LMFDB - Embedded newform 1300.2.bb.d.1049.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(549,1300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1300, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1300.549");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$1300 = 2^{2} \cdot 5^{2} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1300.bb (of order $6$ , degree $2$ , not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.3805522628$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - x^{2} + 1$ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1049.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1300.1049
Dual form			1300.2.bb.d.549.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 + 1.00000i) q^{3} +(3.46410 - 2.00000i) q^{7} +(0.500000 + 0.866025i) q^{9} +(0.866025 - 3.50000i) q^{13} +(-2.59808 + 1.50000i) q^{17} +(1.00000 + 1.73205i) q^{19} +8.00000 q^{21} +(5.19615 + 3.00000i) q^{23} -4.00000i q^{27} +(4.50000 - 7.79423i) q^{29} +2.00000 q^{31} +(-6.06218 - 3.50000i) q^{37} +(5.00000 - 5.19615i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(-3.46410 + 2.00000i) q^{43} +6.00000i q^{47} +(4.50000 - 7.79423i) q^{49} -6.00000 q^{51} +9.00000i q^{53} +4.00000i q^{57} +(-2.50000 - 4.33013i) q^{61} +(3.46410 + 2.00000i) q^{63} +(1.73205 + 1.00000i) q^{67} +(6.00000 + 10.3923i) q^{69} +(3.00000 + 5.19615i) q^{71} -1.00000i q^{73} +4.00000 q^{79} +(5.50000 - 9.52628i) q^{81} +12.0000i q^{83} +(15.5885 - 9.00000i) q^{87} +(3.00000 - 5.19615i) q^{89} +(-4.00000 - 13.8564i) q^{91} +(3.46410 + 2.00000i) q^{93} +(-12.1244 + 7.00000i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q + 2 q^{9} + 4 q^{19} + 32 q^{21} + 18 q^{29} + 8 q^{31} + 20 q^{39} - 6 q^{41} + 18 q^{49} - 24 q^{51} - 10 q^{61} + 24 q^{69} + 12 q^{71} + 16 q^{79} + 22 q^{81} + 12 q^{89} - 16 q^{91}+O(q^{100})$ 4 * q + 2 * q^9 + 4 * q^19 + 32 * q^21 + 18 * q^29 + 8 * q^31 + 20 * q^39 - 6 * q^41 + 18 * q^49 - 24 * q^51 - 10 * q^61 + 24 * q^69 + 12 * q^71 + 16 * q^79 + 22 * q^81 + 12 * q^89 - 16 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$ .

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$		0			0
$2$		0			0
$3$	1.73205	+	1.00000i	1.00000	+	0.577350i	0.908248	−	0.418432i	$-0.137420\pi$
$3$	1.73205	+	1.00000i	1.00000	+	0.577350i	0.0917517	+	0.995782i	$0.470753\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.46410	−	2.00000i	1.30931	−	0.755929i	0.327327	−	0.944911i	$-0.393852\pi$
$7$	3.46410	−	2.00000i	1.30931	−	0.755929i	0.981981	+	0.188982i	$0.0605189\pi$
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$		0			0
$13$	0.866025	−	3.50000i	0.240192	−	0.970725i
$13$	0.866025	−	3.50000i	0.240192	−	0.970725i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.59808	+	1.50000i	−0.630126	+	0.363803i	−0.780801	−	0.624780i	$-0.785189\pi$
$17$	−2.59808	+	1.50000i	−0.630126	+	0.363803i	0.150675	+	0.988583i	$0.451855\pi$
$18$		0			0
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$		0			0
$21$	8.00000			1.74574
$22$		0			0
$23$	5.19615	+	3.00000i	1.08347	+	0.625543i	0.931831	−	0.362892i	$-0.118211\pi$
$23$	5.19615	+	3.00000i	1.08347	+	0.625543i	0.151642	+	0.988436i	$0.451544\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	4.00000i		−	0.769800i
$28$		0			0
$29$	4.50000	−	7.79423i	0.835629	−	1.44735i	−0.0578882	−	0.998323i	$-0.518437\pi$
$29$	4.50000	−	7.79423i	0.835629	−	1.44735i	0.893517	−	0.449029i	$-0.148230\pi$
$30$		0			0
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−6.06218	−	3.50000i	−0.996616	−	0.575396i	−0.0893706	−	0.995998i	$-0.528486\pi$
$37$	−6.06218	−	3.50000i	−0.996616	−	0.575396i	−0.907245	+	0.420602i	$0.861819\pi$
$38$		0			0
$39$	5.00000	−	5.19615i	0.800641	−	0.832050i
$40$		0			0
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	−3.46410	+	2.00000i	−0.528271	+	0.304997i	−0.740312	−	0.672264i	$-0.765322\pi$
$43$	−3.46410	+	2.00000i	−0.528271	+	0.304997i	0.212041	+	0.977261i	$0.431989\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			6.00000i			0.875190i	0.899172	+	0.437595i	$0.144170\pi$
$47$			6.00000i			0.875190i	−0.899172	+	0.437595i	$0.855830\pi$
$48$		0			0
$49$	4.50000	−	7.79423i	0.642857	−	1.11346i
$50$		0			0
$51$	−6.00000			−0.840168
$52$		0			0
$53$			9.00000i			1.23625i	0.786082	+	0.618123i	$0.212106\pi$
$53$			9.00000i			1.23625i	−0.786082	+	0.618123i	$0.787894\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			4.00000i			0.529813i
$58$		0			0
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	0.660415	−	0.750901i	$-0.270381\pi$
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	−0.980507	+	0.196485i	$0.937047\pi$
$62$		0			0
$63$	3.46410	+	2.00000i	0.436436	+	0.251976i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.73205	+	1.00000i	0.211604	+	0.122169i	0.602056	−	0.798454i	$-0.294348\pi$
$67$	1.73205	+	1.00000i	0.211604	+	0.122169i	−0.390453	+	0.920623i	$0.627682\pi$
$68$		0			0
$69$	6.00000	+	10.3923i	0.722315	+	1.25109i
$70$		0			0
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$		0			0
$73$		−	1.00000i		−	0.117041i	−0.998286	−	0.0585206i	$-0.981362\pi$
$73$		−	1.00000i		−	0.117041i	0.998286	−	0.0585206i	$-0.0186383\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$		0			0
$83$			12.0000i			1.31717i	0.752506	+	0.658586i	$0.228845\pi$
$83$			12.0000i			1.31717i	−0.752506	+	0.658586i	$0.771155\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	15.5885	−	9.00000i	1.67126	−	0.964901i
$88$		0			0
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$	−4.00000	−	13.8564i	−0.419314	−	1.45255i
$92$		0			0
$93$	3.46410	+	2.00000i	0.359211	+	0.207390i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−12.1244	+	7.00000i	−1.23104	+	0.710742i	−0.967247	−	0.253837i	$-0.918307\pi$
$97$	−12.1244	+	7.00000i	−1.23104	+	0.710742i	−0.263795	+	0.964579i	$0.584974\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	−0.998240	−	0.0592978i	$-0.981114\pi$
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	0.550474	+	0.834853i	$0.314447\pi$
$102$		0			0
$103$			2.00000i			0.197066i	0.995134	+	0.0985329i	$0.0314150\pi$
$103$			2.00000i			0.197066i	−0.995134	+	0.0985329i	$0.968585\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.19615	+	3.00000i	0.502331	+	0.290021i	0.729676	−	0.683793i	$-0.239671\pi$
$107$	5.19615	+	3.00000i	0.502331	+	0.290021i	−0.227345	+	0.973814i	$0.573004\pi$
$108$		0			0
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$		0			0
$111$	−7.00000	−	12.1244i	−0.664411	−	1.15079i
$112$		0			0
$113$	−7.79423	+	4.50000i	−0.733219	+	0.423324i	−0.819599	−	0.572938i	$-0.805804\pi$
$113$	−7.79423	+	4.50000i	−0.733219	+	0.423324i	0.0863794	+	0.996262i	$0.472470\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.46410	−	1.00000i	0.320256	−	0.0924500i
$118$		0			0
$119$	−6.00000	+	10.3923i	−0.550019	+	0.952661i
$120$		0			0
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$		0			0
$123$	−5.19615	+	3.00000i	−0.468521	+	0.270501i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−8.66025	−	5.00000i	−0.768473	−	0.443678i	0.0638564	−	0.997959i	$-0.479660\pi$
$127$	−8.66025	−	5.00000i	−0.768473	−	0.443678i	−0.832330	+	0.554281i	$0.812993\pi$
$128$		0			0
$129$	−8.00000			−0.704361
$130$		0			0
$131$	6.00000			0.524222			0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000			0.524222			0.262111	+	0.965038i	$0.415581\pi$
$132$		0			0
$133$	6.92820	+	4.00000i	0.600751	+	0.346844i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−12.9904	+	7.50000i	−1.10984	+	0.640768i	−0.938789	−	0.344493i	$-0.888051\pi$
$137$	−12.9904	+	7.50000i	−1.10984	+	0.640768i	−0.171054	+	0.985262i	$0.554717\pi$
$138$		0			0
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	0.296866	−	0.954919i	$-0.404058\pi$
$140$		0			0
$141$	−6.00000	+	10.3923i	−0.505291	+	0.875190i
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$	15.5885	−	9.00000i	1.28571	−	0.742307i
$148$		0			0
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	0.989355	−	0.145519i	$-0.0464853\pi$
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	−0.620701	+	0.784047i	$0.713152\pi$
$150$		0			0
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$		0			0
$153$	−2.59808	−	1.50000i	−0.210042	−	0.121268i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			7.00000i			0.558661i	0.960195	+	0.279330i	$0.0901125\pi$
$157$			7.00000i			0.558661i	−0.960195	+	0.279330i	$0.909888\pi$
$158$		0			0
$159$	−9.00000	+	15.5885i	−0.713746	+	1.23625i
$160$		0			0
$161$	24.0000			1.89146
$162$		0			0
$163$	6.92820	−	4.00000i	0.542659	−	0.313304i	−0.203497	−	0.979076i	$-0.565231\pi$
$163$	6.92820	−	4.00000i	0.542659	−	0.313304i	0.746156	+	0.665771i	$0.231897\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−20.7846	−	12.0000i	−1.60836	−	0.928588i	−0.989737	−	0.142901i	$-0.954357\pi$
$167$	−20.7846	−	12.0000i	−1.60836	−	0.928588i	−0.618624	−	0.785687i	$-0.712310\pi$
$168$		0			0
$169$	−11.5000	−	6.06218i	−0.884615	−	0.466321i
$170$		0			0
$171$	−1.00000	+	1.73205i	−0.0764719	+	0.132453i
$172$		0			0
$173$	5.19615	−	3.00000i	0.395056	−	0.228086i	−0.289292	−	0.957241i	$-0.593420\pi$
$173$	5.19615	−	3.00000i	0.395056	−	0.228086i	0.684349	+	0.729155i	$0.260087\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.0000	−	20.7846i	0.896922	−	1.55351i	0.0655145	−	0.997852i	$-0.479131\pi$
$179$	12.0000	−	20.7846i	0.896922	−	1.55351i	0.831408	−	0.555663i	$-0.187536\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$		−	10.0000i		−	0.739221i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−8.00000	−	13.8564i	−0.581914	−	1.00791i
$190$		0			0
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	0.736839	−	0.676068i	$-0.236317\pi$
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	−0.953912	+	0.300088i	$0.902984\pi$
$192$		0			0
$193$	−9.52628	−	5.50000i	−0.685717	−	0.395899i	0.116289	−	0.993215i	$-0.462900\pi$
$193$	−9.52628	−	5.50000i	−0.685717	−	0.395899i	−0.802005	+	0.597317i	$0.796234\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.19615	+	3.00000i	0.370211	+	0.213741i	0.673550	−	0.739141i	$-0.264768\pi$
$197$	5.19615	+	3.00000i	0.370211	+	0.213741i	−0.303340	+	0.952882i	$0.598102\pi$
$198$		0			0
$199$	13.0000	+	22.5167i	0.921546	+	1.59616i	0.797025	+	0.603947i	$0.206406\pi$
$199$	13.0000	+	22.5167i	0.921546	+	1.59616i	0.124521	+	0.992217i	$0.460261\pi$
$200$		0			0
$201$	2.00000	+	3.46410i	0.141069	+	0.244339i
$202$		0			0
$203$		−	36.0000i		−	2.52670i
$204$		0			0
$205$		0			0
$206$		0			0
$207$			6.00000i			0.417029i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−1.00000	+	1.73205i	−0.0688428	+	0.119239i	−0.898392	−	0.439194i	$-0.855264\pi$
$211$	−1.00000	+	1.73205i	−0.0688428	+	0.119239i	0.829549	+	0.558433i	$0.188597\pi$
$212$		0			0
$213$			12.0000i			0.822226i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	6.92820	−	4.00000i	0.470317	−	0.271538i
$218$		0			0
$219$	1.00000	−	1.73205i	0.0675737	−	0.117041i
$220$		0			0
$221$	3.00000	+	10.3923i	0.201802	+	0.699062i
$222$		0			0
$223$	−22.5167	−	13.0000i	−1.50783	−	0.870544i	−0.999959	−	0.00910984i	$-0.997100\pi$
$223$	−22.5167	−	13.0000i	−1.50783	−	0.870544i	−0.507869	−	0.861435i	$-0.669566\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.19615	+	3.00000i	−0.344881	+	0.199117i	−0.662428	−	0.749125i	$-0.730474\pi$
$227$	−5.19615	+	3.00000i	−0.344881	+	0.199117i	0.317547	+	0.948242i	$0.397141\pi$
$228$		0			0
$229$	−14.0000			−0.925146			−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000			−0.925146			−0.462573	+	0.886581i	$0.653074\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	18.0000i		−	1.17922i	−0.807688	−	0.589610i	$-0.799282\pi$
$233$		−	18.0000i		−	1.17922i	0.807688	−	0.589610i	$-0.200718\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	6.92820	+	4.00000i	0.450035	+	0.259828i
$238$		0			0
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	0.881680	−	0.471848i	$-0.156413\pi$
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	−0.849472	+	0.527633i	$0.823079\pi$
$242$		0			0
$243$	8.66025	−	5.00000i	0.555556	−	0.320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	6.92820	−	2.00000i	0.440831	−	0.127257i
$248$		0			0
$249$	−12.0000	+	20.7846i	−0.760469	+	1.31717i
$250$		0			0
$251$	3.00000	+	5.19615i	0.189358	+	0.327978i	0.945036	−	0.326965i	$-0.106026\pi$
$251$	3.00000	+	5.19615i	0.189358	+	0.327978i	−0.755678	+	0.654943i	$0.772693\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.59808	+	1.50000i	0.162064	+	0.0935674i	0.578838	−	0.815442i	$-0.303506\pi$
$257$	2.59808	+	1.50000i	0.162064	+	0.0935674i	−0.416775	+	0.909010i	$0.636840\pi$
$258$		0			0
$259$	−28.0000			−1.73984
$260$		0			0
$261$	9.00000			0.557086
$262$		0			0
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	10.3923	−	6.00000i	0.635999	−	0.367194i
$268$		0			0
$269$	15.0000	+	25.9808i	0.914566	+	1.58408i	0.807535	+	0.589819i	$0.200801\pi$
$269$	15.0000	+	25.9808i	0.914566	+	1.58408i	0.107031	+	0.994256i	$0.465866\pi$
$270$		0			0
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	−0.961563	−	0.274586i	$-0.911459\pi$
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	0.718580	+	0.695444i	$0.244792\pi$
$272$		0			0
$273$	6.92820	−	28.0000i	0.419314	−	1.69464i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	16.4545	−	9.50000i	0.988654	−	0.570800i	0.0837823	−	0.996484i	$-0.473300\pi$
$277$	16.4545	−	9.50000i	0.988654	−	0.570800i	0.904872	+	0.425684i	$0.139967\pi$
$278$		0			0
$279$	1.00000	+	1.73205i	0.0598684	+	0.103695i
$280$		0			0
$281$	3.00000			0.178965			0.0894825	−	0.995988i	$-0.471479\pi$
$281$	3.00000			0.178965			0.0894825	+	0.995988i	$0.471479\pi$
$282$		0			0
$283$	13.8564	+	8.00000i	0.823678	+	0.475551i	0.851683	−	0.524057i	$-0.175582\pi$
$283$	13.8564	+	8.00000i	0.823678	+	0.475551i	−0.0280052	+	0.999608i	$0.508916\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			12.0000i			0.708338i
$288$		0			0
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$		0			0
$291$	−28.0000			−1.64139
$292$		0			0
$293$	7.79423	−	4.50000i	0.455344	−	0.262893i	−0.254741	−	0.967009i	$-0.581990\pi$
$293$	7.79423	−	4.50000i	0.455344	−	0.262893i	0.710084	+	0.704117i	$0.248657\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	15.0000	−	15.5885i	0.867472	−	0.901504i
$300$		0			0
$301$	−8.00000	+	13.8564i	−0.461112	+	0.798670i
$302$		0			0
$303$	−15.5885	+	9.00000i	−0.895533	+	0.517036i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	26.0000i		−	1.48390i	−0.670456	−	0.741949i	$-0.733902\pi$
$307$		−	26.0000i		−	1.48390i	0.670456	−	0.741949i	$-0.266098\pi$
$308$		0			0
$309$	−2.00000	+	3.46410i	−0.113776	+	0.197066i
$310$		0			0
$311$	6.00000			0.340229			0.170114	−	0.985424i	$-0.445586\pi$
$311$	6.00000			0.340229			0.170114	+	0.985424i	$0.445586\pi$
$312$		0			0
$313$			14.0000i			0.791327i	0.918396	+	0.395663i	$0.129485\pi$
$313$			14.0000i			0.791327i	−0.918396	+	0.395663i	$0.870515\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			15.0000i			0.842484i	0.906948	+	0.421242i	$0.138406\pi$
$317$			15.0000i			0.842484i	−0.906948	+	0.421242i	$0.861594\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	6.00000	+	10.3923i	0.334887	+	0.580042i
$322$		0			0
$323$	−5.19615	−	3.00000i	−0.289122	−	0.166924i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	17.3205	+	10.0000i	0.957826	+	0.553001i
$328$		0			0
$329$	12.0000	+	20.7846i	0.661581	+	1.14589i
$330$		0			0
$331$	−16.0000	−	27.7128i	−0.879440	−	1.52323i	−0.851957	−	0.523612i	$-0.824584\pi$
$331$	−16.0000	−	27.7128i	−0.879440	−	1.52323i	−0.0274825	−	0.999622i	$-0.508749\pi$
$332$		0			0
$333$		−	7.00000i		−	0.383598i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			25.0000i			1.36184i	0.732359	+	0.680918i	$0.238419\pi$
$337$			25.0000i			1.36184i	−0.732359	+	0.680918i	$0.761581\pi$
$338$		0			0
$339$	−18.0000			−0.977626
$340$		0			0
$341$		0			0
$342$		0			0
$343$		−	8.00000i		−	0.431959i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−15.5885	+	9.00000i	−0.836832	+	0.483145i	−0.856186	−	0.516667i	$-0.827172\pi$
$347$	−15.5885	+	9.00000i	−0.836832	+	0.483145i	0.0193540	+	0.999813i	$0.493839\pi$
$348$		0			0
$349$	7.00000	−	12.1244i	0.374701	−	0.649002i	−0.615581	−	0.788074i	$-0.711079\pi$
$349$	7.00000	−	12.1244i	0.374701	−	0.649002i	0.990282	+	0.139072i	$0.0444119\pi$
$350$		0			0
$351$	−14.0000	−	3.46410i	−0.747265	−	0.184900i
$352$		0			0
$353$	−23.3827	−	13.5000i	−1.24453	−	0.718532i	−0.274521	−	0.961581i	$-0.588519\pi$
$353$	−23.3827	−	13.5000i	−1.24453	−	0.718532i	−0.970014	+	0.243049i	$0.921853\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−20.7846	+	12.0000i	−1.10004	+	0.635107i
$358$		0			0
$359$	−36.0000			−1.90001			−0.950004	−	0.312239i	$-0.898921\pi$
$359$	−36.0000			−1.90001			−0.950004	+	0.312239i	$0.898921\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$		0			0
$363$			22.0000i			1.15470i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−19.0526	−	11.0000i	−0.994535	−	0.574195i	−0.0879086	−	0.996129i	$-0.528018\pi$
$367$	−19.0526	−	11.0000i	−0.994535	−	0.574195i	−0.906627	+	0.421933i	$0.861352\pi$
$368$		0			0
$369$	−3.00000			−0.156174
$370$		0			0
$371$	18.0000	+	31.1769i	0.934513	+	1.61862i
$372$		0			0
$373$	−6.06218	+	3.50000i	−0.313888	+	0.181223i	−0.648665	−	0.761074i	$-0.724672\pi$
$373$	−6.06218	+	3.50000i	−0.313888	+	0.181223i	0.334777	+	0.942297i	$0.391339\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−23.3827	−	22.5000i	−1.20427	−	1.15881i
$378$		0			0
$379$	−5.00000	+	8.66025i	−0.256833	+	0.444847i	−0.965392	−	0.260804i	$-0.916012\pi$
$379$	−5.00000	+	8.66025i	−0.256833	+	0.444847i	0.708559	+	0.705652i	$0.249346\pi$
$380$		0			0
$381$	−10.0000	−	17.3205i	−0.512316	−	0.887357i
$382$		0			0
$383$	−31.1769	+	18.0000i	−1.59307	+	0.919757i	−0.600289	+	0.799783i	$0.704948\pi$
$383$	−31.1769	+	18.0000i	−1.59307	+	0.919757i	−0.992777	+	0.119974i	$0.961719\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.46410	−	2.00000i	−0.176090	−	0.101666i
$388$		0			0
$389$	−21.0000			−1.06474			−0.532371	−	0.846511i	$-0.678699\pi$
$389$	−21.0000			−1.06474			−0.532371	+	0.846511i	$0.678699\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$		0			0
$393$	10.3923	+	6.00000i	0.524222	+	0.302660i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	8.66025	−	5.00000i	0.434646	−	0.250943i	−0.266678	−	0.963786i	$-0.585926\pi$
$397$	8.66025	−	5.00000i	0.434646	−	0.250943i	0.701324	+	0.712843i	$0.252593\pi$
$398$		0			0
$399$	8.00000	+	13.8564i	0.400501	+	0.693688i
$400$		0			0
$401$	16.5000	−	28.5788i	0.823971	−	1.42716i	−0.0787327	−	0.996896i	$-0.525087\pi$
$401$	16.5000	−	28.5788i	0.823971	−	1.42716i	0.902703	−	0.430263i	$-0.141579\pi$
$402$		0			0
$403$	1.73205	−	7.00000i	0.0862796	−	0.348695i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−12.5000	−	21.6506i	−0.618085	−	1.07056i	−0.989835	−	0.142222i	$-0.954575\pi$
$409$	−12.5000	−	21.6506i	−0.618085	−	1.07056i	0.371750	−	0.928333i	$-0.378758\pi$
$410$		0			0
$411$	−30.0000			−1.47979
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	32.0000i		−	1.56705i
$418$		0			0
$419$	15.0000	−	25.9808i	0.732798	−	1.26924i	−0.222885	−	0.974845i	$-0.571547\pi$
$419$	15.0000	−	25.9808i	0.732798	−	1.26924i	0.955683	−	0.294398i	$-0.0951193\pi$
$420$		0			0
$421$	5.00000			0.243685			0.121843	−	0.992549i	$-0.461120\pi$
$421$	5.00000			0.243685			0.121843	+	0.992549i	$0.461120\pi$
$422$		0			0
$423$	−5.19615	+	3.00000i	−0.252646	+	0.145865i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−17.3205	−	10.0000i	−0.838198	−	0.483934i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$		0			0
$433$	−0.866025	+	0.500000i	−0.0416185	+	0.0240285i	−0.520665	−	0.853761i	$-0.674316\pi$
$433$	−0.866025	+	0.500000i	−0.0416185	+	0.0240285i	0.479046	+	0.877790i	$0.340983\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			12.0000i			0.574038i
$438$		0			0
$439$	16.0000	−	27.7128i	0.763638	−	1.32266i	−0.177325	−	0.984152i	$-0.556744\pi$
$439$	16.0000	−	27.7128i	0.763638	−	1.32266i	0.940963	−	0.338508i	$-0.109922\pi$
$440$		0			0
$441$	9.00000			0.428571
$442$		0			0
$443$			12.0000i			0.570137i	0.958507	+	0.285069i	$0.0920164\pi$
$443$			12.0000i			0.570137i	−0.958507	+	0.285069i	$0.907984\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			18.0000i			0.851371i
$448$		0			0
$449$	15.0000	+	25.9808i	0.707894	+	1.22611i	0.965637	+	0.259895i	$0.0836878\pi$
$449$	15.0000	+	25.9808i	0.707894	+	1.22611i	−0.257743	+	0.966213i	$0.582979\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−17.3205	−	10.0000i	−0.813788	−	0.469841i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	19.9186	+	11.5000i	0.931752	+	0.537947i	0.887365	−	0.461067i	$-0.152533\pi$
$457$	19.9186	+	11.5000i	0.931752	+	0.537947i	0.0443868	+	0.999014i	$0.485867\pi$
$458$		0			0
$459$	6.00000	+	10.3923i	0.280056	+	0.485071i
$460$		0			0
$461$	19.5000	+	33.7750i	0.908206	+	1.57306i	0.816556	+	0.577267i	$0.195881\pi$
$461$	19.5000	+	33.7750i	0.908206	+	1.57306i	0.0916500	+	0.995791i	$0.470786\pi$
$462$		0			0
$463$			20.0000i			0.929479i	0.885448	+	0.464739i	$0.153852\pi$
$463$			20.0000i			0.929479i	−0.885448	+	0.464739i	$0.846148\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			36.0000i			1.66588i	0.553362	+	0.832941i	$0.313345\pi$
$467$			36.0000i			1.66588i	−0.553362	+	0.832941i	$0.686655\pi$
$468$		0			0
$469$	8.00000			0.369406
$470$		0			0
$471$	−7.00000	+	12.1244i	−0.322543	+	0.558661i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−7.79423	+	4.50000i	−0.356873	+	0.206041i
$478$		0			0
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	−0.583803	−	0.811895i	$-0.698436\pi$
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	0.995023	+	0.0996406i	$0.0317693\pi$
$480$		0			0
$481$	−17.5000	+	18.1865i	−0.797931	+	0.829235i
$482$		0			0
$483$	41.5692	+	24.0000i	1.89146	+	1.09204i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	13.8564	−	8.00000i	0.627894	−	0.362515i	−0.152042	−	0.988374i	$-0.548585\pi$
$487$	13.8564	−	8.00000i	0.627894	−	0.362515i	0.779936	+	0.625859i	$0.215252\pi$
$488$		0			0
$489$	16.0000			0.723545
$490$		0			0
$491$	12.0000	−	20.7846i	0.541552	−	0.937996i	−0.457263	−	0.889332i	$-0.651170\pi$
$491$	12.0000	−	20.7846i	0.541552	−	0.937996i	0.998815	−	0.0486647i	$-0.0154966\pi$
$492$		0			0
$493$			27.0000i			1.21602i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	20.7846	+	12.0000i	0.932317	+	0.538274i
$498$		0			0
$499$	−14.0000			−0.626726			−0.313363	−	0.949633i	$-0.601456\pi$
$499$	−14.0000			−0.626726			−0.313363	+	0.949633i	$0.601456\pi$
$500$		0			0
$501$	−24.0000	−	41.5692i	−1.07224	−	1.85718i
$502$		0			0
$503$	10.3923	−	6.00000i	0.463370	−	0.267527i	−0.250090	−	0.968223i	$-0.580460\pi$
$503$	10.3923	−	6.00000i	0.463370	−	0.267527i	0.713460	+	0.700696i	$0.247127\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−13.8564	−	22.0000i	−0.615385	−	0.977054i
$508$		0			0
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	−0.982988	−	0.183669i	$-0.941202\pi$
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	0.650556	+	0.759458i	$0.274536\pi$
$510$		0			0
$511$	−2.00000	−	3.46410i	−0.0884748	−	0.153243i
$512$		0			0
$513$	6.92820	−	4.00000i	0.305888	−	0.176604i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	12.0000			0.526742
$520$		0			0
$521$	−9.00000			−0.394297			−0.197149	−	0.980374i	$-0.563168\pi$
$521$	−9.00000			−0.394297			−0.197149	+	0.980374i	$0.563168\pi$
$522$		0			0
$523$	−17.3205	−	10.0000i	−0.757373	−	0.437269i	0.0709788	−	0.997478i	$-0.477388\pi$
$523$	−17.3205	−	10.0000i	−0.757373	−	0.437269i	−0.828352	+	0.560208i	$0.810721\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.19615	+	3.00000i	−0.226348	+	0.130682i
$528$		0			0
$529$	6.50000	+	11.2583i	0.282609	+	0.489493i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	7.79423	+	7.50000i	0.337606	+	0.324861i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	41.5692	−	24.0000i	1.79384	−	1.03568i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−19.0000			−0.816874			−0.408437	−	0.912787i	$-0.633926\pi$
$541$	−19.0000			−0.816874			−0.408437	+	0.912787i	$0.633926\pi$
$542$		0			0
$543$	−12.1244	−	7.00000i	−0.520306	−	0.300399i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			22.0000i			0.940652i	0.882493	+	0.470326i	$0.155864\pi$
$547$			22.0000i			0.940652i	−0.882493	+	0.470326i	$0.844136\pi$
$548$		0			0
$549$	2.50000	−	4.33013i	0.106697	−	0.184805i
$550$		0			0
$551$	18.0000			0.766826
$552$		0			0
$553$	13.8564	−	8.00000i	0.589234	−	0.340195i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.59808	−	1.50000i	−0.110084	−	0.0635570i	0.443947	−	0.896053i	$-0.353578\pi$
$557$	−2.59808	−	1.50000i	−0.110084	−	0.0635570i	−0.554031	+	0.832496i	$0.686911\pi$
$558$		0			0
$559$	4.00000	+	13.8564i	0.169182	+	0.586064i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	31.1769	−	18.0000i	1.31395	−	0.758610i	0.331202	−	0.943560i	$-0.392546\pi$
$563$	31.1769	−	18.0000i	1.31395	−	0.758610i	0.982748	+	0.184950i	$0.0592124\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	44.0000i		−	1.84783i
$568$		0			0
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	−0.990668	−	0.136295i	$-0.956481\pi$
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	0.613369	+	0.789797i	$0.289814\pi$
$570$		0			0
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$		0			0
$573$		−	12.0000i		−	0.501307i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	11.0000i		−	0.457936i	−0.973434	−	0.228968i	$-0.926465\pi$
$577$		−	11.0000i		−	0.457936i	0.973434	−	0.228968i	$-0.0735351\pi$
$578$		0			0
$579$	−11.0000	−	19.0526i	−0.457144	−	0.791797i
$580$		0			0
$581$	24.0000	+	41.5692i	0.995688	+	1.72458i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$587$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$588$		0			0
$589$	2.00000	+	3.46410i	0.0824086	+	0.142736i
$590$		0			0
$591$	6.00000	+	10.3923i	0.246807	+	0.427482i
$592$		0			0
$593$		−	9.00000i		−	0.369586i	−0.982777	−	0.184793i	$-0.940839\pi$
$593$		−	9.00000i		−	0.369586i	0.982777	−	0.184793i	$-0.0591614\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			52.0000i			2.12822i
$598$		0			0
$599$	30.0000			1.22577			0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000			1.22577			0.612883	+	0.790173i	$0.290010\pi$
$600$		0			0
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	−0.855648	−	0.517559i	$-0.826841\pi$
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	0.876043	+	0.482233i	$0.160174\pi$
$602$		0			0
$603$			2.00000i			0.0814463i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	19.0526	−	11.0000i	0.773320	−	0.446476i	−0.0607380	−	0.998154i	$-0.519345\pi$
$607$	19.0526	−	11.0000i	0.773320	−	0.446476i	0.834058	+	0.551678i	$0.186012\pi$
$608$		0			0
$609$	36.0000	−	62.3538i	1.45879	−	2.52670i
$610$		0			0
$611$	21.0000	+	5.19615i	0.849569	+	0.210214i
$612$		0			0
$613$	16.4545	+	9.50000i	0.664590	+	0.383701i	0.794024	−	0.607887i	$-0.207983\pi$
$613$	16.4545	+	9.50000i	0.664590	+	0.383701i	−0.129433	+	0.991588i	$0.541316\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−23.3827	+	13.5000i	−0.941351	+	0.543490i	−0.890384	−	0.455211i	$-0.849564\pi$
$617$	−23.3827	+	13.5000i	−0.941351	+	0.543490i	−0.0509678	+	0.998700i	$0.516231\pi$
$618$		0			0
$619$	40.0000			1.60774			0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$		0			0
$621$	12.0000	−	20.7846i	0.481543	−	0.834058i
$622$		0			0
$623$		−	24.0000i		−	0.961540i
$624$		0			0
$625$		0			0
$626$		0			0
$627$		0			0
$628$		0			0
$629$	21.0000			0.837325
$630$		0			0
$631$	14.0000	+	24.2487i	0.557331	+	0.965326i	0.997718	+	0.0675178i	$0.0215080\pi$
$631$	14.0000	+	24.2487i	0.557331	+	0.965326i	−0.440387	+	0.897808i	$0.645159\pi$
$632$		0			0
$633$	−3.46410	+	2.00000i	−0.137686	+	0.0794929i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−23.3827	−	22.5000i	−0.926456	−	0.891482i
$638$		0			0
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$		0			0
$641$	−7.50000	−	12.9904i	−0.296232	−	0.513089i	0.679039	−	0.734103i	$-0.262397\pi$
$641$	−7.50000	−	12.9904i	−0.296232	−	0.513089i	−0.975271	+	0.221013i	$0.929064\pi$
$642$		0			0
$643$	−13.8564	+	8.00000i	−0.546443	+	0.315489i	−0.747686	−	0.664052i	$-0.768835\pi$
$643$	−13.8564	+	8.00000i	−0.546443	+	0.315489i	0.201243	+	0.979541i	$0.435502\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.19615	+	3.00000i	0.204282	+	0.117942i	0.598651	−	0.801010i	$-0.295704\pi$
$647$	5.19615	+	3.00000i	0.204282	+	0.117942i	−0.394369	+	0.918952i	$0.629037\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	16.0000			0.627089
$652$		0			0
$653$	36.3731	+	21.0000i	1.42339	+	0.821794i	0.996587	−	0.0825519i	$-0.0263070\pi$
$653$	36.3731	+	21.0000i	1.42339	+	0.821794i	0.426801	+	0.904345i	$0.359640\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	0.866025	−	0.500000i	0.0337869	−	0.0195069i
$658$		0			0
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	0.725175	−	0.688565i	$-0.241759\pi$
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	−0.958902	+	0.283738i	$0.908425\pi$
$660$		0			0
$661$	3.50000	−	6.06218i	0.136134	−	0.235791i	−0.789896	−	0.613241i	$-0.789865\pi$
$661$	3.50000	−	6.06218i	0.136134	−	0.235791i	0.926030	+	0.377450i	$0.123199\pi$
$662$		0			0
$663$	−5.19615	+	21.0000i	−0.201802	+	0.815572i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	46.7654	−	27.0000i	1.81076	−	1.04544i
$668$		0			0
$669$	−26.0000	−	45.0333i	−1.00522	−	1.74109i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	11.2583	+	6.50000i	0.433977	+	0.250557i	0.701039	−	0.713123i	$-0.252720\pi$
$673$	11.2583	+	6.50000i	0.433977	+	0.250557i	−0.267063	+	0.963679i	$0.586053\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			6.00000i			0.230599i	0.993331	+	0.115299i	$0.0367827\pi$
$677$			6.00000i			0.230599i	−0.993331	+	0.115299i	$0.963217\pi$
$678$		0			0
$679$	−28.0000	+	48.4974i	−1.07454	+	1.86116i
$680$		0			0
$681$	−12.0000			−0.459841
$682$		0			0
$683$	−5.19615	+	3.00000i	−0.198825	+	0.114792i	−0.596107	−	0.802905i	$-0.703287\pi$
$683$	−5.19615	+	3.00000i	−0.198825	+	0.114792i	0.397282	+	0.917697i	$0.369953\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−24.2487	−	14.0000i	−0.925146	−	0.534133i
$688$		0			0
$689$	31.5000	+	7.79423i	1.20005	+	0.296936i
$690$		0			0
$691$	20.0000	−	34.6410i	0.760836	−	1.31781i	−0.181584	−	0.983375i	$-0.558123\pi$
$691$	20.0000	−	34.6410i	0.760836	−	1.31781i	0.942420	−	0.334431i	$-0.108544\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		−	9.00000i		−	0.340899i
$698$		0			0
$699$	18.0000	−	31.1769i	0.680823	−	1.17922i
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$		0			0
$703$		−	14.0000i		−	0.528020i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			36.0000i			1.35392i
$708$		0			0
$709$	−15.5000	−	26.8468i	−0.582115	−	1.00825i	−0.995228	−	0.0975728i	$-0.968892\pi$
$709$	−15.5000	−	26.8468i	−0.582115	−	1.00825i	0.413114	−	0.910679i	$-0.364441\pi$
$710$		0			0
$711$	2.00000	+	3.46410i	0.0750059	+	0.129914i
$712$		0			0
$713$	10.3923	+	6.00000i	0.389195	+	0.224702i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−41.5692	−	24.0000i	−1.55243	−	0.896296i
$718$		0			0
$719$	6.00000	+	10.3923i	0.223762	+	0.387568i	0.955947	−	0.293538i	$-0.0948328\pi$
$719$	6.00000	+	10.3923i	0.223762	+	0.387568i	−0.732185	+	0.681106i	$0.761499\pi$
$720$		0			0
$721$	4.00000	+	6.92820i	0.148968	+	0.258020i
$722$		0			0
$723$			2.00000i			0.0743808i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	32.0000i		−	1.18681i	−0.804902	−	0.593407i	$-0.797782\pi$
$727$		−	32.0000i		−	1.18681i	0.804902	−	0.593407i	$-0.202218\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	6.00000	−	10.3923i	0.221918	−	0.384373i
$732$		0			0
$733$			29.0000i			1.07114i	0.844491	+	0.535570i	$0.179903\pi$
$733$			29.0000i			1.07114i	−0.844491	+	0.535570i	$0.820097\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	10.0000	−	17.3205i	0.367856	−	0.637145i	−0.621374	−	0.783514i	$-0.713425\pi$
$739$	10.0000	−	17.3205i	0.367856	−	0.637145i	0.989230	+	0.146369i	$0.0467586\pi$
$740$		0			0
$741$	14.0000	+	3.46410i	0.514303	+	0.127257i
$742$		0			0
$743$	20.7846	+	12.0000i	0.762513	+	0.440237i	0.830197	−	0.557470i	$-0.188228\pi$
$743$	20.7846	+	12.0000i	0.762513	+	0.440237i	−0.0676840	+	0.997707i	$0.521561\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−10.3923	+	6.00000i	−0.380235	+	0.219529i
$748$		0			0
$749$	24.0000			0.876941
$750$		0			0
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	−0.827225	−	0.561870i	$-0.810082\pi$
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	0.900207	+	0.435463i	$0.143415\pi$
$752$		0			0
$753$			12.0000i			0.437304i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	32.9090	+	19.0000i	1.19610	+	0.690567i	0.959683	−	0.281086i	$-0.0906945\pi$
$757$	32.9090	+	19.0000i	1.19610	+	0.690567i	0.236414	+	0.971652i	$0.424028\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	9.00000	+	15.5885i	0.326250	+	0.565081i	0.981764	−	0.190101i	$-0.0608816\pi$
$761$	9.00000	+	15.5885i	0.326250	+	0.565081i	−0.655515	+	0.755182i	$0.727548\pi$
$762$		0			0
$763$	34.6410	−	20.0000i	1.25409	−	0.724049i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	7.00000	−	12.1244i	0.252426	−	0.437215i	−0.711767	−	0.702416i	$-0.752105\pi$
$769$	7.00000	−	12.1244i	0.252426	−	0.437215i	0.964193	+	0.265200i	$0.0854381\pi$
$770$		0			0
$771$	3.00000	+	5.19615i	0.108042	+	0.187135i
$772$		0			0
$773$	−5.19615	+	3.00000i	−0.186893	+	0.107903i	−0.590527	−	0.807018i	$-0.701080\pi$
$773$	−5.19615	+	3.00000i	−0.186893	+	0.107903i	0.403634	+	0.914920i	$0.367747\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−48.4974	−	28.0000i	−1.73984	−	1.00449i
$778$		0			0
$779$	−6.00000			−0.214972
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−31.1769	−	18.0000i	−1.11417	−	0.643268i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−32.9090	+	19.0000i	−1.17308	+	0.677277i	−0.954403	−	0.298521i	$-0.903507\pi$
$787$	−32.9090	+	19.0000i	−1.17308	+	0.677277i	−0.218675	+	0.975798i	$0.570173\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−18.0000	+	31.1769i	−0.640006	+	1.10852i
$792$		0			0
$793$	−17.3205	+	5.00000i	−0.615069	+	0.177555i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	15.5885	−	9.00000i	0.552171	−	0.318796i	−0.197826	−	0.980237i	$-0.563388\pi$
$797$	15.5885	−	9.00000i	0.552171	−	0.318796i	0.749997	+	0.661441i	$0.230055\pi$
$798$		0			0
$799$	−9.00000	−	15.5885i	−0.318397	−	0.551480i
$800$		0			0
$801$	6.00000			0.212000
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$			60.0000i			2.11210i
$808$		0			0
$809$	7.50000	−	12.9904i	0.263686	−	0.456717i	−0.703533	−	0.710663i	$-0.748395\pi$
$809$	7.50000	−	12.9904i	0.263686	−	0.456717i	0.967219	+	0.253946i	$0.0817284\pi$
$810$		0			0
$811$	−10.0000			−0.351147			−0.175574	−	0.984466i	$-0.556178\pi$
$811$	−10.0000			−0.351147			−0.175574	+	0.984466i	$0.556178\pi$
$812$		0			0
$813$	−13.8564	+	8.00000i	−0.485965	+	0.280572i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−6.92820	−	4.00000i	−0.242387	−	0.139942i
$818$		0			0
$819$	10.0000	−	10.3923i	0.349428	−	0.363137i
$820$		0			0
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	−0.665144	−	0.746715i	$-0.731630\pi$
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	0.979246	+	0.202674i	$0.0649632\pi$
$822$		0			0
$823$	27.7128	−	16.0000i	0.966008	−	0.557725i	0.0679910	−	0.997686i	$-0.478341\pi$
$823$	27.7128	−	16.0000i	0.966008	−	0.557725i	0.898017	+	0.439961i	$0.145008\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	36.0000i		−	1.25184i	−0.779886	−	0.625921i	$-0.784723\pi$
$827$		−	36.0000i		−	1.25184i	0.779886	−	0.625921i	$-0.215277\pi$
$828$		0			0
$829$	−9.50000	+	16.4545i	−0.329949	+	0.571488i	−0.982501	−	0.186256i	$-0.940365\pi$
$829$	−9.50000	+	16.4545i	−0.329949	+	0.571488i	0.652553	+	0.757743i	$0.273698\pi$
$830$		0			0
$831$	38.0000			1.31821
$832$		0			0
$833$			27.0000i			0.935495i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	8.00000i		−	0.276520i
$838$		0			0
$839$	21.0000	+	36.3731i	0.725001	+	1.25574i	0.958974	+	0.283495i	$0.0914938\pi$
$839$	21.0000	+	36.3731i	0.725001	+	1.25574i	−0.233973	+	0.972243i	$0.575173\pi$
$840$		0			0
$841$	−26.0000	−	45.0333i	−0.896552	−	1.55287i
$842$		0			0
$843$	5.19615	+	3.00000i	0.178965	+	0.103325i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	38.1051	+	22.0000i	1.30931	+	0.755929i
$848$		0			0
$849$	16.0000	+	27.7128i	0.549119	+	0.951101i
$850$		0			0
$851$	−21.0000	−	36.3731i	−0.719871	−	1.24685i
$852$		0			0
$853$			5.00000i			0.171197i	0.996330	+	0.0855984i	$0.0272802\pi$
$853$			5.00000i			0.171197i	−0.996330	+	0.0855984i	$0.972720\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	3.00000i		−	0.102478i	−0.998686	−	0.0512390i	$-0.983683\pi$
$857$		−	3.00000i		−	0.102478i	0.998686	−	0.0512390i	$-0.0163170\pi$
$858$		0			0
$859$	−2.00000			−0.0682391			−0.0341196	−	0.999418i	$-0.510863\pi$
$859$	−2.00000			−0.0682391			−0.0341196	+	0.999418i	$0.510863\pi$
$860$		0			0
$861$	−12.0000	+	20.7846i	−0.408959	+	0.708338i
$862$		0			0
$863$			36.0000i			1.22545i	0.790295	+	0.612727i	$0.209928\pi$
$863$			36.0000i			1.22545i	−0.790295	+	0.612727i	$0.790072\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−13.8564	+	8.00000i	−0.470588	+	0.271694i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	5.00000	−	5.19615i	0.169419	−	0.176065i
$872$		0			0
$873$	−12.1244	−	7.00000i	−0.410347	−	0.236914i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−4.33013	+	2.50000i	−0.146218	+	0.0844190i	−0.571324	−	0.820724i	$-0.693570\pi$
$877$	−4.33013	+	2.50000i	−0.146218	+	0.0844190i	0.425106	+	0.905143i	$0.360237\pi$
$878$		0			0
$879$	18.0000			0.607125
$880$		0			0
$881$	−25.5000	+	44.1673i	−0.859117	+	1.48803i	0.0136556	+	0.999907i	$0.495653\pi$
$881$	−25.5000	+	44.1673i	−0.859117	+	1.48803i	−0.872772	+	0.488127i	$0.837680\pi$
$882$		0			0
$883$			26.0000i			0.874970i	0.899226	+	0.437485i	$0.144131\pi$
$883$			26.0000i			0.874970i	−0.899226	+	0.437485i	$0.855869\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.3923	+	6.00000i	0.348939	+	0.201460i	0.664218	−	0.747539i	$-0.268765\pi$
$887$	10.3923	+	6.00000i	0.348939	+	0.201460i	−0.315279	+	0.948999i	$0.602098\pi$
$888$		0			0
$889$	−40.0000			−1.34156
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−10.3923	+	6.00000i	−0.347765	+	0.200782i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	41.5692	−	12.0000i	1.38796	−	0.400668i
$898$		0			0
$899$	9.00000	−	15.5885i	0.300167	−	0.519904i
$900$		0			0
$901$	−13.5000	−	23.3827i	−0.449750	−	0.778990i
$902$		0			0
$903$	−27.7128	+	16.0000i	−0.922225	+	0.532447i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	6.92820	+	4.00000i	0.230047	+	0.132818i	0.610594	−	0.791944i	$-0.290931\pi$
$907$	6.92820	+	4.00000i	0.230047	+	0.132818i	−0.380547	+	0.924762i	$0.624264\pi$
$908$		0			0
$909$	−9.00000			−0.298511
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$	20.7846	−	12.0000i	0.686368	−	0.396275i
$918$		0			0
$919$	19.0000	+	32.9090i	0.626752	+	1.08557i	0.988199	+	0.153174i	$0.0489495\pi$
$919$	19.0000	+	32.9090i	0.626752	+	1.08557i	−0.361447	+	0.932393i	$0.617717\pi$
$920$		0			0
$921$	26.0000	−	45.0333i	0.856729	−	1.48390i
$922$		0			0
$923$	20.7846	−	6.00000i	0.684134	−	0.197492i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1.73205	+	1.00000i	−0.0568880	+	0.0328443i
$928$		0			0
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	0.640768	−	0.767735i	$-0.278616\pi$
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	−0.985262	+	0.171054i	$0.945283\pi$
$930$		0			0
$931$	18.0000			0.589926
$932$		0			0
$933$	10.3923	+	6.00000i	0.340229	+	0.196431i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	47.0000i		−	1.53542i	−0.640796	−	0.767712i	$-0.721395\pi$
$937$		−	47.0000i		−	1.53542i	0.640796	−	0.767712i	$-0.278605\pi$
$938$		0			0
$939$	−14.0000	+	24.2487i	−0.456873	+	0.791327i
$940$		0			0
$941$	−30.0000			−0.977972			−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000			−0.977972			−0.488986	+	0.872292i	$0.662633\pi$
$942$		0			0
$943$	−15.5885	+	9.00000i	−0.507630	+	0.293080i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−15.5885	−	9.00000i	−0.506557	−	0.292461i	0.224860	−	0.974391i	$-0.427807\pi$
$947$	−15.5885	−	9.00000i	−0.506557	−	0.292461i	−0.731417	+	0.681930i	$0.761141\pi$
$948$		0			0
$949$	−3.50000	−	0.866025i	−0.113615	−	0.0281124i
$950$		0			0
$951$	−15.0000	+	25.9808i	−0.486408	+	0.842484i
$952$		0			0
$953$	−5.19615	+	3.00000i	−0.168320	+	0.0971795i	−0.581793	−	0.813337i	$-0.697649\pi$
$953$	−5.19615	+	3.00000i	−0.168320	+	0.0971795i	0.413473	+	0.910516i	$0.364315\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−30.0000	+	51.9615i	−0.968751	+	1.67793i
$960$		0			0
$961$	−27.0000			−0.870968
$962$		0			0
$963$			6.00000i			0.193347i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			58.0000i			1.86515i	0.360971	+	0.932577i	$0.382445\pi$
$967$			58.0000i			1.86515i	−0.360971	+	0.932577i	$0.617555\pi$
$968$		0			0
$969$	−6.00000	−	10.3923i	−0.192748	−	0.333849i
$970$		0			0
$971$	−15.0000	−	25.9808i	−0.481373	−	0.833762i	0.518399	−	0.855139i	$-0.326528\pi$
$971$	−15.0000	−	25.9808i	−0.481373	−	0.833762i	−0.999771	+	0.0213768i	$0.993195\pi$
$972$		0			0
$973$	−55.4256	−	32.0000i	−1.77686	−	1.02587i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	33.7750	+	19.5000i	1.08056	+	0.623860i	0.931047	−	0.364900i	$-0.118897\pi$
$977$	33.7750	+	19.5000i	1.08056	+	0.623860i	0.149511	+	0.988760i	$0.452230\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	5.00000	+	8.66025i	0.159638	+	0.276501i
$982$		0			0
$983$		−	6.00000i		−	0.191370i	−0.995412	−	0.0956851i	$-0.969496\pi$
$983$		−	6.00000i		−	0.191370i	0.995412	−	0.0956851i	$-0.0305042\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			48.0000i			1.52786i
$988$		0			0
$989$	−24.0000			−0.763156
$990$		0			0
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	−0.881471	−	0.472237i	$-0.843446\pi$
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	0.849705	+	0.527258i	$0.176780\pi$
$992$		0			0
$993$		−	64.0000i		−	2.03098i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−4.33013	+	2.50000i	−0.137136	+	0.0791758i	−0.566999	−	0.823719i	$-0.691896\pi$
$997$	−4.33013	+	2.50000i	−0.137136	+	0.0791758i	0.429862	+	0.902895i	$0.358562\pi$
$998$		0			0
$999$	−14.0000	+	24.2487i	−0.442940	+	0.767195i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.bb.d.1049.2		4
5.2	odd	4		52.2.e.b.9.1	✓	2
5.3	odd	4		1300.2.i.b.1101.1		2
5.4	even	2	inner	1300.2.bb.d.1049.1		4
13.3	even	3	inner	1300.2.bb.d.549.1		4
15.2	even	4		468.2.l.d.217.1		2
20.7	even	4		208.2.i.a.113.1		2
35.2	odd	12		2548.2.i.g.165.1		2
35.12	even	12		2548.2.i.b.165.1		2
35.17	even	12		2548.2.l.g.373.1		2
35.27	even	4		2548.2.k.a.1569.1		2
35.32	odd	12		2548.2.l.b.373.1		2
40.27	even	4		832.2.i.i.321.1		2
40.37	odd	4		832.2.i.c.321.1		2
60.47	odd	4		1872.2.t.m.1153.1		2
65.2	even	12		676.2.h.d.361.2		4
65.3	odd	12		1300.2.i.b.601.1		2
65.7	even	12		676.2.d.a.337.1		2
65.12	odd	4		676.2.e.d.529.1		2
65.17	odd	12		676.2.a.b.1.1		1
65.22	odd	12		676.2.a.a.1.1		1
65.29	even	6	inner	1300.2.bb.d.549.2		4
65.32	even	12		676.2.d.a.337.2		2
65.37	even	12		676.2.h.d.361.1		4
65.42	odd	12		52.2.e.b.29.1	yes	2
65.47	even	4		676.2.h.d.485.1		4
65.57	even	4		676.2.h.d.485.2		4
65.62	odd	12		676.2.e.d.653.1		2
195.17	even	12		6084.2.a.c.1.1		1
195.32	odd	12		6084.2.b.k.4393.1		2
195.107	even	12		468.2.l.d.289.1		2
195.137	odd	12		6084.2.b.k.4393.2		2
195.152	even	12		6084.2.a.o.1.1		1
260.7	odd	12		2704.2.f.i.337.1		2
260.87	even	12		2704.2.a.l.1.1		1
260.107	even	12		208.2.i.a.81.1		2
260.147	even	12		2704.2.a.m.1.1		1
260.227	odd	12		2704.2.f.i.337.2		2
455.107	odd	12		2548.2.l.b.1537.1		2
455.172	odd	12		2548.2.i.g.1745.1		2
455.237	even	12		2548.2.k.a.393.1		2
455.367	even	12		2548.2.i.b.1745.1		2
455.432	even	12		2548.2.l.g.1537.1		2
520.107	even	12		832.2.i.i.705.1		2
520.237	odd	12		832.2.i.c.705.1		2
780.107	odd	12		1872.2.t.m.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.e.b.9.1	✓	2	5.2	odd	4
52.2.e.b.29.1	yes	2	65.42	odd	12
208.2.i.a.81.1		2	260.107	even	12
208.2.i.a.113.1		2	20.7	even	4
468.2.l.d.217.1		2	15.2	even	4
468.2.l.d.289.1		2	195.107	even	12
676.2.a.a.1.1		1	65.22	odd	12
676.2.a.b.1.1		1	65.17	odd	12
676.2.d.a.337.1		2	65.7	even	12
676.2.d.a.337.2		2	65.32	even	12
676.2.e.d.529.1		2	65.12	odd	4
676.2.e.d.653.1		2	65.62	odd	12
676.2.h.d.361.1		4	65.37	even	12
676.2.h.d.361.2		4	65.2	even	12
676.2.h.d.485.1		4	65.47	even	4
676.2.h.d.485.2		4	65.57	even	4
832.2.i.c.321.1		2	40.37	odd	4
832.2.i.c.705.1		2	520.237	odd	12
832.2.i.i.321.1		2	40.27	even	4
832.2.i.i.705.1		2	520.107	even	12
1300.2.i.b.601.1		2	65.3	odd	12
1300.2.i.b.1101.1		2	5.3	odd	4
1300.2.bb.d.549.1		4	13.3	even	3	inner
1300.2.bb.d.549.2		4	65.29	even	6	inner
1300.2.bb.d.1049.1		4	5.4	even	2	inner
1300.2.bb.d.1049.2		4	1.1	even	1	trivial
1872.2.t.m.289.1		2	780.107	odd	12
1872.2.t.m.1153.1		2	60.47	odd	4
2548.2.i.b.165.1		2	35.12	even	12
2548.2.i.b.1745.1		2	455.367	even	12
2548.2.i.g.165.1		2	35.2	odd	12
2548.2.i.g.1745.1		2	455.172	odd	12
2548.2.k.a.393.1		2	455.237	even	12
2548.2.k.a.1569.1		2	35.27	even	4
2548.2.l.b.373.1		2	35.32	odd	12
2548.2.l.b.1537.1		2	455.107	odd	12
2548.2.l.g.373.1		2	35.17	even	12
2548.2.l.g.1537.1		2	455.432	even	12
2704.2.a.l.1.1		1	260.87	even	12
2704.2.a.m.1.1		1	260.147	even	12
2704.2.f.i.337.1		2	260.7	odd	12
2704.2.f.i.337.2		2	260.227	odd	12
6084.2.a.c.1.1		1	195.17	even	12
6084.2.a.o.1.1		1	195.152	even	12
6084.2.b.k.4393.1		2	195.32	odd	12
6084.2.b.k.4393.2		2	195.137	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1300.2.bb.d.1049.2

Level	$1300$
Weight	$2$
Character	1300.1049
Analytic conductor	$10.381$
Analytic rank	$0$
Dimension	$4$
Inner twists	$4$