LMFDB - Embedded newform 234.2.y.a.59.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(11,234)]

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([2, 7]))

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

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

chi := DirichletCharacter("234.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.y (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			59.13
Character	$\chi$	$=$	234.59
Dual form			234.2.y.a.119.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.41275 - 1.00207i) q^{3} -1.00000i q^{4} +(-0.593533 - 2.21510i) q^{5} +(0.290392 - 1.70753i) q^{6} +(1.07844 + 4.02481i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.991710 - 2.83134i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.41275 - 1.00207i) q^{3} -1.00000i q^{4} +(-0.593533 - 2.21510i) q^{5} +(0.290392 - 1.70753i) q^{6} +(1.07844 + 4.02481i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.991710 - 2.83134i) q^{9} +(-1.98600 - 1.14662i) q^{10} +(1.17772 + 1.17772i) q^{11} +(-1.00207 - 1.41275i) q^{12} +(-3.59712 + 0.246465i) q^{13} +(3.60855 + 2.08340i) q^{14} +(-3.05820 - 2.53461i) q^{15} -1.00000 q^{16} +(-1.96958 - 3.41141i) q^{17} +(-1.30082 - 2.70331i) q^{18} +(-0.878484 + 3.27855i) q^{19} +(-2.21510 + 0.593533i) q^{20} +(5.55671 + 4.60536i) q^{21} +1.66555 q^{22} +(2.53606 + 4.39258i) q^{23} +(-1.70753 - 0.290392i) 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} +5.23684i q^{29} +(-3.95471 + 0.370231i) q^{30} +(2.27844 - 0.610507i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.84398 + 0.483662i) q^{33} +(-3.80493 - 1.01953i) q^{34} +(8.27525 - 4.77772i) q^{35} +(-2.83134 - 0.991710i) q^{36} +(1.21985 + 4.55256i) q^{37} +(1.69710 + 2.93946i) q^{38} +(-4.83484 + 3.95276i) q^{39} +(-1.14662 + 1.98600i) q^{40} +(3.94620 + 1.05738i) q^{41} +(7.18567 - 0.672706i) q^{42} +(-4.26269 - 2.46107i) q^{43} +(1.17772 - 1.17772i) q^{44} +(-6.86032 - 0.516236i) q^{45} +(4.89928 + 1.31276i) q^{46} +(1.17676 - 4.39173i) q^{47} +(-1.41275 + 1.00207i) q^{48} +(-8.97388 + 5.18107i) q^{49} +(-0.0670178 + 0.250114i) q^{50} +(-6.20099 - 2.84580i) q^{51} +(0.246465 + 3.59712i) q^{52} -6.69581i q^{53} +(-4.54663 - 2.51558i) q^{54} +(1.90975 - 3.30778i) q^{55} +(2.08340 - 3.60855i) q^{56} +(2.04426 + 5.51206i) q^{57} +(3.70300 + 3.70300i) q^{58} +(-6.12345 - 6.12345i) q^{59} +(-2.53461 + 3.05820i) q^{60} +(-5.81123 + 10.0653i) q^{61} +(1.17941 - 2.04279i) q^{62} +(12.4651 + 0.937996i) q^{63} +1.00000i q^{64} +(2.68095 + 7.82168i) q^{65} +(2.35300 - 1.66899i) q^{66} +(-3.59365 + 13.4117i) q^{67} +(-3.41141 + 1.96958i) q^{68} +(7.98448 + 3.66430i) q^{69} +(2.47313 - 9.22985i) q^{70} +(13.5600 + 3.63339i) q^{71} +(-2.70331 + 1.30082i) q^{72} +(6.61207 - 6.61207i) q^{73} +(4.08171 + 2.35658i) q^{74} +(-0.187066 + 0.407617i) q^{75} +(3.27855 + 0.878484i) q^{76} +(-3.46999 + 6.01020i) q^{77} +(-0.623728 + 6.21377i) q^{78} +(-8.13274 - 14.0863i) q^{79} +(0.593533 + 2.21510i) q^{80} +(-7.03302 - 5.61575i) q^{81} +(3.53806 - 2.04270i) q^{82} +(-7.55922 - 2.02549i) q^{83} +(4.60536 - 5.55671i) q^{84} +(-6.38759 + 6.38759i) q^{85} +(-4.75442 + 1.27394i) q^{86} +(5.24768 + 7.39833i) q^{87} -1.66555i 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} +(2.60709 - 3.14565i) q^{93} +(-2.27333 - 3.93752i) q^{94} +7.78371 q^{95} +(-0.290392 + 1.70753i) q^{96} +(8.27047 - 2.21607i) q^{97} +(-2.68192 + 10.0091i) q^{98} +(4.50249 - 2.16657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7}+O(q^{10}) $ 56 * q + 4 * q^7	$ 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) $ 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.41275	−	1.00207i	0.815650	−	0.578546i
$3$	1.41275	−	1.00207i	0.815650	−	0.578546i
$4$		−	1.00000i		−	0.500000i
$5$	−0.593533	−	2.21510i	−0.265436	−	0.990622i	−0.961983	−	0.273110i	$-0.911948\pi$
$5$	−0.593533	−	2.21510i	−0.265436	−	0.990622i	0.696547	−	0.717512i	$-0.254719\pi$
$6$	0.290392	−	1.70753i	0.118552	−	0.697098i
$7$	1.07844	+	4.02481i	0.407614	+	1.52124i	0.799184	+	0.601087i	$0.205266\pi$
$7$	1.07844	+	4.02481i	0.407614	+	1.52124i	−0.391570	+	0.920148i	$0.628068\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.991710	−	2.83134i	0.330570	−	0.943781i
$10$	−1.98600	−	1.14662i	−0.628029	−	0.362593i
$11$	1.17772	+	1.17772i	0.355096	+	0.355096i	0.862001	−	0.506906i	$-0.169211\pi$
$11$	1.17772	+	1.17772i	0.355096	+	0.355096i	−0.506906	+	0.862001i	$0.669211\pi$
$12$	−1.00207	−	1.41275i	−0.289273	−	0.407825i
$13$	−3.59712	+	0.246465i	−0.997661	+	0.0683571i
$13$	−3.59712	+	0.246465i	−0.997661	+	0.0683571i
$14$	3.60855	+	2.08340i	0.964425	+	0.556811i
$15$	−3.05820	−	2.53461i	−0.789623	−	0.654434i
$16$	−1.00000			−0.250000
$17$	−1.96958	−	3.41141i	−0.477693	−	0.827388i	0.521980	−	0.852958i	$-0.325193\pi$
$17$	−1.96958	−	3.41141i	−0.477693	−	0.827388i	−0.999673	+	0.0255693i	$0.991860\pi$
$18$	−1.30082	−	2.70331i	−0.306606	−	0.637176i
$19$	−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	$0.956036\pi$
$20$	−2.21510	+	0.593533i	−0.495311	+	0.132718i
$21$	5.55671	+	4.60536i	1.21257	+	1.00497i
$22$	1.66555			0.355096
$23$	2.53606	+	4.39258i	0.528804	+	0.915916i	0.999436	+	0.0335859i	$0.0106927\pi$
$23$	2.53606	+	4.39258i	0.528804	+	0.915916i	−0.470632	+	0.882330i	$0.655974\pi$
$24$	−1.70753	−	0.290392i	−0.348549	−	0.0592761i
$25$	−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
$29$			5.23684i			0.972456i	0.873832	+	0.486228i	$0.161628\pi$
$29$			5.23684i			0.972456i	−0.873832	+	0.486228i	$0.838372\pi$
$30$	−3.95471	+	0.370231i	−0.722028	+	0.0675946i
$31$	2.27844	−	0.610507i	0.409220	−	0.109650i	−0.0483356	−	0.998831i	$-0.515392\pi$
$31$	2.27844	−	0.610507i	0.409220	−	0.109650i	0.457556	+	0.889181i	$0.348725\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	2.84398	+	0.483662i	0.495073	+	0.0841948i
$34$	−3.80493	−	1.01953i	−0.652541	−	0.174848i
$35$	8.27525	−	4.77772i	1.39877	−	0.807582i
$36$	−2.83134	−	0.991710i	−0.471891	−	0.165285i
$37$	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
$39$	−4.83484	+	3.95276i	−0.774194	+	0.632948i
$40$	−1.14662	+	1.98600i	−0.181296	+	0.314014i
$41$	3.94620	+	1.05738i	0.616292	+	0.165135i	0.553442	−	0.832888i	$-0.313314\pi$
$41$	3.94620	+	1.05738i	0.616292	+	0.165135i	0.0628507	+	0.998023i	$0.479981\pi$
$42$	7.18567	−	0.672706i	1.10877	−	0.103801i
$43$	−4.26269	−	2.46107i	−0.650055	−	0.375309i	0.138422	−	0.990373i	$-0.455797\pi$
$43$	−4.26269	−	2.46107i	−0.650055	−	0.375309i	−0.788477	+	0.615064i	$0.789130\pi$
$44$	1.17772	−	1.17772i	0.177548	−	0.177548i
$45$	−6.86032	−	0.516236i	−1.02268	−	0.0769559i
$46$	4.89928	+	1.31276i	0.722360	+	0.193556i
$47$	1.17676	−	4.39173i	0.171648	−	0.640600i	−0.825450	−	0.564475i	$-0.809079\pi$
$47$	1.17676	−	4.39173i	0.171648	−	0.640600i	0.997098	−	0.0761249i	$-0.0242548\pi$
$48$	−1.41275	+	1.00207i	−0.203913	+	0.144636i
$49$	−8.97388	+	5.18107i	−1.28198	+	0.740153i
$50$	−0.0670178	+	0.250114i	−0.00947775	+	0.0353715i
$51$	−6.20099	−	2.84580i	−0.868312	−	0.398492i
$52$	0.246465	+	3.59712i	0.0341786	+	0.498830i
$53$		−	6.69581i		−	0.919741i	−0.887986	−	0.459870i	$-0.847896\pi$
$53$		−	6.69581i		−	0.919741i	0.887986	−	0.459870i	$-0.152104\pi$
$54$	−4.54663	−	2.51558i	−0.618718	−	0.342327i
$55$	1.90975	−	3.30778i	0.257510	−	0.446021i
$56$	2.08340	−	3.60855i	0.278405	−	0.482212i
$57$	2.04426	+	5.51206i	0.270769	+	0.730090i
$58$	3.70300	+	3.70300i	0.486228	+	0.486228i
$59$	−6.12345	−	6.12345i	−0.797205	−	0.797205i	0.185449	−	0.982654i	$-0.440626\pi$
$59$	−6.12345	−	6.12345i	−0.797205	−	0.797205i	−0.982654	+	0.185449i	$0.940626\pi$
$60$	−2.53461	+	3.05820i	−0.327217	+	0.394811i
$61$	−5.81123	+	10.0653i	−0.744052	+	1.28874i	0.206585	+	0.978429i	$0.433765\pi$
$61$	−5.81123	+	10.0653i	−0.744052	+	1.28874i	−0.950637	+	0.310307i	$0.899568\pi$
$62$	1.17941	−	2.04279i	0.149785	−	0.259435i
$63$	12.4651	+	0.937996i	1.57046	+	0.118176i
$64$			1.00000i			0.125000i
$65$	2.68095	+	7.82168i	0.332531	+	0.970160i
$66$	2.35300	−	1.66899i	0.289634	−	0.205439i
$67$	−3.59365	+	13.4117i	−0.439034	+	1.63850i	0.292190	+	0.956360i	$0.405616\pi$
$67$	−3.59365	+	13.4117i	−0.439034	+	1.63850i	−0.731224	+	0.682138i	$0.761050\pi$
$68$	−3.41141	+	1.96958i	−0.413694	+	0.238846i
$69$	7.98448	+	3.66430i	0.961218	+	0.441129i
$70$	2.47313	−	9.22985i	0.295596	−	1.10318i
$71$	13.5600	+	3.63339i	1.60928	+	0.431205i	0.947827	−	0.318784i	$-0.103275\pi$
$71$	13.5600	+	3.63339i	1.60928	+	0.431205i	0.661450	+	0.749989i	$0.269941\pi$
$72$	−2.70331	+	1.30082i	−0.318588	+	0.153303i
$73$	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	$0.0656866\pi$
$74$	4.08171	+	2.35658i	0.474489	+	0.273946i
$75$	−0.187066	+	0.407617i	−0.0216006	+	0.0470675i
$76$	3.27855	+	0.878484i	0.376075	+	0.100769i
$77$	−3.46999	+	6.01020i	−0.395442	+	0.684926i
$78$	−0.623728	+	6.21377i	−0.0706233	+	0.703571i
$79$	−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
$81$	−7.03302	−	5.61575i	−0.781447	−	0.623972i
$82$	3.53806	−	2.04270i	0.390714	−	0.225579i
$83$	−7.55922	−	2.02549i	−0.829732	−	0.222326i	−0.181135	−	0.983458i	$-0.557977\pi$
$83$	−7.55922	−	2.02549i	−0.829732	−	0.222326i	−0.648597	+	0.761132i	$0.724644\pi$
$84$	4.60536	−	5.55671i	0.502486	−	0.606287i
$85$	−6.38759	+	6.38759i	−0.692832	+	0.692832i
$86$	−4.75442	+	1.27394i	−0.512682	+	0.137373i
$87$	5.24768	+	7.39833i	0.562610	+	0.793184i
$88$		−	1.66555i		−	0.177548i
$89$	−8.95926	+	2.40063i	−0.949679	+	0.254466i	−0.700226	−	0.713921i	$-0.746917\pi$
$89$	−8.95926	+	2.40063i	−0.949679	+	0.254466i	−0.249453	+	0.968387i	$0.580251\pi$
$90$	−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
$93$	2.60709	−	3.14565i	0.270343	−	0.326189i
$94$	−2.27333	−	3.93752i	−0.234476	−	0.406124i
$95$	7.78371			0.798591
$96$	−0.290392	+	1.70753i	−0.0296381	+	0.174274i
$97$	8.27047	−	2.21607i	0.839739	−	0.225007i	0.186781	−	0.982402i	$-0.440195\pi$
$97$	8.27047	−	2.21607i	0.839739	−	0.225007i	0.652958	+	0.757394i	$0.273528\pi$
$98$	−2.68192	+	10.0091i	−0.270915	+	1.01107i
$99$	4.50249	−	2.16657i	0.452517	−	0.217749i
$100$	0.129469	+	0.224246i	0.0129469	+	0.0224246i
$101$	−16.7511			−1.66680			−0.833401	−	0.552669i	$-0.813609\pi$
$101$	−16.7511			−1.66680			−0.833401	+	0.552669i	$0.813609\pi$
$102$	−6.39705	+	2.37247i	−0.633402	+	0.234910i
$103$	−7.55143	−	4.35982i	−0.744065	−	0.429586i	0.0794807	−	0.996836i	$-0.474674\pi$
$103$	−7.55143	−	4.35982i	−0.744065	−	0.429586i	−0.823545	+	0.567251i	$0.808007\pi$
$104$	2.71782	+	2.36927i	0.266505	+	0.232326i
$105$	6.90323	−	15.0421i	0.673686	−	1.46796i
$106$	−4.73466	−	4.73466i	−0.459870	−	0.459870i
$107$	−8.80347	−	5.08268i	−0.851063	−	0.491362i	0.00994628	−	0.999951i	$-0.496834\pi$
$107$	−8.80347	−	5.08268i	−0.851063	−	0.491362i	−0.861009	+	0.508589i	$0.830167\pi$
$108$	−4.99374	+	1.43617i	−0.480523	+	0.138196i
$109$	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	$0.704288\pi$
$110$	−0.988558	−	3.68935i	−0.0942553	−	0.351765i
$111$	6.28533	+	5.20923i	0.596577	+	0.494438i
$112$	−1.07844	−	4.02481i	−0.101903	−	0.380309i
$113$		−	18.6446i		−	1.75394i	−0.480547	−	0.876969i	$-0.659562\pi$
$113$		−	18.6446i		−	1.75394i	0.480547	−	0.876969i	$-0.340438\pi$
$114$	5.34312	+	2.45211i	0.500429	+	0.229661i
$115$	8.22475	−	8.22475i	0.766962	−	0.766962i
$116$	5.23684			0.486228
$117$	−2.86947	+	10.4291i	−0.265283	+	0.964171i
$118$	−8.65986			−0.797205
$119$	11.6062	−	11.6062i	1.06394	−	1.06394i
$120$	0.370231	+	3.95471i	0.0337973	+	0.361014i
$121$		−	8.22595i		−	0.747814i
$122$	3.00811	+	11.2264i	0.272342	+	1.01639i
$123$	6.63455	−	2.46056i	0.598217	−	0.221861i
$124$	−0.610507	−	2.27844i	−0.0548251	−	0.204610i
$125$	−7.68794	−	7.68794i	−0.687630	−	0.687630i
$126$	9.47744	−	8.15091i	0.844318	−	0.726141i
$127$	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	$0.396807\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−8.48827	+	0.794653i	−0.747351	+	0.0699653i
$130$	7.42648	+	3.63504i	0.651346	+	0.318814i
$131$	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	$0.502342\pi$
$132$	0.483662	−	2.84398i	0.0420974	−	0.247536i
$133$	−14.1429			−1.22635
$134$	6.94240	+	12.0246i	0.599732	+	1.03877i
$135$	−10.2092	+	6.14521i	−0.878668	+	0.528895i
$136$	−1.01953	+	3.80493i	−0.0874239	+	0.326270i
$137$	−14.9781	+	4.01336i	−1.27966	+	0.342884i	−0.833725	−	0.552180i	$-0.813796\pi$
$137$	−14.9781	+	4.01336i	−1.27966	+	0.342884i	−0.445937	+	0.895064i	$0.647129\pi$
$138$	8.23693	−	3.05483i	0.701174	−	0.260044i
$139$	17.8840			1.51690			0.758451	−	0.651730i	$-0.225956\pi$
$139$	17.8840			1.51690			0.758451	+	0.651730i	$0.225956\pi$
$140$	−4.77772	−	8.27525i	−0.403791	−	0.699387i
$141$	−2.73836	−	7.38361i	−0.230611	−	0.621812i
$142$	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
$146$		−	9.35088i		−	0.773884i
$147$	−7.48603	+	16.3120i	−0.617437	+	1.34539i
$148$	4.55256	−	1.21985i	0.374218	−	0.100271i
$149$	2.90468	−	2.90468i	0.237961	−	0.237961i	−0.578044	−	0.816005i	$-0.696184\pi$
$149$	2.90468	−	2.90468i	0.237961	−	0.237961i	0.816005	+	0.578044i	$0.196184\pi$
$150$	0.155953	+	0.420504i	0.0127335	+	0.0343340i
$151$	3.42988	+	0.919034i	0.279120	+	0.0747899i	0.395663	−	0.918396i	$-0.370515\pi$
$151$	3.42988	+	0.919034i	0.279120	+	0.0747899i	−0.116543	+	0.993186i	$0.537181\pi$
$152$	2.93946	−	1.69710i	0.238422	−	0.137653i
$153$	−11.6121	+	2.19343i	−0.938785	+	0.177328i
$154$	1.79620	+	6.70351i	0.144742	+	0.540184i
$155$	−2.70466	−	4.68461i	−0.217244	−	0.376277i
$156$	3.95276	+	4.83484i	0.316474	+	0.387097i
$157$	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	$0.0601719\pi$
$158$	−15.7112	−	4.20981i	−1.24992	−	0.334915i
$159$	−6.70968	−	9.45949i	−0.532112	−	0.750187i
$160$	1.98600	+	1.14662i	0.157007	+	0.0906482i
$161$	−14.9443	+	14.9443i	−1.17778	+	1.17778i
$162$	−8.94403	+	1.00217i	−0.702709	+	0.0787376i
$163$	−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	$0.789507\pi$
$164$	1.05738	−	3.94620i	0.0825675	−	0.308146i
$165$	−0.616637	−	6.58676i	−0.0480051	−	0.512778i
$166$	−6.77741	+	3.91294i	−0.526029	+	0.303703i
$167$	0.876603	−	3.27153i	0.0678336	−	0.253158i	−0.923679	−	0.383166i	$-0.874834\pi$
$167$	0.876603	−	3.27153i	0.0678336	−	0.253158i	0.991513	+	0.130008i	$0.0415003\pi$
$168$	−0.672706	−	7.18567i	−0.0519004	−	0.554387i
$169$	12.8785	−	1.77313i	0.990655	−	0.136394i
$170$			9.03342i			0.692832i
$171$	8.41149	+	5.73866i	0.643243	+	0.438846i
$172$	−2.46107	+	4.26269i	−0.187655	+	0.325027i
$173$	−4.29557	+	7.44014i	−0.326586	+	0.565664i	−0.981832	−	0.189752i	$-0.939232\pi$
$173$	−4.29557	+	7.44014i	−0.326586	+	0.565664i	0.655246	+	0.755416i	$0.272565\pi$
$174$	8.94208	+	1.52074i	0.677897	+	0.115287i
$175$	−0.762923	−	0.762923i	−0.0576716	−	0.0576716i
$176$	−1.17772	−	1.17772i	−0.0887739	−	0.0887739i
$177$	−14.7870	−	2.51476i	−1.11146	−	0.189021i
$178$	−4.63765	+	8.03265i	−0.347607	+	0.602072i
$179$	5.02767	−	8.70818i	0.375786	−	0.650880i	−0.614658	−	0.788793i	$-0.710706\pi$
$179$	5.02767	−	8.70818i	0.375786	−	0.650880i	0.990444	+	0.137913i	$0.0440395\pi$
$180$	−0.516236	+	6.86032i	−0.0384780	+	0.511338i
$181$			4.65565i			0.346052i	0.984917	+	0.173026i	$0.0553545\pi$
$181$			4.65565i			0.346052i	−0.984917	+	0.173026i	$0.944646\pi$
$182$	−13.4939	−	6.60484i	−1.00023	−	0.489583i
$183$	1.87638	+	20.0430i	0.138706	+	1.48162i
$184$	1.31276	−	4.89928i	0.0967779	−	0.361180i
$185$	9.36033	−	5.40419i	0.688185	−	0.397324i
$186$	−0.380818	−	4.06780i	−0.0279230	−	0.298266i
$187$	1.69807	−	6.33729i	0.124175	−	0.463429i
$188$	−4.39173	−	1.17676i	−0.320300	−	0.0858242i
$189$	18.5500	−	11.1658i	1.34932	−	0.812191i
$190$	5.50391	−	5.50391i	0.399296	−	0.399296i
$191$	7.46624	+	4.31063i	0.540238	+	0.311906i	0.745175	−	0.666869i	$-0.232366\pi$
$191$	7.46624	+	4.31063i	0.540238	+	0.311906i	−0.204937	+	0.978775i	$0.565699\pi$
$192$	1.00207	+	1.41275i	0.0723182	+	0.101956i
$193$	16.6106	+	4.45081i	1.19566	+	0.320376i	0.801120	−	0.598503i	$-0.204238\pi$
$193$	16.6106	+	4.45081i	1.19566	+	0.320376i	0.394539	+	0.918879i	$0.370904\pi$
$194$	4.28111	−	7.41510i	0.307366	−	0.532373i
$195$	11.6254	+	8.36355i	0.832511	+	0.598926i
$196$	5.18107	+	8.97388i	0.370077	+	0.640992i
$197$	2.41082	+	8.99729i	0.171764	+	0.641030i	0.997080	+	0.0763603i	$0.0243299\pi$
$197$	2.41082	+	8.99729i	0.171764	+	0.641030i	−0.825317	+	0.564670i	$0.809003\pi$
$198$	1.65174	−	4.71574i	0.117384	−	0.335133i
$199$	−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	$0.410908\pi$
$200$	0.250114	+	0.0670178i	0.0176857	+	0.00473888i
$201$	8.36253	+	22.5484i	0.589848	+	1.59044i
$202$	−11.8448	+	11.8448i	−0.833401	+	0.833401i
$203$	−21.0773	+	5.64764i	−1.47934	+	0.396387i
$204$	−2.84580	+	6.20099i	−0.199246	+	0.434156i
$205$		−	9.36880i		−	0.654345i
$206$	−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
$210$	−5.75505	−	15.5177i	−0.397136	−	1.07082i
$211$	8.67046	+	15.0177i	0.596899	+	1.03386i	0.993276	+	0.115772i	$0.0369341\pi$
$211$	8.67046	+	15.0177i	0.596899	+	1.03386i	−0.396377	+	0.918088i	$0.629733\pi$
$212$	−6.69581			−0.459870
$213$	22.7978	−	8.45502i	1.56208	−	0.579328i
$214$	−9.81899	+	2.63099i	−0.671212	+	0.179851i
$215$	−2.92145	+	10.9030i	−0.199241	+	0.743579i
$216$	−2.51558	+	4.54663i	−0.171164	+	0.309359i
$217$	4.91435	+	8.51190i	0.333608	+	0.577825i
$218$	2.98831			0.202394
$219$	2.71542	−	15.9669i	0.183491	−	1.07895i
$220$	−3.30778	−	1.90975i	−0.223010	−	0.128755i
$221$	7.92560	+	11.7858i	0.533133	+	0.792799i
$222$	8.12788	−	0.760914i	0.545508	−	0.0510692i
$223$	−18.9534	−	18.9534i	−1.26921	−	1.26921i	−0.946496	−	0.322717i	$-0.895404\pi$
$223$	−18.9534	−	18.9534i	−1.26921	−	1.26921i	−0.322717	−	0.946496i	$-0.604596\pi$
$224$	−3.60855	−	2.08340i	−0.241106	−	0.139203i
$225$	0.144183	+	0.763313i	0.00961220	+	0.0508875i
$226$	−13.1837	−	13.1837i	−0.876969	−	0.876969i
$227$	1.77646	+	6.62982i	0.117907	+	0.440037i	0.999488	−	0.0319971i	$-0.0101867\pi$
$227$	1.77646	+	6.62982i	0.117907	+	0.440037i	−0.881580	+	0.472034i	$0.843520\pi$
$228$	5.51206	−	2.04426i	0.365045	−	0.135384i
$229$	4.61415	+	17.2203i	0.304912	+	1.13795i	0.933021	+	0.359821i	$0.117162\pi$
$229$	4.61415	+	17.2203i	0.304912	+	1.13795i	−0.628109	+	0.778125i	$0.716171\pi$
$230$		−	11.6316i		−	0.766962i
$231$	1.12042	+	11.9681i	0.0737185	+	0.787441i
$232$	3.70300	−	3.70300i	0.243114	−	0.243114i
$233$	−13.8109			−0.904780			−0.452390	−	0.891820i	$-0.649429\pi$
$233$	−13.8109			−0.904780			−0.452390	+	0.891820i	$0.649429\pi$
$234$	5.34547	+	9.40351i	0.349444	+	0.614727i
$235$	−10.4266			−0.680154
$236$	−6.12345	+	6.12345i	−0.398602	+	0.398602i
$237$	−25.6050	−	11.7508i	−1.66322	−	0.763298i
$238$		−	16.4136i		−	1.06394i
$239$	5.74805	+	21.4520i	0.371811	+	1.38762i	0.857949	+	0.513734i	$0.171738\pi$
$239$	5.74805	+	21.4520i	0.371811	+	1.38762i	−0.486139	+	0.873882i	$0.661595\pi$
$240$	3.05820	+	2.53461i	0.197406	+	0.163608i
$241$	2.57281	+	9.60185i	0.165729	+	0.618510i	0.997946	+	0.0640595i	$0.0204048\pi$
$241$	2.57281	+	9.60185i	0.165729	+	0.618510i	−0.832217	+	0.554450i	$0.812929\pi$
$242$	−5.81663	−	5.81663i	−0.373907	−	0.373907i
$243$	−15.5633	−	0.886045i	−0.998383	−	0.0568398i
$244$	10.0653	+	5.81123i	0.644368	+	0.372026i
$245$	16.8029	+	16.8029i	1.07350	+	1.07350i
$246$	2.95146	−	6.43121i	0.188178	−	0.410039i
$247$	2.35196	−	12.0098i	0.149652	−	0.764167i
$248$	−2.04279	−	1.17941i	−0.129718	−	0.0748925i
$249$	−12.7089	+	4.71337i	−0.805397	+	0.298698i
$250$	−10.8724			−0.687630
$251$	−4.30727	−	7.46042i	−0.271873	−	0.470897i	0.697469	−	0.716615i	$-0.254310\pi$
$251$	−4.30727	−	7.46042i	−0.271873	−	0.470897i	−0.969341	+	0.245718i	$0.920976\pi$
$252$	0.937996	−	12.4651i	0.0590882	−	0.785229i
$253$	−2.18646	+	8.15999i	−0.137462	+	0.513014i
$254$	16.3242	−	4.37406i	1.02427	−	0.274453i
$255$	−2.62324	+	15.4249i	−0.164273	+	0.965943i
$256$	1.00000			0.0625000
$257$	−6.68605	−	11.5806i	−0.417064	−	0.722376i	0.578579	−	0.815627i	$-0.303608\pi$
$257$	−6.68605	−	11.5806i	−0.417064	−	0.722376i	−0.995643	+	0.0932505i	$0.970274\pi$
$258$	−5.44021	+	6.56402i	−0.338693	+	0.408658i
$259$	−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
$263$			4.28811i			0.264416i	0.991222	+	0.132208i	$0.0422067\pi$
$263$			4.28811i			0.264416i	−0.991222	+	0.132208i	$0.957793\pi$
$264$	−1.66899	−	2.35300i	−0.102720	−	0.144817i
$265$	−14.8319	+	3.97419i	−0.911115	+	0.244133i
$266$	−10.0006	+	10.0006i	−0.613173	+	0.613173i
$267$	−10.2516	+	12.3693i	−0.627386	+	0.756988i
$268$	13.4117	+	3.59365i	0.819249	+	0.219517i
$269$	13.1178	−	7.57359i	0.799809	−	0.461770i	−0.0435953	−	0.999049i	$-0.513881\pi$
$269$	13.1178	−	7.57359i	0.799809	−	0.461770i	0.843404	+	0.537279i	$0.180548\pi$
$270$	−2.87367	+	11.5643i	−0.174886	+	0.703782i
$271$	−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
$273$	−21.1232	−	15.1965i	−1.27844	−	0.919734i
$274$	−7.75321	+	13.4290i	−0.468389	+	0.811273i
$275$	−0.416577	−	0.111621i	−0.0251205	−	0.00673102i
$276$	3.66430	−	7.98448i	0.220565	−	0.480609i
$277$	19.0105	+	10.9757i	1.14223	+	0.659468i	0.946982	−	0.321285i	$-0.104115\pi$
$277$	19.0105	+	10.9757i	1.14223	+	0.659468i	0.195250	+	0.980754i	$0.437448\pi$
$278$	12.6459	−	12.6459i	0.758451	−	0.758451i
$279$	0.530999	−	7.05650i	0.0317901	−	0.422461i
$280$	−9.22985	−	2.47313i	−0.551589	−	0.147798i
$281$	0.332682	−	1.24159i	0.0198461	−	0.0740668i	−0.955293	−	0.295662i	$-0.904460\pi$
$281$	0.332682	−	1.24159i	0.0198461	−	0.0740668i	0.975139	+	0.221595i	$0.0711264\pi$
$282$	−7.15731	−	3.28469i	−0.426212	−	0.195600i
$283$	10.7548	−	6.20930i	0.639308	−	0.369105i	−0.145040	−	0.989426i	$-0.546331\pi$
$283$	10.7548	−	6.20930i	0.639308	−	0.369105i	0.784348	+	0.620321i	$0.212998\pi$
$284$	3.63339	−	13.5600i	0.215602	−	0.804639i
$285$	10.9964	−	7.79982i	0.651371	−	0.462022i
$286$	−5.99117	+	0.410499i	−0.354265	+	0.0242733i
$287$			17.0230i			1.00484i
$288$	1.30082	+	2.70331i	0.0766514	+	0.159294i
$289$	0.741523	−	1.28436i	0.0436190	−	0.0755504i
$290$	6.00466	−	10.4004i	0.352606	−	0.610731i
$291$	9.46343	−	11.4183i	0.554756	−	0.669354i
$292$	−6.61207	−	6.61207i	−0.386942	−	0.386942i
$293$	5.77135	+	5.77135i	0.337166	+	0.337166i	0.855300	−	0.518134i	$-0.173373\pi$
$293$	5.77135	+	5.77135i	0.337166	+	0.337166i	−0.518134	+	0.855300i	$0.673373\pi$
$294$	6.24091	+	16.8278i	0.363977	+	0.981414i
$295$	−9.92956	+	17.1985i	−0.578121	+	1.00134i
$296$	2.35658	−	4.08171i	0.136973	−	0.237245i
$297$	4.18982	−	7.57263i	0.243118	−	0.439408i
$298$		−	4.10784i		−	0.237961i
$299$	−10.2051	−	15.1756i	−0.590177	−	0.877626i
$300$	0.407617	+	0.187066i	0.0235338	+	0.0108003i
$301$	5.30825	−	19.8107i	0.305963	−	1.14187i
$302$	3.07515	−	1.77544i	0.176955	−	0.102165i
$303$	−23.6651	+	16.7858i	−1.35953	+	0.964321i
$304$	0.878484	−	3.27855i	0.0503845	−	0.188037i
$305$	25.7449	+	6.89832i	1.47415	+	0.394997i
$306$	−6.66003	+	9.76200i	−0.380728	+	0.558056i
$307$	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	$0.0522968\pi$
$308$	6.01020	+	3.46999i	0.342463	+	0.197721i
$309$	−15.0371	+	1.40774i	−0.855431	+	0.0800835i
$310$	−5.22501	−	1.40004i	−0.296760	−	0.0795167i
$311$	−2.55908	+	4.43246i	−0.145112	+	0.251342i	−0.929415	−	0.369037i	$-0.879688\pi$
$311$	−2.55908	+	4.43246i	−0.145112	+	0.251342i	0.784303	+	0.620379i	$0.213021\pi$
$312$	6.21377	+	0.623728i	0.351786	+	0.0353117i
$313$	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
$315$	−5.32072	−	28.1682i	−0.299789	−	1.58710i
$316$	−14.0863	+	8.13274i	−0.792417	+	0.457502i
$317$	6.13308	+	1.64335i	0.344468	+	0.0922999i	0.426905	−	0.904296i	$-0.359604\pi$
$317$	6.13308	+	1.64335i	0.344468	+	0.0922999i	−0.0824373	+	0.996596i	$0.526270\pi$
$318$	−11.4333	−	1.94441i	−0.641149	−	0.109037i
$319$	−6.16752	+	6.16752i	−0.345315	+	0.345315i
$320$	2.21510	−	0.593533i	0.123828	−	0.0331795i
$321$	−17.5303	+	1.64114i	−0.978445	+	0.0915998i
$322$			21.1344i			1.17778i
$323$	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
$327$	5.10264	+	0.867782i	0.282176	+	0.0479884i
$328$	−2.04270	−	3.53806i	−0.112789	−	0.195357i
$329$	18.9450			1.04447
$330$	−5.09357	−	4.22151i	−0.280392	−	0.232387i
$331$	−2.77374	+	0.743222i	−0.152459	+	0.0408512i	−0.334241	−	0.942488i	$-0.608480\pi$
$331$	−2.77374	+	0.743222i	−0.152459	+	0.0408512i	0.181782	+	0.983339i	$0.441813\pi$
$332$	−2.02549	+	7.55922i	−0.111163	+	0.414866i
$333$	14.0996	+	1.06099i	0.772653	+	0.0581418i
$334$	−1.69347	−	2.93317i	−0.0926624	−	0.160496i
$335$	31.8411			1.73967
$336$	−5.55671	−	4.60536i	−0.303144	−	0.251243i
$337$	−11.4454	−	6.60801i	−0.623471	−	0.359961i	0.154748	−	0.987954i	$-0.450543\pi$
$337$	−11.4454	−	6.60801i	−0.623471	−	0.359961i	−0.778219	+	0.627993i	$0.783877\pi$
$338$	7.85269	−	10.3603i	0.427130	−	0.563525i
$339$	−18.6832	−	26.3401i	−1.01473	−	1.43060i
$340$	6.38759	+	6.38759i	0.346416	+	0.346416i
$341$	3.40237	+	1.96436i	0.184249	+	0.106376i
$342$	10.0057	−	1.88998i	0.541044	−	0.102198i
$343$	−9.90611	−	9.90611i	−0.534880	−	0.534880i
$344$	1.27394	+	4.75442i	0.0686864	+	0.256341i
$345$	3.37772	−	19.8613i	0.181850	−	1.06930i
$346$	2.22355	+	8.29840i	0.119539	+	0.446125i
$347$			3.99079i			0.214237i	0.994246	+	0.107118i	$0.0341624\pi$
$347$			3.99079i			0.214237i	−0.994246	+	0.107118i	$0.965838\pi$
$348$	7.39833	−	5.24768i	0.396592	−	0.281305i
$349$	11.4498	−	11.4498i	0.612895	−	0.612895i	−0.330804	−	0.943699i	$-0.607320\pi$
$349$	11.4498	−	11.4498i	0.612895	−	0.612895i	0.943699	+	0.330804i	$0.107320\pi$
$350$	−1.07894			−0.0576716
$351$	6.39686	+	17.6091i	0.341439	+	0.939904i
$352$	−1.66555			−0.0887739
$353$	1.25545	−	1.25545i	0.0668208	−	0.0668208i	−0.672907	−	0.739727i	$-0.734954\pi$
$353$	1.25545	−	1.25545i	0.0668208	−	0.0668208i	0.739727	+	0.672907i	$0.234954\pi$
$354$	−12.2342	+	8.67779i	−0.650240	+	0.461219i
$355$		−	32.1933i		−	1.70864i
$356$	2.40063	+	8.95926i	0.127233	+	0.474840i
$357$	4.76640	−	28.0268i	0.252265	−	1.48334i
$358$	−2.60251	−	9.71272i	−0.137547	−	0.513333i
$359$	−5.40394	−	5.40394i	−0.285209	−	0.285209i	0.549973	−	0.835182i	$-0.314638\pi$
$359$	−5.40394	−	5.40394i	−0.285209	−	0.285209i	−0.835182	+	0.549973i	$0.814638\pi$
$360$	4.48594	+	5.21601i	0.236430	+	0.274908i
$361$	6.47736	+	3.73970i	0.340913	+	0.196826i
$362$	3.29204	+	3.29204i	0.173026	+	0.173026i
$363$	−8.24299	−	11.6212i	−0.432645	−	0.609955i
$364$	−14.2119	+	4.87127i	−0.744907	+	0.255324i
$365$	−18.5709	−	10.7219i	−0.972043	−	0.561209i
$366$	15.4994	+	12.8458i	0.810166	+	0.671459i
$367$	22.9156			1.19618			0.598092	−	0.801427i	$-0.295926\pi$
$367$	22.9156			1.19618			0.598092	+	0.801427i	$0.295926\pi$
$368$	−2.53606	−	4.39258i	−0.132201	−	0.228979i
$369$	6.90729	−	10.1244i	0.359579	−	0.527057i
$370$	2.79741	−	10.4401i	0.145431	−	0.542754i
$371$	26.9494	−	7.22107i	1.39914	−	0.374899i
$372$	−3.14565	−	2.60709i	−0.163094	−	0.135171i
$373$	−12.3759			−0.640799			−0.320400	−	0.947282i	$-0.603817\pi$
$373$	−12.3759			−0.640799			−0.320400	+	0.947282i	$0.603817\pi$
$374$	−3.28042	−	5.68186i	−0.169627	−	0.293802i
$375$	−18.5650	−	3.15726i	−0.958690	−	0.163040i
$376$	−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	$0.553361\pi$
$380$		−	7.78371i		−	0.399296i
$381$	29.1444	−	2.72843i	1.49311	−	0.139782i
$382$	8.32750	−	2.23135i	0.426072	−	0.114166i
$383$	5.14094	−	5.14094i	0.262690	−	0.262690i	−0.563456	−	0.826146i	$-0.690529\pi$
$383$	5.14094	−	5.14094i	0.262690	−	0.262690i	0.826146	+	0.563456i	$0.190529\pi$
$384$	1.70753	+	0.290392i	0.0871372	+	0.0148190i
$385$	15.3727	+	4.11911i	0.783467	+	0.209929i
$386$	14.8927	−	8.59830i	0.758018	−	0.437642i
$387$	−11.1955	+	9.62849i	−0.569099	+	0.489444i
$388$	−2.21607	−	8.27047i	−0.112504	−	0.419869i
$389$	−12.0896	−	20.9397i	−0.612965	−	1.06169i	−0.990738	−	0.135788i	$-0.956643\pi$
$389$	−12.0896	−	20.9397i	−0.612965	−	1.06169i	0.377773	−	0.925898i	$-0.376690\pi$
$390$	14.1343	−	2.30646i	0.715719	−	0.116792i
$391$	9.98992	−	17.3030i	0.505212	−	0.875053i
$392$	10.0091	+	2.68192i	0.505534	+	0.135457i
$393$	19.4858	−	1.82422i	0.982929	−	0.0920196i
$394$	8.06675	+	4.65734i	0.406397	+	0.234633i
$395$	−26.3755	+	26.3755i	−1.32710	+	1.32710i
$396$	−2.16657	−	4.50249i	−0.108874	−	0.226258i
$397$	−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	$0.722457\pi$
$398$	−1.76204	+	6.57603i	−0.0883231	+	0.329626i
$399$	−19.9804	+	14.1722i	−1.00027	+	0.709498i
$400$	0.224246	−	0.129469i	0.0112123	−	0.00647343i
$401$	−5.30318	+	19.7917i	−0.264828	+	0.988352i	0.697527	+	0.716558i	$0.254284\pi$
$401$	−5.30318	+	19.7917i	−0.264828	+	0.988352i	−0.962356	+	0.271794i	$0.912383\pi$
$402$	21.8573	+	10.0309i	1.09014	+	0.500297i
$403$	−8.04535	+	2.75762i	−0.400768	+	0.137367i
$404$			16.7511i			0.833401i
$405$	−8.26509	+	18.9120i	−0.410695	+	0.939743i
$406$	−10.9104	+	18.8974i	−0.541474	+	0.937861i
$407$	−3.92499	+	6.79828i	−0.194554	+	0.336978i
$408$	2.37247	+	6.39705i	0.117455	+	0.316701i
$409$	12.1240	+	12.1240i	0.599492	+	0.599492i	0.940177	−	0.340686i	$-0.110659\pi$
$409$	12.1240	+	12.1240i	0.599492	+	0.599492i	−0.340686	+	0.940177i	$0.610659\pi$
$410$	−6.62474	−	6.62474i	−0.327173	−	0.327173i
$411$	−17.1385	+	20.6789i	−0.845382	+	1.02002i
$412$	−4.35982	+	7.55143i	−0.214793	+	0.372032i
$413$	18.0419	−	31.2495i	0.887785	−	1.53769i
$414$	8.57554	−	12.5697i	0.421465	−	0.617766i
$415$			17.9466i			0.880964i
$416$	2.36927	−	2.71782i	0.116163	−	0.133252i
$417$	25.2656	−	17.9210i	1.23726	−	0.877597i
$418$	−1.46316	+	5.46057i	−0.0715653	+	0.267085i
$419$	24.0106	−	13.8625i	1.17299	−	0.677228i	0.218611	−	0.975812i	$-0.429848\pi$
$419$	24.0106	−	13.8625i	1.17299	−	0.677228i	0.954383	+	0.298584i	$0.0965142\pi$
$420$	−15.0421	−	6.90323i	−0.733979	−	0.336843i
$421$	−7.55093	+	28.1804i	−0.368010	+	1.37343i	0.495285	+	0.868731i	$0.335064\pi$
$421$	−7.55093	+	28.1804i	−0.368010	+	1.37343i	−0.863295	+	0.504700i	$0.831603\pi$
$422$	16.7500	+	4.48816i	0.815380	+	0.218480i
$423$	−11.2675	−	7.68714i	−0.547845	−	0.373762i
$424$	−4.73466	+	4.73466i	−0.229935	+	0.229935i
$425$	0.883340	+	0.509997i	0.0428483	+	0.0247385i
$426$	10.1419	−	22.0991i	0.491375	−	1.07070i
$427$	−46.7782	−	12.5342i	−2.26376	−	0.606572i
$428$	−5.08268	+	8.80347i	−0.245681	+	0.425532i
$429$	−10.3493	−	1.03885i	−0.499670	−	0.0501561i
$430$	5.64381	+	9.77537i	0.272169	+	0.471410i
$431$	−0.105936	−	0.395359i	−0.00510277	−	0.0190438i	0.963328	−	0.268328i	$-0.0864712\pi$
$431$	−0.105936	−	0.395359i	−0.00510277	−	0.0190438i	−0.968430	+	0.249285i	$0.919805\pi$
$432$	1.43617	+	4.99374i	0.0690978	+	0.240261i
$433$	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	$0.179101\pi$
$434$	9.49379	+	2.54385i	0.455716	+	0.122109i
$435$	13.2733	−	16.0153i	0.636408	−	0.767874i
$436$	2.11305	−	2.11305i	0.101197	−	0.101197i
$437$	−16.6291	+	4.45577i	−0.795480	+	0.213148i
$438$	−9.37024	−	13.2104i	−0.447727	−	0.631219i
$439$			17.1133i			0.816775i	0.912809	+	0.408387i	$0.133909\pi$
$439$			17.1133i			0.816775i	−0.912809	+	0.408387i	$0.866091\pi$
$440$	−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	$0.314768\pi$
$444$	5.20923	−	6.28533i	0.247219	−	0.298288i
$445$	10.6352	+	18.4208i	0.504159	+	0.873228i
$446$	−26.8041			−1.26921
$447$	1.19289	−	7.01428i	0.0564216	−	0.331764i
$448$	−4.02481	+	1.07844i	−0.190154	+	0.0509517i
$449$	−1.17970	+	4.40270i	−0.0556735	+	0.207776i	−0.988160	−	0.153429i	$-0.950968\pi$
$449$	−1.17970	+	4.40270i	−0.0556735	+	0.207776i	0.932486	+	0.361206i	$0.117635\pi$
$450$	0.641697	+	0.437791i	0.0302499	+	0.0206377i
$451$	3.40222	+	5.89281i	0.160204	+	0.277482i
$452$	−18.6446			−0.876969
$453$	5.76649	−	2.13862i	0.270933	−	0.100481i
$454$	5.94413	+	3.43185i	0.278972	+	0.161065i
$455$	−28.5895	+	19.2256i	−1.34030	+	0.901309i
$456$	2.45211	−	5.34312i	0.114830	−	0.250215i
$457$	−6.11788	−	6.11788i	−0.286183	−	0.286183i	0.549386	−	0.835569i	$-0.314862\pi$
$457$	−6.11788	−	6.11788i	−0.286183	−	0.286183i	−0.835569	+	0.549386i	$0.814862\pi$
$458$	15.4393	+	8.91386i	0.721429	+	0.416517i
$459$	−14.2070	+	14.7349i	−0.663127	+	0.687767i
$460$	−8.22475	−	8.22475i	−0.383481	−	0.383481i
$461$	−4.98578	−	18.6072i	−0.232211	−	0.866622i	−0.979386	−	0.201996i	$-0.935257\pi$
$461$	−4.98578	−	18.6072i	−0.232211	−	0.866622i	0.747176	−	0.664627i	$-0.231409\pi$
$462$	9.25497	+	7.67045i	0.430580	+	0.356861i
$463$	−0.871225	−	3.25146i	−0.0404893	−	0.151108i	0.942722	−	0.333580i	$-0.108257\pi$
$463$	−0.871225	−	3.25146i	−0.0404893	−	0.151108i	−0.983211	+	0.182472i	$0.941590\pi$
$464$		−	5.23684i		−	0.243114i
$465$	−8.51532	−	3.90791i	−0.394888	−	0.181225i
$466$	−9.76576	+	9.76576i	−0.452390	+	0.452390i
$467$	25.8396			1.19571			0.597856	−	0.801604i	$-0.296019\pi$
$467$	25.8396			1.19571			0.597856	+	0.801604i	$0.296019\pi$
$468$	10.4291	+	2.86947i	0.482085	+	0.132641i
$469$	−57.8550			−2.67150
$470$	−7.37269	+	7.37269i	−0.340077	+	0.340077i
$471$	−1.32846	−	14.1903i	−0.0612124	−	0.653854i
$472$			8.65986i			0.398602i
$473$	−2.12181	−	7.91870i	−0.0975609	−	0.364102i
$474$	−26.4145	+	9.79636i	−1.21326	+	0.449962i
$475$	−0.227472	−	0.848937i	−0.0104371	−	0.0389519i
$476$	−11.6062	−	11.6062i	−0.531969	−	0.531969i
$477$	−18.9582	−	6.64031i	−0.868034	−	0.304039i
$478$	19.2334	+	11.1044i	0.879713	+	0.507903i
$479$	−14.3660	−	14.3660i	−0.656399	−	0.656399i	0.298127	−	0.954526i	$-0.403638\pi$
$479$	−14.3660	−	14.3660i	−0.656399	−	0.656399i	−0.954526	+	0.298127i	$0.903638\pi$
$480$	3.95471	−	0.370231i	0.180507	−	0.0168987i
$481$	−5.51000	−	16.0754i	−0.251235	−	0.732976i
$482$	8.60879	+	4.97029i	0.392119	+	0.226390i
$483$	−6.13728	+	36.0878i	−0.279256	+	1.64205i
$484$	−8.22595			−0.373907
$485$	−9.81760	−	17.0046i	−0.445794	−	0.772138i
$486$	−11.6314	+	10.3784i	−0.527612	+	0.470772i
$487$	−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	$0.757749\pi$
$488$	11.2264	−	3.00811i	0.508197	−	0.136171i
$489$	−25.0196	+	9.27903i	−1.13143	+	0.419612i
$490$	23.7629			1.07350
$491$	12.9064	+	22.3546i	0.582459	+	1.00885i	0.995187	+	0.0979942i	$0.0312426\pi$
$491$	12.9064	+	22.3546i	0.582459	+	1.00885i	−0.412728	+	0.910854i	$0.635424\pi$
$492$	−2.46056	−	6.63455i	−0.110930	−	0.299109i
$493$	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
$497$			58.4949i			2.62386i
$498$	−5.65373	+	12.3194i	−0.253350	+	0.552047i
$499$	18.3835	−	4.92584i	0.822958	−	0.220511i	0.177319	−	0.984153i	$-0.443258\pi$
$499$	18.3835	−	4.92584i	0.822958	−	0.220511i	0.645639	+	0.763642i	$0.276591\pi$
$500$	−7.68794	+	7.68794i	−0.343815	+	0.343815i
$501$	−2.03988	−	5.50026i	−0.0911352	−	0.245734i
$502$	−8.32102	−	2.22961i	−0.371385	−	0.0995123i
$503$	−2.59687	+	1.49930i	−0.115789	+	0.0668507i	−0.556776	−	0.830663i	$-0.687962\pi$
$503$	−2.59687	+	1.49930i	−0.115789	+	0.0668507i	0.440987	+	0.897513i	$0.354628\pi$
$504$	−8.15091	−	9.47744i	−0.363071	−	0.422159i
$505$	9.94237	+	37.1054i	0.442430	+	1.65117i
$506$	4.22392	+	7.31604i	0.187776	+	0.325238i
$507$	16.4173	−	15.4102i	0.729117	−	0.684389i
$508$	8.45004	−	14.6359i	0.374910	−	0.649363i
$509$	22.8785	+	6.13027i	1.01407	+	0.271719i	0.727329	−	0.686289i	$-0.240761\pi$
$509$	22.8785	+	6.13027i	1.01407	+	0.271719i	0.286741	+	0.958008i	$0.407428\pi$
$510$	9.05212	+	12.7619i	0.400835	+	0.565108i
$511$	33.7431	+	19.4816i	1.49271	+	0.861814i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	17.6338	−	0.321635i	0.778553	−	0.0142005i
$514$	−12.9164	−	3.46095i	−0.569720	−	0.152656i
$515$	−5.17540	+	19.3149i	−0.228055	+	0.851114i
$516$	0.794653	+	8.48827i	0.0349826	+	0.373675i
$517$	6.55812	−	3.78633i	0.288426	−	0.166523i
$518$	−5.08287	+	18.9695i	−0.223329	+	0.833474i
$519$	1.38699	+	14.8155i	0.0608823	+	0.650329i
$520$	3.63504	−	7.42648i	0.159407	−	0.325673i
$521$			9.92644i			0.434885i	0.976073	+	0.217443i	$0.0697715\pi$
$521$			9.92644i			0.434885i	−0.976073	+	0.217443i	$0.930229\pi$
$522$	14.1568	−	6.81217i	0.619626	−	0.298161i
$523$	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	$0.0392157\pi$
$524$	5.64966	−	9.78550i	0.246807	−	0.427482i
$525$	−1.84232	−	0.313315i	−0.0804055	−	0.0136742i
$526$	3.03215	+	3.03215i	0.132208	+	0.132208i
$527$	−6.57026	−	6.57026i	−0.286205	−	0.286205i
$528$	−2.84398	−	0.483662i	−0.123768	−	0.0210487i
$529$	−1.36316	+	2.36106i	−0.0592678	+	0.102655i
$530$	−7.67755	+	13.2979i	−0.333491	+	0.577624i
$531$	−23.4103	+	11.2649i	−1.01592	+	0.488855i
$532$			14.1429i			0.613173i
$533$	−14.4555	−	2.83092i	−0.626139	−	0.122621i
$534$	1.49745	+	15.9954i	0.0648010	+	0.692187i
$535$	−6.03349	+	22.5173i	−0.260850	+	0.973507i
$536$	12.0246	−	6.94240i	0.519383	−	0.299866i
$537$	−1.62338	−	17.3405i	−0.0700541	−	0.748300i
$538$	3.92038	−	14.6311i	0.169020	−	0.630790i
$539$	−16.6706	−	4.46686i	−0.718052	−	0.192401i
$540$	6.14521	+	10.2092i	0.264448	+	0.439334i
$541$	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	$-0.107136\pi$
$542$	−3.05526	−	1.76395i	−0.131235	−	0.0757684i
$543$	4.66529	+	6.57726i	0.200207	+	0.282257i
$544$	3.80493	+	1.01953i	0.163135	+	0.0437119i
$545$	3.42645	−	5.93478i	0.146773	−	0.254218i
$546$	−25.6819	+	4.19082i	−1.09908	+	0.179351i
$547$	−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
$549$	22.7354	+	26.4355i	0.970323	+	1.12824i
$550$	−0.373492	+	0.215636i	−0.0159258	+	0.00919474i
$551$	−17.1692	−	4.60048i	−0.731433	−	0.195987i
$552$	−3.05483	−	8.23693i	−0.130022	−	0.350587i
$553$	47.9240	−	47.9240i	2.03794	−	2.03794i
$554$	21.2035	−	5.68146i	0.900850	−	0.241382i
$555$	7.80840	−	17.0145i	0.331448	−	0.722224i
$556$		−	17.8840i		−	0.758451i
$557$	−43.1111	+	11.5516i	−1.82668	+	0.489457i	−0.997572	−	0.0696359i	$-0.977816\pi$
$557$	−43.1111	+	11.5516i	−1.82668	+	0.489457i	−0.829105	+	0.559093i	$0.811150\pi$
$558$	−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
$561$	−3.95147	−	10.6546i	−0.166831	−	0.449837i
$562$	−0.642692	−	1.11318i	−0.0271103	−	0.0469565i
$563$	1.83546			0.0773554			0.0386777	−	0.999252i	$-0.487685\pi$
$563$	1.83546			0.0773554			0.0386777	+	0.999252i	$0.487685\pi$
$564$	−7.38361	+	2.73836i	−0.310906	+	0.115306i
$565$	−41.2996	+	11.0662i	−1.73749	+	0.465559i
$566$	3.21417	−	11.9955i	0.135102	−	0.504206i
$567$	15.0176	−	34.3629i	0.630679	−	1.44310i
$568$	−7.01918	−	12.1576i	−0.294518	−	0.510121i
$569$	5.90319			0.247475			0.123737	−	0.992315i	$-0.460512\pi$
$569$	5.90319			0.247475			0.123737	+	0.992315i	$0.460512\pi$
$570$	2.26033	−	13.2909i	0.0946748	−	0.556696i
$571$	6.53279	+	3.77171i	0.273389	+	0.157841i	0.630427	−	0.776249i	$-0.282880\pi$
$571$	6.53279	+	3.77171i	0.273389	+	0.157841i	−0.357038	+	0.934090i	$0.616213\pi$
$572$	−3.94613	+	4.52666i	−0.164996	+	0.189269i
$573$	14.8675	−	1.39186i	0.621097	−	0.0581457i
$574$	12.0371	+	12.0371i	0.502419	+	0.502419i
$575$	−1.13740	−	0.656679i	−0.0474329	−	0.0273854i
$576$	2.83134	+	0.991710i	0.117973	+	0.0413212i
$577$	−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	$0.844666\pi$
$578$	−0.383841	−	1.43251i	−0.0159657	−	0.0595847i
$579$	27.9266	−	10.3572i	1.16059	−	0.430429i
$580$	−3.10824	−	11.6001i	−0.129063	−	0.481668i
$581$		−	32.6088i		−	1.35284i
$582$	−1.38233	−	14.7656i	−0.0572992	−	0.612055i
$583$	7.88579	−	7.88579i	0.326596	−	0.326596i
$584$	−9.35088			−0.386942
$585$	24.8046	+	0.166134i	1.02554	+	0.00686878i
$586$	8.16192			0.337166
$587$	−5.58491	+	5.58491i	−0.230514	+	0.230514i	−0.812907	−	0.582393i	$-0.802116\pi$
$587$	−5.58491	+	5.58491i	−0.230514	+	0.230514i	0.582393	+	0.812907i	$0.302116\pi$
$588$	16.3120	+	7.48603i	0.672696	+	0.308719i
$589$			8.00629i			0.329894i
$590$	5.13992	+	19.1824i	0.211607	+	0.789728i
$591$	12.4218	+	10.2951i	0.510964	+	0.423483i
$592$	−1.21985	−	4.55256i	−0.0501357	−	0.187109i
$593$	−17.4187	−	17.4187i	−0.715300	−	0.715300i	0.252339	−	0.967639i	$-0.418800\pi$
$593$	−17.4187	−	17.4187i	−0.715300	−	0.715300i	−0.967639	+	0.252339i	$0.918800\pi$
$594$	−2.39201	−	8.31730i	−0.0981453	−	0.341263i
$595$	−32.5975	−	18.8202i	−1.33637	−	0.771552i
$596$	−2.90468	−	2.90468i	−0.118980	−	0.118980i
$597$	−4.91837	+	10.7171i	−0.201296	+	0.438622i
$598$	−17.9468	−	3.51465i	−0.733901	−	0.143725i
$599$	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	$0.240155\pi$
$600$	0.420504	−	0.155953i	0.0171670	−	0.00636674i
$601$	−29.0425			−1.18467			−0.592334	−	0.805693i	$-0.701793\pi$
$601$	−29.0425			−1.18467			−0.592334	+	0.805693i	$0.701793\pi$
$602$	−10.2548	−	17.7618i	−0.417953	−	0.723915i
$603$	34.4092	+	23.4754i	1.40125	+	0.955991i
$604$	0.919034	−	3.42988i	0.0373949	−	0.139560i
$605$	−18.2213	+	4.88238i	−0.740801	+	0.198497i
$606$	−4.86441	+	28.6032i	−0.197603	+	1.16192i
$607$	−16.4214			−0.666523			−0.333262	−	0.942834i	$-0.608149\pi$
$607$	−16.4214			−0.666523			−0.333262	+	0.942834i	$0.608149\pi$
$608$	−1.69710	−	2.93946i	−0.0688265	−	0.119211i
$609$	−24.1175	+	29.0996i	−0.977292	+	1.17918i
$610$	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	$0.551199\pi$
$614$		−	20.3926i		−	0.822977i
$615$	−9.38820	−	13.2357i	−0.378569	−	0.533717i
$616$	6.70351	−	1.79620i	0.270092	−	0.0723710i
$617$	22.6178	−	22.6178i	0.910560	−	0.910560i	−0.0857562	−	0.996316i	$-0.527331\pi$
$617$	22.6178	−	22.6178i	0.910560	−	0.910560i	0.996316	+	0.0857562i	$0.0273306\pi$
$618$	−9.63742	+	11.6283i	−0.387674	+	0.467757i
$619$	36.9574	+	9.90270i	1.48544	+	0.398023i	0.908196	−	0.418546i	$-0.137460\pi$
$619$	36.9574	+	9.90270i	1.48544	+	0.398023i	0.577247	+	0.816569i	$0.304127\pi$
$620$	−4.68461	+	2.70466i	−0.188139	+	0.108622i
$621$	18.2932	−	18.9729i	0.734080	−	0.761356i
$622$	1.32468	+	4.94377i	0.0531148	+	0.198227i
$623$	−19.3241	−	33.4704i	−0.774205	−	1.34096i
$624$	4.83484	−	3.95276i	0.193549	−	0.158237i
$625$	−13.1138	+	22.7138i	−0.524553	+	0.908552i
$626$	4.87482	+	1.30620i	0.194837	+	0.0522064i
$627$	−4.08410	+	8.89922i	−0.163103	+	0.355401i
$628$	−7.12617	−	4.11430i	−0.284365	−	0.164178i
$629$	13.1280	−	13.1280i	0.523449	−	0.523449i
$630$	−23.6802	−	16.1556i	−0.943444	−	0.643655i
$631$	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	$0.475749\pi$
$632$	−4.20981	+	15.7112i	−0.167457	+	0.624960i
$633$	27.2979	+	12.5278i	1.08500	+	0.497934i
$634$	5.49877	−	3.17472i	0.218384	−	0.126084i
$635$	10.0308	−	37.4353i	0.398059	−	1.48558i
$636$	−9.45949	+	6.70968i	−0.375093	+	0.266056i
$637$	31.0032	−	20.8487i	1.22839	−	0.826055i
$638$			8.72220i			0.345315i
$639$	23.7350	−	34.7898i	0.938942	−	1.37626i
$640$	1.14662	−	1.98600i	0.0453241	−	0.0785036i
$641$	−15.8503	+	27.4536i	−0.626051	+	1.08435i	0.362286	+	0.932067i	$0.381997\pi$
$641$	−15.8503	+	27.4536i	−0.626051	+	1.08435i	−0.988337	+	0.152285i	$0.951337\pi$
$642$	−11.2353	+	13.5562i	−0.443422	+	0.535022i
$643$	1.02379	+	1.02379i	0.0403743	+	0.0403743i	0.727006	−	0.686631i	$-0.240911\pi$
$643$	1.02379	+	1.02379i	0.0403743	+	0.0403743i	−0.686631	+	0.727006i	$0.740911\pi$
$644$	14.9443	+	14.9443i	0.588888	+	0.588888i
$645$	6.79831	+	18.3307i	0.267683	+	0.721770i
$646$	6.68514	−	11.5790i	0.263023	−	0.455570i
$647$	9.55687	−	16.5530i	0.375719	−	0.650765i	−0.614715	−	0.788749i	$-0.710729\pi$
$647$	9.55687	−	16.5530i	0.375719	−	0.650765i	0.990434	+	0.137984i	$0.0440624\pi$
$648$	1.00217	+	8.94403i	0.0393688	+	0.351355i
$649$		−	14.4234i		−	0.566168i
$650$	0.179427	−	0.916207i	0.00703769	−	0.0359366i
$651$	15.4723	+	7.10064i	0.606405	+	0.278296i
$652$	−3.98750	+	14.8816i	−0.156163	+	0.582807i
$653$	−36.6995	+	21.1885i	−1.43616	+	0.829169i	−0.997580	−	0.0695219i	$-0.977853\pi$
$653$	−36.6995	+	21.1885i	−1.43616	+	0.829169i	−0.438583	+	0.898691i	$0.644519\pi$
$654$	4.22172	−	2.99449i	0.165082	−	0.117094i
$655$	6.70653	−	25.0291i	0.262046	−	0.977968i
$656$	−3.94620	−	1.05738i	−0.154073	−	0.0412838i
$657$	−12.1638	−	25.2783i	−0.474555	−	0.986201i
$658$	13.3961	−	13.3961i	0.522235	−	0.522235i
$659$	−6.53926	−	3.77544i	−0.254733	−	0.147070i	0.367196	−	0.930143i	$-0.380318\pi$
$659$	−6.53926	−	3.77544i	−0.254733	−	0.147070i	−0.621930	+	0.783073i	$0.713651\pi$
$660$	−6.58676	+	0.616637i	−0.256389	+	0.0240026i
$661$	−17.1429	−	4.59344i	−0.666783	−	0.178664i	−0.0904779	−	0.995898i	$-0.528839\pi$
$661$	−17.1429	−	4.59344i	−0.666783	−	0.178664i	−0.576305	+	0.817234i	$0.695506\pi$
$662$	−1.43579	+	2.48687i	−0.0558037	+	0.0966549i
$663$	23.0071	+	8.70836i	0.893521	+	0.338205i
$664$	3.91294	+	6.77741i	0.151852	+	0.263015i
$665$	8.39430	+	31.3279i	0.325517	+	1.21485i
$666$	10.7202	−	9.21969i	0.415397	−	0.357256i
$667$	−23.0032	+	13.2809i	−0.890688	+	0.514239i
$668$	−3.27153	−	0.876603i	−0.126579	−	0.0339168i
$669$	−45.7690	−	7.78372i	−1.76953	−	0.300936i
$670$	22.5151	−	22.5151i	0.869834	−	0.869834i
$671$	−18.6981	+	5.01015i	−0.721834	+	0.193415i
$672$	−7.18567	+	0.672706i	−0.277193	+	0.0259502i
$673$			1.13171i			0.0436244i	0.999762	+	0.0218122i	$0.00694358\pi$
$673$			1.13171i			0.0436244i	−0.999762	+	0.0218122i	$0.993056\pi$
$674$	−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	$0.290529\pi$
$678$	−31.8363	−	5.41425i	−1.22267	−	0.207933i
$679$	17.8385	+	30.8972i	0.684578	+	1.18572i
$680$	9.03342			0.346416
$681$	9.15323	+	7.58613i	0.350753	+	0.290701i
$682$	3.79485	−	1.01683i	0.145312	−	0.0389363i
$683$	0.848566	−	3.16689i	0.0324695	−	0.121178i	−0.947789	−	0.318898i	$-0.896687\pi$
$683$	0.848566	−	3.16689i	0.0324695	−	0.121178i	0.980258	+	0.197721i	$0.0633538\pi$
$684$	5.73866	−	8.41149i	0.219423	−	0.321621i
$685$	17.7800	+	30.7958i	0.679337	+	1.17665i
$686$	−14.0094			−0.534880
$687$	23.7745	+	19.7042i	0.907055	+	0.751761i
$688$	4.26269	+	2.46107i	0.162514	+	0.0938273i
$689$	1.65028	+	24.0856i	0.0628708	+	0.917590i
$690$	−11.6556	−	16.4324i	−0.443723	−	0.625573i
$691$	−5.02563	−	5.02563i	−0.191184	−	0.191184i	0.605024	−	0.796207i	$-0.293164\pi$
$691$	−5.02563	−	5.02563i	−0.191184	−	0.191184i	−0.796207	+	0.605024i	$0.793164\pi$
$692$	7.44014	+	4.29557i	0.282832	+	0.163293i
$693$	13.5757	+	15.7851i	0.515699	+	0.599627i
$694$	2.82191	+	2.82191i	0.107118	+	0.107118i
$695$	−10.6148	−	39.6148i	−0.402641	−	1.50268i
$696$	1.52074	−	8.94208i	0.0576434	−	0.338949i
$697$	−4.16519	−	15.5447i	−0.157768	−	0.588797i
$698$		−	16.1925i		−	0.612895i
$699$	−19.5113	+	13.8395i	−0.737984	+	0.523457i
$700$	−0.762923	+	0.762923i	−0.0288358	+	0.0288358i
$701$	44.5315			1.68193			0.840966	−	0.541088i	$-0.181987\pi$
$701$	44.5315			1.68193			0.840966	+	0.541088i	$0.181987\pi$
$702$	16.9748	+	7.92825i	0.640671	+	0.299232i
$703$	−15.9974			−0.603353
$704$	−1.17772	+	1.17772i	−0.0443870	+	0.0443870i
$705$	−14.7301	+	10.4482i	−0.554768	+	0.393500i
$706$		−	1.77547i		−	0.0668208i
$707$	−18.0652	−	67.4202i	−0.679411	−	2.53560i
$708$	−2.51476	+	14.7870i	−0.0945104	+	0.555730i
$709$	−1.42586	−	5.32138i	−0.0535493	−	0.199849i	0.933969	−	0.357355i	$-0.116321\pi$
$709$	−1.42586	−	5.32138i	−0.0535493	−	0.199849i	−0.987518	+	0.157506i	$0.949655\pi$
$710$	−22.7641	−	22.7641i	−0.854321	−	0.854321i
$711$	−47.9485	+	9.05704i	−1.79821	+	0.339666i
$712$	8.03265	+	4.63765i	0.301036	+	0.173803i
$713$	8.45995	+	8.45995i	0.316828	+	0.316828i
$714$	−16.4476	−	23.1883i	−0.615537	−	0.867801i
$715$	−6.05433	+	12.3692i	−0.226419	+	0.462580i
$716$	−8.70818	−	5.02767i	−0.325440	−	0.187893i
$717$	29.6170	+	24.5463i	1.10607	+	0.916700i
$718$	−7.64233			−0.285209
$719$	0.0565881	+	0.0980135i	0.00211038	+	0.00365529i	0.867079	−	0.498171i	$-0.165995\pi$
$719$	0.0565881	+	0.0980135i	0.00211038	+	0.00365529i	−0.864968	+	0.501827i	$0.832662\pi$
$720$	6.86032	+	0.516236i	0.255669	+	0.0192390i
$721$	9.40365	−	35.0949i	0.350210	−	1.30700i
$722$	7.22455	−	1.93581i	0.268870	−	0.0720435i
$723$	13.2565	+	10.9869i	0.493013	+	0.408606i
$724$	4.65565			0.173026
$725$	−0.678006	−	1.17434i	−0.0251805	−	0.0436139i
$726$	−14.0461	−	2.38876i	−0.521300	−	0.0886550i
$727$	−6.21671	+	3.58922i	−0.230565	+	0.133117i	−0.610833	−	0.791760i	$-0.709165\pi$
$727$	−6.21671	+	3.58922i	−0.230565	+	0.133117i	0.380268	+	0.924876i	$0.375832\pi$
$728$	−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
$731$			19.3891i			0.717130i
$732$	20.0430	−	1.87638i	0.740812	−	0.0693532i
$733$	−13.5981	+	3.64360i	−0.502257	+	0.134579i	−0.501047	−	0.865420i	$-0.667052\pi$
$733$	−13.5981	+	3.64360i	−0.502257	+	0.134579i	−0.00120982	+	0.999999i	$0.500385\pi$
$734$	16.2038	−	16.2038i	0.598092	−	0.598092i
$735$	40.5759	+	6.90055i	1.49666	+	0.254531i
$736$	−4.89928	−	1.31276i	−0.180590	−	0.0483889i
$737$	−20.0275	+	11.5629i	−0.737723	+	0.425924i
$738$	−2.27486	−	12.0432i	−0.0837388	−	0.443318i
$739$	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
$741$	−8.71197	−	19.3237i	−0.320042	−	0.709873i
$742$	13.9500	−	24.1622i	0.512122	−	0.887021i
$743$	−38.4128	−	10.2927i	−1.40923	−	0.377602i	−0.527580	−	0.849506i	$-0.676900\pi$
$743$	−38.4128	−	10.2927i	−1.40923	−	0.377602i	−0.881650	+	0.471904i	$0.843567\pi$
$744$	−4.06780	+	0.380818i	−0.149133	+	0.0139615i
$745$	−8.15818	−	4.71013i	−0.298893	−	0.172566i
$746$	−8.75107	+	8.75107i	−0.320400	+	0.320400i
$747$	−13.2314	+	19.3941i	−0.484112	+	0.709592i
$748$	−6.33729	−	1.69807i	−0.231714	−	0.0620877i
$749$	10.9628	−	40.9137i	0.400572	−	1.49495i
$750$	−15.3599	+	10.8949i	−0.560865	+	0.397825i
$751$	−3.61879	+	2.08931i	−0.132051	+	0.0762399i	−0.564570	−	0.825385i	$-0.690958\pi$
$751$	−3.61879	+	2.08931i	−0.132051	+	0.0762399i	0.432519	+	0.901625i	$0.357625\pi$
$752$	−1.17676	+	4.39173i	−0.0429121	+	0.160150i
$753$	−13.5610	−	6.22349i	−0.494189	−	0.226797i
$754$	−14.2328	−	12.4075i	−0.518328	−	0.451854i
$755$		−	8.14299i		−	0.296354i
$756$	−11.1658	−	18.5500i	−0.406096	−	0.674658i
$757$	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	$4.27865e-5\pi$
$758$	−8.10565	+	14.0394i	−0.294410	+	0.509934i
$759$	5.08796	+	13.7190i	0.184681	+	0.497968i
$760$	−5.50391	−	5.50391i	−0.199648	−	0.199648i
$761$	−30.1277	−	30.1277i	−1.09213	−	1.09213i	−0.995301	−	0.0968263i	$-0.969131\pi$
$761$	−30.1277	−	30.1277i	−1.09213	−	1.09213i	−0.0968263	−	0.995301i	$-0.530869\pi$
$762$	18.6789	−	22.5375i	0.676665	−	0.816446i
$763$	−6.22582	+	10.7834i	−0.225390	+	0.390387i
$764$	4.31063	−	7.46624i	0.155953	−	0.270119i
$765$	11.7508	+	24.4201i	0.424852	+	0.882911i
$766$		−	7.27039i		−	0.262690i
$767$	23.5360	+	20.5175i	0.849835	+	0.740846i
$768$	1.41275	−	1.00207i	0.0509781	−	0.0361591i
$769$	−0.262129	+	0.978277i	−0.00945260	+	0.0352776i	−0.970491	−

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.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.41275 - 1.00207i) q^{3} -1.00000i q^{4} +(-0.593533 - 2.21510i) q^{5} +(0.290392 - 1.70753i) q^{6} +(1.07844 + 4.02481i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.991710 - 2.83134i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.41275 - 1.00207i) q^{3} -1.00000i q^{4} +(-0.593533 - 2.21510i) q^{5} +(0.290392 - 1.70753i) q^{6} +(1.07844 + 4.02481i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.991710 - 2.83134i) q^{9} +(-1.98600 - 1.14662i) q^{10} +(1.17772 + 1.17772i) q^{11} +(-1.00207 - 1.41275i) q^{12} +(-3.59712 + 0.246465i) q^{13} +(3.60855 + 2.08340i) q^{14} +(-3.05820 - 2.53461i) q^{15} -1.00000 q^{16} +(-1.96958 - 3.41141i) q^{17} +(-1.30082 - 2.70331i) q^{18} +(-0.878484 + 3.27855i) q^{19} +(-2.21510 + 0.593533i) q^{20} +(5.55671 + 4.60536i) q^{21} +1.66555 q^{22} +(2.53606 + 4.39258i) q^{23} +(-1.70753 - 0.290392i) 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} +5.23684i q^{29} +(-3.95471 + 0.370231i) q^{30} +(2.27844 - 0.610507i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.84398 + 0.483662i) q^{33} +(-3.80493 - 1.01953i) q^{34} +(8.27525 - 4.77772i) q^{35} +(-2.83134 - 0.991710i) q^{36} +(1.21985 + 4.55256i) q^{37} +(1.69710 + 2.93946i) q^{38} +(-4.83484 + 3.95276i) q^{39} +(-1.14662 + 1.98600i) q^{40} +(3.94620 + 1.05738i) q^{41} +(7.18567 - 0.672706i) q^{42} +(-4.26269 - 2.46107i) q^{43} +(1.17772 - 1.17772i) q^{44} +(-6.86032 - 0.516236i) q^{45} +(4.89928 + 1.31276i) q^{46} +(1.17676 - 4.39173i) q^{47} +(-1.41275 + 1.00207i) q^{48} +(-8.97388 + 5.18107i) q^{49} +(-0.0670178 + 0.250114i) q^{50} +(-6.20099 - 2.84580i) q^{51} +(0.246465 + 3.59712i) q^{52} -6.69581i q^{53} +(-4.54663 - 2.51558i) q^{54} +(1.90975 - 3.30778i) q^{55} +(2.08340 - 3.60855i) q^{56} +(2.04426 + 5.51206i) q^{57} +(3.70300 + 3.70300i) q^{58} +(-6.12345 - 6.12345i) q^{59} +(-2.53461 + 3.05820i) q^{60} +(-5.81123 + 10.0653i) q^{61} +(1.17941 - 2.04279i) q^{62} +(12.4651 + 0.937996i) q^{63} +1.00000i q^{64} +(2.68095 + 7.82168i) q^{65} +(2.35300 - 1.66899i) q^{66} +(-3.59365 + 13.4117i) q^{67} +(-3.41141 + 1.96958i) q^{68} +(7.98448 + 3.66430i) q^{69} +(2.47313 - 9.22985i) q^{70} +(13.5600 + 3.63339i) q^{71} +(-2.70331 + 1.30082i) q^{72} +(6.61207 - 6.61207i) q^{73} +(4.08171 + 2.35658i) q^{74} +(-0.187066 + 0.407617i) q^{75} +(3.27855 + 0.878484i) q^{76} +(-3.46999 + 6.01020i) q^{77} +(-0.623728 + 6.21377i) q^{78} +(-8.13274 - 14.0863i) q^{79} +(0.593533 + 2.21510i) q^{80} +(-7.03302 - 5.61575i) q^{81} +(3.53806 - 2.04270i) q^{82} +(-7.55922 - 2.02549i) q^{83} +(4.60536 - 5.55671i) q^{84} +(-6.38759 + 6.38759i) q^{85} +(-4.75442 + 1.27394i) q^{86} +(5.24768 + 7.39833i) q^{87} -1.66555i 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} +(2.60709 - 3.14565i) q^{93} +(-2.27333 - 3.93752i) q^{94} +7.78371 q^{95} +(-0.290392 + 1.70753i) q^{96} +(8.27047 - 2.21607i) q^{97} +(-2.68192 + 10.0091i) q^{98} +(4.50249 - 2.16657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7}+O(q^{10}) \) 56 * q + 4 * q^7	\( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) \) 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

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