LMFDB - Embedded newform 630.2.t.c.311.13

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			311.13
Character	$\chi$	$=$	630.311
Dual form			630.2.t.c.551.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.0292487 + 1.73180i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.840572 + 1.51441i) q^{6} +(2.63859 + 0.194573i) q^{7} +1.00000i q^{8} +(-2.99829 + 0.101306i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.0292487 + 1.73180i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.840572 + 1.51441i) q^{6} +(2.63859 + 0.194573i) q^{7} +1.00000i q^{8} +(-2.99829 + 0.101306i) q^{9} +(0.866025 + 0.500000i) q^{10} +2.09116i q^{11} +(-1.48516 + 0.891232i) q^{12} +(-0.413776 - 0.238893i) q^{13} +(2.18780 + 1.48780i) q^{14} +(0.0292487 + 1.73180i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.44100 + 2.49589i) q^{17} +(-2.64725 - 1.41141i) q^{18} +(4.03431 - 2.32921i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-0.259788 + 4.57521i) q^{21} +(-1.04558 + 1.81100i) q^{22} -2.02764i q^{23} +(-1.73180 + 0.0292487i) q^{24} +1.00000 q^{25} +(-0.238893 - 0.413776i) q^{26} +(-0.263138 - 5.18949i) q^{27} +(1.15079 + 2.38237i) q^{28} +(2.74938 - 1.58735i) q^{29} +(-0.840572 + 1.51441i) q^{30} +(-4.59333 + 2.65196i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.62148 + 0.0611638i) q^{33} +(-2.49589 + 1.44100i) q^{34} +(2.63859 + 0.194573i) q^{35} +(-1.58688 - 2.54594i) q^{36} +(-1.93169 - 3.34578i) q^{37} +4.65842 q^{38} +(0.401614 - 0.723566i) q^{39} +1.00000i q^{40} +(-4.03898 + 6.99572i) q^{41} +(-2.51259 + 3.83235i) q^{42} +(-2.96902 - 5.14250i) q^{43} +(-1.81100 + 1.04558i) q^{44} +(-2.99829 + 0.101306i) q^{45} +(1.01382 - 1.75599i) q^{46} +(0.0525367 - 0.0909962i) q^{47} +(-1.51441 - 0.840572i) q^{48} +(6.92428 + 1.02680i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-4.36455 - 2.42254i) q^{51} -0.477787i q^{52} +(-4.27164 - 2.46623i) q^{53} +(2.36686 - 4.62580i) q^{54} +2.09116i q^{55} +(-0.194573 + 2.63859i) q^{56} +(4.15173 + 6.91851i) q^{57} +3.17471 q^{58} +(1.40971 + 2.44169i) q^{59} +(-1.48516 + 0.891232i) q^{60} +(3.71793 + 2.14655i) q^{61} -5.30392 q^{62} +(-7.93096 - 0.316082i) q^{63} -1.00000 q^{64} +(-0.413776 - 0.238893i) q^{65} +(-3.16688 - 1.75777i) q^{66} +(-2.73588 - 4.73867i) q^{67} -2.88201 q^{68} +(3.51147 - 0.0593058i) q^{69} +(2.18780 + 1.48780i) q^{70} -10.8486i q^{71} +(-0.101306 - 2.99829i) q^{72} +(5.64929 + 3.26162i) q^{73} -3.86338i q^{74} +(0.0292487 + 1.73180i) q^{75} +(4.03431 + 2.32921i) q^{76} +(-0.406885 + 5.51772i) q^{77} +(0.709591 - 0.425819i) q^{78} +(7.81773 - 13.5407i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(8.97947 - 0.607490i) q^{81} +(-6.99572 + 4.03898i) q^{82} +(5.58951 + 9.68132i) q^{83} +(-4.09214 + 2.06262i) q^{84} +(-1.44100 + 2.49589i) q^{85} -5.93804i q^{86} +(2.82940 + 4.71496i) q^{87} -2.09116 q^{88} +(-6.59060 - 11.4153i) q^{89} +(-2.64725 - 1.41141i) q^{90} +(-1.04530 - 0.710851i) q^{91} +(1.75599 - 1.01382i) q^{92} +(-4.72703 - 7.87718i) q^{93} +(0.0909962 - 0.0525367i) q^{94} +(4.03431 - 2.32921i) q^{95} +(-0.891232 - 1.48516i) q^{96} +(7.98211 - 4.60847i) q^{97} +(5.48321 + 4.35137i) q^{98} +(-0.211848 - 6.26991i) 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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
$3$	0.0292487	+	1.73180i	0.0168868	+	0.999857i
$3$	0.0292487	+	1.73180i	0.0168868	+	0.999857i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.840572	+	1.51441i	−0.343162	+	0.618255i
$7$	2.63859	+	0.194573i	0.997292	+	0.0735418i
$7$	2.63859	+	0.194573i	0.997292	+	0.0735418i
$8$			1.00000i			0.353553i
$9$	−2.99829	+	0.101306i	−0.999430	+	0.0337687i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$			2.09116i			0.630509i	0.949007	+	0.315255i	$0.102090\pi$
$11$			2.09116i			0.630509i	−0.949007	+	0.315255i	$0.897910\pi$
$12$	−1.48516	+	0.891232i	−0.428729	+	0.257277i
$13$	−0.413776	−	0.238893i	−0.114761	−	0.0662571i	0.441521	−	0.897251i	$-0.354439\pi$
$13$	−0.413776	−	0.238893i	−0.114761	−	0.0662571i	−0.556282	+	0.830994i	$0.687772\pi$
$14$	2.18780	+	1.48780i	0.584713	+	0.397631i
$15$	0.0292487	+	1.73180i	0.00755199	+	0.447150i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.44100	+	2.49589i	−0.349495	+	0.605343i	−0.986160	−	0.165798i	$-0.946980\pi$
$17$	−1.44100	+	2.49589i	−0.349495	+	0.605343i	0.636665	+	0.771141i	$0.280313\pi$
$18$	−2.64725	−	1.41141i	−0.623962	−	0.332673i
$19$	4.03431	−	2.32921i	0.925535	−	0.534358i	0.0401380	−	0.999194i	$-0.487220\pi$
$19$	4.03431	−	2.32921i	0.925535	−	0.534358i	0.885397	+	0.464837i	$0.153887\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−0.259788	+	4.57521i	−0.0566903	+	0.998392i
$22$	−1.04558	+	1.81100i	−0.222919	+	0.386107i
$23$		−	2.02764i		−	0.422792i	−0.977401	−	0.211396i	$-0.932199\pi$
$23$		−	2.02764i		−	0.422792i	0.977401	−	0.211396i	$-0.0678009\pi$
$24$	−1.73180	+	0.0292487i	−0.353503	+	0.00597037i
$25$	1.00000			0.200000
$26$	−0.238893	−	0.413776i	−0.0468509	−	0.0811481i
$27$	−0.263138	−	5.18949i	−0.0506410	−	0.998717i
$28$	1.15079	+	2.38237i	0.217478	+	0.450226i
$29$	2.74938	−	1.58735i	0.510547	−	0.294764i	−0.222512	−	0.974930i	$-0.571426\pi$
$29$	2.74938	−	1.58735i	0.510547	−	0.294764i	0.733058	+	0.680166i	$0.238092\pi$
$30$	−0.840572	+	1.51441i	−0.153467	+	0.276492i
$31$	−4.59333	+	2.65196i	−0.824987	+	0.476306i	−0.852133	−	0.523325i	$-0.824691\pi$
$31$	−4.59333	+	2.65196i	−0.824987	+	0.476306i	0.0271462	+	0.999631i	$0.491358\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−3.62148	+	0.0611638i	−0.630419	+	0.0106473i
$34$	−2.49589	+	1.44100i	−0.428042	+	0.247130i
$35$	2.63859	+	0.194573i	0.446003	+	0.0328889i
$36$	−1.58688	−	2.54594i	−0.264480	−	0.424324i
$37$	−1.93169	−	3.34578i	−0.317568	−	0.550043i	0.662412	−	0.749140i	$-0.269533\pi$
$37$	−1.93169	−	3.34578i	−0.317568	−	0.550043i	−0.979980	+	0.199096i	$0.936199\pi$
$38$	4.65842			0.755696
$39$	0.401614	−	0.723566i	0.0643098	−	0.115863i
$40$			1.00000i			0.158114i
$41$	−4.03898	+	6.99572i	−0.630783	+	1.09255i	0.356609	+	0.934254i	$0.383933\pi$
$41$	−4.03898	+	6.99572i	−0.630783	+	1.09255i	−0.987392	+	0.158294i	$0.949401\pi$
$42$	−2.51259	+	3.83235i	−0.387700	+	0.591345i
$43$	−2.96902	−	5.14250i	−0.452772	−	0.784224i	0.545785	−	0.837925i	$-0.316231\pi$
$43$	−2.96902	−	5.14250i	−0.452772	−	0.784224i	−0.998557	+	0.0537015i	$0.982898\pi$
$44$	−1.81100	+	1.04558i	−0.273019	+	0.157627i
$45$	−2.99829	+	0.101306i	−0.446959	+	0.0151018i
$46$	1.01382	−	1.75599i	0.149479	−	0.258906i
$47$	0.0525367	−	0.0909962i	0.00766326	−	0.0132732i	−0.862168	−	0.506622i	$-0.830894\pi$
$47$	0.0525367	−	0.0909962i	0.00766326	−	0.0132732i	0.869832	+	0.493349i	$0.164227\pi$
$48$	−1.51441	−	0.840572i	−0.218586	−	0.121326i
$49$	6.92428	+	1.02680i	0.989183	+	0.146685i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	−4.36455	−	2.42254i	−0.611159	−	0.339223i
$52$		−	0.477787i		−	0.0662571i
$53$	−4.27164	−	2.46623i	−0.586755	−	0.338763i	0.177058	−	0.984200i	$-0.443342\pi$
$53$	−4.27164	−	2.46623i	−0.586755	−	0.338763i	−0.763813	+	0.645437i	$0.776675\pi$
$54$	2.36686	−	4.62580i	0.322089	−	0.629491i
$55$			2.09116i			0.281972i
$56$	−0.194573	+	2.63859i	−0.0260010	+	0.352596i
$57$	4.15173	+	6.91851i	0.549911	+	0.916379i
$58$	3.17471			0.416860
$59$	1.40971	+	2.44169i	0.183529	+	0.317881i	0.943080	−	0.332567i	$-0.107915\pi$
$59$	1.40971	+	2.44169i	0.183529	+	0.317881i	−0.759551	+	0.650448i	$0.774581\pi$
$60$	−1.48516	+	0.891232i	−0.191734	+	0.115058i
$61$	3.71793	+	2.14655i	0.476033	+	0.274838i	0.718762	−	0.695256i	$-0.244709\pi$
$61$	3.71793	+	2.14655i	0.476033	+	0.274838i	−0.242729	+	0.970094i	$0.578043\pi$
$62$	−5.30392			−0.673599
$63$	−7.93096	−	0.316082i	−0.999207	−	0.0398226i
$64$	−1.00000			−0.125000
$65$	−0.413776	−	0.238893i	−0.0513226	−	0.0296311i
$66$	−3.16688	−	1.75777i	−0.389816	−	0.216367i
$67$	−2.73588	−	4.73867i	−0.334240	−	0.578921i	0.649098	−	0.760705i	$-0.275146\pi$
$67$	−2.73588	−	4.73867i	−0.334240	−	0.578921i	−0.983339	+	0.181783i	$0.941813\pi$
$68$	−2.88201			−0.349495
$69$	3.51147	−	0.0593058i	0.422731	−	0.00713958i
$70$	2.18780	+	1.48780i	0.261492	+	0.177826i
$71$		−	10.8486i		−	1.28750i	−0.765238	−	0.643748i	$-0.777379\pi$
$71$		−	10.8486i		−	1.28750i	0.765238	−	0.643748i	$-0.222621\pi$
$72$	−0.101306	−	2.99829i	−0.0119390	−	0.353352i
$73$	5.64929	+	3.26162i	0.661199	+	0.381744i	0.792734	−	0.609568i	$-0.208657\pi$
$73$	5.64929	+	3.26162i	0.661199	+	0.381744i	−0.131535	+	0.991312i	$0.541990\pi$
$74$		−	3.86338i		−	0.449109i
$75$	0.0292487	+	1.73180i	0.00337735	+	0.199971i
$76$	4.03431	+	2.32921i	0.462767	+	0.267179i
$77$	−0.406885	+	5.51772i	−0.0463688	+	0.628802i
$78$	0.709591	−	0.425819i	0.0803454	−	0.0482145i
$79$	7.81773	−	13.5407i	0.879563	−	1.52345i	0.0277423	−	0.999615i	$-0.491168\pi$
$79$	7.81773	−	13.5407i	0.879563	−	1.52345i	0.851821	−	0.523833i	$-0.175498\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	8.97947	−	0.607490i	0.997719	−	0.0674989i
$82$	−6.99572	+	4.03898i	−0.772548	+	0.446031i
$83$	5.58951	+	9.68132i	0.613529	+	1.06266i	0.990641	+	0.136495i	$0.0435839\pi$
$83$	5.58951	+	9.68132i	0.613529	+	1.06266i	−0.377112	+	0.926168i	$0.623083\pi$
$84$	−4.09214	+	2.06262i	−0.446489	+	0.225050i
$85$	−1.44100	+	2.49589i	−0.156299	+	0.270718i
$86$		−	5.93804i		−	0.640316i
$87$	2.82940	+	4.71496i	0.303344	+	0.505496i
$88$	−2.09116			−0.222919
$89$	−6.59060	−	11.4153i	−0.698602	−	1.21001i	−0.968951	−	0.247252i	$-0.920472\pi$
$89$	−6.59060	−	11.4153i	−0.698602	−	1.21001i	0.270349	−	0.962762i	$-0.412861\pi$
$90$	−2.64725	−	1.41141i	−0.279044	−	0.148776i
$91$	−1.04530	−	0.710851i	−0.109577	−	0.0745174i
$92$	1.75599	−	1.01382i	0.183074	−	0.105698i
$93$	−4.72703	−	7.87718i	−0.490170	−	0.816826i
$94$	0.0909962	−	0.0525367i	0.00938554	−	0.00541874i
$95$	4.03431	−	2.32921i	0.413912	−	0.238972i
$96$	−0.891232	−	1.48516i	−0.0909610	−	0.151579i
$97$	7.98211	−	4.60847i	0.810460	−	0.467920i	−0.0366553	−	0.999328i	$-0.511670\pi$
$97$	7.98211	−	4.60847i	0.810460	−	0.467920i	0.847116	+	0.531408i	$0.178337\pi$
$98$	5.48321	+	4.35137i	0.553887	+	0.439555i
$99$	−0.211848	−	6.26991i	−0.0212915	−	0.630150i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	18.8631			1.87695			0.938475	−	0.345347i	$-0.112239\pi$
$101$	18.8631			1.87695			0.938475	+	0.345347i	$0.112239\pi$
$102$	−2.56854	−	4.28025i	−0.254323	−	0.423808i
$103$		−	10.1578i		−	1.00087i	−0.865773	−	0.500437i	$-0.833173\pi$
$103$		−	10.1578i		−	1.00087i	0.865773	−	0.500437i	$-0.166827\pi$
$104$	0.238893	−	0.413776i	0.0234254	−	0.0405740i
$105$	−0.259788	+	4.57521i	−0.0253527	+	0.446494i
$106$	−2.46623	−	4.27164i	−0.239542	−	0.414898i
$107$	−15.8802	+	9.16843i	−1.53520	+	0.886346i	−0.536086	+	0.844163i	$0.680098\pi$
$107$	−15.8802	+	9.16843i	−1.53520	+	0.886346i	−0.999110	+	0.0421823i	$0.986569\pi$
$108$	4.36266	−	2.82263i	0.419797	−	0.271607i
$109$	7.08626	−	12.2738i	0.678741	−	1.17561i	−0.296619	−	0.954996i	$-0.595859\pi$
$109$	7.08626	−	12.2738i	0.678741	−	1.17561i	0.975360	−	0.220618i	$-0.0708074\pi$
$110$	−1.04558	+	1.81100i	−0.0996923	+	0.172672i
$111$	5.73774	−	3.44317i	0.544602	−	0.326811i
$112$	−1.48780	+	2.18780i	−0.140584	+	0.206727i
$113$	6.91284	+	3.99113i	0.650305	+	0.375454i	0.788573	−	0.614941i	$-0.210820\pi$
$113$	6.91284	+	3.99113i	0.650305	+	0.375454i	−0.138268	+	0.990395i	$0.544153\pi$
$114$	0.136253	+	8.06747i	0.0127612	+	0.755588i
$115$		−	2.02764i		−	0.189078i
$116$	2.74938	+	1.58735i	0.255273	+	0.147382i
$117$	1.26482	+	0.674354i	0.116933	+	0.0623440i
$118$			2.81942i			0.259549i
$119$	−4.28785	+	6.30525i	−0.393067	+	0.578001i
$120$	−1.73180	+	0.0292487i	−0.158091	+	0.00267003i
$121$	6.62704			0.602458
$122$	2.14655	+	3.71793i	0.194340	+	0.336606i
$123$	−12.2334	−	6.79011i	−1.10304	−	0.612243i
$124$	−4.59333	−	2.65196i	−0.412493	−	0.238153i
$125$	1.00000			0.0894427
$126$	−6.71037	−	4.23921i	−0.597807	−	0.377659i
$127$	0.449694			0.0399039			0.0199520	−	0.999801i	$-0.493649\pi$
$127$	0.449694			0.0399039			0.0199520	+	0.999801i	$0.493649\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	8.81896	−	5.29218i	0.776466	−	0.465950i
$130$	−0.238893	−	0.413776i	−0.0209523	−	0.0362905i
$131$	−10.4428			−0.912392			−0.456196	−	0.889879i	$-0.650788\pi$
$131$	−10.4428			−0.912392			−0.456196	+	0.889879i	$0.650788\pi$
$132$	−1.86371	−	3.10572i	−0.162215	−	0.270318i
$133$	11.0981	−	5.36086i	0.962326	−	0.464845i
$134$		−	5.47175i		−	0.472687i
$135$	−0.263138	−	5.18949i	−0.0226473	−	0.446640i
$136$	−2.49589	−	1.44100i	−0.214021	−	0.123565i
$137$			17.4349i			1.48956i	0.667310	+	0.744780i	$0.267446\pi$
$137$			17.4349i			1.48956i	−0.667310	+	0.744780i	$0.732554\pi$
$138$	3.07068	+	1.70437i	0.261393	+	0.145086i
$139$	11.1168	+	6.41827i	0.942912	+	0.544390i	0.890872	−	0.454255i	$-0.150094\pi$
$139$	11.1168	+	6.41827i	0.942912	+	0.544390i	0.0520399	+	0.998645i	$0.483428\pi$
$140$	1.15079	+	2.38237i	0.0972593	+	0.201347i
$141$	0.159124	+	0.0883217i	0.0134007	+	0.00743803i
$142$	5.42432	−	9.39519i	0.455198	−	0.788427i
$143$	0.499565	−	0.865272i	0.0417757	−	0.0723577i
$144$	1.41141	−	2.64725i	0.117618	−	0.220604i
$145$	2.74938	−	1.58735i	0.228323	−	0.131823i
$146$	3.26162	+	5.64929i	0.269933	+	0.467538i
$147$	−1.57569	+	12.0215i	−0.129960	+	0.991519i
$148$	1.93169	−	3.34578i	0.158784	−	0.275022i
$149$		−	1.19092i		−	0.0975637i	−0.998809	−	0.0487818i	$-0.984466\pi$
$149$		−	1.19092i		−	0.0975637i	0.998809	−	0.0487818i	$-0.0155339\pi$
$150$	−0.840572	+	1.51441i	−0.0686324	+	0.123651i
$151$	1.58349			0.128863			0.0644314	−	0.997922i	$-0.479477\pi$
$151$	1.58349			0.128863			0.0644314	+	0.997922i	$0.479477\pi$
$152$	2.32921	+	4.03431i	0.188924	+	0.327226i
$153$	4.06770	−	7.62939i	0.328854	−	0.616800i
$154$	−3.11123	+	4.57504i	−0.250710	+	0.368667i
$155$	−4.59333	+	2.65196i	−0.368945	+	0.213011i
$156$	0.827433	−	0.0139747i	0.0662477	−	0.00111887i
$157$	−14.5680	+	8.41085i	−1.16266	+	0.671259i	−0.951939	−	0.306288i	$-0.900913\pi$
$157$	−14.5680	+	8.41085i	−1.16266	+	0.671259i	−0.210716	+	0.977547i	$0.567580\pi$
$158$	13.5407	−	7.81773i	1.07724	−	0.621945i
$159$	4.14609	−	7.46978i	0.328806	−	0.592392i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	0.394524	−	5.35010i	0.0310929	−	0.421647i
$162$	8.08020	+	3.96364i	0.634840	+	0.311413i
$163$	−5.01637	−	8.68860i	−0.392912	−	0.680544i	0.599920	−	0.800060i	$-0.295199\pi$
$163$	−5.01637	−	8.68860i	−0.392912	−	0.680544i	−0.992832	+	0.119516i	$0.961866\pi$
$164$	−8.07796			−0.630783
$165$	−3.62148	+	0.0611638i	−0.281932	+	0.00476160i
$166$			11.1790i			0.867661i
$167$	7.17037	−	12.4194i	0.554860	−	0.961045i	−0.443055	−	0.896495i	$-0.646105\pi$
$167$	7.17037	−	12.4194i	0.554860	−	0.961045i	0.997914	−	0.0645506i	$-0.0205614\pi$
$168$	−4.57521	−	0.259788i	−0.352985	−	0.0200431i
$169$	−6.38586	−	11.0606i	−0.491220	−	0.850818i
$170$	−2.49589	+	1.44100i	−0.191426	+	0.110520i
$171$	−11.8601	+	7.39235i	−0.906962	+	0.565307i
$172$	2.96902	−	5.14250i	0.226386	−	0.392112i
$173$	−8.06316	+	13.9658i	−0.613031	+	1.06180i	0.377696	+	0.925930i	$0.376716\pi$
$173$	−8.06316	+	13.9658i	−0.613031	+	1.06180i	−0.990727	+	0.135870i	$0.956617\pi$
$174$	0.0928562	+	5.49797i	0.00703941	+	0.416800i
$175$	2.63859	+	0.194573i	0.199458	+	0.0147084i
$176$	−1.81100	−	1.04558i	−0.136509	−	0.0788137i
$177$	−4.18730	+	2.51276i	−0.314736	+	0.188870i
$178$		−	13.1812i		−	0.987973i
$179$	0.0837491	+	0.0483526i	0.00625970	+	0.00361404i	0.503127	−	0.864213i	$-0.332183\pi$
$179$	0.0837491	+	0.0483526i	0.00625970	+	0.00361404i	−0.496867	+	0.867827i	$0.665516\pi$
$180$	−1.58688	−	2.54594i	−0.118279	−	0.189763i
$181$			20.0938i			1.49356i	0.665072	+	0.746779i	$0.268401\pi$
$181$			20.0938i			1.49356i	−0.665072	+	0.746779i	$0.731599\pi$
$182$	−0.549832	−	1.13827i	−0.0407562	−	0.0843738i
$183$	−3.60866	+	6.50152i	−0.266760	+	0.480606i
$184$	2.02764			0.149479
$185$	−1.93169	−	3.34578i	−0.142021	−	0.245987i
$186$	−0.155133	−	9.18536i	−0.0113749	−	0.673503i
$187$	−5.21932	−	3.01338i	−0.381674	−	0.220360i
$188$	0.105073			0.00766326
$189$	0.315422	−	13.7441i	0.0229436	−	0.999737i
$190$	4.65842			0.337957
$191$	−3.05974	−	1.76654i	−0.221395	−	0.127822i	0.385201	−	0.922833i	$-0.374132\pi$
$191$	−3.05974	−	1.76654i	−0.221395	−	0.127822i	−0.606596	+	0.795010i	$0.707465\pi$
$192$	−0.0292487	−	1.73180i	−0.00211084	−	0.124982i
$193$	−12.6572	−	21.9229i	−0.911084	−	1.57804i	−0.812535	−	0.582912i	$-0.801913\pi$
$193$	−12.6572	−	21.9229i	−0.911084	−	1.57804i	−0.0985491	−	0.995132i	$-0.531420\pi$
$194$	9.21695			0.661738
$195$	0.401614	−	0.723566i	0.0287602	−	0.0518156i
$196$	2.57291	+	6.51000i	0.183779	+	0.465000i
$197$			9.01088i			0.641999i	0.947079	+	0.320999i	$0.104019\pi$
$197$			9.01088i			0.641999i	−0.947079	+	0.320999i	$0.895981\pi$
$198$	2.95149	−	5.53583i	0.209753	−	0.393414i
$199$	−12.3893	−	7.15296i	−0.878254	−	0.507060i	−0.00817145	−	0.999967i	$-0.502601\pi$
$199$	−12.3893	−	7.15296i	−0.878254	−	0.507060i	−0.870082	+	0.492907i	$0.835934\pi$
$200$			1.00000i			0.0707107i
$201$	8.12643	−	4.87660i	0.573194	−	0.343969i
$202$	16.3359	+	9.43156i	1.14939	+	0.663602i
$203$	7.56333	−	3.65342i	0.530842	−	0.256420i
$204$	−0.0842951	−	4.99107i	−0.00590184	−	0.349445i
$205$	−4.03898	+	6.99572i	−0.282095	+	0.488602i
$206$	5.07888	−	8.79688i	0.353863	−	0.612908i
$207$	0.205412	+	6.07944i	0.0142771	+	0.422551i
$208$	0.413776	−	0.238893i	0.0286902	−	0.0165643i
$209$	4.87076	+	8.43640i	0.336917	+	0.583558i
$210$	−2.51259	+	3.83235i	−0.173385	+	0.264457i
$211$	−0.442791	+	0.766937i	−0.0304830	+	0.0527981i	−0.880864	−	0.473369i	$-0.843038\pi$
$211$	−0.442791	+	0.766937i	−0.0304830	+	0.0527981i	0.850381	+	0.526167i	$0.176371\pi$
$212$		−	4.93246i		−	0.338763i
$213$	18.7877	−	0.317309i	1.28731	−	0.0217416i
$214$	−18.3369			−1.25348
$215$	−2.96902	−	5.14250i	−0.202486	−	0.350715i
$216$	5.18949	−	0.263138i	0.353100	−	0.0179043i
$217$	−12.6359	+	6.10369i	−0.857781	+	0.414346i
$218$	12.2738	−	7.08626i	0.831284	−	0.479942i
$219$	−5.48325	+	9.87886i	−0.370524	+	0.667551i
$220$	−1.81100	+	1.04558i	−0.122098	+	0.0704931i
$221$	1.19251	−	0.688493i	0.0802166	−	0.0463131i
$222$	6.69061	−	0.112999i	0.449045	−	0.00758399i
$223$	0.0602532	−	0.0347872i	0.00403485	−	0.00232952i	−0.497981	−	0.867188i	$-0.665925\pi$
$223$	0.0602532	−	0.0347872i	0.00403485	−	0.00232952i	0.502016	+	0.864858i	$0.332592\pi$
$224$	−2.38237	+	1.15079i	−0.159179	+	0.0768903i
$225$	−2.99829	+	0.101306i	−0.199886	+	0.00675374i
$226$	3.99113	+	6.91284i	0.265486	+	0.459835i
$227$	−18.3801			−1.21993			−0.609964	−	0.792429i	$-0.708816\pi$
$227$	−18.3801			−1.21993			−0.609964	+	0.792429i	$0.708816\pi$
$228$	−3.91574	+	7.05476i	−0.259326	+	0.467213i
$229$		−	16.0697i		−	1.06192i	−0.847398	−	0.530958i	$-0.821832\pi$
$229$		−	16.0697i		−	1.06192i	0.847398	−	0.530958i	$-0.178168\pi$
$230$	1.01382	−	1.75599i	0.0668492	−	0.115786i
$231$	−9.56750	−	0.543258i	−0.629495	−	0.0357438i
$232$	1.58735	+	2.74938i	0.104215	+	0.180506i
$233$	−22.4677	+	12.9717i	−1.47191	+	0.849808i	−0.999501	−	0.0315722i	$-0.989949\pi$
$233$	−22.4677	+	12.9717i	−1.47191	+	0.849808i	−0.472408	+	0.881380i	$0.656615\pi$
$234$	0.758190	+	1.21642i	0.0495644	+	0.0795197i
$235$	0.0525367	−	0.0909962i	0.00342711	−	0.00593593i
$236$	−1.40971	+	2.44169i	−0.0917643	+	0.158941i
$237$	23.6785	+	13.1427i	1.53808	+	0.853712i
$238$	−6.86601	+	3.31658i	−0.445058	+	0.214982i
$239$	−8.46444	−	4.88695i	−0.547519	−	0.316110i	0.200602	−	0.979673i	$-0.435710\pi$
$239$	−8.46444	−	4.88695i	−0.547519	−	0.316110i	−0.748121	+	0.663563i	$0.769044\pi$
$240$	−1.51441	−	0.840572i	−0.0977548	−	0.0542587i
$241$			25.6104i			1.64971i	0.565345	+	0.824854i	$0.308743\pi$
$241$			25.6104i			1.64971i	−0.565345	+	0.824854i	$0.691257\pi$
$242$	5.73918	+	3.31352i	0.368929	+	0.213001i
$243$	1.31469	+	15.5329i	0.0843375	+	0.996437i
$244$			4.29310i			0.274838i
$245$	6.92428	+	1.02680i	0.442376	+	0.0655997i
$246$	−7.19934	−	11.9971i	−0.459013	−	0.764906i
$247$	−2.22573			−0.141620
$248$	−2.65196	−	4.59333i	−0.168400	−	0.291677i
$249$	−16.6027	+	9.96311i	−1.05215	+	0.631386i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	−8.02626			−0.506613			−0.253307	−	0.967386i	$-0.581518\pi$
$251$	−8.02626			−0.506613			−0.253307	+	0.967386i	$0.581518\pi$
$252$	−3.69174	−	7.02645i	−0.232558	−	0.442625i
$253$	4.24012			0.266574
$254$	0.389447	+	0.224847i	0.0244361	+	0.0141082i
$255$	−4.36455	−	2.42254i	−0.273318	−	0.151705i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.25239			−0.0781216			−0.0390608	−	0.999237i	$-0.512437\pi$
$257$	−1.25239			−0.0781216			−0.0390608	+	0.999237i	$0.512437\pi$
$258$	10.2835	−	0.173680i	0.640225	−	0.0108129i
$259$	−4.44593	−	9.20400i	−0.276257	−	0.571908i
$260$		−	0.477787i		−	0.0296311i
$261$	−8.08262	+	5.03788i	−0.500302	+	0.311837i
$262$	−9.04374	−	5.22140i	−0.558724	−	0.322579i
$263$		−	7.23219i		−	0.445956i	−0.974824	−	0.222978i	$-0.928422\pi$
$263$		−	7.23219i		−	0.445956i	0.974824	−	0.222978i	$-0.0715778\pi$
$264$	−0.0611638	−	3.62148i	−0.00376437	−	0.222887i
$265$	−4.27164	−	2.46623i	−0.262405	−	0.151499i
$266$	12.2917	+	0.906405i	0.753649	+	0.0555753i
$267$	19.5762	−	11.7475i	1.19804	−	0.718936i
$268$	2.73588	−	4.73867i	0.167120	−	0.289461i
$269$	5.65912	−	9.80188i	0.345043	−	0.597631i	−0.640319	−	0.768109i	$-0.721198\pi$
$269$	5.65912	−	9.80188i	0.345043	−	0.597631i	0.985362	+	0.170478i	$0.0545311\pi$
$270$	2.36686	−	4.62580i	0.144042	−	0.281517i
$271$	3.52208	−	2.03347i	0.213951	−	0.123525i	−0.389195	−	0.921155i	$-0.627247\pi$
$271$	3.52208	−	2.03347i	0.213951	−	0.123525i	0.603146	+	0.797631i	$0.293914\pi$
$272$	−1.44100	−	2.49589i	−0.0873737	−	0.151336i
$273$	1.20048	−	1.83105i	0.0726564	−	0.110820i
$274$	−8.71743	+	15.0990i	−0.526639	+	0.912165i
$275$			2.09116i			0.126102i
$276$	1.80710	+	3.01137i	0.108774	+	0.181263i
$277$	−3.69051			−0.221741			−0.110871	−	0.993835i	$-0.535364\pi$
$277$	−3.69051			−0.221741			−0.110871	+	0.993835i	$0.535364\pi$
$278$	6.41827	+	11.1168i	0.384942	+	0.666739i
$279$	13.5035	−	8.41668i	0.808432	−	0.503893i
$280$	−0.194573	+	2.63859i	−0.0116280	+	0.157686i
$281$	21.3133	−	12.3052i	1.27144	−	0.734068i	0.296184	−	0.955131i	$-0.404286\pi$
$281$	21.3133	−	12.3052i	1.27144	−	0.734068i	0.975260	+	0.221063i	$0.0709527\pi$
$282$	0.0936447	+	0.156051i	0.00557646	+	0.00929269i
$283$	−1.56082	+	0.901139i	−0.0927810	+	0.0535671i	−0.545673	−	0.837998i	$-0.683726\pi$
$283$	−1.56082	+	0.901139i	−0.0927810	+	0.0535671i	0.452892	+	0.891566i	$0.350392\pi$
$284$	9.39519	−	5.42432i	0.557502	−	0.321874i
$285$	4.15173	+	6.91851i	0.245928	+	0.409817i
$286$	0.865272	−	0.499565i	0.0511646	−	0.0295399i
$287$	−12.0184	+	17.6729i	−0.709423	+	1.04320i
$288$	2.54594	−	1.58688i	0.150021	−	0.0935077i
$289$	4.34701	+	7.52924i	0.255707	+	0.442897i
$290$	3.17471			0.186425
$291$	8.21444	+	13.6887i	0.481539	+	0.802443i
$292$			6.52324i			0.381744i
$293$	−11.8910	+	20.5959i	−0.694682	+	1.20322i	0.275606	+	0.961271i	$0.411121\pi$
$293$	−11.8910	+	20.5959i	−0.694682	+	1.20322i	−0.970288	+	0.241953i	$0.922212\pi$
$294$	−7.37535	+	9.62311i	−0.430139	+	0.561231i
$295$	1.40971	+	2.44169i	0.0820765	+	0.142161i
$296$	3.34578	−	1.93169i	0.194470	−	0.112277i
$297$	10.8521	−	0.550265i	0.629700	−	0.0319296i
$298$	0.595458	−	1.03136i	0.0344940	−	0.0597453i
$299$	−0.484389	+	0.838987i	−0.0280130	+	0.0485199i
$300$	−1.48516	+	0.891232i	−0.0857459	+	0.0514553i
$301$	−6.83343	−	14.1466i	−0.393872	−	0.815398i
$302$	1.37135	+	0.791747i	0.0789121	+	0.0455599i
$303$	0.551722	+	32.6672i	0.0316956	+	1.87668i
$304$			4.65842i			0.267179i
$305$	3.71793	+	2.14655i	0.212888	+	0.122911i
$306$	7.33743	−	4.57340i	0.419453	−	0.261444i
$307$		−	5.99873i		−	0.342366i	−0.985239	−	0.171183i	$-0.945241\pi$
$307$		−	5.99873i		−	0.342366i	0.985239	−	0.171183i	$-0.0547589\pi$
$308$	−4.98192	+	2.40649i	−0.283871	+	0.137122i
$309$	17.5913	−	0.297102i	1.00073	−	0.0169015i
$310$	−5.30392			−0.301243
$311$	−11.8641	−	20.5493i	−0.672753	−	1.16524i	−0.977120	−	0.212688i	$-0.931778\pi$
$311$	−11.8641	−	20.5493i	−0.672753	−	1.16524i	0.304367	−	0.952555i	$-0.401555\pi$
$312$	0.723566	+	0.401614i	0.0409638	+	0.0227369i
$313$	2.56825	+	1.48278i	0.145166	+	0.0838116i	0.570824	−	0.821073i	$-0.306624\pi$
$313$	2.56825	+	1.48278i	0.145166	+	0.0838116i	−0.425658	+	0.904884i	$0.639957\pi$
$314$	−16.8217			−0.949304
$315$	−7.93096	−	0.316082i	−0.446859	−	0.0178092i
$316$	15.6355			0.879563
$317$	−11.2152	−	6.47508i	−0.629906	−	0.363677i	0.150809	−	0.988563i	$-0.451812\pi$
$317$	−11.2152	−	6.47508i	−0.629906	−	0.363677i	−0.780716	+	0.624886i	$0.785145\pi$
$318$	7.32551	−	4.39597i	0.410794	−	0.246514i
$319$	3.31942	+	5.74940i	0.185852	+	0.321904i
$320$	−1.00000			−0.0559017
$321$	−16.3424	−	27.2332i	−0.912144	−	1.52001i
$322$	3.01672	−	4.43606i	0.168115	−	0.247212i
$323$			13.4256i			0.747021i
$324$	5.01584	+	7.47271i	0.278658	+	0.415150i
$325$	−0.413776	−	0.238893i	−0.0229521	−	0.0132514i
$326$		−	10.0327i		−	0.555662i
$327$	21.4630	+	11.9130i	1.18691	+	0.658792i
$328$	−6.99572	−	4.03898i	−0.386274	−	0.223015i
$329$	0.156328	−	0.229879i	0.00861864	−	0.0126736i
$330$	−3.16688	−	1.75777i	−0.174331	−	0.0967622i
$331$	−17.0020	+	29.4483i	−0.934514	+	1.61863i	−0.159016	+	0.987276i	$0.550832\pi$
$331$	−17.0020	+	29.4483i	−0.934514	+	1.61863i	−0.775498	+	0.631350i	$0.782501\pi$
$332$	−5.58951	+	9.68132i	−0.306764	+	0.531332i
$333$	6.13071	+	9.83593i	0.335961	+	0.539006i
$334$	12.4194	−	7.17037i	0.679562	−	0.392345i
$335$	−2.73588	−	4.73867i	−0.149477	−	0.258901i
$336$	−3.83235	−	2.51259i	−0.209072	−	0.137073i
$337$	11.3157	−	19.5993i	0.616403	−	1.06764i	−0.373734	−	0.927536i	$-0.621923\pi$
$337$	11.3157	−	19.5993i	0.616403	−	1.06764i	0.990137	−	0.140105i	$-0.0447440\pi$
$338$		−	12.7717i		−	0.694690i
$339$	−6.70966	+	12.0884i	−0.364419	+	0.656553i
$340$	−2.88201			−0.156299
$341$	−5.54568	−	9.60541i	−0.300316	−	0.520162i
$342$	−13.9673	+	0.471926i	−0.755265	+	0.0255189i
$343$	18.0705	+	4.05658i	0.975717	+	0.219035i
$344$	5.14250	−	2.96902i	0.277265	−	0.160079i
$345$	3.51147	−	0.0593058i	0.189051	−	0.00319292i
$346$	−13.9658	+	8.06316i	−0.750806	+	0.433478i
$347$	11.0660	−	6.38896i	0.594054	−	0.342977i	−0.172645	−	0.984984i	$-0.555231\pi$
$347$	11.0660	−	6.38896i	0.594054	−	0.342977i	0.766699	+	0.642007i	$0.221898\pi$
$348$	−2.66857	+	4.80781i	−0.143050	+	0.257726i
$349$	−3.95316	+	2.28236i	−0.211608	+	0.122172i	−0.602058	−	0.798452i	$-0.705653\pi$
$349$	−3.95316	+	2.28236i	−0.211608	+	0.122172i	0.390451	+	0.920624i	$0.372319\pi$
$350$	2.18780	+	1.48780i	0.116943	+	0.0795262i
$351$	−1.13085	+	2.21014i	−0.0603605	+	0.117969i
$352$	−1.04558	−	1.81100i	−0.0557297	−	0.0965266i
$353$	15.9021			0.846384			0.423192	−	0.906040i	$-0.360910\pi$
$353$	15.9021			0.846384			0.423192	+	0.906040i	$0.360910\pi$
$354$	−4.88268	+	0.0824644i	−0.259512	+	0.00438294i
$355$		−	10.8486i		−	0.575786i
$356$	6.59060	−	11.4153i	0.349301	−	0.605007i
$357$	−11.0449	−	7.24130i	−0.584557	−	0.383250i
$358$	0.0483526	+	0.0837491i	0.00255551	+	0.00442628i
$359$	−17.0237	+	9.82867i	−0.898479	+	0.518737i	−0.876706	−	0.481026i	$-0.840264\pi$
$359$	−17.0237	+	9.82867i	−0.898479	+	0.518737i	−0.0217726	+	0.999763i	$0.506931\pi$
$360$	−0.101306	−	2.99829i	−0.00533930	−	0.158024i
$361$	1.35045	−	2.33904i	0.0710761	−	0.123107i
$362$	−10.0469	+	17.4017i	−0.528052	+	0.914614i
$363$	0.193832	+	11.4767i	0.0101736	+	0.602372i
$364$	0.0929646	−	1.26068i	0.00487267	−	0.0660777i
$365$	5.64929	+	3.26162i	0.295697	+	0.170721i
$366$	−6.37595	+	3.82615i	−0.333276	+	0.199996i
$367$			21.9998i			1.14838i	0.818721	+	0.574191i	$0.194683\pi$
$367$			21.9998i			1.14838i	−0.818721	+	0.574191i	$0.805317\pi$
$368$	1.75599	+	1.01382i	0.0915371	+	0.0528490i
$369$	11.4013	−	21.3844i	0.593529	−	1.11323i
$370$		−	3.86338i		−	0.200847i
$371$	−10.7912	−	7.33852i	−0.560253	−	0.380997i
$372$	4.45833	−	8.03232i	0.231154	−	0.416456i
$373$	−23.3319			−1.20808			−0.604041	−	0.796954i	$-0.706444\pi$
$373$	−23.3319			−1.20808			−0.604041	+	0.796954i	$0.706444\pi$
$374$	−3.01338	−	5.21932i	−0.155818	−	0.269885i
$375$	0.0292487	+	1.73180i	0.00151040	+	0.0894300i
$376$	0.0909962	+	0.0525367i	0.00469277	+	0.00270937i
$377$	−1.51683			−0.0781210
$378$	7.14522	−	11.7450i	0.367510	−	0.604099i
$379$	−20.3159			−1.04356			−0.521780	−	0.853080i	$-0.674732\pi$
$379$	−20.3159			−1.04356			−0.521780	+	0.853080i	$0.674732\pi$
$380$	4.03431	+	2.32921i	0.206956	+	0.119486i
$381$	0.0131530	+	0.778782i	0.000673848	+	0.0398982i
$382$	−1.76654	−	3.05974i	−0.0903841	−	0.156550i
$383$	−3.82312			−0.195352			−0.0976762	−	0.995218i	$-0.531141\pi$
$383$	−3.82312			−0.195352			−0.0976762	+	0.995218i	$0.531141\pi$
$384$	0.840572	−	1.51441i	0.0428952	−	0.0772819i
$385$	−0.406885	+	5.51772i	−0.0207368	+	0.281209i
$386$		−	25.3144i		−	1.28847i
$387$	9.42295	+	15.1179i	0.478996	+	0.768487i
$388$	7.98211	+	4.60847i	0.405230	+	0.233960i
$389$			19.3426i			0.980711i	0.871522	+	0.490356i	$0.163133\pi$
$389$			19.3426i			0.980711i	−0.871522	+	0.490356i	$0.836867\pi$
$390$	0.709591	−	0.425819i	0.0359315	−	0.0215622i
$391$	5.06077	+	2.92184i	0.255934	+	0.147764i
$392$	−1.02680	+	6.92428i	−0.0518611	+	0.349729i
$393$	−0.305439	−	18.0849i	−0.0154073	−	0.912262i
$394$	−4.50544	+	7.80365i	−0.226981	+	0.393142i
$395$	7.81773	−	13.5407i	0.393353	−	0.681307i
$396$	5.32398	−	3.31842i	0.267540	−	0.166757i
$397$	−26.2370	+	15.1479i	−1.31680	+	0.760253i	−0.983212	−	0.182467i	$-0.941592\pi$
$397$	−26.2370	+	15.1479i	−1.31680	+	0.760253i	−0.333585	+	0.942720i	$0.608258\pi$
$398$	−7.15296	−	12.3893i	−0.358546	−	0.621019i
$399$	9.60855	+	19.0629i	0.481029	+	0.954339i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$		−	33.0679i		−	1.65133i	−0.564159	−	0.825666i	$-0.690800\pi$
$401$		−	33.0679i		−	1.65133i	0.564159	−	0.825666i	$-0.309200\pi$
$402$	9.47600	−	0.160042i	0.472620	−	0.00798215i
$403$	2.53415			0.126235
$404$	9.43156	+	16.3359i	0.469238	+	0.812743i
$405$	8.97947	−	0.607490i	0.446194	−	0.0301864i
$406$	8.37674	+	0.617714i	0.415731	+	0.0306566i
$407$	6.99658	−	4.03948i	0.346808	−	0.200229i
$408$	2.42254	−	4.36455i	0.119933	−	0.216077i
$409$	−14.7421	+	8.51133i	−0.728948	+	0.420858i	−0.818037	−	0.575165i	$-0.804938\pi$
$409$	−14.7421	+	8.51133i	−0.728948	+	0.420858i	0.0890894	+	0.996024i	$0.471604\pi$
$410$	−6.99572	+	4.03898i	−0.345494	+	0.199471i
$411$	−30.1937	+	0.509947i	−1.48935	+	0.0251538i
$412$	8.79688	−	5.07888i	0.433391	−	0.250219i
$413$	3.24456	+	6.71690i	0.159654	+	0.330517i
$414$	−2.86183	+	5.36766i	−0.140651	+	0.263806i
$415$	5.58951	+	9.68132i	0.274378	+	0.475237i
$416$	0.477787			0.0234254
$417$	−10.7900	+	19.4398i	−0.528390	+	0.951970i
$418$			9.74152i			0.476473i
$419$	−3.89228	+	6.74162i	−0.190150	+	0.329350i	−0.945300	−	0.326203i	$-0.894231\pi$
$419$	−3.89228	+	6.74162i	−0.190150	+	0.329350i	0.755150	+	0.655552i	$0.227564\pi$
$420$	−4.09214	+	2.06262i	−0.199676	+	0.100646i
$421$	15.4668	+	26.7894i	0.753808	+	1.30563i	0.945965	+	0.324269i	$0.105118\pi$
$421$	15.4668	+	26.7894i	0.753808	+	1.30563i	−0.192157	+	0.981364i	$0.561548\pi$
$422$	−0.766937	+	0.442791i	−0.0373339	+	0.0215547i
$423$	−0.148302	+	0.278155i	−0.00721067	+	0.0135244i
$424$	2.46623	−	4.27164i	0.119771	−	0.207449i
$425$	−1.44100	+	2.49589i	−0.0698990	+	0.121069i
$426$	16.4293	+	9.11905i	0.796001	+	0.441820i
$427$	9.39243	+	6.38727i	0.454532	+	0.309102i
$428$	−15.8802	−	9.16843i	−0.767598	−	0.443173i
$429$	1.51309	+	0.839841i	0.0730528	+	0.0405479i
$430$		−	5.93804i		−	0.286358i
$431$	17.0026	+	9.81647i	0.818988	+	0.472843i	0.850067	−	0.526674i	$-0.176561\pi$
$431$	17.0026	+	9.81647i	0.818988	+	0.472843i	−0.0310795	+	0.999517i	$0.509895\pi$
$432$	4.62580	+	2.36686i	0.222559	+	0.113876i
$433$			35.9562i			1.72794i	0.503540	+	0.863972i	$0.332031\pi$
$433$			35.9562i			1.72794i	−0.503540	+	0.863972i	$0.667969\pi$
$434$	−13.9949	−	1.03200i	−0.671775	−	0.0495377i
$435$	2.82940	+	4.71496i	0.135659	+	0.226065i
$436$	14.1725			0.678741
$437$	−4.72280	−	8.18012i	−0.225922	−	0.391308i
$438$	−9.68806	+	5.81372i	−0.462913	+	0.277790i
$439$	21.0814	+	12.1713i	1.00616	+	0.580906i	0.910065	−	0.414467i	$-0.136032\pi$
$439$	21.0814	+	12.1713i	1.00616	+	0.580906i	0.0960937	+	0.995372i	$0.469365\pi$
$440$	−2.09116			−0.0996923
$441$	−20.8650	−	2.37716i	−0.993572	−	0.113198i
$442$	1.37699			0.0654966
$443$	−5.14619	−	2.97116i	−0.244503	−	0.141164i	0.372742	−	0.927935i	$-0.378418\pi$
$443$	−5.14619	−	2.97116i	−0.244503	−	0.141164i	−0.617245	+	0.786771i	$0.711751\pi$
$444$	5.85074	+	3.24745i	0.277664	+	0.154117i
$445$	−6.59060	−	11.4153i	−0.312424	−	0.541135i
$446$	0.0695744			0.00329444
$447$	2.06243	−	0.0348328i	0.0975498	−	0.00164753i
$448$	−2.63859	−	0.194573i	−0.124662	−	0.00919273i
$449$			3.59042i			0.169442i	0.996405	+	0.0847211i	$0.0269999\pi$
$449$			3.59042i			0.169442i	−0.996405	+	0.0847211i	$0.973000\pi$
$450$	−2.64725	−	1.41141i	−0.124792	−	0.0665345i
$451$	−14.6292	−	8.44617i	−0.688862	−	0.397715i
$452$			7.98226i			0.375454i
$453$	0.0463152	+	2.74230i	0.00217608	+	0.128845i
$454$	−15.9176	−	9.19003i	−0.747050	−	0.431310i
$455$	−1.04530	−	0.710851i	−0.0490045	−	0.0333252i
$456$	−6.91851	+	4.15173i	−0.323989	+	0.194423i
$457$	−6.72945	+	11.6558i	−0.314791	+	0.545233i	−0.979393	−	0.201964i	$-0.935268\pi$
$457$	−6.72945	+	11.6558i	−0.314791	+	0.545233i	0.664602	+	0.747197i	$0.268601\pi$
$458$	8.03486	−	13.9168i	0.375444	−	0.650288i
$459$	13.3316	+	6.82131i	0.622265	+	0.318391i
$460$	1.75599	−	1.01382i	0.0818733	−	0.0472695i
$461$	13.5633	+	23.4924i	0.631708	+	1.09415i	0.987202	+	0.159472i	$0.0509791\pi$
$461$	13.5633	+	23.4924i	0.631708	+	1.09415i	−0.355495	+	0.934678i	$0.615688\pi$
$462$	−8.01407	−	5.25423i	−0.372848	−	0.244449i
$463$	−15.9746	+	27.6688i	−0.742403	+	1.28588i	0.208995	+	0.977917i	$0.432981\pi$
$463$	−15.9746	+	27.6688i	−0.742403	+	1.28588i	−0.951398	+	0.307963i	$0.900353\pi$
$464$			3.17471i			0.147382i
$465$	−4.72703	−	7.87718i	−0.219211	−	0.365296i
$466$	−25.9435			−1.20181
$467$	−18.4026	−	31.8743i	−0.851572	−	1.47497i	−0.879789	−	0.475364i	$-0.842316\pi$
$467$	−18.4026	−	31.8743i	−0.851572	−	1.47497i	0.0282177	−	0.999602i	$-0.491017\pi$
$468$	0.0484027	+	1.43254i	0.00223742	+	0.0662193i
$469$	−6.29682	−	13.0357i	−0.290760	−	0.601934i
$470$	0.0909962	−	0.0525367i	0.00419734	−	0.00242334i
$471$	−14.9920	−	24.9830i	−0.690797	−	1.15115i
$472$	−2.44169	+	1.40971i	−0.112388	+	0.0648872i
$473$	10.7538	−	6.20871i	0.494460	−	0.285477i
$474$	13.9348	+	23.2212i	0.640048	+	1.06658i
$475$	4.03431	−	2.32921i	0.185107	−	0.106872i
$476$	−7.60443	−	0.560762i	−0.348549	−	0.0257025i
$477$	13.0575	+	6.96173i	0.597860	+	0.318756i
$478$	−4.88695	−	8.46444i	−0.223524	−	0.387155i
$479$	−17.6491			−0.806406			−0.403203	−	0.915110i	$-0.632103\pi$
$479$	−17.6491			−0.806406			−0.403203	+	0.915110i	$0.632103\pi$
$480$	−0.891232	−	1.48516i	−0.0406790	−	0.0677880i
$481$			1.84587i			0.0841645i
$482$	−12.8052	+	22.1792i	−0.583260	+	1.01024i
$483$	9.27686	+	0.526755i	0.422112	+	0.0239682i
$484$	3.31352	+	5.73918i	0.150614	+	0.260872i
$485$	7.98211	−	4.60847i	0.362449	−	0.209260i
$486$	−6.62790	+	14.1092i	−0.300648	+	0.640009i
$487$	5.44521	−	9.43137i	0.246746	−	0.427376i	−0.715875	−	0.698228i	$-0.753972\pi$
$487$	5.44521	−	9.43137i	0.246746	−	0.427376i	0.962621	+	0.270852i	$0.0873054\pi$
$488$	−2.14655	+	3.71793i	−0.0971698	+	0.168303i
$489$	14.9002	−	8.94149i	0.673812	−	0.404348i
$490$	5.48321	+	4.35137i	0.247706	+	0.196575i
$491$	−21.5186	−	12.4238i	−0.971123	−	0.560678i	−0.0715443	−	0.997437i	$-0.522793\pi$
$491$	−21.5186	−	12.4238i	−0.971123	−	0.560678i	−0.899578	+	0.436760i	$0.856126\pi$
$492$	−0.236270	−	13.9894i	−0.0106519	−	0.630693i
$493$			9.14954i			0.412075i
$494$	−1.92754	−	1.11287i	−0.0867242	−	0.0500702i
$495$	−0.211848	−	6.26991i	−0.00952184	−	0.281812i
$496$		−	5.30392i		−	0.238153i
$497$	2.11086	−	28.6251i	0.0946848	−	1.28401i
$498$	−19.3599	+	0.326972i	−0.867537	+	0.0146520i
$499$	36.8849			1.65119			0.825597	−	0.564261i	$-0.190839\pi$
$499$	36.8849			1.65119			0.825597	+	0.564261i	$0.190839\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	21.7178	+	12.0544i	0.970278	+	0.538552i
$502$	−6.95095	−	4.01313i	−0.310236	−	0.179115i
$503$	4.02007			0.179246			0.0896231	−	0.995976i	$-0.471434\pi$
$503$	4.02007			0.179246			0.0896231	+	0.995976i	$0.471434\pi$
$504$	0.316082	−	7.93096i	0.0140794	−	0.353273i
$505$	18.8631			0.839398
$506$	3.67205	+	2.12006i	0.163243	+	0.0942482i
$507$	18.9681	−	11.3826i	0.842402	−	0.505517i
$508$	0.224847	+	0.389447i	0.00997598	+	0.0172789i
$509$	24.2483			1.07479			0.537394	−	0.843331i	$-0.319409\pi$
$509$	24.2483			1.07479			0.537394	+	0.843331i	$0.319409\pi$
$510$	−2.56854	−	4.28025i	−0.113737	−	0.189533i
$511$	14.2715	+	9.70527i	0.631335	+	0.429336i
$512$		−	1.00000i		−	0.0441942i
$513$	−13.1490	−	20.3231i	−0.580542	−	0.897287i
$514$	−1.08460	−	0.626193i	−0.0478395	−	0.0276202i
$515$		−	10.1578i		−	0.447605i
$516$	8.99264	+	4.99135i	0.395879	+	0.219732i
$517$	0.190288	+	0.109863i	0.00836885	+	0.00483176i
$518$	0.751711	−	10.1939i	0.0330283	−	0.447892i
$519$	−24.4219	−	13.5553i	−1.07200	−	0.595013i
$520$	0.238893	−	0.413776i	0.0104762	−	0.0181453i
$521$	20.9866	−	36.3499i	0.919440	−	1.59252i	0.119173	−	0.992874i	$-0.461976\pi$
$521$	20.9866	−	36.3499i	0.919440	−	1.59252i	0.800267	−	0.599643i	$-0.204691\pi$
$522$	−9.51869	+	0.321617i	−0.416622	+	0.0140768i
$523$	−2.05664	+	1.18740i	−0.0899304	+	0.0519213i	−0.544291	−	0.838897i	$-0.683201\pi$
$523$	−2.05664	+	1.18740i	−0.0899304	+	0.0519213i	0.454360	+	0.890818i	$0.349868\pi$
$524$	−5.22140	−	9.04374i	−0.228098	−	0.395077i
$525$	−0.259788	+	4.57521i	−0.0113381	+	0.199678i
$526$	3.61609	−	6.26326i	0.157669	−	0.273091i
$527$		−	15.2860i		−	0.665867i
$528$	1.75777	−	3.16688i	0.0764972	−	0.137821i
$529$	18.8887			0.821247
$530$	−2.46623	−	4.27164i	−0.107126	−	0.185548i
$531$	−4.47408	−	7.17808i	−0.194158	−	0.311502i
$532$	10.1917	+	6.93079i	0.441865	+	0.300488i
$533$	3.34246	−	1.92977i	0.144778	−	0.0835877i
$534$	22.8273	−	0.385533i	0.987832	−	0.0166837i
$535$	−15.8802	+	9.16843i	−0.686560	+	0.396386i
$536$	4.73867	−	2.73588i	0.204680	−	0.118172i
$537$	−0.0812876	+	0.146451i	−0.00350782	+	0.00631984i
$538$	9.80188	−	5.65912i	0.422589	−	0.243982i
$539$	−2.14720	+	14.4798i	−0.0924865	+	0.623689i
$540$	4.36266	−	2.82263i	0.187739	−	0.121467i
$541$	−4.57807	−	7.92946i	−0.196827	−	0.340914i	0.750671	−	0.660676i	$-0.229730\pi$
$541$	−4.57807	−	7.92946i	−0.196827	−	0.340914i	−0.947498	+	0.319762i	$0.896397\pi$
$542$	4.06694			0.174690
$543$	−34.7985	+	0.587717i	−1.49334	+	0.0252213i
$544$		−	2.88201i		−	0.123565i
$545$	7.08626	−	12.2738i	0.303542	−	0.525750i
$546$	1.95517	−	0.985493i	0.0836736	−	0.0421752i
$547$	−23.0072	−	39.8496i	−0.983717	−	1.70385i	−0.647505	−	0.762061i	$-0.724187\pi$
$547$	−23.0072	−	39.8496i	−0.983717	−	1.70385i	−0.336212	−	0.941786i	$-0.609146\pi$
$548$	−15.0990	+	8.71743i	−0.644998	+	0.372390i
$549$	−11.3649	−	6.05933i	−0.485042	−	0.258606i
$550$	−1.04558	+	1.81100i	−0.0445837	+	0.0772213i
$551$	7.39457	−	12.8078i	0.315019	−	0.545629i
$552$	0.0593058	+	3.51147i	0.00252422	+	0.149458i
$553$	23.2624	−	34.2072i	0.989219	−	1.45464i
$554$	−3.19608	−	1.84526i	−0.135788	−	0.0783974i
$555$	5.73774	−	3.44317i	0.243554	−	0.146154i
$556$			12.8365i			0.544390i
$557$	16.7682	+	9.68111i	0.710490	+	0.410202i	0.811242	−	0.584710i	$-0.198792\pi$
$557$	16.7682	+	9.68111i	0.710490	+	0.410202i	−0.100752	+	0.994912i	$0.532125\pi$
$558$	15.9027	−	0.537320i	0.673215	−	0.0227466i
$559$			2.83712i			0.119997i
$560$	−1.48780	+	2.18780i	−0.0628710	+	0.0924513i
$561$	5.06592	−	9.12698i	0.213883	−	0.385341i
$562$	24.6104			1.03813
$563$	−10.8619	−	18.8134i	−0.457775	−	0.792889i	0.541068	−	0.840979i	$-0.318020\pi$
$563$	−10.8619	−	18.8134i	−0.457775	−	0.792889i	−0.998843	+	0.0480895i	$0.984687\pi$
$564$	0.00307326	+	0.181966i	0.000129408	+	0.00766217i
$565$	6.91284	+	3.99113i	0.290825	+	0.167908i
$566$	−1.80228			−0.0757554
$567$	23.8113	+	0.144252i	0.999982	+	0.00605803i
$568$	10.8486			0.455198
$569$	18.3585	+	10.5993i	0.769629	+	0.444346i	0.832742	−	0.553661i	$-0.186770\pi$
$569$	18.3585	+	10.5993i	0.769629	+	0.444346i	−0.0631131	+	0.998006i	$0.520103\pi$
$570$	0.136253	+	8.06747i	0.00570700	+	0.337909i
$571$	5.52866	+	9.57592i	0.231367	+	0.400740i	0.958211	−	0.286063i	$-0.0923468\pi$
$571$	5.52866	+	9.57592i	0.231367	+	0.400740i	−0.726843	+	0.686803i	$0.759013\pi$
$572$	0.999130			0.0417757
$573$	2.96981	−	5.35053i	0.124066	−	0.223522i
$574$	−19.2447	+	9.29602i	−0.803258	+	0.388008i
$575$		−	2.02764i		−	0.0845583i
$576$	2.99829	−	0.101306i	0.124929	−	0.00422109i
$577$	−27.5702	−	15.9177i	−1.14776	−	0.662662i	−0.199423	−	0.979914i	$-0.563907\pi$
$577$	−27.5702	−	15.9177i	−1.14776	−	0.662662i	−0.948341	+	0.317251i	$0.897240\pi$
$578$			8.69402i			0.361624i
$579$	37.5959	−	22.5610i	1.56243	−	0.937602i
$580$	2.74938	+	1.58735i	0.114162	+	0.0659113i
$581$	12.8647	+	26.6326i	0.533717	+	1.10491i
$582$	0.269584	+	15.9619i	0.0111746	+	0.661644i
$583$	5.15729	−	8.93269i	0.213593	−	0.369954i
$584$	−3.26162	+	5.64929i	−0.134967	+	0.233769i
$585$	1.26482	+	0.674354i	0.0522939	+	0.0278811i
$586$	−20.5959	+	11.8910i	−0.850808	+	0.491214i
$587$	−14.7632	−	25.5706i	−0.609343	−	1.05541i	−0.991349	−	0.131253i	$-0.958100\pi$
$587$	−14.7632	−	25.5706i	−0.609343	−	1.05541i	0.382006	−	0.924160i	$-0.375233\pi$
$588$	−11.1988	+	4.64618i	−0.461830	+	0.191605i
$589$	−12.3540	+	21.3977i	−0.509036	+	0.881676i
$590$			2.81942i			0.116074i
$591$	−15.6051	+	0.263557i	−0.641907	+	0.0108413i
$592$	3.86338			0.158784
$593$	−10.9772	−	19.0131i	−0.450780	−	0.780773i	0.547655	−	0.836704i	$-0.315521\pi$
$593$	−10.9772	−	19.0131i	−0.450780	−	0.780773i	−0.998435	+	0.0559309i	$0.982187\pi$
$594$	9.67329	+	4.94949i	0.396900	+	0.203080i
$595$	−4.28785	+	6.30525i	−0.175785	+	0.258490i
$596$	1.03136	−	0.595458i	0.0422463	−	0.0243909i
$597$	12.0252	−	21.6650i	0.492157	−	0.886691i
$598$	−0.838987	+	0.484389i	−0.0343087	+	0.0198082i
$599$	23.0407	−	13.3026i	0.941418	−	0.543528i	0.0510136	−	0.998698i	$-0.483755\pi$
$599$	23.0407	−	13.3026i	0.941418	−	0.543528i	0.890405	+	0.455170i	$0.150421\pi$
$600$	−1.73180	+	0.0292487i	−0.0707006	+	0.00119407i
$601$	−33.3026	+	19.2273i	−1.35844	+	0.784296i	−0.989414	−	0.145122i	$-0.953642\pi$
$601$	−33.3026	+	19.2273i	−1.35844	+	0.784296i	−0.369027	+	0.929419i	$0.620309\pi$
$602$	1.15539	−	15.6680i	0.0470900	−	0.638582i
$603$	8.68300	+	13.9308i	0.353599	+	0.567304i
$604$	0.791747	+	1.37135i	0.0322157	+	0.0557993i
$605$	6.62704			0.269427
$606$	−15.8558	+	28.5665i	−0.644098	+	1.16043i
$607$		−	23.5753i		−	0.956893i	−0.878117	−	0.478446i	$-0.841200\pi$
$607$		−	23.5753i		−	0.956893i	0.878117	−	0.478446i	$-0.158800\pi$
$608$	−2.32921	+	4.03431i	−0.0944620	+	0.163613i
$609$	6.54822	+	12.9913i	0.265347	+	0.526436i
$610$	2.14655	+	3.71793i	0.0869113	+	0.150535i
$611$	−0.0434768	+	0.0251013i	−0.00175888	+	0.00101549i
$612$	8.64110	−	0.291965i	0.349296	−	0.0118020i
$613$	−7.77138	+	13.4604i	−0.313883	+	0.543661i	−0.979199	−	0.202900i	$-0.934963\pi$
$613$	−7.77138	+	13.4604i	−0.313883	+	0.543661i	0.665316	+	0.746561i	$0.268297\pi$
$614$	2.99936	−	5.19505i	0.121044	−	0.209655i
$615$	−12.2334	−	6.79011i	−0.493296	−	0.273804i
$616$	−5.51772	−	0.406885i	−0.222315	−	0.0163939i
$617$	−11.7195	−	6.76627i	−0.471810	−	0.272400i	0.245187	−	0.969476i	$-0.421151\pi$
$617$	−11.7195	−	6.76627i	−0.471810	−	0.272400i	−0.716997	+	0.697076i	$0.754484\pi$
$618$	15.3830	+	8.53833i	0.618796	+	0.343462i
$619$			23.6194i			0.949345i	0.880163	+	0.474672i	$0.157433\pi$
$619$			23.6194i			0.949345i	−0.880163	+	0.474672i	$0.842567\pi$
$620$	−4.59333	−	2.65196i	−0.184473	−	0.106505i
$621$	−10.5224	+	0.533549i	−0.422249	+	0.0214106i
$622$		−	23.7283i		−	0.951416i
$623$	−15.1688	−	31.4025i	−0.607724	−	1.25811i
$624$	0.425819	+	0.709591i	0.0170464	+	0.0284064i
$625$	1.00000			0.0400000
$626$	1.48278	+	2.56825i	0.0592637	+	0.102648i
$627$	−14.4677	+	8.68195i	−0.577786	+	0.346724i
$628$	−14.5680	−	8.41085i	−0.581328	−	0.335630i
$629$	11.1343			0.443953
$630$	−6.71037	−	4.23921i	−0.267348	−	0.168894i
$631$	29.0626			1.15696			0.578482	−	0.815695i	$-0.303645\pi$
$631$	29.0626			1.15696			0.578482	+	0.815695i	$0.303645\pi$
$632$	13.5407	+	7.81773i	0.538620	+	0.310973i
$633$	−1.34113	−	0.744395i	−0.0533053	−	0.0295871i
$634$	−6.47508	−	11.2152i	−0.257158	−	0.445411i
$635$	0.449694			0.0178456
$636$	8.54206	−	0.144268i	0.338715	−	0.00572061i
$637$	−2.61980	−	2.07903i	−0.103800	−	0.0823742i
$638$			6.63883i			0.262834i
$639$	1.09903	+	32.5273i	0.0434770	+	1.28676i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$		−	5.47596i		−	0.216288i	−0.994135	−	0.108144i	$-0.965509\pi$
$641$		−	5.47596i		−	0.216288i	0.994135	−	0.108144i	$-0.0344907\pi$
$642$	−0.536330	−	31.7558i	−0.0211672	−	1.25330i
$643$	22.6584	+	13.0818i	0.893560	+	0.515897i	0.875105	−	0.483933i	$-0.160792\pi$
$643$	22.6584	+	13.0818i	0.893560	+	0.515897i	0.0184548	+	0.999830i	$0.494125\pi$
$644$	4.83058	−	2.33338i	0.190352	−	0.0919481i
$645$	8.81896	−	5.29218i	0.347246	−	0.208379i
$646$	−6.71281	+	11.6269i	−0.264112	+	0.457455i
$647$	7.13123	−	12.3517i	0.280358	−	0.485594i	−0.691115	−	0.722745i	$-0.742880\pi$
$647$	7.13123	−	12.3517i	0.280358	−	0.485594i	0.971473	+	0.237151i	$0.0762136\pi$
$648$	0.607490	+	8.97947i	0.0238645	+	0.352747i
$649$	−5.10597	+	2.94793i	−0.200427	+	0.115717i
$650$	−0.238893	−	0.413776i	−0.00937017	−	0.0162296i
$651$	−10.9400	−	21.7044i	−0.428772	−	0.850662i
$652$	5.01637	−	8.68860i	0.196456	−	0.340272i
$653$		−	14.4155i		−	0.564123i	−0.959396	−	0.282062i	$-0.908982\pi$
$653$		−	14.4155i		−	0.564123i	0.959396	−	0.282062i	$-0.0910183\pi$
$654$	12.6310	+	21.0485i	0.493912	+	0.823061i
$655$	−10.4428			−0.408034
$656$	−4.03898	−	6.99572i	−0.157696	−	0.273137i
$657$	−17.2686	−	9.20697i	−0.673713	−	0.359198i
$658$	0.250324	−	0.120917i	0.00975863	−	0.00471384i
$659$	−23.0675	+	13.3180i	−0.898581	+	0.518796i	−0.876739	−	0.480966i	$-0.840286\pi$
$659$	−23.0675	+	13.3180i	−0.898581	+	0.518796i	−0.0218413	+	0.999761i	$0.506953\pi$
$660$	−1.86371	−	3.10572i	−0.0725449	−	0.120890i
$661$	10.9321	−	6.31167i	0.425211	−	0.245496i	−0.272093	−	0.962271i	$-0.587716\pi$
$661$	10.9321	−	6.31167i	0.425211	−	0.245496i	0.697304	+	0.716775i	$0.254383\pi$
$662$	−29.4483	+	17.0020i	−1.14454	+	0.660801i
$663$	1.22721	+	2.04505i	0.0476611	+	0.0794231i
$664$	−9.68132	+	5.58951i	−0.375708	+	0.216915i
$665$	11.0981	−	5.36086i	0.430365	−	0.207885i
$666$	0.391384	+	11.5835i	0.0151658	+	0.448852i
$667$	−3.21858	−	5.57474i	−0.124624	−	0.215855i
$668$	14.3407			0.554860
$669$	0.0620069	+	0.103329i	0.00239733	+	0.00399494i
$670$		−	5.47175i		−	0.211392i
$671$	−4.48879	+	7.77481i	−0.173288	+	0.300143i
$672$	−2.06262	−	4.09214i	−0.0795673	−	0.157858i
$673$	−1.51712	−	2.62772i	−0.0584805	−	0.101291i	0.835303	−	0.549790i	$-0.185292\pi$
$673$	−1.51712	−	2.62772i	−0.0584805	−	0.101291i	−0.893784	+	0.448499i	$0.851959\pi$
$674$	19.5993	−	11.3157i	0.754936	−	0.435863i
$675$	−0.263138	−	5.18949i	−0.0101282	−	0.199743i
$676$	6.38586	−	11.0606i	0.245610	−	0.425409i
$677$	−5.58739	+	9.67764i	−0.214741	+	0.371942i	−0.953192	−	0.302365i	$-0.902224\pi$
$677$	−5.58739	+	9.67764i	−0.214741	+	0.371942i	0.738452	+	0.674306i	$0.235557\pi$
$678$	−11.8549	+	7.11405i	−0.455287	+	0.273213i
$679$	21.9582	−	10.6068i	0.842677	−	0.407050i
$680$	−2.49589	−	1.44100i	−0.0957131	−	0.0552600i
$681$	−0.537593	−	31.8307i	−0.0206006	−	1.21975i
$682$		−	11.0914i		−	0.424710i
$683$	23.9631	+	13.8351i	0.916924	+	0.529387i	0.882653	−	0.470026i	$-0.155755\pi$
$683$	23.9631	+	13.8351i	0.916924	+	0.529387i	0.0342719	+	0.999413i	$0.489089\pi$
$684$	−12.3320	−	6.57495i	−0.471526	−	0.251399i
$685$			17.4349i			0.666151i
$686$	13.6213	+	12.5484i	0.520062	+	0.479099i
$687$	27.8296	−	0.470018i	1.06176	−	0.0179323i
$688$	5.93804			0.226386
$689$	1.17833	+	2.04093i	0.0448909	+	0.0777534i
$690$	3.07068	+	1.70437i	0.116899	+	0.0648844i
$691$	−11.7384	−	6.77716i	−0.446549	−	0.257815i	0.259823	−	0.965656i	$-0.416336\pi$
$691$	−11.7384	−	6.77716i	−0.446549	−	0.257815i	−0.706372	+	0.707841i	$0.749669\pi$
$692$	−16.1263			−0.613031
$693$	0.660980	−	16.5849i	0.0251085	−	0.630009i
$694$	12.7779			0.485043
$695$	11.1168	+	6.41827i	0.421683	+	0.243459i
$696$	−4.71496	+	2.82940i	−0.178720	+	0.107248i
$697$	−11.6404	−	20.1617i	−0.440911	−	0.763680i
$698$	−4.56471			−0.172777
$699$	−23.1217	−	38.5303i	−0.874542	−	1.45735i
$700$	1.15079	+	2.38237i	0.0434957	+	0.0900451i
$701$			45.4060i			1.71496i	0.514516	+	0.857481i	$0.327972\pi$
$701$			45.4060i			1.71496i	−0.514516	+	0.857481i	$0.672028\pi$
$702$	−2.08442	+	1.34861i	−0.0786714	+	0.0509002i
$703$	−15.5861	−	8.99862i	−0.587840	−	0.339389i
$704$		−	2.09116i		−	0.0788137i
$705$	0.159124	+	0.0883217i	0.00599296	+	0.00332639i
$706$	13.7716	+	7.95106i	0.518302	+	0.299242i
$707$	49.7720	+	3.67026i	1.87187	+	0.138034i
$708$	−4.26976	−	2.36993i	−0.160467	−	0.0890673i
$709$	10.2957	−	17.8327i	0.386663	−	0.669719i	−0.605336	−	0.795970i	$-0.706961\pi$
$709$	10.2957	−	17.8327i	0.386663	−	0.669719i	0.991998	+	0.126251i	$0.0402944\pi$
$710$	5.42432	−	9.39519i	0.203571	−	0.352595i
$711$	−22.0681	+	41.3909i	−0.827617	+	1.55228i
$712$	11.4153	−	6.59060i	0.427805	−	0.246993i
$713$	5.37722	+	9.31361i	0.201378	+	0.348798i
$714$	−5.94449	−	11.7936i	−0.222467	−	0.441364i
$715$	0.499565	−	0.865272i	0.0186827	−	0.0323594i
$716$			0.0967051i			0.00361404i
$717$	8.21566	−	14.8017i	0.306819	−	0.552779i
$718$	−19.6573			−0.733605
$719$	−19.2776	−	33.3899i	−0.718935	−	1.24523i	−0.961422	−	0.275077i	$-0.911297\pi$
$719$	−19.2776	−	33.3899i	−0.718935	−	1.24523i	0.242488	−	0.970155i	$-0.422037\pi$
$720$	1.41141	−	2.64725i	0.0526002	−	0.0986571i
$721$	1.97643	−	26.8021i	0.0736061	−	0.998164i
$722$	2.33904	−	1.35045i	0.0870501	−	0.0502584i
$723$	−44.3521	+	0.749070i	−1.64947	+	0.0278582i
$724$	−17.4017	+	10.0469i	−0.646729	+	0.373389i
$725$	2.74938	−	1.58735i	0.102109	−	0.0589529i
$726$	−5.57050	+	10.0361i	−0.206741	+	0.372473i
$727$	21.6549	−	12.5025i	0.803137	−	0.463692i	−0.0414296	−	0.999141i	$-0.513191\pi$
$727$	21.6549	−	12.5025i	0.803137	−	0.463692i	0.844567	+	0.535450i	$0.179858\pi$
$728$	0.710851	−	1.04530i	0.0263459	−	0.0387414i
$729$	−26.8615	+	2.73111i	−0.994871	+	0.101152i
$730$	3.26162	+	5.64929i	0.120718	+	0.209090i
$731$	17.1135			0.632966
$732$	−7.43481	+	0.125568i	−0.274798	+	0.00464112i
$733$			49.3523i			1.82287i	0.411444	+	0.911435i	$0.365024\pi$
$733$			49.3523i			1.82287i	−0.411444	+	0.911435i	$0.634976\pi$
$734$	−10.9999	+	19.0524i	−0.406014	+	0.703237i
$735$	−1.57569	+	12.0215i	−0.0581201	+	0.443421i
$736$	1.01382	+	1.75599i	0.0373699	+	0.0647265i
$737$	9.90934	−	5.72116i	0.365015	−	0.210742i
$738$	20.5660	−	12.8187i	0.757046	−	0.471864i
$739$	10.3267	−	17.8864i	0.379874	−	0.657961i	−0.611170	−	0.791500i	$-0.709301\pi$
$739$	10.3267	−	17.8864i	0.379874	−	0.657961i	0.991044	+	0.133539i	$0.0426340\pi$
$740$	1.93169	−	3.34578i	0.0710103	−	0.122993i
$741$	−0.0650998	−	3.85453i	−0.00239150	−	0.141600i
$742$	−5.67622	−	11.7510i	−0.208381	−	0.431391i
$743$	7.62562	+	4.40265i	0.279757	+	0.161518i	0.633313	−	0.773895i	$-0.281694\pi$
$743$	7.62562	+	4.40265i	0.279757	+	0.161518i	−0.353556	+	0.935413i	$0.615028\pi$
$744$	7.87718	−	4.72703i	0.288792	−	0.173301i
$745$		−	1.19092i		−	0.0436318i
$746$	−20.2060	−	11.6660i	−0.739796	−	0.427121i
$747$	−17.7398	−	28.4611i	−0.649064	−	1.04134i
$748$		−	6.02675i		−	0.220360i
$749$	−43.6852	+	21.1018i	−1.59622	+	0.771044i
$750$	−0.840572	+	1.51441i	−0.0306933	+	0.0552985i
$751$	42.7052			1.55833			0.779167	−	0.626816i	$-0.215642\pi$
$751$	42.7052			1.55833			0.779167	+	0.626816i	$0.215642\pi$
$752$	0.0525367	+	0.0909962i	0.00191581	+	0.00331829i
$753$	−0.234758	−	13.8999i	−0.00855505	−	0.506541i
$754$	−1.31362	−	0.758417i	−0.0478391	−	0.0276199i
$755$	1.58349			0.0576292
$756$	12.0605	−	6.59889i	0.438635	−	0.239999i
$757$	−23.4364			−0.851811			−0.425905	−	0.904768i	$-0.640044\pi$
$757$	−23.4364			−0.851811			−0.425905	+	0.904768i	$0.640044\pi$
$758$	−17.5941	−	10.1580i	−0.639047	−	0.368954i
$759$	0.124018	+	7.34306i	0.00450157	+	0.266536i
$760$	2.32921	+	4.03431i	0.0844894	+	0.146340i
$761$	−7.38846			−0.267832			−0.133916	−	0.990993i	$-0.542755\pi$
$761$	−7.38846			−0.267832			−0.133916	+	0.990993i	$0.542755\pi$
$762$	−0.378000	+	0.681022i	−0.0136935	+	0.0246708i
$763$	21.0859	−	31.0066i	0.763360	−	1.12251i
$764$		−	3.53308i		−	0.127822i
$765$	4.06770	−	7.62939i	0.147068	−	0.275841i
$766$	−3.31092	−	1.91156i	−0.119628	−	0.0690675i
$767$		−	1.34708i		−	0.0486403i
$768$	1.48516	−	0.891232i	0.0535912	−	0.0321596i
$769$	−41.7890	−	24.1269i	−1.50695	−	0.870038i	−0.999967	−	0.00808106i	$-0.997428\pi$
$769$	−41.7890	−	24.1269i	−1.50695	−	0.870038i	−0.506982	−	0.861957i	$-0.669239\pi$
$770$	−3.11123	+	4.57504i	−0.112121	+	0.164873i
$771$	−0.0366307	−	2.16889i	−0.00131922	−	0.0781105i
$772$	12.6572	−	21.9229i	0.455542	−	0.789022i
$773$	−12.6336	+	21.8821i	−0.454401	+	0.787045i	−0.998654	−	0.0518761i	$-0.983480\pi$
$773$	−12.6336	+	21.8821i	−0.454401	+	0.787045i	0.544253	+	0.838921i	$0.316813\pi$
$774$	0.601560	+	17.8040i	0.0216226	+	0.639951i
$775$	−4.59333	+	2.65196i	−0.164997	+	0.0952613i
$776$	4.60847	+	7.98211i	0.165435	+	0.286541i
$777$	15.8095	−	7.96868i	0.567162	−	0.285875i
$778$	−9.67132	+	16.7512i	−0.346734	+	0.600561i
$779$			37.6306i			1.34825i
$780$	0.827433	−	0.0139747i	0.0296269	−	0.000500373i
$781$	22.6863			0.811778
$782$	2.92184	+	5.06077i	0.104485	+	0.180973i
$783$	−8.96102	−	13.8502i	−0.320241	−	0.494965i
$784$	−4.35137	+	5.48321i	−0.155406	+	0.195829i
$785$	−14.5680	+	8.41085i	−0.519955	+	0.300196i
$786$	8.77793	−	15.8147i	0.313098	−	0.564092i
$787$	46.9696	−	27.1179i	1.67429	−	0.966649i	0.709091	−	0.705117i	$-0.249106\pi$
$787$	46.9696	−	27.1179i	1.67429	−	0.966649i	0.965195	−	0.261532i	$-0.0842278\pi$
$788$	−7.80365	+	4.50544i	−0.277994	+	0.160500i
$789$	12.5247	−	0.211532i	0.445892	−	0.00753075i
$790$	13.5407	−	7.81773i	0.481757	−	0.278142i
$791$	17.4636	+	11.8760i	0.620933	+	0.422262i
$792$	6.26991	−	0.211848i	0.222792	−	0.00752767i
$793$	−1.02559	−	1.77638i	−0.0364199	−	0.0630811i
$794$	−30.2959			−1.07516
$795$	4.14609	−	7.46978i	0.147047	−	0.264926i
$796$		−	14.3059i		−	0.507060i
$797$	7.63066	−	13.2167i	0.270292	−	0.468159i	−0.698645	−	0.715469i	$-0.746213\pi$
$797$	7.63066	−	13.2167i	0.270292	−	0.468159i	0.968936	+	0.247310i	$0.0795465\pi$
$798$	−1.21020	+	21.3132i	−0.0428406	+	0.754480i
$799$	0.151411	+	0.262252i	0.00535654	+	0.00927780i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	20.9170	+	33.5586i	0.739064	+	1.18573i
$802$	16.5340	−	28.6376i	0.583834	−	1.01123i
$803$	−6.82058	+	11.8136i	−0.240693	+	0.416892i
$804$	8.28648	+	4.59940i	0.292241	+	0.162208i
$805$	0.394524	−	5.35010i	0.0139052	−	0.188566i
$806$	2.19463	+	1.26707i	0.0773027	+	0.0446307i
$807$	17.1405	+	9.51379i	0.603373	+	0.334901i
$808$			18.8631i			0.663602i
$809$	12.9900	+	7.49978i	0.456704	+	0.263678i	0.710657	−	0.703538i	$-0.248398\pi$
$809$	12.9900	+	7.49978i	0.456704	+	0.263678i	−0.253953	+	0.967216i	$0.581731\pi$
$810$	8.08020	+	3.96364i	0.283909	+	0.139268i
$811$		−	15.3625i		−	0.539451i	−0.962937	−	0.269726i	$-0.913067\pi$
$811$		−	15.3625i		−	0.539451i	0.962937	−	0.269726i	$-0.0869330\pi$
$812$	6.94562	+	4.72333i	0.243743	+	0.165756i
$813$	3.62459	+	6.04007i	0.127120	+	0.211834i
$814$	8.07895			0.283167
$815$	−5.01637	−	8.68860i	−0.175716	−	0.304348i
$816$	4.28025	−	2.56854i	0.149839	−	0.0899169i
$817$	−23.9559	−	13.8310i	−0.838112	−	0.483884i
$818$	−17.0227			−0.595183
$819$	3.20613	+	2.02544i	0.112031	+	0.0707747i
$820$	−8.07796			−0.282095
$821$	24.2512	+	14.0014i	0.846372	+	0.488653i	0.859425	−	0.511262i	$-0.170822\pi$
$821$	24.2512	+	14.0014i	0.846372	+	0.488653i	−0.0130533	+	0.999915i	$0.504155\pi$
$822$	−26.4035	−	14.6552i	−0.920929	−	0.511160i
$823$	−1.01689	−	1.76131i	−0.0354466	−	0.0613954i	0.847758	−	0.530383i	$-0.177952\pi$
$823$	−1.01689	−	1.76131i	−0.0354466	−	0.0613954i	−0.883204	+	0.468988i	$0.844619\pi$
$824$	10.1578			0.353863
$825$	−3.62148	+	0.0611638i	−0.126084	+	0.00212945i
$826$	−0.548584	+	7.43929i	−0.0190877	+	0.258846i
$827$			25.2422i			0.877758i	0.898546	+	0.438879i	$0.144624\pi$
$827$			25.2422i			0.877758i	−0.898546	+	0.438879i	$0.855376\pi$
$828$	−5.16225	+	3.21761i	−0.179400	+	0.111820i
$829$	−35.8687	−	20.7088i	−1.24577	−	0.719246i	−0.275508	−	0.961299i	$-0.588846\pi$
$829$	−35.8687	−	20.7088i	−1.24577	−	0.719246i	−0.970263	+	0.242053i	$0.922179\pi$
$830$			11.1790i			0.388030i
$831$	−0.107943	−	6.39124i	−0.00374449	−	0.221710i
$832$	0.413776	+	0.238893i	0.0143451	+	0.00828214i
$833$	−12.5407	+	15.8026i	−0.434510	+	0.547529i
$834$	−19.0643	+	11.4403i	−0.660144	+	0.396146i
$835$	7.17037	−	12.4194i	0.248141	−	0.429792i
$836$	−4.87076	+	8.43640i	−0.168459	+	0.291779i
$837$	14.9710	+	23.1392i	0.517473	+	0.799808i
$838$	−6.74162	+	3.89228i	−0.232885	+	0.134456i
$839$	7.84013	+	13.5795i	0.270671	+	0.468817i	0.969034	−	0.246928i	$-0.0794210\pi$
$839$	7.84013	+	13.5795i	0.270671	+	0.468817i	−0.698363	+	0.715744i	$0.746088\pi$
$840$	−4.57521	−	0.259788i	−0.157860	−	0.00896353i
$841$	−9.46061	+	16.3863i	−0.326228	+	0.565043i
$842$			30.9337i			1.06605i
$843$	21.9336	+	36.5505i	0.755434	+	1.25887i
$844$	−0.885582			−0.0304830
$845$	−6.38586	−	11.0606i	−0.219680	−	0.380497i
$846$	−0.267510	+	0.166739i	−0.00919720	+	0.00573259i
$847$	17.4860	+	1.28945i	0.600827	+	0.0443059i
$848$	4.27164	−	2.46623i	0.146689	−	0.0846908i
$849$	−1.60625	−	2.67667i	−0.0551263	−	0.0918632i
$850$	−2.49589	+	1.44100i	−0.0856084	+	0.0494261i
$851$	−6.78404	+	3.91677i	−0.232554	+	0.134265i
$852$	9.66865	+	16.1120i	0.331242	+	0.551987i
$853$	13.0788	−	7.55104i	0.447809	−	0.258543i	−0.259095	−	0.965852i	$-0.583424\pi$
$853$	13.0788	−	7.55104i	0.447809	−	0.258543i	0.706904	+	0.707309i	$0.250091\pi$
$854$	4.94045	+	10.2278i	0.169059	+	0.349987i
$855$	−11.8601	+	7.39235i	−0.405606	+	0.252813i
$856$	−9.16843	−	15.8802i	−0.313371	−	0.542774i
$857$	2.72299			0.0930155			0.0465077	−	0.998918i	$-0.485191\pi$
$857$	2.72299			0.0930155			0.0465077	+	0.998918i	$0.485191\pi$
$858$	0.890457	+	1.48387i	0.0303997	+	0.0506585i
$859$			28.1990i			0.962136i	0.876683	+	0.481068i	$0.159751\pi$
$859$			28.1990i			0.962136i	−0.876683	+	0.481068i	$0.840249\pi$
$860$	2.96902	−	5.14250i	0.101243	−	0.175358i
$861$	−30.9576	−	20.2966i	−1.05503	−	0.691705i
$862$	9.81647	+	17.0026i	0.334350	+	0.579112i
$863$	10.0634	−	5.81009i	0.342561	−	0.197778i	−0.318843	−	0.947808i	$-0.603294\pi$
$863$	10.0634	−	5.81009i	0.342561	−	0.197778i	0.661404	+	0.750030i	$0.269961\pi$
$864$	2.82263	+	4.36266i	0.0960277	+	0.148421i
$865$	−8.06316	+	13.9658i	−0.274156	+	0.474851i
$866$	−17.9781	+	31.1390i	−0.610920	+	1.05815i
$867$	−12.9120	+	7.74839i	−0.438515	+	0.263149i
$868$	−11.6039	−	7.89117i	−0.393862	−	0.267844i
$869$	28.3158	+	16.3481i	0.960548	+	0.554573i
$870$	0.0928562	+	5.49797i	0.00314812	+	0.186399i
$871$			2.61433i			0.0885832i
$872$	12.2738	+	7.08626i	0.415642	+	0.239971i
$873$	−23.4658	+	14.6262i	−0.794197	+	0.495021i
$874$		−	9.44559i		−	0.319502i
$875$	2.63859	+	0.194573i	0.0892005	+	0.00657778i
$876$	−11.2970	+	0.190796i	−0.381689	+	0.00644641i
$877$	−26.9876			−0.911307			−0.455654	−	0.890157i	$-0.650594\pi$
$877$	−26.9876			−0.911307			−0.455654	+	0.890157i	$0.650594\pi$
$878$	12.1713	+	21.0814i	0.410762	+	0.711461i
$879$	−36.0158	−	19.9905i	−1.21478	−	0.674264i
$880$	−1.81100	−	1.04558i	−0.0610488	−	0.0352465i
$881$	−3.38847			−0.114160			−0.0570802	−	0.998370i	$-0.518179\pi$
$881$	−3.38847			−0.114160			−0.0570802	+	0.998370i	$0.518179\pi$
$882$	−16.8811	−	12.4912i	−0.568415	−	0.420600i
$883$	−28.0287			−0.943241			−0.471621	−	0.881802i	$-0.656331\pi$
$883$	−28.0287			−0.943241			−0.471621	+	0.881802i	$0.656331\pi$
$884$	1.19251	+	0.688493i	0.0401083	+	0.0231565i
$885$	−4.18730	+	2.51276i	−0.140754	+	0.0844655i
$886$	−2.97116	−	5.14619i	−0.0998180	−	0.172890i
$887$	20.1280			0.675833			0.337917	−	0.941176i	$-0.390278\pi$
$887$	20.1280			0.675833			0.337917	+	0.941176i	$0.390278\pi$
$888$	3.44317	+	5.73774i	0.115545	+	0.192546i
$889$	1.18656	+	0.0874986i	0.0397959	+	0.00293461i
$890$		−	13.1812i		−	0.441835i
$891$	1.27036	+	18.7775i	0.0425587	+	0.629071i
$892$	0.0602532	+	0.0347872i	0.00201743	+	0.00116476i
$893$		−	0.489476i		−	0.0163797i
$894$	1.80354	+	1.00105i	0.0603193	+	0.0334801i
$895$	0.0837491	+	0.0483526i	0.00279942	+	0.00161625i
$896$	−2.18780	−	1.48780i	−0.0730892	−	0.0497039i
$897$	−1.46713	−	0.814328i	−0.0489860	−	0.0271896i
$898$	−1.79521	+	3.10939i	−0.0599069	+	0.103762i
$899$	−8.41921	+	14.5825i	−0.280796	+	0.486353i
$900$	−1.58688	−	2.54594i	−0.0528959	−	0.0848647i
$901$	12.3109	−	7.10770i	0.410136	−	0.236792i
$902$	−8.44617	−	14.6292i	−0.281227	−	0.487099i
$903$	24.2993	−	12.2479i	0.808630	−	0.407586i
$904$	−3.99113	+	6.91284i	−0.132743	+	0.229918i
$905$			20.0938i			0.667939i
$906$	−1.33104	+	2.39806i	−0.0442208	+	0.0796702i
$907$	−33.6848			−1.11849			−0.559243	−	0.829004i	$-0.688908\pi$
$907$	−33.6848			−1.11849			−0.559243	+	0.829004i	$0.688908\pi$
$908$	−9.19003	−	15.9176i	−0.304982	−	0.528244i
$909$	−56.5571	+	1.91095i	−1.87588	+	0.0633822i
$910$	−0.549832	−	1.13827i	−0.0182267	−	0.0377331i
$911$	−34.1663	+	19.7259i	−1.13198	+	0.653550i	−0.944432	−	0.328706i	$-0.893388\pi$
$911$	−34.1663	+	19.7259i	−1.13198	+	0.653550i	−0.187549	+	0.982255i	$0.560054\pi$
$912$	−8.06747	+	0.136253i	−0.267141	+	0.00451178i
$913$	−20.2452	+	11.6886i	−0.670019	+	0.386836i
$914$	−11.6558	+	6.72945i	−0.385538	+	0.222591i
$915$	−3.60866	+	6.50152i	−0.119299	+	0.214934i
$916$	13.9168	−	8.03486i	0.459823	−	0.265479i
$917$	−27.5543	−	2.03189i	−0.909922	−	0.0670990i
$918$	8.13484	+	12.5732i	0.268490	+	0.414978i
$919$	24.5657	+	42.5490i	0.810346	+	1.40356i	0.912622	+	0.408804i	$0.134054\pi$
$919$	24.5657	+	42.5490i	0.810346	+	1.40356i	−0.102276	+	0.994756i	$0.532612\pi$
$920$	2.02764			0.0668492
$921$	10.3886	−	0.175455i	0.342317	−	0.00578144i
$922$			27.1267i			0.893370i
$923$	−2.59167	+	4.48890i	−0.0853058	+	0.147754i
$924$	−4.31328	−	8.55733i	−0.141896	−	0.281515i
$925$	−1.93169	−	3.34578i	−0.0635135	−	0.110009i
$926$	−27.6688	+	15.9746i	−0.909254	+	0.524958i
$927$	1.02904	+	30.4559i	0.0337982	+	1.00030i
$928$	−1.58735	+	2.74938i	−0.0521075	+	0.0902528i
$929$	3.80826	−	6.59610i	0.124945	−	0.216411i	−0.796766	−	0.604287i	$-0.793458\pi$
$929$	3.80826	−	6.59610i	0.124945	−	0.216411i	0.921711	+	0.387876i	$0.126791\pi$
$930$	−0.155133	−	9.18536i	−0.00508701	−	0.301200i
$931$	30.3263	−	11.9857i	0.993906	−	0.392815i
$932$	−22.4677	−	12.9717i	−0.735955	−	0.424904i
$933$	35.2403	−	21.1474i	1.15372	−	0.692334i
$934$		−	36.8052i		−	1.20430i
$935$	−5.21932	−	3.01338i	−0.170690	−	0.0985479i
$936$	−0.674354	+	1.26482i	−0.0220419	+	0.0413419i
$937$			35.6260i			1.16385i	0.813243	+	0.581925i	$0.197700\pi$
$937$			35.6260i			1.16385i	−0.813243	+	0.581925i	$0.802300\pi$
$938$	1.06466	−	14.4377i	0.0347623	−	0.471407i
$939$	−2.49276	+	4.49107i	−0.0813482	+	0.146560i
$940$	0.105073			0.00342711
$941$	22.4863	+	38.9474i	0.733032	+	1.26965i	0.955581	+	0.294727i	$0.0952287\pi$
$941$	22.4863	+	38.9474i	0.733032	+	1.26965i	−0.222550	+	0.974921i	$0.571438\pi$
$942$	−0.492013	−	29.1319i	−0.0160307	−	0.949169i
$943$	14.1848	+	8.18959i	0.461920	+	0.266690i
$944$	−2.81942			−0.0917643
$945$	0.315422	−	13.7441i	0.0102607	−	0.447096i
$946$	12.4174			0.403725
$947$	36.7624	+	21.2248i	1.19462	+	0.689712i	0.959350	−	0.282219i	$-0.0910705\pi$
$947$	36.7624	+	21.2248i	1.19462	+	0.689712i	0.235266	+	0.971931i	$0.424404\pi$
$948$	0.457317	+	27.0775i	0.0148530	+	0.879438i
$949$	−1.55836	−	2.69916i	−0.0505865	−	0.0876183i
$950$	4.65842			0.151139
$951$	10.8855	−	19.6119i	0.352988	−	0.635958i
$952$	−6.30525	−	4.28785i	−0.204354	−	0.138970i
$953$			4.59106i			0.148719i	0.997232	+	0.0743595i	$0.0236912\pi$
$953$			4.59106i			0.148719i	−0.997232	+	0.0743595i	$0.976309\pi$
$954$	7.82722	+	12.5578i	0.253416	+	0.406573i
$955$	−3.05974	−	1.76654i	−0.0990108	−	0.0571639i
$956$		−	9.77390i		−	0.316110i
$957$	−9.85974	+	5.91674i	−0.318720	+	0.191261i
$958$	−15.2845	−	8.82453i	−0.493821	−	0.285108i
$959$	−3.39236	+	46.0034i	−0.109545	+	1.48553i
$960$	−0.0292487	−	1.73180i	−0.000943998	−	0.0558937i
$961$	−1.43420	+	2.48410i	−0.0462644	+	0.0801323i
$962$	−0.922936	+	1.59857i	−0.0297566	+	0.0515400i
$963$	46.6846	−	29.0984i	1.50439	−	0.937682i
$964$	−22.1792	+	12.8052i	−0.714345	+	0.412427i
$965$	−12.6572	−	21.9229i	−0.407449	−	0.705723i
$966$	7.77062	+	5.09461i	0.250016	+	0.163916i
$967$	3.39500	−	5.88032i	0.109176	−	0.189098i	−0.806261	−	0.591560i	$-0.798512\pi$
$967$	3.39500	−	5.88032i	0.109176	−	0.189098i	0.915437	+	0.402462i	$0.131845\pi$
$968$			6.62704i			0.213001i
$969$	−23.2505	+	0.392682i	−0.746915	+	0.0126148i
$970$	9.21695			0.295938
$971$	27.3715	+	47.4087i	0.878392	+	1.52142i	0.853105	+	0.521739i	$0.174716\pi$
$971$	27.3715	+	47.4087i	0.878392	+	1.52142i	0.0252864	+	0.999680i	$0.491950\pi$
$972$	−12.7946	+	8.90502i	−0.410386	+	0.285629i
$973$	28.0837	+	19.0982i	0.900323	+	0.612260i
$974$	9.43137	−	5.44521i	0.302201	−	0.174476i
$975$	0.401614	−	0.723566i	0.0128620	−	0.0231726i
$976$	−3.71793	+	2.14655i	−0.119008	+	0.0687094i
$977$	−2.91180	+	1.68113i	−0.0931566	+	0.0537840i	−0.545855	−	0.837880i	$-0.683795\pi$
$977$	−2.91180	+	1.68113i	−0.0931566	+	0.0537840i	0.452698	+	0.891664i	$0.350462\pi$
$978$	17.3747	−	0.293445i	0.555582	−	0.00938332i
$979$	23.8712	−	13.7820i	0.762925	−	0.440475i
$980$	2.57291	+	6.51000i	0.0821885	+	0.207954i
$981$	−20.0033	+	37.5182i	−0.638655	+	1.19786i
$982$	−12.4238	−	21.5186i	−0.396459	−	0.686687i
$983$	49.5842			1.58149			0.790745	−	0.612146i	$-0.209694\pi$
$983$	49.5842			1.58149			0.790745	+	0.612146i	$0.209694\pi$
$984$	6.79011	−	12.2334i	0.216461	−	0.389985i
$985$			9.01088i			0.287111i
$986$	−4.57477	+	7.92373i	−0.145690	+	0.252343i
$987$	0.402678	+	0.264006i	0.0128174	+	0.00840339i
$988$	−1.11287	−	1.92754i	−0.0354050	−	0.0613233i
$989$	−10.4271	+	6.02010i	−0.331563	+	0.191428i
$990$	2.95149	−	5.53583i	0.0938045	−	0.175940i
$991$	−25.0428	+	43.3755i	−0.795512	+	1.37787i	0.127001	+	0.991903i	$0.459465\pi$
$991$	−25.0428	+	43.3755i	−0.795512	+	1.37787i	−0.922513	+	0.385965i	$0.873869\pi$
$992$	2.65196	−	4.59333i	0.0841999	−	0.145838i
$993$	−51.4960	−	28.5828i	−1.63418	−	0.907047i
$994$	16.1406	−	23.7346i	0.511948	−	0.752816i
$995$	−12.3893	−	7.15296i	−0.392767	−	0.226764i
$996$	−16.9296	−	9.39677i	−0.536436	−	0.297748i
$997$			31.2926i			0.991048i	0.868594	+	0.495524i	$0.165024\pi$
$997$			31.2926i			0.991048i	−0.868594	+	0.495524i	$0.834976\pi$
$998$	31.9432	+	18.4424i	1.01115	+	0.583785i
$999$	−16.8546	+	10.9049i	−0.533256	+	0.345015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.c.311.13	✓	32
3.2	odd	2		1890.2.t.c.1151.2		32
7.5	odd	6		630.2.bk.c.131.7	yes	32
9.2	odd	6		630.2.bk.c.101.15	yes	32
9.7	even	3		1890.2.bk.c.521.14		32
21.5	even	6		1890.2.bk.c.341.14		32
63.47	even	6	inner	630.2.t.c.551.13	yes	32
63.61	odd	6		1890.2.t.c.1601.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.13	✓	32	1.1	even	1	trivial
630.2.t.c.551.13	yes	32	63.47	even	6	inner
630.2.bk.c.101.15	yes	32	9.2	odd	6
630.2.bk.c.131.7	yes	32	7.5	odd	6
1890.2.t.c.1151.2		32	3.2	odd	2
1890.2.t.c.1601.2		32	63.61	odd	6
1890.2.bk.c.341.14		32	21.5	even	6
1890.2.bk.c.521.14		32	9.7	even	3

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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.0292487 + 1.73180i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.840572 + 1.51441i) q^{6} +(2.63859 + 0.194573i) q^{7} +1.00000i q^{8} +(-2.99829 + 0.101306i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.0292487 + 1.73180i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.840572 + 1.51441i) q^{6} +(2.63859 + 0.194573i) q^{7} +1.00000i q^{8} +(-2.99829 + 0.101306i) q^{9} +(0.866025 + 0.500000i) q^{10} +2.09116i q^{11} +(-1.48516 + 0.891232i) q^{12} +(-0.413776 - 0.238893i) q^{13} +(2.18780 + 1.48780i) q^{14} +(0.0292487 + 1.73180i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.44100 + 2.49589i) q^{17} +(-2.64725 - 1.41141i) q^{18} +(4.03431 - 2.32921i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-0.259788 + 4.57521i) q^{21} +(-1.04558 + 1.81100i) q^{22} -2.02764i q^{23} +(-1.73180 + 0.0292487i) q^{24} +1.00000 q^{25} +(-0.238893 - 0.413776i) q^{26} +(-0.263138 - 5.18949i) q^{27} +(1.15079 + 2.38237i) q^{28} +(2.74938 - 1.58735i) q^{29} +(-0.840572 + 1.51441i) q^{30} +(-4.59333 + 2.65196i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.62148 + 0.0611638i) q^{33} +(-2.49589 + 1.44100i) q^{34} +(2.63859 + 0.194573i) q^{35} +(-1.58688 - 2.54594i) q^{36} +(-1.93169 - 3.34578i) q^{37} +4.65842 q^{38} +(0.401614 - 0.723566i) q^{39} +1.00000i q^{40} +(-4.03898 + 6.99572i) q^{41} +(-2.51259 + 3.83235i) q^{42} +(-2.96902 - 5.14250i) q^{43} +(-1.81100 + 1.04558i) q^{44} +(-2.99829 + 0.101306i) q^{45} +(1.01382 - 1.75599i) q^{46} +(0.0525367 - 0.0909962i) q^{47} +(-1.51441 - 0.840572i) q^{48} +(6.92428 + 1.02680i) q^{49} +(0.866025 + 0.500000i) q^{50} +(-4.36455 - 2.42254i) q^{51} -0.477787i q^{52} +(-4.27164 - 2.46623i) q^{53} +(2.36686 - 4.62580i) q^{54} +2.09116i q^{55} +(-0.194573 + 2.63859i) q^{56} +(4.15173 + 6.91851i) q^{57} +3.17471 q^{58} +(1.40971 + 2.44169i) q^{59} +(-1.48516 + 0.891232i) q^{60} +(3.71793 + 2.14655i) q^{61} -5.30392 q^{62} +(-7.93096 - 0.316082i) q^{63} -1.00000 q^{64} +(-0.413776 - 0.238893i) q^{65} +(-3.16688 - 1.75777i) q^{66} +(-2.73588 - 4.73867i) q^{67} -2.88201 q^{68} +(3.51147 - 0.0593058i) q^{69} +(2.18780 + 1.48780i) q^{70} -10.8486i q^{71} +(-0.101306 - 2.99829i) q^{72} +(5.64929 + 3.26162i) q^{73} -3.86338i q^{74} +(0.0292487 + 1.73180i) q^{75} +(4.03431 + 2.32921i) q^{76} +(-0.406885 + 5.51772i) q^{77} +(0.709591 - 0.425819i) q^{78} +(7.81773 - 13.5407i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(8.97947 - 0.607490i) q^{81} +(-6.99572 + 4.03898i) q^{82} +(5.58951 + 9.68132i) q^{83} +(-4.09214 + 2.06262i) q^{84} +(-1.44100 + 2.49589i) q^{85} -5.93804i q^{86} +(2.82940 + 4.71496i) q^{87} -2.09116 q^{88} +(-6.59060 - 11.4153i) q^{89} +(-2.64725 - 1.41141i) q^{90} +(-1.04530 - 0.710851i) q^{91} +(1.75599 - 1.01382i) q^{92} +(-4.72703 - 7.87718i) q^{93} +(0.0909962 - 0.0525367i) q^{94} +(4.03431 - 2.32921i) q^{95} +(-0.891232 - 1.48516i) q^{96} +(7.98211 - 4.60847i) q^{97} +(5.48321 + 4.35137i) q^{98} +(-0.211848 - 6.26991i) 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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