LMFDB - Embedded newform 630.2.ba.a.529.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(499,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.32
Character	$\chi$	$=$	630.529
Dual form			630.2.ba.a.499.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.966638 - 1.43722i) q^{3} -1.00000 q^{4} +(-1.59633 - 1.56580i) q^{5} +(1.43722 - 0.966638i) q^{6} +(2.09808 - 1.61186i) q^{7} -1.00000i q^{8} +(-1.13122 + 2.77855i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.966638 - 1.43722i) q^{3} -1.00000 q^{4} +(-1.59633 - 1.56580i) q^{5} +(1.43722 - 0.966638i) q^{6} +(2.09808 - 1.61186i) q^{7} -1.00000i q^{8} +(-1.13122 + 2.77855i) q^{9} +(1.56580 - 1.59633i) q^{10} +(-0.420325 - 0.728025i) q^{11} +(0.966638 + 1.43722i) q^{12} +(-0.875777 + 0.505630i) q^{13} +(1.61186 + 2.09808i) q^{14} +(-0.707328 + 3.80785i) q^{15} +1.00000 q^{16} +(-3.81674 - 2.20360i) q^{17} +(-2.77855 - 1.13122i) q^{18} +(0.952130 + 1.64914i) q^{19} +(1.59633 + 1.56580i) q^{20} +(-4.34468 - 1.45732i) q^{21} +(0.728025 - 0.420325i) q^{22} +(-3.29325 - 1.90136i) q^{23} +(-1.43722 + 0.966638i) q^{24} +(0.0965491 + 4.99907i) q^{25} +(-0.505630 - 0.875777i) q^{26} +(5.08688 - 1.06003i) q^{27} +(-2.09808 + 1.61186i) q^{28} +(-4.01934 + 6.96170i) q^{29} +(-3.80785 - 0.707328i) q^{30} -7.73072 q^{31} +1.00000i q^{32} +(-0.640032 + 1.30784i) q^{33} +(2.20360 - 3.81674i) q^{34} +(-5.87307 - 0.712108i) q^{35} +(1.13122 - 2.77855i) q^{36} +(-3.73933 + 2.15891i) q^{37} +(-1.64914 + 0.952130i) q^{38} +(1.57326 + 0.769926i) q^{39} +(-1.56580 + 1.59633i) q^{40} +(-4.72608 - 8.18582i) q^{41} +(1.45732 - 4.34468i) q^{42} +(-4.27106 - 2.46590i) q^{43} +(0.420325 + 0.728025i) q^{44} +(6.15645 - 2.66422i) q^{45} +(1.90136 - 3.29325i) q^{46} -0.430181i q^{47} +(-0.966638 - 1.43722i) q^{48} +(1.80384 - 6.76359i) q^{49} +(-4.99907 + 0.0965491i) q^{50} +(0.522347 + 7.61560i) q^{51} +(0.875777 - 0.505630i) q^{52} +(-2.64705 - 1.52828i) q^{53} +(1.06003 + 5.08688i) q^{54} +(-0.468962 + 1.82031i) q^{55} +(-1.61186 - 2.09808i) q^{56} +(1.44981 - 2.96254i) q^{57} +(-6.96170 - 4.01934i) q^{58} +4.28660 q^{59} +(0.707328 - 3.80785i) q^{60} +13.1981 q^{61} -7.73072i q^{62} +(2.10523 + 7.65297i) q^{63} -1.00000 q^{64} +(2.18975 + 0.564137i) q^{65} +(-1.30784 - 0.640032i) q^{66} +14.0784i q^{67} +(3.81674 + 2.20360i) q^{68} +(0.450703 + 6.57106i) q^{69} +(0.712108 - 5.87307i) q^{70} -10.6603 q^{71} +(2.77855 + 1.13122i) q^{72} +(-9.21556 - 5.32061i) q^{73} +(-2.15891 - 3.73933i) q^{74} +(7.09145 - 4.97105i) q^{75} +(-0.952130 - 1.64914i) q^{76} +(-2.05535 - 0.849947i) q^{77} +(-0.769926 + 1.57326i) q^{78} +9.85613 q^{79} +(-1.59633 - 1.56580i) q^{80} +(-6.44067 - 6.28631i) q^{81} +(8.18582 - 4.72608i) q^{82} +(9.47556 + 5.47071i) q^{83} +(4.34468 + 1.45732i) q^{84} +(2.64240 + 9.49393i) q^{85} +(2.46590 - 4.27106i) q^{86} +(13.8908 - 0.952755i) q^{87} +(-0.728025 + 0.420325i) q^{88} +(-5.46333 - 9.46277i) q^{89} +(2.66422 + 6.15645i) q^{90} +(-1.02244 + 2.47248i) q^{91} +(3.29325 + 1.90136i) q^{92} +(7.47280 + 11.1108i) q^{93} +0.430181 q^{94} +(1.06230 - 4.12342i) q^{95} +(1.43722 - 0.966638i) q^{96} +(2.02734 + 1.17049i) q^{97} +(6.76359 + 1.80384i) q^{98} +(2.49833 - 0.344337i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 96 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) $ 96 * q - 96 * q^4 - 4 * q^6 + 8 * q^9	$ 96 q - 96 q^{4} - 4 q^{6} + 8 q^{9} + 4 q^{11} - 2 q^{14} - 2 q^{15} + 96 q^{16} + 8 q^{21} + 4 q^{24} + 24 q^{26} + 10 q^{29} + 10 q^{30} - 34 q^{35} - 8 q^{36} + 44 q^{39} + 30 q^{41} - 4 q^{44} - 44 q^{45} - 6 q^{46} - 6 q^{49} - 12 q^{50} + 28 q^{51} - 8 q^{54} + 12 q^{55} + 2 q^{56} + 48 q^{59} + 2 q^{60} + 12 q^{61} - 96 q^{64} - 36 q^{65} + 32 q^{66} + 36 q^{69} + 6 q^{70} - 32 q^{71} - 68 q^{75} - 32 q^{81} - 8 q^{84} + 4 q^{86} - 66 q^{89} - 22 q^{90} + 24 q^{94} - 60 q^{95} - 4 q^{96} - 4 q^{99}+O(q^{100}) $ 96 * q - 96 * q^4 - 4 * q^6 + 8 * q^9 + 4 * q^11 - 2 * q^14 - 2 * q^15 + 96 * q^16 + 8 * q^21 + 4 * q^24 + 24 * q^26 + 10 * q^29 + 10 * q^30 - 34 * q^35 - 8 * q^36 + 44 * q^39 + 30 * q^41 - 4 * q^44 - 44 * q^45 - 6 * q^46 - 6 * q^49 - 12 * q^50 + 28 * q^51 - 8 * q^54 + 12 * q^55 + 2 * q^56 + 48 * q^59 + 2 * q^60 + 12 * q^61 - 96 * q^64 - 36 * q^65 + 32 * q^66 + 36 * q^69 + 6 * q^70 - 32 * q^71 - 68 * q^75 - 32 * q^81 - 8 * q^84 + 4 * q^86 - 66 * q^89 - 22 * q^90 + 24 * q^94 - 60 * q^95 - 4 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.966638	−	1.43722i	−0.558089	−	0.829781i
$3$	−0.966638	−	1.43722i	−0.558089	−	0.829781i
$4$	−1.00000			−0.500000
$5$	−1.59633	−	1.56580i	−0.713901	−	0.700246i
$5$	−1.59633	−	1.56580i	−0.713901	−	0.700246i
$6$	1.43722	−	0.966638i	0.586744	−	0.394628i
$7$	2.09808	−	1.61186i	0.792998	−	0.609224i
$7$	2.09808	−	1.61186i	0.792998	−	0.609224i
$8$		−	1.00000i		−	0.353553i
$9$	−1.13122	+	2.77855i	−0.377074	+	0.926183i
$10$	1.56580	−	1.59633i	0.495149	−	0.504804i
$11$	−0.420325	−	0.728025i	−0.126733	−	0.219508i	0.795676	−	0.605722i	$-0.207116\pi$
$11$	−0.420325	−	0.728025i	−0.126733	−	0.219508i	−0.922409	+	0.386215i	$0.873782\pi$
$12$	0.966638	+	1.43722i	0.279044	+	0.414891i
$13$	−0.875777	+	0.505630i	−0.242897	+	0.140237i	−0.616507	−	0.787349i	$-0.711453\pi$
$13$	−0.875777	+	0.505630i	−0.242897	+	0.140237i	0.373611	+	0.927586i	$0.378120\pi$
$14$	1.61186	+	2.09808i	0.430787	+	0.560734i
$15$	−0.707328	+	3.80785i	−0.182631	+	0.983181i
$16$	1.00000			0.250000
$17$	−3.81674	−	2.20360i	−0.925696	−	0.534451i	−0.0402485	−	0.999190i	$-0.512815\pi$
$17$	−3.81674	−	2.20360i	−0.925696	−	0.534451i	−0.885448	+	0.464739i	$0.846148\pi$
$18$	−2.77855	−	1.13122i	−0.654910	−	0.266632i
$19$	0.952130	+	1.64914i	0.218434	+	0.378338i	0.954329	−	0.298757i	$-0.0965719\pi$
$19$	0.952130	+	1.64914i	0.218434	+	0.378338i	−0.735896	+	0.677095i	$0.763239\pi$
$20$	1.59633	+	1.56580i	0.356951	+	0.350123i
$21$	−4.34468	−	1.45732i	−0.948086	−	0.318014i
$22$	0.728025	−	0.420325i	0.155215	−	0.0896137i
$23$	−3.29325	−	1.90136i	−0.686690	−	0.396460i	0.115681	−	0.993286i	$-0.463095\pi$
$23$	−3.29325	−	1.90136i	−0.686690	−	0.396460i	−0.802371	+	0.596826i	$0.796428\pi$
$24$	−1.43722	+	0.966638i	−0.293372	+	0.197314i
$25$	0.0965491	+	4.99907i	0.0193098	+	0.999814i
$26$	−0.505630	−	0.875777i	−0.0991622	−	0.171754i
$27$	5.08688	−	1.06003i	0.978970	−	0.204003i
$28$	−2.09808	+	1.61186i	−0.396499	+	0.304612i
$29$	−4.01934	+	6.96170i	−0.746373	+	1.29276i	0.203178	+	0.979142i	$0.434873\pi$
$29$	−4.01934	+	6.96170i	−0.746373	+	1.29276i	−0.949551	+	0.313614i	$0.898460\pi$
$30$	−3.80785	−	0.707328i	−0.695214	−	0.129140i
$31$	−7.73072			−1.38848			−0.694239	−	0.719745i	$-0.744259\pi$
$31$	−7.73072			−1.38848			−0.694239	+	0.719745i	$0.744259\pi$
$32$			1.00000i			0.176777i
$33$	−0.640032	+	1.30784i	−0.111415	+	0.227665i
$34$	2.20360	−	3.81674i	0.377914	−	0.654566i
$35$	−5.87307	−	0.712108i	−0.992729	−	0.120368i
$36$	1.13122	−	2.77855i	0.188537	−	0.463092i
$37$	−3.73933	+	2.15891i	−0.614743	+	0.354922i	−0.774819	−	0.632183i	$-0.782159\pi$
$37$	−3.73933	+	2.15891i	−0.614743	+	0.354922i	0.160077	+	0.987105i	$0.448826\pi$
$38$	−1.64914	+	0.952130i	−0.267526	+	0.154456i
$39$	1.57326	+	0.769926i	0.251924	+	0.123287i
$40$	−1.56580	+	1.59633i	−0.247575	+	0.252402i
$41$	−4.72608	−	8.18582i	−0.738090	−	1.27841i	−0.953354	−	0.301854i	$-0.902395\pi$
$41$	−4.72608	−	8.18582i	−0.738090	−	1.27841i	0.215264	−	0.976556i	$-0.430939\pi$
$42$	1.45732	−	4.34468i	0.224870	−	0.670398i
$43$	−4.27106	−	2.46590i	−0.651330	−	0.376046i	0.137635	−	0.990483i	$-0.456050\pi$
$43$	−4.27106	−	2.46590i	−0.651330	−	0.376046i	−0.788966	+	0.614437i	$0.789383\pi$
$44$	0.420325	+	0.728025i	0.0633664	+	0.109754i
$45$	6.15645	−	2.66422i	0.917750	−	0.397159i
$46$	1.90136	−	3.29325i	0.280340	−	0.485563i
$47$		−	0.430181i		−	0.0627484i	−0.999508	−	0.0313742i	$-0.990012\pi$
$47$		−	0.430181i		−	0.0627484i	0.999508	−	0.0313742i	$-0.00998835\pi$
$48$	−0.966638	−	1.43722i	−0.139522	−	0.207445i
$49$	1.80384	−	6.76359i	0.257692	−	0.966227i
$50$	−4.99907	+	0.0965491i	−0.706975	+	0.0136541i
$51$	0.522347	+	7.61560i	0.0731432	+	1.06640i
$52$	0.875777	−	0.505630i	0.121448	−	0.0701183i
$53$	−2.64705	−	1.52828i	−0.363600	−	0.209925i	0.307059	−	0.951691i	$-0.400655\pi$
$53$	−2.64705	−	1.52828i	−0.363600	−	0.209925i	−0.670659	+	0.741766i	$0.733989\pi$
$54$	1.06003	+	5.08688i	0.144252	+	0.692236i
$55$	−0.468962	+	1.82031i	−0.0632348	+	0.245451i
$56$	−1.61186	−	2.09808i	−0.215393	−	0.280367i
$57$	1.44981	−	2.96254i	0.192033	−	0.392398i
$58$	−6.96170	−	4.01934i	−0.914116	−	0.527765i
$59$	4.28660			0.558067			0.279034	−	0.960281i	$-0.409986\pi$
$59$	4.28660			0.558067			0.279034	+	0.960281i	$0.409986\pi$
$60$	0.707328	−	3.80785i	0.0913156	−	0.491591i
$61$	13.1981			1.68984			0.844921	−	0.534892i	$-0.179648\pi$
$61$	13.1981			1.68984			0.844921	+	0.534892i	$0.179648\pi$
$62$		−	7.73072i		−	0.981802i
$63$	2.10523	+	7.65297i	0.265234	+	0.964184i
$64$	−1.00000			−0.125000
$65$	2.18975	+	0.564137i	0.271605	+	0.0699726i
$66$	−1.30784	−	0.640032i	−0.160984	−	0.0787825i
$67$			14.0784i			1.71995i	0.510338	+	0.859974i	$0.329520\pi$
$67$			14.0784i			1.71995i	−0.510338	+	0.859974i	$0.670480\pi$
$68$	3.81674	+	2.20360i	0.462848	+	0.267226i
$69$	0.450703	+	6.57106i	0.0542583	+	0.791062i
$70$	0.712108	−	5.87307i	0.0851132	−	0.701966i
$71$	−10.6603			−1.26514			−0.632571	−	0.774503i	$-0.718000\pi$
$71$	−10.6603			−1.26514			−0.632571	+	0.774503i	$0.718000\pi$
$72$	2.77855	+	1.13122i	0.327455	+	0.133316i
$73$	−9.21556	−	5.32061i	−1.07860	−	0.622730i	−0.148081	−	0.988975i	$-0.547310\pi$
$73$	−9.21556	−	5.32061i	−1.07860	−	0.622730i	−0.930518	+	0.366245i	$0.880643\pi$
$74$	−2.15891	−	3.73933i	−0.250968	−	0.434689i
$75$	7.09145	−	4.97105i	0.818850	−	0.574008i
$76$	−0.952130	−	1.64914i	−0.109217	−	0.189169i
$77$	−2.05535	−	0.849947i	−0.234228	−	0.0968605i
$78$	−0.769926	+	1.57326i	−0.0871770	+	0.178137i
$79$	9.85613			1.10890			0.554451	−	0.832217i	$-0.312928\pi$
$79$	9.85613			1.10890			0.554451	+	0.832217i	$0.312928\pi$
$80$	−1.59633	−	1.56580i	−0.178475	−	0.175062i
$81$	−6.44067	−	6.28631i	−0.715630	−	0.698479i
$82$	8.18582	−	4.72608i	0.903972	−	0.521909i
$83$	9.47556	+	5.47071i	1.04008	+	0.600489i	0.919855	−	0.392258i	$-0.128306\pi$
$83$	9.47556	+	5.47071i	1.04008	+	0.600489i	0.120222	+	0.992747i	$0.461639\pi$
$84$	4.34468	+	1.45732i	0.474043	+	0.159007i
$85$	2.64240	+	9.49393i	0.286608	+	1.02976i
$86$	2.46590	−	4.27106i	0.265904	−	0.460560i
$87$	13.8908	−	0.952755i	1.48925	−	0.102146i
$88$	−0.728025	+	0.420325i	−0.0776077	+	0.0448068i
$89$	−5.46333	−	9.46277i	−0.579112	−	1.00305i	−0.995581	−	0.0939021i	$-0.970066\pi$
$89$	−5.46333	−	9.46277i	−0.579112	−	1.00305i	0.416469	−	0.909150i	$-0.363267\pi$
$90$	2.66422	+	6.15645i	0.280833	+	0.648947i
$91$	−1.02244	+	2.47248i	−0.107181	+	0.259186i
$92$	3.29325	+	1.90136i	0.343345	+	0.198230i
$93$	7.47280	+	11.1108i	0.774894	+	1.15213i
$94$	0.430181			0.0443698
$95$	1.06230	−	4.12342i	0.108990	−	0.423054i
$96$	1.43722	−	0.966638i	0.146686	−	0.0986571i
$97$	2.02734	+	1.17049i	0.205846	+	0.118845i	0.599379	−	0.800465i	$-0.295414\pi$
$97$	2.02734	+	1.17049i	0.205846	+	0.118845i	−0.393534	+	0.919310i	$0.628747\pi$
$98$	6.76359	+	1.80384i	0.683226	+	0.182216i
$99$	2.49833	−	0.344337i	0.251092	−	0.0346072i
$100$	−0.0965491	−	4.99907i	−0.00965491	−	0.499907i
$101$	−2.49744	−	4.32568i	−0.248504	−	0.430422i	0.714607	−	0.699526i	$-0.246606\pi$
$101$	−2.49744	−	4.32568i	−0.248504	−	0.430422i	−0.963111	+	0.269105i	$0.913272\pi$
$102$	−7.61560	+	0.522347i	−0.754056	+	0.0517201i
$103$	2.61374	+	1.50905i	0.257540	+	0.148691i	0.623212	−	0.782053i	$-0.285827\pi$
$103$	2.61374	+	1.50905i	0.257540	+	0.148691i	−0.365672	+	0.930744i	$0.619161\pi$
$104$	0.505630	+	0.875777i	0.0495811	+	0.0858770i
$105$	4.65367	+	9.12926i	0.454152	+	0.890924i
$106$	1.52828	−	2.64705i	0.148439	−	0.257104i
$107$	−4.87464	+	2.81438i	−0.471250	+	0.272076i	−0.716763	−	0.697317i	$-0.754377\pi$
$107$	−4.87464	+	2.81438i	−0.471250	+	0.272076i	0.245513	+	0.969393i	$0.421044\pi$
$108$	−5.08688	+	1.06003i	−0.489485	+	0.102002i
$109$	9.53935	−	16.5226i	0.913704	−	1.58258i	0.104916	−	0.994481i	$-0.466543\pi$
$109$	9.53935	−	16.5226i	0.913704	−	1.58258i	0.808788	−	0.588101i	$-0.200124\pi$
$110$	−1.82031	−	0.468962i	−0.173560	−	0.0447137i
$111$	6.71741	+	3.28738i	0.637588	+	0.312024i
$112$	2.09808	−	1.61186i	0.198250	−	0.152306i
$113$	−2.84618	+	1.64324i	−0.267746	+	0.154583i	−0.627863	−	0.778324i	$-0.716070\pi$
$113$	−2.84618	+	1.64324i	−0.267746	+	0.154583i	0.360117	+	0.932907i	$0.382737\pi$
$114$	2.96254	+	1.44981i	0.277468	+	0.135788i
$115$	2.27997	+	8.19176i	0.212609	+	0.763886i
$116$	4.01934	−	6.96170i	0.373186	−	0.646378i
$117$	−0.414220	−	3.00537i	−0.0382946	−	0.277847i
$118$			4.28660i			0.394613i
$119$	−11.5597	+	1.52873i	−1.05968	+	0.140138i
$120$	3.80785	+	0.707328i	0.347607	+	0.0645699i
$121$	5.14665	−	8.91427i	0.467878	−	0.810388i
$122$			13.1981i			1.19490i
$123$	−7.19644	+	14.7052i	−0.648881	+	1.32592i
$124$	7.73072			0.694239
$125$	7.67341	−	8.13135i	0.686331	−	0.727290i
$126$	−7.65297	+	2.10523i	−0.681781	+	0.187549i
$127$			1.23171i			0.109297i	0.998506	+	0.0546484i	$0.0174038\pi$
$127$			1.23171i			0.109297i	−0.998506	+	0.0546484i	$0.982596\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	0.584523	+	8.52209i	0.0514644	+	0.750329i
$130$	−0.564137	+	2.18975i	−0.0494781	+	0.192053i
$131$	−4.65950	+	8.07049i	−0.407102	+	0.705122i	−0.994564	−	0.104130i	$-0.966794\pi$
$131$	−4.65950	+	8.07049i	−0.407102	+	0.705122i	0.587461	+	0.809252i	$0.300127\pi$
$132$	0.640032	−	1.30784i	0.0557076	−	0.113833i
$133$	4.65581	+	1.92532i	0.403710	+	0.166946i
$134$	−14.0784			−1.21619
$135$	−9.78014	−	6.27286i	−0.841741	−	0.539882i
$136$	−2.20360	+	3.81674i	−0.188957	+	0.327283i
$137$	2.73820	−	1.58090i	0.233940	−	0.135066i	−0.378448	−	0.925623i	$-0.623542\pi$
$137$	2.73820	−	1.58090i	0.233940	−	0.135066i	0.612389	+	0.790557i	$0.290209\pi$
$138$	−6.57106	+	0.450703i	−0.559366	+	0.0383664i
$139$	−6.95211	−	12.0414i	−0.589670	−	1.02134i	−0.994275	−	0.106847i	$-0.965924\pi$
$139$	−6.95211	−	12.0414i	−0.589670	−	1.02134i	0.404605	−	0.914491i	$-0.367409\pi$
$140$	5.87307	+	0.712108i	0.496365	+	0.0601841i
$141$	−0.618266	+	0.415829i	−0.0520674	+	0.0350192i
$142$		−	10.6603i		−	0.894590i
$143$	0.736222	+	0.425058i	0.0615660	+	0.0355452i
$144$	−1.13122	+	2.77855i	−0.0942685	+	0.231546i
$145$	17.3168	−	4.81971i	1.43808	−	0.400255i
$146$	5.32061	−	9.21556i	0.440336	−	0.762685i
$147$	−11.4645	+	3.94542i	−0.945572	+	0.325413i
$148$	3.73933	−	2.15891i	0.307371	−	0.177461i
$149$	−4.46886	+	7.74030i	−0.366104	+	0.634110i	−0.988953	−	0.148232i	$-0.952642\pi$
$149$	−4.46886	+	7.74030i	−0.366104	+	0.634110i	0.622849	+	0.782342i	$0.285975\pi$
$150$	4.97105	+	7.09145i	0.405885	+	0.579014i
$151$	−9.48547	−	16.4293i	−0.771917	−	1.33700i	−0.936511	−	0.350637i	$-0.885965\pi$
$151$	−9.48547	−	16.4293i	−0.771917	−	1.33700i	0.164595	−	0.986361i	$-0.447368\pi$
$152$	1.64914	−	0.952130i	0.133763	−	0.0772280i
$153$	10.4404	−	8.11225i	0.844056	−	0.655837i
$154$	0.849947	−	2.05535i	0.0684907	−	0.165624i
$155$	12.3408	+	12.1047i	0.991236	+	0.972276i
$156$	−1.57326	−	0.769926i	−0.125962	−	0.0616434i
$157$			4.21289i			0.336225i	0.985768	+	0.168112i	$0.0537672\pi$
$157$			4.21289i			0.336225i	−0.985768	+	0.168112i	$0.946233\pi$
$158$			9.85613i			0.784112i
$159$	0.362267	+	5.28169i	0.0287296	+	0.418866i
$160$	1.56580	−	1.59633i	0.123787	−	0.126201i
$161$	−9.97420	+	1.31905i	−0.786077	+	0.103956i
$162$	6.28631	−	6.44067i	0.493899	−	0.506027i
$163$	4.12425	−	2.38114i	0.323036	−	0.186505i	−0.329709	−	0.944083i	$-0.606951\pi$
$163$	4.12425	−	2.38114i	0.323036	−	0.186505i	0.652745	+	0.757578i	$0.273617\pi$
$164$	4.72608	+	8.18582i	0.369045	+	0.639205i
$165$	3.06951	−	1.08558i	0.238961	−	0.0845124i
$166$	−5.47071	+	9.47556i	−0.424610	+	0.735446i
$167$	−3.20663	+	1.85135i	−0.248137	+	0.143262i	−0.618911	−	0.785461i	$-0.712426\pi$
$167$	−3.20663	+	1.85135i	−0.248137	+	0.143262i	0.370774	+	0.928723i	$0.379092\pi$
$168$	−1.45732	+	4.34468i	−0.112435	+	0.335199i
$169$	−5.98868	+	10.3727i	−0.460667	+	0.797899i
$170$	−9.49393	+	2.64240i	−0.728151	+	0.202663i
$171$	−5.65928	+	0.780000i	−0.432776	+	0.0596481i
$172$	4.27106	+	2.46590i	0.325665	+	0.188023i
$173$		−	23.1278i		−	1.75837i	−0.476477	−	0.879187i	$-0.658086\pi$
$173$		−	23.1278i		−	1.75837i	0.476477	−	0.879187i	$-0.341914\pi$
$174$	0.952755	+	13.8908i	0.0722282	+	1.05306i
$175$	8.26034	+	10.3328i	0.624423	+	0.781086i
$176$	−0.420325	−	0.728025i	−0.0316832	−	0.0548769i
$177$	−4.14359	−	6.16080i	−0.311451	−	0.463074i
$178$	9.46277	−	5.46333i	0.709265	−	0.409494i
$179$	2.15690	−	3.73586i	0.161214	−	0.279231i	−0.774090	−	0.633075i	$-0.781792\pi$
$179$	2.15690	−	3.73586i	0.161214	−	0.279231i	0.935304	+	0.353844i	$0.115126\pi$
$180$	−6.15645	+	2.66422i	−0.458875	+	0.198579i
$181$	3.95990			0.294337			0.147168	−	0.989111i	$-0.452984\pi$
$181$	3.95990			0.294337			0.147168	+	0.989111i	$0.452984\pi$
$182$	−2.47248	−	1.02244i	−0.183272	−	0.0757886i
$183$	−12.7578	−	18.9686i	−0.943081	−	1.40220i
$184$	−1.90136	+	3.29325i	−0.140170	+	0.242781i
$185$	9.34963	+	2.40871i	0.687398	+	0.177092i
$186$	−11.1108	+	7.47280i	−0.814681	+	0.547933i
$187$			3.70491i			0.270930i
$188$			0.430181i			0.0313742i
$189$	8.96404	−	10.4233i	0.652038	−	0.758187i
$190$	4.12342	+	1.06230i	0.299144	+	0.0770675i
$191$	12.0276			0.870290			0.435145	−	0.900360i	$-0.356697\pi$
$191$	12.0276			0.870290			0.435145	+	0.900360i	$0.356697\pi$
$192$	0.966638	+	1.43722i	0.0697611	+	0.103723i
$193$		−	19.2814i		−	1.38790i	−0.720021	−	0.693952i	$-0.755868\pi$
$193$		−	19.2814i		−	1.38790i	0.720021	−	0.693952i	$-0.244132\pi$
$194$	−1.17049	+	2.02734i	−0.0840361	+	0.145555i
$195$	−1.30590	−	3.69247i	−0.0935174	−	0.264423i
$196$	−1.80384	+	6.76359i	−0.128846	+	0.483114i
$197$			13.4436i			0.957820i	0.877864	+	0.478910i	$0.158968\pi$
$197$			13.4436i			0.957820i	−0.877864	+	0.478910i	$0.841032\pi$
$198$	0.344337	+	2.49833i	0.0244710	+	0.177549i
$199$	−8.57412	+	14.8508i	−0.607804	+	1.05275i	0.383798	+	0.923417i	$0.374616\pi$
$199$	−8.57412	+	14.8508i	−0.607804	+	1.05275i	−0.991602	+	0.129330i	$0.958717\pi$
$200$	4.99907	−	0.0965491i	0.353487	−	0.00682705i
$201$	20.2338	−	13.6087i	1.42718	−	0.959883i
$202$	4.32568	−	2.49744i	0.304354	−	0.175719i
$203$	2.78838	+	21.0848i	0.195706	+	1.47986i
$204$	−0.522347	−	7.61560i	−0.0365716	−	0.533198i
$205$	−5.27294	+	20.4674i	−0.368278	+	1.42950i
$206$	−1.50905	+	2.61374i	−0.105140	+	0.182108i
$207$	9.00841	−	6.99959i	0.626128	−	0.486505i
$208$	−0.875777	+	0.505630i	−0.0607242	+	0.0350591i
$209$	0.800409	−	1.38635i	0.0553654	−	0.0958958i
$210$	−9.12926	+	4.65367i	−0.629979	+	0.321134i
$211$	−2.66598	−	4.61761i	−0.183533	−	0.317889i	0.759548	−	0.650451i	$-0.225420\pi$
$211$	−2.66598	−	4.61761i	−0.183533	−	0.317889i	−0.943081	+	0.332562i	$0.892087\pi$
$212$	2.64705	+	1.52828i	0.181800	+	0.104962i
$213$	10.3046	+	15.3212i	0.706061	+	1.04979i
$214$	−2.81438	−	4.87464i	−0.192387	−	0.333224i
$215$	2.95693	+	10.6240i	0.201661	+	0.724551i
$216$	−1.06003	−	5.08688i	−0.0721261	−	0.346118i
$217$	−16.2196	+	12.4608i	−1.10106	+	0.845894i
$218$	16.5226	+	9.53935i	1.11905	+	0.646086i
$219$	1.26121	+	18.3879i	0.0852247	+	1.24254i
$220$	0.468962	−	1.82031i	0.0316174	−	0.122726i
$221$	4.45682			0.299798
$222$	−3.28738	+	6.71741i	−0.220634	+	0.450843i
$223$	−8.82525	−	5.09526i	−0.590982	−	0.341204i	0.174504	−	0.984657i	$-0.444168\pi$
$223$	−8.82525	−	5.09526i	−0.590982	−	0.341204i	−0.765486	+	0.643453i	$0.777501\pi$
$224$	1.61186	+	2.09808i	0.107697	+	0.140184i
$225$	−13.9994	−	5.38679i	−0.933292	−	0.359119i
$226$	−1.64324	−	2.84618i	−0.109307	−	0.189325i
$227$	−6.05888	+	3.49809i	−0.402142	+	0.232177i	−0.687408	−	0.726272i	$-0.741251\pi$
$227$	−6.05888	+	3.49809i	−0.402142	+	0.232177i	0.285266	+	0.958448i	$0.407918\pi$
$228$	−1.44981	+	2.96254i	−0.0960163	+	0.196199i
$229$	7.00329	−	12.1301i	0.462790	−	0.801576i	−0.536308	−	0.844022i	$-0.680182\pi$
$229$	7.00329	−	12.1301i	0.462790	−	0.801576i	0.999099	+	0.0424457i	$0.0135149\pi$
$230$	−8.19176	+	2.27997i	−0.540149	+	0.150337i
$231$	0.765211	+	3.77558i	0.0503472	+	0.248415i
$232$	6.96170	+	4.01934i	0.457058	+	0.263883i
$233$	14.8053	−	8.54786i	0.969930	−	0.559989i	0.0707148	−	0.997497i	$-0.477472\pi$
$233$	14.8053	−	8.54786i	0.969930	−	0.559989i	0.899215	+	0.437507i	$0.144139\pi$
$234$	3.00537	−	0.414220i	0.196467	−	0.0270784i
$235$	−0.673577	+	0.686712i	−0.0439393	+	0.0447961i
$236$	−4.28660			−0.279034
$237$	−9.52731	−	14.1655i	−0.618865	−	0.920145i
$238$	−1.52873	−	11.5597i	−0.0990925	−	0.749304i
$239$	1.23115	+	2.13242i	0.0796366	+	0.137935i	0.903093	−	0.429445i	$-0.141291\pi$
$239$	1.23115	+	2.13242i	0.0796366	+	0.137935i	−0.823457	+	0.567379i	$0.807957\pi$
$240$	−0.707328	+	3.80785i	−0.0456578	+	0.245795i
$241$	−9.70241	−	16.8051i	−0.624987	−	1.08251i	−0.988543	−	0.150937i	$-0.951771\pi$
$241$	−9.70241	−	16.8051i	−0.624987	−	1.08251i	0.363556	−	0.931572i	$-0.381563\pi$
$242$	8.91427	+	5.14665i	0.573031	+	0.330839i
$243$	−2.80904	+	15.3333i	−0.180200	+	0.983630i
$244$	−13.1981			−0.844921
$245$	−13.4700	+	7.97248i	−0.860564	+	0.509343i
$246$	−14.7052	−	7.19644i	−0.937567	−	0.458828i
$247$	−1.66771	−	0.962852i	−0.106114	−	0.0612648i
$248$			7.73072i			0.490901i
$249$	−1.29679	−	18.9067i	−0.0821809	−	1.19816i
$250$	8.13135	+	7.67341i	0.514271	+	0.485309i
$251$	14.7856			0.933256			0.466628	−	0.884454i	$-0.345469\pi$
$251$	14.7856			0.933256			0.466628	+	0.884454i	$0.345469\pi$
$252$	−2.10523	−	7.65297i	−0.132617	−	0.482092i
$253$			3.19675i			0.200978i
$254$	−1.23171			−0.0772844
$255$	11.0907	−	12.9749i	0.694523	−	0.812520i
$256$	1.00000			0.0625000
$257$	−27.5921	−	15.9303i	−1.72115	−	0.993704i	−0.916592	−	0.399824i	$-0.869071\pi$
$257$	−27.5921	−	15.9303i	−1.72115	−	0.993704i	−0.804554	−	0.593880i	$-0.797595\pi$
$258$	−8.52209	+	0.584523i	−0.530562	+	0.0363908i
$259$	−4.36556	+	10.5568i	−0.271263	+	0.655968i
$260$	−2.18975	−	0.564137i	−0.135802	−	0.0349863i
$261$	−14.7967	−	19.0432i	−0.915891	−	1.17874i
$262$	−8.07049	−	4.65950i	−0.498596	−	0.287865i
$263$	23.3624	−	13.4883i	1.44059	−	0.831722i	0.442697	−	0.896671i	$-0.354022\pi$
$263$	23.3624	−	13.4883i	1.44059	−	0.831722i	0.997889	+	0.0649488i	$0.0206884\pi$
$264$	1.30784	+	0.640032i	0.0804918	+	0.0393912i
$265$	1.83260	+	6.58438i	0.112576	+	0.404476i
$266$	−1.92532	+	4.65581i	−0.118049	+	0.285466i
$267$	−8.31905	+	16.9991i	−0.509118	+	1.04033i
$268$		−	14.0784i		−	0.859974i
$269$	1.39626	−	2.41839i	0.0851314	−	0.147452i	−0.820316	−	0.571911i	$-0.806202\pi$
$269$	1.39626	−	2.41839i	0.0851314	−	0.147452i	0.905447	+	0.424459i	$0.139536\pi$
$270$	6.27286	−	9.78014i	0.381754	−	0.595201i
$271$	6.60560	+	11.4412i	0.401262	+	0.695005i	0.993878	−	0.110479i	$-0.0352385\pi$
$271$	6.60560	+	11.4412i	0.401262	+	0.695005i	−0.592617	+	0.805484i	$0.701905\pi$
$272$	−3.81674	−	2.20360i	−0.231424	−	0.133613i
$273$	4.54183	−	0.920510i	0.274884	−	0.0557118i
$274$	1.58090	+	2.73820i	0.0955058	+	0.165421i
$275$	3.59886	−	2.17152i	0.217020	−	0.130948i
$276$	−0.450703	−	6.57106i	−0.0271291	−	0.395531i
$277$	−3.79593	+	2.19158i	−0.228075	+	0.131679i	−0.609684	−	0.792645i	$-0.708704\pi$
$277$	−3.79593	+	2.19158i	−0.228075	+	0.131679i	0.381609	+	0.924324i	$0.375370\pi$
$278$	12.0414	−	6.95211i	0.722195	−	0.416960i
$279$	8.74516	−	21.4802i	0.523559	−	1.28598i
$280$	−0.712108	+	5.87307i	−0.0425566	+	0.350983i
$281$	12.2175	−	21.1613i	0.728834	−	1.26238i	−0.228542	−	0.973534i	$-0.573396\pi$
$281$	12.2175	−	21.1613i	0.728834	−	1.26238i	0.957376	−	0.288844i	$-0.0932709\pi$
$282$	−0.415829	−	0.618266i	−0.0247623	−	0.0368172i
$283$		−	24.8049i		−	1.47450i	−0.675622	−	0.737249i	$-0.736125\pi$
$283$		−	24.8049i		−	1.47450i	0.675622	−	0.737249i	$-0.263875\pi$
$284$	10.6603			0.632571
$285$	−6.95313	+	2.45908i	−0.411868	+	0.145664i
$286$	−0.425058	+	0.736222i	−0.0251342	+	0.0435337i
$287$	−23.1100	−	9.55670i	−1.36414	−	0.564114i
$288$	−2.77855	−	1.13122i	−0.163728	−	0.0666579i
$289$	1.21169	+	2.09871i	0.0712759	+	0.123453i
$290$	4.81971	+	17.3168i	0.283023	+	1.01688i
$291$	−0.277456	−	4.04518i	−0.0162647	−	0.237133i
$292$	9.21556	+	5.32061i	0.539300	+	0.311365i
$293$	−2.60830	+	1.50591i	−0.152379	+	0.0879759i	−0.574251	−	0.818680i	$-0.694707\pi$
$293$	−2.60830	+	1.50591i	−0.152379	+	0.0879759i	0.421872	+	0.906655i	$0.361373\pi$
$294$	−3.94542	−	11.4645i	−0.230102	−	0.668620i
$295$	−6.84283	−	6.71195i	−0.398405	−	0.390785i
$296$	2.15891	+	3.73933i	0.125484	+	0.217344i
$297$	−2.90987	−	3.25781i	−0.168848	−	0.189038i
$298$	−7.74030	−	4.46886i	−0.448384	−	0.258874i
$299$	3.84553			0.222393
$300$	−7.09145	+	4.97105i	−0.409425	+	0.287004i
$301$	−12.9357	+	1.71069i	−0.745600	+	0.0986027i
$302$	16.4293	−	9.48547i	0.945401	−	0.545827i
$303$	−3.80286	+	7.77074i	−0.218469	+	0.446418i
$304$	0.952130	+	1.64914i	0.0546084	+	0.0945846i
$305$	−21.0685	−	20.6655i	−1.20638	−	1.18331i
$306$	8.11225	+	10.4404i	0.463747	+	0.596837i
$307$		−	10.9855i		−	0.626976i	−0.949592	−	0.313488i	$-0.898502\pi$
$307$		−	10.9855i		−	0.626976i	0.949592	−	0.313488i	$-0.101498\pi$
$308$	2.05535	+	0.849947i	0.117114	+	0.0484302i
$309$	−0.357708	−	5.21524i	−0.0203493	−	0.296684i
$310$	−12.1047	+	12.3408i	−0.687503	+	0.700910i
$311$	−18.3890			−1.04275			−0.521373	−	0.853329i	$-0.674580\pi$
$311$	−18.3890			−1.04275			−0.521373	+	0.853329i	$0.674580\pi$
$312$	0.769926	−	1.57326i	0.0435885	−	0.0890685i
$313$			17.9290i			1.01341i	0.862120	+	0.506704i	$0.169136\pi$
$313$			17.9290i			1.01341i	−0.862120	+	0.506704i	$0.830864\pi$
$314$	−4.21289			−0.237747
$315$	8.62237	−	15.5131i	0.485815	−	0.874061i
$316$	−9.85613			−0.554451
$317$			6.63686i			0.372763i	0.982477	+	0.186381i	$0.0596760\pi$
$317$			6.63686i			0.372763i	−0.982477	+	0.186381i	$0.940324\pi$
$318$	−5.28169	+	0.362267i	−0.296183	+	0.0203149i
$319$	6.75772			0.378360
$320$	1.59633	+	1.56580i	0.0892376	+	0.0875308i
$321$	8.75691	+	4.28547i	0.488763	+	0.239192i
$322$	−1.31905	−	9.97420i	−0.0735077	−	0.555840i
$323$		−	8.39245i		−	0.466968i
$324$	6.44067	+	6.28631i	0.357815	+	0.349240i
$325$	−2.61223	−	4.32925i	−0.144901	−	0.240144i
$326$	2.38114	+	4.12425i	0.131879	+	0.228421i
$327$	−32.9678	+	2.26123i	−1.82312	+	0.125046i
$328$	−8.18582	+	4.72608i	−0.451986	+	0.260954i
$329$	−0.693390	−	0.902553i	−0.0382278	−	0.0497593i
$330$	1.08558	+	3.06951i	0.0597593	+	0.168971i
$331$	−3.77671			−0.207587			−0.103793	−	0.994599i	$-0.533098\pi$
$331$	−3.77671			−0.207587			−0.103793	+	0.994599i	$0.533098\pi$
$332$	−9.47556	−	5.47071i	−0.520039	−	0.300244i
$333$	−1.76861	−	12.8321i	−0.0969191	−	0.703196i
$334$	−1.85135	−	3.20663i	−0.101301	−	0.175459i
$335$	22.0439	−	22.4738i	1.20439	−	1.22787i
$336$	−4.34468	−	1.45732i	−0.237022	−	0.0795034i
$337$	−24.0531	+	13.8871i	−1.31026	+	0.756478i	−0.982139	−	0.188159i	$-0.939748\pi$
$337$	−24.0531	+	13.8871i	−1.31026	+	0.756478i	−0.328119	+	0.944636i	$0.606415\pi$
$338$	−10.3727	−	5.98868i	−0.564200	−	0.325741i
$339$	5.11292	+	2.50217i	0.277696	+	0.135899i
$340$	−2.64240	−	9.49393i	−0.143304	−	0.514880i
$341$	3.24942	+	5.62815i	0.175966	+	0.304782i
$342$	−0.780000	−	5.65928i	−0.0421776	−	0.306019i
$343$	−7.11733	−	17.0981i	−0.384300	−	0.923208i
$344$	−2.46590	+	4.27106i	−0.132952	+	0.230280i
$345$	9.56948	−	11.1953i	0.515204	−	0.602734i
$346$	23.1278			1.24336
$347$		−	6.15913i		−	0.330640i	−0.986240	−	0.165320i	$-0.947134\pi$
$347$		−	6.15913i		−	0.330640i	0.986240	−	0.165320i	$-0.0528656\pi$
$348$	−13.8908	+	0.952755i	−0.744623	+	0.0510730i
$349$	−15.3833	+	26.6447i	−0.823451	+	1.42626i	0.0796469	+	0.996823i	$0.474621\pi$
$349$	−15.3833	+	26.6447i	−0.823451	+	1.42626i	−0.903098	+	0.429435i	$0.858713\pi$
$350$	−10.3328	+	8.26034i	−0.552311	+	0.441534i
$351$	−3.91899	+	3.50043i	−0.209180	+	0.186839i
$352$	0.728025	−	0.420325i	0.0388038	−	0.0224034i
$353$	19.1527	−	11.0578i	1.01939	−	0.588548i	0.105466	−	0.994423i	$-0.466367\pi$
$353$	19.1527	−	11.0578i	1.01939	−	0.588548i	0.913928	+	0.405875i	$0.133033\pi$
$354$	6.16080	−	4.14359i	0.327443	−	0.220229i
$355$	17.0173	+	16.6918i	0.903186	+	0.885911i
$356$	5.46333	+	9.46277i	0.289556	+	0.501526i
$357$	13.3712	+	15.1361i	0.707677	+	0.801090i
$358$	3.73586	+	2.15690i	0.197446	+	0.113996i
$359$	16.4883	+	28.5585i	0.870217	+	1.50726i	0.861772	+	0.507296i	$0.169355\pi$
$359$	16.4883	+	28.5585i	0.870217	+	1.50726i	0.00844553	+	0.999964i	$0.497312\pi$
$360$	−2.66422	−	6.15645i	−0.140417	−	0.324474i
$361$	7.68690	−	13.3141i	0.404573	−	0.700742i
$362$			3.95990i			0.208127i
$363$	−17.7867	+	1.21998i	−0.933562	+	0.0640322i
$364$	1.02244	−	2.47248i	0.0535906	−	0.129593i
$365$	6.38009	+	22.9232i	0.333949	+	1.19985i
$366$	18.9686	−	12.7578i	0.991504	−	0.666859i
$367$	−3.05465	+	1.76360i	−0.159451	+	0.0920593i	−0.577602	−	0.816318i	$-0.696012\pi$
$367$	−3.05465	+	1.76360i	−0.159451	+	0.0920593i	0.418151	+	0.908378i	$0.362678\pi$
$368$	−3.29325	−	1.90136i	−0.171672	−	0.0991151i
$369$	28.0909	−	3.87168i	1.46236	−	0.201552i
$370$	−2.40871	+	9.34963i	−0.125223	+	0.486064i
$371$	−8.01707	+	1.06023i	−0.416226	+	0.0550442i
$372$	−7.47280	−	11.1108i	−0.387447	−	0.576066i
$373$	−14.8300	−	8.56210i	−0.767868	−	0.443329i	0.0642458	−	0.997934i	$-0.479536\pi$
$373$	−14.8300	−	8.56210i	−0.767868	−	0.443329i	−0.832113	+	0.554606i	$0.812869\pi$
$374$	−3.70491			−0.191576
$375$	−19.1040	−	3.16833i	−0.986525	−	0.163612i
$376$	−0.430181			−0.0221849
$377$		−	8.12920i		−	0.418675i
$378$	10.4233	+	8.96404i	0.536119	+	0.461060i
$379$	10.6327			0.546168			0.273084	−	0.961990i	$-0.411956\pi$
$379$	10.6327			0.546168			0.273084	+	0.961990i	$0.411956\pi$
$380$	−1.06230	+	4.12342i	−0.0544950	+	0.211527i
$381$	1.77024	−	1.19062i	0.0906924	−	0.0609973i
$382$			12.0276i			0.615388i
$383$	12.8423	+	7.41452i	0.656212	+	0.378864i	0.790832	−	0.612033i	$-0.209648\pi$
$383$	12.8423	+	7.41452i	0.656212	+	0.378864i	−0.134620	+	0.990897i	$0.542981\pi$
$384$	−1.43722	+	0.966638i	−0.0733430	+	0.0493285i
$385$	1.95017	+	4.57505i	0.0993897	+	0.233166i
$386$	19.2814			0.981397
$387$	11.6831	−	9.07787i	0.593887	−	0.461454i
$388$	−2.02734	−	1.17049i	−0.102923	−	0.0594225i
$389$	−8.89556	−	15.4076i	−0.451023	−	0.781194i	0.547427	−	0.836853i	$-0.315607\pi$
$389$	−8.89556	−	15.4076i	−0.451023	−	0.781194i	−0.998450	+	0.0556592i	$0.982274\pi$
$390$	3.69247	−	1.30590i	0.186975	−	0.0661268i
$391$	8.37966	+	14.5140i	0.423777	+	0.734004i
$392$	−6.76359	−	1.80384i	−0.341613	−	0.0911078i
$393$	16.1031	−	1.10450i	0.812296	−	0.0557147i
$394$	−13.4436			−0.677281
$395$	−15.7337	−	15.4327i	−0.791646	−	0.776504i
$396$	−2.49833	+	0.344337i	−0.125546	+	0.0173036i
$397$	12.2504	−	7.07278i	0.614831	−	0.354973i	−0.160023	−	0.987113i	$-0.551157\pi$
$397$	12.2504	−	7.07278i	0.614831	−	0.354973i	0.774854	+	0.632141i	$0.217823\pi$
$398$	−14.8508	−	8.57412i	−0.744404	−	0.429782i
$399$	−1.73337	−	8.55253i	−0.0867772	−	0.428162i
$400$	0.0965491	+	4.99907i	0.00482746	+	0.249953i
$401$	10.1838	−	17.6389i	0.508556	−	0.880844i	−0.491395	−	0.870937i	$-0.663513\pi$
$401$	10.1838	−	17.6389i	0.508556	−	0.880844i	0.999951	−	0.00990749i	$-0.00315370\pi$
$402$	13.6087	+	20.2338i	0.678740	+	1.00917i
$403$	6.77038	−	3.90888i	0.337257	−	0.194715i
$404$	2.49744	+	4.32568i	0.124252	+	0.215211i
$405$	0.438351	+	20.1198i	0.0217818	+	0.999763i
$406$	−21.0848	+	2.78838i	−1.04642	+	0.138385i
$407$	3.14347	+	1.81488i	0.155816	+	0.0899605i
$408$	7.61560	−	0.522347i	0.377028	−	0.0258600i
$409$	−5.89927			−0.291700			−0.145850	−	0.989307i	$-0.546592\pi$
$409$	−5.89927			−0.291700			−0.145850	+	0.989307i	$0.546592\pi$
$410$	−20.4674	−	5.27294i	−1.01081	−	0.260412i
$411$	−4.91896	−	2.40725i	−0.242634	−	0.118741i
$412$	−2.61374	−	1.50905i	−0.128770	−	0.0743454i
$413$	8.99360	−	6.90937i	0.442546	−	0.339988i
$414$	6.99959	+	9.00841i	0.344011	+	0.442739i
$415$	−6.56009	−	23.5699i	−0.322022	−	1.15700i
$416$	−0.505630	−	0.875777i	−0.0247906	−	0.0429385i
$417$	−10.5860	+	21.6314i	−0.518399	+	1.05929i
$418$	1.38635	+	0.800409i	0.0678085	+	0.0391493i
$419$	−9.42995	−	16.3332i	−0.460683	−	0.797927i	0.538312	−	0.842746i	$-0.319062\pi$
$419$	−9.42995	−	16.3332i	−0.460683	−	0.797927i	−0.998995	+	0.0448189i	$0.985729\pi$
$420$	−4.65367	−	9.12926i	−0.227076	−	0.445462i
$421$	−3.82844	+	6.63106i	−0.186587	+	0.323178i	−0.944110	−	0.329630i	$-0.893076\pi$
$421$	−3.82844	+	6.63106i	−0.186587	+	0.323178i	0.757523	+	0.652808i	$0.226409\pi$
$422$	4.61761	−	2.66598i	0.224782	−	0.129778i
$423$	1.19528	+	0.486630i	0.0581165	+	0.0236608i
$424$	−1.52828	+	2.64705i	−0.0742196	+	0.128552i
$425$	10.6474	−	19.2929i	0.516476	−	0.935844i
$426$	−15.3212	+	10.3046i	−0.742314	+	0.499261i
$427$	27.6906	−	21.2734i	1.34004	−	1.02949i
$428$	4.87464	−	2.81438i	0.235625	−	0.136038i
$429$	−0.100757	−	1.46899i	−0.00486459	−	0.0709237i
$430$	−10.6240	+	2.95693i	−0.512335	+	0.142596i
$431$	−19.3878	+	33.5806i	−0.933876	+	1.61752i	−0.157250	+	0.987559i	$0.550263\pi$
$431$	−19.3878	+	33.5806i	−0.933876	+	1.61752i	−0.776626	+	0.629962i	$0.783071\pi$
$432$	5.08688	−	1.06003i	0.244743	−	0.0510008i
$433$			34.5032i			1.65812i	0.559163	+	0.829058i	$0.311123\pi$
$433$			34.5032i			1.65812i	−0.559163	+	0.829058i	$0.688877\pi$
$434$	−12.4608	−	16.2196i	−0.598137	−	0.778567i
$435$	−23.6661	−	20.2292i	−1.13470	−	0.969917i
$436$	−9.53935	+	16.5226i	−0.456852	+	0.791291i
$437$		−	7.24136i		−	0.346401i
$438$	−18.3879	+	1.26121i	−0.878609	+	0.0602630i
$439$	−31.7960			−1.51754			−0.758769	−	0.651360i	$-0.774199\pi$
$439$	−31.7960			−1.51754			−0.758769	+	0.651360i	$0.774199\pi$
$440$	1.82031	+	0.468962i	0.0867800	+	0.0223569i
$441$	16.7524	+	12.6632i	0.797734	+	0.603009i
$442$			4.45682i			0.211989i
$443$			0.442872i			0.0210415i	0.999945	+	0.0105207i	$0.00334892\pi$
$443$			0.442872i			0.0210415i	−0.999945	+	0.0105207i	$0.996651\pi$
$444$	−6.71741	−	3.28738i	−0.318794	−	0.156012i
$445$	−6.09550	+	23.6602i	−0.288955	+	1.12160i
$446$	5.09526	−	8.82525i	0.241267	−	0.417887i
$447$	15.4443	−	1.05931i	0.730491	−	0.0501037i
$448$	−2.09808	+	1.61186i	−0.0991248	+	0.0761530i
$449$	8.01243			0.378130			0.189065	−	0.981965i	$-0.439454\pi$
$449$	8.01243			0.378130			0.189065	+	0.981965i	$0.439454\pi$
$450$	5.38679	−	13.9994i	0.253936	−	0.659937i
$451$	−3.97298	+	6.88141i	−0.187081	+	0.324033i
$452$	2.84618	−	1.64324i	0.133873	−	0.0772915i
$453$	−14.4436	+	29.5139i	−0.678619	+	1.38669i
$454$	−3.49809	−	6.05888i	−0.164174	−	0.284357i
$455$	5.50356	−	2.34595i	0.258011	−	0.109980i
$456$	−2.96254	−	1.44981i	−0.138734	−	0.0678938i
$457$			18.3998i			0.860707i	0.902660	+	0.430354i	$0.141611\pi$
$457$			18.3998i			0.860707i	−0.902660	+	0.430354i	$0.858389\pi$
$458$	12.1301	+	7.00329i	0.566800	+	0.327242i
$459$	−21.7512	−	7.16356i	−1.01526	−	0.334366i
$460$	−2.27997	−	8.19176i	−0.106304	−	0.381943i
$461$	−19.0742	+	33.0375i	−0.888374	+	1.53871i	−0.0465771	+	0.998915i	$0.514831\pi$
$461$	−19.0742	+	33.0375i	−0.888374	+	1.53871i	−0.841797	+	0.539794i	$0.818502\pi$
$462$	−3.77558	+	0.765211i	−0.175656	+	0.0356008i
$463$	−37.1001	+	21.4198i	−1.72419	+	0.995461i	−0.814511	+	0.580147i	$0.802995\pi$
$463$	−37.1001	+	21.4198i	−1.72419	+	0.995461i	−0.909678	+	0.415314i	$0.863672\pi$
$464$	−4.01934	+	6.96170i	−0.186593	+	0.323189i
$465$	5.46815	−	29.4374i	0.253579	−	1.36513i
$466$	8.54786	+	14.8053i	0.395972	+	0.685844i
$467$	−5.97156	+	3.44768i	−0.276331	+	0.159540i	−0.631761	−	0.775163i	$-0.717668\pi$
$467$	−5.97156	+	3.44768i	−0.276331	+	0.159540i	0.355430	+	0.934703i	$0.384334\pi$
$468$	0.414220	+	3.00537i	0.0191473	+	0.138923i
$469$	22.6923	+	29.5375i	1.04783	+	1.36392i
$470$	−0.686712	−	0.673577i	−0.0316757	−	0.0310698i
$471$	6.05486	−	4.07234i	0.278993	−	0.187643i
$472$		−	4.28660i		−	0.197307i
$473$			4.14591i			0.190629i
$474$	14.1655	−	9.52731i	0.650641	−	0.437604i
$475$	−8.15223	+	4.91899i	−0.374050	+	0.225699i
$476$	11.5597	−	1.52873i	0.529838	−	0.0700690i
$477$	7.24079	−	5.62614i	0.331533	−	0.257603i
$478$	−2.13242	+	1.23115i	−0.0975345	+	0.0563116i
$479$	11.8565	+	20.5361i	0.541738	+	0.938318i	0.998804	+	0.0488852i	$0.0155669\pi$
$479$	11.8565	+	20.5361i	0.541738	+	0.938318i	−0.457066	+	0.889433i	$0.651100\pi$
$480$	−3.80785	−	0.707328i	−0.173804	−	0.0322849i
$481$	2.18321	−	3.78144i	0.0995460	−	0.172419i
$482$	16.8051	−	9.70241i	0.765450	−	0.441933i
$483$	11.5372	+	13.0601i	0.524961	+	0.594255i
$484$	−5.14665	+	8.91427i	−0.233939	+	0.405194i
$485$	−1.40357	−	5.04290i	−0.0637326	−	0.228986i
$486$	−15.3333	−	2.80904i	−0.695531	−	0.127420i
$487$	5.15393	+	2.97562i	0.233547	+	0.134838i	0.612207	−	0.790697i	$-0.290282\pi$
$487$	5.15393	+	2.97562i	0.233547	+	0.134838i	−0.378660	+	0.925536i	$0.623615\pi$
$488$		−	13.1981i		−	0.597449i
$489$	−7.40888	−	3.62577i	−0.335041	−	0.163963i
$490$	−7.97248	−	13.4700i	−0.360160	−	0.608510i
$491$	10.0161	+	17.3484i	0.452019	+	0.782920i	0.998511	−	0.0545440i	$-0.0173705\pi$
$491$	10.0161	+	17.3484i	0.452019	+	0.782920i	−0.546492	+	0.837464i	$0.684037\pi$
$492$	7.19644	−	14.7052i	0.324440	−	0.662960i
$493$	30.6816	−	17.7140i	1.38183	−	0.797799i
$494$	0.962852	−	1.66771i	0.0433207	−	0.0750337i
$495$	−4.52733	−	3.36221i	−0.203488	−	0.151120i
$496$	−7.73072			−0.347119
$497$	−22.3661	+	17.1828i	−1.00325	+	0.770755i
$498$	18.9067	−	1.29679i	0.847229	−	0.0581107i
$499$	8.24490	−	14.2806i	0.369092	−	0.639286i	−0.620332	−	0.784340i	$-0.713002\pi$
$499$	8.24490	−	14.2806i	0.369092	−	0.639286i	0.989424	+	0.145053i	$0.0463353\pi$
$500$	−7.67341	+	8.13135i	−0.343165	+	0.363645i
$501$	5.76046	+	2.81906i	0.257358	+	0.125946i
$502$			14.7856i			0.659912i
$503$		−	6.58177i		−	0.293467i	−0.989176	−	0.146733i	$-0.953124\pi$
$503$		−	6.58177i		−	0.293467i	0.989176	−	0.146733i	$-0.0468759\pi$
$504$	7.65297	−	2.10523i	0.340891	−	0.0937745i
$505$	−2.78642	+	10.8157i	−0.123994	+	0.481293i
$506$	−3.19675			−0.142113
$507$	20.6968	−	1.41957i	0.919175	−	0.0630454i
$508$		−	1.23171i		−	0.0546484i
$509$	−16.8580	+	29.1989i	−0.747218	+	1.29422i	0.201934	+	0.979399i	$0.435277\pi$
$509$	−16.8580	+	29.1989i	−0.747218	+	1.29422i	−0.949151	+	0.314820i	$0.898056\pi$
$510$	12.9749	+	11.0907i	0.574538	+	0.491102i
$511$	−27.9110	+	3.69112i	−1.23471	+	0.163286i
$512$			1.00000i			0.0441942i
$513$	6.59151	+	7.37968i	0.291022	+	0.325821i
$514$	15.9303	−	27.5921i	0.702655	−	1.21703i
$515$	−1.80954	−	6.50154i	−0.0797379	−	0.286492i
$516$	−0.584523	−	8.52209i	−0.0257322	−	0.375164i
$517$	−0.313183	+	0.180816i	−0.0137738	+	0.00795228i
$518$	−10.5568	−	4.36556i	−0.463840	−	0.191812i
$519$	−33.2398	+	22.3562i	−1.45907	+	0.981329i
$520$	0.564137	−	2.18975i	0.0247391	−	0.0960267i
$521$	7.59172	−	13.1492i	0.332599	−	0.576079i	−0.650422	−	0.759573i	$-0.725408\pi$
$521$	7.59172	−	13.1492i	0.332599	−	0.576079i	0.983021	+	0.183495i	$0.0587411\pi$
$522$	19.0432	−	14.7967i	0.833497	−	0.647632i
$523$	8.15731	−	4.70962i	0.356694	−	0.205938i	−0.310935	−	0.950431i	$-0.600642\pi$
$523$	8.15731	−	4.70962i	0.356694	−	0.205938i	0.667630	+	0.744494i	$0.267309\pi$
$524$	4.65950	−	8.07049i	0.203551	−	0.352561i
$525$	6.86578	−	21.8600i	0.299647	−	0.954050i
$526$	13.4883	+	23.3624i	0.588117	+	1.01865i
$527$	29.5062	+	17.0354i	1.28531	+	0.742073i
$528$	−0.640032	+	1.30784i	−0.0278538	+	0.0569163i
$529$	−4.26968	−	7.39530i	−0.185638	−	0.321535i
$530$	−6.58438	+	1.83260i	−0.286007	+	0.0796030i
$531$	−4.84909	+	11.9105i	−0.210433	+	0.516872i
$532$	−4.65581	−	1.92532i	−0.201855	−	0.0834732i
$533$	8.27799	+	4.77930i	0.358560	+	0.207014i
$534$	−16.9991	−	8.31905i	−0.735623	−	0.360001i
$535$	12.1883	+	3.14003i	0.526946	+	0.135755i
$536$	14.0784			0.608093
$537$	−7.45420	+	0.511277i	−0.321672	+	0.0220632i
$538$	2.41839	+	1.39626i	0.104264	+	0.0601970i
$539$	−5.68226	+	1.52967i	−0.244752	+	0.0658874i
$540$	9.78014	+	6.27286i	0.420870	+	0.269941i
$541$	0.775493	+	1.34319i	0.0333410	+	0.0577484i	0.882214	−	0.470848i	$-0.156052\pi$
$541$	0.775493	+	1.34319i	0.0333410	+	0.0577484i	−0.848873	+	0.528596i	$0.822719\pi$
$542$	−11.4412	+	6.60560i	−0.491443	+	0.283735i
$543$	−3.82779	−	5.69125i	−0.164266	−	0.244235i
$544$	2.20360	−	3.81674i	0.0944785	−	0.163642i
$545$	−41.0991	+	11.4389i	−1.76049	+	0.489989i
$546$	0.920510	+	4.54183i	0.0393942	+	0.194373i
$547$	−10.9103	−	6.29905i	−0.466490	−	0.269328i	0.248280	−	0.968688i	$-0.420135\pi$
$547$	−10.9103	−	6.29905i	−0.466490	−	0.269328i	−0.714769	+	0.699361i	$0.753468\pi$
$548$	−2.73820	+	1.58090i	−0.116970	+	0.0675328i
$549$	−14.9300	+	36.6715i	−0.637195	+	1.56510i
$550$	2.17152	+	3.59886i	0.0925941	+	0.153456i
$551$	−15.3077			−0.652132
$552$	6.57106	−	0.450703i	0.279683	−	0.0191832i
$553$	20.6789	−	15.8867i	0.879356	−	0.675569i
$554$	−2.19158	−	3.79593i	−0.0931113	−	0.161274i
$555$	−5.57584	−	15.7659i	−0.236681	−	0.669223i
$556$	6.95211	+	12.0414i	0.294835	+	0.510669i
$557$	24.3739	+	14.0723i	1.03276	+	0.596262i	0.917773	−	0.397106i	$-0.129985\pi$
$557$	24.3739	+	14.0723i	1.03276	+	0.596262i	0.114983	+	0.993367i	$0.463319\pi$
$558$	21.4802	+	8.74516i	0.909328	+	0.370212i
$559$	4.98733			0.210941
$560$	−5.87307	−	0.712108i	−0.248182	−	0.0300920i
$561$	5.32479	−	3.58131i	0.224813	−	0.151203i
$562$	21.1613	+	12.2175i	0.892636	+	0.515364i
$563$			41.5928i			1.75293i	0.481467	+	0.876464i	$0.340104\pi$
$563$			41.5928i			1.75293i	−0.481467	+	0.876464i	$0.659896\pi$
$564$	0.618266	−	0.415829i	0.0260337	−	0.0175096i
$565$	7.11642	+	1.83338i	0.299390	+	0.0771309i
$566$	24.8049			1.04263
$567$	−23.6456	−	2.80772i	−0.993024	−	0.117913i
$568$			10.6603i			0.447295i
$569$	6.71204			0.281383			0.140692	−	0.990053i	$-0.455067\pi$
$569$	6.71204			0.281383			0.140692	+	0.990053i	$0.455067\pi$
$570$	−2.45908	−	6.95313i	−0.103000	−	0.291235i
$571$	38.2017			1.59869			0.799345	−	0.600872i	$-0.205180\pi$
$571$	38.2017			1.59869			0.799345	+	0.600872i	$0.205180\pi$
$572$	−0.736222	−	0.425058i	−0.0307830	−	0.0177726i
$573$	−11.6264	−	17.2864i	−0.485699	−	0.722150i
$574$	9.55670	−	23.1100i	0.398889	−	0.964594i
$575$	9.18705	−	16.6467i	0.383127	−	0.694217i
$576$	1.13122	−	2.77855i	0.0471343	−	0.115773i
$577$	12.4815	+	7.20619i	0.519611	+	0.299998i	0.736775	−	0.676137i	$-0.236347\pi$
$577$	12.4815	+	7.20619i	0.519611	+	0.299998i	−0.217164	+	0.976135i	$0.569681\pi$
$578$	−2.09871	+	1.21169i	−0.0872947	+	0.0503996i
$579$	−27.7117	+	18.6381i	−1.15166	+	0.774574i
$580$	−17.3168	+	4.81971i	−0.719042	+	0.200127i
$581$	28.6984	−	3.79526i	1.19061	−	0.157454i
$582$	4.04518	−	0.277456i	0.167678	−	0.0115009i
$583$			2.56949i			0.106417i
$584$	−5.32061	+	9.21556i	−0.220168	+	0.381343i
$585$	−4.04457	+	5.44615i	−0.167222	+	0.225171i
$586$	−1.50591	−	2.60830i	−0.0622084	−	0.107748i
$587$	14.5914	+	8.42436i	0.602253	+	0.347711i	0.769927	−	0.638132i	$-0.220292\pi$
$587$	14.5914	+	8.42436i	0.602253	+	0.347711i	−0.167675	+	0.985842i	$0.553626\pi$
$588$	11.4645	−	3.94542i	0.472786	−	0.162706i
$589$	−7.36065	−	12.7490i	−0.303290	−	0.525314i
$590$	6.71195	−	6.84283i	0.276326	−	0.281715i
$591$	19.3215	−	12.9951i	0.794781	−	0.534549i
$592$	−3.73933	+	2.15891i	−0.153686	+	0.0887305i
$593$	31.9833	−	18.4656i	1.31340	−	0.758290i	0.330739	−	0.943722i	$-0.392702\pi$
$593$	31.9833	−	18.4656i	1.31340	−	0.758290i	0.982657	+	0.185433i	$0.0593686\pi$
$594$	3.25781	−	2.90987i	0.133670	−	0.119394i
$595$	20.8468	+	15.6598i	0.854635	+	0.641990i
$596$	4.46886	−	7.74030i	0.183052	−	0.317055i
$597$	29.6320	−	2.03243i	1.21276	−	0.0831820i
$598$			3.84553i			0.157256i
$599$	26.4689			1.08149			0.540745	−	0.841186i	$-0.318142\pi$
$599$	26.4689			1.08149			0.540745	+	0.841186i	$0.318142\pi$
$600$	−4.97105	−	7.09145i	−0.202942	−	0.289507i
$601$	−1.03438	+	1.79159i	−0.0421931	+	0.0730806i	−0.886351	−	0.463014i	$-0.846768\pi$
$601$	−1.03438	+	1.79159i	−0.0421931	+	0.0730806i	0.844158	+	0.536095i	$0.180101\pi$
$602$	−1.71069	−	12.9357i	−0.0697226	−	0.527219i
$603$	−39.1175	−	15.9258i	−1.59299	−	0.648548i
$604$	9.48547	+	16.4293i	0.385958	+	0.668499i
$605$	−22.1737	+	6.17150i	−0.901489	+	0.250907i
$606$	−7.77074	−	3.80286i	−0.315665	−	0.154481i
$607$	3.83639	+	2.21494i	0.155714	+	0.0899016i	0.575832	−	0.817568i	$-0.304678\pi$
$607$	3.83639	+	2.21494i	0.155714	+	0.0899016i	−0.420118	+	0.907469i	$0.638011\pi$
$608$	−1.64914	+	0.952130i	−0.0668814	+	0.0386140i
$609$	27.6082	−	24.3889i	1.11874	−	0.988287i
$610$	20.6655	−	21.0685i	0.836723	−	0.853039i
$611$	0.217513	+	0.376743i	0.00879962	+	0.0152414i
$612$	−10.4404	+	8.11225i	−0.422028	+	0.327918i
$613$	−30.1062	−	17.3818i	−1.21598	−	0.702045i	−0.251923	−	0.967747i	$-0.581063\pi$
$613$	−30.1062	−	17.3818i	−1.21598	−	0.702045i	−0.964055	+	0.265702i	$0.914396\pi$
$614$	10.9855			0.443339
$615$	34.5132	−	12.2061i	1.39171	−	0.492199i
$616$	−0.849947	+	2.05535i	−0.0342453	+	0.0828122i
$617$	4.09862	−	2.36634i	0.165004	−	0.0952653i	−0.415224	−	0.909719i	$-0.636297\pi$
$617$	4.09862	−	2.36634i	0.165004	−	0.0952653i	0.580228	+	0.814454i	$0.302963\pi$
$618$	5.21524	−	0.357708i	0.209788	−	0.0143891i
$619$	−7.30809	−	12.6580i	−0.293737	−	0.508767i	0.680953	−	0.732327i	$-0.261566\pi$
$619$	−7.30809	−	12.6580i	−0.293737	−	0.508767i	−0.974690	+	0.223559i	$0.928232\pi$
$620$	−12.3408	−	12.1047i	−0.495618	−	0.486138i
$621$	−18.7679	−	6.18102i	−0.753128	−	0.248036i
$622$		−	18.3890i		−	0.737333i
$623$	−26.7151	−	11.0475i	−1.07032	−	0.442609i
$624$	1.57326	+	0.769926i	0.0629809	+	0.0308217i
$625$	−24.9814	+	0.965311i	−0.999254	+	0.0386124i
$626$	−17.9290			−0.716588
$627$	−2.76620	+	0.189731i	−0.110471	+	0.00757713i
$628$		−	4.21289i		−	0.168112i
$629$	19.0294			0.758753
$630$	15.5131	+	8.62237i	0.618055	+	0.343523i
$631$	−15.3749			−0.612067			−0.306033	−	0.952021i	$-0.599002\pi$
$631$	−15.3749			−0.612067			−0.306033	+	0.952021i	$0.599002\pi$
$632$		−	9.85613i		−	0.392056i
$633$	−4.05950	+	8.29516i	−0.161351	+	0.329703i
$634$	−6.63686			−0.263583
$635$	1.92861	−	1.96622i	0.0765346	−	0.0780270i
$636$	−0.362267	−	5.28169i	−0.0143648	−	0.209433i
$637$	1.84011	+	6.83547i	0.0729079	+	0.270831i
$638$			6.75772i			0.267541i
$639$	12.0591	−	29.6201i	0.477052	−	1.17175i
$640$	−1.56580	+	1.59633i	−0.0618936	+	0.0631005i
$641$	21.3994	+	37.0648i	0.845225	+	1.46397i	0.885426	+	0.464781i	$0.153867\pi$
$641$	21.3994	+	37.0648i	0.845225	+	1.46397i	−0.0402010	+	0.999192i	$0.512800\pi$
$642$	−4.28547	+	8.75691i	−0.169134	+	0.345607i
$643$	12.6379	−	7.29647i	0.498388	−	0.287745i	−0.229659	−	0.973271i	$-0.573761\pi$
$643$	12.6379	−	7.29647i	0.498388	−	0.287745i	0.728048	+	0.685526i	$0.240428\pi$
$644$	9.97420	−	1.31905i	0.393038	−	0.0519778i
$645$	12.4108	−	14.5193i	0.488674	−	0.571698i
$646$	8.39245			0.330197
$647$	6.95004	+	4.01261i	0.273234	+	0.157752i	0.630356	−	0.776306i	$-0.282909\pi$
$647$	6.95004	+	4.01261i	0.273234	+	0.157752i	−0.357122	+	0.934058i	$0.616242\pi$
$648$	−6.28631	+	6.44067i	−0.246950	+	0.253014i
$649$	−1.80176	−	3.12075i	−0.0707254	−	0.122500i
$650$	4.32925	−	2.61223i	0.169807	−	0.102460i
$651$	33.5875	+	11.2661i	1.31640	+	0.441555i
$652$	−4.12425	+	2.38114i	−0.161518	+	0.0932525i
$653$	9.60899	+	5.54775i	0.376029	+	0.217100i	0.676089	−	0.736820i	$-0.263673\pi$
$653$	9.60899	+	5.54775i	0.376029	+	0.217100i	−0.300060	+	0.953920i	$0.597007\pi$
$654$	−2.26123	−	32.9678i	−0.0884212	−	1.28914i
$655$	20.0749	−	5.58734i	0.784390	−	0.218315i
$656$	−4.72608	−	8.18582i	−0.184523	−	0.319602i
$657$	25.2084	−	19.5871i	0.983474	−	0.764166i
$658$	0.902553	−	0.693390i	0.0351852	−	0.0270312i
$659$	24.4175	−	42.2923i	0.951169	−	1.64747i	0.208269	−	0.978072i	$-0.433217\pi$
$659$	24.4175	−	42.2923i	0.951169	−	1.64747i	0.742900	−	0.669402i	$-0.233450\pi$
$660$	−3.06951	+	1.08558i	−0.119481	+	0.0422562i
$661$	−29.1306			−1.13305			−0.566525	−	0.824044i	$-0.691713\pi$
$661$	−29.1306			−1.13305			−0.566525	+	0.824044i	$0.691713\pi$
$662$		−	3.77671i		−	0.146786i
$663$	−4.30813	−	6.40545i	−0.167314	−	0.248767i
$664$	5.47071	−	9.47556i	0.212305	−	0.367723i
$665$	−4.41756	−	10.3635i	−0.171306	−	0.401880i
$666$	12.8321	−	1.76861i	0.497235	−	0.0685322i
$667$	26.4734	−	15.2844i	1.02505	−	0.591815i
$668$	3.20663	−	1.85135i	0.124068	−	0.0716309i
$669$	1.20779	+	17.6091i	0.0466960	+	0.680808i
$670$	22.4738	+	22.0439i	0.868237	+	0.851630i
$671$	−5.54749	−	9.60853i	−0.214158	−	0.370933i
$672$	1.45732	−	4.34468i	0.0562174	−	0.167600i
$673$	−10.7102	−	6.18352i	−0.412847	−	0.238357i	0.279165	−	0.960243i	$-0.409942\pi$
$673$	−10.7102	−	6.18352i	−0.412847	−	0.238357i	−0.692012	+	0.721886i	$0.743276\pi$
$674$	−13.8871	−	24.0531i	−0.534910	−	0.926492i
$675$	5.79031	+	25.3273i	0.222869	+	0.974848i
$676$	5.98868	−	10.3727i	0.230334	−	0.398950i
$677$		−	35.4377i		−	1.36198i	−0.732292	−	0.680991i	$-0.761549\pi$
$677$		−	35.4377i		−	1.36198i	0.732292	−	0.680991i	$-0.238451\pi$
$678$	−2.50217	+	5.11292i	−0.0960953	+	0.196361i
$679$	6.14018	−	0.812015i	0.235638	−	0.0311623i
$680$	9.49393	−	2.64240i	0.364075	−	0.101331i
$681$	10.8843	+	5.32657i	0.417087	+	0.204114i
$682$	−5.62815	+	3.24942i	−0.215513	+	0.124427i
$683$	35.2245	+	20.3369i	1.34783	+	0.778168i	0.987941	−	0.154828i	$-0.0494823\pi$
$683$	35.2245	+	20.3369i	1.34783	+	0.778168i	0.359886	+	0.932996i	$0.382816\pi$
$684$	5.65928	−	0.780000i	0.216388	−	0.0298240i
$685$	−6.84646	−	1.76383i	−0.261590	−	0.0673925i
$686$	17.0981	−	7.11733i	0.652807	−	0.271741i
$687$	−24.2032	+	1.66008i	−0.923411	+	0.0633359i
$688$	−4.27106	−	2.46590i	−0.162833	−	0.0940114i
$689$	3.09097			0.117757
$690$	11.1953	+	9.56948i	0.426198	+	0.364304i
$691$	13.9169			0.529423			0.264712	−	0.964328i	$-0.414723\pi$
$691$	13.9169			0.529423			0.264712	+	0.964328i	$0.414723\pi$
$692$			23.1278i			0.879187i
$693$	4.68667	−	4.74940i	0.178032	−	0.180415i
$694$	6.15913			0.233797
$695$	−7.75654	+	30.1077i	−0.294222	+	1.14205i
$696$	−0.952755	−	13.8908i	−0.0361141	−	0.526528i
$697$			41.6576i			1.57789i
$698$	−26.6447	−	15.3833i	−1.00852	−	0.582268i
$699$	−26.5966	−	13.0159i	−1.00598	−	0.492306i
$700$	−8.26034	−	10.3328i	−0.312212	−	0.390543i
$701$	−25.4648			−0.961794			−0.480897	−	0.876777i	$-0.659689\pi$
$701$	−25.4648			−0.961794			−0.480897	+	0.876777i	$0.659689\pi$
$702$	−3.50043	−	3.91899i	−0.132115	−	0.147913i
$703$	−7.12066	−	4.11112i	−0.268561	−	0.155054i
$704$	0.420325	+	0.728025i	0.0158416	+	0.0274385i
$705$	1.63806	+	0.304279i	0.0616930	+	0.0114598i
$706$	11.0578	+	19.1527i	0.416166	+	0.720821i
$707$	−12.2122	−	5.05011i	−0.459287	−	0.189929i
$708$	4.14359	+	6.16080i	0.155726	+	0.231537i
$709$	−20.6267			−0.774651			−0.387325	−	0.921943i	$-0.626601\pi$
$709$	−20.6267			−0.774651			−0.387325	+	0.921943i	$0.626601\pi$
$710$	−16.6918	+	17.0173i	−0.626434	+	0.638649i
$711$	−11.1495	+	27.3857i	−0.418138	+	1.02705i
$712$	−9.46277	+	5.46333i	−0.354632	+	0.204747i
$713$	25.4592	+	14.6989i	0.953453	+	0.550476i
$714$	−15.1361	+	13.3712i	−0.566456	+	0.500403i
$715$	−0.509700	−	1.83131i	−0.0190617	−	0.0684871i
$716$	−2.15690	+	3.73586i	−0.0806070	+	0.139616i
$717$	1.87468	−	3.83072i	0.0700113	−	0.143061i
$718$	−28.5585	+	16.4883i	−1.06579	+	0.615337i
$719$	−17.4847	−	30.2844i	−0.652069	−	1.12942i	−0.982620	−	0.185629i	$-0.940568\pi$
$719$	−17.4847	−	30.2844i	−0.652069	−	1.12942i	0.330551	−	0.943788i	$-0.392766\pi$
$720$	6.15645	−	2.66422i	0.229438	−	0.0992896i
$721$	7.91620	−	1.04689i	0.294815	−	0.0389881i
$722$	13.3141	+	7.68690i	0.495499	+	0.286077i
$723$	−14.7739	+	30.1890i	−0.549448	+	1.12274i
$724$	−3.95990			−0.147168
$725$	−35.1901	−	19.4208i	−1.30693	−	0.721271i
$726$	−1.21998	−	17.7867i	−0.0452776	−	0.660128i
$727$	−4.55898	−	2.63213i	−0.169083	−	0.0976203i	0.413070	−	0.910699i	$-0.364456\pi$
$727$	−4.55898	−	2.63213i	−0.169083	−	0.0976203i	−0.582154	+	0.813079i	$0.697790\pi$
$728$	2.47248	+	1.02244i	0.0916361	+	0.0378943i
$729$	24.7527	−	10.7845i	0.916765	−	0.399426i
$730$	−22.9232	+	6.38009i	−0.848424	+	0.236138i
$731$	10.8677	+	18.8234i	0.401956	+	0.696208i
$732$	12.7578	+	18.9686i	0.471541	+	0.701099i
$733$	−23.6730	−	13.6676i	−0.874383	−	0.504825i	−0.00558085	−	0.999984i	$-0.501776\pi$
$733$	−23.6730	−	13.6676i	−0.874383	−	0.504825i	−0.868802	+	0.495159i	$0.835110\pi$
$734$	−1.76360	−	3.05465i	−0.0650958	−	0.112749i
$735$	24.4788	+	11.6528i	0.902914	+	0.429821i
$736$	1.90136	−	3.29325i	0.0700850	−	0.121391i
$737$	10.2494	−	5.91750i	0.377542	−	0.217974i
$738$	3.87168	+	28.0909i	0.142519	+	1.03404i
$739$	−16.5878	+	28.7310i	−0.610193	+	1.05689i	0.381014	+	0.924569i	$0.375575\pi$
$739$	−16.5878	+	28.7310i	−0.610193	+	1.05689i	−0.991207	+	0.132317i	$0.957758\pi$
$740$	−9.34963	−	2.40871i	−0.343699	−	0.0885461i
$741$	0.228237	+	3.32760i	0.00838449	+	0.122242i
$742$	−1.06023	−	8.01707i	−0.0389221	−	0.294316i
$743$	24.0563	−	13.8889i	0.882540	−	0.509534i	0.0110447	−	0.999939i	$-0.496484\pi$
$743$	24.0563	−	13.8889i	0.882540	−	0.509534i	0.871495	+	0.490405i	$0.163151\pi$
$744$	11.1108	−	7.47280i	0.407340	−	0.273966i
$745$	19.2535	−	5.35874i	0.705395	−	0.196329i
$746$	8.56210	−	14.8300i	0.313481	−	0.542964i
$747$	−25.9196	+	20.1397i	−0.948349	+	0.736873i
$748$		−	3.70491i		−	0.135465i
$749$	−5.69100	+	13.7620i	−0.207945	+	0.502853i
$750$	3.16833	−	19.1040i	0.115691	−	0.697578i
$751$	7.47848	−	12.9531i	0.272893	−	0.472665i	−0.696708	−	0.717355i	$-0.745353\pi$
$751$	7.47848	−	12.9531i	0.272893	−	0.472665i	0.969602	+	0.244689i	$0.0786860\pi$
$752$		−	0.430181i		−	0.0156871i
$753$	−14.2923	−	21.2501i	−0.520840	−	0.774398i
$754$	8.12920			0.296048
$755$	−10.5830	+	41.0790i	−0.385156	+	1.49502i
$756$	−8.96404	+	10.4233i	−0.326019	+	0.379093i
$757$			44.3484i			1.61187i	0.592004	+	0.805935i	$0.298337\pi$
$757$			44.3484i			1.61187i	−0.592004	+	0.805935i	$0.701663\pi$
$758$			10.6327i			0.386199i
$759$	4.59445	−	3.09010i	0.166768	−	0.112164i
$760$	−4.12342	−	1.06230i	−0.149572	−	0.0385338i
$761$	−15.3172	+	26.5302i	−0.555250	+	0.961720i	0.442635	+	0.896702i	$0.354044\pi$
$761$	−15.3172	+	26.5302i	−0.555250	+	0.961720i	−0.997884	+	0.0650183i	$0.979289\pi$
$762$	1.19062	+	1.77024i	0.0431316	+	0.0641292i
$763$	−6.61783	−	50.0418i	−0.239582	−	1.81163i
$764$	−12.0276			−0.435145
$765$	−29.3685	−	3.39771i	−1.06182	−	0.122844i
$766$	−7.41452	+	12.8423i	−0.267897	+	0.464012i
$767$	−3.75410	+	2.16743i	−0.135553	+	0.0782614i
$768$	−0.966638	−	1.43722i	−0.0348805	−	0.0518613i
$769$	−11.2438	−	19.4749i	−0.405463	−	0.702283i	0.588912	−	0.808197i	$-0.299556\pi$
$769$	−11.2438	−	19.4749i	−0.405463	−	0.702283i	−0.994375	+	0.105914i	$0.966223\pi$
$770$	−4.57505	+	1.95017i	−0.164874	+	0.0702791i
$771$	3.77616	+	55.0548i	0.135995	+	1.98275i
$772$			19.2814i			0.693952i
$773$	−34.1008	−	19.6881i	−1.22652	−	0.708131i	−0.260220	−	0.965549i	$-0.583795\pi$
$773$	−34.1008	−	19.6881i	−1.22652	−	0.708131i	−0.966300	+	0.257418i	$0.917128\pi$
$774$	9.07787	+	11.6831i	0.326297	+	0.419941i
$775$	−0.746394	−	38.6464i	−0.0268113	−	1.38822i
$776$	1.17049	−	2.02734i	0.0420181	−	0.0727774i
$777$	19.3924	−	3.93033i	0.695699	−	0.141000i
$778$	15.4076	−	8.89556i	0.552388	−	0.318921i
$779$	8.99969	−	15.5879i	0.322448	−	0.558495i
$780$	1.30590	+	3.69247i	0.0467587	+	0.132212i
$781$	4.48078	+	7.76094i	0.160335	+	0.277708i
$782$	−14.5140	+	8.37966i	−0.519019	+	0.299656i
$783$	−13.0663	+	39.6740i	−0.466950	+	1.41783i
$784$	1.80384	−	6.76359i	0.0644229	−	0.241557i
$785$	6.59653	−	6.72516i	0.235440	−	0.240031i
$786$	1.10450	+	16.1031i	0.0393962	+	0.574380i
$787$		−	48.3783i		−	1.72450i	−0.506483	−	0.862250i	$-0.669055\pi$
$787$		−	48.3783i		−	1.72450i	0.506483	−	0.862250i	$-0.330945\pi$
$788$		−	13.4436i		−	0.478910i
$789$	−41.9686	−	20.5387i	−1.49412	−	0.731196i
$790$	15.4327	−	15.7337i	0.549071	−	0.559778i
$791$	−3.32282	+	8.03527i	−0.118146	+	0.285701i
$792$	−0.344337	−	2.49833i	−0.0122355	−	0.0887744i
$793$	−11.5586	+	6.67335i	−0.410457	+	0.236978i
$794$	7.07278	+	12.2504i	0.251004	+	0.434751i
$795$	7.69177	−	8.99857i	0.272799	−	0.319146i
$796$	8.57412	−	14.8508i	0.303902	−	0.526373i
$797$	33.1557	−	19.1424i	1.17443	−	0.678060i	0.219714	−	0.975564i	$-0.429488\pi$
$797$	33.1557	−	19.1424i	1.17443	−	0.678060i	0.954721	+	0.297504i	$0.0961542\pi$
$798$	8.55253	−	1.73337i	0.302756	−	0.0613607i
$799$	−0.947946	+	1.64189i	−0.0335359	+	0.0580859i
$800$	−4.99907	+	0.0965491i	−0.176744	+	0.00341353i
$801$	32.4730	−	4.47565i	1.14738	−	0.158139i
$802$	17.6389	+	10.1838i	0.622851	+	0.359603i
$803$			8.94554i			0.315681i
$804$	−20.2338	+	13.6087i	−0.713590	+	0.479942i
$805$	17.9875	+	13.5119i	0.633976	+	0.476233i
$806$	3.90888	+	6.77038i	0.137685	+	0.238477i
$807$	−4.82544	+	0.330973i	−0.169864	+	0.0116508i
$808$	−4.32568	+	2.49744i	−0.152177	+	0.0878595i
$809$	−12.3800	+	21.4428i	−0.435257	+	0.753888i	−0.997317	−	0.0732093i	$-0.976676\pi$
$809$	−12.3800	+	21.4428i	−0.435257	+	0.753888i	0.562059	+	0.827097i	$0.310009\pi$
$810$	−20.1198	+	0.438351i	−0.706939	+	0.0154021i
$811$	22.6756			0.796249			0.398124	−	0.917331i	$-0.369661\pi$
$811$	22.6756			0.796249			0.398124	+	0.917331i	$0.369661\pi$
$812$	−2.78838	−	21.0848i	−0.0978529	−	0.739930i
$813$	10.0584	−	20.5533i	0.352763	−	0.720834i
$814$	−1.81488	+	3.14347i	−0.0636117	+	0.110179i
$815$	−10.3120	−	2.65666i	−0.361215	−	0.0930587i
$816$	0.522347	+	7.61560i	0.0182858	+	0.266599i
$817$		−	9.39142i		−	0.328564i
$818$		−	5.89927i		−	0.206263i
$819$	−5.71329	−	5.63783i	−0.199638	−	0.197002i
$820$	5.27294	−	20.4674i	0.184139	−	0.714752i
$821$	−15.7008			−0.547960			−0.273980	−	0.961735i	$-0.588340\pi$
$821$	−15.7008			−0.547960			−0.273980	+	0.961735i	$0.588340\pi$
$822$	2.40725	−	4.91896i	0.0839625	−	0.171568i
$823$			7.81595i			0.272447i	0.990678	+	0.136224i	$0.0434965\pi$
$823$			7.81595i			0.272447i	−0.990678	+	0.136224i	$0.956503\pi$
$824$	1.50905	−	2.61374i	0.0525701	−	0.0910541i
$825$	−6.59976	−	3.07329i	−0.229774	−	0.106998i
$826$	6.90937	+	8.99360i	0.240408	+	0.312927i
$827$			26.4090i			0.918333i	0.888350	+	0.459166i	$0.151852\pi$
$827$			26.4090i			0.918333i	−0.888350	+	0.459166i	$0.848148\pi$
$828$	−9.00841	+	6.99959i	−0.313064	+	0.243253i
$829$	2.06847	−	3.58269i	0.0718408	−	0.124432i	−0.827867	−	0.560924i	$-0.810446\pi$
$829$	2.06847	−	3.58269i	0.0718408	−	0.124432i	0.899708	+	0.436492i	$0.143779\pi$
$830$	23.5699	−	6.56009i	0.818123	−	0.227704i
$831$	6.81908	+	3.33713i	0.236551	+	0.115764i
$832$	0.875777	−	0.505630i	0.0303621	−	0.0175296i
$833$	−21.7890	+	21.8399i	−0.754945	+	0.756709i
$834$	−21.6314	−	10.5860i	−0.749034	−	0.366564i
$835$	8.01769	+	2.06557i	0.277464	+	0.0714821i
$836$	−0.800409	+	1.38635i	−0.0276827	+	0.0479479i
$837$	−39.3252	+	8.19481i	−1.35928	+	0.283254i
$838$	16.3332	−	9.42995i	0.564220	−	0.325752i
$839$	−13.7108	+	23.7479i	−0.473350	+	0.819867i	−0.999535	−	0.0305035i	$-0.990289\pi$
$839$	−13.7108	+	23.7479i	−0.473350	+	0.819867i	0.526184	+	0.850371i	$0.323622\pi$
$840$	9.12926	−	4.65367i	0.314989	−	0.160567i
$841$	−17.8102	−	30.8481i	−0.614144	−	1.06373i
$842$	−6.63106	−	3.82844i	−0.228521	−	0.131937i
$843$	−42.2234	+	2.89607i	−1.45425	+	0.0997459i
$844$	2.66598	+	4.61761i	0.0917667	+	0.158945i
$845$	25.8015	−	7.18119i	0.887597	−	0.247041i
$846$	−0.486630	+	1.19528i	−0.0167307	+	0.0410946i
$847$	−3.57044	−	26.9985i	−0.122682	−	0.927678i
$848$	−2.64705	−	1.52828i	−0.0909001	−	0.0524812i
$849$	−35.6502	+	23.9773i	−1.22351	+	0.822900i
$850$	19.2929	+	10.6474i	0.661742	+	0.365204i
$851$	16.4194			0.562850
$852$	−10.3046	−	15.3212i	−0.353031	−	0.524895i
$853$	34.9133	+	20.1572i	1.19541	+	0.690169i	0.959528	−	0.281613i	$-0.0908695\pi$
$853$	34.9133	+	20.1572i	1.19541	+	0.690169i	0.235880	+	0.971782i	$0.424203\pi$
$854$	21.2734	+	27.6906i	0.727961	+	0.947552i
$855$	10.2554	+	7.61616i	0.350728	+	0.260467i
$856$	2.81438	+	4.87464i	0.0961934	+	0.166612i
$857$	−12.9511	+	7.47733i	−0.442402	+	0.255421i	−0.704616	−	0.709589i	$-0.748881\pi$
$857$	−12.9511	+	7.47733i	−0.442402	+	0.255421i	0.262214	+	0.965010i	$0.415547\pi$
$858$	1.46899	−	0.100757i	0.0501506	−	0.00343979i
$859$	5.86938	−	10.1661i	0.200261	−	0.346862i	−0.748352	−	0.663302i	$-0.769154\pi$
$859$	5.86938	−	10.1661i	0.200261	−	0.346862i	0.948612	+	0.316440i	$0.102488\pi$
$860$	−2.95693	−	10.6240i	−0.100830	−	0.362276i
$861$	8.60393	+	42.4522i	0.293221	+	1.44677i
$862$	−33.5806	−	19.3878i	−1.14376	−	0.660350i
$863$	−28.1985	+	16.2804i	−0.959889	+	0.554192i	−0.896139	−	0.443774i	$-0.853639\pi$
$863$	−28.1985	+	16.2804i	−0.959889	+	0.554192i	−0.0637500	+	0.997966i	$0.520306\pi$
$864$	1.06003	+	5.08688i	0.0360630	+	0.173059i
$865$	−36.2135	+	36.9196i	−1.23130	+	1.25531i
$866$	−34.5032			−1.17246
$867$	1.84505	−	3.77016i	0.0626611	−	0.128041i
$868$	16.2196	−	12.4608i	0.550530	−	0.422947i
$869$	−4.14278	−	7.17551i	−0.140534	−	0.243412i
$870$	20.2292	−	23.6661i	0.685835	−	0.802356i
$871$	−7.11845	−	12.3295i	−0.241200	−	0.417770i
$872$	−16.5226	−	9.53935i	−0.559527	−	0.323043i
$873$	−5.54563	+	4.30899i	−0.187691	+	0.145837i
$874$	7.24136			0.244943
$875$	2.99284	−	29.4286i	0.101176	−	0.994869i
$876$	−1.26121	−	18.3879i	−0.0426124	−	0.621270i
$877$	−26.3127	−	15.1916i	−0.888517	−	0.512986i	−0.0150599	−	0.999887i	$-0.504794\pi$
$877$	−26.3127	−	15.1916i	−0.888517	−	0.512986i	−0.873457	+	0.486901i	$0.838127\pi$
$878$		−	31.7960i		−	1.07306i
$879$	4.68561	+	2.29305i	0.158042	+	0.0773427i
$880$	−0.468962	+	1.82031i	−0.0158087	+	0.0613628i
$881$	−56.5236			−1.90433			−0.952164	−	0.305587i	$-0.901147\pi$
$881$	−56.5236			−1.90433			−0.952164	+	0.305587i	$0.901147\pi$
$882$	−12.6632	+	16.7524i	−0.426392	+	0.564083i
$883$			7.98060i			0.268569i	0.990943	+	0.134284i	$0.0428735\pi$
$883$			7.98060i			0.268569i	−0.990943	+	0.134284i	$0.957126\pi$
$884$	−4.45682			−0.149899
$885$	−3.03203	+	16.3227i	−0.101920	+	0.548681i
$886$	−0.442872			−0.0148786
$887$	−21.4791	−	12.4009i	−0.721196	−	0.416383i	0.0939966	−	0.995573i	$-0.470036\pi$
$887$	−21.4791	−	12.4009i	−0.721196	−	0.416383i	−0.815193	+	0.579190i	$0.803369\pi$
$888$	3.28738	−	6.71741i	0.110317	−	0.225422i
$889$	1.98534	+	2.58422i	0.0665862	+	0.0866721i
$890$	−23.6602	−	6.09550i	−0.793092	−	0.204322i
$891$	−1.86941	+	7.33127i	−0.0626277	+	0.245607i
$892$	8.82525	+	5.09526i	0.295491	+	0.170602i
$893$	0.709428	−	0.409589i	0.0237401	−	0.0137064i
$894$	1.05931	+	15.4443i	0.0354287	+	0.516535i
$895$	−9.29272	+	2.58640i	−0.310621	+	0.0864537i
$896$	−1.61186	−	2.09808i	−0.0538483	−	0.0700918i
$897$	−3.71724	−	5.52689i	−0.124115	−	0.184538i
$898$			8.01243i			0.267378i
$899$	31.0724	−	53.8189i	1.03632	−	1.79496i
$900$	13.9994	+	5.38679i	0.466646	+	0.179560i
$901$	6.73541	+	11.6661i	0.224389	+	0.388653i
$902$	−6.88141	−	3.97298i	−0.229126	−	0.132286i
$903$	14.9628	+	16.9378i	0.497929	+	0.563656i
$904$	1.64324	+	2.84618i	0.0546533	+	0.0946624i
$905$	−6.32131	−	6.20040i	−0.210127	−	0.206108i
$906$	−29.5139	−	14.4436i	−0.980535	−	0.479856i
$907$	28.4327	−	16.4156i	0.944093	−	0.545072i	0.0528517	−	0.998602i	$-0.483169\pi$
$907$	28.4327	−	16.4156i	0.944093	−	0.545072i	0.891241	+	0.453530i	$0.149836\pi$
$908$	6.05888	−	3.49809i	0.201071	−	0.116088i
$909$	14.8443	−	2.04594i	0.492354	−	0.0678595i
$910$	2.34595	+	5.50356i	0.0777675	+	0.182441i
$911$	17.2988	−	29.9624i	0.573135	−	0.992698i	−0.423107	−	0.906080i	$-0.639061\pi$
$911$	17.2988	−	29.9624i	0.573135	−	0.992698i	0.996242	−	0.0866186i	$-0.0276062\pi$
$912$	1.44981	−	2.96254i	0.0480082	−	0.0980996i
$913$		−	9.19792i		−	0.304407i
$914$	−18.3998			−0.608612
$915$	−9.33537	+	50.2563i	−0.308618	+	1.66142i
$916$	−7.00329	+	12.1301i	−0.231395	+	0.400788i
$917$	3.23248	+	24.4429i	0.106746	+	0.807177i
$918$	7.16356	−	21.7512i	0.236433	−	0.717897i
$919$	20.7521	+	35.9437i	0.684549	+	1.18567i	0.973578	+	0.228353i	$0.0733341\pi$
$919$	20.7521	+	35.9437i	0.684549	+	1.18567i	−0.289030	+	0.957320i	$0.593333\pi$
$920$	8.19176	−	2.27997i	0.270074	−	0.0751685i
$921$	−15.7886	+	10.6190i	−0.520253	+	0.349908i
$922$	−33.0375	−	19.0742i	−1.08803	−	0.628175i
$923$	9.33602	−	5.39016i	0.307299	−	0.177419i
$924$	−0.765211	−	3.77558i	−0.0251736	−	0.124208i
$925$	−11.1535	−	18.4847i	−0.366726	−	0.607774i
$926$	−21.4198	−	37.1001i	−0.703897	−	1.21919i
$927$	−7.14969	+	5.55535i	−0.234826	+	0.182462i
$928$	−6.96170	−	4.01934i	−0.228529	−	0.131941i
$929$	4.99827			0.163988			0.0819939	−	0.996633i	$-0.473871\pi$
$929$	4.99827			0.163988			0.0819939	+	0.996633i	$0.473871\pi$
$930$	29.4374	+	5.46815i	0.965289	+	0.179308i
$931$	12.8716	−	3.46503i	0.421849	−	0.113562i
$932$	−14.8053	+	8.54786i	−0.484965	+	0.279995i
$933$	17.7755	+	26.4291i	0.581945	+	0.865251i
$934$	−3.44768	−	5.97156i	−0.112812	−	0.195395i
$935$	5.80115	−	5.91427i	0.189718	−	0.193417i
$936$	−3.00537	+	0.414220i	−0.0982336	+	0.0135392i
$937$		−	47.6976i		−	1.55821i	−0.626891	−	0.779107i	$-0.715673\pi$
$937$		−	47.6976i		−	1.55821i	0.626891	−	0.779107i	$-0.284327\pi$
$938$	−29.5375	+	22.6923i	−0.964434	+	0.740930i
$939$	25.7680	−	17.3309i	0.840908	−	0.565572i
$940$	0.673577	−	0.686712i	0.0219697	−	0.0223981i
$941$	−16.6170			−0.541697			−0.270849	−	0.962622i	$-0.587304\pi$
$941$	−16.6170			−0.541697			−0.270849	+	0.962622i	$0.587304\pi$
$942$	4.07234	+	6.05486i	0.132684	+	0.197278i
$943$			35.9439i			1.17049i
$944$	4.28660			0.139517
$945$	−30.6304	+	2.60324i	−0.996408	+	0.0846833i
$946$	−4.14591			−0.134795
$947$			43.5260i			1.41440i	0.707012	+	0.707202i	$0.250043\pi$
$947$			43.5260i			1.41440i	−0.707012	+	0.707202i	$0.749957\pi$
$948$	9.52731	+	14.1655i	0.309433	+	0.460073i
$949$	10.7610			0.349318
$950$	−4.91899	−	8.15223i	−0.159593	−	0.264493i
$951$	9.53864	−	6.41544i	0.309312	−	0.208035i
$952$	1.52873	+	11.5597i	0.0495463	+	0.374652i
$953$			26.0200i			0.842870i	0.906859	+	0.421435i	$0.138473\pi$
$953$			26.0200i			0.842870i	−0.906859	+	0.421435i	$0.861527\pi$
$954$	5.62614	+	7.24079i	0.182153	+	0.234429i
$955$	−19.2001	−	18.8329i	−0.621301	−	0.609418i
$956$	−1.23115	−	2.13242i	−0.0398183	−	0.0689673i
$957$	−6.53227	−	9.71235i	−0.211158	−	0.313956i
$958$	−20.5361	+	11.8565i	−0.663491	+	0.383067i
$959$	3.19677	−	7.73044i	0.103229	−	0.249629i
$960$	0.707328	−	3.80785i	0.0228289	−	0.122898i
$961$	28.7640			0.927870
$962$	3.78144	+	2.18321i	0.121918	+	0.0703897i
$963$	−2.30558	−	16.7281i	−0.0742963	−	0.539056i
$964$	9.70241	+	16.8051i	0.312494	+	0.541255i
$965$	−30.1908	+	30.7795i	−0.971875	+	0.990827i
$966$	−13.0601	+	11.5372i	−0.420202	+	0.371203i
$967$	9.74398	−	5.62569i	0.313345	−	0.180910i	−0.335077	−	0.942191i	$-0.608762\pi$
$967$	9.74398	−	5.62569i	0.313345	−	0.180910i	0.648422	+	0.761281i	$0.275429\pi$
$968$	−8.91427	−	5.14665i	−0.286515	−	0.165420i
$969$	−12.0618	+	8.11246i	−0.387482	+	0.260610i
$970$	5.04290	−	1.40357i	0.161918	−	0.0450658i
$971$	−18.1251	−	31.3936i	−0.581662	−	1.00747i	−0.995282	−	0.0970194i	$-0.969069\pi$
$971$	−18.1251	−	31.3936i	−0.581662	−	1.00747i	0.413620	−	0.910450i	$-0.364264\pi$
$972$	2.80904	−	15.3333i	0.0900999	−	0.491815i
$973$	−33.9950	−	14.0580i	−1.08983	−	0.450678i
$974$	−2.97562	+	5.15393i	−0.0953451	+	0.165143i
$975$	−3.69702	+	7.93918i	−0.118399	+	0.254257i
$976$	13.1981			0.422460
$977$			8.10793i			0.259396i	0.991554	+	0.129698i	$0.0414008\pi$
$977$			8.10793i			0.259396i	−0.991554	+	0.129698i	$0.958599\pi$
$978$	3.62577	−	7.40888i	0.115939	−	0.236910i
$979$	−4.59276	+	7.95489i	−0.146785	+	0.254239i
$980$	13.4700	−	7.97248i	0.430282	−	0.254672i
$981$	35.1178	+	45.1963i	1.12123	+	1.44301i
$982$	−17.3484	+	10.0161i	−0.553608	+	0.319626i
$983$	−20.0545	+	11.5785i	−0.639638	+	0.369295i	−0.784475	−	0.620160i	$-0.787068\pi$
$983$	−20.0545	+	11.5785i	−0.639638	+	0.369295i	0.144837	+	0.989456i	$0.453734\pi$
$984$	14.7052	+	7.19644i	0.468783	+	0.229414i
$985$	21.0500	−	21.4605i	0.670710	−	0.683789i
$986$	17.7140	+	30.6816i	0.564129	+	0.977101i
$987$	−0.626913	+	1.86900i	−0.0199548	+	0.0594909i
$988$	1.66771	+	0.962852i	0.0530569	+	0.0306324i
$989$	9.37710	+	16.2416i	0.298175	+	0.516453i
$990$	3.36221	−	4.52733i	0.106858	−	0.143888i
$991$	6.18252	−	10.7084i	0.196394	−	0.340165i	−0.750962	−	0.660345i	$-0.770410\pi$
$991$	6.18252	−	10.7084i	0.196394	−	0.340165i	0.947357	+	0.320180i	$0.103743\pi$
$992$		−	7.73072i		−	0.245450i
$993$	3.65071	+	5.42798i	0.115852	+	0.172252i
$994$	−17.1828	−	22.3661i	−0.545006	−	0.709408i
$995$	36.9405	−	10.2815i	1.17109	−	0.325945i
$996$	1.29679	+	18.9067i	0.0410905	+	0.599081i
$997$	−8.81145	+	5.08729i	−0.279061	+	0.161116i	−0.632998	−	0.774153i	$-0.718176\pi$
$997$	−8.81145	+	5.08729i	−0.279061	+	0.161116i	0.353937	+	0.935269i	$0.384843\pi$
$998$	14.2806	+	8.24490i	0.452044	+	0.260988i
$999$	−16.7330	+	14.9459i	−0.529409	+	0.472867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.ba.a.529.32	yes	96
3.2	odd	2		1890.2.ba.a.1369.28		96
5.4	even	2	inner	630.2.ba.a.529.17	yes	96
7.2	even	3		630.2.bq.a.79.47	yes	96
9.4	even	3		630.2.bq.a.319.2	yes	96
9.5	odd	6		1890.2.bq.a.739.35		96
15.14	odd	2		1890.2.ba.a.1369.26		96
21.2	odd	6		1890.2.bq.a.289.10		96
35.9	even	6		630.2.bq.a.79.2	yes	96
45.4	even	6		630.2.bq.a.319.47	yes	96
45.14	odd	6		1890.2.bq.a.739.10		96
63.23	odd	6		1890.2.ba.a.1549.26		96
63.58	even	3	inner	630.2.ba.a.499.41	yes	96
105.44	odd	6		1890.2.bq.a.289.35		96
315.149	odd	6		1890.2.ba.a.1549.28		96
315.184	even	6	inner	630.2.ba.a.499.8	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ba.a.499.8	✓	96	315.184	even	6	inner
630.2.ba.a.499.41	yes	96	63.58	even	3	inner
630.2.ba.a.529.17	yes	96	5.4	even	2	inner
630.2.ba.a.529.32	yes	96	1.1	even	1	trivial
630.2.bq.a.79.2	yes	96	35.9	even	6
630.2.bq.a.79.47	yes	96	7.2	even	3
630.2.bq.a.319.2	yes	96	9.4	even	3
630.2.bq.a.319.47	yes	96	45.4	even	6
1890.2.ba.a.1369.26		96	15.14	odd	2
1890.2.ba.a.1369.28		96	3.2	odd	2
1890.2.ba.a.1549.26		96	63.23	odd	6
1890.2.ba.a.1549.28		96	315.149	odd	6
1890.2.bq.a.289.10		96	21.2	odd	6
1890.2.bq.a.289.35		96	105.44	odd	6
1890.2.bq.a.739.10		96	45.14	odd	6
1890.2.bq.a.739.35		96	9.5	odd	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.966638 - 1.43722i) q^{3} -1.00000 q^{4} +(-1.59633 - 1.56580i) q^{5} +(1.43722 - 0.966638i) q^{6} +(2.09808 - 1.61186i) q^{7} -1.00000i q^{8} +(-1.13122 + 2.77855i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.966638 - 1.43722i) q^{3} -1.00000 q^{4} +(-1.59633 - 1.56580i) q^{5} +(1.43722 - 0.966638i) q^{6} +(2.09808 - 1.61186i) q^{7} -1.00000i q^{8} +(-1.13122 + 2.77855i) q^{9} +(1.56580 - 1.59633i) q^{10} +(-0.420325 - 0.728025i) q^{11} +(0.966638 + 1.43722i) q^{12} +(-0.875777 + 0.505630i) q^{13} +(1.61186 + 2.09808i) q^{14} +(-0.707328 + 3.80785i) q^{15} +1.00000 q^{16} +(-3.81674 - 2.20360i) q^{17} +(-2.77855 - 1.13122i) q^{18} +(0.952130 + 1.64914i) q^{19} +(1.59633 + 1.56580i) q^{20} +(-4.34468 - 1.45732i) q^{21} +(0.728025 - 0.420325i) q^{22} +(-3.29325 - 1.90136i) q^{23} +(-1.43722 + 0.966638i) q^{24} +(0.0965491 + 4.99907i) q^{25} +(-0.505630 - 0.875777i) q^{26} +(5.08688 - 1.06003i) q^{27} +(-2.09808 + 1.61186i) q^{28} +(-4.01934 + 6.96170i) q^{29} +(-3.80785 - 0.707328i) q^{30} -7.73072 q^{31} +1.00000i q^{32} +(-0.640032 + 1.30784i) q^{33} +(2.20360 - 3.81674i) q^{34} +(-5.87307 - 0.712108i) q^{35} +(1.13122 - 2.77855i) q^{36} +(-3.73933 + 2.15891i) q^{37} +(-1.64914 + 0.952130i) q^{38} +(1.57326 + 0.769926i) q^{39} +(-1.56580 + 1.59633i) q^{40} +(-4.72608 - 8.18582i) q^{41} +(1.45732 - 4.34468i) q^{42} +(-4.27106 - 2.46590i) q^{43} +(0.420325 + 0.728025i) q^{44} +(6.15645 - 2.66422i) q^{45} +(1.90136 - 3.29325i) q^{46} -0.430181i q^{47} +(-0.966638 - 1.43722i) q^{48} +(1.80384 - 6.76359i) q^{49} +(-4.99907 + 0.0965491i) q^{50} +(0.522347 + 7.61560i) q^{51} +(0.875777 - 0.505630i) q^{52} +(-2.64705 - 1.52828i) q^{53} +(1.06003 + 5.08688i) q^{54} +(-0.468962 + 1.82031i) q^{55} +(-1.61186 - 2.09808i) q^{56} +(1.44981 - 2.96254i) q^{57} +(-6.96170 - 4.01934i) q^{58} +4.28660 q^{59} +(0.707328 - 3.80785i) q^{60} +13.1981 q^{61} -7.73072i q^{62} +(2.10523 + 7.65297i) q^{63} -1.00000 q^{64} +(2.18975 + 0.564137i) q^{65} +(-1.30784 - 0.640032i) q^{66} +14.0784i q^{67} +(3.81674 + 2.20360i) q^{68} +(0.450703 + 6.57106i) q^{69} +(0.712108 - 5.87307i) q^{70} -10.6603 q^{71} +(2.77855 + 1.13122i) q^{72} +(-9.21556 - 5.32061i) q^{73} +(-2.15891 - 3.73933i) q^{74} +(7.09145 - 4.97105i) q^{75} +(-0.952130 - 1.64914i) q^{76} +(-2.05535 - 0.849947i) q^{77} +(-0.769926 + 1.57326i) q^{78} +9.85613 q^{79} +(-1.59633 - 1.56580i) q^{80} +(-6.44067 - 6.28631i) q^{81} +(8.18582 - 4.72608i) q^{82} +(9.47556 + 5.47071i) q^{83} +(4.34468 + 1.45732i) q^{84} +(2.64240 + 9.49393i) q^{85} +(2.46590 - 4.27106i) q^{86} +(13.8908 - 0.952755i) q^{87} +(-0.728025 + 0.420325i) q^{88} +(-5.46333 - 9.46277i) q^{89} +(2.66422 + 6.15645i) q^{90} +(-1.02244 + 2.47248i) q^{91} +(3.29325 + 1.90136i) q^{92} +(7.47280 + 11.1108i) q^{93} +0.430181 q^{94} +(1.06230 - 4.12342i) q^{95} +(1.43722 - 0.966638i) q^{96} +(2.02734 + 1.17049i) q^{97} +(6.76359 + 1.80384i) q^{98} +(2.49833 - 0.344337i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 96 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) \) 96 * q - 96 * q^4 - 4 * q^6 + 8 * q^9	\( 96 q - 96 q^{4} - 4 q^{6} + 8 q^{9} + 4 q^{11} - 2 q^{14} - 2 q^{15} + 96 q^{16} + 8 q^{21} + 4 q^{24} + 24 q^{26} + 10 q^{29} + 10 q^{30} - 34 q^{35} - 8 q^{36} + 44 q^{39} + 30 q^{41} - 4 q^{44} - 44 q^{45} - 6 q^{46} - 6 q^{49} - 12 q^{50} + 28 q^{51} - 8 q^{54} + 12 q^{55} + 2 q^{56} + 48 q^{59} + 2 q^{60} + 12 q^{61} - 96 q^{64} - 36 q^{65} + 32 q^{66} + 36 q^{69} + 6 q^{70} - 32 q^{71} - 68 q^{75} - 32 q^{81} - 8 q^{84} + 4 q^{86} - 66 q^{89} - 22 q^{90} + 24 q^{94} - 60 q^{95} - 4 q^{96} - 4 q^{99}+O(q^{100}) \) 96 * q - 96 * q^4 - 4 * q^6 + 8 * q^9 + 4 * q^11 - 2 * q^14 - 2 * q^15 + 96 * q^16 + 8 * q^21 + 4 * q^24 + 24 * q^26 + 10 * q^29 + 10 * q^30 - 34 * q^35 - 8 * q^36 + 44 * q^39 + 30 * q^41 - 4 * q^44 - 44 * q^45 - 6 * q^46 - 6 * q^49 - 12 * q^50 + 28 * q^51 - 8 * q^54 + 12 * q^55 + 2 * q^56 + 48 * q^59 + 2 * q^60 + 12 * q^61 - 96 * q^64 - 36 * q^65 + 32 * q^66 + 36 * q^69 + 6 * q^70 - 32 * q^71 - 68 * q^75 - 32 * q^81 - 8 * q^84 + 4 * q^86 - 66 * q^89 - 22 * q^90 + 24 * q^94 - 60 * q^95 - 4 * q^96 - 4 * q^99

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