LMFDB - Embedded newform 120.2.w.c.53.11

Newspace parameters

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

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			53.11
Character	$\chi$	$=$	120.53
Dual form			120.2.w.c.77.11

$q$-expansion

$f(q)$	$=$	$q+(0.533177 - 1.30986i) q^{2} +(1.59834 - 0.667305i) q^{3} +(-1.43144 - 1.39677i) q^{4} +(0.143028 + 2.23149i) q^{5} +(-0.0218716 - 2.44939i) q^{6} +(0.582772 - 0.582772i) q^{7} +(-2.59278 + 1.13026i) q^{8} +(2.10941 - 2.13317i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.533177	−	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	−0.588344	−	0.808611i	$-0.700220\pi$
$7$	0.582772	−	0.582772i	0.220267	−	0.220267i	0.808611	+	0.588344i	$0.200220\pi$
$8$	−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	−0.0815911	+	0.996666i	$0.526000\pi$
$13$	−3.88771	+	3.88771i	−1.07826	+	1.07826i	−0.996666	+	0.0815911i	$0.974000\pi$
$14$	−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	0.592277	−	0.805734i	$-0.298229\pi$
$17$	−0.880105	−	0.880105i	−0.213457	−	0.213457i	−0.805734	+	0.592277i	$0.798229\pi$
$18$	−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	−0.458071	−	0.888916i	$-0.651460\pi$
$23$	2.06626	−	2.06626i	0.430844	−	0.430844i	0.888916	+	0.458071i	$0.151460\pi$
$24$	−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	$0.0406359\pi$
$29$			1.37122i			0.254630i	−0.991862	+	0.127315i	$0.959364\pi$
$30$	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	0.477342	−	0.878718i	$-0.341600\pi$
$37$	−2.44147	−	2.44147i	−0.401376	−	0.401376i	−0.878718	+	0.477342i	$0.841600\pi$
$38$	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	$0.0161160\pi$
$41$			0.648104i			0.101217i	−0.998719	+	0.0506084i	$0.983884\pi$
$42$	−1.44018	−	1.41469i	−0.222225	−	0.218292i
$43$	−0.819412	+	0.819412i	−0.124959	+	0.124959i	−0.766821	−	0.641861i	$-0.778162\pi$
$43$	−0.819412	+	0.819412i	−0.124959	+	0.124959i	0.641861	+	0.766821i	$0.278162\pi$
$44$	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	0.0800208	−	0.996793i	$-0.474501\pi$
$47$	−6.28508	−	6.28508i	−0.916772	−	0.916772i	−0.996793	+	0.0800208i	$0.974501\pi$
$48$	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	0.207864	−	0.978158i	$-0.433349\pi$
$53$	−5.60782	−	5.60782i	−0.770293	−	0.770293i	−0.978158	+	0.207864i	$0.933349\pi$
$54$	−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	$-0.869567\pi$
$59$		−	6.12026i		−	0.796790i	0.917214	−	0.398395i	$-0.130433\pi$
$60$	2.38975	−	7.36811i	0.308516	−	0.951219i
$61$		−	5.13471i		−	0.657432i	−0.944429	−	0.328716i	$-0.893384\pi$
$61$		−	5.13471i		−	0.657432i	0.944429	−	0.328716i	$-0.106616\pi$
$62$	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	0.340747	−	0.940155i	$-0.389320\pi$
$67$	−4.90636	−	4.90636i	−0.599408	−	0.599408i	−0.940155	+	0.340747i	$0.889320\pi$
$68$	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	$0.0788601\pi$
$71$			4.13251i			0.490439i	−0.969468	+	0.245220i	$0.921140\pi$
$72$	−3.05821	+	7.91501i	−0.360414	+	0.932793i
$73$	4.69820	+	4.69820i	0.549883	+	0.549883i	0.926407	−	0.376524i	$-0.122881\pi$
$73$	4.69820	+	4.69820i	0.549883	+	0.549883i	−0.376524	+	0.926407i	$0.622881\pi$
$74$	−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	$-0.980276\pi$
$79$		−	1.10079i		−	0.123848i	0.998081	−	0.0619241i	$-0.0197237\pi$
$80$	−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	0.961945	−	0.273242i	$-0.0880960\pi$
$83$	6.27439	+	6.27439i	0.688703	+	0.688703i	−0.273242	+	0.961945i	$0.588096\pi$
$84$	−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	−0.926578	−	0.376104i	$-0.877264\pi$
$97$	−5.42154	+	5.42154i	−0.550474	+	0.550474i	0.376104	+	0.926578i	$0.377264\pi$
$98$	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	0.169569	−	0.985518i	$-0.445762\pi$
$103$	−8.28098	−	8.28098i	−0.815949	−	0.815949i	−0.985518	+	0.169569i	$0.945762\pi$
$104$	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	−0.930788	−	0.365559i	$-0.880878\pi$
$107$	−5.84678	+	5.84678i	−0.565230	+	0.565230i	0.365559	+	0.930788i	$0.380878\pi$
$108$	−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	−0.984248	−	0.176796i	$-0.943427\pi$
$113$	−8.58333	+	8.58333i	−0.807452	+	0.807452i	0.176796	+	0.984248i	$0.443427\pi$
$114$	−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	−0.707756	−	0.706457i	$-0.750293\pi$
$127$	−0.0146460	+	0.0146460i	−0.00129962	+	0.00129962i	0.706457	+	0.707756i	$0.250293\pi$
$128$	−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	0.972782	+	0.231722i	$0.0744360\pi$
$137$	14.0984	+	14.0984i	1.20450	+	1.20450i	0.231722	+	0.972782i	$0.425564\pi$
$138$	−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	$0.194487\pi$
$149$			14.0054i			1.14737i	−0.819076	+	0.573685i	$0.805513\pi$
$150$	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	0.405683	−	0.914014i	$-0.367034\pi$
$157$	−6.36936	−	6.36936i	−0.508330	−	0.508330i	−0.914014	+	0.405683i	$0.867034\pi$
$158$	−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	−0.829510	−	0.558492i	$-0.811380\pi$
$163$	−3.46013	+	3.46013i	−0.271018	+	0.271018i	0.558492	+	0.829510i	$0.311380\pi$
$164$	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	0.669225	−	0.743060i	$-0.266626\pi$
$167$	−0.954151	−	0.954151i	−0.0738345	−	0.0738345i	−0.743060	+	0.669225i	$0.766626\pi$
$168$	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	0.772296	−	0.635262i	$-0.219108\pi$
$173$	1.80240	+	1.80240i	0.137034	+	0.137034i	−0.635262	+	0.772296i	$0.719108\pi$
$174$	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	$-0.645351\pi$
$179$		−	24.0166i		−	1.79508i	0.440930	−	0.897541i	$-0.354649\pi$
$180$	−1.09712	−	13.3715i	−0.0817748	−	0.996651i
$181$			21.7210i			1.61451i	0.590205	+	0.807253i	$0.299047\pi$
$181$			21.7210i			1.61451i	−0.590205	+	0.807253i	$0.700953\pi$
$182$	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	$0.155652\pi$
$191$			12.9839i			0.939479i	−0.882805	+	0.469739i	$0.844348\pi$
$192$	4.79195	−	13.0014i	0.345829	−	0.938297i
$193$	9.48630	+	9.48630i	0.682839	+	0.682839i	0.960639	−	0.277800i	$-0.0896053\pi$
$193$	9.48630	+	9.48630i	0.682839	+	0.682839i	−0.277800	+	0.960639i	$0.589605\pi$
$194$	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	−0.0804765	−	0.996757i	$-0.525644\pi$
$197$	12.8606	−	12.8606i	0.916280	−	0.916280i	0.996757	+	0.0804765i	$0.0256442\pi$
$198$	6.15370	+	14.3770i	0.437324	+	1.02173i
$199$			0.0463625i			0.00328655i	0.999999	+	0.00164328i	$0.000523071\pi$
$199$			0.0463625i			0.00328655i	−0.999999	+	0.00164328i	$0.999477\pi$
$200$	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	$0.00647657\pi$
$211$			0.591066i			0.0406907i	−0.999793	+	0.0203453i	$0.993523\pi$
$212$	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	0.990360	+	0.138517i	$0.0442335\pi$
$223$	16.8577	+	16.8577i	1.12888	+	1.12888i	0.138517	+	0.990360i	$0.455767\pi$
$224$	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	−0.425043	−	0.905173i	$-0.639741\pi$
$227$	7.23390	−	7.23390i	0.480131	−	0.480131i	0.905173	+	0.425043i	$0.139741\pi$
$228$	−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	−0.546122	−	0.837705i	$-0.683897\pi$
$233$	4.45082	−	4.45082i	0.291583	−	0.291583i	0.837705	+	0.546122i	$0.183897\pi$
$234$	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	0.463578	−	0.886056i	$-0.346565\pi$
$257$	−6.77283	−	6.77283i	−0.422477	−	0.422477i	−0.886056	+	0.463578i	$0.846565\pi$
$258$	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	−0.998704	−	0.0508987i	$-0.983791\pi$
$263$	−15.3708	+	15.3708i	−0.947805	+	0.947805i	0.0508987	+	0.998704i	$0.483791\pi$
$264$	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	$0.0944250\pi$
$269$			9.58859i			0.584627i	−0.956323	+	0.292313i	$0.905575\pi$
$270$	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	0.921330	−	0.388782i	$-0.127104\pi$
$277$	8.86336	+	8.86336i	0.532547	+	0.532547i	−0.388782	+	0.921330i	$0.627104\pi$
$278$	−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	$0.118477\pi$
$281$			12.1925i			0.727341i	−0.931528	+	0.363670i	$0.881523\pi$
$282$	−15.2571	+	15.5321i	−0.908550	+	0.924922i
$283$	11.6799	−	11.6799i	0.694298	−	0.694298i	−0.268877	−	0.963175i	$-0.586652\pi$
$283$	11.6799	−	11.6799i	0.694298	−	0.694298i	0.963175	+	0.268877i	$0.0866525\pi$
$284$	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	0.539977	−	0.841680i	$-0.318433\pi$
$293$	−5.16432	−	5.16432i	−0.301703	−	0.301703i	−0.841680	+	0.539977i	$0.818433\pi$
$294$	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	0.394097	−	0.919069i	$-0.371057\pi$
$307$	−9.19824	−	9.19824i	−0.524972	−	0.524972i	−0.919069	+	0.394097i	$0.871057\pi$
$308$	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	$-0.666233\pi$
$311$		−	30.5690i		−	1.73341i	0.498821	−	0.866705i	$-0.333767\pi$
$312$	−0.570656	−	26.9288i	−0.0323071	−	1.52454i
$313$	−16.4612	−	16.4612i	−0.930440	−	0.930440i	0.0672931	−	0.997733i	$-0.478564\pi$
$313$	−16.4612	−	16.4612i	−0.930440	−	0.930440i	−0.997733	+	0.0672931i	$0.978564\pi$
$314$	−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	−0.707124	−	0.707089i	$-0.750008\pi$
$317$	−0.000616701	0	0.000616701i	−3.46374e−5	0	3.46374e-5i	0.707089	+	0.707124i	$0.250008\pi$
$318$	−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	$0.0731283\pi$
$331$			8.28613i			0.455447i	−0.973726	+	0.227724i	$0.926872\pi$
$332$	−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	−0.642374	−	0.766392i	$-0.722050\pi$
$337$	2.27666	−	2.27666i	0.124018	−	0.124018i	0.766392	+	0.642374i	$0.222050\pi$
$338$	−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	−0.000564305		1.00000i	$0.500180\pi$
$347$	−18.6384	+	18.6384i	−1.00056	+	1.00056i	−1.00000		0.000564305i	$0.999820\pi$
$348$	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	−0.367153	−	0.930160i	$-0.619668\pi$
$353$	10.5779	−	10.5779i	0.563007	−	0.563007i	0.930160	+	0.367153i	$0.119668\pi$
$354$	−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	−0.420069	−	0.907492i	$-0.637994\pi$
$367$	9.33767	−	9.33767i	0.487423	−	0.487423i	0.907492	+	0.420069i	$0.137994\pi$
$368$	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	−0.328287	−	0.944578i	$-0.606471\pi$
$373$	11.9025	−	11.9025i	0.616291	−	0.616291i	0.944578	+	0.328287i	$0.106471\pi$
$374$	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	−0.995405	−	0.0957539i	$-0.969474\pi$
$383$	−17.6065	+	17.6065i	−0.899651	+	0.899651i	0.0957539	+	0.995405i	$0.469474\pi$
$384$	−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	$0.219891\pi$
$389$			25.1335i			1.27432i	−0.770731	+	0.637160i	$0.780109\pi$
$390$	−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	0.557692	−	0.830048i	$-0.311687\pi$
$397$	−5.42664	−	5.42664i	−0.272355	−	0.272355i	−0.830048	+	0.557692i	$0.811687\pi$
$398$	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	$-0.958888\pi$
$401$		−	5.15831i		−	0.257594i	0.991671	−	0.128797i	$-0.0411115\pi$
$402$	−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	$0.113879\pi$
$409$			14.1638i			0.700356i	−0.936683	+	0.350178i	$0.886121\pi$
$410$	−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	$0.0374474\pi$
$419$			4.80514i			0.234746i	−0.993088	+	0.117373i	$0.962553\pi$
$420$	−2.90125	−	5.68661i	−0.141566	−	0.277478i
$421$		−	15.2187i		−	0.741716i	−0.928690	−	0.370858i	$-0.879064\pi$
$421$		−	15.2187i		−	0.741716i	0.928690	−	0.370858i	$-0.120936\pi$
$422$	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	$-0.765706\pi$
$431$		−	27.8760i		−	1.34274i	0.741122	−	0.671370i	$-0.234294\pi$
$432$	19.4538	+	7.31764i	0.935974	+	0.352070i
$433$	−2.78003	−	2.78003i	−0.133600	−	0.133600i	0.637145	−	0.770744i	$-0.280115\pi$
$433$	−2.78003	−	2.78003i	−0.133600	−	0.133600i	−0.770744	+	0.637145i	$0.780115\pi$
$434$	−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	$0.0831105\pi$
$439$			10.8174i			0.516286i	−0.966107	+	0.258143i	$0.916889\pi$
$440$	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	0.830376	−	0.557203i	$-0.188126\pi$
$443$	5.74963	+	5.74963i	0.273173	+	0.273173i	−0.557203	+	0.830376i	$0.688126\pi$
$444$	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	−0.817370	−	0.576113i	$-0.804569\pi$
$457$	−5.15748	+	5.15748i	−0.241257	+	0.241257i	0.576113	+	0.817370i	$0.304569\pi$
$458$	−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	0.0815977	−	0.996665i	$-0.473998\pi$
$463$	−19.6899	−	19.6899i	−0.915068	−	0.915068i	−0.996665	+	0.0815977i	$0.973998\pi$
$464$	−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	−0.657355	−	0.753581i	$-0.728325\pi$
$467$	2.07946	−	2.07946i	0.0962257	−	0.0962257i	0.753581	+	0.657355i	$0.228325\pi$
$468$	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	−0.605155	−	0.796107i	$-0.706889\pi$
$487$	4.21395	−	4.21395i	0.190952	−	0.190952i	0.796107	+	0.605155i	$0.206889\pi$
$488$	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	−0.925056	−	0.379832i	$-0.875982\pi$
$503$	−12.2281	+	12.2281i	−0.545224	+	0.545224i	0.379832	+	0.925056i	$0.375982\pi$
$504$	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	$-0.707888\pi$
$509$		−	35.8361i		−	1.58841i	0.607651	−	0.794204i	$-0.292112\pi$
$510$	−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	$-0.869686\pi$
$521$		−	18.1715i		−	0.796107i	0.917362	−	0.398054i	$-0.130314\pi$
$522$	5.34829	−	2.28919i	0.234088	−	0.100195i
$523$	−21.7444	+	21.7444i	−0.950815	+	0.950815i	−0.998846	−	0.0480305i	$-0.984706\pi$
$523$	−21.7444	+	21.7444i	−0.950815	+	0.950815i	0.0480305	+	0.998846i	$0.484706\pi$
$524$	−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	$-0.805537\pi$
$541$		−	26.6843i		−	1.14725i	0.819119	−	0.573623i	$-0.194463\pi$
$542$	−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	0.998880	−	0.0473207i	$-0.0150683\pi$
$547$	22.2551	+	22.2551i	0.951559	+	0.951559i	−0.0473207	+	0.998880i	$0.515068\pi$
$548$	−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	−0.844743	−	0.535172i	$-0.820247\pi$
$557$	−7.30615	+	7.30615i	−0.309572	+	0.309572i	0.535172	+	0.844743i	$0.320247\pi$
$558$	−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	0.995402	−	0.0957856i	$-0.0305363\pi$
$563$	21.3458	+	21.3458i	0.899616	+	0.899616i	−0.0957856	+	0.995402i	$0.530536\pi$
$564$	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	$-0.936350\pi$
$571$		−	9.49296i		−	0.397268i	0.980074	−	0.198634i	$-0.0636505\pi$
$572$	−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	−0.450297	−	0.892879i	$-0.648682\pi$
$577$	10.6312	−	10.6312i	0.442582	−	0.442582i	0.892879	+	0.450297i	$0.148682\pi$
$578$	−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	−0.966441	−	0.256891i	$-0.917302\pi$
$587$	−17.1910	+	17.1910i	−0.709550	+	0.709550i	0.256891	+	0.966441i	$0.417302\pi$
$588$	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	−0.479434	−	0.877578i	$-0.659158\pi$
$593$	9.69544	−	9.69544i	0.398144	−	0.398144i	0.877578	+	0.479434i	$0.159158\pi$
$594$	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	0.372498	−	0.928033i	$-0.378501\pi$
$607$	32.0417	−	32.0417i	1.30053	−	1.30053i	0.928033	−	0.372498i	$-0.121499\pi$
$608$	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	−0.985160	−	0.171638i	$-0.945094\pi$
$613$	−20.1419	+	20.1419i	−0.813522	+	0.813522i	0.171638	+	0.985160i	$0.445094\pi$
$614$	−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	0.543881	−	0.839162i	$-0.316954\pi$
$617$	−7.33463	−	7.33463i	−0.295281	−	0.295281i	−0.839162	+	0.543881i	$0.816954\pi$
$618$	−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	$0.201991\pi$
$641$			30.0187i			1.18567i	−0.805325	+	0.592834i	$0.798009\pi$
$642$	14.4489	+	14.1932i	0.570254	+	0.560160i
$643$	32.7048	−	32.7048i	1.28975	−	1.28975i	0.354812	−	0.934938i	$-0.384545\pi$
$643$	32.7048	−	32.7048i	1.28975	−	1.28975i	0.934938	−	0.354812i	$-0.115455\pi$
$644$	−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	0.755093	−	0.655618i	$-0.227592\pi$
$647$	2.53026	+	2.53026i	0.0994747	+	0.0994747i	−0.655618	+	0.755093i	$0.727592\pi$
$648$	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	0.997806	−	0.0662023i	$-0.0210883\pi$
$653$	23.8061	+	23.8061i	0.931604	+	0.931604i	−0.0662023	+	0.997806i	$0.521088\pi$
$654$	−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	$-0.900994\pi$
$659$		−	15.7130i		−	0.612093i	0.952017	−	0.306047i	$-0.0990063\pi$
$660$	−8.80879	+	27.1593i	−0.342882	+	1.05718i
$661$			25.2637i			0.982643i	0.870978	+	0.491322i	$0.163486\pi$
$661$			25.2637i			0.982643i	−0.870978	+	0.491322i	$0.836514\pi$
$662$	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	0.343613	−	0.939111i	$-0.388349\pi$
$673$	−15.4486	−	15.4486i	−0.595498	−	0.595498i	−0.939111	+	0.343613i	$0.888349\pi$
$674$	−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	−0.629029	−	0.777382i	$-0.716547\pi$
$677$	3.86002	−	3.86002i	0.148353	−	0.148353i	0.777382	+	0.629029i	$0.216547\pi$
$678$	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	0.181451	−	0.983400i	$-0.441921\pi$
$683$	−20.9584	−	20.9584i	−0.801949	−	0.801949i	−0.983400	+	0.181451i	$0.941921\pi$
$684$	−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	$-0.829099\pi$
$691$		−	26.8902i		−	1.02295i	0.859298	−	0.511475i	$-0.170901\pi$
$692$	−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	−0.206768	−	0.978390i	$-0.566295\pi$
$727$	20.8052	−	20.8052i	0.771622	−	0.771622i	0.978390	+	0.206768i	$0.0662946\pi$
$728$	−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	−0.464526	−	0.885559i	$-0.653775\pi$
$733$	11.3990	−	11.3990i	0.421033	−	0.421033i	0.885559	+	0.464526i	$0.153775\pi$
$734$	−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	−0.755142	−	0.655562i	$-0.772432\pi$
$743$	−2.71436	+	2.71436i	−0.0995802	+	0.0995802i	0.655562	+	0.755142i	$0.272432\pi$
$744$	−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	0.712170	−	0.702008i	$-0.247713\pi$
$757$	0.279592	+	0.279592i	0.0101620	+	0.0101620i	−0.702008	+	0.712170i	$0.747713\pi$
$758$	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	$0.120083\pi$
$761$			20.3237i			0.736733i	−0.929681	+	0.368366i	$0.879917\pi$
$762$	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	$0.149952\pi$
$769$			25.1716i			0.907711i	−0.891075	+	0.453855i	$0.850048\pi$
$770$	−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	0.991905	−	0.126980i	$-0.0405284\pi$

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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