LMFDB - Embedded newform 637.2.bb.a.227.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(227,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("637.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bb (of order $12$, degree $4$, not 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.6
Character	$\chi$	$=$	637.227
Dual form			637.2.bb.a.362.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14693 - 1.14693i) q^{2} +(0.445073 - 0.256963i) q^{3} -0.630890i q^{4} +(-0.395109 + 1.47457i) q^{5} +(0.215749 - 0.805186i) q^{6} +(1.57027 + 1.57027i) q^{8} +(-1.36794 + 2.36934i) q^{9} +O(q^{10})$	\(q+(1.14693 - 1.14693i) q^{2} +(0.445073 - 0.256963i) q^{3} -0.630890i q^{4} +(-0.395109 + 1.47457i) q^{5} +(0.215749 - 0.805186i) q^{6} +(1.57027 + 1.57027i) q^{8} +(-1.36794 + 2.36934i) q^{9} +(1.23806 + 2.14439i) q^{10} +(-0.745574 + 2.78252i) q^{11} +(-0.162115 - 0.280792i) q^{12} +(2.94467 - 2.08061i) q^{13} +(0.203057 + 0.757819i) q^{15} +4.86376 q^{16} +6.21574 q^{17} +(1.14854 + 4.28639i) q^{18} +(-2.23387 + 0.598564i) q^{19} +(0.930289 + 0.249270i) q^{20} +(2.33623 + 4.04647i) q^{22} -5.62238i q^{23} +(1.10239 + 0.295384i) q^{24} +(2.31189 + 1.33477i) q^{25} +(0.991014 - 5.76363i) q^{26} +2.94782i q^{27} +(0.379237 - 0.656858i) q^{29} +(1.10206 + 0.636273i) q^{30} +(-8.36292 + 2.24084i) q^{31} +(2.43784 - 2.43784i) q^{32} +(0.383170 + 1.43001i) q^{33} +(7.12901 - 7.12901i) q^{34} +(1.49479 + 0.863019i) q^{36} +(-4.26298 - 4.26298i) q^{37} +(-1.87558 + 3.24860i) q^{38} +(0.775953 - 1.68269i) q^{39} +(-2.93590 + 1.69504i) q^{40} +(1.94919 - 0.522283i) q^{41} +(-2.24252 + 1.29472i) q^{43} +(1.75546 + 0.470375i) q^{44} +(-2.95327 - 2.95327i) q^{45} +(-6.44847 - 6.44847i) q^{46} +(2.13395 + 0.571791i) q^{47} +(2.16473 - 1.24981i) q^{48} +(4.18246 - 1.12069i) q^{50} +(2.76646 - 1.59722i) q^{51} +(-1.31263 - 1.85776i) q^{52} +(2.47328 - 4.28385i) q^{53} +(3.38094 + 3.38094i) q^{54} +(-3.80843 - 2.19880i) q^{55} +(-0.840427 + 0.840427i) q^{57} +(-0.318411 - 1.18833i) q^{58} +(0.623268 - 0.623268i) q^{59} +(0.478100 - 0.128107i) q^{60} +(-4.48249 - 2.58797i) q^{61} +(-7.02159 + 12.1617i) q^{62} +4.13546i q^{64} +(1.90453 + 5.16418i) q^{65} +(2.07959 + 1.20065i) q^{66} +(15.1664 + 4.06383i) q^{67} -3.92145i q^{68} +(-1.44475 - 2.50237i) q^{69} +(-10.3040 - 2.76095i) q^{71} +(-5.86855 + 1.57247i) q^{72} +(-1.80076 - 6.72052i) q^{73} -9.77867 q^{74} +1.37195 q^{75} +(0.377628 + 1.40933i) q^{76} +(-1.03997 - 2.81989i) q^{78} +(-4.24764 - 7.35713i) q^{79} +(-1.92172 + 7.17194i) q^{80} +(-3.34634 - 5.79603i) q^{81} +(1.63656 - 2.83460i) q^{82} +(1.51432 + 1.51432i) q^{83} +(-2.45590 + 9.16553i) q^{85} +(-1.08706 + 4.05696i) q^{86} -0.389800i q^{87} +(-5.54006 + 3.19856i) q^{88} +(5.91573 - 5.91573i) q^{89} -6.77438 q^{90} -3.54710 q^{92} +(-3.14630 + 3.14630i) q^{93} +(3.10329 - 1.79169i) q^{94} -3.53049i q^{95} +(0.458582 - 1.71145i) q^{96} +(0.933928 - 3.48547i) q^{97} +(-5.57284 - 5.57284i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.14693	−	1.14693i	0.811001	−	0.811001i	−0.173783	−	0.984784i	$-0.555599\pi$
$2$	1.14693	−	1.14693i	0.811001	−	0.811001i	0.984784	+	0.173783i	$0.0555992\pi$
$3$	0.445073	−	0.256963i	0.256963	−	0.148358i	−0.365985	−	0.930621i	$-0.619268\pi$
$3$	0.445073	−	0.256963i	0.256963	−	0.148358i	0.622948	+	0.782263i	$0.285935\pi$
$4$		−	0.630890i		−	0.315445i
$5$	−0.395109	+	1.47457i	−0.176698	+	0.659447i	0.819558	+	0.572996i	$0.194219\pi$
$5$	−0.395109	+	1.47457i	−0.176698	+	0.659447i	−0.996256	+	0.0864504i	$0.972448\pi$
$6$	0.215749	−	0.805186i	0.0880791	−	0.328716i
$7$		0			0
$7$		0			0
$8$	1.57027	+	1.57027i	0.555175	+	0.555175i
$9$	−1.36794	+	2.36934i	−0.455980	+	0.789780i
$10$	1.23806	+	2.14439i	0.391509	+	0.678114i
$11$	−0.745574	+	2.78252i	−0.224799	+	0.838961i	0.757686	+	0.652619i	$0.226330\pi$
$11$	−0.745574	+	2.78252i	−0.224799	+	0.838961i	−0.982485	+	0.186342i	$0.940337\pi$
$12$	−0.162115	−	0.280792i	−0.0467987	−	0.0810577i
$13$	2.94467	−	2.08061i	0.816704	−	0.577057i
$13$	2.94467	−	2.08061i	0.816704	−	0.577057i
$14$		0			0
$15$	0.203057	+	0.757819i	0.0524291	+	0.195668i
$16$	4.86376			1.21594
$17$	6.21574			1.50754			0.753769	−	0.657139i	$-0.228234\pi$
$17$	6.21574			1.50754			0.753769	+	0.657139i	$0.228234\pi$
$18$	1.14854	+	4.28639i	0.270712	+	1.01031i
$19$	−2.23387	+	0.598564i	−0.512485	+	0.137320i	−0.505788	−	0.862658i	$-0.668798\pi$
$19$	−2.23387	+	0.598564i	−0.512485	+	0.137320i	−0.00669672	+	0.999978i	$0.502132\pi$
$20$	0.930289	+	0.249270i	0.208019	+	0.0557385i
$21$		0			0
$22$	2.33623	+	4.04647i	0.498086	+	0.862710i
$23$		−	5.62238i		−	1.17235i	−0.810185	−	0.586174i	$-0.800633\pi$
$23$		−	5.62238i		−	1.17235i	0.810185	−	0.586174i	$-0.199367\pi$
$24$	1.10239	+	0.295384i	0.225024	+	0.0602950i
$25$	2.31189	+	1.33477i	0.462378	+	0.266954i
$26$	0.991014	−	5.76363i	0.194354	−	1.13034i
$27$			2.94782i			0.567308i
$28$		0			0
$29$	0.379237	−	0.656858i	0.0704225	−	0.121975i	−0.828664	−	0.559746i	$-0.810899\pi$
$29$	0.379237	−	0.656858i	0.0704225	−	0.121975i	0.899087	+	0.437771i	$0.144232\pi$
$30$	1.10206	+	0.636273i	0.201207	+	0.116167i
$31$	−8.36292	+	2.24084i	−1.50202	+	0.402466i	−0.913777	−	0.406215i	$-0.866848\pi$
$31$	−8.36292	+	2.24084i	−1.50202	+	0.402466i	−0.588247	+	0.808682i	$0.700182\pi$
$32$	2.43784	−	2.43784i	0.430953	−	0.430953i
$33$	0.383170	+	1.43001i	0.0667013	+	0.248933i
$34$	7.12901	−	7.12901i	1.22261	−	1.22261i
$35$		0			0
$36$	1.49479	+	0.863019i	0.249132	+	0.143837i
$37$	−4.26298	−	4.26298i	−0.700830	−	0.700830i	0.263759	−	0.964589i	$-0.415038\pi$
$37$	−4.26298	−	4.26298i	−0.700830	−	0.700830i	−0.964589	+	0.263759i	$0.915038\pi$
$38$	−1.87558	+	3.24860i	−0.304259	+	0.526992i
$39$	0.775953	−	1.68269i	0.124252	−	0.269447i
$40$	−2.93590	+	1.69504i	−0.464207	+	0.268010i
$41$	1.94919	−	0.522283i	0.304412	−	0.0815669i	−0.103380	−	0.994642i	$-0.532966\pi$
$41$	1.94919	−	0.522283i	0.304412	−	0.0815669i	0.407792	+	0.913075i	$0.366299\pi$
$42$		0			0
$43$	−2.24252	+	1.29472i	−0.341981	+	0.197443i	−0.661148	−	0.750256i	$-0.729930\pi$
$43$	−2.24252	+	1.29472i	−0.341981	+	0.197443i	0.319167	+	0.947699i	$0.396597\pi$
$44$	1.75546	+	0.470375i	0.264646	+	0.0709116i
$45$	−2.95327	−	2.95327i	−0.440247	−	0.440247i
$46$	−6.44847	−	6.44847i	−0.950775	−	0.950775i
$47$	2.13395	+	0.571791i	0.311269	+	0.0834043i	0.411072	−	0.911603i	$-0.365155\pi$
$47$	2.13395	+	0.571791i	0.311269	+	0.0834043i	−0.0998029	+	0.995007i	$0.531821\pi$
$48$	2.16473	−	1.24981i	0.312452	−	0.180394i
$49$		0			0
$50$	4.18246	−	1.12069i	0.591488	−	0.158489i
$51$	2.76646	−	1.59722i	0.387382	−	0.223655i
$52$	−1.31263	−	1.85776i	−0.182030	−	0.257625i
$53$	2.47328	−	4.28385i	0.339732	−	0.588433i	−0.644650	−	0.764477i	$-0.722997\pi$
$53$	2.47328	−	4.28385i	0.339732	−	0.588433i	0.984382	+	0.176045i	$0.0563304\pi$
$54$	3.38094	+	3.38094i	0.460087	+	0.460087i
$55$	−3.80843	−	2.19880i	−0.513529	−	0.296486i
$56$		0			0
$57$	−0.840427	+	0.840427i	−0.111317	+	0.111317i
$58$	−0.318411	−	1.18833i	−0.0418094	−	0.156035i
$59$	0.623268	−	0.623268i	0.0811426	−	0.0811426i	−0.665371	−	0.746513i	$-0.731726\pi$
$59$	0.623268	−	0.623268i	0.0811426	−	0.0811426i	0.746513	+	0.665371i	$0.231726\pi$
$60$	0.478100	−	0.128107i	0.0617225	−	0.0165385i
$61$	−4.48249	−	2.58797i	−0.573924	−	0.331355i	0.184791	−	0.982778i	$-0.440839\pi$
$61$	−4.48249	−	2.58797i	−0.573924	−	0.331355i	−0.758715	+	0.651423i	$0.774172\pi$
$62$	−7.02159	+	12.1617i	−0.891742	+	1.54454i
$63$		0			0
$64$			4.13546i			0.516933i
$65$	1.90453	+	5.16418i	0.236228	+	0.640538i
$66$	2.07959	+	1.20065i	0.255980	+	0.147790i
$67$	15.1664	+	4.06383i	1.85287	+	0.496476i	0.999684	−	0.0251264i	$-0.00799882\pi$
$67$	15.1664	+	4.06383i	1.85287	+	0.496476i	0.853189	+	0.521602i	$0.174665\pi$
$68$		−	3.92145i		−	0.475545i
$69$	−1.44475	−	2.50237i	−0.173927	−	0.301250i
$70$		0			0
$71$	−10.3040	−	2.76095i	−1.22286	−	0.327665i	−0.411066	−	0.911606i	$-0.634843\pi$
$71$	−10.3040	−	2.76095i	−1.22286	−	0.327665i	−0.811796	+	0.583941i	$0.801510\pi$
$72$	−5.86855	+	1.57247i	−0.691615	+	0.185318i
$73$	−1.80076	−	6.72052i	−0.210763	−	0.786578i	−0.987615	−	0.156895i	$-0.949852\pi$
$73$	−1.80076	−	6.72052i	−0.210763	−	0.786578i	0.776852	−	0.629683i	$-0.216815\pi$
$74$	−9.77867			−1.13675
$75$	1.37195			0.158419
$76$	0.377628	+	1.40933i	0.0433169	+	0.161661i
$77$		0			0
$78$	−1.03997	−	2.81989i	−0.117753	−	0.319290i
$79$	−4.24764	−	7.35713i	−0.477897	−	0.827742i	0.521782	−	0.853079i	$-0.325267\pi$
$79$	−4.24764	−	7.35713i	−0.477897	−	0.827742i	−0.999679	+	0.0253371i	$0.991934\pi$
$80$	−1.92172	+	7.17194i	−0.214854	+	0.801847i
$81$	−3.34634	−	5.79603i	−0.371815	−	0.644003i
$82$	1.63656	−	2.83460i	0.180727	−	0.313029i
$83$	1.51432	+	1.51432i	0.166218	+	0.166218i	0.785315	−	0.619096i	$-0.212501\pi$
$83$	1.51432	+	1.51432i	0.166218	+	0.166218i	−0.619096	+	0.785315i	$0.712501\pi$
$84$		0			0
$85$	−2.45590	+	9.16553i	−0.266379	+	0.994141i
$86$	−1.08706	+	4.05696i	−0.117221	+	0.437473i
$87$		−	0.389800i		−	0.0417909i
$88$	−5.54006	+	3.19856i	−0.590573	+	0.340967i
$89$	5.91573	−	5.91573i	0.627066	−	0.627066i	−0.320263	−	0.947329i	$-0.603771\pi$
$89$	5.91573	−	5.91573i	0.627066	−	0.627066i	0.947329	+	0.320263i	$0.103771\pi$
$90$	−6.77438			−0.714082
$91$		0			0
$92$	−3.54710			−0.369811
$93$	−3.14630	+	3.14630i	−0.326256	+	0.326256i
$94$	3.10329	−	1.79169i	0.320080	−	0.184798i
$95$		−	3.53049i		−	0.362221i
$96$	0.458582	−	1.71145i	0.0468038	−	0.174674i
$97$	0.933928	−	3.48547i	0.0948260	−	0.353896i	−0.902167	−	0.431387i	$-0.858024\pi$
$97$	0.933928	−	3.48547i	0.0948260	−	0.353896i	0.996993	+	0.0774914i	$0.0246910\pi$
$98$		0			0
$99$	−5.57284	−	5.57284i	−0.560091	−	0.560091i
$100$	0.842092	−	1.45855i	0.0842092	−	0.145855i
$101$	−9.84474	−	17.0516i	−0.979589	−	1.69670i	−0.663876	−	0.747843i	$-0.731090\pi$
$101$	−9.84474	−	17.0516i	−0.979589	−	1.69670i	−0.315713	−	0.948855i	$-0.602244\pi$
$102$	1.34104	−	5.00482i	0.132783	−	0.495551i
$103$	4.70130	+	8.14290i	0.463233	+	0.802344i	0.999120	−	0.0419464i	$-0.0133559\pi$
$103$	4.70130	+	8.14290i	0.463233	+	0.802344i	−0.535887	+	0.844290i	$0.680023\pi$
$104$	7.89105	+	1.35681i	0.773781	+	0.133046i
$105$		0			0
$106$	−2.07659	−	7.74995i	−0.201697	−	0.752742i
$107$	0.0718412			0.00694515			0.00347258	−	0.999994i	$-0.498895\pi$
$107$	0.0718412			0.00694515			0.00347258	+	0.999994i	$0.498895\pi$
$108$	1.85975			0.178954
$109$	1.89580	+	7.07523i	0.181585	+	0.677684i	0.995336	+	0.0964705i	$0.0307553\pi$
$109$	1.89580	+	7.07523i	0.181585	+	0.677684i	−0.813751	+	0.581214i	$0.802578\pi$
$110$	−6.88986	+	1.84613i	−0.656922	+	0.176022i
$111$	−2.99277	−	0.801910i	−0.284061	−	0.0761139i
$112$		0			0
$113$	−8.15754	−	14.1293i	−0.767396	−	1.32917i	−0.938970	−	0.343998i	$-0.888219\pi$
$113$	−8.15754	−	14.1293i	−0.767396	−	1.32917i	0.171574	−	0.985171i	$-0.445115\pi$
$114$			1.92782i			0.180557i
$115$	8.29059	+	2.22146i	0.773101	+	0.207152i
$116$	−0.414405	−	0.239257i	−0.0384765	−	0.0222144i
$117$	0.901544	+	9.82307i	0.0833478	+	0.908143i
$118$		−	1.42969i		−	0.131613i
$119$		0			0
$120$	−0.871127	+	1.50884i	−0.0795227	+	0.137737i
$121$	2.33975	+	1.35085i	0.212704	+	0.122805i
$122$	−8.10931	+	2.17288i	−0.734182	+	0.196724i
$123$	0.733324	−	0.733324i	0.0661216	−	0.0661216i
$124$	1.41372	+	5.27608i	0.126956	+	0.473806i
$125$	−8.27895	+	8.27895i	−0.740492	+	0.740492i
$126$		0			0
$127$	14.9037	+	8.60464i	1.32249	+	0.763538i	0.984125	−	0.177478i	$-0.0567937\pi$
$127$	14.9037	+	8.60464i	1.32249	+	0.763538i	0.338362	+	0.941016i	$0.390127\pi$
$128$	9.61876	+	9.61876i	0.850186	+	0.850186i
$129$	−0.665390	+	1.15249i	−0.0585843	+	0.101471i
$130$	8.10731	+	3.73858i	0.711058	+	0.327895i
$131$	−4.73734	+	2.73511i	−0.413904	+	0.238967i	−0.692466	−	0.721451i	$-0.743476\pi$
$131$	−4.73734	+	2.73511i	−0.413904	+	0.238967i	0.278562	+	0.960418i	$0.410142\pi$
$132$	0.902178	−	0.241738i	0.0785245	−	0.0210406i
$133$		0			0
$134$	22.0557	−	12.7339i	1.90532	−	1.10004i
$135$	−4.34676	−	1.16471i	−0.374110	−	0.100242i
$136$	9.76040	+	9.76040i	0.836947	+	0.836947i
$137$	−1.24060	−	1.24060i	−0.105991	−	0.105991i	0.652122	−	0.758114i	$-0.273879\pi$
$137$	−1.24060	−	1.24060i	−0.105991	−	0.105991i	−0.758114	+	0.652122i	$0.773879\pi$
$138$	−4.52706	−	1.21302i	−0.385369	−	0.103259i
$139$	−7.13953	+	4.12201i	−0.605567	+	0.349624i	−0.771228	−	0.636559i	$-0.780357\pi$
$139$	−7.13953	+	4.12201i	−0.605567	+	0.349624i	0.165662	+	0.986183i	$0.447024\pi$
$140$		0			0
$141$	1.09669	−	0.293858i	0.0923583	−	0.0247473i
$142$	−14.9846	+	8.65135i	−1.25748	+	0.726005i
$143$	3.59387	+	9.74484i	0.300534	+	0.814904i
$144$	−6.65333	+	11.5239i	−0.554444	+	0.960325i
$145$	0.818741	+	0.818741i	0.0679927	+	0.0679927i
$146$	−9.77330	−	5.64262i	−0.808844	−	0.466986i
$147$		0			0
$148$	−2.68947	+	2.68947i	−0.221073	+	0.221073i
$149$	1.15185	+	4.29875i	0.0943628	+	0.352167i	0.996922	−	0.0783988i	$-0.0249807\pi$
$149$	1.15185	+	4.29875i	0.0943628	+	0.352167i	−0.902559	+	0.430566i	$0.858314\pi$
$150$	1.57352	−	1.57352i	0.128478	−	0.128478i
$151$	−8.69443	+	2.32966i	−0.707542	+	0.189585i	−0.594606	−	0.804017i	$-0.702692\pi$
$151$	−8.69443	+	2.32966i	−0.707542	+	0.189585i	−0.112936	+	0.993602i	$0.536025\pi$
$152$	−4.44769	−	2.56788i	−0.360755	−	0.208282i
$153$	−8.50276	+	14.7272i	−0.687407	+	1.19062i
$154$		0			0
$155$		−	13.2171i		−	1.06162i
$156$	−1.06159	−	0.489541i	−0.0849956	−	0.0391946i
$157$	4.21105	+	2.43125i	0.336078	+	0.194035i	0.658537	−	0.752549i	$-0.271176\pi$
$157$	4.21105	+	2.43125i	0.336078	+	0.194035i	−0.322458	+	0.946584i	$0.604509\pi$
$158$	−13.3098	−	3.56636i	−1.05887	−	0.283724i
$159$		−	2.54217i		−	0.201607i
$160$	2.63155	+	4.55797i	0.208042	+	0.360339i
$161$		0			0
$162$	−10.4856	−	2.80962i	−0.823830	−	0.220744i
$163$	6.17099	−	1.65351i	0.483349	−	0.129513i	−0.00891239	−	0.999960i	$-0.502837\pi$
$163$	6.17099	−	1.65351i	0.483349	−	0.129513i	0.492262	+	0.870447i	$0.336170\pi$
$164$	−0.329503	−	1.22972i	−0.0257299	−	0.0960252i
$165$	−2.26004			−0.175944
$166$	3.47364			0.269607
$167$	−2.62064	−	9.78037i	−0.202791	−	0.756828i	−0.990111	−	0.140283i	$-0.955199\pi$
$167$	−2.62064	−	9.78037i	−0.202791	−	0.756828i	0.787320	−	0.616544i	$-0.211468\pi$
$168$		0			0
$169$	4.34213	−	12.2534i	0.334010	−	0.942569i
$170$	7.69547	+	13.3289i	0.590215	+	1.02228i
$171$	1.63760	−	6.11160i	0.125230	−	0.467366i
$172$	0.816825	+	1.41478i	0.0622823	+	0.107876i
$173$	8.82380	−	15.2833i	0.670861	−	1.16197i	−0.306799	−	0.951774i	$-0.599258\pi$
$173$	8.82380	−	15.2833i	0.670861	−	1.16197i	0.977660	−	0.210192i	$-0.0674088\pi$
$174$	−0.447072	−	0.447072i	−0.0338925	−	0.0338925i
$175$		0			0
$176$	−3.62629	+	13.5335i	−0.273342	+	1.02013i
$177$	0.117243	−	0.437557i	0.00881253	−	0.0328888i
$178$		−	13.5698i		−	1.01710i
$179$	−17.5138	+	10.1116i	−1.30904	+	0.755775i	−0.981936	−	0.189213i	$-0.939406\pi$
$179$	−17.5138	+	10.1116i	−1.30904	+	0.755775i	−0.327105	+	0.944988i	$0.606073\pi$
$180$	−1.86319	+	1.86319i	−0.138874	+	0.138874i
$181$	17.4649			1.29815			0.649077	−	0.760722i	$-0.275155\pi$
$181$	17.4649			1.29815			0.649077	+	0.760722i	$0.275155\pi$
$182$		0			0
$183$	−2.66005			−0.196636
$184$	8.82867	−	8.82867i	0.650858	−	0.650858i
$185$	7.97040	−	4.60171i	0.585995	−	0.338324i
$186$			7.21716i			0.529188i
$187$	−4.63429	+	17.2954i	−0.338893	+	1.26477i
$188$	0.360737	−	1.34629i	0.0263094	−	0.0981882i
$189$		0			0
$190$	−4.04922	−	4.04922i	−0.293761	−	0.293761i
$191$	−0.0207944	+	0.0360170i	−0.00150463	+	0.00260610i	−0.866777	−	0.498696i	$-0.833812\pi$
$191$	−0.0207944	+	0.0360170i	−0.00150463	+	0.00260610i	0.865272	+	0.501302i	$0.167146\pi$
$192$	1.06266	+	1.84058i	0.0766910	+	0.132833i
$193$	3.23272	−	12.0647i	0.232696	−	0.868434i	−0.746478	−	0.665411i	$-0.768256\pi$
$193$	3.23272	−	12.0647i	0.232696	−	0.868434i	0.979174	−	0.203024i	$-0.0650769\pi$
$194$	−2.92643	−	5.06873i	−0.210106	−	0.363914i
$195$	2.17466	+	1.80904i	0.155731	+	0.129548i
$196$		0			0
$197$	0.962573	+	3.59237i	0.0685805	+	0.255946i	0.991701	−	0.128565i	$-0.0410369\pi$
$197$	0.962573	+	3.59237i	0.0685805	+	0.255946i	−0.923121	+	0.384510i	$0.874370\pi$
$198$	−12.7833			−0.908469
$199$	8.77707			0.622190			0.311095	−	0.950379i	$-0.399304\pi$
$199$	8.77707			0.622190			0.311095	+	0.950379i	$0.399304\pi$
$200$	1.53434	+	5.72624i	0.108494	+	0.404907i
$201$	7.79442	−	2.08851i	0.549776	−	0.147312i
$202$	−30.8482	−	8.26575i	−2.17047	−	0.581576i
$203$		0			0
$204$	−1.00767	−	1.74533i	−0.0705508	−	0.122198i
$205$			3.08057i			0.215156i
$206$	14.7314	+	3.94726i	1.02638	+	0.275019i
$207$	13.3213	+	7.69108i	0.925898	+	0.534567i
$208$	14.3221	−	10.1196i	0.993062	−	0.701666i
$209$		−	6.66206i		−	0.460824i
$210$		0			0
$211$	−3.33665	+	5.77924i	−0.229704	+	0.397859i	−0.957720	−	0.287701i	$-0.907109\pi$
$211$	−3.33665	+	5.77924i	−0.229704	+	0.397859i	0.728016	+	0.685560i	$0.240443\pi$
$212$	−2.70264	−	1.56037i	−0.185618	−	0.107167i
$213$	−5.29551	+	1.41893i	−0.362842	+	0.0972232i
$214$	0.0823968	−	0.0823968i	0.00563253	−	0.00563253i
$215$	−1.02311	−	3.81830i	−0.0697756	−	0.260406i
$216$	−4.62888	+	4.62888i	−0.314955	+	0.314955i
$217$		0			0
$218$	10.2891	+	5.94043i	0.696868	+	0.402337i
$219$	−2.52840	−	2.52840i	−0.170853	−	0.170853i
$220$	−1.38720	+	2.40270i	−0.0935249	+	0.161990i
$221$	18.3033	−	12.9325i	1.23121	−	0.869936i
$222$	−4.35222	+	2.51276i	−0.292102	+	0.168645i
$223$	6.10027	−	1.63456i	0.408505	−	0.109458i	−0.0487142	−	0.998813i	$-0.515512\pi$
$223$	6.10027	−	1.63456i	0.408505	−	0.109458i	0.457219	+	0.889354i	$0.348846\pi$
$224$		0			0
$225$	−6.32505	+	3.65177i	−0.421670	+	0.243451i
$226$	−25.5614	−	6.84915i	−1.70032	−	0.455599i
$227$	−16.6512	−	16.6512i	−1.10518	−	1.10518i	−0.993775	−	0.111402i	$-0.964466\pi$
$227$	−16.6512	−	16.6512i	−1.10518	−	1.10518i	−0.111402	−	0.993775i	$-0.535534\pi$
$228$	0.530217	+	0.530217i	0.0351145	+	0.0351145i
$229$	−18.2790	−	4.89785i	−1.20791	−	0.323659i	−0.401969	−	0.915653i	$-0.631674\pi$
$229$	−18.2790	−	4.89785i	−1.20791	−	0.323659i	−0.805942	+	0.591995i	$0.798341\pi$
$230$	12.0566	−	6.96086i	0.794986	−	0.458985i
$231$		0			0
$232$	1.62695	−	0.435940i	0.106814	−	0.0286209i
$233$	6.36747	−	3.67626i	0.417147	−	0.240840i	−0.276709	−	0.960954i	$-0.589244\pi$
$233$	6.36747	−	3.67626i	0.417147	−	0.240840i	0.693856	+	0.720114i	$0.255910\pi$
$234$	12.3004	+	10.2324i	0.804100	+	0.668910i
$235$	−1.68629	+	2.92074i	−0.110001	+	0.190528i
$236$	−0.393214	−	0.393214i	−0.0255960	−	0.0255960i
$237$	−3.78102	−	2.18297i	−0.245604	−	0.141799i
$238$		0			0
$239$	−4.08646	+	4.08646i	−0.264331	+	0.264331i	−0.826811	−	0.562480i	$-0.809847\pi$
$239$	−4.08646	+	4.08646i	−0.264331	+	0.264331i	0.562480	+	0.826811i	$0.309847\pi$
$240$	0.987620	+	3.68585i	0.0637506	+	0.237921i
$241$	−20.3223	+	20.3223i	−1.30907	+	1.30907i	−0.386988	+	0.922085i	$0.626485\pi$
$241$	−20.3223	+	20.3223i	−1.30907	+	1.30907i	−0.922085	+	0.386988i	$0.873515\pi$
$242$	4.23286	−	1.13419i	0.272098	−	0.0729086i
$243$	−10.6374	−	6.14150i	−0.682389	−	0.393977i
$244$	−1.63272	+	2.82796i	−0.104524	+	0.181041i
$245$		0			0
$246$		−	1.68214i		−	0.107249i
$247$	−5.33263	+	6.41038i	−0.339307	+	0.407883i
$248$	−16.6508	−	9.61333i	−1.05732	−	0.610447i
$249$	1.06311	+	0.284859i	0.0673718	+	0.0180522i
$250$			18.9907i			1.20108i
$251$	9.72695	+	16.8476i	0.613960	+	1.06341i	0.990566	+	0.137036i	$0.0437576\pi$
$251$	9.72695	+	16.8476i	0.613960	+	1.06341i	−0.376606	+	0.926373i	$0.622909\pi$
$252$		0			0
$253$	15.6444	+	4.19190i	0.983554	+	0.263543i
$254$	26.9624	−	7.22454i	1.69177	−	0.453308i
$255$	1.26215	+	4.71041i	0.0790389	+	0.294977i
$256$	13.7931			0.862070
$257$	25.2048			1.57223			0.786116	−	0.618080i	$-0.212089\pi$
$257$	25.2048			1.57223			0.786116	+	0.618080i	$0.212089\pi$
$258$	0.558668	+	2.08498i	0.0347812	+	0.129805i
$259$		0			0
$260$	3.25803	−	1.20155i	0.202054	−	0.0745170i
$261$	1.03755	+	1.79708i	0.0642225	+	0.111237i
$262$	−2.29642	+	8.57036i	−0.141873	+	0.529479i
$263$	−15.6393	−	27.0881i	−0.964362	−	1.67032i	−0.711320	−	0.702868i	$-0.751902\pi$
$263$	−15.6393	−	27.0881i	−0.964362	−	1.67032i	−0.253041	−	0.967455i	$-0.581431\pi$
$264$	−1.64382	+	2.84718i	−0.101170	+	0.175232i
$265$	5.33961	+	5.33961i	0.328010	+	0.328010i
$266$		0			0
$267$	1.11281	−	4.15306i	0.0681027	−	0.254163i
$268$	2.56383	−	9.56834i	0.156611	−	0.584479i
$269$		−	9.01798i		−	0.549836i	−0.961468	−	0.274918i	$-0.911349\pi$
$269$		−	9.01798i		−	0.549836i	0.961468	−	0.274918i	$-0.0886507\pi$
$270$	−6.32126	+	3.64958i	−0.384700	+	0.222107i
$271$	−2.40845	+	2.40845i	−0.146303	+	0.146303i	−0.776464	−	0.630161i	$-0.782989\pi$
$271$	−2.40845	+	2.40845i	−0.146303	+	0.146303i	0.630161	+	0.776464i	$0.282989\pi$
$272$	30.2318			1.83308
$273$		0			0
$274$	−2.84575			−0.171918
$275$	−5.43770	+	5.43770i	−0.327906	+	0.327906i
$276$	−1.57872	+	0.911475i	−0.0950279	+	0.0548644i
$277$		−	4.02905i		−	0.242082i	−0.992648	−	0.121041i	$-0.961377\pi$
$277$		−	4.02905i		−	0.242082i	0.992648	−	0.121041i	$-0.0386232\pi$
$278$	−3.46088	+	12.9162i	−0.207570	+	0.774661i
$279$	6.13066	−	22.8799i	0.367033	−	1.36979i
$280$		0			0
$281$	−3.28511	−	3.28511i	−0.195973	−	0.195973i	0.602298	−	0.798271i	$-0.294252\pi$
$281$	−3.28511	−	3.28511i	−0.195973	−	0.195973i	−0.798271	+	0.602298i	$0.794252\pi$
$282$	0.920795	−	1.59486i	0.0548326	−	0.0949728i
$283$	−0.514830	−	0.891711i	−0.0306035	−	0.0530067i	0.850318	−	0.526269i	$-0.176410\pi$
$283$	−0.514830	−	0.891711i	−0.0306035	−	0.0530067i	−0.880921	+	0.473262i	$0.843076\pi$
$284$	−1.74186	+	6.50070i	−0.103360	+	0.385745i
$285$	−0.907206	−	1.57133i	−0.0537383	−	0.0930774i
$286$	15.2985	+	7.05473i	0.904622	+	0.417155i
$287$		0			0
$288$	2.44126	+	9.11089i	0.143852	+	0.536864i
$289$	21.6354			1.27267
$290$	1.87807			0.110284
$291$	−0.479970	−	1.79127i	−0.0281364	−	0.105006i
$292$	−4.23991	+	1.13608i	−0.248122	+	0.0664840i
$293$	−24.6989	−	6.61806i	−1.44293	−	0.386631i	−0.549369	−	0.835580i	$-0.685132\pi$
$293$	−24.6989	−	6.61806i	−1.44293	−	0.386631i	−0.893558	+	0.448948i	$0.851799\pi$
$294$		0			0
$295$	0.672792	+	1.16531i	0.0391715	+	0.0678470i
$296$		−	13.3881i		−	0.778166i
$297$	−8.20236	−	2.19782i	−0.475949	−	0.127530i
$298$	6.25144	+	3.60927i	0.362136	+	0.209079i
$299$	−11.6980	−	16.5561i	−0.676512	−	0.957461i
$300$		−	0.865547i		−	0.0499724i
$301$		0			0
$302$	−7.29993	+	12.6438i	−0.420064	+	0.727571i
$303$	−8.76327	−	5.05947i	−0.503436	−	0.290659i
$304$	−10.8650	+	2.91127i	−0.623151	+	0.166973i
$305$	5.58721	−	5.58721i	0.319922	−	0.319922i
$306$	7.13900	+	26.6431i	0.408109	+	1.52309i
$307$	14.0195	−	14.0195i	0.800136	−	0.800136i	−0.182981	−	0.983117i	$-0.558575\pi$
$307$	14.0195	−	14.0195i	0.800136	−	0.800136i	0.983117	+	0.182981i	$0.0585745\pi$
$308$		0			0
$309$	4.18485	+	2.41612i	0.238068	+	0.137449i
$310$	−15.1590	−	15.1590i	−0.860975	−	0.860975i
$311$	−3.20853	+	5.55733i	−0.181939	+	0.315127i	−0.942541	−	0.334091i	$-0.891571\pi$
$311$	−3.20853	+	5.55733i	−0.181939	+	0.315127i	0.760602	+	0.649219i	$0.224904\pi$
$312$	3.86074	−	1.42383i	0.218572	−	0.0806085i
$313$	21.8008	−	12.5867i	1.23225	−	0.711441i	0.264753	−	0.964316i	$-0.414709\pi$
$313$	21.8008	−	12.5867i	1.23225	−	0.711441i	0.967499	+	0.252875i	$0.0813762\pi$
$314$	7.61824	−	2.04130i	0.429922	−	0.115197i
$315$		0			0
$316$	−4.64154	+	2.67979i	−0.261107	+	0.150750i
$317$	23.2745	+	6.23639i	1.30723	+	0.350271i	0.844178	−	0.536062i	$-0.180089\pi$
$317$	23.2745	+	6.23639i	1.30723	+	0.350271i	0.463049	+	0.886333i	$0.346755\pi$
$318$	−2.91569	−	2.91569i	−0.163504	−	0.163504i
$319$	1.54497	+	1.54497i	0.0865017	+	0.0865017i
$320$	−6.09802	−	1.63396i	−0.340890	−	0.0913411i
$321$	0.0319746	−	0.0184606i	0.00178465	−	0.00103037i
$322$		0			0
$323$	−13.8852	+	3.72052i	−0.772591	+	0.207015i
$324$	−3.65665	+	2.11117i	−0.203147	+	0.117287i
$325$	9.58488	−	0.879683i	0.531673	−	0.0487960i
$326$	5.18123	−	8.97415i	0.286962	−	0.497032i
$327$	2.66185	+	2.66185i	0.147200	+	0.147200i
$328$	3.88088	+	2.24063i	0.214286	+	0.123718i
$329$		0			0
$330$	−2.59210	+	2.59210i	−0.142691	+	0.142691i
$331$	−1.52989	−	5.70964i	−0.0840905	−	0.313830i	0.911050	−	0.412296i	$-0.135273\pi$
$331$	−1.52989	−	5.70964i	−0.0840905	−	0.313830i	−0.995140	+	0.0984660i	$0.968606\pi$
$332$	0.955370	−	0.955370i	0.0524328	−	0.0524328i
$333$	15.9320	−	4.26895i	0.873066	−	0.233937i
$334$	−14.2231	−	8.21169i	−0.778252	−	0.449324i
$335$	−11.9848	+	20.7583i	−0.654799	+	1.13414i
$336$		0			0
$337$			11.5318i			0.628179i	0.949393	+	0.314089i	$0.101699\pi$
$337$			11.5318i			0.628179i	−0.949393	+	0.314089i	$0.898301\pi$
$338$	−9.07366	−	19.0339i	−0.493542	−	1.03531i
$339$	−7.26140	−	4.19237i	−0.394385	−	0.227698i
$340$	5.78244	+	1.54940i	0.313597	+	0.0840280i
$341$		−	24.9407i		−	1.35061i
$342$	−5.13136	−	8.88778i	−0.277472	−	0.480596i
$343$		0			0
$344$	−5.55442	−	1.48830i	−0.299474	−	0.0802439i
$345$	4.26075	−	1.14166i	0.229391	−	0.0614652i
$346$	−7.40855	−	27.6491i	−0.398286	−	1.48642i
$347$	9.07305			0.487067			0.243533	−	0.969893i	$-0.421693\pi$
$347$	9.07305			0.487067			0.243533	+	0.969893i	$0.421693\pi$
$348$	−0.245921			−0.0131827
$349$	7.77792	+	29.0276i	0.416342	+	1.55381i	0.782132	+	0.623113i	$0.214132\pi$
$349$	7.77792	+	29.0276i	0.416342	+	1.55381i	−0.365789	+	0.930698i	$0.619201\pi$
$350$		0			0
$351$	6.13326	+	8.68035i	0.327369	+	0.463323i
$352$	4.96574	+	8.60092i	0.264675	+	0.458431i
$353$	−7.50007	+	27.9907i	−0.399189	+	1.48979i	0.415338	+	0.909667i	$0.363663\pi$
$353$	−7.50007	+	27.9907i	−0.399189	+	1.48979i	−0.814527	+	0.580125i	$0.803004\pi$
$354$	−0.367377	−	0.636316i	−0.0195259	−	0.0338198i
$355$	8.14242	−	14.1031i	0.432155	−	0.748514i
$356$	−3.73217	−	3.73217i	−0.197805	−	0.197805i
$357$		0			0
$358$	−8.48978	+	31.6843i	−0.448699	+	1.67457i
$359$	2.28482	−	8.52708i	0.120588	−	0.450042i	−0.879056	−	0.476719i	$-0.841826\pi$
$359$	2.28482	−	8.52708i	0.120588	−	0.450042i	0.999644	+	0.0266770i	$0.00849258\pi$
$360$		−	9.27487i		−	0.488828i
$361$	−11.8226	+	6.82577i	−0.622241	+	0.359251i
$362$	20.0310	−	20.0310i	1.05280	−	1.05280i
$363$	1.38848			0.0728763
$364$		0			0
$365$	10.6214			0.555947
$366$	−3.05089	+	3.05089i	−0.159472	+	0.159472i
$367$	11.5082	−	6.64427i	0.600724	−	0.346828i	−0.168602	−	0.985684i	$-0.553925\pi$
$367$	11.5082	−	6.64427i	0.600724	−	0.346828i	0.769326	+	0.638856i	$0.220592\pi$
$368$		−	27.3459i		−	1.42550i
$369$	−1.42890	+	5.33274i	−0.0743858	+	0.277611i
$370$	3.86364	−	14.4193i	0.200861	−	0.749624i
$371$		0			0
$372$	1.98497	+	1.98497i	0.102916	+	0.102916i
$373$	4.12496	−	7.14464i	0.213582	−	0.369935i	−0.739251	−	0.673430i	$-0.764820\pi$
$373$	4.12496	−	7.14464i	0.213582	−	0.369935i	0.952833	+	0.303495i	$0.0981535\pi$
$374$	14.5214	+	25.1518i	0.750884	+	1.30057i
$375$	−1.55735	+	5.81212i	−0.0804214	+	0.300137i
$376$	2.45302	+	4.24875i	0.126505	+	0.219113i
$377$	−0.249937	−	2.72327i	−0.0128724	−	0.140256i
$378$		0			0
$379$	0.896568	+	3.34604i	0.0460536	+	0.171874i	0.985122	−	0.171855i	$-0.0549762\pi$
$379$	0.896568	+	3.34604i	0.0460536	+	0.171874i	−0.939069	+	0.343730i	$0.888310\pi$
$380$	−2.22735			−0.114261
$381$	8.84430			0.453107
$382$	0.0174592	+	0.0651586i	0.000893291	+	0.00333381i
$383$	−33.2559	+	8.91088i	−1.69930	+	0.455325i	−0.972762	−	0.231806i	$-0.925537\pi$
$383$	−33.2559	+	8.91088i	−1.69930	+	0.455325i	−0.726534	+	0.687131i	$0.758870\pi$
$384$	6.75272	+	1.80939i	0.344598	+	0.0923348i
$385$		0			0
$386$	−10.1296	−	17.5450i	−0.515584	−	0.893018i
$387$		−	7.08439i		−	0.360120i
$388$	−2.19894	−	0.589205i	−0.111635	−	0.0299124i
$389$	−8.07601	−	4.66269i	−0.409470	−	0.236408i	0.281092	−	0.959681i	$-0.409303\pi$
$389$	−8.07601	−	4.66269i	−0.409470	−	0.236408i	−0.690562	+	0.723273i	$0.742637\pi$
$390$	4.56902	−	0.419337i	0.231362	−	0.0212340i
$391$		−	34.9473i		−	1.76736i
$392$		0			0
$393$	−1.40564	+	2.43465i	−0.0709053	+	0.122812i
$394$	5.22420	+	3.01619i	0.263191	+	0.151954i
$395$	12.5269	−	3.35656i	0.630295	−	0.168887i
$396$	−3.51584	+	3.51584i	−0.176678	+	0.176678i
$397$	5.12022	+	19.1089i	0.256977	+	0.959049i	0.966980	+	0.254852i	$0.0820266\pi$
$397$	5.12022	+	19.1089i	0.256977	+	0.959049i	−0.710004	+	0.704198i	$0.751307\pi$
$398$	10.0667	−	10.0667i	0.504596	−	0.504596i
$399$		0			0
$400$	11.2445	+	6.49199i	0.562223	+	0.324600i
$401$	8.51496	+	8.51496i	0.425217	+	0.425217i	0.886995	−	0.461778i	$-0.152788\pi$
$401$	8.51496	+	8.51496i	0.425217	+	0.425217i	−0.461778	+	0.886995i	$0.652788\pi$
$402$	6.54427	−	11.3350i	0.326399	−	0.565339i
$403$	−19.9637	+	23.9985i	−0.994463	+	1.19545i
$404$	−10.7577	+	6.21095i	−0.535214	+	0.309006i
$405$	9.86881	−	2.64434i	0.490385	−	0.131398i
$406$		0			0
$407$	15.0402	−	8.68346i	0.745514	−	0.430423i
$408$	6.85216	+	1.83603i	0.339232	+	0.0908970i
$409$	13.7865	+	13.7865i	0.681696	+	0.681696i	0.960382	−	0.278686i	$-0.0898988\pi$
$409$	13.7865	+	13.7865i	0.681696	+	0.681696i	−0.278686	+	0.960382i	$0.589899\pi$
$410$	3.53319	+	3.53319i	0.174492	+	0.174492i
$411$	−0.870943	−	0.233368i	−0.0429605	−	0.0115112i
$412$	5.13727	−	2.96600i	0.253095	−	0.146125i
$413$		0			0
$414$	24.0998	−	6.45751i	1.18444	−	0.317369i
$415$	−2.83129	+	1.63465i	−0.138983	+	0.0802417i
$416$	2.10644	−	12.2508i	0.103277	−	0.600645i
$417$	−2.11841	+	3.66919i	−0.103739	+	0.179681i
$418$	−7.64091	−	7.64091i	−0.373729	−	0.373729i
$419$	3.34749	+	1.93268i	0.163536	+	0.0944174i	0.579534	−	0.814948i	$-0.303235\pi$
$419$	3.34749	+	1.93268i	0.163536	+	0.0944174i	−0.415999	+	0.909365i	$0.636568\pi$
$420$		0			0
$421$	3.65782	−	3.65782i	0.178271	−	0.178271i	−0.612331	−	0.790602i	$-0.709768\pi$
$421$	3.65782	−	3.65782i	0.178271	−	0.178271i	0.790602	+	0.612331i	$0.209768\pi$
$422$	2.80148	+	10.4553i	0.136374	+	0.508955i
$423$	−4.27389	+	4.27389i	−0.207803	+	0.207803i
$424$	10.6105	−	2.84309i	0.515293	−	0.138072i
$425$	14.3701	+	8.29658i	0.697052	+	0.402443i
$426$	−4.44616	+	7.70097i	−0.215417	+	0.373113i
$427$		0			0
$428$		−	0.0453239i		−	0.00219081i
$429$	4.10360	+	3.41368i	0.198124	+	0.164814i
$430$	−5.55275	−	3.20588i	−0.267778	−	0.154601i
$431$	9.71910	+	2.60423i	0.468153	+	0.125441i	0.485181	−	0.874414i	$-0.338754\pi$
$431$	9.71910	+	2.60423i	0.468153	+	0.125441i	−0.0170280	+	0.999855i	$0.505420\pi$
$432$			14.3375i			0.689812i
$433$	3.80951	+	6.59826i	0.183073	+	0.317092i	0.942926	−	0.333004i	$-0.108062\pi$
$433$	3.80951	+	6.59826i	0.183073	+	0.317092i	−0.759852	+	0.650096i	$0.774729\pi$
$434$		0			0
$435$	0.574786	+	0.154013i	0.0275589	+	0.00738438i
$436$	4.46369	−	1.19604i	0.213772	−	0.0572800i
$437$	3.36536	+	12.5597i	0.160987	+	0.600811i
$438$	−5.79978			−0.277124
$439$	−22.3628			−1.06732			−0.533658	−	0.845700i	$-0.679183\pi$
$439$	−22.3628			−1.06732			−0.533658	+	0.845700i	$0.679183\pi$
$440$	−2.52756	−	9.43298i	−0.120497	−	0.449700i
$441$		0			0
$442$	6.15988	−	35.8252i	0.292996	−	1.70403i
$443$	−12.8459	−	22.2497i	−0.610326	−	1.05712i	−0.991185	−	0.132483i	$-0.957705\pi$
$443$	−12.8459	−	22.2497i	−0.610326	−	1.05712i	0.380859	−	0.924633i	$-0.375628\pi$
$444$	−0.505917	+	1.88811i	−0.0240097	+	0.0896056i
$445$	6.38578	+	11.0605i	0.302715	+	0.524318i
$446$	5.12185	−	8.87130i	0.242527	−	0.420068i
$447$	1.61727	+	1.61727i	0.0764945	+	0.0764945i
$448$		0			0
$449$	−0.821652	+	3.06645i	−0.0387761	+	0.144715i	−0.982600	−	0.185735i	$-0.940534\pi$
$449$	−0.821652	+	3.06645i	−0.0387761	+	0.144715i	0.943824	+	0.330449i	$0.107200\pi$
$450$	−3.06606	+	11.4427i	−0.144535	+	0.539414i
$451$			5.81305i			0.273726i
$452$	−8.91401	+	5.14650i	−0.419280	+	0.242071i
$453$	−3.27102	+	3.27102i	−0.153686	+	0.153686i
$454$	−38.1954			−1.79260
$455$		0			0
$456$	−2.63940			−0.123601
$457$	−23.2165	+	23.2165i	−1.08602	+	1.08602i	−0.0900871	+	0.995934i	$0.528715\pi$
$457$	−23.2165	+	23.2165i	−1.08602	+	1.08602i	−0.995934	+	0.0900871i	$0.971285\pi$
$458$	−26.5822	+	15.3472i	−1.24210	+	0.717129i
$459$			18.3229i			0.855239i
$460$	1.40149	−	5.23045i	0.0653450	−	0.243871i
$461$	1.38662	−	5.17492i	0.0645811	−	0.241020i	−0.926088	−	0.377307i	$-0.876850\pi$
$461$	1.38662	−	5.17492i	0.0645811	−	0.241020i	0.990669	+	0.136287i	$0.0435169\pi$
$462$		0			0
$463$	−17.0182	−	17.0182i	−0.790903	−	0.790903i	0.190738	−	0.981641i	$-0.438912\pi$
$463$	−17.0182	−	17.0182i	−0.790903	−	0.790903i	−0.981641	+	0.190738i	$0.938912\pi$
$464$	1.84452	−	3.19480i	0.0856295	−	0.148315i
$465$	−3.39630	−	5.88256i	−0.157500	−	0.272797i
$466$	3.08663	−	11.5194i	0.142985	−	0.533628i
$467$	3.73447	+	6.46829i	0.172811	+	0.299317i	0.939401	−	0.342819i	$-0.111382\pi$
$467$	3.73447	+	6.46829i	0.172811	+	0.299317i	−0.766591	+	0.642136i	$0.778049\pi$
$468$	6.19727	−	0.568775i	0.286469	−	0.0262916i
$469$		0			0
$470$	1.41582	+	5.28393i	0.0653071	+	0.243729i
$471$	2.49897			0.115146
$472$	1.95740			0.0900967
$473$	−1.93062	−	7.20516i	−0.0887698	−	0.331294i
$474$	−6.84028	+	1.83285i	−0.314184	+	0.0841854i
$475$	−5.96340	−	1.59789i	−0.273620	−	0.0733162i
$476$		0			0
$477$	6.76661	+	11.7201i	0.309822	+	0.536627i
$478$			9.37376i			0.428746i
$479$	20.1369	+	5.39566i	0.920078	+	0.246534i	0.687619	−	0.726072i	$-0.258656\pi$
$479$	20.1369	+	5.39566i	0.920078	+	0.246534i	0.232459	+	0.972606i	$0.425323\pi$
$480$	2.34246	+	1.35242i	0.106918	+	0.0617293i
$481$	−21.4227	−	3.68347i	−0.976789	−	0.167952i
$482$			46.6164i			2.12332i
$483$		0			0
$484$	0.852240	−	1.47612i	0.0387382	−	0.0670965i
$485$	4.77055	+	2.75428i	0.216620	+	0.125065i
$486$	−19.2442	+	5.15647i	−0.872934	+	0.233902i
$487$	−13.2023	+	13.2023i	−0.598255	+	0.598255i	−0.939848	−	0.341593i	$-0.889034\pi$
$487$	−13.2023	+	13.2023i	−0.598255	+	0.598255i	0.341593	+	0.939848i	$0.389034\pi$
$488$	−2.97492	−	11.1025i	−0.134668	−	0.502588i
$489$	2.32165	−	2.32165i	0.104989	−	0.104989i
$490$		0			0
$491$	26.9636	+	15.5675i	1.21685	+	0.702550i	0.964243	−	0.265019i	$-0.0853781\pi$
$491$	26.9636	+	15.5675i	1.21685	+	0.702550i	0.252609	+	0.967569i	$0.418711\pi$
$492$	−0.462646	−	0.462646i	−0.0208577	−	0.0208577i
$493$	2.35724	−	4.08286i	0.106165	−	0.183883i
$494$	1.23611	+	13.4684i	0.0556150	+	0.605972i
$495$	10.4194	−	6.01565i	0.468317	−	0.270383i
$496$	−40.6752	+	10.8989i	−1.82637	+	0.489374i
$497$		0			0
$498$	1.54602	−	0.892597i	0.0692790	−	0.0399982i
$499$	17.9002	+	4.79636i	0.801325	+	0.214714i	0.636166	−	0.771553i	$-0.280519\pi$
$499$	17.9002	+	4.79636i	0.801325	+	0.214714i	0.165159	+	0.986267i	$0.447186\pi$
$500$	5.22310	+	5.22310i	0.233584	+	0.233584i
$501$	−3.67957	−	3.67957i	−0.164391	−	0.164391i
$502$	30.4791	+	8.16684i	1.36035	+	0.364504i
$503$	22.0368	−	12.7230i	0.982573	−	0.567289i	0.0795268	−	0.996833i	$-0.474659\pi$
$503$	22.0368	−	12.7230i	0.982573	−	0.567289i	0.903046	+	0.429544i	$0.141326\pi$
$504$		0			0
$505$	29.0335	−	7.77950i	1.29197	−	0.346183i
$506$	22.7508	−	13.1352i	1.01140	−	0.583930i
$507$	−1.21611	−	6.56943i	−0.0540091	−	0.291759i
$508$	5.42858	−	9.40257i	0.240854	−	0.417172i
$509$	17.5363	+	17.5363i	0.777285	+	0.777285i	0.979368	−	0.202084i	$-0.0647713\pi$
$509$	17.5363	+	17.5363i	0.777285	+	0.777285i	−0.202084	+	0.979368i	$0.564771\pi$
$510$	6.85009	+	3.95490i	0.303327	+	0.175126i
$511$		0			0
$512$	−3.41779	+	3.41779i	−0.151046	+	0.151046i
$513$	−1.76446	−	6.58505i	−0.0779027	−	0.290737i
$514$	28.9081	−	28.9081i	1.27508	−	1.27508i
$515$	−13.8648	+	3.71506i	−0.610955	+	0.163705i
$516$	0.727094	+	0.419788i	0.0320085	+	0.0184801i
$517$	−3.18204	+	5.51145i	−0.139946	+	0.242393i
$518$		0			0
$519$		−	9.06957i		−	0.398110i
$520$	−5.11853	+	11.0998i	−0.224462	+	0.486758i
$521$	3.53287	+	2.03970i	0.154778	+	0.0893610i	0.575389	−	0.817880i	$-0.304851\pi$
$521$	3.53287	+	2.03970i	0.154778	+	0.0893610i	−0.420611	+	0.907241i	$0.638184\pi$
$522$	3.25112	+	0.871134i	0.142298	+	0.0381285i
$523$			29.4455i			1.28756i	0.765209	+	0.643781i	$0.222635\pi$
$523$			29.4455i			1.28756i	−0.765209	+	0.643781i	$0.777365\pi$
$524$	1.72555	+	2.98874i	0.0753810	+	0.130564i
$525$		0			0
$526$	−49.0053	−	13.1309i	−2.13673	−	0.572536i
$527$	−51.9817	+	13.9285i	−2.26436	+	0.606733i
$528$	1.86365	+	6.95522i	0.0811048	+	0.302687i
$529$	−8.61121			−0.374400
$530$	12.2483			0.532033
$531$	0.624142	+	2.32933i	0.0270854	+	0.101084i
$532$		0			0
$533$	4.65304	−	5.59345i	0.201546	−	0.242279i
$534$	−3.48695	−	6.03957i	−0.150895	−	0.261358i
$535$	−0.0283851	+	0.105935i	−0.00122720	+	0.00457996i
$536$	17.4341	+	30.1967i	0.753038	+	1.30430i
$537$	−5.19661	+	9.00079i	−0.224250	+	0.388413i
$538$	−10.3430	−	10.3430i	−0.445917	−	0.445917i
$539$		0			0
$540$	−0.734804	+	2.74233i	−0.0316209	+	0.118011i
$541$	−9.74099	+	36.3539i	−0.418798	+	1.56298i	0.358307	+	0.933604i	$0.383354\pi$
$541$	−9.74099	+	36.3539i	−0.418798	+	1.56298i	−0.777105	+	0.629371i	$0.783312\pi$
$542$			5.52463i			0.237303i
$543$	7.77315	−	4.48783i	0.333578	−	0.192591i
$544$	15.1530	−	15.1530i	0.649678	−	0.649678i
$545$	−11.1820			−0.478982
$546$		0			0
$547$	−36.7251			−1.57025			−0.785125	−	0.619337i	$-0.787401\pi$
$547$	−36.7251			−1.57025			−0.785125	+	0.619337i	$0.787401\pi$
$548$	−0.782679	+	0.782679i	−0.0334344	+	0.0334344i
$549$	12.2636	−	7.08037i	0.523396	−	0.302183i
$550$			12.4733i			0.531864i
$551$	−0.453995	+	1.69433i	−0.0193408	+	0.0721810i
$552$	1.66076	−	6.19805i	0.0706867	−	0.263806i
$553$		0			0
$554$	−4.62103	−	4.62103i	−0.196329	−	0.196329i
$555$	2.36494	−	4.09620i	0.100386	−	0.173874i
$556$	2.60053	+	4.50425i	0.110287	+	0.191023i
$557$	−5.17843	+	19.3262i	−0.219417	+	0.818876i	0.765148	+	0.643855i	$0.222666\pi$
$557$	−5.17843	+	19.3262i	−0.219417	+	0.818876i	−0.984565	+	0.175021i	$0.944001\pi$
$558$	−19.2102	−	33.2731i	−0.813233	−	1.40856i
$559$	−3.90967	+	8.47832i	−0.165361	+	0.358595i
$560$		0			0
$561$	2.38168	+	8.88857i	0.100555	+	0.375276i
$562$	−7.53556			−0.317869
$563$	−15.6920			−0.661340			−0.330670	−	0.943746i	$-0.607275\pi$
$563$	−15.6920			−0.661340			−0.330670	+	0.943746i	$0.607275\pi$
$564$	−0.185392	−	0.691893i	−0.00780642	−	0.0291340i
$565$	24.0577	−	6.44624i	1.01211	−	0.271195i
$566$	−1.61320	−	0.432256i	−0.0678079	−	0.0181691i
$567$		0			0
$568$	−11.8447	−	20.5155i	−0.496991	−	0.860813i
$569$			5.07533i			0.212769i	0.994325	+	0.106385i	$0.0339275\pi$
$569$			5.07533i			0.212769i	−0.994325	+	0.106385i	$0.966073\pi$
$570$	−2.84270	−	0.761699i	−0.119068	−	0.0319041i
$571$	−17.5642	−	10.1407i	−0.735038	−	0.424374i	0.0852246	−	0.996362i	$-0.472839\pi$
$571$	−17.5642	−	10.1407i	−0.735038	−	0.424374i	−0.820262	+	0.571988i	$0.806173\pi$
$572$	6.14792	−	2.26733i	0.257057	−	0.0948020i
$573$			0.0213736i			0.000892895i
$574$		0			0
$575$	7.50459	−	12.9983i	0.312963	−	0.542068i
$576$	−9.79832	−	5.65706i	−0.408263	−	0.235711i
$577$	25.2962	−	6.77811i	1.05310	−	0.282176i	0.309566	−	0.950878i	$-0.399816\pi$
$577$	25.2962	−	6.77811i	1.05310	−	0.282176i	0.743531	+	0.668702i	$0.233150\pi$
$578$	24.8143	−	24.8143i	1.03214	−	1.03214i
$579$	−1.66138	−	6.20036i	−0.0690446	−	0.257678i
$580$	0.516535	−	0.516535i	0.0214480	−	0.0214480i
$581$		0			0
$582$	−2.60495	−	1.50397i	−0.107979	−	0.0623416i
$583$	10.0759	+	10.0759i	0.417301	+	0.417301i
$584$	7.72537	−	13.3807i	0.319678	−	0.553698i
$585$	−14.8410	−	2.55180i	−0.613599	−	0.105504i
$586$	−35.9183	+	20.7375i	−1.48377	+	0.856657i
$587$	−1.75410	+	0.470009i	−0.0723994	+	0.0193994i	−0.294837	−	0.955548i	$-0.595265\pi$
$587$	−1.75410	+	0.470009i	−0.0723994	+	0.0193994i	0.222438	+	0.974947i	$0.428599\pi$
$588$		0			0
$589$	17.3404	−	10.0115i	0.714498	−	0.412516i
$590$	2.10817	+	0.564883i	0.0867921	+	0.0232559i
$591$	1.35152	+	1.35152i	0.0555942	+	0.0555942i
$592$	−20.7341	−	20.7341i	−0.852166	−	0.852166i
$593$	−30.9506	−	8.29320i	−1.27099	−	0.340561i	−0.440580	−	0.897713i	$-0.645227\pi$
$593$	−30.9506	−	8.29320i	−1.27099	−	0.340561i	−0.830410	+	0.557153i	$0.811894\pi$
$594$	−11.9283	+	6.88679i	−0.489423	+	0.282568i
$595$		0			0
$596$	2.71203	−	0.726687i	0.111089	−	0.0297663i
$597$	3.90644	−	2.25538i	0.159880	−	0.0923067i
$598$	−32.4054	−	5.57186i	−1.32515	−	0.227850i
$599$	1.81349	−	3.14105i	0.0740970	−	0.128340i	−0.826596	−	0.562795i	$-0.809726\pi$
$599$	1.81349	−	3.14105i	0.0740970	−	0.128340i	0.900693	+	0.434456i	$0.143059\pi$
$600$	2.15433	+	2.15433i	0.0879501	+	0.0879501i
$601$	−22.0032	−	12.7035i	−0.897529	−	0.518189i	−0.0211313	−	0.999777i	$-0.506727\pi$
$601$	−22.0032	−	12.7035i	−0.897529	−	0.518189i	−0.876398	+	0.481588i	$0.840060\pi$
$602$		0			0
$603$	−30.3753	+	30.3753i	−1.23698	+	1.23698i
$604$	1.46976	+	5.48522i	0.0598037	+	0.223191i
$605$	−2.91638	+	2.91638i	−0.118568	+	0.118568i
$606$	−15.8537	+	4.24798i	−0.644012	+	0.172563i
$607$	−3.52942	−	2.03771i	−0.143255	−	0.0827081i	0.426660	−	0.904412i	$-0.359690\pi$
$607$	−3.52942	−	2.03771i	−0.143255	−	0.0827081i	−0.569914	+	0.821704i	$0.693024\pi$
$608$	−3.98661	+	6.90502i	−0.161679	+	0.280035i
$609$		0			0
$610$		−	12.8162i		−	0.518915i
$611$	7.47345	−	2.75619i	0.302344	−	0.111503i
$612$	9.29124	+	5.36430i	0.375576	+	0.216839i
$613$	−22.4119	−	6.00524i	−0.905207	−	0.242550i	−0.223956	−	0.974599i	$-0.571897\pi$
$613$	−22.4119	−	6.00524i	−0.905207	−	0.242550i	−0.681251	+	0.732050i	$0.738564\pi$
$614$		−	32.1588i		−	1.29782i
$615$	0.791593	+	1.37108i	0.0319201	+	0.0552872i
$616$		0			0
$617$	0.685439	+	0.183663i	0.0275948	+	0.00739399i	0.272590	−	0.962130i	$-0.412120\pi$
$617$	0.685439	+	0.183663i	0.0275948	+	0.00739399i	−0.244995	+	0.969524i	$0.578786\pi$
$618$	7.57085	−	2.02860i	0.304544	−	0.0816023i
$619$	3.54491	+	13.2298i	0.142482	+	0.531751i	0.999855	+	0.0170541i	$0.00542874\pi$
$619$	3.54491	+	13.2298i	0.142482	+	0.531751i	−0.857372	+	0.514697i	$0.827905\pi$
$620$	−8.33851			−0.334882
$621$	16.5738			0.665083
$622$	2.69391	+	10.0538i	0.108016	+	0.403121i
$623$		0			0
$624$	3.77405	−	8.18422i	0.151083	−	0.327631i
$625$	−2.26294	−	3.91952i	−0.0905174	−	0.156781i
$626$	10.5679	−	39.4399i	0.422378	−	1.57634i
$627$	−1.71190	−	2.96510i	−0.0683669	−	0.118415i
$628$	1.53385	−	2.65671i	0.0612073	−	0.106014i
$629$	−26.4976	−	26.4976i	−1.05653	−	1.05653i
$630$		0			0
$631$	−0.371814	+	1.38763i	−0.0148017	+	0.0552407i	−0.972932	−	0.231093i	$-0.925770\pi$
$631$	−0.371814	+	1.38763i	−0.0148017	+	0.0552407i	0.958130	+	0.286334i	$0.0924365\pi$
$632$	4.88274	−	18.2226i	0.194225	−	0.724858i
$633$			3.42958i			0.136314i
$634$	33.8469	−	19.5415i	1.34423	−	0.776093i
$635$	−18.5767	+	18.5767i	−0.737194	+	0.737194i
$636$	−1.60383			−0.0635960
$637$		0			0
$638$	3.54394			0.140306
$639$	20.6369	−	20.6369i	0.816384	−	0.816384i
$640$	−17.9840	+	10.3830i	−0.710879	+	0.410426i
$641$		−	11.0407i		−	0.436083i	−0.975939	−	0.218042i	$-0.930033\pi$
$641$		−	11.0407i		−	0.436083i	0.975939	−	0.218042i	$-0.0699669\pi$
$642$	0.0154997	−	0.0578455i	0.000611723	−	0.00228298i
$643$	−11.5604	+	43.1441i	−0.455899	+	1.70144i	0.229532	+	0.973301i	$0.426281\pi$
$643$	−11.5604	+	43.1441i	−0.455899	+	1.70144i	−0.685431	+	0.728138i	$0.740386\pi$
$644$		0			0
$645$	−1.43652	−	1.43652i	−0.0565630	−	0.0565630i
$646$	−11.6581	+	20.1924i	−0.458682	+	0.794461i
$647$	5.20304	+	9.01192i	0.204552	+	0.354295i	0.949990	−	0.312280i	$-0.101093\pi$
$647$	5.20304	+	9.01192i	0.204552	+	0.354295i	−0.745438	+	0.666575i	$0.767759\pi$
$648$	3.84668	−	14.3560i	0.151112	−	0.563957i
$649$	1.26956	+	2.19895i	0.0498347	+	0.0863163i
$650$	9.98423	−	12.0021i	0.391614	−	0.470761i
$651$		0			0
$652$	−1.04318	−	3.89321i	−0.0408542	−	0.152470i
$653$	−10.4386			−0.408493			−0.204246	−	0.978920i	$-0.565474\pi$
$653$	−10.4386			−0.408493			−0.204246	+	0.978920i	$0.565474\pi$
$654$	6.10589			0.238759
$655$	−2.16133	−	8.06620i	−0.0844502	−	0.315172i
$656$	9.48038	−	2.54026i	0.370146	−	0.0991804i
$657$	18.3865	+	4.92666i	0.717327	+	0.192207i
$658$		0			0
$659$	−3.86557	−	6.69537i	−0.150581	−	0.260815i	0.780860	−	0.624706i	$-0.214781\pi$
$659$	−3.86557	−	6.69537i	−0.150581	−	0.260815i	−0.931441	+	0.363892i	$0.881448\pi$
$660$			1.42584i			0.0555006i
$661$	−43.2687	−	11.5938i	−1.68296	−	0.450947i	−0.714401	−	0.699737i	$-0.753301\pi$
$661$	−43.2687	−	11.5938i	−1.68296	−	0.450947i	−0.968558	+	0.248790i	$0.919967\pi$
$662$	−8.30322	−	4.79387i	−0.322714	−	0.186319i
$663$	4.82312	−	10.4592i	0.187315	−	0.406201i
$664$			4.75580i			0.184561i
$665$		0			0
$666$	13.3766	−	23.1690i	0.518334	−	0.897780i
$667$	−3.69311	−	2.13222i	−0.142998	−	0.0825597i
$668$	−6.17033	+	1.65334i	−0.238737	+	0.0639695i
$669$	2.29505	−	2.29505i	0.0887316	−	0.0887316i
$670$	10.0625	+	37.5539i	0.388750	+	1.45083i
$671$	10.5431	−	10.5431i	0.407012	−	0.407012i
$672$		0			0
$673$	−19.6804	−	11.3625i	−0.758625	−	0.437992i	0.0701768	−	0.997535i	$-0.477644\pi$
$673$	−19.6804	−	11.3625i	−0.758625	−	0.437992i	−0.828802	+	0.559542i	$0.810977\pi$
$674$	13.2262	+	13.2262i	0.509454	+	0.509454i
$675$	−3.93466	+	6.81503i	−0.151445	+	0.262311i
$676$	−7.73054	−	2.73941i	−0.297329	−	0.105362i
$677$	7.56955	−	4.37028i	0.290921	−	0.167964i	−0.347436	−	0.937704i	$-0.612948\pi$
$677$	7.56955	−	4.37028i	0.290921	−	0.167964i	0.638357	+	0.769740i	$0.279614\pi$
$678$	−13.1367	+	3.51996i	−0.504510	+	0.135183i
$679$		0			0
$680$	−18.2488	+	10.5359i	−0.699809	+	0.404035i
$681$	−11.6897	−	3.13226i	−0.447952	−	0.120028i
$682$	−28.6052	−	28.6052i	−1.09535	−	1.09535i
$683$	1.57793	+	1.57793i	0.0603777	+	0.0603777i	0.736651	−	0.676273i	$-0.236406\pi$
$683$	1.57793	+	1.57793i	0.0603777	+	0.0603777i	−0.676273	+	0.736651i	$0.736406\pi$
$684$	−3.85575	−	1.03314i	−0.147428	−	0.0395032i
$685$	2.31951	−	1.33917i	0.0886240	−	0.0511671i
$686$		0			0
$687$	−9.39407	+	2.51713i	−0.358406	+	0.0960346i
$688$	−10.9071	+	6.29720i	−0.415828	+	0.240078i
$689$	−1.63002	−	17.7605i	−0.0620990	−	0.676620i
$690$	3.57737	−	6.19618i	0.136188	−	0.235885i
$691$	3.25857	+	3.25857i	0.123962	+	0.123962i	0.766366	−	0.642404i	$-0.222063\pi$
$691$	3.25857	+	3.25857i	0.123962	+	0.123962i	−0.642404	+	0.766366i	$0.722063\pi$
$692$	−9.64206	−	5.56685i	−0.366536	−	0.211620i
$693$		0			0
$694$	10.4061	−	10.4061i	0.395012	−	0.395012i
$695$	−3.25729	−	12.1564i	−0.123556	−	0.461117i
$696$	0.612091	−	0.612091i	0.0232013	−	0.0232013i
$697$	12.1156	−	3.24638i	0.458913	−	0.122965i
$698$	42.2133	+	24.3718i	1.59780	+	0.922488i
$699$	1.88933	−	3.27241i	0.0714609	−	0.123774i
$700$		0			0
$701$		−	10.7910i		−	0.407569i	−0.979016	−	0.203784i	$-0.934676\pi$
$701$		−	10.7910i		−	0.407569i	0.979016	−	0.203784i	$-0.0653242\pi$
$702$	16.9901	+	2.92133i	0.641252	+	0.110258i
$703$	12.0746	+	6.97128i	0.455403	+	0.262927i
$704$	−11.5070	−	3.08329i	−0.433686	−	0.116206i
$705$			1.73326i			0.0652782i
$706$	23.5012	+	40.7053i	0.884481	+	1.53197i
$707$		0			0
$708$	−0.276050	−	0.0739674i	−0.0103746	−	0.00277987i
$709$	−22.3737	+	5.99502i	−0.840262	+	0.225148i	−0.653186	−	0.757198i	$-0.726568\pi$
$709$	−22.3737	+	5.99502i	−0.840262	+	0.225148i	−0.187076	+	0.982345i	$0.559901\pi$
$710$	−6.83646	−	25.5140i	−0.256568	−	0.957524i
$711$	23.2421			0.871646
$712$	18.5786			0.696262
$713$	12.5988	+	47.0195i	0.471830	+	1.76090i
$714$		0			0
$715$	−15.7894	+	1.44912i	−0.590490	+	0.0541941i
$716$	6.37929	+	11.0493i	0.238405	+	0.412930i
$717$	−0.768705	+	2.86885i	−0.0287078	+	0.107139i
$718$	−7.15942	−	12.4005i	−0.267187	−	0.462782i
$719$	−17.9493	+	31.0890i	−0.669394	+	1.15942i	0.308679	+	0.951166i	$0.400113\pi$
$719$	−17.9493	+	31.0890i	−0.669394	+	1.15942i	−0.978074	+	0.208259i	$0.933220\pi$
$720$	−14.3640	−	14.3640i	−0.535314	−	0.535314i
$721$		0			0
$722$	−5.73099	+	21.3883i	−0.213285	+	0.795991i
$723$	−3.82283	+	14.2670i	−0.142172	+	0.530595i
$724$		−	11.0184i		−	0.409496i
$725$	1.75351	−	1.01239i	0.0651236	−	0.0375991i
$726$	1.59249	−	1.59249i	0.0591027	−	0.0591027i
$727$	−40.7770			−1.51234			−0.756168	−	0.654377i	$-0.772931\pi$
$727$	−40.7770			−1.51234			−0.756168	+	0.654377i	$0.772931\pi$
$728$		0			0
$729$	13.7655			0.509832
$730$	12.1819	−	12.1819i	0.450874	−	0.450874i
$731$	−13.9389	+	8.04764i	−0.515549	+	0.297653i
$732$			1.67820i			0.0620279i
$733$	6.43098	−	24.0007i	0.237533	−	0.886487i	−0.739457	−	0.673204i	$-0.764918\pi$
$733$	6.43098	−	24.0007i	0.237533	−	0.886487i	0.976990	−	0.213283i	$-0.0684157\pi$
$734$	5.57860	−	20.8196i	0.205910	−	0.768466i
$735$		0			0
$736$	−13.7065	−	13.7065i	−0.505227	−	0.505227i
$737$	−22.6154	+	39.1710i	−0.833048	+	1.44288i
$738$	4.47742	+	7.75512i	0.164816	+	0.285470i
$739$	−10.9878	+	41.0071i	−0.404194	+	1.50847i	0.401344	+	0.915927i	$0.368543\pi$
$739$	−10.9878	+	41.0071i	−0.404194	+	1.50847i	−0.805538	+	0.592544i	$0.798124\pi$
$740$	−2.90317	−	5.02844i	−0.106723	−	0.184849i
$741$	−0.726179	+	4.22338i	−0.0266768	+	0.155150i
$742$		0			0
$743$	−6.30753	−	23.5400i	−0.231401	−	0.863600i	−0.979738	−	0.200282i	$-0.935814\pi$
$743$	−6.30753	−	23.5400i	−0.231401	−	0.863600i	0.748337	−	0.663318i	$-0.230852\pi$
$744$	−9.88108			−0.362258
$745$	−6.79390			−0.248909
$746$	−3.46336	−	12.9254i	−0.126802	−	0.473233i
$747$	−5.65945	+	1.51644i	−0.207068	+	0.0554838i
$748$	10.9115	+	2.92373i	0.398964	+	0.106902i
$749$		0			0
$750$	4.87992	+	8.45226i	0.178189	+	0.308633i
$751$		−	28.4458i		−	1.03800i	−0.854774	−	0.519001i	$-0.826304\pi$
$751$		−	28.4458i		−	1.03800i	0.854774	−	0.519001i	$-0.173696\pi$
$752$	10.3790	+	2.78105i	0.378484	+	0.101415i
$753$	8.65841	+	4.99894i	0.315530	+	0.182171i
$754$	−3.41006	−	2.83674i	−0.124187	−	0.103308i
$755$		−	13.7410i		−	0.500086i
$756$		0			0
$757$	−26.0081	+	45.0474i	−0.945282	+	1.63728i	−0.190095	+	0.981766i	$0.560880\pi$
$757$	−26.0081	+	45.0474i	−0.945282	+	1.63728i	−0.755187	+	0.655510i	$0.772454\pi$
$758$	4.86597	+	2.80937i	0.176740	+	0.102041i
$759$	8.04006	−	2.15433i	0.291836	−	0.0781972i
$760$	5.54383	−	5.54383i	0.201096	−	0.201096i
$761$	−1.53417	−	5.72561i	−0.0556137	−	0.207553i	0.932528	−	0.361098i	$-0.117598\pi$
$761$	−1.53417	−	5.72561i	−0.0556137	−	0.207553i	−0.988142	+	0.153544i	$0.950931\pi$
$762$	10.1438	−	10.1438i	0.367470	−	0.367470i
$763$		0			0
$764$	0.0227228	+	0.0131190i	0.000822080	+	0.000474628i
$765$	−18.3567	−	18.3567i	−0.663690	−	0.663690i
$766$	−27.9220	+	48.3623i	−1.00886	+	1.74740i
$767$	0.538541	−	3.13210i	0.0194456	−	0.113093i
$768$	6.13895	−	3.54433i	0.221520	−	0.127895i
$769$	−0.310861	+	0.0832949i	−0.0112099	+	0.00300369i	−0.264420	−	0.964408i	$-0.585180\pi$
$769$	−0.310861	+	0.0832949i	−0.0112099	+	0.00300369i	0.253210	+	0.967411i	$0.418514\pi$
$770$		0			0
$771$	11.2180	−	6.47670i	0.404005	−	0.233253i
$772$	−7.61148	−	2.03949i	−0.273943	−	0.0734028i
$773$	−22.4820	−	22.4820i	−0.808623	−	0.808623i	0.175802	−	0.984425i	$-0.443748\pi$
$773$	−22.4820	−	22.4820i	−0.808623	−	0.808623i	−0.984425	+	0.175802i	$0.943748\pi$
$774$	−8.12529	−	8.12529i	−0.292057	−	0.292057i
$775$	−22.3251	−	5.98200i	−0.801942	−	0.214880i
$776$	6.93965	−	4.00661i	0.249119	−	0.143829i
$777$		0			0
$778$	−14.6104	+	3.91484i	−0.523807	+	0.140354i
$779$	−4.04161	+	2.33343i	−0.144806	+	0.0836037i
$780$	1.14131	−	1.37197i	0.0408653	−	0.0491244i
$781$	15.3648	−	26.6126i	0.549796	−	0.952274i
$782$	−40.0820	−	40.0820i	−1.43333	−	1.43333i
$783$	1.93630	+	1.11792i	0.0691976	+	0.0399513i
$784$		0			0
$785$	−5.24887	+	5.24887i	−0.187340	+	0.187340i
$786$	1.18019	+	4.40454i	0.0420960	+	0.157105i
$787$	−23.7400	+	23.7400i	−0.846239	+	0.846239i	−0.989662	−	0.143423i	$-0.954189\pi$
$787$	−23.7400	+	23.7400i	−0.846239	+	0.846239i	0.143423	+	0.989662i	$0.454189\pi$
$788$	2.26639	−	0.607277i	0.0807368	−	0.0216334i
$789$	−13.9213	−	8.03746i	−0.495611	−	0.286141i
$790$	10.5177	−	18.2172i	0.374202	−	0.648137i
$791$		0			0
$792$		−	17.5017i		−	0.621897i
$793$	−18.5840	+	1.70561i	−0.659937	+	0.0605678i
$794$	27.7891	+	16.0440i	0.986198	+	0.569382i
$795$	3.74860	+	1.00444i	0.132949	+	0.0356237i
$796$		−	5.53736i		−	0.196267i
$797$	−6.34434	−	10.9887i	−0.224728	−	0.389240i	0.731510	−	0.681831i	$-0.238816\pi$
$797$	−6.34434	−	10.9887i	−0.224728	−	0.389240i	−0.956238	+	0.292591i	$0.905483\pi$
$798$		0			0
$799$	13.2641	+	3.55410i	0.469250	+	0.125735i
$800$	8.88996	−	2.38206i	0.314308	−	0.0842185i
$801$	5.92402	+	22.1087i	0.209315	+	0.781174i
$802$	19.5321			0.689703
$803$	20.0426			0.707287
$804$	−1.31762	−	4.91742i	−0.0464688	−	0.173424i
$805$		0			0
$806$	4.62759	+	50.4215i	0.163000	+	1.77602i
$807$	−2.31729	−	4.01366i	−0.0815724	−	0.141288i
$808$	11.3167	−	42.2346i	0.398121	−	1.48581i
$809$	21.4022	+	37.0698i	0.752463	+	1.30330i	0.946626	+	0.322334i	$0.104467\pi$
$809$	21.4022	+	37.0698i	0.752463	+	1.30330i	−0.194163	+	0.980969i	$0.562199\pi$
$810$	8.28595	−	14.3517i	0.291138	−	0.504267i
$811$	−1.51360	−	1.51360i	−0.0531496	−	0.0531496i	0.680032	−	0.733182i	$-0.261966\pi$
$811$	−1.51360	−	1.51360i	−0.0531496	−	0.0531496i	−0.733182	+	0.680032i	$0.761966\pi$
$812$		0			0
$813$	−0.453053	+	1.69082i	−0.0158893	+	0.0592995i
$814$	7.29072	−	27.2093i	0.255539	−	0.953686i
$815$			9.75286i			0.341628i
$816$	13.4554	−	7.76847i	0.471033	−	0.271951i
$817$	4.23453	−	4.23453i	0.148147	−	0.148147i
$818$	31.6242			1.10571
$819$		0			0
$820$	1.94350			0.0678699
$821$	26.6039	−	26.6039i	0.928481	−	0.928481i	−0.0691268	−	0.997608i	$-0.522021\pi$
$821$	26.6039	−	26.6039i	0.928481	−	0.928481i	0.997608	+	0.0691268i	$0.0220213\pi$
$822$	−1.26657	+	0.731252i	−0.0441766	+	0.0255054i
$823$			44.4969i			1.55107i	0.631308	+	0.775533i	$0.282519\pi$
$823$			44.4969i			1.55107i	−0.631308	+	0.775533i	$0.717481\pi$
$824$	−5.40424	+	20.1689i	−0.188266	+	0.702616i
$825$	−1.02289	+	3.81747i	−0.0356124	+	0.132907i
$826$		0			0
$827$	12.3898	+	12.3898i	0.430835	+	0.430835i	0.888912	−	0.458077i	$-0.151462\pi$
$827$	12.3898	+	12.3898i	0.430835	+	0.430835i	−0.458077	+	0.888912i	$0.651462\pi$
$828$	4.85222	−	8.40430i	0.168626	−	0.292070i
$829$	21.1381	+	36.6122i	0.734155	+	1.27159i	0.955093	+	0.296306i	$0.0957548\pi$
$829$	21.1381	+	36.6122i	0.734155	+	1.27159i	−0.220938	+	0.975288i	$0.570912\pi$
$830$	−1.37247	+	5.12212i	−0.0476390	+	0.177791i
$831$	−1.03532	−	1.79322i	−0.0359147	−	0.0622061i
$832$	8.60428	+	12.1776i	0.298300	+	0.422181i
$833$		0			0
$834$	1.77864	+	6.63796i	0.0615891	+	0.229854i
$835$	15.4573			0.534920
$836$	−4.20302			−0.145365
$837$	−6.60558	−	24.6524i	−0.228322	−	0.852110i
$838$	6.05597	−	1.62269i	0.209200	−	0.0560550i
$839$	−25.6907	−	6.88379i	−0.886940	−	0.237655i	−0.213541	−	0.976934i	$-0.568500\pi$
$839$	−25.6907	−	6.88379i	−0.886940	−	0.237655i	−0.673399	+	0.739279i	$0.735166\pi$
$840$		0			0
$841$	14.2124	+	24.6165i	0.490081	+	0.848846i
$842$		−	8.39052i		−	0.289156i
$843$	−2.30626	−	0.617962i	−0.0794320	−	0.0212837i
$844$	3.64606	+	2.10506i	0.125503	+	0.0724590i
$845$	16.3529	+	11.2442i	0.562555	+	0.386812i
$846$			9.80368i			0.337058i
$847$		0			0
$848$	12.0295	−	20.8356i	0.413093	−	0.715498i
$849$	−0.458274	−	0.264585i	−0.0157279	−	0.00908052i
$850$	25.9971	−	6.96589i	0.891691	−	0.238928i
$851$	−23.9681	+	23.9681i	−0.821616	+	0.821616i
$852$	0.895186	+	3.34088i	0.0306686	+	0.114457i
$853$	0.950856	−	0.950856i	0.0325567	−	0.0325567i	−0.690641	−	0.723198i	$-0.742672\pi$
$853$	0.950856	−	0.950856i	0.0325567	−	0.0325567i	0.723198	+	0.690641i	$0.242672\pi$
$854$		0			0
$855$	8.36494	+	4.82950i	0.286075	+	0.165165i
$856$	0.112810	+	0.112810i	0.00385578	+	0.00385578i
$857$	21.1903	−	36.7026i	0.723845	−	1.25374i	−0.235602	−	0.971850i	$-0.575706\pi$
$857$	21.1903	−	36.7026i	0.723845	−	1.25374i	0.959447	−	0.281887i	$-0.0909605\pi$
$858$	8.62178	−	0.791292i	0.294343	−	0.0270142i
$859$	5.83030	−	3.36613i	0.198927	−	0.114851i	−0.397228	−	0.917720i	$-0.630028\pi$
$859$	5.83030	−	3.36613i	0.198927	−	0.114851i	0.596155	+	0.802869i	$0.296694\pi$
$860$	−2.40893	+	0.645470i	−0.0821437	+	0.0220103i
$861$		0			0
$862$	14.1340	−	8.16026i	0.481405	−	0.277939i
$863$	17.8200	+	4.77484i	0.606598	+	0.162537i	0.549028	−	0.835804i	$-0.314998\pi$
$863$	17.8200	+	4.77484i	0.606598	+	0.162537i	0.0575702	+	0.998341i	$0.481665\pi$
$864$	7.18631	+	7.18631i	0.244483	+	0.244483i
$865$	19.0499	+	19.0499i	0.647715	+	0.647715i
$866$	11.9370	+	3.19850i	0.405634	+	0.108689i
$867$	9.62934	−	5.55950i	0.327030	−	0.188811i
$868$		0			0
$869$	23.6383	−	6.33386i	0.801874	−	0.214861i
$870$	0.835881	−	0.482596i	0.0283390	−	0.0163615i
$871$	53.1153	−	19.5888i	1.79974	−	0.663740i
$872$	−8.13311	+	14.0870i	−0.275422	+	0.477045i
$873$	6.98070	+	6.98070i	0.236261	+	0.236261i
$874$	18.2649	+	10.5452i	0.617819	+	0.356698i
$875$		0			0
$876$	−1.59514	+	1.59514i	−0.0538948	+	0.0538948i
$877$	3.89991	+	14.5547i	0.131691	+	0.491476i	0.999990	−	0.00456529i	$-0.00145318\pi$
$877$	3.89991	+	14.5547i	0.131691	+	0.491476i	−0.868299	+	0.496041i	$0.834787\pi$
$878$	−25.6485	+	25.6485i	−0.865595	+	0.865595i
$879$	−12.6934	+	3.40120i	−0.428139	+	0.114719i
$880$	−18.5233	−	10.6944i	−0.624420	−	0.360509i
$881$	22.3633	−	38.7344i	0.753439	−	1.30500i	−0.192707	−	0.981256i	$-0.561727\pi$
$881$	22.3633	−	38.7344i	0.753439	−	1.30500i	0.946146	−	0.323739i	$-0.104940\pi$
$882$		0			0
$883$			46.5076i			1.56510i	0.622585	+	0.782552i	$0.286083\pi$
$883$			46.5076i			1.56510i	−0.622585	+	0.782552i	$0.713917\pi$
$884$	−8.15899	−	11.5474i	−0.274417	−	0.388380i
$885$	0.598884	+	0.345766i	0.0201313	+	0.0116228i
$886$	−40.2522	−	10.7855i	−1.35230	−	0.362347i
$887$			46.0518i			1.54627i	0.634244	+	0.773133i	$0.281312\pi$
$887$			46.0518i			1.54627i	−0.634244	+	0.773133i	$0.718688\pi$
$888$	−3.44024	−	5.95867i	−0.115447	−	0.199960i
$889$		0			0
$890$	20.0096	+	5.36156i	0.670724	+	0.179720i
$891$	18.6225	−	4.98988i	0.623877	−	0.167167i
$892$	−1.03123	−	3.84860i	−0.0345281	−	0.128861i
$893$	−5.10923			−0.170974
$894$	3.70980			0.124074
$895$	−7.99036	−	29.8204i	−0.267088	−	0.996787i
$896$		0			0
$897$	−9.46076	−	4.36271i	−0.315885	−	0.145667i
$898$	2.57462	+	4.45937i	0.0859161	+	0.148811i
$899$	−1.69962	+	6.34305i	−0.0566854	+	0.211553i
$900$	2.30386	+	3.99041i	0.0767954	+	0.133014i
$901$	15.3733	−	26.6273i	0.512158	−	0.887085i
$902$	6.66715	+	6.66715i	0.221992	+	0.221992i
$903$		0			0
$904$	9.37724	−	34.9963i	0.311882	−	1.16396i
$905$	−6.90054	+	25.7532i	−0.229382	+	0.856064i
$906$			7.50325i			0.249279i
$907$	27.6067	−	15.9387i	0.916666	−	0.529237i	0.0340961	−	0.999419i	$-0.489145\pi$
$907$	27.6067	−	15.9387i	0.916666	−	0.529237i	0.882570	+	0.470181i	$0.155811\pi$
$908$	−10.5051	+	10.5051i	−0.348623	+	0.348623i
$909$	53.8681			1.78669
$910$		0			0
$911$	34.8516			1.15469			0.577343	−	0.816502i	$-0.304090\pi$
$911$	34.8516			1.15469			0.577343	+	0.816502i	$0.304090\pi$
$912$	−4.08763	+	4.08763i	−0.135355	+	0.135355i
$913$	−5.34267	+	3.08459i	−0.176817	+	0.102085i
$914$			53.2553i			1.76153i
$915$	1.05101	−	3.92242i	0.0347453	−	0.129671i
$916$	−3.09000	+	11.5320i	−0.102096	+	0.381029i
$917$		0			0
$918$	21.0150	+	21.0150i	0.693599	+	0.693599i
$919$	1.90511	−	3.29975i	0.0628439	−	0.108849i	−0.832892	−	0.553436i	$-0.813316\pi$
$919$	1.90511	−	3.29975i	0.0628439	−	0.108849i	0.895736	+	0.444587i	$0.146650\pi$
$920$	9.53018	+	16.5068i	0.314201	+	0.544212i
$921$	2.63721	−	9.84221i	0.0868991	−	0.324312i
$922$	−4.34491	−	7.52561i	−0.143092	−	0.247843i
$923$	−36.0864	+	13.3085i	−1.18780	+	0.438056i
$924$		0			0
$925$	−4.16544	−	15.5456i	−0.136959	−	0.511137i
$926$	−39.0373			−1.28285
$927$	−25.7244			−0.844900
$928$	−0.676794	−	2.52583i	−0.0222169	−	0.0829145i
$929$	−36.3444	+	9.73846i	−1.19242	+	0.319509i	−0.799843	−	0.600210i	$-0.795084\pi$
$929$	−36.3444	+	9.73846i	−1.19242	+	0.319509i	−0.392579	+	0.919718i	$0.628417\pi$
$930$	−10.6422	−	2.85157i	−0.348971	−	0.0935065i
$931$		0			0
$932$	−2.31931	−	4.01717i	−0.0759717	−	0.131587i
$933$			3.29789i			0.107968i
$934$	11.7018	+	3.13550i	0.382895	+	0.102597i
$935$	−23.6722	−	13.6672i	−0.774164	−	0.446964i
$936$	−14.0092	+	16.8406i	−0.457906	+	0.550451i
$937$		−	38.0350i		−	1.24255i	−0.783593	−	0.621275i	$-0.786615\pi$
$937$		−	38.0350i		−	1.24255i	0.783593	−	0.621275i	$-0.213385\pi$
$938$		0			0
$939$	6.46863	−	11.2040i	0.211096	−	0.365628i
$940$	1.84266	+	1.06386i	0.0601010	+	0.0346993i
$941$	25.3679	−	6.79732i	0.826971	−	0.221586i	0.179579	−	0.983744i	$-0.442526\pi$
$941$	25.3679	−	6.79732i	0.826971	−	0.221586i	0.647392	+	0.762157i	$0.275860\pi$
$942$	2.86614	−	2.86614i	0.0933838	−	0.0933838i
$943$	−2.93648	−	10.9591i	−0.0956248	−	0.356877i
$944$	3.03143	−	3.03143i	0.0986645	−	0.0986645i
$945$		0			0
$946$	−10.4781	−	6.04952i	−0.340672	−	0.196687i
$947$	−5.51091	−	5.51091i	−0.179081	−	0.179081i	0.611874	−	0.790955i	$-0.290416\pi$
$947$	−5.51091	−	5.51091i	−0.179081	−	0.179081i	−0.790955	+	0.611874i	$0.790416\pi$
$948$	−1.37722	+	2.38541i	−0.0447299	+	0.0774745i
$949$	−19.2854	−	16.0430i	−0.626031	−	0.520779i
$950$	−8.67226	+	5.00693i	−0.281365	+	0.162446i
$951$	11.9614	−	3.20505i	0.387875	−	0.103931i
$952$		0			0
$953$	−7.95143	+	4.59076i	−0.257572	+	0.148709i	−0.623227	−	0.782041i	$-0.714179\pi$
$953$	−7.95143	+	4.59076i	−0.257572	+	0.148709i	0.365654	+	0.930751i	$0.380845\pi$
$954$	21.2029	+	5.68131i	0.686470	+	0.183939i
$955$	−0.0448934	−	0.0448934i	−0.00145272	−	0.00145272i
$956$	2.57811	+	2.57811i	0.0833820	+	0.0833820i
$957$	1.08462	+	0.290624i	0.0350609	+	0.00939455i
$958$	29.2840	−	16.9071i	0.946124	−	0.546245i
$959$		0			0
$960$	−3.13393	+	0.839735i	−0.101147	+	0.0271023i
$961$	38.0702	−	21.9798i	1.22807	−	0.709027i
$962$	−28.7949	+	20.3456i	−0.928386	+	0.655968i
$963$	−0.0982745	+	0.170216i	−0.00316685	+	0.00548515i
$964$	12.8211	+	12.8211i	0.412940	+	0.412940i
$965$	16.5129	+	9.53373i	0.531569	+	0.306902i
$966$		0			0
$967$	29.3315	−	29.3315i	0.943237	−	0.943237i	−0.0552359	−	0.998473i	$-0.517591\pi$
$967$	29.3315	−	29.3315i	0.943237	−	0.943237i	0.998473	+	0.0552359i	$0.0175911\pi$
$968$	1.55283	+	5.79525i	0.0499099	+	0.186266i
$969$	−5.22388	+	5.22388i	−0.167815	+	0.167815i
$970$	8.63045	−	2.31252i	0.277107	−	0.0742506i
$971$	−32.5158	−	18.7730i	−1.04348	−	0.602455i	−0.122665	−	0.992448i	$-0.539144\pi$
$971$	−32.5158	−	18.7730i	−1.04348	−	0.602455i	−0.920818	+	0.389993i	$0.872478\pi$
$972$	−3.87461	+	6.71102i	−0.124278	+	0.215256i
$973$		0			0
$974$			30.2843i			0.970371i
$975$	4.03993	−	2.85448i	0.129381	−	0.0914166i
$976$	−21.8017	−	12.5872i	−0.697857	−	0.402908i
$977$	27.8219	+	7.45485i	0.890101	+	0.238502i	0.674760	−	0.738037i	$-0.264247\pi$
$977$	27.8219	+	7.45485i	0.890101	+	0.238502i	0.215341	+	0.976539i	$0.430914\pi$
$978$		−	5.32554i		−	0.170292i
$979$	12.0500	+	20.8712i	0.385120	+	0.667047i
$980$		0			0
$981$	−19.3570	−	5.18669i	−0.618021	−	0.165598i
$982$	48.7801	−	13.0706i	1.55664	−	0.417099i
$983$	−5.09738	−	19.0237i	−0.162581	−	0.606762i	−0.998336	−	0.0576591i	$-0.981636\pi$
$983$	−5.09738	−	19.0237i	−0.162581	−	0.606762i	0.835755	−	0.549102i	$-0.185030\pi$
$984$	2.30303			0.0734181
$985$	−5.67752			−0.180901
$986$	−1.97916	−	7.38633i	−0.0630293	−	0.235229i
$987$		0			0
$988$	4.04424	+	3.36430i	0.128665	+	0.107033i
$989$	7.27941	+	12.6083i	0.231472	+	0.400921i
$990$	5.05080	−	18.8498i	0.160525	−	0.599087i
$991$	−17.6102	−	30.5018i	−0.559407	−	0.968921i	−0.997546	−	0.0700140i	$-0.977696\pi$
$991$	−17.6102	−	30.5018i	−0.559407	−	0.968921i	0.438139	−	0.898907i	$-0.355638\pi$
$992$	−14.9246	+	25.8502i	−0.473858	+	0.820746i
$993$	−2.14808	−	2.14808i	−0.0681673	−	0.0681673i
$994$		0			0
$995$	−3.46790	+	12.9424i	−0.109940	+	0.410301i
$996$	0.179715	−	0.670705i	0.00569448	−	0.0212521i
$997$			36.6156i			1.15963i	0.814749	+	0.579814i	$0.196875\pi$
$997$			36.6156i			1.15963i	−0.814749	+	0.579814i	$0.803125\pi$
$998$	26.0314	−	15.0292i	0.824009	−	0.475742i
$999$	12.5665	−	12.5665i	0.397586	−	0.397586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bb.a.227.6		28
7.2	even	3		91.2.w.a.19.2	✓	28
7.3	odd	6		637.2.bd.b.97.6		28
7.4	even	3		637.2.bd.a.97.6		28
7.5	odd	6		637.2.x.a.19.2		28
7.6	odd	2		91.2.ba.a.45.6	yes	28
13.11	odd	12		637.2.x.a.570.2		28
21.2	odd	6		819.2.gh.b.19.6		28
21.20	even	2		819.2.et.b.136.2		28
91.11	odd	12		637.2.bd.b.440.6		28
91.24	even	12		637.2.bd.a.440.6		28
91.37	odd	12		91.2.ba.a.89.6	yes	28
91.76	even	12		91.2.w.a.24.2	yes	28
91.89	even	12	inner	637.2.bb.a.362.6		28
273.128	even	12		819.2.et.b.271.2		28
273.167	odd	12		819.2.gh.b.388.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.2	✓	28	7.2	even	3
91.2.w.a.24.2	yes	28	91.76	even	12
91.2.ba.a.45.6	yes	28	7.6	odd	2
91.2.ba.a.89.6	yes	28	91.37	odd	12
637.2.x.a.19.2		28	7.5	odd	6
637.2.x.a.570.2		28	13.11	odd	12
637.2.bb.a.227.6		28	1.1	even	1	trivial
637.2.bb.a.362.6		28	91.89	even	12	inner
637.2.bd.a.97.6		28	7.4	even	3
637.2.bd.a.440.6		28	91.24	even	12
637.2.bd.b.97.6		28	7.3	odd	6
637.2.bd.b.440.6		28	91.11	odd	12
819.2.et.b.136.2		28	21.20	even	2
819.2.et.b.271.2		28	273.128	even	12
819.2.gh.b.19.6		28	21.2	odd	6
819.2.gh.b.388.6		28	273.167	odd	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.14693 - 1.14693i) q^{2} +(0.445073 - 0.256963i) q^{3} -0.630890i q^{4} +(-0.395109 + 1.47457i) q^{5} +(0.215749 - 0.805186i) q^{6} +(1.57027 + 1.57027i) q^{8} +(-1.36794 + 2.36934i) q^{9} +O(q^{10})\)	\(q+(1.14693 - 1.14693i) q^{2} +(0.445073 - 0.256963i) q^{3} -0.630890i q^{4} +(-0.395109 + 1.47457i) q^{5} +(0.215749 - 0.805186i) q^{6} +(1.57027 + 1.57027i) q^{8} +(-1.36794 + 2.36934i) q^{9} +(1.23806 + 2.14439i) q^{10} +(-0.745574 + 2.78252i) q^{11} +(-0.162115 - 0.280792i) q^{12} +(2.94467 - 2.08061i) q^{13} +(0.203057 + 0.757819i) q^{15} +4.86376 q^{16} +6.21574 q^{17} +(1.14854 + 4.28639i) q^{18} +(-2.23387 + 0.598564i) q^{19} +(0.930289 + 0.249270i) q^{20} +(2.33623 + 4.04647i) q^{22} -5.62238i q^{23} +(1.10239 + 0.295384i) q^{24} +(2.31189 + 1.33477i) q^{25} +(0.991014 - 5.76363i) q^{26} +2.94782i q^{27} +(0.379237 - 0.656858i) q^{29} +(1.10206 + 0.636273i) q^{30} +(-8.36292 + 2.24084i) q^{31} +(2.43784 - 2.43784i) q^{32} +(0.383170 + 1.43001i) q^{33} +(7.12901 - 7.12901i) q^{34} +(1.49479 + 0.863019i) q^{36} +(-4.26298 - 4.26298i) q^{37} +(-1.87558 + 3.24860i) q^{38} +(0.775953 - 1.68269i) q^{39} +(-2.93590 + 1.69504i) q^{40} +(1.94919 - 0.522283i) q^{41} +(-2.24252 + 1.29472i) q^{43} +(1.75546 + 0.470375i) q^{44} +(-2.95327 - 2.95327i) q^{45} +(-6.44847 - 6.44847i) q^{46} +(2.13395 + 0.571791i) q^{47} +(2.16473 - 1.24981i) q^{48} +(4.18246 - 1.12069i) q^{50} +(2.76646 - 1.59722i) q^{51} +(-1.31263 - 1.85776i) q^{52} +(2.47328 - 4.28385i) q^{53} +(3.38094 + 3.38094i) q^{54} +(-3.80843 - 2.19880i) q^{55} +(-0.840427 + 0.840427i) q^{57} +(-0.318411 - 1.18833i) q^{58} +(0.623268 - 0.623268i) q^{59} +(0.478100 - 0.128107i) q^{60} +(-4.48249 - 2.58797i) q^{61} +(-7.02159 + 12.1617i) q^{62} +4.13546i q^{64} +(1.90453 + 5.16418i) q^{65} +(2.07959 + 1.20065i) q^{66} +(15.1664 + 4.06383i) q^{67} -3.92145i q^{68} +(-1.44475 - 2.50237i) q^{69} +(-10.3040 - 2.76095i) q^{71} +(-5.86855 + 1.57247i) q^{72} +(-1.80076 - 6.72052i) q^{73} -9.77867 q^{74} +1.37195 q^{75} +(0.377628 + 1.40933i) q^{76} +(-1.03997 - 2.81989i) q^{78} +(-4.24764 - 7.35713i) q^{79} +(-1.92172 + 7.17194i) q^{80} +(-3.34634 - 5.79603i) q^{81} +(1.63656 - 2.83460i) q^{82} +(1.51432 + 1.51432i) q^{83} +(-2.45590 + 9.16553i) q^{85} +(-1.08706 + 4.05696i) q^{86} -0.389800i q^{87} +(-5.54006 + 3.19856i) q^{88} +(5.91573 - 5.91573i) q^{89} -6.77438 q^{90} -3.54710 q^{92} +(-3.14630 + 3.14630i) q^{93} +(3.10329 - 1.79169i) q^{94} -3.53049i q^{95} +(0.458582 - 1.71145i) q^{96} +(0.933928 - 3.48547i) q^{97} +(-5.57284 - 5.57284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

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