LMFDB - Embedded newform 637.2.c.f.246.2

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			246.2
Root			$-2.12549i$ of defining polynomial
Character	$\chi$	$=$	637.246
Dual form			637.2.c.f.246.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12549i q^{2} -0.178854 q^{3} -2.51771 q^{4} +3.60603i q^{5} +0.380153i q^{6} +1.10038i q^{8} -2.96801 q^{9} +O(q^{10})$	\(q-2.12549i q^{2} -0.178854 q^{3} -2.51771 q^{4} +3.60603i q^{5} +0.380153i q^{6} +1.10038i q^{8} -2.96801 q^{9} +7.66457 q^{10} -3.99236i q^{11} +0.450303 q^{12} +(-2.51771 - 2.58092i) q^{13} -0.644954i q^{15} -2.69656 q^{16} -4.78916 q^{17} +6.30848i q^{18} -3.15060i q^{19} -9.07892i q^{20} -8.48572 q^{22} +2.17885 q^{23} -0.196808i q^{24} -8.00343 q^{25} +(-5.48572 + 5.35136i) q^{26} +1.06740 q^{27} -6.57198 q^{29} -1.37084 q^{30} +1.48672i q^{31} +7.93228i q^{32} +0.714051i q^{33} +10.1793i q^{34} +7.47259 q^{36} -4.96503i q^{37} -6.69656 q^{38} +(0.450303 + 0.461609i) q^{39} -3.96801 q^{40} -2.11931i q^{41} -1.43145 q^{43} +10.0516i q^{44} -10.7027i q^{45} -4.63113i q^{46} -1.01893i q^{47} +0.482292 q^{48} +17.0112i q^{50} +0.856562 q^{51} +(6.33885 + 6.49800i) q^{52} +6.03542 q^{53} -2.26876i q^{54} +14.3966 q^{55} +0.563498i q^{57} +13.9687i q^{58} +4.90322i q^{59} +1.62380i q^{60} -2.03542 q^{61} +3.16000 q^{62} +11.4669 q^{64} +(9.30686 - 9.07892i) q^{65} +1.51771 q^{66} +3.91090i q^{67} +12.0577 q^{68} -0.389698 q^{69} -8.80684i q^{71} -3.26595i q^{72} -3.08878i q^{73} -10.5531 q^{74} +1.43145 q^{75} +7.93228i q^{76} +(0.981145 - 0.957115i) q^{78} +1.96801 q^{79} -9.72388i q^{80} +8.71312 q^{81} -4.50457 q^{82} +7.66020i q^{83} -17.2698i q^{85} +3.04253i q^{86} +1.17543 q^{87} +4.39312 q^{88} +12.7992i q^{89} -22.7485 q^{90} -5.48572 q^{92} -0.265906i q^{93} -2.16572 q^{94} +11.3611 q^{95} -1.41872i q^{96} +1.35900i q^{97} +11.8494i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.12549i		−	1.50295i	−0.659762	−	0.751474i	$-0.729343\pi$
$2$		−	2.12549i		−	1.50295i	0.659762	−	0.751474i	$-0.270657\pi$
$3$	−0.178854			−0.103262			−0.0516308	−	0.998666i	$-0.516442\pi$
$3$	−0.178854			−0.103262			−0.0516308	+	0.998666i	$0.516442\pi$
$4$	−2.51771			−1.25885
$5$			3.60603i			1.61266i	0.591463	+	0.806332i	$0.298551\pi$
$5$			3.60603i			1.61266i	−0.591463	+	0.806332i	$0.701449\pi$
$6$			0.380153i			0.155197i
$7$		0			0
$7$		0			0
$8$			1.10038i			0.389044i
$9$	−2.96801			−0.989337
$10$	7.66457			2.42375
$11$		−	3.99236i		−	1.20374i	−0.798594	−	0.601871i	$-0.794422\pi$
$11$		−	3.99236i		−	1.20374i	0.798594	−	0.601871i	$-0.205578\pi$
$12$	0.450303			0.129991
$13$	−2.51771	−	2.58092i	−0.698287	−	0.715818i
$13$	−2.51771	−	2.58092i	−0.698287	−	0.715818i
$14$		0			0
$15$		−	0.644954i		−	0.166526i
$16$	−2.69656			−0.674141
$17$	−4.78916			−1.16154			−0.580771	−	0.814067i	$-0.697249\pi$
$17$	−4.78916			−1.16154			−0.580771	+	0.814067i	$0.697249\pi$
$18$			6.30848i			1.48692i
$19$		−	3.15060i		−	0.722796i	−0.932412	−	0.361398i	$-0.882299\pi$
$19$		−	3.15060i		−	0.722796i	0.932412	−	0.361398i	$-0.117701\pi$
$20$		−	9.07892i		−	2.03011i
$21$		0			0
$22$	−8.48572			−1.80916
$23$	2.17885			0.454323			0.227161	−	0.973857i	$-0.427056\pi$
$23$	2.17885			0.454323			0.227161	+	0.973857i	$0.427056\pi$
$24$		−	0.196808i		−	0.0401733i
$25$	−8.00343			−1.60069
$26$	−5.48572	+	5.35136i	−1.07584	+	1.04949i
$27$	1.06740			0.205422
$28$		0			0
$29$	−6.57198			−1.22039			−0.610193	−	0.792253i	$-0.708908\pi$
$29$	−6.57198			−1.22039			−0.610193	+	0.792253i	$0.708908\pi$
$30$	−1.37084			−0.250280
$31$			1.48672i			0.267022i	0.991047	+	0.133511i	$0.0426252\pi$
$31$			1.48672i			0.267022i	−0.991047	+	0.133511i	$0.957375\pi$
$32$			7.93228i			1.40224i
$33$			0.714051i			0.124300i
$34$			10.1793i			1.74574i
$35$		0			0
$36$	7.47259			1.24543
$37$		−	4.96503i		−	0.816246i	−0.912927	−	0.408123i	$-0.866183\pi$
$37$		−	4.96503i		−	0.816246i	0.912927	−	0.408123i	$-0.133817\pi$
$38$	−6.69656			−1.08633
$39$	0.450303	+	0.461609i	0.0721062	+	0.0739166i
$40$	−3.96801			−0.627398
$41$		−	2.11931i		−	0.330981i	−0.986211	−	0.165490i	$-0.947079\pi$
$41$		−	2.11931i		−	0.330981i	0.986211	−	0.165490i	$-0.0529207\pi$
$42$		0			0
$43$	−1.43145			−0.218294			−0.109147	−	0.994026i	$-0.534812\pi$
$43$	−1.43145			−0.218294			−0.109147	+	0.994026i	$0.534812\pi$
$44$			10.0516i			1.51533i
$45$		−	10.7027i		−	1.59547i
$46$		−	4.63113i		−	0.682823i
$47$		−	1.01893i		−	0.148626i	−0.997235	−	0.0743129i	$-0.976324\pi$
$47$		−	1.01893i		−	0.148626i	0.997235	−	0.0743129i	$-0.0236764\pi$
$48$	0.482292			0.0696129
$49$		0			0
$50$			17.0112i			2.40575i
$51$	0.856562			0.119943
$52$	6.33885	+	6.49800i	0.879041	+	0.901111i
$53$	6.03542			0.829028			0.414514	−	0.910043i	$-0.363952\pi$
$53$	6.03542			0.829028			0.414514	+	0.910043i	$0.363952\pi$
$54$		−	2.26876i		−	0.308739i
$55$	14.3966			1.94123
$56$		0			0
$57$			0.563498i			0.0746371i
$58$			13.9687i			1.83418i
$59$			4.90322i			0.638345i	0.947697	+	0.319172i	$0.103405\pi$
$59$			4.90322i			0.638345i	−0.947697	+	0.319172i	$0.896595\pi$
$60$			1.62380i			0.209632i
$61$	−2.03542			−0.260608			−0.130304	−	0.991474i	$-0.541595\pi$
$61$	−2.03542			−0.260608			−0.130304	+	0.991474i	$0.541595\pi$
$62$	3.16000			0.401320
$63$		0			0
$64$	11.4669			1.43336
$65$	9.30686	−	9.07892i	1.15437	−	1.12610i
$66$	1.51771			0.186817
$67$			3.91090i			0.477793i	0.971045	+	0.238896i	$0.0767856\pi$
$67$			3.91090i			0.477793i	−0.971045	+	0.238896i	$0.923214\pi$
$68$	12.0577			1.46221
$69$	−0.389698			−0.0469141
$70$		0			0
$71$		−	8.80684i		−	1.04518i	−0.852584	−	0.522590i	$-0.824966\pi$
$71$		−	8.80684i		−	1.04518i	0.852584	−	0.522590i	$-0.175034\pi$
$72$		−	3.26595i		−	0.384896i
$73$		−	3.08878i		−	0.361515i	−0.983528	−	0.180757i	$-0.942145\pi$
$73$		−	3.08878i		−	0.361515i	0.983528	−	0.180757i	$-0.0578549\pi$
$74$	−10.5531			−1.22678
$75$	1.43145			0.165289
$76$			7.93228i			0.909895i
$77$		0			0
$78$	0.981145	−	0.957115i	0.111093	−	0.108372i
$79$	1.96801			0.221419			0.110709	−	0.993853i	$-0.464688\pi$
$79$	1.96801			0.221419			0.110709	+	0.993853i	$0.464688\pi$
$80$		−	9.72388i		−	1.08716i
$81$	8.71312			0.968125
$82$	−4.50457			−0.497447
$83$			7.66020i			0.840816i	0.907335	+	0.420408i	$0.138113\pi$
$83$			7.66020i			0.840816i	−0.907335	+	0.420408i	$0.861887\pi$
$84$		0			0
$85$		−	17.2698i		−	1.87318i
$86$			3.04253i			0.328084i
$87$	1.17543			0.126019
$88$	4.39312			0.468309
$89$			12.7992i			1.35671i	0.734733	+	0.678356i	$0.237307\pi$
$89$			12.7992i			1.35671i	−0.734733	+	0.678356i	$0.762693\pi$
$90$	−22.7485			−2.39791
$91$		0			0
$92$	−5.48572			−0.571926
$93$		−	0.265906i		−	0.0275731i
$94$	−2.16572			−0.223377
$95$	11.3611			1.16563
$96$		−	1.41872i		−	0.144798i
$97$			1.35900i			0.137986i	0.997617	+	0.0689930i	$0.0219786\pi$
$97$			1.35900i			0.137986i	−0.997617	+	0.0689930i	$0.978021\pi$
$98$		0			0
$99$			11.8494i			1.19091i
$100$	20.1503			2.01503
$101$	−4.28801			−0.426673			−0.213336	−	0.976979i	$-0.568433\pi$
$101$	−4.28801			−0.426673			−0.213336	+	0.976979i	$0.568433\pi$
$102$		−	1.82061i		−	0.180268i
$103$	−14.4349			−1.42231			−0.711155	−	0.703035i	$-0.751828\pi$
$103$	−14.4349			−1.42231			−0.711155	+	0.703035i	$0.751828\pi$
$104$	2.84000	−	2.77044i	0.278485	−	0.271664i
$105$		0			0
$106$		−	12.8282i		−	1.24599i
$107$	−9.71884			−0.939556			−0.469778	−	0.882785i	$-0.655666\pi$
$107$	−9.71884			−0.939556			−0.469778	+	0.882785i	$0.655666\pi$
$108$	−2.68741			−0.258597
$109$		−	6.64855i		−	0.636816i	−0.947954	−	0.318408i	$-0.896852\pi$
$109$		−	6.64855i		−	0.636816i	0.947954	−	0.318408i	$-0.103148\pi$
$110$		−	30.5997i		−	2.91757i
$111$			0.888018i			0.0842869i
$112$		0			0
$113$	17.5434			1.65035			0.825173	−	0.564880i	$-0.191078\pi$
$113$	17.5434			1.65035			0.825173	+	0.564880i	$0.191078\pi$
$114$	1.19771			0.112176
$115$			7.85701i			0.732670i
$116$	16.5463			1.53629
$117$	7.47259	+	7.66020i	0.690841	+	0.708186i
$118$	10.4217			0.959399
$119$		0			0
$120$	0.709696			0.0647861
$121$	−4.93893			−0.448994
$122$			4.32626i			0.391681i
$123$			0.379048i			0.0341776i
$124$		−	3.74312i		−	0.336142i
$125$		−	10.8304i		−	0.968704i
$126$		0			0
$127$	−19.5143			−1.73162			−0.865809	−	0.500375i	$-0.833195\pi$
$127$	−19.5143			−1.73162			−0.865809	+	0.500375i	$0.833195\pi$
$128$		−	8.50814i		−	0.752020i
$129$	0.256021			0.0225414
$130$	−19.2972	−	19.7816i	−1.69247	−	1.73497i
$131$	19.0743			1.66653			0.833263	−	0.552877i	$-0.186470\pi$
$131$	19.0743			1.66653			0.833263	+	0.552877i	$0.186470\pi$
$132$		−	1.79777i		−	0.156476i
$133$		0			0
$134$	8.31259			0.718098
$135$			3.84909i			0.331277i
$136$		−	5.26991i		−	0.451891i
$137$			6.42890i			0.549258i	0.961550	+	0.274629i	$0.0885551\pi$
$137$			6.42890i			0.549258i	−0.961550	+	0.274629i	$0.911445\pi$
$138$			0.828298i			0.0705094i
$139$	−2.42854			−0.205986			−0.102993	−	0.994682i	$-0.532842\pi$
$139$	−2.42854			−0.205986			−0.102993	+	0.994682i	$0.532842\pi$
$140$		0			0
$141$			0.182240i			0.0153473i
$142$	−18.7188			−1.57085
$143$	−10.3040	+	10.0516i	−0.861660	+	0.840557i
$144$	8.00343			0.666952
$145$		−	23.6987i		−	1.96807i
$146$	−6.56518			−0.543338
$147$		0			0
$148$			12.5005i			1.02753i
$149$		−	0.115353i		−	0.00945007i	−0.999989	−	0.00472503i	$-0.998496\pi$
$149$		−	0.115353i		−	0.00945007i	0.999989	−	0.00472503i	$-0.00150403\pi$
$150$		−	3.04253i		−	0.248421i
$151$		−	11.8031i		−	0.960523i	−0.877125	−	0.480262i	$-0.840542\pi$
$151$		−	11.8031i		−	0.960523i	0.877125	−	0.480262i	$-0.159458\pi$
$152$	3.46686			0.281200
$153$	14.2143			1.14916
$154$		0			0
$155$	−5.36114			−0.430617
$156$	−1.13373	−	1.16220i	−0.0907712	−	0.0930502i
$157$	−13.1469			−1.04923			−0.524617	−	0.851338i	$-0.675791\pi$
$157$	−13.1469			−1.04923			−0.524617	+	0.851338i	$0.675791\pi$
$158$		−	4.18299i		−	0.332781i
$159$	−1.07946			−0.0856068
$160$	−28.6040			−2.26135
$161$		0			0
$162$		−	18.5197i		−	1.45504i
$163$		−	18.6485i		−	1.46066i	−0.683094	−	0.730331i	$-0.739366\pi$
$163$		−	18.6485i		−	1.46066i	0.683094	−	0.730331i	$-0.260634\pi$
$164$			5.33581i			0.416656i
$165$	−2.57489			−0.200455
$166$	16.2817			1.26370
$167$		−	0.972672i		−	0.0752676i	−0.999292	−	0.0376338i	$-0.988018\pi$
$167$		−	0.972672i		−	0.0752676i	0.999292	−	0.0376338i	$-0.0119820\pi$
$168$		0			0
$169$	−0.322293	+	12.9960i	−0.0247917	+	0.999693i
$170$	−36.7068			−2.81529
$171$			9.35101i			0.715089i
$172$	3.60397			0.274800
$173$	−2.45710			−0.186810			−0.0934050	−	0.995628i	$-0.529775\pi$
$173$	−2.45710			−0.186810			−0.0934050	+	0.995628i	$0.529775\pi$
$174$		−	2.49836i		−	0.189400i
$175$		0			0
$176$			10.7656i			0.811491i
$177$		−	0.876962i		−	0.0659165i
$178$	27.2046			2.03907
$179$	−14.4726			−1.08173			−0.540866	−	0.841109i	$-0.681903\pi$
$179$	−14.4726			−1.08173			−0.540866	+	0.841109i	$0.681903\pi$
$180$			26.9463i			2.00846i
$181$	−9.17885			−0.682259			−0.341129	−	0.940016i	$-0.610809\pi$
$181$	−9.17885			−0.682259			−0.341129	+	0.940016i	$0.610809\pi$
$182$		0			0
$183$	0.364043			0.0269108
$184$			2.39757i			0.176752i
$185$	17.9040			1.31633
$186$	−0.565180			−0.0414410
$187$			19.1200i			1.39820i
$188$			2.56536i			0.187098i
$189$		0			0
$190$		−	24.1480i		−	1.75188i
$191$	17.5840			1.27234			0.636168	−	0.771551i	$-0.280518\pi$
$191$	17.5840			1.27234			0.636168	+	0.771551i	$0.280518\pi$
$192$	−2.05090			−0.148011
$193$		−	19.7558i		−	1.42206i	−0.703164	−	0.711028i	$-0.748230\pi$
$193$		−	19.7558i		−	1.42206i	0.703164	−	0.711028i	$-0.251770\pi$
$194$	2.88855			0.207386
$195$	−1.66457	+	1.62380i	−0.119203	+	0.116283i
$196$		0			0
$197$		−	7.66020i		−	0.545767i	−0.962047	−	0.272883i	$-0.912023\pi$
$197$		−	7.66020i		−	0.545767i	0.962047	−	0.272883i	$-0.0879773\pi$
$198$	25.1857			1.78987
$199$	6.54342			0.463851			0.231925	−	0.972734i	$-0.425498\pi$
$199$	6.54342			0.463851			0.231925	+	0.972734i	$0.425498\pi$
$200$		−	8.80684i		−	0.622737i
$201$		−	0.699482i		−	0.0493377i
$202$			9.11412i			0.641267i
$203$		0			0
$204$	−2.15657			−0.150990
$205$	7.64229			0.533761
$206$			30.6812i			2.13766i
$207$	−6.46686			−0.449478
$208$	6.78916	+	6.95961i	0.470743	+	0.482562i
$209$	−12.5783			−0.870060
$210$		0			0
$211$	20.0452			1.37997			0.689983	−	0.723825i	$-0.257618\pi$
$211$	20.0452			1.37997			0.689983	+	0.723825i	$0.257618\pi$
$212$	−15.1954			−1.04363
$213$			1.57514i			0.107927i
$214$			20.6573i			1.41210i
$215$		−	5.16184i		−	0.352035i
$216$			1.17455i			0.0799183i
$217$		0			0
$218$	−14.1314			−0.957102
$219$			0.552443i			0.0373306i
$220$	−36.2463			−2.44373
$221$	12.0577	+	12.3604i	0.811089	+	0.831452i
$222$	1.88747			0.126679
$223$		−	27.7139i		−	1.85586i	−0.372752	−	0.927931i	$-0.621586\pi$
$223$		−	27.7139i		−	1.85586i	0.372752	−	0.927931i	$-0.378414\pi$
$224$		0			0
$225$	23.7543			1.58362
$226$		−	37.2884i		−	2.48038i
$227$		−	11.3711i		−	0.754726i	−0.926065	−	0.377363i	$-0.876831\pi$
$227$		−	11.3711i		−	0.754726i	0.926065	−	0.377363i	$-0.123169\pi$
$228$		−	1.41872i		−	0.0939573i
$229$		−	8.71113i		−	0.575647i	−0.957683	−	0.287824i	$-0.907068\pi$
$229$		−	8.71113i		−	0.575647i	0.957683	−	0.287824i	$-0.0929317\pi$
$230$	16.7000			1.10116
$231$		0			0
$232$		−	7.23170i		−	0.474784i
$233$	3.36456			0.220420			0.110210	−	0.993908i	$-0.464848\pi$
$233$	3.36456			0.220420			0.110210	+	0.993908i	$0.464848\pi$
$234$	16.2817	−	15.8829i	1.06437	−	1.03830i
$235$	3.67428			0.239684
$236$		−	12.3449i		−	0.803583i
$237$	−0.351987			−0.0228640
$238$		0			0
$239$			19.8798i			1.28592i	0.765902	+	0.642958i	$0.222293\pi$
$239$			19.8798i			1.28592i	−0.765902	+	0.642958i	$0.777707\pi$
$240$			1.73916i			0.112262i
$241$		−	18.8719i		−	1.21565i	−0.794073	−	0.607823i	$-0.792043\pi$
$241$		−	18.8719i		−	1.21565i	0.794073	−	0.607823i	$-0.207957\pi$
$242$			10.4976i			0.674814i
$243$	−4.76059			−0.305392
$244$	5.12458			0.328068
$245$		0			0
$246$	0.805663			0.0513672
$247$	−8.13144	+	7.93228i	−0.517391	+	0.504719i
$248$	−1.63596			−0.103883
$249$		−	1.37006i		−	0.0868240i
$250$	−23.0200			−1.45591
$251$	9.79601			0.618319			0.309159	−	0.951010i	$-0.399952\pi$
$251$	9.79601			0.618319			0.309159	+	0.951010i	$0.399952\pi$
$252$		0			0
$253$		−	8.69877i		−	0.546887i
$254$			41.4775i			2.60253i
$255$			3.08878i			0.193427i
$256$	4.84976			0.303110
$257$	−20.9394			−1.30617			−0.653083	−	0.757286i	$-0.726525\pi$
$257$	−20.9394			−1.30617			−0.653083	+	0.757286i	$0.726525\pi$
$258$		−	0.544170i		−	0.0338785i
$259$		0			0
$260$	−23.4320	+	22.8581i	−1.45319	+	1.41760i
$261$	19.5057			1.20737
$262$		−	40.5421i		−	2.50470i
$263$	−7.38679			−0.455489			−0.227745	−	0.973721i	$-0.573135\pi$
$263$	−7.38679			−0.455489			−0.227745	+	0.973721i	$0.573135\pi$
$264$	−0.785730			−0.0483583
$265$			21.7639i			1.33694i
$266$		0			0
$267$		−	2.28919i		−	0.140096i
$268$		−	9.84651i		−	0.601471i
$269$	22.7892			1.38948			0.694740	−	0.719261i	$-0.255520\pi$
$269$	22.7892			1.38948			0.694740	+	0.719261i	$0.255520\pi$
$270$	8.18120			0.497892
$271$		−	4.16633i		−	0.253086i	−0.991961	−	0.126543i	$-0.959612\pi$
$271$		−	4.16633i		−	0.253086i	0.991961	−	0.126543i	$-0.0403882\pi$
$272$	12.9143			0.783042
$273$		0			0
$274$	13.6646			0.825507
$275$			31.9526i			1.92681i
$276$	0.981145			0.0590580
$277$	−0.777101			−0.0466915			−0.0233457	−	0.999727i	$-0.507432\pi$
$277$	−0.777101			−0.0466915			−0.0233457	+	0.999727i	$0.507432\pi$
$278$			5.16184i			0.309587i
$279$		−	4.41259i		−	0.264175i
$280$		0			0
$281$			11.8988i			0.709824i	0.934900	+	0.354912i	$0.115489\pi$
$281$			11.8988i			0.709824i	−0.934900	+	0.354912i	$0.884511\pi$
$282$	0.387349			0.0230663
$283$	15.9040			0.945397			0.472698	−	0.881224i	$-0.343280\pi$
$283$	15.9040			0.945397			0.472698	+	0.881224i	$0.343280\pi$
$284$			22.1730i			1.31573i
$285$	−2.03199			−0.120365
$286$	21.3646	+	21.9010i	1.26331	+	1.29503i
$287$		0			0
$288$		−	23.5431i		−	1.38729i
$289$	5.93602			0.349178
$290$	−50.3714			−2.95791
$291$		−	0.243064i		−	0.0142487i
$292$			7.77666i			0.455094i
$293$			6.73698i			0.393579i	0.980446	+	0.196789i	$0.0630515\pi$
$293$			6.73698i			0.393579i	−0.980446	+	0.196789i	$0.936949\pi$
$294$		0			0
$295$	−17.6811			−1.02944
$296$	5.46344			0.317556
$297$		−	4.26146i		−	0.247275i
$298$	−0.245181			−0.0142030
$299$	−5.48572	−	5.62345i	−0.317247	−	0.325212i
$300$	−3.60397			−0.208075
$301$		0			0
$302$	−25.0874			−1.44362
$303$	0.766929			0.0440589
$304$			8.49578i			0.487266i
$305$		−	7.33976i		−	0.420274i
$306$		−	30.2123i		−	1.72712i
$307$		−	14.7179i		−	0.839996i	−0.907525	−	0.419998i	$-0.862031\pi$
$307$		−	14.7179i		−	0.839996i	0.907525	−	0.419998i	$-0.137969\pi$
$308$		0			0
$309$	2.58174			0.146870
$310$			11.3950i			0.647195i
$311$	−28.6578			−1.62503			−0.812517	−	0.582938i	$-0.801903\pi$
$311$	−28.6578			−1.62503			−0.812517	+	0.582938i	$0.801903\pi$
$312$	−0.507947	+	0.495506i	−0.0287568	+	0.0280525i
$313$	−32.8251			−1.85538			−0.927692	−	0.373347i	$-0.878210\pi$
$313$	−32.8251			−1.85538			−0.927692	+	0.373347i	$0.878210\pi$
$314$			27.9435i			1.57694i
$315$		0			0
$316$	−4.95488			−0.278734
$317$		−	10.4121i		−	0.584802i	−0.956296	−	0.292401i	$-0.905546\pi$
$317$		−	10.4121i		−	0.584802i	0.956296	−	0.292401i	$-0.0944542\pi$
$318$			2.29438i			0.128663i
$319$			26.2377i			1.46903i
$320$			41.3498i			2.31152i
$321$	1.73826			0.0970201
$322$		0			0
$323$			15.0887i			0.839558i
$324$	−21.9371			−1.21873
$325$	20.1503	+	20.6562i	1.11774	+	1.14580i
$326$	−39.6371			−2.19530
$327$			1.18912i			0.0657587i
$328$	2.33205			0.128766
$329$		0			0
$330$			5.47290i			0.301273i
$331$			4.46015i			0.245152i	0.992459	+	0.122576i	$0.0391155\pi$
$331$			4.46015i			0.245152i	−0.992459	+	0.122576i	$0.960885\pi$
$332$		−	19.2861i		−	1.05846i
$333$			14.7363i			0.807542i
$334$	−2.06740			−0.113123
$335$	−14.1028			−0.770519
$336$		0			0
$337$	10.7949			0.588034			0.294017	−	0.955800i	$-0.405008\pi$
$337$	10.7949			0.588034			0.294017	+	0.955800i	$0.405008\pi$
$338$	27.6229	+	0.685030i	1.50249	+	0.0372607i
$339$	−3.13772			−0.170417
$340$			43.4804i			2.35805i
$341$	5.93550			0.321425
$342$	19.8755			1.07474
$343$		0			0
$344$		−	1.57514i		−	0.0849259i
$345$		−	1.40526i		−	0.0756567i
$346$			5.22255i			0.280766i
$347$	−4.07031			−0.218506			−0.109253	−	0.994014i	$-0.534846\pi$
$347$	−4.07031			−0.218506			−0.109253	+	0.994014i	$0.534846\pi$
$348$	−2.95938			−0.158640
$349$		−	23.8727i		−	1.27788i	−0.769258	−	0.638938i	$-0.779374\pi$
$349$		−	23.8727i		−	1.27788i	0.769258	−	0.638938i	$-0.220626\pi$
$350$		0			0
$351$	−2.68741	−	2.75489i	−0.143444	−	0.147045i
$352$	31.6685			1.68794
$353$			26.0839i			1.38831i	0.719826	+	0.694154i	$0.244221\pi$
$353$			26.0839i			1.38831i	−0.719826	+	0.694154i	$0.755779\pi$
$354$	−1.86397			−0.0990691
$355$	31.7577			1.68552
$356$		−	32.2246i		−	1.70790i
$357$		0			0
$358$			30.7613i			1.62579i
$359$			22.8944i			1.20832i	0.796863	+	0.604160i	$0.206491\pi$
$359$			22.8944i			1.20832i	−0.796863	+	0.604160i	$0.793509\pi$
$360$	11.7771			0.620708
$361$	9.07374			0.477565
$362$			19.5096i			1.02540i
$363$	0.883349			0.0463638
$364$		0			0
$365$	11.1382			0.583002
$366$		−	0.773770i		−	0.0404456i
$367$	−18.1601			−0.947947			−0.473974	−	0.880539i	$-0.657181\pi$
$367$	−18.1601			−0.947947			−0.473974	+	0.880539i	$0.657181\pi$
$368$	−5.87542			−0.306277
$369$			6.29014i			0.327452i
$370$		−	38.0548i		−	1.97838i
$371$		0			0
$372$			0.669473i			0.0347105i
$373$	−15.8691			−0.821673			−0.410836	−	0.911709i	$-0.634763\pi$
$373$	−15.8691			−0.821673			−0.410836	+	0.911709i	$0.634763\pi$
$374$	40.6394			2.10142
$375$			1.93707i			0.100030i
$376$	1.12121			0.0578220
$377$	16.5463	+	16.9618i	0.852179	+	0.873575i
$378$		0			0
$379$			27.7634i			1.42611i	0.701108	+	0.713055i	$0.252689\pi$
$379$			27.7634i			1.42611i	−0.701108	+	0.713055i	$0.747311\pi$
$380$	−28.6040			−1.46736
$381$	3.49022			0.178810
$382$		−	37.3747i		−	1.91226i
$383$		−	26.2469i		−	1.34115i	−0.741841	−	0.670576i	$-0.766047\pi$
$383$		−	26.2469i		−	1.34115i	0.741841	−	0.670576i	$-0.233953\pi$
$384$			1.52172i			0.0776548i
$385$		0			0
$386$	−41.9908			−2.13728
$387$	4.24855			0.215966
$388$		−	3.42158i		−	0.173704i
$389$	25.2554			1.28050			0.640250	−	0.768167i	$-0.278831\pi$
$389$	25.2554			1.28050			0.640250	+	0.768167i	$0.278831\pi$
$390$	3.45138	+	3.53803i	0.174767	+	0.179155i
$391$	−10.4349			−0.527714
$392$		0			0
$393$	−3.41151			−0.172088
$394$	−16.2817			−0.820259
$395$			7.09670i			0.357074i
$396$		−	29.8332i		−	1.49918i
$397$			14.9765i			0.751651i	0.926690	+	0.375826i	$0.122641\pi$
$397$			14.9765i			0.751651i	−0.926690	+	0.375826i	$0.877359\pi$
$398$		−	13.9080i		−	0.697143i
$399$		0			0
$400$	21.5817			1.07909
$401$			5.34408i			0.266871i	0.991058	+	0.133435i	$0.0426008\pi$
$401$			5.34408i			0.266871i	−0.991058	+	0.133435i	$0.957399\pi$
$402$	−1.48674			−0.0741520
$403$	3.83709	−	3.74312i	0.191139	−	0.186458i
$404$	10.7960			0.537119
$405$			31.4198i			1.56126i
$406$		0			0
$407$	−19.8222			−0.982549
$408$			0.942546i			0.0466630i
$409$		−	3.36517i		−	0.166397i	−0.996533	−	0.0831985i	$-0.973486\pi$
$409$		−	3.36517i		−	0.166397i	0.996533	−	0.0831985i	$-0.0265136\pi$
$410$		−	16.2436i		−	0.802215i
$411$		−	1.14984i		−	0.0567173i
$412$	36.3428			1.79048
$413$		0			0
$414$			13.7453i			0.675542i
$415$	−27.6229			−1.35595
$416$	20.4726	−	19.9712i	1.00375	−	0.979167i
$417$	0.434355			0.0212705
$418$			26.7351i			1.30766i
$419$	−28.8639			−1.41010			−0.705048	−	0.709160i	$-0.749074\pi$
$419$	−28.8639			−1.41010			−0.705048	+	0.709160i	$0.749074\pi$
$420$		0			0
$421$		−	16.6125i		−	0.809644i	−0.914395	−	0.404822i	$-0.867333\pi$
$421$		−	16.6125i		−	0.809644i	0.914395	−	0.404822i	$-0.132667\pi$
$422$		−	42.6058i		−	2.07402i
$423$			3.02419i			0.147041i
$424$			6.64127i			0.322529i
$425$	38.3297			1.85926
$426$	3.34795			0.162209
$427$		0			0
$428$	24.4692			1.18276
$429$	1.84291	−	1.79777i	0.0889764	−	0.0867972i
$430$	−10.9714			−0.529090
$431$			20.5554i			0.990120i	0.868859	+	0.495060i	$0.164854\pi$
$431$			20.5554i			0.990120i	−0.868859	+	0.495060i	$0.835146\pi$
$432$	−2.87832			−0.138483
$433$	−19.4092			−0.932748			−0.466374	−	0.884588i	$-0.654440\pi$
$433$	−19.4092			−0.932748			−0.466374	+	0.884588i	$0.654440\pi$
$434$		0			0
$435$			4.23862i			0.203226i
$436$			16.7391i			0.801658i
$437$		−	6.86469i		−	0.328383i
$438$	1.17421			0.0561060
$439$	−13.4251			−0.640746			−0.320373	−	0.947292i	$-0.603808\pi$
$439$	−13.4251			−0.640746			−0.320373	+	0.947292i	$0.603808\pi$
$440$			15.8417i			0.755225i
$441$		0			0
$442$	26.2720	−	25.6285i	1.24963	−	1.21902i
$443$	−33.5532			−1.59416			−0.797080	−	0.603874i	$-0.793623\pi$
$443$	−33.5532			−1.59416			−0.797080	+	0.603874i	$0.793623\pi$
$444$		−	2.23577i		−	0.106105i
$445$	−46.1542			−2.18792
$446$	−58.9057			−2.78927
$447$			0.0206313i			0.000975829i
$448$		0			0
$449$		−	34.4284i		−	1.62478i	−0.583117	−	0.812388i	$-0.698167\pi$
$449$		−	34.4284i		−	1.62478i	0.583117	−	0.812388i	$-0.301833\pi$
$450$		−	50.4894i		−	2.38010i
$451$	−8.46105			−0.398415
$452$	−44.1692			−2.07754
$453$			2.11104i			0.0991852i
$454$	−24.1691			−1.13431
$455$		0			0
$456$	−0.620064			−0.0290371
$457$		−	13.4793i		−	0.630537i	−0.949002	−	0.315269i	$-0.897905\pi$
$457$		−	13.4793i		−	0.630537i	0.949002	−	0.315269i	$-0.102095\pi$
$458$	−18.5154			−0.865168
$459$	−5.11197			−0.238606
$460$		−	19.7816i		−	0.922324i
$461$		−	1.35900i		−	0.0632951i	−0.999499	−	0.0316476i	$-0.989925\pi$
$461$		−	1.35900i		−	0.0632951i	0.999499	−	0.0316476i	$-0.0100754\pi$
$462$		0			0
$463$		−	2.49836i		−	0.116109i	−0.998313	−	0.0580543i	$-0.981510\pi$
$463$		−	2.49836i		−	0.116109i	0.998313	−	0.0580543i	$-0.0184897\pi$
$464$	17.7218			0.822712
$465$	0.958863			0.0444662
$466$		−	7.15135i		−	0.331280i
$467$	26.2182			1.21323			0.606617	−	0.794994i	$-0.292526\pi$
$467$	26.2182			1.21323			0.606617	+	0.794994i	$0.292526\pi$
$468$	−18.8138	−	19.2861i	−0.869668	−	0.891502i
$469$		0			0
$470$		−	7.80965i		−	0.360232i
$471$	2.35137			0.108346
$472$	−5.39542			−0.248344
$473$			5.71485i			0.262769i
$474$			0.748146i			0.0343635i
$475$			25.2156i			1.15697i
$476$		0			0
$477$	−17.9132			−0.820188
$478$	42.2542			1.93266
$479$		−	23.8461i		−	1.08956i	−0.838580	−	0.544778i	$-0.816614\pi$
$479$		−	23.8461i		−	1.08956i	0.838580	−	0.544778i	$-0.183386\pi$
$480$	5.11595			0.233510
$481$	−12.8143	+	12.5005i	−0.584284	+	0.569974i
$482$	−40.1120			−1.82705
$483$		0			0
$484$	12.4348			0.565217
$485$	−4.90061			−0.222525
$486$			10.1186i			0.458989i
$487$			10.5947i			0.480090i	0.970762	+	0.240045i	$0.0771622\pi$
$487$			10.5947i			0.480090i	−0.970762	+	0.240045i	$0.922838\pi$
$488$		−	2.23974i		−	0.101388i
$489$			3.33536i			0.150830i
$490$		0			0
$491$	19.7704			0.892224			0.446112	−	0.894977i	$-0.352808\pi$
$491$	19.7704			0.892224			0.446112	+	0.894977i	$0.352808\pi$
$492$		−	0.954332i		−	0.0430246i
$493$	31.4742			1.41753
$494$	16.8600	+	17.2833i	0.758567	+	0.777612i
$495$	−42.7291			−1.92053
$496$		−	4.00902i		−	0.180010i
$497$		0			0
$498$	−2.91205			−0.130492
$499$		−	13.1906i		−	0.590492i	−0.955421	−	0.295246i	$-0.904598\pi$
$499$		−	13.1906i		−	0.590492i	0.955421	−	0.295246i	$-0.0954017\pi$
$500$			27.2679i			1.21946i
$501$			0.173967i			0.00777226i
$502$		−	20.8213i		−	0.929301i
$503$	37.9046			1.69008			0.845040	−	0.534703i	$-0.179576\pi$
$503$	37.9046			1.69008			0.845040	+	0.534703i	$0.179576\pi$
$504$		0			0
$505$		−	15.4627i		−	0.688080i
$506$	−18.4891			−0.821943
$507$	0.0576435	−	2.32439i	0.00256004	−	0.103230i
$508$	49.1314			2.17985
$509$		−	27.6626i		−	1.22612i	−0.790035	−	0.613062i	$-0.789938\pi$
$509$		−	27.6626i		−	1.22612i	0.790035	−	0.613062i	$-0.210062\pi$
$510$	6.56518			0.290711
$511$		0			0
$512$		−	27.3244i		−	1.20758i
$513$		−	3.36296i		−	0.148478i
$514$			44.5066i			1.96310i
$515$		−	52.0525i		−	2.29371i
$516$	−0.644585			−0.0283763
$517$	−4.06792			−0.178907
$518$		0			0
$519$	0.439464			0.0192903
$520$	9.99029	+	10.2411i	0.438103	+	0.449103i
$521$	15.5668			0.681993			0.340996	−	0.940065i	$-0.389236\pi$
$521$	15.5668			0.681993			0.340996	+	0.940065i	$0.389236\pi$
$522$		−	41.4592i		−	1.81462i
$523$	27.2338			1.19085			0.595425	−	0.803411i	$-0.296984\pi$
$523$	27.2338			1.19085			0.595425	+	0.803411i	$0.296984\pi$
$524$	−48.0234			−2.09791
$525$		0			0
$526$			15.7005i			0.684577i
$527$		−	7.12011i		−	0.310157i
$528$		−	1.92548i		−	0.0837959i
$529$	−18.2526			−0.793591
$530$	46.2589			2.00936
$531$		−	14.5528i		−	0.631538i
$532$		0			0
$533$	−5.46977	+	5.33581i	−0.236922	+	0.231119i
$534$	−4.86566			−0.210557
$535$		−	35.0464i		−	1.51519i
$536$	−4.30349			−0.185883
$537$	2.58849			0.111701
$538$		−	48.4381i		−	2.08832i
$539$		0			0
$540$		−	9.69089i		−	0.417029i
$541$			24.2055i			1.04068i	0.853961	+	0.520338i	$0.174194\pi$
$541$			24.2055i			1.04068i	−0.853961	+	0.520338i	$0.825806\pi$
$542$	−8.85548			−0.380376
$543$	1.64168			0.0704512
$544$		−	37.9889i		−	1.62876i
$545$	23.9749			1.02697
$546$		0			0
$547$	−22.2177			−0.949960			−0.474980	−	0.879997i	$-0.657545\pi$
$547$	−22.2177			−0.949960			−0.474980	+	0.879997i	$0.657545\pi$
$548$		−	16.1861i		−	0.691436i
$549$	6.04114			0.257829
$550$	67.9148			2.89590
$551$			20.7057i			0.882091i
$552$		−	0.428817i		−	0.0182517i
$553$		0			0
$554$			1.65172i			0.0701749i
$555$	−3.20221			−0.135926
$556$	6.11436			0.259306
$557$		−	22.3204i		−	0.945746i	−0.881131	−	0.472873i	$-0.843217\pi$
$557$		−	22.3204i		−	0.945746i	0.881131	−	0.472873i	$-0.156783\pi$
$558$	−9.37891			−0.397041
$559$	3.60397	+	3.69445i	0.152432	+	0.156259i
$560$		0			0
$561$		−	3.41970i		−	0.144380i
$562$	25.2908			1.06683
$563$	−26.7039			−1.12543			−0.562717	−	0.826649i	$-0.690244\pi$
$563$	−26.7039			−1.12543			−0.562717	+	0.826649i	$0.690244\pi$
$564$		−	0.458826i		−	0.0193201i
$565$			63.2620i			2.66145i
$566$		−	33.8039i		−	1.42088i
$567$		0			0
$568$	9.69090			0.406621
$569$	−6.61021			−0.277114			−0.138557	−	0.990354i	$-0.544246\pi$
$569$	−6.61021			−0.277114			−0.138557	+	0.990354i	$0.544246\pi$
$570$			4.31897i			0.180902i
$571$	42.1286			1.76303			0.881513	−	0.472159i	$-0.156525\pi$
$571$	42.1286			1.76303			0.881513	+	0.472159i	$0.156525\pi$
$572$	25.9424	−	25.3070i	1.08470	−	1.05814i
$573$	−3.14498			−0.131383
$574$		0			0
$575$	−17.4383			−0.727227
$576$	−34.0338			−1.41807
$577$		−	15.8839i		−	0.661255i	−0.943761	−	0.330628i	$-0.892740\pi$
$577$		−	15.8839i		−	0.661255i	0.943761	−	0.330628i	$-0.107260\pi$
$578$		−	12.6170i		−	0.524796i
$579$			3.53342i			0.146844i
$580$			59.6665i			2.47752i
$581$		0			0
$582$	−0.516630			−0.0214150
$583$		−	24.0955i		−	0.997936i
$584$	3.39885			0.140645
$585$	−27.6229	+	26.9463i	−1.14207	+	1.11409i
$586$	14.3194			0.591528
$587$		−	18.5676i		−	0.766366i	−0.923672	−	0.383183i	$-0.874828\pi$
$587$		−	18.5676i		−	0.766366i	0.923672	−	0.383183i	$-0.125172\pi$
$588$		0			0
$589$	4.68404			0.193003
$590$			37.5811i			1.54719i
$591$			1.37006i			0.0563567i
$592$			13.3885i			0.550265i
$593$		−	20.6099i		−	0.846349i	−0.906048	−	0.423175i	$-0.860916\pi$
$593$		−	20.6099i		−	0.846349i	0.906048	−	0.423175i	$-0.139084\pi$
$594$	−9.05770			−0.371642
$595$		0			0
$596$			0.290425i			0.0118963i
$597$	−1.17032			−0.0478980
$598$	−11.9526	+	11.6598i	−0.488777	+	0.476806i
$599$	−13.6045			−0.555864			−0.277932	−	0.960601i	$-0.589649\pi$
$599$	−13.6045			−0.555864			−0.277932	+	0.960601i	$0.589649\pi$
$600$			1.57514i			0.0643049i
$601$	−12.1503			−0.495621			−0.247810	−	0.968809i	$-0.579711\pi$
$601$	−12.1503			−0.495621			−0.247810	+	0.968809i	$0.579711\pi$
$602$		0			0
$603$		−	11.6076i		−	0.472698i
$604$			29.7168i			1.20916i
$605$		−	17.8099i		−	0.724076i
$606$		−	1.63010i		−	0.0662183i
$607$	35.2332			1.43007			0.715035	−	0.699088i	$-0.246411\pi$
$607$	35.2332			1.43007			0.715035	+	0.699088i	$0.246411\pi$
$608$	24.9914			1.01354
$609$		0			0
$610$	−15.6006			−0.631650
$611$	−2.62977	+	2.56536i	−0.106389	+	0.103783i
$612$	−35.7874			−1.44662
$613$		−	30.0621i		−	1.21419i	−0.794627	−	0.607097i	$-0.792334\pi$
$613$		−	30.0621i		−	1.21419i	0.794627	−	0.607097i	$-0.207666\pi$
$614$	−31.2828			−1.26247
$615$	−1.36686			−0.0551170
$616$		0			0
$617$			7.01712i			0.282499i	0.989974	+	0.141249i	$0.0451119\pi$
$617$			7.01712i			0.282499i	−0.989974	+	0.141249i	$0.954888\pi$
$618$		−	5.48746i		−	0.220738i
$619$			43.8482i			1.76241i	0.472737	+	0.881203i	$0.343266\pi$
$619$			43.8482i			1.76241i	−0.472737	+	0.881203i	$0.656734\pi$
$620$	13.4978			0.542084
$621$	2.32572			0.0933279
$622$			60.9118i			2.44234i
$623$		0			0
$624$	−1.21427	−	1.24476i	−0.0486097	−	0.0498302i
$625$	−0.962290			−0.0384916
$626$			69.7694i			2.78855i
$627$	2.24969			0.0898438
$628$	33.1000			1.32083
$629$			23.7783i			0.948103i
$630$		0			0
$631$			23.4936i			0.935267i	0.883922	+	0.467634i	$0.154893\pi$
$631$			23.4936i			0.935267i	−0.883922	+	0.467634i	$0.845107\pi$
$632$			2.16557i			0.0861416i
$633$	−3.58517			−0.142498
$634$	−22.1308			−0.878927
$635$		−	70.3692i		−	2.79252i
$636$	2.71777			0.107766
$637$		0			0
$638$	55.7680			2.20788
$639$			26.1388i			1.03403i
$640$	30.6806			1.21276
$641$	−7.40466			−0.292467			−0.146233	−	0.989250i	$-0.546715\pi$
$641$	−7.40466			−0.292467			−0.146233	+	0.989250i	$0.546715\pi$
$642$		−	3.69465i		−	0.145816i
$643$			39.9607i			1.57590i	0.615742	+	0.787948i	$0.288856\pi$
$643$			39.9607i			1.57590i	−0.615742	+	0.787948i	$0.711144\pi$
$644$		0			0
$645$			0.923218i			0.0363517i
$646$	32.0709			1.26181
$647$	−27.2468			−1.07118			−0.535591	−	0.844478i	$-0.679911\pi$
$647$	−27.2468			−1.07118			−0.535591	+	0.844478i	$0.679911\pi$
$648$			9.58777i			0.376643i
$649$	19.5754			0.768402
$650$	43.9046	−	42.8292i	1.72208	−	1.67990i
$651$		0			0
$652$			46.9514i			1.83876i
$653$	19.1451			0.749205			0.374603	−	0.927185i	$-0.377779\pi$
$653$	19.1451			0.749205			0.374603	+	0.927185i	$0.377779\pi$
$654$	2.52747			0.0988319
$655$			68.7823i			2.68755i
$656$			5.71485i			0.223128i
$657$			9.16755i			0.357660i
$658$		0			0
$659$	41.5725			1.61943			0.809717	−	0.586820i	$-0.199620\pi$
$659$	41.5725			1.61943			0.809717	+	0.586820i	$0.199620\pi$
$660$	6.48281			0.252343
$661$		−	34.2046i		−	1.33041i	−0.746662	−	0.665203i	$-0.768345\pi$
$661$		−	34.2046i		−	1.33041i	0.746662	−	0.665203i	$-0.231655\pi$
$662$	9.48000			0.368451
$663$	−2.15657	−	2.21072i	−0.0837543	−	0.0858571i
$664$	−8.42915			−0.327115
$665$		0			0
$666$	31.3218			1.21369
$667$	−14.3194			−0.554449
$668$			2.44890i			0.0947510i
$669$			4.95676i			0.191639i
$670$			29.9754i			1.15805i
$671$			8.12611i			0.313705i
$672$		0			0
$673$	−21.4308			−0.826098			−0.413049	−	0.910709i	$-0.635536\pi$
$673$	−21.4308			−0.826098			−0.413049	+	0.910709i	$0.635536\pi$
$674$		−	22.9444i		−	0.883786i
$675$	−8.54290			−0.328816
$676$	0.811439	−	32.7201i	0.0312092	−	1.25847i
$677$	9.78166			0.375940			0.187970	−	0.982175i	$-0.439809\pi$
$677$	9.78166			0.375940			0.187970	+	0.982175i	$0.439809\pi$
$678$			6.66919i			0.256129i
$679$		0			0
$680$	19.0034			0.728748
$681$			2.03377i			0.0779342i
$682$		−	12.6159i		−	0.483086i
$683$		−	15.2764i		−	0.584533i	−0.956337	−	0.292267i	$-0.905591\pi$
$683$		−	15.2764i		−	0.584533i	0.956337	−	0.292267i	$-0.0944095\pi$
$684$		−	23.5431i		−	0.900193i
$685$	−23.1828			−0.885769
$686$		0			0
$687$			1.55802i			0.0594423i
$688$	3.85999			0.147161
$689$	−15.1954	−	15.5769i	−0.578899	−	0.593434i
$690$	−2.98687			−0.113708
$691$			42.4572i			1.61515i	0.589767	+	0.807573i	$0.299220\pi$
$691$			42.4572i			1.61515i	−0.589767	+	0.807573i	$0.700780\pi$
$692$	6.18627			0.235167
$693$		0			0
$694$			8.65141i			0.328403i
$695$		−	8.75738i		−	0.332186i
$696$			1.29342i			0.0490270i
$697$			10.1497i			0.384448i
$698$	−50.7412			−1.92058
$699$	−0.601767			−0.0227609
$700$		0			0
$701$	2.79985			0.105749			0.0528744	−	0.998601i	$-0.483162\pi$
$701$	2.79985			0.105749			0.0528744	+	0.998601i	$0.483162\pi$
$702$	−5.85548	+	5.71207i	−0.221001	+	0.215588i
$703$	−15.6428			−0.589980
$704$		−	45.7798i		−	1.72539i
$705$	−0.657161			−0.0247501
$706$	55.4412			2.08656
$707$		0			0
$708$			2.20793i			0.0829793i
$709$			14.5664i			0.547052i	0.961865	+	0.273526i	$0.0881900\pi$
$709$			14.5664i			0.547052i	−0.961865	+	0.273526i	$0.911810\pi$
$710$		−	67.5006i		−	2.53325i
$711$	−5.84108			−0.219058
$712$	−14.0840			−0.527821
$713$			3.23934i			0.121314i
$714$		0			0
$715$	−36.2463	−	37.1563i	−1.35554	−	1.38957i
$716$	36.4377			1.36174
$717$		−	3.55558i		−	0.132786i
$718$	48.6618			1.81604
$719$	−34.5057			−1.28685			−0.643423	−	0.765511i	$-0.722486\pi$
$719$	−34.5057			−1.28685			−0.643423	+	0.765511i	$0.722486\pi$
$720$			28.8606i			1.07557i
$721$		0			0
$722$		−	19.2861i		−	0.717756i
$723$			3.37532i			0.125530i
$724$	23.1097			0.858864
$725$	52.5984			1.95345
$726$		−	1.87755i		−	0.0696824i
$727$	−35.7571			−1.32616			−0.663078	−	0.748550i	$-0.730750\pi$
$727$	−35.7571			−1.32616			−0.663078	+	0.748550i	$0.730750\pi$
$728$		0			0
$729$	−25.2879			−0.936590
$730$		−	23.6742i		−	0.876222i
$731$	6.85543			0.253557
$732$	−0.916554			−0.0338768
$733$		−	41.0500i		−	1.51622i	−0.652129	−	0.758108i	$-0.726124\pi$
$733$		−	41.0500i		−	1.51622i	0.652129	−	0.758108i	$-0.273876\pi$
$734$			38.5990i			1.42472i
$735$		0			0
$736$			17.2833i			0.637071i
$737$	15.6137			0.575139
$738$	13.3696			0.492143
$739$			0.726409i			0.0267214i	0.999911	+	0.0133607i	$0.00425297\pi$
$739$			0.726409i			0.0267214i	−0.999911	+	0.0133607i	$0.995747\pi$
$740$	−45.0771			−1.65707
$741$	1.45434	−	1.41872i	0.0534266	−	0.0521181i
$742$		0			0
$743$			16.4547i			0.603664i	0.953361	+	0.301832i	$0.0975981\pi$
$743$			16.4547i			0.603664i	−0.953361	+	0.301832i	$0.902402\pi$
$744$	0.292598			0.0107272
$745$	0.415965			0.0152398
$746$			33.7297i			1.23493i
$747$		−	22.7356i		−	0.831850i
$748$		−	48.1387i		−	1.76012i
$749$		0			0
$750$	4.11723			0.150340
$751$	−25.1707			−0.918494			−0.459247	−	0.888309i	$-0.651881\pi$
$751$	−25.1707			−0.918494			−0.459247	+	0.888309i	$0.651881\pi$
$752$			2.74760i			0.100195i
$753$	−1.75206			−0.0638486
$754$	36.0520	−	35.1690i	1.31294	−	1.28078i
$755$	42.5623			1.54900
$756$		0			0
$757$	44.0743			1.60191			0.800953	−	0.598727i	$-0.204327\pi$
$757$	44.0743			1.60191			0.800953	+	0.598727i	$0.204327\pi$
$758$	59.0108			2.14337
$759$			1.55581i			0.0564724i
$760$			12.5016i			0.453481i
$761$			38.7022i			1.40295i	0.712692	+	0.701477i	$0.247476\pi$
$761$			38.7022i			1.40295i	−0.712692	+	0.701477i	$0.752524\pi$
$762$		−	7.41844i		−	0.268742i
$763$		0			0
$764$	−44.2715			−1.60169
$765$			51.2570i			1.85320i
$766$	−55.7874			−2.01568
$767$	12.6548	−	12.3449i	0.456939	−	0.445747i
$768$	−0.867401			−0.0312996
$769$		−	36.1506i		−	1.30362i	−0.758381	−	0.651811i	$-0.774009\pi$
$769$		−	36.1506i		−	1.30362i	0.758381	−	0.651811i	$-0.225991\pi$
$770$		0			0
$771$	3.74511			0.134877
$772$			49.7394i			1.79016i
$773$			30.0731i			1.08165i	0.841134	+	0.540827i	$0.181889\pi$
$773$			30.0731i			1.08165i	−0.841134	+	0.540827i	$0.818111\pi$
$774$		−	9.03026i		−	0.324586i
$775$		−	11.8988i		−	0.427418i
$776$	−1.49543			−0.0536827
$777$		0			0
$778$		−	53.6801i		−	1.92453i
$779$	−6.67709			−0.239232
$780$	4.19091	−	4.08827i	0.150059	−	0.146383i
$781$	−35.1601			−1.25813
$782$			22.1792i			0.793127i
$783$	−7.01496			−0.250694
$784$		0			0
$785$		−	47.4079i		−	1.69206i
$786$			7.25114i			0.258640i
$787$			36.8472i			1.31346i	0.754126	+	0.656730i	$0.228061\pi$
$787$			36.8472i			1.31346i	−0.754126	+	0.656730i	$0.771939\pi$
$788$			19.2861i			0.687040i
$789$	1.32116			0.0470345
$790$	15.0840			0.536663
$791$		0			0
$792$	−13.0388			−0.463315
$793$	5.12458	+	5.25325i	0.181979	+	0.186548i
$794$	31.8325			1.12969
$795$		−	3.89256i		−	0.138055i
$796$	−16.4744			−0.583920
$797$	−27.5910			−0.977323			−0.488661	−	0.872474i	$-0.662515\pi$
$797$	−27.5910			−0.977323			−0.488661	+	0.872474i	$0.662515\pi$
$798$		0			0
$799$			4.87980i			0.172635i
$800$		−	63.4854i		−	2.24455i
$801$		−	37.9882i		−	1.34225i
$802$	11.3588			0.401093
$803$	−12.3315			−0.435170
$804$			1.76109i			0.0621089i
$805$		0			0
$806$	−7.95596	−	8.15570i	−0.280237	−	0.287272i
$807$	−4.07594			−0.143480
$808$		−	4.71845i		−	0.165995i
$809$	35.7102			1.25550			0.627752	−	0.778413i	$-0.283975\pi$
$809$	35.7102			1.25550			0.627752	+	0.778413i	$0.283975\pi$
$810$	66.7824			2.34649
$811$			2.22418i			0.0781015i	0.999237	+	0.0390508i	$0.0124334\pi$
$811$			2.22418i			0.0781015i	−0.999237	+	0.0390508i	$0.987567\pi$
$812$		0			0
$813$			0.745166i			0.0261341i
$814$			42.1319i			1.47672i
$815$	67.2469			2.35556
$816$	−2.30977			−0.0808582
$817$			4.50992i			0.157782i
$818$	−7.15264			−0.250086
$819$		0			0
$820$	−19.2411			−0.671927
$821$		−	53.3694i		−	1.86260i	−0.364248	−	0.931302i	$-0.618674\pi$
$821$		−	53.3694i		−	1.86260i	0.364248	−	0.931302i	$-0.381326\pi$
$822$	−2.44397			−0.0852432
$823$	−51.2086			−1.78502			−0.892509	−	0.451029i	$-0.851057\pi$
$823$	−51.2086			−1.78502			−0.892509	+	0.451029i	$0.851057\pi$
$824$		−	15.8839i		−	0.553342i
$825$		−	5.71485i		−	0.198966i
$826$		0			0
$827$		−	8.97196i		−	0.311986i	−0.987758	−	0.155993i	$-0.950142\pi$
$827$		−	8.97196i		−	0.311986i	0.987758	−	0.155993i	$-0.0498577\pi$
$828$	16.2817			0.565827
$829$	−40.5716			−1.40911			−0.704554	−	0.709650i	$-0.748853\pi$
$829$	−40.5716			−1.40911			−0.704554	+	0.709650i	$0.748853\pi$
$830$			58.7122i			2.03793i
$831$	0.138988			0.00482144
$832$	−28.8702	−	29.5951i	−1.00089	−	1.02602i
$833$		0			0
$834$		−	0.923218i		−	0.0319684i
$835$	3.50748			0.121381
$836$	31.6685			1.09528
$837$			1.58693i			0.0548522i
$838$			61.3500i			2.11930i
$839$			32.3005i			1.11514i	0.830131	+	0.557568i	$0.188266\pi$
$839$			32.3005i			1.11514i	−0.830131	+	0.557568i	$0.811734\pi$
$840$		0			0
$841$	14.1909			0.489342
$842$	−35.3097			−1.21685
$843$		−	2.12816i		−	0.0732976i
$844$	−50.4679			−1.73718
$845$	−46.8639	−	1.16220i	−1.61217	−	0.0399808i
$846$	6.42788			0.220995
$847$		0			0
$848$	−16.2749			−0.558882
$849$	−2.84451			−0.0976232
$850$		−	81.4693i		−	2.79437i
$851$		−	10.8181i		−	0.370839i
$852$		−	3.96575i		−	0.135864i
$853$		−	35.5887i		−	1.21853i	−0.792965	−	0.609267i	$-0.791464\pi$
$853$		−	35.5887i		−	1.21853i	0.792965	−	0.609267i	$-0.208536\pi$
$854$		0			0
$855$	−33.7200			−1.15320
$856$		−	10.6945i		−	0.365529i
$857$	−46.0229			−1.57211			−0.786055	−	0.618156i	$-0.787880\pi$
$857$	−46.0229			−1.57211			−0.786055	+	0.618156i	$0.787880\pi$
$858$	−3.82115	−	3.91708i	−0.130452	−	0.133727i
$859$	25.2458			0.861377			0.430689	−	0.902501i	$-0.358271\pi$
$859$	25.2458			0.861377			0.430689	+	0.902501i	$0.358271\pi$
$860$			12.9960i			0.443160i
$861$		0			0
$862$	43.6903			1.48810
$863$			13.8337i			0.470904i	0.971886	+	0.235452i	$0.0756570\pi$
$863$			13.8337i			0.470904i	−0.971886	+	0.235452i	$0.924343\pi$
$864$			8.46696i			0.288052i
$865$		−	8.86038i		−	0.301262i
$866$			41.2541i			1.40187i
$867$	−1.06168			−0.0360567
$868$		0			0
$869$		−	7.85701i		−	0.266531i
$870$	9.00915			0.305439
$871$	10.0937	−	9.84651i	0.342013	−	0.333636i
$872$	7.31596			0.247750
$873$		−	4.03354i		−	0.136515i
$874$	−14.5908			−0.493542
$875$		0			0
$876$		−	1.39089i		−	0.0469938i
$877$		−	3.65416i		−	0.123392i	−0.998095	−	0.0616961i	$-0.980349\pi$
$877$		−	3.65416i		−	0.123392i	0.998095	−	0.0616961i	$-0.0196509\pi$
$878$			28.5349i			0.963008i
$879$		−	1.20494i		−	0.0406416i
$880$	−38.8212			−1.30866
$881$	−36.6320			−1.23416			−0.617082	−	0.786899i	$-0.711685\pi$
$881$	−36.6320			−1.23416			−0.617082	+	0.786899i	$0.711685\pi$
$882$		0			0
$883$	7.11145			0.239319			0.119660	−	0.992815i	$-0.461820\pi$
$883$	7.11145			0.239319			0.119660	+	0.992815i	$0.461820\pi$
$884$	−30.3578	−	31.1200i	−1.02104	−	1.04668i
$885$	3.16235			0.106301
$886$			71.3169i			2.39594i
$887$	−6.73546			−0.226155			−0.113077	−	0.993586i	$-0.536071\pi$
$887$	−6.73546			−0.226155			−0.113077	+	0.993586i	$0.536071\pi$
$888$	−0.977160			−0.0327913
$889$		0			0
$890$			98.1004i			3.28833i
$891$		−	34.7859i		−	1.16537i
$892$			69.7756i			2.33626i
$893$	−3.21023			−0.107426
$894$	0.0438517			0.00146662
$895$		−	52.1885i		−	1.74447i
$896$		0			0
$897$	0.981145	+	1.00578i	0.0327595	+	0.0335820i
$898$	−73.1772			−2.44195
$899$		−	9.77066i		−	0.325870i
$900$	−59.8063			−1.99354
$901$	−28.9046			−0.962950
$902$			17.9839i			0.598798i
$903$		0			0
$904$			19.3045i			0.642058i
$905$		−	33.0992i		−	1.10025i
$906$	4.48699			0.149070
$907$	4.93260			0.163784			0.0818921	−	0.996641i	$-0.473904\pi$
$907$	4.93260			0.163784			0.0818921	+	0.996641i	$0.473904\pi$
$908$			28.6291i			0.950090i
$909$	12.7269			0.422123
$910$		0			0
$911$	−26.6258			−0.882152			−0.441076	−	0.897470i	$-0.645403\pi$
$911$	−26.6258			−0.882152			−0.441076	+	0.897470i	$0.645403\pi$
$912$		−	1.51951i		−	0.0503159i
$913$	30.5823			1.01213
$914$	−28.6502			−0.947665
$915$			1.31275i			0.0433981i
$916$			21.9321i			0.724656i
$917$		0			0
$918$			10.8654i			0.358613i
$919$	−32.3836			−1.06824			−0.534118	−	0.845410i	$-0.679356\pi$
$919$	−32.3836			−1.06824			−0.534118	+	0.845410i	$0.679356\pi$
$920$	−8.64572			−0.285041
$921$			2.63237i			0.0867394i
$922$	−2.88855			−0.0951293
$923$	−22.7297	+	22.1730i	−0.748158	+	0.729835i
$924$		0			0
$925$			39.7373i			1.30655i
$926$	−5.31024			−0.174505
$927$	42.8429			1.40714
$928$		−	52.1308i		−	1.71128i
$929$			28.0271i			0.919539i	0.888038	+	0.459769i	$0.152068\pi$
$929$			28.0271i			0.919539i	−0.888038	+	0.459769i	$0.847932\pi$
$930$		−	2.03805i		−	0.0668304i
$931$		0			0
$932$	−8.47099			−0.277476
$933$	5.12557			0.167804
$934$		−	55.7266i		−	1.82343i
$935$	−68.9473			−2.25482
$936$	−8.42915	+	8.22271i	−0.275516	+	0.268768i
$937$	14.1324			0.461686			0.230843	−	0.972991i	$-0.425852\pi$
$937$	14.1324			0.461686			0.230843	+	0.972991i	$0.425852\pi$
$938$		0			0
$939$	5.87091			0.191590
$940$	−9.25076			−0.301727
$941$			8.97295i			0.292510i	0.989247	+	0.146255i	$0.0467220\pi$
$941$			8.97295i			0.292510i	−0.989247	+	0.146255i	$0.953278\pi$
$942$		−	4.99782i		−	0.162838i
$943$		−	4.61767i		−	0.150372i
$944$		−	13.2218i		−	0.430334i
$945$		0			0
$946$	12.1469			0.394929
$947$			46.2958i			1.50441i	0.658929	+	0.752205i	$0.271010\pi$
$947$			46.2958i			1.50441i	−0.658929	+	0.752205i	$0.728990\pi$
$948$	0.886202			0.0287825
$949$	−7.97190	+	7.77666i	−0.258779	+	0.252441i
$950$	53.5954			1.73887
$951$			1.86225i			0.0603876i
$952$		0			0
$953$	−19.1097			−0.619023			−0.309512	−	0.950896i	$-0.600166\pi$
$953$	−19.1097			−0.619023			−0.309512	+	0.950896i	$0.600166\pi$
$954$			38.0743i			1.23270i
$955$			63.4085i			2.05185i
$956$		−	50.0514i		−	1.61878i
$957$		−	4.69273i		−	0.151694i
$958$	−50.6846			−1.63755
$959$		0			0
$960$		−	7.39560i		−	0.238692i
$961$	28.7897			0.928699
$962$	26.5697	+	27.2368i	0.856641	+	0.878149i
$963$	28.8456			0.929538
$964$			47.5139i			1.53032i
$965$	71.2400			2.29330
$966$		0			0
$967$			22.5432i			0.724942i	0.931995	+	0.362471i	$0.118067\pi$
$967$			22.5432i			0.724942i	−0.931995	+	0.362471i	$0.881933\pi$
$968$		−	5.43472i		−	0.174678i
$969$		−	2.69868i		−	0.0866941i
$970$			10.4162i			0.334444i
$971$	27.2857			0.875640			0.437820	−	0.899063i	$-0.355751\pi$
$971$	27.2857			0.875640			0.437820	+	0.899063i	$0.355751\pi$
$972$	11.9858			0.384444
$973$		0			0
$974$	22.5188			0.721550
$975$	−3.60397	−	3.69445i	−0.115419	−	0.118317i
$976$	5.48863			0.175687
$977$		−	56.1841i		−	1.79749i	−0.438474	−	0.898744i	$-0.644481\pi$
$977$		−	56.1841i		−	1.79749i	0.438474	−	0.898744i	$-0.355519\pi$
$978$	7.08928			0.226690
$979$	51.0990			1.63313
$980$		0			0
$981$			19.7330i			0.630026i
$982$		−	42.0217i		−	1.34097i
$983$		−	26.4890i		−	0.844869i	−0.906393	−	0.422435i	$-0.861176\pi$
$983$		−	26.4890i		−	0.844869i	0.906393	−	0.422435i	$-0.138824\pi$
$984$	−0.417098			−0.0132966
$985$	27.6229			0.880138
$986$		−	66.8982i		−	2.13047i
$987$		0			0
$988$	20.4726	−	19.9712i	0.651320	−	0.635368i
$989$	−3.11892			−0.0991758
$990$			90.8203i			2.88646i
$991$	5.11258			0.162407			0.0812033	−	0.996698i	$-0.474124\pi$
$991$	5.11258			0.162407			0.0812033	+	0.996698i	$0.474124\pi$
$992$	−11.7930			−0.374430
$993$		−	0.797717i		−	0.0253148i
$994$		0			0
$995$			23.5957i			0.748035i
$996$			3.44941i			0.109299i
$997$	2.03542			0.0644623			0.0322311	−	0.999480i	$-0.489739\pi$
$997$	2.03542			0.0644623			0.0322311	+	0.999480i	$0.489739\pi$
$998$	−28.0365			−0.887480
$999$		−	5.29970i		−	0.167675i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.c.f.246.2		8
7.2	even	3		91.2.r.a.25.2	✓	16
7.3	odd	6		637.2.r.f.324.7		16
7.4	even	3		91.2.r.a.51.7	yes	16
7.5	odd	6		637.2.r.f.116.2		16
7.6	odd	2		637.2.c.e.246.2		8
13.5	odd	4		8281.2.a.ck.1.2		8
13.8	odd	4		8281.2.a.ck.1.7		8
13.12	even	2	inner	637.2.c.f.246.7		8
21.2	odd	6		819.2.dl.e.298.7		16
21.11	odd	6		819.2.dl.e.415.2		16
91.12	odd	6		637.2.r.f.116.7		16
91.18	odd	12		1183.2.e.i.170.7		16
91.25	even	6		91.2.r.a.51.2	yes	16
91.34	even	4		8281.2.a.cj.1.7		8
91.38	odd	6		637.2.r.f.324.2		16
91.44	odd	12		1183.2.e.i.508.7		16
91.51	even	6		91.2.r.a.25.7	yes	16
91.60	odd	12		1183.2.e.i.170.2		16
91.83	even	4		8281.2.a.cj.1.2		8
91.86	odd	12		1183.2.e.i.508.2		16
91.90	odd	2		637.2.c.e.246.7		8
273.116	odd	6		819.2.dl.e.415.7		16
273.233	odd	6		819.2.dl.e.298.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.r.a.25.2	✓	16	7.2	even	3
91.2.r.a.25.7	yes	16	91.51	even	6
91.2.r.a.51.2	yes	16	91.25	even	6
91.2.r.a.51.7	yes	16	7.4	even	3
637.2.c.e.246.2		8	7.6	odd	2
637.2.c.e.246.7		8	91.90	odd	2
637.2.c.f.246.2		8	1.1	even	1	trivial
637.2.c.f.246.7		8	13.12	even	2	inner
637.2.r.f.116.2		16	7.5	odd	6
637.2.r.f.116.7		16	91.12	odd	6
637.2.r.f.324.2		16	91.38	odd	6
637.2.r.f.324.7		16	7.3	odd	6
819.2.dl.e.298.2		16	273.233	odd	6
819.2.dl.e.298.7		16	21.2	odd	6
819.2.dl.e.415.2		16	21.11	odd	6
819.2.dl.e.415.7		16	273.116	odd	6
1183.2.e.i.170.2		16	91.60	odd	12
1183.2.e.i.170.7		16	91.18	odd	12
1183.2.e.i.508.2		16	91.86	odd	12
1183.2.e.i.508.7		16	91.44	odd	12
8281.2.a.cj.1.2		8	91.83	even	4
8281.2.a.cj.1.7		8	91.34	even	4
8281.2.a.ck.1.2		8	13.5	odd	4
8281.2.a.ck.1.7		8	13.8	odd	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)

\(f(q)\)	\(=\)	\(q-2.12549i q^{2} -0.178854 q^{3} -2.51771 q^{4} +3.60603i q^{5} +0.380153i q^{6} +1.10038i q^{8} -2.96801 q^{9} +O(q^{10})\)	\(q-2.12549i q^{2} -0.178854 q^{3} -2.51771 q^{4} +3.60603i q^{5} +0.380153i q^{6} +1.10038i q^{8} -2.96801 q^{9} +7.66457 q^{10} -3.99236i q^{11} +0.450303 q^{12} +(-2.51771 - 2.58092i) q^{13} -0.644954i q^{15} -2.69656 q^{16} -4.78916 q^{17} +6.30848i q^{18} -3.15060i q^{19} -9.07892i q^{20} -8.48572 q^{22} +2.17885 q^{23} -0.196808i q^{24} -8.00343 q^{25} +(-5.48572 + 5.35136i) q^{26} +1.06740 q^{27} -6.57198 q^{29} -1.37084 q^{30} +1.48672i q^{31} +7.93228i q^{32} +0.714051i q^{33} +10.1793i q^{34} +7.47259 q^{36} -4.96503i q^{37} -6.69656 q^{38} +(0.450303 + 0.461609i) q^{39} -3.96801 q^{40} -2.11931i q^{41} -1.43145 q^{43} +10.0516i q^{44} -10.7027i q^{45} -4.63113i q^{46} -1.01893i q^{47} +0.482292 q^{48} +17.0112i q^{50} +0.856562 q^{51} +(6.33885 + 6.49800i) q^{52} +6.03542 q^{53} -2.26876i q^{54} +14.3966 q^{55} +0.563498i q^{57} +13.9687i q^{58} +4.90322i q^{59} +1.62380i q^{60} -2.03542 q^{61} +3.16000 q^{62} +11.4669 q^{64} +(9.30686 - 9.07892i) q^{65} +1.51771 q^{66} +3.91090i q^{67} +12.0577 q^{68} -0.389698 q^{69} -8.80684i q^{71} -3.26595i q^{72} -3.08878i q^{73} -10.5531 q^{74} +1.43145 q^{75} +7.93228i q^{76} +(0.981145 - 0.957115i) q^{78} +1.96801 q^{79} -9.72388i q^{80} +8.71312 q^{81} -4.50457 q^{82} +7.66020i q^{83} -17.2698i q^{85} +3.04253i q^{86} +1.17543 q^{87} +4.39312 q^{88} +12.7992i q^{89} -22.7485 q^{90} -5.48572 q^{92} -0.265906i q^{93} -2.16572 q^{94} +11.3611 q^{95} -1.41872i q^{96} +1.35900i q^{97} +11.8494i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 6 q^{4} + 12 q^{9}+O(q^{10}) \) 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

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