LMFDB - Embedded newform 234.2.z.a.137.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(41,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("234.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			137.12
Character	$\chi$	$=$	234.137
Dual form			234.2.z.a.41.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 + 0.258819i) q^{2} +(0.161445 - 1.72451i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.21510 - 0.593533i) q^{5} +(0.602280 - 1.62396i) q^{6} +(2.94637 - 2.94637i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.94787 - 0.556826i) q^{9} +(-1.98600 - 1.14662i) q^{10} +(-0.431075 + 1.60879i) q^{11} +(1.00207 - 1.41275i) q^{12} +(1.58511 - 3.23843i) q^{13} +(3.60855 - 2.08340i) q^{14} +(-1.38117 + 3.72413i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.96958 + 3.41141i) q^{17} +(-2.70331 - 1.30082i) q^{18} +(-0.878484 + 3.27855i) q^{19} +(-1.62156 - 1.62156i) q^{20} +(-4.60536 - 5.55671i) q^{21} +(-0.832773 + 1.44241i) q^{22} +5.07211 q^{23} +(1.33357 - 1.10525i) q^{24} +(0.224246 + 0.129469i) q^{25} +(2.36927 - 2.71782i) q^{26} +(-1.43617 + 4.99374i) q^{27} +(4.02481 - 1.07844i) q^{28} +(-4.53523 + 2.61842i) q^{29} +(-2.29799 + 3.23976i) q^{30} +(-0.610507 + 2.27844i) q^{31} +(0.258819 + 0.965926i) q^{32} +(2.70479 + 1.00312i) q^{33} +(1.01953 + 3.80493i) q^{34} +(-8.27525 + 4.77772i) q^{35} +(-2.27452 - 1.95616i) q^{36} +(1.21985 + 4.55256i) q^{37} +(-1.69710 + 2.93946i) q^{38} +(-5.32879 - 3.25637i) q^{39} +(-1.14662 - 1.98600i) q^{40} +(2.88882 - 2.88882i) q^{41} +(-3.01026 - 6.55933i) q^{42} +4.92213i q^{43} +(-1.17772 + 1.17772i) q^{44} +(6.19933 + 2.98308i) q^{45} +(4.89928 + 1.31276i) q^{46} +(4.39173 - 1.17676i) q^{47} +(1.57419 - 0.722440i) q^{48} -10.3621i q^{49} +(0.183096 + 0.183096i) q^{50} +(6.20099 - 2.84580i) q^{51} +(2.99196 - 2.01200i) q^{52} +6.69581i q^{53} +(-2.67971 + 4.45187i) q^{54} +(1.90975 - 3.30778i) q^{55} +4.16679 q^{56} +(5.51206 + 2.04426i) q^{57} +(-5.05840 + 1.35539i) q^{58} +(-8.36478 + 2.24134i) q^{59} +(-3.05820 + 2.53461i) q^{60} +11.6225 q^{61} +(-1.17941 + 2.04279i) q^{62} +(-10.3261 + 7.04489i) q^{63} +1.00000i q^{64} +(-5.43330 + 6.23261i) q^{65} +(2.35300 + 1.66899i) q^{66} +(-9.81803 - 9.81803i) q^{67} +3.93916i q^{68} +(0.818866 - 8.74691i) q^{69} +(-9.22985 + 2.47313i) q^{70} +(-13.5600 - 3.63339i) q^{71} +(-1.69072 - 2.47820i) q^{72} +(6.61207 - 6.61207i) q^{73} +4.71315i q^{74} +(0.259473 - 0.365813i) q^{75} +(-2.40006 + 2.40006i) q^{76} +(3.46999 + 6.01020i) q^{77} +(-4.30441 - 4.52461i) q^{78} +(-8.13274 + 14.0863i) q^{79} +(-0.593533 - 2.21510i) q^{80} +(8.37989 + 3.28290i) q^{81} +(3.53806 - 2.04270i) q^{82} +(-2.02549 - 7.55922i) q^{83} +(-1.21000 - 7.11494i) q^{84} +(-2.33802 - 8.72561i) q^{85} +(-1.27394 + 4.75442i) q^{86} +(3.78330 + 8.24379i) q^{87} +(-1.44241 + 0.832773i) q^{88} +(8.95926 - 2.40063i) q^{89} +(5.21601 + 4.48594i) q^{90} +(-4.87127 - 14.2119i) q^{91} +(4.39258 + 2.53606i) q^{92} +(3.83063 + 1.42067i) q^{93} +4.54666 q^{94} +(3.89185 - 6.74089i) q^{95} +(1.70753 - 0.290392i) q^{96} +(-6.05440 - 6.05440i) q^{97} +(2.68192 - 10.0091i) q^{98} +(2.16657 - 4.50249i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	0.161445	−	1.72451i	0.0932102	−	0.995646i
$3$	0.161445	−	1.72451i	0.0932102	−	0.995646i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−2.21510	−	0.593533i	−0.990622	−	0.265436i	−0.273110	−	0.961983i	$-0.588052\pi$
$5$	−2.21510	−	0.593533i	−0.990622	−	0.265436i	−0.717512	+	0.696547i	$0.754719\pi$
$6$	0.602280	−	1.62396i	0.245880	−	0.662981i
$7$	2.94637	−	2.94637i	1.11362	−	1.11362i	0.120965	−	0.992657i	$-0.461401\pi$
$7$	2.94637	−	2.94637i	1.11362	−	1.11362i	0.992657	−	0.120965i	$-0.0385989\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.94787	−	0.556826i	−0.982624	−	0.185609i
$10$	−1.98600	−	1.14662i	−0.628029	−	0.362593i
$11$	−0.431075	+	1.60879i	−0.129974	+	0.485070i	−0.999968	−	0.00799251i	$-0.997456\pi$
$11$	−0.431075	+	1.60879i	−0.129974	+	0.485070i	0.869994	+	0.493062i	$0.164123\pi$
$12$	1.00207	−	1.41275i	0.289273	−	0.407825i
$13$	1.58511	−	3.23843i	0.439631	−	0.898178i
$13$	1.58511	−	3.23843i	0.439631	−	0.898178i
$14$	3.60855	−	2.08340i	0.964425	−	0.556811i
$15$	−1.38117	+	3.72413i	−0.356617	+	0.961567i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.96958	+	3.41141i	0.477693	+	0.827388i	0.999673	−	0.0255693i	$-0.00813984\pi$
$17$	1.96958	+	3.41141i	0.477693	+	0.827388i	−0.521980	+	0.852958i	$0.674807\pi$
$18$	−2.70331	−	1.30082i	−0.637176	−	0.306606i
$19$	−0.878484	+	3.27855i	−0.201538	+	0.752150i	0.788939	+	0.614472i	$0.210631\pi$
$19$	−0.878484	+	3.27855i	−0.201538	+	0.752150i	−0.990477	+	0.137678i	$0.956036\pi$
$20$	−1.62156	−	1.62156i	−0.362593	−	0.362593i
$21$	−4.60536	−	5.55671i	−1.00497	−	1.21257i
$22$	−0.832773	+	1.44241i	−0.177548	+	0.307522i
$23$	5.07211			1.05761			0.528804	−	0.848744i	$-0.322641\pi$
$23$	5.07211			1.05761			0.528804	+	0.848744i	$0.322641\pi$
$24$	1.33357	−	1.10525i	0.272214	−	0.225609i
$25$	0.224246	+	0.129469i	0.0448492	+	0.0258937i
$26$	2.36927	−	2.71782i	0.464652	−	0.533009i
$27$	−1.43617	+	4.99374i	−0.276391	+	0.961045i
$28$	4.02481	−	1.07844i	0.760618	−	0.203807i
$29$	−4.53523	+	2.61842i	−0.842172	+	0.486228i	−0.858002	−	0.513647i	$-0.828294\pi$
$29$	−4.53523	+	2.61842i	−0.842172	+	0.486228i	0.0158300	+	0.999875i	$0.494961\pi$
$30$	−2.29799	+	3.23976i	−0.419553	+	0.591497i
$31$	−0.610507	+	2.27844i	−0.109650	+	0.409220i	−0.998831	−	0.0483356i	$-0.984608\pi$
$31$	−0.610507	+	2.27844i	−0.109650	+	0.409220i	0.889181	+	0.457556i	$0.151275\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	2.70479	+	1.00312i	0.470843	+	0.174622i
$34$	1.01953	+	3.80493i	0.174848	+	0.652541i
$35$	−8.27525	+	4.77772i	−1.39877	+	0.807582i
$36$	−2.27452	−	1.95616i	−0.379086	−	0.326027i
$37$	1.21985	+	4.55256i	0.200543	+	0.748436i	0.990762	+	0.135612i	$0.0432999\pi$
$37$	1.21985	+	4.55256i	0.200543	+	0.748436i	−0.790219	+	0.612824i	$0.790033\pi$
$38$	−1.69710	+	2.93946i	−0.275306	+	0.476844i
$39$	−5.32879	−	3.25637i	−0.853290	−	0.521437i
$40$	−1.14662	−	1.98600i	−0.181296	−	0.314014i
$41$	2.88882	−	2.88882i	0.451157	−	0.451157i	−0.444581	−	0.895739i	$-0.646647\pi$
$41$	2.88882	−	2.88882i	0.451157	−	0.451157i	0.895739	+	0.444581i	$0.146647\pi$
$42$	−3.01026	−	6.55933i	−0.464493	−	1.01213i
$43$			4.92213i			0.750619i	0.926900	+	0.375309i	$0.122463\pi$
$43$			4.92213i			0.750619i	−0.926900	+	0.375309i	$0.877537\pi$
$44$	−1.17772	+	1.17772i	−0.177548	+	0.177548i
$45$	6.19933	+	2.98308i	0.924141	+	0.444692i
$46$	4.89928	+	1.31276i	0.722360	+	0.193556i
$47$	4.39173	−	1.17676i	0.640600	−	0.171648i	0.0761249	−	0.997098i	$-0.475745\pi$
$47$	4.39173	−	1.17676i	0.640600	−	0.171648i	0.564475	+	0.825450i	$0.309079\pi$
$48$	1.57419	−	0.722440i	0.227215	−	0.104275i
$49$		−	10.3621i		−	1.48031i
$50$	0.183096	+	0.183096i	0.0258937	+	0.0258937i
$51$	6.20099	−	2.84580i	0.868312	−	0.398492i
$52$	2.99196	−	2.01200i	0.414911	−	0.279015i
$53$			6.69581i			0.919741i	0.887986	+	0.459870i	$0.152104\pi$
$53$			6.69581i			0.919741i	−0.887986	+	0.459870i	$0.847896\pi$
$54$	−2.67971	+	4.45187i	−0.364662	+	0.605823i
$55$	1.90975	−	3.30778i	0.257510	−	0.446021i
$56$	4.16679			0.556811
$57$	5.51206	+	2.04426i	0.730090	+	0.270769i
$58$	−5.05840	+	1.35539i	−0.664200	+	0.177972i
$59$	−8.36478	+	2.24134i	−1.08900	+	0.291797i	−0.758279	−	0.651930i	$-0.773959\pi$
$59$	−8.36478	+	2.24134i	−1.08900	+	0.291797i	−0.330723	+	0.943728i	$0.607293\pi$
$60$	−3.05820	+	2.53461i	−0.394811	+	0.327217i
$61$	11.6225			1.48810			0.744052	−	0.668122i	$-0.232902\pi$
$61$	11.6225			1.48810			0.744052	+	0.668122i	$0.232902\pi$
$62$	−1.17941	+	2.04279i	−0.149785	+	0.259435i
$63$	−10.3261	+	7.04489i	−1.30097	+	0.887573i
$64$			1.00000i			0.125000i
$65$	−5.43330	+	6.23261i	−0.673917	+	0.773061i
$66$	2.35300	+	1.66899i	0.289634	+	0.205439i
$67$	−9.81803	−	9.81803i	−1.19946	−	1.19946i	−0.974327	−	0.225137i	$-0.927717\pi$
$67$	−9.81803	−	9.81803i	−1.19946	−	1.19946i	−0.225137	−	0.974327i	$-0.572283\pi$
$68$			3.93916i			0.477693i
$69$	0.818866	−	8.74691i	0.0985798	−	1.05300i
$70$	−9.22985	+	2.47313i	−1.10318	+	0.295596i
$71$	−13.5600	−	3.63339i	−1.60928	−	0.431205i	−0.661450	−	0.749989i	$-0.730059\pi$
$71$	−13.5600	−	3.63339i	−1.60928	−	0.431205i	−0.947827	+	0.318784i	$0.896725\pi$
$72$	−1.69072	−	2.47820i	−0.199254	−	0.292058i
$73$	6.61207	−	6.61207i	0.773884	−	0.773884i	−0.204899	−	0.978783i	$-0.565687\pi$
$73$	6.61207	−	6.61207i	0.773884	−	0.773884i	0.978783	+	0.204899i	$0.0656866\pi$
$74$			4.71315i			0.547893i
$75$	0.259473	−	0.365813i	0.0299614	−	0.0422404i
$76$	−2.40006	+	2.40006i	−0.275306	+	0.275306i
$77$	3.46999	+	6.01020i	0.395442	+	0.684926i
$78$	−4.30441	−	4.52461i	−0.487378	−	0.512311i
$79$	−8.13274	+	14.0863i	−0.915004	+	1.58483i	−0.108109	+	0.994139i	$0.534480\pi$
$79$	−8.13274	+	14.0863i	−0.915004	+	1.58483i	−0.806895	+	0.590695i	$0.798854\pi$
$80$	−0.593533	−	2.21510i	−0.0663591	−	0.247655i
$81$	8.37989	+	3.28290i	0.931099	+	0.364767i
$82$	3.53806	−	2.04270i	0.390714	−	0.225579i
$83$	−2.02549	−	7.55922i	−0.222326	−	0.829732i	−0.983458	−	0.181135i	$-0.942023\pi$
$83$	−2.02549	−	7.55922i	−0.222326	−	0.829732i	0.761132	−	0.648597i	$-0.224644\pi$
$84$	−1.21000	−	7.11494i	−0.132022	−	0.776303i
$85$	−2.33802	−	8.72561i	−0.253594	−	0.946426i
$86$	−1.27394	+	4.75442i	−0.137373	+	0.512682i
$87$	3.78330	+	8.24379i	0.405612	+	0.883827i
$88$	−1.44241	+	0.832773i	−0.153761	+	0.0887739i
$89$	8.95926	−	2.40063i	0.949679	−	0.254466i	0.249453	−	0.968387i	$-0.419749\pi$
$89$	8.95926	−	2.40063i	0.949679	−	0.254466i	0.700226	+	0.713921i	$0.253083\pi$
$90$	5.21601	+	4.48594i	0.549816	+	0.472860i
$91$	−4.87127	−	14.2119i	−0.510648	−	1.48981i
$92$	4.39258	+	2.53606i	0.457958	+	0.264402i
$93$	3.83063	+	1.42067i	0.397218	+	0.147316i
$94$	4.54666			0.468952
$95$	3.89185	−	6.74089i	0.399296	−	0.691600i
$96$	1.70753	−	0.290392i	0.174274	−	0.0296381i
$97$	−6.05440	−	6.05440i	−0.614731	−	0.614731i	0.329444	−	0.944175i	$-0.393139\pi$
$97$	−6.05440	−	6.05440i	−0.614731	−	0.614731i	−0.944175	+	0.329444i	$0.893139\pi$
$98$	2.68192	−	10.0091i	0.270915	−	1.01107i
$99$	2.16657	−	4.50249i	0.217749	−	0.452517i
$100$	0.129469	+	0.224246i	0.0129469	+	0.0224246i
$101$	−8.37557	−	14.5069i	−0.833401	−	1.44349i	−0.895326	−	0.445412i	$-0.853057\pi$
$101$	−8.37557	−	14.5069i	−0.833401	−	1.44349i	0.0619252	−	0.998081i	$-0.480276\pi$
$102$	6.72624	−	1.14390i	0.665997	−	0.113263i
$103$	7.55143	−	4.35982i	0.744065	−	0.429586i	−0.0794807	−	0.996836i	$-0.525326\pi$
$103$	7.55143	−	4.35982i	0.744065	−	0.429586i	0.823545	+	0.567251i	$0.191993\pi$
$104$	3.41076	−	1.16907i	0.334452	−	0.114637i
$105$	6.90323	+	15.0421i	0.673686	+	1.46796i
$106$	−1.73300	+	6.46766i	−0.168324	+	0.628195i
$107$	8.80347	+	5.08268i	0.851063	+	0.491362i	0.861009	−	0.508589i	$-0.169833\pi$
$107$	8.80347	+	5.08268i	0.851063	+	0.491362i	−0.00994628	+	0.999951i	$0.503166\pi$
$108$	−3.74063	+	3.60662i	−0.359942	+	0.347047i
$109$	2.11305	+	2.11305i	0.202394	+	0.202394i	0.801025	−	0.598631i	$-0.204288\pi$
$109$	2.11305	+	2.11305i	0.202394	+	0.202394i	−0.598631	+	0.801025i	$0.704288\pi$
$110$	2.70079	−	2.70079i	0.257510	−	0.257510i
$111$	8.04787	−	1.36866i	0.763870	−	0.129908i
$112$	4.02481	+	1.07844i	0.380309	+	0.101903i
$113$	−16.1467	−	9.32231i	−1.51895	−	0.876969i	−0.999751	−	0.0223181i	$-0.992895\pi$
$113$	−16.1467	−	9.32231i	−1.51895	−	0.876969i	−0.519203	−	0.854651i	$-0.673771\pi$
$114$	4.79515	+	3.40123i	0.449107	+	0.318554i
$115$	−11.2352	−	3.01047i	−1.04769	−	0.280728i
$116$	−5.23684			−0.486228
$117$	−6.47595	+	8.66384i	−0.598702	+	0.800972i
$118$	−8.65986			−0.797205
$119$	15.8544	+	4.24816i	1.45337	+	0.389428i
$120$	−3.61000	+	1.65673i	−0.329546	+	0.151238i
$121$	7.12389	+	4.11298i	0.647626	+	0.373907i
$122$	11.2264	+	3.00811i	1.01639	+	0.272342i
$123$	−4.51541	−	5.44818i	−0.407141	−	0.491246i
$124$	−1.66793	+	1.66793i	−0.149785	+	0.149785i
$125$	7.68794	+	7.68794i	0.687630	+	0.687630i
$126$	−11.7976	+	4.13225i	−1.05102	+	0.368130i
$127$	14.6359	+	8.45004i	1.29873	+	0.749820i	0.980184	−	0.198089i	$-0.0634735\pi$
$127$	14.6359	+	8.45004i	1.29873	+	0.749820i	0.318542	+	0.947909i	$0.396807\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	8.48827	+	0.794653i	0.747351	+	0.0699653i
$130$	−6.86128	+	4.61400i	−0.601774	+	0.404675i
$131$	9.78550	−	5.64966i	0.854963	−	0.493613i	−0.00735903	−	0.999973i	$-0.502342\pi$
$131$	9.78550	−	5.64966i	0.854963	−	0.493613i	0.862322	+	0.506360i	$0.169009\pi$
$132$	1.84085	+	2.22113i	0.160226	+	0.193324i
$133$	7.07146	+	12.2481i	0.613173	+	1.06205i
$134$	−6.94240	−	12.0246i	−0.599732	−	1.03877i
$135$	6.14521	−	10.2092i	0.528895	−	0.878668i
$136$	−1.01953	+	3.80493i	−0.0874239	+	0.326270i
$137$	−10.9647	−	10.9647i	−0.936777	−	0.936777i	0.0613396	−	0.998117i	$-0.480463\pi$
$137$	−10.9647	−	10.9647i	−0.936777	−	0.936777i	−0.998117	+	0.0613396i	$0.980463\pi$
$138$	3.05483	−	8.23693i	0.260044	−	0.701174i
$139$	−8.94201	+	15.4880i	−0.758451	+	1.31368i	0.185189	+	0.982703i	$0.440710\pi$
$139$	−8.94201	+	15.4880i	−0.758451	+	1.31368i	−0.943640	+	0.330973i	$0.892623\pi$
$140$	−9.55544			−0.807582
$141$	−1.32032	−	7.76357i	−0.111191	−	0.653811i
$142$	−12.1576	−	7.01918i	−1.02024	−	0.589036i
$143$	4.52666	+	3.94613i	0.378538	+	0.329992i
$144$	−0.991710	−	2.83134i	−0.0826425	−	0.235945i
$145$	11.6001	−	3.10824i	0.963336	−	0.258125i
$146$	8.09810	−	4.67544i	0.670203	−	0.386942i
$147$	−17.8696	−	1.67291i	−1.47386	−	0.137980i
$148$	−1.21985	+	4.55256i	−0.100271	+	0.374218i
$149$	−1.06319	−	3.96787i	−0.0870997	−	0.325061i	0.908604	−	0.417659i	$-0.137149\pi$
$149$	−1.06319	−	3.96787i	−0.0870997	−	0.325061i	−0.995704	+	0.0925986i	$0.970483\pi$
$150$	0.345311	−	0.286191i	0.0281945	−	0.0233674i
$151$	−0.919034	−	3.42988i	−0.0747899	−	0.279120i	0.918396	−	0.395663i	$-0.129485\pi$
$151$	−0.919034	−	3.42988i	−0.0747899	−	0.279120i	−0.993186	+	0.116543i	$0.962819\pi$
$152$	−2.93946	+	1.69710i	−0.238422	+	0.137653i
$153$	−3.90650	−	11.1531i	−0.315822	−	0.901675i
$154$	1.79620	+	6.70351i	0.144742	+	0.540184i
$155$	2.70466	−	4.68461i	0.217244	−	0.376277i
$156$	−2.98668	−	5.48450i	−0.239126	−	0.439111i
$157$	4.11430	+	7.12617i	0.328357	+	0.568731i	0.982186	−	0.187912i	$-0.0601719\pi$
$157$	4.11430	+	7.12617i	0.328357	+	0.568731i	−0.653829	+	0.756642i	$0.726839\pi$
$158$	−11.5014	+	11.5014i	−0.915004	+	0.915004i
$159$	11.5470	+	1.08100i	0.915737	+	0.0857292i
$160$		−	2.29324i		−	0.181296i
$161$	14.9443	−	14.9443i	1.17778	−	1.17778i
$162$	7.24467	+	5.33992i	0.569195	+	0.419543i
$163$	−14.8816	−	3.98750i	−1.16561	−	0.312325i	−0.376408	−	0.926454i	$-0.622841\pi$
$163$	−14.8816	−	3.98750i	−1.16561	−	0.312325i	−0.789206	+	0.614129i	$0.789507\pi$
$164$	3.94620	−	1.05738i	0.308146	−	0.0825675i
$165$	−5.39598	−	3.82740i	−0.420076	−	0.297963i
$166$		−	7.82588i		−	0.607406i
$167$	−2.39493	−	2.39493i	−0.185325	−	0.185325i	0.608347	−	0.793671i	$-0.291833\pi$
$167$	−2.39493	−	2.39493i	−0.185325	−	0.185325i	−0.793671	+	0.608347i	$0.791833\pi$
$168$	0.672706	−	7.18567i	0.0519004	−	0.554387i
$169$	−7.97483	−	10.2666i	−0.613448	−	0.789735i
$170$		−	9.03342i		−	0.692832i
$171$	4.41524	−	9.17557i	0.337642	−	0.701673i
$172$	−2.46107	+	4.26269i	−0.187655	+	0.325027i
$173$	−8.59114			−0.653172			−0.326586	−	0.945167i	$-0.605898\pi$
$173$	−8.59114			−0.653172			−0.326586	+	0.945167i	$0.605898\pi$
$174$	1.52074	+	8.94208i	0.115287	+	0.677897i
$175$	1.04217	−	0.279249i	0.0787809	−	0.0211093i
$176$	−1.60879	+	0.431075i	−0.121267	+	0.0324935i
$177$	2.51476	+	14.7870i	0.189021	+	1.11146i
$178$	9.27530			0.695213
$179$	−5.02767	+	8.70818i	−0.375786	+	0.650880i	−0.990444	−	0.137913i	$-0.955961\pi$
$179$	−5.02767	+	8.70818i	−0.375786	+	0.650880i	0.614658	+	0.788793i	$0.289294\pi$
$180$	3.87723	+	5.68309i	0.288992	+	0.423592i
$181$			4.65565i			0.346052i	0.984917	+	0.173026i	$0.0553545\pi$
$181$			4.65565i			0.346052i	−0.984917	+	0.173026i	$0.944646\pi$
$182$	−1.02697	−	14.9884i	−0.0761240	−	1.11102i
$183$	1.87638	−	20.0430i	0.138706	−	1.48162i
$184$	3.58652	+	3.58652i	0.264402	+	0.264402i
$185$		−	10.8084i		−	0.794648i
$186$	3.33241	+	2.36370i	0.244344	+	0.173315i
$187$	−6.33729	+	1.69807i	−0.463429	+	0.124175i
$188$	4.39173	+	1.17676i	0.320300	+	0.0858242i
$189$	10.4819	+	18.9449i	0.762446	+	1.37804i
$190$	5.50391	−	5.50391i	0.399296	−	0.399296i
$191$			8.62127i			0.623813i	0.950113	+	0.311906i	$0.100968\pi$
$191$			8.62127i			0.623813i	−0.950113	+	0.311906i	$0.899032\pi$
$192$	1.72451	+	0.161445i	0.124456	+	0.0116513i
$193$	−12.1598	+	12.1598i	−0.875283	+	0.875283i	−0.993042	−	0.117759i	$-0.962429\pi$
$193$	−12.1598	+	12.1598i	−0.875283	+	0.875283i	0.117759	+	0.993042i	$0.462429\pi$
$194$	−4.28111	−	7.41510i	−0.307366	−	0.532373i
$195$	9.87103	+	10.3760i	0.706879	+	0.743041i
$196$	5.18107	−	8.97388i	0.370077	−	0.640992i
$197$	−2.41082	−	8.99729i	−0.171764	−	0.641030i	−0.997080	−	0.0763603i	$-0.975670\pi$
$197$	−2.41082	−	8.99729i	−0.171764	−	0.641030i	0.825317	−	0.564670i	$-0.190997\pi$
$198$	3.25808	−	3.78832i	0.231542	−	0.269224i
$199$	−5.89590	+	3.40400i	−0.417950	+	0.241303i	−0.694200	−	0.719782i	$-0.744242\pi$
$199$	−5.89590	+	3.40400i	−0.417950	+	0.241303i	0.276250	+	0.961086i	$0.410908\pi$
$200$	0.0670178	+	0.250114i	0.00473888	+	0.0176857i
$201$	−18.5164	+	15.3462i	−1.30604	+	1.08244i
$202$	−4.33552	−	16.1804i	−0.305046	−	1.13845i
$203$	−5.64764	+	21.0773i	−0.396387	+	1.47934i
$204$	6.79312	+	0.635956i	0.475613	+	0.0445258i
$205$	−8.11362	+	4.68440i	−0.566680	+	0.327173i
$206$	8.42253	−	2.25681i	0.586825	−	0.157239i
$207$	−14.9519	−	2.82428i	−1.03923	−	0.196301i
$208$	3.59712	−	0.246465i	0.249415	−	0.0170893i
$209$	−4.89581	−	2.82660i	−0.338651	−	0.195520i
$210$	2.77483	+	16.3162i	0.191481	+	1.12593i
$211$	−17.3409			−1.19380			−0.596899	−	0.802316i	$-0.703601\pi$
$211$	−17.3409			−1.19380			−0.596899	+	0.802316i	$0.703601\pi$
$212$	−3.34791	+	5.79875i	−0.229935	+	0.398259i
$213$	−8.45502	+	22.7978i	−0.579328	+	1.56208i
$214$	7.18800	+	7.18800i	0.491362	+	0.491362i
$215$	2.92145	−	10.9030i	0.199241	−	0.743579i
$216$	−4.54663	+	2.51558i	−0.309359	+	0.171164i
$217$	4.91435	+	8.51190i	0.333608	+	0.577825i
$218$	1.49415	+	2.58795i	0.101197	+	0.175278i
$219$	−10.3351	−	12.4701i	−0.698381	−	0.842649i
$220$	3.30778	−	1.90975i	0.223010	−	0.128755i
$221$	14.1696	−	0.970865i	0.953151	−	0.0653074i
$222$	8.12788	+	0.760914i	0.545508	+	0.0510692i
$223$	−6.93742	+	25.8908i	−0.464564	+	1.73378i	0.193767	+	0.981048i	$0.437930\pi$
$223$	−6.93742	+	25.8908i	−0.464564	+	1.73378i	−0.658331	+	0.752729i	$0.728737\pi$
$224$	3.60855	+	2.08340i	0.241106	+	0.139203i
$225$	−0.588957	−	0.506523i	−0.0392638	−	0.0337682i
$226$	−13.1837	−	13.1837i	−0.876969	−	0.876969i
$227$	−4.85337	+	4.85337i	−0.322129	+	0.322129i	−0.849583	−	0.527454i	$-0.823147\pi$
$227$	−4.85337	+	4.85337i	−0.322129	+	0.322129i	0.527454	+	0.849583i	$0.323147\pi$
$228$	3.75145	+	4.52641i	0.248446	+	0.299769i
$229$	−17.2203	−	4.61415i	−1.13795	−	0.304912i	−0.359821	−	0.933021i	$-0.617162\pi$
$229$	−17.2203	−	4.61415i	−1.13795	−	0.304912i	−0.778125	+	0.628109i	$0.783829\pi$
$230$	−10.0732	−	5.81578i	−0.664209	−	0.383481i
$231$	10.9249	−	5.01372i	0.718804	−	0.329879i
$232$	−5.05840	−	1.35539i	−0.332100	−	0.0889859i
$233$	13.8109			0.904780			0.452390	−	0.891820i	$-0.350571\pi$
$233$	13.8109			0.904780			0.452390	+	0.891820i	$0.350571\pi$
$234$	−8.49766	+	6.69252i	−0.555509	+	0.437504i
$235$	−10.4266			−0.680154
$236$	−8.36478	−	2.24134i	−0.544501	−	0.145899i
$237$	22.9790	+	16.2991i	1.49265	+	1.05874i
$238$	14.2146	+	8.20682i	0.921398	+	0.531969i
$239$	21.4520	+	5.74805i	1.38762	+	0.371811i	0.873882	−	0.486139i	$-0.161595\pi$
$239$	21.4520	+	5.74805i	1.38762	+	0.371811i	0.513734	+	0.857949i	$0.328262\pi$
$240$	−3.91578	+	0.665939i	−0.252763	+	0.0429862i
$241$	7.02904	−	7.02904i	0.452781	−	0.452781i	−0.443496	−	0.896276i	$-0.646262\pi$
$241$	7.02904	−	7.02904i	0.452781	−	0.452781i	0.896276	+	0.443496i	$0.146262\pi$
$242$	5.81663	+	5.81663i	0.373907	+	0.373907i
$243$	7.01429	−	13.9212i	0.449967	−	0.893045i
$244$	10.0653	+	5.81123i	0.644368	+	0.372026i
$245$	−6.15028	+	22.9532i	−0.392927	+	1.46642i
$246$	−2.95146	−	6.43121i	−0.188178	−	0.410039i
$247$	9.22484	+	8.04177i	0.586962	+	0.511686i
$248$	−2.04279	+	1.17941i	−0.129718	+	0.0748925i
$249$	−13.3630	+	2.27258i	−0.846843	+	0.144019i
$250$	5.43619	+	9.41576i	0.343815	+	0.595505i
$251$	4.30727	+	7.46042i	0.271873	+	0.470897i	0.969341	−	0.245718i	$-0.0790237\pi$
$251$	4.30727	+	7.46042i	0.271873	+	0.470897i	−0.697469	+	0.716615i	$0.745690\pi$
$252$	−12.4651	+	0.937996i	−0.785229	+	0.0590882i
$253$	−2.18646	+	8.15999i	−0.137462	+	0.513014i
$254$	11.9502	+	11.9502i	0.749820	+	0.749820i
$255$	−15.4249	+	2.62324i	−0.965943	+	0.164273i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−13.3721			−0.834128			−0.417064	−	0.908877i	$-0.636941\pi$
$257$	−13.3721			−0.834128			−0.417064	+	0.908877i	$0.636941\pi$
$258$	7.99337	+	2.96450i	0.497645	+	0.184562i
$259$	17.0076	+	9.81936i	1.05680	+	0.610145i
$260$	−7.82168	+	2.68095i	−0.485080	+	0.166266i
$261$	14.8273	−	5.19342i	0.917786	−	0.321465i
$262$	10.9143	−	2.92448i	0.674288	−	0.180675i
$263$	−3.71361	+	2.14406i	−0.228991	+	0.132208i	−0.610107	−	0.792319i	$-0.708873\pi$
$263$	−3.71361	+	2.14406i	−0.228991	+	0.132208i	0.381115	+	0.924527i	$0.375540\pi$
$264$	1.20326	+	2.62189i	0.0740554	+	0.161366i
$265$	3.97419	−	14.8319i	0.244133	−	0.911115i
$266$	3.66046	+	13.6610i	0.224437	+	0.837610i
$267$	−2.69348	−	15.8379i	−0.164838	−	0.969264i
$268$	−3.59365	−	13.4117i	−0.219517	−	0.819249i
$269$	−13.1178	+	7.57359i	−0.799809	+	0.461770i	−0.843404	−	0.537279i	$-0.819452\pi$
$269$	−13.1178	+	7.57359i	−0.799809	+	0.461770i	0.0435953	+	0.999049i	$0.486119\pi$
$270$	8.57815	−	8.27083i	0.522050	−	0.503347i
$271$	−0.913090	−	3.40770i	−0.0554663	−	0.207003i	0.932631	−	0.360830i	$-0.117507\pi$
$271$	−0.913090	−	3.40770i	−0.0554663	−	0.207003i	−0.988098	+	0.153827i	$0.950840\pi$
$272$	−1.96958	+	3.41141i	−0.119423	+	0.206847i
$273$	−25.2950	+	6.10611i	−1.53093	+	0.369559i
$274$	−7.75321	−	13.4290i	−0.468389	−	0.811273i
$275$	−0.304955	+	0.304955i	−0.0183895	+	0.0183895i
$276$	5.08261	−	7.16561i	0.305937	−	0.431319i
$277$		−	21.9515i		−	1.31894i	−0.751732	−	0.659468i	$-0.770782\pi$
$277$		−	21.9515i		−	1.31894i	0.751732	−	0.659468i	$-0.229218\pi$
$278$	−12.6459	+	12.6459i	−0.758451	+	0.758451i
$279$	3.06839	−	6.37661i	0.183700	−	0.381757i
$280$	−9.22985	−	2.47313i	−0.551589	−	0.147798i
$281$	1.24159	−	0.332682i	0.0740668	−	0.0198461i	−0.221595	−	0.975139i	$-0.571126\pi$
$281$	1.24159	−	0.332682i	0.0740668	−	0.0198461i	0.295662	+	0.955293i	$0.404460\pi$
$282$	0.734034	−	7.84076i	0.0437111	−	0.466910i
$283$			12.4186i			0.738210i	0.929388	+	0.369105i	$0.120336\pi$
$283$			12.4186i			0.738210i	−0.929388	+	0.369105i	$0.879664\pi$
$284$	−9.92662	−	9.92662i	−0.589036	−	0.589036i
$285$	−10.9964	−	7.79982i	−0.651371	−	0.462022i
$286$	3.35109	+	4.98325i	0.198154	+	0.294666i
$287$		−	17.0230i		−	1.00484i
$288$	−0.225112	−	2.99154i	−0.0132649	−	0.176278i
$289$	0.741523	−	1.28436i	0.0436190	−	0.0755504i
$290$	12.0093			0.705211
$291$	−11.4183	+	9.46343i	−0.669354	+	0.554756i
$292$	9.03226	−	2.42019i	0.528573	−	0.141631i
$293$	7.88381	−	2.11246i	0.460577	−	0.123411i	−0.0210673	−	0.999778i	$-0.506706\pi$
$293$	7.88381	−	2.11246i	0.460577	−	0.123411i	0.481644	+	0.876367i	$0.340040\pi$
$294$	−16.8278	−	6.24091i	−0.981414	−	0.363977i
$295$	19.8591			1.15624
$296$	−2.35658	+	4.08171i	−0.136973	+	0.237245i
$297$	−7.41480	−	4.46318i	−0.430250	−	0.258980i
$298$		−	4.10784i		−	0.237961i
$299$	8.03987	−	16.4257i	0.464958	−	0.949921i
$300$	0.407617	−	0.187066i	0.0235338	−	0.0108003i
$301$	14.5024	+	14.5024i	0.835905	+	0.835905i
$302$		−	3.55087i		−	0.204330i
$303$	−26.3695	+	12.1017i	−1.51489	+	0.695224i
$304$	−3.27855	+	0.878484i	−0.188037	+	0.0503845i
$305$	−25.7449	−	6.89832i	−1.47415	−	0.394997i
$306$	−0.886753	−	11.7842i	−0.0506923	−	0.673655i
$307$	14.4197	−	14.4197i	0.822977	−	0.822977i	−0.163557	−	0.986534i	$-0.552297\pi$
$307$	14.4197	−	14.4197i	0.822977	−	0.822977i	0.986534	+	0.163557i	$0.0522968\pi$
$308$			6.93998i			0.395442i
$309$	−6.29942	−	13.7264i	−0.358361	−	0.780867i
$310$	3.82497	−	3.82497i	0.217244	−	0.217244i
$311$	2.55908	+	4.43246i	0.145112	+	0.251342i	0.929415	−	0.369037i	$-0.120312\pi$
$311$	2.55908	+	4.43246i	0.145112	+	0.251342i	−0.784303	+	0.620379i	$0.786979\pi$
$312$	−1.46542	−	6.07063i	−0.0829633	−	0.343682i
$313$	2.52339	−	4.37065i	0.142631	−	0.247043i	−0.785856	−	0.618410i	$-0.787777\pi$
$313$	2.52339	−	4.37065i	0.142631	−	0.247043i	0.928486	+	0.371366i	$0.121111\pi$
$314$	2.12972	+	7.94821i	0.120187	+	0.448544i
$315$	27.0547	−	9.47622i	1.52436	−	0.533925i
$316$	−14.0863	+	8.13274i	−0.792417	+	0.457502i
$317$	1.64335	+	6.13308i	0.0922999	+	0.344468i	0.996596	−	0.0824373i	$-0.0262704\pi$
$317$	1.64335	+	6.13308i	0.0922999	+	0.344468i	−0.904296	+	0.426905i	$0.859604\pi$
$318$	10.8738	+	4.03275i	0.609770	+	0.226146i
$319$	−2.25747	−	8.42500i	−0.126394	−	0.471709i
$320$	0.593533	−	2.21510i	0.0331795	−	0.123828i
$321$	10.1864	−	14.3611i	0.568550	−	0.801558i
$322$	18.3030	−	10.5672i	1.01998	−	0.588888i
$323$	−12.9147	+	3.46048i	−0.718593	+	0.192547i
$324$	5.61575	+	7.03302i	0.311986	+	0.390723i
$325$	0.774730	−	0.520982i	0.0429743	−	0.0288989i
$326$	−13.3424	−	7.70326i	−0.738969	−	0.426644i
$327$	3.98512	−	3.30284i	0.220378	−	0.182647i
$328$	4.08540			0.225579
$329$	9.47249	−	16.4068i	0.522235	−	0.904538i
$330$	−4.22151	−	5.09357i	−0.232387	−	0.280392i
$331$	2.03052	+	2.03052i	0.111607	+	0.111607i	0.760705	−	0.649098i	$-0.224853\pi$
$331$	2.03052	+	2.03052i	0.111607	+	0.111607i	−0.649098	+	0.760705i	$0.724853\pi$
$332$	2.02549	−	7.55922i	0.111163	−	0.414866i
$333$	−1.06099	−	14.0996i	−0.0581418	−	0.772653i
$334$	−1.69347	−	2.93317i	−0.0926624	−	0.160496i
$335$	15.9206	+	27.5752i	0.869834	+	1.50660i
$336$	2.50957	−	6.76672i	0.136908	−	0.369155i
$337$	11.4454	−	6.60801i	0.623471	−	0.359961i	−0.154748	−	0.987954i	$-0.549457\pi$
$337$	11.4454	−	6.60801i	0.623471	−	0.359961i	0.778219	+	0.627993i	$0.216123\pi$
$338$	−5.04591	−	11.9808i	−0.274462	−	0.651668i
$339$	−18.6832	+	26.3401i	−1.01473	+	1.43060i
$340$	2.33802	−	8.72561i	0.126797	−	0.473213i
$341$	−3.40237	−	1.96436i	−0.184249	−	0.106376i
$342$	6.63960	−	7.72017i	0.359029	−	0.417459i
$343$	−9.90611	−	9.90611i	−0.534880	−	0.534880i
$344$	−3.48048	+	3.48048i	−0.187655	+	0.187655i
$345$	−7.00545	+	18.8892i	−0.377161	+	1.01696i
$346$	−8.29840	−	2.22355i	−0.446125	−	0.119539i
$347$	3.45612	+	1.99539i	0.185534	+	0.107118i	0.589890	−	0.807483i	$-0.299171\pi$
$347$	3.45612	+	1.99539i	0.185534	+	0.107118i	−0.404356	+	0.914602i	$0.632504\pi$
$348$	−0.845460	+	9.03098i	−0.0453214	+	0.484111i
$349$	−15.6408	−	4.19093i	−0.837230	−	0.224335i	−0.185365	−	0.982670i	$-0.559347\pi$
$349$	−15.6408	−	4.19093i	−0.837230	−	0.224335i	−0.651866	+	0.758335i	$0.726013\pi$
$350$	1.07894			0.0576716
$351$	13.8954	+	12.5666i	0.741680	+	0.670754i
$352$	−1.66555			−0.0887739
$353$	1.71497	+	0.459526i	0.0912789	+	0.0244581i	0.304169	−	0.952618i	$-0.401621\pi$
$353$	1.71497	+	0.459526i	0.0912789	+	0.0244581i	−0.212891	+	0.977076i	$0.568288\pi$
$354$	−1.39809	+	14.9340i	−0.0743076	+	0.793734i
$355$	27.8802	+	16.0966i	1.47973	+	0.854321i
$356$	8.95926	+	2.40063i	0.474840	+	0.127233i
$357$	9.88560	−	26.6552i	0.523202	−	1.41074i
$358$	−7.11020	+	7.11020i	−0.375786	+	0.375786i
$359$	5.40394	+	5.40394i	0.285209	+	0.285209i	0.835182	−	0.549973i	$-0.185362\pi$
$359$	5.40394	+	5.40394i	0.285209	+	0.285209i	−0.549973	+	0.835182i	$0.685362\pi$
$360$	2.27423	+	6.49294i	0.119862	+	0.342208i
$361$	6.47736	+	3.73970i	0.340913	+	0.196826i
$362$	−1.20497	+	4.49702i	−0.0633319	+	0.236358i
$363$	8.24299	−	11.6212i	0.432645	−	0.609955i
$364$	2.88732	−	14.7435i	0.151337	−	0.772770i
$365$	−18.5709	+	10.7219i	−0.972043	+	0.561209i
$366$	6.99997	−	18.8745i	0.365894	−	0.986584i
$367$	−11.4578	−	19.8455i	−0.598092	−	1.03593i	−0.993102	−	0.117250i	$-0.962592\pi$
$367$	−11.4578	−	19.8455i	−0.598092	−	1.03593i	0.395010	−	0.918677i	$-0.370741\pi$
$368$	2.53606	+	4.39258i	0.132201	+	0.228979i
$369$	−10.1244	+	6.90729i	−0.527057	+	0.359579i
$370$	2.79741	−	10.4401i	0.145431	−	0.542754i
$371$	19.7283	+	19.7283i	1.02424	+	1.02424i
$372$	2.60709	+	3.14565i	0.135171	+	0.163094i
$373$	6.18794	−	10.7178i	0.320400	−	0.554948i	−0.660171	−	0.751115i	$-0.729516\pi$
$373$	6.18794	−	10.7178i	0.320400	−	0.554948i	0.980570	+	0.196167i	$0.0628495\pi$
$374$	−6.56085			−0.339253
$375$	14.4991	−	12.0167i	0.748730	−	0.620542i
$376$	3.93752	+	2.27333i	0.203062	+	0.117238i
$377$	1.29070	+	18.8375i	0.0664743	+	0.970182i
$378$	5.22144	+	21.0122i	0.268562	+	1.08075i
$379$	−15.6589	+	4.19579i	−0.804344	+	0.215523i	−0.637490	−	0.770458i	$-0.720027\pi$
$379$	−15.6589	+	4.19579i	−0.804344	+	0.215523i	−0.166854	+	0.985982i	$0.553361\pi$
$380$	6.74089	−	3.89185i	0.345800	−	0.199648i
$381$	16.9351	−	23.8755i	0.867610	−	1.22318i
$382$	−2.23135	+	8.32750i	−0.114166	+	0.426072i
$383$	−1.88172	−	7.02266i	−0.0961512	−	0.358841i	0.901040	−	0.433735i	$-0.142805\pi$
$383$	−1.88172	−	7.02266i	−0.0961512	−	0.358841i	−0.997191	+	0.0748943i	$0.976138\pi$
$384$	1.62396	+	0.602280i	0.0828726	+	0.0307350i
$385$	−4.11911	−	15.3727i	−0.209929	−	0.783467i
$386$	−14.8927	+	8.59830i	−0.758018	+	0.437642i
$387$	2.74077	−	14.5098i	0.139321	−	0.737576i
$388$	−2.21607	−	8.27047i	−0.112504	−	0.419869i
$389$	12.0896	−	20.9397i	0.612965	−	1.06169i	−0.377773	−	0.925898i	$-0.623310\pi$
$389$	12.0896	−	20.9397i	0.612965	−	1.06169i	0.990738	−	0.135788i	$-0.0433566\pi$
$390$	6.84918	+	12.5773i	0.346822	+	0.636874i
$391$	9.98992	+	17.3030i	0.505212	+	0.875053i
$392$	7.32714	−	7.32714i	0.370077	−	0.370077i
$393$	−8.16308	−	17.7873i	−0.411773	−	0.897251i
$394$		−	9.31468i		−	0.469267i
$395$	26.3755	−	26.3755i	1.32710	−	1.32710i
$396$	4.12755	−	2.81598i	0.207417	−	0.141508i
$397$	−16.2930	−	4.36571i	−0.817724	−	0.219109i	−0.174373	−	0.984680i	$-0.555790\pi$
$397$	−16.2930	−	4.36571i	−0.817724	−	0.219109i	−0.643351	+	0.765571i	$0.722457\pi$
$398$	−6.57603	+	1.76204i	−0.329626	+	0.0883231i
$399$	22.2637	−	10.2174i	1.11458	−	0.511510i
$400$			0.258937i			0.0129469i
$401$	14.4886	+	14.4886i	0.723524	+	0.723524i	0.969321	−	0.245798i	$-0.0790498\pi$
$401$	14.4886	+	14.4886i	0.723524	+	0.723524i	−0.245798	+	0.969321i	$0.579050\pi$
$402$	−21.8573	+	10.0309i	−1.09014	+	0.500297i
$403$	6.41085	+	5.58867i	0.319347	+	0.278391i
$404$		−	16.7511i		−	0.833401i
$405$	−16.6138	−	12.2457i	−0.825544	−	0.608493i
$406$	−10.9104	+	18.8974i	−0.541474	+	0.937861i
$407$	−7.84998			−0.389109
$408$	6.39705	+	2.37247i	0.316701	+	0.117455i
$409$	−16.5616	+	4.43768i	−0.818921	+	0.219429i	−0.643875	−	0.765131i	$-0.722674\pi$
$409$	−16.5616	+	4.43768i	−0.818921	+	0.219429i	−0.175046	+	0.984560i	$0.556007\pi$
$410$	−9.04957	+	2.42482i	−0.446926	+	0.119754i
$411$	−20.6789	+	17.1385i	−1.02002	+	0.845382i
$412$	8.71964			0.429586
$413$	−18.0419	+	31.2495i	−0.887785	+	1.53769i
$414$	−13.7115	−	6.59789i	−0.673882	−	0.324269i
$415$			17.9466i			0.880964i
$416$	3.53834	+	0.692936i	0.173481	+	0.0339740i
$417$	25.2656	+	17.9210i	1.23726	+	0.877597i
$418$	−3.99742	−	3.99742i	−0.195520	−	0.195520i
$419$		−	27.7250i		−	1.35446i	−0.735773	−	0.677228i	$-0.763181\pi$
$419$		−	27.7250i		−	1.35446i	0.735773	−	0.677228i	$-0.236819\pi$
$420$	−1.54268	+	16.4785i	−0.0752749	+	0.804066i
$421$	28.1804	−	7.55093i	1.37343	−	0.368010i	0.504700	−	0.863295i	$-0.331603\pi$
$421$	28.1804	−	7.55093i	1.37343	−	0.368010i	0.868731	+	0.495285i	$0.164936\pi$
$422$	−16.7500	−	4.48816i	−0.815380	−	0.218480i
$423$	−13.6015	+	1.02351i	−0.661328	+	0.0497647i
$424$	−4.73466	+	4.73466i	−0.229935	+	0.229935i
$425$			1.01999i			0.0494770i
$426$	−14.0674	+	19.8327i	−0.681569	+	0.960895i
$427$	34.2440	−	34.2440i	1.65718	−	1.65718i
$428$	5.08268	+	8.80347i	0.245681	+	0.425532i
$429$	7.53594	−	7.16919i	0.363839	−	0.346132i
$430$	5.64381	−	9.77537i	0.272169	−	0.471410i
$431$	0.105936	+	0.395359i	0.00510277	+	0.0190438i	0.968430	−	0.249285i	$-0.0801955\pi$
$431$	0.105936	+	0.395359i	0.00510277	+	0.0190438i	−0.963328	+	0.268328i	$0.913529\pi$
$432$	−5.04279	+	1.25311i	−0.242621	+	0.0602902i
$433$	16.7881	−	9.69262i	0.806785	−	0.465798i	−0.0390532	−	0.999237i	$-0.512434\pi$
$433$	16.7881	−	9.69262i	0.806785	−	0.465798i	0.845838	+	0.533440i	$0.179101\pi$
$434$	2.54385	+	9.49379i	0.122109	+	0.455716i
$435$	−3.48741	−	20.5063i	−0.167209	−	0.983202i
$436$	0.773431	+	2.88648i	0.0370406	+	0.138237i
$437$	−4.45577	+	16.6291i	−0.213148	+	0.795480i
$438$	−6.75545	−	14.7201i	−0.322788	−	0.703353i
$439$	14.8206	−	8.55666i	0.707348	−	0.408387i	−0.102731	−	0.994709i	$-0.532758\pi$
$439$	14.8206	−	8.55666i	0.707348	−	0.408387i	0.810078	+	0.586322i	$0.199425\pi$
$440$	3.68935	−	0.988558i	0.175883	−	0.0471276i
$441$	−5.76991	+	30.5463i	−0.274758	+	1.45458i
$442$	13.9381	+	2.72958i	0.662966	+	0.129833i
$443$	2.12505	+	1.22690i	0.100964	+	0.0582916i	0.549632	−	0.835407i	$-0.314768\pi$
$443$	2.12505	+	1.22690i	0.100964	+	0.0582916i	−0.448668	+	0.893699i	$0.648101\pi$
$444$	7.65399	+	2.83864i	0.363242	+	0.134716i
$445$	−21.2705			−1.00832
$446$	−13.4021	+	23.2131i	−0.634606	+	1.09917i
$447$	−7.01428	+	1.19289i	−0.331764	+	0.0564216i
$448$	2.94637	+	2.94637i	0.139203	+	0.139203i
$449$	1.17970	−	4.40270i	0.0556735	−	0.207776i	−0.932486	−	0.361206i	$-0.882365\pi$
$449$	1.17970	−	4.40270i	0.0556735	−	0.207776i	0.988160	+	0.153429i	$0.0490318\pi$
$450$	−0.437791	−	0.641697i	−0.0206377	−	0.0302499i
$451$	3.40222	+	5.89281i	0.160204	+	0.277482i
$452$	−9.32231	−	16.1467i	−0.438484	−	0.759477i
$453$	−6.06324	+	1.03115i	−0.284876	+	0.0484475i
$454$	−5.94413	+	3.43185i	−0.278972	+	0.161065i
$455$	2.35508	+	34.3720i	0.110408	+	1.61139i
$456$	2.45211	+	5.34312i	0.114830	+	0.250215i
$457$	−2.23930	+	8.35718i	−0.104750	+	0.390933i	−0.998317	−	0.0579980i	$-0.981528\pi$
$457$	−2.23930	+	8.35718i	−0.104750	+	0.390933i	0.893567	+	0.448931i	$0.148195\pi$
$458$	−15.4393	−	8.91386i	−0.721429	−	0.416517i
$459$	−19.8643	+	4.93619i	−0.927188	+	0.230402i
$460$	−8.22475	−	8.22475i	−0.383481	−	0.383481i
$461$	13.6214	−	13.6214i	0.634412	−	0.634412i	−0.314760	−	0.949171i	$-0.601924\pi$
$461$	13.6214	−	13.6214i	0.634412	−	0.634412i	0.949171	+	0.314760i	$0.101924\pi$
$462$	11.8503	−	2.01532i	0.551324	−	0.0937611i
$463$	3.25146	+	0.871225i	0.151108	+	0.0404893i	0.333580	−	0.942722i	$-0.391743\pi$
$463$	3.25146	+	0.871225i	0.151108	+	0.0404893i	−0.182472	+	0.983211i	$0.558410\pi$
$464$	−4.53523	−	2.61842i	−0.210543	−	0.121557i
$465$	−7.64201	−	5.42052i	−0.354390	−	0.251371i
$466$	13.3403	+	3.57452i	0.617976	+	0.165586i
$467$	−25.8396			−1.19571			−0.597856	−	0.801604i	$-0.703981\pi$
$467$	−25.8396			−1.19571			−0.597856	+	0.801604i	$0.703981\pi$
$468$	−9.94026	+	4.26513i	−0.459489	+	0.197155i
$469$	−57.8550			−2.67150
$470$	−10.0713	−	2.69859i	−0.464554	−	0.124477i
$471$	12.9534	−	5.94467i	0.596861	−	0.273916i
$472$	−7.49966	−	4.32993i	−0.345200	−	0.199301i
$473$	−7.91870	−	2.12181i	−0.364102	−	0.0975609i
$474$	17.9775	+	21.6912i	0.825733	+	0.996309i
$475$	−0.621465	+	0.621465i	−0.0285148	+	0.0285148i
$476$	11.6062	+	11.6062i	0.531969	+	0.531969i
$477$	3.72840	−	19.7384i	0.170712	−	0.903759i
$478$	19.2334	+	11.1044i	0.879713	+	0.507903i
$479$	5.25832	−	19.6243i	0.240259	−	0.896657i	−0.735449	−	0.677580i	$-0.763029\pi$
$479$	5.25832	−	19.6243i	0.240259	−	0.896657i	0.975708	−	0.219077i	$-0.0703047\pi$
$480$	−3.95471	−	0.370231i	−0.180507	−	0.0168987i
$481$	16.6767	+	3.26591i	0.760393	+	0.148913i
$482$	8.60879	−	4.97029i	0.392119	−	0.226390i
$483$	−23.3589	−	28.1843i	−1.06287	−	1.28243i
$484$	4.11298	+	7.12389i	0.186954	+	0.323813i
$485$	9.81760	+	17.0046i	0.445794	+	0.772138i
$486$	10.3784	−	11.6314i	0.470772	−	0.527612i
$487$	−9.75089	+	36.3908i	−0.441855	+	1.64902i	0.282255	+	0.959340i	$0.408918\pi$
$487$	−9.75089	+	36.3908i	−0.441855	+	1.64902i	−0.724109	+	0.689685i	$0.757749\pi$
$488$	8.21832	+	8.21832i	0.372026	+	0.372026i
$489$	−9.27903	+	25.0196i	−0.419612	+	1.13143i
$490$	−11.8814	+	20.5792i	−0.536748	+	0.929675i
$491$	25.8129			1.16492			0.582459	−	0.812860i	$-0.302091\pi$
$491$	25.8129			1.16492			0.582459	+	0.812860i	$0.302091\pi$
$492$	−1.18637	−	6.97597i	−0.0534857	−	0.314501i
$493$	−17.8650	−	10.3144i	−0.804599	−	0.464535i
$494$	6.82914	+	10.1553i	0.307258	+	0.456909i
$495$	−7.47155	+	8.68751i	−0.335821	+	0.390474i
$496$	−2.27844	+	0.610507i	−0.102305	+	0.0274126i
$497$	−50.6581	+	29.2475i	−2.27233	+	1.31193i
$498$	−13.4958	−	1.26345i	−0.604762	−	0.0566164i
$499$	−4.92584	+	18.3835i	−0.220511	+	0.822958i	0.763642	+	0.645639i	$0.223409\pi$
$499$	−4.92584	+	18.3835i	−0.220511	+	0.822958i	−0.984153	+	0.177319i	$0.943258\pi$
$500$	2.81398	+	10.5019i	0.125845	+	0.469660i
$501$	−4.51672	+	3.74342i	−0.201792	+	0.167244i
$502$	2.22961	+	8.32102i	0.0995123	+	0.371385i
$503$	2.59687	−	1.49930i	0.115789	−	0.0668507i	−0.440987	−	0.897513i	$-0.645372\pi$
$503$	2.59687	−	1.49930i	0.115789	−	0.0668507i	0.556776	+	0.830663i	$0.312038\pi$
$504$	−12.2832	−	2.32018i	−0.547136	−	0.103349i
$505$	9.94237	+	37.1054i	0.442430	+	1.65117i
$506$	−4.22392	+	7.31604i	−0.187776	+	0.325238i
$507$	−18.9923	+	12.0952i	−0.843476	+	0.537166i
$508$	8.45004	+	14.6359i	0.374910	+	0.649363i
$509$	16.7482	−	16.7482i	0.742351	−	0.742351i	−0.230679	−	0.973030i	$-0.574095\pi$
$509$	16.7482	−	16.7482i	0.742351	−	0.742351i	0.973030	+	0.230679i	$0.0740947\pi$
$510$	−15.5782	−	1.45840i	−0.689815	−	0.0645790i
$511$		−	38.9632i		−	1.72363i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−15.1105	−	9.09547i	−0.667147	−	0.401575i
$514$	−12.9164	−	3.46095i	−0.569720	−	0.152656i
$515$	−19.3149	+	5.17540i	−0.851114	+	0.228055i
$516$	6.95373	+	4.93233i	0.306121	+	0.217134i
$517$			7.57267i			0.333046i
$518$	13.8867	+	13.8867i	0.610145	+	0.610145i
$519$	−1.38699	+	14.8155i	−0.0608823	+	0.650329i
$520$	−8.24904	+	0.565203i	−0.361745	+	0.0247858i
$521$		−	9.92644i		−	0.434885i	−0.976073	−	0.217443i	$-0.930229\pi$
$521$		−	9.92644i		−	0.434885i	0.976073	−	0.217443i	$-0.0697715\pi$
$522$	15.6662	−	1.17888i	0.685692	−	0.0515980i
$523$	8.91409	−	15.4397i	0.389786	−	0.675129i	−0.602635	−	0.798017i	$-0.705882\pi$
$523$	8.91409	−	15.4397i	0.389786	−	0.675129i	0.992421	+	0.122888i	$0.0392157\pi$
$524$	11.2993			0.493613
$525$	−0.313315	−	1.84232i	−0.0136742	−	0.0804055i
$526$	−4.14200	+	1.10984i	−0.180600	+	0.0483915i
$527$	−8.97514	+	2.40488i	−0.390963	+	0.104758i
$528$	0.483662	+	2.84398i	0.0210487	+	0.123768i
$529$	2.72632			0.118536
$530$	7.67755	−	13.2979i	0.333491	−	0.577624i
$531$	25.9063	−	1.94944i	1.12424	−	0.0845986i
$532$			14.1429i			0.613173i
$533$	−4.77612	−	13.9343i	−0.206877	−	0.603563i
$534$	1.49745	−	15.9954i	0.0648010	−	0.692187i
$535$	−16.4838	−	16.4838i	−0.712656	−	0.712656i
$536$		−	13.8848i		−	0.599732i
$537$	14.2057	+	10.0762i	0.613020	+	0.434819i
$538$	−14.6311	+	3.92038i	−0.630790	+	0.169020i
$539$	16.6706	+	4.46686i	0.718052	+	0.192401i
$540$	10.4265	−	5.76882i	0.448685	−	0.248251i
$541$	29.6359	−	29.6359i	1.27415	−	1.27415i	0.330258	−	0.943891i	$-0.392864\pi$
$541$	29.6359	−	29.6359i	1.27415	−	1.27415i	0.943891	−	0.330258i	$-0.107136\pi$
$542$		−	3.52791i		−	0.151537i
$543$	8.02872	+	0.751631i	0.344545	+	0.0322556i
$544$	−2.78540	+	2.78540i	−0.119423	+	0.119423i
$545$	−3.42645	−	5.93478i	−0.146773	−	0.254218i
$546$	−26.0135	−	0.648786i	−1.11328	−	0.0277655i
$547$	−11.2632	+	19.5084i	−0.481580	+	0.834120i	−0.999777	−	0.0211411i	$-0.993270\pi$
$547$	−11.2632	+	19.5084i	−0.481580	+	0.834120i	0.518197	+	0.855261i	$0.326603\pi$
$548$	−4.01336	−	14.9781i	−0.171442	−	0.639831i
$549$	−34.2615	−	6.47169i	−1.46225	−	0.276205i
$550$	−0.373492	+	0.215636i	−0.0159258	+	0.00919474i
$551$	−4.60048	−	17.1692i	−0.195987	−	0.731433i
$552$	6.76402	−	5.60597i	0.287896	−	0.238606i
$553$	17.5414	+	65.4655i	0.745937	+	2.78387i
$554$	5.68146	−	21.2035i	0.241382	−	0.900850i
$555$	−18.6392	−	1.74496i	−0.791188	−	0.0740692i
$556$	−15.4880	+	8.94201i	−0.656838	+	0.379226i
$557$	43.1111	−	11.5516i	1.82668	−	0.489457i	0.829105	−	0.559093i	$-0.188850\pi$
$557$	43.1111	−	11.5516i	1.82668	−	0.489457i	0.997572	+	0.0696359i	$0.0221838\pi$
$558$	4.61422	−	5.36517i	0.195336	−	0.227126i
$559$	15.9400	+	7.80214i	0.674189	+	0.329996i
$560$	−8.27525	−	4.77772i	−0.349693	−	0.201896i
$561$	1.90522	+	11.2029i	0.0804385	+	0.472986i
$562$	1.28538			0.0542207
$563$	0.917730	−	1.58956i	0.0386777	−	0.0669918i	−0.846039	−	0.533122i	$-0.821019\pi$
$563$	0.917730	−	1.58956i	0.0386777	−	0.0669918i	0.884716	+	0.466130i	$0.154352\pi$
$564$	2.73836	−	7.38361i	0.115306	−	0.310906i
$565$	30.2334	+	30.2334i	1.27193	+	1.27193i
$566$	−3.21417	+	11.9955i	−0.135102	+	0.504206i
$567$	34.3629	−	15.0176i	1.44310	−	0.630679i
$568$	−7.01918	−	12.1576i	−0.294518	−	0.510121i
$569$	2.95160	+	5.11231i	0.123737	+	0.214319i	0.921239	−	0.388998i	$-0.127179\pi$
$569$	2.95160	+	5.11231i	0.123737	+	0.214319i	−0.797501	+	0.603317i	$0.793845\pi$
$570$	−8.60297	−	10.3801i	−0.360339	−	0.434776i
$571$	−6.53279	+	3.77171i	−0.273389	+	0.157841i	−0.630427	−	0.776249i	$-0.717120\pi$
$571$	−6.53279	+	3.77171i	−0.273389	+	0.157841i	0.357038	+	0.934090i	$0.383787\pi$
$572$	1.94714	+	5.68078i	0.0814140	+	0.237525i
$573$	14.8675	+	1.39186i	0.621097	+	0.0581457i
$574$	4.40588	−	16.4430i	0.183898	−	0.686317i
$575$	1.13740	+	0.656679i	0.0474329	+	0.0273854i
$576$	0.556826	−	2.94787i	0.0232011	−	0.122828i
$577$	−9.95468	−	9.95468i	−0.414419	−	0.414419i	0.468856	−	0.883275i	$-0.344666\pi$
$577$	−9.95468	−	9.95468i	−0.414419	−	0.414419i	−0.883275	+	0.468856i	$0.844666\pi$
$578$	1.04867	−	1.04867i	0.0436190	−	0.0436190i
$579$	19.0066	+	22.9329i	0.789888	+	0.953058i
$580$	11.6001	+	3.10824i	0.481668	+	0.129063i
$581$	−28.2401	−	16.3044i	−1.17159	−	0.676421i
$582$	−13.4786	+	6.18569i	−0.558705	+	0.256405i
$583$	−10.7722	−	2.88640i	−0.446139	−	0.119542i
$584$	9.35088			0.386942
$585$	19.4871	−	15.3475i	0.805694	−	0.634543i
$586$	8.16192			0.337166
$587$	−7.62913	−	2.04422i	−0.314888	−	0.0843739i	0.0979138	−	0.995195i	$-0.468783\pi$
$587$	−7.62913	−	2.04422i	−0.314888	−	0.0843739i	−0.412802	+	0.910821i	$0.635450\pi$
$588$	−14.6391	−	10.3836i	−0.603706	−	0.428212i
$589$	−6.93365	−	4.00315i	−0.285696	−	0.164947i
$590$	19.1824	+	5.13992i	0.789728	+	0.211607i
$591$	−15.9051	+	2.70491i	−0.654250	+	0.111265i
$592$	−3.33270	+	3.33270i	−0.136973	+	0.136973i
$593$	17.4187	+	17.4187i	0.715300	+	0.715300i	0.967639	−	0.252339i	$-0.0811998\pi$
$593$	17.4187	+	17.4187i	0.715300	+	0.715300i	−0.252339	+	0.967639i	$0.581200\pi$
$594$	−6.00699	−	6.23019i	−0.246470	−	0.255628i
$595$	−32.5975	−	18.8202i	−1.33637	−	0.771552i
$596$	1.06319	−	3.96787i	0.0435499	−	0.162530i
$597$	4.91837	+	10.7171i	0.201296	+	0.438622i
$598$	12.0172	−	13.7851i	0.491420	−	0.563715i
$599$	41.2663	−	23.8251i	1.68610	−	0.973468i	0.728635	−	0.684902i	$-0.240155\pi$
$599$	41.2663	−	23.8251i	1.68610	−	0.973468i	0.957460	−	0.288566i	$-0.0931783\pi$
$600$	0.442144	−	0.0751934i	0.0180504	−	0.00306976i
$601$	14.5212	+	25.1515i	0.592334	+	1.02595i	0.993917	+	0.110130i	$0.0351267\pi$
$601$	14.5212	+	25.1515i	0.592334	+	1.02595i	−0.401583	+	0.915822i	$0.631540\pi$
$602$	10.2548	+	17.7618i	0.417953	+	0.723915i
$603$	23.4754	+	34.4092i	0.955991	+	1.40125i
$604$	0.919034	−	3.42988i	0.0373949	−	0.139560i
$605$	−13.3389	−	13.3389i	−0.542304	−	0.542304i
$606$	−28.6032	+	4.86441i	−1.16192	+	0.197603i
$607$	8.21069	−	14.2213i	0.333262	−	0.577226i	−0.649888	−	0.760030i	$-0.725184\pi$
$607$	8.21069	−	14.2213i	0.333262	−	0.577226i	0.983149	+	0.182804i	$0.0585174\pi$
$608$	−3.39420			−0.137653
$609$	35.4362	+	13.1422i	1.43595	+	0.532550i
$610$	−23.0822	−	13.3265i	−0.934572	−	0.539575i
$611$	3.15054	−	16.0876i	0.127457	−	0.650835i
$612$	2.19343	−	11.6121i	0.0886640	−	0.469392i
$613$	−19.6188	+	5.25684i	−0.792396	+	0.212322i	−0.632243	−	0.774770i	$-0.717865\pi$
$613$	−19.6188	+	5.25684i	−0.792396	+	0.212322i	−0.160153	+	0.987092i	$0.551199\pi$
$614$	17.6605	−	10.1963i	0.712719	−	0.411488i
$615$	6.76840	+	14.7483i	0.272928	+	0.594709i
$616$	−1.79620	+	6.70351i	−0.0723710	+	0.270092i
$617$	−8.27870	−	30.8965i	−0.333288	−	1.24385i	−0.905713	−	0.423891i	$-0.860664\pi$
$617$	−8.27870	−	30.8965i	−0.333288	−	1.24385i	0.572425	−	0.819957i	$-0.306003\pi$
$618$	−2.53212	−	14.8891i	−0.101857	−	0.598927i
$619$	−9.90270	−	36.9574i	−0.398023	−	1.48544i	−0.816569	−	0.577247i	$-0.804127\pi$
$619$	−9.90270	−	36.9574i	−0.398023	−	1.48544i	0.418546	−	0.908196i	$-0.362540\pi$
$620$	4.68461	−	2.70466i	0.188139	−	0.108622i
$621$	−7.28442	+	25.3288i	−0.292314	+	1.01641i
$622$	1.32468	+	4.94377i	0.0531148	+	0.198227i
$623$	19.3241	−	33.4704i	0.774205	−	1.34096i
$624$	0.155704	−	6.24306i	0.00623315	−	0.249922i
$625$	−13.1138	−	22.7138i	−0.524553	−	0.908552i
$626$	3.56862	−	3.56862i	0.142631	−	0.142631i
$627$	−5.66490	+	7.98654i	−0.226234	+	0.318952i
$628$			8.22860i			0.328357i
$629$	−13.1280	+	13.1280i	−0.523449	+	0.523449i
$630$	28.5855	−	2.15105i	1.13887	−	0.0856998i
$631$	16.0911	+	4.31160i	0.640577	+	0.171642i	0.564465	−	0.825457i	$-0.309083\pi$
$631$	16.0911	+	4.31160i	0.640577	+	0.171642i	0.0761122	+	0.997099i	$0.475749\pi$
$632$	−15.7112	+	4.20981i	−0.624960	+	0.167457i
$633$	−2.79960	+	29.9046i	−0.111274	+	1.18860i
$634$			6.34943i			0.252168i
$635$	−27.4046	−	27.4046i	−1.08752	−	1.08752i
$636$	9.45949	+	6.70968i	0.375093	+	0.266056i
$637$	−33.5571	−	16.4252i	−1.32958	−	0.650789i
$638$		−	8.72220i		−	0.345315i
$639$	37.9500	+	18.2614i	1.50128	+	0.722408i
$640$	1.14662	−	1.98600i	0.0453241	−	0.0785036i
$641$	−31.7007			−1.25210			−0.626051	−	0.779782i	$-0.715330\pi$
$641$	−31.7007			−1.25210			−0.626051	+	0.779782i	$0.715330\pi$
$642$	13.5562	−	11.2353i	0.535022	−	0.443422i
$643$	−1.39852	+	0.374733i	−0.0551524	+	0.0147780i	−0.286290	−	0.958143i	$-0.592422\pi$
$643$	−1.39852	+	0.374733i	−0.0551524	+	0.0147780i	0.231137	+	0.972921i	$0.425755\pi$
$644$	20.4143	−	5.46999i	0.804436	−	0.215548i
$645$	−18.3307	−	6.79831i	−0.721770	−	0.267683i
$646$	−13.3703			−0.526047
$647$	−9.55687	+	16.5530i	−0.375719	+	0.650765i	−0.990434	−	0.137984i	$-0.955938\pi$
$647$	−9.55687	+	16.5530i	−0.375719	+	0.650765i	0.614715	+	0.788749i	$0.289271\pi$
$648$	3.60411	+	8.24684i	0.141583	+	0.323966i
$649$		−	14.4234i		−	0.566168i
$650$	0.883172	−	0.302715i	0.0346409	−	0.0118735i
$651$	15.4723	−	7.10064i	0.606405	−	0.278296i
$652$	−10.8941	−	10.8941i	−0.426644	−	0.426644i
$653$			42.3769i			1.65834i	0.558998	+	0.829169i	$0.311186\pi$
$653$			42.3769i			1.65834i	−0.558998	+	0.829169i	$0.688814\pi$
$654$	4.70417	−	2.15887i	0.183948	−	0.0844186i
$655$	−25.0291	+	6.70653i	−0.977968	+	0.262046i
$656$	3.94620	+	1.05738i	0.154073	+	0.0412838i
$657$	−23.1733	+	15.8098i	−0.904077	+	0.616797i
$658$	13.3961	−	13.3961i	0.522235	−	0.522235i
$659$		−	7.55088i		−	0.294141i	−0.989126	−	0.147070i	$-0.953016\pi$
$659$		−	7.55088i		−	0.294141i	0.989126	−	0.147070i	$-0.0469844\pi$
$660$	−2.75935	−	6.01262i	−0.107408	−	0.234041i
$661$	12.5495	−	12.5495i	0.488119	−	0.488119i	−0.419593	−	0.907712i	$-0.637827\pi$
$661$	12.5495	−	12.5495i	0.488119	−	0.488119i	0.907712	+	0.419593i	$0.137827\pi$
$662$	1.43579	+	2.48687i	0.0558037	+	0.0966549i
$663$	0.613343	−	24.5924i	0.0238203	−	0.955089i
$664$	3.91294	−	6.77741i	0.151852	−	0.263015i
$665$	−8.39430	−	31.3279i	−0.325517	−	1.21485i
$666$	2.62441	−	13.8938i	0.101694	−	0.538373i
$667$	−23.0032	+	13.2809i	−0.890688	+	0.514239i
$668$	−0.876603	−	3.27153i	−0.0339168	−	0.126579i
$669$	43.5289	+	16.1436i	1.68293	+	0.624147i
$670$	8.24109	+	30.7562i	0.318381	+	1.18821i
$671$	−5.01015	+	18.6981i	−0.193415	+	0.721834i
$672$	4.17542	−	5.88662i	0.161070	−	0.227081i
$673$	0.980093	−	0.565857i	0.0377798	−	0.0218122i	−0.480991	−	0.876725i	$-0.659723\pi$
$673$	0.980093	−	0.565857i	0.0377798	−	0.0218122i	0.518771	+	0.854913i	$0.326390\pi$
$674$	12.7657	−	3.42056i	0.491716	−	0.131755i
$675$	−0.968587	+	0.933887i	−0.0372810	+	0.0359453i
$676$	−1.77313	−	12.8785i	−0.0681972	−	0.495327i
$677$	6.04206	+	3.48838i	0.232215	+	0.134070i	0.611594	−	0.791172i	$-0.290529\pi$
$677$	6.04206	+	3.48838i	0.232215	+	0.134070i	−0.379378	+	0.925242i	$0.623862\pi$
$678$	−24.8639	+	20.6070i	−0.954893	+	0.791408i
$679$	−35.6770			−1.36916
$680$	4.51671	−	7.82317i	0.173208	−	0.300005i
$681$	7.58613	+	9.15323i	0.290701	+	0.350753i
$682$	−2.77802	−	2.77802i	−0.106376	−	0.106376i
$683$	−0.848566	+	3.16689i	−0.0324695	+	0.121178i	−0.980258	−	0.197721i	$-0.936646\pi$
$683$	−0.848566	+	3.16689i	−0.0324695	+	0.121178i	0.947789	+	0.318898i	$0.103313\pi$
$684$	8.41149	−	5.73866i	0.321621	−	0.219423i
$685$	17.7800	+	30.7958i	0.679337	+	1.17665i
$686$	−7.00468	−	12.1325i	−0.267440	−	0.463219i
$687$	−10.7373	+	28.9516i	−0.409653	+	1.10457i
$688$	−4.26269	+	2.46107i	−0.162514	+	0.0938273i
$689$	21.6839	+	10.6136i	0.826091	+	0.404347i
$690$	−11.6556	+	16.4324i	−0.443723	+	0.625573i
$691$	−1.83951	+	6.86513i	−0.0699781	+	0.261162i	−0.992048	−	0.125862i	$-0.959830\pi$
$691$	−1.83951	+	6.86513i	−0.0699781	+	0.261162i	0.922070	+	0.387024i	$0.126497\pi$
$692$	−7.44014	−	4.29557i	−0.282832	−	0.163293i
$693$	−6.88245	−	19.6495i	−0.261443	−	0.746422i
$694$	2.82191	+	2.82191i	0.107118	+	0.107118i
$695$	29.0001	−	29.0001i	1.10004	−	1.10004i
$696$	−3.15404	+	8.50444i	−0.119554	+	0.322360i
$697$	15.5447	+	4.16519i	0.588797	+	0.157768i
$698$	−14.0231	−	8.09625i	−0.530783	−	0.306448i
$699$	2.22969	−	23.8170i	0.0843347	−	0.900841i
$700$	1.04217	+	0.279249i	0.0393904	+	0.0105546i
$701$	−44.5315			−1.68193			−0.840966	−	0.541088i	$-0.818013\pi$
$701$	−44.5315			−1.68193			−0.840966	+	0.541088i	$0.818013\pi$
$702$	10.1694	+	15.7348i	0.383820	+	0.593870i
$703$	−15.9974			−0.603353
$704$	−1.60879	−	0.431075i	−0.0606337	−	0.0162468i
$705$	−1.68331	+	17.9807i	−0.0633973	+	0.677193i
$706$	1.53760	+	0.887736i	0.0578685	+	0.0334104i
$707$	−67.4202	−	18.0652i	−2.53560	−	0.679411i
$708$	−5.21566	+	14.0633i	−0.196016	+	0.528531i
$709$	−3.89552	+	3.89552i	−0.146299	+	0.146299i	−0.776463	−	0.630163i	$-0.782988\pi$
$709$	−3.89552	+	3.89552i	−0.146299	+	0.146299i	0.630163	+	0.776463i	$0.282988\pi$
$710$	22.7641	+	22.7641i	0.854321	+	0.854321i
$711$	31.8179	−	36.9961i	1.19326	−	1.38746i
$712$	8.03265	+	4.63765i	0.301036	+	0.173803i
$713$	−3.09656	+	11.5565i	−0.115967	+	0.432795i
$714$	16.4476	−	23.1883i	0.615537	−	0.867801i
$715$	−7.68484	−	11.4278i	−0.287397	−	0.427375i
$716$	−8.70818	+	5.02767i	−0.325440	+	0.187893i
$717$	13.3759	−	36.0662i	0.499532	−	1.34692i
$718$	3.82116	+	6.61845i	0.142605	+	0.246998i
$719$	−0.0565881	−	0.0980135i	−0.00211038	−	0.00365529i	0.864968	−	0.501827i	$-0.167338\pi$
$719$	−0.0565881	−	0.0980135i	−0.00211038	−	0.00365529i	−0.867079	+	0.498171i	$0.834005\pi$
$720$	0.516236	+	6.86032i	0.0192390	+	0.255669i
$721$	9.40365	−	35.0949i	0.350210	−	1.30700i
$722$	5.28874	+	5.28874i	0.196826	+	0.196826i
$723$	−10.9869	−	13.2565i	−0.408606	−	0.493013i
$724$	−2.32783	+	4.03191i	−0.0865130	+	0.149845i
$725$	−1.35601			−0.0503610
$726$	10.9699	−	9.09177i	0.407131	−	0.337427i
$727$	6.21671	+	3.58922i	0.230565	+	0.133117i	0.610833	−	0.791760i	$-0.290835\pi$
$727$	6.21671	+	3.58922i	0.230565	+	0.133117i	−0.380268	+	0.924876i	$0.624168\pi$
$728$	6.60484	−	13.4939i	0.244792	−	0.500115i
$729$	−22.8748	−	14.3437i	−0.847216	−	0.531249i
$730$	−20.7131	+	5.55006i	−0.766626	+	0.205417i
$731$	−16.7914	+	9.69453i	−0.621053	+	0.358565i
$732$	11.6465	−	16.4196i	0.430468	−	0.606886i
$733$	3.64360	−	13.5981i	0.134579	−	0.502257i	−0.865420	−	0.501047i	$-0.832948\pi$
$733$	3.64360	−	13.5981i	0.134579	−	0.502257i	0.999999	−	0.00120982i	$-0.000385098\pi$
$734$	−5.93100	−	22.1348i	−0.218917	−	0.817009i
$735$	38.5900	+	14.3119i	1.42341	+	0.527902i
$736$	1.31276	+	4.89928i	0.0483889	+	0.180590i
$737$	20.0275	−	11.5629i	0.737723	−	0.425924i
$738$	−11.5672	+	4.05154i	−0.425794	+	0.149139i
$739$	0.395975	+	1.47780i	0.0145662	+	0.0543618i	0.972826	−	0.231536i	$-0.0743750\pi$
$739$	0.395975	+	1.47780i	0.0145662	+	0.0543618i	−0.958260	+	0.285897i	$0.907708\pi$
$740$	5.40419	−	9.36033i	0.198662	−	0.344093i
$741$	15.3574	−	14.6100i	0.564169	−	0.536713i
$742$	13.9500	+	24.1622i	0.512122	+	0.887021i
$743$	−28.1201	+	28.1201i	−1.03163	+	1.03163i	−0.0321446	+	0.999483i	$0.510234\pi$
$743$	−28.1201	+	28.1201i	−1.03163	+	1.03163i	−0.999483	+	0.0321446i	$0.989766\pi$
$744$	1.70410	+	3.71323i	0.0624754	+	0.136134i
$745$			9.42025i			0.345131i
$746$	8.75107	−	8.75107i	0.320400	−	0.320400i
$747$	1.76170	+	23.4115i	0.0644573	+	0.856580i
$748$	−6.33729	−	1.69807i	−0.231714	−	0.0620877i
$749$	40.9137	−	10.9628i	1.49495	−	0.400572i
$750$	17.1152	−	7.85464i	0.624959	−	0.286811i
$751$		−	4.17861i		−	0.152480i	−0.997090	−	0.0762399i	$-0.975709\pi$
$751$		−	4.17861i		−	0.152480i	0.997090	−	0.0762399i	$-0.0242915\pi$
$752$	3.21497	+	3.21497i	0.117238	+	0.117238i
$753$	13.5610	−	6.22349i	0.494189	−	0.226797i
$754$	−3.62879	+	18.5297i	−0.132153	+	0.674812i
$755$			8.14299i			0.296354i
$756$	−0.394845	+	21.6477i	−0.0143604	+	0.787318i
$757$	13.7536	−	23.8220i	0.499884	−	0.865824i	−0.500116	−	0.865958i	$-0.666709\pi$
$757$	13.7536	−	23.8220i	0.499884	−	0.865824i	1.00000		0.000134418i	$4.27865e-5\pi$
$758$	−16.2113			−0.588821
$759$	13.7190	+	5.08796i	0.497968	+	0.184681i
$760$	7.51848	−	2.01457i	0.272724	−	0.0730762i
$761$	−41.1552	+	11.0275i	−1.49187	+	0.399746i	−0.910369	−	0.413797i	$-0.864202\pi$
$761$	−41.1552	+	11.0275i	−1.49187	+	0.399746i	−0.581505	+	0.813543i	$0.697536\pi$
$762$	22.5375	−	18.6789i	0.816446	−	0.676665i
$763$	12.4516			0.450780
$764$	−4.31063	+	7.46624i	−0.155953	+	0.270119i
$765$	2.03353	+	27.0239i	0.0735226	+	0.977050i
$766$		−	7.27039i		−	0.262690i
$767$	−6.00073	+	30.6415i	−0.216674	+	1.10640i
$768$	1.41275	+	1.00207i	0.0509781	+	0.0361591i
$769$	−0.716149	−	0.716149i	−0.0258250	−	0.0258250i	0.694076	−	0.719901i	$-0.255813\pi$
$769$	−0.716149	−	0.716149i	−0.0258250	−	0.0258250i	−0.719901	+	0.694076i	$0.755813\pi$
$770$		−	15.9150i		−	0.573538i

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.161445 - 1.72451i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-2.21510 - 0.593533i) q^{5} +(0.602280 - 1.62396i) q^{6} +(2.94637 - 2.94637i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.94787 - 0.556826i) q^{9} +(-1.98600 - 1.14662i) q^{10} +(-0.431075 + 1.60879i) q^{11} +(1.00207 - 1.41275i) q^{12} +(1.58511 - 3.23843i) q^{13} +(3.60855 - 2.08340i) q^{14} +(-1.38117 + 3.72413i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.96958 + 3.41141i) q^{17} +(-2.70331 - 1.30082i) q^{18} +(-0.878484 + 3.27855i) q^{19} +(-1.62156 - 1.62156i) q^{20} +(-4.60536 - 5.55671i) q^{21} +(-0.832773 + 1.44241i) q^{22} +5.07211 q^{23} +(1.33357 - 1.10525i) q^{24} +(0.224246 + 0.129469i) q^{25} +(2.36927 - 2.71782i) q^{26} +(-1.43617 + 4.99374i) q^{27} +(4.02481 - 1.07844i) q^{28} +(-4.53523 + 2.61842i) q^{29} +(-2.29799 + 3.23976i) q^{30} +(-0.610507 + 2.27844i) q^{31} +(0.258819 + 0.965926i) q^{32} +(2.70479 + 1.00312i) q^{33} +(1.01953 + 3.80493i) q^{34} +(-8.27525 + 4.77772i) q^{35} +(-2.27452 - 1.95616i) q^{36} +(1.21985 + 4.55256i) q^{37} +(-1.69710 + 2.93946i) q^{38} +(-5.32879 - 3.25637i) q^{39} +(-1.14662 - 1.98600i) q^{40} +(2.88882 - 2.88882i) q^{41} +(-3.01026 - 6.55933i) q^{42} +4.92213i q^{43} +(-1.17772 + 1.17772i) q^{44} +(6.19933 + 2.98308i) q^{45} +(4.89928 + 1.31276i) q^{46} +(4.39173 - 1.17676i) q^{47} +(1.57419 - 0.722440i) q^{48} -10.3621i q^{49} +(0.183096 + 0.183096i) q^{50} +(6.20099 - 2.84580i) q^{51} +(2.99196 - 2.01200i) q^{52} +6.69581i q^{53} +(-2.67971 + 4.45187i) q^{54} +(1.90975 - 3.30778i) q^{55} +4.16679 q^{56} +(5.51206 + 2.04426i) q^{57} +(-5.05840 + 1.35539i) q^{58} +(-8.36478 + 2.24134i) q^{59} +(-3.05820 + 2.53461i) q^{60} +11.6225 q^{61} +(-1.17941 + 2.04279i) q^{62} +(-10.3261 + 7.04489i) q^{63} +1.00000i q^{64} +(-5.43330 + 6.23261i) q^{65} +(2.35300 + 1.66899i) q^{66} +(-9.81803 - 9.81803i) q^{67} +3.93916i q^{68} +(0.818866 - 8.74691i) q^{69} +(-9.22985 + 2.47313i) q^{70} +(-13.5600 - 3.63339i) q^{71} +(-1.69072 - 2.47820i) q^{72} +(6.61207 - 6.61207i) q^{73} +4.71315i q^{74} +(0.259473 - 0.365813i) q^{75} +(-2.40006 + 2.40006i) q^{76} +(3.46999 + 6.01020i) q^{77} +(-4.30441 - 4.52461i) q^{78} +(-8.13274 + 14.0863i) q^{79} +(-0.593533 - 2.21510i) q^{80} +(8.37989 + 3.28290i) q^{81} +(3.53806 - 2.04270i) q^{82} +(-2.02549 - 7.55922i) q^{83} +(-1.21000 - 7.11494i) q^{84} +(-2.33802 - 8.72561i) q^{85} +(-1.27394 + 4.75442i) q^{86} +(3.78330 + 8.24379i) q^{87} +(-1.44241 + 0.832773i) q^{88} +(8.95926 - 2.40063i) q^{89} +(5.21601 + 4.48594i) q^{90} +(-4.87127 - 14.2119i) q^{91} +(4.39258 + 2.53606i) q^{92} +(3.83063 + 1.42067i) q^{93} +4.54666 q^{94} +(3.89185 - 6.74089i) q^{95} +(1.70753 - 0.290392i) q^{96} +(-6.05440 - 6.05440i) q^{97} +(2.68192 - 10.0091i) q^{98} +(2.16657 - 4.50249i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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