LMFDB - Embedded newform 234.2.y.a.119.13

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			119.13
Character	$\chi$	$=$	234.119
Dual form			234.2.y.a.59.13

$q$-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} +(-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} + 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}+ \cdots - 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

Character values

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

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

Coefficient data

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

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

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

$2$	0.707107	+	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	0.696547	+	0.717512i	$0.254719\pi$
$5$	−0.593533	+	2.21510i	−0.265436	+	0.990622i	−0.961983	+	0.273110i	$0.911948\pi$
$6$	0.290392	+	1.70753i	0.118552	+	0.697098i
$7$	1.07844	−	4.02481i	0.407614	−	1.52124i	−0.391570	−	0.920148i	$-0.628068\pi$
$7$	1.07844	−	4.02481i	0.407614	−	1.52124i	0.799184	−	0.601087i	$-0.205266\pi$
$8$	−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	−0.506906	−	0.862001i	$-0.669211\pi$
$11$	1.17772	−	1.17772i	0.355096	−	0.355096i	0.862001	+	0.506906i	$0.169211\pi$
$12$	−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	−0.999673	−	0.0255693i	$-0.991860\pi$
$17$	−1.96958	+	3.41141i	−0.477693	+	0.827388i	0.521980	+	0.852958i	$0.325193\pi$
$18$	−1.30082	+	2.70331i	−0.306606	+	0.637176i
$19$	−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	$-0.210631\pi$
$20$	−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	−0.470632	−	0.882330i	$-0.655974\pi$
$23$	2.53606	−	4.39258i	0.528804	−	0.915916i	0.999436	−	0.0335859i	$-0.0106927\pi$
$24$	−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	$-0.838372\pi$
$29$		−	5.23684i		−	0.972456i	0.873832	−	0.486228i	$-0.161628\pi$
$30$	−3.95471	−	0.370231i	−0.722028	−	0.0675946i
$31$	2.27844	+	0.610507i	0.409220	+	0.109650i	0.457556	−	0.889181i	$-0.348725\pi$
$31$	2.27844	+	0.610507i	0.409220	+	0.109650i	−0.0483356	+	0.998831i	$0.515392\pi$
$32$	−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	−0.790219	−	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
$39$	−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	0.0628507	−	0.998023i	$-0.479981\pi$
$41$	3.94620	−	1.05738i	0.616292	−	0.165135i	0.553442	+	0.832888i	$0.313314\pi$
$42$	7.18567	+	0.672706i	1.10877	+	0.103801i
$43$	−4.26269	+	2.46107i	−0.650055	+	0.375309i	−0.788477	−	0.615064i	$-0.789130\pi$
$43$	−4.26269	+	2.46107i	−0.650055	+	0.375309i	0.138422	+	0.990373i	$0.455797\pi$
$44$	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	0.997098	+	0.0761249i	$0.0242548\pi$
$47$	1.17676	+	4.39173i	0.171648	+	0.640600i	−0.825450	+	0.564475i	$0.809079\pi$
$48$	−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	$0.152104\pi$
$53$			6.69581i			0.919741i	−0.887986	+	0.459870i	$0.847896\pi$
$54$	−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	−0.982654	−	0.185449i	$-0.940626\pi$
$59$	−6.12345	+	6.12345i	−0.797205	+	0.797205i	0.185449	+	0.982654i	$0.440626\pi$
$60$	−2.53461	−	3.05820i	−0.327217	−	0.394811i
$61$	−5.81123	−	10.0653i	−0.744052	−	1.28874i	−0.950637	−	0.310307i	$-0.899568\pi$
$61$	−5.81123	−	10.0653i	−0.744052	−	1.28874i	0.206585	−	0.978429i	$-0.433765\pi$
$62$	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	−0.731224	−	0.682138i	$-0.761050\pi$
$67$	−3.59365	−	13.4117i	−0.439034	−	1.63850i	0.292190	−	0.956360i	$-0.405616\pi$
$68$	−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	0.661450	−	0.749989i	$-0.269941\pi$
$71$	13.5600	−	3.63339i	1.60928	−	0.431205i	0.947827	+	0.318784i	$0.103275\pi$
$72$	−2.70331	−	1.30082i	−0.318588	−	0.153303i
$73$	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	$0.565687\pi$
$74$	4.08171	−	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	−0.108109	+	0.994139i	$0.534480\pi$
$79$	−8.13274	+	14.0863i	−0.915004	+	1.58483i	−0.806895	+	0.590695i	$0.798854\pi$
$80$	0.593533	−	2.21510i	0.0663591	−	0.247655i
$81$	−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	−0.648597	−	0.761132i	$-0.724644\pi$
$83$	−7.55922	+	2.02549i	−0.829732	+	0.222326i	−0.181135	+	0.983458i	$0.557977\pi$
$84$	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	−0.249453	−	0.968387i	$-0.580251\pi$
$89$	−8.95926	−	2.40063i	−0.949679	−	0.254466i	−0.700226	+	0.713921i	$0.746917\pi$
$90$	−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	0.652958	−	0.757394i	$-0.273528\pi$
$97$	8.27047	+	2.21607i	0.839739	+	0.225007i	0.186781	+	0.982402i	$0.440195\pi$
$98$	−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	−0.823545	−	0.567251i	$-0.808007\pi$
$103$	−7.55143	+	4.35982i	−0.744065	+	0.429586i	0.0794807	+	0.996836i	$0.474674\pi$
$104$	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	−0.861009	−	0.508589i	$-0.830167\pi$
$107$	−8.80347	+	5.08268i	−0.851063	+	0.491362i	0.00994628	+	0.999951i	$0.496834\pi$
$108$	−4.99374	−	1.43617i	−0.480523	−	0.138196i
$109$	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	$0.204288\pi$
$110$	−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	$0.340438\pi$
$113$			18.6446i			1.75394i	−0.480547	+	0.876969i	$0.659562\pi$
$114$	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	0.318542	−	0.947909i	$-0.396807\pi$
$127$	14.6359	−	8.45004i	1.29873	−	0.749820i	0.980184	+	0.198089i	$0.0634735\pi$
$128$	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	−0.00735903	−	0.999973i	$-0.502342\pi$
$131$	9.78550	−	5.64966i	0.854963	−	0.493613i	0.862322	+	0.506360i	$0.169009\pi$
$132$	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	−0.445937	−	0.895064i	$-0.647129\pi$
$137$	−14.9781	−	4.01336i	−1.27966	−	0.342884i	−0.833725	+	0.552180i	$0.813796\pi$
$138$	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	0.816005	−	0.578044i	$-0.196184\pi$
$149$	2.90468	+	2.90468i	0.237961	+	0.237961i	−0.578044	+	0.816005i	$0.696184\pi$
$150$	0.155953	−	0.420504i	0.0127335	−	0.0343340i
$151$	3.42988	−	0.919034i	0.279120	−	0.0747899i	−0.116543	−	0.993186i	$-0.537181\pi$
$151$	3.42988	−	0.919034i	0.279120	−	0.0747899i	0.395663	+	0.918396i	$0.370515\pi$
$152$	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	0.982186	−	0.187912i	$-0.0601719\pi$
$157$	4.11430	+	7.12617i	0.328357	+	0.568731i	−0.653829	+	0.756642i	$0.726839\pi$
$158$	−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	−0.789206	−	0.614129i	$-0.789507\pi$
$163$	−14.8816	+	3.98750i	−1.16561	+	0.312325i	−0.376408	+	0.926454i	$0.622841\pi$
$164$	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	0.991513	−	0.130008i	$-0.0415003\pi$
$167$	0.876603	+	3.27153i	0.0678336	+	0.253158i	−0.923679	+	0.383166i	$0.874834\pi$
$168$	−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	0.655246	−	0.755416i	$-0.272565\pi$
$173$	−4.29557	−	7.44014i	−0.326586	−	0.565664i	−0.981832	+	0.189752i	$0.939232\pi$
$174$	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	0.990444	−	0.137913i	$-0.0440395\pi$
$179$	5.02767	+	8.70818i	0.375786	+	0.650880i	−0.614658	+	0.788793i	$0.710706\pi$
$180$	−0.516236	−	6.86032i	−0.0384780	−	0.511338i
$181$		−	4.65565i		−	0.346052i	−0.984917	−	0.173026i	$-0.944646\pi$
$181$		−	4.65565i		−	0.346052i	0.984917	−	0.173026i	$-0.0553545\pi$
$182$	−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	−0.204937	−	0.978775i	$-0.565699\pi$
$191$	7.46624	−	4.31063i	0.540238	−	0.311906i	0.745175	+	0.666869i	$0.232366\pi$
$192$	1.00207	−	1.41275i	0.0723182	−	0.101956i
$193$	16.6106	−	4.45081i	1.19566	−	0.320376i	0.394539	−	0.918879i	$-0.370904\pi$
$193$	16.6106	−	4.45081i	1.19566	−	0.320376i	0.801120	+	0.598503i	$0.204238\pi$
$194$	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	−0.825317	−	0.564670i	$-0.809003\pi$
$197$	2.41082	−	8.99729i	0.171764	−	0.641030i	0.997080	−	0.0763603i	$-0.0243299\pi$
$198$	1.65174	+	4.71574i	0.117384	+	0.335133i
$199$	−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	$0.744242\pi$
$200$	0.250114	−	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	−0.396377	−	0.918088i	$-0.629733\pi$
$211$	8.67046	−	15.0177i	0.596899	−	1.03386i	0.993276	−	0.115772i	$-0.0369341\pi$
$212$	−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	−0.322717	+	0.946496i	$0.604596\pi$
$223$	−18.9534	+	18.9534i	−1.26921	+	1.26921i	−0.946496	+	0.322717i	$0.895404\pi$
$224$	−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	−0.881580	−	0.472034i	$-0.843520\pi$
$227$	1.77646	−	6.62982i	0.117907	−	0.440037i	0.999488	+	0.0319971i	$0.0101867\pi$
$228$	5.51206	+	2.04426i	0.365045	+	0.135384i
$229$	4.61415	−	17.2203i	0.304912	−	1.13795i	−0.628109	−	0.778125i	$-0.716171\pi$
$229$	4.61415	−	17.2203i	0.304912	−	1.13795i	0.933021	−	0.359821i	$-0.117162\pi$
$230$			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	−0.486139	−	0.873882i	$-0.661595\pi$
$239$	5.74805	−	21.4520i	0.371811	−	1.38762i	0.857949	−	0.513734i	$-0.171738\pi$
$240$	3.05820	−	2.53461i	0.197406	−	0.163608i
$241$	2.57281	−	9.60185i	0.165729	−	0.618510i	−0.832217	−	0.554450i	$-0.812929\pi$
$241$	2.57281	−	9.60185i	0.165729	−	0.618510i	0.997946	−	0.0640595i	$-0.0204048\pi$
$242$	−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	−0.969341	−	0.245718i	$-0.920976\pi$
$251$	−4.30727	+	7.46042i	−0.271873	+	0.470897i	0.697469	+	0.716615i	$0.254310\pi$
$252$	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	−0.995643	−	0.0932505i	$-0.970274\pi$
$257$	−6.68605	+	11.5806i	−0.417064	+	0.722376i	0.578579	+	0.815627i	$0.303608\pi$
$258$	−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	$-0.957793\pi$
$263$		−	4.28811i		−	0.264416i	0.991222	−	0.132208i	$-0.0422067\pi$
$264$	−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	0.843404	−	0.537279i	$-0.180548\pi$
$269$	13.1178	+	7.57359i	0.799809	+	0.461770i	−0.0435953	+	0.999049i	$0.513881\pi$
$270$	−2.87367	−	11.5643i	−0.174886	−	0.703782i
$271$	−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
$273$	−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	0.195250	−	0.980754i	$-0.437448\pi$
$277$	19.0105	−	10.9757i	1.14223	−	0.659468i	0.946982	+	0.321285i	$0.104115\pi$
$278$	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	0.975139	−	0.221595i	$-0.0711264\pi$
$281$	0.332682	+	1.24159i	0.0198461	+	0.0740668i	−0.955293	+	0.295662i	$0.904460\pi$
$282$	−7.15731	+	3.28469i	−0.426212	+	0.195600i
$283$	10.7548	+	6.20930i	0.639308	+	0.369105i	0.784348	−	0.620321i	$-0.212998\pi$
$283$	10.7548	+	6.20930i	0.639308	+	0.369105i	−0.145040	+	0.989426i	$0.546331\pi$
$284$	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	−0.518134	−	0.855300i	$-0.673373\pi$
$293$	5.77135	−	5.77135i	0.337166	−	0.337166i	0.855300	+	0.518134i	$0.173373\pi$
$294$	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	0.986534	−	0.163557i	$-0.0522968\pi$
$307$	14.4197	+	14.4197i	0.822977	+	0.822977i	−0.163557	+	0.986534i	$0.552297\pi$
$308$	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	0.784303	−	0.620379i	$-0.213021\pi$
$311$	−2.55908	−	4.43246i	−0.145112	−	0.251342i	−0.929415	+	0.369037i	$0.879688\pi$
$312$	6.21377	−	0.623728i	0.351786	−	0.0353117i
$313$	2.52339	−	4.37065i	0.142631	−	0.247043i	−0.785856	−	0.618410i	$-0.787777\pi$
$313$	2.52339	−	4.37065i	0.142631	−	0.247043i	0.928486	+	0.371366i	$0.121111\pi$
$314$	−2.12972	+	7.94821i	−0.120187	+	0.448544i
$315$	−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	−0.0824373	−	0.996596i	$-0.526270\pi$
$317$	6.13308	−	1.64335i	0.344468	−	0.0922999i	0.426905	+	0.904296i	$0.359604\pi$
$318$	−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	0.181782	−	0.983339i	$-0.441813\pi$
$331$	−2.77374	−	0.743222i	−0.152459	−	0.0408512i	−0.334241	+	0.942488i	$0.608480\pi$
$332$	−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	−0.778219	−	0.627993i	$-0.783877\pi$
$337$	−11.4454	+	6.60801i	−0.623471	+	0.359961i	0.154748	+	0.987954i	$0.450543\pi$
$338$	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	$-0.965838\pi$
$347$		−	3.99079i		−	0.214237i	0.994246	−	0.107118i	$-0.0341624\pi$
$348$	7.39833	+	5.24768i	0.396592	+	0.281305i
$349$	11.4498	+	11.4498i	0.612895	+	0.612895i	0.943699	−	0.330804i	$-0.107320\pi$
$349$	11.4498	+	11.4498i	0.612895	+	0.612895i	−0.330804	+	0.943699i	$0.607320\pi$
$350$	−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	0.739727	−	0.672907i	$-0.234954\pi$
$353$	1.25545	+	1.25545i	0.0668208	+	0.0668208i	−0.672907	+	0.739727i	$0.734954\pi$
$354$	−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	−0.835182	−	0.549973i	$-0.814638\pi$
$359$	−5.40394	+	5.40394i	−0.285209	+	0.285209i	0.549973	+	0.835182i	$0.314638\pi$
$360$	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	−0.166854	−	0.985982i	$-0.553361\pi$
$379$	−15.6589	−	4.19579i	−0.804344	−	0.215523i	−0.637490	+	0.770458i	$0.720027\pi$
$380$			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	0.826146	−	0.563456i	$-0.190529\pi$
$383$	5.14094	+	5.14094i	0.262690	+	0.262690i	−0.563456	+	0.826146i	$0.690529\pi$
$384$	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	0.377773	+	0.925898i	$0.376690\pi$
$389$	−12.0896	+	20.9397i	−0.612965	+	1.06169i	−0.990738	+	0.135788i	$0.956643\pi$
$390$	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	−0.643351	−	0.765571i	$-0.722457\pi$
$397$	−16.2930	+	4.36571i	−0.817724	+	0.219109i	−0.174373	+	0.984680i	$0.555790\pi$
$398$	−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	−0.962356	−	0.271794i	$-0.912383\pi$
$401$	−5.30318	−	19.7917i	−0.264828	−	0.988352i	0.697527	−	0.716558i	$-0.254284\pi$
$402$	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	−0.340686	−	0.940177i	$-0.610659\pi$
$409$	12.1240	−	12.1240i	0.599492	−	0.599492i	0.940177	+	0.340686i	$0.110659\pi$
$410$	−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	0.954383	−	0.298584i	$-0.0965142\pi$
$419$	24.0106	+	13.8625i	1.17299	+	0.677228i	0.218611	+	0.975812i	$0.429848\pi$
$420$	−15.0421	+	6.90323i	−0.733979	+	0.336843i
$421$	−7.55093	−	28.1804i	−0.368010	−	1.37343i	−0.863295	−	0.504700i	$-0.831603\pi$
$421$	−7.55093	−	28.1804i	−0.368010	−	1.37343i	0.495285	−	0.868731i	$-0.335064\pi$
$422$	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	−0.968430	−	0.249285i	$-0.919805\pi$
$431$	−0.105936	+	0.395359i	−0.00510277	+	0.0190438i	0.963328	+	0.268328i	$0.0864712\pi$
$432$	1.43617	−	4.99374i	0.0690978	−	0.240261i
$433$	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	$0.512434\pi$
$434$	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	$-0.866091\pi$
$439$		−	17.1133i		−	0.816775i	0.912809	−	0.408387i	$-0.133909\pi$
$440$	−3.68935	−	0.988558i	−0.175883	−	0.0471276i
$441$	5.76991	−	30.5463i	0.274758	−	1.45458i
$442$	13.9381	−	2.72958i	0.662966	−	0.129833i
$443$	2.12505	+	1.22690i	0.100964	+	0.0582916i	0.549632	−	0.835407i	$-0.314768\pi$
$443$	2.12505	+	1.22690i	0.100964	+	0.0582916i	−0.448668	+	0.893699i	$0.648101\pi$
$444$	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	0.932486	−	0.361206i	$-0.117635\pi$
$449$	−1.17970	−	4.40270i	−0.0556735	−	0.207776i	−0.988160	+	0.153429i	$0.950968\pi$
$450$	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	−0.835569	−	0.549386i	$-0.814862\pi$
$457$	−6.11788	+	6.11788i	−0.286183	+	0.286183i	0.549386	+	0.835569i	$0.314862\pi$
$458$	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	0.747176	+	0.664627i	$0.231409\pi$
$461$	−4.98578	+	18.6072i	−0.232211	+	0.866622i	−0.979386	+	0.201996i	$0.935257\pi$
$462$	9.25497	−	7.67045i	0.430580	−	0.356861i
$463$	−0.871225	+	3.25146i	−0.0404893	+	0.151108i	−0.983211	−	0.182472i	$-0.941590\pi$
$463$	−0.871225	+	3.25146i	−0.0404893	+	0.151108i	0.942722	+	0.333580i	$0.108257\pi$
$464$			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	−0.954526	−	0.298127i	$-0.903638\pi$
$479$	−14.3660	+	14.3660i	−0.656399	+	0.656399i	0.298127	+	0.954526i	$0.403638\pi$
$480$	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	−0.724109	−	0.689685i	$-0.757749\pi$
$487$	−9.75089	−	36.3908i	−0.441855	−	1.64902i	0.282255	−	0.959340i	$-0.408918\pi$
$488$	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	−0.412728	−	0.910854i	$-0.635424\pi$
$491$	12.9064	−	22.3546i	0.582459	−	1.00885i	0.995187	−	0.0979942i	$-0.0312426\pi$
$492$	−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	0.645639	−	0.763642i	$-0.276591\pi$
$499$	18.3835	+	4.92584i	0.822958	+	0.220511i	0.177319	+	0.984153i	$0.443258\pi$
$500$	−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	0.440987	−	0.897513i	$-0.354628\pi$
$503$	−2.59687	−	1.49930i	−0.115789	−	0.0668507i	−0.556776	+	0.830663i	$0.687962\pi$
$504$	−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	0.286741	−	0.958008i	$-0.407428\pi$
$509$	22.8785	−	6.13027i	1.01407	−	0.271719i	0.727329	+	0.686289i	$0.240761\pi$
$510$	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	$-0.930229\pi$
$521$		−	9.92644i		−	0.434885i	0.976073	−	0.217443i	$-0.0697715\pi$
$522$	14.1568	+	6.81217i	0.619626	+	0.298161i
$523$	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	$0.705882\pi$
$524$	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	0.943891	+	0.330258i	$0.107136\pi$
$541$	29.6359	+	29.6359i	1.27415	+	1.27415i	0.330258	+	0.943891i	$0.392864\pi$
$542$	−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	−0.999777	−	0.0211411i	$-0.993270\pi$
$547$	−11.2632	+	19.5084i	−0.481580	+	0.834120i	0.518197	+	0.855261i	$0.326603\pi$
$548$	4.01336	−	14.9781i	0.171442	−	0.639831i
$549$	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	−0.829105	−	0.559093i	$-0.811150\pi$
$557$	−43.1111	−	11.5516i	−1.82668	−	0.489457i	−0.997572	+	0.0696359i	$0.977816\pi$
$558$	−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	−0.357038	−	0.934090i	$-0.616213\pi$
$571$	6.53279	−	3.77171i	0.273389	−	0.157841i	0.630427	+	0.776249i	$0.282880\pi$
$572$	−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	−0.883275	−	0.468856i	$-0.844666\pi$
$577$	−9.95468	+	9.95468i	−0.414419	+	0.414419i	0.468856	+	0.883275i	$0.344666\pi$
$578$	−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	0.582393	−	0.812907i	$-0.302116\pi$
$587$	−5.58491	−	5.58491i	−0.230514	−	0.230514i	−0.812907	+	0.582393i	$0.802116\pi$
$588$	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	−0.967639	−	0.252339i	$-0.918800\pi$
$593$	−17.4187	+	17.4187i	−0.715300	+	0.715300i	0.252339	+	0.967639i	$0.418800\pi$
$594$	−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	0.728635	−	0.684902i	$-0.240155\pi$
$599$	41.2663	−	23.8251i	1.68610	−	0.973468i	0.957460	−	0.288566i	$-0.0931783\pi$
$600$	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	−0.160153	−	0.987092i	$-0.551199\pi$
$613$	−19.6188	−	5.25684i	−0.792396	−	0.212322i	−0.632243	+	0.774770i	$0.717865\pi$
$614$			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	0.996316	−	0.0857562i	$-0.0273306\pi$
$617$	22.6178	+	22.6178i	0.910560	+	0.910560i	−0.0857562	+	0.996316i	$0.527331\pi$
$618$	−9.63742	−	11.6283i	−0.387674	−	0.467757i
$619$	36.9574	−	9.90270i	1.48544	−	0.398023i	0.577247	−	0.816569i	$-0.304127\pi$
$619$	36.9574	−	9.90270i	1.48544	−	0.398023i	0.908196	+	0.418546i	$0.137460\pi$
$620$	−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	0.0761122	−	0.997099i	$-0.475749\pi$
$631$	16.0911	−	4.31160i	0.640577	−	0.171642i	0.564465	+	0.825457i	$0.309083\pi$
$632$	−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	−0.988337	−	0.152285i	$-0.951337\pi$
$641$	−15.8503	−	27.4536i	−0.626051	−	1.08435i	0.362286	−	0.932067i	$-0.381997\pi$
$642$	−11.2353	−	13.5562i	−0.443422	−	0.535022i
$643$	1.02379	−	1.02379i	0.0403743	−	0.0403743i	−0.686631	−	0.727006i	$-0.740911\pi$
$643$	1.02379	−	1.02379i	0.0403743	−	0.0403743i	0.727006	+	0.686631i	$0.240911\pi$
$644$	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	0.990434	−	0.137984i	$-0.0440624\pi$
$647$	9.55687	+	16.5530i	0.375719	+	0.650765i	−0.614715	+	0.788749i	$0.710729\pi$
$648$	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	−0.438583	−	0.898691i	$-0.644519\pi$
$653$	−36.6995	−	21.1885i	−1.43616	−	0.829169i	−0.997580	+	0.0695219i	$0.977853\pi$
$654$	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	−0.621930	−	0.783073i	$-0.713651\pi$
$659$	−6.53926	+	3.77544i	−0.254733	+	0.147070i	0.367196	+	0.930143i	$0.380318\pi$
$660$	−6.58676	−	0.616637i	−0.256389	−	0.0240026i
$661$	−17.1429	+	4.59344i	−0.666783	+	0.178664i	−0.576305	−	0.817234i	$-0.695506\pi$
$661$	−17.1429	+	4.59344i	−0.666783	+	0.178664i	−0.0904779	+	0.995898i	$0.528839\pi$
$662$	−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	$-0.993056\pi$
$673$		−	1.13171i		−	0.0436244i	0.999762	−	0.0218122i	$-0.00694358\pi$
$674$	−12.7657	−	3.42056i	−0.491716	−	0.131755i
$675$	0.968587	−	0.933887i	0.0372810	−	0.0359453i
$676$	−1.77313	+	12.8785i	−0.0681972	+	0.495327i
$677$	6.04206	+	3.48838i	0.232215	+	0.134070i	0.611594	−	0.791172i	$-0.290529\pi$
$677$	6.04206	+	3.48838i	0.232215	+	0.134070i	−0.379378	+	0.925242i	$0.623862\pi$
$678$	−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	0.980258	−	0.197721i	$-0.0633538\pi$
$683$	0.848566	+	3.16689i	0.0324695	+	0.121178i	−0.947789	+	0.318898i	$0.896687\pi$
$684$	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	−0.796207	−	0.605024i	$-0.793164\pi$
$691$	−5.02563	+	5.02563i	−0.191184	+	0.191184i	0.605024	+	0.796207i	$0.293164\pi$
$692$	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	−0.987518	−	0.157506i	$-0.949655\pi$
$709$	−1.42586	+	5.32138i	−0.0535493	+	0.199849i	0.933969	+	0.357355i	$0.116321\pi$
$710$	−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	−0.864968	−	0.501827i	$-0.832662\pi$
$719$	0.0565881	−	0.0980135i	0.00211038	−	0.00365529i	0.867079	+	0.498171i	$0.165995\pi$
$720$	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	0.380268	−	0.924876i	$-0.375832\pi$
$727$	−6.21671	−	3.58922i	−0.230565	−	0.133117i	−0.610833	+	0.791760i	$0.709165\pi$
$728$	−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	−0.00120982	−	0.999999i	$-0.500385\pi$
$733$	−13.5981	−	3.64360i	−0.502257	−	0.134579i	−0.501047	+	0.865420i	$0.667052\pi$
$734$	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	−0.958260	−	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
$741$	−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	−0.881650	−	0.471904i	$-0.843567\pi$
$743$	−38.4128	+	10.2927i	−1.40923	+	0.377602i	−0.527580	+	0.849506i	$0.676900\pi$
$744$	−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	0.432519	−	0.901625i	$-0.357625\pi$
$751$	−3.61879	−	2.08931i	−0.132051	−	0.0762399i	−0.564570	+	0.825385i	$0.690958\pi$
$752$	−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	1.00000		0.000134418i	$-4.27865e-5\pi$
$757$	13.7536	+	23.8220i	0.499884	+	0.865824i	−0.500116	+	0.865958i	$0.666709\pi$
$758$	−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	−0.0968263	+	0.995301i	$0.530869\pi$
$761$	−30.1277	+	30.1277i	−1.09213	+	1.09213i	−0.995301	+	0.0968263i	$0.969131\pi$
$762$	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	0.961038	−	0.276415i	$-0.0891463\pi$
$769$	−0.262129	−	0.978277i	−0.00945260	−	0.0352776i	−0.970491	+	0.241137i	$0.922480\pi$
$770$	13.7828	+	7.95752i	0.496698	+	0.286

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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

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