LMFDB - Embedded newform 570.2.x.b.103.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(103,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("570.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.x (of order $12$, degree $4$, 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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.2
Character	$\chi$	$=$	570.103
Dual form			570.2.x.b.487.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.02196 - 1.98887i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.613926 + 0.613926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.02196 - 1.98887i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.613926 + 0.613926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.50189 + 1.65660i) q^{10} -3.43469 q^{11} +(-0.707107 - 0.707107i) q^{12} +(2.02663 + 0.543034i) q^{13} +(0.434111 - 0.751903i) q^{14} +(-1.65660 + 1.50189i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.55366 - 5.79834i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-3.87290 + 2.00016i) q^{19} +(-1.87948 - 1.21143i) q^{20} +(0.751903 + 0.434111i) q^{21} +(3.31765 - 0.888962i) q^{22} +(-0.621386 + 2.31904i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-2.91121 + 4.06508i) q^{25} -2.09812 q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.224712 + 0.838638i) q^{28} +(4.59281 + 7.95499i) q^{29} +(1.21143 - 1.87948i) q^{30} +8.09976i q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.888962 + 3.31765i) q^{33} +(3.00144 + 5.19865i) q^{34} +(1.84842 + 0.593613i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-7.31205 - 7.31205i) q^{37} +(3.22325 - 2.93439i) q^{38} -2.09812i q^{39} +(2.12898 + 0.683710i) q^{40} +(-6.91637 - 3.99317i) q^{41} +(-0.838638 - 0.224712i) q^{42} +(3.61605 - 0.968917i) q^{43} +(-2.97452 + 1.71734i) q^{44} +(1.87948 + 1.21143i) q^{45} -2.40085i q^{46} +(-7.08481 - 1.89837i) q^{47} +(-0.965926 - 0.258819i) q^{48} +6.24619i q^{49} +(1.75989 - 4.68004i) q^{50} +(-5.19865 + 3.00144i) q^{51} +(2.02663 - 0.543034i) q^{52} +(-3.31055 - 0.887059i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(3.51010 + 6.83114i) q^{55} -0.868222i q^{56} +(2.93439 + 3.22325i) q^{57} +(-6.49522 - 6.49522i) q^{58} +(-3.68131 + 6.37621i) q^{59} +(-0.683710 + 2.12898i) q^{60} +(3.34665 + 5.79656i) q^{61} +(-2.09637 - 7.82377i) q^{62} +(0.224712 - 0.838638i) q^{63} -1.00000i q^{64} +(-0.991106 - 4.58566i) q^{65} +(-1.71734 - 2.97452i) q^{66} +(1.38830 - 5.18119i) q^{67} +(-4.24468 - 4.24468i) q^{68} +2.40085 q^{69} +(-1.93908 - 0.0949781i) q^{70} +(-5.85711 - 3.38160i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-11.4942 + 3.07985i) q^{73} +(8.95539 + 5.17040i) q^{74} +(4.68004 + 1.75989i) q^{75} +(-2.35395 + 3.66864i) q^{76} +(2.10864 - 2.10864i) q^{77} +(0.543034 + 2.02663i) q^{78} +(6.09173 - 10.5512i) q^{79} +(-2.23339 - 0.109394i) q^{80} +(0.500000 - 0.866025i) q^{81} +(7.71421 + 2.06702i) q^{82} +(0.509987 + 0.509987i) q^{83} +0.868222 q^{84} +(-9.94437 + 9.01569i) q^{85} +(-3.24206 + 1.87180i) q^{86} +(6.49522 - 6.49522i) q^{87} +(2.42869 - 2.42869i) q^{88} +(-6.81651 - 11.8065i) q^{89} +(-2.12898 - 0.683710i) q^{90} +(-1.57758 + 0.910818i) q^{91} +(0.621386 + 2.31904i) q^{92} +(7.82377 - 2.09637i) q^{93} +7.33473 q^{94} +(7.93600 + 5.65861i) q^{95} +1.00000 q^{96} +(3.26511 - 0.874883i) q^{97} +(-1.61663 - 6.03336i) q^{98} +(2.97452 - 1.71734i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 20 q^{6} - 8 q^{7}+O(q^{10}) $ 40 * q + 20 * q^6 - 8 * q^7	$ 40 q + 20 q^{6} - 8 q^{7} + 12 q^{10} + 8 q^{11} + 24 q^{13} + 20 q^{16} + 36 q^{21} - 8 q^{23} + 16 q^{25} + 4 q^{28} - 4 q^{35} - 20 q^{36} + 24 q^{38} + 12 q^{41} - 4 q^{42} - 12 q^{43} - 16 q^{47} + 24 q^{52} + 72 q^{53} + 8 q^{55} - 24 q^{57} - 16 q^{58} + 12 q^{60} + 24 q^{61} - 4 q^{63} + 4 q^{66} - 36 q^{67} - 24 q^{70} - 72 q^{71} - 32 q^{73} + 8 q^{76} - 88 q^{77} + 24 q^{78} + 20 q^{81} + 8 q^{82} - 88 q^{83} - 24 q^{85} - 48 q^{86} + 16 q^{87} - 24 q^{91} + 8 q^{92} - 96 q^{95} + 40 q^{96} - 60 q^{97} - 48 q^{98}+O(q^{100}) $ 40 * q + 20 * q^6 - 8 * q^7 + 12 * q^10 + 8 * q^11 + 24 * q^13 + 20 * q^16 + 36 * q^21 - 8 * q^23 + 16 * q^25 + 4 * q^28 - 4 * q^35 - 20 * q^36 + 24 * q^38 + 12 * q^41 - 4 * q^42 - 12 * q^43 - 16 * q^47 + 24 * q^52 + 72 * q^53 + 8 * q^55 - 24 * q^57 - 16 * q^58 + 12 * q^60 + 24 * q^61 - 4 * q^63 + 4 * q^66 - 36 * q^67 - 24 * q^70 - 72 * q^71 - 32 * q^73 + 8 * q^76 - 88 * q^77 + 24 * q^78 + 20 * q^81 + 8 * q^82 - 88 * q^83 - 24 * q^85 - 48 * q^86 + 16 * q^87 - 24 * q^91 + 8 * q^92 - 96 * q^95 + 40 * q^96 - 60 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−1.02196	−	1.98887i	−0.457033	−	0.889450i
$5$	−1.02196	−	1.98887i	−0.457033	−	0.889450i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−0.613926	+	0.613926i	−0.232042	+	0.232042i	−0.813545	−	0.581502i	$-0.802465\pi$
$7$	−0.613926	+	0.613926i	−0.232042	+	0.232042i	0.581502	+	0.813545i	$0.302465\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	1.50189	+	1.65660i	0.474940	+	0.523862i
$11$	−3.43469			−1.03560			−0.517798	−	0.855503i	$-0.673248\pi$
$11$	−3.43469			−1.03560			−0.517798	+	0.855503i	$0.673248\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	2.02663	+	0.543034i	0.562086	+	0.150610i	0.528665	−	0.848831i	$-0.322693\pi$
$13$	2.02663	+	0.543034i	0.562086	+	0.150610i	0.0334215	+	0.999441i	$0.489360\pi$
$14$	0.434111	−	0.751903i	0.116021	−	0.200954i
$15$	−1.65660	+	1.50189i	−0.427732	+	0.387787i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.55366	−	5.79834i	−0.376818	−	1.40630i	−0.850670	−	0.525700i	$-0.823804\pi$
$17$	−1.55366	−	5.79834i	−0.376818	−	1.40630i	0.473852	−	0.880604i	$-0.342863\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	−3.87290	+	2.00016i	−0.888504	+	0.458869i
$19$	−3.87290	+	2.00016i	−0.888504	+	0.458869i
$20$	−1.87948	−	1.21143i	−0.420264	−	0.270885i
$21$	0.751903	+	0.434111i	0.164079	+	0.0947308i
$22$	3.31765	−	0.888962i	0.707326	−	0.189527i
$23$	−0.621386	+	2.31904i	−0.129568	+	0.483554i	−0.999961	−	0.00880293i	$-0.997198\pi$
$23$	−0.621386	+	2.31904i	−0.129568	+	0.483554i	0.870393	+	0.492357i	$0.163865\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−2.91121	+	4.06508i	−0.582241	+	0.813016i
$26$	−2.09812			−0.411476
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−0.224712	+	0.838638i	−0.0424667	+	0.158488i
$29$	4.59281	+	7.95499i	0.852864	+	1.47720i	0.878612	+	0.477536i	$0.158470\pi$
$29$	4.59281	+	7.95499i	0.852864	+	1.47720i	−0.0257482	+	0.999668i	$0.508197\pi$
$30$	1.21143	−	1.87948i	0.221176	−	0.343144i
$31$			8.09976i			1.45476i	0.686235	+	0.727380i	$0.259262\pi$
$31$			8.09976i			1.45476i	−0.686235	+	0.727380i	$0.740738\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	0.888962	+	3.31765i	0.154748	+	0.577529i
$34$	3.00144	+	5.19865i	0.514743	+	0.891561i
$35$	1.84842	+	0.593613i	0.312441	+	0.100339i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−7.31205	−	7.31205i	−1.20209	−	1.20209i	−0.973529	−	0.228564i	$-0.926597\pi$
$37$	−7.31205	−	7.31205i	−1.20209	−	1.20209i	−0.228564	−	0.973529i	$-0.573403\pi$
$38$	3.22325	−	2.93439i	0.522881	−	0.476021i
$39$		−	2.09812i		−	0.335968i
$40$	2.12898	+	0.683710i	0.336621	+	0.108104i
$41$	−6.91637	−	3.99317i	−1.08016	−	0.623628i	−0.149218	−	0.988804i	$-0.547676\pi$
$41$	−6.91637	−	3.99317i	−1.08016	−	0.623628i	−0.930939	+	0.365176i	$0.881009\pi$
$42$	−0.838638	−	0.224712i	−0.129405	−	0.0346739i
$43$	3.61605	−	0.968917i	0.551442	−	0.147758i	0.0276704	−	0.999617i	$-0.491191\pi$
$43$	3.61605	−	0.968917i	0.551442	−	0.147758i	0.523772	+	0.851859i	$0.324524\pi$
$44$	−2.97452	+	1.71734i	−0.448426	+	0.258899i
$45$	1.87948	+	1.21143i	0.280176	+	0.180590i
$46$		−	2.40085i		−	0.353986i
$47$	−7.08481	−	1.89837i	−1.03343	−	0.276905i	−0.298039	−	0.954554i	$-0.596333\pi$
$47$	−7.08481	−	1.89837i	−1.03343	−	0.276905i	−0.735386	+	0.677648i	$0.762999\pi$
$48$	−0.965926	−	0.258819i	−0.139419	−	0.0373573i
$49$			6.24619i			0.892313i
$50$	1.75989	−	4.68004i	0.248886	−	0.661858i
$51$	−5.19865	+	3.00144i	−0.727957	+	0.420286i
$52$	2.02663	−	0.543034i	0.281043	−	0.0753052i
$53$	−3.31055	−	0.887059i	−0.454739	−	0.121847i	0.0241769	−	0.999708i	$-0.492303\pi$
$53$	−3.31055	−	0.887059i	−0.454739	−	0.121847i	−0.478916	+	0.877861i	$0.658970\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	3.51010	+	6.83114i	0.473302	+	0.921111i
$56$		−	0.868222i		−	0.116021i
$57$	2.93439	+	3.22325i	0.388669	+	0.426930i
$58$	−6.49522	−	6.49522i	−0.852864	−	0.852864i
$59$	−3.68131	+	6.37621i	−0.479265	+	0.830112i	−0.999717	−	0.0237793i	$-0.992430\pi$
$59$	−3.68131	+	6.37621i	−0.479265	+	0.830112i	0.520452	+	0.853891i	$0.325763\pi$
$60$	−0.683710	+	2.12898i	−0.0882666	+	0.274850i
$61$	3.34665	+	5.79656i	0.428494	+	0.742174i	0.996740	−	0.0806853i	$-0.0257109\pi$
$61$	3.34665	+	5.79656i	0.428494	+	0.742174i	−0.568245	+	0.822859i	$0.692378\pi$
$62$	−2.09637	−	7.82377i	−0.266240	−	0.993620i
$63$	0.224712	−	0.838638i	0.0283111	−	0.105659i
$64$		−	1.00000i		−	0.125000i
$65$	−0.991106	−	4.58566i	−0.122932	−	0.568781i
$66$	−1.71734	−	2.97452i	−0.211390	−	0.366139i
$67$	1.38830	−	5.18119i	0.169607	−	0.632983i	−0.827800	−	0.561023i	$-0.810408\pi$
$67$	1.38830	−	5.18119i	0.169607	−	0.632983i	0.997408	−	0.0719600i	$-0.0229254\pi$
$68$	−4.24468	−	4.24468i	−0.514743	−	0.514743i
$69$	2.40085			0.289029
$70$	−1.93908	−	0.0949781i	−0.231764	−	0.0113521i
$71$	−5.85711	−	3.38160i	−0.695111	−	0.401323i	0.110413	−	0.993886i	$-0.464783\pi$
$71$	−5.85711	−	3.38160i	−0.695111	−	0.401323i	−0.805524	+	0.592563i	$0.798116\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	−11.4942	+	3.07985i	−1.34529	+	0.360469i	−0.858394	−	0.512991i	$-0.828538\pi$
$73$	−11.4942	+	3.07985i	−1.34529	+	0.360469i	−0.486896	+	0.873460i	$0.661871\pi$
$74$	8.95539	+	5.17040i	1.04104	+	0.601046i
$75$	4.68004	+	1.75989i	0.540405	+	0.203214i
$76$	−2.35395	+	3.66864i	−0.270016	+	0.420822i
$77$	2.10864	−	2.10864i	0.240302	−	0.240302i
$78$	0.543034	+	2.02663i	0.0614865	+	0.229471i
$79$	6.09173	−	10.5512i	0.685373	−	1.18710i	−0.287947	−	0.957646i	$-0.592973\pi$
$79$	6.09173	−	10.5512i	0.685373	−	1.18710i	0.973320	−	0.229454i	$-0.0736940\pi$
$80$	−2.23339	−	0.109394i	−0.249701	−	0.0122306i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	7.71421	+	2.06702i	0.851892	+	0.228264i
$83$	0.509987	+	0.509987i	0.0559783	+	0.0559783i	0.734542	−	0.678563i	$-0.237397\pi$
$83$	0.509987	+	0.509987i	0.0559783	+	0.0559783i	−0.678563	+	0.734542i	$0.737397\pi$
$84$	0.868222			0.0947308
$85$	−9.94437	+	9.01569i	−1.07862	+	0.977888i
$86$	−3.24206	+	1.87180i	−0.349600	+	0.201842i
$87$	6.49522	−	6.49522i	0.696361	−	0.696361i
$88$	2.42869	−	2.42869i	0.258899	−	0.258899i
$89$	−6.81651	−	11.8065i	−0.722548	−	1.25149i	−0.959975	−	0.280085i	$-0.909637\pi$
$89$	−6.81651	−	11.8065i	−0.722548	−	1.25149i	0.237427	−	0.971405i	$-0.423696\pi$
$90$	−2.12898	−	0.683710i	−0.224414	−	0.0720694i
$91$	−1.57758	+	0.910818i	−0.165376	+	0.0954797i
$92$	0.621386	+	2.31904i	0.0647840	+	0.241777i
$93$	7.82377	−	2.09637i	0.811287	−	0.217384i
$94$	7.33473			0.756520
$95$	7.93600	+	5.65861i	0.814217	+	0.580561i
$96$	1.00000			0.102062
$97$	3.26511	−	0.874883i	0.331521	−	0.0888309i	−0.0892189	−	0.996012i	$-0.528437\pi$
$97$	3.26511	−	0.874883i	0.331521	−	0.0888309i	0.420740	+	0.907181i	$0.361770\pi$
$98$	−1.61663	−	6.03336i	−0.163305	−	0.609461i
$99$	2.97452	−	1.71734i	0.298951	−	0.172599i
$100$	−0.488638	+	4.97607i	−0.0488638	+	0.497607i
$101$	−0.315763	−	0.546917i	−0.0314196	−	0.0544203i	0.849888	−	0.526963i	$-0.176669\pi$
$101$	−0.315763	−	0.546917i	−0.0314196	−	0.0544203i	−0.881308	+	0.472543i	$0.843336\pi$
$102$	4.24468	−	4.24468i	0.420286	−	0.420286i
$103$	−8.61495	+	8.61495i	−0.848856	+	0.848856i	−0.989991	−	0.141134i	$-0.954925\pi$
$103$	−8.61495	+	8.61495i	−0.848856	+	0.848856i	0.141134	+	0.989991i	$0.454925\pi$
$104$	−1.81703	+	1.04906i	−0.178174	+	0.102869i
$105$	0.0949781	−	1.93908i	0.00926892	−	0.189235i
$106$	3.42733			0.332892
$107$	1.70625	+	1.70625i	0.164949	+	0.164949i	0.784755	−	0.619806i	$-0.212789\pi$
$107$	1.70625	+	1.70625i	0.164949	+	0.164949i	−0.619806	+	0.784755i	$0.712789\pi$
$108$	0.965926	+	0.258819i	0.0929463	+	0.0249049i
$109$	8.39549	−	14.5414i	0.804142	−	1.39282i	−0.112727	−	0.993626i	$-0.535958\pi$
$109$	8.39549	−	14.5414i	0.804142	−	1.39282i	0.916869	−	0.399189i	$-0.130708\pi$
$110$	−5.15853	−	5.68989i	−0.491846	−	0.542510i
$111$	−5.17040	+	8.95539i	−0.490752	+	0.850008i
$112$	0.224712	+	0.838638i	0.0212333	+	0.0792439i
$113$	10.7091	−	10.7091i	1.00743	−	1.00743i	0.00745440	−	0.999972i	$-0.497627\pi$
$113$	10.7091	−	10.7091i	1.00743	−	1.00743i	0.999972	−	0.00745440i	$-0.00237283\pi$
$114$	−3.66864	−	2.35395i	−0.343600	−	0.220467i
$115$	5.24731	−	1.13411i	0.489314	−	0.105756i
$116$	7.95499	+	4.59281i	0.738602	+	0.426432i
$117$	−2.02663	+	0.543034i	−0.187362	+	0.0502035i
$118$	1.90558	−	7.11174i	0.175423	−	0.654688i
$119$	4.51358	+	2.60592i	0.413760	+	0.238884i
$120$	0.109394	−	2.23339i	0.00998624	−	0.203880i
$121$	0.797063			0.0724602
$122$	−4.73287	−	4.73287i	−0.428494	−	0.428494i
$123$	−2.06702	+	7.71421i	−0.186377	+	0.695567i
$124$	4.04988	+	7.01460i	0.363690	+	0.629930i
$125$	11.0600	+	1.63567i	0.989240	+	0.146299i
$126$			0.868222i			0.0773474i
$127$	0.663238	−	2.47524i	0.0588529	−	0.219642i	−0.930236	−	0.366962i	$-0.880398\pi$
$127$	0.663238	−	2.47524i	0.0588529	−	0.219642i	0.989089	+	0.147320i	$0.0470646\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−1.87180	−	3.24206i	−0.164803	−	0.285448i
$130$	2.14419	+	4.17289i	0.188058	+	0.365987i
$131$	−6.69434	+	11.5949i	−0.584887	+	1.01305i	0.410002	+	0.912085i	$0.365528\pi$
$131$	−6.69434	+	11.5949i	−0.584887	+	1.01305i	−0.994889	+	0.100970i	$0.967805\pi$
$132$	2.42869	+	2.42869i	0.211390	+	0.211390i
$133$	1.14972	−	3.60563i	0.0996935	−	0.312647i
$134$			5.36396i			0.463376i
$135$	0.683710	−	2.12898i	0.0588444	−	0.183233i
$136$	5.19865	+	3.00144i	0.445781	+	0.257372i
$137$	11.0367	+	2.95728i	0.942931	+	0.252658i	0.697360	−	0.716721i	$-0.254358\pi$
$137$	11.0367	+	2.95728i	0.942931	+	0.252658i	0.245571	+	0.969379i	$0.421025\pi$
$138$	−2.31904	+	0.621386i	−0.197410	+	0.0528959i
$139$	2.38720	−	1.37825i	0.202479	−	0.116902i	−0.395332	−	0.918538i	$-0.629370\pi$
$139$	2.38720	−	1.37825i	0.202479	−	0.116902i	0.597811	+	0.801637i	$0.296037\pi$
$140$	1.89759	−	0.410129i	0.160376	−	0.0346622i
$141$			7.33473i			0.617696i
$142$	6.53276	+	1.75045i	0.548217	+	0.146894i
$143$	−6.96084	−	1.86515i	−0.582094	−	0.155972i
$144$			1.00000i			0.0833333i
$145$	11.1278	−	17.2642i	0.924111	−	1.43371i
$146$	10.3054	−	5.94982i	0.852880	−	0.492410i
$147$	6.03336	−	1.61663i	0.497623	−	0.133338i
$148$	−9.98844	−	2.67639i	−0.821045	−	0.219998i
$149$	−1.62389	−	0.937552i	−0.133034	−	0.0768072i	0.432006	−	0.901871i	$-0.357806\pi$
$149$	−1.62389	−	0.937552i	−0.133034	−	0.0768072i	−0.565040	+	0.825064i	$0.691139\pi$
$150$	−4.97607	−	0.488638i	−0.406294	−	0.0398971i
$151$		−	20.5987i		−	1.67630i	−0.545442	−	0.838148i	$-0.683638\pi$
$151$		−	20.5987i		−	1.67630i	0.545442	−	0.838148i	$-0.316362\pi$
$152$	1.32422	−	4.15288i	0.107409	−	0.336843i
$153$	4.24468	+	4.24468i	0.343162	+	0.343162i
$154$	−1.49104	+	2.58255i	−0.120151	+	0.208108i
$155$	16.1094	−	8.27761i	1.29394	−	0.664874i
$156$	−1.04906	−	1.81703i	−0.0839921	−	0.145479i
$157$	−5.39127	−	20.1205i	−0.430270	−	1.60579i	−0.752138	−	0.659005i	$-0.770978\pi$
$157$	−5.39127	−	20.1205i	−0.430270	−	1.60579i	0.321868	−	0.946784i	$-0.395689\pi$
$158$	−3.15331	+	11.7683i	−0.250864	+	0.936237i
$159$			3.42733i			0.271805i
$160$	2.18560	−	0.472378i	0.172787	−	0.0373447i
$161$	−1.04224	−	1.80521i	−0.0821397	−	0.142270i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	8.04341	+	8.04341i	0.630008	+	0.630008i	0.948070	−	0.318062i	$-0.103032\pi$
$163$	8.04341	+	8.04341i	0.630008	+	0.630008i	−0.318062	+	0.948070i	$0.603032\pi$
$164$	−7.98634			−0.623628
$165$	5.68989	−	5.15853i	0.442958	−	0.401591i
$166$	−0.624604	−	0.360615i	−0.0484786	−	0.0279892i
$167$	−2.16746	+	8.08906i	−0.167723	+	0.625951i	0.829954	+	0.557831i	$0.188366\pi$
$167$	−2.16746	+	8.08906i	−0.167723	+	0.625951i	−0.997677	+	0.0681191i	$0.978300\pi$
$168$	−0.838638	+	0.224712i	−0.0647024	+	0.0173369i
$169$	−7.44599	−	4.29894i	−0.572768	−	0.330688i
$170$	7.27209	−	11.2823i	0.557744	−	0.865311i
$171$	2.35395	−	3.66864i	0.180011	−	0.280548i
$172$	2.64713	−	2.64713i	0.201842	−	0.201842i
$173$	−1.17612	−	4.38935i	−0.0894189	−	0.333716i	0.906695	−	0.421786i	$-0.138597\pi$
$173$	−1.17612	−	4.38935i	−0.0894189	−	0.333716i	−0.996114	+	0.0880702i	$0.971930\pi$
$174$	−4.59281	+	7.95499i	−0.348180	+	0.603066i
$175$	−0.708393	−	4.28292i	−0.0535495	−	0.323759i
$176$	−1.71734	+	2.97452i	−0.129450	+	0.224213i
$177$	7.11174	+	1.90558i	0.534551	+	0.143232i
$178$	9.64000	+	9.64000i	0.722548	+	0.722548i
$179$	10.7866			0.806229			0.403114	−	0.915150i	$-0.367928\pi$
$179$	10.7866			0.806229			0.403114	+	0.915150i	$0.367928\pi$
$180$	2.23339	+	0.109394i	0.166467	+	0.00815373i
$181$	2.11107	−	1.21883i	0.156915	−	0.0905948i	−0.419487	−	0.907762i	$-0.637790\pi$
$181$	2.11107	−	1.21883i	0.156915	−	0.0905948i	0.576401	+	0.817167i	$0.304457\pi$
$182$	1.28809	−	1.28809i	0.0954797	−	0.0954797i
$183$	4.73287	−	4.73287i	0.349864	−	0.349864i
$184$	−1.20043	−	2.07920i	−0.0884966	−	0.153281i
$185$	−7.07011	+	22.0153i	−0.519805	+	1.61860i
$186$	−7.01460	+	4.04988i	−0.514335	+	0.296952i
$187$	5.33634	+	19.9155i	0.390231	+	1.45636i
$188$	−7.08481	+	1.89837i	−0.516713	+	0.138453i
$189$	−0.868222			−0.0631539
$190$	−9.13015	−	3.41181i	−0.662370	−	0.247519i
$191$	−18.6474			−1.34928			−0.674639	−	0.738148i	$-0.735701\pi$
$191$	−18.6474			−1.34928			−0.674639	+	0.738148i	$0.735701\pi$
$192$	−0.965926	+	0.258819i	−0.0697097	+	0.0186787i
$193$	−4.77536	−	17.8219i	−0.343738	−	1.28285i	−0.894080	−	0.447908i	$-0.852169\pi$
$193$	−4.77536	−	17.8219i	−0.343738	−	1.28285i	0.550342	−	0.834939i	$-0.314497\pi$
$194$	−2.92741	+	1.69014i	−0.210176	+	0.121345i
$195$	−4.17289	+	2.14419i	−0.298827	+	0.153549i
$196$	3.12309	+	5.40936i	0.223078	+	0.386383i
$197$	8.24972	−	8.24972i	0.587768	−	0.587768i	−0.349258	−	0.937027i	$-0.613566\pi$
$197$	8.24972	−	8.24972i	0.587768	−	0.587768i	0.937027	+	0.349258i	$0.113566\pi$
$198$	−2.42869	+	2.42869i	−0.172599	+	0.172599i
$199$	−12.5164	+	7.22633i	−0.887262	+	0.512261i	−0.873046	−	0.487638i	$-0.837859\pi$
$199$	−12.5164	+	7.22633i	−0.887262	+	0.512261i	−0.0142163	+	0.999899i	$0.504525\pi$
$200$	−0.815913	−	4.93298i	−0.0576937	−	0.348814i
$201$	−5.36396			−0.378345
$202$	0.446556	+	0.446556i	0.0314196	+	0.0314196i
$203$	−7.70342	−	2.06413i	−0.540674	−	0.144873i
$204$	−3.00144	+	5.19865i	−0.210143	+	0.363978i
$205$	−0.873656	+	17.8366i	−0.0610188	+	1.24576i
$206$	6.09169	−	10.5511i	0.424428	−	0.735131i
$207$	−0.621386	−	2.31904i	−0.0431893	−	0.161185i
$208$	1.48360	−	1.48360i	0.102869	−	0.102869i
$209$	13.3022	−	6.86993i	0.920132	−	0.475203i
$210$	0.410129	+	1.89759i	0.0283016	+	0.130946i
$211$	7.87286	+	4.54540i	0.541990	+	0.312918i	0.745885	−	0.666075i	$-0.232027\pi$
$211$	7.87286	+	4.54540i	0.541990	+	0.312918i	−0.203895	+	0.978993i	$0.565360\pi$
$212$	−3.31055	+	0.887059i	−0.227370	+	0.0609235i
$213$	−1.75045	+	6.53276i	−0.119939	+	0.447617i
$214$	−2.08972	−	1.20650i	−0.142850	−	0.0824746i
$215$	−5.62250	−	6.20166i	−0.383451	−	0.422950i
$216$	−1.00000			−0.0680414
$217$	−4.97265	−	4.97265i	−0.337566	−	0.337566i
$218$	−4.34583	+	16.2188i	−0.294336	+	1.09848i
$219$	5.94982	+	10.3054i	0.402051	+	0.696373i
$220$	6.45541	+	4.16089i	0.435224	+	0.280527i
$221$		−	12.5948i		−	0.847217i
$222$	2.67639	−	9.98844i	0.179628	−	0.670380i
$223$	−1.87366	−	6.99260i	−0.125470	−	0.468259i	0.874386	−	0.485230i	$-0.161264\pi$
$223$	−1.87366	−	6.99260i	−0.125470	−	0.468259i	−0.999856	+	0.0169712i	$0.994598\pi$
$224$	−0.434111	−	0.751903i	−0.0290053	−	0.0502386i
$225$	0.488638	−	4.97607i	0.0325759	−	0.331738i
$226$	−7.57247	+	13.1159i	−0.503713	+	0.872457i
$227$	9.05115	+	9.05115i	0.600746	+	0.600746i	0.940510	−	0.339765i	$-0.110347\pi$
$227$	9.05115	+	9.05115i	0.600746	+	0.600746i	−0.339765	+	0.940510i	$0.610347\pi$
$228$	4.15288	+	1.32422i	0.275031	+	0.0876989i
$229$		−	25.8553i		−	1.70857i	−0.519808	−	0.854283i	$-0.673997\pi$
$229$		−	25.8553i		−	1.70857i	0.519808	−	0.854283i	$-0.326003\pi$
$230$	−4.77498	+	2.45357i	−0.314853	+	0.161783i
$231$	−2.58255	−	1.49104i	−0.169919	−	0.0981029i
$232$	−8.87264	−	2.37742i	−0.582517	−	0.156085i
$233$	−13.6047	+	3.64538i	−0.891276	+	0.238817i	−0.675266	−	0.737575i	$-0.735971\pi$
$233$	−13.6047	+	3.64538i	−0.891276	+	0.238817i	−0.216010	+	0.976391i	$0.569304\pi$
$234$	1.81703	−	1.04906i	0.118783	−	0.0685793i
$235$	3.46476	+	16.0308i	0.226016	+	1.04573i
$236$			7.36261i			0.479265i
$237$	−11.7683	−	3.15331i	−0.764434	−	0.204829i
$238$	−5.03425	−	1.34892i	−0.326322	−	0.0874377i
$239$			9.02234i			0.583607i	0.956478	+	0.291803i	$0.0942553\pi$
$239$			9.02234i			0.583607i	−0.956478	+	0.291803i	$0.905745\pi$
$240$	0.472378	+	2.18560i	0.0304918	+	0.141080i
$241$	−13.1064	+	7.56697i	−0.844256	+	0.487431i	−0.858709	−	0.512464i	$-0.828733\pi$
$241$	−13.1064	+	7.56697i	−0.844256	+	0.487431i	0.0144526	+	0.999896i	$0.495399\pi$
$242$	−0.769903	+	0.206295i	−0.0494913	+	0.0132611i
$243$	−0.965926	−	0.258819i	−0.0619642	−	0.0166032i
$244$	5.79656	+	3.34665i	0.371087	+	0.214247i
$245$	12.4229	−	6.38334i	0.793667	−	0.407817i
$246$		−	7.98634i		−	0.509190i
$247$	−8.93509	+	1.95047i	−0.568526	+	0.124106i
$248$	−5.72740	−	5.72740i	−0.363690	−	0.363690i
$249$	0.360615	−	0.624604i	0.0228531	−	0.0395826i
$250$	−11.1065	+	1.28261i	−0.702438	+	0.0811196i
$251$	6.82936	+	11.8288i	0.431066	+	0.746628i	0.996965	−	0.0778465i	$-0.0248044\pi$
$251$	6.82936	+	11.8288i	0.431066	+	0.746628i	−0.565900	+	0.824474i	$0.691471\pi$
$252$	−0.224712	−	0.838638i	−0.0141556	−	0.0528293i
$253$	2.13427	−	7.96519i	0.134180	−	0.500767i
$254$			2.56256i			0.160789i
$255$	11.2823	+	7.27209i	0.706524	+	0.455396i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.22862	+	4.58526i	−0.0766389	+	0.286020i	−0.993600	−	0.112956i	$-0.963968\pi$
$257$	−1.22862	+	4.58526i	−0.0766389	+	0.286020i	0.916961	+	0.398977i	$0.130635\pi$
$258$	2.64713	+	2.64713i	0.164803	+	0.164803i
$259$	8.97811			0.557873
$260$	−3.15115	−	3.47575i	−0.195426	−	0.215557i
$261$	−7.95499	−	4.59281i	−0.492401	−	0.284288i
$262$	3.46525	−	12.9325i	0.214084	−	0.798971i
$263$	−20.4875	+	5.48962i	−1.26332	+	0.338504i	−0.827466	−	0.561516i	$-0.810218\pi$
$263$	−20.4875	+	5.48962i	−1.26332	+	0.338504i	−0.435849	+	0.900020i	$0.643552\pi$
$264$	−2.97452	−	1.71734i	−0.183069	−	0.105695i
$265$	1.61900	+	7.49079i	0.0994541	+	0.460156i
$266$	−0.177341	+	3.78034i	−0.0108735	+	0.231787i
$267$	−9.64000	+	9.64000i	−0.589958	+	0.589958i
$268$	−1.38830	−	5.18119i	−0.0848036	−	0.316491i
$269$	−10.6663	+	18.4746i	−0.650337	+	1.12642i	0.332705	+	0.943031i	$0.392039\pi$
$269$	−10.6663	+	18.4746i	−0.650337	+	1.12642i	−0.983041	+	0.183385i	$0.941295\pi$
$270$	−0.109394	+	2.23339i	−0.00665749	+	0.135920i
$271$	−2.34724	+	4.06555i	−0.142585	+	0.246964i	−0.928469	−	0.371409i	$-0.878875\pi$
$271$	−2.34724	+	4.06555i	−0.142585	+	0.246964i	0.785884	+	0.618373i	$0.212208\pi$
$272$	−5.79834	−	1.55366i	−0.351576	−	0.0942045i
$273$	1.28809	+	1.28809i	0.0779588	+	0.0779588i
$274$	−11.4261			−0.690273
$275$	9.99908	−	13.9623i	0.602967	−	0.841957i
$276$	2.07920	−	1.20043i	0.125153	−	0.0722571i
$277$	−9.13094	+	9.13094i	−0.548625	+	0.548625i	−0.926043	−	0.377418i	$-0.876812\pi$
$277$	−9.13094	+	9.13094i	−0.548625	+	0.548625i	0.377418	+	0.926043i	$0.376812\pi$
$278$	−1.94914	+	1.94914i	−0.116902	+	0.116902i
$279$	−4.04988	−	7.01460i	−0.242460	−	0.419953i
$280$	−1.72678	+	0.887286i	−0.103195	+	0.0530255i
$281$	−16.0448	+	9.26345i	−0.957150	+	0.552611i	−0.895295	−	0.445474i	$-0.853035\pi$
$281$	−16.0448	+	9.26345i	−0.957150	+	0.552611i	−0.0618554	+	0.998085i	$0.519702\pi$
$282$	−1.89837	−	7.08481i	−0.113046	−	0.421894i
$283$	−4.26152	+	1.14187i	−0.253321	+	0.0678771i	−0.383245	−	0.923647i	$-0.625193\pi$
$283$	−4.26152	+	1.14187i	−0.253321	+	0.0678771i	0.129924	+	0.991524i	$0.458527\pi$
$284$	−6.76321			−0.401323
$285$	3.41181	−	9.13015i	0.202098	−	0.540823i
$286$	7.20639			0.426123
$287$	6.69765	−	1.79463i	0.395350	−	0.105934i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	−16.4845	+	9.51731i	−0.969674	+	0.559842i
$290$	−6.28031	+	19.5560i	−0.368792	+	1.14837i
$291$	−1.69014	−	2.92741i	−0.0990780	−	0.171608i
$292$	−8.41431	+	8.41431i	−0.492410	+	0.492410i
$293$	12.4994	−	12.4994i	0.730225	−	0.730225i	−0.240439	−	0.970664i	$-0.577292\pi$
$293$	12.4994	−	12.4994i	0.730225	−	0.730225i	0.970664	+	0.240439i	$0.0772916\pi$
$294$	−5.40936	+	3.12309i	−0.315480	+	0.182143i
$295$	16.4436	+	0.805424i	0.957382	+	0.0468936i
$296$	10.3408			0.601046
$297$	−2.42869	−	2.42869i	−0.140927	−	0.140927i
$298$	1.81121	+	0.485313i	0.104921	+	0.0281134i
$299$	−2.51864	+	4.36241i	−0.145657	+	0.252285i
$300$	4.93298	−	0.815913i	0.284806	−	0.0471067i
$301$	−1.62514	+	2.81483i	−0.0936717	+	0.162244i
$302$	5.33133	+	19.8968i	0.306784	+	1.14493i
$303$	−0.446556	+	0.446556i	−0.0256540	+	0.0256540i
$304$	−0.204258	+	4.35411i	−0.0117150	+	0.249725i
$305$	8.10848	−	12.5799i	0.464290	−	0.720322i
$306$	−5.19865	−	3.00144i	−0.297187	−	0.171581i
$307$	−22.3007	+	5.97544i	−1.27277	+	0.341037i	−0.831090	−	0.556138i	$-0.812283\pi$
$307$	−22.3007	+	5.97544i	−1.27277	+	0.341037i	−0.441676	+	0.897175i	$0.645616\pi$
$308$	0.771817	−	2.88046i	0.0439783	−	0.164129i
$309$	10.5511	+	6.09169i	0.600232	+	0.346544i
$310$	−13.4181	+	12.1650i	−0.762094	+	0.690924i
$311$	11.8891			0.674169			0.337084	−	0.941474i	$-0.390559\pi$
$311$	11.8891			0.674169			0.337084	+	0.941474i	$0.390559\pi$
$312$	1.48360	+	1.48360i	0.0839921	+	0.0839921i
$313$	2.47206	−	9.22586i	0.139729	−	0.521477i	−0.860204	−	0.509950i	$-0.829664\pi$
$313$	2.47206	−	9.22586i	0.139729	−	0.521477i	0.999934	−	0.0115271i	$-0.00366927\pi$
$314$	10.4151	+	18.0395i	0.587760	+	1.01803i
$315$	−1.89759	+	0.410129i	−0.106917	+	0.0231081i
$316$		−	12.1835i		−	0.685373i
$317$	1.88878	−	7.04900i	0.106084	−	0.395912i	−0.892382	−	0.451281i	$-0.850967\pi$
$317$	1.88878	−	7.04900i	0.106084	−	0.395912i	0.998466	+	0.0553698i	$0.0176338\pi$
$318$	−0.887059	−	3.31055i	−0.0497438	−	0.185646i
$319$	−15.7749	−	27.3229i	−0.883223	−	1.52979i
$320$	−1.98887	+	1.02196i	−0.111181	+	0.0571292i
$321$	1.20650	−	2.08972i	0.0673402	−	0.116637i
$322$	1.47394	+	1.47394i	0.0821397	+	0.0821397i
$323$	17.6148	+	19.3488i	0.980113	+	1.07660i
$324$		−	1.00000i		−	0.0555556i
$325$	−8.10741	+	6.65753i	−0.449718	+	0.369293i
$326$	−9.85112	−	5.68755i	−0.545603	−	0.315004i
$327$	−16.2188	−	4.34583i	−0.896904	−	0.240325i
$328$	7.71421	−	2.06702i	0.425946	−	0.114132i
$329$	5.51500	−	3.18409i	0.304052	−	0.175545i
$330$	−4.16089	+	6.45541i	−0.229050	+	0.355359i
$331$		−	28.8103i		−	1.58356i	−0.610809	−	0.791778i	$-0.709156\pi$
$331$		−	28.8103i		−	1.58356i	0.610809	−	0.791778i	$-0.290844\pi$
$332$	0.696655	+	0.186668i	0.0382339	+	0.0102447i
$333$	9.98844	+	2.67639i	0.547363	+	0.146666i
$334$		−	8.37441i		−	0.458228i
$335$	−11.7235	+	2.53382i	−0.640523	+	0.138437i
$336$	0.751903	−	0.434111i	0.0410197	−	0.0236827i
$337$	−18.1892	+	4.87377i	−0.990827	+	0.265491i	−0.717598	−	0.696458i	$-0.754758\pi$
$337$	−18.1892	+	4.87377i	−0.990827	+	0.265491i	−0.273229	+	0.961949i	$0.588092\pi$
$338$	8.30492	+	2.22530i	0.451728	+	0.121040i
$339$	−13.1159	−	7.57247i	−0.712358	−	0.411280i
$340$	−4.10423	+	12.7800i	−0.222583	+	0.693093i
$341$		−	27.8201i		−	1.50654i
$342$	−1.32422	+	4.15288i	−0.0716059	+	0.224562i
$343$	−8.13218	−	8.13218i	−0.439096	−	0.439096i
$344$	−1.87180	+	3.24206i	−0.100921	+	0.174800i
$345$	−2.45357	−	4.77498i	−0.132096	−	0.257076i
$346$	2.27209	+	3.93538i	0.122148	+	0.211567i
$347$	−3.59302	−	13.4093i	−0.192883	−	0.719850i	−0.992805	−	0.119745i	$-0.961792\pi$
$347$	−3.59302	−	13.4093i	−0.192883	−	0.719850i	0.799921	−	0.600105i	$-0.204874\pi$
$348$	2.37742	−	8.87264i	0.127443	−	0.475623i
$349$			4.57374i			0.244827i	0.992479	+	0.122413i	$0.0390633\pi$
$349$			4.57374i			0.244827i	−0.992479	+	0.122413i	$0.960937\pi$
$350$	1.79276	+	3.95364i	0.0958269	+	0.211331i
$351$	1.04906	+	1.81703i	0.0559947	+	0.0969857i
$352$	0.888962	−	3.31765i	0.0473818	−	0.176831i
$353$	25.5016	+	25.5016i	1.35731	+	1.35731i	0.877217	+	0.480093i	$0.159397\pi$
$353$	25.5016	+	25.5016i	1.35731	+	1.35731i	0.480093	+	0.877217i	$0.340603\pi$
$354$	−7.36261			−0.391318
$355$	−0.739853	+	15.1049i	−0.0392673	+	0.801684i
$356$	−11.8065	−	6.81651i	−0.625745	−	0.361274i
$357$	1.34892	−	5.03425i	0.0713926	−	0.266441i
$358$	−10.4191	+	2.79178i	−0.550665	+	0.147550i
$359$	−17.8973	−	10.3330i	−0.944582	−	0.545354i	−0.0531880	−	0.998585i	$-0.516938\pi$
$359$	−17.8973	−	10.3330i	−0.944582	−	0.545354i	−0.891394	+	0.453230i	$0.850272\pi$
$360$	−2.18560	+	0.472378i	−0.115191	+	0.0248965i
$361$	10.9987	−	15.4929i	0.578879	−	0.815414i
$362$	−1.72368	+	1.72368i	−0.0905948	+	0.0905948i
$363$	−0.206295	−	0.769903i	−0.0108277	−	0.0404094i
$364$	−0.910818	+	1.57758i	−0.0477398	+	0.0826878i
$365$	17.8720	+	19.7129i	0.935462	+	1.03182i
$366$	−3.34665	+	5.79656i	−0.174932	+	0.302991i
$367$	4.28460	+	1.14806i	0.223655	+	0.0599280i	0.368906	−	0.929467i	$-0.379732\pi$
$367$	4.28460	+	1.14806i	0.223655	+	0.0599280i	−0.145251	+	0.989395i	$0.546399\pi$
$368$	1.69766	+	1.69766i	0.0884966	+	0.0884966i
$369$	7.98634			0.415752
$370$	1.13122	−	23.0950i	0.0588093	−	1.20065i
$371$	2.57702	−	1.48784i	0.133792	−	0.0772450i
$372$	5.72740	−	5.72740i	0.296952	−	0.296952i
$373$	−14.0859	+	14.0859i	−0.729339	+	0.729339i	−0.970488	−	0.241149i	$-0.922476\pi$
$373$	−14.0859	+	14.0859i	−0.729339	+	0.729339i	0.241149	+	0.970488i	$0.422476\pi$
$374$	−10.3090	−	17.8557i	−0.533066	−	0.923298i
$375$	−1.28261	−	11.1065i	−0.0662339	−	0.573538i
$376$	6.35206	−	3.66737i	0.327583	−	0.189130i
$377$	4.98811	+	18.6159i	0.256901	+	0.958766i
$378$	0.838638	−	0.224712i	0.0431349	−	0.0115580i
$379$	3.48826			0.179180			0.0895900	−	0.995979i	$-0.471444\pi$
$379$	3.48826			0.179180			0.0895900	+	0.995979i	$0.471444\pi$
$380$	9.70208	+	0.932500i	0.497706	+	0.0478363i
$381$	−2.56256			−0.131284
$382$	18.0120	−	4.82630i	0.921574	−	0.246935i
$383$	−4.70488	−	17.5589i	−0.240408	−	0.897216i	−0.975636	−	0.219396i	$-0.929591\pi$
$383$	−4.70488	−	17.5589i	−0.240408	−	0.897216i	0.735228	−	0.677820i	$-0.237075\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	−6.34876	−	2.03887i	−0.323563	−	0.103911i
$386$	9.22528	+	15.9787i	0.469555	+	0.813292i
$387$	−2.64713	+	2.64713i	−0.134561	+	0.134561i
$388$	2.39022	−	2.39022i	0.121345	−	0.121345i
$389$	19.5339	−	11.2779i	0.990410	−	0.571813i	0.0850132	−	0.996380i	$-0.472907\pi$
$389$	19.5339	−	11.2779i	0.990410	−	0.571813i	0.905397	+	0.424566i	$0.139573\pi$
$390$	3.47575	−	3.15115i	0.176001	−	0.159565i
$391$	14.4120			0.728848
$392$	−4.41672	−	4.41672i	−0.223078	−	0.223078i
$393$	12.9325	+	3.46525i	0.652357	+	0.174799i
$394$	−5.83344	+	10.1038i	−0.293884	+	0.509022i
$395$	−27.2104	−	1.33279i	−1.36910	−	0.0670601i
$396$	1.71734	−	2.97452i	0.0862997	−	0.149475i
$397$	4.70104	+	17.5445i	0.235939	+	0.880535i	0.977724	+	0.209897i	$0.0673128\pi$
$397$	4.70104	+	17.5445i	0.235939	+	0.880535i	−0.741785	+	0.670638i	$0.766021\pi$
$398$	10.2196	−	10.2196i	0.512261	−	0.512261i
$399$	−3.78034	−	0.177341i	−0.189254	−	0.00887817i
$400$	2.06486	+	4.55372i	0.103243	+	0.227686i
$401$	25.5333	+	14.7417i	1.27507	+	0.736165i	0.975939	−	0.218046i	$-0.0699682\pi$
$401$	25.5333	+	14.7417i	1.27507	+	0.736165i	0.299136	+	0.954210i	$0.403302\pi$
$402$	5.18119	−	1.38830i	0.258414	−	0.0692419i
$403$	−4.39845	+	16.4152i	−0.219102	+	0.817700i
$404$	−0.546917	−	0.315763i	−0.0272102	−	0.0157098i
$405$	−2.23339	−	0.109394i	−0.110978	−	0.00543582i
$406$	7.97517			0.395801
$407$	25.1146	+	25.1146i	1.24488	+	1.24488i
$408$	1.55366	−	5.79834i	0.0769177	−	0.287061i
$409$	−5.03256	−	8.71666i	−0.248844	−	0.431011i	0.714361	−	0.699777i	$-0.246717\pi$
$409$	−5.03256	−	8.71666i	−0.248844	−	0.431011i	−0.963205	+	0.268766i	$0.913384\pi$
$410$	−3.77257	−	17.4550i	−0.186314	−	0.862039i
$411$		−	11.4261i		−	0.563606i
$412$	−3.15329	+	11.7682i	−0.155352	+	0.579780i
$413$	−1.65447	−	6.17457i	−0.0814112	−	0.303831i
$414$	1.20043	+	2.07920i	0.0589977	+	0.102187i
$415$	0.493112	−	1.53548i	0.0242059	−	0.0753738i
$416$	−1.04906	+	1.81703i	−0.0514344	+	0.0890871i
$417$	−1.94914	−	1.94914i	−0.0954497	−	0.0954497i
$418$	−11.0709	+	10.0787i	−0.541493	+	0.492965i
$419$			23.4141i			1.14385i	0.820305	+	0.571927i	$0.193804\pi$
$419$			23.4141i			1.14385i	−0.820305	+	0.571927i	$0.806196\pi$
$420$	−0.887286	−	1.72678i	−0.0432951	−	0.0842583i
$421$	34.3191	+	19.8141i	1.67261	+	0.965682i	0.966168	+	0.257912i	$0.0830345\pi$
$421$	34.3191	+	19.8141i	1.67261	+	0.965682i	0.706443	+	0.707770i	$0.250299\pi$
$422$	−8.78104	−	2.35287i	−0.427454	−	0.114536i
$423$	7.08481	−	1.89837i	0.344475	−	0.0923018i
$424$	2.96816	−	1.71367i	0.144147	−	0.0832230i
$425$	28.0937	+	10.5644i	1.36275	+	0.512449i
$426$		−	6.76321i		−	0.327679i
$427$	−5.61325	−	1.50407i	−0.271644	−	0.0727869i
$428$	2.33078	+	0.624530i	0.112662	+	0.0301878i
$429$			7.20639i			0.347928i
$430$	7.03602	+	4.53513i	0.339307	+	0.218703i
$431$	−22.2597	+	12.8516i	−1.07221	+	0.619042i	−0.928785	−	0.370619i	$-0.879146\pi$
$431$	−22.2597	+	12.8516i	−1.07221	+	0.619042i	−0.143427	+	0.989661i	$0.545812\pi$
$432$	0.965926	−	0.258819i	0.0464731	−	0.0124524i
$433$	−13.4524	−	3.60456i	−0.646481	−	0.173224i	−0.0793436	−	0.996847i	$-0.525282\pi$
$433$	−13.4524	−	3.60456i	−0.646481	−	0.173224i	−0.567137	+	0.823623i	$0.691949\pi$
$434$	6.09023	+	3.51620i	0.292341	+	0.168783i
$435$	−19.5560	−	6.28031i	−0.937638	−	0.301118i
$436$		−	16.7910i		−	0.804142i
$437$	−2.23190	−	10.2243i	−0.106766	−	0.489094i
$438$	−8.41431	−	8.41431i	−0.402051	−	0.402051i
$439$	14.6188	−	25.3205i	0.697716	−	1.20848i	−0.271540	−	0.962427i	$-0.587533\pi$
$439$	14.6188	−	25.3205i	0.697716	−	1.20848i	0.969256	−	0.246053i	$-0.0791338\pi$
$440$	−7.31236	−	2.34833i	−0.348603	−	0.111952i
$441$	−3.12309	−	5.40936i	−0.148719	−	0.257589i
$442$	3.25977	+	12.1656i	0.155051	+	0.578660i
$443$	−6.81750	+	25.4433i	−0.323909	+	1.20885i	0.591495	+	0.806309i	$0.298538\pi$
$443$	−6.81750	+	25.4433i	−0.323909	+	1.20885i	−0.915404	+	0.402537i	$0.868129\pi$
$444$			10.3408i			0.490752i
$445$	−16.5155	+	25.6229i	−0.782909	+	1.21464i
$446$	3.61964	+	6.26940i	0.171395	+	0.296864i
$447$	−0.485313	+	1.81121i	−0.0229545	+	0.0856673i
$448$	0.613926	+	0.613926i	0.0290053	+	0.0290053i
$449$	−5.29306			−0.249795			−0.124898	−	0.992170i	$-0.539860\pi$
$449$	−5.29306			−0.249795			−0.124898	+	0.992170i	$0.539860\pi$
$450$	0.815913	+	4.93298i	0.0384625	+	0.232543i
$451$	23.7556	+	13.7153i	1.11861	+	0.645827i
$452$	3.91980	−	14.6289i	0.184372	−	0.688085i
$453$	−19.8968	+	5.33133i	−0.934833	+	0.250488i
$454$	−11.0853	−	6.40013i	−0.520261	−	0.300373i
$455$	3.42372	+	2.20679i	0.160507	+	0.103456i
$456$	−4.35411	−	0.204258i	−0.203900	−	0.00956526i
$457$	2.27360	−	2.27360i	0.106355	−	0.106355i	−0.651927	−	0.758282i	$-0.726039\pi$
$457$	2.27360	−	2.27360i	0.106355	−	0.106355i	0.758282	+	0.651927i	$0.226039\pi$
$458$	6.69184	+	24.9743i	0.312689	+	1.16697i
$459$	3.00144	−	5.19865i	0.140095	−	0.242652i
$460$	3.97725	−	3.60582i	0.185440	−	0.168122i
$461$	1.46637	−	2.53982i	0.0682956	−	0.118291i	−0.829856	−	0.557978i	$-0.811577\pi$
$461$	1.46637	−	2.53982i	0.0682956	−	0.118291i	0.898151	+	0.439687i	$0.144911\pi$
$462$	2.88046	+	0.771817i	0.134011	+	0.0359082i
$463$	9.36466	+	9.36466i	0.435213	+	0.435213i	0.890397	−	0.455184i	$-0.150427\pi$
$463$	9.36466	+	9.36466i	0.435213	+	0.435213i	−0.455184	+	0.890397i	$0.650427\pi$
$464$	9.18563			0.426432
$465$	−12.1650	−	13.4181i	−0.564137	−	0.622247i
$466$	12.1977	−	7.04233i	0.565046	−	0.326230i
$467$	−28.8274	+	28.8274i	−1.33397	+	1.33397i	−0.432191	+	0.901782i	$0.642259\pi$
$467$	−28.8274	+	28.8274i	−1.33397	+	1.33397i	−0.901782	+	0.432191i	$0.857741\pi$
$468$	−1.48360	+	1.48360i	−0.0685793	+	0.0685793i
$469$	2.32856	+	4.03318i	0.107523	+	0.186235i
$470$	−7.49578	−	14.5878i	−0.345755	−	0.672886i
$471$	−18.0395	+	10.4151i	−0.831218	+	0.479904i
$472$	−1.90558	−	7.11174i	−0.0877116	−	0.327344i
$473$	−12.4200	+	3.32793i	−0.571072	+	0.153018i
$474$	12.1835			0.559604
$475$	3.14399	−	21.5665i	0.144256	−	0.989540i
$476$	5.21184			0.238884
$477$	3.31055	−	0.887059i	0.151580	−	0.0406157i
$478$	−2.33515	−	8.71491i	−0.106807	−	0.398611i
$479$	5.07080	−	2.92763i	0.231691	−	0.133767i	−0.379661	−	0.925126i	$-0.623959\pi$
$479$	5.07080	−	2.92763i	0.231691	−	0.133767i	0.611352	+	0.791359i	$0.290626\pi$
$480$	−1.02196	−	1.98887i	−0.0466458	−	0.0907791i
$481$	−10.8481	−	18.7895i	−0.494632	−	0.856727i
$482$	10.7013	−	10.7013i	0.487431	−	0.487431i
$483$	−1.47394	+	1.47394i	−0.0670668	+	0.0670668i
$484$	0.690276	−	0.398531i	0.0313762	−	0.0181151i
$485$	−5.07683	−	5.59978i	−0.230527	−	0.254273i
$486$	1.00000			0.0453609
$487$	11.5436	+	11.5436i	0.523092	+	0.523092i	0.918504	−	0.395412i	$-0.129398\pi$
$487$	11.5436	+	11.5436i	0.523092	+	0.523092i	−0.395412	+	0.918504i	$0.629398\pi$
$488$	−6.46523	−	1.73235i	−0.292667	−	0.0784199i
$489$	5.68755	−	9.85112i	0.257200	−	0.445483i
$490$	−10.3474	+	9.38111i	−0.467449	+	0.423795i
$491$	16.6098	−	28.7690i	0.749590	−	1.29833i	−0.198429	−	0.980115i	$-0.563584\pi$
$491$	16.6098	−	28.7690i	0.749590	−	1.29833i	0.948019	−	0.318213i	$-0.103083\pi$
$492$	2.06702	+	7.71421i	0.0931883	+	0.347784i
$493$	38.9900	−	38.9900i	1.75602	−	1.75602i
$494$	8.12581	−	4.19658i	0.365598	−	0.188813i
$495$	−6.45541	−	4.16089i	−0.290149	−	0.187018i
$496$	7.01460	+	4.04988i	0.314965	+	0.181845i
$497$	5.67189	−	1.51978i	0.254419	−	0.0681713i
$498$	−0.186668	+	0.696655i	−0.00836480	+	0.0312178i
$499$	2.88335	+	1.66470i	0.129076	+	0.0745222i	0.563148	−	0.826356i	$-0.309590\pi$
$499$	2.88335	+	1.66470i	0.129076	+	0.0745222i	−0.434072	+	0.900878i	$0.642923\pi$
$500$	10.3961	−	4.11349i	0.464928	−	0.183961i
$501$	8.37441			0.374141
$502$	−9.65818	−	9.65818i	−0.431066	−	0.431066i
$503$	7.34618	−	27.4163i	0.327550	−	1.22243i	−0.584174	−	0.811629i	$-0.698581\pi$
$503$	7.34618	−	27.4163i	0.327550	−	1.22243i	0.911724	−	0.410804i	$-0.134752\pi$
$504$	0.434111	+	0.751903i	0.0193368	+	0.0334924i
$505$	−0.765051	+	1.18694i	−0.0340443	+	0.0528180i
$506$			8.24617i			0.366587i
$507$	−2.22530	+	8.30492i	−0.0988289	+	0.368834i
$508$	−0.663238	−	2.47524i	−0.0294264	−	0.109821i
$509$	0.324841	+	0.562642i	0.0143983	+	0.0249386i	0.873135	−	0.487479i	$-0.162083\pi$
$509$	0.324841	+	0.562642i	0.0143983	+	0.0249386i	−0.858736	+	0.512417i	$0.828750\pi$
$510$	−12.7800	−	4.10423i	−0.565908	−	0.181739i
$511$	5.16576	−	8.94737i	0.228520	−	0.395808i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−4.15288	−	1.32422i	−0.183354	−	0.0584660i
$514$		−	4.74701i		−	0.209381i
$515$	25.9381	+	8.32990i	1.14297	+	0.367059i
$516$	−3.24206	−	1.87180i	−0.142724	−	0.0824016i
$517$	24.3341	+	6.52030i	1.07021	+	0.286762i
$518$	−8.67219	+	2.32371i	−0.381034	+	0.102098i
$519$	−3.93538	+	2.27209i	−0.172744	+	0.0997338i
$520$	3.94337	+	2.54173i	0.172928	+	0.111462i
$521$			24.3018i			1.06468i	0.846530	+	0.532341i	$0.178687\pi$
$521$			24.3018i			1.06468i	−0.846530	+	0.532341i	$0.821313\pi$
$522$	8.87264	+	2.37742i	0.388345	+	0.104057i
$523$	17.2183	+	4.61362i	0.752902	+	0.201739i	0.614805	−	0.788679i	$-0.289235\pi$
$523$	17.2183	+	4.61362i	0.752902	+	0.201739i	0.138097	+	0.990419i	$0.455901\pi$
$524$			13.3887i			0.584887i
$525$	−3.95364	+	1.79276i	−0.172551	+	0.0782424i
$526$	18.3686	−	10.6051i	0.800910	−	0.462405i
$527$	46.9652	−	12.5843i	2.04584	−	0.548180i
$528$	3.31765	+	0.888962i	0.144382	+	0.0386871i
$529$	14.9267	+	8.61796i	0.648989	+	0.374694i
$530$	−3.50259	−	6.81652i	−0.152143	−	0.296091i
$531$		−	7.36261i		−	0.319510i
$532$	−0.807124	−	3.69742i	−0.0349933	−	0.160304i
$533$	−11.8485	−	11.8485i	−0.513216	−	0.513216i
$534$	6.81651	−	11.8065i	0.294979	−	0.510919i
$535$	1.64979	−	5.13722i	0.0713267	−	0.222101i
$536$	2.68198	+	4.64533i	0.115844	+	0.200648i
$537$	−2.79178	−	10.4191i	−0.120474	−	0.449616i
$538$	5.52129	−	20.6057i	0.238040	−	0.888376i
$539$		−	21.4537i		−	0.924076i
$540$	−0.472378	−	2.18560i	−0.0203279	−	0.0940534i
$541$	12.0869	+	20.9352i	0.519657	+	0.900073i	0.999739	+	0.0228492i	$0.00727375\pi$
$541$	12.0869	+	20.9352i	0.519657	+	0.900073i	−0.480082	+	0.877224i	$0.659393\pi$
$542$	1.21502	−	4.53453i	0.0521897	−	0.194775i
$543$	−1.72368	−	1.72368i	−0.0739703	−	0.0739703i
$544$	6.00288			0.257372
$545$	−37.5008	−	1.83683i	−1.60636	−	0.0786811i
$546$	−1.57758	−	0.910818i	−0.0675143	−	0.0389794i
$547$	−2.03188	+	7.58307i	−0.0868768	+	0.324229i	−0.995663	−	0.0930335i	$-0.970344\pi$
$547$	−2.03188	+	7.58307i	−0.0868768	+	0.324229i	0.908786	+	0.417262i	$0.137010\pi$
$548$	11.0367	−	2.95728i	0.471465	−	0.126329i
$549$	−5.79656	−	3.34665i	−0.247391	−	0.142831i
$550$	−6.04466	+	16.0745i	−0.257745	+	0.685418i
$551$	−33.6988	−	21.6225i	−1.43562	−	0.921149i
$552$	−1.69766	+	1.69766i	−0.0722571	+	0.0722571i
$553$	2.73777	+	10.2175i	0.116422	+	0.434493i
$554$	6.45655	−	11.1831i	0.274312	−	0.475123i
$555$	23.0950	+	1.13122i	0.980330	+	0.0480176i
$556$	1.37825	−	2.38720i	0.0584508	−	0.101240i
$557$	−22.8766	−	6.12976i	−0.969312	−	0.259726i	−0.260775	−	0.965400i	$-0.583978\pi$
$557$	−22.8766	−	6.12976i	−0.969312	−	0.259726i	−0.708537	+	0.705673i	$0.750645\pi$
$558$	5.72740	+	5.72740i	0.242460	+	0.242460i
$559$	7.85455			0.332212
$560$	1.43830	−	1.30398i	0.0607791	−	0.0551031i
$561$	17.8557	−	10.3090i	0.753869	−	0.435247i
$562$	13.1005	−	13.1005i	0.552611	−	0.552611i
$563$	−10.8352	+	10.8352i	−0.456650	+	0.456650i	−0.897554	−	0.440904i	$-0.854658\pi$
$563$	−10.8352	+	10.8352i	−0.456650	+	0.456650i	0.440904	+	0.897554i	$0.354658\pi$
$564$	3.66737	+	6.35206i	0.154424	+	0.267470i
$565$	−32.2432	−	10.3548i	−1.35648	−	0.435628i
$566$	3.82077	−	2.20592i	0.160599	−	0.0927219i
$567$	0.224712	+	0.838638i	0.00943704	+	0.0352195i
$568$	6.53276	−	1.75045i	0.274108	−	0.0734471i
$569$	7.17316			0.300714			0.150357	−	0.988632i	$-0.451958\pi$
$569$	7.17316			0.300714			0.150357	+	0.988632i	$0.451958\pi$
$570$	−0.932500	+	9.70208i	−0.0390581	+	0.406376i
$571$	−7.60097			−0.318091			−0.159045	−	0.987271i	$-0.550842\pi$
$571$	−7.60097			−0.318091			−0.159045	+	0.987271i	$0.550842\pi$
$572$	−6.96084	+	1.86515i	−0.291047	+	0.0779859i
$573$	4.82630	+	18.0120i	0.201622	+	0.752462i
$574$	−6.00495	+	3.46696i	−0.250642	+	0.144708i
$575$	−7.61812	−	9.27720i	−0.317698	−	0.386886i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−12.8271	+	12.8271i	−0.534000	+	0.534000i	−0.921760	−	0.387760i	$-0.873249\pi$
$577$	−12.8271	+	12.8271i	−0.534000	+	0.534000i	0.387760	+	0.921760i	$0.373249\pi$
$578$	13.4595	−	13.4595i	0.559842	−	0.559842i
$579$	−15.9787	+	9.22528i	−0.664050	+	0.383390i
$580$	1.00485	−	20.5151i	0.0417242	−	0.851843i
$581$	−0.626188			−0.0259787
$582$	2.39022	+	2.39022i	0.0990780	+	0.0990780i
$583$	11.3707	+	3.04677i	0.470926	+	0.126184i
$584$	5.94982	−	10.3054i	0.246205	−	0.426440i
$585$	3.15115	+	3.47575i	0.130284	+	0.143704i
$586$	−8.83843	+	15.3086i	−0.365112	+	0.632393i
$587$	−0.511523	−	1.90903i	−0.0211128	−	0.0787941i	0.954566	−	0.298001i	$-0.0963198\pi$
$587$	−0.511523	−	1.90903i	−0.0211128	−	0.0787941i	−0.975678	+	0.219207i	$0.929653\pi$
$588$	4.41672	−	4.41672i	0.182143	−	0.182143i
$589$	−16.2008	−	31.3696i	−0.667544	−	1.29256i
$590$	−16.0917	+	3.47793i	−0.662487	+	0.143184i
$591$	−10.1038	−	5.83344i	−0.415615	−	0.239955i
$592$	−9.98844	+	2.67639i	−0.410522	+	0.109999i
$593$	5.62151	−	20.9798i	0.230848	−	0.861535i	−0.749129	−	0.662424i	$-0.769528\pi$
$593$	5.62151	−	20.9798i	0.230848	−	0.861535i	0.979977	−	0.199111i	$-0.0638056\pi$
$594$	2.97452	+	1.71734i	0.122046	+	0.0704634i
$595$	0.570143	−	11.6401i	0.0233736	−	0.477196i
$596$	−1.87510			−0.0768072
$597$	10.2196	+	10.2196i	0.418259	+	0.418259i
$598$	1.30374	−	4.86564i	0.0533140	−	0.198971i
$599$	−18.3712	−	31.8198i	−0.750626	−	1.30012i	−0.947520	−	0.319697i	$-0.896419\pi$
$599$	−18.3712	−	31.8198i	−0.750626	−	1.30012i	0.196894	−	0.980425i	$-0.436915\pi$
$600$	−4.55372	+	2.06486i	−0.185905	+	0.0842976i
$601$			8.49788i			0.346636i	0.984866	+	0.173318i	$0.0554488\pi$
$601$			8.49788i			0.346636i	−0.984866	+	0.173318i	$0.944551\pi$
$602$	0.841236	−	3.13953i	0.0342862	−	0.127958i
$603$	1.38830	+	5.18119i	0.0565358	+	0.210994i
$604$	−10.2993	−	17.8390i	−0.419074	−	0.725858i
$605$	−0.814564	−	1.58525i	−0.0331167	−	0.0644497i
$606$	0.315763	−	0.546917i	0.0128270	−	0.0222170i
$607$	−13.4891	−	13.4891i	−0.547506	−	0.547506i	0.378212	−	0.925719i	$-0.376539\pi$
$607$	−13.4891	−	13.4891i	−0.547506	−	0.547506i	−0.925719	+	0.378212i	$0.876539\pi$
$608$	−0.929629	−	4.25861i	−0.0377014	−	0.172710i
$609$			7.97517i			0.323170i
$610$	−4.57627	+	14.2499i	−0.185288	+	0.576960i
$611$	−13.3274	−	7.69458i	−0.539169	−	0.311289i
$612$	5.79834	+	1.55366i	0.234384	+	0.0628030i
$613$	−1.37465	+	0.368335i	−0.0555215	+	0.0148769i	−0.286473	−	0.958088i	$-0.592483\pi$
$613$	−1.37465	+	0.368335i	−0.0555215	+	0.0148769i	0.230951	+	0.972965i	$0.425816\pi$
$614$	19.9942	−	11.5437i	0.806901	−	0.465865i
$615$	17.4550	−	3.77257i	0.703852	−	0.152125i
$616$			2.98207i			0.120151i
$617$	0.940845	+	0.252099i	0.0378770	+	0.0101491i	0.277708	−	0.960666i	$-0.410425\pi$
$617$	0.940845	+	0.252099i	0.0378770	+	0.0101491i	−0.239831	+	0.970815i	$0.577092\pi$
$618$	−11.7682	−	3.15329i	−0.473388	−	0.126844i
$619$			29.5159i			1.18634i	0.805076	+	0.593171i	$0.202124\pi$
$619$			29.5159i			1.18634i	−0.805076	+	0.593171i	$0.797876\pi$
$620$	9.81232	−	15.2233i	0.394072	−	0.611383i
$621$	−2.07920	+	1.20043i	−0.0834353	+	0.0481714i
$622$	−11.4840	+	3.07712i	−0.460466	+	0.123381i
$623$	11.4332	+	3.06351i	0.458060	+	0.122737i
$624$	−1.81703	−	1.04906i	−0.0727393	−	0.0419960i
$625$	−8.04976	−	23.6686i	−0.321990	−	0.946743i
$626$			9.55132i			0.381747i
$627$	−10.0787	−	11.0709i	−0.402505	−	0.442128i
$628$	−14.7292	−	14.7292i	−0.587760	−	0.587760i
$629$	−31.0373	+	53.7582i	−1.23754	+	2.14348i
$630$	1.72678	−	0.887286i	0.0687966	−	0.0353503i
$631$	16.9218	+	29.3094i	0.673646	+	1.16679i	0.976863	+	0.213867i	$0.0686059\pi$
$631$	16.9218	+	29.3094i	0.673646	+	1.16679i	−0.303217	+	0.952922i	$0.598061\pi$
$632$	3.15331	+	11.7683i	0.125432	+	0.468118i
$633$	2.35287	−	8.78104i	0.0935183	−	0.349015i
$634$			7.29767i			0.289827i
$635$	−5.60073	+	1.21049i	−0.222258	+	0.0480370i
$636$	1.71367	+	2.96816i	0.0679513	+	0.117695i
$637$	−3.39189	+	12.6587i	−0.134392	+	0.501557i
$638$	22.3090	+	22.3090i	0.883223	+	0.883223i
$639$	6.76321			0.267548
$640$	1.65660	−	1.50189i	0.0654828	−	0.0593675i
$641$	18.2235	+	10.5214i	0.719787	+	0.415569i	0.814674	−	0.579919i	$-0.196916\pi$
$641$	18.2235	+	10.5214i	0.719787	+	0.415569i	−0.0948875	+	0.995488i	$0.530249\pi$
$642$	−0.624530	+	2.33078i	−0.0246482	+	0.0919885i
$643$	−38.7893	+	10.3936i	−1.52970	+	0.409882i	−0.922921	−	0.384989i	$-0.874205\pi$
$643$	−38.7893	+	10.3936i	−1.52970	+	0.409882i	−0.606779	+	0.794871i	$0.707539\pi$
$644$	−1.80521	−	1.04224i	−0.0711351	−	0.0410699i
$645$	−4.53513	+	7.03602i	−0.178571	+	0.277043i
$646$	−22.0224	−	14.1305i	−0.866461	−	0.555956i
$647$	18.3048	−	18.3048i	0.719635	−	0.719635i	−0.248895	−	0.968530i	$-0.580067\pi$
$647$	18.3048	−	18.3048i	0.719635	−	0.719635i	0.968530	+	0.248895i	$0.0800675\pi$
$648$	0.258819	+	0.965926i	0.0101674	+	0.0379452i
$649$	12.6441	−	21.9003i	0.496325	−	0.859661i
$650$	6.10806	−	8.52903i	0.239578	−	0.334536i
$651$	−3.51620	+	6.09023i	−0.137811	+	0.238695i
$652$	10.9875	+	2.94409i	0.430304	+	0.115300i
$653$	25.0858	+	25.0858i	0.981683	+	0.981683i	0.999835	−	0.0181523i	$-0.00577837\pi$
$653$	25.0858	+	25.0858i	0.981683	+	0.981683i	−0.0181523	+	0.999835i	$0.505778\pi$
$654$	16.7910			0.656579
$655$	29.9022	+	1.46464i	1.16837	+	0.0572282i
$656$	−6.91637	+	3.99317i	−0.270039	+	0.155907i
$657$	8.41431	−	8.41431i	0.328274	−	0.328274i
$658$	−4.50298	+	4.50298i	−0.175545	+	0.175545i
$659$	7.77987	+	13.4751i	0.303061	+	0.524917i	0.976828	−	0.214027i	$-0.0686581\pi$
$659$	7.77987	+	13.4751i	0.303061	+	0.524917i	−0.673767	+	0.738944i	$0.735325\pi$
$660$	2.34833	−	7.31236i	0.0914086	−	0.284633i
$661$	−17.3474	+	10.0156i	−0.674737	+	0.389560i	−0.797869	−	0.602831i	$-0.794039\pi$
$661$	−17.3474	+	10.0156i	−0.674737	+	0.389560i	0.123132	+	0.992390i	$0.460706\pi$
$662$	7.45665	+	27.8286i	0.289811	+	1.08159i
$663$	−12.1656	+	3.25977i	−0.472474	+	0.126599i
$664$	−0.721230			−0.0279892
$665$	−8.34609	+	1.39815i	−0.323647	+	0.0542179i
$666$	−10.3408			−0.400698
$667$	−21.3019	+	5.70782i	−0.824812	+	0.221008i
$668$	2.16746	+	8.08906i	0.0838615	+	0.312975i
$669$	−6.26940	+	3.61964i	−0.242389	+	0.139943i
$670$	10.6682	−	5.48174i	0.412149	−	0.211778i
$671$	−11.4947	−	19.9094i	−0.443747	−	0.768593i
$672$	−0.613926	+	0.613926i	−0.0236827	+	0.0236827i
$673$	−18.3228	+	18.3228i	−0.706292	+	0.706292i	−0.965753	−	0.259462i	$-0.916455\pi$
$673$	−18.3228	+	18.3228i	−0.706292	+	0.706292i	0.259462	+	0.965753i	$0.416455\pi$
$674$	16.3080	−	9.41540i	0.628159	−	0.362668i
$675$	−4.93298	+	0.815913i	−0.189870	+	0.0314045i
$676$	−8.59789			−0.330688
$677$	−27.4272	−	27.4272i	−1.05411	−	1.05411i	−0.998450	−	0.0556615i	$-0.982273\pi$
$677$	−27.4272	−	27.4272i	−1.05411	−	1.05411i	−0.0556615	−	0.998450i	$-0.517727\pi$
$678$	14.6289	+	3.91980i	0.561819	+	0.150539i
$679$	−1.46742	+	2.54165i	−0.0563144	+	0.0975395i
$680$	0.656678	−	13.4068i	0.0251825	−	0.514127i
$681$	6.40013	−	11.0853i	0.245253	−	0.424791i
$682$	7.20038	+	26.8722i	0.275717	+	1.02899i
$683$	−0.411760	+	0.411760i	−0.0157556	+	0.0157556i	−0.714941	−	0.699185i	$-0.753546\pi$
$683$	−0.411760	+	0.411760i	−0.0157556	+	0.0157556i	0.699185	+	0.714941i	$0.253546\pi$
$684$	0.204258	−	4.35411i	0.00781000	−	0.166484i
$685$	−5.39741	−	24.9728i	−0.206225	−	0.954162i
$686$	9.95984	+	5.75032i	0.380269	+	0.219548i
$687$	−24.9743	+	6.69184i	−0.952829	+	0.255310i
$688$	0.968917	−	3.61605i	0.0369396	−	0.137861i
$689$	−6.22756	−	3.59548i	−0.237251	−	0.136977i
$690$	3.60582	+	3.97725i	0.137271	+	0.151411i
$691$	23.4429			0.891809			0.445904	−	0.895081i	$-0.352882\pi$
$691$	23.4429			0.891809			0.445904	+	0.895081i	$0.352882\pi$
$692$	−3.21322	−	3.21322i	−0.122148	−	0.122148i
$693$	−0.771817	+	2.88046i	−0.0293189	+	0.109420i
$694$	6.94118	+	12.0225i	0.263483	+	0.456367i
$695$	−5.18077	−	3.33931i	−0.196518	−	0.126667i
$696$			9.18563i			0.348180i
$697$	−12.4081	+	46.3075i	−0.469989	+	1.75402i
$698$	−1.18377	−	4.41789i	−0.0448064	−	0.167220i
$699$	7.04233	+	12.1977i	0.266365	+	0.461358i
$700$	−2.75495	−	3.35492i	−0.104127	−	0.126804i
$701$	−12.7019	+	22.0003i	−0.479744	+	0.830940i	−0.999730	−	0.0232343i	$-0.992604\pi$
$701$	−12.7019	+	22.0003i	−0.479744	+	0.830940i	0.519987	+	0.854174i	$0.325937\pi$
$702$	−1.48360	−	1.48360i	−0.0559947	−	0.0559947i
$703$	42.9441	+	13.6935i	1.61967	+	0.516462i
$704$			3.43469i			0.129450i
$705$	14.5878	−	7.49578i	0.549409	−	0.282308i
$706$	−31.2329	−	18.0323i	−1.17547	−	0.678655i
$707$	0.529622	+	0.141912i	0.0199185	+	0.00533714i
$708$	7.11174	−	1.90558i	0.267275	−	0.0716162i
$709$	33.2345	−	19.1880i	1.24815	−	0.720619i	0.277409	−	0.960752i	$-0.410524\pi$
$709$	33.2345	−	19.1880i	1.24815	−	0.720619i	0.970740	+	0.240133i	$0.0771909\pi$
$710$	−3.19479	−	14.7817i	−0.119898	−	0.554747i
$711$			12.1835i			0.456915i
$712$	13.1685	+	3.52848i	0.493510	+	0.132236i
$713$	−18.7837	−	5.03308i	−0.703455	−	0.188490i
$714$			5.21184i			0.195048i
$715$	3.40414	+	15.7503i	0.127307	+	0.589028i
$716$	9.34148	−	5.39330i	0.349107	−	0.201557i
$717$	8.71491	−	2.33515i	0.325464	−	0.0872079i
$718$	19.9618	+	5.34875i	0.744968	+	0.199614i
$719$	−13.4949	−	7.79129i	−0.503275	−	0.290566i	0.226790	−	0.973944i	$-0.427177\pi$
$719$	−13.4949	−	7.79129i	−0.503275	−	0.290566i	−0.730065	+	0.683378i	$0.760510\pi$
$720$	1.98887	−	1.02196i	0.0741208	−	0.0380861i
$721$		−	10.5779i		−	0.393941i
$722$	−6.61408	+	17.8116i	−0.246151	+	0.662880i
$723$	10.7013	+	10.7013i	0.397986	+	0.397986i
$724$	1.21883	−	2.11107i	0.0452974	−	0.0784574i
$725$	−45.7083	−	4.48845i	−1.69756	−	0.166697i
$726$	0.398531	+	0.690276i	0.0147909	+	0.0256186i
$727$	2.98632	+	11.1451i	0.110757	+	0.413349i	0.998934	−	0.0461506i	$-0.0146954\pi$
$727$	2.98632	+	11.1451i	0.110757	+	0.413349i	−0.888178	+	0.459500i	$0.848029\pi$
$728$	0.471474	−	1.75957i	0.0174740	−	0.0652138i
$729$			1.00000i			0.0370370i
$730$	−22.3651	−	14.4156i	−0.827769	−	0.533546i
$731$	−11.2362	−	19.4617i	−0.415587	−	0.719817i
$732$	1.73235	−	6.46523i	0.0640296	−	0.238962i
$733$	−32.4470	−	32.4470i	−1.19846	−	1.19846i	−0.974629	−	0.223828i	$-0.928144\pi$
$733$	−32.4470	−	32.4470i	−1.19846	−	1.19846i	−0.223828	−	0.974629i	$-0.571856\pi$
$734$	−4.43575			−0.163726
$735$	−9.38111	−	10.3474i	−0.346027	−	0.381671i
$736$	−2.07920	−	1.20043i	−0.0766403	−	0.0442483i
$737$	−4.76836	+	17.7958i	−0.175645	+	0.655515i
$738$	−7.71421	+	2.06702i	−0.283964	+	0.0760880i
$739$	−1.07249	−	0.619204i	−0.0394523	−	0.0227778i	0.480144	−	0.877190i	$-0.340584\pi$
$739$	−1.07249	−	0.619204i	−0.0394523	−	0.0227778i	−0.519596	+	0.854412i	$0.673918\pi$
$740$	4.88476	+	22.6009i	0.179567	+	0.830824i
$741$	4.19658	+	8.12581i	0.154165	+	0.298509i
$742$	−2.10413	+	2.10413i	−0.0772450	+	0.0772450i
$743$	5.77539	+	21.5541i	0.211879	+	0.790742i	0.987242	+	0.159227i	$0.0509001\pi$
$743$	5.77539	+	21.5541i	0.211879	+	0.790742i	−0.775363	+	0.631515i	$0.782433\pi$
$744$	−4.04988	+	7.01460i	−0.148476	+	0.257168i
$745$	−0.205125	+	4.18784i	−0.00751519	+	0.153431i
$746$	9.96022	−	17.2516i	0.364670	−	0.631626i
$747$	−0.696655	−	0.186668i	−0.0254893	−	0.00682983i
$748$	14.5791	+	14.5791i	0.533066	+	0.533066i
$749$	−2.09502			−0.0765504
$750$	4.11349	+	10.3961i	0.150203	+	0.379612i
$751$	20.9019	−	12.0677i	0.762721	−	0.440357i	−0.0675506	−	0.997716i	$-0.521518\pi$
$751$	20.9019	−	12.0677i	0.762721	−	0.440357i	0.830272	+	0.557358i	$0.188185\pi$
$752$	−5.18644	+	5.18644i	−0.189130	+	0.189130i
$753$	9.65818	−	9.65818i	0.351964	−	0.351964i
$754$	−9.63628	−	16.6905i	−0.350933	−	0.607833i
$755$	−40.9681	+	21.0510i	−1.49098	+	0.766123i
$756$	−0.751903	+	0.434111i	−0.0273464	+	0.0157885i
$757$	7.33374	+	27.3699i	0.266549	+	0.994775i	0.961295	+	0.275520i	$0.0888500\pi$
$757$	7.33374	+	27.3699i	0.266549	+	0.994775i	−0.694746	+	0.719255i	$0.744483\pi$
$758$	−3.36940	+	0.902829i	−0.122382	+	0.0327922i
$759$	−8.24617			−0.299317
$760$	−9.61284	+	1.61036i	−0.348694	+	0.0584138i
$761$	18.5587			0.672752			0.336376	−	0.941728i	$-0.390799\pi$
$761$	18.5587			0.672752			0.336376	+	0.941728i	$0.390799\pi$
$762$	2.47524	−	0.663238i	0.0896685	−	0.0240266i
$763$	3.77314	+	14.0816i	0.136597	+	0.509787i
$764$	−16.1491	+	9.32369i	−0.584254	+	0.337319i
$765$	4.10423	−	12.7800i	0.148389	−	0.462062i
$766$	9.08914	+	15.7428i	0.328404	+	0.568812i
$767$	−10.9231	+	10.9231i	−0.394412	+	0.394412i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	−17.7686	+	10.2587i	−0.640752	+	0.369938i	−0.784904	−	0.619617i	$-0.787288\pi$
$769$	−17.7686	+	10.2587i	−0.640752	+	0.369938i	0.144152	+	0.989556i	$0.453954\pi$
$770$	6.66013	+	0.326220i	0.240014	+	0.0117562i
$771$	4.74701			0.170959
$772$	−13.0465	−	13.0465i	−0.469555	−	0.469555i
$773$	3.57868	+	0.958905i	0.128716	+	0.0344894i	0.322602	−	0.946535i	$-0.395442\pi$
$773$	3.57868	+	0.958905i	0.128716	+	0.0344894i	−0.193886	+	0.981024i	$0.562109\pi$
$774$	1.87180	−	3.24206i	0.0672806	−	0.116533i
$775$	−32.9262	−	23.5801i	−1.18274	−	0.847021i
$776$	−1.69014	+	2.92741i	−0.0606726	+	0.105088i
$777$	−2.32371	−	8.67219i	−0.0833625	−	0.311113i
$778$	−15.9494	+	15.9494i	−0.571813	+	0.571813i
$779$	34.7734	+	1.63127i	1.24589	+	0.0584465i
$780$	−2.54173	+	3.94337i	−0.0910087	+	0.141195i
$781$	20.1173	+	11.6147i	0.719855	+	0.415608i
$782$	−13.9210	+	3.73011i	−0.497812	+	0.133388i
$783$	−2.37742	+	8.87264i	−0.0849619	+	0.317082i
$784$	5.40936	+	3.12309i	0.193191	+	0.111539i
$785$	−34.5074	+	31.2848i	−1.23162	+	1.11660i
$786$	−13.3887			−0.477559
$787$	−28.3253	−	28.3253i	−1.00969	−	1.00969i	−0.999953	−	0.00973546i	$-0.996901\pi$
$787$	−28.3253	−	28.3253i	−1.00969	−	1.00969i	−0.00973546	−	0.999953i	$-0.503099\pi$
$788$	3.01961	−	11.2693i	0.107569	−	0.401453i
$789$	10.6051	+	18.3686i	0.377552	+	0.653940i
$790$	26.6282	−	5.75519i	0.947388	−	0.204761i
$791$			13.1492i			0.467531i
$792$	−0.888962	+	3.31765i	−0.0315879	+	0.117888i
$793$	3.63469	+	13.5648i	0.129071	+	0.481701i
$794$	−9.08172	−	15.7300i	−0.322298	−	0.558237i
$795$	6.81652	−	3.50259i	0.241757	−	0.124224i
$796$	−7.22633	+	12.5164i	−0.256131	+	0.443631i
$797$	−5.21830	−	5.21830i	−0.184842	−	0.184842i	0.608620	−	0.793462i	$-0.291723\pi$
$797$	−5.21830	−	5.21830i	−0.184842	−	0.184842i	−0.793462	+	0.608620i	$0.791723\pi$
$798$	3.69742	−	0.807124i	0.130887	−	0.0285719i
$799$			44.0295i			1.55765i
$800$	−3.17309	−	3.86413i	−0.112186	−	0.136618i
$801$	11.8065	+	6.81651i	0.417164	+	0.240849i
$802$	−28.4787	−	7.63086i	−1.00562	−	0.269455i
$803$	39.4788	−	10.5783i	1.39318	−	0.373301i
$804$	−4.64533	+	2.68198i	−0.163828	+	0.0945862i
$805$	−2.52520	+	3.91772i	−0.0890016	+	0.138081i
$806$		−	16.9943i		−	0.598598i
$807$	20.6057	+	5.52129i	0.725356	+	0.194359i
$808$	0.610007	+	0.163451i	0.0214600	+	0.00575018i
$809$		−	16.8017i		−	0.590717i	−0.955386	−	0.295359i	$-0.904561\pi$
$809$		−	16.8017i		−	0.590717i	0.955386	−	0.295359i	$-0.0954391\pi$
$810$	2.18560	−	0.472378i	0.0767943	−	0.0165977i
$811$	26.0252	−	15.0257i	0.913869	−	0.527623i	0.0321952	−	0.999482i	$-0.489750\pi$
$811$	26.0252	−	15.0257i	0.913869	−	0.527623i	0.881674	+	0.471859i	$0.156417\pi$
$812$	−7.70342	+	2.06413i	−0.270337	+	0.0724366i
$813$	4.53453	+	1.21502i	0.159033	+	0.0426127i
$814$	−30.7589	−	17.7587i	−1.07810	−	0.622442i
$815$	7.77727	−	24.2173i	0.272426	−	0.848295i
$816$			6.00288i			0.210143i
$817$	−12.0666	+	10.9852i	−0.422157	+	0.384324i
$818$	7.11712	+	7.11712i	0.248844	+	0.248844i
$819$	0.910818	−	1.57758i	0.0318266	−	0.0551252i
$820$	8.16170	+	15.8838i	0.285019	+	0.554686i
$821$	−6.60085	−	11.4330i	−0.230371	−	0.399015i	0.727546	−	0.686059i	$-0.240661\pi$
$821$	−6.60085	−	11.4330i	−0.230371	−	0.399015i	−0.957917	+	0.287044i	$0.907327\pi$
$822$	2.95728	+	11.0367i	0.103147	+	0.384950i
$823$	8.86779	−	33.0951i	0.309112	−	1.15362i	−0.620236	−	0.784415i	$-0.712963\pi$
$823$	8.86779	−	33.0951i	0.309112	−	1.15362i	0.929348	−	0.369206i	$-0.120370\pi$
$824$		−	12.1834i		−	0.424428i
$825$	−16.0745	−	6.04466i	−0.559641	−	0.210448i
$826$	3.19619	+	5.53597i	0.111210	+	0.192621i
$827$	7.85091	−	29.3000i	0.273003	−	1.01886i	−0.684165	−	0.729327i	$-0.739833\pi$
$827$	7.85091	−	29.3000i	0.273003	−	1.01886i	0.957168	−	0.289534i	$-0.0935002\pi$
$828$	−1.69766	−	1.69766i	−0.0589977	−	0.0589977i
$829$	33.5350			1.16472			0.582359	−	0.812932i	$-0.302130\pi$
$829$	33.5350			1.16472			0.582359	+	0.812932i	$0.302130\pi$
$830$	−0.0788981	+	1.61079i	−0.00273859	+	0.0559113i
$831$	11.1831	+	6.45655i	0.387936	+	0.223975i
$832$	0.543034	−	2.02663i	0.0188263	−	0.0702608i
$833$	36.2175	−	9.70446i	1.25486	−	0.336240i
$834$	2.38720	+	1.37825i	0.0826619	+	0.0477248i
$835$	18.3031	−	3.95589i	0.633406	−	0.136899i
$836$	8.08507	−	12.6006i	0.279628	−	0.435802i
$837$	−5.72740	+	5.72740i	−0.197968	+	0.197968i
$838$	−6.06001	−	22.6163i	−0.209340	−	0.781266i
$839$	26.0625	−	45.1416i	0.899777	−	1.55846i	0.0719990	−	0.997405i	$-0.477062\pi$
$839$	26.0625	−	45.1416i	0.899777	−	1.55846i	0.827778	−	0.561055i	$-0.189605\pi$
$840$	1.30398	+	1.43830i	0.0449915	+	0.0496259i
$841$	−27.6879	+	47.9568i	−0.954755	+	1.65368i
$842$	−38.2780	−	10.2566i	−1.31915	−	0.353464i
$843$	13.1005	+	13.1005i	0.451205	+	0.451205i
$844$	9.09080			0.312918
$845$	−0.940555	+	19.2024i	−0.0323561	+	0.660584i
$846$	−6.35206	+	3.66737i	−0.218388	+	0.126087i
$847$	−0.489337	+	0.489337i	−0.0168138	+	0.0168138i
$848$	−2.42349	+	2.42349i	−0.0832230	+	0.0832230i
$849$	2.20592	+	3.82077i	0.0757071	+	0.131129i
$850$	−29.8707	−	2.93324i	−1.02456	−	0.100609i
$851$	21.5006	−	12.4134i	0.737030	−	0.425524i
$852$	1.75045	+	6.53276i	0.0599693	+	0.223809i
$853$	−19.0817	+	5.11294i	−0.653346	+	0.175064i	−0.570241	−	0.821477i	$-0.693150\pi$
$853$	−19.0817	+	5.11294i	−0.653346	+	0.175064i	−0.0831050	+	0.996541i	$0.526484\pi$
$854$	5.81127			0.198858
$855$	−9.70208	−	0.932500i	−0.331804	−	0.0318908i
$856$	−2.41300			−0.0824746
$857$	−8.39996	+	2.25076i	−0.286937	+	0.0768846i	−0.399417	−	0.916769i	$-0.630787\pi$
$857$	−8.39996	+	2.25076i	−0.286937	+	0.0768846i	0.112480	+	0.993654i	$0.464121\pi$
$858$	−1.86515	−	6.96084i	−0.0636752	−	0.237639i
$859$	−37.9093	+	21.8869i	−1.29345	+	0.746773i	−0.979264	−	0.202589i	$-0.935064\pi$
$859$	−37.9093	+	21.8869i	−1.29345	+	0.746773i	−0.314185	+	0.949362i	$0.601731\pi$
$860$	−7.97005	−	2.55954i	−0.271777	−	0.0872797i
$861$	−3.46696	−	6.00495i	−0.118154	−	0.204648i
$862$	18.1750	−	18.1750i	0.619042	−	0.619042i
$863$	−14.4173	+	14.4173i	−0.490772	+	0.490772i	−0.908549	−	0.417778i	$-0.862809\pi$
$863$	−14.4173	+	14.4173i	−0.490772	+	0.490772i	0.417778	+	0.908549i	$0.362809\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	−7.52789	+	6.82488i	−0.255956	+	0.232053i
$866$	13.9269			0.473257
$867$	13.4595	+	13.4595i	0.457109	+	0.457109i
$868$	−6.79277	−	1.82012i	−0.230562	−	0.0617788i
$869$	−20.9232	+	36.2400i	−0.709770	+	1.22936i
$870$	20.5151	+	1.00485i	0.695527	+	0.0340676i
$871$	5.62712	−	9.74646i	0.190668	−	0.330246i
$872$	4.34583	+	16.2188i	0.147168	+	0.549239i
$873$	−2.39022	+	2.39022i	−0.0808968	+	0.0808968i
$874$	4.80209	+	9.29826i	0.162433	+	0.314518i
$875$	−7.79423	+	5.78587i	−0.263493	+	0.195598i
$876$	10.3054	+	5.94982i	0.348187	+	0.201026i
$877$	32.9368	−	8.82539i	1.11220	−	0.298012i	0.344475	−	0.938795i	$-0.388057\pi$
$877$	32.9368	−	8.82539i	1.11220	−	0.298012i	0.767722	+	0.640783i	$0.221390\pi$
$878$	−7.56724	+	28.2413i	−0.255382	+	0.953098i
$879$	−15.3086	−	8.83843i	−0.516347	−	0.298113i
$880$	7.67099	+	0.375733i	0.258589	+	0.0126660i
$881$	−25.2086			−0.849298			−0.424649	−	0.905358i	$-0.639602\pi$
$881$	−25.2086			−0.849298			−0.424649	+	0.905358i	$0.639602\pi$
$882$	4.41672	+	4.41672i	0.148719	+	0.148719i
$883$	6.62717	−	24.7329i	0.223022	−	0.832330i	−0.760165	−	0.649730i	$-0.774882\pi$
$883$	6.62717	−	24.7329i	0.223022	−	0.832330i	0.983187	−	0.182600i	$-0.0584513\pi$
$884$	−6.29739	−	10.9074i	−0.211804	−	0.366856i
$885$	−3.47793	−	16.0917i	−0.116909	−	0.540918i
$886$		−	26.3408i		−	0.884936i
$887$	1.04505	−	3.90017i	0.0350892	−	0.130955i	−0.946159	−	0.323701i	$-0.895073\pi$
$887$	1.04505	−	3.90017i	0.0350892	−	0.130955i	0.981249	+	0.192746i	$0.0617394\pi$
$888$	−2.67639	−	9.98844i	−0.0898139	−	0.335190i
$889$	1.11243	+	1.92679i	0.0373099	+	0.0646226i
$890$	9.32103	−	29.0244i	0.312442	−	0.972899i
$891$	−1.71734	+	2.97452i	−0.0575331	+	0.0996503i
$892$	−5.11894	−	5.11894i	−0.171395	−	0.171395i
$893$	31.2358	−	6.81858i	1.04527	−	0.228175i
$894$		−	1.87510i		−	0.0627129i
$895$	−11.0235	−	21.4532i	−0.368473	−	0.717100i
$896$	−0.751903	−	0.434111i	−0.0251193	−	0.0145026i
$897$	4.86564	+	1.30374i	0.162459	+	0.0435307i
$898$	5.11271	−	1.36995i	0.170613	−	0.0457157i
$899$	−64.4335	+	37.2007i	−2.14898	+	1.24071i
$900$	−2.06486	−	4.55372i	−0.0688287	−	0.151791i
$901$			20.5739i			0.685416i
$902$	−26.4959	−	7.09955i	−0.882217	−	0.236389i
$903$	3.13953	+	0.841236i	0.104477	+	0.0279946i
$904$			15.1449i			0.503713i
$905$	−4.58152	−	2.95306i	−0.152295	−	0.0981629i
$906$	17.8390	−	10.2993i	0.592660	−	0.342173i
$907$	49.3062	−	13.2116i	1.63718	−	0.438682i	0.681200	−	0.732098i	$-0.261459\pi$
$907$	49.3062	−	13.2116i	1.63718	−	0.438682i	0.955985	+	0.293415i	$0.0947919\pi$
$908$	12.3641	+	3.31295i	0.410317	+	0.109944i
$909$	0.546917	+	0.315763i	0.0181401	+	0.0104732i
$910$	−3.87822	−	1.24547i	−0.128562	−	0.0412870i
$911$		−	14.6706i		−	0.486059i	−0.970019	−	0.243029i	$-0.921859\pi$
$911$		−	14.6706i		−	0.486059i	0.970019	−	0.243029i	$-0.0781411\pi$
$912$	4.25861	−	0.929629i	0.141017	−	0.0307831i
$913$	−1.75164	−	1.75164i	−0.0579710	−	0.0579710i
$914$	−1.60768	+	2.78458i	−0.0531773	+	0.0921057i
$915$	−14.2499	−	4.57627i	−0.471086	−	0.151287i
$916$	−12.9276	−	22.3913i	−0.427142	−	0.739831i
$917$	−3.00860	−	11.2283i	−0.0993529	−	0.370790i
$918$	−1.55366	+	5.79834i	−0.0512784	+	0.191374i
$919$		−	43.7927i		−	1.44459i	−0.691587	−	0.722293i	$-0.743088\pi$
$919$		−	43.7927i		−	1.44459i	0.691587	−	0.722293i	$-0.256912\pi$
$920$	−2.90847	+	4.51234i	−0.0958894	+	0.148768i
$921$	11.5437	+	19.9942i	0.380377	+	0.658832i
$922$	−0.759048	+	2.83281i	−0.0249979	+	0.0932935i
$923$	−10.0339	−	10.0339i	−0.330269	−	0.330269i
$924$	−2.98207			−0.0981029
$925$	51.0109	−	8.43718i	1.67723	−	0.277413i
$926$	−11.4693	−	6.62182i	−0.376905	−	0.217606i
$927$	3.15329	−	11.7682i	0.103568	−	0.386520i
$928$	−8.87264	+	2.37742i	−0.291259	+	0.0780425i
$929$	−6.78461	−	3.91710i	−0.222596	−	0.128516i	0.384556	−	0.923102i	$-0.374355\pi$
$929$	−6.78461	−	3.91710i	−0.222596	−	0.128516i	−0.607152	+	0.794586i	$0.707688\pi$
$930$	15.2233	+	9.81232i	0.499192	+	0.321759i
$931$	−12.4934	−	24.1909i	−0.409455	−	0.792824i
$932$	−9.95936	+	9.95936i	−0.326230	+	0.326230i
$933$	−3.07712	−	11.4840i	−0.100741	−	0.375969i
$934$	20.3841	−	35.3062i	0.666987	−	1.15525i
$935$	34.1558	−	30.9660i	1.11701	−	1.01270i
$936$	1.04906	−	1.81703i	0.0342896	−	0.0593914i
$937$	0.445277	+	0.119312i	0.0145466	+	0.00389774i	0.266085	−	0.963950i	$-0.414270\pi$
$937$	0.445277	+	0.119312i	0.0145466	+	0.00389774i	−0.251538	+	0.967847i	$0.580936\pi$
$938$	−3.29307	−	3.29307i	−0.107523	−	0.107523i
$939$	−9.55132			−0.311695
$940$	11.0160	+	12.1507i	0.359302	+	0.396312i
$941$	−2.70036	+	1.55906i	−0.0880294	+	0.0508238i	−0.543368	−	0.839494i	$-0.682851\pi$
$941$	−2.70036	+	1.55906i	−0.0880294	+	0.0508238i	0.455339	+	0.890318i	$0.349518\pi$
$942$	14.7292	−	14.7292i	0.479904	−	0.479904i
$943$	13.5581	−	13.5581i	0.441512	−	0.441512i
$944$	3.68131	+	6.37621i	0.119816	+	0.207528i
$945$	0.887286	+	1.72678i	0.0288634	+	0.0561722i
$946$	11.1355	−	6.42906i	0.362045	−	0.209027i
$947$	2.46054	+	9.18285i	0.0799567	+	0.298402i	0.994311	−	0.106512i	$-0.0339681\pi$
$947$	2.46054	+	9.18285i	0.0799567	+	0.298402i	−0.914355	+	0.404914i	$0.867301\pi$
$948$	−11.7683	+	3.15331i	−0.382217	+	0.102415i
$949$	−24.9669			−0.810459
$950$	2.54497	+	21.6454i	0.0825698	+	0.702269i
$951$	−7.29767			−0.236643
$952$	−5.03425	+	1.34892i	−0.163161	+	0.0437188i
$953$	−3.80552	−	14.2024i	−0.123273	−	0.460061i	0.876499	−	0.481403i	$-0.159873\pi$
$953$	−3.80552	−	14.2024i	−0.123273	−	0.460061i	−0.999772	+	0.0213423i	$0.993206\pi$
$954$	−2.96816	+	1.71367i	−0.0960977	+	0.0554820i
$955$	19.0568	+	37.0872i	0.616665	+	1.20011i
$956$	4.51117	+	7.81357i	0.145902	+	0.252709i
$957$	−22.3090	+	22.3090i	−0.721149	+	0.721149i
$958$	−4.14029	+	4.14029i	−0.133767	+	0.133767i
$959$	−8.59128	+	4.96018i	−0.277427	+	0.160173i
$960$	1.50189	+	1.65660i	0.0484734	+	0.0534665i
$961$	−34.6062			−1.11633
$962$	15.3416	+	15.3416i	0.494632	+	0.494632i
$963$	−2.33078	−	0.624530i	−0.0751083	−	0.0201252i
$964$	−7.56697	+	13.1064i	−0.243716	+	0.422128i
$965$	−30.5652	+	27.7108i	−0.983928	+	0.892041i
$966$	1.04224	−	1.80521i	0.0335334	−	0.0580816i
$967$	1.29093	+	4.81782i	0.0415135	+	0.154931i	0.983571	−	0.180520i	$-0.0577781\pi$
$967$	1.29093	+	4.81782i	0.0415135	+	0.154931i	−0.942058	+	0.335451i	$0.891111\pi$
$968$	−0.563608	+	0.563608i	−0.0181151	+	0.0181151i
$969$	14.1305	−	22.0224i	0.453936	−	0.707462i
$970$	6.35317	+	4.09499i	0.203988	+	0.131482i
$971$	−43.2525	−	24.9718i	−1.38804	−	0.801385i	−0.394945	−	0.918705i	$-0.629236\pi$
$971$	−43.2525	−	24.9718i	−1.38804	−	0.801385i	−0.993094	+	0.117320i	$0.962570\pi$
$972$	−0.965926	+	0.258819i	−0.0309821	+	0.00830162i
$973$	−0.619419	+	2.31170i	−0.0198577	+	0.0741098i
$974$	−14.1380	−	8.16258i	−0.453011	−	0.261546i
$975$	8.52903	+	6.10806i	0.273148	+	0.195615i
$976$	6.69329			0.214247
$977$	−5.00444	−	5.00444i	−0.160106	−	0.160106i	0.622508	−	0.782614i	$-0.286114\pi$
$977$	−5.00444	−	5.00444i	−0.160106	−	0.160106i	−0.782614	+	0.622508i	$0.786114\pi$
$978$	−2.94409	+	10.9875i	−0.0941417	+	0.351341i
$979$	23.4126	+	40.5517i	0.748269	+	1.29604i
$980$	7.56684	−	11.7396i	0.241714	−	0.375007i
$981$			16.7910i			0.536095i
$982$	−8.59787	+	32.0877i	−0.274369	+	1.02396i
$983$	11.9513	+	44.6027i	0.381186	+	1.42261i	0.844092	+	0.536198i	$0.180140\pi$
$983$	11.9513	+	44.6027i	0.381186	+	1.42261i	−0.462906	+	0.886407i	$0.653193\pi$
$984$	−3.99317	−	6.91637i	−0.127298	−	0.220486i
$985$	−24.8385	−	7.97676i	−0.791420	−	0.254161i
$986$	−27.5701	+	47.7529i	−0.878012	+	1.52076i
$987$	−4.50298	−	4.50298i	−0.143331	−	0.143331i
$988$	−6.76278	+	6.15670i	−0.215153	+	0.195871i
$989$			8.98785i			0.285797i
$990$	7.31236	+	2.34833i	0.232402	+	0.0746348i
$991$	−0.786094	−	0.453851i	−0.0249711	−	0.0144171i	0.487462	−	0.873144i	$-0.337923\pi$
$991$	−0.786094	−	0.453851i	−0.0249711	−	0.0144171i	−0.512434	+	0.858727i	$0.671256\pi$
$992$	−7.82377	−	2.09637i	−0.248405	−	0.0665599i
$993$	−27.8286	+	7.45665i	−0.883113	+	0.236630i
$994$	−5.08527	+	2.93598i	−0.161295	+	0.0931238i
$995$	27.1634	+	17.5084i	0.861139	+	0.555055i
$996$		−	0.721230i		−	0.0228531i
$997$	−22.5232	−	6.03508i	−0.713318	−	0.191133i	−0.116130	−	0.993234i	$-0.537049\pi$
$997$	−22.5232	−	6.03508i	−0.713318	−	0.191133i	−0.597188	+	0.802101i	$0.703716\pi$
$998$	−3.21596	−	0.861713i	−0.101799	−	0.0272770i
$999$		−	10.3408i		−	0.327168i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.x.b.103.2	✓	40
5.2	odd	4	inner	570.2.x.b.217.5	yes	40
19.12	odd	6	inner	570.2.x.b.373.5	yes	40
95.12	even	12	inner	570.2.x.b.487.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.x.b.103.2	✓	40	1.1	even	1	trivial
570.2.x.b.217.5	yes	40	5.2	odd	4	inner
570.2.x.b.373.5	yes	40	19.12	odd	6	inner
570.2.x.b.487.2	yes	40	95.12	even	12	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.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.02196 - 1.98887i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.613926 + 0.613926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.02196 - 1.98887i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.613926 + 0.613926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.50189 + 1.65660i) q^{10} -3.43469 q^{11} +(-0.707107 - 0.707107i) q^{12} +(2.02663 + 0.543034i) q^{13} +(0.434111 - 0.751903i) q^{14} +(-1.65660 + 1.50189i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.55366 - 5.79834i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-3.87290 + 2.00016i) q^{19} +(-1.87948 - 1.21143i) q^{20} +(0.751903 + 0.434111i) q^{21} +(3.31765 - 0.888962i) q^{22} +(-0.621386 + 2.31904i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-2.91121 + 4.06508i) q^{25} -2.09812 q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.224712 + 0.838638i) q^{28} +(4.59281 + 7.95499i) q^{29} +(1.21143 - 1.87948i) q^{30} +8.09976i q^{31} +(-0.258819 + 0.965926i) q^{32} +(0.888962 + 3.31765i) q^{33} +(3.00144 + 5.19865i) q^{34} +(1.84842 + 0.593613i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-7.31205 - 7.31205i) q^{37} +(3.22325 - 2.93439i) q^{38} -2.09812i q^{39} +(2.12898 + 0.683710i) q^{40} +(-6.91637 - 3.99317i) q^{41} +(-0.838638 - 0.224712i) q^{42} +(3.61605 - 0.968917i) q^{43} +(-2.97452 + 1.71734i) q^{44} +(1.87948 + 1.21143i) q^{45} -2.40085i q^{46} +(-7.08481 - 1.89837i) q^{47} +(-0.965926 - 0.258819i) q^{48} +6.24619i q^{49} +(1.75989 - 4.68004i) q^{50} +(-5.19865 + 3.00144i) q^{51} +(2.02663 - 0.543034i) q^{52} +(-3.31055 - 0.887059i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(3.51010 + 6.83114i) q^{55} -0.868222i q^{56} +(2.93439 + 3.22325i) q^{57} +(-6.49522 - 6.49522i) q^{58} +(-3.68131 + 6.37621i) q^{59} +(-0.683710 + 2.12898i) q^{60} +(3.34665 + 5.79656i) q^{61} +(-2.09637 - 7.82377i) q^{62} +(0.224712 - 0.838638i) q^{63} -1.00000i q^{64} +(-0.991106 - 4.58566i) q^{65} +(-1.71734 - 2.97452i) q^{66} +(1.38830 - 5.18119i) q^{67} +(-4.24468 - 4.24468i) q^{68} +2.40085 q^{69} +(-1.93908 - 0.0949781i) q^{70} +(-5.85711 - 3.38160i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-11.4942 + 3.07985i) q^{73} +(8.95539 + 5.17040i) q^{74} +(4.68004 + 1.75989i) q^{75} +(-2.35395 + 3.66864i) q^{76} +(2.10864 - 2.10864i) q^{77} +(0.543034 + 2.02663i) q^{78} +(6.09173 - 10.5512i) q^{79} +(-2.23339 - 0.109394i) q^{80} +(0.500000 - 0.866025i) q^{81} +(7.71421 + 2.06702i) q^{82} +(0.509987 + 0.509987i) q^{83} +0.868222 q^{84} +(-9.94437 + 9.01569i) q^{85} +(-3.24206 + 1.87180i) q^{86} +(6.49522 - 6.49522i) q^{87} +(2.42869 - 2.42869i) q^{88} +(-6.81651 - 11.8065i) q^{89} +(-2.12898 - 0.683710i) q^{90} +(-1.57758 + 0.910818i) q^{91} +(0.621386 + 2.31904i) q^{92} +(7.82377 - 2.09637i) q^{93} +7.33473 q^{94} +(7.93600 + 5.65861i) q^{95} +1.00000 q^{96} +(3.26511 - 0.874883i) q^{97} +(-1.61663 - 6.03336i) q^{98} +(2.97452 - 1.71734i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 20 q^{6} - 8 q^{7}+O(q^{10}) \) 40 * q + 20 * q^6 - 8 * q^7	\( 40 q + 20 q^{6} - 8 q^{7} + 12 q^{10} + 8 q^{11} + 24 q^{13} + 20 q^{16} + 36 q^{21} - 8 q^{23} + 16 q^{25} + 4 q^{28} - 4 q^{35} - 20 q^{36} + 24 q^{38} + 12 q^{41} - 4 q^{42} - 12 q^{43} - 16 q^{47} + 24 q^{52} + 72 q^{53} + 8 q^{55} - 24 q^{57} - 16 q^{58} + 12 q^{60} + 24 q^{61} - 4 q^{63} + 4 q^{66} - 36 q^{67} - 24 q^{70} - 72 q^{71} - 32 q^{73} + 8 q^{76} - 88 q^{77} + 24 q^{78} + 20 q^{81} + 8 q^{82} - 88 q^{83} - 24 q^{85} - 48 q^{86} + 16 q^{87} - 24 q^{91} + 8 q^{92} - 96 q^{95} + 40 q^{96} - 60 q^{97} - 48 q^{98}+O(q^{100}) \) 40 * q + 20 * q^6 - 8 * q^7 + 12 * q^10 + 8 * q^11 + 24 * q^13 + 20 * q^16 + 36 * q^21 - 8 * q^23 + 16 * q^25 + 4 * q^28 - 4 * q^35 - 20 * q^36 + 24 * q^38 + 12 * q^41 - 4 * q^42 - 12 * q^43 - 16 * q^47 + 24 * q^52 + 72 * q^53 + 8 * q^55 - 24 * q^57 - 16 * q^58 + 12 * q^60 + 24 * q^61 - 4 * q^63 + 4 * q^66 - 36 * q^67 - 24 * q^70 - 72 * q^71 - 32 * q^73 + 8 * q^76 - 88 * q^77 + 24 * q^78 + 20 * q^81 + 8 * q^82 - 88 * q^83 - 24 * q^85 - 48 * q^86 + 16 * q^87 - 24 * q^91 + 8 * q^92 - 96 * q^95 + 40 * q^96 - 60 * q^97 - 48 * q^98

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