LMFDB - Embedded newform 5292.2.bm.b.4625.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5292,2,Mod(2285,5292)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5292, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("5292.2285");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5292.bm (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:	$42.2568327497$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3x^{14} - 9x^{12} - 9x^{10} + 225x^{8} - 81x^{6} - 729x^{4} - 2187x^{2} + 6561 $ x^16 - 3x^14 - 9x^12 - 9x^10 + 225x^8 - 81x^6 - 729x^4 - 2187*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{37}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4625.8
Root			$-1.71965 + 0.206851i$ of defining polynomial
Character	$\chi$	$=$	5292.4625
Dual form			5292.2.bm.b.2285.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.18671 q^{5} +O(q^{10})$	$q+4.18671 q^{5} -1.42285i q^{11} +(0.850739 - 0.491174i) q^{13} +(-0.185474 - 0.321250i) q^{17} +(-4.30823 - 2.48736i) q^{19} -5.75936i q^{23} +12.5285 q^{25} +(-7.31732 - 4.22466i) q^{29} +(6.28007 + 3.62580i) q^{31} +(-1.73222 + 3.00030i) q^{37} +(-1.06981 - 1.85297i) q^{41} +(3.00875 - 5.21130i) q^{43} +(-4.13542 - 7.16276i) q^{47} +(4.30627 - 2.48623i) q^{53} -5.95706i q^{55} +(-2.27883 + 3.94705i) q^{59} +(6.50416 - 3.75518i) q^{61} +(3.56180 - 2.05640i) q^{65} +(5.03205 - 8.71577i) q^{67} -10.9555i q^{71} +(-8.25191 + 4.76424i) q^{73} +(4.25553 + 7.37079i) q^{79} +(0.972254 - 1.68399i) q^{83} +(-0.776524 - 1.34498i) q^{85} +(3.90368 - 6.76137i) q^{89} +(-18.0373 - 10.4138i) q^{95} +(3.34099 + 1.92892i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 16 q^{25} + 12 q^{29} - 2 q^{37} + 4 q^{43} + 36 q^{53} - 24 q^{65} + 14 q^{67} + 20 q^{79} + 6 q^{85} - 60 q^{95}+O(q^{100}) $ 16 * q + 16 * q^25 + 12 * q^29 - 2 * q^37 + 4 * q^43 + 36 * q^53 - 24 * q^65 + 14 * q^67 + 20 * q^79 + 6 * q^85 - 60 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$	$2647$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$	4.18671			1.87235			0.936177	−	0.351529i	$-0.114338\pi$
$5$	4.18671			1.87235			0.936177	+	0.351529i	$0.114338\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	1.42285i		−	0.429005i	−0.976723	−	0.214503i	$-0.931187\pi$
$11$		−	1.42285i		−	0.429005i	0.976723	−	0.214503i	$-0.0688130\pi$
$12$		0			0
$13$	0.850739	−	0.491174i	0.235952	−	0.136227i	−0.377363	−	0.926066i	$-0.623169\pi$
$13$	0.850739	−	0.491174i	0.235952	−	0.136227i	0.613315	+	0.789838i	$0.289836\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.185474	−	0.321250i	−0.0449840	−	0.0779145i	0.842657	−	0.538451i	$-0.180990\pi$
$17$	−0.185474	−	0.321250i	−0.0449840	−	0.0779145i	−0.887641	+	0.460537i	$0.847657\pi$
$18$		0			0
$19$	−4.30823	−	2.48736i	−0.988375	−	0.570638i	−0.0835867	−	0.996501i	$-0.526638\pi$
$19$	−4.30823	−	2.48736i	−0.988375	−	0.570638i	−0.904788	+	0.425862i	$0.859971\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	5.75936i		−	1.20091i	−0.799659	−	0.600455i	$-0.794986\pi$
$23$		−	5.75936i		−	1.20091i	0.799659	−	0.600455i	$-0.205014\pi$
$24$		0			0
$25$	12.5285			2.50571
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−7.31732	−	4.22466i	−1.35879	−	0.784499i	−0.369332	−	0.929298i	$-0.620413\pi$
$29$	−7.31732	−	4.22466i	−1.35879	−	0.784499i	−0.989461	+	0.144798i	$0.953747\pi$
$30$		0			0
$31$	6.28007	+	3.62580i	1.12793	+	0.651213i	0.943414	−	0.331616i	$-0.107594\pi$
$31$	6.28007	+	3.62580i	1.12793	+	0.651213i	0.184519	+	0.982829i	$0.440927\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.73222	+	3.00030i	−0.284776	+	0.493246i	−0.972555	−	0.232674i	$-0.925252\pi$
$37$	−1.73222	+	3.00030i	−0.284776	+	0.493246i	0.687779	+	0.725920i	$0.258586\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.06981	−	1.85297i	−0.167077	−	0.289386i	0.770314	−	0.637665i	$-0.220099\pi$
$41$	−1.06981	−	1.85297i	−0.167077	−	0.289386i	−0.937391	+	0.348279i	$0.886766\pi$
$42$		0			0
$43$	3.00875	−	5.21130i	0.458830	−	0.794716i	−0.540070	−	0.841620i	$-0.681602\pi$
$43$	3.00875	−	5.21130i	0.458830	−	0.794716i	0.998899	+	0.0469039i	$0.0149354\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.13542	−	7.16276i	−0.603213	−	1.04480i	−0.992331	−	0.123608i	$-0.960553\pi$
$47$	−4.13542	−	7.16276i	−0.603213	−	1.04480i	0.389118	−	0.921188i	$-0.372780\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.30627	−	2.48623i	0.591512	−	0.341509i	−0.174183	−	0.984713i	$-0.555729\pi$
$53$	4.30627	−	2.48623i	0.591512	−	0.341509i	0.765695	+	0.643204i	$0.222395\pi$
$54$		0			0
$55$		−	5.95706i		−	0.803250i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.27883	+	3.94705i	−0.296678	+	0.513862i	−0.975374	−	0.220558i	$-0.929212\pi$
$59$	−2.27883	+	3.94705i	−0.296678	+	0.513862i	0.678696	+	0.734420i	$0.262546\pi$
$60$		0			0
$61$	6.50416	−	3.75518i	0.832772	−	0.480801i	−0.0220288	−	0.999757i	$-0.507013\pi$
$61$	6.50416	−	3.75518i	0.832772	−	0.480801i	0.854801	+	0.518956i	$0.173679\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.56180	−	2.05640i	0.441786	−	0.255066i
$66$		0			0
$67$	5.03205	−	8.71577i	0.614763	−	1.06480i	−0.375663	−	0.926756i	$-0.622585\pi$
$67$	5.03205	−	8.71577i	0.614763	−	1.06480i	0.990426	−	0.138044i	$-0.0440816\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	10.9555i		−	1.30018i	−0.759857	−	0.650090i	$-0.774731\pi$
$71$		−	10.9555i		−	1.30018i	0.759857	−	0.650090i	$-0.225269\pi$
$72$		0			0
$73$	−8.25191	+	4.76424i	−0.965813	+	0.557612i	−0.897957	−	0.440083i	$-0.854949\pi$
$73$	−8.25191	+	4.76424i	−0.965813	+	0.557612i	−0.0678555	+	0.997695i	$0.521616\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.25553	+	7.37079i	0.478784	+	0.829278i	0.999704	−	0.0243272i	$-0.00774434\pi$
$79$	4.25553	+	7.37079i	0.478784	+	0.829278i	−0.520920	+	0.853606i	$0.674411\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.972254	−	1.68399i	0.106719	−	0.184842i	−0.807720	−	0.589566i	$-0.799299\pi$
$83$	0.972254	−	1.68399i	0.106719	−	0.184842i	0.914439	+	0.404724i	$0.132632\pi$
$84$		0			0
$85$	−0.776524	−	1.34498i	−0.0842259	−	0.145884i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.90368	−	6.76137i	0.413789	−	0.716703i	−0.581512	−	0.813538i	$-0.697538\pi$
$89$	3.90368	−	6.76137i	0.413789	−	0.716703i	0.995300	+	0.0968347i	$0.0308718\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−18.0373	−	10.4138i	−1.85059	−	1.06844i
$96$		0			0
$97$	3.34099	+	1.92892i	0.339226	+	0.195852i	0.659930	−	0.751327i	$-0.270586\pi$
$97$	3.34099	+	1.92892i	0.339226	+	0.195852i	−0.320704	+	0.947180i	$0.603919\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	9.01274			0.896801			0.448401	−	0.893833i	$-0.351994\pi$
$101$	9.01274			0.896801			0.448401	+	0.893833i	$0.351994\pi$
$102$		0			0
$103$		−	6.88598i		−	0.678495i	−0.940697	−	0.339248i	$-0.889828\pi$
$103$		−	6.88598i		−	0.678495i	0.940697	−	0.339248i	$-0.110172\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.84062	−	5.68149i	−0.951329	−	0.549250i	−0.0578356	−	0.998326i	$-0.518420\pi$
$107$	−9.84062	−	5.68149i	−0.951329	−	0.549250i	−0.893494	+	0.449076i	$0.851753\pi$
$108$		0			0
$109$	7.99650	+	13.8503i	0.765926	+	1.32662i	0.939756	+	0.341846i	$0.111052\pi$
$109$	7.99650	+	13.8503i	0.765926	+	1.32662i	−0.173830	+	0.984776i	$0.555614\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.17043	+	1.25310i	−0.204177	+	0.117881i	−0.598602	−	0.801046i	$-0.704277\pi$
$113$	−2.17043	+	1.25310i	−0.204177	+	0.117881i	0.394426	+	0.918928i	$0.370944\pi$
$114$		0			0
$115$		−	24.1128i		−	2.24853i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	8.97550			0.815955
$122$		0			0
$123$		0			0
$124$		0			0
$125$	31.5199			2.81922
$126$		0			0
$127$	−1.91140			−0.169609			−0.0848046	−	0.996398i	$-0.527027\pi$
$127$	−1.91140			−0.169609			−0.0848046	+	0.996398i	$0.527027\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.65182			0.755913			0.377957	−	0.925823i	$-0.376627\pi$
$131$	8.65182			0.755913			0.377957	+	0.925823i	$0.376627\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$			11.6594i			0.996131i	0.867139	+	0.498065i	$0.165956\pi$
$137$			11.6594i			0.996131i	−0.867139	+	0.498065i	$0.834044\pi$
$138$		0			0
$139$	4.82663	−	2.78666i	0.409390	−	0.236361i	−0.281138	−	0.959667i	$-0.590712\pi$
$139$	4.82663	−	2.78666i	0.409390	−	0.236361i	0.690528	+	0.723306i	$0.257378\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.698867	−	1.21047i	−0.0584422	−	0.101225i
$144$		0			0
$145$	−30.6355	−	17.6874i	−2.54414	−	1.46886i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			15.4758i			1.26783i	0.773405	+	0.633913i	$0.218552\pi$
$149$			15.4758i			1.26783i	−0.773405	+	0.633913i	$0.781448\pi$
$150$		0			0
$151$	−16.6346			−1.35371			−0.676854	−	0.736117i	$-0.736657\pi$
$151$	−16.6346			−1.35371			−0.676854	+	0.736117i	$0.736657\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	26.2928	+	15.1802i	2.11189	+	1.21930i
$156$		0			0
$157$	14.5559	+	8.40387i	1.16169	+	0.670702i	0.951708	−	0.307004i	$-0.0993264\pi$
$157$	14.5559	+	8.40387i	1.16169	+	0.670702i	0.209981	+	0.977705i	$0.432660\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1.75553	+	3.04066i	−0.137503	+	0.238163i	−0.926551	−	0.376169i	$-0.877241\pi$
$163$	−1.75553	+	3.04066i	−0.137503	+	0.238163i	0.789048	+	0.614332i	$0.210574\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.05253	+	7.01918i	0.313594	+	0.543160i	0.979138	−	0.203198i	$-0.0651336\pi$
$167$	4.05253	+	7.01918i	0.313594	+	0.543160i	−0.665544	+	0.746359i	$0.731800\pi$
$168$		0			0
$169$	−6.01750	+	10.4226i	−0.462884	+	0.801739i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.54844	−	11.3422i	−0.497868	−	0.862334i	0.502128	−	0.864793i	$-0.332550\pi$
$173$	−6.54844	−	11.3422i	−0.497868	−	0.862334i	−0.999997	+	0.00245951i	$0.999217\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−11.0140	+	6.35893i	−0.823225	+	0.475289i	−0.851527	−	0.524310i	$-0.824323\pi$
$179$	−11.0140	+	6.35893i	−0.823225	+	0.475289i	0.0283026	+	0.999599i	$0.490990\pi$
$180$		0			0
$181$		−	26.5518i		−	1.97358i	−0.161998	−	0.986791i	$-0.551794\pi$
$181$		−	26.5518i		−	1.97358i	0.161998	−	0.986791i	$-0.448206\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−7.25232	+	12.5614i	−0.533201	+	0.923532i
$186$		0			0
$187$	−0.457090	+	0.263901i	−0.0334257	+	0.0192983i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.09735	+	0.633555i	−0.0794014	+	0.0458424i	−0.539175	−	0.842194i	$-0.681264\pi$
$191$	−1.09735	+	0.633555i	−0.0794014	+	0.0458424i	0.459774	+	0.888036i	$0.347931\pi$
$192$		0			0
$193$	−9.31732	+	16.1381i	−0.670676	+	1.16164i	0.307037	+	0.951697i	$0.400662\pi$
$193$	−9.31732	+	16.1381i	−0.670676	+	1.16164i	−0.977713	+	0.209947i	$0.932671\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			5.94312i			0.423430i	0.977331	+	0.211715i	$0.0679049\pi$
$197$			5.94312i			0.423430i	−0.977331	+	0.211715i	$0.932095\pi$
$198$		0			0
$199$	−4.87291	+	2.81337i	−0.345431	+	0.199435i	−0.662671	−	0.748910i	$-0.730577\pi$
$199$	−4.87291	+	2.81337i	−0.345431	+	0.199435i	0.317240	+	0.948345i	$0.397244\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−4.47900	−	7.75786i	−0.312827	−	0.541832i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.53913	+	6.12996i	−0.244807	+	0.424018i
$210$		0			0
$211$	1.05305	+	1.82393i	0.0724948	+	0.125565i	0.899994	−	0.435902i	$-0.143571\pi$
$211$	1.05305	+	1.82393i	0.0724948	+	0.125565i	−0.827499	+	0.561467i	$0.810237\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	12.5968	−	21.8182i	0.859092	−	1.48799i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.315579	−	0.182200i	−0.0212281	−	0.0122561i
$222$		0			0
$223$	−5.52351	−	3.18900i	−0.369882	−	0.213551i	0.303525	−	0.952823i	$-0.401836\pi$
$223$	−5.52351	−	3.18900i	−0.369882	−	0.213551i	−0.673407	+	0.739272i	$0.735170\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	11.4473			0.759783			0.379892	−	0.925031i	$-0.375961\pi$
$227$	11.4473			0.759783			0.379892	+	0.925031i	$0.375961\pi$
$228$		0			0
$229$			5.64298i			0.372899i	0.982465	+	0.186449i	$0.0596980\pi$
$229$			5.64298i			0.372899i	−0.982465	+	0.186449i	$0.940302\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.7788	+	6.22316i	0.706145	+	0.407693i	0.809632	−	0.586938i	$-0.199667\pi$
$233$	10.7788	+	6.22316i	0.706145	+	0.407693i	−0.103487	+	0.994631i	$0.533000\pi$
$234$		0			0
$235$	−17.3138	−	29.9884i	−1.12943	−	1.95623i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−3.52450	+	2.03487i	−0.227981	+	0.131625i	−0.609640	−	0.792678i	$-0.708686\pi$
$239$	−3.52450	+	2.03487i	−0.227981	+	0.131625i	0.381659	+	0.924303i	$0.375353\pi$
$240$		0			0
$241$			4.92128i			0.317007i	0.987358	+	0.158504i	$0.0506670\pi$
$241$			4.92128i			0.317007i	−0.987358	+	0.158504i	$0.949333\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.88690			−0.310946
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−4.65020			−0.293518			−0.146759	−	0.989172i	$-0.546884\pi$
$251$	−4.65020			−0.293518			−0.146759	+	0.989172i	$0.546884\pi$
$252$		0			0
$253$	−8.19470			−0.515196
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.8940			0.679551			0.339775	−	0.940507i	$-0.389649\pi$
$257$	10.8940			0.679551			0.339775	+	0.940507i	$0.389649\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$			18.0698i			1.11423i	0.830436	+	0.557114i	$0.188092\pi$
$263$			18.0698i			1.11423i	−0.830436	+	0.557114i	$0.811908\pi$
$264$		0			0
$265$	18.0291	−	10.4091i	1.10752	−	0.639427i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.49205	−	2.58430i	−0.0909718	−	0.157568i	0.816948	−	0.576711i	$-0.195664\pi$
$269$	−1.49205	−	2.58430i	−0.0909718	−	0.157568i	−0.907920	+	0.419143i	$0.862331\pi$
$270$		0			0
$271$	−8.97274	−	5.18041i	−0.545055	−	0.314688i	0.202070	−	0.979371i	$-0.435233\pi$
$271$	−8.97274	−	5.18041i	−0.545055	−	0.314688i	−0.747125	+	0.664683i	$0.768566\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	17.8262i		−	1.07496i
$276$		0			0
$277$	−11.8869			−0.714215			−0.357107	−	0.934063i	$-0.616237\pi$
$277$	−11.8869			−0.714215			−0.357107	+	0.934063i	$0.616237\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	12.0740	+	6.97095i	0.720277	+	0.415852i	0.814855	−	0.579665i	$-0.196817\pi$
$281$	12.0740	+	6.97095i	0.720277	+	0.415852i	−0.0945775	+	0.995518i	$0.530150\pi$
$282$		0			0
$283$	2.19593	+	1.26782i	0.130535	+	0.0753642i	0.563845	−	0.825880i	$-0.309321\pi$
$283$	2.19593	+	1.26782i	0.130535	+	0.0753642i	−0.433311	+	0.901245i	$0.642655\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.43120	−	14.6033i	0.495953	−	0.859016i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.95496	+	6.85020i	0.231052	+	0.400193i	0.958118	−	0.286374i	$-0.0924501\pi$
$293$	3.95496	+	6.85020i	0.231052	+	0.400193i	−0.727066	+	0.686567i	$0.759117\pi$
$294$		0			0
$295$	−9.54080	+	16.5251i	−0.555487	+	0.962131i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.82885	−	4.89971i	−0.163596	−	0.283357i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	27.2310	−	15.7218i	1.55924	−	0.900230i
$306$		0			0
$307$			13.9676i			0.797170i	0.917131	+	0.398585i	$0.130499\pi$
$307$			13.9676i			0.797170i	−0.917131	+	0.398585i	$0.869501\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	16.3163	−	28.2607i	0.925215	−	1.60252i	0.134001	−	0.990981i	$-0.457218\pi$
$311$	16.3163	−	28.2607i	0.925215	−	1.60252i	0.791215	−	0.611539i	$-0.209449\pi$
$312$		0			0
$313$	13.6110	−	7.85832i	0.769340	−	0.444178i	−0.0632994	−	0.997995i	$-0.520162\pi$
$313$	13.6110	−	7.85832i	0.769340	−	0.444178i	0.832639	+	0.553816i	$0.186829\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−25.1366	+	14.5126i	−1.41181	+	0.815111i	−0.995559	−	0.0941377i	$-0.969991\pi$
$317$	−25.1366	+	14.5126i	−1.41181	+	0.815111i	−0.416254	+	0.909248i	$0.636657\pi$
$318$		0			0
$319$	−6.01105	+	10.4114i	−0.336554	+	0.582929i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			1.84535i			0.102678i
$324$		0			0
$325$	10.6585	−	6.15370i	0.591228	−	0.341346i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−6.58510	−	11.4057i	−0.361950	−	0.626915i	0.626332	−	0.779556i	$-0.284555\pi$
$331$	−6.58510	−	11.4057i	−0.361950	−	0.626915i	−0.988282	+	0.152641i	$0.951222\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	21.0677	−	36.4904i	1.15105	−	1.99368i
$336$		0			0
$337$	8.31732	+	14.4060i	0.453073	+	0.784746i	0.998575	−	0.0533635i	$-0.0169942\pi$
$337$	8.31732	+	14.4060i	0.453073	+	0.784746i	−0.545502	+	0.838110i	$0.683661\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	5.15896	−	8.93559i	0.279374	−	0.483889i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	21.4012	+	12.3560i	1.14888	+	0.663305i	0.948614	−	0.316437i	$-0.102487\pi$
$347$	21.4012	+	12.3560i	1.14888	+	0.663305i	0.200264	+	0.979742i	$0.435820\pi$
$348$		0			0
$349$	26.7994	+	15.4727i	1.43454	+	0.828232i	0.997463	−	0.0711915i	$-0.0226802\pi$
$349$	26.7994	+	15.4727i	1.43454	+	0.828232i	0.437078	+	0.899424i	$0.356013\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−23.3516			−1.24288			−0.621440	−	0.783462i	$-0.713452\pi$
$353$	−23.3516			−1.24288			−0.621440	+	0.783462i	$0.713452\pi$
$354$		0			0
$355$		−	45.8676i		−	2.43440i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	18.3902	+	10.6176i	0.970596	+	0.560374i	0.899418	−	0.437090i	$-0.143991\pi$
$359$	18.3902	+	10.6176i	0.970596	+	0.560374i	0.0711782	+	0.997464i	$0.477324\pi$
$360$		0			0
$361$	2.87387	+	4.97769i	0.151256	+	0.261984i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−34.5483	+	19.9465i	−1.80834	+	1.04405i
$366$		0			0
$367$			13.8769i			0.724370i	0.932106	+	0.362185i	$0.117969\pi$
$367$			13.8769i			0.724370i	−0.932106	+	0.362185i	$0.882031\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−32.1457			−1.66444			−0.832221	−	0.554445i	$-0.812931\pi$
$373$	−32.1457			−1.66444			−0.832221	+	0.554445i	$0.812931\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−8.30017			−0.427481
$378$		0			0
$379$	1.95340			0.100339			0.0501696	−	0.998741i	$-0.484024\pi$
$379$	1.95340			0.100339			0.0501696	+	0.998741i	$0.484024\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.57633			−0.0805469			−0.0402734	−	0.999189i	$-0.512823\pi$
$383$	−1.57633			−0.0805469			−0.0402734	+	0.999189i	$0.512823\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$			11.2519i			0.570496i	0.958454	+	0.285248i	$0.0920760\pi$
$389$			11.2519i			0.570496i	−0.958454	+	0.285248i	$0.907924\pi$
$390$		0			0
$391$	−1.85019	+	1.06821i	−0.0935682	+	0.0540216i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	17.8167	+	30.8594i	0.896453	+	1.55270i
$396$		0			0
$397$	0.548160	+	0.316480i	0.0275114	+	0.0158837i	0.513693	−	0.857974i	$-0.328277\pi$
$397$	0.548160	+	0.316480i	0.0275114	+	0.0158837i	−0.486181	+	0.873858i	$0.661611\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	8.52206i		−	0.425571i	−0.977099	−	0.212786i	$-0.931746\pi$
$401$		−	8.52206i		−	0.425571i	0.977099	−	0.212786i	$-0.0682536\pi$
$402$		0			0
$403$	7.12359			0.354851
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.26897	+	2.46469i	0.211605	+	0.122170i
$408$		0			0
$409$	12.1822	+	7.03338i	0.602370	+	0.347778i	0.769973	−	0.638076i	$-0.220269\pi$
$409$	12.1822	+	7.03338i	0.602370	+	0.347778i	−0.167603	+	0.985855i	$0.553603\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	4.07054	−	7.05039i	0.199815	−	0.346090i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.9339	−	18.9381i	−0.534156	−	0.925185i	−0.999204	−	0.0398995i	$-0.987296\pi$
$419$	−10.9339	−	18.9381i	−0.534156	−	0.925185i	0.465048	−	0.885286i	$-0.346037\pi$
$420$		0			0
$421$	13.3616	−	23.1430i	0.651206	−	1.12792i	−0.331625	−	0.943411i	$-0.607597\pi$
$421$	13.3616	−	23.1430i	0.651206	−	1.12792i	0.982831	−	0.184510i	$-0.0590698\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.32371	−	4.02479i	−0.112717	−	0.195231i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	17.2686	−	9.97000i	0.831797	−	0.480238i	−0.0226706	−	0.999743i	$-0.507217\pi$
$431$	17.2686	−	9.97000i	0.831797	−	0.480238i	0.854468	+	0.519505i	$0.173884\pi$
$432$		0			0
$433$		−	20.2826i		−	0.974719i	−0.873201	−	0.487359i	$-0.837960\pi$
$433$		−	20.2826i		−	0.974719i	0.873201	−	0.487359i	$-0.162040\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−14.3256	+	24.8126i	−0.685285	+	1.18695i
$438$		0			0
$439$	−24.5936	+	14.1991i	−1.17379	+	0.677687i	−0.954569	−	0.297989i	$-0.903684\pi$
$439$	−24.5936	+	14.1991i	−1.17379	+	0.677687i	−0.219219	+	0.975676i	$0.570351\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.6570	−	6.15281i	0.506328	−	0.292329i	−0.224995	−	0.974360i	$-0.572236\pi$
$443$	10.6570	−	6.15281i	0.506328	−	0.292329i	0.731323	+	0.682031i	$0.238903\pi$
$444$		0			0
$445$	16.3436	−	28.3079i	0.774759	−	1.34192i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	36.1924i		−	1.70803i	−0.520251	−	0.854013i	$-0.674162\pi$
$449$		−	36.1924i		−	1.70803i	0.520251	−	0.854013i	$-0.325838\pi$
$450$		0			0
$451$	−2.63650	+	1.52218i	−0.124148	+	0.0716769i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	4.20892	+	7.29007i	0.196885	+	0.341015i	0.947517	−	0.319706i	$-0.103584\pi$
$457$	4.20892	+	7.29007i	0.196885	+	0.341015i	−0.750632	+	0.660721i	$0.770251\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−9.07730	+	15.7224i	−0.422772	+	0.732263i	−0.996209	−	0.0869865i	$-0.972276\pi$
$461$	−9.07730	+	15.7224i	−0.422772	+	0.732263i	0.573437	+	0.819249i	$0.305610\pi$
$462$		0			0
$463$	−7.64690	−	13.2448i	−0.355381	−	0.615539i	0.631802	−	0.775130i	$-0.282316\pi$
$463$	−7.64690	−	13.2448i	−0.355381	−	0.615539i	−0.987183	+	0.159591i	$0.948982\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	13.3932	−	23.1977i	0.619763	−	1.07346i	−0.369766	−	0.929125i	$-0.620562\pi$
$467$	13.3932	−	23.1977i	0.619763	−	1.07346i	0.989529	−	0.144336i	$-0.0461045\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−7.41490	−	4.28100i	−0.340938	−	0.196840i
$474$		0			0
$475$	−53.9758	−	31.1630i	−2.47658	−	1.42985i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−28.5551			−1.30471			−0.652357	−	0.757912i	$-0.726220\pi$
$479$	−28.5551			−1.30471			−0.652357	+	0.757912i	$0.726220\pi$
$480$		0			0
$481$			3.40329i			0.155177i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	13.9877	+	8.07583i	0.635151	+	0.366705i
$486$		0			0
$487$	6.57635	+	11.3906i	0.298003	+	0.516156i	0.975679	−	0.219204i	$-0.0703462\pi$
$487$	6.57635	+	11.3906i	0.298003	+	0.516156i	−0.677676	+	0.735361i	$0.737013\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−28.6854	+	16.5615i	−1.29455	+	0.747411i	−0.979458	−	0.201649i	$-0.935370\pi$
$491$	−28.6854	+	16.5615i	−1.29455	+	0.747411i	−0.315096	+	0.949060i	$0.602037\pi$
$492$		0			0
$493$			3.13425i			0.141160i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−6.55305			−0.293355			−0.146677	−	0.989184i	$-0.546858\pi$
$499$	−6.55305			−0.293355			−0.146677	+	0.989184i	$0.546858\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	12.4969			0.557210			0.278605	−	0.960406i	$-0.410128\pi$
$503$	12.4969			0.557210			0.278605	+	0.960406i	$0.410128\pi$
$504$		0			0
$505$	37.7337			1.67913
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−6.60474			−0.292750			−0.146375	−	0.989229i	$-0.546761\pi$
$509$	−6.60474			−0.292750			−0.146375	+	0.989229i	$0.546761\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	28.8296i		−	1.27038i
$516$		0			0
$517$	−10.1915	+	5.88408i	−0.448223	+	0.258782i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	7.98920	+	13.8377i	0.350013	+	0.606241i	0.986251	−	0.165252i	$-0.0528438\pi$
$521$	7.98920	+	13.8377i	0.350013	+	0.606241i	−0.636238	+	0.771493i	$0.719510\pi$
$522$		0			0
$523$	10.1857	+	5.88074i	0.445391	+	0.257147i	0.705882	−	0.708330i	$-0.250551\pi$
$523$	10.1857	+	5.88074i	0.445391	+	0.257147i	−0.260491	+	0.965476i	$0.583884\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	2.68996i		−	0.117176i
$528$		0			0
$529$	−10.1702			−0.442183
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.82026	−	1.05093i	−0.0788444	−	0.0455208i
$534$		0			0
$535$	−41.1999	−	23.7867i	−1.78122	−	1.02839i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	0.205980	−	0.356768i	0.00885576	−	0.0153386i	−0.861564	−	0.507650i	$-0.830514\pi$
$541$	0.205980	−	0.356768i	0.00885576	−	0.0153386i	0.870419	+	0.492311i	$0.163848\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	33.4790	+	57.9874i	1.43408	+	2.48391i
$546$		0			0
$547$	11.9166	−	20.6402i	0.509519	−	0.882513i	−0.490420	−	0.871486i	$-0.663157\pi$
$547$	11.9166	−	20.6402i	0.509519	−	0.882513i	0.999939	−	0.0110266i	$-0.00350995\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	21.0165	+	36.4016i	0.895331	+	1.55076i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	37.1935	−	21.4737i	1.57594	−	0.909869i	0.580522	−	0.814245i	$-0.302849\pi$
$557$	37.1935	−	21.4737i	1.57594	−	0.909869i	0.995418	−	0.0956241i	$-0.0304847\pi$
$558$		0			0
$559$		−	5.91128i		−	0.250020i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	15.9454	−	27.6182i	0.672019	−	1.16397i	−0.305312	−	0.952252i	$-0.598761\pi$
$563$	15.9454	−	27.6182i	0.672019	−	1.16397i	0.977331	−	0.211718i	$-0.0679058\pi$
$564$		0			0
$565$	−9.08695	+	5.24635i	−0.382291	+	0.220716i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	0.428895	−	0.247623i	0.0179802	−	0.0103809i	−0.490983	−	0.871169i	$-0.663362\pi$
$569$	0.428895	−	0.247623i	0.0179802	−	0.0103809i	0.508963	+	0.860788i	$0.330029\pi$
$570$		0			0
$571$	−1.34182	+	2.32411i	−0.0561535	+	0.0972608i	−0.892736	−	0.450581i	$-0.851217\pi$
$571$	−1.34182	+	2.32411i	−0.0561535	+	0.0972608i	0.836582	+	0.547841i	$0.184550\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	72.1564i		−	3.00913i
$576$		0			0
$577$	36.3955	−	21.0130i	1.51517	−	0.874781i	0.515324	−	0.856995i	$-0.327672\pi$
$577$	36.3955	−	21.0130i	1.51517	−	0.874781i	0.999842	−	0.0177861i	$-0.00566180\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−3.53753	−	6.12717i	−0.146509	−	0.253762i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.71916	−	2.97768i	0.0709575	−	0.122902i	−0.828364	−	0.560191i	$-0.810728\pi$
$587$	1.71916	−	2.97768i	0.0709575	−	0.122902i	0.899321	+	0.437289i	$0.144061\pi$
$588$		0			0
$589$	−18.0373	−	31.2415i	−0.743214	−	1.28728i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−4.55126	+	7.88301i	−0.186898	+	0.323716i	−0.944214	−	0.329332i	$-0.893177\pi$
$593$	−4.55126	+	7.88301i	−0.186898	+	0.323716i	0.757317	+	0.653048i	$0.226510\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	6.71186	+	3.87510i	0.274239	+	0.158332i	0.630813	−	0.775935i	$-0.282722\pi$
$599$	6.71186	+	3.87510i	0.274239	+	0.158332i	−0.356573	+	0.934267i	$0.616055\pi$
$600$		0			0
$601$	22.0034	+	12.7037i	0.897536	+	0.518193i	0.876400	−	0.481584i	$-0.159938\pi$
$601$	22.0034	+	12.7037i	0.897536	+	0.518193i	0.0211361	+	0.999777i	$0.493272\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	37.5778			1.52776
$606$		0			0
$607$		−	13.5208i		−	0.548794i	−0.961616	−	0.274397i	$-0.911522\pi$
$607$		−	13.5208i		−	0.548794i	0.961616	−	0.274397i	$-0.0884783\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−7.03633	−	4.06243i	−0.284659	−	0.164348i
$612$		0			0
$613$	−2.41817	−	4.18840i	−0.0976691	−	0.169168i	0.813050	−	0.582193i	$-0.197805\pi$
$613$	−2.41817	−	4.18840i	−0.0976691	−	0.169168i	−0.910719	+	0.413026i	$0.864472\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.30333	+	3.06188i	−0.213504	+	0.123267i	−0.602939	−	0.797787i	$-0.706004\pi$
$617$	−5.30333	+	3.06188i	−0.213504	+	0.123267i	0.389435	+	0.921054i	$0.372670\pi$
$618$		0			0
$619$			5.70784i			0.229417i	0.993399	+	0.114709i	$0.0365935\pi$
$619$			5.70784i			0.229417i	−0.993399	+	0.114709i	$0.963407\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	69.3218			2.77287
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.28513			0.0512414
$630$		0			0
$631$	−19.0525			−0.758468			−0.379234	−	0.925301i	$-0.623812\pi$
$631$	−19.0525			−0.758468			−0.379234	+	0.925301i	$0.623812\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8.00247			−0.317569
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$			15.3367i			0.605764i	0.953028	+	0.302882i	$0.0979489\pi$
$641$			15.3367i			0.605764i	−0.953028	+	0.302882i	$0.902051\pi$
$642$		0			0
$643$	11.3209	−	6.53612i	0.446453	−	0.257759i	−0.259878	−	0.965641i	$-0.583682\pi$
$643$	11.3209	−	6.53612i	0.446453	−	0.257759i	0.706331	+	0.707882i	$0.250349\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−17.8533	−	30.9228i	−0.701885	−	1.21570i	−0.967804	−	0.251705i	$-0.919009\pi$
$647$	−17.8533	−	30.9228i	−0.701885	−	1.21570i	0.265919	−	0.963995i	$-0.414325\pi$
$648$		0			0
$649$	5.61605	+	3.24243i	0.220449	+	0.127277i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			27.2660i			1.06700i	0.845799	+	0.533501i	$0.179124\pi$
$653$			27.2660i			1.06700i	−0.845799	+	0.533501i	$0.820876\pi$
$654$		0			0
$655$	36.2227			1.41534
$656$		0			0
$657$		0			0
$658$		0			0
$659$	14.7911	+	8.53963i	0.576179	+	0.332657i	0.759613	−	0.650375i	$-0.225388\pi$
$659$	14.7911	+	8.53963i	0.576179	+	0.332657i	−0.183435	+	0.983032i	$0.558722\pi$
$660$		0			0
$661$	−40.6657	−	23.4784i	−1.58171	−	0.913203i	−0.994609	−	0.103692i	$-0.966934\pi$
$661$	−40.6657	−	23.4784i	−1.58171	−	0.913203i	−0.587105	−	0.809511i	$-0.699732\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−24.3313	+	42.1431i	−0.942112	+	1.63179i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−5.34305	−	9.25444i	−0.206266	−	0.357264i
$672$		0			0
$673$	7.76077	−	13.4421i	0.299156	−	0.518153i	−0.676787	−	0.736179i	$-0.736628\pi$
$673$	7.76077	−	13.4421i	0.299156	−	0.518153i	0.975943	+	0.218026i	$0.0699616\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.07869	−	15.7248i	−0.348922	−	0.604351i	0.637136	−	0.770751i	$-0.280119\pi$
$677$	−9.07869	−	15.7248i	−0.348922	−	0.604351i	−0.986058	+	0.166400i	$0.946786\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−17.4866	+	10.0959i	−0.669104	+	0.386308i	−0.795737	−	0.605642i	$-0.792916\pi$
$683$	−17.4866	+	10.0959i	−0.669104	+	0.386308i	0.126633	+	0.991950i	$0.459583\pi$
$684$		0			0
$685$			48.8146i			1.86511i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.44234	−	4.23026i	0.0930458	−	0.161160i
$690$		0			0
$691$	−0.0695792	+	0.0401716i	−0.00264692	+	0.00152820i	−0.501323	−	0.865260i	$-0.667153\pi$
$691$	−0.0695792	+	0.0401716i	−0.00264692	+	0.00152820i	0.498676	+	0.866788i	$0.333820\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	20.2077	−	11.6669i	0.766523	−	0.442552i
$696$		0			0
$697$	−0.396844	+	0.687355i	−0.0150316	+	0.0260354i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	35.1490i		−	1.32756i	−0.747928	−	0.663780i	$-0.768951\pi$
$701$		−	35.1490i		−	1.32756i	0.747928	−	0.663780i	$-0.231049\pi$
$702$		0			0
$703$	14.9256	−	8.61731i	0.562930	−	0.325008i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.782968	−	1.35614i	−0.0294050	−	0.0509309i	0.850948	−	0.525249i	$-0.176028\pi$
$709$	−0.782968	−	1.35614i	−0.0294050	−	0.0509309i	−0.880353	+	0.474318i	$0.842695\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	20.8823	−	36.1691i	0.782047	−	1.35455i
$714$		0			0
$715$	−2.92595	−	5.06790i	−0.109424	−	0.189529i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−12.9393	+	22.4116i	−0.482556	+	0.835811i	−0.999799	−	0.0200268i	$-0.993625\pi$
$719$	−12.9393	+	22.4116i	−0.482556	+	0.835811i	0.517243	+	0.855838i	$0.326958\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−91.6754	−	52.9288i	−3.40474	−	1.96573i
$726$		0			0
$727$	−0.990545	−	0.571891i	−0.0367373	−	0.0212103i	0.481519	−	0.876436i	$-0.340085\pi$
$727$	−0.990545	−	0.571891i	−0.0367373	−	0.0212103i	−0.518256	+	0.855225i	$0.673419\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.23217			−0.0825599
$732$		0			0
$733$			23.2565i			0.859000i	0.903067	+	0.429500i	$0.141310\pi$
$733$			23.2565i			0.859000i	−0.903067	+	0.429500i	$0.858690\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.4012	−	7.15985i	−0.456805	−	0.263736i
$738$		0			0
$739$	18.0758	+	31.3082i	0.664929	+	1.15169i	0.979305	+	0.202392i	$0.0648714\pi$
$739$	18.0758	+	31.3082i	0.664929	+	1.15169i	−0.314376	+	0.949299i	$0.601795\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−6.43940	+	3.71779i	−0.236239	+	0.136392i	−0.613447	−	0.789736i	$-0.710217\pi$
$743$	−6.43940	+	3.71779i	−0.236239	+	0.136392i	0.377208	+	0.926129i	$0.376884\pi$
$744$		0			0
$745$			64.7926i			2.37382i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	7.35595			0.268423			0.134211	−	0.990953i	$-0.457150\pi$
$751$	7.35595			0.268423			0.134211	+	0.990953i	$0.457150\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−69.6445			−2.53462
$756$		0			0
$757$	7.65326			0.278163			0.139081	−	0.990281i	$-0.455585\pi$
$757$	7.65326			0.278163			0.139081	+	0.990281i	$0.455585\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−43.4407			−1.57472			−0.787362	−	0.616492i	$-0.788553\pi$
$761$	−43.4407			−1.57472			−0.787362	+	0.616492i	$0.788553\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$			4.47721i			0.161663i
$768$		0			0
$769$	18.8491	−	10.8825i	0.679716	−	0.392434i	−0.120032	−	0.992770i	$-0.538300\pi$
$769$	18.8491	−	10.8825i	0.679716	−	0.392434i	0.799748	+	0.600336i	$0.204966\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	7.25734	+	12.5701i	0.261028	+	0.452114i	0.966515	−	0.256609i	$-0.0826051\pi$
$773$	7.25734	+	12.5701i	0.261028	+	0.452114i	−0.705487	+	0.708723i	$0.749272\pi$
$774$		0			0
$775$	78.6801	+	45.4260i	2.82627	+	1.63175i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			10.6440i			0.381362i
$780$		0			0
$781$	−15.5880			−0.557784
$782$		0			0
$783$		0			0
$784$		0			0
$785$	60.9415	+	35.1846i	2.17509	+	1.25579i
$786$		0			0
$787$	11.4291	+	6.59861i	0.407405	+	0.235215i	0.689674	−	0.724120i	$-0.257754\pi$
$787$	11.4291	+	6.59861i	0.407405	+	0.235215i	−0.282269	+	0.959335i	$0.591087\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	3.68889	−	6.38935i	0.130996	−	0.226892i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−24.8899	−	43.1106i	−0.881646	−	1.52706i	−0.849511	−	0.527572i	$-0.823103\pi$
$797$	−24.8899	−	43.1106i	−0.881646	−	1.52706i	−0.0321352	−	0.999484i	$-0.510231\pi$
$798$		0			0
$799$	−1.53402	+	2.65701i	−0.0542698	+	0.0939981i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	6.77880	+	11.7412i	0.239219	+	0.414339i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−24.4123	+	14.0944i	−0.858290	+	0.495534i	−0.863439	−	0.504453i	$-0.831694\pi$
$809$	−24.4123	+	14.0944i	−0.858290	+	0.495534i	0.00514934	+	0.999987i	$0.498361\pi$
$810$		0			0
$811$			33.5981i			1.17979i	0.807480	+	0.589894i	$0.200831\pi$
$811$			33.5981i			1.17979i	−0.807480	+	0.589894i	$0.799169\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−7.34988	+	12.7304i	−0.257455	+	0.445925i
$816$		0			0
$817$	−25.9247	+	14.9677i	−0.906992	+	0.523652i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−46.9123	+	27.0848i	−1.63725	+	0.945267i	−0.655475	+	0.755217i	$0.727532\pi$
$821$	−46.9123	+	27.0848i	−1.63725	+	0.945267i	−0.981774	+	0.190050i	$0.939135\pi$
$822$		0			0
$823$	−14.2695	+	24.7155i	−0.497404	+	0.861529i	−0.999996	−	0.00299479i	$-0.999047\pi$
$823$	−14.2695	+	24.7155i	−0.497404	+	0.861529i	0.502591	+	0.864524i	$0.332380\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			37.2062i			1.29379i	0.762581	+	0.646893i	$0.223932\pi$
$827$			37.2062i			1.29379i	−0.762581	+	0.646893i	$0.776068\pi$
$828$		0			0
$829$	1.92557	−	1.11173i	0.0668777	−	0.0386119i	−0.466188	−	0.884686i	$-0.654373\pi$
$829$	1.92557	−	1.11173i	0.0668777	−	0.0386119i	0.533066	+	0.846074i	$0.321040\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	16.9668	+	29.3873i	0.587159	+	1.01699i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−27.8383	+	48.2173i	−0.961084	+	1.66465i	−0.241297	+	0.970451i	$0.577573\pi$
$839$	−27.8383	+	48.2173i	−0.961084	+	1.66465i	−0.719787	+	0.694195i	$0.755760\pi$
$840$		0			0
$841$	21.1955	+	36.7116i	0.730878	+	1.26592i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−25.1935	+	43.6364i	−0.866683	+	1.50114i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	17.2798	+	9.97650i	0.592344	+	0.341990i
$852$		0			0
$853$	16.2574	+	9.38622i	0.556643	+	0.321378i	0.751797	−	0.659395i	$-0.229187\pi$
$853$	16.2574	+	9.38622i	0.556643	+	0.321378i	−0.195154	+	0.980773i	$0.562521\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−23.7032			−0.809687			−0.404844	−	0.914386i	$-0.632674\pi$
$857$	−23.7032			−0.809687			−0.404844	+	0.914386i	$0.632674\pi$
$858$		0			0
$859$			16.7705i			0.572203i	0.958199	+	0.286102i	$0.0923595\pi$
$859$			16.7705i			0.572203i	−0.958199	+	0.286102i	$0.907640\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	29.2235	+	16.8722i	0.994778	+	0.574335i	0.906699	−	0.421778i	$-0.138594\pi$
$863$	29.2235	+	16.8722i	0.994778	+	0.574335i	0.0880791	+	0.996113i	$0.471927\pi$
$864$		0			0
$865$	−27.4164	−	47.4866i	−0.932186	−	1.61459i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	10.4875	−	6.05497i	0.355765	−	0.205401i
$870$		0			0
$871$		−	9.88645i		−	0.334990i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−39.4174			−1.33103			−0.665515	−	0.746384i	$-0.731788\pi$
$877$	−39.4174			−1.33103			−0.665515	+	0.746384i	$0.731788\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	26.2496			0.884372			0.442186	−	0.896923i	$-0.354203\pi$
$881$	26.2496			0.884372			0.442186	+	0.896923i	$0.354203\pi$
$882$		0			0
$883$	−43.5087			−1.46418			−0.732091	−	0.681206i	$-0.761456\pi$
$883$	−43.5087			−1.46418			−0.732091	+	0.681206i	$0.761456\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.67776			−0.190640			−0.0953202	−	0.995447i	$-0.530387\pi$
$887$	−5.67776			−0.190640			−0.0953202	+	0.995447i	$0.530387\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$			41.1451i			1.37687i
$894$		0			0
$895$	−46.1124	+	26.6230i	−1.54137	+	0.889909i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−30.6355	−	53.0623i	−1.02175	−	1.76973i
$900$		0			0
$901$	−1.59740	−	0.922259i	−0.0532171	−	0.0307249i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	111.165i		−	3.69524i
$906$		0			0
$907$	14.6548			0.486605			0.243303	−	0.969950i	$-0.421769\pi$
$907$	14.6548			0.486605			0.243303	+	0.969950i	$0.421769\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−7.19133	−	4.15192i	−0.238260	−	0.137559i	0.376117	−	0.926572i	$-0.377259\pi$
$911$	−7.19133	−	4.15192i	−0.238260	−	0.137559i	−0.614377	+	0.789013i	$0.710592\pi$
$912$		0			0
$913$	−2.39607	−	1.38337i	−0.0792983	−	0.0457829i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	18.5554	−	32.1388i	0.612085	−	1.06016i	−0.378804	−	0.925477i	$-0.623665\pi$
$919$	18.5554	−	32.1388i	0.612085	−	1.06016i	0.990889	−	0.134685i	$-0.0430021\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−5.38106	−	9.32027i	−0.177120	−	0.306781i
$924$		0			0
$925$	−21.7022	+	37.5894i	−0.713566	+	1.23593i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.94493	+	6.83283i	0.129429	+	0.224178i	0.923456	−	0.383705i	$-0.125352\pi$
$929$	3.94493	+	6.83283i	0.129429	+	0.224178i	−0.794026	+	0.607883i	$0.792019\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.91370	+	1.10488i	−0.0625848	+	0.0361333i
$936$		0			0
$937$		−	13.2688i		−	0.433472i	−0.976230	−	0.216736i	$-0.930459\pi$
$937$		−	13.2688i		−	0.433472i	0.976230	−	0.216736i	$-0.0695411\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−3.96461	+	6.86691i	−0.129243	+	0.223855i	−0.923383	−	0.383879i	$-0.874588\pi$
$941$	−3.96461	+	6.86691i	−0.129243	+	0.223855i	0.794141	+	0.607734i	$0.207921\pi$
$942$		0			0
$943$	−10.6719	+	6.16144i	−0.347526	+	0.200644i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−26.8152	+	15.4817i	−0.871375	+	0.503089i	−0.867805	−	0.496905i	$-0.834470\pi$
$947$	−26.8152	+	15.4817i	−0.871375	+	0.503089i	−0.00357041	+	0.999994i	$0.501136\pi$
$948$		0			0
$949$	−4.68014	+	8.10625i	−0.151924	+	0.263140i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			34.1087i			1.10489i	0.833549	+	0.552445i	$0.186305\pi$
$953$			34.1087i			1.10489i	−0.833549	+	0.552445i	$0.813695\pi$
$954$		0			0
$955$	−4.59428	+	2.65251i	−0.148668	+	0.0858332i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	10.7928	+	18.6937i	0.348156	+	0.603023i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−39.0089	+	67.5655i	−1.25574	+	2.17501i
$966$		0			0
$967$	29.1066	+	50.4142i	0.936007	+	1.62121i	0.772829	+	0.634614i	$0.218841\pi$
$967$	29.1066	+	50.4142i	0.936007	+	1.62121i	0.163177	+	0.986597i	$0.447826\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−4.91896	+	8.51988i	−0.157857	+	0.273416i	−0.934096	−	0.357023i	$-0.883792\pi$
$971$	−4.91896	+	8.51988i	−0.157857	+	0.273416i	0.776239	+	0.630439i	$0.217125\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−29.0356	−	16.7637i	−0.928930	−	0.536318i	−0.0424567	−	0.999098i	$-0.513518\pi$
$977$	−29.0356	−	16.7637i	−0.928930	−	0.536318i	−0.886473	+	0.462781i	$0.846852\pi$
$978$		0			0
$979$	−9.62041	−	5.55434i	−0.307470	−	0.177518i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	48.4718			1.54601			0.773006	−	0.634399i	$-0.218752\pi$
$983$	48.4718			1.54601			0.773006	+	0.634399i	$0.218752\pi$
$984$		0			0
$985$			24.8821i			0.792811i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−30.0138	−	17.3285i	−0.954382	−	0.551013i
$990$		0			0
$991$	26.5005	+	45.9003i	0.841818	+	1.45807i	0.888357	+	0.459154i	$0.151848\pi$
$991$	26.5005	+	45.9003i	0.841818	+	1.45807i	−0.0465389	+	0.998916i	$0.514819\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−20.4015	+	11.7788i	−0.646770	+	0.373413i
$996$		0			0
$997$		−	8.74551i		−	0.276973i	−0.990364	−	0.138487i	$-0.955776\pi$
$997$		−	8.74551i		−	0.276973i	0.990364	−	0.138487i	$-0.0442238\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5292.2.bm.b.4625.8		16
3.2	odd	2		1764.2.bm.b.1685.8		16
7.2	even	3		756.2.x.a.629.1		16
7.3	odd	6		5292.2.w.a.521.8		16
7.4	even	3		5292.2.w.a.521.1		16
7.5	odd	6		756.2.x.a.629.8		16
7.6	odd	2	inner	5292.2.bm.b.4625.1		16
9.4	even	3		1764.2.w.a.509.7		16
9.5	odd	6		5292.2.w.a.1097.8		16
21.2	odd	6		252.2.x.a.209.4	yes	16
21.5	even	6		252.2.x.a.209.5	yes	16
21.11	odd	6		1764.2.w.a.1109.2		16
21.17	even	6		1764.2.w.a.1109.7		16
21.20	even	2		1764.2.bm.b.1685.1		16
28.19	even	6		3024.2.cc.c.2897.8		16
28.23	odd	6		3024.2.cc.c.2897.1		16
63.2	odd	6		2268.2.f.b.1133.2		16
63.4	even	3		1764.2.bm.b.1697.1		16
63.5	even	6		756.2.x.a.125.1		16
63.13	odd	6		1764.2.w.a.509.2		16
63.16	even	3		2268.2.f.b.1133.16		16
63.23	odd	6		756.2.x.a.125.8		16
63.31	odd	6		1764.2.bm.b.1697.8		16
63.32	odd	6	inner	5292.2.bm.b.2285.1		16
63.40	odd	6		252.2.x.a.41.4	✓	16
63.41	even	6		5292.2.w.a.1097.1		16
63.47	even	6		2268.2.f.b.1133.15		16
63.58	even	3		252.2.x.a.41.5	yes	16
63.59	even	6	inner	5292.2.bm.b.2285.8		16
63.61	odd	6		2268.2.f.b.1133.1		16
84.23	even	6		1008.2.cc.c.209.5		16
84.47	odd	6		1008.2.cc.c.209.4		16
252.23	even	6		3024.2.cc.c.881.8		16
252.103	even	6		1008.2.cc.c.545.5		16
252.131	odd	6		3024.2.cc.c.881.1		16
252.247	odd	6		1008.2.cc.c.545.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.x.a.41.4	✓	16	63.40	odd	6
252.2.x.a.41.5	yes	16	63.58	even	3
252.2.x.a.209.4	yes	16	21.2	odd	6
252.2.x.a.209.5	yes	16	21.5	even	6
756.2.x.a.125.1		16	63.5	even	6
756.2.x.a.125.8		16	63.23	odd	6
756.2.x.a.629.1		16	7.2	even	3
756.2.x.a.629.8		16	7.5	odd	6
1008.2.cc.c.209.4		16	84.47	odd	6
1008.2.cc.c.209.5		16	84.23	even	6
1008.2.cc.c.545.4		16	252.247	odd	6
1008.2.cc.c.545.5		16	252.103	even	6
1764.2.w.a.509.2		16	63.13	odd	6
1764.2.w.a.509.7		16	9.4	even	3
1764.2.w.a.1109.2		16	21.11	odd	6
1764.2.w.a.1109.7		16	21.17	even	6
1764.2.bm.b.1685.1		16	21.20	even	2
1764.2.bm.b.1685.8		16	3.2	odd	2
1764.2.bm.b.1697.1		16	63.4	even	3
1764.2.bm.b.1697.8		16	63.31	odd	6
2268.2.f.b.1133.1		16	63.61	odd	6
2268.2.f.b.1133.2		16	63.2	odd	6
2268.2.f.b.1133.15		16	63.47	even	6
2268.2.f.b.1133.16		16	63.16	even	3
3024.2.cc.c.881.1		16	252.131	odd	6
3024.2.cc.c.881.8		16	252.23	even	6
3024.2.cc.c.2897.1		16	28.23	odd	6
3024.2.cc.c.2897.8		16	28.19	even	6
5292.2.w.a.521.1		16	7.4	even	3
5292.2.w.a.521.8		16	7.3	odd	6
5292.2.w.a.1097.1		16	63.41	even	6
5292.2.w.a.1097.8		16	9.5	odd	6
5292.2.bm.b.2285.1		16	63.32	odd	6	inner
5292.2.bm.b.2285.8		16	63.59	even	6	inner
5292.2.bm.b.4625.1		16	7.6	odd	2	inner
5292.2.bm.b.4625.8		16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5292.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+4.18671 q^{5} +O(q^{10})\)	\(q+4.18671 q^{5} -1.42285i q^{11} +(0.850739 - 0.491174i) q^{13} +(-0.185474 - 0.321250i) q^{17} +(-4.30823 - 2.48736i) q^{19} -5.75936i q^{23} +12.5285 q^{25} +(-7.31732 - 4.22466i) q^{29} +(6.28007 + 3.62580i) q^{31} +(-1.73222 + 3.00030i) q^{37} +(-1.06981 - 1.85297i) q^{41} +(3.00875 - 5.21130i) q^{43} +(-4.13542 - 7.16276i) q^{47} +(4.30627 - 2.48623i) q^{53} -5.95706i q^{55} +(-2.27883 + 3.94705i) q^{59} +(6.50416 - 3.75518i) q^{61} +(3.56180 - 2.05640i) q^{65} +(5.03205 - 8.71577i) q^{67} -10.9555i q^{71} +(-8.25191 + 4.76424i) q^{73} +(4.25553 + 7.37079i) q^{79} +(0.972254 - 1.68399i) q^{83} +(-0.776524 - 1.34498i) q^{85} +(3.90368 - 6.76137i) q^{89} +(-18.0373 - 10.4138i) q^{95} +(3.34099 + 1.92892i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 16 q^{25} + 12 q^{29} - 2 q^{37} + 4 q^{43} + 36 q^{53} - 24 q^{65} + 14 q^{67} + 20 q^{79} + 6 q^{85} - 60 q^{95}+O(q^{100}) \) 16 * q + 16 * q^25 + 12 * q^29 - 2 * q^37 + 4 * q^43 + 36 * q^53 - 24 * q^65 + 14 * q^67 + 20 * q^79 + 6 * q^85 - 60 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more