LMFDB - Embedded newform 570.2.bb.b.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("570.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			71.1
Character	$\chi$	$=$	570.71
Dual form			570.2.bb.b.281.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(-1.66038 - 0.493094i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(-1.72889 + 0.104526i) q^{6} +(0.222334 + 0.385093i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.51372 + 1.63745i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(-1.66038 - 0.493094i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(-1.72889 + 0.104526i) q^{6} +(0.222334 + 0.385093i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.51372 + 1.63745i) q^{9} +(0.342020 - 0.939693i) q^{10} +(4.81206 + 2.77824i) q^{11} +(-1.58888 + 0.689539i) q^{12} +(0.572158 - 0.100887i) q^{13} +(0.340635 + 0.285827i) q^{14} +(-1.44500 + 0.954969i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-2.45646 - 6.74906i) q^{17} +(2.92216 + 0.678954i) q^{18} +(-0.681885 - 4.30523i) q^{19} -1.00000i q^{20} +(-0.179271 - 0.749032i) q^{21} +(5.47207 + 0.964873i) q^{22} +(0.902317 + 1.07534i) q^{23} +(-1.25722 + 1.19138i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(0.503147 - 0.290492i) q^{26} +(-3.36631 - 3.95828i) q^{27} +(0.417851 + 0.152085i) q^{28} +(-1.13984 - 0.414868i) q^{29} +(-1.03124 + 1.39160i) q^{30} +(7.02717 - 4.05714i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-6.61990 - 6.98573i) q^{33} +(-4.61663 - 5.50188i) q^{34} +(0.437912 + 0.0772157i) q^{35} +(2.97815 - 0.361430i) q^{36} -10.2910i q^{37} +(-2.11324 - 3.81238i) q^{38} +(-0.999746 - 0.114617i) q^{39} +(-0.342020 - 0.939693i) q^{40} +(-1.88811 + 10.7080i) q^{41} +(-0.424644 - 0.642546i) q^{42} +(7.72217 + 6.47967i) q^{43} +(5.47207 - 0.964873i) q^{44} +(2.87014 - 0.873089i) q^{45} +(1.21569 + 0.701878i) q^{46} +(-4.36116 + 11.9822i) q^{47} +(-0.773925 + 1.54953i) q^{48} +(3.40114 - 5.89094i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(0.750728 + 12.4173i) q^{51} +(0.373450 - 0.445060i) q^{52} +(2.07004 - 1.73697i) q^{53} +(-4.51711 - 2.56822i) q^{54} +(5.22139 - 1.90043i) q^{55} +0.444667 q^{56} +(-0.990697 + 7.48455i) q^{57} -1.21299 q^{58} +(-7.63063 + 2.77732i) q^{59} +(-0.493094 + 1.66038i) q^{60} +(-6.62392 + 5.55813i) q^{61} +(5.21576 - 6.21590i) q^{62} +(-0.0716854 + 1.33207i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.290492 - 0.503147i) q^{65} +(-8.60993 - 4.30030i) q^{66} +(0.152065 - 0.417795i) q^{67} +(-6.21996 - 3.59110i) q^{68} +(-0.967945 - 2.23040i) q^{69} +(0.437912 - 0.0772157i) q^{70} +(0.665505 + 0.558425i) q^{71} +(2.67493 - 1.35822i) q^{72} +(-1.06384 + 6.03333i) q^{73} +(-3.51971 - 9.67033i) q^{74} +(-0.197281 + 1.72078i) q^{75} +(-3.28970 - 2.85969i) q^{76} +2.47079i q^{77} +(-0.978656 + 0.234228i) q^{78} +(8.58092 + 1.51305i) q^{79} +(-0.642788 - 0.766044i) q^{80} +(3.63754 + 8.23215i) q^{81} +(1.88811 + 10.7080i) q^{82} +(5.55205 - 3.20548i) q^{83} +(-0.618798 - 0.458559i) q^{84} +(-6.74906 - 2.45646i) q^{85} +(9.47264 + 3.44776i) q^{86} +(1.68800 + 1.25089i) q^{87} +(4.81206 - 2.77824i) q^{88} +(-0.586446 - 3.32590i) q^{89} +(2.39844 - 1.80208i) q^{90} +(0.166061 + 0.197904i) q^{91} +(1.38243 + 0.243760i) q^{92} +(-13.6683 + 3.27133i) q^{93} +12.7512i q^{94} +(-3.73631 - 2.24500i) q^{95} +(-0.197281 + 1.72078i) q^{96} +(-4.67071 - 12.8327i) q^{97} +(1.18120 - 6.69893i) q^{98} +(7.54693 + 14.8632i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{6} + 42 q^{8}+O(q^{10}) $ 84 * q - 6 * q^6 + 42 * q^8	$ 84 q - 6 q^{6} + 42 q^{8} + 24 q^{13} - 24 q^{14} + 12 q^{17} - 12 q^{19} + 36 q^{22} + 24 q^{27} - 12 q^{28} - 12 q^{29} + 36 q^{33} + 12 q^{34} + 6 q^{36} + 18 q^{38} + 12 q^{39} + 6 q^{41} + 24 q^{43} + 36 q^{44} + 12 q^{47} - 12 q^{48} - 54 q^{49} - 42 q^{50} + 96 q^{51} + 12 q^{52} - 60 q^{53} - 18 q^{54} - 96 q^{57} - 24 q^{58} - 18 q^{59} - 48 q^{61} - 12 q^{62} - 114 q^{63} - 42 q^{64} - 24 q^{66} + 6 q^{67} - 54 q^{68} - 48 q^{69} + 48 q^{71} + 84 q^{73} + 24 q^{74} - 12 q^{79} - 36 q^{81} - 6 q^{82} + 36 q^{83} + 18 q^{84} + 12 q^{86} + 6 q^{87} - 12 q^{89} - 24 q^{90} + 24 q^{91} - 6 q^{93} - 12 q^{95} - 42 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) $ 84 * q - 6 * q^6 + 42 * q^8 + 24 * q^13 - 24 * q^14 + 12 * q^17 - 12 * q^19 + 36 * q^22 + 24 * q^27 - 12 * q^28 - 12 * q^29 + 36 * q^33 + 12 * q^34 + 6 * q^36 + 18 * q^38 + 12 * q^39 + 6 * q^41 + 24 * q^43 + 36 * q^44 + 12 * q^47 - 12 * q^48 - 54 * q^49 - 42 * q^50 + 96 * q^51 + 12 * q^52 - 60 * q^53 - 18 * q^54 - 96 * q^57 - 24 * q^58 - 18 * q^59 - 48 * q^61 - 12 * q^62 - 114 * q^63 - 42 * q^64 - 24 * q^66 + 6 * q^67 - 54 * q^68 - 48 * q^69 + 48 * q^71 + 84 * q^73 + 24 * q^74 - 12 * q^79 - 36 * q^81 - 6 * q^82 + 36 * q^83 + 18 * q^84 + 12 * q^86 + 6 * q^87 - 12 * q^89 - 24 * q^90 + 24 * q^91 - 6 * q^93 - 12 * q^95 - 42 * q^97 + 36 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$	$1$

Coefficient data

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

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

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

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	−1.66038	−	0.493094i	−0.958620	−	0.284688i
$3$	−1.66038	−	0.493094i	−0.958620	−	0.284688i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	0.642788	−	0.766044i	0.287463	−	0.342585i
$5$	0.642788	−	0.766044i	0.287463	−	0.342585i
$6$	−1.72889	+	0.104526i	−0.705818	+	0.0426727i
$7$	0.222334	+	0.385093i	0.0840342	+	0.145552i	0.904979	−	0.425456i	$-0.139886\pi$
$7$	0.222334	+	0.385093i	0.0840342	+	0.145552i	−0.820945	+	0.571007i	$0.806553\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	2.51372	+	1.63745i	0.837906	+	0.545815i
$10$	0.342020	−	0.939693i	0.108156	−	0.297157i
$11$	4.81206	+	2.77824i	1.45089	+	0.837671i	0.998532	−	0.0541652i	$-0.0172498\pi$
$11$	4.81206	+	2.77824i	1.45089	+	0.837671i	0.452358	+	0.891837i	$0.350583\pi$
$12$	−1.58888	+	0.689539i	−0.458670	+	0.199053i
$13$	0.572158	−	0.100887i	0.158688	−	0.0279810i	−0.0937396	−	0.995597i	$-0.529882\pi$
$13$	0.572158	−	0.100887i	0.158688	−	0.0279810i	0.252428	+	0.967616i	$0.418771\pi$
$14$	0.340635	+	0.285827i	0.0910385	+	0.0763904i
$15$	−1.44500	+	0.954969i	−0.373098	+	0.246572i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−2.45646	−	6.74906i	−0.595778	−	1.63689i	−0.759595	−	0.650396i	$-0.774603\pi$
$17$	−2.45646	−	6.74906i	−0.595778	−	1.63689i	0.163817	−	0.986491i	$-0.447619\pi$
$18$	2.92216	+	0.678954i	0.688760	+	0.160031i
$19$	−0.681885	−	4.30523i	−0.156435	−	0.987688i
$19$	−0.681885	−	4.30523i	−0.156435	−	0.987688i
$20$		−	1.00000i		−	0.223607i
$21$	−0.179271	−	0.749032i	−0.0391201	−	0.163452i
$22$	5.47207	+	0.964873i	1.16665	+	0.205712i
$23$	0.902317	+	1.07534i	0.188146	+	0.224224i	0.851869	−	0.523755i	$-0.175469\pi$
$23$	0.902317	+	1.07534i	0.188146	+	0.224224i	−0.663723	+	0.747978i	$0.731025\pi$
$24$	−1.25722	+	1.19138i	−0.256629	+	0.243190i
$25$	−0.173648	−	0.984808i	−0.0347296	−	0.196962i
$26$	0.503147	−	0.290492i	0.0986753	−	0.0569702i
$27$	−3.36631	−	3.95828i	−0.647846	−	0.761771i
$28$	0.417851	+	0.152085i	0.0789663	+	0.0287414i
$29$	−1.13984	−	0.414868i	−0.211663	−	0.0770390i	0.234013	−	0.972234i	$-0.424814\pi$
$29$	−1.13984	−	0.414868i	−0.211663	−	0.0770390i	−0.445676	+	0.895195i	$0.647036\pi$
$30$	−1.03124	+	1.39160i	−0.188278	+	0.254070i
$31$	7.02717	−	4.05714i	1.26212	−	0.728683i	0.288633	−	0.957440i	$-0.406799\pi$
$31$	7.02717	−	4.05714i	1.26212	−	0.728683i	0.973484	+	0.228756i	$0.0734659\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	−6.61990	−	6.98573i	−1.15238	−	1.21606i
$34$	−4.61663	−	5.50188i	−0.791745	−	0.943565i
$35$	0.437912	+	0.0772157i	0.0740206	+	0.0130518i
$36$	2.97815	−	0.361430i	0.496358	−	0.0602383i
$37$		−	10.2910i		−	1.69182i	−0.533324	−	0.845911i	$-0.679057\pi$
$37$		−	10.2910i		−	1.69182i	0.533324	−	0.845911i	$-0.320943\pi$
$38$	−2.11324	−	3.81238i	−0.342813	−	0.618449i
$39$	−0.999746	−	0.114617i	−0.160088	−	0.0183534i
$40$	−0.342020	−	0.939693i	−0.0540781	−	0.148578i
$41$	−1.88811	+	10.7080i	−0.294874	+	1.67231i	0.372841	+	0.927895i	$0.378384\pi$
$41$	−1.88811	+	10.7080i	−0.294874	+	1.67231i	−0.667715	+	0.744417i	$0.732727\pi$
$42$	−0.424644	−	0.642546i	−0.0655239	−	0.0991469i
$43$	7.72217	+	6.47967i	1.17762	+	0.988140i	0.999992	+	0.00404205i	$0.00128663\pi$
$43$	7.72217	+	6.47967i	1.17762	+	0.988140i	0.177627	+	0.984098i	$0.443158\pi$
$44$	5.47207	−	0.964873i	0.824945	−	0.145460i
$45$	2.87014	−	0.873089i	0.427856	−	0.130152i
$46$	1.21569	+	0.701878i	0.179243	+	0.103486i
$47$	−4.36116	+	11.9822i	−0.636141	+	1.74778i	0.0273786	+	0.999625i	$0.491284\pi$
$47$	−4.36116	+	11.9822i	−0.636141	+	1.74778i	−0.663520	+	0.748159i	$0.730938\pi$
$48$	−0.773925	+	1.54953i	−0.111706	+	0.223655i
$49$	3.40114	−	5.89094i	0.485876	−	0.841563i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	0.750728	+	12.4173i	0.105123	+	1.73876i
$52$	0.373450	−	0.445060i	0.0517882	−	0.0617187i
$53$	2.07004	−	1.73697i	0.284342	−	0.238591i	−0.489450	−	0.872032i	$-0.662802\pi$
$53$	2.07004	−	1.73697i	0.284342	−	0.238591i	0.773791	+	0.633440i	$0.218358\pi$
$54$	−4.51711	−	2.56822i	−0.614700	−	0.349491i
$55$	5.22139	−	1.90043i	0.704052	−	0.256254i
$56$	0.444667			0.0594212
$57$	−0.990697	+	7.48455i	−0.131221	+	0.991353i
$58$	−1.21299			−0.159274
$59$	−7.63063	+	2.77732i	−0.993423	+	0.361576i	−0.787045	−	0.616896i	$-0.788390\pi$
$59$	−7.63063	+	2.77732i	−0.993423	+	0.361576i	−0.206378	+	0.978472i	$0.566168\pi$
$60$	−0.493094	+	1.66038i	−0.0636582	+	0.214354i
$61$	−6.62392	+	5.55813i	−0.848106	+	0.711645i	−0.959372	−	0.282145i	$-0.908954\pi$
$61$	−6.62392	+	5.55813i	−0.848106	+	0.711645i	0.111266	+	0.993791i	$0.464510\pi$
$62$	5.21576	−	6.21590i	0.662402	−	0.789420i
$63$	−0.0716854	+	1.33207i	−0.00903151	+	0.167826i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.290492	−	0.503147i	0.0360311	−	0.0624078i
$66$	−8.60993	−	4.30030i	−1.05981	−	0.529330i
$67$	0.152065	−	0.417795i	0.0185777	−	0.0510418i	−0.930057	−	0.367415i	$-0.880243\pi$
$67$	0.152065	−	0.417795i	0.0185777	−	0.0510418i	0.948635	+	0.316373i	$0.102465\pi$
$68$	−6.21996	−	3.59110i	−0.754282	−	0.435485i
$69$	−0.967945	−	2.23040i	−0.116527	−	0.268508i
$70$	0.437912	−	0.0772157i	0.0523405	−	0.00922904i
$71$	0.665505	+	0.558425i	0.0789809	+	0.0662729i	0.681423	−	0.731889i	$-0.261361\pi$
$71$	0.665505	+	0.558425i	0.0789809	+	0.0662729i	−0.602442	+	0.798162i	$0.705806\pi$
$72$	2.67493	−	1.35822i	0.315243	−	0.160068i
$73$	−1.06384	+	6.03333i	−0.124513	+	0.706148i	0.857083	+	0.515178i	$0.172274\pi$
$73$	−1.06384	+	6.03333i	−0.124513	+	0.706148i	−0.981596	+	0.190969i	$0.938837\pi$
$74$	−3.51971	−	9.67033i	−0.409158	−	1.12415i
$75$	−0.197281	+	1.72078i	−0.0227800	+	0.198698i
$76$	−3.28970	−	2.85969i	−0.377355	−	0.328029i
$77$			2.47079i			0.281572i
$78$	−0.978656	+	0.234228i	−0.110811	+	0.0265211i
$79$	8.58092	+	1.51305i	0.965429	+	0.170231i	0.634072	−	0.773274i	$-0.281382\pi$
$79$	8.58092	+	1.51305i	0.965429	+	0.170231i	0.331357	+	0.943505i	$0.392494\pi$
$80$	−0.642788	−	0.766044i	−0.0718658	−	0.0856464i
$81$	3.63754	+	8.23215i	0.404171	+	0.914683i
$82$	1.88811	+	10.7080i	0.208507	+	1.18250i
$83$	5.55205	−	3.20548i	0.609416	−	0.351847i	−0.163321	−	0.986573i	$-0.552221\pi$
$83$	5.55205	−	3.20548i	0.609416	−	0.351847i	0.772737	+	0.634726i	$0.218887\pi$
$84$	−0.618798	−	0.458559i	−0.0675164	−	0.0500328i
$85$	−6.74906	−	2.45646i	−0.732038	−	0.266440i
$86$	9.47264	+	3.44776i	1.02146	+	0.371781i
$87$	1.68800	+	1.25089i	0.180972	+	0.134109i
$88$	4.81206	−	2.77824i	0.512967	−	0.296162i
$89$	−0.586446	−	3.32590i	−0.0621631	−	0.352545i	−0.999985	−	0.00542844i	$-0.998272\pi$
$89$	−0.586446	−	3.32590i	−0.0621631	−	0.352545i	0.937822	−	0.347116i	$-0.112839\pi$
$90$	2.39844	−	1.80208i	0.252818	−	0.189956i
$91$	0.166061	+	0.197904i	0.0174079	+	0.0207459i
$92$	1.38243	+	0.243760i	0.144128	+	0.0254137i
$93$	−13.6683	+	3.27133i	−1.41734	+	0.339221i
$94$			12.7512i			1.31519i
$95$	−3.73631	−	2.24500i	−0.383337	−	0.230332i
$96$	−0.197281	+	1.72078i	−0.0201349	+	0.175626i
$97$	−4.67071	−	12.8327i	−0.474239	−	1.30296i	−0.914316	−	0.405001i	$-0.867271\pi$
$97$	−4.67071	−	12.8327i	−0.474239	−	1.30296i	0.440078	−	0.897960i	$-0.354951\pi$
$98$	1.18120	−	6.69893i	0.119319	−	0.676694i
$99$	7.54693	+	14.8632i	0.758495	+	1.49381i
$100$	−0.766044	−	0.642788i	−0.0766044	−	0.0642788i
$101$	−4.42869	+	0.780897i	−0.440671	+	0.0777022i	−0.389582	−	0.920992i	$-0.627380\pi$
$101$	−4.42869	+	0.780897i	−0.440671	+	0.0777022i	−0.0510893	+	0.998694i	$0.516269\pi$
$102$	4.95241	+	11.4116i	0.490361	+	1.12992i
$103$	−9.26885	−	5.35138i	−0.913287	−	0.527287i	−0.0318000	−	0.999494i	$-0.510124\pi$
$103$	−9.26885	−	5.35138i	−0.913287	−	0.527287i	−0.881487	+	0.472208i	$0.843457\pi$
$104$	0.198708	−	0.545947i	0.0194850	−	0.0535345i
$105$	−0.689025	−	0.344139i	−0.0672420	−	0.0335845i
$106$	1.35112	−	2.34021i	0.131233	−	0.227302i
$107$	8.40290	+	14.5543i	0.812339	+	1.40701i	0.911223	+	0.411914i	$0.135140\pi$
$107$	8.40290	+	14.5543i	0.812339	+	1.40701i	−0.0988836	+	0.995099i	$0.531527\pi$
$108$	−5.12307	−	0.868397i	−0.492968	−	0.0835615i
$109$	−3.90885	+	4.65839i	−0.374400	+	0.446192i	−0.920038	−	0.391828i	$-0.871843\pi$
$109$	−3.90885	+	4.65839i	−0.374400	+	0.446192i	0.545638	+	0.838021i	$0.316287\pi$
$110$	4.25651	−	3.57164i	0.405843	−	0.340542i
$111$	−5.07441	+	17.0869i	−0.481641	+	1.62182i
$112$	0.417851	−	0.152085i	0.0394832	−	0.0143707i
$113$	−14.8266			−1.39477			−0.697386	−	0.716696i	$-0.745653\pi$
$113$	−14.8266			−1.39477			−0.697386	+	0.716696i	$0.745653\pi$
$114$	1.62892	+	7.37202i	0.152562	+	0.690453i
$115$	1.40376			0.130901
$116$	−1.13984	+	0.414868i	−0.105831	+	0.0385195i
$117$	1.60344	+	0.683277i	0.148238	+	0.0631690i
$118$	−6.22054	+	5.21966i	−0.572648	+	0.480508i
$119$	2.05286	−	2.44651i	0.188186	−	0.224271i
$120$	0.104526	+	1.72889i	0.00954190	+	0.157826i
$121$	9.93726	+	17.2118i	0.903387	+	1.56471i
$122$	−4.32346	+	7.48845i	−0.391427	+	0.677972i
$123$	8.41505	−	16.8484i	0.758759	−	1.51917i
$124$	2.77525	−	7.62492i	0.249224	−	0.684738i
$125$	−0.866025	−	0.500000i	−0.0774597	−	0.0447214i
$126$	0.388234	+	1.27626i	0.0345866	+	0.113698i
$127$	−19.1253	+	3.37231i	−1.69710	+	0.299244i	−0.936679	−	0.350190i	$-0.886117\pi$
$127$	−19.1253	+	3.37231i	−1.69710	+	0.299244i	−0.760418	+	0.649434i	$0.775006\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	−9.62664	−	14.5665i	−0.847578	−	1.28250i
$130$	0.100887	−	0.572158i	0.00884837	−	0.0501816i
$131$	4.01584	+	11.0334i	0.350866	+	0.963996i	0.982093	+	0.188398i	$0.0603294\pi$
$131$	4.01584	+	11.0334i	0.350866	+	0.963996i	−0.631227	+	0.775598i	$0.717448\pi$
$132$	−9.56148	−	1.09619i	−0.832220	−	0.0954110i
$133$	1.50631	−	1.21979i	0.130614	−	0.105769i
$134$		−	0.444608i		−	0.0384083i
$135$	−5.19604	+	0.0344086i	−0.447204	+	0.00296142i
$136$	−7.07308	−	1.24718i	−0.606512	−	0.106944i
$137$	0.211419	+	0.251959i	0.0180627	+	0.0215263i	0.775000	−	0.631961i	$-0.217750\pi$
$137$	0.211419	+	0.251959i	0.0180627	+	0.0215263i	−0.756937	+	0.653487i	$0.773305\pi$
$138$	−1.67241	−	1.76483i	−0.142365	−	0.150232i
$139$	1.57383	+	8.92561i	0.133490	+	0.757060i	0.975899	+	0.218222i	$0.0700256\pi$
$139$	1.57383	+	8.92561i	0.133490	+	0.757060i	−0.842409	+	0.538838i	$0.818863\pi$
$140$	0.385093	−	0.222334i	0.0325463	−	0.0187906i
$141$	13.1495	−	17.7445i	1.10739	−	1.49436i
$142$	0.816363	+	0.297132i	0.0685076	+	0.0249347i
$143$	3.03355	+	1.10412i	0.253678	+	0.0923312i
$144$	2.04907	−	2.19119i	0.170756	−	0.182599i
$145$	−1.05048	+	0.606496i	−0.0872377	+	0.0503667i
$146$	1.06384	+	6.03333i	0.0880439	+	0.499322i
$147$	−8.55196	+	8.10411i	−0.705354	+	0.668416i
$148$	−6.61490	−	7.88333i	−0.543741	−	0.648006i
$149$	10.9677	+	1.93390i	0.898509	+	0.158431i	0.603781	−	0.797150i	$-0.293660\pi$
$149$	10.9677	+	1.93390i	0.898509	+	0.158431i	0.294727	+	0.955581i	$0.404771\pi$
$150$	0.403158	+	1.68448i	0.0329177	+	0.137537i
$151$			12.5080i			1.01788i	0.860801	+	0.508941i	$0.169963\pi$
$151$			12.5080i			1.01788i	−0.860801	+	0.508941i	$0.830037\pi$
$152$	−4.06938	−	1.56209i	−0.330071	−	0.126702i
$153$	4.87638	−	20.9875i	0.394232	−	1.69674i
$154$	0.845059	+	2.32178i	0.0680968	+	0.187094i
$155$	1.40903	−	7.99100i	0.113176	−	0.641853i
$156$	−0.839525	+	0.554823i	−0.0672158	+	0.0444214i
$157$	13.9233	+	11.6830i	1.11120	+	0.932406i	0.998127	−	0.0611803i	$-0.0194865\pi$
$157$	13.9233	+	11.6830i	1.11120	+	0.932406i	0.113072	+	0.993587i	$0.463931\pi$
$158$	8.58092	−	1.51305i	0.682661	−	0.120372i
$159$	−4.29354	+	1.86330i	−0.340500	+	0.147770i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	−0.213490	+	0.586560i	−0.0168254	+	0.0462274i
$162$	6.23373	+	6.49158i	0.489768	+	0.510026i
$163$	1.53525	−	2.65913i	0.120250	−	0.208279i	−0.799616	−	0.600511i	$-0.794964\pi$
$163$	1.53525	−	2.65913i	0.120250	−	0.208279i	0.919866	+	0.392232i	$0.128297\pi$
$164$	5.43661	+	9.41648i	0.424528	+	0.735304i
$165$	−9.60657	+	0.580799i	−0.747871	+	0.0452151i
$166$	4.12088	−	4.91107i	0.319842	−	0.381173i
$167$	−2.39302	+	2.00799i	−0.185178	+	0.155383i	−0.730664	−	0.682737i	$-0.760789\pi$
$167$	−2.39302	+	2.00799i	−0.185178	+	0.155383i	0.545486	+	0.838120i	$0.316345\pi$
$168$	−0.738316	−	0.219263i	−0.0569623	−	0.0169165i
$169$	−11.8988	+	4.33082i	−0.915294	+	0.333140i
$170$	−7.18220			−0.550849
$171$	5.33552	−	11.9387i	0.408017	−	0.912974i
$172$	10.0806			0.768636
$173$	−3.80358	+	1.38439i	−0.289181	+	0.105253i	−0.482537	−	0.875875i	$-0.660285\pi$
$173$	−3.80358	+	1.38439i	−0.289181	+	0.105253i	0.193357	+	0.981129i	$0.438063\pi$
$174$	2.01403	+	0.598119i	0.152683	+	0.0453433i
$175$	0.340635	−	0.285827i	0.0257496	−	0.0216065i
$176$	3.57164	−	4.25651i	0.269222	−	0.320847i
$177$	14.0392	−	0.848789i	1.05525	−	0.0637989i
$178$	−1.68860	−	2.92475i	−0.126566	−	0.219219i
$179$	−2.74135	+	4.74815i	−0.204898	+	0.354894i	−0.950100	−	0.311945i	$-0.899020\pi$
$179$	−2.74135	+	4.74815i	−0.204898	+	0.354894i	0.745202	+	0.666839i	$0.232353\pi$
$180$	1.63745	−	2.51372i	0.122048	−	0.187361i
$181$	5.53236	−	15.2000i	0.411217	−	1.12981i	−0.545327	−	0.838223i	$-0.683595\pi$
$181$	5.53236	−	15.2000i	0.411217	−	1.12981i	0.956544	−	0.291587i	$-0.0941831\pi$
$182$	0.223733	+	0.129172i	0.0165842	+	0.00957490i
$183$	13.7389	−	5.96239i	1.01561	−	0.440752i
$184$	1.38243	−	0.243760i	0.101914	−	0.0179702i
$185$	−7.88333	−	6.61490i	−0.579594	−	0.486337i
$186$	−11.7252	+	7.74888i	−0.859730	+	0.568176i
$187$	6.92991	−	39.3015i	0.506765	−	2.87401i
$188$	4.36116	+	11.9822i	0.318071	+	0.873892i
$189$	0.775863	−	2.17640i	0.0564357	−	0.158310i
$190$	−4.27881	−	0.831714i	−0.310418	−	0.0603389i
$191$		−	10.2693i		−	0.743060i	−0.928421	−	0.371530i	$-0.878833\pi$
$191$		−	10.2693i		−	0.743060i	0.928421	−	0.371530i	$-0.121167\pi$
$192$	0.403158	+	1.68448i	0.0290954	+	0.121567i
$193$	1.70443	+	0.300537i	0.122688	+	0.0216332i	0.234655	−	0.972079i	$-0.424604\pi$
$193$	1.70443	+	0.300537i	0.122688	+	0.0216332i	−0.111967	+	0.993712i	$0.535715\pi$
$194$	−8.77806	−	10.4613i	−0.630228	−	0.751077i
$195$	−0.730426	+	0.692175i	−0.0523069	+	0.0495677i
$196$	−1.18120	−	6.69893i	−0.0843716	−	0.478495i
$197$	−10.8069	+	6.23935i	−0.769958	+	0.444536i	−0.832860	−	0.553484i	$-0.813298\pi$
$197$	−10.8069	+	6.23935i	−0.769958	+	0.444536i	0.0629015	+	0.998020i	$0.479965\pi$
$198$	12.1753	+	11.3856i	0.865261	+	0.809142i
$199$	−1.77434	−	0.645806i	−0.125779	−	0.0457800i	0.278364	−	0.960476i	$-0.410208\pi$
$199$	−1.77434	−	0.645806i	−0.125779	−	0.0457800i	−0.404143	+	0.914696i	$0.632430\pi$
$200$	−0.939693	−	0.342020i	−0.0664463	−	0.0241845i
$201$	−0.458498	+	0.618716i	−0.0323399	+	0.0436409i
$202$	−3.89452	+	2.24850i	−0.274018	+	0.158204i
$203$	−0.0936620	−	0.531183i	−0.00657378	−	0.0372818i
$204$	8.55675	+	9.02961i	0.599092	+	0.632199i
$205$	6.98917	+	8.32937i	0.488145	+	0.581748i
$206$	−10.5402	−	1.85851i	−0.734367	−	0.129489i
$207$	0.507359	+	4.18059i	0.0352639	+	0.290571i
$208$		−	0.580985i		−	0.0402840i
$209$	8.67971	−	22.6115i	0.600388	−	1.56407i
$210$	−0.765174	−	0.0877244i	−0.0528020	−	0.00605356i
$211$	−4.70698	−	12.9323i	−0.324042	−	0.890298i	−0.989586	−	0.143940i	$-0.954023\pi$
$211$	−4.70698	−	12.9323i	−0.324042	−	0.890298i	0.665545	−	0.746358i	$-0.268199\pi$
$212$	0.469240	−	2.66119i	0.0322275	−	0.182771i
$213$	−0.829634	−	1.25535i	−0.0568456	−	0.0860154i
$214$	12.8740	+	10.8026i	0.880048	+	0.738448i
$215$	9.92742	−	1.75047i	0.677045	−	0.119381i
$216$	−5.11112	+	0.936168i	−0.347768	+	0.0636982i
$217$	3.12475	+	1.80408i	0.212122	+	0.122469i
$218$	−2.07986	+	5.71436i	−0.140866	+	0.387025i
$219$	4.74137	−	9.49304i	0.320392	−	0.641480i
$220$	2.77824	−	4.81206i	0.187309	−	0.324429i
$221$	−2.08637	−	3.61370i	−0.140345	−	0.243084i
$222$	1.07568	+	17.7920i	0.0721946	+	1.19412i
$223$	−12.2735	+	14.6270i	−0.821893	+	0.979494i	−0.999990	−	0.00451918i	$-0.998561\pi$
$223$	−12.2735	+	14.6270i	−0.821893	+	0.979494i	0.178097	+	0.984013i	$0.443006\pi$
$224$	0.340635	−	0.285827i	0.0227596	−	0.0190976i
$225$	1.17607	−	2.75987i	0.0784045	−	0.183991i
$226$	−13.9325	+	5.07100i	−0.926774	+	0.337318i
$227$	4.10376			0.272376			0.136188	−	0.990683i	$-0.456515\pi$
$227$	4.10376			0.272376			0.136188	+	0.990683i	$0.456515\pi$
$228$	4.05206	+	6.37031i	0.268354	+	0.421884i
$229$	10.5425			0.696666			0.348333	−	0.937371i	$-0.386748\pi$
$229$	10.5425			0.696666			0.348333	+	0.937371i	$0.386748\pi$
$230$	1.31910	−	0.480113i	0.0869788	−	0.0316577i
$231$	1.21833	−	4.10244i	0.0801602	−	0.269921i
$232$	−0.929205	+	0.779696i	−0.0610053	+	0.0511895i
$233$	−0.604787	+	0.720757i	−0.0396209	+	0.0472183i	−0.785491	−	0.618873i	$-0.787590\pi$
$233$	−0.604787	+	0.720757i	−0.0396209	+	0.0472183i	0.745870	+	0.666091i	$0.232034\pi$
$234$	1.74044	+	0.0936613i	0.113776	+	0.00612283i
$235$	6.37560	+	11.0429i	0.415898	+	0.720357i
$236$	−4.06017	+	7.03242i	−0.264295	+	0.457772i
$237$	−13.5015	−	6.74343i	−0.877017	−	0.438033i
$238$	1.09231	−	3.00109i	0.0708037	−	0.194531i
$239$	−10.6163	−	6.12934i	−0.686713	−	0.396474i	0.115666	−	0.993288i	$-0.463100\pi$
$239$	−10.6163	−	6.12934i	−0.686713	−	0.396474i	−0.802380	+	0.596814i	$0.796433\pi$
$240$	0.689539	+	1.58888i	0.0445096	+	0.102562i
$241$	10.8691	−	1.91651i	0.700137	−	0.123453i	0.187762	−	0.982215i	$-0.439877\pi$
$241$	10.8691	−	1.91651i	0.700137	−	0.123453i	0.512375	+	0.858762i	$0.328766\pi$
$242$	15.2248	+	12.7751i	0.978685	+	0.821214i
$243$	−1.98048	−	15.4621i	−0.127048	−	0.991897i
$244$	−1.50152	+	8.51555i	−0.0961250	+	0.545152i
$245$	−2.32651	−	6.39204i	−0.148636	−	0.408373i
$246$	2.14508	−	18.7104i	0.136765	−	1.19293i
$247$	−0.824488	−	2.39448i	−0.0524609	−	0.152357i
$248$		−	8.11428i		−	0.515257i
$249$	−10.7991	+	2.58462i	−0.684365	+	0.163794i
$250$	−0.984808	−	0.173648i	−0.0622847	−	0.0109825i
$251$	6.67507	+	7.95504i	0.421327	+	0.502118i	0.934399	−	0.356227i	$-0.115937\pi$
$251$	6.67507	+	7.95504i	0.421327	+	0.502118i	−0.513072	+	0.858345i	$0.671493\pi$
$252$	0.801327	+	1.06651i	0.0504788	+	0.0671836i
$253$	1.35445	+	7.68145i	0.0851533	+	0.482929i
$254$	−16.8185	+	9.71017i	−1.05529	+	0.609270i
$255$	9.99473	+	7.40657i	0.625894	+	0.463817i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−5.34640	−	1.94593i	−0.333499	−	0.121384i	0.169843	−	0.985471i	$-0.445674\pi$
$257$	−5.34640	−	1.94593i	−0.333499	−	0.121384i	−0.503342	+	0.864087i	$0.667896\pi$
$258$	−14.0281	−	10.3955i	−0.873351	−	0.647195i
$259$	3.96298	−	2.28803i	0.246247	−	0.142171i
$260$	−0.100887	−	0.572158i	−0.00625674	−	0.0354837i
$261$	−2.18591	−	2.90928i	−0.135304	−	0.180080i
$262$	7.54731	+	8.99454i	0.466275	+	0.555685i
$263$	−13.6233	−	2.40216i	−0.840049	−	0.148123i	−0.262962	−	0.964806i	$-0.584700\pi$
$263$	−13.6233	−	2.40216i	−0.840049	−	0.148123i	−0.577087	+	0.816683i	$0.695811\pi$
$264$	−9.35977	+	2.24014i	−0.576054	+	0.137871i
$265$		−	2.70224i		−	0.165998i
$266$	0.998277	−	1.66141i	0.0612083	−	0.101868i
$267$	−0.666259	+	5.81143i	−0.0407744	+	0.355653i
$268$	−0.152065	−	0.417795i	−0.00928885	−	0.0255209i
$269$	−0.523143	+	2.96689i	−0.0318966	+	0.180895i	−0.996594	−	0.0824670i	$-0.973720\pi$
$269$	−0.523143	+	2.96689i	−0.0318966	+	0.180895i	0.964697	+	0.263362i	$0.0848312\pi$
$270$	−4.87091	+	1.80948i	−0.296434	+	0.110122i
$271$	−13.9461	−	11.7022i	−0.847166	−	0.710857i	0.111998	−	0.993708i	$-0.464275\pi$
$271$	−13.9461	−	11.7022i	−0.847166	−	0.710857i	−0.959164	+	0.282852i	$0.908720\pi$
$272$	−7.07308	+	1.24718i	−0.428869	+	0.0756211i
$273$	−0.178139	−	0.410479i	−0.0107815	−	0.0248433i
$274$	0.284843	+	0.164454i	0.0172080	+	0.00993506i
$275$	1.90043	−	5.22139i	0.114600	−	0.314861i
$276$	−2.17516	−	1.08640i	−0.130929	−	0.0653937i
$277$	4.07017	−	7.04975i	0.244553	−	0.423578i	−0.717453	−	0.696607i	$-0.754692\pi$
$277$	4.07017	−	7.04975i	0.244553	−	0.423578i	0.962006	+	0.273029i	$0.0880254\pi$
$278$	4.53165	+	7.84905i	0.271790	+	0.470754i
$279$	24.3077	+	1.30811i	1.45526	+	0.0783147i
$280$	0.285827	−	0.340635i	0.0170814	−	0.0203568i
$281$	−12.2941	+	10.3160i	−0.733403	+	0.615398i	−0.931057	−	0.364874i	$-0.881112\pi$
$281$	−12.2941	+	10.3160i	−0.733403	+	0.615398i	0.197654	+	0.980272i	$0.436668\pi$
$282$	6.28754	−	21.1718i	0.374417	−	1.26076i
$283$	14.7603	−	5.37232i	0.877410	−	0.319351i	0.136246	−	0.990675i	$-0.456496\pi$
$283$	14.7603	−	5.37232i	0.877410	−	0.319351i	0.741164	+	0.671324i	$0.234274\pi$
$284$	0.868755			0.0515511
$285$	5.09669	+	5.56990i	0.301902	+	0.329932i
$286$	3.22823			0.190889
$287$	−4.54338	+	1.65365i	−0.268187	+	0.0976122i
$288$	1.17607	−	2.75987i	0.0693004	−	0.162627i
$289$	−26.4928	+	22.2301i	−1.55840	+	1.30765i
$290$	−0.779696	+	0.929205i	−0.0457853	+	0.0545648i
$291$	1.42744	+	23.6102i	0.0836778	+	1.38405i
$292$	3.06320	+	5.30562i	0.179260	+	0.310488i
$293$	9.08186	−	15.7302i	0.530568	−	0.918971i	−0.468796	−	0.883306i	$-0.655312\pi$
$293$	9.08186	−	15.7302i	0.530568	−	0.918971i	0.999364	−	0.0356640i	$-0.0113546\pi$
$294$	−5.26444	+	10.5403i	−0.307029	+	0.614724i
$295$	−2.77732	+	7.63063i	−0.161702	+	0.444272i
$296$	−8.91223	−	5.14548i	−0.518013	−	0.299075i
$297$	−5.20180	−	28.3999i	−0.301839	−	1.64793i
$298$	10.9677	−	1.93390i	0.635341	−	0.112028i
$299$	0.624756	+	0.524232i	0.0361306	+	0.0303171i
$300$	0.954969	+	1.44500i	0.0551352	+	0.0834273i
$301$	−0.778378	+	4.41440i	−0.0448650	+	0.254442i
$302$	4.27797	+	11.7536i	0.246170	+	0.676346i
$303$	7.73836	+	0.887174i	0.444557	+	0.0509668i
$304$	−4.35824	−	0.0760704i	−0.249962	−	0.00436294i
$305$			8.64691i			0.495121i
$306$	−2.59586	−	21.3896i	−0.148395	−	1.22276i
$307$	−8.97655	−	1.58281i	−0.512319	−	0.0903356i	−0.0884883	−	0.996077i	$-0.528204\pi$
$307$	−8.97655	−	1.58281i	−0.512319	−	0.0903356i	−0.423830	+	0.905742i	$0.639315\pi$
$308$	1.58819	+	1.89273i	0.0904956	+	0.107848i
$309$	12.7511	+	13.4557i	0.725384	+	0.765470i
$310$	−1.40903	−	7.99100i	−0.0800275	−	0.453858i
$311$	−13.7320	+	7.92819i	−0.778672	+	0.449567i	−0.835959	−	0.548791i	$-0.815088\pi$
$311$	−13.7320	+	7.92819i	−0.778672	+	0.449567i	0.0572874	+	0.998358i	$0.481755\pi$
$312$	−0.599135	+	0.808497i	−0.0339193	+	0.0457721i
$313$	−21.8931	−	7.96845i	−1.23747	−	0.450404i	−0.361323	−	0.932441i	$-0.617675\pi$
$313$	−21.8931	−	7.96845i	−1.23747	−	0.450404i	−0.876151	+	0.482037i	$0.839897\pi$
$314$	17.0794	+	6.21640i	0.963848	+	0.350812i
$315$	0.974350	+	0.911155i	0.0548984	+	0.0513378i
$316$	7.54593	−	4.35665i	0.424492	−	0.245080i
$317$	4.11350	+	23.3288i	0.231037	+	1.31028i	0.850801	+	0.525489i	$0.176118\pi$
$317$	4.11350	+	23.3288i	0.231037	+	1.31028i	−0.619763	+	0.784789i	$0.712771\pi$
$318$	−3.39732	+	3.21941i	−0.190512	+	0.180535i
$319$	−4.33237	−	5.16312i	−0.242566	−	0.289079i
$320$	−0.984808	−	0.173648i	−0.0550524	−	0.00970723i
$321$	−6.77539	−	28.3090i	−0.378165	−	1.58005i
$322$			0.624204i			0.0347856i
$323$	−27.3812	+	15.1777i	−1.52353	+	0.844510i
$324$	8.07804	+	3.96802i	0.448780	+	0.220446i
$325$	−0.198708	−	0.545947i	−0.0110224	−	0.0302837i
$326$	0.533186	−	3.02385i	0.0295305	−	0.167476i
$327$	8.78719	−	5.80726i	0.485933	−	0.321142i
$328$	8.32937	+	6.98917i	0.459912	+	0.385912i
$329$	−5.58390	+	0.984592i	−0.307850	+	0.0542823i
$330$	−8.82858	+	3.83141i	−0.485997	+	0.210912i
$331$	6.47697	+	3.73948i	0.356007	+	0.205541i	0.667328	−	0.744764i	$-0.267438\pi$
$331$	6.47697	+	3.73948i	0.356007	+	0.205541i	−0.311321	+	0.950305i	$0.600771\pi$
$332$	2.19267	−	6.02432i	0.120339	−	0.330628i
$333$	16.8509	−	25.8685i	0.923423	−	1.41759i
$334$	−1.56194	+	2.70535i	−0.0854653	+	0.148030i
$335$	−0.222304	−	0.385042i	−0.0121458	−	0.0210371i
$336$	−0.768783	+	0.0464794i	−0.0419405	+	0.00253566i
$337$	2.42483	−	2.88980i	0.132089	−	0.157418i	−0.695946	−	0.718095i	$-0.745015\pi$
$337$	2.42483	−	2.88980i	0.132089	−	0.157418i	0.828035	+	0.560677i	$0.189459\pi$
$338$	−9.70000	+	8.13927i	−0.527611	+	0.442718i
$339$	24.6178	+	7.31092i	1.33706	+	0.397074i
$340$	−6.74906	+	2.45646i	−0.366019	+	0.133220i
$341$	45.0868			2.44159
$342$	0.930478	−	13.0436i	0.0503145	−	0.705314i
$343$	6.13742			0.331389
$344$	9.47264	−	3.44776i	0.510730	−	0.185891i
$345$	−2.33077	−	0.692184i	−0.125484	−	0.0372659i
$346$	−3.10070	+	2.60180i	−0.166695	+	0.139874i
$347$	11.5692	−	13.7877i	0.621070	−	0.740162i	−0.360184	−	0.932881i	$-0.617286\pi$
$347$	11.5692	−	13.7877i	0.621070	−	0.740162i	0.981254	+	0.192719i	$0.0617306\pi$
$348$	2.09713	−	0.126790i	0.112418	−	0.00679663i
$349$	−14.5795	−	25.2525i	−0.780425	−	1.35174i	−0.931694	−	0.363243i	$-0.881670\pi$
$349$	−14.5795	−	25.2525i	−0.780425	−	1.35174i	0.151270	−	0.988493i	$-0.451664\pi$
$350$	0.222334	−	0.385093i	0.0118842	−	0.0205841i
$351$	−2.32540	−	1.92515i	−0.124121	−	0.102757i
$352$	1.90043	−	5.22139i	0.101293	−	0.278301i
$353$	26.1191	+	15.0799i	1.39018	+	0.802620i	0.993335	−	0.115266i	$-0.0367719\pi$
$353$	26.1191	+	15.0799i	1.39018	+	0.802620i	0.396844	+	0.917886i	$0.370105\pi$
$354$	12.9022	−	5.59929i	0.685746	−	0.297599i
$355$	0.855557	−	0.150858i	0.0454082	−	0.00800670i
$356$	−2.58709	−	2.17083i	−0.137116	−	0.115054i
$357$	−4.61489	+	3.04987i	−0.244246	+	0.161416i
$358$	−0.952060	+	5.39940i	−0.0503179	+	0.285367i
$359$	−8.36291	−	22.9769i	−0.441378	−	1.21267i	−0.938587	−	0.345044i	$-0.887864\pi$
$359$	−8.36291	−	22.9769i	−0.441378	−	1.21267i	0.497209	−	0.867631i	$-0.334358\pi$
$360$	0.678954	−	2.92216i	0.0357840	−	0.154011i
$361$	−18.0701	+	5.87135i	−0.951056	+	0.309018i
$362$		−	16.1755i		−	0.850167i
$363$	−8.01256	−	33.4782i	−0.420550	−	1.75715i
$364$	0.254420	+	0.0448611i	0.0133352	+	0.00235136i
$365$	3.93797	+	4.69310i	0.206123	+	0.245648i
$366$	10.8711	−	10.3018i	0.568241	−	0.538483i
$367$	0.963383	+	5.46362i	0.0502882	+	0.285198i	0.999573	−	0.0292189i	$-0.00930199\pi$
$367$	0.963383	+	5.46362i	0.0502882	+	0.285198i	−0.949285	+	0.314417i	$0.898191\pi$
$368$	1.21569	−	0.701878i	0.0633721	−	0.0365879i
$369$	−22.2800	+	23.8253i	−1.15985	+	1.24029i
$370$	−9.67033	−	3.51971i	−0.502737	−	0.182981i
$371$	1.12913	+	0.410971i	0.0586217	+	0.0213366i
$372$	−8.36776	+	11.2918i	−0.433848	+	0.585453i
$373$	2.06219	−	1.19060i	0.106776	−	0.0616471i	−0.445661	−	0.895202i	$-0.647031\pi$
$373$	2.06219	−	1.19060i	0.106776	−	0.0616471i	0.552437	+	0.833555i	$0.313698\pi$
$374$	−6.92991	−	39.3015i	−0.358337	−	2.03223i
$375$	1.19138	+	1.25722i	0.0615228	+	0.0649226i
$376$	8.19631	+	9.76798i	0.422692	+	0.503745i
$377$	−0.694023	−	0.122375i	−0.0357440	−	0.00630263i
$378$	−0.0153004	−	2.31051i	−0.000786966	−	0.118840i
$379$			12.6046i			0.647453i	0.946151	+	0.323727i	$0.104936\pi$
$379$			12.6046i			0.647453i	−0.946151	+	0.323727i	$0.895064\pi$
$380$	−4.30523	+	0.681885i	−0.220854	+	0.0349800i
$381$	33.4181	+	3.83126i	1.71206	+	0.196282i
$382$	−3.51230	−	9.64998i	−0.179705	−	0.493736i
$383$	−3.25982	+	18.4874i	−0.166569	+	0.944660i	0.780863	+	0.624703i	$0.214780\pi$
$383$	−3.25982	+	18.4874i	−0.166569	+	0.944660i	−0.947432	+	0.319958i	$0.896331\pi$
$384$	0.954969	+	1.44500i	0.0487331	+	0.0737400i
$385$	1.89273	+	1.58819i	0.0964626	+	0.0809417i
$386$	1.70443	−	0.300537i	0.0867533	−	0.0152970i
$387$	8.80123	+	28.9327i	0.447392	+	1.47073i
$388$	−11.8267	−	6.82812i	−0.600407	−	0.346645i
$389$	1.38473	−	3.80452i	0.0702086	−	0.192897i	−0.899626	−	0.436662i	$-0.856161\pi$
$389$	1.38473	−	3.80452i	0.0702086	−	0.192897i	0.969834	+	0.243766i	$0.0783827\pi$
$390$	−0.449638	+	0.900253i	−0.0227683	+	0.0455861i
$391$	5.04103	−	8.73131i	0.254936	−	0.441562i
$392$	−3.40114	−	5.89094i	−0.171783	−	0.297537i
$393$	−1.22730	−	20.2999i	−0.0619091	−	1.02399i
$394$	−8.02116	+	9.55925i	−0.404100	+	0.481588i
$395$	6.67477	−	5.60080i	0.335844	−	0.281807i
$396$	15.3352	+	6.53480i	0.770621	+	0.328386i
$397$	5.81827	−	2.11768i	0.292010	−	0.106283i	−0.191861	−	0.981422i	$-0.561452\pi$
$397$	5.81827	−	2.11768i	0.292010	−	0.106283i	0.483872	+	0.875139i	$0.339230\pi$
$398$	−1.88821			−0.0946475
$399$	−3.10252	+	1.28256i	−0.155320	+	0.0642082i
$400$	−1.00000			−0.0500000
$401$	−21.3894	+	7.78510i	−1.06814	+	0.388770i	−0.815479	−	0.578786i	$-0.803526\pi$
$401$	−21.3894	+	7.78510i	−1.06814	+	0.388770i	−0.252656	+	0.967556i	$0.581304\pi$
$402$	−0.219234	+	0.738218i	−0.0109344	+	0.0368190i
$403$	3.61134	−	3.03027i	0.179894	−	0.150949i
$404$	−2.89062	+	3.44491i	−0.143814	+	0.171391i
$405$	8.64436	+	2.50500i	0.429542	+	0.124475i
$406$	−0.269689	−	0.467115i	−0.0133844	−	0.0231825i
$407$	28.5908	−	49.5207i	1.41719	−	2.45465i
$408$	11.1290	+	5.55848i	0.550969	+	0.275186i
$409$	−1.26608	+	3.47851i	−0.0626034	+	0.172001i	−0.967051	−	0.254584i	$-0.918061\pi$
$409$	−1.26608	+	3.47851i	−0.0626034	+	0.172001i	0.904447	+	0.426586i	$0.140284\pi$
$410$	9.41648	+	5.43661i	0.465047	+	0.268495i
$411$	−0.226796	−	0.522596i	−0.0111870	−	0.0257778i
$412$	−10.5402	+	1.85851i	−0.519276	+	0.0915624i
$413$	−2.76607	−	2.32101i	−0.136110	−	0.114209i
$414$	1.90661	+	3.75495i	0.0937047	+	0.184546i
$415$	1.11325	−	6.31356i	0.0546473	−	0.309920i
$416$	−0.198708	−	0.545947i	−0.00974248	−	0.0267673i
$417$	1.78802	−	15.5959i	0.0875595	−	0.763736i
$418$	0.422684	−	24.2165i	0.0206742	−	1.18447i
$419$		−	15.7444i		−	0.769166i	−0.923090	−	0.384583i	$-0.874345\pi$
$419$		−	15.7444i		−	0.769166i	0.923090	−	0.384583i	$-0.125655\pi$
$420$	−0.749032	+	0.179271i	−0.0365490	+	0.00874753i
$421$	35.9573	+	6.34023i	1.75245	+	0.309004i	0.955489	−	0.295027i	$-0.0953287\pi$
$421$	35.9573	+	6.34023i	1.75245	+	0.309004i	0.796961	+	0.604031i	$0.206440\pi$
$422$	−8.84623	−	10.5425i	−0.430628	−	0.513202i
$423$	−30.5829	+	22.9787i	−1.48699	+	1.11726i
$424$	−0.469240	−	2.66119i	−0.0227883	−	0.129239i
$425$	−6.21996	+	3.59110i	−0.301713	+	0.174194i
$426$	−1.20896	−	0.895895i	−0.0585742	−	0.0434062i
$427$	−3.61312	−	1.31507i	−0.174851	−	0.0636406i
$428$	15.7923	+	5.74792i	0.763349	+	0.277836i
$429$	−4.49240	−	3.32908i	−0.216895	−	0.160730i
$430$	8.73003	−	5.04029i	0.420999	−	0.243064i
$431$	−0.964321	−	5.46894i	−0.0464497	−	0.263430i	0.952735	−	0.303803i	$-0.0982564\pi$
$431$	−0.964321	−	5.46894i	−0.0464497	−	0.263430i	−0.999185	+	0.0403733i	$0.987145\pi$
$432$	−4.48270	+	2.62782i	−0.215674	+	0.126431i
$433$	−5.45238	−	6.49789i	−0.262025	−	0.312269i	0.618952	−	0.785429i	$-0.287558\pi$
$433$	−5.45238	−	6.49789i	−0.262025	−	0.312269i	−0.880976	+	0.473160i	$0.843113\pi$
$434$	3.55334	+	0.626549i	0.170566	+	0.0300753i
$435$	2.04326	−	0.489027i	0.0979667	−	0.0234470i
$436$			6.08109i			0.291231i
$437$	4.01431	−	4.61794i	0.192031	−	0.220906i
$438$	1.20862	−	10.5422i	0.0577502	−	0.503725i
$439$	−2.37823	−	6.53415i	−0.113507	−	0.311858i	0.869912	−	0.493207i	$-0.164176\pi$
$439$	−2.37823	−	6.53415i	−0.113507	−	0.311858i	−0.983419	+	0.181350i	$0.941953\pi$
$440$	0.964873	−	5.47207i	0.0459985	−	0.260871i
$441$	18.1956	−	9.23898i	0.866456	−	0.439951i
$442$	−3.19651	−	2.68219i	−0.152042	−	0.127579i
$443$	−5.86804	+	1.03469i	−0.278799	+	0.0491598i	−0.311299	−	0.950312i	$-0.600764\pi$
$443$	−5.86804	+	1.03469i	−0.278799	+	0.0491598i	0.0325003	+	0.999472i	$0.489653\pi$
$444$	7.09602	+	16.3511i	0.336762	+	0.775988i
$445$	−2.92475	−	1.68860i	−0.138646	−	0.0800475i
$446$	−6.53058	+	17.9426i	−0.309232	+	0.849608i
$447$	−17.2569	−	8.61911i	−0.816225	−	0.407670i
$448$	0.222334	−	0.385093i	0.0105043	−	0.0181939i
$449$	−6.07689	−	10.5255i	−0.286786	−	0.496728i	0.686255	−	0.727362i	$-0.259254\pi$
$449$	−6.07689	−	10.5255i	−0.286786	−	0.496728i	−0.973041	+	0.230633i	$0.925920\pi$
$450$	0.161211	−	2.99567i	0.00759957	−	0.141217i
$451$	−38.8352	+	46.2820i	−1.82868	+	2.17933i
$452$	−11.3578	+	9.53037i	−0.534228	+	0.448271i
$453$	6.16760	−	20.7679i	0.289779	−	0.975763i
$454$	3.85627	−	1.40357i	0.180984	−	0.0658727i
$455$	0.258345			0.0121114
$456$	5.98646	+	4.60025i	0.280342	+	0.215426i
$457$	3.45056			0.161410			0.0807052	−	0.996738i	$-0.474283\pi$
$457$	3.45056			0.161410			0.0807052	+	0.996738i	$0.474283\pi$
$458$	9.90667	−	3.60573i	0.462909	−	0.168485i
$459$	−18.4455	+	32.4427i	−0.860961	+	1.51430i
$460$	1.07534	−	0.902317i	0.0501380	−	0.0420707i
$461$	0.761610	−	0.907651i	0.0354717	−	0.0422735i	−0.748017	−	0.663680i	$-0.768994\pi$
$461$	0.761610	−	0.907651i	0.0354717	−	0.0422735i	0.783489	+	0.621406i	$0.213438\pi$
$462$	−0.258262	−	4.27173i	−0.0120154	−	0.198739i
$463$	11.7087	+	20.2801i	0.544151	+	0.942498i	0.998660	+	0.0517552i	$0.0164815\pi$
$463$	11.7087	+	20.2801i	0.544151	+	0.942498i	−0.454509	+	0.890742i	$0.650185\pi$
$464$	−0.606496	+	1.05048i	−0.0281559	+	0.0487674i
$465$	−6.27984	+	12.5733i	−0.291220	+	0.583073i
$466$	−0.321800	+	0.884139i	−0.0149071	+	0.0409570i
$467$	7.07218	+	4.08312i	0.327261	+	0.188944i	0.654625	−	0.755954i	$-0.272827\pi$
$467$	7.07218	+	4.08312i	0.327261	+	0.188944i	−0.327363	+	0.944899i	$0.606160\pi$
$468$	1.66751	−	0.507251i	0.0770806	−	0.0234477i
$469$	0.194699	−	0.0343307i	0.00899038	−	0.00158525i
$470$	9.76798	+	8.19631i	0.450563	+	0.378068i
$471$	−17.3571	−	26.2637i	−0.799773	−	1.21017i
$472$	−1.41008	+	7.99698i	−0.0649043	+	0.368091i
$473$	19.1574	+	52.6346i	0.880859	+	2.42014i
$474$	−14.9936	−	1.71897i	−0.688681	−	0.0789548i
$475$	−4.12142	+	1.41912i	−0.189104	+	0.0651138i
$476$		−	3.19369i		−	0.146382i
$477$	8.04768	−	0.976671i	0.368478	−	0.0447187i
$478$	−12.0724	−	2.12870i	−0.552181	−	0.0973643i
$479$	15.7946	+	18.8232i	0.721673	+	0.860056i	0.994792	−	0.101924i	$-0.0324999\pi$
$479$	15.7946	+	18.8232i	0.721673	+	0.860056i	−0.273119	+	0.961980i	$0.588055\pi$
$480$	1.19138	+	1.25722i	0.0543790	+	0.0573840i
$481$	−1.03822	−	5.88805i	−0.0473389	−	0.268472i
$482$	9.55808	−	5.51836i	0.435359	−	0.251355i
$483$	0.643704	−	0.868642i	0.0292896	−	0.0395246i
$484$	18.6759	+	6.79748i	0.848906	+	0.308977i
$485$	−12.8327	−	4.67071i	−0.582702	−	0.212086i
$486$	−7.14940	−	13.8523i	−0.324303	−	0.628353i
$487$	−29.8464	+	17.2318i	−1.35247	+	0.780849i	−0.988595	−	0.150599i	$-0.951880\pi$
$487$	−29.8464	+	17.2318i	−1.35247	+	0.780849i	−0.363875	+	0.931448i	$0.618546\pi$
$488$	1.50152	+	8.51555i	0.0679706	+	0.385481i
$489$	−3.86030	+	3.65814i	−0.174569	+	0.165427i
$490$	−4.37242	−	5.21084i	−0.197526	−	0.235402i
$491$	3.04513	+	0.536938i	0.137425	+	0.0242317i	0.241937	−	0.970292i	$-0.422217\pi$
$491$	3.04513	+	0.536938i	0.137425	+	0.0242317i	−0.104513	+	0.994524i	$0.533328\pi$
$492$	−4.38362	−	18.3157i	−0.197629	−	0.825735i
$493$			8.71194i			0.392366i
$494$	−1.59373	−	1.96808i	−0.0717051	−	0.0885483i
$495$	16.2369	+	3.77260i	0.729796	+	0.169566i
$496$	−2.77525	−	7.62492i	−0.124612	−	0.342369i
$497$	−0.0670815	+	0.380438i	−0.00300902	+	0.0170650i
$498$	−9.26384	+	6.12226i	−0.415123	+	0.274345i
$499$	20.7639	+	17.4230i	0.929519	+	0.779959i	0.975731	−	0.218972i	$-0.0702705\pi$
$499$	20.7639	+	17.4230i	0.929519	+	0.779959i	−0.0462119	+	0.998932i	$0.514715\pi$
$500$	−0.984808	+	0.173648i	−0.0440419	+	0.00776578i
$501$	4.96345	−	2.15403i	0.221751	−	0.0962350i
$502$	8.99330	+	5.19229i	0.401391	+	0.231743i
$503$	6.31706	−	17.3560i	0.281664	−	0.773865i	−0.715501	−	0.698612i	$-0.753801\pi$
$503$	6.31706	−	17.3560i	0.281664	−	0.773865i	0.997164	−	0.0752527i	$-0.0239763\pi$
$504$	1.11777	+	0.728119i	0.0497893	+	0.0324330i
$505$	−2.24850	+	3.89452i	−0.100057	+	0.173304i
$506$	3.89997	+	6.75495i	0.173375	+	0.300294i
$507$	21.8920	−	1.32356i	0.972260	−	0.0587813i
$508$	−12.4832	+	14.8768i	−0.553850	+	0.660053i
$509$	7.03448	−	5.90263i	0.311798	−	0.261630i	−0.473437	−	0.880828i	$-0.656987\pi$
$509$	7.03448	−	5.90263i	0.311798	−	0.261630i	0.785235	+	0.619198i	$0.212542\pi$
$510$	11.9252	+	3.54150i	0.528055	+	0.156820i
$511$	−2.55992	+	0.931735i	−0.113244	+	0.0412175i
$512$	−1.00000			−0.0441942
$513$	−14.7459	+	17.1918i	−0.651047	+	0.759038i
$514$	−5.68952			−0.250954
$515$	−10.0573	+	3.66056i	−0.443177	+	0.161303i
$516$	−16.7376	−	4.97067i	−0.736830	−	0.218822i
$517$	−54.2756	+	45.5427i	−2.38704	+	2.00296i
$518$	2.94143	−	3.50546i	0.129239	−	0.154021i
$519$	6.99801	−	0.423089i	0.307179	−	0.0185715i
$520$	−0.290492	−	0.503147i	−0.0127389	−	0.0220645i
$521$	9.57030	−	16.5762i	0.419282	−	0.726218i	−0.576585	−	0.817037i	$-0.695615\pi$
$521$	9.57030	−	16.5762i	0.419282	−	0.726218i	0.995867	+	0.0908189i	$0.0289484\pi$
$522$	−3.04912	−	1.98621i	−0.133456	−	0.0869340i
$523$	−7.14932	+	19.6426i	−0.312618	+	0.858911i	0.679508	+	0.733668i	$0.262193\pi$
$523$	−7.14932	+	19.6426i	−0.312618	+	0.858911i	−0.992126	+	0.125243i	$0.960029\pi$
$524$	10.1685	+	5.87077i	0.444212	+	0.256466i
$525$	−0.706522	+	0.306616i	−0.0308352	+	0.0133818i
$526$	−13.6233	+	2.40216i	−0.594005	+	0.104739i
$527$	−44.6438	−	37.4606i	−1.94471	−	1.63181i
$528$	−8.02914	+	5.30627i	−0.349423	+	0.230926i
$529$	3.65173	−	20.7100i	0.158771	−	0.900434i
$530$	−0.924222	−	2.53928i	−0.0401456	−	0.110299i
$531$	−23.7289	−	5.51334i	−1.02975	−	0.239259i
$532$	0.369836	−	1.90265i	0.0160344	−	0.0824903i
$533$			6.31717i			0.273627i
$534$	1.36155	+	5.68883i	0.0589199	+	0.246180i
$535$	16.5505	+	2.91830i	0.715540	+	0.126169i
$536$	−0.285789	−	0.340590i	−0.0123442	−	0.0147112i
$537$	6.89296	−	6.53199i	0.297453	−	0.281876i
$538$	0.523143	+	2.96689i	0.0225543	+	0.127912i
$539$	32.7329	−	18.8984i	1.40991	−	0.814010i
$540$	−3.95828	+	3.36631i	−0.170337	+	0.144863i
$541$	−9.50811	−	3.46067i	−0.408785	−	0.148786i	0.129439	−	0.991587i	$-0.458682\pi$
$541$	−9.50811	−	3.46067i	−0.408785	−	0.148786i	−0.538224	+	0.842802i	$0.680905\pi$
$542$	−17.1074	−	6.22660i	−0.734828	−	0.267455i
$543$	−16.6809	+	22.5098i	−0.715844	+	0.965990i
$544$	−6.21996	+	3.59110i	−0.266679	+	0.153967i
$545$	1.05597	+	5.98871i	0.0452328	+	0.256528i
$546$	−0.307788	−	0.324797i	−0.0131721	−	0.0139000i
$547$	3.35894	+	4.00303i	0.143618	+	0.171157i	0.833058	−	0.553185i	$-0.186588\pi$
$547$	3.35894	+	4.00303i	0.143618	+	0.171157i	−0.689440	+	0.724343i	$0.742143\pi$
$548$	0.323912	+	0.0571144i	0.0138368	+	0.00243981i
$549$	−25.7518	+	3.12525i	−1.09906	+	0.133382i
$550$		−	5.55648i		−	0.236929i
$551$	−1.00886	+	5.19017i	−0.0429790	+	0.221108i
$552$	−2.41555	−	0.276934i	−0.102813	−	0.0117871i
$553$	1.32516	+	3.64085i	0.0563516	+	0.154825i
$554$	1.41356	−	8.01668i	0.0600563	−	0.340596i
$555$	9.82755	+	14.8705i	0.417156	+	0.631216i
$556$	6.94289	+	5.82578i	0.294444	+	0.247068i
$557$	3.85969	−	0.680567i	0.163540	−	0.0288366i	−0.0912785	−	0.995825i	$-0.529095\pi$
$557$	3.85969	−	0.680567i	0.163540	−	0.0288366i	0.254819	+	0.966989i	$0.417984\pi$
$558$	23.2891	−	7.08448i	0.985907	−	0.299910i
$559$	5.07201	+	2.92833i	0.214523	+	0.123855i
$560$	0.152085	−	0.417851i	0.00642677	−	0.0176574i
$561$	−30.8856	+	61.8382i	−1.30399	+	2.61081i
$562$	−8.02439	+	13.8986i	−0.338488	+	0.586279i
$563$	11.6267	+	20.1381i	0.490009	+	0.848720i	0.999934	−	0.0114987i	$-0.00366023\pi$
$563$	11.6267	+	20.1381i	0.490009	+	0.848720i	−0.509925	+	0.860219i	$0.670327\pi$
$564$	−1.33283	−	22.0455i	−0.0561225	−	0.928281i
$565$	−9.53037	+	11.3578i	−0.400946	+	0.477828i
$566$	12.0327	−	10.0967i	0.505773	−	0.424394i
$567$	−2.36140	+	3.23108i	−0.0991693	+	0.135692i
$568$	0.816363	−	0.297132i	0.0342538	−	0.0124674i
$569$	19.6957			0.825686			0.412843	−	0.910802i	$-0.364536\pi$
$569$	19.6957			0.825686			0.412843	+	0.910802i	$0.364536\pi$
$570$	6.69434	+	3.49082i	0.280395	+	0.146214i
$571$	−13.4022			−0.560865			−0.280432	−	0.959874i	$-0.590478\pi$
$571$	−13.4022			−0.560865			−0.280432	+	0.959874i	$0.590478\pi$
$572$	3.03355	−	1.10412i	0.126839	−	0.0461656i
$573$	−5.06373	+	17.0509i	−0.211540	+	0.712312i
$574$	−3.70380	+	3.10785i	−0.154593	+	0.129719i
$575$	0.902317	−	1.07534i	0.0376292	−	0.0448448i
$576$	0.161211	−	2.99567i	0.00671714	−	0.124819i
$577$	1.55790	+	2.69836i	0.0648563	+	0.112334i	0.896630	−	0.442780i	$-0.146008\pi$
$577$	1.55790	+	2.69836i	0.0648563	+	0.112334i	−0.831774	+	0.555114i	$0.812674\pi$
$578$	−17.2920	+	29.9506i	−0.719251	+	1.24578i
$579$	−2.68181	−	1.33945i	−0.111452	−	0.0556657i
$580$	−0.414868	+	1.13984i	−0.0172264	+	0.0473292i
$581$	2.46881	+	1.42537i	0.102424	+	0.0591343i
$582$	9.41651	+	21.6981i	0.390327	+	0.899416i
$583$	14.7869	−	2.60732i	0.612409	−	0.107984i
$584$	4.69310	+	3.93797i	0.194202	+	0.162955i
$585$	1.55409	−	0.789105i	0.0642538	−	0.0326255i
$586$	3.15410	−	17.8878i	0.130295	−	0.738937i
$587$	5.26810	+	14.4740i	0.217438	+	0.597405i	0.999673	−	0.0255783i	$-0.00814271\pi$
$587$	5.26810	+	14.4740i	0.217438	+	0.597405i	−0.782235	+	0.622983i	$0.785920\pi$
$588$	−1.34196	+	11.7052i	−0.0553414	+	0.482715i
$589$	−22.2586	−	27.4871i	−0.917151	−	1.13259i
$590$			8.12034i			0.334309i
$591$	21.0201	−	5.03089i	0.864652	−	0.206943i
$592$	−10.1346	−	1.78701i	−0.416530	−	0.0734455i
$593$	16.5495	+	19.7230i	0.679608	+	0.809926i	0.990057	−	0.140664i	$-0.0449239\pi$
$593$	16.5495	+	19.7230i	0.679608	+	0.809926i	−0.310449	+	0.950590i	$0.600479\pi$
$594$	−14.6014	−	24.9080i	−0.599104	−	1.02199i
$595$	−0.554578	−	3.14517i	−0.0227355	−	0.128939i
$596$	9.64483	−	5.56844i	0.395068	−	0.228092i
$597$	2.62763	+	1.94720i	0.107542	+	0.0796935i
$598$	0.766376	+	0.278938i	0.0313395	+	0.0114066i
$599$	−30.8938	−	11.2444i	−1.26229	−	0.459435i	−0.377751	−	0.925907i	$-0.623302\pi$
$599$	−30.8938	−	11.2444i	−1.26229	−	0.459435i	−0.884536	+	0.466473i	$0.845525\pi$
$600$	1.39160	+	1.03124i	0.0568117	+	0.0421002i
$601$	37.9759	−	21.9254i	1.54907	−	0.894357i	0.550858	−	0.834599i	$-0.314300\pi$
$601$	37.9759	−	21.9254i	1.54907	−	0.894357i	0.998213	−	0.0597579i	$-0.0190329\pi$
$602$	0.778378	+	4.41440i	0.0317243	+	0.179918i
$603$	1.06637	−	0.801220i	0.0434257	−	0.0326282i
$604$	8.03996	+	9.58165i	0.327141	+	0.389872i
$605$	19.5726	+	3.45117i	0.795738	+	0.140310i
$606$	7.57511	−	1.81300i	0.307718	−	0.0736482i
$607$		−	31.5174i		−	1.27925i	−0.768686	−	0.639627i	$-0.779089\pi$
$607$		−	31.5174i		−	1.27925i	0.768686	−	0.639627i	$-0.220911\pi$
$608$	−4.12142	+	1.41912i	−0.167146	+	0.0575530i
$609$	−0.106409	+	0.928150i	−0.00431191	+	0.0376105i
$610$	2.95742	+	8.12544i	0.119742	+	0.328989i
$611$	−1.28643	+	7.29570i	−0.0520433	+	0.295152i
$612$	−9.75500	−	19.2119i	−0.394323	−	0.776593i
$613$	30.7470	+	25.7998i	1.24186	+	1.04204i	0.997376	+	0.0723891i	$0.0230623\pi$
$613$	30.7470	+	25.7998i	1.24186	+	1.04204i	0.244482	+	0.969654i	$0.421382\pi$
$614$	−8.97655	+	1.58281i	−0.362264	+	0.0638769i
$615$	−7.49751	−	17.2762i	−0.302329	−	0.696644i
$616$	2.13976	+	1.23539i	0.0862135	+	0.0497754i
$617$	4.23165	−	11.6264i	0.170360	−	0.468059i	−0.824904	−	0.565273i	$-0.808771\pi$
$617$	4.23165	−	11.6264i	0.170360	−	0.468059i	0.995264	+	0.0972136i	$0.0309930\pi$
$618$	16.5842	+	8.28312i	0.667115	+	0.333196i
$619$	−10.2668	+	17.7827i	−0.412659	+	0.714746i	−0.995180	−	0.0980700i	$-0.968733\pi$
$619$	−10.2668	+	17.7827i	−0.412659	+	0.714746i	0.582521	+	0.812816i	$0.302066\pi$
$620$	−4.05714	−	7.02717i	−0.162939	−	0.282218i
$621$	1.21902	−	7.19155i	0.0489175	−	0.288587i
$622$	−10.1923	+	12.1467i	−0.408673	+	0.487038i
$623$	1.15039	−	0.965296i	0.0460896	−	0.0386738i
$624$	−0.286480	+	0.964655i	−0.0114684	+	0.0386171i
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	−23.2982			−0.931183
$627$	−25.5612	+	33.2637i	−1.02082	+	1.32842i
$628$	18.1756			0.725283
$629$	−69.4542	+	25.2793i	−2.76932	+	1.00795i
$630$	1.22722	+	0.522959i	0.0488937	+	0.0208352i
$631$	−8.38135	+	7.03279i	−0.333656	+	0.279971i	−0.794188	−	0.607673i	$-0.792103\pi$
$631$	−8.38135	+	7.03279i	−0.333656	+	0.279971i	0.460531	+	0.887643i	$0.347659\pi$
$632$	5.60080	−	6.67477i	0.222788	−	0.265508i
$633$	1.43852	+	23.7935i	0.0571761	+	0.945708i
$634$	11.8444	+	20.5150i	0.470400	+	0.814756i
$635$	−9.71017	+	16.8185i	−0.385336	+	0.667422i
$636$	−2.09133	+	4.18721i	−0.0829268	+	0.166034i
$637$	1.35167	−	3.71368i	0.0535551	−	0.147141i
$638$	−5.83698	−	3.36998i	−0.231088	−	0.133419i
$639$	0.758500	+	2.49345i	0.0300058	+	0.0986394i
$640$	−0.984808	+	0.173648i	−0.0389279	+	0.00686405i
$641$	7.40295	+	6.21181i	0.292399	+	0.245352i	0.777172	−	0.629288i	$-0.216653\pi$
$641$	7.40295	+	6.21181i	0.292399	+	0.245352i	−0.484773	+	0.874640i	$0.661098\pi$
$642$	−16.0490	−	24.2844i	−0.633405	−	0.958430i
$643$	4.19670	−	23.8006i	0.165501	−	0.938606i	−0.783044	−	0.621966i	$-0.786334\pi$
$643$	4.19670	−	23.8006i	0.165501	−	0.938606i	0.948546	−	0.316640i	$-0.102555\pi$
$644$	0.213490	+	0.586560i	0.00841270	+	0.0231137i
$645$	−17.3464	−	1.98871i	−0.683015	−	0.0783052i
$646$	−20.5389	+	23.6273i	−0.808091	+	0.929604i
$647$			43.6069i			1.71436i	0.515013	+	0.857182i	$0.327787\pi$
$647$			43.6069i			1.71436i	−0.515013	+	0.857182i	$0.672213\pi$
$648$	8.94802	+	0.965870i	0.351511	+	0.0379430i
$649$	−44.4351	−	7.83510i	−1.74423	−	0.307555i
$650$	−0.373450	−	0.445060i	−0.0146479	−	0.0174567i
$651$	−4.29869	−	4.53625i	−0.168479	−	0.177790i
$652$	−0.533186	−	3.02385i	−0.0208812	−	0.118423i
$653$	−23.5475	+	13.5952i	−0.921486	+	0.532020i	−0.884109	−	0.467281i	$-0.845234\pi$
$653$	−23.5475	+	13.5952i	−0.921486	+	0.532020i	−0.0373768	+	0.999301i	$0.511900\pi$
$654$	6.27106	−	8.46243i	0.245218	−	0.330907i
$655$	11.0334	+	4.01584i	0.431112	+	0.156912i
$656$	10.2175	+	3.71886i	0.398926	+	0.145197i
$657$	−12.5534	+	13.4241i	−0.489756	+	0.523724i
$658$	−4.91040	+	2.83502i	−0.191427	+	0.110521i
$659$	−6.57672	−	37.2985i	−0.256193	−	1.45294i	−0.792992	−	0.609232i	$-0.791478\pi$
$659$	−6.57672	−	37.2985i	−0.256193	−	1.45294i	0.536800	−	0.843710i	$-0.319633\pi$
$660$	−6.98573	+	6.61990i	−0.271919	+	0.257679i
$661$	3.67938	+	4.38491i	0.143111	+	0.170553i	0.832839	−	0.553516i	$-0.186714\pi$
$661$	3.67938	+	4.38491i	0.143111	+	0.170553i	−0.689728	+	0.724069i	$0.742270\pi$
$662$	7.36534	+	1.29871i	0.286262	+	0.0504757i
$663$	1.68227	+	7.02890i	0.0653341	+	0.272980i
$664$		−	6.41095i		−	0.248793i
$665$	0.0338260	−	1.93796i	0.00131172	−	0.0751510i
$666$	6.98708	−	30.0718i	0.270744	−	1.16526i
$667$	−0.582373	−	1.60006i	−0.0225496	−	0.0619544i
$668$	−0.542454	+	3.07641i	−0.0209882	+	0.119030i
$669$	27.5911	−	18.2343i	1.06673	−	0.704980i
$670$	−0.340590	−	0.285789i	−0.0131581	−	0.0110410i
$671$	−47.3165	+	8.34318i	−1.82663	+	0.322085i
$672$	−0.706522	+	0.306616i	−0.0272547	+	0.0118280i
$673$	21.7474	+	12.5559i	0.838301	+	0.483993i	0.856686	−	0.515838i	$-0.172519\pi$
$673$	21.7474	+	12.5559i	0.838301	+	0.483993i	−0.0183855	+	0.999831i	$0.505853\pi$
$674$	1.29023	−	3.54487i	0.0496977	−	0.136543i
$675$	−3.31359	+	4.00251i	−0.127540	+	0.154057i
$676$	−6.33123	+	10.9660i	−0.243509	+	0.421770i
$677$	−7.36986	−	12.7650i	−0.283247	−	0.490597i	0.688936	−	0.724822i	$-0.258078\pi$
$677$	−7.36986	−	12.7650i	−0.283247	−	0.490597i	−0.972182	+	0.234225i	$0.924745\pi$
$678$	25.6337	−	1.54977i	0.984455	−	0.0595186i
$679$	3.90332	−	4.65179i	0.149796	−	0.178519i
$680$	−5.50188	+	4.61663i	−0.210988	+	0.177040i
$681$	−6.81380	−	2.02354i	−0.261105	−	0.0775422i
$682$	42.3678	−	15.4206i	1.62235	−	0.590486i
$683$	47.0397			1.79993			0.899963	−	0.435967i	$-0.143594\pi$
$683$	47.0397			1.79993			0.899963	+	0.435967i	$0.143594\pi$
$684$	−3.58679	−	12.5752i	−0.137144	−	0.480824i
$685$	0.328909			0.0125670
$686$	5.76729	−	2.09912i	0.220196	−	0.0801448i
$687$	−17.5045	−	5.19843i	−0.667838	−	0.198332i
$688$	7.72217	−	6.47967i	0.294405	−	0.247035i
$689$	1.00915	−	1.20266i	0.0384456	−	0.0458177i
$690$	−2.42695	+	0.146729i	−0.0923922	+	0.00558589i
$691$	−20.5332	−	35.5645i	−0.781120	−	1.35294i	−0.931290	−	0.364279i	$-0.881316\pi$
$691$	−20.5332	−	35.5645i	−0.781120	−	1.35294i	0.150170	−	0.988660i	$-0.452018\pi$
$692$	−2.02384	+	3.50539i	−0.0769349	+	0.133255i
$693$	−4.04578	+	6.21086i	−0.153686	+	0.235931i
$694$	6.15587	−	16.9131i	0.233674	−	0.642013i
$695$	7.84905	+	4.53165i	0.297731	+	0.171895i
$696$	1.92730	−	0.836405i	0.0730540	−	0.0317039i
$697$	76.9072	−	13.5608i	2.91307	−	0.513652i
$698$	−22.3371	−	18.7431i	−0.845474	−	0.709437i
$699$	1.35958	−	0.898513i	0.0514239	−	0.0339849i
$700$	0.0772157	−	0.437912i	0.00291848	−	0.0165515i
$701$	−9.80359	−	26.9351i	−0.370276	−	1.01733i	−0.975255	−	0.221084i	$-0.929040\pi$
$701$	−9.80359	−	26.9351i	−0.370276	−	1.01733i	0.604978	−	0.796242i	$-0.293182\pi$
$702$	−2.84360	−	1.01371i	−0.107325	−	0.0382601i
$703$	−44.3050	+	7.01725i	−1.67099	+	0.264660i
$704$		−	5.55648i		−	0.209418i
$705$	−5.14074	−	21.4791i	−0.193611	−	0.808950i
$706$	29.7015	+	5.23718i	1.11783	+	0.197104i
$707$	−1.28536	−	1.53184i	−0.0483411	−	0.0576107i
$708$	10.2091	−	9.67444i	0.383680	−	0.363588i
$709$	−5.15552	−	29.2384i	−0.193620	−	1.09807i	−0.914371	−	0.404878i	$-0.867314\pi$
$709$	−5.15552	−	29.2384i	−0.193620	−	1.09807i	0.720751	−	0.693194i	$-0.243797\pi$
$710$	0.752364	−	0.434378i	0.0282357	−	0.0163019i
$711$	19.0925	+	17.8542i	0.716023	+	0.669583i
$712$	−3.17354	−	1.15507i	−0.118933	−	0.0432882i
$713$	10.7035	+	3.89577i	0.400851	+	0.145898i
$714$	−3.29346	+	4.44433i	−0.123255	+	0.166325i
$715$	2.79573	−	1.61412i	0.104554	−	0.0603645i
$716$	0.952060	+	5.39940i	0.0355802	+	0.201785i
$717$	14.6048	+	15.4119i	0.545426	+	0.575567i
$718$	−15.7171	−	18.7309i	−0.586558	−	0.699033i
$719$	−28.3624	−	5.00105i	−1.05774	−	0.186508i	−0.382385	−	0.924003i	$-0.624897\pi$
$719$	−28.3624	−	5.00105i	−1.05774	−	0.186508i	−0.675352	+	0.737495i	$0.736008\pi$
$720$	−0.361430	−	2.97815i	−0.0134697	−	0.110989i
$721$		−	4.75916i		−	0.177241i
$722$	−14.9722	+	11.6976i	−0.557207	+	0.435339i
$723$	−18.9918	−	2.17734i	−0.706311	−	0.0809760i
$724$	−5.53236	−	15.2000i	−0.205609	−	0.564905i
$725$	−0.210634	+	1.19456i	−0.00782274	+	0.0443650i
$726$	−18.9796	−	28.7187i	−0.704397	−	1.06585i
$727$	10.7666	+	9.03422i	0.399310	+	0.335061i	0.820227	−	0.572038i	$-0.193847\pi$
$727$	10.7666	+	9.03422i	0.399310	+	0.335061i	−0.420917	+	0.907099i	$0.638292\pi$
$728$	0.254420	−	0.0448611i	0.00942943	−	0.00166266i
$729$	−4.33595	+	26.6496i	−0.160591	+	0.987021i
$730$	5.30562	+	3.06320i	0.196370	+	0.113374i
$731$	24.7625	−	68.0344i	0.915873	−	2.51634i
$732$	6.69206	−	13.3986i	0.247346	−	0.495228i
$733$	0.265583	−	0.460003i	0.00980953	−	0.0169906i	−0.861079	−	0.508471i	$-0.830211\pi$
$733$	0.265583	−	0.460003i	0.00980953	−	0.0169906i	0.870889	+	0.491481i	$0.163544\pi$
$734$	2.77395	+	4.80462i	0.102388	+	0.177342i
$735$	0.711016	+	11.7604i	0.0262262	+	0.433789i
$736$	0.902317	−	1.07534i	0.0332598	−	0.0396375i
$737$	1.89248	−	1.58798i	0.0697104	−	0.0584940i
$738$	−12.7876	+	30.0086i	−0.470719	+	1.10463i
$739$	36.1209	−	13.1470i	1.32873	−	0.483618i	0.422485	−	0.906370i	$-0.361158\pi$
$739$	36.1209	−	13.1470i	1.32873	−	0.483618i	0.906246	+	0.422752i	$0.138936\pi$
$740$	−10.2910			−0.378303
$741$	0.188258	+	4.38230i	0.00691583	+	0.160988i
$742$	1.20160			0.0441121
$743$	2.24712	−	0.817884i	0.0824387	−	0.0300052i	−0.300472	−	0.953791i	$-0.597144\pi$
$743$	2.24712	−	0.817884i	0.0824387	−	0.0300052i	0.382910	+	0.923786i	$0.374922\pi$
$744$	−4.00110	+	13.4728i	−0.146687	+	0.493936i
$745$	8.53135	−	7.15865i	0.312565	−	0.262273i
$746$	1.53061	−	1.82411i	0.0560397	−	0.0667855i
$747$	19.2051	+	1.03352i	0.702677	+	0.0378144i
$748$	−19.9539	−	34.5611i	−0.729586	−	1.26368i
$749$	−3.73650	+	6.47180i	−0.136529	+	0.236474i
$750$	1.54953	+	0.773925i	0.0565808	+	0.0282597i
$751$	12.4842	−	34.2999i	0.455553	−	1.25162i	−0.473210	−	0.880950i	$-0.656905\pi$
$751$	12.4842	−	34.2999i	0.455553	−	1.25162i	0.928763	−	0.370673i	$-0.120873\pi$
$752$	11.0429	+	6.37560i	0.402692	+	0.232494i
$753$	−7.16057	−	16.4998i	−0.260946	−	0.601287i
$754$	−0.694023	+	0.122375i	−0.0252748	+	0.00445663i
$755$	9.58165	+	8.03996i	0.348712	+	0.292604i
$756$	−0.804618	−	2.16593i	−0.0292637	−	0.0787743i
$757$	−0.592373	+	3.35951i	−0.0215301	+	0.122104i	−0.993679	−	0.112262i	$-0.964190\pi$
$757$	−0.592373	+	3.35951i	−0.0215301	+	0.122104i	0.972148	+	0.234366i	$0.0753014\pi$
$758$	4.31102	+	11.8444i	0.156583	+	0.430209i
$759$	1.53878	−	13.4220i	0.0558542	−	0.487187i
$760$	−3.81238	+	2.11324i	−0.138289	+	0.0766552i
$761$			29.2171i			1.05912i	0.848273	+	0.529560i	$0.177643\pi$
$761$			29.2171i			1.05912i	−0.848273	+	0.529560i	$0.822357\pi$
$762$	32.7131	−	7.82946i	1.18507	−	0.283631i
$763$	−2.66298	−	0.469556i	−0.0964064	−	0.0169991i
$764$	−6.60097	−	7.86673i	−0.238815	−	0.284608i
$765$	−12.9429	−	17.2260i	−0.467952	−	0.622809i
$766$	3.25982	+	18.4874i	0.117782	+	0.667976i
$767$	−4.08573	+	2.35890i	−0.147527	+	0.0851749i
$768$	1.39160	+	1.03124i	0.0502150	+	0.0372117i
$769$	13.0276	+	4.74166i	0.469788	+	0.170989i	0.566056	−	0.824367i	$-0.308469\pi$
$769$	13.0276	+	4.74166i	0.469788	+	0.170989i	−0.0962685	+	0.995355i	$0.530691\pi$
$770$	2.32178	+	0.845059i	0.0836711	+	0.0304538i
$771$	7.91752	+	5.86725i	0.285142	+	0.211304i
$772$	1.49885	−	0.865363i	0.0539449	−	0.0311451i
$773$	2.97940	+	16.8970i	0.107161	+	0.607743i	0.990335	+	0.138696i	$0.0442912\pi$
$773$	2.97940	+	16.8970i	0.107161	+	0.607743i	−0.883173	+	0.469046i	$0.844598\pi$
$774$	18.1660	+	24.1776i	0.652964	+	0.869047i
$775$	−5.21576	−	6.21590i	−0.187355	−	0.223282i
$776$	−13.4488	−	2.37138i	−0.482783	−	0.0851276i
$777$	−7.70825	+	1.84487i	−0.276532	+	0.0661843i
$778$		−	4.04868i		−	0.145152i
$779$	47.3880	+	0.827130i	1.69785	+	0.0296350i
$780$	−0.114617	+	0.999746i	−0.00410396	+	0.0357967i
$781$	1.65101	+	4.53611i	0.0590777	+	0.162315i
$782$	1.75073	−	9.92888i	0.0626060	−	0.355056i
$783$	2.19489	+	5.90837i	0.0784389	+	0.211148i
$784$	−5.21084	−	4.37242i	−0.186101	−	0.156158i
$785$	17.8994	−	3.15615i	0.638858	−	0.112648i
$786$	−8.09625	−	18.6559i	−0.288784	−	0.665433i
$787$	15.9379	+	9.20177i	0.568126	+	0.328008i	0.756401	−	0.654109i	$-0.226956\pi$
$787$	15.9379	+	9.20177i	0.568126	+	0.328008i	−0.188274	+	0.982116i	$0.560289\pi$
$788$	−4.26797	+	11.7262i	−0.152040	+	0.417727i
$789$	21.4354	+	10.7061i	0.763119	+	0.381146i
$790$	4.35665	−	7.54593i	0.155002	−	0.268472i
$791$	−3.29646	−	5.70963i	−0.117208	−	0.203011i
$792$	16.6454	+	0.895768i	0.591467	+	0.0318297i
$793$	−3.22919	+	3.84840i	−0.114672	+	0.136661i
$794$	4.74309	−	3.97993i	0.168326	−	0.141242i
$795$	−1.33246	+	4.48675i	−0.0472575	+	0.159129i
$796$	−1.77434	+	0.645806i	−0.0628897	+	0.0228900i
$797$	−37.7276			−1.33638			−0.668190	−	0.743990i	$-0.732931\pi$
$797$	−37.7276			−1.33638			−0.668190	+	0.743990i	$0.732931\pi$
$798$	−2.47675	+	2.26633i	−0.0876760	+	0.0802273i
$799$	91.5816			3.23992
$800$	−0.939693	+	0.342020i	−0.0332232	+	0.0120922i
$801$	3.97182	−	9.32064i	0.140337	−	0.329329i
$802$	−17.4368	+	14.6312i	−0.615715	+	0.516646i
$803$	−21.8813	+	26.0771i	−0.772174	+	0.920241i
$804$	0.0464733	+	0.768681i	0.00163899	+	0.0271093i
$805$	0.312102	+	0.540577i	0.0110002	+	0.0190528i
$806$	2.35713	−	4.08268i	0.0830265	−	0.143806i
$807$	2.33157	−	4.66821i	0.0820752	−	0.164329i
$808$	−1.53807	+	4.22581i	−0.0541090	+	0.148663i
$809$	21.0514	+	12.1540i	0.740128	+	0.427313i	0.822116	−	0.569320i	$-0.192794\pi$
$809$	21.0514	+	12.1540i	0.740128	+	0.427313i	−0.0819879	+	0.996633i	$0.526127\pi$
$810$	8.97980	−	0.602611i	0.315518	−	0.0211736i
$811$	7.54627	−	1.33061i	0.264985	−	0.0467241i	−0.0395768	−	0.999217i	$-0.512601\pi$
$811$	7.54627	−	1.33061i	0.264985	−	0.0467241i	0.304562	+	0.952492i	$0.401490\pi$
$812$	−0.413187	−	0.346705i	−0.0145000	−	0.0121670i
$813$	17.3856	+	26.3068i	0.609738	+	0.922620i
$814$	9.92947	−	56.3128i	0.348028	−	1.97376i
$815$	−1.05017	−	2.88532i	−0.0367859	−	0.101069i
$816$	12.3590	+	1.41691i	0.432651	+	0.0496018i
$817$	22.6308	−	37.6641i	0.791753	−	1.31770i
$818$			3.70176i			0.129429i
$819$	0.0933735	+	0.769389i	0.00326273	+	0.0268846i
$820$	10.7080	+	1.88811i	0.373940	+	0.0659358i
$821$	−26.2870	−	31.3276i	−0.917422	−	1.09334i	−0.995344	−	0.0963815i	$-0.969273\pi$
$821$	−26.2870	−	31.3276i	−0.917422	−	1.09334i	0.0779226	−	0.996959i	$-0.475171\pi$
$822$	−0.391857	−	0.413511i	−0.0136676	−	0.0144229i
$823$	−5.89867	−	33.4530i	−0.205615	−	1.16610i	−0.896469	−	0.443106i	$-0.853877\pi$
$823$	−5.89867	−	33.4530i	−0.205615	−	1.16610i	0.690854	−	0.722994i	$-0.257235\pi$
$824$	−9.26885	+	5.35138i	−0.322896	+	0.186424i
$825$	−5.73007	+	7.73239i	−0.199495	+	0.269207i
$826$	−3.39309	−	1.23498i	−0.118061	−	0.0429706i
$827$	−17.9625	−	6.53780i	−0.624616	−	0.227342i	0.0102702	−	0.999947i	$-0.496731\pi$
$827$	−17.9625	−	6.53780i	−0.624616	−	0.227342i	−0.634886	+	0.772606i	$0.718953\pi$
$828$	3.07589	+	2.87640i	0.106895	+	0.0999617i
$829$	−18.4081	+	10.6279i	−0.639340	+	0.369123i	−0.784360	−	0.620306i	$-0.787009\pi$
$829$	−18.4081	+	10.6279i	−0.639340	+	0.369123i	0.145021	+	0.989429i	$0.453675\pi$
$830$	−1.11325	−	6.31356i	−0.0386415	−	0.219147i
$831$	−10.2342	+	9.69827i	−0.355021	+	0.336429i
$832$	−0.373450	−	0.445060i	−0.0129470	−	0.0154297i
$833$	−48.1130	−	8.48362i	−1.66702	−	0.293940i
$834$	−3.65394	−	15.2669i	−0.126525	−	0.528650i
$835$			3.12387i			0.108106i
$836$	−7.88532	−	22.9006i	−0.272720	−	0.792034i
$837$	−39.7149	−	14.1579i	−1.37275	−	0.489369i
$838$	−5.38492	−	14.7949i	−0.186019	−	0.511082i
$839$	7.97543	−	45.2309i	0.275342	−	1.56154i	−0.462529	−	0.886604i	$-0.653058\pi$
$839$	7.97543	−	45.2309i	0.275342	−	1.56154i	0.737872	−	0.674941i	$-0.235831\pi$
$840$	−0.642546	+	0.424644i	−0.0221699	+	0.0146516i
$841$	−21.0882	−	17.6951i	−0.727178	−	0.610175i
$842$	35.9573	−	6.34023i	1.23917	−	0.218499i
$843$	25.4996	−	11.0663i	0.878251	−	0.381142i
$844$	−11.9185	−	6.88114i	−0.410251	−	0.236859i
$845$	−4.33082	+	11.8988i	−0.148985	+	0.409332i
$846$	−20.8794	+	32.0529i	−0.717848	+	1.10200i
$847$	−4.41877	+	7.65354i	−0.151831	+	0.262979i
$848$	−1.35112	−	2.34021i	−0.0463977	−	0.0803632i
$849$	−27.1568	+	1.64186i	−0.932018	+	0.0563484i
$850$	−4.61663	+	5.50188i	−0.158349	+	0.188713i
$851$	11.0663	−	9.28570i	0.379347	−	0.318310i
$852$	−1.44246	−	0.428378i	−0.0494180	−	0.0146760i
$853$	12.7434	−	4.63821i	0.436325	−	0.158809i	−0.114513	−	0.993422i	$-0.536531\pi$
$853$	12.7434	−	4.63821i	0.436325	−	0.158809i	0.550837	+	0.834613i	$0.314308\pi$
$854$	−3.84500			−0.131573
$855$	−5.71596	−	11.7613i	−0.195482	−	0.402227i
$856$	16.8058			0.574411
$857$	25.6793	−	9.34649i	0.877188	−	0.319270i	0.136113	−	0.990693i	$-0.456539\pi$
$857$	25.6793	−	9.34649i	0.877188	−	0.319270i	0.741074	+	0.671423i	$0.234317\pi$
$858$	−5.36009	−	1.59182i	−0.182990	−	0.0543439i
$859$	18.2808	−	15.3394i	0.623734	−	0.523375i	−0.275241	−	0.961375i	$-0.588758\pi$
$859$	18.2808	−	15.3394i	0.623734	−	0.523375i	0.898975	+	0.438001i	$0.144313\pi$
$860$	6.47967	−	7.72217i	0.220955	−	0.263324i
$861$	8.35914	−	0.505381i	0.284879	−	0.0172233i
$862$	−2.77665	−	4.80930i	−0.0945732	−	0.163806i
$863$	8.32509	−	14.4195i	0.283389	−	0.490845i	−0.688828	−	0.724925i	$-0.741874\pi$
$863$	8.32509	−	14.4195i	0.283389	−	0.490845i	0.972217	+	0.234080i	$0.0752078\pi$
$864$	−3.31359	+	4.00251i	−0.112731	+	0.136168i
$865$	−1.38439	+	3.80358i	−0.0470706	+	0.129325i
$866$	−7.34597	−	4.24120i	−0.249626	−	0.144122i
$867$	54.9497	−	23.8470i	1.86619	−	0.809886i
$868$	3.55334	−	0.626549i	0.120608	−	0.0212665i
$869$	37.0882	+	31.1207i	1.25813	+	1.05570i
$870$	1.75278	−	1.15837i	0.0594247	−	0.0392724i
$871$	0.0448552	−	0.254386i	0.00151986	−	0.00861955i
$872$	2.07986	+	5.71436i	0.0704328	+	0.193513i
$873$	9.27196	−	39.9057i	0.313808	−	1.35060i
$874$	2.19279	−	5.71242i	0.0741722	−	0.193226i
$875$		−	0.444667i		−	0.0150325i
$876$	−2.46990	−	10.3198i	−0.0834504	−	0.348673i
$877$	−32.9754	−	5.81446i	−1.11350	−	0.196340i	−0.413516	−	0.910497i	$-0.635699\pi$
$877$	−32.9754	−	5.81446i	−1.11350	−	0.196340i	−0.699986	+	0.714157i	$0.746810\pi$
$878$	−4.46962	−	5.32668i	−0.150842	−	0.179767i
$879$	−22.8358	+	21.6400i	−0.770233	+	0.729897i
$880$	−0.964873	−	5.47207i	−0.0325259	−	0.184463i
$881$	15.3252	−	8.84799i	0.516318	−	0.298096i	−0.219109	−	0.975700i	$-0.570315\pi$
$881$	15.3252	−	8.84799i	0.516318	−	0.298096i	0.735427	+	0.677604i	$0.236982\pi$
$882$	13.9383	−	14.9051i	0.469328	−	0.501879i
$883$	−1.45743	−	0.530460i	−0.0490463	−	0.0178514i	0.317381	−	0.948298i	$-0.397197\pi$
$883$	−1.45743	−	0.530460i	−0.0490463	−	0.0178514i	−0.366427	+	0.930447i	$0.619419\pi$
$884$	−3.92110	−	1.42716i	−0.131881	−	0.0480007i
$885$	8.37402	−	11.3003i	0.281490	−	0.379854i
$886$	−5.16026	+	2.97928i	−0.173362	+	0.100091i
$887$	3.00085	+	17.0187i	0.100759	+	0.571431i	0.992830	+	0.119536i	$0.0381407\pi$
$887$	3.00085	+	17.0187i	0.100759	+	0.571431i	−0.892071	+	0.451895i	$0.850748\pi$
$888$	12.2605	+	12.9380i	0.411435	+	0.434171i
$889$	−5.55085	−	6.61525i	−0.186170	−	0.221868i
$890$	−3.32590	−	0.586446i	−0.111484	−	0.0196577i
$891$	−5.36684	+	49.7195i	−0.179796	+	1.66567i
$892$			19.0941i			0.639319i
$893$	54.5600	+	10.6054i	1.82578	+	0.354895i
$894$	−19.1641	−	2.19710i	−0.640944	−	0.0734819i
$895$	1.87519	+	5.15205i	0.0626808	+	0.172214i
$896$	0.0772157	−	0.437912i	0.00257959	−	0.0146296i
$897$	−0.778836	−	1.17849i	−0.0260046	−	0.0393486i
$898$	−9.31034	−	7.81230i	−0.310690	−	0.260700i
$899$	−9.69302	+	1.70914i	−0.323280	+	0.0570030i
$900$	−0.873089	−	2.87014i	−0.0291030	−	0.0956714i
$901$	−16.8079	−	9.70403i	−0.559951	−	0.323288i
$902$	−20.6638	+	56.7733i	−0.688029	+	1.89034i
$903$	3.46912	−	6.94577i	0.115445	−	0.231141i
$904$	−7.41331	+	12.8402i	−0.246563	+	0.427060i
$905$	−8.08777	−	14.0084i	−0.268847	−	0.465656i
$906$	−1.30741	−	21.6249i	−0.0434358	−	0.718440i
$907$	−18.3324	+	21.8477i	−0.608718	+	0.725442i	−0.979087	−	0.203443i	$-0.934787\pi$
$907$	−18.3324	+	21.8477i	−0.608718	+	0.725442i	0.370369	+	0.928885i	$0.379231\pi$
$908$	3.14366	−	2.63785i	0.104326	−	0.0875400i
$909$	−12.4111	−	5.28878i	−0.411652	−	0.175418i
$910$	0.242765	−	0.0883592i	0.00804757	−	0.00292908i
$911$	−22.7881			−0.755003			−0.377502	−	0.926009i	$-0.623217\pi$
$911$	−22.7881			−0.755003			−0.377502	+	0.926009i	$0.623217\pi$
$912$	7.19881	+	2.27533i	0.238376	+	0.0753435i
$913$	35.6224			1.17893
$914$	3.24247	−	1.18016i	0.107251	−	0.0390363i
$915$	4.26374	−	14.3572i	0.140955	−	0.474633i
$916$	8.07600	−	6.77656i	0.266838	−	0.223904i
$917$	−3.35604	+	3.99958i	−0.110826	+	0.132078i
$918$	−6.23700	+	36.7949i	−0.205852	+	1.21441i
$919$	0.796711	+	1.37994i	0.0262811	+	0.0455201i	0.878867	−	0.477067i	$-0.158300\pi$
$919$	0.796711	+	1.37994i	0.0262811	+	0.0455201i	−0.852586	+	0.522587i	$0.824967\pi$
$920$	0.701878	−	1.21569i	0.0231402	−	0.0400801i
$921$	14.1240	+	7.05434i	0.465401	+	0.232448i
$922$	0.405244	−	1.11340i	0.0133460	−	0.0366678i
$923$	0.437112	+	0.252367i	0.0143877	+	0.00830675i
$924$	−1.70370	−	3.92578i	−0.0560477	−	0.129149i
$925$	−10.1346	+	1.78701i	−0.333224	+	0.0587564i
$926$	17.9388	+	15.0525i	0.589506	+	0.494655i
$927$	−14.5367	−	28.6291i	−0.477447	−	0.940303i
$928$	−0.210634	+	1.19456i	−0.00691439	+	0.0392135i
$929$	−12.3421	−	33.9096i	−0.404930	−	1.11254i	−0.959821	−	0.280613i	$-0.909462\pi$
$929$	−12.3421	−	33.9096i	−0.404930	−	1.11254i	0.554891	−	0.831923i	$-0.312760\pi$
$930$	−1.60079	+	13.9629i	−0.0524920	+	0.457861i
$931$	−27.6811	−	10.6257i	−0.907210	−	0.348245i
$932$			0.940881i			0.0308196i
$933$	26.7097	−	6.39262i	0.874437	−	0.209285i
$934$	8.04219	+	1.41805i	0.263148	+	0.0464002i
$935$	−25.6522	−	30.5711i	−0.838917	−	0.999782i
$936$	1.39346	−	1.04698i	0.0455465	−	0.0342217i
$937$	−2.44097	−	13.8435i	−0.0797432	−	0.452246i	−0.998368	−	0.0571143i	$-0.981810\pi$
$937$	−2.44097	−	13.8435i	−0.0797432	−	0.452246i	0.918624	−	0.395132i	$-0.129301\pi$
$938$	0.171216	−	0.0988514i	0.00559039	−	0.00322761i
$939$	32.4217	+	24.0260i	1.05804	+	0.784060i
$940$	11.9822	+	4.36116i	0.390816	+	0.142246i
$941$	4.11836	+	1.49896i	0.134255	+	0.0488648i	0.408274	−	0.912860i	$-0.366131\pi$
$941$	4.11836	+	1.49896i	0.134255	+	0.0488648i	−0.274019	+	0.961724i	$0.588353\pi$
$942$	−25.2931	−	18.7434i	−0.824092	−	0.610691i
$943$	−13.2184	+	7.63167i	−0.430452	+	0.248521i
$944$	1.41008	+	7.99698i	0.0458943	+	0.260279i
$945$	−1.16850	−	1.99331i	−0.0380115	−	0.0648423i
$946$	36.0042	+	42.9081i	1.17060	+	1.39506i
$947$	1.86422	+	0.328712i	0.0605789	+	0.0106817i	0.203855	−	0.979001i	$-0.434653\pi$
$947$	1.86422	+	0.328712i	0.0605789	+	0.0106817i	−0.143277	+	0.989683i	$0.545764\pi$
$948$	−14.6773	+	3.51283i	−0.476698	+	0.114091i
$949$			3.55935i			0.115541i
$950$	−3.38750	+	2.74315i	−0.109905	+	0.0889994i
$951$	4.67333	−	40.7630i	0.151543	−	1.32183i
$952$	−1.09231	−	3.00109i	−0.0354018	−	0.0972657i
$953$	1.00895	−	5.72202i	0.0326830	−	0.185354i	−0.964096	−	0.265555i	$-0.914445\pi$
$953$	1.00895	−	5.72202i	0.0326830	−	0.185354i	0.996779	+	0.0802004i	$0.0255560\pi$
$954$	7.22831	−	3.67024i	0.234025	−	0.118828i
$955$	−7.86673	−	6.60097i	−0.254562	−	0.213602i
$956$	−12.0724	+	2.12870i	−0.390451	+	0.0688470i
$957$	4.64747	+	10.7090i	0.150231	+	0.346173i
$958$	21.2800	+	12.2860i	0.687525	+	0.396943i
$959$	−0.0500222	+	0.137435i	−0.00161530	+	0.00443800i
$960$	1.54953	+	0.773925i	0.0500108	+	0.0249783i
$961$	17.4207	−	30.1736i	0.561959	−	0.973342i
$962$	−2.98944	−	5.17787i	−0.0963835	−	0.166941i
$963$	−2.70929	+	50.3446i	−0.0873055	+	1.62233i
$964$	7.09427	−	8.45462i	0.228491	−	0.272305i
$965$	1.32581	−	1.11249i	0.0426794	−	0.0358123i
$966$	0.307791	−	1.03642i	0.00990303	−	0.0333461i
$967$	−28.3298	+	10.3112i	−0.911026	+	0.331586i	−0.754662	−	0.656113i	$-0.772199\pi$
$967$	−28.3298	+	10.3112i	−0.911026	+	0.331586i	−0.156364	+	0.987700i	$0.549977\pi$
$968$	19.8745			0.638791
$969$	52.9473	−	11.6992i	1.70091	−	0.375832i
$970$	−13.6562			−0.438476
$971$	−13.5984	+	4.94943i	−0.436395	+	0.158835i	−0.550869	−	0.834591i	$-0.685704\pi$
$971$	−13.5984	+	4.94943i	−0.436395	+	0.158835i	0.114475	+	0.993426i	$0.463482\pi$
$972$	−11.4560	−	10.5717i	−0.367451	−	0.339086i
$973$	−3.08728	+	2.59053i	−0.0989735	+	0.0830486i
$974$	−22.1528	+	26.4007i	−0.709822	+	0.845933i
$975$	0.0607282	+	1.00446i	0.00194486	+	0.0321685i
$976$	4.32346	+	7.48845i	0.138390	+	0.239699i
$977$	−3.69968	+	6.40804i	−0.118363	+	0.205011i	−0.919119	−	0.393979i	$-0.871098\pi$
$977$	−3.69968	+	6.40804i	−0.118363	+	0.205011i	0.800756	+	0.598991i	$0.204431\pi$
$978$	−2.37633	+	4.75783i	−0.0759868	+	0.152139i
$979$	6.41814	−	17.6337i	0.205125	−	0.563576i
$980$	−5.89094	−	3.40114i	−0.188179	−	0.108645i
$981$	−17.4536	+	5.30933i	−0.557250	+	0.169514i
$982$	3.04513	−	0.536938i	0.0971739	−	0.0171344i
$983$	−5.98976	−	5.02601i	−0.191044	−	0.160305i	0.542249	−	0.840218i	$-0.317573\pi$
$983$	−5.98976	−	5.02601i	−0.191044	−	0.160305i	−0.733293	+	0.679913i	$0.762017\pi$
$984$	−10.3836	−	15.7118i	−0.331017	−	0.500875i
$985$	−2.16691	+	12.2891i	−0.0690433	+	0.391564i
$986$	2.97966	+	8.18655i	0.0948917	+	0.260713i
$987$	9.75688	+	1.11859i	0.310565	+	0.0356051i
$988$	−2.17074	−	1.30431i	−0.0690603	−	0.0414956i
$989$			14.1507i			0.449965i
$990$	16.5480	−	2.00828i	0.525931	−	0.0638273i
$991$	34.3347	+	6.05413i	1.09068	+	0.192316i	0.689932	−	0.723874i	$-0.257640\pi$
$991$	34.3347	+	6.05413i	1.09068	+	0.192316i	0.400744	+	0.916190i	$0.368752\pi$
$992$	−5.21576	−	6.21590i	−0.165600	−	0.197355i
$993$	−8.91031	−	9.40271i	−0.282760	−	0.298386i
$994$	0.0670815	+	0.380438i	0.00212770	+	0.0120668i
$995$	−1.63524	+	0.944106i	−0.0518406	+	0.0299302i
$996$	−6.61123	+	8.92147i	−0.209485	+	0.282687i
$997$	47.1603	+	17.1649i	1.49358	+	0.543619i	0.954389	−	0.298564i	$-0.0965078\pi$
$997$	47.1603	+	17.1649i	1.49358	+	0.543619i	0.539191	+	0.842183i	$0.318730\pi$
$998$	25.4707	+	9.27057i	0.806260	+	0.293455i
$999$	−40.7345	+	34.6425i	−1.28878	+	1.09604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bb.b.71.1	yes	84
3.2	odd	2		570.2.bb.a.71.1	✓	84
19.15	odd	18		570.2.bb.a.281.1	yes	84
57.53	even	18	inner	570.2.bb.b.281.1	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bb.a.71.1	✓	84	3.2	odd	2
570.2.bb.a.281.1	yes	84	19.15	odd	18
570.2.bb.b.71.1	yes	84	1.1	even	1	trivial
570.2.bb.b.281.1	yes	84	57.53	even	18	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.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(-1.66038 - 0.493094i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(-1.72889 + 0.104526i) q^{6} +(0.222334 + 0.385093i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.51372 + 1.63745i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(-1.66038 - 0.493094i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.642788 - 0.766044i) q^{5} +(-1.72889 + 0.104526i) q^{6} +(0.222334 + 0.385093i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.51372 + 1.63745i) q^{9} +(0.342020 - 0.939693i) q^{10} +(4.81206 + 2.77824i) q^{11} +(-1.58888 + 0.689539i) q^{12} +(0.572158 - 0.100887i) q^{13} +(0.340635 + 0.285827i) q^{14} +(-1.44500 + 0.954969i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-2.45646 - 6.74906i) q^{17} +(2.92216 + 0.678954i) q^{18} +(-0.681885 - 4.30523i) q^{19} -1.00000i q^{20} +(-0.179271 - 0.749032i) q^{21} +(5.47207 + 0.964873i) q^{22} +(0.902317 + 1.07534i) q^{23} +(-1.25722 + 1.19138i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(0.503147 - 0.290492i) q^{26} +(-3.36631 - 3.95828i) q^{27} +(0.417851 + 0.152085i) q^{28} +(-1.13984 - 0.414868i) q^{29} +(-1.03124 + 1.39160i) q^{30} +(7.02717 - 4.05714i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-6.61990 - 6.98573i) q^{33} +(-4.61663 - 5.50188i) q^{34} +(0.437912 + 0.0772157i) q^{35} +(2.97815 - 0.361430i) q^{36} -10.2910i q^{37} +(-2.11324 - 3.81238i) q^{38} +(-0.999746 - 0.114617i) q^{39} +(-0.342020 - 0.939693i) q^{40} +(-1.88811 + 10.7080i) q^{41} +(-0.424644 - 0.642546i) q^{42} +(7.72217 + 6.47967i) q^{43} +(5.47207 - 0.964873i) q^{44} +(2.87014 - 0.873089i) q^{45} +(1.21569 + 0.701878i) q^{46} +(-4.36116 + 11.9822i) q^{47} +(-0.773925 + 1.54953i) q^{48} +(3.40114 - 5.89094i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(0.750728 + 12.4173i) q^{51} +(0.373450 - 0.445060i) q^{52} +(2.07004 - 1.73697i) q^{53} +(-4.51711 - 2.56822i) q^{54} +(5.22139 - 1.90043i) q^{55} +0.444667 q^{56} +(-0.990697 + 7.48455i) q^{57} -1.21299 q^{58} +(-7.63063 + 2.77732i) q^{59} +(-0.493094 + 1.66038i) q^{60} +(-6.62392 + 5.55813i) q^{61} +(5.21576 - 6.21590i) q^{62} +(-0.0716854 + 1.33207i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.290492 - 0.503147i) q^{65} +(-8.60993 - 4.30030i) q^{66} +(0.152065 - 0.417795i) q^{67} +(-6.21996 - 3.59110i) q^{68} +(-0.967945 - 2.23040i) q^{69} +(0.437912 - 0.0772157i) q^{70} +(0.665505 + 0.558425i) q^{71} +(2.67493 - 1.35822i) q^{72} +(-1.06384 + 6.03333i) q^{73} +(-3.51971 - 9.67033i) q^{74} +(-0.197281 + 1.72078i) q^{75} +(-3.28970 - 2.85969i) q^{76} +2.47079i q^{77} +(-0.978656 + 0.234228i) q^{78} +(8.58092 + 1.51305i) q^{79} +(-0.642788 - 0.766044i) q^{80} +(3.63754 + 8.23215i) q^{81} +(1.88811 + 10.7080i) q^{82} +(5.55205 - 3.20548i) q^{83} +(-0.618798 - 0.458559i) q^{84} +(-6.74906 - 2.45646i) q^{85} +(9.47264 + 3.44776i) q^{86} +(1.68800 + 1.25089i) q^{87} +(4.81206 - 2.77824i) q^{88} +(-0.586446 - 3.32590i) q^{89} +(2.39844 - 1.80208i) q^{90} +(0.166061 + 0.197904i) q^{91} +(1.38243 + 0.243760i) q^{92} +(-13.6683 + 3.27133i) q^{93} +12.7512i q^{94} +(-3.73631 - 2.24500i) q^{95} +(-0.197281 + 1.72078i) q^{96} +(-4.67071 - 12.8327i) q^{97} +(1.18120 - 6.69893i) q^{98} +(7.54693 + 14.8632i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{6} + 42 q^{8}+O(q^{10}) \) 84 * q - 6 * q^6 + 42 * q^8	\( 84 q - 6 q^{6} + 42 q^{8} + 24 q^{13} - 24 q^{14} + 12 q^{17} - 12 q^{19} + 36 q^{22} + 24 q^{27} - 12 q^{28} - 12 q^{29} + 36 q^{33} + 12 q^{34} + 6 q^{36} + 18 q^{38} + 12 q^{39} + 6 q^{41} + 24 q^{43} + 36 q^{44} + 12 q^{47} - 12 q^{48} - 54 q^{49} - 42 q^{50} + 96 q^{51} + 12 q^{52} - 60 q^{53} - 18 q^{54} - 96 q^{57} - 24 q^{58} - 18 q^{59} - 48 q^{61} - 12 q^{62} - 114 q^{63} - 42 q^{64} - 24 q^{66} + 6 q^{67} - 54 q^{68} - 48 q^{69} + 48 q^{71} + 84 q^{73} + 24 q^{74} - 12 q^{79} - 36 q^{81} - 6 q^{82} + 36 q^{83} + 18 q^{84} + 12 q^{86} + 6 q^{87} - 12 q^{89} - 24 q^{90} + 24 q^{91} - 6 q^{93} - 12 q^{95} - 42 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) \) 84 * q - 6 * q^6 + 42 * q^8 + 24 * q^13 - 24 * q^14 + 12 * q^17 - 12 * q^19 + 36 * q^22 + 24 * q^27 - 12 * q^28 - 12 * q^29 + 36 * q^33 + 12 * q^34 + 6 * q^36 + 18 * q^38 + 12 * q^39 + 6 * q^41 + 24 * q^43 + 36 * q^44 + 12 * q^47 - 12 * q^48 - 54 * q^49 - 42 * q^50 + 96 * q^51 + 12 * q^52 - 60 * q^53 - 18 * q^54 - 96 * q^57 - 24 * q^58 - 18 * q^59 - 48 * q^61 - 12 * q^62 - 114 * q^63 - 42 * q^64 - 24 * q^66 + 6 * q^67 - 54 * q^68 - 48 * q^69 + 48 * q^71 + 84 * q^73 + 24 * q^74 - 12 * q^79 - 36 * q^81 - 6 * q^82 + 36 * q^83 + 18 * q^84 + 12 * q^86 + 6 * q^87 - 12 * q^89 - 24 * q^90 + 24 * q^91 - 6 * q^93 - 12 * q^95 - 42 * q^97 + 36 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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