LMFDB - Embedded newform 234.2.y.a.119.7

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			119.7
Character	$\chi$	$=$	234.119
Dual form			234.2.y.a.59.7

$q$-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} +(1.71950 + 0.208098i) q^{3} +1.00000i q^{4} +(-0.313114 + 1.16856i) q^{5} +(-1.06873 - 1.36302i) q^{6} +(-1.16567 + 4.35033i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.91339 + 0.715650i) q^{9} +(1.04770 - 0.604889i) q^{10} +(0.617934 - 0.617934i) q^{11} +(-0.208098 + 1.71950i) q^{12} +(-1.15311 + 3.41619i) q^{13} +(3.90040 - 2.25190i) q^{14} +(-0.781574 + 1.94418i) q^{15} -1.00000 q^{16} +(1.49284 - 2.58567i) q^{17} +(-1.55404 - 2.56612i) q^{18} +(-1.92262 - 7.17533i) q^{19} +(-1.16856 - 0.313114i) q^{20} +(-2.90966 + 7.23783i) q^{21} -0.873890 q^{22} +(-0.0774220 + 0.134099i) q^{23} +(1.36302 - 1.06873i) q^{24} +(3.06264 + 1.76822i) q^{25} +(3.23098 - 1.60024i) q^{26} +(4.86066 + 1.83683i) q^{27} +(-4.35033 - 1.16567i) q^{28} -9.39503i q^{29} +(1.92740 - 0.822086i) q^{30} +(4.22454 + 1.13196i) q^{31} +(0.707107 + 0.707107i) q^{32} +(1.19113 - 0.933949i) q^{33} +(-2.88394 + 0.772750i) q^{34} +(-4.71862 - 2.72429i) q^{35} +(-0.715650 + 2.91339i) q^{36} +(-1.18157 + 4.40968i) q^{37} +(-3.71422 + 6.43322i) q^{38} +(-2.69367 + 5.63419i) q^{39} +(0.604889 + 1.04770i) q^{40} +(5.46211 - 1.46357i) q^{41} +(7.17536 - 3.06048i) q^{42} +(2.01197 - 1.16161i) q^{43} +(0.617934 + 0.617934i) q^{44} +(-1.74850 + 3.18038i) q^{45} +(0.149568 - 0.0400766i) q^{46} +(-1.69254 - 6.31666i) q^{47} +(-1.71950 - 0.208098i) q^{48} +(-11.5044 - 6.64206i) q^{49} +(-0.915297 - 3.41593i) q^{50} +(3.10501 - 4.13542i) q^{51} +(-3.41619 - 1.15311i) q^{52} +0.732667i q^{53} +(-2.13817 - 4.73585i) q^{54} +(0.528607 + 0.915574i) q^{55} +(2.25190 + 3.90040i) q^{56} +(-1.81279 - 12.7381i) q^{57} +(-6.64329 + 6.64329i) q^{58} +(-10.1664 + 10.1664i) q^{59} +(-1.94418 - 0.781574i) q^{60} +(-1.64418 - 2.84781i) q^{61} +(-2.18678 - 3.78761i) q^{62} +(-6.50935 + 11.8400i) q^{63} -1.00000i q^{64} +(-3.63096 - 2.41712i) q^{65} +(-1.50266 - 0.181855i) q^{66} +(-1.37933 - 5.14774i) q^{67} +(2.58567 + 1.49284i) q^{68} +(-0.161033 + 0.214472i) q^{69} +(1.41020 + 5.26293i) q^{70} +(-14.6948 + 3.93745i) q^{71} +(2.56612 - 1.55404i) q^{72} +(0.594627 + 0.594627i) q^{73} +(3.95361 - 2.28262i) q^{74} +(4.89827 + 3.67779i) q^{75} +(7.17533 - 1.92262i) q^{76} +(1.96791 + 3.40852i) q^{77} +(5.88869 - 2.07926i) q^{78} +(1.78813 - 3.09714i) q^{79} +(0.313114 - 1.16856i) q^{80} +(7.97569 + 4.16994i) q^{81} +(-4.89719 - 2.82739i) q^{82} +(-2.44316 + 0.654644i) q^{83} +(-7.23783 - 2.90966i) q^{84} +(2.55407 + 2.55407i) q^{85} +(-2.24406 - 0.601294i) q^{86} +(1.95509 - 16.1548i) q^{87} -0.873890i q^{88} +(5.91054 + 1.58372i) q^{89} +(3.48525 - 1.01249i) q^{90} +(-13.5174 - 8.99852i) q^{91} +(-0.134099 - 0.0774220i) q^{92} +(7.02855 + 2.82553i) q^{93} +(-3.26974 + 5.66336i) q^{94} +8.98678 q^{95} +(1.06873 + 1.36302i) q^{96} +(10.7725 + 2.88649i) q^{97} +(3.43818 + 12.8315i) q^{98} +(2.24251 - 1.35806i) 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
$3$	1.71950	+	0.208098i	0.992756	+	0.120145i
$3$	1.71950	+	0.208098i	0.992756	+	0.120145i
$4$			1.00000i			0.500000i
$5$	−0.313114	+	1.16856i	−0.140029	+	0.522594i	0.859898	+	0.510466i	$0.170527\pi$
$5$	−0.313114	+	1.16856i	−0.140029	+	0.522594i	−0.999926	+	0.0121279i	$0.996139\pi$
$6$	−1.06873	−	1.36302i	−0.436305	−	0.556451i
$7$	−1.16567	+	4.35033i	−0.440581	+	1.64427i	0.286767	+	0.958000i	$0.407419\pi$
$7$	−1.16567	+	4.35033i	−0.440581	+	1.64427i	−0.727348	+	0.686269i	$0.759247\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.91339	+	0.715650i	0.971130	+	0.238550i
$10$	1.04770	−	0.604889i	0.331312	−	0.191283i
$11$	0.617934	−	0.617934i	0.186314	−	0.186314i	−0.607786	−	0.794101i	$-0.707942\pi$
$11$	0.617934	−	0.617934i	0.186314	−	0.186314i	0.794101	+	0.607786i	$0.207942\pi$
$12$	−0.208098	+	1.71950i	−0.0600727	+	0.496378i
$13$	−1.15311	+	3.41619i	−0.319814	+	0.947480i
$13$	−1.15311	+	3.41619i	−0.319814	+	0.947480i
$14$	3.90040	−	2.25190i	1.04242	−	0.601844i
$15$	−0.781574	+	1.94418i	−0.201802	+	0.501985i
$16$	−1.00000			−0.250000
$17$	1.49284	−	2.58567i	0.362066	−	0.627117i	−0.626234	−	0.779635i	$-0.715405\pi$
$17$	1.49284	−	2.58567i	0.362066	−	0.627117i	0.988301	+	0.152518i	$0.0487381\pi$
$18$	−1.55404	−	2.56612i	−0.366290	−	0.604840i
$19$	−1.92262	−	7.17533i	−0.441080	−	1.64613i	−0.726083	−	0.687607i	$-0.758661\pi$
$19$	−1.92262	−	7.17533i	−0.441080	−	1.64613i	0.285003	−	0.958527i	$-0.408005\pi$
$20$	−1.16856	−	0.313114i	−0.261297	−	0.0700144i
$21$	−2.90966	+	7.23783i	−0.634940	+	1.57942i
$22$	−0.873890			−0.186314
$23$	−0.0774220	+	0.134099i	−0.0161436	+	0.0279615i	−0.873984	−	0.485954i	$-0.838472\pi$
$23$	−0.0774220	+	0.134099i	−0.0161436	+	0.0279615i	0.857841	+	0.513916i	$0.171806\pi$
$24$	1.36302	−	1.06873i	0.278225	−	0.218153i
$25$	3.06264	+	1.76822i	0.612529	+	0.353644i
$26$	3.23098	−	1.60024i	0.633647	−	0.313833i
$27$	4.86066	+	1.83683i	0.935435	+	0.353499i
$28$	−4.35033	−	1.16567i	−0.822135	−	0.220290i
$29$		−	9.39503i		−	1.74461i	−0.488959	−	0.872307i	$-0.662623\pi$
$29$		−	9.39503i		−	1.74461i	0.488959	−	0.872307i	$-0.337377\pi$
$30$	1.92740	−	0.822086i	0.351893	−	0.150092i
$31$	4.22454	+	1.13196i	0.758749	+	0.203306i	0.617395	−	0.786653i	$-0.288188\pi$
$31$	4.22454	+	1.13196i	0.758749	+	0.203306i	0.141354	+	0.989959i	$0.454855\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	1.19113	−	0.933949i	0.207349	−	0.162580i
$34$	−2.88394	+	0.772750i	−0.494592	+	0.132525i
$35$	−4.71862	−	2.72429i	−0.797592	−	0.460490i
$36$	−0.715650	+	2.91339i	−0.119275	+	0.485565i
$37$	−1.18157	+	4.40968i	−0.194249	+	0.724947i	0.798211	+	0.602378i	$0.205780\pi$
$37$	−1.18157	+	4.40968i	−0.194249	+	0.724947i	−0.992460	+	0.122569i	$0.960887\pi$
$38$	−3.71422	+	6.43322i	−0.602527	+	1.04361i
$39$	−2.69367	+	5.63419i	−0.431333	+	0.902193i
$40$	0.604889	+	1.04770i	0.0956414	+	0.165656i
$41$	5.46211	−	1.46357i	0.853038	−	0.228571i	0.194299	−	0.980942i	$-0.437757\pi$
$41$	5.46211	−	1.46357i	0.853038	−	0.228571i	0.658739	+	0.752372i	$0.271090\pi$
$42$	7.17536	−	3.06048i	1.10718	−	0.472242i
$43$	2.01197	−	1.16161i	0.306822	−	0.177144i	−0.338681	−	0.940901i	$-0.609981\pi$
$43$	2.01197	−	1.16161i	0.306822	−	0.177144i	0.645504	+	0.763757i	$0.276648\pi$
$44$	0.617934	+	0.617934i	0.0931570	+	0.0931570i
$45$	−1.74850	+	3.18038i	−0.260651	+	0.474103i
$46$	0.149568	−	0.0400766i	0.0220526	−	0.00590897i
$47$	−1.69254	−	6.31666i	−0.246883	−	0.921379i	−0.972428	−	0.233204i	$-0.925079\pi$
$47$	−1.69254	−	6.31666i	−0.246883	−	0.921379i	0.725545	−	0.688175i	$-0.241588\pi$
$48$	−1.71950	−	0.208098i	−0.248189	−	0.0300363i
$49$	−11.5044	−	6.64206i	−1.64348	−	0.948866i
$50$	−0.915297	−	3.41593i	−0.129443	−	0.483086i
$51$	3.10501	−	4.13542i	0.434789	−	0.579074i
$52$	−3.41619	−	1.15311i	−0.473740	−	0.159907i
$53$			0.732667i			0.100640i	0.998733	+	0.0503198i	$0.0160240\pi$
$53$			0.732667i			0.100640i	−0.998733	+	0.0503198i	$0.983976\pi$
$54$	−2.13817	−	4.73585i	−0.290968	−	0.644467i
$55$	0.528607	+	0.915574i	0.0712773	+	0.123456i
$56$	2.25190	+	3.90040i	0.300922	+	0.521212i
$57$	−1.81279	−	12.7381i	−0.240110	−	1.68720i
$58$	−6.64329	+	6.64329i	−0.872307	+	0.872307i
$59$	−10.1664	+	10.1664i	−1.32355	+	1.32355i	−0.412673	+	0.910879i	$0.635405\pi$
$59$	−10.1664	+	10.1664i	−1.32355	+	1.32355i	−0.910879	+	0.412673i	$0.864595\pi$
$60$	−1.94418	−	0.781574i	−0.250992	−	0.100901i
$61$	−1.64418	−	2.84781i	−0.210516	−	0.364625i	0.741360	−	0.671108i	$-0.234181\pi$
$61$	−1.64418	−	2.84781i	−0.210516	−	0.364625i	−0.951876	+	0.306483i	$0.900848\pi$
$62$	−2.18678	−	3.78761i	−0.277721	−	0.481028i
$63$	−6.50935	+	11.8400i	−0.820102	+	1.49170i
$64$		−	1.00000i		−	0.125000i
$65$	−3.63096	−	2.41712i	−0.450365	−	0.299807i
$66$	−1.50266	−	0.181855i	−0.184964	−	0.0223848i
$67$	−1.37933	−	5.14774i	−0.168512	−	0.628896i	−0.997566	−	0.0697276i	$-0.977787\pi$
$67$	−1.37933	−	5.14774i	−0.168512	−	0.628896i	0.829054	−	0.559169i	$-0.188880\pi$
$68$	2.58567	+	1.49284i	0.313559	+	0.181033i
$69$	−0.161033	+	0.214472i	−0.0193861	+	0.0258194i
$70$	1.41020	+	5.26293i	0.168551	+	0.629041i
$71$	−14.6948	+	3.93745i	−1.74395	+	0.467290i	−0.983318	−	0.181895i	$-0.941777\pi$
$71$	−14.6948	+	3.93745i	−1.74395	+	0.467290i	−0.760631	+	0.649185i	$0.775110\pi$
$72$	2.56612	−	1.55404i	0.302420	−	0.183145i
$73$	0.594627	+	0.594627i	0.0695959	+	0.0695959i	0.741048	−	0.671452i	$-0.234329\pi$
$73$	0.594627	+	0.594627i	0.0695959	+	0.0695959i	−0.671452	+	0.741048i	$0.734329\pi$
$74$	3.95361	−	2.28262i	0.459598	−	0.265349i
$75$	4.89827	+	3.67779i	0.565603	+	0.424674i
$76$	7.17533	−	1.92262i	0.823067	−	0.220540i
$77$	1.96791	+	3.40852i	0.224264	+	0.388437i
$78$	5.88869	−	2.07926i	0.666763	−	0.235430i
$79$	1.78813	−	3.09714i	0.201181	−	0.348455i	−0.747728	−	0.664005i	$-0.768855\pi$
$79$	1.78813	−	3.09714i	0.201181	−	0.348455i	0.948909	+	0.315549i	$0.102189\pi$
$80$	0.313114	−	1.16856i	0.0350072	−	0.130649i
$81$	7.97569	+	4.16994i	0.886188	+	0.463326i
$82$	−4.89719	−	2.82739i	−0.540804	−	0.312233i
$83$	−2.44316	+	0.654644i	−0.268172	+	0.0718565i	−0.390399	−	0.920646i	$-0.627663\pi$
$83$	−2.44316	+	0.654644i	−0.268172	+	0.0718565i	0.122227	+	0.992502i	$0.460996\pi$
$84$	−7.23783	−	2.90966i	−0.789712	−	0.317470i
$85$	2.55407	+	2.55407i	0.277028	+	0.277028i
$86$	−2.24406	−	0.601294i	−0.241983	−	0.0648392i
$87$	1.95509	−	16.1548i	0.209607	−	1.73198i
$88$		−	0.873890i		−	0.0931570i
$89$	5.91054	+	1.58372i	0.626516	+	0.167874i	0.558088	−	0.829782i	$-0.311535\pi$
$89$	5.91054	+	1.58372i	0.626516	+	0.167874i	0.0684275	+	0.997656i	$0.478202\pi$
$90$	3.48525	−	1.01249i	0.367377	−	0.106726i
$91$	−13.5174	−	8.99852i	−1.41701	−	0.943301i
$92$	−0.134099	−	0.0774220i	−0.0139808	−	0.00807180i
$93$	7.02855	+	2.82553i	0.728826	+	0.292994i
$94$	−3.26974	+	5.66336i	−0.337248	+	0.584131i
$95$	8.98678			0.922024
$96$	1.06873	+	1.36302i	0.109076	+	0.139113i
$97$	10.7725	+	2.88649i	1.09378	+	0.293078i	0.760231	−	0.649653i	$-0.225086\pi$
$97$	10.7725	+	2.88649i	1.09378	+	0.293078i	0.333552	+	0.942732i	$0.391753\pi$
$98$	3.43818	+	12.8315i	0.347309	+	1.29618i
$99$	2.24251	−	1.35806i	0.225380	−	0.136490i
$100$	−1.76822	+	3.06264i	−0.176822	+	0.306264i
$101$	12.0245			1.19648			0.598240	−	0.801317i	$-0.295867\pi$
$101$	12.0245			1.19648			0.598240	+	0.801317i	$0.295867\pi$
$102$	−5.11976	+	0.728605i	−0.506931	+	0.0721426i
$103$	3.12107	−	1.80195i	0.307528	−	0.177551i	−0.338292	−	0.941041i	$-0.609849\pi$
$103$	3.12107	−	1.80195i	0.307528	−	0.177551i	0.645820	+	0.763490i	$0.276516\pi$
$104$	1.60024	+	3.23098i	0.156917	+	0.316824i
$105$	−7.54676	−	5.66637i	−0.736489	−	0.552981i
$106$	0.518074	−	0.518074i	0.0503198	−	0.0503198i
$107$	1.48317	−	0.856309i	0.143384	−	0.0827825i	−0.426592	−	0.904444i	$-0.640286\pi$
$107$	1.48317	−	0.856309i	0.143384	−	0.0827825i	0.569976	+	0.821662i	$0.306953\pi$
$108$	−1.83683	+	4.86066i	−0.176749	+	0.467717i
$109$	13.3881	−	13.3881i	1.28235	−	1.28235i	0.343021	−	0.939328i	$-0.388550\pi$
$109$	13.3881	−	13.3881i	1.28235	−	1.28235i	0.939328	−	0.343021i	$-0.111450\pi$
$110$	0.273627	−	1.02119i	0.0260893	−	0.0973667i
$111$	−2.94936	+	7.33658i	−0.279941	+	0.696357i
$112$	1.16567	−	4.35033i	0.110145	−	0.411067i
$113$		−	11.0455i		−	1.03908i	−0.854447	−	0.519539i	$-0.826104\pi$
$113$		−	11.0455i		−	1.03908i	0.854447	−	0.519539i	$-0.173896\pi$
$114$	−7.72536	+	10.2890i	−0.723547	+	0.963656i
$115$	−0.132460	−	0.132460i	−0.0123520	−	0.0123520i
$116$	9.39503			0.872307
$117$	−5.80424	+	9.12747i	−0.536602	+	0.843835i
$118$	14.3775			1.32355
$119$	9.50836	+	9.50836i	0.871630	+	0.871630i
$120$	0.822086	+	1.92740i	0.0750458	+	0.175947i
$121$			10.2363i			0.930574i
$122$	−0.851092	+	3.17632i	−0.0770543	+	0.287571i
$123$	9.69668	−	1.37996i	0.874320	−	0.124427i
$124$	−1.13196	+	4.22454i	−0.101653	+	0.379374i
$125$	−7.30243	+	7.30243i	−0.653149	+	0.653149i
$126$	12.9749	−	3.76933i	1.15590	−	0.335799i
$127$	−2.84302	+	1.64142i	−0.252277	+	0.145652i	−0.620807	−	0.783964i	$-0.713195\pi$
$127$	−2.84302	+	1.64142i	−0.252277	+	0.145652i	0.368529	+	0.929616i	$0.379861\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	3.70132	−	1.57871i	0.325883	−	0.138998i
$130$	0.858309	+	4.27664i	0.0752787	+	0.375086i
$131$	−17.6981	+	10.2180i	−1.54629	+	0.892752i	−0.547871	+	0.836563i	$0.684562\pi$
$131$	−17.6981	+	10.2180i	−1.54629	+	0.892752i	−0.998420	+	0.0561893i	$0.982105\pi$
$132$	0.933949	+	1.19113i	0.0812899	+	0.103675i
$133$	33.4562			2.90102
$134$	−2.66467	+	4.61534i	−0.230192	+	0.398704i
$135$	−3.66838	+	5.10482i	−0.315724	+	0.439353i
$136$	−0.772750	−	2.88394i	−0.0662627	−	0.247296i
$137$	−1.96845	−	0.527444i	−0.168176	−	0.0450626i	0.173748	−	0.984790i	$-0.444412\pi$
$137$	−1.96845	−	0.527444i	−0.168176	−	0.0450626i	−0.341924	+	0.939727i	$0.611079\pi$
$138$	0.265522	−	0.0377871i	0.0226028	−	0.00321665i
$139$	−15.9409			−1.35209			−0.676045	−	0.736861i	$-0.736307\pi$
$139$	−15.9409			−1.35209			−0.676045	+	0.736861i	$0.736307\pi$
$140$	2.72429	−	4.71862i	0.230245	−	0.398796i
$141$	−1.59585	−	11.2137i	−0.134395	−	0.944367i
$142$	13.1750	+	7.60657i	1.10562	+	0.638329i
$143$	1.39844	+	2.82352i	0.116943	+	0.236115i
$144$	−2.91339	−	0.715650i	−0.242783	−	0.0596375i
$145$	10.9786	+	2.94171i	0.911725	+	0.244296i
$146$		−	0.840930i		−	0.0695959i
$147$	−18.3997	−	13.8151i	−1.51758	−	1.13945i
$148$	−4.40968	−	1.18157i	−0.362473	−	0.0971245i
$149$	−6.13782	−	6.13782i	−0.502830	−	0.502830i	0.409486	−	0.912316i	$-0.365708\pi$
$149$	−6.13782	−	6.13782i	−0.502830	−	0.502830i	−0.912316	+	0.409486i	$0.865708\pi$
$150$	−0.863009	−	6.06419i	−0.0704644	−	0.495139i
$151$	5.35919	−	1.43599i	0.436125	−	0.116859i	−0.0340750	−	0.999419i	$-0.510848\pi$
$151$	5.35919	−	1.43599i	0.436125	−	0.116859i	0.470200	+	0.882560i	$0.344182\pi$
$152$	−6.43322	−	3.71422i	−0.521803	−	0.301263i
$153$	6.19965	−	6.46472i	0.501212	−	0.522642i
$154$	1.01866	−	3.80171i	0.0820864	−	0.306350i
$155$	−2.64552	+	4.58217i	−0.212493	+	0.368049i
$156$	−5.63419	−	2.69367i	−0.451097	−	0.215666i
$157$	0.734808	+	1.27273i	0.0586441	+	0.101575i	0.893857	−	0.448352i	$-0.147989\pi$
$157$	0.734808	+	1.27273i	0.0586441	+	0.101575i	−0.835213	+	0.549927i	$0.814656\pi$
$158$	−3.45441	+	0.925606i	−0.274818	+	0.0736373i
$159$	−0.152466	+	1.25982i	−0.0120914	+	0.0999105i
$160$	−1.04770	+	0.604889i	−0.0828279	+	0.0478207i
$161$	−0.493126	−	0.493126i	−0.0388637	−	0.0388637i
$162$	−2.69107	−	8.58825i	−0.211431	−	0.674757i
$163$	9.71328	−	2.60267i	0.760803	−	0.203857i	0.142498	−	0.989795i	$-0.454486\pi$
$163$	9.71328	−	2.60267i	0.760803	−	0.203857i	0.618305	+	0.785939i	$0.287820\pi$
$164$	1.46357	+	5.46211i	0.114285	+	0.426519i
$165$	0.718413	+	1.68434i	0.0559284	+	0.131125i
$166$	2.19048	+	1.26467i	0.170014	+	0.0981578i
$167$	−3.66589	−	13.6813i	−0.283675	−	1.05869i	−0.949802	−	0.312851i	$-0.898716\pi$
$167$	−3.66589	−	13.6813i	−0.283675	−	1.05869i	0.666128	−	0.745838i	$-0.267951\pi$
$168$	3.06048	+	7.17536i	0.236121	+	0.553591i
$169$	−10.3407	−	7.87845i	−0.795438	−	0.606035i
$170$		−	3.61201i		−	0.277028i
$171$	−0.466328	−	22.2805i	−0.0356610	−	1.70383i
$172$	1.16161	+	2.01197i	0.0885720	+	0.153411i
$173$	3.50709	+	6.07445i	0.266639	+	0.461832i	0.967992	−	0.250982i	$-0.0807536\pi$
$173$	3.50709	+	6.07445i	0.266639	+	0.461832i	−0.701353	+	0.712814i	$0.747420\pi$
$174$	−12.8056	+	10.0407i	−0.970792	+	0.761185i
$175$	−11.2623	+	11.2623i	−0.851353	+	0.851353i
$176$	−0.617934	+	0.617934i	−0.0465785	+	0.0465785i
$177$	−19.5968	+	15.3656i	−1.47298	+	1.15495i
$178$	−3.05952	−	5.29924i	−0.229321	−	0.397195i
$179$	3.22379	+	5.58377i	0.240958	+	0.417351i	0.960987	−	0.276592i	$-0.0892052\pi$
$179$	3.22379	+	5.58377i	0.240958	+	0.417351i	−0.720030	+	0.693943i	$0.755872\pi$
$180$	−3.18038	−	1.74850i	−0.237052	−	0.130326i
$181$			2.29864i			0.170857i	0.996344	+	0.0854284i	$0.0272259\pi$
$181$			2.29864i			0.170857i	−0.996344	+	0.0854284i	$0.972774\pi$
$182$	3.19533	+	15.9212i	0.236854	+	1.18016i
$183$	−2.23456	−	5.23897i	−0.165183	−	0.387276i
$184$	0.0400766	+	0.149568i	0.00295448	+	0.0110263i
$185$	−4.78299	−	2.76146i	−0.351653	−	0.203027i
$186$	−2.97198	−	6.96788i	−0.217916	−	0.510910i
$187$	−0.675299	−	2.52025i	−0.0493827	−	0.184299i
$188$	6.31666	−	1.69254i	0.460690	−	0.123441i
$189$	−13.6567	+	19.0043i	−0.993382	+	1.38236i
$190$	−6.35461	−	6.35461i	−0.461012	−	0.461012i
$191$	−5.83377	+	3.36813i	−0.422117	+	0.243709i	−0.695983	−	0.718059i	$-0.745031\pi$
$191$	−5.83377	+	3.36813i	−0.422117	+	0.243709i	0.273866	+	0.961768i	$0.411698\pi$
$192$	0.208098	−	1.71950i	0.0150182	−	0.124095i
$193$	6.26833	−	1.67959i	0.451204	−	0.120900i	−0.0260585	−	0.999660i	$-0.508296\pi$
$193$	6.26833	−	1.67959i	0.451204	−	0.120900i	0.477263	+	0.878761i	$0.341629\pi$
$194$	−5.57626	−	9.65837i	−0.400352	−	0.693431i
$195$	−5.74045	−	4.91185i	−0.411082	−	0.351745i
$196$	6.64206	−	11.5044i	0.474433	−	0.821742i
$197$	3.37597	−	12.5993i	0.240528	−	0.897662i	−0.735051	−	0.678012i	$-0.762842\pi$
$197$	3.37597	−	12.5993i	0.240528	−	0.897662i	0.975579	−	0.219650i	$-0.0704916\pi$
$198$	−2.54598	−	0.625400i	−0.180935	−	0.0444452i
$199$	−4.37034	−	2.52321i	−0.309805	−	0.178866i	0.337034	−	0.941492i	$-0.390576\pi$
$199$	−4.37034	−	2.52321i	−0.309805	−	0.178866i	−0.646839	+	0.762626i	$0.723909\pi$
$200$	3.41593	−	0.915297i	0.241543	−	0.0647213i
$201$	−1.30054	−	9.13860i	−0.0917327	−	0.644587i
$202$	−8.50258	−	8.50258i	−0.598240	−	0.598240i
$203$	40.8715	+	10.9515i	2.86861	+	0.768643i
$204$	4.13542	+	3.10501i	0.289537	+	0.217394i
$205$			6.84104i			0.477799i
$206$	−3.48110	−	0.932758i	−0.242540	−	0.0649883i
$207$	−0.321528	+	0.335275i	−0.0223478	+	0.0233032i
$208$	1.15311	−	3.41619i	0.0799534	−	0.236870i
$209$	−5.62193	−	3.24582i	−0.388877	−	0.224518i
$210$	1.32964	+	9.34309i	0.0917537	+	0.644735i
$211$	−4.68443	+	8.11367i	−0.322489	+	0.558568i	−0.981001	−	0.194003i	$-0.937853\pi$
$211$	−4.68443	+	8.11367i	−0.322489	+	0.558568i	0.658512	+	0.752570i	$0.271186\pi$
$212$	−0.732667			−0.0503198
$213$	−26.0871	+	3.71252i	−1.78746	+	0.254377i
$214$	−1.65426	−	0.443258i	−0.113083	−	0.0303005i
$215$	0.727433	+	2.71482i	0.0496105	+	0.185149i
$216$	4.73585	−	2.13817i	0.322233	−	0.145484i
$217$	−9.84880	+	17.0586i	−0.668580	+	1.15801i
$218$	−18.9337			−1.28235
$219$	0.898724	+	1.14621i	0.0607301	+	0.0774534i
$220$	−0.915574	+	0.528607i	−0.0617280	+	0.0356387i
$221$	7.11174	+	8.08137i	0.478388	+	0.543611i
$222$	7.27326	−	3.10223i	0.488149	−	0.208208i
$223$	−13.4141	+	13.4141i	−0.898272	+	0.898272i	−0.995283	−	0.0970112i	$-0.969072\pi$
$223$	−13.4141	+	13.4141i	−0.898272	+	0.898272i	0.0970112	+	0.995283i	$0.469072\pi$
$224$	−3.90040	+	2.25190i	−0.260606	+	0.150461i
$225$	7.65725	+	7.34329i	0.510483	+	0.489553i
$226$	−7.81038	+	7.81038i	−0.519539	+	0.519539i
$227$	1.04029	−	3.88241i	0.0690464	−	0.257685i	−0.922771	−	0.385349i	$-0.874081\pi$
$227$	1.04029	−	3.88241i	0.0690464	−	0.257685i	0.991817	+	0.127664i	$0.0407479\pi$
$228$	12.7381	−	1.81279i	0.843602	−	0.120055i
$229$	5.53707	−	20.6646i	0.365900	−	1.36556i	−0.500296	−	0.865854i	$-0.666776\pi$
$229$	5.53707	−	20.6646i	0.365900	−	1.36556i	0.866196	−	0.499704i	$-0.166558\pi$
$230$			0.187327i			0.0123520i
$231$	2.67452	+	6.27048i	0.175971	+	0.412567i
$232$	−6.64329	−	6.64329i	−0.436153	−	0.436153i
$233$	−1.72841			−0.113232			−0.0566158	−	0.998396i	$-0.518031\pi$
$233$	−1.72841			−0.113232			−0.0566158	+	0.998396i	$0.518031\pi$
$234$	10.5583	−	2.34988i	0.690219	−	0.153616i
$235$	7.91133			0.516078
$236$	−10.1664	−	10.1664i	−0.661776	−	0.661776i
$237$	3.71921	−	4.95344i	0.241589	−	0.321760i
$238$		−	13.4469i		−	0.871630i
$239$	0.420695	−	1.57006i	0.0272125	−	0.101558i	−0.950984	−	0.309240i	$-0.899925\pi$
$239$	0.420695	−	1.57006i	0.0272125	−	0.101558i	0.978196	+	0.207682i	$0.0665919\pi$
$240$	0.781574	−	1.94418i	0.0504504	−	0.125496i
$241$	2.16228	−	8.06975i	0.139285	−	0.519819i	−0.860658	−	0.509183i	$-0.829948\pi$
$241$	2.16228	−	8.06975i	0.139285	−	0.519819i	0.999943	−	0.0106359i	$-0.00338558\pi$
$242$	7.23817	−	7.23817i	0.465287	−	0.465287i
$243$	12.8465	+	8.82995i	0.824102	+	0.566441i
$244$	2.84781	−	1.64418i	0.182312	−	0.105258i
$245$	11.3638	−	11.3638i	0.726007	−	0.726007i
$246$	−7.83237	−	5.88081i	−0.499373	−	0.374947i
$247$	26.7293	+	1.70586i	1.70074	+	0.108541i
$248$	3.78761	−	2.18678i	0.240514	−	0.138861i
$249$	−4.33726	+	0.617246i	−0.274863	+	0.0391163i
$250$	10.3272			0.653149
$251$	7.58570	−	13.1388i	0.478805	−	0.829315i	−0.520899	−	0.853618i	$-0.674403\pi$
$251$	7.58570	−	13.1388i	0.478805	−	0.829315i	0.999705	+	0.0243030i	$0.00773664\pi$
$252$	−11.8400	−	6.50935i	−0.745849	−	0.410051i
$253$	0.0350225	+	0.130706i	0.00220185	+	0.00821741i
$254$	3.17098	+	0.849661i	0.198965	+	0.0533125i
$255$	3.86024	+	4.92324i	0.241738	+	0.308305i
$256$	1.00000			0.0625000
$257$	−10.5262	+	18.2319i	−0.656607	+	1.13728i	0.324881	+	0.945755i	$0.394676\pi$
$257$	−10.5262	+	18.2319i	−0.656607	+	1.13728i	−0.981488	+	0.191522i	$0.938658\pi$
$258$	−3.73354	−	1.50091i	−0.232440	−	0.0934427i
$259$	−17.8062	−	10.2804i	−1.10643	−	0.638795i
$260$	2.41712	−	3.63096i	0.149904	−	0.225182i
$261$	6.72356	−	27.3714i	0.416178	−	1.69425i
$262$	19.7397	+	5.28923i	1.21952	+	0.326770i
$263$			29.9839i			1.84889i	0.381319	+	0.924444i	$0.375470\pi$
$263$			29.9839i			1.84889i	−0.381319	+	0.924444i	$0.624530\pi$
$264$	0.181855	−	1.50266i	0.0111924	−	0.0924822i
$265$	−0.856163	−	0.229408i	−0.0525937	−	0.0140924i
$266$	−23.6571	−	23.6571i	−1.45051	−	1.45051i
$267$	9.83362	+	3.95319i	0.601808	+	0.241931i
$268$	5.14774	−	1.37933i	0.314448	−	0.0842561i
$269$	−13.2251	−	7.63551i	−0.806348	−	0.465545i	0.0393383	−	0.999226i	$-0.487475\pi$
$269$	−13.2251	−	7.63551i	−0.806348	−	0.465545i	−0.845686	+	0.533681i	$0.820808\pi$
$270$	6.20359	−	1.01571i	0.377539	−	0.0618144i
$271$	−3.28534	+	12.2611i	−0.199570	+	0.744806i	0.791466	+	0.611213i	$0.209318\pi$
$271$	−3.28534	+	12.2611i	−0.199570	+	0.744806i	−0.991036	+	0.133593i	$0.957349\pi$
$272$	−1.49284	+	2.58567i	−0.0905166	+	0.156779i
$273$	−21.3707	−	18.2859i	−1.29341	−	1.10672i
$274$	1.01894	+	1.76486i	0.0615567	+	0.106619i
$275$	2.98515	−	0.799869i	0.180011	−	0.0482339i
$276$	−0.214472	−	0.161033i	−0.0129097	−	0.00969306i
$277$	−25.7220	+	14.8506i	−1.54549	+	0.892286i	−0.547008	+	0.837128i	$0.684233\pi$
$277$	−25.7220	+	14.8506i	−1.54549	+	0.892286i	−0.998478	+	0.0551587i	$0.982434\pi$
$278$	11.2719	+	11.2719i	0.676045	+	0.676045i
$279$	11.4976	+	6.32113i	0.688345	+	0.378436i
$280$	−5.26293	+	1.41020i	−0.314520	+	0.0842755i
$281$	−4.24522	−	15.8434i	−0.253249	−	0.945137i	−0.969056	−	0.246840i	$-0.920608\pi$
$281$	−4.24522	−	15.8434i	−0.253249	−	0.945137i	0.715808	−	0.698297i	$-0.246059\pi$
$282$	−6.80087	+	9.05775i	−0.404986	+	0.539381i
$283$	11.0257	+	6.36571i	0.655412	+	0.378402i	0.790527	−	0.612428i	$-0.209807\pi$
$283$	11.0257	+	6.36571i	0.655412	+	0.378402i	−0.135114	+	0.990830i	$0.543140\pi$
$284$	−3.93745	−	14.6948i	−0.233645	−	0.871974i
$285$	15.4528	+	1.87013i	0.915345	+	0.110777i
$286$	1.00769	−	2.98538i	0.0595858	−	0.176529i
$287$			25.4680i			1.50333i
$288$	1.55404	+	2.56612i	0.0915725	+	0.151210i
$289$	4.04287	+	7.00246i	0.237816	+	0.411909i
$290$	−5.68295	−	9.84317i	−0.333715	−	0.578011i
$291$	17.9227	+	7.20506i	1.05065	+	0.422368i
$292$	−0.594627	+	0.594627i	−0.0347979	+	0.0347979i
$293$	−19.8453	+	19.8453i	−1.15938	+	1.15938i	−0.174765	+	0.984610i	$0.555917\pi$
$293$	−19.8453	+	19.8453i	−1.15938	+	1.15938i	−0.984610	+	0.174765i	$0.944083\pi$
$294$	3.24177	+	22.7793i	0.189064	+	1.32851i
$295$	−8.69677	−	15.0632i	−0.506346	−	0.877016i
$296$	2.28262	+	3.95361i	0.132674	+	0.229799i
$297$	4.13861	−	1.86853i	0.240147	−	0.108423i
$298$			8.68019i			0.502830i
$299$	−0.368831	−	0.419118i	−0.0213301	−	0.0242382i
$300$	−3.67779	+	4.89827i	−0.212337	+	0.282802i
$301$	2.70810	+	10.1068i	0.156092	+	0.582545i
$302$	−4.80492	−	2.77412i	−0.276492	−	0.159633i
$303$	20.6761	+	2.50226i	1.18781	+	0.143751i
$304$	1.92262	+	7.17533i	0.110270	+	0.411533i
$305$	3.84264	−	1.02963i	0.220029	−	0.0589566i
$306$	−8.95506	+	0.187429i	−0.511927	+	0.0107146i
$307$	−20.4736	−	20.4736i	−1.16849	−	1.16849i	−0.982563	−	0.185929i	$-0.940471\pi$
$307$	−20.4736	−	20.4736i	−1.16849	−	1.16849i	−0.185929	−	0.982563i	$-0.559529\pi$
$308$	−3.40852	+	1.96791i	−0.194218	+	0.112132i
$309$	5.74167	−	2.44897i	0.326632	−	0.139317i
$310$	5.11075	−	1.36942i	0.290271	−	0.0777779i
$311$	−9.98758	−	17.2990i	−0.566344	−	0.980936i	−0.996923	−	0.0783834i	$-0.975024\pi$
$311$	−9.98758	−	17.2990i	−0.566344	−	0.980936i	0.430580	−	0.902553i	$-0.358309\pi$
$312$	2.07926	+	5.88869i	0.117715	+	0.333381i
$313$	−15.1464	+	26.2344i	−0.856126	+	1.48285i	0.0194703	+	0.999810i	$0.493802\pi$
$313$	−15.1464	+	26.2344i	−0.856126	+	1.48285i	−0.875596	+	0.483043i	$0.839531\pi$
$314$	0.380365	−	1.41954i	0.0214652	−	0.0801093i
$315$	−11.7975	−	11.3138i	−0.664716	−	0.637461i
$316$	3.09714	+	1.78813i	0.174228	+	0.100590i
$317$	11.4787	−	3.07571i	0.644708	−	0.172749i	0.0783730	−	0.996924i	$-0.475027\pi$
$317$	11.4787	−	3.07571i	0.644708	−	0.172749i	0.566335	+	0.824175i	$0.308361\pi$
$318$	0.998640	−	0.783020i	0.0560010	−	0.0439096i
$319$	−5.80551	−	5.80551i	−0.325046	−	0.325046i
$320$	1.16856	+	0.313114i	0.0653243	+	0.0175036i
$321$	2.72852	−	1.16378i	0.152291	−	0.0649560i
$322$			0.697385i			0.0388637i
$323$	−21.4232	−	5.74033i	−1.19202	−	0.319401i
$324$	−4.16994	+	7.97569i	−0.231663	+	0.443094i
$325$	−9.57212	+	8.42363i	−0.530965	+	0.467259i
$326$	−8.70869	−	5.02796i	−0.482330	−	0.278473i
$327$	25.8070	−	20.2349i	1.42713	−	1.11899i
$328$	2.82739	−	4.89719i	0.156117	−	0.270402i
$329$	29.4525			1.62377
$330$	0.683010	−	1.69900i	0.0375985	−	0.0935269i
$331$	4.94458	+	1.32490i	0.271779	+	0.0728228i	0.392134	−	0.919908i	$-0.371737\pi$
$331$	4.94458	+	1.32490i	0.271779	+	0.0728228i	−0.120356	+	0.992731i	$0.538404\pi$
$332$	−0.654644	−	2.44316i	−0.0359282	−	0.134086i
$333$	−6.59816	+	12.0015i	−0.361577	+	0.657680i
$334$	−7.08195	+	12.2663i	−0.387507	+	0.671182i
$335$	6.44731			0.352254
$336$	2.90966	−	7.23783i	0.158735	−	0.394856i
$337$	−1.14176	+	0.659198i	−0.0621959	+	0.0359088i	−0.530775	−	0.847512i	$-0.678099\pi$
$337$	−1.14176	+	0.659198i	−0.0621959	+	0.0359088i	0.468580	+	0.883421i	$0.344766\pi$
$338$	1.74107	+	12.8829i	0.0947018	+	0.700736i
$339$	2.29855	−	18.9929i	0.124840	−	1.03155i
$340$	−2.55407	+	2.55407i	−0.138514	+	0.138514i
$341$	3.30996	−	1.91101i	0.179244	−	0.103487i
$342$	−15.4249	+	16.0844i	−0.834084	+	0.869745i
$343$	20.0128	−	20.0128i	1.08059	−	1.08059i
$344$	0.601294	−	2.24406i	0.0324196	−	0.120992i
$345$	−0.200201	−	0.255330i	−0.0107785	−	0.0137465i
$346$	1.81540	−	6.77517i	0.0975966	−	0.364236i
$347$		−	17.4642i		−	0.937528i	−0.883323	−	0.468764i	$-0.844699\pi$
$347$		−	17.4642i		−	0.937528i	0.883323	−	0.468764i	$-0.155301\pi$
$348$	16.1548	+	1.95509i	0.865988	+	0.104804i
$349$	−8.64403	−	8.64403i	−0.462704	−	0.462704i	0.436836	−	0.899541i	$-0.356099\pi$
$349$	−8.64403	−	8.64403i	−0.462704	−	0.462704i	−0.899541	+	0.436836i	$0.856099\pi$
$350$	15.9274			0.851353
$351$	−11.8798	+	14.4869i	−0.634098	+	0.773253i
$352$	0.873890			0.0465785
$353$	4.04671	+	4.04671i	0.215385	+	0.215385i	0.806550	−	0.591166i	$-0.201332\pi$
$353$	4.04671	+	4.04671i	0.215385	+	0.215385i	−0.591166	+	0.806550i	$0.701332\pi$
$354$	24.7221	+	2.99192i	1.31396	+	0.159019i
$355$		−	18.4045i		−	0.976812i
$356$	−1.58372	+	5.91054i	−0.0839372	+	0.313258i
$357$	14.3710	+	18.3283i	0.760594	+	0.970039i
$358$	1.66876	−	6.22789i	0.0881966	−	0.329154i
$359$	15.3645	−	15.3645i	0.810906	−	0.810906i	−0.173864	−	0.984770i	$-0.555625\pi$
$359$	15.3645	−	15.3645i	0.810906	−	0.810906i	0.984770	+	0.173864i	$0.0556252\pi$
$360$	1.01249	+	3.48525i	0.0533631	+	0.183689i
$361$	−31.3344	+	18.0909i	−1.64918	+	0.952154i
$362$	1.62539	−	1.62539i	0.0854284	−	0.0854284i
$363$	−2.13015	+	17.6014i	−0.111804	+	0.923833i
$364$	8.99852	−	13.5174i	0.471651	−	0.708505i
$365$	−0.881042	+	0.508670i	−0.0461158	+	0.0266250i
$366$	−2.12444	+	5.28459i	−0.111046	+	0.276230i
$367$	−6.75568			−0.352644			−0.176322	−	0.984333i	$-0.556420\pi$
$367$	−6.75568			−0.352644			−0.176322	+	0.984333i	$0.556420\pi$
$368$	0.0774220	−	0.134099i	0.00403590	−	0.00699038i
$369$	16.9607	−	0.354985i	0.882936	−	0.0184798i
$370$	1.42944	+	5.33474i	0.0743130	+	0.277340i
$371$	−3.18734	−	0.854045i	−0.165479	−	0.0443398i
$372$	−2.82553	+	7.02855i	−0.146497	+	0.364413i
$373$	7.29564			0.377754			0.188877	−	0.982001i	$-0.439515\pi$
$373$	7.29564			0.377754			0.188877	+	0.982001i	$0.439515\pi$
$374$	−1.30458	+	2.25959i	−0.0674580	+	0.116841i
$375$	−14.0762	+	11.0369i	−0.726891	+	0.569945i
$376$	−5.66336	−	3.26974i	−0.292065	−	0.168624i
$377$	32.0952	+	10.8335i	1.65299	+	0.557952i
$378$	23.0949	−	3.78132i	1.18787	−	0.194490i
$379$	−13.1722	−	3.52948i	−0.676611	−	0.181297i	−0.0958799	−	0.995393i	$-0.530566\pi$
$379$	−13.1722	−	3.52948i	−0.676611	−	0.181297i	−0.580731	+	0.814096i	$0.697233\pi$
$380$			8.98678i			0.461012i
$381$	−5.23017	+	2.23080i	−0.267949	+	0.114287i
$382$	6.50672	+	1.74347i	0.332913	+	0.0892038i
$383$	19.7959	+	19.7959i	1.01152	+	1.01152i	0.999933	+	0.0115914i	$0.00368975\pi$
$383$	19.7959	+	19.7959i	1.01152	+	1.01152i	0.0115914	+	0.999933i	$0.496310\pi$
$384$	−1.36302	+	1.06873i	−0.0695564	+	0.0545382i
$385$	−4.59923	+	1.23236i	−0.234398	+	0.0628068i
$386$	−5.62003	−	3.24473i	−0.286052	−	0.165152i
$387$	6.69296	−	1.94436i	0.340222	−	0.0988374i
$388$	−2.88649	+	10.7725i	−0.146539	+	0.546892i
$389$	9.21923	−	15.9682i	0.467433	−	0.809618i	−0.531874	−	0.846823i	$-0.678512\pi$
$389$	9.21923	−	15.9682i	0.467433	−	0.809618i	0.999308	+	0.0372049i	$0.0118454\pi$
$390$	0.585907	+	7.53231i	0.0296686	+	0.381413i
$391$	0.231157	+	0.400376i	0.0116901	+	0.0202479i
$392$	−12.8315	+	3.43818i	−0.648088	+	0.173655i
$393$	−32.5583	+	13.8870i	−1.64235	+	0.700505i
$394$	−11.2962	+	6.52187i	−0.569095	+	0.328567i
$395$	3.05929	+	3.05929i	0.153930	+	0.153930i
$396$	1.35806	+	2.24251i	0.0682450	+	0.112690i
$397$	5.23300	−	1.40218i	0.262637	−	0.0703733i	−0.125098	−	0.992144i	$-0.539924\pi$
$397$	5.23300	−	1.40218i	0.262637	−	0.0703733i	0.387734	+	0.921771i	$0.373258\pi$
$398$	1.30611	+	4.87448i	0.0654695	+	0.244335i
$399$	57.5280	+	6.96216i	2.88000	+	0.348544i
$400$	−3.06264	−	1.76822i	−0.153132	−	0.0884109i
$401$	7.83810	+	29.2522i	0.391416	+	1.46079i	0.827799	+	0.561024i	$0.189593\pi$
$401$	7.83810	+	29.2522i	0.391416	+	1.46079i	−0.436383	+	0.899761i	$0.643741\pi$
$402$	−5.54235	+	7.38158i	−0.276427	+	0.368160i
$403$	−8.73832	+	13.1265i	−0.435287	+	0.653880i
$404$			12.0245i			0.598240i
$405$	−7.37010	+	8.01438i	−0.366223	+	0.398238i
$406$	−21.1566	−	36.6444i	−1.04999	−	1.81863i
$407$	1.99476	+	3.45502i	0.0988765	+	0.171259i
$408$	−0.728605	−	5.11976i	−0.0360713	−	0.253466i
$409$	−20.5962	+	20.5962i	−1.01841	+	1.01841i	−0.0185873	+	0.999827i	$0.505917\pi$
$409$	−20.5962	+	20.5962i	−1.01841	+	1.01841i	−0.999827	+	0.0185873i	$0.994083\pi$
$410$	4.83735	−	4.83735i	0.238900	−	0.238900i
$411$	−3.27500	−	1.31657i	−0.161544	−	0.0649417i
$412$	1.80195	+	3.12107i	0.0887757	+	0.153764i
$413$	−32.3765	−	56.0778i	−1.59314	−	2.75941i
$414$	0.464430	−	0.00972048i	0.0228255	−	0.000477736i
$415$		−	3.05995i		−	0.150207i
$416$	−3.23098	+	1.60024i	−0.158412	+	0.0784583i
$417$	−27.4104	−	3.31727i	−1.34230	−	0.162447i
$418$	1.68016	+	6.27045i	0.0821794	+	0.306698i
$419$	−14.1052	−	8.14363i	−0.689083	−	0.397843i	0.114185	−	0.993459i	$-0.463574\pi$
$419$	−14.1052	−	8.14363i	−0.689083	−	0.397843i	−0.803269	+	0.595617i	$0.796908\pi$
$420$	5.66637	−	7.54676i	0.276491	−	0.368244i
$421$	1.11148	+	4.14810i	0.0541702	+	0.202166i	0.987707	−	0.156315i	$-0.0499615\pi$
$421$	1.11148	+	4.14810i	0.0541702	+	0.202166i	−0.933537	+	0.358481i	$0.883295\pi$
$422$	9.04962	−	2.42484i	0.440529	−	0.118039i
$423$	−0.410523	−	19.6142i	−0.0199603	−	0.953673i
$424$	0.518074	+	0.518074i	0.0251599	+	0.0251599i
$425$	9.14406	−	5.27932i	0.443552	−	0.256085i
$426$	21.0715	+	15.8212i	1.02092	+	0.766541i
$427$	14.3055	−	3.83314i	0.692291	−	0.185499i
$428$	0.856309	+	1.48317i	0.0413913	+	0.0716918i
$429$	1.81705	+	5.14607i	0.0877279	+	0.248455i
$430$	1.40529	−	2.43404i	0.0677692	−	0.117380i
$431$	−1.03304	+	3.85536i	−0.0497599	+	0.185706i	−0.986332	−	0.164767i	$-0.947313\pi$
$431$	−1.03304	+	3.85536i	−0.0497599	+	0.185706i	0.936573	+	0.350474i	$0.113979\pi$
$432$	−4.86066	−	1.83683i	−0.233859	−	0.0883747i
$433$	11.4946	+	6.63644i	0.552397	+	0.318927i	0.750088	−	0.661338i	$-0.230011\pi$
$433$	11.4946	+	6.63644i	0.552397	+	0.318927i	−0.197691	+	0.980264i	$0.563344\pi$
$434$	19.0264	−	5.09811i	0.913297	−	0.244717i
$435$	18.2656	+	7.34292i	0.875770	+	0.352066i
$436$	13.3881	+	13.3881i	0.641174	+	0.641174i
$437$	1.11106	+	0.297707i	0.0531490	+	0.0142412i
$438$	0.174996	−	1.44598i	0.00836162	−	0.0690917i
$439$			7.67553i			0.366333i	0.983082	+	0.183166i	$0.0586347\pi$
$439$			7.67553i			0.366333i	−0.983082	+	0.183166i	$0.941365\pi$
$440$	1.02119	+	0.273627i	0.0486833	+	0.0130447i
$441$	−28.7634	−	27.5840i	−1.36969	−	1.31353i
$442$	0.685628	−	10.7431i	0.0326120	−	0.510999i
$443$	−24.5458	−	14.1715i	−1.16620	−	0.673309i	−0.213422	−	0.976960i	$-0.568461\pi$
$443$	−24.5458	−	14.1715i	−1.16620	−	0.673309i	−0.952783	+	0.303651i	$0.901794\pi$
$444$	−7.33658	−	2.94936i	−0.348179	−	0.139970i
$445$	−3.70134	+	6.41091i	−0.175460	+	0.303906i
$446$	18.9703			0.898272
$447$	−9.27674	−	11.8313i	−0.438775	−	0.559600i
$448$	4.35033	+	1.16567i	0.205534	+	0.0550726i
$449$	−5.89447	−	21.9985i	−0.278177	−	1.03817i	−0.953682	−	0.300816i	$-0.902741\pi$
$449$	−5.89447	−	21.9985i	−0.278177	−	1.03817i	0.675505	−	0.737355i	$-0.263926\pi$
$450$	−0.222003	−	10.6070i	−0.0104653	−	0.500018i
$451$	2.47083	−	4.27961i	0.116347	−	0.201519i
$452$	11.0455			0.519539
$453$	9.51398	−	1.35396i	0.447006	−	0.0636145i
$454$	−3.48088	+	2.00968i	−0.163366	+	0.0943191i
$455$	14.7478	−	12.9783i	0.691386	−	0.608432i
$456$	−10.2890	−	7.72536i	−0.481828	−	0.361773i
$457$	15.3176	−	15.3176i	0.716529	−	0.716529i	−0.251364	−	0.967893i	$-0.580879\pi$
$457$	15.3176	−	15.3176i	0.716529	−	0.716529i	0.967893	+	0.251364i	$0.0808791\pi$
$458$	−18.5274	+	10.6968i	−0.865729	+	0.499829i
$459$	12.0056	−	9.82598i	0.560375	−	0.458637i
$460$	0.132460	−	0.132460i	0.00617599	−	0.00617599i
$461$	−3.49531	+	13.0447i	−0.162793	+	0.607552i	0.835518	+	0.549462i	$0.185167\pi$
$461$	−3.49531	+	13.0447i	−0.162793	+	0.607552i	−0.998311	+	0.0580892i	$0.981499\pi$
$462$	2.54273	−	6.32507i	0.118298	−	0.294269i
$463$	1.05528	−	3.93837i	0.0490432	−	0.183032i	−0.937059	−	0.349171i	$-0.886463\pi$
$463$	1.05528	−	3.93837i	0.0490432	−	0.183032i	0.986102	+	0.166139i	$0.0531300\pi$
$464$			9.39503i			0.436153i
$465$	−5.50252	+	7.32854i	−0.255173	+	0.339853i
$466$	1.22217	+	1.22217i	0.0566158	+	0.0566158i
$467$	0.722546			0.0334354			0.0167177	−	0.999860i	$-0.494678\pi$
$467$	0.722546			0.0334354			0.0167177	+	0.999860i	$0.494678\pi$
$468$	−9.12747	−	5.80424i	−0.421918	−	0.268301i
$469$	24.0022			1.10832
$470$	−5.59415	−	5.59415i	−0.258039	−	0.258039i
$471$	0.998655	+	2.34137i	0.0460156	+	0.107885i
$472$			14.3775i			0.661776i
$473$	0.525465	−	1.96106i	0.0241609	−	0.0901698i
$474$	−6.13249	+	0.872729i	−0.281674	+	0.0400858i
$475$	6.79924	−	25.3751i	0.311970	−	1.16429i
$476$	−9.50836	+	9.50836i	−0.435815	+	0.435815i
$477$	−0.524333	+	2.13455i	−0.0240076	+	0.0977341i
$478$	−1.40767	+	0.812720i	−0.0643855	+	0.0371730i
$479$	−13.3370	+	13.3370i	−0.609383	+	0.609383i	−0.942785	−	0.333402i	$-0.891803\pi$
$479$	−13.3370	+	13.3370i	−0.609383	+	0.609383i	0.333402	+	0.942785i	$0.391803\pi$
$480$	−1.92740	+	0.822086i	−0.0879733	+	0.0375229i
$481$	−13.7018	−	9.12129i	−0.624749	−	0.415895i
$482$	−7.23514	+	4.17721i	−0.329552	+	0.190267i
$483$	−0.745313	−	0.950550i	−0.0339129	−	0.0432515i
$484$	−10.2363			−0.465287
$485$	−6.74604	+	11.6845i	−0.306322	+	0.530565i
$486$	−2.84012	−	15.3275i	−0.128830	−	0.695272i
$487$	5.72342	+	21.3601i	0.259353	+	0.967919i	0.965617	+	0.259970i	$0.0837127\pi$
$487$	5.72342	+	21.3601i	0.259353	+	0.967919i	−0.706264	+	0.707949i	$0.749621\pi$
$488$	−3.17632	−	0.851092i	−0.143785	−	0.0385271i
$489$	17.2436	−	2.45398i	0.779784	−	0.110973i
$490$	−16.0709			−0.726007
$491$	18.3786	−	31.8326i	0.829414	−	1.43659i	−0.0690851	−	0.997611i	$-0.522008\pi$
$491$	18.3786	−	31.8326i	0.829414	−	1.43659i	0.898499	−	0.438976i	$-0.144659\pi$
$492$	1.37996	+	9.69668i	0.0622133	+	0.437160i
$493$	−24.2925	−	14.0253i	−1.09408	−	0.631666i
$494$	−17.6942	−	20.1067i	−0.796101	−	0.904642i
$495$	0.884808	+	3.04572i	0.0397692	+	0.136895i
$496$	−4.22454	−	1.13196i	−0.189687	−	0.0508265i
$497$		−	68.5168i		−	3.07340i
$498$	3.50336	+	2.63045i	0.156989	+	0.117873i
$499$	−0.0527664	−	0.0141387i	−0.00236215	−	0.000632935i	0.257638	−	0.966242i	$-0.417056\pi$
$499$	−0.0527664	−	0.0141387i	−0.00236215	−	0.000632935i	−0.260000	+	0.965609i	$0.583723\pi$
$500$	−7.30243	−	7.30243i	−0.326575	−	0.326575i
$501$	−3.45646	−	24.2879i	−0.154423	−	1.08510i
$502$	−14.6545	+	3.92665i	−0.654060	+	0.175255i
$503$	6.26294	+	3.61591i	0.279251	+	0.161226i	0.633084	−	0.774083i	$-0.281789\pi$
$503$	6.26294	+	3.61591i	0.279251	+	0.161226i	−0.353833	+	0.935308i	$0.615122\pi$
$504$	3.76933	+	12.9749i	0.167899	+	0.577950i
$505$	−3.76503	+	14.0513i	−0.167541	+	0.625273i
$506$	0.0676583	−	0.117188i	0.00300778	−	0.00520963i
$507$	−16.1414	−	15.6989i	−0.716864	−	0.697213i
$508$	−1.64142	−	2.84302i	−0.0728262	−	0.126139i
$509$	−36.4154	+	9.75747i	−1.61408	+	0.432492i	−0.949256	−	0.314505i	$-0.898161\pi$
$509$	−36.4154	+	9.75747i	−1.61408	+	0.432492i	−0.664827	+	0.746997i	$0.731495\pi$
$510$	0.751651	−	6.21086i	0.0332836	−	0.275022i
$511$	−3.27996	+	1.89369i	−0.145097	+	0.0837718i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	3.83466	−	38.4084i	0.169304	−	1.69577i
$514$	20.3351	−	5.44877i	0.896942	−	0.240335i
$515$	1.12843	+	4.21136i	0.0497246	+	0.185575i
$516$	1.57871	+	3.70132i	0.0694988	+	0.162941i
$517$	−4.94916	−	2.85740i	−0.217664	−	0.125668i
$518$	5.32154	+	19.8603i	0.233815	+	0.872610i
$519$	4.76637	+	11.1749i	0.209220	+	0.490522i
$520$	−4.27664	+	0.858309i	−0.187543	+	0.0376394i
$521$			35.0558i			1.53582i	0.640555	+	0.767912i	$0.278704\pi$
$521$			35.0558i			1.53582i	−0.640555	+	0.767912i	$0.721296\pi$
$522$	−24.1088	+	14.6002i	−1.05521	+	0.639035i
$523$	14.4334	+	24.9994i	0.631128	+	1.09315i	0.987321	+	0.158734i	$0.0507411\pi$
$523$	14.4334	+	24.9994i	0.631128	+	1.09315i	−0.356193	+	0.934412i	$0.615926\pi$
$524$	−10.2180	−	17.6981i	−0.446376	−	0.773146i
$525$	−21.7093	+	17.0220i	−0.947473	+	0.742900i
$526$	21.2018	−	21.2018i	0.924444	−	0.924444i
$527$	9.23342	−	9.23342i	0.402214	−	0.402214i
$528$	−1.19113	+	0.933949i	−0.0518373	+	0.0406449i
$529$	11.4880	+	19.8978i	0.499479	+	0.865123i
$530$	0.443182	+	0.767614i	0.0192506	+	0.0333430i
$531$	−36.8943	+	22.3431i	−1.60108	+	0.969608i
$532$			33.4562i			1.45051i
$533$	−1.29856	+	20.3472i	−0.0562469	+	0.881337i
$534$	−4.15810	−	9.74875i	−0.179938	−	0.421870i
$535$	0.536244	+	2.00129i	0.0231839	+	0.0865234i
$536$	−4.61534	−	2.66467i	−0.199352	−	0.115096i
$537$	4.38136	+	10.2722i	0.189069	+	0.443278i
$538$	3.95243	+	14.7507i	0.170401	+	0.635946i
$539$	−11.2133	+	3.00460i	−0.482991	+	0.129417i
$540$	−5.10482	−	3.66838i	−0.219676	−	0.157862i
$541$	−10.8347	−	10.8347i	−0.465819	−	0.465819i	0.434738	−	0.900557i	$-0.356841\pi$
$541$	−10.8347	−	10.8347i	−0.465819	−	0.465819i	−0.900557	+	0.434738i	$0.856841\pi$
$542$	10.9930	−	6.34679i	0.472188	−	0.272618i
$543$	−0.478342	+	3.95253i	−0.0205276	+	0.169619i
$544$	2.88394	−	0.772750i	0.123648	−	0.0331314i
$545$	11.4528	+	19.8368i	0.490582	+	0.849714i
$546$	2.18123	+	28.0415i	0.0933480	+	1.20006i
$547$	2.42762	−	4.20476i	0.103798	−	0.179783i	−0.809449	−	0.587191i	$-0.800234\pi$
$547$	2.42762	−	4.20476i	0.103798	−	0.179783i	0.913246	+	0.407408i	$0.133567\pi$
$548$	0.527444	−	1.96845i	0.0225313	−	0.0840880i
$549$	−2.75211	−	9.47345i	−0.117457	−	0.404317i
$550$	−2.67641	−	1.54523i	−0.114123	−	0.0658888i
$551$	−67.4125	+	18.0631i	−2.87187	+	0.769515i
$552$	0.0377871	+	0.265522i	0.00160833	+	0.0113014i
$553$	11.3892	+	11.3892i	0.484318	+	0.484318i
$554$	28.6892	+	7.68724i	1.21889	+	0.326599i
$555$	−7.64972	−	5.74368i	−0.324713	−	0.243806i
$556$		−	15.9409i		−	0.676045i
$557$	−15.3310	−	4.10794i	−0.649596	−	0.174059i	−0.0810500	−	0.996710i	$-0.525827\pi$
$557$	−15.3310	−	4.10794i	−0.649596	−	0.174059i	−0.568546	+	0.822651i	$0.692494\pi$
$558$	−3.66034	−	12.5998i	−0.154954	−	0.533391i
$559$	1.64827	+	8.21273i	0.0697144	+	0.347361i
$560$	4.71862	+	2.72429i	0.199398	+	0.115122i
$561$	−0.636721	−	4.47411i	−0.0268824	−	0.188897i
$562$	−8.20114	+	14.2048i	−0.345944	+	0.599193i
$563$	−27.6993			−1.16739			−0.583694	−	0.811974i	$-0.698393\pi$
$563$	−27.6993			−1.16739			−0.583694	+	0.811974i	$0.698393\pi$
$564$	11.2137	−	1.59585i	0.472183	−	0.0671975i
$565$	12.9073	+	3.45851i	0.543016	+	0.145501i
$566$	−3.29514	−	12.2976i	−0.138505	−	0.516907i
$567$	−27.4376	+	29.8361i	−1.15227	+	1.25300i
$568$	−7.60657	+	13.1750i	−0.319165	+	0.552810i
$569$	25.9156			1.08644			0.543219	−	0.839591i	$-0.317205\pi$
$569$	25.9156			1.08644			0.543219	+	0.839591i	$0.317205\pi$
$570$	−9.60440	−	12.2492i	−0.402284	−	0.513061i
$571$	30.2989	−	17.4931i	1.26797	−	0.732061i	0.293364	−	0.956001i	$-0.405225\pi$
$571$	30.2989	−	17.4931i	1.26797	−	0.732061i	0.974603	+	0.223939i	$0.0718917\pi$
$572$	−2.82352	+	1.39844i	−0.118057	+	0.0584716i
$573$	−10.7321	+	4.57752i	−0.448340	+	0.191228i
$574$	18.0086	−	18.0086i	0.751664	−	0.751664i
$575$	−0.474232	+	0.273798i	−0.0197768	+	0.0114182i
$576$	0.715650	−	2.91339i	0.0298188	−	0.121391i
$577$	24.5361	−	24.5361i	1.02145	−	1.02145i	0.0216855	−	0.999765i	$-0.493097\pi$
$577$	24.5361	−	24.5361i	1.02145	−	1.02145i	0.999765	−	0.0216855i	$-0.00690324\pi$
$578$	2.09274	−	7.81023i	0.0870467	−	0.324863i
$579$	11.1279	−	1.58364i	0.462461	−	0.0658140i
$580$	−2.94171	+	10.9786i	−0.122148	+	0.455863i
$581$		−	11.3917i		−	0.472605i
$582$	−7.57852	−	17.7680i	−0.314140	−	0.736508i
$583$	0.452740	+	0.452740i	0.0187506	+	0.0187506i
$584$	0.840930			0.0347979
$585$	−8.84858	−	9.64052i	−0.365844	−	0.398586i
$586$	28.0655			1.15938
$587$	23.4877	+	23.4877i	0.969441	+	0.969441i	0.999547	−	0.0301056i	$-0.00958437\pi$
$587$	23.4877	+	23.4877i	0.969441	+	0.969441i	−0.0301056	+	0.999547i	$0.509584\pi$
$588$	13.8151	−	18.3997i	0.569725	−	0.758789i
$589$		−	32.4888i		−	1.33868i
$590$	−4.50178	+	16.8009i	−0.185335	+	0.691681i
$591$	8.42688	−	20.9620i	0.346635	−	0.862261i
$592$	1.18157	−	4.40968i	0.0485622	−	0.181237i
$593$	11.1144	−	11.1144i	0.456413	−	0.456413i	−0.441063	−	0.897476i	$-0.645398\pi$
$593$	11.1144	−	11.1144i	0.456413	−	0.456413i	0.897476	+	0.441063i	$0.145398\pi$
$594$	−4.24769	−	1.60519i	−0.174285	−	0.0658618i
$595$	−14.0883	+	8.13386i	−0.577562	+	0.333456i
$596$	6.13782	−	6.13782i	0.251415	−	0.251415i
$597$	−6.98974	−	5.24813i	−0.286071	−	0.214792i
$598$	−0.0355582	+	0.557164i	−0.00145408	+	0.0227841i
$599$	25.6875	−	14.8307i	1.04956	−	0.605965i	0.127035	−	0.991898i	$-0.459454\pi$
$599$	25.6875	−	14.8307i	1.04956	−	0.605965i	0.922527	+	0.385933i	$0.126121\pi$
$600$	6.06419	−	0.863009i	0.247569	−	0.0352322i
$601$	−8.85590			−0.361240			−0.180620	−	0.983553i	$-0.557810\pi$
$601$	−8.85590			−0.361240			−0.180620	+	0.983553i	$0.557810\pi$
$602$	5.23165	−	9.06149i	0.213226	−	0.369319i
$603$	−0.334554	−	15.9845i	−0.0136241	−	0.650939i
$604$	1.43599	+	5.35919i	0.0584297	+	0.218062i
$605$	−11.9617	−	3.20513i	−0.486313	−	0.130307i
$606$	−12.8509	−	16.3896i	−0.522030	−	0.665782i
$607$	−23.3967			−0.949641			−0.474821	−	0.880083i	$-0.657487\pi$
$607$	−23.3967			−0.949641			−0.474821	+	0.880083i	$0.657487\pi$
$608$	3.71422	−	6.43322i	0.150632	−	0.260902i
$609$	67.9997	+	27.3364i	2.75549	+	1.10773i
$610$	−3.44522	−	1.98910i	−0.139493	−	0.0805363i
$611$	23.5306	+	1.50172i	0.951945	+	0.0607531i
$612$	6.46472	+	6.19965i	0.261321	+	0.250606i
$613$	−39.6701	−	10.6296i	−1.60226	−	0.429324i	−0.656536	−	0.754295i	$-0.727979\pi$
$613$	−39.6701	−	10.6296i	−1.60226	−	0.429324i	−0.945724	+	0.324970i	$0.894646\pi$
$614$			28.9541i			1.16849i
$615$	−1.42361	+	11.7632i	−0.0574053	+	0.474338i
$616$	3.80171	+	1.01866i	0.153175	+	0.0410432i
$617$	0.0336444	+	0.0336444i	0.00135447	+	0.00135447i	0.707784	−	0.706429i	$-0.249695\pi$
$617$	0.0336444	+	0.0336444i	0.00135447	+	0.00135447i	−0.706429	+	0.707784i	$0.749695\pi$
$618$	−5.79166	−	2.32829i	−0.232975	−	0.0936575i
$619$	−17.6846	+	4.73858i	−0.710806	+	0.190460i	−0.596066	−	0.802936i	$-0.703270\pi$
$619$	−17.6846	+	4.73858i	−0.710806	+	0.190460i	−0.114740	+	0.993396i	$0.536603\pi$
$620$	−4.58217	−	2.64552i	−0.184025	−	0.106247i
$621$	−0.622639	+	0.509598i	−0.0249857	+	0.0204495i
$622$	−5.16995	+	19.2945i	−0.207296	+	0.773640i
$623$	−13.7794	+	23.8667i	−0.552061	+	0.956198i
$624$	2.69367	−	5.63419i	0.107833	−	0.225548i
$625$	2.59428	+	4.49342i	0.103771	+	0.179737i
$626$	29.2606	−	7.84036i	1.16949	−	0.313364i
$627$	−8.99149	−	6.75112i	−0.359086	−	0.269614i
$628$	−1.27273	+	0.734808i	−0.0507873	+	0.0293220i
$629$	9.63809	+	9.63809i	0.384296	+	0.384296i
$630$	0.342041	+	16.3422i	0.0136272	+	0.651088i
$631$	25.1823	−	6.74757i	1.00249	−	0.268616i	0.280002	−	0.960000i	$-0.409665\pi$
$631$	25.1823	−	6.74757i	1.00249	−	0.268616i	0.722488	+	0.691383i	$0.242998\pi$
$632$	−0.925606	−	3.45441i	−0.0368186	−	0.137409i
$633$	−9.74333	+	12.9767i	−0.387263	+	0.515776i
$634$	−10.2915	−	5.94181i	−0.408729	−	0.235980i
$635$	−1.02790	−	3.83618i	−0.0407911	−	0.152234i
$636$	−1.25982	−	0.152466i	−0.0499553	−	0.00604569i
$637$	35.9563	−	31.6422i	1.42464	−	1.25371i
$638$			8.21023i			0.325046i
$639$	−45.6294	+	0.955020i	−1.80507	+	0.0377800i
$640$	−0.604889	−	1.04770i	−0.0239103	−	0.0414139i
$641$	10.9417	+	18.9515i	0.432169	+	0.748539i	0.997060	−	0.0766266i	$-0.0244149\pi$
$641$	10.9417	+	18.9515i	0.432169	+	0.748539i	−0.564890	+	0.825166i	$0.691082\pi$
$642$	−2.75227	−	1.10643i	−0.108623	−	0.0436674i
$643$	28.0855	−	28.0855i	1.10758	−	1.10758i	0.114116	−	0.993467i	$-0.463597\pi$
$643$	28.0855	−	28.0855i	1.10758	−	1.10758i	0.993467	−	0.114116i	$-0.0364034\pi$
$644$	0.493126	−	0.493126i	0.0194319	−	0.0194319i
$645$	0.685876	+	4.81951i	0.0270064	+	0.189768i
$646$	11.0895	+	19.2075i	0.436309	+	0.755710i
$647$	22.0957	+	38.2709i	0.868671	+	1.50458i	0.863355	+	0.504597i	$0.168359\pi$
$647$	22.0957	+	38.2709i	0.868671	+	1.50458i	0.00531608	+	0.999986i	$0.498308\pi$
$648$	8.58825	−	2.69107i	0.337379	−	0.105715i
$649$			12.5643i			0.493193i
$650$	12.7249	+	0.812104i	0.499112	+	0.0318533i
$651$	−20.4849	+	27.2829i	−0.802867	+	1.06930i
$652$	2.60267	+	9.71328i	0.101928	+	0.380401i
$653$	−36.4471	−	21.0428i	−1.42629	−	0.823467i	−0.429462	−	0.903085i	$-0.641297\pi$
$653$	−36.4471	−	21.0428i	−1.42629	−	0.823467i	−0.996825	+	0.0796179i	$0.974630\pi$
$654$	−32.5565	−	3.94005i	−1.27306	−	0.154068i
$655$	−6.39880	−	23.8806i	−0.250022	−	0.933094i
$656$	−5.46211	+	1.46357i	−0.213259	+	0.0571427i
$657$	1.30684	+	2.15793i	0.0509846	+	0.0841888i
$658$	−20.8260	−	20.8260i	−0.811884	−	0.811884i
$659$	23.5924	−	13.6211i	0.919031	−	0.530603i	0.0357053	−	0.999362i	$-0.488632\pi$
$659$	23.5924	−	13.6211i	0.919031	−	0.530603i	0.883326	+	0.468759i	$0.155299\pi$
$660$	−1.68434	+	0.718413i	−0.0655627	+	0.0279642i
$661$	43.7890	−	11.7332i	1.70320	−	0.456370i	0.729455	−	0.684029i	$-0.239774\pi$
$661$	43.7890	−	11.7332i	1.70320	−	0.456370i	0.973741	+	0.227658i	$0.0731070\pi$
$662$	−2.55950	−	4.43319i	−0.0994778	−	0.172301i
$663$	10.5470	+	15.3759i	0.409610	+	0.597150i
$664$	−1.26467	+	2.19048i	−0.0490789	+	0.0850071i
$665$	−10.4756	+	39.0954i	−0.406226	+	1.51606i
$666$	13.1520	−	3.82076i	0.509628	−	0.148051i
$667$	1.25986	+	0.727382i	0.0487821	+	0.0281644i
$668$	13.6813	−	3.66589i	0.529344	−	0.141837i
$669$	−25.8570	+	20.2741i	−0.999688	+	0.783842i
$670$	−4.55894	−	4.55894i	−0.176127	−	0.176127i
$671$	−2.77576	−	0.743762i	−0.107157	−	0.0287126i
$672$	−7.17536	+	3.06048i	−0.276796	+	0.118061i
$673$		−	16.5879i		−	0.639416i	−0.947516	−	0.319708i	$-0.896415\pi$
$673$		−	16.5879i		−	0.639416i	0.947516	−	0.319708i	$-0.103585\pi$
$674$	1.27347	+	0.341226i	0.0490523	+	0.0131435i
$675$	11.6386	+	14.2203i	0.447968	+	0.547339i
$676$	7.87845	−	10.3407i	0.303017	−	0.397719i
$677$	28.0789	+	16.2113i	1.07916	+	0.623053i	0.930669	−	0.365861i	$-0.119226\pi$
$677$	28.0789	+	16.2113i	1.07916	+	0.623053i	0.148490	+	0.988914i	$0.452559\pi$
$678$	−15.0553	+	11.8047i	−0.578195	+	0.453355i
$679$	−25.1143	+	43.4993i	−0.963799	+	1.66935i
$680$	3.61201			0.138514
$681$	2.59670	−	6.45934i	0.0995059	−	0.247523i
$682$	−3.69178	−	0.989210i	−0.141366	−	0.0378788i
$683$	5.52744	+	20.6287i	0.211502	+	0.789335i	0.987369	+	0.158438i	$0.0506459\pi$
$683$	5.52744	+	20.6287i	0.211502	+	0.789335i	−0.775867	+	0.630896i	$0.782687\pi$
$684$	22.2805	−	0.466328i	0.851915	−	0.0178305i
$685$	1.23270	−	2.13509i	0.0470989	−	0.0815777i
$686$	−28.3024			−1.08059
$687$	13.8213	−	34.3807i	0.527315	−	1.31170i
$688$	−2.01197	+	1.16161i	−0.0767056	+	0.0442860i
$689$	−2.50293	−	0.844842i	−0.0953540	−	0.0321859i
$690$	−0.0389823	+	0.322109i	−0.00148403	+	0.0122625i
$691$	22.3355	−	22.3355i	0.849683	−	0.849683i	−0.140410	−	0.990093i	$-0.544842\pi$
$691$	22.3355	−	22.3355i	0.849683	−	0.849683i	0.990093	+	0.140410i	$0.0448421\pi$
$692$	−6.07445	+	3.50709i	−0.230916	+	0.133319i
$693$	3.29398	+	11.3387i	0.125128	+	0.430721i
$694$	−12.3491	+	12.3491i	−0.468764	+	0.468764i
$695$	4.99131	−	18.6278i	0.189331	−	0.706594i
$696$	−10.0407	−	12.8056i	−0.380592	−	0.485396i
$697$	4.36974	−	16.3081i	0.165516	−	0.617712i
$698$			12.2245i			0.462704i
$699$	−2.97200	−	0.359677i	−0.112411	−	0.0136042i
$700$	−11.2623	−	11.2623i	−0.425677	−	0.425677i
$701$	−26.8613			−1.01454			−0.507268	−	0.861788i	$-0.669345\pi$
$701$	−26.8613			−1.01454			−0.507268	+	0.861788i	$0.669345\pi$
$702$	18.6441	−	1.84347i	0.703675	−	0.0695771i
$703$	33.9126			1.27904
$704$	−0.617934	−	0.617934i	−0.0232893	−	0.0232893i
$705$	13.6036	+	1.64633i	0.512340	+	0.0620044i
$706$		−	5.72291i		−	0.215385i
$707$	−14.0165	+	52.3104i	−0.527145	+	1.96733i
$708$	−15.3656	−	19.5968i	−0.577473	−	0.736492i
$709$	−0.0289495	+	0.108041i	−0.00108722	+	0.00405757i	−0.966467	−	0.256790i	$-0.917335\pi$
$709$	−0.0289495	+	0.108041i	−0.00108722	+	0.00405757i	0.965380	+	0.260847i	$0.0840019\pi$
$710$	−13.0140	+	13.0140i	−0.488406	+	0.488406i
$711$	7.42600	−	7.74349i	0.278497	−	0.290404i
$712$	5.29924	−	3.05952i	0.198597	−	0.114660i
$713$	−0.478867	+	0.478867i	−0.0179337	+	0.0179337i
$714$	2.79826	−	23.1219i	0.104722	−	0.865316i
$715$	−3.73731	+	0.750068i	−0.139768	+	0.0280510i
$716$	−5.58377	+	3.22379i	−0.208675	+	0.120479i
$717$	1.05011	−	2.61217i	0.0392172	−	0.0975533i
$718$	−21.7286			−0.810906
$719$	−14.2985	+	24.7657i	−0.533244	+	0.923605i	0.466003	+	0.884783i	$0.345694\pi$
$719$	−14.2985	+	24.7657i	−0.533244	+	0.923605i	−0.999246	+	0.0388216i	$0.987640\pi$
$720$	1.74850	−	3.18038i	0.0651628	−	0.118526i
$721$	4.20094	+	15.6781i	0.156451	+	0.583884i
$722$	34.9490	+	9.36455i	1.30067	+	0.348512i
$723$	5.39736	−	13.4260i	0.200730	−	0.499319i
$724$	−2.29864			−0.0854284
$725$	16.6125	−	28.7736i	0.616972	−	1.06863i
$726$	13.9523	−	10.9398i	0.517819	−	0.406015i
$727$	7.41724	+	4.28235i	0.275090	+	0.158823i	0.631199	−	0.775621i	$-0.282563\pi$
$727$	7.41724	+	4.28235i	0.275090	+	0.158823i	−0.356108	+	0.934445i	$0.615897\pi$
$728$	−15.9212	+	3.19533i	−0.590078	+	0.118427i
$729$	20.2521	+	17.8565i	0.750077	+	0.661350i
$730$	0.982674	+	0.263307i	0.0363704	+	0.00974542i
$731$		−	6.93639i		−	0.256551i
$732$	5.23897	−	2.23456i	0.193638	−	0.0825917i
$733$	36.4164	+	9.75774i	1.34507	+	0.360410i	0.858312	−	0.513127i	$-0.171513\pi$
$733$	36.4164	+	9.75774i	1.34507	+	0.360410i	0.486757	+	0.873538i	$0.338180\pi$
$734$	4.77699	+	4.77699i	0.176322	+	0.176322i
$735$	21.9049	−	17.1753i	0.807974	−	0.633522i
$736$	−0.149568	+	0.0400766i	−0.00551314	+	0.00147724i
$737$	−4.03330	−	2.32863i	−0.148568	−	0.0857760i
$738$	−12.2440	−	11.7420i	−0.450708	−	0.432228i
$739$	−10.9861	+	41.0008i	−0.404131	+	1.50824i	0.401522	+	0.915850i	$0.368481\pi$
$739$	−10.9861	+	41.0008i	−0.404131	+	1.50824i	−0.805653	+	0.592388i	$0.798185\pi$
$740$	2.76146	−	4.78299i	0.101513	−	0.175826i
$741$	45.6061	+	8.49554i	1.67538	+	0.312091i
$742$	1.64989	+	2.85769i	0.0605693	+	0.104909i
$743$	−25.1016	+	6.72595i	−0.920888	+	0.246751i	−0.687965	−	0.725744i	$-0.741496\pi$
$743$	−25.1016	+	6.72595i	−0.920888	+	0.246751i	−0.232923	+	0.972495i	$0.574829\pi$
$744$	6.96788	−	2.97198i	0.255455	−	0.108958i
$745$	9.09423	−	5.25055i	0.333187	−	0.192365i
$746$	−5.15880	−	5.15880i	−0.188877	−	0.188877i
$747$	−7.58638	+	0.158782i	−0.277571	+	0.00580954i
$748$	2.52025	−	0.675299i	0.0921494	−	0.0246914i
$749$	1.99634	+	7.45045i	0.0729448	+	0.272234i
$750$	17.7577	+	2.14907i	0.648418	+	0.0784728i
$751$	−9.79314	−	5.65407i	−0.357357	−	0.206320i	0.310564	−	0.950553i	$-0.399482\pi$
$751$	−9.79314	−	5.65407i	−0.357357	−	0.206320i	−0.667921	+	0.744232i	$0.732815\pi$
$752$	1.69254	+	6.31666i	0.0617207	+	0.230345i
$753$	15.7778	−	21.0137i	0.574975	−	0.765782i
$754$	−15.0343	−	30.3552i	−0.547518	−	1.10547i
$755$			6.71215i			0.244280i
$756$	−19.0043	−	13.6567i	−0.691181	−	0.496691i
$757$	0.110287	+	0.191023i	0.00400845	+	0.00694284i	0.868023	−	0.496525i	$-0.165391\pi$
$757$	0.110287	+	0.191023i	0.00400845	+	0.00694284i	−0.864014	+	0.503467i	$0.832057\pi$
$758$	6.81844	+	11.8099i	0.247657	+	0.428954i
$759$	0.0330218	+	0.232037i	0.00119862	+	0.00842243i
$760$	6.35461	−	6.35461i	0.230506	−	0.230506i
$761$	−15.6816	+	15.6816i	−0.568457	+	0.568457i	−0.931696	−	0.363239i	$-0.881671\pi$
$761$	−15.6816	+	15.6816i	−0.568457	+	0.568457i	0.363239	+	0.931696i	$0.381671\pi$
$762$	5.27570	+	2.12087i	0.191118	+	0.0768310i
$763$	42.6366	+	73.8488i	1.54355	+	2.67350i
$764$	−3.36813	−	5.83377i	−0.121855	−	0.211058i
$765$	5.61319	+	9.26884i	0.202945	+	0.335116i
$766$		−	27.9957i		−	1.01152i
$767$	−23.0074	−	46.4533i	−0.830750	−	1.67733i
$768$	1.71950	+	0.208098i	0.0620473	+	0.00750908i
$769$	−0.432535	−	1.61424i	−0.0155976	−	0.0582110i	0.957688	−	0.287807i	$-0.0929262\pi$
$769$	−0.432535	−	1.61424i	−0.0155976	−	0.0582110i	−0.973286	+	0.229596i	$0.926260\pi$
$770$	4.12355	+	2.38073i	0.148603	+

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} +(1.71950 + 0.208098i) q^{3} +1.00000i q^{4} +(-0.313114 + 1.16856i) q^{5} +(-1.06873 - 1.36302i) q^{6} +(-1.16567 + 4.35033i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.91339 + 0.715650i) q^{9} +(1.04770 - 0.604889i) q^{10} +(0.617934 - 0.617934i) q^{11} +(-0.208098 + 1.71950i) q^{12} +(-1.15311 + 3.41619i) q^{13} +(3.90040 - 2.25190i) q^{14} +(-0.781574 + 1.94418i) q^{15} -1.00000 q^{16} +(1.49284 - 2.58567i) q^{17} +(-1.55404 - 2.56612i) q^{18} +(-1.92262 - 7.17533i) q^{19} +(-1.16856 - 0.313114i) q^{20} +(-2.90966 + 7.23783i) q^{21} -0.873890 q^{22} +(-0.0774220 + 0.134099i) q^{23} +(1.36302 - 1.06873i) q^{24} +(3.06264 + 1.76822i) q^{25} +(3.23098 - 1.60024i) q^{26} +(4.86066 + 1.83683i) q^{27} +(-4.35033 - 1.16567i) q^{28} -9.39503i q^{29} +(1.92740 - 0.822086i) q^{30} +(4.22454 + 1.13196i) q^{31} +(0.707107 + 0.707107i) q^{32} +(1.19113 - 0.933949i) q^{33} +(-2.88394 + 0.772750i) q^{34} +(-4.71862 - 2.72429i) q^{35} +(-0.715650 + 2.91339i) q^{36} +(-1.18157 + 4.40968i) q^{37} +(-3.71422 + 6.43322i) q^{38} +(-2.69367 + 5.63419i) q^{39} +(0.604889 + 1.04770i) q^{40} +(5.46211 - 1.46357i) q^{41} +(7.17536 - 3.06048i) q^{42} +(2.01197 - 1.16161i) q^{43} +(0.617934 + 0.617934i) q^{44} +(-1.74850 + 3.18038i) q^{45} +(0.149568 - 0.0400766i) q^{46} +(-1.69254 - 6.31666i) q^{47} +(-1.71950 - 0.208098i) q^{48} +(-11.5044 - 6.64206i) q^{49} +(-0.915297 - 3.41593i) q^{50} +(3.10501 - 4.13542i) q^{51} +(-3.41619 - 1.15311i) q^{52} +0.732667i q^{53} +(-2.13817 - 4.73585i) q^{54} +(0.528607 + 0.915574i) q^{55} +(2.25190 + 3.90040i) q^{56} +(-1.81279 - 12.7381i) q^{57} +(-6.64329 + 6.64329i) q^{58} +(-10.1664 + 10.1664i) q^{59} +(-1.94418 - 0.781574i) q^{60} +(-1.64418 - 2.84781i) q^{61} +(-2.18678 - 3.78761i) q^{62} +(-6.50935 + 11.8400i) q^{63} -1.00000i q^{64} +(-3.63096 - 2.41712i) q^{65} +(-1.50266 - 0.181855i) q^{66} +(-1.37933 - 5.14774i) q^{67} +(2.58567 + 1.49284i) q^{68} +(-0.161033 + 0.214472i) q^{69} +(1.41020 + 5.26293i) q^{70} +(-14.6948 + 3.93745i) q^{71} +(2.56612 - 1.55404i) q^{72} +(0.594627 + 0.594627i) q^{73} +(3.95361 - 2.28262i) q^{74} +(4.89827 + 3.67779i) q^{75} +(7.17533 - 1.92262i) q^{76} +(1.96791 + 3.40852i) q^{77} +(5.88869 - 2.07926i) q^{78} +(1.78813 - 3.09714i) q^{79} +(0.313114 - 1.16856i) q^{80} +(7.97569 + 4.16994i) q^{81} +(-4.89719 - 2.82739i) q^{82} +(-2.44316 + 0.654644i) q^{83} +(-7.23783 - 2.90966i) q^{84} +(2.55407 + 2.55407i) q^{85} +(-2.24406 - 0.601294i) q^{86} +(1.95509 - 16.1548i) q^{87} -0.873890i q^{88} +(5.91054 + 1.58372i) q^{89} +(3.48525 - 1.01249i) q^{90} +(-13.5174 - 8.99852i) q^{91} +(-0.134099 - 0.0774220i) q^{92} +(7.02855 + 2.82553i) q^{93} +(-3.26974 + 5.66336i) q^{94} +8.98678 q^{95} +(1.06873 + 1.36302i) q^{96} +(10.7725 + 2.88649i) q^{97} +(3.43818 + 12.8315i) q^{98} +(2.24251 - 1.35806i) 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

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