LMFDB - Embedded newform 637.2.u.i.30.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(30,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("637.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.u (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			30.3
Root			$-1.08105 + 0.911778i$ of defining polynomial
Character	$\chi$	$=$	637.30
Dual form			637.2.u.i.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.713220 + 0.411778i) q^{2} -2.66029 q^{3} +(-0.660878 + 1.14467i) q^{4} +(2.73845 + 1.58105i) q^{5} +(1.89737 - 1.09545i) q^{6} -2.73565i q^{8} +4.07715 q^{9} +O(q^{10})$	\(q+(-0.713220 + 0.411778i) q^{2} -2.66029 q^{3} +(-0.660878 + 1.14467i) q^{4} +(2.73845 + 1.58105i) q^{5} +(1.89737 - 1.09545i) q^{6} -2.73565i q^{8} +4.07715 q^{9} -2.60416 q^{10} -5.94270i q^{11} +(1.75813 - 3.04517i) q^{12} +(0.0766193 + 3.60474i) q^{13} +(-7.28508 - 4.20604i) q^{15} +(-0.195274 - 0.338225i) q^{16} +(1.34982 - 2.33796i) q^{17} +(-2.90791 + 1.67888i) q^{18} -1.95705i q^{19} +(-3.61956 + 2.08976i) q^{20} +(2.44707 + 4.23845i) q^{22} +(-1.36471 - 2.36374i) q^{23} +7.27763i q^{24} +(2.49941 + 4.32911i) q^{25} +(-1.53900 - 2.53942i) q^{26} -2.86554 q^{27} +(2.99923 - 5.19481i) q^{29} +6.92783 q^{30} +(-0.997270 + 0.575774i) q^{31} +(5.01684 + 2.89647i) q^{32} +15.8093i q^{33} +2.22331i q^{34} +(-2.69450 + 4.66701i) q^{36} +(5.63310 - 3.25227i) q^{37} +(0.805869 + 1.39581i) q^{38} +(-0.203830 - 9.58965i) q^{39} +(4.32519 - 7.49145i) q^{40} +(3.23351 + 1.86687i) q^{41} +(3.49562 + 6.05460i) q^{43} +(6.80245 + 3.92740i) q^{44} +(11.1651 + 6.44617i) q^{45} +(1.94667 + 1.12391i) q^{46} +(-0.394969 - 0.228035i) q^{47} +(0.519487 + 0.899778i) q^{48} +(-3.56527 - 2.05841i) q^{50} +(-3.59092 + 6.21965i) q^{51} +(-4.17688 - 2.29459i) q^{52} +(-0.199643 - 0.345792i) q^{53} +(2.04376 - 1.17997i) q^{54} +(9.39568 - 16.2738i) q^{55} +5.20632i q^{57} +4.94006i q^{58} +(4.16200 + 2.40293i) q^{59} +(9.62910 - 5.55936i) q^{60} +1.15703 q^{61} +(0.474182 - 0.821308i) q^{62} -3.98971 q^{64} +(-5.48944 + 9.99254i) q^{65} +(-6.50993 - 11.2755i) q^{66} +6.27918i q^{67} +(1.78413 + 3.09021i) q^{68} +(3.63052 + 6.28825i) q^{69} +(3.90335 - 2.25360i) q^{71} -11.1537i q^{72} +(7.19299 - 4.15288i) q^{73} +(-2.67843 + 4.63917i) q^{74} +(-6.64917 - 11.5167i) q^{75} +(2.24018 + 1.29337i) q^{76} +(4.09418 + 6.75560i) q^{78} +(3.95705 - 6.85381i) q^{79} -1.23495i q^{80} -4.60828 q^{81} -3.07494 q^{82} +6.19795i q^{83} +(7.39284 - 4.26826i) q^{85} +(-4.98630 - 2.87884i) q^{86} +(-7.97882 + 13.8197i) q^{87} -16.2571 q^{88} +(3.08423 - 1.78068i) q^{89} -10.6176 q^{90} +3.60762 q^{92} +(2.65303 - 1.53173i) q^{93} +0.375600 q^{94} +(3.09418 - 5.35928i) q^{95} +(-13.3462 - 7.70546i) q^{96} +(2.96831 - 1.71375i) q^{97} -24.2293i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 6 q^{5} + 18 q^{6} + 8 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 + 6 * q^5 + 18 * q^6 + 8 * q^9	$ 12 q + 4 q^{4} + 6 q^{5} + 18 q^{6} + 8 q^{9} + 24 q^{10} - 2 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} - 12 q^{18} + 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} - 24 q^{26} - 12 q^{27} + 8 q^{29} - 16 q^{30} - 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} + 2 q^{38} - 10 q^{39} + 46 q^{40} - 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} - 42 q^{47} + 2 q^{48} - 18 q^{50} - 26 q^{51} - 26 q^{52} + 22 q^{53} + 12 q^{54} + 6 q^{55} + 18 q^{59} + 66 q^{60} + 28 q^{61} + 4 q^{62} - 52 q^{64} - 42 q^{65} - 26 q^{66} + 8 q^{68} - 4 q^{69} - 24 q^{71} - 30 q^{73} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} + 28 q^{82} - 48 q^{85} - 60 q^{86} + 2 q^{87} + 28 q^{88} - 12 q^{89} - 24 q^{90} + 24 q^{92} + 18 q^{93} + 8 q^{94} - 22 q^{95} - 6 q^{96} - 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 + 6 * q^5 + 18 * q^6 + 8 * q^9 + 24 * q^10 - 2 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 - 12 * q^18 + 12 * q^20 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 12 * q^27 + 8 * q^29 - 16 * q^30 - 18 * q^31 - 36 * q^32 - 10 * q^36 + 42 * q^37 + 2 * q^38 - 10 * q^39 + 46 * q^40 - 30 * q^41 + 2 * q^43 + 24 * q^44 - 12 * q^46 - 42 * q^47 + 2 * q^48 - 18 * q^50 - 26 * q^51 - 26 * q^52 + 22 * q^53 + 12 * q^54 + 6 * q^55 + 18 * q^59 + 66 * q^60 + 28 * q^61 + 4 * q^62 - 52 * q^64 - 42 * q^65 - 26 * q^66 + 8 * q^68 - 4 * q^69 - 24 * q^71 - 30 * q^73 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 + 28 * q^79 - 4 * q^81 + 28 * q^82 - 48 * q^85 - 60 * q^86 + 2 * q^87 + 28 * q^88 - 12 * q^89 - 24 * q^90 + 24 * q^92 + 18 * q^93 + 8 * q^94 - 22 * q^95 - 6 * q^96 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.713220	+	0.411778i	−0.504323	+	0.291171i	−0.730497	−	0.682916i	$-0.760712\pi$
$2$	−0.713220	+	0.411778i	−0.504323	+	0.291171i	0.226174	+	0.974087i	$0.427378\pi$
$3$	−2.66029			−1.53592			−0.767960	−	0.640498i	$-0.778728\pi$
$3$	−2.66029			−1.53592			−0.767960	+	0.640498i	$0.778728\pi$
$4$	−0.660878	+	1.14467i	−0.330439	+	0.572337i
$5$	2.73845	+	1.58105i	1.22467	+	0.707065i	0.965911	−	0.258876i	$-0.0833520\pi$
$5$	2.73845	+	1.58105i	1.22467	+	0.707065i	0.258762	+	0.965941i	$0.416685\pi$
$6$	1.89737	−	1.09545i	0.774600	−	0.447215i
$7$		0			0
$7$		0			0
$8$		−	2.73565i		−	0.967199i
$9$	4.07715			1.35905
$10$	−2.60416			−0.823508
$11$		−	5.94270i		−	1.79179i	−0.444265	−	0.895895i	$-0.646535\pi$
$11$		−	5.94270i		−	1.79179i	0.444265	−	0.895895i	$-0.353465\pi$
$12$	1.75813	−	3.04517i	0.507528	−	0.879064i
$13$	0.0766193	+	3.60474i	0.0212504	+	0.999774i
$13$	0.0766193	+	3.60474i	0.0212504	+	0.999774i
$14$		0			0
$15$	−7.28508	−	4.20604i	−1.88100	−	1.08600i
$16$	−0.195274	−	0.338225i	−0.0488186	−	0.0845563i
$17$	1.34982	−	2.33796i	0.327380	−	0.567038i	−0.654611	−	0.755966i	$-0.727168\pi$
$17$	1.34982	−	2.33796i	0.327380	−	0.567038i	0.981991	+	0.188927i	$0.0605010\pi$
$18$	−2.90791	+	1.67888i	−0.685401	+	0.395716i
$19$		−	1.95705i		−	0.448978i	−0.974477	−	0.224489i	$-0.927929\pi$
$19$		−	1.95705i		−	0.448978i	0.974477	−	0.224489i	$-0.0720712\pi$
$20$	−3.61956	+	2.08976i	−0.809359	+	0.467284i
$21$		0			0
$22$	2.44707	+	4.23845i	0.521717	+	0.903641i
$23$	−1.36471	−	2.36374i	−0.284561	−	0.492874i	0.687941	−	0.725766i	$-0.258515\pi$
$23$	−1.36471	−	2.36374i	−0.284561	−	0.492874i	−0.972503	+	0.232892i	$0.925181\pi$
$24$			7.27763i			1.48554i
$25$	2.49941	+	4.32911i	0.499883	+	0.865822i
$26$	−1.53900	−	2.53942i	−0.301822	−	0.498022i
$27$	−2.86554			−0.551474
$28$		0			0
$29$	2.99923	−	5.19481i	0.556942	−	0.964652i	−0.440807	−	0.897602i	$-0.645308\pi$
$29$	2.99923	−	5.19481i	0.556942	−	0.964652i	0.997750	−	0.0670505i	$-0.0213589\pi$
$30$	6.92783			1.26484
$31$	−0.997270	+	0.575774i	−0.179115	+	0.103412i	−0.586877	−	0.809676i	$-0.699643\pi$
$31$	−0.997270	+	0.575774i	−0.179115	+	0.103412i	0.407762	+	0.913088i	$0.366309\pi$
$32$	5.01684	+	2.89647i	0.886860	+	0.512029i
$33$			15.8093i			2.75205i
$34$			2.22331i			0.381294i
$35$		0			0
$36$	−2.69450	+	4.66701i	−0.449083	+	0.777835i
$37$	5.63310	−	3.25227i	0.926075	−	0.534670i	0.0405072	−	0.999179i	$-0.487103\pi$
$37$	5.63310	−	3.25227i	0.926075	−	0.534670i	0.885568	+	0.464509i	$0.153769\pi$
$38$	0.805869	+	1.39581i	0.130729	+	0.226430i
$39$	−0.203830	−	9.58965i	−0.0326389	−	1.53557i
$40$	4.32519	−	7.49145i	0.683873	−	1.18450i
$41$	3.23351	+	1.86687i	0.504990	+	0.291556i	0.730772	−	0.682622i	$-0.239160\pi$
$41$	3.23351	+	1.86687i	0.504990	+	0.291556i	−0.225782	+	0.974178i	$0.572494\pi$
$42$		0			0
$43$	3.49562	+	6.05460i	0.533078	+	0.923318i	0.999254	+	0.0386258i	$0.0122980\pi$
$43$	3.49562	+	6.05460i	0.533078	+	0.923318i	−0.466176	+	0.884692i	$0.654369\pi$
$44$	6.80245	+	3.92740i	1.02551	+	0.592077i
$45$	11.1651	+	6.44617i	1.66439	+	0.960938i
$46$	1.94667	+	1.12391i	0.287021	+	0.165712i
$47$	−0.394969	−	0.228035i	−0.0576121	−	0.0332624i	0.470917	−	0.882177i	$-0.343923\pi$
$47$	−0.394969	−	0.228035i	−0.0576121	−	0.0332624i	−0.528529	+	0.848915i	$0.677256\pi$
$48$	0.519487	+	0.899778i	0.0749815	+	0.129872i
$49$		0			0
$50$	−3.56527	−	2.05841i	−0.504205	−	0.291103i
$51$	−3.59092	+	6.21965i	−0.502829	+	0.870926i
$52$	−4.17688	−	2.29459i	−0.579230	−	0.318202i
$53$	−0.199643	−	0.345792i	−0.0274231	−	0.0474982i	0.851988	−	0.523561i	$-0.175397\pi$
$53$	−0.199643	−	0.345792i	−0.0274231	−	0.0474982i	−0.879411	+	0.476063i	$0.842063\pi$
$54$	2.04376	−	1.17997i	0.278121	−	0.160573i
$55$	9.39568	−	16.2738i	1.26691	−	2.19436i
$56$		0			0
$57$			5.20632i			0.689594i
$58$			4.94006i			0.648662i
$59$	4.16200	+	2.40293i	0.541846	+	0.312835i	0.745827	−	0.666140i	$-0.232055\pi$
$59$	4.16200	+	2.40293i	0.541846	+	0.312835i	−0.203981	+	0.978975i	$0.565388\pi$
$60$	9.62910	−	5.55936i	1.24311	−	0.717711i
$61$	1.15703			0.148142			0.0740711	−	0.997253i	$-0.476401\pi$
$61$	1.15703			0.148142			0.0740711	+	0.997253i	$0.476401\pi$
$62$	0.474182	−	0.821308i	0.0602212	−	0.104306i
$63$		0			0
$64$	−3.98971			−0.498714
$65$	−5.48944	+	9.99254i	−0.680881	+	1.23942i
$66$	−6.50993	−	11.2755i	−0.801316	−	1.38792i
$67$			6.27918i			0.767124i	0.923515	+	0.383562i	$0.125303\pi$
$67$			6.27918i			0.767124i	−0.923515	+	0.383562i	$0.874697\pi$
$68$	1.78413	+	3.09021i	0.216358	+	0.374743i
$69$	3.63052	+	6.28825i	0.437063	+	0.757016i
$70$		0			0
$71$	3.90335	−	2.25360i	0.463242	−	0.267453i	−0.250165	−	0.968203i	$-0.580485\pi$
$71$	3.90335	−	2.25360i	0.463242	−	0.267453i	0.713406	+	0.700751i	$0.247151\pi$
$72$		−	11.1537i		−	1.31447i
$73$	7.19299	−	4.15288i	0.841876	−	0.486057i	−0.0160254	−	0.999872i	$-0.505101\pi$
$73$	7.19299	−	4.15288i	0.841876	−	0.486057i	0.857901	+	0.513814i	$0.171768\pi$
$74$	−2.67843	+	4.63917i	−0.311361	+	0.539293i
$75$	−6.64917	−	11.5167i	−0.767780	−	1.32983i
$76$	2.24018	+	1.29337i	0.256966	+	0.148360i
$77$		0			0
$78$	4.09418	+	6.75560i	0.463575	+	0.764921i
$79$	3.95705	−	6.85381i	0.445203	−	0.771114i	−0.552864	−	0.833272i	$-0.686465\pi$
$79$	3.95705	−	6.85381i	0.445203	−	0.771114i	0.998066	+	0.0621581i	$0.0197983\pi$
$80$		−	1.23495i		−	0.138072i
$81$	−4.60828			−0.512031
$82$	−3.07494			−0.339571
$83$			6.19795i			0.680313i	0.940369	+	0.340156i	$0.110480\pi$
$83$			6.19795i			0.680313i	−0.940369	+	0.340156i	$0.889520\pi$
$84$		0			0
$85$	7.39284	−	4.26826i	0.801866	−	0.462958i
$86$	−4.98630	−	2.87884i	−0.537687	−	0.310434i
$87$	−7.97882	+	13.8197i	−0.855419	+	1.48163i
$88$	−16.2571			−1.73302
$89$	3.08423	−	1.78068i	0.326928	−	0.188752i	−0.327549	−	0.944834i	$-0.606222\pi$
$89$	3.08423	−	1.78068i	0.326928	−	0.188752i	0.654476	+	0.756083i	$0.272889\pi$
$90$	−10.6176			−1.11919
$91$		0			0
$92$	3.60762			0.376120
$93$	2.65303	−	1.53173i	0.275106	−	0.158833i
$94$	0.375600			0.0387402
$95$	3.09418	−	5.35928i	0.317457	−	0.549851i
$96$	−13.3462	−	7.70546i	−1.36215	−	0.786435i
$97$	2.96831	−	1.71375i	0.301386	−	0.174005i	−0.341679	−	0.939817i	$-0.610996\pi$
$97$	2.96831	−	1.71375i	0.301386	−	0.174005i	0.643065	+	0.765811i	$0.277662\pi$
$98$		0			0
$99$		−	24.2293i		−	2.43513i
$100$	−6.60723			−0.660723
$101$	−13.3295			−1.32633			−0.663167	−	0.748472i	$-0.730788\pi$
$101$	−13.3295			−1.32633			−0.663167	+	0.748472i	$0.730788\pi$
$102$		−	5.91465i		−	0.585637i
$103$	−5.82248	+	10.0848i	−0.573706	+	0.993688i	0.422475	+	0.906375i	$0.361161\pi$
$103$	−5.82248	+	10.0848i	−0.573706	+	0.993688i	−0.996181	+	0.0873131i	$0.972172\pi$
$104$	9.86130	−	0.209604i	0.966981	−	0.0205533i
$105$		0			0
$106$	0.284779	+	0.164417i	0.0276602	+	0.0159696i
$107$	−1.96483	−	3.40318i	−0.189947	−	0.328998i	0.755285	−	0.655396i	$-0.227498\pi$
$107$	−1.96483	−	3.40318i	−0.189947	−	0.328998i	−0.945232	+	0.326398i	$0.894165\pi$
$108$	1.89377	−	3.28011i	0.182228	−	0.315629i
$109$	−9.74566	+	5.62666i	−0.933465	+	0.538936i	−0.887906	−	0.460025i	$-0.847840\pi$
$109$	−9.74566	+	5.62666i	−0.933465	+	0.538936i	−0.0455595	+	0.998962i	$0.514507\pi$
$110$			15.4757i			1.47555i
$111$	−14.9857	+	8.65199i	−1.42238	+	0.821210i
$112$		0			0
$113$	2.88709	+	5.00059i	0.271595	+	0.470416i	0.969270	−	0.245998i	$-0.0791157\pi$
$113$	2.88709	+	5.00059i	0.271595	+	0.470416i	−0.697676	+	0.716414i	$0.745782\pi$
$114$	−2.14385	−	3.71325i	−0.200790	−	0.347778i
$115$		−	8.63066i		−	0.804813i
$116$	3.96424	+	6.86627i	0.368071	+	0.637517i
$117$	0.312389	+	14.6971i	0.0288803	+	1.35874i
$118$	−3.95790			−0.364354
$119$		0			0
$120$	−11.5063	+	19.9294i	−1.05037	+	1.81930i
$121$	−24.3156			−2.21051
$122$	−0.825215	+	0.476438i	−0.0747115	+	0.0431347i
$123$	−8.60209	−	4.96642i	−0.775625	−	0.447807i
$124$		−	1.52207i		−	0.136686i
$125$		−	0.00370455i		−	0.000331345i
$126$		0			0
$127$	3.06558	−	5.30975i	0.272027	−	0.471164i	−0.697354	−	0.716727i	$-0.745639\pi$
$127$	3.06558	−	5.30975i	0.272027	−	0.471164i	0.969381	+	0.245563i	$0.0789728\pi$
$128$	−7.18812	+	4.15007i	−0.635346	+	0.366817i
$129$	−9.29938	−	16.1070i	−0.818765	−	1.41814i
$130$	−0.199529	−	9.38731i	−0.0174998	−	0.823322i
$131$	5.11084	−	8.85224i	0.446537	−	0.773424i	−0.551621	−	0.834095i	$-0.685991\pi$
$131$	5.11084	−	8.85224i	0.446537	−	0.773424i	0.998158	+	0.0606707i	$0.0193240\pi$
$132$	−18.0965	−	10.4480i	−1.57510	−	0.909383i
$133$		0			0
$134$	−2.58563	−	4.47844i	−0.223364	−	0.386878i
$135$	−7.84715	−	4.53056i	−0.675375	−	0.389928i
$136$	−6.39584	−	3.69264i	−0.548439	−	0.316641i
$137$	17.2751	+	9.97376i	1.47591	+	0.852116i	0.999631	−	0.0271788i	$-0.00865233\pi$
$137$	17.2751	+	9.97376i	1.47591	+	0.852116i	0.476278	+	0.879295i	$0.341986\pi$
$138$	−5.17872	−	2.98994i	−0.440842	−	0.254520i
$139$	−10.1637	−	17.6041i	−0.862077	−	1.49316i	−0.869921	−	0.493192i	$-0.835830\pi$
$139$	−10.1637	−	17.6041i	−0.862077	−	1.49316i	0.00784365	−	0.999969i	$-0.497503\pi$
$140$		0			0
$141$	1.05073	+	0.606641i	0.0884877	+	0.0510884i
$142$	−1.85596	+	3.21462i	−0.155749	+	0.269765i
$143$	21.4219	−	0.455325i	1.79139	−	0.0380762i
$144$	−0.796164	−	1.37900i	−0.0663470	−	0.114916i
$145$	16.4265	−	9.48383i	1.36414	−	0.787589i
$146$	−3.42013	+	5.92383i	−0.283052	+	0.490260i
$147$		0			0
$148$			8.59741i			0.706703i
$149$		−	10.7162i		−	0.877901i	−0.898511	−	0.438951i	$-0.855350\pi$
$149$		−	10.7162i		−	0.877901i	0.898511	−	0.438951i	$-0.144650\pi$
$150$	9.48465	+	5.47597i	0.774418	+	0.447111i
$151$	7.57267	−	4.37208i	0.616255	−	0.355795i	−0.159155	−	0.987254i	$-0.550877\pi$
$151$	7.57267	−	4.37208i	0.616255	−	0.355795i	0.775409	+	0.631459i	$0.217544\pi$
$152$	−5.35380			−0.434251
$153$	5.50343	−	9.53222i	0.444926	−	0.770634i
$154$		0			0
$155$	−3.64130			−0.292476
$156$	11.1117	+	6.10427i	0.889651	+	0.488733i
$157$	3.25367	+	5.63552i	0.259671	+	0.449763i	0.966154	−	0.257967i	$-0.0830525\pi$
$157$	3.25367	+	5.63552i	0.259671	+	0.449763i	−0.706483	+	0.707730i	$0.749719\pi$
$158$			6.51770i			0.518520i
$159$	0.531109	+	0.919907i	0.0421197	+	0.0729534i
$160$	9.15891	+	15.8637i	0.724075	+	1.25414i
$161$		0			0
$162$	3.28672	−	1.89759i	0.258229	−	0.149089i
$163$			2.61267i			0.204640i	0.994752	+	0.102320i	$0.0326266\pi$
$163$			2.61267i			0.204640i	−0.994752	+	0.102320i	$0.967373\pi$
$164$	−4.27392	+	2.46755i	−0.333737	+	0.192683i
$165$	−24.9952	+	43.2930i	−1.94588	+	3.37036i
$166$	−2.55218	−	4.42050i	−0.198087	−	0.343097i
$167$	3.36558	+	1.94312i	0.260436	+	0.150363i	0.624534	−	0.780998i	$-0.285289\pi$
$167$	3.36558	+	1.94312i	0.260436	+	0.150363i	−0.364097	+	0.931361i	$0.618622\pi$
$168$		0			0
$169$	−12.9883	+	0.552385i	−0.999097	+	0.0424911i
$170$	−3.51515	+	6.08842i	−0.269600	+	0.466961i
$171$		−	7.97919i		−	0.610184i
$172$	−9.24072			−0.704599
$173$	13.9768			1.06263			0.531317	−	0.847173i	$-0.321697\pi$
$173$	13.9768			1.06263			0.531317	+	0.847173i	$0.321697\pi$
$174$		−	13.1420i		−	0.996293i
$175$		0			0
$176$	−2.00997	+	1.16046i	−0.151507	+	0.0874727i
$177$	−11.0721	−	6.39250i	−0.832232	−	0.480490i
$178$	−1.46649	+	2.54004i	−0.109918	+	0.190384i
$179$	25.2843			1.88984			0.944919	−	0.327305i	$-0.106140\pi$
$179$	25.2843			1.88984			0.944919	+	0.327305i	$0.106140\pi$
$180$	−14.7575	+	8.52026i	−1.09996	+	0.635063i
$181$	0.864474			0.0642559			0.0321279	−	0.999484i	$-0.489772\pi$
$181$	0.864474			0.0642559			0.0321279	+	0.999484i	$0.489772\pi$
$182$		0			0
$183$	−3.07803			−0.227535
$184$	−6.46638	+	3.73336i	−0.476708	+	0.275227i
$185$	20.5680			1.51219
$186$	−1.26146	+	2.18492i	−0.0924950	+	0.160206i
$187$	−13.8938	−	8.02158i	−1.01601	−	0.586596i
$188$	0.522052	−	0.301407i	0.0380746	−	0.0219824i
$189$		0			0
$190$			5.09647i			0.369737i
$191$	14.6676			1.06131			0.530657	−	0.847587i	$-0.321945\pi$
$191$	14.6676			1.06131			0.530657	+	0.847587i	$0.321945\pi$
$192$	10.6138			0.765985
$193$		−	16.4959i		−	1.18740i	−0.804686	−	0.593700i	$-0.797667\pi$
$193$		−	16.4959i		−	1.18740i	0.804686	−	0.593700i	$-0.202333\pi$
$194$	−1.41137	+	2.44457i	−0.101331	+	0.175510i
$195$	14.6035	−	26.5831i	1.04578	−	1.90365i
$196$		0			0
$197$	9.53510	+	5.50509i	0.679348	+	0.392222i	0.799609	−	0.600521i	$-0.205040\pi$
$197$	9.53510	+	5.50509i	0.679348	+	0.392222i	−0.120262	+	0.992742i	$0.538373\pi$
$198$	9.97709	+	17.2808i	0.709041	+	1.22809i
$199$	10.6059	−	18.3699i	0.751829	−	1.30221i	−0.195106	−	0.980782i	$-0.562505\pi$
$199$	10.6059	−	18.3699i	0.751829	−	1.30221i	0.946935	−	0.321425i	$-0.104162\pi$
$200$	11.8429	−	6.83753i	0.837423	−	0.483486i
$201$		−	16.7045i		−	1.17824i
$202$	9.50686	−	5.48879i	0.668901	−	0.386190i
$203$		0			0
$204$	−4.74632	−	8.22086i	−0.332309	−	0.575576i
$205$	5.90322	+	10.2247i	0.412299	+	0.714122i
$206$		−	9.59027i		−	0.668186i
$207$	−5.56412	−	9.63734i	−0.386733	−	0.669842i
$208$	1.20425	−	0.729828i	0.0834998	−	0.0506044i
$209$	−11.6301			−0.804474
$210$		0			0
$211$	8.96788	−	15.5328i	0.617375	−	1.06932i	−0.372588	−	0.927997i	$-0.621530\pi$
$211$	8.96788	−	15.5328i	0.617375	−	1.06932i	0.989963	−	0.141327i	$-0.0451370\pi$
$212$	0.527759			0.0362466
$213$	−10.3840	+	5.99523i	−0.711503	+	0.410786i
$214$	2.80271	+	1.61815i	0.191589	+	0.110614i
$215$			22.1070i			1.50768i
$216$			7.83913i			0.533385i
$217$		0			0
$218$	4.63387	−	8.02610i	0.313845	−	0.543596i
$219$	−19.1355	+	11.0479i	−1.29305	+	0.746545i
$220$	12.4188	+	21.5100i	0.837275	+	1.45020i
$221$	8.53115	+	4.68662i	0.573867	+	0.315256i
$222$	7.12540	−	12.3415i	0.478225	−	0.828311i
$223$	13.8834	+	8.01558i	0.929700	+	0.536763i	0.886717	−	0.462313i	$-0.152980\pi$
$223$	13.8834	+	8.01558i	0.929700	+	0.536763i	0.0429835	+	0.999076i	$0.486314\pi$
$224$		0			0
$225$	10.1905	+	17.6505i	0.679366	+	1.17670i
$226$	−4.11826	−	2.37768i	−0.273943	−	0.158161i
$227$	−14.1812	−	8.18751i	−0.941239	−	0.543424i	−0.0508902	−	0.998704i	$-0.516206\pi$
$227$	−14.1812	−	8.18751i	−0.941239	−	0.543424i	−0.890348	+	0.455280i	$0.849539\pi$
$228$	−5.95954	−	3.44074i	−0.394680	−	0.227869i
$229$	−23.3917	−	13.5052i	−1.54577	−	0.892449i	−0.998458	−	0.0555193i	$-0.982319\pi$
$229$	−23.3917	−	13.5052i	−1.54577	−	0.892449i	−0.547310	−	0.836930i	$-0.684348\pi$
$230$	3.55392	+	6.15556i	0.234338	+	0.405886i
$231$		0			0
$232$	−14.2112	−	8.20484i	−0.933011	−	0.538674i
$233$	5.78406	−	10.0183i	0.378926	−	0.656320i	−0.611980	−	0.790873i	$-0.709627\pi$
$233$	5.78406	−	10.0183i	0.378926	−	0.656320i	0.990906	+	0.134554i	$0.0429601\pi$
$234$	−6.27473	−	10.3536i	−0.410192	−	0.676837i
$235$	−0.721069	−	1.24893i	−0.0470374	−	0.0814711i
$236$	−5.50114	+	3.17609i	−0.358094	+	0.206746i
$237$	−10.5269	+	18.2331i	−0.683796	+	1.18437i
$238$		0			0
$239$			14.6731i			0.949122i	0.880223	+	0.474561i	$0.157393\pi$
$239$			14.6731i			0.949122i	−0.880223	+	0.474561i	$0.842607\pi$
$240$			3.28533i			0.212067i
$241$	12.4246	+	7.17334i	0.800338	+	0.462076i	0.843589	−	0.536989i	$-0.180438\pi$
$241$	12.4246	+	7.17334i	0.800338	+	0.462076i	−0.0432510	+	0.999064i	$0.513772\pi$
$242$	17.3424	−	10.0126i	1.11481	−	0.643637i
$243$	20.8560			1.33791
$244$	−0.764654	+	1.32442i	−0.0489519	+	0.0847872i
$245$		0			0
$246$	8.18025			0.521554
$247$	7.05464	−	0.149948i	0.448876	−	0.00954094i
$248$	1.57512	+	2.72818i	0.100020	+	0.173240i
$249$		−	16.4883i		−	1.04491i
$250$	0.00152545	+	0.00264216i	9.64781e−5	+	0.000167105i
$251$	−4.30726	−	7.46040i	−0.271872	−	0.470896i	0.697469	−	0.716615i	$-0.254309\pi$
$251$	−4.30726	−	7.46040i	−0.271872	−	0.470896i	−0.969341	+	0.245719i	$0.920976\pi$
$252$		0			0
$253$	−14.0470	+	8.11004i	−0.883128	+	0.509874i
$254$			5.04936i			0.316825i
$255$	−19.6671	+	11.3548i	−1.23160	+	0.711066i
$256$	7.40753	−	12.8302i	0.462970	−	0.801888i
$257$	−5.18197	−	8.97544i	−0.323243	−	0.559873i	0.657912	−	0.753094i	$-0.271440\pi$
$257$	−5.18197	−	8.97544i	−0.323243	−	0.559873i	−0.981155	+	0.193222i	$0.938106\pi$
$258$	13.2650	+	7.65856i	0.825844	+	0.476801i
$259$		0			0
$260$	−7.81035	−	12.8875i	−0.484377	−	0.799247i
$261$	12.2283	−	21.1800i	0.756913	−	1.31101i
$262$			8.41813i			0.520074i
$263$	−22.0826			−1.36167			−0.680835	−	0.732436i	$-0.738383\pi$
$263$	−22.0826			−1.36167			−0.680835	+	0.732436i	$0.738383\pi$
$264$	43.2488			2.66178
$265$		−	1.26258i		−	0.0775596i
$266$		0			0
$267$	−8.20495	+	4.73713i	−0.502135	+	0.289908i
$268$	−7.18761	−	4.14977i	−0.439053	−	0.253488i
$269$	6.46995	−	11.2063i	0.394480	−	0.683259i	−0.598555	−	0.801082i	$-0.704258\pi$
$269$	6.46995	−	11.2063i	0.394480	−	0.683259i	0.993035	+	0.117823i	$0.0375915\pi$
$270$	7.46233			0.454143
$271$	−15.3069	+	8.83745i	−0.929829	+	0.536837i	−0.886757	−	0.462235i	$-0.847048\pi$
$271$	−15.3069	+	8.83745i	−0.929829	+	0.536837i	−0.0430712	+	0.999072i	$0.513714\pi$
$272$	−1.05434			−0.0639289
$273$		0			0
$274$	−16.4279			−0.992446
$275$	25.7266	−	14.8533i	1.55137	−	0.895685i
$276$	−9.59732			−0.577691
$277$	−9.00751	+	15.6015i	−0.541209	+	0.937401i	0.457626	+	0.889145i	$0.348700\pi$
$277$	−9.00751	+	15.6015i	−0.541209	+	0.937401i	−0.998835	+	0.0482562i	$0.984634\pi$
$278$	14.4980	+	8.37041i	0.869530	+	0.502024i
$279$	−4.06602	+	2.34752i	−0.243426	+	0.140542i
$280$		0			0
$281$		−	2.44178i		−	0.145665i	−0.997344	−	0.0728323i	$-0.976796\pi$
$281$		−	2.44178i		−	0.145665i	0.997344	−	0.0728323i	$-0.0232038\pi$
$282$	−0.999205			−0.0595018
$283$	−28.7240			−1.70746			−0.853732	−	0.520713i	$-0.825666\pi$
$283$	−28.7240			−1.70746			−0.853732	+	0.520713i	$0.825666\pi$
$284$			5.95741i			0.353507i
$285$	−8.23143	+	14.2573i	−0.487588	+	0.844527i
$286$	−15.0910	+	9.14580i	−0.892350	+	0.540802i
$287$		0			0
$288$	20.4544	+	11.8094i	1.20529	+	0.695873i
$289$	4.85596	+	8.41078i	0.285645	+	0.494752i
$290$	−7.81046	+	13.5281i	−0.458646	+	0.794399i
$291$	−7.89657	+	4.55909i	−0.462905	+	0.267258i
$292$			10.9782i			0.642449i
$293$	−25.4013	+	14.6654i	−1.48396	+	0.856763i	−0.999834	−	0.0182359i	$-0.994195\pi$
$293$	−25.4013	+	14.6654i	−1.48396	+	0.856763i	−0.484124	+	0.874999i	$0.660862\pi$
$294$		0			0
$295$	7.59829	+	13.1606i	0.442390	+	0.766241i
$296$	−8.89708	−	15.4102i	−0.517132	−	0.895699i
$297$			17.0291i			0.988126i
$298$	4.41267	+	7.64298i	0.255619	+	0.442746i
$299$	8.41611	−	5.10052i	0.486716	−	0.294971i
$300$	17.5772			1.01482
$301$		0			0
$302$	−3.60065	+	6.23651i	−0.207194	+	0.358871i
$303$	35.4603			2.03714
$304$	−0.661923	+	0.382161i	−0.0379639	+	0.0219185i
$305$	3.16846	+	1.82931i	0.181426	+	0.104746i
$306$			9.06476i			0.518198i
$307$		−	7.06910i		−	0.403455i	−0.979442	−	0.201728i	$-0.935344\pi$
$307$		−	7.06910i		−	0.403455i	0.979442	−	0.201728i	$-0.0646555\pi$
$308$		0			0
$309$	15.4895	−	26.8286i	0.881166	−	1.52623i
$310$	2.59705	−	1.49941i	0.147503	−	0.0851607i
$311$	11.1343	+	19.2852i	0.631368	+	1.09356i	0.987272	+	0.159039i	$0.0508396\pi$
$311$	11.1343	+	19.2852i	0.631368	+	1.09356i	−0.355904	+	0.934522i	$0.615827\pi$
$312$	−26.2340	+	0.557607i	−1.48520	+	0.0315683i
$313$	−14.0420	+	24.3214i	−0.793700	+	1.37473i	0.129961	+	0.991519i	$0.458515\pi$
$313$	−14.0420	+	24.3214i	−0.793700	+	1.37473i	−0.923661	+	0.383210i	$0.874819\pi$
$314$	−4.64117	−	2.67958i	−0.261916	−	0.151217i
$315$		0			0
$316$	5.23025	+	9.05906i	0.294225	+	0.509612i
$317$	−16.9009	−	9.75774i	−0.949249	−	0.548049i	−0.0564015	−	0.998408i	$-0.517963\pi$
$317$	−16.9009	−	9.75774i	−0.949249	−	0.548049i	−0.892848	+	0.450359i	$0.851296\pi$
$318$	−0.757595	−	0.437398i	−0.0424838	−	0.0245281i
$319$	−30.8712	−	17.8235i	−1.72845	−	0.997924i
$320$	−10.9256	−	6.30792i	−0.610762	−	0.352624i
$321$	5.22702	+	9.05346i	0.291744	+	0.505315i
$322$		0			0
$323$	−4.57550	−	2.64167i	−0.254588	−	0.146986i
$324$	3.04551	−	5.27498i	0.169195	−	0.293054i
$325$	−15.4138	+	9.34142i	−0.855004	+	0.518169i
$326$	−1.07584	−	1.86341i	−0.0595853	−	0.103205i
$327$	25.9263	−	14.9686i	1.43373	−	0.827764i
$328$	5.10711	−	8.84577i	0.281993	−	0.488426i
$329$		0			0
$330$		−	41.1700i		−	2.26633i
$331$			15.6308i			0.859145i	0.903032	+	0.429573i	$0.141336\pi$
$331$			15.6308i			0.859145i	−0.903032	+	0.429573i	$0.858664\pi$
$332$	−7.09463	−	4.09609i	−0.389368	−	0.224802i
$333$	22.9670	−	13.2600i	1.25858	−	0.726644i
$334$	−3.20053			−0.175125
$335$	−9.92767	+	17.1952i	−0.542407	+	0.939476i
$336$		0			0
$337$	21.7501			1.18480			0.592401	−	0.805643i	$-0.298180\pi$
$337$	21.7501			1.18480			0.592401	+	0.805643i	$0.298180\pi$
$338$	9.03603	−	5.74225i	0.491495	−	0.312337i
$339$	−7.68050	−	13.3030i	−0.417148	−	0.722521i
$340$			11.2832i			0.611917i
$341$	3.42165	+	5.92647i	0.185293	+	0.320937i
$342$	3.28565	+	5.69092i	0.177668	+	0.307730i
$343$		0			0
$344$	16.5633	−	9.56281i	0.893032	−	0.515592i
$345$			22.9601i			1.23613i
$346$	−9.96851	+	5.75532i	−0.535910	+	0.309408i
$347$	7.97952	−	13.8209i	0.428363	−	0.741946i	−0.568365	−	0.822777i	$-0.692424\pi$
$347$	7.97952	−	13.8209i	0.428363	−	0.741946i	0.996728	+	0.0808303i	$0.0257572\pi$
$348$	−10.5460	−	18.2663i	−0.565327	−	0.979176i
$349$	−5.90375	−	3.40853i	−0.316021	−	0.182455i	0.333597	−	0.942716i	$-0.391738\pi$
$349$	−5.90375	−	3.40853i	−0.316021	−	0.182455i	−0.649617	+	0.760261i	$0.725071\pi$
$350$		0			0
$351$	−0.219556	−	10.3295i	−0.0117190	−	0.551349i
$352$	17.2128	−	29.8135i	0.917448	−	1.58907i
$353$			14.0033i			0.745318i	0.927968	+	0.372659i	$0.121554\pi$
$353$			14.0033i			0.745318i	−0.927968	+	0.372659i	$0.878446\pi$
$354$	10.5292			0.559619
$355$	14.2522			0.756427
$356$			4.70725i			0.249484i
$357$		0			0
$358$	−18.0333	+	10.4115i	−0.953088	+	0.550266i
$359$	4.68947	+	2.70747i	0.247501	+	0.142895i	0.618619	−	0.785691i	$-0.287692\pi$
$359$	4.68947	+	2.70747i	0.247501	+	0.142895i	−0.371119	+	0.928586i	$0.621026\pi$
$360$	17.6345	−	30.5438i	0.929418	−	1.60980i
$361$	15.1700			0.798419
$362$	−0.616561	+	0.355972i	−0.0324057	+	0.0187094i
$363$	64.6867			3.39517
$364$		0			0
$365$	26.2636			1.37470
$366$	2.19531	−	1.26747i	0.114751	−	0.0662515i
$367$	−30.0317			−1.56764			−0.783822	−	0.620985i	$-0.786733\pi$
$367$	−30.0317			−1.56764			−0.783822	+	0.620985i	$0.786733\pi$
$368$	−0.532985	+	0.923157i	−0.0277838	+	0.0481229i
$369$	13.1835	+	7.61152i	0.686307	+	0.396240i
$370$	−14.6695	+	8.46943i	−0.762630	+	0.440305i
$371$		0			0
$372$			4.04914i			0.209938i
$373$	21.4098			1.10856			0.554278	−	0.832332i	$-0.312995\pi$
$373$	21.4098			1.10856			0.554278	+	0.832332i	$0.312995\pi$
$374$	13.2124			0.683199
$375$			0.00985519i			0.000508920i
$376$	−0.623826	+	1.08050i	−0.0321713	+	0.0557224i
$377$	18.9557	+	10.4134i	0.976270	+	0.536317i
$378$		0			0
$379$	−8.20693	−	4.73827i	−0.421562	−	0.243389i	0.274184	−	0.961677i	$-0.411592\pi$
$379$	−8.20693	−	4.73827i	−0.421562	−	0.243389i	−0.695745	+	0.718289i	$0.744926\pi$
$380$	4.08975	+	7.08366i	0.209800	+	0.363384i
$381$	−8.15535	+	14.1255i	−0.417811	+	0.723670i
$382$	−10.4613	+	6.03982i	−0.535245	+	0.309024i
$383$			5.43061i			0.277491i	0.990328	+	0.138746i	$0.0443070\pi$
$383$			5.43061i			0.277491i	−0.990328	+	0.138746i	$0.955693\pi$
$384$	19.1225	−	11.0404i	0.975842	−	0.563402i
$385$		0			0
$386$	6.79264	+	11.7652i	0.345736	+	0.598833i
$387$	14.2522	+	24.6855i	0.724480	+	1.25484i
$388$			4.53033i			0.229993i
$389$	−5.32109	−	9.21640i	−0.269790	−	0.467290i	0.699018	−	0.715105i	$-0.253621\pi$
$389$	−5.32109	−	9.21640i	−0.269790	−	0.467290i	−0.968807	+	0.247815i	$0.920288\pi$
$390$	0.530805	+	24.9730i	0.0268784	+	1.26456i
$391$	−7.36845			−0.372638
$392$		0			0
$393$	−13.5963	+	23.5495i	−0.685845	+	1.18792i
$394$	−9.06750			−0.456814
$395$	21.6724	−	12.5126i	1.09046	−	0.629575i
$396$	27.7346	+	16.0126i	1.39372	+	0.804663i
$397$		−	37.1854i		−	1.86628i	−0.359512	−	0.933140i	$-0.617057\pi$
$397$		−	37.1854i		−	1.86628i	0.359512	−	0.933140i	$-0.382943\pi$
$398$			17.4690i			0.875644i
$399$		0			0
$400$	0.976143	−	1.69073i	0.0488072	−	0.0845365i
$401$	0.776487	−	0.448305i	0.0387759	−	0.0223873i	−0.480487	−	0.877002i	$-0.659540\pi$
$401$	0.776487	−	0.448305i	0.0387759	−	0.0223873i	0.519263	+	0.854615i	$0.326207\pi$
$402$	6.87853	+	11.9140i	0.343070	+	0.594214i
$403$	−2.15192	−	3.55078i	−0.107195	−	0.176877i
$404$	8.80916	−	15.2579i	0.438272	−	0.759110i
$405$	−12.6196	−	7.28590i	−0.627071	−	0.362039i
$406$		0			0
$407$	−19.3273	−	33.4758i	−0.958016	−	1.65933i
$408$	17.0148	+	9.82350i	0.842359	+	0.486336i
$409$	21.2846	+	12.2886i	1.05245	+	0.607635i	0.923335	−	0.383995i	$-0.125452\pi$
$409$	21.2846	+	12.2886i	1.05245	+	0.607635i	0.129119	+	0.991629i	$0.458785\pi$
$410$	−8.42059	−	4.86163i	−0.415863	−	0.240099i
$411$	−45.9567	−	26.5331i	−2.26688	−	1.30878i
$412$	−7.69589	−	13.3297i	−0.379149	−	0.656706i
$413$		0			0
$414$	7.93689	+	4.58237i	0.390077	+	0.225211i
$415$	−9.79924	+	16.9728i	−0.481026	+	0.833161i
$416$	−10.0566	+	18.3063i	−0.493067	+	0.897540i
$417$	27.0385	+	46.8321i	1.32408	+	2.29338i
$418$	8.29486	−	4.78904i	0.405715	−	0.234239i
$419$	−3.82279	+	6.62126i	−0.186755	+	0.323470i	−0.944167	−	0.329468i	$-0.893131\pi$
$419$	−3.82279	+	6.62126i	−0.186755	+	0.323470i	0.757411	+	0.652938i	$0.226464\pi$
$420$		0			0
$421$		−	25.0780i		−	1.22223i	−0.791544	−	0.611113i	$-0.790722\pi$
$421$		−	25.0780i		−	1.22223i	0.791544	−	0.611113i	$-0.209278\pi$
$422$			14.7711i			0.719046i
$423$	−1.61035	−	0.929736i	−0.0782979	−	0.0452053i
$424$	−0.945966	+	0.546154i	−0.0459402	+	0.0265236i
$425$	13.4951			0.654606
$426$	4.93741	−	8.55184i	0.239218	−	0.414338i
$427$		0			0
$428$	5.19405			0.251064
$429$	−56.9884	+	1.21130i	−2.75143	+	0.0584820i
$430$	−9.10317	−	15.7671i	−0.438994	−	0.760359i
$431$		−	7.75404i		−	0.373499i	−0.982408	−	0.186750i	$-0.940205\pi$
$431$		−	7.75404i		−	0.373499i	0.982408	−	0.186750i	$-0.0597953\pi$
$432$	0.559567	+	0.969199i	0.0269222	+	0.0466306i
$433$	−17.9880	−	31.1561i	−0.864448	−	1.49727i	−0.867594	−	0.497273i	$-0.834335\pi$
$433$	−17.9880	−	31.1561i	−0.864448	−	1.49727i	0.00314644	−	0.999995i	$-0.498998\pi$
$434$		0			0
$435$	−43.6992	+	25.2298i	−2.09522	+	1.20967i
$436$		−	14.8741i		−	0.712342i
$437$	−4.62596	+	2.67080i	−0.221290	+	0.127762i
$438$	9.09853	−	15.7591i	0.434745	−	0.753000i
$439$	14.1175	+	24.4523i	0.673792	+	1.16704i	0.976820	+	0.214061i	$0.0686691\pi$
$439$	14.1175	+	24.4523i	0.673792	+	1.16704i	−0.303028	+	0.952982i	$0.597998\pi$
$440$	−44.5194	−	25.7033i	−2.12238	−	1.22536i
$441$		0			0
$442$	−8.01444	+	0.170348i	−0.381208	+	0.00810264i
$443$	−14.3959	+	24.9344i	−0.683970	+	1.18467i	0.289790	+	0.957090i	$0.406415\pi$
$443$	−14.3959	+	24.9344i	−0.683970	+	1.18467i	−0.973759	+	0.227580i	$0.926919\pi$
$444$		−	22.8716i		−	1.08544i
$445$	11.2614			0.533840
$446$	−13.2026			−0.625159
$447$			28.5081i			1.34839i
$448$		0			0
$449$	−25.2795	+	14.5951i	−1.19301	+	0.688785i	−0.958988	−	0.283446i	$-0.908522\pi$
$449$	−25.2795	+	14.5951i	−1.19301	+	0.688785i	−0.234023	+	0.972231i	$0.575189\pi$
$450$	−14.5361	−	8.39244i	−0.685240	−	0.395624i
$451$	11.0942	−	19.2158i	0.522408	−	0.904836i
$452$	−7.63205			−0.358982
$453$	−20.1455	+	11.6310i	−0.946518	+	0.546473i
$454$	13.4858			0.632918
$455$		0			0
$456$	14.2427			0.666974
$457$	27.4399	−	15.8424i	1.28358	−	0.741077i	0.306081	−	0.952006i	$-0.400982\pi$
$457$	27.4399	−	15.8424i	1.28358	−	0.741077i	0.977501	+	0.210929i	$0.0676489\pi$
$458$	22.2446			1.03942
$459$	−3.86797	+	6.69952i	−0.180541	+	0.312707i
$460$	9.87929	+	5.70381i	0.460624	+	0.265942i
$461$	19.1407	−	11.0509i	0.891471	−	0.514691i	0.0170480	−	0.999855i	$-0.494573\pi$
$461$	19.1407	−	11.0509i	0.891471	−	0.514691i	0.874424	+	0.485163i	$0.161240\pi$
$462$		0			0
$463$			38.8811i			1.80696i	0.428632	+	0.903479i	$0.358996\pi$
$463$			38.8811i			1.80696i	−0.428632	+	0.903479i	$0.641004\pi$
$464$	−2.34269			−0.108757
$465$	9.68693			0.449220
$466$			9.52699i			0.441329i
$467$	−6.64116	+	11.5028i	−0.307316	+	0.532287i	−0.977774	−	0.209660i	$-0.932764\pi$
$467$	−6.64116	+	11.5028i	−0.307316	+	0.532287i	0.670458	+	0.741947i	$0.266098\pi$
$468$	−17.0298	−	9.35538i	−0.787203	−	0.432453i
$469$		0			0
$470$	1.02856	+	0.593841i	0.0474440	+	0.0273918i
$471$	−8.65571	−	14.9921i	−0.398834	−	0.690801i
$472$	6.57358	−	11.3858i	0.302574	−	0.524073i
$473$	35.9807	−	20.7734i	1.65439	−	0.955164i
$474$		−	17.3390i		−	0.796406i
$475$	8.47228	−	4.89147i	0.388735	−	0.224436i
$476$		0			0
$477$	−0.813975	−	1.40985i	−0.0372694	−	0.0645524i
$478$	−6.04205	−	10.4651i	−0.276357	−	0.478664i
$479$			6.63512i			0.303166i	0.988445	+	0.151583i	$0.0484371\pi$
$479$			6.63512i			0.303166i	−0.988445	+	0.151583i	$0.951563\pi$
$480$	−24.3654	−	42.2021i	−1.11212	−	1.92625i
$481$	12.1552	+	20.0566i	0.554229	+	0.914504i
$482$	−11.8153			−0.538172
$483$		0			0
$484$	16.0697	−	27.8335i	0.730439	−	1.26516i
$485$	10.8381			0.492133
$486$	−14.8749	+	8.58804i	−0.674740	+	0.389561i
$487$	−28.9860	−	16.7351i	−1.31348	−	0.758338i	−0.330809	−	0.943698i	$-0.607322\pi$
$487$	−28.9860	−	16.7351i	−1.31348	−	0.758338i	−0.982671	+	0.185359i	$0.940655\pi$
$488$		−	3.16522i		−	0.143283i
$489$		−	6.95047i		−	0.314311i
$490$		0			0
$491$	−18.6643	+	32.3276i	−0.842310	+	1.45892i	0.0456264	+	0.998959i	$0.485472\pi$
$491$	−18.6643	+	32.3276i	−0.842310	+	1.45892i	−0.887937	+	0.459966i	$0.847862\pi$
$492$	11.3699	−	6.56439i	0.512593	−	0.295946i
$493$	−8.09684	−	14.0241i	−0.364663	−	0.631615i
$494$	−4.96977	+	3.01189i	−0.223601	+	0.135511i
$495$	38.3076	−	66.3507i	1.72180	−	2.98224i
$496$	0.389483	+	0.224868i	0.0174883	+	0.0100969i
$497$		0			0
$498$	6.78954	+	11.7598i	0.304246	+	0.526970i
$499$	−29.5598	−	17.0663i	−1.32328	−	0.763994i	−0.339027	−	0.940777i	$-0.610098\pi$
$499$	−29.5598	−	17.0663i	−1.32328	−	0.763994i	−0.984250	+	0.176783i	$0.943431\pi$
$500$	0.00424050	+	0.00244826i	0.000189641	+	0.000109489i
$501$	−8.95342	−	5.16926i	−0.400009	−	0.230946i
$502$	6.14405	+	3.54727i	0.274223	+	0.158322i
$503$	7.65447	+	13.2579i	0.341296	+	0.591142i	0.984674	−	0.174407i	$-0.0558008\pi$
$503$	7.65447	+	13.2579i	0.341296	+	0.591142i	−0.643378	+	0.765549i	$0.722467\pi$
$504$		0			0
$505$	−36.5022	−	21.0745i	−1.62433	−	0.937805i
$506$	6.67907	−	11.5685i	0.296921	−	0.514282i
$507$	34.5526	−	1.46950i	1.53453	−	0.0652630i
$508$	4.05195	+	7.01819i	0.179776	+	0.311382i
$509$	−16.0189	+	9.24851i	−0.710025	+	0.409933i	−0.811070	−	0.584949i	$-0.801115\pi$
$509$	−16.0189	+	9.24851i	−0.710025	+	0.409933i	0.101046	+	0.994882i	$0.467781\pi$
$510$	9.35133	−	16.1970i	0.414084	−	0.717214i
$511$		0			0
$512$		−	4.39924i		−	0.194421i
$513$			5.60801i			0.247599i
$514$	7.39178	+	4.26765i	0.326037	+	0.188238i
$515$	−31.8892	+	18.4112i	−1.40520	+	0.811295i
$516$	24.5830			1.08221
$517$	−1.35515	+	2.34718i	−0.0595992	+	0.103229i
$518$		0			0
$519$	−37.1823			−1.63212
$520$	27.3361	+	15.0172i	1.19877	+	0.658547i
$521$	11.7932	+	20.4265i	0.516671	+	0.894901i	0.999813	+	0.0193585i	$0.00616239\pi$
$521$	11.7932	+	20.4265i	0.516671	+	0.894901i	−0.483141	+	0.875542i	$0.660504\pi$
$522$			20.1414i			0.881564i
$523$	6.15294	+	10.6572i	0.269049	+	0.466007i	0.968617	−	0.248560i	$-0.0799572\pi$
$523$	6.15294	+	10.6572i	0.269049	+	0.466007i	−0.699567	+	0.714567i	$0.746624\pi$
$524$	6.75529	+	11.7005i	0.295106	+	0.511139i
$525$		0			0
$526$	15.7498	−	9.09312i	0.686722	−	0.396479i
$527$			3.10877i			0.135420i
$528$	5.34711	−	3.08715i	0.232703	−	0.134351i
$529$	7.77515	−	13.4670i	0.338050	−	0.585520i
$530$	0.519902	+	0.900497i	0.0225831	+	0.0391151i
$531$	16.9691	+	9.79712i	0.736397	+	0.425159i
$532$		0			0
$533$	−6.48183	+	11.7990i	−0.280759	+	0.511072i
$534$	3.90129	−	6.75724i	0.168825	−	0.292414i
$535$		−	12.4259i		−	0.537220i
$536$	17.1777			0.741962
$537$	−67.2636			−2.90264
$538$			10.6567i			0.459444i
$539$		0			0
$540$	10.3720	−	5.98829i	0.446341	−	0.257695i
$541$	16.8365	+	9.72054i	0.723857	+	0.417919i	0.816170	−	0.577811i	$-0.196093\pi$
$541$	16.8365	+	9.72054i	0.723857	+	0.417919i	−0.0923139	+	0.995730i	$0.529426\pi$
$542$	7.27813	−	12.6061i	0.312623	−	0.541478i
$543$	−2.29975			−0.0986919
$544$	13.5437	−	7.81944i	0.580680	−	0.335256i
$545$	−35.5841			−1.52425
$546$		0			0
$547$	40.2163			1.71953			0.859763	−	0.510693i	$-0.170611\pi$
$547$	40.2163			1.71953			0.859763	+	0.510693i	$0.170611\pi$
$548$	−22.8334	+	13.1829i	−0.975395	+	0.563145i
$549$	4.71738			0.201333
$550$	−12.2325	+	21.1873i	−0.521595	+	0.903429i
$551$	−10.1665	−	5.86963i	−0.433107	−	0.250055i
$552$	17.2024	−	9.93184i	0.732185	−	0.422727i
$553$		0			0
$554$		−	14.8364i		−	0.630337i
$555$	−54.7168			−2.32260
$556$	26.8680			1.13945
$557$		−	7.96399i		−	0.337445i	−0.985664	−	0.168722i	$-0.946036\pi$
$557$		−	7.96399i		−	0.337445i	0.985664	−	0.168722i	$-0.0539642\pi$
$558$	1.93331	−	3.34860i	0.0818437	−	0.141757i
$559$	−21.5574	+	13.0647i	−0.911781	+	0.552578i
$560$		0			0
$561$	36.9615	+	21.3397i	1.56052	+	0.900965i
$562$	1.00547	+	1.74153i	0.0424133	+	0.0734620i
$563$	0.711981	−	1.23319i	0.0300064	−	0.0519726i	−0.850632	−	0.525761i	$-0.823781\pi$
$563$	0.711981	−	1.23319i	0.0300064	−	0.0519726i	0.880639	+	0.473789i	$0.157114\pi$
$564$	−1.38881	+	0.801831i	−0.0584795	+	0.0337632i
$565$			18.2585i			0.768140i
$566$	20.4865	−	11.8279i	0.861113	−	0.497164i
$567$		0			0
$568$	−6.16506	−	10.6782i	−0.258680	−	0.448047i
$569$	−9.25946	−	16.0379i	−0.388177	−	0.672342i	0.604028	−	0.796963i	$-0.293562\pi$
$569$	−9.25946	−	16.0379i	−0.388177	−	0.672342i	−0.992204	+	0.124622i	$0.960228\pi$
$570$		−	13.5581i		−	0.567886i
$571$	2.17883	+	3.77384i	0.0911812	+	0.157930i	0.908008	−	0.418952i	$-0.137602\pi$
$571$	2.17883	+	3.77384i	0.0911812	+	0.157930i	−0.816827	+	0.576882i	$0.804269\pi$
$572$	−13.6360	+	24.8220i	−0.570151	+	1.03786i
$573$	−39.0202			−1.63009
$574$		0			0
$575$	6.82194	−	11.8159i	0.284494	−	0.492759i
$576$	−16.2667			−0.677778
$577$	8.28280	−	4.78208i	0.344818	−	0.199081i	−0.317583	−	0.948231i	$-0.602871\pi$
$577$	8.28280	−	4.78208i	0.344818	−	0.199081i	0.662400	+	0.749150i	$0.269538\pi$
$578$	−6.92674	−	3.99916i	−0.288115	−	0.166343i
$579$			43.8839i			1.82375i
$580$			25.0706i			1.04100i
$581$		0			0
$582$	3.75466	−	6.50327i	0.155636	−	0.269569i
$583$	−2.05494	+	1.18642i	−0.0851068	+	0.0491364i
$584$	−11.3608	−	19.6775i	−0.470114	−	0.814262i
$585$	−22.3813	+	40.7411i	−0.925352	+	1.68444i
$586$	12.0778	−	20.9194i	0.498929	−	0.864171i
$587$	2.04428	+	1.18027i	0.0843765	+	0.0487148i	0.541595	−	0.840640i	$-0.317821\pi$
$587$	2.04428	+	1.18027i	0.0843765	+	0.0487148i	−0.457218	+	0.889355i	$0.651154\pi$
$588$		0			0
$589$	1.12682	+	1.95171i	0.0464297	+	0.0804186i
$590$	−10.8385	−	6.25762i	−0.446214	−	0.257622i
$591$	−25.3661	−	14.6452i	−1.04342	−	0.602421i
$592$	−2.20000	−	1.27017i	−0.0904194	−	0.0522037i
$593$	−35.0127	−	20.2146i	−1.43780	−	0.830114i	−0.440103	−	0.897947i	$-0.645058\pi$
$593$	−35.0127	−	20.2146i	−1.43780	−	0.830114i	−0.997697	+	0.0678337i	$0.978391\pi$
$594$	−7.01219	−	12.1455i	−0.287714	−	0.498335i
$595$		0			0
$596$	12.2665	+	7.08207i	0.502455	+	0.290093i
$597$	−28.2147	+	48.8693i	−1.15475	+	2.00009i
$598$	−3.90226	+	7.10336i	−0.159575	+	0.290478i
$599$	19.2936	+	33.4176i	0.788316	+	1.36540i	0.926998	+	0.375067i	$0.122380\pi$
$599$	19.2936	+	33.4176i	0.788316	+	1.36540i	−0.138681	+	0.990337i	$0.544286\pi$
$600$	−31.5057	+	18.1898i	−1.28621	+	0.742596i
$601$	4.08115	−	7.06877i	0.166474	−	0.288341i	−0.770704	−	0.637193i	$-0.780095\pi$
$601$	4.08115	−	7.06877i	0.166474	−	0.288341i	0.937178	+	0.348852i	$0.113429\pi$
$602$		0			0
$603$			25.6012i			1.04256i
$604$			11.5576i			0.470274i
$605$	−66.5872	−	38.4442i	−2.70716	−	1.56298i
$606$	−25.2910	+	14.6018i	−1.02738	+	0.593157i
$607$	−7.58525			−0.307876			−0.153938	−	0.988081i	$-0.549196\pi$
$607$	−7.58525			−0.307876			−0.153938	+	0.988081i	$0.549196\pi$
$608$	5.66853	−	9.81819i	0.229889	−	0.398180i
$609$		0			0
$610$	−3.01308			−0.121996
$611$	0.791746	−	1.44123i	0.0320306	−	0.0583060i
$612$	7.27419	+	12.5993i	0.294042	+	0.509295i
$613$			15.5778i			0.629183i	0.949227	+	0.314592i	$0.101868\pi$
$613$			15.5778i			0.629183i	−0.949227	+	0.314592i	$0.898132\pi$
$614$	2.91090	+	5.04183i	0.117474	+	0.203472i
$615$	−15.7043	−	27.2006i	−0.633258	−	1.09683i
$616$		0			0
$617$	20.6709	−	11.9343i	0.832177	−	0.480458i	−0.0224202	−	0.999749i	$-0.507137\pi$
$617$	20.6709	−	11.9343i	0.832177	−	0.480458i	0.854598	+	0.519291i	$0.173804\pi$
$618$			25.5129i			1.02628i
$619$	−16.8843	+	9.74814i	−0.678636	+	0.391811i	−0.799341	−	0.600878i	$-0.794818\pi$
$619$	−16.8843	+	9.74814i	−0.678636	+	0.391811i	0.120705	+	0.992688i	$0.461485\pi$
$620$	2.40646	−	4.16810i	0.0966456	−	0.167395i
$621$	3.91063	+	6.77341i	0.156928	+	0.271807i
$622$	−15.8824	−	9.16972i	−0.636827	−	0.367672i
$623$		0			0
$624$	−3.20366	+	1.94155i	−0.128249	+	0.0777244i
$625$	12.5029	−	21.6557i	0.500117	−	0.866228i
$626$		−	23.1287i		−	0.924410i
$627$	30.9396			1.23561
$628$	−8.60111			−0.343222
$629$		−	17.5599i		−	0.700161i
$630$		0			0
$631$	−22.2239	+	12.8309i	−0.884718	+	0.510792i	−0.872211	−	0.489130i	$-0.837314\pi$
$631$	−22.2239	+	12.8309i	−0.884718	+	0.510792i	−0.0125066	+	0.999922i	$0.503981\pi$
$632$	−18.7496	−	10.8251i	−0.745820	−	0.430600i
$633$	−23.8572	+	41.3219i	−0.948238	+	1.64240i
$634$	16.0721			0.638304
$635$	16.7899	−	9.69366i	0.666287	−	0.384681i
$636$	−1.40399			−0.0556719
$637$		0			0
$638$	29.3573			1.16227
$639$	15.9145	−	9.18826i	0.629569	−	0.363482i
$640$	−26.2458			−1.03746
$641$	−0.553020	+	0.957859i	−0.0218430	+	0.0378332i	−0.876740	−	0.480964i	$-0.840287\pi$
$641$	−0.553020	+	0.957859i	−0.0218430	+	0.0378332i	0.854897	+	0.518797i	$0.173620\pi$
$642$	−7.45603	−	4.30474i	−0.294266	−	0.169895i
$643$	−10.9437	+	6.31833i	−0.431576	+	0.249171i	−0.700018	−	0.714125i	$-0.746825\pi$
$643$	−10.9437	+	6.31833i	−0.431576	+	0.249171i	0.268442	+	0.963296i	$0.413491\pi$
$644$		0			0
$645$		−	58.8110i		−	2.31568i
$646$	4.35112			0.171192
$647$	25.7148			1.01095			0.505477	−	0.862840i	$-0.331317\pi$
$647$	25.7148			1.01095			0.505477	+	0.862840i	$0.331317\pi$
$648$			12.6066i			0.495236i
$649$	14.2799	−	24.7335i	0.560535	−	0.970875i
$650$	7.14685	−	13.0096i	0.280323	−	0.510277i
$651$		0			0
$652$	−2.99066	−	1.72666i	−0.117123	−	0.0676211i
$653$	−12.6303	−	21.8764i	−0.494263	−	0.856089i	0.505715	−	0.862701i	$-0.331229\pi$
$653$	−12.6303	−	21.8764i	−0.494263	−	0.856089i	−0.999978	+	0.00661158i	$0.997895\pi$
$654$	−12.3275	+	21.3518i	−0.482041	+	0.834920i
$655$	27.9916	−	16.1610i	1.09372	−	0.631461i
$656$		−	1.45821i		−	0.0569335i
$657$	29.3269	−	16.9319i	1.14415	−	0.660577i
$658$		0			0
$659$	−11.4882	−	19.8982i	−0.447517	−	0.775123i	0.550707	−	0.834699i	$-0.314358\pi$
$659$	−11.4882	−	19.8982i	−0.447517	−	0.775123i	−0.998224	+	0.0595764i	$0.981025\pi$
$660$	−33.0376	−	57.2228i	−1.28599	−	2.22739i
$661$			30.4326i			1.18369i	0.806051	+	0.591845i	$0.201600\pi$
$661$			30.4326i			1.18369i	−0.806051	+	0.591845i	$0.798400\pi$
$662$	−6.43641	−	11.1482i	−0.250158	−	0.433287i
$663$	−22.6954	−	12.4678i	−0.881415	−	0.484208i
$664$	16.9554			0.657998
$665$		0			0
$666$	−10.9204	+	18.9146i	−0.423155	+	0.732926i
$667$	−16.3723			−0.633937
$668$	−4.44847	+	2.56833i	−0.172117	+	0.0993715i
$669$	−36.9339	−	21.3238i	−1.42795	−	0.824425i
$670$		−	16.3520i		−	0.631733i
$671$		−	6.87586i		−	0.265440i
$672$		0			0
$673$	5.41933	−	9.38656i	0.208900	−	0.361825i	−0.742468	−	0.669881i	$-0.766345\pi$
$673$	5.41933	−	9.38656i	0.208900	−	0.361825i	0.951368	+	0.308056i	$0.0996784\pi$
$674$	−15.5126	+	8.95620i	−0.597523	+	0.344980i
$675$	−7.16218	−	12.4053i	−0.275672	−	0.477479i
$676$	7.95135	−	15.2324i	0.305821	−	0.585861i
$677$	−9.06044	+	15.6931i	−0.348221	+	0.603137i	−0.985934	−	0.167138i	$-0.946547\pi$
$677$	−9.06044	+	15.6931i	−0.348221	+	0.603137i	0.637712	+	0.770275i	$0.279881\pi$
$678$	10.9558	+	6.32532i	0.420754	+	0.242923i
$679$		0			0
$680$	−11.6765	−	20.2242i	−0.447772	−	0.775564i
$681$	37.7261	+	21.7812i	1.44567	+	0.834656i
$682$	−4.88078	−	2.81792i	−0.186895	−	0.107904i
$683$	−32.7662	−	18.9176i	−1.25376	−	0.723861i	−0.281909	−	0.959441i	$-0.590968\pi$
$683$	−32.7662	−	18.9176i	−1.25376	−	0.723861i	−0.971855	+	0.235580i	$0.924301\pi$
$684$	9.13357	+	5.27327i	0.349231	+	0.201628i
$685$	31.5380	+	54.6254i	1.20500	+	2.08713i
$686$		0			0
$687$	62.2288	+	35.9278i	2.37418	+	1.37073i
$688$	1.36521	−	2.36462i	0.0520482	−	0.0901502i
$689$	1.23119	−	0.746155i	0.0469047	−	0.0284262i
$690$	−9.45446	−	16.3756i	−0.359925	−	0.623408i
$691$	26.0034	−	15.0131i	0.989216	−	0.571124i	0.0841761	−	0.996451i	$-0.473174\pi$
$691$	26.0034	−	15.0131i	0.989216	−	0.571124i	0.905040	+	0.425327i	$0.139841\pi$
$692$	−9.23693	+	15.9988i	−0.351135	+	0.608184i
$693$		0			0
$694$			13.1432i			0.498907i
$695$		−	64.2774i		−	2.43818i
$696$	37.8059	+	21.8273i	1.43303	+	0.827360i
$697$	8.72934	−	5.03988i	0.330647	−	0.190899i
$698$	5.61423			0.212502
$699$	−15.3873	+	26.6516i	−0.582001	+	1.00805i
$700$		0			0
$701$	0.116177			0.00438796			0.00219398	−	0.999998i	$-0.499302\pi$
$701$	0.116177			0.00438796			0.00219398	+	0.999998i	$0.499302\pi$
$702$	4.41006	+	7.27682i	0.166447	+	0.274646i
$703$	−6.36485	−	11.0242i	−0.240055	−	0.415787i
$704$			23.7097i			0.893591i
$705$	1.91825	+	3.32251i	0.0722456	+	0.125133i
$706$	−5.76624	−	9.98741i	−0.217015	−	0.375881i
$707$		0			0
$708$	14.6347	−	8.44932i	0.550004	−	0.317545i
$709$			6.72993i			0.252748i	0.991983	+	0.126374i	$0.0403339\pi$
$709$			6.72993i			0.252748i	−0.991983	+	0.126374i	$0.959666\pi$
$710$	−10.1649	+	5.86873i	−0.381483	+	0.220249i
$711$	16.1335	−	27.9440i	0.605053	−	1.04798i
$712$	−4.87132	−	8.43738i	−0.182561	−	0.316204i
$713$	2.72196	+	1.57153i	0.101938	+	0.0588541i
$714$		0			0
$715$	59.3826	+	32.6221i	2.22078	+	1.22000i
$716$	−16.7098	+	28.9423i	−0.624476	+	1.08162i
$717$		−	39.0347i		−	1.45778i
$718$	−4.45950			−0.166427
$719$	46.8078			1.74564			0.872818	−	0.488046i	$-0.162290\pi$
$719$	46.8078			1.74564			0.872818	+	0.488046i	$0.162290\pi$
$720$		−	5.03509i		−	0.187647i
$721$		0			0
$722$	−10.8195	+	6.24666i	−0.402661	+	0.232476i
$723$	−33.0530	−	19.0832i	−1.22926	−	0.709711i
$724$	−0.571312	+	0.989541i	−0.0212326	+	0.0367760i
$725$	29.9852			1.11362
$726$	−46.1359	+	26.6366i	−1.71226	+	0.988576i
$727$	−13.3362			−0.494611			−0.247305	−	0.968938i	$-0.579545\pi$
$727$	−13.3362			−0.494611			−0.247305	+	0.968938i	$0.579545\pi$
$728$		0			0
$729$	−41.6582			−1.54290
$730$	−18.7317	+	10.8148i	−0.693291	+	0.400272i
$731$	18.8739			0.698076
$732$	2.03420	−	3.52334i	0.0751863	−	0.130226i
$733$	−25.5142	−	14.7306i	−0.942387	−	0.544087i	−0.0516792	−	0.998664i	$-0.516457\pi$
$733$	−25.5142	−	14.7306i	−0.942387	−	0.544087i	−0.890708	+	0.454576i	$0.849791\pi$
$734$	21.4193	−	12.3664i	0.790599	−	0.456453i
$735$		0			0
$736$		−	15.8113i		−	0.582814i
$737$	37.3153			1.37453
$738$	−12.5370			−0.461494
$739$			12.0302i			0.442537i	0.975213	+	0.221269i	$0.0710198\pi$
$739$			12.0302i			0.442537i	−0.975213	+	0.221269i	$0.928980\pi$
$740$	−13.5929	+	23.5436i	−0.499685	+	0.865480i
$741$	−18.7674	+	0.398904i	−0.689438	+	0.0146541i
$742$		0			0
$743$	−18.9509	−	10.9413i	−0.695242	−	0.401398i	0.110331	−	0.993895i	$-0.464809\pi$
$743$	−18.9509	−	10.9413i	−0.695242	−	0.401398i	−0.805573	+	0.592497i	$0.798142\pi$
$744$	−4.19027	−	7.25777i	−0.153623	−	0.266083i
$745$	16.9427	−	29.3457i	0.620734	−	1.07514i
$746$	−15.2699	+	8.81607i	−0.559070	+	0.322779i
$747$			25.2700i			0.924580i
$748$	18.3642	−	10.6026i	0.671461	−	0.387668i
$749$		0			0
$750$	−0.00405815	−	0.00702892i	−0.000148183	−	0.000256660i
$751$	17.3746	+	30.0937i	0.634008	+	1.09813i	0.986724	+	0.162403i	$0.0519245\pi$
$751$	17.3746	+	30.0937i	0.634008	+	1.09813i	−0.352717	+	0.935730i	$0.614742\pi$
$752$			0.178118i			0.00649529i
$753$	11.4586	+	19.8468i	0.417574	+	0.723259i
$754$	−17.8076	+	0.378504i	−0.648515	+	0.0137843i
$755$	27.6498			1.00628
$756$		0			0
$757$	−21.9632	+	38.0413i	−0.798265	+	1.38264i	0.122481	+	0.992471i	$0.460915\pi$
$757$	−21.9632	+	38.0413i	−0.798265	+	1.38264i	−0.920745	+	0.390164i	$0.872418\pi$
$758$	7.80447			0.283471
$759$	37.3691	−	21.5751i	1.35641	−	0.783126i
$760$	−14.6611	−	8.46461i	−0.531815	−	0.307044i
$761$		−	0.141391i		−	0.00512543i	−0.999997	−	0.00256272i	$-0.999184\pi$
$761$		−	0.141391i		−	0.00512543i	0.999997	−	0.00256272i	$-0.000815739\pi$
$762$		−	13.4328i		−	0.486618i
$763$		0			0
$764$	−9.69352	+	16.7897i	−0.350699	+	0.607429i
$765$	30.1418	−	17.4024i	1.08978	−	0.629183i
$766$	−2.23620	−	3.87322i	−0.0807973	−	0.139945i
$767$	−8.34305	+	15.1870i	−0.301250	+	0.548372i
$768$	−19.7062	+	34.1321i	−0.711086	+	1.23164i
$769$	−11.8200	−	6.82429i	−0.426241	−	0.246090i	0.271503	−	0.962438i	$-0.412479\pi$
$769$	−11.8200	−	6.82429i	−0.426241	−	0.246090i	−0.697744	+	0.716347i	$0.745813\pi$
$770$		0			0
$771$	13.7856	+	23.8773i	0.496475	+	0.859920i
$772$	18.8824	+	10.9018i	0.679593	+	0.392363i
$773$	15.2328	+	8.79469i	0.547887	+	0.316323i	0.748269	−	0.663395i	$-0.230885\pi$
$773$	15.2328	+	8.79469i	0.547887	+	0.316323i	−0.200382	+	0.979718i	$0.564218\pi$
$774$	−20.3299	−	11.7375i	−0.730744	−	0.421895i
$775$	−4.98518	−	2.87820i	−0.179073	−	0.103388i
$776$	−4.68824	−	8.12026i	−0.168298	−	0.291500i
$777$		0			0
$778$	7.59022	+	4.38221i	0.272123	+	0.157110i
$779$	3.65356	−	6.32814i	0.130902	−	0.226729i
$780$	20.7778	+	34.2844i	0.743965	+	1.22758i
$781$	−13.3924	−	23.1964i	−0.479219	−	0.830032i
$782$	5.25533	−	3.03416i	0.187930	−	0.108501i
$783$	−8.59441	+	14.8860i	−0.307139	+	0.531981i
$784$		0			0
$785$			20.5768i			0.734418i
$786$		−	22.3947i		−	0.798792i
$787$	2.57075	+	1.48422i	0.0916374	+	0.0529069i	0.545118	−	0.838359i	$-0.316485\pi$
$787$	2.57075	+	1.48422i	0.0916374	+	0.0529069i	−0.453481	+	0.891266i	$0.649818\pi$
$788$	−12.6031	+	7.27639i	−0.448966	+	0.259210i
$789$	58.7461			2.09142
$790$	−10.3048	+	17.8484i	−0.366628	+	0.635018i
$791$		0			0
$792$	−66.2829			−2.35526
$793$	0.0886506	+	4.17078i	0.00314807	+	0.148109i
$794$	15.3121	+	26.5214i	0.543407	+	0.941208i
$795$			3.35883i			0.119125i
$796$	14.0184	+	24.2805i	0.496867	+	0.860600i
$797$	−4.72611	−	8.18586i	−0.167407	−	0.289958i	0.770100	−	0.637923i	$-0.220206\pi$
$797$	−4.72611	−	8.18586i	−0.167407	−	0.289958i	−0.937508	+	0.347965i	$0.886873\pi$
$798$		0			0
$799$	−1.06628	+	0.615614i	−0.0377221	+	0.0217789i
$800$			28.9579i			1.02382i
$801$	12.5749	−	7.26011i	0.444312	−	0.256523i
$802$	−0.369204	+	0.639481i	−0.0130371	+	0.0225809i
$803$	−24.6793	−	42.7458i	−0.870913	−	1.50847i
$804$	19.1212	+	11.0396i	0.674351	+	0.389337i
$805$		0			0
$806$	2.99693	+	1.64637i	0.105562	+	0.0579911i
$807$	−17.2120	+	29.8120i	−0.605890	+	1.04943i
$808$			36.4648i			1.28283i
$809$	−1.16255			−0.0408729			−0.0204365	−	0.999791i	$-0.506506\pi$
$809$	−1.16255			−0.0408729			−0.0204365	+	0.999791i	$0.506506\pi$
$810$	12.0007			0.421662
$811$			19.5561i			0.686706i	0.939206	+	0.343353i	$0.111563\pi$
$811$			19.5561i			0.686706i	−0.939206	+	0.343353i	$0.888437\pi$
$812$		0			0
$813$	40.7209	−	23.5102i	1.42814	−	0.824538i
$814$	27.5692	+	15.9171i	0.966299	+	0.557893i
$815$	−4.13075	+	7.15467i	−0.144694	+	0.250617i
$816$	2.80486			0.0981897
$817$	11.8491	−	6.84111i	0.414549	−	0.239340i
$818$	−20.2408			−0.707702
$819$		0			0
$820$	−15.6052			−0.544958
$821$	−10.9283	+	6.30945i	−0.381400	+	0.220201i	−0.678427	−	0.734668i	$-0.737338\pi$
$821$	−10.9283	+	6.30945i	−0.381400	+	0.220201i	0.297027	+	0.954869i	$0.404005\pi$
$822$	43.7030			1.52432
$823$	−3.28404	+	5.68812i	−0.114474	+	0.198275i	−0.917570	−	0.397575i	$-0.869852\pi$
$823$	−3.28404	+	5.68812i	−0.114474	+	0.198275i	0.803095	+	0.595851i	$0.203185\pi$
$824$	27.5886	+	15.9283i	0.961094	+	0.554888i
$825$	−68.4403	+	39.5140i	−2.38278	+	1.37570i
$826$		0			0
$827$			17.3050i			0.601754i	0.953663	+	0.300877i	$0.0972794\pi$
$827$			17.3050i			0.601754i	−0.953663	+	0.300877i	$0.902721\pi$
$828$	14.7088			0.511167
$829$	−3.75674			−0.130477			−0.0652385	−	0.997870i	$-0.520781\pi$
$829$	−3.75674			−0.130477			−0.0652385	+	0.997870i	$0.520781\pi$
$830$		−	16.1404i		−	0.560243i
$831$	23.9626	−	41.5044i	0.831253	−	1.43977i
$832$	−0.305689	−	14.3819i	−0.0105979	−	0.498602i
$833$		0			0
$834$	−38.5688	−	22.2677i	−1.33553	−	0.771068i
$835$	6.14432	+	10.6423i	0.212633	+	0.368291i
$836$	7.68610	−	13.3127i	0.265829	−	0.460430i
$837$	2.85772	−	1.64991i	0.0987773	−	0.0570291i
$838$		−	6.29656i		−	0.217511i
$839$	40.1340	−	23.1714i	1.38558	−	0.799965i	0.392766	−	0.919638i	$-0.371518\pi$
$839$	40.1340	−	23.1714i	1.38558	−	0.799965i	0.992813	+	0.119674i	$0.0381849\pi$
$840$		0			0
$841$	−3.49071	−	6.04609i	−0.120369	−	0.208486i
$842$	10.3266	+	17.8861i	0.355877	+	0.616396i
$843$			6.49586i			0.223729i
$844$	11.8534	+	20.5306i	0.408009	+	0.706693i
$845$	−36.4411	−	19.0224i	−1.25361	−	0.654389i
$846$	1.53138			0.0526499
$847$		0			0
$848$	−0.0779704	+	0.135049i	−0.00267751	+	0.00463759i
$849$	76.4142			2.62253
$850$	−9.62495	+	5.55697i	−0.330133	+	0.190602i
$851$	−15.3751	−	8.87679i	−0.527050	−	0.304293i
$852$		−	15.8485i		−	0.542959i
$853$		−	15.3103i		−	0.524215i	−0.965039	−	0.262107i	$-0.915583\pi$
$853$		−	15.3103i		−	0.524215i	0.965039	−	0.262107i	$-0.0844174\pi$
$854$		0			0
$855$	12.6155	−	21.8506i	0.431440	−	0.747275i
$856$	−9.30993	+	5.37509i	−0.318207	+	0.183717i
$857$	−1.29624	−	2.24515i	−0.0442787	−	0.0766929i	0.843037	−	0.537856i	$-0.180766\pi$
$857$	−1.29624	−	2.24515i	−0.0442787	−	0.0766929i	−0.887315	+	0.461163i	$0.847432\pi$
$858$	40.1465	−	24.3305i	1.37058	−	0.830629i
$859$	−6.88689	+	11.9284i	−0.234978	+	0.406993i	−0.959266	−	0.282504i	$-0.908835\pi$
$859$	−6.88689	+	11.9284i	−0.234978	+	0.406993i	0.724289	+	0.689497i	$0.242168\pi$
$860$	−25.3053	−	14.6100i	−0.862903	−	0.498197i
$861$		0			0
$862$	3.19294	+	5.53034i	0.108752	+	0.188364i
$863$	25.7723	+	14.8796i	0.877298	+	0.506508i	0.869767	−	0.493463i	$-0.164269\pi$
$863$	25.7723	+	14.8796i	0.877298	+	0.506508i	0.00753143	+	0.999972i	$0.497603\pi$
$864$	−14.3760	−	8.29996i	−0.489080	−	0.282370i
$865$	38.2747	+	22.0979i	1.30138	+	0.751351i
$866$	25.6588	+	14.8141i	0.871922	+	0.503404i
$867$	−12.9183	−	22.3751i	−0.438728	−	0.759899i
$868$		0			0
$869$	−40.7301	−	23.5155i	−1.38167	−	0.797710i
$870$	20.7781	−	35.9888i	0.704444	−	1.22013i
$871$	−22.6348	+	0.481106i	−0.766951	+	0.0163017i
$872$	15.3926	+	26.6607i	0.521259	+	0.902847i
$873$	12.1023	−	6.98724i	0.409599	−	0.236482i
$874$	2.19955	−	3.80974i	0.0744009	−	0.128866i
$875$		0			0
$876$		−	29.2051i		−	0.986750i
$877$		−	1.44332i		−	0.0487374i	−0.999703	−	0.0243687i	$-0.992242\pi$
$877$		−	1.44332i		−	0.0487374i	0.999703	−	0.0243687i	$-0.00775757\pi$
$878$	−20.1378	−	11.6266i	−0.679618	−	0.392378i
$879$	67.5748	−	39.0143i	2.27924	−	1.31592i
$880$	−7.33894			−0.247396
$881$	17.9402	−	31.0733i	0.604420	−	1.04689i	−0.387723	−	0.921776i	$-0.626738\pi$
$881$	17.9402	−	31.0733i	0.604420	−	1.04689i	0.992143	−	0.125110i	$-0.0399284\pi$
$882$		0			0
$883$	10.5626			0.355458			0.177729	−	0.984079i	$-0.443125\pi$
$883$	10.5626			0.355458			0.177729	+	0.984079i	$0.443125\pi$
$884$	−11.0027	+	6.66810i	−0.370061	+	0.224273i
$885$	−20.2137	−	35.0111i	−0.679475	−	1.17689i
$886$		−	23.7116i		−	0.796608i
$887$	6.11401	+	10.5898i	0.205288	+	0.355570i	0.950225	−	0.311566i	$-0.100853\pi$
$887$	6.11401	+	10.5898i	0.205288	+	0.355570i	−0.744936	+	0.667136i	$0.767520\pi$
$888$	23.6688	+	40.9956i	0.794274	+	1.37572i
$889$		0			0
$890$	−8.03183	+	4.63718i	−0.269228	+	0.155439i
$891$			27.3856i			0.917452i
$892$	−18.3504	+	10.5946i	−0.614418	+	0.354735i
$893$	−0.446276	+	0.772973i	−0.0149341	+	0.0258666i
$894$	−11.7390	−	20.3326i	−0.392611	−	0.680022i
$895$	69.2399	+	39.9757i	2.31443	+	1.33624i
$896$		0			0
$897$	−22.3893	+	13.5689i	−0.747557	+	0.453051i
$898$	12.0199	−	20.8190i	0.401109	−	0.694741i
$899$			6.90751i			0.230378i
$900$	−26.9387			−0.897956
$901$	−1.07793			−0.0359110
$902$			18.2735i			0.608440i
$903$		0			0
$904$	13.6799	−	7.89807i	0.454985	−	0.262686i
$905$	2.36732	+	1.36677i	0.0786924	+	0.0454331i
$906$	9.57879	−	16.5909i	0.318234	−	0.551197i
$907$	−4.52555			−0.150269			−0.0751343	−	0.997173i	$-0.523939\pi$
$907$	−4.52555			−0.150269			−0.0751343	+	0.997173i	$0.523939\pi$
$908$	18.7441	−	10.8219i	0.622044	−	0.359137i
$909$	−54.3464			−1.80256
$910$		0			0
$911$	−57.2723			−1.89751			−0.948757	−	0.316006i	$-0.897658\pi$
$911$	−57.2723			−1.89751			−0.948757	+	0.316006i	$0.897658\pi$
$912$	1.76091	−	1.01666i	0.0583095	−	0.0336650i
$913$	36.8325			1.21898
$914$	−13.0471	+	22.5983i	−0.431560	+	0.747484i
$915$	−8.42904	−	4.86651i	−0.278655	−	0.160882i
$916$	30.9181	−	17.8506i	1.02156	−	0.589800i
$917$		0			0
$918$		−	6.37098i		−	0.210274i
$919$	−40.7551			−1.34439			−0.672193	−	0.740376i	$-0.734648\pi$
$919$	−40.7551			−1.34439			−0.672193	+	0.740376i	$0.734648\pi$
$920$	−23.6105			−0.778415
$921$			18.8059i			0.619675i
$922$	−9.10103	+	15.7634i	−0.299726	+	0.519141i
$923$	8.42270	+	13.8979i	0.277236	+	0.457454i
$924$		0			0
$925$	28.1589	+	16.2575i	0.925858	+	0.534545i
$926$	−16.0104	−	27.7308i	−0.526134	−	0.911291i
$927$	−23.7391	+	41.1174i	−0.779696	+	1.35047i
$928$	30.0932	−	17.3743i	0.987859	−	0.570341i
$929$		−	52.2791i		−	1.71522i	−0.514298	−	0.857611i	$-0.671948\pi$
$929$		−	52.2791i		−	1.71522i	0.514298	−	0.857611i	$-0.328052\pi$
$930$	−6.90891	+	3.98886i	−0.226552	+	0.130800i
$931$		0			0
$932$	7.64511	+	13.2417i	0.250424	+	0.433747i
$933$	−29.6205	−	51.3042i	−0.969731	−	1.67962i
$934$		−	10.9387i		−	0.357926i
$935$	−25.3650	−	43.9334i	−0.829523	−	1.43678i
$936$	40.2061	−	0.854586i	1.31418	−	0.0279330i
$937$	6.38634			0.208633			0.104316	−	0.994544i	$-0.466735\pi$
$937$	6.38634			0.208633			0.104316	+	0.994544i	$0.466735\pi$
$938$		0			0
$939$	37.3558	−	64.7021i	1.21906	−	2.11147i
$940$	1.90615			0.0621719
$941$	−21.9720	+	12.6855i	−0.716266	+	0.413536i	−0.813377	−	0.581737i	$-0.802373\pi$
$941$	−21.9720	+	12.6855i	−0.716266	+	0.413536i	0.0971107	+	0.995274i	$0.469040\pi$
$942$	12.3469	+	7.12846i	0.402282	+	0.232258i
$943$		−	10.1909i		−	0.331862i
$944$		−	1.87692i		−	0.0610887i
$945$		0			0
$946$	−17.1081	+	29.6321i	−0.556232	+	0.963422i
$947$	−23.5612	+	13.6031i	−0.765635	+	0.442040i	−0.831315	−	0.555801i	$-0.812412\pi$
$947$	−23.5612	+	13.6031i	−0.765635	+	0.442040i	0.0656800	+	0.997841i	$0.479078\pi$
$948$	−13.9140	−	24.0997i	−0.451905	−	0.782723i
$949$	15.5211	+	25.6107i	0.503838	+	0.831357i
$950$	−4.02840	+	6.97740i	−0.130699	+	0.226377i
$951$	44.9613	+	25.9584i	1.45797	+	0.841760i
$952$		0			0
$953$	13.2939	+	23.0258i	0.430633	+	0.745878i	0.996928	−	0.0783248i	$-0.0249571\pi$
$953$	13.2939	+	23.0258i	0.430633	+	0.745878i	−0.566295	+	0.824203i	$0.691624\pi$
$954$	1.16109	+	0.670354i	0.0375916	+	0.0217035i
$955$	40.1667	+	23.1902i	1.29976	+	0.750418i
$956$	−16.7959	−	9.69711i	−0.543218	−	0.313627i
$957$	82.1264	+	47.4157i	2.65477	+	1.53273i
$958$	−2.73220	−	4.73230i	−0.0882732	−	0.152894i
$959$		0			0
$960$	29.0654	+	16.7809i	0.938082	+	0.541602i
$961$	−14.8370	+	25.6984i	−0.478612	+	0.828980i
$962$	−16.9282	−	9.29957i	−0.545787	−	0.299830i
$963$	−8.01091	−	13.8753i	−0.258148	−	0.447125i
$964$	−16.4223	+	9.48141i	−0.528926	+	0.305376i
$965$	26.0808	−	45.1732i	0.839569	−	1.45418i
$966$		0			0
$967$		−	35.2467i		−	1.13346i	−0.823904	−	0.566729i	$-0.808209\pi$
$967$		−	35.2467i		−	1.13346i	0.823904	−	0.566729i	$-0.191791\pi$
$968$			66.5191i			2.13801i
$969$	12.1722	+	7.02760i	0.391026	+	0.225759i
$970$	−7.72995	+	4.46289i	−0.248194	+	0.143295i
$971$	−36.9783			−1.18669			−0.593344	−	0.804949i	$-0.702193\pi$
$971$	−36.9783			−1.18669			−0.593344	+	0.804949i	$0.702193\pi$
$972$	−13.7833	+	23.8733i	−0.442098	+	0.765737i
$973$		0			0
$974$	27.5645			0.883224
$975$	41.0052	−	24.8509i	1.31322	−	0.795866i
$976$	−0.225938	−	0.391336i	−0.00723209	−	0.0125264i
$977$			24.7525i			0.791902i	0.918272	+	0.395951i	$0.129585\pi$
$977$			24.7525i			0.791902i	−0.918272	+	0.395951i	$0.870415\pi$
$978$	2.86205	+	4.95721i	0.0915182	+	0.158514i
$979$	−10.5820	−	18.3286i	−0.338204	−	0.585786i
$980$		0			0
$981$	−39.7346	+	22.9408i	−1.26863	+	0.732442i
$982$		−	30.7423i		−	0.981025i
$983$	3.94679	−	2.27868i	0.125883	−	0.0726786i	−0.435736	−	0.900074i	$-0.643512\pi$
$983$	3.94679	−	2.27868i	0.125883	−	0.0726786i	0.561619	+	0.827396i	$0.310179\pi$
$984$	−13.5864	+	23.5323i	−0.433119	+	0.750183i
$985$	17.4076	+	30.1509i	0.554652	+	0.960686i
$986$	11.5497	+	6.66820i	0.367816	+	0.212359i
$987$		0			0
$988$	−4.49062	+	8.17436i	−0.142866	+	0.260061i
$989$	9.54101	−	16.5255i	0.303386	−	0.525481i
$990$			63.0969i			2.00535i
$991$	−27.1963			−0.863919			−0.431960	−	0.901893i	$-0.642178\pi$
$991$	−27.1963			−0.863919			−0.431960	+	0.901893i	$0.642178\pi$
$992$	−6.67085			−0.211800
$993$		−	41.5824i		−	1.31958i
$994$		0			0
$995$	58.0873	−	33.5367i	1.84149	−	1.06319i
$996$	18.8738	+	10.8968i	0.598039	+	0.345278i
$997$	−15.1137	+	26.1777i	−0.478656	+	0.829057i	−0.999700	−	0.0244727i	$-0.992209\pi$
$997$	−15.1137	+	26.1777i	−0.478656	+	0.829057i	0.521044	+	0.853530i	$0.325543\pi$
$998$	28.1102			0.889812
$999$	−16.1419	+	9.31952i	−0.510707	+	0.294857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.u.i.30.3		12
7.2	even	3		637.2.q.h.589.4		12
7.3	odd	6		637.2.k.h.459.3		12
7.4	even	3		637.2.k.g.459.3		12
7.5	odd	6		91.2.q.a.43.4	yes	12
7.6	odd	2		637.2.u.h.30.3		12
13.10	even	6		637.2.k.g.569.4		12
21.5	even	6		819.2.ct.a.316.3		12
28.19	even	6		1456.2.cc.c.225.6		12
91.10	odd	6		637.2.u.h.361.3		12
91.19	even	12		1183.2.a.p.1.2		6
91.23	even	6		637.2.q.h.491.4		12
91.33	even	12		1183.2.a.m.1.5		6
91.58	odd	12		8281.2.a.ch.1.2		6
91.61	odd	6		1183.2.c.i.337.5		12
91.62	odd	6		637.2.k.h.569.4		12
91.72	odd	12		8281.2.a.by.1.5		6
91.75	odd	6		91.2.q.a.36.4	✓	12
91.82	odd	6		1183.2.c.i.337.8		12
91.88	even	6	inner	637.2.u.i.361.3		12
273.257	even	6		819.2.ct.a.127.3		12
364.75	even	6		1456.2.cc.c.673.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.4	✓	12	91.75	odd	6
91.2.q.a.43.4	yes	12	7.5	odd	6
637.2.k.g.459.3		12	7.4	even	3
637.2.k.g.569.4		12	13.10	even	6
637.2.k.h.459.3		12	7.3	odd	6
637.2.k.h.569.4		12	91.62	odd	6
637.2.q.h.491.4		12	91.23	even	6
637.2.q.h.589.4		12	7.2	even	3
637.2.u.h.30.3		12	7.6	odd	2
637.2.u.h.361.3		12	91.10	odd	6
637.2.u.i.30.3		12	1.1	even	1	trivial
637.2.u.i.361.3		12	91.88	even	6	inner
819.2.ct.a.127.3		12	273.257	even	6
819.2.ct.a.316.3		12	21.5	even	6
1183.2.a.m.1.5		6	91.33	even	12
1183.2.a.p.1.2		6	91.19	even	12
1183.2.c.i.337.5		12	91.61	odd	6
1183.2.c.i.337.8		12	91.82	odd	6
1456.2.cc.c.225.6		12	28.19	even	6
1456.2.cc.c.673.6		12	364.75	even	6
8281.2.a.by.1.5		6	91.72	odd	12
8281.2.a.ch.1.2		6	91.58	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.713220 + 0.411778i) q^{2} -2.66029 q^{3} +(-0.660878 + 1.14467i) q^{4} +(2.73845 + 1.58105i) q^{5} +(1.89737 - 1.09545i) q^{6} -2.73565i q^{8} +4.07715 q^{9} +O(q^{10})\)	\(q+(-0.713220 + 0.411778i) q^{2} -2.66029 q^{3} +(-0.660878 + 1.14467i) q^{4} +(2.73845 + 1.58105i) q^{5} +(1.89737 - 1.09545i) q^{6} -2.73565i q^{8} +4.07715 q^{9} -2.60416 q^{10} -5.94270i q^{11} +(1.75813 - 3.04517i) q^{12} +(0.0766193 + 3.60474i) q^{13} +(-7.28508 - 4.20604i) q^{15} +(-0.195274 - 0.338225i) q^{16} +(1.34982 - 2.33796i) q^{17} +(-2.90791 + 1.67888i) q^{18} -1.95705i q^{19} +(-3.61956 + 2.08976i) q^{20} +(2.44707 + 4.23845i) q^{22} +(-1.36471 - 2.36374i) q^{23} +7.27763i q^{24} +(2.49941 + 4.32911i) q^{25} +(-1.53900 - 2.53942i) q^{26} -2.86554 q^{27} +(2.99923 - 5.19481i) q^{29} +6.92783 q^{30} +(-0.997270 + 0.575774i) q^{31} +(5.01684 + 2.89647i) q^{32} +15.8093i q^{33} +2.22331i q^{34} +(-2.69450 + 4.66701i) q^{36} +(5.63310 - 3.25227i) q^{37} +(0.805869 + 1.39581i) q^{38} +(-0.203830 - 9.58965i) q^{39} +(4.32519 - 7.49145i) q^{40} +(3.23351 + 1.86687i) q^{41} +(3.49562 + 6.05460i) q^{43} +(6.80245 + 3.92740i) q^{44} +(11.1651 + 6.44617i) q^{45} +(1.94667 + 1.12391i) q^{46} +(-0.394969 - 0.228035i) q^{47} +(0.519487 + 0.899778i) q^{48} +(-3.56527 - 2.05841i) q^{50} +(-3.59092 + 6.21965i) q^{51} +(-4.17688 - 2.29459i) q^{52} +(-0.199643 - 0.345792i) q^{53} +(2.04376 - 1.17997i) q^{54} +(9.39568 - 16.2738i) q^{55} +5.20632i q^{57} +4.94006i q^{58} +(4.16200 + 2.40293i) q^{59} +(9.62910 - 5.55936i) q^{60} +1.15703 q^{61} +(0.474182 - 0.821308i) q^{62} -3.98971 q^{64} +(-5.48944 + 9.99254i) q^{65} +(-6.50993 - 11.2755i) q^{66} +6.27918i q^{67} +(1.78413 + 3.09021i) q^{68} +(3.63052 + 6.28825i) q^{69} +(3.90335 - 2.25360i) q^{71} -11.1537i q^{72} +(7.19299 - 4.15288i) q^{73} +(-2.67843 + 4.63917i) q^{74} +(-6.64917 - 11.5167i) q^{75} +(2.24018 + 1.29337i) q^{76} +(4.09418 + 6.75560i) q^{78} +(3.95705 - 6.85381i) q^{79} -1.23495i q^{80} -4.60828 q^{81} -3.07494 q^{82} +6.19795i q^{83} +(7.39284 - 4.26826i) q^{85} +(-4.98630 - 2.87884i) q^{86} +(-7.97882 + 13.8197i) q^{87} -16.2571 q^{88} +(3.08423 - 1.78068i) q^{89} -10.6176 q^{90} +3.60762 q^{92} +(2.65303 - 1.53173i) q^{93} +0.375600 q^{94} +(3.09418 - 5.35928i) q^{95} +(-13.3462 - 7.70546i) q^{96} +(2.96831 - 1.71375i) q^{97} -24.2293i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 6 q^{5} + 18 q^{6} + 8 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 + 6 * q^5 + 18 * q^6 + 8 * q^9	\( 12 q + 4 q^{4} + 6 q^{5} + 18 q^{6} + 8 q^{9} + 24 q^{10} - 2 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} - 12 q^{18} + 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} - 24 q^{26} - 12 q^{27} + 8 q^{29} - 16 q^{30} - 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} + 2 q^{38} - 10 q^{39} + 46 q^{40} - 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} - 42 q^{47} + 2 q^{48} - 18 q^{50} - 26 q^{51} - 26 q^{52} + 22 q^{53} + 12 q^{54} + 6 q^{55} + 18 q^{59} + 66 q^{60} + 28 q^{61} + 4 q^{62} - 52 q^{64} - 42 q^{65} - 26 q^{66} + 8 q^{68} - 4 q^{69} - 24 q^{71} - 30 q^{73} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} + 28 q^{82} - 48 q^{85} - 60 q^{86} + 2 q^{87} + 28 q^{88} - 12 q^{89} - 24 q^{90} + 24 q^{92} + 18 q^{93} + 8 q^{94} - 22 q^{95} - 6 q^{96} - 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 + 6 * q^5 + 18 * q^6 + 8 * q^9 + 24 * q^10 - 2 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 - 12 * q^18 + 12 * q^20 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 12 * q^27 + 8 * q^29 - 16 * q^30 - 18 * q^31 - 36 * q^32 - 10 * q^36 + 42 * q^37 + 2 * q^38 - 10 * q^39 + 46 * q^40 - 30 * q^41 + 2 * q^43 + 24 * q^44 - 12 * q^46 - 42 * q^47 + 2 * q^48 - 18 * q^50 - 26 * q^51 - 26 * q^52 + 22 * q^53 + 12 * q^54 + 6 * q^55 + 18 * q^59 + 66 * q^60 + 28 * q^61 + 4 * q^62 - 52 * q^64 - 42 * q^65 - 26 * q^66 + 8 * q^68 - 4 * q^69 - 24 * q^71 - 30 * q^73 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 + 28 * q^79 - 4 * q^81 + 28 * q^82 - 48 * q^85 - 60 * q^86 + 2 * q^87 + 28 * q^88 - 12 * q^89 - 24 * q^90 + 24 * q^92 + 18 * q^93 + 8 * q^94 - 22 * q^95 - 6 * q^96 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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