LMFDB - Embedded newform 630.2.t.c.551.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(311,630)]

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([5, 0, 1]))

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

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

chi := DirichletCharacter("630.311");

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.t (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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			551.9
Character	$\chi$	$=$	630.551
Dual form			630.2.t.c.311.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-1.69871 + 0.338184i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-1.30204 + 1.14223i) q^{6} +(-2.46207 - 0.968625i) q^{7} -1.00000i q^{8} +(2.77126 - 1.14896i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-1.69871 + 0.338184i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-1.30204 + 1.14223i) q^{6} +(-2.46207 - 0.968625i) q^{7} -1.00000i q^{8} +(2.77126 - 1.14896i) q^{9} +(0.866025 - 0.500000i) q^{10} +0.656579i q^{11} +(-0.556482 + 1.64022i) q^{12} +(2.39457 - 1.38250i) q^{13} +(-2.61652 + 0.392179i) q^{14} +(-1.69871 + 0.338184i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.36928 - 5.83577i) q^{17} +(1.82551 - 2.38066i) q^{18} +(-0.633612 - 0.365816i) q^{19} +(0.500000 - 0.866025i) q^{20} +(4.50992 + 0.812788i) q^{21} +(0.328290 + 0.568614i) q^{22} -7.20086i q^{23} +(0.338184 + 1.69871i) q^{24} +1.00000 q^{25} +(1.38250 - 2.39457i) q^{26} +(-4.31903 + 2.88894i) q^{27} +(-2.06989 + 1.64790i) q^{28} +(6.21225 + 3.58664i) q^{29} +(-1.30204 + 1.14223i) q^{30} +(-6.93952 - 4.00653i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.222044 - 1.11534i) q^{33} +(-5.83577 - 3.36928i) q^{34} +(-2.46207 - 0.968625i) q^{35} +(0.390607 - 2.97446i) q^{36} +(1.05061 - 1.81971i) q^{37} -0.731632 q^{38} +(-3.60015 + 3.15828i) q^{39} -1.00000i q^{40} +(-3.35799 - 5.81621i) q^{41} +(4.31210 - 1.55107i) q^{42} +(6.29106 - 10.8964i) q^{43} +(0.568614 + 0.328290i) q^{44} +(2.77126 - 1.14896i) q^{45} +(-3.60043 - 6.23613i) q^{46} +(2.92933 + 5.07374i) q^{47} +(1.14223 + 1.30204i) q^{48} +(5.12353 + 4.76964i) q^{49} +(0.866025 - 0.500000i) q^{50} +(7.69702 + 8.77388i) q^{51} -2.76501i q^{52} +(-5.77309 + 3.33309i) q^{53} +(-2.29592 + 4.66141i) q^{54} +0.656579i q^{55} +(-0.968625 + 2.46207i) q^{56} +(1.20004 + 0.407140i) q^{57} +7.17328 q^{58} +(-4.62900 + 8.01766i) q^{59} +(-0.556482 + 1.64022i) q^{60} +(1.35595 - 0.782856i) q^{61} -8.01306 q^{62} +(-7.93594 + 0.144487i) q^{63} -1.00000 q^{64} +(2.39457 - 1.38250i) q^{65} +(-0.749967 - 0.854892i) q^{66} +(3.28370 - 5.68754i) q^{67} -6.73857 q^{68} +(2.43521 + 12.2322i) q^{69} +(-2.61652 + 0.392179i) q^{70} -1.54080i q^{71} +(-1.14896 - 2.77126i) q^{72} +(5.95292 - 3.43692i) q^{73} -2.10122i q^{74} +(-1.69871 + 0.338184i) q^{75} +(-0.633612 + 0.365816i) q^{76} +(0.635979 - 1.61654i) q^{77} +(-1.53868 + 4.53523i) q^{78} +(7.53532 + 13.0516i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(6.35980 - 6.36812i) q^{81} +(-5.81621 - 3.35799i) q^{82} +(-8.71114 + 15.0881i) q^{83} +(2.95885 - 3.49931i) q^{84} +(-3.36928 - 5.83577i) q^{85} -12.5821i q^{86} +(-11.7658 - 3.99180i) q^{87} +0.656579 q^{88} +(-1.32440 + 2.29393i) q^{89} +(1.82551 - 2.38066i) q^{90} +(-7.23471 + 1.08438i) q^{91} +(-6.23613 - 3.60043i) q^{92} +(13.1432 + 4.45912i) q^{93} +(5.07374 + 2.92933i) q^{94} +(-0.633612 - 0.365816i) q^{95} +(1.64022 + 0.556482i) q^{96} +(4.02448 + 2.32353i) q^{97} +(6.82193 + 1.56886i) q^{98} +(0.754380 + 1.81955i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) $ 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9	$ 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9 + 4 * q^12 + 2 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 + 16 * q^20 + 16 * q^21 + 4 * q^24 + 32 * q^25 + 12 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 + 2 * q^30 + 18 * q^31 + 16 * q^33 - 2 * q^35 + 2 * q^37 - 18 * q^39 - 6 * q^41 + 6 * q^42 - 28 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^47 + 2 * q^48 + 32 * q^49 - 26 * q^51 - 36 * q^53 - 32 * q^54 - 6 * q^56 + 18 * q^57 - 30 * q^59 + 4 * q^60 + 54 * q^61 - 94 * q^63 - 32 * q^64 - 44 * q^66 + 4 * q^67 + 12 * q^68 + 28 * q^69 + 4 * q^72 - 30 * q^73 + 2 * q^75 - 6 * q^77 - 22 * q^78 + 4 * q^79 - 16 * q^80 + 26 * q^81 - 24 * q^82 + 6 * q^83 - 4 * q^84 + 6 * q^85 - 8 * q^87 - 12 * q^89 - 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 42 * q^94 + 2 * q^96 + 96 * q^97 - 24 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−1.69871	+	0.338184i	−0.980753	+	0.195250i
$3$	−1.69871	+	0.338184i	−0.980753	+	0.195250i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.30204	+	1.14223i	−0.531555	+	0.466315i
$7$	−2.46207	−	0.968625i	−0.930573	−	0.366106i
$7$	−2.46207	−	0.968625i	−0.930573	−	0.366106i
$8$		−	1.00000i		−	0.353553i
$9$	2.77126	−	1.14896i	0.923755	−	0.382985i
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$			0.656579i			0.197966i	0.995089	+	0.0989831i	$0.0315590\pi$
$11$			0.656579i			0.197966i	−0.995089	+	0.0989831i	$0.968441\pi$
$12$	−0.556482	+	1.64022i	−0.160642	+	0.473491i
$13$	2.39457	−	1.38250i	0.664133	−	0.383438i	−0.129717	−	0.991551i	$-0.541407\pi$
$13$	2.39457	−	1.38250i	0.664133	−	0.383438i	0.793850	+	0.608114i	$0.208073\pi$
$14$	−2.61652	+	0.392179i	−0.699295	+	0.104814i
$15$	−1.69871	+	0.338184i	−0.438606	+	0.0873187i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.36928	−	5.83577i	−0.817172	−	1.41538i	−0.907758	−	0.419494i	$-0.862207\pi$
$17$	−3.36928	−	5.83577i	−0.817172	−	1.41538i	0.0905864	−	0.995889i	$-0.471126\pi$
$18$	1.82551	−	2.38066i	0.430276	−	0.561126i
$19$	−0.633612	−	0.365816i	−0.145361	−	0.0839240i	0.425556	−	0.904932i	$-0.360079\pi$
$19$	−0.633612	−	0.365816i	−0.145361	−	0.0839240i	−0.570916	+	0.821008i	$0.693412\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	4.50992	+	0.812788i	0.984145	+	0.177365i
$22$	0.328290	+	0.568614i	0.0699916	+	0.121229i
$23$		−	7.20086i		−	1.50148i	−0.660596	−	0.750741i	$-0.729696\pi$
$23$		−	7.20086i		−	1.50148i	0.660596	−	0.750741i	$-0.270304\pi$
$24$	0.338184	+	1.69871i	0.0690315	+	0.346749i
$25$	1.00000			0.200000
$26$	1.38250	−	2.39457i	0.271131	−	0.469613i
$27$	−4.31903	+	2.88894i	−0.831197	+	0.555977i
$28$	−2.06989	+	1.64790i	−0.391172	+	0.311424i
$29$	6.21225	+	3.58664i	1.15359	+	0.666023i	0.949758	−	0.312984i	$-0.101329\pi$
$29$	6.21225	+	3.58664i	1.15359	+	0.666023i	0.203827	+	0.979007i	$0.434662\pi$
$30$	−1.30204	+	1.14223i	−0.237719	+	0.208542i
$31$	−6.93952	−	4.00653i	−1.24637	−	0.719594i	−0.275990	−	0.961161i	$-0.589006\pi$
$31$	−6.93952	−	4.00653i	−1.24637	−	0.719594i	−0.970384	+	0.241566i	$0.922339\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−0.222044	−	1.11534i	−0.0386530	−	0.194156i
$34$	−5.83577	−	3.36928i	−1.00083	−	0.577828i
$35$	−2.46207	−	0.968625i	−0.416165	−	0.163728i
$36$	0.390607	−	2.97446i	0.0651012	−	0.495744i
$37$	1.05061	−	1.81971i	0.172719	−	0.299158i	−0.766651	−	0.642065i	$-0.778078\pi$
$37$	1.05061	−	1.81971i	0.172719	−	0.299158i	0.939369	+	0.342907i	$0.111411\pi$
$38$	−0.731632			−0.118686
$39$	−3.60015	+	3.15828i	−0.576485	+	0.505730i
$40$		−	1.00000i		−	0.158114i
$41$	−3.35799	−	5.81621i	−0.524430	−	0.908339i	−0.999595	−	0.0284427i	$-0.990945\pi$
$41$	−3.35799	−	5.81621i	−0.524430	−	0.908339i	0.475166	−	0.879896i	$-0.342388\pi$
$42$	4.31210	−	1.55107i	0.665371	−	0.239335i
$43$	6.29106	−	10.8964i	0.959378	−	1.66169i	0.235364	−	0.971907i	$-0.424372\pi$
$43$	6.29106	−	10.8964i	0.959378	−	1.66169i	0.724015	−	0.689785i	$-0.242295\pi$
$44$	0.568614	+	0.328290i	0.0857219	+	0.0494915i
$45$	2.77126	−	1.14896i	0.413116	−	0.171276i
$46$	−3.60043	−	6.23613i	−0.530854	−	0.919467i
$47$	2.92933	+	5.07374i	0.427286	+	0.740082i	0.996631	−	0.0820173i	$-0.0261363\pi$
$47$	2.92933	+	5.07374i	0.427286	+	0.740082i	−0.569344	+	0.822099i	$0.692803\pi$
$48$	1.14223	+	1.30204i	0.164867	+	0.187933i
$49$	5.12353	+	4.76964i	0.731933	+	0.681377i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	7.69702	+	8.77388i	1.07780	+	1.22859i
$52$		−	2.76501i		−	0.383438i
$53$	−5.77309	+	3.33309i	−0.792994	+	0.457835i	−0.841016	−	0.541011i	$-0.818042\pi$
$53$	−5.77309	+	3.33309i	−0.792994	+	0.457835i	0.0480213	+	0.998846i	$0.484708\pi$
$54$	−2.29592	+	4.66141i	−0.312435	+	0.634338i
$55$			0.656579i			0.0885332i
$56$	−0.968625	+	2.46207i	−0.129438	+	0.329007i
$57$	1.20004	+	0.407140i	0.158949	+	0.0539270i
$58$	7.17328			0.941898
$59$	−4.62900	+	8.01766i	−0.602645	+	1.04381i	0.389774	+	0.920910i	$0.372553\pi$
$59$	−4.62900	+	8.01766i	−0.602645	+	1.04381i	−0.992419	+	0.122901i	$0.960780\pi$
$60$	−0.556482	+	1.64022i	−0.0718415	+	0.211752i
$61$	1.35595	−	0.782856i	0.173611	−	0.100234i	−0.410676	−	0.911781i	$-0.634707\pi$
$61$	1.35595	−	0.782856i	0.173611	−	0.100234i	0.584287	+	0.811547i	$0.301374\pi$
$62$	−8.01306			−1.01766
$63$	−7.93594	+	0.144487i	−0.999834	+	0.0182037i
$64$	−1.00000			−0.125000
$65$	2.39457	−	1.38250i	0.297009	−	0.171478i
$66$	−0.749967	−	0.854892i	−0.0923145	−	0.105230i
$67$	3.28370	−	5.68754i	0.401168	−	0.694843i	−0.592699	−	0.805424i	$-0.701938\pi$
$67$	3.28370	−	5.68754i	0.401168	−	0.694843i	0.993867	+	0.110581i	$0.0352710\pi$
$68$	−6.73857			−0.817172
$69$	2.43521	+	12.2322i	0.293165	+	1.47258i
$70$	−2.61652	+	0.392179i	−0.312734	+	0.0468743i
$71$		−	1.54080i		−	0.182859i	−0.995812	−	0.0914294i	$-0.970856\pi$
$71$		−	1.54080i		−	0.182859i	0.995812	−	0.0914294i	$-0.0291436\pi$
$72$	−1.14896	−	2.77126i	−0.135406	−	0.326597i
$73$	5.95292	−	3.43692i	0.696736	−	0.402261i	−0.109395	−	0.993998i	$-0.534891\pi$
$73$	5.95292	−	3.43692i	0.696736	−	0.402261i	0.806131	+	0.591738i	$0.201558\pi$
$74$		−	2.10122i		−	0.244261i
$75$	−1.69871	+	0.338184i	−0.196151	+	0.0390501i
$76$	−0.633612	+	0.365816i	−0.0726803	+	0.0419620i
$77$	0.635979	−	1.61654i	0.0724766	−	0.184222i
$78$	−1.53868	+	4.53523i	−0.174221	+	0.513513i
$79$	7.53532	+	13.0516i	0.847790	+	1.46842i	0.883176	+	0.469042i	$0.155401\pi$
$79$	7.53532	+	13.0516i	0.847790	+	1.46842i	−0.0353856	+	0.999374i	$0.511266\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	6.35980	−	6.36812i	0.706645	−	0.707568i
$82$	−5.81621	−	3.35799i	−0.642293	−	0.370828i
$83$	−8.71114	+	15.0881i	−0.956172	+	1.65614i	−0.224508	+	0.974472i	$0.572078\pi$
$83$	−8.71114	+	15.0881i	−0.956172	+	1.65614i	−0.731664	+	0.681666i	$0.761256\pi$
$84$	2.95885	−	3.49931i	0.322838	−	0.381806i
$85$	−3.36928	−	5.83577i	−0.365450	−	0.632978i
$86$		−	12.5821i		−	1.35677i
$87$	−11.7658	−	3.99180i	−1.26142	−	0.427966i
$88$	0.656579			0.0699916
$89$	−1.32440	+	2.29393i	−0.140386	+	0.243156i	−0.927642	−	0.373470i	$-0.878168\pi$
$89$	−1.32440	+	2.29393i	−0.140386	+	0.243156i	0.787256	+	0.616627i	$0.211501\pi$
$90$	1.82551	−	2.38066i	0.192425	−	0.250943i
$91$	−7.23471	+	1.08438i	−0.758403	+	0.113674i
$92$	−6.23613	−	3.60043i	−0.650161	−	0.375371i
$93$	13.1432	+	4.45912i	1.36289	+	0.462390i
$94$	5.07374	+	2.92933i	0.523317	+	0.302137i
$95$	−0.633612	−	0.365816i	−0.0650072	−	0.0375319i
$96$	1.64022	+	0.556482i	0.167404	+	0.0567957i
$97$	4.02448	+	2.32353i	0.408624	+	0.235919i	0.690198	−	0.723620i	$-0.257523\pi$
$97$	4.02448	+	2.32353i	0.408624	+	0.235919i	−0.281575	+	0.959539i	$0.590857\pi$
$98$	6.82193	+	1.56886i	0.689119	+	0.158479i
$99$	0.754380	+	1.81955i	0.0758181	+	0.182872i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	4.53706			0.451454			0.225727	−	0.974191i	$-0.427524\pi$
$101$	4.53706			0.451454			0.225727	+	0.974191i	$0.427524\pi$
$102$	11.0528	+	3.74989i	1.09439	+	0.371295i
$103$			3.79379i			0.373814i	0.982378	+	0.186907i	$0.0598462\pi$
$103$			3.79379i			0.373814i	−0.982378	+	0.186907i	$0.940154\pi$
$104$	−1.38250	−	2.39457i	−0.135566	−	0.234807i
$105$	4.50992	+	0.812788i	0.440123	+	0.0793199i
$106$	−3.33309	+	5.77309i	−0.323739	+	0.560732i
$107$	5.69580	+	3.28847i	0.550634	+	0.317909i	0.749378	−	0.662143i	$-0.230353\pi$
$107$	5.69580	+	3.28847i	0.550634	+	0.317909i	−0.198744	+	0.980052i	$0.563686\pi$
$108$	0.342384	+	5.18486i	0.0329460	+	0.498913i
$109$	−4.84359	−	8.38935i	−0.463932	−	0.803554i	0.535221	−	0.844712i	$-0.320228\pi$
$109$	−4.84359	−	8.38935i	−0.463932	−	0.803554i	−0.999153	+	0.0411586i	$0.986895\pi$
$110$	0.328290	+	0.568614i	0.0313012	+	0.0542153i
$111$	−1.16929	+	3.44646i	−0.110984	+	0.327124i
$112$	0.392179	+	2.61652i	0.0370574	+	0.247238i
$113$	−10.5658	+	6.10019i	−0.993950	+	0.573857i	−0.906453	−	0.422307i	$-0.861220\pi$
$113$	−10.5658	+	6.10019i	−0.993950	+	0.573857i	−0.0874975	+	0.996165i	$0.527887\pi$
$114$	1.24283	−	0.247426i	0.116402	−	0.0231736i
$115$		−	7.20086i		−	0.671483i
$116$	6.21225	−	3.58664i	0.576793	−	0.333011i
$117$	5.04754	−	6.58253i	0.466645	−	0.608555i
$118$			9.25800i			0.852268i
$119$	2.64272	+	17.6316i	0.242258	+	1.61629i
$120$	0.338184	+	1.69871i	0.0308718	+	0.155071i
$121$	10.5689			0.960809
$122$	0.782856	−	1.35595i	0.0708764	−	0.122762i
$123$	7.67121	+	8.74446i	0.691690	+	0.788462i
$124$	−6.93952	+	4.00653i	−0.623187	+	0.359797i
$125$	1.00000			0.0894427
$126$	−6.80048	+	4.09310i	−0.605835	+	0.364642i
$127$	2.97414			0.263912			0.131956	−	0.991256i	$-0.457874\pi$
$127$	2.97414			0.263912			0.131956	+	0.991256i	$0.457874\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−7.00172	+	20.6375i	−0.616467	+	1.81703i
$130$	1.38250	−	2.39457i	0.121254	−	0.210017i
$131$	9.31698			0.814028			0.407014	−	0.913422i	$-0.366570\pi$
$131$	9.31698			0.814028			0.407014	+	0.913422i	$0.366570\pi$
$132$	−1.07694	−	0.365374i	−0.0937353	−	0.0318018i
$133$	1.20566	+	1.51440i	0.104544	+	0.131315i
$134$		−	6.56740i		−	0.567337i
$135$	−4.31903	+	2.88894i	−0.371723	+	0.248641i
$136$	−5.83577	+	3.36928i	−0.500413	+	0.288914i
$137$			17.0995i			1.46091i	0.682963	+	0.730453i	$0.260691\pi$
$137$			17.0995i			1.46091i	−0.682963	+	0.730453i	$0.739309\pi$
$138$	8.22506	+	9.37579i	0.700163	+	0.798120i
$139$	12.6560	−	7.30697i	1.07347	−	0.619769i	0.144343	−	0.989528i	$-0.453893\pi$
$139$	12.6560	−	7.30697i	1.07347	−	0.619769i	0.929128	+	0.369759i	$0.120560\pi$
$140$	−2.06989	+	1.64790i	−0.174937	+	0.139273i
$141$	−6.69195	−	7.62819i	−0.563564	−	0.642410i
$142$	−0.770398	−	1.33437i	−0.0646504	−	0.111978i
$143$	0.907724	+	1.57222i	0.0759077	+	0.131476i
$144$	−2.38066	−	1.82551i	−0.198388	−	0.152126i
$145$	6.21225	+	3.58664i	0.515899	+	0.297854i
$146$	3.43692	−	5.95292i	0.284441	−	0.492667i
$147$	−10.3164	−	6.36956i	−0.850885	−	0.525352i
$148$	−1.05061	−	1.81971i	−0.0863595	−	0.149579i
$149$			8.71460i			0.713928i	0.934118	+	0.356964i	$0.116188\pi$
$149$			8.71460i			0.713928i	−0.934118	+	0.356964i	$0.883812\pi$
$150$	−1.30204	+	1.14223i	−0.106311	+	0.0932629i
$151$	−8.62341			−0.701763			−0.350882	−	0.936420i	$-0.614118\pi$
$151$	−8.62341			−0.701763			−0.350882	+	0.936420i	$0.614118\pi$
$152$	−0.365816	+	0.633612i	−0.0296716	+	0.0513927i
$153$	−16.0422	−	12.3013i	−1.29694	−	0.994502i
$154$	−0.257496	−	1.71796i	−0.0207496	−	0.138437i
$155$	−6.93952	−	4.00653i	−0.557395	−	0.321812i
$156$	0.935081	+	4.69696i	0.0748664	+	0.376058i
$157$	13.9806	+	8.07171i	1.11577	+	0.644193i	0.940319	−	0.340295i	$-0.110527\pi$
$157$	13.9806	+	8.07171i	1.11577	+	0.644193i	0.175455	+	0.984487i	$0.443860\pi$
$158$	13.0516	+	7.53532i	1.03833	+	0.599478i
$159$	8.67963	−	7.61434i	0.688339	−	0.603856i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	−6.97493	+	17.7290i	−0.549702	+	1.39724i
$162$	2.32369	−	8.69485i	0.182567	−	0.683132i
$163$	−1.04426	+	1.80871i	−0.0817928	+	0.141669i	−0.904020	−	0.427490i	$-0.859398\pi$
$163$	−1.04426	+	1.80871i	−0.0817928	+	0.141669i	0.822227	+	0.569159i	$0.192731\pi$
$164$	−6.71598			−0.524430
$165$	−0.222044	−	1.11534i	−0.0172861	−	0.0868292i
$166$			17.4223i			1.35223i
$167$	−3.73797	−	6.47435i	−0.289253	−	0.501001i	0.684379	−	0.729127i	$-0.260073\pi$
$167$	−3.73797	−	6.47435i	−0.289253	−	0.501001i	−0.973632	+	0.228126i	$0.926740\pi$
$168$	0.812788	−	4.50992i	0.0627079	−	0.347948i
$169$	−2.67737	+	4.63733i	−0.205951	+	0.356718i
$170$	−5.83577	−	3.36928i	−0.447583	−	0.258412i
$171$	−2.17621	−	0.285781i	−0.166419	−	0.0218542i
$172$	−6.29106	−	10.8964i	−0.479689	−	0.830846i
$173$	−8.95135	−	15.5042i	−0.680559	−	1.17876i	−0.974811	−	0.223034i	$-0.928404\pi$
$173$	−8.95135	−	15.5042i	−0.680559	−	1.17876i	0.294252	−	0.955728i	$-0.404930\pi$
$174$	−12.1854	+	2.42589i	−0.923770	+	0.183906i
$175$	−2.46207	−	0.968625i	−0.186115	−	0.0732212i
$176$	0.568614	−	0.328290i	0.0428609	−	0.0247458i
$177$	5.15191	−	15.1852i	0.387241	−	1.14139i
$178$			2.64880i			0.198536i
$179$	8.68355	−	5.01345i	0.649039	−	0.374723i	−0.139049	−	0.990286i	$-0.544405\pi$
$179$	8.68355	−	5.01345i	0.649039	−	0.374723i	0.788088	+	0.615563i	$0.211071\pi$
$180$	0.390607	−	2.97446i	0.0291141	−	0.221703i
$181$			8.57389i			0.637292i	0.947874	+	0.318646i	$0.103228\pi$
$181$			8.57389i			0.637292i	−0.947874	+	0.318646i	$0.896772\pi$
$182$	−5.72325	+	4.55645i	−0.424236	+	0.337747i
$183$	−2.03862	+	1.78841i	−0.150699	+	0.132203i
$184$	−7.20086			−0.530854
$185$	1.05061	−	1.81971i	0.0772422	−	0.133787i
$186$	13.6119	−	2.70989i	0.998074	−	0.198699i
$187$	3.83165	−	2.21220i	0.280198	−	0.161772i
$188$	5.85866			0.427286
$189$	13.4320	−	2.92925i	0.977037	−	0.213071i
$190$	−0.731632			−0.0530782
$191$	9.27965	−	5.35761i	0.671452	−	0.387663i	−0.125175	−	0.992135i	$-0.539949\pi$
$191$	9.27965	−	5.35761i	0.671452	−	0.387663i	0.796627	+	0.604472i	$0.206616\pi$
$192$	1.69871	−	0.338184i	0.122594	−	0.0244063i
$193$	0.618062	−	1.07052i	0.0444891	−	0.0770574i	−0.842923	−	0.538034i	$-0.819167\pi$
$193$	0.618062	−	1.07052i	0.0444891	−	0.0770574i	0.887412	+	0.460976i	$0.152501\pi$
$194$	4.64707			0.333640
$195$	−3.60015	+	3.15828i	−0.257812	+	0.226169i
$196$	6.69239	−	2.05229i	0.478028	−	0.146592i
$197$		−	15.5323i		−	1.10663i	−0.832972	−	0.553315i	$-0.813363\pi$
$197$		−	15.5323i		−	1.10663i	0.832972	−	0.553315i	$-0.186637\pi$
$198$	1.56309	+	1.19859i	0.111084	+	0.0851801i
$199$	14.8736	−	8.58726i	1.05436	−	0.608735i	0.130493	−	0.991449i	$-0.458344\pi$
$199$	14.8736	−	8.58726i	1.05436	−	0.608735i	0.923867	+	0.382715i	$0.125011\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−3.65464	+	10.7720i	−0.257778	+	0.759798i
$202$	3.92921	−	2.26853i	0.276458	−	0.159613i
$203$	−11.8208	−	14.8479i	−0.829661	−	1.04212i
$204$	11.4469	−	2.27887i	0.801444	−	0.159553i
$205$	−3.35799	−	5.81621i	−0.234532	−	0.406222i
$206$	1.89690	+	3.28552i	0.132163	+	0.228913i
$207$	−8.27346	−	19.9555i	−0.575045	−	1.38700i
$208$	−2.39457	−	1.38250i	−0.166033	−	0.0958594i
$209$	0.240187	−	0.416017i	0.0166141	−	0.0287765i
$210$	4.31210	−	1.55107i	0.297563	−	0.107034i
$211$	−11.1982	−	19.3958i	−0.770913	−	1.33526i	−0.937063	−	0.349160i	$-0.886467\pi$
$211$	−11.1982	−	19.3958i	−0.770913	−	1.33526i	0.166150	−	0.986100i	$-0.446866\pi$
$212$			6.66619i			0.457835i
$213$	0.521072	+	2.61737i	0.0357033	+	0.179339i
$214$	6.57695			0.449591
$215$	6.29106	−	10.8964i	0.429047	−	0.743131i
$216$	2.88894	+	4.31903i	0.196568	+	0.293873i
$217$	13.2047	+	16.5861i	0.896395	+	1.12594i
$218$	−8.38935	−	4.84359i	−0.568198	−	0.328049i
$219$	−8.95000	+	7.85152i	−0.604785	+	0.530557i
$220$	0.568614	+	0.328290i	0.0383360	+	0.0221333i
$221$	−16.1360	−	9.31610i	−1.08542	−	0.626669i
$222$	0.710597	+	3.56937i	0.0476922	+	0.239560i
$223$	−2.68635	−	1.55096i	−0.179891	−	0.103860i	0.407350	−	0.913272i	$-0.366453\pi$
$223$	−2.68635	−	1.55096i	−0.179891	−	0.103860i	−0.587241	+	0.809412i	$0.699786\pi$
$224$	1.64790	+	2.06989i	0.110105	+	0.138300i
$225$	2.77126	−	1.14896i	0.184751	−	0.0765970i
$226$	−6.10019	+	10.5658i	−0.405778	+	0.702829i
$227$	−28.9648			−1.92246			−0.961229	−	0.275751i	$-0.911074\pi$
$227$	−28.9648			−1.92246			−0.961229	+	0.275751i	$0.911074\pi$
$228$	0.952613	−	0.835695i	0.0630884	−	0.0553452i
$229$		−	26.2751i		−	1.73631i	−0.496295	−	0.868154i	$-0.665306\pi$
$229$		−	26.2751i		−	1.73631i	0.496295	−	0.868154i	$-0.334694\pi$
$230$	−3.60043	−	6.23613i	−0.237405	−	0.411198i
$231$	−0.533660	+	2.96112i	−0.0351122	+	0.194827i
$232$	3.58664	−	6.21225i	0.235475	−	0.407854i
$233$	4.26732	+	2.46374i	0.279562	+	0.161405i	0.633225	−	0.773968i	$-0.281731\pi$
$233$	4.26732	+	2.46374i	0.279562	+	0.161405i	−0.353663	+	0.935373i	$0.615064\pi$
$234$	1.08003	−	8.22441i	0.0706039	−	0.537647i
$235$	2.92933	+	5.07374i	0.191088	+	0.330975i
$236$	4.62900	+	8.01766i	0.301322	+	0.521906i
$237$	−17.2142	−	19.6226i	−1.11818	−	1.27462i
$238$	11.1045	+	13.9481i	0.719796	+	0.904119i
$239$	−13.4424	+	7.76099i	−0.869518	+	0.502016i	−0.867188	−	0.497981i	$-0.834075\pi$
$239$	−13.4424	+	7.76099i	−0.869518	+	0.502016i	−0.00232989	+	0.999997i	$0.500742\pi$
$240$	1.14223	+	1.30204i	0.0737308	+	0.0840462i
$241$		−	10.5676i		−	0.680717i	−0.940296	−	0.340359i	$-0.889452\pi$
$241$		−	10.5676i		−	0.680717i	0.940296	−	0.340359i	$-0.110548\pi$
$242$	9.15294	−	5.28445i	0.588373	−	0.339697i
$243$	−8.64990	+	12.9684i	−0.554891	+	0.831923i
$244$		−	1.56571i		−	0.100234i
$245$	5.12353	+	4.76964i	0.327330	+	0.304721i
$246$	11.0157	+	3.73732i	0.702335	+	0.238283i
$247$	−2.02297			−0.128718
$248$	−4.00653	+	6.93952i	−0.254415	+	0.440660i
$249$	9.69518	−	28.5764i	0.614407	−	1.81096i
$250$	0.866025	−	0.500000i	0.0547723	−	0.0316228i
$251$	1.92533			0.121526			0.0607630	−	0.998152i	$-0.480647\pi$
$251$	1.92533			0.121526			0.0607630	+	0.998152i	$0.480647\pi$
$252$	−3.84284	+	6.94497i	−0.242076	+	0.437492i
$253$	4.72793			0.297243
$254$	2.57568	−	1.48707i	0.161612	−	0.0933070i
$255$	7.69702	+	8.77388i	0.482006	+	0.549441i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.54242			−0.220970			−0.110485	−	0.993878i	$-0.535240\pi$
$257$	−3.54242			−0.220970			−0.110485	+	0.993878i	$0.535240\pi$
$258$	4.25507	+	21.3734i	0.264909	+	1.33065i
$259$	−4.34928	+	3.46259i	−0.270251	+	0.215155i
$260$		−	2.76501i		−	0.171478i
$261$	21.3367	+	2.80194i	1.32071	+	0.173436i
$262$	8.06874	−	4.65849i	0.498488	−	0.287802i
$263$			9.51881i			0.586955i	0.955966	+	0.293477i	$0.0948126\pi$
$263$			9.51881i			0.586955i	−0.955966	+	0.293477i	$0.905187\pi$
$264$	−1.11534	+	0.222044i	−0.0686445	+	0.0136659i
$265$	−5.77309	+	3.33309i	−0.354638	+	0.204750i
$266$	1.80133	+	0.708678i	0.110446	+	0.0434518i
$267$	1.47401	−	4.34463i	0.0902080	−	0.265887i
$268$	−3.28370	−	5.68754i	−0.200584	−	0.347422i
$269$	1.90191	+	3.29420i	0.115961	+	0.200851i	0.918164	−	0.396201i	$-0.129672\pi$
$269$	1.90191	+	3.29420i	0.115961	+	0.200851i	−0.802202	+	0.597052i	$0.796338\pi$
$270$	−2.29592	+	4.66141i	−0.139725	+	0.283685i
$271$	−1.08398	−	0.625837i	−0.0658472	−	0.0380169i	0.466715	−	0.884408i	$-0.345437\pi$
$271$	−1.08398	−	0.625837i	−0.0658472	−	0.0380169i	−0.532562	+	0.846391i	$0.678771\pi$
$272$	−3.36928	+	5.83577i	−0.204293	+	0.353846i
$273$	11.9230	−	4.28871i	0.721612	−	0.259564i
$274$	8.54973	+	14.8086i	0.516508	+	0.894618i
$275$			0.656579i			0.0395932i
$276$	11.8110	+	4.00715i	0.710939	+	0.241202i
$277$	−15.0419			−0.903781			−0.451891	−	0.892073i	$-0.649250\pi$
$277$	−15.0419			−0.903781			−0.451891	+	0.892073i	$0.649250\pi$
$278$	7.30697	−	12.6560i	0.438243	−	0.759059i
$279$	−23.8346	−	3.12996i	−1.42694	−	0.187386i
$280$	−0.968625	+	2.46207i	−0.0578864	+	0.147137i
$281$	27.1483	+	15.6741i	1.61953	+	0.935038i	0.987041	+	0.160471i	$0.0513012\pi$
$281$	27.1483	+	15.6741i	1.61953	+	0.935038i	0.632492	+	0.774567i	$0.282032\pi$
$282$	−9.60950	−	3.26023i	−0.572237	−	0.194144i
$283$	18.2738	+	10.5504i	1.08627	+	0.627157i	0.932580	−	0.360963i	$-0.117552\pi$
$283$	18.2738	+	10.5504i	1.08627	+	0.627157i	0.153687	+	0.988120i	$0.450885\pi$
$284$	−1.33437	−	0.770398i	−0.0791802	−	0.0457147i
$285$	1.20004	+	0.407140i	0.0710842	+	0.0241169i
$286$	1.57222	+	0.907724i	0.0929675	+	0.0536748i
$287$	2.63386	+	17.5725i	0.155472	+	1.03727i
$288$	−2.97446	−	0.390607i	−0.175272	−	0.0230168i
$289$	−14.2042	+	24.6023i	−0.835539	+	1.44720i
$290$	7.17328			0.421230
$291$	−7.62222	−	2.58601i	−0.446822	−	0.151594i
$292$		−	6.87383i		−	0.402261i
$293$	−6.76886	−	11.7240i	−0.395441	−	0.684924i	0.597716	−	0.801708i	$-0.296075\pi$
$293$	−6.76886	−	11.7240i	−0.395441	−	0.684924i	−0.993157	+	0.116784i	$0.962742\pi$
$294$	−12.1191	−	0.357984i	−0.706798	−	0.0208781i
$295$	−4.62900	+	8.01766i	−0.269511	+	0.466806i
$296$	−1.81971	−	1.05061i	−0.105768	−	0.0610654i
$297$	−1.89682	−	2.83579i	−0.110065	−	0.164549i
$298$	4.35730	+	7.54707i	0.252412	+	0.437190i
$299$	−9.95521	−	17.2429i	−0.575725	−	0.997185i
$300$	−0.556482	+	1.64022i	−0.0321285	+	0.0946983i
$301$	−26.0436	+	20.7341i	−1.50113	+	1.19509i
$302$	−7.46809	+	4.31171i	−0.429741	+	0.248111i
$303$	−7.70716	+	1.53436i	−0.442765	+	0.0881466i
$304$			0.731632i			0.0419620i
$305$	1.35595	−	0.782856i	0.0776412	−	0.0448262i
$306$	−20.0436	−	2.63213i	−1.14582	−	0.150469i
$307$		−	14.6424i		−	0.835688i	−0.908519	−	0.417844i	$-0.862786\pi$
$307$		−	14.6424i		−	0.835688i	0.908519	−	0.417844i	$-0.137214\pi$
$308$	−1.08198	−	1.35905i	−0.0616513	−	0.0774388i
$309$	−1.28300	−	6.44457i	−0.0729873	−	0.366619i
$310$	−8.01306			−0.455111
$311$	−2.40758	+	4.17005i	−0.136521	+	0.236462i	−0.926178	−	0.377088i	$-0.876926\pi$
$311$	−2.40758	+	4.17005i	−0.136521	+	0.236462i	0.789656	+	0.613549i	$0.210259\pi$
$312$	3.15828	+	3.60015i	0.178803	+	0.203818i
$313$	−6.26856	+	3.61916i	−0.354320	+	0.204567i	−0.666586	−	0.745428i	$-0.732245\pi$
$313$	−6.26856	+	3.61916i	−0.354320	+	0.204567i	0.312266	+	0.949995i	$0.398912\pi$
$314$	16.1434			0.911026
$315$	−7.93594	+	0.144487i	−0.447139	+	0.00814093i
$316$	15.0706			0.847790
$317$	3.23740	−	1.86912i	0.181831	−	0.104980i	−0.406322	−	0.913730i	$-0.633189\pi$
$317$	3.23740	−	1.86912i	0.181831	−	0.104980i	0.588153	+	0.808750i	$0.299855\pi$
$318$	3.70961	−	10.9340i	0.208025	−	0.613150i
$319$	−2.35492	+	4.07883i	−0.131850	+	0.228371i
$320$	−1.00000			−0.0559017
$321$	−10.7877	−	3.65995i	−0.602108	−	0.204279i
$322$	2.82402	+	18.8412i	0.157377	+	1.04998i
$323$			4.93016i			0.274321i
$324$	−2.33505	−	8.69181i	−0.129725	−	0.482878i
$325$	2.39457	−	1.38250i	0.132827	−	0.0766875i
$326$			2.08852i			0.115673i
$327$	11.0650	+	12.6131i	0.611897	+	0.697505i
$328$	−5.81621	+	3.35799i	−0.321146	+	0.185414i
$329$	−2.29764	−	15.3293i	−0.126673	−	0.845132i
$330$	−0.749967	−	0.854892i	−0.0412843	−	0.0470602i
$331$	2.40059	+	4.15794i	0.131948	+	0.228541i	0.924428	−	0.381358i	$-0.124543\pi$
$331$	2.40059	+	4.15794i	0.131948	+	0.228541i	−0.792479	+	0.609899i	$0.791210\pi$
$332$	8.71114	+	15.0881i	0.478086	+	0.828069i
$333$	0.820750	−	6.24999i	0.0449768	−	0.342497i
$334$	−6.47435	−	3.73797i	−0.354261	−	0.204533i
$335$	3.28370	−	5.68754i	0.179408	−	0.310743i
$336$	−1.55107	−	4.31210i	−0.0846175	−	0.235244i
$337$	−12.0518	−	20.8744i	−0.656505	−	1.13710i	−0.981514	−	0.191389i	$-0.938701\pi$
$337$	−12.0518	−	20.8744i	−0.656505	−	1.13710i	0.325009	−	0.945711i	$-0.394633\pi$
$338$			5.35473i			0.291259i
$339$	15.8854	−	13.9357i	0.862774	−	0.756882i
$340$	−6.73857			−0.365450
$341$	2.63061	−	4.55634i	0.142455	−	0.246740i
$342$	−2.02755	+	0.840613i	−0.109637	+	0.0454551i
$343$	−7.99448	−	16.7059i	−0.431661	−	0.902036i
$344$	−10.8964	−	6.29106i	−0.587497	−	0.339191i
$345$	2.43521	+	12.2322i	0.131107	+	0.658560i
$346$	−15.5042	−	8.95135i	−0.833511	−	0.481228i
$347$	18.7841	+	10.8450i	1.00838	+	0.582190i	0.910718	−	0.413029i	$-0.135529\pi$
$347$	18.7841	+	10.8450i	1.00838	+	0.582190i	0.0976652	+	0.995219i	$0.468863\pi$
$348$	−9.33989	+	8.19356i	−0.500671	+	0.439221i
$349$	16.3083	+	9.41562i	0.872965	+	0.504007i	0.868332	−	0.495983i	$-0.165192\pi$
$349$	16.3083	+	9.41562i	0.872965	+	0.504007i	0.00463264	+	0.999989i	$0.498525\pi$
$350$	−2.61652	+	0.392179i	−0.139859	+	0.0209628i
$351$	−6.34823	+	12.8888i	−0.338843	+	0.687955i
$352$	0.328290	−	0.568614i	0.0174979	−	0.0303073i
$353$	−9.54427			−0.507990			−0.253995	−	0.967205i	$-0.581745\pi$
$353$	−9.54427			−0.507990			−0.253995	+	0.967205i	$0.581745\pi$
$354$	−3.13091	−	15.7267i	−0.166406	−	0.835865i
$355$		−	1.54080i		−	0.0817770i
$356$	1.32440	+	2.29393i	0.0701932	+	0.121578i
$357$	−10.4520	−	29.0574i	−0.553176	−	1.53788i
$358$	5.01345	−	8.68355i	0.264969	−	0.458940i
$359$	−8.21398	−	4.74234i	−0.433517	−	0.250291i	0.267327	−	0.963606i	$-0.413860\pi$
$359$	−8.21398	−	4.74234i	−0.433517	−	0.250291i	−0.700844	+	0.713315i	$0.747193\pi$
$360$	−1.14896	−	2.77126i	−0.0605553	−	0.146058i
$361$	−9.23236	−	15.9909i	−0.485914	−	0.841627i
$362$	4.28694	+	7.42520i	0.225317	+	0.390260i
$363$	−17.9536	+	3.57423i	−0.942317	+	0.187598i
$364$	−2.67826	+	6.80763i	−0.140379	+	0.356817i
$365$	5.95292	−	3.43692i	0.311590	−	0.179896i
$366$	−0.871290	+	2.56811i	−0.0455430	+	0.134237i
$367$		−	0.361215i		−	0.0188553i	−0.999956	−	0.00942764i	$-0.996999\pi$
$367$		−	0.361215i		−	0.0188553i	0.999956	−	0.00942764i	$-0.00300095\pi$
$368$	−6.23613	+	3.60043i	−0.325081	+	0.187685i
$369$	−15.9884	−	12.2601i	−0.832325	−	0.638234i
$370$		−	2.10122i		−	0.109237i
$371$	17.4422	−	2.61433i	0.905556	−	0.135730i
$372$	10.4333	−	9.15279i	0.540942	−	0.474550i
$373$	9.48709			0.491223			0.245611	−	0.969368i	$-0.421011\pi$
$373$	9.48709			0.491223			0.245611	+	0.969368i	$0.421011\pi$
$374$	2.21220	−	3.83165i	0.114390	−	0.198130i
$375$	−1.69871	+	0.338184i	−0.0877213	+	0.0174637i
$376$	5.07374	−	2.92933i	0.261658	−	0.151069i
$377$	19.8342			1.02151
$378$	10.1679	−	9.25282i	0.522978	−	0.475914i
$379$	30.4526			1.56424			0.782122	−	0.623125i	$-0.214137\pi$
$379$	30.4526			1.56424			0.782122	+	0.623125i	$0.214137\pi$
$380$	−0.633612	+	0.365816i	−0.0325036	+	0.0187660i
$381$	−5.05221	+	1.00580i	−0.258833	+	0.0515289i
$382$	5.35761	−	9.27965i	0.274119	−	0.474788i
$383$	21.0775			1.07701			0.538505	−	0.842622i	$-0.318989\pi$
$383$	21.0775			1.07701			0.538505	+	0.842622i	$0.318989\pi$
$384$	1.30204	−	1.14223i	0.0664444	−	0.0582893i
$385$	0.635979	−	1.61654i	0.0324125	−	0.0823866i
$386$		−	1.23612i		−	0.0629171i
$387$	4.91467	−	37.4251i	0.249827	−	1.90242i
$388$	4.02448	−	2.32353i	0.204312	−	0.117960i
$389$			30.8294i			1.56311i	0.623834	+	0.781557i	$0.285574\pi$
$389$			30.8294i			1.56311i	−0.623834	+	0.781557i	$0.714426\pi$
$390$	−1.53868	+	4.53523i	−0.0779139	+	0.229650i
$391$	−42.0226	+	24.2617i	−2.12517	+	1.22697i
$392$	4.76964	−	5.12353i	0.240903	−	0.258777i
$393$	−15.8269	+	3.15085i	−0.798361	+	0.158939i
$394$	−7.76614	−	13.4514i	−0.391253	−	0.677669i
$395$	7.53532	+	13.0516i	0.379143	+	0.656696i
$396$	1.95297	+	0.256465i	0.0981405	+	0.0128878i
$397$	12.1734	+	7.02834i	0.610968	+	0.352742i	0.773344	−	0.633987i	$-0.218583\pi$
$397$	12.1734	+	7.02834i	0.610968	+	0.352742i	−0.162376	+	0.986729i	$0.551916\pi$
$398$	8.58726	−	14.8736i	0.430440	−	0.745545i
$399$	−2.56021	−	2.16479i	−0.128171	−	0.108375i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$		−	33.9774i		−	1.69675i	−0.529397	−	0.848374i	$-0.677582\pi$
$401$		−	33.9774i		−	1.69675i	0.529397	−	0.848374i	$-0.322418\pi$
$402$	2.22099	+	11.1561i	0.110773	+	0.556418i
$403$	−22.1562			−1.10368
$404$	2.26853	−	3.92921i	0.112863	−	0.195485i
$405$	6.35980	−	6.36812i	0.316021	−	0.316434i
$406$	−17.6611	−	6.94822i	−0.876505	−	0.344835i
$407$	1.19478	+	0.689808i	0.0592231	+	0.0341925i
$408$	8.77388	−	7.69702i	0.434372	−	0.381059i
$409$	9.95136	+	5.74542i	0.492063	+	0.284093i	0.725430	−	0.688296i	$-0.241641\pi$
$409$	9.95136	+	5.74542i	0.492063	+	0.284093i	−0.233367	+	0.972389i	$0.574974\pi$
$410$	−5.81621	−	3.35799i	−0.287242	−	0.165839i
$411$	−5.78276	−	29.0471i	−0.285242	−	1.43279i
$412$	3.28552	+	1.89690i	0.161866	+	0.0934534i
$413$	19.1630	−	15.2562i	0.942950	−	0.750711i
$414$	−17.1428	−	13.1452i	−0.842521	−	0.646052i
$415$	−8.71114	+	15.0881i	−0.427613	+	0.740647i
$416$	−2.76501			−0.135566
$417$	−19.0279	+	16.6925i	−0.931800	+	0.817436i
$418$		−	0.480375i		−	0.0234959i
$419$	14.4601	+	25.0456i	0.706421	+	1.22356i	0.966176	+	0.257883i	$0.0830249\pi$
$419$	14.4601	+	25.0456i	0.706421	+	1.22356i	−0.259755	+	0.965675i	$0.583642\pi$
$420$	2.95885	−	3.49931i	0.144377	−	0.170749i
$421$	−0.473626	+	0.820343i	−0.0230831	+	0.0399811i	−0.877336	−	0.479876i	$-0.840682\pi$
$421$	−0.473626	+	0.820343i	−0.0230831	+	0.0399811i	0.854253	+	0.519857i	$0.174015\pi$
$422$	−19.3958	−	11.1982i	−0.944172	−	0.545118i
$423$	13.9474	+	10.6950i	0.678148	+	0.520010i
$424$	3.33309	+	5.77309i	0.161869	+	0.280366i
$425$	−3.36928	−	5.83577i	−0.163434	−	0.283077i
$426$	1.75995	+	2.00618i	0.0852698	+	0.0971995i
$427$	−4.09672	+	0.614038i	−0.198254	+	0.0297154i
$428$	5.69580	−	3.28847i	0.275317	−	0.158954i
$429$	−2.07366	−	2.36378i	−0.100117	−	0.114124i
$430$		−	12.5821i		−	0.606764i
$431$	−10.1746	+	5.87431i	−0.490094	+	0.282956i	−0.724613	−	0.689156i	$-0.757982\pi$
$431$	−10.1746	+	5.87431i	−0.490094	+	0.282956i	0.234520	+	0.972111i	$0.424648\pi$
$432$	4.66141	+	2.29592i	0.224272	+	0.110462i
$433$			31.4858i			1.51311i	0.653930	+	0.756555i	$0.273119\pi$
$433$			31.4858i			1.51311i	−0.653930	+	0.756555i	$0.726881\pi$
$434$	19.7287	+	7.76166i	0.947007	+	0.372571i
$435$	−11.7658	−	3.99180i	−0.564126	−	0.191392i
$436$	−9.68718			−0.463932
$437$	−2.63419	+	4.56255i	−0.126010	+	0.218256i
$438$	−3.82516	+	11.2746i	−0.182773	+	0.538722i
$439$	24.8076	−	14.3227i	1.18400	−	0.683583i	0.227064	−	0.973880i	$-0.427087\pi$
$439$	24.8076	−	14.3227i	1.18400	−	0.683583i	0.956937	+	0.290296i	$0.0937539\pi$
$440$	0.656579			0.0313012
$441$	19.6788	+	7.33121i	0.937083	+	0.349105i
$442$	−18.6322			−0.886243
$443$	10.9899	−	6.34500i	0.522144	−	0.301460i	−0.215667	−	0.976467i	$-0.569193\pi$
$443$	10.9899	−	6.34500i	0.522144	−	0.301460i	0.737811	+	0.675007i	$0.235859\pi$
$444$	2.40008	+	2.73586i	0.113903	+	0.129838i
$445$	−1.32440	+	2.29393i	−0.0627827	+	0.108743i
$446$	−3.10192			−0.146880
$447$	−2.94714	−	14.8036i	−0.139395	−	0.700188i
$448$	2.46207	+	0.968625i	0.116322	+	0.0457632i
$449$		−	3.80547i		−	0.179591i	−0.995960	−	0.0897956i	$-0.971379\pi$
$449$		−	3.80547i		−	0.179591i	0.995960	−	0.0897956i	$-0.0286214\pi$
$450$	1.82551	−	2.38066i	0.0860552	−	0.112225i
$451$	3.81880	−	2.20479i	0.179820	−	0.103819i
$452$			12.2004i			0.573857i
$453$	14.6487	−	2.91630i	0.688257	−	0.137020i
$454$	−25.0842	+	14.4824i	−1.17726	+	0.679692i
$455$	−7.23471	+	1.08438i	−0.339168	+	0.0508364i
$456$	0.407140	−	1.20004i	0.0190661	−	0.0561970i
$457$	20.1887	+	34.9678i	0.944386	+	1.63572i	0.756977	+	0.653442i	$0.226676\pi$
$457$	20.1887	+	34.9678i	0.944386	+	1.63572i	0.187409	+	0.982282i	$0.439991\pi$
$458$	−13.1376	−	22.7549i	−0.613878	−	1.06327i
$459$	31.4113	+	15.4712i	1.46615	+	0.722133i
$460$	−6.23613	−	3.60043i	−0.290761	−	0.167871i
$461$	7.52397	−	13.0319i	0.350426	−	0.606956i	−0.635898	−	0.771773i	$-0.719370\pi$
$461$	7.52397	−	13.0319i	0.350426	−	0.606956i	0.986324	+	0.164817i	$0.0527034\pi$
$462$	1.01840	+	2.83124i	0.0473801	+	0.131721i
$463$	−12.4404	−	21.5474i	−0.578156	−	1.00139i	−0.995691	−	0.0927341i	$-0.970439\pi$
$463$	−12.4404	−	21.5474i	−0.578156	−	1.00139i	0.417535	−	0.908661i	$-0.362894\pi$
$464$		−	7.17328i		−	0.333011i
$465$	13.1432	+	4.45912i	0.609502	+	0.206787i
$466$	4.92748			0.228261
$467$	17.4957	−	30.3035i	0.809605	−	1.40228i	−0.103533	−	0.994626i	$-0.533015\pi$
$467$	17.4957	−	30.3035i	0.809605	−	1.40228i	0.913138	−	0.407651i	$-0.133652\pi$
$468$	−3.17687	−	7.66256i	−0.146851	−	0.354202i
$469$	−13.5938	+	10.8224i	−0.627702	+	0.499733i
$470$	5.07374	+	2.92933i	0.234034	+	0.135120i
$471$	−26.4788	−	8.98352i	−1.22008	−	0.413939i
$472$	8.01766	+	4.62900i	0.369043	+	0.213067i
$473$	7.15438	+	4.13058i	0.328959	+	0.189924i
$474$	−24.7192	−	8.38654i	−1.13539	−	0.385207i
$475$	−0.633612	−	0.365816i	−0.0290721	−	0.0167848i
$476$	16.5908	+	6.52715i	0.760438	+	0.299171i
$477$	−12.1692	+	15.8699i	−0.557188	+	0.726633i
$478$	−7.76099	+	13.4424i	−0.354979	+	0.614842i
$479$	12.1246			0.553985			0.276993	−	0.960872i	$-0.410662\pi$
$479$	12.1246			0.553985			0.276993	+	0.960872i	$0.410662\pi$
$480$	1.64022	+	0.556482i	0.0748655	+	0.0253998i
$481$		−	5.80988i		−	0.264908i
$482$	−5.28379	−	9.15179i	−0.240670	−	0.416853i
$483$	5.85277	−	32.4753i	0.266310	−	1.47768i
$484$	5.28445	−	9.15294i	0.240202	−	0.416043i
$485$	4.02448	+	2.32353i	0.182742	+	0.105506i
$486$	−1.00683	+	15.5559i	−0.0456709	+	0.705630i
$487$	3.55858	+	6.16364i	0.161255	+	0.279301i	0.935319	−	0.353806i	$-0.115113\pi$
$487$	3.55858	+	6.16364i	0.161255	+	0.279301i	−0.774064	+	0.633107i	$0.781779\pi$
$488$	−0.782856	−	1.35595i	−0.0354382	−	0.0613808i
$489$	1.16222	−	3.42564i	0.0525576	−	0.154913i
$490$	6.82193	+	1.56886i	0.308183	+	0.0708739i
$491$	16.3865	−	9.46076i	0.739513	−	0.426958i	−0.0823791	−	0.996601i	$-0.526252\pi$
$491$	16.3865	−	9.46076i	0.739513	−	0.426958i	0.821892	+	0.569643i	$0.192919\pi$
$492$	11.4085	−	2.27123i	0.514336	−	0.102395i
$493$		−	48.3377i		−	2.17702i
$494$	−1.75194	+	1.01148i	−0.0788236	+	0.0455088i
$495$	0.754380	+	1.81955i	0.0339069	+	0.0817829i
$496$			8.01306i			0.359797i
$497$	−1.49245	+	3.79354i	−0.0669457	+	0.170164i
$498$	−5.89193	−	29.5955i	−0.264024	−	1.32621i
$499$	−19.0082			−0.850925			−0.425463	−	0.904976i	$-0.639889\pi$
$499$	−19.0082			−0.850925			−0.425463	+	0.904976i	$0.639889\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	8.53927	+	9.73396i	0.381506	+	0.434881i
$502$	1.66739	−	0.962667i	0.0744192	−	0.0429659i
$503$	26.9377			1.20109			0.600546	−	0.799590i	$-0.294950\pi$
$503$	26.9377			1.20109			0.600546	+	0.799590i	$0.294950\pi$
$504$	0.144487	+	7.93594i	0.00643597	+	0.353495i
$505$	4.53706			0.201896
$506$	4.09451	−	2.36397i	0.182023	−	0.105091i
$507$	2.97981	−	8.78295i	0.132338	−	0.390065i
$508$	1.48707	−	2.57568i	0.0659780	−	0.114277i
$509$	−19.3033			−0.855602			−0.427801	−	0.903873i	$-0.640712\pi$
$509$	−19.3033			−0.855602			−0.427801	+	0.903873i	$0.640712\pi$
$510$	11.0528	+	3.74989i	0.489424	+	0.166048i
$511$	−17.9856	+	2.69577i	−0.795634	+	0.119254i
$512$			1.00000i			0.0441942i
$513$	3.79341	−	0.250499i	0.167483	−	0.0110598i
$514$	−3.06783	+	1.77121i	−0.135316	+	0.0781248i
$515$			3.79379i			0.167175i
$516$	14.3717	+	16.3824i	0.632680	+	0.721195i
$517$	−3.33132	+	1.92334i	−0.146511	+	0.0845882i
$518$	−2.03529	+	5.17333i	−0.0894256	+	0.227303i
$519$	20.4491	+	23.3100i	0.897614	+	1.02320i
$520$	−1.38250	−	2.39457i	−0.0606268	−	0.105009i
$521$	−2.29540	−	3.97574i	−0.100563	−	0.174180i	0.811354	−	0.584556i	$-0.198731\pi$
$521$	−2.29540	−	3.97574i	−0.100563	−	0.174180i	−0.911917	+	0.410375i	$0.865398\pi$
$522$	19.8791	−	8.24178i	0.870083	−	0.360733i
$523$	−7.54094	−	4.35376i	−0.329742	−	0.190377i	0.325985	−	0.945375i	$-0.394304\pi$
$523$	−7.54094	−	4.35376i	−0.329742	−	0.190377i	−0.655727	+	0.754998i	$0.727638\pi$
$524$	4.65849	−	8.06874i	0.203507	−	0.352484i
$525$	4.50992	+	0.812788i	0.196829	+	0.0354730i
$526$	4.75941	+	8.24353i	0.207520	+	0.359435i
$527$			53.9966i			2.35213i
$528$	−0.854892	+	0.749967i	−0.0372044	+	0.0326381i
$529$	−28.8523			−1.25445
$530$	−3.33309	+	5.77309i	−0.144780	+	0.250767i
$531$	−3.61624	+	27.5376i	−0.156932	+	1.19503i
$532$	1.91433	−	0.286931i	0.0829969	−	0.0124400i
$533$	−16.0819	−	9.28487i	−0.696583	−	0.402172i
$534$	−0.895782	−	4.49956i	−0.0387643	−	0.194715i
$535$	5.69580	+	3.28847i	0.246251	+	0.142173i
$536$	−5.68754	−	3.28370i	−0.245664	−	0.141834i
$537$	−13.0554	+	11.4531i	−0.563382	+	0.494236i
$538$	3.29420	+	1.90191i	0.142023	+	0.0819970i
$539$	−3.13165	+	3.36400i	−0.134890	+	0.144898i
$540$	0.342384	+	5.18486i	0.0147339	+	0.223121i
$541$	−5.63297	+	9.75660i	−0.242180	+	0.419469i	−0.961335	−	0.275381i	$-0.911196\pi$
$541$	−5.63297	+	9.75660i	−0.242180	+	0.419469i	0.719155	+	0.694850i	$0.244529\pi$
$542$	−1.25167			−0.0537640
$543$	−2.89955	−	14.5646i	−0.124432	−	0.625026i
$544$			6.73857i			0.288914i
$545$	−4.84359	−	8.38935i	−0.207477	−	0.359360i
$546$	8.18126	−	9.67562i	0.350125	−	0.414078i
$547$	−18.9696	+	32.8563i	−0.811082	+	1.40484i	0.101025	+	0.994884i	$0.467788\pi$
$547$	−18.9696	+	32.8563i	−0.811082	+	1.40484i	−0.912107	+	0.409952i	$0.865546\pi$
$548$	14.8086	+	8.54973i	0.632591	+	0.365226i
$549$	2.85822	−	3.72742i	0.121986	−	0.159082i
$550$	0.328290	+	0.568614i	0.0139983	+	0.0242458i
$551$	−2.62410	−	4.54508i	−0.111791	−	0.193627i
$552$	12.2322	−	2.43521i	0.520637	−	0.103650i
$553$	−5.91039	−	39.4327i	−0.251335	−	1.67685i
$554$	−13.0267	+	7.52096i	−0.553451	+	0.319535i
$555$	−1.16929	+	3.44646i	−0.0496335	+	0.146294i
$556$		−	14.6139i		−	0.619769i
$557$	18.9332	−	10.9311i	0.802224	−	0.463164i	−0.0420244	−	0.999117i	$-0.513381\pi$
$557$	18.9332	−	10.9311i	0.802224	−	0.463164i	0.844248	+	0.535952i	$0.180047\pi$
$558$	−22.2063	+	9.20665i	−0.940068	+	0.389749i
$559$		−	34.7897i		−	1.47145i
$560$	0.392179	+	2.61652i	0.0165726	+	0.110568i
$561$	−5.76075	+	5.05370i	−0.243219	+	0.213368i
$562$	31.3482			1.32234
$563$	−11.5145	+	19.9438i	−0.485280	+	0.840530i	−0.999857	−	0.0169145i	$-0.994616\pi$
$563$	−11.5145	+	19.9438i	−0.485280	+	0.840530i	0.514577	+	0.857444i	$0.327949\pi$
$564$	−9.95219	+	1.98130i	−0.419063	+	0.0834279i
$565$	−10.5658	+	6.10019i	−0.444508	+	0.256637i
$566$	21.1008			0.886934
$567$	−21.8266	+	9.51845i	−0.916630	+	0.399737i
$568$	−1.54080			−0.0646504
$569$	−18.3294	+	10.5825i	−0.768409	+	0.443641i	−0.832307	−	0.554315i	$-0.812980\pi$
$569$	−18.3294	+	10.5825i	−0.768409	+	0.443641i	0.0638975	+	0.997956i	$0.479647\pi$
$570$	1.24283	−	0.247426i	0.0520566	−	0.0103635i
$571$	−5.38408	+	9.32549i	−0.225317	+	0.390260i	−0.956414	−	0.292013i	$-0.905675\pi$
$571$	−5.38408	+	9.32549i	−0.225317	+	0.390260i	0.731098	+	0.682273i	$0.239008\pi$
$572$	1.81545			0.0759077
$573$	−13.9516	+	12.2393i	−0.582837	+	0.511303i
$574$	11.0673	+	13.9013i	0.461938	+	0.580230i
$575$		−	7.20086i		−	0.300297i
$576$	−2.77126	+	1.14896i	−0.115469	+	0.0478731i
$577$	10.1757	−	5.87494i	0.423620	−	0.244577i	−0.273005	−	0.962013i	$-0.588018\pi$
$577$	10.1757	−	5.87494i	0.423620	−	0.244577i	0.696625	+	0.717436i	$0.254684\pi$
$578$			28.4083i			1.18163i
$579$	−0.687881	+	2.02752i	−0.0285874	+	0.0842608i
$580$	6.21225	−	3.58664i	0.257949	−	0.148927i
$581$	36.0621	−	28.7101i	1.49611	−	1.19110i
$582$	−7.89404	+	1.57156i	−0.327218	+	0.0651433i
$583$	−2.18844	−	3.79049i	−0.0906359	−	0.156986i
$584$	−3.43692	−	5.95292i	−0.142221	−	0.246333i
$585$	5.04754	−	6.58253i	0.208690	−	0.272154i
$586$	−11.7240	−	6.76886i	−0.484315	−	0.279619i
$587$	12.5348	−	21.7109i	0.517366	−	0.896105i	−0.482430	−	0.875934i	$-0.660246\pi$
$587$	12.5348	−	21.7109i	0.517366	−	0.896105i	0.999797	−	0.0201704i	$-0.00642087\pi$
$588$	−10.6744	+	5.74951i	−0.440205	+	0.237106i
$589$	2.93131	+	5.07718i	0.120782	+	0.209201i
$590$			9.25800i			0.381146i
$591$	5.25277	+	26.3849i	0.216070	+	1.08533i
$592$	−2.10122			−0.0863595
$593$	−16.2045	+	28.0670i	−0.665438	+	1.15257i	0.313728	+	0.949513i	$0.398422\pi$
$593$	−16.2045	+	28.0670i	−0.665438	+	1.15257i	−0.979166	+	0.203060i	$0.934911\pi$
$594$	−3.06059	−	1.50745i	−0.125577	−	0.0618515i
$595$	2.64272	+	17.6316i	0.108341	+	0.722826i
$596$	7.54707	+	4.35730i	0.309140	+	0.178482i
$597$	−22.3619	+	19.6173i	−0.915211	+	0.802883i
$598$	−17.2429	−	9.95521i	−0.705116	−	0.407099i
$599$	−7.43975	−	4.29534i	−0.303980	−	0.175503i	0.340249	−	0.940335i	$-0.389488\pi$
$599$	−7.43975	−	4.29534i	−0.303980	−	0.175503i	−0.644229	+	0.764832i	$0.722822\pi$
$600$	0.338184	+	1.69871i	0.0138063	+	0.0693497i
$601$	28.6965	+	16.5680i	1.17056	+	0.675821i	0.953811	−	0.300407i	$-0.0971227\pi$
$601$	28.6965	+	16.5680i	1.17056	+	0.675821i	0.216745	+	0.976228i	$0.430456\pi$
$602$	−12.1874	+	30.9780i	−0.496720	+	1.26257i
$603$	2.56528	−	19.5345i	0.104466	−	0.795506i
$604$	−4.31171	+	7.46809i	−0.175441	+	0.303872i
$605$	10.5689			0.429687
$606$	−5.90742	+	5.18237i	−0.239973	+	0.210520i
$607$			23.9742i			0.973083i	0.873658	+	0.486541i	$0.161742\pi$
$607$			23.9742i			0.973083i	−0.873658	+	0.486541i	$0.838258\pi$
$608$	0.365816	+	0.633612i	0.0148358	+	0.0256964i
$609$	25.1016	+	21.2247i	1.01717	+	0.860068i
$610$	0.782856	−	1.35595i	0.0316969	−	0.0549006i
$611$	14.0289	+	8.09961i	0.567550	+	0.327675i
$612$	−18.6744	+	7.74232i	−0.754866	+	0.312965i
$613$	16.0872	+	27.8638i	0.649754	+	1.12541i	0.983181	+	0.182631i	$0.0584615\pi$
$613$	16.0872	+	27.8638i	0.649754	+	1.12541i	−0.333427	+	0.942776i	$0.608205\pi$
$614$	−7.32121	−	12.6807i	−0.295460	−	0.511752i
$615$	7.67121	+	8.74446i	0.309333	+	0.352611i
$616$	−1.61654	−	0.635979i	−0.0651323	−	0.0256243i
$617$	−32.2651	+	18.6283i	−1.29894	+	0.749946i	−0.980222	−	0.197902i	$-0.936587\pi$
$617$	−32.2651	+	18.6283i	−1.29894	+	0.749946i	−0.318723	+	0.947848i	$0.603254\pi$
$618$	−4.33340	−	4.93966i	−0.174315	−	0.198702i
$619$			22.7167i			0.913060i	0.889708	+	0.456530i	$0.150908\pi$
$619$			22.7167i			0.913060i	−0.889708	+	0.456530i	$0.849092\pi$
$620$	−6.93952	+	4.00653i	−0.278698	+	0.160906i
$621$	20.8029	+	31.1007i	0.834790	+	1.24803i
$622$			4.81516i			0.193070i
$623$	5.48272	−	4.36496i	0.219661	−	0.174878i
$624$	4.53523	+	1.53868i	0.181554	+	0.0615963i
$625$	1.00000			0.0400000
$626$	−3.61916	+	6.26856i	−0.144651	+	0.250542i
$627$	−0.267320	+	0.787921i	−0.0106757	+	0.0314665i
$628$	13.9806	−	8.07171i	0.557887	−	0.322096i
$629$	−14.1592			−0.564564
$630$	−6.80048	+	4.09310i	−0.270938	+	0.163073i
$631$	−4.22820			−0.168322			−0.0841610	−	0.996452i	$-0.526821\pi$
$631$	−4.22820			−0.168322			−0.0841610	+	0.996452i	$0.526821\pi$
$632$	13.0516	−	7.53532i	0.519163	−	0.299739i
$633$	25.5818	+	29.1609i	1.01679	+	1.15904i
$634$	1.86912	−	3.23740i	0.0742321	−	0.128574i
$635$	2.97414			0.118025
$636$	−2.25440	−	11.3239i	−0.0893926	−	0.449024i
$637$	18.8627	+	4.33791i	0.747366	+	0.171874i
$638$			4.70983i			0.186464i
$639$	−1.77031	−	4.26995i	−0.0700322	−	0.168917i
$640$	−0.866025	+	0.500000i	−0.0342327	+	0.0197642i
$641$		−	32.2594i		−	1.27417i	−0.770794	−	0.637085i	$-0.780140\pi$
$641$		−	32.2594i		−	1.27417i	0.770794	−	0.637085i	$-0.219860\pi$
$642$	−11.1724	+	2.22422i	−0.440938	+	0.0877828i
$643$	17.8975	−	10.3331i	0.705810	−	0.407500i	−0.103698	−	0.994609i	$-0.533067\pi$
$643$	17.8975	−	10.3331i	0.705810	−	0.407500i	0.809508	+	0.587109i	$0.199734\pi$
$644$	11.8663	+	14.9050i	0.467597	+	0.587338i
$645$	−7.00172	+	20.6375i	−0.275693	+	0.812600i
$646$	2.46508	+	4.26964i	0.0969872	+	0.167987i
$647$	11.2156	+	19.4260i	0.440930	+	0.763714i	0.997759	−	0.0669137i	$-0.0213152\pi$
$647$	11.2156	+	19.4260i	0.440930	+	0.763714i	−0.556828	+	0.830628i	$0.687982\pi$
$648$	−6.36812	−	6.35980i	−0.250163	−	0.249837i
$649$	−5.26423	−	3.03931i	−0.206639	−	0.119303i
$650$	1.38250	−	2.39457i	0.0542263	−	0.0939226i
$651$	−28.0402	−	23.7095i	−1.09898	−	0.929248i
$652$	1.04426	+	1.80871i	0.0408964	+	0.0708347i
$653$		−	2.87083i		−	0.112344i	−0.998421	−	0.0561722i	$-0.982110\pi$
$653$		−	2.87083i		−	0.112344i	0.998421	−	0.0561722i	$-0.0178896\pi$
$654$	15.8891	+	5.39074i	0.621314	+	0.210795i
$655$	9.31698			0.364044
$656$	−3.35799	+	5.81621i	−0.131107	+	0.227085i
$657$	12.5482	−	16.3642i	0.489553	−	0.638430i
$658$	−9.65447	−	12.1268i	−0.376370	−	0.472750i
$659$	32.1692	+	18.5729i	1.25313	+	0.723497i	0.971731	−	0.236092i	$-0.0758667\pi$
$659$	32.1692	+	18.5729i	1.25313	+	0.723497i	0.281404	+	0.959589i	$0.409200\pi$
$660$	−1.07694	−	0.365374i	−0.0419197	−	0.0142222i
$661$	−36.8474	−	21.2739i	−1.43320	−	0.827457i	−0.435835	−	0.900027i	$-0.643547\pi$
$661$	−36.8474	−	21.2739i	−1.43320	−	0.827457i	−0.997363	+	0.0725692i	$0.976880\pi$
$662$	4.15794	+	2.40059i	0.161603	+	0.0933015i
$663$	30.5609	+	10.3685i	1.18689	+	0.402678i
$664$	15.0881	+	8.71114i	0.585533	+	0.338058i
$665$	1.20566	+	1.51440i	0.0467533	+	0.0587258i
$666$	−2.41420	−	5.82302i	−0.0935485	−	0.225638i
$667$	25.8269	−	44.7335i	1.00002	−	1.73209i
$668$	−7.47594			−0.289253
$669$	5.08785	+	1.72616i	0.196707	+	0.0667374i
$670$		−	6.56740i		−	0.253721i
$671$	0.514007	+	0.890286i	0.0198430	+	0.0343691i
$672$	−3.49931	−	2.95885i	−0.134989	−	0.114140i
$673$	−21.7915	+	37.7439i	−0.839999	+	1.45492i	0.0498957	+	0.998754i	$0.484111\pi$
$673$	−21.7915	+	37.7439i	−0.839999	+	1.45492i	−0.889895	+	0.456166i	$0.849222\pi$
$674$	−20.8744	−	12.0518i	−0.804051	−	0.464219i
$675$	−4.31903	+	2.88894i	−0.166239	+	0.111195i
$676$	2.67737	+	4.63733i	0.102976	+	0.178359i
$677$	−2.64816	−	4.58674i	−0.101777	−	0.176283i	0.810640	−	0.585545i	$-0.199119\pi$
$677$	−2.64816	−	4.58674i	−0.101777	−	0.176283i	−0.912417	+	0.409262i	$0.865786\pi$
$678$	6.78929	−	20.0113i	0.260741	−	0.768530i
$679$	−7.65789	−	9.61890i	−0.293883	−	0.369139i
$680$	−5.83577	+	3.36928i	−0.223792	+	0.129206i
$681$	49.2029	−	9.79541i	1.88546	−	0.375361i
$682$		−	5.26121i		−	0.201462i
$683$	−15.0590	+	8.69432i	−0.576216	+	0.332679i	−0.759628	−	0.650357i	$-0.774619\pi$
$683$	−15.0590	+	8.69432i	−0.576216	+	0.332679i	0.183412	+	0.983036i	$0.441286\pi$
$684$	−1.33560	+	1.74177i	−0.0510679	+	0.0665981i
$685$			17.0995i			0.653337i
$686$	−15.2764	−	10.4705i	−0.583255	−	0.399767i
$687$	8.88581	+	44.6339i	0.339015	+	1.70289i
$688$	−12.5821			−0.479689
$689$	−9.21603	+	15.9626i	−0.351103	+	0.608128i
$690$	8.22506	+	9.37579i	0.313123	+	0.356930i
$691$	8.87459	−	5.12375i	0.337605	−	0.194917i	−0.321607	−	0.946873i	$-0.604223\pi$
$691$	8.87459	−	5.12375i	0.337605	−	0.194917i	0.659213	+	0.751957i	$0.270890\pi$
$692$	−17.9027			−0.680559
$693$	−0.0948673	−	5.21057i	−0.00360371	−	0.197933i
$694$	21.6900			0.823341
$695$	12.6560	−	7.30697i	0.480071	−	0.277169i
$696$	−3.99180	+	11.7658i	−0.151309	+	0.445981i
$697$	−22.6280	+	39.1929i	−0.857098	+	1.48454i
$698$	18.8312			0.712773
$699$	−8.08216	−	2.74205i	−0.305695	−	0.103714i
$700$	−2.06989	+	1.64790i	−0.0782344	+	0.0622847i
$701$		−	34.2446i		−	1.29340i	−0.762745	−	0.646699i	$-0.776149\pi$
$701$		−	34.2446i		−	1.29340i	0.762745	−	0.646699i	$-0.223851\pi$
$702$	0.946695	+	14.3362i	0.0357307	+	0.541084i
$703$	−1.33136	+	0.768659i	−0.0502130	+	0.0289905i
$704$		−	0.656579i		−	0.0247458i
$705$	−6.69195	−	7.62819i	−0.252033	−	0.287294i
$706$	−8.26558	+	4.77214i	−0.311079	+	0.179602i
$707$	−11.1705	−	4.39471i	−0.420111	−	0.165280i
$708$	−10.5748	−	12.0543i	−0.397425	−	0.453027i
$709$	−3.24108	−	5.61372i	−0.121721	−	0.210828i	0.798725	−	0.601696i	$-0.205508\pi$
$709$	−3.24108	−	5.61372i	−0.121721	−	0.210828i	−0.920447	+	0.390868i	$0.872175\pi$
$710$	−0.770398	−	1.33437i	−0.0289125	−	0.0500780i
$711$	35.8780	+	27.5116i	1.34553	+	1.03176i
$712$	2.29393	+	1.32440i	0.0859687	+	0.0496341i
$713$	−28.8505	+	49.9705i	−1.08046	+	1.87141i
$714$	−23.5804	−	19.9384i	−0.882473	−	0.746178i
$715$	0.907724	+	1.57222i	0.0339469	+	0.0587978i
$716$		−	10.0269i		−	0.374723i
$717$	20.2102	−	17.7297i	0.754764	−	0.662128i
$718$	−9.48468			−0.353965
$719$	13.4027	−	23.2142i	0.499838	−	0.865745i	−0.500162	−	0.865932i	$-0.666726\pi$
$719$	13.4027	−	23.2142i	0.499838	−	0.865745i	1.00000		0.000186880i	$5.94858e-5\pi$
$720$	−2.38066	−	1.82551i	−0.0887218	−	0.0680326i
$721$	3.67476	−	9.34057i	0.136855	−	0.347861i
$722$	−15.9909	−	9.23236i	−0.595120	−	0.343593i
$723$	3.57378	+	17.9513i	0.132910	+	0.667616i
$724$	7.42520	+	4.28694i	0.275956	+	0.159323i
$725$	6.21225	+	3.58664i	0.230717	+	0.133205i
$726$	−13.7611	+	12.0722i	−0.510723	+	0.448040i
$727$	35.4292	+	20.4551i	1.31400	+	0.758637i	0.982756	−	0.184909i	$-0.0591991\pi$
$727$	35.4292	+	20.4551i	1.31400	+	0.758637i	0.331242	+	0.943546i	$0.392532\pi$
$728$	1.08438	+	7.23471i	0.0401897	+	0.268136i
$729$	10.3080	−	24.9549i	0.381778	−	0.924254i
$730$	3.43692	−	5.95292i	0.127206	−	0.220327i
$731$	−84.7855			−3.13591
$732$	0.529498	+	2.65970i	0.0195708	+	0.0983052i
$733$			21.5290i			0.795190i	0.917561	+	0.397595i	$0.130155\pi$
$733$			21.5290i			0.795190i	−0.917561	+	0.397595i	$0.869845\pi$
$734$	−0.180608	−	0.312821i	−0.00666635	−	0.0115464i
$735$	−10.3164	−	6.36956i	−0.380527	−	0.234945i
$736$	−3.60043	+	6.23613i	−0.132714	+	0.229867i
$737$	3.73432	+	2.15601i	0.137555	+	0.0794177i
$738$	−19.9764	−	2.62331i	−0.735342	−	0.0965654i
$739$	−17.3918	−	30.1235i	−0.639769	−	1.10811i	−0.985483	−	0.169772i	$-0.945697\pi$
$739$	−17.3918	−	30.1235i	−0.639769	−	1.10811i	0.345714	−	0.938340i	$-0.387637\pi$
$740$	−1.05061	−	1.81971i	−0.0386211	−	0.0668937i
$741$	3.43645	−	0.684135i	0.126241	−	0.0251323i
$742$	13.7982	−	10.9852i	0.506550	−	0.403279i
$743$	24.8388	−	14.3407i	0.911248	−	0.526109i	0.0304153	−	0.999537i	$-0.490317\pi$
$743$	24.8388	−	14.3407i	0.911248	−	0.526109i	0.880832	+	0.473428i	$0.156984\pi$
$744$	4.45912	−	13.1432i	0.163479	−	0.481853i
$745$			8.71460i			0.319278i
$746$	8.21606	−	4.74354i	0.300811	−	0.173674i
$747$	−6.80527	+	51.8219i	−0.248992	+	1.89606i
$748$		−	4.42441i		−	0.161772i
$749$	−10.8381	−	13.6135i	−0.396017	−	0.497428i
$750$	−1.30204	+	1.14223i	−0.0475437	+	0.0417085i
$751$	−15.3233			−0.559157			−0.279578	−	0.960123i	$-0.590195\pi$
$751$	−15.3233			−0.559157			−0.279578	+	0.960123i	$0.590195\pi$
$752$	2.92933	−	5.07374i	0.106822	−	0.185020i
$753$	−3.27059	+	0.651116i	−0.119187	+	0.0237280i
$754$	17.1769	−	9.91709i	0.625546	−	0.361159i
$755$	−8.62341			−0.313838
$756$	4.17921	−	13.0971i	0.151997	−	0.476337i
$757$	0.00588405			0.000213860			0.000106930	−	1.00000i	$-0.499966\pi$
$757$	0.00588405			0.000213860			0.000106930		1.00000i	$0.499966\pi$
$758$	26.3727	−	15.2263i	0.957900	−	0.553044i
$759$	−8.03141	+	1.59891i	−0.291522	+	0.0580368i
$760$	−0.365816	+	0.633612i	−0.0132695	+	0.0229835i
$761$	−5.65870			−0.205128			−0.102564	−	0.994726i	$-0.532705\pi$
$761$	−5.65870			−0.205128			−0.102564	+	0.994726i	$0.532705\pi$
$762$	−3.87244	+	3.39716i	−0.140284	+	0.123066i
$763$	3.79911	+	25.3467i	0.137537	+	0.917614i
$764$		−	10.7152i		−	0.387663i
$765$	−16.0422	−	12.3013i	−0.580008	−	0.444755i
$766$	18.2537	−	10.5388i	0.659531	−	0.380781i
$767$			25.5984i			0.924306i
$768$	0.556482	−	1.64022i	0.0200803	−	0.0591864i
$769$	13.4866	−	7.78647i	0.486338	−	0.280787i	−0.236716	−	0.971579i	$-0.576071\pi$
$769$	13.4866	−	7.78647i	0.486338	−	0.280787i	0.723054	+	0.690791i	$0.242738\pi$
$770$	−0.257496	−	1.71796i	−0.00927953	−	0.0619108i
$771$	6.01756	−	1.19799i	0.216717	−	0.0431445i
$772$	−0.618062	−	1.07052i	−0.0222446	−	0.0385287i
$773$	−9.05480	−	15.6834i	−0.325678	−	0.564092i	0.655971	−	0.754786i	$-0.272259\pi$
$773$	−9.05480	−	15.6834i	−0.325678	−	0.564092i	−0.981649	+	0.190695i	$0.938926\pi$
$774$	−14.4563	−	34.8684i	−0.519621	−	1.25332i
$775$	−6.93952	−	4.00653i	−0.249275	−	0.143919i
$776$	2.32353	−	4.02448i	0.0834100	−	0.144470i
$777$	6.21719	−	7.35281i	0.223041	−	0.263781i
$778$	15.4147	+	26.6991i	0.552644	+	0.957208i
$779$			4.91363i			0.176049i
$780$	0.935081	+	4.69696i	0.0334813	+	0.168178i
$781$	1.01166			0.0361999
$782$	−24.2617	+	42.0226i	−0.867598	+	1.50272i
$783$	−37.1925	+	2.45602i	−1.32915	+	0.0877710i
$784$	1.56886	−	6.82193i	0.0560308	−	0.243640i
$785$	13.9806	+	8.07171i	0.498989	+	0.288092i
$786$	−12.1311	+	10.6422i	−0.432701	+	0.379593i
$787$	37.9890	+	21.9330i	1.35416	+	0.781826i	0.988830	−	0.149050i	$-0.0476216\pi$
$787$	37.9890	+	21.9330i	1.35416	+	0.781826i	0.365334	+	0.930877i	$0.380955\pi$
$788$	−13.4514	−	7.76614i	−0.479185	−	0.276657i
$789$	−3.21911	−	16.1697i	−0.114603	−	0.575658i
$790$	13.0516	+	7.53532i	0.464354	+	0.268095i
$791$	31.9226	−	4.78473i	1.13504	−	0.170125i
$792$	1.81955	−	0.754380i	0.0646551	−	0.0268057i
$793$	2.16460	−	3.74920i	0.0768673	−	0.133138i
$794$	14.0567			0.498853
$795$	8.67963	−	7.61434i	0.307835	−	0.270053i
$796$		−	17.1745i		−	0.608735i
$797$	5.25439	+	9.10087i	0.186120	+	0.322369i	0.943953	−	0.330079i	$-0.107075\pi$
$797$	5.25439	+	9.10087i	0.186120	+	0.322369i	−0.757833	+	0.652448i	$0.773742\pi$
$798$	−3.29960	−	0.594662i	−0.116805	−	0.0210508i
$799$	19.7395	−	34.1898i	0.698333	−	1.20955i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	−1.03464	+	7.87877i	−0.0365573	+	0.278383i
$802$	−16.9887	−	29.4253i	−0.599891	−	1.03904i
$803$	2.25661	+	3.90856i	0.0796340	+	0.137930i
$804$	7.50150	+	8.55101i	0.264558	+	0.301571i
$805$	−6.97493	+	17.7290i	−0.245834	+	0.624864i
$806$	−19.1878	+	11.0781i	−0.675862	+	0.390209i
$807$	−4.34484	−	4.95271i	−0.152946	−	0.174344i
$808$		−	4.53706i		−	0.159613i
$809$	−27.9421	+	16.1324i	−0.982392	+	0.567184i	−0.902992	−	0.429658i	$-0.858634\pi$
$809$	−27.9421	+	16.1324i	−0.982392	+	0.567184i	−0.0794007	+	0.996843i	$0.525301\pi$
$810$	2.32369	−	8.69485i	0.0816463	−	0.305506i
$811$		−	48.8854i		−	1.71660i	−0.513151	−	0.858299i	$-0.671522\pi$
$811$		−	48.8854i		−	1.71660i	0.513151	−	0.858299i	$-0.328478\pi$
$812$	−18.7691	+	2.81321i	−0.658665	+	0.0987242i
$813$	2.05302	+	0.696534i	0.0720027	+	0.0244285i
$814$	1.37962			0.0483555
$815$	−1.04426	+	1.80871i	−0.0365789	+	0.0633564i
$816$	3.74989	−	11.0528i	0.131272	−	0.386924i
$817$	−7.97219	+	4.60275i	−0.278912	+	0.161030i
$818$	11.4908			0.401768
$819$	−18.8034	+	11.3174i	−0.657043	+	0.395464i
$820$	−6.71598			−0.234532
$821$	30.1804	−	17.4247i	1.05330	−	0.608126i	0.129732	−	0.991549i	$-0.458588\pi$
$821$	30.1804	−	17.4247i	1.05330	−	0.608126i	0.923573	+	0.383424i	$0.125255\pi$
$822$	−19.5316	−	22.2642i	−0.681242	−	0.776551i
$823$	21.1920	−	36.7055i	0.738705	−	1.27947i	−0.214373	−	0.976752i	$-0.568771\pi$
$823$	21.1920	−	36.7055i	0.738705	−	1.27947i	0.953079	−	0.302723i	$-0.0978957\pi$
$824$	3.79379			0.132163
$825$	−0.222044	−	1.11534i	−0.00773060	−	0.0388312i
$826$	8.96753	−	22.7938i	0.312020	−	0.793098i
$827$		−	9.24262i		−	0.321397i	−0.987004	−	0.160699i	$-0.948625\pi$
$827$		−	9.24262i		−	0.321397i	0.987004	−	0.160699i	$-0.0513748\pi$
$828$	−21.4187	−	2.81271i	−0.744351	−	0.0977483i
$829$	11.4514	−	6.61149i	0.397725	−	0.229626i	−0.287777	−	0.957697i	$-0.592916\pi$
$829$	11.4514	−	6.61149i	0.397725	−	0.229626i	0.685502	+	0.728071i	$0.259583\pi$
$830$			17.4223i			0.604736i
$831$	25.5519	−	5.08693i	0.886387	−	0.176464i
$832$	−2.39457	+	1.38250i	−0.0830167	+	0.0479297i
$833$	10.5719	−	45.9700i	0.366294	−	1.59277i
$834$	−8.13239	+	23.9701i	−0.281601	+	0.830016i
$835$	−3.73797	−	6.47435i	−0.129358	−	0.224054i
$836$	−0.240187	−	0.416017i	−0.00830705	−	0.0143882i
$837$	41.5466	−	2.74355i	1.43606	−	0.0948309i
$838$	25.0456	+	14.4601i	0.865186	+	0.499515i
$839$	9.52343	−	16.4951i	0.328785	−	0.569473i	−0.653486	−	0.756939i	$-0.726694\pi$
$839$	9.52343	−	16.4951i	0.328785	−	0.569473i	0.982271	+	0.187466i	$0.0600274\pi$
$840$	0.812788	−	4.50992i	0.0280438	−	0.155607i
$841$	11.2280	+	19.4475i	0.387172	+	0.670602i
$842$			0.947251i			0.0326444i
$843$	−51.4180	−	17.4447i	−1.77093	−	0.600827i
$844$	−22.3963			−0.770913
$845$	−2.67737	+	4.63733i	−0.0921042	+	0.159529i
$846$	17.4264	+	2.28843i	0.599130	+	0.0786780i
$847$	−26.0213	−	10.2373i	−0.894103	−	0.351758i
$848$	5.77309	+	3.33309i	0.198249	+	0.114459i
$849$	−34.6100	−	11.7422i	−1.18781	−	0.402992i
$850$	−5.83577	−	3.36928i	−0.200165	−	0.115566i
$851$	−13.1034	−	7.56528i	−0.449180	−	0.259334i
$852$	2.52725	+	0.857425i	0.0865821	+	0.0293749i
$853$	−15.0469	−	8.68732i	−0.515195	−	0.297448i	0.219771	−	0.975551i	$-0.429469\pi$
$853$	−15.0469	−	8.68732i	−0.515195	−	0.297448i	−0.734967	+	0.678103i	$0.762802\pi$
$854$	−3.24085	+	2.58013i	−0.110899	+	0.0882903i
$855$	−2.17621	−	0.285781i	−0.0744249	−	0.00977350i
$856$	3.28847	−	5.69580i	0.112398	−	0.194679i
$857$	−15.8907			−0.542816			−0.271408	−	0.962464i	$-0.587489\pi$
$857$	−15.8907			−0.542816			−0.271408	+	0.962464i	$0.587489\pi$
$858$	−2.97774	−	1.01026i	−0.101658	−	0.0344898i
$859$			1.97486i			0.0673812i	0.999432	+	0.0336906i	$0.0107261\pi$
$859$			1.97486i			0.0673812i	−0.999432	+	0.0336906i	$0.989274\pi$
$860$	−6.29106	−	10.8964i	−0.214524	−	0.371566i
$861$	−10.4169	−	28.9600i	−0.355008	−	0.986953i
$862$	−5.87431	+	10.1746i	−0.200080	+	0.346549i
$863$	−23.5615	−	13.6032i	−0.802043	−	0.463060i	0.0421423	−	0.999112i	$-0.486582\pi$
$863$	−23.5615	−	13.6032i	−0.802043	−	0.463060i	−0.844185	+	0.536052i	$0.819915\pi$
$864$	5.18486	−	0.342384i	0.176393	−	0.0116482i
$865$	−8.95135	−	15.5042i	−0.304355	−	0.527159i
$866$	15.7429	+	27.2675i	0.534965	+	0.926587i
$867$	15.8087	−	46.5960i	0.536892	−	1.58248i
$868$	20.9664	−	3.14255i	0.711645	−	0.106665i
$869$	−8.56939	+	4.94754i	−0.290697	+	0.167834i
$870$	−12.1854	+	2.42589i	−0.413122	+	0.0822453i
$871$		−	18.1589i		−	0.615291i
$872$	−8.38935	+	4.84359i	−0.284099	+	0.164025i
$873$	13.8225	+	1.81518i	0.467821	+	0.0614345i
$874$			5.26838i			0.178206i
$875$	−2.46207	−	0.968625i	−0.0832330	−	0.0327455i
$876$	2.32462	+	11.6767i	0.0785416	+	0.394519i
$877$	−8.85975			−0.299173			−0.149586	−	0.988749i	$-0.547794\pi$
$877$	−8.85975			−0.299173			−0.149586	+	0.988749i	$0.547794\pi$
$878$	14.3227	−	24.8076i	0.483366	−	0.837215i
$879$	15.4632	+	17.6266i	0.521562	+	0.594532i
$880$	0.568614	−	0.328290i	0.0191680	−	0.0110666i
$881$	−13.6049			−0.458361			−0.229180	−	0.973384i	$-0.573605\pi$
$881$	−13.6049			−0.458361			−0.229180	+	0.973384i	$0.573605\pi$
$882$	20.7079	−	3.49036i	0.697271	−	0.117527i
$883$	35.3206			1.18863			0.594316	−	0.804232i	$-0.297423\pi$
$883$	35.3206			1.18863			0.594316	+	0.804232i	$0.297423\pi$
$884$	−16.1360	+	9.31610i	−0.542711	+	0.313334i
$885$	5.15191	−	15.1852i	0.173180	−	0.510444i
$886$	6.34500	−	10.9899i	0.213164	−	0.369212i
$887$	16.0126			0.537651			0.268826	−	0.963189i	$-0.413364\pi$
$887$	16.0126			0.537651			0.268826	+	0.963189i	$0.413364\pi$
$888$	3.44646	+	1.16929i	0.115656	+	0.0392387i
$889$	−7.32252	−	2.88082i	−0.245589	−	0.0966197i
$890$			2.64880i			0.0887881i
$891$	4.18117	+	4.17572i	0.140075	+	0.139892i
$892$	−2.68635	+	1.55096i	−0.0899455	+	0.0519301i
$893$		−	4.28638i		−	0.143438i
$894$	−9.95411	−	11.3467i	−0.332915	−	0.379492i
$895$	8.68355	−	5.01345i	0.290259	−	0.167581i
$896$	2.61652	−	0.392179i	0.0874119	−	0.0131018i
$897$	22.7423	+	25.9241i	0.759345	+	0.865582i
$898$	−1.90273	−	3.29563i	−0.0634951	−	0.109977i
$899$	−28.7400	−	49.7791i	−0.958532	−	1.66023i
$900$	0.390607	−	2.97446i	0.0130202	−	0.0991487i
$901$	38.9023	+	22.4603i	1.29602	+	0.748260i
$902$	2.20479	−	3.81880i	0.0734114	−	0.127152i
$903$	37.2287	−	44.0288i	1.23889	−	1.46519i
$904$	6.10019	+	10.5658i	0.202889	+	0.351414i
$905$			8.57389i			0.285006i
$906$	11.2280	−	9.84995i	0.373026	−	0.327243i
$907$	−23.4420			−0.778378			−0.389189	−	0.921158i	$-0.627245\pi$
$907$	−23.4420			−0.778378			−0.389189	+	0.921158i	$0.627245\pi$
$908$	−14.4824	+	25.0842i	−0.480615	+	0.832449i
$909$	12.5734	−	5.21287i	0.417033	−	0.172900i
$910$	−5.72325	+	4.55645i	−0.189724	+	0.151045i
$911$	−32.0609	−	18.5104i	−1.06222	−	0.613275i	−0.136178	−	0.990684i	$-0.543482\pi$
$911$	−32.0609	−	18.5104i	−1.06222	−	0.613275i	−0.926047	+	0.377409i	$0.876815\pi$
$912$	−0.247426	−	1.24283i	−0.00819310	−	0.0411544i
$913$	−9.90656	−	5.71956i	−0.327859	−	0.189290i
$914$	34.9678	+	20.1887i	1.15663	+	0.667781i
$915$	−2.03862	+	1.78841i	−0.0673946	+	0.0591229i
$916$	−22.7549	−	13.1376i	−0.751843	−	0.434077i
$917$	−22.9390	−	9.02466i	−0.757513	−	0.298020i
$918$	34.9385	−	2.30718i	1.15314	−	0.0761483i
$919$	−1.61312	+	2.79400i	−0.0532118	+	0.0921656i	−0.891404	−	0.453209i	$-0.850279\pi$
$919$	−1.61312	+	2.79400i	−0.0532118	+	0.0921656i	0.838193	+	0.545374i	$0.183613\pi$
$920$	−7.20086			−0.237405
$921$	4.95183	+	24.8733i	0.163168	+	0.819603i
$922$		−	15.0479i		−	0.495577i
$923$	−2.13016	−	3.68954i	−0.0701150	−	0.121443i
$924$	2.29758	+	1.94272i	0.0755847	+	0.0639109i
$925$	1.05061	−	1.81971i	0.0345438	−	0.0598316i
$926$	−21.5474	−	12.4404i	−0.708093	−	0.408818i
$927$	4.35890	+	10.5136i	0.143165	+	0.345312i
$928$	−3.58664	−	6.21225i	−0.117737	−	0.203927i
$929$	−27.1070	−	46.9507i	−0.889353	−	1.54040i	−0.840642	−	0.541591i	$-0.817822\pi$
$929$	−27.1070	−	46.9507i	−0.889353	−	1.54040i	−0.0487105	−	0.998813i	$-0.515511\pi$
$930$	13.6119	−	2.70989i	0.446352	−	0.0888607i
$931$	−1.50152	−	4.89637i	−0.0492104	−	0.160472i
$932$	4.26732	−	2.46374i	0.139781	−	0.0807025i
$933$	2.67955	−	7.89793i	0.0877244	−	0.258567i
$934$		−	34.9914i		−	1.14495i
$935$	3.83165	−	2.21220i	0.125308	−	0.0723468i
$936$	−6.58253	−	5.04754i	−0.215157	−	0.164984i
$937$			44.7766i			1.46279i	0.681956	+	0.731393i	$0.261130\pi$
$937$			44.7766i			1.46279i	−0.681956	+	0.731393i	$0.738870\pi$
$938$	−6.36135	+	16.1694i	−0.207705	+	0.527949i
$939$	9.42456	−	8.26784i	0.307559	−	0.269811i
$940$	5.85866			0.191088
$941$	7.41316	−	12.8400i	0.241662	−	0.418571i	−0.719526	−	0.694466i	$-0.755641\pi$
$941$	7.41316	−	12.8400i	0.241662	−	0.418571i	0.961188	+	0.275895i	$0.0889741\pi$
$942$	−27.4231	+	5.45944i	−0.893492	+	0.177878i
$943$	−41.8817	+	24.1804i	−1.36386	+	0.787422i
$944$	9.25800			0.301322
$945$	13.4320	−	2.92925i	0.436944	−	0.0952884i
$946$	8.26117			0.268594
$947$	−10.5450	+	6.08814i	−0.342665	+	0.197838i	−0.661450	−	0.749989i	$-0.730059\pi$
$947$	−10.5450	+	6.08814i	−0.342665	+	0.197838i	0.318785	+	0.947827i	$0.396725\pi$
$948$	−25.6007	+	5.09665i	−0.831473	+	0.165531i
$949$	9.50310	−	16.4599i	0.308484	−	0.534310i
$950$	−0.731632			−0.0237373
$951$	−4.86732	+	4.26993i	−0.157834	+	0.138462i
$952$	17.6316	−	2.64272i	0.571444	−	0.0856511i
$953$			54.1766i			1.75495i	0.479619	+	0.877477i	$0.340775\pi$
$953$			54.1766i			1.75495i	−0.479619	+	0.877477i	$0.659225\pi$
$954$	−2.60386	+	19.8283i	−0.0843031	+	0.641965i
$955$	9.27965	−	5.35761i	0.300282	−	0.173368i
$956$			15.5220i			0.502016i
$957$	2.62093	−	7.72517i	0.0847228	−	0.249719i
$958$	10.5002	−	6.06228i	0.339245	−	0.195863i
$959$	16.5630	−	42.1000i	0.534846	−	1.35948i
$960$	1.69871	−	0.338184i	0.0548258	−	0.0109148i
$961$	16.6046	+	28.7600i	0.535632	+	0.927742i
$962$	−2.90494	−	5.03150i	−0.0936590	−	0.162222i
$963$	19.5629	+	2.56900i	0.630405	+	0.0827850i
$964$	−9.15179	−	5.28379i	−0.294759	−	0.170179i
$965$	0.618062	−	1.07052i	0.0198961	−	0.0344611i
$966$	−11.1690	−	31.0508i	−0.359357	−	0.999043i
$967$	−6.01241	−	10.4138i	−0.193346	−	0.334885i	0.753011	−	0.658008i	$-0.228601\pi$
$967$	−6.01241	−	10.4138i	−0.193346	−	0.334885i	−0.946357	+	0.323123i	$0.895267\pi$
$968$		−	10.5689i		−	0.339697i
$969$	−1.66730	−	8.37493i	−0.0535613	−	0.269041i
$970$	4.64707			0.149208
$971$	−29.0141	+	50.2539i	−0.931107	+	1.61272i	−0.149673	+	0.988736i	$0.547822\pi$
$971$	−29.0141	+	50.2539i	−0.931107	+	1.61272i	−0.781434	+	0.623988i	$0.785511\pi$
$972$	6.90601	+	13.9752i	0.221510	+	0.448256i
$973$	−38.2377	+	5.73127i	−1.22584	+	0.183736i
$974$	6.16364	+	3.55858i	0.197496	+	0.114024i
$975$	−3.60015	+	3.15828i	−0.115297	+	0.101146i
$976$	−1.35595	−	0.782856i	−0.0434028	−	0.0250586i
$977$	−6.60356	−	3.81257i	−0.211267	−	0.121975i	0.390633	−	0.920546i	$-0.372256\pi$
$977$	−6.60356	−	3.81257i	−0.211267	−	0.121975i	−0.601900	+	0.798572i	$0.705589\pi$
$978$	−0.706304	−	3.54780i	−0.0225851	−	0.113446i
$979$	−1.50615	−	0.869575i	−0.0481367	−	0.0277917i
$980$	6.69239	−	2.05229i	0.213781	−	0.0655580i
$981$	−23.0619	−	17.6840i	−0.736308	−	0.564607i
$982$	9.46076	−	16.3865i	0.301905	−	0.522915i
$983$	−14.8972			−0.475148			−0.237574	−	0.971369i	$-0.576352\pi$
$983$	−14.8972			−0.475148			−0.237574	+	0.971369i	$0.576352\pi$
$984$	8.74446	−	7.67121i	0.278763	−	0.244549i
$985$		−	15.5323i		−	0.494900i
$986$	−24.1688	−	41.8617i	−0.769693	−	1.33315i
$987$	9.08716	+	25.2631i	0.289247	+	0.804133i
$988$	−1.01148	+	1.75194i	−0.0321796	+	0.0557367i
$989$	−78.4637	−	45.3011i	−2.49500	−	1.44049i
$990$	1.56309	+	1.19859i	0.0496783	+	0.0380937i
$991$	−23.9760	−	41.5276i	−0.761622	−	1.31917i	−0.942014	−	0.335573i	$-0.891070\pi$
$991$	−23.9760	−	41.5276i	−0.761622	−	1.31917i	0.180393	−	0.983595i	$-0.442263\pi$
$992$	4.00653	+	6.93952i	0.127208	+	0.220330i
$993$	−5.48406	−	6.25131i	−0.174031	−	0.198379i
$994$	0.604267	+	4.03153i	0.0191662	+	0.127872i
$995$	14.8736	−	8.58726i	0.471524	−	0.272234i
$996$	−19.9003	−	22.6845i	−0.630565	−	0.718785i
$997$		−	1.95332i		−	0.0618624i	−0.999522	−	0.0309312i	$-0.990153\pi$
$997$		−	1.95332i		−	0.0618624i	0.999522	−	0.0309312i	$-0.00984728\pi$
$998$	−16.4616	+	9.50411i	−0.521083	+	0.300847i
$999$	0.719424	+	10.8945i	0.0227616	+	0.344687i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.c.551.9	yes	32
3.2	odd	2		1890.2.t.c.1601.5		32
7.3	odd	6		630.2.bk.c.101.11	yes	32
9.4	even	3		1890.2.bk.c.341.8		32
9.5	odd	6		630.2.bk.c.131.3	yes	32
21.17	even	6		1890.2.bk.c.521.8		32
63.31	odd	6		1890.2.t.c.1151.5		32
63.59	even	6	inner	630.2.t.c.311.9	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.9	✓	32	63.59	even	6	inner
630.2.t.c.551.9	yes	32	1.1	even	1	trivial
630.2.bk.c.101.11	yes	32	7.3	odd	6
630.2.bk.c.131.3	yes	32	9.5	odd	6
1890.2.t.c.1151.5		32	63.31	odd	6
1890.2.t.c.1601.5		32	3.2	odd	2
1890.2.bk.c.341.8		32	9.4	even	3
1890.2.bk.c.521.8		32	21.17	even	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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.69871 + 0.338184i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-1.30204 + 1.14223i) q^{6} +(-2.46207 - 0.968625i) q^{7} -1.00000i q^{8} +(2.77126 - 1.14896i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.69871 + 0.338184i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-1.30204 + 1.14223i) q^{6} +(-2.46207 - 0.968625i) q^{7} -1.00000i q^{8} +(2.77126 - 1.14896i) q^{9} +(0.866025 - 0.500000i) q^{10} +0.656579i q^{11} +(-0.556482 + 1.64022i) q^{12} +(2.39457 - 1.38250i) q^{13} +(-2.61652 + 0.392179i) q^{14} +(-1.69871 + 0.338184i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.36928 - 5.83577i) q^{17} +(1.82551 - 2.38066i) q^{18} +(-0.633612 - 0.365816i) q^{19} +(0.500000 - 0.866025i) q^{20} +(4.50992 + 0.812788i) q^{21} +(0.328290 + 0.568614i) q^{22} -7.20086i q^{23} +(0.338184 + 1.69871i) q^{24} +1.00000 q^{25} +(1.38250 - 2.39457i) q^{26} +(-4.31903 + 2.88894i) q^{27} +(-2.06989 + 1.64790i) q^{28} +(6.21225 + 3.58664i) q^{29} +(-1.30204 + 1.14223i) q^{30} +(-6.93952 - 4.00653i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.222044 - 1.11534i) q^{33} +(-5.83577 - 3.36928i) q^{34} +(-2.46207 - 0.968625i) q^{35} +(0.390607 - 2.97446i) q^{36} +(1.05061 - 1.81971i) q^{37} -0.731632 q^{38} +(-3.60015 + 3.15828i) q^{39} -1.00000i q^{40} +(-3.35799 - 5.81621i) q^{41} +(4.31210 - 1.55107i) q^{42} +(6.29106 - 10.8964i) q^{43} +(0.568614 + 0.328290i) q^{44} +(2.77126 - 1.14896i) q^{45} +(-3.60043 - 6.23613i) q^{46} +(2.92933 + 5.07374i) q^{47} +(1.14223 + 1.30204i) q^{48} +(5.12353 + 4.76964i) q^{49} +(0.866025 - 0.500000i) q^{50} +(7.69702 + 8.77388i) q^{51} -2.76501i q^{52} +(-5.77309 + 3.33309i) q^{53} +(-2.29592 + 4.66141i) q^{54} +0.656579i q^{55} +(-0.968625 + 2.46207i) q^{56} +(1.20004 + 0.407140i) q^{57} +7.17328 q^{58} +(-4.62900 + 8.01766i) q^{59} +(-0.556482 + 1.64022i) q^{60} +(1.35595 - 0.782856i) q^{61} -8.01306 q^{62} +(-7.93594 + 0.144487i) q^{63} -1.00000 q^{64} +(2.39457 - 1.38250i) q^{65} +(-0.749967 - 0.854892i) q^{66} +(3.28370 - 5.68754i) q^{67} -6.73857 q^{68} +(2.43521 + 12.2322i) q^{69} +(-2.61652 + 0.392179i) q^{70} -1.54080i q^{71} +(-1.14896 - 2.77126i) q^{72} +(5.95292 - 3.43692i) q^{73} -2.10122i q^{74} +(-1.69871 + 0.338184i) q^{75} +(-0.633612 + 0.365816i) q^{76} +(0.635979 - 1.61654i) q^{77} +(-1.53868 + 4.53523i) q^{78} +(7.53532 + 13.0516i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(6.35980 - 6.36812i) q^{81} +(-5.81621 - 3.35799i) q^{82} +(-8.71114 + 15.0881i) q^{83} +(2.95885 - 3.49931i) q^{84} +(-3.36928 - 5.83577i) q^{85} -12.5821i q^{86} +(-11.7658 - 3.99180i) q^{87} +0.656579 q^{88} +(-1.32440 + 2.29393i) q^{89} +(1.82551 - 2.38066i) q^{90} +(-7.23471 + 1.08438i) q^{91} +(-6.23613 - 3.60043i) q^{92} +(13.1432 + 4.45912i) q^{93} +(5.07374 + 2.92933i) q^{94} +(-0.633612 - 0.365816i) q^{95} +(1.64022 + 0.556482i) q^{96} +(4.02448 + 2.32353i) q^{97} +(6.82193 + 1.56886i) q^{98} +(0.754380 + 1.81955i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9	\( 32 q + 2 q^{3} + 16 q^{4} + 32 q^{5} + 2 q^{6} - 2 q^{7} + 6 q^{9} + 4 q^{12} + 2 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} + 16 q^{20} + 16 q^{21} + 4 q^{24} + 32 q^{25} + 12 q^{26} + 8 q^{27} + 2 q^{28} + 6 q^{29} + 2 q^{30} + 18 q^{31} + 16 q^{33} - 2 q^{35} + 2 q^{37} - 18 q^{39} - 6 q^{41} + 6 q^{42} - 28 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{47} + 2 q^{48} + 32 q^{49} - 26 q^{51} - 36 q^{53} - 32 q^{54} - 6 q^{56} + 18 q^{57} - 30 q^{59} + 4 q^{60} + 54 q^{61} - 94 q^{63} - 32 q^{64} - 44 q^{66} + 4 q^{67} + 12 q^{68} + 28 q^{69} + 4 q^{72} - 30 q^{73} + 2 q^{75} - 6 q^{77} - 22 q^{78} + 4 q^{79} - 16 q^{80} + 26 q^{81} - 24 q^{82} + 6 q^{83} - 4 q^{84} + 6 q^{85} - 8 q^{87} - 12 q^{89} - 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 42 q^{94} + 2 q^{96} + 96 q^{97} - 24 q^{98} - 24 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 16 * q^4 + 32 * q^5 + 2 * q^6 - 2 * q^7 + 6 * q^9 + 4 * q^12 + 2 * q^15 - 16 * q^16 + 6 * q^17 - 4 * q^18 + 16 * q^20 + 16 * q^21 + 4 * q^24 + 32 * q^25 + 12 * q^26 + 8 * q^27 + 2 * q^28 + 6 * q^29 + 2 * q^30 + 18 * q^31 + 16 * q^33 - 2 * q^35 + 2 * q^37 - 18 * q^39 - 6 * q^41 + 6 * q^42 - 28 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^47 + 2 * q^48 + 32 * q^49 - 26 * q^51 - 36 * q^53 - 32 * q^54 - 6 * q^56 + 18 * q^57 - 30 * q^59 + 4 * q^60 + 54 * q^61 - 94 * q^63 - 32 * q^64 - 44 * q^66 + 4 * q^67 + 12 * q^68 + 28 * q^69 + 4 * q^72 - 30 * q^73 + 2 * q^75 - 6 * q^77 - 22 * q^78 + 4 * q^79 - 16 * q^80 + 26 * q^81 - 24 * q^82 + 6 * q^83 - 4 * q^84 + 6 * q^85 - 8 * q^87 - 12 * q^89 - 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 42 * q^94 + 2 * q^96 + 96 * q^97 - 24 * q^98 - 24 * q^99

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