LMFDB - Embedded newform 3850.2.c.r.1849.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3850,2,Mod(1849,3850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3850, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3850.1849");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3850.c (of order $2$, degree $1$, 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:	$30.7424047782$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1849.3
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	3850.1849
Dual form			3850.2.c.r.1849.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -0.732051i q^{3} -1.00000 q^{4} +0.732051 q^{6} -1.00000i q^{7} -1.00000i q^{8} +2.46410 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -0.732051i q^{3} -1.00000 q^{4} +0.732051 q^{6} -1.00000i q^{7} -1.00000i q^{8} +2.46410 q^{9} +1.00000 q^{11} +0.732051i q^{12} +0.267949i q^{13} +1.00000 q^{14} +1.00000 q^{16} -4.73205i q^{17} +2.46410i q^{18} +4.46410 q^{19} -0.732051 q^{21} +1.00000i q^{22} +1.73205i q^{23} -0.732051 q^{24} -0.267949 q^{26} -4.00000i q^{27} +1.00000i q^{28} +0.464102 q^{29} +2.46410 q^{31} +1.00000i q^{32} -0.732051i q^{33} +4.73205 q^{34} -2.46410 q^{36} +1.46410i q^{37} +4.46410i q^{38} +0.196152 q^{39} -9.46410 q^{41} -0.732051i q^{42} -2.26795i q^{43} -1.00000 q^{44} -1.73205 q^{46} -6.00000i q^{47} -0.732051i q^{48} -1.00000 q^{49} -3.46410 q^{51} -0.267949i q^{52} +4.73205i q^{53} +4.00000 q^{54} -1.00000 q^{56} -3.26795i q^{57} +0.464102i q^{58} +6.92820 q^{59} +6.39230 q^{61} +2.46410i q^{62} -2.46410i q^{63} -1.00000 q^{64} +0.732051 q^{66} -6.73205i q^{67} +4.73205i q^{68} +1.26795 q^{69} -8.66025 q^{71} -2.46410i q^{72} +2.92820i q^{73} -1.46410 q^{74} -4.46410 q^{76} -1.00000i q^{77} +0.196152i q^{78} -7.66025 q^{79} +4.46410 q^{81} -9.46410i q^{82} +3.00000i q^{83} +0.732051 q^{84} +2.26795 q^{86} -0.339746i q^{87} -1.00000i q^{88} +1.73205 q^{89} +0.267949 q^{91} -1.73205i q^{92} -1.80385i q^{93} +6.00000 q^{94} +0.732051 q^{96} -7.19615i q^{97} -1.00000i q^{98} +2.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + 4 q^{11} + 4 q^{14} + 4 q^{16} + 4 q^{19} + 4 q^{21} + 4 q^{24} - 8 q^{26} - 12 q^{29} - 4 q^{31} + 12 q^{34} + 4 q^{36} - 20 q^{39} - 24 q^{41} - 4 q^{44} - 4 q^{49} + 16 q^{54} - 4 q^{56} - 16 q^{61} - 4 q^{64} - 4 q^{66} + 12 q^{69} + 8 q^{74} - 4 q^{76} + 4 q^{79} + 4 q^{81} - 4 q^{84} + 16 q^{86} + 8 q^{91} + 24 q^{94} - 4 q^{96} - 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 + 4 * q^11 + 4 * q^14 + 4 * q^16 + 4 * q^19 + 4 * q^21 + 4 * q^24 - 8 * q^26 - 12 * q^29 - 4 * q^31 + 12 * q^34 + 4 * q^36 - 20 * q^39 - 24 * q^41 - 4 * q^44 - 4 * q^49 + 16 * q^54 - 4 * q^56 - 16 * q^61 - 4 * q^64 - 4 * q^66 + 12 * q^69 + 8 * q^74 - 4 * q^76 + 4 * q^79 + 4 * q^81 - 4 * q^84 + 16 * q^86 + 8 * q^91 + 24 * q^94 - 4 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3850\mathbb{Z}\right)^\times$.

$n$	$1751$	$2201$	$2927$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	− 0.732051i	− 0.422650i	−0.977416	−	0.211325i	$-0.932222\pi$
$3$	− 0.732051i	− 0.422650i	0.977416	−	0.211325i	$-0.0677778\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	0.732051	0.298858
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	− 1.00000i	− 0.353553i
$9$	2.46410	0.821367
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.732051i	0.211325i
$13$	0.267949i	0.0743157i	0.999309	+	0.0371579i	$0.0118304\pi$
$13$	0.267949i	0.0743157i	−0.999309	+	0.0371579i	$0.988170\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	− 4.73205i	− 1.14769i	−0.818964	−	0.573845i	$-0.805451\pi$
$17$	− 4.73205i	− 1.14769i	0.818964	−	0.573845i	$-0.194549\pi$
$18$	2.46410i	0.580794i
$19$	4.46410	1.02414	0.512068	−	0.858945i	$-0.328880\pi$
$19$	4.46410	1.02414	0.512068	+	0.858945i	$0.328880\pi$
$20$	0	0
$21$	−0.732051	−0.159747
$22$	1.00000i	0.213201i
$23$	1.73205i	0.361158i	0.983561	+	0.180579i	$0.0577971\pi$
$23$	1.73205i	0.361158i	−0.983561	+	0.180579i	$0.942203\pi$
$24$	−0.732051	−0.149429
$25$	0	0
$26$	−0.267949	−0.0525492
$27$	− 4.00000i	− 0.769800i
$28$	1.00000i	0.188982i
$29$	0.464102	0.0861815	0.0430908	−	0.999071i	$-0.486280\pi$
$29$	0.464102	0.0861815	0.0430908	+	0.999071i	$0.486280\pi$
$30$	0	0
$31$	2.46410	0.442566	0.221283	−	0.975210i	$-0.428976\pi$
$31$	2.46410	0.442566	0.221283	+	0.975210i	$0.428976\pi$
$32$	1.00000i	0.176777i
$33$	− 0.732051i	− 0.127434i
$34$	4.73205	0.811540
$35$	0	0
$36$	−2.46410	−0.410684
$37$	1.46410i	0.240697i	0.992732	+	0.120348i	$0.0384012\pi$
$37$	1.46410i	0.240697i	−0.992732	+	0.120348i	$0.961599\pi$
$38$	4.46410i	0.724173i
$39$	0.196152	0.0314095
$40$	0	0
$41$	−9.46410	−1.47804	−0.739022	−	0.673681i	$-0.764712\pi$
$41$	−9.46410	−1.47804	−0.739022	+	0.673681i	$0.764712\pi$
$42$	− 0.732051i	− 0.112958i
$43$	− 2.26795i	− 0.345859i	−0.984934	−	0.172930i	$-0.944677\pi$
$43$	− 2.26795i	− 0.345859i	0.984934	−	0.172930i	$-0.0553233\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−1.73205	−0.255377
$47$	− 6.00000i	− 0.875190i	−0.899172	−	0.437595i	$-0.855830\pi$
$47$	− 6.00000i	− 0.875190i	0.899172	−	0.437595i	$-0.144170\pi$
$48$	− 0.732051i	− 0.105662i
$49$	−1.00000	−0.142857
$50$	0	0
$51$	−3.46410	−0.485071
$52$	− 0.267949i	− 0.0371579i
$53$	4.73205i	0.649997i	0.945715	+	0.324999i	$0.105364\pi$
$53$	4.73205i	0.649997i	−0.945715	+	0.324999i	$0.894636\pi$
$54$	4.00000	0.544331
$55$	0	0
$56$	−1.00000	−0.133631
$57$	− 3.26795i	− 0.432850i
$58$	0.464102i	0.0609395i
$59$	6.92820	0.901975	0.450988	−	0.892530i	$-0.351072\pi$
$59$	6.92820	0.901975	0.450988	+	0.892530i	$0.351072\pi$
$60$	0	0
$61$	6.39230	0.818451	0.409225	−	0.912433i	$-0.365799\pi$
$61$	6.39230	0.818451	0.409225	+	0.912433i	$0.365799\pi$
$62$	2.46410i	0.312941i
$63$	− 2.46410i	− 0.310448i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	0.732051	0.0901092
$67$	− 6.73205i	− 0.822451i	−0.911534	−	0.411225i	$-0.865101\pi$
$67$	− 6.73205i	− 0.822451i	0.911534	−	0.411225i	$-0.134899\pi$
$68$	4.73205i	0.573845i
$69$	1.26795	0.152643
$70$	0	0
$71$	−8.66025	−1.02778	−0.513892	−	0.857855i	$-0.671797\pi$
$71$	−8.66025	−1.02778	−0.513892	+	0.857855i	$0.671797\pi$
$72$	− 2.46410i	− 0.290397i
$73$	2.92820i	0.342720i	0.985208	+	0.171360i	$0.0548162\pi$
$73$	2.92820i	0.342720i	−0.985208	+	0.171360i	$0.945184\pi$
$74$	−1.46410	−0.170198
$75$	0	0
$76$	−4.46410	−0.512068
$77$	− 1.00000i	− 0.113961i
$78$	0.196152i	0.0222099i
$79$	−7.66025	−0.861846	−0.430923	−	0.902389i	$-0.641812\pi$
$79$	−7.66025	−0.861846	−0.430923	+	0.902389i	$0.641812\pi$
$80$	0	0
$81$	4.46410	0.496011
$82$	− 9.46410i	− 1.04514i
$83$	3.00000i	0.329293i	0.986353	+	0.164646i	$0.0526483\pi$
$83$	3.00000i	0.329293i	−0.986353	+	0.164646i	$0.947352\pi$
$84$	0.732051	0.0798733
$85$	0	0
$86$	2.26795	0.244559
$87$	− 0.339746i	− 0.0364246i
$88$	− 1.00000i	− 0.106600i
$89$	1.73205	0.183597	0.0917985	−	0.995778i	$-0.470738\pi$
$89$	1.73205	0.183597	0.0917985	+	0.995778i	$0.470738\pi$
$90$	0	0
$91$	0.267949	0.0280887
$92$	− 1.73205i	− 0.180579i
$93$	− 1.80385i	− 0.187050i
$94$	6.00000	0.618853
$95$	0	0
$96$	0.732051	0.0747146
$97$	− 7.19615i	− 0.730659i	−0.930878	−	0.365329i	$-0.880956\pi$
$97$	− 7.19615i	− 0.730659i	0.930878	−	0.365329i	$-0.119044\pi$
$98$	− 1.00000i	− 0.101015i
$99$	2.46410	0.247652
$100$	0	0
$101$	11.1962	1.11406	0.557029	−	0.830493i	$-0.311941\pi$
$101$	11.1962	1.11406	0.557029	+	0.830493i	$0.311941\pi$
$102$	− 3.46410i	− 0.342997i
$103$	− 7.92820i	− 0.781189i	−0.920563	−	0.390595i	$-0.872269\pi$
$103$	− 7.92820i	− 0.781189i	0.920563	−	0.390595i	$-0.127731\pi$
$104$	0.267949	0.0262746
$105$	0	0
$106$	−4.73205	−0.459617
$107$	− 4.26795i	− 0.412598i	−0.978489	−	0.206299i	$-0.933858\pi$
$107$	− 4.26795i	− 0.412598i	0.978489	−	0.206299i	$-0.0661420\pi$
$108$	4.00000i	0.384900i
$109$	7.00000	0.670478	0.335239	−	0.942133i	$-0.391183\pi$
$109$	7.00000	0.670478	0.335239	+	0.942133i	$0.391183\pi$
$110$	0	0
$111$	1.07180	0.101730
$112$	− 1.00000i	− 0.0944911i
$113$	− 6.92820i	− 0.651751i	−0.945413	−	0.325875i	$-0.894341\pi$
$113$	− 6.92820i	− 0.651751i	0.945413	−	0.325875i	$-0.105659\pi$
$114$	3.26795	0.306071
$115$	0	0
$116$	−0.464102	−0.0430908
$117$	0.660254i	0.0610405i
$118$	6.92820i	0.637793i
$119$	−4.73205	−0.433786
$120$	0	0
$121$	1.00000	0.0909091
$122$	6.39230i	0.578732i
$123$	6.92820i	0.624695i
$124$	−2.46410	−0.221283
$125$	0	0
$126$	2.46410	0.219520
$127$	1.46410i	0.129918i	0.997888	+	0.0649590i	$0.0206917\pi$
$127$	1.46410i	0.129918i	−0.997888	+	0.0649590i	$0.979308\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−1.66025	−0.146177
$130$	0	0
$131$	6.46410	0.564771	0.282386	−	0.959301i	$-0.408874\pi$
$131$	6.46410	0.564771	0.282386	+	0.959301i	$0.408874\pi$
$132$	0.732051i	0.0637168i
$133$	− 4.46410i	− 0.387087i
$134$	6.73205	0.581561
$135$	0	0
$136$	−4.73205	−0.405770
$137$	− 5.53590i	− 0.472964i	−0.971636	−	0.236482i	$-0.924006\pi$
$137$	− 5.53590i	− 0.472964i	0.971636	−	0.236482i	$-0.0759944\pi$
$138$	1.26795i	0.107935i
$139$	1.00000	0.0848189	0.0424094	−	0.999100i	$-0.486497\pi$
$139$	1.00000	0.0848189	0.0424094	+	0.999100i	$0.486497\pi$
$140$	0	0
$141$	−4.39230	−0.369899
$142$	− 8.66025i	− 0.726752i
$143$	0.267949i	0.0224070i
$144$	2.46410	0.205342
$145$	0	0
$146$	−2.92820	−0.242340
$147$	0.732051i	0.0603785i
$148$	− 1.46410i	− 0.120348i
$149$	−13.8564	−1.13516	−0.567581	−	0.823318i	$-0.692120\pi$
$149$	−13.8564	−1.13516	−0.567581	+	0.823318i	$0.692120\pi$
$150$	0	0
$151$	−1.80385	−0.146795	−0.0733975	−	0.997303i	$-0.523384\pi$
$151$	−1.80385	−0.146795	−0.0733975	+	0.997303i	$0.523384\pi$
$152$	− 4.46410i	− 0.362086i
$153$	− 11.6603i	− 0.942676i
$154$	1.00000	0.0805823
$155$	0	0
$156$	−0.196152	−0.0157048
$157$	− 11.8038i	− 0.942050i	−0.882120	−	0.471025i	$-0.843884\pi$
$157$	− 11.8038i	− 0.942050i	0.882120	−	0.471025i	$-0.156116\pi$
$158$	− 7.66025i	− 0.609417i
$159$	3.46410	0.274721
$160$	0	0
$161$	1.73205	0.136505
$162$	4.46410i	0.350733i
$163$	12.3923i	0.970640i	0.874337	+	0.485320i	$0.161297\pi$
$163$	12.3923i	0.970640i	−0.874337	+	0.485320i	$0.838703\pi$
$164$	9.46410	0.739022
$165$	0	0
$166$	−3.00000	−0.232845
$167$	− 5.66025i	− 0.438004i	−0.975724	−	0.219002i	$-0.929720\pi$
$167$	− 5.66025i	− 0.438004i	0.975724	−	0.219002i	$-0.0702801\pi$
$168$	0.732051i	0.0564789i
$169$	12.9282	0.994477
$170$	0	0
$171$	11.0000	0.841191
$172$	2.26795i	0.172930i
$173$	− 6.12436i	− 0.465626i	−0.972522	−	0.232813i	$-0.925207\pi$
$173$	− 6.12436i	− 0.465626i	0.972522	−	0.232813i	$-0.0747930\pi$
$174$	0.339746	0.0257561
$175$	0	0
$176$	1.00000	0.0753778
$177$	− 5.07180i	− 0.381220i
$178$	1.73205i	0.129823i
$179$	9.12436	0.681986	0.340993	−	0.940066i	$-0.389237\pi$
$179$	9.12436	0.681986	0.340993	+	0.940066i	$0.389237\pi$
$180$	0	0
$181$	−6.53590	−0.485810	−0.242905	−	0.970050i	$-0.578100\pi$
$181$	−6.53590	−0.485810	−0.242905	+	0.970050i	$0.578100\pi$
$182$	0.267949i	0.0198617i
$183$	− 4.67949i	− 0.345918i
$184$	1.73205	0.127688
$185$	0	0
$186$	1.80385	0.132265
$187$	− 4.73205i	− 0.346042i
$188$	6.00000i	0.437595i
$189$	−4.00000	−0.290957
$190$	0	0
$191$	25.0526	1.81274	0.906370	−	0.422485i	$-0.138842\pi$
$191$	25.0526	1.81274	0.906370	+	0.422485i	$0.138842\pi$
$192$	0.732051i	0.0528312i
$193$	− 15.3205i	− 1.10279i	−0.834243	−	0.551397i	$-0.814095\pi$
$193$	− 15.3205i	− 1.10279i	0.834243	−	0.551397i	$-0.185905\pi$
$194$	7.19615	0.516654
$195$	0	0
$196$	1.00000	0.0714286
$197$	− 25.3923i	− 1.80913i	−0.426339	−	0.904563i	$-0.640197\pi$
$197$	− 25.3923i	− 1.80913i	0.426339	−	0.904563i	$-0.359803\pi$
$198$	2.46410i	0.175116i
$199$	15.7846	1.11894	0.559471	−	0.828850i	$-0.311004\pi$
$199$	15.7846	1.11894	0.559471	+	0.828850i	$0.311004\pi$
$200$	0	0
$201$	−4.92820	−0.347609
$202$	11.1962i	0.787759i
$203$	− 0.464102i	− 0.0325735i
$204$	3.46410	0.242536
$205$	0	0
$206$	7.92820	0.552384
$207$	4.26795i	0.296643i
$208$	0.267949i	0.0185789i
$209$	4.46410	0.308788
$210$	0	0
$211$	8.00000	0.550743	0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000	0.550743	0.275371	+	0.961338i	$0.411199\pi$
$212$	− 4.73205i	− 0.324999i
$213$	6.33975i	0.434392i
$214$	4.26795	0.291751
$215$	0	0
$216$	−4.00000	−0.272166
$217$	− 2.46410i	− 0.167274i
$218$	7.00000i	0.474100i
$219$	2.14359	0.144851
$220$	0	0
$221$	1.26795	0.0852915
$222$	1.07180i	0.0719343i
$223$	14.0000i	0.937509i	0.883328	+	0.468755i	$0.155297\pi$
$223$	14.0000i	0.937509i	−0.883328	+	0.468755i	$0.844703\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	6.92820	0.460857
$227$	− 15.9282i	− 1.05719i	−0.848874	−	0.528596i	$-0.822719\pi$
$227$	− 15.9282i	− 1.05719i	0.848874	−	0.528596i	$-0.177281\pi$
$228$	3.26795i	0.216425i
$229$	−3.85641	−0.254839	−0.127419	−	0.991849i	$-0.540669\pi$
$229$	−3.85641	−0.254839	−0.127419	+	0.991849i	$0.540669\pi$
$230$	0	0
$231$	−0.732051	−0.0481654
$232$	− 0.464102i	− 0.0304698i
$233$	− 7.26795i	− 0.476139i	−0.971248	−	0.238070i	$-0.923485\pi$
$233$	− 7.26795i	− 0.476139i	0.971248	−	0.238070i	$-0.0765146\pi$
$234$	−0.660254	−0.0431622
$235$	0	0
$236$	−6.92820	−0.450988
$237$	5.60770i	0.364259i
$238$	− 4.73205i	− 0.306733i
$239$	−22.3923	−1.44844	−0.724219	−	0.689570i	$-0.757799\pi$
$239$	−22.3923	−1.44844	−0.724219	+	0.689570i	$0.757799\pi$
$240$	0	0
$241$	2.00000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	1.00000i	0.0642824i
$243$	− 15.2679i	− 0.979439i
$244$	−6.39230	−0.409225
$245$	0	0
$246$	−6.92820	−0.441726
$247$	1.19615i	0.0761094i
$248$	− 2.46410i	− 0.156471i
$249$	2.19615	0.139176
$250$	0	0
$251$	12.5885	0.794576	0.397288	−	0.917694i	$-0.369951\pi$
$251$	12.5885	0.794576	0.397288	+	0.917694i	$0.369951\pi$
$252$	2.46410i	0.155224i
$253$	1.73205i	0.108893i
$254$	−1.46410	−0.0918659
$255$	0	0
$256$	1.00000	0.0625000
$257$	3.58846i	0.223842i	0.993717	+	0.111921i	$0.0357003\pi$
$257$	3.58846i	0.223842i	−0.993717	+	0.111921i	$0.964300\pi$
$258$	− 1.66025i	− 0.103363i
$259$	1.46410	0.0909748
$260$	0	0
$261$	1.14359	0.0707867
$262$	6.46410i	0.399354i
$263$	19.2679i	1.18811i	0.804423	+	0.594056i	$0.202474\pi$
$263$	19.2679i	1.18811i	−0.804423	+	0.594056i	$0.797526\pi$
$264$	−0.732051	−0.0450546
$265$	0	0
$266$	4.46410	0.273712
$267$	− 1.26795i	− 0.0775972i
$268$	6.73205i	0.411225i
$269$	−12.5885	−0.767532	−0.383766	−	0.923430i	$-0.625373\pi$
$269$	−12.5885	−0.767532	−0.383766	+	0.923430i	$0.625373\pi$
$270$	0	0
$271$	2.58846	0.157238	0.0786188	−	0.996905i	$-0.474949\pi$
$271$	2.58846	0.157238	0.0786188	+	0.996905i	$0.474949\pi$
$272$	− 4.73205i	− 0.286923i
$273$	− 0.196152i	− 0.0118717i
$274$	5.53590	0.334436
$275$	0	0
$276$	−1.26795	−0.0763216
$277$	25.4641i	1.52999i	0.644036	+	0.764995i	$0.277258\pi$
$277$	25.4641i	1.52999i	−0.644036	+	0.764995i	$0.722742\pi$
$278$	1.00000i	0.0599760i
$279$	6.07180	0.363509
$280$	0	0
$281$	12.5885	0.750964	0.375482	−	0.926830i	$-0.377477\pi$
$281$	12.5885	0.750964	0.375482	+	0.926830i	$0.377477\pi$
$282$	− 4.39230i	− 0.261558i
$283$	0.143594i	0.00853575i	0.999991	+	0.00426787i	$0.00135851\pi$
$283$	0.143594i	0.00853575i	−0.999991	+	0.00426787i	$0.998641\pi$
$284$	8.66025	0.513892
$285$	0	0
$286$	−0.267949	−0.0158442
$287$	9.46410i	0.558648i
$288$	2.46410i	0.145199i
$289$	−5.39230	−0.317194
$290$	0	0
$291$	−5.26795	−0.308813
$292$	− 2.92820i	− 0.171360i
$293$	5.32051i	0.310827i	0.987849	+	0.155414i	$0.0496711\pi$
$293$	5.32051i	0.310827i	−0.987849	+	0.155414i	$0.950329\pi$
$294$	−0.732051	−0.0426941
$295$	0	0
$296$	1.46410	0.0850992
$297$	− 4.00000i	− 0.232104i
$298$	− 13.8564i	− 0.802680i
$299$	−0.464102	−0.0268397
$300$	0	0
$301$	−2.26795	−0.130722
$302$	− 1.80385i	− 0.103800i
$303$	− 8.19615i	− 0.470857i
$304$	4.46410	0.256034
$305$	0	0
$306$	11.6603	0.666572
$307$	2.14359i	0.122341i	0.998127	+	0.0611707i	$0.0194834\pi$
$307$	2.14359i	0.122341i	−0.998127	+	0.0611707i	$0.980517\pi$
$308$	1.00000i	0.0569803i
$309$	−5.80385	−0.330169
$310$	0	0
$311$	32.3205	1.83273	0.916364	−	0.400346i	$-0.131110\pi$
$311$	32.3205	1.83273	0.916364	+	0.400346i	$0.131110\pi$
$312$	− 0.196152i	− 0.0111049i
$313$	− 17.8564i	− 1.00930i	−0.863323	−	0.504652i	$-0.831621\pi$
$313$	− 17.8564i	− 1.00930i	0.863323	−	0.504652i	$-0.168379\pi$
$314$	11.8038	0.666130
$315$	0	0
$316$	7.66025	0.430923
$317$	− 34.0526i	− 1.91258i	−0.292416	−	0.956291i	$-0.594459\pi$
$317$	− 34.0526i	− 1.91258i	0.292416	−	0.956291i	$-0.405541\pi$
$318$	3.46410i	0.194257i
$319$	0.464102	0.0259847
$320$	0	0
$321$	−3.12436	−0.174385
$322$	1.73205i	0.0965234i
$323$	− 21.1244i	− 1.17539i
$324$	−4.46410	−0.248006
$325$	0	0
$326$	−12.3923	−0.686346
$327$	− 5.12436i	− 0.283378i
$328$	9.46410i	0.522568i
$329$	−6.00000	−0.330791
$330$	0	0
$331$	22.5359	1.23869	0.619343	−	0.785121i	$-0.287399\pi$
$331$	22.5359	1.23869	0.619343	+	0.785121i	$0.287399\pi$
$332$	− 3.00000i	− 0.164646i
$333$	3.60770i	0.197700i
$334$	5.66025	0.309715
$335$	0	0
$336$	−0.732051	−0.0399366
$337$	6.19615i	0.337526i	0.985657	+	0.168763i	$0.0539772\pi$
$337$	6.19615i	0.337526i	−0.985657	+	0.168763i	$0.946023\pi$
$338$	12.9282i	0.703202i
$339$	−5.07180	−0.275462
$340$	0	0
$341$	2.46410	0.133439
$342$	11.0000i	0.594812i
$343$	1.00000i	0.0539949i
$344$	−2.26795	−0.122280
$345$	0	0
$346$	6.12436	0.329247
$347$	− 11.3205i	− 0.607717i	−0.952717	−	0.303858i	$-0.901725\pi$
$347$	− 11.3205i	− 0.607717i	0.952717	−	0.303858i	$-0.0982750\pi$
$348$	0.339746i	0.0182123i
$349$	10.8038	0.578317	0.289158	−	0.957281i	$-0.406625\pi$
$349$	10.8038	0.578317	0.289158	+	0.957281i	$0.406625\pi$
$350$	0	0
$351$	1.07180	0.0572083
$352$	1.00000i	0.0533002i
$353$	20.6603i	1.09963i	0.835285	+	0.549817i	$0.185303\pi$
$353$	20.6603i	1.09963i	−0.835285	+	0.549817i	$0.814697\pi$
$354$	5.07180	0.269563
$355$	0	0
$356$	−1.73205	−0.0917985
$357$	3.46410i	0.183340i
$358$	9.12436i	0.482237i
$359$	−5.07180	−0.267679	−0.133840	−	0.991003i	$-0.542731\pi$
$359$	−5.07180	−0.267679	−0.133840	+	0.991003i	$0.542731\pi$
$360$	0	0
$361$	0.928203	0.0488528
$362$	− 6.53590i	− 0.343519i
$363$	− 0.732051i	− 0.0384227i
$364$	−0.267949	−0.0140444
$365$	0	0
$366$	4.67949	0.244601
$367$	10.4641i	0.546222i	0.961983	+	0.273111i	$0.0880526\pi$
$367$	10.4641i	0.546222i	−0.961983	+	0.273111i	$0.911947\pi$
$368$	1.73205i	0.0902894i
$369$	−23.3205	−1.21402
$370$	0	0
$371$	4.73205	0.245676
$372$	1.80385i	0.0935251i
$373$	4.78461i	0.247738i	0.992299	+	0.123869i	$0.0395302\pi$
$373$	4.78461i	0.247738i	−0.992299	+	0.123869i	$0.960470\pi$
$374$	4.73205	0.244689
$375$	0	0
$376$	−6.00000	−0.309426
$377$	0.124356i	0.00640464i
$378$	− 4.00000i	− 0.205738i
$379$	−13.6603	−0.701680	−0.350840	−	0.936435i	$-0.614104\pi$
$379$	−13.6603	−0.701680	−0.350840	+	0.936435i	$0.614104\pi$
$380$	0	0
$381$	1.07180	0.0549098
$382$	25.0526i	1.28180i
$383$	23.7846i	1.21534i	0.794191	+	0.607668i	$0.207895\pi$
$383$	23.7846i	1.21534i	−0.794191	+	0.607668i	$0.792105\pi$
$384$	−0.732051	−0.0373573
$385$	0	0
$386$	15.3205	0.779793
$387$	− 5.58846i	− 0.284077i
$388$	7.19615i	0.365329i
$389$	−34.0526	−1.72653	−0.863267	−	0.504748i	$-0.831585\pi$
$389$	−34.0526	−1.72653	−0.863267	+	0.504748i	$0.831585\pi$
$390$	0	0
$391$	8.19615	0.414497
$392$	1.00000i	0.0505076i
$393$	− 4.73205i	− 0.238700i
$394$	25.3923	1.27925
$395$	0	0
$396$	−2.46410	−0.123826
$397$	− 18.3923i	− 0.923083i	−0.887119	−	0.461542i	$-0.847296\pi$
$397$	− 18.3923i	− 0.923083i	0.887119	−	0.461542i	$-0.152704\pi$
$398$	15.7846i	0.791211i
$399$	−3.26795	−0.163602
$400$	0	0
$401$	−3.00000	−0.149813	−0.0749064	−	0.997191i	$-0.523866\pi$
$401$	−3.00000	−0.149813	−0.0749064	+	0.997191i	$0.523866\pi$
$402$	− 4.92820i	− 0.245796i
$403$	0.660254i	0.0328896i
$404$	−11.1962	−0.557029
$405$	0	0
$406$	0.464102	0.0230330
$407$	1.46410i	0.0725728i
$408$	3.46410i	0.171499i
$409$	−1.41154	−0.0697963	−0.0348981	−	0.999391i	$-0.511111\pi$
$409$	−1.41154	−0.0697963	−0.0348981	+	0.999391i	$0.511111\pi$
$410$	0	0
$411$	−4.05256	−0.199898
$412$	7.92820i	0.390595i
$413$	− 6.92820i	− 0.340915i
$414$	−4.26795	−0.209758
$415$	0	0
$416$	−0.267949	−0.0131373
$417$	− 0.732051i	− 0.0358487i
$418$	4.46410i	0.218346i
$419$	10.3923	0.507697	0.253849	−	0.967244i	$-0.418303\pi$
$419$	10.3923	0.507697	0.253849	+	0.967244i	$0.418303\pi$
$420$	0	0
$421$	1.41154	0.0687944	0.0343972	−	0.999408i	$-0.489049\pi$
$421$	1.41154	0.0687944	0.0343972	+	0.999408i	$0.489049\pi$
$422$	8.00000i	0.389434i
$423$	− 14.7846i	− 0.718852i
$424$	4.73205	0.229809
$425$	0	0
$426$	−6.33975	−0.307162
$427$	− 6.39230i	− 0.309345i
$428$	4.26795i	0.206299i
$429$	0.196152	0.00947033
$430$	0	0
$431$	−2.53590	−0.122150	−0.0610750	−	0.998133i	$-0.519453\pi$
$431$	−2.53590	−0.122150	−0.0610750	+	0.998133i	$0.519453\pi$
$432$	− 4.00000i	− 0.192450i
$433$	33.0526i	1.58840i	0.607653	+	0.794202i	$0.292111\pi$
$433$	33.0526i	1.58840i	−0.607653	+	0.794202i	$0.707889\pi$
$434$	2.46410	0.118281
$435$	0	0
$436$	−7.00000	−0.335239
$437$	7.73205i	0.369874i
$438$	2.14359i	0.102425i
$439$	−0.392305	−0.0187237	−0.00936184	−	0.999956i	$-0.502980\pi$
$439$	−0.392305	−0.0187237	−0.00936184	+	0.999956i	$0.502980\pi$
$440$	0	0
$441$	−2.46410	−0.117338
$442$	1.26795i	0.0603102i
$443$	20.7846i	0.987507i	0.869602	+	0.493753i	$0.164375\pi$
$443$	20.7846i	0.987507i	−0.869602	+	0.493753i	$0.835625\pi$
$444$	−1.07180	−0.0508652
$445$	0	0
$446$	−14.0000	−0.662919
$447$	10.1436i	0.479776i
$448$	1.00000i	0.0472456i
$449$	−39.9282	−1.88433	−0.942164	−	0.335152i	$-0.891212\pi$
$449$	−39.9282	−1.88433	−0.942164	+	0.335152i	$0.891212\pi$
$450$	0	0
$451$	−9.46410	−0.445647
$452$	6.92820i	0.325875i
$453$	1.32051i	0.0620429i
$454$	15.9282	0.747548
$455$	0	0
$456$	−3.26795	−0.153036
$457$	− 16.1962i	− 0.757624i	−0.925474	−	0.378812i	$-0.876333\pi$
$457$	− 16.1962i	− 0.757624i	0.925474	−	0.378812i	$-0.123667\pi$
$458$	− 3.85641i	− 0.180198i
$459$	−18.9282	−0.883493
$460$	0	0
$461$	−18.9282	−0.881574	−0.440787	−	0.897612i	$-0.645301\pi$
$461$	−18.9282	−0.881574	−0.440787	+	0.897612i	$0.645301\pi$
$462$	− 0.732051i	− 0.0340581i
$463$	11.5885i	0.538561i	0.963062	+	0.269281i	$0.0867859\pi$
$463$	11.5885i	0.538561i	−0.963062	+	0.269281i	$0.913214\pi$
$464$	0.464102	0.0215454
$465$	0	0
$466$	7.26795	0.336681
$467$	− 24.9282i	− 1.15354i	−0.816907	−	0.576770i	$-0.804313\pi$
$467$	− 24.9282i	− 1.15354i	0.816907	−	0.576770i	$-0.195687\pi$
$468$	− 0.660254i	− 0.0305203i
$469$	−6.73205	−0.310857
$470$	0	0
$471$	−8.64102	−0.398157
$472$	− 6.92820i	− 0.318896i
$473$	− 2.26795i	− 0.104280i
$474$	−5.60770	−0.257570
$475$	0	0
$476$	4.73205	0.216893
$477$	11.6603i	0.533886i
$478$	− 22.3923i	− 1.02420i
$479$	24.2487	1.10795	0.553976	−	0.832533i	$-0.313110\pi$
$479$	24.2487	1.10795	0.553976	+	0.832533i	$0.313110\pi$
$480$	0	0
$481$	−0.392305	−0.0178876
$482$	2.00000i	0.0910975i
$483$	− 1.26795i	− 0.0576937i
$484$	−1.00000	−0.0454545
$485$	0	0
$486$	15.2679	0.692568
$487$	27.4449i	1.24365i	0.783158	+	0.621823i	$0.213608\pi$
$487$	27.4449i	1.24365i	−0.783158	+	0.621823i	$0.786392\pi$
$488$	− 6.39230i	− 0.289366i
$489$	9.07180	0.410241
$490$	0	0
$491$	−30.1244	−1.35949	−0.679747	−	0.733447i	$-0.737910\pi$
$491$	−30.1244	−1.35949	−0.679747	+	0.733447i	$0.737910\pi$
$492$	− 6.92820i	− 0.312348i
$493$	− 2.19615i	− 0.0989097i
$494$	−1.19615	−0.0538174
$495$	0	0
$496$	2.46410	0.110641
$497$	8.66025i	0.388465i
$498$	2.19615i	0.0984119i
$499$	−30.3923	−1.36055	−0.680273	−	0.732959i	$-0.738139\pi$
$499$	−30.3923	−1.36055	−0.680273	+	0.732959i	$0.738139\pi$
$500$	0	0
$501$	−4.14359	−0.185122
$502$	12.5885i	0.561850i
$503$	0.928203i	0.0413865i	0.999786	+	0.0206933i	$0.00658734\pi$
$503$	0.928203i	0.0413865i	−0.999786	+	0.0206933i	$0.993413\pi$
$504$	−2.46410	−0.109760
$505$	0	0
$506$	−1.73205	−0.0769991
$507$	− 9.46410i	− 0.420316i
$508$	− 1.46410i	− 0.0649590i
$509$	12.5885	0.557974	0.278987	−	0.960295i	$-0.410001\pi$
$509$	12.5885	0.557974	0.278987	+	0.960295i	$0.410001\pi$
$510$	0	0
$511$	2.92820	0.129536
$512$	1.00000i	0.0441942i
$513$	− 17.8564i	− 0.788380i
$514$	−3.58846	−0.158280
$515$	0	0
$516$	1.66025	0.0730886
$517$	− 6.00000i	− 0.263880i
$518$	1.46410i	0.0643289i
$519$	−4.48334	−0.196797
$520$	0	0
$521$	−21.5885	−0.945807	−0.472904	−	0.881114i	$-0.656794\pi$
$521$	−21.5885	−0.945807	−0.472904	+	0.881114i	$0.656794\pi$
$522$	1.14359i	0.0500537i
$523$	− 25.9282i	− 1.13376i	−0.823800	−	0.566881i	$-0.808150\pi$
$523$	− 25.9282i	− 1.13376i	0.823800	−	0.566881i	$-0.191850\pi$
$524$	−6.46410	−0.282386
$525$	0	0
$526$	−19.2679	−0.840123
$527$	− 11.6603i	− 0.507929i
$528$	− 0.732051i	− 0.0318584i
$529$	20.0000	0.869565
$530$	0	0
$531$	17.0718	0.740853
$532$	4.46410i	0.193543i
$533$	− 2.53590i	− 0.109842i
$534$	1.26795	0.0548695
$535$	0	0
$536$	−6.73205	−0.290780
$537$	− 6.67949i	− 0.288241i
$538$	− 12.5885i	− 0.542727i
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	−12.3205	−0.529700	−0.264850	−	0.964290i	$-0.585322\pi$
$541$	−12.3205	−0.529700	−0.264850	+	0.964290i	$0.585322\pi$
$542$	2.58846i	0.111184i
$543$	4.78461i	0.205327i
$544$	4.73205	0.202885
$545$	0	0
$546$	0.196152	0.00839455
$547$	28.8038i	1.23156i	0.787917	+	0.615782i	$0.211160\pi$
$547$	28.8038i	1.23156i	−0.787917	+	0.615782i	$0.788840\pi$
$548$	5.53590i	0.236482i
$549$	15.7513	0.672249
$550$	0	0
$551$	2.07180	0.0882615
$552$	− 1.26795i	− 0.0539675i
$553$	7.66025i	0.325747i
$554$	−25.4641	−1.08187
$555$	0	0
$556$	−1.00000	−0.0424094
$557$	18.7128i	0.792887i	0.918059	+	0.396444i	$0.129756\pi$
$557$	18.7128i	0.792887i	−0.918059	+	0.396444i	$0.870244\pi$
$558$	6.07180i	0.257040i
$559$	0.607695	0.0257028
$560$	0	0
$561$	−3.46410	−0.146254
$562$	12.5885i	0.531012i
$563$	− 2.78461i	− 0.117357i	−0.998277	−	0.0586787i	$-0.981311\pi$
$563$	− 2.78461i	− 0.117357i	0.998277	−	0.0586787i	$-0.0186887\pi$
$564$	4.39230	0.184949
$565$	0	0
$566$	−0.143594	−0.00603569
$567$	− 4.46410i	− 0.187475i
$568$	8.66025i	0.363376i
$569$	−15.8038	−0.662532	−0.331266	−	0.943537i	$-0.607476\pi$
$569$	−15.8038	−0.662532	−0.331266	+	0.943537i	$0.607476\pi$
$570$	0	0
$571$	23.5885	0.987146	0.493573	−	0.869704i	$-0.335691\pi$
$571$	23.5885	0.987146	0.493573	+	0.869704i	$0.335691\pi$
$572$	− 0.267949i	− 0.0112035i
$573$	− 18.3397i	− 0.766154i
$574$	−9.46410	−0.395024
$575$	0	0
$576$	−2.46410	−0.102671
$577$	− 20.2487i	− 0.842965i	−0.906837	−	0.421482i	$-0.861510\pi$
$577$	− 20.2487i	− 0.842965i	0.906837	−	0.421482i	$-0.138490\pi$
$578$	− 5.39230i	− 0.224290i
$579$	−11.2154	−0.466096
$580$	0	0
$581$	3.00000	0.124461
$582$	− 5.26795i	− 0.218364i
$583$	4.73205i	0.195982i
$584$	2.92820	0.121170
$585$	0	0
$586$	−5.32051	−0.219788
$587$	19.6077i	0.809296i	0.914472	+	0.404648i	$0.132606\pi$
$587$	19.6077i	0.809296i	−0.914472	+	0.404648i	$0.867394\pi$
$588$	− 0.732051i	− 0.0301893i
$589$	11.0000	0.453247
$590$	0	0
$591$	−18.5885	−0.764627
$592$	1.46410i	0.0601742i
$593$	− 31.5167i	− 1.29423i	−0.762391	−	0.647117i	$-0.775974\pi$
$593$	− 31.5167i	− 1.29423i	0.762391	−	0.647117i	$-0.224026\pi$
$594$	4.00000	0.164122
$595$	0	0
$596$	13.8564	0.567581
$597$	− 11.5551i	− 0.472920i
$598$	− 0.464102i	− 0.0189785i
$599$	0.679492	0.0277633	0.0138816	−	0.999904i	$-0.495581\pi$
$599$	0.679492	0.0277633	0.0138816	+	0.999904i	$0.495581\pi$
$600$	0	0
$601$	−41.8564	−1.70736	−0.853679	−	0.520799i	$-0.825634\pi$
$601$	−41.8564	−1.70736	−0.853679	+	0.520799i	$0.825634\pi$
$602$	− 2.26795i	− 0.0924347i
$603$	− 16.5885i	− 0.675534i
$604$	1.80385	0.0733975
$605$	0	0
$606$	8.19615	0.332946
$607$	42.7846i	1.73657i	0.496062	+	0.868287i	$0.334779\pi$
$607$	42.7846i	1.73657i	−0.496062	+	0.868287i	$0.665221\pi$
$608$	4.46410i	0.181043i
$609$	−0.339746	−0.0137672
$610$	0	0
$611$	1.60770	0.0650404
$612$	11.6603i	0.471338i
$613$	24.3923i	0.985196i	0.870257	+	0.492598i	$0.163953\pi$
$613$	24.3923i	0.985196i	−0.870257	+	0.492598i	$0.836047\pi$
$614$	−2.14359	−0.0865084
$615$	0	0
$616$	−1.00000	−0.0402911
$617$	8.32051i	0.334971i	0.985875	+	0.167486i	$0.0535647\pi$
$617$	8.32051i	0.334971i	−0.985875	+	0.167486i	$0.946435\pi$
$618$	− 5.80385i	− 0.233465i
$619$	30.4449	1.22368	0.611841	−	0.790981i	$-0.290429\pi$
$619$	30.4449	1.22368	0.611841	+	0.790981i	$0.290429\pi$
$620$	0	0
$621$	6.92820	0.278019
$622$	32.3205i	1.29593i
$623$	− 1.73205i	− 0.0693932i
$624$	0.196152	0.00785238
$625$	0	0
$626$	17.8564	0.713686
$627$	− 3.26795i	− 0.130509i
$628$	11.8038i	0.471025i
$629$	6.92820	0.276246
$630$	0	0
$631$	27.1769	1.08190	0.540948	−	0.841056i	$-0.318066\pi$
$631$	27.1769	1.08190	0.540948	+	0.841056i	$0.318066\pi$
$632$	7.66025i	0.304709i
$633$	− 5.85641i	− 0.232771i
$634$	34.0526	1.35240
$635$	0	0
$636$	−3.46410	−0.137361
$637$	− 0.267949i	− 0.0106165i
$638$	0.464102i	0.0183740i
$639$	−21.3397	−0.844187
$640$	0	0
$641$	12.7128	0.502126	0.251063	−	0.967971i	$-0.419220\pi$
$641$	12.7128	0.502126	0.251063	+	0.967971i	$0.419220\pi$
$642$	− 3.12436i	− 0.123308i
$643$	23.1244i	0.911936i	0.889996	+	0.455968i	$0.150707\pi$
$643$	23.1244i	0.911936i	−0.889996	+	0.455968i	$0.849293\pi$
$644$	−1.73205	−0.0682524
$645$	0	0
$646$	21.1244	0.831127
$647$	6.00000i	0.235884i	0.993020	+	0.117942i	$0.0376297\pi$
$647$	6.00000i	0.235884i	−0.993020	+	0.117942i	$0.962370\pi$
$648$	− 4.46410i	− 0.175366i
$649$	6.92820	0.271956
$650$	0	0
$651$	−1.80385	−0.0706984
$652$	− 12.3923i	− 0.485320i
$653$	27.3731i	1.07119i	0.844475	+	0.535595i	$0.179913\pi$
$653$	27.3731i	1.07119i	−0.844475	+	0.535595i	$0.820087\pi$
$654$	5.12436	0.200378
$655$	0	0
$656$	−9.46410	−0.369511
$657$	7.21539i	0.281499i
$658$	− 6.00000i	− 0.233904i
$659$	−24.1244	−0.939751	−0.469876	−	0.882733i	$-0.655701\pi$
$659$	−24.1244	−0.939751	−0.469876	+	0.882733i	$0.655701\pi$
$660$	0	0
$661$	−3.66025	−0.142367	−0.0711837	−	0.997463i	$-0.522678\pi$
$661$	−3.66025	−0.142367	−0.0711837	+	0.997463i	$0.522678\pi$
$662$	22.5359i	0.875883i
$663$	− 0.928203i	− 0.0360484i
$664$	3.00000	0.116423
$665$	0	0
$666$	−3.60770	−0.139795
$667$	0.803848i	0.0311251i
$668$	5.66025i	0.219002i
$669$	10.2487	0.396238
$670$	0	0
$671$	6.39230	0.246772
$672$	− 0.732051i	− 0.0282395i
$673$	− 26.6410i	− 1.02694i	−0.858109	−	0.513468i	$-0.828361\pi$
$673$	− 26.6410i	− 1.02694i	0.858109	−	0.513468i	$-0.171639\pi$
$674$	−6.19615	−0.238667
$675$	0	0
$676$	−12.9282	−0.497239
$677$	− 9.33975i	− 0.358956i	−0.983762	−	0.179478i	$-0.942559\pi$
$677$	− 9.33975i	− 0.358956i	0.983762	−	0.179478i	$-0.0574408\pi$
$678$	− 5.07180i	− 0.194781i
$679$	−7.19615	−0.276163
$680$	0	0
$681$	−11.6603	−0.446822
$682$	2.46410i	0.0943553i
$683$	21.1244i	0.808301i	0.914693	+	0.404151i	$0.132433\pi$
$683$	21.1244i	0.808301i	−0.914693	+	0.404151i	$0.867567\pi$
$684$	−11.0000	−0.420596
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	2.82309i	0.107707i
$688$	− 2.26795i	− 0.0864648i
$689$	−1.26795	−0.0483050
$690$	0	0
$691$	50.2487	1.91155	0.955776	−	0.294097i	$-0.0950189\pi$
$691$	50.2487	1.91155	0.955776	+	0.294097i	$0.0950189\pi$
$692$	6.12436i	0.232813i
$693$	− 2.46410i	− 0.0936035i
$694$	11.3205	0.429721
$695$	0	0
$696$	−0.339746	−0.0128780
$697$	44.7846i	1.69634i
$698$	10.8038i	0.408932i
$699$	−5.32051	−0.201240
$700$	0	0
$701$	−39.0000	−1.47301	−0.736505	−	0.676432i	$-0.763525\pi$
$701$	−39.0000	−1.47301	−0.736505	+	0.676432i	$0.763525\pi$
$702$	1.07180i	0.0404524i
$703$	6.53590i	0.246506i
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	−20.6603	−0.777559
$707$	− 11.1962i	− 0.421075i
$708$	5.07180i	0.190610i
$709$	−12.9808	−0.487503	−0.243751	−	0.969838i	$-0.578378\pi$
$709$	−12.9808	−0.487503	−0.243751	+	0.969838i	$0.578378\pi$
$710$	0	0
$711$	−18.8756	−0.707892
$712$	− 1.73205i	− 0.0649113i
$713$	4.26795i	0.159836i
$714$	−3.46410	−0.129641
$715$	0	0
$716$	−9.12436	−0.340993
$717$	16.3923i	0.612182i
$718$	− 5.07180i	− 0.189278i
$719$	−18.0000	−0.671287	−0.335643	−	0.941989i	$-0.608954\pi$
$719$	−18.0000	−0.671287	−0.335643	+	0.941989i	$0.608954\pi$
$720$	0	0
$721$	−7.92820	−0.295262
$722$	0.928203i	0.0345441i
$723$	− 1.46410i	− 0.0544505i
$724$	6.53590	0.242905
$725$	0	0
$726$	0.732051	0.0271690
$727$	40.7128i	1.50995i	0.655751	+	0.754977i	$0.272352\pi$
$727$	40.7128i	1.50995i	−0.655751	+	0.754977i	$0.727648\pi$
$728$	− 0.267949i	− 0.00993086i
$729$	2.21539	0.0820515
$730$	0	0
$731$	−10.7321	−0.396939
$732$	4.67949i	0.172959i
$733$	− 39.1962i	− 1.44774i	−0.689935	−	0.723871i	$-0.742361\pi$
$733$	− 39.1962i	− 1.44774i	0.689935	−	0.723871i	$-0.257639\pi$
$734$	−10.4641	−0.386237
$735$	0	0
$736$	−1.73205	−0.0638442
$737$	− 6.73205i	− 0.247978i
$738$	− 23.3205i	− 0.858440i
$739$	−29.4641	−1.08385	−0.541927	−	0.840425i	$-0.682305\pi$
$739$	−29.4641	−1.08385	−0.541927	+	0.840425i	$0.682305\pi$
$740$	0	0
$741$	0.875644	0.0321676
$742$	4.73205i	0.173719i
$743$	− 1.94744i	− 0.0714447i	−0.999362	−	0.0357223i	$-0.988627\pi$
$743$	− 1.94744i	− 0.0714447i	0.999362	−	0.0357223i	$-0.0113732\pi$
$744$	−1.80385	−0.0661323
$745$	0	0
$746$	−4.78461	−0.175177
$747$	7.39230i	0.270470i
$748$	4.73205i	0.173021i
$749$	−4.26795	−0.155947
$750$	0	0
$751$	16.9090	0.617017	0.308508	−	0.951222i	$-0.400170\pi$
$751$	16.9090	0.617017	0.308508	+	0.951222i	$0.400170\pi$
$752$	− 6.00000i	− 0.218797i
$753$	− 9.21539i	− 0.335827i
$754$	−0.124356	−0.00452877
$755$	0	0
$756$	4.00000	0.145479
$757$	24.7846i	0.900812i	0.892824	+	0.450406i	$0.148721\pi$
$757$	24.7846i	0.900812i	−0.892824	+	0.450406i	$0.851279\pi$
$758$	− 13.6603i	− 0.496163i
$759$	1.26795	0.0460236
$760$	0	0
$761$	25.5167	0.924978	0.462489	−	0.886625i	$-0.346956\pi$
$761$	25.5167	0.924978	0.462489	+	0.886625i	$0.346956\pi$
$762$	1.07180i	0.0388271i
$763$	− 7.00000i	− 0.253417i
$764$	−25.0526	−0.906370
$765$	0	0
$766$	−23.7846	−0.859373
$767$	1.85641i	0.0670310i
$768$	− 0.732051i	− 0.0264156i
$769$	39.9090	1.43915	0.719577	−	0.694413i	$-0.244336\pi$
$769$	39.9090	1.43915	0.719577	+	0.694413i	$0.244336\pi$
$770$	0	0
$771$	2.62693	0.0946067
$772$	15.3205i	0.551397i
$773$	12.0000i	0.431610i	0.976436	+	0.215805i	$0.0692376\pi$
$773$	12.0000i	0.431610i	−0.976436	+	0.215805i	$0.930762\pi$
$774$	5.58846	0.200873
$775$	0	0
$776$	−7.19615	−0.258327
$777$	− 1.07180i	− 0.0384505i
$778$	− 34.0526i	− 1.22084i
$779$	−42.2487	−1.51372
$780$	0	0
$781$	−8.66025	−0.309888
$782$	8.19615i	0.293094i
$783$	− 1.85641i	− 0.0663426i
$784$	−1.00000	−0.0357143
$785$	0	0
$786$	4.73205	0.168787
$787$	− 34.7846i	− 1.23994i	−0.784627	−	0.619969i	$-0.787145\pi$
$787$	− 34.7846i	− 1.23994i	0.784627	−	0.619969i	$-0.212855\pi$
$788$	25.3923i	0.904563i
$789$	14.1051	0.502155
$790$	0	0
$791$	−6.92820	−0.246339
$792$	− 2.46410i	− 0.0875580i
$793$	1.71281i	0.0608238i
$794$	18.3923	0.652718
$795$	0	0
$796$	−15.7846	−0.559471
$797$	35.6603i	1.26315i	0.775314	+	0.631576i	$0.217591\pi$
$797$	35.6603i	1.26315i	−0.775314	+	0.631576i	$0.782409\pi$
$798$	− 3.26795i	− 0.115684i
$799$	−28.3923	−1.00445
$800$	0	0
$801$	4.26795	0.150801
$802$	− 3.00000i	− 0.105934i
$803$	2.92820i	0.103334i
$804$	4.92820	0.173804
$805$	0	0
$806$	−0.660254	−0.0232565
$807$	9.21539i	0.324397i
$808$	− 11.1962i	− 0.393879i
$809$	0.339746	0.0119448	0.00597242	−	0.999982i	$-0.498099\pi$
$809$	0.339746	0.0119448	0.00597242	+	0.999982i	$0.498099\pi$
$810$	0	0
$811$	−18.7846	−0.659617	−0.329808	−	0.944048i	$-0.606984\pi$
$811$	−18.7846	−0.659617	−0.329808	+	0.944048i	$0.606984\pi$
$812$	0.464102i	0.0162868i
$813$	− 1.89488i	− 0.0664564i
$814$	−1.46410	−0.0513167
$815$	0	0
$816$	−3.46410	−0.121268
$817$	− 10.1244i	− 0.354206i
$818$	− 1.41154i	− 0.0493534i
$819$	0.660254	0.0230711
$820$	0	0
$821$	−51.2487	−1.78859	−0.894296	−	0.447476i	$-0.852323\pi$
$821$	−51.2487	−1.78859	−0.894296	+	0.447476i	$0.852323\pi$
$822$	− 4.05256i	− 0.141349i
$823$	28.7846i	1.00337i	0.865051	+	0.501684i	$0.167286\pi$
$823$	28.7846i	1.00337i	−0.865051	+	0.501684i	$0.832714\pi$
$824$	−7.92820	−0.276192
$825$	0	0
$826$	6.92820	0.241063
$827$	− 12.8038i	− 0.445233i	−0.974906	−	0.222617i	$-0.928540\pi$
$827$	− 12.8038i	− 0.445233i	0.974906	−	0.222617i	$-0.0714598\pi$
$828$	− 4.26795i	− 0.148321i
$829$	28.9282	1.00472	0.502359	−	0.864659i	$-0.332466\pi$
$829$	28.9282	1.00472	0.502359	+	0.864659i	$0.332466\pi$
$830$	0	0
$831$	18.6410	0.646650
$832$	− 0.267949i	− 0.00928947i
$833$	4.73205i	0.163956i
$834$	0.732051	0.0253488
$835$	0	0
$836$	−4.46410	−0.154394
$837$	− 9.85641i	− 0.340687i
$838$	10.3923i	0.358996i
$839$	50.7846	1.75328	0.876640	−	0.481147i	$-0.159780\pi$
$839$	50.7846	1.75328	0.876640	+	0.481147i	$0.159780\pi$
$840$	0	0
$841$	−28.7846	−0.992573
$842$	1.41154i	0.0486450i
$843$	− 9.21539i	− 0.317395i
$844$	−8.00000	−0.275371
$845$	0	0
$846$	14.7846	0.508305
$847$	− 1.00000i	− 0.0343604i
$848$	4.73205i	0.162499i
$849$	0.105118	0.00360763
$850$	0	0
$851$	−2.53590	−0.0869295
$852$	− 6.33975i	− 0.217196i
$853$	8.24871i	0.282430i	0.989979	+	0.141215i	$0.0451010\pi$
$853$	8.24871i	0.282430i	−0.989979	+	0.141215i	$0.954899\pi$
$854$	6.39230	0.218740
$855$	0	0
$856$	−4.26795	−0.145876
$857$	− 26.1962i	− 0.894844i	−0.894323	−	0.447422i	$-0.852342\pi$
$857$	− 26.1962i	− 0.894844i	0.894323	−	0.447422i	$-0.147658\pi$
$858$	0.196152i	0.00669653i
$859$	−5.80385	−0.198025	−0.0990124	−	0.995086i	$-0.531568\pi$
$859$	−5.80385	−0.198025	−0.0990124	+	0.995086i	$0.531568\pi$
$860$	0	0
$861$	6.92820	0.236113
$862$	− 2.53590i	− 0.0863730i
$863$	12.8038i	0.435848i	0.975966	+	0.217924i	$0.0699285\pi$
$863$	12.8038i	0.435848i	−0.975966	+	0.217924i	$0.930072\pi$
$864$	4.00000	0.136083
$865$	0	0
$866$	−33.0526	−1.12317
$867$	3.94744i	0.134062i
$868$	2.46410i	0.0836371i
$869$	−7.66025	−0.259856
$870$	0	0
$871$	1.80385	0.0611210
$872$	− 7.00000i	− 0.237050i
$873$	− 17.7321i	− 0.600139i
$874$	−7.73205	−0.261541
$875$	0	0
$876$	−2.14359	−0.0724253
$877$	7.00000i	0.236373i	0.992991	+	0.118187i	$0.0377081\pi$
$877$	7.00000i	0.236373i	−0.992991	+	0.118187i	$0.962292\pi$
$878$	− 0.392305i	− 0.0132396i
$879$	3.89488	0.131371
$880$	0	0
$881$	−46.5167	−1.56719	−0.783593	−	0.621274i	$-0.786615\pi$
$881$	−46.5167	−1.56719	−0.783593	+	0.621274i	$0.786615\pi$
$882$	− 2.46410i	− 0.0829706i
$883$	0.392305i	0.0132021i	0.999978	+	0.00660105i	$0.00210120\pi$
$883$	0.392305i	0.0132021i	−0.999978	+	0.00660105i	$0.997899\pi$
$884$	−1.26795	−0.0426457
$885$	0	0
$886$	−20.7846	−0.698273
$887$	18.0000i	0.604381i	0.953248	+	0.302190i	$0.0977178\pi$
$887$	18.0000i	0.604381i	−0.953248	+	0.302190i	$0.902282\pi$
$888$	− 1.07180i	− 0.0359671i
$889$	1.46410	0.0491044
$890$	0	0
$891$	4.46410	0.149553
$892$	− 14.0000i	− 0.468755i
$893$	− 26.7846i	− 0.896313i
$894$	−10.1436	−0.339253
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	0.339746i	0.0113438i
$898$	− 39.9282i	− 1.33242i
$899$	1.14359	0.0381410
$900$	0	0
$901$	22.3923	0.745996
$902$	− 9.46410i	− 0.315120i
$903$	1.66025i	0.0552498i
$904$	−6.92820	−0.230429
$905$	0	0
$906$	−1.32051	−0.0438709
$907$	45.6603i	1.51612i	0.652183	+	0.758062i	$0.273854\pi$
$907$	45.6603i	1.51612i	−0.652183	+	0.758062i	$0.726146\pi$
$908$	15.9282i	0.528596i
$909$	27.5885	0.915051
$910$	0	0
$911$	33.0333	1.09444	0.547221	−	0.836988i	$-0.315686\pi$
$911$	33.0333	1.09444	0.547221	+	0.836988i	$0.315686\pi$
$912$	− 3.26795i	− 0.108213i
$913$	3.00000i	0.0992855i
$914$	16.1962	0.535721
$915$	0	0
$916$	3.85641	0.127419
$917$	− 6.46410i	− 0.213463i
$918$	− 18.9282i	− 0.624724i
$919$	−28.7846	−0.949517	−0.474758	−	0.880116i	$-0.657465\pi$
$919$	−28.7846	−0.949517	−0.474758	+	0.880116i	$0.657465\pi$
$920$	0	0
$921$	1.56922	0.0517075
$922$	− 18.9282i	− 0.623367i
$923$	− 2.32051i	− 0.0763805i
$924$	0.732051	0.0240827
$925$	0	0
$926$	−11.5885	−0.380820
$927$	− 19.5359i	− 0.641643i
$928$	0.464102i	0.0152349i
$929$	19.7321	0.647388	0.323694	−	0.946162i	$-0.395075\pi$
$929$	19.7321	0.647388	0.323694	+	0.946162i	$0.395075\pi$
$930$	0	0
$931$	−4.46410	−0.146305
$932$	7.26795i	0.238070i
$933$	− 23.6603i	− 0.774602i
$934$	24.9282	0.815676
$935$	0	0
$936$	0.660254	0.0215811
$937$	52.5885i	1.71799i	0.511984	+	0.858995i	$0.328911\pi$
$937$	52.5885i	1.71799i	−0.511984	+	0.858995i	$0.671089\pi$
$938$	− 6.73205i	− 0.219809i
$939$	−13.0718	−0.426582
$940$	0	0
$941$	−43.1769	−1.40753	−0.703764	−	0.710434i	$-0.748499\pi$
$941$	−43.1769	−1.40753	−0.703764	+	0.710434i	$0.748499\pi$
$942$	− 8.64102i	− 0.281540i
$943$	− 16.3923i	− 0.533807i
$944$	6.92820	0.225494
$945$	0	0
$946$	2.26795	0.0737374
$947$	20.1962i	0.656287i	0.944628	+	0.328143i	$0.106423\pi$
$947$	20.1962i	0.656287i	−0.944628	+	0.328143i	$0.893577\pi$
$948$	− 5.60770i	− 0.182129i
$949$	−0.784610	−0.0254695
$950$	0	0
$951$	−24.9282	−0.808352
$952$	4.73205i	0.153367i
$953$	− 43.2679i	− 1.40159i	−0.713365	−	0.700793i	$-0.752830\pi$
$953$	− 43.2679i	− 1.40159i	0.713365	−	0.700793i	$-0.247170\pi$
$954$	−11.6603	−0.377515
$955$	0	0
$956$	22.3923	0.724219
$957$	− 0.339746i	− 0.0109824i
$958$	24.2487i	0.783440i
$959$	−5.53590	−0.178763
$960$	0	0
$961$	−24.9282	−0.804136
$962$	− 0.392305i	− 0.0126484i
$963$	− 10.5167i	− 0.338895i
$964$	−2.00000	−0.0644157
$965$	0	0
$966$	1.26795	0.0407956
$967$	− 43.9090i	− 1.41202i	−0.708203	−	0.706009i	$-0.750494\pi$
$967$	− 43.9090i	− 1.41202i	0.708203	−	0.706009i	$-0.249506\pi$
$968$	− 1.00000i	− 0.0321412i
$969$	−15.4641	−0.496779
$970$	0	0
$971$	−52.6410	−1.68933	−0.844665	−	0.535295i	$-0.820201\pi$
$971$	−52.6410	−1.68933	−0.844665	+	0.535295i	$0.820201\pi$
$972$	15.2679i	0.489720i
$973$	− 1.00000i	− 0.0320585i
$974$	−27.4449	−0.879390
$975$	0	0
$976$	6.39230	0.204613
$977$	30.2487i	0.967742i	0.875139	+	0.483871i	$0.160770\pi$
$977$	30.2487i	0.967742i	−0.875139	+	0.483871i	$0.839230\pi$
$978$	9.07180i	0.290084i
$979$	1.73205	0.0553566
$980$	0	0
$981$	17.2487	0.550709
$982$	− 30.1244i	− 0.961307i
$983$	27.0000i	0.861166i	0.902551	+	0.430583i	$0.141692\pi$
$983$	27.0000i	0.861166i	−0.902551	+	0.430583i	$0.858308\pi$
$984$	6.92820	0.220863
$985$	0	0
$986$	2.19615	0.0699397
$987$	4.39230i	0.139809i
$988$	− 1.19615i	− 0.0380547i
$989$	3.92820	0.124910
$990$	0	0
$991$	−17.8564	−0.567227	−0.283614	−	0.958939i	$-0.591533\pi$
$991$	−17.8564	−0.567227	−0.283614	+	0.958939i	$0.591533\pi$
$992$	2.46410i	0.0782353i
$993$	− 16.4974i	− 0.523530i
$994$	−8.66025	−0.274687
$995$	0	0
$996$	−2.19615	−0.0695878
$997$	20.1436i	0.637954i	0.947762	+	0.318977i	$0.103339\pi$
$997$	20.1436i	0.637954i	−0.947762	+	0.318977i	$0.896661\pi$
$998$	− 30.3923i	− 0.962052i
$999$	5.85641	0.185289

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.c.r.1849.3		4
5.2	odd	4		3850.2.a.bk.1.1	✓	2
5.3	odd	4		3850.2.a.bl.1.2	yes	2
5.4	even	2	inner	3850.2.c.r.1849.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3850.2.a.bk.1.1	✓	2	5.2	odd	4
3850.2.a.bl.1.2	yes	2	5.3	odd	4
3850.2.c.r.1849.2		4	5.4	even	2	inner
3850.2.c.r.1849.3		4	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:	\( N \)	\(=\)	\( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3850.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -0.732051i q^{3} -1.00000 q^{4} +0.732051 q^{6} -1.00000i q^{7} -1.00000i q^{8} +2.46410 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -0.732051i q^{3} -1.00000 q^{4} +0.732051 q^{6} -1.00000i q^{7} -1.00000i q^{8} +2.46410 q^{9} +1.00000 q^{11} +0.732051i q^{12} +0.267949i q^{13} +1.00000 q^{14} +1.00000 q^{16} -4.73205i q^{17} +2.46410i q^{18} +4.46410 q^{19} -0.732051 q^{21} +1.00000i q^{22} +1.73205i q^{23} -0.732051 q^{24} -0.267949 q^{26} -4.00000i q^{27} +1.00000i q^{28} +0.464102 q^{29} +2.46410 q^{31} +1.00000i q^{32} -0.732051i q^{33} +4.73205 q^{34} -2.46410 q^{36} +1.46410i q^{37} +4.46410i q^{38} +0.196152 q^{39} -9.46410 q^{41} -0.732051i q^{42} -2.26795i q^{43} -1.00000 q^{44} -1.73205 q^{46} -6.00000i q^{47} -0.732051i q^{48} -1.00000 q^{49} -3.46410 q^{51} -0.267949i q^{52} +4.73205i q^{53} +4.00000 q^{54} -1.00000 q^{56} -3.26795i q^{57} +0.464102i q^{58} +6.92820 q^{59} +6.39230 q^{61} +2.46410i q^{62} -2.46410i q^{63} -1.00000 q^{64} +0.732051 q^{66} -6.73205i q^{67} +4.73205i q^{68} +1.26795 q^{69} -8.66025 q^{71} -2.46410i q^{72} +2.92820i q^{73} -1.46410 q^{74} -4.46410 q^{76} -1.00000i q^{77} +0.196152i q^{78} -7.66025 q^{79} +4.46410 q^{81} -9.46410i q^{82} +3.00000i q^{83} +0.732051 q^{84} +2.26795 q^{86} -0.339746i q^{87} -1.00000i q^{88} +1.73205 q^{89} +0.267949 q^{91} -1.73205i q^{92} -1.80385i q^{93} +6.00000 q^{94} +0.732051 q^{96} -7.19615i q^{97} -1.00000i q^{98} +2.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} - 4 q^{6} - 4 q^{9} + 4 q^{11} + 4 q^{14} + 4 q^{16} + 4 q^{19} + 4 q^{21} + 4 q^{24} - 8 q^{26} - 12 q^{29} - 4 q^{31} + 12 q^{34} + 4 q^{36} - 20 q^{39} - 24 q^{41} - 4 q^{44} - 4 q^{49} + 16 q^{54} - 4 q^{56} - 16 q^{61} - 4 q^{64} - 4 q^{66} + 12 q^{69} + 8 q^{74} - 4 q^{76} + 4 q^{79} + 4 q^{81} - 4 q^{84} + 16 q^{86} + 8 q^{91} + 24 q^{94} - 4 q^{96} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 4 * q^6 - 4 * q^9 + 4 * q^11 + 4 * q^14 + 4 * q^16 + 4 * q^19 + 4 * q^21 + 4 * q^24 - 8 * q^26 - 12 * q^29 - 4 * q^31 + 12 * q^34 + 4 * q^36 - 20 * q^39 - 24 * q^41 - 4 * q^44 - 4 * q^49 + 16 * q^54 - 4 * q^56 - 16 * q^61 - 4 * q^64 - 4 * q^66 + 12 * q^69 + 8 * q^74 - 4 * q^76 + 4 * q^79 + 4 * q^81 - 4 * q^84 + 16 * q^86 + 8 * q^91 + 24 * q^94 - 4 * q^96 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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