LMFDB - Embedded newform 637.2.g.k.373.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(263,637)]

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([4, 2]))

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

//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);

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: 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 7x^{6} + 38x^{4} - 16x^{3} + 15x^{2} + 3x + 1 $ x^8 - x^7 + 7x^6 + 38x^4 - 16x^3 + 15x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.4
Root			$1.37054 + 2.37385i$ of defining polynomial
Character	$\chi$	$=$	637.373
Dual form			637.2.g.k.263.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37054 + 2.37385i) q^{2} +1.36482 q^{3} +(-2.75677 + 4.77486i) q^{4} +(-0.370541 + 0.641796i) q^{5} +(1.87054 + 3.23987i) q^{6} -9.63087 q^{8} -1.13727 q^{9} +O(q^{10})$	\(q+(1.37054 + 2.37385i) q^{2} +1.36482 q^{3} +(-2.75677 + 4.77486i) q^{4} +(-0.370541 + 0.641796i) q^{5} +(1.87054 + 3.23987i) q^{6} -9.63087 q^{8} -1.13727 q^{9} -2.03137 q^{10} -1.36482 q^{11} +(-3.76249 + 6.51682i) q^{12} +(0.301907 + 3.59289i) q^{13} +(-0.505722 + 0.875935i) q^{15} +(-7.68598 - 13.3125i) q^{16} +(2.07436 - 3.59289i) q^{17} +(-1.55867 - 2.69970i) q^{18} +7.26606 q^{19} +(-2.04299 - 3.53856i) q^{20} +(-1.87054 - 3.23987i) q^{22} +(1.16673 + 2.02083i) q^{23} -13.1444 q^{24} +(2.22540 + 3.85450i) q^{25} +(-8.11519 + 5.64088i) q^{26} -5.64662 q^{27} +(0.203815 - 0.353017i) q^{29} -2.77245 q^{30} +(1.38622 + 2.40101i) q^{31} +(11.4370 - 19.8095i) q^{32} -1.86273 q^{33} +11.3720 q^{34} +(3.13518 - 5.43029i) q^{36} +(3.05295 + 5.28787i) q^{37} +(9.95843 + 17.2485i) q^{38} +(0.412049 + 4.90364i) q^{39} +(3.56863 - 6.18106i) q^{40} +(-0.627306 + 1.08653i) q^{41} +(0.870541 + 1.50782i) q^{43} +(3.76249 - 6.51682i) q^{44} +(0.421404 - 0.729894i) q^{45} +(-3.19809 + 5.53926i) q^{46} +(2.92921 - 5.07355i) q^{47} +(-10.4900 - 18.1692i) q^{48} +(-6.10000 + 10.5655i) q^{50} +(2.83112 - 4.90364i) q^{51} +(-17.9878 - 8.46319i) q^{52} +(-2.28389 - 3.95582i) q^{53} +(-7.73893 - 13.4042i) q^{54} +(0.505722 - 0.875935i) q^{55} +9.91685 q^{57} +1.11734 q^{58} +(5.49213 - 9.51264i) q^{59} +(-2.78831 - 4.82950i) q^{60} +6.52497 q^{61} +(-3.79975 + 6.58137i) q^{62} +31.9557 q^{64} +(-2.41777 - 1.13755i) q^{65} +(-2.55295 - 4.42184i) q^{66} -13.7597 q^{67} +(11.4370 + 19.8095i) q^{68} +(1.59237 + 2.75807i) q^{69} +(2.40763 + 4.17014i) q^{71} +10.9529 q^{72} +(-3.03494 - 5.25666i) q^{73} +(-8.36839 + 14.4945i) q^{74} +(3.03727 + 5.26070i) q^{75} +(-20.0308 + 34.6944i) q^{76} +(-11.0758 + 7.69879i) q^{78} +(4.56291 - 7.90320i) q^{79} +11.3919 q^{80} -4.29482 q^{81} -3.43900 q^{82} +11.7368 q^{83} +(1.53727 + 2.66263i) q^{85} +(-2.38622 + 4.13306i) q^{86} +(0.278170 - 0.481805i) q^{87} +13.1444 q^{88} +(0.880503 + 1.52508i) q^{89} +2.31021 q^{90} -12.8656 q^{92} +(1.89195 + 3.27695i) q^{93} +16.0584 q^{94} +(-2.69237 + 4.66332i) q^{95} +(15.6095 - 27.0364i) q^{96} +(-4.76691 - 8.25652i) q^{97} +1.55217 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 2 q^{3} - 5 q^{4} + 7 q^{5} + 5 q^{6} - 12 q^{8} + 14 q^{9}+O(q^{10}) $ 8 * q + q^2 + 2 * q^3 - 5 * q^4 + 7 * q^5 + 5 * q^6 - 12 * q^8 + 14 * q^9	$ 8 q + q^{2} + 2 q^{3} - 5 q^{4} + 7 q^{5} + 5 q^{6} - 12 q^{8} + 14 q^{9} - 22 q^{10} - 2 q^{11} - 12 q^{12} + 4 q^{13} - 3 q^{15} - 19 q^{16} + 4 q^{17} + 3 q^{18} + 2 q^{19} + 2 q^{20} - 5 q^{22} + 2 q^{23} - 6 q^{24} - 5 q^{25} + 3 q^{26} - 52 q^{27} - q^{29} - 8 q^{30} + 4 q^{31} + 33 q^{32} - 38 q^{33} + 6 q^{34} + 34 q^{36} + 10 q^{37} + 23 q^{38} - 19 q^{39} + 17 q^{40} + 22 q^{41} - 3 q^{43} + 12 q^{44} + 11 q^{45} - 24 q^{46} - 2 q^{47} - 11 q^{48} - 43 q^{50} - 7 q^{51} - 34 q^{52} - 2 q^{53} - 5 q^{54} + 3 q^{55} - 34 q^{57} - 22 q^{58} + 8 q^{59} + 11 q^{60} + 16 q^{61} + 5 q^{62} + 28 q^{64} + 4 q^{65} - 6 q^{66} - 12 q^{67} + 33 q^{68} + 18 q^{69} + 14 q^{71} + 10 q^{72} + 8 q^{73} - 20 q^{74} + 7 q^{75} - 32 q^{76} - q^{78} + 26 q^{79} + 14 q^{80} + 48 q^{81} - 28 q^{82} - 5 q^{85} - 12 q^{86} - 13 q^{87} + 6 q^{88} + q^{89} + 52 q^{90} + 24 q^{92} + 7 q^{93} + 66 q^{94} - 21 q^{95} + 58 q^{96} - 3 q^{97} + 46 q^{99}+O(q^{100}) $ 8 * q + q^2 + 2 * q^3 - 5 * q^4 + 7 * q^5 + 5 * q^6 - 12 * q^8 + 14 * q^9 - 22 * q^10 - 2 * q^11 - 12 * q^12 + 4 * q^13 - 3 * q^15 - 19 * q^16 + 4 * q^17 + 3 * q^18 + 2 * q^19 + 2 * q^20 - 5 * q^22 + 2 * q^23 - 6 * q^24 - 5 * q^25 + 3 * q^26 - 52 * q^27 - q^29 - 8 * q^30 + 4 * q^31 + 33 * q^32 - 38 * q^33 + 6 * q^34 + 34 * q^36 + 10 * q^37 + 23 * q^38 - 19 * q^39 + 17 * q^40 + 22 * q^41 - 3 * q^43 + 12 * q^44 + 11 * q^45 - 24 * q^46 - 2 * q^47 - 11 * q^48 - 43 * q^50 - 7 * q^51 - 34 * q^52 - 2 * q^53 - 5 * q^54 + 3 * q^55 - 34 * q^57 - 22 * q^58 + 8 * q^59 + 11 * q^60 + 16 * q^61 + 5 * q^62 + 28 * q^64 + 4 * q^65 - 6 * q^66 - 12 * q^67 + 33 * q^68 + 18 * q^69 + 14 * q^71 + 10 * q^72 + 8 * q^73 - 20 * q^74 + 7 * q^75 - 32 * q^76 - q^78 + 26 * q^79 + 14 * q^80 + 48 * q^81 - 28 * q^82 - 5 * q^85 - 12 * q^86 - 13 * q^87 + 6 * q^88 + q^89 + 52 * q^90 + 24 * q^92 + 7 * q^93 + 66 * q^94 - 21 * q^95 + 58 * q^96 - 3 * q^97 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.37054	+	2.37385i	0.969119	+	1.67856i	0.698116	+	0.715984i	$0.254022\pi$
$2$	1.37054	+	2.37385i	0.969119	+	1.67856i	0.271003	+	0.962579i	$0.412645\pi$
$3$	1.36482			0.787979			0.393989	−	0.919115i	$-0.371095\pi$
$3$	1.36482			0.787979			0.393989	+	0.919115i	$0.371095\pi$
$4$	−2.75677	+	4.77486i	−1.37838	+	2.38743i
$5$	−0.370541	+	0.641796i	−0.165711	+	0.287020i	−0.936908	−	0.349577i	$-0.886325\pi$
$5$	−0.370541	+	0.641796i	−0.165711	+	0.287020i	0.771197	+	0.636597i	$0.219659\pi$
$6$	1.87054	+	3.23987i	0.763645	+	1.32267i
$7$		0			0
$7$		0			0
$8$	−9.63087			−3.40503
$9$	−1.13727			−0.379089
$10$	−2.03137			−0.642374
$11$	−1.36482			−0.411509			−0.205754	−	0.978604i	$-0.565965\pi$
$11$	−1.36482			−0.411509			−0.205754	+	0.978604i	$0.565965\pi$
$12$	−3.76249	+	6.51682i	−1.08614	+	1.88124i
$13$	0.301907	+	3.59289i	0.0837339	+	0.996488i
$13$	0.301907	+	3.59289i	0.0837339	+	0.996488i
$14$		0			0
$15$	−0.505722	+	0.875935i	−0.130577	+	0.226166i
$16$	−7.68598	−	13.3125i	−1.92149	−	3.32813i
$17$	2.07436	−	3.59289i	0.503105	−	0.871404i	−0.496888	−	0.867814i	$-0.665524\pi$
$17$	2.07436	−	3.59289i	0.503105	−	0.871404i	0.999994	−	0.00358919i	$-0.00114248\pi$
$18$	−1.55867	−	2.69970i	−0.367383	−	0.636325i
$19$	7.26606			1.66695			0.833474	−	0.552559i	$-0.186349\pi$
$19$	7.26606			1.66695			0.833474	+	0.552559i	$0.186349\pi$
$20$	−2.04299	−	3.53856i	−0.456826	−	0.791246i
$21$		0			0
$22$	−1.87054	−	3.23987i	−0.398801	−	0.690743i
$23$	1.16673	+	2.02083i	0.243279	+	0.421372i	0.961646	−	0.274292i	$-0.0884435\pi$
$23$	1.16673	+	2.02083i	0.243279	+	0.421372i	−0.718367	+	0.695664i	$0.755110\pi$
$24$	−13.1444			−2.68309
$25$	2.22540	+	3.85450i	0.445080	+	0.770901i
$26$	−8.11519	+	5.64088i	−1.59152	+	1.10627i
$27$	−5.64662			−1.08669
$28$		0			0
$29$	0.203815	−	0.353017i	0.0378474	−	0.0655536i	−0.846481	−	0.532419i	$-0.821283\pi$
$29$	0.203815	−	0.353017i	0.0378474	−	0.0655536i	0.884329	+	0.466865i	$0.154617\pi$
$30$	−2.77245			−0.506178
$31$	1.38622	+	2.40101i	0.248973	+	0.431234i	0.963241	−	0.268638i	$-0.0865736\pi$
$31$	1.38622	+	2.40101i	0.248973	+	0.431234i	−0.714268	+	0.699872i	$0.753240\pi$
$32$	11.4370	−	19.8095i	2.02180	−	3.50186i
$33$	−1.86273			−0.324260
$34$	11.3720			1.95027
$35$		0			0
$36$	3.13518	−	5.43029i	0.522530	−	0.905049i
$37$	3.05295	+	5.28787i	0.501902	+	0.869320i	0.999998	+	0.00219764i	$0.000699531\pi$
$37$	3.05295	+	5.28787i	0.501902	+	0.869320i	−0.498096	+	0.867122i	$0.665967\pi$
$38$	9.95843	+	17.2485i	1.61547	+	2.79808i
$39$	0.412049	+	4.90364i	0.0659806	+	0.785212i
$40$	3.56863	−	6.18106i	0.564251	−	0.977311i
$41$	−0.627306	+	1.08653i	−0.0979688	+	0.169687i	−0.910844	−	0.412751i	$-0.864568\pi$
$41$	−0.627306	+	1.08653i	−0.0979688	+	0.169687i	0.812875	+	0.582438i	$0.197901\pi$
$42$		0			0
$43$	0.870541	+	1.50782i	0.132756	+	0.229941i	0.924738	−	0.380604i	$-0.124284\pi$
$43$	0.870541	+	1.50782i	0.132756	+	0.229941i	−0.791982	+	0.610545i	$0.790951\pi$
$44$	3.76249	−	6.51682i	0.567216	−	0.982447i
$45$	0.421404	−	0.729894i	0.0628193	−	0.108806i
$46$	−3.19809	+	5.53926i	−0.471533	+	0.816719i
$47$	2.92921	−	5.07355i	0.427270	−	0.740053i	−0.569360	−	0.822089i	$-0.692809\pi$
$47$	2.92921	−	5.07355i	0.427270	−	0.740053i	0.996629	+	0.0820357i	$0.0261422\pi$
$48$	−10.4900	−	18.1692i	−1.51410	−	2.62249i
$49$		0			0
$50$	−6.10000	+	10.5655i	−0.862670	+	1.49419i
$51$	2.83112	−	4.90364i	0.396436	−	0.686648i
$52$	−17.9878	−	8.46319i	−2.49446	−	1.17363i
$53$	−2.28389	−	3.95582i	−0.313717	−	0.543373i	0.665447	−	0.746445i	$-0.268241\pi$
$53$	−2.28389	−	3.95582i	−0.313717	−	0.543373i	−0.979164	+	0.203072i	$0.934908\pi$
$54$	−7.73893	−	13.4042i	−1.05313	−	1.82408i
$55$	0.505722	−	0.875935i	0.0681915	−	0.118111i
$56$		0			0
$57$	9.91685			1.31352
$58$	1.11734			0.146715
$59$	5.49213	−	9.51264i	0.715014	−	1.23844i	−0.247940	−	0.968775i	$-0.579754\pi$
$59$	5.49213	−	9.51264i	0.715014	−	1.23844i	0.962954	−	0.269665i	$-0.0869130\pi$
$60$	−2.78831	−	4.82950i	−0.359969	−	0.623485i
$61$	6.52497			0.835437			0.417719	−	0.908576i	$-0.362830\pi$
$61$	6.52497			0.835437			0.417719	+	0.908576i	$0.362830\pi$
$62$	−3.79975	+	6.58137i	−0.482569	+	0.835834i
$63$		0			0
$64$	31.9557			3.99446
$65$	−2.41777	−	1.13755i	−0.299887	−	0.141096i
$66$	−2.55295	−	4.42184i	−0.314247	−	0.544291i
$67$	−13.7597			−1.68101			−0.840505	−	0.541804i	$-0.817742\pi$
$67$	−13.7597			−1.68101			−0.840505	+	0.541804i	$0.817742\pi$
$68$	11.4370	+	19.8095i	1.38694	+	2.40226i
$69$	1.59237	+	2.75807i	0.191699	+	0.332032i
$70$		0			0
$71$	2.40763	+	4.17014i	0.285733	+	0.494904i	0.972787	−	0.231703i	$-0.0744296\pi$
$71$	2.40763	+	4.17014i	0.285733	+	0.494904i	−0.687054	+	0.726607i	$0.741096\pi$
$72$	10.9529			1.29081
$73$	−3.03494	−	5.25666i	−0.355212	−	0.615246i	0.631942	−	0.775016i	$-0.282258\pi$
$73$	−3.03494	−	5.25666i	−0.355212	−	0.615246i	−0.987154	+	0.159770i	$0.948925\pi$
$74$	−8.36839	+	14.4945i	−0.972805	+	1.68495i
$75$	3.03727	+	5.26070i	0.350713	+	0.607453i
$76$	−20.0308	+	34.6944i	−2.29769	+	3.97972i
$77$		0			0
$78$	−11.0758	+	7.69879i	−1.25408	+	0.871716i
$79$	4.56291	−	7.90320i	0.513368	−	0.889179i	−0.486512	−	0.873674i	$-0.661731\pi$
$79$	4.56291	−	7.90320i	0.513368	−	0.889179i	0.999880	−	0.0155052i	$-0.00493564\pi$
$80$	11.3919			1.27365
$81$	−4.29482			−0.477202
$82$	−3.43900			−0.379774
$83$	11.7368			1.28828			0.644139	−	0.764908i	$-0.277216\pi$
$83$	11.7368			1.28828			0.644139	+	0.764908i	$0.277216\pi$
$84$		0			0
$85$	1.53727	+	2.66263i	0.166740	+	0.288802i
$86$	−2.38622	+	4.13306i	−0.257313	+	0.445679i
$87$	0.278170	−	0.481805i	0.0298230	−	0.0516549i
$88$	13.1444			1.40120
$89$	0.880503	+	1.52508i	0.0933331	+	0.161658i	0.908912	−	0.416989i	$-0.136915\pi$
$89$	0.880503	+	1.52508i	0.0933331	+	0.161658i	−0.815579	+	0.578646i	$0.803581\pi$
$90$	2.31021			0.243517
$91$		0			0
$92$	−12.8656			−1.34133
$93$	1.89195	+	3.27695i	0.196186	+	0.339803i
$94$	16.0584			1.65630
$95$	−2.69237	+	4.66332i	−0.276231	+	0.478447i
$96$	15.6095	−	27.0364i	1.59313	−	2.75939i
$97$	−4.76691	−	8.25652i	−0.484006	−	0.838323i	0.515825	−	0.856694i	$-0.327485\pi$
$97$	−4.76691	−	8.25652i	−0.484006	−	0.838323i	−0.999831	+	0.0183708i	$0.994152\pi$
$98$		0			0
$99$	1.55217			0.155998
$100$	−24.5396			−2.45396
$101$	−7.49361			−0.745642			−0.372821	−	0.927903i	$-0.621609\pi$
$101$	−7.49361			−0.745642			−0.372821	+	0.927903i	$0.621609\pi$
$102$	15.5207			1.53678
$103$	−1.40424	+	2.43221i	−0.138364	+	0.239653i	−0.926877	−	0.375364i	$-0.877518\pi$
$103$	−1.40424	+	2.43221i	−0.138364	+	0.239653i	0.788514	+	0.615017i	$0.210851\pi$
$104$	−2.90763	−	34.6027i	−0.285116	−	3.39307i
$105$		0			0
$106$	6.26033	−	10.8432i	0.608057	−	1.05319i
$107$	−0.743235	−	1.28732i	−0.0718512	−	0.124450i	0.827861	−	0.560933i	$-0.189557\pi$
$107$	−0.743235	−	1.28732i	−0.0718512	−	0.124450i	−0.899713	+	0.436483i	$0.856224\pi$
$108$	15.5664	−	26.9618i	1.49788	−	2.59440i
$109$	−1.43561	−	2.48654i	−0.137506	−	0.238168i	0.789046	−	0.614334i	$-0.210575\pi$
$109$	−1.43561	−	2.48654i	−0.137506	−	0.238168i	−0.926552	+	0.376167i	$0.877242\pi$
$110$	2.77245			0.264343
$111$	4.16673	+	7.21698i	0.395488	+	0.685006i
$112$		0			0
$113$	6.20972	+	10.7555i	0.584161	+	1.01180i	0.994979	+	0.100079i	$0.0319096\pi$
$113$	6.20972	+	10.7555i	0.584161	+	1.01180i	−0.410819	+	0.911717i	$0.634757\pi$
$114$	13.5915	+	23.5411i	1.27296	+	2.20483i
$115$	−1.72928			−0.161256
$116$	1.12374	+	1.94637i	0.104336	+	0.180716i
$117$	−0.343349	−	4.08608i	−0.0317426	−	0.377758i
$118$	30.1087			2.77173
$119$		0			0
$120$	4.87054	−	8.43602i	0.444618	−	0.770100i
$121$	−9.13727			−0.830661
$122$	8.94274	+	15.4893i	0.809638	+	1.40233i
$123$	−0.856160	+	1.48291i	−0.0771973	+	0.133710i
$124$	−15.2860			−1.37272
$125$	−7.00382			−0.626440
$126$		0			0
$127$	−2.71526	+	4.70296i	−0.240940	+	0.417321i	−0.960982	−	0.276610i	$-0.910789\pi$
$127$	−2.71526	+	4.70296i	−0.240940	+	0.417321i	0.720042	+	0.693930i	$0.244122\pi$
$128$	20.9226	+	36.2390i	1.84931	+	3.20310i
$129$	1.18813	+	2.05790i	0.104609	+	0.181188i
$130$	−0.613284	−	7.29847i	−0.0537886	−	0.640119i
$131$	5.66100	−	9.80515i	0.494604	−	0.856680i	−0.505376	−	0.862899i	$-0.668646\pi$
$131$	5.66100	−	9.80515i	0.494604	−	0.856680i	0.999981	+	0.00621925i	$0.00197966\pi$
$132$	5.13512	−	8.89428i	0.446954	−	0.774148i
$133$		0			0
$134$	−18.8582	−	32.6633i	−1.62910	−	2.82168i
$135$	2.09231	−	3.62398i	0.180077	−	0.311902i
$136$	−19.9779	+	34.6027i	−1.71309	+	2.96715i
$137$	6.98771	−	12.1031i	0.597000	−	1.03403i	−0.396261	−	0.918138i	$-0.629693\pi$
$137$	6.98771	−	12.1031i	0.597000	−	1.03403i	0.993261	−	0.115897i	$-0.0369741\pi$
$138$	−4.36482	+	7.56009i	−0.371558	+	0.643558i
$139$	−5.21544	−	9.03340i	−0.442368	−	0.766203i	0.555497	−	0.831518i	$-0.312528\pi$
$139$	−5.21544	−	9.03340i	−0.442368	−	0.766203i	−0.997865	+	0.0653153i	$0.979195\pi$
$140$		0			0
$141$	3.99785	−	6.92447i	0.336679	−	0.583146i
$142$	−6.59951	+	11.4307i	−0.553818	+	0.959242i
$143$	−0.412049	−	4.90364i	−0.0344572	−	0.410063i
$144$	8.74102	+	15.1399i	0.728418	+	1.26166i
$145$	0.151043	+	0.261615i	0.0125435	+	0.0217259i
$146$	8.31901	−	14.4089i	0.688486	−	1.19249i
$147$		0			0
$148$	−33.6651			−2.76725
$149$	8.16433			0.668848			0.334424	−	0.942423i	$-0.391458\pi$
$149$	8.16433			0.668848			0.334424	+	0.942423i	$0.391458\pi$
$150$	−8.32540	+	14.4200i	−0.679766	+	1.17739i
$151$	1.23094	+	2.13205i	0.100173	+	0.173504i	0.911756	−	0.410733i	$-0.134727\pi$
$151$	1.23094	+	2.13205i	0.100173	+	0.173504i	−0.811583	+	0.584237i	$0.801394\pi$
$152$	−69.9785			−5.67600
$153$	−2.35910	+	4.08608i	−0.190722	+	0.330340i
$154$		0			0
$155$	−2.05461			−0.165030
$156$	−24.5501	−	11.5507i	−1.96558	−	0.924798i
$157$	6.45991	+	11.1889i	0.515557	+	0.892971i	0.999837	+	0.0180576i	$0.00574822\pi$
$157$	6.45991	+	11.1889i	0.515557	+	0.892971i	−0.484280	+	0.874913i	$0.660918\pi$
$158$	25.0146			1.99006
$159$	−3.11710	−	5.39897i	−0.247202	−	0.428167i
$160$	8.47577	+	14.6805i	0.670069	+	1.16059i
$161$		0			0
$162$	−5.88622	−	10.1952i	−0.462465	−	0.801014i
$163$	−6.02742			−0.472104			−0.236052	−	0.971740i	$-0.575854\pi$
$163$	−6.02742			−0.472104			−0.236052	+	0.971740i	$0.575854\pi$
$164$	−3.45867	−	5.99060i	−0.270077	−	0.467787i
$165$	0.690219	−	1.19549i	0.0537334	−	0.0930691i
$166$	16.0857	+	27.8613i	1.24850	+	2.16246i
$167$	−3.82558	+	6.62610i	−0.296032	+	0.512743i	−0.975224	−	0.221218i	$-0.928997\pi$
$167$	−3.82558	+	6.62610i	−0.296032	+	0.512743i	0.679192	+	0.733960i	$0.262330\pi$
$168$		0			0
$169$	−12.8177	+	2.16944i	−0.985977	+	0.166880i
$170$	−4.21378	+	7.29847i	−0.323182	+	0.559767i
$171$	−8.26345			−0.631922
$172$	−9.59951			−0.731956
$173$	−0.164460			−0.0125036			−0.00625182	−	0.999980i	$-0.501990\pi$
$173$	−0.164460			−0.0125036			−0.00625182	+	0.999980i	$0.501990\pi$
$174$	1.52497			0.115608
$175$		0			0
$176$	10.4900	+	18.1692i	0.790711	+	1.36955i
$177$	7.49576	−	12.9830i	0.563416	−	0.975865i
$178$	−2.41353	+	4.18036i	−0.180902	+	0.313331i
$179$	0.768633			0.0574503			0.0287252	−	0.999587i	$-0.490855\pi$
$179$	0.768633			0.0574503			0.0287252	+	0.999587i	$0.490855\pi$
$180$	2.32343	+	4.02429i	0.173178	+	0.299953i
$181$	−9.92152			−0.737461			−0.368730	−	0.929536i	$-0.620207\pi$
$181$	−9.92152			−0.737461			−0.368730	+	0.929536i	$0.620207\pi$
$182$		0			0
$183$	8.90541			0.658307
$184$	−11.2366	−	19.4624i	−0.828373	−	1.43478i
$185$	−4.52497			−0.332683
$186$	−5.18598	+	8.98238i	−0.380254	+	0.658620i
$187$	−2.83112	+	4.90364i	−0.207032	+	0.358590i
$188$	16.1503	+	27.9732i	1.17788	+	2.04015i
$189$		0			0
$190$	−14.7600			−1.07080
$191$	9.89693			0.716117			0.358058	−	0.933699i	$-0.383439\pi$
$191$	9.89693			0.716117			0.358058	+	0.933699i	$0.383439\pi$
$192$	43.6138			3.14755
$193$	8.70075			0.626293			0.313147	−	0.949705i	$-0.398617\pi$
$193$	8.70075			0.626293			0.313147	+	0.949705i	$0.398617\pi$
$194$	13.0665	−	22.6318i	0.938119	−	1.62487i
$195$	−3.29982	−	1.55255i	−0.236305	−	0.111180i
$196$		0			0
$197$	13.0093	−	22.5328i	0.926874	−	1.60539i	0.138354	−	0.990383i	$-0.455819\pi$
$197$	13.0093	−	22.5328i	0.926874	−	1.60539i	0.788520	−	0.615009i	$-0.210848\pi$
$198$	2.12731	+	3.68460i	0.151181	+	0.261853i
$199$	−5.06648	+	8.77540i	−0.359153	+	0.622072i	−0.987820	−	0.155603i	$-0.950268\pi$
$199$	−5.06648	+	8.77540i	−0.359153	+	0.622072i	0.628666	+	0.777675i	$0.283601\pi$
$200$	−21.4325	−	37.1222i	−1.51551	−	2.62494i
$201$	−18.7795			−1.32460
$202$	−10.2703	−	17.7887i	−0.722615	−	1.25161i
$203$		0			0
$204$	15.6095	+	27.0364i	1.09288	+	1.89293i
$205$	−0.464885	−	0.805205i	−0.0324690	−	0.0562380i
$206$	−7.69827			−0.536364
$207$	−1.32688	−	2.29822i	−0.0922246	−	0.159738i
$208$	45.5099	−	31.6340i	3.15554	−	2.19342i
$209$	−9.91685			−0.685963
$210$		0			0
$211$	−8.33911	+	14.4438i	−0.574088	+	0.994349i	0.422052	+	0.906572i	$0.361310\pi$
$211$	−8.33911	+	14.4438i	−0.574088	+	0.994349i	−0.996140	+	0.0877779i	$0.972023\pi$
$212$	25.1846			1.72969
$213$	3.28598	+	5.69148i	0.225152	+	0.389974i
$214$	2.03727	−	3.52865i	0.139265	−	0.241214i
$215$	−1.29028			−0.0879967
$216$	54.3819			3.70022
$217$		0			0
$218$	3.93511	−	6.81582i	0.266520	−	0.461625i
$219$	−4.14214	−	7.17439i	−0.279900	−	0.484801i
$220$	2.78831	+	4.82950i	0.187988	+	0.325605i
$221$	13.5351	+	6.36821i	0.910470	+	0.428372i
$222$	−11.4213	+	19.7823i	−0.766550	+	1.32770i
$223$	−0.535180	+	0.926959i	−0.0358383	+	0.0620738i	−0.883388	−	0.468642i	$-0.844743\pi$
$223$	−0.535180	+	0.926959i	−0.0358383	+	0.0620738i	0.847550	+	0.530716i	$0.178077\pi$
$224$		0			0
$225$	−2.53087	−	4.38360i	−0.168725	−	0.292240i
$226$	−17.0213	+	29.4818i	−1.13224	+	1.96110i
$227$	12.2332	−	21.1885i	0.811947	−	1.40633i	−0.0995534	−	0.995032i	$-0.531741\pi$
$227$	12.2332	−	21.1885i	0.811947	−	1.40633i	0.911500	−	0.411300i	$-0.134925\pi$
$228$	−27.3384	+	47.3516i	−1.81053	+	3.13593i
$229$	−2.36482	+	4.09599i	−0.156272	+	0.270670i	−0.933521	−	0.358522i	$-0.883281\pi$
$229$	−2.36482	+	4.09599i	−0.156272	+	0.270670i	0.777250	+	0.629192i	$0.216614\pi$
$230$	−2.37005	−	4.10505i	−0.156276	−	0.270679i
$231$		0			0
$232$	−1.96291	+	3.39986i	−0.128871	+	0.223212i
$233$	−10.2753	+	17.7974i	−0.673160	+	1.16595i	0.303843	+	0.952722i	$0.401730\pi$
$233$	−10.2753	+	17.7974i	−0.673160	+	1.16595i	−0.977003	+	0.213226i	$0.931603\pi$
$234$	9.22915	−	6.41519i	0.603328	−	0.419374i
$235$	2.17079	+	3.75991i	0.141607	+	0.245270i
$236$	30.2810	+	52.4482i	1.97113	+	3.41409i
$237$	6.22755	−	10.7864i	0.404523	−	0.700654i
$238$		0			0
$239$	6.25461			0.404577			0.202289	−	0.979326i	$-0.435162\pi$
$239$	6.25461			0.404577			0.202289	+	0.979326i	$0.435162\pi$
$240$	15.5479			1.00361
$241$	6.07220	−	10.5174i	0.391145	−	0.677483i	−0.601456	−	0.798906i	$-0.705412\pi$
$241$	6.07220	−	10.5174i	0.391145	−	0.677483i	0.992601	+	0.121423i	$0.0387458\pi$
$242$	−12.5230	−	21.6905i	−0.805009	−	1.39432i
$243$	11.0782			0.710668
$244$	−17.9878	+	31.1558i	−1.15155	+	1.99455i
$245$		0			0
$246$	−4.69361			−0.299254
$247$	2.19367	+	26.1061i	0.139580	+	1.66109i
$248$	−13.3506	−	23.1238i	−0.847761	−	1.46836i
$249$	16.0186			1.01514
$250$	−9.59902	−	16.6260i	−0.607095	−	1.05152i
$251$	3.15719	+	5.46842i	0.199280	+	0.345163i	0.948295	−	0.317390i	$-0.102806\pi$
$251$	3.15719	+	5.46842i	0.199280	+	0.345163i	−0.749015	+	0.662553i	$0.769473\pi$
$252$		0			0
$253$	−1.59237	−	2.75807i	−0.100112	−	0.173398i
$254$	−14.8855			−0.933999
$255$	2.09809	+	3.63400i	0.131388	+	0.227570i
$256$	−25.3948	+	43.9850i	−1.58717	+	2.74907i
$257$	−12.1781	−	21.0931i	−0.759649	−	1.31575i	−0.943030	−	0.332709i	$-0.892037\pi$
$257$	−12.1781	−	21.0931i	−0.759649	−	1.31575i	0.183380	−	0.983042i	$-0.441296\pi$
$258$	−3.25677	+	5.64088i	−0.202757	+	0.351186i
$259$		0			0
$260$	12.0969	−	8.40855i	0.750216	−	0.521476i
$261$	−0.231792	+	0.401475i	−0.0143475	+	0.0248507i
$262$	31.0346			1.91732
$263$	−9.57910			−0.590672			−0.295336	−	0.955393i	$-0.595432\pi$
$263$	−9.57910			−0.590672			−0.295336	+	0.955393i	$0.595432\pi$
$264$	17.9397			1.10411
$265$	3.38510			0.207945
$266$		0			0
$267$	1.20173	+	2.08145i	0.0735445	+	0.127383i
$268$	37.9322	−	65.7004i	2.31708	−	4.01329i
$269$	−14.6995	+	25.4603i	−0.896245	+	1.55234i	−0.0639886	+	0.997951i	$0.520382\pi$
$269$	−14.6995	+	25.4603i	−0.896245	+	1.55234i	−0.832256	+	0.554391i	$0.812951\pi$
$270$	11.4704			0.698064
$271$	0.150192	+	0.260141i	0.00912354	+	0.0158024i	0.870551	−	0.492078i	$-0.163763\pi$
$271$	0.150192	+	0.260141i	0.00912354	+	0.0158024i	−0.861428	+	0.507880i	$0.830429\pi$
$272$	−63.7738			−3.86686
$273$		0			0
$274$	38.3078			2.31426
$275$	−3.03727	−	5.26070i	−0.183154	−	0.317232i
$276$	−17.5592			−1.05694
$277$	16.3855	−	28.3805i	0.984509	−	1.70522i	0.340408	−	0.940278i	$-0.389435\pi$
$277$	16.3855	−	28.3805i	0.984509	−	1.70522i	0.644100	−	0.764941i	$-0.277232\pi$
$278$	14.2959	−	24.7613i	0.857414	−	1.48508i
$279$	−1.57651	−	2.73059i	−0.0943831	−	0.163476i
$280$		0			0
$281$	4.29482			0.256207			0.128104	−	0.991761i	$-0.459111\pi$
$281$	4.29482			0.256207			0.128104	+	0.991761i	$0.459111\pi$
$282$	21.9169			1.30513
$283$	−21.1003			−1.25428			−0.627140	−	0.778907i	$-0.715775\pi$
$283$	−21.1003			−1.25428			−0.627140	+	0.778907i	$0.715775\pi$
$284$	−26.5491			−1.57540
$285$	−3.67460	+	6.36460i	−0.217665	+	0.377006i
$286$	11.0758	−	7.69879i	0.654924	−	0.455239i
$287$		0			0
$288$	−13.0070	+	22.5287i	−0.766442	+	1.32752i
$289$	−0.105901	−	0.183427i	−0.00622950	−	0.0107898i
$290$	−0.414022	+	0.717107i	−0.0243122	+	0.0421100i
$291$	−6.50597	−	11.2687i	−0.381387	−	0.660581i
$292$	33.4664			1.95847
$293$	−8.88192	−	15.3839i	−0.518887	−	0.898739i	−0.999759	−	0.0219482i	$-0.993013\pi$
$293$	−8.88192	−	15.3839i	−0.518887	−	0.898739i	0.480872	−	0.876791i	$-0.340320\pi$
$294$		0			0
$295$	4.07012	+	7.04965i	0.236971	+	0.410446i
$296$	−29.4026	−	50.9268i	−1.70899	−	2.96006i
$297$	7.70662			0.447184
$298$	11.1895	+	19.3809i	0.648193	+	1.12270i
$299$	−6.90837	+	4.80202i	−0.399522	+	0.277708i
$300$	−33.4921			−1.93367
$301$		0			0
$302$	−3.37411	+	5.84413i	−0.194158	+	0.336292i
$303$	−10.2274			−0.587550
$304$	−55.8467	−	96.7294i	−3.20303	−	5.54781i
$305$	−2.41777	+	4.18770i	−0.138441	+	0.239787i
$306$	−12.9330			−0.739328
$307$	18.0156			1.02821			0.514103	−	0.857729i	$-0.328125\pi$
$307$	18.0156			1.02821			0.514103	+	0.857729i	$0.328125\pi$
$308$		0			0
$309$	−1.91653	+	3.31953i	−0.109028	+	0.188842i
$310$	−2.81593	−	4.87733i	−0.159934	−	0.277014i
$311$	−8.62724	−	14.9428i	−0.489206	−	0.847330i	0.510717	−	0.859749i	$-0.329380\pi$
$311$	−8.62724	−	14.9428i	−0.489206	−	0.847330i	−0.999923	+	0.0124194i	$0.996047\pi$
$312$	−3.96839	−	47.2264i	−0.224666	−	2.67367i
$313$	−3.40763	+	5.90219i	−0.192611	+	0.333611i	−0.946115	−	0.323832i	$-0.895029\pi$
$313$	−3.40763	+	5.90219i	−0.192611	+	0.333611i	0.753504	+	0.657443i	$0.228362\pi$
$314$	−17.7071	+	30.6697i	−0.999272	+	1.73079i
$315$		0			0
$316$	25.1578	+	43.5745i	1.41523	+	2.45126i
$317$	12.5385	−	21.7173i	0.704233	−	1.21977i	−0.262735	−	0.964868i	$-0.584625\pi$
$317$	12.5385	−	21.7173i	0.704233	−	1.21977i	0.966968	−	0.254899i	$-0.0820421\pi$
$318$	8.54423	−	14.7990i	0.479136	−	0.829889i
$319$	−0.278170	+	0.481805i	−0.0155745	+	0.0269759i
$320$	−11.8409	+	20.5090i	−0.661927	+	1.14649i
$321$	−1.01438	−	1.75696i	−0.0566172	−	0.0980639i
$322$		0			0
$323$	15.0724	−	26.1061i	0.838650	−	1.45258i
$324$	11.8398	−	20.5071i	0.657767	−	1.13929i
$325$	−13.1769	+	9.15931i	−0.730925	+	0.508067i
$326$	−8.26083	−	14.3082i	−0.457525	−	0.792456i
$327$	−1.95934	−	3.39368i	−0.108352	−	0.187671i
$328$	6.04151	−	10.4642i	0.333586	−	0.577789i
$329$		0			0
$330$	3.78389			0.208296
$331$	−2.99534			−0.164639			−0.0823193	−	0.996606i	$-0.526233\pi$
$331$	−2.99534			−0.164639			−0.0823193	+	0.996606i	$0.526233\pi$
$332$	−32.3555	+	56.0414i	−1.77574	+	3.07567i
$333$	−3.47202	−	6.01372i	−0.190266	−	0.329550i
$334$	−20.9724			−1.14756
$335$	5.09852	−	8.83089i	0.278562	−	0.482483i
$336$		0			0
$337$	−29.4888			−1.60636			−0.803179	−	0.595738i	$-0.796860\pi$
$337$	−29.4888			−1.60636			−0.803179	+	0.595738i	$0.796860\pi$
$338$	−22.7171	−	27.4540i	−1.23565	−	1.49330i
$339$	8.47514	+	14.6794i	0.460306	+	0.797274i
$340$	−16.9515			−0.919326
$341$	−1.89195	−	3.27695i	−0.102455	−	0.177457i
$342$	−11.3254	−	19.6162i	−0.612407	−	1.06072i
$343$		0			0
$344$	−8.38407	−	14.5216i	−0.452039	−	0.782954i
$345$	−2.36015			−0.127066
$346$	−0.225399	−	0.390402i	−0.0121175	−	0.0209881i
$347$	2.99343	−	5.18477i	0.160696	−	0.278333i	−0.774423	−	0.632668i	$-0.781960\pi$
$347$	2.99343	−	5.18477i	0.160696	−	0.278333i	0.935118	+	0.354336i	$0.115293\pi$
$348$	1.53370	+	2.65644i	0.0822149	+	0.142400i
$349$	15.1681	−	26.2719i	0.811929	−	1.40630i	−0.0995840	−	0.995029i	$-0.531751\pi$
$349$	15.1681	−	26.2719i	0.811929	−	1.40630i	0.911513	−	0.411272i	$-0.134915\pi$
$350$		0			0
$351$	−1.70476	−	20.2877i	−0.0909931	−	1.08288i
$352$	−15.6095	+	27.0364i	−0.831988	+	1.44104i
$353$	−28.6063			−1.52256			−0.761280	−	0.648424i	$-0.775428\pi$
$353$	−28.6063			−1.52256			−0.761280	+	0.648424i	$0.775428\pi$
$354$	41.0930			2.18407
$355$	−3.56850			−0.189396
$356$	−9.70936			−0.514595
$357$		0			0
$358$	1.05344	+	1.82462i	0.0556762	+	0.0964340i
$359$	−11.7309	+	20.3185i	−0.619132	+	1.07237i	0.370513	+	0.928827i	$0.379182\pi$
$359$	−11.7309	+	20.3185i	−0.619132	+	1.07237i	−0.989644	+	0.143540i	$0.954151\pi$
$360$	−4.05849	+	7.02952i	−0.213901	+	0.370488i
$361$	33.7956			1.77871
$362$	−13.5978	−	23.5522i	−0.714687	−	1.23787i
$363$	−12.4707			−0.654543
$364$		0			0
$365$	4.49827			0.235450
$366$	12.2052	+	21.1401i	0.637978	+	1.10501i
$367$	36.5197			1.90631			0.953156	−	0.302479i	$-0.0978143\pi$
$367$	36.5197			1.90631			0.953156	+	0.302479i	$0.0978143\pi$
$368$	17.9349	−	31.0641i	0.934920	−	1.61933i
$369$	0.713415	−	1.23567i	0.0371389	−	0.0643265i
$370$	−6.20166	−	10.7416i	−0.322409	−	0.558429i
$371$		0			0
$372$	−20.8626			−1.08168
$373$	−13.0498			−0.675694			−0.337847	−	0.941201i	$-0.609699\pi$
$373$	−13.0498			−0.675694			−0.337847	+	0.941201i	$0.609699\pi$
$374$	−15.5207			−0.802555
$375$	−9.55894			−0.493622
$376$	−28.2109	+	48.8627i	−1.45487	+	2.51990i
$377$	1.32988	+	0.625705i	0.0684925	+	0.0322254i
$378$		0			0
$379$	−15.3018	+	26.5036i	−0.786003	+	1.36140i	0.142395	+	0.989810i	$0.454520\pi$
$379$	−15.3018	+	26.5036i	−0.786003	+	1.36140i	−0.928398	+	0.371587i	$0.878814\pi$
$380$	−14.8445	−	25.7114i	−0.761505	−	1.31897i
$381$	−3.70584	+	6.41870i	−0.189856	+	0.328840i
$382$	13.5641	+	23.4938i	0.694002	+	1.20205i
$383$	−4.88598			−0.249662			−0.124831	−	0.992178i	$-0.539839\pi$
$383$	−4.88598			−0.249662			−0.124831	+	0.992178i	$0.539839\pi$
$384$	28.5555	+	49.4596i	1.45722	+	2.52398i
$385$		0			0
$386$	11.9247	+	20.6542i	0.606953	+	1.05127i
$387$	−0.990038	−	1.71480i	−0.0503265	−	0.0871680i
$388$	52.5650			2.66858
$389$	0.927126	+	1.60583i	0.0470072	+	0.0814188i	0.888572	−	0.458738i	$-0.151698\pi$
$389$	0.927126	+	1.60583i	0.0470072	+	0.0814188i	−0.841564	+	0.540157i	$0.818365\pi$
$390$	−0.837022	−	9.96110i	−0.0423842	−	0.504400i
$391$	9.68082			0.489580
$392$		0			0
$393$	7.72625	−	13.3823i	0.389738	−	0.675046i
$394$	71.3191			3.59300
$395$	3.38149	+	5.85692i	0.170141	+	0.294693i
$396$	−4.27896	+	7.41137i	−0.215026	+	0.372435i
$397$	21.5134			1.07973			0.539863	−	0.841753i	$-0.318476\pi$
$397$	21.5134			1.07973			0.539863	+	0.841753i	$0.318476\pi$
$398$	−27.7753			−1.39225
$399$		0			0
$400$	34.2087	−	59.2513i	1.71044	−	2.96256i
$401$	7.28266	+	12.6139i	0.363678	+	0.629910i	0.988563	−	0.150808i	$-0.0481874\pi$
$401$	7.28266	+	12.6139i	0.363678	+	0.629910i	−0.624885	+	0.780717i	$0.714854\pi$
$402$	−25.7380	−	44.5795i	−1.28370	−	2.22343i
$403$	−8.20805	+	5.70543i	−0.408872	+	0.284208i
$404$	20.6581	−	35.7809i	1.02778	−	1.78017i
$405$	1.59141	−	2.75640i	0.0790776	−	0.136966i
$406$		0			0
$407$	−4.16673	−	7.21698i	−0.206537	−	0.357733i
$408$	−27.2662	+	47.2264i	−1.34988	+	2.33805i
$409$	11.0645	−	19.1643i	0.547105	−	0.947613i	−0.451366	−	0.892339i	$-0.649063\pi$
$409$	11.0645	−	19.1643i	0.547105	−	0.947613i	0.998471	−	0.0552745i	$-0.0176034\pi$
$410$	1.27429	−	2.20713i	0.0629326	−	0.109003i
$411$	9.53696	−	16.5185i	0.470423	−	0.814797i
$412$	−7.74232	−	13.4101i	−0.381437	−	0.660668i
$413$		0			0
$414$	3.63709	−	6.29962i	0.178753	−	0.309610i
$415$	−4.34896	+	7.53261i	−0.213482	+	0.369761i
$416$	74.6263	+	35.1113i	3.65885	+	1.72147i
$417$	−7.11813	−	12.3290i	−0.348576	−	0.603752i
$418$	−13.5915	−	23.5411i	−0.664780	−	1.15143i
$419$	−1.68795	+	2.92362i	−0.0824618	+	0.142828i	−0.904307	−	0.426883i	$-0.859612\pi$
$419$	−1.68795	+	2.92362i	−0.0824618	+	0.142828i	0.821845	+	0.569711i	$0.192945\pi$
$420$		0			0
$421$	−25.1101			−1.22379			−0.611895	−	0.790939i	$-0.709593\pi$
$421$	−25.1101			−1.22379			−0.611895	+	0.790939i	$0.709593\pi$
$422$	−45.7164			−2.22544
$423$	−3.33130	+	5.76998i	−0.161973	+	0.280546i
$424$	21.9959	+	38.0980i	1.06821	+	1.85020i
$425$	18.4651			0.895688
$426$	−9.00714	+	15.6008i	−0.436397	+	0.755862i
$427$		0			0
$428$	8.19570			0.396154
$429$	−0.562372	−	6.69259i	−0.0271516	−	0.323121i
$430$	−1.76839	−	3.06294i	−0.0852792	−	0.147708i
$431$	10.7948			0.519969			0.259985	−	0.965613i	$-0.416282\pi$
$431$	10.7948			0.519969			0.259985	+	0.965613i	$0.416282\pi$
$432$	43.3998	+	75.1707i	2.08808	+	3.61665i
$433$	7.25910	+	12.5731i	0.348850	+	0.604226i	0.986045	−	0.166476i	$-0.0532389\pi$
$433$	7.25910	+	12.5731i	0.348850	+	0.604226i	−0.637195	+	0.770702i	$0.719906\pi$
$434$		0			0
$435$	0.206147	+	0.357057i	0.00988398	+	0.0171196i
$436$	15.8305			0.758144
$437$	8.47750	+	14.6835i	0.405534	+	0.702405i
$438$	11.3539	−	19.6656i	0.542512	−	0.939659i
$439$	7.21544	+	12.4975i	0.344374	+	0.596473i	0.985240	−	0.171180i	$-0.0547578\pi$
$439$	7.21544	+	12.4975i	0.344374	+	0.596473i	−0.640866	+	0.767653i	$0.721425\pi$
$440$	−4.87054	+	8.43602i	−0.232194	+	0.402172i
$441$		0			0
$442$	3.43327	+	40.8582i	0.163304	+	1.94343i
$443$	15.1215	−	26.1912i	0.718445	−	1.24438i	−0.243171	−	0.969984i	$-0.578187\pi$
$443$	15.1215	−	26.1912i	0.718445	−	1.24438i	0.961616	−	0.274400i	$-0.0884792\pi$
$444$	−45.9467			−2.18054
$445$	−1.30505			−0.0618653
$446$	−2.93395			−0.138926
$447$	11.1428			0.527038
$448$		0			0
$449$	−15.6380	−	27.0858i	−0.738003	−	1.27826i	−0.953393	−	0.301731i	$-0.902435\pi$
$449$	−15.6380	−	27.0858i	−0.738003	−	1.27826i	0.215390	−	0.976528i	$-0.430898\pi$
$450$	6.93733	−	12.0158i	0.327029	−	0.566431i
$451$	0.856160	−	1.48291i	0.0403150	−	0.0698276i
$452$	−68.4749			−3.22079
$453$	1.68001	+	2.90987i	0.0789338	+	0.136717i
$454$	67.0645			3.14749
$455$		0			0
$456$	−95.5080			−4.47257
$457$	−10.3233	−	17.8805i	−0.482904	−	0.836415i	0.516903	−	0.856044i	$-0.327085\pi$
$457$	−10.3233	−	17.8805i	−0.482904	−	0.836415i	−0.999807	+	0.0196293i	$0.993751\pi$
$458$	−12.9643			−0.605783
$459$	−11.7131	+	20.2877i	−0.546721	+	0.946948i
$460$	4.76722	−	8.25707i	0.222273	−	0.384988i
$461$	−13.6480	−	23.6391i	−0.635653	−	1.10098i	−0.986376	−	0.164504i	$-0.947398\pi$
$461$	−13.6480	−	23.6391i	−0.635653	−	1.10098i	0.350724	−	0.936479i	$-0.385936\pi$
$462$		0			0
$463$	5.65977			0.263032			0.131516	−	0.991314i	$-0.458016\pi$
$463$	5.65977			0.263032			0.131516	+	0.991314i	$0.458016\pi$
$464$	−6.26606			−0.290894
$465$	−2.80417			−0.130040
$466$	−56.3311			−2.60949
$467$	−21.1073	+	36.5588i	−0.976727	+	1.69174i	−0.302614	+	0.953113i	$0.597859\pi$
$467$	−21.1073	+	36.5588i	−0.976727	+	1.69174i	−0.674114	+	0.738628i	$0.735474\pi$
$468$	20.4570	+	9.62491i	0.945624	+	0.444912i
$469$		0			0
$470$	−5.95031	+	10.3062i	−0.274467	+	0.475391i
$471$	8.81661	+	15.2708i	0.406248	+	0.703642i
$472$	−52.8940	+	91.6151i	−2.43464	+	4.21692i
$473$	−1.18813	−	2.05790i	−0.0546303	−	0.0946225i
$474$	34.1405			1.56812
$475$	16.1699	+	28.0070i	0.741925	+	1.28505i
$476$		0			0
$477$	2.59740	+	4.49882i	0.118927	+	0.205987i
$478$	8.57220	+	14.8475i	0.392083	+	0.679108i
$479$	32.5316			1.48641			0.743204	−	0.669065i	$-0.233305\pi$
$479$	32.5316			1.48641			0.743204	+	0.669065i	$0.233305\pi$
$480$	11.5679	+	20.0362i	0.528000	+	0.914523i
$481$	−18.0770	+	12.5654i	−0.824241	+	0.572931i
$482$	33.2888			1.51626
$483$		0			0
$484$	25.1893	−	43.6292i	1.14497	−	1.98314i
$485$	7.06534			0.320820
$486$	15.1832	+	26.2980i	0.688722	+	1.19290i
$487$	−13.4291	+	23.2600i	−0.608533	+	1.05401i	0.382950	+	0.923769i	$0.374908\pi$
$487$	−13.4291	+	23.2600i	−0.608533	+	1.05401i	−0.991482	+	0.130240i	$0.958425\pi$
$488$	−62.8412			−2.84469
$489$	−8.22634			−0.372008
$490$		0			0
$491$	−21.8439	+	37.8348i	−0.985802	+	1.70746i	−0.347485	+	0.937685i	$0.612964\pi$
$491$	−21.8439	+	37.8348i	−0.985802	+	1.70746i	−0.638317	+	0.769774i	$0.720369\pi$
$492$	−4.72046	−	8.17608i	−0.212815	−	0.368606i
$493$	−0.845567	−	1.46457i	−0.0380824	−	0.0659607i
$494$	−58.9654	+	40.9870i	−2.65298	+	1.84409i
$495$	−0.575141	+	0.996173i	−0.0258507	+	0.0447747i
$496$	21.3090	−	36.9082i	0.956801	−	1.65723i
$497$		0			0
$498$	21.9541	+	38.0257i	0.983788	+	1.70397i
$499$	9.05098	−	15.6768i	0.405177	−	0.701788i	−0.589165	−	0.808013i	$-0.700543\pi$
$499$	9.05098	−	15.6768i	0.405177	−	0.701788i	0.994342	+	0.106225i	$0.0338764\pi$
$500$	19.3079	−	33.4422i	0.863474	−	1.49558i
$501$	−5.22122	+	9.04343i	−0.233267	+	0.404030i
$502$	−8.65412	+	14.9894i	−0.386252	+	0.669009i
$503$	14.2077	+	24.6085i	0.633492	+	1.09724i	0.986833	+	0.161745i	$0.0517123\pi$
$503$	14.2077	+	24.6085i	0.633492	+	1.09724i	−0.353341	+	0.935495i	$0.614954\pi$
$504$		0			0
$505$	2.77669	−	4.80937i	0.123561	−	0.214014i
$506$	4.36482	−	7.56009i	0.194040	−	0.336087i
$507$	−17.4939	+	2.96089i	−0.776929	+	0.131498i
$508$	−14.9707	−	25.9299i	−0.664215	−	1.15045i
$509$	−8.73956	−	15.1374i	−0.387374	−	0.670952i	0.604721	−	0.796437i	$-0.293285\pi$
$509$	−8.73956	−	15.1374i	−0.387374	−	0.670952i	−0.992095	+	0.125485i	$0.959951\pi$
$510$	−5.75104	+	9.96110i	−0.254660	+	0.441085i
$511$		0			0
$512$	−55.5280			−2.45402
$513$	−41.0287			−1.81146
$514$	33.3812	−	57.8179i	1.47238	−	2.55024i
$515$	−1.04066	−	1.80247i	−0.0458568	−	0.0794263i
$516$	−13.1016			−0.576766
$517$	−3.99785	+	6.92447i	−0.175825	+	0.304538i
$518$		0			0
$519$	−0.224458			−0.00985260
$520$	23.2852	+	10.9556i	1.02113	+	0.480435i
$521$	−9.65437	−	16.7219i	−0.422966	−	0.732598i	0.573263	−	0.819372i	$-0.305678\pi$
$521$	−9.65437	−	16.7219i	−0.422966	−	0.732598i	−0.996228	+	0.0867740i	$0.972344\pi$
$522$	−1.27072			−0.0556179
$523$	5.01144	+	8.68007i	0.219135	+	0.379553i	0.954544	−	0.298071i	$-0.0963431\pi$
$523$	5.01144	+	8.68007i	0.219135	+	0.379553i	−0.735409	+	0.677624i	$0.763010\pi$
$524$	31.2121	+	54.0610i	1.36351	+	2.36167i
$525$		0			0
$526$	−13.1285	−	22.7393i	−0.572432	−	0.991481i
$527$	11.5021			0.501039
$528$	14.3169	+	24.7976i	0.623064	+	1.07918i
$529$	8.77750	−	15.2031i	0.381630	−	0.661003i
$530$	4.63942	+	8.03571i	0.201524	+	0.349049i
$531$	−6.24602	+	10.8184i	−0.271054	+	0.469479i
$532$		0			0
$533$	−4.09316	−	1.92581i	−0.177294	−	0.0834162i
$534$	−3.29403	+	5.70543i	−0.142547	+	0.246898i
$535$	1.10160			0.0476261
$536$	132.518			5.72389
$537$	1.04904			0.0452696
$538$	−80.5851			−3.47427
$539$		0			0
$540$	11.5360	+	19.9809i	0.496430	+	0.859842i
$541$	−8.80763	+	15.2553i	−0.378670	+	0.655875i	−0.990869	−	0.134829i	$-0.956952\pi$
$541$	−8.80763	+	15.2553i	−0.378670	+	0.655875i	0.612199	+	0.790703i	$0.290285\pi$
$542$	−0.411690	+	0.713067i	−0.0176836	+	0.0306289i
$543$	−13.5411			−0.581103
$544$	−47.4489	−	82.1839i	−2.03435	−	3.52361i
$545$	2.12780			0.0911451
$546$		0			0
$547$	2.98425			0.127597			0.0637987	−	0.997963i	$-0.479678\pi$
$547$	2.98425			0.127597			0.0637987	+	0.997963i	$0.479678\pi$
$548$	38.5269	+	66.7306i	1.64579	+	2.85059i
$549$	−7.42064			−0.316705
$550$	8.32540	−	14.4200i	0.354996	−	0.614871i
$551$	1.48093	−	2.56504i	0.0630896	−	0.109274i
$552$	−15.3359	−	26.5626i	−0.652740	−	1.13058i
$553$		0			0
$554$	89.8279			3.81642
$555$	−6.17577			−0.262147
$556$	57.5109			2.43901
$557$	7.25596			0.307445			0.153722	−	0.988114i	$-0.450874\pi$
$557$	7.25596			0.307445			0.153722	+	0.988114i	$0.450874\pi$
$558$	4.32134	−	7.48478i	0.182937	−	0.316856i
$559$	−5.15461	+	3.58298i	−0.218017	+	0.151544i
$560$		0			0
$561$	−3.86397	+	6.69259i	−0.163137	+	0.282561i
$562$	5.88622	+	10.1952i	0.248295	+	0.430060i
$563$	−2.13967	+	3.70601i	−0.0901762	+	0.156190i	−0.907585	−	0.419868i	$-0.862076\pi$
$563$	−2.13967	+	3.70601i	−0.0901762	+	0.156190i	0.817409	+	0.576058i	$0.195410\pi$
$564$	22.0423	+	38.1783i	0.928146	+	1.60760i
$565$	−9.20382			−0.387207
$566$	−28.9188	−	50.0888i	−1.21555	−	2.10539i
$567$		0			0
$568$	−23.1876	−	40.1621i	−0.972929	−	1.68516i
$569$	9.88131	+	17.1149i	0.414246	+	0.717495i	0.995349	−	0.0963347i	$-0.0307119\pi$
$569$	9.88131	+	17.1149i	0.414246	+	0.717495i	−0.581103	+	0.813830i	$0.697379\pi$
$570$	−20.1448			−0.843771
$571$	9.96182	+	17.2544i	0.416889	+	0.722073i	0.995625	−	0.0934422i	$-0.0297870\pi$
$571$	9.96182	+	17.2544i	0.416889	+	0.722073i	−0.578736	+	0.815515i	$0.696454\pi$
$572$	24.5501	+	11.5507i	1.02649	+	0.482960i
$573$	13.5075			0.564285
$574$		0			0
$575$	−5.19286	+	8.99430i	−0.216557	+	0.375088i
$576$	−36.3422			−1.51426
$577$	14.3650	+	24.8809i	0.598023	+	1.03581i	0.993113	+	0.117163i	$0.0373801\pi$
$577$	14.3650	+	24.8809i	0.598023	+	1.03581i	−0.395090	+	0.918642i	$0.629287\pi$
$578$	0.290284	−	0.502787i	0.0120742	−	0.0209132i
$579$	11.8749			0.493506
$580$	−1.66556			−0.0691587
$581$		0			0
$582$	17.8334	−	30.8883i	0.739218	−	1.28036i
$583$	3.11710	+	5.39897i	0.129097	+	0.223603i
$584$	29.2291	+	50.6263i	1.20951	+	2.09493i
$585$	2.74965	+	1.29370i	0.113684	+	0.0534879i
$586$	24.3461	−	42.1686i	1.00573	−	1.74197i
$587$	−15.7694	+	27.3134i	−0.650872	+	1.12734i	0.332040	+	0.943265i	$0.392263\pi$
$587$	−15.7694	+	27.3134i	−0.650872	+	1.12734i	−0.982912	+	0.184078i	$0.941070\pi$
$588$		0			0
$589$	10.0724	+	17.4459i	0.415025	+	0.718845i
$590$	−11.1565	+	19.3237i	−0.459307	+	0.795542i
$591$	17.7553	−	30.7531i	0.730357	−	1.26502i
$592$	46.9298	−	81.2848i	1.92880	−	3.34079i
$593$	5.55903	−	9.62852i	0.228282	−	0.395396i	−0.729017	−	0.684496i	$-0.760023\pi$
$593$	5.55903	−	9.62852i	0.228282	−	0.395396i	0.957299	+	0.289099i	$0.0933558\pi$
$594$	10.5622	+	18.2943i	0.433374	+	0.750626i
$595$		0			0
$596$	−22.5071	+	38.9835i	−0.921928	+	1.59683i
$597$	−6.91483	+	11.9768i	−0.283005	+	0.490179i
$598$	−20.8675	−	9.81805i	−0.853334	−	0.401490i
$599$	3.64786	+	6.31828i	0.149048	+	0.258158i	0.930876	−	0.365336i	$-0.119046\pi$
$599$	3.64786	+	6.31828i	0.149048	+	0.258158i	−0.781828	+	0.623494i	$0.785713\pi$
$600$	−29.2515	−	50.6652i	−1.19419	−	2.06840i
$601$	0.586291	−	1.01548i	0.0239153	−	0.0414225i	−0.853820	−	0.520568i	$-0.825720\pi$
$601$	0.586291	−	1.01548i	0.0239153	−	0.0414225i	0.877735	+	0.479146i	$0.159053\pi$
$602$		0			0
$603$	15.6484			0.637253
$604$	−13.5737			−0.552304
$605$	3.38573	−	5.86426i	0.137650	−	0.238416i
$606$	−14.0171	−	24.2783i	−0.569406	−	0.986240i
$607$	0.633838			0.0257267			0.0128633	−	0.999917i	$-0.495905\pi$
$607$	0.633838			0.0257267			0.0128633	+	0.999917i	$0.495905\pi$
$608$	83.1020	−	143.937i	3.37023	−	5.83741i
$609$		0			0
$610$	−13.2546			−0.536664
$611$	19.1130	+	8.99260i	0.773231	+	0.363802i
$612$	−13.0070	−	22.5287i	−0.525775	−	0.910669i
$613$	−30.8550			−1.24622			−0.623110	−	0.782134i	$-0.714131\pi$
$613$	−30.8550			−1.24622			−0.623110	+	0.782134i	$0.714131\pi$
$614$	24.6911	+	42.7663i	0.996453	+	1.72591i
$615$	−0.634485	−	1.09896i	−0.0255849	−	0.0443143i
$616$		0			0
$617$	−16.9105	−	29.2898i	−0.680790	−	1.17916i	−0.974740	−	0.223341i	$-0.928304\pi$
$617$	−16.9105	−	29.2898i	−0.680790	−	1.17916i	0.293951	−	0.955821i	$-0.405030\pi$
$618$	−10.5068			−0.422644
$619$	0.202399	+	0.350565i	0.00813509	+	0.0140904i	0.870064	−	0.492938i	$-0.164077\pi$
$619$	0.202399	+	0.350565i	0.00813509	+	0.0140904i	−0.861929	+	0.507029i	$0.830744\pi$
$620$	5.66408	−	9.81048i	0.227475	−	0.393998i
$621$	−6.58807	−	11.4109i	−0.264370	−	0.457902i
$622$	23.6480	−	40.9595i	0.948197	−	1.64233i
$623$		0			0
$624$	62.1128	−	43.1747i	2.48650	−	1.72837i
$625$	−8.53179	+	14.7775i	−0.341272	+	0.591100i
$626$	−18.6812			−0.746650
$627$	−13.5347			−0.540524
$628$	−71.2338			−2.84254
$629$	25.3316			1.01004
$630$		0			0
$631$	−15.2254	−	26.3712i	−0.606114	−	1.04982i	−0.991874	−	0.127221i	$-0.959394\pi$
$631$	−15.2254	−	26.3712i	−0.606114	−	1.04982i	0.385761	−	0.922599i	$-0.373939\pi$
$632$	−43.9448	+	76.1147i	−1.74803	+	3.02768i
$633$	−11.3814	+	19.7131i	−0.452369	+	0.783526i
$634$	68.7381			2.72994
$635$	−2.01223	−	3.48528i	−0.0798529	−	0.138309i
$636$	34.3724			1.36296
$637$		0			0
$638$	−1.52497			−0.0603743
$639$	−2.73812	−	4.74256i	−0.108318	−	0.187613i
$640$	−31.0107			−1.22581
$641$	−4.82282	+	8.35337i	−0.190490	+	0.329938i	−0.945413	−	0.325875i	$-0.894341\pi$
$641$	−4.82282	+	8.35337i	−0.190490	+	0.329938i	0.754923	+	0.655814i	$0.227674\pi$
$642$	2.78050	−	4.81597i	0.109738	−	0.190071i
$643$	−4.06648	−	7.04335i	−0.160366	−	0.277763i	0.774634	−	0.632410i	$-0.217934\pi$
$643$	−4.06648	−	7.04335i	−0.160366	−	0.277763i	−0.935000	+	0.354647i	$0.884601\pi$
$644$		0			0
$645$	−1.76101			−0.0693395
$646$	82.6293			3.25101
$647$	−11.5227			−0.453005			−0.226503	−	0.974011i	$-0.572729\pi$
$647$	−11.5227			−0.453005			−0.226503	+	0.974011i	$0.572729\pi$
$648$	41.3629			1.62489
$649$	−7.49576	+	12.9830i	−0.294234	+	0.509629i
$650$	−39.8023	−	18.7268i	−1.56118	−	0.734526i
$651$		0			0
$652$	16.6162	−	28.7801i	0.650740	−	1.12711i
$653$	−21.2020	−	36.7229i	−0.829697	−	1.43708i	−0.898276	−	0.439431i	$-0.855180\pi$
$653$	−21.2020	−	36.7229i	−0.829697	−	1.43708i	0.0685797	−	0.997646i	$-0.478153\pi$
$654$	5.37072	−	9.30236i	0.210012	−	0.363751i
$655$	4.19527	+	7.26642i	0.163923	+	0.283922i
$656$	19.2858			0.752986
$657$	3.45153	+	5.97823i	0.134657	+	0.233233i
$658$		0			0
$659$	1.25044	+	2.16582i	0.0487101	+	0.0843684i	0.889352	−	0.457222i	$-0.151156\pi$
$659$	1.25044	+	2.16582i	0.0487101	+	0.0843684i	−0.840642	+	0.541591i	$0.817822\pi$
$660$	3.80554	+	6.59139i	0.148130	+	0.256570i
$661$	14.8394			0.577184			0.288592	−	0.957452i	$-0.406813\pi$
$661$	14.8394			0.577184			0.288592	+	0.957452i	$0.406813\pi$
$662$	−4.10523	−	7.11047i	−0.159554	−	0.276356i
$663$	18.4730	+	8.69146i	0.717431	+	0.337548i
$664$	−113.035			−4.38663
$665$		0			0
$666$	9.51710	−	16.4841i	0.368780	−	0.638746i
$667$	0.951183			0.0368300
$668$	−21.0924	−	36.5332i	−0.816091	−	1.41351i
$669$	−0.730424	+	1.26513i	−0.0282398	+	0.0489128i
$670$	27.9509			1.07984
$671$	−8.90541			−0.343790
$672$		0			0
$673$	−19.8046	+	34.3025i	−0.763410	+	1.32226i	0.177674	+	0.984089i	$0.443143\pi$
$673$	−19.8046	+	34.3025i	−0.763410	+	1.32226i	−0.941083	+	0.338175i	$0.890190\pi$
$674$	−40.4156	−	70.0019i	−1.55675	−	2.69637i
$675$	−12.5660	−	21.7649i	−0.483665	−	0.837733i
$676$	24.9766	−	67.1833i	0.960640	−	2.58397i
$677$	−8.51604	+	14.7502i	−0.327298	+	0.566897i	−0.981975	−	0.189012i	$-0.939471\pi$
$677$	−8.51604	+	14.7502i	−0.327298	+	0.566897i	0.654677	+	0.755909i	$0.272805\pi$
$678$	−23.2311	+	40.2374i	−0.892183	+	1.54531i
$679$		0			0
$680$	−14.8052	−	25.6434i	−0.567755	−	0.983380i
$681$	16.6961	−	28.9185i	0.639797	−	1.10816i
$682$	5.18598	−	8.98238i	0.198581	−	0.343953i
$683$	−16.4456	+	28.4846i	−0.629272	+	1.08993i	0.358426	+	0.933558i	$0.383314\pi$
$683$	−16.4456	+	28.4846i	−0.629272	+	1.08993i	−0.987698	+	0.156374i	$0.950020\pi$
$684$	22.7804	−	39.4568i	0.871030	−	1.50867i
$685$	5.17846	+	8.96936i	0.197859	+	0.342702i
$686$		0			0
$687$	−3.22755	+	5.59028i	−0.123139	+	0.213283i
$688$	13.3819	−	23.1782i	0.510181	−	0.883659i
$689$	13.5233	−	9.40006i	0.515196	−	0.358114i
$690$	−3.23469	−	5.60265i	−0.123143	−	0.213289i
$691$	11.8961	+	20.6047i	0.452550	+	0.783839i	0.998544	−	0.0539500i	$-0.0171812\pi$
$691$	11.8961	+	20.6047i	0.452550	+	0.783839i	−0.545994	+	0.837789i	$0.683848\pi$
$692$	0.453377	−	0.785272i	0.0172348	−	0.0298515i
$693$		0			0
$694$	16.4105			0.622933
$695$	7.73013			0.293221
$696$	−2.67902	+	4.64020i	−0.101548	+	0.175886i
$697$	2.60251	+	4.50768i	0.0985772	+	0.170741i
$698$	83.1539			3.14742
$699$	−14.0240	+	24.2903i	−0.530436	+	0.918742i
$700$		0			0
$701$	29.7796			1.12476			0.562380	−	0.826879i	$-0.309886\pi$
$701$	29.7796			1.12476			0.562380	+	0.826879i	$0.309886\pi$
$702$	45.8234	−	31.8519i	1.72949	−	1.20217i
$703$	22.1829	+	38.4219i	0.836644	+	1.44911i
$704$	−43.6138			−1.64376
$705$	2.96273	+	5.13160i	0.111583	+	0.193267i
$706$	−39.2061	−	67.9069i	−1.47554	−	2.55571i
$707$		0			0
$708$	41.3281	+	71.5824i	1.55321	+	2.69023i
$709$	11.9304			0.448054			0.224027	−	0.974583i	$-0.428080\pi$
$709$	11.9304			0.448054			0.224027	+	0.974583i	$0.428080\pi$
$710$	−4.89078	−	8.47107i	−0.183548	−	0.317914i
$711$	−5.18925	+	8.98805i	−0.194612	+	0.337078i
$712$	−8.48001	−	14.6878i	−0.317802	−	0.550449i
$713$	−3.23469	+	5.60265i	−0.121140	+	0.209821i
$714$		0			0
$715$	3.29982	+	1.55255i	0.123406	+	0.0580621i
$716$	−2.11894	+	3.67011i	−0.0791885	+	0.137159i
$717$	8.53642			0.318798
$718$	−64.3106			−2.40005
$719$	32.3638			1.20697			0.603484	−	0.797375i	$-0.293779\pi$
$719$	32.3638			1.20697			0.603484	+	0.797375i	$0.293779\pi$
$720$	−12.9556			−0.482827
$721$		0			0
$722$	46.3182	+	80.2255i	1.72379	+	2.98568i
$723$	8.28746	−	14.3543i	0.308214	−	0.533842i
$724$	27.3513	−	47.3738i	1.01650	−	1.76063i
$725$	1.81427			0.0673805
$726$	−17.0916	−	29.6036i	−0.634330	−	1.09869i
$727$	−31.4897			−1.16789			−0.583943	−	0.811794i	$-0.698491\pi$
$727$	−31.4897			−1.16789			−0.583943	+	0.811794i	$0.698491\pi$
$728$		0			0
$729$	28.0042			1.03719
$730$	6.16507	+	10.6782i	0.228179	+	0.395218i
$731$	7.22325			0.267161
$732$	−24.5501	+	42.5221i	−0.907399	+	1.57166i
$733$	−1.33112	+	2.30557i	−0.0491661	+	0.0851581i	−0.889561	−	0.456816i	$-0.848990\pi$
$733$	−1.33112	+	2.30557i	−0.0491661	+	0.0851581i	0.840395	+	0.541974i	$0.182323\pi$
$734$	50.0517	+	86.6921i	1.84744	+	3.19986i
$735$		0			0
$736$	53.3755			1.96745
$737$	18.7795			0.691750
$738$	3.91106			0.143968
$739$	−35.5828			−1.30893			−0.654467	−	0.756091i	$-0.727107\pi$
$739$	−35.5828			−1.30893			−0.654467	+	0.756091i	$0.727107\pi$
$740$	12.4743	−	21.6061i	0.458564	−	0.794256i
$741$	2.99397	+	35.6302i	0.109986	+	1.30891i
$742$		0			0
$743$	−12.1203	+	20.9929i	−0.444650	+	0.770156i	−0.998028	−	0.0627740i	$-0.980005\pi$
$743$	−12.1203	+	20.9929i	−0.444650	+	0.770156i	0.553378	+	0.832930i	$0.313339\pi$
$744$	−18.2211	−	31.5599i	−0.668018	−	1.15704i
$745$	−3.02522	+	5.23983i	−0.110835	+	0.191973i
$746$	−17.8853	−	30.9783i	−0.654828	−	1.13419i
$747$	−13.3479			−0.488373
$748$	−15.6095	−	27.0364i	−0.570739	−	0.988549i
$749$		0			0
$750$	−13.1009	−	22.6915i	−0.478378	−	0.828575i
$751$	14.5705	+	25.2368i	0.531684	+	0.920904i	0.999316	+	0.0369807i	$0.0117740\pi$
$751$	14.5705	+	25.2368i	0.531684	+	0.920904i	−0.467632	+	0.883923i	$0.654893\pi$
$752$	−90.0555			−3.28399
$753$	4.30900	+	7.46340i	0.157029	+	0.271981i
$754$	0.337334	+	4.01449i	0.0122850	+	0.146199i
$755$	−1.82446			−0.0663988
$756$		0			0
$757$	2.49495	−	4.32138i	0.0906805	−	0.157063i	−0.817117	−	0.576472i	$-0.804429\pi$
$757$	2.49495	−	4.32138i	0.0906805	−	0.157063i	0.907798	+	0.419408i	$0.137762\pi$
$758$	−83.8872			−3.04692
$759$	−2.17330	−	3.76426i	−0.0788858	−	0.136634i
$760$	25.9299	−	44.9119i	0.940576	−	1.62913i
$761$	−11.8372			−0.429097			−0.214548	−	0.976713i	$-0.568828\pi$
$761$	−11.8372			−0.429097			−0.214548	+	0.976713i	$0.568828\pi$
$762$	−20.3160			−0.735971
$763$		0			0
$764$	−27.2835	+	47.2564i	−0.987083	+	1.70968i
$765$	−1.74828	−	3.02812i	−0.0632094	−	0.109482i
$766$	−6.69643	−	11.5986i	−0.241952	−	0.419073i
$767$	35.8360	+	16.8607i	1.29396	+	0.608803i
$768$	−34.6593	+	60.0316i	−1.25066	+	2.16621i
$769$	17.9092	−	31.0196i	0.645821	−	1.11859i	−0.338291	−	0.941042i	$-0.609849\pi$
$769$	17.9092	−	31.0196i	0.645821	−	1.11859i	0.984111	−	0.177553i	$-0.0568180\pi$
$770$		0			0
$771$	−16.6209	−	28.7883i	−0.598588	−	1.03678i
$772$	−23.9859	+	41.5448i	−0.863272	+	1.49523i
$773$	9.97669	−	17.2801i	0.358837	−	0.621523i	−0.628930	−	0.777462i	$-0.716507\pi$
$773$	9.97669	−	17.2801i	0.358837	−	0.621523i	0.987767	+	0.155939i	$0.0498402\pi$
$774$	2.71378	−	4.70040i	0.0975447	−	0.168952i
$775$	−6.16980	+	10.6864i	−0.221626	+	0.383867i
$776$	45.9095	+	79.5176i	1.64805	+	2.85451i
$777$		0			0
$778$	−2.54133	+	4.40171i	−0.0911110	+	0.157809i
$779$	−4.55804	+	7.89476i	−0.163309	+	0.282859i
$780$	16.5100	−	11.4762i	0.591154	−	0.410912i
$781$	−3.28598	−	5.69148i	−0.117582	−	0.203657i
$782$	13.2680	+	22.9808i	0.474461	+	0.821791i
$783$	−1.15086	+	1.99335i	−0.0411285	+	0.0712367i
$784$		0			0
$785$	−9.57464			−0.341734
$786$	42.3566			1.51081
$787$	−1.39809	+	2.42157i	−0.0498367	+	0.0863196i	−0.889868	−	0.456219i	$-0.849203\pi$
$787$	−1.39809	+	2.42157i	−0.0498367	+	0.0863196i	0.840031	+	0.542539i	$0.182537\pi$
$788$	71.7271	+	124.235i	2.55517	+	4.42569i
$789$	−13.0737			−0.465437
$790$	−9.26895	+	16.0543i	−0.329774	+	0.571186i
$791$		0			0
$792$	−14.9487			−0.531179
$793$	1.96994	+	23.4435i	0.0699545	+	0.832503i
$794$	29.4850	+	51.0695i	1.04638	+	1.81239i
$795$	4.62005			0.163856
$796$	−27.9342	−	48.3835i	−0.990101	−	1.71491i
$797$	−0.842809	−	1.45979i	−0.0298538	−	0.0517083i	0.850712	−	0.525631i	$-0.176171\pi$
$797$	−0.842809	−	1.45979i	−0.0298538	−	0.0517083i	−0.880566	+	0.473923i	$0.842838\pi$
$798$		0			0
$799$	−12.1525	−	21.0487i	−0.429923	−	0.744649i
$800$	101.808			3.59945
$801$	−1.00137	−	1.73442i	−0.0353816	−	0.0612827i
$802$	−19.9624	+	34.5758i	−0.704895	+	1.22091i
$803$	4.14214	+	7.17439i	0.146173	+	0.253179i
$804$	51.7705	−	89.6692i	1.82581	−	3.16239i
$805$		0			0
$806$	−24.7933	−	11.6651i	−0.873307	−	0.410887i
$807$	−20.0622	+	34.7487i	−0.706222	+	1.22321i
$808$	72.1700			2.53893
$809$	−43.4372			−1.52717			−0.763585	−	0.645708i	$-0.776562\pi$
$809$	−43.4372			−1.52717			−0.763585	+	0.645708i	$0.776562\pi$
$810$	8.72435			0.306542
$811$	5.60812			0.196928			0.0984639	−	0.995141i	$-0.468607\pi$
$811$	5.60812			0.196928			0.0984639	+	0.995141i	$0.468607\pi$
$812$		0			0
$813$	0.204986	+	0.355045i	0.00718916	+	0.0124520i
$814$	11.4213	−	19.7823i	0.400318	−	0.693371i
$815$	2.23341	−	3.86837i	0.0782328	−	0.135503i
$816$	−87.0397			−3.04700
$817$	6.32540	+	10.9559i	0.221298	+	0.383299i
$818$	60.6574			2.12084
$819$		0			0
$820$	5.12632			0.179019
$821$	11.9724	+	20.7368i	0.417839	+	0.723718i	0.995722	−	0.0924014i	$-0.0294543\pi$
$821$	11.9724	+	20.7368i	0.417839	+	0.723718i	−0.577883	+	0.816120i	$0.696121\pi$
$822$	52.2832			1.82358
$823$	−17.7058	+	30.6674i	−0.617187	+	1.06900i	0.372810	+	0.927908i	$0.378394\pi$
$823$	−17.7058	+	30.6674i	−0.617187	+	1.06900i	−0.989997	+	0.141091i	$0.954939\pi$
$824$	13.5241	−	23.4244i	0.471133	−	0.816026i
$825$	−4.14532	−	7.17991i	−0.144322	−	0.249972i
$826$		0			0
$827$	−16.1563			−0.561811			−0.280905	−	0.959735i	$-0.590635\pi$
$827$	−16.1563			−0.561811			−0.280905	+	0.959735i	$0.590635\pi$
$828$	14.6316			0.508483
$829$	−52.7010			−1.83038			−0.915190	−	0.403022i	$-0.867960\pi$
$829$	−52.7010			−1.83038			−0.915190	+	0.403022i	$0.867960\pi$
$830$	−23.8417			−0.827557
$831$	22.3632	−	38.7343i	0.775772	−	1.34368i
$832$	9.64766	+	114.813i	0.334472	+	3.98044i
$833$		0			0
$834$	19.5114	−	33.7947i	0.675624	−	1.17021i
$835$	−2.83507	−	4.91048i	−0.0981116	−	0.169934i
$836$	27.3384	−	47.3516i	0.945520	−	1.63769i
$837$	−7.82749	−	13.5576i	−0.270558	−	0.468619i
$838$	−9.25363			−0.319661
$839$	11.2169	+	19.4283i	0.387251	+	0.670738i	0.992079	−	0.125618i	$-0.0400913\pi$
$839$	11.2169	+	19.4283i	0.387251	+	0.670738i	−0.604828	+	0.796356i	$0.706758\pi$
$840$		0			0
$841$	14.4169	+	24.9708i	0.497135	+	0.861063i
$842$	−34.4144	−	59.6075i	−1.18600	−	2.05421i
$843$	5.86165			0.201886
$844$	−45.9779	−	79.6361i	−1.58263	−	2.74119i
$845$	3.35715	−	9.03021i	0.115489	−	0.310649i
$846$	−18.2627			−0.627886
$847$		0			0
$848$	−35.1079	+	60.8086i	−1.20561	+	2.08818i
$849$	−28.7980			−0.988346
$850$	25.3071	+	43.8333i	0.868028	+	1.50347i
$851$	−7.12392	+	12.3390i	−0.244205	+	0.422975i
$852$	−36.2347			−1.24138
$853$	30.8521			1.05635			0.528177	−	0.849134i	$-0.322876\pi$
$853$	30.8521			1.05635			0.528177	+	0.849134i	$0.322876\pi$
$854$		0			0
$855$	3.06195	−	5.30345i	0.104716	−	0.181374i
$856$	7.15800	+	12.3980i	0.244655	+	0.423756i
$857$	−13.3700	−	23.1575i	−0.456710	−	0.791045i	0.542075	−	0.840330i	$-0.317639\pi$
$857$	−13.3700	−	23.1575i	−0.456710	−	0.791045i	−0.998785	+	0.0492854i	$0.984306\pi$
$858$	15.1164	−	10.5075i	0.516066	−	0.358719i
$859$	2.57902	−	4.46699i	0.0879950	−	0.152412i	−0.818669	−	0.574266i	$-0.805287\pi$
$859$	2.57902	−	4.46699i	0.0879950	−	0.152412i	0.906664	+	0.421855i	$0.138621\pi$
$860$	3.55701	−	6.16092i	0.121293	−	0.210086i
$861$		0			0
$862$	14.7948	+	25.6253i	0.503912	+	0.872801i
$863$	−4.08407	+	7.07382i	−0.139023	+	0.240796i	−0.927127	−	0.374747i	$-0.877730\pi$
$863$	−4.08407	+	7.07382i	−0.139023	+	0.240796i	0.788104	+	0.615542i	$0.211063\pi$
$864$	−64.5806	+	111.857i	−2.19708	+	3.80545i
$865$	0.0609391	−	0.105550i	0.00207199	−	0.00358879i
$866$	−19.8978	+	34.4640i	−0.676154	+	1.17113i
$867$	−0.144536	−	0.250344i	−0.00490871	−	0.00850214i
$868$		0			0
$869$	−6.22755	+	10.7864i	−0.211255	+	0.365905i
$870$	−0.565065	+	0.978722i	−0.0191575	+	0.0331818i
$871$	−4.15414	−	49.4369i	−0.140758	−	1.67511i
$872$	13.8261	+	23.9476i	0.468212	+	0.810968i
$873$	5.42125	+	9.38988i	0.183481	+	0.317799i
$874$	−23.2375	+	40.2486i	−0.786021	+	1.36143i
$875$		0			0
$876$	45.6756			1.54324
$877$	15.6184			0.527398			0.263699	−	0.964605i	$-0.415058\pi$
$877$	15.6184			0.527398			0.263699	+	0.964605i	$0.415058\pi$
$878$	−19.7781	+	34.2567i	−0.667479	+	1.15611i
$879$	−12.1222	−	20.9963i	−0.408872	−	0.708187i
$880$	−15.5479			−0.524118
$881$	23.2188	−	40.2161i	0.782260	−	1.35491i	−0.148362	−	0.988933i	$-0.547400\pi$
$881$	23.2188	−	40.2161i	0.782260	−	1.35491i	0.930622	−	0.365981i	$-0.119266\pi$
$882$		0			0
$883$	15.6588			0.526960			0.263480	−	0.964665i	$-0.415130\pi$
$883$	15.6588			0.526960			0.263480	+	0.964665i	$0.415130\pi$
$884$	−67.7204	+	47.0726i	−2.27768	+	1.58322i
$885$	5.55497	+	9.62149i	0.186728	+	0.323423i
$886$	82.8986			2.78503
$887$	−15.7554	−	27.2891i	−0.529013	−	0.916278i	−0.999428	−	0.0338320i	$-0.989229\pi$
$887$	−15.7554	−	27.2891i	−0.529013	−	0.916278i	0.470414	−	0.882446i	$-0.344104\pi$
$888$	−40.1292	−	69.5059i	−1.34665	−	2.33246i
$889$		0			0
$890$	−1.78862	−	3.09799i	−0.0599548	−	0.103845i
$891$	5.86165			0.196373
$892$	−2.95073	−	5.11082i	−0.0987978	−	0.171123i
$893$	21.2838	−	36.8647i	0.712236	−	1.23363i
$894$	15.2717	+	26.4514i	0.510762	+	0.884666i
$895$	−0.284810	+	0.493305i	−0.00952015	+	0.0164894i
$896$		0			0
$897$	−9.42868	+	6.55389i	−0.314815	+	0.218828i
$898$	42.8651	−	74.2445i	1.43043	−	2.47757i
$899$	1.13013			0.0376920
$900$	27.9081			0.930270
$901$	−18.9504			−0.631330
$902$	4.69361			0.156280
$903$		0			0
$904$	−59.8050	−	103.585i	−1.98908	−	3.44520i
$905$	3.67633	−	6.36759i	0.122205	−	0.211666i
$906$	−4.60505	+	7.97618i	−0.152993	+	0.264991i
$907$	−0.747991			−0.0248366			−0.0124183	−	0.999923i	$-0.503953\pi$
$907$	−0.747991			−0.0248366			−0.0124183	+	0.999923i	$0.503953\pi$
$908$	67.4482	+	116.824i	2.23835	+	3.87693i
$909$	8.52224			0.282665
$910$		0			0
$911$	24.9000			0.824973			0.412486	−	0.910964i	$-0.364660\pi$
$911$	24.9000			0.824973			0.412486	+	0.910964i	$0.364660\pi$
$912$	−76.2207	−	132.018i	−2.52392	−	4.37156i
$913$	−16.0186			−0.530138
$914$	28.2970	−	49.0119i	0.935983	−	1.62117i
$915$	−3.29982	+	5.71546i	−0.109089	+	0.188947i
$916$	−13.0385	−	22.5834i	−0.430804	−	0.746175i
$917$		0			0
$918$	−64.2132			−2.11935
$919$	0.586495			0.0193467			0.00967334	−	0.999953i	$-0.496921\pi$
$919$	0.586495			0.0193467			0.00967334	+	0.999953i	$0.496921\pi$
$920$	16.6545			0.549082
$921$	24.5881			0.810204
$922$	37.4104	−	64.7967i	1.23205	−	2.13397i
$923$	−14.2560	+	9.90934i	−0.469240	+	0.326170i
$924$		0			0
$925$	−13.5881	+	23.5352i	−0.446773	+	0.773833i
$926$	7.75694	+	13.4354i	0.254909	+	0.441515i
$927$	1.59700	−	2.76608i	0.0524523	−	0.0908500i
$928$	−4.66206	−	8.07493i	−0.153040	−	0.265073i
$929$	−50.1949			−1.64684			−0.823421	−	0.567431i	$-0.807938\pi$
$929$	−50.1949			−1.64684			−0.823421	+	0.567431i	$0.807938\pi$
$930$	−3.84324	−	6.65668i	−0.126025	−	0.218281i
$931$		0			0
$932$	−56.6534	−	98.1266i	−1.85574	−	3.21424i
$933$	−11.7746	−	20.3943i	−0.385484	−	0.667678i
$934$	−115.713			−3.78626
$935$	−2.09809	−	3.63400i	−0.0686150	−	0.118845i
$936$	3.30675	+	39.3525i	0.108085	+	1.28628i
$937$	22.7130			0.742003			0.371001	−	0.928632i	$-0.379015\pi$
$937$	22.7130			0.742003			0.371001	+	0.928632i	$0.379015\pi$
$938$		0			0
$939$	−4.65080	+	8.05542i	−0.151773	+	0.262879i
$940$	−23.9374			−0.780752
$941$	24.9367	+	43.1916i	0.812914	+	1.40801i	0.910816	+	0.412812i	$0.135453\pi$
$941$	24.9367	+	43.1916i	0.812914	+	1.40801i	−0.0979030	+	0.995196i	$0.531213\pi$
$942$	−24.1670	+	41.8586i	−0.787405	+	1.36383i
$943$	−2.92758			−0.0953351
$944$	−168.849			−5.49558
$945$		0			0
$946$	3.25677	−	5.64088i	0.105887	−	0.183401i
$947$	−0.133207	−	0.230722i	−0.00432865	−	0.00749745i	0.863853	−	0.503744i	$-0.168045\pi$
$947$	−0.133207	−	0.230722i	−0.00432865	−	0.00749745i	−0.868182	+	0.496247i	$0.834711\pi$
$948$	34.3358	+	59.4713i	1.11517	+	1.93154i
$949$	17.9703	−	12.4912i	0.583342	−	0.405482i
$950$	−44.3229	+	76.7696i	−1.43803	+	2.49073i
$951$	17.1128	−	29.6402i	0.554920	−	0.961150i
$952$		0			0
$953$	−3.91014	−	6.77257i	−0.126662	−	0.219385i	0.795719	−	0.605665i	$-0.207093\pi$
$953$	−3.91014	−	6.77257i	−0.126662	−	0.219385i	−0.922381	+	0.386281i	$0.873760\pi$
$954$	−7.11968	+	12.3316i	−0.230508	+	0.399252i
$955$	−3.66722	+	6.35181i	−0.118668	+	0.205540i
$956$	−17.2425	+	29.8649i	−0.557662	+	0.965899i
$957$	−0.379652	+	0.657576i	−0.0122724	+	0.0212564i
$958$	44.5859	+	77.2251i	1.44051	+	2.49503i
$959$		0			0
$960$	−16.1607	+	27.9911i	−0.521584	+	0.903410i
$961$	11.6568	−	20.1901i	0.376025	−	0.651294i
$962$	−54.6035	−	25.6907i	−1.76049	−	0.828302i
$963$	0.845257	+	1.46403i	0.0272380	+	0.0471776i
$964$	33.4793	+	57.9878i	1.07829	+	1.86766i
$965$	−3.22398	+	5.58410i	−0.103784	+	0.179759i
$966$		0			0
$967$	39.8224			1.28060			0.640301	−	0.768124i	$-0.278810\pi$
$967$	39.8224			1.28060			0.640301	+	0.768124i	$0.278810\pi$
$968$	87.9999			2.82842
$969$	20.5711	−	35.6302i	0.660838	−	1.14461i
$970$	9.68333	+	16.7720i	0.310913	+	0.538517i
$971$	−45.9295			−1.47395			−0.736974	−	0.675921i	$-0.763746\pi$
$971$	−45.9295			−1.47395			−0.736974	+	0.675921i	$0.763746\pi$
$972$	−30.5401	+	52.8969i	−0.979573	+	1.69667i
$973$		0			0
$974$	−73.6208			−2.35896
$975$	−17.9841	+	12.5008i	−0.575954	+	0.400346i
$976$	−50.1508	−	86.8637i	−1.60529	−	2.78044i
$977$	−28.6627			−0.917002			−0.458501	−	0.888694i	$-0.651613\pi$
$977$	−28.6627			−0.917002			−0.458501	+	0.888694i	$0.651613\pi$
$978$	−11.2745	−	19.5281i	−0.360520	−	0.624439i
$979$	−1.20173	−	2.08145i	−0.0384074	−	0.0665235i
$980$		0			0
$981$	1.63267	+	2.82787i	0.0521271	+	0.0902868i
$982$	−119.752			−3.82144
$983$	23.0600	+	39.9411i	0.735500	+	1.27392i	0.954503	+	0.298200i	$0.0963862\pi$
$983$	23.0600	+	39.9411i	0.735500	+	1.27392i	−0.219003	+	0.975724i	$0.570280\pi$
$984$	8.24557	−	14.2817i	0.262859	−	0.455285i
$985$	9.64095	+	16.6986i	0.307186	+	0.532062i
$986$	2.31777	−	4.01449i	0.0738128	−	0.127848i
$987$		0			0
$988$	−130.700	−	61.4940i	−4.15814	−	1.95638i
$989$	−2.03137	+	3.51843i	−0.0645937	+	0.111880i
$990$	−3.15302			−0.100209
$991$	37.8249			1.20155			0.600773	−	0.799419i	$-0.294859\pi$
$991$	37.8249			1.20155			0.600773	+	0.799419i	$0.294859\pi$
$992$	63.4171			2.01350
$993$	−4.08809			−0.129732
$994$		0			0
$995$	−3.75468	−	6.50329i	−0.119031	−	0.206168i
$996$	−44.1595	+	76.4864i	−1.39925	+	2.42357i
$997$	−19.1874	+	33.2335i	−0.607671	+	1.05252i	0.383952	+	0.923353i	$0.374563\pi$
$997$	−19.1874	+	33.2335i	−0.607671	+	1.05252i	−0.991623	+	0.129164i	$0.958771\pi$
$998$	49.6189			1.57066
$999$	−17.2389	−	29.8586i	−0.545414	−	0.944684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.g.k.373.4		8
7.2	even	3		91.2.f.c.22.4	✓	8
7.3	odd	6		637.2.h.i.165.1		8
7.4	even	3		637.2.h.h.165.1		8
7.5	odd	6		637.2.f.i.295.4		8
7.6	odd	2		637.2.g.j.373.4		8
13.3	even	3		637.2.h.h.471.1		8
21.2	odd	6		819.2.o.h.568.1		8
28.23	odd	6		1456.2.s.q.113.3		8
91.3	odd	6		637.2.g.j.263.4		8
91.9	even	3		1183.2.a.k.1.1		4
91.16	even	3		91.2.f.c.29.4	yes	8
91.30	even	6		1183.2.a.l.1.4		4
91.55	odd	6		637.2.h.i.471.1		8
91.58	odd	12		1183.2.c.g.337.8		8
91.61	odd	6		8281.2.a.bp.1.1		4
91.68	odd	6		637.2.f.i.393.4		8
91.72	odd	12		1183.2.c.g.337.1		8
91.81	even	3	inner	637.2.g.k.263.4		8
91.82	odd	6		8281.2.a.bt.1.4		4
273.107	odd	6		819.2.o.h.757.1		8
364.107	odd	6		1456.2.s.q.1121.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.4	✓	8	7.2	even	3
91.2.f.c.29.4	yes	8	91.16	even	3
637.2.f.i.295.4		8	7.5	odd	6
637.2.f.i.393.4		8	91.68	odd	6
637.2.g.j.263.4		8	91.3	odd	6
637.2.g.j.373.4		8	7.6	odd	2
637.2.g.k.263.4		8	91.81	even	3	inner
637.2.g.k.373.4		8	1.1	even	1	trivial
637.2.h.h.165.1		8	7.4	even	3
637.2.h.h.471.1		8	13.3	even	3
637.2.h.i.165.1		8	7.3	odd	6
637.2.h.i.471.1		8	91.55	odd	6
819.2.o.h.568.1		8	21.2	odd	6
819.2.o.h.757.1		8	273.107	odd	6
1183.2.a.k.1.1		4	91.9	even	3
1183.2.a.l.1.4		4	91.30	even	6
1183.2.c.g.337.1		8	91.72	odd	12
1183.2.c.g.337.8		8	91.58	odd	12
1456.2.s.q.113.3		8	28.23	odd	6
1456.2.s.q.1121.3		8	364.107	odd	6
8281.2.a.bp.1.1		4	91.61	odd	6
8281.2.a.bt.1.4		4	91.82	odd	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.37054 + 2.37385i) q^{2} +1.36482 q^{3} +(-2.75677 + 4.77486i) q^{4} +(-0.370541 + 0.641796i) q^{5} +(1.87054 + 3.23987i) q^{6} -9.63087 q^{8} -1.13727 q^{9} +O(q^{10})\)	\(q+(1.37054 + 2.37385i) q^{2} +1.36482 q^{3} +(-2.75677 + 4.77486i) q^{4} +(-0.370541 + 0.641796i) q^{5} +(1.87054 + 3.23987i) q^{6} -9.63087 q^{8} -1.13727 q^{9} -2.03137 q^{10} -1.36482 q^{11} +(-3.76249 + 6.51682i) q^{12} +(0.301907 + 3.59289i) q^{13} +(-0.505722 + 0.875935i) q^{15} +(-7.68598 - 13.3125i) q^{16} +(2.07436 - 3.59289i) q^{17} +(-1.55867 - 2.69970i) q^{18} +7.26606 q^{19} +(-2.04299 - 3.53856i) q^{20} +(-1.87054 - 3.23987i) q^{22} +(1.16673 + 2.02083i) q^{23} -13.1444 q^{24} +(2.22540 + 3.85450i) q^{25} +(-8.11519 + 5.64088i) q^{26} -5.64662 q^{27} +(0.203815 - 0.353017i) q^{29} -2.77245 q^{30} +(1.38622 + 2.40101i) q^{31} +(11.4370 - 19.8095i) q^{32} -1.86273 q^{33} +11.3720 q^{34} +(3.13518 - 5.43029i) q^{36} +(3.05295 + 5.28787i) q^{37} +(9.95843 + 17.2485i) q^{38} +(0.412049 + 4.90364i) q^{39} +(3.56863 - 6.18106i) q^{40} +(-0.627306 + 1.08653i) q^{41} +(0.870541 + 1.50782i) q^{43} +(3.76249 - 6.51682i) q^{44} +(0.421404 - 0.729894i) q^{45} +(-3.19809 + 5.53926i) q^{46} +(2.92921 - 5.07355i) q^{47} +(-10.4900 - 18.1692i) q^{48} +(-6.10000 + 10.5655i) q^{50} +(2.83112 - 4.90364i) q^{51} +(-17.9878 - 8.46319i) q^{52} +(-2.28389 - 3.95582i) q^{53} +(-7.73893 - 13.4042i) q^{54} +(0.505722 - 0.875935i) q^{55} +9.91685 q^{57} +1.11734 q^{58} +(5.49213 - 9.51264i) q^{59} +(-2.78831 - 4.82950i) q^{60} +6.52497 q^{61} +(-3.79975 + 6.58137i) q^{62} +31.9557 q^{64} +(-2.41777 - 1.13755i) q^{65} +(-2.55295 - 4.42184i) q^{66} -13.7597 q^{67} +(11.4370 + 19.8095i) q^{68} +(1.59237 + 2.75807i) q^{69} +(2.40763 + 4.17014i) q^{71} +10.9529 q^{72} +(-3.03494 - 5.25666i) q^{73} +(-8.36839 + 14.4945i) q^{74} +(3.03727 + 5.26070i) q^{75} +(-20.0308 + 34.6944i) q^{76} +(-11.0758 + 7.69879i) q^{78} +(4.56291 - 7.90320i) q^{79} +11.3919 q^{80} -4.29482 q^{81} -3.43900 q^{82} +11.7368 q^{83} +(1.53727 + 2.66263i) q^{85} +(-2.38622 + 4.13306i) q^{86} +(0.278170 - 0.481805i) q^{87} +13.1444 q^{88} +(0.880503 + 1.52508i) q^{89} +2.31021 q^{90} -12.8656 q^{92} +(1.89195 + 3.27695i) q^{93} +16.0584 q^{94} +(-2.69237 + 4.66332i) q^{95} +(15.6095 - 27.0364i) q^{96} +(-4.76691 - 8.25652i) q^{97} +1.55217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 2 q^{3} - 5 q^{4} + 7 q^{5} + 5 q^{6} - 12 q^{8} + 14 q^{9}+O(q^{10}) \) 8 * q + q^2 + 2 * q^3 - 5 * q^4 + 7 * q^5 + 5 * q^6 - 12 * q^8 + 14 * q^9	\( 8 q + q^{2} + 2 q^{3} - 5 q^{4} + 7 q^{5} + 5 q^{6} - 12 q^{8} + 14 q^{9} - 22 q^{10} - 2 q^{11} - 12 q^{12} + 4 q^{13} - 3 q^{15} - 19 q^{16} + 4 q^{17} + 3 q^{18} + 2 q^{19} + 2 q^{20} - 5 q^{22} + 2 q^{23} - 6 q^{24} - 5 q^{25} + 3 q^{26} - 52 q^{27} - q^{29} - 8 q^{30} + 4 q^{31} + 33 q^{32} - 38 q^{33} + 6 q^{34} + 34 q^{36} + 10 q^{37} + 23 q^{38} - 19 q^{39} + 17 q^{40} + 22 q^{41} - 3 q^{43} + 12 q^{44} + 11 q^{45} - 24 q^{46} - 2 q^{47} - 11 q^{48} - 43 q^{50} - 7 q^{51} - 34 q^{52} - 2 q^{53} - 5 q^{54} + 3 q^{55} - 34 q^{57} - 22 q^{58} + 8 q^{59} + 11 q^{60} + 16 q^{61} + 5 q^{62} + 28 q^{64} + 4 q^{65} - 6 q^{66} - 12 q^{67} + 33 q^{68} + 18 q^{69} + 14 q^{71} + 10 q^{72} + 8 q^{73} - 20 q^{74} + 7 q^{75} - 32 q^{76} - q^{78} + 26 q^{79} + 14 q^{80} + 48 q^{81} - 28 q^{82} - 5 q^{85} - 12 q^{86} - 13 q^{87} + 6 q^{88} + q^{89} + 52 q^{90} + 24 q^{92} + 7 q^{93} + 66 q^{94} - 21 q^{95} + 58 q^{96} - 3 q^{97} + 46 q^{99}+O(q^{100}) \) 8 * q + q^2 + 2 * q^3 - 5 * q^4 + 7 * q^5 + 5 * q^6 - 12 * q^8 + 14 * q^9 - 22 * q^10 - 2 * q^11 - 12 * q^12 + 4 * q^13 - 3 * q^15 - 19 * q^16 + 4 * q^17 + 3 * q^18 + 2 * q^19 + 2 * q^20 - 5 * q^22 + 2 * q^23 - 6 * q^24 - 5 * q^25 + 3 * q^26 - 52 * q^27 - q^29 - 8 * q^30 + 4 * q^31 + 33 * q^32 - 38 * q^33 + 6 * q^34 + 34 * q^36 + 10 * q^37 + 23 * q^38 - 19 * q^39 + 17 * q^40 + 22 * q^41 - 3 * q^43 + 12 * q^44 + 11 * q^45 - 24 * q^46 - 2 * q^47 - 11 * q^48 - 43 * q^50 - 7 * q^51 - 34 * q^52 - 2 * q^53 - 5 * q^54 + 3 * q^55 - 34 * q^57 - 22 * q^58 + 8 * q^59 + 11 * q^60 + 16 * q^61 + 5 * q^62 + 28 * q^64 + 4 * q^65 - 6 * q^66 - 12 * q^67 + 33 * q^68 + 18 * q^69 + 14 * q^71 + 10 * q^72 + 8 * q^73 - 20 * q^74 + 7 * q^75 - 32 * q^76 - q^78 + 26 * q^79 + 14 * q^80 + 48 * q^81 - 28 * q^82 - 5 * q^85 - 12 * q^86 - 13 * q^87 + 6 * q^88 + q^89 + 52 * q^90 + 24 * q^92 + 7 * q^93 + 66 * q^94 - 21 * q^95 + 58 * q^96 - 3 * q^97 + 46 * q^99

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