LMFDB - Embedded newform 931.2.bj.a.129.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(117,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([15, 13]))

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

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

chi := DirichletCharacter("931.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.bj (of order $18$, degree $6$, 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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 133)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			129.3
Character	$\chi$	$=$	931.129
Dual form			931.2.bj.a.166.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.84540 + 0.325394i) q^{2} +(2.57736 + 0.938083i) q^{3} +(1.42023 - 0.516922i) q^{4} +(0.854536 - 2.34782i) q^{5} +(-5.06151 - 0.892480i) q^{6} +(0.792944 - 0.457807i) q^{8} +(3.46466 + 2.90719i) q^{9} +O(q^{10})$	\(q+(-1.84540 + 0.325394i) q^{2} +(2.57736 + 0.938083i) q^{3} +(1.42023 - 0.516922i) q^{4} +(0.854536 - 2.34782i) q^{5} +(-5.06151 - 0.892480i) q^{6} +(0.792944 - 0.457807i) q^{8} +(3.46466 + 2.90719i) q^{9} +(-0.812995 + 4.61072i) q^{10} +5.95494 q^{11} +4.14536 q^{12} +(-0.144307 + 0.818407i) q^{13} +(4.40490 - 5.24955i) q^{15} +(-3.62990 + 3.04584i) q^{16} +(-2.15947 - 2.57355i) q^{17} +(-7.33966 - 4.23756i) q^{18} +(-1.39034 + 4.13122i) q^{19} -3.77617i q^{20} +(-10.9892 + 1.93770i) q^{22} +(-0.293617 + 1.66519i) q^{23} +(2.47317 - 0.436086i) q^{24} +(-0.951798 - 0.798653i) q^{25} -1.55724i q^{26} +(2.08834 + 3.61710i) q^{27} +(-1.44808 - 3.97856i) q^{29} +(-6.42062 + 11.1208i) q^{30} +(-1.44184 - 2.49735i) q^{31} +(4.53042 - 5.39914i) q^{32} +(15.3480 + 5.58623i) q^{33} +(4.82250 + 4.04655i) q^{34} +(6.42341 + 2.33793i) q^{36} +(5.74728 - 3.31819i) q^{37} +(1.22147 - 8.07615i) q^{38} +(-1.13967 + 1.97396i) q^{39} +(-0.397247 - 2.25290i) q^{40} +(0.0114298 + 0.0648215i) q^{41} +(8.34767 - 7.00453i) q^{43} +(8.45739 - 3.07824i) q^{44} +(9.78624 - 5.65009i) q^{45} -3.16848i q^{46} +(1.20091 - 1.43119i) q^{47} +(-12.2128 + 4.44510i) q^{48} +(2.01632 + 1.16412i) q^{50} +(-3.15152 - 8.65874i) q^{51} +(0.218103 + 1.23692i) q^{52} +(3.10913 + 8.54226i) q^{53} +(-5.03079 - 5.99547i) q^{54} +(5.08871 - 13.9811i) q^{55} +(-7.45884 + 9.34338i) q^{57} +(3.96688 + 6.87084i) q^{58} +(-3.97141 + 3.33241i) q^{59} +(3.54236 - 9.73256i) q^{60} +(-8.30925 - 1.46514i) q^{61} +(3.47340 + 4.13944i) q^{62} +(-1.86509 + 3.23043i) q^{64} +(1.79816 + 1.03817i) q^{65} +(-30.1410 - 5.31467i) q^{66} +(-0.678216 - 0.119588i) q^{67} +(-4.39727 - 2.53876i) q^{68} +(-2.31884 + 4.01635i) q^{69} +(5.06930 + 6.04136i) q^{71} +(4.07822 + 0.719100i) q^{72} +(-3.52159 + 9.67549i) q^{73} +(-9.52630 + 7.99351i) q^{74} +(-1.70392 - 2.95128i) q^{75} +(0.160907 + 6.58598i) q^{76} +(1.46082 - 4.01358i) q^{78} +(-6.71483 - 8.00242i) q^{79} +(4.04921 + 11.1251i) q^{80} +(-0.366871 - 2.08063i) q^{81} +(-0.0421850 - 0.115902i) q^{82} +(8.03504 + 4.63903i) q^{83} +(-7.88758 + 2.87084i) q^{85} +(-13.1256 + 15.6424i) q^{86} -11.6126i q^{87} +(4.72194 - 2.72621i) q^{88} +(1.71992 - 0.626000i) q^{89} +(-16.2210 + 13.6110i) q^{90} +(0.443767 + 2.51673i) q^{92} +(-1.37344 - 7.78914i) q^{93} +(-1.75046 + 3.03188i) q^{94} +(8.51125 + 6.79455i) q^{95} +(16.7414 - 9.66563i) q^{96} +(-8.16455 - 2.97165i) q^{97} +(20.6319 + 17.3122i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 3 q^{2} + 9 q^{3} - 3 q^{4} + 9 q^{5} - 18 q^{8} - 3 q^{9}+O(q^{10}) $ 66 * q - 3 * q^2 + 9 * q^3 - 3 * q^4 + 9 * q^5 - 18 * q^8 - 3 * q^9	$ 66 q - 3 q^{2} + 9 q^{3} - 3 q^{4} + 9 q^{5} - 18 q^{8} - 3 q^{9} + 9 q^{10} - 12 q^{11} - 6 q^{12} + 30 q^{13} + 9 q^{15} - 15 q^{16} - 18 q^{17} + 36 q^{18} - 12 q^{19} - 3 q^{23} + 36 q^{24} - 27 q^{25} - 12 q^{27} - 6 q^{29} + 3 q^{30} + 9 q^{31} + 60 q^{32} + 9 q^{33} + 36 q^{34} + 27 q^{36} - 36 q^{37} - 18 q^{38} + 12 q^{39} - 9 q^{40} - 54 q^{41} + 12 q^{43} + 18 q^{44} + 27 q^{45} - 45 q^{47} - 63 q^{48} - 63 q^{50} - 3 q^{51} - 57 q^{52} + 27 q^{53} + 9 q^{54} + 45 q^{55} - 54 q^{57} + 30 q^{58} - 36 q^{59} - 78 q^{60} + 42 q^{61} + 45 q^{62} - 36 q^{64} + 45 q^{65} - 9 q^{66} + 30 q^{67} + 9 q^{68} - 6 q^{71} - 6 q^{72} - 60 q^{73} + 9 q^{74} + 21 q^{75} - 54 q^{76} + 3 q^{78} + 27 q^{79} + 45 q^{80} + 24 q^{81} + 9 q^{82} - 36 q^{83} - 48 q^{85} - 48 q^{86} - 9 q^{88} + 9 q^{89} + 18 q^{90} + 48 q^{92} - 3 q^{93} - 90 q^{94} - 75 q^{95} - 63 q^{96} + 27 q^{97} + 48 q^{99}+O(q^{100}) $ 66 * q - 3 * q^2 + 9 * q^3 - 3 * q^4 + 9 * q^5 - 18 * q^8 - 3 * q^9 + 9 * q^10 - 12 * q^11 - 6 * q^12 + 30 * q^13 + 9 * q^15 - 15 * q^16 - 18 * q^17 + 36 * q^18 - 12 * q^19 - 3 * q^23 + 36 * q^24 - 27 * q^25 - 12 * q^27 - 6 * q^29 + 3 * q^30 + 9 * q^31 + 60 * q^32 + 9 * q^33 + 36 * q^34 + 27 * q^36 - 36 * q^37 - 18 * q^38 + 12 * q^39 - 9 * q^40 - 54 * q^41 + 12 * q^43 + 18 * q^44 + 27 * q^45 - 45 * q^47 - 63 * q^48 - 63 * q^50 - 3 * q^51 - 57 * q^52 + 27 * q^53 + 9 * q^54 + 45 * q^55 - 54 * q^57 + 30 * q^58 - 36 * q^59 - 78 * q^60 + 42 * q^61 + 45 * q^62 - 36 * q^64 + 45 * q^65 - 9 * q^66 + 30 * q^67 + 9 * q^68 - 6 * q^71 - 6 * q^72 - 60 * q^73 + 9 * q^74 + 21 * q^75 - 54 * q^76 + 3 * q^78 + 27 * q^79 + 45 * q^80 + 24 * q^81 + 9 * q^82 - 36 * q^83 - 48 * q^85 - 48 * q^86 - 9 * q^88 + 9 * q^89 + 18 * q^90 + 48 * q^92 - 3 * q^93 - 90 * q^94 - 75 * q^95 - 63 * q^96 + 27 * q^97 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−1.84540	+	0.325394i	−1.30489	+	0.230088i	−0.782518	−	0.622627i	$-0.786065\pi$
$2$	−1.84540	+	0.325394i	−1.30489	+	0.230088i	−0.522376	+	0.852716i	$0.674954\pi$
$3$	2.57736	+	0.938083i	1.48804	+	0.541602i	0.952933	−	0.303182i	$-0.0980488\pi$
$3$	2.57736	+	0.938083i	1.48804	+	0.541602i	0.535108	+	0.844784i	$0.320271\pi$
$4$	1.42023	−	0.516922i	0.710115	−	0.258461i
$5$	0.854536	−	2.34782i	0.382160	−	1.04998i	−0.588285	−	0.808654i	$-0.700197\pi$
$5$	0.854536	−	2.34782i	0.382160	−	1.04998i	0.970445	−	0.241323i	$-0.0775812\pi$
$6$	−5.06151	−	0.892480i	−2.06635	−	0.364353i
$7$		0			0
$7$		0			0
$8$	0.792944	−	0.457807i	0.280348	−	0.161859i
$9$	3.46466	+	2.90719i	1.15489	+	0.969065i
$10$	−0.812995	+	4.61072i	−0.257091	+	1.45804i
$11$	5.95494			1.79548			0.897742	−	0.440522i	$-0.145207\pi$
$11$	5.95494			1.79548			0.897742	+	0.440522i	$0.145207\pi$
$12$	4.14536			1.19666
$13$	−0.144307	+	0.818407i	−0.0400236	+	0.226985i	−0.998258	−	0.0589985i	$-0.981209\pi$
$13$	−0.144307	+	0.818407i	−0.0400236	+	0.226985i	0.958234	+	0.285984i	$0.0923204\pi$
$14$		0			0
$15$	4.40490	−	5.24955i	1.13734	−	1.35543i
$16$	−3.62990	+	3.04584i	−0.907474	+	0.761461i
$17$	−2.15947	−	2.57355i	−0.523748	−	0.624178i	0.437715	−	0.899114i	$-0.355788\pi$
$17$	−2.15947	−	2.57355i	−0.523748	−	0.624178i	−0.961463	+	0.274936i	$0.911343\pi$
$18$	−7.33966	−	4.23756i	−1.72997	−	0.998801i
$19$	−1.39034	+	4.13122i	−0.318967	+	0.947766i
$19$	−1.39034	+	4.13122i	−0.318967	+	0.947766i
$20$		−	3.77617i		−	0.844378i
$21$		0			0
$22$	−10.9892	+	1.93770i	−2.34292	+	0.413119i
$23$	−0.293617	+	1.66519i	−0.0612235	+	0.347215i	0.938773	+	0.344536i	$0.111964\pi$
$23$	−0.293617	+	1.66519i	−0.0612235	+	0.347215i	−0.999996	+	0.00267907i	$0.999147\pi$
$24$	2.47317	−	0.436086i	0.504833	−	0.0890156i
$25$	−0.951798	−	0.798653i	−0.190360	−	0.159731i
$26$		−	1.55724i		−	0.305401i
$27$	2.08834	+	3.61710i	0.401900	+	0.696112i
$28$		0			0
$29$	−1.44808	−	3.97856i	−0.268901	−	0.738800i	−0.998491	−	0.0549151i	$-0.982511\pi$
$29$	−1.44808	−	3.97856i	−0.268901	−	0.738800i	0.729590	−	0.683885i	$-0.239711\pi$
$30$	−6.42062	+	11.1208i	−1.17224	+	2.03038i
$31$	−1.44184	−	2.49735i	−0.258963	−	0.448537i	0.707001	−	0.707212i	$-0.250047\pi$
$31$	−1.44184	−	2.49735i	−0.258963	−	0.448537i	−0.965964	+	0.258675i	$0.916714\pi$
$32$	4.53042	−	5.39914i	0.800872	−	0.954442i
$33$	15.3480	+	5.58623i	2.67175	+	0.972438i
$34$	4.82250	+	4.04655i	0.827051	+	0.693978i
$35$		0			0
$36$	6.42341	+	2.33793i	1.07057	+	0.389655i
$37$	5.74728	−	3.31819i	0.944847	−	0.545507i	0.0533703	−	0.998575i	$-0.483004\pi$
$37$	5.74728	−	3.31819i	0.944847	−	0.545507i	0.891476	+	0.453067i	$0.149670\pi$
$38$	1.22147	−	8.07615i	0.198148	−	1.31012i
$39$	−1.13967	+	1.97396i	−0.182493	+	0.316087i
$40$	−0.397247	−	2.25290i	−0.0628103	−	0.356215i
$41$	0.0114298	+	0.0648215i	0.00178503	+	0.0101234i	0.985687	−	0.168584i	$-0.0539195\pi$
$41$	0.0114298	+	0.0648215i	0.00178503	+	0.0101234i	−0.983902	+	0.178708i	$0.942808\pi$
$42$		0			0
$43$	8.34767	−	7.00453i	1.27301	−	1.06818i	0.278840	−	0.960338i	$-0.410050\pi$
$43$	8.34767	−	7.00453i	1.27301	−	1.06818i	0.994168	−	0.107843i	$-0.0343942\pi$
$44$	8.45739	−	3.07824i	1.27500	−	0.464062i
$45$	9.78624	−	5.65009i	1.45885	−	0.842266i
$46$		−	3.16848i		−	0.467166i
$47$	1.20091	−	1.43119i	0.175171	−	0.208760i	−0.671314	−	0.741173i	$-0.734270\pi$
$47$	1.20091	−	1.43119i	0.175171	−	0.208760i	0.846485	+	0.532412i	$0.178714\pi$
$48$	−12.2128	+	4.44510i	−1.76277	+	0.641595i
$49$		0			0
$50$	2.01632	+	1.16412i	0.285151	+	0.164632i
$51$	−3.15152	−	8.65874i	−0.441301	−	1.21247i
$52$	0.218103	+	1.23692i	0.0302454	+	0.171530i
$53$	3.10913	+	8.54226i	0.427072	+	1.17337i	0.947582	+	0.319514i	$0.103520\pi$
$53$	3.10913	+	8.54226i	0.427072	+	1.17337i	−0.520510	+	0.853856i	$0.674258\pi$
$54$	−5.03079	−	5.99547i	−0.684604	−	0.815880i
$55$	5.08871	−	13.9811i	0.686162	−	1.88521i
$56$		0			0
$57$	−7.45884	+	9.34338i	−0.987948	+	1.23756i
$58$	3.96688	+	6.87084i	0.520877	+	0.902185i
$59$	−3.97141	+	3.33241i	−0.517033	+	0.433843i	−0.863596	−	0.504184i	$-0.831793\pi$
$59$	−3.97141	+	3.33241i	−0.517033	+	0.433843i	0.346563	+	0.938027i	$0.387349\pi$
$60$	3.54236	−	9.73256i	0.457317	−	1.25647i
$61$	−8.30925	−	1.46514i	−1.06389	−	0.187593i	−0.385808	−	0.922579i	$-0.626077\pi$
$61$	−8.30925	−	1.46514i	−1.06389	−	0.187593i	−0.678082	+	0.734986i	$0.737189\pi$
$62$	3.47340	+	4.13944i	0.441122	+	0.525709i
$63$		0			0
$64$	−1.86509	+	3.23043i	−0.233136	+	0.403803i
$65$	1.79816	+	1.03817i	0.223034	+	0.128769i
$66$	−30.1410	−	5.31467i	−3.71010	−	0.654191i
$67$	−0.678216	−	0.119588i	−0.0828573	−	0.0146100i	0.132066	−	0.991241i	$-0.457839\pi$
$67$	−0.678216	−	0.119588i	−0.0828573	−	0.0146100i	−0.214923	+	0.976631i	$0.568950\pi$
$68$	−4.39727	−	2.53876i	−0.533247	−	0.307870i
$69$	−2.31884	+	4.01635i	−0.279156	+	0.483512i
$70$		0			0
$71$	5.06930	+	6.04136i	0.601616	+	0.716978i	0.977794	−	0.209570i	$-0.0672063\pi$
$71$	5.06930	+	6.04136i	0.601616	+	0.716978i	−0.376178	+	0.926547i	$0.622762\pi$
$72$	4.07822	+	0.719100i	0.480622	+	0.0847467i
$73$	−3.52159	+	9.67549i	−0.412171	+	1.13243i	0.543863	+	0.839174i	$0.316961\pi$
$73$	−3.52159	+	9.67549i	−0.412171	+	1.13243i	−0.956034	+	0.293256i	$0.905261\pi$
$74$	−9.52630	+	7.99351i	−1.10741	+	0.929227i
$75$	−1.70392	−	2.95128i	−0.196752	−	0.340785i
$76$	0.160907	+	6.58598i	0.0184573	+	0.755463i
$77$		0			0
$78$	1.46082	−	4.01358i	0.165406	−	0.454449i
$79$	−6.71483	−	8.00242i	−0.755477	−	0.900343i	0.242076	−	0.970257i	$-0.422172\pi$
$79$	−6.71483	−	8.00242i	−0.755477	−	0.900343i	−0.997553	+	0.0699147i	$0.977727\pi$
$80$	4.04921	+	11.1251i	0.452716	+	1.24383i
$81$	−0.366871	−	2.08063i	−0.0407635	−	0.231181i
$82$	−0.0421850	−	0.115902i	−0.00465855	−	0.0127993i
$83$	8.03504	+	4.63903i	0.881960	+	0.509200i	0.871304	−	0.490744i	$-0.163275\pi$
$83$	8.03504	+	4.63903i	0.881960	+	0.509200i	0.0106557	+	0.999943i	$0.496608\pi$
$84$		0			0
$85$	−7.88758	+	2.87084i	−0.855528	+	0.311387i
$86$	−13.1256	+	15.6424i	−1.41536	+	1.68677i
$87$		−	11.6126i		−	1.24500i
$88$	4.72194	−	2.72621i	0.503360	−	0.290615i
$89$	1.71992	−	0.626000i	0.182311	−	0.0663558i	−0.249252	−	0.968439i	$-0.580185\pi$
$89$	1.71992	−	0.626000i	0.182311	−	0.0663558i	0.431563	+	0.902083i	$0.357962\pi$
$90$	−16.2210	+	13.6110i	−1.70985	+	1.43473i
$91$		0			0
$92$	0.443767	+	2.51673i	0.0462659	+	0.262387i
$93$	−1.37344	−	7.78914i	−0.142419	−	0.807696i
$94$	−1.75046	+	3.03188i	−0.180546	+	0.312715i
$95$	8.51125	+	6.79455i	0.873235	+	0.697106i
$96$	16.7414	−	9.66563i	1.70866	−	0.986495i
$97$	−8.16455	−	2.97165i	−0.828984	−	0.301726i	−0.107542	−	0.994201i	$-0.534298\pi$
$97$	−8.16455	−	2.97165i	−0.828984	−	0.301726i	−0.721442	+	0.692475i	$0.756520\pi$
$98$		0			0
$99$	20.6319	+	17.3122i	2.07358	+	1.73994i
$100$	−1.76461	−	0.642267i	−0.176461	−	0.0642267i
$101$	−1.32709	+	1.58157i	−0.132051	+	0.157372i	−0.828018	−	0.560702i	$-0.810531\pi$
$101$	−1.32709	+	1.58157i	−0.132051	+	0.157372i	0.695967	+	0.718074i	$0.254976\pi$
$102$	8.63331	+	14.9533i	0.854825	+	1.48060i
$103$	2.35870	−	4.08539i	0.232410	−	0.402546i	−0.726107	−	0.687582i	$-0.758672\pi$
$103$	2.35870	−	4.08539i	0.232410	−	0.402546i	0.958517	+	0.285036i	$0.0920056\pi$
$104$	0.260245	+	0.715016i	0.0255191	+	0.0701131i
$105$		0			0
$106$	−8.51718	−	14.7522i	−0.827262	−	1.43286i
$107$			5.34815i			0.517026i	0.966008	+	0.258513i	$0.0832324\pi$
$107$			5.34815i			0.517026i	−0.966008	+	0.258513i	$0.916768\pi$
$108$	4.83568	+	4.05761i	0.465313	+	0.390444i
$109$	−11.9720	+	2.11099i	−1.14671	+	0.202196i	−0.714539	−	0.699596i	$-0.753364\pi$
$109$	−11.9720	+	2.11099i	−1.14671	+	0.202196i	−0.432171	+	0.901792i	$0.642252\pi$
$110$	−4.84134	+	27.4566i	−0.461603	+	2.61788i
$111$	17.9256	−	3.16076i	1.70142	−	0.300006i
$112$		0			0
$113$			13.1973i			1.24150i	0.784008	+	0.620750i	$0.213172\pi$
$113$			13.1973i			1.24150i	−0.784008	+	0.620750i	$0.786828\pi$
$114$	10.7243	−	19.6693i	1.00442	−	1.84220i
$115$	3.65865	+	2.11232i	0.341171	+	0.196975i
$116$	−4.11321	−	4.90193i	−0.381902	−	0.455133i
$117$	−2.87925	+	2.41597i	−0.266186	+	0.223357i
$118$	6.24449	−	7.44189i	0.574852	−	0.685082i
$119$		0			0
$120$	1.08956	−	6.17919i	0.0994626	−	0.564081i
$121$	24.4614			2.22376
$122$	15.8106			1.43143
$123$	−0.0313492	+	0.177790i	−0.00282667	+	0.0160308i
$124$	−3.33868	−	2.80149i	−0.299823	−	0.251581i
$125$	8.13037	−	4.69407i	0.727202	−	0.419850i
$126$		0			0
$127$	−7.55726	−	1.33255i	−0.670598	−	0.118245i	−0.172026	−	0.985092i	$-0.555031\pi$
$127$	−7.55726	−	1.33255i	−0.670598	−	0.118245i	−0.498573	+	0.866848i	$0.666142\pi$
$128$	−2.43050	+	6.67774i	−0.214828	+	0.590234i
$129$	28.0858	−	10.2224i	2.47282	−	0.900031i
$130$	−3.65613	−	1.33072i	−0.320664	−	0.116712i
$131$	−0.750788	+	0.132384i	−0.0655967	+	0.0115665i	−0.206350	−	0.978478i	$-0.566159\pi$
$131$	−0.750788	+	0.132384i	−0.0655967	+	0.0115665i	0.140754	+	0.990045i	$0.455047\pi$
$132$	24.6854			2.14859
$133$		0			0
$134$	1.29049			0.111482
$135$	10.2769	−	1.81209i	0.884491	−	0.155960i
$136$	−2.89053	−	1.05207i	−0.247861	−	0.0902139i
$137$	−0.129452	+	0.0471168i	−0.0110599	+	0.00402546i	−0.347544	−	0.937664i	$-0.612984\pi$
$137$	−0.129452	+	0.0471168i	−0.0110599	+	0.00402546i	0.336484	+	0.941689i	$0.390762\pi$
$138$	2.97229	−	8.16631i	0.253018	−	0.695162i
$139$	2.42098	+	0.426884i	0.205345	+	0.0362078i	0.275374	−	0.961337i	$-0.411198\pi$
$139$	2.42098	+	0.426884i	0.205345	+	0.0362078i	−0.0700296	+	0.997545i	$0.522309\pi$
$140$		0			0
$141$	4.43775	−	2.56214i	0.373726	−	0.215771i
$142$	−11.3207	−	9.49920i	−0.950013	−	0.797155i
$143$	−0.859342	+	4.87357i	−0.0718618	+	0.407548i
$144$	−21.4312			−1.78593
$145$	−10.5784			−0.878486
$146$	3.35040	−	19.0010i	0.277281	−	1.57254i
$147$		0			0
$148$	6.44721	−	7.68349i	0.529958	−	0.631579i
$149$	4.49502	−	3.77177i	0.368246	−	0.308995i	−0.439821	−	0.898085i	$-0.644958\pi$
$149$	4.49502	−	3.77177i	0.368246	−	0.308995i	0.808067	+	0.589090i	$0.200514\pi$
$150$	4.10475	+	4.89185i	0.335151	+	0.399418i
$151$	−1.41973	−	0.819682i	−0.115536	−	0.0667048i	0.441118	−	0.897449i	$-0.354582\pi$
$151$	−1.41973	−	0.819682i	−0.115536	−	0.0667048i	−0.556654	+	0.830744i	$0.687915\pi$
$152$	0.788833	+	3.91233i	0.0639828	+	0.317332i
$153$		−	15.1945i		−	1.22840i
$154$		0			0
$155$	−7.09543	+	1.25112i	−0.569918	+	0.100492i
$156$	−0.598206	+	3.39260i	−0.0478948	+	0.271625i
$157$	−5.53919	+	0.976709i	−0.442076	+	0.0779499i	−0.390256	−	0.920707i	$-0.627613\pi$
$157$	−5.53919	+	0.976709i	−0.442076	+	0.0779499i	−0.0518202	+	0.998656i	$0.516502\pi$
$158$	14.9955	+	12.5827i	1.19298	+	1.00103i
$159$			24.9331i			1.97732i
$160$	−8.80480	−	15.2504i	−0.696081	−	1.20565i
$161$		0			0
$162$	1.35405	+	3.72021i	0.106384	+	0.292288i
$163$	−0.734783	+	1.27268i	−0.0575527	+	0.0996842i	−0.893366	−	0.449329i	$-0.851663\pi$
$163$	−0.734783	+	1.27268i	−0.0575527	+	0.0996842i	0.835814	+	0.549013i	$0.184996\pi$
$164$	0.0497405	+	0.0861531i	0.00388408	+	0.00672743i
$165$	26.2309	−	31.2608i	2.04207	−	2.43365i
$166$	−16.3374	−	5.94631i	−1.26802	−	0.461523i
$167$	−15.5832	−	13.0758i	−1.20586	−	1.01184i	−0.999443	−	0.0333754i	$-0.989374\pi$
$167$	−15.5832	−	13.0758i	−1.20586	−	1.01184i	−0.206420	−	0.978464i	$-0.566181\pi$
$168$		0			0
$169$	11.5670	+	4.21006i	0.889772	+	0.323851i
$170$	13.6216	−	7.86442i	1.04473	−	0.603173i
$171$	−16.8273	+	10.2713i	−1.28682	+	0.785463i
$172$	8.23482	−	14.2631i	0.627899	−	1.08755i
$173$	3.09387	+	17.5462i	0.235223	+	1.33401i	0.842144	+	0.539252i	$0.181293\pi$
$173$	3.09387	+	17.5462i	0.235223	+	1.33401i	−0.606922	+	0.794762i	$0.707596\pi$
$174$	3.77867	+	21.4299i	0.286460	+	1.62460i
$175$		0			0
$176$	−21.6158	+	18.1378i	−1.62935	+	1.36719i
$177$	−13.3618	+	4.86331i	−1.00434	+	0.365549i
$178$	−2.97024	+	1.71487i	−0.222629	+	0.128535i
$179$		−	6.85003i		−	0.511995i	−0.966677	−	0.255998i	$-0.917596\pi$
$179$		−	6.85003i		−	0.511995i	0.966677	−	0.255998i	$-0.0824039\pi$
$180$	10.9781	−	13.0831i	0.818257	−	0.975160i
$181$	−6.54081	+	2.38066i	−0.486175	+	0.176953i	−0.573465	−	0.819230i	$-0.694401\pi$
$181$	−6.54081	+	2.38066i	−0.486175	+	0.176953i	0.0872907	+	0.996183i	$0.472179\pi$
$182$		0			0
$183$	−20.0415	−	11.5710i	−1.48151	−	0.855351i
$184$	0.529511	+	1.45482i	0.0390361	+	0.107251i
$185$	−2.87926	−	16.3291i	−0.211687	−	1.20054i
$186$	5.06907	+	13.9272i	0.371682	+	1.02119i
$187$	−12.8595	−	15.3254i	−0.940380	−	1.12070i
$188$	0.965757	−	2.65339i	0.0704350	−	0.193519i
$189$		0			0
$190$	−17.9175	−	9.76914i	−1.29988	−	0.708728i
$191$	−2.89966	−	5.02236i	−0.209812	−	0.363405i	0.741843	−	0.670573i	$-0.233952\pi$
$191$	−2.89966	−	5.02236i	−0.209812	−	0.363405i	−0.951655	+	0.307168i	$0.900619\pi$
$192$	−7.83742	+	6.57637i	−0.565617	+	0.474609i
$193$	−8.27901	+	22.7464i	−0.595936	+	1.63732i	0.163353	+	0.986568i	$0.447769\pi$
$193$	−8.27901	+	22.7464i	−0.595936	+	1.63732i	−0.759289	+	0.650754i	$0.774453\pi$
$194$	16.0338	+	2.82719i	1.15116	+	0.202981i
$195$	3.66061	+	4.36255i	0.262142	+	0.312409i
$196$		0			0
$197$	4.05822	−	7.02905i	0.289136	−	0.500799i	−0.684467	−	0.729043i	$-0.739965\pi$
$197$	4.05822	−	7.02905i	0.289136	−	0.500799i	0.973604	+	0.228244i	$0.0732986\pi$
$198$	−43.7073	−	25.2344i	−3.10614	−	1.79333i
$199$	24.1063	+	4.25060i	1.70885	+	0.301317i	0.940773	−	0.339038i	$-0.110102\pi$
$199$	24.1063	+	4.25060i	1.70885	+	0.301317i	0.768079	+	0.640355i	$0.221213\pi$
$200$	−1.12035	−	0.197548i	−0.0792208	−	0.0139688i
$201$	−1.63583	−	0.944444i	−0.115382	−	0.0666160i
$202$	1.93439	−	3.35045i	0.136103	−	0.235737i
$203$		0			0
$204$	−8.95178	−	10.6683i	−0.626750	−	0.746931i
$205$	0.161956	+	0.0285572i	0.0113115	+	0.00199452i
$206$	−3.02339	+	8.30669i	−0.210649	+	0.578754i
$207$	−5.85831	+	4.91570i	−0.407181	+	0.341665i
$208$	−1.96892	−	3.41027i	−0.136520	−	0.236460i
$209$	−8.27942	+	24.6012i	−0.572699	+	1.70170i
$210$		0			0
$211$	1.81256	−	4.97996i	0.124782	−	0.342835i	−0.861535	−	0.507699i	$-0.830496\pi$
$211$	1.81256	−	4.97996i	0.124782	−	0.342835i	0.986316	+	0.164864i	$0.0527185\pi$
$212$	8.83136	+	10.5248i	0.606540	+	0.722846i
$213$	7.39813	+	20.3262i	0.506912	+	1.39273i
$214$	−1.74026	−	9.86948i	−0.118961	−	0.674664i
$215$	−9.31197	−	25.5844i	−0.635071	−	1.74484i
$216$	3.31187	+	1.91211i	0.225344	+	0.130102i
$217$		0			0
$218$	21.4062	−	7.79123i	1.44981	−	0.527689i
$219$	−18.1528	+	21.6337i	−1.22665	+	1.46187i
$220$		−	22.4869i		−	1.51607i
$221$	2.41784	−	1.39594i	0.162642	−	0.0939012i
$222$	−32.0513	+	11.6657i	−2.15114	+	0.782952i
$223$	−4.52242	+	3.79476i	−0.302844	+	0.254116i	−0.781527	−	0.623872i	$-0.785559\pi$
$223$	−4.52242	+	3.79476i	−0.302844	+	0.254116i	0.478683	+	0.877988i	$0.341114\pi$
$224$		0			0
$225$	−0.975815	−	5.53412i	−0.0650543	−	0.368941i
$226$	−4.29433	−	24.3543i	−0.285654	−	1.62003i
$227$	−6.58643	+	11.4080i	−0.437157	+	0.757178i	−0.997469	−	0.0711035i	$-0.977348\pi$
$227$	−6.58643	+	11.4080i	−0.437157	+	0.757178i	0.560312	+	0.828282i	$0.310681\pi$
$228$	−5.76348	+	17.1254i	−0.381696	+	1.13416i
$229$	−8.33194	+	4.81045i	−0.550590	+	0.317883i	−0.749360	−	0.662163i	$-0.769639\pi$
$229$	−8.33194	+	4.81045i	−0.550590	+	0.317883i	0.198770	+	0.980046i	$0.436305\pi$
$230$	−7.43900	−	2.70758i	−0.490513	−	0.178532i
$231$		0			0
$232$	−2.96966	−	2.49184i	−0.194968	−	0.163597i
$233$	−7.73968	−	2.81701i	−0.507043	−	0.184549i	0.0758159	−	0.997122i	$-0.475844\pi$
$233$	−7.73968	−	2.81701i	−0.507043	−	0.184549i	−0.582859	+	0.812573i	$0.698066\pi$
$234$	4.52721	−	5.39532i	0.295953	−	0.352703i
$235$	−2.33395	−	4.04252i	−0.152250	−	0.263705i
$236$	−3.91772	+	6.78569i	−0.255022	+	0.441711i
$237$	−9.79961	−	26.9242i	−0.636553	−	1.74891i
$238$		0			0
$239$	−12.7030	−	22.0022i	−0.821686	−	1.42320i	−0.904426	−	0.426631i	$-0.859700\pi$
$239$	−12.7030	−	22.0022i	−0.821686	−	1.42320i	0.0827395	−	0.996571i	$-0.473633\pi$
$240$			32.4720i			2.09606i
$241$	−20.7142	−	17.3813i	−1.33432	−	1.11963i	−0.983047	−	0.183352i	$-0.941305\pi$
$241$	−20.7142	−	17.3813i	−1.33432	−	1.11963i	−0.351271	−	0.936274i	$-0.614250\pi$
$242$	−45.1410	+	7.95957i	−2.90177	+	0.511660i
$243$	3.18206	−	18.0463i	0.204129	−	1.15767i
$244$	−12.5584	+	2.21439i	−0.803970	+	0.141762i
$245$		0			0
$246$		−	0.338295i		−	0.0215689i
$247$	−3.18038	−	1.73403i	−0.202363	−	0.110334i
$248$	−2.28660	−	1.32017i	−0.145200	−	0.0838310i
$249$	16.3574	+	19.4940i	1.03661	+	1.23538i
$250$	−13.4764	+	11.3080i	−0.852319	+	0.715181i
$251$	−15.3004	+	18.2343i	−0.965752	+	1.15094i	0.0227511	+	0.999741i	$0.492757\pi$
$251$	−15.3004	+	18.2343i	−0.965752	+	1.15094i	−0.988504	+	0.151198i	$0.951687\pi$
$252$		0			0
$253$	−1.74848	+	9.91610i	−0.109926	+	0.623420i
$254$	14.3798			0.902266
$255$	−23.0222			−1.44171
$256$	3.60782	−	20.4610i	0.225489	−	1.27881i
$257$	3.33176	+	2.79568i	0.207829	+	0.174389i	0.740761	−	0.671769i	$-0.234465\pi$
$257$	3.33176	+	2.79568i	0.207829	+	0.174389i	−0.532931	+	0.846158i	$0.678910\pi$
$258$	−48.5032	+	28.0033i	−3.01968	+	1.74341i
$259$		0			0
$260$	3.09045	+	0.544929i	0.191661	+	0.0337951i
$261$	6.54935	−	17.9942i	0.405395	−	1.11381i
$262$	1.34243	−	0.488603i	0.0829354	−	0.0301860i
$263$	−18.7659	−	6.83025i	−1.15716	−	0.421171i	−0.309077	−	0.951037i	$-0.600020\pi$
$263$	−18.7659	−	6.83025i	−1.15716	−	0.421171i	−0.848081	+	0.529866i	$0.822242\pi$
$264$	14.7276	−	2.59687i	0.906419	−	0.159826i
$265$	22.7125			1.39522
$266$		0			0
$267$	5.02009			0.307225
$268$	−1.02504	+	0.180742i	−0.0626143	+	0.0110406i
$269$	9.39860	+	3.42081i	0.573043	+	0.208570i	0.612255	−	0.790660i	$-0.290263\pi$
$269$	9.39860	+	3.42081i	0.573043	+	0.208570i	−0.0392123	+	0.999231i	$0.512485\pi$
$270$	−18.3753	+	6.68805i	−1.11828	+	0.407022i
$271$	8.89284	−	24.4329i	0.540202	−	1.48419i	−0.306368	−	0.951913i	$-0.599114\pi$
$271$	8.89284	−	24.4329i	0.540202	−	1.48419i	0.846569	−	0.532279i	$-0.178664\pi$
$272$	15.6773	+	2.76433i	0.950575	+	0.167612i
$273$		0			0
$274$	0.223560	−	0.129072i	0.0135057	−	0.00779754i
$275$	−5.66790	−	4.75593i	−0.341787	−	0.286794i
$276$	−1.21715	+	6.90280i	−0.0732639	+	0.415500i
$277$	−2.41705			−0.145227			−0.0726133	−	0.997360i	$-0.523134\pi$
$277$	−2.41705			−0.145227			−0.0726133	+	0.997360i	$0.523134\pi$
$278$	−4.60657			−0.276284
$279$	2.26478	−	12.8442i	0.135589	−	0.768961i
$280$		0			0
$281$	−1.90037	+	2.26478i	−0.113367	+	0.135105i	−0.819744	−	0.572731i	$-0.805884\pi$
$281$	−1.90037	+	2.26478i	−0.113367	+	0.135105i	0.706377	+	0.707836i	$0.250328\pi$
$282$	−7.35572	+	6.17218i	−0.438027	+	0.367548i
$283$	−11.4903	−	13.6936i	−0.683026	−	0.813999i	0.307467	−	0.951559i	$-0.400519\pi$
$283$	−11.4903	−	13.6936i	−0.683026	−	0.813999i	−0.990493	+	0.137560i	$0.956074\pi$
$284$	10.3225	+	5.95969i	0.612527	+	0.353643i
$285$	15.5627	+	25.4963i	0.921856	+	1.51027i
$286$		−	9.27331i		−	0.548342i
$287$		0			0
$288$	31.3927	−	5.53538i	1.84983	−	0.326176i
$289$	0.992143	−	5.62672i	0.0583614	−	0.330984i
$290$	19.5213	−	3.44213i	1.14633	−	0.202129i
$291$	−18.2553	−	15.3180i	−1.07015	−	0.897960i
$292$			15.5618i			0.910686i
$293$	−13.9063	−	24.0864i	−0.812414	−	1.40714i	−0.911170	−	0.412031i	$-0.864820\pi$
$293$	−13.9063	−	24.0864i	−0.812414	−	1.40714i	0.0987558	−	0.995112i	$-0.468514\pi$
$294$		0			0
$295$	4.43018	+	12.1718i	0.257935	+	0.708670i
$296$	3.03818	−	5.26228i	0.176591	−	0.305864i
$297$	12.4359	+	21.5396i	0.721605	+	1.24986i
$298$	−7.06779	+	8.42306i	−0.409426	+	0.487935i
$299$	−1.32043	−	0.480597i	−0.0763625	−	0.0277937i
$300$	−3.94555	−	3.31071i	−0.227796	−	0.191144i
$301$		0			0
$302$	2.88669	+	1.05067i	0.166110	+	0.0604592i
$303$	−4.90404	+	2.83135i	−0.281730	+	0.162657i
$304$	−7.53624	−	19.2307i	−0.432233	−	1.10295i
$305$	−10.5404	+	18.2566i	−0.603544	+	1.04537i
$306$	4.94419	+	28.0399i	0.282640	+	1.60293i
$307$	5.34757	+	30.3276i	0.305202	+	1.73088i	0.622554	+	0.782577i	$0.286095\pi$
$307$	5.34757	+	30.3276i	0.305202	+	1.73088i	−0.317352	+	0.948308i	$0.602794\pi$
$308$		0			0
$309$	9.91167	−	8.31688i	0.563855	−	0.473131i
$310$	12.6868	−	4.61761i	0.720561	−	0.262263i
$311$	27.4345	−	15.8393i	1.55567	−	0.898164i	0.558002	−	0.829840i	$-0.311568\pi$
$311$	27.4345	−	15.8393i	1.55567	−	0.898164i	0.997663	−	0.0683241i	$-0.0217652\pi$
$312$			2.08699i			0.118152i
$313$	−8.47869	+	10.1045i	−0.479244	+	0.571140i	−0.950448	−	0.310884i	$-0.899375\pi$
$313$	−8.47869	+	10.1045i	−0.479244	+	0.571140i	0.471204	+	0.882024i	$0.343819\pi$
$314$	9.90421	−	3.60484i	0.558927	−	0.203433i
$315$		0			0
$316$	−13.6732	−	7.89424i	−0.769179	−	0.444086i
$317$	2.35364	+	6.46657i	0.132193	+	0.363199i	0.988075	−	0.153973i	$-0.0492070\pi$
$317$	2.35364	+	6.46657i	0.132193	+	0.363199i	−0.855882	+	0.517172i	$0.826985\pi$
$318$	−8.11308	−	46.0115i	−0.454959	−	2.58020i
$319$	−8.62322	−	23.6921i	−0.482808	−	1.32650i
$320$	5.99067	+	7.13941i	0.334889	+	0.399105i
$321$	−5.01701	+	13.7841i	−0.280022	+	0.769355i
$322$		0			0
$323$	13.6343	−	5.34310i	0.758633	−	0.297298i
$324$	−1.59656	−	2.76533i	−0.0886980	−	0.153629i
$325$	0.790975	−	0.663707i	0.0438754	−	0.0368158i
$326$	0.941846	−	2.58770i	0.0521640	−	0.143319i
$327$	−32.8365	−	5.78996i	−1.81586	−	0.320185i
$328$	0.0387389	+	0.0461672i	0.00213900	+	0.00254916i
$329$		0			0
$330$	−38.2344	+	66.2240i	−2.10474	+	3.64551i
$331$	−23.9087	−	13.8037i	−1.31414	−	0.758719i	−0.331361	−	0.943504i	$-0.607508\pi$
$331$	−23.9087	−	13.8037i	−1.31414	−	0.758719i	−0.982779	+	0.184785i	$0.940841\pi$
$332$	13.8096	+	2.43501i	0.757901	+	0.133638i
$333$	29.5590	+	5.21205i	1.61982	+	0.285618i
$334$	33.0120	+	19.0595i	1.80633	+	1.04289i
$335$	−0.860331	+	1.49014i	−0.0470049	+	0.0814149i
$336$		0			0
$337$	−4.69940	−	5.60053i	−0.255993	−	0.305080i	0.622707	−	0.782455i	$-0.286033\pi$
$337$	−4.69940	−	5.60053i	−0.255993	−	0.305080i	−0.878700	+	0.477375i	$0.841588\pi$
$338$	−22.7157	−	4.00539i	−1.23557	−	0.217865i
$339$	−12.3802	+	34.0143i	−0.672400	+	1.84740i
$340$	−9.71818	+	8.15452i	−0.527042	+	0.442241i
$341$	−8.58610	−	14.8716i	−0.464964	−	0.805340i
$342$	27.7109	−	24.4301i	1.49843	−	1.32103i
$343$		0			0
$344$	3.41252	−	9.37582i	0.183991	−	0.505510i
$345$	7.44813	+	8.87634i	0.400994	+	0.477886i
$346$	−11.4189	−	31.3730i	−0.613881	−	1.68663i
$347$	3.53520	+	20.0491i	0.189779	+	1.07629i	0.919659	+	0.392717i	$0.128465\pi$
$347$	3.53520	+	20.0491i	0.189779	+	1.07629i	−0.729880	+	0.683575i	$0.760424\pi$
$348$	−6.00281	−	16.4926i	−0.321784	−	0.884095i
$349$	−6.58470	−	3.80168i	−0.352471	−	0.203499i	0.313302	−	0.949653i	$-0.398565\pi$
$349$	−6.58470	−	3.80168i	−0.352471	−	0.203499i	−0.665773	+	0.746154i	$0.731898\pi$
$350$		0			0
$351$	−3.26163	+	1.18713i	−0.174093	+	0.0633646i
$352$	26.9784	−	32.1516i	1.43795	−	1.71369i
$353$			13.3070i			0.708262i	0.935196	+	0.354131i	$0.115223\pi$
$353$			13.3070i			0.708262i	−0.935196	+	0.354131i	$0.884777\pi$
$354$	23.0754	−	13.3226i	1.22644	−	0.708088i
$355$	18.5159	−	6.73925i	0.982723	−	0.357682i
$356$	2.11909	−	1.77813i	0.112312	−	0.0942406i
$357$		0			0
$358$	2.22895	+	12.6410i	0.117804	+	0.668099i
$359$	4.18271	+	23.7213i	0.220755	+	1.25196i	0.870636	+	0.491928i	$0.163708\pi$
$359$	4.18271	+	23.7213i	0.220755	+	1.25196i	−0.649881	+	0.760036i	$0.725181\pi$
$360$	5.17330	−	8.96041i	0.272657	−	0.472255i
$361$	−15.1339	−	11.4876i	−0.796521	−	0.604611i
$362$	11.2958	−	6.52161i	0.593692	−	0.342768i
$363$	63.0458	+	22.9468i	3.30904	+	1.20439i
$364$		0			0
$365$	19.7070	+	16.5361i	1.03151	+	0.865539i
$366$	40.7497	+	14.8317i	2.13002	+	0.775264i
$367$	−14.0438	+	16.7368i	−0.733081	+	0.873652i	−0.995831	−	0.0912121i	$-0.970926\pi$
$367$	−14.0438	+	16.7368i	−0.733081	+	0.873652i	0.262751	+	0.964864i	$0.415370\pi$
$368$	−4.00610	−	6.93877i	−0.208832	−	0.361708i
$369$	−0.148848	+	0.257813i	−0.00774874	+	0.0134212i
$370$	10.6268	+	29.1968i	0.552459	+	1.51787i
$371$		0			0
$372$	−5.97697	−	10.3524i	−0.309891	−	0.536748i
$373$		−	0.0722462i		−	0.00374077i	−0.999998	−	0.00187038i	$-0.999405\pi$
$373$		−	0.0722462i		−	0.00374077i	0.999998	−	0.00187038i	$-0.000595362\pi$
$374$	28.7177	+	24.0970i	1.48496	+	1.24603i
$375$	25.3583	−	4.47136i	1.30950	−	0.230900i
$376$	0.297047	−	1.68464i	0.0153190	−	0.0868786i
$377$	3.46505	−	0.610982i	0.178459	−	0.0314672i
$378$		0			0
$379$			19.2649i			0.989571i	0.869015	+	0.494785i	$0.164753\pi$
$379$			19.2649i			0.989571i	−0.869015	+	0.494785i	$0.835247\pi$
$380$	15.6002	+	5.25017i	0.800272	+	0.269328i
$381$	−18.2277	−	10.5238i	−0.933836	−	0.539150i
$382$	6.98527	+	8.32472i	0.357397	+	0.425930i
$383$	−1.85143	+	1.55353i	−0.0946036	+	0.0793819i	−0.688863	−	0.724892i	$-0.741890\pi$
$383$	−1.85143	+	1.55353i	−0.0946036	+	0.0793819i	0.594259	+	0.804274i	$0.297445\pi$
$384$	−12.5285	+	14.9309i	−0.639345	+	0.761941i
$385$		0			0
$386$	7.87655	−	44.6701i	0.400906	−	2.27365i
$387$	49.2854			2.50532
$388$	−13.1316			−0.666658
$389$	−2.81394	+	15.9587i	−0.142672	+	0.809136i	0.826534	+	0.562887i	$0.190309\pi$
$389$	−2.81394	+	15.9587i	−0.142672	+	0.809136i	−0.969207	+	0.246249i	$0.920802\pi$
$390$	−8.17484	−	6.85950i	−0.413949	−	0.347344i
$391$	4.91950	−	2.84028i	0.248790	−	0.143639i
$392$		0			0
$393$	−2.05924	−	0.363100i	−0.103875	−	0.0183160i
$394$	−5.20183	+	14.2919i	−0.262065	+	0.720016i
$395$	−24.5263	+	8.92684i	−1.23405	+	0.449158i
$396$	38.2510	+	13.9222i	1.92219	+	0.699619i
$397$	8.07027	−	1.42301i	0.405035	−	0.0714186i	0.0325807	−	0.999469i	$-0.489627\pi$
$397$	8.07027	−	1.42301i	0.405035	−	0.0714186i	0.372454	+	0.928050i	$0.378516\pi$
$398$	−45.8689			−2.29920
$399$		0			0
$400$	5.88750			0.294375
$401$	−14.2250	+	2.50825i	−0.710361	+	0.125256i	−0.517142	−	0.855900i	$-0.673004\pi$
$401$	−14.2250	+	2.50825i	−0.710361	+	0.125256i	−0.193219	+	0.981156i	$0.561893\pi$
$402$	3.32607	+	1.21059i	0.165889	+	0.0603787i
$403$	2.25192	−	0.819631i	0.112176	−	0.0408287i
$404$	−1.06723	+	2.93220i	−0.0530968	+	0.145882i
$405$	−5.19844	−	0.916626i	−0.258313	−	0.0455475i
$406$		0			0
$407$	34.2247	−	19.7596i	1.69646	−	0.979449i
$408$	−6.46301	−	5.42311i	−0.319967	−	0.268484i
$409$	−0.618090	+	3.50536i	−0.0305626	+	0.173329i	−0.996268	−	0.0863100i	$-0.972492\pi$
$409$	−0.618090	+	3.50536i	−0.0305626	+	0.173329i	0.965706	+	0.259639i	$0.0836036\pi$
$410$	−0.308166			−0.0152192
$411$	−0.377845			−0.0186377
$412$	1.23807	−	7.02147i	0.0609955	−	0.345923i
$413$		0			0
$414$	9.21138	−	10.9777i	0.452714	−	0.539524i
$415$	17.7578	−	14.9006i	0.871698	−	0.731441i
$416$	3.76493	+	4.48686i	0.184591	+	0.219987i
$417$	5.83928	+	3.37131i	0.285951	+	0.165094i
$418$	7.27377	−	48.0930i	0.355771	−	2.35231i
$419$		−	21.2892i		−	1.04005i	−0.854152	−	0.520023i	$-0.825924\pi$
$419$		−	21.2892i		−	1.04005i	0.854152	−	0.520023i	$-0.174076\pi$
$420$		0			0
$421$	−20.0541	+	3.53608i	−0.977377	+	0.172338i	−0.639448	−	0.768834i	$-0.720837\pi$
$421$	−20.0541	+	3.53608i	−0.977377	+	0.172338i	−0.337928	+	0.941172i	$0.609726\pi$
$422$	−1.72444	+	9.77981i	−0.0839447	+	0.476074i
$423$	8.32149	−	1.46730i	0.404605	−	0.0713427i
$424$	6.37607	+	5.35016i	0.309649	+	0.259827i
$425$			4.17417i			0.202477i
$426$	−20.2665	−	35.1026i	−0.981916	−	1.70073i
$427$		0			0
$428$	2.76458	+	7.59561i	0.133631	+	0.367148i
$429$	−6.78665	+	11.7548i	−0.327662	+	0.567528i
$430$	25.5093	+	44.1834i	1.23017	+	2.13071i
$431$	−12.9727	+	15.4602i	−0.624871	+	0.744693i	−0.981900	−	0.189401i	$-0.939345\pi$
$431$	−12.9727	+	15.4602i	−0.624871	+	0.744693i	0.357028	+	0.934094i	$0.383790\pi$
$432$	−18.5976	−	6.76896i	−0.894776	−	0.325672i
$433$	10.8336	+	9.09050i	0.520631	+	0.436862i	0.864852	−	0.502027i	$-0.167412\pi$
$433$	10.8336	+	9.09050i	0.520631	+	0.436862i	−0.344220	+	0.938889i	$0.611857\pi$
$434$		0			0
$435$	−27.2643	−	9.92339i	−1.30722	−	0.475790i
$436$	−15.9118	+	9.18668i	−0.762037	+	0.439962i
$437$	−6.47102	−	3.52818i	−0.309551	−	0.168776i
$438$	26.4597	−	45.8296i	1.26429	−	2.18982i
$439$	0.294279	+	1.66894i	0.0140451	+	0.0796540i	0.991025	−	0.133679i	$-0.0426791\pi$
$439$	0.294279	+	1.66894i	0.0140451	+	0.0796540i	−0.976980	+	0.213333i	$0.931568\pi$
$440$	−2.36559	−	13.4159i	−0.112775	−	0.639578i
$441$		0			0
$442$	−4.00765	+	3.36282i	−0.190625	+	0.159953i
$443$	−36.6501	+	13.3395i	−1.74130	+	0.633780i	−0.999328	−	0.0366545i	$-0.988330\pi$
$443$	−36.6501	+	13.3395i	−1.74130	+	0.633780i	−0.741969	+	0.670435i	$0.766108\pi$
$444$	23.8245	−	13.7551i	1.13066	−	0.652789i
$445$		−	4.57300i		−	0.216781i
$446$	7.11088	−	8.47442i	0.336710	−	0.401275i
$447$	15.1235	−	5.50451i	0.715318	−	0.260354i
$448$		0			0
$449$	8.99854	+	5.19531i	0.424667	+	0.245182i	0.697072	−	0.717001i	$-0.254486\pi$
$449$	8.99854	+	5.19531i	0.424667	+	0.245182i	−0.272405	+	0.962183i	$0.587819\pi$
$450$	3.60154	+	9.89514i	0.169778	+	0.466461i
$451$	0.0680637	+	0.386008i	0.00320499	+	0.0181764i
$452$	6.82198	+	18.7432i	0.320879	+	0.881608i
$453$	−2.89023	−	3.44444i	−0.135795	−	0.161834i
$454$	8.44250	−	23.1956i	0.396226	−	1.08862i
$455$		0			0
$456$	−1.63698	+	10.8235i	−0.0766588	+	0.506856i
$457$	−8.14231	−	14.1029i	−0.380881	−	0.659706i	0.610307	−	0.792165i	$-0.291046\pi$
$457$	−8.14231	−	14.1029i	−0.380881	−	0.659706i	−0.991188	+	0.132459i	$0.957713\pi$
$458$	13.8105	−	11.5884i	0.645320	−	0.541488i
$459$	4.79911	−	13.1855i	0.224003	−	0.615444i
$460$	6.28803	+	1.10875i	0.293181	+	0.0516957i
$461$	3.91224	+	4.66242i	0.182211	+	0.217151i	0.849416	−	0.527723i	$-0.176954\pi$
$461$	3.91224	+	4.66242i	0.182211	+	0.217151i	−0.667205	+	0.744874i	$0.732510\pi$
$462$		0			0
$463$	−15.7937	+	27.3555i	−0.733996	+	1.27132i	0.221166	+	0.975236i	$0.429014\pi$
$463$	−15.7937	+	27.3555i	−0.733996	+	1.27132i	−0.955162	+	0.296082i	$0.904320\pi$
$464$	17.3744	+	10.0311i	0.806588	+	0.465684i
$465$	−19.4611	−	3.43152i	−0.902488	−	0.159133i
$466$	15.1994	+	2.68007i	0.704100	+	0.124152i
$467$	−9.92214	−	5.72855i	−0.459142	−	0.265086i	0.252541	−	0.967586i	$-0.418734\pi$
$467$	−9.92214	−	5.72855i	−0.459142	−	0.265086i	−0.711683	+	0.702500i	$0.752067\pi$
$468$	−2.84032	+	4.91958i	−0.131294	+	0.227408i
$469$		0			0
$470$	5.62248	+	6.70061i	0.259346	+	0.309076i
$471$	−15.1927	−	2.67889i	−0.700045	−	0.123437i
$472$	−1.62351	+	4.46055i	−0.0747280	+	0.205314i
$473$	49.7099	−	41.7116i	2.28566	−	1.91790i
$474$	26.8451	+	46.4971i	1.23304	+	2.13568i
$475$	4.62273	−	2.82168i	0.212106	−	0.129468i
$476$		0			0
$477$	−14.0619	+	38.6349i	−0.643852	+	1.76897i
$478$	30.6014	+	36.4693i	1.39968	+	1.66807i
$479$	−8.62844	−	23.7065i	−0.394244	−	1.08318i	−0.965044	−	0.262087i	$-0.915589\pi$
$479$	−8.62844	−	23.7065i	−0.394244	−	1.08318i	0.570801	−	0.821089i	$-0.306633\pi$
$480$	−8.38705	−	47.5653i	−0.382815	−	2.17105i
$481$	1.88626	+	5.18245i	0.0860060	+	0.236300i
$482$	43.8817	+	25.3351i	1.99876	+	1.15398i
$483$		0			0
$484$	34.7408	−	12.6446i	1.57913	−	0.574755i
$485$	−13.9538	+	16.6295i	−0.633609	+	0.755106i
$486$			34.3381i			1.55761i
$487$	11.3453	−	6.55023i	0.514106	−	0.296819i	−0.220414	−	0.975406i	$-0.570741\pi$
$487$	11.3453	−	6.55023i	0.514106	−	0.296819i	0.734520	+	0.678587i	$0.237407\pi$
$488$	−7.25953	+	2.64225i	−0.328623	+	0.119609i
$489$	−3.08768	+	2.59087i	−0.139630	+	0.117163i
$490$		0			0
$491$	−0.369555	−	2.09585i	−0.0166778	−	0.0945844i	0.975333	−	0.220740i	$-0.0708472\pi$
$491$	−0.369555	−	2.09585i	−0.0166778	−	0.0945844i	−0.992010	+	0.126156i	$0.959736\pi$
$492$	0.0473805	+	0.268708i	0.00213608	+	0.0121143i
$493$	−7.11196	+	12.3183i	−0.320307	+	0.554787i
$494$	6.43331	+	2.16510i	0.289448	+	0.0974127i
$495$	58.2765	−	33.6460i	2.61934	−	1.51227i
$496$	12.8403	+	4.67348i	0.576546	+	0.209845i
$497$		0			0
$498$	−36.5291	−	30.6516i	−1.63691	−	1.37353i
$499$	12.2986	+	4.47632i	0.550561	+	0.200388i	0.602296	−	0.798273i	$-0.294253\pi$
$499$	12.2986	+	4.47632i	0.550561	+	0.200388i	−0.0517350	+	0.998661i	$0.516475\pi$
$500$	9.12053	−	10.8694i	0.407883	−	0.486095i
$501$	−27.8973	−	48.3195i	−1.24636	−	2.15876i
$502$	22.3020	−	38.6282i	0.995387	−	1.72406i
$503$	−7.02082	−	19.2895i	−0.313043	−	0.860078i	−0.992038	−	0.125936i	$-0.959807\pi$
$503$	−7.02082	−	19.2895i	−0.313043	−	0.860078i	0.678996	−	0.734142i	$-0.262416\pi$
$504$		0			0
$505$	2.57919	+	4.46728i	0.114772	+	0.198792i
$506$		−	18.8681i		−	0.838789i
$507$	25.8631	+	21.7017i	1.14862	+	0.963805i
$508$	−11.4219	+	2.01398i	−0.506764	+	0.0893561i
$509$	−1.73629	+	9.84698i	−0.0769596	+	0.436460i	0.921844	+	0.387561i	$0.126682\pi$
$509$	−1.73629	+	9.84698i	−0.0769596	+	0.436460i	−0.998804	+	0.0488989i	$0.984429\pi$
$510$	42.4852	−	7.49129i	1.88128	−	0.331720i
$511$		0			0
$512$			24.7200i			1.09248i
$513$	−17.8465	+	3.59835i	−0.787944	+	0.158871i
$514$	−7.05811	−	4.07500i	−0.311320	−	0.179741i
$515$	−7.57617	−	9.02892i	−0.333846	−	0.397862i
$516$	34.6041	−	29.0363i	1.52336	−	1.27825i
$517$	7.15135	−	8.52265i	0.314516	−	0.374826i
$518$		0			0
$519$	−8.48578	+	48.1253i	−0.372484	+	2.11246i
$520$	1.90112			0.0833695
$521$	11.8011			0.517017			0.258508	−	0.966009i	$-0.416769\pi$
$521$	11.8011			0.517017			0.258508	+	0.966009i	$0.416769\pi$
$522$	−6.23097	+	35.3376i	−0.272722	+	1.54668i
$523$	−2.02944	−	1.70290i	−0.0887412	−	0.0744627i	0.597338	−	0.801990i	$-0.296225\pi$
$523$	−2.02944	−	1.70290i	−0.0887412	−	0.0744627i	−0.686079	+	0.727527i	$0.740670\pi$
$524$	−0.997860	+	0.576115i	−0.0435917	+	0.0251677i
$525$		0			0
$526$	36.8532	+	6.49821i	1.60687	+	0.283335i
$527$	−3.31344	+	9.10360i	−0.144336	+	0.396559i
$528$	−72.7266	+	26.4703i	−3.16502	+	1.15197i
$529$	18.9263	+	6.88861i	0.822882	+	0.299505i
$530$	−41.9137	+	7.39051i	−1.82061	+	0.321023i
$531$	−23.4475			−1.01754
$532$		0			0
$533$	−0.0546998			−0.00236931
$534$	−9.26408	+	1.63351i	−0.400896	+	0.0706887i
$535$	12.5565	+	4.57019i	0.542865	+	0.197587i
$536$	−0.592536	+	0.215665i	−0.0255937	+	0.00931533i
$537$	6.42589	−	17.6550i	0.277298	−	0.761869i
$538$	−18.4573	−	3.25451i	−0.795749	−	0.140312i
$539$		0			0
$540$	13.6588	−	7.88591i	0.587781	−	0.339356i
$541$	−15.7897	−	13.2492i	−0.678853	−	0.569626i	0.236818	−	0.971554i	$-0.423896\pi$
$541$	−15.7897	−	13.2492i	−0.678853	−	0.569626i	−0.915671	+	0.401928i	$0.868340\pi$
$542$	−8.46054	+	47.9821i	−0.363411	+	2.06101i
$543$	−19.0913			−0.819286
$544$	−23.6783			−1.01520
$545$	−5.27430	+	29.9120i	−0.225926	+	1.28129i
$546$		0			0
$547$	−16.1337	+	19.2274i	−0.689828	+	0.822105i	−0.991335	−	0.131359i	$-0.958066\pi$
$547$	−16.1337	+	19.2274i	−0.689828	+	0.822105i	0.301507	+	0.953464i	$0.402510\pi$
$548$	−0.159496	+	0.133833i	−0.00681335	+	0.00571708i
$549$	−24.5293	−	29.2328i	−1.04688	−	1.24763i
$550$	12.0071	+	6.93230i	0.511984	+	0.295594i
$551$	18.4496	−	0.450756i	0.785980	−	0.0192029i
$552$			4.24632i			0.180736i
$553$		0			0
$554$	4.46042	−	0.786493i	0.189505	−	0.0334149i
$555$	7.89714	−	44.7869i	0.335215	−	1.90110i
$556$	3.65901	−	0.645182i	0.155177	−	0.0273618i
$557$	−21.3231	−	17.8922i	−0.903487	−	0.758116i	0.0673818	−	0.997727i	$-0.478535\pi$
$557$	−21.3231	−	17.8922i	−0.903487	−	0.758116i	−0.970869	+	0.239612i	$0.922980\pi$
$558$			24.4396i			1.03461i
$559$	4.52793	+	7.84260i	0.191511	+	0.331707i
$560$		0			0
$561$	−18.7671	−	51.5623i	−0.792349	−	2.17696i
$562$	2.77000	−	4.79779i	0.116846	−	0.202382i
$563$	9.56314	+	16.5638i	0.403038	+	0.698082i	0.994091	−	0.108550i	$-0.0346209\pi$
$563$	9.56314	+	16.5638i	0.403038	+	0.698082i	−0.591053	+	0.806633i	$0.701288\pi$
$564$	4.97821	−	5.93280i	0.209620	−	0.249816i
$565$	30.9849	+	11.2776i	1.30355	+	0.474452i
$566$	25.6599	+	21.5313i	1.07857	+	0.905026i
$567$		0			0
$568$	6.78545	+	2.46970i	0.284711	+	0.103626i
$569$	37.2818	−	21.5246i	1.56293	−	0.902359i	0.565974	−	0.824423i	$-0.308500\pi$
$569$	37.2818	−	21.5246i	1.56293	−	0.902359i	0.996958	−	0.0779363i	$-0.0248331\pi$
$570$	−37.0157	−	41.9868i	−1.55042	−	1.75863i
$571$	4.02236	−	6.96693i	0.168330	−	0.291557i	−0.769503	−	0.638644i	$-0.779496\pi$
$571$	4.02236	−	6.96693i	0.168330	−	0.291557i	0.937833	+	0.347087i	$0.112829\pi$
$572$	1.29879	+	7.36581i	0.0543051	+	0.307980i
$573$	−2.76208	−	15.6645i	−0.115388	−	0.654396i
$574$		0			0
$575$	1.60937	−	1.35042i	0.0671154	−	0.0563165i
$576$	−15.8534	+	5.77016i	−0.660558	+	0.240423i
$577$	1.02666	−	0.592741i	0.0427403	−	0.0246761i	−0.478478	−	0.878100i	$-0.658811\pi$
$577$	1.02666	−	0.592741i	0.0427403	−	0.0246761i	0.521218	+	0.853424i	$0.325478\pi$
$578$			10.7064i			0.445327i
$579$	−42.6760	+	50.8593i	−1.77355	+	2.11364i
$580$	−15.0237	+	5.46819i	−0.623826	+	0.227054i
$581$		0			0
$582$	38.6728	+	22.3277i	1.60304	+	0.925514i
$583$	18.5147	+	50.8687i	0.766800	+	2.10677i
$584$	1.63708	+	9.28433i	0.0677428	+	0.384188i
$585$	3.21185	+	8.82448i	0.132794	+	0.364847i
$586$	33.5002	+	39.9240i	1.38388	+	1.64925i
$587$	−1.48615	+	4.08315i	−0.0613398	+	0.168530i	−0.966577	−	0.256377i	$-0.917471\pi$
$587$	−1.48615	+	4.08315i	−0.0613398	+	0.168530i	0.905237	+	0.424907i	$0.139693\pi$
$588$		0			0
$589$	12.3217	−	2.48440i	0.507709	−	0.102368i
$590$	−12.1361	−	21.0203i	−0.499634	−	0.865392i
$591$	17.0533	−	14.3094i	0.701481	−	0.588612i
$592$	−10.7553	+	29.5500i	−0.442041	+	1.21450i
$593$	41.2649	+	7.27612i	1.69455	+	0.298794i	0.935784	−	0.352573i	$-0.114693\pi$
$593$	41.2649	+	7.27612i	1.69455	+	0.298794i	0.758762	+	0.651368i	$0.225804\pi$
$594$	−29.9581	−	35.7027i	−1.22920	−	1.46490i
$595$		0			0
$596$	4.43425	−	7.68035i	0.181634	−	0.314599i
$597$	58.1433	+	33.5691i	2.37965	+	1.37389i
$598$	2.59310	+	0.457234i	0.106040	+	0.0186977i
$599$	−20.2318	−	3.56740i	−0.826647	−	0.145760i	−0.255710	−	0.966754i	$-0.582309\pi$
$599$	−20.2318	−	3.56740i	−0.826647	−	0.145760i	−0.570938	+	0.820993i	$0.693420\pi$
$600$	−2.70223	−	1.56014i	−0.110318	−	0.0636923i
$601$	−10.4938	+	18.1758i	−0.428052	+	0.741408i	−0.996700	−	0.0811730i	$-0.974133\pi$
$601$	−10.4938	+	18.1758i	−0.428052	+	0.741408i	0.568648	+	0.822581i	$0.307467\pi$
$602$		0			0
$603$	−2.00212	−	2.38604i	−0.0815328	−	0.0971670i
$604$	−2.44006	−	0.430248i	−0.0992845	−	0.0175065i
$605$	20.9031	−	57.4308i	0.849832	−	2.33490i
$606$	8.12861	−	6.82072i	0.330202	−	0.277073i
$607$	14.0195	+	24.2824i	0.569032	+	0.985593i	0.996662	+	0.0816391i	$0.0260155\pi$
$607$	14.0195	+	24.2824i	0.569032	+	0.985593i	−0.427629	+	0.903954i	$0.640651\pi$
$608$	16.0062	+	26.2228i	0.649136	+	1.06347i
$609$		0			0
$610$	13.5107	−	37.1205i	0.547034	−	1.50296i
$611$	0.997995	+	1.18936i	0.0403746	+	0.0481165i
$612$	−7.85435	−	21.5797i	−0.317493	−	0.872306i
$613$	3.52534	+	19.9932i	0.142387	+	0.807517i	0.969428	+	0.245375i	$0.0789112\pi$
$613$	3.52534	+	19.9932i	0.142387	+	0.807517i	−0.827041	+	0.562141i	$0.809978\pi$
$614$	−19.7368	−	54.2264i	−0.796512	−	2.18840i
$615$	0.390631	+	0.225531i	0.0157517	+	0.00909427i
$616$		0			0
$617$	12.8361	−	4.67194i	0.516760	−	0.188085i	−0.0704569	−	0.997515i	$-0.522446\pi$
$617$	12.8361	−	4.67194i	0.516760	−	0.188085i	0.587217	+	0.809430i	$0.300224\pi$
$618$	−15.5847	+	18.5732i	−0.626910	+	0.747122i
$619$		−	45.0707i		−	1.81155i	−0.423764	−	0.905773i	$-0.639291\pi$
$619$		−	45.0707i		−	1.81155i	0.423764	−	0.905773i	$-0.360709\pi$
$620$	−9.43041	+	5.44465i	−0.378734	+	0.218662i
$621$	−6.63632	+	2.41542i	−0.266307	+	0.0969276i
$622$	−45.4735	+	38.1568i	−1.82332	+	1.52995i
$623$		0			0
$624$	−1.87550	−	10.6365i	−0.0750803	−	0.425801i
$625$	−5.15191	−	29.2179i	−0.206076	−	1.16872i
$626$	12.3586	−	21.4057i	0.493950	−	0.855546i
$627$	−44.4170	+	55.6393i	−1.77384	+	2.22202i
$628$	−7.36205	+	4.25048i	−0.293778	+	0.169613i
$629$	−20.9506	−	7.62539i	−0.835355	−	0.304044i
$630$		0			0
$631$	−6.59750	−	5.53596i	−0.262642	−	0.220383i	0.501951	−	0.864896i	$-0.332616\pi$
$631$	−6.59750	−	5.53596i	−0.262642	−	0.220383i	−0.764593	+	0.644513i	$0.777060\pi$
$632$	−8.98805	−	3.27138i	−0.357525	−	0.130129i
$633$	9.34324	−	11.1348i	0.371360	−	0.442570i
$634$	−6.44758	−	11.1675i	−0.256066	−	0.443519i
$635$	−9.58653	+	16.6044i	−0.380430	+	0.658924i
$636$	12.8885	+	35.4108i	0.511061	+	1.40413i
$637$		0			0
$638$	23.6225	+	40.9154i	0.935225	+	1.61986i
$639$			35.6687i			1.41103i
$640$	13.6012	+	11.4127i	0.537634	+	0.451128i
$641$	10.2479	−	1.80698i	0.404768	−	0.0713715i	0.0324421	−	0.999474i	$-0.489672\pi$
$641$	10.2479	−	1.80698i	0.404768	−	0.0713715i	0.372326	+	0.928102i	$0.378560\pi$
$642$	4.77312	−	27.0697i	0.188380	−	1.06836i
$643$	−9.79011	+	1.72626i	−0.386084	+	0.0680771i	−0.363322	−	0.931664i	$-0.618357\pi$
$643$	−9.79011	+	1.72626i	−0.386084	+	0.0680771i	−0.0227628	+	0.999741i	$0.507246\pi$
$644$		0			0
$645$		−	74.6757i		−	2.94035i
$646$	−23.4221	+	14.2967i	−0.921531	+	0.562495i
$647$	29.3237	+	16.9301i	1.15284	+	0.665590i	0.949576	−	0.313535i	$-0.101513\pi$
$647$	29.3237	+	16.9301i	1.15284	+	0.665590i	0.203259	+	0.979125i	$0.434847\pi$
$648$	−1.24343	−	1.48187i	−0.0488467	−	0.0582132i
$649$	−23.6495	+	19.8443i	−0.928325	+	0.778957i
$650$	−1.24370	+	1.48218i	−0.0487819	+	0.0581360i
$651$		0			0
$652$	−0.385685	+	2.18733i	−0.0151046	+	0.0856624i
$653$	16.2439			0.635672			0.317836	−	0.948146i	$-0.397044\pi$
$653$	16.2439			0.635672			0.317836	+	0.948146i	$0.397044\pi$
$654$	62.4804			2.44318
$655$	−0.330762	+	1.87584i	−0.0129239	+	0.0732952i
$656$	−0.238925	−	0.200482i	−0.00932845	−	0.00782750i
$657$	−40.3296	+	23.2843i	−1.57341	+	0.908408i
$658$		0			0
$659$	−9.45469	−	1.66712i	−0.368303	−	0.0649417i	−0.0135660	−	0.999908i	$-0.504318\pi$
$659$	−9.45469	−	1.66712i	−0.368303	−	0.0649417i	−0.354737	+	0.934966i	$0.615429\pi$
$660$	21.0946	−	57.9568i	0.821105	−	2.25597i
$661$	−21.9748	+	7.99817i	−0.854720	+	0.311093i	−0.731963	−	0.681344i	$-0.761396\pi$
$661$	−21.9748	+	7.99817i	−0.854720	+	0.311093i	−0.122757	+	0.992437i	$0.539174\pi$
$662$	48.6127	+	17.6936i	1.88939	+	0.687680i
$663$	7.54116	−	1.32971i	0.292874	−	0.0516417i
$664$	8.49512			0.329674
$665$		0			0
$666$	−56.2441			−2.17941
$667$	7.05023	−	1.24315i	0.272986	−	0.0481348i
$668$	−28.8909	−	10.5154i	−1.11782	−	0.406854i
$669$	−15.2157	+	5.53807i	−0.588274	+	0.214114i
$670$	1.10277	−	3.02984i	0.0426038	−	0.117053i
$671$	−49.4811	−	8.72485i	−1.91020	−	0.336819i
$672$		0			0
$673$	−20.6850	+	11.9425i	−0.797348	+	0.460349i	−0.842543	−	0.538629i	$-0.818942\pi$
$673$	−20.6850	+	11.9425i	−0.797348	+	0.460349i	0.0451949	+	0.998978i	$0.485609\pi$
$674$	10.4946	+	8.80605i	0.404239	+	0.339196i
$675$	0.901138	−	5.11061i	0.0346848	−	0.196707i
$676$	18.6041			0.715543
$677$	−9.90298			−0.380602			−0.190301	−	0.981726i	$-0.560946\pi$
$677$	−9.90298			−0.380602			−0.190301	+	0.981726i	$0.560946\pi$
$678$	11.7784	−	66.7984i	0.452345	−	2.56538i
$679$		0			0
$680$	−4.94012	+	5.88741i	−0.189445	+	0.225772i
$681$	−27.6773	+	23.2240i	−1.06060	+	0.889946i
$682$	20.6839	+	24.6501i	0.792027	+	0.943901i
$683$	5.38502	+	3.10904i	0.206052	+	0.118964i	0.599475	−	0.800393i	$-0.295376\pi$
$683$	5.38502	+	3.10904i	0.206052	+	0.118964i	−0.393423	+	0.919357i	$0.628709\pi$
$684$	−18.5892	+	23.2860i	−0.710777	+	0.890361i
$685$			0.344193i			0.0131510i
$686$		0			0
$687$	−25.9870	+	4.58221i	−0.991467	+	0.174822i
$688$	−8.96647	+	50.8514i	−0.341844	+	1.93869i
$689$	−7.43972	+	1.31182i	−0.283431	+	0.0499765i
$690$	−16.6331	−	13.9568i	−0.633210	−	0.531327i
$691$		−	30.8239i		−	1.17260i	−0.810096	−	0.586298i	$-0.800585\pi$
$691$		−	30.8239i		−	1.17260i	0.810096	−	0.586298i	$-0.199415\pi$
$692$	13.4640	+	23.3204i	0.511826	+	0.886508i
$693$		0			0
$694$	−13.0477	−	35.8483i	−0.495284	−	1.36078i
$695$	3.07106	−	5.31923i	0.116492	−	0.201770i
$696$	−5.31633	−	9.20815i	−0.201515	−	0.349034i
$697$	0.142139	−	0.169395i	0.00538391	−	0.00641629i
$698$	13.3884	+	4.87299i	0.506760	+	0.184445i
$699$	−17.3054	−	14.5209i	−0.654549	−	0.549232i
$700$		0			0
$701$	2.43588	+	0.886588i	0.0920019	+	0.0334860i	0.387611	−	0.921823i	$-0.373300\pi$
$701$	2.43588	+	0.886588i	0.0920019	+	0.0334860i	−0.295609	+	0.955309i	$0.595523\pi$
$702$	5.63271	−	3.25205i	0.212593	−	0.122741i
$703$	5.71748	+	28.3567i	0.215639	+	1.06949i
$704$	−11.1065	+	19.2370i	−0.418592	+	0.725022i
$705$	−2.22321	−	12.6085i	−0.0837311	−	0.474863i
$706$	−4.33002	−	24.5568i	−0.162963	−	0.924207i
$707$		0			0
$708$	−16.4629	+	13.8140i	−0.618715	+	0.519163i
$709$	−11.3421	+	4.12819i	−0.425962	+	0.155038i	−0.546101	−	0.837720i	$-0.683888\pi$
$709$	−11.3421	+	4.12819i	−0.425962	+	0.155038i	0.120138	+	0.992757i	$0.461666\pi$
$710$	−31.9764	+	18.4616i	−1.20005	+	0.692850i
$711$		−	47.2470i		−	1.77190i
$712$	1.07721	−	1.28377i	0.0403703	−	0.0481115i
$713$	4.58190	−	1.66768i	0.171594	−	0.0624549i
$714$		0			0
$715$	10.7079	+	6.18222i	0.400453	+	0.231202i
$716$	−3.54093	−	9.72862i	−0.132331	−	0.363575i
$717$	−12.1003	−	68.6240i	−0.451893	−	2.56281i
$718$	−15.4375	−	42.4143i	−0.576124	−	1.58289i
$719$	−6.82136	−	8.12938i	−0.254394	−	0.303175i	0.623699	−	0.781664i	$-0.285629\pi$
$719$	−6.82136	−	8.12938i	−0.254394	−	0.303175i	−0.878093	+	0.478489i	$0.841184\pi$
$720$	−18.3137	+	50.3166i	−0.682513	+	1.87519i
$721$		0			0
$722$	31.6661	+	16.2748i	1.17849	+	0.605684i
$723$	−37.0829	−	64.2294i	−1.37913	−	2.38872i
$724$	−8.05885	+	6.76218i	−0.299505	+	0.251314i
$725$	−1.79921	+	4.94330i	−0.0668211	+	0.183589i
$726$	−123.811	−	21.8313i	−4.59507	−	0.810235i
$727$	0.735074	+	0.876026i	0.0272624	+	0.0324900i	0.779503	−	0.626398i	$-0.215472\pi$
$727$	0.735074	+	0.876026i	0.0272624	+	0.0324900i	−0.752241	+	0.658888i	$0.771027\pi$
$728$		0			0
$729$	21.9612	−	38.0379i	0.813377	−	1.40881i
$730$	−41.7480	−	24.1032i	−1.54516	−	0.892099i
$731$	−36.0530	−	6.35712i	−1.33347	−	0.235127i
$732$	−34.4448	−	6.07356i	−1.27312	−	0.224485i
$733$	−26.6024	−	15.3589i	−0.982584	−	0.567295i	−0.0795346	−	0.996832i	$-0.525343\pi$
$733$	−26.6024	−	15.3589i	−0.982584	−	0.567295i	−0.903049	+	0.429537i	$0.858677\pi$
$734$	20.4704	−	35.4558i	0.755576	−	1.30870i
$735$		0			0
$736$	7.66037	+	9.12927i	0.282365	+	0.336510i
$737$	−4.03874	−	0.712139i	−0.148769	−	0.0262320i
$738$	0.190794	−	0.524202i	0.00702322	−	0.0192961i
$739$	−19.7433	+	16.5666i	−0.726269	+	0.609412i	−0.929112	−	0.369799i	$-0.879426\pi$
$739$	−19.7433	+	16.5666i	−0.726269	+	0.609412i	0.202843	+	0.979211i	$0.434982\pi$
$740$	−12.5301	−	21.7027i	−0.460614	−	0.797807i
$741$	−6.57033	−	7.45269i	−0.241367	−	0.273781i
$742$		0			0
$743$	11.7640	−	32.3214i	0.431580	−	1.18576i	−0.513262	−	0.858232i	$-0.671563\pi$
$743$	11.7640	−	32.3214i	0.431580	−	1.18576i	0.944842	−	0.327525i	$-0.106215\pi$
$744$	−4.65498	−	5.54759i	−0.170660	−	0.203384i
$745$	−5.01427	−	13.7766i	−0.183709	−	0.504735i
$746$	0.0235084	+	0.133323i	0.000860705	+	0.00488130i
$747$	14.3521	+	39.4321i	0.525116	+	1.44274i
$748$	−26.1855	−	15.1182i	−0.957436	−	0.552776i
$749$		0			0
$750$	−45.3413	+	16.5029i	−1.65563	+	0.602600i
$751$	21.3505	−	25.4446i	0.779092	−	0.928486i	−0.219800	−	0.975545i	$-0.570540\pi$
$751$	21.3505	−	25.4446i	0.779092	−	0.928486i	0.998892	+	0.0470591i	$0.0149849\pi$
$752$			8.85285i			0.322830i
$753$	−56.5399	+	32.6433i	−2.06043	+	1.18959i
$754$	−6.19559	+	2.25501i	−0.225630	+	0.0821227i
$755$	−3.13767	+	2.63282i	−0.114192	+	0.0958182i
$756$		0			0
$757$	−4.57638	−	25.9540i	−0.166331	−	0.943313i	−0.947681	−	0.319219i	$-0.896579\pi$
$757$	−4.57638	−	25.9540i	−0.166331	−	0.943313i	0.781350	−	0.624094i	$-0.214532\pi$
$758$	−6.26867	−	35.5514i	−0.227688	−	1.29129i
$759$	−13.8086	+	23.9171i	−0.501219	+	0.868138i
$760$	9.85953	+	1.49119i	0.357643	+	0.0540912i
$761$	8.70020	−	5.02307i	0.315382	−	0.182086i	−0.333950	−	0.942591i	$-0.608382\pi$
$761$	8.70020	−	5.02307i	0.315382	−	0.182086i	0.649332	+	0.760505i	$0.275048\pi$
$762$	37.0618	+	13.4894i	1.34261	+	0.488670i
$763$		0			0
$764$	−6.71435	−	5.63401i	−0.242917	−	0.203831i
$765$	−35.6739	−	12.9842i	−1.28979	−	0.469446i
$766$	2.91112	−	3.46933i	0.105183	−	0.125352i
$767$	−2.15416	−	3.73112i	−0.0777823	−	0.134723i
$768$	28.4928	−	49.3509i	1.02814	−	1.78080i
$769$	2.21251	+	6.07883i	0.0797853	+	0.219208i	0.973171	−	0.230081i	$-0.0738993\pi$
$769$	2.21251	+	6.07883i	0.0797853	+	0.219208i	−0.893386	+	0.449290i	$0.851677\pi$
$770$		0			0
$771$	5.96457	+	10.3309i	0.214809	+	0.372059i
$772$			36.5847i			1.31671i
$773$	33.6272	+	28.2166i	1.20949	+	1.01488i	0.999307	+	0.0372184i	$0.0118497\pi$
$773$	33.6272	+	28.2166i	1.20949	+	1.01488i	0.210181	+	0.977663i	$0.432595\pi$
$774$	−90.9511	+	16.0371i	−3.26917	+	0.576443i
$775$	−0.622170	+	3.52850i	−0.0223490	+	0.126748i
$776$	−7.83447	+	1.38143i	−0.281241	+	0.0495904i
$777$		0			0
$778$		−	30.3657i		−	1.08866i
$779$	−0.283683	−	0.0429052i	−0.0101640	−	0.00153724i
$780$	7.45401	+	4.30357i	0.266896	+	0.154093i
$781$	30.1874	+	35.9760i	1.08019	+	1.28732i
$782$	−8.15424	+	6.84222i	−0.291595	+	0.244677i
$783$	11.3668	−	13.5464i	0.406216	−	0.484109i
$784$		0			0
$785$	−2.44030	+	13.8397i	−0.0870982	+	0.493959i
$786$	3.91827			0.139760
$787$	−21.7807			−0.776398			−0.388199	−	0.921576i	$-0.626903\pi$
$787$	−21.7807			−0.776398			−0.388199	+	0.921576i	$0.626903\pi$
$788$	2.13014	−	12.0807i	0.0758833	−	0.430355i
$789$	−41.9593	−	35.2080i	−1.49379	−	1.25344i
$790$	42.3561	−	24.4543i	1.50696	−	0.870044i
$791$		0			0
$792$	24.2855	+	4.28220i	0.862949	+	0.152161i
$793$	2.39817	−	6.58892i	0.0851615	−	0.233979i
$794$	−14.4298	+	5.25203i	−0.512095	+	0.186387i
$795$	58.5384	+	21.3062i	2.07614	+	0.755655i
$796$	36.4338	−	6.42425i	1.29136	−	0.227702i
$797$	36.1577			1.28077			0.640386	−	0.768053i	$-0.278774\pi$
$797$	36.1577			1.28077			0.640386	+	0.768053i	$0.278774\pi$
$798$		0			0
$799$	−6.27657			−0.222049
$800$	−8.62408	+	1.52066i	−0.304907	+	0.0537634i
$801$	7.77884	+	2.83127i	0.274852	+	0.100038i
$802$	25.4346	−	9.25742i	0.898126	−	0.326891i
$803$	−20.9709	+	57.6170i	−0.740046	+	2.03326i
$804$	−2.81145	−	0.495735i	−0.0991523	−	0.0174832i
$805$		0			0
$806$	−3.88898	+	2.24530i	−0.136984	+	0.0790875i
$807$	21.0146	+	17.6333i	0.739748	+	0.620723i
$808$	−0.328259	+	1.86165i	−0.0115481	+	0.0654926i
$809$	−8.11547			−0.285325			−0.142662	−	0.989771i	$-0.545566\pi$
$809$	−8.11547			−0.285325			−0.142662	+	0.989771i	$0.545566\pi$
$810$	9.89147			0.347551
$811$	−4.56743	+	25.9032i	−0.160384	+	0.909584i	0.793312	+	0.608815i	$0.208355\pi$
$811$	−4.56743	+	25.9032i	−0.160384	+	0.909584i	−0.953697	+	0.300770i	$0.902756\pi$
$812$		0			0
$813$	45.8401	−	54.6302i	1.60768	−	1.91596i
$814$	−56.7286	+	47.6009i	−1.98834	+	1.66841i
$815$	2.36013	+	2.81269i	0.0826717	+	0.0985243i
$816$	37.8129	+	21.8313i	1.32371	+	0.764247i
$817$	17.3311	+	44.2247i	0.606338	+	1.54723i
$818$		−	6.66991i		−	0.233208i
$819$		0			0
$820$	0.244777	−	0.0431608i	0.00854798	−	0.00150724i
$821$	−3.17586	+	18.0112i	−0.110838	+	0.628595i	0.877889	+	0.478865i	$0.158952\pi$
$821$	−3.17586	+	18.0112i	−0.110838	+	0.628595i	−0.988727	+	0.149730i	$0.952159\pi$
$822$	0.697274	−	0.122948i	0.0243202	−	0.00428831i
$823$	−17.4055	−	14.6049i	−0.606716	−	0.509095i	0.286880	−	0.957966i	$-0.407382\pi$
$823$	−17.4055	−	14.6049i	−0.606716	−	0.509095i	−0.893596	+	0.448871i	$0.851826\pi$
$824$		−	4.31932i		−	0.150471i
$825$	−10.1468	−	17.5747i	−0.353265	−	0.611873i
$826$		0			0
$827$	14.3070	+	39.3081i	0.497502	+	1.36688i	0.893681	+	0.448703i	$0.148114\pi$
$827$	14.3070	+	39.3081i	0.497502	+	1.36688i	−0.396178	+	0.918174i	$0.629664\pi$
$828$	−5.77911	+	10.0097i	−0.200838	+	0.347862i
$829$	−8.20208	−	14.2064i	−0.284870	−	0.493409i	0.687708	−	0.725988i	$-0.258617\pi$
$829$	−8.20208	−	14.2064i	−0.284870	−	0.493409i	−0.972578	+	0.232579i	$0.925284\pi$
$830$	−27.9217	+	33.2758i	−0.969177	+	1.15502i
$831$	−6.22961	−	2.26739i	−0.216103	−	0.0786550i
$832$	−2.37466	−	1.99258i	−0.0823265	−	0.0690802i
$833$		0			0
$834$	−11.8728	−	4.32135i	−0.411122	−	0.149636i
$835$	−44.0161	+	25.4127i	−1.52324	+	0.879443i
$836$	0.958192	+	39.2191i	0.0331398	+	1.35642i
$837$	6.02211	−	10.4306i	0.208155	−	0.360534i
$838$	6.92737	+	39.2871i	0.239302	+	1.35715i
$839$	−1.89393	−	10.7410i	−0.0653859	−	0.370822i	−0.999889	−	0.0148681i	$-0.995267\pi$
$839$	−1.89393	−	10.7410i	−0.0653859	−	0.370822i	0.934504	−	0.355954i	$-0.115844\pi$
$840$		0			0
$841$	8.48327	−	7.11831i	0.292527	−	0.245459i
$842$	35.8572	−	13.0509i	1.23572	−	0.449765i
$843$	−7.02250	+	4.05444i	−0.241868	+	0.139642i
$844$		−	8.00965i		−	0.275703i
$845$	19.7689	−	23.5597i	0.680071	−	0.810477i
$846$	−14.8790	+	5.41552i	−0.511551	+	0.186189i
$847$		0			0
$848$	−37.3042	−	21.5376i	−1.28103	−	0.739604i
$849$	−16.7689	−	46.0721i	−0.575507	−	1.58119i
$850$	−1.35825	−	7.70300i	−0.0465875	−	0.264211i
$851$	3.83791	+	10.5446i	0.131562	+	0.361463i
$852$	21.0141	+	25.0436i	0.719931	+	0.857981i
$853$	−4.40339	+	12.0982i	−0.150769	+	0.414235i	−0.991968	−	0.126491i	$-0.959628\pi$
$853$	−4.40339	+	12.0982i	−0.150769	+	0.414235i	0.841198	+	0.540727i	$0.181851\pi$
$854$		0			0
$855$	9.73550	+	48.2846i	0.332947	+	1.65130i
$856$	2.44842	+	4.24079i	0.0836853	+	0.144947i
$857$	26.6928	−	22.3979i	0.911807	−	0.765097i	−0.0606547	−	0.998159i	$-0.519319\pi$
$857$	26.6928	−	22.3979i	0.911807	−	0.765097i	0.972462	+	0.233062i	$0.0748744\pi$
$858$	8.69913	−	23.9007i	0.296983	−	0.815955i
$859$	11.8950	+	2.09741i	0.405852	+	0.0715626i	0.372848	−	0.927893i	$-0.378381\pi$
$859$	11.8950	+	2.09741i	0.405852	+	0.0715626i	0.0330042	+	0.999455i	$0.489493\pi$
$860$	−26.4503	−	31.5222i	−0.901947	−	1.07490i
$861$		0			0
$862$	18.9091	−	32.7515i	0.644046	−	1.11552i
$863$	33.4423	+	19.3079i	1.13839	+	0.657250i	0.946031	−	0.324075i	$-0.105053\pi$
$863$	33.4423	+	19.3079i	1.13839	+	0.657250i	0.192358	+	0.981325i	$0.438386\pi$
$864$	28.9903	+	5.11177i	0.986269	+	0.173906i
$865$	43.8392	+	7.73003i	1.49058	+	0.262829i
$866$	−22.9504	−	13.2504i	−0.779885	−	0.450267i
$867$	7.83545	−	13.5714i	0.266106	−	0.460909i
$868$		0			0
$869$	−39.9864	−	47.6540i	−1.35645	−	1.61655i
$870$	53.5425	+	9.44099i	1.81526	+	0.320079i
$871$	0.195743	−	0.537800i	0.00663250	−	0.0182227i
$872$	−8.52671	+	7.15476i	−0.288751	+	0.242291i
$873$	−19.6482	−	34.0317i	−0.664991	−	1.15180i
$874$	13.0897	+	4.40527i	0.442764	+	0.149010i
$875$		0			0
$876$	−14.5983	+	40.1084i	−0.493230	+	1.35514i
$877$	2.88768	+	3.44140i	0.0975100	+	0.116208i	0.812593	−	0.582832i	$-0.198055\pi$
$877$	2.88768	+	3.44140i	0.0975100	+	0.116208i	−0.715083	+	0.699040i	$0.753611\pi$
$878$	−1.08612	−	2.98410i	−0.0366549	−	0.100708i
$879$	−13.2465	−	75.1246i	−0.446793	−	2.53389i
$880$	24.1128	+	66.2495i	0.812844	+	2.23327i
$881$	19.5809	+	11.3050i	0.659696	+	0.380876i	0.792161	−	0.610312i	$-0.208956\pi$
$881$	19.5809	+	11.3050i	0.659696	+	0.380876i	−0.132465	+	0.991188i	$0.542289\pi$
$882$		0			0
$883$	−12.9244	+	4.70410i	−0.434941	+	0.158305i	−0.550205	−	0.835029i	$-0.685451\pi$
$883$	−12.9244	+	4.70410i	−0.434941	+	0.158305i	0.115265	+	0.993335i	$0.463228\pi$
$884$	2.71230	−	3.23239i	0.0912245	−	0.108717i
$885$			35.5270i			1.19423i
$886$	63.2934	−	36.5424i	2.12638	−	1.22767i
$887$	38.4222	−	13.9845i	1.29009	−	0.469555i	0.396334	−	0.918107i	$-0.370282\pi$
$887$	38.4222	−	13.9845i	1.29009	−	0.469555i	0.893757	+	0.448552i	$0.148060\pi$
$888$	12.7669	−	10.7127i	0.428431	−	0.359496i
$889$		0			0
$890$	1.48802	+	8.43901i	0.0498787	+	0.282876i
$891$	−2.18470	−	12.3900i	−0.0731901	−	0.415082i
$892$	−4.46129	+	7.72718i	−0.149375	+	0.258725i
$893$	4.24287	+	6.95106i	0.141982	+	0.232608i
$894$	−26.1178	+	15.0791i	−0.873509	+	0.504321i
$895$	−16.0826	−	5.85359i	−0.537583	−	0.195664i
$896$		0			0
$897$	−2.95239	−	2.47735i	−0.0985773	−	0.0827162i
$898$	−18.2964	−	6.65935i	−0.610559	−	0.222225i
$899$	−7.84795	+	9.35282i	−0.261744	+	0.311934i
$900$	−4.24659	−	7.35531i	−0.141553	−	0.245177i
$901$	15.2699	−	26.4482i	0.508714	−	0.881119i
$902$	−0.251209	−	0.690192i	−0.00836435	−	0.0229809i
$903$		0			0
$904$	6.04183	+	10.4647i	0.200948	+	0.348052i
$905$			17.3910i			0.578097i
$906$	6.45442	+	5.41591i	0.214434	+	0.179931i
$907$	5.58381	−	0.984576i	0.185407	−	0.0326923i	−0.0801735	−	0.996781i	$-0.525547\pi$
$907$	5.58381	−	0.984576i	0.185407	−	0.0326923i	0.265581	+	0.964089i	$0.414436\pi$
$908$	−3.45719	+	19.6067i	−0.114731	+	0.650672i
$909$	−9.19586	+	1.62148i	−0.305007	+	0.0537810i
$910$		0			0
$911$			39.4091i			1.30568i	0.757495	+	0.652841i	$0.226423\pi$
$911$			39.4091i			1.30568i	−0.757495	+	0.652841i	$0.773577\pi$
$912$	−1.38367	−	56.6340i	−0.0458178	−	1.87534i
$913$	47.8482	+	27.6252i	1.58354	+	0.914260i
$914$	19.6148	+	23.3760i	0.648800	+	0.773210i
$915$	−44.2927	+	37.1660i	−1.46427	+	1.22867i
$916$	−9.34665	+	11.1389i	−0.308822	+	0.368040i
$917$		0			0
$918$	−4.56582	+	25.8940i	−0.150694	+	0.854630i
$919$	−45.6581			−1.50612			−0.753062	−	0.657950i	$-0.771424\pi$
$919$	−45.6581			−1.50612			−0.753062	+	0.657950i	$0.771424\pi$
$920$	3.86814			0.127529
$921$	−14.6671	+	83.1815i	−0.483299	+	2.74092i
$922$	−8.73676	−	7.33101i	−0.287730	−	0.241434i
$923$	−5.67583	+	3.27694i	−0.186822	+	0.107862i
$924$		0			0
$925$	−8.12033	−	1.43183i	−0.266995	−	0.0470784i
$926$	20.2444	−	55.6210i	0.665272	−	1.82782i
$927$	20.0491	−	7.29729i	0.658500	−	0.239674i
$928$	−28.0412	−	10.2062i	−0.920498	−	0.335034i
$929$	42.6278	−	7.51643i	1.39857	−	0.246606i	0.577016	−	0.816733i	$-0.304217\pi$
$929$	42.6278	−	7.51643i	1.39857	−	0.246606i	0.821557	+	0.570127i	$0.193106\pi$
$930$	37.0301			1.21427
$931$		0			0
$932$	−12.4483			−0.407758
$933$	85.5671	−	15.0878i	2.80134	−	0.493952i
$934$	20.1743	+	7.34286i	0.660125	+	0.240266i
$935$	−46.9701	+	17.0957i	−1.53609	+	0.559090i
$936$	−1.17703	+	3.23387i	−0.0384725	+	0.105702i
$937$	45.9844	+	8.10829i	1.50224	+	0.264886i	0.863428	−	0.504473i	$-0.168313\pi$
$937$	45.9844	+	8.10829i	1.50224	+	0.264886i	0.638817	+	0.769359i	$0.279424\pi$
$938$		0			0
$939$	−31.3315	+	18.0893i	−1.02246	+	0.590320i
$940$	−5.40441	−	4.53484i	−0.176273	−	0.147910i
$941$	2.23252	−	12.6612i	0.0727781	−	0.412745i	−0.926553	−	0.376165i	$-0.877243\pi$
$941$	2.23252	−	12.6612i	0.0727781	−	0.412745i	0.999331	−	0.0365798i	$-0.0116463\pi$
$942$	28.9084			0.941885
$943$	−0.111296			−0.00362429
$944$	4.26581	−	24.1926i	0.138840	−	0.787402i
$945$		0			0
$946$	−78.1619	+	93.1497i	−2.54126	+	3.02856i
$947$	6.66819	−	5.59528i	0.216687	−	0.181822i	−0.527983	−	0.849255i	$-0.677051\pi$
$947$	6.66819	−	5.59528i	0.216687	−	0.181822i	0.744670	+	0.667433i	$0.232607\pi$
$948$	−27.8354	−	33.1729i	−0.904052	−	1.07741i
$949$	−7.41030	−	4.27834i	−0.240549	−	0.138881i
$950$	−7.61263	+	6.71133i	−0.246986	+	0.217744i
$951$			18.8746i			0.612050i
$952$		0			0
$953$	−1.25278	+	0.220898i	−0.0405814	+	0.00715559i	−0.193902	−	0.981021i	$-0.562114\pi$
$953$	−1.25278	+	0.220898i	−0.0405814	+	0.00715559i	0.153321	+	0.988176i	$0.451003\pi$
$954$	13.3784	−	75.8724i	0.433140	−	2.45646i
$955$	−14.2694	+	2.51609i	−0.461748	+	0.0814187i
$956$	−29.4145	−	24.6817i	−0.951334	−	0.798264i
$957$		−	69.1524i		−	2.23538i
$958$	23.6368	+	40.9402i	0.763672	+	1.32272i
$959$		0			0
$960$	8.74278	+	24.0206i	0.282172	+	0.775261i
$961$	11.3422	−	19.6452i	0.365876	−	0.633717i
$962$	−5.16724	−	8.94992i	−0.166598	−	0.288557i
$963$	−15.5481	+	18.5295i	−0.501031	+	0.597106i
$964$	−38.4037	−	13.9778i	−1.23690	−	0.450194i
$965$	46.3297	+	38.8752i	1.49141	+	1.25144i
$966$		0			0
$967$	47.3977	+	17.2513i	1.52421	+	0.554766i	0.962195	−	0.272363i	$-0.0878051\pi$
$967$	47.3977	+	17.2513i	1.52421	+	0.554766i	0.562012	+	0.827129i	$0.310027\pi$
$968$	19.3965	−	11.1986i	0.623427	−	0.359936i
$969$	40.1528	−	0.981003i	1.28989	−	0.0315144i
$970$	20.3392	−	35.2285i	0.653052	−	1.13112i
$971$	3.89518	+	22.0906i	0.125002	+	0.708922i	0.981307	+	0.192451i	$0.0616436\pi$
$971$	3.89518	+	22.0906i	0.125002	+	0.708922i	−0.856304	+	0.516471i	$0.827245\pi$
$972$	−4.80929	−	27.2748i	−0.154258	−	0.874841i
$973$		0			0
$974$	−18.8053	+	15.7795i	−0.602559	+	0.505607i
$975$	2.66124	−	0.968612i	0.0852279	−	0.0310204i
$976$	34.6243	−	19.9904i	1.10830	−	0.639876i
$977$		−	45.0887i		−	1.44252i	−0.692667	−	0.721258i	$-0.743564\pi$
$977$		−	45.0887i		−	1.44252i	0.692667	−	0.721258i	$-0.256436\pi$
$978$	4.85495	−	5.78591i	0.155244	−	0.185013i
$979$	10.2420	−	3.72779i	0.327337	−	0.119141i
$980$		0			0
$981$	−47.6160	−	27.4911i	−1.52026	−	0.877723i
$982$	1.36395	+	3.74743i	0.0435255	+	0.119585i
$983$	1.68662	+	9.56532i	0.0537949	+	0.305086i	0.999819	−	0.0190093i	$-0.00605121\pi$
$983$	1.68662	+	9.56532i	0.0537949	+	0.305086i	−0.946024	+	0.324095i	$0.894940\pi$
$984$	0.0565354	+	0.155330i	0.00180228	+	0.00495173i
$985$	−13.0350	−	15.5345i	−0.415331	−	0.494972i
$986$	9.11611	−	25.0463i	0.290316	−	0.797637i
$987$		0			0
$988$	−5.41323	−	0.818717i	−0.172218	−	0.0260469i
$989$	9.21283	+	15.9571i	0.292951	+	0.507406i
$990$	−96.5952	+	81.0530i	−3.07000	+	2.57603i
$991$	2.67080	−	7.33797i	0.0848408	−	0.233098i	−0.890016	−	0.455928i	$-0.849307\pi$
$991$	2.67080	−	7.33797i	0.0848408	−	0.233098i	0.974857	+	0.222830i	$0.0715295\pi$
$992$	−20.0157	−	3.52931i	−0.635499	−	0.112056i
$993$	−48.6723	−	58.0054i	−1.54457	−	1.84075i
$994$		0			0
$995$	30.5793	−	52.9650i	0.969431	−	1.67910i
$996$	33.3081	+	19.2305i	1.05541	+	0.609341i
$997$	23.6322	+	4.16700i	0.748440	+	0.131970i	0.534843	−	0.844952i	$-0.320371\pi$
$997$	23.6322	+	4.16700i	0.748440	+	0.131970i	0.213597	+	0.976922i	$0.431482\pi$
$998$	−24.1524	−	4.25871i	−0.764530	−	0.134807i
$999$	24.0045	+	13.8590i	0.759468	+	0.438479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.bj.a.129.3		66
7.2	even	3		133.2.bb.a.110.9	yes	66
7.3	odd	6		931.2.be.a.832.9		66
7.4	even	3		931.2.be.b.832.9		66
7.5	odd	6		931.2.bf.a.509.9		66
7.6	odd	2		133.2.bf.a.129.3	yes	66
19.14	odd	18		931.2.bf.a.717.9		66
133.33	even	18	inner	931.2.bj.a.166.3		66
133.52	even	18		931.2.be.b.489.9		66
133.90	even	18		133.2.bb.a.52.9	✓	66
133.109	odd	18		931.2.be.a.489.9		66
133.128	odd	18		133.2.bf.a.33.3	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.bb.a.52.9	✓	66	133.90	even	18
133.2.bb.a.110.9	yes	66	7.2	even	3
133.2.bf.a.33.3	yes	66	133.128	odd	18
133.2.bf.a.129.3	yes	66	7.6	odd	2
931.2.be.a.489.9		66	133.109	odd	18
931.2.be.a.832.9		66	7.3	odd	6
931.2.be.b.489.9		66	133.52	even	18
931.2.be.b.832.9		66	7.4	even	3
931.2.bf.a.509.9		66	7.5	odd	6
931.2.bf.a.717.9		66	19.14	odd	18
931.2.bj.a.129.3		66	1.1	even	1	trivial
931.2.bj.a.166.3		66	133.33	even	18	inner

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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.bj (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.84540 + 0.325394i) q^{2} +(2.57736 + 0.938083i) q^{3} +(1.42023 - 0.516922i) q^{4} +(0.854536 - 2.34782i) q^{5} +(-5.06151 - 0.892480i) q^{6} +(0.792944 - 0.457807i) q^{8} +(3.46466 + 2.90719i) q^{9} +O(q^{10})\)	\(q+(-1.84540 + 0.325394i) q^{2} +(2.57736 + 0.938083i) q^{3} +(1.42023 - 0.516922i) q^{4} +(0.854536 - 2.34782i) q^{5} +(-5.06151 - 0.892480i) q^{6} +(0.792944 - 0.457807i) q^{8} +(3.46466 + 2.90719i) q^{9} +(-0.812995 + 4.61072i) q^{10} +5.95494 q^{11} +4.14536 q^{12} +(-0.144307 + 0.818407i) q^{13} +(4.40490 - 5.24955i) q^{15} +(-3.62990 + 3.04584i) q^{16} +(-2.15947 - 2.57355i) q^{17} +(-7.33966 - 4.23756i) q^{18} +(-1.39034 + 4.13122i) q^{19} -3.77617i q^{20} +(-10.9892 + 1.93770i) q^{22} +(-0.293617 + 1.66519i) q^{23} +(2.47317 - 0.436086i) q^{24} +(-0.951798 - 0.798653i) q^{25} -1.55724i q^{26} +(2.08834 + 3.61710i) q^{27} +(-1.44808 - 3.97856i) q^{29} +(-6.42062 + 11.1208i) q^{30} +(-1.44184 - 2.49735i) q^{31} +(4.53042 - 5.39914i) q^{32} +(15.3480 + 5.58623i) q^{33} +(4.82250 + 4.04655i) q^{34} +(6.42341 + 2.33793i) q^{36} +(5.74728 - 3.31819i) q^{37} +(1.22147 - 8.07615i) q^{38} +(-1.13967 + 1.97396i) q^{39} +(-0.397247 - 2.25290i) q^{40} +(0.0114298 + 0.0648215i) q^{41} +(8.34767 - 7.00453i) q^{43} +(8.45739 - 3.07824i) q^{44} +(9.78624 - 5.65009i) q^{45} -3.16848i q^{46} +(1.20091 - 1.43119i) q^{47} +(-12.2128 + 4.44510i) q^{48} +(2.01632 + 1.16412i) q^{50} +(-3.15152 - 8.65874i) q^{51} +(0.218103 + 1.23692i) q^{52} +(3.10913 + 8.54226i) q^{53} +(-5.03079 - 5.99547i) q^{54} +(5.08871 - 13.9811i) q^{55} +(-7.45884 + 9.34338i) q^{57} +(3.96688 + 6.87084i) q^{58} +(-3.97141 + 3.33241i) q^{59} +(3.54236 - 9.73256i) q^{60} +(-8.30925 - 1.46514i) q^{61} +(3.47340 + 4.13944i) q^{62} +(-1.86509 + 3.23043i) q^{64} +(1.79816 + 1.03817i) q^{65} +(-30.1410 - 5.31467i) q^{66} +(-0.678216 - 0.119588i) q^{67} +(-4.39727 - 2.53876i) q^{68} +(-2.31884 + 4.01635i) q^{69} +(5.06930 + 6.04136i) q^{71} +(4.07822 + 0.719100i) q^{72} +(-3.52159 + 9.67549i) q^{73} +(-9.52630 + 7.99351i) q^{74} +(-1.70392 - 2.95128i) q^{75} +(0.160907 + 6.58598i) q^{76} +(1.46082 - 4.01358i) q^{78} +(-6.71483 - 8.00242i) q^{79} +(4.04921 + 11.1251i) q^{80} +(-0.366871 - 2.08063i) q^{81} +(-0.0421850 - 0.115902i) q^{82} +(8.03504 + 4.63903i) q^{83} +(-7.88758 + 2.87084i) q^{85} +(-13.1256 + 15.6424i) q^{86} -11.6126i q^{87} +(4.72194 - 2.72621i) q^{88} +(1.71992 - 0.626000i) q^{89} +(-16.2210 + 13.6110i) q^{90} +(0.443767 + 2.51673i) q^{92} +(-1.37344 - 7.78914i) q^{93} +(-1.75046 + 3.03188i) q^{94} +(8.51125 + 6.79455i) q^{95} +(16.7414 - 9.66563i) q^{96} +(-8.16455 - 2.97165i) q^{97} +(20.6319 + 17.3122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 3 q^{2} + 9 q^{3} - 3 q^{4} + 9 q^{5} - 18 q^{8} - 3 q^{9}+O(q^{10}) \) 66 * q - 3 * q^2 + 9 * q^3 - 3 * q^4 + 9 * q^5 - 18 * q^8 - 3 * q^9	\( 66 q - 3 q^{2} + 9 q^{3} - 3 q^{4} + 9 q^{5} - 18 q^{8} - 3 q^{9} + 9 q^{10} - 12 q^{11} - 6 q^{12} + 30 q^{13} + 9 q^{15} - 15 q^{16} - 18 q^{17} + 36 q^{18} - 12 q^{19} - 3 q^{23} + 36 q^{24} - 27 q^{25} - 12 q^{27} - 6 q^{29} + 3 q^{30} + 9 q^{31} + 60 q^{32} + 9 q^{33} + 36 q^{34} + 27 q^{36} - 36 q^{37} - 18 q^{38} + 12 q^{39} - 9 q^{40} - 54 q^{41} + 12 q^{43} + 18 q^{44} + 27 q^{45} - 45 q^{47} - 63 q^{48} - 63 q^{50} - 3 q^{51} - 57 q^{52} + 27 q^{53} + 9 q^{54} + 45 q^{55} - 54 q^{57} + 30 q^{58} - 36 q^{59} - 78 q^{60} + 42 q^{61} + 45 q^{62} - 36 q^{64} + 45 q^{65} - 9 q^{66} + 30 q^{67} + 9 q^{68} - 6 q^{71} - 6 q^{72} - 60 q^{73} + 9 q^{74} + 21 q^{75} - 54 q^{76} + 3 q^{78} + 27 q^{79} + 45 q^{80} + 24 q^{81} + 9 q^{82} - 36 q^{83} - 48 q^{85} - 48 q^{86} - 9 q^{88} + 9 q^{89} + 18 q^{90} + 48 q^{92} - 3 q^{93} - 90 q^{94} - 75 q^{95} - 63 q^{96} + 27 q^{97} + 48 q^{99}+O(q^{100}) \) 66 * q - 3 * q^2 + 9 * q^3 - 3 * q^4 + 9 * q^5 - 18 * q^8 - 3 * q^9 + 9 * q^10 - 12 * q^11 - 6 * q^12 + 30 * q^13 + 9 * q^15 - 15 * q^16 - 18 * q^17 + 36 * q^18 - 12 * q^19 - 3 * q^23 + 36 * q^24 - 27 * q^25 - 12 * q^27 - 6 * q^29 + 3 * q^30 + 9 * q^31 + 60 * q^32 + 9 * q^33 + 36 * q^34 + 27 * q^36 - 36 * q^37 - 18 * q^38 + 12 * q^39 - 9 * q^40 - 54 * q^41 + 12 * q^43 + 18 * q^44 + 27 * q^45 - 45 * q^47 - 63 * q^48 - 63 * q^50 - 3 * q^51 - 57 * q^52 + 27 * q^53 + 9 * q^54 + 45 * q^55 - 54 * q^57 + 30 * q^58 - 36 * q^59 - 78 * q^60 + 42 * q^61 + 45 * q^62 - 36 * q^64 + 45 * q^65 - 9 * q^66 + 30 * q^67 + 9 * q^68 - 6 * q^71 - 6 * q^72 - 60 * q^73 + 9 * q^74 + 21 * q^75 - 54 * q^76 + 3 * q^78 + 27 * q^79 + 45 * q^80 + 24 * q^81 + 9 * q^82 - 36 * q^83 - 48 * q^85 - 48 * q^86 - 9 * q^88 + 9 * q^89 + 18 * q^90 + 48 * q^92 - 3 * q^93 - 90 * q^94 - 75 * q^95 - 63 * q^96 + 27 * q^97 + 48 * q^99

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