LMFDB - Embedded newform 234.2.z.a.41.12

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			41.12
Character	$\chi$	$=$	234.41
Dual form			234.2.z.a.137.12

$q$-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 $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.965926	−	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	−0.717512	−	0.696547i	$-0.754719\pi$
$5$	−2.21510	+	0.593533i	−0.990622	+	0.265436i	−0.273110	+	0.961983i	$0.588052\pi$
$6$	0.602280	+	1.62396i	0.245880	+	0.662981i
$7$	2.94637	+	2.94637i	1.11362	+	1.11362i	0.992657	+	0.120965i	$0.0385989\pi$
$7$	2.94637	+	2.94637i	1.11362	+	1.11362i	0.120965	+	0.992657i	$0.461401\pi$
$8$	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	0.869994	−	0.493062i	$-0.164123\pi$
$11$	−0.431075	−	1.60879i	−0.129974	−	0.485070i	−0.999968	+	0.00799251i	$0.997456\pi$
$12$	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	−0.521980	−	0.852958i	$-0.674807\pi$
$17$	1.96958	−	3.41141i	0.477693	−	0.827388i	0.999673	+	0.0255693i	$0.00813984\pi$
$18$	−2.70331	+	1.30082i	−0.637176	+	0.306606i
$19$	−0.878484	−	3.27855i	−0.201538	−	0.752150i	−0.990477	−	0.137678i	$-0.956036\pi$
$19$	−0.878484	−	3.27855i	−0.201538	−	0.752150i	0.788939	−	0.614472i	$-0.210631\pi$
$20$	−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	0.0158300	−	0.999875i	$-0.494961\pi$
$29$	−4.53523	−	2.61842i	−0.842172	−	0.486228i	−0.858002	+	0.513647i	$0.828294\pi$
$30$	−2.29799	−	3.23976i	−0.419553	−	0.591497i
$31$	−0.610507	−	2.27844i	−0.109650	−	0.409220i	0.889181	−	0.457556i	$-0.151275\pi$
$31$	−0.610507	−	2.27844i	−0.109650	−	0.409220i	−0.998831	+	0.0483356i	$0.984608\pi$
$32$	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	−0.790219	−	0.612824i	$-0.790033\pi$
$37$	1.21985	−	4.55256i	0.200543	−	0.748436i	0.990762	−	0.135612i	$-0.0432999\pi$
$38$	−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	0.895739	−	0.444581i	$-0.146647\pi$
$41$	2.88882	+	2.88882i	0.451157	+	0.451157i	−0.444581	+	0.895739i	$0.646647\pi$
$42$	−3.01026	+	6.55933i	−0.464493	+	1.01213i
$43$		−	4.92213i		−	0.750619i	−0.926900	−	0.375309i	$-0.877537\pi$
$43$		−	4.92213i		−	0.750619i	0.926900	−	0.375309i	$-0.122463\pi$
$44$	−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	0.564475	−	0.825450i	$-0.309079\pi$
$47$	4.39173	+	1.17676i	0.640600	+	0.171648i	0.0761249	+	0.997098i	$0.475745\pi$
$48$	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	$-0.847896\pi$
$53$		−	6.69581i		−	0.919741i	0.887986	−	0.459870i	$-0.152104\pi$
$54$	−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	−0.330723	−	0.943728i	$-0.607293\pi$
$59$	−8.36478	−	2.24134i	−1.08900	−	0.291797i	−0.758279	+	0.651930i	$0.773959\pi$
$60$	−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	−0.225137	+	0.974327i	$0.572283\pi$
$67$	−9.81803	+	9.81803i	−1.19946	+	1.19946i	−0.974327	+	0.225137i	$0.927717\pi$
$68$		−	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	−0.947827	−	0.318784i	$-0.896725\pi$
$71$	−13.5600	+	3.63339i	−1.60928	+	0.431205i	−0.661450	+	0.749989i	$0.730059\pi$
$72$	−1.69072	+	2.47820i	−0.199254	+	0.292058i
$73$	6.61207	+	6.61207i	0.773884	+	0.773884i	0.978783	−	0.204899i	$-0.0656866\pi$
$73$	6.61207	+	6.61207i	0.773884	+	0.773884i	−0.204899	+	0.978783i	$0.565687\pi$
$74$		−	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	−0.806895	−	0.590695i	$-0.798854\pi$
$79$	−8.13274	−	14.0863i	−0.915004	−	1.58483i	−0.108109	−	0.994139i	$-0.534480\pi$
$80$	−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	0.761132	+	0.648597i	$0.224644\pi$
$83$	−2.02549	+	7.55922i	−0.222326	+	0.829732i	−0.983458	+	0.181135i	$0.942023\pi$
$84$	−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	0.700226	−	0.713921i	$-0.253083\pi$
$89$	8.95926	+	2.40063i	0.949679	+	0.254466i	0.249453	+	0.968387i	$0.419749\pi$
$90$	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	−0.944175	−	0.329444i	$-0.893139\pi$
$97$	−6.05440	+	6.05440i	−0.614731	+	0.614731i	0.329444	+	0.944175i	$0.393139\pi$
$98$	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	0.0619252	+	0.998081i	$0.480276\pi$
$101$	−8.37557	+	14.5069i	−0.833401	+	1.44349i	−0.895326	+	0.445412i	$0.853057\pi$
$102$	6.72624	+	1.14390i	0.665997	+	0.113263i
$103$	7.55143	+	4.35982i	0.744065	+	0.429586i	0.823545	−	0.567251i	$-0.191993\pi$
$103$	7.55143	+	4.35982i	0.744065	+	0.429586i	−0.0794807	+	0.996836i	$0.525326\pi$
$104$	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	−0.00994628	−	0.999951i	$-0.503166\pi$
$107$	8.80347	−	5.08268i	0.851063	−	0.491362i	0.861009	+	0.508589i	$0.169833\pi$
$108$	−3.74063	−	3.60662i	−0.359942	−	0.347047i
$109$	2.11305	−	2.11305i	0.202394	−	0.202394i	−0.598631	−	0.801025i	$-0.704288\pi$
$109$	2.11305	−	2.11305i	0.202394	−	0.202394i	0.801025	+	0.598631i	$0.204288\pi$
$110$	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	−0.519203	+	0.854651i	$0.673771\pi$
$113$	−16.1467	+	9.32231i	−1.51895	+	0.876969i	−0.999751	+	0.0223181i	$0.992895\pi$
$114$	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	0.318542	−	0.947909i	$-0.396807\pi$
$127$	14.6359	−	8.45004i	1.29873	−	0.749820i	0.980184	+	0.198089i	$0.0634735\pi$
$128$	−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	0.862322	−	0.506360i	$-0.169009\pi$
$131$	9.78550	+	5.64966i	0.854963	+	0.493613i	−0.00735903	+	0.999973i	$0.502342\pi$
$132$	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	−0.998117	−	0.0613396i	$-0.980463\pi$
$137$	−10.9647	+	10.9647i	−0.936777	+	0.936777i	0.0613396	+	0.998117i	$0.480463\pi$
$138$	3.05483	+	8.23693i	0.260044	+	0.701174i
$139$	−8.94201	−	15.4880i	−0.758451	−	1.31368i	−0.943640	−	0.330973i	$-0.892623\pi$
$139$	−8.94201	−	15.4880i	−0.758451	−	1.31368i	0.185189	−	0.982703i	$-0.440710\pi$
$140$	−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	−0.995704	−	0.0925986i	$-0.970483\pi$
$149$	−1.06319	+	3.96787i	−0.0870997	+	0.325061i	0.908604	+	0.417659i	$0.137149\pi$
$150$	0.345311	+	0.286191i	0.0281945	+	0.0233674i
$151$	−0.919034	+	3.42988i	−0.0747899	+	0.279120i	−0.993186	−	0.116543i	$-0.962819\pi$
$151$	−0.919034	+	3.42988i	−0.0747899	+	0.279120i	0.918396	+	0.395663i	$0.129485\pi$
$152$	−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	−0.653829	−	0.756642i	$-0.726839\pi$
$157$	4.11430	−	7.12617i	0.328357	−	0.568731i	0.982186	+	0.187912i	$0.0601719\pi$
$158$	−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	−0.789206	−	0.614129i	$-0.789507\pi$
$163$	−14.8816	+	3.98750i	−1.16561	+	0.312325i	−0.376408	+	0.926454i	$0.622841\pi$
$164$	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	−0.793671	−	0.608347i	$-0.791833\pi$
$167$	−2.39493	+	2.39493i	−0.185325	+	0.185325i	0.608347	+	0.793671i	$0.291833\pi$
$168$	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	0.614658	−	0.788793i	$-0.289294\pi$
$179$	−5.02767	−	8.70818i	−0.375786	−	0.650880i	−0.990444	+	0.137913i	$0.955961\pi$
$180$	3.87723	−	5.68309i	0.288992	−	0.423592i
$181$		−	4.65565i		−	0.346052i	−0.984917	−	0.173026i	$-0.944646\pi$
$181$		−	4.65565i		−	0.346052i	0.984917	−	0.173026i	$-0.0553545\pi$
$182$	−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	$-0.899032\pi$
$191$		−	8.62127i		−	0.623813i	0.950113	−	0.311906i	$-0.100968\pi$
$192$	1.72451	−	0.161445i	0.124456	−	0.0116513i
$193$	−12.1598	−	12.1598i	−0.875283	−	0.875283i	0.117759	−	0.993042i	$-0.462429\pi$
$193$	−12.1598	−	12.1598i	−0.875283	−	0.875283i	−0.993042	+	0.117759i	$0.962429\pi$
$194$	−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	0.825317	+	0.564670i	$0.190997\pi$
$197$	−2.41082	+	8.99729i	−0.171764	+	0.641030i	−0.997080	+	0.0763603i	$0.975670\pi$
$198$	3.25808	+	3.78832i	0.231542	+	0.269224i
$199$	−5.89590	−	3.40400i	−0.417950	−	0.241303i	0.276250	−	0.961086i	$-0.410908\pi$
$199$	−5.89590	−	3.40400i	−0.417950	−	0.241303i	−0.694200	+	0.719782i	$0.744242\pi$
$200$	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	−0.658331	−	0.752729i	$-0.728737\pi$
$223$	−6.93742	−	25.8908i	−0.464564	−	1.73378i	0.193767	−	0.981048i	$-0.437930\pi$
$224$	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	0.527454	−	0.849583i	$-0.323147\pi$
$227$	−4.85337	−	4.85337i	−0.322129	−	0.322129i	−0.849583	+	0.527454i	$0.823147\pi$
$228$	3.75145	−	4.52641i	0.248446	−	0.299769i
$229$	−17.2203	+	4.61415i	−1.13795	+	0.304912i	−0.778125	−	0.628109i	$-0.783829\pi$
$229$	−17.2203	+	4.61415i	−1.13795	+	0.304912i	−0.359821	+	0.933021i	$0.617162\pi$
$230$	−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	0.513734	−	0.857949i	$-0.328262\pi$
$239$	21.4520	−	5.74805i	1.38762	−	0.371811i	0.873882	+	0.486139i	$0.161595\pi$
$240$	−3.91578	−	0.665939i	−0.252763	−	0.0429862i
$241$	7.02904	+	7.02904i	0.452781	+	0.452781i	0.896276	−	0.443496i	$-0.146262\pi$
$241$	7.02904	+	7.02904i	0.452781	+	0.452781i	−0.443496	+	0.896276i	$0.646262\pi$
$242$	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	−0.697469	−	0.716615i	$-0.745690\pi$
$251$	4.30727	−	7.46042i	0.271873	−	0.470897i	0.969341	+	0.245718i	$0.0790237\pi$
$252$	−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	0.381115	−	0.924527i	$-0.375540\pi$
$263$	−3.71361	−	2.14406i	−0.228991	−	0.132208i	−0.610107	+	0.792319i	$0.708873\pi$
$264$	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	0.0435953	−	0.999049i	$-0.486119\pi$
$269$	−13.1178	−	7.57359i	−0.799809	−	0.461770i	−0.843404	+	0.537279i	$0.819452\pi$
$270$	8.57815	+	8.27083i	0.522050	+	0.503347i
$271$	−0.913090	+	3.40770i	−0.0554663	+	0.207003i	−0.988098	−	0.153827i	$-0.950840\pi$
$271$	−0.913090	+	3.40770i	−0.0554663	+	0.207003i	0.932631	+	0.360830i	$0.117507\pi$
$272$	−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	$0.229218\pi$
$277$			21.9515i			1.31894i	−0.751732	+	0.659468i	$0.770782\pi$
$278$	−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	0.295662	−	0.955293i	$-0.404460\pi$
$281$	1.24159	+	0.332682i	0.0740668	+	0.0198461i	−0.221595	+	0.975139i	$0.571126\pi$
$282$	0.734034	+	7.84076i	0.0437111	+	0.466910i
$283$		−	12.4186i		−	0.738210i	−0.929388	−	0.369105i	$-0.879664\pi$
$283$		−	12.4186i		−	0.738210i	0.929388	−	0.369105i	$-0.120336\pi$
$284$	−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	0.481644	−	0.876367i	$-0.340040\pi$
$293$	7.88381	+	2.11246i	0.460577	+	0.123411i	−0.0210673	+	0.999778i	$0.506706\pi$
$294$	−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	0.986534	−	0.163557i	$-0.0522968\pi$
$307$	14.4197	+	14.4197i	0.822977	+	0.822977i	−0.163557	+	0.986534i	$0.552297\pi$
$308$		−	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	−0.784303	−	0.620379i	$-0.786979\pi$
$311$	2.55908	−	4.43246i	0.145112	−	0.251342i	0.929415	+	0.369037i	$0.120312\pi$
$312$	−1.46542	+	6.07063i	−0.0829633	+	0.343682i
$313$	2.52339	+	4.37065i	0.142631	+	0.247043i	0.928486	−	0.371366i	$-0.121111\pi$
$313$	2.52339	+	4.37065i	0.142631	+	0.247043i	−0.785856	+	0.618410i	$0.787777\pi$
$314$	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	−0.904296	−	0.426905i	$-0.859604\pi$
$317$	1.64335	−	6.13308i	0.0922999	−	0.344468i	0.996596	+	0.0824373i	$0.0262704\pi$
$318$	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	−0.649098	−	0.760705i	$-0.724853\pi$
$331$	2.03052	−	2.03052i	0.111607	−	0.111607i	0.760705	+	0.649098i	$0.224853\pi$
$332$	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	0.778219	−	0.627993i	$-0.216123\pi$
$337$	11.4454	+	6.60801i	0.623471	+	0.359961i	−0.154748	+	0.987954i	$0.549457\pi$
$338$	−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	−0.404356	−	0.914602i	$-0.632504\pi$
$347$	3.45612	−	1.99539i	0.185534	−	0.107118i	0.589890	+	0.807483i	$0.299171\pi$
$348$	−0.845460	−	9.03098i	−0.0453214	−	0.484111i
$349$	−15.6408	+	4.19093i	−0.837230	+	0.224335i	−0.651866	−	0.758335i	$-0.726013\pi$
$349$	−15.6408	+	4.19093i	−0.837230	+	0.224335i	−0.185365	+	0.982670i	$0.559347\pi$
$350$	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	−0.212891	−	0.977076i	$-0.568288\pi$
$353$	1.71497	−	0.459526i	0.0912789	−	0.0244581i	0.304169	+	0.952618i	$0.401621\pi$
$354$	−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	−0.549973	−	0.835182i	$-0.685362\pi$
$359$	5.40394	−	5.40394i	0.285209	−	0.285209i	0.835182	+	0.549973i	$0.185362\pi$
$360$	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	0.395010	+	0.918677i	$0.370741\pi$
$367$	−11.4578	+	19.8455i	−0.598092	+	1.03593i	−0.993102	+	0.117250i	$0.962592\pi$
$368$	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	0.980570	−	0.196167i	$-0.0628495\pi$
$373$	6.18794	+	10.7178i	0.320400	+	0.554948i	−0.660171	+	0.751115i	$0.729516\pi$
$374$	−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	−0.166854	−	0.985982i	$-0.553361\pi$
$379$	−15.6589	−	4.19579i	−0.804344	−	0.215523i	−0.637490	+	0.770458i	$0.720027\pi$
$380$	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	−0.997191	−	0.0748943i	$-0.976138\pi$
$383$	−1.88172	+	7.02266i	−0.0961512	+	0.358841i	0.901040	+	0.433735i	$0.142805\pi$
$384$	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	0.990738	+	0.135788i	$0.0433566\pi$
$389$	12.0896	+	20.9397i	0.612965	+	1.06169i	−0.377773	+	0.925898i	$0.623310\pi$
$390$	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	−0.643351	−	0.765571i	$-0.722457\pi$
$397$	−16.2930	+	4.36571i	−0.817724	+	0.219109i	−0.174373	+	0.984680i	$0.555790\pi$
$398$	−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	−0.245798	−	0.969321i	$-0.579050\pi$
$401$	14.4886	−	14.4886i	0.723524	−	0.723524i	0.969321	+	0.245798i	$0.0790498\pi$
$402$	−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	−0.175046	−	0.984560i	$-0.556007\pi$
$409$	−16.5616	−	4.43768i	−0.818921	−	0.219429i	−0.643875	+	0.765131i	$0.722674\pi$
$410$	−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	$0.236819\pi$
$419$			27.7250i			1.35446i	−0.735773	+	0.677228i	$0.763181\pi$
$420$	−1.54268	−	16.4785i	−0.0752749	−	0.804066i
$421$	28.1804	+	7.55093i	1.37343	+	0.368010i	0.868731	−	0.495285i	$-0.164936\pi$
$421$	28.1804	+	7.55093i	1.37343	+	0.368010i	0.504700	+	0.863295i	$0.331603\pi$
$422$	−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	−0.963328	−	0.268328i	$-0.913529\pi$
$431$	0.105936	−	0.395359i	0.00510277	−	0.0190438i	0.968430	+	0.249285i	$0.0801955\pi$
$432$	−5.04279	−	1.25311i	−0.242621	−	0.0602902i
$433$	16.7881	+	9.69262i	0.806785	+	0.465798i	0.845838	−	0.533440i	$-0.179101\pi$
$433$	16.7881	+	9.69262i	0.806785	+	0.465798i	−0.0390532	+	0.999237i	$0.512434\pi$
$434$	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	0.810078	−	0.586322i	$-0.199425\pi$
$439$	14.8206	+	8.55666i	0.707348	+	0.408387i	−0.102731	+	0.994709i	$0.532758\pi$
$440$	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	−0.448668	−	0.893699i	$-0.648101\pi$
$443$	2.12505	−	1.22690i	0.100964	−	0.0582916i	0.549632	+	0.835407i	$0.314768\pi$
$444$	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	0.988160	−	0.153429i	$-0.0490318\pi$
$449$	1.17970	+	4.40270i	0.0556735	+	0.207776i	−0.932486	+	0.361206i	$0.882365\pi$
$450$	−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	0.893567	−	0.448931i	$-0.148195\pi$
$457$	−2.23930	−	8.35718i	−0.104750	−	0.390933i	−0.998317	+	0.0579980i	$0.981528\pi$
$458$	−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	0.949171	−	0.314760i	$-0.101924\pi$
$461$	13.6214	+	13.6214i	0.634412	+	0.634412i	−0.314760	+	0.949171i	$0.601924\pi$
$462$	11.8503	+	2.01532i	0.551324	+	0.0937611i
$463$	3.25146	−	0.871225i	0.151108	−	0.0404893i	−0.182472	−	0.983211i	$-0.558410\pi$
$463$	3.25146	−	0.871225i	0.151108	−	0.0404893i	0.333580	+	0.942722i	$0.391743\pi$
$464$	−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	0.975708	+	0.219077i	$0.0703047\pi$
$479$	5.25832	+	19.6243i	0.240259	+	0.896657i	−0.735449	+	0.677580i	$0.763029\pi$
$480$	−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	−0.724109	−	0.689685i	$-0.757749\pi$
$487$	−9.75089	−	36.3908i	−0.441855	−	1.64902i	0.282255	−	0.959340i	$-0.408918\pi$
$488$	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	−0.984153	−	0.177319i	$-0.943258\pi$
$499$	−4.92584	−	18.3835i	−0.220511	−	0.822958i	0.763642	−	0.645639i	$-0.223409\pi$
$500$	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	0.556776	−	0.830663i	$-0.312038\pi$
$503$	2.59687	+	1.49930i	0.115789	+	0.0668507i	−0.440987	+	0.897513i	$0.645372\pi$
$504$	−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	0.973030	−	0.230679i	$-0.0740947\pi$
$509$	16.7482	+	16.7482i	0.742351	+	0.742351i	−0.230679	+	0.973030i	$0.574095\pi$
$510$	−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	$0.0697715\pi$
$521$			9.92644i			0.434885i	−0.976073	+	0.217443i	$0.930229\pi$
$522$	15.6662	+	1.17888i	0.685692	+	0.0515980i
$523$	8.91409	+	15.4397i	0.389786	+	0.675129i	0.992421	−	0.122888i	$-0.0392157\pi$
$523$	8.91409	+	15.4397i	0.389786	+	0.675129i	−0.602635	+	0.798017i	$0.705882\pi$
$524$	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	0.943891	+	0.330258i	$0.107136\pi$
$541$	29.6359	+	29.6359i	1.27415	+	1.27415i	0.330258	+	0.943891i	$0.392864\pi$
$542$			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	0.518197	−	0.855261i	$-0.326603\pi$
$547$	−11.2632	−	19.5084i	−0.481580	−	0.834120i	−0.999777	+	0.0211411i	$0.993270\pi$
$548$	−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	0.997572	−	0.0696359i	$-0.0221838\pi$
$557$	43.1111	+	11.5516i	1.82668	+	0.489457i	0.829105	+	0.559093i	$0.188850\pi$
$558$	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	0.884716	−	0.466130i	$-0.154352\pi$
$563$	0.917730	+	1.58956i	0.0386777	+	0.0669918i	−0.846039	+	0.533122i	$0.821019\pi$
$564$	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	−0.797501	−	0.603317i	$-0.793845\pi$
$569$	2.95160	−	5.11231i	0.123737	−	0.214319i	0.921239	+	0.388998i	$0.127179\pi$
$570$	−8.60297	+	10.3801i	−0.360339	+	0.434776i
$571$	−6.53279	−	3.77171i	−0.273389	−	0.157841i	0.357038	−	0.934090i	$-0.383787\pi$
$571$	−6.53279	−	3.77171i	−0.273389	−	0.157841i	−0.630427	+	0.776249i	$0.717120\pi$
$572$	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	−0.883275	−	0.468856i	$-0.844666\pi$
$577$	−9.95468	+	9.95468i	−0.414419	+	0.414419i	0.468856	+	0.883275i	$0.344666\pi$
$578$	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	−0.412802	−	0.910821i	$-0.635450\pi$
$587$	−7.62913	+	2.04422i	−0.314888	+	0.0843739i	0.0979138	+	0.995195i	$0.468783\pi$
$588$	−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	−0.252339	−	0.967639i	$-0.581200\pi$
$593$	17.4187	−	17.4187i	0.715300	−	0.715300i	0.967639	+	0.252339i	$0.0811998\pi$
$594$	−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	0.957460	+	0.288566i	$0.0931783\pi$
$599$	41.2663	+	23.8251i	1.68610	+	0.973468i	0.728635	+	0.684902i	$0.240155\pi$
$600$	0.442144	+	0.0751934i	0.0180504	+	0.00306976i
$601$	14.5212	−	25.1515i	0.592334	−	1.02595i	−0.401583	−	0.915822i	$-0.631540\pi$
$601$	14.5212	−	25.1515i	0.592334	−	1.02595i	0.993917	−	0.110130i	$-0.0351267\pi$
$602$	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	0.983149	−	0.182804i	$-0.0585174\pi$
$607$	8.21069	+	14.2213i	0.333262	+	0.577226i	−0.649888	+	0.760030i	$0.725184\pi$
$608$	−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	−0.160153	−	0.987092i	$-0.551199\pi$
$613$	−19.6188	−	5.25684i	−0.792396	−	0.212322i	−0.632243	+	0.774770i	$0.717865\pi$
$614$	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	0.572425	+	0.819957i	$0.306003\pi$
$617$	−8.27870	+	30.8965i	−0.333288	+	1.24385i	−0.905713	+	0.423891i	$0.860664\pi$
$618$	−2.53212	+	14.8891i	−0.101857	+	0.598927i
$619$	−9.90270	+	36.9574i	−0.398023	+	1.48544i	0.418546	+	0.908196i	$0.362540\pi$
$619$	−9.90270	+	36.9574i	−0.398023	+	1.48544i	−0.816569	+	0.577247i	$0.804127\pi$
$620$	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	0.0761122	−	0.997099i	$-0.475749\pi$
$631$	16.0911	−	4.31160i	0.640577	−	0.171642i	0.564465	+	0.825457i	$0.309083\pi$
$632$	−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	0.231137	−	0.972921i	$-0.425755\pi$
$643$	−1.39852	−	0.374733i	−0.0551524	−	0.0147780i	−0.286290	+	0.958143i	$0.592422\pi$
$644$	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	0.614715	−	0.788749i	$-0.289271\pi$
$647$	−9.55687	−	16.5530i	−0.375719	−	0.650765i	−0.990434	+	0.137984i	$0.955938\pi$
$648$	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	$-0.688814\pi$
$653$		−	42.3769i		−	1.65834i	0.558998	−	0.829169i	$-0.311186\pi$
$654$	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	$0.0469844\pi$
$659$			7.55088i			0.294141i	−0.989126	+	0.147070i	$0.953016\pi$
$660$	−2.75935	+	6.01262i	−0.107408	+	0.234041i
$661$	12.5495	+	12.5495i	0.488119	+	0.488119i	0.907712	−	0.419593i	$-0.137827\pi$
$661$	12.5495	+	12.5495i	0.488119	+	0.488119i	−0.419593	+	0.907712i	$0.637827\pi$
$662$	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	0.518771	−	0.854913i	$-0.326390\pi$
$673$	0.980093	+	0.565857i	0.0377798	+	0.0218122i	−0.480991	+	0.876725i	$0.659723\pi$
$674$	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	−0.379378	−	0.925242i	$-0.623862\pi$
$677$	6.04206	−	3.48838i	0.232215	−	0.134070i	0.611594	+	0.791172i	$0.290529\pi$
$678$	−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	0.947789	−	0.318898i	$-0.103313\pi$
$683$	−0.848566	−	3.16689i	−0.0324695	−	0.121178i	−0.980258	+	0.197721i	$0.936646\pi$
$684$	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	0.922070	−	0.387024i	$-0.126497\pi$
$691$	−1.83951	−	6.86513i	−0.0699781	−	0.261162i	−0.992048	+	0.125862i	$0.959830\pi$
$692$	−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	0.630163	−	0.776463i	$-0.282988\pi$
$709$	−3.89552	−	3.89552i	−0.146299	−	0.146299i	−0.776463	+	0.630163i	$0.782988\pi$
$710$	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	−0.867079	−	0.498171i	$-0.834005\pi$
$719$	−0.0565881	+	0.0980135i	−0.00211038	+	0.00365529i	0.864968	+	0.501827i	$0.167338\pi$
$720$	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	−0.380268	−	0.924876i	$-0.624168\pi$
$727$	6.21671	−	3.58922i	0.230565	−	0.133117i	0.610833	+	0.791760i	$0.290835\pi$
$728$	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	0.999999	+	0.00120982i	$0.000385098\pi$
$733$	3.64360	+	13.5981i	0.134579	+	0.502257i	−0.865420	+	0.501047i	$0.832948\pi$
$734$	−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	−0.958260	−	0.285897i	$-0.907708\pi$
$739$	0.395975	−	1.47780i	0.0145662	−	0.0543618i	0.972826	+	0.231536i	$0.0743750\pi$
$740$	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	−0.999483	−	0.0321446i	$-0.989766\pi$
$743$	−28.1201	−	28.1201i	−1.03163	−	1.03163i	−0.0321446	−	0.999483i	$-0.510234\pi$
$744$	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	$0.0242915\pi$
$751$			4.17861i			0.152480i	−0.997090	+	0.0762399i	$0.975709\pi$
$752$	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	1.00000		0.000134418i	$-4.27865e-5\pi$
$757$	13.7536	+	23.8220i	0.499884	+	0.865824i	−0.500116	+	0.865958i	$0.666709\pi$
$758$	−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	−0.581505	−	0.813543i	$-0.697536\pi$
$761$	−41.1552	−	11.0275i	−1.49187	−	0.399746i	−0.910369	+	0.413797i	$0.864202\pi$
$762$	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	−0.719901	−	0.694076i	$-0.755813\pi$
$769$	−0.716149	+	0.716149i	−0.0258250	+	0.0258250i	0.694076	+	0.719901i	$0.255813\pi$
$770$			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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