LMFDB - Embedded newform 570.2.x.b.103.9

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			103.9
Character	$\chi$	$=$	570.103
Dual form			570.2.x.b.487.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.89255 + 1.19091i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.32404 - 2.32404i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.89255 + 1.19091i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.32404 - 2.32404i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(2.13629 + 0.660499i) q^{10} +3.35986 q^{11} +(0.707107 + 0.707107i) q^{12} +(-5.53140 - 1.48213i) q^{13} +(1.64335 - 2.84636i) q^{14} +(-0.660499 + 2.13629i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.215133 - 0.802888i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-3.50954 + 2.58518i) q^{19} +(2.23445 + 0.0850797i) q^{20} +(2.84636 + 1.64335i) q^{21} +(3.24538 - 0.869596i) q^{22} +(0.220355 - 0.822375i) q^{23} +(0.866025 + 0.500000i) q^{24} +(2.16349 + 4.50770i) q^{25} -5.72653 q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.850659 - 3.17470i) q^{28} +(-2.58935 - 4.48489i) q^{29} +(-0.0850797 + 2.23445i) q^{30} +5.68857i q^{31} +(0.258819 - 0.965926i) q^{32} +(0.869596 + 3.24538i) q^{33} +(-0.415606 - 0.719850i) q^{34} +(7.16608 - 1.63065i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(4.63392 + 4.63392i) q^{37} +(-2.72086 + 3.40542i) q^{38} -5.72653i q^{39} +(2.18033 - 0.496137i) q^{40} +(2.08112 + 1.20154i) q^{41} +(3.17470 + 0.850659i) q^{42} +(1.14348 - 0.306394i) q^{43} +(2.90972 - 1.67993i) q^{44} +(-2.23445 - 0.0850797i) q^{45} -0.851385i q^{46} +(-8.20582 - 2.19874i) q^{47} +(0.965926 + 0.258819i) q^{48} -3.80235i q^{49} +(3.25645 + 3.79415i) q^{50} +(0.719850 - 0.415606i) q^{51} +(-5.53140 + 1.48213i) q^{52} +(0.607538 + 0.162789i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(6.35870 + 4.00128i) q^{55} -3.28669i q^{56} +(-3.40542 - 2.72086i) q^{57} +(-3.66189 - 3.66189i) q^{58} +(-6.16345 + 10.6754i) q^{59} +(0.496137 + 2.18033i) q^{60} +(-5.60453 - 9.70733i) q^{61} +(1.47231 + 5.49473i) q^{62} +(-0.850659 + 3.17470i) q^{63} -1.00000i q^{64} +(-8.70337 - 9.39239i) q^{65} +(1.67993 + 2.90972i) q^{66} +(-0.751997 + 2.80649i) q^{67} +(-0.587755 - 0.587755i) q^{68} +0.851385 q^{69} +(6.49986 - 3.42981i) q^{70} +(-6.35845 - 3.67106i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(8.79077 - 2.35548i) q^{73} +(5.67536 + 3.27667i) q^{74} +(-3.79415 + 3.25645i) q^{75} +(-1.74676 + 3.99360i) q^{76} +(7.80846 - 7.80846i) q^{77} +(-1.48213 - 5.53140i) q^{78} +(0.524789 - 0.908960i) q^{79} +(1.97763 - 1.04354i) q^{80} +(0.500000 - 0.866025i) q^{81} +(2.32119 + 0.621961i) q^{82} +(-9.97246 - 9.97246i) q^{83} +3.28669 q^{84} +(0.549014 - 1.77571i) q^{85} +(1.02522 - 0.591908i) q^{86} +(3.66189 - 3.66189i) q^{87} +(2.37578 - 2.37578i) q^{88} +(2.07845 + 3.59999i) q^{89} +(-2.18033 + 0.496137i) q^{90} +(-16.2998 + 9.41067i) q^{91} +(-0.220355 - 0.822375i) q^{92} +(-5.49473 + 1.47231i) q^{93} -8.49529 q^{94} +(-9.72068 + 0.713042i) q^{95} +1.00000 q^{96} +(9.00085 - 2.41177i) q^{97} +(-0.984122 - 3.67279i) q^{98} +(-2.90972 + 1.67993i) 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
$5$	1.89255	+	1.19091i	0.846374	+	0.532589i
$5$	1.89255	+	1.19091i	0.846374	+	0.532589i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	2.32404	−	2.32404i	0.878406	−	0.878406i	−0.114964	−	0.993370i	$-0.536675\pi$
$7$	2.32404	−	2.32404i	0.878406	−	0.878406i	0.993370	+	0.114964i	$0.0366752\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	2.13629	+	0.660499i	0.675555	+	0.208868i
$11$	3.35986			1.01304			0.506518	−	0.862229i	$-0.330932\pi$
$11$	3.35986			1.01304			0.506518	+	0.862229i	$0.330932\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	−5.53140	−	1.48213i	−1.53413	−	0.411070i	−0.609769	−	0.792579i	$-0.708738\pi$
$13$	−5.53140	−	1.48213i	−1.53413	−	0.411070i	−0.924365	+	0.381509i	$0.875405\pi$
$14$	1.64335	−	2.84636i	0.439203	−	0.760722i
$15$	−0.660499	+	2.13629i	−0.170540	+	0.551588i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.215133	−	0.802888i	−0.0521775	−	0.194729i	0.934917	−	0.354865i	$-0.115473\pi$
$17$	−0.215133	−	0.802888i	−0.0521775	−	0.194729i	−0.987095	+	0.160136i	$0.948807\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	−3.50954	+	2.58518i	−0.805144	+	0.593080i
$19$	−3.50954	+	2.58518i	−0.805144	+	0.593080i
$20$	2.23445	+	0.0850797i	0.499638	+	0.0190244i
$21$	2.84636	+	1.64335i	0.621127	+	0.358608i
$22$	3.24538	−	0.869596i	0.691917	−	0.185398i
$23$	0.220355	−	0.822375i	0.0459471	−	0.171477i	−0.939140	−	0.343536i	$-0.888375\pi$
$23$	0.220355	−	0.822375i	0.0459471	−	0.171477i	0.985087	+	0.172059i	$0.0550420\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	2.16349	+	4.50770i	0.432698	+	0.901539i
$26$	−5.72653			−1.12306
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	0.850659	−	3.17470i	0.160759	−	0.599962i
$29$	−2.58935	−	4.48489i	−0.480830	−	0.832822i	0.518928	−	0.854818i	$-0.326331\pi$
$29$	−2.58935	−	4.48489i	−0.480830	−	0.832822i	−0.999758	+	0.0219956i	$0.992998\pi$
$30$	−0.0850797	+	2.23445i	−0.0155333	+	0.407953i
$31$			5.68857i			1.02170i	0.859671	+	0.510848i	$0.170669\pi$
$31$			5.68857i			1.02170i	−0.859671	+	0.510848i	$0.829331\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	0.869596	+	3.24538i	0.151377	+	0.564948i
$34$	−0.415606	−	0.719850i	−0.0712758	−	0.123453i
$35$	7.16608	−	1.63065i	1.21129	−	0.275630i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	4.63392	+	4.63392i	0.761811	+	0.761811i	0.976650	−	0.214839i	$-0.0689225\pi$
$37$	4.63392	+	4.63392i	0.761811	+	0.761811i	−0.214839	+	0.976650i	$0.568923\pi$
$38$	−2.72086	+	3.40542i	−0.441382	+	0.552433i
$39$		−	5.72653i		−	0.916978i
$40$	2.18033	−	0.496137i	0.344741	−	0.0784462i
$41$	2.08112	+	1.20154i	0.325017	+	0.187648i	0.653626	−	0.756817i	$-0.273247\pi$
$41$	2.08112	+	1.20154i	0.325017	+	0.187648i	−0.328610	+	0.944466i	$0.606580\pi$
$42$	3.17470	+	0.850659i	0.489867	+	0.131260i
$43$	1.14348	−	0.306394i	0.174379	−	0.0467247i	−0.170573	−	0.985345i	$-0.554562\pi$
$43$	1.14348	−	0.306394i	0.174379	−	0.0467247i	0.344952	+	0.938620i	$0.387895\pi$
$44$	2.90972	−	1.67993i	0.438658	−	0.253259i
$45$	−2.23445	−	0.0850797i	−0.333092	−	0.0126829i
$46$		−	0.851385i		−	0.125530i
$47$	−8.20582	−	2.19874i	−1.19694	−	0.320720i	−0.395316	−	0.918545i	$-0.629365\pi$
$47$	−8.20582	−	2.19874i	−1.19694	−	0.320720i	−0.801626	+	0.597826i	$0.796031\pi$
$48$	0.965926	+	0.258819i	0.139419	+	0.0373573i
$49$		−	3.80235i		−	0.543193i
$50$	3.25645	+	3.79415i	0.460531	+	0.536574i
$51$	0.719850	−	0.415606i	0.100799	−	0.0581964i
$52$	−5.53140	+	1.48213i	−0.767067	+	0.205535i
$53$	0.607538	+	0.162789i	0.0834518	+	0.0223608i	0.300303	−	0.953844i	$-0.402912\pi$
$53$	0.607538	+	0.162789i	0.0834518	+	0.0223608i	−0.216852	+	0.976205i	$0.569579\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	6.35870	+	4.00128i	0.857407	+	0.539532i
$56$		−	3.28669i		−	0.439203i
$57$	−3.40542	−	2.72086i	−0.451059	−	0.360387i
$58$	−3.66189	−	3.66189i	−0.480830	−	0.480830i
$59$	−6.16345	+	10.6754i	−0.802412	+	1.38982i	0.115612	+	0.993294i	$0.463117\pi$
$59$	−6.16345	+	10.6754i	−0.802412	+	1.38982i	−0.918024	+	0.396525i	$0.870216\pi$
$60$	0.496137	+	2.18033i	0.0640510	+	0.281480i
$61$	−5.60453	−	9.70733i	−0.717586	−	1.24290i	−0.961954	−	0.273213i	$-0.911914\pi$
$61$	−5.60453	−	9.70733i	−0.717586	−	1.24290i	0.244367	−	0.969683i	$-0.421420\pi$
$62$	1.47231	+	5.49473i	0.186983	+	0.697832i
$63$	−0.850659	+	3.17470i	−0.107173	+	0.399975i
$64$		−	1.00000i		−	0.125000i
$65$	−8.70337	−	9.39239i	−1.07952	−	1.16498i
$66$	1.67993	+	2.90972i	0.206785	+	0.358162i
$67$	−0.751997	+	2.80649i	−0.0918710	+	0.342867i	−0.996526	−	0.0832764i	$-0.973462\pi$
$67$	−0.751997	+	2.80649i	−0.0918710	+	0.342867i	0.904655	+	0.426144i	$0.140128\pi$
$68$	−0.587755	−	0.587755i	−0.0712758	−	0.0712758i
$69$	0.851385			0.102495
$70$	6.49986	−	3.42981i	0.776882	−	0.409940i
$71$	−6.35845	−	3.67106i	−0.754610	−	0.435674i	0.0727473	−	0.997350i	$-0.476823\pi$
$71$	−6.35845	−	3.67106i	−0.754610	−	0.435674i	−0.827357	+	0.561676i	$0.810157\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	8.79077	−	2.35548i	1.02888	−	0.275688i	0.295383	−	0.955379i	$-0.404553\pi$
$73$	8.79077	−	2.35548i	1.02888	−	0.275688i	0.733499	+	0.679691i	$0.237886\pi$
$74$	5.67536	+	3.27667i	0.659748	+	0.380906i
$75$	−3.79415	+	3.25645i	−0.438110	+	0.376022i
$76$	−1.74676	+	3.99360i	−0.200367	+	0.458097i
$77$	7.80846	−	7.80846i	0.889857	−	0.889857i
$78$	−1.48213	−	5.53140i	−0.167819	−	0.626308i
$79$	0.524789	−	0.908960i	0.0590433	−	0.102266i	−0.834993	−	0.550261i	$-0.814528\pi$
$79$	0.524789	−	0.908960i	0.0590433	−	0.102266i	0.894036	+	0.447995i	$0.147862\pi$
$80$	1.97763	−	1.04354i	0.221106	−	0.116672i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	2.32119	+	0.621961i	0.256332	+	0.0686841i
$83$	−9.97246	−	9.97246i	−1.09462	−	1.09462i	−0.995028	−	0.0995914i	$-0.968246\pi$
$83$	−9.97246	−	9.97246i	−1.09462	−	1.09462i	−0.0995914	−	0.995028i	$-0.531754\pi$
$84$	3.28669			0.358608
$85$	0.549014	−	1.77571i	0.0595489	−	0.192603i
$86$	1.02522	−	0.591908i	0.110552	−	0.0638271i
$87$	3.66189	−	3.66189i	0.392596	−	0.392596i
$88$	2.37578	−	2.37578i	0.253259	−	0.253259i
$89$	2.07845	+	3.59999i	0.220316	+	0.381598i	0.954904	−	0.296915i	$-0.0959580\pi$
$89$	2.07845	+	3.59999i	0.220316	+	0.381598i	−0.734588	+	0.678513i	$0.762625\pi$
$90$	−2.18033	+	0.496137i	−0.229827	+	0.0522975i
$91$	−16.2998	+	9.41067i	−1.70868	+	0.986506i
$92$	−0.220355	−	0.822375i	−0.0229736	−	0.0857385i
$93$	−5.49473	+	1.47231i	−0.569777	+	0.152671i
$94$	−8.49529			−0.876222
$95$	−9.72068	+	0.713042i	−0.997320	+	0.0731565i
$96$	1.00000			0.102062
$97$	9.00085	−	2.41177i	0.913898	−	0.244878i	0.228923	−	0.973445i	$-0.426480\pi$
$97$	9.00085	−	2.41177i	0.913898	−	0.244878i	0.684975	+	0.728566i	$0.259813\pi$
$98$	−0.984122	−	3.67279i	−0.0994113	−	0.371008i
$99$	−2.90972	+	1.67993i	−0.292438	+	0.168839i
$100$	4.12748	+	2.82203i	0.412748	+	0.282203i
$101$	−4.93960	−	8.55564i	−0.491509	−	0.851318i	0.508443	−	0.861095i	$-0.330221\pi$
$101$	−4.93960	−	8.55564i	−0.491509	−	0.851318i	−0.999952	+	0.00977708i	$0.996888\pi$
$102$	0.587755	−	0.587755i	0.0581964	−	0.0581964i
$103$	−6.25029	+	6.25029i	−0.615859	+	0.615859i	−0.944467	−	0.328608i	$-0.893421\pi$
$103$	−6.25029	+	6.25029i	−0.615859	+	0.615859i	0.328608	+	0.944467i	$0.393421\pi$
$104$	−4.95932	+	2.86326i	−0.486301	+	0.280766i
$105$	3.42981	+	6.49986i	0.334715	+	0.634321i
$106$	0.628970			0.0610909
$107$	−8.80608	−	8.80608i	−0.851316	−	0.851316i	0.138979	−	0.990295i	$-0.455618\pi$
$107$	−8.80608	−	8.80608i	−0.851316	−	0.851316i	−0.990295	+	0.138979i	$0.955618\pi$
$108$	−0.965926	−	0.258819i	−0.0929463	−	0.0249049i
$109$	−7.97689	+	13.8164i	−0.764047	+	1.32337i	0.176701	+	0.984265i	$0.443457\pi$
$109$	−7.97689	+	13.8164i	−0.764047	+	1.32337i	−0.940749	+	0.339104i	$0.889876\pi$
$110$	7.17764	+	2.21918i	0.684361	+	0.211591i
$111$	−3.27667	+	5.67536i	−0.311008	+	0.538682i
$112$	−0.850659	−	3.17470i	−0.0803797	−	0.299981i
$113$	8.83236	−	8.83236i	0.830879	−	0.830879i	−0.156758	−	0.987637i	$-0.550104\pi$
$113$	8.83236	−	8.83236i	0.830879	−	0.830879i	0.987637	+	0.156758i	$0.0501043\pi$
$114$	−3.99360	−	1.74676i	−0.374035	−	0.163599i
$115$	1.39640	−	1.29396i	0.130215	−	0.120663i
$116$	−4.48489	−	2.58935i	−0.416411	−	0.240415i
$117$	5.53140	−	1.48213i	0.511378	−	0.137023i
$118$	−3.19043	+	11.9069i	−0.293703	+	1.09612i
$119$	−2.36593	−	1.36597i	−0.216884	−	0.125218i
$120$	1.04354	+	1.97763i	0.0952620	+	0.180532i
$121$	0.288665			0.0262423
$122$	−7.92600	−	7.92600i	−0.717586	−	0.717586i
$123$	−0.621961	+	2.32119i	−0.0560803	+	0.209295i
$124$	2.84428	+	4.92644i	0.255424	+	0.442408i
$125$	−1.27373	+	11.1075i	−0.113926	+	0.993489i
$126$			3.28669i			0.292802i
$127$	1.80240	−	6.72666i	0.159937	−	0.596895i	−0.838694	−	0.544602i	$-0.816681\pi$
$127$	1.80240	−	6.72666i	0.159937	−	0.596895i	0.998632	−	0.0522923i	$-0.0166527\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	0.591908	+	1.02522i	0.0521146	+	0.0902652i
$130$	−10.8377	−	6.81975i	−0.950532	−	0.598132i
$131$	4.56401	−	7.90510i	0.398759	−	0.690672i	−0.594814	−	0.803864i	$-0.702774\pi$
$131$	4.56401	−	7.90510i	0.398759	−	0.690672i	0.993573	+	0.113192i	$0.0361075\pi$
$132$	2.37578	+	2.37578i	0.206785	+	0.206785i
$133$	−2.14826	+	14.1644i	−0.186278	+	1.22821i
$134$			2.90549i			0.250996i
$135$	−0.496137	−	2.18033i	−0.0427007	−	0.187653i
$136$	−0.719850	−	0.415606i	−0.0617266	−	0.0356379i
$137$	14.9103	+	3.99521i	1.27388	+	0.341334i	0.831515	−	0.555503i	$-0.187474\pi$
$137$	14.9103	+	3.99521i	1.27388	+	0.341334i	0.442361	+	0.896837i	$0.354141\pi$
$138$	0.822375	−	0.220355i	0.0700052	−	0.0187578i
$139$	−4.89461	+	2.82591i	−0.415156	+	0.239690i	−0.693002	−	0.720935i	$-0.743713\pi$
$139$	−4.89461	+	2.82591i	−0.415156	+	0.239690i	0.277847	+	0.960625i	$0.410379\pi$
$140$	5.39068	−	4.99523i	0.455596	−	0.422174i
$141$		−	8.49529i		−	0.715432i
$142$	−7.09193	−	1.90028i	−0.595142	−	0.159468i
$143$	−18.5847	−	4.97976i	−1.55413	−	0.416429i
$144$			1.00000i			0.0833333i
$145$	0.440602	−	11.5715i	0.0365900	−	0.960964i
$146$	7.88159	−	4.55044i	0.652285	−	0.376597i
$147$	3.67279	−	0.984122i	0.302927	−	0.0811690i
$148$	6.33005	+	1.69613i	0.520327	+	0.139421i
$149$	10.9702	+	6.33366i	0.898715	+	0.518873i	0.876783	−	0.480886i	$-0.159685\pi$
$149$	10.9702	+	6.33366i	0.898715	+	0.518873i	0.0219320	+	0.999759i	$0.493018\pi$
$150$	−2.82203	+	4.12748i	−0.230418	+	0.337008i
$151$			18.0547i			1.46927i	0.678461	+	0.734636i	$0.262647\pi$
$151$			18.0547i			1.46927i	−0.678461	+	0.734636i	$0.737353\pi$
$152$	−0.653625	+	4.30961i	−0.0530160	+	0.349556i
$153$	0.587755	+	0.587755i	0.0475172	+	0.0475172i
$154$	5.52142	−	9.56337i	0.444928	−	0.770639i
$155$	−6.77455	+	10.7659i	−0.544145	+	0.864738i
$156$	−2.86326	−	4.95932i	−0.229245	−	0.397063i
$157$	−4.41038	−	16.4598i	−0.351987	−	1.31363i	−0.884234	−	0.467043i	$-0.845319\pi$
$157$	−4.41038	−	16.4598i	−0.351987	−	1.31363i	0.532248	−	0.846589i	$-0.321347\pi$
$158$	0.271651	−	1.01381i	0.0216114	−	0.0806547i
$159$			0.628970i			0.0498805i
$160$	1.64015	−	1.51983i	0.129666	−	0.120153i
$161$	−1.39912	−	2.42335i	−0.110266	−	0.190987i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	−4.83093	−	4.83093i	−0.378388	−	0.378388i	0.492132	−	0.870520i	$-0.336218\pi$
$163$	−4.83093	−	4.83093i	−0.378388	−	0.378388i	−0.870520	+	0.492132i	$0.836218\pi$
$164$	2.40307			0.187648
$165$	−2.21918	+	7.17764i	−0.172763	+	0.558779i
$166$	−12.2137	−	7.05159i	−0.947969	−	0.547310i
$167$	−0.641405	+	2.39376i	−0.0496334	+	0.185234i	−0.986292	−	0.165009i	$-0.947235\pi$
$167$	−0.641405	+	2.39376i	−0.0496334	+	0.185234i	0.936659	+	0.350244i	$0.113901\pi$
$168$	3.17470	−	0.850659i	0.244934	−	0.0656298i
$169$	17.1413	+	9.89656i	1.31856	+	0.761273i
$170$	0.0707192	−	1.85730i	0.00542391	−	0.142448i
$171$	1.74676	−	3.99360i	0.133578	−	0.305398i
$172$	0.837085	−	0.837085i	0.0638271	−	0.0638271i
$173$	−6.05836	−	22.6101i	−0.460608	−	1.71901i	−0.671054	−	0.741408i	$-0.734158\pi$
$173$	−6.05836	−	22.6101i	−0.460608	−	1.71901i	0.210446	−	0.977606i	$-0.432508\pi$
$174$	2.58935	−	4.48489i	0.196298	−	0.339998i
$175$	15.5041	+	5.44804i	1.17200	+	0.411833i
$176$	1.67993	−	2.90972i	0.126630	−	0.219329i
$177$	−11.9069	−	3.19043i	−0.894975	−	0.239808i
$178$	2.93938	+	2.93938i	0.220316	+	0.220316i
$179$	22.6709			1.69451			0.847253	−	0.531190i	$-0.178255\pi$
$179$	22.6709			1.69451			0.847253	+	0.531190i	$0.178255\pi$
$180$	−1.97763	+	1.04354i	−0.147404	+	0.0777811i
$181$	0.818680	−	0.472665i	0.0608520	−	0.0351329i	−0.469265	−	0.883057i	$-0.655481\pi$
$181$	0.818680	−	0.472665i	0.0608520	−	0.0351329i	0.530117	+	0.847924i	$0.322148\pi$
$182$	−13.3087	+	13.3087i	−0.986506	+	0.986506i
$183$	7.92600	−	7.92600i	0.585907	−	0.585907i
$184$	−0.425692	−	0.737321i	−0.0313825	−	0.0543560i
$185$	3.25136	+	14.2885i	0.239045	+	1.05051i
$186$	−4.92644	+	2.84428i	−0.361224	+	0.208553i
$187$	−0.722818	−	2.69759i	−0.0528577	−	0.197268i
$188$	−8.20582	+	2.19874i	−0.598471	+	0.160360i
$189$	−3.28669			−0.239072
$190$	−9.20490	+	3.20464i	−0.667794	+	0.232489i
$191$	24.9547			1.80566			0.902830	−	0.429997i	$-0.141485\pi$
$191$	24.9547			1.80566			0.902830	+	0.429997i	$0.141485\pi$
$192$	0.965926	−	0.258819i	0.0697097	−	0.0186787i
$193$	6.66413	+	24.8709i	0.479695	+	1.79024i	0.602847	+	0.797857i	$0.294033\pi$
$193$	6.66413	+	24.8709i	0.479695	+	1.79024i	−0.123152	+	0.992388i	$0.539300\pi$
$194$	8.06994	−	4.65918i	0.579388	−	0.334510i
$195$	6.81975	−	10.8377i	0.488373	−	0.776106i
$196$	−1.90118	−	3.29294i	−0.135798	−	0.235210i
$197$	1.19736	−	1.19736i	0.0853084	−	0.0853084i	−0.663165	−	0.748473i	$-0.730787\pi$
$197$	1.19736	−	1.19736i	0.0853084	−	0.0853084i	0.748473	+	0.663165i	$0.230787\pi$
$198$	−2.37578	+	2.37578i	−0.168839	+	0.168839i
$199$	−8.78902	+	5.07435i	−0.623037	+	0.359711i	−0.778051	−	0.628202i	$-0.783791\pi$
$199$	−8.78902	+	5.07435i	−0.623037	+	0.359711i	0.155013	+	0.987912i	$0.450458\pi$
$200$	4.71724	+	1.65761i	0.333559	+	0.117210i
$201$	−2.90549			−0.204938
$202$	−6.98565	−	6.98565i	−0.491509	−	0.491509i
$203$	−16.4408	−	4.40531i	−1.15392	−	0.309192i
$204$	0.415606	−	0.719850i	0.0290982	−	0.0503996i
$205$	2.50771	+	4.75239i	0.175146	+	0.331921i
$206$	−4.41962	+	7.65501i	−0.307929	+	0.533350i
$207$	0.220355	+	0.822375i	0.0153157	+	0.0571590i
$208$	−4.04927	+	4.04927i	−0.280766	+	0.280766i
$209$	−11.7916	+	8.68583i	−0.815640	+	0.600811i
$210$	4.99523	+	5.39068i	0.344703	+	0.371993i
$211$	−22.5018	−	12.9914i	−1.54909	−	0.894368i	−0.998211	−	0.0597823i	$-0.980959\pi$
$211$	−22.5018	−	12.9914i	−1.54909	−	0.894368i	−0.550879	−	0.834585i	$-0.685707\pi$
$212$	0.607538	−	0.162789i	0.0417259	−	0.0111804i
$213$	1.90028	−	7.09193i	0.130205	−	0.485931i
$214$	−10.7852	−	6.22684i	−0.737262	−	0.425658i
$215$	2.52898	+	0.781909i	0.172475	+	0.0533258i
$216$	−1.00000			−0.0680414
$217$	13.2205	+	13.2205i	0.897464	+	0.897464i
$218$	−4.12914	+	15.4102i	−0.279661	+	1.04371i
$219$	4.55044	+	7.88159i	0.307490	+	0.532589i
$220$	7.50744	+	0.285856i	0.506151	+	0.0192724i
$221$			4.75995i			0.320189i
$222$	−1.69613	+	6.33005i	−0.113837	+	0.424845i
$223$	−1.11134	−	4.14757i	−0.0744206	−	0.277742i	0.918681	−	0.395001i	$-0.129256\pi$
$223$	−1.11134	−	4.14757i	−0.0744206	−	0.277742i	−0.993101	+	0.117259i	$0.962589\pi$
$224$	−1.64335	−	2.84636i	−0.109801	−	0.190180i
$225$	−4.12748	−	2.82203i	−0.275166	−	0.188136i
$226$	6.24542	−	10.8174i	0.415439	−	0.719562i
$227$	2.66464	+	2.66464i	0.176858	+	0.176858i	0.789985	−	0.613127i	$-0.210088\pi$
$227$	2.66464	+	2.66464i	0.176858	+	0.176858i	−0.613127	+	0.789985i	$0.710088\pi$
$228$	−4.30961	−	0.653625i	−0.285411	−	0.0432873i
$229$			17.6122i			1.16384i	0.813245	+	0.581922i	$0.197699\pi$
$229$			17.6122i			1.16384i	−0.813245	+	0.581922i	$0.802301\pi$
$230$	1.01392	−	1.61129i	0.0668558	−	0.106245i
$231$	9.56337	+	5.52142i	0.629224	+	0.363283i
$232$	−5.00224	−	1.34035i	−0.328413	−	0.0879981i
$233$	−12.2081	+	3.27116i	−0.799782	+	0.214301i	−0.635488	−	0.772111i	$-0.719201\pi$
$233$	−12.2081	+	3.27116i	−0.799782	+	0.214301i	−0.164294	+	0.986411i	$0.552534\pi$
$234$	4.95932	−	2.86326i	0.324201	−	0.187177i
$235$	−12.9114	−	13.9336i	−0.842248	−	0.908927i
$236$			12.3269i			0.802412i
$237$	1.01381	+	0.271651i	0.0658543	+	0.0176456i
$238$	−2.63885	−	0.707077i	−0.171051	−	0.0458330i
$239$		−	14.6676i		−	0.948770i	−0.880318	−	0.474385i	$-0.842671\pi$
$239$		−	14.6676i		−	0.948770i	0.880318	−	0.474385i	$-0.157329\pi$
$240$	1.51983	+	1.64015i	0.0981048	+	0.105872i
$241$	8.41878	−	4.86058i	0.542301	−	0.313098i	−0.203710	−	0.979031i	$-0.565300\pi$
$241$	8.41878	−	4.86058i	0.542301	−	0.313098i	0.746011	+	0.665934i	$0.231967\pi$
$242$	0.278829	−	0.0747119i	0.0179238	−	0.00480267i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	−9.70733	−	5.60453i	−0.621448	−	0.358793i
$245$	4.52824	−	7.19614i	0.289299	−	0.459745i
$246$			2.40307i			0.153214i
$247$	23.2442	−	9.09803i	1.47900	−	0.578894i
$248$	4.02242	+	4.02242i	0.255424	+	0.255424i
$249$	7.05159	−	12.2137i	0.446877	−	0.774013i
$250$	1.64451	+	11.0587i	0.104008	+	0.699416i
$251$	11.6996	+	20.2643i	0.738471	+	1.27907i	0.953184	+	0.302392i	$0.0977852\pi$
$251$	11.6996	+	20.2643i	0.738471	+	1.27907i	−0.214713	+	0.976677i	$0.568881\pi$
$252$	0.850659	+	3.17470i	0.0535865	+	0.199987i
$253$	0.740361	−	2.76306i	0.0465461	−	0.173712i
$254$		−	6.96395i		−	0.436957i
$255$	1.85730	+	0.0707192i	0.116309	+	0.00442861i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.38531	−	12.6342i	0.211170	−	0.788098i	−0.776310	−	0.630352i	$-0.782911\pi$
$257$	3.38531	−	12.6342i	0.211170	−	0.788098i	0.987480	−	0.157746i	$-0.0504227\pi$
$258$	0.837085	+	0.837085i	0.0521146	+	0.0521146i
$259$	21.5388			1.33836
$260$	−12.2335	−	3.78236i	−0.758691	−	0.234572i
$261$	4.48489	+	2.58935i	0.277607	+	0.160277i
$262$	2.36251	−	8.81699i	0.145956	−	0.544715i
$263$	9.40629	−	2.52041i	0.580016	−	0.155415i	0.0431300	−	0.999069i	$-0.486267\pi$
$263$	9.40629	−	2.52041i	0.580016	−	0.155415i	0.536886	+	0.843655i	$0.319600\pi$
$264$	2.90972	+	1.67993i	0.179081	+	0.103393i
$265$	0.955929	+	1.03161i	0.0587223	+	0.0633711i
$266$	1.59095	+	14.2378i	0.0975473	+	0.872973i
$267$	−2.93938	+	2.93938i	−0.179887	+	0.179887i
$268$	0.751997	+	2.80649i	0.0459355	+	0.171434i
$269$	−2.00916	+	3.47997i	−0.122501	+	0.212178i	−0.920753	−	0.390145i	$-0.872425\pi$
$269$	−2.00916	+	3.47997i	−0.122501	+	0.212178i	0.798252	+	0.602323i	$0.205758\pi$
$270$	−1.04354	−	1.97763i	−0.0635080	−	0.120355i
$271$	−11.0969	+	19.2203i	−0.674086	+	1.16755i	0.302649	+	0.953102i	$0.402129\pi$
$271$	−11.0969	+	19.2203i	−0.674086	+	1.16755i	−0.976735	+	0.214450i	$0.931204\pi$
$272$	−0.802888	−	0.215133i	−0.0486823	−	0.0130444i
$273$	−13.3087	−	13.3087i	−0.805479	−	0.805479i
$274$	15.4363			0.932542
$275$	7.26902	+	15.1452i	0.438338	+	0.913292i
$276$	0.737321	−	0.425692i	0.0443815	−	0.0256237i
$277$	5.93572	−	5.93572i	0.356643	−	0.356643i	−0.505931	−	0.862574i	$-0.668851\pi$
$277$	5.93572	−	5.93572i	0.356643	−	0.356643i	0.862574	+	0.505931i	$0.168851\pi$
$278$	−3.99643	+	3.99643i	−0.239690	+	0.239690i
$279$	−2.84428	−	4.92644i	−0.170283	−	0.294938i
$280$	3.91414	−	6.22023i	0.233915	−	0.371730i
$281$	3.49878	−	2.02002i	0.208720	−	0.120504i	−0.391996	−	0.919967i	$-0.628215\pi$
$281$	3.49878	−	2.02002i	0.208720	−	0.120504i	0.600716	+	0.799462i	$0.294882\pi$
$282$	−2.19874	−	8.20582i	−0.130933	−	0.488649i
$283$	23.0042	−	6.16396i	1.36746	−	0.366410i	0.500909	−	0.865500i	$-0.332999\pi$
$283$	23.0042	−	6.16396i	1.36746	−	0.366410i	0.866550	+	0.499090i	$0.166332\pi$
$284$	−7.34211			−0.435674
$285$	−3.20464	−	9.20490i	−0.189827	−	0.545251i
$286$	−19.2403			−1.13770
$287$	7.62904	−	2.04419i	0.450328	−	0.120665i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	14.1241	−	8.15454i	0.830828	−	0.479679i
$290$	−2.56935	−	11.2913i	−0.150877	−	0.663047i
$291$	4.65918	+	8.06994i	0.273126	+	0.473069i
$292$	6.43529	−	6.43529i	0.376597	−	0.376597i
$293$	14.4801	−	14.4801i	0.845938	−	0.845938i	−0.143685	−	0.989623i	$-0.545895\pi$
$293$	14.4801	−	14.4801i	0.845938	−	0.845938i	0.989623	+	0.143685i	$0.0458952\pi$
$294$	3.29294	−	1.90118i	0.192048	−	0.110879i
$295$	−24.3780	+	12.8636i	−1.41934	+	0.748951i
$296$	6.55335			0.380906
$297$	−2.37578	−	2.37578i	−0.137857	−	0.137857i
$298$	12.2357	+	3.27854i	0.708794	+	0.189921i
$299$	−2.43774	+	4.22229i	−0.140978	+	0.244181i
$300$	−1.65761	+	4.71724i	−0.0957019	+	0.272350i
$301$	1.94542	−	3.36957i	0.112132	−	0.194219i
$302$	4.67291	+	17.4395i	0.268896	+	1.00353i
$303$	6.98565	−	6.98565i	0.401315	−	0.401315i
$304$	0.484057	+	4.33194i	0.0277626	+	0.248454i
$305$	0.953663	−	25.0461i	0.0546066	−	1.43413i
$306$	0.719850	+	0.415606i	0.0411511	+	0.0237586i
$307$	−13.8216	+	3.70348i	−0.788839	+	0.211369i	−0.630678	−	0.776045i	$-0.717223\pi$
$307$	−13.8216	+	3.70348i	−0.788839	+	0.211369i	−0.158161	+	0.987413i	$0.550557\pi$
$308$	2.85810	−	10.6666i	0.162855	−	0.607784i
$309$	−7.65501	−	4.41962i	−0.435478	−	0.251423i
$310$	−3.75729	+	12.1524i	−0.213400	+	0.690212i
$311$	−20.9262			−1.18662			−0.593309	−	0.804975i	$-0.702179\pi$
$311$	−20.9262			−1.18662			−0.593309	+	0.804975i	$0.702179\pi$
$312$	−4.04927	−	4.04927i	−0.229245	−	0.229245i
$313$	−0.449181	+	1.67637i	−0.0253892	+	0.0947539i	−0.977458	−	0.211131i	$-0.932285\pi$
$313$	−0.449181	+	1.67637i	−0.0253892	+	0.0947539i	0.952069	+	0.305884i	$0.0989521\pi$
$314$	−8.52020	−	14.7574i	−0.480823	−	0.832809i
$315$	−5.39068	+	4.99523i	−0.303731	+	0.281449i
$316$		−	1.04958i		−	0.0590433i
$317$	6.42459	−	23.9769i	0.360841	−	1.34668i	−0.512132	−	0.858907i	$-0.671144\pi$
$317$	6.42459	−	23.9769i	0.360841	−	1.34668i	0.872973	−	0.487769i	$-0.162189\pi$
$318$	0.162789	+	0.607538i	0.00912877	+	0.0340690i
$319$	−8.69986	−	15.0686i	−0.487098	−	0.843679i
$320$	1.19091	−	1.89255i	0.0665736	−	0.105797i
$321$	6.22684	−	10.7852i	0.347548	−	0.601972i
$322$	−1.97866	−	1.97866i	−0.110266	−	0.110266i
$323$	2.83063	+	2.26161i	0.157500	+	0.125839i
$324$		−	1.00000i		−	0.0555556i
$325$	−5.28611	−	28.1404i	−0.293221	−	1.56095i
$326$	−5.91666	−	3.41599i	−0.327694	−	0.189194i
$327$	−15.4102	−	4.12914i	−0.852184	−	0.228342i
$328$	2.32119	−	0.621961i	0.128166	−	0.0343420i
$329$	−24.1806	+	13.9607i	−1.33312	+	0.769679i
$330$	−0.285856	+	7.50744i	−0.0157358	+	0.413271i
$331$			24.0347i			1.32107i	0.750797	+	0.660533i	$0.229669\pi$
$331$			24.0347i			1.32107i	−0.750797	+	0.660533i	$0.770331\pi$
$332$	−13.6226	−	3.65017i	−0.747639	−	0.200329i
$333$	−6.33005	−	1.69613i	−0.346884	−	0.0929474i
$334$			2.47820i			0.135601i
$335$	−4.76546	+	4.41586i	−0.260365	+	0.241264i
$336$	2.84636	−	1.64335i	0.155282	−	0.0896519i
$337$	27.8258	−	7.45590i	1.51577	−	0.406149i	0.597421	−	0.801928i	$-0.296192\pi$
$337$	27.8258	−	7.45590i	1.51577	−	0.406149i	0.918346	+	0.395779i	$0.129525\pi$
$338$	19.1187	+	5.12283i	1.03992	+	0.278645i
$339$	10.8174	+	6.24542i	0.587520	+	0.339205i
$340$	−0.412395	−	1.81232i	−0.0223653	−	0.0982867i
$341$			19.1128i			1.03502i
$342$	0.653625	−	4.30961i	0.0353440	−	0.233037i
$343$	7.43147	+	7.43147i	0.401262	+	0.401262i
$344$	0.591908	−	1.02522i	0.0319136	−	0.0552759i
$345$	1.61129	+	1.01392i	0.0867488	+	0.0545876i
$346$	−11.7038	−	20.2717i	−0.629203	−	1.08981i
$347$	5.65938	+	21.1211i	0.303811	+	1.13384i	0.933964	+	0.357368i	$0.116326\pi$
$347$	5.65938	+	21.1211i	0.303811	+	1.13384i	−0.630152	+	0.776471i	$0.717008\pi$
$348$	1.34035	−	5.00224i	0.0718501	−	0.268148i
$349$			31.7750i			1.70088i	0.526076	+	0.850438i	$0.323663\pi$
$349$			31.7750i			1.70088i	−0.526076	+	0.850438i	$0.676337\pi$
$350$	16.3859	+	1.24964i	0.875862	+	0.0667961i
$351$	2.86326	+	4.95932i	0.152830	+	0.264709i
$352$	0.869596	−	3.24538i	0.0463496	−	0.172979i
$353$	−10.3062	−	10.3062i	−0.548545	−	0.548545i	0.377475	−	0.926020i	$-0.376792\pi$
$353$	−10.3062	−	10.3062i	−0.548545	−	0.548545i	−0.926020	+	0.377475i	$0.876792\pi$
$354$	−12.3269			−0.655167
$355$	−7.66181	−	14.5200i	−0.406647	−	0.770640i
$356$	3.59999	+	2.07845i	0.190799	+	0.110158i
$357$	0.707077	−	2.63885i	0.0374225	−	0.139663i
$358$	21.8984	−	5.86767i	1.15737	−	0.310116i
$359$	32.6835	+	18.8698i	1.72497	+	0.995912i	0.907647	+	0.419734i	$0.137877\pi$
$359$	32.6835	+	18.8698i	1.72497	+	0.995912i	0.817324	+	0.576179i	$0.195457\pi$
$360$	−1.64015	+	1.51983i	−0.0864437	+	0.0801023i
$361$	5.63374	−	18.1455i	0.296513	−	0.955029i
$362$	0.668450	−	0.668450i	0.0351329	−	0.0351329i
$363$	0.0747119	+	0.278829i	0.00392136	+	0.0146347i
$364$	−9.41067	+	16.2998i	−0.493253	+	0.854339i
$365$	19.4421	+	6.01112i	1.01765	+	0.314636i
$366$	5.60453	−	9.70733i	0.292953	−	0.507410i
$367$	23.3540	+	6.25768i	1.21907	+	0.326648i	0.810314	−	0.585996i	$-0.199297\pi$
$367$	23.3540	+	6.25768i	1.21907	+	0.326648i	0.408754	+	0.912644i	$0.365963\pi$
$368$	−0.602020	−	0.602020i	−0.0313825	−	0.0313825i
$369$	−2.40307			−0.125099
$370$	6.83870	+	12.9601i	0.355527	+	0.673763i
$371$	1.79027	−	1.03362i	0.0929464	−	0.0536626i
$372$	−4.02242	+	4.02242i	−0.208553	+	0.208553i
$373$	−15.7126	+	15.7126i	−0.813567	+	0.813567i	−0.985167	−	0.171600i	$-0.945106\pi$
$373$	−15.7126	+	15.7126i	−0.813567	+	0.813567i	0.171600	+	0.985167i	$0.445106\pi$
$374$	−1.39638	−	2.41860i	−0.0722049	−	0.125063i
$375$	−11.0587	+	1.64451i	−0.571071	+	0.0849224i
$376$	−7.35714	+	4.24764i	−0.379415	+	0.219056i
$377$	7.67553	+	28.6455i	0.395310	+	1.47532i
$378$	−3.17470	+	0.850659i	−0.163289	+	0.0437532i
$379$	−3.29453			−0.169228			−0.0846142	−	0.996414i	$-0.526966\pi$
$379$	−3.29453			−0.169228			−0.0846142	+	0.996414i	$0.526966\pi$
$380$	−8.06183	+	5.47785i	−0.413563	+	0.281008i
$381$	6.96395			0.356774
$382$	24.1044	−	6.45876i	1.23329	−	0.330459i
$383$	3.95726	+	14.7687i	0.202207	+	0.754646i	0.990283	+	0.139068i	$0.0444107\pi$
$383$	3.95726	+	14.7687i	0.202207	+	0.754646i	−0.788076	+	0.615578i	$0.788923\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	24.0770	−	5.47876i	1.22708	−	0.279224i
$386$	12.8741	+	22.2986i	0.655275	+	1.13497i
$387$	−0.837085	+	0.837085i	−0.0425514	+	0.0425514i
$388$	6.58908	−	6.58908i	0.334510	−	0.334510i
$389$	12.4895	−	7.21084i	0.633245	−	0.365604i	−0.148763	−	0.988873i	$-0.547529\pi$
$389$	12.4895	−	7.21084i	0.633245	−	0.365604i	0.782008	+	0.623269i	$0.214196\pi$
$390$	3.78236	−	12.2335i	0.191527	−	0.619469i
$391$	−0.707681			−0.0357890
$392$	−2.68867	−	2.68867i	−0.135798	−	0.135798i
$393$	8.81699	+	2.36251i	0.444758	+	0.119173i
$394$	0.846662	−	1.46646i	0.0426542	−	0.0738793i
$395$	2.07567	−	1.09528i	0.104439	−	0.0551095i
$396$	−1.67993	+	2.90972i	−0.0844197	+	0.146219i
$397$	−4.52807	−	16.8990i	−0.227257	−	0.848136i	−0.981488	−	0.191526i	$-0.938656\pi$
$397$	−4.52807	−	16.8990i	−0.227257	−	0.848136i	0.754230	−	0.656610i	$-0.228010\pi$
$398$	−7.17621	+	7.17621i	−0.359711	+	0.359711i
$399$	−14.2378	+	1.59095i	−0.712779	+	0.0796470i
$400$	4.98552	+	0.380212i	0.249276	+	0.0190106i
$401$	12.0308	+	6.94597i	0.600788	+	0.346865i	0.769352	−	0.638826i	$-0.220579\pi$
$401$	12.0308	+	6.94597i	0.600788	+	0.346865i	−0.168563	+	0.985691i	$0.553913\pi$
$402$	−2.80649	+	0.751997i	−0.139975	+	0.0375062i
$403$	8.43122	−	31.4657i	0.419989	−	1.56742i
$404$	−8.55564	−	4.93960i	−0.425659	−	0.245754i
$405$	1.97763	−	1.04354i	0.0982692	−	0.0518541i
$406$	−17.0208			−0.844728
$407$	15.5693	+	15.5693i	0.771742	+	0.771742i
$408$	0.215133	−	0.802888i	0.0106507	−	0.0397489i
$409$	−7.10446	−	12.3053i	−0.351293	−	0.608458i	0.635183	−	0.772362i	$-0.280925\pi$
$409$	−7.10446	−	12.3053i	−0.351293	−	0.608458i	−0.986476	+	0.163904i	$0.947591\pi$
$410$	3.65227	+	3.94141i	0.180373	+	0.194652i
$411$			15.4363i			0.761417i
$412$	−2.28776	+	8.53805i	−0.112710	+	0.420640i
$413$	10.4860	+	39.1342i	0.515981	+	1.92567i
$414$	0.425692	+	0.737321i	0.0209216	+	0.0362373i
$415$	−6.99712	−	30.7496i	−0.343475	−	1.50944i
$416$	−2.86326	+	4.95932i	−0.140383	+	0.243151i
$417$	−3.99643	−	3.99643i	−0.195706	−	0.195706i
$418$	−9.14172	+	11.4417i	−0.447136	+	0.559634i
$419$			18.3478i			0.896350i	0.893946	+	0.448175i	$0.147926\pi$
$419$			18.3478i			0.896350i	−0.893946	+	0.448175i	$0.852074\pi$
$420$	6.22023	+	3.91414i	0.303516	+	0.190991i
$421$	−20.5657	−	11.8736i	−1.00231	−	0.578685i	−0.0933800	−	0.995631i	$-0.529767\pi$
$421$	−20.5657	−	11.8736i	−1.00231	−	0.578685i	−0.908931	+	0.416946i	$0.863100\pi$
$422$	−25.0975	−	6.72486i	−1.22173	−	0.327361i
$423$	8.20582	−	2.19874i	0.398981	−	0.106907i
$424$	0.544704	−	0.314485i	0.0264532	−	0.0152727i
$425$	3.15374	−	2.70680i	0.152979	−	0.131299i
$426$		−	7.34211i		−	0.355726i
$427$	−35.5854	−	9.53508i	−1.72210	−	0.461435i
$428$	−12.0293	−	3.22325i	−0.581460	−	0.155802i
$429$		−	19.2403i		−	0.928932i
$430$	2.64518	+	0.100719i	0.127562	+	0.00485709i
$431$	−0.231076	+	0.133412i	−0.0111306	+	0.00642623i	−0.505555	−	0.862794i	$-0.668712\pi$
$431$	−0.231076	+	0.133412i	−0.0111306	+	0.00642623i	0.494424	+	0.869221i	$0.335379\pi$
$432$	−0.965926	+	0.258819i	−0.0464731	+	0.0124524i
$433$	34.2386	+	9.17422i	1.64540	+	0.440885i	0.958321	−	0.285694i	$-0.0922240\pi$
$433$	34.2386	+	9.17422i	1.64540	+	0.440885i	0.687083	+	0.726579i	$0.258891\pi$
$434$	16.1917	+	9.34829i	0.777227	+	0.448732i
$435$	11.2913	−	2.56935i	0.541376	−	0.123191i
$436$			15.9538i			0.764047i
$437$	1.35264	+	3.45581i	0.0647055	+	0.165314i
$438$	6.43529	+	6.43529i	0.307490	+	0.307490i
$439$	7.06742	−	12.2411i	0.337310	−	0.584237i	−0.646616	−	0.762816i	$-0.723816\pi$
$439$	7.06742	−	12.2411i	0.337310	−	0.584237i	0.983926	+	0.178578i	$0.0571498\pi$
$440$	7.32561	−	1.66695i	0.349235	−	0.0794688i
$441$	1.90118	+	3.29294i	0.0905322	+	0.156806i
$442$	1.23197	+	4.59776i	0.0585987	+	0.218693i
$443$	−7.10427	+	26.5135i	−0.337534	+	1.25969i	0.563562	+	0.826074i	$0.309431\pi$
$443$	−7.10427	+	26.5135i	−0.337534	+	1.25969i	−0.901096	+	0.433620i	$0.857236\pi$
$444$			6.55335i			0.311008i
$445$	−0.353668	+	9.28839i	−0.0167655	+	0.440312i
$446$	−2.14694	−	3.71861i	−0.101660	−	0.176081i
$447$	−3.27854	+	12.2357i	−0.155070	+	0.578728i
$448$	−2.32404	−	2.32404i	−0.109801	−	0.109801i
$449$	−29.7390			−1.40347			−0.701735	−	0.712438i	$-0.747591\pi$
$449$	−29.7390			−1.40347			−0.701735	+	0.712438i	$0.747591\pi$
$450$	−4.71724	−	1.65761i	−0.222373	−	0.0781403i
$451$	6.99228	+	4.03699i	0.329254	+	0.190095i
$452$	3.23287	−	12.0652i	0.152061	−	0.567501i
$453$	−17.4395	+	4.67291i	−0.819381	+	0.219552i
$454$	3.26350	+	1.88418i	0.153164	+	0.0884291i
$455$	−42.0553	−	1.60131i	−1.97158	−	0.0750707i
$456$	−4.33194	+	0.484057i	−0.202862	+	0.0226681i
$457$	−24.0479	+	24.0479i	−1.12491	+	1.12491i	−0.133923	+	0.990992i	$0.542758\pi$
$457$	−24.0479	+	24.0479i	−1.12491	+	1.12491i	−0.990992	+	0.133923i	$0.957242\pi$
$458$	4.55836	+	17.0120i	0.212998	+	0.794920i
$459$	−0.415606	+	0.719850i	−0.0193988	+	0.0335997i
$460$	0.562338	−	1.81881i	0.0262192	−	0.0848023i
$461$	4.26325	−	7.38416i	0.198559	−	0.343915i	−0.749502	−	0.662002i	$-0.769707\pi$
$461$	4.26325	−	7.38416i	0.198559	−	0.343915i	0.948061	+	0.318087i	$0.103040\pi$
$462$	10.6666	+	2.85810i	0.496253	+	0.132971i
$463$	−6.31787	−	6.31787i	−0.293616	−	0.293616i	0.544891	−	0.838507i	$-0.316571\pi$
$463$	−6.31787	−	6.31787i	−0.293616	−	0.293616i	−0.838507	+	0.544891i	$0.816571\pi$
$464$	−5.17870			−0.240415
$465$	−12.1524	−	3.75729i	−0.563556	−	0.174240i
$466$	−10.9455	+	6.31940i	−0.507041	+	0.292740i
$467$	−16.4576	+	16.4576i	−0.761567	+	0.761567i	−0.976606	−	0.215039i	$-0.931012\pi$
$467$	−16.4576	+	16.4576i	−0.761567	+	0.761567i	0.215039	+	0.976606i	$0.431012\pi$
$468$	4.04927	−	4.04927i	0.187177	−	0.187177i
$469$	4.77473	+	8.27008i	0.220477	+	0.381877i
$470$	−16.0778	−	10.1171i	−0.741611	−	0.466666i
$471$	14.7574	−	8.52020i	0.679986	−	0.392590i
$472$	3.19043	+	11.9069i	0.146852	+	0.548058i
$473$	3.84193	−	1.02944i	0.176652	−	0.0473338i
$474$	1.04958			0.0482087
$475$	−19.2460	−	10.2269i	−0.883068	−	0.469244i
$476$	−2.73194			−0.125218
$477$	−0.607538	+	0.162789i	−0.0278173	+	0.00745361i
$478$	−3.79626	−	14.1678i	−0.173637	−	0.648022i
$479$	−5.99334	+	3.46026i	−0.273843	+	0.158103i	−0.630633	−	0.776081i	$-0.717205\pi$
$479$	−5.99334	+	3.46026i	−0.273843	+	0.158103i	0.356790	+	0.934185i	$0.383871\pi$
$480$	1.89255	+	1.19091i	0.0863827	+	0.0543572i
$481$	−18.7640	−	32.5001i	−0.855563	−	1.48188i
$482$	6.87390	−	6.87390i	0.313098	−	0.313098i
$483$	1.97866	−	1.97866i	0.0900319	−	0.0900319i
$484$	0.249991	−	0.144332i	0.0113632	−	0.00656056i
$485$	19.9068	+	6.15477i	0.903919	+	0.279474i
$486$	1.00000			0.0453609
$487$	−19.5607	−	19.5607i	−0.886378	−	0.886378i	0.107795	−	0.994173i	$-0.465621\pi$
$487$	−19.5607	−	19.5607i	−0.886378	−	0.886378i	−0.994173	+	0.107795i	$0.965621\pi$
$488$	−10.8271	−	2.90112i	−0.490121	−	0.131327i
$489$	3.41599	−	5.91666i	0.154476	−	0.267561i
$490$	2.51145	−	8.12294i	0.113456	−	0.366957i
$491$	3.74829	−	6.49223i	0.169158	−	0.292990i	−0.768966	−	0.639290i	$-0.779229\pi$
$491$	3.74829	−	6.49223i	0.169158	−	0.292990i	0.938124	+	0.346299i	$0.112562\pi$
$492$	0.621961	+	2.32119i	0.0280402	+	0.104647i
$493$	−3.04381	+	3.04381i	−0.137086	+	0.137086i
$494$	20.0975	−	14.8041i	0.904228	−	0.666067i
$495$	−7.50744	−	0.285856i	−0.337434	−	0.0128483i
$496$	4.92644	+	2.84428i	0.221204	+	0.127712i
$497$	−23.3090	+	6.24563i	−1.04555	+	0.280155i
$498$	3.65017	−	13.6226i	0.163568	−	0.610445i
$499$	−32.0819	−	18.5225i	−1.43618	−	0.829180i	−0.438600	−	0.898682i	$-0.644526\pi$
$499$	−32.0819	−	18.5225i	−1.43618	−	0.829180i	−0.997582	+	0.0695023i	$0.977859\pi$
$500$	4.45069	+	10.2563i	0.199041	+	0.458675i
$501$	−2.47820			−0.110718
$502$	16.5457	+	16.5457i	0.738471	+	0.738471i
$503$	2.48405	−	9.27062i	0.110758	−	0.413356i	−0.888176	−	0.459503i	$-0.848028\pi$
$503$	2.48405	−	9.27062i	0.110758	−	0.413356i	0.998935	+	0.0461468i	$0.0146942\pi$
$504$	1.64335	+	2.84636i	0.0732005	+	0.126787i
$505$	0.840519	−	22.0746i	0.0374026	−	0.982306i
$506$		−	2.86053i		−	0.127166i
$507$	−5.12283	+	19.1187i	−0.227513	+	0.849090i
$508$	−1.80240	−	6.72666i	−0.0799687	−	0.298447i
$509$	−14.6149	−	25.3138i	−0.647795	−	1.12201i	−0.983648	−	0.180099i	$-0.942358\pi$
$509$	−14.6149	−	25.3138i	−0.647795	−	1.12201i	0.335854	−	0.941914i	$-0.390975\pi$
$510$	1.81232	−	0.412395i	0.0802507	−	0.0182612i
$511$	14.9559	−	25.9044i	0.661610	−	1.14594i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	4.30961	+	0.653625i	0.190274	+	0.0288582i
$514$		−	13.0799i		−	0.576928i
$515$	−19.2725	+	4.38548i	−0.849247	+	0.193247i
$516$	1.02522	+	0.591908i	0.0451326	+	0.0260573i
$517$	−27.5704	−	7.38747i	−1.21255	−	0.324900i
$518$	20.8049	−	5.57466i	0.914116	−	0.244937i
$519$	20.2717	−	11.7038i	0.889827	−	0.513742i
$520$	−12.7956	−	0.487211i	−0.561126	−	0.0213656i
$521$		−	21.4684i		−	0.940546i	−0.882521	−	0.470273i	$-0.844155\pi$
$521$		−	21.4684i		−	0.940546i	0.882521	−	0.470273i	$-0.155845\pi$
$522$	5.00224	+	1.34035i	0.218942	+	0.0586654i
$523$	15.5467	+	4.16571i	0.679808	+	0.182154i	0.582169	−	0.813068i	$-0.302204\pi$
$523$	15.5467	+	4.16571i	0.679808	+	0.182154i	0.0976391	+	0.995222i	$0.468871\pi$
$524$		−	9.12802i		−	0.398759i
$525$	−1.24964	+	16.3859i	−0.0545388	+	0.715139i
$526$	8.43344	−	4.86905i	0.367716	−	0.212301i
$527$	4.56729	−	1.22380i	0.198954	−	0.0533096i
$528$	3.24538	+	0.869596i	0.141237	+	0.0378443i
$529$	19.2908	+	11.1376i	0.838732	+	0.484242i
$530$	1.19036	+	0.749044i	0.0517058	+	0.0325364i
$531$		−	12.3269i		−	0.534942i
$532$	5.22174	+	13.3408i	0.226391	+	0.578399i
$533$	−9.73068	−	9.73068i	−0.421482	−	0.421482i
$534$	−2.07845	+	3.59999i	−0.0899434	+	0.155787i
$535$	−6.17874	−	27.1532i	−0.267130	−	1.17393i
$536$	1.45275	+	2.51623i	0.0627491	+	0.108685i
$537$	5.86767	+	21.8984i	0.253209	+	0.944988i
$538$	−1.04002	+	3.88141i	−0.0448384	+	0.167339i
$539$		−	12.7754i		−	0.550275i
$540$	−1.51983	−	1.64015i	−0.0654032	−	0.0705810i
$541$	5.40375	+	9.35956i	0.232325	+	0.402399i	0.958492	−	0.285120i	$-0.0920333\pi$
$541$	5.40375	+	9.35956i	0.232325	+	0.402399i	−0.726167	+	0.687519i	$0.758700\pi$
$542$	−5.74416	+	21.4375i	−0.246733	+	0.920819i
$543$	0.668450	+	0.668450i	0.0286859	+	0.0286859i
$544$	−0.831211			−0.0356379
$545$	−31.5507	+	16.6485i	−1.35148	+	0.713142i
$546$	−16.2998	−	9.41067i	−0.697565	−	0.402739i
$547$	−10.1670	+	37.9438i	−0.434710	+	1.62236i	0.307050	+	0.951693i	$0.400658\pi$
$547$	−10.1670	+	37.9438i	−0.434710	+	1.62236i	−0.741760	+	0.670665i	$0.766009\pi$
$548$	14.9103	−	3.99521i	0.636938	−	0.170667i
$549$	9.70733	+	5.60453i	0.414299	+	0.239195i
$550$	10.9412	+	12.7478i	0.466535	+	0.543568i
$551$	20.6816	+	9.04596i	0.881068	+	0.385371i
$552$	0.602020	−	0.602020i	0.0256237	−	0.0256237i
$553$	−0.892832	−	3.33209i	−0.0379671	−	0.141695i
$554$	4.19719	−	7.26974i	0.178321	−	0.308862i
$555$	−12.9601	+	6.83870i	−0.550125	+	0.290287i
$556$	−2.82591	+	4.89461i	−0.119845	+	0.207578i
$557$	−16.3266	−	4.37469i	−0.691779	−	0.185362i	−0.104234	−	0.994553i	$-0.533239\pi$
$557$	−16.3266	−	4.37469i	−0.691779	−	0.185362i	−0.587546	+	0.809191i	$0.699906\pi$
$558$	−4.02242	−	4.02242i	−0.170283	−	0.170283i
$559$	−6.77916			−0.286728
$560$	2.17086	−	7.02134i	0.0917354	−	0.296706i
$561$	2.41860	−	1.39638i	0.102113	−	0.0589551i
$562$	2.85674	−	2.85674i	0.120504	−	0.120504i
$563$	0.0412095	−	0.0412095i	0.00173677	−	0.00173677i	−0.706238	−	0.707975i	$-0.749609\pi$
$563$	0.0412095	−	0.0412095i	0.00173677	−	0.00173677i	0.707975	+	0.706238i	$0.249609\pi$
$564$	−4.24764	−	7.35714i	−0.178858	−	0.309791i
$565$	27.2342	−	6.19718i	1.14575	−	0.260717i
$566$	20.6250	−	11.9079i	0.866934	−	0.500525i
$567$	−0.850659	−	3.17470i	−0.0357243	−	0.133325i
$568$	−7.09193	+	1.90028i	−0.297571	+	0.0797339i
$569$	−36.7771			−1.54178			−0.770889	−	0.636969i	$-0.780188\pi$
$569$	−36.7771			−1.54178			−0.770889	+	0.636969i	$0.780188\pi$
$570$	−5.47785	−	8.06183i	−0.229442	−	0.337673i
$571$	5.36345			0.224453			0.112227	−	0.993683i	$-0.464202\pi$
$571$	5.36345			0.224453			0.112227	+	0.993683i	$0.464202\pi$
$572$	−18.5847	+	4.97976i	−0.777067	+	0.208214i
$573$	6.45876	+	24.1044i	0.269818	+	1.00698i
$574$	6.84001	−	3.94908i	0.285496	−	0.164831i
$575$	4.18375	−	0.785906i	0.174474	−	0.0327745i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−15.9109	+	15.9109i	−0.662379	+	0.662379i	−0.955940	−	0.293561i	$-0.905160\pi$
$577$	−15.9109	+	15.9109i	−0.662379	+	0.662379i	0.293561	+	0.955940i	$0.405160\pi$
$578$	11.5323	−	11.5323i	0.479679	−	0.479679i
$579$	−22.2986	+	12.8741i	−0.926699	+	0.535030i
$580$	−5.40420	−	10.2415i	−0.224397	−	0.425257i
$581$	−46.3529			−1.92304
$582$	6.58908	+	6.58908i	0.273126	+	0.273126i
$583$	2.04124	+	0.546950i	0.0845397	+	0.0226523i
$584$	4.55044	−	7.88159i	0.188299	−	0.326143i
$585$	12.2335	+	3.78236i	0.505794	+	0.156381i
$586$	10.2390	−	17.7345i	0.422969	−	0.732604i
$587$	1.24148	+	4.63328i	0.0512415	+	0.191236i	0.986802	−	0.161930i	$-0.0517718\pi$
$587$	1.24148	+	4.63328i	0.0512415	+	0.191236i	−0.935561	+	0.353166i	$0.885105\pi$
$588$	2.68867	−	2.68867i	0.110879	−	0.110879i
$589$	−14.7059	−	19.9643i	−0.605948	−	0.822613i
$590$	−20.2180	+	18.7348i	−0.832362	+	0.771301i
$591$	1.46646	+	0.846662i	0.0603222	+	0.0348270i
$592$	6.33005	−	1.69613i	0.260163	−	0.0697106i
$593$	0.0979587	−	0.365587i	0.00402268	−	0.0150129i	−0.963885	−	0.266318i	$-0.914193\pi$
$593$	0.0979587	−	0.365587i	0.00402268	−	0.0150129i	0.967908	+	0.251305i	$0.0808597\pi$
$594$	−2.90972	−	1.67993i	−0.119387	−	0.0689284i
$595$	−2.85089	−	5.40276i	−0.116875	−	0.221491i
$596$	12.6673			0.518873
$597$	−7.17621	−	7.17621i	−0.293703	−	0.293703i
$598$	−1.26187	+	4.70935i	−0.0516016	+	0.192580i
$599$	−8.63466	−	14.9557i	−0.352803	−	0.611072i	0.633937	−	0.773385i	$-0.281438\pi$
$599$	−8.63466	−	14.9557i	−0.352803	−	0.611072i	−0.986739	+	0.162313i	$0.948105\pi$
$600$	−0.380212	+	4.98552i	−0.0155221	+	0.203533i
$601$		−	5.49417i		−	0.224112i	−0.993702	−	0.112056i	$-0.964256\pi$
$601$		−	5.49417i		−	0.224112i	0.993702	−	0.112056i	$-0.0357436\pi$
$602$	1.00702	−	3.75826i	0.0410432	−	0.153175i
$603$	−0.751997	−	2.80649i	−0.0306237	−	0.114289i
$604$	9.02736	+	15.6359i	0.367318	+	0.636214i
$605$	0.546312	+	0.343772i	0.0222108	+	0.0139763i
$606$	4.93960	−	8.55564i	0.200658	−	0.347549i
$607$	−19.7187	−	19.7187i	−0.800359	−	0.800359i	0.182792	−	0.983152i	$-0.441486\pi$
$607$	−19.7187	−	19.7187i	−0.800359	−	0.800359i	−0.983152	+	0.182792i	$0.941486\pi$
$608$	1.58875	+	4.05905i	0.0644324	+	0.164616i
$609$		−	17.0208i		−	0.689718i
$610$	−5.56123	−	24.4395i	−0.225168	−	0.989525i
$611$	42.1308	+	24.3242i	1.70443	+	0.984054i
$612$	0.802888	+	0.215133i	0.0324548	+	0.00869625i
$613$	13.1009	−	3.51036i	0.529139	−	0.141782i	0.0156482	−	0.999878i	$-0.495019\pi$
$613$	13.1009	−	3.51036i	0.529139	−	0.141782i	0.513491	+	0.858095i	$0.328352\pi$
$614$	−12.3921	+	7.15458i	−0.500104	+	0.288735i
$615$	−3.94141	+	3.65227i	−0.158933	+	0.147274i
$616$		−	11.0428i		−	0.444928i
$617$	38.3659	+	10.2801i	1.54455	+	0.413862i	0.927734	−	0.373243i	$-0.121754\pi$
$617$	38.3659	+	10.2801i	1.54455	+	0.413862i	0.616820	+	0.787104i	$0.288421\pi$
$618$	−8.53805	−	2.28776i	−0.343451	−	0.0920273i
$619$			41.6336i			1.67340i	0.547665	+	0.836698i	$0.315517\pi$
$619$			41.6336i			1.67340i	−0.547665	+	0.836698i	$0.684483\pi$
$620$	−0.483981	+	12.7108i	−0.0194372	+	0.510478i
$621$	−0.737321	+	0.425692i	−0.0295877	+	0.0170824i
$622$	−20.2132	+	5.41610i	−0.810474	+	0.217166i
$623$	13.1969	+	3.53611i	0.528724	+	0.141671i
$624$	−4.95932	−	2.86326i	−0.198532	−	0.114622i
$625$	−15.6386	+	19.5047i	−0.625546	+	0.780188i
$626$			1.73550i			0.0693647i
$627$	−11.4417	−	9.14172i	−0.456939	−	0.365085i
$628$	−12.0494	−	12.0494i	−0.480823	−	0.480823i
$629$	2.72361	−	4.71743i	0.108597	−	0.188096i
$630$	−3.91414	+	6.22023i	−0.155943	+	0.247820i
$631$	8.01752	+	13.8868i	0.319173	+	0.552823i	0.980316	−	0.197437i	$-0.0632617\pi$
$631$	8.01752	+	13.8868i	0.319173	+	0.552823i	−0.661143	+	0.750260i	$0.729928\pi$
$632$	−0.271651	−	1.01381i	−0.0108057	−	0.0403273i
$633$	6.72486	−	25.0975i	0.267289	−	0.997537i
$634$		−	24.8227i		−	0.985835i
$635$	11.4220	−	10.5840i	0.453266	−	0.420015i
$636$	0.314485	+	0.544704i	0.0124701	+	0.0215989i
$637$	−5.63560	+	21.0323i	−0.223291	+	0.833332i
$638$	−12.3035	−	12.3035i	−0.487098	−	0.487098i
$639$	7.34211			0.290449
$640$	0.660499	−	2.13629i	0.0261085	−	0.0844443i
$641$	−21.2101	−	12.2456i	−0.837747	−	0.483673i	0.0187508	−	0.999824i	$-0.494031\pi$
$641$	−21.2101	−	12.2456i	−0.837747	−	0.483673i	−0.856498	+	0.516151i	$0.827364\pi$
$642$	3.22325	−	12.0293i	0.127212	−	0.474760i
$643$	−44.8101	+	12.0068i	−1.76714	+	0.473504i	−0.988145	−	0.153526i	$-0.950937\pi$
$643$	−44.8101	+	12.0068i	−1.76714	+	0.473504i	−0.778995	+	0.627030i	$0.784270\pi$
$644$	−2.42335	−	1.39912i	−0.0954933	−	0.0551331i
$645$	−0.100719	+	2.64518i	−0.00396579	+	0.104154i
$646$	3.31952	+	1.45193i	0.130605	+	0.0571254i
$647$	9.74555	−	9.74555i	0.383137	−	0.383137i	−0.489094	−	0.872231i	$-0.662673\pi$
$647$	9.74555	−	9.74555i	0.383137	−	0.383137i	0.872231	+	0.489094i	$0.162673\pi$
$648$	−0.258819	−	0.965926i	−0.0101674	−	0.0379452i
$649$	−20.7083	+	35.8679i	−0.812873	+	1.40794i
$650$	−12.3893	−	25.8134i	−0.485947	−	1.01249i
$651$	−9.34829	+	16.1917i	−0.366388	+	0.634603i
$652$	−6.59918	−	1.76824i	−0.258444	−	0.0692498i
$653$	−28.2367	−	28.2367i	−1.10499	−	1.10499i	−0.993799	−	0.111189i	$-0.964534\pi$
$653$	−28.2367	−	28.2367i	−1.10499	−	1.10499i	−0.111189	−	0.993799i	$-0.535466\pi$
$654$	−15.9538			−0.623842
$655$	18.0518	−	9.52548i	0.705344	−	0.372191i
$656$	2.08112	−	1.20154i	0.0812541	−	0.0469121i
$657$	−6.43529	+	6.43529i	−0.251065	+	0.251065i
$658$	−19.7434	+	19.7434i	−0.769679	+	0.769679i
$659$	−2.41936	−	4.19046i	−0.0942450	−	0.163237i	0.815048	−	0.579393i	$-0.196710\pi$
$659$	−2.41936	−	4.19046i	−0.0942450	−	0.163237i	−0.909293	+	0.416156i	$0.863377\pi$
$660$	1.66695	+	7.32561i	0.0648860	+	0.285149i
$661$	40.6683	−	23.4798i	1.58181	−	0.913260i	0.587217	−	0.809429i	$-0.300223\pi$
$661$	40.6683	−	23.4798i	1.58181	−	0.913260i	0.994595	−	0.103831i	$-0.0331100\pi$
$662$	6.22063	+	23.2157i	0.241772	+	0.902304i
$663$	−4.59776	+	1.23197i	−0.178562	+	0.0478456i
$664$	−14.1032			−0.547310
$665$	−20.9341	+	24.2484i	−0.811791	+	0.940313i
$666$	−6.55335			−0.253937
$667$	−4.25883	+	1.14115i	−0.164903	+	0.0441855i
$668$	0.641405	+	2.39376i	0.0248167	+	0.0926172i
$669$	3.71861	−	2.14694i	0.143770	−	0.0830054i
$670$	−3.46017	+	5.49879i	−0.133678	+	0.212437i
$671$	−18.8304	−	32.6153i	−0.726941	−	1.25910i
$672$	2.32404	−	2.32404i	0.0896519	−	0.0896519i
$673$	−14.1915	+	14.1915i	−0.547042	+	0.547042i	−0.925584	−	0.378542i	$-0.876425\pi$
$673$	−14.1915	+	14.1915i	−0.547042	+	0.547042i	0.378542	+	0.925584i	$0.376425\pi$
$674$	24.9479	−	14.4037i	0.960958	−	0.554809i
$675$	1.65761	−	4.71724i	0.0638013	−	0.181567i
$676$	19.7931			0.761273
$677$	14.9031	+	14.9031i	0.572774	+	0.572774i	0.932903	−	0.360128i	$-0.117267\pi$
$677$	14.9031	+	14.9031i	0.572774	+	0.572774i	−0.360128	+	0.932903i	$0.617267\pi$
$678$	12.0652	+	3.23287i	0.463363	+	0.124158i
$679$	15.3133	−	26.5234i	0.587671	−	1.01788i
$680$	−0.867405	−	1.64383i	−0.0332635	−	0.0630379i
$681$	−1.88418	+	3.26350i	−0.0722021	+	0.125058i
$682$	4.94676	+	18.4615i	0.189421	+	0.706929i
$683$	3.54587	−	3.54587i	0.135679	−	0.135679i	−0.636006	−	0.771684i	$-0.719414\pi$
$683$	3.54587	−	3.54587i	0.135679	−	0.135679i	0.771684	+	0.636006i	$0.219414\pi$
$684$	−0.484057	−	4.33194i	−0.0185084	−	0.165636i
$685$	23.4606	+	25.3179i	0.896384	+	0.967349i
$686$	9.10165	+	5.25484i	0.347503	+	0.200631i
$687$	−17.0120	+	4.55836i	−0.649050	+	0.173912i
$688$	0.306394	−	1.14348i	0.0116812	−	0.0435947i
$689$	−3.11926	−	1.80091i	−0.118834	−	0.0686091i
$690$	1.81881	+	0.562338i	0.0692408	+	0.0214079i
$691$	25.8653			0.983962			0.491981	−	0.870606i	$-0.336273\pi$
$691$	25.8653			0.983962			0.491981	+	0.870606i	$0.336273\pi$
$692$	−16.5517	−	16.5517i	−0.629203	−	0.629203i
$693$	−2.85810	+	10.6666i	−0.108570	+	0.405189i
$694$	10.9331	+	18.9366i	0.415014	+	0.718825i
$695$	−12.6287	−	0.480854i	−0.479033	−	0.0182398i
$696$		−	5.17870i		−	0.196298i
$697$	0.516981	−	1.92940i	0.0195820	−	0.0730812i
$698$	8.22397	+	30.6923i	0.311282	+	1.16172i
$699$	−6.31940	−	10.9455i	−0.239022	−	0.413997i
$700$	16.1510	−	3.03392i	0.610450	−	0.114671i
$701$	5.01822	−	8.69181i	0.189535	−	0.328285i	−0.755560	−	0.655079i	$-0.772635\pi$
$701$	5.01822	−	8.69181i	0.189535	−	0.328285i	0.945095	+	0.326794i	$0.105968\pi$
$702$	4.04927	+	4.04927i	0.152830	+	0.152830i
$703$	−28.2424	−	4.28343i	−1.06518	−	0.161553i
$704$		−	3.35986i		−	0.126630i
$705$	10.1171	−	16.0778i	0.381031	−	0.605523i
$706$	−12.6225	−	7.28759i	−0.475053	−	0.274272i
$707$	−31.3635	−	8.40383i	−1.17955	−	0.316059i
$708$	−11.9069	+	3.19043i	−0.447487	+	0.119904i
$709$	−6.56715	+	3.79154i	−0.246634	+	0.142394i	−0.618222	−	0.786003i	$-0.712147\pi$
$709$	−6.56715	+	3.79154i	−0.246634	+	0.142394i	0.371588	+	0.928398i	$0.378813\pi$
$710$	−11.1588	−	12.0422i	−0.418782	−	0.451936i
$711$			1.04958i			0.0393622i
$712$	4.01526	+	1.07589i	0.150478	+	0.0403205i
$713$	4.67813	+	1.25350i	0.175197	+	0.0469440i
$714$		−	2.73194i		−	0.102240i
$715$	−29.2421	−	31.5571i	−1.09359	−	1.18017i
$716$	19.6336	−	11.3355i	0.733742	−	0.423626i
$717$	14.1678	−	3.79626i	0.529107	−	0.141774i
$718$	36.4537	+	9.76775i	1.36044	+	0.364529i
$719$	42.1115	+	24.3131i	1.57049	+	0.906725i	0.996108	+	0.0881401i	$0.0280923\pi$
$719$	42.1115	+	24.3131i	1.57049	+	0.906725i	0.574386	+	0.818585i	$0.305241\pi$
$720$	−1.19091	+	1.89255i	−0.0443824	+	0.0705312i
$721$			29.0519i			1.08195i
$722$	0.745361	−	18.9854i	0.0277395	−	0.706562i
$723$	6.87390	+	6.87390i	0.255643	+	0.255643i
$724$	0.472665	−	0.818680i	0.0175665	−	0.0304260i
$725$	14.6145	−	21.3750i	0.542768	−	0.793848i
$726$	0.144332	+	0.249991i	0.00535668	+	0.00927804i
$727$	−0.985193	−	3.67679i	−0.0365388	−	0.136365i	0.945247	−	0.326356i	$-0.105821\pi$
$727$	−0.985193	−	3.67679i	−0.0365388	−	0.136365i	−0.981786	+	0.189991i	$0.939154\pi$
$728$	−4.87132	+	18.1800i	−0.180543	+	0.673796i
$729$			1.00000i			0.0370370i
$730$	20.3354	+	0.774300i	0.752649	+	0.0286581i
$731$	−0.492001	−	0.852170i	−0.0181973	−	0.0315187i
$732$	2.90112	−	10.8271i	0.107228	−	0.400182i
$733$	−12.4051	−	12.4051i	−0.458193	−	0.458193i	0.439869	−	0.898062i	$-0.355025\pi$
$733$	−12.4051	−	12.4051i	−0.458193	−	0.458193i	−0.898062	+	0.439869i	$0.855025\pi$
$734$	24.1778			0.892420
$735$	8.12294	+	2.51145i	0.299619	+	0.0926362i
$736$	−0.737321	−	0.425692i	−0.0271780	−	0.0156912i
$737$	−2.52660	+	9.42942i	−0.0930687	+	0.347337i
$738$	−2.32119	+	0.621961i	−0.0854442	+	0.0228947i
$739$	5.03031	+	2.90425i	0.185043	+	0.106835i	0.589660	−	0.807652i	$-0.299262\pi$
$739$	5.03031	+	2.90425i	0.185043	+	0.106835i	−0.404617	+	0.914486i	$0.632595\pi$
$740$	9.96000	+	10.7485i	0.366137	+	0.395123i
$741$	14.8041	+	20.0975i	0.543841	+	0.738299i
$742$	1.46175	−	1.46175i	0.0536626	−	0.0536626i
$743$	−12.1650	−	45.4005i	−0.446292	−	1.66558i	−0.712504	−	0.701668i	$-0.752439\pi$
$743$	−12.1650	−	45.4005i	−0.446292	−	1.66558i	0.266212	−	0.963914i	$-0.414228\pi$
$744$	−2.84428	+	4.92644i	−0.104276	+	0.180612i
$745$	13.2189	+	25.0513i	0.484303	+	0.917807i
$746$	−11.1105	+	19.2439i	−0.406783	+	0.704570i
$747$	13.6226	+	3.65017i	0.498426	+	0.133553i
$748$	−1.97478	−	1.97478i	−0.0722049	−	0.0722049i
$749$	−40.9314			−1.49560
$750$	−10.2563	+	4.45069i	−0.374507	+	0.162516i
$751$	−2.33666	+	1.34907i	−0.0852659	+	0.0492283i	−0.542027	−	0.840361i	$-0.682343\pi$
$751$	−2.33666	+	1.34907i	−0.0852659	+	0.0492283i	0.456761	+	0.889590i	$0.349010\pi$
$752$	−6.00708	+	6.00708i	−0.219056	+	0.219056i
$753$	−16.5457	+	16.5457i	−0.602959	+	0.602959i
$754$	14.8280	+	25.6828i	0.540003	+	0.935313i
$755$	−21.5015	+	34.1695i	−0.782519	+	1.24355i
$756$	−2.84636	+	1.64335i	−0.103521	+	0.0597679i
$757$	1.30634	+	4.87532i	0.0474797	+	0.177197i	0.985594	−	0.169130i	$-0.0540957\pi$
$757$	1.30634	+	4.87532i	0.0474797	+	0.177197i	−0.938114	+	0.346326i	$0.887429\pi$
$758$	−3.18227	+	0.852686i	−0.115585	+	0.0309709i
$759$	2.86053			0.103831
$760$	−6.36936	+	7.37775i	−0.231041	+	0.267619i
$761$	6.69955			0.242858			0.121429	−	0.992600i	$-0.461252\pi$
$761$	6.69955			0.242858			0.121429	+	0.992600i	$0.461252\pi$
$762$	6.72666	−	1.80240i	0.243681	−	0.0652942i
$763$	13.5712	+	50.6485i	0.491311	+	1.83360i
$764$	21.6114	−	12.4774i	0.781874	−	0.451415i
$765$	0.412395	+	1.81232i	0.0149102	+	0.0655244i
$766$	7.64485	+	13.2413i	0.276220	+	0.478426i
$767$	49.9149	−	49.9149i	1.80232	−	1.80232i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−35.1666	+	20.3035i	−1.26814	+	0.732162i	−0.974636	−	0.223796i	$-0.928155\pi$
$769$	−35.1666	+	20.3035i	−1.26814	+	0.732162i	−0.293505	+	0.955958i	$0.594822\pi$
$770$	21.8386	−	11.5237i	0.787010	−	0.415284i
$771$	13.0799			0.471059
$772$	18.2067	+	18.2067i	0.655275	+	0.655275i
$773$	26.7838	+	7.17668i	0.963345	+	0.258127i	0.706015	−	0.708196i	$-0.250491\pi$
$773$	26.7838	+	7.17668i	0.963345	+	0.258127i	0.257329	+	0.966324i	$0.417158\pi$
$774$	−0.591908	+	1.02522i	−0.0212757	+	0.0368506i
$775$	−25.6423	+	12.3071i	−0.921100	+	0.442086i
$776$	4.65918	−	8.06994i	0.167255	−	0.289694i
$777$	5.57466	+	20.8049i	0.199990	+	0.746372i
$778$	10.1977	−	10.1977i	0.365604	−	0.365604i
$779$	−10.4100	+	1.16322i	−0.372975	+	0.0416768i
$780$	0.487211	−	12.7956i	0.0174449	−	0.458157i
$781$	−21.3635	−	12.3342i	−0.764447	−	0.441354i
$782$	−0.683567	+	0.183161i	−0.0244443	+	0.00654983i
$783$	−1.34035	+	5.00224i	−0.0479001	+	0.178766i
$784$	−3.29294	−	1.90118i	−0.117605	−	0.0678992i
$785$	11.2552	−	36.4033i	0.401714	−	1.29929i
$786$	9.12802			0.325586
$787$	7.63086	+	7.63086i	0.272011	+	0.272011i	0.829909	−	0.557898i	$-0.188392\pi$
$787$	7.63086	+	7.63086i	0.272011	+	0.272011i	−0.557898	+	0.829909i	$0.688392\pi$
$788$	0.438265	−	1.63563i	0.0156125	−	0.0582668i
$789$	4.86905	+	8.43344i	0.173343	+	0.300239i
$790$	1.72147	−	1.59518i	0.0612471	−	0.0567540i
$791$		−	41.0536i		−	1.45970i
$792$	−0.869596	+	3.24538i	−0.0308997	+	0.115319i
$793$	16.6133	+	62.0018i	0.589956	+	2.20175i
$794$	−8.74756	−	15.1512i	−0.310439	−	0.537697i
$795$	−0.749044	+	1.19036i	−0.0265658	+	0.0422176i
$796$	−5.07435	+	8.78902i	−0.179855	+	0.311519i
$797$	24.8629	+	24.8629i	0.880688	+	0.880688i	0.993604	−	0.112917i	$-0.0360193\pi$
$797$	24.8629	+	24.8629i	0.880688	+	0.880688i	−0.112917	+	0.993604i	$0.536019\pi$
$798$	−13.3408	+	5.22174i	−0.472261	+	0.184848i
$799$			7.06138i			0.249814i
$800$	4.91405	−	0.923091i	0.173738	−	0.0326362i
$801$	−3.59999	−	2.07845i	−0.127199	−	0.0734385i
$802$	13.4186	+	3.59550i	0.473827	+	0.126961i
$803$	29.5358	−	7.91409i	1.04229	−	0.279282i
$804$	−2.51623	+	1.45275i	−0.0887406	+	0.0512344i
$805$	0.238073	−	6.25253i	0.00839098	−	0.220373i
$806$		−	32.5757i		−	1.14743i
$807$	−3.88141	−	1.04002i	−0.136632	−	0.0366104i
$808$	−9.54258	−	2.55693i	−0.335707	−	0.0899524i
$809$		−	32.2087i		−	1.13240i	−0.824269	−	0.566199i	$-0.808413\pi$
$809$		−	32.2087i		−	1.13240i	0.824269	−	0.566199i	$-0.191587\pi$
$810$	1.64015	−	1.51983i	0.0576291	−	0.0534015i
$811$	−6.60201	+	3.81167i	−0.231828	+	0.133846i	−0.611415	−	0.791310i	$-0.709399\pi$
$811$	−6.60201	+	3.81167i	−0.231828	+	0.133846i	0.379587	+	0.925156i	$0.376066\pi$
$812$	−16.4408	+	4.40531i	−0.576960	+	0.154596i
$813$	−21.4375	−	5.74416i	−0.751846	−	0.201456i
$814$	19.0684	+	11.0092i	0.668348	+	0.385871i
$815$	−3.38960	−	14.8960i	−0.118732	−	0.521783i
$816$		−	0.831211i		−	0.0290982i
$817$	−3.22100	+	4.03140i	−0.112689	+	0.141041i
$818$	−10.0472	−	10.0472i	−0.351293	−	0.351293i
$819$	9.41067	−	16.2998i	0.328835	−	0.569560i
$820$	4.54793	+	2.86183i	0.158821	+	0.0999395i
$821$	−3.06848	−	5.31476i	−0.107091	−	0.185486i	0.807500	−	0.589868i	$-0.200820\pi$
$821$	−3.06848	−	5.31476i	−0.107091	−	0.185486i	−0.914590	+	0.404381i	$0.867487\pi$
$822$	3.99521	+	14.9103i	0.139349	+	0.520058i
$823$	10.2358	−	38.2003i	0.356796	−	1.33158i	−0.521414	−	0.853304i	$-0.674595\pi$
$823$	10.2358	−	38.2003i	0.356796	−	1.33158i	0.878209	−	0.478276i	$-0.158738\pi$
$824$			8.83924i			0.307929i
$825$	−12.7478	+	10.9412i	−0.443822	+	0.380924i
$826$	20.2574	+	35.0868i	0.704844	+	1.22083i
$827$	0.586233	−	2.18785i	0.0203853	−	0.0760790i	−0.954984	−	0.296658i	$-0.904128\pi$
$827$	0.586233	−	2.18785i	0.0203853	−	0.0760790i	0.975369	+	0.220579i	$0.0707946\pi$
$828$	0.602020	+	0.602020i	0.0209216	+	0.0209216i
$829$	54.5778			1.89557			0.947783	−	0.318917i	$-0.103319\pi$
$829$	54.5778			1.89557			0.947783	+	0.318917i	$0.103319\pi$
$830$	−14.7173	−	27.8909i	−0.510845	−	0.968107i
$831$	7.26974	+	4.19719i	0.252184	+	0.145599i
$832$	−1.48213	+	5.53140i	−0.0513838	+	0.191767i
$833$	−3.05287	+	0.818013i	−0.105776	+	0.0283425i
$834$	−4.89461	−	2.82591i	−0.169487	−	0.0978531i
$835$	−4.06463	+	3.76645i	−0.140662	+	0.130343i
$836$	−5.86888	+	13.4179i	−0.202979	+	0.464069i
$837$	4.02242	−	4.02242i	0.139035	−	0.139035i
$838$	4.74877	+	17.7226i	0.164043	+	0.612218i
$839$	25.0388	−	43.3685i	0.864436	−	1.49725i	−0.00317075	−	0.999995i	$-0.501009\pi$
$839$	25.0388	−	43.3685i	0.864436	−	1.49725i	0.867606	−	0.497252i	$-0.165657\pi$
$840$	7.02134	+	2.17086i	0.242259	+	0.0749017i
$841$	1.09053	−	1.88885i	0.0376045	−	0.0651328i
$842$	−22.9381	−	6.14624i	−0.790498	−	0.211813i
$843$	2.85674	+	2.85674i	0.0983915	+	0.0983915i
$844$	−25.9829			−0.894368
$845$	20.6550	+	39.1434i	0.710552	+	1.34658i
$846$	7.35714	−	4.24764i	0.252944	−	0.146037i
$847$	0.670869	−	0.670869i	0.0230513	−	0.0230513i
$848$	0.444749	−	0.444749i	0.0152727	−	0.0152727i
$849$	11.9079	+	20.6250i	0.408677	+	0.707849i
$850$	2.34571	−	3.43081i	0.0804571	−	0.117676i
$851$	4.83192	−	2.78971i	0.165636	−	0.0956300i
$852$	−1.90028	−	7.09193i	−0.0651025	−	0.242966i
$853$	30.3150	−	8.12288i	1.03797	−	0.278122i	0.300696	−	0.953720i	$-0.402781\pi$
$853$	30.3150	−	8.12288i	1.03797	−	0.278122i	0.737270	+	0.675598i	$0.236114\pi$
$854$	−36.8407			−1.26066
$855$	8.06183	−	5.47785i	0.275709	−	0.187339i
$856$	−12.4537			−0.425658
$857$	−44.4765	+	11.9174i	−1.51929	+	0.407092i	−0.919508	−	0.393072i	$-0.871412\pi$
$857$	−44.4765	+	11.9174i	−1.51929	+	0.407092i	−0.599781	+	0.800164i	$0.704746\pi$
$858$	−4.97976	−	18.5847i	−0.170006	−	0.634472i
$859$	11.5340	−	6.65918i	0.393537	−	0.227208i	−0.290155	−	0.956980i	$-0.593707\pi$
$859$	11.5340	−	6.65918i	0.393537	−	0.227208i	0.683691	+	0.729771i	$0.260373\pi$
$860$	2.58111	−	0.587336i	0.0880152	−	0.0200280i
$861$	3.94908	+	6.84001i	0.134584	+	0.233107i
$862$	−0.188673	+	0.188673i	−0.00642623	+	0.00642623i
$863$	−10.9076	+	10.9076i	−0.371300	+	0.371300i	−0.867951	−	0.496650i	$-0.834563\pi$
$863$	−10.9076	+	10.9076i	−0.371300	+	0.371300i	0.496650	+	0.867951i	$0.334563\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	15.4607	−	50.0057i	0.525681	−	1.70024i
$866$	35.4465			1.20452
$867$	11.5323	+	11.5323i	0.391656	+	0.391656i
$868$	18.0595	+	4.83903i	0.612980	+	0.164247i
$869$	1.76322	−	3.05398i	0.0598130	−	0.103599i
$870$	10.2415	−	5.40420i	0.347221	−	0.183219i
$871$	8.31919	−	14.4093i	0.281885	−	0.488239i
$872$	4.12914	+	15.4102i	0.139830	+	0.521854i
$873$	−6.58908	+	6.58908i	−0.223007	+	0.223007i
$874$	2.20098	+	2.98797i	0.0744492	+	0.101070i
$875$	22.8542	+	28.7746i	0.772613	+	0.972760i
$876$	7.88159	+	4.55044i	0.266294	+	0.153745i
$877$	52.6333	−	14.1030i	1.77730	−	0.476226i	0.787212	−	0.616682i	$-0.211524\pi$
$877$	52.6333	−	14.1030i	1.77730	−	0.476226i	0.990087	+	0.140456i	$0.0448570\pi$
$878$	3.65837	−	13.6532i	0.123464	−	0.460773i
$879$	17.7345	+	10.2390i	0.598169	+	0.345353i
$880$	6.64456	−	3.50616i	0.223988	−	0.118193i
$881$	36.8050			1.23999			0.619997	−	0.784605i	$-0.287134\pi$
$881$	36.8050			1.23999			0.619997	+	0.784605i	$0.287134\pi$
$882$	2.68867	+	2.68867i	0.0905322	+	0.0905322i
$883$	−1.14605	+	4.27713i	−0.0385678	+	0.143937i	−0.982525	−	0.186131i	$-0.940405\pi$
$883$	−1.14605	+	4.27713i	−0.0385678	+	0.143937i	0.943957	+	0.330068i	$0.107072\pi$
$884$	2.37998	+	4.12224i	0.0800473	+	0.138646i
$885$	−18.7348	−	20.2180i	−0.629764	−	0.679621i
$886$			27.4488i			0.922160i
$887$	2.31329	−	8.63333i	0.0776728	−	0.289879i	−0.916153	−	0.400828i	$-0.868722\pi$
$887$	2.31329	−	8.63333i	0.0776728	−	0.289879i	0.993826	+	0.110949i	$0.0353891\pi$
$888$	1.69613	+	6.33005i	0.0569184	+	0.212422i
$889$	−11.4442	−	19.8219i	−0.383826	−	0.664806i
$890$	2.06240	+	9.06343i	0.0691317	+	0.303807i
$891$	1.67993	−	2.90972i	0.0562798	−	0.0974794i
$892$	−3.03623	−	3.03623i	−0.101660	−	0.101660i
$893$	34.4828	−	13.4969i	1.15392	−	0.451657i
$894$			12.6673i			0.423658i
$895$	42.9059	+	26.9989i	1.43419	+	0.902475i
$896$	−2.84636	−	1.64335i	−0.0950902	−	0.0549004i
$897$	−4.70935	−	1.26187i	−0.157241	−	0.0421325i
$898$	−28.7257	+	7.69702i	−0.958587	+	0.256853i
$899$	25.5126	−	14.7297i	0.850892	−	0.491263i
$900$	−4.98552	−	0.380212i	−0.166184	−	0.0126737i
$901$		−	0.522807i		−	0.0174172i
$902$	7.79887	+	2.08970i	0.259674	+	0.0695795i
$903$	3.75826	+	1.00702i	0.125067	+	0.0335117i
$904$		−	12.4908i		−	0.415439i
$905$	2.11229	+	0.0804284i	0.0702150	+	0.00267353i
$906$	−15.6359	+	9.02736i	−0.519466	+	0.299914i
$907$	32.2523	−	8.64197i	1.07092	−	0.286952i	0.320048	−	0.947401i	$-0.396301\pi$
$907$	32.2523	−	8.64197i	1.07092	−	0.286952i	0.750870	+	0.660450i	$0.229634\pi$
$908$	3.63996	+	0.975325i	0.120796	+	0.0323673i
$909$	8.55564	+	4.93960i	0.283773	+	0.163836i
$910$	−41.0368	+	9.33797i	−1.36036	+	0.309551i
$911$			18.6575i			0.618151i	0.951037	+	0.309076i	$0.100020\pi$
$911$			18.6575i			0.618151i	−0.951037	+	0.309076i	$0.899980\pi$
$912$	−4.05905	+	1.58875i	−0.134409	+	0.0526088i
$913$	−33.5061	−	33.5061i	−1.10889	−	1.10889i
$914$	−17.0045	+	29.4526i	−0.562457	+	0.974205i
$915$	24.4395	−	5.56123i	0.807944	−	0.183849i
$916$	8.80608	+	15.2526i	0.290961	+	0.503959i
$917$	−7.76483	−	28.9787i	−0.256417	−	0.956962i
$918$	−0.215133	+	0.802888i	−0.00710046	+	0.0264993i
$919$		−	51.1261i		−	1.68649i	−0.537526	−	0.843247i	$-0.680641\pi$
$919$		−	51.1261i		−	1.68649i	0.537526	−	0.843247i	$-0.319359\pi$
$920$	0.0724355	−	1.90238i	0.00238813	−	0.0627195i
$921$	−7.15458	−	12.3921i	−0.235751	−	0.408333i
$922$	2.20682	−	8.23596i	0.0726777	−	0.271237i
$923$	29.7302	+	29.7302i	0.978580	+	0.978580i
$924$	11.0428			0.363283
$925$	−10.8629	+	30.9137i	−0.357169	+	1.01644i
$926$	−7.73778	−	4.46741i	−0.254279	−	0.146808i
$927$	2.28776	−	8.53805i	0.0751400	−	0.280426i
$928$	−5.00224	+	1.34035i	−0.164207	+	0.0439990i
$929$	−2.67635	−	1.54519i	−0.0878081	−	0.0506960i	0.455453	−	0.890260i	$-0.349477\pi$
$929$	−2.67635	−	1.54519i	−0.0878081	−	0.0506960i	−0.543261	+	0.839564i	$0.682811\pi$
$930$	−12.7108	−	0.483981i	−0.416804	−	0.0158704i
$931$	9.82975	+	13.3445i	0.322157	+	0.437349i
$932$	−8.93698	+	8.93698i	−0.292740	+	0.292740i
$933$	−5.41610	−	20.2132i	−0.177315	−	0.661750i
$934$	−11.6373	+	20.1564i	−0.380784	+	0.659536i
$935$	1.84461	−	5.96614i	0.0603252	−	0.195114i
$936$	2.86326	−	4.95932i	0.0935887	−	0.162100i
$937$	23.3631	+	6.26011i	0.763238	+	0.204509i	0.619382	−	0.785090i	$-0.287383\pi$
$937$	23.3631	+	6.26011i	0.763238	+	0.204509i	0.143856	+	0.989599i	$0.454050\pi$
$938$	6.75249	+	6.75249i	0.220477	+	0.220477i
$939$	−1.73550			−0.0566360
$940$	−18.1484	−	5.61113i	−0.591936	−	0.183015i
$941$	−35.6792	+	20.5994i	−1.16311	+	0.671521i	−0.952047	−	0.305952i	$-0.901025\pi$
$941$	−35.6792	+	20.5994i	−1.16311	+	0.671521i	−0.211061	+	0.977473i	$0.567692\pi$
$942$	12.0494	−	12.0494i	0.392590	−	0.392590i
$943$	1.44670	−	1.44670i	0.0471109	−	0.0471109i
$944$	6.16345	+	10.6754i	0.200603	+	0.347455i
$945$	−6.22023	−	3.91414i	−0.202344	−	0.127327i
$946$	3.44458	−	1.98873i	0.111993	−	0.0646592i
$947$	5.66389	+	21.1379i	0.184052	+	0.686890i	0.994832	+	0.101539i	$0.0323767\pi$
$947$	5.66389	+	21.1379i	0.184052	+	0.686890i	−0.810780	+	0.585351i	$0.800957\pi$
$948$	1.01381	−	0.271651i	0.0329271	−	0.00882280i
$949$	−52.1164			−1.69177
$950$	−21.2372	−	4.89723i	−0.689025	−	0.158887i
$951$	24.8227			0.804931
$952$	−2.63885	+	0.707077i	−0.0855256	+	0.0229165i
$953$	0.993195	+	3.70665i	0.0321727	+	0.120070i	0.980145	−	0.198284i	$-0.0635367\pi$
$953$	0.993195	+	3.70665i	0.0321727	+	0.120070i	−0.947972	+	0.318354i	$0.896870\pi$
$954$	−0.544704	+	0.314485i	−0.0176354	+	0.0101818i
$955$	47.2280	+	29.7187i	1.52826	+	0.961675i
$956$	−7.33381	−	12.7025i	−0.237192	−	0.410829i
$957$	12.3035	−	12.3035i	0.397714	−	0.397714i
$958$	−4.89354	+	4.89354i	−0.158103	+	0.158103i
$959$	43.9373	−	25.3672i	1.41881	−	0.819150i
$960$	2.13629	+	0.660499i	0.0689485	+	0.0213175i
$961$	−1.35980			−0.0438644
$962$	−26.5362	−	26.5362i	−0.855563	−	0.855563i
$963$	12.0293	+	3.22325i	0.387640	+	0.103868i
$964$	4.86058	−	8.41878i	0.156549	−	0.271151i
$965$	−17.0067	+	55.0057i	−0.547464	+	1.77070i
$966$	1.39912	−	2.42335i	0.0450160	−	0.0779699i
$967$	−10.9472	−	40.8557i	−0.352040	−	1.31383i	−0.884169	−	0.467167i	$-0.845275\pi$
$967$	−10.9472	−	40.8557i	−0.352040	−	1.31383i	0.532130	−	0.846663i	$-0.321392\pi$
$968$	0.204117	−	0.204117i	0.00656056	−	0.00656056i
$969$	−1.45193	+	3.31952i	−0.0466427	+	0.106638i
$970$	20.8214	+	0.792804i	0.668535	+	0.0254554i
$971$	−26.3710	−	15.2253i	−0.846287	−	0.488604i	0.0131096	−	0.999914i	$-0.495827\pi$
$971$	−26.3710	−	15.2253i	−0.846287	−	0.488604i	−0.859396	+	0.511310i	$0.829160\pi$
$972$	0.965926	−	0.258819i	0.0309821	−	0.00830162i
$973$	−4.80776	+	17.9428i	−0.154130	+	0.575220i
$974$	−23.9568	−	13.8315i	−0.767626	−	0.443189i
$975$	25.8134	−	12.3893i	0.826692	−	0.396774i
$976$	−11.2091			−0.358793
$977$	6.49346	+	6.49346i	0.207744	+	0.207744i	0.803308	−	0.595564i	$-0.203071\pi$
$977$	6.49346	+	6.49346i	0.207744	+	0.207744i	−0.595564	+	0.803308i	$0.703071\pi$
$978$	1.76824	−	6.59918i	0.0565422	−	0.211018i
$979$	6.98331	+	12.0955i	0.223188	+	0.386572i
$980$	0.323503	−	8.49617i	0.0103339	−	0.271400i
$981$		−	15.9538i		−	0.509365i
$982$	1.94026	−	7.24114i	0.0619161	−	0.231074i
$983$	7.19462	+	26.8507i	0.229473	+	0.856404i	0.980563	+	0.196204i	$0.0628616\pi$
$983$	7.19462	+	26.8507i	0.229473	+	0.856404i	−0.751090	+	0.660199i	$0.770472\pi$
$984$	1.20154	+	2.08112i	0.0383036	+	0.0663437i
$985$	3.69201	−	0.840121i	0.117637	−	0.0267685i
$986$	−2.15230	+	3.72789i	−0.0685431	+	0.118720i
$987$	−19.7434	−	19.7434i	−0.628440	−	0.628440i
$988$	15.5811	−	19.5012i	0.495701	−	0.620417i
$989$		−	1.00788i		−	0.0320488i
$990$	−7.32561	+	1.66695i	−0.232823	+	0.0529792i
$991$	−21.3858	−	12.3471i	−0.679342	−	0.392218i	0.120265	−	0.992742i	$-0.461625\pi$
$991$	−21.3858	−	12.3471i	−0.679342	−	0.392218i	−0.799607	+	0.600524i	$0.794959\pi$
$992$	5.49473	+	1.47231i	0.174458	+	0.0467459i
$993$	−23.2157	+	6.22063i	−0.736728	+	0.197406i
$994$	−20.8983	+	12.0656i	−0.662854	+	0.382699i
$995$	−22.6767	−	0.863447i	−0.718901	−	0.0273731i
$996$		−	14.1032i		−	0.446877i
$997$	−24.4145	−	6.54185i	−0.773215	−	0.207182i	−0.149424	−	0.988773i	$-0.547742\pi$
$997$	−24.4145	−	6.54185i	−0.773215	−	0.207182i	−0.623791	+	0.781591i	$0.714409\pi$
$998$	−35.7827	−	9.58794i	−1.13268	−	0.303501i
$999$		−	6.55335i		−	0.207339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.x.b.103.9	✓	40
5.2	odd	4	inner	570.2.x.b.217.7	yes	40
19.12	odd	6	inner	570.2.x.b.373.7	yes	40
95.12	even	12	inner	570.2.x.b.487.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.x.b.103.9	✓	40	1.1	even	1	trivial
570.2.x.b.217.7	yes	40	5.2	odd	4	inner
570.2.x.b.373.7	yes	40	19.12	odd	6	inner
570.2.x.b.487.9	yes	40	95.12	even	12	inner

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.89255 + 1.19091i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.32404 - 2.32404i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.89255 + 1.19091i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.32404 - 2.32404i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(2.13629 + 0.660499i) q^{10} +3.35986 q^{11} +(0.707107 + 0.707107i) q^{12} +(-5.53140 - 1.48213i) q^{13} +(1.64335 - 2.84636i) q^{14} +(-0.660499 + 2.13629i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.215133 - 0.802888i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-3.50954 + 2.58518i) q^{19} +(2.23445 + 0.0850797i) q^{20} +(2.84636 + 1.64335i) q^{21} +(3.24538 - 0.869596i) q^{22} +(0.220355 - 0.822375i) q^{23} +(0.866025 + 0.500000i) q^{24} +(2.16349 + 4.50770i) q^{25} -5.72653 q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.850659 - 3.17470i) q^{28} +(-2.58935 - 4.48489i) q^{29} +(-0.0850797 + 2.23445i) q^{30} +5.68857i q^{31} +(0.258819 - 0.965926i) q^{32} +(0.869596 + 3.24538i) q^{33} +(-0.415606 - 0.719850i) q^{34} +(7.16608 - 1.63065i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(4.63392 + 4.63392i) q^{37} +(-2.72086 + 3.40542i) q^{38} -5.72653i q^{39} +(2.18033 - 0.496137i) q^{40} +(2.08112 + 1.20154i) q^{41} +(3.17470 + 0.850659i) q^{42} +(1.14348 - 0.306394i) q^{43} +(2.90972 - 1.67993i) q^{44} +(-2.23445 - 0.0850797i) q^{45} -0.851385i q^{46} +(-8.20582 - 2.19874i) q^{47} +(0.965926 + 0.258819i) q^{48} -3.80235i q^{49} +(3.25645 + 3.79415i) q^{50} +(0.719850 - 0.415606i) q^{51} +(-5.53140 + 1.48213i) q^{52} +(0.607538 + 0.162789i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(6.35870 + 4.00128i) q^{55} -3.28669i q^{56} +(-3.40542 - 2.72086i) q^{57} +(-3.66189 - 3.66189i) q^{58} +(-6.16345 + 10.6754i) q^{59} +(0.496137 + 2.18033i) q^{60} +(-5.60453 - 9.70733i) q^{61} +(1.47231 + 5.49473i) q^{62} +(-0.850659 + 3.17470i) q^{63} -1.00000i q^{64} +(-8.70337 - 9.39239i) q^{65} +(1.67993 + 2.90972i) q^{66} +(-0.751997 + 2.80649i) q^{67} +(-0.587755 - 0.587755i) q^{68} +0.851385 q^{69} +(6.49986 - 3.42981i) q^{70} +(-6.35845 - 3.67106i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(8.79077 - 2.35548i) q^{73} +(5.67536 + 3.27667i) q^{74} +(-3.79415 + 3.25645i) q^{75} +(-1.74676 + 3.99360i) q^{76} +(7.80846 - 7.80846i) q^{77} +(-1.48213 - 5.53140i) q^{78} +(0.524789 - 0.908960i) q^{79} +(1.97763 - 1.04354i) q^{80} +(0.500000 - 0.866025i) q^{81} +(2.32119 + 0.621961i) q^{82} +(-9.97246 - 9.97246i) q^{83} +3.28669 q^{84} +(0.549014 - 1.77571i) q^{85} +(1.02522 - 0.591908i) q^{86} +(3.66189 - 3.66189i) q^{87} +(2.37578 - 2.37578i) q^{88} +(2.07845 + 3.59999i) q^{89} +(-2.18033 + 0.496137i) q^{90} +(-16.2998 + 9.41067i) q^{91} +(-0.220355 - 0.822375i) q^{92} +(-5.49473 + 1.47231i) q^{93} -8.49529 q^{94} +(-9.72068 + 0.713042i) q^{95} +1.00000 q^{96} +(9.00085 - 2.41177i) q^{97} +(-0.984122 - 3.67279i) q^{98} +(-2.90972 + 1.67993i) 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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