LMFDB - Embedded newform 120.2.w.c.77.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,2,Mod(53,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("120.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	120.w (of order $4$, degree $2$, 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:	$0.958204824255$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.11
Character	$\chi$	$=$	120.77
Dual form			120.2.w.c.53.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.533177 + 1.30986i) q^{2} +(1.59834 + 0.667305i) q^{3} +(-1.43144 + 1.39677i) q^{4} +(0.143028 - 2.23149i) q^{5} +(-0.0218716 + 2.44939i) q^{6} +(0.582772 + 0.582772i) q^{7} +(-2.59278 - 1.13026i) q^{8} +(2.10941 + 2.13317i) q^{9} +O(q^{10})$	\(q+(0.533177 + 1.30986i) q^{2} +(1.59834 + 0.667305i) q^{3} +(-1.43144 + 1.39677i) q^{4} +(0.143028 - 2.23149i) q^{5} +(-0.0218716 + 2.44939i) q^{6} +(0.582772 + 0.582772i) q^{7} +(-2.59278 - 1.13026i) q^{8} +(2.10941 + 2.13317i) q^{9} +(2.99919 - 1.00243i) q^{10} -3.68607 q^{11} +(-3.22001 + 1.27731i) q^{12} +(-3.88771 - 3.88771i) q^{13} +(-0.452626 + 1.07407i) q^{14} +(1.71769 - 3.47124i) q^{15} +(0.0980619 - 3.99880i) q^{16} +(-0.880105 + 0.880105i) q^{17} +(-1.66945 + 3.90038i) q^{18} +6.32919 q^{19} +(2.91214 + 3.39403i) q^{20} +(0.542584 + 1.32036i) q^{21} +(-1.96533 - 4.82821i) q^{22} +(2.06626 + 2.06626i) q^{23} +(-3.38993 - 3.53672i) q^{24} +(-4.95909 - 0.638332i) q^{25} +(3.01950 - 7.16518i) q^{26} +(1.94809 + 4.81715i) q^{27} +(-1.64820 - 0.0202063i) q^{28} -1.37122i q^{29} +(5.46266 + 0.399139i) q^{30} +3.32075 q^{31} +(5.29013 - 2.00362i) q^{32} +(-5.89160 - 2.45973i) q^{33} +(-1.62206 - 0.683558i) q^{34} +(1.38380 - 1.21710i) q^{35} +(-5.99904 - 0.107144i) q^{36} +(-2.44147 + 2.44147i) q^{37} +(3.37458 + 8.29032i) q^{38} +(-3.61961 - 8.80819i) q^{39} +(-2.89300 + 5.62410i) q^{40} -0.648104i q^{41} +(-1.44018 + 1.41469i) q^{42} +(-0.819412 - 0.819412i) q^{43} +(5.27640 - 5.14859i) q^{44} +(5.06184 - 4.40202i) q^{45} +(-1.60482 + 3.80818i) q^{46} +(-6.28508 + 6.28508i) q^{47} +(2.82515 - 6.32602i) q^{48} -6.32075i q^{49} +(-1.80795 - 6.83603i) q^{50} +(-1.99401 + 0.819412i) q^{51} +(10.9953 + 0.134798i) q^{52} +(-5.60782 + 5.60782i) q^{53} +(-5.27109 + 5.12011i) q^{54} +(-0.527212 + 8.22542i) q^{55} +(-0.852318 - 2.16968i) q^{56} +(10.1162 + 4.22349i) q^{57} +(1.79611 - 0.731106i) q^{58} +6.12026i q^{59} +(2.38975 + 7.36811i) q^{60} +5.13471i q^{61} +(1.77055 + 4.34971i) q^{62} +(-0.0138443 + 2.47245i) q^{63} +(5.44503 + 5.86102i) q^{64} +(-9.23144 + 8.11933i) q^{65} +(0.0806201 - 9.02862i) q^{66} +(-4.90636 + 4.90636i) q^{67} +(0.0305156 - 2.48912i) q^{68} +(1.92377 + 4.68141i) q^{69} +(2.33203 + 1.16365i) q^{70} -4.13251i q^{71} +(-3.05821 - 7.91501i) q^{72} +(4.69820 - 4.69820i) q^{73} +(-4.49972 - 1.89624i) q^{74} +(-7.50036 - 4.32950i) q^{75} +(-9.05987 + 8.84042i) q^{76} +(-2.14814 - 2.14814i) q^{77} +(9.60756 - 9.43750i) q^{78} +1.10079i q^{79} +(-8.90925 - 0.790765i) q^{80} +(-0.100786 + 8.99944i) q^{81} +(0.848922 - 0.345554i) q^{82} +(6.27439 - 6.27439i) q^{83} +(-2.62091 - 1.13215i) q^{84} +(1.83806 + 2.08982i) q^{85} +(0.636420 - 1.51020i) q^{86} +(0.915024 - 2.19169i) q^{87} +(9.55717 + 4.16621i) q^{88} +15.3562 q^{89} +(8.46487 + 4.28322i) q^{90} -4.53130i q^{91} +(-5.84382 - 0.0716428i) q^{92} +(5.30771 + 2.21595i) q^{93} +(-11.5836 - 4.88148i) q^{94} +(0.905253 - 14.1235i) q^{95} +(9.79248 + 0.327652i) q^{96} +(-5.42154 - 5.42154i) q^{97} +(8.27927 - 3.37008i) q^{98} +(-7.77542 - 7.86299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{6}+O(q^{10}) $ 32 * q - 4 * q^6	$ 32 q - 4 q^{6} + 4 q^{10} - 8 q^{12} - 28 q^{15} + 28 q^{16} - 20 q^{18} - 52 q^{22} - 8 q^{25} + 12 q^{28} - 32 q^{30} - 32 q^{31} + 8 q^{33} - 20 q^{36} + 24 q^{40} + 16 q^{42} + 24 q^{46} + 44 q^{48} + 8 q^{52} + 8 q^{55} - 16 q^{57} + 28 q^{58} + 56 q^{60} + 48 q^{63} + 16 q^{66} + 20 q^{70} + 32 q^{72} - 64 q^{73} - 88 q^{76} + 64 q^{78} + 48 q^{81} + 64 q^{82} - 8 q^{87} - 52 q^{88} + 84 q^{90} - 52 q^{96} + 16 q^{97}+O(q^{100}) $ 32 * q - 4 * q^6 + 4 * q^10 - 8 * q^12 - 28 * q^15 + 28 * q^16 - 20 * q^18 - 52 * q^22 - 8 * q^25 + 12 * q^28 - 32 * q^30 - 32 * q^31 + 8 * q^33 - 20 * q^36 + 24 * q^40 + 16 * q^42 + 24 * q^46 + 44 * q^48 + 8 * q^52 + 8 * q^55 - 16 * q^57 + 28 * q^58 + 56 * q^60 + 48 * q^63 + 16 * q^66 + 20 * q^70 + 32 * q^72 - 64 * q^73 - 88 * q^76 + 64 * q^78 + 48 * q^81 + 64 * q^82 - 8 * q^87 - 52 * q^88 + 84 * q^90 - 52 * q^96 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.533177	+	1.30986i	0.377013	+	0.926208i
$2$	0.533177	+	1.30986i	0.377013	+	0.926208i
$3$	1.59834	+	0.667305i	0.922805	+	0.385268i
$3$	1.59834	+	0.667305i	0.922805	+	0.385268i
$4$	−1.43144	+	1.39677i	−0.715722	+	0.698385i
$5$	0.143028	−	2.23149i	0.0639642	−	0.997952i
$5$	0.143028	−	2.23149i	0.0639642	−	0.997952i
$6$	−0.0218716	+	2.44939i	−0.00892904	+	0.999960i
$7$	0.582772	+	0.582772i	0.220267	+	0.220267i	0.808611	−	0.588344i	$-0.200220\pi$
$7$	0.582772	+	0.582772i	0.220267	+	0.220267i	−0.588344	+	0.808611i	$0.700220\pi$
$8$	−2.59278	−	1.13026i	−0.916687	−	0.399606i
$9$	2.10941	+	2.13317i	0.703136	+	0.711055i
$10$	2.99919	−	1.00243i	0.948426	−	0.316997i
$11$	−3.68607			−1.11139			−0.555695	−	0.831386i	$-0.687548\pi$
$11$	−3.68607			−1.11139			−0.555695	+	0.831386i	$0.687548\pi$
$12$	−3.22001	+	1.27731i	−0.929537	+	0.368728i
$13$	−3.88771	−	3.88771i	−1.07826	−	1.07826i	−0.996666	−	0.0815911i	$-0.974000\pi$
$13$	−3.88771	−	3.88771i	−1.07826	−	1.07826i	−0.0815911	−	0.996666i	$-0.526000\pi$
$14$	−0.452626	+	1.07407i	−0.120969	+	0.287057i
$15$	1.71769	−	3.47124i	0.443506	−	0.896271i
$16$	0.0980619	−	3.99880i	0.0245155	−	0.999699i
$17$	−0.880105	+	0.880105i	−0.213457	+	0.213457i	−0.805734	−	0.592277i	$-0.798229\pi$
$17$	−0.880105	+	0.880105i	−0.213457	+	0.213457i	0.592277	+	0.805734i	$0.298229\pi$
$18$	−1.66945	+	3.90038i	−0.393493	+	0.919328i
$19$	6.32919			1.45201			0.726007	−	0.687687i	$-0.241374\pi$
$19$	6.32919			1.45201			0.726007	+	0.687687i	$0.241374\pi$
$20$	2.91214	+	3.39403i	0.651175	+	0.758928i
$21$	0.542584	+	1.32036i	0.118402	+	0.288125i
$22$	−1.96533	−	4.82821i	−0.419009	−	1.02938i
$23$	2.06626	+	2.06626i	0.430844	+	0.430844i	0.888916	−	0.458071i	$-0.151460\pi$
$23$	2.06626	+	2.06626i	0.430844	+	0.430844i	−0.458071	+	0.888916i	$0.651460\pi$
$24$	−3.38993	−	3.53672i	−0.691967	−	0.721929i
$25$	−4.95909	−	0.638332i	−0.991817	−	0.127666i
$26$	3.01950	−	7.16518i	0.592173	−	1.40521i
$27$	1.94809	+	4.81715i	0.374910	+	0.927061i
$28$	−1.64820	−	0.0202063i	−0.311481	−	0.00381863i
$29$		−	1.37122i		−	0.254630i	−0.991862	−	0.127315i	$-0.959364\pi$
$29$		−	1.37122i		−	0.254630i	0.991862	−	0.127315i	$-0.0406359\pi$
$30$	5.46266	+	0.399139i	0.997341	+	0.0728724i
$31$	3.32075			0.596425			0.298212	−	0.954500i	$-0.403610\pi$
$31$	3.32075			0.596425			0.298212	+	0.954500i	$0.403610\pi$
$32$	5.29013	−	2.00362i	0.935172	−	0.354194i
$33$	−5.89160	−	2.45973i	−1.02560	−	0.428184i
$34$	−1.62206	−	0.683558i	−0.278181	−	0.117229i
$35$	1.38380	−	1.21710i	0.233905	−	0.205727i
$36$	−5.99904	−	0.107144i	−0.999841	−	0.0178574i
$37$	−2.44147	+	2.44147i	−0.401376	+	0.401376i	−0.878718	−	0.477342i	$-0.841600\pi$
$37$	−2.44147	+	2.44147i	−0.401376	+	0.401376i	0.477342	+	0.878718i	$0.341600\pi$
$38$	3.37458	+	8.29032i	0.547429	+	1.34487i
$39$	−3.61961	−	8.80819i	−0.579602	−	1.41044i
$40$	−2.89300	+	5.62410i	−0.457423	+	0.889249i
$41$		−	0.648104i		−	0.101217i	−0.998719	−	0.0506084i	$-0.983884\pi$
$41$		−	0.648104i		−	0.101217i	0.998719	−	0.0506084i	$-0.0161160\pi$
$42$	−1.44018	+	1.41469i	−0.222225	+	0.218292i
$43$	−0.819412	−	0.819412i	−0.124959	−	0.124959i	0.641861	−	0.766821i	$-0.278162\pi$
$43$	−0.819412	−	0.819412i	−0.124959	−	0.124959i	−0.766821	+	0.641861i	$0.778162\pi$
$44$	5.27640	−	5.14859i	0.795447	−	0.776179i
$45$	5.06184	−	4.40202i	0.754574	−	0.656214i
$46$	−1.60482	+	3.80818i	−0.236617	+	0.561485i
$47$	−6.28508	+	6.28508i	−0.916772	+	0.916772i	−0.996793	−	0.0800208i	$-0.974501\pi$
$47$	−6.28508	+	6.28508i	−0.916772	+	0.916772i	0.0800208	+	0.996793i	$0.474501\pi$
$48$	2.82515	−	6.32602i	0.407776	−	0.913082i
$49$		−	6.32075i		−	0.902965i
$50$	−1.80795	−	6.83603i	−0.255683	−	0.966761i
$51$	−1.99401	+	0.819412i	−0.279217	+	0.114741i
$52$	10.9953	+	0.134798i	1.52477	+	0.0186931i
$53$	−5.60782	+	5.60782i	−0.770293	+	0.770293i	−0.978158	−	0.207864i	$-0.933349\pi$
$53$	−5.60782	+	5.60782i	−0.770293	+	0.770293i	0.207864	+	0.978158i	$0.433349\pi$
$54$	−5.27109	+	5.12011i	−0.717305	+	0.696759i
$55$	−0.527212	+	8.22542i	−0.0710892	+	1.10911i
$56$	−0.852318	−	2.16968i	−0.113896	−	0.289936i
$57$	10.1162	+	4.22349i	1.33993	+	0.559415i
$58$	1.79611	−	0.731106i	0.235840	−	0.0959989i
$59$			6.12026i			0.796790i	0.917214	+	0.398395i	$0.130433\pi$
$59$			6.12026i			0.796790i	−0.917214	+	0.398395i	$0.869567\pi$
$60$	2.38975	+	7.36811i	0.308516	+	0.951219i
$61$			5.13471i			0.657432i	0.944429	+	0.328716i	$0.106616\pi$
$61$			5.13471i			0.657432i	−0.944429	+	0.328716i	$0.893384\pi$
$62$	1.77055	+	4.34971i	0.224860	+	0.552413i
$63$	−0.0138443	+	2.47245i	−0.00174421	+	0.311500i
$64$	5.44503	+	5.86102i	0.680629	+	0.732628i
$65$	−9.23144	+	8.11933i	−1.14502	+	1.00708i
$66$	0.0806201	−	9.02862i	0.00992365	−	1.11135i
$67$	−4.90636	+	4.90636i	−0.599408	+	0.599408i	−0.940155	−	0.340747i	$-0.889320\pi$
$67$	−4.90636	+	4.90636i	−0.599408	+	0.599408i	0.340747	+	0.940155i	$0.389320\pi$
$68$	0.0305156	−	2.48912i	0.00370056	−	0.301851i
$69$	1.92377	+	4.68141i	0.231594	+	0.563576i
$70$	2.33203	+	1.16365i	0.278731	+	0.139083i
$71$		−	4.13251i		−	0.490439i	−0.969468	−	0.245220i	$-0.921140\pi$
$71$		−	4.13251i		−	0.490439i	0.969468	−	0.245220i	$-0.0788601\pi$
$72$	−3.05821	−	7.91501i	−0.360414	−	0.932793i
$73$	4.69820	−	4.69820i	0.549883	−	0.549883i	−0.376524	−	0.926407i	$-0.622881\pi$
$73$	4.69820	−	4.69820i	0.549883	−	0.549883i	0.926407	+	0.376524i	$0.122881\pi$
$74$	−4.49972	−	1.89624i	−0.523082	−	0.220433i
$75$	−7.50036	−	4.32950i	−0.866068	−	0.499927i
$76$	−9.05987	+	8.84042i	−1.03924	+	1.01407i
$77$	−2.14814	−	2.14814i	−0.244803	−	0.244803i
$78$	9.60756	−	9.43750i	1.08784	−	1.06859i
$79$			1.10079i			0.123848i	0.998081	+	0.0619241i	$0.0197237\pi$
$79$			1.10079i			0.123848i	−0.998081	+	0.0619241i	$0.980276\pi$
$80$	−8.90925	−	0.790765i	−0.996084	−	0.0884103i
$81$	−0.100786	+	8.99944i	−0.0111985	+	0.999937i
$82$	0.848922	−	0.345554i	0.0937478	−	0.0381601i
$83$	6.27439	−	6.27439i	0.688703	−	0.688703i	−0.273242	−	0.961945i	$-0.588096\pi$
$83$	6.27439	−	6.27439i	0.688703	−	0.688703i	0.961945	+	0.273242i	$0.0880960\pi$
$84$	−2.62091	−	1.13215i	−0.285965	−	0.123528i
$85$	1.83806	+	2.08982i	0.199366	+	0.226673i
$86$	0.636420	−	1.51020i	0.0686269	−	0.162849i
$87$	0.915024	−	2.19169i	0.0981009	−	0.234974i
$88$	9.55717	+	4.16621i	1.01880	+	0.444119i
$89$	15.3562			1.62775			0.813875	−	0.581040i	$-0.197354\pi$
$89$	15.3562			1.62775			0.813875	+	0.581040i	$0.197354\pi$
$90$	8.46487	+	4.28322i	0.892276	+	0.451491i
$91$		−	4.53130i		−	0.475009i
$92$	−5.84382	−	0.0716428i	−0.609260	−	0.00746928i
$93$	5.30771	+	2.21595i	0.550384	+	0.229784i
$94$	−11.5836	−	4.88148i	−1.19476	−	0.503486i
$95$	0.905253	−	14.1235i	0.0928770	−	1.44904i
$96$	9.79248	+	0.327652i	0.999441	+	0.0334409i
$97$	−5.42154	−	5.42154i	−0.550474	−	0.550474i	0.376104	−	0.926578i	$-0.377264\pi$
$97$	−5.42154	−	5.42154i	−0.550474	−	0.550474i	−0.926578	+	0.376104i	$0.877264\pi$
$98$	8.27927	−	3.37008i	0.836333	−	0.340430i
$99$	−7.77542	−	7.86299i	−0.781459	−	0.790260i
$100$	7.99026	−	6.01297i	0.799026	−	0.601297i
$101$	9.84442			0.979556			0.489778	−	0.871847i	$-0.337078\pi$
$101$	9.84442			0.979556			0.489778	+	0.871847i	$0.337078\pi$
$102$	−2.13647	−	2.17497i	−0.211542	−	0.215354i
$103$	−8.28098	+	8.28098i	−0.815949	+	0.815949i	−0.985518	−	0.169569i	$-0.945762\pi$
$103$	−8.28098	+	8.28098i	−0.815949	+	0.815949i	0.169569	+	0.985518i	$0.445762\pi$
$104$	5.68587	+	14.4741i	0.557545	+	1.41930i
$105$	3.02397	−	1.02192i	0.295109	−	0.0997293i
$106$	−10.3354	−	4.35547i	−1.00386	−	0.423041i
$107$	−5.84678	−	5.84678i	−0.565230	−	0.565230i	0.365559	−	0.930788i	$-0.380878\pi$
$107$	−5.84678	−	5.84678i	−0.565230	−	0.565230i	−0.930788	+	0.365559i	$0.880878\pi$
$108$	−9.51704	−	4.17444i	−0.915777	−	0.401686i
$109$	11.7033			1.12097			0.560487	−	0.828163i	$-0.310614\pi$
$109$	11.7033			1.12097			0.560487	+	0.828163i	$0.310614\pi$
$110$	−11.0552	+	3.69503i	−1.05407	+	0.352308i
$111$	−5.53152	+	2.27311i	−0.525029	+	0.215754i
$112$	2.38754	−	2.27324i	0.225601	−	0.214801i
$113$	−8.58333	−	8.58333i	−0.807452	−	0.807452i	0.176796	−	0.984248i	$-0.443427\pi$
$113$	−8.58333	−	8.58333i	−0.807452	−	0.807452i	−0.984248	+	0.176796i	$0.943427\pi$
$114$	−0.138429	+	15.5027i	−0.0129651	+	1.45196i
$115$	4.90636	−	4.31530i	0.457521	−	0.402403i
$116$	1.91529	+	1.96283i	0.177830	+	0.182244i
$117$	0.0923560	−	16.4939i	0.00853832	−	1.52486i
$118$	−8.01666	+	3.26318i	−0.737993	+	0.300400i
$119$	−1.02580			−0.0940350
$120$	−8.37700	+	7.05874i	−0.764712	+	0.644372i
$121$	2.58708			0.235189
$122$	−6.72573	+	2.73771i	−0.608919	+	0.247861i
$123$	0.432483	−	1.03589i	0.0389956	−	0.0934033i
$124$	−4.75347	+	4.63833i	−0.426874	+	0.416535i
$125$	−2.13372	+	10.9748i	−0.190846	+	0.981620i
$126$	−3.24594	+	1.30012i	−0.289171	+	0.115824i
$127$	−0.0146460	−	0.0146460i	−0.00129962	−	0.00129962i	0.706457	−	0.707756i	$-0.250293\pi$
$127$	−0.0146460	−	0.0146460i	−0.00129962	−	0.00129962i	−0.707756	+	0.706457i	$0.750293\pi$
$128$	−4.77393	+	10.2572i	−0.421959	+	0.906615i
$129$	−0.762905	−	1.85650i	−0.0671701	−	0.163456i
$130$	−15.5571	−	7.76281i	−1.36445	−	0.680843i
$131$	5.23989			0.457811			0.228906	−	0.973449i	$-0.426485\pi$
$131$	5.23989			0.457811			0.228906	+	0.973449i	$0.426485\pi$
$132$	11.8692	−	4.70826i	1.03308	−	0.409801i
$133$	3.68847	+	3.68847i	0.319831	+	0.319831i
$134$	−9.04259	−	3.81066i	−0.781161	−	0.329191i
$135$	11.0281	−	3.65816i	0.949143	−	0.314844i
$136$	3.27666	−	1.28717i	0.280972	−	0.110374i
$137$	14.0984	−	14.0984i	1.20450	−	1.20450i	0.231722	−	0.972782i	$-0.425564\pi$
$137$	14.0984	−	14.0984i	1.20450	−	1.20450i	0.972782	−	0.231722i	$-0.0744360\pi$
$138$	−5.10627	+	5.01588i	−0.434674	+	0.426980i
$139$	−9.22166			−0.782171			−0.391085	−	0.920354i	$-0.627900\pi$
$139$	−9.22166			−0.782171			−0.391085	+	0.920354i	$0.627900\pi$
$140$	−0.280830	+	3.67506i	−0.0237345	+	0.310599i
$141$	−14.2398	+	5.85165i	−1.19921	+	0.492798i
$142$	5.41300	−	2.20336i	0.454249	−	0.184902i
$143$	14.3304	+	14.3304i	1.19836	+	1.19836i
$144$	8.73695	−	8.22592i	0.728079	−	0.685493i
$145$	−3.05987	−	0.196124i	−0.254109	−	0.0162872i
$146$	8.65895	+	3.64899i	0.716619	+	0.301993i
$147$	4.21787	−	10.1027i	0.347884	−	0.833260i
$148$	0.0846526	−	6.90501i	0.00695840	−	0.567589i
$149$		−	14.0054i		−	1.14737i	−0.819076	−	0.573685i	$-0.805513\pi$
$149$		−	14.0054i		−	1.14737i	0.819076	−	0.573685i	$-0.194487\pi$
$150$	1.67199	−	12.1328i	0.136517	−	0.990638i
$151$	13.1301			1.06851			0.534255	−	0.845323i	$-0.320592\pi$
$151$	13.1301			1.06851			0.534255	+	0.845323i	$0.320592\pi$
$152$	−16.4102	−	7.15361i	−1.33104	−	0.580234i
$153$	−3.73391	−	0.0209077i	−0.301869	−	0.00169028i
$154$	1.66841	−	3.95909i	0.134444	−	0.319032i
$155$	0.474962	−	7.41023i	0.0381498	−	0.595204i
$156$	17.4843	+	7.55265i	1.39986	+	0.604696i
$157$	−6.36936	+	6.36936i	−0.508330	+	0.508330i	−0.914014	−	0.405683i	$-0.867034\pi$
$157$	−6.36936	+	6.36936i	−0.508330	+	0.508330i	0.405683	+	0.914014i	$0.367034\pi$
$158$	−1.44187	+	0.586914i	−0.114709	+	0.0466924i
$159$	−12.7054	+	5.22110i	−1.00760	+	0.414060i
$160$	−3.71442	−	12.0914i	−0.293651	−	0.955913i
$161$			2.40831i			0.189802i
$162$	−11.8417	+	4.66628i	−0.930372	+	0.366618i
$163$	−3.46013	−	3.46013i	−0.271018	−	0.271018i	0.558492	−	0.829510i	$-0.311380\pi$
$163$	−3.46013	−	3.46013i	−0.271018	−	0.271018i	−0.829510	+	0.558492i	$0.811380\pi$
$164$	0.905253	+	0.927724i	0.0706884	+	0.0724431i
$165$	−6.33152	+	12.7952i	−0.492908	+	0.996108i
$166$	11.5639	+	4.87318i	0.897533	+	0.378232i
$167$	−0.954151	+	0.954151i	−0.0738345	+	0.0738345i	−0.743060	−	0.669225i	$-0.766626\pi$
$167$	−0.954151	+	0.954151i	−0.0738345	+	0.0738345i	0.669225	+	0.743060i	$0.266626\pi$
$168$	0.0855420	−	4.03666i	0.00659971	−	0.311435i
$169$			17.2286i			1.32528i
$170$	−1.75735	+	3.52185i	−0.134783	+	0.270113i
$171$	13.3508	+	13.5012i	1.02096	+	1.03246i
$172$	2.31747	+	0.0284113i	0.176706	+	0.00216634i
$173$	1.80240	−	1.80240i	0.137034	−	0.137034i	−0.635262	−	0.772296i	$-0.719108\pi$
$173$	1.80240	−	1.80240i	0.137034	−	0.137034i	0.772296	+	0.635262i	$0.219108\pi$
$174$	3.35867	+	0.0299909i	0.254620	+	0.00227360i
$175$	−2.51801	−	3.26202i	−0.190344	−	0.246585i
$176$	−0.361463	+	14.7398i	−0.0272463	+	1.11106i
$177$	−4.08408	+	9.78228i	−0.306978	+	0.735281i
$178$	8.18756	+	20.1144i	0.613683	+	1.50763i
$179$			24.0166i			1.79508i	0.440930	+	0.897541i	$0.354649\pi$
$179$			24.0166i			1.79508i	−0.440930	+	0.897541i	$0.645351\pi$
$180$	−1.09712	+	13.3715i	−0.0817748	+	0.996651i
$181$		−	21.7210i		−	1.61451i	−0.590205	−	0.807253i	$-0.700953\pi$
$181$		−	21.7210i		−	1.61451i	0.590205	−	0.807253i	$-0.299047\pi$
$182$	5.93535	−	2.41599i	0.439957	−	0.179085i
$183$	−3.42641	+	8.20703i	−0.253288	+	0.606681i
$184$	−3.02195	−	7.69276i	−0.222781	−	0.567117i
$185$	5.09892	+	5.79732i	0.374880	+	0.426228i
$186$	−0.0726302	+	8.13383i	−0.00532550	+	0.596401i
$187$	3.24412	−	3.24412i	0.237234	−	0.237234i
$188$	0.217921	−	17.7755i	0.0158935	−	1.29641i
$189$	−1.67201	+	3.94259i	−0.121621	+	0.286781i
$190$	18.9824	−	6.34458i	1.37713	−	0.460285i
$191$		−	12.9839i		−	0.939479i	−0.882805	−	0.469739i	$-0.844348\pi$
$191$		−	12.9839i		−	0.939479i	0.882805	−	0.469739i	$-0.155652\pi$
$192$	4.79195	+	13.0014i	0.345829	+	0.938297i
$193$	9.48630	−	9.48630i	0.682839	−	0.682839i	−0.277800	−	0.960639i	$-0.589605\pi$
$193$	9.48630	−	9.48630i	0.682839	−	0.682839i	0.960639	+	0.277800i	$0.0896053\pi$
$194$	4.21079	−	9.99208i	0.302317	−	0.717389i
$195$	−20.1731	+	6.81731i	−1.44462	+	0.488197i
$196$	8.82864	+	9.04780i	0.630617	+	0.646272i
$197$	12.8606	+	12.8606i	0.916280	+	0.916280i	0.996757	−	0.0804765i	$-0.0256442\pi$
$197$	12.8606	+	12.8606i	0.916280	+	0.916280i	−0.0804765	+	0.996757i	$0.525644\pi$
$198$	6.15370	−	14.3770i	0.437324	−	1.02173i
$199$		−	0.0463625i		−	0.00328655i	−0.999999	−	0.00164328i	$-0.999477\pi$
$199$		−	0.0463625i		−	0.00328655i	0.999999	−	0.00164328i	$-0.000523071\pi$
$200$	12.1363	+	7.26010i	0.858169	+	0.513367i
$201$	−11.1161	+	4.56802i	−0.784069	+	0.322203i
$202$	5.24882	+	12.8948i	0.369306	+	0.907273i
$203$	0.799111	−	0.799111i	0.0560866	−	0.0560866i
$204$	1.70978	−	3.95812i	0.119708	−	0.277123i
$205$	−1.44624	−	0.0926972i	−0.101010	−	0.00647425i
$206$	−15.2621	−	6.43165i	−1.06336	−	0.448115i
$207$	−0.0490858	+	8.76625i	−0.00341170	+	0.609296i
$208$	−15.9274	+	15.1649i	−1.10437	+	1.05150i
$209$	−23.3298			−1.61376
$210$	2.95088	+	3.41609i	0.203630	+	0.235733i
$211$		−	0.591066i		−	0.0406907i	−0.999793	−	0.0203453i	$-0.993523\pi$
$211$		−	0.591066i		−	0.0406907i	0.999793	−	0.0203453i	$-0.00647657\pi$
$212$	0.194439	−	15.8601i	0.0133541	−	1.08928i
$213$	2.75765	−	6.60518i	0.188951	−	0.452579i
$214$	4.54107	−	10.7758i	0.310421	−	0.736619i
$215$	−1.94571	+	1.71131i	−0.132696	+	0.116710i
$216$	0.393647	−	14.6917i	0.0267843	−	0.999641i
$217$	1.93524	+	1.93524i	0.131373	+	0.131373i
$218$	6.23994	+	15.3296i	0.422622	+	1.03825i
$219$	10.6445	−	4.37421i	0.719287	−	0.295582i
$220$	−10.7343	−	12.5106i	−0.723710	−	0.843465i
$221$	6.84318			0.460322
$222$	−5.92673	−	6.03353i	−0.397776	−	0.404944i
$223$	16.8577	−	16.8577i	1.12888	−	1.12888i	0.138517	−	0.990360i	$-0.455767\pi$
$223$	16.8577	−	16.8577i	1.12888	−	1.12888i	0.990360	−	0.138517i	$-0.0442335\pi$
$224$	4.25060	+	1.91529i	0.284005	+	0.127970i
$225$	−9.09907	−	11.9251i	−0.606605	−	0.795003i
$226$	6.66649	−	15.8194i	0.443448	−	1.05229i
$227$	7.23390	+	7.23390i	0.480131	+	0.480131i	0.905173	−	0.425043i	$-0.139741\pi$
$227$	7.23390	+	7.23390i	0.480131	+	0.480131i	−0.425043	+	0.905173i	$0.639741\pi$
$228$	−20.3800	+	8.08434i	−1.34970	+	0.535399i
$229$	−23.0081			−1.52042			−0.760210	−	0.649677i	$-0.774904\pi$
$229$	−23.0081			−1.52042			−0.760210	+	0.649677i	$0.774904\pi$
$230$	8.26838	+	4.12581i	0.545201	+	0.272048i
$231$	−2.00000	−	4.86692i	−0.131590	−	0.320220i
$232$	−1.54984	+	3.55529i	−0.101752	+	0.233416i
$233$	4.45082	+	4.45082i	0.291583	+	0.291583i	0.837705	−	0.546122i	$-0.183897\pi$
$233$	4.45082	+	4.45082i	0.291583	+	0.291583i	−0.546122	+	0.837705i	$0.683897\pi$
$234$	21.6539	−	8.67320i	1.41556	−	0.566985i
$235$	13.1261	+	14.9240i	0.856254	+	0.973536i
$236$	−8.54860	−	8.76081i	−0.556466	−	0.570280i
$237$	−0.734560	+	1.75944i	−0.0477148	+	0.114288i
$238$	−0.546934	−	1.34365i	−0.0354524	−	0.0870959i
$239$	−4.03472			−0.260984			−0.130492	−	0.991449i	$-0.541656\pi$
$239$	−4.03472			−0.260984			−0.130492	+	0.991449i	$0.541656\pi$
$240$	−13.7124	−	7.20910i	−0.885129	−	0.465345i
$241$	−11.4612			−0.738279			−0.369139	−	0.929374i	$-0.620347\pi$
$241$	−11.4612			−0.738279			−0.369139	+	0.929374i	$0.620347\pi$
$242$	1.37937	+	3.38871i	0.0886696	+	0.217834i
$243$	−6.16646	+	14.3169i	−0.395578	+	0.918432i
$244$	−7.17201	−	7.35005i	−0.459141	−	0.470538i
$245$	−14.1047	−	0.904047i	−0.901116	−	0.0577574i
$246$	1.58746	+	0.0141751i	0.101213	+	0.000903769i
$247$	−24.6060	−	24.6060i	−1.56564	−	1.56564i
$248$	−8.60999	−	3.75331i	−0.546735	−	0.238335i
$249$	14.2156	−	5.84170i	0.900874	−	0.370203i
$250$	−15.5131	+	3.05667i	−0.981136	+	0.193321i
$251$	−17.4804			−1.10335			−0.551677	−	0.834058i	$-0.686012\pi$
$251$	−17.4804			−1.10335			−0.551677	+	0.834058i	$0.686012\pi$
$252$	−3.43363	−	3.55851i	−0.216299	−	0.224165i
$253$	−7.61636	−	7.61636i	−0.478836	−	0.478836i
$254$	0.0113752	−	0.0269930i	0.000713745	−	0.00169369i
$255$	1.54331	+	4.56681i	0.0966458	+	0.285984i
$256$	−15.9808	−	0.784260i	−0.998798	−	0.0490162i
$257$	−6.77283	+	6.77283i	−0.422477	+	0.422477i	−0.886056	−	0.463578i	$-0.846565\pi$
$257$	−6.77283	+	6.77283i	−0.422477	+	0.422477i	0.463578	+	0.886056i	$0.346565\pi$
$258$	2.02498	−	1.98914i	0.126070	−	0.123838i
$259$	−2.84565			−0.176820
$260$	1.87344	−	24.5166i	0.116186	−	1.52045i
$261$	2.92505	−	2.89247i	0.181056	−	0.179040i
$262$	2.79379	+	6.86350i	0.172601	+	0.424028i
$263$	−15.3708	−	15.3708i	−0.947805	−	0.947805i	0.0508987	−	0.998704i	$-0.483791\pi$
$263$	−15.3708	−	15.3708i	−0.947805	−	0.947805i	−0.998704	+	0.0508987i	$0.983791\pi$
$264$	12.4955	+	13.0366i	0.769046	+	0.802345i
$265$	11.7117	+	13.3159i	0.719445	+	0.817987i
$266$	−2.86476	+	6.79798i	−0.175649	+	0.416811i
$267$	24.5444	+	10.2472i	1.50209	+	0.627121i
$268$	0.170117	−	13.8762i	0.0103916	−	0.847627i
$269$		−	9.58859i		−	0.584627i	−0.956323	−	0.292313i	$-0.905575\pi$
$269$		−	9.58859i		−	0.584627i	0.956323	−	0.292313i	$-0.0944250\pi$
$270$	10.6716	+	12.4947i	0.649451	+	0.760404i
$271$	−20.9078			−1.27006			−0.635030	−	0.772487i	$-0.719012\pi$
$271$	−20.9078			−1.27006			−0.635030	+	0.772487i	$0.719012\pi$
$272$	3.43306	+	3.60567i	0.208160	+	0.218626i
$273$	3.02376	−	7.24257i	0.183006	−	0.438341i
$274$	25.9837	+	10.9499i	1.56974	+	0.661507i
$275$	18.2795	+	2.35293i	1.10230	+	0.141887i
$276$	−9.29263	−	4.01412i	−0.559350	−	0.241621i
$277$	8.86336	−	8.86336i	0.532547	−	0.532547i	−0.388782	−	0.921330i	$-0.627104\pi$
$277$	8.86336	−	8.86336i	0.532547	−	0.532547i	0.921330	+	0.388782i	$0.127104\pi$
$278$	−4.91678	−	12.0790i	−0.294889	−	0.724453i
$279$	7.00483	+	7.08372i	0.419368	+	0.424091i
$280$	−4.96353	+	1.59161i	−0.296628	+	0.0951170i
$281$		−	12.1925i		−	0.727341i	−0.931528	−	0.363670i	$-0.881523\pi$
$281$		−	12.1925i		−	0.727341i	0.931528	−	0.363670i	$-0.118477\pi$
$282$	−15.2571	−	15.5321i	−0.908550	−	0.924922i
$283$	11.6799	+	11.6799i	0.694298	+	0.694298i	0.963175	−	0.268877i	$-0.0866525\pi$
$283$	11.6799	+	11.6799i	0.694298	+	0.694298i	−0.268877	+	0.963175i	$0.586652\pi$
$284$	5.77217	+	5.91546i	0.342516	+	0.351018i
$285$	10.8716	−	21.9701i	0.643977	−	1.30140i
$286$	−11.1301	+	26.4113i	−0.658135	+	1.56173i
$287$	0.377697	−	0.377697i	0.0222947	−	0.0222947i
$288$	15.4331	+	7.05827i	0.909405	+	0.415912i
$289$			15.4508i			0.908872i
$290$	−1.37456	−	4.11256i	−0.0807170	−	0.241498i
$291$	−5.04767	−	12.2833i	−0.295900	−	0.720060i
$292$	−0.162900	+	13.2875i	−0.00953298	+	0.777594i
$293$	−5.16432	+	5.16432i	−0.301703	+	0.301703i	−0.841680	−	0.539977i	$-0.818433\pi$
$293$	−5.16432	+	5.16432i	−0.301703	+	0.301703i	0.539977	+	0.841680i	$0.318433\pi$
$294$	15.4820	+	0.138245i	0.902929	+	0.00806261i
$295$	13.6573	+	0.875370i	0.795158	+	0.0509660i
$296$	9.08971	−	3.57071i	0.528328	−	0.207544i
$297$	−7.18079	−	17.7563i	−0.416672	−	1.03033i
$298$	18.3451	−	7.46739i	1.06270	−	0.432574i
$299$		−	16.0660i		−	0.929122i
$300$	16.7837	−	4.27886i	0.969005	−	0.247040i
$301$		−	0.955061i		−	0.0550488i
$302$	7.00066	+	17.1985i	0.402843	+	0.989663i
$303$	15.7348	+	6.56923i	0.903939	+	0.377392i
$304$	0.620652	−	25.3091i	0.0355968	−	1.45158i
$305$	11.4580	+	0.734409i	0.656086	+	0.0420521i
$306$	−1.96345	−	4.90203i	−0.112243	−	0.280230i
$307$	−9.19824	+	9.19824i	−0.524972	+	0.524972i	−0.919069	−	0.394097i	$-0.871057\pi$
$307$	−9.19824	+	9.19824i	−0.524972	+	0.524972i	0.394097	+	0.919069i	$0.371057\pi$
$308$	6.07539	+	0.0744818i	0.346177	+	0.00424399i
$309$	−18.7618	+	7.70992i	−1.06732	+	0.438602i
$310$	9.95956	−	3.32883i	0.565665	−	0.189065i
$311$			30.5690i			1.73341i	0.498821	+	0.866705i	$0.333767\pi$
$311$			30.5690i			1.73341i	−0.498821	+	0.866705i	$0.666233\pi$
$312$	−0.570656	+	26.9288i	−0.0323071	+	1.52454i
$313$	−16.4612	+	16.4612i	−0.930440	+	0.930440i	−0.997733	−	0.0672931i	$-0.978564\pi$
$313$	−16.4612	+	16.4612i	−0.930440	+	0.930440i	0.0672931	+	0.997733i	$0.478564\pi$
$314$	−11.7389	−	4.94694i	−0.662467	−	0.279172i
$315$	5.51527	+	0.384524i	0.310750	+	0.0216655i
$316$	−1.53755	−	1.57571i	−0.0864937	−	0.0886408i
$317$	−0.000616701	0	0.000616701i	−3.46374e−5	0	3.46374e-5i	0.707089	−	0.707124i	$-0.250008\pi$
$317$	−0.000616701	0	0.000616701i	−3.46374e−5	0	3.46374e-5i	−0.707124	+	0.707089i	$0.750008\pi$
$318$	−13.6131	−	13.8584i	−0.763385	−	0.777141i
$319$			5.05442i			0.282993i
$320$	13.8576	−	11.3122i	0.774664	−	0.632374i
$321$	−5.44358	−	13.2468i	−0.303831	−	0.739362i
$322$	−3.15454	+	1.28406i	−0.175796	+	0.0715578i
$323$	−5.57034	+	5.57034i	−0.309942	+	0.309942i
$324$	−12.4259	−	13.0230i	−0.690327	−	0.723498i
$325$	16.7978	+	21.7611i	0.931777	+	1.20709i
$326$	2.68740	−	6.37713i	0.148842	−	0.353196i
$327$	18.7059	+	7.80967i	1.03444	+	0.431876i
$328$	−0.732524	+	1.68039i	−0.0404469	+	0.0927841i
$329$	−7.32553			−0.403870
$330$	−20.1357	−	1.47125i	−1.10844	−	0.0809897i
$331$		−	8.28613i		−	0.455447i	−0.973726	−	0.227724i	$-0.926872\pi$
$331$		−	8.28613i		−	0.455447i	0.973726	−	0.227724i	$-0.0731283\pi$
$332$	−0.217550	+	17.7453i	−0.0119396	+	0.973901i
$333$	−10.3581	−	0.0579994i	−0.567622	−	0.00317835i
$334$	−1.75853	−	0.741069i	−0.0962226	−	0.0405495i
$335$	10.2467	+	11.6502i	0.559839	+	0.636521i
$336$	5.33305	−	2.04021i	0.290942	−	0.111302i
$337$	2.27666	+	2.27666i	0.124018	+	0.124018i	0.766392	−	0.642374i	$-0.222050\pi$
$337$	2.27666	+	2.27666i	0.124018	+	0.124018i	−0.642374	+	0.766392i	$0.722050\pi$
$338$	−22.5670	+	9.18590i	−1.22748	+	0.499647i
$339$	−7.99142	−	19.4468i	−0.434035	−	1.05621i
$340$	−5.55009	−	0.424111i	−0.300996	−	0.0230006i
$341$	−12.2405			−0.662861
$342$	−10.5663	+	24.6862i	−0.571357	+	1.33488i
$343$	7.76296	−	7.76296i	0.419161	−	0.419161i
$344$	1.19841	+	3.05070i	0.0646139	+	0.164483i
$345$	10.7217	−	3.62329i	0.577235	−	0.195071i
$346$	3.32189	+	1.39989i	0.178586	+	0.0752584i
$347$	−18.6384	−	18.6384i	−1.00056	−	1.00056i	−1.00000		0.000564305i	$-0.999820\pi$
$347$	−18.6384	−	18.6384i	−1.00056	−	1.00056i	−0.000564305	−	1.00000i	$-0.500180\pi$
$348$	1.75148	+	4.41536i	0.0938892	+	0.236688i
$349$	17.7267			0.948889			0.474445	−	0.880285i	$-0.342649\pi$
$349$	17.7267			0.948889			0.474445	+	0.880285i	$0.342649\pi$
$350$	2.93022	−	5.03747i	0.156627	−	0.269264i
$351$	11.1541	−	26.3013i	0.595360	−	1.40386i
$352$	−19.4998	+	7.38548i	−1.03934	+	0.393648i
$353$	10.5779	+	10.5779i	0.563007	+	0.563007i	0.930160	−	0.367153i	$-0.119668\pi$
$353$	10.5779	+	10.5779i	0.563007	+	0.563007i	−0.367153	+	0.930160i	$0.619668\pi$
$354$	−14.9909	−	0.133860i	−0.796758	−	0.00711457i
$355$	−9.22166	−	0.591066i	−0.489435	−	0.0313705i
$356$	−21.9815	+	21.4490i	−1.16502	+	1.13680i
$357$	−1.63958	−	0.684521i	−0.0867759	−	0.0362287i
$358$	−31.4582	+	12.8051i	−1.66262	+	0.676770i
$359$	24.7266			1.30502			0.652510	−	0.757780i	$-0.273716\pi$
$359$	24.7266			1.30502			0.652510	+	0.757780i	$0.273716\pi$
$360$	−18.0997	+	5.69229i	−0.953936	+	0.300010i
$361$	21.0586			1.10835
$362$	28.4513	−	11.5811i	1.49537	−	0.608691i
$363$	4.13505	+	1.72637i	0.217034	+	0.0906111i
$364$	6.32919	+	6.48630i	0.331739	+	0.339974i
$365$	−9.81201	−	11.1560i	−0.513584	−	0.583930i
$366$	−12.5769	−	0.112304i	−0.657406	−	0.00587024i
$367$	9.33767	+	9.33767i	0.487423	+	0.487423i	0.907492	−	0.420069i	$-0.137994\pi$
$367$	9.33767	+	9.33767i	0.487423	+	0.487423i	−0.420069	+	0.907492i	$0.637994\pi$
$368$	8.46516	−	8.05992i	0.441277	−	0.420152i
$369$	1.38251	−	1.36712i	0.0719707	−	0.0711692i
$370$	−4.87503	+	9.76985i	−0.253441	+	0.507911i
$371$	−6.53616			−0.339341
$372$	−10.6929	+	4.24164i	−0.554399	+	0.219919i
$373$	11.9025	+	11.9025i	0.616291	+	0.616291i	0.944578	−	0.328287i	$-0.106471\pi$
$373$	11.9025	+	11.9025i	0.616291	+	0.616291i	−0.328287	+	0.944578i	$0.606471\pi$
$374$	5.97903	+	2.51964i	0.309168	+	0.130288i
$375$	−10.7340	+	16.1177i	−0.554301	+	0.832317i
$376$	23.3996	−	9.19207i	1.20674	−	0.474045i
$377$	−5.33092	+	5.33092i	−0.274557	+	0.274557i
$378$	−6.05570	−	0.0879865i	−0.311472	−	0.00452554i
$379$	2.73341			0.140406			0.0702029	−	0.997533i	$-0.477635\pi$
$379$	2.73341			0.140406			0.0702029	+	0.997533i	$0.477635\pi$
$380$	18.4315	+	21.4814i	0.945515	+	1.10197i
$381$	−0.0136360	−	0.0331827i	−0.000698593	−	0.00170000i
$382$	17.0070	−	6.92270i	0.870153	−	0.354196i
$383$	−17.6065	−	17.6065i	−0.899651	−	0.899651i	0.0957539	−	0.995405i	$-0.469474\pi$
$383$	−17.6065	−	17.6065i	−0.899651	−	0.899651i	−0.995405	+	0.0957539i	$0.969474\pi$
$384$	−14.4750	+	13.2088i	−0.738676	+	0.674060i
$385$	−5.10079	+	4.48630i	−0.259960	+	0.228643i
$386$	17.4836	+	7.36780i	0.889890	+	0.375011i
$387$	0.0194659	−	3.47642i	0.000989506	−	0.176716i
$388$	15.3333	+	0.187980i	0.778429	+	0.00954322i
$389$		−	25.1335i		−	1.27432i	−0.770731	−	0.637160i	$-0.780109\pi$
$389$		−	25.1335i		−	1.27432i	0.770731	−	0.637160i	$-0.219891\pi$
$390$	−19.6855	−	22.7890i	−0.996815	−	1.15397i
$391$	−3.63704			−0.183933
$392$	−7.14408	+	16.3883i	−0.360831	+	0.827736i
$393$	8.37515	+	3.49660i	0.422470	+	0.176380i
$394$	−9.98855	+	23.7025i	−0.503216	+	1.19412i
$395$	2.45639	+	0.157444i	0.123594	+	0.00792185i
$396$	22.1129	+	0.394941i	1.11121	+	0.0198465i
$397$	−5.42664	+	5.42664i	−0.272355	+	0.272355i	−0.830048	−	0.557692i	$-0.811687\pi$
$397$	−5.42664	+	5.42664i	−0.272355	+	0.272355i	0.557692	+	0.830048i	$0.311687\pi$
$398$	0.0607282	−	0.0247195i	0.00304403	−	0.00123907i
$399$	3.43411	+	8.35678i	0.171921	+	0.418362i
$400$	−3.03886	+	19.7678i	−0.151943	+	0.988389i
$401$			5.15831i			0.257594i	0.991671	+	0.128797i	$0.0411115\pi$
$401$			5.15831i			0.257594i	−0.991671	+	0.128797i	$0.958888\pi$
$402$	−11.9103	−	12.1249i	−0.594032	−	0.604736i
$403$	−12.9101	−	12.9101i	−0.643099	−	0.643099i
$404$	−14.0917	+	13.7504i	−0.701090	+	0.684108i
$405$	20.0677	+	1.51208i	0.997173	+	0.0751357i
$406$	1.47279	+	0.620652i	0.0730933	+	0.0308025i
$407$	8.99944	−	8.99944i	0.446085	−	0.446085i
$408$	6.09617	+	0.129186i	0.301806	+	0.00639565i
$409$		−	14.1638i		−	0.700356i	−0.936683	−	0.350178i	$-0.886121\pi$
$409$		−	14.1638i		−	0.700356i	0.936683	−	0.350178i	$-0.113879\pi$
$410$	−0.649681	−	1.94379i	−0.0320854	−	0.0959967i
$411$	31.9419	−	13.1261i	1.57558	−	0.647464i
$412$	0.287124	−	23.4204i	0.0141456	−	1.15384i
$413$	−3.56672	+	3.56672i	−0.175507	+	0.175507i
$414$	−11.5087	+	4.60967i	−0.565621	+	0.226553i
$415$	−13.1038	−	14.8986i	−0.643241	−	0.731345i
$416$	−28.3560	−	12.7770i	−1.39027	−	0.626444i
$417$	−14.7394	−	6.15365i	−0.721791	−	0.301346i
$418$	−12.4389	−	30.5587i	−0.608407	−	1.49467i
$419$		−	4.80514i		−	0.234746i	−0.993088	−	0.117373i	$-0.962553\pi$
$419$		−	4.80514i		−	0.234746i	0.993088	−	0.117373i	$-0.0374474\pi$
$420$	−2.90125	+	5.68661i	−0.141566	+	0.277478i
$421$			15.2187i			0.741716i	0.928690	+	0.370858i	$0.120936\pi$
$421$			15.2187i			0.741716i	−0.928690	+	0.370858i	$0.879064\pi$
$422$	0.774212	−	0.315143i	0.0376880	−	0.0153409i
$423$	−26.6649	−	0.149308i	−1.29649	−	0.00725958i
$424$	20.8781	−	8.20157i	1.01393	−	0.398304i
$425$	4.92631	−	3.80272i	0.238961	−	0.184459i
$426$	10.1221	+	0.0903846i	0.490420	+	0.00437915i
$427$	−2.99236	+	2.99236i	−0.144811	+	0.144811i
$428$	16.5359	+	0.202724i	0.799295	+	0.00979903i
$429$	13.3421	+	32.4676i	0.644164	+	1.56755i
$430$	−3.27898	−	1.63617i	−0.158126	−	0.0789029i
$431$			27.8760i			1.34274i	0.741122	+	0.671370i	$0.234294\pi$
$431$			27.8760i			1.34274i	−0.741122	+	0.671370i	$0.765706\pi$
$432$	19.4538	−	7.31764i	0.935974	−	0.352070i
$433$	−2.78003	+	2.78003i	−0.133600	+	0.133600i	−0.770744	−	0.637145i	$-0.780115\pi$
$433$	−2.78003	+	2.78003i	−0.133600	+	0.133600i	0.637145	+	0.770744i	$0.280115\pi$
$434$	−1.50306	+	3.56672i	−0.0721492	+	0.171208i
$435$	−4.75985	−	2.35534i	−0.228218	−	0.112930i
$436$	−16.7526	+	16.3468i	−0.802305	+	0.782872i
$437$	13.0777	+	13.0777i	0.625592	+	0.625592i
$438$	11.4050	+	11.6105i	0.544951	+	0.554771i
$439$		−	10.8174i		−	0.516286i	−0.966107	−	0.258143i	$-0.916889\pi$
$439$		−	10.8174i		−	0.516286i	0.966107	−	0.258143i	$-0.0831105\pi$
$440$	10.6638	−	20.7308i	0.508376	−	0.988303i
$441$	13.4832	−	13.3331i	0.642058	−	0.634907i
$442$	3.64863	+	8.96358i	0.173548	+	0.426354i
$443$	5.74963	−	5.74963i	0.273173	−	0.273173i	−0.557203	−	0.830376i	$-0.688126\pi$
$443$	5.74963	−	5.74963i	0.273173	−	0.273173i	0.830376	+	0.557203i	$0.188126\pi$
$444$	4.74305	−	10.9801i	0.225095	−	0.521092i
$445$	2.19637	−	34.2671i	0.104118	−	1.62442i
$446$	31.0693	+	13.0930i	1.47118	+	0.619973i
$447$	9.34590	−	22.3855i	0.442046	−	1.05880i
$448$	−0.242427	+	6.58885i	−0.0114536	+	0.311294i
$449$	−6.91183			−0.326189			−0.163095	−	0.986610i	$-0.552148\pi$
$449$	−6.91183			−0.326189			−0.163095	+	0.986610i	$0.552148\pi$
$450$	10.7687	−	18.2766i	0.507640	−	0.861569i
$451$			2.38895i			0.112491i
$452$	24.2755	+	0.297608i	1.14182	+	0.0139983i
$453$	20.9864	+	8.76176i	0.986026	+	0.411663i
$454$	−5.61841	+	13.3323i	−0.263685	+	0.625716i
$455$	−10.1115	−	0.648104i	−0.474036	−	0.0303836i
$456$	−21.4555	−	22.3845i	−1.00475	−	1.04825i
$457$	−5.15748	−	5.15748i	−0.241257	−	0.241257i	0.576113	−	0.817370i	$-0.304569\pi$
$457$	−5.15748	−	5.15748i	−0.241257	−	0.241257i	−0.817370	+	0.576113i	$0.804569\pi$
$458$	−12.2674	−	30.1373i	−0.573219	−	1.40823i
$459$	−5.95412	−	2.52507i	−0.277915	−	0.117860i
$460$	−0.995701	+	13.0302i	−0.0464248	+	0.607535i
$461$	18.4555			0.859558			0.429779	−	0.902934i	$-0.358592\pi$
$461$	18.4555			0.859558			0.429779	+	0.902934i	$0.358592\pi$
$462$	5.30861	−	5.21464i	0.246979	−	0.242607i
$463$	−19.6899	+	19.6899i	−0.915068	+	0.915068i	−0.996665	−	0.0815977i	$-0.973998\pi$
$463$	−19.6899	+	19.6899i	−0.915068	+	0.915068i	0.0815977	+	0.996665i	$0.473998\pi$
$464$	−5.48325	−	0.134465i	−0.254553	−	0.00624238i
$465$	5.70403	−	11.5271i	0.264518	−	0.534559i
$466$	−3.45685	+	8.20301i	−0.160136	+	0.379997i
$467$	2.07946	+	2.07946i	0.0962257	+	0.0962257i	0.753581	−	0.657355i	$-0.228325\pi$
$467$	2.07946	+	2.07946i	0.0962257	+	0.0962257i	−0.657355	+	0.753581i	$0.728325\pi$
$468$	22.9060	+	23.7391i	1.05883	+	1.09734i
$469$	−5.71858			−0.264060
$470$	−12.5498	+	25.1505i	−0.578877	+	1.16011i
$471$	−14.4307	+	5.93013i	−0.664933	+	0.273246i
$472$	6.91747	−	15.8685i	0.318402	−	0.730407i
$473$	3.02041	+	3.02041i	0.138879	+	0.138879i
$474$	−2.69626	−	0.0240759i	−0.123843	−	0.00110584i
$475$	−31.3870	−	4.04012i	−1.44013	−	0.185374i
$476$	1.46838	−	1.43281i	0.0673029	−	0.0656727i
$477$	−23.7916	−	0.133219i	−1.08934	−	0.00609967i
$478$	−2.15122	−	5.28490i	−0.0983945	−	0.241725i
$479$	−19.7088			−0.900517			−0.450259	−	0.892898i	$-0.648668\pi$
$479$	−19.7088			−0.900517			−0.450259	+	0.892898i	$0.648668\pi$
$480$	2.13175	−	21.8049i	0.0973008	−	0.995255i
$481$	18.9835			0.865573
$482$	−6.11083	−	15.0125i	−0.278341	−	0.683799i
$483$	−1.60708	+	3.84931i	−0.0731246	+	0.175150i
$484$	−3.70326	+	3.61356i	−0.168330	+	0.164253i
$485$	−12.8735	+	11.3227i	−0.584557	+	0.514136i
$486$	−22.0409	−	0.443697i	−0.999797	−	0.0201265i
$487$	4.21395	+	4.21395i	0.190952	+	0.190952i	0.796107	−	0.605155i	$-0.206889\pi$
$487$	4.21395	+	4.21395i	0.190952	+	0.190952i	−0.605155	+	0.796107i	$0.706889\pi$
$488$	5.80354	−	13.3132i	0.262714	−	0.602659i
$489$	−3.22151	−	7.83943i	−0.145682	−	0.354511i
$490$	−6.33613	−	18.9571i	−0.286237	−	0.856396i
$491$	−27.7215			−1.25105			−0.625527	−	0.780203i	$-0.715116\pi$
$491$	−27.7215			−1.25105			−0.625527	+	0.780203i	$0.715116\pi$
$492$	0.827831	+	2.08690i	0.0373215	+	0.0940848i
$493$	1.20682	+	1.20682i	0.0543525	+	0.0543525i
$494$	19.1110	−	45.3497i	0.859843	−	2.04038i
$495$	−18.6583	+	16.2261i	−0.838627	+	0.729311i
$496$	0.325640	−	13.2790i	0.0146216	−	0.596246i
$497$	2.40831	−	2.40831i	0.108028	−	0.108028i
$498$	15.2312	+	15.5057i	0.682527	+	0.694825i
$499$	5.14705			0.230414			0.115207	−	0.993342i	$-0.463247\pi$
$499$	5.14705			0.230414			0.115207	+	0.993342i	$0.463247\pi$
$500$	−12.2750	−	18.6902i	−0.548957	−	0.835851i
$501$	−2.16177	+	0.888353i	−0.0965809	+	0.0396887i
$502$	−9.32016	−	22.8968i	−0.415979	−	1.02193i
$503$	−12.2281	−	12.2281i	−0.545224	−	0.545224i	0.379832	−	0.925056i	$-0.375982\pi$
$503$	−12.2281	−	12.2281i	−0.545224	−	0.545224i	−0.925056	+	0.379832i	$0.875982\pi$
$504$	2.83040	−	6.39488i	0.126076	−	0.284851i
$505$	1.40803	−	21.9677i	0.0626565	−	0.977550i
$506$	5.91546	−	14.0372i	0.262974	−	0.624030i
$507$	−11.4967	+	27.5372i	−0.510587	+	1.22297i
$508$	0.0414220		0.000507817i	0.00183780		2.25307e-5i
$509$			35.8361i			1.58841i	0.607651	+	0.794204i	$0.292112\pi$
$509$			35.8361i			1.58841i	−0.607651	+	0.794204i	$0.707888\pi$
$510$	−5.15900	+	4.45643i	−0.228444	+	0.197334i
$511$	5.47596			0.242242
$512$	−7.49332	−	21.3506i	−0.331161	−	0.943574i
$513$	12.3298	+	30.4886i	0.544375	+	1.34611i
$514$	−12.4825	−	5.26031i	−0.550581	−	0.232022i
$515$	17.2945	+	19.6633i	0.762086	+	0.866469i
$516$	3.68516	+	1.59187i	0.162230	+	0.0700783i
$517$	23.1672	−	23.1672i	1.01889	−	1.01889i
$518$	−1.51723	−	3.72738i	−0.0666634	−	0.163772i
$519$	4.08361	−	1.67811i	0.179251	−	0.0736608i
$520$	33.1120	−	10.6177i	1.45206	−	0.465619i
$521$			18.1715i			0.796107i	0.917362	+	0.398054i	$0.130314\pi$
$521$			18.1715i			0.796107i	−0.917362	+	0.398054i	$0.869686\pi$
$522$	5.34829	+	2.28919i	0.234088	+	0.100195i
$523$	−21.7444	−	21.7444i	−0.950815	−	0.950815i	0.0480305	−	0.998846i	$-0.484706\pi$
$523$	−21.7444	−	21.7444i	−0.950815	−	0.950815i	−0.998846	+	0.0480305i	$0.984706\pi$
$524$	−7.50061	+	7.31893i	−0.327666	+	0.319729i
$525$	−1.84789	−	6.89411i	−0.0806487	−	0.300884i
$526$	11.9382	−	28.3289i	0.520529	−	1.23520i
$527$	−2.92261	+	2.92261i	−0.127311	+	0.127311i
$528$	−10.4137	+	23.3181i	−0.453198	+	1.01479i
$529$		−	14.4612i		−	0.628746i
$530$	−11.1974	+	22.4404i	−0.486386	+	0.974748i
$531$	−13.0555	+	12.9101i	−0.566561	+	0.560252i
$532$	−10.4318	−	0.127889i	−0.452275	−	0.00554471i
$533$	−2.51964	+	2.51964i	−0.109138	+	0.109138i
$534$	−0.335864	+	37.6133i	−0.0145342	+	1.62768i
$535$	−13.8833	+	12.2108i	−0.600227	+	0.527918i
$536$	18.2666	−	7.17567i	0.788996	−	0.309942i
$537$	−16.0264	+	38.3867i	−0.691589	+	1.65651i
$538$	12.5597	−	5.11242i	0.541486	−	0.220412i
$539$			23.2987i			1.00355i
$540$	−10.6764	+	20.6401i	−0.459440	+	0.888209i
$541$			26.6843i			1.14725i	0.819119	+	0.573623i	$0.194463\pi$
$541$			26.6843i			1.14725i	−0.819119	+	0.573623i	$0.805537\pi$
$542$	−11.1476	−	27.3862i	−0.478830	−	1.17634i
$543$	14.4945	−	34.7176i	0.622019	−	1.48987i
$544$	−2.89247	+	6.41927i	−0.124014	+	0.275224i
$545$	1.67390	−	26.1158i	0.0717022	−	1.11868i
$546$	11.0989	+	0.0991067i	0.474990	+	0.00424138i
$547$	22.2551	−	22.2551i	0.951559	−	0.951559i	−0.0473207	−	0.998880i	$-0.515068\pi$
$547$	22.2551	−	22.2551i	0.951559	−	0.951559i	0.998880	+	0.0473207i	$0.0150683\pi$
$548$	−0.488829	+	39.8732i	−0.0208817	+	1.70330i
$549$	−10.9532	+	10.8312i	−0.467470	+	0.462264i
$550$	6.66422	+	25.1981i	0.284163	+	1.07445i
$551$		−	8.67873i		−	0.369726i
$552$	0.303295	−	14.3122i	0.0129091	−	0.609169i
$553$	−0.641507	+	0.641507i	−0.0272797	+	0.0272797i
$554$	16.3355	+	6.88398i	0.694027	+	0.292472i
$555$	4.28125	+	12.6687i	0.181729	+	0.537754i
$556$	13.2003	−	12.8805i	0.559817	−	0.546257i
$557$	−7.30615	−	7.30615i	−0.309572	−	0.309572i	0.535172	−	0.844743i	$-0.320247\pi$
$557$	−7.30615	−	7.30615i	−0.309572	−	0.309572i	−0.844743	+	0.535172i	$0.820247\pi$
$558$	−5.54383	+	12.9522i	−0.234689	+	0.548310i
$559$			6.37128i			0.269476i
$560$	−4.73122	−	5.65290i	−0.199931	−	0.238878i
$561$	7.35005	−	3.02041i	0.310319	−	0.127522i
$562$	15.9704	−	6.50074i	0.673669	−	0.274217i
$563$	21.3458	−	21.3458i	0.899616	−	0.899616i	−0.0957856	−	0.995402i	$-0.530536\pi$
$563$	21.3458	−	21.3458i	0.899616	−	0.899616i	0.995402	+	0.0957856i	$0.0305363\pi$
$564$	12.2100	−	28.2660i	0.514134	−	1.19021i
$565$	−20.3813	+	17.9260i	−0.857447	+	0.754150i
$566$	−9.07152	+	21.5264i	−0.381304	+	0.904823i
$567$	−5.30335	+	5.18588i	−0.222720	+	0.217787i
$568$	−4.67081	+	10.7147i	−0.195983	+	0.449579i
$569$	−35.6410			−1.49415			−0.747075	−	0.664740i	$-0.768542\pi$
$569$	−35.6410			−1.49415			−0.747075	+	0.664740i	$0.768542\pi$
$570$	34.5742	+	2.52622i	1.44815	+	0.105812i
$571$			9.49296i			0.397268i	0.980074	+	0.198634i	$0.0636505\pi$
$571$			9.49296i			0.397268i	−0.980074	+	0.198634i	$0.936350\pi$
$572$	−40.5293	−	0.496873i	−1.69462	−	0.0207753i
$573$	8.66419	−	20.7527i	0.361952	−	0.866955i
$574$	0.696108	+	0.293349i	0.0290550	+	0.0122441i
$575$	−8.92779	−	11.5657i	−0.372314	−	0.482323i
$576$	−1.01673	+	23.9785i	−0.0423636	+	0.999102i
$577$	10.6312	+	10.6312i	0.442582	+	0.442582i	0.892879	−	0.450297i	$-0.148682\pi$
$577$	10.6312	+	10.6312i	0.442582	+	0.442582i	−0.450297	+	0.892879i	$0.648682\pi$
$578$	−20.2384	+	8.23803i	−0.841805	+	0.342657i
$579$	21.4926	−	8.83212i	0.893203	−	0.367050i
$580$	4.65397	−	3.99320i	0.193246	−	0.165809i
$581$	7.31307			0.303397
$582$	13.3981	−	13.1609i	0.555367	−	0.545537i
$583$	20.6708	−	20.6708i	0.856097	−	0.856097i
$584$	−17.4916	+	6.87124i	−0.723808	+	0.284334i
$585$	−36.7927	−	2.56519i	−1.52119	−	0.106057i
$586$	−9.51801	−	4.01102i	−0.393186	−	0.165694i
$587$	−17.1910	−	17.1910i	−0.709550	−	0.709550i	0.256891	−	0.966441i	$-0.417302\pi$
$587$	−17.1910	−	17.1910i	−0.709550	−	0.709550i	−0.966441	+	0.256891i	$0.917302\pi$
$588$	8.07357	+	20.3529i	0.332949	+	0.839339i
$589$	21.0177			0.866018
$590$	6.13515	+	18.3558i	0.252580	+	0.755697i
$591$	11.9737	+	29.1376i	0.492534	+	1.19856i
$592$	9.52355	+	10.0024i	0.391415	+	0.411095i
$593$	9.69544	+	9.69544i	0.398144	+	0.398144i	0.877578	−	0.479434i	$-0.159158\pi$
$593$	9.69544	+	9.69544i	0.398144	+	0.398144i	−0.479434	+	0.877578i	$0.659158\pi$
$594$	19.4296	−	18.8731i	0.797206	−	0.774372i
$595$	−0.146719	+	2.28906i	−0.00601487	+	0.0938424i
$596$	19.5624	+	20.0480i	0.801307	+	0.821198i
$597$	0.0309379	−	0.0741033i	0.00126621	−	0.00303285i
$598$	21.0442	−	8.56604i	0.860560	−	0.350291i
$599$	26.8502			1.09707			0.548535	−	0.836128i	$-0.315186\pi$
$599$	26.8502			1.09707			0.548535	+	0.836128i	$0.315186\pi$
$600$	14.5534	+	19.7028i	0.594139	+	0.804363i
$601$	−42.9566			−1.75224			−0.876119	−	0.482095i	$-0.839876\pi$
$601$	−42.9566			−1.75224			−0.876119	+	0.482095i	$0.839876\pi$
$602$	1.25099	−	0.509217i	0.0509866	−	0.0207541i
$603$	−20.8156	−	0.116555i	−0.847677	−	0.00474649i
$604$	−18.7950	+	18.3397i	−0.764756	+	0.746232i
$605$	0.370026	−	5.77305i	0.0150437	−	0.234708i
$606$	−0.215313	+	24.1128i	−0.00874650	+	0.979517i
$607$	32.0417	+	32.0417i	1.30053	+	1.30053i	0.928033	+	0.372498i	$0.121499\pi$
$607$	32.0417	+	32.0417i	1.30053	+	1.30053i	0.372498	+	0.928033i	$0.378501\pi$
$608$	33.4822	−	12.6813i	1.35788	−	0.514294i
$609$	1.81051	−	0.744004i	0.0733654	−	0.0301486i
$610$	5.14720	+	15.4000i	0.208404	+	0.623526i
$611$	48.8691			1.97703
$612$	5.37408	−	5.18549i	0.217234	−	0.209611i
$613$	−20.1419	−	20.1419i	−0.813522	−	0.813522i	0.171638	−	0.985160i	$-0.445094\pi$
$613$	−20.1419	−	20.1419i	−0.813522	−	0.813522i	−0.985160	+	0.171638i	$0.945094\pi$
$614$	−16.9527	−	7.14408i	−0.684154	−	0.288311i
$615$	−2.24973	−	1.11324i	−0.0907177	−	0.0448903i
$616$	3.14170	+	7.99760i	0.126583	+	0.322232i
$617$	−7.33463	+	7.33463i	−0.295281	+	0.295281i	−0.839162	−	0.543881i	$-0.816954\pi$
$617$	−7.33463	+	7.33463i	−0.295281	+	0.295281i	0.543881	+	0.839162i	$0.316954\pi$
$618$	−20.1022	−	20.4645i	−0.808631	−	0.823202i
$619$	11.9287			0.479456			0.239728	−	0.970840i	$-0.422942\pi$
$619$	11.9287			0.479456			0.239728	+	0.970840i	$0.422942\pi$
$620$	9.67051	+	11.2707i	0.388377	+	0.452644i
$621$	−5.92821	+	13.9787i	−0.237891	+	0.560947i
$622$	−40.0410	+	16.2987i	−1.60550	+	0.653519i
$623$	8.94914	+	8.94914i	0.358540	+	0.358540i
$624$	−35.5771	+	13.6104i	−1.42422	+	0.544850i
$625$	24.1851	+	6.33109i	0.967403	+	0.253244i
$626$	−30.3385	−	12.7850i	−1.21257	−	0.510993i
$627$	−37.2890	−	15.5681i	−1.48918	−	0.621729i
$628$	0.220843	−	18.0139i	0.00881260	−	0.718834i
$629$		−	4.29751i		−	0.171353i
$630$	2.43695	+	7.42923i	0.0970903	+	0.295988i
$631$	7.13985			0.284233			0.142116	−	0.989850i	$-0.454609\pi$
$631$	7.13985			0.284233			0.142116	+	0.989850i	$0.454609\pi$
$632$	1.24417	−	2.85410i	0.0494905	−	0.113530i
$633$	0.394421	−	0.944728i	0.0156768	−	0.0375496i
$634$	0.000478978	−	0.00113660i	1.90227e−5	−	4.51402e-5i
$635$	−0.0347772	+	0.0305876i	−0.00138009	+	0.00121383i
$636$	10.8943	−	25.2202i	0.431988	−	1.00005i
$637$	−24.5733	+	24.5733i	−0.973628	+	0.973628i
$638$	−6.62057	+	2.69490i	−0.262111	+	0.106692i
$639$	8.81533	−	8.71716i	0.348729	−	0.344846i
$640$	22.2060	+	12.1200i	0.877768	+	0.479086i
$641$		−	30.0187i		−	1.18567i	−0.805325	−	0.592834i	$-0.798009\pi$
$641$		−	30.0187i		−	1.18567i	0.805325	−	0.592834i	$-0.201991\pi$
$642$	14.4489	−	14.1932i	0.570254	−	0.560160i
$643$	32.7048	+	32.7048i	1.28975	+	1.28975i	0.934938	+	0.354812i	$0.115455\pi$
$643$	32.7048	+	32.7048i	1.28975	+	1.28975i	0.354812	+	0.934938i	$0.384545\pi$
$644$	−3.36386	−	3.44736i	−0.132555	−	0.135845i
$645$	−4.25188	+	1.43688i	−0.167418	+	0.0565772i
$646$	−10.2663	−	4.32637i	−0.403923	−	0.170219i
$647$	2.53026	−	2.53026i	0.0994747	−	0.0994747i	−0.655618	−	0.755093i	$-0.727592\pi$
$647$	2.53026	−	2.53026i	0.0994747	−	0.0994747i	0.755093	+	0.655618i	$0.227592\pi$
$648$	10.4330	−	23.2197i	0.409847	−	0.912154i
$649$		−	22.5597i		−	0.885545i
$650$	−19.5477	+	33.6053i	−0.766725	+	1.31811i
$651$	1.80179	+	4.38458i	0.0706176	+	0.171845i
$652$	9.78598	+	0.119972i	0.383248	+	0.00469847i
$653$	23.8061	−	23.8061i	0.931604	−	0.931604i	−0.0662023	−	0.997806i	$-0.521088\pi$
$653$	23.8061	−	23.8061i	0.931604	−	0.931604i	0.997806	+	0.0662023i	$0.0210883\pi$
$654$	−0.255970	+	28.6660i	−0.0100092	+	1.12093i
$655$	0.749453	−	11.6928i	0.0292835	−	0.456874i
$656$	−2.59164	−	0.0635543i	−0.101186	−	0.00248138i
$657$	19.9325	+	0.111610i	0.777640	+	0.00435432i
$658$	−3.90581	−	9.59539i	−0.152264	−	0.374067i
$659$			15.7130i			0.612093i	0.952017	+	0.306047i	$0.0990063\pi$
$659$			15.7130i			0.612093i	−0.952017	+	0.306047i	$0.900994\pi$
$660$	−8.80879	−	27.1593i	−0.342882	−	1.05718i
$661$		−	25.2637i		−	0.982643i	−0.870978	−	0.491322i	$-0.836514\pi$
$661$		−	25.2637i		−	0.982643i	0.870978	−	0.491322i	$-0.163486\pi$
$662$	10.8536	−	4.41798i	0.421839	−	0.171710i
$663$	10.9378	+	4.56649i	0.424788	+	0.177348i
$664$	−23.3598	+	9.17644i	−0.906536	+	0.356115i
$665$	8.75834	−	7.70323i	0.339634	−	0.298718i
$666$	−5.44675	−	13.5986i	−0.211057	−	0.526935i
$667$	2.83330	−	2.83330i	0.109706	−	0.109706i
$668$	0.0330830	−	2.69854i	0.00128002	−	0.104410i
$669$	38.1937	−	15.6952i	1.47665	−	0.606812i
$670$	−9.79680	+	19.6334i	−0.378483	+	0.758505i
$671$		−	18.9269i		−	0.730664i
$672$	5.51584	+	5.89773i	0.212778	+	0.227510i
$673$	−15.4486	+	15.4486i	−0.595498	+	0.595498i	−0.939111	−	0.343613i	$-0.888349\pi$
$673$	−15.4486	+	15.4486i	−0.595498	+	0.595498i	0.343613	+	0.939111i	$0.388349\pi$
$674$	−1.76824	+	4.19597i	−0.0681099	+	0.161623i
$675$	−6.58581	−	25.1322i	−0.253488	−	0.967339i
$676$	−24.0644	−	24.6618i	−0.925554	−	0.948529i
$677$	3.86002	+	3.86002i	0.148353	+	0.148353i	0.777382	−	0.629029i	$-0.216547\pi$
$677$	3.86002	+	3.86002i	0.148353	+	0.148353i	−0.629029	+	0.777382i	$0.716547\pi$
$678$	21.2117	−	20.8362i	0.814630	−	0.800210i
$679$		−	6.31904i		−	0.242503i
$680$	−2.40366	−	7.49594i	−0.0921761	−	0.287456i
$681$	6.73505	+	16.3895i	0.258088	+	0.628046i
$682$	−6.52637	−	16.0333i	−0.249908	−	0.613947i
$683$	−20.9584	+	20.9584i	−0.801949	+	0.801949i	−0.983400	−	0.181451i	$-0.941921\pi$
$683$	−20.9584	+	20.9584i	−0.801949	+	0.801949i	0.181451	+	0.983400i	$0.441921\pi$
$684$	−37.9691	−	0.678136i	−1.45178	−	0.0259292i
$685$	−29.4439	−	33.4768i	−1.12499	−	1.27908i
$686$	14.3074	+	6.02932i	0.546259	+	0.230201i
$687$	−36.7749	−	15.3534i	−1.40305	−	0.585770i
$688$	−3.35702	+	3.19631i	−0.127985	+	0.121858i
$689$	43.6032			1.66115
$690$	10.4625	+	12.1120i	0.398302	+	0.461095i
$691$			26.8902i			1.02295i	0.859298	+	0.511475i	$0.170901\pi$
$691$			26.8902i			1.02295i	−0.859298	+	0.511475i	$0.829099\pi$
$692$	−0.0624943	+	5.09759i	−0.00237568	+	0.193781i
$693$	0.0510309	−	9.11363i	0.00193850	−	0.346198i
$694$	14.4761	−	34.3513i	0.549504	−	1.30396i
$695$	−1.31896	+	20.5780i	−0.0500309	+	0.780569i
$696$	−4.84963	+	4.64836i	−0.183825	+	0.176196i
$697$	0.570399	+	0.570399i	0.0216054	+	0.0216054i
$698$	9.45148	+	23.2194i	0.357744	+	0.878869i
$699$	4.14389	+	10.0840i	0.156736	+	0.381412i
$700$	8.16069	+	1.15231i	0.308445	+	0.0435531i
$701$	−35.7956			−1.35198			−0.675990	−	0.736911i	$-0.736284\pi$
$701$	−35.7956			−1.35198			−0.675990	+	0.736911i	$0.736284\pi$
$702$	40.3980	+	0.586964i	1.52472	+	0.0221535i
$703$	−15.4525	+	15.4525i	−0.582804	+	0.582804i
$704$	−20.0708	−	21.6041i	−0.756445	−	0.814236i
$705$	11.0212	+	32.6128i	0.415083	+	1.22827i
$706$	−8.21566	+	19.4955i	−0.309200	+	0.733723i
$707$	5.73705	+	5.73705i	0.215764	+	0.215764i
$708$	−7.81748	−	19.7073i	−0.293799	−	0.740646i
$709$	−31.6856			−1.18998			−0.594988	−	0.803735i	$-0.702843\pi$
$709$	−31.6856			−1.18998			−0.594988	+	0.803735i	$0.702843\pi$
$710$	−4.14257	−	12.3942i	−0.155468	−	0.465145i
$711$	−2.34816	+	2.32201i	−0.0880628	+	0.0870821i
$712$	−39.8152	−	17.3564i	−1.49214	−	0.650459i
$713$	6.86153	+	6.86153i	0.256966	+	0.256966i
$714$	0.0224359	−	2.51259i	0.000839642	−	0.0940312i
$715$	34.0277	−	29.9284i	1.27256	−	1.11926i
$716$	−33.5456	−	34.3784i	−1.25366	−	1.28478i
$717$	−6.44887	−	2.69238i	−0.240837	−	0.100549i
$718$	13.1837	+	32.3883i	0.492010	+	1.20872i
$719$	47.9558			1.78845			0.894225	−	0.447618i	$-0.147728\pi$
$719$	47.9558			1.78845			0.894225	+	0.447618i	$0.147728\pi$
$720$	−17.1064	−	20.6729i	−0.637518	−	0.770435i
$721$	−9.65184			−0.359453
$722$	11.2280	+	27.5837i	0.417861	+	1.02656i
$723$	−18.3189	−	7.64809i	−0.681287	−	0.284435i
$724$	30.3392	+	31.0923i	1.12755	+	1.15554i
$725$	−0.875297	+	6.80002i	−0.0325077	+	0.252546i
$726$	−0.0565836	+	6.33678i	−0.00210002	+	0.235180i
$727$	20.8052	+	20.8052i	0.771622	+	0.771622i	0.978390	−	0.206768i	$-0.0662946\pi$
$727$	20.8052	+	20.8052i	0.771622	+	0.771622i	−0.206768	+	0.978390i	$0.566295\pi$
$728$	−5.12153	+	11.7487i	−0.189817	+	0.435435i
$729$	−19.4099	+	18.7685i	−0.718884	+	0.695130i
$730$	9.38116	−	18.8004i	0.347212	−	0.695835i
$731$	1.44234			0.0533468
$732$	−6.55862	−	16.5338i	−0.242414	−	0.611108i
$733$	11.3990	+	11.3990i	0.421033	+	0.421033i	0.885559	−	0.464526i	$-0.153775\pi$
$733$	11.3990	+	11.3990i	0.421033	+	0.421033i	−0.464526	+	0.885559i	$0.653775\pi$
$734$	−7.25237	+	17.2096i	−0.267690	+	0.635219i
$735$	−21.9409	−	10.8571i	−0.809302	−	0.400470i
$736$	15.0708	+	6.79077i	0.555516	+	0.250311i
$737$	18.0852	−	18.0852i	0.666176	−	0.666176i
$738$	2.52785	+	1.08198i	0.0930514	+	0.0398281i
$739$	9.60683			0.353393			0.176697	−	0.984265i	$-0.443459\pi$
$739$	9.60683			0.353393			0.176697	+	0.984265i	$0.443459\pi$
$740$	−15.3964	−	1.17651i	−0.565981	−	0.0432495i
$741$	−22.9092	−	55.7487i	−0.841591	−	2.04798i
$742$	−3.48493	−	8.56143i	−0.127936	−	0.314300i
$743$	−2.71436	−	2.71436i	−0.0995802	−	0.0995802i	0.655562	−	0.755142i	$-0.272432\pi$
$743$	−2.71436	−	2.71436i	−0.0995802	−	0.0995802i	−0.755142	+	0.655562i	$0.772432\pi$
$744$	−11.2571	−	11.7446i	−0.412706	−	0.430577i
$745$	−31.2530	−	2.00318i	−1.14502	−	0.0733907i
$746$	−9.24445	+	21.9368i	−0.338463	+	0.803163i
$747$	26.6196	+	0.149054i	0.973958	+	0.00545359i
$748$	−0.112483	+	9.17508i	−0.00411277	+	0.335474i
$749$		−	6.81468i		−	0.249003i
$750$	−26.8350	−	5.46636i	−0.979877	−	0.199603i
$751$	−18.9690			−0.692189			−0.346094	−	0.938200i	$-0.612492\pi$
$751$	−18.9690			−0.692189			−0.346094	+	0.938200i	$0.612492\pi$
$752$	24.5164	+	25.7491i	0.894022	+	0.938972i
$753$	−27.9397	−	11.6648i	−1.01818	−	0.425087i
$754$	−9.82507	−	4.14041i	−0.357808	−	0.150785i
$755$	1.87797	−	29.2996i	0.0683464	−	1.06632i
$756$	−3.11352	−	7.97901i	−0.113237	−	0.290194i
$757$	0.279592	−	0.279592i	0.0101620	−	0.0101620i	−0.702008	−	0.712170i	$-0.747713\pi$
$757$	0.279592	−	0.279592i	0.0101620	−	0.0101620i	0.712170	+	0.702008i	$0.247713\pi$
$758$	1.45739	+	3.58037i	0.0529349	+	0.130045i
$759$	−7.09113	−	17.2560i	−0.257392	−	0.626353i
$760$	−18.3103	+	35.5960i	−0.664185	+	1.29120i
$761$		−	20.3237i		−	0.736733i	−0.929681	−	0.368366i	$-0.879917\pi$
$761$		−	20.3237i		−	0.736733i	0.929681	−	0.368366i	$-0.120083\pi$
$762$	0.0361941	−	0.0355534i	0.00131117	−	0.00128797i
$763$	6.82036	+	6.82036i	0.246914	+	0.246914i
$764$	18.1355	+	18.5857i	0.656118	+	0.672406i
$765$	−0.580710	+	8.32919i	−0.0209956	+	0.301142i
$766$	13.6746	−	32.4494i	0.494083	−	1.17244i
$767$	23.7938	−	23.7938i	0.859144	−	0.859144i
$768$	−25.0194	−	11.9176i	−0.902811	−	0.430038i
$769$		−	25.1716i		−	0.907711i	−0.891075	−	0.453855i	$-0.850048\pi$
$769$		−	25.1716i		−	0.907711i	0.891075	−	0.453855i	$-0.149952\pi$
$770$	−8.59603	−	4.28930i	−0.309779	−	0.154576i
$771$	−15.3448	+	6.30577i	−0.552631	+	0.227097i
$772$	−0.328916	+	26.8293i	−0.0118379	+	0.965607i
$773$	24.0474	−	24.0474i	0.864925	−	0.864925i	−0.126980	−	0.991905i	$-0.540528\pi$
$773$	24.0474	−	24.0474i	0.864925	−	0.864925i	0.991905	+	0.126980i	$0.0405284\pi$
$774$	4.56398	−	1.82805i	0.164049	−	0.0657079i
$775$	−16.4679	−	2.11974i	−0.591545	−	0.0761434i
$776$	7.92913	+	20.1846i	0.284639	+	0.724585i
$777$	−4.54832	−	1.89891i	−0.163170	−	0.0681231i
$778$	32.9213	−	13.4006i	1.18029	−	0.480436i
$779$		−	4.10197i		−	0.146968i
$780$	19.3544	−	37.9358i	0.692999	−	1.35832i
$781$			15.2327i			0.545070i
$782$	−1.93919	−	4.76400i	−0.0693453	−	0.170360i
$783$	6.60539	−	2.67127i	0.236058	−	0.0954634i
$784$	−25.2754	−	0.619825i	−0.902693	−	0.0221366i
$785$	13.3022	+	15.1242i	0.474774	+	0.539804i
$786$	−0.114605	+	12.8345i	−0.00408782	+	0.457793i
$787$	6.79695	−	6.79695i	0.242285	−	0.242285i	−0.575510	−	0.817795i	$-0.695196\pi$
$787$	6.79695	−	6.79695i	0.242285	−	0.242285i	0.817795	+	0.575510i	$0.195196\pi$
$788$	−36.3725	−	0.445912i	−1.29572	−	0.0158850i
$789$	−14.3108	−	34.8249i	−0.509479	−	1.23980i
$790$	1.10346	+	3.30146i	0.0392595	+	0.117461i
$791$		−	10.0043i		−	0.355710i
$792$	11.2728	+	29.1752i	0.400560	+	1.03670i
$793$	19.9623	−	19.9623i	0.708881	−	0.708881i
$794$	−10.0015	−	4.21476i	−0.354939	−	0.149576i
$795$	9.83361	+	29.0986i	0.348762	+	1.03202i
$796$	0.0647578	+	0.0663654i	0.00229528	+	0.00235226i
$797$	6.72322	+	6.72322i	0.238149	+	0.238149i	0.816083	−	0.577935i	$-0.196141\pi$
$797$	6.72322	+	6.72322i	0.238149	+	0.238149i	−0.577935	+	0.816083i	$0.696141\pi$
$798$	−9.11519	+	8.95384i	−0.322674	+	0.316963i
$799$		−	11.0630i		−	0.391382i
$800$	−27.5132	+	6.55927i	−0.972738	+	0.231905i
$801$	32.3924	+	32.7572i	1.14453	+	1.15742i
$802$	−6.75665	+	2.75030i	−0.238585	+	0.0971164i
$803$	−17.3179	+	17.3179i	−0.611135	+	0.611135i
$804$	9.53159	−	22.0655i	0.336153	−	0.778190i
$805$	5.37412	+	0.344457i	0.189413	+	0.0121405i
$806$	10.0270	−	23.7938i	0.353187	−	0.838101i
$807$	6.39851	−	15.3259i	0.225238	−	0.539496i
$808$	−25.5244	−	11.1267i	−0.897946	−	0.391437i
$809$	−35.3381			−1.24242			−0.621212	−	0.783643i	$-0.713359\pi$
$809$	−35.3381			−1.24242			−0.621212	+	0.783643i	$0.713359\pi$
$810$	8.71906	+	27.0920i	0.306356	+	0.951917i
$811$			37.1596i			1.30485i	0.757854	+	0.652425i	$0.226248\pi$
$811$			37.1596i			1.30485i	−0.757854	+	0.652425i	$0.773752\pi$
$812$	−0.0277074	+	2.26006i	−0.000972338	+	0.0793125i
$813$	−33.4179	−	13.9519i	−1.17202	−	0.489314i
$814$	16.5863	+	6.98967i	0.581348	+	0.244988i
$815$	−8.21613	+	7.22634i	−0.287798	+	0.253128i
$816$	3.08113	+	8.05399i	0.107861	+	0.281946i
$817$	−5.18621	−	5.18621i	−0.181443	−	0.181443i
$818$	18.5526	−	7.55184i	0.648676	−	0.264044i
$819$	9.66601	−	9.55836i	0.337758	−	0.333996i
$820$	2.19968	−	1.88737i	0.0768163	−	0.0659098i
$821$	28.5674			0.997010			0.498505	−	0.866887i	$-0.333882\pi$
$821$	28.5674			0.997010			0.498505	+	0.866887i	$0.333882\pi$
$822$	34.2241	+	34.8408i	1.19370	+	1.21521i
$823$	−28.5682	+	28.5682i	−0.995823	+	0.995823i	−0.999991	−	0.00416817i	$-0.998673\pi$
$823$	−28.5682	+	28.5682i	−0.995823	+	0.995823i	0.00416817	+	0.999991i	$0.498673\pi$
$824$	30.8304	−	12.1111i	1.07403	−	0.421911i
$825$	27.6468	+	15.9588i	0.962539	+	0.555614i
$826$	−6.57357	−	2.77019i	−0.228724	−	0.0963872i
$827$	−5.31276	−	5.31276i	−0.184743	−	0.184743i	0.608676	−	0.793419i	$-0.291701\pi$
$827$	−5.31276	−	5.31276i	−0.184743	−	0.184743i	−0.793419	+	0.608676i	$0.791701\pi$
$828$	−12.1742	−	12.6170i	−0.423082	−	0.438469i
$829$	4.51176			0.156700			0.0783500	−	0.996926i	$-0.475035\pi$
$829$	4.51176			0.156700			0.0783500	+	0.996926i	$0.475035\pi$
$830$	12.5284	−	25.1077i	0.434868	−	0.871502i
$831$	20.0813	−	8.25214i	0.696611	−	0.286263i
$832$	1.61725	−	43.9547i	0.0560679	−	1.52385i
$833$	5.56292	+	5.56292i	0.192744	+	0.192744i
$834$	0.201692	−	22.5875i	0.00698403	−	0.782140i
$835$	1.99271	+	2.26565i	0.0689605	+	0.0784060i
$836$	33.3953	−	32.5864i	1.15500	−	1.12702i
$837$	6.46913	+	15.9966i	0.223606	+	0.552922i
$838$	6.29404	−	2.56199i	0.217424	−	0.0885025i
$839$	−42.7255			−1.47505			−0.737523	−	0.675322i	$-0.764005\pi$
$839$	−42.7255			−1.47505			−0.737523	+	0.675322i	$0.764005\pi$
$840$	−8.99552	−	0.768242i	−0.310375	−	0.0265069i
$841$	27.1197			0.935164
$842$	−19.9343	+	8.11428i	−0.686983	+	0.279637i
$843$	8.13608	−	19.4877i	0.280221	−	0.671193i
$844$	0.825584	+	0.846078i	0.0284178	+	0.0291232i
$845$	38.4454	+	2.46418i	1.32256	+	0.0847702i
$846$	−14.0215	−	35.0068i	−0.482071	−	1.20356i
$847$	1.50768	+	1.50768i	0.0518045	+	0.0518045i
$848$	21.8746	+	22.9745i	0.751178	+	0.788946i
$849$	10.8744	+	26.4625i	0.373210	+	0.908192i
$850$	7.60761	+	4.42524i	0.260939	+	0.151784i
$851$	−10.0894			−0.345861
$852$	5.27851	+	13.3067i	0.180839	+	0.455881i
$853$	28.1027	+	28.1027i	0.962217	+	0.962217i	0.999312	−	0.0370946i	$-0.0118103\pi$
$853$	28.1027	+	28.1027i	0.962217	+	0.962217i	−0.0370946	+	0.999312i	$0.511810\pi$
$854$	−5.51503	−	2.32410i	−0.188720	−	0.0795292i
$855$	32.0373	−	27.8612i	1.09565	−	0.952833i
$856$	8.55106	+	21.7678i	0.292269	+	0.744008i
$857$	−35.8406	+	35.8406i	−1.22429	+	1.22429i	−0.258198	+	0.966092i	$0.583129\pi$
$857$	−35.8406	+	35.8406i	−1.22429	+	1.22429i	−0.966092	+	0.258198i	$0.916871\pi$
$858$	−35.4141	+	34.7872i	−1.20902	+	1.18762i
$859$	1.55128			0.0529289			0.0264645	−	0.999650i	$-0.491575\pi$
$859$	1.55128			0.0529289			0.0264645	+	0.999650i	$0.491575\pi$
$860$	0.394864	−	5.16735i	0.0134647	−	0.176205i
$861$	0.855728	−	0.351651i	0.0291631	−	0.0119842i
$862$	−36.5136	+	14.8629i	−1.24366	+	0.506231i
$863$	−22.7893	−	22.7893i	−0.775758	−	0.775758i	0.203348	−	0.979107i	$-0.434818\pi$
$863$	−22.7893	−	22.7893i	−0.775758	−	0.775758i	−0.979107	+	0.203348i	$0.934818\pi$
$864$	19.9574	+	21.5801i	0.678965	+	0.734171i
$865$	−3.76425	−	4.27984i	−0.127988	−	0.145519i
$866$	−5.12369	−	2.15919i	−0.174110	−	0.0733723i
$867$	−10.3104	+	24.6957i	−0.350160	+	0.838712i
$868$	−5.47328	−	0.0671001i	−0.185775	−	0.00227753i
$869$		−	4.05757i		−	0.137644i
$870$	0.547309	−	7.49054i	0.0185555	−	0.253953i
$871$	38.1490			1.29263
$872$	−30.3441	−	13.2278i	−1.02758	−	0.447948i
$873$	0.128793	−	23.0013i	0.00435900	−	0.778476i
$874$	−10.1572	+	24.1027i	−0.343572	+	0.815285i
$875$	−7.63931	+	5.15236i	−0.258256	+	0.174182i
$876$	−9.12720	+	21.1293i	−0.308379	+	0.713894i
$877$	−22.8089	+	22.8089i	−0.770202	+	0.770202i	−0.978142	−	0.207940i	$-0.933324\pi$
$877$	−22.8089	+	22.8089i	−0.770202	+	0.770202i	0.207940	+	0.978142i	$0.433324\pi$
$878$	14.1692	−	5.76759i	0.478188	−	0.194647i
$879$	−11.7005	+	4.80819i	−0.394649	+	0.162176i
$880$	32.8401	+	2.91481i	1.10704	+	0.0982583i
$881$		−	1.47551i		−	0.0497114i	−0.999691	−	0.0248557i	$-0.992087\pi$
$881$		−	1.47551i		−	0.0497114i	0.999691	−	0.0248557i	$-0.00791262\pi$
$882$	24.6533	+	10.5522i	0.830121	+	0.355310i
$883$	3.02812	+	3.02812i	0.101904	+	0.101904i	0.756221	−	0.654316i	$-0.227044\pi$
$883$	3.02812	+	3.02812i	0.101904	+	0.101904i	−0.654316	+	0.756221i	$0.727044\pi$
$884$	−9.79563	+	9.55836i	−0.329463	+	0.321482i
$885$	21.2449	+	10.5127i	0.714140	+	0.353381i
$886$	10.5968	+	4.46561i	0.356005	+	0.150025i
$887$	−19.9170	+	19.9170i	−0.668749	+	0.668749i	−0.957426	−	0.288678i	$-0.906784\pi$
$887$	−19.9170	+	19.9170i	−0.668749	+	0.668749i	0.288678	+	0.957426i	$0.406784\pi$
$888$	16.9112	+	0.358371i	0.567504	+	0.0120261i
$889$		−	0.0170705i		−	0.000572528i
$890$	46.0560	−	15.3935i	1.54380	−	0.515992i
$891$	0.371504	−	33.1725i	0.0124459	−	1.11132i
$892$	−0.584504	+	47.6773i	−0.0195706	+	1.59635i
$893$	−39.7794	+	39.7794i	−1.33117	+	1.33117i
$894$	34.3048	+	0.306321i	1.14733	+	0.0102449i
$895$	53.5927	+	3.43505i	1.79141	+	0.114821i
$896$	−8.75970	+	3.19548i	−0.292641	+	0.106754i
$897$	10.7209	−	25.6790i	0.357961	−	0.857398i
$898$	−3.68523	−	9.05349i	−0.122978	−	0.302119i
$899$		−	4.55350i		−	0.151868i
$900$	29.6814	+	4.36072i	0.989379	+	0.145357i
$901$		−	9.87094i		−	0.328849i
$902$	−3.12918	+	1.27374i	−0.104190	+	0.0424108i
$903$	0.637317	−	1.52652i	0.0212086	−	0.0507993i
$904$	12.5533	+	31.9561i	0.417518	+	1.06284i
$905$	−48.4701	−	3.10671i	−1.61120	−	0.103271i
$906$	−0.287176	+	32.1607i	−0.00954077	+	1.06847i
$907$	−6.11318	+	6.11318i	−0.202985	+	0.202985i	−0.801278	−	0.598293i	$-0.795846\pi$
$907$	−6.11318	+	6.11318i	−0.202985	+	0.202985i	0.598293	+	0.801278i	$0.295846\pi$
$908$	−20.4590	−	0.250819i	−0.678956	−	0.00832372i
$909$	20.7659	+	20.9998i	0.688762	+	0.696518i
$910$	−4.54232	−	13.5902i	−0.150577	−	0.450511i
$911$			28.1492i			0.932625i	0.884620	+	0.466313i	$0.154418\pi$
$911$			28.1492i			0.932625i	−0.884620	+	0.466313i	$0.845582\pi$
$912$	17.8809	−	40.0385i	0.592096	−	1.32581i
$913$	−23.1278	+	23.1278i	−0.765419	+	0.765419i
$914$	4.00570	−	9.50541i	0.132497	−	0.314411i
$915$	17.8238	+	8.81984i	0.589238	+	0.291575i
$916$	32.9349	−	32.1371i	1.08820	−	1.06184i
$917$	3.05366	+	3.05366i	0.100841	+	0.100841i
$918$	0.132878	−	9.14535i	0.00438561	−	0.301842i
$919$			49.4285i			1.63049i	0.579113	+	0.815247i	$0.303399\pi$
$919$			49.4285i			1.63049i	−0.579113	+	0.815247i	$0.696601\pi$
$920$	−17.5985	+	5.64317i	−0.580206	+	0.186050i
$921$	−20.8400	+	8.56393i	−0.686701	+	0.282191i
$922$	9.84005	+	24.1740i	0.324065	+	0.796129i
$923$	−16.0660	+	16.0660i	−0.528819	+	0.528819i
$924$	9.66086	+	4.17318i	0.317819	+	0.137288i
$925$	13.6660	−	10.5490i	0.449334	−	0.346849i
$926$	−36.2892	−	15.2927i	−1.19254	−	0.502550i
$927$	−35.1327	−	0.196722i	−1.15391	−	0.00646120i
$928$	−2.74741	−	7.25396i	−0.0901883	−	0.238123i
$929$	38.9204			1.27694			0.638468	−	0.769649i	$-0.279569\pi$
$929$	38.9204			1.27694			0.638468	+	0.769649i	$0.279569\pi$
$930$	18.1402	+	1.32544i	0.594839	+	0.0434629i
$931$		−	40.0052i		−	1.31112i
$932$	−12.5879	−	0.154322i	−0.412329	−	0.00505499i
$933$	−20.3988	+	48.8598i	−0.667828	+	1.59960i
$934$	−1.61507	+	3.83251i	−0.0528466	+	0.125403i
$935$	−6.77522	−	7.70323i	−0.221574	−	0.251922i
$936$	−18.8818	+	42.6607i	−0.617172	+	1.39441i
$937$	−4.49303	−	4.49303i	−0.146781	−	0.146781i	0.629897	−	0.776678i	$-0.283097\pi$
$937$	−4.49303	−	4.49303i	−0.146781	−	0.146781i	−0.776678	+	0.629897i	$0.783097\pi$
$938$	−3.04902	−	7.49052i	−0.0995540	−	0.244574i
$939$	−37.2952	+	15.3260i	−1.21708	+	0.500145i
$940$	−39.6348	−	3.02869i	−1.29274	−	0.0987851i
$941$	−23.2736			−0.758696			−0.379348	−	0.925254i	$-0.623852\pi$
$941$	−23.2736			−0.758696			−0.379348	+	0.925254i	$0.623852\pi$
$942$	−15.4618	−	15.7404i	−0.503771	−	0.512849i
$943$	1.33915	−	1.33915i	0.0436087	−	0.0436087i
$944$	24.4737	+	0.600164i	0.796550	+	0.0195337i
$945$	8.55871	+	4.29497i	0.278415	+	0.139715i
$946$	−2.34589	+	5.56671i	−0.0762713	+	0.180989i
$947$	28.1797	+	28.1797i	0.915717	+	0.915717i	0.996714	−	0.0809978i	$-0.0258107\pi$
$947$	28.1797	+	28.1797i	0.915717	+	0.915717i	−0.0809978	+	0.996714i	$0.525811\pi$
$948$	−1.40605	−	3.54454i	−0.0456663	−	0.115121i
$949$	−36.5305			−1.18583
$950$	−11.4428	−	43.2665i	−0.371255	−	1.40375i
$951$	−0.000574173	−	0.00139723i	−1.86188e−5	−	4.53082e-5i
$952$	2.65968	+	1.15942i	0.0862006	+	0.0375770i
$953$	−28.5653	−	28.5653i	−0.925321	−	0.925321i	0.0720776	−	0.997399i	$-0.477037\pi$
$953$	−28.5653	−	28.5653i	−0.925321	−	0.925321i	−0.997399	+	0.0720776i	$0.977037\pi$
$954$	−12.5106	−	31.2346i	−0.405047	−	1.01126i
$955$	−28.9733	−	1.85706i	−0.937555	−	0.0600930i
$956$	5.77547	−	5.63557i	0.186792	−	0.182267i
$957$	−3.37284	+	8.07871i	−0.109028	+	0.261148i
$958$	−10.5083	−	25.8157i	−0.339507	−	0.834066i
$959$	16.4323			0.530625
$960$	29.6979	−	8.83361i	0.958497	−	0.285104i
$961$	−19.9726			−0.644277
$962$	10.1216	+	24.8656i	0.326332	+	0.801700i
$963$	0.138895	−	24.8054i	0.00447584	−	0.799343i
$964$	16.4060	−	16.0086i	0.528402	−	0.515603i
$965$	−19.8118	−	22.5254i	−0.637763	−	0.725118i
$966$	−5.89890	−	0.0526736i	−0.189794	−	0.00169475i
$967$	−37.0606	−	37.0606i	−1.19179	−	1.19179i	−0.976565	−	0.215225i	$-0.930952\pi$
$967$	−37.0606	−	37.0606i	−1.19179	−	1.19179i	−0.215225	−	0.976565i	$-0.569048\pi$
$968$	−6.70774	−	2.92407i	−0.215595	−	0.0939832i
$969$	−12.6204	+	5.18621i	−0.405427	+	0.166605i
$970$	−21.6949	−	10.8255i	−0.696583	−	0.347585i
$971$	11.8114			0.379044			0.189522	−	0.981876i	$-0.439306\pi$
$971$	11.8114			0.379044			0.189522	+	0.981876i	$0.439306\pi$
$972$	−11.1706	−	29.1070i	−0.358296	−	0.933608i
$973$	−5.37412	−	5.37412i	−0.172287	−	0.172287i
$974$	−3.27288	+	7.76644i	−0.104870	+	0.248853i
$975$	12.3274	+	45.9911i	0.394793	+	1.47289i
$976$	20.5327	+	0.503519i	0.657234	+	0.0161173i
$977$	5.34002	−	5.34002i	0.170842	−	0.170842i	−0.616507	−	0.787349i	$-0.711453\pi$
$977$	5.34002	−	5.34002i	0.170842	−	0.170842i	0.787349	+	0.616507i	$0.211453\pi$
$978$	8.55088	−	8.39953i	0.273427	−	0.268587i
$979$	−56.6038			−1.80907
$980$	21.4528	−	18.4069i	0.685285	−	0.587988i
$981$	24.6871	+	24.9651i	0.788197	+	0.797074i
$982$	−14.7805	−	36.3111i	−0.471664	−	1.15874i
$983$	42.6490	+	42.6490i	1.36029	+	1.36029i	0.873540	+	0.486753i	$0.161819\pi$
$983$	42.6490	+	42.6490i	1.36029	+	1.36029i	0.486753	+	0.873540i	$0.338181\pi$
$984$	−2.29216	+	2.19703i	−0.0730714	+	0.0700387i
$985$	30.5377	−	26.8589i	0.973013	−	0.855795i
$986$	−0.937311	+	2.22421i	−0.0298501	+	0.0708333i
$987$	−11.7087	−	4.88836i	−0.372693	−	0.155598i
$988$	69.5912	+	0.853159i	2.21399	+	0.0271426i
$989$		−	3.38623i		−	0.107676i
$990$	−31.2021	−	15.7882i	−0.991667	−	0.501783i
$991$	−31.5197			−1.00126			−0.500629	−	0.865662i	$-0.666898\pi$
$991$	−31.5197			−1.00126			−0.500629	+	0.865662i	$0.666898\pi$
$992$	17.5672	−	6.65353i	0.557760	−	0.211250i
$993$	5.52938	−	13.2441i	0.175469	−	0.420289i
$994$	4.43860	+	1.87048i	0.140784	+	0.0593282i
$995$	−0.103457	−	0.00663115i	−0.00327982	−	0.000210222i
$996$	−12.1892	+	28.2179i	−0.386231	+	0.894120i
$997$	38.3474	−	38.3474i	1.21447	−	1.21447i	0.244935	−	0.969540i	$-0.421233\pi$
$997$	38.3474	−	38.3474i	1.21447	−	1.21447i	0.969540	−	0.244935i	$-0.0787666\pi$
$998$	2.74429	+	6.74190i	0.0868690	+	0.213411i
$999$	−16.5172	−	7.00473i	−0.522580	−	0.221620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.2.w.c.77.11	yes	32
3.2	odd	2	inner	120.2.w.c.77.6	yes	32
4.3	odd	2		480.2.bi.c.17.3		32
5.2	odd	4		600.2.w.j.293.3		32
5.3	odd	4	inner	120.2.w.c.53.14	yes	32
5.4	even	2		600.2.w.j.557.6		32
8.3	odd	2		480.2.bi.c.17.14		32
8.5	even	2	inner	120.2.w.c.77.3	yes	32
12.11	even	2		480.2.bi.c.17.6		32
15.2	even	4		600.2.w.j.293.14		32
15.8	even	4	inner	120.2.w.c.53.3	✓	32
15.14	odd	2		600.2.w.j.557.11		32
20.3	even	4		480.2.bi.c.113.11		32
24.5	odd	2	inner	120.2.w.c.77.14	yes	32
24.11	even	2		480.2.bi.c.17.11		32
40.3	even	4		480.2.bi.c.113.6		32
40.13	odd	4	inner	120.2.w.c.53.6	yes	32
40.29	even	2		600.2.w.j.557.14		32
40.37	odd	4		600.2.w.j.293.11		32
60.23	odd	4		480.2.bi.c.113.14		32
120.29	odd	2		600.2.w.j.557.3		32
120.53	even	4	inner	120.2.w.c.53.11	yes	32
120.77	even	4		600.2.w.j.293.6		32
120.83	odd	4		480.2.bi.c.113.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.w.c.53.3	✓	32	15.8	even	4	inner
120.2.w.c.53.6	yes	32	40.13	odd	4	inner
120.2.w.c.53.11	yes	32	120.53	even	4	inner
120.2.w.c.53.14	yes	32	5.3	odd	4	inner
120.2.w.c.77.3	yes	32	8.5	even	2	inner
120.2.w.c.77.6	yes	32	3.2	odd	2	inner
120.2.w.c.77.11	yes	32	1.1	even	1	trivial
120.2.w.c.77.14	yes	32	24.5	odd	2	inner
480.2.bi.c.17.3		32	4.3	odd	2
480.2.bi.c.17.6		32	12.11	even	2
480.2.bi.c.17.11		32	24.11	even	2
480.2.bi.c.17.14		32	8.3	odd	2
480.2.bi.c.113.3		32	120.83	odd	4
480.2.bi.c.113.6		32	40.3	even	4
480.2.bi.c.113.11		32	20.3	even	4
480.2.bi.c.113.14		32	60.23	odd	4
600.2.w.j.293.3		32	5.2	odd	4
600.2.w.j.293.6		32	120.77	even	4
600.2.w.j.293.11		32	40.37	odd	4
600.2.w.j.293.14		32	15.2	even	4
600.2.w.j.557.3		32	120.29	odd	2
600.2.w.j.557.6		32	5.4	even	2
600.2.w.j.557.11		32	15.14	odd	2
600.2.w.j.557.14		32	40.29	even	2

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	120.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.533177 + 1.30986i) q^{2} +(1.59834 + 0.667305i) q^{3} +(-1.43144 + 1.39677i) q^{4} +(0.143028 - 2.23149i) q^{5} +(-0.0218716 + 2.44939i) q^{6} +(0.582772 + 0.582772i) q^{7} +(-2.59278 - 1.13026i) q^{8} +(2.10941 + 2.13317i) q^{9} +O(q^{10})\)	\(q+(0.533177 + 1.30986i) q^{2} +(1.59834 + 0.667305i) q^{3} +(-1.43144 + 1.39677i) q^{4} +(0.143028 - 2.23149i) q^{5} +(-0.0218716 + 2.44939i) q^{6} +(0.582772 + 0.582772i) q^{7} +(-2.59278 - 1.13026i) q^{8} +(2.10941 + 2.13317i) q^{9} +(2.99919 - 1.00243i) q^{10} -3.68607 q^{11} +(-3.22001 + 1.27731i) q^{12} +(-3.88771 - 3.88771i) q^{13} +(-0.452626 + 1.07407i) q^{14} +(1.71769 - 3.47124i) q^{15} +(0.0980619 - 3.99880i) q^{16} +(-0.880105 + 0.880105i) q^{17} +(-1.66945 + 3.90038i) q^{18} +6.32919 q^{19} +(2.91214 + 3.39403i) q^{20} +(0.542584 + 1.32036i) q^{21} +(-1.96533 - 4.82821i) q^{22} +(2.06626 + 2.06626i) q^{23} +(-3.38993 - 3.53672i) q^{24} +(-4.95909 - 0.638332i) q^{25} +(3.01950 - 7.16518i) q^{26} +(1.94809 + 4.81715i) q^{27} +(-1.64820 - 0.0202063i) q^{28} -1.37122i q^{29} +(5.46266 + 0.399139i) q^{30} +3.32075 q^{31} +(5.29013 - 2.00362i) q^{32} +(-5.89160 - 2.45973i) q^{33} +(-1.62206 - 0.683558i) q^{34} +(1.38380 - 1.21710i) q^{35} +(-5.99904 - 0.107144i) q^{36} +(-2.44147 + 2.44147i) q^{37} +(3.37458 + 8.29032i) q^{38} +(-3.61961 - 8.80819i) q^{39} +(-2.89300 + 5.62410i) q^{40} -0.648104i q^{41} +(-1.44018 + 1.41469i) q^{42} +(-0.819412 - 0.819412i) q^{43} +(5.27640 - 5.14859i) q^{44} +(5.06184 - 4.40202i) q^{45} +(-1.60482 + 3.80818i) q^{46} +(-6.28508 + 6.28508i) q^{47} +(2.82515 - 6.32602i) q^{48} -6.32075i q^{49} +(-1.80795 - 6.83603i) q^{50} +(-1.99401 + 0.819412i) q^{51} +(10.9953 + 0.134798i) q^{52} +(-5.60782 + 5.60782i) q^{53} +(-5.27109 + 5.12011i) q^{54} +(-0.527212 + 8.22542i) q^{55} +(-0.852318 - 2.16968i) q^{56} +(10.1162 + 4.22349i) q^{57} +(1.79611 - 0.731106i) q^{58} +6.12026i q^{59} +(2.38975 + 7.36811i) q^{60} +5.13471i q^{61} +(1.77055 + 4.34971i) q^{62} +(-0.0138443 + 2.47245i) q^{63} +(5.44503 + 5.86102i) q^{64} +(-9.23144 + 8.11933i) q^{65} +(0.0806201 - 9.02862i) q^{66} +(-4.90636 + 4.90636i) q^{67} +(0.0305156 - 2.48912i) q^{68} +(1.92377 + 4.68141i) q^{69} +(2.33203 + 1.16365i) q^{70} -4.13251i q^{71} +(-3.05821 - 7.91501i) q^{72} +(4.69820 - 4.69820i) q^{73} +(-4.49972 - 1.89624i) q^{74} +(-7.50036 - 4.32950i) q^{75} +(-9.05987 + 8.84042i) q^{76} +(-2.14814 - 2.14814i) q^{77} +(9.60756 - 9.43750i) q^{78} +1.10079i q^{79} +(-8.90925 - 0.790765i) q^{80} +(-0.100786 + 8.99944i) q^{81} +(0.848922 - 0.345554i) q^{82} +(6.27439 - 6.27439i) q^{83} +(-2.62091 - 1.13215i) q^{84} +(1.83806 + 2.08982i) q^{85} +(0.636420 - 1.51020i) q^{86} +(0.915024 - 2.19169i) q^{87} +(9.55717 + 4.16621i) q^{88} +15.3562 q^{89} +(8.46487 + 4.28322i) q^{90} -4.53130i q^{91} +(-5.84382 - 0.0716428i) q^{92} +(5.30771 + 2.21595i) q^{93} +(-11.5836 - 4.88148i) q^{94} +(0.905253 - 14.1235i) q^{95} +(9.79248 + 0.327652i) q^{96} +(-5.42154 - 5.42154i) q^{97} +(8.27927 - 3.37008i) q^{98} +(-7.77542 - 7.86299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{6}+O(q^{10}) \) 32 * q - 4 * q^6	\( 32 q - 4 q^{6} + 4 q^{10} - 8 q^{12} - 28 q^{15} + 28 q^{16} - 20 q^{18} - 52 q^{22} - 8 q^{25} + 12 q^{28} - 32 q^{30} - 32 q^{31} + 8 q^{33} - 20 q^{36} + 24 q^{40} + 16 q^{42} + 24 q^{46} + 44 q^{48} + 8 q^{52} + 8 q^{55} - 16 q^{57} + 28 q^{58} + 56 q^{60} + 48 q^{63} + 16 q^{66} + 20 q^{70} + 32 q^{72} - 64 q^{73} - 88 q^{76} + 64 q^{78} + 48 q^{81} + 64 q^{82} - 8 q^{87} - 52 q^{88} + 84 q^{90} - 52 q^{96} + 16 q^{97}+O(q^{100}) \) 32 * q - 4 * q^6 + 4 * q^10 - 8 * q^12 - 28 * q^15 + 28 * q^16 - 20 * q^18 - 52 * q^22 - 8 * q^25 + 12 * q^28 - 32 * q^30 - 32 * q^31 + 8 * q^33 - 20 * q^36 + 24 * q^40 + 16 * q^42 + 24 * q^46 + 44 * q^48 + 8 * q^52 + 8 * q^55 - 16 * q^57 + 28 * q^58 + 56 * q^60 + 48 * q^63 + 16 * q^66 + 20 * q^70 + 32 * q^72 - 64 * q^73 - 88 * q^76 + 64 * q^78 + 48 * q^81 + 64 * q^82 - 8 * q^87 - 52 * q^88 + 84 * q^90 - 52 * q^96 + 16 * q^97

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