LMFDB - Embedded newform 570.2.bf.a.29.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(29,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 17]))

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

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

chi := DirichletCharacter("570.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bf (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.11
Character	$\chi$	$=$	570.29
Dual form			570.2.bf.a.59.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(0.144472 + 1.72602i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-2.21146 - 0.330832i) q^{5} +(-0.441997 - 1.67471i) q^{6} +(2.42894 + 1.40235i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.95826 + 0.498722i) q^{9} +O(q^{10})$	\(q+(-0.984808 + 0.173648i) q^{2} +(0.144472 + 1.72602i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-2.21146 - 0.330832i) q^{5} +(-0.441997 - 1.67471i) q^{6} +(2.42894 + 1.40235i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.95826 + 0.498722i) q^{9} +(2.23531 - 0.0582100i) q^{10} +(5.08124 - 2.93365i) q^{11} +(0.726091 + 1.57251i) q^{12} +(2.44808 + 2.05418i) q^{13} +(-2.63556 - 0.959265i) q^{14} +(0.251527 - 3.86481i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.740904 + 4.20188i) q^{17} +(2.82671 - 1.00484i) q^{18} +(-1.47061 + 4.10333i) q^{19} +(-2.19124 + 0.445483i) q^{20} +(-2.06956 + 4.39499i) q^{21} +(-4.49462 + 3.77143i) q^{22} +(-7.84429 + 2.85509i) q^{23} +(-0.988124 - 1.42254i) q^{24} +(4.78110 + 1.46324i) q^{25} +(-2.76759 - 1.59787i) q^{26} +(-1.28819 - 5.03394i) q^{27} +(2.76209 + 0.487031i) q^{28} +(-0.140039 + 0.794199i) q^{29} +(0.423411 + 3.84977i) q^{30} +(-0.327703 - 0.189199i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(5.79763 + 8.34646i) q^{33} +(-1.45930 - 4.00938i) q^{34} +(-4.90757 - 3.90481i) q^{35} +(-2.60928 + 1.48043i) q^{36} -0.577661 q^{37} +(0.735732 - 4.29636i) q^{38} +(-3.19186 + 4.52219i) q^{39} +(2.08060 - 0.819221i) q^{40} +(-6.13650 + 5.14914i) q^{41} +(1.27494 - 4.68760i) q^{42} +(-0.0911924 + 0.250549i) q^{43} +(3.77143 - 4.49462i) q^{44} +(6.70705 - 0.124218i) q^{45} +(7.22933 - 4.17386i) q^{46} +(1.53141 - 8.68509i) q^{47} +(1.22013 + 1.22934i) q^{48} +(0.433177 + 0.750284i) q^{49} +(-4.96255 - 0.610783i) q^{50} +(-7.14546 + 1.88587i) q^{51} +(3.00301 + 1.09301i) q^{52} +(1.39838 + 3.84201i) q^{53} +(2.14275 + 4.73377i) q^{54} +(-12.2075 + 4.80662i) q^{55} -2.80470 q^{56} +(-7.29487 - 1.94548i) q^{57} -0.806451i q^{58} +(1.97667 + 11.2102i) q^{59} +(-1.08548 - 3.71776i) q^{60} +(-5.56123 + 2.02412i) q^{61} +(0.355578 + 0.129420i) q^{62} +(-7.88482 - 2.93714i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-4.73423 - 5.35263i) q^{65} +(-7.15890 - 7.21291i) q^{66} +(-0.0547307 + 0.310393i) q^{67} +(2.13335 + 3.69507i) q^{68} +(-6.06120 - 13.1269i) q^{69} +(5.51107 + 2.99330i) q^{70} +(11.7903 + 4.29132i) q^{71} +(2.31256 - 1.91103i) q^{72} +(0.930133 + 1.10849i) q^{73} +(0.568885 - 0.100310i) q^{74} +(-1.83484 + 8.46365i) q^{75} +(0.0215007 + 4.35885i) q^{76} +16.4561 q^{77} +(2.35810 - 5.00775i) q^{78} +(0.149928 + 0.178677i) q^{79} +(-1.90673 + 1.16807i) q^{80} +(8.50255 - 2.95070i) q^{81} +(5.14914 - 6.13650i) q^{82} +(-1.81869 + 3.15006i) q^{83} +(-0.441578 + 4.83778i) q^{84} +(-0.248364 - 9.53739i) q^{85} +(0.0462996 - 0.262578i) q^{86} +(-1.39103 - 0.126969i) q^{87} +(-2.93365 + 5.08124i) q^{88} +(11.3272 + 9.50467i) q^{89} +(-6.58359 + 1.28700i) q^{90} +(3.06556 + 8.42254i) q^{91} +(-6.39472 + 5.36581i) q^{92} +(0.279217 - 0.592954i) q^{93} +8.81907i q^{94} +(4.60970 - 8.58782i) q^{95} +(-1.41507 - 0.998789i) q^{96} +(-2.19206 - 12.4318i) q^{97} +(-0.556881 - 0.663665i) q^{98} +(-13.5685 + 11.2126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) $ 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$	$-1$

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 $

$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$3$	0.144472	+	1.72602i	0.0834110	+	0.996515i
$3$	0.144472	+	1.72602i	0.0834110	+	0.996515i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	−2.21146	−	0.330832i	−0.988994	−	0.147953i
$5$	−2.21146	−	0.330832i	−0.988994	−	0.147953i
$6$	−0.441997	−	1.67471i	−0.180444	−	0.683696i
$7$	2.42894	+	1.40235i	0.918054	+	0.530039i	0.883014	−	0.469347i	$-0.155511\pi$
$7$	2.42894	+	1.40235i	0.918054	+	0.530039i	0.0350404	+	0.999386i	$0.488844\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−2.95826	+	0.498722i	−0.986085	+	0.166241i
$10$	2.23531	−	0.0582100i	0.706867	−	0.0184076i
$11$	5.08124	−	2.93365i	1.53205	−	0.884530i	0.532784	−	0.846251i	$-0.321146\pi$
$11$	5.08124	−	2.93365i	1.53205	−	0.884530i	0.999267	−	0.0382790i	$-0.0121876\pi$
$12$	0.726091	+	1.57251i	0.209605	+	0.453945i
$13$	2.44808	+	2.05418i	0.678974	+	0.569727i	0.915706	−	0.401848i	$-0.131632\pi$
$13$	2.44808	+	2.05418i	0.678974	+	0.569727i	−0.236732	+	0.971575i	$0.576076\pi$
$14$	−2.63556	−	0.959265i	−0.704382	−	0.256374i
$15$	0.251527	−	3.86481i	0.0649439	−	0.997889i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.740904	+	4.20188i	0.179696	+	1.01910i	0.932583	+	0.360955i	$0.117549\pi$
$17$	0.740904	+	4.20188i	0.179696	+	1.01910i	−0.752887	+	0.658149i	$0.771340\pi$
$18$	2.82671	−	1.00484i	0.666262	−	0.236843i
$19$	−1.47061	+	4.10333i	−0.337381	+	0.941368i
$19$	−1.47061	+	4.10333i	−0.337381	+	0.941368i
$20$	−2.19124	+	0.445483i	−0.489977	+	0.0996131i
$21$	−2.06956	+	4.39499i	−0.451616	+	0.959066i
$22$	−4.49462	+	3.77143i	−0.958256	+	0.804072i
$23$	−7.84429	+	2.85509i	−1.63565	+	0.595327i	−0.986270	−	0.165140i	$-0.947192\pi$
$23$	−7.84429	+	2.85509i	−1.63565	+	0.595327i	−0.649377	+	0.760467i	$0.724970\pi$
$24$	−0.988124	−	1.42254i	−0.201700	−	0.290374i
$25$	4.78110	+	1.46324i	0.956220	+	0.292648i
$26$	−2.76759	−	1.59787i	−0.542769	−	0.313368i
$27$	−1.28819	−	5.03394i	−0.247912	−	0.968783i
$28$	2.76209	+	0.487031i	0.521986	+	0.0920403i
$29$	−0.140039	+	0.794199i	−0.0260045	+	0.147479i	−0.995045	−	0.0994211i	$-0.968301\pi$
$29$	−0.140039	+	0.794199i	−0.0260045	+	0.147479i	0.969041	+	0.246900i	$0.0794120\pi$
$30$	0.423411	+	3.84977i	0.0773040	+	0.702868i
$31$	−0.327703	−	0.189199i	−0.0588571	−	0.0339812i	0.470283	−	0.882516i	$-0.344152\pi$
$31$	−0.327703	−	0.189199i	−0.0588571	−	0.0339812i	−0.529140	+	0.848535i	$0.677485\pi$
$32$	−0.642788	+	0.766044i	−0.113630	+	0.135419i
$33$	5.79763	+	8.34646i	1.00924	+	1.45293i
$34$	−1.45930	−	4.00938i	−0.250267	−	0.687604i
$35$	−4.90757	−	3.90481i	−0.829530	−	0.660034i
$36$	−2.60928	+	1.48043i	−0.434880	+	0.246738i
$37$	−0.577661			−0.0949669			−0.0474834	−	0.998872i	$-0.515120\pi$
$37$	−0.577661			−0.0949669			−0.0474834	+	0.998872i	$0.515120\pi$
$38$	0.735732	−	4.29636i	0.119351	−	0.696961i
$39$	−3.19186	+	4.52219i	−0.511107	+	0.724129i
$40$	2.08060	−	0.819221i	0.328971	−	0.129530i
$41$	−6.13650	+	5.14914i	−0.958361	+	0.804160i	−0.980686	−	0.195590i	$-0.937338\pi$
$41$	−6.13650	+	5.14914i	−0.958361	+	0.804160i	0.0223246	+	0.999751i	$0.492893\pi$
$42$	1.27494	−	4.68760i	0.196728	−	0.723312i
$43$	−0.0911924	+	0.250549i	−0.0139067	+	0.0382084i	−0.946452	−	0.322845i	$-0.895361\pi$
$43$	−0.0911924	+	0.250549i	−0.0139067	+	0.0382084i	0.932545	+	0.361054i	$0.117583\pi$
$44$	3.77143	−	4.49462i	0.568565	−	0.677589i
$45$	6.70705	−	0.124218i	0.999829	−	0.0185174i
$46$	7.22933	−	4.17386i	1.06591	−	0.615402i
$47$	1.53141	−	8.68509i	0.223380	−	1.26685i	−0.642379	−	0.766388i	$-0.722052\pi$
$47$	1.53141	−	8.68509i	0.223380	−	1.26685i	0.865758	−	0.500462i	$-0.166837\pi$
$48$	1.22013	+	1.22934i	0.176111	+	0.177440i
$49$	0.433177	+	0.750284i	0.0618824	+	0.107183i
$50$	−4.96255	−	0.610783i	−0.701811	−	0.0863777i
$51$	−7.14546	+	1.88587i	−1.00056	+	0.264074i
$52$	3.00301	+	1.09301i	0.416442	+	0.151573i
$53$	1.39838	+	3.84201i	0.192082	+	0.527741i	0.997925	−	0.0643884i	$-0.0205096\pi$
$53$	1.39838	+	3.84201i	0.192082	+	0.527741i	−0.805843	+	0.592129i	$0.798287\pi$
$54$	2.14275	+	4.73377i	0.291592	+	0.644185i
$55$	−12.2075	+	4.80662i	−1.64606	+	0.648125i
$56$	−2.80470			−0.374794
$57$	−7.29487	−	1.94548i	−0.966229	−	0.257685i
$58$		−	0.806451i		−	0.105892i
$59$	1.97667	+	11.2102i	0.257340	+	1.45945i	0.789993	+	0.613116i	$0.210084\pi$
$59$	1.97667	+	11.2102i	0.257340	+	1.45945i	−0.532653	+	0.846334i	$0.678805\pi$
$60$	−1.08548	−	3.71776i	−0.140135	−	0.479960i
$61$	−5.56123	+	2.02412i	−0.712042	+	0.259162i	−0.672544	−	0.740057i	$-0.734798\pi$
$61$	−5.56123	+	2.02412i	−0.712042	+	0.259162i	−0.0394986	+	0.999220i	$0.512576\pi$
$62$	0.355578	+	0.129420i	0.0451585	+	0.0164363i
$63$	−7.88482	−	2.93714i	−0.993394	−	0.370045i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−4.73423	−	5.35263i	−0.587209	−	0.663912i
$66$	−7.15890	−	7.21291i	−0.881200	−	0.887848i
$67$	−0.0547307	+	0.310393i	−0.00668642	+	0.0379206i	−0.987968	−	0.154656i	$-0.950573\pi$
$67$	−0.0547307	+	0.310393i	−0.00668642	+	0.0379206i	0.981282	+	0.192576i	$0.0616843\pi$
$68$	2.13335	+	3.69507i	0.258707	+	0.448093i
$69$	−6.06120	−	13.1269i	−0.729683	−	1.58029i
$70$	5.51107	+	2.99330i	0.658699	+	0.357768i
$71$	11.7903	+	4.29132i	1.39925	+	0.509286i	0.927956	−	0.372690i	$-0.121565\pi$
$71$	11.7903	+	4.29132i	1.39925	+	0.509286i	0.471295	+	0.881976i	$0.343787\pi$
$72$	2.31256	−	1.91103i	0.272538	−	0.225217i
$73$	0.930133	+	1.10849i	0.108864	+	0.129739i	0.817725	−	0.575609i	$-0.195235\pi$
$73$	0.930133	+	1.10849i	0.108864	+	0.129739i	−0.708861	+	0.705348i	$0.750791\pi$
$74$	0.568885	−	0.100310i	0.0661315	−	0.0116608i
$75$	−1.83484	+	8.46365i	−0.211869	+	0.977298i
$76$	0.0215007	+	4.35885i	0.00246630	+	0.499994i
$77$	16.4561			1.87534
$78$	2.35810	−	5.00775i	0.267003	−	0.567015i
$79$	0.149928	+	0.178677i	0.0168682	+	0.0201028i	0.774413	−	0.632681i	$-0.218046\pi$
$79$	0.149928	+	0.178677i	0.0168682	+	0.0201028i	−0.757544	+	0.652784i	$0.773601\pi$
$80$	−1.90673	+	1.16807i	−0.213179	+	0.130594i
$81$	8.50255	−	2.95070i	0.944728	−	0.327855i
$82$	5.14914	−	6.13650i	0.568627	−	0.677664i
$83$	−1.81869	+	3.15006i	−0.199627	+	0.345764i	−0.948408	−	0.317054i	$-0.897306\pi$
$83$	−1.81869	+	3.15006i	−0.199627	+	0.345764i	0.748780	+	0.662818i	$0.230640\pi$
$84$	−0.441578	+	4.83778i	−0.0481801	+	0.527845i
$85$	−0.248364	−	9.53739i	−0.0269389	−	1.03448i
$86$	0.0462996	−	0.262578i	0.00499262	−	0.0283145i
$87$	−1.39103	−	0.126969i	−0.149134	−	0.0136125i
$88$	−2.93365	+	5.08124i	−0.312729	+	0.541662i
$89$	11.3272	+	9.50467i	1.20068	+	1.00749i	0.999610	+	0.0279174i	$0.00888755\pi$
$89$	11.3272	+	9.50467i	1.20068	+	1.00749i	0.201074	+	0.979576i	$0.435557\pi$
$90$	−6.58359	+	1.28700i	−0.693971	+	0.135662i
$91$	3.06556	+	8.42254i	0.321358	+	0.882923i
$92$	−6.39472	+	5.36581i	−0.666696	+	0.559424i
$93$	0.279217	−	0.592954i	0.0289534	−	0.0614864i
$94$			8.81907i			0.909617i
$95$	4.60970	−	8.58782i	0.472946	−	0.881092i
$96$	−1.41507	−	0.998789i	−0.144425	−	0.101938i
$97$	−2.19206	−	12.4318i	−0.222570	−	1.26226i	−0.867276	−	0.497828i	$-0.834131\pi$
$97$	−2.19206	−	12.4318i	−0.222570	−	1.26226i	0.644705	−	0.764431i	$-0.276980\pi$
$98$	−0.556881	−	0.663665i	−0.0562535	−	0.0670403i
$99$	−13.5685	+	11.2126i	−1.36369	+	1.12691i
$100$	4.99322	−	0.260235i	0.499322	−	0.0260235i
$101$	6.16510	−	7.34728i	0.613450	−	0.731081i	−0.366479	−	0.930426i	$-0.619437\pi$
$101$	6.16510	−	7.34728i	0.613450	−	0.731081i	0.979929	+	0.199345i	$0.0638814\pi$
$102$	6.70943	−	3.09801i	0.664333	−	0.306749i
$103$	4.45159	+	7.71039i	0.438629	+	0.759727i	0.997584	−	0.0694708i	$-0.0221311\pi$
$103$	4.45159	+	7.71039i	0.438629	+	0.759727i	−0.558955	+	0.829198i	$0.688798\pi$
$104$	−3.14718	−	0.554934i	−0.308607	−	0.0544157i
$105$	6.03076	−	9.03467i	0.588542	−	0.881693i
$106$	−2.04429	−	3.54082i	−0.198559	−	0.343915i
$107$	2.42461	+	1.39985i	0.234396	+	0.135329i	0.612598	−	0.790394i	$-0.290124\pi$
$107$	2.42461	+	1.39985i	0.234396	+	0.135329i	−0.378202	+	0.925723i	$0.623458\pi$
$108$	−2.93221	−	4.28977i	−0.282152	−	0.412784i
$109$	−4.43192	+	12.1766i	−0.424501	+	1.16631i	0.524604	+	0.851347i	$0.324213\pi$
$109$	−4.43192	+	12.1766i	−0.424501	+	1.16631i	−0.949105	+	0.314960i	$0.898009\pi$
$110$	11.1874	−	6.85341i	1.06667	−	0.653447i
$111$	−0.0834559	−	0.997051i	−0.00792128	−	0.0946359i
$112$	2.76209	−	0.487031i	0.260993	−	0.0460201i
$113$		−	9.30807i		−	0.875629i	−0.899065	−	0.437815i	$-0.855753\pi$
$113$		−	9.30807i		−	0.875629i	0.899065	−	0.437815i	$-0.144247\pi$
$114$	7.52187	+	0.649180i	0.704488	+	0.0608012i
$115$	18.2919	−	3.71877i	1.70573	−	0.346777i
$116$	0.140039	+	0.794199i	0.0130023	+	0.0737396i
$117$	−8.26650	−	4.85588i	−0.764238	−	0.448926i
$118$	−3.89328	−	10.6967i	−0.358405	−	0.984710i
$119$	−4.09289	+	11.2451i	−0.375195	+	1.03084i
$120$	1.71458	+	3.47278i	0.156519	+	0.317020i
$121$	11.7127	−	20.2869i	1.06479	−	1.84427i
$122$	5.12526	−	2.95907i	0.464019	−	0.267901i
$123$	−9.77405	−	9.84779i	−0.881296	−	0.887946i
$124$	−0.372650	−	0.0657082i	−0.0334649	−	0.00590077i
$125$	−10.0891	−	4.81764i	−0.902398	−	0.430903i
$126$	8.27506	+	1.52334i	0.737201	+	0.135710i
$127$	−9.55303	−	8.01594i	−0.847694	−	0.711300i	0.111587	−	0.993755i	$-0.464407\pi$
$127$	−9.55303	−	8.01594i	−0.847694	−	0.711300i	−0.959281	+	0.282455i	$0.908851\pi$
$128$	−0.342020	+	0.939693i	−0.0302306	+	0.0830579i
$129$	−0.445626	−	0.121202i	−0.0392352	−	0.0106713i
$130$	5.59178	+	4.44922i	0.490432	+	0.390223i
$131$	5.96444	−	1.05169i	0.521116	−	0.0918868i	0.0930978	−	0.995657i	$-0.470323\pi$
$131$	5.96444	−	1.05169i	0.521116	−	0.0918868i	0.428018	+	0.903770i	$0.359212\pi$
$132$	8.30265	+	5.86020i	0.722653	+	0.510065i
$133$	−9.32633	+	7.90444i	−0.808696	+	0.685402i
$134$		−	0.315182i		−	0.0272276i
$135$	1.18338	+	11.5585i	0.101850	+	0.994800i
$136$	−2.74258	−	3.26848i	−0.235174	−	0.280270i
$137$	18.0494	−	6.56946i	1.54207	−	0.561267i	0.575527	−	0.817782i	$-0.304797\pi$
$137$	18.0494	−	6.56946i	1.54207	−	0.561267i	0.966540	+	0.256516i	$0.0825746\pi$
$138$	8.24858	+	11.8749i	0.702166	+	1.01086i
$139$	1.23736	+	1.03826i	0.104951	+	0.0880645i	0.693753	−	0.720213i	$-0.255956\pi$
$139$	1.23736	+	1.03826i	0.104951	+	0.0880645i	−0.588802	+	0.808277i	$0.700400\pi$
$140$	−5.94713	−	1.99084i	−0.502624	−	0.168257i
$141$	15.2118	+	1.38849i	1.28107	+	0.116932i
$142$	−12.3564	−	2.17876i	−1.03692	−	0.182837i
$143$	18.4655	+	3.25597i	1.54416	+	0.272278i
$144$	−1.94558	+	2.28357i	−0.162132	+	0.190298i
$145$	0.572436	−	1.71001i	0.0475383	−	0.142009i
$146$	−1.10849	−	0.930133i	−0.0917393	−	0.0769784i
$147$	−1.23242	+	0.856064i	−0.101648	+	0.0706070i
$148$	−0.542824	+	0.197572i	−0.0446198	+	0.0162403i
$149$	−12.1342	−	14.4610i	−0.994073	−	1.18469i	−0.982785	−	0.184754i	$-0.940851\pi$
$149$	−12.1342	−	14.4610i	−0.994073	−	1.18469i	−0.0112880	−	0.999936i	$-0.503593\pi$
$150$	0.337270	−	8.65368i	0.0275379	−	0.706570i
$151$		−	2.05253i		−	0.167033i	−0.996506	−	0.0835163i	$-0.973385\pi$
$151$		−	2.05253i		−	0.167033i	0.996506	−	0.0835163i	$-0.0266151\pi$
$152$	−0.778080	−	4.28889i	−0.0631106	−	0.347875i
$153$	−4.28735	−	12.0607i	−0.346612	−	0.975051i
$154$	−16.2061	+	2.85756i	−1.30592	+	0.230269i
$155$	0.662108	+	0.526821i	0.0531818	+	0.0423153i
$156$	−1.45269	+	5.34115i	−0.116309	+	0.427634i
$157$	1.00557	−	2.76277i	0.0802528	−	0.220493i	−0.893077	−	0.449905i	$-0.851458\pi$
$157$	1.00557	−	2.76277i	0.0802528	−	0.220493i	0.973329	+	0.229412i	$0.0736802\pi$
$158$	−0.178677	−	0.149928i	−0.0142148	−	0.0119276i
$159$	−6.42934	+	2.96869i	−0.509880	+	0.235432i
$160$	1.67493	−	1.48142i	0.132415	−	0.117117i
$161$	−23.0572	−	4.06560i	−1.81716	−	0.320414i
$162$	−7.86100	+	4.38232i	−0.617618	+	0.344308i
$163$	12.2818	−	7.09091i	0.961986	−	0.555403i	0.0652022	−	0.997872i	$-0.479231\pi$
$163$	12.2818	−	7.09091i	0.961986	−	0.555403i	0.896784	+	0.442469i	$0.145897\pi$
$164$	−4.00532	+	6.93742i	−0.312763	+	0.541721i
$165$	−10.0599	−	20.3759i	−0.783166	−	1.58626i
$166$	1.24406	−	3.41802i	0.0965575	−	0.265290i
$167$	3.24444	+	8.91402i	0.251062	+	0.689788i	0.999642	+	0.0267434i	$0.00851371\pi$
$167$	3.24444	+	8.91402i	0.251062	+	0.689788i	−0.748580	+	0.663044i	$0.769264\pi$
$168$	−0.405201	−	4.84096i	−0.0312620	−	0.373488i
$169$	−0.484006	−	2.74493i	−0.0372312	−	0.211149i
$170$	1.90074	+	9.34937i	0.145780	+	0.717064i
$171$	2.30402	−	12.8721i	0.176193	−	0.984356i
$172$			0.266629i			0.0203303i
$173$	−1.47394	+	0.259896i	−0.112062	+	0.0197595i	−0.229398	−	0.973333i	$-0.573676\pi$
$173$	−1.47394	+	0.259896i	−0.112062	+	0.0197595i	0.117336	+	0.993092i	$0.462565\pi$
$174$	1.39195	−	0.116510i	0.105523	−	0.00883258i
$175$	9.56104	+	10.2589i	0.722747	+	0.775501i
$176$	2.00674	−	5.51347i	0.151264	−	0.415593i
$177$	−19.0635	+	5.03133i	−1.43290	+	0.378178i
$178$	−12.8056	−	7.39332i	−0.959821	−	0.554153i
$179$	−6.01949	−	10.4261i	−0.449918	−	0.779280i	0.548463	−	0.836175i	$-0.315213\pi$
$179$	−6.01949	−	10.4261i	−0.449918	−	0.779280i	−0.998380	+	0.0568949i	$0.981880\pi$
$180$	6.26008	−	2.41067i	0.466599	−	0.179681i
$181$	12.8250	+	2.26140i	0.953277	+	0.168088i	0.628593	−	0.777734i	$-0.283631\pi$
$181$	12.8250	+	2.26140i	0.953277	+	0.168088i	0.324684	+	0.945823i	$0.394742\pi$
$182$	−4.48154	−	7.76226i	−0.332194	−	0.575377i
$183$	−4.29711	−	9.30633i	−0.317651	−	0.687944i
$184$	5.36581	−	6.39472i	0.395573	−	0.471425i
$185$	1.27747	+	0.191109i	0.0939217	+	0.0140506i
$186$	−0.172010	+	0.632431i	−0.0126123	+	0.0463721i
$187$	16.0916	+	19.1772i	1.17673	+	1.40237i
$188$	−1.53141	−	8.68509i	−0.111690	−	0.633425i
$189$	3.93042	−	14.0337i	0.285896	−	1.02080i
$190$	−3.04841	+	9.25782i	−0.221155	+	0.671633i
$191$		−	22.7737i		−	1.64785i	−0.566699	−	0.823925i	$-0.691780\pi$
$191$		−	22.7737i		−	1.64785i	0.566699	−	0.823925i	$-0.308220\pi$
$192$	1.56701	+	0.737891i	0.113089	+	0.0532527i
$193$	16.0924	−	13.5031i	1.15836	−	0.971976i	0.158475	−	0.987363i	$-0.449342\pi$
$193$	16.0924	−	13.5031i	1.15836	−	0.971976i	0.999882	+	0.0153865i	$0.00489788\pi$
$194$	4.31752	+	11.8623i	0.309980	+	0.851663i
$195$	8.55476	−	8.94466i	0.612619	−	0.640540i
$196$	0.663665	+	0.556881i	0.0474046	+	0.0397772i
$197$	−3.42024	+	5.92404i	−0.243682	+	0.422070i	−0.961760	−	0.273892i	$-0.911689\pi$
$197$	−3.42024	+	5.92404i	−0.243682	+	0.422070i	0.718078	+	0.695963i	$0.245022\pi$
$198$	11.4153	−	13.3984i	0.811253	−	0.952185i
$199$	1.29993	−	7.37224i	0.0921493	−	0.522604i	−0.903434	−	0.428726i	$-0.858962\pi$
$199$	1.29993	−	7.37224i	0.0921493	−	0.522604i	0.995584	−	0.0938782i	$-0.0299264\pi$
$200$	−4.87218	+	1.12335i	−0.344515	+	0.0794325i
$201$	−0.543651	−	0.0496229i	−0.0383462	−	0.00350013i
$202$	−4.79559	+	8.30621i	−0.337417	+	0.584423i
$203$	−1.45389	+	1.73268i	−0.102043	+	0.121610i
$204$	−6.06953	+	4.21603i	−0.424952	+	0.295181i
$205$	15.2741	−	9.35696i	1.06679	−	0.653518i
$206$	−5.72286	−	6.82024i	−0.398730	−	0.475188i
$207$	21.7815	−	12.3582i	1.51392	−	0.858954i
$208$	3.19574			0.221584
$209$	4.56523	+	25.1643i	0.315784	+	1.74065i
$210$	−4.37029	+	9.94464i	−0.301578	+	0.686245i
$211$	−9.93375	+	1.75159i	−0.683868	+	0.120584i	−0.504779	−	0.863249i	$-0.668426\pi$
$211$	−9.93375	+	1.75159i	−0.683868	+	0.120584i	−0.179089	+	0.983833i	$0.557315\pi$
$212$	2.62809	+	3.13204i	0.180498	+	0.215109i
$213$	−5.70351	+	20.9702i	−0.390798	+	1.43685i
$214$	−2.63086	−	0.957553i	−0.179842	−	0.0654570i
$215$	0.284558	−	0.523910i	0.0194067	−	0.0357304i
$216$	3.63257	+	3.71543i	0.247165	+	0.252803i
$217$	−0.530647	−	0.919108i	−0.0360227	−	0.0623931i
$218$	2.25015	−	12.7612i	0.152399	−	0.864298i
$219$	−1.77889	+	1.76557i	−0.120206	+	0.119306i
$220$	−9.82733	+	8.69196i	−0.662559	+	0.586012i
$221$	−6.81762	+	11.8085i	−0.458603	+	0.794323i
$222$	0.255324	+	0.967412i	0.0171362	+	0.0649284i
$223$	−19.0599	−	6.93723i	−1.27634	−	0.464551i	−0.387123	−	0.922028i	$-0.626531\pi$
$223$	−19.0599	−	6.93723i	−1.27634	−	0.464551i	−0.889222	+	0.457477i	$0.848753\pi$
$224$	−2.63556	+	0.959265i	−0.176096	+	0.0640936i
$225$	−14.8735	−	1.94420i	−0.991565	−	0.129614i
$226$	1.61633	+	9.16666i	0.107517	+	0.609757i
$227$			27.1644i			1.80297i	0.432814	+	0.901483i	$0.357521\pi$
$227$			27.1644i			1.80297i	−0.432814	+	0.901483i	$0.642479\pi$
$228$	−7.52033	+	0.666842i	−0.498046	+	0.0441627i
$229$	−0.853480			−0.0563995			−0.0281998	−	0.999602i	$-0.508977\pi$
$229$	−0.853480			−0.0563995			−0.0281998	+	0.999602i	$0.508977\pi$
$230$	−17.3682	+	6.83862i	−1.14523	+	0.450925i
$231$	2.37744	+	28.4034i	0.156424	+	1.86881i
$232$	−0.275823	−	0.757816i	−0.0181086	−	0.0497531i
$233$	−10.1506	−	3.69452i	−0.664989	−	0.242036i	−0.0125999	−	0.999921i	$-0.504011\pi$
$233$	−10.1506	−	3.69452i	−0.664989	−	0.242036i	−0.652389	+	0.757885i	$0.726233\pi$
$234$	8.98412	+	3.34664i	0.587311	+	0.218777i
$235$	−6.25996	+	18.7001i	−0.408355	+	1.21986i
$236$	5.69159	+	9.85813i	0.370491	+	0.641709i
$237$	−0.286739	+	0.284592i	−0.0186257	+	0.0184862i
$238$	2.07802	−	11.7850i	0.134698	−	0.763909i
$239$	17.8849	−	10.3259i	1.15688	−	0.667924i	0.206325	−	0.978484i	$-0.433850\pi$
$239$	17.8849	−	10.3259i	1.15688	−	0.667924i	0.950554	+	0.310559i	$0.100516\pi$
$240$	−2.29157	−	3.12229i	−0.147920	−	0.201543i
$241$	0.922717	−	1.09965i	0.0594374	−	0.0708348i	−0.735507	−	0.677518i	$-0.763056\pi$
$241$	0.922717	−	1.09965i	0.0594374	−	0.0708348i	0.794944	+	0.606683i	$0.207500\pi$
$242$	−8.01193	+	22.0126i	−0.515026	+	1.41502i
$243$	6.32133	+	14.2492i	0.405513	+	0.914089i
$244$	−4.53355	+	3.80410i	−0.290231	+	0.243533i
$245$	−0.709734	−	1.80253i	−0.0453433	−	0.115159i
$246$	11.3356	+	8.00094i	0.722732	+	0.510121i
$247$	−12.0291	+	7.02436i	−0.765395	+	0.446950i
$248$	0.378398			0.0240283
$249$	−5.69980	−	2.68399i	−0.361210	−	0.170091i
$250$	10.7724	+	2.99249i	0.681308	+	0.189262i
$251$	9.26299	+	25.4498i	0.584675	+	1.60638i	0.780095	+	0.625661i	$0.215171\pi$
$251$	9.26299	+	25.4498i	0.584675	+	1.60638i	−0.195421	+	0.980719i	$0.562607\pi$
$252$	−8.41387	−	0.0632468i	−0.530024	−	0.00398417i
$253$	−31.4829	+	37.5198i	−1.97931	+	2.35885i
$254$	10.7998	+	6.23529i	0.677643	+	0.391237i
$255$	16.4258	−	1.80657i	1.02862	−	0.113132i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	23.9090	+	4.21581i	1.49140	+	0.262975i	0.859125	−	0.511766i	$-0.171009\pi$
$257$	23.9090	+	4.21581i	1.49140	+	0.262975i	0.632279	+	0.774741i	$0.282120\pi$
$258$	0.459903	+	0.0419786i	0.0286323	+	0.00261347i
$259$	−1.40311	−	0.810083i	−0.0871847	−	0.0503361i
$260$	−6.27943	−	3.41063i	−0.389434	−	0.211518i
$261$	0.0181857	−	2.41929i	0.00112567	−	0.149750i
$262$	−5.69121	+	2.07143i	−0.351604	+	0.127973i
$263$	−17.5337	+	14.7126i	−1.08118	+	0.907215i	−0.996018	−	0.0891523i	$-0.971584\pi$
$263$	−17.5337	+	14.7126i	−1.08118	+	0.907215i	−0.0851589	+	0.996367i	$0.527140\pi$
$264$	−9.19413	−	4.32943i	−0.565859	−	0.266458i
$265$	−1.82140	−	8.95908i	−0.111887	−	0.550352i
$266$	7.81205	−	9.40386i	0.478988	−	0.576587i
$267$	−14.7687	+	20.9241i	−0.903832	+	1.28054i
$268$	0.0547307	+	0.310393i	0.00334321	+	0.0189603i
$269$	9.51096	−	7.98064i	0.579893	−	0.486588i	−0.305019	−	0.952346i	$-0.598663\pi$
$269$	9.51096	−	7.98064i	0.579893	−	0.486588i	0.884912	+	0.465758i	$0.154218\pi$
$270$	−3.17252	−	11.1774i	−0.193074	−	0.680237i
$271$	−24.9123	−	9.06735i	−1.51332	−	0.550802i	−0.553848	−	0.832618i	$-0.686841\pi$
$271$	−24.9123	−	9.06735i	−1.51332	−	0.550802i	−0.959468	+	0.281816i	$0.909063\pi$
$272$	3.26848	+	2.74258i	0.198181	+	0.166293i
$273$	−14.0946	+	6.50802i	−0.853041	+	0.393883i
$274$	−16.6345	+	9.60390i	−1.00492	+	0.580193i
$275$	28.5866	−	6.59102i	1.72383	−	0.397453i
$276$	−10.1853	−	10.2622i	−0.613084	−	0.617710i
$277$	−0.521644	+	0.301171i	−0.0313426	+	0.0180956i	−0.515589	−	0.856836i	$-0.672427\pi$
$277$	−0.521644	+	0.301171i	−0.0313426	+	0.0180956i	0.484247	+	0.874931i	$0.339094\pi$
$278$	−1.39885	−	0.807627i	−0.0838975	−	0.0484382i
$279$	1.06379	+	0.396267i	0.0636872	+	0.0237239i
$280$	6.20248	+	0.927885i	0.370669	+	0.0554517i
$281$	−8.68753	+	3.16200i	−0.518255	+	0.188629i	−0.587886	−	0.808943i	$-0.700040\pi$
$281$	−8.68753	+	3.16200i	−0.518255	+	0.188629i	0.0696316	+	0.997573i	$0.477818\pi$
$282$	−15.2218	+	1.27411i	−0.906447	+	0.0758721i
$283$	5.42480	−	0.956539i	0.322471	−	0.0568604i	−0.0100694	−	0.999949i	$-0.503205\pi$
$283$	5.42480	−	0.956539i	0.322471	−	0.0568604i	0.332541	+	0.943089i	$0.392094\pi$
$284$	12.5470			0.744526
$285$	15.4887	+	6.71572i	0.917470	+	0.397805i
$286$	−18.7504			−1.10873
$287$	−22.1261	+	3.90143i	−1.30606	+	0.230294i
$288$	1.51949	−	2.58673i	0.0895366	−	0.152424i
$289$	−1.13206	+	0.412034i	−0.0665915	+	0.0242373i
$290$	−0.266800	+	1.78343i	−0.0156670	+	0.104727i
$291$	21.1408	−	5.57959i	1.23930	−	0.327081i
$292$	1.25317	+	0.723515i	0.0733359	+	0.0423405i
$293$	10.8441	−	6.26085i	0.633520	−	0.365763i	−0.148594	−	0.988898i	$-0.547475\pi$
$293$	10.8441	−	6.26085i	0.633520	−	0.365763i	0.782114	+	0.623135i	$0.214141\pi$
$294$	1.06504	−	1.05707i	0.0621145	−	0.0616494i
$295$	−0.662615	−	25.4449i	−0.0385789	−	1.48146i
$296$	0.500269	−	0.288830i	0.0290775	−	0.0167879i
$297$	−21.3134	−	21.7996i	−1.23673	−	1.26494i
$298$	14.4610	+	12.1342i	0.837702	+	0.702916i
$299$	−25.0683	−	9.12410i	−1.44973	−	0.527660i
$300$	1.17055	+	8.58078i	0.0675818	+	0.495412i
$301$	−0.572859	+	0.480686i	−0.0330191	+	0.0277063i
$302$	0.356418	+	2.02135i	0.0205096	+	0.116316i
$303$	13.5722	+	9.57957i	0.779702	+	0.550332i
$304$	1.51102	+	4.08862i	0.0866628	+	0.234499i
$305$	12.9681	−	2.63643i	0.742550	−	0.150962i
$306$	6.31654	+	11.1330i	0.361093	+	0.636431i
$307$	11.9257	−	10.0068i	0.680635	−	0.571121i	−0.235557	−	0.971861i	$-0.575691\pi$
$307$	11.9257	−	10.0068i	0.680635	−	0.571121i	0.916192	+	0.400740i	$0.131247\pi$
$308$	15.4636	−	5.62830i	0.881122	−	0.320702i
$309$	−12.6651	+	8.79745i	−0.720493	+	0.500470i
$310$	−0.743530	−	0.403843i	−0.0422297	−	0.0229368i
$311$	−20.1822	−	11.6522i	−1.14443	−	0.660737i	−0.196906	−	0.980422i	$-0.563089\pi$
$311$	−20.1822	−	11.6522i	−1.14443	−	0.660737i	−0.947524	+	0.319686i	$0.896423\pi$
$312$	0.503143	−	5.51226i	0.0284849	−	0.312070i
$313$	−1.39481	−	0.245942i	−0.0788392	−	0.0139015i	0.134089	−	0.990969i	$-0.457189\pi$
$313$	−1.39481	−	0.245942i	−0.0788392	−	0.0139015i	−0.212929	+	0.977068i	$0.568300\pi$
$314$	−0.510539	+	2.89541i	−0.0288114	+	0.163397i
$315$	16.4652	+	9.10392i	0.927712	+	0.512948i
$316$	0.201998	+	0.116623i	0.0113633	+	0.00656058i
$317$	11.2821	−	13.4455i	0.633667	−	0.755175i	−0.349689	−	0.936866i	$-0.613713\pi$
$317$	11.2821	−	13.4455i	0.633667	−	0.755175i	0.983356	+	0.181691i	$0.0581571\pi$
$318$	5.81616	−	4.04003i	0.326154	−	0.226554i
$319$	1.61834	+	4.44634i	0.0906094	+	0.248947i
$320$	−1.39224	+	1.74976i	−0.0778285	+	0.0978148i
$321$	−2.06587	+	4.38715i	−0.115306	+	0.244867i
$322$	23.4129			1.30475
$323$	−18.3313	−	3.13914i	−1.01998	−	0.174667i
$324$	6.98059	−	5.68079i	0.387810	−	0.315599i
$325$	8.69873	+	13.4034i	0.482519	+	0.743485i
$326$	−10.8639	+	9.11590i	−0.601696	+	0.504883i
$327$	−21.6573	−	5.89038i	−1.19765	−	0.325739i
$328$	2.73980	−	7.52754i	0.151280	−	0.415639i
$329$	15.8993	−	18.9480i	0.876554	−	1.04464i
$330$	13.4453	+	18.3195i	0.740142	+	1.00845i
$331$	1.47859	−	0.853667i	0.0812709	−	0.0469218i	−0.458814	−	0.888532i	$-0.651726\pi$
$331$	1.47859	−	0.853667i	0.0812709	−	0.0469218i	0.540085	+	0.841611i	$0.318392\pi$
$332$	−0.631624	+	3.58212i	−0.0346649	+	0.196594i
$333$	1.70887	−	0.288092i	0.0936454	−	0.0157874i
$334$	−4.74305	−	8.21521i	−0.259528	−	0.449516i
$335$	0.223723	−	0.668316i	0.0122233	−	0.0365140i
$336$	1.23967	+	4.69705i	0.0676295	+	0.256245i
$337$	25.3177	+	9.21487i	1.37914	+	0.501966i	0.921918	−	0.387386i	$-0.126622\pi$
$337$	25.3177	+	9.21487i	1.37914	+	0.501966i	0.457223	+	0.889352i	$0.348844\pi$
$338$	0.953305	+	2.61918i	0.0518530	+	0.142465i
$339$	16.0659	−	1.34476i	0.872578	−	0.0730371i
$340$	−3.49537	−	8.87727i	−0.189563	−	0.481438i
$341$	−2.22018			−0.120230
$342$	−0.0337928	+	13.0767i	−0.00182731	+	0.707104i
$343$		−	17.2031i		−	0.928877i
$344$	−0.0462996	−	0.262578i	−0.00249631	−	0.0141573i
$345$	9.06131	+	31.0348i	0.487845	+	1.67086i
$346$	1.40642	−	0.511895i	0.0756096	−	0.0275196i
$347$	−2.97628	−	1.08328i	−0.159775	−	0.0581534i	0.260894	−	0.965367i	$-0.415983\pi$
$347$	−2.97628	−	1.08328i	−0.159775	−	0.0581534i	−0.420670	+	0.907214i	$0.638205\pi$
$348$	−1.35057	+	0.356449i	−0.0723981	+	0.0191077i
$349$	3.83396	−	6.64061i	0.205227	−	0.355464i	−0.744978	−	0.667089i	$-0.767540\pi$
$349$	3.83396	−	6.64061i	0.205227	−	0.355464i	0.950205	+	0.311625i	$0.100873\pi$
$350$	−11.1972	−	8.44280i	−0.598517	−	0.451287i
$351$	7.18704	−	14.9696i	0.383616	−	0.799020i
$352$	−1.01885	+	5.77817i	−0.0543048	+	0.307978i
$353$	−3.71414	−	6.43309i	−0.197684	−	0.342399i	0.750093	−	0.661332i	$-0.230009\pi$
$353$	−3.71414	−	6.43309i	−0.197684	−	0.342399i	−0.947777	+	0.318934i	$0.896675\pi$
$354$	17.9002	−	8.26523i	0.951384	−	0.439292i
$355$	−24.6541	−	13.3907i	−1.30850	−	0.710703i
$356$	13.8949	+	5.05733i	0.736429	+	0.268038i
$357$	−20.0006	−	5.43979i	−1.05854	−	0.287904i
$358$	7.73850	+	9.22239i	0.408993	+	0.487418i
$359$	−21.2531	+	3.74750i	−1.12170	+	0.197786i	−0.703586	−	0.710610i	$-0.748419\pi$
$359$	−21.2531	+	3.74750i	−1.12170	+	0.197786i	−0.418111	+	0.908396i	$0.637308\pi$
$360$	−5.74637	+	3.46110i	−0.302860	+	0.182416i
$361$	−14.6746	−	12.0688i	−0.772348	−	0.635199i
$362$	−13.0229			−0.684467
$363$	36.7077	+	17.2853i	1.92665	+	0.907245i
$364$	5.76136	+	6.86612i	0.301977	+	0.359883i
$365$	−1.69023	−	2.75910i	−0.0884706	−	0.144418i
$366$	5.84785	+	8.41877i	0.305672	+	0.440056i
$367$	4.65967	−	5.55318i	0.243233	−	0.289874i	−0.630592	−	0.776115i	$-0.717188\pi$
$367$	4.65967	−	5.55318i	0.243233	−	0.289874i	0.873825	+	0.486241i	$0.161632\pi$
$368$	−4.17386	+	7.22933i	−0.217577	+	0.376855i
$369$	15.5854	−	18.2929i	0.811341	−	0.952289i
$370$	−1.29125	+	0.0336256i	−0.0671290	+	0.00174811i
$371$	−1.99127	+	11.2930i	−0.103382	+	0.586306i
$372$	0.0595758	−	0.652692i	0.00308886	−	0.0338405i
$373$	−5.38050	+	9.31930i	−0.278592	+	0.482535i	−0.971035	−	0.238937i	$-0.923201\pi$
$373$	−5.38050	+	9.31930i	−0.278592	+	0.482535i	0.692443	+	0.721472i	$0.256534\pi$
$374$	−19.1772	−	16.0916i	−0.991629	−	0.832075i
$375$	6.85772	−	18.1100i	0.354131	−	0.935196i
$376$	3.01630	+	8.28721i	0.155554	+	0.427380i
$377$	−1.97425	+	1.65659i	−0.101679	+	0.0853190i
$378$	−1.43379	+	14.5030i	−0.0737462	+	0.745952i
$379$			30.9213i			1.58832i	0.607708	+	0.794161i	$0.292089\pi$
$379$			30.9213i			1.58832i	−0.607708	+	0.794161i	$0.707911\pi$
$380$	1.39450	−	9.64652i	0.0715362	−	0.494856i
$381$	12.4555	−	17.6467i	0.638114	−	0.904070i
$382$	3.95462	+	22.4277i	0.202336	+	1.14750i
$383$	−5.21084	−	6.21003i	−0.266261	−	0.317318i	0.616303	−	0.787509i	$-0.288629\pi$
$383$	−5.21084	−	6.21003i	−0.266261	−	0.317318i	−0.882565	+	0.470191i	$0.844185\pi$
$384$	−1.67134	−	0.454573i	−0.0852900	−	0.0231973i
$385$	−36.3919	−	5.44419i	−1.85470	−	0.277461i
$386$	−13.5031	+	16.0924i	−0.687291	+	0.819082i
$387$	0.144816	−	0.786668i	0.00736142	−	0.0399886i
$388$	−6.31180	−	10.9324i	−0.320433	−	0.555006i
$389$	1.30120	+	0.229437i	0.0659736	+	0.0116329i	0.206538	−	0.978439i	$-0.433780\pi$
$389$	1.30120	+	0.229437i	0.0659736	+	0.0116329i	−0.140564	+	0.990072i	$0.544892\pi$
$390$	−6.87157	+	10.2943i	−0.347956	+	0.521271i
$391$	−17.8086	−	30.8454i	−0.900619	−	1.55992i
$392$	−0.750284	−	0.433177i	−0.0378951	−	0.0218787i
$393$	2.67693	+	10.1428i	0.135033	+	0.511636i
$394$	2.33959	−	6.42796i	0.117867	−	0.323836i
$395$	−0.272448	−	0.444739i	−0.0137083	−	0.0223772i
$396$	−8.91530	+	15.1771i	−0.448011	+	0.762680i
$397$	0.339352	−	0.0598368i	0.0170316	−	0.00300312i	−0.165126	−	0.986272i	$-0.552803\pi$
$397$	0.339352	−	0.0598368i	0.0170316	−	0.00300312i	0.182157	+	0.983269i	$0.441692\pi$
$398$			7.48597i			0.375238i
$399$	−14.9906	−	14.9554i	−0.750468	−	0.748707i
$400$	4.60309	−	1.95232i	0.230154	−	0.0976162i
$401$	−4.53340	−	25.7102i	−0.226387	−	1.28391i	−0.860016	−	0.510268i	$-0.829546\pi$
$401$	−4.53340	−	25.7102i	−0.226387	−	1.28391i	0.633628	−	0.773638i	$-0.281565\pi$
$402$	0.544008	−	0.0455350i	0.0271327	−	0.00227108i
$403$	−0.413592	−	1.13633i	−0.0206025	−	0.0566048i
$404$	3.28038	−	9.01277i	0.163205	−	0.448402i
$405$	−19.7792	+	3.71243i	−0.982838	+	0.184472i
$406$	1.13093	−	1.95882i	0.0561270	−	0.0972148i
$407$	−2.93523	+	1.69466i	−0.145494	+	0.0840011i
$408$	5.24522	−	5.20594i	0.259677	−	0.257732i
$409$	9.60037	+	1.69280i	0.474708	+	0.0837038i	0.405883	−	0.913925i	$-0.366964\pi$
$409$	9.60037	+	1.69280i	0.474708	+	0.0837038i	0.0688245	+	0.997629i	$0.478075\pi$
$410$	−13.4173	+	11.8671i	−0.662631	+	0.586076i
$411$	13.9466	+	30.2045i	0.687936	+	1.48988i
$412$	6.82024	+	5.72286i	0.336009	+	0.281945i
$413$	−10.9195	+	30.0010i	−0.537313	+	1.47625i
$414$	−19.3046	+	15.9528i	−0.948770	+	0.784036i
$415$	5.06410	−	6.36455i	0.248587	−	0.312424i
$416$	−3.14718	+	0.554934i	−0.154303	+	0.0272079i
$417$	−1.61330	+	2.28570i	−0.0790035	+	0.111931i
$418$	−8.86561	−	23.9892i	−0.433631	−	1.17335i
$419$			18.9014i			0.923392i	0.887038	+	0.461696i	$0.152759\pi$
$419$			18.9014i			0.923392i	−0.887038	+	0.461696i	$0.847241\pi$
$420$	2.57702	−	10.5525i	0.125746	−	0.514907i
$421$	−21.2072	−	25.2737i	−1.03358	−	1.23177i	−0.972322	−	0.233645i	$-0.924935\pi$
$421$	−21.2072	−	25.2737i	−1.03358	−	1.23177i	−0.0612531	−	0.998122i	$-0.519510\pi$
$422$	9.47868	−	3.44996i	0.461415	−	0.167941i
$423$	−0.198872	+	26.4565i	−0.00966951	+	1.28636i
$424$	−3.13204	−	2.62809i	−0.152105	−	0.127631i
$425$	−2.60603	+	21.1737i	−0.126411	+	1.02708i
$426$	1.97542	−	21.6420i	0.0957095	−	1.04856i
$427$	−16.3464	−	2.88232i	−0.791060	−	0.139485i
$428$	2.75716	+	0.486162i	0.133273	+	0.0234995i
$429$	−2.95210	+	32.3421i	−0.142529	+	1.56149i
$430$	−0.189259	+	0.565363i	−0.00912688	+	0.0272642i
$431$	1.20151	+	1.00818i	0.0578746	+	0.0485626i	0.671266	−	0.741216i	$-0.265751\pi$
$431$	1.20151	+	1.00818i	0.0578746	+	0.0485626i	−0.613392	+	0.789779i	$0.710195\pi$
$432$	−4.22256	−	3.02819i	−0.203158	−	0.145694i
$433$	35.7640	−	13.0170i	1.71871	−	0.625558i	0.720980	−	0.692956i	$-0.243692\pi$
$433$	35.7640	−	13.0170i	1.71871	−	0.625558i	0.997726	+	0.0673985i	$0.0214699\pi$
$434$	0.682187	+	0.812999i	0.0327460	+	0.0390252i
$435$	3.03420	+	0.740985i	0.145479	+	0.0355275i
$436$			12.9581i			0.620579i
$437$	−0.179482	−	36.3864i	−0.00858579	−	1.74060i
$438$	1.44528	−	2.04765i	0.0690581	−	0.0978404i
$439$	24.2706	−	4.27957i	1.15837	−	0.204253i	0.438745	−	0.898612i	$-0.355423\pi$
$439$	24.2706	−	4.27957i	1.15837	−	0.204253i	0.719629	+	0.694359i	$0.244312\pi$
$440$	8.16869	−	10.2664i	0.389427	−	0.489432i
$441$	−1.65563	−	2.00350i	−0.0788395	−	0.0954046i
$442$	4.66352	−	12.8129i	0.221821	−	0.609449i
$443$	−20.8019	−	17.4549i	−0.988330	−	0.829307i	−0.00300464	−	0.999995i	$-0.500956\pi$
$443$	−20.8019	−	17.4549i	−0.988330	−	0.829307i	−0.985325	+	0.170688i	$0.945401\pi$
$444$	−0.419435	−	0.908378i	−0.0199055	−	0.0431097i
$445$	−21.9053	−	24.7666i	−1.03841	−	1.17405i
$446$	19.9750	+	3.52212i	0.945842	+	0.166777i
$447$	23.2068	−	23.0330i	1.09764	−	1.08942i
$448$	2.42894	−	1.40235i	0.114757	−	0.0662549i
$449$	4.16071	−	7.20657i	0.196356	−	0.340099i	−0.750988	−	0.660316i	$-0.770422\pi$
$449$	4.16071	−	7.20657i	0.196356	−	0.340099i	0.947344	+	0.320217i	$0.103756\pi$
$450$	14.9851	−	0.668084i	0.706405	−	0.0314938i
$451$	−16.0753	+	44.1664i	−0.756954	+	2.07971i
$452$	−3.18355	−	8.74672i	−0.149741	−	0.411411i
$453$	3.54270	−	0.296534i	0.166451	−	0.0139324i
$454$	−4.71705	−	26.7517i	−0.221382	−	1.25552i
$455$	−3.99290	−	19.6403i	−0.187190	−	0.920751i
$456$	7.29028	−	1.96260i	0.341399	−	0.0919073i
$457$			20.3458i			0.951736i	0.879517	+	0.475868i	$0.157866\pi$
$457$			20.3458i			0.951736i	−0.879517	+	0.475868i	$0.842134\pi$
$458$	0.840514	−	0.148205i	0.0392746	−	0.00692518i
$459$	20.1976	−	9.14247i	0.942742	−	0.426734i
$460$	15.9168	−	9.75068i	0.742127	−	0.454628i
$461$	3.68782	−	10.1322i	0.171759	−	0.471904i	−0.823708	−	0.567015i	$-0.808098\pi$
$461$	3.68782	−	10.1322i	0.171759	−	0.471904i	0.995467	+	0.0951107i	$0.0303205\pi$
$462$	−7.27352	−	27.5590i	−0.338395	−	1.28216i
$463$	32.5056	+	18.7671i	1.51066	+	0.872181i	0.999923	+	0.0124456i	$0.00396167\pi$
$463$	32.5056	+	18.7671i	1.51066	+	0.872181i	0.510740	+	0.859736i	$0.329372\pi$
$464$	0.403226	+	0.698407i	0.0187193	+	0.0324227i
$465$	−0.813644	+	1.21892i	−0.0377319	+	0.0565260i
$466$	10.6379	+	1.87576i	0.492793	+	0.0868928i
$467$	12.8925	+	22.3305i	0.596594	+	1.03333i	0.993320	+	0.115394i	$0.0368132\pi$
$467$	12.8925	+	22.3305i	0.596594	+	1.03333i	−0.396725	+	0.917937i	$0.629853\pi$
$468$	−9.42877	−	1.73572i	−0.435845	−	0.0802338i
$469$	−0.568218	+	0.677176i	−0.0262379	+	0.0312691i
$470$	2.91763	−	19.5030i	0.134580	−	0.899606i
$471$	4.91385	+	1.33648i	0.226418	+	0.0615816i
$472$	−7.31697	−	8.72002i	−0.336791	−	0.401372i
$473$	0.271654	+	1.54063i	0.0124907	+	0.0708381i
$474$	0.232964	−	0.330060i	0.0107004	−	0.0151602i
$475$	−13.0353	+	17.4666i	−0.598100	+	0.801421i
$476$			11.9668i			0.548498i
$477$	−6.05286	−	10.6683i	−0.277141	−	0.488466i
$478$	−15.8201	+	13.2747i	−0.723596	+	0.607169i
$479$	−1.44121	−	3.95968i	−0.0658504	−	0.180922i	0.902403	−	0.430893i	$-0.141801\pi$
$479$	−1.44121	−	3.95968i	−0.0658504	−	0.180922i	−0.968253	+	0.249970i	$0.919579\pi$
$480$	2.79894	+	2.67693i	0.127753	+	0.122185i
$481$	−1.41416	−	1.18662i	−0.0644800	−	0.0541052i
$482$	−0.717747	+	1.24317i	−0.0326925	+	0.0566250i
$483$	3.68617	−	40.3844i	0.167726	−	1.83755i
$484$	4.06776	−	23.0694i	0.184898	−	1.04861i
$485$	0.734819	+	28.2176i	0.0333664	+	1.28130i
$486$	−8.69965	−	12.9351i	−0.394624	−	0.586747i
$487$	−14.5391	+	25.1824i	−0.658827	+	1.14112i	0.322092	+	0.946708i	$0.395614\pi$
$487$	−14.5391	+	25.1824i	−0.658827	+	1.14112i	−0.980920	+	0.194414i	$0.937719\pi$
$488$	3.80410	−	4.53355i	0.172204	−	0.205224i
$489$	14.0134	+	20.1742i	0.633708	+	0.912307i
$490$	1.01196	+	1.65190i	0.0457156	+	0.0746253i
$491$	25.0503	+	29.8538i	1.13050	+	1.34728i	0.929987	+	0.367593i	$0.119818\pi$
$491$	25.0503	+	29.8538i	1.13050	+	1.34728i	0.200518	+	0.979690i	$0.435738\pi$
$492$	−12.5527	−	5.91098i	−0.565921	−	0.266487i
$493$	−3.44088			−0.154970
$494$	10.6266	−	9.00648i	0.478114	−	0.405221i
$495$	33.7157	−	20.3074i	1.51541	−	0.912748i
$496$	−0.372650	+	0.0657082i	−0.0167325	+	0.00295038i
$497$	22.6200	+	26.9575i	1.01465	+	1.20921i
$498$	6.07928	+	1.65345i	0.272419	+	0.0740930i
$499$	−11.7882	−	4.29054i	−0.527711	−	0.192071i	0.0644052	−	0.997924i	$-0.479485\pi$
$499$	−11.7882	−	4.29054i	−0.527711	−	0.192071i	−0.592116	+	0.805853i	$0.701707\pi$
$500$	−11.1284	−	1.07642i	−0.497677	−	0.0481389i
$501$	−14.9170	+	6.88778i	−0.666443	+	0.307723i
$502$	−13.5416	−	23.4547i	−0.604390	−	1.04683i
$503$	4.61087	−	26.1495i	0.205588	−	1.16595i	−0.690923	−	0.722929i	$-0.742795\pi$
$503$	4.61087	−	26.1495i	0.205588	−	1.16595i	0.896511	−	0.443021i	$-0.146093\pi$
$504$	8.29703	−	1.39877i	0.369579	−	0.0623060i
$505$	−16.0646	+	14.2086i	−0.714864	+	0.632274i
$506$	24.4893	−	42.4167i	1.08868	−	1.88565i
$507$	4.66787	−	1.23197i	0.207307	−	0.0547136i
$508$	−11.7185	−	4.26519i	−0.519925	−	0.189237i
$509$	1.93283	−	0.703491i	0.0856710	−	0.0311817i	−0.298829	−	0.954307i	$-0.596596\pi$
$509$	1.93283	−	0.703491i	0.0856710	−	0.0311817i	0.384500	+	0.923125i	$0.374374\pi$
$510$	−15.8625	+	4.63143i	−0.702405	+	0.205083i
$511$	0.704749	+	3.99683i	0.0311763	+	0.176809i
$512$			1.00000i			0.0441942i
$513$	22.5503	+	2.11710i	0.995622	+	0.0934724i
$514$	−24.2779			−1.07085
$515$	−7.29367	−	18.5239i	−0.321398	−	0.816262i
$516$	−0.460205	+	0.0385204i	−0.0202594	+	0.00169577i
$517$	−17.6976	−	48.6236i	−0.778338	−	2.13847i
$518$	1.52246	+	0.554130i	0.0668930	+	0.0243471i
$519$	−0.661528	−	2.50650i	−0.0290378	−	0.110023i
$520$	6.77628	+	2.26840i	0.297160	+	0.0994760i
$521$	1.30575	+	2.26163i	0.0572061	+	0.0990838i	0.893210	−	0.449639i	$-0.148447\pi$
$521$	1.30575	+	2.26163i	0.0572061	+	0.0990838i	−0.836004	+	0.548723i	$0.815114\pi$
$522$	0.402195	+	2.38569i	0.0176036	+	0.104419i
$523$	1.55123	−	8.79748i	0.0678307	−	0.384687i	−0.931926	−	0.362647i	$-0.881873\pi$
$523$	1.55123	−	8.79748i	0.0678307	−	0.384687i	0.999757	−	0.0220395i	$-0.00701596\pi$
$524$	5.24504	−	3.02823i	0.229131	−	0.132289i
$525$	−16.3257	+	17.9846i	−0.712513	+	0.784914i
$526$	14.7126	−	17.5337i	0.641498	−	0.764508i
$527$	0.552195	−	1.51714i	0.0240540	−	0.0660879i
$528$	9.80625	+	2.66712i	0.426762	+	0.116071i
$529$	35.7623	−	30.0081i	1.55488	−	1.30470i
$530$	3.34945	+	8.50669i	0.145491	+	0.369507i
$531$	−11.4383	−	32.1770i	−0.496380	−	1.39636i
$532$	−6.06041	+	10.6175i	−0.262752	+	0.460329i
$533$	−25.5999			−1.10885
$534$	10.9109	−	23.1708i	0.472162	−	1.00270i
$535$	−4.89881	−	3.89785i	−0.211794	−	0.168519i
$536$	−0.107798	−	0.296174i	−0.00465619	−	0.0127928i
$537$	17.1259	−	11.8960i	0.739037	−	0.513350i
$538$	−7.98064	+	9.51096i	−0.344070	+	0.410046i
$539$	4.40215	+	2.54158i	0.189614	+	0.109474i
$540$	5.06527	+	10.4567i	0.217974	+	0.449986i
$541$	−7.17164	+	40.6724i	−0.308333	+	1.74864i	0.299054	+	0.954236i	$0.403329\pi$
$541$	−7.17164	+	40.6724i	−0.308333	+	1.74864i	−0.607387	+	0.794406i	$0.707782\pi$
$542$	26.1084	+	4.60361i	1.12145	+	0.197742i
$543$	−2.05035	+	22.4629i	−0.0879889	+	0.963976i
$544$	−3.69507	−	2.13335i	−0.158425	−	0.0914666i
$545$	13.8294	−	25.4618i	0.592387	−	1.09067i
$546$	12.7503	−	8.85664i	0.545663	−	0.379029i
$547$	−29.6537	+	10.7931i	−1.26790	+	0.461478i	−0.886412	−	0.462896i	$-0.846810\pi$
$547$	−29.6537	+	10.7931i	−1.26790	+	0.461478i	−0.381487	+	0.924374i	$0.624588\pi$
$548$	14.7140	−	12.3465i	0.628552	−	0.527418i
$549$	15.4421	−	8.76138i	0.659051	−	0.373926i
$550$	−27.0078	+	11.4549i	−1.15161	+	0.488438i
$551$	−3.05292	−	1.74258i	−0.130059	−	0.0742365i
$552$	11.8126	+	8.33761i	0.502777	+	0.354872i
$553$	0.113598	+	0.644249i	0.00483070	+	0.0273963i
$554$	0.461421	−	0.387179i	0.0196039	−	0.0164496i
$555$	−0.145297	+	2.23255i	−0.00616752	+	0.0947664i
$556$	1.51784	+	0.552449i	0.0643708	+	0.0234291i
$557$	−3.04384	−	2.55408i	−0.128971	−	0.108220i	0.576020	−	0.817435i	$-0.304605\pi$
$557$	−3.04384	−	2.55408i	−0.128971	−	0.108220i	−0.704992	+	0.709215i	$0.749049\pi$
$558$	−1.11644	−	0.205522i	−0.0472625	−	0.00870046i
$559$	−0.737919	+	0.426038i	−0.0312106	+	0.0180195i
$560$	−6.26938	+	0.163262i	−0.264930	+	0.00689907i
$561$	−30.7753	+	30.5449i	−1.29934	+	1.28960i
$562$	8.00648	−	4.62254i	0.337733	−	0.194990i
$563$	−29.3130	−	16.9238i	−1.23539	−	0.713255i	−0.267245	−	0.963629i	$-0.586113\pi$
$563$	−29.3130	−	16.9238i	−1.23539	−	0.713255i	−0.968149	+	0.250374i	$0.919447\pi$
$564$	14.7693	−	3.89800i	0.621901	−	0.164135i
$565$	−3.07941	+	20.5844i	−0.129552	+	0.865993i
$566$	−5.17629	+	1.88401i	−0.217576	+	0.0791911i
$567$	24.7901	+	4.75649i	1.04109	+	0.199754i
$568$	−12.3564	+	2.17876i	−0.518461	+	0.0914187i
$569$	0.590427			0.0247520			0.0123760	−	0.999923i	$-0.496060\pi$
$569$	0.590427			0.0247520			0.0123760	+	0.999923i	$0.496060\pi$
$570$	−16.4195	−	3.92411i	−0.687739	−	0.164363i
$571$	34.7096			1.45255			0.726275	−	0.687404i	$-0.241250\pi$
$571$	34.7096			1.45255			0.726275	+	0.687404i	$0.241250\pi$
$572$	18.4655	−	3.25597i	0.772082	−	0.136139i
$573$	39.3078	−	3.29017i	1.64211	−	0.137449i
$574$	21.1125	−	7.68432i	0.881219	−	0.320737i
$575$	−41.6820	+	2.17237i	−1.73826	+	0.0905939i
$576$	−1.04722	+	2.81129i	−0.0436342	+	0.117137i
$577$	−24.0060	−	13.8599i	−0.999383	−	0.576994i	−0.0913174	−	0.995822i	$-0.529108\pi$
$577$	−24.0060	−	13.8599i	−0.999383	−	0.576994i	−0.908066	+	0.418828i	$0.862441\pi$
$578$	1.04331	−	0.602354i	0.0433959	−	0.0250546i
$579$	25.6315	+	25.8249i	1.06521	+	1.07325i
$580$	−0.0469435	−	1.80267i	−0.00194922	−	0.0748517i
$581$	−8.83499	+	5.10088i	−0.366537	+	0.211620i
$582$	−19.8507	+	9.16588i	−0.822840	+	0.379938i
$583$	18.3766	+	15.4198i	0.761082	+	0.638624i
$584$	−1.35976	−	0.494914i	−0.0562674	−	0.0204797i
$585$	16.6745	+	13.4734i	0.689407	+	0.557056i
$586$	−9.59219	+	8.04880i	−0.396250	+	0.332493i
$587$	5.05176	+	28.6499i	0.208508	+	1.18251i	0.891823	+	0.452385i	$0.149427\pi$
$587$	5.05176	+	28.6499i	0.208508	+	1.18251i	−0.683315	+	0.730124i	$0.739462\pi$
$588$	−0.865304	+	1.22595i	−0.0356845	+	0.0505573i
$589$	1.25827	−	1.06643i	0.0518461	−	0.0439416i
$590$	5.07102	+	24.9433i	0.208770	+	1.02690i
$591$	−10.7191	−	5.04754i	−0.440925	−	0.207628i
$592$	−0.442514	+	0.371313i	−0.0181872	+	0.0152609i
$593$	38.9574	−	14.1793i	1.59979	−	0.582276i	0.620405	−	0.784282i	$-0.286968\pi$
$593$	38.9574	−	14.1793i	1.59979	−	0.582276i	0.979384	+	0.202006i	$0.0647460\pi$
$594$	24.7751	+	17.7673i	1.01653	+	0.729003i
$595$	12.7715	−	23.5141i	0.523581	−	0.963983i
$596$	−16.3484	−	9.43874i	−0.669655	−	0.386626i
$597$	12.9124	+	1.17861i	0.528470	+	0.0482372i
$598$	26.2718	+	4.63243i	1.07433	+	0.189434i
$599$	4.28225	−	24.2858i	0.174968	−	0.992293i	−0.763213	−	0.646147i	$-0.776379\pi$
$599$	4.28225	−	24.2858i	0.174968	−	0.992293i	0.938181	−	0.346146i	$-0.112510\pi$
$600$	−2.64280	−	8.24716i	−0.107892	−	0.336689i
$601$	−4.73014	−	2.73095i	−0.192946	−	0.111398i	0.400415	−	0.916334i	$-0.368866\pi$
$601$	−4.73014	−	2.73095i	−0.192946	−	0.111398i	−0.593361	+	0.804936i	$0.702199\pi$
$602$	0.480686	−	0.572859i	0.0195913	−	0.0233480i
$603$	0.00710744	−	0.945518i	0.000289437	−	0.0385045i
$604$	−0.702007	−	1.92875i	−0.0285643	−	0.0784797i
$605$	−32.6136	+	40.9888i	−1.32593	+	1.66643i
$606$	−15.0295	−	7.07725i	−0.610531	−	0.287494i
$607$	17.1854			0.697535			0.348767	−	0.937209i	$-0.386600\pi$
$607$	17.1854			0.697535			0.348767	+	0.937209i	$0.386600\pi$
$608$	−2.19804	−	3.76412i	−0.0891424	−	0.152655i
$609$	−3.20068	−	2.25912i	−0.129698	−	0.0915440i
$610$	−12.3132	+	4.84826i	−0.498549	+	0.196300i
$611$	21.5897	−	18.1159i	0.873427	−	0.732892i
$612$	−8.15380	−	9.86701i	−0.329598	−	0.398850i
$613$	10.1908	−	27.9989i	0.411602	−	1.13087i	−0.544737	−	0.838607i	$-0.683371\pi$
$613$	10.1908	−	27.9989i	0.411602	−	1.13087i	0.956339	−	0.292260i	$-0.0944072\pi$
$614$	−10.0068	+	11.9257i	−0.403843	+	0.481282i
$615$	18.3569	+	25.0116i	0.740223	+	1.00856i
$616$	−14.2514	+	8.22803i	−0.574204	+	0.331517i
$617$	7.35764	−	41.7272i	0.296207	−	1.67987i	−0.366048	−	0.930596i	$-0.619289\pi$
$617$	7.35764	−	41.7272i	0.296207	−	1.67987i	0.662255	−	0.749279i	$-0.269600\pi$
$618$	10.9450	−	10.8631i	0.440274	−	0.436977i
$619$	−9.94278	−	17.2214i	−0.399634	−	0.692187i	0.594046	−	0.804431i	$-0.297530\pi$
$619$	−9.94278	−	17.2214i	−0.399634	−	0.692187i	−0.993681	+	0.112244i	$0.964196\pi$
$620$	0.802361	+	0.268595i	0.0322236	+	0.0107870i
$621$	24.4772	+	35.8098i	0.982238	+	1.43700i
$622$	21.8990	+	7.97059i	0.878070	+	0.319591i
$623$	14.1843	+	38.9711i	0.568282	+	1.56134i
$624$	0.461695	+	5.51589i	0.0184826	+	0.220812i
$625$	20.7178	+	13.9918i	0.828714	+	0.559673i
$626$	1.41632			0.0566077
$627$	−42.7743	+	11.5152i	−1.70824	+	0.459873i
$628$		−	2.94008i		−	0.117322i
$629$	−0.427991	−	2.42726i	−0.0170651	−	0.0967812i
$630$	−17.7960	−	6.10645i	−0.709009	−	0.243287i
$631$	−15.0088	+	5.46277i	−0.597492	+	0.217469i	−0.623021	−	0.782205i	$-0.714095\pi$
$631$	−15.0088	+	5.46277i	−0.597492	+	0.217469i	0.0255294	+	0.999674i	$0.491873\pi$
$632$	−0.219180	−	0.0797751i	−0.00871852	−	0.00317328i
$633$	−4.45842	−	16.8927i	−0.177206	−	0.671427i
$634$	−8.77593	+	15.2004i	−0.348537	+	0.603683i
$635$	18.4742	+	20.8874i	0.733126	+	0.828890i
$636$	−5.02626	+	4.98862i	−0.199304	+	0.197812i
$637$	−0.480768	+	2.72657i	−0.0190487	+	0.108031i
$638$	−2.36585	−	4.09777i	−0.0936649	−	0.162232i
$639$	−37.0189	−	6.81473i	−1.46444	−	0.269587i
$640$	1.06724	−	1.96494i	0.0421865	−	0.0776711i
$641$	8.79759	+	3.20206i	0.347484	+	0.126474i	0.509865	−	0.860254i	$-0.329695\pi$
$641$	8.79759	+	3.20206i	0.347484	+	0.126474i	−0.162381	+	0.986728i	$0.551917\pi$
$642$	1.27267	−	4.67924i	0.0502281	−	0.184675i
$643$	−6.26523	−	7.46661i	−0.247076	−	0.294454i	0.628225	−	0.778032i	$-0.283782\pi$
$643$	−6.26523	−	7.46661i	−0.247076	−	0.294454i	−0.875302	+	0.483577i	$0.839337\pi$
$644$	−23.0572	+	4.06560i	−0.908579	+	0.160207i
$645$	0.945387	+	0.415461i	0.0372246	+	0.0163588i
$646$	18.5979	−	0.0917371i	0.731724	−	0.00360935i
$647$	11.8796			0.467034			0.233517	−	0.972353i	$-0.424976\pi$
$647$	11.8796			0.467034			0.233517	+	0.972353i	$0.424976\pi$
$648$	−5.88808	+	6.80665i	−0.231306	+	0.267391i
$649$	42.9309	+	51.1631i	1.68519	+	2.00833i
$650$	−10.8940	−	11.6892i	−0.427300	−	0.458489i
$651$	1.50973	−	1.04869i	0.0591710	−	0.0411014i
$652$	9.11590	−	10.8639i	0.357006	−	0.425463i
$653$	−2.15300	+	3.72910i	−0.0842532	+	0.145931i	−0.905073	−	0.425257i	$-0.860184\pi$
$653$	−2.15300	+	3.72910i	−0.0842532	+	0.145931i	0.820820	+	0.571188i	$0.193517\pi$
$654$	22.3511	+	2.04015i	0.873998	+	0.0797760i
$655$	−13.5381	+	0.352546i	−0.528976	+	0.0137751i
$656$	−1.39103	+	7.88894i	−0.0543107	+	0.308011i
$657$	−3.30440	−	2.81532i	−0.128917	−	0.109836i
$658$	−12.3674	+	21.4210i	−0.482132	+	0.835078i
$659$	−2.44487	−	2.05149i	−0.0952387	−	0.0799147i	0.593925	−	0.804520i	$-0.297578\pi$
$659$	−2.44487	−	2.05149i	−0.0952387	−	0.0799147i	−0.689164	+	0.724606i	$0.742022\pi$
$660$	−16.4222	−	15.7064i	−0.639234	−	0.611370i
$661$	−2.66247	−	7.31507i	−0.103558	−	0.284523i	0.877083	−	0.480340i	$-0.159487\pi$
$661$	−2.66247	−	7.31507i	−0.103558	−	0.284523i	−0.980641	+	0.195816i	$0.937264\pi$
$662$	−1.30789	+	1.09745i	−0.0508327	+	0.0426537i
$663$	−21.3665	−	10.0613i	−0.829807	−	0.390749i
$664$		−	3.63738i		−	0.141158i
$665$	23.2398	−	14.3949i	0.901202	−	0.558210i
$666$	−1.63288	+	0.580457i	−0.0632728	+	0.0224923i
$667$	−1.16900	−	6.62975i	−0.0452640	−	0.256705i
$668$	6.09755	+	7.26678i	0.235921	+	0.281160i
$669$	9.22014	−	33.8999i	0.356471	−	1.31065i
$670$	−0.104272	+	0.697011i	−0.00402838	+	0.0269279i
$671$	−22.3199	+	26.5998i	−0.861649	+	1.02687i
$672$	−2.03647	−	4.41043i	−0.0785585	−	0.170136i
$673$	3.97910	+	6.89200i	0.153383	+	0.265667i	0.932469	−	0.361250i	$-0.117650\pi$
$673$	3.97910	+	6.89200i	0.153383	+	0.265667i	−0.779086	+	0.626917i	$0.784317\pi$
$674$	−26.5332	−	4.67851i	−1.02202	−	0.180210i
$675$	1.20692	−	25.9527i	0.0464545	−	0.998920i
$676$	−1.39364	−	2.41385i	−0.0536015	−	0.0928405i
$677$	8.19808	+	4.73316i	0.315078	+	0.181910i	0.649196	−	0.760621i	$-0.275105\pi$
$677$	8.19808	+	4.73316i	0.315078	+	0.181910i	−0.334119	+	0.942531i	$0.608439\pi$
$678$	−15.5883	+	4.11413i	−0.598664	+	0.158002i
$679$	12.1094	−	33.2702i	0.464715	−	1.27679i
$680$	4.98379	+	8.13544i	0.191119	+	0.311980i
$681$	−46.8862	+	3.92450i	−1.79668	+	0.150387i
$682$	2.18645	−	0.385530i	0.0837235	−	0.0147627i
$683$		−	12.9727i		−	0.496385i	−0.968711	−	0.248193i	$-0.920163\pi$
$683$		−	12.9727i		−	0.496385i	0.968711	−	0.248193i	$-0.0798366\pi$
$684$	−2.23746	−	12.8839i	−0.0855513	−	0.492627i
$685$	−42.0890	+	8.55676i	−1.60814	+	0.326937i
$686$	2.98728	+	16.9417i	0.114055	+	0.646837i
$687$	−0.123304	−	1.47312i	−0.00470434	−	0.0562030i
$688$	0.0911924	+	0.250549i	0.00347668	+	0.00955210i
$689$	−4.46885	+	12.2781i	−0.170249	+	0.467757i
$690$	−14.3128	−	28.9898i	−0.544878	−	1.10362i
$691$	9.46593	−	16.3955i	0.360101	−	0.623713i	−0.627876	−	0.778313i	$-0.716076\pi$
$691$	9.46593	−	16.3955i	0.360101	−	0.623713i	0.987977	+	0.154600i	$0.0494090\pi$
$692$	−1.29616	+	0.748340i	−0.0492727	+	0.0284476i
$693$	−48.6812	+	8.20700i	−1.84925	+	0.311758i
$694$	3.11918	+	0.549995i	0.118402	+	0.0208775i
$695$	−2.39287	−	2.70544i	−0.0907668	−	0.102623i
$696$	1.26815	−	0.585557i	0.0480692	−	0.0221955i
$697$	−26.1826	−	21.9698i	−0.991737	−	0.832166i
$698$	−2.62258	+	7.20549i	−0.0992662	+	0.272732i
$699$	4.91032	−	18.0539i	0.185725	−	0.682860i
$700$	12.4932	+	6.37016i	0.472198	+	0.240769i
$701$	36.6308	−	6.45900i	1.38353	−	0.243953i	0.568170	−	0.822911i	$-0.307652\pi$
$701$	36.6308	−	6.45900i	1.38353	−	0.243953i	0.815357	+	0.578958i	$0.196541\pi$
$702$	−4.47840	+	15.9902i	−0.169026	+	0.603512i
$703$	0.849513	−	2.37033i	0.0320400	−	0.0893988i
$704$		−	5.86731i		−	0.221133i
$705$	−33.1810	−	8.10315i	−1.24967	−	0.305182i
$706$	4.77481	+	5.69040i	0.179702	+	0.214161i
$707$	25.2781	−	9.20049i	0.950682	−	0.346020i
$708$	−16.1930	+	11.2480i	−0.608570	+	0.422726i
$709$	−6.29278	−	5.28027i	−0.236330	−	0.198305i	0.516929	−	0.856028i	$-0.327075\pi$
$709$	−6.29278	−	5.28027i	−0.236330	−	0.198305i	−0.753259	+	0.657724i	$0.771519\pi$
$710$	26.6048	+	8.90611i	0.998459	+	0.334240i
$711$	−0.532636	−	0.453801i	−0.0199754	−	0.0170189i
$712$	−14.5620	−	2.56767i	−0.545734	−	0.0962277i
$713$	3.11077	+	0.548513i	0.116499	+	0.0205420i
$714$	20.6413	+	1.88408i	0.772482	+	0.0705099i
$715$	−39.7585	−	13.3094i	−1.48688	−	0.497744i
$716$	−9.22239	−	7.73850i	−0.344657	−	0.289201i
$717$	20.4065	+	29.3778i	0.762093	+	1.09714i
$718$	20.2795	−	7.38113i	0.756824	−	0.275462i
$719$	−20.8681	−	24.8696i	−0.778249	−	0.927481i	0.220604	−	0.975364i	$-0.429197\pi$
$719$	−20.8681	−	24.8696i	−0.778249	−	0.927481i	−0.998853	+	0.0478821i	$0.984753\pi$
$720$	5.05806	−	4.40637i	0.188503	−	0.164216i
$721$			24.9708i			0.929961i
$722$	16.5474	+	9.33721i	0.615830	+	0.347495i
$723$	2.03132	+	1.43375i	0.0755457	+	0.0533219i
$724$	12.8250	−	2.26140i	0.476639	−	0.0840442i
$725$	−1.83165	+	3.59224i	−0.0680256	+	0.133412i
$726$	−39.1516	−	10.6485i	−1.45305	−	0.395203i
$727$	1.29903	−	3.56904i	0.0481782	−	0.132368i	−0.913270	−	0.407355i	$-0.866451\pi$
$727$	1.29903	−	3.56904i	0.0481782	−	0.132368i	0.961448	+	0.274987i	$0.0886734\pi$
$728$	−6.86612	−	5.76136i	−0.254475	−	0.213530i
$729$	−23.6811	+	12.9693i	−0.877080	+	0.480345i
$730$	2.14366	+	2.42368i	0.0793405	+	0.0897042i
$731$	−1.12034	−	0.197546i	−0.0414373	−	0.00730652i
$732$	−7.22091	−	7.27540i	−0.266893	−	0.268906i
$733$	−11.0282	+	6.36716i	−0.407337	+	0.235176i	−0.689645	−	0.724148i	$-0.742233\pi$
$733$	−11.0282	+	6.36716i	−0.407337	+	0.235176i	0.282308	+	0.959324i	$0.408900\pi$
$734$	−3.62458	+	6.27796i	−0.133786	+	0.231724i
$735$	3.00866	−	1.48543i	0.110976	−	0.0547908i
$736$	2.85509	−	7.84429i	0.105240	−	0.289144i
$737$	0.632487	+	1.73774i	0.0232980	+	0.0640106i
$738$	−12.1721	+	20.7213i	−0.448060	+	0.762763i
$739$	4.53532	+	25.7211i	0.166834	+	0.946164i	0.947153	+	0.320782i	$0.103946\pi$
$739$	4.53532	+	25.7211i	0.166834	+	0.946164i	−0.780319	+	0.625382i	$0.784943\pi$
$740$	1.26580	−	0.257338i	0.0465316	−	0.00945994i
$741$	−13.8620	−	19.7476i	−0.509234	−	0.725448i
$742$		−	11.4673i		−	0.420976i
$743$	−29.0022	+	5.11387i	−1.06399	+	0.187610i	−0.678125	−	0.734947i	$-0.737207\pi$
$743$	−29.0022	+	5.11387i	−1.06399	+	0.187610i	−0.385862	+	0.922556i	$0.626096\pi$
$744$	0.0546680	+	0.653121i	0.00200423	+	0.0239446i
$745$	22.0501	+	35.9943i	0.807855	+	1.31873i
$746$	3.68048	−	10.1120i	0.134752	−	0.370228i
$747$	3.80914	−	10.2257i	0.139369	−	0.374139i
$748$	21.6801	+	12.5170i	0.792703	+	0.457667i
$749$	3.92616	+	6.80031i	0.143459	+	0.248478i
$750$	−3.60877	+	19.0257i	−0.131774	+	0.694720i
$751$	25.9604	+	4.57753i	0.947310	+	0.167036i	0.625899	−	0.779904i	$-0.284732\pi$
$751$	25.9604	+	4.57753i	0.947310	+	0.167036i	0.321410	+	0.946940i	$0.395843\pi$
$752$	−4.40953	−	7.63754i	−0.160799	−	0.278512i
$753$	−42.5886	+	19.6648i	−1.55201	+	0.716627i
$754$	1.65659	−	1.97425i	0.0603296	−	0.0718981i
$755$	−0.679043	+	4.53909i	−0.0247129	+	0.165194i
$756$	−1.10640	−	14.5316i	−0.0402395	−	0.528509i
$757$	5.17672	+	6.16937i	0.188151	+	0.224230i	0.851871	−	0.523751i	$-0.175468\pi$
$757$	5.17672	+	6.16937i	0.188151	+	0.224230i	−0.663720	+	0.747981i	$0.731023\pi$
$758$	−5.36943	−	30.4516i	−0.195026	−	1.10605i
$759$	−69.3081	−	48.9193i	−2.51573	−	1.77566i
$760$	0.301789	+	9.74212i	0.0109470	+	0.353384i
$761$			37.1501i			1.34669i	0.739328	+	0.673345i	$0.235143\pi$
$761$			37.1501i			1.34669i	−0.739328	+	0.673345i	$0.764857\pi$
$762$	−9.20194	+	19.5415i	−0.333351	+	0.707915i
$763$	−27.8408	+	23.3612i	−1.00790	+	0.845731i
$764$	−7.78907	−	21.4003i	−0.281799	−	0.774236i
$765$	5.49123	+	28.0902i	0.198536	+	1.01560i
$766$	6.21003	+	5.21084i	0.224378	+	0.188275i
$767$	−18.1888	+	31.5040i	−0.656760	+	1.13754i
$768$	1.72488	+	0.157442i	0.0622413	+	0.00568120i
$769$	−2.04832	+	11.6166i	−0.0738644	+	0.418906i	0.925344	+	0.379128i	$0.123776\pi$
$769$	−2.04832	+	11.6166i	−0.0738644	+	0.418906i	−0.999209	+	0.0397776i	$0.987335\pi$
$770$	36.7844	−	0.957907i	1.32562	−	0.0345206i
$771$	−3.82236	+	41.8764i	−0.137659	+	1.50814i
$772$	10.5036	−	18.1927i	0.378032	−	0.654770i
$773$	−11.3515	+	13.5282i	−0.408284	+	0.486574i	−0.930527	−	0.366222i	$-0.880651\pi$
$773$	−11.3515	+	13.5282i	−0.408284	+	0.486574i	0.522243	+	0.852797i	$0.325095\pi$
$774$	−0.00601255	+	0.799864i	−0.000216117	+	0.0287505i
$775$	−1.28993	−	1.38409i	−0.0463358	−	0.0497179i
$776$	8.11429	+	9.67023i	0.291286	+	0.347141i
$777$	1.19551	−	2.53882i	0.0428886	−	0.0910795i
$778$	−1.32128			−0.0473701
$779$	−12.1042	−	32.7525i	−0.433678	−	1.17348i
$780$	4.97959	−	11.3311i	0.178298	−	0.405720i
$781$	72.4986	−	12.7835i	2.59420	−	0.457428i
$782$	22.8943	+	27.2843i	0.818698	+	0.975686i
$783$	4.17835	−	0.318130i	0.149322	−	0.0113691i
$784$	0.814106	+	0.296310i	0.0290752	+	0.0105825i
$785$	−3.13778	+	5.77707i	−0.111992	+	0.206193i
$786$	−4.39754	−	9.52384i	−0.156855	−	0.339704i
$787$	11.4307	+	19.7985i	0.407460	+	0.705741i	0.994604	−	0.103741i	$-0.0330813\pi$
$787$	11.4307	+	19.7985i	0.407460	+	0.705741i	−0.587144	+	0.809482i	$0.699748\pi$
$788$	−1.18784	+	6.73657i	−0.0423150	+	0.239980i
$789$	−27.9272	−	28.1379i	−0.994236	−	1.00174i
$790$	0.345537	+	0.390672i	0.0122936	+	0.0138995i
$791$	13.0532	−	22.6088i	0.464118	−	0.803875i
$792$	6.14437	−	16.4947i	0.218331	−	0.586113i
$793$	−17.7722	−	6.46856i	−0.631110	−	0.229705i
$794$	−0.323805	+	0.117856i	−0.0114914	+	0.00418254i
$795$	15.2004	−	4.43809i	0.539101	−	0.157403i
$796$	−1.29993	−	7.37224i	−0.0460746	−	0.261302i
$797$		−	3.93646i		−	0.139437i	−0.997567	−	0.0697184i	$-0.977790\pi$
$797$		−	3.93646i		−	0.139437i	0.997567	−	0.0697184i	$-0.0222101\pi$
$798$	17.3598	+	12.1251i	0.614531	+	0.429225i
$799$	37.6283			1.33119
$800$	−4.19414	+	2.72198i	−0.148285	+	0.0962366i
$801$	−38.2490	−	22.4681i	−1.35146	−	0.793872i
$802$	8.92905	+	24.5324i	0.315296	+	0.866268i
$803$	7.97816	+	2.90381i	0.281543	+	0.102473i
$804$	−0.527837	+	0.139309i	−0.0186154	+	0.00491306i
$805$	49.6449	+	16.6189i	1.74975	+	0.585741i
$806$	0.604630	+	1.04725i	0.0212972	+	0.0368878i
$807$	15.1488	+	15.2631i	0.533262	+	0.537286i
$808$	−1.66549	+	9.44548i	−0.0585918	+	0.332291i
$809$	−9.24481	+	5.33749i	−0.325030	+	0.187656i	−0.653632	−	0.756812i	$-0.726756\pi$
$809$	−9.24481	+	5.33749i	−0.325030	+	0.187656i	0.328602	+	0.944468i	$0.393422\pi$
$810$	18.8341	−	7.09065i	0.661762	−	0.249140i
$811$	−26.0094	+	30.9968i	−0.913313	+	1.08844i	0.0824599	+	0.996594i	$0.473722\pi$
$811$	−26.0094	+	30.9968i	−0.913313	+	1.08844i	−0.995773	+	0.0918496i	$0.970722\pi$
$812$	−0.773600	+	2.12545i	−0.0271480	+	0.0745886i
$813$	12.0512	−	44.3090i	0.422655	−	1.55399i
$814$	2.59637	−	2.17861i	0.0910026	−	0.0763602i
$815$	−29.5066	+	11.6180i	−1.03357	+	0.406962i
$816$	−4.26153	+	6.03767i	−0.149183	+	0.211361i
$817$	−0.893977	−	0.742652i	−0.0312763	−	0.0259821i
$818$	−9.74847			−0.340847
$819$	−13.2692	−	23.3872i	−0.463664	−	0.817214i
$820$	11.1527	−	14.0167i	0.389470	−	0.489485i
$821$	0.837425	+	2.30081i	0.0292263	+	0.0802987i	0.953448	−	0.301558i	$-0.0975068\pi$
$821$	0.837425	+	2.30081i	0.0292263	+	0.0802987i	−0.924221	+	0.381857i	$0.875285\pi$
$822$	−18.9797	−	27.3238i	−0.661993	−	0.953027i
$823$	−20.9121	+	24.9221i	−0.728951	+	0.868730i	−0.995468	−	0.0951006i	$-0.969683\pi$
$823$	−20.9121	+	24.9221i	−0.728951	+	0.868730i	0.266517	+	0.963830i	$0.414127\pi$
$824$	−7.71039	−	4.45159i	−0.268604	−	0.155079i
$825$	15.5062	+	48.3886i	0.539855	+	1.68468i
$826$	5.54397	−	31.4414i	0.192899	−	1.09399i
$827$	−43.8897	−	7.73894i	−1.52620	−	0.269109i	−0.653331	−	0.757072i	$-0.726629\pi$
$827$	−43.8897	−	7.73894i	−1.52620	−	0.269109i	−0.872864	+	0.487963i	$0.837740\pi$
$828$	16.2412	−	19.0626i	0.564420	−	0.662472i
$829$	6.38872	+	3.68853i	0.221889	+	0.128108i	0.606825	−	0.794836i	$-0.292443\pi$
$829$	6.38872	+	3.68853i	0.221889	+	0.128108i	−0.384935	+	0.922944i	$0.625776\pi$
$830$	−3.88197	+	7.14723i	−0.134745	+	0.248084i
$831$	−0.595189	−	0.856855i	−0.0206469	−	0.0297240i
$832$	3.00301	−	1.09301i	0.104111	−	0.0378932i
$833$	−2.83166	+	2.37604i	−0.0981111	+	0.0823250i
$834$	1.19188	−	2.53112i	0.0412715	−	0.0876454i
$835$	−4.22590	−	20.7864i	−0.146243	−	0.719342i
$836$	12.8966	+	22.0853i	0.446038	+	0.763835i
$837$	−0.530275	+	1.89336i	−0.0183290	+	0.0654441i
$838$	−3.28219	−	18.6142i	−0.113381	−	0.643017i
$839$	−9.19197	+	7.71298i	−0.317342	+	0.266282i	−0.787519	−	0.616291i	$-0.788635\pi$
$839$	−9.19197	+	7.71298i	−0.317342	+	0.266282i	0.470177	+	0.882572i	$0.344190\pi$
$840$	−0.705457	+	10.8396i	−0.0243406	+	0.374003i
$841$	26.6399	+	9.69615i	0.918619	+	0.334350i
$842$	25.2737	+	21.2072i	0.870991	+	0.730848i
$843$	−6.71277	−	14.5380i	−0.231200	−	0.500715i
$844$	−8.73559	+	5.04350i	−0.300692	+	0.173604i
$845$	0.162247	+	6.23043i	0.00558148	+	0.214333i
$846$	−4.39826	−	26.0891i	−0.151215	−	0.896960i
$847$	56.8988	−	32.8505i	1.95507	−	1.12876i
$848$	3.54082	+	2.04429i	0.121592	+	0.0702013i
$849$	2.43473	+	9.22510i	0.0835599	+	0.316605i
$850$	−1.11034	−	21.3046i	−0.0380845	−	0.730741i
$851$	4.53134	−	1.64927i	0.155332	−	0.0565363i
$852$	1.81269	+	21.6563i	0.0621017	+	0.741931i
$853$	8.58918	−	1.51450i	0.294088	−	0.0518556i	−0.0246576	−	0.999696i	$-0.507850\pi$
$853$	8.58918	−	1.51450i	0.294088	−	0.0518556i	0.318746	+	0.947840i	$0.396738\pi$
$854$	16.5986			0.567993
$855$	−9.35375	+	27.7039i	−0.319891	+	0.947454i
$856$	−2.79970			−0.0956917
$857$	23.0739	−	4.06855i	0.788189	−	0.138979i	0.234957	−	0.972006i	$-0.424505\pi$
$857$	23.0739	−	4.06855i	0.788189	−	0.138979i	0.553233	+	0.833027i	$0.313394\pi$
$858$	−2.70891	−	32.3634i	−0.0924805	−	1.10487i
$859$	26.0132	−	9.46803i	0.887559	−	0.323045i	0.142303	−	0.989823i	$-0.454549\pi$
$859$	26.0132	−	9.46803i	0.887559	−	0.323045i	0.745256	+	0.666778i	$0.232327\pi$
$860$	0.0882093	−	0.589639i	0.00300791	−	0.0201065i
$861$	−9.93054	−	37.6264i	−0.338432	−	1.28230i
$862$	−1.35832	−	0.784229i	−0.0462647	−	0.0267109i
$863$	27.0699	−	15.6288i	0.921470	−	0.532011i	0.0373662	−	0.999302i	$-0.488103\pi$
$863$	27.0699	−	15.6288i	0.921470	−	0.532011i	0.884104	+	0.467291i	$0.154770\pi$
$864$	4.68425	+	2.24895i	0.159362	+	0.0765107i
$865$	3.34554	−	0.0871217i	0.113752	−	0.00296223i
$866$	−32.9602	+	19.0296i	−1.12003	+	0.646652i
$867$	−0.874728	−	1.89442i	−0.0297073	−	0.0643378i
$868$	−0.812999	−	0.682187i	−0.0275950	−	0.0231549i
$869$	1.28600	+	0.468065i	0.0436245	+	0.0158780i
$870$	−3.11678	−	0.202844i	−0.105669	−	0.00687705i
$871$	−0.771588	+	0.647440i	−0.0261443	+	0.0219377i
$872$	−2.25015	−	12.7612i	−0.0761995	−	0.432149i
$873$	12.6847	+	35.6832i	0.429312	+	1.20769i
$874$	6.49519	+	35.8024i	0.219703	+	1.21104i
$875$	−17.7499	−	25.8503i	−0.600055	−	0.873898i
$876$	−1.06775	+	2.26751i	−0.0360760	+	0.0766121i
$877$	2.06607	−	1.73364i	0.0697661	−	0.0585408i	−0.607238	−	0.794520i	$-0.707722\pi$
$877$	2.06607	−	1.73364i	0.0697661	−	0.0585408i	0.677004	+	0.735979i	$0.263278\pi$
$878$	−23.1588	+	8.42910i	−0.781570	+	0.284468i
$879$	12.3730	+	17.8126i	0.417331	+	0.600804i
$880$	−6.26185	+	11.5289i	−0.211087	+	0.388640i
$881$	−4.01643	−	2.31889i	−0.135317	−	0.0781254i	0.430813	−	0.902441i	$-0.358227\pi$
$881$	−4.01643	−	2.31889i	−0.135317	−	0.0781254i	−0.566130	+	0.824316i	$0.691560\pi$
$882$	1.97838	+	1.68556i	0.0666156	+	0.0567558i
$883$	−45.7386	−	8.06495i	−1.53923	−	0.271407i	−0.661271	−	0.750147i	$-0.729983\pi$
$883$	−45.7386	−	8.06495i	−1.53923	−	0.271407i	−0.877957	+	0.478740i	$0.841094\pi$
$884$	−2.36773	+	13.4281i	−0.0796355	+	0.451635i
$885$	43.8226	−	4.81977i	1.47308	−	0.162015i
$886$	23.5169	+	13.5775i	0.790066	+	0.456145i
$887$	−24.6246	+	29.3464i	−0.826812	+	0.985357i	0.173187	+	0.984889i	$0.444593\pi$
$887$	−24.6246	+	29.3464i	−0.826812	+	0.985357i	−1.00000		0.000467769i	$0.999851\pi$
$888$	0.570801	+	0.821744i	0.0191548	+	0.0275759i
$889$	−11.9626	−	32.8670i	−0.401213	−	1.10232i
$890$	25.8731	+	20.5865i	0.867270	+	0.690062i
$891$	34.5472	−	39.9367i	1.15737	−	1.33793i
$892$	−20.2831			−0.679129
$893$	33.3856	+	19.0563i	1.11721	+	0.637694i
$894$	−18.8546	+	26.7129i	−0.630593	+	0.893414i
$895$	9.86258	+	25.0482i	0.329670	+	0.837270i
$896$	−2.14853	+	1.80283i	−0.0717772	+	0.0602282i
$897$	12.1267	−	44.5864i	0.404898	−	1.48870i
$898$	−2.84610	+	7.81959i	−0.0949755	+	0.260943i
$899$	0.196153	−	0.233766i	0.00654207	−	0.00779653i
$900$	−14.6414	+	3.26007i	−0.488048	+	0.108669i
$901$	−15.1076	+	8.72238i	−0.503307	+	0.290584i
$902$	8.16162	−	46.2868i	0.271752	−	1.54118i
$903$	−0.912433	−	0.919318i	−0.0303639	−	0.0305930i
$904$	4.65403	+	8.06102i	0.154791	+	0.268106i
$905$	−27.6139	−	9.24392i	−0.917917	−	0.307278i
$906$	−3.43739	+	0.907212i	−0.114199	+	0.0301401i
$907$	40.9197	+	14.8935i	1.35872	+	0.494532i	0.915657	−	0.401961i	$-0.131671\pi$
$907$	40.9197	+	14.8935i	1.35872	+	0.494532i	0.443059	+	0.896493i	$0.353893\pi$
$908$	9.29078	+	25.5262i	0.308325	+	0.847117i
$909$	−14.5737	+	24.8098i	−0.483379	+	0.822889i
$910$	7.34274	+	18.6486i	0.243410	+	0.618194i
$911$	−31.7331			−1.05137			−0.525683	−	0.850681i	$-0.676190\pi$
$911$	−31.7331			−1.05137			−0.525683	+	0.850681i	$0.676190\pi$
$912$	−6.83872	+	3.19873i	−0.226453	+	0.105921i
$913$			21.3416i			0.706305i
$914$	−3.53301	−	20.0367i	−0.116862	−	0.662755i
$915$	6.42404	+	22.0022i	0.212372	+	0.727370i
$916$	−0.802009	+	0.291907i	−0.0264991	+	0.00964489i
$917$	15.9621	+	5.80974i	0.527116	+	0.191855i
$918$	−18.3032	+	12.5109i	−0.604094	+	0.412920i
$919$	11.1214	−	19.2628i	0.366861	−	0.635423i	−0.622212	−	0.782849i	$-0.713766\pi$
$919$	11.1214	−	19.2628i	0.366861	−	0.635423i	0.989073	+	0.147426i	$0.0470990\pi$
$920$	−13.9818	+	12.3665i	−0.460968	+	0.407711i
$921$	18.9949	+	19.1382i	0.625903	+	0.630625i
$922$	−1.87236	+	10.6187i	−0.0616628	+	0.349707i
$923$	20.0484	+	34.7248i	0.659901	+	1.14298i
$924$	11.9486	+	25.8773i	0.393080	+	0.851302i
$925$	−2.76185	−	0.845258i	−0.0908092	−	0.0277919i
$926$	−35.2706	−	12.8375i	−1.15906	−	0.421865i
$927$	−17.0143	−	20.5892i	−0.558823	−	0.676238i
$928$	−0.518377	−	0.617777i	−0.0170166	−	0.0202795i
$929$	30.0418	−	5.29719i	0.985641	−	0.173795i	0.342479	−	0.939525i	$-0.388733\pi$
$929$	30.0418	−	5.29719i	0.985641	−	0.173795i	0.643162	+	0.765730i	$0.277622\pi$
$930$	0.589620	−	1.34169i	0.0193344	−	0.0439957i
$931$	−3.71570	+	0.674092i	−0.121777	+	0.0220925i
$932$	−10.8021			−0.353833
$933$	17.1961	−	36.5183i	0.562976	−	1.19555i
$934$	−16.5743	−	19.7525i	−0.542327	−	0.646321i
$935$	−29.2414	−	47.7332i	−0.956297	−	1.56104i
$936$	9.58693	+	0.0720647i	0.313359	+	0.00235551i
$937$	−24.4549	+	29.1442i	−0.798907	+	0.952101i	−0.999620	−	0.0275495i	$-0.991230\pi$
$937$	−24.4549	+	29.1442i	−0.798907	+	0.952101i	0.200713	+	0.979650i	$0.435674\pi$
$938$	0.441995	−	0.765558i	0.0144317	−	0.0249964i
$939$	0.222989	−	2.44299i	0.00727697	−	0.0797240i
$940$	0.513358	+	19.7133i	0.0167439	+	0.642979i
$941$	9.74496	−	55.2664i	0.317677	−	1.80163i	−0.239125	−	0.970989i	$-0.576861\pi$
$941$	9.74496	−	55.2664i	0.317677	−	1.80163i	0.556802	−	0.830645i	$-0.312028\pi$
$942$	−5.07128	−	0.462892i	−0.165231	−	0.0150818i
$943$	33.4353	−	57.9116i	1.08880	−	1.88586i
$944$	8.72002	+	7.31697i	0.283813	+	0.238147i
$945$	−13.3347	+	29.7345i	−0.433779	+	0.967264i
$946$	−0.535054	−	1.47005i	−0.0173961	−	0.0477954i
$947$	−29.3545	+	24.6313i	−0.953891	+	0.800410i	−0.979949	−	0.199250i	$-0.936149\pi$
$947$	−29.3545	+	24.6313i	−0.953891	+	0.800410i	0.0260571	+	0.999660i	$0.491705\pi$
$948$	−0.172111	+	0.365500i	−0.00558989	+	0.0118709i
$949$			4.62433i			0.150112i
$950$	9.80422	−	19.4648i	0.318091	−	0.631521i
$951$	24.8371	+	17.5306i	0.805398	+	0.568469i
$952$	−2.07802	−	11.7850i	−0.0673489	−	0.381954i
$953$	−25.0402	−	29.8418i	−0.811133	−	0.966670i	0.188749	−	0.982025i	$-0.439557\pi$
$953$	−25.0402	−	29.8418i	−0.811133	−	0.966670i	−0.999882	+	0.0153550i	$0.995112\pi$
$954$	7.81342	+	9.45511i	0.252969	+	0.306121i
$955$	−7.53428	+	50.3632i	−0.243803	+	1.62971i
$956$	13.2747	−	15.8201i	0.429334	−	0.511660i
$957$	−7.44065	+	3.43565i	−0.240522	+	0.111059i
$958$	2.10690	+	3.64926i	0.0680709	+	0.117902i
$959$	53.0537	+	9.35481i	1.71319	+	0.302082i
$960$	−3.22126	−	2.15023i	−0.103966	−	0.0693984i
$961$	−15.4284	−	26.7228i	−0.497691	−	0.862025i
$962$	1.59873	+	0.923026i	0.0515450	+	0.0297595i
$963$	−7.87075	−	2.93190i	−0.253631	−	0.0944793i
$964$	0.490968	−	1.34892i	0.0158130	−	0.0434459i
$965$	−40.0550	+	24.5377i	−1.28941	+	0.789898i
$966$	3.38250	+	40.4109i	0.108830	+	1.30020i
$967$	5.09325	−	0.898077i	0.163788	−	0.0288802i	−0.0911528	−	0.995837i	$-0.529055\pi$
$967$	5.09325	−	0.898077i	0.163788	−	0.0288802i	0.254941	+	0.966957i	$0.417944\pi$
$968$			23.4253i			0.752918i
$969$	2.76985	−	32.0936i	0.0889805	−	1.03099i
$970$	−5.62360	−	27.6614i	−0.180563	−	0.888153i
$971$	−6.52849	−	37.0249i	−0.209509	−	1.18819i	−0.890184	−	0.455601i	$-0.849424\pi$
$971$	−6.52849	−	37.0249i	−0.209509	−	1.18819i	0.680675	−	0.732586i	$-0.261687\pi$
$972$	10.8136	+	11.2279i	0.346847	+	0.360135i
$973$	1.54946	+	4.25709i	0.0496733	+	0.136476i
$974$	9.94530	−	27.3245i	0.318668	−	0.875533i
$975$	−21.8777	+	16.9506i	−0.700647	+	0.542852i
$976$	−2.95907	+	5.12526i	−0.0947175	+	0.164055i
$977$	3.61366	−	2.08635i	0.115611	−	0.0667482i	−0.441079	−	0.897468i	$-0.645404\pi$
$977$	3.61366	−	2.08635i	0.115611	−	0.0667482i	0.556691	+	0.830720i	$0.312071\pi$
$978$	−17.3037	−	17.4343i	−0.553311	−	0.557486i
$979$	85.4398	+	15.0653i	2.73067	+	0.481490i
$980$	−1.28343	−	1.45108i	−0.0409978	−	0.0463531i
$981$	7.03801	−	38.2318i	0.224706	−	1.22065i
$982$	−29.8538	−	25.0503i	−0.952673	−	0.799387i
$983$	−3.62177	+	9.95074i	−0.115517	+	0.317379i	−0.983955	−	0.178418i	$-0.942902\pi$
$983$	−3.62177	+	9.95074i	−0.115517	+	0.317379i	0.868438	+	0.495798i	$0.165124\pi$
$984$	13.3885	+	3.64142i	0.426809	+	0.116084i
$985$	9.52359	−	11.9692i	0.303447	−	0.381372i
$986$	3.38861	−	0.597503i	0.107915	−	0.0190284i
$987$	35.0015	+	24.7049i	1.11411	+	0.786366i
$988$	−8.90121	+	10.7149i	−0.283185	+	0.340888i
$989$		−	2.22574i		−	0.0707745i
$990$	−29.6772	+	25.8535i	−0.943203	+	0.821679i
$991$	−32.4916	−	38.7220i	−1.03213	−	1.23005i	−0.972761	−	0.231810i	$-0.925535\pi$
$991$	−32.4916	−	38.7220i	−1.03213	−	1.23005i	−0.0593702	−	0.998236i	$-0.518909\pi$
$992$	0.355578	−	0.129420i	0.0112896	−	0.00410908i
$993$	1.68706	+	2.42875i	0.0535372	+	0.0770739i
$994$	−26.9575	−	22.6200i	−0.855040	−	0.717464i
$995$	−5.31370	+	15.8734i	−0.168456	+	0.503219i
$996$	−6.27404	−	0.572676i	−0.198801	−	0.0181459i
$997$	16.6998	+	2.94463i	0.528889	+	0.0932573i	0.431715	−	0.902010i	$-0.357909\pi$
$997$	16.6998	+	2.94463i	0.528889	+	0.0932573i	0.0971737	+	0.995267i	$0.469020\pi$
$998$	12.3541	+	2.17836i	0.391063	+	0.0689549i
$999$	0.744135	+	2.90791i	0.0235434	+	0.0920022i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bf.a.29.11	✓	240
3.2	odd	2	inner	570.2.bf.a.29.21	yes	240
5.4	even	2	inner	570.2.bf.a.29.30	yes	240
15.14	odd	2	inner	570.2.bf.a.29.20	yes	240
19.2	odd	18	inner	570.2.bf.a.59.20	yes	240
57.2	even	18	inner	570.2.bf.a.59.30	yes	240
95.59	odd	18	inner	570.2.bf.a.59.21	yes	240
285.59	even	18	inner	570.2.bf.a.59.11	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bf.a.29.11	✓	240	1.1	even	1	trivial
570.2.bf.a.29.20	yes	240	15.14	odd	2	inner
570.2.bf.a.29.21	yes	240	3.2	odd	2	inner
570.2.bf.a.29.30	yes	240	5.4	even	2	inner
570.2.bf.a.59.11	yes	240	285.59	even	18	inner
570.2.bf.a.59.20	yes	240	19.2	odd	18	inner
570.2.bf.a.59.21	yes	240	95.59	odd	18	inner
570.2.bf.a.59.30	yes	240	57.2	even	18	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(0.144472 + 1.72602i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-2.21146 - 0.330832i) q^{5} +(-0.441997 - 1.67471i) q^{6} +(2.42894 + 1.40235i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.95826 + 0.498722i) q^{9} +O(q^{10})\)	\(q+(-0.984808 + 0.173648i) q^{2} +(0.144472 + 1.72602i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-2.21146 - 0.330832i) q^{5} +(-0.441997 - 1.67471i) q^{6} +(2.42894 + 1.40235i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.95826 + 0.498722i) q^{9} +(2.23531 - 0.0582100i) q^{10} +(5.08124 - 2.93365i) q^{11} +(0.726091 + 1.57251i) q^{12} +(2.44808 + 2.05418i) q^{13} +(-2.63556 - 0.959265i) q^{14} +(0.251527 - 3.86481i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.740904 + 4.20188i) q^{17} +(2.82671 - 1.00484i) q^{18} +(-1.47061 + 4.10333i) q^{19} +(-2.19124 + 0.445483i) q^{20} +(-2.06956 + 4.39499i) q^{21} +(-4.49462 + 3.77143i) q^{22} +(-7.84429 + 2.85509i) q^{23} +(-0.988124 - 1.42254i) q^{24} +(4.78110 + 1.46324i) q^{25} +(-2.76759 - 1.59787i) q^{26} +(-1.28819 - 5.03394i) q^{27} +(2.76209 + 0.487031i) q^{28} +(-0.140039 + 0.794199i) q^{29} +(0.423411 + 3.84977i) q^{30} +(-0.327703 - 0.189199i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(5.79763 + 8.34646i) q^{33} +(-1.45930 - 4.00938i) q^{34} +(-4.90757 - 3.90481i) q^{35} +(-2.60928 + 1.48043i) q^{36} -0.577661 q^{37} +(0.735732 - 4.29636i) q^{38} +(-3.19186 + 4.52219i) q^{39} +(2.08060 - 0.819221i) q^{40} +(-6.13650 + 5.14914i) q^{41} +(1.27494 - 4.68760i) q^{42} +(-0.0911924 + 0.250549i) q^{43} +(3.77143 - 4.49462i) q^{44} +(6.70705 - 0.124218i) q^{45} +(7.22933 - 4.17386i) q^{46} +(1.53141 - 8.68509i) q^{47} +(1.22013 + 1.22934i) q^{48} +(0.433177 + 0.750284i) q^{49} +(-4.96255 - 0.610783i) q^{50} +(-7.14546 + 1.88587i) q^{51} +(3.00301 + 1.09301i) q^{52} +(1.39838 + 3.84201i) q^{53} +(2.14275 + 4.73377i) q^{54} +(-12.2075 + 4.80662i) q^{55} -2.80470 q^{56} +(-7.29487 - 1.94548i) q^{57} -0.806451i q^{58} +(1.97667 + 11.2102i) q^{59} +(-1.08548 - 3.71776i) q^{60} +(-5.56123 + 2.02412i) q^{61} +(0.355578 + 0.129420i) q^{62} +(-7.88482 - 2.93714i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-4.73423 - 5.35263i) q^{65} +(-7.15890 - 7.21291i) q^{66} +(-0.0547307 + 0.310393i) q^{67} +(2.13335 + 3.69507i) q^{68} +(-6.06120 - 13.1269i) q^{69} +(5.51107 + 2.99330i) q^{70} +(11.7903 + 4.29132i) q^{71} +(2.31256 - 1.91103i) q^{72} +(0.930133 + 1.10849i) q^{73} +(0.568885 - 0.100310i) q^{74} +(-1.83484 + 8.46365i) q^{75} +(0.0215007 + 4.35885i) q^{76} +16.4561 q^{77} +(2.35810 - 5.00775i) q^{78} +(0.149928 + 0.178677i) q^{79} +(-1.90673 + 1.16807i) q^{80} +(8.50255 - 2.95070i) q^{81} +(5.14914 - 6.13650i) q^{82} +(-1.81869 + 3.15006i) q^{83} +(-0.441578 + 4.83778i) q^{84} +(-0.248364 - 9.53739i) q^{85} +(0.0462996 - 0.262578i) q^{86} +(-1.39103 - 0.126969i) q^{87} +(-2.93365 + 5.08124i) q^{88} +(11.3272 + 9.50467i) q^{89} +(-6.58359 + 1.28700i) q^{90} +(3.06556 + 8.42254i) q^{91} +(-6.39472 + 5.36581i) q^{92} +(0.279217 - 0.592954i) q^{93} +8.81907i q^{94} +(4.60970 - 8.58782i) q^{95} +(-1.41507 - 0.998789i) q^{96} +(-2.19206 - 12.4318i) q^{97} +(-0.556881 - 0.663665i) q^{98} +(-13.5685 + 11.2126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) \) 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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