LMFDB - Embedded newform 770.2.bd.a.263.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(263,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 8, 6]))

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

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

chi := DirichletCharacter("770.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.14848095564$
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			263.3
Character	$\chi$	$=$	770.263
Dual form			770.2.bd.a.527.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-2.59645 + 0.695717i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.04774 + 0.898208i) q^{5} -2.68804i q^{6} +(1.70855 + 2.02011i) q^{7} +(0.707107 - 0.707107i) q^{8} +(3.65945 - 2.11279i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$

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	−0.912785	−	0.408440i	$-0.866073\pi$
$3$	−2.59645	+	0.695717i	−1.49906	+	0.401672i	−0.586275	+	0.810112i	$0.699406\pi$
$4$	−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	−0.106418	−	0.994322i	$-0.533938\pi$
$13$	3.20138	−	3.20138i	0.887904	−	0.887904i	0.994322	+	0.106418i	$0.0339381\pi$
$14$	−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	0.0646443	−	0.997908i	$-0.479409\pi$
$17$	2.55460	−	0.684504i	0.619582	−	0.166017i	0.554938	+	0.831892i	$0.312742\pi$
$18$	1.09366	+	4.08159i	0.257778	+	0.962040i
$19$	−2.02033	−	3.49931i	−0.463495	−	0.802797i	0.535637	−	0.844448i	$-0.320071\pi$
$19$	−2.02033	−	3.49931i	−0.463495	−	0.802797i	−0.999132	+	0.0416513i	$0.986738\pi$
$20$	−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	−0.528946	−	0.848656i	$-0.677413\pi$
$23$	1.69515	−	6.32637i	0.353462	−	1.31914i	0.882408	−	0.470484i	$-0.155921\pi$
$24$	−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	−0.0288777	−	0.999583i	$-0.509193\pi$
$31$	4.73942	−	8.20892i	0.851225	−	1.47437i	0.880103	−	0.474783i	$-0.157473\pi$
$32$	−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	0.720191	−	0.693776i	$-0.244054\pi$
$37$	6.06455	+	1.62499i	0.997006	+	0.267147i	0.276816	+	0.960923i	$0.410721\pi$
$38$	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	$0.170549\pi$
$41$			6.53792i			1.02105i	−0.859862	+	0.510526i	$0.829451\pi$
$42$	5.43014	−	4.59267i	0.837889	−	0.708664i
$43$	−7.25627	+	7.25627i	−1.10657	+	1.10657i	−0.112972	+	0.993598i	$0.536037\pi$
$43$	−7.25627	+	7.25627i	−1.10657	+	1.10657i	−0.993598	+	0.112972i	$0.963963\pi$
$44$	−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	0.585405	−	0.810741i	$-0.300936\pi$
$47$	4.70990	+	1.26201i	0.687010	+	0.184084i	0.101605	+	0.994825i	$0.467602\pi$
$48$	−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	0.216498	−	0.976283i	$-0.430536\pi$
$53$	6.49482	−	1.74028i	0.892132	−	0.239046i	0.675634	+	0.737237i	$0.263870\pi$
$54$	−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	0.273704	−	0.961814i	$-0.411751\pi$
$59$	−3.24450	−	1.87322i	−0.422399	−	0.243872i	−0.696103	+	0.717942i	$0.745084\pi$
$60$	4.69195	+	3.75679i	0.605728	+	0.485000i
$61$	−1.95267	+	1.12738i	−0.250014	+	0.144346i	−0.619771	−	0.784783i	$-0.712774\pi$
$61$	−1.95267	+	1.12738i	−0.250014	+	0.144346i	0.369757	+	0.929129i	$0.379441\pi$
$62$	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	0.997440	−	0.0715127i	$-0.0227826\pi$
$67$	0.801143	+	2.98991i	0.0978752	+	0.365275i	−0.899564	+	0.436788i	$0.856116\pi$
$68$	−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	−0.999922	−	0.0125156i	$-0.996016\pi$
$73$	−1.19806	−	4.47121i	−0.140222	−	0.523315i	0.859700	−	0.510800i	$-0.170651\pi$
$74$	−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	0.962629	−	0.270824i	$-0.0872960\pi$
$79$	2.19338	+	3.79904i	0.246774	+	0.427426i	−0.715855	+	0.698249i	$0.753963\pi$
$80$	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	−0.325410	−	0.945573i	$-0.605502\pi$
$83$	5.64995	−	5.64995i	0.620163	−	0.620163i	0.945573	+	0.325410i	$0.105502\pi$
$84$	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	0.604193	−	0.796838i	$-0.293496\pi$
$89$	15.0601	−	8.69497i	1.59637	−	0.921665i	0.992179	−	0.124827i	$-0.0398376\pi$
$90$	−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	−0.352140	−	0.935947i	$-0.614546\pi$
$97$	5.74983	−	5.74983i	0.583807	−	0.583807i	0.935947	+	0.352140i	$0.114546\pi$
$98$	−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	−0.383908	−	0.923371i	$-0.625422\pi$
$101$	−13.8239	−	7.98121i	−1.37553	−	0.794160i	−0.991617	+	0.129211i	$0.958755\pi$
$102$	−1.83998	−	6.86688i	−0.182185	−	0.679922i
$103$	−3.64713	+	13.6113i	−0.359363	+	1.34116i	0.515542	+	0.856864i	$0.327591\pi$
$103$	−3.64713	+	13.6113i	−0.359363	+	1.34116i	−0.874904	+	0.484296i	$0.839076\pi$
$104$		−	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	0.412767	+	0.910837i	$0.364562\pi$
$107$	−4.13885	+	15.4464i	−0.400118	+	1.49326i	−0.812885	+	0.582424i	$0.802104\pi$
$108$	3.18214	−	0.852651i	0.306201	−	0.0820463i
$109$	1.79806	−	3.11433i	0.172223	−	0.298298i	−0.766974	−	0.641678i	$-0.778238\pi$
$109$	1.79806	−	3.11433i	0.172223	−	0.298298i	0.939197	+	0.343380i	$0.111572\pi$
$110$	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	−0.997829	−	0.0658550i	$-0.979023\pi$
$113$	−11.3071	−	11.3071i	−1.06368	−	1.06368i	−0.0658550	−	0.997829i	$-0.520977\pi$
$114$	−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	0.920924	−	0.389742i	$-0.127436\pi$
$127$	5.98612	+	5.98612i	0.531182	+	0.531182i	−0.389742	+	0.920924i	$0.627436\pi$
$128$	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	−0.0567680	−	0.998387i	$-0.518080\pi$
$131$	8.92152	−	5.15084i	0.779477	−	0.450031i	0.836245	+	0.548356i	$0.184746\pi$
$132$	−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	0.981265	+	0.192660i	$0.0617116\pi$
$137$	2.66627	+	9.95066i	0.227795	+	0.850142i	−0.753471	+	0.657482i	$0.771622\pi$
$138$	−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	−0.899128	−	0.437686i	$-0.855798\pi$
$149$	−10.1145	−	17.5188i	−0.828611	−	1.43520i	0.0705173	−	0.997511i	$-0.477535\pi$
$150$	9.88819	−	9.10291i	0.807367	−	0.743249i
$151$	11.2742	+	6.50916i	0.917481	+	0.529708i	0.882831	−	0.469692i	$-0.155635\pi$
$151$	11.2742	+	6.50916i	0.917481	+	0.529708i	0.0346504	+	0.999399i	$0.488968\pi$
$152$	−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	−0.961449	−	0.274984i	$-0.911327\pi$
$157$	−3.33675	−	12.4529i	−0.266302	−	0.993852i	0.695147	−	0.718868i	$-0.255339\pi$
$158$	−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	0.617951	+	0.786216i	$0.287963\pi$
$163$	−3.96188	+	14.7859i	−0.310318	+	1.15812i	−0.928270	+	0.371907i	$0.878704\pi$
$164$	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	−0.999313	−	0.0370650i	$-0.988199\pi$
$167$	−13.3930	−	13.3930i	−1.03638	−	1.03638i	−0.0370650	−	0.999313i	$-0.511801\pi$
$168$	−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	0.276710	−	0.960953i	$-0.410756\pi$
$173$	0.471822	+	0.126424i	0.0358719	+	0.00961186i	−0.240838	+	0.970565i	$0.577422\pi$
$174$			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	0.518430	−	0.855120i	$-0.326517\pi$
$179$	0.496211	+	0.286488i	0.0370886	+	0.0214131i	−0.481341	+	0.876533i	$0.659850\pi$
$180$	−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	0.946290	−	0.323319i	$-0.104799\pi$
$191$	2.66929	+	4.62334i	0.193143	+	0.334533i	−0.753147	+	0.657852i	$0.771465\pi$
$192$	0.695717	+	2.59645i	0.0502090	+	0.187383i
$193$	5.17346	+	19.3076i	0.372394	+	1.38979i	0.857115	+	0.515125i	$0.172254\pi$
$193$	5.17346	+	19.3076i	0.372394	+	1.38979i	−0.484721	+	0.874669i	$0.661079\pi$
$194$	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	0.904492	−	0.426491i	$-0.140251\pi$
$197$	6.70905	+	6.70905i	0.478000	+	0.478000i	−0.426491	+	0.904492i	$0.640251\pi$
$198$	11.5314	−	7.96475i	0.819499	−	0.566030i
$199$	−2.58858	−	1.49452i	−0.183499	−	0.105943i	0.405436	−	0.914123i	$-0.367120\pi$
$199$	−2.58858	−	1.49452i	−0.183499	−	0.105943i	−0.588936	+	0.808180i	$0.700453\pi$
$200$	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	$-0.892853\pi$
$211$		−	9.59556i		−	0.660586i	0.943879	−	0.330293i	$-0.107147\pi$
$212$	−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	0.997821	+	0.0659793i	$0.0210171\pi$
$223$	15.8859	+	15.8859i	1.06380	+	1.06380i	0.0659793	+	0.997821i	$0.478983\pi$
$224$	−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	0.116748	−	0.993162i	$-0.462753\pi$
$227$	10.7641	−	2.88422i	0.714436	−	0.191433i	0.597688	+	0.801729i	$0.296086\pi$
$228$	−2.81115	−	10.4914i	−0.186173	−	0.694807i
$229$	18.5411	−	10.7047i	1.22523	−	0.707389i	0.259204	−	0.965823i	$-0.416540\pi$
$229$	18.5411	−	10.7047i	1.22523	−	0.707389i	0.966029	+	0.258434i	$0.0832064\pi$
$230$	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	0.0694681	−	0.997584i	$-0.477870\pi$
$233$	−5.63503	−	1.50990i	−0.369163	−	0.0989169i	−0.438631	+	0.898667i	$0.644536\pi$
$234$	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	0.973561	−	0.228425i	$-0.0733577\pi$
$241$	19.5996	+	11.3158i	1.26252	+	0.728916i	0.288959	+	0.957342i	$0.406691\pi$
$242$	−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	0.754320	−	0.656507i	$-0.227967\pi$
$257$	17.3029	+	4.63630i	1.07933	+	0.289205i	0.325007	+	0.945712i	$0.394633\pi$
$258$	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	−0.916249	−	0.400610i	$-0.868798\pi$
$263$	−5.23914	−	19.5527i	−0.323059	−	1.20567i	0.593189	−	0.805063i	$-0.297869\pi$
$264$	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	0.284086	−	0.958799i	$-0.408310\pi$
$269$	−6.62961	−	3.82761i	−0.404215	−	0.233373i	−0.688301	+	0.725425i	$0.741643\pi$
$270$	−0.810411	−	7.32176i	−0.0493200	−	0.445588i
$271$	−3.39858	+	1.96217i	−0.206449	+	0.119194i	−0.599660	−	0.800255i	$-0.704698\pi$
$271$	−3.39858	+	1.96217i	−0.206449	+	0.119194i	0.393211	+	0.919448i	$0.371364\pi$
$272$	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	0.0358900	−	0.999356i	$-0.488573\pi$
$277$	9.43093	−	2.52701i	0.566650	−	0.151833i	0.530760	+	0.847522i	$0.321907\pi$
$278$	−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	$0.00944575\pi$
$281$			0.994731i			0.0593407i	−0.999560	+	0.0296703i	$0.990554\pi$
$282$	3.39235	−	12.6604i	0.202011	−	0.753917i
$283$	3.37200	+	12.5845i	0.200445	+	0.748070i	0.990790	+	0.135408i	$0.0432345\pi$
$283$	3.37200	+	12.5845i	0.200445	+	0.748070i	−0.790345	+	0.612662i	$0.790099\pi$
$284$	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	−0.920423	−	0.390925i	$-0.872155\pi$
$293$	−9.06354	+	9.06354i	−0.529498	+	0.529498i	0.390925	+	0.920423i	$0.372155\pi$
$294$	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	0.994505	−	0.104692i	$-0.0333857\pi$
$307$	15.5908	+	15.5908i	0.889813	+	0.889813i	−0.104692	+	0.994505i	$0.533386\pi$
$308$	−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	−0.730163	−	0.683273i	$-0.760556\pi$
$311$	3.99701	−	6.92303i	0.226650	−	0.392569i	0.956813	+	0.290704i	$0.0938894\pi$
$312$	3.14981	+	11.7553i	0.178323	+	0.665511i
$313$	2.35326	−	8.78249i	0.133014	−	0.496416i	−0.866984	−	0.498336i	$-0.833945\pi$
$313$	2.35326	−	8.78249i	0.133014	−	0.496416i	0.999998	+	0.00192030i	$0.000611252\pi$
$314$	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	0.248227	−	0.968702i	$-0.420152\pi$
$317$	−0.376636	−	0.100919i	−0.0211540	−	0.00566819i	−0.269381	+	0.963034i	$0.586819\pi$
$318$	−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	0.895181	−	0.445702i	$-0.147046\pi$
$331$	1.12074	+	1.94118i	0.0616015	+	0.106697i	−0.833580	+	0.552399i	$0.813713\pi$
$332$	−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	0.522341	−	0.852736i	$-0.325059\pi$
$337$	−6.06525	−	6.06525i	−0.330395	−	0.330395i	−0.852736	+	0.522341i	$0.825059\pi$
$338$	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	−0.876889	−	0.480693i	$-0.840385\pi$
$347$	−26.0037	+	6.96766i	−1.39595	+	0.374044i	−0.519061	+	0.854737i	$0.673718\pi$
$348$	−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	−0.996267	−	0.0863226i	$-0.972488\pi$
$353$	−34.1176	+	9.14179i	−1.81590	+	0.486569i	−0.819631	+	0.572891i	$0.805822\pi$
$354$	−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	0.705341	−	0.708868i	$-0.250794\pi$
$359$	−4.94954	−	8.57286i	−0.261227	−	0.452458i	−0.966568	+	0.256410i	$0.917460\pi$
$360$	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	0.999996	−	0.00269244i	$-0.000857030\pi$
$367$	2.54078	+	9.48234i	0.132628	+	0.494974i	−0.867368	+	0.497666i	$0.834190\pi$
$368$	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	0.0319557	−	0.999489i	$-0.489826\pi$
$373$	−8.50002	−	2.27757i	−0.440114	−	0.117928i	−0.472070	+	0.881561i	$0.656493\pi$
$374$	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	$-0.891411\pi$
$379$		−	13.0265i		−	0.669126i	0.942373	−	0.334563i	$-0.108589\pi$
$380$	−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	0.837158	+	0.546960i	$0.184215\pi$
$383$	−3.15714	+	11.7826i	−0.161322	+	0.602063i	−0.998481	+	0.0551023i	$0.982451\pi$
$384$	−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	0.0607111	−	0.998155i	$-0.480663\pi$
$389$	−15.2531	−	8.80636i	−0.773361	−	0.446500i	−0.834072	+	0.551655i	$0.813996\pi$
$390$	−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	0.455088	−	0.890447i	$-0.349608\pi$
$397$	8.04928	+	2.15680i	0.403982	+	0.108247i	−0.0511057	+	0.998693i	$0.516275\pi$
$398$	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	0.997019	+	0.0771616i	$0.0245857\pi$
$401$	11.3208	+	19.6082i	0.565333	+	0.979186i	−0.431685	+	0.902024i	$0.642081\pi$
$402$	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	−0.810421	−	0.585848i	$-0.800762\pi$
$409$	2.06583	−	3.57813i	0.102149	−	0.176927i	0.912570	+	0.408921i	$0.134095\pi$
$410$	−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	$-0.721154\pi$
$419$		−	31.4492i		−	1.53640i	0.640213	−	0.768198i	$-0.278846\pi$
$420$	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	0.940211	−	0.340592i	$-0.110628\pi$
$431$	23.1554	+	13.3688i	1.11536	+	0.643951i	0.175144	+	0.984543i	$0.443961\pi$
$432$	−3.18214	−	0.852651i	−0.153101	−	0.0410232i
$433$	−0.525794	−	0.525794i	−0.0252680	−	0.0252680i	0.694360	−	0.719628i	$-0.255688\pi$
$433$	−0.525794	−	0.525794i	−0.0252680	−	0.0252680i	−0.719628	+	0.694360i	$0.755688\pi$
$434$	−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	0.996428	−	0.0844504i	$-0.0269135\pi$
$439$	8.90637	+	15.4263i	0.425078	+	0.736256i	−0.571350	+	0.820706i	$0.693580\pi$
$440$	−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	−0.868232	−	0.496159i	$-0.834743\pi$
$443$	2.77319	−	10.3497i	0.131758	−	0.491729i	0.999990	+	0.00442990i	$0.00141009\pi$
$444$	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	$0.318576\pi$
$449$			35.6800i			1.68385i	−0.539598	+	0.841923i	$0.681424\pi$
$450$	−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	−0.931213	−	0.364476i	$-0.881248\pi$
$457$	1.22876	−	4.58580i	0.0574790	−	0.214515i	0.988692	+	0.149961i	$0.0479149\pi$
$458$	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	$0.0111884\pi$
$461$			1.50907i			0.0702842i	−0.999382	+	0.0351421i	$0.988812\pi$
$462$	−20.3978	−	11.8448i	−0.948990	−	0.551071i
$463$	14.2220	+	14.2220i	0.660952	+	0.660952i	0.955604	−	0.294653i	$-0.0952039\pi$
$463$	14.2220	+	14.2220i	0.660952	+	0.660952i	−0.294653	+	0.955604i	$0.595204\pi$
$464$	−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	0.342566	−	0.939494i	$-0.388704\pi$
$467$	3.66271	+	0.981421i	0.169490	+	0.0454148i	−0.173076	+	0.984908i	$0.555371\pi$
$468$	−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	−0.847430	−	0.530907i	$-0.821851\pi$
$479$	0.789292	−	1.36709i	0.0360637	−	0.0624641i	0.883494	+	0.468443i	$0.155185\pi$
$480$	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	0.965523	−	0.260317i	$-0.0838270\pi$
$487$	−0.0177171	−	0.0661211i	−0.000802838	−	0.00299623i	−0.966326	+	0.257321i	$0.917160\pi$
$488$	−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	$-0.796689\pi$
$491$		−	26.4205i		−	1.19234i	0.802858	−	0.596170i	$-0.203311\pi$
$492$	−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	−0.119218	−	0.992868i	$-0.538039\pi$
$499$	15.2129	−	8.78316i	0.681022	−	0.393188i	0.800240	+	0.599680i	$0.204705\pi$
$500$	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	0.227805	−	0.973707i	$-0.426845\pi$
$503$	26.9471	−	26.9471i	1.20151	−	1.20151i	0.973707	−	0.227805i	$-0.0731550\pi$
$504$	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	−0.589938	−	0.807448i	$-0.700848\pi$
$509$	−4.18815	+	2.41803i	−0.185637	+	0.107177i	0.404302	+	0.914626i	$0.367515\pi$
$510$	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	−0.940943	−	0.338566i	$-0.890058\pi$
$521$	−4.04614	+	7.00812i	−0.177265	+	0.307031i	0.763678	+	0.645597i	$0.223392\pi$
$522$	−2.36970	−	8.84385i	−0.103719	−	0.387085i
$523$	−1.07264	−	0.287414i	−0.0469034	−	0.0125677i	0.235291	−	0.971925i	$-0.424396\pi$
$523$	−1.07264	−	0.287414i	−0.0469034	−	0.0125677i	−0.282194	+	0.959357i	$0.591062\pi$
$524$	−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	−0.408273	−	0.912860i	$-0.633869\pi$
$541$	4.14369	−	2.39236i	0.178151	−	0.102856i	0.586424	+	0.810004i	$0.300535\pi$
$542$	−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	0.633653	−	0.773617i	$-0.281555\pi$
$547$	−3.27348	−	3.27348i	−0.139964	−	0.139964i	−0.773617	+	0.633653i	$0.781555\pi$
$548$	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	−0.995074	−	0.0991383i	$-0.968391\pi$
$557$	−42.6530	+	11.4288i	−1.80726	+	0.484255i	−0.812190	+	0.583393i	$0.801725\pi$
$558$	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	0.995331	+	0.0965222i	$0.0307719\pi$
$563$	4.30918	+	16.0821i	0.181610	+	0.677778i	−0.813721	+	0.581256i	$0.802561\pi$
$564$	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	−0.889442	−	0.457048i	$-0.848907\pi$
$569$	−20.0499	−	34.7275i	−0.840536	−	1.45585i	0.0489060	−	0.998803i	$-0.484427\pi$
$570$	−24.1395	+	2.67189i	−1.01109	+	0.111913i
$571$	22.5866	+	13.0404i	0.945219	+	0.545723i	0.891593	−	0.452838i	$-0.149589\pi$
$571$	22.5866	+	13.0404i	0.945219	+	0.545723i	0.0536268	+	0.998561i	$0.482922\pi$
$572$	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	0.966233	−	0.257669i	$-0.0829544\pi$
$577$	0.0148009	+	0.0552379i	0.000616171	+	0.00229958i	−0.965617	+	0.259969i	$0.916288\pi$
$578$	−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	−0.966586	−	0.256343i	$-0.917482\pi$
$587$	−17.2078	+	17.2078i	−0.710242	+	0.710242i	0.256343	+	0.966586i	$0.417482\pi$
$588$	−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	0.796939	−	0.604059i	$-0.206451\pi$
$593$	28.8586	+	7.73263i	1.18508	+	0.317541i	0.388140	+	0.921600i	$0.373118\pi$
$594$	−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	0.332606	−	0.943066i	$-0.392072\pi$
$599$	−7.77821	−	4.49075i	−0.317809	−	0.183487i	−0.650416	+	0.759579i	$0.725405\pi$
$600$	−13.1149	+	2.93926i	−0.535413	+	0.119995i
$601$			42.9190i			1.75070i	0.483488	+	0.875351i	$0.339370\pi$
$601$			42.9190i			1.75070i	−0.483488	+	0.875351i	$0.660630\pi$
$602$	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	0.552473	+	0.833531i	$0.313684\pi$
$607$	−8.44441	+	31.5150i	−0.342748	+	1.27915i	−0.895221	+	0.445622i	$0.852982\pi$
$608$	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	−0.782504	−	0.622646i	$-0.786058\pi$
$613$	−10.3036	−	38.4536i	−0.416158	−	1.55312i	0.366346	−	0.930479i	$-0.380609\pi$
$614$	−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	−0.597374	−	0.801963i	$-0.703789\pi$
$617$	5.08189	−	5.08189i	0.204589	−	0.204589i	0.801963	+	0.597374i	$0.203789\pi$
$618$	36.5877	+	9.80365i	1.47177	+	0.394361i
$619$	−27.4630	−	15.8558i	−1.10383	−	0.637298i	−0.166607	−	0.986023i	$-0.553281\pi$
$619$	−27.4630	−	15.8558i	−1.10383	−	0.637298i	−0.937225	+	0.348726i	$0.886615\pi$
$620$	−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	−0.707048	−	0.707166i	$-0.749974\pi$
$641$	6.55481	−	11.3533i	0.258899	−	0.448427i	0.965947	+	0.258739i	$0.0833069\pi$
$642$	41.5206	+	11.1254i	1.63869	+	0.439085i
$643$	8.98489	+	8.98489i	0.354329	+	0.354329i	0.861718	−	0.507388i	$-0.169389\pi$
$643$	8.98489	+	8.98489i	0.354329	+	0.354329i	−0.507388	+	0.861718i	$0.669389\pi$
$644$	−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	−0.694583	−	0.719413i	$-0.744411\pi$
$647$	−11.5166	−	42.9804i	−0.452763	−	1.68973i	0.241820	−	0.970321i	$-0.422256\pi$
$648$	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	−0.488059	−	0.872811i	$-0.662295\pi$
$653$	9.48094	−	35.3833i	0.371018	−	1.38466i	0.859077	−	0.511847i	$-0.171038\pi$
$654$	−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	−0.846300	−	0.532707i	$-0.821175\pi$
$661$	0.981802	−	1.70053i	0.0381877	−	0.0661430i	0.884488	+	0.466564i	$0.154508\pi$
$662$	−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	−0.400968	+	0.916092i	$0.631326\pi$
$673$	−34.1675	+	34.1675i	−1.31706	+	1.31706i	−0.916092	+	0.400968i	$0.868674\pi$
$674$	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	−0.593436	−	0.804881i	$-0.702229\pi$
$677$	8.40252	−	31.3586i	0.322935	−	1.20521i	0.916371	−	0.400330i	$-0.131104\pi$
$678$	−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	−0.284656	−	0.958630i	$-0.591879\pi$
$683$	−1.35535	+	0.363164i	−0.0518609	+	0.0138961i	0.232795	+	0.972526i	$0.425213\pi$
$684$	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	0.996001	+	0.0893466i	$0.0284779\pi$
$691$	15.1249	+	26.1970i	0.575377	+	0.996582i	−0.420624	+	0.907235i	$0.638189\pi$
$692$	−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	$0.0967449\pi$
$701$			15.8475i			0.598550i	−0.954167	+	0.299275i	$0.903255\pi$
$702$	−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	−0.612445	−	0.790514i	$-0.709814\pi$
$709$	−6.23238	+	3.59827i	−0.234062	+	0.135136i	0.378382	+	0.925649i	$0.376480\pi$
$710$	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	−0.998355	−	0.0573267i	$-0.981742\pi$
$719$	−38.8239	+	22.4150i	−1.44789	+	0.835938i	−0.449531	+	0.893265i	$0.648409\pi$
$720$	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	−0.563883	−	0.825854i	$-0.690693\pi$
$727$	7.06351	−	7.06351i	0.261971	−	0.261971i	0.825854	+	0.563883i	$0.190693\pi$
$728$	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	0.181381	−	0.983413i	$-0.441943\pi$
$733$	−4.14896	−	1.11171i	−0.153245	−	0.0410620i	−0.334626	+	0.942351i	$0.608610\pi$
$734$	−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	−0.491872	−	0.870668i	$-0.663687\pi$
$739$	13.8121	−	23.9232i	0.508085	−	0.880028i	0.999956	−	0.00936063i	$-0.00297962\pi$
$740$	−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	−0.789940	−	0.613184i	$-0.789889\pi$
$743$	−4.81804	+	4.81804i	−0.176757	+	0.176757i	0.613184	+	0.789940i	$0.289889\pi$
$744$	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	−0.984202	−	0.177052i	$-0.943344\pi$
$751$	−17.6877	−	30.6359i	−0.645432	−	1.11792i	0.338769	−	0.940869i	$-0.389989\pi$
$752$	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	−0.250309	+	0.968166i	$0.580532\pi$
$757$	−33.5247	+	33.5247i	−1.21848	+	1.21848i	−0.968166	+	0.250309i	$0.919468\pi$
$758$	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	0.187797	−	0.982208i	$-0.439865\pi$
$761$	31.2362	−	18.0343i	1.13231	−	0.653741i	0.944516	+	0.328467i	$0.106532\pi$
$762$	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	0.0113334	−	0.999936i	$-0.496392\pi$
$773$	14.4885	−	3.88219i	0.521116	−	0.139633i	0.509783	+	0.860303i	$0.329726\pi$
$774$	−37.5530	−	21.6812i	−1.34981	−	0.779315i
$775$	46.2470	−	10.3647i	1.66124	−	0.372311i
$776$		−	8.13149i		−	0.291903i
$777$	−28.8350	−	34.0931i	−1.03445	−	1.22308i
$778$	12.4541	−	12.4541i	0.446500	−	0.446500i
$779$	22.8782	−	13.2087i	0.819697	−	0.473253i
$780$	27.0476	−	2.99377i	0.968461	−	0.107194i
$781$	6.09594	+	17.0883i	0.218130	+	0.611467i
$782$	16.7315	+	4.48319i	0.598317	+	0.160318i
$783$	5.04745	−	5.04745i	0.180381	−	0.180381i
$784$	−6.55896	+	2.44542i	−0.234248	+	0.0873365i
$785$	4.35253	−	28.4974i	0.155348	−	1.01712i
$786$	−13.8457	−	23.9814i	−0.493859	−	0.855389i
$787$	−29.5199	+	7.90983i	−1.05227	+	0.281955i	−0.743189	−	0.669081i	$-0.766688\pi$
$787$	−29.5199	+	7.90983i	−1.05227	+	0.281955i	−0.309080	+	0.951036i	$0.600021\pi$
$788$	−2.45568	−	9.16474i	−0.0874801	−	0.326480i
$789$	27.2063	+	47.1227i	0.968571	+	1.67761i
$790$	−9.69664	−	1.48101i	−0.344991	−	0.0526919i
$791$	3.52278	−	42.1604i	0.125256	−	1.49905i
$792$	−13.9688	+	1.13199i	−0.496361	+	0.0402235i
$793$	−2.64209	+	9.86042i	−0.0938234	+	0.350154i
$794$	−4.16662	+	7.21679i	−0.147868	+	0.256114i
$795$	−40.1699	+	4.44621i	−1.42468	+	0.157691i
$796$	1.49452	+	2.58858i	0.0529717	+	0.0917497i
$797$	−21.9988	+	21.9988i	−0.779239	+	0.779239i	−0.979701	−	0.200462i	$-0.935756\pi$
$797$	−21.9988	+	21.9988i	−0.779239	+	0.779239i	0.200462	+	0.979701i	$0.435756\pi$
$798$	−27.0418	−	9.72305i	−0.957271	−	0.344192i
$799$	12.8958			0.456220
$800$	−4.22314	−	2.67676i	−0.149311	−	0.0946379i
$801$	36.7412	−	63.6377i	1.29819	−	2.24853i
$802$	−21.8701	+	5.86007i	−0.772260	+	0.206926i
$803$	−12.6321	+	8.72505i	−0.445778	+	0.307900i
$804$			8.32051i			0.293442i
$805$	38.7336	−	1.04117i	1.36518	−	0.0366962i
$806$	42.9149			1.51161
$807$	19.8764	+	5.32586i	0.699682	+	0.187479i
$808$	−15.4185	+	4.13138i	−0.542421	+	0.145341i
$809$	14.0707	−	24.3711i	0.494698	−	0.856842i	−0.505283	−	0.862954i	$-0.668612\pi$
$809$	14.0707	−	24.3711i	0.494698	−	0.856842i	0.999981	+	0.00611117i	$0.00194526\pi$
$810$	−3.10607	−	7.96005i	−0.109136	−	0.279688i
$811$			42.4074i			1.48912i	0.667553	+	0.744562i	$0.267342\pi$
$811$			42.4074i			1.48912i	−0.667553	+	0.744562i	$0.732658\pi$
$812$	1.01751	+	5.64170i	0.0357075	+	0.197985i
$813$	7.45914	−	7.45914i	0.261603	−	0.261603i
$814$	20.4834	+	3.74724i	0.717944	+	0.131341i
$815$	−21.3937	+	26.7191i	−0.749389	+	0.935929i
$816$	−6.15668	−	3.55456i	−0.215527	−	0.124434i
$817$	40.0520	+	10.7319i	1.40124	+	0.375461i
$818$	2.92153	+	2.92153i	0.102149	+	0.102149i
$819$	45.7897	−	21.5701i	1.60002	−	0.753721i
$820$	11.7796	−	8.65809i	0.411362	−	0.302354i
$821$	−28.0932	+	16.2196i	−0.980460	+	0.566069i	−0.902409	−	0.430881i	$-0.858203\pi$
$821$	−28.0932	+	16.2196i	−0.980460	+	0.566069i	−0.0780508	+	0.996949i	$0.524870\pi$
$822$	26.7478	−	7.16705i	0.932936	−	0.249980i
$823$	−35.6548	+	9.55368i	−1.24285	+	0.333021i	−0.819570	−	0.572979i	$-0.805788\pi$
$823$	−35.6548	+	9.55368i	−1.24285	+	0.333021i	−0.423279	+	0.905999i	$0.639121\pi$
$824$	7.04572	+	12.2035i	0.245449	+	0.425131i
$825$	−9.82637	+	43.4796i	−0.342110	+	1.51376i
$826$	9.87770	+	0.825346i	0.343689	+	0.0287175i
$827$	37.0076	+	37.0076i	1.28688	+	1.28688i	0.936671	+	0.350210i	$0.113890\pi$
$827$	37.0076	+	37.0076i	1.28688	+	1.28688i	0.350210	+	0.936671i	$0.386110\pi$
$828$	−7.16296	+	26.7325i	−0.248930	+	0.929020i
$829$	−16.5715	−	9.56754i	−0.575551	−	0.332294i	0.183812	−	0.982961i	$-0.441156\pi$
$829$	−16.5715	−	9.56754i	−0.575551	−	0.332294i	−0.759363	+	0.650667i	$0.774489\pi$
$830$	1.96558	+	17.7583i	0.0682261	+	0.616398i
$831$	−22.7288	+	13.1225i	−0.788455	+	0.455215i
$832$	−3.20138	−	3.20138i	−0.110988	−	0.110988i
$833$	1.75745	+	18.4294i	0.0608922	+	0.638542i
$834$		−	3.36396i		−	0.116484i
$835$	−15.3956	−	39.4549i	−0.532786	−	1.36539i
$836$	12.6222	−	4.50276i	0.436549	−	0.155731i
$837$	8.08214	+	30.1630i	0.279360	+	1.04258i
$838$	30.3776	+	8.13966i	1.04938	+	0.281180i
$839$			22.1231i			0.763775i	0.924209	+	0.381887i	$0.124726\pi$
$839$			22.1231i			0.763775i	−0.924209	+	0.381887i	$0.875274\pi$
$840$	−15.4659	−	3.70168i	−0.533623	−	0.127720i
$841$	−24.3051			−0.838108
$842$	−0.452589	+	1.68909i	−0.0155973	+	0.0582098i
$843$	−0.692051	−	2.58277i	−0.0238355	−	0.0889553i
$844$	−4.79778	+	8.31000i	−0.165146	+	0.286042i
$845$	6.73449	−	15.3533i	0.231674	−	0.528170i
$846$			20.6041i			0.708384i
$847$	−28.6150	−	5.30887i	−0.983222	−	0.182415i
$848$	4.75454	+	4.75454i	0.163272	+	0.163272i
$849$	−17.5105	−	30.3290i	−0.600957	−	1.04089i
$850$	−9.72882	+	8.95620i	−0.333696	+	0.307195i
$851$	20.5606	−	35.6120i	0.704809	−	1.22076i
$852$	−14.2034	−	3.80580i	−0.486602	−	0.130385i
$853$	29.9751	−	29.9751i	1.02633	−	1.02633i	0.0266822	−	0.999644i	$-0.491506\pi$
$853$	29.9751	−	29.9751i	1.02633	−	1.02633i	0.999644	−	0.0266822i	$-0.00849423\pi$
$854$	3.40258	−	4.89999i	0.116434	−	0.167674i
$855$	−22.6110	−	30.7630i	−0.773280	−	1.05207i
$856$	7.99565	+	13.8489i	0.273286	+	0.473345i
$857$	−32.5284	+	8.71596i	−1.11115	+	0.297732i	−0.767297	−	0.641292i	$-0.778399\pi$
$857$	−32.5284	+	8.71596i	−1.11115	+	0.297732i	−0.343853	+	0.939024i	$0.611732\pi$
$858$	−17.2922	+	36.4714i	−0.590346	+	1.24511i
$859$	−10.7169	+	6.18738i	−0.365654	+	0.211111i	−0.671558	−	0.740952i	$-0.734375\pi$
$859$	−10.7169	+	6.18738i	−0.365654	+	0.211111i	0.305904	+	0.952062i	$0.401041\pi$
$860$	22.6833	+	3.46451i	0.773493	+	0.118139i
$861$	26.5207	−	38.1919i	0.903823	−	1.30158i
$862$	−18.9063	+	18.9063i	−0.643951	+	0.643951i
$863$	−9.21470	+	34.3897i	−0.313672	+	1.17064i	0.611547	+	0.791208i	$0.290547\pi$
$863$	−9.21470	+	34.3897i	−0.313672	+	1.17064i	−0.925219	+	0.379433i	$0.876119\pi$
$864$	1.64719	−	2.85302i	0.0560387	−	0.0970619i
$865$	0.852611	+	0.682677i	0.0289896	+	0.0232117i
$866$	0.643963	−	0.371792i	0.0218828	−	0.0126340i
$867$	19.0177	−	19.0177i	0.645875	−	0.645875i
$868$	−23.5995	−	8.48535i	−0.801021	−	0.288012i
$869$	9.42327	−	11.0852i	0.319663	−	0.376040i
$870$	−5.23148	+	11.9267i	−0.177364	+	0.404355i
$871$	12.1366	+	7.00707i	0.411233	+	0.237426i
$872$	−0.930743	−	3.47358i	−0.0315189	−	0.117630i
$873$	8.89307	−	33.1894i	0.300985	−	1.12329i
$874$		−	26.4645i		−	0.895173i
$875$	−15.1589	+	25.4009i	−0.512464	+	0.858709i
$876$		−	12.4428i		−	0.420402i
$877$	−5.50042	+	20.5278i	−0.185736	+	0.693176i	0.808736	+	0.588172i	$0.200152\pi$
$877$	−5.50042	+	20.5278i	−0.185736	+	0.693176i	−0.994472	+	0.105004i	$0.966515\pi$
$878$	−17.2058	+	4.61027i	−0.580667	+	0.155589i
$879$	17.2274	−	29.8387i	0.581065	−	1.00643i
$880$	6.66852	−	3.24512i	0.224796	−	0.109393i
$881$	26.8797			0.905599			0.452799	−	0.891612i	$-0.350425\pi$
$881$	26.8797			0.905599			0.452799	+	0.891612i	$0.350425\pi$
$882$	−29.4454	+	2.80795i	−0.991479	+	0.0945487i
$883$	15.4309	+	15.4309i	0.519292	+	0.519292i	0.917357	−	0.398065i	$-0.130318\pi$
$883$	15.4309	+	15.4309i	0.519292	+	0.519292i	−0.398065	+	0.917357i	$0.630318\pi$
$884$	−10.3696	+	5.98690i	−0.348768	+	0.201361i
$885$	17.5781	+	14.0746i	0.590880	+	0.473112i
$886$	9.27928	+	5.35740i	0.311744	+	0.179985i
$887$	5.46875	−	20.4096i	0.183623	−	0.685289i	−0.811299	−	0.584632i	$-0.801239\pi$
$887$	5.46875	−	20.4096i	0.183623	−	0.685289i	0.994921	−	0.100657i	$-0.0320944\pi$
$888$	−11.9337	+	11.9337i	−0.400470	+	0.400470i
$889$	−1.86500	+	22.3202i	−0.0625501	+	0.748596i
$890$	−5.87100	+	38.4393i	−0.196796	+	1.28849i
$891$	12.4668	+	2.28067i	0.417653	+	0.0764055i
$892$	−5.81465	−	21.7006i	−0.194689	−	0.726589i
$893$	−5.09937	−	19.0311i	−0.170644	−	0.636851i
$894$	−47.0913	+	27.1882i	−1.57497	+	0.909308i
$895$	0.758784	+	1.03235i	0.0253634	+	0.0345077i
$896$	1.12749	+	2.39348i	0.0376670	+	0.0799606i
$897$	56.3618	+	56.3618i	1.88186	+	1.88186i
$898$	−34.4643	−	9.23468i	−1.15009	−	0.308165i
$899$	−10.2692	+	17.7868i	−0.342498	+	0.593223i
$900$	−14.3097	−	15.5441i	−0.476989	−	0.518137i
$901$	15.4005	−	8.89146i	0.513064	−	0.296217i
$902$	1.75145	+	21.6130i	0.0583168	+	0.719634i
$903$	71.8228	−	12.9536i	2.39011	−	0.431069i
$904$	−15.9907			−0.531842
$905$	−37.9153	−	16.6310i	−1.26035	−	0.552832i
$906$	17.4969	−	30.3055i	0.581295	−	1.00683i
$907$	9.26877	+	34.5915i	0.307764	+	1.14859i	0.930539	+	0.366192i	$0.119339\pi$
$907$	9.26877	+	34.5915i	0.307764	+	1.14859i	−0.622775	+	0.782401i	$0.713995\pi$
$908$	−10.7641	−	2.88422i	−0.357218	−	0.0957163i
$909$	−67.4503			−2.23719
$910$	−18.4239	+	19.4417i	−0.610746	+	0.644486i
$911$	−4.86361			−0.161138			−0.0805692	−	0.996749i	$-0.525674\pi$
$911$	−4.86361			−0.161138			−0.0805692	+	0.996749i	$0.525674\pi$
$912$	−2.81115	+	10.4914i	−0.0930865	+	0.347404i
$913$	−23.9455	−	11.3533i	−0.792479	−	0.375739i
$914$	4.11152	+	2.37378i	0.135997	+	0.0785178i
$915$	12.6254	−	4.92652i	0.417382	−	0.162866i
$916$	−21.4095			−0.707389
$917$	25.6482	+	9.22195i	0.846977	+	0.304535i
$918$	−6.16083	−	6.16083i	−0.203338	−	0.203338i
$919$	12.3549	+	21.3992i	0.407549	+	0.705896i	0.994614	−	0.103644i	$-0.0330502\pi$
$919$	12.3549	+	21.3992i	0.407549	+	0.705896i	−0.587065	+	0.809539i	$0.699717\pi$
$920$	−1.61117	−	14.5563i	−0.0531187	−	0.479908i
$921$	−51.3274	−	29.6339i	−1.69130	−	0.976470i
$922$	−1.45765	−	0.390575i	−0.0480050	−	0.0128629i
$923$	−17.5126	+	17.5126i	−0.576435	+	0.576435i
$924$	16.7206	−	16.6371i	0.550066	−	0.547319i
$925$	14.5596	+	27.8119i	0.478717	+	0.914450i
$926$	−17.4183	+	10.0565i	−0.572401	+	0.330476i
$927$	15.4112	+	57.5155i	0.506171	+	1.88906i
$928$	2.09293	−	0.560800i	0.0687039	−	0.0184092i
$929$	−1.18457	+	0.683910i	−0.0388644	+	0.0224383i	−0.519306	−	0.854588i	$-0.673810\pi$
$929$	−1.18457	+	0.683910i	−0.0388644	+	0.0224383i	0.480442	+	0.877027i	$0.340476\pi$
$930$	−33.7422	−	45.9075i	−1.10645	−	1.50537i
$931$	26.5025	−	9.88111i	0.868584	−	0.323840i
$932$	4.12513	+	4.12513i	0.135123	+	0.135123i
$933$	−5.56157	+	20.7561i	−0.182078	+	0.679523i
$934$	−1.89596	+	3.28390i	−0.0620377	+	0.107452i
$935$	−3.72535	−	19.2567i	−0.121832	−	0.629762i
$936$	−9.56551	−	16.5679i	−0.312658	−	0.541540i
$937$	−3.18623	−	3.18623i	−0.104089	−	0.104089i	0.653144	−	0.757234i	$-0.273450\pi$
$937$	−3.18623	−	3.18623i	−0.104089	−	0.104089i	−0.757234	+	0.653144i	$0.773450\pi$
$938$	−5.28863	−	6.25301i	−0.172680	−	0.204168i
$939$			24.4405i			0.797585i
$940$	−3.96345	−	10.1573i	−0.129273	−	0.331294i
$941$	8.34076	+	4.81554i	0.271901	+	0.156982i	0.629751	−	0.776797i	$-0.283157\pi$
$941$	8.34076	+	4.81554i	0.271901	+	0.156982i	−0.357850	+	0.933779i	$0.616490\pi$
$942$	−33.4740	+	8.96933i	−1.09064	+	0.292237i
$943$	41.3613	+	11.0827i	1.34691	+	0.360904i
$944$		−	3.74643i		−	0.121936i
$945$	−17.1345	−	9.28788i	−0.557385	−	0.302135i
$946$	−22.0438	+	25.9316i	−0.716706	+	0.843108i
$947$	−0.696763	−	0.186697i	−0.0226418	−	0.00606684i	0.247480	−	0.968893i	$-0.420397\pi$
$947$	−0.696763	−	0.186697i	−0.0226418	−	0.00606684i	−0.270122	+	0.962826i	$0.587064\pi$
$948$	3.05194	+	11.3900i	0.0991224	+	0.369930i
$949$	−18.1495	−	10.4786i	−0.589157	−	0.340150i
$950$	17.0643	+	10.8159i	0.553638	+	0.350913i
$951$	1.04813			0.0339878
$952$	6.88617	−	1.24195i	0.223182	−	0.0402520i
$953$	20.0111	−	20.0111i	0.648222	−	0.648222i	−0.304341	−	0.952563i	$-0.598436\pi$
$953$	20.0111	−	20.0111i	0.648222	−	0.648222i	0.952563	+	0.304341i	$0.0984364\pi$
$954$	14.2062	+	24.6059i	0.459944	+	0.796646i
$955$	1.31328	+	11.8650i	0.0424966	+	0.383941i
$956$	1.95832	+	1.13064i	0.0633365	+	0.0365674i
$957$	−10.9783	−	15.8944i	−0.354878	−	0.513793i
$958$	1.11623	+	1.11623i	0.0360637	+	0.0360637i
$959$	−15.5459	+	22.3874i	−0.502005	+	0.722927i
$960$	−0.907507	+	5.94174i	−0.0292897	+	0.191769i
$961$	−29.4242	−	50.9643i	−0.949169	−	1.64401i
$962$	7.35705	+	27.4569i	0.237201	+	0.885246i
$963$	17.4890	+	65.2699i	0.563576	+	2.10329i
$964$	−11.3158	−	19.5996i	−0.364458	−	0.631260i
$965$	−6.74837	+	44.1838i	−0.217238	+	1.42233i
$966$	−19.8501	−	42.1383i	−0.638665	−	1.35578i
$967$	−23.3924	−	23.3924i	−0.752247	−	0.752247i	0.222651	−	0.974898i	$-0.428529\pi$
$967$	−23.3924	−	23.3924i	−0.752247	−	0.752247i	−0.974898	+	0.222651i	$0.928529\pi$
$968$	−1.09903	+	10.9450i	−0.0353243	+	0.351784i
$969$	24.8770	+	14.3627i	0.799165	+	0.461398i
$970$	2.00032	+	18.0722i	0.0642265	+	0.580263i
$971$	8.75447	+	15.1632i	0.280944	+	0.486610i	0.971618	−	0.236557i	$-0.0760191\pi$
$971$	8.75447	+	15.1632i	0.280944	+	0.486610i	−0.690673	+	0.723167i	$0.742686\pi$
$972$	−14.2516	+	14.2516i	−0.457122	+	0.457122i
$973$	2.13818	+	2.52807i	0.0685469	+	0.0810463i
$974$	0.0684536			0.00219340
$975$	−59.3768	+	13.3073i	−1.90158	+	0.426175i
$976$	−1.95267	−	1.12738i	−0.0625036	−	0.0360865i
$977$	1.29855	+	4.84627i	0.0415444	+	0.155046i	0.983582	−	0.180461i	$-0.0577590\pi$
$977$	1.29855	+	4.84627i	0.0415444	+	0.155046i	−0.942038	+	0.335507i	$0.891092\pi$
$978$	39.7452	+	10.6497i	1.27091	+	0.340540i
$979$	−43.9439	−	37.3557i	−1.40445	−	1.19389i
$980$	13.9757	−	7.04843i	0.446437	−	0.225154i
$981$		−	15.1956i		−	0.485160i
$982$	25.5202	+	6.83812i	0.814383	+	0.218213i
$983$	17.8218	−	4.77533i	0.568427	−	0.152310i	0.0368518	−	0.999321i	$-0.488267\pi$
$983$	17.8218	−	4.77533i	0.568427	−	0.152310i	0.531575	+	0.847011i	$0.321600\pi$
$984$	−15.2197	−	8.78711i	−0.485187	−	0.280123i
$985$	7.71225	+	19.7645i	0.245733	+	0.629749i
$986$		−	5.73049i		−	0.182496i
$987$	−22.3941	−	26.4776i	−0.712811	−	0.842792i
$988$	12.9357	+	12.9357i	0.411539	+	0.411539i
$989$	33.6054	+	58.2063i	1.06859	+	1.85085i
$990$	30.7672	−	5.95214i	0.977847	−	0.189171i
$991$	1.97065	−	3.41327i	0.0625999	−	0.108426i	−0.833027	−	0.553232i	$-0.813394\pi$
$991$	1.97065	−	3.41327i	0.0625999	−	0.108426i	0.895627	+	0.444806i	$0.146727\pi$
$992$	−2.45331	+	9.15586i	−0.0778925	+	0.290699i
$993$	−4.26046	−	4.26046i	−0.135202	−	0.135202i
$994$	13.0931	−	6.16777i	0.415289	−	0.195630i
$995$	−3.95834	−	5.38545i	−0.125488	−	0.170730i
$996$	18.6006	−	10.7390i	0.589382	−	0.340280i
$997$	−50.0498	+	13.4108i	−1.58509	+	0.424725i	−0.940498	−	0.339799i	$-0.889641\pi$
$997$	−50.0498	+	13.4108i	−1.58509	+	0.424725i	−0.644596	+	0.764524i	$0.722974\pi$
$998$	4.54650	+	16.9678i	0.143917	+	0.537105i
$999$	−17.9127	+	10.3419i	−0.566732	+	0.327203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bd.a.263.3	✓	192
5.2	odd	4	inner	770.2.bd.a.417.22	yes	192
7.2	even	3	inner	770.2.bd.a.373.46	yes	192
11.10	odd	2	inner	770.2.bd.a.263.27	yes	192
35.2	odd	12	inner	770.2.bd.a.527.27	yes	192
55.32	even	4	inner	770.2.bd.a.417.46	yes	192
77.65	odd	6	inner	770.2.bd.a.373.22	yes	192
385.142	even	12	inner	770.2.bd.a.527.3	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bd.a.263.3	✓	192	1.1	even	1	trivial
770.2.bd.a.263.27	yes	192	11.10	odd	2	inner
770.2.bd.a.373.22	yes	192	77.65	odd	6	inner
770.2.bd.a.373.46	yes	192	7.2	even	3	inner
770.2.bd.a.417.22	yes	192	5.2	odd	4	inner
770.2.bd.a.417.46	yes	192	55.32	even	4	inner
770.2.bd.a.527.3	yes	192	385.142	even	12	inner
770.2.bd.a.527.27	yes	192	35.2	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
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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