LMFDB - Embedded newform 3450.2.d.y.2899.3

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:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2899.3
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	3450.2899
Dual form			3450.2.d.y.2899.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -3.44949i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -3.44949i q^{7} -1.00000i q^{8} -1.00000 q^{9} +2.00000 q^{11} +1.00000i q^{12} -6.89898i q^{13} +3.44949 q^{14} +1.00000 q^{16} -0.550510i q^{17} -1.00000i q^{18} +2.89898 q^{19} -3.44949 q^{21} +2.00000i q^{22} -1.00000i q^{23} -1.00000 q^{24} +6.89898 q^{26} +1.00000i q^{27} +3.44949i q^{28} -5.00000 q^{29} +2.00000 q^{31} +1.00000i q^{32} -2.00000i q^{33} +0.550510 q^{34} +1.00000 q^{36} -6.34847i q^{37} +2.89898i q^{38} -6.89898 q^{39} +4.89898 q^{41} -3.44949i q^{42} -1.10102i q^{43} -2.00000 q^{44} +1.00000 q^{46} +5.89898i q^{47} -1.00000i q^{48} -4.89898 q^{49} -0.550510 q^{51} +6.89898i q^{52} +8.89898i q^{53} -1.00000 q^{54} -3.44949 q^{56} -2.89898i q^{57} -5.00000i q^{58} -10.0000 q^{59} +4.89898 q^{61} +2.00000i q^{62} +3.44949i q^{63} -1.00000 q^{64} +2.00000 q^{66} -2.00000i q^{67} +0.550510i q^{68} -1.00000 q^{69} -8.79796 q^{71} +1.00000i q^{72} -11.8990i q^{73} +6.34847 q^{74} -2.89898 q^{76} -6.89898i q^{77} -6.89898i q^{78} -10.0000 q^{79} +1.00000 q^{81} +4.89898i q^{82} +7.44949i q^{83} +3.44949 q^{84} +1.10102 q^{86} +5.00000i q^{87} -2.00000i q^{88} -4.34847 q^{89} -23.7980 q^{91} +1.00000i q^{92} -2.00000i q^{93} -5.89898 q^{94} +1.00000 q^{96} +16.6969i q^{97} -4.89898i q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 8 q^{11} + 4 q^{14} + 4 q^{16} - 8 q^{19} - 4 q^{21} - 4 q^{24} + 8 q^{26} - 20 q^{29} + 8 q^{31} + 12 q^{34} + 4 q^{36} - 8 q^{39} - 8 q^{44} + 4 q^{46} - 12 q^{51} - 4 q^{54} - 4 q^{56} - 40 q^{59} - 4 q^{64} + 8 q^{66} - 4 q^{69} + 4 q^{71} - 4 q^{74} + 8 q^{76} - 40 q^{79} + 4 q^{81} + 4 q^{84} + 24 q^{86} + 12 q^{89} - 56 q^{91} - 4 q^{94} + 4 q^{96} - 8 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 8 * q^11 + 4 * q^14 + 4 * q^16 - 8 * q^19 - 4 * q^21 - 4 * q^24 + 8 * q^26 - 20 * q^29 + 8 * q^31 + 12 * q^34 + 4 * q^36 - 8 * q^39 - 8 * q^44 + 4 * q^46 - 12 * q^51 - 4 * q^54 - 4 * q^56 - 40 * q^59 - 4 * q^64 + 8 * q^66 - 4 * q^69 + 4 * q^71 - 4 * q^74 + 8 * q^76 - 40 * q^79 + 4 * q^81 + 4 * q^84 + 24 * q^86 + 12 * q^89 - 56 * q^91 - 4 * q^94 + 4 * q^96 - 8 * 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
$7$	− 3.44949i	− 1.30378i	−0.758312	−	0.651892i	$-0.773975\pi$
$7$	− 3.44949i	− 1.30378i	0.758312	−	0.651892i	$-0.226025\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	1.00000i	0.288675i
$13$	− 6.89898i	− 1.91343i	−0.291022	−	0.956716i	$-0.593995\pi$
$13$	− 6.89898i	− 1.91343i	0.291022	−	0.956716i	$-0.406005\pi$
$14$	3.44949	0.921915
$15$	0	0
$16$	1.00000	0.250000
$17$	− 0.550510i	− 0.133518i	−0.997769	−	0.0667592i	$-0.978734\pi$
$17$	− 0.550510i	− 0.133518i	0.997769	−	0.0667592i	$-0.0212659\pi$
$18$	− 1.00000i	− 0.235702i
$19$	2.89898	0.665072	0.332536	−	0.943091i	$-0.392096\pi$
$19$	2.89898	0.665072	0.332536	+	0.943091i	$0.392096\pi$
$20$	0	0
$21$	−3.44949	−0.752740
$22$	2.00000i	0.426401i
$23$	− 1.00000i	− 0.208514i
$23$	− 1.00000i	− 0.208514i
$24$	−1.00000	−0.204124
$25$	0	0
$26$	6.89898	1.35300
$27$	1.00000i	0.192450i
$28$	3.44949i	0.651892i
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	1.00000i	0.176777i
$33$	− 2.00000i	− 0.348155i
$34$	0.550510	0.0944117
$35$	0	0
$36$	1.00000	0.166667
$37$	− 6.34847i	− 1.04368i	−0.853043	−	0.521841i	$-0.825245\pi$
$37$	− 6.34847i	− 1.04368i	0.853043	−	0.521841i	$-0.174755\pi$
$38$	2.89898i	0.470277i
$39$	−6.89898	−1.10472
$40$	0	0
$41$	4.89898	0.765092	0.382546	−	0.923936i	$-0.375047\pi$
$41$	4.89898	0.765092	0.382546	+	0.923936i	$0.375047\pi$
$42$	− 3.44949i	− 0.532268i
$43$	− 1.10102i	− 0.167904i	−0.996470	−	0.0839520i	$-0.973246\pi$
$43$	− 1.10102i	− 0.167904i	0.996470	−	0.0839520i	$-0.0267543\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	1.00000	0.147442
$47$	5.89898i	0.860455i	0.902721	+	0.430227i	$0.141567\pi$
$47$	5.89898i	0.860455i	−0.902721	+	0.430227i	$0.858433\pi$
$48$	− 1.00000i	− 0.144338i
$49$	−4.89898	−0.699854
$50$	0	0
$51$	−0.550510	−0.0770869
$52$	6.89898i	0.956716i
$53$	8.89898i	1.22237i	0.791488	+	0.611184i	$0.209307\pi$
$53$	8.89898i	1.22237i	−0.791488	+	0.611184i	$0.790693\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−3.44949	−0.460957
$57$	− 2.89898i	− 0.383979i
$58$	− 5.00000i	− 0.656532i
$59$	−10.0000	−1.30189	−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000	−1.30189	−0.650945	+	0.759125i	$0.725627\pi$
$60$	0	0
$61$	4.89898	0.627250	0.313625	−	0.949547i	$-0.398457\pi$
$61$	4.89898	0.627250	0.313625	+	0.949547i	$0.398457\pi$
$62$	2.00000i	0.254000i
$63$	3.44949i	0.434595i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	2.00000	0.246183
$67$	− 2.00000i	− 0.244339i	−0.992509	−	0.122169i	$-0.961015\pi$
$67$	− 2.00000i	− 0.244339i	0.992509	−	0.122169i	$-0.0389851\pi$
$68$	0.550510i	0.0667592i
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−8.79796	−1.04413	−0.522063	−	0.852907i	$-0.674837\pi$
$71$	−8.79796	−1.04413	−0.522063	+	0.852907i	$0.674837\pi$
$72$	1.00000i	0.117851i
$73$	− 11.8990i	− 1.39267i	−0.717717	−	0.696335i	$-0.754813\pi$
$73$	− 11.8990i	− 1.39267i	0.717717	−	0.696335i	$-0.245187\pi$
$74$	6.34847	0.737995
$75$	0	0
$76$	−2.89898	−0.332536
$77$	− 6.89898i	− 0.786212i
$78$	− 6.89898i	− 0.781156i
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	4.89898i	0.541002i
$83$	7.44949i	0.817688i	0.912604	+	0.408844i	$0.134068\pi$
$83$	7.44949i	0.817688i	−0.912604	+	0.408844i	$0.865932\pi$
$84$	3.44949	0.376370
$85$	0	0
$86$	1.10102	0.118726
$87$	5.00000i	0.536056i
$88$	− 2.00000i	− 0.213201i
$89$	−4.34847	−0.460937	−0.230468	−	0.973080i	$-0.574026\pi$
$89$	−4.34847	−0.460937	−0.230468	+	0.973080i	$0.574026\pi$
$90$	0	0
$91$	−23.7980	−2.49470
$92$	1.00000i	0.104257i
$93$	− 2.00000i	− 0.207390i
$94$	−5.89898	−0.608433
$95$	0	0
$96$	1.00000	0.102062
$97$	16.6969i	1.69532i	0.530542	+	0.847659i	$0.321988\pi$
$97$	16.6969i	1.69532i	−0.530542	+	0.847659i	$0.678012\pi$
$98$	− 4.89898i	− 0.494872i
$99$	−2.00000	−0.201008
$100$	0	0
$101$	15.6969	1.56190	0.780952	−	0.624591i	$-0.214734\pi$
$101$	15.6969	1.56190	0.780952	+	0.624591i	$0.214734\pi$
$102$	− 0.550510i	− 0.0545086i
$103$	− 11.2474i	− 1.10824i	−0.832435	−	0.554122i	$-0.813054\pi$
$103$	− 11.2474i	− 1.10824i	0.832435	−	0.554122i	$-0.186946\pi$
$104$	−6.89898	−0.676501
$105$	0	0
$106$	−8.89898	−0.864345
$107$	− 2.00000i	− 0.193347i	−0.995316	−	0.0966736i	$-0.969180\pi$
$107$	− 2.00000i	− 0.193347i	0.995316	−	0.0966736i	$-0.0308203\pi$
$108$	− 1.00000i	− 0.0962250i
$109$	1.44949	0.138836	0.0694180	−	0.997588i	$-0.477886\pi$
$109$	1.44949	0.138836	0.0694180	+	0.997588i	$0.477886\pi$
$110$	0	0
$111$	−6.34847	−0.602570
$112$	− 3.44949i	− 0.325946i
$113$	0.348469i	0.0327812i	0.999866	+	0.0163906i	$0.00521753\pi$
$113$	0.348469i	0.0327812i	−0.999866	+	0.0163906i	$0.994782\pi$
$114$	2.89898	0.271514
$115$	0	0
$116$	5.00000	0.464238
$117$	6.89898i	0.637811i
$118$	− 10.0000i	− 0.920575i
$119$	−1.89898	−0.174079
$120$	0	0
$121$	−7.00000	−0.636364
$122$	4.89898i	0.443533i
$123$	− 4.89898i	− 0.441726i
$124$	−2.00000	−0.179605
$125$	0	0
$126$	−3.44949	−0.307305
$127$	− 17.7980i	− 1.57931i	−0.613549	−	0.789657i	$-0.710259\pi$
$127$	− 17.7980i	− 1.57931i	0.613549	−	0.789657i	$-0.289741\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−1.10102	−0.0969395
$130$	0	0
$131$	−0.898979	−0.0785442	−0.0392721	−	0.999229i	$-0.512504\pi$
$131$	−0.898979	−0.0785442	−0.0392721	+	0.999229i	$0.512504\pi$
$132$	2.00000i	0.174078i
$133$	− 10.0000i	− 0.867110i
$134$	2.00000	0.172774
$135$	0	0
$136$	−0.550510	−0.0472059
$137$	− 7.65153i	− 0.653714i	−0.945074	−	0.326857i	$-0.894010\pi$
$137$	− 7.65153i	− 0.653714i	0.945074	−	0.326857i	$-0.105990\pi$
$138$	− 1.00000i	− 0.0851257i
$139$	13.6969	1.16176	0.580880	−	0.813990i	$-0.302709\pi$
$139$	13.6969	1.16176	0.580880	+	0.813990i	$0.302709\pi$
$140$	0	0
$141$	5.89898	0.496784
$142$	− 8.79796i	− 0.738308i
$143$	− 13.7980i	− 1.15384i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	11.8990	0.984767
$147$	4.89898i	0.404061i
$148$	6.34847i	0.521841i
$149$	−20.0000	−1.63846	−0.819232	−	0.573462i	$-0.805600\pi$
$149$	−20.0000	−1.63846	−0.819232	+	0.573462i	$0.805600\pi$
$150$	0	0
$151$	10.6969	0.870505	0.435252	−	0.900309i	$-0.356659\pi$
$151$	10.6969	0.870505	0.435252	+	0.900309i	$0.356659\pi$
$152$	− 2.89898i	− 0.235138i
$153$	0.550510i	0.0445061i
$154$	6.89898	0.555936
$155$	0	0
$156$	6.89898	0.552360
$157$	0.898979i	0.0717464i	0.999356	+	0.0358732i	$0.0114212\pi$
$157$	0.898979i	0.0717464i	−0.999356	+	0.0358732i	$0.988579\pi$
$158$	− 10.0000i	− 0.795557i
$159$	8.89898	0.705735
$160$	0	0
$161$	−3.44949	−0.271858
$162$	1.00000i	0.0785674i
$163$	1.79796i	0.140827i	0.997518	+	0.0704135i	$0.0224319\pi$
$163$	1.79796i	0.140827i	−0.997518	+	0.0704135i	$0.977568\pi$
$164$	−4.89898	−0.382546
$165$	0	0
$166$	−7.44949	−0.578193
$167$	− 7.00000i	− 0.541676i	−0.962625	−	0.270838i	$-0.912699\pi$
$167$	− 7.00000i	− 0.541676i	0.962625	−	0.270838i	$-0.0873008\pi$
$168$	3.44949i	0.266134i
$169$	−34.5959	−2.66122
$170$	0	0
$171$	−2.89898	−0.221691
$172$	1.10102i	0.0839520i
$173$	0.202041i	0.0153609i	0.999971	+	0.00768045i	$0.00244479\pi$
$173$	0.202041i	0.0153609i	−0.999971	+	0.00768045i	$0.997555\pi$
$174$	−5.00000	−0.379049
$175$	0	0
$176$	2.00000	0.150756
$177$	10.0000i	0.751646i
$178$	− 4.34847i	− 0.325932i
$179$	−12.8990	−0.964115	−0.482057	−	0.876140i	$-0.660110\pi$
$179$	−12.8990	−0.964115	−0.482057	+	0.876140i	$0.660110\pi$
$180$	0	0
$181$	−3.65153	−0.271416	−0.135708	−	0.990749i	$-0.543331\pi$
$181$	−3.65153	−0.271416	−0.135708	+	0.990749i	$0.543331\pi$
$182$	− 23.7980i	− 1.76402i
$183$	− 4.89898i	− 0.362143i
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	2.00000	0.146647
$187$	− 1.10102i	− 0.0805146i
$188$	− 5.89898i	− 0.430227i
$189$	3.44949	0.250913
$190$	0	0
$191$	2.00000	0.144715	0.0723575	−	0.997379i	$-0.476948\pi$
$191$	2.00000	0.144715	0.0723575	+	0.997379i	$0.476948\pi$
$192$	1.00000i	0.0721688i
$193$	19.6969i	1.41782i	0.705301	+	0.708908i	$0.250812\pi$
$193$	19.6969i	1.41782i	−0.705301	+	0.708908i	$0.749188\pi$
$194$	−16.6969	−1.19877
$195$	0	0
$196$	4.89898	0.349927
$197$	5.89898i	0.420285i	0.977671	+	0.210142i	$0.0673928\pi$
$197$	5.89898i	0.420285i	−0.977671	+	0.210142i	$0.932607\pi$
$198$	− 2.00000i	− 0.142134i
$199$	10.1464	0.719261	0.359631	−	0.933095i	$-0.382903\pi$
$199$	10.1464	0.719261	0.359631	+	0.933095i	$0.382903\pi$
$200$	0	0
$201$	−2.00000	−0.141069
$202$	15.6969i	1.10443i
$203$	17.2474i	1.21053i
$204$	0.550510	0.0385434
$205$	0	0
$206$	11.2474	0.783647
$207$	1.00000i	0.0695048i
$208$	− 6.89898i	− 0.478358i
$209$	5.79796	0.401053
$210$	0	0
$211$	−8.79796	−0.605676	−0.302838	−	0.953042i	$-0.597934\pi$
$211$	−8.79796	−0.605676	−0.302838	+	0.953042i	$0.597934\pi$
$212$	− 8.89898i	− 0.611184i
$213$	8.79796i	0.602826i
$214$	2.00000	0.136717
$215$	0	0
$216$	1.00000	0.0680414
$217$	− 6.89898i	− 0.468333i
$218$	1.44949i	0.0981718i
$219$	−11.8990	−0.804059
$220$	0	0
$221$	−3.79796	−0.255478
$222$	− 6.34847i	− 0.426081i
$223$	4.69694i	0.314530i	0.987556	+	0.157265i	$0.0502677\pi$
$223$	4.69694i	0.314530i	−0.987556	+	0.157265i	$0.949732\pi$
$224$	3.44949	0.230479
$225$	0	0
$226$	−0.348469	−0.0231798
$227$	− 29.2474i	− 1.94122i	−0.240655	−	0.970611i	$-0.577362\pi$
$227$	− 29.2474i	− 1.94122i	0.240655	−	0.970611i	$-0.422638\pi$
$228$	2.89898i	0.191990i
$229$	−12.8990	−0.852389	−0.426194	−	0.904632i	$-0.640146\pi$
$229$	−12.8990	−0.852389	−0.426194	+	0.904632i	$0.640146\pi$
$230$	0	0
$231$	−6.89898	−0.453920
$232$	5.00000i	0.328266i
$233$	− 2.69694i	− 0.176682i	−0.996090	−	0.0883412i	$-0.971843\pi$
$233$	− 2.69694i	− 0.176682i	0.996090	−	0.0883412i	$-0.0281566\pi$
$234$	−6.89898	−0.451000
$235$	0	0
$236$	10.0000	0.650945
$237$	10.0000i	0.649570i
$238$	− 1.89898i	− 0.123093i
$239$	17.8990	1.15779	0.578894	−	0.815403i	$-0.303484\pi$
$239$	17.8990	1.15779	0.578894	+	0.815403i	$0.303484\pi$
$240$	0	0
$241$	−8.00000	−0.515325	−0.257663	−	0.966235i	$-0.582952\pi$
$241$	−8.00000	−0.515325	−0.257663	+	0.966235i	$0.582952\pi$
$242$	− 7.00000i	− 0.449977i
$243$	− 1.00000i	− 0.0641500i
$244$	−4.89898	−0.313625
$245$	0	0
$246$	4.89898	0.312348
$247$	− 20.0000i	− 1.27257i
$248$	− 2.00000i	− 0.127000i
$249$	7.44949	0.472092
$250$	0	0
$251$	19.2474	1.21489	0.607444	−	0.794362i	$-0.292195\pi$
$251$	19.2474	1.21489	0.607444	+	0.794362i	$0.292195\pi$
$252$	− 3.44949i	− 0.217297i
$253$	− 2.00000i	− 0.125739i
$254$	17.7980	1.11674
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 27.7980i	− 1.73399i	−0.498318	−	0.866995i	$-0.666049\pi$
$257$	− 27.7980i	− 1.73399i	0.498318	−	0.866995i	$-0.333951\pi$
$258$	− 1.10102i	− 0.0685465i
$259$	−21.8990	−1.36074
$260$	0	0
$261$	5.00000	0.309492
$262$	− 0.898979i	− 0.0555391i
$263$	0.202041i	0.0124584i	0.999981	+	0.00622919i	$0.00198283\pi$
$263$	0.202041i	0.0124584i	−0.999981	+	0.00622919i	$0.998017\pi$
$264$	−2.00000	−0.123091
$265$	0	0
$266$	10.0000	0.613139
$267$	4.34847i	0.266122i
$268$	2.00000i	0.122169i
$269$	15.7980	0.963219	0.481609	−	0.876386i	$-0.340052\pi$
$269$	15.7980	0.963219	0.481609	+	0.876386i	$0.340052\pi$
$270$	0	0
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	− 0.550510i	− 0.0333796i
$273$	23.7980i	1.44032i
$274$	7.65153	0.462246
$275$	0	0
$276$	1.00000	0.0601929
$277$	− 13.5959i	− 0.816900i	−0.912781	−	0.408450i	$-0.866070\pi$
$277$	− 13.5959i	− 0.816900i	0.912781	−	0.408450i	$-0.133930\pi$
$278$	13.6969i	0.821488i
$279$	−2.00000	−0.119737
$280$	0	0
$281$	−25.2474	−1.50614	−0.753068	−	0.657942i	$-0.771427\pi$
$281$	−25.2474	−1.50614	−0.753068	+	0.657942i	$0.771427\pi$
$282$	5.89898i	0.351279i
$283$	27.5959i	1.64041i	0.572072	+	0.820204i	$0.306140\pi$
$283$	27.5959i	1.64041i	−0.572072	+	0.820204i	$0.693860\pi$
$284$	8.79796	0.522063
$285$	0	0
$286$	13.7980	0.815890
$287$	− 16.8990i	− 0.997515i
$288$	− 1.00000i	− 0.0589256i
$289$	16.6969	0.982173
$290$	0	0
$291$	16.6969	0.978792
$292$	11.8990i	0.696335i
$293$	11.7980i	0.689244i	0.938742	+	0.344622i	$0.111993\pi$
$293$	11.7980i	0.689244i	−0.938742	+	0.344622i	$0.888007\pi$
$294$	−4.89898	−0.285714
$295$	0	0
$296$	−6.34847	−0.368997
$297$	2.00000i	0.116052i
$298$	− 20.0000i	− 1.15857i
$299$	−6.89898	−0.398978
$300$	0	0
$301$	−3.79796	−0.218911
$302$	10.6969i	0.615540i
$303$	− 15.6969i	− 0.901766i
$304$	2.89898	0.166268
$305$	0	0
$306$	−0.550510	−0.0314706
$307$	− 29.8990i	− 1.70642i	−0.521564	−	0.853212i	$-0.674651\pi$
$307$	− 29.8990i	− 1.70642i	0.521564	−	0.853212i	$-0.325349\pi$
$308$	6.89898i	0.393106i
$309$	−11.2474	−0.639845
$310$	0	0
$311$	−24.5959	−1.39471	−0.697353	−	0.716728i	$-0.745639\pi$
$311$	−24.5959	−1.39471	−0.697353	+	0.716728i	$0.745639\pi$
$312$	6.89898i	0.390578i
$313$	3.10102i	0.175280i	0.996152	+	0.0876400i	$0.0279325\pi$
$313$	3.10102i	0.175280i	−0.996152	+	0.0876400i	$0.972067\pi$
$314$	−0.898979	−0.0507323
$315$	0	0
$316$	10.0000	0.562544
$317$	− 28.5959i	− 1.60611i	−0.595907	−	0.803053i	$-0.703207\pi$
$317$	− 28.5959i	− 1.60611i	0.595907	−	0.803053i	$-0.296793\pi$
$318$	8.89898i	0.499030i
$319$	−10.0000	−0.559893
$320$	0	0
$321$	−2.00000	−0.111629
$322$	− 3.44949i	− 0.192233i
$323$	− 1.59592i	− 0.0887992i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−1.79796	−0.0995797
$327$	− 1.44949i	− 0.0801570i
$328$	− 4.89898i	− 0.270501i
$329$	20.3485	1.12185
$330$	0	0
$331$	12.7980	0.703439	0.351720	−	0.936105i	$-0.385597\pi$
$331$	12.7980	0.703439	0.351720	+	0.936105i	$0.385597\pi$
$332$	− 7.44949i	− 0.408844i
$333$	6.34847i	0.347894i
$334$	7.00000	0.383023
$335$	0	0
$336$	−3.44949	−0.188185
$337$	32.4949i	1.77011i	0.465487	+	0.885055i	$0.345879\pi$
$337$	32.4949i	1.77011i	−0.465487	+	0.885055i	$0.654121\pi$
$338$	− 34.5959i	− 1.88177i
$339$	0.348469	0.0189263
$340$	0	0
$341$	4.00000	0.216612
$342$	− 2.89898i	− 0.156759i
$343$	− 7.24745i	− 0.391325i
$344$	−1.10102	−0.0593630
$345$	0	0
$346$	−0.202041	−0.0108618
$347$	− 3.30306i	− 0.177318i	−0.996062	−	0.0886588i	$-0.971742\pi$
$347$	− 3.30306i	− 0.177318i	0.996062	−	0.0886588i	$-0.0282581\pi$
$348$	− 5.00000i	− 0.268028i
$349$	−22.8990	−1.22575	−0.612877	−	0.790178i	$-0.709988\pi$
$349$	−22.8990	−1.22575	−0.612877	+	0.790178i	$0.709988\pi$
$350$	0	0
$351$	6.89898	0.368240
$352$	2.00000i	0.106600i
$353$	26.0000i	1.38384i	0.721974	+	0.691920i	$0.243235\pi$
$353$	26.0000i	1.38384i	−0.721974	+	0.691920i	$0.756765\pi$
$354$	−10.0000	−0.531494
$355$	0	0
$356$	4.34847	0.230468
$357$	1.89898i	0.100505i
$358$	− 12.8990i	− 0.681732i
$359$	25.7980	1.36156	0.680782	−	0.732486i	$-0.261640\pi$
$359$	25.7980	1.36156	0.680782	+	0.732486i	$0.261640\pi$
$360$	0	0
$361$	−10.5959	−0.557680
$362$	− 3.65153i	− 0.191920i
$363$	7.00000i	0.367405i
$364$	23.7980	1.24735
$365$	0	0
$366$	4.89898	0.256074
$367$	− 27.7980i	− 1.45104i	−0.688200	−	0.725521i	$-0.741599\pi$
$367$	− 27.7980i	− 1.45104i	0.688200	−	0.725521i	$-0.258401\pi$
$368$	− 1.00000i	− 0.0521286i
$369$	−4.89898	−0.255031
$370$	0	0
$371$	30.6969	1.59371
$372$	2.00000i	0.103695i
$373$	− 21.2474i	− 1.10015i	−0.835115	−	0.550076i	$-0.814599\pi$
$373$	− 21.2474i	− 1.10015i	0.835115	−	0.550076i	$-0.185401\pi$
$374$	1.10102	0.0569324
$375$	0	0
$376$	5.89898	0.304217
$377$	34.4949i	1.77658i
$378$	3.44949i	0.177423i
$379$	−30.2929	−1.55604	−0.778020	−	0.628240i	$-0.783776\pi$
$379$	−30.2929	−1.55604	−0.778020	+	0.628240i	$0.783776\pi$
$380$	0	0
$381$	−17.7980	−0.911817
$382$	2.00000i	0.102329i
$383$	− 9.79796i	− 0.500652i	−0.968162	−	0.250326i	$-0.919462\pi$
$383$	− 9.79796i	− 0.500652i	0.968162	−	0.250326i	$-0.0805379\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−19.6969	−1.00255
$387$	1.10102i	0.0559680i
$388$	− 16.6969i	− 0.847659i
$389$	4.20204	0.213052	0.106526	−	0.994310i	$-0.466027\pi$
$389$	4.20204	0.213052	0.106526	+	0.994310i	$0.466027\pi$
$390$	0	0
$391$	−0.550510	−0.0278405
$392$	4.89898i	0.247436i
$393$	0.898979i	0.0453475i
$394$	−5.89898	−0.297186
$395$	0	0
$396$	2.00000	0.100504
$397$	28.0000i	1.40528i	0.711546	+	0.702640i	$0.247995\pi$
$397$	28.0000i	1.40528i	−0.711546	+	0.702640i	$0.752005\pi$
$398$	10.1464i	0.508594i
$399$	−10.0000	−0.500626
$400$	0	0
$401$	10.6969	0.534180	0.267090	−	0.963672i	$-0.413938\pi$
$401$	10.6969	0.534180	0.267090	+	0.963672i	$0.413938\pi$
$402$	− 2.00000i	− 0.0997509i
$403$	− 13.7980i	− 0.687325i
$404$	−15.6969	−0.780952
$405$	0	0
$406$	−17.2474	−0.855977
$407$	− 12.6969i	− 0.629364i
$408$	0.550510i	0.0272543i
$409$	3.69694	0.182802	0.0914009	−	0.995814i	$-0.470866\pi$
$409$	3.69694	0.182802	0.0914009	+	0.995814i	$0.470866\pi$
$410$	0	0
$411$	−7.65153	−0.377422
$412$	11.2474i	0.554122i
$413$	34.4949i	1.69738i
$414$	−1.00000	−0.0491473
$415$	0	0
$416$	6.89898	0.338250
$417$	− 13.6969i	− 0.670742i
$418$	5.79796i	0.283587i
$419$	20.1464	0.984217	0.492109	−	0.870534i	$-0.336226\pi$
$419$	20.1464	0.984217	0.492109	+	0.870534i	$0.336226\pi$
$420$	0	0
$421$	36.4949	1.77865	0.889326	−	0.457273i	$-0.151174\pi$
$421$	36.4949	1.77865	0.889326	+	0.457273i	$0.151174\pi$
$422$	− 8.79796i	− 0.428278i
$423$	− 5.89898i	− 0.286818i
$424$	8.89898	0.432173
$425$	0	0
$426$	−8.79796	−0.426263
$427$	− 16.8990i	− 0.817799i
$428$	2.00000i	0.0966736i
$429$	−13.7980	−0.666172
$430$	0	0
$431$	40.6969	1.96030	0.980151	−	0.198251i	$-0.0635261\pi$
$431$	40.6969	1.96030	0.980151	+	0.198251i	$0.0635261\pi$
$432$	1.00000i	0.0481125i
$433$	− 12.6969i	− 0.610176i	−0.952324	−	0.305088i	$-0.901314\pi$
$433$	− 12.6969i	− 0.610176i	0.952324	−	0.305088i	$-0.0986859\pi$
$434$	6.89898	0.331162
$435$	0	0
$436$	−1.44949	−0.0694180
$437$	− 2.89898i	− 0.138677i
$438$	− 11.8990i	− 0.568555i
$439$	−18.6969	−0.892356	−0.446178	−	0.894944i	$-0.647215\pi$
$439$	−18.6969	−0.892356	−0.446178	+	0.894944i	$0.647215\pi$
$440$	0	0
$441$	4.89898	0.233285
$442$	− 3.79796i	− 0.180650i
$443$	34.6969i	1.64850i	0.566225	+	0.824251i	$0.308403\pi$
$443$	34.6969i	1.64850i	−0.566225	+	0.824251i	$0.691597\pi$
$444$	6.34847	0.301285
$445$	0	0
$446$	−4.69694	−0.222406
$447$	20.0000i	0.945968i
$448$	3.44949i	0.162973i
$449$	15.7980	0.745552	0.372776	−	0.927921i	$-0.378406\pi$
$449$	15.7980	0.745552	0.372776	+	0.927921i	$0.378406\pi$
$450$	0	0
$451$	9.79796	0.461368
$452$	− 0.348469i	− 0.0163906i
$453$	− 10.6969i	− 0.502586i
$454$	29.2474	1.37265
$455$	0	0
$456$	−2.89898	−0.135757
$457$	39.5959i	1.85222i	0.377255	+	0.926109i	$0.376868\pi$
$457$	39.5959i	1.85222i	−0.377255	+	0.926109i	$0.623132\pi$
$458$	− 12.8990i	− 0.602730i
$459$	0.550510	0.0256956
$460$	0	0
$461$	−27.4949	−1.28057	−0.640283	−	0.768140i	$-0.721183\pi$
$461$	−27.4949	−1.28057	−0.640283	+	0.768140i	$0.721183\pi$
$462$	− 6.89898i	− 0.320970i
$463$	− 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
$466$	2.69694	0.124933
$467$	23.9444i	1.10801i	0.832512	+	0.554007i	$0.186902\pi$
$467$	23.9444i	1.10801i	−0.832512	+	0.554007i	$0.813098\pi$
$468$	− 6.89898i	− 0.318905i
$469$	−6.89898	−0.318565
$470$	0	0
$471$	0.898979	0.0414228
$472$	10.0000i	0.460287i
$473$	− 2.20204i	− 0.101250i
$474$	−10.0000	−0.459315
$475$	0	0
$476$	1.89898	0.0870396
$477$	− 8.89898i	− 0.407456i
$478$	17.8990i	0.818680i
$479$	30.0000	1.37073	0.685367	−	0.728197i	$-0.259642\pi$
$479$	30.0000	1.37073	0.685367	+	0.728197i	$0.259642\pi$
$480$	0	0
$481$	−43.7980	−1.99702
$482$	− 8.00000i	− 0.364390i
$483$	3.44949i	0.156957i
$484$	7.00000	0.318182
$485$	0	0
$486$	1.00000	0.0453609
$487$	− 24.8990i	− 1.12828i	−0.825679	−	0.564140i	$-0.809208\pi$
$487$	− 24.8990i	− 1.12828i	0.825679	−	0.564140i	$-0.190792\pi$
$488$	− 4.89898i	− 0.221766i
$489$	1.79796	0.0813065
$490$	0	0
$491$	34.8990	1.57497	0.787484	−	0.616335i	$-0.211383\pi$
$491$	34.8990	1.57497	0.787484	+	0.616335i	$0.211383\pi$
$492$	4.89898i	0.220863i
$493$	2.75255i	0.123969i
$494$	20.0000	0.899843
$495$	0	0
$496$	2.00000	0.0898027
$497$	30.3485i	1.36131i
$498$	7.44949i	0.333820i
$499$	−12.1010	−0.541716	−0.270858	−	0.962619i	$-0.587307\pi$
$499$	−12.1010	−0.541716	−0.270858	+	0.962619i	$0.587307\pi$
$500$	0	0
$501$	−7.00000	−0.312737
$502$	19.2474i	0.859056i
$503$	14.6969i	0.655304i	0.944798	+	0.327652i	$0.106257\pi$
$503$	14.6969i	0.655304i	−0.944798	+	0.327652i	$0.893743\pi$
$504$	3.44949	0.153652
$505$	0	0
$506$	2.00000	0.0889108
$507$	34.5959i	1.53646i
$508$	17.7980i	0.789657i
$509$	15.0000	0.664863	0.332432	−	0.943127i	$-0.392131\pi$
$509$	15.0000	0.664863	0.332432	+	0.943127i	$0.392131\pi$
$510$	0	0
$511$	−41.0454	−1.81574
$512$	1.00000i	0.0441942i
$513$	2.89898i	0.127993i
$514$	27.7980	1.22612
$515$	0	0
$516$	1.10102	0.0484697
$517$	11.7980i	0.518874i
$518$	− 21.8990i	− 0.962186i
$519$	0.202041	0.00886862
$520$	0	0
$521$	−8.14643	−0.356901	−0.178451	−	0.983949i	$-0.557109\pi$
$521$	−8.14643	−0.356901	−0.178451	+	0.983949i	$0.557109\pi$
$522$	5.00000i	0.218844i
$523$	16.0000i	0.699631i	0.936819	+	0.349816i	$0.113756\pi$
$523$	16.0000i	0.699631i	−0.936819	+	0.349816i	$0.886244\pi$
$524$	0.898979	0.0392721
$525$	0	0
$526$	−0.202041	−0.00880941
$527$	− 1.10102i	− 0.0479612i
$528$	− 2.00000i	− 0.0870388i
$529$	−1.00000	−0.0434783
$530$	0	0
$531$	10.0000	0.433963
$532$	10.0000i	0.433555i
$533$	− 33.7980i	− 1.46395i
$534$	−4.34847	−0.188177
$535$	0	0
$536$	−2.00000	−0.0863868
$537$	12.8990i	0.556632i
$538$	15.7980i	0.681098i
$539$	−9.79796	−0.422028
$540$	0	0
$541$	23.5959	1.01447	0.507234	−	0.861808i	$-0.330668\pi$
$541$	23.5959	1.01447	0.507234	+	0.861808i	$0.330668\pi$
$542$	− 8.00000i	− 0.343629i
$543$	3.65153i	0.156702i
$544$	0.550510	0.0236029
$545$	0	0
$546$	−23.7980	−1.01846
$547$	8.79796i	0.376174i	0.982152	+	0.188087i	$0.0602286\pi$
$547$	8.79796i	0.376174i	−0.982152	+	0.188087i	$0.939771\pi$
$548$	7.65153i	0.326857i
$549$	−4.89898	−0.209083
$550$	0	0
$551$	−14.4949	−0.617503
$552$	1.00000i	0.0425628i
$553$	34.4949i	1.46687i
$554$	13.5959	0.577635
$555$	0	0
$556$	−13.6969	−0.580880
$557$	− 0.696938i	− 0.0295302i	−0.999891	−	0.0147651i	$-0.995300\pi$
$557$	− 0.696938i	− 0.0295302i	0.999891	−	0.0147651i	$-0.00470005\pi$
$558$	− 2.00000i	− 0.0846668i
$559$	−7.59592	−0.321273
$560$	0	0
$561$	−1.10102	−0.0464851
$562$	− 25.2474i	− 1.06500i
$563$	6.00000i	0.252870i	0.991975	+	0.126435i	$0.0403535\pi$
$563$	6.00000i	0.252870i	−0.991975	+	0.126435i	$0.959647\pi$
$564$	−5.89898	−0.248392
$565$	0	0
$566$	−27.5959	−1.15994
$567$	− 3.44949i	− 0.144865i
$568$	8.79796i	0.369154i
$569$	−4.49490	−0.188436	−0.0942180	−	0.995552i	$-0.530035\pi$
$569$	−4.49490	−0.188436	−0.0942180	+	0.995552i	$0.530035\pi$
$570$	0	0
$571$	3.30306	0.138229	0.0691144	−	0.997609i	$-0.477983\pi$
$571$	3.30306	0.138229	0.0691144	+	0.997609i	$0.477983\pi$
$572$	13.7980i	0.576922i
$573$	− 2.00000i	− 0.0835512i
$574$	16.8990	0.705350
$575$	0	0
$576$	1.00000	0.0416667
$577$	− 2.00000i	− 0.0832611i	−0.999133	−	0.0416305i	$-0.986745\pi$
$577$	− 2.00000i	− 0.0832611i	0.999133	−	0.0416305i	$-0.0132552\pi$
$578$	16.6969i	0.694501i
$579$	19.6969	0.818577
$580$	0	0
$581$	25.6969	1.06609
$582$	16.6969i	0.692110i
$583$	17.7980i	0.737116i
$584$	−11.8990	−0.492383
$585$	0	0
$586$	−11.7980	−0.487369
$587$	− 4.89898i	− 0.202203i	−0.994876	−	0.101101i	$-0.967763\pi$
$587$	− 4.89898i	− 0.202203i	0.994876	−	0.101101i	$-0.0322366\pi$
$588$	− 4.89898i	− 0.202031i
$589$	5.79796	0.238901
$590$	0	0
$591$	5.89898	0.242652
$592$	− 6.34847i	− 0.260920i
$593$	4.40408i	0.180854i	0.995903	+	0.0904270i	$0.0288232\pi$
$593$	4.40408i	0.180854i	−0.995903	+	0.0904270i	$0.971177\pi$
$594$	−2.00000	−0.0820610
$595$	0	0
$596$	20.0000	0.819232
$597$	− 10.1464i	− 0.415266i
$598$	− 6.89898i	− 0.282120i
$599$	−37.3939	−1.52787	−0.763936	−	0.645292i	$-0.776736\pi$
$599$	−37.3939	−1.52787	−0.763936	+	0.645292i	$0.776736\pi$
$600$	0	0
$601$	37.0000	1.50926	0.754631	−	0.656150i	$-0.227816\pi$
$601$	37.0000	1.50926	0.754631	+	0.656150i	$0.227816\pi$
$602$	− 3.79796i	− 0.154793i
$603$	2.00000i	0.0814463i
$604$	−10.6969	−0.435252
$605$	0	0
$606$	15.6969	0.637645
$607$	18.0000i	0.730597i	0.930890	+	0.365299i	$0.119033\pi$
$607$	18.0000i	0.730597i	−0.930890	+	0.365299i	$0.880967\pi$
$608$	2.89898i	0.117569i
$609$	17.2474	0.698902
$610$	0	0
$611$	40.6969	1.64642
$612$	− 0.550510i	− 0.0222531i
$613$	− 34.1464i	− 1.37916i	−0.724209	−	0.689581i	$-0.757795\pi$
$613$	− 34.1464i	− 1.37916i	0.724209	−	0.689581i	$-0.242205\pi$
$614$	29.8990	1.20662
$615$	0	0
$616$	−6.89898	−0.277968
$617$	− 36.4949i	− 1.46923i	−0.678485	−	0.734615i	$-0.737363\pi$
$617$	− 36.4949i	− 1.46923i	0.678485	−	0.734615i	$-0.262637\pi$
$618$	− 11.2474i	− 0.452439i
$619$	−4.49490	−0.180665	−0.0903326	−	0.995912i	$-0.528793\pi$
$619$	−4.49490	−0.180665	−0.0903326	+	0.995912i	$0.528793\pi$
$620$	0	0
$621$	1.00000	0.0401286
$622$	− 24.5959i	− 0.986206i
$623$	15.0000i	0.600962i
$624$	−6.89898	−0.276180
$625$	0	0
$626$	−3.10102	−0.123942
$627$	− 5.79796i	− 0.231548i
$628$	− 0.898979i	− 0.0358732i
$629$	−3.49490	−0.139351
$630$	0	0
$631$	10.5505	0.420009	0.210005	−	0.977700i	$-0.432652\pi$
$631$	10.5505	0.420009	0.210005	+	0.977700i	$0.432652\pi$
$632$	10.0000i	0.397779i
$633$	8.79796i	0.349687i
$634$	28.5959	1.13569
$635$	0	0
$636$	−8.89898	−0.352867
$637$	33.7980i	1.33912i
$638$	− 10.0000i	− 0.395904i
$639$	8.79796	0.348042
$640$	0	0
$641$	−29.4495	−1.16318	−0.581592	−	0.813480i	$-0.697570\pi$
$641$	−29.4495	−1.16318	−0.581592	+	0.813480i	$0.697570\pi$
$642$	− 2.00000i	− 0.0789337i
$643$	0.202041i	0.00796772i	0.999992	+	0.00398386i	$0.00126811\pi$
$643$	0.202041i	0.00796772i	−0.999992	+	0.00398386i	$0.998732\pi$
$644$	3.44949	0.135929
$645$	0	0
$646$	1.59592	0.0627906
$647$	− 18.5959i	− 0.731081i	−0.930795	−	0.365540i	$-0.880884\pi$
$647$	− 18.5959i	− 0.731081i	0.930795	−	0.365540i	$-0.119116\pi$
$648$	− 1.00000i	− 0.0392837i
$649$	−20.0000	−0.785069
$650$	0	0
$651$	−6.89898	−0.270392
$652$	− 1.79796i	− 0.0704135i
$653$	29.6969i	1.16213i	0.813857	+	0.581066i	$0.197364\pi$
$653$	29.6969i	1.16213i	−0.813857	+	0.581066i	$0.802636\pi$
$654$	1.44949	0.0566795
$655$	0	0
$656$	4.89898	0.191273
$657$	11.8990i	0.464223i
$658$	20.3485i	0.793266i
$659$	18.5505	0.722625	0.361313	−	0.932445i	$-0.382329\pi$
$659$	18.5505	0.722625	0.361313	+	0.932445i	$0.382329\pi$
$660$	0	0
$661$	−16.5505	−0.643740	−0.321870	−	0.946784i	$-0.604311\pi$
$661$	−16.5505	−0.643740	−0.321870	+	0.946784i	$0.604311\pi$
$662$	12.7980i	0.497407i
$663$	3.79796i	0.147501i
$664$	7.44949	0.289096
$665$	0	0
$666$	−6.34847	−0.245998
$667$	5.00000i	0.193601i
$668$	7.00000i	0.270838i
$669$	4.69694	0.181594
$670$	0	0
$671$	9.79796	0.378246
$672$	− 3.44949i	− 0.133067i
$673$	12.5959i	0.485537i	0.970084	+	0.242768i	$0.0780555\pi$
$673$	12.5959i	0.485537i	−0.970084	+	0.242768i	$0.921944\pi$
$674$	−32.4949	−1.25166
$675$	0	0
$676$	34.5959	1.33061
$677$	25.3939i	0.975966i	0.872853	+	0.487983i	$0.162267\pi$
$677$	25.3939i	0.975966i	−0.872853	+	0.487983i	$0.837733\pi$
$678$	0.348469i	0.0133829i
$679$	57.5959	2.21033
$680$	0	0
$681$	−29.2474	−1.12076
$682$	4.00000i	0.153168i
$683$	− 16.8990i	− 0.646621i	−0.946293	−	0.323311i	$-0.895204\pi$
$683$	− 16.8990i	− 0.646621i	0.946293	−	0.323311i	$-0.104796\pi$
$684$	2.89898	0.110845
$685$	0	0
$686$	7.24745	0.276709
$687$	12.8990i	0.492127i
$688$	− 1.10102i	− 0.0419760i
$689$	61.3939	2.33892
$690$	0	0
$691$	−28.7980	−1.09553	−0.547763	−	0.836634i	$-0.684520\pi$
$691$	−28.7980	−1.09553	−0.547763	+	0.836634i	$0.684520\pi$
$692$	− 0.202041i	− 0.00768045i
$693$	6.89898i	0.262071i
$694$	3.30306	0.125383
$695$	0	0
$696$	5.00000	0.189525
$697$	− 2.69694i	− 0.102154i
$698$	− 22.8990i	− 0.866739i
$699$	−2.69694	−0.102008
$700$	0	0
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	6.89898i	0.260385i
$703$	− 18.4041i	− 0.694123i
$704$	−2.00000	−0.0753778
$705$	0	0
$706$	−26.0000	−0.978523
$707$	− 54.1464i	− 2.03639i
$708$	− 10.0000i	− 0.375823i
$709$	25.9444	0.974362	0.487181	−	0.873301i	$-0.338025\pi$
$709$	25.9444	0.974362	0.487181	+	0.873301i	$0.338025\pi$
$710$	0	0
$711$	10.0000	0.375029
$712$	4.34847i	0.162966i
$713$	− 2.00000i	− 0.0749006i
$714$	−1.89898	−0.0710675
$715$	0	0
$716$	12.8990	0.482057
$717$	− 17.8990i	− 0.668450i
$718$	25.7980i	0.962771i
$719$	−9.20204	−0.343178	−0.171589	−	0.985169i	$-0.554890\pi$
$719$	−9.20204	−0.343178	−0.171589	+	0.985169i	$0.554890\pi$
$720$	0	0
$721$	−38.7980	−1.44491
$722$	− 10.5959i	− 0.394339i
$723$	8.00000i	0.297523i
$724$	3.65153	0.135708
$725$	0	0
$726$	−7.00000	−0.259794
$727$	− 19.3939i	− 0.719279i	−0.933091	−	0.359640i	$-0.882900\pi$
$727$	− 19.3939i	− 0.719279i	0.933091	−	0.359640i	$-0.117100\pi$
$728$	23.7980i	0.882011i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−0.606123	−0.0224183
$732$	4.89898i	0.181071i
$733$	5.85357i	0.216207i	0.994140	+	0.108103i	$0.0344777\pi$
$733$	5.85357i	0.216207i	−0.994140	+	0.108103i	$0.965522\pi$
$734$	27.7980	1.02604
$735$	0	0
$736$	1.00000	0.0368605
$737$	− 4.00000i	− 0.147342i
$738$	− 4.89898i	− 0.180334i
$739$	26.5959	0.978347	0.489173	−	0.872187i	$-0.337299\pi$
$739$	26.5959	0.978347	0.489173	+	0.872187i	$0.337299\pi$
$740$	0	0
$741$	−20.0000	−0.734718
$742$	30.6969i	1.12692i
$743$	− 44.2929i	− 1.62495i	−0.582998	−	0.812474i	$-0.698120\pi$
$743$	− 44.2929i	− 1.62495i	0.582998	−	0.812474i	$-0.301880\pi$
$744$	−2.00000	−0.0733236
$745$	0	0
$746$	21.2474	0.777924
$747$	− 7.44949i	− 0.272563i
$748$	1.10102i	0.0402573i
$749$	−6.89898	−0.252083
$750$	0	0
$751$	−0.752551	−0.0274610	−0.0137305	−	0.999906i	$-0.504371\pi$
$751$	−0.752551	−0.0274610	−0.0137305	+	0.999906i	$0.504371\pi$
$752$	5.89898i	0.215114i
$753$	− 19.2474i	− 0.701416i
$754$	−34.4949	−1.25623
$755$	0	0
$756$	−3.44949	−0.125457
$757$	35.2474i	1.28109i	0.767921	+	0.640545i	$0.221292\pi$
$757$	35.2474i	1.28109i	−0.767921	+	0.640545i	$0.778708\pi$
$758$	− 30.2929i	− 1.10029i
$759$	−2.00000	−0.0725954
$760$	0	0
$761$	38.0908	1.38079	0.690395	−	0.723432i	$-0.257437\pi$
$761$	38.0908	1.38079	0.690395	+	0.723432i	$0.257437\pi$
$762$	− 17.7980i	− 0.644752i
$763$	− 5.00000i	− 0.181012i
$764$	−2.00000	−0.0723575
$765$	0	0
$766$	9.79796	0.354015
$767$	68.9898i	2.49108i
$768$	− 1.00000i	− 0.0360844i
$769$	20.2929	0.731779	0.365890	−	0.930658i	$-0.380765\pi$
$769$	20.2929	0.731779	0.365890	+	0.930658i	$0.380765\pi$
$770$	0	0
$771$	−27.7980	−1.00112
$772$	− 19.6969i	− 0.708908i
$773$	− 1.10102i	− 0.0396010i	−0.999804	−	0.0198005i	$-0.993697\pi$
$773$	− 1.10102i	− 0.0396010i	0.999804	−	0.0198005i	$-0.00630310\pi$
$774$	−1.10102	−0.0395754
$775$	0	0
$776$	16.6969	0.599385
$777$	21.8990i	0.785622i
$778$	4.20204i	0.150650i
$779$	14.2020	0.508841
$780$	0	0
$781$	−17.5959	−0.629631
$782$	− 0.550510i	− 0.0196862i
$783$	− 5.00000i	− 0.178685i
$784$	−4.89898	−0.174964
$785$	0	0
$786$	−0.898979	−0.0320655
$787$	28.0000i	0.998092i	0.866575	+	0.499046i	$0.166316\pi$
$787$	28.0000i	0.998092i	−0.866575	+	0.499046i	$0.833684\pi$
$788$	− 5.89898i	− 0.210142i
$789$	0.202041	0.00719285
$790$	0	0
$791$	1.20204	0.0427397
$792$	2.00000i	0.0710669i
$793$	− 33.7980i	− 1.20020i
$794$	−28.0000	−0.993683
$795$	0	0
$796$	−10.1464	−0.359631
$797$	25.1010i	0.889124i	0.895748	+	0.444562i	$0.146641\pi$
$797$	25.1010i	0.889124i	−0.895748	+	0.444562i	$0.853359\pi$
$798$	− 10.0000i	− 0.353996i
$799$	3.24745	0.114886
$800$	0	0
$801$	4.34847	0.153646
$802$	10.6969i	0.377722i
$803$	− 23.7980i	− 0.839812i
$804$	2.00000	0.0705346
$805$	0	0
$806$	13.7980	0.486012
$807$	− 15.7980i	− 0.556114i
$808$	− 15.6969i	− 0.552216i
$809$	47.3939	1.66628	0.833140	−	0.553062i	$-0.186541\pi$
$809$	47.3939	1.66628	0.833140	+	0.553062i	$0.186541\pi$
$810$	0	0
$811$	26.2020	0.920078	0.460039	−	0.887899i	$-0.347835\pi$
$811$	26.2020	0.920078	0.460039	+	0.887899i	$0.347835\pi$
$812$	− 17.2474i	− 0.605267i
$813$	8.00000i	0.280572i
$814$	12.6969	0.445027
$815$	0	0
$816$	−0.550510	−0.0192717
$817$	− 3.19184i	− 0.111668i
$818$	3.69694i	0.129260i
$819$	23.7980	0.831568
$820$	0	0
$821$	−32.2020	−1.12386	−0.561929	−	0.827185i	$-0.689941\pi$
$821$	−32.2020	−1.12386	−0.561929	+	0.827185i	$0.689941\pi$
$822$	− 7.65153i	− 0.266878i
$823$	32.0908i	1.11862i	0.828960	+	0.559308i	$0.188933\pi$
$823$	32.0908i	1.11862i	−0.828960	+	0.559308i	$0.811067\pi$
$824$	−11.2474	−0.391823
$825$	0	0
$826$	−34.4949	−1.20023
$827$	− 39.2474i	− 1.36477i	−0.730994	−	0.682384i	$-0.760943\pi$
$827$	− 39.2474i	− 1.36477i	0.730994	−	0.682384i	$-0.239057\pi$
$828$	− 1.00000i	− 0.0347524i
$829$	42.8990	1.48994	0.744972	−	0.667096i	$-0.232463\pi$
$829$	42.8990	1.48994	0.744972	+	0.667096i	$0.232463\pi$
$830$	0	0
$831$	−13.5959	−0.471637
$832$	6.89898i	0.239179i
$833$	2.69694i	0.0934434i
$834$	13.6969	0.474286
$835$	0	0
$836$	−5.79796	−0.200527
$837$	2.00000i	0.0691301i
$838$	20.1464i	0.695947i
$839$	38.6969	1.33597	0.667983	−	0.744176i	$-0.267158\pi$
$839$	38.6969	1.33597	0.667983	+	0.744176i	$0.267158\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	36.4949i	1.25770i
$843$	25.2474i	0.869568i
$844$	8.79796	0.302838
$845$	0	0
$846$	5.89898	0.202811
$847$	24.1464i	0.829681i
$848$	8.89898i	0.305592i
$849$	27.5959	0.947089
$850$	0	0
$851$	−6.34847	−0.217623
$852$	− 8.79796i	− 0.301413i
$853$	− 52.9898i	− 1.81434i	−0.420769	−	0.907168i	$-0.638240\pi$
$853$	− 52.9898i	− 1.81434i	0.420769	−	0.907168i	$-0.361760\pi$
$854$	16.8990	0.578271
$855$	0	0
$856$	−2.00000	−0.0683586
$857$	− 6.49490i	− 0.221861i	−0.993828	−	0.110931i	$-0.964617\pi$
$857$	− 6.49490i	− 0.221861i	0.993828	−	0.110931i	$-0.0353832\pi$
$858$	− 13.7980i	− 0.471055i
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	0	0
$861$	−16.8990	−0.575916
$862$	40.6969i	1.38614i
$863$	38.3939i	1.30694i	0.756951	+	0.653471i	$0.226688\pi$
$863$	38.3939i	1.30694i	−0.756951	+	0.653471i	$0.773312\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	12.6969	0.431460
$867$	− 16.6969i	− 0.567058i
$868$	6.89898i	0.234167i
$869$	−20.0000	−0.678454
$870$	0	0
$871$	−13.7980	−0.467526
$872$	− 1.44949i	− 0.0490859i
$873$	− 16.6969i	− 0.565106i
$874$	2.89898	0.0980594
$875$	0	0
$876$	11.8990	0.402029
$877$	29.5959i	0.999383i	0.866203	+	0.499692i	$0.166553\pi$
$877$	29.5959i	0.999383i	−0.866203	+	0.499692i	$0.833447\pi$
$878$	− 18.6969i	− 0.630991i
$879$	11.7980	0.397935
$880$	0	0
$881$	−40.8990	−1.37792	−0.688961	−	0.724799i	$-0.741933\pi$
$881$	−40.8990	−1.37792	−0.688961	+	0.724799i	$0.741933\pi$
$882$	4.89898i	0.164957i
$883$	9.40408i	0.316473i	0.987401	+	0.158236i	$0.0505808\pi$
$883$	9.40408i	0.316473i	−0.987401	+	0.158236i	$0.949419\pi$
$884$	3.79796	0.127739
$885$	0	0
$886$	−34.6969	−1.16567
$887$	− 19.8990i	− 0.668142i	−0.942548	−	0.334071i	$-0.891577\pi$
$887$	− 19.8990i	− 0.668142i	0.942548	−	0.334071i	$-0.108423\pi$
$888$	6.34847i	0.213041i
$889$	−61.3939	−2.05908
$890$	0	0
$891$	2.00000	0.0670025
$892$	− 4.69694i	− 0.157265i
$893$	17.1010i	0.572264i
$894$	−20.0000	−0.668900
$895$	0	0
$896$	−3.44949	−0.115239
$897$	6.89898i	0.230350i
$898$	15.7980i	0.527185i
$899$	−10.0000	−0.333519
$900$	0	0
$901$	4.89898	0.163209
$902$	9.79796i	0.326236i
$903$	3.79796i	0.126388i
$904$	0.348469	0.0115899
$905$	0	0
$906$	10.6969	0.355382
$907$	− 46.4949i	− 1.54384i	−0.635721	−	0.771919i	$-0.719297\pi$
$907$	− 46.4949i	− 1.54384i	0.635721	−	0.771919i	$-0.280703\pi$
$908$	29.2474i	0.970611i
$909$	−15.6969	−0.520635
$910$	0	0
$911$	50.6969	1.67966	0.839832	−	0.542846i	$-0.182653\pi$
$911$	50.6969	1.67966	0.839832	+	0.542846i	$0.182653\pi$
$912$	− 2.89898i	− 0.0959948i
$913$	14.8990i	0.493084i
$914$	−39.5959	−1.30972
$915$	0	0
$916$	12.8990	0.426194
$917$	3.10102i	0.102405i
$918$	0.550510i	0.0181695i
$919$	−25.9444	−0.855826	−0.427913	−	0.903820i	$-0.640751\pi$
$919$	−25.9444	−0.855826	−0.427913	+	0.903820i	$0.640751\pi$
$920$	0	0
$921$	−29.8990	−0.985205
$922$	− 27.4949i	− 0.905496i
$923$	60.6969i	1.99786i
$924$	6.89898	0.226960
$925$	0	0
$926$	4.00000	0.131448
$927$	11.2474i	0.369415i
$928$	− 5.00000i	− 0.164133i
$929$	−15.7980	−0.518314	−0.259157	−	0.965835i	$-0.583445\pi$
$929$	−15.7980	−0.518314	−0.259157	+	0.965835i	$0.583445\pi$
$930$	0	0
$931$	−14.2020	−0.465453
$932$	2.69694i	0.0883412i
$933$	24.5959i	0.805234i
$934$	−23.9444	−0.783484
$935$	0	0
$936$	6.89898	0.225500
$937$	3.79796i	0.124074i	0.998074	+	0.0620370i	$0.0197597\pi$
$937$	3.79796i	0.124074i	−0.998074	+	0.0620370i	$0.980240\pi$
$938$	− 6.89898i	− 0.225260i
$939$	3.10102	0.101198
$940$	0	0
$941$	2.00000	0.0651981	0.0325991	−	0.999469i	$-0.489622\pi$
$941$	2.00000	0.0651981	0.0325991	+	0.999469i	$0.489622\pi$
$942$	0.898979i	0.0292903i
$943$	− 4.89898i	− 0.159533i
$944$	−10.0000	−0.325472
$945$	0	0
$946$	2.20204	0.0715945
$947$	39.5959i	1.28669i	0.765575	+	0.643347i	$0.222455\pi$
$947$	39.5959i	1.28669i	−0.765575	+	0.643347i	$0.777545\pi$
$948$	− 10.0000i	− 0.324785i
$949$	−82.0908	−2.66478
$950$	0	0
$951$	−28.5959	−0.927286
$952$	1.89898i	0.0615463i
$953$	− 32.8434i	− 1.06390i	−0.846775	−	0.531951i	$-0.821459\pi$
$953$	− 32.8434i	− 1.06390i	0.846775	−	0.531951i	$-0.178541\pi$
$954$	8.89898	0.288115
$955$	0	0
$956$	−17.8990	−0.578894
$957$	10.0000i	0.323254i
$958$	30.0000i	0.969256i
$959$	−26.3939	−0.852303
$960$	0	0
$961$	−27.0000	−0.870968
$962$	− 43.7980i	− 1.41210i
$963$	2.00000i	0.0644491i
$964$	8.00000	0.257663
$965$	0	0
$966$	−3.44949	−0.110986
$967$	9.59592i	0.308584i	0.988025	+	0.154292i	$0.0493096\pi$
$967$	9.59592i	0.308584i	−0.988025	+	0.154292i	$0.950690\pi$
$968$	7.00000i	0.224989i
$969$	−1.59592	−0.0512683
$970$	0	0
$971$	−8.14643	−0.261431	−0.130716	−	0.991420i	$-0.541727\pi$
$971$	−8.14643	−0.261431	−0.130716	+	0.991420i	$0.541727\pi$
$972$	1.00000i	0.0320750i
$973$	− 47.2474i	− 1.51468i
$974$	24.8990	0.797815
$975$	0	0
$976$	4.89898	0.156813
$977$	− 49.2474i	− 1.57557i	−0.615953	−	0.787783i	$-0.711229\pi$
$977$	− 49.2474i	− 1.57557i	0.615953	−	0.787783i	$-0.288771\pi$
$978$	1.79796i	0.0574924i
$979$	−8.69694	−0.277955
$980$	0	0
$981$	−1.44949	−0.0462786
$982$	34.8990i	1.11367i
$983$	− 24.0000i	− 0.765481i	−0.923856	−	0.382741i	$-0.874980\pi$
$983$	− 24.0000i	− 0.765481i	0.923856	−	0.382741i	$-0.125020\pi$
$984$	−4.89898	−0.156174
$985$	0	0
$986$	−2.75255	−0.0876591
$987$	− 20.3485i	− 0.647699i
$988$	20.0000i	0.636285i
$989$	−1.10102	−0.0350104
$990$	0	0
$991$	37.7980	1.20069	0.600346	−	0.799740i	$-0.295030\pi$
$991$	37.7980	1.20069	0.600346	+	0.799740i	$0.295030\pi$
$992$	2.00000i	0.0635001i
$993$	− 12.7980i	− 0.406131i
$994$	−30.3485	−0.962595
$995$	0	0
$996$	−7.44949	−0.236046
$997$	30.8990i	0.978580i	0.872121	+	0.489290i	$0.162744\pi$
$997$	30.8990i	0.978580i	−0.872121	+	0.489290i	$0.837256\pi$
$998$	− 12.1010i	− 0.383051i
$999$	6.34847	0.200857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3450.2.d.y.2899.3		4
5.2	odd	4		3450.2.a.bf.1.2	✓	2
5.3	odd	4		3450.2.a.bl.1.1	yes	2
5.4	even	2	inner	3450.2.d.y.2899.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3450.2.a.bf.1.2	✓	2	5.2	odd	4
3450.2.a.bl.1.1	yes	2	5.3	odd	4
3450.2.d.y.2899.2		4	5.4	even	2	inner
3450.2.d.y.2899.3		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3450.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -3.44949i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -3.44949i q^{7} -1.00000i q^{8} -1.00000 q^{9} +2.00000 q^{11} +1.00000i q^{12} -6.89898i q^{13} +3.44949 q^{14} +1.00000 q^{16} -0.550510i q^{17} -1.00000i q^{18} +2.89898 q^{19} -3.44949 q^{21} +2.00000i q^{22} -1.00000i q^{23} -1.00000 q^{24} +6.89898 q^{26} +1.00000i q^{27} +3.44949i q^{28} -5.00000 q^{29} +2.00000 q^{31} +1.00000i q^{32} -2.00000i q^{33} +0.550510 q^{34} +1.00000 q^{36} -6.34847i q^{37} +2.89898i q^{38} -6.89898 q^{39} +4.89898 q^{41} -3.44949i q^{42} -1.10102i q^{43} -2.00000 q^{44} +1.00000 q^{46} +5.89898i q^{47} -1.00000i q^{48} -4.89898 q^{49} -0.550510 q^{51} +6.89898i q^{52} +8.89898i q^{53} -1.00000 q^{54} -3.44949 q^{56} -2.89898i q^{57} -5.00000i q^{58} -10.0000 q^{59} +4.89898 q^{61} +2.00000i q^{62} +3.44949i q^{63} -1.00000 q^{64} +2.00000 q^{66} -2.00000i q^{67} +0.550510i q^{68} -1.00000 q^{69} -8.79796 q^{71} +1.00000i q^{72} -11.8990i q^{73} +6.34847 q^{74} -2.89898 q^{76} -6.89898i q^{77} -6.89898i q^{78} -10.0000 q^{79} +1.00000 q^{81} +4.89898i q^{82} +7.44949i q^{83} +3.44949 q^{84} +1.10102 q^{86} +5.00000i q^{87} -2.00000i q^{88} -4.34847 q^{89} -23.7980 q^{91} +1.00000i q^{92} -2.00000i q^{93} -5.89898 q^{94} +1.00000 q^{96} +16.6969i q^{97} -4.89898i q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 8 q^{11} + 4 q^{14} + 4 q^{16} - 8 q^{19} - 4 q^{21} - 4 q^{24} + 8 q^{26} - 20 q^{29} + 8 q^{31} + 12 q^{34} + 4 q^{36} - 8 q^{39} - 8 q^{44} + 4 q^{46} - 12 q^{51} - 4 q^{54} - 4 q^{56} - 40 q^{59} - 4 q^{64} + 8 q^{66} - 4 q^{69} + 4 q^{71} - 4 q^{74} + 8 q^{76} - 40 q^{79} + 4 q^{81} + 4 q^{84} + 24 q^{86} + 12 q^{89} - 56 q^{91} - 4 q^{94} + 4 q^{96} - 8 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 8 * q^11 + 4 * q^14 + 4 * q^16 - 8 * q^19 - 4 * q^21 - 4 * q^24 + 8 * q^26 - 20 * q^29 + 8 * q^31 + 12 * q^34 + 4 * q^36 - 8 * q^39 - 8 * q^44 + 4 * q^46 - 12 * q^51 - 4 * q^54 - 4 * q^56 - 40 * q^59 - 4 * q^64 + 8 * q^66 - 4 * q^69 + 4 * q^71 - 4 * q^74 + 8 * q^76 - 40 * q^79 + 4 * q^81 + 4 * q^84 + 24 * q^86 + 12 * q^89 - 56 * q^91 - 4 * q^94 + 4 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more