LMFDB - Embedded newform 770.2.bd.a.527.3

Newspace parameters

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bd (of order $12$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			527.3
Character	$\chi$	$=$	770.527
Dual form			770.2.bd.a.263.3

$q$-expansion

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-2.59645 - 0.695717i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.04774 - 0.898208i) q^{5} +2.68804i q^{6} +(1.70855 - 2.02011i) q^{7} +(0.707107 + 0.707107i) q^{8} +(3.65945 + 2.11279i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-2.59645 - 0.695717i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.04774 - 0.898208i) q^{5} +2.68804i q^{6} +(1.70855 - 2.02011i) q^{7} +(0.707107 + 0.707107i) q^{8} +(3.65945 + 2.11279i) q^{9} +(-1.39760 - 1.74549i) q^{10} +(-1.11436 + 3.12381i) q^{11} +(2.59645 - 0.695717i) q^{12} +(3.20138 + 3.20138i) q^{13} +(-2.39348 - 1.12749i) q^{14} +(-5.94174 + 0.907507i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.55460 + 0.684504i) q^{17} +(1.09366 - 4.08159i) q^{18} +(-2.02033 + 3.49931i) q^{19} +(-1.32429 + 1.80174i) q^{20} +(-5.84160 + 4.05644i) q^{21} +(3.30579 + 0.267890i) q^{22} +(1.69515 + 6.32637i) q^{23} +(-1.34402 - 2.32791i) q^{24} +(3.38645 - 3.67858i) q^{25} +(2.26372 - 3.92088i) q^{26} +(-2.32948 - 2.32948i) q^{27} +(-0.469598 + 2.60374i) q^{28} -2.16677 q^{29} +(2.41442 + 5.50440i) q^{30} +(4.73942 + 8.20892i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(5.06667 - 7.33554i) q^{33} -2.64472i q^{34} +(1.68419 - 5.67129i) q^{35} -4.22557 q^{36} +(6.06455 - 1.62499i) q^{37} +(3.90297 + 1.04580i) q^{38} +(-6.08497 - 10.5395i) q^{39} +(2.08310 + 0.812839i) q^{40} -6.53792i q^{41} +(5.43014 + 4.59267i) q^{42} +(-7.25627 - 7.25627i) q^{43} +(-0.596839 - 3.26248i) q^{44} +(9.39131 + 1.03948i) q^{45} +(5.67207 - 3.27477i) q^{46} +(4.70990 - 1.26201i) q^{47} +(-1.90073 + 1.90073i) q^{48} +(-1.16168 - 6.90293i) q^{49} +(-4.42972 - 2.31897i) q^{50} +(-6.15668 - 3.55456i) q^{51} +(-4.37317 - 1.17179i) q^{52} +(6.49482 + 1.74028i) q^{53} +(-1.64719 + 2.85302i) q^{54} +(0.523909 + 7.39767i) q^{55} +(2.63656 - 0.220302i) q^{56} +(7.68021 - 7.68021i) q^{57} +(0.560800 + 2.09293i) q^{58} +(-3.24450 + 1.87322i) q^{59} +(4.69195 - 3.75679i) q^{60} +(-1.95267 - 1.12738i) q^{61} +(6.70256 - 6.70256i) q^{62} +(10.5204 - 3.78268i) q^{63} +1.00000i q^{64} +(9.43109 + 3.68008i) q^{65} +(-8.39694 - 2.99546i) q^{66} +(0.801143 - 2.98991i) q^{67} +(-2.55460 + 0.684504i) q^{68} -17.6054i q^{69} +(-5.91394 - 0.158968i) q^{70} -5.47033 q^{71} +(1.09366 + 4.08159i) q^{72} +(-1.19806 + 4.47121i) q^{73} +(-3.13924 - 5.43733i) q^{74} +(-11.3520 + 7.19525i) q^{75} -4.04066i q^{76} +(4.40649 + 7.58834i) q^{77} +(-8.60545 + 8.60545i) q^{78} +(2.19338 - 3.79904i) q^{79} +(0.245997 - 2.22250i) q^{80} +(-1.91063 - 3.30931i) q^{81} +(-6.31515 + 1.69214i) q^{82} +(5.64995 + 5.64995i) q^{83} +(3.03075 - 6.43378i) q^{84} +(5.84598 - 0.892881i) q^{85} +(-5.13096 + 8.88708i) q^{86} +(5.62590 + 1.50745i) q^{87} +(-2.99684 + 1.42089i) q^{88} +(15.0601 + 8.69497i) q^{89} +(-1.42659 - 9.34035i) q^{90} +(11.9369 - 0.997403i) q^{91} +(-4.63123 - 4.63123i) q^{92} +(-6.59459 - 24.6113i) q^{93} +(-2.43803 - 4.22278i) q^{94} +(-0.993991 + 8.98034i) q^{95} +(2.32791 + 1.34402i) q^{96} +(5.74983 + 5.74983i) q^{97} +(-6.36706 + 2.90871i) q^{98} +(-10.6779 + 9.07703i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{5}+O(q^{10}) $ 192 * q + 8 * q^5	$ 192 q + 8 q^{5} + 4 q^{11} + 16 q^{15} + 96 q^{16} + 24 q^{22} - 8 q^{23} + 24 q^{25} - 8 q^{26} - 16 q^{33} - 160 q^{36} - 40 q^{37} - 40 q^{42} + 32 q^{45} - 40 q^{47} + 40 q^{53} + 8 q^{55} + 16 q^{56} + 32 q^{58} - 48 q^{67} - 72 q^{70} + 32 q^{71} - 48 q^{75} - 72 q^{77} - 8 q^{80} + 64 q^{81} + 16 q^{82} - 12 q^{88} - 112 q^{91} - 16 q^{92} + 80 q^{93} - 64 q^{97}+O(q^{100}) $ 192 * q + 8 * q^5 + 4 * q^11 + 16 * q^15 + 96 * q^16 + 24 * q^22 - 8 * q^23 + 24 * q^25 - 8 * q^26 - 16 * q^33 - 160 * q^36 - 40 * q^37 - 40 * q^42 + 32 * q^45 - 40 * q^47 + 40 * q^53 + 8 * q^55 + 16 * q^56 + 32 * q^58 - 48 * q^67 - 72 * q^70 + 32 * q^71 - 48 * q^75 - 72 * q^77 - 8 * q^80 + 64 * q^81 + 16 * q^82 - 12 * q^88 - 112 * q^91 - 16 * q^92 + 80 * q^93 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	−2.59645	−	0.695717i	−1.49906	−	0.401672i	−0.586275	−	0.810112i	$-0.699406\pi$
$3$	−2.59645	−	0.695717i	−1.49906	−	0.401672i	−0.912785	+	0.408440i	$0.866073\pi$
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	2.04774	−	0.898208i	0.915775	−	0.401691i
$5$	2.04774	−	0.898208i	0.915775	−	0.401691i
$6$			2.68804i			1.09739i
$7$	1.70855	−	2.02011i	0.645773	−	0.763529i
$7$	1.70855	−	2.02011i	0.645773	−	0.763529i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	3.65945	+	2.11279i	1.21982	+	0.704262i
$10$	−1.39760	−	1.74549i	−0.441958	−	0.551972i
$11$	−1.11436	+	3.12381i	−0.335993	+	0.941864i
$11$	−1.11436	+	3.12381i	−0.335993	+	0.941864i
$12$	2.59645	−	0.695717i	0.749530	−	0.200836i
$13$	3.20138	+	3.20138i	0.887904	+	0.887904i	0.994322	−	0.106418i	$-0.0339381\pi$
$13$	3.20138	+	3.20138i	0.887904	+	0.887904i	−0.106418	+	0.994322i	$0.533938\pi$
$14$	−2.39348	−	1.12749i	−0.639685	−	0.301336i
$15$	−5.94174	+	0.907507i	−1.53415	+	0.234317i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.55460	+	0.684504i	0.619582	+	0.166017i	0.554938	−	0.831892i	$-0.312742\pi$
$17$	2.55460	+	0.684504i	0.619582	+	0.166017i	0.0646443	+	0.997908i	$0.479409\pi$
$18$	1.09366	−	4.08159i	0.257778	−	0.962040i
$19$	−2.02033	+	3.49931i	−0.463495	+	0.802797i	−0.999132	−	0.0416513i	$-0.986738\pi$
$19$	−2.02033	+	3.49931i	−0.463495	+	0.802797i	0.535637	+	0.844448i	$0.320071\pi$
$20$	−1.32429	+	1.80174i	−0.296120	+	0.402881i
$21$	−5.84160	+	4.05644i	−1.27474	+	0.885188i
$22$	3.30579	+	0.267890i	0.704796	+	0.0571144i
$23$	1.69515	+	6.32637i	0.353462	+	1.31914i	0.882408	+	0.470484i	$0.155921\pi$
$23$	1.69515	+	6.32637i	0.353462	+	1.31914i	−0.528946	+	0.848656i	$0.677413\pi$
$24$	−1.34402	−	2.32791i	−0.274347	−	0.475183i
$25$	3.38645	−	3.67858i	0.677289	−	0.735717i
$26$	2.26372	−	3.92088i	0.443952	−	0.768947i
$27$	−2.32948	−	2.32948i	−0.448310	−	0.448310i
$28$	−0.469598	+	2.60374i	−0.0887456	+	0.492061i
$29$	−2.16677			−0.402358			−0.201179	−	0.979554i	$-0.564477\pi$
$29$	−2.16677			−0.402358			−0.201179	+	0.979554i	$0.564477\pi$
$30$	2.41442	+	5.50440i	0.440811	+	1.00496i
$31$	4.73942	+	8.20892i	0.851225	+	1.47437i	0.880103	+	0.474783i	$0.157473\pi$
$31$	4.73942	+	8.20892i	0.851225	+	1.47437i	−0.0288777	+	0.999583i	$0.509193\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	5.06667	−	7.33554i	0.881995	−	1.27695i
$34$		−	2.64472i		−	0.453566i
$35$	1.68419	−	5.67129i	0.284680	−	0.958622i
$36$	−4.22557			−0.704262
$37$	6.06455	−	1.62499i	0.997006	−	0.267147i	0.276816	−	0.960923i	$-0.410721\pi$
$37$	6.06455	−	1.62499i	0.997006	−	0.267147i	0.720191	+	0.693776i	$0.244054\pi$
$38$	3.90297	+	1.04580i	0.633146	+	0.169651i
$39$	−6.08497	−	10.5395i	−0.974376	−	1.68767i
$40$	2.08310	+	0.812839i	0.329367	+	0.128521i
$41$		−	6.53792i		−	1.02105i	−0.859862	−	0.510526i	$-0.829451\pi$
$41$		−	6.53792i		−	1.02105i	0.859862	−	0.510526i	$-0.170549\pi$
$42$	5.43014	+	4.59267i	0.837889	+	0.708664i
$43$	−7.25627	−	7.25627i	−1.10657	−	1.10657i	−0.993598	−	0.112972i	$-0.963963\pi$
$43$	−7.25627	−	7.25627i	−1.10657	−	1.10657i	−0.112972	−	0.993598i	$-0.536037\pi$
$44$	−0.596839	−	3.26248i	−0.0899768	−	0.491838i
$45$	9.39131	+	1.03948i	1.39997	+	0.154956i
$46$	5.67207	−	3.27477i	0.836301	−	0.482839i
$47$	4.70990	−	1.26201i	0.687010	−	0.184084i	0.101605	−	0.994825i	$-0.467602\pi$
$47$	4.70990	−	1.26201i	0.687010	−	0.184084i	0.585405	+	0.810741i	$0.300936\pi$
$48$	−1.90073	+	1.90073i	−0.274347	+	0.274347i
$49$	−1.16168	−	6.90293i	−0.165954	−	0.986133i
$50$	−4.42972	−	2.31897i	−0.626457	−	0.327952i
$51$	−6.15668	−	3.55456i	−0.862107	−	0.497738i
$52$	−4.37317	−	1.17179i	−0.606450	−	0.162498i
$53$	6.49482	+	1.74028i	0.892132	+	0.239046i	0.675634	−	0.737237i	$-0.263870\pi$
$53$	6.49482	+	1.74028i	0.892132	+	0.239046i	0.216498	+	0.976283i	$0.430536\pi$
$54$	−1.64719	+	2.85302i	−0.224155	+	0.388247i
$55$	0.523909	+	7.39767i	0.0706439	+	0.997502i
$56$	2.63656	−	0.220302i	0.352326	−	0.0294391i
$57$	7.68021	−	7.68021i	1.01727	−	1.01727i
$58$	0.560800	+	2.09293i	0.0736367	+	0.274816i
$59$	−3.24450	+	1.87322i	−0.422399	+	0.243872i	−0.696103	−	0.717942i	$-0.745084\pi$
$59$	−3.24450	+	1.87322i	−0.422399	+	0.243872i	0.273704	+	0.961814i	$0.411751\pi$
$60$	4.69195	−	3.75679i	0.605728	−	0.485000i
$61$	−1.95267	−	1.12738i	−0.250014	−	0.144346i	0.369757	−	0.929129i	$-0.379441\pi$
$61$	−1.95267	−	1.12738i	−0.250014	−	0.144346i	−0.619771	+	0.784783i	$0.712774\pi$
$62$	6.70256	−	6.70256i	0.851225	−	0.851225i
$63$	10.5204	−	3.78268i	1.32545	−	0.476573i
$64$			1.00000i			0.125000i
$65$	9.43109	+	3.68008i	1.16978	+	0.456458i
$66$	−8.39694	−	2.99546i	−1.03359	−	0.368715i
$67$	0.801143	−	2.98991i	0.0978752	−	0.365275i	−0.899564	−	0.436788i	$-0.856116\pi$
$67$	0.801143	−	2.98991i	0.0978752	−	0.365275i	0.997440	+	0.0715127i	$0.0227826\pi$
$68$	−2.55460	+	0.684504i	−0.309791	+	0.0830083i
$69$		−	17.6054i		−	2.11945i
$70$	−5.91394	−	0.158968i	−0.706851	−	0.0190003i
$71$	−5.47033			−0.649209			−0.324605	−	0.945850i	$-0.605231\pi$
$71$	−5.47033			−0.649209			−0.324605	+	0.945850i	$0.605231\pi$
$72$	1.09366	+	4.08159i	0.128889	+	0.481020i
$73$	−1.19806	+	4.47121i	−0.140222	+	0.523315i	0.859700	+	0.510800i	$0.170651\pi$
$73$	−1.19806	+	4.47121i	−0.140222	+	0.523315i	−0.999922	+	0.0125156i	$0.996016\pi$
$74$	−3.13924	−	5.43733i	−0.364930	−	0.632077i
$75$	−11.3520	+	7.19525i	−1.31081	+	0.830836i
$76$		−	4.04066i		−	0.463495i
$77$	4.40649	+	7.58834i	0.502166	+	0.864771i
$78$	−8.60545	+	8.60545i	−0.974376	+	0.974376i
$79$	2.19338	−	3.79904i	0.246774	−	0.427426i	−0.715855	−	0.698249i	$-0.753963\pi$
$79$	2.19338	−	3.79904i	0.246774	−	0.427426i	0.962629	+	0.270824i	$0.0872960\pi$
$80$	0.245997	−	2.22250i	0.0275033	−	0.248483i
$81$	−1.91063	−	3.30931i	−0.212292	−	0.367701i
$82$	−6.31515	+	1.69214i	−0.697391	+	0.186865i
$83$	5.64995	+	5.64995i	0.620163	+	0.620163i	0.945573	−	0.325410i	$-0.105502\pi$
$83$	5.64995	+	5.64995i	0.620163	+	0.620163i	−0.325410	+	0.945573i	$0.605502\pi$
$84$	3.03075	−	6.43378i	0.330682	−	0.701983i
$85$	5.84598	−	0.892881i	0.634085	−	0.0968465i
$86$	−5.13096	+	8.88708i	−0.553285	+	0.958318i
$87$	5.62590	+	1.50745i	0.603159	+	0.161616i
$88$	−2.99684	+	1.42089i	−0.319464	+	0.151468i
$89$	15.0601	+	8.69497i	1.59637	+	0.921665i	0.992179	+	0.124827i	$0.0398376\pi$
$89$	15.0601	+	8.69497i	1.59637	+	0.921665i	0.604193	+	0.796838i	$0.293496\pi$
$90$	−1.42659	−	9.34035i	−0.150376	−	0.984559i
$91$	11.9369	−	0.997403i	1.25132	−	0.104556i
$92$	−4.63123	−	4.63123i	−0.482839	−	0.482839i
$93$	−6.59459	−	24.6113i	−0.683827	−	2.55208i
$94$	−2.43803	−	4.22278i	−0.251463	−	0.435547i
$95$	−0.993991	+	8.98034i	−0.101981	+	0.921363i
$96$	2.32791	+	1.34402i	0.237592	+	0.137174i
$97$	5.74983	+	5.74983i	0.583807	+	0.583807i	0.935947	−	0.352140i	$-0.114546\pi$
$97$	5.74983	+	5.74983i	0.583807	+	0.583807i	−0.352140	+	0.935947i	$0.614546\pi$
$98$	−6.36706	+	2.90871i	−0.643170	+	0.293824i
$99$	−10.6779	+	9.07703i	−1.07317	+	0.912275i
$100$	−1.09346	+	4.87897i	−0.109346	+	0.487897i
$101$	−13.8239	+	7.98121i	−1.37553	+	0.794160i	−0.991617	−	0.129211i	$-0.958755\pi$
$101$	−13.8239	+	7.98121i	−1.37553	+	0.794160i	−0.383908	+	0.923371i	$0.625422\pi$
$102$	−1.83998	+	6.86688i	−0.182185	+	0.679922i
$103$	−3.64713	−	13.6113i	−0.359363	−	1.34116i	−0.874904	−	0.484296i	$-0.839076\pi$
$103$	−3.64713	−	13.6113i	−0.359363	−	1.34116i	0.515542	−	0.856864i	$-0.327591\pi$
$104$			4.52744i			0.443952i
$105$	−8.31853	+	13.5535i	−0.811805	+	1.32269i
$106$		−	6.72393i		−	0.653086i
$107$	−4.13885	−	15.4464i	−0.400118	−	1.49326i	−0.812885	−	0.582424i	$-0.802104\pi$
$107$	−4.13885	−	15.4464i	−0.400118	−	1.49326i	0.412767	−	0.910837i	$-0.364562\pi$
$108$	3.18214	+	0.852651i	0.306201	+	0.0820463i
$109$	1.79806	+	3.11433i	0.172223	+	0.298298i	0.939197	−	0.343380i	$-0.111572\pi$
$109$	1.79806	+	3.11433i	0.172223	+	0.298298i	−0.766974	+	0.641678i	$0.778238\pi$
$110$	7.01000	−	2.42072i	0.668378	−	0.230806i
$111$	−16.8768			−1.60188
$112$	−0.895188	−	2.48971i	−0.0845873	−	0.235255i
$113$	−11.3071	+	11.3071i	−1.06368	+	1.06368i	−0.0658550	+	0.997829i	$0.520977\pi$
$113$	−11.3071	+	11.3071i	−1.06368	+	1.06368i	−0.997829	+	0.0658550i	$0.979023\pi$
$114$	−9.40630	−	5.43073i	−0.880980	−	0.508634i
$115$	9.15361	+	11.4321i	0.853578	+	1.06605i
$116$	1.87647	−	1.08338i	0.174226	−	0.100590i
$117$	4.95147	+	18.4791i	0.457764	+	1.70840i
$118$	2.64913	+	2.64913i	0.243872	+	0.243872i
$119$	5.74745	−	3.99106i	0.526868	−	0.365860i
$120$	−4.84315	−	3.55974i	−0.442117	−	0.324958i
$121$	−8.51639	−	6.96212i	−0.774217	−	0.632920i
$122$	−0.583573	+	2.17792i	−0.0528342	+	0.197180i
$123$	−4.54854	+	16.9754i	−0.410128	+	1.53062i
$124$	−8.20892	−	4.73942i	−0.737183	−	0.425613i
$125$	3.63041	−	10.5745i	0.324714	−	0.945812i
$126$	−6.37668	−	9.18293i	−0.568080	−	0.818080i
$127$	5.98612	−	5.98612i	0.531182	−	0.531182i	−0.389742	−	0.920924i	$-0.627436\pi$
$127$	5.98612	−	5.98612i	0.531182	−	0.531182i	0.920924	+	0.389742i	$0.127436\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	13.7922	+	23.8888i	1.21434	+	2.10329i
$130$	1.11374	−	10.0622i	0.0976813	−	0.882514i
$131$	8.92152	+	5.15084i	0.779477	+	0.450031i	0.836245	−	0.548356i	$-0.184746\pi$
$131$	8.92152	+	5.15084i	0.779477	+	0.450031i	−0.0567680	+	0.998387i	$0.518080\pi$
$132$	−0.720101	+	8.88610i	−0.0626767	+	0.773436i
$133$	3.61715	+	10.0600i	0.313646	+	0.872317i
$134$	−3.09538			−0.267400
$135$	−6.86253	−	2.67781i	−0.590633	−	0.230469i
$136$	1.32236	+	2.29039i	0.113391	+	0.196400i
$137$	2.66627	−	9.95066i	0.227795	−	0.850142i	−0.753471	−	0.657482i	$-0.771622\pi$
$137$	2.66627	−	9.95066i	0.227795	−	0.850142i	0.981265	−	0.192660i	$-0.0617116\pi$
$138$	−17.0056	+	4.55663i	−1.44761	+	0.387886i
$139$	1.25145			0.106147			0.0530735	−	0.998591i	$-0.483098\pi$
$139$	1.25145			0.106147			0.0530735	+	0.998591i	$0.483098\pi$
$140$	1.37709	+	5.75357i	0.116385	+	0.486266i
$141$	−13.1070			−1.10381
$142$	1.41583	+	5.28394i	0.118813	+	0.443418i
$143$	−13.5680	+	6.43301i	−1.13461	+	0.537955i
$144$	3.65945	−	2.11279i	0.304954	−	0.176065i
$145$	−4.43696	+	1.94621i	−0.368470	+	0.161624i
$146$	4.62893			0.383093
$147$	−1.78624	+	18.7313i	−0.147327	+	1.54493i
$148$	−4.43956	+	4.43956i	−0.364930	+	0.364930i
$149$	−10.1145	+	17.5188i	−0.828611	+	1.43520i	0.0705173	+	0.997511i	$0.477535\pi$
$149$	−10.1145	+	17.5188i	−0.828611	+	1.43520i	−0.899128	+	0.437686i	$0.855798\pi$
$150$	9.88819	+	9.10291i	0.807367	+	0.743249i
$151$	11.2742	−	6.50916i	0.917481	−	0.529708i	0.0346504	−	0.999399i	$-0.488968\pi$
$151$	11.2742	−	6.50916i	0.917481	−	0.529708i	0.882831	+	0.469692i	$0.155635\pi$
$152$	−3.90297	+	1.04580i	−0.316573	+	0.0848255i
$153$	7.90224	+	7.90224i	0.638858	+	0.638858i
$154$	6.18929	−	6.22035i	0.498747	−	0.501250i
$155$	17.0784	+	12.5527i	1.37177	+	1.00826i
$156$	10.5395	+	6.08497i	0.843834	+	0.487188i
$157$	−3.33675	+	12.4529i	−0.266302	+	0.993852i	0.695147	+	0.718868i	$0.255339\pi$
$157$	−3.33675	+	12.4529i	−0.266302	+	0.993852i	−0.961449	+	0.274984i	$0.911327\pi$
$158$	−4.23728	−	1.13538i	−0.337100	−	0.0903257i
$159$	−15.6527	−	9.03711i	−1.24134	−	0.716689i
$160$	−2.21043	+	0.337609i	−0.174750	+	0.0266903i
$161$	15.6762	+	7.38458i	1.23546	+	0.581986i
$162$	−2.70204	+	2.70204i	−0.212292	+	0.212292i
$163$	−3.96188	−	14.7859i	−0.310318	−	1.15812i	−0.928270	−	0.371907i	$-0.878704\pi$
$163$	−3.96188	−	14.7859i	−0.310318	−	1.15812i	0.617951	−	0.786216i	$-0.287963\pi$
$164$	3.26896	+	5.66201i	0.255263	+	0.442128i
$165$	3.78638	−	19.5722i	0.294769	−	1.52369i
$166$	3.99512	−	6.91975i	0.310081	−	0.537076i
$167$	−13.3930	+	13.3930i	−1.03638	+	1.03638i	−0.0370650	+	0.999313i	$0.511801\pi$
$167$	−13.3930	+	13.3930i	−1.03638	+	1.03638i	−0.999313	+	0.0370650i	$0.988199\pi$
$168$	−6.99897	−	1.26230i	−0.539982	−	0.0973884i
$169$			7.49770i			0.576746i
$170$	−2.37551	−	5.41569i	−0.182193	−	0.415364i
$171$	−14.7866	+	8.53704i	−1.13076	+	0.652844i
$172$	9.91224	+	2.65598i	0.755802	+	0.202516i
$173$	0.471822	−	0.126424i	0.0358719	−	0.00961186i	−0.240838	−	0.970565i	$-0.577422\pi$
$173$	0.471822	−	0.126424i	0.0358719	−	0.00961186i	0.276710	+	0.960953i	$0.410756\pi$
$174$		−	5.82436i		−	0.441543i
$175$	−1.64521	−	13.1261i	−0.124366	−	0.992236i
$176$	2.14812	+	2.52697i	0.161920	+	0.190478i
$177$	9.72742	−	2.60645i	0.731158	−	0.195913i
$178$	4.50085	−	16.7974i	0.337353	−	1.25902i
$179$	0.496211	−	0.286488i	0.0370886	−	0.0214131i	−0.481341	−	0.876533i	$-0.659850\pi$
$179$	0.496211	−	0.286488i	0.0370886	−	0.0214131i	0.518430	+	0.855120i	$0.326517\pi$
$180$	−8.65286	+	3.79544i	−0.644946	+	0.282895i
$181$	−18.5157			−1.37626			−0.688131	−	0.725586i	$-0.741569\pi$
$181$	−18.5157			−1.37626			−0.688131	+	0.725586i	$0.741569\pi$
$182$	−4.05291	−	11.2720i	−0.300422	−	0.835536i
$183$	4.28568	+	4.28568i	0.316807	+	0.316807i
$184$	−3.27477	+	5.67207i	−0.241419	+	0.418151i
$185$	10.9590	−	8.77478i	0.805723	−	0.645135i
$186$	−22.0659	+	12.7398i	−1.61795	+	0.934125i
$187$	−4.98502	+	7.21731i	−0.364540	+	0.527782i
$188$	−3.44789	+	3.44789i	−0.251463	+	0.251463i
$189$	−8.68586	+	0.725760i	−0.631804	+	0.0527913i
$190$	8.93161	−	1.36416i	0.647967	−	0.0989667i
$191$	2.66929	−	4.62334i	0.193143	−	0.334533i	−0.753147	−	0.657852i	$-0.771465\pi$
$191$	2.66929	−	4.62334i	0.193143	−	0.334533i	0.946290	+	0.323319i	$0.104799\pi$
$192$	0.695717	−	2.59645i	0.0502090	−	0.187383i
$193$	5.17346	−	19.3076i	0.372394	−	1.38979i	−0.484721	−	0.874669i	$-0.661079\pi$
$193$	5.17346	−	19.3076i	0.372394	−	1.38979i	0.857115	−	0.515125i	$-0.172254\pi$
$194$	4.06574	−	7.04207i	0.291903	−	0.505591i
$195$	−21.9271	−	16.1165i	−1.57023	−	1.15413i
$196$	4.45751	+	5.39728i	0.318394	+	0.385520i
$197$	6.70905	−	6.70905i	0.478000	−	0.478000i	−0.426491	−	0.904492i	$-0.640251\pi$
$197$	6.70905	−	6.70905i	0.478000	−	0.478000i	0.904492	+	0.426491i	$0.140251\pi$
$198$	11.5314	+	7.96475i	0.819499	+	0.566030i
$199$	−2.58858	+	1.49452i	−0.183499	+	0.105943i	−0.588936	−	0.808180i	$-0.700453\pi$
$199$	−2.58858	+	1.49452i	−0.183499	+	0.105943i	0.405436	+	0.914123i	$0.367120\pi$
$200$	4.99573	−	0.206573i	0.353252	−	0.0146069i
$201$	−4.16026	+	7.20578i	−0.293442	+	0.508256i
$202$	11.2871	+	11.2871i	0.794160	+	0.794160i
$203$	−3.70204	+	4.37710i	−0.259832	+	0.307212i
$204$	7.10912			0.497738
$205$	−5.87241	−	13.3879i	−0.410147	−	0.935054i
$206$	−12.2035	+	7.04572i	−0.850261	+	0.490899i
$207$	−7.16296	+	26.7325i	−0.497860	+	1.85804i
$208$	4.37317	−	1.17179i	0.303225	−	0.0812488i
$209$	−8.67981	−	10.2106i	−0.600395	−	0.706284i
$210$	15.2447	+	4.52718i	1.05198	+	0.312405i
$211$			9.59556i			0.660586i	0.943879	+	0.330293i	$0.107147\pi$
$211$			9.59556i			0.660586i	−0.943879	+	0.330293i	$0.892853\pi$
$212$	−6.49482	+	1.74028i	−0.446066	+	0.119523i
$213$	14.2034	+	3.80580i	0.973204	+	0.260769i
$214$	−13.8489	+	7.99565i	−0.946690	+	0.546572i
$215$	−21.3766	−	8.34128i	−1.45787	−	0.568871i
$216$		−	3.29439i		−	0.224155i
$217$	24.6805	+	4.45124i	1.67542	+	0.302170i
$218$	2.54284	−	2.54284i	0.172223	−	0.172223i
$219$	6.22139	−	10.7758i	0.420402	−	0.728158i
$220$	−4.15255	−	6.14462i	−0.279965	−	0.414270i
$221$	5.98690	+	10.3696i	0.402723	+	0.697536i
$222$	4.36805	+	16.3018i	0.293164	+	1.09410i
$223$	15.8859	−	15.8859i	1.06380	−	1.06380i	0.0659793	−	0.997821i	$-0.478983\pi$
$223$	15.8859	−	15.8859i	1.06380	−	1.06380i	0.997821	−	0.0659793i	$-0.0210171\pi$
$224$	−2.17318	+	1.50907i	−0.145202	+	0.100829i
$225$	20.1646	−	6.30677i	1.34431	−	0.420451i
$226$	13.8483	+	7.99534i	0.921178	+	0.531842i
$227$	10.7641	+	2.88422i	0.714436	+	0.191433i	0.597688	−	0.801729i	$-0.296086\pi$
$227$	10.7641	+	2.88422i	0.714436	+	0.191433i	0.116748	+	0.993162i	$0.462753\pi$
$228$	−2.81115	+	10.4914i	−0.186173	+	0.694807i
$229$	18.5411	+	10.7047i	1.22523	+	0.707389i	0.966029	−	0.258434i	$-0.0832064\pi$
$229$	18.5411	+	10.7047i	1.22523	+	0.707389i	0.259204	+	0.965823i	$0.416540\pi$
$230$	8.67348	−	11.8006i	0.571912	−	0.778106i
$231$	−6.16189	−	22.7684i	−0.405423	−	1.49805i
$232$	−1.53213	−	1.53213i	−0.100590	−	0.100590i
$233$	−5.63503	+	1.50990i	−0.369163	+	0.0989169i	−0.438631	−	0.898667i	$-0.644536\pi$
$233$	−5.63503	+	1.50990i	−0.369163	+	0.0989169i	0.0694681	+	0.997584i	$0.477870\pi$
$234$	16.5679	−	9.56551i	1.08308	−	0.625317i
$235$	8.51109	−	6.81474i	0.555202	−	0.444545i
$236$	1.87322	−	3.24450i	0.121936	−	0.211199i
$237$	−8.33805	+	8.33805i	−0.541615	+	0.541615i
$238$	−5.34262	−	4.51865i	−0.346311	−	0.292900i
$239$	−2.26127			−0.146269			−0.0731347	−	0.997322i	$-0.523300\pi$
$239$	−2.26127			−0.146269			−0.0731347	+	0.997322i	$0.523300\pi$
$240$	−2.18495	+	5.59945i	−0.141038	+	0.361443i
$241$	19.5996	−	11.3158i	1.26252	−	0.728916i	0.288959	−	0.957342i	$-0.406691\pi$
$241$	19.5996	−	11.3158i	1.26252	−	0.728916i	0.973561	+	0.228425i	$0.0733577\pi$
$242$	−4.52069	+	10.0281i	−0.290601	+	0.644633i
$243$	5.21646	+	19.4681i	0.334636	+	1.24888i
$244$	2.25475			0.144346
$245$	−8.57908	−	13.0920i	−0.548097	−	0.836414i
$246$	17.5742			1.12049
$247$	−17.6705	+	4.73479i	−1.12435	+	0.301267i
$248$	−2.45331	+	9.15586i	−0.155785	+	0.581398i
$249$	−10.7390	−	18.6006i	−0.680559	−	1.17876i
$250$	−11.1538	−	0.769828i	−0.705429	−	0.0486882i
$251$	−7.90057			−0.498680			−0.249340	−	0.968416i	$-0.580214\pi$
$251$	−7.90057			−0.498680			−0.249340	+	0.968416i	$0.580214\pi$
$252$	−7.21962	+	8.53611i	−0.454793	+	0.537725i
$253$	−21.6514	−	1.75456i	−1.36121	−	0.110308i
$254$	−7.33147	−	4.23283i	−0.460017	−	0.265591i
$255$	−15.8000	−	1.74882i	−0.989433	−	0.109516i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	17.3029	−	4.63630i	1.07933	−	0.289205i	0.325007	−	0.945712i	$-0.394633\pi$
$257$	17.3029	−	4.63630i	1.07933	−	0.289205i	0.754320	+	0.656507i	$0.227967\pi$
$258$	19.5052	−	19.5052i	1.21434	−	1.21434i
$259$	7.07896	−	15.0274i	0.439865	−	0.933760i
$260$	−10.0076	+	1.52850i	−0.620645	+	0.0947938i
$261$	−7.92917	−	4.57791i	−0.490804	−	0.283366i
$262$	2.66627	−	9.95066i	0.164723	−	0.614754i
$263$	−5.23914	+	19.5527i	−0.323059	+	1.20567i	0.593189	+	0.805063i	$0.297869\pi$
$263$	−5.23914	+	19.5527i	−0.323059	+	1.20567i	−0.916249	+	0.400610i	$0.868798\pi$
$264$	8.76969	−	1.60433i	0.539737	−	0.0987395i
$265$	14.8628	−	2.27006i	0.913016	−	0.139449i
$266$	8.78107	−	6.09763i	0.538402	−	0.373870i
$267$	−33.0536	−	33.0536i	−2.02285	−	2.02285i
$268$	0.801143	+	2.98991i	0.0489376	+	0.182638i
$269$	−6.62961	+	3.82761i	−0.404215	+	0.233373i	−0.688301	−	0.725425i	$-0.741643\pi$
$269$	−6.62961	+	3.82761i	−0.404215	+	0.233373i	0.284086	+	0.958799i	$0.408310\pi$
$270$	−0.810411	+	7.32176i	−0.0493200	+	0.445588i
$271$	−3.39858	−	1.96217i	−0.206449	−	0.119194i	0.393211	−	0.919448i	$-0.371364\pi$
$271$	−3.39858	−	1.96217i	−0.206449	−	0.119194i	−0.599660	+	0.800255i	$0.704698\pi$
$272$	1.87010	−	1.87010i	0.113391	−	0.113391i
$273$	−31.6874	−	5.71498i	−1.91781	−	0.345886i
$274$	−10.3017			−0.622347
$275$	7.71747	+	14.6779i	0.465381	+	0.885110i
$276$	8.80272	+	15.2468i	0.529862	+	0.917747i
$277$	9.43093	+	2.52701i	0.566650	+	0.151833i	0.530760	−	0.847522i	$-0.321907\pi$
$277$	9.43093	+	2.52701i	0.566650	+	0.151833i	0.0358900	+	0.999356i	$0.488573\pi$
$278$	−0.323900	−	1.20881i	−0.0194262	−	0.0724997i
$279$			40.0535i			2.39794i
$280$	5.20111	−	2.81930i	0.310826	−	0.168486i
$281$		−	0.994731i		−	0.0593407i	−0.999560	−	0.0296703i	$-0.990554\pi$
$281$		−	0.994731i		−	0.0593407i	0.999560	−	0.0296703i	$-0.00944575\pi$
$282$	3.39235	+	12.6604i	0.202011	+	0.753917i
$283$	3.37200	−	12.5845i	0.200445	−	0.748070i	−0.790345	−	0.612662i	$-0.790099\pi$
$283$	3.37200	−	12.5845i	0.200445	−	0.748070i	0.990790	−	0.135408i	$-0.0432345\pi$
$284$	4.73745	−	2.73517i	0.281116	−	0.162302i
$285$	8.82862	−	22.6255i	0.522962	−	1.34022i
$286$	9.72547	+	11.4407i	0.575079	+	0.676503i
$287$	−13.2073	−	11.1704i	−0.779603	−	0.659368i
$288$	−2.98793	−	2.98793i	−0.176065	−	0.176065i
$289$	−8.66498	−	5.00273i	−0.509705	−	0.294278i
$290$	3.02826	+	3.78206i	0.177826	+	0.222090i
$291$	−10.9289	−	18.9294i	−0.640663	−	1.10966i
$292$	−1.19806	−	4.47121i	−0.0701110	−	0.261658i
$293$	−9.06354	−	9.06354i	−0.529498	−	0.529498i	0.390925	−	0.920423i	$-0.372155\pi$
$293$	−9.06354	−	9.06354i	−0.529498	−	0.529498i	−0.920423	+	0.390925i	$0.872155\pi$
$294$	18.5554	−	3.12264i	1.08217	−	0.182116i
$295$	−4.96135	+	6.75009i	−0.288861	+	0.393005i
$296$	5.43733	+	3.13924i	0.316038	+	0.182465i
$297$	9.87276	−	4.68098i	0.572876	−	0.271618i
$298$	19.5397	+	5.23564i	1.13190	+	0.303293i
$299$	−14.8263	+	25.6800i	−0.857429	+	1.48511i
$300$	6.23348	−	11.9073i	0.359890	−	0.687466i
$301$	−27.0562	+	2.26072i	−1.55949	+	0.130306i
$302$	−9.20534	−	9.20534i	−0.529708	−	0.529708i
$303$	41.4456	−	11.1053i	2.38099	−	0.637984i
$304$	2.02033	+	3.49931i	0.115874	+	0.200699i
$305$	−5.01118	−	0.554663i	−0.286939	−	0.0317599i
$306$	5.58773	−	9.67822i	0.319429	−	0.553267i
$307$	15.5908	−	15.5908i	0.889813	−	0.889813i	−0.104692	−	0.994505i	$-0.533386\pi$
$307$	15.5908	−	15.5908i	0.889813	−	0.889813i	0.994505	+	0.104692i	$0.0333857\pi$
$308$	−7.61030	−	4.36845i	−0.433637	−	0.248916i
$309$			37.8784i			2.15483i
$310$	7.70478	−	19.7454i	0.437602	−	1.12146i
$311$	3.99701	+	6.92303i	0.226650	+	0.392569i	0.956813	−	0.290704i	$-0.0938894\pi$
$311$	3.99701	+	6.92303i	0.226650	+	0.392569i	−0.730163	+	0.683273i	$0.760556\pi$
$312$	3.14981	−	11.7553i	0.178323	−	0.665511i
$313$	2.35326	+	8.78249i	0.133014	+	0.496416i	0.999998	−	0.00192030i	$-0.000611252\pi$
$313$	2.35326	+	8.78249i	0.133014	+	0.496416i	−0.866984	+	0.498336i	$0.833945\pi$
$314$	12.8922			0.727550
$315$	18.1454	−	17.1955i	1.02238	−	0.968855i
$316$			4.38676i			0.246774i
$317$	−0.376636	+	0.100919i	−0.0211540	+	0.00566819i	−0.269381	−	0.963034i	$-0.586819\pi$
$317$	−0.376636	+	0.100919i	−0.0211540	+	0.00566819i	0.248227	+	0.968702i	$0.420152\pi$
$318$	−4.67795	+	17.4584i	−0.262327	+	0.979016i
$319$	2.41456	−	6.76857i	0.135190	−	0.378967i
$320$	0.898208	+	2.04774i	0.0502113	+	0.114472i
$321$			42.9853i			2.39921i
$322$	3.07565	−	17.0533i	0.171399	−	0.950345i
$323$	−7.55643	+	7.55643i	−0.420451	+	0.420451i
$324$	3.30931	+	1.91063i	0.183850	+	0.106146i
$325$	22.6179	−	0.935248i	1.25461	−	0.0518782i
$326$	−13.2567	+	7.65376i	−0.734221	+	0.423903i
$327$	−2.50188	−	9.33713i	−0.138354	−	0.516345i
$328$	4.62301	−	4.62301i	0.255263	−	0.255263i
$329$	5.49772	−	11.6707i	0.303099	−	0.643429i
$330$	−19.8852	+	1.40829i	−1.09465	+	0.0775238i
$331$	1.12074	−	1.94118i	0.0616015	−	0.106697i	−0.833580	−	0.552399i	$-0.813713\pi$
$331$	1.12074	−	1.94118i	0.0616015	−	0.106697i	0.895181	+	0.445702i	$0.147046\pi$
$332$	−7.71797	−	2.06802i	−0.423579	−	0.113498i
$333$	25.6262	+	6.86652i	1.40431	+	0.376283i
$334$	16.4030	+	9.47025i	0.897530	+	0.518189i
$335$	−1.04503	−	6.84214i	−0.0570960	−	0.373826i
$336$	0.592181	+	7.08719i	0.0323061	+	0.386638i
$337$	−6.06525	+	6.06525i	−0.330395	+	0.330395i	−0.852736	−	0.522341i	$-0.825059\pi$
$337$	−6.06525	+	6.06525i	−0.330395	+	0.330395i	0.522341	+	0.852736i	$0.325059\pi$
$338$	7.24222	−	1.94055i	0.393925	−	0.105552i
$339$	37.2249	−	21.4918i	2.02178	−	1.16728i
$340$	−4.61633	+	3.69625i	−0.250355	+	0.200457i
$341$	−30.9246	+	5.65734i	−1.67466	+	0.306362i
$342$	12.0732	+	12.0732i	0.652844	+	0.652844i
$343$	−15.9295	−	9.44732i	−0.860111	−	0.510107i
$344$		−	10.2619i		−	0.553285i
$345$	−15.8134	−	36.0513i	−0.851362	−	1.94094i
$346$	−0.244233	−	0.423024i	−0.0131300	−	0.0227419i
$347$	−26.0037	−	6.96766i	−1.39595	−	0.374044i	−0.519061	−	0.854737i	$-0.673718\pi$
$347$	−26.0037	−	6.96766i	−1.39595	−	0.374044i	−0.876889	+	0.480693i	$0.840385\pi$
$348$	−5.62590	+	1.50745i	−0.301580	+	0.0808080i
$349$	−4.88249			−0.261354			−0.130677	−	0.991425i	$-0.541715\pi$
$349$	−4.88249			−0.261354			−0.130677	+	0.991425i	$0.541715\pi$
$350$	−12.2530	+	4.98643i	−0.654949	+	0.266536i
$351$		−	14.9151i		−	0.796111i
$352$	1.88489	−	2.72895i	0.100465	−	0.145454i
$353$	−34.1176	−	9.14179i	−1.81590	−	0.486569i	−0.819631	−	0.572891i	$-0.805822\pi$
$353$	−34.1176	−	9.14179i	−1.81590	−	0.486569i	−0.996267	+	0.0863226i	$0.972488\pi$
$354$	−5.03528	−	8.72137i	−0.267622	−	0.463535i
$355$	−11.2018	+	4.91349i	−0.594530	+	0.260781i
$356$	−17.3899			−0.921665
$357$	−17.6996	+	6.36400i	−0.936763	+	0.336818i
$358$	−0.405155	−	0.405155i	−0.0214131	−	0.0214131i
$359$	−4.94954	+	8.57286i	−0.261227	+	0.452458i	−0.966568	−	0.256410i	$-0.917460\pi$
$359$	−4.94954	+	8.57286i	−0.261227	+	0.452458i	0.705341	+	0.708868i	$0.250794\pi$
$360$	5.90564	+	7.37568i	0.311254	+	0.388733i
$361$	1.33655	+	2.31497i	0.0703447	+	0.121841i
$362$	4.79222	+	17.8848i	0.251873	+	0.940005i
$363$	17.2687	+	24.0018i	0.906372	+	1.25977i
$364$	−9.83894	+	6.83222i	−0.515701	+	0.358105i
$365$	1.56277	+	10.2320i	0.0817991	+	0.535565i
$366$	3.03044	−	5.24887i	0.158403	−	0.274363i
$367$	2.54078	−	9.48234i	0.132628	−	0.494974i	−0.867368	−	0.497666i	$-0.834190\pi$
$367$	2.54078	−	9.48234i	0.132628	−	0.494974i	0.999996	+	0.00269244i	$0.000857030\pi$
$368$	6.32637	+	1.69515i	0.329785	+	0.0883656i
$369$	13.8132	−	23.9252i	0.719088	−	1.24550i
$370$	−11.3122	−	8.31452i	−0.588093	−	0.432251i
$371$	14.6123	−	10.1469i	0.758634	−	0.526800i
$372$	18.0168	+	18.0168i	0.934125	+	0.934125i
$373$	−8.50002	+	2.27757i	−0.440114	+	0.117928i	−0.472070	−	0.881561i	$-0.656493\pi$
$373$	−8.50002	+	2.27757i	−0.440114	+	0.117928i	0.0319557	+	0.999489i	$0.489826\pi$
$374$	8.26160	+	2.94718i	0.427197	+	0.152395i
$375$	−16.7830	+	24.9304i	−0.866673	+	1.28740i
$376$	4.22278	+	2.43803i	0.217773	+	0.125732i
$377$	−6.93664	−	6.93664i	−0.357255	−	0.357255i
$378$	2.94910	+	8.20206i	0.151685	+	0.421868i
$379$			13.0265i			0.669126i	0.942373	+	0.334563i	$0.108589\pi$
$379$			13.0265i			0.669126i	−0.942373	+	0.334563i	$0.891411\pi$
$380$	−3.62935	−	8.27420i	−0.186182	−	0.424457i
$381$	−19.7073	+	11.3780i	−1.00964	+	0.582913i
$382$	−5.15667	−	1.38173i	−0.263838	−	0.0706952i
$383$	−3.15714	−	11.7826i	−0.161322	−	0.602063i	−0.998481	−	0.0551023i	$-0.982451\pi$
$383$	−3.15714	−	11.7826i	−0.161322	−	0.602063i	0.837158	−	0.546960i	$-0.184215\pi$
$384$	−2.68804			−0.137174
$385$	15.8392	+	11.5810i	0.807242	+	0.590221i
$386$	−19.9887			−1.01740
$387$	−11.2230	−	41.8849i	−0.570498	−	2.12913i
$388$	−7.85441	−	2.10458i	−0.398747	−	0.106844i
$389$	−15.2531	+	8.80636i	−0.773361	+	0.446500i	−0.834072	−	0.551655i	$-0.813996\pi$
$389$	−15.2531	+	8.80636i	−0.773361	+	0.446500i	0.0607111	+	0.998155i	$0.480663\pi$
$390$	−9.89221	+	25.3512i	−0.500912	+	1.28371i
$391$			17.3217i			0.875996i
$392$	4.05968	−	5.70254i	0.205045	−	0.288022i
$393$	−19.5808	−	19.5808i	−0.987718	−	0.987718i
$394$	−8.21688	−	4.74402i	−0.413960	−	0.239000i
$395$	1.07913	−	9.74955i	0.0542969	−	0.490553i
$396$	4.70882	−	13.1999i	0.236627	−	0.663319i
$397$	8.04928	−	2.15680i	0.403982	−	0.108247i	−0.0511057	−	0.998693i	$-0.516275\pi$
$397$	8.04928	−	2.15680i	0.403982	−	0.108247i	0.455088	+	0.890447i	$0.349608\pi$
$398$	2.11356	+	2.11356i	0.105943	+	0.105943i
$399$	−2.39280	−	28.6369i	−0.119790	−	1.43364i
$400$	−1.49252	−	4.77204i	−0.0746262	−	0.238602i
$401$	11.3208	−	19.6082i	0.565333	−	0.979186i	−0.431685	−	0.902024i	$-0.642081\pi$
$401$	11.3208	−	19.6082i	0.565333	−	0.979186i	0.997019	−	0.0771616i	$-0.0245857\pi$
$402$	8.03700	+	2.15351i	0.400849	+	0.107407i
$403$	−11.1072	+	41.4526i	−0.553289	+	2.06490i
$404$	7.98121	−	13.8239i	0.397080	−	0.687763i
$405$	−6.88491	−	5.06045i	−0.342114	−	0.251456i
$406$	5.18611	+	2.44302i	0.257383	+	0.121245i
$407$	−1.68195	+	20.7553i	−0.0833710	+	1.02880i
$408$	−1.83998	−	6.86688i	−0.0910923	−	0.339961i
$409$	2.06583	+	3.57813i	0.102149	+	0.176927i	0.912570	−	0.408921i	$-0.134095\pi$
$409$	2.06583	+	3.57813i	0.102149	+	0.176927i	−0.810421	+	0.585848i	$0.800762\pi$
$410$	−11.4119	+	9.13737i	−0.563592	+	0.451262i
$411$	−13.8457	+	23.9814i	−0.682957	+	1.18292i
$412$	9.96415	+	9.96415i	0.490899	+	0.490899i
$413$	−1.75932	+	9.75475i	−0.0865702	+	0.480000i
$414$	27.6756			1.36018
$415$	16.6444	+	6.49478i	0.817043	+	0.318816i
$416$	−2.26372	−	3.92088i	−0.110988	−	0.192237i
$417$	−3.24934	−	0.870657i	−0.159121	−	0.0426363i
$418$	−7.61621	+	11.0268i	−0.372521	+	0.539336i
$419$			31.4492i			1.53640i	0.640213	+	0.768198i	$0.278846\pi$
$419$			31.4492i			1.53640i	−0.640213	+	0.768198i	$0.721154\pi$
$420$	0.427312	−	15.8969i	0.0208507	−	0.775691i
$421$	1.74867			0.0852250			0.0426125	−	0.999092i	$-0.486432\pi$
$421$	1.74867			0.0852250			0.0426125	+	0.999092i	$0.486432\pi$
$422$	9.26860	−	2.48351i	0.451188	−	0.120896i
$423$	19.9020	+	5.33273i	0.967670	+	0.259286i
$424$	3.36197	+	5.82310i	0.163272	+	0.282795i
$425$	11.1690	−	7.07929i	0.541777	−	0.343396i
$426$		−	14.7045i		−	0.712435i
$427$	−5.61368	+	2.01843i	−0.271665	+	0.0976786i
$428$	11.3076	+	11.3076i	0.546572	+	0.546572i
$429$	39.7042	−	7.26349i	1.91694	−	0.350685i
$430$	−2.52440	+	22.8070i	−0.121737	+	1.09985i
$431$	23.1554	−	13.3688i	1.11536	−	0.643951i	0.175144	−	0.984543i	$-0.443961\pi$
$431$	23.1554	−	13.3688i	1.11536	−	0.643951i	0.940211	+	0.340592i	$0.110628\pi$
$432$	−3.18214	+	0.852651i	−0.153101	+	0.0410232i
$433$	−0.525794	+	0.525794i	−0.0252680	+	0.0252680i	−0.719628	−	0.694360i	$-0.755688\pi$
$433$	−0.525794	+	0.525794i	−0.0252680	+	0.0252680i	0.694360	+	0.719628i	$0.255688\pi$
$434$	−2.08821	−	24.9916i	−0.100237	−	1.19963i
$435$	12.8744	−	1.96636i	0.617278	−	0.0942795i
$436$	−3.11433	−	1.79806i	−0.149149	−	0.0861113i
$437$	−25.5627	−	6.84950i	−1.22283	−	0.327656i
$438$	−12.0188	−	3.22043i	−0.574280	−	0.153878i
$439$	8.90637	−	15.4263i	0.425078	−	0.736256i	−0.571350	−	0.820706i	$-0.693580\pi$
$439$	8.90637	−	15.4263i	0.425078	−	0.736256i	0.996428	+	0.0844504i	$0.0269135\pi$
$440$	−4.86048	+	5.60140i	−0.231714	+	0.267036i
$441$	10.3333	−	27.7153i	0.492062	−	1.31978i
$442$	8.46676	−	8.46676i	0.402723	−	0.402723i
$443$	2.77319	+	10.3497i	0.131758	+	0.491729i	0.999990	−	0.00442990i	$-0.00141009\pi$
$443$	2.77319	+	10.3497i	0.131758	+	0.491729i	−0.868232	+	0.496159i	$0.834743\pi$
$444$	14.6158	−	8.43842i	0.693634	−	0.400470i
$445$	38.6491	+	4.27788i	1.83214	+	0.202791i
$446$	−19.4562	−	11.2330i	−0.921278	−	0.531900i
$447$	38.4499	−	38.4499i	1.81862	−	1.81862i
$448$	2.02011	+	1.70855i	0.0954412	+	0.0807216i
$449$		−	35.6800i		−	1.68385i	−0.539598	−	0.841923i	$-0.681424\pi$
$449$		−	35.6800i		−	1.68385i	0.539598	−	0.841923i	$-0.318576\pi$
$450$	−11.3109	−	17.8452i	−0.533199	−	0.841231i
$451$	20.4232	+	7.28562i	0.961693	+	0.343066i
$452$	4.13869	−	15.4458i	0.194668	−	0.726510i
$453$	−33.8014	+	9.05706i	−1.58813	+	0.425538i
$454$		−	11.1438i		−	0.523004i
$455$	23.5477	−	12.7642i	1.10393	−	0.598396i
$456$	10.8615			0.508634
$457$	1.22876	+	4.58580i	0.0574790	+	0.214515i	0.988692	−	0.149961i	$-0.0479149\pi$
$457$	1.22876	+	4.58580i	0.0574790	+	0.214515i	−0.931213	+	0.364476i	$0.881248\pi$
$458$	5.54118	−	20.6800i	0.258922	−	0.966311i
$459$	−4.35637	−	7.54545i	−0.203338	−	0.352191i
$460$	−13.6433	−	5.32373i	−0.636124	−	0.248220i
$461$		−	1.50907i		−	0.0702842i	−0.999382	−	0.0351421i	$-0.988812\pi$
$461$		−	1.50907i		−	0.0702842i	0.999382	−	0.0351421i	$-0.0111884\pi$
$462$	−20.3978	+	11.8448i	−0.948990	+	0.551071i
$463$	14.2220	−	14.2220i	0.660952	−	0.660952i	−0.294653	−	0.955604i	$-0.595204\pi$
$463$	14.2220	−	14.2220i	0.660952	−	0.660952i	0.955604	+	0.294653i	$0.0952039\pi$
$464$	−1.08338	+	1.87647i	−0.0502948	+	0.0871131i
$465$	−35.6101	−	44.4742i	−1.65138	−	2.06244i
$466$	2.91690	+	5.05223i	0.135123	+	0.234040i
$467$	3.66271	−	0.981421i	0.169490	−	0.0454148i	−0.173076	−	0.984908i	$-0.555371\pi$
$467$	3.66271	−	0.981421i	0.169490	−	0.0454148i	0.342566	+	0.939494i	$0.388704\pi$
$468$	−13.5277	−	13.5277i	−0.625317	−	0.625317i
$469$	−4.67114	−	6.72682i	−0.215693	−	0.310616i
$470$	−8.78537	−	6.45729i	−0.405239	−	0.297853i
$471$	17.3274	−	30.0120i	0.798405	−	1.38288i
$472$	−3.61878	−	0.969648i	−0.166568	−	0.0446317i
$473$	30.7533	−	14.5811i	1.41404	−	0.670439i
$474$	10.2120	+	5.89589i	0.469052	+	0.270807i
$475$	6.03078	+	19.2822i	0.276711	+	0.884727i
$476$	−2.98191	+	6.33009i	−0.136675	+	0.290139i
$477$	20.0906	+	20.0906i	0.919888	+	0.919888i
$478$	0.585260	+	2.18422i	0.0267692	+	0.0999039i
$479$	0.789292	+	1.36709i	0.0360637	+	0.0624641i	0.883494	−	0.468443i	$-0.155185\pi$
$479$	0.789292	+	1.36709i	0.0360637	+	0.0624641i	−0.847430	+	0.530907i	$0.821851\pi$
$480$	5.97416	+	0.661251i	0.272682	+	0.0301818i
$481$	24.6172	+	14.2127i	1.12245	+	0.648045i
$482$	−16.0030	−	16.0030i	−0.728916	−	0.728916i
$483$	−35.5649	−	30.0799i	−1.61826	−	1.36868i
$484$	10.8565	+	1.77118i	0.493476	+	0.0805081i
$485$	16.9387	+	6.60959i	0.769146	+	0.300126i
$486$	17.4546	−	10.0774i	0.791758	−	0.457122i
$487$	−0.0177171	+	0.0661211i	−0.000802838	+	0.00299623i	−0.966326	−	0.257321i	$-0.917160\pi$
$487$	−0.0177171	+	0.0661211i	−0.000802838	+	0.00299623i	0.965523	+	0.260317i	$0.0838270\pi$
$488$	−0.583573	−	2.17792i	−0.0264171	−	0.0985900i
$489$			41.1473i			1.86074i
$490$	−10.4254	+	11.6752i	−0.470973	+	0.527432i
$491$			26.4205i			1.19234i	0.802858	+	0.596170i	$0.203311\pi$
$491$			26.4205i			1.19234i	−0.802858	+	0.596170i	$0.796689\pi$
$492$	−4.54854	−	16.9754i	−0.205064	−	0.765309i
$493$	−5.53522	−	1.48316i	−0.249294	−	0.0667981i
$494$	9.14691	+	15.8429i	0.411539	+	0.712806i
$495$	−13.7125	+	28.1783i	−0.616330	+	1.26652i
$496$	9.47884			0.425613
$497$	−9.34636	+	11.0507i	−0.419242	+	0.495690i
$498$	−15.1873	+	15.1873i	−0.680559	+	0.680559i
$499$	15.2129	+	8.78316i	0.681022	+	0.393188i	0.800240	−	0.599680i	$-0.204705\pi$
$499$	15.2129	+	8.78316i	0.681022	+	0.393188i	−0.119218	+	0.992868i	$0.538039\pi$
$500$	2.14322	+	10.9730i	0.0958477	+	0.490727i
$501$	44.0918	−	25.4564i	1.96988	−	1.13731i
$502$	2.04482	+	7.63137i	0.0912647	+	0.340605i
$503$	26.9471	+	26.9471i	1.20151	+	1.20151i	0.973707	+	0.227805i	$0.0731550\pi$
$503$	26.9471	+	26.9471i	1.20151	+	1.20151i	0.227805	+	0.973707i	$0.426845\pi$
$504$	10.1138	+	4.76431i	0.450506	+	0.212219i
$505$	−21.1388	+	28.7601i	−0.940666	+	1.27981i
$506$	3.90902	+	21.3678i	0.173777	+	0.949913i
$507$	5.21627	−	19.4674i	0.231663	−	0.864578i
$508$	−2.19107	+	8.17719i	−0.0972131	+	0.362804i
$509$	−4.18815	−	2.41803i	−0.185637	−	0.107177i	0.404302	−	0.914626i	$-0.367515\pi$
$509$	−4.18815	−	2.41803i	−0.185637	−	0.107177i	−0.589938	+	0.807448i	$0.700848\pi$
$510$	2.40010	+	15.7142i	0.106278	+	0.695838i
$511$	6.98538	+	10.0595i	0.309015	+	0.445006i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	12.8579	−	3.44527i	0.567691	−	0.152112i
$514$	−8.95665	−	15.5134i	−0.395061	−	0.684266i
$515$	−19.6941	−	24.5964i	−0.867827	−	1.08385i
$516$	−23.8888	−	13.7922i	−1.05165	−	0.607169i
$517$	−1.30625	+	16.1192i	−0.0574487	+	0.708921i
$518$	−16.3476	−	2.94836i	−0.718271	−	0.129544i
$519$	−1.31302			−0.0576350
$520$	4.06658	+	9.27100i	0.178331	+	0.406560i
$521$	−4.04614	−	7.00812i	−0.177265	−	0.307031i	0.763678	−	0.645597i	$-0.223392\pi$
$521$	−4.04614	−	7.00812i	−0.177265	−	0.307031i	−0.940943	+	0.338566i	$0.890058\pi$
$522$	−2.36970	+	8.84385i	−0.103719	+	0.387085i
$523$	−1.07264	+	0.287414i	−0.0469034	+	0.0125677i	−0.282194	−	0.959357i	$-0.591062\pi$
$523$	−1.07264	+	0.287414i	−0.0469034	+	0.0125677i	0.235291	+	0.971925i	$0.424396\pi$
$524$	−10.3017			−0.450031
$525$	−4.86030	+	35.2257i	−0.212121	+	1.53738i
$526$	20.2425			0.882614
$527$	6.48830	+	24.2147i	0.282635	+	1.05481i
$528$	−3.81942	−	8.05564i	−0.166219	−	0.350577i
$529$	−17.2309	+	9.94826i	−0.749169	+	0.432533i
$530$	−6.03949	−	13.7688i	−0.262339	−	0.598080i
$531$	−15.8308			−0.686999
$532$	−8.16257	−	6.90368i	−0.353892	−	0.299313i
$533$	20.9304	−	20.9304i	0.906596	−	0.906596i
$534$	−23.3725	+	40.4823i	−1.01143	+	1.75184i
$535$	−22.3494	−	27.9126i	−0.966248	−	1.20677i
$536$	2.68068	−	1.54769i	0.115788	−	0.0668500i
$537$	−1.48770	+	0.398629i	−0.0641991	+	0.0172021i
$538$	5.41306	+	5.41306i	0.233373	+	0.233373i
$539$	22.8580	+	4.06351i	0.984564	+	0.175028i
$540$	7.28203	−	1.11222i	0.313369	−	0.0478621i
$541$	4.14369	+	2.39236i	0.178151	+	0.102856i	0.586424	−	0.810004i	$-0.300535\pi$
$541$	4.14369	+	2.39236i	0.178151	+	0.102856i	−0.408273	+	0.912860i	$0.633869\pi$
$542$	−1.01570	+	3.79063i	−0.0436279	+	0.162821i
$543$	48.0751	+	12.8817i	2.06310	+	0.552806i
$544$	−2.29039	−	1.32236i	−0.0981998	−	0.0566957i
$545$	6.47926	+	4.76229i	0.277541	+	0.203994i
$546$	2.68106	+	32.0868i	0.114739	+	1.37319i
$547$	−3.27348	+	3.27348i	−0.139964	+	0.139964i	−0.773617	−	0.633653i	$-0.781555\pi$
$547$	−3.27348	+	3.27348i	−0.139964	+	0.139964i	0.633653	+	0.773617i	$0.281555\pi$
$548$	2.66627	+	9.95066i	0.113897	+	0.425071i
$549$	−4.76381	−	8.25116i	−0.203315	−	0.352151i
$550$	12.1803	−	11.2534i	0.519371	−	0.479848i
$551$	4.37758	−	7.58219i	0.186491	−	0.323012i
$552$	12.4489	−	12.4489i	0.529862	−	0.529862i
$553$	−3.92697	−	10.9217i	−0.166992	−	0.464439i
$554$		−	9.76362i		−	0.414816i
$555$	−34.5593	+	15.1589i	−1.46696	+	0.643460i
$556$	−1.08379	+	0.625727i	−0.0459630	+	0.0265367i
$557$	−42.6530	−	11.4288i	−1.80726	−	0.484255i	−0.812190	−	0.583393i	$-0.801725\pi$
$557$	−42.6530	−	11.4288i	−1.80726	−	0.484255i	−0.995074	+	0.0991383i	$0.968391\pi$
$558$	38.6887	−	10.3666i	1.63783	−	0.438854i
$559$		−	46.4602i		−	1.96506i
$560$	−4.06938	−	4.29420i	−0.171963	−	0.181463i
$561$	17.9645	−	15.2712i	0.758464	−	0.644752i
$562$	−0.960836	+	0.257455i	−0.0405304	+	0.0108601i
$563$	4.30918	−	16.0821i	0.181610	−	0.677778i	−0.813721	−	0.581256i	$-0.802561\pi$
$563$	4.30918	−	16.0821i	0.181610	−	0.677778i	0.995331	−	0.0965222i	$-0.0307719\pi$
$564$	11.3510	−	6.55351i	0.477964	−	0.275953i
$565$	−12.9979	+	33.3101i	−0.546824	+	1.40137i
$566$	−13.0284			−0.547625
$567$	−9.94958	−	1.79445i	−0.417843	−	0.0753600i
$568$	−3.86811	−	3.86811i	−0.162302	−	0.162302i
$569$	−20.0499	+	34.7275i	−0.840536	+	1.45585i	0.0489060	+	0.998803i	$0.484427\pi$
$569$	−20.0499	+	34.7275i	−0.840536	+	1.45585i	−0.889442	+	0.457048i	$0.848907\pi$
$570$	−24.1395	−	2.67189i	−1.01109	−	0.111913i
$571$	22.5866	−	13.0404i	0.945219	−	0.545723i	0.0536268	−	0.998561i	$-0.482922\pi$
$571$	22.5866	−	13.0404i	0.945219	−	0.545723i	0.891593	+	0.452838i	$0.149589\pi$
$572$	8.53374	−	12.3552i	0.356814	−	0.516595i
$573$	−10.1472	+	10.1472i	−0.423906	+	0.423906i
$574$	−7.37147	+	15.6484i	−0.307679	+	0.653152i
$575$	29.0126	+	15.1882i	1.20991	+	0.633391i
$576$	−2.11279	+	3.65945i	−0.0880327	+	0.152477i
$577$	0.0148009	−	0.0552379i	0.000616171	−	0.00229958i	−0.965617	−	0.259969i	$-0.916288\pi$
$577$	0.0148009	−	0.0552379i	0.000616171	−	0.00229958i	0.966233	+	0.257669i	$0.0829544\pi$
$578$	−2.58960	+	9.66453i	−0.107713	+	0.401992i
$579$	−26.8653	+	46.5320i	−1.11648	+	1.93380i
$580$	2.86942	−	3.90395i	0.119146	−	0.162102i
$581$	21.0668	−	1.76026i	0.873997	−	0.0730281i
$582$	−15.4558	+	15.4558i	−0.640663	+	0.640663i
$583$	−12.6739	+	18.3493i	−0.524899	+	0.759950i
$584$	−4.00878	+	2.31447i	−0.165884	+	0.0957733i
$585$	26.7374	+	33.3930i	1.10546	+	1.38063i
$586$	−6.40889	+	11.1005i	−0.264749	+	0.458559i
$587$	−17.2078	−	17.2078i	−0.710242	−	0.710242i	0.256343	−	0.966586i	$-0.417482\pi$
$587$	−17.2078	−	17.2078i	−0.710242	−	0.710242i	−0.966586	+	0.256343i	$0.917482\pi$
$588$	−7.81873	−	17.1149i	−0.322439	−	0.705807i
$589$	−38.3008			−1.57815
$590$	7.80418	+	3.04525i	0.321293	+	0.125371i
$591$	−22.0873	+	12.7521i	−0.908551	+	0.524552i
$592$	1.62499	−	6.06455i	0.0667868	−	0.249252i
$593$	28.8586	−	7.73263i	1.18508	−	0.317541i	0.388140	−	0.921600i	$-0.373118\pi$
$593$	28.8586	−	7.73263i	1.18508	−	0.317541i	0.796939	+	0.604059i	$0.206451\pi$
$594$	−7.07674	−	8.32483i	−0.290362	−	0.341572i
$595$	8.18446	−	13.3350i	0.335530	−	0.546684i
$596$		−	20.2290i		−	0.828611i
$597$	7.76087	−	2.07952i	0.317631	−	0.0851090i
$598$	28.6423	+	7.67467i	1.17127	+	0.313841i
$599$	−7.77821	+	4.49075i	−0.317809	+	0.183487i	−0.650416	−	0.759579i	$-0.725405\pi$
$599$	−7.77821	+	4.49075i	−0.317809	+	0.183487i	0.332606	+	0.943066i	$0.392072\pi$
$600$	−13.1149	−	2.93926i	−0.535413	−	0.119995i
$601$		−	42.9190i		−	1.75070i	−0.483488	−	0.875351i	$-0.660630\pi$
$601$		−	42.9190i		−	1.75070i	0.483488	−	0.875351i	$-0.339370\pi$
$602$	9.18634	+	25.5491i	0.374407	+	1.04131i
$603$	9.24878	−	9.24878i	0.376639	−	0.376639i
$604$	−6.50916	+	11.2742i	−0.264854	+	0.458740i
$605$	−23.6927	−	6.60710i	−0.963247	−	0.268617i
$606$	−21.4538	−	37.1591i	−0.871502	−	1.50949i
$607$	−8.44441	−	31.5150i	−0.342748	−	1.27915i	−0.895221	−	0.445622i	$-0.852982\pi$
$607$	−8.44441	−	31.5150i	−0.342748	−	1.27915i	0.552473	−	0.833531i	$-0.313684\pi$
$608$	2.85718	−	2.85718i	0.115874	−	0.115874i
$609$	12.6574	−	8.78936i	0.512903	−	0.356163i
$610$	0.761225	+	4.98399i	0.0308211	+	0.201796i
$611$	19.1184	+	11.0380i	0.773447	+	0.446550i
$612$	−10.7947	−	2.89242i	−0.436348	−	0.116919i
$613$	−10.3036	+	38.4536i	−0.416158	+	1.55312i	0.366346	+	0.930479i	$0.380609\pi$
$613$	−10.3036	+	38.4536i	−0.416158	+	1.55312i	−0.782504	+	0.622646i	$0.786058\pi$
$614$	−19.0947	−	11.0243i	−0.770600	−	0.444906i
$615$	5.93321	+	38.8466i	0.239250	+	1.56645i
$616$	−2.24991	+	8.48162i	−0.0906514	+	0.341734i
$617$	5.08189	+	5.08189i	0.204589	+	0.204589i	0.801963	−	0.597374i	$-0.203789\pi$
$617$	5.08189	+	5.08189i	0.204589	+	0.204589i	−0.597374	+	0.801963i	$0.703789\pi$
$618$	36.5877	−	9.80365i	1.47177	−	0.394361i
$619$	−27.4630	+	15.8558i	−1.10383	+	0.637298i	−0.937225	−	0.348726i	$-0.886615\pi$
$619$	−27.4630	+	15.8558i	−1.10383	+	0.637298i	−0.166607	+	0.986023i	$0.553281\pi$
$620$	−21.0667	−	2.33177i	−0.846059	−	0.0936461i
$621$	10.7884	−	18.6860i	0.432922	−	0.749844i
$622$	5.65263	−	5.65263i	0.226650	−	0.226650i
$623$	43.2959	−	15.5673i	1.73461	−	0.623690i
$624$	−12.1699			−0.487188
$625$	−2.06397	−	24.9147i	−0.0825588	−	0.996586i
$626$	7.87417	−	4.54615i	0.314715	−	0.181701i
$627$	15.4330	+	32.5501i	0.616334	+	1.29992i
$628$	−3.33675	−	12.4529i	−0.133151	−	0.496926i
$629$	16.6048			0.662078
$630$	−21.3059	−	13.0766i	−0.848849	−	0.520985i
$631$	−26.5850			−1.05833			−0.529165	−	0.848519i	$-0.677495\pi$
$631$	−26.5850			−1.05833			−0.529165	+	0.848519i	$0.677495\pi$
$632$	4.23728	−	1.13538i	0.168550	−	0.0451628i
$633$	6.67579	−	24.9144i	0.265339	−	0.990258i
$634$	0.194961	+	0.337682i	0.00774289	+	0.0134111i
$635$	6.88121	−	17.6348i	0.273073	−	0.699815i
$636$	18.0742			0.716689
$637$	18.3800	−	25.8179i	0.728240	−	1.02294i
$638$	−7.16287	−	0.580456i	−0.283581	−	0.0229805i
$639$	−20.0184	−	11.5576i	−0.791916	−	0.457213i
$640$	1.74549	−	1.39760i	0.0689965	−	0.0552448i
$641$	6.55481	+	11.3533i	0.258899	+	0.448427i	0.965947	−	0.258739i	$-0.0833069\pi$
$641$	6.55481	+	11.3533i	0.258899	+	0.448427i	−0.707048	+	0.707166i	$0.749974\pi$
$642$	41.5206	−	11.1254i	1.63869	−	0.439085i
$643$	8.98489	−	8.98489i	0.354329	−	0.354329i	−0.507388	−	0.861718i	$-0.669389\pi$
$643$	8.98489	−	8.98489i	0.354329	−	0.354329i	0.861718	+	0.507388i	$0.169389\pi$
$644$	−17.2683	+	1.44288i	−0.680466	+	0.0568573i
$645$	49.7000	+	36.5297i	1.95693	+	1.43836i
$646$	9.25470	+	5.34320i	0.364121	+	0.210225i
$647$	−11.5166	+	42.9804i	−0.452763	+	1.68973i	0.241820	+	0.970321i	$0.422256\pi$
$647$	−11.5166	+	42.9804i	−0.452763	+	1.68973i	−0.694583	+	0.719413i	$0.744411\pi$
$648$	0.989015	−	3.69105i	0.0388522	−	0.144998i
$649$	−2.23602	−	12.2227i	−0.0877713	−	0.479781i
$650$	−6.75731	−	21.6051i	−0.265044	−	0.847423i
$651$	−60.9848	−	28.7280i	−2.39018	−	1.12594i
$652$	10.8241	+	10.8241i	0.423903	+	0.423903i
$653$	9.48094	+	35.3833i	0.371018	+	1.38466i	0.859077	+	0.511847i	$0.171038\pi$
$653$	9.48094	+	35.3833i	0.371018	+	1.38466i	−0.488059	+	0.872811i	$0.662295\pi$
$654$	−8.37144	+	4.83326i	−0.327349	+	0.188995i
$655$	22.8954	+	2.53419i	0.894599	+	0.0990189i
$656$	−5.66201	−	3.26896i	−0.221064	−	0.127631i
$657$	−13.8309	+	13.8309i	−0.539596	+	0.539596i
$658$	−12.6960	−	2.28978i	−0.494941	−	0.0892650i
$659$	−32.0226			−1.24742			−0.623711	−	0.781655i	$-0.714376\pi$
$659$	−32.0226			−1.24742			−0.623711	+	0.781655i	$0.714376\pi$
$660$	6.50699	+	18.8432i	0.253284	+	0.733470i
$661$	0.981802	+	1.70053i	0.0381877	+	0.0661430i	0.884488	−	0.466564i	$-0.154508\pi$
$661$	0.981802	+	1.70053i	0.0381877	+	0.0661430i	−0.846300	+	0.532707i	$0.821175\pi$
$662$	−2.16511	−	0.580138i	−0.0841492	−	0.0225477i
$663$	−8.33037	−	31.0894i	−0.323525	−	1.20741i
$664$			7.99023i			0.310081i
$665$	16.4430	+	17.3514i	0.637631	+	0.672857i
$666$		−	26.5302i		−	1.02802i
$667$	−3.67298	−	13.7078i	−0.142219	−	0.530767i
$668$	4.90216	−	18.2951i	0.189670	−	0.707859i
$669$	−52.2991	+	30.1949i	−2.02200	+	1.16740i
$670$	−6.33852	+	2.78029i	−0.244878	+	0.107412i
$671$	5.69770	−	4.84348i	0.219957	−	0.186980i
$672$	6.69244	−	2.40630i	0.258166	−	0.0928252i
$673$	−34.1675	−	34.1675i	−1.31706	−	1.31706i	−0.916092	−	0.400968i	$-0.868674\pi$
$673$	−34.1675	−	34.1675i	−1.31706	−	1.31706i	−0.400968	−	0.916092i	$-0.631326\pi$
$674$	7.42838	+	4.28878i	0.286130	+	0.165197i
$675$	−16.4579	+	0.680533i	−0.633464	+	0.0261937i
$676$	−3.74885	−	6.49320i	−0.144187	−	0.249738i
$677$	8.40252	+	31.3586i	0.322935	+	1.20521i	0.916371	+	0.400330i	$0.131104\pi$
$677$	8.40252	+	31.3586i	0.322935	+	1.20521i	−0.593436	+	0.804881i	$0.702229\pi$
$678$	−30.3940	−	30.3940i	−1.16728	−	1.16728i
$679$	21.4392	−	1.79138i	0.822760	−	0.0687469i
$680$	4.76509	+	3.50237i	0.182733	+	0.134310i
$681$	−25.9418	−	14.9775i	−0.994090	−	0.573938i
$682$	13.4684	+	28.4066i	0.515733	+	1.08774i
$683$	−1.35535	−	0.363164i	−0.0518609	−	0.0138961i	0.232795	−	0.972526i	$-0.425213\pi$
$683$	−1.35535	−	0.363164i	−0.0518609	−	0.0138961i	−0.284656	+	0.958630i	$0.591879\pi$
$684$	8.53704	−	14.7866i	0.326422	−	0.565379i
$685$	−3.47794	−	22.7712i	−0.132885	−	0.870042i
$686$	−5.00256	+	17.8318i	−0.190999	+	0.680823i
$687$	−40.6937	−	40.6937i	−1.55256	−	1.55256i
$688$	−9.91224	+	2.65598i	−0.377901	+	0.101258i
$689$	15.2211	+	26.3637i	0.579878	+	1.00438i
$690$	−30.7301	+	24.6053i	−1.16987	+	0.936707i
$691$	15.1249	−	26.1970i	0.575377	−	0.996582i	−0.420624	−	0.907235i	$-0.638189\pi$
$691$	15.1249	−	26.1970i	0.575377	−	0.996582i	0.996001	−	0.0893466i	$-0.0284779\pi$
$692$	−0.345397	+	0.345397i	−0.0131300	+	0.0131300i
$693$	0.0927986	+	37.0791i	0.00352513	+	1.40852i
$694$			26.9210i			1.02191i
$695$	2.56265	−	1.12407i	0.0972068	−	0.0426383i
$696$	2.91218	+	5.04404i	0.110386	+	0.191194i
$697$	4.47523	−	16.7018i	0.169512	−	0.632626i
$698$	1.26368	+	4.71613i	0.0478311	+	0.178508i
$699$	15.6815			0.593130
$700$	7.98782	+	10.5449i	0.301911	+	0.398559i
$701$		−	15.8475i		−	0.598550i	−0.954167	−	0.299275i	$-0.903255\pi$
$701$		−	15.8475i		−	0.598550i	0.954167	−	0.299275i	$-0.0967449\pi$
$702$	−14.4069	+	3.86032i	−0.543754	+	0.145698i
$703$	−6.56603	+	24.5048i	−0.247643	+	0.924215i
$704$	−3.12381	−	1.11436i	−0.117733	−	0.0419991i
$705$	−26.8397	+	11.7728i	−1.01084	+	0.443391i
$706$			35.3212i			1.32933i
$707$	−7.49591	+	41.5620i	−0.281913	+	1.56310i
$708$	−7.12097	+	7.12097i	−0.267622	+	0.267622i
$709$	−6.23238	−	3.59827i	−0.234062	−	0.135136i	0.378382	−	0.925649i	$-0.376480\pi$
$709$	−6.23238	−	3.59827i	−0.234062	−	0.135136i	−0.612445	+	0.790514i	$0.709814\pi$
$710$	7.64531	+	9.54840i	0.286923	+	0.358345i
$711$	16.0531	−	9.26828i	0.602039	−	0.347588i
$712$	4.50085	+	16.7974i	0.168676	+	0.629509i
$713$	−43.8987	+	43.8987i	−1.64402	+	1.64402i
$714$	10.7281	+	15.4494i	0.401491	+	0.578179i
$715$	−22.0055	+	25.3600i	−0.822960	+	0.948410i
$716$	−0.286488	+	0.496211i	−0.0107066	+	0.0185443i
$717$	5.87128	+	1.57320i	0.219267	+	0.0587524i
$718$	9.56178	+	2.56207i	0.356843	+	0.0956157i
$719$	−38.8239	−	22.4150i	−1.44789	−	0.835938i	−0.449531	−	0.893265i	$-0.648409\pi$
$719$	−38.8239	−	22.4150i	−1.44789	−	0.835938i	−0.998355	+	0.0573267i	$0.981742\pi$
$720$	5.59587	−	7.61338i	0.208546	−	0.283734i
$721$	−33.7276	−	15.8880i	−1.25608	−	0.591701i
$722$	1.89017	−	1.89017i	0.0703447	−	0.0703447i
$723$	−58.7619	+	15.7452i	−2.18538	+	0.585571i
$724$	16.0351	−	9.25786i	0.595939	−	0.344066i
$725$	−7.33763	+	7.97063i	−0.272513	+	0.296022i
$726$	18.7145	−	22.8924i	0.694559	−	0.849617i
$727$	7.06351	+	7.06351i	0.261971	+	0.261971i	0.825854	−	0.563883i	$-0.190693\pi$
$727$	7.06351	+	7.06351i	0.261971	+	0.261971i	−0.563883	+	0.825854i	$0.690693\pi$
$728$	9.14592	+	7.73538i	0.338970	+	0.286692i
$729$		−	42.7134i		−	1.58198i
$730$	9.47884	−	4.15775i	0.350827	−	0.153885i
$731$	−13.5699	−	23.5038i	−0.501902	−	0.869320i
$732$	−5.85435	−	1.56867i	−0.216383	−	0.0579797i
$733$	−4.14896	+	1.11171i	−0.153245	+	0.0410620i	−0.334626	−	0.942351i	$-0.608610\pi$
$733$	−4.14896	+	1.11171i	−0.153245	+	0.0410620i	0.181381	+	0.983413i	$0.441943\pi$
$734$	−9.81684			−0.362346
$735$	13.1669	+	39.9612i	0.485667	+	1.47399i
$736$		−	6.54954i		−	0.241419i
$737$	8.44714	+	5.83446i	0.311154	+	0.214915i
$738$	−26.6851	−	7.15025i	−0.982293	−	0.263204i
$739$	13.8121	+	23.9232i	0.508085	+	0.880028i	0.999956	+	0.00936063i	$0.00297962\pi$
$739$	13.8121	+	23.9232i	0.508085	+	0.880028i	−0.491872	+	0.870668i	$0.663687\pi$
$740$	−5.10340	+	13.0787i	−0.187605	+	0.480782i
$741$	49.1746			1.80647
$742$	−13.5831	−	11.4882i	−0.498651	−	0.421746i
$743$	−4.81804	−	4.81804i	−0.176757	−	0.176757i	0.613184	−	0.789940i	$-0.289889\pi$
$743$	−4.81804	−	4.81804i	−0.176757	−	0.176757i	−0.789940	+	0.613184i	$0.789889\pi$
$744$	12.7398	−	22.0659i	0.467063	−	0.808976i
$745$	−4.97627	+	44.9588i	−0.182316	+	1.64716i
$746$	4.39993	+	7.62091i	0.161093	+	0.279021i
$747$	8.73859	+	32.6129i	0.319728	+	1.19324i
$748$	0.708495	−	8.74288i	0.0259051	−	0.319671i
$749$	−38.2749	−	18.0301i	−1.39853	−	0.658806i
$750$	28.4247	+	9.75871i	1.03792	+	0.356338i
$751$	−17.6877	+	30.6359i	−0.645432	+	1.11792i	0.338769	+	0.940869i	$0.389989\pi$
$751$	−17.6877	+	30.6359i	−0.645432	+	1.11792i	−0.984202	+	0.177052i	$0.943344\pi$
$752$	1.26201	−	4.70990i	0.0460209	−	0.171752i
$753$	20.5134	+	5.49656i	0.747551	+	0.200306i
$754$	−4.90495	+	8.49562i	−0.178628	+	0.309392i
$755$	17.2400	−	23.4556i	0.627428	−	0.853637i
$756$	7.15930	−	4.97146i	0.260381	−	0.180810i
$757$	−33.5247	−	33.5247i	−1.21848	−	1.21848i	−0.968166	−	0.250309i	$-0.919468\pi$
$757$	−33.5247	−	33.5247i	−1.21848	−	1.21848i	−0.250309	−	0.968166i	$-0.580532\pi$
$758$	12.5826	−	3.37150i	0.457021	−	0.122458i
$759$	54.9961	+	19.6189i	1.99623	+	0.712120i
$760$	−7.05292	+	5.64720i	−0.255836	+	0.204846i
$761$	31.2362	+	18.0343i	1.13231	+	0.653741i	0.944516	−	0.328467i	$-0.106532\pi$
$761$	31.2362	+	18.0343i	1.13231	+	0.653741i	0.187797	+	0.982208i	$0.439865\pi$
$762$	16.0909	+	16.0909i	0.582913	+	0.582913i
$763$	9.36336	+	1.68873i	0.338976	+	0.0611360i
$764$			5.33858i			0.193143i
$765$	23.2795	+	9.08385i	0.841674	+	0.328427i
$766$	−10.5640	+	6.09912i	−0.381692	+	0.220370i
$767$	−16.3838	−	4.39002i	−0.591584	−	0.158514i
$768$	0.695717	+	2.59645i	0.0251045	+	0.0936913i
$769$	−28.7886			−1.03814			−0.519072	−	0.854730i	$-0.673723\pi$
$769$	−28.7886			−1.03814			−0.519072	+	0.854730i	$0.673723\pi$
$770$	7.08687	−	18.2969i	0.255393	−	0.659374i
$771$	−48.1517			−1.73414
$772$	5.17346	+	19.3076i	0.186197	+	0.694897i
$773$	14.4885	+	3.88219i	0.521116	+	0.139633i	0.509783	−	0.860303i	$-0.329726\pi$
$773$	14.4885	+	3.88219i	0.521116	+	0.139633i	0.0113334	+	0.999936i	$0.496392\pi$

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-2.59645 - 0.695717i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.04774 - 0.898208i) q^{5} +2.68804i q^{6} +(1.70855 - 2.02011i) q^{7} +(0.707107 + 0.707107i) q^{8} +(3.65945 + 2.11279i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-2.59645 - 0.695717i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.04774 - 0.898208i) q^{5} +2.68804i q^{6} +(1.70855 - 2.02011i) q^{7} +(0.707107 + 0.707107i) q^{8} +(3.65945 + 2.11279i) q^{9} +(-1.39760 - 1.74549i) q^{10} +(-1.11436 + 3.12381i) q^{11} +(2.59645 - 0.695717i) q^{12} +(3.20138 + 3.20138i) q^{13} +(-2.39348 - 1.12749i) q^{14} +(-5.94174 + 0.907507i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.55460 + 0.684504i) q^{17} +(1.09366 - 4.08159i) q^{18} +(-2.02033 + 3.49931i) q^{19} +(-1.32429 + 1.80174i) q^{20} +(-5.84160 + 4.05644i) q^{21} +(3.30579 + 0.267890i) q^{22} +(1.69515 + 6.32637i) q^{23} +(-1.34402 - 2.32791i) q^{24} +(3.38645 - 3.67858i) q^{25} +(2.26372 - 3.92088i) q^{26} +(-2.32948 - 2.32948i) q^{27} +(-0.469598 + 2.60374i) q^{28} -2.16677 q^{29} +(2.41442 + 5.50440i) q^{30} +(4.73942 + 8.20892i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(5.06667 - 7.33554i) q^{33} -2.64472i q^{34} +(1.68419 - 5.67129i) q^{35} -4.22557 q^{36} +(6.06455 - 1.62499i) q^{37} +(3.90297 + 1.04580i) q^{38} +(-6.08497 - 10.5395i) q^{39} +(2.08310 + 0.812839i) q^{40} -6.53792i q^{41} +(5.43014 + 4.59267i) q^{42} +(-7.25627 - 7.25627i) q^{43} +(-0.596839 - 3.26248i) q^{44} +(9.39131 + 1.03948i) q^{45} +(5.67207 - 3.27477i) q^{46} +(4.70990 - 1.26201i) q^{47} +(-1.90073 + 1.90073i) q^{48} +(-1.16168 - 6.90293i) q^{49} +(-4.42972 - 2.31897i) q^{50} +(-6.15668 - 3.55456i) q^{51} +(-4.37317 - 1.17179i) q^{52} +(6.49482 + 1.74028i) q^{53} +(-1.64719 + 2.85302i) q^{54} +(0.523909 + 7.39767i) q^{55} +(2.63656 - 0.220302i) q^{56} +(7.68021 - 7.68021i) q^{57} +(0.560800 + 2.09293i) q^{58} +(-3.24450 + 1.87322i) q^{59} +(4.69195 - 3.75679i) q^{60} +(-1.95267 - 1.12738i) q^{61} +(6.70256 - 6.70256i) q^{62} +(10.5204 - 3.78268i) q^{63} +1.00000i q^{64} +(9.43109 + 3.68008i) q^{65} +(-8.39694 - 2.99546i) q^{66} +(0.801143 - 2.98991i) q^{67} +(-2.55460 + 0.684504i) q^{68} -17.6054i q^{69} +(-5.91394 - 0.158968i) q^{70} -5.47033 q^{71} +(1.09366 + 4.08159i) q^{72} +(-1.19806 + 4.47121i) q^{73} +(-3.13924 - 5.43733i) q^{74} +(-11.3520 + 7.19525i) q^{75} -4.04066i q^{76} +(4.40649 + 7.58834i) q^{77} +(-8.60545 + 8.60545i) q^{78} +(2.19338 - 3.79904i) q^{79} +(0.245997 - 2.22250i) q^{80} +(-1.91063 - 3.30931i) q^{81} +(-6.31515 + 1.69214i) q^{82} +(5.64995 + 5.64995i) q^{83} +(3.03075 - 6.43378i) q^{84} +(5.84598 - 0.892881i) q^{85} +(-5.13096 + 8.88708i) q^{86} +(5.62590 + 1.50745i) q^{87} +(-2.99684 + 1.42089i) q^{88} +(15.0601 + 8.69497i) q^{89} +(-1.42659 - 9.34035i) q^{90} +(11.9369 - 0.997403i) q^{91} +(-4.63123 - 4.63123i) q^{92} +(-6.59459 - 24.6113i) q^{93} +(-2.43803 - 4.22278i) q^{94} +(-0.993991 + 8.98034i) q^{95} +(2.32791 + 1.34402i) q^{96} +(5.74983 + 5.74983i) q^{97} +(-6.36706 + 2.90871i) q^{98} +(-10.6779 + 9.07703i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{5}+O(q^{10}) \) 192 * q + 8 * q^5	\( 192 q + 8 q^{5} + 4 q^{11} + 16 q^{15} + 96 q^{16} + 24 q^{22} - 8 q^{23} + 24 q^{25} - 8 q^{26} - 16 q^{33} - 160 q^{36} - 40 q^{37} - 40 q^{42} + 32 q^{45} - 40 q^{47} + 40 q^{53} + 8 q^{55} + 16 q^{56} + 32 q^{58} - 48 q^{67} - 72 q^{70} + 32 q^{71} - 48 q^{75} - 72 q^{77} - 8 q^{80} + 64 q^{81} + 16 q^{82} - 12 q^{88} - 112 q^{91} - 16 q^{92} + 80 q^{93} - 64 q^{97}+O(q^{100}) \) 192 * q + 8 * q^5 + 4 * q^11 + 16 * q^15 + 96 * q^16 + 24 * q^22 - 8 * q^23 + 24 * q^25 - 8 * q^26 - 16 * q^33 - 160 * q^36 - 40 * q^37 - 40 * q^42 + 32 * q^45 - 40 * q^47 + 40 * q^53 + 8 * q^55 + 16 * q^56 + 32 * q^58 - 48 * q^67 - 72 * q^70 + 32 * q^71 - 48 * q^75 - 72 * q^77 - 8 * q^80 + 64 * q^81 + 16 * q^82 - 12 * q^88 - 112 * q^91 - 16 * q^92 + 80 * q^93 - 64 * q^97

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