5219	−	7.36751i	0.509190	−	0.356539i
$428$	5.48714	−	3.84214i	0.265231	−	0.185717i
$429$	20.7126	−	11.9584i	1.00001	−	0.577358i
$430$	17.9338	−	15.2909i	0.864842	−	0.737392i
$431$	−7.43648	+	8.86245i	−0.358203	+	0.426889i	−0.914809	−	0.403887i	$-0.867659\pi$
$431$	−7.43648	+	8.86245i	−0.358203	+	0.426889i	0.556606	+	0.830776i	$0.312103\pi$
$432$	0.906308	−	0.422618i	0.0436048	−	0.0203332i
$433$	−5.03501	−	2.34786i	−0.241967	−	0.112831i	0.297852	−	0.954612i	$-0.403730\pi$
$433$	−5.03501	−	2.34786i	−0.241967	−	0.112831i	−0.539819	+	0.841781i	$0.681507\pi$
$434$	−5.96025	−	7.10315i	−0.286101	−	0.340962i
$435$	−10.4743	−	14.7105i	−0.502205	−	0.705316i
$436$		−	0.544392i		−	0.0260717i
$437$	−11.7161	−	15.9787i	−0.560456	−	0.764365i
$438$	−8.10449	+	8.10449i	−0.387248	+	0.387248i
$439$	−3.85015	−	21.8353i	−0.183758	−	1.04214i	−0.927541	−	0.373722i	$-0.878082\pi$
$439$	−3.85015	−	21.8353i	−0.183758	−	1.04214i	0.743783	−	0.668421i	$-0.233030\pi$
$440$	−5.36197	+	11.7397i	−0.255622	+	0.559667i
$441$	1.29871	−	0.472690i	0.0618431	−	0.0225091i
$442$	−6.84309	−	14.6751i	−0.325493	−	0.698021i
$443$	−12.6142	+	1.10360i	−0.599321	+	0.0524338i	−0.382780	−	0.923840i	$-0.625033\pi$
$443$	−12.6142	+	1.10360i	−0.599321	+	0.0524338i	−0.216541	+	0.976273i	$0.569478\pi$
$444$	8.59881	+	4.96453i	0.408082	+	0.235606i
$445$	3.52616	−	0.650476i	0.167156	−	0.0308355i
$446$	−1.35674	+	7.69445i	−0.0642435	+	0.364343i
$447$	7.00628	+	10.0060i	0.331386	+	0.473268i
$448$	2.79653	+	0.749327i	0.132123	+	0.0354024i
$449$	−3.99278	+	6.91569i	−0.188431	+	0.326372i	−0.944727	−	0.327857i	$-0.893673\pi$
$449$	−3.99278	+	6.91569i	−0.188431	+	0.326372i	0.756296	+	0.654229i	$0.227007\pi$
$450$	2.80291	−	4.14049i	0.132131	−	0.195185i
$451$	−0.226529	+	0.622384i	−0.0106668	+	0.0293069i
$452$	−0.723441	+	1.55143i	−0.0340278	+	0.0729729i
$453$	0.263893	−	3.01631i	0.0123988	−	0.141719i
$454$	14.7746	−	2.60516i	0.693405	−	0.122266i
$455$	−25.2794	−	8.97577i	−1.18512	−	0.420791i
$456$	2.87402	+	3.27719i	0.134588	+	0.153469i
$457$	2.00876	+	2.00876i	0.0939660	+	0.0939660i	0.752527	−	0.658561i	$-0.228835\pi$
$457$	2.00876	+	2.00876i	0.0939660	+	0.0939660i	−0.658561	+	0.752527i	$0.728835\pi$
$458$	−0.806414	+	1.15168i	−0.0376813	+	0.0538144i
$459$	−2.99343	+	2.51178i	−0.139721	+	0.117240i
$460$	7.13030	−	7.24368i	0.332452	−	0.337738i
$461$	−3.59099	−	1.30701i	−0.167249	−	0.0608736i	0.257039	−	0.966401i	$-0.417253\pi$
$461$	−3.59099	−	1.30701i	−0.167249	−	0.0608736i	−0.424288	+	0.905527i	$0.639475\pi$
$462$	−1.45642	−	16.6469i	−0.0677586	−	0.774485i
$463$	−8.13855	−	30.3735i	−0.378231	−	1.41158i	−0.848567	−	0.529089i	$-0.822534\pi$
$463$	−8.13855	−	30.3735i	−0.378231	−	1.41158i	0.470336	−	0.882487i	$-0.344133\pi$
$464$	4.03801	+	6.99404i	0.187460	+	0.324690i
$465$	6.90269	−	1.90805i	0.320105	−	0.0884838i
$466$	26.3100	+	4.63916i	1.21879	+	0.214905i
$467$	−0.613797	+	2.29072i	−0.0284031	+	0.106002i	−0.978672	−	0.205428i	$-0.934141\pi$
$467$	−0.613797	+	2.29072i	−0.0284031	+	0.106002i	0.950269	+	0.311430i	$0.100808\pi$
$468$	4.00251	−	1.07247i	0.185016	−	0.0495750i
$469$	−30.0428	−	25.2089i	−1.38725	−	1.16404i
$470$	15.3397	−	18.5768i	0.707568	−	0.856883i
$471$	−5.41428	−	14.8756i	−0.249477	−	0.685432i
$472$	−0.958134	−	0.0838258i	−0.0441017	−	0.00385840i
$473$	49.8320	+	34.8928i	2.29128	+	1.60437i
$474$	−2.12566			−0.0976346
$475$	20.7458	+	6.67916i	0.951883	+	0.306461i
$476$	−11.3133			−0.518545
$477$	−6.93490	−	4.85587i	−0.317527	−	0.222335i
$478$	−24.3991	−	2.13465i	−1.11599	−	0.0976365i
$479$	−3.97342	−	10.9169i	−0.181550	−	0.498805i	0.815216	−	0.579156i	$-0.196618\pi$
$479$	−3.97342	−	10.9169i	−0.181550	−	0.498805i	−0.996767	+	0.0803515i	$0.974396\pi$
$480$	−1.42376	+	1.72421i	−0.0649855	+	0.0786991i
$481$	31.5174	+	26.4463i	1.43707	+	1.20585i
$482$	−2.92427	+	0.783556i	−0.133197	+	0.0356900i
$483$	−3.40614	+	12.7119i	−0.154985	+	0.578410i
$484$	−21.9751	−	3.87481i	−0.998870	−	0.176128i
$485$	−19.9791	+	5.52267i	−0.907206	+	0.250771i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−2.90399	−	10.8378i	−0.131592	−	0.491109i	0.868397	−	0.495870i	$-0.165151\pi$
$487$	−2.90399	−	10.8378i	−0.131592	−	0.491109i	−0.999989	+	0.00476187i	$0.998484\pi$
$488$	−0.386679	−	4.41976i	−0.0175041	−	0.200073i
$489$	2.93306	+	1.06755i	0.132638	+	0.0482761i
$490$	−2.16791	+	2.20239i	−0.0979364	+	0.0994937i
$491$	7.18885	−	6.03216i	0.324428	−	0.272228i	−0.465997	−	0.884786i	$-0.654304\pi$
$491$	7.18885	−	6.03216i	0.324428	−	0.272228i	0.790425	+	0.612559i	$0.209860\pi$
$492$	−0.0658187	+	0.0939989i	−0.00296734	+	0.00423780i
$493$	−22.3150	−	22.3150i	−1.00502	−	1.00502i
$494$	9.37009	+	15.4414i	0.421580	+	0.694742i
$495$	12.1623	+	4.31839i	0.546656	+	0.194097i
$496$	−3.15409	+	0.556150i	−0.141623	+	0.0249719i
$497$	−1.67892	+	19.1902i	−0.0753099	+	0.860797i
$498$	−4.48660	+	9.62155i	−0.201050	+	0.431152i
$499$	3.01705	−	8.28927i	0.135062	−	0.371079i	−0.853663	−	0.520826i	$-0.825624\pi$
$499$	3.01705	−	8.28927i	0.135062	−	0.371079i	0.988724	+	0.149748i	$0.0478461\pi$
$500$	−1.68037	+	11.0533i	−0.0751485	+	0.494320i
$501$	3.88474	−	6.72857i	0.173557	−	0.300610i
$502$	−0.232366	−	0.0622624i	−0.0103710	−	0.00277890i
$503$	2.20294	+	3.14613i	0.0982244	+	0.140279i	0.865256	−	0.501330i	$-0.167156\pi$
$503$	2.20294	+	3.14613i	0.0982244	+	0.140279i	−0.767031	+	0.641609i	$0.778267\pi$
$504$	0.502742	−	2.85119i	0.0223939	−	0.127002i
$505$	−32.3469	+	5.96709i	−1.43942	+	0.265532i
$506$	22.7214	+	13.1182i	1.01009	+	0.583176i
$507$	4.15445	−	0.363467i	0.184506	−	0.0161421i
$508$	−1.60275	−	3.43710i	−0.0711103	−	0.152497i
$509$	−5.05198	+	1.83877i	−0.223925	+	0.0815021i	−0.451546	−	0.892248i	$-0.649127\pi$
$509$	−5.05198	+	1.83877i	−0.223925	+	0.0815021i	0.227621	+	0.973750i	$0.426905\pi$
$510$	3.63015	−	7.94798i	0.160746	−	0.351942i
$511$	5.76217	+	32.6789i	0.254903	+	1.44563i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	3.01423	−	3.14871i	0.133082	−	0.139019i
$514$		−	0.603345i		−	0.0266124i
$515$	−13.6031	−	19.1047i	−0.599423	−	0.841853i
$516$	6.77481	+	8.07391i	0.298245	+	0.355434i
$517$	56.3599	+	26.2810i	2.47870	+	1.15584i
$518$	26.0531	−	12.1487i	1.14471	−	0.533785i
$519$	−6.93036	+	8.25928i	−0.304209	+	0.362542i
$520$	−7.05067	+	6.01162i	−0.309192	+	0.263627i
$521$	−11.1461	+	6.43518i	−0.488318	+	0.281931i	−0.723876	−	0.689930i	$-0.757641\pi$
$521$	−11.1461	+	6.43518i	−0.488318	+	0.281931i	0.235558	+	0.971860i	$0.424308\pi$
$522$	6.61549	−	4.63222i	0.289552	−	0.202747i
$523$	−3.47582	+	2.43379i	−0.151987	+	0.106422i	−0.647096	−	0.762408i	$-0.724017\pi$
$523$	−3.47582	+	2.43379i	−0.151987	+	0.106422i	0.495109	+	0.868831i	$0.335128\pi$
$524$	6.86289	−	3.96229i	0.299807	−	0.173093i
$525$	−5.16502	−	13.5231i	−0.225420	−	0.590196i
$526$	−1.15379	+	1.37503i	−0.0503075	+	0.0599542i
$527$	11.3426	−	5.28914i	0.494091	−	0.230399i
$528$	−5.23106	−	2.43928i	−0.227653	−	0.106156i
$529$	1.50258	+	1.79070i	0.0653294	+	0.0778565i
$530$	18.6682	+	3.14008i	0.810895	+	0.136396i
$531$			0.961793i			0.0417383i
$532$	12.5448	−	1.37388i	0.543885	−	0.0595653i
$533$	−0.336227	+	0.336227i	−0.0145636	+	0.0145636i
$534$	0.278454	+	1.57919i	0.0120499	+	0.0683383i
$535$	13.6246	+	6.22289i	0.589043	+	0.269039i
$536$	−12.7291	+	4.63300i	−0.549812	+	0.200115i
$537$	8.81600	+	18.9060i	0.380438	+	0.815853i
$538$	5.22381	−	0.457024i	0.225214	−	0.0197037i
$539$	−6.90828	−	3.98850i	−0.297561	−	0.171797i
$540$	1.84174	+	1.26807i	0.0792558	+	0.0545689i
$541$	−2.22457	+	12.6162i	−0.0956417	+	0.542411i	0.898907	+	0.438139i	$0.144362\pi$
$541$	−2.22457	+	12.6162i	−0.0956417	+	0.542411i	−0.994549	+	0.104272i	$0.966749\pi$
$542$	−1.76217	−	2.51664i	−0.0756918	−	0.108099i
$543$	1.09793	+	0.294189i	0.0471166	+	0.0126249i
$544$	−1.95382	+	3.38412i	−0.0837694	+	0.145093i
$545$	1.04938	−	0.616945i	0.0449504	−	0.0264270i
$546$	4.10314	−	11.2733i	0.175598	−	0.482452i
$547$	−8.11200	+	17.3962i	−0.346844	+	0.743809i	−0.999909	−	0.0134925i	$-0.995705\pi$
$547$	−8.11200	+	17.3962i	−0.346844	+	0.743809i	0.653065	+	0.757302i	$0.273483\pi$
$548$	0.162051	−	1.85225i	0.00692246	−	0.0791240i
$549$	−4.36924	+	0.770414i	−0.186474	+	0.0328805i
$550$	−28.7061	+	2.96847i	−1.22403	+	0.126576i
$551$	27.4539	+	22.0341i	1.16958	+	0.938684i
$552$	3.21422	+	3.21422i	0.136806	+	0.136806i
$553$	−3.52988	+	5.04118i	−0.150106	+	0.214373i
$554$	17.7219	−	14.8704i	0.752931	−	0.631784i
$555$	0.175129	+	22.2013i	0.00743382	+	0.942395i
$556$	18.2227	+	6.63253i	0.772816	+	0.281282i
$557$	2.22053	+	25.3807i	0.0940867	+	1.07542i	0.885658	+	0.464338i	$0.153708\pi$
$557$	2.22053	+	25.3807i	0.0940867	+	1.07542i	−0.791571	+	0.611077i	$0.790737\pi$
$558$	0.828931	+	3.09361i	0.0350914	+	0.130963i
$559$	21.8368	+	37.8225i	0.923599	+	1.59972i
$560$	1.72482	+	6.23981i	0.0728869	+	0.263680i
$561$	22.2116	+	3.91651i	0.937776	+	0.165355i
$562$	−4.19678	+	15.6626i	−0.177030	+	0.660686i
$563$	2.71239	−	0.726784i	0.114314	−	0.0306303i	−0.201209	−	0.979548i	$-0.564487\pi$
$563$	2.71239	−	0.726784i	0.114314	−	0.0306303i	0.315522	+	0.948918i	$0.397820\pi$
$564$	8.25342	+	6.92544i	0.347532	+	0.291614i
$565$	−3.81040	+	0.363675i	−0.160305	+	0.0152999i
$566$	−9.37053	−	25.7453i	−0.393873	−	1.08216i
$567$	−2.88416	−	0.252331i	−0.121123	−	0.0105969i
$568$	5.45034	+	3.81637i	0.228691	+	0.160131i
$569$	−39.1835			−1.64266			−0.821328	−	0.570456i	$-0.806767\pi$
$569$	−39.1835			−1.64266			−0.821328	+	0.570456i	$0.806767\pi$
$570$	−3.06010	+	9.25396i	−0.128174	+	0.387606i
$571$	17.1294			0.716845			0.358423	−	0.933559i	$-0.383315\pi$
$571$	17.1294			0.716845			0.358423	+	0.933559i	$0.383315\pi$
$572$	−19.5915	−	13.7181i	−0.819162	−	0.573584i
$573$	5.32253	+	0.465661i	0.222352	+	0.0194533i
$574$	0.113628	+	0.312190i	0.00474274	+	0.0130306i
$575$	22.0436	+	5.53537i	0.919281	+	0.230841i
$576$	−0.766044	−	0.642788i	−0.0319185	−	0.0267828i
$577$	18.2068	−	4.87850i	0.757959	−	0.203094i	0.140913	−	0.990022i	$-0.454996\pi$
$577$	18.2068	−	4.87850i	0.757959	−	0.203094i	0.617045	+	0.786927i	$0.288329\pi$
$578$	−0.447844	+	1.67138i	−0.0186278	+	0.0695201i
$579$	17.7870	+	3.13632i	0.739202	+	0.130341i
$580$	−8.90563	+	15.7099i	−0.369786	+	0.652318i
$581$	15.3679	+	26.6180i	0.637568	+	1.10430i
$582$	−2.39926	−	8.95415i	−0.0994524	−	0.371161i
$583$	4.25879	+	48.6782i	0.176381	+	2.01604i
$584$	10.7703	+	3.92006i	0.445677	+	0.162213i
$585$	6.60325	+	6.49989i	0.273011	+	0.268738i
$586$	−19.9874	+	16.7714i	−0.825671	+	0.692820i
$587$	4.34853	−	6.21034i	0.179483	−	0.256328i	−0.719322	−	0.694677i	$-0.755548\pi$
$587$	4.34853	−	6.21034i	0.179483	−	0.256328i	0.898805	+	0.438348i	$0.144436\pi$
$588$	−0.977260	−	0.977260i	−0.0403015	−	0.0403015i
$589$	−11.9349	+	7.24230i	−0.491770	+	0.298414i
$590$	−0.924244	−	1.94191i	−0.0380505	−	0.0799471i
$591$	17.2288	−	3.03790i	0.708697	−	0.124962i
$592$	0.865374	−	9.89127i	0.0355667	−	0.406529i
$593$	−5.60159	+	12.0126i	−0.230030	+	0.493300i	−0.987114	−	0.160017i	$-0.948845\pi$
$593$	−5.60159	+	12.0126i	−0.230030	+	0.493300i	0.757085	+	0.653317i	$0.226623\pi$
$594$	−1.97409	+	5.42376i	−0.0809977	+	0.222539i
$595$	−12.8211	−	21.8077i	−0.525613	−	0.894028i
$596$	6.10754	−	10.5786i	0.250175	−	0.433315i
$597$	−25.8606	−	6.92933i	−1.05840	−	0.283599i
$598$	10.8037	+	15.4292i	0.441795	+	0.630948i
$599$	−5.04867	+	28.6324i	−0.206283	+	1.16989i	0.689125	+	0.724642i	$0.257995\pi$
$599$	−5.04867	+	28.6324i	−0.206283	+	1.16989i	−0.895408	+	0.445246i	$0.853116\pi$
$600$	−4.93712	−	0.790454i	−0.201557	−	0.0322701i
$601$	−8.93726	−	5.15993i	−0.364558	−	0.210478i	0.306520	−	0.951864i	$-0.400835\pi$
$601$	−8.93726	−	5.15993i	−0.364558	−	0.210478i	−0.671078	+	0.741386i	$0.734169\pi$
$602$	30.3983	−	2.65951i	1.23894	−	0.108393i
$603$	5.72479	+	12.2768i	0.233131	+	0.499952i
$604$	−2.84523	+	1.03558i	−0.115771	+	0.0421371i
$605$	−17.4347	−	46.7508i	−0.708822	−	1.90069i
$606$	−2.55437	−	14.4866i	−0.103764	−	0.588477i
$607$	14.6081	−	14.6081i	0.592924	−	0.592924i	−0.345496	−	0.938420i	$-0.612289\pi$
$607$	14.6081	−	14.6081i	0.592924	−	0.592924i	0.938420	+	0.345496i	$0.112289\pi$
$608$	1.75553	−	3.98975i	0.0711962	−	0.161806i
$609$		−	23.3815i		−	0.947467i
$610$	8.08136	−	5.75416i	0.327205	−	0.232979i
$611$	28.6970	+	34.1998i	1.16096	+	1.38357i
$612$	3.54153	+	1.65144i	0.143158	+	0.0667555i
$613$	22.6344	−	10.5546i	0.914194	−	0.426296i	0.0921667	−	0.995744i	$-0.470621\pi$
$613$	22.6344	−	10.5546i	0.914194	−	0.426296i	0.822027	+	0.569448i	$0.192843\pi$
$614$	21.6089	−	25.7525i	0.872066	−	1.03929i
$615$	−0.255784	−	0.0203465i	−0.0103142	−	0.000820449i
$616$	−14.4717	+	8.35525i	−0.583082	+	0.336643i
$617$	21.7709	−	15.2442i	0.876464	−	0.613707i	−0.0463615	−	0.998925i	$-0.514763\pi$
$617$	21.7709	−	15.2442i	0.876464	−	0.613707i	0.922826	+	0.385218i	$0.125874\pi$
$618$	8.59159	−	6.01590i	0.345604	−	0.241995i
$619$	24.6440	−	14.2282i	0.990528	−	0.571881i	0.0850957	−	0.996373i	$-0.472880\pi$
$619$	24.6440	−	14.2282i	0.990528	−	0.571881i	0.905432	+	0.424491i	$0.139547\pi$
$620$	−4.64649	−	5.44958i	−0.186607	−	0.218861i
$621$	2.92185	−	3.48213i	0.117250	−	0.139733i
$622$	−2.30266	+	1.07375i	−0.0923283	+	0.0430534i
$623$	4.20760	+	1.96203i	0.168574	+	0.0786073i
$624$	−2.66352	−	3.17426i	−0.106626	−	0.127072i
$625$	−23.2109	+	9.28736i	−0.928435	+	0.371494i
$626$		−	2.03186i		−	0.0812093i
$627$	−25.1050	−	1.64546i	−1.00260	−	0.0657134i
$628$	−11.1937	+	11.1937i	−0.446678	+	0.446678i
$629$	6.73741	+	38.2097i	0.268638	+	1.52352i
$630$	6.06574	−	2.26209i	0.241665	−	0.0901239i
$631$	−7.47099	+	2.71922i	−0.297416	+	0.108250i	−0.486418	−	0.873726i	$-0.661697\pi$
$631$	−7.47099	+	2.71922i	−0.297416	+	0.108250i	0.189003	+	0.981977i	$0.439475\pi$
$632$	0.898341	+	1.92650i	0.0357341	+	0.0766320i
$633$	10.7792	−	0.943056i	0.428434	−	0.0374831i
$634$	−0.658795	−	0.380355i	−0.0261641	−	0.0151058i
$635$	4.80904	−	6.98465i	0.190841	−	0.277177i
$636$	−1.47010	+	8.33733i	−0.0582931	+	0.330597i
$637$	−3.28477	−	4.69114i	−0.130147	−	0.185870i
$638$	−45.0252	−	12.0645i	−1.78256	−	0.477637i
$639$	3.32682	−	5.76222i	0.131607	−	0.227950i
$640$	2.16437	+	0.561682i	0.0855544	+	0.0222024i
$641$	−8.90256	+	24.4596i	−0.351630	+	0.966095i	0.630217	+	0.776419i	$0.282966\pi$
$641$	−8.90256	+	24.4596i	−0.351630	+	0.966095i	−0.981847	+	0.189676i	$0.939256\pi$
$642$	−2.83094	+	6.07096i	−0.111728	+	0.239602i
$643$	−2.01856	+	23.0722i	−0.0796042	+	0.909880i	0.846445	+	0.532477i	$0.178739\pi$
$643$	−2.01856	+	23.0722i	−0.0796042	+	0.909880i	−0.926049	+	0.377403i	$0.876817\pi$
$644$	12.9604	−	2.28526i	0.510710	−	0.0900519i
$645$	−7.88565	+	22.2092i	−0.310497	+	0.874485i
$646$	−2.59111	+	16.8348i	−0.101946	+	0.662355i
$647$	−14.8926	−	14.8926i	−0.585488	−	0.585488i	0.350918	−	0.936406i	$-0.385869\pi$
$647$	−14.8926	−	14.8926i	−0.585488	−	0.585488i	−0.936406	+	0.350918i	$0.885869\pi$
$648$	−0.573576	+	0.819152i	−0.0225322	+	0.0321793i
$649$	4.25256	−	3.56832i	0.166927	−	0.140069i
$650$	−19.5784	−	6.77814i	−0.767929	−	0.265861i
$651$	8.71331	+	3.17138i	0.341501	+	0.124296i
$652$	−0.272039	−	3.10942i	−0.0106539	−	0.121774i
$653$	−5.32640	−	19.8784i	−0.208438	−	0.777902i	−0.988374	−	0.152042i	$-0.951415\pi$
$653$	−5.32640	−	19.8784i	−0.208438	−	0.777902i	0.779936	−	0.625859i	$-0.215252\pi$
$654$	0.272196	+	0.471457i	0.0106437	+	0.0184354i
$655$	15.4153	+	8.73863i	0.602325	+	0.341446i
$656$	0.113008	+	0.0199264i	0.00441223	+	0.000777994i
$657$	2.96645	−	11.0709i	0.115732	−	0.431919i
$658$	30.1300	−	8.07331i	1.17459	−	0.314730i
$659$	−22.6780	−	19.0291i	−0.883409	−	0.741268i	0.0834682	−	0.996510i	$-0.473400\pi$
$659$	−22.6780	−	19.0291i	−0.883409	−	0.741268i	−0.966877	+	0.255242i	$0.917845\pi$
$660$	−1.22623	−	12.8478i	−0.0477311	−	0.500102i
$661$	−3.85534	−	10.5925i	−0.149955	−	0.411999i	0.841857	−	0.539700i	$-0.181462\pi$
$661$	−3.85534	−	10.5925i	−0.149955	−	0.411999i	−0.991813	+	0.127701i	$0.959240\pi$
$662$	−19.5235	−	1.70808i	−0.758801	−	0.0663865i
$663$	13.2638	+	9.28742i	0.515124	+	0.360694i
$664$	10.6162			0.411989
$665$	16.8650	+	22.6245i	0.653996	+	0.877340i
$666$	−9.92905			−0.384743
$667$	30.0713	+	21.0562i	1.16437	+	0.815298i
$668$	−7.73991	−	0.677155i	−0.299466	−	0.0261999i
$669$	−2.67225	−	7.34196i	−0.103315	−	0.283857i
$670$	−23.3562	−	19.2863i	−0.902327	−	0.745093i
$671$	19.6165	+	16.4602i	0.757288	+	0.635440i
$672$	−2.79653	+	0.749327i	−0.107878	+	0.0289059i
$673$	10.4858	−	39.1334i	0.404196	−	1.50848i	−0.401338	−	0.915930i	$-0.631455\pi$
$673$	10.4858	−	39.1334i	0.404196	−	1.50848i	0.805534	−	0.592550i	$-0.201879\pi$
$674$	−20.0128	−	3.52880i	−0.770865	−	0.135924i
$675$	−0.357147	+	4.98723i	−0.0137466	+	0.191959i
$676$	−2.08516	−	3.61160i	−0.0801985	−	0.138908i
$677$	−2.21364	−	8.26143i	−0.0850772	−	0.317513i	0.910252	−	0.414056i	$-0.135888\pi$
$677$	−2.21364	−	8.26143i	−0.0850772	−	0.317513i	−0.995329	+	0.0965431i	$0.969221\pi$
$678$	−0.149194	−	1.70529i	−0.00572976	−	0.0654914i
$679$	−25.2198	−	9.17925i	−0.967847	−	0.352267i
$680$	−8.73748	+	0.0689232i	−0.335067	+	0.00264309i
$681$	−11.4926	+	9.64342i	−0.440396	+	0.369536i
$682$	10.6030	−	15.1426i	0.406009	−	0.579841i
$683$	−15.7131	−	15.7131i	−0.601244	−	0.601244i	0.339399	−	0.940643i	$-0.389776\pi$
$683$	−15.7131	−	15.7131i	−0.601244	−	0.601244i	−0.940643	+	0.339399i	$0.889776\pi$
$684$	−4.12757	−	1.40112i	−0.157822	−	0.0535732i
$685$	3.75406	−	1.78673i	0.143435	−	0.0682675i
$686$	16.0179	−	2.82438i	0.611564	−	0.107835i
$687$	0.122536	−	1.40059i	0.00467503	−	0.0534359i
$688$	4.45429	−	9.55225i	0.169818	−	0.364176i
$689$	−11.9982	+	32.9648i	−0.457096	+	1.25586i
$690$	−2.55318	+	9.83836i	−0.0971978	+	0.374540i
$691$	−3.54649	+	6.14270i	−0.134915	+	0.233679i	−0.925565	−	0.378589i	$-0.876409\pi$
$691$	−3.54649	+	6.14270i	−0.134915	+	0.233679i	0.790650	+	0.612268i	$0.209743\pi$
$692$	10.4143	+	2.79052i	0.395894	+	0.106079i
$693$	9.58475	+	13.6884i	0.364095	+	0.519981i
$694$	−1.49350	+	8.47008i	−0.0566926	+	0.321520i
$695$	7.86640	+	42.6428i	0.298389	+	1.61753i
$696$	−6.99404	−	4.03801i	−0.265108	−	0.153060i
$697$	−0.446701	+	0.0390813i	−0.0169200	+	0.00148031i
$698$	−2.02142	−	4.33495i	−0.0765119	−	0.164080i
$699$	−25.1047	+	9.13737i	−0.949547	+	0.345607i
$700$	−10.0732	+	10.3962i	−0.380733	+	0.392940i
$701$	−9.03635	−	51.2477i	−0.341298	−	1.93560i	−0.352890	−	0.935665i	$-0.614801\pi$
$701$	−9.03635	−	51.2477i	−0.341298	−	1.93560i	0.0115915	−	0.999933i	$-0.496310\pi$
$702$	−2.93004	+	2.93004i	−0.110587	+	0.110587i
$703$	−12.1109	−	41.5507i	−0.456773	−	1.56711i
$704$			5.77184i			0.217534i
$705$	−3.99618	+	23.7578i	−0.150505	+	0.894771i
$706$	11.7336	+	13.9836i	0.441600	+	0.526278i
$707$	−38.5980	−	17.9986i	−1.45163	−	0.676905i
$708$	0.871681	−	0.406471i	0.0327598	−	0.0152761i
$709$	8.25988	−	9.84375i	0.310206	−	0.369690i	−0.588305	−	0.808639i	$-0.700205\pi$
$709$	8.25988	−	9.84375i	0.310206	−	0.369690i	0.898512	+	0.438949i	$0.144649\pi$
$710$	−1.17975	+	14.8311i	−0.0442753	+	0.556603i
$711$	1.84087	−	1.06283i	0.0690381	−	0.0398592i
$712$	1.31355	−	0.919760i	0.0492275	−	0.0344695i
$713$	−11.9255	+	8.35033i	−0.446614	+	0.312722i
$714$	9.79762	−	5.65666i	0.366667	−	0.211695i
$715$	4.24067	−	53.3112i	0.158592	−	1.99373i
$716$	13.4088	−	15.9800i	0.501111	−	0.597201i
$717$	22.1976	−	10.3509i	0.828984	−	0.386562i
$718$	24.5775	+	11.4607i	0.917224	+	0.427709i
$719$	−10.4678	−	12.4750i	−0.390381	−	0.465238i	0.534681	−	0.845054i	$-0.320432\pi$
$719$	−10.4678	−	12.4750i	−0.390381	−	0.465238i	−0.925062	+	0.379816i	$0.875987\pi$
$720$	0.370907	−	2.20509i	0.0138229	−	0.0821789i
$721$		−	30.3658i		−	1.13088i
$722$	0.828756	−	18.9819i	0.0308431	−	0.706434i
$723$	2.14071	−	2.14071i	0.0796140	−	0.0796140i
$724$	−0.197379	−	1.11939i	−0.00733552	−	0.0416018i
$725$	−40.3751	+	0.637015i	−1.49949	+	0.0236582i
$726$	20.9684	−	7.63188i	0.778211	−	0.283246i
$727$	−17.1277	−	36.7305i	−0.635231	−	1.36226i	−0.915493	−	0.402334i	$-0.868199\pi$
$727$	−17.1277	−	36.7305i	−0.635231	−	1.36226i	0.280262	−	0.959924i	$-0.409579\pi$
$728$	−11.9511	+	1.04559i	−0.442938	+	0.0387521i
$729$	0.866025	+	0.500000i	0.0320750	+	0.0185185i
$730$	4.64932	+	25.2034i	0.172079	+	0.932820i
$731$	−7.15179	+	40.5598i	−0.264519	+	1.50016i
$732$	2.54475	+	3.63428i	0.0940567	+	0.134327i
$733$	12.4318	+	3.33110i	0.459180	+	0.123037i	0.480991	−	0.876725i	$-0.340277\pi$
$733$	12.4318	+	3.33110i	0.459180	+	0.123037i	−0.0218118	+	0.999762i	$0.506943\pi$
$734$	−0.251805	+	0.436139i	−0.00929430	+	0.0160982i
$735$	0.776275	−	2.99128i	0.0286333	−	0.110335i
$736$	1.55468	−	4.27146i	0.0573064	−	0.157448i
$737$	33.0425	−	70.8600i	1.21714	−	2.61016i
$738$	0.0100012	−	0.114315i	0.000368151	−	0.00420799i
$739$	−1.60833	+	0.283592i	−0.0591635	+	0.0104321i	−0.203152	−	0.979147i	$-0.565118\pi$
$739$	−1.60833	+	0.283592i	−0.0591635	+	0.0104321i	0.143988	+	0.989579i	$0.454007\pi$
$740$	20.0472	−	9.54142i	0.736951	−	0.350749i
$741$	−15.8354	−	8.68762i	−0.581730	−	0.319148i
$742$	17.3315	+	17.3315i	0.636259	+	0.636259i
$743$	25.1931	−	35.9795i	0.924246	−	1.31996i	−0.0230945	−	0.999733i	$-0.507352\pi$
$743$	25.1931	−	35.9795i	0.924246	−	1.31996i	0.947341	−	0.320227i	$-0.103759\pi$
$744$	2.45344	−	2.05868i	0.0899476	−	0.0754750i
$745$	27.3129	−	0.215450i	1.00067	−	0.00789349i
$746$	−6.56566	−	2.38971i	−0.240386	−	0.0874933i
$747$	−0.925264	−	10.5758i	−0.0338536	−	0.386949i
$748$	−5.83748	−	21.7858i	−0.213439	−	0.796566i
$749$	9.69677	+	16.7953i	0.354312	+	0.613687i
$750$	−4.07143	−	10.4127i	−0.148667	−	0.380217i
$751$	2.38558	+	0.420642i	0.0870509	+	0.0153494i	0.217004	−	0.976171i	$-0.430372\pi$
$751$	2.38558	+	0.420642i	0.0870509	+	0.0153494i	−0.129953	+	0.991520i	$0.541483\pi$
$752$	2.78854	−	10.4070i	0.101687	−	0.379503i
$753$	0.232366	−	0.0622624i	0.00846790	−	0.00226897i
$754$	−25.6354	−	21.5107i	−0.933587	−	0.783373i
$755$	−5.22062	−	4.31091i	−0.189998	−	0.156890i
$756$	0.990209	+	2.72058i	0.0360136	+	0.0989464i
$757$	−23.7647	−	2.07914i	−0.863743	−	0.0755677i	−0.353332	−	0.935498i	$-0.614951\pi$
$757$	−23.7647	−	2.07914i	−0.863743	−	0.0755677i	−0.510411	+	0.859930i	$0.670507\pi$
$758$	−23.5772	−	16.5089i	−0.856362	−	0.599631i
$759$	−26.2364			−0.952322
$760$	9.68019	−	1.13750i	0.351137	−	0.0412614i
$761$	47.3499			1.71643			0.858216	−	0.513290i	$-0.171573\pi$
$761$	47.3499			1.71643			0.858216	+	0.513290i	$0.171573\pi$
$762$	3.10657	+	2.17524i	0.112539	+	0.0788007i
$763$	1.57011	+	0.137367i	0.0568419	+	0.00497303i
$764$	−1.82737	−	5.02065i	−0.0661118	−	0.181641i
$765$	0.830183	+	8.69823i	0.0300153	+	0.314485i
$766$	2.88080	+	2.41728i	0.104088	+	0.0873398i
$767$	3.84959	−	1.03150i	0.139001	−	0.0372451i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	14.8699	+	2.62196i	0.536222	+	0.0945504i	0.435200	−	0.900334i	$-0.356678\pi$
$769$	14.8699	+	2.62196i	0.536222	+	0.0945504i	0.101022	+	0.994884i	$0.467789\pi$
$770$	−32.5061	−	18.4271i	−1.17144	−	0.664066i
$771$	0.301673	+	0.522512i	0.0108645	+	0.0188178i
$772$	−4.67463	−	17.4459i	−0.168244	−	0.627893i
$773$	1.97245	+	22.5452i	0.0709442	+	0.810896i	0.945426	+	0.325837i	$0.105646\pi$
$773$	1.97245	+	22.5452i	0.0709442	+	0.810896i	−0.874482	+	0.485059i	$0.838798\pi$
$774$	−9.90412	−	3.60480i	−0.355996	−	0.129572i
$775$	5.23894	−	15.1325i	0.188188	−	0.543575i
$776$	−7.10124	+	5.95865i	−0.254920	+	0.213903i
$777$	−16.4882	+	23.5477i	−0.591512	+	0.844767i
$778$	19.1837	+	19.1837i	0.687768	+	0.687768i
$779$	0.490579	−	0.0975824i	0.0175768	−	0.00349625i
$780$	3.10025	−	8.73156i	0.111007	−	0.312640i
$781$	−37.8203	+	6.66874i	−1.35332	+	0.238626i
$782$	−1.54811	+	17.6950i	−0.0553602	+	0.632770i
$783$	−3.41307	+	7.31936i	−0.121973	+	0.261573i
$784$	−0.472690	+	1.29871i	−0.0168818	+	0.0463823i
$785$	−34.2627	−	8.89159i	−1.22289	−	0.317355i
$786$	−3.96229	+	6.86289i	−0.141330	+	0.244791i
$787$	−7.18676	−	1.92569i	−0.256180	−	0.0686433i	0.128443	−	0.991717i	$-0.459002\pi$
$787$	−7.18676	−	1.92569i	−0.256180	−	0.0686433i	−0.384624	+	0.923074i	$0.625669\pi$
$788$	−10.0345	−	14.3307i	−0.357463	−	0.510510i
$789$	0.311694	−	1.76770i	0.0110966	−	0.0629319i
$790$	−2.69548	+	3.91490i	−0.0959007	+	0.139286i
$791$	−4.29201	−	2.47799i	−0.152606	−	0.0881073i
$792$	5.74988	−	0.503049i	0.204313	−	0.0178751i
$793$	7.76947	+	16.6617i	0.275902	+	0.591674i
$794$	−18.8072	+	6.84527i	−0.667443	+	0.242929i
$795$	−17.7372	+	6.61471i	−0.629073	+	0.234600i
$796$	4.64906	+	26.3661i	0.164782	+	0.934523i
$797$	18.1969	−	18.1969i	0.644566	−	0.644566i	−0.307109	−	0.951674i	$-0.599362\pi$
$797$	18.1969	−	18.1969i	0.644566	−	0.644566i	0.951674	+	0.307109i	$0.0993615\pi$
$798$	−10.1772	+	7.46220i	−0.360267	+	0.264159i
$799$			42.1012i			1.48943i
$800$	1.37012	+	4.80861i	0.0484412	+	0.170010i
$801$	−1.03074	−	1.22839i	−0.0364195	−	0.0434031i
$802$	−14.5023	−	6.76252i	−0.512093	−	0.238793i
$803$	−59.9557	+	27.9578i	−2.11579	+	0.986610i
$804$	8.70720	−	10.3768i	0.307079	−	0.365963i
$805$	19.0927	+	22.3927i	0.672931	+	0.789240i
$806$	11.4932	−	6.63561i	0.404831	−	0.233730i
$807$	−4.29544	+	3.00770i	−0.151207	+	0.105876i
$808$	−12.0498	+	8.43734i	−0.423909	+	0.296825i
$809$	−31.3922	+	18.1243i	−1.10369	+	0.637216i	−0.937188	−	0.348826i	$-0.886581\pi$
$809$	−31.3922	+	18.1243i	−1.10369	+	0.637216i	−0.166502	+	0.986041i	$0.553247\pi$
$810$	−2.22903	−	0.177309i	−0.0783200	−	0.00623001i
$811$	−8.81066	+	10.5001i	−0.309384	+	0.368710i	−0.898222	−	0.439541i	$-0.855141\pi$
$811$	−8.81066	+	10.5001i	−0.309384	+	0.368710i	0.588838	+	0.808251i	$0.299586\pi$
$812$	−21.1909	+	9.88146i	−0.743653	+	0.346771i
$813$	2.78441	+	1.29839i	0.0976535	+	0.0455366i
$814$	36.8375	+	43.9012i	1.29115	+	1.53874i
$815$	5.68546	−	4.04821i	0.199153	−	0.141803i
$816$		−	3.90764i		−	0.136795i
$817$	3.00471	−	45.8433i	0.105122	−	1.60385i
$818$	−11.4284	+	11.4284i	−0.399584	+	0.399584i
$819$	2.08322	+	11.8145i	0.0727935	+	0.412833i
$820$	0.0896588	+	0.240418i	0.00313102	+	0.00839576i
$821$	−29.6353	+	10.7864i	−1.03428	+	0.376446i	−0.802708	−	0.596372i	$-0.796608\pi$
$821$	−29.6353	+	10.7864i	−1.03428	+	0.376446i	−0.231569	+	0.972818i	$0.574386\pi$
$822$	0.785783	+	1.68512i	0.0274073	+	0.0587752i
$823$	25.7777	−	2.25526i	0.898554	−	0.0786133i	0.371488	−	0.928438i	$-0.378848\pi$
$823$	25.7777	−	2.25526i	0.898554	−	0.0786133i	0.527066	+	0.849824i	$0.323292\pi$
$824$	−9.08322	−	5.24420i	−0.316429	−	0.182690i
$825$	23.3760	−	16.9238i	0.813848	−	0.589212i
$826$	0.483534	−	2.74226i	0.0168243	−	0.0954154i
$827$	−21.7358	−	31.0419i	−0.755826	−	1.07943i	−0.994125	−	0.108240i	$-0.965479\pi$
$827$	−21.7358	−	31.0419i	−0.755826	−	1.07943i	0.238298	−	0.971192i	$-0.423410\pi$
$828$	−4.39070	−	1.17649i	−0.152588	−	0.0408857i
$829$	−13.9916	+	24.2342i	−0.485949	+	0.841688i	−0.999870	−	0.0161499i	$-0.994859\pi$
$829$	−13.9916	+	24.2342i	−0.485949	+	0.841688i	0.513921	+	0.857838i	$0.328192\pi$
$830$	12.0311	+	20.4639i	0.417605	+	0.710314i
$831$	−7.91240	+	21.7391i	−0.274478	+	0.754122i
$832$	−1.75121	+	3.75548i	−0.0607122	+	0.130198i
$833$	0.470691	−	5.38002i	0.0163085	−	0.186407i
$834$	−19.0976	+	3.36742i	−0.661296	+	0.116604i
$835$	−7.46615	−	15.6870i	−0.258377	−	0.542870i
$836$	9.11854	+	23.4483i	0.315371	+	0.810975i
$837$	−2.26468	−	2.26468i	−0.0782788	−	0.0782788i
$838$	−3.94438	+	5.63316i	−0.136256	+	0.194594i
$839$	−19.4998	+	16.3622i	−0.673206	+	0.564887i	−0.914012	−	0.405686i	$-0.867033\pi$
$839$	−19.4998	+	16.3622i	−0.673206	+	0.564887i	0.240806	+	0.970573i	$0.422588\pi$
$840$	−4.61364	−	4.54143i	−0.159186	−	0.156694i
$841$	−34.0377	−	12.3887i	−1.17371	−	0.427197i
$842$	−0.415836	−	4.75303i	−0.0143307	−	0.163800i
$843$	−4.19678	−	15.6626i	−0.144545	−	0.539448i
$844$	−5.41018	−	9.37070i	−0.186226	−	0.322553i
$845$	4.59871	−	8.11232i	0.158201	−	0.279072i
$846$	−10.6104	−	1.87090i	−0.364793	−	0.0643228i
$847$	16.7206	−	62.4021i	0.574526	−	2.14416i
$848$	8.17748	−	2.19115i	0.280816	−	0.0752444i
$849$	20.9878	+	17.6108i	0.720299	+	0.604402i
$850$	−10.0348	−	16.7644i	−0.344191	−	0.575013i
$851$	−15.4365	−	42.4115i	−0.529158	−	1.45385i
$852$	−6.62832	−	0.579903i	−0.227083	−	0.0198671i
$853$	−7.94036	−	5.55990i	−0.271873	−	0.190367i	0.429687	−	0.902978i	$-0.358624\pi$
$853$	−7.94036	−	5.55990i	−0.271873	−	0.190367i	−0.701560	+	0.712611i	$0.747513\pi$
$854$	12.8449			0.439542
$855$	−1.97685	−	9.54422i	−0.0676070	−	0.326405i
$856$	6.69857			0.228952
$857$	−19.9385	−	13.9611i	−0.681086	−	0.476902i	0.181119	−	0.983461i	$-0.442028\pi$
$857$	−19.9385	−	13.9611i	−0.681086	−	0.476902i	−0.862205	+	0.506560i	$0.830917\pi$
$858$	23.8258	+	2.08449i	0.813400	+	0.0711633i
$859$	−5.74738	−	15.7908i	−0.196098	−	0.538775i	0.802202	−	0.597052i	$-0.203662\pi$
$859$	−5.74738	−	15.7908i	−0.196098	−	0.538775i	−0.998300	+	0.0582772i	$0.981439\pi$
$860$	23.4610	−	2.23918i	0.800012	−	0.0763554i
$861$	−0.254500	−	0.213551i	−0.00867333	−	0.00727779i
$862$	−11.1749	+	2.99431i	−0.380619	+	0.101986i
$863$	7.30471	−	27.2615i	0.248655	−	0.927994i	−0.722856	−	0.690999i	$-0.757171\pi$
$863$	7.30471	−	27.2615i	0.248655	−	0.927994i	0.971511	−	0.236995i	$-0.0761625\pi$
$864$	0.984808	+	0.173648i	0.0335038	+	0.00590763i
$865$	6.42328	+	23.2372i	0.218398	+	0.790090i
$866$	−2.77776	−	4.81122i	−0.0943921	−	0.163492i
$867$	−0.447844	−	1.67138i	−0.0152096	−	0.0567629i
$868$	−0.808152	−	9.23722i	−0.0274305	−	0.313532i
$869$	−11.5290	−	4.19623i	−0.391096	−	0.142347i
$870$	−0.142445	−	18.0580i	−0.00482935	−	0.612223i
$871$	42.9986	−	36.0801i	1.45695	−	1.22253i
$872$	0.312250	−	0.445940i	0.0105741	−	0.0151014i
$873$	6.55489	+	6.55489i	0.221849	+	0.221849i
$874$	−0.432241	−	19.8091i	−0.0146208	−	0.670051i
$875$	−31.4556	−	7.63557i	−1.06339	−	0.258129i
$876$	−11.2874	+	1.99027i	−0.381364	+	0.0672448i
$877$	−3.05587	+	34.9287i	−0.103189	+	1.17946i	0.751290	+	0.659972i	$0.229432\pi$
$877$	−3.05587	+	34.9287i	−0.103189	+	1.17946i	−0.854479	+	0.519486i	$0.826123\pi$
$878$	9.37036	−	20.0948i	0.316234	−	0.678167i
$879$	8.92388	−	24.5182i	0.300995	−	0.826977i
$880$	−11.1259	+	6.54108i	−0.375053	+	0.220500i
$881$	−16.6880	+	28.9045i	−0.562233	+	0.973817i	0.435068	+	0.900398i	$0.356724\pi$
$881$	−16.6880	+	28.9045i	−0.562233	+	0.973817i	−0.997301	+	0.0734192i	$0.976609\pi$
$882$	1.33496	+	0.357702i	0.0449505	+	0.0120444i
$883$	5.92760	+	8.46549i	0.199480	+	0.284886i	0.906412	−	0.422395i	$-0.138810\pi$
$883$	5.92760	+	8.46549i	0.199480	+	0.284886i	−0.706932	+	0.707281i	$0.749922\pi$
$884$	2.81173	−	15.9461i	0.0945688	−	0.536327i
$885$	1.77137	+	1.21962i	0.0595441	+	0.0409971i
$886$	−10.9660	−	6.33121i	−0.368409	−	0.212701i
$887$	31.0868	−	2.71975i	1.04379	−	0.0913201i	0.447659	−	0.894204i	$-0.352258\pi$
$887$	31.0868	−	2.71975i	1.04379	−	0.0913201i	0.596135	+	0.802884i	$0.296702\pi$
$888$	4.19620	+	8.99878i	0.140815	+	0.301979i
$889$	10.3176	−	3.75529i	0.346040	−	0.125948i
$890$	3.26156	+	1.48968i	0.109328	+	0.0499342i
$891$	−1.00227	−	5.68415i	−0.0335773	−	0.190426i
$892$	−5.52473	+	5.52473i	−0.184982	+	0.184982i
$893$	−5.11274	−	46.6840i	−0.171091	−	1.56222i
$894$			12.2151i			0.408533i
$895$	45.9991	+	7.73728i	1.53758	+	0.258629i
$896$	1.86098	+	2.21783i	0.0621711	+	0.0740927i
$897$	−17.0709	−	7.96027i	−0.569979	−	0.265786i
$898$	−7.23737	+	3.37484i	−0.241514	+	0.112620i
$899$	16.6260	−	19.8141i	0.554507	−	0.660836i
$900$	4.67090	−	1.78401i	0.155697	−	0.0594669i
$901$	−28.6498	+	16.5410i	−0.954462	+	0.551059i
$902$	−0.542546	+	0.379895i	−0.0180648	+	0.0126491i
$903$	−24.9960	+	17.5024i	−0.831813	+	0.582442i
$904$	−1.48247	+	0.855904i	−0.0493062	+	0.0284669i
$905$	1.93407	−	1.64905i	0.0642906	−	0.0548161i
$906$	1.94625	−	2.31945i	0.0646599	−	0.0770587i
$907$	5.34845	−	2.49402i	0.177592	−	0.0828126i	−0.331789	−	0.943354i	$-0.607652\pi$
$907$	5.34845	−	2.49402i	0.177592	−	0.0828126i	0.509381	+	0.860541i	$0.329874\pi$
$908$	13.5969	+	6.34033i	0.451228	+	0.210411i
$909$	9.45544	+	11.2686i	0.313617	+	0.373754i
$910$	−15.5594	−	21.8522i	−0.515789	−	0.724393i
$911$			12.0373i			0.398814i	0.979917	+	0.199407i	$0.0639015\pi$
$911$			12.0373i			0.398814i	−0.979917	+	0.199407i	$0.936098\pi$
$912$	0.474541	+	4.33299i	0.0157136	+	0.143480i
$913$	−43.3280	+	43.3280i	−1.43395	+	1.43395i
$914$	0.493303	+	2.79766i	0.0163170	+	0.0925385i
$915$	−4.12159	+	9.02393i	−0.136255	+	0.298322i
$916$	−1.32115	+	0.480860i	−0.0436521	+	0.0158881i
$917$	9.69616	+	20.7935i	0.320195	+	0.686661i
$918$	−3.89277	+	0.340573i	−0.128481	+	0.0112406i
$919$	37.8083	+	21.8286i	1.24718	+	0.720059i	0.970546	−	0.240916i	$-0.0774479\pi$
$919$	37.8083	+	21.8286i	1.24718	+	0.720059i	0.276633	+	0.960976i	$0.410781\pi$
$920$	9.99560	−	1.84391i	0.329545	−	0.0607918i
$921$	−5.83762	+	33.1068i	−0.192356	+	1.09091i
$922$	−2.19189	−	3.13035i	−0.0721861	−	0.103092i
$923$	−26.6313	−	7.13583i	−0.876580	−	0.234879i
$924$	8.35525	−	14.4717i	0.274868	−	0.476085i
$925$	41.1112	+	27.8303i	1.35173	+	0.915054i
$926$	10.7548	−	29.5486i	0.353425	−	0.971027i
$927$	−4.43259	+	9.50571i	−0.145585	+	0.312209i
$928$	−0.703872	+	8.04529i	−0.0231057	+	0.264100i
$929$	2.58049	−	0.455010i	0.0846630	−	0.0149284i	−0.131156	−	0.991362i	$-0.541869\pi$
$929$	2.58049	−	0.455010i	0.0846630	−	0.0149284i	0.215819	+	0.976433i	$0.430758\pi$
$930$	6.74877	+	2.39623i	0.221301	+	0.0785756i
$931$	0.131420	+	6.02280i	0.00430711	+	0.197389i
$932$	18.8910	+	18.8910i	0.618795	+	0.618795i
$933$	1.45729	−	2.08122i	0.0477095	−	0.0681362i
$934$	−1.81670	+	1.52439i	−0.0594441	+	0.0498795i
$935$	35.3790	−	35.9416i	1.15702	−	1.17542i
$936$	3.89381	+	1.41723i	0.127273	+	0.0463237i
$937$	−2.25487	−	25.7733i	−0.0736634	−	0.841977i	−0.939701	−	0.341998i	$-0.888897\pi$
$937$	−2.25487	−	25.7733i	−0.0736634	−	0.841977i	0.866037	−	0.499979i	$-0.166659\pi$
$938$	−10.1504	−	37.8817i	−0.331422	−	1.23688i
$939$	1.01593	+	1.75964i	0.0331536	+	0.0574237i
$940$	23.2208	−	6.41872i	0.757377	−	0.209356i
$941$	−59.5361	−	10.4978i	−1.94082	−	0.342219i	−0.999994	−	0.00333638i	$-0.998938\pi$
$941$	−59.5361	−	10.4978i	−1.94082	−	0.342219i	−0.940829	−	0.338883i	$-0.889951\pi$
$942$	4.09718	−	15.2909i	0.133493	−	0.498204i
$943$	0.503840	−	0.135003i	0.0164073	−	0.00439632i
$944$	−0.736777	−	0.618229i	−0.0239800	−	0.0201216i
$945$	−4.12204	+	4.99190i	−0.134090	+	0.162386i
$946$	20.8063	+	57.1650i	0.676473	+	1.85859i
$947$	33.6465	+	2.94369i	1.09336	+	0.0956570i	0.619542	−	0.784964i	$-0.287318\pi$
$947$	33.6465	+	2.94369i	1.09336	+	0.0956570i	0.473822	+	0.880621i	$0.342874\pi$
$948$	−1.74123	−	1.21923i	−0.0565527	−	0.0395986i
$949$	−47.4930			−1.54169
$950$	13.1630	+	17.3706i	0.427063	+	0.563575i
$951$	0.760711			0.0246677
$952$	−9.26733	−	6.48905i	−0.300356	−	0.210311i
$953$	−0.787470	−	0.0688947i	−0.0255086	−	0.00223172i	0.0743943	−	0.997229i	$-0.476298\pi$
$953$	−0.787470	−	0.0688947i	−0.0255086	−	0.00223172i	−0.0999029	+	0.994997i	$0.531853\pi$
$954$	−2.89553	−	7.95539i	−0.0937461	−	0.257565i
$955$	7.60695	−	9.21222i	0.246155	−	0.298101i
$956$	−18.7622	−	15.7434i	−0.606813	−	0.509177i
$957$	45.0252	−	12.0645i	1.45546	−	0.389989i
$958$	3.00683	−	11.2216i	0.0971463	−	0.362555i
$959$	5.30129	+	0.934760i	0.171187	+	0.0301850i
$960$	−2.15524	+	0.595756i	−0.0695602	+	0.0192279i
$961$	−10.3712	−	17.9635i	−0.334556	−	0.579467i
$962$	10.6486	+	39.7412i	0.343325	+	1.28131i
$963$	−0.583818	−	6.67308i	−0.0188133	−	0.215037i
$964$	−2.84485	−	1.03544i	−0.0916265	−	0.0333493i
$965$	28.3314	−	28.7819i	0.912020	−	0.926522i
$966$	−10.0814	+	8.45928i	−0.324363	+	0.272173i
$967$	−29.7625	+	42.5052i	−0.957097	+	1.36688i	−0.0269706	+	0.999636i	$0.508586\pi$
$967$	−29.7625	+	42.5052i	−0.957097	+	1.36688i	−0.930126	+	0.367240i	$0.880303\pi$
$968$	−15.7785	−	15.7785i	−0.507139	−	0.507139i
$969$	−6.17342	−	15.8749i	−0.198319	−	0.509975i
$970$	−19.5336	−	6.93566i	−0.627187	−	0.222691i
$971$	−20.8472	+	3.67593i	−0.669019	+	0.117966i	−0.497834	−	0.867273i	$-0.665871\pi$
$971$	−20.8472	+	3.67593i	−0.669019	+	0.117966i	−0.171186	+	0.985239i	$0.554760\pi$
$972$	0.0871557	−	0.996195i	0.00279552	−	0.0319530i
$973$	−23.7274	+	50.8837i	−0.760667	+	1.63126i
$974$	3.83751	−	10.5435i	0.122962	−	0.337835i
$975$	20.3445	−	3.91917i	0.651545	−	0.125514i
$976$	2.21832	−	3.84224i	0.0710067	−	0.122987i
$977$	50.9392	+	13.6491i	1.62969	+	0.436674i	0.953828	−	0.300354i	$-0.0971046\pi$
$977$	50.9392	+	13.6491i	1.62969	+	0.436674i	0.675862	+	0.737028i	$0.263771\pi$
$978$	1.79030	+	2.55682i	0.0572476	+	0.0817580i
$979$	−1.60719	+	9.11484i	−0.0513661	+	0.291311i
$980$	−3.03909	+	0.560626i	−0.0970801	+	0.0179085i
$981$	−0.471457	−	0.272196i	−0.0150525	−	0.00869055i
$982$	9.34867	−	0.817903i	0.298328	−	0.0261003i
$983$	−24.5176	−	52.5781i	−0.781989	−	1.67698i	−0.734982	−	0.678086i	$-0.762810\pi$
$983$	−24.5176	−	52.5781i	−0.781989	−	1.67698i	−0.0470067	−	0.998895i	$-0.514968\pi$
$984$	−0.107831	+	0.0392473i	−0.00343753	+	0.00125116i
$985$	16.2522	−	35.5832i	0.517839	−	1.13377i
$986$	−5.48002	−	31.0788i	−0.174520	−	0.989749i
$987$	−22.0567	+	22.0567i	−0.702072	+	0.702072i
$988$	−1.18131	+	18.0233i	−0.0375824	+	0.573399i
$989$		−	47.9094i		−	1.52343i
$990$	7.48587	+	10.5134i	0.237917	+	0.334139i
$991$	12.4874	+	14.8819i	0.396674	+	0.472738i	0.927003	−	0.375054i	$-0.122376\pi$
$991$	12.4874	+	14.8819i	0.396674	+	0.472738i	−0.530329	+	0.847792i	$0.677931\pi$
$992$	−2.90267	−	1.35354i	−0.0921599	−	0.0429749i
$993$	17.7619	−	8.28249i	0.563655	−	0.262837i
$994$	−12.3823	+	14.7567i	−0.392743	+	0.468053i
$995$	−45.5550	+	38.8417i	−1.44419	+	1.23136i
$996$	−9.19391	+	5.30811i	−0.291320	+	0.168194i
$997$	−18.2867	+	12.8045i	−0.579147	+	0.405523i	−0.826116	−	0.563500i	$-0.809454\pi$
$997$	−18.2867	+	12.8045i	−0.579147	+	0.405523i	0.246969	+	0.969023i	$0.420565\pi$
$998$	7.22595	−	5.05966i	0.228733	−	0.160161i
$999$	8.59881	−	4.96453i	0.272054	−	0.157071i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bh.a.67.7	✓	120
5.3	odd	4	inner	570.2.bh.a.523.9	yes	120
19.2	odd	18	inner	570.2.bh.a.97.9	yes	120
95.78	even	36	inner	570.2.bh.a.553.7	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.a.67.7	✓	120	1.1	even	1	trivial
570.2.bh.a.97.9	yes	120	19.2	odd	18	inner
570.2.bh.a.523.9	yes	120	5.3	odd	4	inner
570.2.bh.a.553.7	yes	120	95.78	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)

\(f(q)\)	\(=\)	\(q+(0.819152 + 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-1.42376 + 1.72421i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-2.79653 + 0.749327i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +O(q^{10})\)	\(q+(0.819152 + 0.573576i) q^{2} +(-0.996195 - 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-1.42376 + 1.72421i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(-2.79653 + 0.749327i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +(-2.15524 + 0.595756i) q^{10} +(-2.88592 - 4.99856i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(-0.361148 - 4.12794i) q^{13} +(-2.72058 - 0.990209i) q^{14} +(1.56862 - 1.59356i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(2.24133 - 3.20095i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-2.09658 + 3.82156i) q^{19} +(-2.10718 - 0.748182i) q^{20} +(2.85119 - 0.502742i) q^{21} +(0.503049 - 5.74988i) q^{22} +(-1.92105 + 4.11971i) q^{23} +(0.342020 - 0.939693i) q^{24} +(-0.945812 - 4.90973i) q^{25} +(2.07185 - 3.58856i) q^{26} +(-0.965926 - 0.258819i) q^{27} +(-1.66061 - 2.37159i) q^{28} +(1.40239 - 7.95333i) q^{29} +(2.19897 - 0.405647i) q^{30} +(2.77366 + 1.60137i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(2.43928 + 5.23106i) q^{33} +(3.67198 - 1.33649i) q^{34} +(2.68959 - 5.88867i) q^{35} +(0.173648 + 0.984808i) q^{36} +(-7.02090 + 7.02090i) q^{37} +(-3.90938 + 1.92789i) q^{38} +4.14371i q^{39} +(-1.29696 - 1.82151i) q^{40} +(-0.0737608 - 0.0879047i) q^{41} +(2.62392 + 1.22355i) q^{42} +(-9.55225 + 4.45429i) q^{43} +(3.71007 - 4.42149i) q^{44} +(-1.70154 + 1.45078i) q^{45} +(-3.93660 + 2.27280i) q^{46} +(-8.82560 + 6.17975i) q^{47} +(0.819152 - 0.573576i) q^{48} +(1.19689 - 0.691027i) q^{49} +(2.04134 - 4.56431i) q^{50} +(-2.51178 + 2.99343i) q^{51} +(3.75548 - 1.75121i) q^{52} +(-7.67276 - 3.57787i) q^{53} +(-0.642788 - 0.766044i) q^{54} +(12.7274 + 2.14082i) q^{55} -2.89518i q^{56} +(2.42167 - 3.62429i) q^{57} +(5.71061 - 5.71061i) q^{58} +(0.167014 + 0.947182i) q^{59} +(2.03396 + 0.928988i) q^{60} +(-4.16908 + 1.51742i) q^{61} +(1.35354 + 2.90267i) q^{62} +(-2.88416 + 0.252331i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(7.63163 + 5.25450i) q^{65} +(-1.00227 + 5.68415i) q^{66} +(7.76967 + 11.0962i) q^{67} +(3.77449 + 1.01137i) q^{68} +(2.27280 - 3.93660i) q^{69} +(5.58078 - 3.28103i) q^{70} +(2.27568 - 6.25238i) q^{71} +(-0.422618 + 0.906308i) q^{72} +(0.998934 - 11.4179i) q^{73} +(-9.77821 + 1.72416i) q^{74} +(0.514302 + 4.97348i) q^{75} +(-4.30817 - 0.663089i) q^{76} +(11.8161 + 11.8161i) q^{77} +(-2.37673 + 3.39433i) q^{78} +(1.62835 - 1.36634i) q^{79} +(-0.0176381 - 2.23600i) q^{80} +(0.939693 + 0.342020i) q^{81} +(-0.0100012 - 0.114315i) q^{82} +(-2.74768 - 10.2545i) q^{83} +(1.44759 + 2.50730i) q^{84} +(2.32800 + 8.42192i) q^{85} +(-10.3796 - 1.83021i) q^{86} +(-2.09023 + 7.80084i) q^{87} +(5.57517 - 1.49386i) q^{88} +(-1.22839 - 1.03074i) q^{89} +(-2.22595 + 0.212451i) q^{90} +(4.10314 + 11.2733i) q^{91} +(-4.52829 - 0.396174i) q^{92} +(-2.62353 - 1.83702i) q^{93} -10.7741 q^{94} +(-3.60416 - 9.05594i) q^{95} +1.00000 q^{96} +(7.59355 + 5.31706i) q^{97} +(1.37679 + 0.120454i) q^{98} +(-1.97409 - 5.42376i) 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	\( 120 q - 12 q^{5} + 12 q^{7} - 12 q^{10} + 48 q^{13} + 12 q^{17} + 36 q^{21} - 36 q^{22} - 96 q^{23} + 12 q^{25} + 12 q^{26} + 12 q^{30} + 24 q^{38} + 60 q^{41} + 96 q^{43} - 48 q^{47} - 24 q^{52} - 72 q^{53} + 108 q^{55} + 12 q^{57} + 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} + 24 q^{66} + 72 q^{67} + 12 q^{68} - 48 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} + 12 q^{80} - 72 q^{82} + 12 q^{83} - 108 q^{85} - 24 q^{86} + 12 q^{87} - 48 q^{91} - 84 q^{92} - 48 q^{93} - 204 q^{95} + 120 q^{96} + 24 q^{97} - 96 q^{98}+O(q^{100}) \) 120 * q - 12 * q^5 + 12 * q^7 - 12 * q^10 + 48 * q^13 + 12 * q^17 + 36 * q^21 - 36 * q^22 - 96 * q^23 + 12 * q^25 + 12 * q^26 + 12 * q^30 + 24 * q^38 + 60 * q^41 + 96 * q^43 - 48 * q^47 - 24 * q^52 - 72 * q^53 + 108 * 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 - 48 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 + 12 * q^80 - 72 * q^82 + 12 * q^83 - 108 * q^85 - 24 * q^86 + 12 * q^87 - 48 * q^91 - 84 * q^92 - 48 * q^93 - 204 * q^95 + 120 * q^96 + 24 * q^97 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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