LMFDB - Embedded newform 234.2.z.a.137.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("234.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			137.4
Character	$\chi$	$=$	234.137
Dual form			234.2.z.a.41.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.679534 - 1.59318i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.16856 - 0.313114i) q^{5} +(0.244033 + 1.71477i) q^{6} +(-3.18466 + 3.18466i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.07647 + 2.16525i) q^{9} +(1.04770 + 0.604889i) q^{10} +(-0.226179 + 0.844113i) q^{11} +(0.208098 - 1.71950i) q^{12} +(3.53506 + 0.709476i) q^{13} +(3.90040 - 2.25190i) q^{14} +(0.295226 + 2.07450i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.49284 - 2.58567i) q^{17} +(2.56612 - 1.55404i) q^{18} +(-1.92262 + 7.17533i) q^{19} +(-0.855443 - 0.855443i) q^{20} +(7.23783 + 2.90966i) q^{21} +(0.436945 - 0.756811i) q^{22} -0.154844 q^{23} +(-0.646048 + 1.60705i) 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} +(-8.13634 + 4.69752i) q^{29} +(0.251752 - 2.08022i) q^{30} +(-1.13196 + 4.22454i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(1.49852 - 0.213258i) q^{33} +(0.772750 + 2.88394i) q^{34} +(4.71862 - 2.72429i) q^{35} +(-2.88090 + 0.836924i) q^{36} +(-1.18157 - 4.40968i) q^{37} +(3.71422 - 6.43322i) q^{38} +(-1.27187 - 6.11411i) q^{39} +(0.604889 + 1.04770i) q^{40} +(3.99854 - 3.99854i) q^{41} +(-6.23813 - 4.68381i) q^{42} -2.32322i q^{43} +(-0.617934 + 0.617934i) q^{44} +(3.10444 - 1.88004i) q^{45} +(0.149568 + 0.0400766i) q^{46} +(-6.31666 + 1.69254i) q^{47} +(1.03997 - 1.38509i) q^{48} -13.2841i q^{49} +(2.50064 + 2.50064i) q^{50} +(-3.10501 + 4.13542i) q^{51} +(2.70671 + 2.38195i) q^{52} +0.732667i q^{53} +(-4.21963 - 3.03228i) q^{54} +(0.528607 - 0.915574i) q^{55} +4.50379 q^{56} +(12.7381 - 1.81279i) q^{57} +(9.07491 - 2.43161i) q^{58} +(-13.8876 + 3.72116i) q^{59} +(-0.781574 + 1.94418i) q^{60} +3.28837 q^{61} +(2.18678 - 3.78761i) q^{62} +(-0.282730 - 13.5084i) q^{63} +1.00000i q^{64} +(-3.90877 - 1.93594i) q^{65} +(-1.50266 - 0.181855i) q^{66} +(-3.76841 - 3.76841i) q^{67} -2.98568i q^{68} +(0.105222 + 0.246695i) q^{69} +(-5.26293 + 1.41020i) q^{70} +(14.6948 + 3.93745i) q^{71} +(2.99934 - 0.0627760i) q^{72} +(0.594627 - 0.594627i) q^{73} +4.56524i q^{74} +(-0.735925 + 6.08092i) q^{75} +(-5.25271 + 5.25271i) q^{76} +(-1.96791 - 3.40852i) q^{77} +(-0.353919 + 6.23496i) q^{78} +(1.78813 - 3.09714i) q^{79} +(-0.313114 - 1.16856i) q^{80} +(-0.376573 - 8.99212i) q^{81} +(-4.89719 + 2.82739i) q^{82} +(-0.654644 - 2.44316i) q^{83} +(4.81332 + 6.13876i) q^{84} +(0.934856 + 3.48893i) q^{85} +(-0.601294 + 2.24406i) q^{86} +(13.0129 + 9.77055i) q^{87} +(0.756811 - 0.436945i) 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} +(7.49967 - 1.06729i) q^{93} +6.53948 q^{94} +(4.49339 - 7.78278i) q^{95} +(-1.36302 + 1.06873i) q^{96} +(-7.88603 - 7.88603i) q^{97} +(-3.43818 + 12.8315i) q^{98} +(-1.35806 - 2.24251i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−0.679534	−	1.59318i	−0.392329	−	0.919825i
$3$	−0.679534	−	1.59318i	−0.392329	−	0.919825i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−1.16856	−	0.313114i	−0.522594	−	0.140029i	−0.0121279	−	0.999926i	$-0.503861\pi$
$5$	−1.16856	−	0.313114i	−0.522594	−	0.140029i	−0.510466	+	0.859898i	$0.670527\pi$
$6$	0.244033	+	1.71477i	0.0996262	+	0.700053i
$7$	−3.18466	+	3.18466i	−1.20369	+	1.20369i	−0.230652	+	0.973036i	$0.574086\pi$
$7$	−3.18466	+	3.18466i	−1.20369	+	1.20369i	−0.973036	+	0.230652i	$0.925914\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.07647	+	2.16525i	−0.692156	+	0.721748i
$10$	1.04770	+	0.604889i	0.331312	+	0.191283i
$11$	−0.226179	+	0.844113i	−0.0681957	+	0.254510i	−0.991604	−	0.129308i	$-0.958724\pi$
$11$	−0.226179	+	0.844113i	−0.0681957	+	0.254510i	0.923409	+	0.383818i	$0.125391\pi$
$12$	0.208098	−	1.71950i	0.0600727	−	0.496378i
$13$	3.53506	+	0.709476i	0.980449	+	0.196773i
$13$	3.53506	+	0.709476i	0.980449	+	0.196773i
$14$	3.90040	−	2.25190i	1.04242	−	0.601844i
$15$	0.295226	+	2.07450i	0.0762271	+	0.535633i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.49284	−	2.58567i	−0.362066	−	0.627117i	0.626234	−	0.779635i	$-0.284595\pi$
$17$	−1.49284	−	2.58567i	−0.362066	−	0.627117i	−0.988301	+	0.152518i	$0.951262\pi$
$18$	2.56612	−	1.55404i	0.604840	−	0.366290i
$19$	−1.92262	+	7.17533i	−0.441080	+	1.64613i	0.285003	+	0.958527i	$0.408005\pi$
$19$	−1.92262	+	7.17533i	−0.441080	+	1.64613i	−0.726083	+	0.687607i	$0.758661\pi$
$20$	−0.855443	−	0.855443i	−0.191283	−	0.191283i
$21$	7.23783	+	2.90966i	1.57942	+	0.634940i
$22$	0.436945	−	0.756811i	0.0931570	−	0.161353i
$23$	−0.154844			−0.0322872			−0.0161436	−	0.999870i	$-0.505139\pi$
$23$	−0.154844			−0.0322872			−0.0161436	+	0.999870i	$0.505139\pi$
$24$	−0.646048	+	1.60705i	−0.131874	+	0.328039i
$25$	−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
$29$	−8.13634	+	4.69752i	−1.51088	+	0.872307i	−0.510961	+	0.859604i	$0.670710\pi$
$29$	−8.13634	+	4.69752i	−1.51088	+	0.872307i	−0.999919	+	0.0127028i	$0.995956\pi$
$30$	0.251752	−	2.08022i	0.0459635	−	0.379794i
$31$	−1.13196	+	4.22454i	−0.203306	+	0.758749i	0.786653	+	0.617395i	$0.211812\pi$
$31$	−1.13196	+	4.22454i	−0.203306	+	0.758749i	−0.989959	+	0.141354i	$0.954855\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	1.49852	−	0.213258i	0.260860	−	0.0371235i
$34$	0.772750	+	2.88394i	0.132525	+	0.494592i
$35$	4.71862	−	2.72429i	0.797592	−	0.460490i
$36$	−2.88090	+	0.836924i	−0.480149	+	0.139487i
$37$	−1.18157	−	4.40968i	−0.194249	−	0.724947i	−0.992460	−	0.122569i	$-0.960887\pi$
$37$	−1.18157	−	4.40968i	−0.194249	−	0.724947i	0.798211	−	0.602378i	$-0.205780\pi$
$38$	3.71422	−	6.43322i	0.602527	−	1.04361i
$39$	−1.27187	−	6.11411i	−0.203662	−	0.979041i
$40$	0.604889	+	1.04770i	0.0956414	+	0.165656i
$41$	3.99854	−	3.99854i	0.624467	−	0.624467i	−0.322203	−	0.946670i	$-0.604424\pi$
$41$	3.99854	−	3.99854i	0.624467	−	0.624467i	0.946670	+	0.322203i	$0.104424\pi$
$42$	−6.23813	−	4.68381i	−0.962565	−	0.722727i
$43$		−	2.32322i		−	0.354288i	−0.984185	−	0.177144i	$-0.943314\pi$
$43$		−	2.32322i		−	0.354288i	0.984185	−	0.177144i	$-0.0566858\pi$
$44$	−0.617934	+	0.617934i	−0.0931570	+	0.0931570i
$45$	3.10444	−	1.88004i	0.462782	−	0.280260i
$46$	0.149568	+	0.0400766i	0.0220526	+	0.00590897i
$47$	−6.31666	+	1.69254i	−0.921379	+	0.246883i	−0.688175	−	0.725545i	$-0.741588\pi$
$47$	−6.31666	+	1.69254i	−0.921379	+	0.246883i	−0.233204	+	0.972428i	$0.574921\pi$
$48$	1.03997	−	1.38509i	0.150107	−	0.199920i
$49$		−	13.2841i		−	1.89773i
$50$	2.50064	+	2.50064i	0.353644	+	0.353644i
$51$	−3.10501	+	4.13542i	−0.434789	+	0.579074i
$52$	2.70671	+	2.38195i	0.375354	+	0.330318i
$53$			0.732667i			0.100640i	0.998733	+	0.0503198i	$0.0160240\pi$
$53$			0.732667i			0.100640i	−0.998733	+	0.0503198i	$0.983976\pi$
$54$	−4.21963	−	3.03228i	−0.574219	−	0.412641i
$55$	0.528607	−	0.915574i	0.0712773	−	0.123456i
$56$	4.50379			0.601844
$57$	12.7381	−	1.81279i	1.68720	−	0.240110i
$58$	9.07491	−	2.43161i	1.19159	−	0.319286i
$59$	−13.8876	+	3.72116i	−1.80801	+	0.484454i	−0.995181	−	0.0980543i	$-0.968738\pi$
$59$	−13.8876	+	3.72116i	−1.80801	+	0.484454i	−0.812825	+	0.582508i	$0.802071\pi$
$60$	−0.781574	+	1.94418i	−0.100901	+	0.250992i
$61$	3.28837			0.421032			0.210516	−	0.977590i	$-0.432486\pi$
$61$	3.28837			0.421032			0.210516	+	0.977590i	$0.432486\pi$
$62$	2.18678	−	3.78761i	0.277721	−	0.481028i
$63$	−0.282730	−	13.5084i	−0.0356206	−	1.70190i
$64$			1.00000i			0.125000i
$65$	−3.90877	−	1.93594i	−0.484823	−	0.240124i
$66$	−1.50266	−	0.181855i	−0.184964	−	0.0223848i
$67$	−3.76841	−	3.76841i	−0.460384	−	0.460384i	0.438397	−	0.898781i	$-0.355546\pi$
$67$	−3.76841	−	3.76841i	−0.460384	−	0.460384i	−0.898781	+	0.438397i	$0.855546\pi$
$68$		−	2.98568i		−	0.362066i
$69$	0.105222	+	0.246695i	0.0126672	+	0.0296986i
$70$	−5.26293	+	1.41020i	−0.629041	+	0.168551i
$71$	14.6948	+	3.93745i	1.74395	+	0.467290i	0.983318	−	0.181895i	$-0.0582232\pi$
$71$	14.6948	+	3.93745i	1.74395	+	0.467290i	0.760631	+	0.649185i	$0.224890\pi$
$72$	2.99934	−	0.0627760i	0.353476	−	0.00739822i
$73$	0.594627	−	0.594627i	0.0695959	−	0.0695959i	−0.671452	−	0.741048i	$-0.734329\pi$
$73$	0.594627	−	0.594627i	0.0695959	−	0.0695959i	0.741048	+	0.671452i	$0.234329\pi$
$74$			4.56524i			0.530698i
$75$	−0.735925	+	6.08092i	−0.0849772	+	0.702164i
$76$	−5.25271	+	5.25271i	−0.602527	+	0.602527i
$77$	−1.96791	−	3.40852i	−0.224264	−	0.388437i
$78$	−0.353919	+	6.23496i	−0.0400734	+	0.705970i
$79$	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
$81$	−0.376573	−	8.99212i	−0.0418415	−	0.999124i
$82$	−4.89719	+	2.82739i	−0.540804	+	0.312233i
$83$	−0.654644	−	2.44316i	−0.0718565	−	0.268172i	0.920646	−	0.390399i	$-0.127663\pi$
$83$	−0.654644	−	2.44316i	−0.0718565	−	0.268172i	−0.992502	+	0.122227i	$0.960996\pi$
$84$	4.81332	+	6.13876i	0.525176	+	0.669793i
$85$	0.934856	+	3.48893i	0.101399	+	0.378428i
$86$	−0.601294	+	2.24406i	−0.0648392	+	0.241983i
$87$	13.0129	+	9.77055i	1.39513	+	1.04751i
$88$	0.756811	−	0.436945i	0.0806764	−	0.0465785i
$89$	−5.91054	+	1.58372i	−0.626516	+	0.167874i	−0.558088	−	0.829782i	$-0.688465\pi$
$89$	−5.91054	+	1.58372i	−0.626516	+	0.167874i	−0.0684275	+	0.997656i	$0.521798\pi$
$90$	−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
$93$	7.49967	−	1.06729i	0.777679	−	0.110673i
$94$	6.53948			0.674496
$95$	4.49339	−	7.78278i	0.461012	−	0.798496i
$96$	−1.36302	+	1.06873i	−0.139113	+	0.109076i
$97$	−7.88603	−	7.88603i	−0.800705	−	0.800705i	0.182501	−	0.983206i	$-0.441581\pi$
$97$	−7.88603	−	7.88603i	−0.800705	−	0.800705i	−0.983206	+	0.182501i	$0.941581\pi$
$98$	−3.43818	+	12.8315i	−0.347309	+	1.29618i
$99$	−1.35806	−	2.24251i	−0.136490	−	0.225380i
$100$	−1.76822	−	3.06264i	−0.176822	−	0.306264i
$101$	6.01223	+	10.4135i	0.598240	+	1.03618i	0.993081	+	0.117432i	$0.0374662\pi$
$101$	6.01223	+	10.4135i	0.598240	+	1.03618i	−0.394841	+	0.918749i	$0.629200\pi$
$102$	4.06954	−	3.19087i	0.402944	−	0.315943i
$103$	−3.12107	+	1.80195i	−0.307528	+	0.177551i	−0.645820	−	0.763490i	$-0.723484\pi$
$103$	−3.12107	+	1.80195i	−0.307528	+	0.177551i	0.338292	+	0.941041i	$0.390151\pi$
$104$	−1.99799	−	3.00134i	−0.195919	−	0.294306i
$105$	−7.54676	−	5.66637i	−0.736489	−	0.552981i
$106$	0.189628	−	0.707702i	0.0184183	−	0.0687381i
$107$	−1.48317	−	0.856309i	−0.143384	−	0.0827825i	0.426592	−	0.904444i	$-0.359714\pi$
$107$	−1.48317	−	0.856309i	−0.143384	−	0.0827825i	−0.569976	+	0.821662i	$0.693047\pi$
$108$	3.29104	+	4.02108i	0.316681	+	0.386928i
$109$	13.3881	+	13.3881i	1.28235	+	1.28235i	0.939328	+	0.343021i	$0.111450\pi$
$109$	13.3881	+	13.3881i	1.28235	+	1.28235i	0.343021	+	0.939328i	$0.388550\pi$
$110$	−0.747563	+	0.747563i	−0.0712773	+	0.0712773i
$111$	−6.22251	+	4.87899i	−0.590615	+	0.463093i
$112$	−4.35033	−	1.16567i	−0.411067	−	0.110145i
$113$	9.56572	+	5.52277i	0.899867	+	0.519539i	0.877157	−	0.480204i	$-0.159437\pi$
$113$	9.56572	+	5.52277i	0.899867	+	0.519539i	0.0227101	+	0.999742i	$0.492771\pi$
$114$	−12.7732	−	1.54584i	−1.19632	−	0.144782i
$115$	0.180944	+	0.0484838i	0.0168731	+	0.00452114i
$116$	−9.39503			−0.872307
$117$	−8.87662	+	6.18107i	−0.820644	+	0.571440i
$118$	14.3775			1.32355
$119$	12.9887	+	3.48030i	1.19067	+	0.319039i
$120$	1.25813	−	1.67565i	0.114851	−	0.152965i
$121$	8.86491	+	5.11816i	0.805901	+	0.465287i
$122$	−3.17632	−	0.851092i	−0.287571	−	0.0770543i
$123$	−9.08755	−	3.65326i	−0.819397	−	0.329404i
$124$	−3.09257	+	3.09257i	−0.277721	+	0.277721i
$125$	7.30243	+	7.30243i	0.653149	+	0.653149i
$126$	−3.22314	+	13.1213i	−0.287140	+	1.16894i
$127$	−2.84302	−	1.64142i	−0.252277	−	0.145652i	0.368529	−	0.929616i	$-0.379861\pi$
$127$	−2.84302	−	1.64142i	−0.252277	−	0.145652i	−0.620807	+	0.783964i	$0.713195\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−3.70132	+	1.57871i	−0.325883	+	0.138998i
$130$	3.27452	+	2.88164i	0.287195	+	0.252736i
$131$	−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	$0.982105\pi$
$132$	1.40439	+	0.564575i	0.122236	+	0.0491399i
$133$	−16.7281	−	28.9739i	−1.45051	−	2.51236i
$134$	2.66467	+	4.61534i	0.230192	+	0.398704i
$135$	−5.10482	−	3.66838i	−0.439353	−	0.315724i
$136$	−0.772750	+	2.88394i	−0.0662627	+	0.247296i
$137$	−1.44100	−	1.44100i	−0.123113	−	0.123113i	0.642866	−	0.765979i	$-0.277745\pi$
$137$	−1.44100	−	1.44100i	−0.123113	−	0.123113i	−0.765979	+	0.642866i	$0.777745\pi$
$138$	−0.0377871	−	0.265522i	−0.00321665	−	0.0226028i
$139$	7.97045	−	13.8052i	0.676045	−	1.17094i	−0.300118	−	0.953902i	$-0.597026\pi$
$139$	7.97045	−	13.8052i	0.676045	−	1.17094i	0.976162	−	0.217042i	$-0.0696407\pi$
$140$	5.44859			0.460490
$141$	6.98892	+	8.91345i	0.588573	+	0.750648i
$142$	−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
$146$	−0.728267	+	0.420465i	−0.0602718	+	0.0347979i
$147$	−21.1640	+	9.02702i	−1.74558	+	0.744536i
$148$	1.18157	−	4.40968i	0.0971245	−	0.362473i
$149$	2.24660	+	8.38442i	0.184049	+	0.686878i	0.994832	+	0.101533i	$0.0323746\pi$
$149$	2.24660	+	8.38442i	0.184049	+	0.686878i	−0.810784	+	0.585346i	$0.800959\pi$
$150$	2.28471	−	5.68324i	0.186545	−	0.464035i
$151$	−1.43599	−	5.35919i	−0.116859	−	0.436125i	0.882560	−	0.470200i	$-0.155818\pi$
$151$	−1.43599	−	5.35919i	−0.116859	−	0.436125i	−0.999419	+	0.0340750i	$0.989152\pi$
$152$	6.43322	−	3.71422i	0.521803	−	0.301263i
$153$	8.69844	+	2.13670i	0.703227	+	0.172742i
$154$	1.01866	+	3.80171i	0.0820864	+	0.306350i
$155$	2.64552	−	4.58217i	0.212493	−	0.368049i
$156$	1.95559	−	5.93091i	0.156572	−	0.474853i
$157$	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	$0.814656\pi$
$158$	−2.52880	+	2.52880i	−0.201181	+	0.201181i
$159$	1.16727	−	0.497872i	0.0925708	−	0.0394838i
$160$			1.20978i			0.0956414i
$161$	0.493126	−	0.493126i	0.0388637	−	0.0388637i
$162$	−1.96359	+	8.78318i	−0.154274	+	0.690072i
$163$	9.71328	+	2.60267i	0.760803	+	0.203857i	0.618305	−	0.785939i	$-0.287820\pi$
$163$	9.71328	+	2.60267i	0.760803	+	0.203857i	0.142498	+	0.989795i	$0.454486\pi$
$164$	5.46211	−	1.46357i	0.426519	−	0.114285i
$165$	−1.81788	−	0.220004i	−0.141522	−	0.0171273i
$166$			2.52935i			0.196316i
$167$	10.0154	+	10.0154i	0.775014	+	0.775014i	0.978978	−	0.203964i	$-0.0653827\pi$
$167$	10.0154	+	10.0154i	0.775014	+	0.775014i	−0.203964	+	0.978978i	$0.565383\pi$
$168$	−3.06048	−	7.17536i	−0.236121	−	0.553591i
$169$	11.9933	+	5.01608i	0.922561	+	0.385852i
$170$		−	3.61201i		−	0.277028i
$171$	−11.5441	−	19.0623i	−0.882798	−	1.45773i
$172$	1.16161	−	2.01197i	0.0885720	−	0.153411i
$173$	7.01417			0.533278			0.266639	−	0.963797i	$-0.414087\pi$
$173$	7.01417			0.533278			0.266639	+	0.963797i	$0.414087\pi$
$174$	−10.0407	−	12.8056i	−0.761185	−	0.970792i
$175$	15.3847	−	4.12231i	1.16297	−	0.311617i
$176$	−0.844113	+	0.226179i	−0.0636274	+	0.0170489i
$177$	15.3656	+	19.5968i	1.15495	+	1.47298i
$178$	6.11904			0.458641
$179$	−3.22379	+	5.58377i	−0.240958	+	0.417351i	−0.960987	−	0.276592i	$-0.910795\pi$
$179$	−3.22379	+	5.58377i	−0.240958	+	0.417351i	0.720030	+	0.693943i	$0.244128\pi$
$180$	3.62854	−	0.0759450i	0.270455	−	0.00566061i
$181$		−	2.29864i		−	0.170857i	−0.996344	−	0.0854284i	$-0.972774\pi$
$181$		−	2.29864i		−	0.170857i	0.996344	−	0.0854284i	$-0.0272259\pi$
$182$	15.3858	−	5.19334i	1.14047	−	0.384956i
$183$	−2.23456	−	5.23897i	−0.165183	−	0.387276i
$184$	0.109491	+	0.109491i	0.00807180	+	0.00807180i
$185$			5.52292i			0.406054i
$186$	−7.52036	−	0.910128i	−0.551419	−	0.0667338i
$187$	2.52025	−	0.675299i	0.184299	−	0.0493827i
$188$	−6.31666	−	1.69254i	−0.460690	−	0.123441i
$189$	−21.3293	+	9.62987i	−1.55147	+	0.700470i
$190$	−6.35461	+	6.35461i	−0.461012	+	0.461012i
$191$		−	6.73626i		−	0.487418i	−0.969848	−	0.243709i	$-0.921636\pi$
$191$		−	6.73626i		−	0.487418i	0.969848	−	0.243709i	$-0.0783642\pi$
$192$	1.59318	−	0.679534i	0.114978	−	0.0490412i
$193$	−4.58874	+	4.58874i	−0.330304	+	0.330304i	−0.852702	−	0.522398i	$-0.825038\pi$
$193$	−4.58874	+	4.58874i	−0.330304	+	0.330304i	0.522398	+	0.852702i	$0.325038\pi$
$194$	5.57626	+	9.65837i	0.400352	+	0.693431i
$195$	−0.428163	+	7.54292i	−0.0306614	+	0.540160i
$196$	6.64206	−	11.5044i	0.474433	−	0.821742i
$197$	−3.37597	−	12.5993i	−0.240528	−	0.897662i	−0.975579	−	0.219650i	$-0.929508\pi$
$197$	−3.37597	−	12.5993i	−0.240528	−	0.897662i	0.735051	−	0.678012i	$-0.237158\pi$
$198$	0.731380	+	2.51759i	0.0519769	+	0.178917i
$199$	−4.37034	+	2.52321i	−0.309805	+	0.178866i	−0.646839	−	0.762626i	$-0.723909\pi$
$199$	−4.37034	+	2.52321i	−0.309805	+	0.178866i	0.337034	+	0.941492i	$0.390576\pi$
$200$	0.915297	+	3.41593i	0.0647213	+	0.241543i
$201$	−3.44300	+	8.56452i	−0.242851	+	0.604095i
$202$	−3.11216	−	11.6147i	−0.218971	−	0.817210i
$203$	10.9515	−	40.8715i	0.768643	−	2.86861i
$204$	−4.75673	+	2.02887i	−0.333038	+	0.142049i
$205$	−5.92452	+	3.42052i	−0.413786	+	0.238900i
$206$	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
$210$	5.82305	+	7.42654i	0.401828	+	0.512480i
$211$	9.36885			0.644979			0.322489	−	0.946573i	$-0.395480\pi$
$211$	9.36885			0.644979			0.322489	+	0.946573i	$0.395480\pi$
$212$	−0.366333	+	0.634508i	−0.0251599	+	0.0435782i
$213$	−3.71252	−	26.0871i	−0.254377	−	1.78746i
$214$	1.21100	+	1.21100i	0.0827825	+	0.0827825i
$215$	−0.727433	+	2.71482i	−0.0496105	+	0.185149i
$216$	−2.13817	−	4.73585i	−0.145484	−	0.322233i
$217$	−9.84880	−	17.0586i	−0.668580	−	1.15801i
$218$	−9.46683	−	16.3970i	−0.641174	−	1.11055i
$219$	−1.35142	−	0.543281i	−0.0913205	−	0.0367115i
$220$	0.915574	−	0.528607i	0.0617280	−	0.0356387i
$221$	−3.44280	−	10.1996i	−0.231588	−	0.686101i
$222$	7.27326	−	3.10223i	0.488149	−	0.208208i
$223$	−4.90989	+	18.3239i	−0.328790	+	1.22706i	0.581656	+	0.813435i	$0.302405\pi$
$223$	−4.90989	+	18.3239i	−0.328790	+	1.22706i	−0.910446	+	0.413627i	$0.864262\pi$
$224$	3.90040	+	2.25190i	0.260606	+	0.150461i
$225$	10.1881	−	2.95973i	0.679207	−	0.197315i
$226$	−7.81038	−	7.81038i	−0.519539	−	0.519539i
$227$	−2.84212	+	2.84212i	−0.188638	+	0.188638i	−0.795107	−	0.606469i	$-0.792585\pi$
$227$	−2.84212	+	2.84212i	−0.188638	+	0.188638i	0.606469	+	0.795107i	$0.292585\pi$
$228$	11.9379	+	4.79913i	0.790608	+	0.317830i
$229$	−20.6646	−	5.53707i	−1.36556	−	0.365900i	−0.499704	−	0.866196i	$-0.666558\pi$
$229$	−20.6646	−	5.53707i	−1.36556	−	0.365900i	−0.865854	+	0.500296i	$0.833224\pi$
$230$	−0.162230	−	0.0936635i	−0.0106971	−	0.00617599i
$231$	−4.09313	+	5.45145i	−0.269308	+	0.358679i
$232$	9.07491	+	2.43161i	0.595797	+	0.159643i
$233$	1.72841			0.113232			0.0566158	−	0.998396i	$-0.481969\pi$
$233$	1.72841			0.113232			0.0566158	+	0.998396i	$0.481969\pi$
$234$	10.1739	−	3.67301i	0.665091	−	0.240112i
$235$	7.91133			0.516078
$236$	−13.8876	−	3.72116i	−0.904003	−	0.242227i
$237$	−6.14941	−	0.744213i	−0.399447	−	0.0483418i
$238$	−11.6453	−	6.72343i	−0.754854	−	0.435815i
$239$	1.57006	+	0.420695i	0.101558	+	0.0272125i	0.309240	−	0.950984i	$-0.399925\pi$
$239$	1.57006	+	0.420695i	0.101558	+	0.0272125i	−0.207682	+	0.978196i	$0.566592\pi$
$240$	−1.64895	+	1.29292i	−0.106439	+	0.0834577i
$241$	5.90747	−	5.90747i	0.380534	−	0.380534i	−0.490761	−	0.871294i	$-0.663281\pi$
$241$	5.90747	−	5.90747i	0.380534	−	0.380534i	0.871294	+	0.490761i	$0.163281\pi$
$242$	−7.23817	−	7.23817i	−0.465287	−	0.465287i
$243$	−14.0702	+	6.71040i	−0.902604	+	0.430473i
$244$	2.84781	+	1.64418i	0.182312	+	0.105258i
$245$	−4.15944	+	15.5232i	−0.265737	+	0.991744i
$246$	7.83237	+	5.88081i	0.499373	+	0.374947i
$247$	−11.8873	+	24.0012i	−0.756372	+	1.52716i
$248$	3.78761	−	2.18678i	0.240514	−	0.138861i
$249$	−3.44755	+	2.70318i	−0.218480	+	0.171307i
$250$	−5.16360	−	8.94361i	−0.326575	−	0.565644i
$251$	−7.58570	−	13.1388i	−0.478805	−	0.829315i	0.520899	−	0.853618i	$-0.325597\pi$
$251$	−7.58570	−	13.1388i	−0.478805	−	0.829315i	−0.999705	+	0.0243030i	$0.992263\pi$
$252$	6.50935	−	11.8400i	0.410051	−	0.745849i
$253$	0.0350225	−	0.130706i	0.00220185	−	0.00821741i
$254$	2.32132	+	2.32132i	0.145652	+	0.145652i
$255$	4.92324	−	3.86024i	0.308305	−	0.241738i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−21.0524			−1.31321			−0.656607	−	0.754233i	$-0.728009\pi$
$257$	−21.0524			−1.31321			−0.656607	+	0.754233i	$0.728009\pi$
$258$	3.98380	−	0.566944i	0.248020	−	0.0352964i
$259$	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
$263$	25.9668	−	14.9920i	1.60118	−	0.924444i	0.609932	−	0.792454i	$-0.291197\pi$
$263$	25.9668	−	14.9920i	1.60118	−	0.924444i	0.991251	−	0.131990i	$-0.0421367\pi$
$264$	−1.21041	−	0.908820i	−0.0744958	−	0.0559340i
$265$	0.229408	−	0.856163i	0.0140924	−	0.0525937i
$266$	8.65909	+	32.3162i	0.530923	+	1.98143i
$267$	6.53957	+	8.34037i	0.400215	+	0.510423i
$268$	−1.37933	−	5.14774i	−0.0842561	−	0.314448i
$269$	13.2251	−	7.63551i	0.806348	−	0.465545i	−0.0393383	−	0.999226i	$-0.512525\pi$
$269$	13.2251	−	7.63551i	0.806348	−	0.465545i	0.845686	+	0.533681i	$0.179192\pi$
$270$	3.98143	+	4.86461i	0.242302	+	0.296051i
$271$	−3.28534	−	12.2611i	−0.199570	−	0.744806i	−0.991036	−	0.133593i	$-0.957349\pi$
$271$	−3.28534	−	12.2611i	−0.199570	−	0.744806i	0.791466	−	0.611213i	$-0.209318\pi$
$272$	1.49284	−	2.58567i	0.0905166	−	0.156779i
$273$	23.5218	+	15.4209i	1.42361	+	0.933315i
$274$	1.01894	+	1.76486i	0.0615567	+	0.106619i
$275$	2.18528	−	2.18528i	0.131778	−	0.131778i
$276$	−0.0322227	+	0.266255i	−0.00193958	+	0.0160267i
$277$			29.7012i			1.78457i	0.451470	+	0.892286i	$0.350900\pi$
$277$			29.7012i			1.78457i	−0.451470	+	0.892286i	$0.649100\pi$
$278$	−11.2719	+	11.2719i	−0.676045	+	0.676045i
$279$	−6.79668	−	11.2231i	−0.406906	−	0.671908i
$280$	−5.26293	−	1.41020i	−0.314520	−	0.0842755i
$281$	−15.8434	+	4.24522i	−0.945137	+	0.253249i	−0.698297	−	0.715808i	$-0.746059\pi$
$281$	−15.8434	+	4.24522i	−0.945137	+	0.253249i	−0.246840	+	0.969056i	$0.579392\pi$
$282$	−4.44380	−	10.4186i	−0.264625	−	0.620419i
$283$			12.7314i			0.756805i	0.925641	+	0.378402i	$0.123526\pi$
$283$			12.7314i			0.756805i	−0.925641	+	0.378402i	$0.876474\pi$
$284$	10.7573	+	10.7573i	0.638329	+	0.638329i
$285$	−15.4528	−	1.87013i	−0.915345	−	0.110777i
$286$	2.08157	−	2.36537i	0.123086	−	0.139867i
$287$			25.4680i			1.50333i
$288$	2.62890	+	1.44531i	0.154909	+	0.0851655i
$289$	4.04287	−	7.00246i	0.237816	−	0.411909i
$290$	−11.3659			−0.667429
$291$	−7.20506	+	17.9227i	−0.422368	+	1.05065i
$292$	0.812276	−	0.217649i	0.0475349	−	0.0127369i
$293$	−27.1092	+	7.26389i	−1.58374	+	0.424361i	−0.940080	−	0.340954i	$-0.889250\pi$
$293$	−27.1092	+	7.26389i	−1.58374	+	0.424361i	−0.643656	+	0.765315i	$0.722583\pi$
$294$	22.7793	−	3.24177i	1.32851	−	0.189064i
$295$	17.3935			1.01269
$296$	−2.28262	+	3.95361i	−0.132674	+	0.229799i
$297$	−2.64988	+	3.68750i	−0.153762	+	0.213970i
$298$		−	8.68019i		−	0.502830i
$299$	−0.547383	−	0.109858i	−0.0316560	−	0.00635326i
$300$	−3.67779	+	4.89827i	−0.212337	+	0.282802i
$301$	7.39867	+	7.39867i	0.426452	+	0.426452i
$302$			5.54824i			0.319266i
$303$	12.5051	−	16.6549i	0.718398	−	0.956800i
$304$	−7.17533	+	1.92262i	−0.411533	+	0.110270i
$305$	−3.84264	−	1.02963i	−0.220029	−	0.0589566i
$306$	−7.84903	−	4.31521i	−0.448699	−	0.246684i
$307$	−20.4736	+	20.4736i	−1.16849	+	1.16849i	−0.185929	+	0.982563i	$0.559529\pi$
$307$	−20.4736	+	20.4736i	−1.16849	+	1.16849i	−0.982563	+	0.185929i	$0.940471\pi$
$308$		−	3.93582i		−	0.224264i
$309$	4.99171	+	3.74795i	0.283968	+	0.213213i
$310$	−3.74133	+	3.74133i	−0.212493	+	0.212493i
$311$	9.98758	+	17.2990i	0.566344	+	0.980936i	0.996923	+	0.0783834i	$0.0249758\pi$
$311$	9.98758	+	17.2990i	0.566344	+	0.980936i	−0.430580	+	0.902553i	$0.641691\pi$
$312$	−3.42398	+	5.22268i	−0.193845	+	0.295676i
$313$	−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
$315$	−3.89928	+	15.8739i	−0.219700	+	0.894391i
$316$	3.09714	−	1.78813i	0.174228	−	0.100590i
$317$	3.07571	+	11.4787i	0.172749	+	0.644708i	0.996924	+	0.0783730i	$0.0249725\pi$
$317$	3.07571	+	11.4787i	0.172749	+	0.644708i	−0.824175	+	0.566335i	$0.808361\pi$
$318$	−1.25636	+	0.178795i	−0.0704530	+	0.0100263i
$319$	−2.12496	−	7.93047i	−0.118975	−	0.444021i
$320$	0.313114	−	1.16856i	0.0175036	−	0.0653243i
$321$	−0.356392	+	2.94486i	−0.0198919	+	0.164366i
$322$	−0.603953	+	0.348692i	−0.0336570	+	0.0194319i
$323$	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
$327$	12.2320	−	30.4274i	0.676433	−	1.68264i
$328$	−5.65479			−0.312233
$329$	14.7262	−	25.5066i	0.811884	−	1.40622i
$330$	1.69900	+	0.683010i	0.0935269	+	0.0375985i
$331$	−3.61968	−	3.61968i	−0.198956	−	0.198956i	0.600597	−	0.799552i	$-0.294930\pi$
$331$	−3.61968	−	3.61968i	−0.198956	−	0.198956i	−0.799552	+	0.600597i	$0.794930\pi$
$332$	0.654644	−	2.44316i	0.0359282	−	0.134086i
$333$	12.0015	+	6.59816i	0.657680	+	0.361577i
$334$	−7.08195	−	12.2663i	−0.387507	−	0.671182i
$335$	3.22366	+	5.58354i	0.176127	+	0.305061i
$336$	1.09908	+	7.72298i	0.0599595	+	0.421323i
$337$	1.14176	−	0.659198i	0.0621959	−	0.0359088i	−0.468580	−	0.883421i	$-0.655234\pi$
$337$	1.14176	−	0.659198i	0.0621959	−	0.0359088i	0.530775	+	0.847512i	$0.321901\pi$
$338$	−10.2864	−	7.94925i	−0.559505	−	0.432382i
$339$	2.29855	−	18.9929i	0.124840	−	1.03155i
$340$	−0.934856	+	3.48893i	−0.0506997	+	0.189214i
$341$	−3.30996	−	1.91101i	−0.179244	−	0.103487i
$342$	6.21705	+	21.4006i	0.336179	+	1.15721i
$343$	20.0128	+	20.0128i	1.08059	+	1.08059i
$344$	−1.64277	+	1.64277i	−0.0885720	+	0.0885720i
$345$	−0.0457140	−	0.321223i	−0.00246116	−	0.0172941i
$346$	−6.77517	−	1.81540i	−0.364236	−	0.0975966i
$347$	15.1245	+	8.73211i	0.811923	+	0.468764i	0.847623	−	0.530598i	$-0.178033\pi$
$347$	15.1245	+	8.73211i	0.811923	+	0.468764i	−0.0357000	+	0.999363i	$0.511366\pi$
$348$	6.38425	+	14.9680i	0.342232	+	0.802370i
$349$	11.8080	+	3.16394i	0.632066	+	0.169362i	0.560607	−	0.828082i	$-0.310568\pi$
$349$	11.8080	+	3.16394i	0.632066	+	0.169362i	0.0714590	+	0.997444i	$0.477235\pi$
$350$	−15.9274			−0.851353
$351$	15.8795	+	9.94184i	0.847587	+	0.530656i
$352$	0.873890			0.0465785
$353$	5.52791	+	1.48120i	0.294221	+	0.0788363i	0.402910	−	0.915240i	$-0.367999\pi$
$353$	5.52791	+	1.48120i	0.294221	+	0.0788363i	−0.108689	+	0.994076i	$0.534665\pi$
$354$	−9.76997	−	22.9059i	−0.519268	−	1.21744i
$355$	−15.9388	−	9.20227i	−0.845944	−	0.488406i
$356$	−5.91054	−	1.58372i	−0.313258	−	0.0839372i
$357$	−3.28148	−	23.0583i	−0.173674	−	1.22038i
$358$	4.55913	−	4.55913i	0.240958	−	0.240958i
$359$	−15.3645	−	15.3645i	−0.810906	−	0.810906i	0.173864	−	0.984770i	$-0.444375\pi$
$359$	−15.3645	−	15.3645i	−0.810906	−	0.810906i	−0.984770	+	0.173864i	$0.944375\pi$
$360$	−3.52456	−	0.865778i	−0.185760	−	0.0456305i
$361$	−31.3344	−	18.0909i	−1.64918	−	0.952154i
$362$	−0.594932	+	2.22032i	−0.0312690	+	0.116697i
$363$	2.13015	−	17.6014i	0.111804	−	0.923833i
$364$	−16.2057	+	1.03425i	−0.849408	+	0.0542092i
$365$	−0.881042	+	0.508670i	−0.0461158	+	0.0266250i
$366$	0.802472	+	5.63881i	0.0419459	+	0.294745i
$367$	3.37784	+	5.85059i	0.176322	+	0.305398i	0.940618	−	0.339467i	$-0.110247\pi$
$367$	3.37784	+	5.85059i	0.176322	+	0.305398i	−0.764296	+	0.644866i	$0.776913\pi$
$368$	−0.0774220	−	0.134099i	−0.00403590	−	0.00699038i
$369$	0.354985	+	16.9607i	0.0184798	+	0.882936i
$370$	1.42944	−	5.33474i	0.0743130	−	0.277340i
$371$	−2.33330	−	2.33330i	−0.121139	−	0.121139i
$372$	7.02855	+	2.82553i	0.364413	+	0.146497i
$373$	−3.64782	+	6.31821i	−0.188877	+	0.327145i	−0.944876	−	0.327428i	$-0.893818\pi$
$373$	−3.64782	+	6.31821i	−0.188877	+	0.327145i	0.755999	+	0.654573i	$0.227151\pi$
$374$	−2.60915			−0.134916
$375$	6.67186	−	16.5964i	0.344533	−	0.857033i
$376$	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	−0.580731	−	0.814096i	$-0.697233\pi$
$379$	−13.1722	+	3.52948i	−0.676611	+	0.181297i	−0.0958799	+	0.995393i	$0.530566\pi$
$380$	7.78278	−	4.49339i	0.399248	−	0.230506i
$381$	−0.683152	+	5.64486i	−0.0349989	+	0.289195i
$382$	−1.74347	+	6.50672i	−0.0892038	+	0.332913i
$383$	−7.24581	−	27.0417i	−0.370244	−	1.38177i	−0.860172	−	0.510005i	$-0.829644\pi$
$383$	−7.24581	−	27.0417i	−0.370244	−	1.38177i	0.489928	−	0.871763i	$-0.337023\pi$
$384$	−1.71477	+	0.244033i	−0.0875067	+	0.0124533i
$385$	1.23236	+	4.59923i	0.0628068	+	0.234398i
$386$	5.62003	−	3.24473i	0.286052	−	0.165152i
$387$	5.03034	+	4.82409i	0.255707	+	0.245222i
$388$	−2.88649	−	10.7725i	−0.146539	−	0.546892i
$389$	−9.21923	+	15.9682i	−0.467433	+	0.809618i	−0.999308	−	0.0372049i	$-0.988155\pi$
$389$	−9.21923	+	15.9682i	−0.467433	+	0.809618i	0.531874	+	0.846823i	$0.321488\pi$
$390$	2.36583	−	7.17509i	0.119798	−	0.363325i
$391$	0.231157	+	0.400376i	0.0116901	+	0.0202479i
$392$	−9.39330	+	9.39330i	−0.474433	+	0.474433i
$393$	28.3056	+	21.2529i	1.42783	+	1.07206i
$394$			13.0437i			0.657134i
$395$	−3.05929	+	3.05929i	−0.153930	+	0.153930i
$396$	−0.0548593	−	2.62110i	−0.00275679	−	0.131715i
$397$	5.23300	+	1.40218i	0.262637	+	0.0703733i	0.387734	−	0.921771i	$-0.373258\pi$
$397$	5.23300	+	1.40218i	0.262637	+	0.0703733i	−0.125098	+	0.992144i	$0.539924\pi$
$398$	4.87448	−	1.30611i	0.244335	−	0.0654695i
$399$	−34.7934	+	46.3397i	−1.74185	+	2.31988i
$400$		−	3.53644i		−	0.176822i
$401$	−21.4141	−	21.4141i	−1.06937	−	1.06937i	−0.997407	−	0.0719617i	$-0.977074\pi$
$401$	−21.4141	−	21.4141i	−1.06937	−	1.06937i	−0.0719617	−	0.997407i	$-0.522926\pi$
$402$	5.54235	−	7.38158i	0.276427	−	0.368160i
$403$	−6.99876	+	14.1309i	−0.348633	+	0.703909i
$404$			12.0245i			0.598240i
$405$	−2.37551	+	10.6257i	−0.118040	+	0.527996i
$406$	−21.1566	+	36.6444i	−1.04999	+	1.81863i
$407$	3.98952			0.197753
$408$	5.11976	−	0.728605i	0.253466	−	0.0360713i
$409$	28.1349	−	7.53872i	1.39118	−	0.372766i	0.516011	−	0.856582i	$-0.327416\pi$
$409$	28.1349	−	7.53872i	1.39118	−	0.372766i	0.875169	+	0.483817i	$0.160750\pi$
$410$	6.60794	−	1.77059i	0.326343	−	0.0874433i
$411$	−1.31657	+	3.27500i	−0.0649417	+	0.161544i
$412$	−3.60390			−0.177551
$413$	32.3765	−	56.0778i	1.59314	−	2.75941i
$414$	−0.397348	+	0.240633i	−0.0195286	+	0.0118265i
$415$			3.05995i			0.150207i
$416$	−0.229639	−	3.59823i	−0.0112590	−	0.176418i
$417$	−27.4104	−	3.31727i	−1.34230	−	0.162447i
$418$	4.59029	+	4.59029i	0.224518	+	0.224518i
$419$			16.2873i			0.795685i	0.917454	+	0.397843i	$0.130241\pi$
$419$			16.2873i			0.795685i	−0.917454	+	0.397843i	$0.869759\pi$
$420$	−3.70250	−	8.68060i	−0.180664	−	0.423570i
$421$	−4.14810	+	1.11148i	−0.202166	+	0.0541702i	−0.358481	−	0.933537i	$-0.616705\pi$
$421$	−4.14810	+	1.11148i	−0.202166	+	0.0541702i	0.156315	+	0.987707i	$0.450039\pi$
$422$	−9.04962	−	2.42484i	−0.440529	−	0.118039i
$423$	9.45156	−	17.1916i	0.459550	−	0.835885i
$424$	0.518074	−	0.518074i	0.0251599	−	0.0251599i
$425$			10.5586i			0.512170i
$426$	−3.16582	+	26.1591i	−0.153385	+	1.26741i
$427$	−10.4723	+	10.4723i	−0.506792	+	0.506792i
$428$	−0.856309	−	1.48317i	−0.0413913	−	0.0716918i
$429$	5.44867	+	0.309286i	0.263064	+	0.0149325i
$430$	1.40529	−	2.43404i	0.0677692	−	0.117380i
$431$	1.03304	+	3.85536i	0.0497599	+	0.185706i	0.986332	−	0.164767i	$-0.0526873\pi$
$431$	1.03304	+	3.85536i	0.0497599	+	0.185706i	−0.936573	+	0.350474i	$0.886021\pi$
$432$	0.839587	+	5.12787i	0.0403946	+	0.246715i
$433$	11.4946	−	6.63644i	0.552397	−	0.318927i	−0.197691	−	0.980264i	$-0.563344\pi$
$433$	11.4946	−	6.63644i	0.552397	−	0.318927i	0.750088	+	0.661338i	$0.230011\pi$
$434$	5.09811	+	19.0264i	0.244717	+	0.913297i
$435$	−12.1470	−	15.4920i	−0.582406	−	0.742783i
$436$	4.90039	+	18.2885i	0.234686	+	0.875860i
$437$	0.297707	−	1.11106i	0.0142412	−	0.0531490i
$438$	1.16476	+	0.874542i	0.0556544	+	0.0417872i
$439$	−6.64720	+	3.83776i	−0.317254	+	0.183166i	−0.650168	−	0.759791i	$-0.725301\pi$
$439$	−6.64720	+	3.83776i	−0.317254	+	0.183166i	0.332914	+	0.942957i	$0.391968\pi$
$440$	−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	$0.901794\pi$
$444$	−7.82835	+	1.11407i	−0.371517	+	0.0528714i
$445$	7.40268			0.350921
$446$	9.48517	−	16.4288i	0.449136	−	0.777926i
$447$	11.8313	−	9.27674i	0.559600	−	0.438775i
$448$	−3.18466	−	3.18466i	−0.150461	−	0.150461i
$449$	5.89447	−	21.9985i	0.278177	−	1.03817i	−0.675505	−	0.737355i	$-0.736074\pi$
$449$	5.89447	−	21.9985i	0.278177	−	1.03817i	0.953682	−	0.300816i	$-0.0972590\pi$
$450$	−10.6070	+	0.222003i	−0.500018	+	0.0104653i
$451$	2.47083	+	4.27961i	0.116347	+	0.201519i
$452$	5.52277	+	9.56572i	0.259769	+	0.449934i
$453$	−7.56237	+	5.92955i	−0.355311	+	0.278595i
$454$	3.48088	−	2.00968i	0.163366	−	0.0943191i
$455$	18.6134	−	6.28280i	0.872610	−	0.294542i
$456$	−10.2890	−	7.72536i	−0.481828	−	0.361773i
$457$	5.60664	−	20.9243i	0.262268	−	0.978796i	−0.701634	−	0.712538i	$-0.747546\pi$
$457$	5.60664	−	20.9243i	0.262268	−	0.978796i	0.963902	−	0.266259i	$-0.0857875\pi$
$458$	18.5274	+	10.6968i	0.865729	+	0.499829i
$459$	−2.50673	−	15.3102i	−0.117004	−	0.714617i
$460$	0.132460	+	0.132460i	0.00617599	+	0.00617599i
$461$	9.54937	−	9.54937i	0.444759	−	0.444759i	−0.448849	−	0.893608i	$-0.648166\pi$
$461$	9.54937	−	9.54937i	0.444759	−	0.444759i	0.893608	+	0.448849i	$0.148166\pi$
$462$	5.36460	−	4.20631i	0.249584	−	0.195695i
$463$	−3.93837	−	1.05528i	−0.183032	−	0.0490432i	0.166139	−	0.986102i	$-0.446870\pi$
$463$	−3.93837	−	1.05528i	−0.183032	−	0.0490432i	−0.349171	+	0.937059i	$0.613537\pi$
$464$	−8.13634	−	4.69752i	−0.377720	−	0.218077i
$465$	−9.09797	−	1.10105i	−0.421908	−	0.0510601i
$466$	−1.66951	−	0.447344i	−0.0773386	−	0.0207228i
$467$	−0.722546			−0.0334354			−0.0167177	−	0.999860i	$-0.505322\pi$
$467$	−0.722546			−0.0334354			−0.0167177	+	0.999860i	$0.505322\pi$
$468$	−10.7779	+	0.914649i	−0.498209	+	0.0422797i
$469$	24.0022			1.10832
$470$	−7.64176	−	2.04760i	−0.352488	−	0.0944489i
$471$	1.52836	−	2.03555i	0.0704230	−	0.0937930i
$472$	12.4512	+	7.18873i	0.573115	+	0.330888i
$473$	1.96106	+	0.525465i	0.0901698	+	0.0241609i
$474$	5.74725	+	2.31044i	0.263980	+	0.106122i
$475$	18.5759	−	18.5759i	0.852319	−	0.852319i
$476$	9.50836	+	9.50836i	0.435815	+	0.435815i
$477$	−1.58640	−	1.52136i	−0.0726364	−	0.0696582i
$478$	−1.40767	−	0.812720i	−0.0643855	−	0.0371730i
$479$	4.88168	−	18.2187i	0.223050	−	0.832433i	−0.760127	−	0.649775i	$-0.774863\pi$
$479$	4.88168	−	18.2187i	0.223050	−	0.832433i	0.983177	−	0.182658i	$-0.0584701\pi$
$480$	1.92740	−	0.822086i	0.0879733	−	0.0375229i
$481$	−1.04836	−	16.4268i	−0.0478010	−	0.748996i
$482$	−7.23514	+	4.17721i	−0.329552	+	0.190267i
$483$	−1.12074	−	0.450544i	−0.0509952	−	0.0205005i
$484$	5.11816	+	8.86491i	0.232644	+	0.402950i
$485$	6.74604	+	11.6845i	0.306322	+	0.530565i
$486$	15.3275	−	2.84012i	0.695272	−	0.128830i
$487$	5.72342	−	21.3601i	0.259353	−	0.967919i	−0.706264	−	0.707949i	$-0.749621\pi$
$487$	5.72342	−	21.3601i	0.259353	−	0.967919i	0.965617	−	0.259970i	$-0.0837127\pi$
$488$	−2.32523	−	2.32523i	−0.105258	−	0.105258i
$489$	−2.45398	−	17.2436i	−0.110973	−	0.779784i
$490$	8.03543	−	13.9178i	0.363004	−	0.628741i
$491$	36.7572			1.65883			0.829414	−	0.558635i	$-0.188675\pi$
$491$	36.7572			1.65883			0.829414	+	0.558635i	$0.188675\pi$
$492$	−6.04342	−	7.70759i	−0.272458	−	0.347485i
$493$	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
$497$	−59.3373	+	34.2584i	−2.66164	+	1.53670i
$498$	4.02972	−	1.71878i	0.180576	−	0.0770203i
$499$	0.0141387	−	0.0527664i	0.000632935	−	0.00236215i	−0.965609	−	0.260000i	$-0.916277\pi$
$499$	0.0141387	−	0.0527664i	0.000632935	−	0.00236215i	0.966242	+	0.257638i	$0.0829441\pi$
$500$	2.67288	+	9.97531i	0.119535	+	0.446109i
$501$	9.15055	−	22.7621i	0.408816	−	1.01694i
$502$	3.92665	+	14.6545i	0.175255	+	0.654060i
$503$	−6.26294	+	3.61591i	−0.279251	+	0.161226i	−0.633084	−	0.774083i	$-0.718211\pi$
$503$	−6.26294	+	3.61591i	−0.279251	+	0.161226i	0.353833	+	0.935308i	$0.384878\pi$
$504$	−9.35197	+	9.75181i	−0.416570	+	0.434380i
$505$	−3.76503	−	14.0513i	−0.167541	−	0.625273i
$506$	−0.0676583	+	0.117188i	−0.00300778	+	0.00520963i
$507$	−0.158310	−	22.5161i	−0.00703081	−	0.999975i
$508$	−1.64142	−	2.84302i	−0.0728262	−	0.126139i
$509$	−26.6579	+	26.6579i	−1.18159	+	1.18159i	−0.202258	+	0.979332i	$0.564828\pi$
$509$	−26.6579	+	26.6579i	−1.18159	+	1.18159i	−0.979332	+	0.202258i	$0.935172\pi$
$510$	−5.75459	+	2.45448i	−0.254817	+	0.108686i
$511$			3.78737i			0.167544i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−22.5251	+	31.3453i	−0.994508	+	1.38393i
$514$	20.3351	+	5.44877i	0.896942	+	0.240335i
$515$	4.21136	−	1.12843i	0.185575	−	0.0497246i
$516$	−3.99479	−	0.483457i	−0.175861	−	0.0212830i
$517$		−	5.71479i		−	0.251336i
$518$	−14.5387	−	14.5387i	−0.638795	−	0.638795i
$519$	−4.76637	−	11.1749i	−0.209220	−	0.490522i
$520$	1.39500	+	4.13283i	0.0611749	+	0.181237i
$521$			35.0558i			1.53582i	0.640555	+	0.767912i	$0.278704\pi$
$521$			35.0558i			1.53582i	−0.640555	+	0.767912i	$0.721296\pi$
$522$	−13.5787	+	24.6986i	−0.594323	+	1.08103i
$523$	14.4334	−	24.9994i	0.631128	−	1.09315i	−0.356193	−	0.934412i	$-0.615926\pi$
$523$	14.4334	−	24.9994i	0.631128	−	1.09315i	0.987321	−	0.158734i	$-0.0507411\pi$
$524$	−20.4360			−0.892752
$525$	−17.0220	−	21.7093i	−0.742900	−	0.947473i
$526$	−28.9622	+	7.76041i	−1.26281	+	0.338370i
$527$	12.6131	−	3.37967i	0.549435	−	0.147221i
$528$	0.933949	+	1.19113i	0.0406449	+	0.0518373i
$529$	−22.9760			−0.998958
$530$	−0.443182	+	0.767614i	−0.0192506	+	0.0333430i
$531$	20.7798	−	37.7968i	0.901768	−	1.64024i
$532$		−	33.4562i		−	1.45051i
$533$	16.9719	−	11.2982i	0.735136	−	0.489380i
$534$	−4.15810	−	9.74875i	−0.179938	−	0.421870i
$535$	1.46505	+	1.46505i	0.0633395	+	0.0633395i
$536$			5.32933i			0.230192i
$537$	11.0867	+	1.34173i	0.478424	+	0.0578999i
$538$	−14.7507	+	3.95243i	−0.635946	+	0.170401i
$539$	11.2133	+	3.00460i	0.482991	+	0.129417i
$540$	−2.58671	−	5.72932i	−0.111314	−	0.246551i
$541$	−10.8347	+	10.8347i	−0.465819	+	0.465819i	−0.900557	−	0.434738i	$-0.856841\pi$
$541$	−10.8347	+	10.8347i	−0.465819	+	0.465819i	0.434738	+	0.900557i	$0.356841\pi$
$542$			12.6936i			0.545236i
$543$	−3.66216	+	1.56201i	−0.157158	+	0.0670321i
$544$	−2.11119	+	2.11119i	−0.0905166	+	0.0905166i
$545$	−11.4528	−	19.8368i	−0.490582	−	0.849714i
$546$	−18.7291	−	20.9833i	−0.801533	−	0.898004i
$547$	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
$549$	−6.82819	+	7.12012i	−0.291420	+	0.303879i
$550$	−2.67641	+	1.54523i	−0.114123	+	0.0658888i
$551$	−18.0631	−	67.4125i	−0.769515	−	2.87187i
$552$	0.100037	−	0.248843i	0.00425784	−	0.0105914i
$553$	4.16873	+	15.5579i	0.177273	+	0.661590i
$554$	7.68724	−	28.6892i	0.326599	−	1.21889i
$555$	8.79903	−	3.75302i	0.373498	−	0.159307i
$556$	13.8052	−	7.97045i	0.585472	−	0.338022i
$557$	15.3310	−	4.10794i	0.649596	−	0.174059i	0.0810500	−	0.996710i	$-0.474173\pi$
$557$	15.3310	−	4.10794i	0.649596	−	0.174059i	0.568546	+	0.822651i	$0.307506\pi$
$558$	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
$561$	−2.78847	−	3.55633i	−0.117729	−	0.150148i
$562$	16.4023			0.691888
$563$	−13.8497	+	23.9883i	−0.583694	+	1.01099i	0.411343	+	0.911481i	$0.365060\pi$
$563$	−13.8497	+	23.9883i	−0.583694	+	1.01099i	−0.995037	+	0.0995068i	$0.968273\pi$
$564$	1.59585	+	11.2137i	0.0671975	+	0.472183i
$565$	−9.44883	−	9.44883i	−0.397515	−	0.397515i
$566$	3.29514	−	12.2976i	0.138505	−	0.516907i
$567$	29.8361	+	27.4376i	1.25300	+	1.15227i
$568$	−7.60657	−	13.1750i	−0.319165	−	0.552810i
$569$	12.9578	+	22.4436i	0.543219	+	0.940883i	0.998717	+	0.0506463i	$0.0161281\pi$
$569$	12.9578	+	22.4436i	0.543219	+	0.940883i	−0.455497	+	0.890237i	$0.650539\pi$
$570$	14.4422	+	5.80588i	0.604919	+	0.243182i
$571$	−30.2989	+	17.4931i	−1.26797	+	0.732061i	−0.974603	−	0.223939i	$-0.928108\pi$
$571$	−30.2989	+	17.4931i	−1.26797	+	0.732061i	−0.293364	+	0.956001i	$0.594775\pi$
$572$	−2.62284	+	1.74602i	−0.109667	+	0.0730049i
$573$	−10.7321	+	4.57752i	−0.448340	+	0.191228i
$574$	6.59160	−	24.6002i	0.275128	−	1.02679i
$575$	0.474232	+	0.273798i	0.0197768	+	0.0114182i
$576$	−2.16525	−	2.07647i	−0.0902185	−	0.0865194i
$577$	24.5361	+	24.5361i	1.02145	+	1.02145i	0.999765	+	0.0216855i	$0.00690324\pi$
$577$	24.5361	+	24.5361i	1.02145	+	1.02145i	0.0216855	+	0.999765i	$0.493097\pi$
$578$	−5.71748	+	5.71748i	−0.237816	+	0.237816i
$579$	10.4289	+	4.19250i	0.433410	+	0.174234i
$580$	10.9786	+	2.94171i	0.455863	+	0.122148i
$581$	9.86546	+	5.69583i	0.409288	+	0.236303i
$582$	11.5983	−	15.4472i	0.480765	−	0.640307i
$583$	−0.618454	−	0.165714i	−0.0256137	−	0.00686318i
$584$	−0.840930			−0.0347979
$585$	12.3082	−	4.44353i	0.508882	−	0.183717i
$586$	28.0655			1.15938
$587$	32.0848	+	8.59709i	1.32428	+	0.354840i	0.850580	−	0.525846i	$-0.176251\pi$
$587$	32.0848	+	8.59709i	1.32428	+	0.354840i	0.473701	+	0.880686i	$0.342918\pi$
$588$	−22.8421	−	2.76440i	−0.941993	−	0.114002i
$589$	−28.1361	−	16.2444i	−1.15933	−	0.669338i
$590$	−16.8009	−	4.50178i	−0.691681	−	0.185335i
$591$	−17.7789	+	13.9402i	−0.731326	+	0.573423i
$592$	3.22811	−	3.22811i	0.132674	−	0.132674i
$593$	−11.1144	−	11.1144i	−0.456413	−	0.456413i	0.441063	−	0.897476i	$-0.354602\pi$
$593$	−11.1144	−	11.1144i	−0.456413	−	0.456413i	−0.897476	+	0.441063i	$0.854602\pi$
$594$	3.51398	−	2.87601i	0.144180	−	0.118004i
$595$	−14.0883	−	8.13386i	−0.577562	−	0.333456i
$596$	−2.24660	+	8.38442i	−0.0920243	+	0.343439i
$597$	6.98974	+	5.24813i	0.286071	+	0.214792i
$598$	0.500298	+	0.247788i	0.0204587	+	0.0101328i
$599$	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	$0.126121\pi$
$600$	4.82023	−	3.77948i	0.196785	−	0.154297i
$601$	4.42795	+	7.66944i	0.180620	+	0.312843i	0.942092	−	0.335355i	$-0.108856\pi$
$601$	4.42795	+	7.66944i	0.180620	+	0.312843i	−0.761472	+	0.648198i	$0.775523\pi$
$602$	−5.23165	−	9.06149i	−0.213226	−	0.369319i
$603$	15.9845	−	0.334554i	0.650939	−	0.0136241i
$604$	1.43599	−	5.35919i	0.0584297	−	0.218062i
$605$	−8.75658	−	8.75658i	−0.356006	−	0.356006i
$606$	−16.3896	+	12.8509i	−0.665782	+	0.522030i
$607$	11.6983	−	20.2621i	0.474821	−	0.822413i	−0.524764	−	0.851248i	$-0.675846\pi$
$607$	11.6983	−	20.2621i	0.474821	−	0.822413i	0.999584	+	0.0288346i	$0.00917961\pi$
$608$	7.42845			0.301263
$609$	−72.5576	+	10.3258i	−2.94018	+	0.418425i
$610$	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	−0.945724	−	0.324970i	$-0.894646\pi$
$613$	−39.6701	+	10.6296i	−1.60226	+	0.429324i	−0.656536	+	0.754295i	$0.727979\pi$
$614$	25.0750	−	14.4770i	1.01194	−	0.584246i
$615$	9.47543	+	7.11448i	0.382086	+	0.286884i
$616$	−1.01866	+	3.80171i	−0.0410432	+	0.153175i
$617$	−0.0123147	−	0.0459591i	−0.000495771	−	0.00185024i	0.965677	−	0.259744i	$-0.0836382\pi$
$617$	−0.0123147	−	0.0459591i	−0.000495771	−	0.00185024i	−0.966173	+	0.257894i	$0.916972\pi$
$618$	−3.85158	−	4.91219i	−0.154933	−	0.197597i
$619$	4.73858	+	17.6846i	0.190460	+	0.710806i	0.993396	+	0.114740i	$0.0366035\pi$
$619$	4.73858	+	17.6846i	0.190460	+	0.710806i	−0.802936	+	0.596066i	$0.796730\pi$
$620$	4.58217	−	2.64552i	0.184025	−	0.106247i
$621$	−0.752644	−	0.284423i	−0.0302026	−	0.0114135i
$622$	−5.16995	−	19.2945i	−0.207296	−	0.773640i
$623$	13.7794	−	23.8667i	0.552061	−	0.956198i
$624$	4.65904	−	4.15853i	0.186511	−	0.166474i
$625$	2.59428	+	4.49342i	0.103771	+	0.179737i
$626$	21.4203	−	21.4203i	0.856126	−	0.856126i
$627$	−1.35090	+	11.1624i	−0.0539497	+	0.445784i
$628$			1.46962i			0.0586441i
$629$	−9.63809	+	9.63809i	−0.384296	+	0.384296i
$630$	7.87488	−	14.3238i	0.313743	−	0.570673i
$631$	25.1823	+	6.74757i	1.00249	+	0.268616i	0.722488	−	0.691383i	$-0.242998\pi$
$631$	25.1823	+	6.74757i	1.00249	+	0.268616i	0.280002	+	0.960000i	$0.409665\pi$
$632$	−3.45441	+	0.925606i	−0.137409	+	0.0368186i
$633$	−6.36646	−	14.9263i	−0.253044	−	0.593267i
$634$		−	11.8836i		−	0.471959i
$635$	2.80828	+	2.80828i	0.111443	+	0.111443i
$636$	1.25982	+	0.152466i	0.0499553	+	0.00604569i
$637$	9.42477	−	46.9602i	0.373423	−	1.86063i
$638$			8.21023i			0.325046i
$639$	−39.0388	+	23.6418i	−1.54435	+	0.935255i
$640$	−0.604889	+	1.04770i	−0.0239103	+	0.0414139i
$641$	21.8833			0.864339			0.432169	−	0.901792i	$-0.357748\pi$
$641$	21.8833			0.864339			0.432169	+	0.901792i	$0.357748\pi$
$642$	1.10643	−	2.75227i	0.0436674	−	0.108623i
$643$	−38.3655	+	10.2800i	−1.51299	+	0.405404i	−0.917426	−	0.397907i	$-0.869737\pi$
$643$	−38.3655	+	10.2800i	−1.51299	+	0.405404i	−0.595561	+	0.803310i	$0.703070\pi$
$644$	0.673622	−	0.180496i	0.0265444	−	0.00711256i
$645$	4.81951	−	0.685876i	0.189768	−	0.0270064i
$646$	−22.1789			−0.872618
$647$	−22.0957	+	38.2709i	−0.868671	+	1.50458i	−0.00531608	+	0.999986i	$0.501692\pi$
$647$	−22.0957	+	38.2709i	−0.868671	+	1.50458i	−0.863355	+	0.504597i	$0.831641\pi$
$648$	−6.09211	+	6.62467i	−0.239321	+	0.260241i
$649$		−	12.5643i		−	0.493193i
$650$	7.06576	+	10.6140i	0.277142	+	0.416317i
$651$	−20.4849	+	27.2829i	−0.802867	+	1.06930i
$652$	7.11062	+	7.11062i	0.278473	+	0.278473i
$653$			42.0855i			1.64693i	0.567364	+	0.823467i	$0.307963\pi$
$653$			42.0855i			1.64693i	−0.567364	+	0.823467i	$0.692037\pi$
$654$	−19.6904	+	26.2247i	−0.769957	+	1.02547i
$655$	23.8806	−	6.39880i	0.933094	−	0.250022i
$656$	5.46211	+	1.46357i	0.213259	+	0.0571427i
$657$	0.0527902	+	2.52224i	0.00205954	+	0.0984019i
$658$	−20.8260	+	20.8260i	−0.811884	+	0.811884i
$659$			27.2422i			1.06121i	0.847621	+	0.530603i	$0.178034\pi$
$659$			27.2422i			1.06121i	−0.847621	+	0.530603i	$0.821966\pi$
$660$	−1.46433	−	1.09947i	−0.0569990	−	0.0427968i
$661$	−32.0558	+	32.0558i	−1.24683	+	1.24683i	−0.289713	+	0.957114i	$0.593560\pi$
$661$	−32.0558	+	32.0558i	−1.24683	+	1.24683i	−0.957114	+	0.289713i	$0.906440\pi$
$662$	2.55950	+	4.43319i	0.0994778	+	0.172301i
$663$	−13.9104	+	12.4160i	−0.540235	+	0.482198i
$664$	−1.26467	+	2.19048i	−0.0490789	+	0.0850071i
$665$	10.4756	+	39.0954i	0.406226	+	1.51606i
$666$	−9.88486	−	9.47956i	−0.383030	−	0.367326i
$667$	1.25986	−	0.727382i	0.0487821	−	0.0281644i
$668$	3.66589	+	13.6813i	0.141837	+	0.529344i
$669$	32.5298	−	4.62940i	1.25768	−	0.178983i
$670$	−1.66869	−	6.22762i	−0.0644670	−	0.240594i
$671$	−0.743762	+	2.77576i	−0.0287126	+	0.107157i
$672$	0.937229	−	7.74429i	0.0361544	−	0.298742i
$673$	14.3655	−	8.29395i	0.553751	−	0.319708i	−0.196883	−	0.980427i	$-0.563082\pi$
$673$	14.3655	−	8.29395i	0.553751	−	0.319708i	0.750633	+	0.660719i	$0.229748\pi$
$674$	−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	$0.452559\pi$
$678$	−7.13594	+	17.7508i	−0.274054	+	0.681715i
$679$	50.2286			1.92760
$680$	1.80600	−	3.12809i	0.0692571	−	0.119957i
$681$	6.45934	+	2.59670i	0.247523	+	0.0995059i
$682$	2.70257	+	2.70257i	0.103487	+	0.103487i
$683$	−5.52744	+	20.6287i	−0.211502	+	0.789335i	0.775867	+	0.630896i	$0.217313\pi$
$683$	−5.52744	+	20.6287i	−0.211502	+	0.789335i	−0.987369	+	0.158438i	$0.949354\pi$
$684$	−0.466328	−	22.2805i	−0.0178305	−	0.851915i
$685$	1.23270	+	2.13509i	0.0470989	+	0.0815777i
$686$	−14.1512	−	24.5106i	−0.540295	−	0.935818i
$687$	5.22076	+	36.6852i	0.199184	+	1.39963i
$688$	2.01197	−	1.16161i	0.0767056	−	0.0442860i
$689$	−0.519810	+	2.59002i	−0.0198032	+	0.0986719i
$690$	−0.0389823	+	0.322109i	−0.00148403	+	0.0122625i
$691$	8.17537	−	30.5109i	0.311006	−	1.16069i	−0.616645	−	0.787241i	$-0.711509\pi$
$691$	8.17537	−	30.5109i	0.311006	−	1.16069i	0.927651	−	0.373448i	$-0.121825\pi$
$692$	6.07445	+	3.50709i	0.230916	+	0.133319i
$693$	11.4666	+	2.81667i	0.435579	+	0.106996i
$694$	−12.3491	−	12.3491i	−0.468764	−	0.468764i
$695$	−13.6365	+	13.6365i	−0.517263	+	0.517263i
$696$	−2.29270	−	16.1104i	−0.0869047	−	0.610661i
$697$	−16.3081	−	4.36974i	−0.617712	−	0.165516i
$698$	−10.5867	−	6.11225i	−0.400714	−	0.231352i
$699$	−1.17451	−	2.75367i	−0.0444241	−	0.104153i
$700$	15.3847	+	4.12231i	0.581485	+	0.155809i
$701$	26.8613			1.01454			0.507268	−	0.861788i	$-0.330655\pi$
$701$	26.8613			1.01454			0.507268	+	0.861788i	$0.330655\pi$
$702$	−12.7653	−	13.7130i	−0.481796	−	0.517564i
$703$	33.9126			1.27904
$704$	−0.844113	−	0.226179i	−0.0318137	−	0.00852446i
$705$	−5.37602	−	12.6042i	−0.202473	−	0.474702i
$706$	−4.95619	−	2.86146i	−0.186529	−	0.107692i
$707$	−52.3104	−	14.0165i	−1.96733	−	0.527145i
$708$	3.50858	+	24.6541i	0.131861	+	0.926557i
$709$	−0.0790916	+	0.0790916i	−0.00297035	+	0.00297035i	−0.708590	−	0.705620i	$-0.750669\pi$
$709$	−0.0790916	+	0.0790916i	−0.00297035	+	0.00297035i	0.705620	+	0.708590i	$0.250669\pi$
$710$	13.0140	+	13.0140i	0.488406	+	0.488406i
$711$	2.99306	+	10.3028i	0.112249	+	0.386387i
$712$	5.29924	+	3.05952i	0.198597	+	0.114660i
$713$	0.175277	−	0.654144i	0.00656419	−	0.0244979i
$714$	−2.79826	+	23.1219i	−0.104722	+	0.865316i
$715$	2.51824	−	2.86157i	0.0941767	−	0.107017i
$716$	−5.58377	+	3.22379i	−0.208675	+	0.120479i
$717$	−0.396662	−	2.78726i	−0.0148136	−	0.104092i
$718$	10.8643	+	18.8176i	0.405453	+	0.702265i
$719$	14.2985	+	24.7657i	0.533244	+	0.923605i	0.999246	+	0.0388216i	$0.0123604\pi$
$719$	14.2985	+	24.7657i	0.533244	+	0.923605i	−0.466003	+	0.884783i	$0.654306\pi$
$720$	3.18038	+	1.74850i	0.118526	+	0.0651628i
$721$	4.20094	−	15.6781i	0.156451	−	0.583884i
$722$	25.5844	+	25.5844i	0.952154	+	0.952154i
$723$	−13.4260	−	5.39736i	−0.499319	−	0.200730i
$724$	1.14932	−	1.99068i	0.0427142	−	0.0739831i
$725$	33.2249			1.23394
$726$	−6.61315	+	16.4503i	−0.245437	+	0.610528i
$727$	−7.41724	−	4.28235i	−0.275090	−	0.158823i	0.356108	−	0.934445i	$-0.384103\pi$
$727$	−7.41724	−	4.28235i	−0.275090	−	0.158823i	−0.631199	+	0.775621i	$0.717437\pi$
$728$	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
$731$	−6.00709	+	3.46819i	−0.222180	+	0.128276i
$732$	0.684302	−	5.65436i	0.0252925	−	0.208991i
$733$	−9.75774	+	36.4164i	−0.360410	+	1.34507i	0.513127	+	0.858312i	$0.328487\pi$
$733$	−9.75774	+	36.4164i	−0.360410	+	1.34507i	−0.873538	+	0.486757i	$0.838180\pi$
$734$	−1.74850	−	6.52549i	−0.0645383	−	0.240860i
$735$	27.5579	−	3.92182i	1.01649	−	0.144659i
$736$	0.0400766	+	0.149568i	0.00147724	+	0.00551314i
$737$	4.03330	−	2.32863i	0.148568	−	0.0857760i
$738$	4.04685	−	16.4746i	0.148967	−	0.606439i
$739$	−10.9861	−	41.0008i	−0.404131	−	1.50824i	−0.805653	−	0.592388i	$-0.798185\pi$
$739$	−10.9861	−	41.0008i	−0.404131	−	1.50824i	0.401522	−	0.915850i	$-0.368481\pi$
$740$	−2.76146	+	4.78299i	−0.101513	+	0.175826i
$741$	46.3161	+	2.62907i	1.70146	+	0.0965811i
$742$	1.64989	+	2.85769i	0.0605693	+	0.104909i
$743$	−18.3756	+	18.3756i	−0.674137	+	0.674137i	−0.958667	−	0.284530i	$-0.908162\pi$
$743$	−18.3756	+	18.3756i	−0.674137	+	0.674137i	0.284530	+	0.958667i	$0.408162\pi$
$744$	−6.05776	−	4.54837i	−0.222088	−	0.166751i
$745$		−	10.5011i		−	0.384731i
$746$	5.15880	−	5.15880i	0.188877	−	0.188877i
$747$	6.64939	+	3.65568i	0.243289	+	0.133754i
$748$	2.52025	+	0.675299i	0.0921494	+	0.0246914i
$749$	7.45045	−	1.99634i	0.272234	−	0.0729448i
$750$	−10.7400	+	14.3041i	−0.392169	+	0.522310i
$751$		−	11.3081i		−	0.412640i	−0.978485	−	0.206320i	$-0.933851\pi$
$751$		−	11.3081i		−	0.412640i	0.978485	−	0.206320i	$-0.0661488\pi$
$752$	−4.62411	−	4.62411i	−0.168624	−	0.168624i
$753$	−15.7778	+	21.0137i	−0.574975	+	0.765782i
$754$	33.8055	−	2.15747i	1.23112	−	0.0785703i
$755$			6.71215i			0.244280i
$756$	−23.2866	−	2.32492i	−0.846926	−	0.0845564i
$757$	0.110287	−	0.191023i	0.00400845	−	0.00694284i	−0.864014	−	0.503467i	$-0.832057\pi$
$757$	0.110287	−	0.191023i	0.00400845	−	0.00694284i	0.868023	+	0.496525i	$0.165391\pi$
$758$	13.6369			0.495313
$759$	−0.232037	+	0.0330218i	−0.00842243	+	0.00119862i
$760$	−8.68056	+	2.32595i	−0.314877	+	0.0843710i
$761$	−21.4214	+	5.73986i	−0.776527	+	0.208070i	−0.625253	−	0.780422i	$-0.715004\pi$
$761$	−21.4214	+	5.73986i	−0.776527	+	0.208070i	−0.151274	+	0.988492i	$0.548338\pi$
$762$	2.12087	−	5.27570i	0.0768310	−	0.191118i
$763$	−85.2732			−3.08710
$764$	3.36813	−	5.83377i	0.121855	−	0.211058i
$765$	−9.49559	−	5.22045i	−0.343314	−	0.188746i
$766$			27.9957i			1.01152i
$767$	−51.7334	+	3.30163i	−1.86799	+	0.119215i
$768$	1.71950	+	0.208098i	0.0620473	+	0.00750908i
$769$	−1.18171	−	1.18171i	−0.0426134	−	0.0426134i	0.685479	−	0.728092i	$-0.259593\pi$
$769$	−1.18171	−	1.18171i	−0.0426134	−	0.0426134i	−0.728092	+	0.685479i	$0.759593\pi$
$770$		−	4.76147i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.679534 - 1.59318i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.16856 - 0.313114i) q^{5} +(0.244033 + 1.71477i) q^{6} +(-3.18466 + 3.18466i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.07647 + 2.16525i) q^{9} +(1.04770 + 0.604889i) q^{10} +(-0.226179 + 0.844113i) q^{11} +(0.208098 - 1.71950i) q^{12} +(3.53506 + 0.709476i) q^{13} +(3.90040 - 2.25190i) q^{14} +(0.295226 + 2.07450i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.49284 - 2.58567i) q^{17} +(2.56612 - 1.55404i) q^{18} +(-1.92262 + 7.17533i) q^{19} +(-0.855443 - 0.855443i) q^{20} +(7.23783 + 2.90966i) q^{21} +(0.436945 - 0.756811i) q^{22} -0.154844 q^{23} +(-0.646048 + 1.60705i) 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} +(-8.13634 + 4.69752i) q^{29} +(0.251752 - 2.08022i) q^{30} +(-1.13196 + 4.22454i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(1.49852 - 0.213258i) q^{33} +(0.772750 + 2.88394i) q^{34} +(4.71862 - 2.72429i) q^{35} +(-2.88090 + 0.836924i) q^{36} +(-1.18157 - 4.40968i) q^{37} +(3.71422 - 6.43322i) q^{38} +(-1.27187 - 6.11411i) q^{39} +(0.604889 + 1.04770i) q^{40} +(3.99854 - 3.99854i) q^{41} +(-6.23813 - 4.68381i) q^{42} -2.32322i q^{43} +(-0.617934 + 0.617934i) q^{44} +(3.10444 - 1.88004i) q^{45} +(0.149568 + 0.0400766i) q^{46} +(-6.31666 + 1.69254i) q^{47} +(1.03997 - 1.38509i) q^{48} -13.2841i q^{49} +(2.50064 + 2.50064i) q^{50} +(-3.10501 + 4.13542i) q^{51} +(2.70671 + 2.38195i) q^{52} +0.732667i q^{53} +(-4.21963 - 3.03228i) q^{54} +(0.528607 - 0.915574i) q^{55} +4.50379 q^{56} +(12.7381 - 1.81279i) q^{57} +(9.07491 - 2.43161i) q^{58} +(-13.8876 + 3.72116i) q^{59} +(-0.781574 + 1.94418i) q^{60} +3.28837 q^{61} +(2.18678 - 3.78761i) q^{62} +(-0.282730 - 13.5084i) q^{63} +1.00000i q^{64} +(-3.90877 - 1.93594i) q^{65} +(-1.50266 - 0.181855i) q^{66} +(-3.76841 - 3.76841i) q^{67} -2.98568i q^{68} +(0.105222 + 0.246695i) q^{69} +(-5.26293 + 1.41020i) q^{70} +(14.6948 + 3.93745i) q^{71} +(2.99934 - 0.0627760i) q^{72} +(0.594627 - 0.594627i) q^{73} +4.56524i q^{74} +(-0.735925 + 6.08092i) q^{75} +(-5.25271 + 5.25271i) q^{76} +(-1.96791 - 3.40852i) q^{77} +(-0.353919 + 6.23496i) q^{78} +(1.78813 - 3.09714i) q^{79} +(-0.313114 - 1.16856i) q^{80} +(-0.376573 - 8.99212i) q^{81} +(-4.89719 + 2.82739i) q^{82} +(-0.654644 - 2.44316i) q^{83} +(4.81332 + 6.13876i) q^{84} +(0.934856 + 3.48893i) q^{85} +(-0.601294 + 2.24406i) q^{86} +(13.0129 + 9.77055i) q^{87} +(0.756811 - 0.436945i) 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} +(7.49967 - 1.06729i) q^{93} +6.53948 q^{94} +(4.49339 - 7.78278i) q^{95} +(-1.36302 + 1.06873i) q^{96} +(-7.88603 - 7.88603i) q^{97} +(-3.43818 + 12.8315i) q^{98} +(-1.35806 - 2.24251i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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