LMFDB - Embedded newform 3450.2.d.l.2899.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3450,2,Mod(2899,3450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3450, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3450.2899");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3450.d (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:	$27.5483886973$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2899.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	3450.2899
Dual form			3450.2.d.l.2899.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +5.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +5.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} -3.00000 q^{11} +1.00000i q^{12} -5.00000i q^{13} -5.00000 q^{14} +1.00000 q^{16} +6.00000i q^{17} -1.00000i q^{18} +1.00000 q^{19} +5.00000 q^{21} -3.00000i q^{22} -1.00000i q^{23} -1.00000 q^{24} +5.00000 q^{26} +1.00000i q^{27} -5.00000i q^{28} +5.00000 q^{29} -8.00000 q^{31} +1.00000i q^{32} +3.00000i q^{33} -6.00000 q^{34} +1.00000 q^{36} +4.00000i q^{37} +1.00000i q^{38} -5.00000 q^{39} -7.00000 q^{41} +5.00000i q^{42} +7.00000i q^{43} +3.00000 q^{44} +1.00000 q^{46} -6.00000i q^{47} -1.00000i q^{48} -18.0000 q^{49} +6.00000 q^{51} +5.00000i q^{52} -8.00000i q^{53} -1.00000 q^{54} +5.00000 q^{56} -1.00000i q^{57} +5.00000i q^{58} +10.0000 q^{59} -12.0000 q^{61} -8.00000i q^{62} -5.00000i q^{63} -1.00000 q^{64} -3.00000 q^{66} -12.0000i q^{67} -6.00000i q^{68} -1.00000 q^{69} +10.0000 q^{71} +1.00000i q^{72} -15.0000i q^{73} -4.00000 q^{74} -1.00000 q^{76} -15.0000i q^{77} -5.00000i q^{78} +5.00000 q^{79} +1.00000 q^{81} -7.00000i q^{82} +9.00000i q^{83} -5.00000 q^{84} -7.00000 q^{86} -5.00000i q^{87} +3.00000i q^{88} -14.0000 q^{89} +25.0000 q^{91} +1.00000i q^{92} +8.00000i q^{93} +6.00000 q^{94} +1.00000 q^{96} +16.0000i q^{97} -18.0000i q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 2 q^{6} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 + 2 * q^6 - 2 * q^9	$ 2 q - 2 q^{4} + 2 q^{6} - 2 q^{9} - 6 q^{11} - 10 q^{14} + 2 q^{16} + 2 q^{19} + 10 q^{21} - 2 q^{24} + 10 q^{26} + 10 q^{29} - 16 q^{31} - 12 q^{34} + 2 q^{36} - 10 q^{39} - 14 q^{41} + 6 q^{44} + 2 q^{46} - 36 q^{49} + 12 q^{51} - 2 q^{54} + 10 q^{56} + 20 q^{59} - 24 q^{61} - 2 q^{64} - 6 q^{66} - 2 q^{69} + 20 q^{71} - 8 q^{74} - 2 q^{76} + 10 q^{79} + 2 q^{81} - 10 q^{84} - 14 q^{86} - 28 q^{89} + 50 q^{91} + 12 q^{94} + 2 q^{96} + 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 + 2 * q^6 - 2 * q^9 - 6 * q^11 - 10 * q^14 + 2 * q^16 + 2 * q^19 + 10 * q^21 - 2 * q^24 + 10 * q^26 + 10 * q^29 - 16 * q^31 - 12 * q^34 + 2 * q^36 - 10 * q^39 - 14 * q^41 + 6 * q^44 + 2 * q^46 - 36 * q^49 + 12 * q^51 - 2 * q^54 + 10 * q^56 + 20 * q^59 - 24 * q^61 - 2 * q^64 - 6 * q^66 - 2 * q^69 + 20 * q^71 - 8 * q^74 - 2 * q^76 + 10 * q^79 + 2 * q^81 - 10 * q^84 - 14 * q^86 - 28 * q^89 + 50 * q^91 + 12 * q^94 + 2 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3450\mathbb{Z}\right)^\times$.

$n$	$277$	$1151$	$1201$
$\chi(n)$	$-1$	$1$	$1$

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
$3$	− 1.00000i	− 0.577350i
$3$	− 1.00000i	− 0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	5.00000i	1.88982i	0.327327	+	0.944911i	$0.393852\pi$
$7$	5.00000i	1.88982i	−0.327327	+	0.944911i	$0.606148\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	1.00000i	0.288675i
$13$	− 5.00000i	− 1.38675i	−0.720577	−	0.693375i	$-0.756123\pi$
$13$	− 5.00000i	− 1.38675i	0.720577	−	0.693375i	$-0.243877\pi$
$14$	−5.00000	−1.33631
$15$	0	0
$16$	1.00000	0.250000
$17$	6.00000i	1.45521i	0.685994	+	0.727607i	$0.259367\pi$
$17$	6.00000i	1.45521i	−0.685994	+	0.727607i	$0.740633\pi$
$18$	− 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
$21$	5.00000	1.09109
$22$	− 3.00000i	− 0.639602i
$23$	− 1.00000i	− 0.208514i
$23$	− 1.00000i	− 0.208514i
$24$	−1.00000	−0.204124
$25$	0	0
$26$	5.00000	0.980581
$27$	1.00000i	0.192450i
$28$	− 5.00000i	− 0.944911i
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	0	0
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	1.00000i	0.176777i
$33$	3.00000i	0.522233i
$34$	−6.00000	−1.02899
$35$	0	0
$36$	1.00000	0.166667
$37$	4.00000i	0.657596i	0.944400	+	0.328798i	$0.106644\pi$
$37$	4.00000i	0.657596i	−0.944400	+	0.328798i	$0.893356\pi$
$38$	1.00000i	0.162221i
$39$	−5.00000	−0.800641
$40$	0	0
$41$	−7.00000	−1.09322	−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000	−1.09322	−0.546608	+	0.837389i	$0.684081\pi$
$42$	5.00000i	0.771517i
$43$	7.00000i	1.06749i	0.845645	+	0.533745i	$0.179216\pi$
$43$	7.00000i	1.06749i	−0.845645	+	0.533745i	$0.820784\pi$
$44$	3.00000	0.452267
$45$	0	0
$46$	1.00000	0.147442
$47$	− 6.00000i	− 0.875190i	−0.899172	−	0.437595i	$-0.855830\pi$
$47$	− 6.00000i	− 0.875190i	0.899172	−	0.437595i	$-0.144170\pi$
$48$	− 1.00000i	− 0.144338i
$49$	−18.0000	−2.57143
$50$	0	0
$51$	6.00000	0.840168
$52$	5.00000i	0.693375i
$53$	− 8.00000i	− 1.09888i	−0.835532	−	0.549442i	$-0.814840\pi$
$53$	− 8.00000i	− 1.09888i	0.835532	−	0.549442i	$-0.185160\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	5.00000	0.668153
$57$	− 1.00000i	− 0.132453i
$58$	5.00000i	0.656532i
$59$	10.0000	1.30189	0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000	1.30189	0.650945	+	0.759125i	$0.274373\pi$
$60$	0	0
$61$	−12.0000	−1.53644	−0.768221	−	0.640184i	$-0.778858\pi$
$61$	−12.0000	−1.53644	−0.768221	+	0.640184i	$0.778858\pi$
$62$	− 8.00000i	− 1.01600i
$63$	− 5.00000i	− 0.629941i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−3.00000	−0.369274
$67$	− 12.0000i	− 1.46603i	−0.680211	−	0.733017i	$-0.738112\pi$
$67$	− 12.0000i	− 1.46603i	0.680211	−	0.733017i	$-0.261888\pi$
$68$	− 6.00000i	− 0.727607i
$69$	−1.00000	−0.120386
$70$	0	0
$71$	10.0000	1.18678	0.593391	−	0.804914i	$-0.297789\pi$
$71$	10.0000	1.18678	0.593391	+	0.804914i	$0.297789\pi$
$72$	1.00000i	0.117851i
$73$	− 15.0000i	− 1.75562i	−0.479012	−	0.877809i	$-0.659005\pi$
$73$	− 15.0000i	− 1.75562i	0.479012	−	0.877809i	$-0.340995\pi$
$74$	−4.00000	−0.464991
$75$	0	0
$76$	−1.00000	−0.114708
$77$	− 15.0000i	− 1.70941i
$78$	− 5.00000i	− 0.566139i
$79$	5.00000	0.562544	0.281272	−	0.959628i	$-0.409244\pi$
$79$	5.00000	0.562544	0.281272	+	0.959628i	$0.409244\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 7.00000i	− 0.773021i
$83$	9.00000i	0.987878i	0.869496	+	0.493939i	$0.164443\pi$
$83$	9.00000i	0.987878i	−0.869496	+	0.493939i	$0.835557\pi$
$84$	−5.00000	−0.545545
$85$	0	0
$86$	−7.00000	−0.754829
$87$	− 5.00000i	− 0.536056i
$88$	3.00000i	0.319801i
$89$	−14.0000	−1.48400	−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000	−1.48400	−0.741999	+	0.670402i	$0.766122\pi$
$90$	0	0
$91$	25.0000	2.62071
$92$	1.00000i	0.104257i
$93$	8.00000i	0.829561i
$94$	6.00000	0.618853
$95$	0	0
$96$	1.00000	0.102062
$97$	16.0000i	1.62455i	0.583272	+	0.812277i	$0.301772\pi$
$97$	16.0000i	1.62455i	−0.583272	+	0.812277i	$0.698228\pi$
$98$	− 18.0000i	− 1.81827i
$99$	3.00000	0.301511
$100$	0	0
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	6.00000i	0.594089i
$103$	− 19.0000i	− 1.87213i	−0.351833	−	0.936063i	$-0.614441\pi$
$103$	− 19.0000i	− 1.87213i	0.351833	−	0.936063i	$-0.385559\pi$
$104$	−5.00000	−0.490290
$105$	0	0
$106$	8.00000	0.777029
$107$	− 12.0000i	− 1.16008i	−0.814587	−	0.580042i	$-0.803036\pi$
$107$	− 12.0000i	− 1.16008i	0.814587	−	0.580042i	$-0.196964\pi$
$108$	− 1.00000i	− 0.0962250i
$109$	−12.0000	−1.14939	−0.574696	−	0.818367i	$-0.694880\pi$
$109$	−12.0000	−1.14939	−0.574696	+	0.818367i	$0.694880\pi$
$110$	0	0
$111$	4.00000	0.379663
$112$	5.00000i	0.472456i
$113$	10.0000i	0.940721i	0.882474	+	0.470360i	$0.155876\pi$
$113$	10.0000i	0.940721i	−0.882474	+	0.470360i	$0.844124\pi$
$114$	1.00000	0.0936586
$115$	0	0
$116$	−5.00000	−0.464238
$117$	5.00000i	0.462250i
$118$	10.0000i	0.920575i
$119$	−30.0000	−2.75010
$120$	0	0
$121$	−2.00000	−0.181818
$122$	− 12.0000i	− 1.08643i
$123$	7.00000i	0.631169i
$124$	8.00000	0.718421
$125$	0	0
$126$	5.00000	0.445435
$127$	6.00000i	0.532414i	0.963916	+	0.266207i	$0.0857705\pi$
$127$	6.00000i	0.532414i	−0.963916	+	0.266207i	$0.914230\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	7.00000	0.616316
$130$	0	0
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	− 3.00000i	− 0.261116i
$133$	5.00000i	0.433555i
$134$	12.0000	1.03664
$135$	0	0
$136$	6.00000	0.514496
$137$	− 8.00000i	− 0.683486i	−0.939793	−	0.341743i	$-0.888983\pi$
$137$	− 8.00000i	− 0.683486i	0.939793	−	0.341743i	$-0.111017\pi$
$138$	− 1.00000i	− 0.0851257i
$139$	−2.00000	−0.169638	−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000	−0.169638	−0.0848189	+	0.996396i	$0.527031\pi$
$140$	0	0
$141$	−6.00000	−0.505291
$142$	10.0000i	0.839181i
$143$	15.0000i	1.25436i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	15.0000	1.24141
$147$	18.0000i	1.48461i
$148$	− 4.00000i	− 0.328798i
$149$	20.0000	1.63846	0.819232	−	0.573462i	$-0.194400\pi$
$149$	20.0000	1.63846	0.819232	+	0.573462i	$0.194400\pi$
$150$	0	0
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	− 1.00000i	− 0.0811107i
$153$	− 6.00000i	− 0.485071i
$154$	15.0000	1.20873
$155$	0	0
$156$	5.00000	0.400320
$157$	4.00000i	0.319235i	0.987179	+	0.159617i	$0.0510260\pi$
$157$	4.00000i	0.319235i	−0.987179	+	0.159617i	$0.948974\pi$
$158$	5.00000i	0.397779i
$159$	−8.00000	−0.634441
$160$	0	0
$161$	5.00000	0.394055
$162$	1.00000i	0.0785674i
$163$	− 12.0000i	− 0.939913i	−0.882690	−	0.469956i	$-0.844270\pi$
$163$	− 12.0000i	− 0.939913i	0.882690	−	0.469956i	$-0.155730\pi$
$164$	7.00000	0.546608
$165$	0	0
$166$	−9.00000	−0.698535
$167$	− 12.0000i	− 0.928588i	−0.885681	−	0.464294i	$-0.846308\pi$
$167$	− 12.0000i	− 0.928588i	0.885681	−	0.464294i	$-0.153692\pi$
$168$	− 5.00000i	− 0.385758i
$169$	−12.0000	−0.923077
$170$	0	0
$171$	−1.00000	−0.0764719
$172$	− 7.00000i	− 0.533745i
$173$	− 21.0000i	− 1.59660i	−0.602260	−	0.798300i	$-0.705733\pi$
$173$	− 21.0000i	− 1.59660i	0.602260	−	0.798300i	$-0.294267\pi$
$174$	5.00000	0.379049
$175$	0	0
$176$	−3.00000	−0.226134
$177$	− 10.0000i	− 0.751646i
$178$	− 14.0000i	− 1.04934i
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	0	0
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	25.0000i	1.85312i
$183$	12.0000i	0.887066i
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	−8.00000	−0.586588
$187$	− 18.0000i	− 1.31629i
$188$	6.00000i	0.437595i
$189$	−5.00000	−0.363696
$190$	0	0
$191$	−13.0000	−0.940647	−0.470323	−	0.882494i	$-0.655863\pi$
$191$	−13.0000	−0.940647	−0.470323	+	0.882494i	$0.655863\pi$
$192$	1.00000i	0.0721688i
$193$	− 6.00000i	− 0.431889i	−0.976406	−	0.215945i	$-0.930717\pi$
$193$	− 6.00000i	− 0.431889i	0.976406	−	0.215945i	$-0.0692831\pi$
$194$	−16.0000	−1.14873
$195$	0	0
$196$	18.0000	1.28571
$197$	− 11.0000i	− 0.783718i	−0.920025	−	0.391859i	$-0.871832\pi$
$197$	− 11.0000i	− 0.783718i	0.920025	−	0.391859i	$-0.128168\pi$
$198$	3.00000i	0.213201i
$199$	1.00000	0.0708881	0.0354441	−	0.999372i	$-0.488715\pi$
$199$	1.00000	0.0708881	0.0354441	+	0.999372i	$0.488715\pi$
$200$	0	0
$201$	−12.0000	−0.846415
$202$	− 10.0000i	− 0.703598i
$203$	25.0000i	1.75466i
$204$	−6.00000	−0.420084
$205$	0	0
$206$	19.0000	1.32379
$207$	1.00000i	0.0695048i
$208$	− 5.00000i	− 0.346688i
$209$	−3.00000	−0.207514
$210$	0	0
$211$	10.0000	0.688428	0.344214	−	0.938891i	$-0.388145\pi$
$211$	10.0000	0.688428	0.344214	+	0.938891i	$0.388145\pi$
$212$	8.00000i	0.549442i
$213$	− 10.0000i	− 0.685189i
$214$	12.0000	0.820303
$215$	0	0
$216$	1.00000	0.0680414
$217$	− 40.0000i	− 2.71538i
$218$	− 12.0000i	− 0.812743i
$219$	−15.0000	−1.01361
$220$	0	0
$221$	30.0000	2.01802
$222$	4.00000i	0.268462i
$223$	14.0000i	0.937509i	0.883328	+	0.468755i	$0.155297\pi$
$223$	14.0000i	0.937509i	−0.883328	+	0.468755i	$0.844703\pi$
$224$	−5.00000	−0.334077
$225$	0	0
$226$	−10.0000	−0.665190
$227$	8.00000i	0.530979i	0.964114	+	0.265489i	$0.0855335\pi$
$227$	8.00000i	0.530979i	−0.964114	+	0.265489i	$0.914466\pi$
$228$	1.00000i	0.0662266i
$229$	−16.0000	−1.05731	−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000	−1.05731	−0.528655	+	0.848837i	$0.677303\pi$
$230$	0	0
$231$	−15.0000	−0.986928
$232$	− 5.00000i	− 0.328266i
$233$	− 7.00000i	− 0.458585i	−0.973358	−	0.229293i	$-0.926359\pi$
$233$	− 7.00000i	− 0.458585i	0.973358	−	0.229293i	$-0.0736413\pi$
$234$	−5.00000	−0.326860
$235$	0	0
$236$	−10.0000	−0.650945
$237$	− 5.00000i	− 0.324785i
$238$	− 30.0000i	− 1.94461i
$239$	−24.0000	−1.55243	−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000	−1.55243	−0.776215	+	0.630468i	$0.782863\pi$
$240$	0	0
$241$	−18.0000	−1.15948	−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000	−1.15948	−0.579741	+	0.814801i	$0.696846\pi$
$242$	− 2.00000i	− 0.128565i
$243$	− 1.00000i	− 0.0641500i
$244$	12.0000	0.768221
$245$	0	0
$246$	−7.00000	−0.446304
$247$	− 5.00000i	− 0.318142i
$248$	8.00000i	0.508001i
$249$	9.00000	0.570352
$250$	0	0
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	5.00000i	0.314970i
$253$	3.00000i	0.188608i
$254$	−6.00000	−0.376473
$255$	0	0
$256$	1.00000	0.0625000
$257$	6.00000i	0.374270i	0.982334	+	0.187135i	$0.0599201\pi$
$257$	6.00000i	0.374270i	−0.982334	+	0.187135i	$0.940080\pi$
$258$	7.00000i	0.435801i
$259$	−20.0000	−1.24274
$260$	0	0
$261$	−5.00000	−0.309492
$262$	− 4.00000i	− 0.247121i
$263$	4.00000i	0.246651i	0.992366	+	0.123325i	$0.0393559\pi$
$263$	4.00000i	0.246651i	−0.992366	+	0.123325i	$0.960644\pi$
$264$	3.00000	0.184637
$265$	0	0
$266$	−5.00000	−0.306570
$267$	14.0000i	0.856786i
$268$	12.0000i	0.733017i
$269$	−3.00000	−0.182913	−0.0914566	−	0.995809i	$-0.529152\pi$
$269$	−3.00000	−0.182913	−0.0914566	+	0.995809i	$0.529152\pi$
$270$	0	0
$271$	−28.0000	−1.70088	−0.850439	−	0.526073i	$-0.823664\pi$
$271$	−28.0000	−1.70088	−0.850439	+	0.526073i	$0.823664\pi$
$272$	6.00000i	0.363803i
$273$	− 25.0000i	− 1.51307i
$274$	8.00000	0.483298
$275$	0	0
$276$	1.00000	0.0601929
$277$	− 1.00000i	− 0.0600842i	−0.999549	−	0.0300421i	$-0.990436\pi$
$277$	− 1.00000i	− 0.0600842i	0.999549	−	0.0300421i	$-0.00956413\pi$
$278$	− 2.00000i	− 0.119952i
$279$	8.00000	0.478947
$280$	0	0
$281$	2.00000	0.119310	0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000	0.119310	0.0596550	+	0.998219i	$0.481000\pi$
$282$	− 6.00000i	− 0.357295i
$283$	− 20.0000i	− 1.18888i	−0.804141	−	0.594438i	$-0.797374\pi$
$283$	− 20.0000i	− 1.18888i	0.804141	−	0.594438i	$-0.202626\pi$
$284$	−10.0000	−0.593391
$285$	0	0
$286$	−15.0000	−0.886969
$287$	− 35.0000i	− 2.06598i
$288$	− 1.00000i	− 0.0589256i
$289$	−19.0000	−1.11765
$290$	0	0
$291$	16.0000	0.937937
$292$	15.0000i	0.877809i
$293$	28.0000i	1.63578i	0.575376	+	0.817889i	$0.304856\pi$
$293$	28.0000i	1.63578i	−0.575376	+	0.817889i	$0.695144\pi$
$294$	−18.0000	−1.04978
$295$	0	0
$296$	4.00000	0.232495
$297$	− 3.00000i	− 0.174078i
$298$	20.0000i	1.15857i
$299$	−5.00000	−0.289157
$300$	0	0
$301$	−35.0000	−2.01737
$302$	− 10.0000i	− 0.575435i
$303$	10.0000i	0.574485i
$304$	1.00000	0.0573539
$305$	0	0
$306$	6.00000	0.342997
$307$	12.0000i	0.684876i	0.939540	+	0.342438i	$0.111253\pi$
$307$	12.0000i	0.684876i	−0.939540	+	0.342438i	$0.888747\pi$
$308$	15.0000i	0.854704i
$309$	−19.0000	−1.08087
$310$	0	0
$311$	28.0000	1.58773	0.793867	−	0.608091i	$-0.208065\pi$
$311$	28.0000	1.58773	0.793867	+	0.608091i	$0.208065\pi$
$312$	5.00000i	0.283069i
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	−4.00000	−0.225733
$315$	0	0
$316$	−5.00000	−0.281272
$317$	9.00000i	0.505490i	0.967533	+	0.252745i	$0.0813334\pi$
$317$	9.00000i	0.505490i	−0.967533	+	0.252745i	$0.918667\pi$
$318$	− 8.00000i	− 0.448618i
$319$	−15.0000	−0.839839
$320$	0	0
$321$	−12.0000	−0.669775
$322$	5.00000i	0.278639i
$323$	6.00000i	0.333849i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	12.0000	0.664619
$327$	12.0000i	0.663602i
$328$	7.00000i	0.386510i
$329$	30.0000	1.65395
$330$	0	0
$331$	4.00000	0.219860	0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000	0.219860	0.109930	+	0.993939i	$0.464937\pi$
$332$	− 9.00000i	− 0.493939i
$333$	− 4.00000i	− 0.219199i
$334$	12.0000	0.656611
$335$	0	0
$336$	5.00000	0.272772
$337$	8.00000i	0.435788i	0.975972	+	0.217894i	$0.0699187\pi$
$337$	8.00000i	0.435788i	−0.975972	+	0.217894i	$0.930081\pi$
$338$	− 12.0000i	− 0.652714i
$339$	10.0000	0.543125
$340$	0	0
$341$	24.0000	1.29967
$342$	− 1.00000i	− 0.0540738i
$343$	− 55.0000i	− 2.96972i
$344$	7.00000	0.377415
$345$	0	0
$346$	21.0000	1.12897
$347$	− 4.00000i	− 0.214731i	−0.994220	−	0.107366i	$-0.965758\pi$
$347$	− 4.00000i	− 0.214731i	0.994220	−	0.107366i	$-0.0342415\pi$
$348$	5.00000i	0.268028i
$349$	−1.00000	−0.0535288	−0.0267644	−	0.999642i	$-0.508520\pi$
$349$	−1.00000	−0.0535288	−0.0267644	+	0.999642i	$0.508520\pi$
$350$	0	0
$351$	5.00000	0.266880
$352$	− 3.00000i	− 0.159901i
$353$	− 9.00000i	− 0.479022i	−0.970894	−	0.239511i	$-0.923013\pi$
$353$	− 9.00000i	− 0.479022i	0.970894	−	0.239511i	$-0.0769871\pi$
$354$	10.0000	0.531494
$355$	0	0
$356$	14.0000	0.741999
$357$	30.0000i	1.58777i
$358$	− 6.00000i	− 0.317110i
$359$	7.00000	0.369446	0.184723	−	0.982791i	$-0.440861\pi$
$359$	7.00000	0.369446	0.184723	+	0.982791i	$0.440861\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	− 14.0000i	− 0.735824i
$363$	2.00000i	0.104973i
$364$	−25.0000	−1.31036
$365$	0	0
$366$	−12.0000	−0.627250
$367$	1.00000i	0.0521996i	0.999659	+	0.0260998i	$0.00830876\pi$
$367$	1.00000i	0.0521996i	−0.999659	+	0.0260998i	$0.991691\pi$
$368$	− 1.00000i	− 0.0521286i
$369$	7.00000	0.364405
$370$	0	0
$371$	40.0000	2.07670
$372$	− 8.00000i	− 0.414781i
$373$	26.0000i	1.34623i	0.739538	+	0.673114i	$0.235044\pi$
$373$	26.0000i	1.34623i	−0.739538	+	0.673114i	$0.764956\pi$
$374$	18.0000	0.930758
$375$	0	0
$376$	−6.00000	−0.309426
$377$	− 25.0000i	− 1.28757i
$378$	− 5.00000i	− 0.257172i
$379$	−12.0000	−0.616399	−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000	−0.616399	−0.308199	+	0.951322i	$0.599726\pi$
$380$	0	0
$381$	6.00000	0.307389
$382$	− 13.0000i	− 0.665138i
$383$	9.00000i	0.459879i	0.973205	+	0.229939i	$0.0738528\pi$
$383$	9.00000i	0.459879i	−0.973205	+	0.229939i	$0.926147\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	6.00000	0.305392
$387$	− 7.00000i	− 0.355830i
$388$	− 16.0000i	− 0.812277i
$389$	38.0000	1.92668	0.963338	−	0.268290i	$-0.0864585\pi$
$389$	38.0000	1.92668	0.963338	+	0.268290i	$0.0864585\pi$
$390$	0	0
$391$	6.00000	0.303433
$392$	18.0000i	0.909137i
$393$	4.00000i	0.201773i
$394$	11.0000	0.554172
$395$	0	0
$396$	−3.00000	−0.150756
$397$	− 2.00000i	− 0.100377i	−0.998740	−	0.0501886i	$-0.984018\pi$
$397$	− 2.00000i	− 0.100377i	0.998740	−	0.0501886i	$-0.0159822\pi$
$398$	1.00000i	0.0501255i
$399$	5.00000	0.250313
$400$	0	0
$401$	20.0000	0.998752	0.499376	−	0.866385i	$-0.333563\pi$
$401$	20.0000	0.998752	0.499376	+	0.866385i	$0.333563\pi$
$402$	− 12.0000i	− 0.598506i
$403$	40.0000i	1.99254i
$404$	10.0000	0.497519
$405$	0	0
$406$	−25.0000	−1.24073
$407$	− 12.0000i	− 0.594818i
$408$	− 6.00000i	− 0.297044i
$409$	−17.0000	−0.840596	−0.420298	−	0.907386i	$-0.638074\pi$
$409$	−17.0000	−0.840596	−0.420298	+	0.907386i	$0.638074\pi$
$410$	0	0
$411$	−8.00000	−0.394611
$412$	19.0000i	0.936063i
$413$	50.0000i	2.46034i
$414$	−1.00000	−0.0491473
$415$	0	0
$416$	5.00000	0.245145
$417$	2.00000i	0.0979404i
$418$	− 3.00000i	− 0.146735i
$419$	1.00000	0.0488532	0.0244266	−	0.999702i	$-0.492224\pi$
$419$	1.00000	0.0488532	0.0244266	+	0.999702i	$0.492224\pi$
$420$	0	0
$421$	−18.0000	−0.877266	−0.438633	−	0.898666i	$-0.644537\pi$
$421$	−18.0000	−0.877266	−0.438633	+	0.898666i	$0.644537\pi$
$422$	10.0000i	0.486792i
$423$	6.00000i	0.291730i
$424$	−8.00000	−0.388514
$425$	0	0
$426$	10.0000	0.484502
$427$	− 60.0000i	− 2.90360i
$428$	12.0000i	0.580042i
$429$	15.0000	0.724207
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	1.00000i	0.0481125i
$433$	28.0000i	1.34559i	0.739827	+	0.672797i	$0.234907\pi$
$433$	28.0000i	1.34559i	−0.739827	+	0.672797i	$0.765093\pi$
$434$	40.0000	1.92006
$435$	0	0
$436$	12.0000	0.574696
$437$	− 1.00000i	− 0.0478365i
$438$	− 15.0000i	− 0.716728i
$439$	12.0000	0.572729	0.286364	−	0.958121i	$-0.407553\pi$
$439$	12.0000	0.572729	0.286364	+	0.958121i	$0.407553\pi$
$440$	0	0
$441$	18.0000	0.857143
$442$	30.0000i	1.42695i
$443$	4.00000i	0.190046i	0.995475	+	0.0950229i	$0.0302924\pi$
$443$	4.00000i	0.190046i	−0.995475	+	0.0950229i	$0.969708\pi$
$444$	−4.00000	−0.189832
$445$	0	0
$446$	−14.0000	−0.662919
$447$	− 20.0000i	− 0.945968i
$448$	− 5.00000i	− 0.236228i
$449$	2.00000	0.0943858	0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000	0.0943858	0.0471929	+	0.998886i	$0.484972\pi$
$450$	0	0
$451$	21.0000	0.988851
$452$	− 10.0000i	− 0.470360i
$453$	10.0000i	0.469841i
$454$	−8.00000	−0.375459
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	− 18.0000i	− 0.842004i	−0.907060	−	0.421002i	$-0.861678\pi$
$457$	− 18.0000i	− 0.842004i	0.907060	−	0.421002i	$-0.138322\pi$
$458$	− 16.0000i	− 0.747631i
$459$	−6.00000	−0.280056
$460$	0	0
$461$	7.00000	0.326023	0.163011	−	0.986624i	$-0.447879\pi$
$461$	7.00000	0.326023	0.163011	+	0.986624i	$0.447879\pi$
$462$	− 15.0000i	− 0.697863i
$463$	− 4.00000i	− 0.185896i	−0.995671	−	0.0929479i	$-0.970371\pi$
$463$	− 4.00000i	− 0.185896i	0.995671	−	0.0929479i	$-0.0296290\pi$
$464$	5.00000	0.232119
$465$	0	0
$466$	7.00000	0.324269
$467$	21.0000i	0.971764i	0.874024	+	0.485882i	$0.161502\pi$
$467$	21.0000i	0.971764i	−0.874024	+	0.485882i	$0.838498\pi$
$468$	− 5.00000i	− 0.231125i
$469$	60.0000	2.77054
$470$	0	0
$471$	4.00000	0.184310
$472$	− 10.0000i	− 0.460287i
$473$	− 21.0000i	− 0.965581i
$474$	5.00000	0.229658
$475$	0	0
$476$	30.0000	1.37505
$477$	8.00000i	0.366295i
$478$	− 24.0000i	− 1.09773i
$479$	25.0000	1.14228	0.571140	−	0.820853i	$-0.306501\pi$
$479$	25.0000	1.14228	0.571140	+	0.820853i	$0.306501\pi$
$480$	0	0
$481$	20.0000	0.911922
$482$	− 18.0000i	− 0.819878i
$483$	− 5.00000i	− 0.227508i
$484$	2.00000	0.0909091
$485$	0	0
$486$	1.00000	0.0453609
$487$	2.00000i	0.0906287i	0.998973	+	0.0453143i	$0.0144289\pi$
$487$	2.00000i	0.0906287i	−0.998973	+	0.0453143i	$0.985571\pi$
$488$	12.0000i	0.543214i
$489$	−12.0000	−0.542659
$490$	0	0
$491$	−32.0000	−1.44414	−0.722070	−	0.691820i	$-0.756809\pi$
$491$	−32.0000	−1.44414	−0.722070	+	0.691820i	$0.756809\pi$
$492$	− 7.00000i	− 0.315584i
$493$	30.0000i	1.35113i
$494$	5.00000	0.224961
$495$	0	0
$496$	−8.00000	−0.359211
$497$	50.0000i	2.24281i
$498$	9.00000i	0.403300i
$499$	6.00000	0.268597	0.134298	−	0.990941i	$-0.457122\pi$
$499$	6.00000	0.268597	0.134298	+	0.990941i	$0.457122\pi$
$500$	0	0
$501$	−12.0000	−0.536120
$502$	12.0000i	0.535586i
$503$	19.0000i	0.847168i	0.905857	+	0.423584i	$0.139228\pi$
$503$	19.0000i	0.847168i	−0.905857	+	0.423584i	$0.860772\pi$
$504$	−5.00000	−0.222718
$505$	0	0
$506$	−3.00000	−0.133366
$507$	12.0000i	0.532939i
$508$	− 6.00000i	− 0.266207i
$509$	−30.0000	−1.32973	−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000	−1.32973	−0.664863	+	0.746965i	$0.731510\pi$
$510$	0	0
$511$	75.0000	3.31780
$512$	1.00000i	0.0441942i
$513$	1.00000i	0.0441511i
$514$	−6.00000	−0.264649
$515$	0	0
$516$	−7.00000	−0.308158
$517$	18.0000i	0.791639i
$518$	− 20.0000i	− 0.878750i
$519$	−21.0000	−0.921798
$520$	0	0
$521$	−4.00000	−0.175243	−0.0876216	−	0.996154i	$-0.527927\pi$
$521$	−4.00000	−0.175243	−0.0876216	+	0.996154i	$0.527927\pi$
$522$	− 5.00000i	− 0.218844i
$523$	1.00000i	0.0437269i	0.999761	+	0.0218635i	$0.00695991\pi$
$523$	1.00000i	0.0437269i	−0.999761	+	0.0218635i	$0.993040\pi$
$524$	4.00000	0.174741
$525$	0	0
$526$	−4.00000	−0.174408
$527$	− 48.0000i	− 2.09091i
$528$	3.00000i	0.130558i
$529$	−1.00000	−0.0434783
$530$	0	0
$531$	−10.0000	−0.433963
$532$	− 5.00000i	− 0.216777i
$533$	35.0000i	1.51602i
$534$	−14.0000	−0.605839
$535$	0	0
$536$	−12.0000	−0.518321
$537$	6.00000i	0.258919i
$538$	− 3.00000i	− 0.129339i
$539$	54.0000	2.32594
$540$	0	0
$541$	−39.0000	−1.67674	−0.838370	−	0.545101i	$-0.816491\pi$
$541$	−39.0000	−1.67674	−0.838370	+	0.545101i	$0.816491\pi$
$542$	− 28.0000i	− 1.20270i
$543$	14.0000i	0.600798i
$544$	−6.00000	−0.257248
$545$	0	0
$546$	25.0000	1.06990
$547$	30.0000i	1.28271i	0.767245	+	0.641354i	$0.221627\pi$
$547$	30.0000i	1.28271i	−0.767245	+	0.641354i	$0.778373\pi$
$548$	8.00000i	0.341743i
$549$	12.0000	0.512148
$550$	0	0
$551$	5.00000	0.213007
$552$	1.00000i	0.0425628i
$553$	25.0000i	1.06311i
$554$	1.00000	0.0424859
$555$	0	0
$556$	2.00000	0.0848189
$557$	− 10.0000i	− 0.423714i	−0.977301	−	0.211857i	$-0.932049\pi$
$557$	− 10.0000i	− 0.423714i	0.977301	−	0.211857i	$-0.0679510\pi$
$558$	8.00000i	0.338667i
$559$	35.0000	1.48034
$560$	0	0
$561$	−18.0000	−0.759961
$562$	2.00000i	0.0843649i
$563$	21.0000i	0.885044i	0.896758	+	0.442522i	$0.145916\pi$
$563$	21.0000i	0.885044i	−0.896758	+	0.442522i	$0.854084\pi$
$564$	6.00000	0.252646
$565$	0	0
$566$	20.0000	0.840663
$567$	5.00000i	0.209980i
$568$	− 10.0000i	− 0.419591i
$569$	30.0000	1.25767	0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000	1.25767	0.628833	+	0.777541i	$0.283533\pi$
$570$	0	0
$571$	4.00000	0.167395	0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000	0.167395	0.0836974	+	0.996491i	$0.473327\pi$
$572$	− 15.0000i	− 0.627182i
$573$	13.0000i	0.543083i
$574$	35.0000	1.46087
$575$	0	0
$576$	1.00000	0.0416667
$577$	23.0000i	0.957503i	0.877951	+	0.478751i	$0.158910\pi$
$577$	23.0000i	0.957503i	−0.877951	+	0.478751i	$0.841090\pi$
$578$	− 19.0000i	− 0.790296i
$579$	−6.00000	−0.249351
$580$	0	0
$581$	−45.0000	−1.86691
$582$	16.0000i	0.663221i
$583$	24.0000i	0.993978i
$584$	−15.0000	−0.620704
$585$	0	0
$586$	−28.0000	−1.15667
$587$	42.0000i	1.73353i	0.498721	+	0.866763i	$0.333803\pi$
$587$	42.0000i	1.73353i	−0.498721	+	0.866763i	$0.666197\pi$
$588$	− 18.0000i	− 0.742307i
$589$	−8.00000	−0.329634
$590$	0	0
$591$	−11.0000	−0.452480
$592$	4.00000i	0.164399i
$593$	− 3.00000i	− 0.123195i	−0.998101	−	0.0615976i	$-0.980380\pi$
$593$	− 3.00000i	− 0.123195i	0.998101	−	0.0615976i	$-0.0196196\pi$
$594$	3.00000	0.123091
$595$	0	0
$596$	−20.0000	−0.819232
$597$	− 1.00000i	− 0.0409273i
$598$	− 5.00000i	− 0.204465i
$599$	44.0000	1.79779	0.898896	−	0.438163i	$-0.144371\pi$
$599$	44.0000	1.79779	0.898896	+	0.438163i	$0.144371\pi$
$600$	0	0
$601$	−38.0000	−1.55005	−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000	−1.55005	−0.775026	+	0.631929i	$0.782263\pi$
$602$	− 35.0000i	− 1.42649i
$603$	12.0000i	0.488678i
$604$	10.0000	0.406894
$605$	0	0
$606$	−10.0000	−0.406222
$607$	− 22.0000i	− 0.892952i	−0.894795	−	0.446476i	$-0.852679\pi$
$607$	− 22.0000i	− 0.892952i	0.894795	−	0.446476i	$-0.147321\pi$
$608$	1.00000i	0.0405554i
$609$	25.0000	1.01305
$610$	0	0
$611$	−30.0000	−1.21367
$612$	6.00000i	0.242536i
$613$	− 10.0000i	− 0.403896i	−0.979396	−	0.201948i	$-0.935273\pi$
$613$	− 10.0000i	− 0.403896i	0.979396	−	0.201948i	$-0.0647272\pi$
$614$	−12.0000	−0.484281
$615$	0	0
$616$	−15.0000	−0.604367
$617$	− 2.00000i	− 0.0805170i	−0.999189	−	0.0402585i	$-0.987182\pi$
$617$	− 2.00000i	− 0.0805170i	0.999189	−	0.0402585i	$-0.0128181\pi$
$618$	− 19.0000i	− 0.764292i
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	0	0
$621$	1.00000	0.0401286
$622$	28.0000i	1.12270i
$623$	− 70.0000i	− 2.80449i
$624$	−5.00000	−0.200160
$625$	0	0
$626$	0	0
$627$	3.00000i	0.119808i
$628$	− 4.00000i	− 0.159617i
$629$	−24.0000	−0.956943
$630$	0	0
$631$	29.0000	1.15447	0.577236	−	0.816577i	$-0.304131\pi$
$631$	29.0000	1.15447	0.577236	+	0.816577i	$0.304131\pi$
$632$	− 5.00000i	− 0.198889i
$633$	− 10.0000i	− 0.397464i
$634$	−9.00000	−0.357436
$635$	0	0
$636$	8.00000	0.317221
$637$	90.0000i	3.56593i
$638$	− 15.0000i	− 0.593856i
$639$	−10.0000	−0.395594
$640$	0	0
$641$	−36.0000	−1.42191	−0.710957	−	0.703235i	$-0.751738\pi$
$641$	−36.0000	−1.42191	−0.710957	+	0.703235i	$0.751738\pi$
$642$	− 12.0000i	− 0.473602i
$643$	− 1.00000i	− 0.0394362i	−0.999806	−	0.0197181i	$-0.993723\pi$
$643$	− 1.00000i	− 0.0394362i	0.999806	−	0.0197181i	$-0.00627687\pi$
$644$	−5.00000	−0.197028
$645$	0	0
$646$	−6.00000	−0.236067
$647$	24.0000i	0.943537i	0.881722	+	0.471769i	$0.156384\pi$
$647$	24.0000i	0.943537i	−0.881722	+	0.471769i	$0.843616\pi$
$648$	− 1.00000i	− 0.0392837i
$649$	−30.0000	−1.17760
$650$	0	0
$651$	−40.0000	−1.56772
$652$	12.0000i	0.469956i
$653$	− 11.0000i	− 0.430463i	−0.976563	−	0.215232i	$-0.930949\pi$
$653$	− 11.0000i	− 0.430463i	0.976563	−	0.215232i	$-0.0690506\pi$
$654$	−12.0000	−0.469237
$655$	0	0
$656$	−7.00000	−0.273304
$657$	15.0000i	0.585206i
$658$	30.0000i	1.16952i
$659$	−3.00000	−0.116863	−0.0584317	−	0.998291i	$-0.518610\pi$
$659$	−3.00000	−0.116863	−0.0584317	+	0.998291i	$0.518610\pi$
$660$	0	0
$661$	40.0000	1.55582	0.777910	−	0.628376i	$-0.216280\pi$
$661$	40.0000	1.55582	0.777910	+	0.628376i	$0.216280\pi$
$662$	4.00000i	0.155464i
$663$	− 30.0000i	− 1.16510i
$664$	9.00000	0.349268
$665$	0	0
$666$	4.00000	0.154997
$667$	− 5.00000i	− 0.193601i
$668$	12.0000i	0.464294i
$669$	14.0000	0.541271
$670$	0	0
$671$	36.0000	1.38976
$672$	5.00000i	0.192879i
$673$	− 45.0000i	− 1.73462i	−0.497766	−	0.867311i	$-0.665846\pi$
$673$	− 45.0000i	− 1.73462i	0.497766	−	0.867311i	$-0.334154\pi$
$674$	−8.00000	−0.308148
$675$	0	0
$676$	12.0000	0.461538
$677$	24.0000i	0.922395i	0.887298	+	0.461197i	$0.152580\pi$
$677$	24.0000i	0.922395i	−0.887298	+	0.461197i	$0.847420\pi$
$678$	10.0000i	0.384048i
$679$	−80.0000	−3.07012
$680$	0	0
$681$	8.00000	0.306561
$682$	24.0000i	0.919007i
$683$	10.0000i	0.382639i	0.981528	+	0.191320i	$0.0612767\pi$
$683$	10.0000i	0.382639i	−0.981528	+	0.191320i	$0.938723\pi$
$684$	1.00000	0.0382360
$685$	0	0
$686$	55.0000	2.09991
$687$	16.0000i	0.610438i
$688$	7.00000i	0.266872i
$689$	−40.0000	−1.52388
$690$	0	0
$691$	−10.0000	−0.380418	−0.190209	−	0.981744i	$-0.560917\pi$
$691$	−10.0000	−0.380418	−0.190209	+	0.981744i	$0.560917\pi$
$692$	21.0000i	0.798300i
$693$	15.0000i	0.569803i
$694$	4.00000	0.151838
$695$	0	0
$696$	−5.00000	−0.189525
$697$	− 42.0000i	− 1.59086i
$698$	− 1.00000i	− 0.0378506i
$699$	−7.00000	−0.264764
$700$	0	0
$701$	12.0000	0.453234	0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000	0.453234	0.226617	+	0.973984i	$0.427233\pi$
$702$	5.00000i	0.188713i
$703$	4.00000i	0.150863i
$704$	3.00000	0.113067
$705$	0	0
$706$	9.00000	0.338719
$707$	− 50.0000i	− 1.88044i
$708$	10.0000i	0.375823i
$709$	−12.0000	−0.450669	−0.225335	−	0.974281i	$-0.572348\pi$
$709$	−12.0000	−0.450669	−0.225335	+	0.974281i	$0.572348\pi$
$710$	0	0
$711$	−5.00000	−0.187515
$712$	14.0000i	0.524672i
$713$	8.00000i	0.299602i
$714$	−30.0000	−1.12272
$715$	0	0
$716$	6.00000	0.224231
$717$	24.0000i	0.896296i
$718$	7.00000i	0.261238i
$719$	22.0000	0.820462	0.410231	−	0.911982i	$-0.365448\pi$
$719$	22.0000	0.820462	0.410231	+	0.911982i	$0.365448\pi$
$720$	0	0
$721$	95.0000	3.53798
$722$	− 18.0000i	− 0.669891i
$723$	18.0000i	0.669427i
$724$	14.0000	0.520306
$725$	0	0
$726$	−2.00000	−0.0742270
$727$	32.0000i	1.18681i	0.804902	+	0.593407i	$0.202218\pi$
$727$	32.0000i	1.18681i	−0.804902	+	0.593407i	$0.797782\pi$
$728$	− 25.0000i	− 0.926562i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−42.0000	−1.55343
$732$	− 12.0000i	− 0.443533i
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	−1.00000	−0.0369107
$735$	0	0
$736$	1.00000	0.0368605
$737$	36.0000i	1.32608i
$738$	7.00000i	0.257674i
$739$	24.0000	0.882854	0.441427	−	0.897297i	$-0.354472\pi$
$739$	24.0000	0.882854	0.441427	+	0.897297i	$0.354472\pi$
$740$	0	0
$741$	−5.00000	−0.183680
$742$	40.0000i	1.46845i
$743$	− 11.0000i	− 0.403551i	−0.979432	−	0.201775i	$-0.935329\pi$
$743$	− 11.0000i	− 0.403551i	0.979432	−	0.201775i	$-0.0646711\pi$
$744$	8.00000	0.293294
$745$	0	0
$746$	−26.0000	−0.951928
$747$	− 9.00000i	− 0.329293i
$748$	18.0000i	0.658145i
$749$	60.0000	2.19235
$750$	0	0
$751$	−43.0000	−1.56909	−0.784546	−	0.620070i	$-0.787104\pi$
$751$	−43.0000	−1.56909	−0.784546	+	0.620070i	$0.787104\pi$
$752$	− 6.00000i	− 0.218797i
$753$	− 12.0000i	− 0.437304i
$754$	25.0000	0.910446
$755$	0	0
$756$	5.00000	0.181848
$757$	28.0000i	1.01768i	0.860862	+	0.508839i	$0.169925\pi$
$757$	28.0000i	1.01768i	−0.860862	+	0.508839i	$0.830075\pi$
$758$	− 12.0000i	− 0.435860i
$759$	3.00000	0.108893
$760$	0	0
$761$	51.0000	1.84875	0.924374	−	0.381487i	$-0.124588\pi$
$761$	51.0000	1.84875	0.924374	+	0.381487i	$0.124588\pi$
$762$	6.00000i	0.217357i
$763$	− 60.0000i	− 2.17215i
$764$	13.0000	0.470323
$765$	0	0
$766$	−9.00000	−0.325183
$767$	− 50.0000i	− 1.80540i
$768$	− 1.00000i	− 0.0360844i
$769$	2.00000	0.0721218	0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000	0.0721218	0.0360609	+	0.999350i	$0.488519\pi$
$770$	0	0
$771$	6.00000	0.216085
$772$	6.00000i	0.215945i
$773$	12.0000i	0.431610i	0.976436	+	0.215805i	$0.0692376\pi$
$773$	12.0000i	0.431610i	−0.976436	+	0.215805i	$0.930762\pi$
$774$	7.00000	0.251610
$775$	0	0
$776$	16.0000	0.574367
$777$	20.0000i	0.717496i
$778$	38.0000i	1.36237i
$779$	−7.00000	−0.250801
$780$	0	0
$781$	−30.0000	−1.07348
$782$	6.00000i	0.214560i
$783$	5.00000i	0.178685i
$784$	−18.0000	−0.642857
$785$	0	0
$786$	−4.00000	−0.142675
$787$	− 17.0000i	− 0.605985i	−0.952993	−	0.302992i	$-0.902014\pi$
$787$	− 17.0000i	− 0.605985i	0.952993	−	0.302992i	$-0.0979856\pi$
$788$	11.0000i	0.391859i
$789$	4.00000	0.142404
$790$	0	0
$791$	−50.0000	−1.77780
$792$	− 3.00000i	− 0.106600i
$793$	60.0000i	2.13066i
$794$	2.00000	0.0709773
$795$	0	0
$796$	−1.00000	−0.0354441
$797$	42.0000i	1.48772i	0.668338	+	0.743858i	$0.267006\pi$
$797$	42.0000i	1.48772i	−0.668338	+	0.743858i	$0.732994\pi$
$798$	5.00000i	0.176998i
$799$	36.0000	1.27359
$800$	0	0
$801$	14.0000	0.494666
$802$	20.0000i	0.706225i
$803$	45.0000i	1.58802i
$804$	12.0000	0.423207
$805$	0	0
$806$	−40.0000	−1.40894
$807$	3.00000i	0.105605i
$808$	10.0000i	0.351799i
$809$	−19.0000	−0.668004	−0.334002	−	0.942572i	$-0.608399\pi$
$809$	−19.0000	−0.668004	−0.334002	+	0.942572i	$0.608399\pi$
$810$	0	0
$811$	−30.0000	−1.05344	−0.526721	−	0.850038i	$-0.676579\pi$
$811$	−30.0000	−1.05344	−0.526721	+	0.850038i	$0.676579\pi$
$812$	− 25.0000i	− 0.877328i
$813$	28.0000i	0.982003i
$814$	12.0000	0.420600
$815$	0	0
$816$	6.00000	0.210042
$817$	7.00000i	0.244899i
$818$	− 17.0000i	− 0.594391i
$819$	−25.0000	−0.873571
$820$	0	0
$821$	9.00000	0.314102	0.157051	−	0.987590i	$-0.449801\pi$
$821$	9.00000	0.314102	0.157051	+	0.987590i	$0.449801\pi$
$822$	− 8.00000i	− 0.279032i
$823$	− 50.0000i	− 1.74289i	−0.490493	−	0.871445i	$-0.663183\pi$
$823$	− 50.0000i	− 1.74289i	0.490493	−	0.871445i	$-0.336817\pi$
$824$	−19.0000	−0.661896
$825$	0	0
$826$	−50.0000	−1.73972
$827$	− 27.0000i	− 0.938882i	−0.882964	−	0.469441i	$-0.844455\pi$
$827$	− 27.0000i	− 0.938882i	0.882964	−	0.469441i	$-0.155545\pi$
$828$	− 1.00000i	− 0.0347524i
$829$	31.0000	1.07667	0.538337	−	0.842729i	$-0.319053\pi$
$829$	31.0000	1.07667	0.538337	+	0.842729i	$0.319053\pi$
$830$	0	0
$831$	−1.00000	−0.0346896
$832$	5.00000i	0.173344i
$833$	− 108.000i	− 3.74198i
$834$	−2.00000	−0.0692543
$835$	0	0
$836$	3.00000	0.103757
$837$	− 8.00000i	− 0.276520i
$838$	1.00000i	0.0345444i
$839$	−7.00000	−0.241667	−0.120833	−	0.992673i	$-0.538557\pi$
$839$	−7.00000	−0.241667	−0.120833	+	0.992673i	$0.538557\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	− 18.0000i	− 0.620321i
$843$	− 2.00000i	− 0.0688837i
$844$	−10.0000	−0.344214
$845$	0	0
$846$	−6.00000	−0.206284
$847$	− 10.0000i	− 0.343604i
$848$	− 8.00000i	− 0.274721i
$849$	−20.0000	−0.686398
$850$	0	0
$851$	4.00000	0.137118
$852$	10.0000i	0.342594i
$853$	− 9.00000i	− 0.308154i	−0.988059	−	0.154077i	$-0.950760\pi$
$853$	− 9.00000i	− 0.308154i	0.988059	−	0.154077i	$-0.0492404\pi$
$854$	60.0000	2.05316
$855$	0	0
$856$	−12.0000	−0.410152
$857$	− 22.0000i	− 0.751506i	−0.926720	−	0.375753i	$-0.877384\pi$
$857$	− 22.0000i	− 0.751506i	0.926720	−	0.375753i	$-0.122616\pi$
$858$	15.0000i	0.512092i
$859$	30.0000	1.02359	0.511793	−	0.859109i	$-0.328981\pi$
$859$	30.0000	1.02359	0.511793	+	0.859109i	$0.328981\pi$
$860$	0	0
$861$	−35.0000	−1.19280
$862$	0	0
$863$	− 18.0000i	− 0.612727i	−0.951915	−	0.306364i	$-0.900888\pi$
$863$	− 18.0000i	− 0.612727i	0.951915	−	0.306364i	$-0.0991123\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−28.0000	−0.951479
$867$	19.0000i	0.645274i
$868$	40.0000i	1.35769i
$869$	−15.0000	−0.508840
$870$	0	0
$871$	−60.0000	−2.03302
$872$	12.0000i	0.406371i
$873$	− 16.0000i	− 0.541518i
$874$	1.00000	0.0338255
$875$	0	0
$876$	15.0000	0.506803
$877$	42.0000i	1.41824i	0.705088	+	0.709120i	$0.250907\pi$
$877$	42.0000i	1.41824i	−0.705088	+	0.709120i	$0.749093\pi$
$878$	12.0000i	0.404980i
$879$	28.0000	0.944417
$880$	0	0
$881$	−24.0000	−0.808581	−0.404290	−	0.914631i	$-0.632481\pi$
$881$	−24.0000	−0.808581	−0.404290	+	0.914631i	$0.632481\pi$
$882$	18.0000i	0.606092i
$883$	− 8.00000i	− 0.269221i	−0.990899	−	0.134611i	$-0.957022\pi$
$883$	− 8.00000i	− 0.269221i	0.990899	−	0.134611i	$-0.0429784\pi$
$884$	−30.0000	−1.00901
$885$	0	0
$886$	−4.00000	−0.134383
$887$	22.0000i	0.738688i	0.929293	+	0.369344i	$0.120418\pi$
$887$	22.0000i	0.738688i	−0.929293	+	0.369344i	$0.879582\pi$
$888$	− 4.00000i	− 0.134231i
$889$	−30.0000	−1.00617
$890$	0	0
$891$	−3.00000	−0.100504
$892$	− 14.0000i	− 0.468755i
$893$	− 6.00000i	− 0.200782i
$894$	20.0000	0.668900
$895$	0	0
$896$	5.00000	0.167038
$897$	5.00000i	0.166945i
$898$	2.00000i	0.0667409i
$899$	−40.0000	−1.33407
$900$	0	0
$901$	48.0000	1.59911
$902$	21.0000i	0.699224i
$903$	35.0000i	1.16473i
$904$	10.0000	0.332595
$905$	0	0
$906$	−10.0000	−0.332228
$907$	− 37.0000i	− 1.22856i	−0.789086	−	0.614282i	$-0.789446\pi$
$907$	− 37.0000i	− 1.22856i	0.789086	−	0.614282i	$-0.210554\pi$
$908$	− 8.00000i	− 0.265489i
$909$	10.0000	0.331679
$910$	0	0
$911$	−15.0000	−0.496972	−0.248486	−	0.968635i	$-0.579933\pi$
$911$	−15.0000	−0.496972	−0.248486	+	0.968635i	$0.579933\pi$
$912$	− 1.00000i	− 0.0331133i
$913$	− 27.0000i	− 0.893570i
$914$	18.0000	0.595387
$915$	0	0
$916$	16.0000	0.528655
$917$	− 20.0000i	− 0.660458i
$918$	− 6.00000i	− 0.198030i
$919$	12.0000	0.395843	0.197922	−	0.980218i	$-0.436581\pi$
$919$	12.0000	0.395843	0.197922	+	0.980218i	$0.436581\pi$
$920$	0	0
$921$	12.0000	0.395413
$922$	7.00000i	0.230533i
$923$	− 50.0000i	− 1.64577i
$924$	15.0000	0.493464
$925$	0	0
$926$	4.00000	0.131448
$927$	19.0000i	0.624042i
$928$	5.00000i	0.164133i
$929$	43.0000	1.41078	0.705392	−	0.708817i	$-0.250771\pi$
$929$	43.0000	1.41078	0.705392	+	0.708817i	$0.250771\pi$
$930$	0	0
$931$	−18.0000	−0.589926
$932$	7.00000i	0.229293i
$933$	− 28.0000i	− 0.916679i
$934$	−21.0000	−0.687141
$935$	0	0
$936$	5.00000	0.163430
$937$	− 20.0000i	− 0.653372i	−0.945133	−	0.326686i	$-0.894068\pi$
$937$	− 20.0000i	− 0.653372i	0.945133	−	0.326686i	$-0.105932\pi$
$938$	60.0000i	1.95907i
$939$	0	0
$940$	0	0
$941$	−48.0000	−1.56476	−0.782378	−	0.622804i	$-0.785993\pi$
$941$	−48.0000	−1.56476	−0.782378	+	0.622804i	$0.785993\pi$
$942$	4.00000i	0.130327i
$943$	7.00000i	0.227951i
$944$	10.0000	0.325472
$945$	0	0
$946$	21.0000	0.682769
$947$	32.0000i	1.03986i	0.854209	+	0.519930i	$0.174042\pi$
$947$	32.0000i	1.03986i	−0.854209	+	0.519930i	$0.825958\pi$
$948$	5.00000i	0.162392i
$949$	−75.0000	−2.43460
$950$	0	0
$951$	9.00000	0.291845
$952$	30.0000i	0.972306i
$953$	12.0000i	0.388718i	0.980930	+	0.194359i	$0.0622627\pi$
$953$	12.0000i	0.388718i	−0.980930	+	0.194359i	$0.937737\pi$
$954$	−8.00000	−0.259010
$955$	0	0
$956$	24.0000	0.776215
$957$	15.0000i	0.484881i
$958$	25.0000i	0.807713i
$959$	40.0000	1.29167
$960$	0	0
$961$	33.0000	1.06452
$962$	20.0000i	0.644826i
$963$	12.0000i	0.386695i
$964$	18.0000	0.579741
$965$	0	0
$966$	5.00000	0.160872
$967$	− 8.00000i	− 0.257263i	−0.991692	−	0.128631i	$-0.958942\pi$
$967$	− 8.00000i	− 0.257263i	0.991692	−	0.128631i	$-0.0410584\pi$
$968$	2.00000i	0.0642824i
$969$	6.00000	0.192748
$970$	0	0
$971$	−49.0000	−1.57248	−0.786242	−	0.617918i	$-0.787976\pi$
$971$	−49.0000	−1.57248	−0.786242	+	0.617918i	$0.787976\pi$
$972$	1.00000i	0.0320750i
$973$	− 10.0000i	− 0.320585i
$974$	−2.00000	−0.0640841
$975$	0	0
$976$	−12.0000	−0.384111
$977$	8.00000i	0.255943i	0.991778	+	0.127971i	$0.0408466\pi$
$977$	8.00000i	0.255943i	−0.991778	+	0.127971i	$0.959153\pi$
$978$	− 12.0000i	− 0.383718i
$979$	42.0000	1.34233
$980$	0	0
$981$	12.0000	0.383131
$982$	− 32.0000i	− 1.02116i
$983$	31.0000i	0.988746i	0.869250	+	0.494373i	$0.164602\pi$
$983$	31.0000i	0.988746i	−0.869250	+	0.494373i	$0.835398\pi$
$984$	7.00000	0.223152
$985$	0	0
$986$	−30.0000	−0.955395
$987$	− 30.0000i	− 0.954911i
$988$	5.00000i	0.159071i
$989$	7.00000	0.222587
$990$	0	0
$991$	4.00000	0.127064	0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000	0.127064	0.0635321	+	0.997980i	$0.479763\pi$
$992$	− 8.00000i	− 0.254000i
$993$	− 4.00000i	− 0.126936i
$994$	−50.0000	−1.58590
$995$	0	0
$996$	−9.00000	−0.285176
$997$	− 1.00000i	− 0.0316703i	−0.999875	−	0.0158352i	$-0.994959\pi$
$997$	− 1.00000i	− 0.0316703i	0.999875	−	0.0158352i	$-0.00504070\pi$
$998$	6.00000i	0.189927i
$999$	−4.00000	−0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3450.2.d.l.2899.2		2
5.2	odd	4		3450.2.a.a.1.1	✓	1
5.3	odd	4		3450.2.a.bb.1.1	yes	1
5.4	even	2	inner	3450.2.d.l.2899.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3450.2.a.a.1.1	✓	1	5.2	odd	4
3450.2.a.bb.1.1	yes	1	5.3	odd	4
3450.2.d.l.2899.1		2	5.4	even	2	inner
3450.2.d.l.2899.2		2	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:	\( N \)	\(=\)	\( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3450.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +5.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} +5.00000i q^{7} -1.00000i q^{8} -1.00000 q^{9} -3.00000 q^{11} +1.00000i q^{12} -5.00000i q^{13} -5.00000 q^{14} +1.00000 q^{16} +6.00000i q^{17} -1.00000i q^{18} +1.00000 q^{19} +5.00000 q^{21} -3.00000i q^{22} -1.00000i q^{23} -1.00000 q^{24} +5.00000 q^{26} +1.00000i q^{27} -5.00000i q^{28} +5.00000 q^{29} -8.00000 q^{31} +1.00000i q^{32} +3.00000i q^{33} -6.00000 q^{34} +1.00000 q^{36} +4.00000i q^{37} +1.00000i q^{38} -5.00000 q^{39} -7.00000 q^{41} +5.00000i q^{42} +7.00000i q^{43} +3.00000 q^{44} +1.00000 q^{46} -6.00000i q^{47} -1.00000i q^{48} -18.0000 q^{49} +6.00000 q^{51} +5.00000i q^{52} -8.00000i q^{53} -1.00000 q^{54} +5.00000 q^{56} -1.00000i q^{57} +5.00000i q^{58} +10.0000 q^{59} -12.0000 q^{61} -8.00000i q^{62} -5.00000i q^{63} -1.00000 q^{64} -3.00000 q^{66} -12.0000i q^{67} -6.00000i q^{68} -1.00000 q^{69} +10.0000 q^{71} +1.00000i q^{72} -15.0000i q^{73} -4.00000 q^{74} -1.00000 q^{76} -15.0000i q^{77} -5.00000i q^{78} +5.00000 q^{79} +1.00000 q^{81} -7.00000i q^{82} +9.00000i q^{83} -5.00000 q^{84} -7.00000 q^{86} -5.00000i q^{87} +3.00000i q^{88} -14.0000 q^{89} +25.0000 q^{91} +1.00000i q^{92} +8.00000i q^{93} +6.00000 q^{94} +1.00000 q^{96} +16.0000i q^{97} -18.0000i q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 + 2 * q^6 - 2 * q^9	\( 2 q - 2 q^{4} + 2 q^{6} - 2 q^{9} - 6 q^{11} - 10 q^{14} + 2 q^{16} + 2 q^{19} + 10 q^{21} - 2 q^{24} + 10 q^{26} + 10 q^{29} - 16 q^{31} - 12 q^{34} + 2 q^{36} - 10 q^{39} - 14 q^{41} + 6 q^{44} + 2 q^{46} - 36 q^{49} + 12 q^{51} - 2 q^{54} + 10 q^{56} + 20 q^{59} - 24 q^{61} - 2 q^{64} - 6 q^{66} - 2 q^{69} + 20 q^{71} - 8 q^{74} - 2 q^{76} + 10 q^{79} + 2 q^{81} - 10 q^{84} - 14 q^{86} - 28 q^{89} + 50 q^{91} + 12 q^{94} + 2 q^{96} + 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 + 2 * q^6 - 2 * q^9 - 6 * q^11 - 10 * q^14 + 2 * q^16 + 2 * q^19 + 10 * q^21 - 2 * q^24 + 10 * q^26 + 10 * q^29 - 16 * q^31 - 12 * q^34 + 2 * q^36 - 10 * q^39 - 14 * q^41 + 6 * q^44 + 2 * q^46 - 36 * q^49 + 12 * q^51 - 2 * q^54 + 10 * q^56 + 20 * q^59 - 24 * q^61 - 2 * q^64 - 6 * q^66 - 2 * q^69 + 20 * q^71 - 8 * q^74 - 2 * q^76 + 10 * q^79 + 2 * q^81 - 10 * q^84 - 14 * q^86 - 28 * q^89 + 50 * q^91 + 12 * q^94 + 2 * q^96 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more