LMFDB - Embedded newform 2366.2.d.b.337.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,2,Mod(337,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2366.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2366.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:	$18.8926051182$
Analytic rank:	$0$
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:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.2
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	2366.337
Dual form			2366.2.d.b.337.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -2.00000 q^{3} -1.00000 q^{4} -2.00000i q^{6} +1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -2.00000 q^{3} -1.00000 q^{4} -2.00000i q^{6} +1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} +2.00000 q^{12} -1.00000 q^{14} +1.00000 q^{16} -6.00000 q^{17} +1.00000i q^{18} -2.00000i q^{19} -2.00000i q^{21} +2.00000i q^{24} +5.00000 q^{25} +4.00000 q^{27} -1.00000i q^{28} -6.00000 q^{29} +4.00000i q^{31} +1.00000i q^{32} -6.00000i q^{34} -1.00000 q^{36} +2.00000i q^{37} +2.00000 q^{38} -6.00000i q^{41} +2.00000 q^{42} -8.00000 q^{43} -12.0000i q^{47} -2.00000 q^{48} -1.00000 q^{49} +5.00000i q^{50} +12.0000 q^{51} +6.00000 q^{53} +4.00000i q^{54} +1.00000 q^{56} +4.00000i q^{57} -6.00000i q^{58} -6.00000i q^{59} +8.00000 q^{61} -4.00000 q^{62} +1.00000i q^{63} -1.00000 q^{64} +4.00000i q^{67} +6.00000 q^{68} -1.00000i q^{72} +2.00000i q^{73} -2.00000 q^{74} -10.0000 q^{75} +2.00000i q^{76} +8.00000 q^{79} -11.0000 q^{81} +6.00000 q^{82} +6.00000i q^{83} +2.00000i q^{84} -8.00000i q^{86} +12.0000 q^{87} -6.00000i q^{89} -8.00000i q^{93} +12.0000 q^{94} -2.00000i q^{96} +10.0000i q^{97} -1.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{3} - 2 q^{4} + 2 q^{9}+O(q^{10}) $ 2 * q - 4 * q^3 - 2 * q^4 + 2 * q^9	$ 2 q - 4 q^{3} - 2 q^{4} + 2 q^{9} + 4 q^{12} - 2 q^{14} + 2 q^{16} - 12 q^{17} + 10 q^{25} + 8 q^{27} - 12 q^{29} - 2 q^{36} + 4 q^{38} + 4 q^{42} - 16 q^{43} - 4 q^{48} - 2 q^{49} + 24 q^{51} + 12 q^{53} + 2 q^{56} + 16 q^{61} - 8 q^{62} - 2 q^{64} + 12 q^{68} - 4 q^{74} - 20 q^{75} + 16 q^{79} - 22 q^{81} + 12 q^{82} + 24 q^{87} + 24 q^{94}+O(q^{100}) $ 2 * q - 4 * q^3 - 2 * q^4 + 2 * q^9 + 4 * q^12 - 2 * q^14 + 2 * q^16 - 12 * q^17 + 10 * q^25 + 8 * q^27 - 12 * q^29 - 2 * q^36 + 4 * q^38 + 4 * q^42 - 16 * q^43 - 4 * q^48 - 2 * q^49 + 24 * q^51 + 12 * q^53 + 2 * q^56 + 16 * q^61 - 8 * q^62 - 2 * q^64 + 12 * q^68 - 4 * q^74 - 20 * q^75 + 16 * q^79 - 22 * q^81 + 12 * q^82 + 24 * q^87 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2366\mathbb{Z}\right)^\times$.

$n$	$339$	$2199$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	−2.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	−1.00000	−0.500000
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	− 2.00000i	− 0.816497i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	− 1.00000i	− 0.353553i
$9$	1.00000	0.333333
$10$	0	0
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	2.00000	0.577350
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	1.00000i	0.235702i
$19$	− 2.00000i	− 0.458831i	−0.973329	−	0.229416i	$-0.926318\pi$
$19$	− 2.00000i	− 0.458831i	0.973329	−	0.229416i	$-0.0736815\pi$
$20$	0	0
$21$	− 2.00000i	− 0.436436i
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	2.00000i	0.408248i
$25$	5.00000	1.00000
$26$	0	0
$27$	4.00000	0.769800
$28$	− 1.00000i	− 0.188982i
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	4.00000i	0.718421i	0.933257	+	0.359211i	$0.116954\pi$
$31$	4.00000i	0.718421i	−0.933257	+	0.359211i	$0.883046\pi$
$32$	1.00000i	0.176777i
$33$	0	0
$34$	− 6.00000i	− 1.02899i
$35$	0	0
$36$	−1.00000	−0.166667
$37$	2.00000i	0.328798i	0.986394	+	0.164399i	$0.0525685\pi$
$37$	2.00000i	0.328798i	−0.986394	+	0.164399i	$0.947432\pi$
$38$	2.00000	0.324443
$39$	0	0
$40$	0	0
$41$	− 6.00000i	− 0.937043i	−0.883452	−	0.468521i	$-0.844787\pi$
$41$	− 6.00000i	− 0.937043i	0.883452	−	0.468521i	$-0.155213\pi$
$42$	2.00000	0.308607
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	− 12.0000i	− 1.75038i	−0.483779	−	0.875190i	$-0.660736\pi$
$47$	− 12.0000i	− 1.75038i	0.483779	−	0.875190i	$-0.339264\pi$
$48$	−2.00000	−0.288675
$49$	−1.00000	−0.142857
$50$	5.00000i	0.707107i
$51$	12.0000	1.68034
$52$	0	0
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	4.00000i	0.544331i
$55$	0	0
$56$	1.00000	0.133631
$57$	4.00000i	0.529813i
$58$	− 6.00000i	− 0.787839i
$59$	− 6.00000i	− 0.781133i	−0.920575	−	0.390567i	$-0.872279\pi$
$59$	− 6.00000i	− 0.781133i	0.920575	−	0.390567i	$-0.127721\pi$
$60$	0	0
$61$	8.00000	1.02430	0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000	1.02430	0.512148	+	0.858898i	$0.328850\pi$
$62$	−4.00000	−0.508001
$63$	1.00000i	0.125988i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	0	0
$67$	4.00000i	0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$	4.00000i	0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$	6.00000	0.727607
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	− 1.00000i	− 0.117851i
$73$	2.00000i	0.234082i	0.993127	+	0.117041i	$0.0373409\pi$
$73$	2.00000i	0.234082i	−0.993127	+	0.117041i	$0.962659\pi$
$74$	−2.00000	−0.232495
$75$	−10.0000	−1.15470
$76$	2.00000i	0.229416i
$77$	0	0
$78$	0	0
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	6.00000	0.662589
$83$	6.00000i	0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$	6.00000i	0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$	2.00000i	0.218218i
$85$	0	0
$86$	− 8.00000i	− 0.862662i
$87$	12.0000	1.28654
$88$	0	0
$89$	− 6.00000i	− 0.635999i	−0.948091	−	0.317999i	$-0.896989\pi$
$89$	− 6.00000i	− 0.635999i	0.948091	−	0.317999i	$-0.103011\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	− 8.00000i	− 0.829561i
$94$	12.0000	1.23771
$95$	0	0
$96$	− 2.00000i	− 0.204124i
$97$	10.0000i	1.01535i	0.861550	+	0.507673i	$0.169494\pi$
$97$	10.0000i	1.01535i	−0.861550	+	0.507673i	$0.830506\pi$
$98$	− 1.00000i	− 0.101015i
$99$	0	0
$100$	−5.00000	−0.500000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	12.0000i	1.18818i
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	0	0
$105$	0	0
$106$	6.00000i	0.582772i
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	−4.00000	−0.384900
$109$	− 2.00000i	− 0.191565i	−0.995402	−	0.0957826i	$-0.969465\pi$
$109$	− 2.00000i	− 0.191565i	0.995402	−	0.0957826i	$-0.0305354\pi$
$110$	0	0
$111$	− 4.00000i	− 0.379663i
$112$	1.00000i	0.0944911i
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	−4.00000	−0.374634
$115$	0	0
$116$	6.00000	0.557086
$117$	0	0
$118$	6.00000	0.552345
$119$	− 6.00000i	− 0.550019i
$120$	0	0
$121$	11.0000	1.00000
$122$	8.00000i	0.724286i
$123$	12.0000i	1.08200i
$124$	− 4.00000i	− 0.359211i
$125$	0	0
$126$	−1.00000	−0.0890871
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	16.0000	1.40872
$130$	0	0
$131$	18.0000	1.57267	0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000	1.57267	0.786334	+	0.617802i	$0.211977\pi$
$132$	0	0
$133$	2.00000	0.173422
$134$	−4.00000	−0.345547
$135$	0	0
$136$	6.00000i	0.514496i
$137$	18.0000i	1.53784i	0.639343	+	0.768922i	$0.279207\pi$
$137$	18.0000i	1.53784i	−0.639343	+	0.768922i	$0.720793\pi$
$138$	0	0
$139$	14.0000	1.18746	0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000	1.18746	0.593732	+	0.804663i	$0.297654\pi$
$140$	0	0
$141$	24.0000i	2.02116i
$142$	0	0
$143$	0	0
$144$	1.00000	0.0833333
$145$	0	0
$146$	−2.00000	−0.165521
$147$	2.00000	0.164957
$148$	− 2.00000i	− 0.164399i
$149$	18.0000i	1.47462i	0.675556	+	0.737309i	$0.263904\pi$
$149$	18.0000i	1.47462i	−0.675556	+	0.737309i	$0.736096\pi$
$150$	− 10.0000i	− 0.816497i
$151$	8.00000i	0.651031i	0.945537	+	0.325515i	$0.105538\pi$
$151$	8.00000i	0.651031i	−0.945537	+	0.325515i	$0.894462\pi$
$152$	−2.00000	−0.162221
$153$	−6.00000	−0.485071
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−4.00000	−0.319235	−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000	−0.319235	−0.159617	+	0.987179i	$0.551026\pi$
$158$	8.00000i	0.636446i
$159$	−12.0000	−0.951662
$160$	0	0
$161$	0	0
$162$	− 11.0000i	− 0.864242i
$163$	− 16.0000i	− 1.25322i	−0.779334	−	0.626608i	$-0.784443\pi$
$163$	− 16.0000i	− 1.25322i	0.779334	−	0.626608i	$-0.215557\pi$
$164$	6.00000i	0.468521i
$165$	0	0
$166$	−6.00000	−0.465690
$167$	− 12.0000i	− 0.928588i	−0.885681	−	0.464294i	$-0.846308\pi$
$167$	− 12.0000i	− 0.928588i	0.885681	−	0.464294i	$-0.153692\pi$
$168$	−2.00000	−0.154303
$169$	0	0
$170$	0	0
$171$	− 2.00000i	− 0.152944i
$172$	8.00000	0.609994
$173$	12.0000	0.912343	0.456172	−	0.889892i	$-0.349220\pi$
$173$	12.0000	0.912343	0.456172	+	0.889892i	$0.349220\pi$
$174$	12.0000i	0.909718i
$175$	5.00000i	0.377964i
$176$	0	0
$177$	12.0000i	0.901975i
$178$	6.00000	0.449719
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	0	0
$181$	−20.0000	−1.48659	−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−20.0000	−1.48659	−0.743294	+	0.668965i	$0.766738\pi$
$182$	0	0
$183$	−16.0000	−1.18275
$184$	0	0
$185$	0	0
$186$	8.00000	0.586588
$187$	0	0
$188$	12.0000i	0.875190i
$189$	4.00000i	0.290957i
$190$	0	0
$191$	24.0000	1.73658	0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000	1.73658	0.868290	+	0.496058i	$0.165220\pi$
$192$	2.00000	0.144338
$193$	14.0000i	1.00774i	0.863779	+	0.503871i	$0.168091\pi$
$193$	14.0000i	1.00774i	−0.863779	+	0.503871i	$0.831909\pi$
$194$	−10.0000	−0.717958
$195$	0	0
$196$	1.00000	0.0714286
$197$	18.0000i	1.28245i	0.767354	+	0.641223i	$0.221573\pi$
$197$	18.0000i	1.28245i	−0.767354	+	0.641223i	$0.778427\pi$
$198$	0	0
$199$	−20.0000	−1.41776	−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000	−1.41776	−0.708881	+	0.705328i	$0.750800\pi$
$200$	− 5.00000i	− 0.353553i
$201$	− 8.00000i	− 0.564276i
$202$	0	0
$203$	− 6.00000i	− 0.421117i
$204$	−12.0000	−0.840168
$205$	0	0
$206$	4.00000i	0.278693i
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−4.00000	−0.275371	−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000	−0.275371	−0.137686	+	0.990476i	$0.543966\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	12.0000i	0.820303i
$215$	0	0
$216$	− 4.00000i	− 0.272166i
$217$	−4.00000	−0.271538
$218$	2.00000	0.135457
$219$	− 4.00000i	− 0.270295i
$220$	0	0
$221$	0	0
$222$	4.00000	0.268462
$223$	− 8.00000i	− 0.535720i	−0.963458	−	0.267860i	$-0.913684\pi$
$223$	− 8.00000i	− 0.535720i	0.963458	−	0.267860i	$-0.0863164\pi$
$224$	−1.00000	−0.0668153
$225$	5.00000	0.333333
$226$	6.00000i	0.399114i
$227$	− 18.0000i	− 1.19470i	−0.801980	−	0.597351i	$-0.796220\pi$
$227$	− 18.0000i	− 1.19470i	0.801980	−	0.597351i	$-0.203780\pi$
$228$	− 4.00000i	− 0.264906i
$229$	− 4.00000i	− 0.264327i	−0.991228	−	0.132164i	$-0.957808\pi$
$229$	− 4.00000i	− 0.264327i	0.991228	−	0.132164i	$-0.0421925\pi$
$230$	0	0
$231$	0	0
$232$	6.00000i	0.393919i
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	0	0
$235$	0	0
$236$	6.00000i	0.390567i
$237$	−16.0000	−1.03931
$238$	6.00000	0.388922
$239$	− 24.0000i	− 1.55243i	−0.630468	−	0.776215i	$-0.717137\pi$
$239$	− 24.0000i	− 1.55243i	0.630468	−	0.776215i	$-0.282863\pi$
$240$	0	0
$241$	− 10.0000i	− 0.644157i	−0.946713	−	0.322078i	$-0.895619\pi$
$241$	− 10.0000i	− 0.644157i	0.946713	−	0.322078i	$-0.104381\pi$
$242$	11.0000i	0.707107i
$243$	10.0000	0.641500
$244$	−8.00000	−0.512148
$245$	0	0
$246$	−12.0000	−0.765092
$247$	0	0
$248$	4.00000	0.254000
$249$	− 12.0000i	− 0.760469i
$250$	0	0
$251$	18.0000	1.13615	0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000	1.13615	0.568075	+	0.822977i	$0.307688\pi$
$252$	− 1.00000i	− 0.0629941i
$253$	0	0
$254$	16.0000i	1.00393i
$255$	0	0
$256$	1.00000	0.0625000
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	16.0000i	0.996116i
$259$	−2.00000	−0.124274
$260$	0	0
$261$	−6.00000	−0.371391
$262$	18.0000i	1.11204i
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	0	0
$266$	2.00000i	0.122628i
$267$	12.0000i	0.734388i
$268$	− 4.00000i	− 0.244339i
$269$	−12.0000	−0.731653	−0.365826	−	0.930683i	$-0.619214\pi$
$269$	−12.0000	−0.731653	−0.365826	+	0.930683i	$0.619214\pi$
$270$	0	0
$271$	− 16.0000i	− 0.971931i	−0.873978	−	0.485965i	$-0.838468\pi$
$271$	− 16.0000i	− 0.971931i	0.873978	−	0.485965i	$-0.161532\pi$
$272$	−6.00000	−0.363803
$273$	0	0
$274$	−18.0000	−1.08742
$275$	0	0
$276$	0	0
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	14.0000i	0.839664i
$279$	4.00000i	0.239474i
$280$	0	0
$281$	− 6.00000i	− 0.357930i	−0.983855	−	0.178965i	$-0.942725\pi$
$281$	− 6.00000i	− 0.357930i	0.983855	−	0.178965i	$-0.0572749\pi$
$282$	−24.0000	−1.42918
$283$	22.0000	1.30776	0.653882	−	0.756596i	$-0.273139\pi$
$283$	22.0000	1.30776	0.653882	+	0.756596i	$0.273139\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	6.00000	0.354169
$288$	1.00000i	0.0589256i
$289$	19.0000	1.11765
$290$	0	0
$291$	− 20.0000i	− 1.17242i
$292$	− 2.00000i	− 0.117041i
$293$	24.0000i	1.40209i	0.713115	+	0.701047i	$0.247284\pi$
$293$	24.0000i	1.40209i	−0.713115	+	0.701047i	$0.752716\pi$
$294$	2.00000i	0.116642i
$295$	0	0
$296$	2.00000	0.116248
$297$	0	0
$298$	−18.0000	−1.04271
$299$	0	0
$300$	10.0000	0.577350
$301$	− 8.00000i	− 0.461112i
$302$	−8.00000	−0.460348
$303$	0	0
$304$	− 2.00000i	− 0.114708i
$305$	0	0
$306$	− 6.00000i	− 0.342997i
$307$	2.00000i	0.114146i	0.998370	+	0.0570730i	$0.0181768\pi$
$307$	2.00000i	0.114146i	−0.998370	+	0.0570730i	$0.981823\pi$
$308$	0	0
$309$	−8.00000	−0.455104
$310$	0	0
$311$	24.0000	1.36092	0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000	1.36092	0.680458	+	0.732787i	$0.261781\pi$
$312$	0	0
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	− 4.00000i	− 0.225733i
$315$	0	0
$316$	−8.00000	−0.450035
$317$	− 6.00000i	− 0.336994i	−0.985702	−	0.168497i	$-0.946109\pi$
$317$	− 6.00000i	− 0.336994i	0.985702	−	0.168497i	$-0.0538913\pi$
$318$	− 12.0000i	− 0.672927i
$319$	0	0
$320$	0	0
$321$	−24.0000	−1.33955
$322$	0	0
$323$	12.0000i	0.667698i
$324$	11.0000	0.611111
$325$	0	0
$326$	16.0000	0.886158
$327$	4.00000i	0.221201i
$328$	−6.00000	−0.331295
$329$	12.0000	0.661581
$330$	0	0
$331$	− 8.00000i	− 0.439720i	−0.975531	−	0.219860i	$-0.929440\pi$
$331$	− 8.00000i	− 0.439720i	0.975531	−	0.219860i	$-0.0705600\pi$
$332$	− 6.00000i	− 0.329293i
$333$	2.00000i	0.109599i
$334$	12.0000	0.656611
$335$	0	0
$336$	− 2.00000i	− 0.109109i
$337$	−14.0000	−0.762629	−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000	−0.762629	−0.381314	+	0.924445i	$0.624528\pi$
$338$	0	0
$339$	−12.0000	−0.651751
$340$	0	0
$341$	0	0
$342$	2.00000	0.108148
$343$	− 1.00000i	− 0.0539949i
$344$	8.00000i	0.431331i
$345$	0	0
$346$	12.0000i	0.645124i
$347$	−24.0000	−1.28839	−0.644194	−	0.764862i	$-0.722807\pi$
$347$	−24.0000	−1.28839	−0.644194	+	0.764862i	$0.722807\pi$
$348$	−12.0000	−0.643268
$349$	− 28.0000i	− 1.49881i	−0.662114	−	0.749403i	$-0.730341\pi$
$349$	− 28.0000i	− 1.49881i	0.662114	−	0.749403i	$-0.269659\pi$
$350$	−5.00000	−0.267261
$351$	0	0
$352$	0	0
$353$	− 18.0000i	− 0.958043i	−0.877803	−	0.479022i	$-0.840992\pi$
$353$	− 18.0000i	− 0.958043i	0.877803	−	0.479022i	$-0.159008\pi$
$354$	−12.0000	−0.637793
$355$	0	0
$356$	6.00000i	0.317999i
$357$	12.0000i	0.635107i
$358$	12.0000i	0.634220i
$359$	− 24.0000i	− 1.26667i	−0.773877	−	0.633336i	$-0.781685\pi$
$359$	− 24.0000i	− 1.26667i	0.773877	−	0.633336i	$-0.218315\pi$
$360$	0	0
$361$	15.0000	0.789474
$362$	− 20.0000i	− 1.05118i
$363$	−22.0000	−1.15470
$364$	0	0
$365$	0	0
$366$	− 16.0000i	− 0.836333i
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	0	0
$369$	− 6.00000i	− 0.312348i
$370$	0	0
$371$	6.00000i	0.311504i
$372$	8.00000i	0.414781i
$373$	14.0000	0.724893	0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000	0.724893	0.362446	+	0.932005i	$0.381942\pi$
$374$	0	0
$375$	0	0
$376$	−12.0000	−0.618853
$377$	0	0
$378$	−4.00000	−0.205738
$379$	16.0000i	0.821865i	0.911666	+	0.410932i	$0.134797\pi$
$379$	16.0000i	0.821865i	−0.911666	+	0.410932i	$0.865203\pi$
$380$	0	0
$381$	−32.0000	−1.63941
$382$	24.0000i	1.22795i
$383$	− 36.0000i	− 1.83951i	−0.392488	−	0.919757i	$-0.628386\pi$
$383$	− 36.0000i	− 1.83951i	0.392488	−	0.919757i	$-0.371614\pi$
$384$	2.00000i	0.102062i
$385$	0	0
$386$	−14.0000	−0.712581
$387$	−8.00000	−0.406663
$388$	− 10.0000i	− 0.507673i
$389$	−18.0000	−0.912636	−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000	−0.912636	−0.456318	+	0.889817i	$0.650832\pi$
$390$	0	0
$391$	0	0
$392$	1.00000i	0.0505076i
$393$	−36.0000	−1.81596
$394$	−18.0000	−0.906827
$395$	0	0
$396$	0	0
$397$	20.0000i	1.00377i	0.864934	+	0.501886i	$0.167360\pi$
$397$	20.0000i	1.00377i	−0.864934	+	0.501886i	$0.832640\pi$
$398$	− 20.0000i	− 1.00251i
$399$	−4.00000	−0.200250
$400$	5.00000	0.250000
$401$	− 18.0000i	− 0.898877i	−0.893311	−	0.449439i	$-0.851624\pi$
$401$	− 18.0000i	− 0.898877i	0.893311	−	0.449439i	$-0.148376\pi$
$402$	8.00000	0.399004
$403$	0	0
$404$	0	0
$405$	0	0
$406$	6.00000	0.297775
$407$	0	0
$408$	− 12.0000i	− 0.594089i
$409$	− 14.0000i	− 0.692255i	−0.938187	−	0.346128i	$-0.887496\pi$
$409$	− 14.0000i	− 0.692255i	0.938187	−	0.346128i	$-0.112504\pi$
$410$	0	0
$411$	− 36.0000i	− 1.77575i
$412$	−4.00000	−0.197066
$413$	6.00000	0.295241
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−28.0000	−1.37117
$418$	0	0
$419$	6.00000	0.293119	0.146560	−	0.989202i	$-0.453180\pi$
$419$	6.00000	0.293119	0.146560	+	0.989202i	$0.453180\pi$
$420$	0	0
$421$	10.0000i	0.487370i	0.969854	+	0.243685i	$0.0783563\pi$
$421$	10.0000i	0.487370i	−0.969854	+	0.243685i	$0.921644\pi$
$422$	− 4.00000i	− 0.194717i
$423$	− 12.0000i	− 0.583460i
$424$	− 6.00000i	− 0.291386i
$425$	−30.0000	−1.45521
$426$	0	0
$427$	8.00000i	0.387147i
$428$	−12.0000	−0.580042
$429$	0	0
$430$	0	0
$431$	− 24.0000i	− 1.15604i	−0.816023	−	0.578020i	$-0.803826\pi$
$431$	− 24.0000i	− 1.15604i	0.816023	−	0.578020i	$-0.196174\pi$
$432$	4.00000	0.192450
$433$	34.0000	1.63394	0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000	1.63394	0.816968	+	0.576683i	$0.195653\pi$
$434$	− 4.00000i	− 0.192006i
$435$	0	0
$436$	2.00000i	0.0957826i
$437$	0	0
$438$	4.00000	0.191127
$439$	−8.00000	−0.381819	−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000	−0.381819	−0.190910	+	0.981608i	$0.561144\pi$
$440$	0	0
$441$	−1.00000	−0.0476190
$442$	0	0
$443$	−12.0000	−0.570137	−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000	−0.570137	−0.285069	+	0.958507i	$0.592016\pi$
$444$	4.00000i	0.189832i
$445$	0	0
$446$	8.00000	0.378811
$447$	− 36.0000i	− 1.70274i
$448$	− 1.00000i	− 0.0472456i
$449$	18.0000i	0.849473i	0.905317	+	0.424736i	$0.139633\pi$
$449$	18.0000i	0.849473i	−0.905317	+	0.424736i	$0.860367\pi$
$450$	5.00000i	0.235702i
$451$	0	0
$452$	−6.00000	−0.282216
$453$	− 16.0000i	− 0.751746i
$454$	18.0000	0.844782
$455$	0	0
$456$	4.00000	0.187317
$457$	10.0000i	0.467780i	0.972263	+	0.233890i	$0.0751456\pi$
$457$	10.0000i	0.467780i	−0.972263	+	0.233890i	$0.924854\pi$
$458$	4.00000	0.186908
$459$	−24.0000	−1.12022
$460$	0	0
$461$	− 12.0000i	− 0.558896i	−0.960161	−	0.279448i	$-0.909849\pi$
$461$	− 12.0000i	− 0.558896i	0.960161	−	0.279448i	$-0.0901514\pi$
$462$	0	0
$463$	32.0000i	1.48717i	0.668644	+	0.743583i	$0.266875\pi$
$463$	32.0000i	1.48717i	−0.668644	+	0.743583i	$0.733125\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	6.00000i	0.277945i
$467$	6.00000	0.277647	0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000	0.277647	0.138823	+	0.990317i	$0.455668\pi$
$468$	0	0
$469$	−4.00000	−0.184703
$470$	0	0
$471$	8.00000	0.368621
$472$	−6.00000	−0.276172
$473$	0	0
$474$	− 16.0000i	− 0.734904i
$475$	− 10.0000i	− 0.458831i
$476$	6.00000i	0.275010i
$477$	6.00000	0.274721
$478$	24.0000	1.09773
$479$	− 36.0000i	− 1.64488i	−0.568850	−	0.822441i	$-0.692612\pi$
$479$	− 36.0000i	− 1.64488i	0.568850	−	0.822441i	$-0.307388\pi$
$480$	0	0
$481$	0	0
$482$	10.0000	0.455488
$483$	0	0
$484$	−11.0000	−0.500000
$485$	0	0
$486$	10.0000i	0.453609i
$487$	16.0000i	0.725029i	0.931978	+	0.362515i	$0.118082\pi$
$487$	16.0000i	0.725029i	−0.931978	+	0.362515i	$0.881918\pi$
$488$	− 8.00000i	− 0.362143i
$489$	32.0000i	1.44709i
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	− 12.0000i	− 0.541002i
$493$	36.0000	1.62136
$494$	0	0
$495$	0	0
$496$	4.00000i	0.179605i
$497$	0	0
$498$	12.0000	0.537733
$499$	4.00000i	0.179065i	0.995984	+	0.0895323i	$0.0285372\pi$
$499$	4.00000i	0.179065i	−0.995984	+	0.0895323i	$0.971463\pi$
$500$	0	0
$501$	24.0000i	1.07224i
$502$	18.0000i	0.803379i
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	1.00000	0.0445435
$505$	0	0
$506$	0	0
$507$	0	0
$508$	−16.0000	−0.709885
$509$	− 36.0000i	− 1.59567i	−0.602875	−	0.797836i	$-0.705978\pi$
$509$	− 36.0000i	− 1.59567i	0.602875	−	0.797836i	$-0.294022\pi$
$510$	0	0
$511$	−2.00000	−0.0884748
$512$	1.00000i	0.0441942i
$513$	− 8.00000i	− 0.353209i
$514$	− 18.0000i	− 0.793946i
$515$	0	0
$516$	−16.0000	−0.704361
$517$	0	0
$518$	− 2.00000i	− 0.0878750i
$519$	−24.0000	−1.05348
$520$	0	0
$521$	6.00000	0.262865	0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000	0.262865	0.131432	+	0.991325i	$0.458042\pi$
$522$	− 6.00000i	− 0.262613i
$523$	2.00000	0.0874539	0.0437269	−	0.999044i	$-0.486077\pi$
$523$	2.00000	0.0874539	0.0437269	+	0.999044i	$0.486077\pi$
$524$	−18.0000	−0.786334
$525$	− 10.0000i	− 0.436436i
$526$	0	0
$527$	− 24.0000i	− 1.04546i
$528$	0	0
$529$	−23.0000	−1.00000
$530$	0	0
$531$	− 6.00000i	− 0.260378i
$532$	−2.00000	−0.0867110
$533$	0	0
$534$	−12.0000	−0.519291
$535$	0	0
$536$	4.00000	0.172774
$537$	−24.0000	−1.03568
$538$	− 12.0000i	− 0.517357i
$539$	0	0
$540$	0	0
$541$	38.0000i	1.63375i	0.576816	+	0.816874i	$0.304295\pi$
$541$	38.0000i	1.63375i	−0.576816	+	0.816874i	$0.695705\pi$
$542$	16.0000	0.687259
$543$	40.0000	1.71656
$544$	− 6.00000i	− 0.257248i
$545$	0	0
$546$	0	0
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	− 18.0000i	− 0.768922i
$549$	8.00000	0.341432
$550$	0	0
$551$	12.0000i	0.511217i
$552$	0	0
$553$	8.00000i	0.340195i
$554$	10.0000i	0.424859i
$555$	0	0
$556$	−14.0000	−0.593732
$557$	6.00000i	0.254228i	0.991888	+	0.127114i	$0.0405714\pi$
$557$	6.00000i	0.254228i	−0.991888	+	0.127114i	$0.959429\pi$
$558$	−4.00000	−0.169334
$559$	0	0
$560$	0	0
$561$	0	0
$562$	6.00000	0.253095
$563$	−30.0000	−1.26435	−0.632175	−	0.774826i	$-0.717837\pi$
$563$	−30.0000	−1.26435	−0.632175	+	0.774826i	$0.717837\pi$
$564$	− 24.0000i	− 1.01058i
$565$	0	0
$566$	22.0000i	0.924729i
$567$	− 11.0000i	− 0.461957i
$568$	0	0
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	0	0
$571$	−32.0000	−1.33916	−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000	−1.33916	−0.669579	+	0.742741i	$0.733526\pi$
$572$	0	0
$573$	−48.0000	−2.00523
$574$	6.00000i	0.250435i
$575$	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	$-0.0132552\pi$
$578$	19.0000i	0.790296i
$579$	− 28.0000i	− 1.16364i
$580$	0	0
$581$	−6.00000	−0.248922
$582$	20.0000	0.829027
$583$	0	0
$584$	2.00000	0.0827606
$585$	0	0
$586$	−24.0000	−0.991431
$587$	42.0000i	1.73353i	0.498721	+	0.866763i	$0.333803\pi$
$587$	42.0000i	1.73353i	−0.498721	+	0.866763i	$0.666197\pi$
$588$	−2.00000	−0.0824786
$589$	8.00000	0.329634
$590$	0	0
$591$	− 36.0000i	− 1.48084i
$592$	2.00000i	0.0821995i
$593$	− 6.00000i	− 0.246390i	−0.992382	−	0.123195i	$-0.960686\pi$
$593$	− 6.00000i	− 0.246390i	0.992382	−	0.123195i	$-0.0393141\pi$
$594$	0	0
$595$	0	0
$596$	− 18.0000i	− 0.737309i
$597$	40.0000	1.63709
$598$	0	0
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	10.0000i	0.408248i
$601$	26.0000	1.06056	0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000	1.06056	0.530281	+	0.847822i	$0.322086\pi$
$602$	8.00000	0.326056
$603$	4.00000i	0.162893i
$604$	− 8.00000i	− 0.325515i
$605$	0	0
$606$	0	0
$607$	32.0000	1.29884	0.649420	−	0.760430i	$-0.275012\pi$
$607$	32.0000	1.29884	0.649420	+	0.760430i	$0.275012\pi$
$608$	2.00000	0.0811107
$609$	12.0000i	0.486265i
$610$	0	0
$611$	0	0
$612$	6.00000	0.242536
$613$	− 2.00000i	− 0.0807792i	−0.999184	−	0.0403896i	$-0.987140\pi$
$613$	− 2.00000i	− 0.0807792i	0.999184	−	0.0403896i	$-0.0128599\pi$
$614$	−2.00000	−0.0807134
$615$	0	0
$616$	0	0
$617$	− 6.00000i	− 0.241551i	−0.992680	−	0.120775i	$-0.961462\pi$
$617$	− 6.00000i	− 0.241551i	0.992680	−	0.120775i	$-0.0385381\pi$
$618$	− 8.00000i	− 0.321807i
$619$	26.0000i	1.04503i	0.852631	+	0.522514i	$0.175006\pi$
$619$	26.0000i	1.04503i	−0.852631	+	0.522514i	$0.824994\pi$
$620$	0	0
$621$	0	0
$622$	24.0000i	0.962312i
$623$	6.00000	0.240385
$624$	0	0
$625$	25.0000	1.00000
$626$	− 10.0000i	− 0.399680i
$627$	0	0
$628$	4.00000	0.159617
$629$	− 12.0000i	− 0.478471i
$630$	0	0
$631$	− 16.0000i	− 0.636950i	−0.947931	−	0.318475i	$-0.896829\pi$
$631$	− 16.0000i	− 0.636950i	0.947931	−	0.318475i	$-0.103171\pi$
$632$	− 8.00000i	− 0.318223i
$633$	8.00000	0.317971
$634$	6.00000	0.238290
$635$	0	0
$636$	12.0000	0.475831
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	− 24.0000i	− 0.947204i
$643$	− 14.0000i	− 0.552106i	−0.961142	−	0.276053i	$-0.910973\pi$
$643$	− 14.0000i	− 0.552106i	0.961142	−	0.276053i	$-0.0890266\pi$
$644$	0	0
$645$	0	0
$646$	−12.0000	−0.472134
$647$	12.0000	0.471769	0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000	0.471769	0.235884	+	0.971781i	$0.424201\pi$
$648$	11.0000i	0.432121i
$649$	0	0
$650$	0	0
$651$	8.00000	0.313545
$652$	16.0000i	0.626608i
$653$	18.0000	0.704394	0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000	0.704394	0.352197	+	0.935926i	$0.385435\pi$
$654$	−4.00000	−0.156412
$655$	0	0
$656$	− 6.00000i	− 0.234261i
$657$	2.00000i	0.0780274i
$658$	12.0000i	0.467809i
$659$	−24.0000	−0.934907	−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000	−0.934907	−0.467454	+	0.884018i	$0.654829\pi$
$660$	0	0
$661$	− 40.0000i	− 1.55582i	−0.628376	−	0.777910i	$-0.716280\pi$
$661$	− 40.0000i	− 1.55582i	0.628376	−	0.777910i	$-0.283720\pi$
$662$	8.00000	0.310929
$663$	0	0
$664$	6.00000	0.232845
$665$	0	0
$666$	−2.00000	−0.0774984
$667$	0	0
$668$	12.0000i	0.464294i
$669$	16.0000i	0.618596i
$670$	0	0
$671$	0	0
$672$	2.00000	0.0771517
$673$	−26.0000	−1.00223	−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000	−1.00223	−0.501113	+	0.865382i	$0.667076\pi$
$674$	− 14.0000i	− 0.539260i
$675$	20.0000	0.769800
$676$	0	0
$677$	−12.0000	−0.461197	−0.230599	−	0.973049i	$-0.574068\pi$
$677$	−12.0000	−0.461197	−0.230599	+	0.973049i	$0.574068\pi$
$678$	− 12.0000i	− 0.460857i
$679$	−10.0000	−0.383765
$680$	0	0
$681$	36.0000i	1.37952i
$682$	0	0
$683$	− 12.0000i	− 0.459167i	−0.973289	−	0.229584i	$-0.926264\pi$
$683$	− 12.0000i	− 0.459167i	0.973289	−	0.229584i	$-0.0737364\pi$
$684$	2.00000i	0.0764719i
$685$	0	0
$686$	1.00000	0.0381802
$687$	8.00000i	0.305219i
$688$	−8.00000	−0.304997
$689$	0	0
$690$	0	0
$691$	46.0000i	1.74992i	0.484193	+	0.874961i	$0.339113\pi$
$691$	46.0000i	1.74992i	−0.484193	+	0.874961i	$0.660887\pi$
$692$	−12.0000	−0.456172
$693$	0	0
$694$	− 24.0000i	− 0.911028i
$695$	0	0
$696$	− 12.0000i	− 0.454859i
$697$	36.0000i	1.36360i
$698$	28.0000	1.05982
$699$	−12.0000	−0.453882
$700$	− 5.00000i	− 0.188982i
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	0	0
$703$	4.00000	0.150863
$704$	0	0
$705$	0	0
$706$	18.0000	0.677439
$707$	0	0
$708$	− 12.0000i	− 0.450988i
$709$	− 46.0000i	− 1.72757i	−0.503864	−	0.863783i	$-0.668089\pi$
$709$	− 46.0000i	− 1.72757i	0.503864	−	0.863783i	$-0.331911\pi$
$710$	0	0
$711$	8.00000	0.300023
$712$	−6.00000	−0.224860
$713$	0	0
$714$	−12.0000	−0.449089
$715$	0	0
$716$	−12.0000	−0.448461
$717$	48.0000i	1.79259i
$718$	24.0000	0.895672
$719$	−12.0000	−0.447524	−0.223762	−	0.974644i	$-0.571834\pi$
$719$	−12.0000	−0.447524	−0.223762	+	0.974644i	$0.571834\pi$
$720$	0	0
$721$	4.00000i	0.148968i
$722$	15.0000i	0.558242i
$723$	20.0000i	0.743808i
$724$	20.0000	0.743294
$725$	−30.0000	−1.11417
$726$	− 22.0000i	− 0.816497i
$727$	−44.0000	−1.63187	−0.815935	−	0.578144i	$-0.803777\pi$
$727$	−44.0000	−1.63187	−0.815935	+	0.578144i	$0.803777\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	48.0000	1.77534
$732$	16.0000	0.591377
$733$	40.0000i	1.47743i	0.674016	+	0.738717i	$0.264568\pi$
$733$	40.0000i	1.47743i	−0.674016	+	0.738717i	$0.735432\pi$
$734$	8.00000i	0.295285i
$735$	0	0
$736$	0	0
$737$	0	0
$738$	6.00000	0.220863
$739$	− 16.0000i	− 0.588570i	−0.955718	−	0.294285i	$-0.904919\pi$
$739$	− 16.0000i	− 0.588570i	0.955718	−	0.294285i	$-0.0950814\pi$
$740$	0	0
$741$	0	0
$742$	−6.00000	−0.220267
$743$	− 24.0000i	− 0.880475i	−0.897881	−	0.440237i	$-0.854894\pi$
$743$	− 24.0000i	− 0.880475i	0.897881	−	0.440237i	$-0.145106\pi$
$744$	−8.00000	−0.293294
$745$	0	0
$746$	14.0000i	0.512576i
$747$	6.00000i	0.219529i
$748$	0	0
$749$	12.0000i	0.438470i
$750$	0	0
$751$	40.0000	1.45962	0.729810	−	0.683650i	$-0.239608\pi$
$751$	40.0000	1.45962	0.729810	+	0.683650i	$0.239608\pi$
$752$	− 12.0000i	− 0.437595i
$753$	−36.0000	−1.31191
$754$	0	0
$755$	0	0
$756$	− 4.00000i	− 0.145479i
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	−16.0000	−0.581146
$759$	0	0
$760$	0	0
$761$	− 18.0000i	− 0.652499i	−0.945284	−	0.326250i	$-0.894215\pi$
$761$	− 18.0000i	− 0.652499i	0.945284	−	0.326250i	$-0.105785\pi$
$762$	− 32.0000i	− 1.15924i
$763$	2.00000	0.0724049
$764$	−24.0000	−0.868290
$765$	0	0
$766$	36.0000	1.30073
$767$	0	0
$768$	−2.00000	−0.0721688
$769$	− 14.0000i	− 0.504853i	−0.967616	−	0.252426i	$-0.918771\pi$
$769$	− 14.0000i	− 0.504853i	0.967616	−	0.252426i	$-0.0812286\pi$
$770$	0	0
$771$	36.0000	1.29651
$772$	− 14.0000i	− 0.503871i
$773$	− 24.0000i	− 0.863220i	−0.902060	−	0.431610i	$-0.857946\pi$
$773$	− 24.0000i	− 0.863220i	0.902060	−	0.431610i	$-0.142054\pi$
$774$	− 8.00000i	− 0.287554i
$775$	20.0000i	0.718421i
$776$	10.0000	0.358979
$777$	4.00000	0.143499
$778$	− 18.0000i	− 0.645331i
$779$	−12.0000	−0.429945
$780$	0	0
$781$	0	0
$782$	0	0
$783$	−24.0000	−0.857690
$784$	−1.00000	−0.0357143
$785$	0	0
$786$	− 36.0000i	− 1.28408i
$787$	− 22.0000i	− 0.784215i	−0.919919	−	0.392108i	$-0.871746\pi$
$787$	− 22.0000i	− 0.784215i	0.919919	−	0.392108i	$-0.128254\pi$
$788$	− 18.0000i	− 0.641223i
$789$	0	0
$790$	0	0
$791$	6.00000i	0.213335i
$792$	0	0
$793$	0	0
$794$	−20.0000	−0.709773
$795$	0	0
$796$	20.0000	0.708881
$797$	12.0000	0.425062	0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000	0.425062	0.212531	+	0.977154i	$0.431829\pi$
$798$	− 4.00000i	− 0.141598i
$799$	72.0000i	2.54718i
$800$	5.00000i	0.176777i
$801$	− 6.00000i	− 0.212000i
$802$	18.0000	0.635602
$803$	0	0
$804$	8.00000i	0.282138i
$805$	0	0
$806$	0	0
$807$	24.0000	0.844840
$808$	0	0
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	0	0
$811$	− 2.00000i	− 0.0702295i	−0.999383	−	0.0351147i	$-0.988820\pi$
$811$	− 2.00000i	− 0.0702295i	0.999383	−	0.0351147i	$-0.0111797\pi$
$812$	6.00000i	0.210559i
$813$	32.0000i	1.12229i
$814$	0	0
$815$	0	0
$816$	12.0000	0.420084
$817$	16.0000i	0.559769i
$818$	14.0000	0.489499
$819$	0	0
$820$	0	0
$821$	− 6.00000i	− 0.209401i	−0.994504	−	0.104701i	$-0.966612\pi$
$821$	− 6.00000i	− 0.209401i	0.994504	−	0.104701i	$-0.0333885\pi$
$822$	36.0000	1.25564
$823$	40.0000	1.39431	0.697156	−	0.716919i	$-0.254448\pi$
$823$	40.0000	1.39431	0.697156	+	0.716919i	$0.254448\pi$
$824$	− 4.00000i	− 0.139347i
$825$	0	0
$826$	6.00000i	0.208767i
$827$	− 36.0000i	− 1.25184i	−0.779886	−	0.625921i	$-0.784723\pi$
$827$	− 36.0000i	− 1.25184i	0.779886	−	0.625921i	$-0.215277\pi$
$828$	0	0
$829$	−56.0000	−1.94496	−0.972480	−	0.232986i	$-0.925151\pi$
$829$	−56.0000	−1.94496	−0.972480	+	0.232986i	$0.925151\pi$
$830$	0	0
$831$	−20.0000	−0.693792
$832$	0	0
$833$	6.00000	0.207888
$834$	− 28.0000i	− 0.969561i
$835$	0	0
$836$	0	0
$837$	16.0000i	0.553041i
$838$	6.00000i	0.207267i
$839$	12.0000i	0.414286i	0.978311	+	0.207143i	$0.0664165\pi$
$839$	12.0000i	0.414286i	−0.978311	+	0.207143i	$0.933583\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−10.0000	−0.344623
$843$	12.0000i	0.413302i
$844$	4.00000	0.137686
$845$	0	0
$846$	12.0000	0.412568
$847$	11.0000i	0.377964i
$848$	6.00000	0.206041
$849$	−44.0000	−1.51008
$850$	− 30.0000i	− 1.02899i
$851$	0	0
$852$	0	0
$853$	44.0000i	1.50653i	0.657716	+	0.753266i	$0.271523\pi$
$853$	44.0000i	1.50653i	−0.657716	+	0.753266i	$0.728477\pi$
$854$	−8.00000	−0.273754
$855$	0	0
$856$	− 12.0000i	− 0.410152i
$857$	18.0000	0.614868	0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000	0.614868	0.307434	+	0.951569i	$0.400530\pi$
$858$	0	0
$859$	14.0000	0.477674	0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000	0.477674	0.238837	+	0.971060i	$0.423234\pi$
$860$	0	0
$861$	−12.0000	−0.408959
$862$	24.0000	0.817443
$863$	24.0000i	0.816970i	0.912765	+	0.408485i	$0.133943\pi$
$863$	24.0000i	0.816970i	−0.912765	+	0.408485i	$0.866057\pi$
$864$	4.00000i	0.136083i
$865$	0	0
$866$	34.0000i	1.15537i
$867$	−38.0000	−1.29055
$868$	4.00000	0.135769
$869$	0	0
$870$	0	0
$871$	0	0
$872$	−2.00000	−0.0677285
$873$	10.0000i	0.338449i
$874$	0	0
$875$	0	0
$876$	4.00000i	0.135147i
$877$	22.0000i	0.742887i	0.928456	+	0.371444i	$0.121137\pi$
$877$	22.0000i	0.742887i	−0.928456	+	0.371444i	$0.878863\pi$
$878$	− 8.00000i	− 0.269987i
$879$	− 48.0000i	− 1.61900i
$880$	0	0
$881$	54.0000	1.81931	0.909653	−	0.415369i	$-0.136347\pi$
$881$	54.0000	1.81931	0.909653	+	0.415369i	$0.136347\pi$
$882$	− 1.00000i	− 0.0336718i
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	0	0
$885$	0	0
$886$	− 12.0000i	− 0.403148i
$887$	−36.0000	−1.20876	−0.604381	−	0.796696i	$-0.706579\pi$
$887$	−36.0000	−1.20876	−0.604381	+	0.796696i	$0.706579\pi$
$888$	−4.00000	−0.134231
$889$	16.0000i	0.536623i
$890$	0	0
$891$	0	0
$892$	8.00000i	0.267860i
$893$	−24.0000	−0.803129
$894$	36.0000	1.20402
$895$	0	0
$896$	1.00000	0.0334077
$897$	0	0
$898$	−18.0000	−0.600668
$899$	− 24.0000i	− 0.800445i
$900$	−5.00000	−0.166667
$901$	−36.0000	−1.19933
$902$	0	0
$903$	16.0000i	0.532447i
$904$	− 6.00000i	− 0.199557i
$905$	0	0
$906$	16.0000	0.531564
$907$	−44.0000	−1.46100	−0.730498	−	0.682915i	$-0.760712\pi$
$907$	−44.0000	−1.46100	−0.730498	+	0.682915i	$0.760712\pi$
$908$	18.0000i	0.597351i
$909$	0	0
$910$	0	0
$911$	48.0000	1.59031	0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000	1.59031	0.795155	+	0.606406i	$0.207389\pi$
$912$	4.00000i	0.132453i
$913$	0	0
$914$	−10.0000	−0.330771
$915$	0	0
$916$	4.00000i	0.132164i
$917$	18.0000i	0.594412i
$918$	− 24.0000i	− 0.792118i
$919$	56.0000	1.84727	0.923635	−	0.383274i	$-0.125203\pi$
$919$	56.0000	1.84727	0.923635	+	0.383274i	$0.125203\pi$
$920$	0	0
$921$	− 4.00000i	− 0.131804i
$922$	12.0000	0.395199
$923$	0	0
$924$	0	0
$925$	10.0000i	0.328798i
$926$	−32.0000	−1.05159
$927$	4.00000	0.131377
$928$	− 6.00000i	− 0.196960i
$929$	− 6.00000i	− 0.196854i	−0.995144	−	0.0984268i	$-0.968619\pi$
$929$	− 6.00000i	− 0.196854i	0.995144	−	0.0984268i	$-0.0313810\pi$
$930$	0	0
$931$	2.00000i	0.0655474i
$932$	−6.00000	−0.196537
$933$	−48.0000	−1.57145
$934$	6.00000i	0.196326i
$935$	0	0
$936$	0	0
$937$	2.00000	0.0653372	0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000	0.0653372	0.0326686	+	0.999466i	$0.489599\pi$
$938$	− 4.00000i	− 0.130605i
$939$	20.0000	0.652675
$940$	0	0
$941$	24.0000i	0.782378i	0.920310	+	0.391189i	$0.127936\pi$
$941$	24.0000i	0.782378i	−0.920310	+	0.391189i	$0.872064\pi$
$942$	8.00000i	0.260654i
$943$	0	0
$944$	− 6.00000i	− 0.195283i
$945$	0	0
$946$	0	0
$947$	24.0000i	0.779895i	0.920837	+	0.389948i	$0.127507\pi$
$947$	24.0000i	0.779895i	−0.920837	+	0.389948i	$0.872493\pi$
$948$	16.0000	0.519656
$949$	0	0
$950$	10.0000	0.324443
$951$	12.0000i	0.389127i
$952$	−6.00000	−0.194461
$953$	54.0000	1.74923	0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000	1.74923	0.874616	+	0.484817i	$0.161114\pi$
$954$	6.00000i	0.194257i
$955$	0	0
$956$	24.0000i	0.776215i
$957$	0	0
$958$	36.0000	1.16311
$959$	−18.0000	−0.581250
$960$	0	0
$961$	15.0000	0.483871
$962$	0	0
$963$	12.0000	0.386695
$964$	10.0000i	0.322078i
$965$	0	0
$966$	0	0
$967$	− 32.0000i	− 1.02905i	−0.857475	−	0.514525i	$-0.827968\pi$
$967$	− 32.0000i	− 1.02905i	0.857475	−	0.514525i	$-0.172032\pi$
$968$	− 11.0000i	− 0.353553i
$969$	− 24.0000i	− 0.770991i
$970$	0	0
$971$	−6.00000	−0.192549	−0.0962746	−	0.995355i	$-0.530693\pi$
$971$	−6.00000	−0.192549	−0.0962746	+	0.995355i	$0.530693\pi$
$972$	−10.0000	−0.320750
$973$	14.0000i	0.448819i
$974$	−16.0000	−0.512673
$975$	0	0
$976$	8.00000	0.256074
$977$	6.00000i	0.191957i	0.995383	+	0.0959785i	$0.0305980\pi$
$977$	6.00000i	0.191957i	−0.995383	+	0.0959785i	$0.969402\pi$
$978$	−32.0000	−1.02325
$979$	0	0
$980$	0	0
$981$	− 2.00000i	− 0.0638551i
$982$	12.0000i	0.382935i
$983$	− 36.0000i	− 1.14822i	−0.818778	−	0.574111i	$-0.805348\pi$
$983$	− 36.0000i	− 1.14822i	0.818778	−	0.574111i	$-0.194652\pi$
$984$	12.0000	0.382546
$985$	0	0
$986$	36.0000i	1.14647i
$987$	−24.0000	−0.763928
$988$	0	0
$989$	0	0
$990$	0	0
$991$	−16.0000	−0.508257	−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000	−0.508257	−0.254128	+	0.967170i	$0.581789\pi$
$992$	−4.00000	−0.127000
$993$	16.0000i	0.507745i
$994$	0	0
$995$	0	0
$996$	12.0000i	0.380235i
$997$	8.00000	0.253363	0.126681	−	0.991943i	$-0.459567\pi$
$997$	8.00000	0.253363	0.126681	+	0.991943i	$0.459567\pi$
$998$	−4.00000	−0.126618
$999$	8.00000i	0.253109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.d.b.337.2		2
13.5	odd	4		2366.2.a.j.1.1		1
13.8	odd	4		14.2.a.a.1.1	✓	1
13.12	even	2	inner	2366.2.d.b.337.1		2
39.8	even	4		126.2.a.b.1.1		1
52.47	even	4		112.2.a.c.1.1		1
65.8	even	4		350.2.c.d.99.2		2
65.34	odd	4		350.2.a.f.1.1		1
65.47	even	4		350.2.c.d.99.1		2
91.34	even	4		98.2.a.a.1.1		1
91.47	even	12		98.2.c.a.67.1		2
91.60	odd	12		98.2.c.b.79.1		2
91.73	even	12		98.2.c.a.79.1		2
91.86	odd	12		98.2.c.b.67.1		2
104.21	odd	4		448.2.a.g.1.1		1
104.99	even	4		448.2.a.a.1.1		1
117.34	odd	12		1134.2.f.l.757.1		2
117.47	even	12		1134.2.f.f.757.1		2
117.86	even	12		1134.2.f.f.379.1		2
117.112	odd	12		1134.2.f.l.379.1		2
143.21	even	4		1694.2.a.e.1.1		1
156.47	odd	4		1008.2.a.h.1.1		1
195.8	odd	4		3150.2.g.j.2899.1		2
195.47	odd	4		3150.2.g.j.2899.2		2
195.164	even	4		3150.2.a.i.1.1		1
208.21	odd	4		1792.2.b.c.897.2		2
208.99	even	4		1792.2.b.g.897.2		2
208.125	odd	4		1792.2.b.c.897.1		2
208.203	even	4		1792.2.b.g.897.1		2
221.203	odd	4		4046.2.a.f.1.1		1
247.151	even	4		5054.2.a.c.1.1		1
260.47	odd	4		2800.2.g.h.449.1		2
260.99	even	4		2800.2.a.g.1.1		1
260.203	odd	4		2800.2.g.h.449.2		2
273.47	odd	12		882.2.g.d.361.1		2
273.86	even	12		882.2.g.c.361.1		2
273.125	odd	4		882.2.a.i.1.1		1
273.164	odd	12		882.2.g.d.667.1		2
273.242	even	12		882.2.g.c.667.1		2
299.229	even	4		7406.2.a.a.1.1		1
312.125	even	4		4032.2.a.w.1.1		1
312.203	odd	4		4032.2.a.r.1.1		1
364.47	odd	12		784.2.i.i.753.1		2
364.151	even	12		784.2.i.c.177.1		2
364.255	odd	12		784.2.i.i.177.1		2
364.307	odd	4		784.2.a.b.1.1		1
364.359	even	12		784.2.i.c.753.1		2
455.34	even	4		2450.2.a.t.1.1		1
455.307	odd	4		2450.2.c.c.99.1		2
455.398	odd	4		2450.2.c.c.99.2		2
728.125	even	4		3136.2.a.e.1.1		1
728.307	odd	4		3136.2.a.z.1.1		1
1092.671	even	4		7056.2.a.bd.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.2.a.a.1.1	✓	1	13.8	odd	4
98.2.a.a.1.1		1	91.34	even	4
98.2.c.a.67.1		2	91.47	even	12
98.2.c.a.79.1		2	91.73	even	12
98.2.c.b.67.1		2	91.86	odd	12
98.2.c.b.79.1		2	91.60	odd	12
112.2.a.c.1.1		1	52.47	even	4
126.2.a.b.1.1		1	39.8	even	4
350.2.a.f.1.1		1	65.34	odd	4
350.2.c.d.99.1		2	65.47	even	4
350.2.c.d.99.2		2	65.8	even	4
448.2.a.a.1.1		1	104.99	even	4
448.2.a.g.1.1		1	104.21	odd	4
784.2.a.b.1.1		1	364.307	odd	4
784.2.i.c.177.1		2	364.151	even	12
784.2.i.c.753.1		2	364.359	even	12
784.2.i.i.177.1		2	364.255	odd	12
784.2.i.i.753.1		2	364.47	odd	12
882.2.a.i.1.1		1	273.125	odd	4
882.2.g.c.361.1		2	273.86	even	12
882.2.g.c.667.1		2	273.242	even	12
882.2.g.d.361.1		2	273.47	odd	12
882.2.g.d.667.1		2	273.164	odd	12
1008.2.a.h.1.1		1	156.47	odd	4
1134.2.f.f.379.1		2	117.86	even	12
1134.2.f.f.757.1		2	117.47	even	12
1134.2.f.l.379.1		2	117.112	odd	12
1134.2.f.l.757.1		2	117.34	odd	12
1694.2.a.e.1.1		1	143.21	even	4
1792.2.b.c.897.1		2	208.125	odd	4
1792.2.b.c.897.2		2	208.21	odd	4
1792.2.b.g.897.1		2	208.203	even	4
1792.2.b.g.897.2		2	208.99	even	4
2366.2.a.j.1.1		1	13.5	odd	4
2366.2.d.b.337.1		2	13.12	even	2	inner
2366.2.d.b.337.2		2	1.1	even	1	trivial
2450.2.a.t.1.1		1	455.34	even	4
2450.2.c.c.99.1		2	455.307	odd	4
2450.2.c.c.99.2		2	455.398	odd	4
2800.2.a.g.1.1		1	260.99	even	4
2800.2.g.h.449.1		2	260.47	odd	4
2800.2.g.h.449.2		2	260.203	odd	4
3136.2.a.e.1.1		1	728.125	even	4
3136.2.a.z.1.1		1	728.307	odd	4
3150.2.a.i.1.1		1	195.164	even	4
3150.2.g.j.2899.1		2	195.8	odd	4
3150.2.g.j.2899.2		2	195.47	odd	4
4032.2.a.r.1.1		1	312.203	odd	4
4032.2.a.w.1.1		1	312.125	even	4
4046.2.a.f.1.1		1	221.203	odd	4
5054.2.a.c.1.1		1	247.151	even	4
7056.2.a.bd.1.1		1	1092.671	even	4
7406.2.a.a.1.1		1	299.229	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -2.00000 q^{3} -1.00000 q^{4} -2.00000i q^{6} +1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -2.00000 q^{3} -1.00000 q^{4} -2.00000i q^{6} +1.00000i q^{7} -1.00000i q^{8} +1.00000 q^{9} +2.00000 q^{12} -1.00000 q^{14} +1.00000 q^{16} -6.00000 q^{17} +1.00000i q^{18} -2.00000i q^{19} -2.00000i q^{21} +2.00000i q^{24} +5.00000 q^{25} +4.00000 q^{27} -1.00000i q^{28} -6.00000 q^{29} +4.00000i q^{31} +1.00000i q^{32} -6.00000i q^{34} -1.00000 q^{36} +2.00000i q^{37} +2.00000 q^{38} -6.00000i q^{41} +2.00000 q^{42} -8.00000 q^{43} -12.0000i q^{47} -2.00000 q^{48} -1.00000 q^{49} +5.00000i q^{50} +12.0000 q^{51} +6.00000 q^{53} +4.00000i q^{54} +1.00000 q^{56} +4.00000i q^{57} -6.00000i q^{58} -6.00000i q^{59} +8.00000 q^{61} -4.00000 q^{62} +1.00000i q^{63} -1.00000 q^{64} +4.00000i q^{67} +6.00000 q^{68} -1.00000i q^{72} +2.00000i q^{73} -2.00000 q^{74} -10.0000 q^{75} +2.00000i q^{76} +8.00000 q^{79} -11.0000 q^{81} +6.00000 q^{82} +6.00000i q^{83} +2.00000i q^{84} -8.00000i q^{86} +12.0000 q^{87} -6.00000i q^{89} -8.00000i q^{93} +12.0000 q^{94} -2.00000i q^{96} +10.0000i q^{97} -1.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{3} - 2 q^{4} + 2 q^{9}+O(q^{10}) \) 2 * q - 4 * q^3 - 2 * q^4 + 2 * q^9	\( 2 q - 4 q^{3} - 2 q^{4} + 2 q^{9} + 4 q^{12} - 2 q^{14} + 2 q^{16} - 12 q^{17} + 10 q^{25} + 8 q^{27} - 12 q^{29} - 2 q^{36} + 4 q^{38} + 4 q^{42} - 16 q^{43} - 4 q^{48} - 2 q^{49} + 24 q^{51} + 12 q^{53} + 2 q^{56} + 16 q^{61} - 8 q^{62} - 2 q^{64} + 12 q^{68} - 4 q^{74} - 20 q^{75} + 16 q^{79} - 22 q^{81} + 12 q^{82} + 24 q^{87} + 24 q^{94}+O(q^{100}) \) 2 * q - 4 * q^3 - 2 * q^4 + 2 * q^9 + 4 * q^12 - 2 * q^14 + 2 * q^16 - 12 * q^17 + 10 * q^25 + 8 * q^27 - 12 * q^29 - 2 * q^36 + 4 * q^38 + 4 * q^42 - 16 * q^43 - 4 * q^48 - 2 * q^49 + 24 * q^51 + 12 * q^53 + 2 * q^56 + 16 * q^61 - 8 * q^62 - 2 * q^64 + 12 * q^68 - 4 * q^74 - 20 * q^75 + 16 * q^79 - 22 * q^81 + 12 * q^82 + 24 * q^87 + 24 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more