LMFDB - Embedded newform 245.2.b.e.99.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,2,Mod(99,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("245.99"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(245, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-16,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$1.95633484952$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.4
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	245.99
Dual form			245.2.b.e.99.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.44949i q^{2} +1.73205i q^{3} -4.00000 q^{4} +(-1.41421 + 1.73205i) q^{5} -4.24264 q^{6} -4.89898i q^{8} +(-4.24264 - 3.46410i) q^{10} +5.00000 q^{11} -6.92820i q^{12} -1.73205i q^{13} +(-3.00000 - 2.44949i) q^{15} +4.00000 q^{16} +1.73205i q^{17} -2.82843 q^{19} +(5.65685 - 6.92820i) q^{20} +12.2474i q^{22} +2.44949i q^{23} +8.48528 q^{24} +(-1.00000 - 4.89898i) q^{25} +4.24264 q^{26} +5.19615i q^{27} -5.00000 q^{29} +(6.00000 - 7.34847i) q^{30} +1.41421 q^{31} +8.66025i q^{33} -4.24264 q^{34} +2.44949i q^{37} -6.92820i q^{38} +3.00000 q^{39} +(8.48528 + 6.92820i) q^{40} +9.89949 q^{41} -20.0000 q^{44} -6.00000 q^{46} -8.66025i q^{47} +6.92820i q^{48} +(12.0000 - 2.44949i) q^{50} -3.00000 q^{51} +6.92820i q^{52} +7.34847i q^{53} -12.7279 q^{54} +(-7.07107 + 8.66025i) q^{55} -4.89898i q^{57} -12.2474i q^{58} +1.41421 q^{59} +(12.0000 + 9.79796i) q^{60} -2.82843 q^{61} +3.46410i q^{62} +8.00000 q^{64} +(3.00000 + 2.44949i) q^{65} -21.2132 q^{66} +7.34847i q^{67} -6.92820i q^{68} -4.24264 q^{69} +2.00000 q^{71} +13.8564i q^{73} -6.00000 q^{74} +(8.48528 - 1.73205i) q^{75} +11.3137 q^{76} +7.34847i q^{78} +3.00000 q^{79} +(-5.65685 + 6.92820i) q^{80} -9.00000 q^{81} +24.2487i q^{82} -13.8564i q^{83} +(-3.00000 - 2.44949i) q^{85} -8.66025i q^{87} -24.4949i q^{88} +16.9706 q^{89} -9.79796i q^{92} +2.44949i q^{93} +21.2132 q^{94} +(4.00000 - 4.89898i) q^{95} -1.73205i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{4} + 20 q^{11} - 12 q^{15} + 16 q^{16} - 4 q^{25} - 20 q^{29} + 24 q^{30} + 12 q^{39} - 80 q^{44} - 24 q^{46} + 48 q^{50} - 12 q^{51} + 48 q^{60} + 32 q^{64} + 12 q^{65} + 8 q^{71} - 24 q^{74}+ \cdots + 16 q^{95}+O(q^{100}) $ 4 * q - 16 * q^4 + 20 * q^11 - 12 * q^15 + 16 * q^16 - 4 * q^25 - 20 * q^29 + 24 * q^30 + 12 * q^39 - 80 * q^44 - 24 * q^46 + 48 * q^50 - 12 * q^51 + 48 * q^60 + 32 * q^64 + 12 * q^65 + 8 * q^71 - 24 * q^74 + 12 * q^79 - 36 * q^81 - 12 * q^85 + 16 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$1$	$-1$

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 $

$2$			2.44949i			1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$2$			2.44949i			1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$3$			1.73205i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$3$			1.73205i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$4$	−4.00000			−2.00000
$5$	−1.41421	+	1.73205i	−0.632456	+	0.774597i
$5$	−1.41421	+	1.73205i	−0.632456	+	0.774597i
$6$	−4.24264			−1.73205
$7$		0			0
$7$		0			0
$8$		−	4.89898i		−	1.73205i
$9$		0			0
$10$	−4.24264	−	3.46410i	−1.34164	−	1.09545i
$11$	5.00000			1.50756			0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000			1.50756			0.753778	+	0.657129i	$0.228229\pi$
$12$		−	6.92820i		−	2.00000i
$13$		−	1.73205i		−	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$		−	1.73205i		−	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$14$		0			0
$15$	−3.00000	−	2.44949i	−0.774597	−	0.632456i
$16$	4.00000			1.00000
$17$			1.73205i			0.420084i	0.977692	+	0.210042i	$0.0673601\pi$
$17$			1.73205i			0.420084i	−0.977692	+	0.210042i	$0.932640\pi$
$18$		0			0
$19$	−2.82843			−0.648886			−0.324443	−	0.945905i	$-0.605177\pi$
$19$	−2.82843			−0.648886			−0.324443	+	0.945905i	$0.605177\pi$
$20$	5.65685	−	6.92820i	1.26491	−	1.54919i
$21$		0			0
$22$			12.2474i			2.61116i
$23$			2.44949i			0.510754i	0.966842	+	0.255377i	$0.0821996\pi$
$23$			2.44949i			0.510754i	−0.966842	+	0.255377i	$0.917800\pi$
$24$	8.48528			1.73205
$25$	−1.00000	−	4.89898i	−0.200000	−	0.979796i
$26$	4.24264			0.832050
$27$			5.19615i			1.00000i
$28$		0			0
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$	6.00000	−	7.34847i	1.09545	−	1.34164i
$31$	1.41421			0.254000			0.127000	−	0.991903i	$-0.459465\pi$
$31$	1.41421			0.254000			0.127000	+	0.991903i	$0.459465\pi$
$32$		0			0
$33$			8.66025i			1.50756i
$34$	−4.24264			−0.727607
$35$		0			0
$36$		0			0
$37$			2.44949i			0.402694i	0.979520	+	0.201347i	$0.0645318\pi$
$37$			2.44949i			0.402694i	−0.979520	+	0.201347i	$0.935468\pi$
$38$		−	6.92820i		−	1.12390i
$39$	3.00000			0.480384
$40$	8.48528	+	6.92820i	1.34164	+	1.09545i
$41$	9.89949			1.54604			0.773021	−	0.634381i	$-0.218745\pi$
$41$	9.89949			1.54604			0.773021	+	0.634381i	$0.218745\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	−20.0000			−3.01511
$45$		0			0
$46$	−6.00000			−0.884652
$47$		−	8.66025i		−	1.26323i	−0.775283	−	0.631614i	$-0.782393\pi$
$47$		−	8.66025i		−	1.26323i	0.775283	−	0.631614i	$-0.217607\pi$
$48$			6.92820i			1.00000i
$49$		0			0
$50$	12.0000	−	2.44949i	1.69706	−	0.346410i
$51$	−3.00000			−0.420084
$52$			6.92820i			0.960769i
$53$			7.34847i			1.00939i	0.863298	+	0.504695i	$0.168395\pi$
$53$			7.34847i			1.00939i	−0.863298	+	0.504695i	$0.831605\pi$
$54$	−12.7279			−1.73205
$55$	−7.07107	+	8.66025i	−0.953463	+	1.16775i
$56$		0			0
$57$		−	4.89898i		−	0.648886i
$58$		−	12.2474i		−	1.60817i
$59$	1.41421			0.184115			0.0920575	−	0.995754i	$-0.470656\pi$
$59$	1.41421			0.184115			0.0920575	+	0.995754i	$0.470656\pi$
$60$	12.0000	+	9.79796i	1.54919	+	1.26491i
$61$	−2.82843			−0.362143			−0.181071	−	0.983470i	$-0.557957\pi$
$61$	−2.82843			−0.362143			−0.181071	+	0.983470i	$0.557957\pi$
$62$			3.46410i			0.439941i
$63$		0			0
$64$	8.00000			1.00000
$65$	3.00000	+	2.44949i	0.372104	+	0.303822i
$66$	−21.2132			−2.61116
$67$			7.34847i			0.897758i	0.893592	+	0.448879i	$0.148177\pi$
$67$			7.34847i			0.897758i	−0.893592	+	0.448879i	$0.851823\pi$
$68$		−	6.92820i		−	0.840168i
$69$	−4.24264			−0.510754
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$		0			0
$73$			13.8564i			1.62177i	0.585206	+	0.810885i	$0.301014\pi$
$73$			13.8564i			1.62177i	−0.585206	+	0.810885i	$0.698986\pi$
$74$	−6.00000			−0.697486
$75$	8.48528	−	1.73205i	0.979796	−	0.200000i
$76$	11.3137			1.29777
$77$		0			0
$78$			7.34847i			0.832050i
$79$	3.00000			0.337526			0.168763	−	0.985657i	$-0.446023\pi$
$79$	3.00000			0.337526			0.168763	+	0.985657i	$0.446023\pi$
$80$	−5.65685	+	6.92820i	−0.632456	+	0.774597i
$81$	−9.00000			−1.00000
$82$			24.2487i			2.67782i
$83$		−	13.8564i		−	1.52094i	−0.649374	−	0.760469i	$-0.724969\pi$
$83$		−	13.8564i		−	1.52094i	0.649374	−	0.760469i	$-0.275031\pi$
$84$		0			0
$85$	−3.00000	−	2.44949i	−0.325396	−	0.265684i
$86$		0			0
$87$		−	8.66025i		−	0.928477i
$88$		−	24.4949i		−	2.61116i
$89$	16.9706			1.79888			0.899438	−	0.437048i	$-0.143976\pi$
$89$	16.9706			1.79888			0.899438	+	0.437048i	$0.143976\pi$
$90$		0			0
$91$		0			0
$92$		−	9.79796i		−	1.02151i
$93$			2.44949i			0.254000i
$94$	21.2132			2.18797
$95$	4.00000	−	4.89898i	0.410391	−	0.502625i
$96$		0			0
$97$		−	1.73205i		−	0.175863i	−0.996127	−	0.0879316i	$-0.971974\pi$
$97$		−	1.73205i		−	0.175863i	0.996127	−	0.0879316i	$-0.0280257\pi$
$98$		0			0
$99$		0			0
$100$	4.00000	+	19.5959i	0.400000	+	1.95959i
$101$	11.3137			1.12576			0.562878	−	0.826540i	$-0.309694\pi$
$101$	11.3137			1.12576			0.562878	+	0.826540i	$0.309694\pi$
$102$		−	7.34847i		−	0.727607i
$103$		−	8.66025i		−	0.853320i	−0.904412	−	0.426660i	$-0.859690\pi$
$103$		−	8.66025i		−	0.853320i	0.904412	−	0.426660i	$-0.140310\pi$
$104$	−8.48528			−0.832050
$105$		0			0
$106$	−18.0000			−1.74831
$107$		−	14.6969i		−	1.42081i	−0.703795	−	0.710403i	$-0.748513\pi$
$107$		−	14.6969i		−	1.42081i	0.703795	−	0.710403i	$-0.251487\pi$
$108$		−	20.7846i		−	2.00000i
$109$	−9.00000			−0.862044			−0.431022	−	0.902342i	$-0.641847\pi$
$109$	−9.00000			−0.862044			−0.431022	+	0.902342i	$0.641847\pi$
$110$	−21.2132	−	17.3205i	−2.02260	−	1.65145i
$111$	−4.24264			−0.402694
$112$		0			0
$113$			17.1464i			1.61300i	0.591234	+	0.806500i	$0.298641\pi$
$113$			17.1464i			1.61300i	−0.591234	+	0.806500i	$0.701359\pi$
$114$	12.0000			1.12390
$115$	−4.24264	−	3.46410i	−0.395628	−	0.323029i
$116$	20.0000			1.85695
$117$		0			0
$118$			3.46410i			0.318896i
$119$		0			0
$120$	−12.0000	+	14.6969i	−1.09545	+	1.34164i
$121$	14.0000			1.27273
$122$		−	6.92820i		−	0.627250i
$123$			17.1464i			1.54604i
$124$	−5.65685			−0.508001
$125$	9.89949	+	5.19615i	0.885438	+	0.464758i
$126$		0			0
$127$		−	17.1464i		−	1.52150i	−0.649045	−	0.760750i	$-0.724831\pi$
$127$		−	17.1464i		−	1.52150i	0.649045	−	0.760750i	$-0.275169\pi$
$128$			19.5959i			1.73205i
$129$		0			0
$130$	−6.00000	+	7.34847i	−0.526235	+	0.644503i
$131$	−12.7279			−1.11204			−0.556022	−	0.831168i	$-0.687673\pi$
$131$	−12.7279			−1.11204			−0.556022	+	0.831168i	$0.687673\pi$
$132$		−	34.6410i		−	3.01511i
$133$		0			0
$134$	−18.0000			−1.55496
$135$	−9.00000	−	7.34847i	−0.774597	−	0.632456i
$136$	8.48528			0.727607
$137$		−	9.79796i		−	0.837096i	−0.908195	−	0.418548i	$-0.862539\pi$
$137$		−	9.79796i		−	0.837096i	0.908195	−	0.418548i	$-0.137461\pi$
$138$		−	10.3923i		−	0.884652i
$139$	9.89949			0.839664			0.419832	−	0.907602i	$-0.362089\pi$
$139$	9.89949			0.839664			0.419832	+	0.907602i	$0.362089\pi$
$140$		0			0
$141$	15.0000			1.26323
$142$			4.89898i			0.411113i
$143$		−	8.66025i		−	0.724207i
$144$		0			0
$145$	7.07107	−	8.66025i	0.587220	−	0.719195i
$146$	−33.9411			−2.80899
$147$		0			0
$148$		−	9.79796i		−	0.805387i
$149$	−4.00000			−0.327693			−0.163846	−	0.986486i	$-0.552390\pi$
$149$	−4.00000			−0.327693			−0.163846	+	0.986486i	$0.552390\pi$
$150$	4.24264	+	20.7846i	0.346410	+	1.69706i
$151$	5.00000			0.406894			0.203447	−	0.979086i	$-0.434786\pi$
$151$	5.00000			0.406894			0.203447	+	0.979086i	$0.434786\pi$
$152$			13.8564i			1.12390i
$153$		0			0
$154$		0			0
$155$	−2.00000	+	2.44949i	−0.160644	+	0.196748i
$156$	−12.0000			−0.960769
$157$		−	10.3923i		−	0.829396i	−0.909959	−	0.414698i	$-0.863887\pi$
$157$		−	10.3923i		−	0.829396i	0.909959	−	0.414698i	$-0.136113\pi$
$158$			7.34847i			0.584613i
$159$	−12.7279			−1.00939
$160$		0			0
$161$		0			0
$162$		−	22.0454i		−	1.73205i
$163$			2.44949i			0.191859i	0.995388	+	0.0959294i	$0.0305823\pi$
$163$			2.44949i			0.191859i	−0.995388	+	0.0959294i	$0.969418\pi$
$164$	−39.5980			−3.09208
$165$	−15.0000	−	12.2474i	−1.16775	−	0.953463i
$166$	33.9411			2.63434
$167$		−	1.73205i		−	0.134030i	−0.997752	−	0.0670151i	$-0.978652\pi$
$167$		−	1.73205i		−	0.134030i	0.997752	−	0.0670151i	$-0.0213476\pi$
$168$		0			0
$169$	10.0000			0.769231
$170$	6.00000	−	7.34847i	0.460179	−	0.563602i
$171$		0			0
$172$		0			0
$173$			15.5885i			1.18517i	0.805508	+	0.592584i	$0.201892\pi$
$173$			15.5885i			1.18517i	−0.805508	+	0.592584i	$0.798108\pi$
$174$	21.2132			1.60817
$175$		0			0
$176$	20.0000			1.50756
$177$			2.44949i			0.184115i
$178$			41.5692i			3.11574i
$179$	−2.00000			−0.149487			−0.0747435	−	0.997203i	$-0.523814\pi$
$179$	−2.00000			−0.149487			−0.0747435	+	0.997203i	$0.523814\pi$
$180$		0			0
$181$	−9.89949			−0.735824			−0.367912	−	0.929861i	$-0.619927\pi$
$181$	−9.89949			−0.735824			−0.367912	+	0.929861i	$0.619927\pi$
$182$		0			0
$183$		−	4.89898i		−	0.362143i
$184$	12.0000			0.884652
$185$	−4.24264	−	3.46410i	−0.311925	−	0.254686i
$186$	−6.00000			−0.439941
$187$			8.66025i			0.633300i
$188$			34.6410i			2.52646i
$189$		0			0
$190$	12.0000	+	9.79796i	0.870572	+	0.710819i
$191$	17.0000			1.23008			0.615038	−	0.788497i	$-0.289140\pi$
$191$	17.0000			1.23008			0.615038	+	0.788497i	$0.289140\pi$
$192$			13.8564i			1.00000i
$193$		−	9.79796i		−	0.705273i	−0.935760	−	0.352636i	$-0.885285\pi$
$193$		−	9.79796i		−	0.705273i	0.935760	−	0.352636i	$-0.114715\pi$
$194$	4.24264			0.304604
$195$	−4.24264	+	5.19615i	−0.303822	+	0.372104i
$196$		0			0
$197$			17.1464i			1.22163i	0.791772	+	0.610816i	$0.209159\pi$
$197$			17.1464i			1.22163i	−0.791772	+	0.610816i	$0.790841\pi$
$198$		0			0
$199$	−18.3848			−1.30326			−0.651631	−	0.758536i	$-0.725915\pi$
$199$	−18.3848			−1.30326			−0.651631	+	0.758536i	$0.725915\pi$
$200$	−24.0000	+	4.89898i	−1.69706	+	0.346410i
$201$	−12.7279			−0.897758
$202$			27.7128i			1.94987i
$203$		0			0
$204$	12.0000			0.840168
$205$	−14.0000	+	17.1464i	−0.977802	+	1.19756i
$206$	21.2132			1.47799
$207$		0			0
$208$		−	6.92820i		−	0.480384i
$209$	−14.1421			−0.978232
$210$		0			0
$211$	9.00000			0.619586			0.309793	−	0.950804i	$-0.399740\pi$
$211$	9.00000			0.619586			0.309793	+	0.950804i	$0.399740\pi$
$212$		−	29.3939i		−	2.01878i
$213$			3.46410i			0.237356i
$214$	36.0000			2.46091
$215$		0			0
$216$	25.4558			1.73205
$217$		0			0
$218$		−	22.0454i		−	1.49310i
$219$	−24.0000			−1.62177
$220$	28.2843	−	34.6410i	1.90693	−	2.33550i
$221$	3.00000			0.201802
$222$		−	10.3923i		−	0.697486i
$223$		−	25.9808i		−	1.73980i	−0.493228	−	0.869900i	$-0.664183\pi$
$223$		−	25.9808i		−	1.73980i	0.493228	−	0.869900i	$-0.335817\pi$
$224$		0			0
$225$		0			0
$226$	−42.0000			−2.79380
$227$			1.73205i			0.114960i	0.998347	+	0.0574801i	$0.0183066\pi$
$227$			1.73205i			0.114960i	−0.998347	+	0.0574801i	$0.981693\pi$
$228$			19.5959i			1.29777i
$229$	7.07107			0.467269			0.233635	−	0.972324i	$-0.424938\pi$
$229$	7.07107			0.467269			0.233635	+	0.972324i	$0.424938\pi$
$230$	8.48528	−	10.3923i	0.559503	−	0.685248i
$231$		0			0
$232$			24.4949i			1.60817i
$233$		−	14.6969i		−	0.962828i	−0.876493	−	0.481414i	$-0.840123\pi$
$233$		−	14.6969i		−	0.962828i	0.876493	−	0.481414i	$-0.159877\pi$
$234$		0			0
$235$	15.0000	+	12.2474i	0.978492	+	0.798935i
$236$	−5.65685			−0.368230
$237$			5.19615i			0.337526i
$238$		0			0
$239$	−19.0000			−1.22901			−0.614504	−	0.788914i	$-0.710644\pi$
$239$	−19.0000			−1.22901			−0.614504	+	0.788914i	$0.710644\pi$
$240$	−12.0000	−	9.79796i	−0.774597	−	0.632456i
$241$	−18.3848			−1.18427			−0.592134	−	0.805840i	$-0.701714\pi$
$241$	−18.3848			−1.18427			−0.592134	+	0.805840i	$0.701714\pi$
$242$			34.2929i			2.20443i
$243$		0			0
$244$	11.3137			0.724286
$245$		0			0
$246$	−42.0000			−2.67782
$247$			4.89898i			0.311715i
$248$		−	6.92820i		−	0.439941i
$249$	24.0000			1.52094
$250$	−12.7279	+	24.2487i	−0.804984	+	1.53362i
$251$	9.89949			0.624851			0.312425	−	0.949942i	$-0.398859\pi$
$251$	9.89949			0.624851			0.312425	+	0.949942i	$0.398859\pi$
$252$		0			0
$253$			12.2474i			0.769991i
$254$	42.0000			2.63531
$255$	4.24264	−	5.19615i	0.265684	−	0.325396i
$256$	−32.0000			−2.00000
$257$			3.46410i			0.216085i	0.994146	+	0.108042i	$0.0344582\pi$
$257$			3.46410i			0.216085i	−0.994146	+	0.108042i	$0.965542\pi$
$258$		0			0
$259$		0			0
$260$	−12.0000	−	9.79796i	−0.744208	−	0.607644i
$261$		0			0
$262$		−	31.1769i		−	1.92612i
$263$		−	9.79796i		−	0.604168i	−0.953281	−	0.302084i	$-0.902318\pi$
$263$		−	9.79796i		−	0.604168i	0.953281	−	0.302084i	$-0.0976823\pi$
$264$	42.4264			2.61116
$265$	−12.7279	−	10.3923i	−0.781870	−	0.638394i
$266$		0			0
$267$			29.3939i			1.79888i
$268$		−	29.3939i		−	1.79552i
$269$	21.2132			1.29339			0.646696	−	0.762748i	$-0.276150\pi$
$269$	21.2132			1.29339			0.646696	+	0.762748i	$0.276150\pi$
$270$	18.0000	−	22.0454i	1.09545	−	1.34164i
$271$	−22.6274			−1.37452			−0.687259	−	0.726413i	$-0.741186\pi$
$271$	−22.6274			−1.37452			−0.687259	+	0.726413i	$0.741186\pi$
$272$			6.92820i			0.420084i
$273$		0			0
$274$	24.0000			1.44989
$275$	−5.00000	−	24.4949i	−0.301511	−	1.47710i
$276$	16.9706			1.02151
$277$		−	26.9444i		−	1.61893i	−0.587167	−	0.809466i	$-0.699757\pi$
$277$		−	26.9444i		−	1.61893i	0.587167	−	0.809466i	$-0.300243\pi$
$278$			24.2487i			1.45434i
$279$		0			0
$280$		0			0
$281$	−5.00000			−0.298275			−0.149137	−	0.988816i	$-0.547650\pi$
$281$	−5.00000			−0.298275			−0.149137	+	0.988816i	$0.547650\pi$
$282$			36.7423i			2.18797i
$283$			1.73205i			0.102960i	0.998674	+	0.0514799i	$0.0163938\pi$
$283$			1.73205i			0.102960i	−0.998674	+	0.0514799i	$0.983606\pi$
$284$	−8.00000			−0.474713
$285$	8.48528	+	6.92820i	0.502625	+	0.410391i
$286$	21.2132			1.25436
$287$		0			0
$288$		0			0
$289$	14.0000			0.823529
$290$	21.2132	+	17.3205i	1.24568	+	1.01710i
$291$	3.00000			0.175863
$292$		−	55.4256i		−	3.24354i
$293$			22.5167i			1.31544i	0.753264	+	0.657719i	$0.228478\pi$
$293$			22.5167i			1.31544i	−0.753264	+	0.657719i	$0.771522\pi$
$294$		0			0
$295$	−2.00000	+	2.44949i	−0.116445	+	0.142615i
$296$	12.0000			0.697486
$297$			25.9808i			1.50756i
$298$		−	9.79796i		−	0.567581i
$299$	4.24264			0.245358
$300$	−33.9411	+	6.92820i	−1.95959	+	0.400000i
$301$		0			0
$302$			12.2474i			0.704761i
$303$			19.5959i			1.12576i
$304$	−11.3137			−0.648886
$305$	4.00000	−	4.89898i	0.229039	−	0.280515i
$306$		0			0
$307$		−	1.73205i		−	0.0988534i	−0.998778	−	0.0494267i	$-0.984261\pi$
$307$		−	1.73205i		−	0.0988534i	0.998778	−	0.0494267i	$-0.0157394\pi$
$308$		0			0
$309$	15.0000			0.853320
$310$	−6.00000	−	4.89898i	−0.340777	−	0.278243i
$311$	−8.48528			−0.481156			−0.240578	−	0.970630i	$-0.577337\pi$
$311$	−8.48528			−0.481156			−0.240578	+	0.970630i	$0.577337\pi$
$312$		−	14.6969i		−	0.832050i
$313$		−	8.66025i		−	0.489506i	−0.969585	−	0.244753i	$-0.921293\pi$
$313$		−	8.66025i		−	0.489506i	0.969585	−	0.244753i	$-0.0787070\pi$
$314$	25.4558			1.43656
$315$		0			0
$316$	−12.0000			−0.675053
$317$			19.5959i			1.10062i	0.834962	+	0.550308i	$0.185490\pi$
$317$			19.5959i			1.10062i	−0.834962	+	0.550308i	$0.814510\pi$
$318$		−	31.1769i		−	1.74831i
$319$	−25.0000			−1.39973
$320$	−11.3137	+	13.8564i	−0.632456	+	0.774597i
$321$	25.4558			1.42081
$322$		0			0
$323$		−	4.89898i		−	0.272587i
$324$	36.0000			2.00000
$325$	−8.48528	+	1.73205i	−0.470679	+	0.0960769i
$326$	−6.00000			−0.332309
$327$		−	15.5885i		−	0.862044i
$328$		−	48.4974i		−	2.67782i
$329$		0			0
$330$	30.0000	−	36.7423i	1.65145	−	2.02260i
$331$	−18.0000			−0.989369			−0.494685	−	0.869072i	$-0.664716\pi$
$331$	−18.0000			−0.989369			−0.494685	+	0.869072i	$0.664716\pi$
$332$			55.4256i			3.04188i
$333$		0			0
$334$	4.24264			0.232147
$335$	−12.7279	−	10.3923i	−0.695401	−	0.567792i
$336$		0			0
$337$		−	17.1464i		−	0.934025i	−0.884251	−	0.467013i	$-0.845330\pi$
$337$		−	17.1464i		−	0.934025i	0.884251	−	0.467013i	$-0.154670\pi$
$338$			24.4949i			1.33235i
$339$	−29.6985			−1.61300
$340$	12.0000	+	9.79796i	0.650791	+	0.531369i
$341$	7.07107			0.382920
$342$		0			0
$343$		0			0
$344$		0			0
$345$	6.00000	−	7.34847i	0.323029	−	0.395628i
$346$	−38.1838			−2.05277
$347$			7.34847i			0.394486i	0.980355	+	0.197243i	$0.0631989\pi$
$347$			7.34847i			0.394486i	−0.980355	+	0.197243i	$0.936801\pi$
$348$			34.6410i			1.85695i
$349$	−19.7990			−1.05982			−0.529908	−	0.848055i	$-0.677773\pi$
$349$	−19.7990			−1.05982			−0.529908	+	0.848055i	$0.677773\pi$
$350$		0			0
$351$	9.00000			0.480384
$352$		0			0
$353$		−	22.5167i		−	1.19844i	−0.800584	−	0.599220i	$-0.795477\pi$
$353$		−	22.5167i		−	1.19844i	0.800584	−	0.599220i	$-0.204523\pi$
$354$	−6.00000			−0.318896
$355$	−2.82843	+	3.46410i	−0.150117	+	0.183855i
$356$	−67.8823			−3.59775
$357$		0			0
$358$		−	4.89898i		−	0.258919i
$359$	−4.00000			−0.211112			−0.105556	−	0.994413i	$-0.533662\pi$
$359$	−4.00000			−0.211112			−0.105556	+	0.994413i	$0.533662\pi$
$360$		0			0
$361$	−11.0000			−0.578947
$362$		−	24.2487i		−	1.27448i
$363$			24.2487i			1.27273i
$364$		0			0
$365$	−24.0000	−	19.5959i	−1.25622	−	1.02570i
$366$	12.0000			0.627250
$367$			1.73205i			0.0904123i	0.998978	+	0.0452062i	$0.0143945\pi$
$367$			1.73205i			0.0904123i	−0.998978	+	0.0452062i	$0.985606\pi$
$368$			9.79796i			0.510754i
$369$		0			0
$370$	8.48528	−	10.3923i	0.441129	−	0.540270i
$371$		0			0
$372$		−	9.79796i		−	0.508001i
$373$		−	14.6969i		−	0.760979i	−0.924785	−	0.380489i	$-0.875756\pi$
$373$		−	14.6969i		−	0.760979i	0.924785	−	0.380489i	$-0.124244\pi$
$374$	−21.2132			−1.09691
$375$	−9.00000	+	17.1464i	−0.464758	+	0.885438i
$376$	−42.4264			−2.18797
$377$			8.66025i			0.446026i
$378$		0			0
$379$	−26.0000			−1.33553			−0.667765	−	0.744372i	$-0.732749\pi$
$379$	−26.0000			−1.33553			−0.667765	+	0.744372i	$0.732749\pi$
$380$	−16.0000	+	19.5959i	−0.820783	+	1.00525i
$381$	29.6985			1.52150
$382$			41.6413i			2.13056i
$383$		−	20.7846i		−	1.06204i	−0.847358	−	0.531022i	$-0.821808\pi$
$383$		−	20.7846i		−	1.06204i	0.847358	−	0.531022i	$-0.178192\pi$
$384$	−33.9411			−1.73205
$385$		0			0
$386$	24.0000			1.22157
$387$		0			0
$388$			6.92820i			0.351726i
$389$	5.00000			0.253510			0.126755	−	0.991934i	$-0.459544\pi$
$389$	5.00000			0.253510			0.126755	+	0.991934i	$0.459544\pi$
$390$	−12.7279	−	10.3923i	−0.644503	−	0.526235i
$391$	−4.24264			−0.214560
$392$		0			0
$393$		−	22.0454i		−	1.11204i
$394$	−42.0000			−2.11593
$395$	−4.24264	+	5.19615i	−0.213470	+	0.261447i
$396$		0			0
$397$			15.5885i			0.782362i	0.920314	+	0.391181i	$0.127933\pi$
$397$			15.5885i			0.782362i	−0.920314	+	0.391181i	$0.872067\pi$
$398$		−	45.0333i		−	2.25732i
$399$		0			0
$400$	−4.00000	−	19.5959i	−0.200000	−	0.979796i
$401$	−11.0000			−0.549314			−0.274657	−	0.961542i	$-0.588564\pi$
$401$	−11.0000			−0.549314			−0.274657	+	0.961542i	$0.588564\pi$
$402$		−	31.1769i		−	1.55496i
$403$		−	2.44949i		−	0.122018i
$404$	−45.2548			−2.25151
$405$	12.7279	−	15.5885i	0.632456	−	0.774597i
$406$		0			0
$407$			12.2474i			0.607083i
$408$			14.6969i			0.727607i
$409$	11.3137			0.559427			0.279713	−	0.960084i	$-0.409761\pi$
$409$	11.3137			0.559427			0.279713	+	0.960084i	$0.409761\pi$
$410$	−42.0000	−	34.2929i	−2.07423	−	1.69360i
$411$	16.9706			0.837096
$412$			34.6410i			1.70664i
$413$		0			0
$414$		0			0
$415$	24.0000	+	19.5959i	1.17811	+	0.961926i
$416$		0			0
$417$			17.1464i			0.839664i
$418$		−	34.6410i		−	1.69435i
$419$	29.6985			1.45087			0.725433	−	0.688293i	$-0.241640\pi$
$419$	29.6985			1.45087			0.725433	+	0.688293i	$0.241640\pi$
$420$		0			0
$421$	9.00000			0.438633			0.219317	−	0.975654i	$-0.429617\pi$
$421$	9.00000			0.438633			0.219317	+	0.975654i	$0.429617\pi$
$422$			22.0454i			1.07315i
$423$		0			0
$424$	36.0000			1.74831
$425$	8.48528	−	1.73205i	0.411597	−	0.0840168i
$426$	−8.48528			−0.411113
$427$		0			0
$428$			58.7878i			2.84161i
$429$	15.0000			0.724207
$430$		0			0
$431$	19.0000			0.915198			0.457599	−	0.889159i	$-0.348710\pi$
$431$	19.0000			0.915198			0.457599	+	0.889159i	$0.348710\pi$
$432$			20.7846i			1.00000i
$433$			10.3923i			0.499422i	0.968320	+	0.249711i	$0.0803357\pi$
$433$			10.3923i			0.499422i	−0.968320	+	0.249711i	$0.919664\pi$
$434$		0			0
$435$	15.0000	+	12.2474i	0.719195	+	0.587220i
$436$	36.0000			1.72409
$437$		−	6.92820i		−	0.331421i
$438$		−	58.7878i		−	2.80899i
$439$	7.07107			0.337484			0.168742	−	0.985660i	$-0.446030\pi$
$439$	7.07107			0.337484			0.168742	+	0.985660i	$0.446030\pi$
$440$	42.4264	+	34.6410i	2.02260	+	1.65145i
$441$		0			0
$442$			7.34847i			0.349531i
$443$		−	14.6969i		−	0.698273i	−0.937072	−	0.349136i	$-0.886475\pi$
$443$		−	14.6969i		−	0.698273i	0.937072	−	0.349136i	$-0.113525\pi$
$444$	16.9706			0.805387
$445$	−24.0000	+	29.3939i	−1.13771	+	1.39340i
$446$	63.6396			3.01342
$447$		−	6.92820i		−	0.327693i
$448$		0			0
$449$	23.0000			1.08544			0.542719	−	0.839915i	$-0.317395\pi$
$449$	23.0000			1.08544			0.542719	+	0.839915i	$0.317395\pi$
$450$		0			0
$451$	49.4975			2.33075
$452$		−	68.5857i		−	3.22600i
$453$			8.66025i			0.406894i
$454$	−4.24264			−0.199117
$455$		0			0
$456$	−24.0000			−1.12390
$457$			2.44949i			0.114582i	0.998358	+	0.0572911i	$0.0182463\pi$
$457$			2.44949i			0.114582i	−0.998358	+	0.0572911i	$0.981754\pi$
$458$			17.3205i			0.809334i
$459$	−9.00000			−0.420084
$460$	16.9706	+	13.8564i	0.791257	+	0.646058i
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$		−	34.2929i		−	1.59372i	−0.604161	−	0.796862i	$-0.706492\pi$
$463$		−	34.2929i		−	1.59372i	0.604161	−	0.796862i	$-0.293508\pi$
$464$	−20.0000			−0.928477
$465$	−4.24264	−	3.46410i	−0.196748	−	0.160644i
$466$	36.0000			1.66767
$467$			15.5885i			0.721348i	0.932692	+	0.360674i	$0.117453\pi$
$467$			15.5885i			0.721348i	−0.932692	+	0.360674i	$0.882547\pi$
$468$		0			0
$469$		0			0
$470$	−30.0000	+	36.7423i	−1.38380	+	1.69480i
$471$	18.0000			0.829396
$472$		−	6.92820i		−	0.318896i
$473$		0			0
$474$	−12.7279			−0.584613
$475$	2.82843	+	13.8564i	0.129777	+	0.635776i
$476$		0			0
$477$		0			0
$478$		−	46.5403i		−	2.12870i
$479$	21.2132			0.969256			0.484628	−	0.874720i	$-0.338955\pi$
$479$	21.2132			0.969256			0.484628	+	0.874720i	$0.338955\pi$
$480$		0			0
$481$	4.24264			0.193448
$482$		−	45.0333i		−	2.05121i
$483$		0			0
$484$	−56.0000			−2.54545
$485$	3.00000	+	2.44949i	0.136223	+	0.111226i
$486$		0			0
$487$			7.34847i			0.332991i	0.986042	+	0.166495i	$0.0532451\pi$
$487$			7.34847i			0.332991i	−0.986042	+	0.166495i	$0.946755\pi$
$488$			13.8564i			0.627250i
$489$	−4.24264			−0.191859
$490$		0			0
$491$	23.0000			1.03798			0.518988	−	0.854782i	$-0.326309\pi$
$491$	23.0000			1.03798			0.518988	+	0.854782i	$0.326309\pi$
$492$		−	68.5857i		−	3.09208i
$493$		−	8.66025i		−	0.390038i
$494$	−12.0000			−0.539906
$495$		0			0
$496$	5.65685			0.254000
$497$		0			0
$498$			58.7878i			2.63434i
$499$	17.0000			0.761025			0.380512	−	0.924776i	$-0.375748\pi$
$499$	17.0000			0.761025			0.380512	+	0.924776i	$0.375748\pi$
$500$	−39.5980	−	20.7846i	−1.77088	−	0.929516i
$501$	3.00000			0.134030
$502$			24.2487i			1.08227i
$503$		−	1.73205i		−	0.0772283i	−0.999254	−	0.0386142i	$-0.987706\pi$
$503$		−	1.73205i		−	0.0772283i	0.999254	−	0.0386142i	$-0.0122943\pi$
$504$		0			0
$505$	−16.0000	+	19.5959i	−0.711991	+	0.872007i
$506$	−30.0000			−1.33366
$507$			17.3205i			0.769231i
$508$			68.5857i			3.04300i
$509$	−12.7279			−0.564155			−0.282078	−	0.959392i	$-0.591024\pi$
$509$	−12.7279			−0.564155			−0.282078	+	0.959392i	$0.591024\pi$
$510$	12.7279	+	10.3923i	0.563602	+	0.460179i
$511$		0			0
$512$		−	39.1918i		−	1.73205i
$513$		−	14.6969i		−	0.648886i
$514$	−8.48528			−0.374270
$515$	15.0000	+	12.2474i	0.660979	+	0.539687i
$516$		0			0
$517$		−	43.3013i		−	1.90439i
$518$		0			0
$519$	−27.0000			−1.18517
$520$	12.0000	−	14.6969i	0.526235	−	0.644503i
$521$	−8.48528			−0.371747			−0.185873	−	0.982574i	$-0.559511\pi$
$521$	−8.48528			−0.371747			−0.185873	+	0.982574i	$0.559511\pi$
$522$		0			0
$523$		−	20.7846i		−	0.908848i	−0.890786	−	0.454424i	$-0.849845\pi$
$523$		−	20.7846i		−	0.908848i	0.890786	−	0.454424i	$-0.150155\pi$
$524$	50.9117			2.22409
$525$		0			0
$526$	24.0000			1.04645
$527$			2.44949i			0.106701i
$528$			34.6410i			1.50756i
$529$	17.0000			0.739130
$530$	25.4558	−	31.1769i	1.10573	−	1.35424i
$531$		0			0
$532$		0			0
$533$		−	17.1464i		−	0.742694i
$534$	−72.0000			−3.11574
$535$	25.4558	+	20.7846i	1.10055	+	0.898597i
$536$	36.0000			1.55496
$537$		−	3.46410i		−	0.149487i
$538$			51.9615i			2.24022i
$539$		0			0
$540$	36.0000	+	29.3939i	1.54919	+	1.26491i
$541$	3.00000			0.128980			0.0644900	−	0.997918i	$-0.479458\pi$
$541$	3.00000			0.128980			0.0644900	+	0.997918i	$0.479458\pi$
$542$		−	55.4256i		−	2.38073i
$543$		−	17.1464i		−	0.735824i
$544$		0			0
$545$	12.7279	−	15.5885i	0.545204	−	0.667736i
$546$		0			0
$547$		−	34.2929i		−	1.46626i	−0.680090	−	0.733128i	$-0.738059\pi$
$547$		−	34.2929i		−	1.46626i	0.680090	−	0.733128i	$-0.261941\pi$
$548$			39.1918i			1.67419i
$549$		0			0
$550$	60.0000	−	12.2474i	2.55841	−	0.522233i
$551$	14.1421			0.602475
$552$			20.7846i			0.884652i
$553$		0			0
$554$	66.0000			2.80407
$555$	6.00000	−	7.34847i	0.254686	−	0.311925i
$556$	−39.5980			−1.67933
$557$			24.4949i			1.03788i	0.854810	+	0.518941i	$0.173674\pi$
$557$			24.4949i			1.03788i	−0.854810	+	0.518941i	$0.826326\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−15.0000			−0.633300
$562$		−	12.2474i		−	0.516627i
$563$		−	10.3923i		−	0.437983i	−0.975727	−	0.218992i	$-0.929723\pi$
$563$		−	10.3923i		−	0.437983i	0.975727	−	0.218992i	$-0.0702768\pi$
$564$	−60.0000			−2.52646
$565$	−29.6985	−	24.2487i	−1.24942	−	1.02015i
$566$	−4.24264			−0.178331
$567$		0			0
$568$		−	9.79796i		−	0.411113i
$569$	−4.00000			−0.167689			−0.0838444	−	0.996479i	$-0.526720\pi$
$569$	−4.00000			−0.167689			−0.0838444	+	0.996479i	$0.526720\pi$
$570$	−16.9706	+	20.7846i	−0.710819	+	0.870572i
$571$	−2.00000			−0.0836974			−0.0418487	−	0.999124i	$-0.513325\pi$
$571$	−2.00000			−0.0836974			−0.0418487	+	0.999124i	$0.513325\pi$
$572$			34.6410i			1.44841i
$573$			29.4449i			1.23008i
$574$		0			0
$575$	12.0000	−	2.44949i	0.500435	−	0.102151i
$576$		0			0
$577$			1.73205i			0.0721062i	0.999350	+	0.0360531i	$0.0114785\pi$
$577$			1.73205i			0.0721062i	−0.999350	+	0.0360531i	$0.988521\pi$
$578$			34.2929i			1.42639i
$579$	16.9706			0.705273
$580$	−28.2843	+	34.6410i	−1.17444	+	1.43839i
$581$		0			0
$582$			7.34847i			0.304604i
$583$			36.7423i			1.52171i
$584$	67.8823			2.80899
$585$		0			0
$586$	−55.1543			−2.27840
$587$			34.6410i			1.42979i	0.699233	+	0.714894i	$0.253525\pi$
$587$			34.6410i			1.42979i	−0.699233	+	0.714894i	$0.746475\pi$
$588$		0			0
$589$	−4.00000			−0.164817
$590$	−6.00000	−	4.89898i	−0.247016	−	0.201688i
$591$	−29.6985			−1.22163
$592$			9.79796i			0.402694i
$593$		−	8.66025i		−	0.355634i	−0.984064	−	0.177817i	$-0.943096\pi$
$593$		−	8.66025i		−	0.355634i	0.984064	−	0.177817i	$-0.0569035\pi$
$594$	−63.6396			−2.61116
$595$		0			0
$596$	16.0000			0.655386
$597$		−	31.8434i		−	1.30326i
$598$			10.3923i			0.424973i
$599$	−37.0000			−1.51178			−0.755890	−	0.654699i	$-0.772795\pi$
$599$	−37.0000			−1.51178			−0.755890	+	0.654699i	$0.772795\pi$
$600$	−8.48528	−	41.5692i	−0.346410	−	1.69706i
$601$	19.7990			0.807618			0.403809	−	0.914843i	$-0.367686\pi$
$601$	19.7990			0.807618			0.403809	+	0.914843i	$0.367686\pi$
$602$		0			0
$603$		0			0
$604$	−20.0000			−0.813788
$605$	−19.7990	+	24.2487i	−0.804943	+	0.985850i
$606$	−48.0000			−1.94987
$607$			39.8372i			1.61694i	0.588537	+	0.808470i	$0.299704\pi$
$607$			39.8372i			1.61694i	−0.588537	+	0.808470i	$0.700296\pi$
$608$		0			0
$609$		0			0
$610$	12.0000	+	9.79796i	0.485866	+	0.396708i
$611$	−15.0000			−0.606835
$612$		0			0
$613$		−	9.79796i		−	0.395736i	−0.980229	−	0.197868i	$-0.936598\pi$
$613$		−	9.79796i		−	0.395736i	0.980229	−	0.197868i	$-0.0634017\pi$
$614$	4.24264			0.171219
$615$	−29.6985	−	24.2487i	−1.19756	−	0.977802i
$616$		0			0
$617$		−	17.1464i		−	0.690289i	−0.938550	−	0.345145i	$-0.887830\pi$
$617$		−	17.1464i		−	0.690289i	0.938550	−	0.345145i	$-0.112170\pi$
$618$			36.7423i			1.47799i
$619$	1.41421			0.0568420			0.0284210	−	0.999596i	$-0.490952\pi$
$619$	1.41421			0.0568420			0.0284210	+	0.999596i	$0.490952\pi$
$620$	8.00000	−	9.79796i	0.321288	−	0.393496i
$621$	−12.7279			−0.510754
$622$		−	20.7846i		−	0.833387i
$623$		0			0
$624$	12.0000			0.480384
$625$	−23.0000	+	9.79796i	−0.920000	+	0.391918i
$626$	21.2132			0.847850
$627$		−	24.4949i		−	0.978232i
$628$			41.5692i			1.65879i
$629$	−4.24264			−0.169165
$630$		0			0
$631$	−33.0000			−1.31371			−0.656855	−	0.754017i	$-0.728113\pi$
$631$	−33.0000			−1.31371			−0.656855	+	0.754017i	$0.728113\pi$
$632$		−	14.6969i		−	0.584613i
$633$			15.5885i			0.619586i
$634$	−48.0000			−1.90632
$635$	29.6985	+	24.2487i	1.17855	+	0.962281i
$636$	50.9117			2.01878
$637$		0			0
$638$		−	61.2372i		−	2.42441i
$639$		0			0
$640$	−33.9411	−	27.7128i	−1.34164	−	1.09545i
$641$	−16.0000			−0.631962			−0.315981	−	0.948766i	$-0.602334\pi$
$641$	−16.0000			−0.631962			−0.315981	+	0.948766i	$0.602334\pi$
$642$			62.3538i			2.46091i
$643$			46.7654i			1.84425i	0.386897	+	0.922123i	$0.373547\pi$
$643$			46.7654i			1.84425i	−0.386897	+	0.922123i	$0.626453\pi$
$644$		0			0
$645$		0			0
$646$	12.0000			0.472134
$647$			13.8564i			0.544752i	0.962191	+	0.272376i	$0.0878094\pi$
$647$			13.8564i			0.544752i	−0.962191	+	0.272376i	$0.912191\pi$
$648$			44.0908i			1.73205i
$649$	7.07107			0.277564
$650$	−4.24264	−	20.7846i	−0.166410	−	0.815239i
$651$		0			0
$652$		−	9.79796i		−	0.383718i
$653$			19.5959i			0.766848i	0.923573	+	0.383424i	$0.125255\pi$
$653$			19.5959i			0.766848i	−0.923573	+	0.383424i	$0.874745\pi$
$654$	38.1838			1.49310
$655$	18.0000	−	22.0454i	0.703318	−	0.861385i
$656$	39.5980			1.54604
$657$		0			0
$658$		0			0
$659$	37.0000			1.44132			0.720658	−	0.693291i	$-0.243840\pi$
$659$	37.0000			1.44132			0.720658	+	0.693291i	$0.243840\pi$
$660$	60.0000	+	48.9898i	2.33550	+	1.90693i
$661$	−48.0833			−1.87022			−0.935111	−	0.354355i	$-0.884701\pi$
$661$	−48.0833			−1.87022			−0.935111	+	0.354355i	$0.884701\pi$
$662$		−	44.0908i		−	1.71364i
$663$			5.19615i			0.201802i
$664$	−67.8823			−2.63434
$665$		0			0
$666$		0			0
$667$		−	12.2474i		−	0.474223i
$668$			6.92820i			0.268060i
$669$	45.0000			1.73980
$670$	25.4558	−	31.1769i	0.983445	−	1.20447i
$671$	−14.1421			−0.545951
$672$		0			0
$673$			34.2929i			1.32189i	0.750433	+	0.660946i	$0.229845\pi$
$673$			34.2929i			1.32189i	−0.750433	+	0.660946i	$0.770155\pi$
$674$	42.0000			1.61778
$675$	25.4558	−	5.19615i	0.979796	−	0.200000i
$676$	−40.0000			−1.53846
$677$		−	32.9090i		−	1.26479i	−0.774644	−	0.632397i	$-0.782071\pi$
$677$		−	32.9090i		−	1.26479i	0.774644	−	0.632397i	$-0.217929\pi$
$678$		−	72.7461i		−	2.79380i
$679$		0			0
$680$	−12.0000	+	14.6969i	−0.460179	+	0.563602i
$681$	−3.00000			−0.114960
$682$			17.3205i			0.663237i
$683$		−	44.0908i		−	1.68709i	−0.537060	−	0.843544i	$-0.680465\pi$
$683$		−	44.0908i		−	1.68709i	0.537060	−	0.843544i	$-0.319535\pi$
$684$		0			0
$685$	16.9706	+	13.8564i	0.648412	+	0.529426i
$686$		0			0
$687$			12.2474i			0.467269i
$688$		0			0
$689$	12.7279			0.484895
$690$	18.0000	+	14.6969i	0.685248	+	0.559503i
$691$	−2.82843			−0.107598			−0.0537992	−	0.998552i	$-0.517133\pi$
$691$	−2.82843			−0.107598			−0.0537992	+	0.998552i	$0.517133\pi$
$692$		−	62.3538i		−	2.37034i
$693$		0			0
$694$	−18.0000			−0.683271
$695$	−14.0000	+	17.1464i	−0.531050	+	0.650401i
$696$	−42.4264			−1.60817
$697$			17.1464i			0.649467i
$698$		−	48.4974i		−	1.83565i
$699$	25.4558			0.962828
$700$		0			0
$701$	−47.0000			−1.77517			−0.887583	−	0.460648i	$-0.847617\pi$
$701$	−47.0000			−1.77517			−0.887583	+	0.460648i	$0.847617\pi$
$702$			22.0454i			0.832050i
$703$		−	6.92820i		−	0.261302i
$704$	40.0000			1.50756
$705$	−21.2132	+	25.9808i	−0.798935	+	0.978492i
$706$	55.1543			2.07576
$707$		0			0
$708$		−	9.79796i		−	0.368230i
$709$	−25.0000			−0.938895			−0.469447	−	0.882960i	$-0.655547\pi$
$709$	−25.0000			−0.938895			−0.469447	+	0.882960i	$0.655547\pi$
$710$	−8.48528	−	6.92820i	−0.318447	−	0.260011i
$711$		0			0
$712$		−	83.1384i		−	3.11574i
$713$			3.46410i			0.129732i
$714$		0			0
$715$	15.0000	+	12.2474i	0.560968	+	0.458029i
$716$	8.00000			0.298974
$717$		−	32.9090i		−	1.22901i
$718$		−	9.79796i		−	0.365657i
$719$	−52.3259			−1.95143			−0.975713	−	0.219051i	$-0.929704\pi$
$719$	−52.3259			−1.95143			−0.975713	+	0.219051i	$0.929704\pi$
$720$		0			0
$721$		0			0
$722$		−	26.9444i		−	1.00277i
$723$		−	31.8434i		−	1.18427i
$724$	39.5980			1.47165
$725$	5.00000	+	24.4949i	0.185695	+	0.909718i
$726$	−59.3970			−2.20443
$727$		−	38.1051i		−	1.41324i	−0.707593	−	0.706620i	$-0.750219\pi$
$727$		−	38.1051i		−	1.41324i	0.707593	−	0.706620i	$-0.249781\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	48.0000	−	58.7878i	1.77656	−	2.17583i
$731$		0			0
$732$			19.5959i			0.724286i
$733$		−	32.9090i		−	1.21552i	−0.794121	−	0.607760i	$-0.792068\pi$
$733$		−	32.9090i		−	1.21552i	0.794121	−	0.607760i	$-0.207932\pi$
$734$	−4.24264			−0.156599
$735$		0			0
$736$		0			0
$737$			36.7423i			1.35342i
$738$		0			0
$739$	19.0000			0.698926			0.349463	−	0.936950i	$-0.386364\pi$
$739$	19.0000			0.698926			0.349463	+	0.936950i	$0.386364\pi$
$740$	16.9706	+	13.8564i	0.623850	+	0.509372i
$741$	−8.48528			−0.311715
$742$		0			0
$743$			17.1464i			0.629041i	0.949251	+	0.314521i	$0.101844\pi$
$743$			17.1464i			0.629041i	−0.949251	+	0.314521i	$0.898156\pi$
$744$	12.0000			0.439941
$745$	5.65685	−	6.92820i	0.207251	−	0.253830i
$746$	36.0000			1.31805
$747$		0			0
$748$		−	34.6410i		−	1.26660i
$749$		0			0
$750$	−42.0000	−	22.0454i	−1.53362	−	0.804984i
$751$	45.0000			1.64207			0.821037	−	0.570875i	$-0.193396\pi$
$751$	45.0000			1.64207			0.821037	+	0.570875i	$0.193396\pi$
$752$		−	34.6410i		−	1.26323i
$753$			17.1464i			0.624851i
$754$	−21.2132			−0.772539
$755$	−7.07107	+	8.66025i	−0.257343	+	0.315179i
$756$		0			0
$757$			34.2929i			1.24640i	0.782064	+	0.623198i	$0.214167\pi$
$757$			34.2929i			1.24640i	−0.782064	+	0.623198i	$0.785833\pi$
$758$		−	63.6867i		−	2.31321i
$759$	−21.2132			−0.769991
$760$	−24.0000	−	19.5959i	−0.870572	−	0.710819i
$761$	−12.7279			−0.461387			−0.230693	−	0.973026i	$-0.574099\pi$
$761$	−12.7279			−0.461387			−0.230693	+	0.973026i	$0.574099\pi$
$762$			72.7461i			2.63531i
$763$		0			0
$764$	−68.0000			−2.46015
$765$		0			0
$766$	50.9117			1.83951
$767$		−	2.44949i		−	0.0884459i
$768$		−	55.4256i		−	2.00000i
$769$	−39.5980			−1.42794			−0.713970	−	0.700176i	$-0.753105\pi$
$769$	−39.5980			−1.42794			−0.713970	+	0.700176i	$0.753105\pi$
$770$		0			0
$771$	−6.00000			−0.216085
$772$			39.1918i			1.41055i
$773$			25.9808i			0.934463i	0.884135	+	0.467232i	$0.154749\pi$
$773$			25.9808i			0.934463i	−0.884135	+	0.467232i	$0.845251\pi$
$774$		0			0
$775$	−1.41421	−	6.92820i	−0.0508001	−	0.248868i
$776$	−8.48528			−0.304604
$777$		0			0
$778$			12.2474i			0.439092i
$779$	−28.0000			−1.00320
$780$	16.9706	−	20.7846i	0.607644	−	0.744208i
$781$	10.0000			0.357828
$782$		−	10.3923i		−	0.371628i
$783$		−	25.9808i		−	0.928477i
$784$		0			0
$785$	18.0000	+	14.6969i	0.642448	+	0.524556i
$786$	54.0000			1.92612
$787$		−	22.5167i		−	0.802632i	−0.915940	−	0.401316i	$-0.868553\pi$
$787$		−	22.5167i		−	0.802632i	0.915940	−	0.401316i	$-0.131447\pi$
$788$		−	68.5857i		−	2.44326i
$789$	16.9706			0.604168
$790$	−12.7279	−	10.3923i	−0.452839	−	0.369742i
$791$		0			0
$792$		0			0
$793$			4.89898i			0.173968i
$794$	−38.1838			−1.35509
$795$	18.0000	−	22.0454i	0.638394	−	0.781870i
$796$	73.5391			2.60652
$797$		−	1.73205i		−	0.0613524i	−0.999529	−	0.0306762i	$-0.990234\pi$
$797$		−	1.73205i		−	0.0613524i	0.999529	−	0.0306762i	$-0.00976607\pi$
$798$		0			0
$799$	15.0000			0.530662
$800$		0			0
$801$		0			0
$802$		−	26.9444i		−	0.951439i
$803$			69.2820i			2.44491i
$804$	50.9117			1.79552
$805$		0			0
$806$	6.00000			0.211341
$807$			36.7423i			1.29339i
$808$		−	55.4256i		−	1.94987i
$809$	5.00000			0.175791			0.0878953	−	0.996130i	$-0.471986\pi$
$809$	5.00000			0.175791			0.0878953	+	0.996130i	$0.471986\pi$
$810$	38.1838	+	31.1769i	1.34164	+	1.09545i
$811$	−49.4975			−1.73809			−0.869046	−	0.494732i	$-0.835266\pi$
$811$	−49.4975			−1.73809			−0.869046	+	0.494732i	$0.835266\pi$
$812$		0			0
$813$		−	39.1918i		−	1.37452i
$814$	−30.0000			−1.05150
$815$	−4.24264	−	3.46410i	−0.148613	−	0.121342i
$816$	−12.0000			−0.420084
$817$		0			0
$818$			27.7128i			0.968956i
$819$		0			0
$820$	56.0000	−	68.5857i	1.95560	−	2.39512i
$821$	−11.0000			−0.383903			−0.191951	−	0.981404i	$-0.561482\pi$
$821$	−11.0000			−0.383903			−0.191951	+	0.981404i	$0.561482\pi$
$822$			41.5692i			1.44989i
$823$		−	26.9444i		−	0.939222i	−0.882873	−	0.469611i	$-0.844394\pi$
$823$		−	26.9444i		−	0.939222i	0.882873	−	0.469611i	$-0.155606\pi$
$824$	−42.4264			−1.47799
$825$	42.4264	−	8.66025i	1.47710	−	0.301511i
$826$		0			0
$827$			17.1464i			0.596240i	0.954528	+	0.298120i	$0.0963595\pi$
$827$			17.1464i			0.596240i	−0.954528	+	0.298120i	$0.903640\pi$
$828$		0			0
$829$	−18.3848			−0.638530			−0.319265	−	0.947666i	$-0.603436\pi$
$829$	−18.3848			−0.638530			−0.319265	+	0.947666i	$0.603436\pi$
$830$	−48.0000	+	58.7878i	−1.66610	+	2.04055i
$831$	46.6690			1.61893
$832$		−	13.8564i		−	0.480384i
$833$		0			0
$834$	−42.0000			−1.45434
$835$	3.00000	+	2.44949i	0.103819	+	0.0847681i
$836$	56.5685			1.95646
$837$			7.34847i			0.254000i
$838$			72.7461i			2.51297i
$839$	9.89949			0.341769			0.170884	−	0.985291i	$-0.445338\pi$
$839$	9.89949			0.341769			0.170884	+	0.985291i	$0.445338\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$			22.0454i			0.759735i
$843$		−	8.66025i		−	0.298275i
$844$	−36.0000			−1.23917
$845$	−14.1421	+	17.3205i	−0.486504	+	0.595844i
$846$		0			0
$847$		0			0
$848$			29.3939i			1.00939i
$849$	−3.00000			−0.102960
$850$	4.24264	+	20.7846i	0.145521	+	0.712906i
$851$	−6.00000			−0.205677
$852$		−	13.8564i		−	0.474713i
$853$		−	38.1051i		−	1.30469i	−0.757920	−	0.652347i	$-0.773784\pi$
$853$		−	38.1051i		−	1.30469i	0.757920	−	0.652347i	$-0.226216\pi$
$854$		0			0
$855$		0			0
$856$	−72.0000			−2.46091
$857$			38.1051i			1.30165i	0.759229	+	0.650823i	$0.225576\pi$
$857$			38.1051i			1.30165i	−0.759229	+	0.650823i	$0.774424\pi$
$858$			36.7423i			1.25436i
$859$	−2.82843			−0.0965047			−0.0482523	−	0.998835i	$-0.515365\pi$
$859$	−2.82843			−0.0965047			−0.0482523	+	0.998835i	$0.515365\pi$
$860$		0			0
$861$		0			0
$862$			46.5403i			1.58517i
$863$			2.44949i			0.0833816i	0.999131	+	0.0416908i	$0.0132744\pi$
$863$			2.44949i			0.0833816i	−0.999131	+	0.0416908i	$0.986726\pi$
$864$		0			0
$865$	−27.0000	−	22.0454i	−0.918028	−	0.749566i
$866$	−25.4558			−0.865025
$867$			24.2487i			0.823529i
$868$		0			0
$869$	15.0000			0.508840
$870$	−30.0000	+	36.7423i	−1.01710	+	1.24568i
$871$	12.7279			0.431269
$872$			44.0908i			1.49310i
$873$		0			0
$874$	16.9706			0.574038
$875$		0			0
$876$	96.0000			3.24354
$877$		−	48.9898i		−	1.65427i	−0.562005	−	0.827134i	$-0.689970\pi$
$877$		−	48.9898i		−	1.65427i	0.562005	−	0.827134i	$-0.310030\pi$
$878$			17.3205i			0.584539i
$879$	−39.0000			−1.31544
$880$	−28.2843	+	34.6410i	−0.953463	+	1.16775i
$881$	−39.5980			−1.33409			−0.667045	−	0.745018i	$-0.732441\pi$
$881$	−39.5980			−1.33409			−0.667045	+	0.745018i	$0.732441\pi$
$882$		0			0
$883$			34.2929i			1.15405i	0.816728	+	0.577023i	$0.195786\pi$
$883$			34.2929i			1.15405i	−0.816728	+	0.577023i	$0.804214\pi$
$884$	−12.0000			−0.403604
$885$	−4.24264	−	3.46410i	−0.142615	−	0.116445i
$886$	36.0000			1.20944
$887$		−	45.0333i		−	1.51207i	−0.654531	−	0.756035i	$-0.727134\pi$
$887$		−	45.0333i		−	1.51207i	0.654531	−	0.756035i	$-0.272866\pi$
$888$			20.7846i			0.697486i
$889$		0			0
$890$	−72.0000	−	58.7878i	−2.41345	−	1.97057i
$891$	−45.0000			−1.50756
$892$			103.923i			3.47960i
$893$			24.4949i			0.819690i
$894$	16.9706			0.567581
$895$	2.82843	−	3.46410i	0.0945439	−	0.115792i
$896$		0			0
$897$			7.34847i			0.245358i
$898$			56.3383i			1.88003i
$899$	−7.07107			−0.235833
$900$		0			0
$901$	−12.7279			−0.424029
$902$			121.244i			4.03697i
$903$		0			0
$904$	84.0000			2.79380
$905$	14.0000	−	17.1464i	0.465376	−	0.569967i
$906$	−21.2132			−0.704761
$907$			7.34847i			0.244002i	0.992530	+	0.122001i	$0.0389311\pi$
$907$			7.34847i			0.244002i	−0.992530	+	0.122001i	$0.961069\pi$
$908$		−	6.92820i		−	0.229920i
$909$		0			0
$910$		0			0
$911$	44.0000			1.45779			0.728893	−	0.684628i	$-0.240035\pi$
$911$	44.0000			1.45779			0.728893	+	0.684628i	$0.240035\pi$
$912$		−	19.5959i		−	0.648886i
$913$		−	69.2820i		−	2.29290i
$914$	−6.00000			−0.198462
$915$	8.48528	+	6.92820i	0.280515	+	0.229039i
$916$	−28.2843			−0.934539
$917$		0			0
$918$		−	22.0454i		−	0.727607i
$919$	45.0000			1.48441			0.742207	−	0.670171i	$-0.233779\pi$
$919$	45.0000			1.48441			0.742207	+	0.670171i	$0.233779\pi$
$920$	−16.9706	+	20.7846i	−0.559503	+	0.685248i
$921$	3.00000			0.0988534
$922$		0			0
$923$		−	3.46410i		−	0.114022i
$924$		0			0
$925$	12.0000	−	2.44949i	0.394558	−	0.0805387i
$926$	84.0000			2.76041
$927$		0			0
$928$		0			0
$929$	−12.7279			−0.417590			−0.208795	−	0.977959i	$-0.566954\pi$
$929$	−12.7279			−0.417590			−0.208795	+	0.977959i	$0.566954\pi$
$930$	8.48528	−	10.3923i	0.278243	−	0.340777i
$931$		0			0
$932$			58.7878i			1.92566i
$933$		−	14.6969i		−	0.481156i
$934$	−38.1838			−1.24941
$935$	−15.0000	−	12.2474i	−0.490552	−	0.400534i
$936$		0			0
$937$			22.5167i			0.735587i	0.929907	+	0.367794i	$0.119887\pi$
$937$			22.5167i			0.735587i	−0.929907	+	0.367794i	$0.880113\pi$
$938$		0			0
$939$	15.0000			0.489506
$940$	−60.0000	−	48.9898i	−1.95698	−	1.59787i
$941$	−28.2843			−0.922041			−0.461020	−	0.887390i	$-0.652517\pi$
$941$	−28.2843			−0.922041			−0.461020	+	0.887390i	$0.652517\pi$
$942$			44.0908i			1.43656i
$943$			24.2487i			0.789647i
$944$	5.65685			0.184115
$945$		0			0
$946$		0			0
$947$		−	31.8434i		−	1.03477i	−0.855753	−	0.517385i	$-0.826905\pi$
$947$		−	31.8434i		−	1.03477i	0.855753	−	0.517385i	$-0.173095\pi$
$948$		−	20.7846i		−	0.675053i
$949$	24.0000			0.779073
$950$	−33.9411	+	6.92820i	−1.10120	+	0.224781i
$951$	−33.9411			−1.10062
$952$		0			0
$953$		−	17.1464i		−	0.555427i	−0.960664	−	0.277714i	$-0.910423\pi$
$953$		−	17.1464i		−	0.555427i	0.960664	−	0.277714i	$-0.0895766\pi$
$954$		0			0
$955$	−24.0416	+	29.4449i	−0.777969	+	0.952813i
$956$	76.0000			2.45802
$957$		−	43.3013i		−	1.39973i
$958$			51.9615i			1.67880i
$959$		0			0
$960$	−24.0000	−	19.5959i	−0.774597	−	0.632456i
$961$	−29.0000			−0.935484
$962$			10.3923i			0.335061i
$963$		0			0
$964$	73.5391			2.36854
$965$	16.9706	+	13.8564i	0.546302	+	0.446054i
$966$		0			0
$967$		−	34.2929i		−	1.10278i	−0.834246	−	0.551392i	$-0.814097\pi$
$967$		−	34.2929i		−	1.10278i	0.834246	−	0.551392i	$-0.185903\pi$
$968$		−	68.5857i		−	2.20443i
$969$	8.48528			0.272587
$970$	−6.00000	+	7.34847i	−0.192648	+	0.235945i
$971$	26.8701			0.862301			0.431151	−	0.902280i	$-0.358108\pi$
$971$	26.8701			0.862301			0.431151	+	0.902280i	$0.358108\pi$
$972$		0			0
$973$		0			0
$974$	−18.0000			−0.576757
$975$	−3.00000	−	14.6969i	−0.0960769	−	0.470679i
$976$	−11.3137			−0.362143
$977$			24.4949i			0.783661i	0.920037	+	0.391831i	$0.128158\pi$
$977$			24.4949i			0.783661i	−0.920037	+	0.391831i	$0.871842\pi$
$978$		−	10.3923i		−	0.332309i
$979$	84.8528			2.71191
$980$		0			0
$981$		0			0
$982$			56.3383i			1.79783i
$983$			25.9808i			0.828658i	0.910127	+	0.414329i	$0.135984\pi$
$983$			25.9808i			0.828658i	−0.910127	+	0.414329i	$0.864016\pi$
$984$	84.0000			2.67782
$985$	−29.6985	−	24.2487i	−0.946272	−	0.772628i
$986$	21.2132			0.675566
$987$		0			0
$988$		−	19.5959i		−	0.623429i
$989$		0			0
$990$		0			0
$991$	−30.0000			−0.952981			−0.476491	−	0.879180i	$-0.658091\pi$
$991$	−30.0000			−0.952981			−0.476491	+	0.879180i	$0.658091\pi$
$992$		0			0
$993$		−	31.1769i		−	0.989369i
$994$		0			0
$995$	26.0000	−	31.8434i	0.824255	−	1.00950i
$996$	−96.0000			−3.04188
$997$		−	46.7654i		−	1.48107i	−0.672015	−	0.740537i	$-0.734571\pi$
$997$		−	46.7654i		−	1.48107i	0.672015	−	0.740537i	$-0.265429\pi$
$998$			41.6413i			1.31813i
$999$	−12.7279			−0.402694

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.b.e.99.4	yes	4
3.2	odd	2		2205.2.d.i.1324.2		4
5.2	odd	4		1225.2.a.bb.1.2		4
5.3	odd	4		1225.2.a.bb.1.3		4
5.4	even	2	inner	245.2.b.e.99.1	✓	4
7.2	even	3		245.2.j.a.214.2		4
7.3	odd	6		245.2.j.a.79.1		4
7.4	even	3		245.2.j.f.79.1		4
7.5	odd	6		245.2.j.f.214.2		4
7.6	odd	2	inner	245.2.b.e.99.3	yes	4
15.14	odd	2		2205.2.d.i.1324.4		4
21.20	even	2		2205.2.d.i.1324.1		4
35.4	even	6		245.2.j.a.79.2		4
35.9	even	6		245.2.j.f.214.1		4
35.13	even	4		1225.2.a.bb.1.4		4
35.19	odd	6		245.2.j.a.214.1		4
35.24	odd	6		245.2.j.f.79.2		4
35.27	even	4		1225.2.a.bb.1.1		4
35.34	odd	2	inner	245.2.b.e.99.2	yes	4
105.104	even	2		2205.2.d.i.1324.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.2.b.e.99.1	✓	4	5.4	even	2	inner
245.2.b.e.99.2	yes	4	35.34	odd	2	inner
245.2.b.e.99.3	yes	4	7.6	odd	2	inner
245.2.b.e.99.4	yes	4	1.1	even	1	trivial
245.2.j.a.79.1		4	7.3	odd	6
245.2.j.a.79.2		4	35.4	even	6
245.2.j.a.214.1		4	35.19	odd	6
245.2.j.a.214.2		4	7.2	even	3
245.2.j.f.79.1		4	7.4	even	3
245.2.j.f.79.2		4	35.24	odd	6
245.2.j.f.214.1		4	35.9	even	6
245.2.j.f.214.2		4	7.5	odd	6
1225.2.a.bb.1.1		4	35.27	even	4
1225.2.a.bb.1.2		4	5.2	odd	4
1225.2.a.bb.1.3		4	5.3	odd	4
1225.2.a.bb.1.4		4	35.13	even	4
2205.2.d.i.1324.1		4	21.20	even	2
2205.2.d.i.1324.2		4	3.2	odd	2
2205.2.d.i.1324.3		4	105.104	even	2
2205.2.d.i.1324.4		4	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.44949i q^{2} +1.73205i q^{3} -4.00000 q^{4} +(-1.41421 + 1.73205i) q^{5} -4.24264 q^{6} -4.89898i q^{8} +(-4.24264 - 3.46410i) q^{10} +5.00000 q^{11} -6.92820i q^{12} -1.73205i q^{13} +(-3.00000 - 2.44949i) q^{15} +4.00000 q^{16} +1.73205i q^{17} -2.82843 q^{19} +(5.65685 - 6.92820i) q^{20} +12.2474i q^{22} +2.44949i q^{23} +8.48528 q^{24} +(-1.00000 - 4.89898i) q^{25} +4.24264 q^{26} +5.19615i q^{27} -5.00000 q^{29} +(6.00000 - 7.34847i) q^{30} +1.41421 q^{31} +8.66025i q^{33} -4.24264 q^{34} +2.44949i q^{37} -6.92820i q^{38} +3.00000 q^{39} +(8.48528 + 6.92820i) q^{40} +9.89949 q^{41} -20.0000 q^{44} -6.00000 q^{46} -8.66025i q^{47} +6.92820i q^{48} +(12.0000 - 2.44949i) q^{50} -3.00000 q^{51} +6.92820i q^{52} +7.34847i q^{53} -12.7279 q^{54} +(-7.07107 + 8.66025i) q^{55} -4.89898i q^{57} -12.2474i q^{58} +1.41421 q^{59} +(12.0000 + 9.79796i) q^{60} -2.82843 q^{61} +3.46410i q^{62} +8.00000 q^{64} +(3.00000 + 2.44949i) q^{65} -21.2132 q^{66} +7.34847i q^{67} -6.92820i q^{68} -4.24264 q^{69} +2.00000 q^{71} +13.8564i q^{73} -6.00000 q^{74} +(8.48528 - 1.73205i) q^{75} +11.3137 q^{76} +7.34847i q^{78} +3.00000 q^{79} +(-5.65685 + 6.92820i) q^{80} -9.00000 q^{81} +24.2487i q^{82} -13.8564i q^{83} +(-3.00000 - 2.44949i) q^{85} -8.66025i q^{87} -24.4949i q^{88} +16.9706 q^{89} -9.79796i q^{92} +2.44949i q^{93} +21.2132 q^{94} +(4.00000 - 4.89898i) q^{95} -1.73205i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{4} + 20 q^{11} - 12 q^{15} + 16 q^{16} - 4 q^{25} - 20 q^{29} + 24 q^{30} + 12 q^{39} - 80 q^{44} - 24 q^{46} + 48 q^{50} - 12 q^{51} + 48 q^{60} + 32 q^{64} + 12 q^{65} + 8 q^{71} - 24 q^{74}+ \cdots + 16 q^{95}+O(q^{100}) \) 4 * q - 16 * q^4 + 20 * q^11 - 12 * q^15 + 16 * q^16 - 4 * q^25 - 20 * q^29 + 24 * q^30 + 12 * q^39 - 80 * q^44 - 24 * q^46 + 48 * q^50 - 12 * q^51 + 48 * q^60 + 32 * q^64 + 12 * q^65 + 8 * q^71 - 24 * q^74 + 12 * q^79 - 36 * q^81 - 12 * q^85 + 16 * q^95

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