LMFDB - Embedded newform 1260.2.s.h.541.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1260,2,Mod(361,1260)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1260.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1260, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.s (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,0,3,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.4406832.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 6x^{4} + 7x^{3} + 24x^{2} + 5x + 1 $ x^6 - x^5 + 6x^4 + 7x^3 + 24x^2 + 5x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.1
Root			$1.43310 - 2.48220i$ of defining polynomial
Character	$\chi$	$=$	1260.541
Dual form			1260.2.s.h.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +(-1.69175 + 2.03420i) q^{7} +(-1.19175 - 2.06417i) q^{11} +1.38350 q^{13} +(0.415795 + 0.720178i) q^{17} +(2.10755 - 3.65038i) q^{19} +(2.79930 - 4.84853i) q^{23} +(-0.500000 - 0.866025i) q^{25} +10.0467 q^{29} +(0.500000 + 0.866025i) q^{31} +(0.915795 + 2.48220i) q^{35} +(-2.29930 + 3.98250i) q^{37} +8.81369 q^{41} -1.83159 q^{43} +(6.21509 - 10.7649i) q^{47} +(-1.27596 - 6.88273i) q^{49} +(0.831590 + 1.44036i) q^{53} -2.38350 q^{55} +(-4.19175 - 7.26033i) q^{59} +(-2.60755 + 4.51640i) q^{61} +(0.691751 - 1.19815i) q^{65} +(-0.691751 - 1.19815i) q^{67} +3.61650 q^{71} +(6.29930 + 10.9107i) q^{73} +(6.21509 + 1.06781i) q^{77} +(5.93914 - 10.2869i) q^{79} -3.93541 q^{83} +0.831590 q^{85} +(0.360161 - 0.623817i) q^{89} +(-2.34054 + 2.81432i) q^{91} +(-2.10755 - 3.65038i) q^{95} -2.44809 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} - q^{7} + 2 q^{11} - 10 q^{13} - 2 q^{17} - q^{19} - 6 q^{23} - 3 q^{25} + 24 q^{29} + 3 q^{31} + q^{35} + 9 q^{37} - 20 q^{41} - 2 q^{43} + 10 q^{47} - 3 q^{49} - 4 q^{53} + 4 q^{55} - 16 q^{59}+ \cdots - 24 q^{97}+O(q^{100}) $ 6 * q + 3 * q^5 - q^7 + 2 * q^11 - 10 * q^13 - 2 * q^17 - q^19 - 6 * q^23 - 3 * q^25 + 24 * q^29 + 3 * q^31 + q^35 + 9 * q^37 - 20 * q^41 - 2 * q^43 + 10 * q^47 - 3 * q^49 - 4 * q^53 + 4 * q^55 - 16 * q^59 - 2 * q^61 - 5 * q^65 + 5 * q^67 + 40 * q^71 + 15 * q^73 + 10 * q^77 + 13 * q^79 + 4 * q^83 - 4 * q^85 + 2 * q^89 - 37 * q^91 + q^95 - 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−1.69175	+	2.03420i	−0.639422	+	0.768856i
$7$	−1.69175	+	2.03420i	−0.639422	+	0.768856i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.19175	−	2.06417i	−0.359326	−	0.622372i	0.628522	−	0.777792i	$-0.283660\pi$
$11$	−1.19175	−	2.06417i	−0.359326	−	0.622372i	−0.987848	+	0.155420i	$0.950327\pi$
$12$		0			0
$13$	1.38350			0.383715			0.191857	−	0.981423i	$-0.438549\pi$
$13$	1.38350			0.383715			0.191857	+	0.981423i	$0.438549\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.415795	+	0.720178i	0.100845	+	0.174669i	0.912033	−	0.410117i	$-0.134512\pi$
$17$	0.415795	+	0.720178i	0.100845	+	0.174669i	−0.811188	+	0.584786i	$0.801179\pi$
$18$		0			0
$19$	2.10755	−	3.65038i	0.483504	−	0.837454i	−0.516316	−	0.856398i	$-0.672697\pi$
$19$	2.10755	−	3.65038i	0.483504	−	0.837454i	0.999821	+	0.0189440i	$0.00603043\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.79930	−	4.84853i	0.583694	−	1.01099i	−0.411343	−	0.911481i	$-0.634940\pi$
$23$	2.79930	−	4.84853i	0.583694	−	1.01099i	0.995037	−	0.0995068i	$-0.0317265\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	10.0467			1.86562			0.932811	−	0.360366i	$-0.117348\pi$
$29$	10.0467			1.86562			0.932811	+	0.360366i	$0.117348\pi$
$30$		0			0
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	0.907428	−	0.420208i	$-0.138043\pi$
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	−0.817625	+	0.575751i	$0.804710\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.915795	+	2.48220i	0.154798	+	0.419568i
$36$		0			0
$37$	−2.29930	+	3.98250i	−0.378002	+	0.654719i	−0.990771	−	0.135543i	$-0.956722\pi$
$37$	−2.29930	+	3.98250i	−0.378002	+	0.654719i	0.612769	+	0.790262i	$0.290055\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	8.81369			1.37647			0.688233	−	0.725489i	$-0.258387\pi$
$41$	8.81369			1.37647			0.688233	+	0.725489i	$0.258387\pi$
$42$		0			0
$43$	−1.83159			−0.279315			−0.139657	−	0.990200i	$-0.544600\pi$
$43$	−1.83159			−0.279315			−0.139657	+	0.990200i	$0.544600\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.21509	−	10.7649i	0.906564	−	1.57022i	0.0877610	−	0.996142i	$-0.472029\pi$
$47$	6.21509	−	10.7649i	0.906564	−	1.57022i	0.818803	−	0.574074i	$-0.194638\pi$
$48$		0			0
$49$	−1.27596	−	6.88273i	−0.182279	−	0.983247i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.831590	+	1.44036i	0.114228	+	0.197848i	0.917471	−	0.397803i	$-0.130227\pi$
$53$	0.831590	+	1.44036i	0.114228	+	0.197848i	−0.803243	+	0.595651i	$0.796894\pi$
$54$		0			0
$55$	−2.38350			−0.321391
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.19175	−	7.26033i	−0.545720	−	0.945214i	−0.998561	−	0.0536230i	$-0.982923\pi$
$59$	−4.19175	−	7.26033i	−0.545720	−	0.945214i	0.452842	−	0.891591i	$-0.350410\pi$
$60$		0			0
$61$	−2.60755	+	4.51640i	−0.333862	+	0.578266i	−0.983266	−	0.182178i	$-0.941685\pi$
$61$	−2.60755	+	4.51640i	−0.333862	+	0.578266i	0.649403	+	0.760444i	$0.275019\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.691751	−	1.19815i	0.0858012	−	0.148612i
$66$		0			0
$67$	−0.691751	−	1.19815i	−0.0845109	−	0.146377i	0.820672	−	0.571400i	$-0.193599\pi$
$67$	−0.691751	−	1.19815i	−0.0845109	−	0.146377i	−0.905183	+	0.425023i	$0.860266\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.61650			0.429199			0.214600	−	0.976702i	$-0.431155\pi$
$71$	3.61650			0.429199			0.214600	+	0.976702i	$0.431155\pi$
$72$		0			0
$73$	6.29930	+	10.9107i	0.737277	+	1.27700i	0.953717	+	0.300705i	$0.0972221\pi$
$73$	6.29930	+	10.9107i	0.737277	+	1.27700i	−0.216440	+	0.976296i	$0.569445\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.21509	+	1.06781i	0.708276	+	0.121688i
$78$		0			0
$79$	5.93914	−	10.2869i	0.668205	−	1.15737i	−0.310201	−	0.950671i	$-0.600396\pi$
$79$	5.93914	−	10.2869i	0.668205	−	1.15737i	0.978406	−	0.206694i	$-0.0662704\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.93541			−0.431968			−0.215984	−	0.976397i	$-0.569296\pi$
$83$	−3.93541			−0.431968			−0.215984	+	0.976397i	$0.569296\pi$
$84$		0			0
$85$	0.831590			0.0901986
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.360161	−	0.623817i	0.0381770	−	0.0661245i	−0.846306	−	0.532698i	$-0.821178\pi$
$89$	0.360161	−	0.623817i	0.0381770	−	0.0661245i	0.884483	+	0.466573i	$0.154512\pi$
$90$		0			0
$91$	−2.34054	+	2.81432i	−0.245355	+	0.295021i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.10755	−	3.65038i	−0.216230	−	0.374521i
$96$		0			0
$97$	−2.44809			−0.248566			−0.124283	−	0.992247i	$-0.539663\pi$
$97$	−2.44809			−0.248566			−0.124283	+	0.992247i	$0.539663\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.57525	−	11.3887i	−0.654262	−	1.13322i	−0.982078	−	0.188474i	$-0.939646\pi$
$101$	−6.57525	−	11.3887i	−0.654262	−	1.13322i	0.327816	−	0.944742i	$-0.393687\pi$
$102$		0			0
$103$	−3.13089	+	5.42286i	−0.308496	+	0.534330i	−0.978033	−	0.208448i	$-0.933159\pi$
$103$	−3.13089	+	5.42286i	−0.308496	+	0.534330i	0.669538	+	0.742778i	$0.266492\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.79930	+	10.0447i	−0.560639	+	0.971056i	0.436802	+	0.899558i	$0.356111\pi$
$107$	−5.79930	+	10.0447i	−0.560639	+	0.971056i	−0.997441	+	0.0714977i	$0.977222\pi$
$108$		0			0
$109$	−6.49105	−	11.2428i	−0.621730	−	1.07687i	−0.989164	−	0.146818i	$-0.953097\pi$
$109$	−6.49105	−	11.2428i	−0.621730	−	1.07687i	0.367434	−	0.930050i	$-0.380236\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	16.7670			1.57731			0.788654	−	0.614838i	$-0.210779\pi$
$113$	16.7670			1.57731			0.788654	+	0.614838i	$0.210779\pi$
$114$		0			0
$115$	−2.79930	−	4.84853i	−0.261036	−	0.452127i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.16841	−	0.372551i	−0.198778	−	0.0341517i
$120$		0			0
$121$	2.65946	−	4.60632i	0.241769	−	0.418756i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	13.8137			1.22577			0.612883	−	0.790173i	$-0.290010\pi$
$127$	13.8137			1.22577			0.612883	+	0.790173i	$0.290010\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.616498	−	1.06781i	0.0538637	−	0.0932946i	−0.837836	−	0.545921i	$-0.816180\pi$
$131$	0.616498	−	1.06781i	0.0538637	−	0.0932946i	0.891700	+	0.452627i	$0.149513\pi$
$132$		0			0
$133$	3.86016	+	10.4627i	0.334718	+	0.907232i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.200703	−	0.347627i	−0.0171472	−	0.0296998i	0.857324	−	0.514776i	$-0.172125\pi$
$137$	−0.200703	−	0.347627i	−0.0171472	−	0.0296998i	−0.874472	+	0.485077i	$0.838792\pi$
$138$		0			0
$139$	−0.888732			−0.0753812			−0.0376906	−	0.999289i	$-0.512000\pi$
$139$	−0.888732			−0.0753812			−0.0376906	+	0.999289i	$0.512000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.64879	−	2.85579i	−0.137879	−	0.238813i
$144$		0			0
$145$	5.02334	−	8.70068i	0.417166	−	0.722552i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	8.37455	+	14.5051i	0.681511	+	1.18041i	0.974520	+	0.224302i	$0.0720103\pi$
$151$	8.37455	+	14.5051i	0.681511	+	1.18041i	−0.293008	+	0.956110i	$0.594656\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.00000			0.0803219
$156$		0			0
$157$	−1.83159	−	3.17241i	−0.146177	−	0.253186i	0.783635	−	0.621222i	$-0.213364\pi$
$157$	−1.83159	−	3.17241i	−0.146177	−	0.253186i	−0.929811	+	0.368036i	$0.880030\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.12717	+	13.8968i	0.404077	+	1.09522i
$162$		0			0
$163$	−8.04668	+	13.9373i	−0.630265	+	1.09165i	0.357233	+	0.934015i	$0.383720\pi$
$163$	−8.04668	+	13.9373i	−0.630265	+	1.09165i	−0.987497	+	0.157635i	$0.949613\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−11.5986			−0.897526			−0.448763	−	0.893651i	$-0.648135\pi$
$167$	−11.5986			−0.897526			−0.448763	+	0.893651i	$0.648135\pi$
$168$		0			0
$169$	−11.0859			−0.852763
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.21509	−	10.7649i	0.472525	−	0.818437i	−0.526981	−	0.849877i	$-0.676676\pi$
$173$	6.21509	−	10.7649i	0.472525	−	0.818437i	0.999506	+	0.0314403i	$0.0100094\pi$
$174$		0			0
$175$	2.60755	+	0.447998i	0.197112	+	0.0338655i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.55191	+	2.68799i	0.115995	+	0.200910i	0.918177	−	0.396170i	$-0.129661\pi$
$179$	1.55191	+	2.68799i	0.115995	+	0.200910i	−0.802182	+	0.597080i	$0.796328\pi$
$180$		0			0
$181$	−2.98210			−0.221658			−0.110829	−	0.993840i	$-0.535351\pi$
$181$	−2.98210			−0.221658			−0.110829	+	0.993840i	$0.535351\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.29930	+	3.98250i	0.169048	+	0.292799i
$186$		0			0
$187$	0.991049	−	1.71655i	0.0724726	−	0.125526i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−7.55191	+	13.0803i	−0.546437	+	0.946457i	0.452078	+	0.891979i	$0.350683\pi$
$191$	−7.55191	+	13.0803i	−0.546437	+	0.946457i	−0.998515	+	0.0544784i	$0.982650\pi$
$192$		0			0
$193$	8.89789	+	15.4116i	0.640484	+	1.10935i	0.985325	+	0.170690i	$0.0545997\pi$
$193$	8.89789	+	15.4116i	0.640484	+	1.10935i	−0.344840	+	0.938661i	$0.612067\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	17.1684			1.22320			0.611599	−	0.791168i	$-0.290526\pi$
$197$	17.1684			1.22320			0.611599	+	0.791168i	$0.290526\pi$
$198$		0			0
$199$	−10.3746	−	17.9692i	−0.735432	−	1.27381i	−0.954533	−	0.298104i	$-0.903646\pi$
$199$	−10.3746	−	17.9692i	−0.735432	−	1.27381i	0.219101	−	0.975702i	$-0.429688\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−16.9965	+	20.4370i	−1.19292	+	1.43439i
$204$		0			0
$205$	4.40684	−	7.63288i	0.307787	−	0.533103i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−10.0467			−0.694944
$210$		0			0
$211$	3.12173			0.214909			0.107454	−	0.994210i	$-0.465730\pi$
$211$	3.12173			0.214909			0.107454	+	0.994210i	$0.465730\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.915795	+	1.58620i	−0.0624567	+	0.108178i
$216$		0			0
$217$	−2.60755	−	0.447998i	−0.177012	−	0.0304121i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.575253	+	0.996368i	0.0386957	+	0.0670230i
$222$		0			0
$223$	−7.32636			−0.490609			−0.245305	−	0.969446i	$-0.578888\pi$
$223$	−7.32636			−0.490609			−0.245305	+	0.969446i	$0.578888\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.6309	−	21.8773i	−0.838341	−	1.45205i	−0.891281	−	0.453452i	$-0.850192\pi$
$227$	−12.6309	−	21.8773i	−0.838341	−	1.45205i	0.0529391	−	0.998598i	$-0.483141\pi$
$228$		0			0
$229$	5.16318	−	8.94289i	0.341193	−	0.590963i	−0.643462	−	0.765478i	$-0.722503\pi$
$229$	5.16318	−	8.94289i	0.341193	−	0.590963i	0.984654	+	0.174515i	$0.0558358\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−13.0467	+	22.5975i	−0.854717	+	1.48041i	0.0221911	+	0.999754i	$0.492936\pi$
$233$	−13.0467	+	22.5975i	−0.854717	+	1.48041i	−0.876908	+	0.480659i	$0.840398\pi$
$234$		0			0
$235$	−6.21509	−	10.7649i	−0.405428	−	0.702222i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.86037			−0.443760			−0.221880	−	0.975074i	$-0.571219\pi$
$239$	−6.86037			−0.443760			−0.221880	+	0.975074i	$0.571219\pi$
$240$		0			0
$241$	1.43914	+	2.49266i	0.0927029	+	0.160566i	0.908648	−	0.417564i	$-0.137116\pi$
$241$	1.43914	+	2.49266i	0.0927029	+	0.160566i	−0.815945	+	0.578130i	$0.803783\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−6.59859	−	2.33635i	−0.421569	−	0.149264i
$246$		0			0
$247$	2.91580	−	5.05031i	0.185528	−	0.321343i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−24.1400			−1.52371			−0.761853	−	0.647750i	$-0.775710\pi$
$251$	−24.1400			−1.52371			−0.761853	+	0.647750i	$0.775710\pi$
$252$		0			0
$253$	−13.3443			−0.838947
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−12.2295	+	21.1821i	−0.762854	+	1.32130i	0.178519	+	0.983936i	$0.442869\pi$
$257$	−12.2295	+	21.1821i	−0.762854	+	1.32130i	−0.941374	+	0.337366i	$0.890464\pi$
$258$		0			0
$259$	−4.21137	−	11.4146i	−0.261682	−	0.709271i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−9.43018	−	16.3336i	−0.581490	−	1.00717i	−0.995303	−	0.0968085i	$-0.969137\pi$
$263$	−9.43018	−	16.3336i	−0.581490	−	1.00717i	0.413813	−	0.910362i	$-0.364197\pi$
$264$		0			0
$265$	1.66318			0.102168
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2.59859	+	4.50090i	0.158439	+	0.274425i	0.934306	−	0.356472i	$-0.116021\pi$
$269$	2.59859	+	4.50090i	0.158439	+	0.274425i	−0.775867	+	0.630897i	$0.782687\pi$
$270$		0			0
$271$	−13.9910	+	24.2332i	−0.849896	+	1.47206i	0.0314051	+	0.999507i	$0.490002\pi$
$271$	−13.9910	+	24.2332i	−0.849896	+	1.47206i	−0.881301	+	0.472556i	$0.843332\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.19175	+	2.06417i	−0.0718653	+	0.124474i
$276$		0			0
$277$	3.08420	+	5.34200i	0.185312	+	0.320970i	0.943682	−	0.330855i	$-0.107337\pi$
$277$	3.08420	+	5.34200i	0.185312	+	0.320970i	−0.758370	+	0.651825i	$0.774004\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	11.5698			0.690197			0.345099	−	0.938566i	$-0.387845\pi$
$281$	11.5698			0.690197			0.345099	+	0.938566i	$0.387845\pi$
$282$		0			0
$283$	14.8979	+	25.8039i	0.885588	+	1.53388i	0.845038	+	0.534705i	$0.179577\pi$
$283$	14.8979	+	25.8039i	0.885588	+	1.53388i	0.0405493	+	0.999178i	$0.487089\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−14.9106	+	17.9288i	−0.880143	+	1.05830i
$288$		0			0
$289$	8.15423	−	14.1235i	0.479661	−	0.830796i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−19.6632			−1.14874			−0.574368	−	0.818597i	$-0.694752\pi$
$293$	−19.6632			−1.14874			−0.574368	+	0.818597i	$0.694752\pi$
$294$		0			0
$295$	−8.38350			−0.488106
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.87283	−	6.70795i	0.223972	−	0.387931i
$300$		0			0
$301$	3.09859	−	3.72582i	0.178600	−	0.214753i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.60755	+	4.51640i	0.149308	+	0.258608i
$306$		0			0
$307$	19.8137			1.13083			0.565413	−	0.824808i	$-0.308717\pi$
$307$	19.8137			1.13083			0.565413	+	0.824808i	$0.308717\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−11.0233	−	19.0930i	−0.625076	−	1.08266i	−0.988526	−	0.151050i	$-0.951734\pi$
$311$	−11.0233	−	19.0930i	−0.625076	−	1.08266i	0.363450	−	0.931614i	$-0.381599\pi$
$312$		0			0
$313$	5.25261	−	9.09780i	0.296895	−	0.514238i	−0.678529	−	0.734574i	$-0.737382\pi$
$313$	5.25261	−	9.09780i	0.296895	−	0.514238i	0.975424	+	0.220336i	$0.0707154\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.36911	+	4.10342i	−0.133063	+	0.230471i	−0.924856	−	0.380318i	$-0.875814\pi$
$317$	−2.36911	+	4.10342i	−0.133063	+	0.230471i	0.791793	+	0.610789i	$0.209148\pi$
$318$		0			0
$319$	−11.9731	−	20.7381i	−0.670367	−	1.16111i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.50523			0.195036
$324$		0			0
$325$	−0.691751	−	1.19815i	−0.0383715	−	0.0664613i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	11.3835	+	30.8542i	0.627593	+	1.70105i
$330$		0			0
$331$	−8.93018	+	15.4675i	−0.490847	+	0.850173i	−0.999944	−	0.0105365i	$-0.996646\pi$
$331$	−8.93018	+	15.4675i	−0.490847	+	0.850173i	0.509097	+	0.860709i	$0.329979\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.38350			−0.0755888
$336$		0			0
$337$	−11.4769			−0.625185			−0.312592	−	0.949887i	$-0.601197\pi$
$337$	−11.4769			−0.625185			−0.312592	+	0.949887i	$0.601197\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.19175	−	2.06417i	0.0645369	−	0.111781i
$342$		0			0
$343$	16.1595	+	9.04831i	0.872529	+	0.488563i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.78491	+	4.82360i	0.149502	+	0.258944i	0.931043	−	0.364908i	$-0.118900\pi$
$347$	2.78491	+	4.82360i	0.149502	+	0.258944i	−0.781542	+	0.623853i	$0.785566\pi$
$348$		0			0
$349$	3.66318			0.196086			0.0980428	−	0.995182i	$-0.468742\pi$
$349$	3.66318			0.196086			0.0980428	+	0.995182i	$0.468742\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.200703	−	0.347627i	−0.0106823	−	0.0185023i	0.860635	−	0.509223i	$-0.170067\pi$
$353$	−0.200703	−	0.347627i	−0.0106823	−	0.0185023i	−0.871317	+	0.490720i	$0.836734\pi$
$354$		0			0
$355$	1.80825	−	3.13198i	0.0959719	−	0.166228i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−13.4068	+	23.2213i	−0.707586	+	1.22558i	0.258164	+	0.966101i	$0.416883\pi$
$359$	−13.4068	+	23.2213i	−0.707586	+	1.22558i	−0.965750	+	0.259474i	$0.916451\pi$
$360$		0			0
$361$	0.616498	+	1.06781i	0.0324472	+	0.0562003i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	12.5986			0.659441
$366$		0			0
$367$	−0.261566	−	0.453046i	−0.0136536	−	0.0236488i	0.859118	−	0.511778i	$-0.171013\pi$
$367$	−0.261566	−	0.453046i	−0.0136536	−	0.0236488i	−0.872771	+	0.488129i	$0.837680\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.33682	−	0.745102i	−0.225156	−	0.0386838i
$372$		0			0
$373$	−16.1219	+	27.9240i	−0.834762	+	1.44585i	0.0594617	+	0.998231i	$0.481062\pi$
$373$	−16.1219	+	27.9240i	−0.834762	+	1.44585i	−0.894224	+	0.447620i	$0.852272\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	13.8996			0.715866
$378$		0			0
$379$	19.5236			1.00286			0.501429	−	0.865199i	$-0.332808\pi$
$379$	19.5236			1.00286			0.501429	+	0.865199i	$0.332808\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.401405	−	0.695254i	0.0205108	−	0.0355258i	−0.855588	−	0.517658i	$-0.826804\pi$
$383$	0.401405	−	0.695254i	0.0205108	−	0.0355258i	0.876099	+	0.482132i	$0.160137\pi$
$384$		0			0
$385$	4.03229	−	4.84853i	0.205505	−	0.247104i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−14.9588	−	25.9093i	−0.758439	−	1.31365i	−0.943646	−	0.330955i	$-0.892629\pi$
$389$	−14.9588	−	25.9093i	−0.758439	−	1.31365i	0.185207	−	0.982699i	$-0.440704\pi$
$390$		0			0
$391$	4.65574			0.235451
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−5.93914	−	10.2869i	−0.298830	−	0.517589i
$396$		0			0
$397$	−14.7295	+	25.5122i	−0.739252	+	1.28042i	0.213581	+	0.976925i	$0.431487\pi$
$397$	−14.7295	+	25.5122i	−0.739252	+	1.28042i	−0.952833	+	0.303496i	$0.901846\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−13.2618	+	22.9701i	−0.662261	+	1.14707i	0.317759	+	0.948172i	$0.397070\pi$
$401$	−13.2618	+	22.9701i	−0.662261	+	1.14707i	−0.980020	+	0.198899i	$0.936263\pi$
$402$		0			0
$403$	0.691751	+	1.19815i	0.0344586	+	0.0596840i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	10.9608			0.543305
$408$		0			0
$409$	−15.7618	−	27.3002i	−0.779370	−	1.34991i	−0.932306	−	0.361672i	$-0.882206\pi$
$409$	−15.7618	−	27.3002i	−0.779370	−	1.34991i	0.152936	−	0.988236i	$-0.451127\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	21.8604	+	3.75580i	1.07568	+	0.184811i
$414$		0			0
$415$	−1.96771	+	3.40817i	−0.0965909	+	0.167300i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.802810			−0.0392199			−0.0196099	−	0.999808i	$-0.506242\pi$
$419$	−0.802810			−0.0392199			−0.0196099	+	0.999808i	$0.506242\pi$
$420$		0			0
$421$	37.8425			1.84433			0.922164	−	0.386798i	$-0.126419\pi$
$421$	37.8425			1.84433			0.922164	+	0.386798i	$0.126419\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.415795	−	0.720178i	0.0201690	−	0.0349338i
$426$		0			0
$427$	−4.77596	−	12.9449i	−0.231125	−	0.626448i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	8.59859	+	14.8932i	0.414180	+	0.717380i	0.995342	−	0.0964074i	$-0.0307352\pi$
$431$	8.59859	+	14.8932i	0.414180	+	0.717380i	−0.581162	+	0.813788i	$0.697402\pi$
$432$		0			0
$433$	12.1505			0.583916			0.291958	−	0.956431i	$-0.405693\pi$
$433$	12.1505			0.583916			0.291958	+	0.956431i	$0.405693\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−11.7993	−	20.4370i	−0.564437	−	0.977633i
$438$		0			0
$439$	15.6363	−	27.0829i	0.746281	−	1.29260i	−0.203313	−	0.979114i	$-0.565171\pi$
$439$	15.6363	−	27.0829i	0.746281	−	1.29260i	0.949594	−	0.313483i	$-0.101496\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.43018	−	5.94125i	0.162973	−	0.282278i	−0.772961	−	0.634454i	$-0.781225\pi$
$443$	3.43018	−	5.94125i	0.162973	−	0.282278i	0.935934	+	0.352177i	$0.114558\pi$
$444$		0			0
$445$	−0.360161	−	0.623817i	−0.0170733	−	0.0295718i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	27.1038			1.27911			0.639554	−	0.768746i	$-0.279119\pi$
$449$	27.1038			1.27911			0.639554	+	0.768746i	$0.279119\pi$
$450$		0			0
$451$	−10.5037	−	18.1930i	−0.494601	−	0.856674i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.26700	+	3.43413i	0.0593981	+	0.160995i
$456$		0			0
$457$	−9.90684	+	17.1592i	−0.463423	+	0.802671i	−0.999129	−	0.0417330i	$-0.986712\pi$
$457$	−9.90684	+	17.1592i	−0.463423	+	0.802671i	0.535706	+	0.844404i	$0.320045\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−3.82415			−0.178108			−0.0890541	−	0.996027i	$-0.528384\pi$
$461$	−3.82415			−0.178108			−0.0890541	+	0.996027i	$0.528384\pi$
$462$		0			0
$463$	−8.95332			−0.416096			−0.208048	−	0.978119i	$-0.566711\pi$
$463$	−8.95332			−0.416096			−0.208048	+	0.978119i	$0.566711\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.16841	−	8.95195i	0.239165	−	0.414247i	−0.721310	−	0.692613i	$-0.756459\pi$
$467$	5.16841	−	8.95195i	0.239165	−	0.414247i	0.960475	+	0.278366i	$0.0897928\pi$
$468$		0			0
$469$	3.60755	+	0.619807i	0.166581	+	0.0286200i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.18280	+	3.78072i	0.100365	+	0.173838i
$474$		0			0
$475$	−4.21509			−0.193402
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−20.1972	−	34.9826i	−0.922833	−	1.59839i	−0.795009	−	0.606597i	$-0.792534\pi$
$479$	−20.1972	−	34.9826i	−0.922833	−	1.59839i	−0.127824	−	0.991797i	$-0.540799\pi$
$480$		0			0
$481$	−3.18108	+	5.50980i	−0.145045	+	0.251225i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.22404	+	2.12011i	−0.0555810	+	0.0962691i
$486$		0			0
$487$	6.57002	+	11.3796i	0.297716	+	0.515660i	0.975613	−	0.219497i	$-0.0704418\pi$
$487$	6.57002	+	11.3796i	0.297716	+	0.515660i	−0.677897	+	0.735157i	$0.737108\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	17.1972			0.776098			0.388049	−	0.921639i	$-0.373149\pi$
$491$	17.1972			0.776098			0.388049	+	0.921639i	$0.373149\pi$
$492$		0			0
$493$	4.17736	+	7.23540i	0.188139	+	0.325866i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.11821	+	7.35669i	−0.274439	+	0.329993i
$498$		0			0
$499$	1.33159	−	2.30638i	0.0596102	−	0.103248i	−0.834680	−	0.550735i	$-0.814348\pi$
$499$	1.33159	−	2.30638i	0.0596102	−	0.103248i	0.894290	+	0.447487i	$0.147681\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	−13.1505			−0.585190
$506$		0			0
$507$		0			0
$508$		0			0
$509$	12.0288	−	20.8345i	0.533166	−	0.923471i	−0.466083	−	0.884741i	$-0.654335\pi$
$509$	12.0288	−	20.8345i	0.533166	−	0.923471i	0.999250	−	0.0387303i	$-0.0123313\pi$
$510$		0			0
$511$	−32.8514	−	5.64415i	−1.45326	−	0.249683i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.13089	+	5.42286i	0.137963	+	0.238960i
$516$		0			0
$517$	−29.6274			−1.30301
$518$		0			0
$519$		0			0
$520$		0			0
$521$	8.81369	+	15.2658i	0.386135	+	0.668805i	0.991926	−	0.126819i	$-0.0404767\pi$
$521$	8.81369	+	15.2658i	0.386135	+	0.668805i	−0.605791	+	0.795624i	$0.707143\pi$
$522$		0			0
$523$	8.09316	−	14.0178i	0.353889	−	0.612954i	−0.633038	−	0.774121i	$-0.718192\pi$
$523$	8.09316	−	14.0178i	0.353889	−	0.612954i	0.986927	+	0.161167i	$0.0515257\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.415795	+	0.720178i	−0.0181123	+	0.0313715i
$528$		0			0
$529$	−4.17213	−	7.22634i	−0.181397	−	0.314189i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	12.1938			0.528170
$534$		0			0
$535$	5.79930	+	10.0447i	0.250725	+	0.434269i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−12.6865	+	10.8363i	−0.546447	+	0.466752i
$540$		0			0
$541$	8.77968	−	15.2068i	0.377468	−	0.653793i	−0.613225	−	0.789908i	$-0.710128\pi$
$541$	8.77968	−	15.2068i	0.377468	−	0.653793i	0.990693	+	0.136115i	$0.0434615\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−12.9821			−0.556092
$546$		0			0
$547$	−7.96419			−0.340524			−0.170262	−	0.985399i	$-0.554461\pi$
$547$	−7.96419			−0.340524			−0.170262	+	0.985399i	$0.554461\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	21.1738	−	36.6742i	0.902036	−	1.56237i
$552$		0			0
$553$	10.8781	+	29.4843i	0.462582	+	1.25380i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−13.7670	−	23.8452i	−0.583327	−	1.01035i	−0.995082	−	0.0990569i	$-0.968417\pi$
$557$	−13.7670	−	23.8452i	−0.583327	−	1.01035i	0.411755	−	0.911295i	$-0.364916\pi$
$558$		0			0
$559$	−2.53401			−0.107177
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−11.4873	−	19.8966i	−0.484133	−	0.838543i	0.515701	−	0.856769i	$-0.327532\pi$
$563$	−11.4873	−	19.8966i	−0.484133	−	0.838543i	−0.999834	+	0.0182256i	$0.994198\pi$
$564$		0			0
$565$	8.38350	−	14.5207i	0.352697	−	0.610888i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.62194	−	2.80928i	0.0679951	−	0.117771i	−0.830024	−	0.557728i	$-0.811673\pi$
$569$	1.62194	−	2.80928i	0.0679951	−	0.117771i	0.898019	+	0.439957i	$0.145006\pi$
$570$		0			0
$571$	14.1075	+	24.4350i	0.590382	+	1.02257i	0.994181	+	0.107724i	$0.0343564\pi$
$571$	14.1075	+	24.4350i	0.590382	+	1.02257i	−0.403798	+	0.914848i	$0.632310\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−5.59859			−0.233478
$576$		0			0
$577$	8.73843	+	15.1354i	0.363786	+	0.630095i	0.988581	−	0.150694i	$-0.0481507\pi$
$577$	8.73843	+	15.1354i	0.363786	+	0.630095i	−0.624795	+	0.780789i	$0.714817\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	6.65774	−	8.00543i	0.276210	−	0.332121i
$582$		0			0
$583$	1.98210	−	3.43309i	0.0820901	−	0.142184i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	10.1580			0.419264			0.209632	−	0.977780i	$-0.432773\pi$
$587$	10.1580			0.419264			0.209632	+	0.977780i	$0.432773\pi$
$588$		0			0
$589$	4.21509			0.173680
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−2.69547	+	4.66870i	−0.110690	+	0.191720i	−0.916049	−	0.401067i	$-0.868639\pi$
$593$	−2.69547	+	4.66870i	−0.110690	+	0.191720i	0.805359	+	0.592788i	$0.201973\pi$
$594$		0			0
$595$	−1.40684	+	1.69162i	−0.0576750	+	0.0693498i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	11.4948	+	19.9095i	0.469664	+	0.813481i	0.999398	−	0.0346821i	$-0.0110419\pi$
$599$	11.4948	+	19.9095i	0.469664	+	0.813481i	−0.529735	+	0.848163i	$0.677709\pi$
$600$		0			0
$601$	38.2727			1.56117			0.780587	−	0.625047i	$-0.214920\pi$
$601$	38.2727			1.56117			0.780587	+	0.625047i	$0.214920\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.65946	−	4.60632i	−0.108122	−	0.187273i
$606$		0			0
$607$	−5.86016	+	10.1501i	−0.237857	+	0.411980i	−0.960099	−	0.279660i	$-0.909778\pi$
$607$	−5.86016	+	10.1501i	−0.237857	+	0.411980i	0.722242	+	0.691640i	$0.243111\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	8.59859	−	14.8932i	0.347862	−	0.602515i
$612$		0			0
$613$	−13.9910	−	24.2332i	−0.565093	−	0.978770i	−0.997041	−	0.0768714i	$-0.975507\pi$
$613$	−13.9910	−	24.2332i	−0.565093	−	0.978770i	0.431948	−	0.901899i	$-0.357826\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	31.0680			1.25075			0.625376	−	0.780324i	$-0.284946\pi$
$617$	31.0680			1.25075			0.625376	+	0.780324i	$0.284946\pi$
$618$		0			0
$619$	−3.65051	−	6.32286i	−0.146726	−	0.254137i	0.783289	−	0.621657i	$-0.213540\pi$
$619$	−3.65051	−	6.32286i	−0.146726	−	0.254137i	−0.930016	+	0.367520i	$0.880207\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.659667	+	1.78798i	0.0264290	+	0.0716340i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−3.82415			−0.152479
$630$		0			0
$631$	−22.4877			−0.895223			−0.447611	−	0.894228i	$-0.647725\pi$
$631$	−22.4877			−0.895223			−0.447611	+	0.894228i	$0.647725\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	6.90684	−	11.9630i	0.274090	−	0.474737i
$636$		0			0
$637$	−1.76529	−	9.52227i	−0.0699433	−	0.377286i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−22.0054	−	38.1145i	−0.869163	−	1.50543i	−0.862854	−	0.505454i	$-0.831325\pi$
$641$	−22.0054	−	38.1145i	−0.869163	−	1.50543i	−0.00630878	−	0.999980i	$-0.502008\pi$
$642$		0			0
$643$	−10.1863			−0.401709			−0.200854	−	0.979621i	$-0.564372\pi$
$643$	−10.1863			−0.401709			−0.200854	+	0.979621i	$0.564372\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.2762	+	28.1911i	0.639882	+	1.10831i	0.985458	+	0.169918i	$0.0543501\pi$
$647$	16.2762	+	28.1911i	0.639882	+	1.10831i	−0.345576	+	0.938391i	$0.612317\pi$
$648$		0			0
$649$	−9.99105	+	17.3050i	−0.392183	+	0.679281i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	10.4625	−	18.1215i	0.409428	−	0.709151i	−0.585397	−	0.810747i	$-0.699061\pi$
$653$	10.4625	−	18.1215i	0.409428	−	0.709151i	0.994826	+	0.101596i	$0.0323948\pi$
$654$		0			0
$655$	−0.616498	−	1.06781i	−0.0240886	−	0.0417226i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	37.7207			1.46939			0.734696	−	0.678397i	$-0.237325\pi$
$659$	37.7207			1.46939			0.734696	+	0.678397i	$0.237325\pi$
$660$		0			0
$661$	−4.61278	−	7.98956i	−0.179416	−	0.310758i	0.762265	−	0.647266i	$-0.224088\pi$
$661$	−4.61278	−	7.98956i	−0.179416	−	0.310758i	−0.941681	+	0.336508i	$0.890754\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	10.9910	+	1.88835i	0.426215	+	0.0732273i
$666$		0			0
$667$	28.1237	−	48.7116i	1.08895	−	1.88612i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	12.4302			0.479862
$672$		0			0
$673$	−30.2797			−1.16720			−0.583598	−	0.812043i	$-0.698356\pi$
$673$	−30.2797			−1.16720			−0.583598	+	0.812043i	$0.698356\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	16.8927	−	29.2590i	0.649238	−	1.12451i	−0.334067	−	0.942549i	$-0.608421\pi$
$677$	16.8927	−	29.2590i	0.649238	−	1.12451i	0.983305	−	0.181964i	$-0.0582453\pi$
$678$		0			0
$679$	4.14156	−	4.97991i	0.158938	−	0.191111i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	16.5663	+	28.6937i	0.633892	+	1.09793i	0.986749	+	0.162256i	$0.0518769\pi$
$683$	16.5663	+	28.6937i	0.633892	+	1.09793i	−0.352857	+	0.935677i	$0.614790\pi$
$684$		0			0
$685$	−0.401405			−0.0153369
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.15051	+	1.99274i	0.0438308	+	0.0759172i
$690$		0			0
$691$	−22.4821	+	38.9401i	−0.855259	+	1.48135i	0.0211450	+	0.999776i	$0.493269\pi$
$691$	−22.4821	+	38.9401i	−0.855259	+	1.48135i	−0.876404	+	0.481576i	$0.840064\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.444366	+	0.769664i	−0.0168558	+	0.0291950i
$696$		0			0
$697$	3.66469	+	6.34743i	0.138810	+	0.240426i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	42.5702			1.60786			0.803928	−	0.594727i	$-0.202740\pi$
$701$	42.5702			1.60786			0.803928	+	0.594727i	$0.202740\pi$
$702$		0			0
$703$	9.69175	+	16.7866i	0.365531	+	0.633119i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	34.2906	+	5.89141i	1.28963	+	0.221569i
$708$		0			0
$709$	−5.10232	+	8.83747i	−0.191622	+	0.331898i	−0.945788	−	0.324785i	$-0.894708\pi$
$709$	−5.10232	+	8.83747i	−0.191622	+	0.331898i	0.754166	+	0.656684i	$0.228041\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	5.59859			0.209669
$714$		0			0
$715$	−3.29758			−0.123323
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.04668	+	1.81291i	−0.0390347	+	0.0676100i	−0.884883	−	0.465814i	$-0.845762\pi$
$719$	−1.04668	+	1.81291i	−0.0390347	+	0.0676100i	0.845848	+	0.533424i	$0.179095\pi$
$720$		0			0
$721$	−5.73450	−	15.5430i	−0.213564	−	0.578851i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−5.02334	−	8.70068i	−0.186562	−	0.323135i
$726$		0			0
$727$	34.8211			1.29144			0.645722	−	0.763572i	$-0.276556\pi$
$727$	34.8211			1.29144			0.645722	+	0.763572i	$0.276556\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.761566	−	1.31907i	−0.0281675	−	0.0487876i
$732$		0			0
$733$	23.7384	−	41.1162i	0.876799	−	1.51866i	0.0219652	−	0.999759i	$-0.493008\pi$
$733$	23.7384	−	41.1162i	0.876799	−	1.51866i	0.854834	−	0.518902i	$-0.173659\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.64879	+	2.85579i	−0.0607340	+	0.105194i
$738$		0			0
$739$	20.1363	+	34.8771i	0.740727	+	1.28298i	0.952165	+	0.305585i	$0.0988520\pi$
$739$	20.1363	+	34.8771i	0.740727	+	1.28298i	−0.211438	+	0.977391i	$0.567815\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	27.7853			1.01934			0.509672	−	0.860369i	$-0.329767\pi$
$743$	27.7853			1.01934			0.509672	+	0.860369i	$0.329767\pi$
$744$		0			0
$745$	3.00000	+	5.19615i	0.109911	+	0.190372i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−10.6219	−	28.7900i	−0.388117	−	1.05197i
$750$		0			0
$751$	0.901405	−	1.56128i	0.0328927	−	0.0569719i	−0.849110	−	0.528215i	$-0.822861\pi$
$751$	0.901405	−	1.56128i	0.0328927	−	0.0569719i	0.882003	+	0.471243i	$0.156195\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	16.7491			0.609562
$756$		0			0
$757$	21.8708			0.794909			0.397454	−	0.917622i	$-0.369894\pi$
$757$	21.8708			0.794909			0.397454	+	0.917622i	$0.369894\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−11.0233	+	19.0930i	−0.399596	+	0.692120i	−0.993676	−	0.112286i	$-0.964183\pi$
$761$	−11.0233	+	19.0930i	−0.399596	+	0.692120i	0.594080	+	0.804406i	$0.297516\pi$
$762$		0			0
$763$	33.8514	+	5.81596i	1.22550	+	0.210552i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.79930	−	10.0447i	−0.209400	−	0.362692i
$768$		0			0
$769$	−28.2727			−1.01954			−0.509769	−	0.860311i	$-0.670269\pi$
$769$	−28.2727			−1.01954			−0.509769	+	0.860311i	$0.670269\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−19.9965	−	34.6349i	−0.719224	−	1.24573i	−0.961308	−	0.275477i	$-0.911164\pi$
$773$	−19.9965	−	34.6349i	−0.719224	−	1.24573i	0.242084	−	0.970255i	$-0.422169\pi$
$774$		0			0
$775$	0.500000	−	0.866025i	0.0179605	−	0.0311086i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	18.5753	−	32.1733i	0.665528	−	1.15273i
$780$		0			0
$781$	−4.30997	−	7.46508i	−0.154223	−	0.267122i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.66318			−0.130745
$786$		0			0
$787$	−17.5807	−	30.4507i	−0.626684	−	1.08545i	−0.988213	−	0.153088i	$-0.951078\pi$
$787$	−17.5807	−	30.4507i	−0.626684	−	1.08545i	0.361529	−	0.932361i	$-0.382255\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−28.3656	+	34.1075i	−1.00856	+	1.21272i
$792$		0			0
$793$	−3.60755	+	6.24845i	−0.128108	+	0.221889i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−49.0968			−1.73910			−0.869549	−	0.493847i	$-0.835590\pi$
$797$	−49.0968			−1.73910			−0.869549	+	0.493847i	$0.835590\pi$
$798$		0			0
$799$	10.3368			0.365690
$800$		0			0
$801$		0			0
$802$		0			0
$803$	15.0144	−	26.0057i	0.529846	−	0.917721i
$804$		0			0
$805$	14.5986	+	2.50816i	0.514533	+	0.0884011i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	6.64528	+	11.5100i	0.233636	+	0.404669i	0.958875	−	0.283828i	$-0.0916044\pi$
$809$	6.64528	+	11.5100i	0.233636	+	0.404669i	−0.725240	+	0.688496i	$0.758271\pi$
$810$		0			0
$811$	−44.9358			−1.57791			−0.788955	−	0.614451i	$-0.789378\pi$
$811$	−44.9358			−1.57791			−0.788955	+	0.614451i	$0.789378\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	8.04668	+	13.9373i	0.281863	+	0.488201i
$816$		0			0
$817$	−3.86016	+	6.68599i	−0.135050	+	0.233913i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.22053	−	12.5063i	0.251998	−	0.436474i	−0.712078	−	0.702101i	$-0.752246\pi$
$821$	7.22053	−	12.5063i	0.251998	−	0.436474i	0.964076	+	0.265627i	$0.0855789\pi$
$822$		0			0
$823$	−13.0556	−	22.6130i	−0.455091	−	0.788240i	0.543603	−	0.839343i	$-0.317060\pi$
$823$	−13.0556	−	22.6130i	−0.455091	−	0.788240i	−0.998693	+	0.0511023i	$0.983727\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−32.5236			−1.13095			−0.565477	−	0.824764i	$-0.691308\pi$
$827$	−32.5236			−1.13095			−0.565477	+	0.824764i	$0.691308\pi$
$828$		0			0
$829$	19.5198	+	33.8093i	0.677952	+	1.17425i	0.975597	+	0.219570i	$0.0704655\pi$
$829$	19.5198	+	33.8093i	0.677952	+	1.17425i	−0.297645	+	0.954677i	$0.596201\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	4.42625	−	3.78072i	0.153361	−	0.130994i
$834$		0			0
$835$	−5.79930	+	10.0447i	−0.200693	+	0.347610i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	35.7099			1.23284			0.616421	−	0.787417i	$-0.288582\pi$
$839$	35.7099			1.23284			0.616421	+	0.787417i	$0.288582\pi$
$840$		0			0
$841$	71.9358			2.48055
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−5.54296	+	9.60069i	−0.190684	+	0.330274i
$846$		0			0
$847$	4.87104	+	13.2026i	0.167371	+	0.453647i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	12.8728	+	22.2964i	0.441275	+	0.764311i
$852$		0			0
$853$	−44.0968			−1.50985			−0.754923	−	0.655814i	$-0.772326\pi$
$853$	−44.0968			−1.50985			−0.754923	+	0.655814i	$0.772326\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	2.15402	+	3.73087i	0.0735799	+	0.127444i	0.900468	−	0.434923i	$-0.143224\pi$
$857$	2.15402	+	3.73087i	0.0735799	+	0.127444i	−0.826888	+	0.562367i	$0.809891\pi$
$858$		0			0
$859$	−11.6363	+	20.1547i	−0.397026	+	0.687670i	−0.993358	−	0.115069i	$-0.963291\pi$
$859$	−11.6363	+	20.1547i	−0.397026	+	0.687670i	0.596331	+	0.802738i	$0.296625\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−27.4590	+	47.5603i	−0.934714	+	1.61897i	−0.159571	+	0.987186i	$0.551011\pi$
$863$	−27.4590	+	47.5603i	−0.934714	+	1.61897i	−0.775143	+	0.631786i	$0.782322\pi$
$864$		0			0
$865$	−6.21509	−	10.7649i	−0.211319	−	0.366016i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−28.3119			−0.960415
$870$		0			0
$871$	−0.957039	−	1.65764i	−0.0324280	−	0.0561670i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.69175	−	2.03420i	0.0571916	−	0.0687686i
$876$		0			0
$877$	3.04668	−	5.27701i	0.102879	−	0.178192i	−0.809991	−	0.586443i	$-0.800528\pi$
$877$	3.04668	−	5.27701i	0.102879	−	0.178192i	0.912870	+	0.408251i	$0.133861\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−21.3264			−0.718503			−0.359252	−	0.933241i	$-0.616968\pi$
$881$	−21.3264			−0.718503			−0.359252	+	0.933241i	$0.616968\pi$
$882$		0			0
$883$	−24.3761			−0.820320			−0.410160	−	0.912014i	$-0.634527\pi$
$883$	−24.3761			−0.820320			−0.410160	+	0.912014i	$0.634527\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	22.1649	−	38.3907i	0.744224	−	1.28903i	−0.206332	−	0.978482i	$-0.566153\pi$
$887$	22.1649	−	38.3907i	0.744224	−	1.28903i	0.950556	−	0.310552i	$-0.100514\pi$
$888$		0			0
$889$	−23.3693	+	28.0998i	−0.783782	+	0.942438i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−26.1972	−	45.3749i	−0.876656	−	1.51841i
$894$		0			0
$895$	3.10382			0.103749
$896$		0			0
$897$		0			0
$898$		0			0
$899$	5.02334	+	8.70068i	0.167538	+	0.290184i
$900$		0			0
$901$	−0.691542	+	1.19779i	−0.0230386	+	0.0399040i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.49105	+	2.58257i	−0.0495641	+	0.0858476i
$906$		0			0
$907$	−5.29930	−	9.17865i	−0.175960	−	0.304772i	0.764533	−	0.644585i	$-0.222970\pi$
$907$	−5.29930	−	9.17865i	−0.175960	−	0.304772i	−0.940493	+	0.339813i	$0.889636\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−24.1400			−0.799795			−0.399898	−	0.916560i	$-0.630954\pi$
$911$	−24.1400			−0.799795			−0.399898	+	0.916560i	$0.630954\pi$
$912$		0			0
$913$	4.69003	+	8.12338i	0.155217	+	0.268845i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.12917	+	3.06054i	0.0372885	+	0.101068i
$918$		0			0
$919$	−4.99477	+	8.65120i	−0.164762	+	0.285377i	−0.936571	−	0.350478i	$-0.886019\pi$
$919$	−4.99477	+	8.65120i	−0.164762	+	0.285377i	0.771809	+	0.635855i	$0.219352\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	5.00343			0.164690
$924$		0			0
$925$	4.59859			0.151201
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−22.8370	+	39.5549i	−0.749259	+	1.29775i	0.198920	+	0.980016i	$0.436257\pi$
$929$	−22.8370	+	39.5549i	−0.749259	+	1.29775i	−0.948178	+	0.317738i	$0.897077\pi$
$930$		0			0
$931$	−27.8137	−	9.84795i	−0.911557	−	0.322753i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.991049	−	1.71655i	−0.0324108	−	0.0561371i
$936$		0			0
$937$	−15.4948			−0.506192			−0.253096	−	0.967441i	$-0.581449\pi$
$937$	−15.4948			−0.506192			−0.253096	+	0.967441i	$0.581449\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−9.90161	−	17.1501i	−0.322783	−	0.559077i	0.658278	−	0.752775i	$-0.271285\pi$
$941$	−9.90161	−	17.1501i	−0.322783	−	0.559077i	−0.981061	+	0.193698i	$0.937952\pi$
$942$		0			0
$943$	24.6721	−	42.7334i	0.803435	−	1.39159i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−5.07898	+	8.79704i	−0.165045	+	0.285866i	−0.936671	−	0.350210i	$-0.886110\pi$
$947$	−5.07898	+	8.79704i	−0.165045	+	0.285866i	0.771627	+	0.636076i	$0.219443\pi$
$948$		0			0
$949$	8.71509	+	15.0950i	0.282904	+	0.490004i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−8.09337			−0.262170			−0.131085	−	0.991371i	$-0.541846\pi$
$953$	−8.09337			−0.262170			−0.131085	+	0.991371i	$0.541846\pi$
$954$		0			0
$955$	7.55191	+	13.0803i	0.244374	+	0.423268i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.04668	+	0.179829i	0.0337991	+	0.00580698i
$960$		0			0
$961$	15.0000	−	25.9808i	0.483871	−	0.838089i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	17.7958			0.572867
$966$		0			0
$967$	29.2513			0.940659			0.470329	−	0.882491i	$-0.344135\pi$
$967$	29.2513			0.940659			0.470329	+	0.882491i	$0.344135\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−8.19719	+	14.1979i	−0.263060	+	0.455634i	−0.967054	−	0.254573i	$-0.918065\pi$
$971$	−8.19719	+	14.1979i	−0.263060	+	0.455634i	0.703993	+	0.710207i	$0.251398\pi$
$972$		0			0
$973$	1.50351	−	1.80786i	0.0482004	−	0.0579573i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	15.5484	+	26.9306i	0.497437	+	0.861587i	0.999996	−	0.00295656i	$-0.000941104\pi$
$977$	15.5484	+	26.9306i	0.497437	+	0.861587i	−0.502558	+	0.864543i	$0.667608\pi$
$978$		0			0
$979$	−1.71689			−0.0548720
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−2.18280	−	3.78072i	−0.0696205	−	0.120586i	0.829114	−	0.559080i	$-0.188846\pi$
$983$	−2.18280	−	3.78072i	−0.0696205	−	0.120586i	−0.898734	+	0.438494i	$0.855512\pi$
$984$		0			0
$985$	8.58420	−	14.8683i	0.273516	−	0.473743i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−5.12717	+	8.88051i	−0.163034	+	0.282384i
$990$		0			0
$991$	−13.6490	−	23.6408i	−0.433575	−	0.750974i	0.563603	−	0.826046i	$-0.309415\pi$
$991$	−13.6490	−	23.6408i	−0.433575	−	0.750974i	−0.997178	+	0.0750720i	$0.976081\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−20.7491			−0.657791
$996$		0			0
$997$	−15.2422	−	26.4002i	−0.482724	−	0.836102i	0.517079	−	0.855937i	$-0.327019\pi$
$997$	−15.2422	−	26.4002i	−0.482724	−	0.836102i	−0.999803	+	0.0198351i	$0.993686\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.s.h.541.1	yes	6
3.2	odd	2		1260.2.s.g.541.1	yes	6
7.2	even	3		8820.2.a.bn.1.3		3
7.4	even	3	inner	1260.2.s.h.361.1	yes	6
7.5	odd	6		8820.2.a.bp.1.3		3
21.2	odd	6		8820.2.a.bq.1.1		3
21.5	even	6		8820.2.a.bo.1.1		3
21.11	odd	6		1260.2.s.g.361.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.s.g.361.1	✓	6	21.11	odd	6
1260.2.s.g.541.1	yes	6	3.2	odd	2
1260.2.s.h.361.1	yes	6	7.4	even	3	inner
1260.2.s.h.541.1	yes	6	1.1	even	1	trivial
8820.2.a.bn.1.3		3	7.2	even	3
8820.2.a.bo.1.1		3	21.5	even	6
8820.2.a.bp.1.3		3	7.5	odd	6
8820.2.a.bq.1.1		3	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{5} +(-1.69175 + 2.03420i) q^{7} +(-1.19175 - 2.06417i) q^{11} +1.38350 q^{13} +(0.415795 + 0.720178i) q^{17} +(2.10755 - 3.65038i) q^{19} +(2.79930 - 4.84853i) q^{23} +(-0.500000 - 0.866025i) q^{25} +10.0467 q^{29} +(0.500000 + 0.866025i) q^{31} +(0.915795 + 2.48220i) q^{35} +(-2.29930 + 3.98250i) q^{37} +8.81369 q^{41} -1.83159 q^{43} +(6.21509 - 10.7649i) q^{47} +(-1.27596 - 6.88273i) q^{49} +(0.831590 + 1.44036i) q^{53} -2.38350 q^{55} +(-4.19175 - 7.26033i) q^{59} +(-2.60755 + 4.51640i) q^{61} +(0.691751 - 1.19815i) q^{65} +(-0.691751 - 1.19815i) q^{67} +3.61650 q^{71} +(6.29930 + 10.9107i) q^{73} +(6.21509 + 1.06781i) q^{77} +(5.93914 - 10.2869i) q^{79} -3.93541 q^{83} +0.831590 q^{85} +(0.360161 - 0.623817i) q^{89} +(-2.34054 + 2.81432i) q^{91} +(-2.10755 - 3.65038i) q^{95} -2.44809 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} - q^{7} + 2 q^{11} - 10 q^{13} - 2 q^{17} - q^{19} - 6 q^{23} - 3 q^{25} + 24 q^{29} + 3 q^{31} + q^{35} + 9 q^{37} - 20 q^{41} - 2 q^{43} + 10 q^{47} - 3 q^{49} - 4 q^{53} + 4 q^{55} - 16 q^{59}+ \cdots - 24 q^{97}+O(q^{100}) \) 6 * q + 3 * q^5 - q^7 + 2 * q^11 - 10 * q^13 - 2 * q^17 - q^19 - 6 * q^23 - 3 * q^25 + 24 * q^29 + 3 * q^31 + q^35 + 9 * q^37 - 20 * q^41 - 2 * q^43 + 10 * q^47 - 3 * q^49 - 4 * q^53 + 4 * q^55 - 16 * q^59 - 2 * q^61 - 5 * q^65 + 5 * q^67 + 40 * q^71 + 15 * q^73 + 10 * q^77 + 13 * q^79 + 4 * q^83 - 4 * q^85 + 2 * q^89 - 37 * q^91 + q^95 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more