LMFDB - Embedded newform 2150.2.b.o.1549.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2150,2,Mod(1549,2150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2150, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2150.1549");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2150 = 2 \cdot 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2150.b (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:	$17.1678364346$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 430)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1549.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2150.1549
Dual form			2150.2.b.o.1549.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.41421i q^{3} -1.00000 q^{4} -1.41421 q^{6} -1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.41421i q^{3} -1.00000 q^{4} -1.41421 q^{6} -1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{9} +3.41421 q^{11} +1.41421i q^{12} +3.82843i q^{13} -1.00000 q^{14} +1.00000 q^{16} +1.41421i q^{17} -1.00000i q^{18} +1.00000 q^{19} -1.41421 q^{21} -3.41421i q^{22} +9.07107i q^{23} +1.41421 q^{24} +3.82843 q^{26} -5.65685i q^{27} +1.00000i q^{28} +7.24264 q^{29} +2.41421 q^{31} -1.00000i q^{32} -4.82843i q^{33} +1.41421 q^{34} -1.00000 q^{36} +6.24264i q^{37} -1.00000i q^{38} +5.41421 q^{39} +3.82843 q^{41} +1.41421i q^{42} +1.00000i q^{43} -3.41421 q^{44} +9.07107 q^{46} +7.07107i q^{47} -1.41421i q^{48} +6.00000 q^{49} +2.00000 q^{51} -3.82843i q^{52} +5.65685i q^{53} -5.65685 q^{54} +1.00000 q^{56} -1.41421i q^{57} -7.24264i q^{58} +6.82843 q^{59} -14.0711 q^{61} -2.41421i q^{62} -1.00000i q^{63} -1.00000 q^{64} -4.82843 q^{66} -7.24264i q^{67} -1.41421i q^{68} +12.8284 q^{69} -7.89949 q^{71} +1.00000i q^{72} -0.757359i q^{73} +6.24264 q^{74} -1.00000 q^{76} -3.41421i q^{77} -5.41421i q^{78} +5.58579 q^{79} -5.00000 q^{81} -3.82843i q^{82} -7.65685i q^{83} +1.41421 q^{84} +1.00000 q^{86} -10.2426i q^{87} +3.41421i q^{88} -5.07107 q^{89} +3.82843 q^{91} -9.07107i q^{92} -3.41421i q^{93} +7.07107 q^{94} -1.41421 q^{96} +17.5563i q^{97} -6.00000i q^{98} +3.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^9	$ 4 q - 4 q^{4} + 4 q^{9} + 8 q^{11} - 4 q^{14} + 4 q^{16} + 4 q^{19} + 4 q^{26} + 12 q^{29} + 4 q^{31} - 4 q^{36} + 16 q^{39} + 4 q^{41} - 8 q^{44} + 8 q^{46} + 24 q^{49} + 8 q^{51} + 4 q^{56} + 16 q^{59} - 28 q^{61} - 4 q^{64} - 8 q^{66} + 40 q^{69} + 8 q^{71} + 8 q^{74} - 4 q^{76} + 28 q^{79} - 20 q^{81} + 4 q^{86} + 8 q^{89} + 4 q^{91} + 8 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^9 + 8 * q^11 - 4 * q^14 + 4 * q^16 + 4 * q^19 + 4 * q^26 + 12 * q^29 + 4 * q^31 - 4 * q^36 + 16 * q^39 + 4 * q^41 - 8 * q^44 + 8 * q^46 + 24 * q^49 + 8 * q^51 + 4 * q^56 + 16 * q^59 - 28 * q^61 - 4 * q^64 - 8 * q^66 + 40 * q^69 + 8 * q^71 + 8 * q^74 - 4 * q^76 + 28 * q^79 - 20 * q^81 + 4 * q^86 + 8 * q^89 + 4 * q^91 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2150\mathbb{Z}\right)^\times$.

$n$	$1377$	$1551$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	− 1.41421i	− 0.816497i	−0.912871	−	0.408248i	$-0.866140\pi$
$3$	− 1.41421i	− 0.816497i	0.912871	−	0.408248i	$-0.133860\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.41421	−0.577350
$7$	− 1.00000i	− 0.377964i	−0.981981	−	0.188982i	$-0.939481\pi$
$7$	− 1.00000i	− 0.377964i	0.981981	−	0.188982i	$-0.0605189\pi$
$8$	1.00000i	0.353553i
$9$	1.00000	0.333333
$10$	0	0
$11$	3.41421	1.02942	0.514712	−	0.857363i	$-0.327899\pi$
$11$	3.41421	1.02942	0.514712	+	0.857363i	$0.327899\pi$
$12$	1.41421i	0.408248i
$13$	3.82843i	1.06181i	0.847430	+	0.530907i	$0.178149\pi$
$13$	3.82843i	1.06181i	−0.847430	+	0.530907i	$0.821851\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	1.41421i	0.342997i	0.985184	+	0.171499i	$0.0548609\pi$
$17$	1.41421i	0.342997i	−0.985184	+	0.171499i	$0.945139\pi$
$18$	− 1.00000i	− 0.235702i
$19$	1.00000	0.229416	0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000	0.229416	0.114708	+	0.993399i	$0.463407\pi$
$20$	0	0
$21$	−1.41421	−0.308607
$22$	− 3.41421i	− 0.727913i
$23$	9.07107i	1.89145i	0.324970	+	0.945724i	$0.394646\pi$
$23$	9.07107i	1.89145i	−0.324970	+	0.945724i	$0.605354\pi$
$24$	1.41421	0.288675
$25$	0	0
$26$	3.82843	0.750816
$27$	− 5.65685i	− 1.08866i
$28$	1.00000i	0.188982i
$29$	7.24264	1.34492	0.672462	−	0.740131i	$-0.265237\pi$
$29$	7.24264	1.34492	0.672462	+	0.740131i	$0.265237\pi$
$30$	0	0
$31$	2.41421	0.433606	0.216803	−	0.976215i	$-0.430437\pi$
$31$	2.41421	0.433606	0.216803	+	0.976215i	$0.430437\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 4.82843i	− 0.840521i
$34$	1.41421	0.242536
$35$	0	0
$36$	−1.00000	−0.166667
$37$	6.24264i	1.02628i	0.858304	+	0.513142i	$0.171519\pi$
$37$	6.24264i	1.02628i	−0.858304	+	0.513142i	$0.828481\pi$
$38$	− 1.00000i	− 0.162221i
$39$	5.41421	0.866968
$40$	0	0
$41$	3.82843	0.597900	0.298950	−	0.954269i	$-0.403364\pi$
$41$	3.82843	0.597900	0.298950	+	0.954269i	$0.403364\pi$
$42$	1.41421i	0.218218i
$43$	1.00000i	0.152499i
$43$	1.00000i	0.152499i
$44$	−3.41421	−0.514712
$45$	0	0
$46$	9.07107	1.33746
$47$	7.07107i	1.03142i	0.856763	+	0.515711i	$0.172472\pi$
$47$	7.07107i	1.03142i	−0.856763	+	0.515711i	$0.827528\pi$
$48$	− 1.41421i	− 0.204124i
$49$	6.00000	0.857143
$50$	0	0
$51$	2.00000	0.280056
$52$	− 3.82843i	− 0.530907i
$53$	5.65685i	0.777029i	0.921443	+	0.388514i	$0.127012\pi$
$53$	5.65685i	0.777029i	−0.921443	+	0.388514i	$0.872988\pi$
$54$	−5.65685	−0.769800
$55$	0	0
$56$	1.00000	0.133631
$57$	− 1.41421i	− 0.187317i
$58$	− 7.24264i	− 0.951005i
$59$	6.82843	0.888985	0.444493	−	0.895782i	$-0.353384\pi$
$59$	6.82843	0.888985	0.444493	+	0.895782i	$0.353384\pi$
$60$	0	0
$61$	−14.0711	−1.80162	−0.900808	−	0.434218i	$-0.857025\pi$
$61$	−14.0711	−1.80162	−0.900808	+	0.434218i	$0.857025\pi$
$62$	− 2.41421i	− 0.306605i
$63$	− 1.00000i	− 0.125988i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−4.82843	−0.594338
$67$	− 7.24264i	− 0.884829i	−0.896811	−	0.442415i	$-0.854122\pi$
$67$	− 7.24264i	− 0.884829i	0.896811	−	0.442415i	$-0.145878\pi$
$68$	− 1.41421i	− 0.171499i
$69$	12.8284	1.54436
$70$	0	0
$71$	−7.89949	−0.937498	−0.468749	−	0.883332i	$-0.655295\pi$
$71$	−7.89949	−0.937498	−0.468749	+	0.883332i	$0.655295\pi$
$72$	1.00000i	0.117851i
$73$	− 0.757359i	− 0.0886422i	−0.999017	−	0.0443211i	$-0.985888\pi$
$73$	− 0.757359i	− 0.0886422i	0.999017	−	0.0443211i	$-0.0141125\pi$
$74$	6.24264	0.725692
$75$	0	0
$76$	−1.00000	−0.114708
$77$	− 3.41421i	− 0.389086i
$78$	− 5.41421i	− 0.613039i
$79$	5.58579	0.628450	0.314225	−	0.949349i	$-0.398255\pi$
$79$	5.58579	0.628450	0.314225	+	0.949349i	$0.398255\pi$
$80$	0	0
$81$	−5.00000	−0.555556
$82$	− 3.82843i	− 0.422779i
$83$	− 7.65685i	− 0.840449i	−0.907420	−	0.420224i	$-0.861951\pi$
$83$	− 7.65685i	− 0.840449i	0.907420	−	0.420224i	$-0.138049\pi$
$84$	1.41421	0.154303
$85$	0	0
$86$	1.00000	0.107833
$87$	− 10.2426i	− 1.09813i
$88$	3.41421i	0.363956i
$89$	−5.07107	−0.537532	−0.268766	−	0.963205i	$-0.586616\pi$
$89$	−5.07107	−0.537532	−0.268766	+	0.963205i	$0.586616\pi$
$90$	0	0
$91$	3.82843	0.401328
$92$	− 9.07107i	− 0.945724i
$93$	− 3.41421i	− 0.354037i
$94$	7.07107	0.729325
$95$	0	0
$96$	−1.41421	−0.144338
$97$	17.5563i	1.78258i	0.453436	+	0.891289i	$0.350198\pi$
$97$	17.5563i	1.78258i	−0.453436	+	0.891289i	$0.649802\pi$
$98$	− 6.00000i	− 0.606092i
$99$	3.41421	0.343141
$100$	0	0
$101$	−1.41421	−0.140720	−0.0703598	−	0.997522i	$-0.522415\pi$
$101$	−1.41421	−0.140720	−0.0703598	+	0.997522i	$0.522415\pi$
$102$	− 2.00000i	− 0.198030i
$103$	− 4.82843i	− 0.475759i	−0.971295	−	0.237880i	$-0.923548\pi$
$103$	− 4.82843i	− 0.475759i	0.971295	−	0.237880i	$-0.0764523\pi$
$104$	−3.82843	−0.375408
$105$	0	0
$106$	5.65685	0.549442
$107$	− 16.0711i	− 1.55365i	−0.629717	−	0.776824i	$-0.716829\pi$
$107$	− 16.0711i	− 1.55365i	0.629717	−	0.776824i	$-0.283171\pi$
$108$	5.65685i	0.544331i
$109$	5.17157	0.495347	0.247673	−	0.968844i	$-0.420334\pi$
$109$	5.17157	0.495347	0.247673	+	0.968844i	$0.420334\pi$
$110$	0	0
$111$	8.82843	0.837957
$112$	− 1.00000i	− 0.0944911i
$113$	− 14.8995i	− 1.40163i	−0.713345	−	0.700813i	$-0.752821\pi$
$113$	− 14.8995i	− 1.40163i	0.713345	−	0.700813i	$-0.247179\pi$
$114$	−1.41421	−0.132453
$115$	0	0
$116$	−7.24264	−0.672462
$117$	3.82843i	0.353938i
$118$	− 6.82843i	− 0.628608i
$119$	1.41421	0.129641
$120$	0	0
$121$	0.656854	0.0597140
$122$	14.0711i	1.27393i
$123$	− 5.41421i	− 0.488183i
$124$	−2.41421	−0.216803
$125$	0	0
$126$	−1.00000	−0.0890871
$127$	− 20.4853i	− 1.81777i	−0.417042	−	0.908887i	$-0.636933\pi$
$127$	− 20.4853i	− 1.81777i	0.417042	−	0.908887i	$-0.363067\pi$
$128$	1.00000i	0.0883883i
$129$	1.41421	0.124515
$130$	0	0
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	4.82843i	0.420261i
$133$	− 1.00000i	− 0.0867110i
$134$	−7.24264	−0.625669
$135$	0	0
$136$	−1.41421	−0.121268
$137$	− 18.0711i	− 1.54392i	−0.635674	−	0.771958i	$-0.719278\pi$
$137$	− 18.0711i	− 1.54392i	0.635674	−	0.771958i	$-0.280722\pi$
$138$	− 12.8284i	− 1.09203i
$139$	−2.24264	−0.190218	−0.0951092	−	0.995467i	$-0.530320\pi$
$139$	−2.24264	−0.190218	−0.0951092	+	0.995467i	$0.530320\pi$
$140$	0	0
$141$	10.0000	0.842152
$142$	7.89949i	0.662911i
$143$	13.0711i	1.09306i
$144$	1.00000	0.0833333
$145$	0	0
$146$	−0.757359	−0.0626795
$147$	− 8.48528i	− 0.699854i
$148$	− 6.24264i	− 0.513142i
$149$	−20.5563	−1.68404	−0.842021	−	0.539445i	$-0.818634\pi$
$149$	−20.5563	−1.68404	−0.842021	+	0.539445i	$0.818634\pi$
$150$	0	0
$151$	−6.48528	−0.527765	−0.263882	−	0.964555i	$-0.585003\pi$
$151$	−6.48528	−0.527765	−0.263882	+	0.964555i	$0.585003\pi$
$152$	1.00000i	0.0811107i
$153$	1.41421i	0.114332i
$154$	−3.41421	−0.275125
$155$	0	0
$156$	−5.41421	−0.433484
$157$	− 1.75736i	− 0.140253i	−0.997538	−	0.0701263i	$-0.977660\pi$
$157$	− 1.75736i	− 0.140253i	0.997538	−	0.0701263i	$-0.0223402\pi$
$158$	− 5.58579i	− 0.444381i
$159$	8.00000	0.634441
$160$	0	0
$161$	9.07107	0.714900
$162$	5.00000i	0.392837i
$163$	2.34315i	0.183529i	0.995781	+	0.0917647i	$0.0292508\pi$
$163$	2.34315i	0.183529i	−0.995781	+	0.0917647i	$0.970749\pi$
$164$	−3.82843	−0.298950
$165$	0	0
$166$	−7.65685	−0.594287
$167$	17.5563i	1.35855i	0.733883	+	0.679276i	$0.237706\pi$
$167$	17.5563i	1.35855i	−0.733883	+	0.679276i	$0.762294\pi$
$168$	− 1.41421i	− 0.109109i
$169$	−1.65685	−0.127450
$170$	0	0
$171$	1.00000	0.0764719
$172$	− 1.00000i	− 0.0762493i
$173$	17.4853i	1.32938i	0.747119	+	0.664691i	$0.231437\pi$
$173$	17.4853i	1.32938i	−0.747119	+	0.664691i	$0.768563\pi$
$174$	−10.2426	−0.776493
$175$	0	0
$176$	3.41421	0.257356
$177$	− 9.65685i	− 0.725854i
$178$	5.07107i	0.380093i
$179$	−0.514719	−0.0384719	−0.0192359	−	0.999815i	$-0.506123\pi$
$179$	−0.514719	−0.0384719	−0.0192359	+	0.999815i	$0.506123\pi$
$180$	0	0
$181$	−0.928932	−0.0690470	−0.0345235	−	0.999404i	$-0.510991\pi$
$181$	−0.928932	−0.0690470	−0.0345235	+	0.999404i	$0.510991\pi$
$182$	− 3.82843i	− 0.283782i
$183$	19.8995i	1.47101i
$184$	−9.07107	−0.668728
$185$	0	0
$186$	−3.41421	−0.250342
$187$	4.82843i	0.353090i
$188$	− 7.07107i	− 0.515711i
$189$	−5.65685	−0.411476
$190$	0	0
$191$	0.100505	0.00727229	0.00363615	−	0.999993i	$-0.498843\pi$
$191$	0.100505	0.00727229	0.00363615	+	0.999993i	$0.498843\pi$
$192$	1.41421i	0.102062i
$193$	1.17157i	0.0843317i	0.999111	+	0.0421658i	$0.0134258\pi$
$193$	1.17157i	0.0843317i	−0.999111	+	0.0421658i	$0.986574\pi$
$194$	17.5563	1.26047
$195$	0	0
$196$	−6.00000	−0.428571
$197$	3.14214i	0.223868i	0.993716	+	0.111934i	$0.0357045\pi$
$197$	3.14214i	0.223868i	−0.993716	+	0.111934i	$0.964295\pi$
$198$	− 3.41421i	− 0.242638i
$199$	19.8995	1.41064	0.705319	−	0.708890i	$-0.250804\pi$
$199$	19.8995	1.41064	0.705319	+	0.708890i	$0.250804\pi$
$200$	0	0
$201$	−10.2426	−0.722460
$202$	1.41421i	0.0995037i
$203$	− 7.24264i	− 0.508334i
$204$	−2.00000	−0.140028
$205$	0	0
$206$	−4.82843	−0.336412
$207$	9.07107i	0.630483i
$208$	3.82843i	0.265454i
$209$	3.41421	0.236166
$210$	0	0
$211$	9.65685	0.664805	0.332403	−	0.943138i	$-0.392141\pi$
$211$	9.65685	0.664805	0.332403	+	0.943138i	$0.392141\pi$
$212$	− 5.65685i	− 0.388514i
$213$	11.1716i	0.765464i
$214$	−16.0711	−1.09860
$215$	0	0
$216$	5.65685	0.384900
$217$	− 2.41421i	− 0.163887i
$218$	− 5.17157i	− 0.350263i
$219$	−1.07107	−0.0723761
$220$	0	0
$221$	−5.41421	−0.364199
$222$	− 8.82843i	− 0.592525i
$223$	− 12.1421i	− 0.813098i	−0.913629	−	0.406549i	$-0.866732\pi$
$223$	− 12.1421i	− 0.813098i	0.913629	−	0.406549i	$-0.133268\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	−14.8995	−0.991100
$227$	− 14.8284i	− 0.984197i	−0.870539	−	0.492099i	$-0.836230\pi$
$227$	− 14.8284i	− 0.984197i	0.870539	−	0.492099i	$-0.163770\pi$
$228$	1.41421i	0.0936586i
$229$	4.82843	0.319071	0.159536	−	0.987192i	$-0.449000\pi$
$229$	4.82843	0.319071	0.159536	+	0.987192i	$0.449000\pi$
$230$	0	0
$231$	−4.82843	−0.317687
$232$	7.24264i	0.475503i
$233$	− 8.48528i	− 0.555889i	−0.960597	−	0.277945i	$-0.910347\pi$
$233$	− 8.48528i	− 0.555889i	0.960597	−	0.277945i	$-0.0896532\pi$
$234$	3.82843	0.250272
$235$	0	0
$236$	−6.82843	−0.444493
$237$	− 7.89949i	− 0.513127i
$238$	− 1.41421i	− 0.0916698i
$239$	−14.4142	−0.932378	−0.466189	−	0.884685i	$-0.654373\pi$
$239$	−14.4142	−0.932378	−0.466189	+	0.884685i	$0.654373\pi$
$240$	0	0
$241$	−18.5858	−1.19722	−0.598608	−	0.801042i	$-0.704279\pi$
$241$	−18.5858	−1.19722	−0.598608	+	0.801042i	$0.704279\pi$
$242$	− 0.656854i	− 0.0422242i
$243$	− 9.89949i	− 0.635053i
$244$	14.0711	0.900808
$245$	0	0
$246$	−5.41421	−0.345198
$247$	3.82843i	0.243597i
$248$	2.41421i	0.153303i
$249$	−10.8284	−0.686224
$250$	0	0
$251$	22.9706	1.44989	0.724945	−	0.688807i	$-0.241865\pi$
$251$	22.9706	1.44989	0.724945	+	0.688807i	$0.241865\pi$
$252$	1.00000i	0.0629941i
$253$	30.9706i	1.94710i
$254$	−20.4853	−1.28536
$255$	0	0
$256$	1.00000	0.0625000
$257$	10.8995i	0.679892i	0.940445	+	0.339946i	$0.110409\pi$
$257$	10.8995i	0.679892i	−0.940445	+	0.339946i	$0.889591\pi$
$258$	− 1.41421i	− 0.0880451i
$259$	6.24264	0.387899
$260$	0	0
$261$	7.24264	0.448308
$262$	− 6.00000i	− 0.370681i
$263$	0.514719i	0.0317389i	0.999874	+	0.0158695i	$0.00505162\pi$
$263$	0.514719i	0.0317389i	−0.999874	+	0.0158695i	$0.994948\pi$
$264$	4.82843	0.297169
$265$	0	0
$266$	−1.00000	−0.0613139
$267$	7.17157i	0.438893i
$268$	7.24264i	0.442415i
$269$	−14.8284	−0.904105	−0.452053	−	0.891991i	$-0.649308\pi$
$269$	−14.8284	−0.904105	−0.452053	+	0.891991i	$0.649308\pi$
$270$	0	0
$271$	−10.8995	−0.662097	−0.331049	−	0.943614i	$-0.607402\pi$
$271$	−10.8995	−0.662097	−0.331049	+	0.943614i	$0.607402\pi$
$272$	1.41421i	0.0857493i
$273$	− 5.41421i	− 0.327683i
$274$	−18.0711	−1.09171
$275$	0	0
$276$	−12.8284	−0.772181
$277$	− 16.4853i	− 0.990505i	−0.868749	−	0.495252i	$-0.835076\pi$
$277$	− 16.4853i	− 0.990505i	0.868749	−	0.495252i	$-0.164924\pi$
$278$	2.24264i	0.134505i
$279$	2.41421	0.144535
$280$	0	0
$281$	−12.6569	−0.755045	−0.377522	−	0.926000i	$-0.623224\pi$
$281$	−12.6569	−0.755045	−0.377522	+	0.926000i	$0.623224\pi$
$282$	− 10.0000i	− 0.595491i
$283$	27.2426i	1.61941i	0.586839	+	0.809703i	$0.300372\pi$
$283$	27.2426i	1.61941i	−0.586839	+	0.809703i	$0.699628\pi$
$284$	7.89949	0.468749
$285$	0	0
$286$	13.0711	0.772908
$287$	− 3.82843i	− 0.225985i
$288$	− 1.00000i	− 0.0589256i
$289$	15.0000	0.882353
$290$	0	0
$291$	24.8284	1.45547
$292$	0.757359i	0.0443211i
$293$	− 22.9706i	− 1.34195i	−0.741478	−	0.670977i	$-0.765875\pi$
$293$	− 22.9706i	− 1.34195i	0.741478	−	0.670977i	$-0.234125\pi$
$294$	−8.48528	−0.494872
$295$	0	0
$296$	−6.24264	−0.362846
$297$	− 19.3137i	− 1.12070i
$298$	20.5563i	1.19080i
$299$	−34.7279	−2.00837
$300$	0	0
$301$	1.00000	0.0576390
$302$	6.48528i	0.373186i
$303$	2.00000i	0.114897i
$304$	1.00000	0.0573539
$305$	0	0
$306$	1.41421	0.0808452
$307$	20.0711i	1.14552i	0.819724	+	0.572758i	$0.194127\pi$
$307$	20.0711i	1.14552i	−0.819724	+	0.572758i	$0.805873\pi$
$308$	3.41421i	0.194543i
$309$	−6.82843	−0.388456
$310$	0	0
$311$	10.0711	0.571078	0.285539	−	0.958367i	$-0.407827\pi$
$311$	10.0711	0.571078	0.285539	+	0.958367i	$0.407827\pi$
$312$	5.41421i	0.306519i
$313$	21.3137i	1.20472i	0.798224	+	0.602361i	$0.205773\pi$
$313$	21.3137i	1.20472i	−0.798224	+	0.602361i	$0.794227\pi$
$314$	−1.75736	−0.0991735
$315$	0	0
$316$	−5.58579	−0.314225
$317$	− 29.1421i	− 1.63679i	−0.574659	−	0.818393i	$-0.694865\pi$
$317$	− 29.1421i	− 1.63679i	0.574659	−	0.818393i	$-0.305135\pi$
$318$	− 8.00000i	− 0.448618i
$319$	24.7279	1.38450
$320$	0	0
$321$	−22.7279	−1.26855
$322$	− 9.07107i	− 0.505511i
$323$	1.41421i	0.0786889i
$324$	5.00000	0.277778
$325$	0	0
$326$	2.34315	0.129775
$327$	− 7.31371i	− 0.404449i
$328$	3.82843i	0.211390i
$329$	7.07107	0.389841
$330$	0	0
$331$	−2.68629	−0.147652	−0.0738260	−	0.997271i	$-0.523521\pi$
$331$	−2.68629	−0.147652	−0.0738260	+	0.997271i	$0.523521\pi$
$332$	7.65685i	0.420224i
$333$	6.24264i	0.342095i
$334$	17.5563	0.960641
$335$	0	0
$336$	−1.41421	−0.0771517
$337$	19.6569i	1.07078i	0.844606	+	0.535389i	$0.179835\pi$
$337$	19.6569i	1.07078i	−0.844606	+	0.535389i	$0.820165\pi$
$338$	1.65685i	0.0901210i
$339$	−21.0711	−1.14442
$340$	0	0
$341$	8.24264	0.446364
$342$	− 1.00000i	− 0.0540738i
$343$	− 13.0000i	− 0.701934i
$344$	−1.00000	−0.0539164
$345$	0	0
$346$	17.4853	0.940015
$347$	13.7574i	0.738534i	0.929323	+	0.369267i	$0.120391\pi$
$347$	13.7574i	0.738534i	−0.929323	+	0.369267i	$0.879609\pi$
$348$	10.2426i	0.549063i
$349$	27.4558	1.46968	0.734839	−	0.678242i	$-0.237258\pi$
$349$	27.4558	1.46968	0.734839	+	0.678242i	$0.237258\pi$
$350$	0	0
$351$	21.6569	1.15596
$352$	− 3.41421i	− 0.181978i
$353$	4.38478i	0.233378i	0.993168	+	0.116689i	$0.0372281\pi$
$353$	4.38478i	0.233378i	−0.993168	+	0.116689i	$0.962772\pi$
$354$	−9.65685	−0.513256
$355$	0	0
$356$	5.07107	0.268766
$357$	− 2.00000i	− 0.105851i
$358$	0.514719i	0.0272037i
$359$	37.5269	1.98059	0.990297	−	0.138965i	$-0.0443775\pi$
$359$	37.5269	1.98059	0.990297	+	0.138965i	$0.0443775\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	0.928932i	0.0488236i
$363$	− 0.928932i	− 0.0487563i
$364$	−3.82843	−0.200664
$365$	0	0
$366$	19.8995	1.04016
$367$	8.68629i	0.453421i	0.973962	+	0.226710i	$0.0727971\pi$
$367$	8.68629i	0.453421i	−0.973962	+	0.226710i	$0.927203\pi$
$368$	9.07107i	0.472862i
$369$	3.82843	0.199300
$370$	0	0
$371$	5.65685	0.293689
$372$	3.41421i	0.177019i
$373$	− 10.7279i	− 0.555471i	−0.960658	−	0.277735i	$-0.910416\pi$
$373$	− 10.7279i	− 0.555471i	0.960658	−	0.277735i	$-0.0895838\pi$
$374$	4.82843	0.249672
$375$	0	0
$376$	−7.07107	−0.364662
$377$	27.7279i	1.42806i
$378$	5.65685i	0.290957i
$379$	24.1421	1.24010	0.620049	−	0.784563i	$-0.287113\pi$
$379$	24.1421	1.24010	0.620049	+	0.784563i	$0.287113\pi$
$380$	0	0
$381$	−28.9706	−1.48421
$382$	− 0.100505i	− 0.00514229i
$383$	14.3137i	0.731396i	0.930734	+	0.365698i	$0.119170\pi$
$383$	14.3137i	0.731396i	−0.930734	+	0.365698i	$0.880830\pi$
$384$	1.41421	0.0721688
$385$	0	0
$386$	1.17157	0.0596315
$387$	1.00000i	0.0508329i
$388$	− 17.5563i	− 0.891289i
$389$	−15.1716	−0.769229	−0.384615	−	0.923077i	$-0.625666\pi$
$389$	−15.1716	−0.769229	−0.384615	+	0.923077i	$0.625666\pi$
$390$	0	0
$391$	−12.8284	−0.648761
$392$	6.00000i	0.303046i
$393$	− 8.48528i	− 0.428026i
$394$	3.14214	0.158299
$395$	0	0
$396$	−3.41421	−0.171571
$397$	3.51472i	0.176399i	0.996103	+	0.0881993i	$0.0281112\pi$
$397$	3.51472i	0.176399i	−0.996103	+	0.0881993i	$0.971889\pi$
$398$	− 19.8995i	− 0.997472i
$399$	−1.41421	−0.0707992
$400$	0	0
$401$	38.1127	1.90326	0.951629	−	0.307251i	$-0.0994090\pi$
$401$	38.1127	1.90326	0.951629	+	0.307251i	$0.0994090\pi$
$402$	10.2426i	0.510856i
$403$	9.24264i	0.460409i
$404$	1.41421	0.0703598
$405$	0	0
$406$	−7.24264	−0.359446
$407$	21.3137i	1.05648i
$408$	2.00000i	0.0990148i
$409$	−15.2132	−0.752244	−0.376122	−	0.926570i	$-0.622743\pi$
$409$	−15.2132	−0.752244	−0.376122	+	0.926570i	$0.622743\pi$
$410$	0	0
$411$	−25.5563	−1.26060
$412$	4.82843i	0.237880i
$413$	− 6.82843i	− 0.336005i
$414$	9.07107	0.445819
$415$	0	0
$416$	3.82843	0.187704
$417$	3.17157i	0.155313i
$418$	− 3.41421i	− 0.166995i
$419$	−26.7990	−1.30922	−0.654608	−	0.755968i	$-0.727166\pi$
$419$	−26.7990	−1.30922	−0.654608	+	0.755968i	$0.727166\pi$
$420$	0	0
$421$	−7.24264	−0.352985	−0.176492	−	0.984302i	$-0.556475\pi$
$421$	−7.24264	−0.352985	−0.176492	+	0.984302i	$0.556475\pi$
$422$	− 9.65685i	− 0.470088i
$423$	7.07107i	0.343807i
$424$	−5.65685	−0.274721
$425$	0	0
$426$	11.1716	0.541264
$427$	14.0711i	0.680947i
$428$	16.0711i	0.776824i
$429$	18.4853	0.892478
$430$	0	0
$431$	34.9706	1.68447	0.842236	−	0.539108i	$-0.181239\pi$
$431$	34.9706	1.68447	0.842236	+	0.539108i	$0.181239\pi$
$432$	− 5.65685i	− 0.272166i
$433$	− 21.9289i	− 1.05384i	−0.849916	−	0.526919i	$-0.823347\pi$
$433$	− 21.9289i	− 1.05384i	0.849916	−	0.526919i	$-0.176653\pi$
$434$	−2.41421	−0.115886
$435$	0	0
$436$	−5.17157	−0.247673
$437$	9.07107i	0.433928i
$438$	1.07107i	0.0511776i
$439$	−7.31371	−0.349064	−0.174532	−	0.984651i	$-0.555841\pi$
$439$	−7.31371	−0.349064	−0.174532	+	0.984651i	$0.555841\pi$
$440$	0	0
$441$	6.00000	0.285714
$442$	5.41421i	0.257528i
$443$	− 24.0711i	− 1.14365i	−0.820375	−	0.571825i	$-0.806235\pi$
$443$	− 24.0711i	− 1.14365i	0.820375	−	0.571825i	$-0.193765\pi$
$444$	−8.82843	−0.418979
$445$	0	0
$446$	−12.1421	−0.574947
$447$	29.0711i	1.37501i
$448$	1.00000i	0.0472456i
$449$	−13.7574	−0.649250	−0.324625	−	0.945843i	$-0.605238\pi$
$449$	−13.7574	−0.649250	−0.324625	+	0.945843i	$0.605238\pi$
$450$	0	0
$451$	13.0711	0.615493
$452$	14.8995i	0.700813i
$453$	9.17157i	0.430918i
$454$	−14.8284	−0.695933
$455$	0	0
$456$	1.41421	0.0662266
$457$	13.5147i	0.632192i	0.948727	+	0.316096i	$0.102372\pi$
$457$	13.5147i	0.632192i	−0.948727	+	0.316096i	$0.897628\pi$
$458$	− 4.82843i	− 0.225618i
$459$	8.00000	0.373408
$460$	0	0
$461$	−0.928932	−0.0432647	−0.0216323	−	0.999766i	$-0.506886\pi$
$461$	−0.928932	−0.0432647	−0.0216323	+	0.999766i	$0.506886\pi$
$462$	4.82843i	0.224639i
$463$	7.68629i	0.357212i	0.983921	+	0.178606i	$0.0571588\pi$
$463$	7.68629i	0.357212i	−0.983921	+	0.178606i	$0.942841\pi$
$464$	7.24264	0.336231
$465$	0	0
$466$	−8.48528	−0.393073
$467$	35.0711i	1.62290i	0.584425	+	0.811448i	$0.301320\pi$
$467$	35.0711i	1.62290i	−0.584425	+	0.811448i	$0.698680\pi$
$468$	− 3.82843i	− 0.176969i
$469$	−7.24264	−0.334434
$470$	0	0
$471$	−2.48528	−0.114516
$472$	6.82843i	0.314304i
$473$	3.41421i	0.156986i
$474$	−7.89949	−0.362836
$475$	0	0
$476$	−1.41421	−0.0648204
$477$	5.65685i	0.259010i
$478$	14.4142i	0.659291i
$479$	−14.8284	−0.677528	−0.338764	−	0.940871i	$-0.610009\pi$
$479$	−14.8284	−0.677528	−0.338764	+	0.940871i	$0.610009\pi$
$480$	0	0
$481$	−23.8995	−1.08972
$482$	18.5858i	0.846559i
$483$	− 12.8284i	− 0.583714i
$484$	−0.656854	−0.0298570
$485$	0	0
$486$	−9.89949	−0.449050
$487$	− 9.21320i	− 0.417490i	−0.977970	−	0.208745i	$-0.933062\pi$
$487$	− 9.21320i	− 0.417490i	0.977970	−	0.208745i	$-0.0669379\pi$
$488$	− 14.0711i	− 0.636967i
$489$	3.31371	0.149851
$490$	0	0
$491$	−28.6274	−1.29194	−0.645969	−	0.763364i	$-0.723546\pi$
$491$	−28.6274	−1.29194	−0.645969	+	0.763364i	$0.723546\pi$
$492$	5.41421i	0.244092i
$493$	10.2426i	0.461305i
$494$	3.82843	0.172249
$495$	0	0
$496$	2.41421	0.108401
$497$	7.89949i	0.354341i
$498$	10.8284i	0.485233i
$499$	−16.4558	−0.736665	−0.368332	−	0.929694i	$-0.620071\pi$
$499$	−16.4558	−0.736665	−0.368332	+	0.929694i	$0.620071\pi$
$500$	0	0
$501$	24.8284	1.10925
$502$	− 22.9706i	− 1.02523i
$503$	− 20.3431i	− 0.907056i	−0.891242	−	0.453528i	$-0.850165\pi$
$503$	− 20.3431i	− 0.907056i	0.891242	−	0.453528i	$-0.149835\pi$
$504$	1.00000	0.0445435
$505$	0	0
$506$	30.9706	1.37681
$507$	2.34315i	0.104063i
$508$	20.4853i	0.908887i
$509$	3.51472	0.155787	0.0778936	−	0.996962i	$-0.475181\pi$
$509$	3.51472	0.155787	0.0778936	+	0.996962i	$0.475181\pi$
$510$	0	0
$511$	−0.757359	−0.0335036
$512$	− 1.00000i	− 0.0441942i
$513$	− 5.65685i	− 0.249756i
$514$	10.8995	0.480756
$515$	0	0
$516$	−1.41421	−0.0622573
$517$	24.1421i	1.06177i
$518$	− 6.24264i	− 0.274286i
$519$	24.7279	1.08544
$520$	0	0
$521$	3.07107	0.134546	0.0672730	−	0.997735i	$-0.478570\pi$
$521$	3.07107	0.134546	0.0672730	+	0.997735i	$0.478570\pi$
$522$	− 7.24264i	− 0.317002i
$523$	− 14.7279i	− 0.644007i	−0.946738	−	0.322004i	$-0.895644\pi$
$523$	− 14.7279i	− 0.644007i	0.946738	−	0.322004i	$-0.104356\pi$
$524$	−6.00000	−0.262111
$525$	0	0
$526$	0.514719	0.0224428
$527$	3.41421i	0.148725i
$528$	− 4.82843i	− 0.210130i
$529$	−59.2843	−2.57758
$530$	0	0
$531$	6.82843	0.296328
$532$	1.00000i	0.0433555i
$533$	14.6569i	0.634859i
$534$	7.17157	0.310344
$535$	0	0
$536$	7.24264	0.312834
$537$	0.727922i	0.0314122i
$538$	14.8284i	0.639299i
$539$	20.4853	0.882364
$540$	0	0
$541$	36.1421	1.55387	0.776936	−	0.629580i	$-0.216773\pi$
$541$	36.1421	1.55387	0.776936	+	0.629580i	$0.216773\pi$
$542$	10.8995i	0.468173i
$543$	1.31371i	0.0563766i
$544$	1.41421	0.0606339
$545$	0	0
$546$	−5.41421	−0.231707
$547$	12.0000i	0.513083i	0.966533	+	0.256541i	$0.0825830\pi$
$547$	12.0000i	0.513083i	−0.966533	+	0.256541i	$0.917417\pi$
$548$	18.0711i	0.771958i
$549$	−14.0711	−0.600539
$550$	0	0
$551$	7.24264	0.308547
$552$	12.8284i	0.546014i
$553$	− 5.58579i	− 0.237532i
$554$	−16.4853	−0.700392
$555$	0	0
$556$	2.24264	0.0951092
$557$	− 36.1716i	− 1.53264i	−0.642460	−	0.766319i	$-0.722086\pi$
$557$	− 36.1716i	− 1.53264i	0.642460	−	0.766319i	$-0.277914\pi$
$558$	− 2.41421i	− 0.102202i
$559$	−3.82843	−0.161925
$560$	0	0
$561$	6.82843	0.288296
$562$	12.6569i	0.533897i
$563$	− 16.0711i	− 0.677315i	−0.940910	−	0.338657i	$-0.890027\pi$
$563$	− 16.0711i	− 0.677315i	0.940910	−	0.338657i	$-0.109973\pi$
$564$	−10.0000	−0.421076
$565$	0	0
$566$	27.2426	1.14509
$567$	5.00000i	0.209980i
$568$	− 7.89949i	− 0.331455i
$569$	16.7990	0.704250	0.352125	−	0.935953i	$-0.385459\pi$
$569$	16.7990	0.704250	0.352125	+	0.935953i	$0.385459\pi$
$570$	0	0
$571$	33.0000	1.38101	0.690504	−	0.723329i	$-0.257389\pi$
$571$	33.0000	1.38101	0.690504	+	0.723329i	$0.257389\pi$
$572$	− 13.0711i	− 0.546529i
$573$	− 0.142136i	− 0.00593780i
$574$	−3.82843	−0.159795
$575$	0	0
$576$	−1.00000	−0.0416667
$577$	8.41421i	0.350288i	0.984543	+	0.175144i	$0.0560391\pi$
$577$	8.41421i	0.350288i	−0.984543	+	0.175144i	$0.943961\pi$
$578$	− 15.0000i	− 0.623918i
$579$	1.65685	0.0688565
$580$	0	0
$581$	−7.65685	−0.317660
$582$	− 24.8284i	− 1.02917i
$583$	19.3137i	0.799892i
$584$	0.757359	0.0313398
$585$	0	0
$586$	−22.9706	−0.948905
$587$	− 3.55635i	− 0.146786i	−0.997303	−	0.0733931i	$-0.976617\pi$
$587$	− 3.55635i	− 0.146786i	0.997303	−	0.0733931i	$-0.0233828\pi$
$588$	8.48528i	0.349927i
$589$	2.41421	0.0994759
$590$	0	0
$591$	4.44365	0.182787
$592$	6.24264i	0.256571i
$593$	1.24264i	0.0510291i	0.999674	+	0.0255146i	$0.00812242\pi$
$593$	1.24264i	0.0510291i	−0.999674	+	0.0255146i	$0.991878\pi$
$594$	−19.3137	−0.792451
$595$	0	0
$596$	20.5563	0.842021
$597$	− 28.1421i	− 1.15178i
$598$	34.7279i	1.42013i
$599$	−38.1421	−1.55845	−0.779223	−	0.626747i	$-0.784386\pi$
$599$	−38.1421	−1.55845	−0.779223	+	0.626747i	$0.784386\pi$
$600$	0	0
$601$	−28.0000	−1.14214	−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000	−1.14214	−0.571072	+	0.820900i	$0.693472\pi$
$602$	− 1.00000i	− 0.0407570i
$603$	− 7.24264i	− 0.294943i
$604$	6.48528	0.263882
$605$	0	0
$606$	2.00000	0.0812444
$607$	− 6.00000i	− 0.243532i	−0.992559	−	0.121766i	$-0.961144\pi$
$607$	− 6.00000i	− 0.243532i	0.992559	−	0.121766i	$-0.0388558\pi$
$608$	− 1.00000i	− 0.0405554i
$609$	−10.2426	−0.415053
$610$	0	0
$611$	−27.0711	−1.09518
$612$	− 1.41421i	− 0.0571662i
$613$	43.8284i	1.77021i	0.465388	+	0.885107i	$0.345915\pi$
$613$	43.8284i	1.77021i	−0.465388	+	0.885107i	$0.654085\pi$
$614$	20.0711	0.810002
$615$	0	0
$616$	3.41421	0.137563
$617$	− 40.2843i	− 1.62178i	−0.585196	−	0.810892i	$-0.698982\pi$
$617$	− 40.2843i	− 1.62178i	0.585196	−	0.810892i	$-0.301018\pi$
$618$	6.82843i	0.274680i
$619$	19.8995	0.799828	0.399914	−	0.916553i	$-0.369040\pi$
$619$	19.8995	0.799828	0.399914	+	0.916553i	$0.369040\pi$
$620$	0	0
$621$	51.3137	2.05915
$622$	− 10.0711i	− 0.403813i
$623$	5.07107i	0.203168i
$624$	5.41421	0.216742
$625$	0	0
$626$	21.3137	0.851867
$627$	− 4.82843i	− 0.192829i
$628$	1.75736i	0.0701263i
$629$	−8.82843	−0.352012
$630$	0	0
$631$	45.6985	1.81923	0.909614	−	0.415454i	$-0.136377\pi$
$631$	45.6985	1.81923	0.909614	+	0.415454i	$0.136377\pi$
$632$	5.58579i	0.222191i
$633$	− 13.6569i	− 0.542811i
$634$	−29.1421	−1.15738
$635$	0	0
$636$	−8.00000	−0.317221
$637$	22.9706i	0.910127i
$638$	− 24.7279i	− 0.978988i
$639$	−7.89949	−0.312499
$640$	0	0
$641$	−30.7696	−1.21532	−0.607662	−	0.794196i	$-0.707893\pi$
$641$	−30.7696	−1.21532	−0.607662	+	0.794196i	$0.707893\pi$
$642$	22.7279i	0.897000i
$643$	14.2721i	0.562836i	0.959585	+	0.281418i	$0.0908047\pi$
$643$	14.2721i	0.562836i	−0.959585	+	0.281418i	$0.909195\pi$
$644$	−9.07107	−0.357450
$645$	0	0
$646$	1.41421	0.0556415
$647$	− 44.7990i	− 1.76123i	−0.473832	−	0.880615i	$-0.657130\pi$
$647$	− 44.7990i	− 1.76123i	0.473832	−	0.880615i	$-0.342870\pi$
$648$	− 5.00000i	− 0.196419i
$649$	23.3137	0.915143
$650$	0	0
$651$	−3.41421	−0.133814
$652$	− 2.34315i	− 0.0917647i
$653$	− 9.41421i	− 0.368407i	−0.982888	−	0.184203i	$-0.941030\pi$
$653$	− 9.41421i	− 0.368407i	0.982888	−	0.184203i	$-0.0589705\pi$
$654$	−7.31371	−0.285989
$655$	0	0
$656$	3.82843	0.149475
$657$	− 0.757359i	− 0.0295474i
$658$	− 7.07107i	− 0.275659i
$659$	12.3848	0.482442	0.241221	−	0.970470i	$-0.422452\pi$
$659$	12.3848	0.482442	0.241221	+	0.970470i	$0.422452\pi$
$660$	0	0
$661$	−28.8701	−1.12292	−0.561458	−	0.827506i	$-0.689759\pi$
$661$	−28.8701	−1.12292	−0.561458	+	0.827506i	$0.689759\pi$
$662$	2.68629i	0.104406i
$663$	7.65685i	0.297368i
$664$	7.65685	0.297144
$665$	0	0
$666$	6.24264	0.241897
$667$	65.6985i	2.54386i
$668$	− 17.5563i	− 0.679276i
$669$	−17.1716	−0.663891
$670$	0	0
$671$	−48.0416	−1.85463
$672$	1.41421i	0.0545545i
$673$	17.5858i	0.677882i	0.940808	+	0.338941i	$0.110069\pi$
$673$	17.5858i	0.677882i	−0.940808	+	0.338941i	$0.889931\pi$
$674$	19.6569	0.757154
$675$	0	0
$676$	1.65685	0.0637252
$677$	7.45584i	0.286551i	0.989683	+	0.143276i	$0.0457636\pi$
$677$	7.45584i	0.286551i	−0.989683	+	0.143276i	$0.954236\pi$
$678$	21.0711i	0.809229i
$679$	17.5563	0.673751
$680$	0	0
$681$	−20.9706	−0.803594
$682$	− 8.24264i	− 0.315627i
$683$	− 20.4853i	− 0.783848i	−0.919998	−	0.391924i	$-0.871810\pi$
$683$	− 20.4853i	− 0.783848i	0.919998	−	0.391924i	$-0.128190\pi$
$684$	−1.00000	−0.0382360
$685$	0	0
$686$	−13.0000	−0.496342
$687$	− 6.82843i	− 0.260521i
$688$	1.00000i	0.0381246i
$689$	−21.6569	−0.825060
$690$	0	0
$691$	1.51472	0.0576226	0.0288113	−	0.999585i	$-0.490828\pi$
$691$	1.51472	0.0576226	0.0288113	+	0.999585i	$0.490828\pi$
$692$	− 17.4853i	− 0.664691i
$693$	− 3.41421i	− 0.129695i
$694$	13.7574	0.522222
$695$	0	0
$696$	10.2426	0.388246
$697$	5.41421i	0.205078i
$698$	− 27.4558i	− 1.03922i
$699$	−12.0000	−0.453882
$700$	0	0
$701$	36.7279	1.38719	0.693597	−	0.720363i	$-0.256025\pi$
$701$	36.7279	1.38719	0.693597	+	0.720363i	$0.256025\pi$
$702$	− 21.6569i	− 0.817385i
$703$	6.24264i	0.235446i
$704$	−3.41421	−0.128678
$705$	0	0
$706$	4.38478	0.165023
$707$	1.41421i	0.0531870i
$708$	9.65685i	0.362927i
$709$	−35.2132	−1.32246	−0.661230	−	0.750183i	$-0.729965\pi$
$709$	−35.2132	−1.32246	−0.661230	+	0.750183i	$0.729965\pi$
$710$	0	0
$711$	5.58579	0.209483
$712$	− 5.07107i	− 0.190046i
$713$	21.8995i	0.820143i
$714$	−2.00000	−0.0748481
$715$	0	0
$716$	0.514719	0.0192359
$717$	20.3848i	0.761283i
$718$	− 37.5269i	− 1.40049i
$719$	−8.62742	−0.321748	−0.160874	−	0.986975i	$-0.551431\pi$
$719$	−8.62742	−0.321748	−0.160874	+	0.986975i	$0.551431\pi$
$720$	0	0
$721$	−4.82843	−0.179820
$722$	18.0000i	0.669891i
$723$	26.2843i	0.977523i
$724$	0.928932	0.0345235
$725$	0	0
$726$	−0.928932	−0.0344759
$727$	14.0000i	0.519231i	0.965712	+	0.259616i	$0.0835959\pi$
$727$	14.0000i	0.519231i	−0.965712	+	0.259616i	$0.916404\pi$
$728$	3.82843i	0.141891i
$729$	−29.0000	−1.07407
$730$	0	0
$731$	−1.41421	−0.0523066
$732$	− 19.8995i	− 0.735506i
$733$	36.2426i	1.33865i	0.742969	+	0.669326i	$0.233417\pi$
$733$	36.2426i	1.33865i	−0.742969	+	0.669326i	$0.766583\pi$
$734$	8.68629	0.320617
$735$	0	0
$736$	9.07107	0.334364
$737$	− 24.7279i	− 0.910865i
$738$	− 3.82843i	− 0.140926i
$739$	−41.9706	−1.54391	−0.771956	−	0.635676i	$-0.780721\pi$
$739$	−41.9706	−1.54391	−0.771956	+	0.635676i	$0.780721\pi$
$740$	0	0
$741$	5.41421	0.198896
$742$	− 5.65685i	− 0.207670i
$743$	− 20.3137i	− 0.745238i	−0.927984	−	0.372619i	$-0.878460\pi$
$743$	− 20.3137i	− 0.745238i	0.927984	−	0.372619i	$-0.121540\pi$
$744$	3.41421	0.125171
$745$	0	0
$746$	−10.7279	−0.392777
$747$	− 7.65685i	− 0.280150i
$748$	− 4.82843i	− 0.176545i
$749$	−16.0711	−0.587224
$750$	0	0
$751$	16.7279	0.610411	0.305205	−	0.952287i	$-0.401275\pi$
$751$	16.7279	0.610411	0.305205	+	0.952287i	$0.401275\pi$
$752$	7.07107i	0.257855i
$753$	− 32.4853i	− 1.18383i
$754$	27.7279	1.00979
$755$	0	0
$756$	5.65685	0.205738
$757$	48.4264i	1.76009i	0.474892	+	0.880044i	$0.342487\pi$
$757$	48.4264i	1.76009i	−0.474892	+	0.880044i	$0.657513\pi$
$758$	− 24.1421i	− 0.876882i
$759$	43.7990	1.58980
$760$	0	0
$761$	−39.1716	−1.41997	−0.709984	−	0.704218i	$-0.751298\pi$
$761$	−39.1716	−1.41997	−0.709984	+	0.704218i	$0.751298\pi$
$762$	28.9706i	1.04949i
$763$	− 5.17157i	− 0.187224i
$764$	−0.100505	−0.00363615
$765$	0	0
$766$	14.3137	0.517175
$767$	26.1421i	0.943938i
$768$	− 1.41421i	− 0.0510310i
$769$	−21.0000	−0.757279	−0.378640	−	0.925544i	$-0.623608\pi$
$769$	−21.0000	−0.757279	−0.378640	+	0.925544i	$0.623608\pi$
$770$	0	0
$771$	15.4142	0.555129
$772$	− 1.17157i	− 0.0421658i
$773$	− 10.9289i	− 0.393086i	−0.980495	−	0.196543i	$-0.937028\pi$
$773$	− 10.9289i	− 0.393086i	0.980495	−	0.196543i	$-0.0629716\pi$
$774$	1.00000	0.0359443
$775$	0	0
$776$	−17.5563	−0.630236
$777$	− 8.82843i	− 0.316718i
$778$	15.1716i	0.543927i
$779$	3.82843	0.137168
$780$	0	0
$781$	−26.9706	−0.965083
$782$	12.8284i	0.458744i
$783$	− 40.9706i	− 1.46417i
$784$	6.00000	0.214286
$785$	0	0
$786$	−8.48528	−0.302660
$787$	− 22.7574i	− 0.811212i	−0.914048	−	0.405606i	$-0.867060\pi$
$787$	− 22.7574i	− 0.811212i	0.914048	−	0.405606i	$-0.132940\pi$
$788$	− 3.14214i	− 0.111934i
$789$	0.727922	0.0259147
$790$	0	0
$791$	−14.8995	−0.529765
$792$	3.41421i	0.121319i
$793$	− 53.8701i	− 1.91298i
$794$	3.51472	0.124733
$795$	0	0
$796$	−19.8995	−0.705319
$797$	− 24.9411i	− 0.883460i	−0.897148	−	0.441730i	$-0.854365\pi$
$797$	− 24.9411i	− 0.883460i	0.897148	−	0.441730i	$-0.145635\pi$
$798$	1.41421i	0.0500626i
$799$	−10.0000	−0.353775
$800$	0	0
$801$	−5.07107	−0.179177
$802$	− 38.1127i	− 1.34581i
$803$	− 2.58579i	− 0.0912504i
$804$	10.2426	0.361230
$805$	0	0
$806$	9.24264	0.325558
$807$	20.9706i	0.738199i
$808$	− 1.41421i	− 0.0497519i
$809$	−10.7990	−0.379672	−0.189836	−	0.981816i	$-0.560796\pi$
$809$	−10.7990	−0.379672	−0.189836	+	0.981816i	$0.560796\pi$
$810$	0	0
$811$	14.1127	0.495564	0.247782	−	0.968816i	$-0.420298\pi$
$811$	14.1127	0.495564	0.247782	+	0.968816i	$0.420298\pi$
$812$	7.24264i	0.254167i
$813$	15.4142i	0.540600i
$814$	21.3137	0.747045
$815$	0	0
$816$	2.00000	0.0700140
$817$	1.00000i	0.0349856i
$818$	15.2132i	0.531917i
$819$	3.82843	0.133776
$820$	0	0
$821$	8.14214	0.284162	0.142081	−	0.989855i	$-0.454621\pi$
$821$	8.14214	0.284162	0.142081	+	0.989855i	$0.454621\pi$
$822$	25.5563i	0.891380i
$823$	30.4853i	1.06265i	0.847168	+	0.531325i	$0.178306\pi$
$823$	30.4853i	1.06265i	−0.847168	+	0.531325i	$0.821694\pi$
$824$	4.82843	0.168206
$825$	0	0
$826$	−6.82843	−0.237591
$827$	− 21.5269i	− 0.748564i	−0.927315	−	0.374282i	$-0.877889\pi$
$827$	− 21.5269i	− 0.748564i	0.927315	−	0.374282i	$-0.122111\pi$
$828$	− 9.07107i	− 0.315241i
$829$	5.24264	0.182084	0.0910422	−	0.995847i	$-0.470980\pi$
$829$	5.24264	0.182084	0.0910422	+	0.995847i	$0.470980\pi$
$830$	0	0
$831$	−23.3137	−0.808744
$832$	− 3.82843i	− 0.132727i
$833$	8.48528i	0.293998i
$834$	3.17157	0.109823
$835$	0	0
$836$	−3.41421	−0.118083
$837$	− 13.6569i	− 0.472050i
$838$	26.7990i	0.925756i
$839$	−31.0122	−1.07066	−0.535330	−	0.844643i	$-0.679813\pi$
$839$	−31.0122	−1.07066	−0.535330	+	0.844643i	$0.679813\pi$
$840$	0	0
$841$	23.4558	0.808822
$842$	7.24264i	0.249598i
$843$	17.8995i	0.616491i
$844$	−9.65685	−0.332403
$845$	0	0
$846$	7.07107	0.243108
$847$	− 0.656854i	− 0.0225698i
$848$	5.65685i	0.194257i
$849$	38.5269	1.32224
$850$	0	0
$851$	−56.6274	−1.94116
$852$	− 11.1716i	− 0.382732i
$853$	31.9411i	1.09364i	0.837249	+	0.546822i	$0.184162\pi$
$853$	31.9411i	1.09364i	−0.837249	+	0.546822i	$0.815838\pi$
$854$	14.0711	0.481502
$855$	0	0
$856$	16.0711	0.549298
$857$	− 32.9289i	− 1.12483i	−0.826855	−	0.562415i	$-0.809872\pi$
$857$	− 32.9289i	− 1.12483i	0.826855	−	0.562415i	$-0.190128\pi$
$858$	− 18.4853i	− 0.631077i
$859$	33.4853	1.14250	0.571252	−	0.820775i	$-0.306458\pi$
$859$	33.4853	1.14250	0.571252	+	0.820775i	$0.306458\pi$
$860$	0	0
$861$	−5.41421	−0.184516
$862$	− 34.9706i	− 1.19110i
$863$	− 35.1716i	− 1.19725i	−0.801028	−	0.598627i	$-0.795713\pi$
$863$	− 35.1716i	− 1.19725i	0.801028	−	0.598627i	$-0.204287\pi$
$864$	−5.65685	−0.192450
$865$	0	0
$866$	−21.9289	−0.745175
$867$	− 21.2132i	− 0.720438i
$868$	2.41421i	0.0819437i
$869$	19.0711	0.646942
$870$	0	0
$871$	27.7279	0.939525
$872$	5.17157i	0.175132i
$873$	17.5563i	0.594192i
$874$	9.07107	0.306833
$875$	0	0
$876$	1.07107	0.0361880
$877$	− 26.6274i	− 0.899144i	−0.893244	−	0.449572i	$-0.851577\pi$
$877$	− 26.6274i	− 0.899144i	0.893244	−	0.449572i	$-0.148423\pi$
$878$	7.31371i	0.246826i
$879$	−32.4853	−1.09570
$880$	0	0
$881$	−40.7990	−1.37455	−0.687276	−	0.726396i	$-0.741194\pi$
$881$	−40.7990	−1.37455	−0.687276	+	0.726396i	$0.741194\pi$
$882$	− 6.00000i	− 0.202031i
$883$	− 16.2132i	− 0.545618i	−0.962068	−	0.272809i	$-0.912047\pi$
$883$	− 16.2132i	− 0.545618i	0.962068	−	0.272809i	$-0.0879527\pi$
$884$	5.41421	0.182100
$885$	0	0
$886$	−24.0711	−0.808683
$887$	− 6.11270i	− 0.205244i	−0.994720	−	0.102622i	$-0.967277\pi$
$887$	− 6.11270i	− 0.205244i	0.994720	−	0.102622i	$-0.0327233\pi$
$888$	8.82843i	0.296263i
$889$	−20.4853	−0.687054
$890$	0	0
$891$	−17.0711	−0.571902
$892$	12.1421i	0.406549i
$893$	7.07107i	0.236624i
$894$	29.0711	0.972282
$895$	0	0
$896$	1.00000	0.0334077
$897$	49.1127i	1.63983i
$898$	13.7574i	0.459089i
$899$	17.4853	0.583167
$900$	0	0
$901$	−8.00000	−0.266519
$902$	− 13.0711i	− 0.435219i
$903$	− 1.41421i	− 0.0470621i
$904$	14.8995	0.495550
$905$	0	0
$906$	9.17157	0.304705
$907$	4.89949i	0.162685i	0.996686	+	0.0813425i	$0.0259208\pi$
$907$	4.89949i	0.162685i	−0.996686	+	0.0813425i	$0.974079\pi$
$908$	14.8284i	0.492099i
$909$	−1.41421	−0.0469065
$910$	0	0
$911$	16.3848	0.542852	0.271426	−	0.962459i	$-0.412505\pi$
$911$	16.3848	0.542852	0.271426	+	0.962459i	$0.412505\pi$
$912$	− 1.41421i	− 0.0468293i
$913$	− 26.1421i	− 0.865178i
$914$	13.5147	0.447027
$915$	0	0
$916$	−4.82843	−0.159536
$917$	− 6.00000i	− 0.198137i
$918$	− 8.00000i	− 0.264039i
$919$	15.1005	0.498120	0.249060	−	0.968488i	$-0.419878\pi$
$919$	15.1005	0.498120	0.249060	+	0.968488i	$0.419878\pi$
$920$	0	0
$921$	28.3848	0.935310
$922$	0.928932i	0.0305928i
$923$	− 30.2426i	− 0.995449i
$924$	4.82843	0.158844
$925$	0	0
$926$	7.68629	0.252587
$927$	− 4.82843i	− 0.158586i
$928$	− 7.24264i	− 0.237751i
$929$	−25.7990	−0.846437	−0.423219	−	0.906028i	$-0.639100\pi$
$929$	−25.7990	−0.846437	−0.423219	+	0.906028i	$0.639100\pi$
$930$	0	0
$931$	6.00000	0.196642
$932$	8.48528i	0.277945i
$933$	− 14.2426i	− 0.466283i
$934$	35.0711	1.14756
$935$	0	0
$936$	−3.82843	−0.125136
$937$	− 50.4264i	− 1.64736i	−0.567056	−	0.823679i	$-0.691918\pi$
$937$	− 50.4264i	− 1.64736i	0.567056	−	0.823679i	$-0.308082\pi$
$938$	7.24264i	0.236481i
$939$	30.1421	0.983651
$940$	0	0
$941$	−38.9289	−1.26905	−0.634523	−	0.772904i	$-0.718804\pi$
$941$	−38.9289	−1.26905	−0.634523	+	0.772904i	$0.718804\pi$
$942$	2.48528i	0.0809748i
$943$	34.7279i	1.13090i
$944$	6.82843	0.222246
$945$	0	0
$946$	3.41421	0.111006
$947$	17.1838i	0.558397i	0.960233	+	0.279199i	$0.0900688\pi$
$947$	17.1838i	0.558397i	−0.960233	+	0.279199i	$0.909931\pi$
$948$	7.89949i	0.256564i
$949$	2.89949	0.0941216
$950$	0	0
$951$	−41.2132	−1.33643
$952$	1.41421i	0.0458349i
$953$	− 28.8995i	− 0.936146i	−0.883690	−	0.468073i	$-0.844948\pi$
$953$	− 28.8995i	− 0.936146i	0.883690	−	0.468073i	$-0.155052\pi$
$954$	5.65685	0.183147
$955$	0	0
$956$	14.4142	0.466189
$957$	− 34.9706i	− 1.13044i
$958$	14.8284i	0.479085i
$959$	−18.0711	−0.583545
$960$	0	0
$961$	−25.1716	−0.811986
$962$	23.8995i	0.770551i
$963$	− 16.0711i	− 0.517883i
$964$	18.5858	0.598608
$965$	0	0
$966$	−12.8284	−0.412748
$967$	− 27.7574i	− 0.892616i	−0.894879	−	0.446308i	$-0.852738\pi$
$967$	− 27.7574i	− 0.892616i	0.894879	−	0.446308i	$-0.147262\pi$
$968$	0.656854i	0.0211121i
$969$	2.00000	0.0642493
$970$	0	0
$971$	6.92893	0.222360	0.111180	−	0.993800i	$-0.464537\pi$
$971$	6.92893	0.222360	0.111180	+	0.993800i	$0.464537\pi$
$972$	9.89949i	0.317526i
$973$	2.24264i	0.0718958i
$974$	−9.21320	−0.295210
$975$	0	0
$976$	−14.0711	−0.450404
$977$	2.92893i	0.0937048i	0.998902	+	0.0468524i	$0.0149191\pi$
$977$	2.92893i	0.0937048i	−0.998902	+	0.0468524i	$0.985081\pi$
$978$	− 3.31371i	− 0.105961i
$979$	−17.3137	−0.553349
$980$	0	0
$981$	5.17157	0.165116
$982$	28.6274i	0.913538i
$983$	− 38.6569i	− 1.23296i	−0.787370	−	0.616481i	$-0.788558\pi$
$983$	− 38.6569i	− 1.23296i	0.787370	−	0.616481i	$-0.211442\pi$
$984$	5.41421	0.172599
$985$	0	0
$986$	10.2426	0.326192
$987$	− 10.0000i	− 0.318304i
$988$	− 3.82843i	− 0.121798i
$989$	−9.07107	−0.288443
$990$	0	0
$991$	−49.2548	−1.56463	−0.782316	−	0.622882i	$-0.785962\pi$
$991$	−49.2548	−1.56463	−0.782316	+	0.622882i	$0.785962\pi$
$992$	− 2.41421i	− 0.0766514i
$993$	3.79899i	0.120557i
$994$	7.89949	0.250557
$995$	0	0
$996$	10.8284	0.343112
$997$	− 42.8284i	− 1.35639i	−0.734882	−	0.678195i	$-0.762762\pi$
$997$	− 42.8284i	− 1.35639i	0.734882	−	0.678195i	$-0.237238\pi$
$998$	16.4558i	0.520901i
$999$	35.3137	1.11728

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2150.2.b.o.1549.1		4
5.2	odd	4		430.2.a.g.1.1	✓	2
5.3	odd	4		2150.2.a.v.1.2		2
5.4	even	2	inner	2150.2.b.o.1549.4		4
15.2	even	4		3870.2.a.bc.1.1		2
20.7	even	4		3440.2.a.j.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.a.g.1.1	✓	2	5.2	odd	4
2150.2.a.v.1.2		2	5.3	odd	4
2150.2.b.o.1549.1		4	1.1	even	1	trivial
2150.2.b.o.1549.4		4	5.4	even	2	inner
3440.2.a.j.1.2		2	20.7	even	4
3870.2.a.bc.1.1		2	15.2	even	4

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:	\( N \)	\(=\)	\( 2150 = 2 \cdot 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2150.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.41421i q^{3} -1.00000 q^{4} -1.41421 q^{6} -1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.41421i q^{3} -1.00000 q^{4} -1.41421 q^{6} -1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{9} +3.41421 q^{11} +1.41421i q^{12} +3.82843i q^{13} -1.00000 q^{14} +1.00000 q^{16} +1.41421i q^{17} -1.00000i q^{18} +1.00000 q^{19} -1.41421 q^{21} -3.41421i q^{22} +9.07107i q^{23} +1.41421 q^{24} +3.82843 q^{26} -5.65685i q^{27} +1.00000i q^{28} +7.24264 q^{29} +2.41421 q^{31} -1.00000i q^{32} -4.82843i q^{33} +1.41421 q^{34} -1.00000 q^{36} +6.24264i q^{37} -1.00000i q^{38} +5.41421 q^{39} +3.82843 q^{41} +1.41421i q^{42} +1.00000i q^{43} -3.41421 q^{44} +9.07107 q^{46} +7.07107i q^{47} -1.41421i q^{48} +6.00000 q^{49} +2.00000 q^{51} -3.82843i q^{52} +5.65685i q^{53} -5.65685 q^{54} +1.00000 q^{56} -1.41421i q^{57} -7.24264i q^{58} +6.82843 q^{59} -14.0711 q^{61} -2.41421i q^{62} -1.00000i q^{63} -1.00000 q^{64} -4.82843 q^{66} -7.24264i q^{67} -1.41421i q^{68} +12.8284 q^{69} -7.89949 q^{71} +1.00000i q^{72} -0.757359i q^{73} +6.24264 q^{74} -1.00000 q^{76} -3.41421i q^{77} -5.41421i q^{78} +5.58579 q^{79} -5.00000 q^{81} -3.82843i q^{82} -7.65685i q^{83} +1.41421 q^{84} +1.00000 q^{86} -10.2426i q^{87} +3.41421i q^{88} -5.07107 q^{89} +3.82843 q^{91} -9.07107i q^{92} -3.41421i q^{93} +7.07107 q^{94} -1.41421 q^{96} +17.5563i q^{97} -6.00000i q^{98} +3.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^9	\( 4 q - 4 q^{4} + 4 q^{9} + 8 q^{11} - 4 q^{14} + 4 q^{16} + 4 q^{19} + 4 q^{26} + 12 q^{29} + 4 q^{31} - 4 q^{36} + 16 q^{39} + 4 q^{41} - 8 q^{44} + 8 q^{46} + 24 q^{49} + 8 q^{51} + 4 q^{56} + 16 q^{59} - 28 q^{61} - 4 q^{64} - 8 q^{66} + 40 q^{69} + 8 q^{71} + 8 q^{74} - 4 q^{76} + 28 q^{79} - 20 q^{81} + 4 q^{86} + 8 q^{89} + 4 q^{91} + 8 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^9 + 8 * q^11 - 4 * q^14 + 4 * q^16 + 4 * q^19 + 4 * q^26 + 12 * q^29 + 4 * q^31 - 4 * q^36 + 16 * q^39 + 4 * q^41 - 8 * q^44 + 8 * q^46 + 24 * q^49 + 8 * q^51 + 4 * q^56 + 16 * q^59 - 28 * q^61 - 4 * q^64 - 8 * q^66 + 40 * q^69 + 8 * q^71 + 8 * q^74 - 4 * q^76 + 28 * q^79 - 20 * q^81 + 4 * q^86 + 8 * q^89 + 4 * q^91 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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