LMFDB - Embedded newform 637.2.g.l.263.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(263,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("637.263"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,2,2,-4,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			263.6
Root			$-0.181721 - 0.314749i$ of defining polynomial
Character	$\chi$	$=$	637.263
Dual form			637.2.g.l.373.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.19402 - 2.06810i) q^{2} +2.75148 q^{3} +(-1.85136 - 3.20665i) q^{4} +(0.491140 + 0.850679i) q^{5} +(3.28532 - 5.69033i) q^{6} -4.06616 q^{8} +4.57063 q^{9} +2.34572 q^{10} -0.587802 q^{11} +(-5.09398 - 8.82303i) q^{12} +(-2.39227 + 2.69760i) q^{13} +(1.35136 + 2.34063i) q^{15} +(-1.15235 + 1.99593i) q^{16} +(-3.22710 - 5.58950i) q^{17} +(5.45742 - 9.45253i) q^{18} +3.82689 q^{19} +(1.81855 - 3.14983i) q^{20} +(-0.701847 + 1.21563i) q^{22} +(-4.13001 + 7.15338i) q^{23} -11.1880 q^{24} +(2.01756 - 3.49452i) q^{25} +(2.72249 + 8.16844i) q^{26} +4.32156 q^{27} +(1.98009 + 3.42962i) q^{29} +6.45420 q^{30} +(-1.49436 + 2.58831i) q^{31} +(-1.31430 - 2.27644i) q^{32} -1.61733 q^{33} -15.4129 q^{34} +(-8.46189 - 14.6564i) q^{36} +(-0.877941 + 1.52064i) q^{37} +(4.56938 - 7.91440i) q^{38} +(-6.58228 + 7.42239i) q^{39} +(-1.99705 - 3.45900i) q^{40} +(1.83584 + 3.17977i) q^{41} +(-3.19042 + 5.52598i) q^{43} +(1.08823 + 1.88488i) q^{44} +(2.24482 + 3.88814i) q^{45} +(9.86261 + 17.0825i) q^{46} +(-2.17030 - 3.75906i) q^{47} +(-3.17067 + 5.49176i) q^{48} +(-4.81802 - 8.34505i) q^{50} +(-8.87930 - 15.3794i) q^{51} +(13.0792 + 2.67695i) q^{52} +(-0.212770 + 0.368529i) q^{53} +(5.16002 - 8.93742i) q^{54} +(-0.288693 - 0.500031i) q^{55} +10.5296 q^{57} +9.45706 q^{58} +(3.00431 + 5.20362i) q^{59} +(5.00371 - 8.66669i) q^{60} -2.20674 q^{61} +(3.56859 + 6.18097i) q^{62} -10.8866 q^{64} +(-3.46973 - 0.710156i) q^{65} +(-1.93112 + 3.34479i) q^{66} +7.01303 q^{67} +(-11.9491 + 20.6964i) q^{68} +(-11.3636 + 19.6824i) q^{69} +(-1.80127 + 3.11988i) q^{71} -18.5849 q^{72} +(2.46714 - 4.27321i) q^{73} +(2.09656 + 3.63134i) q^{74} +(5.55128 - 9.61510i) q^{75} +(-7.08496 - 12.2715i) q^{76} +(7.49088 + 22.4753i) q^{78} +(-1.39270 - 2.41223i) q^{79} -2.26386 q^{80} -1.82122 q^{81} +8.76812 q^{82} +2.86819 q^{83} +(3.16992 - 5.49045i) q^{85} +(7.61885 + 13.1962i) q^{86} +(5.44818 + 9.43652i) q^{87} +2.39010 q^{88} +(-1.04656 + 1.81269i) q^{89} +10.7214 q^{90} +30.5845 q^{92} +(-4.11170 + 7.12167i) q^{93} -10.3655 q^{94} +(1.87954 + 3.25546i) q^{95} +(-3.61628 - 6.26357i) q^{96} +(3.84852 - 6.66584i) q^{97} -2.68663 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} - 6 q^{9} + 8 q^{10} - 8 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} + q^{20} - 5 q^{22} - q^{23}+ \cdots - 20 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^4 - q^5 + 9 * q^6 - 6 * q^8 - 6 * q^9 + 8 * q^10 - 8 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 + 8 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 + q^20 - 5 * q^22 - q^23 - 22 * q^24 + 7 * q^25 - 5 * q^26 + 8 * q^27 + 3 * q^29 + 10 * q^30 - 16 * q^31 + 8 * q^32 + 32 * q^33 - 32 * q^34 - 21 * q^36 - 13 * q^37 + 17 * q^38 - 23 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 + 7 * q^45 + 16 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 + 25 * q^52 - 2 * q^53 + 18 * q^54 - 9 * q^55 + 42 * q^57 + 16 * q^58 - 13 * q^59 + 20 * q^60 - 10 * q^61 - 5 * q^62 - 30 * q^64 + 19 * q^65 - 18 * q^66 + 22 * q^67 - 29 * q^68 - 23 * q^69 + 6 * q^71 - 50 * q^72 + 30 * q^73 - 3 * q^74 + 3 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 - 14 * q^80 + 12 * q^81 + 2 * q^82 + 54 * q^83 - q^85 - 7 * q^86 - 16 * q^87 - 4 * q^89 + 16 * q^90 + 54 * q^92 - 7 * q^93 + 90 * q^94 - 6 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.19402	−	2.06810i	0.844299	−	1.46237i	−0.0419302	−	0.999121i	$-0.513351\pi$
$2$	1.19402	−	2.06810i	0.844299	−	1.46237i	0.886229	−	0.463248i	$-0.153316\pi$
$3$	2.75148			1.58857			0.794283	−	0.607548i	$-0.207847\pi$
$3$	2.75148			1.58857			0.794283	+	0.607548i	$0.207847\pi$
$4$	−1.85136	−	3.20665i	−0.925680	−	1.60333i
$5$	0.491140	+	0.850679i	0.219644	+	0.380435i	0.954699	−	0.297572i	$-0.0961769\pi$
$5$	0.491140	+	0.850679i	0.219644	+	0.380435i	−0.735055	+	0.678008i	$0.762844\pi$
$6$	3.28532	−	5.69033i	1.34122	−	2.32307i
$7$		0			0
$7$		0			0
$8$	−4.06616			−1.43761
$9$	4.57063			1.52354
$10$	2.34572			0.741782
$11$	−0.587802			−0.177229			−0.0886146	−	0.996066i	$-0.528244\pi$
$11$	−0.587802			−0.177229			−0.0886146	+	0.996066i	$0.528244\pi$
$12$	−5.09398	−	8.82303i	−1.47051	−	2.54699i
$13$	−2.39227	+	2.69760i	−0.663496	+	0.748179i
$13$	−2.39227	+	2.69760i	−0.663496	+	0.748179i
$14$		0			0
$15$	1.35136	+	2.34063i	0.348920	+	0.604347i
$16$	−1.15235	+	1.99593i	−0.288088	+	0.498983i
$17$	−3.22710	−	5.58950i	−0.782687	−	1.35565i	−0.930371	−	0.366619i	$-0.880515\pi$
$17$	−3.22710	−	5.58950i	−0.782687	−	1.35565i	0.147685	−	0.989035i	$-0.452818\pi$
$18$	5.45742	−	9.45253i	1.28633	−	2.22798i
$19$	3.82689			0.877950			0.438975	−	0.898499i	$-0.355342\pi$
$19$	3.82689			0.877950			0.438975	+	0.898499i	$0.355342\pi$
$20$	1.81855	−	3.14983i	0.406641	−	0.704323i
$21$		0			0
$22$	−0.701847	+	1.21563i	−0.149634	+	0.259174i
$23$	−4.13001	+	7.15338i	−0.861166	+	1.49158i	0.00963902	+	0.999954i	$0.496932\pi$
$23$	−4.13001	+	7.15338i	−0.861166	+	1.49158i	−0.870805	+	0.491629i	$0.836402\pi$
$24$	−11.1880			−2.28373
$25$	2.01756	−	3.49452i	0.403513	−	0.698904i
$26$	2.72249	+	8.16844i	0.533925	+	1.60196i
$27$	4.32156			0.831685
$28$		0			0
$29$	1.98009	+	3.42962i	0.367694	+	0.636864i	0.989205	−	0.146541i	$-0.0468141\pi$
$29$	1.98009	+	3.42962i	0.367694	+	0.636864i	−0.621511	+	0.783406i	$0.713481\pi$
$30$	6.45420			1.17837
$31$	−1.49436	+	2.58831i	−0.268395	+	0.464874i	−0.968448	−	0.249218i	$-0.919827\pi$
$31$	−1.49436	+	2.58831i	−0.268395	+	0.464874i	0.700053	+	0.714091i	$0.253160\pi$
$32$	−1.31430	−	2.27644i	−0.232338	−	0.402421i
$33$	−1.61733			−0.281540
$34$	−15.4129			−2.64329
$35$		0			0
$36$	−8.46189	−	14.6564i	−1.41031	−	2.44274i
$37$	−0.877941	+	1.52064i	−0.144333	+	0.249991i	−0.929124	−	0.369769i	$-0.879437\pi$
$37$	−0.877941	+	1.52064i	−0.144333	+	0.249991i	0.784791	+	0.619760i	$0.212770\pi$
$38$	4.56938	−	7.91440i	0.741252	−	1.28389i
$39$	−6.58228	+	7.42239i	−1.05401	+	1.18853i
$40$	−1.99705	−	3.45900i	−0.315762	−	0.546916i
$41$	1.83584	+	3.17977i	0.286710	+	0.496597i	0.973023	−	0.230710i	$-0.0741049\pi$
$41$	1.83584	+	3.17977i	0.286710	+	0.496597i	−0.686312	+	0.727307i	$0.740772\pi$
$42$		0			0
$43$	−3.19042	+	5.52598i	−0.486535	+	0.842703i	−0.999880	−	0.0154788i	$-0.995073\pi$
$43$	−3.19042	+	5.52598i	−0.486535	+	0.842703i	0.513345	+	0.858182i	$0.328406\pi$
$44$	1.08823	+	1.88488i	0.164058	+	0.284156i
$45$	2.24482	+	3.88814i	0.334638	+	0.579610i
$46$	9.86261	+	17.0825i	1.45416	+	2.51868i
$47$	−2.17030	−	3.75906i	−0.316570	−	0.548316i	0.663200	−	0.748442i	$-0.269198\pi$
$47$	−2.17030	−	3.75906i	−0.316570	−	0.548316i	−0.979770	+	0.200127i	$0.935865\pi$
$48$	−3.17067	+	5.49176i	−0.457647	+	0.792668i
$49$		0			0
$50$	−4.81802	−	8.34505i	−0.681370	−	1.18017i
$51$	−8.87930	−	15.3794i	−1.24335	−	2.15355i
$52$	13.0792	+	2.67695i	1.81376	+	0.371226i
$53$	−0.212770	+	0.368529i	−0.0292263	+	0.0506214i	−0.880269	−	0.474476i	$-0.842638\pi$
$53$	−0.212770	+	0.368529i	−0.0292263	+	0.0506214i	0.851042	+	0.525097i	$0.175971\pi$
$54$	5.16002	−	8.93742i	0.702190	−	1.21623i
$55$	−0.288693	−	0.500031i	−0.0389274	−	0.0674242i
$56$		0			0
$57$	10.5296			1.39468
$58$	9.45706			1.24177
$59$	3.00431	+	5.20362i	0.391128	+	0.677454i	0.992599	−	0.121441i	$-0.0387516\pi$
$59$	3.00431	+	5.20362i	0.391128	+	0.677454i	−0.601470	+	0.798895i	$0.705418\pi$
$60$	5.00371	−	8.66669i	0.645977	−	1.11886i
$61$	−2.20674			−0.282544			−0.141272	−	0.989971i	$-0.545119\pi$
$61$	−2.20674			−0.282544			−0.141272	+	0.989971i	$0.545119\pi$
$62$	3.56859	+	6.18097i	0.453211	+	0.784985i
$63$		0			0
$64$	−10.8866			−1.36083
$65$	−3.46973	−	0.710156i	−0.430367	−	0.0880841i
$66$	−1.93112	+	3.34479i	−0.237704	+	0.411716i
$67$	7.01303			0.856778			0.428389	−	0.903594i	$-0.359081\pi$
$67$	7.01303			0.856778			0.428389	+	0.903594i	$0.359081\pi$
$68$	−11.9491	+	20.6964i	−1.44904	+	2.50980i
$69$	−11.3636	+	19.6824i	−1.36802	+	2.36948i
$70$		0			0
$71$	−1.80127	+	3.11988i	−0.213771	+	0.370262i	−0.952892	−	0.303311i	$-0.901908\pi$
$71$	−1.80127	+	3.11988i	−0.213771	+	0.370262i	0.739121	+	0.673573i	$0.235241\pi$
$72$	−18.5849			−2.19026
$73$	2.46714	−	4.27321i	0.288756	−	0.500141i	−0.684757	−	0.728772i	$-0.740092\pi$
$73$	2.46714	−	4.27321i	0.288756	−	0.500141i	0.973513	+	0.228631i	$0.0734249\pi$
$74$	2.09656	+	3.63134i	0.243720	+	0.422135i
$75$	5.55128	−	9.61510i	0.641007	−	1.11026i
$76$	−7.08496	−	12.2715i	−0.812701	−	1.40764i
$77$		0			0
$78$	7.49088	+	22.4753i	0.848175	+	2.54483i
$79$	−1.39270	−	2.41223i	−0.156691	−	0.271397i	0.776982	−	0.629522i	$-0.216749\pi$
$79$	−1.39270	−	2.41223i	−0.156691	−	0.271397i	−0.933674	+	0.358125i	$0.883416\pi$
$80$	−2.26386			−0.253108
$81$	−1.82122			−0.202357
$82$	8.76812			0.968277
$83$	2.86819			0.314825			0.157412	−	0.987533i	$-0.449685\pi$
$83$	2.86819			0.314825			0.157412	+	0.987533i	$0.449685\pi$
$84$		0			0
$85$	3.16992	−	5.49045i	0.343826	−	0.595523i
$86$	7.61885	+	13.1962i	0.821562	+	1.42299i
$87$	5.44818	+	9.43652i	0.584106	+	1.01170i
$88$	2.39010			0.254786
$89$	−1.04656	+	1.81269i	−0.110935	+	0.192145i	−0.916147	−	0.400842i	$-0.868718\pi$
$89$	−1.04656	+	1.81269i	−0.110935	+	0.192145i	0.805213	+	0.592986i	$0.202051\pi$
$90$	10.7214			1.13014
$91$		0			0
$92$	30.5845			3.18866
$93$	−4.11170	+	7.12167i	−0.426363	+	0.738483i
$94$	−10.3655			−1.06912
$95$	1.87954	+	3.25546i	0.192837	+	0.334003i
$96$	−3.61628	−	6.26357i	−0.369085	−	0.639273i
$97$	3.84852	−	6.66584i	0.390758	−	0.676813i	−0.601791	−	0.798653i	$-0.705546\pi$
$97$	3.84852	−	6.66584i	0.390758	−	0.676813i	0.992550	+	0.121840i	$0.0388795\pi$
$98$		0			0
$99$	−2.68663			−0.270016
$100$	−14.9409			−1.49409
$101$	2.63732			0.262423			0.131212	−	0.991354i	$-0.458113\pi$
$101$	2.63732			0.262423			0.131212	+	0.991354i	$0.458113\pi$
$102$	−42.4082			−4.19903
$103$	−5.43095	−	9.40669i	−0.535128	−	0.926868i	−0.999157	−	0.0410486i	$-0.986930\pi$
$103$	−5.43095	−	9.40669i	−0.535128	−	0.926868i	0.464029	−	0.885820i	$-0.346403\pi$
$104$	9.72736	−	10.9689i	0.953846	−	1.07559i
$105$		0			0
$106$	0.508103	+	0.880061i	0.0493514	+	0.0854791i
$107$	7.99024	−	13.8395i	0.772446	−	1.33792i	−0.163773	−	0.986498i	$-0.552366\pi$
$107$	7.99024	−	13.8395i	0.772446	−	1.33792i	0.936219	−	0.351418i	$-0.114300\pi$
$108$	−8.00077	−	13.8577i	−0.769874	−	1.33346i
$109$	−4.61738	+	7.99754i	−0.442265	+	0.766026i	−0.997857	−	0.0654294i	$-0.979158\pi$
$109$	−4.61738	+	7.99754i	−0.442265	+	0.766026i	0.555592	+	0.831455i	$0.312492\pi$
$110$	−1.37882			−0.131465
$111$	−2.41564	+	4.18400i	−0.229282	+	0.397128i
$112$		0			0
$113$	−5.09012	+	8.81635i	−0.478838	+	0.829372i	−0.999706	−	0.0242655i	$-0.992275\pi$
$113$	−5.09012	+	8.81635i	−0.478838	+	0.829372i	0.520867	+	0.853638i	$0.325609\pi$
$114$	12.5726	−	21.7763i	1.17753	−	2.03954i
$115$	−8.11364			−0.756601
$116$	7.33173	−	12.6989i	0.680734	−	1.17907i
$117$	−10.9342	+	12.3297i	−1.01087	+	1.13988i
$118$	14.3488			1.32092
$119$		0			0
$120$	−5.49485	−	9.51736i	−0.501609	−	0.868813i
$121$	−10.6545			−0.968590
$122$	−2.63489	+	4.56376i	−0.238552	+	0.413184i
$123$	5.05128	+	8.74908i	0.455459	+	0.788878i
$124$	11.0664			0.993792
$125$	8.87502			0.793806
$126$		0			0
$127$	−2.12513	−	3.68083i	−0.188575	−	0.326621i	0.756201	−	0.654340i	$-0.227053\pi$
$127$	−2.12513	−	3.68083i	−0.188575	−	0.326621i	−0.944775	+	0.327719i	$0.893720\pi$
$128$	−10.3702	+	17.9617i	−0.916606	+	1.58761i
$129$	−8.77838	+	15.2046i	−0.772893	+	1.33869i
$130$	−5.61160	+	6.32781i	−0.492170	+	0.554986i
$131$	−1.08478	−	1.87890i	−0.0947779	−	0.164160i	0.814738	−	0.579829i	$-0.196881\pi$
$131$	−1.08478	−	1.87890i	−0.0947779	−	0.164160i	−0.909516	+	0.415669i	$0.863547\pi$
$132$	2.99425	+	5.18620i	0.260616	+	0.451401i
$133$		0			0
$134$	8.37369	−	14.5037i	0.723376	−	1.25292i
$135$	2.12249	+	3.67626i	0.182675	+	0.316402i
$136$	13.1219	+	22.7278i	1.12519	+	1.94889i
$137$	−4.18158	−	7.24271i	−0.357257	−	0.618787i	0.630245	−	0.776396i	$-0.282955\pi$
$137$	−4.18158	−	7.24271i	−0.357257	−	0.618787i	−0.987501	+	0.157610i	$0.949621\pi$
$138$	27.1367	+	47.0022i	2.31003	+	4.00110i
$139$	−0.288457	+	0.499622i	−0.0244666	+	0.0423774i	−0.877999	−	0.478662i	$-0.841122\pi$
$139$	−0.288457	+	0.499622i	−0.0244666	+	0.0423774i	0.853533	+	0.521039i	$0.174455\pi$
$140$		0			0
$141$	−5.97152	−	10.3430i	−0.502893	−	0.871036i
$142$	4.30149	+	7.45040i	0.360973	+	0.625224i
$143$	1.40618	−	1.58566i	0.117591	−	0.132599i
$144$	−5.26698	+	9.12267i	−0.438915	+	0.760223i
$145$	−1.94500	+	3.36885i	−0.161524	+	0.279767i
$146$	−5.89161	−	10.2046i	−0.487593	−	0.844537i
$147$		0			0
$148$	6.50154			0.534423
$149$	2.80662			0.229928			0.114964	−	0.993370i	$-0.463325\pi$
$149$	2.80662			0.229928			0.114964	+	0.993370i	$0.463325\pi$
$150$	−13.2567	−	22.9612i	−1.08240	−	1.87478i
$151$	11.5054	−	19.9280i	0.936300	−	1.62172i	0.164000	−	0.986460i	$-0.447560\pi$
$151$	11.5054	−	19.9280i	0.936300	−	1.62172i	0.772300	−	0.635258i	$-0.219106\pi$
$152$	−15.5608			−1.26215
$153$	−14.7499	−	25.5476i	−1.19246	−	2.06540i
$154$		0			0
$155$	−2.93576			−0.235806
$156$	35.9872	+	7.36556i	2.88128	+	0.589717i
$157$	11.2880	−	19.5513i	0.900879	−	1.56037i	0.0745227	−	0.997219i	$-0.476257\pi$
$157$	11.2880	−	19.5513i	0.900879	−	1.56037i	0.826356	−	0.563148i	$-0.190410\pi$
$158$	−6.65165			−0.529177
$159$	−0.585433	+	1.01400i	−0.0464278	+	0.0804154i
$160$	1.29101	−	2.23610i	0.102064	−	0.176779i
$161$		0			0
$162$	−2.17457	+	3.76646i	−0.170850	+	0.295921i
$163$	8.17714			0.640483			0.320242	−	0.947336i	$-0.396236\pi$
$163$	8.17714			0.640483			0.320242	+	0.947336i	$0.396236\pi$
$164$	6.79761	−	11.7738i	0.530804	−	0.919380i
$165$	−0.794333	−	1.37583i	−0.0618388	−	0.107108i
$166$	3.42467	−	5.93170i	0.265806	−	0.460389i
$167$	−1.16386	−	2.01586i	−0.0900619	−	0.155992i	0.817475	−	0.575964i	$-0.195373\pi$
$167$	−1.16386	−	2.01586i	−0.0900619	−	0.155992i	−0.907537	+	0.419972i	$0.862040\pi$
$168$		0			0
$169$	−1.55408	−	12.9068i	−0.119545	−	0.992829i
$170$	−7.56988	−	13.1114i	−0.580583	−	1.00560i
$171$	17.4913			1.33760
$172$	23.6265			1.80150
$173$	8.13372			0.618396			0.309198	−	0.950998i	$-0.399939\pi$
$173$	8.13372			0.618396			0.309198	+	0.950998i	$0.399939\pi$
$174$	26.0209			1.97264
$175$		0			0
$176$	0.677355	−	1.17321i	0.0510576	−	0.0884343i
$177$	8.26630	+	14.3177i	0.621333	+	1.07618i
$178$	2.49922	+	4.32877i	0.187324	+	0.324455i
$179$	−20.9925			−1.56906			−0.784528	−	0.620093i	$-0.787095\pi$
$179$	−20.9925			−1.56906			−0.784528	+	0.620093i	$0.787095\pi$
$180$	8.31194	−	14.3967i	0.619536	−	1.07307i
$181$	1.60807			0.119527			0.0597635	−	0.998213i	$-0.480965\pi$
$181$	1.60807			0.119527			0.0597635	+	0.998213i	$0.480965\pi$
$182$		0			0
$183$	−6.07180			−0.448841
$184$	16.7933	−	29.0868i	1.23802	−	2.14431i
$185$	−1.72477			−0.126807
$186$	9.81889	+	17.0068i	0.719956	+	1.24700i
$187$	1.89690	+	3.28552i	0.138715	+	0.240261i
$188$	−8.03601	+	13.9188i	−0.586086	+	1.01513i
$189$		0			0
$190$	8.97683			0.651247
$191$	−11.5622			−0.836614			−0.418307	−	0.908306i	$-0.637376\pi$
$191$	−11.5622			−0.836614			−0.418307	+	0.908306i	$0.637376\pi$
$192$	−29.9543			−2.16176
$193$	23.5788			1.69724			0.848621	−	0.529001i	$-0.177433\pi$
$193$	23.5788			1.69724			0.848621	+	0.529001i	$0.177433\pi$
$194$	−9.19041	−	15.9183i	−0.659833	−	1.14286i
$195$	−9.54689	−	1.95398i	−0.683667	−	0.139927i
$196$		0			0
$197$	0.735472	+	1.27387i	0.0524002	+	0.0907598i	0.891036	−	0.453933i	$-0.149980\pi$
$197$	0.735472	+	1.27387i	0.0524002	+	0.0907598i	−0.838636	+	0.544693i	$0.816646\pi$
$198$	−3.20788	+	5.55622i	−0.227974	+	0.394863i
$199$	4.69700	+	8.13543i	0.332961	+	0.576706i	0.983091	−	0.183117i	$-0.0586189\pi$
$199$	4.69700	+	8.13543i	0.332961	+	0.576706i	−0.650130	+	0.759823i	$0.725286\pi$
$200$	−8.20374	+	14.2093i	−0.580092	+	1.00475i
$201$	19.2962			1.36105
$202$	3.14901	−	5.45425i	0.221564	−	0.383760i
$203$		0			0
$204$	−32.8776	+	56.9456i	−2.30189	+	3.98699i
$205$	−1.80331	+	3.12343i	−0.125949	+	0.218150i
$206$	−25.9386			−1.80723
$207$	−18.8767	+	32.6955i	−1.31202	+	2.27249i
$208$	−2.62749	−	7.88340i	−0.182183	−	0.546615i
$209$	−2.24946			−0.155598
$210$		0			0
$211$	4.47109	+	7.74416i	0.307803	+	0.533130i	0.977881	−	0.209160i	$-0.0670730\pi$
$211$	4.47109	+	7.74416i	0.307803	+	0.533130i	−0.670079	+	0.742290i	$0.733740\pi$
$212$	1.57566			0.108217
$213$	−4.95615	+	8.58430i	−0.339589	+	0.588186i
$214$	−19.0810	−	33.0493i	−1.30435	−	2.25920i
$215$	−6.26778			−0.427459
$216$	−17.5722			−1.19563
$217$		0			0
$218$	11.0265	+	19.0984i	0.746808	+	1.29351i
$219$	6.78827	−	11.7576i	0.458709	−	0.794507i
$220$	−1.06895	+	1.85148i	−0.0720686	+	0.124827i
$221$	22.7983	+	4.66618i	1.53358	+	0.313881i
$222$	5.76863	+	9.99156i	0.387165	+	0.670589i
$223$	10.9098	+	18.8963i	0.730574	+	1.26539i	0.956638	+	0.291279i	$0.0940809\pi$
$223$	10.9098	+	18.8963i	0.730574	+	1.26539i	−0.226064	+	0.974112i	$0.572586\pi$
$224$		0			0
$225$	9.22154	−	15.9722i	0.614769	−	1.06481i
$226$	12.1554	+	21.0538i	0.808565	+	1.40048i
$227$	−9.27627	−	16.0670i	−0.615687	−	1.06640i	−0.990263	−	0.139206i	$-0.955545\pi$
$227$	−9.27627	−	16.0670i	−0.615687	−	1.06640i	0.374576	−	0.927196i	$-0.377788\pi$
$228$	−19.4941	−	33.7648i	−1.29103	−	2.23613i
$229$	9.67525	+	16.7580i	0.639359	+	1.10740i	0.985574	+	0.169247i	$0.0541334\pi$
$229$	9.67525	+	16.7580i	0.639359	+	1.10740i	−0.346215	+	0.938155i	$0.612533\pi$
$230$	−9.68784	+	16.7798i	−0.638797	+	1.10643i
$231$		0			0
$232$	−8.05137	−	13.9454i	−0.528599	−	0.915560i
$233$	−8.08170	−	13.9979i	−0.529450	−	0.917034i	−0.999410	−	0.0343462i	$-0.989065\pi$
$233$	−8.08170	−	13.9979i	−0.529450	−	0.917034i	0.469960	−	0.882688i	$-0.344268\pi$
$234$	12.4435	+	37.3349i	0.813458	+	2.44066i
$235$	2.13184	−	3.69245i	0.139066	−	0.240869i
$236$	11.1241	−	19.2676i	0.724119	−	1.25421i
$237$	−3.83199	−	6.63720i	−0.248915	−	0.431133i
$238$		0			0
$239$	16.1037			1.04166			0.520831	−	0.853660i	$-0.325622\pi$
$239$	16.1037			1.04166			0.520831	+	0.853660i	$0.325622\pi$
$240$	−6.22897			−0.402079
$241$	−2.00300	−	3.46930i	−0.129025	−	0.223477i	0.794274	−	0.607559i	$-0.207851\pi$
$241$	−2.00300	−	3.46930i	−0.129025	−	0.223477i	−0.923299	+	0.384082i	$0.874518\pi$
$242$	−12.7217	+	22.0346i	−0.817779	+	1.41643i
$243$	−17.9757			−1.15314
$244$	4.08548	+	7.07625i	0.261546	+	0.453011i
$245$		0			0
$246$	24.1253			1.53817
$247$	−9.15497	+	10.3234i	−0.582517	+	0.656864i
$248$	6.07631	−	10.5245i	0.385846	−	0.668305i
$249$	7.89176			0.500120
$250$	10.5969	−	18.3544i	0.670209	−	1.16084i
$251$	1.62344	−	2.81188i	0.102471	−	0.177484i	−0.810231	−	0.586110i	$-0.800659\pi$
$251$	1.62344	−	2.81188i	0.102471	−	0.177484i	0.912702	+	0.408626i	$0.133992\pi$
$252$		0			0
$253$	2.42763	−	4.20477i	0.152624	−	0.264352i
$254$	−10.1498			−0.636853
$255$	8.72195	−	15.1069i	0.546190	−	0.946029i
$256$	13.8778	+	24.0371i	0.867365	+	1.50232i
$257$	−13.4462	+	23.2895i	−0.838751	+	1.45276i	0.0521891	+	0.998637i	$0.483380\pi$
$257$	−13.4462	+	23.2895i	−0.838751	+	1.45276i	−0.890940	+	0.454122i	$0.849953\pi$
$258$	20.9631	+	36.3092i	1.30511	+	2.26051i
$259$		0			0
$260$	4.14650	+	12.4410i	0.257155	+	0.771556i
$261$	9.05027	+	15.6755i	0.560198	+	0.970291i
$262$	−5.18100			−0.320084
$263$	−3.80706			−0.234753			−0.117377	−	0.993087i	$-0.537448\pi$
$263$	−3.80706			−0.234753			−0.117377	+	0.993087i	$0.537448\pi$
$264$	6.57631			0.404744
$265$	−0.418000			−0.0256775
$266$		0			0
$267$	−2.87958	+	4.98757i	−0.176227	+	0.305235i
$268$	−12.9836	−	22.4883i	−0.793102	−	1.37369i
$269$	−11.9190	−	20.6444i	−0.726716	−	1.25871i	−0.958264	−	0.285886i	$-0.907712\pi$
$269$	−11.9190	−	20.6444i	−0.726716	−	1.25871i	0.231548	−	0.972824i	$-0.425621\pi$
$270$	10.1372			0.616929
$271$	4.95068	−	8.57482i	0.300732	−	0.520883i	−0.675570	−	0.737296i	$-0.736102\pi$
$271$	4.95068	−	8.57482i	0.300732	−	0.520883i	0.976302	+	0.216413i	$0.0694357\pi$
$272$	14.8750			0.901931
$273$		0			0
$274$	−19.9715			−1.20653
$275$	−1.18593	+	2.05409i	−0.0715142	+	0.123866i
$276$	84.1526			5.06539
$277$	−5.89289	−	10.2068i	−0.354069	−	0.613266i	0.632889	−	0.774243i	$-0.281869\pi$
$277$	−5.89289	−	10.2068i	−0.354069	−	0.613266i	−0.986958	+	0.160977i	$0.948536\pi$
$278$	0.688846	+	1.19312i	0.0413142	+	0.0715584i
$279$	−6.83017	+	11.8302i	−0.408912	+	0.708256i
$280$		0			0
$281$	12.9976			0.775372			0.387686	−	0.921791i	$-0.373274\pi$
$281$	12.9976			0.775372			0.387686	+	0.921791i	$0.373274\pi$
$282$	−28.5204			−1.69837
$283$	16.8050			0.998952			0.499476	−	0.866328i	$-0.333526\pi$
$283$	16.8050			0.998952			0.499476	+	0.866328i	$0.333526\pi$
$284$	13.3392			0.791534
$285$	5.17151	+	8.95733i	0.306334	+	0.530586i
$286$	−1.60029	−	4.80143i	−0.0946270	−	0.283914i
$287$		0			0
$288$	−6.00719	−	10.4048i	−0.353977	−	0.613107i
$289$	−12.3283	+	21.3533i	−0.725197	+	1.25608i
$290$	4.64474	+	8.04493i	0.272749	+	0.472414i
$291$	10.5891	−	18.3409i	0.620746	−	1.07516i
$292$	−18.2702			−1.06918
$293$	−7.04782	+	12.2072i	−0.411738	+	0.713151i	−0.995080	−	0.0990757i	$-0.968411\pi$
$293$	−7.04782	+	12.2072i	−0.411738	+	0.713151i	0.583342	+	0.812227i	$0.301745\pi$
$294$		0			0
$295$	−2.95108	+	5.11141i	−0.171818	+	0.297598i
$296$	3.56985	−	6.18316i	0.207493	−	0.359389i
$297$	−2.54022			−0.147399
$298$	3.35116	−	5.80438i	0.194128	−	0.336239i
$299$	−9.41686	−	28.2539i	−0.544591	−	1.63397i
$300$	−41.1097			−2.37347
$301$		0			0
$302$	−27.4754	−	47.5888i	−1.58103	−	2.73843i
$303$	7.25654			0.416877
$304$	−4.40993	+	7.63822i	−0.252927	+	0.438082i
$305$	−1.08382	−	1.87723i	−0.0620593	−	0.107490i
$306$	−70.4466			−4.02716
$307$	−15.8786			−0.906240			−0.453120	−	0.891450i	$-0.649689\pi$
$307$	−15.8786			−0.906240			−0.453120	+	0.891450i	$0.649689\pi$
$308$		0			0
$309$	−14.9431	−	25.8823i	−0.850086	−	1.47239i
$310$	−3.50535	+	6.07145i	−0.199091	+	0.344835i
$311$	−14.3017	+	24.7713i	−0.810975	+	1.40465i	0.101208	+	0.994865i	$0.467729\pi$
$311$	−14.3017	+	24.7713i	−0.810975	+	1.40465i	−0.912183	+	0.409784i	$0.865604\pi$
$312$	26.7646	−	30.1806i	1.51525	−	1.70864i
$313$	−9.28962	−	16.0901i	−0.525080	−	0.909465i	−0.999573	−	0.0292063i	$-0.990702\pi$
$313$	−9.28962	−	16.0901i	−0.525080	−	0.909465i	0.474493	−	0.880259i	$-0.342631\pi$
$314$	−26.9561	−	46.6893i	−1.52122	−	2.63483i
$315$		0			0
$316$	−5.15679	+	8.93182i	−0.290092	+	0.502454i
$317$	−15.3223	−	26.5389i	−0.860584	−	1.49057i	−0.871366	−	0.490633i	$-0.836766\pi$
$317$	−15.3223	−	26.5389i	−0.860584	−	1.49057i	0.0107826	−	0.999942i	$-0.496568\pi$
$318$	1.39804	+	2.42147i	0.0783979	+	0.135789i
$319$	−1.16390	−	2.01594i	−0.0651660	−	0.112871i
$320$	−5.34685	−	9.26102i	−0.298898	−	0.517707i
$321$	21.9850	−	38.0791i	1.22708	−	2.12537i
$322$		0			0
$323$	−12.3498	−	21.3904i	−0.687160	−	1.19020i
$324$	3.37173	+	5.84001i	0.187318	+	0.324445i
$325$	4.60026	+	13.8024i	0.255177	+	0.765620i
$326$	9.76366	−	16.9112i	0.540759	−	0.936622i
$327$	−12.7046	+	22.0051i	−0.702568	+	1.21688i
$328$	−7.46483	−	12.9295i	−0.412177	−	0.713911i
$329$		0			0
$330$	−3.79379			−0.208842
$331$	27.2277			1.49657			0.748284	−	0.663378i	$-0.230878\pi$
$331$	27.2277			1.49657			0.748284	+	0.663378i	$0.230878\pi$
$332$	−5.31005	−	9.19728i	−0.291427	−	0.504766i
$333$	−4.01275	+	6.95028i	−0.219897	+	0.380873i
$334$	−5.55867			−0.304157
$335$	3.44438	+	5.96584i	0.188187	+	0.325949i
$336$		0			0
$337$	−12.3160			−0.670898			−0.335449	−	0.942058i	$-0.608888\pi$
$337$	−12.3160			−0.670898			−0.335449	+	0.942058i	$0.608888\pi$
$338$	−28.5481	−	12.1969i	−1.55281	−	0.663426i
$339$	−14.0054	+	24.2580i	−0.760666	+	1.31751i
$340$	−23.4746			−1.27309
$341$	0.878389	−	1.52141i	0.0475674	−	0.0823892i
$342$	20.8850	−	36.1738i	1.12933	−	1.95606i
$343$		0			0
$344$	12.9728	−	22.4695i	0.699445	−	1.21148i
$345$	−22.3245			−1.20191
$346$	9.71182	−	16.8214i	0.522111	−	0.904322i
$347$	−3.07253	−	5.32177i	−0.164942	−	0.285688i	0.771693	−	0.635996i	$-0.219410\pi$
$347$	−3.07253	−	5.32177i	−0.164942	−	0.285688i	−0.936635	+	0.350308i	$0.886077\pi$
$348$	20.1731	−	34.9408i	1.08139	−	1.87302i
$349$	6.51563	+	11.2854i	0.348774	+	0.604094i	0.986032	−	0.166557i	$-0.0532649\pi$
$349$	6.51563	+	11.2854i	0.348774	+	0.604094i	−0.637258	+	0.770650i	$0.719932\pi$
$350$		0			0
$351$	−10.3383	+	11.6578i	−0.551820	+	0.622249i
$352$	0.772550	+	1.33810i	0.0411771	+	0.0713208i
$353$	−31.6665			−1.68544			−0.842718	−	0.538356i	$-0.819046\pi$
$353$	−31.6665			−1.68544			−0.842718	+	0.538356i	$0.819046\pi$
$354$	39.4805			2.09836
$355$	−3.53870			−0.187814
$356$	7.75021			0.410761
$357$		0			0
$358$	−25.0655	+	43.4147i	−1.32475	+	2.29454i
$359$	−9.96610	−	17.2618i	−0.525991	−	0.911043i	−0.999542	−	0.0302764i	$-0.990361\pi$
$359$	−9.96610	−	17.2618i	−0.525991	−	0.911043i	0.473551	−	0.880767i	$-0.342972\pi$
$360$	−9.12780	−	15.8098i	−0.481077	−	0.833251i
$361$	−4.35488			−0.229204
$362$	1.92007	−	3.32566i	0.100917	−	0.174793i
$363$	−29.3156			−1.53867
$364$		0			0
$365$	4.84684			0.253695
$366$	−7.24984	+	12.5571i	−0.378955	+	0.656370i
$367$	−19.7190			−1.02932			−0.514662	−	0.857393i	$-0.672082\pi$
$367$	−19.7190			−1.02932			−0.514662	+	0.857393i	$0.672082\pi$
$368$	−9.51844	−	16.4864i	−0.496183	−	0.859414i
$369$	8.39096	+	14.5336i	0.436816	+	0.756588i
$370$	−2.05940	+	3.56699i	−0.107063	+	0.185439i
$371$		0			0
$372$	30.4490			1.57870
$373$	17.5469			0.908544			0.454272	−	0.890863i	$-0.349899\pi$
$373$	17.5469			0.908544			0.454272	+	0.890863i	$0.349899\pi$
$374$	9.05972			0.468467
$375$	24.4194			1.26101
$376$	8.82478	+	15.2850i	0.455103	+	0.788262i
$377$	−13.9887	−	2.86308i	−0.720452	−	0.147456i
$378$		0			0
$379$	5.85068	+	10.1337i	0.300529	+	0.520532i	0.976256	−	0.216620i	$-0.0695034\pi$
$379$	5.85068	+	10.1337i	0.300529	+	0.520532i	−0.675727	+	0.737152i	$0.736170\pi$
$380$	6.95942	−	12.0541i	0.357010	−	0.618360i
$381$	−5.84725	−	10.1277i	−0.299563	−	0.518859i
$382$	−13.8055	+	23.9119i	−0.706352	+	1.22344i
$383$	21.5288			1.10007			0.550036	−	0.835141i	$-0.314614\pi$
$383$	21.5288			1.10007			0.550036	+	0.835141i	$0.314614\pi$
$384$	−28.5334	+	49.4213i	−1.45609	+	2.52202i
$385$		0			0
$386$	28.1536	−	48.7634i	1.43298	−	2.48199i
$387$	−14.5823	+	25.2572i	−0.741258	+	1.28390i
$388$	−28.5000			−1.44687
$389$	−13.2455	+	22.9419i	−0.671574	+	1.16320i	0.305884	+	0.952069i	$0.401048\pi$
$389$	−13.2455	+	22.9419i	−0.671574	+	1.16320i	−0.977458	+	0.211131i	$0.932285\pi$
$390$	−15.4402	+	17.4108i	−0.781845	+	0.881632i
$391$	53.3118			2.69609
$392$		0			0
$393$	−2.98476	−	5.16975i	−0.150561	−	0.260779i
$394$	3.51267			0.176966
$395$	1.36802	−	2.36949i	0.0688327	−	0.119222i
$396$	4.97392	+	8.61508i	0.249949	+	0.432924i
$397$	33.7989			1.69632			0.848160	−	0.529740i	$-0.177711\pi$
$397$	33.7989			1.69632			0.848160	+	0.529740i	$0.177711\pi$
$398$	22.4332			1.12447
$399$		0			0
$400$	4.64989	+	8.05384i	0.232494	+	0.402692i
$401$	−10.8059	+	18.7164i	−0.539623	+	0.934655i	0.459301	+	0.888281i	$0.348100\pi$
$401$	−10.8059	+	18.7164i	−0.539623	+	0.934655i	−0.998924	+	0.0463741i	$0.985233\pi$
$402$	23.0400	−	39.9065i	1.14913	−	1.99035i
$403$	−3.40730	−	10.2231i	−0.169730	−	0.509250i
$404$	−4.88264	−	8.45697i	−0.242920	−	0.420750i
$405$	−0.894473	−	1.54927i	−0.0444467	−	0.0769839i
$406$		0			0
$407$	0.516056	−	0.893835i	0.0255799	−	0.0443058i
$408$	36.1047	+	62.5351i	1.78745	+	3.09595i
$409$	3.87109	+	6.70492i	0.191413	+	0.331537i	0.945719	−	0.324986i	$-0.105360\pi$
$409$	3.87109	+	6.70492i	0.191413	+	0.331537i	−0.754306	+	0.656523i	$0.772026\pi$
$410$	4.30637	+	7.45886i	0.212677	+	0.368367i
$411$	−11.5055	−	19.9282i	−0.567526	−	0.982984i
$412$	−20.1093	+	34.8303i	−0.990714	+	1.71597i
$413$		0			0
$414$	45.0783	+	78.0780i	2.21548	+	3.83732i
$415$	1.40868	+	2.43991i	0.0691495	+	0.119770i
$416$	9.28509	+	1.90040i	0.455239	+	0.0931746i
$417$	−0.793683	+	1.37470i	−0.0388668	+	0.0673193i
$418$	−2.68589	+	4.65211i	−0.131371	+	0.227542i
$419$	−4.05097	−	7.01649i	−0.197903	−	0.342778i	0.749945	−	0.661500i	$-0.230080\pi$
$419$	−4.05097	−	7.01649i	−0.197903	−	0.342778i	−0.947848	+	0.318722i	$0.896746\pi$
$420$		0			0
$421$	−32.1124			−1.56506			−0.782530	−	0.622612i	$-0.786071\pi$
$421$	−32.1124			−1.56506			−0.782530	+	0.622612i	$0.786071\pi$
$422$	21.3543			1.03951
$423$	−9.91963	−	17.1813i	−0.482309	−	0.835384i
$424$	0.865159	−	1.49850i	0.0420158	−	0.0727735i
$425$	−26.0435			−1.26330
$426$	11.8355	+	20.4996i	0.573430	+	0.993210i
$427$		0			0
$428$	−59.1713			−2.86015
$429$	3.86908	−	4.36290i	0.186801	−	0.210643i
$430$	−7.48384	+	12.9624i	−0.360903	+	0.625102i
$431$	−29.5281			−1.42232			−0.711159	−	0.703031i	$-0.751829\pi$
$431$	−29.5281			−1.42232			−0.711159	+	0.703031i	$0.751829\pi$
$432$	−4.97996	+	8.62554i	−0.239598	+	0.414997i
$433$	11.0455	−	19.1314i	0.530813	−	0.919395i	−0.468540	−	0.883442i	$-0.655220\pi$
$433$	11.0455	−	19.1314i	0.530813	−	0.919395i	0.999353	−	0.0359531i	$-0.0114467\pi$
$434$		0			0
$435$	−5.35164	+	9.26931i	−0.256591	+	0.444429i
$436$	34.1938			1.63758
$437$	−15.8051	+	27.3752i	−0.756060	+	1.30953i
$438$	−16.2106	−	28.0777i	−0.774575	−	1.34160i
$439$	−3.17790	+	5.50428i	−0.151673	+	0.262705i	−0.931843	−	0.362863i	$-0.881799\pi$
$439$	−3.17790	+	5.50428i	−0.151673	+	0.262705i	0.780170	+	0.625568i	$0.215133\pi$
$440$	1.17387	+	2.03321i	0.0559622	+	0.0969294i
$441$		0			0
$442$	36.8718	−	41.5777i	1.75381	−	1.97765i
$443$	6.78135	+	11.7456i	0.322192	+	0.558052i	0.980940	−	0.194311i	$-0.0622472\pi$
$443$	6.78135	+	11.7456i	0.322192	+	0.558052i	−0.658748	+	0.752363i	$0.728914\pi$
$444$	17.8889			0.848967
$445$	−2.05602			−0.0974648
$446$	52.1060			2.46729
$447$	7.72237			0.365255
$448$		0			0
$449$	−10.9559	+	18.9762i	−0.517041	+	0.895541i	0.482763	+	0.875751i	$0.339633\pi$
$449$	−10.9559	+	18.9762i	−0.517041	+	0.895541i	−0.999804	+	0.0197900i	$0.993700\pi$
$450$	−22.0214	−	38.1421i	−1.03810	−	1.79804i
$451$	−1.07911	−	1.86908i	−0.0508134	−	0.0880115i
$452$	37.6946			1.77300
$453$	31.6570	−	54.8315i	1.48737	−	2.57621i
$454$	−44.3041			−2.07930
$455$		0			0
$456$	−42.8151			−2.00500
$457$	−7.60732	+	13.1763i	−0.355855	+	0.616359i	−0.987264	−	0.159091i	$-0.949144\pi$
$457$	−7.60732	+	13.1763i	−0.355855	+	0.616359i	0.631409	+	0.775450i	$0.282477\pi$
$458$	46.2097			2.15924
$459$	−13.9461	−	24.1554i	−0.650949	−	1.12748i
$460$	15.0213	+	26.0176i	0.700371	+	1.21308i
$461$	−8.10813	+	14.0437i	−0.377633	+	0.654080i	−0.990717	−	0.135937i	$-0.956595\pi$
$461$	−8.10813	+	14.0437i	−0.377633	+	0.654080i	0.613084	+	0.790018i	$0.289929\pi$
$462$		0			0
$463$	−1.44769			−0.0672799			−0.0336400	−	0.999434i	$-0.510710\pi$
$463$	−1.44769			−0.0672799			−0.0336400	+	0.999434i	$0.510710\pi$
$464$	−9.12705			−0.423713
$465$	−8.07768			−0.374593
$466$	−38.5988			−1.78805
$467$	7.00337	+	12.1302i	0.324078	+	0.561319i	0.981325	−	0.192356i	$-0.0616128\pi$
$467$	7.00337	+	12.1302i	0.324078	+	0.561319i	−0.657248	+	0.753675i	$0.728279\pi$
$468$	59.7803	+	12.2353i	2.76334	+	0.565579i
$469$		0			0
$470$	−5.09091	−	8.81772i	−0.234826	−	0.406731i
$471$	31.0586	−	53.7951i	1.43111	−	2.47875i
$472$	−12.2160	−	21.1588i	−0.562288	−	0.973912i
$473$	1.87534	−	3.24818i	0.0862282	−	0.149352i
$474$	−18.3019			−0.840633
$475$	7.72100	−	13.3732i	0.354264	−	0.613603i
$476$		0			0
$477$	−0.972495	+	1.68441i	−0.0445275	+	0.0771239i
$478$	19.2281	−	33.3041i	0.879474	−	1.52329i
$479$	30.0243			1.37185			0.685923	−	0.727674i	$-0.259399\pi$
$479$	30.0243			1.37185			0.685923	+	0.727674i	$0.259399\pi$
$480$	3.55219	−	6.15258i	0.162135	−	0.280826i
$481$	−2.00180	−	6.00611i	−0.0912742	−	0.273855i
$482$	−9.56649			−0.435742
$483$		0			0
$484$	19.7253	+	34.1652i	0.896605	+	1.55296i
$485$	7.56065			0.343312
$486$	−21.4633	+	37.1756i	−0.973597	+	1.68632i
$487$	14.2452	+	24.6733i	0.645510	+	1.11806i	0.984184	+	0.177152i	$0.0566884\pi$
$487$	14.2452	+	24.6733i	0.645510	+	1.11806i	−0.338674	+	0.940904i	$0.609978\pi$
$488$	8.97297			0.406187
$489$	22.4992			1.01745
$490$		0			0
$491$	14.2339	+	24.6538i	0.642365	+	1.11261i	0.984903	+	0.173105i	$0.0553799\pi$
$491$	14.2339	+	24.6538i	0.642365	+	1.11261i	−0.342539	+	0.939504i	$0.611287\pi$
$492$	18.7035	−	32.3954i	0.843218	−	1.46050i
$493$	12.7799	−	22.1354i	0.575578	−	0.996930i
$494$	10.4187	+	31.2598i	0.468759	+	1.40644i
$495$	−1.31951	−	2.28546i	−0.0593076	−	0.102724i
$496$	−3.44406	−	5.96528i	−0.154643	−	0.267849i
$497$		0			0
$498$	9.42290	−	16.3209i	0.422250	−	0.731359i
$499$	13.1164	+	22.7183i	0.587172	+	1.01701i	0.994601	+	0.103775i	$0.0330921\pi$
$499$	13.1164	+	22.7183i	0.587172	+	1.01701i	−0.407429	+	0.913237i	$0.633575\pi$
$500$	−16.4309	−	28.4591i	−0.734811	−	1.27273i
$501$	−3.20233	−	5.54659i	−0.143069	−	0.247803i
$502$	−3.87684	−	6.71488i	−0.173032	−	0.299700i
$503$	4.26588	−	7.38872i	0.190206	−	0.329447i	−0.755112	−	0.655595i	$-0.772418\pi$
$503$	4.26588	−	7.38872i	0.190206	−	0.329447i	0.945318	+	0.326149i	$0.105751\pi$
$504$		0			0
$505$	1.29529	+	2.24352i	0.0576398	+	0.0998351i
$506$	−5.79726	−	10.0412i	−0.257720	−	0.446384i
$507$	−4.27602	−	35.5127i	−0.189905	−	1.57717i
$508$	−7.86876	+	13.6291i	−0.349120	+	0.604693i
$509$	−6.51298	+	11.2808i	−0.288683	+	0.500014i	−0.973496	−	0.228706i	$-0.926551\pi$
$509$	−6.51298	+	11.2808i	−0.288683	+	0.500014i	0.684813	+	0.728719i	$0.259884\pi$
$510$	−20.8283	−	36.0758i	−0.922295	−	1.59746i
$511$		0			0
$512$	24.8008			1.09605
$513$	16.5382			0.730177
$514$	32.1100	+	55.6162i	1.41631	+	2.45312i
$515$	5.33472	−	9.24000i	0.235076	−	0.407163i
$516$	65.0078			2.86181
$517$	1.27571	+	2.20959i	0.0561055	+	0.0971775i
$518$		0			0
$519$	22.3798			0.982363
$520$	14.1085	+	2.88761i	0.618698	+	0.126630i
$521$	2.23285	−	3.86741i	0.0978230	−	0.169434i	−0.812960	−	0.582319i	$-0.802145\pi$
$521$	2.23285	−	3.86741i	0.0978230	−	0.169434i	0.910783	+	0.412885i	$0.135479\pi$
$522$	43.2248			1.89190
$523$	−1.45406	+	2.51850i	−0.0635815	+	0.110126i	−0.896064	−	0.443925i	$-0.853586\pi$
$523$	−1.45406	+	2.51850i	−0.0635815	+	0.110126i	0.832482	+	0.554051i	$0.186919\pi$
$524$	−4.01665	+	6.95704i	−0.175468	+	0.303920i
$525$		0			0
$526$	−4.54570	+	7.87339i	−0.198202	+	0.343296i
$527$	19.2898			0.840277
$528$	1.86373	−	3.22807i	0.0811084	−	0.140484i
$529$	−22.6139	−	39.1684i	−0.983213	−	1.70297i
$530$	−0.499100	+	0.864466i	−0.0216795	+	0.0375500i
$531$	13.7316	+	23.7838i	0.595901	+	1.03213i
$532$		0			0
$533$	−12.9696	−	2.65451i	−0.561775	−	0.114980i
$534$	6.87654	+	11.9105i	0.297577	+	0.515418i
$535$	15.6973			0.678654
$536$	−28.5161			−1.23171
$537$	−57.7605			−2.49255
$538$	−56.9262			−2.45426
$539$		0			0
$540$	7.85899	−	13.6122i	0.338197	−	0.585775i
$541$	9.23193	+	15.9902i	0.396912	+	0.687471i	0.993343	−	0.115193i	$-0.0367486\pi$
$541$	9.23193	+	15.9902i	0.396912	+	0.687471i	−0.596431	+	0.802664i	$0.703415\pi$
$542$	−11.8224	−	20.4770i	−0.507815	−	0.879562i
$543$	4.42458			0.189877
$544$	−8.48277	+	14.6926i	−0.363696	+	0.629940i
$545$	−9.07112			−0.388564
$546$		0			0
$547$	34.9817			1.49571			0.747856	−	0.663861i	$-0.231083\pi$
$547$	34.9817			1.49571			0.747856	+	0.663861i	$0.231083\pi$
$548$	−15.4832	+	26.8177i	−0.661411	+	1.14560i
$549$	−10.0862			−0.430469
$550$	2.83204	+	4.90524i	0.120759	+	0.209160i
$551$	7.57760	+	13.1248i	0.322817	+	0.559135i
$552$	46.2063	−	80.0317i	1.96667	−	3.40638i
$553$		0			0
$554$	−28.1449			−1.19576
$555$	−4.74566			−0.201442
$556$	2.13615			0.0905930
$557$	0.0531413			0.00225167			0.00112583	−	0.999999i	$-0.499642\pi$
$557$	0.0531413			0.00225167			0.00112583	+	0.999999i	$0.499642\pi$
$558$	16.3107	+	28.2510i	0.690487	+	1.19596i
$559$	−7.27451	−	21.8261i	−0.307679	−	0.923146i
$560$		0			0
$561$	5.21927	+	9.04004i	0.220358	+	0.381671i
$562$	15.5194	−	26.8804i	0.654646	−	1.13388i
$563$	3.99253	+	6.91527i	0.168265	+	0.291444i	0.937810	−	0.347149i	$-0.112850\pi$
$563$	3.99253	+	6.91527i	0.168265	+	0.291444i	−0.769545	+	0.638593i	$0.779517\pi$
$564$	−22.1109	+	38.2972i	−0.931037	+	1.61260i
$565$	−9.99985			−0.420697
$566$	20.0655	−	34.7544i	0.843414	−	1.46084i
$567$		0			0
$568$	7.32424	−	12.6860i	0.307318	−	0.532291i
$569$	13.3621	−	23.1438i	0.560167	−	0.970237i	−0.437315	−	0.899308i	$-0.644070\pi$
$569$	13.3621	−	23.1438i	0.560167	−	0.970237i	0.997481	−	0.0709285i	$-0.0225962\pi$
$570$	24.6995			1.03455
$571$	−6.74647	+	11.6852i	−0.282331	+	0.489012i	−0.971958	−	0.235153i	$-0.924441\pi$
$571$	−6.74647	+	11.6852i	−0.282331	+	0.489012i	0.689627	+	0.724164i	$0.257774\pi$
$572$	−7.68799	−	1.57352i	−0.321451	−	0.0657920i
$573$	−31.8132			−1.32902
$574$		0			0
$575$	16.6651	+	28.8648i	0.694982	+	1.20374i
$576$	−49.7587			−2.07328
$577$	6.00662	−	10.4038i	0.250059	−	0.433115i	−0.713483	−	0.700673i	$-0.752883\pi$
$577$	6.00662	−	10.4038i	0.250059	−	0.433115i	0.963542	+	0.267558i	$0.0862167\pi$
$578$	29.4406	+	50.9925i	1.22457	+	2.12101i
$579$	64.8767			2.69618
$580$	14.4036			0.598078
$581$		0			0
$582$	−25.2872	−	43.7988i	−1.04819	−	1.81552i
$583$	0.125067	−	0.216622i	0.00517974	−	0.00897158i
$584$	−10.0318	+	17.3756i	−0.415118	+	0.719005i
$585$	−15.8589	−	3.24586i	−0.655683	−	0.134200i
$586$	16.8305	+	29.1512i	0.695260	+	1.20422i
$587$	5.21177	+	9.02705i	0.215113	+	0.372586i	0.953307	−	0.302002i	$-0.0976548\pi$
$587$	5.21177	+	9.02705i	0.215113	+	0.372586i	−0.738195	+	0.674588i	$0.764321\pi$
$588$		0			0
$589$	−5.71876	+	9.90518i	−0.235637	+	0.408136i
$590$	7.04728	+	12.2062i	0.290132	+	0.502523i
$591$	2.02364	+	3.50504i	0.0832412	+	0.144178i
$592$	−2.02339	−	3.50462i	−0.0831610	−	0.144039i
$593$	−11.1751	−	19.3558i	−0.458905	−	0.794847i	0.539998	−	0.841666i	$-0.318425\pi$
$593$	−11.1751	−	19.3558i	−0.458905	−	0.794847i	−0.998903	+	0.0468194i	$0.985091\pi$
$594$	−3.03307	+	5.25344i	−0.124449	+	0.215551i
$595$		0			0
$596$	−5.19607	−	8.99986i	−0.212839	−	0.368649i
$597$	12.9237	+	22.3845i	0.528931	+	0.916135i
$598$	−69.6759	−	14.2607i	−2.84926	−	0.583163i
$599$	−0.579463	+	1.00366i	−0.0236762	+	0.0410084i	−0.877621	−	0.479356i	$-0.840870\pi$
$599$	−0.579463	+	1.00366i	−0.0236762	+	0.0410084i	0.853945	+	0.520364i	$0.174204\pi$
$600$	−22.5724	+	39.0966i	−0.921515	+	1.59611i
$601$	21.0907	+	36.5301i	0.860306	+	1.49009i	0.871633	+	0.490158i	$0.163061\pi$
$601$	21.0907	+	36.5301i	0.860306	+	1.49009i	−0.0113271	+	0.999936i	$0.503606\pi$
$602$		0			0
$603$	32.0540			1.30534
$604$	−85.2029			−3.46686
$605$	−5.23284	−	9.06355i	−0.212745	−	0.368486i
$606$	8.66444	−	15.0072i	0.351969	−	0.609628i
$607$	18.1569			0.736965			0.368482	−	0.929635i	$-0.379877\pi$
$607$	18.1569			0.736965			0.368482	+	0.929635i	$0.379877\pi$
$608$	−5.02970	−	8.71169i	−0.203981	−	0.353306i
$609$		0			0
$610$	−5.17640			−0.209586
$611$	15.3324	+	3.13811i	0.620282	+	0.126954i
$612$	−54.6147	+	94.5955i	−2.20767	+	3.82380i
$613$	−0.902645			−0.0364575			−0.0182288	−	0.999834i	$-0.505803\pi$
$613$	−0.902645			−0.0364575			−0.0182288	+	0.999834i	$0.505803\pi$
$614$	−18.9594	+	32.8386i	−0.765137	+	1.32526i
$615$	−4.96177	+	8.59404i	−0.200078	+	0.346545i
$616$		0			0
$617$	13.0218	−	22.5544i	0.524238	−	0.908008i	−0.475363	−	0.879790i	$-0.657683\pi$
$617$	13.0218	−	22.5544i	0.524238	−	0.908008i	0.999602	−	0.0282180i	$-0.00898327\pi$
$618$	−71.3696			−2.87091
$619$	13.4171	−	23.2390i	0.539277	−	0.934056i	−0.459666	−	0.888092i	$-0.652031\pi$
$619$	13.4171	−	23.2390i	0.539277	−	0.934056i	0.998943	−	0.0459638i	$-0.0146359\pi$
$620$	5.43515	+	9.41396i	0.218281	+	0.378074i
$621$	−17.8481	+	30.9138i	−0.716218	+	1.24053i
$622$	34.1530	+	59.1547i	1.36941	+	2.37189i
$623$		0			0
$624$	−7.22948	−	21.6910i	−0.289411	−	0.868335i
$625$	−5.72894	−	9.92281i	−0.229158	−	0.396912i
$626$	−44.3679			−1.77330
$627$	−6.18933			−0.247178
$628$	−83.5925			−3.33570
$629$	11.3328			0.451869
$630$		0			0
$631$	16.8061	−	29.1089i	0.669039	−	1.15881i	−0.309135	−	0.951018i	$-0.600039\pi$
$631$	16.8061	−	29.1089i	0.669039	−	1.15881i	0.978173	−	0.207791i	$-0.0666273\pi$
$632$	5.66296	+	9.80853i	0.225260	+	0.390162i
$633$	12.3021	+	21.3079i	0.488965	+	0.846913i
$634$	−73.1802			−2.90636
$635$	2.08747	−	3.61561i	0.0828388	−	0.143481i
$636$	4.33539			0.171909
$637$		0			0
$638$	−5.55889			−0.220078
$639$	−8.23293	+	14.2598i	−0.325690	+	0.564111i
$640$	−20.3729			−0.805310
$641$	−10.5921	−	18.3460i	−0.418361	−	0.724622i	0.577414	−	0.816452i	$-0.304062\pi$
$641$	−10.5921	−	18.3460i	−0.418361	−	0.724622i	−0.995775	+	0.0918294i	$0.970729\pi$
$642$	−52.5010	−	90.9343i	−2.07205	−	3.58889i
$643$	0.330770	−	0.572910i	0.0130443	−	0.0225933i	−0.859430	−	0.511254i	$-0.829181\pi$
$643$	0.330770	−	0.572910i	0.0130443	−	0.0225933i	0.872474	+	0.488661i	$0.162514\pi$
$644$		0			0
$645$	−17.2457			−0.679047
$646$	−58.9834			−2.32067
$647$	40.0323			1.57383			0.786916	−	0.617060i	$-0.211676\pi$
$647$	40.0323			1.57383			0.786916	+	0.617060i	$0.211676\pi$
$648$	7.40537			0.290910
$649$	−1.76594	−	3.05870i	−0.0693193	−	0.120065i
$650$	34.0376	+	6.96654i	1.33506	+	0.273250i
$651$		0			0
$652$	−15.1388	−	26.2212i	−0.592883	−	1.02690i
$653$	−6.35602	+	11.0089i	−0.248730	+	0.430813i	−0.963174	−	0.268880i	$-0.913347\pi$
$653$	−6.35602	+	11.0089i	−0.248730	+	0.430813i	0.714444	+	0.699693i	$0.246680\pi$
$654$	30.3391	+	52.5489i	1.18635	+	2.05482i
$655$	1.06556	−	1.84560i	0.0416349	−	0.0721138i
$656$	−8.46215			−0.330391
$657$	11.2764	−	19.5313i	0.439933	−	0.761987i
$658$		0			0
$659$	7.09522	−	12.2893i	0.276391	−	0.478723i	−0.694094	−	0.719884i	$-0.744195\pi$
$659$	7.09522	−	12.2893i	0.276391	−	0.478723i	0.970485	+	0.241161i	$0.0775283\pi$
$660$	−2.94119	+	5.09430i	−0.114486	+	0.198295i
$661$	−50.1780			−1.95170			−0.975848	−	0.218449i	$-0.929900\pi$
$661$	−50.1780			−1.95170			−0.975848	+	0.218449i	$0.929900\pi$
$662$	32.5104	−	56.3096i	1.26355	−	2.18853i
$663$	62.7291	+	12.8389i	2.43620	+	0.498621i
$664$	−11.6625			−0.452594
$665$		0			0
$666$	9.58259	+	16.5975i	0.371318	+	0.643141i
$667$	−32.7112			−1.26658
$668$	−4.30944	+	7.46417i	−0.166737	+	0.288797i
$669$	30.0181	+	51.9928i	1.16057	+	2.01016i
$670$	16.4506			0.635542
$671$	1.29713			0.0500751
$672$		0			0
$673$	0.937137	+	1.62317i	0.0361240	+	0.0625685i	0.883522	−	0.468389i	$-0.155166\pi$
$673$	0.937137	+	1.62317i	0.0361240	+	0.0625685i	−0.847398	+	0.530958i	$0.821832\pi$
$674$	−14.7056	+	25.4708i	−0.566438	+	0.981100i
$675$	8.71902	−	15.1018i	0.335595	−	0.581268i
$676$	−38.5104	+	28.8785i	−1.48117	+	1.11071i
$677$	−1.00439	−	1.73966i	−0.0386020	−	0.0668607i	0.846079	−	0.533058i	$-0.178957\pi$
$677$	−1.00439	−	1.73966i	−0.0386020	−	0.0668607i	−0.884681	+	0.466197i	$0.845624\pi$
$678$	33.4453	+	57.9290i	1.28446	+	2.22475i
$679$		0			0
$680$	−12.8894	+	22.3251i	−0.494286	+	0.856128i
$681$	−25.5234	−	44.2079i	−0.978061	−	1.69405i
$682$	−2.09762	−	3.63319i	−0.0803222	−	0.139122i
$683$	7.05061	+	12.2120i	0.269784	+	0.467280i	0.968806	−	0.247820i	$-0.0797143\pi$
$683$	7.05061	+	12.2120i	0.269784	+	0.467280i	−0.699022	+	0.715100i	$0.746381\pi$
$684$	−32.3828	−	56.0886i	−1.23819	−	2.14460i
$685$	4.10748	−	7.11437i	0.156939	−	0.271826i
$686$		0			0
$687$	26.6212	+	46.1094i	1.01566	+	1.75918i
$688$	−7.35298	−	12.7357i	−0.280330	−	0.485546i
$689$	−0.485139	−	1.45559i	−0.0184823	−	0.0554536i
$690$	−26.6559	+	46.1693i	−1.01477	+	1.75764i
$691$	−17.8460	+	30.9102i	−0.678895	+	1.17588i	0.296419	+	0.955058i	$0.404207\pi$
$691$	−17.8460	+	30.9102i	−0.678895	+	1.17588i	−0.975314	+	0.220822i	$0.929126\pi$
$692$	−15.0585	−	26.0820i	−0.572437	−	0.991489i
$693$		0			0
$694$	−14.6746			−0.557041
$695$	−0.566691			−0.0214958
$696$	−22.1532	−	38.3704i	−0.839714	−	1.45443i
$697$	11.8489	−	20.5229i	0.448809	−	0.777360i
$698$	31.1191			1.17788
$699$	−22.2366	−	38.5150i	−0.841066	−	1.45677i
$700$		0			0
$701$	−6.15865			−0.232609			−0.116305	−	0.993214i	$-0.537105\pi$
$701$	−6.15865			−0.232609			−0.116305	+	0.993214i	$0.537105\pi$
$702$	11.7654	+	35.3004i	0.444057	+	1.33233i
$703$	−3.35979	+	5.81932i	−0.126717	+	0.219480i
$704$	6.39918			0.241178
$705$	5.86571	−	10.1597i	0.220915	−	0.382637i
$706$	−37.8103	+	65.4894i	−1.42301	+	2.46473i
$707$		0			0
$708$	30.6078	−	53.0143i	1.15031	−	1.99240i
$709$	34.0371			1.27829			0.639144	−	0.769087i	$-0.279289\pi$
$709$	34.0371			1.27829			0.639144	+	0.769087i	$0.279289\pi$
$710$	−4.22527	+	7.31838i	−0.158571	+	0.274654i
$711$	−6.36553	−	11.0254i	−0.238726	−	0.413486i
$712$	4.25547	−	7.37069i	0.159480	−	0.276228i
$713$	−12.3434	−	21.3794i	−0.462265	−	0.800667i
$714$		0			0
$715$	2.03952	+	0.417432i	0.0762736	+	0.0156111i
$716$	38.8648	+	67.3158i	1.45244	+	2.51571i
$717$	44.3090			1.65475
$718$	−47.5989			−1.77637
$719$	22.9648			0.856444			0.428222	−	0.903674i	$-0.359140\pi$
$719$	22.9648			0.856444			0.428222	+	0.903674i	$0.359140\pi$
$720$	−10.3473			−0.385621
$721$		0			0
$722$	−5.19981	+	9.00633i	−0.193517	+	0.335181i
$723$	−5.51122	−	9.54571i	−0.204964	−	0.355009i
$724$	−2.97712	−	5.15653i	−0.110644	−	0.191641i
$725$	15.9798			0.593476
$726$	−35.0034	+	60.6276i	−1.29910	+	2.25010i
$727$	−1.06558			−0.0395203			−0.0197601	−	0.999805i	$-0.506290\pi$
$727$	−1.06558			−0.0395203			−0.0197601	+	0.999805i	$0.506290\pi$
$728$		0			0
$729$	−43.9962			−1.62949
$730$	5.78721	−	10.0237i	0.214194	−	0.370996i
$731$	41.1833			1.52322
$732$	11.2411	+	19.4702i	0.415483	+	0.719637i
$733$	−13.1689	−	22.8092i	−0.486404	−	0.842476i	0.513474	−	0.858105i	$-0.328358\pi$
$733$	−13.1689	−	22.8092i	−0.486404	−	0.842476i	−0.999878	+	0.0156289i	$0.995025\pi$
$734$	−23.5448	+	40.7809i	−0.869056	+	1.50525i
$735$		0			0
$736$	21.7123			0.800326
$737$	−4.12228			−0.151846
$738$	40.0759			1.47521
$739$	34.2149			1.25862			0.629308	−	0.777156i	$-0.283338\pi$
$739$	34.2149			1.25862			0.629308	+	0.777156i	$0.283338\pi$
$740$	3.19317	+	5.53073i	0.117383	+	0.203314i
$741$	−25.1897	+	28.4047i	−0.925366	+	1.04347i
$742$		0			0
$743$	−11.2391	−	19.4667i	−0.412322	−	0.714163i	0.582821	−	0.812600i	$-0.301949\pi$
$743$	−11.2391	−	19.4667i	−0.412322	−	0.714163i	−0.995143	+	0.0984379i	$0.968615\pi$
$744$	16.7188	−	28.9579i	0.612942	−	1.06165i
$745$	1.37845	+	2.38754i	0.0505023	+	0.0874726i
$746$	20.9513	−	36.2888i	0.767083	−	1.32863i
$747$	13.1094			0.479649
$748$	7.02368	−	12.1654i	0.256811	−	0.444810i
$749$		0			0
$750$	29.1573	−	50.5018i	1.06467	−	1.84407i
$751$	21.2712	−	36.8428i	0.776197	−	1.34441i	−0.157923	−	0.987451i	$-0.550480\pi$
$751$	21.2712	−	36.8428i	0.776197	−	1.34441i	0.934119	−	0.356961i	$-0.116187\pi$
$752$	10.0038			0.364801
$753$	4.46686	−	7.73683i	0.162781	−	0.281946i
$754$	−22.6239	+	25.5114i	−0.823912	+	0.929069i
$755$	22.6031			0.822612
$756$		0			0
$757$	5.61902	+	9.73243i	0.204227	+	0.353731i	0.949886	−	0.312596i	$-0.101199\pi$
$757$	5.61902	+	9.73243i	0.204227	+	0.353731i	−0.745659	+	0.666327i	$0.767865\pi$
$758$	27.9433			1.01495
$759$	6.67956	−	11.5693i	0.242453	−	0.419941i
$760$	−7.64252	−	13.2372i	−0.277223	−	0.480165i
$761$	−12.8084			−0.464306			−0.232153	−	0.972679i	$-0.574577\pi$
$761$	−12.8084			−0.464306			−0.232153	+	0.972679i	$0.574577\pi$
$762$	−27.9269			−1.01168
$763$		0			0
$764$	21.4059	+	37.0760i	0.774437	+	1.34136i
$765$	14.4885	−	25.0948i	0.523833	−	0.907306i
$766$	25.7058	−	44.5238i	0.928789	−	1.60871i
$767$	−21.2244	−	4.34404i	−0.766369	−	0.156854i
$768$	38.1846	+	66.1377i	1.37787	+	2.38654i
$769$	−25.6759	−	44.4719i	−0.925895	−	1.60370i	−0.790115	−	0.612958i	$-0.789979\pi$
$769$	−25.6759	−	44.4719i	−0.925895	−	1.60370i	−0.135780	−	0.990739i	$-0.543354\pi$
$770$		0			0
$771$	−36.9969	+	64.0805i	−1.33241	+	2.30780i
$772$	−43.6529	−	75.6091i	−1.57110	−	2.72123i
$773$	10.0023	+	17.3245i	0.359759	+	0.623120i	0.987920	−	0.154963i	$-0.0495257\pi$
$773$	10.0023	+	17.3245i	0.359759	+	0.623120i	−0.628162	+	0.778083i	$0.716192\pi$
$774$	34.8230	+	60.3151i	1.25169	+	2.16798i
$775$	6.02993	+	10.4441i	0.216602	+	0.375165i
$776$	−15.6487	+	27.1044i	−0.561756	+	0.972990i
$777$		0			0
$778$	31.6308	+	54.7861i	1.13402	+	1.96418i
$779$	7.02558	+	12.1687i	0.251717	+	0.435987i
$780$	11.4090	+	34.2311i	0.408508	+	1.22567i
$781$	1.05879	−	1.83388i	0.0378864	−	0.0656212i
$782$	63.6552	−	110.254i	2.27631	−	3.94268i
$783$	8.55708	+	14.8213i	0.305805	+	0.529670i
$784$		0			0
$785$	22.1759			0.791492
$786$	−14.2554			−0.508474
$787$	14.6596	+	25.3911i	0.522558	+	0.905096i	0.999656	+	0.0262462i	$0.00835537\pi$
$787$	14.6596	+	25.3911i	0.522558	+	0.905096i	−0.477098	+	0.878850i	$0.658311\pi$
$788$	2.72325	−	4.71680i	0.0970117	−	0.168029i
$789$	−10.4750			−0.372921
$790$	−3.26689	−	5.65842i	−0.116231	−	0.201318i
$791$		0			0
$792$	10.9243			0.388177
$793$	5.27912	−	5.95291i	0.187467	−	0.211394i
$794$	40.3566	−	69.8996i	1.43220	−	2.48064i
$795$	−1.15012			−0.0407905
$796$	17.3917	−	30.1232i	0.616431	−	1.06769i
$797$	1.55050	−	2.68554i	0.0549215	−	0.0951269i	−0.837258	−	0.546809i	$-0.815842\pi$
$797$	1.55050	−	2.68554i	0.0549215	−	0.0951269i	0.892179	+	0.451682i	$0.149176\pi$
$798$		0			0
$799$	−14.0075	+	24.2618i	−0.495551	+	0.858319i
$800$	−10.6068			−0.375005
$801$	−4.78343	+	8.28514i	−0.169014	+	0.292741i
$802$	25.8050	+	44.6956i	0.911206	+	1.57826i
$803$	−1.45019	+	2.51180i	−0.0511761	+	0.0886395i
$804$	−35.7242	−	61.8762i	−1.25990	−	2.18220i
$805$		0			0
$806$	−25.2108	−	5.15995i	−0.888013	−	0.181751i
$807$	−32.7950	−	56.8025i	−1.15444	−	1.99954i
$808$	−10.7238			−0.377261
$809$	7.99003			0.280914			0.140457	−	0.990087i	$-0.455143\pi$
$809$	7.99003			0.280914			0.140457	+	0.990087i	$0.455143\pi$
$810$	−4.27207			−0.150105
$811$	48.2554			1.69448			0.847239	−	0.531213i	$-0.178263\pi$
$811$	48.2554			1.69448			0.847239	+	0.531213i	$0.178263\pi$
$812$		0			0
$813$	13.6217	−	23.5934i	0.477733	−	0.827458i
$814$	−1.23236	−	2.13451i	−0.0431942	−	0.0748146i
$815$	4.01612	+	6.95612i	0.140679	+	0.243662i
$816$	40.9283			1.43278
$817$	−12.2094	+	21.1473i	−0.427153	+	0.739851i
$818$	18.4886			0.646439
$819$		0			0
$820$	13.3543			0.466353
$821$	13.7760	−	23.8607i	0.480785	−	0.832743i	−0.518972	−	0.854791i	$-0.673685\pi$
$821$	13.7760	−	23.8607i	0.480785	−	0.832743i	0.999757	+	0.0220477i	$0.00701856\pi$
$822$	−54.9513			−1.91665
$823$	−10.2137	−	17.6907i	−0.356028	−	0.616659i	0.631265	−	0.775567i	$-0.282536\pi$
$823$	−10.2137	−	17.6907i	−0.356028	−	0.616659i	−0.987293	+	0.158908i	$0.949203\pi$
$824$	22.0831	+	38.2491i	0.769303	+	1.33247i
$825$	−3.26306	+	5.65178i	−0.113605	+	0.196770i
$826$		0			0
$827$	−27.7142			−0.963719			−0.481859	−	0.876249i	$-0.660038\pi$
$827$	−27.7142			−0.963719			−0.481859	+	0.876249i	$0.660038\pi$
$828$	139.791			4.85806
$829$	−9.25664			−0.321496			−0.160748	−	0.986995i	$-0.551391\pi$
$829$	−9.25664			−0.321496			−0.160748	+	0.986995i	$0.551391\pi$
$830$	6.72797			0.233531
$831$	−16.2142	−	28.0837i	−0.562463	−	0.974214i
$832$	26.0437	−	29.3677i	0.902904	−	1.01814i
$833$		0			0
$834$	1.89535	+	3.28283i	0.0656304	+	0.113675i
$835$	1.14323	−	1.98014i	0.0395632	−	0.0685255i
$836$	4.16456	+	7.21323i	0.144034	+	0.249475i
$837$	−6.45797	+	11.1855i	−0.223220	+	0.386628i
$838$	−19.3477			−0.668357
$839$	−15.1870	+	26.3046i	−0.524312	+	0.908135i	0.475287	+	0.879831i	$0.342344\pi$
$839$	−15.1870	+	26.3046i	−0.524312	+	0.908135i	−0.999599	+	0.0283045i	$0.990989\pi$
$840$		0			0
$841$	6.65848	−	11.5328i	0.229603	−	0.397683i
$842$	−38.3428	+	66.4116i	−1.32138	+	2.28869i
$843$	35.7626			1.23173
$844$	16.5552	−	28.6745i	0.569854	−	0.987016i
$845$	10.2163	−	7.66106i	0.351450	−	0.263548i
$846$	−47.3769			−1.62885
$847$		0			0
$848$	−0.490373	−	0.849350i	−0.0168395	−	0.0291668i
$849$	46.2385			1.58690
$850$	−31.0964	+	53.8606i	−1.06660	+	1.84740i
$851$	−7.25180	−	12.5605i	−0.248589	−	0.430568i
$852$	36.7025			1.25741
$853$	5.30773			0.181733			0.0908666	−	0.995863i	$-0.471036\pi$
$853$	5.30773			0.181733			0.0908666	+	0.995863i	$0.471036\pi$
$854$		0			0
$855$	8.59069	+	14.8795i	0.293795	+	0.508868i
$856$	−32.4896	+	56.2737i	−1.11047	+	1.92340i
$857$	−8.31857	+	14.4082i	−0.284157	+	0.492175i	−0.972404	−	0.233302i	$-0.925047\pi$
$857$	−8.31857	+	14.4082i	−0.284157	+	0.492175i	0.688247	+	0.725476i	$0.258380\pi$
$858$	−4.40316	−	13.2110i	−0.150321	−	0.451017i
$859$	−5.29426	−	9.16993i	−0.180638	−	0.312874i	0.761460	−	0.648212i	$-0.224483\pi$
$859$	−5.29426	−	9.16993i	−0.180638	−	0.312874i	−0.942098	+	0.335338i	$0.891150\pi$
$860$	11.6039	+	20.0986i	0.395690	+	0.685356i
$861$		0			0
$862$	−35.2571	+	61.0671i	−1.20086	+	2.07995i
$863$	28.0316	+	48.5522i	0.954207	+	1.65273i	0.736173	+	0.676793i	$0.236631\pi$
$863$	28.0316	+	48.5522i	0.954207	+	1.65273i	0.218033	+	0.975941i	$0.430036\pi$
$864$	−5.67984	−	9.83777i	−0.193232	−	0.334688i
$865$	3.99480	+	6.91919i	0.135827	+	0.235260i
$866$	−26.3771	−	45.6864i	−0.896329	−	1.55249i
$867$	−33.9212	+	58.7532i	−1.15202	+	1.99536i
$868$		0			0
$869$	0.818634	+	1.41792i	0.0277703	+	0.0480995i
$870$	12.7799	+	22.1354i	0.433279	+	0.750462i
$871$	−16.7771	+	18.9183i	−0.568469	+	0.641024i
$872$	18.7750	−	32.5193i	0.635803	−	1.10124i
$873$	17.5902	−	30.4671i	0.595337	−	1.03115i
$874$	37.7432	+	65.3731i	1.27668	+	2.21128i
$875$		0			0
$876$	−50.2702			−1.69847
$877$	−3.66051			−0.123607			−0.0618033	−	0.998088i	$-0.519685\pi$
$877$	−3.66051			−0.123607			−0.0618033	+	0.998088i	$0.519685\pi$
$878$	7.58894	+	13.1444i	0.256114	+	0.443603i
$879$	−19.3919	+	33.5878i	−0.654073	+	1.13289i
$880$	1.33071			0.0448581
$881$	5.11493	+	8.85932i	0.172326	+	0.298478i	0.939233	−	0.343281i	$-0.111538\pi$
$881$	5.11493	+	8.85932i	0.172326	+	0.298478i	−0.766906	+	0.641759i	$0.778205\pi$
$882$		0			0
$883$	−3.98979			−0.134267			−0.0671335	−	0.997744i	$-0.521385\pi$
$883$	−3.98979			−0.134267			−0.0671335	+	0.997744i	$0.521385\pi$
$884$	−27.2451	−	81.7451i	−0.916353	−	2.74938i
$885$	−8.11982	+	14.0639i	−0.272945	+	0.472754i
$886$	32.3882			1.08810
$887$	−7.11039	+	12.3155i	−0.238743	+	0.413516i	−0.960354	−	0.278784i	$-0.910069\pi$
$887$	−7.11039	+	12.3155i	−0.238743	+	0.413516i	0.721611	+	0.692299i	$0.243402\pi$
$888$	9.82237	−	17.0128i	0.329617	−	0.570913i
$889$		0			0
$890$	−2.45493	+	4.25206i	−0.0822894	+	0.142529i
$891$	1.07052			0.0358636
$892$	40.3960	−	69.9678i	1.35256	−	2.34270i
$893$	−8.30550	−	14.3855i	−0.277933	−	0.481394i
$894$	9.22065	−	15.9706i	0.308385	−	0.534138i
$895$	−10.3103	−	17.8579i	−0.344635	−	0.596924i
$896$		0			0
$897$	−25.9103	−	77.7400i	−0.865119	−	2.59566i
$898$	26.1631	+	45.3158i	0.873074	+	1.51221i
$899$	−11.8359			−0.394749
$900$	−68.2896			−2.27632
$901$	2.74652			0.0915000
$902$	−5.15392			−0.171607
$903$		0			0
$904$	20.6973	−	35.8487i	0.688381	−	1.19231i
$905$	0.789789	+	1.36795i	0.0262535	+	0.0454723i
$906$	−75.5980	−	130.940i	−2.51158	−	4.35018i
$907$	43.4253			1.44191			0.720956	−	0.692981i	$-0.243703\pi$
$907$	43.4253			1.44191			0.720956	+	0.692981i	$0.243703\pi$
$908$	−34.3474	+	59.4915i	−1.13986	+	1.97429i
$909$	12.0542			0.399814
$910$		0			0
$911$	24.8617			0.823706			0.411853	−	0.911250i	$-0.364882\pi$
$911$	24.8617			0.823706			0.411853	+	0.911250i	$0.364882\pi$
$912$	−12.1338	+	21.0164i	−0.401791	+	0.695923i
$913$	−1.68593			−0.0557961
$914$	18.1666	+	31.4654i	0.600896	+	1.04078i
$915$	−2.98210	−	5.16516i	−0.0985853	−	0.170755i
$916$	35.8248	−	62.0503i	1.18368	−	2.05020i
$917$		0			0
$918$	−66.6076			−2.19838
$919$	−1.66327			−0.0548664			−0.0274332	−	0.999624i	$-0.508733\pi$
$919$	−1.66327			−0.0548664			−0.0274332	+	0.999624i	$0.508733\pi$
$920$	32.9914			1.08769
$921$	−43.6896			−1.43962
$922$	19.3625	+	33.5369i	0.637671	+	1.10448i
$923$	−4.10708	−	12.3227i	−0.135186	−	0.405607i
$924$		0			0
$925$	3.54260	+	6.13597i	0.116480	+	0.201749i
$926$	−1.72857	+	2.99397i	−0.0568044	+	0.0983880i
$927$	−24.8229	−	42.9945i	−0.815291	−	1.41212i
$928$	5.20488	−	9.01512i	0.170859	−	0.295936i
$929$	−9.49521			−0.311528			−0.155764	−	0.987794i	$-0.549784\pi$
$929$	−9.49521			−0.311528			−0.155764	+	0.987794i	$0.549784\pi$
$930$	−9.64490	+	16.7055i	−0.316269	+	0.547793i
$931$		0			0
$932$	−29.9243	+	51.8304i	−0.980202	+	1.69776i
$933$	−39.3508	+	68.1576i	−1.28829	+	2.23138i
$934$	33.4486			1.09447
$935$	−1.86328	+	3.22730i	−0.0609359	+	0.105544i
$936$	44.4602	−	50.1347i	1.45323	−	1.63870i
$937$	6.41678			0.209627			0.104813	−	0.994492i	$-0.466575\pi$
$937$	6.41678			0.209627			0.104813	+	0.994492i	$0.466575\pi$
$938$		0			0
$939$	−25.5602	−	44.2715i	−0.834125	−	1.44475i
$940$	−15.7872			−0.514922
$941$	−25.7593	+	44.6164i	−0.839730	+	1.45445i	0.0503911	+	0.998730i	$0.483953\pi$
$941$	−25.7593	+	44.6164i	−0.839730	+	1.45445i	−0.890121	+	0.455725i	$0.849380\pi$
$942$	−74.1691	−	128.465i	−2.41656	−	4.18561i
$943$	−30.3282			−0.987621
$944$	−13.8481			−0.450717
$945$		0			0
$946$	−4.47838	−	7.75678i	−0.145605	−	0.252195i
$947$	4.20109	−	7.27651i	0.136517	−	0.236455i	−0.789659	−	0.613546i	$-0.789742\pi$
$947$	4.20109	−	7.27651i	0.136517	−	0.236455i	0.926176	+	0.377091i	$0.123076\pi$
$948$	−14.1888	+	24.5757i	−0.460831	+	0.798182i
$949$	5.62534	+	16.8780i	0.182606	+	0.547883i
$950$	−18.4380	−	31.9356i	−0.598209	−	1.03613i
$951$	−42.1589	−	73.0213i	−1.36709	−	2.36788i
$952$		0			0
$953$	18.0455	−	31.2558i	0.584552	−	1.01247i	−0.410379	−	0.911915i	$-0.634604\pi$
$953$	18.0455	−	31.2558i	0.584552	−	1.01247i	0.994931	−	0.100559i	$-0.0320631\pi$
$954$	2.32235	+	4.02244i	0.0751890	+	0.130231i
$955$	−5.67867	−	9.83575i	−0.183758	−	0.318277i
$956$	−29.8138	−	51.6390i	−0.964246	−	1.67012i
$957$	−3.20245	−	5.54681i	−0.103521	−	0.179303i
$958$	35.8496	−	62.0933i	1.15825	−	2.00614i
$959$		0			0
$960$	−14.7117	−	25.4815i	−0.474820	−	0.822412i
$961$	11.0338	+	19.1111i	0.355928	+	0.616486i
$962$	−14.8114	−	3.03148i	−0.477540	−	0.0977390i
$963$	36.5205	−	63.2553i	1.17686	−	2.03837i
$964$	−7.41656	+	12.8459i	−0.238871	+	0.413737i
$965$	11.5805	+	20.0580i	0.372790	+	0.645691i
$966$		0			0
$967$	3.18338			0.102371			0.0511853	−	0.998689i	$-0.483700\pi$
$967$	3.18338			0.102371			0.0511853	+	0.998689i	$0.483700\pi$
$968$	43.3229			1.39245
$969$	−33.9801	−	58.8553i	−1.09160	−	1.89070i
$970$	9.02756	−	15.6362i	0.289857	−	0.502048i
$971$	−37.7476			−1.21138			−0.605690	−	0.795701i	$-0.707103\pi$
$971$	−37.7476			−1.21138			−0.605690	+	0.795701i	$0.707103\pi$
$972$	33.2795	+	57.6419i	1.06744	+	1.84886i
$973$		0			0
$974$	68.0359			2.18001
$975$	12.6575	+	37.9771i	0.405365	+	1.21624i
$976$	2.54294	−	4.40451i	0.0813977	−	0.140985i
$977$	−21.3076			−0.681692			−0.340846	−	0.940119i	$-0.610713\pi$
$977$	−21.3076			−0.681692			−0.340846	+	0.940119i	$0.610713\pi$
$978$	26.8645	−	46.5307i	0.859032	−	1.48789i
$979$	0.615168	−	1.06550i	0.0196609	−	0.0340536i
$980$		0			0
$981$	−21.1044	+	36.5538i	−0.673810	+	1.16707i
$982$	67.9819			2.16939
$983$	−11.0158	+	19.0799i	−0.351350	+	0.608556i	−0.986486	−	0.163844i	$-0.947611\pi$
$983$	−11.0158	+	19.0799i	−0.351350	+	0.608556i	0.635136	+	0.772400i	$0.280944\pi$
$984$	−20.5393	−	35.5752i	−0.654770	−	1.13409i
$985$	−0.722439	+	1.25130i	−0.0230188	+	0.0398698i
$986$	−30.5189	−	52.8603i	−0.971919	−	1.68341i
$987$		0			0
$988$	50.0528	+	10.2444i	1.59239	+	0.325918i
$989$	−26.3529	−	45.6446i	−0.837975	−	1.45141i
$990$	−6.30208			−0.200293
$991$	−22.0259			−0.699676			−0.349838	−	0.936810i	$-0.613763\pi$
$991$	−22.0259			−0.699676			−0.349838	+	0.936810i	$0.613763\pi$
$992$	7.85617			0.249434
$993$	74.9164			2.37740
$994$		0			0
$995$	−4.61376	+	7.99127i	−0.146266	+	0.253340i
$996$	−14.6105	−	25.3061i	−0.462951	−	0.801855i
$997$	5.04102	+	8.73130i	0.159651	+	0.276523i	0.934743	−	0.355325i	$-0.115630\pi$
$997$	5.04102	+	8.73130i	0.159651	+	0.276523i	−0.775092	+	0.631848i	$0.782297\pi$
$998$	62.6450			1.98299
$999$	−3.79408	+	6.57153i	−0.120039	+	0.207914i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.g.l.263.6		12
7.2	even	3		637.2.h.l.471.1		12
7.3	odd	6		637.2.f.k.393.6		12
7.4	even	3		637.2.f.j.393.6		12
7.5	odd	6		91.2.h.b.16.1	yes	12
7.6	odd	2		91.2.g.b.81.6	yes	12
13.9	even	3		637.2.h.l.165.1		12
21.5	even	6		819.2.s.d.289.6		12
21.20	even	2		819.2.n.d.172.1		12
91.3	odd	6		8281.2.a.bz.1.1		6
91.9	even	3	inner	637.2.g.l.373.6		12
91.10	odd	6		8281.2.a.ce.1.6		6
91.48	odd	6		91.2.h.b.74.1	yes	12
91.55	odd	6		1183.2.e.h.508.6		12
91.61	odd	6		91.2.g.b.9.6	✓	12
91.62	odd	6		1183.2.e.g.508.1		12
91.68	odd	6		1183.2.e.h.170.6		12
91.74	even	3		637.2.f.j.295.6		12
91.75	odd	6		1183.2.e.g.170.1		12
91.81	even	3		8281.2.a.ca.1.1		6
91.87	odd	6		637.2.f.k.295.6		12
91.88	even	6		8281.2.a.cf.1.6		6
273.152	even	6		819.2.n.d.100.1		12
273.230	even	6		819.2.s.d.802.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.6	✓	12	91.61	odd	6
91.2.g.b.81.6	yes	12	7.6	odd	2
91.2.h.b.16.1	yes	12	7.5	odd	6
91.2.h.b.74.1	yes	12	91.48	odd	6
637.2.f.j.295.6		12	91.74	even	3
637.2.f.j.393.6		12	7.4	even	3
637.2.f.k.295.6		12	91.87	odd	6
637.2.f.k.393.6		12	7.3	odd	6
637.2.g.l.263.6		12	1.1	even	1	trivial
637.2.g.l.373.6		12	91.9	even	3	inner
637.2.h.l.165.1		12	13.9	even	3
637.2.h.l.471.1		12	7.2	even	3
819.2.n.d.100.1		12	273.152	even	6
819.2.n.d.172.1		12	21.20	even	2
819.2.s.d.289.6		12	21.5	even	6
819.2.s.d.802.6		12	273.230	even	6
1183.2.e.g.170.1		12	91.75	odd	6
1183.2.e.g.508.1		12	91.62	odd	6
1183.2.e.h.170.6		12	91.68	odd	6
1183.2.e.h.508.6		12	91.55	odd	6
8281.2.a.bz.1.1		6	91.3	odd	6
8281.2.a.ca.1.1		6	91.81	even	3
8281.2.a.ce.1.6		6	91.10	odd	6
8281.2.a.cf.1.6		6	91.88	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.19402 - 2.06810i) q^{2} +2.75148 q^{3} +(-1.85136 - 3.20665i) q^{4} +(0.491140 + 0.850679i) q^{5} +(3.28532 - 5.69033i) q^{6} -4.06616 q^{8} +4.57063 q^{9} +2.34572 q^{10} -0.587802 q^{11} +(-5.09398 - 8.82303i) q^{12} +(-2.39227 + 2.69760i) q^{13} +(1.35136 + 2.34063i) q^{15} +(-1.15235 + 1.99593i) q^{16} +(-3.22710 - 5.58950i) q^{17} +(5.45742 - 9.45253i) q^{18} +3.82689 q^{19} +(1.81855 - 3.14983i) q^{20} +(-0.701847 + 1.21563i) q^{22} +(-4.13001 + 7.15338i) q^{23} -11.1880 q^{24} +(2.01756 - 3.49452i) q^{25} +(2.72249 + 8.16844i) q^{26} +4.32156 q^{27} +(1.98009 + 3.42962i) q^{29} +6.45420 q^{30} +(-1.49436 + 2.58831i) q^{31} +(-1.31430 - 2.27644i) q^{32} -1.61733 q^{33} -15.4129 q^{34} +(-8.46189 - 14.6564i) q^{36} +(-0.877941 + 1.52064i) q^{37} +(4.56938 - 7.91440i) q^{38} +(-6.58228 + 7.42239i) q^{39} +(-1.99705 - 3.45900i) q^{40} +(1.83584 + 3.17977i) q^{41} +(-3.19042 + 5.52598i) q^{43} +(1.08823 + 1.88488i) q^{44} +(2.24482 + 3.88814i) q^{45} +(9.86261 + 17.0825i) q^{46} +(-2.17030 - 3.75906i) q^{47} +(-3.17067 + 5.49176i) q^{48} +(-4.81802 - 8.34505i) q^{50} +(-8.87930 - 15.3794i) q^{51} +(13.0792 + 2.67695i) q^{52} +(-0.212770 + 0.368529i) q^{53} +(5.16002 - 8.93742i) q^{54} +(-0.288693 - 0.500031i) q^{55} +10.5296 q^{57} +9.45706 q^{58} +(3.00431 + 5.20362i) q^{59} +(5.00371 - 8.66669i) q^{60} -2.20674 q^{61} +(3.56859 + 6.18097i) q^{62} -10.8866 q^{64} +(-3.46973 - 0.710156i) q^{65} +(-1.93112 + 3.34479i) q^{66} +7.01303 q^{67} +(-11.9491 + 20.6964i) q^{68} +(-11.3636 + 19.6824i) q^{69} +(-1.80127 + 3.11988i) q^{71} -18.5849 q^{72} +(2.46714 - 4.27321i) q^{73} +(2.09656 + 3.63134i) q^{74} +(5.55128 - 9.61510i) q^{75} +(-7.08496 - 12.2715i) q^{76} +(7.49088 + 22.4753i) q^{78} +(-1.39270 - 2.41223i) q^{79} -2.26386 q^{80} -1.82122 q^{81} +8.76812 q^{82} +2.86819 q^{83} +(3.16992 - 5.49045i) q^{85} +(7.61885 + 13.1962i) q^{86} +(5.44818 + 9.43652i) q^{87} +2.39010 q^{88} +(-1.04656 + 1.81269i) q^{89} +10.7214 q^{90} +30.5845 q^{92} +(-4.11170 + 7.12167i) q^{93} -10.3655 q^{94} +(1.87954 + 3.25546i) q^{95} +(-3.61628 - 6.26357i) q^{96} +(3.84852 - 6.66584i) q^{97} -2.68663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} - 6 q^{9} + 8 q^{10} - 8 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} + q^{20} - 5 q^{22} - q^{23}+ \cdots - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^4 - q^5 + 9 * q^6 - 6 * q^8 - 6 * q^9 + 8 * q^10 - 8 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 + 8 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 + q^20 - 5 * q^22 - q^23 - 22 * q^24 + 7 * q^25 - 5 * q^26 + 8 * q^27 + 3 * q^29 + 10 * q^30 - 16 * q^31 + 8 * q^32 + 32 * q^33 - 32 * q^34 - 21 * q^36 - 13 * q^37 + 17 * q^38 - 23 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 + 7 * q^45 + 16 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 + 25 * q^52 - 2 * q^53 + 18 * q^54 - 9 * q^55 + 42 * q^57 + 16 * q^58 - 13 * q^59 + 20 * q^60 - 10 * q^61 - 5 * q^62 - 30 * q^64 + 19 * q^65 - 18 * q^66 + 22 * q^67 - 29 * q^68 - 23 * q^69 + 6 * q^71 - 50 * q^72 + 30 * q^73 - 3 * q^74 + 3 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 - 14 * q^80 + 12 * q^81 + 2 * q^82 + 54 * q^83 - q^85 - 7 * q^86 - 16 * q^87 - 4 * q^89 + 16 * q^90 + 54 * q^92 - 7 * q^93 + 90 * q^94 - 6 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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