LMFDB - Embedded newform 637.2.c.e.246.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(246,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("637.246");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.c (of order $2$, degree $1$, 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:	$8$
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} + 11x^{6} + 36x^{4} + 31x^{2} + 3 $ x^8 + 11x^6 + 36x^4 + 31*x^2 + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			246.6
Root			$1.07305i$ of defining polynomial
Character	$\chi$	$=$	637.246
Dual form			637.2.c.e.246.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.07305i q^{2} +2.43140 q^{3} +0.848553 q^{4} +0.625432i q^{5} +2.60903i q^{6} +3.05665i q^{8} +2.91173 q^{9} +O(q^{10})$	\(q+1.07305i q^{2} +2.43140 q^{3} +0.848553 q^{4} +0.625432i q^{5} +2.60903i q^{6} +3.05665i q^{8} +2.91173 q^{9} -0.671123 q^{10} -0.708521i q^{11} +2.06318 q^{12} +(-0.848553 + 3.50428i) q^{13} +1.52068i q^{15} -1.58285 q^{16} -3.34313 q^{17} +3.12445i q^{18} -5.20276i q^{19} +0.530712i q^{20} +0.760282 q^{22} +4.43140 q^{23} +7.43196i q^{24} +4.60883 q^{25} +(-3.76028 - 0.910544i) q^{26} -0.214623 q^{27} -6.59711 q^{29} -1.63177 q^{30} -4.39061i q^{31} +4.41482i q^{32} -1.72270i q^{33} -3.58737i q^{34} +2.47076 q^{36} +0.423409i q^{37} +5.58285 q^{38} +(-2.06318 + 8.52032i) q^{39} -1.91173 q^{40} -5.01604i q^{41} +11.2059 q^{43} -0.601218i q^{44} +1.82109i q^{45} +4.75514i q^{46} -8.07269i q^{47} -3.84855 q^{48} +4.94553i q^{50} -8.12851 q^{51} +(-0.720042 + 2.97356i) q^{52} -0.697106 q^{53} -0.230302i q^{54} +0.443132 q^{55} -12.6500i q^{57} -7.07906i q^{58} -9.86319i q^{59} +1.29038i q^{60} -4.69711 q^{61} +4.71136 q^{62} -7.90305 q^{64} +(-2.19169 - 0.530712i) q^{65} +1.84855 q^{66} -10.4208i q^{67} -2.83683 q^{68} +10.7745 q^{69} +14.0876i q^{71} +8.90015i q^{72} +5.08383i q^{73} -0.454341 q^{74} +11.2059 q^{75} -4.41482i q^{76} +(-9.14277 - 2.21390i) q^{78} -3.91173 q^{79} -0.989966i q^{80} -9.25702 q^{81} +5.38249 q^{82} +10.2035i q^{83} -2.09090i q^{85} +12.0246i q^{86} -16.0402 q^{87} +2.16570 q^{88} +13.3791i q^{89} -1.95413 q^{90} +3.76028 q^{92} -10.6753i q^{93} +8.66244 q^{94} +3.25397 q^{95} +10.7342i q^{96} -0.202023i q^{97} -2.06302i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 6 q^{4} + 12 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 - 6 * q^4 + 12 * q^9	$ 8 q - 4 q^{3} - 6 q^{4} + 12 q^{9} - 6 q^{10} + 18 q^{12} + 6 q^{13} - 2 q^{16} + 8 q^{17} - 18 q^{22} + 12 q^{23} - 6 q^{26} - 16 q^{27} - 8 q^{29} - 38 q^{30} - 28 q^{36} + 34 q^{38} - 18 q^{39} - 4 q^{40} + 8 q^{43} - 18 q^{48} - 16 q^{51} - 42 q^{52} + 20 q^{53} - 12 q^{55} - 12 q^{61} - 22 q^{62} + 44 q^{64} + 30 q^{65} + 2 q^{66} - 2 q^{68} + 28 q^{69} - 42 q^{74} + 8 q^{75} + 10 q^{78} - 20 q^{79} + 24 q^{81} - 16 q^{82} - 68 q^{87} - 4 q^{88} + 108 q^{90} + 6 q^{92} - 26 q^{94} + 16 q^{95}+O(q^{100}) $ 8 * q - 4 * q^3 - 6 * q^4 + 12 * q^9 - 6 * q^10 + 18 * q^12 + 6 * q^13 - 2 * q^16 + 8 * q^17 - 18 * q^22 + 12 * q^23 - 6 * q^26 - 16 * q^27 - 8 * q^29 - 38 * q^30 - 28 * q^36 + 34 * q^38 - 18 * q^39 - 4 * q^40 + 8 * q^43 - 18 * q^48 - 16 * q^51 - 42 * q^52 + 20 * q^53 - 12 * q^55 - 12 * q^61 - 22 * q^62 + 44 * q^64 + 30 * q^65 + 2 * q^66 - 2 * q^68 + 28 * q^69 - 42 * q^74 + 8 * q^75 + 10 * q^78 - 20 * q^79 + 24 * q^81 - 16 * q^82 - 68 * q^87 - 4 * q^88 + 108 * q^90 + 6 * q^92 - 26 * q^94 + 16 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.07305i			0.758764i	0.925240	+	0.379382i	$0.123863\pi$
$2$			1.07305i			0.758764i	−0.925240	+	0.379382i	$0.876137\pi$
$3$	2.43140			1.40377			0.701886	−	0.712289i	$-0.252342\pi$
$3$	2.43140			1.40377			0.701886	+	0.712289i	$0.252342\pi$
$4$	0.848553			0.424277
$5$			0.625432i			0.279702i	0.990173	+	0.139851i	$0.0446623\pi$
$5$			0.625432i			0.279702i	−0.990173	+	0.139851i	$0.955338\pi$
$6$			2.60903i			1.06513i
$7$		0			0
$7$		0			0
$8$			3.05665i			1.08069i
$9$	2.91173			0.970576
$10$	−0.671123			−0.212228
$11$		−	0.708521i		−	0.213627i	−0.994279	−	0.106814i	$-0.965935\pi$
$11$		−	0.708521i		−	0.213627i	0.994279	−	0.106814i	$-0.0340648\pi$
$12$	2.06318			0.595588
$13$	−0.848553	+	3.50428i	−0.235346	+	0.971912i
$13$	−0.848553	+	3.50428i	−0.235346	+	0.971912i
$14$		0			0
$15$			1.52068i			0.392637i
$16$	−1.58285			−0.395713
$17$	−3.34313			−0.810829			−0.405414	−	0.914133i	$-0.632873\pi$
$17$	−3.34313			−0.810829			−0.405414	+	0.914133i	$0.632873\pi$
$18$			3.12445i			0.736439i
$19$		−	5.20276i		−	1.19360i	−0.802392	−	0.596798i	$-0.796439\pi$
$19$		−	5.20276i		−	1.19360i	0.802392	−	0.596798i	$-0.203561\pi$
$20$			0.530712i			0.118671i
$21$		0			0
$22$	0.760282			0.162093
$23$	4.43140			0.924012			0.462006	−	0.886877i	$-0.347130\pi$
$23$	4.43140			0.924012			0.462006	+	0.886877i	$0.347130\pi$
$24$			7.43196i			1.51704i
$25$	4.60883			0.921767
$26$	−3.76028	−	0.910544i	−0.737452	−	0.178572i
$27$	−0.214623			−0.0413042
$28$		0			0
$29$	−6.59711			−1.22505			−0.612526	−	0.790450i	$-0.709847\pi$
$29$	−6.59711			−1.22505			−0.612526	+	0.790450i	$0.709847\pi$
$30$	−1.63177			−0.297919
$31$		−	4.39061i		−	0.788576i	−0.918987	−	0.394288i	$-0.870991\pi$
$31$		−	4.39061i		−	0.788576i	0.918987	−	0.394288i	$-0.129009\pi$
$32$			4.41482i			0.780437i
$33$		−	1.72270i		−	0.299884i
$34$		−	3.58737i		−	0.615228i
$35$		0			0
$36$	2.47076			0.411793
$37$			0.423409i			0.0696080i	0.999394	+	0.0348040i	$0.0110807\pi$
$37$			0.423409i			0.0696080i	−0.999394	+	0.0348040i	$0.988919\pi$
$38$	5.58285			0.905658
$39$	−2.06318	+	8.52032i	−0.330373	+	1.36434i
$40$	−1.91173			−0.302271
$41$		−	5.01604i		−	0.783374i	−0.920099	−	0.391687i	$-0.871892\pi$
$41$		−	5.01604i		−	0.783374i	0.920099	−	0.391687i	$-0.128108\pi$
$42$		0			0
$43$	11.2059			1.70889			0.854445	−	0.519542i	$-0.173897\pi$
$43$	11.2059			1.70889			0.854445	+	0.519542i	$0.173897\pi$
$44$		−	0.601218i		−	0.0906370i
$45$			1.82109i			0.271472i
$46$			4.75514i			0.701107i
$47$		−	8.07269i		−	1.17752i	−0.808307	−	0.588762i	$-0.799616\pi$
$47$		−	8.07269i		−	1.17752i	0.808307	−	0.588762i	$-0.200384\pi$
$48$	−3.84855			−0.555491
$49$		0			0
$50$			4.94553i			0.699404i
$51$	−8.12851			−1.13822
$52$	−0.720042	+	2.97356i	−0.0998519	+	0.412359i
$53$	−0.697106			−0.0957549			−0.0478774	−	0.998853i	$-0.515246\pi$
$53$	−0.697106			−0.0957549			−0.0478774	+	0.998853i	$0.515246\pi$
$54$		−	0.230302i		−	0.0313401i
$55$	0.443132			0.0597519
$56$		0			0
$57$		−	12.6500i		−	1.67554i
$58$		−	7.07906i		−	0.929526i
$59$		−	9.86319i		−	1.28408i	−0.766672	−	0.642039i	$-0.778089\pi$
$59$		−	9.86319i		−	1.28408i	0.766672	−	0.642039i	$-0.221911\pi$
$60$			1.29038i			0.166587i
$61$	−4.69711			−0.601403			−0.300701	−	0.953718i	$-0.597221\pi$
$61$	−4.69711			−0.601403			−0.300701	+	0.953718i	$0.597221\pi$
$62$	4.71136			0.598344
$63$		0			0
$64$	−7.90305			−0.987881
$65$	−2.19169	−	0.530712i	−0.271845	−	0.0658267i
$66$	1.84855			0.227541
$67$		−	10.4208i		−	1.27311i	−0.771233	−	0.636553i	$-0.780360\pi$
$67$		−	10.4208i		−	1.27311i	0.771233	−	0.636553i	$-0.219640\pi$
$68$	−2.83683			−0.344016
$69$	10.7745			1.29710
$70$		0			0
$71$			14.0876i			1.67189i	0.548812	+	0.835946i	$0.315080\pi$
$71$			14.0876i			1.67189i	−0.548812	+	0.835946i	$0.684920\pi$
$72$			8.90015i			1.04889i
$73$			5.08383i			0.595017i	0.954719	+	0.297509i	$0.0961557\pi$
$73$			5.08383i			0.595017i	−0.954719	+	0.297509i	$0.903844\pi$
$74$	−0.454341			−0.0528161
$75$	11.2059			1.29395
$76$		−	4.41482i		−	0.506415i
$77$		0			0
$78$	−9.14277	−	2.21390i	−1.03521	−	0.250675i
$79$	−3.91173			−0.440104			−0.220052	−	0.975488i	$-0.570623\pi$
$79$	−3.91173			−0.440104			−0.220052	+	0.975488i	$0.570623\pi$
$80$		−	0.989966i		−	0.110682i
$81$	−9.25702			−1.02856
$82$	5.38249			0.594396
$83$			10.2035i			1.11998i	0.828499	+	0.559990i	$0.189195\pi$
$83$			10.2035i			1.11998i	−0.828499	+	0.559990i	$0.810805\pi$
$84$		0			0
$85$		−	2.09090i		−	0.226790i
$86$			12.0246i			1.29665i
$87$	−16.0402			−1.71969
$88$	2.16570			0.230865
$89$			13.3791i			1.41818i	0.705117	+	0.709090i	$0.250894\pi$
$89$			13.3791i			1.41818i	−0.705117	+	0.709090i	$0.749106\pi$
$90$	−1.95413			−0.205983
$91$		0			0
$92$	3.76028			0.392036
$93$		−	10.6753i		−	1.10698i
$94$	8.66244			0.893463
$95$	3.25397			0.333851
$96$			10.7342i			1.09556i
$97$		−	0.202023i		−	0.0205123i	−0.999947	−	0.0102562i	$-0.996735\pi$
$97$		−	0.202023i		−	0.0205123i	0.999947	−	0.0102562i	$-0.00326470\pi$
$98$		0			0
$99$		−	2.06302i		−	0.207341i
$100$	3.91084			0.391084
$101$	−17.3345			−1.72484			−0.862421	−	0.506191i	$-0.831053\pi$
$101$	−17.3345			−1.72484			−0.862421	+	0.506191i	$0.831053\pi$
$102$		−	8.72234i		−	0.863640i
$103$	−10.8148			−1.06561			−0.532806	−	0.846237i	$-0.678862\pi$
$103$	−10.8148			−1.06561			−0.532806	+	0.846237i	$0.678862\pi$
$104$	−10.7114	−	2.59373i	−1.05034	−	0.254336i
$105$		0			0
$106$		−	0.748033i		−	0.0726554i
$107$	−6.11678			−0.591332			−0.295666	−	0.955291i	$-0.595542\pi$
$107$	−6.11678			−0.591332			−0.295666	+	0.955291i	$0.595542\pi$
$108$	−0.182119			−0.0175244
$109$		−	11.3992i		−	1.09184i	−0.837837	−	0.545921i	$-0.816180\pi$
$109$		−	11.3992i		−	1.09184i	0.837837	−	0.545921i	$-0.183820\pi$
$110$			0.475505i			0.0453376i
$111$			1.02948i			0.0977137i
$112$		0			0
$113$	−0.923456			−0.0868714			−0.0434357	−	0.999056i	$-0.513830\pi$
$113$	−0.923456			−0.0868714			−0.0434357	+	0.999056i	$0.513830\pi$
$114$	13.5742			1.27134
$115$			2.77154i			0.258448i
$116$	−5.59800			−0.519761
$117$	−2.47076	+	10.2035i	−0.228422	+	0.943314i
$118$	10.5837			0.974312
$119$		0			0
$120$	−4.64819			−0.424319
$121$	10.4980			0.954363
$122$		−	5.04025i		−	0.456323i
$123$		−	12.1960i		−	1.09968i
$124$		−	3.72566i		−	0.334574i
$125$			6.00967i			0.537521i
$126$		0			0
$127$	8.50972			0.755116			0.377558	−	0.925986i	$-0.376764\pi$
$127$	8.50972			0.755116			0.377558	+	0.925986i	$0.376764\pi$
$128$			0.349236i			0.0308684i
$129$	27.2462			2.39889
$130$	0.569483	−	2.35180i	0.0499470	−	0.206267i
$131$	7.00305			0.611859			0.305930	−	0.952054i	$-0.401033\pi$
$131$	7.00305			0.611859			0.305930	+	0.952054i	$0.401033\pi$
$132$		−	1.46180i		−	0.127234i
$133$		0			0
$134$	11.1821			0.965988
$135$		−	0.134232i		−	0.0115528i
$136$		−	10.2188i		−	0.876255i
$137$		−	6.21694i		−	0.531149i	−0.964090	−	0.265575i	$-0.914438\pi$
$137$		−	6.21694i		−	0.531149i	0.964090	−	0.265575i	$-0.0855617\pi$
$138$			11.5617i			0.984195i
$139$	−6.53140			−0.553986			−0.276993	−	0.960872i	$-0.589338\pi$
$139$	−6.53140			−0.553986			−0.276993	+	0.960872i	$0.589338\pi$
$140$		0			0
$141$		−	19.6280i		−	1.65297i
$142$	−15.1168			−1.26857
$143$	2.48285	+	0.601218i	0.207627	+	0.0502763i
$144$	−4.60883			−0.384070
$145$		−	4.12604i		−	0.342649i
$146$	−5.45523			−0.451478
$147$		0			0
$148$			0.359285i			0.0295330i
$149$			3.69738i			0.302901i	0.988465	+	0.151451i	$0.0483945\pi$
$149$			3.69738i			0.302901i	−0.988465	+	0.151451i	$0.951606\pi$
$150$			12.0246i			0.981804i
$151$		−	4.87774i		−	0.396945i	−0.980106	−	0.198473i	$-0.936402\pi$
$151$		−	4.87774i		−	0.396945i	0.980106	−	0.198473i	$-0.0635981\pi$
$152$	15.9030			1.28991
$153$	−9.73430			−0.786971
$154$		0			0
$155$	2.74603			0.220566
$156$	−1.75071	+	7.22994i	−0.140169	+	0.578858i
$157$	9.51968			0.759753			0.379876	−	0.925037i	$-0.375967\pi$
$157$	9.51968			0.759753			0.379876	+	0.925037i	$0.375967\pi$
$158$		−	4.19750i		−	0.333935i
$159$	−1.69495			−0.134418
$160$	−2.76117			−0.218290
$161$		0			0
$162$		−	9.93329i		−	0.780433i
$163$		−	23.7089i		−	1.85702i	−0.371305	−	0.928511i	$-0.621090\pi$
$163$		−	23.7089i		−	1.85702i	0.371305	−	0.928511i	$-0.378910\pi$
$164$		−	4.25637i		−	0.332367i
$165$	1.07743			0.0838780
$166$	−10.9489			−0.849801
$167$		−	1.13193i		−	0.0875914i	−0.999041	−	0.0437957i	$-0.986055\pi$
$167$		−	1.13193i		−	0.0875914i	0.999041	−	0.0437957i	$-0.0139451\pi$
$168$		0			0
$169$	−11.5599	−	5.94713i	−0.889224	−	0.457472i
$170$	2.24365			0.172080
$171$		−	15.1490i		−	1.15848i
$172$	9.50884			0.725042
$173$	11.9892			0.911519			0.455760	−	0.890103i	$-0.349368\pi$
$173$	11.9892			0.911519			0.455760	+	0.890103i	$0.349368\pi$
$174$		−	17.2121i		−	1.30484i
$175$		0			0
$176$			1.12148i			0.0845350i
$177$		−	23.9814i		−	1.80255i
$178$	−14.3565			−1.07607
$179$	−9.47076			−0.707878			−0.353939	−	0.935269i	$-0.615158\pi$
$179$	−9.47076			−0.707878			−0.353939	+	0.935269i	$0.615158\pi$
$180$			1.54529i			0.115179i
$181$	11.4314			0.849690			0.424845	−	0.905266i	$-0.360329\pi$
$181$	11.4314			0.849690			0.424845	+	0.905266i	$0.360329\pi$
$182$		0			0
$183$	−11.4206			−0.844233
$184$			13.5453i			0.998571i
$185$	−0.264813			−0.0194695
$186$	11.4552			0.839938
$187$			2.36868i			0.173215i
$188$		−	6.85011i		−	0.499595i
$189$		0			0
$190$			3.49169i			0.253314i
$191$	15.6875			1.13511			0.567555	−	0.823335i	$-0.307889\pi$
$191$	15.6875			1.13511			0.567555	+	0.823335i	$0.307889\pi$
$192$	−19.2155			−1.38676
$193$			23.0071i			1.65609i	0.560662	+	0.828045i	$0.310547\pi$
$193$			23.0071i			1.65609i	−0.560662	+	0.828045i	$0.689453\pi$
$194$	0.216782			0.0155640
$195$	−5.32888	−	1.29038i	−0.381609	−	0.0924057i
$196$		0			0
$197$			10.2035i			0.726970i	0.931600	+	0.363485i	$0.118413\pi$
$197$			10.2035i			0.726970i	−0.931600	+	0.363485i	$0.881587\pi$
$198$	2.21373			0.157323
$199$	11.9235			0.845231			0.422616	−	0.906309i	$-0.361112\pi$
$199$	11.9235			0.845231			0.422616	+	0.906309i	$0.361112\pi$
$200$			14.0876i			0.996145i
$201$		−	25.3372i		−	1.78715i
$202$		−	18.6008i		−	1.30875i
$203$		0			0
$204$	−6.89747			−0.482920
$205$	3.13719			0.219111
$206$		−	11.6049i		−	0.808548i
$207$	12.9030			0.896824
$208$	1.34313	−	5.54675i	0.0931296	−	0.384598i
$209$	−3.68627			−0.254984
$210$		0			0
$211$	−15.5893			−1.07321			−0.536606	−	0.843833i	$-0.680294\pi$
$211$	−15.5893			−1.07321			−0.536606	+	0.843833i	$0.680294\pi$
$212$	−0.591531			−0.0406265
$213$			34.2527i			2.34696i
$214$		−	6.56365i		−	0.448682i
$215$			7.00855i			0.477979i
$216$		−	0.656028i		−	0.0446370i
$217$		0			0
$218$	12.2319			0.828451
$219$			12.3608i			0.835269i
$220$	0.376021			0.0253513
$221$	2.83683	−	11.7153i	0.190826	−	0.788054i
$222$	−1.10469			−0.0741417
$223$			6.76662i			0.453126i	0.973996	+	0.226563i	$0.0727490\pi$
$223$			6.76662i			0.453126i	−0.973996	+	0.226563i	$0.927251\pi$
$224$		0			0
$225$	13.4197			0.894645
$226$		−	0.990919i		−	0.0659149i
$227$		−	16.8245i		−	1.11668i	−0.829612	−	0.558340i	$-0.811438\pi$
$227$		−	16.8245i		−	1.11668i	0.829612	−	0.558340i	$-0.188562\pi$
$228$		−	10.7342i		−	0.710891i
$229$			11.0257i			0.728599i	0.931282	+	0.364300i	$0.118692\pi$
$229$			11.0257i			0.728599i	−0.931282	+	0.364300i	$0.881308\pi$
$230$	−2.97402			−0.196101
$231$		0			0
$232$		−	20.1651i		−	1.32390i
$233$	−17.3549			−1.13695			−0.568477	−	0.822699i	$-0.692467\pi$
$233$	−17.3549			−1.13695			−0.568477	+	0.822699i	$0.692467\pi$
$234$	−10.9489	−	2.65126i	−0.715753	−	0.173318i
$235$	5.04892			0.329355
$236$		−	8.36944i		−	0.544804i
$237$	−9.51100			−0.617806
$238$		0			0
$239$			19.7223i			1.27573i	0.770148	+	0.637865i	$0.220182\pi$
$239$			19.7223i			1.27573i	−0.770148	+	0.637865i	$0.779818\pi$
$240$		−	2.40701i		−	0.155372i
$241$			2.78413i			0.179341i	0.995971	+	0.0896706i	$0.0285814\pi$
$241$			2.78413i			0.179341i	−0.995971	+	0.0896706i	$0.971419\pi$
$242$			11.2649i			0.724137i
$243$	−21.8637			−1.40256
$244$	−3.98574			−0.255161
$245$		0			0
$246$	13.0870			0.834397
$247$	18.2319	+	4.41482i	1.16007	+	0.280908i
$248$	13.4206			0.852207
$249$			24.8088i			1.57220i
$250$	−6.44871			−0.407852
$251$	23.5608			1.48714			0.743572	−	0.668655i	$-0.233130\pi$
$251$	23.5608			1.48714			0.743572	+	0.668655i	$0.233130\pi$
$252$		0			0
$253$		−	3.13974i		−	0.197394i
$254$			9.13140i			0.572955i
$255$		−	5.08383i		−	0.318362i
$256$	−16.1808			−1.01130
$257$	−3.43229			−0.214101			−0.107050	−	0.994254i	$-0.534141\pi$
$257$	−3.43229			−0.214101			−0.107050	+	0.994254i	$0.534141\pi$
$258$			29.2367i			1.82019i
$259$		0			0
$260$	−1.85976	−	0.450337i	−0.115338	−	0.0279287i
$261$	−19.2090			−1.18901
$262$			7.51465i			0.464257i
$263$	−21.4491			−1.32261			−0.661303	−	0.750119i	$-0.729996\pi$
$263$	−21.4491			−1.32261			−0.661303	+	0.750119i	$0.729996\pi$
$264$	5.26570			0.324082
$265$		−	0.435992i		−	0.0267828i
$266$		0			0
$267$			32.5300i			1.99080i
$268$		−	8.84262i		−	0.540149i
$269$	−14.6569			−0.893645			−0.446822	−	0.894623i	$-0.647444\pi$
$269$	−14.6569			−0.893645			−0.446822	+	0.894623i	$0.647444\pi$
$270$	0.144038			0.00876589
$271$		−	2.04366i		−	0.124143i	−0.998072	−	0.0620717i	$-0.980229\pi$
$271$		−	2.04366i		−	0.124143i	0.998072	−	0.0620717i	$-0.0197707\pi$
$272$	5.29168			0.320856
$273$		0			0
$274$	6.67112			0.403017
$275$		−	3.26546i		−	0.196914i
$276$	9.14277			0.550330
$277$	5.43356			0.326471			0.163236	−	0.986587i	$-0.447807\pi$
$277$	5.43356			0.326471			0.163236	+	0.986587i	$0.447807\pi$
$278$		−	7.00855i		−	0.420345i
$279$		−	12.7843i		−	0.765373i
$280$		0			0
$281$		−	20.2356i		−	1.20715i	−0.797305	−	0.603577i	$-0.793742\pi$
$281$		−	20.2356i		−	1.20715i	0.797305	−	0.603577i	$-0.206258\pi$
$282$	21.0619			1.25422
$283$	1.73519			0.103146			0.0515731	−	0.998669i	$-0.483576\pi$
$283$	1.73519			0.103146			0.0515731	+	0.998669i	$0.483576\pi$
$284$			11.9541i			0.709345i
$285$	7.91173			0.468650
$286$	−0.645140	+	2.66424i	−0.0381479	+	0.157540i
$287$		0			0
$288$			12.8548i			0.757474i
$289$	−5.82346			−0.342556
$290$	4.42747			0.259990
$291$		−	0.491200i		−	0.0287947i
$292$			4.31390i			0.252452i
$293$			27.2441i			1.59162i	0.605547	+	0.795810i	$0.292954\pi$
$293$			27.2441i			1.59162i	−0.605547	+	0.795810i	$0.707046\pi$
$294$		0			0
$295$	6.16875			0.359159
$296$	−1.29421			−0.0752247
$297$			0.152065i			0.00882369i
$298$	−3.96750			−0.229831
$299$	−3.76028	+	15.5289i	−0.217463	+	0.898058i
$300$	9.50884			0.548993
$301$		0			0
$302$	5.23409			0.301188
$303$	−42.1471			−2.42129
$304$			8.23520i			0.472321i
$305$		−	2.93772i		−	0.168213i
$306$		−	10.4454i		−	0.597126i
$307$			12.7138i			0.725612i	0.931865	+	0.362806i	$0.118181\pi$
$307$			12.7138i			0.725612i	−0.931865	+	0.362806i	$0.881819\pi$
$308$		0			0
$309$	−26.2951			−1.49588
$310$			2.94664i			0.167358i
$311$	9.61879			0.545431			0.272716	−	0.962095i	$-0.412078\pi$
$311$	9.61879			0.545431			0.272716	+	0.962095i	$0.412078\pi$
$312$	−26.0437	−	6.30641i	−1.47443	−	0.357030i
$313$	9.02547			0.510149			0.255075	−	0.966921i	$-0.417900\pi$
$313$	9.02547			0.510149			0.255075	+	0.966921i	$0.417900\pi$
$314$			10.2151i			0.576473i
$315$		0			0
$316$	−3.31931			−0.186726
$317$			24.6262i			1.38314i	0.722307	+	0.691572i	$0.243082\pi$
$317$			24.6262i			1.38314i	−0.722307	+	0.691572i	$0.756918\pi$
$318$		−	1.81877i		−	0.101992i
$319$			4.67419i			0.261704i
$320$		−	4.94282i		−	0.276312i
$321$	−14.8724			−0.830095
$322$		0			0
$323$			17.3935i			0.967802i
$324$	−7.85507			−0.436393
$325$	−3.91084	+	16.1506i	−0.216934	+	0.895876i
$326$	25.4409			1.40904
$327$		−	27.7160i		−	1.53270i
$328$	15.3323			0.846584
$329$		0			0
$330$			1.15614i			0.0636436i
$331$			13.1718i			0.723989i	0.932180	+	0.361994i	$0.117904\pi$
$331$			13.1718i			0.723989i	−0.932180	+	0.361994i	$0.882096\pi$
$332$			8.65821i			0.475181i
$333$			1.23285i			0.0675599i
$334$	1.21462			0.0664612
$335$	6.51752			0.356090
$336$		0			0
$337$	17.0307			0.927720			0.463860	−	0.885909i	$-0.346464\pi$
$337$	17.0307			0.927720			0.463860	+	0.885909i	$0.346464\pi$
$338$	6.38160	−	12.4044i	0.347113	−	0.674712i
$339$	−2.24529			−0.121948
$340$		−	1.77424i		−	0.0962218i
$341$	−3.11084			−0.168461
$342$	16.2558			0.879010
$343$		0			0
$344$			34.2527i			1.84678i
$345$			6.73874i			0.362802i
$346$			12.8650i			0.691628i
$347$	0.459917			0.0246897			0.0123448	−	0.999924i	$-0.496070\pi$
$347$	0.459917			0.0246897			0.0123448	+	0.999924i	$0.496070\pi$
$348$	−13.6110			−0.729626
$349$		−	6.87822i		−	0.368183i	−0.982909	−	0.184091i	$-0.941066\pi$
$349$		−	6.87822i		−	0.368183i	0.982909	−	0.184091i	$-0.0589342\pi$
$350$		0			0
$351$	0.182119	−	0.752098i	0.00972078	−	0.0401440i
$352$	3.12799			0.166723
$353$		−	1.53326i		−	0.0816073i	−0.999167	−	0.0408036i	$-0.987008\pi$
$353$		−	1.53326i		−	0.0816073i	0.999167	−	0.0408036i	$-0.0129918\pi$
$354$	25.7334			1.36771
$355$	−8.81084			−0.467631
$356$			11.3529i			0.601701i
$357$		0			0
$358$		−	10.1626i		−	0.537112i
$359$			27.2068i			1.43592i	0.696085	+	0.717959i	$0.254923\pi$
$359$			27.2068i			1.43592i	−0.696085	+	0.717959i	$0.745077\pi$
$360$	−5.56644			−0.293377
$361$	−8.06875			−0.424671
$362$			12.2665i			0.644714i
$363$	25.5249			1.33971
$364$		0			0
$365$	−3.17959			−0.166427
$366$		−	12.2549i		−	0.640574i
$367$	−26.9814			−1.40842			−0.704208	−	0.709994i	$-0.748698\pi$
$367$	−26.9814			−1.40842			−0.704208	+	0.709994i	$0.748698\pi$
$368$	−7.01426			−0.365643
$369$		−	14.6053i		−	0.760324i
$370$		−	0.284159i		−	0.0147727i
$371$		0			0
$372$		−	9.05859i		−	0.469666i
$373$	3.97238			0.205682			0.102841	−	0.994698i	$-0.467207\pi$
$373$	3.97238			0.205682			0.102841	+	0.994698i	$0.467207\pi$
$374$	−2.54172			−0.131429
$375$			14.6119i			0.754558i
$376$	24.6754			1.27254
$377$	5.59800	−	23.1181i	0.288311	−	1.19064i
$378$		0			0
$379$		−	11.4059i		−	0.585884i	−0.956130	−	0.292942i	$-0.905366\pi$
$379$		−	11.4059i		−	0.585884i	0.956130	−	0.292942i	$-0.0946343\pi$
$380$	2.76117			0.141645
$381$	20.6906			1.06001
$382$			16.8336i			0.861281i
$383$			23.7920i			1.21571i	0.794047	+	0.607856i	$0.207970\pi$
$383$			23.7920i			1.21571i	−0.794047	+	0.607856i	$0.792030\pi$
$384$			0.849134i			0.0433322i
$385$		0			0
$386$	−24.6879			−1.25658
$387$	32.6287			1.65861
$388$		−	0.171427i		−	0.00870290i
$389$	28.4110			1.44049			0.720247	−	0.693717i	$-0.244028\pi$
$389$	28.4110			1.44049			0.720247	+	0.693717i	$0.244028\pi$
$390$	1.38464	−	5.71818i	0.0701142	−	0.289551i
$391$	−14.8148			−0.749216
$392$		0			0
$393$	17.0272			0.858911
$394$	−10.9489			−0.551599
$395$		−	2.44652i		−	0.123098i
$396$		−	1.75058i		−	0.0879701i
$397$		−	9.85912i		−	0.494815i	−0.968912	−	0.247408i	$-0.920421\pi$
$397$		−	9.85912i		−	0.494815i	0.968912	−	0.247408i	$-0.0795786\pi$
$398$			12.7945i			0.641332i
$399$		0			0
$400$	−7.29510			−0.364755
$401$		−	12.6194i		−	0.630184i	−0.949061	−	0.315092i	$-0.897965\pi$
$401$		−	12.6194i		−	0.630184i	0.949061	−	0.315092i	$-0.102035\pi$
$402$	27.1883			1.35603
$403$	15.3859	+	3.72566i	0.766426	+	0.185588i
$404$	−14.7092			−0.731810
$405$		−	5.78964i		−	0.287689i
$406$		0			0
$407$	0.299994			0.0148701
$408$		−	24.8460i		−	1.23006i
$409$			18.0573i			0.892878i	0.894814	+	0.446439i	$0.147308\pi$
$409$			18.0573i			0.892878i	−0.894814	+	0.446439i	$0.852692\pi$
$410$			3.36638i			0.166254i
$411$		−	15.1159i		−	0.745613i
$412$	−9.17691			−0.452114
$413$		0			0
$414$			13.8457i			0.680478i
$415$	−6.38160			−0.313260
$416$	−15.4708	−	3.74621i	−0.758516	−	0.183673i
$417$	−15.8805			−0.777671
$418$		−	3.95557i		−	0.193473i
$419$	−14.2805			−0.697647			−0.348823	−	0.937188i	$-0.613419\pi$
$419$	−14.2805			−0.697647			−0.348823	+	0.937188i	$0.613419\pi$
$420$		0			0
$421$			4.27439i			0.208321i	0.994561	+	0.104160i	$0.0332155\pi$
$421$			4.27439i			0.208321i	−0.994561	+	0.104160i	$0.966784\pi$
$422$		−	16.7282i		−	0.814316i
$423$		−	23.5055i		−	1.14288i
$424$		−	2.13081i		−	0.103481i
$425$	−15.4080			−0.747395
$426$	−36.7550			−1.78079
$427$		0			0
$428$	−5.19042			−0.250888
$429$	6.03682	+	1.46180i	0.291461	+	0.0705765i
$430$	−7.52056			−0.362674
$431$			14.6067i			0.703580i	0.936079	+	0.351790i	$0.114427\pi$
$431$			14.6067i			0.703580i	−0.936079	+	0.351790i	$0.885573\pi$
$432$	0.339716			0.0163446
$433$	−28.0099			−1.34607			−0.673035	−	0.739611i	$-0.735009\pi$
$433$	−28.0099			−1.34607			−0.673035	+	0.739611i	$0.735009\pi$
$434$		0			0
$435$		−	10.0321i		−	0.481001i
$436$		−	9.67279i		−	0.463243i
$437$		−	23.0556i		−	1.10290i
$438$	−13.2639			−0.633772
$439$	17.0774			0.815061			0.407531	−	0.913192i	$-0.366390\pi$
$439$	17.0774			0.815061			0.407531	+	0.913192i	$0.366390\pi$
$440$			1.35450i			0.0645733i
$441$		0			0
$442$	12.5711	+	3.04407i	0.597947	+	0.144792i
$443$	13.8157			0.656402			0.328201	−	0.944608i	$-0.393558\pi$
$443$	13.8157			0.656402			0.328201	+	0.944608i	$0.393558\pi$
$444$			0.873567i			0.0414576i
$445$	−8.36771			−0.396668
$446$	−7.26096			−0.343816
$447$			8.98984i			0.425205i
$448$		0			0
$449$		−	32.6410i		−	1.54042i	−0.637789	−	0.770211i	$-0.720151\pi$
$449$		−	32.6410i		−	1.54042i	0.637789	−	0.770211i	$-0.279849\pi$
$450$			14.4001i			0.678825i
$451$	−3.55397			−0.167350
$452$	−0.783601			−0.0368575
$453$		−	11.8598i		−	0.557220i
$454$	18.0536			0.847298
$455$		0			0
$456$	38.6667			1.81074
$457$		−	3.17034i		−	0.148302i	−0.997247	−	0.0741511i	$-0.976375\pi$
$457$		−	3.17034i		−	0.148302i	0.997247	−	0.0741511i	$-0.0236247\pi$
$458$	−11.8312			−0.552835
$459$	0.717513			0.0334906
$460$			2.35180i			0.109653i
$461$			0.202023i			0.00940915i	0.999989	+	0.00470458i	$0.00149752\pi$
$461$			0.202023i			0.00940915i	−0.999989	+	0.00470458i	$0.998502\pi$
$462$		0			0
$463$			17.2121i			0.799912i	0.916534	+	0.399956i	$0.130975\pi$
$463$			17.2121i			0.799912i	−0.916534	+	0.399956i	$0.869025\pi$
$464$	10.4422			0.484769
$465$	6.67670			0.309625
$466$		−	18.6227i		−	0.862681i
$467$	−0.191169			−0.00884625			−0.00442312	−	0.999990i	$-0.501408\pi$
$467$	−0.191169			−0.00884625			−0.00442312	+	0.999990i	$0.501408\pi$
$468$	−2.09657	+	8.65821i	−0.0969139	+	0.400226i
$469$		0			0
$470$			5.41777i			0.249903i
$471$	23.1462			1.06652
$472$	30.1483			1.38769
$473$		−	7.93965i		−	0.365065i
$474$		−	10.2058i		−	0.468769i
$475$		−	23.9787i		−	1.10022i
$476$		0			0
$477$	−2.02978			−0.0929374
$478$	−21.1631			−0.967978
$479$			21.4785i			0.981377i	0.871335	+	0.490688i	$0.163255\pi$
$479$			21.4785i			0.981377i	−0.871335	+	0.490688i	$0.836745\pi$
$480$	−6.71352			−0.306429
$481$	−1.48374	−	0.359285i	−0.0676528	−	0.0163820i
$482$	−2.98752			−0.136078
$483$		0			0
$484$	8.90811			0.404914
$485$	0.126352			0.00573733
$486$		−	23.4609i		−	1.06421i
$487$			19.0484i			0.863167i	0.902073	+	0.431584i	$0.142045\pi$
$487$			19.0484i			0.863167i	−0.902073	+	0.431584i	$0.857955\pi$
$488$		−	14.3574i		−	0.649930i
$489$		−	57.6458i		−	2.60684i
$490$		0			0
$491$	−35.7559			−1.61364			−0.806821	−	0.590796i	$-0.798814\pi$
$491$	−35.7559			−1.61364			−0.806821	+	0.590796i	$0.798814\pi$
$492$		−	10.3490i		−	0.466568i
$493$	22.0550			0.993308
$494$	−4.73735	+	19.5639i	−0.213143	+	0.880220i
$495$	1.29028			0.0579937
$496$			6.94968i			0.312050i
$497$		0			0
$498$	−26.6213			−1.19293
$499$			17.6891i			0.791875i	0.918277	+	0.395937i	$0.129580\pi$
$499$			17.6891i			0.791875i	−0.918277	+	0.395937i	$0.870420\pi$
$500$			5.09953i			0.228058i
$501$		−	2.75218i		−	0.122958i
$502$			25.2820i			1.12839i
$503$	−11.3305			−0.505203			−0.252601	−	0.967570i	$-0.581286\pi$
$503$	−11.3305			−0.505203			−0.252601	+	0.967570i	$0.581286\pi$
$504$		0			0
$505$		−	10.8415i		−	0.482441i
$506$	3.36912			0.149776
$507$	−28.1068	−	14.4599i	−1.24827	−	0.642186i
$508$	7.22095			0.320378
$509$			19.3514i			0.857735i	0.903367	+	0.428868i	$0.141087\pi$
$509$			19.3514i			0.857735i	−0.903367	+	0.428868i	$0.858913\pi$
$510$	5.45523			0.241562
$511$		0			0
$512$		−	16.6645i		−	0.736472i
$513$			1.11663i			0.0493005i
$514$		−	3.68304i		−	0.162452i
$515$		−	6.76391i		−	0.298053i
$516$	23.1198			1.01779
$517$	−5.71967			−0.251551
$518$		0			0
$519$	29.1505			1.27957
$520$	1.62220	−	6.69923i	0.0711383	−	0.293781i
$521$	7.71099			0.337825			0.168912	−	0.985631i	$-0.445975\pi$
$521$	7.71099			0.337825			0.168912	+	0.985631i	$0.445975\pi$
$522$		−	20.6123i		−	0.902176i
$523$	35.0501			1.53263			0.766317	−	0.642462i	$-0.222087\pi$
$523$	35.0501			1.53263			0.766317	+	0.642462i	$0.222087\pi$
$524$	5.94246			0.259597
$525$		0			0
$526$		−	23.0160i		−	1.00355i
$527$			14.6784i			0.639401i
$528$			2.72678i			0.118668i
$529$	−3.36265			−0.146202
$530$	0.467844			0.0203218
$531$		−	28.7189i		−	1.24630i
$532$		0			0
$533$	17.5776	+	4.25637i	0.761370	+	0.184364i
$534$	−34.9065			−1.51055
$535$		−	3.82563i		−	0.165396i
$536$	31.8529			1.37583
$537$	−23.0272			−0.993699
$538$		−	15.7276i		−	0.678066i
$539$		0			0
$540$		−	0.113903i		−	0.00490160i
$541$		−	12.1335i		−	0.521659i	−0.965385	−	0.260829i	$-0.916004\pi$
$541$		−	12.1335i		−	0.521659i	0.965385	−	0.260829i	$-0.0839960\pi$
$542$	2.19296			0.0941956
$543$	27.7944			1.19277
$544$		−	14.7593i		−	0.632801i
$545$	7.12940			0.305390
$546$		0			0
$547$	−5.12546			−0.219149			−0.109575	−	0.993979i	$-0.534949\pi$
$547$	−5.12546			−0.219149			−0.109575	+	0.993979i	$0.534949\pi$
$548$		−	5.27541i		−	0.225354i
$549$	−13.6767			−0.583707
$550$	3.50401			0.149412
$551$			34.3232i			1.46222i
$552$			32.9340i			1.40177i
$553$		0			0
$554$			5.83051i			0.247715i
$555$	−0.643868			−0.0273307
$556$	−5.54224			−0.235043
$557$		−	37.5586i		−	1.59141i	−0.605685	−	0.795705i	$-0.707101\pi$
$557$		−	37.5586i		−	1.59141i	0.605685	−	0.795705i	$-0.292899\pi$
$558$	13.7182			0.580738
$559$	−9.50884	+	39.2687i	−0.402181	+	1.66089i
$560$		0			0
$561$			5.75922i			0.243154i
$562$	21.7139			0.915945
$563$	28.7009			1.20960			0.604799	−	0.796378i	$-0.293253\pi$
$563$	28.7009			1.20960			0.604799	+	0.796378i	$0.293253\pi$
$564$		−	16.6554i		−	0.701318i
$565$		−	0.577559i		−	0.0242981i
$566$			1.86195i			0.0782636i
$567$		0			0
$568$	−43.0610			−1.80680
$569$	−17.9483			−0.752434			−0.376217	−	0.926532i	$-0.622775\pi$
$569$	−17.9483			−0.752434			−0.376217	+	0.926532i	$0.622775\pi$
$570$			8.48972i			0.355595i
$571$	−17.8274			−0.746053			−0.373027	−	0.927821i	$-0.621680\pi$
$571$	−17.8274			−0.746053			−0.373027	+	0.927821i	$0.621680\pi$
$572$	2.10683	+	0.510165i	0.0880911	+	0.0213311i
$573$	38.1428			1.59344
$574$		0			0
$575$	20.4236			0.851724
$576$	−23.0115			−0.958814
$577$		−	33.0570i		−	1.37618i	−0.725624	−	0.688091i	$-0.758449\pi$
$577$		−	33.0570i		−	1.37618i	0.725624	−	0.688091i	$-0.241551\pi$
$578$		−	6.24889i		−	0.259920i
$579$			55.9396i			2.32477i
$580$		−	3.50117i		−	0.145378i
$581$		0			0
$582$	0.527085			0.0218484
$583$			0.493914i			0.0204558i
$584$	−15.5395			−0.643029
$585$	−6.38160	−	1.54529i	−0.263847	−	0.0638899i
$586$	−29.2345			−1.20766
$587$		−	14.7295i		−	0.607953i	−0.952680	−	0.303976i	$-0.901686\pi$
$587$		−	14.7295i		−	0.607953i	0.952680	−	0.303976i	$-0.0983144\pi$
$588$		0			0
$589$	−22.8433			−0.941241
$590$			6.61941i			0.272517i
$591$			24.8088i			1.02050i
$592$		−	0.670193i		−	0.0275448i
$593$		−	9.20987i		−	0.378204i	−0.981957	−	0.189102i	$-0.939442\pi$
$593$		−	9.20987i		−	0.378204i	0.981957	−	0.189102i	$-0.0605577\pi$
$594$	−0.163174			−0.00669510
$595$		0			0
$596$			3.13743i			0.128514i
$597$	28.9907			1.18651
$598$	−16.6633	−	4.03499i	−0.681414	−	0.165003i
$599$	−10.5745			−0.432064			−0.216032	−	0.976386i	$-0.569312\pi$
$599$	−10.5745			−0.432064			−0.216032	+	0.976386i	$0.569312\pi$
$600$			34.2527i			1.39836i
$601$	−4.08916			−0.166800			−0.0834001	−	0.996516i	$-0.526578\pi$
$601$	−4.08916			−0.166800			−0.0834001	+	0.996516i	$0.526578\pi$
$602$		0			0
$603$		−	30.3426i		−	1.23565i
$604$		−	4.13902i		−	0.168414i
$605$			6.56578i			0.266937i
$606$		−	45.2261i		−	1.83719i
$607$	−3.60706			−0.146406			−0.0732030	−	0.997317i	$-0.523322\pi$
$607$	−3.60706			−0.146406			−0.0732030	+	0.997317i	$0.523322\pi$
$608$	22.9693			0.931527
$609$		0			0
$610$	3.15233			0.127634
$611$	28.2890	+	6.85011i	1.14445	+	0.277126i
$612$	−8.26007			−0.333893
$613$		−	38.4845i		−	1.55437i	−0.629271	−	0.777186i	$-0.716646\pi$
$613$		−	38.4845i		−	1.55437i	0.629271	−	0.777186i	$-0.283354\pi$
$614$	−13.6426			−0.550569
$615$	7.62778			0.307582
$616$		0			0
$617$		−	3.09503i		−	0.124601i	−0.998057	−	0.0623007i	$-0.980156\pi$
$617$		−	3.09503i		−	0.124601i	0.998057	−	0.0623007i	$-0.0198438\pi$
$618$		−	28.2161i		−	1.13502i
$619$			12.2692i			0.493142i	0.969125	+	0.246571i	$0.0793039\pi$
$619$			12.2692i			0.493142i	−0.969125	+	0.246571i	$0.920696\pi$
$620$	2.33015			0.0935810
$621$	−0.951081			−0.0381655
$622$			10.3215i			0.413854i
$623$		0			0
$624$	3.26570	−	13.4864i	0.130733	−	0.539888i
$625$	19.2855			0.771421
$626$			9.68482i			0.387083i
$627$	−8.96281			−0.357940
$628$	8.07795			0.322345
$629$		−	1.41551i		−	0.0564402i
$630$		0			0
$631$			5.31780i			0.211698i	0.994382	+	0.105849i	$0.0337561\pi$
$631$			5.31780i			0.211698i	−0.994382	+	0.105849i	$0.966244\pi$
$632$		−	11.9568i		−	0.475616i
$633$	−37.9039			−1.50655
$634$	−26.4253			−1.04948
$635$			5.32225i			0.211207i
$636$	−1.43825			−0.0570304
$637$		0			0
$638$	−5.01566			−0.198572
$639$			41.0193i			1.62270i
$640$	−0.218423			−0.00863394
$641$	−12.1904			−0.481493			−0.240746	−	0.970588i	$-0.577392\pi$
$641$	−12.1904			−0.481493			−0.240746	+	0.970588i	$0.577392\pi$
$642$		−	15.9589i		−	0.629847i
$643$			18.9733i			0.748235i	0.927381	+	0.374117i	$0.122054\pi$
$643$			18.9733i			0.748235i	−0.927381	+	0.374117i	$0.877946\pi$
$644$		0			0
$645$			17.0406i			0.670974i
$646$	−18.6642			−0.734334
$647$	19.7117			0.774948			0.387474	−	0.921881i	$-0.373348\pi$
$647$	19.7117			0.774948			0.387474	+	0.921881i	$0.373348\pi$
$648$		−	28.2955i		−	1.11155i
$649$	−6.98827			−0.274314
$650$	−17.3305	−	4.19655i	−0.679759	−	0.164602i
$651$		0			0
$652$		−	20.1182i		−	0.787891i
$653$	−20.3973			−0.798206			−0.399103	−	0.916906i	$-0.630678\pi$
$653$	−20.3973			−0.798206			−0.399103	+	0.916906i	$0.630678\pi$
$654$	29.7408			1.16296
$655$			4.37993i			0.171138i
$656$			7.93965i			0.309991i
$657$			14.8027i			0.577510i
$658$		0			0
$659$	32.6628			1.27236			0.636181	−	0.771540i	$-0.280513\pi$
$659$	32.6628			1.27236			0.636181	+	0.771540i	$0.280513\pi$
$660$	0.914258			0.0355875
$661$		−	9.73692i		−	0.378722i	−0.981908	−	0.189361i	$-0.939358\pi$
$661$		−	9.73692i		−	0.378722i	0.981908	−	0.189361i	$-0.0606417\pi$
$662$	−14.1341			−0.549337
$663$	6.89747	−	28.4846i	0.267876	−	1.10625i
$664$	−31.1886			−1.21035
$665$		0			0
$666$	−1.32292			−0.0512620
$667$	−29.2345			−1.13196
$668$		−	0.960502i		−	0.0371630i
$669$			16.4524i			0.636086i
$670$			6.99365i			0.270188i
$671$			3.32800i			0.128476i
$672$		0			0
$673$	−39.4512			−1.52073			−0.760367	−	0.649494i	$-0.774981\pi$
$673$	−39.4512			−1.52073			−0.760367	+	0.649494i	$0.774981\pi$
$674$			18.2748i			0.703921i
$675$	−0.989161			−0.0380728
$676$	−9.80920	−	5.04646i	−0.377277	−	0.194094i
$677$	48.6339			1.86915			0.934576	−	0.355764i	$-0.115779\pi$
$677$	48.6339			1.86915			0.934576	+	0.355764i	$0.115779\pi$
$678$		−	2.40932i		−	0.0925296i
$679$		0			0
$680$	6.39117			0.245090
$681$		−	40.9072i		−	1.56757i
$682$		−	3.33810i		−	0.127822i
$683$		−	5.70773i		−	0.218400i	−0.994020	−	0.109200i	$-0.965171\pi$
$683$		−	5.70773i		−	0.218400i	0.994020	−	0.109200i	$-0.0348289\pi$
$684$		−	12.8548i		−	0.491514i
$685$	3.88828			0.148563
$686$		0			0
$687$			26.8080i			1.02279i
$688$	−17.7373			−0.676230
$689$	0.591531	−	2.44285i	0.0225356	−	0.0930653i
$690$	−7.23104			−0.275281
$691$			41.7732i			1.58913i	0.607182	+	0.794563i	$0.292300\pi$
$691$			41.7732i			1.58913i	−0.607182	+	0.794563i	$0.707700\pi$
$692$	10.1734			0.386736
$693$		0			0
$694$			0.493517i			0.0187336i
$695$		−	4.08495i		−	0.154951i
$696$		−	49.0295i		−	1.85846i
$697$			16.7693i			0.635182i
$698$	7.38071			0.279364
$699$	−42.1967			−1.59603
$700$		0			0
$701$	22.4361			0.847399			0.423700	−	0.905803i	$-0.360731\pi$
$701$	22.4361			0.847399			0.423700	+	0.905803i	$0.360731\pi$
$702$	0.807042	+	0.195424i	0.0304598	+	0.00737579i
$703$	2.20290			0.0830838
$704$			5.59948i			0.211038i
$705$	12.2760			0.462340
$706$	1.64527			0.0619207
$707$		0			0
$708$		−	20.3495i		−	0.764780i
$709$			28.7468i			1.07961i	0.841790	+	0.539804i	$0.181502\pi$
$709$			28.7468i			1.07961i	−0.841790	+	0.539804i	$0.818498\pi$
$710$		−	9.45452i		−	0.354822i
$711$	−11.3899			−0.427154
$712$	−40.8953			−1.53261
$713$		−	19.4566i		−	0.728654i
$714$		0			0
$715$	−0.376021	+	1.55286i	−0.0140624	+	0.0580735i
$716$	−8.03644			−0.300336
$717$			47.9529i			1.79083i
$718$	−29.1944			−1.08952
$719$	−4.20899			−0.156969			−0.0784844	−	0.996915i	$-0.525008\pi$
$719$	−4.20899			−0.156969			−0.0784844	+	0.996915i	$0.525008\pi$
$720$		−	2.88251i		−	0.107425i
$721$		0			0
$722$		−	8.65821i		−	0.322225i
$723$			6.76934i			0.251754i
$724$	9.70015			0.360503
$725$	−30.4050			−1.12921
$726$			27.3896i			1.01652i
$727$	43.4680			1.61214			0.806070	−	0.591820i	$-0.201591\pi$
$727$	43.4680			1.61214			0.806070	+	0.591820i	$0.201591\pi$
$728$		0			0
$729$	−25.3884			−0.940312
$730$		−	3.41187i		−	0.126279i
$731$	−37.4630			−1.38562
$732$	−9.69096			−0.358188
$733$			9.09421i			0.335902i	0.985795	+	0.167951i	$0.0537151\pi$
$733$			9.09421i			0.335902i	−0.985795	+	0.167951i	$0.946285\pi$
$734$		−	28.9525i		−	1.06866i
$735$		0			0
$736$			19.5639i			0.721133i
$737$	−7.38337			−0.271970
$738$	15.6723			0.576907
$739$			9.60867i			0.353461i	0.984259	+	0.176730i	$0.0565520\pi$
$739$			9.60867i			0.353461i	−0.984259	+	0.176730i	$0.943448\pi$
$740$	−0.224708			−0.00826044
$741$	44.3292	+	10.7342i	1.62847	+	0.394331i
$742$		0			0
$743$		−	32.1771i		−	1.18046i	−0.807234	−	0.590231i	$-0.799036\pi$
$743$		−	32.1771i		−	1.18046i	0.807234	−	0.590231i	$-0.200964\pi$
$744$	32.6308			1.19630
$745$	−2.31246			−0.0847220
$746$			4.26258i			0.156064i
$747$			29.7098i			1.08703i
$748$			2.00995i			0.0734911i
$749$		0			0
$750$	−15.6794			−0.572531
$751$	−7.79784			−0.284547			−0.142274	−	0.989827i	$-0.545441\pi$
$751$	−7.79784			−0.284547			−0.142274	+	0.989827i	$0.545441\pi$
$752$			12.7779i			0.465961i
$753$	57.2858			2.08761
$754$	24.8070	+	6.00696i	0.903417	+	0.218760i
$755$	3.05070			0.111026
$756$		0			0
$757$	17.9970			0.654110			0.327055	−	0.945005i	$-0.393944\pi$
$757$	17.9970			0.654110			0.327055	+	0.945005i	$0.393944\pi$
$758$	12.2392			0.444548
$759$		−	7.63399i		−	0.277096i
$760$			9.94627i			0.360789i
$761$		−	40.6790i		−	1.47461i	−0.675559	−	0.737306i	$-0.736098\pi$
$761$		−	40.6790i		−	1.47461i	0.675559	−	0.737306i	$-0.263902\pi$
$762$			22.2021i			0.804299i
$763$		0			0
$764$	13.3117			0.481601
$765$		−	6.08814i		−	0.220117i
$766$	−25.5301			−0.922439
$767$	34.5633	+	8.36944i	1.24801	+	0.302203i
$768$	−39.3422			−1.41964
$769$		−	39.3098i		−	1.41755i	−0.705435	−	0.708774i	$-0.749248\pi$
$769$		−	39.3098i		−	1.41755i	0.705435	−	0.708774i	$-0.250752\pi$
$770$		0			0
$771$	−8.34529			−0.300548
$772$			19.5228i			0.702640i
$773$		−	13.4736i		−	0.484611i	−0.970200	−	0.242306i	$-0.922096\pi$
$773$		−	13.4736i		−	0.484611i	0.970200	−	0.242306i	$-0.0779036\pi$
$774$			35.0124i			1.25849i
$775$		−	20.2356i		−	0.726884i
$776$	0.617515			0.0221675
$777$		0			0
$778$			30.4866i			1.09300i
$779$	−26.0973			−0.935032
$780$	−4.52183	−	1.09495i	−0.161908	−	0.0392056i
$781$	9.98137			0.357161
$782$		−	15.8971i		−	0.568478i
$783$	1.41589			0.0505998
$784$		0			0
$785$			5.95391i			0.212504i
$786$			18.2712i			0.651711i
$787$			39.8291i			1.41975i	0.704326	+	0.709877i	$0.251249\pi$
$787$			39.8291i			1.41975i	−0.704326	+	0.709877i	$0.748751\pi$
$788$			8.65821i			0.308436i
$789$	−52.1514			−1.85664
$790$	2.62525			0.0934022
$791$		0			0
$792$	6.30594			0.224072
$793$	3.98574	−	16.4600i	0.141538	−	0.584510i
$794$	10.5794			0.375448
$795$		−	1.06007i		−	0.0375969i
$796$	10.1177			0.358612
$797$	−21.2530			−0.752821			−0.376410	−	0.926453i	$-0.622842\pi$
$797$	−21.2530			−0.752821			−0.376410	+	0.926453i	$0.622842\pi$
$798$		0			0
$799$			26.9881i			0.954770i
$800$			20.3472i			0.719382i
$801$			38.9563i			1.37645i
$802$	13.5413			0.478161
$803$	3.60200			0.127112
$804$		−	21.5000i		−	0.758246i
$805$		0			0
$806$	−3.99784	+	16.5099i	−0.140818	+	0.581537i
$807$	−35.6368			−1.25447
$808$		−	52.9854i		−	1.86402i
$809$	21.4175			0.753000			0.376500	−	0.926417i	$-0.377128\pi$
$809$	21.4175			0.753000			0.376500	+	0.926417i	$0.377128\pi$
$810$	6.21260			0.218288
$811$			11.0116i			0.386669i	0.981133	+	0.193335i	$0.0619303\pi$
$811$			11.0116i			0.386669i	−0.981133	+	0.193335i	$0.938070\pi$
$812$		0			0
$813$		−	4.96896i		−	0.174269i
$814$			0.321910i			0.0112829i
$815$	14.8283			0.519412
$816$	12.8662			0.450408
$817$		−	58.3019i		−	2.03972i
$818$	−19.3765			−0.677484
$819$		0			0
$820$	2.66207			0.0929636
$821$		−	38.6685i		−	1.34954i	−0.738029	−	0.674769i	$-0.764243\pi$
$821$		−	38.6685i		−	1.34954i	0.738029	−	0.674769i	$-0.235757\pi$
$822$	16.2202			0.565744
$823$	20.4566			0.713073			0.356537	−	0.934281i	$-0.383957\pi$
$823$	20.4566			0.713073			0.356537	+	0.934281i	$0.383957\pi$
$824$		−	33.0570i		−	1.15160i
$825$		−	7.93965i		−	0.276423i
$826$		0			0
$827$		−	27.3451i		−	0.950881i	−0.879748	−	0.475440i	$-0.842289\pi$
$827$		−	27.3451i		−	0.950881i	0.879748	−	0.475440i	$-0.157711\pi$
$828$	10.9489			0.380501
$829$	−25.0086			−0.868585			−0.434292	−	0.900772i	$-0.643002\pi$
$829$	−25.0086			−0.868585			−0.434292	+	0.900772i	$0.643002\pi$
$830$		−	6.84780i		−	0.237691i
$831$	13.2112			0.458291
$832$	6.70616	−	27.6945i	0.232494	−	0.960133i
$833$		0			0
$834$		−	17.0406i		−	0.590069i
$835$	0.707945			0.0244994
$836$	−3.12799			−0.108184
$837$			0.942324i			0.0325715i
$838$		−	15.3237i		−	0.529350i
$839$			8.76981i			0.302768i	0.988475	+	0.151384i	$0.0483729\pi$
$839$			8.76981i			0.302768i	−0.988475	+	0.151384i	$0.951627\pi$
$840$		0			0
$841$	14.5218			0.500753
$842$	−4.58665			−0.158066
$843$		−	49.2009i		−	1.69457i
$844$	−13.2284			−0.455339
$845$	3.71952	−	7.22994i	0.127956	−	0.248717i
$846$	25.2227			0.867174
$847$		0			0
$848$	1.10342			0.0378914
$849$	4.21894			0.144794
$850$		−	16.5336i		−	0.567097i
$851$			1.87630i			0.0643186i
$852$			29.0652i			0.995758i
$853$			19.8232i			0.678734i	0.940654	+	0.339367i	$0.110213\pi$
$853$			19.8232i			0.678734i	−0.940654	+	0.339367i	$0.889787\pi$
$854$		0			0
$855$	9.47469			0.324028
$856$		−	18.6969i		−	0.639047i
$857$	−2.67037			−0.0912181			−0.0456090	−	0.998959i	$-0.514523\pi$
$857$	−2.67037			−0.0912181			−0.0456090	+	0.998959i	$0.514523\pi$
$858$	−1.56860	+	6.47784i	−0.0535510	+	0.221150i
$859$	38.9597			1.32929			0.664644	−	0.747160i	$-0.268583\pi$
$859$	38.9597			1.32929			0.664644	+	0.747160i	$0.268583\pi$
$860$			5.94713i			0.202795i
$861$		0			0
$862$	−15.6738			−0.533851
$863$		−	24.7976i		−	0.844121i	−0.906568	−	0.422060i	$-0.861307\pi$
$863$		−	24.7976i		−	0.844121i	0.906568	−	0.422060i	$-0.138693\pi$
$864$		−	0.947521i		−	0.0322353i
$865$			7.49840i			0.254953i
$866$		−	30.0561i		−	1.02135i
$867$	−14.1592			−0.480871
$868$		0			0
$869$			2.77154i			0.0940181i
$870$	10.7650			0.364967
$871$	36.5175	+	8.84262i	1.23735	+	0.299621i
$872$	34.8433			1.17994
$873$		−	0.588237i		−	0.0199088i
$874$	24.7399			0.836839
$875$		0			0
$876$			10.4888i			0.354385i
$877$			1.97840i			0.0668059i	0.999442	+	0.0334029i	$0.0106345\pi$
$877$			1.97840i			0.0668059i	−0.999442	+	0.0334029i	$0.989366\pi$
$878$			18.3250i			0.618440i
$879$			66.2415i			2.23427i
$880$	−0.701412			−0.0236446
$881$	17.1466			0.577683			0.288841	−	0.957377i	$-0.406730\pi$
$881$	17.1466			0.577683			0.288841	+	0.957377i	$0.406730\pi$
$882$		0			0
$883$	10.2168			0.343822			0.171911	−	0.985112i	$-0.445006\pi$
$883$	10.2168			0.343822			0.171911	+	0.985112i	$0.445006\pi$
$884$	2.40720	−	9.94102i	0.0809628	−	0.334353i
$885$	14.9987			0.504177
$886$			14.8250i			0.498055i
$887$	−50.9931			−1.71218			−0.856090	−	0.516826i	$-0.827113\pi$
$887$	−50.9931			−1.71218			−0.856090	+	0.516826i	$0.827113\pi$
$888$	−3.14676			−0.105598
$889$		0			0
$890$		−	8.97901i		−	0.300977i
$891$			6.55879i			0.219728i
$892$			5.74184i			0.192251i
$893$	−42.0003			−1.40549
$894$	−9.64659			−0.322630
$895$		−	5.92331i		−	0.197995i
$896$		0			0
$897$	−9.14277	+	37.7570i	−0.305268	+	1.26067i
$898$	35.0255			1.16882
$899$			28.9653i			0.966047i
$900$	11.3873			0.379577
$901$	2.33052			0.0776408
$902$		−	3.81360i		−	0.126979i
$903$		0			0
$904$		−	2.82268i		−	0.0938811i
$905$			7.14957i			0.237660i
$906$	12.7262			0.422799
$907$	5.78538			0.192100			0.0960501	−	0.995376i	$-0.469379\pi$
$907$	5.78538			0.192100			0.0960501	+	0.995376i	$0.469379\pi$
$908$		−	14.2765i		−	0.473782i
$909$	−50.4732			−1.67409
$910$		0			0
$911$	−1.70706			−0.0565573			−0.0282787	−	0.999600i	$-0.509003\pi$
$911$	−1.70706			−0.0565573			−0.0282787	+	0.999600i	$0.509003\pi$
$912$			20.0231i			0.663032i
$913$	7.22940			0.239258
$914$	3.40195			0.112526
$915$		−	7.14279i		−	0.236133i
$916$			9.35590i			0.309128i
$917$		0			0
$918$			0.769931i			0.0254115i
$919$	37.2050			1.22728			0.613640	−	0.789586i	$-0.289705\pi$
$919$	37.2050			1.22728			0.613640	+	0.789586i	$0.289705\pi$
$920$	−8.47164			−0.279302
$921$			30.9123i			1.01859i
$922$	−0.216782			−0.00713933
$923$	−49.3669	−	11.9541i	−1.62493	−	0.393474i
$924$		0			0
$925$			1.95142i			0.0641623i
$926$	−18.4695			−0.606945
$927$	−31.4897			−1.03426
$928$		−	29.1251i		−	0.956077i
$929$			19.9046i			0.653048i	0.945189	+	0.326524i	$0.105877\pi$
$929$			19.9046i			0.653048i	−0.945189	+	0.326524i	$0.894123\pi$
$930$			7.16447i			0.234932i
$931$		0			0
$932$	−14.7265			−0.482383
$933$	23.3872			0.765661
$934$		−	0.205135i		−	0.00671222i
$935$	−1.48145			−0.0484485
$936$	−31.1886	−	7.55225i	−1.01943	−	0.246853i
$937$	−7.16949			−0.234217			−0.117109	−	0.993119i	$-0.537363\pi$
$937$	−7.16949			−0.234217			−0.117109	+	0.993119i	$0.537363\pi$
$938$		0			0
$939$	21.9446			0.716134
$940$	4.28428			0.139738
$941$			3.06072i			0.0997766i	0.998755	+	0.0498883i	$0.0158865\pi$
$941$			3.06072i			0.0997766i	−0.998755	+	0.0498883i	$0.984113\pi$
$942$			24.8371i			0.809237i
$943$		−	22.2281i		−	0.723846i
$944$			15.6120i			0.508126i
$945$		0			0
$946$	8.51968			0.276999
$947$		−	44.2056i		−	1.43649i	−0.695791	−	0.718244i	$-0.744946\pi$
$947$		−	44.2056i		−	1.43649i	0.695791	−	0.718244i	$-0.255054\pi$
$948$	−8.07058			−0.262120
$949$	−17.8151	−	4.31390i	−0.578304	−	0.140035i
$950$	25.7304			0.834806
$951$			59.8762i			1.94162i
$952$		0			0
$953$	13.7002			0.443791			0.221896	−	0.975070i	$-0.428776\pi$
$953$	13.7002			0.443791			0.221896	+	0.975070i	$0.428776\pi$
$954$		−	2.17807i		−	0.0705176i
$955$			9.81149i			0.317492i
$956$			16.7354i			0.541262i
$957$			11.3648i			0.367373i
$958$	−23.0476			−0.744634
$959$		0			0
$960$		−	12.0180i		−	0.387879i
$961$	11.7226			0.378147
$962$	0.385532	−	1.59214i	0.0124301	−	0.0513325i
$963$	−17.8104			−0.573933
$964$			2.36248i			0.0760903i
$965$	−14.3894			−0.463211
$966$		0			0
$967$			43.9429i			1.41311i	0.707659	+	0.706554i	$0.249751\pi$
$967$			43.9429i			1.41311i	−0.707659	+	0.706554i	$0.750249\pi$
$968$			32.0887i			1.03137i
$969$			42.2907i			1.35857i
$970$			0.135582i			0.00435329i
$971$	21.3171			0.684098			0.342049	−	0.939682i	$-0.388879\pi$
$971$	21.3171			0.684098			0.342049	+	0.939682i	$0.388879\pi$
$972$	−18.5525			−0.595072
$973$		0			0
$974$	−20.4400			−0.654941
$975$	−9.50884	+	39.2687i	−0.304527	+	1.25761i
$976$	7.43482			0.237983
$977$			16.4466i			0.526173i	0.964772	+	0.263087i	$0.0847405\pi$
$977$			16.4466i			0.526173i	−0.964772	+	0.263087i	$0.915260\pi$
$978$	61.8572			1.97797
$979$	9.47937			0.302962
$980$		0			0
$981$		−	33.1913i		−	1.05972i
$982$		−	38.3681i		−	1.22437i
$983$		−	11.7104i		−	0.373504i	−0.982407	−	0.186752i	$-0.940204\pi$
$983$		−	11.7104i		−	0.373504i	0.982407	−	0.186752i	$-0.0597961\pi$
$984$	37.2790			1.18841
$985$	−6.38160			−0.203335
$986$			23.6662i			0.753687i
$987$		0			0
$988$	15.4708	+	3.74621i	0.492190	+	0.119183i
$989$	49.6581			1.57903
$990$			1.38454i			0.0440036i
$991$	−31.3747			−0.996650			−0.498325	−	0.866990i	$-0.666051\pi$
$991$	−31.3747			−0.996650			−0.498325	+	0.866990i	$0.666051\pi$
$992$	19.3837			0.615434
$993$			32.0260i			1.01632i
$994$		0			0
$995$			7.45731i			0.236413i
$996$			21.0516i			0.667046i
$997$	4.69711			0.148759			0.0743794	−	0.997230i	$-0.476302\pi$
$997$	4.69711			0.148759			0.0743794	+	0.997230i	$0.476302\pi$
$998$	−18.9814			−0.600847
$999$		−	0.0908732i		−	0.00287510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.c.e.246.6		8
7.2	even	3		637.2.r.f.116.6		16
7.3	odd	6		91.2.r.a.51.3	yes	16
7.4	even	3		637.2.r.f.324.3		16
7.5	odd	6		91.2.r.a.25.6	yes	16
7.6	odd	2		637.2.c.f.246.6		8
13.5	odd	4		8281.2.a.cj.1.6		8
13.8	odd	4		8281.2.a.cj.1.3		8
13.12	even	2	inner	637.2.c.e.246.3		8
21.5	even	6		819.2.dl.e.298.3		16
21.17	even	6		819.2.dl.e.415.6		16
91.5	even	12		1183.2.e.i.508.3		16
91.12	odd	6		91.2.r.a.25.3	✓	16
91.25	even	6		637.2.r.f.324.6		16
91.31	even	12		1183.2.e.i.170.3		16
91.34	even	4		8281.2.a.ck.1.3		8
91.38	odd	6		91.2.r.a.51.6	yes	16
91.47	even	12		1183.2.e.i.508.6		16
91.51	even	6		637.2.r.f.116.3		16
91.73	even	12		1183.2.e.i.170.6		16
91.83	even	4		8281.2.a.ck.1.6		8
91.90	odd	2		637.2.c.f.246.3		8
273.38	even	6		819.2.dl.e.415.3		16
273.194	even	6		819.2.dl.e.298.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.r.a.25.3	✓	16	91.12	odd	6
91.2.r.a.25.6	yes	16	7.5	odd	6
91.2.r.a.51.3	yes	16	7.3	odd	6
91.2.r.a.51.6	yes	16	91.38	odd	6
637.2.c.e.246.3		8	13.12	even	2	inner
637.2.c.e.246.6		8	1.1	even	1	trivial
637.2.c.f.246.3		8	91.90	odd	2
637.2.c.f.246.6		8	7.6	odd	2
637.2.r.f.116.3		16	91.51	even	6
637.2.r.f.116.6		16	7.2	even	3
637.2.r.f.324.3		16	7.4	even	3
637.2.r.f.324.6		16	91.25	even	6
819.2.dl.e.298.3		16	21.5	even	6
819.2.dl.e.298.6		16	273.194	even	6
819.2.dl.e.415.3		16	273.38	even	6
819.2.dl.e.415.6		16	21.17	even	6
1183.2.e.i.170.3		16	91.31	even	12
1183.2.e.i.170.6		16	91.73	even	12
1183.2.e.i.508.3		16	91.5	even	12
1183.2.e.i.508.6		16	91.47	even	12
8281.2.a.cj.1.3		8	13.8	odd	4
8281.2.a.cj.1.6		8	13.5	odd	4
8281.2.a.ck.1.3		8	91.34	even	4
8281.2.a.ck.1.6		8	91.83	even	4

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.07305i q^{2} +2.43140 q^{3} +0.848553 q^{4} +0.625432i q^{5} +2.60903i q^{6} +3.05665i q^{8} +2.91173 q^{9} +O(q^{10})\)	\(q+1.07305i q^{2} +2.43140 q^{3} +0.848553 q^{4} +0.625432i q^{5} +2.60903i q^{6} +3.05665i q^{8} +2.91173 q^{9} -0.671123 q^{10} -0.708521i q^{11} +2.06318 q^{12} +(-0.848553 + 3.50428i) q^{13} +1.52068i q^{15} -1.58285 q^{16} -3.34313 q^{17} +3.12445i q^{18} -5.20276i q^{19} +0.530712i q^{20} +0.760282 q^{22} +4.43140 q^{23} +7.43196i q^{24} +4.60883 q^{25} +(-3.76028 - 0.910544i) q^{26} -0.214623 q^{27} -6.59711 q^{29} -1.63177 q^{30} -4.39061i q^{31} +4.41482i q^{32} -1.72270i q^{33} -3.58737i q^{34} +2.47076 q^{36} +0.423409i q^{37} +5.58285 q^{38} +(-2.06318 + 8.52032i) q^{39} -1.91173 q^{40} -5.01604i q^{41} +11.2059 q^{43} -0.601218i q^{44} +1.82109i q^{45} +4.75514i q^{46} -8.07269i q^{47} -3.84855 q^{48} +4.94553i q^{50} -8.12851 q^{51} +(-0.720042 + 2.97356i) q^{52} -0.697106 q^{53} -0.230302i q^{54} +0.443132 q^{55} -12.6500i q^{57} -7.07906i q^{58} -9.86319i q^{59} +1.29038i q^{60} -4.69711 q^{61} +4.71136 q^{62} -7.90305 q^{64} +(-2.19169 - 0.530712i) q^{65} +1.84855 q^{66} -10.4208i q^{67} -2.83683 q^{68} +10.7745 q^{69} +14.0876i q^{71} +8.90015i q^{72} +5.08383i q^{73} -0.454341 q^{74} +11.2059 q^{75} -4.41482i q^{76} +(-9.14277 - 2.21390i) q^{78} -3.91173 q^{79} -0.989966i q^{80} -9.25702 q^{81} +5.38249 q^{82} +10.2035i q^{83} -2.09090i q^{85} +12.0246i q^{86} -16.0402 q^{87} +2.16570 q^{88} +13.3791i q^{89} -1.95413 q^{90} +3.76028 q^{92} -10.6753i q^{93} +8.66244 q^{94} +3.25397 q^{95} +10.7342i q^{96} -0.202023i q^{97} -2.06302i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 6 q^{4} + 12 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 - 6 * q^4 + 12 * q^9	\( 8 q - 4 q^{3} - 6 q^{4} + 12 q^{9} - 6 q^{10} + 18 q^{12} + 6 q^{13} - 2 q^{16} + 8 q^{17} - 18 q^{22} + 12 q^{23} - 6 q^{26} - 16 q^{27} - 8 q^{29} - 38 q^{30} - 28 q^{36} + 34 q^{38} - 18 q^{39} - 4 q^{40} + 8 q^{43} - 18 q^{48} - 16 q^{51} - 42 q^{52} + 20 q^{53} - 12 q^{55} - 12 q^{61} - 22 q^{62} + 44 q^{64} + 30 q^{65} + 2 q^{66} - 2 q^{68} + 28 q^{69} - 42 q^{74} + 8 q^{75} + 10 q^{78} - 20 q^{79} + 24 q^{81} - 16 q^{82} - 68 q^{87} - 4 q^{88} + 108 q^{90} + 6 q^{92} - 26 q^{94} + 16 q^{95}+O(q^{100}) \) 8 * q - 4 * q^3 - 6 * q^4 + 12 * q^9 - 6 * q^10 + 18 * q^12 + 6 * q^13 - 2 * q^16 + 8 * q^17 - 18 * q^22 + 12 * q^23 - 6 * q^26 - 16 * q^27 - 8 * q^29 - 38 * q^30 - 28 * q^36 + 34 * q^38 - 18 * q^39 - 4 * q^40 + 8 * q^43 - 18 * q^48 - 16 * q^51 - 42 * q^52 + 20 * q^53 - 12 * q^55 - 12 * q^61 - 22 * q^62 + 44 * q^64 + 30 * q^65 + 2 * q^66 - 2 * q^68 + 28 * q^69 - 42 * q^74 + 8 * q^75 + 10 * q^78 - 20 * q^79 + 24 * q^81 - 16 * q^82 - 68 * q^87 - 4 * q^88 + 108 * q^90 + 6 * q^92 - 26 * q^94 + 16 * q^95

Introduction

L-functions

Modular forms

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