LMFDB - Embedded newform 3024.2.df.e.1601.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(17,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.18
Character	$\chi$	$=$	3024.1601
Dual form			3024.2.df.e.17.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+1.58600 q^{5} +(1.06431 + 2.42224i) q^{7} +3.95252i q^{11} +(5.09214 - 2.93995i) q^{13} +(3.19652 + 5.53653i) q^{17} +(6.37856 + 3.68267i) q^{19} -2.43102i q^{23} -2.48459 q^{25} +(-4.34058 - 2.50604i) q^{29} +(-0.855353 - 0.493838i) q^{31} +(1.68800 + 3.84168i) q^{35} +(0.183332 - 0.317540i) q^{37} +(-5.58681 - 9.67664i) q^{41} +(-1.26688 + 2.19430i) q^{43} +(-0.543280 - 0.940989i) q^{47} +(-4.73448 + 5.15604i) q^{49} +(-6.89030 + 3.97812i) q^{53} +6.26871i q^{55} +(-2.73420 + 4.73577i) q^{59} +(12.4765 - 7.20330i) q^{61} +(8.07615 - 4.66277i) q^{65} +(-5.70501 + 9.88137i) q^{67} +9.65277i q^{71} +(7.64694 - 4.41497i) q^{73} +(-9.57394 + 4.20672i) q^{77} +(-5.30654 - 9.19120i) q^{79} +(2.96819 - 5.14105i) q^{83} +(5.06969 + 8.78096i) q^{85} +(-4.70952 + 8.15712i) q^{89} +(12.5409 + 9.20535i) q^{91} +(10.1164 + 5.84072i) q^{95} +(10.4826 + 6.05213i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{25} - 18 q^{29} - 18 q^{31} + 6 q^{41} + 6 q^{43} + 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} - 6 q^{79} + 18 q^{89} - 6 q^{91} - 54 q^{95}+O(q^{100}) $ 48 * q + 48 * q^25 - 18 * q^29 - 18 * q^31 + 6 * q^41 + 6 * q^43 + 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 - 6 * q^79 + 18 * q^89 - 6 * q^91 - 54 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.58600			0.709283			0.354641	−	0.935002i	$-0.384603\pi$
$5$	1.58600			0.709283			0.354641	+	0.935002i	$0.384603\pi$
$6$		0			0
$7$	1.06431	+	2.42224i	0.402272	+	0.915520i
$7$	1.06431	+	2.42224i	0.402272	+	0.915520i
$8$		0			0
$9$		0			0
$10$		0			0
$11$			3.95252i			1.19173i	0.803085	+	0.595865i	$0.203191\pi$
$11$			3.95252i			1.19173i	−0.803085	+	0.595865i	$0.796809\pi$
$12$		0			0
$13$	5.09214	−	2.93995i	1.41231	−	0.815395i	0.416700	−	0.909044i	$-0.363187\pi$
$13$	5.09214	−	2.93995i	1.41231	−	0.815395i	0.995605	+	0.0936493i	$0.0298532\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.19652	+	5.53653i	0.775269	+	1.34281i	0.934643	+	0.355588i	$0.115719\pi$
$17$	3.19652	+	5.53653i	0.775269	+	1.34281i	−0.159374	+	0.987218i	$0.550947\pi$
$18$		0			0
$19$	6.37856	+	3.68267i	1.46334	+	0.844862i	0.999164	−	0.0408799i	$-0.0130161\pi$
$19$	6.37856	+	3.68267i	1.46334	+	0.844862i	0.464179	+	0.885741i	$0.346349\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	2.43102i		−	0.506903i	−0.967348	−	0.253451i	$-0.918434\pi$
$23$		−	2.43102i		−	0.506903i	0.967348	−	0.253451i	$-0.0815658\pi$
$24$		0			0
$25$	−2.48459			−0.496918
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.34058	−	2.50604i	−0.806026	−	0.465359i	0.0395477	−	0.999218i	$-0.487408\pi$
$29$	−4.34058	−	2.50604i	−0.806026	−	0.465359i	−0.845574	+	0.533858i	$0.820742\pi$
$30$		0			0
$31$	−0.855353	−	0.493838i	−0.153626	−	0.0886960i	0.421216	−	0.906960i	$-0.361603\pi$
$31$	−0.855353	−	0.493838i	−0.153626	−	0.0886960i	−0.574842	+	0.818264i	$0.694937\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.68800	+	3.84168i	0.285325	+	0.649362i
$36$		0			0
$37$	0.183332	−	0.317540i	0.0301396	−	0.0522033i	−0.850562	−	0.525874i	$-0.823738\pi$
$37$	0.183332	−	0.317540i	0.0301396	−	0.0522033i	0.880702	+	0.473671i	$0.157071\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.58681	−	9.67664i	−0.872513	−	1.51124i	−0.859389	−	0.511323i	$-0.829156\pi$
$41$	−5.58681	−	9.67664i	−0.872513	−	1.51124i	−0.0131240	−	0.999914i	$-0.504178\pi$
$42$		0			0
$43$	−1.26688	+	2.19430i	−0.193197	+	0.334627i	−0.946308	−	0.323266i	$-0.895219\pi$
$43$	−1.26688	+	2.19430i	−0.193197	+	0.334627i	0.753111	+	0.657894i	$0.228552\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.543280	−	0.940989i	−0.0792456	−	0.137257i	0.823679	−	0.567056i	$-0.191918\pi$
$47$	−0.543280	−	0.940989i	−0.0792456	−	0.137257i	−0.902925	+	0.429799i	$0.858584\pi$
$48$		0			0
$49$	−4.73448	+	5.15604i	−0.676354	+	0.736577i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.89030	+	3.97812i	−0.946455	+	0.546436i	−0.891978	−	0.452079i	$-0.850683\pi$
$53$	−6.89030	+	3.97812i	−0.946455	+	0.546436i	−0.0544773	+	0.998515i	$0.517349\pi$
$54$		0			0
$55$			6.26871i			0.845273i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.73420	+	4.73577i	−0.355963	+	0.616545i	−0.987282	−	0.158977i	$-0.949180\pi$
$59$	−2.73420	+	4.73577i	−0.355963	+	0.616545i	0.631320	+	0.775523i	$0.282514\pi$
$60$		0			0
$61$	12.4765	−	7.20330i	1.59745	−	0.922288i	0.605473	−	0.795865i	$-0.292984\pi$
$61$	12.4765	−	7.20330i	1.59745	−	0.922288i	0.991976	−	0.126423i	$-0.0403496\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	8.07615	−	4.66277i	1.00172	−	0.578345i
$66$		0			0
$67$	−5.70501	+	9.88137i	−0.696978	+	1.20720i	0.272531	+	0.962147i	$0.412139\pi$
$67$	−5.70501	+	9.88137i	−0.696978	+	1.20720i	−0.969509	+	0.245055i	$0.921194\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			9.65277i			1.14557i	0.819705	+	0.572787i	$0.194138\pi$
$71$			9.65277i			1.14557i	−0.819705	+	0.572787i	$0.805862\pi$
$72$		0			0
$73$	7.64694	−	4.41497i	0.895007	−	0.516733i	0.0194302	−	0.999811i	$-0.493815\pi$
$73$	7.64694	−	4.41497i	0.895007	−	0.516733i	0.875577	+	0.483079i	$0.160481\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−9.57394	+	4.20672i	−1.09105	+	0.479400i
$78$		0			0
$79$	−5.30654	−	9.19120i	−0.597032	−	1.03409i	−0.993257	−	0.115937i	$-0.963013\pi$
$79$	−5.30654	−	9.19120i	−0.597032	−	1.03409i	0.396224	−	0.918154i	$-0.370320\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.96819	−	5.14105i	0.325801	−	0.564303i	−0.655873	−	0.754871i	$-0.727699\pi$
$83$	2.96819	−	5.14105i	0.325801	−	0.564303i	0.981674	+	0.190568i	$0.0610328\pi$
$84$		0			0
$85$	5.06969	+	8.78096i	0.549885	+	0.952429i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.70952	+	8.15712i	−0.499208	+	0.864653i	−1.00000		0.000914461i	$-0.999709\pi$
$89$	−4.70952	+	8.15712i	−0.499208	+	0.864653i	0.500792	+	0.865568i	$0.333042\pi$
$90$		0			0
$91$	12.5409	+	9.20535i	1.31464	+	0.964983i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	10.1164	+	5.84072i	1.03792	+	0.599246i
$96$		0			0
$97$	10.4826	+	6.05213i	1.06435	+	0.614501i	0.926631	−	0.375971i	$-0.122691\pi$
$97$	10.4826	+	6.05213i	1.06435	+	0.614501i	0.137715	+	0.990472i	$0.456024\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.0243106			−0.00241900			−0.00120950	−	0.999999i	$-0.500385\pi$
$101$	−0.0243106			−0.00241900			−0.00120950	+	0.999999i	$0.500385\pi$
$102$		0			0
$103$			1.42747i			0.140653i	0.997524	+	0.0703266i	$0.0224041\pi$
$103$			1.42747i			0.140653i	−0.997524	+	0.0703266i	$0.977596\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−10.9445	−	6.31880i	−1.05804	−	0.610862i	−0.133153	−	0.991095i	$-0.542510\pi$
$107$	−10.9445	−	6.31880i	−1.05804	−	0.610862i	−0.924890	+	0.380234i	$0.875844\pi$
$108$		0			0
$109$	0.0726028	+	0.125752i	0.00695408	+	0.0120448i	0.869482	−	0.493965i	$-0.164453\pi$
$109$	0.0726028	+	0.125752i	0.00695408	+	0.0120448i	−0.862527	+	0.506010i	$0.831120\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	9.35867	−	5.40323i	0.880390	−	0.508293i	0.00960284	−	0.999954i	$-0.496943\pi$
$113$	9.35867	−	5.40323i	0.880390	−	0.508293i	0.870787	+	0.491661i	$0.163610\pi$
$114$		0			0
$115$		−	3.85561i		−	0.359537i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−10.0087	+	13.6353i	−0.917496	+	1.24995i
$120$		0			0
$121$	−4.62241			−0.420219
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.8706			−1.06174
$126$		0			0
$127$	3.63647			0.322685			0.161342	−	0.986899i	$-0.448418\pi$
$127$	3.63647			0.322685			0.161342	+	0.986899i	$0.448418\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	5.01984			0.438585			0.219293	−	0.975659i	$-0.429625\pi$
$131$	5.01984			0.438585			0.219293	+	0.975659i	$0.429625\pi$
$132$		0			0
$133$	−2.13151	+	19.3699i	−0.184825	+	1.67958i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	9.30911i		−	0.795331i	−0.917531	−	0.397665i	$-0.869820\pi$
$137$		−	9.30911i		−	0.795331i	0.917531	−	0.397665i	$-0.130180\pi$
$138$		0			0
$139$	3.82307	−	2.20725i	0.324269	−	0.187217i	−0.329025	−	0.944321i	$-0.606720\pi$
$139$	3.82307	−	2.20725i	0.324269	−	0.187217i	0.653294	+	0.757105i	$0.273387\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	11.6202	+	20.1268i	0.971730	+	1.68309i
$144$		0			0
$145$	−6.88418	−	3.97459i	−0.571700	−	0.330071i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	2.89473i		−	0.237145i	−0.992945	−	0.118573i	$-0.962168\pi$
$149$		−	2.89473i		−	0.237145i	0.992945	−	0.118573i	$-0.0378318\pi$
$150$		0			0
$151$	−2.77117			−0.225515			−0.112757	−	0.993623i	$-0.535968\pi$
$151$	−2.77117			−0.225515			−0.112757	+	0.993623i	$0.535968\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.35659	−	0.783230i	−0.108964	−	0.0629105i
$156$		0			0
$157$	0.146366	+	0.0845044i	0.0116813	+	0.00674418i	0.505829	−	0.862634i	$-0.331187\pi$
$157$	0.146366	+	0.0845044i	0.0116813	+	0.00674418i	−0.494148	+	0.869378i	$0.664520\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.88851	−	2.58736i	0.464079	−	0.203913i
$162$		0			0
$163$	3.55929	−	6.16487i	0.278785	−	0.482870i	−0.692298	−	0.721612i	$-0.743402\pi$
$163$	3.55929	−	6.16487i	0.278785	−	0.482870i	0.971083	+	0.238742i	$0.0767350\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.19494	+	2.06970i	0.0924675	+	0.160158i	0.908549	−	0.417779i	$-0.137191\pi$
$167$	1.19494	+	2.06970i	0.0924675	+	0.160158i	−0.816081	+	0.577937i	$0.803858\pi$
$168$		0			0
$169$	10.7866	−	18.6829i	0.829737	−	1.43715i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.57971	+	6.20023i	0.272160	+	0.471395i	0.969415	−	0.245429i	$-0.0789287\pi$
$173$	3.57971	+	6.20023i	0.272160	+	0.471395i	−0.697255	+	0.716823i	$0.745595\pi$
$174$		0			0
$175$	−2.64438	−	6.01827i	−0.199896	−	0.454939i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.02286	+	4.63200i	−0.599657	+	0.346212i	−0.768906	−	0.639361i	$-0.779199\pi$
$179$	−8.02286	+	4.63200i	−0.599657	+	0.346212i	0.169250	+	0.985573i	$0.445866\pi$
$180$		0			0
$181$		−	21.5541i		−	1.60210i	−0.598595	−	0.801052i	$-0.704274\pi$
$181$		−	21.5541i		−	1.60210i	0.598595	−	0.801052i	$-0.295726\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.290765	−	0.503620i	0.0213775	−	0.0370269i
$186$		0			0
$187$	−21.8832	+	12.6343i	−1.60026	+	0.923911i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.91100	−	1.68067i	0.210633	−	0.121609i	−0.390973	−	0.920402i	$-0.627861\pi$
$191$	2.91100	−	1.68067i	0.210633	−	0.121609i	0.601605	+	0.798793i	$0.294528\pi$
$192$		0			0
$193$	−4.17845	+	7.23728i	−0.300771	+	0.520951i	−0.976311	−	0.216373i	$-0.930577\pi$
$193$	−4.17845	+	7.23728i	−0.300771	+	0.520951i	0.675540	+	0.737324i	$0.263911\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			5.57159i			0.396959i	0.980105	+	0.198480i	$0.0636003\pi$
$197$			5.57159i			0.396959i	−0.980105	+	0.198480i	$0.936400\pi$
$198$		0			0
$199$	11.6605	−	6.73222i	0.826594	−	0.477234i	−0.0260910	−	0.999660i	$-0.508306\pi$
$199$	11.6605	−	6.73222i	0.826594	−	0.477234i	0.852685	+	0.522425i	$0.174973\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.45048	−	13.1811i	0.101804	−	0.925134i
$204$		0			0
$205$	−8.86070	−	15.3472i	−0.618858	−	1.07189i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−14.5558	+	25.2114i	−1.00685	+	1.74391i
$210$		0			0
$211$	−7.23362	−	12.5290i	−0.497983	−	0.862532i	0.502014	−	0.864859i	$-0.332592\pi$
$211$	−7.23362	−	12.5290i	−0.497983	−	0.862532i	−0.999997	+	0.00232753i	$0.999259\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.00928	+	3.48017i	−0.137031	+	0.237345i
$216$		0			0
$217$	0.285831	−	2.59747i	0.0194035	−	0.176328i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	32.5542	+	18.7952i	2.18983	+	1.26430i
$222$		0			0
$223$	18.3399	+	10.5885i	1.22813	+	0.709060i	0.966638	−	0.256146i	$-0.0824529\pi$
$223$	18.3399	+	10.5885i	1.22813	+	0.709060i	0.261490	+	0.965206i	$0.415786\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.47672			0.562620			0.281310	−	0.959617i	$-0.409231\pi$
$227$	8.47672			0.562620			0.281310	+	0.959617i	$0.409231\pi$
$228$		0			0
$229$			19.7783i			1.30699i	0.756932	+	0.653494i	$0.226697\pi$
$229$			19.7783i			1.30699i	−0.756932	+	0.653494i	$0.773303\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	23.7957	+	13.7385i	1.55891	+	0.900037i	0.997362	+	0.0725933i	$0.0231275\pi$
$233$	23.7957	+	13.7385i	1.55891	+	0.900037i	0.561548	+	0.827444i	$0.310206\pi$
$234$		0			0
$235$	−0.861645	−	1.49241i	−0.0562075	−	0.0973543i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.979306	−	0.565402i	0.0633460	−	0.0365728i	−0.467992	−	0.883732i	$-0.655023\pi$
$239$	0.979306	−	0.565402i	0.0633460	−	0.0365728i	0.531339	+	0.847160i	$0.321689\pi$
$240$		0			0
$241$			1.45825i			0.0939339i	0.998896	+	0.0469669i	$0.0149555\pi$
$241$			1.45825i			0.0939339i	−0.998896	+	0.0469669i	$0.985044\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.50890	+	8.17750i	−0.479726	+	0.522441i
$246$		0			0
$247$	43.3074			2.75558
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.61932			0.102210			0.0511052	−	0.998693i	$-0.483726\pi$
$251$	1.61932			0.102210			0.0511052	+	0.998693i	$0.483726\pi$
$252$		0			0
$253$	9.60865			0.604091
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.95518			−0.558609			−0.279305	−	0.960203i	$-0.590104\pi$
$257$	−8.95518			−0.558609			−0.279305	+	0.960203i	$0.590104\pi$
$258$		0			0
$259$	0.964280	+	0.106112i	0.0599174	+	0.00659345i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	2.71686i		−	0.167529i	−0.996486	−	0.0837643i	$-0.973306\pi$
$263$		−	2.71686i		−	0.167529i	0.996486	−	0.0837643i	$-0.0266943\pi$
$264$		0			0
$265$	−10.9280	+	6.30931i	−0.671304	+	0.387578i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	8.87918	+	15.3792i	0.541373	+	0.937686i	0.998826	+	0.0484519i	$0.0154288\pi$
$269$	8.87918	+	15.3792i	0.541373	+	0.937686i	−0.457452	+	0.889234i	$0.651238\pi$
$270$		0			0
$271$	−2.76570	−	1.59678i	−0.168004	−	0.0969973i	0.413640	−	0.910440i	$-0.364257\pi$
$271$	−2.76570	−	1.59678i	−0.168004	−	0.0969973i	−0.581644	+	0.813443i	$0.697590\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	9.82039i		−	0.592192i
$276$		0			0
$277$	6.63542			0.398684			0.199342	−	0.979930i	$-0.436120\pi$
$277$	6.63542			0.398684			0.199342	+	0.979930i	$0.436120\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.88306	+	3.97394i	0.410609	+	0.237065i	0.691051	−	0.722806i	$-0.257148\pi$
$281$	6.88306	+	3.97394i	0.410609	+	0.237065i	−0.280442	+	0.959871i	$0.590481\pi$
$282$		0			0
$283$	−21.9793	−	12.6898i	−1.30653	−	0.754328i	−0.325019	−	0.945708i	$-0.605371\pi$
$283$	−21.9793	−	12.6898i	−1.30653	−	0.754328i	−0.981516	+	0.191379i	$0.938704\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	17.4930	−	23.8315i	1.03258	−	1.40673i
$288$		0			0
$289$	−11.9354	+	20.6728i	−0.702085	+	1.21605i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.29543	−	7.43990i	−0.250942	−	0.434644i	0.712844	−	0.701323i	$-0.247407\pi$
$293$	−4.29543	−	7.43990i	−0.250942	−	0.434644i	−0.963785	+	0.266679i	$0.914074\pi$
$294$		0			0
$295$	−4.33645	+	7.51096i	−0.252478	+	0.437305i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.14707	−	12.3791i	−0.413326	−	0.715901i
$300$		0			0
$301$	−6.66347	−	0.733263i	−0.384076	−	0.0422646i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	19.7878	−	11.4245i	1.13304	−	0.654163i
$306$		0			0
$307$			24.2144i			1.38199i	0.722861	+	0.690994i	$0.242827\pi$
$307$			24.2144i			1.38199i	−0.722861	+	0.690994i	$0.757173\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	12.7009	−	21.9986i	0.720201	−	1.24742i	−0.240718	−	0.970595i	$-0.577383\pi$
$311$	12.7009	−	21.9986i	0.720201	−	1.24742i	0.960919	−	0.276830i	$-0.0892837\pi$
$312$		0			0
$313$	−20.0407	+	11.5705i	−1.13276	+	0.654002i	−0.944629	−	0.328141i	$-0.893578\pi$
$313$	−20.0407	+	11.5705i	−1.13276	+	0.654002i	−0.188136	+	0.982143i	$0.560245\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.22166	+	3.01472i	−0.293277	+	0.169324i	−0.639419	−	0.768859i	$-0.720825\pi$
$317$	−5.22166	+	3.01472i	−0.293277	+	0.169324i	0.346142	+	0.938182i	$0.387492\pi$
$318$		0			0
$319$	9.90516	−	17.1562i	0.554583	−	0.960565i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			47.0868i			2.61998i
$324$		0			0
$325$	−12.6519	+	7.30457i	−0.701800	+	0.405184i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.70108	−	2.31746i	0.0937836	−	0.127766i
$330$		0			0
$331$	−8.70940	−	15.0851i	−0.478712	−	0.829153i	0.520990	−	0.853563i	$-0.325563\pi$
$331$	−8.70940	−	15.0851i	−0.478712	−	0.829153i	−0.999702	+	0.0244093i	$0.992230\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−9.04818	+	15.6719i	−0.494355	+	0.856247i
$336$		0			0
$337$	−0.760462	−	1.31716i	−0.0414250	−	0.0717502i	0.844570	−	0.535446i	$-0.179856\pi$
$337$	−0.760462	−	1.31716i	−0.0414250	−	0.0717502i	−0.885995	+	0.463696i	$0.846523\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.95191	−	3.38080i	0.105702	−	0.183081i
$342$		0			0
$343$	−17.5281	−	5.98040i	−0.946429	−	0.322911i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−19.0030	−	10.9714i	−1.02013	−	0.588975i	−0.105992	−	0.994367i	$-0.533802\pi$
$347$	−19.0030	−	10.9714i	−1.02013	−	0.588975i	−0.914143	+	0.405392i	$0.867135\pi$
$348$		0			0
$349$	4.95655	+	2.86167i	0.265318	+	0.153182i	0.626758	−	0.779214i	$-0.284381\pi$
$349$	4.95655	+	2.86167i	0.265318	+	0.153182i	−0.361440	+	0.932395i	$0.617715\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.84540			−0.204670			−0.102335	−	0.994750i	$-0.532631\pi$
$353$	−3.84540			−0.204670			−0.102335	+	0.994750i	$0.532631\pi$
$354$		0			0
$355$			15.3093i			0.812535i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−10.8763	−	6.27946i	−0.574031	−	0.331417i	0.184727	−	0.982790i	$-0.440860\pi$
$359$	−10.8763	−	6.27946i	−0.574031	−	0.331417i	−0.758758	+	0.651373i	$0.774193\pi$
$360$		0			0
$361$	17.6241	+	30.5258i	0.927582	+	1.60662i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	12.1281	−	7.00215i	0.634813	−	0.366509i
$366$		0			0
$367$		−	1.22224i		−	0.0638006i	−0.999491	−	0.0319003i	$-0.989844\pi$
$367$		−	1.22224i		−	0.0638006i	0.999491	−	0.0319003i	$-0.0101559\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−16.9694	−	12.4560i	−0.881006	−	0.646683i
$372$		0			0
$373$	13.1525			0.681010			0.340505	−	0.940243i	$-0.389402\pi$
$373$	13.1525			0.681010			0.340505	+	0.940243i	$0.389402\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−29.4705			−1.51781
$378$		0			0
$379$	−22.9852			−1.18067			−0.590336	−	0.807157i	$-0.701005\pi$
$379$	−22.9852			−1.18067			−0.590336	+	0.807157i	$0.701005\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−27.9366			−1.42749			−0.713746	−	0.700404i	$-0.753003\pi$
$383$	−27.9366			−1.42749			−0.713746	+	0.700404i	$0.753003\pi$
$384$		0			0
$385$	−15.1843	+	6.67187i	−0.773864	+	0.340030i
$386$		0			0
$387$		0			0
$388$		0			0
$389$			14.3116i			0.725627i	0.931862	+	0.362814i	$0.118184\pi$
$389$			14.3116i			0.725627i	−0.931862	+	0.362814i	$0.881816\pi$
$390$		0			0
$391$	13.4594	−	7.77080i	0.680672	−	0.392986i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−8.41619	−	14.5773i	−0.423465	−	0.733462i
$396$		0			0
$397$	−3.97038	−	2.29230i	−0.199267	−	0.115047i	0.397046	−	0.917799i	$-0.370035\pi$
$397$	−3.97038	−	2.29230i	−0.199267	−	0.115047i	−0.596314	+	0.802751i	$0.703369\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			11.0739i			0.553003i	0.961013	+	0.276502i	$0.0891751\pi$
$401$			11.0739i			0.553003i	−0.961013	+	0.276502i	$0.910825\pi$
$402$		0			0
$403$	−5.80744			−0.289289
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.25508	+	0.724623i	0.0622122	+	0.0359182i
$408$		0			0
$409$	5.31691	+	3.06972i	0.262904	+	0.151788i	0.625659	−	0.780097i	$-0.284830\pi$
$409$	5.31691	+	3.06972i	0.262904	+	0.151788i	−0.362754	+	0.931885i	$0.618164\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−14.3812	−	1.58254i	−0.707653	−	0.0778718i
$414$		0			0
$415$	4.70756	−	8.15372i	0.231085	−	0.400251i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−8.83059	−	15.2950i	−0.431402	−	0.747211i	0.565592	−	0.824685i	$-0.308648\pi$
$419$	−8.83059	−	15.2950i	−0.431402	−	0.747211i	−0.996994	+	0.0774744i	$0.975314\pi$
$420$		0			0
$421$	11.3569	−	19.6707i	0.553501	−	0.958693i	−0.444517	−	0.895770i	$-0.646625\pi$
$421$	11.3569	−	19.6707i	0.553501	−	0.958693i	0.998018	−	0.0629223i	$-0.0200420\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−7.94204	−	13.7560i	−0.385245	−	0.667265i
$426$		0			0
$427$	30.7270	+	22.5545i	1.48698	+	1.09149i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	18.4152	−	10.6320i	0.887031	−	0.512128i	0.0140610	−	0.999901i	$-0.495524\pi$
$431$	18.4152	−	10.6320i	0.887031	−	0.512128i	0.872970	+	0.487773i	$0.162191\pi$
$432$		0			0
$433$		−	16.1075i		−	0.774079i	−0.922063	−	0.387039i	$-0.873498\pi$
$433$		−	16.1075i		−	0.774079i	0.922063	−	0.387039i	$-0.126502\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	8.95263	−	15.5064i	0.428262	−	0.741772i
$438$		0			0
$439$	11.2480	−	6.49401i	0.536836	−	0.309942i	−0.206960	−	0.978349i	$-0.566357\pi$
$439$	11.2480	−	6.49401i	0.536836	−	0.309942i	0.743796	+	0.668407i	$0.233024\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	15.4357	−	8.91183i	0.733374	−	0.423414i	−0.0862809	−	0.996271i	$-0.527498\pi$
$443$	15.4357	−	8.91183i	0.733374	−	0.423414i	0.819655	+	0.572857i	$0.194165\pi$
$444$		0			0
$445$	−7.46931	+	12.9372i	−0.354079	+	0.613284i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	5.71118i		−	0.269527i	−0.990878	−	0.134764i	$-0.956972\pi$
$449$		−	5.71118i		−	0.269527i	0.990878	−	0.134764i	$-0.0430275\pi$
$450$		0			0
$451$	38.2471	−	22.0820i	1.80099	−	1.03980i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	19.8899	+	14.5997i	0.932452	+	0.684446i
$456$		0			0
$457$	4.75884	+	8.24255i	0.222609	+	0.385570i	0.955599	−	0.294669i	$-0.0952093\pi$
$457$	4.75884	+	8.24255i	0.222609	+	0.385570i	−0.732990	+	0.680239i	$0.761876\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	20.1348	−	34.8746i	0.937773	−	1.62427i	0.168160	−	0.985760i	$-0.446218\pi$
$461$	20.1348	−	34.8746i	0.937773	−	1.62427i	0.769613	−	0.638510i	$-0.220449\pi$
$462$		0			0
$463$	−6.92014	−	11.9860i	−0.321606	−	0.557038i	0.659213	−	0.751956i	$-0.270889\pi$
$463$	−6.92014	−	11.9860i	−0.321606	−	0.557038i	−0.980820	+	0.194917i	$0.937556\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−10.5793	+	18.3238i	−0.489549	+	0.847924i	−0.999928	−	0.0120256i	$-0.996172\pi$
$467$	−10.5793	+	18.3238i	−0.489549	+	0.847924i	0.510378	+	0.859950i	$0.329505\pi$
$468$		0			0
$469$	−30.0070	−	3.30203i	−1.38559	−	0.152474i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−8.67301	−	5.00736i	−0.398785	−	0.230239i
$474$		0			0
$475$	−15.8481	−	9.14992i	−0.727162	−	0.419827i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.34127			−0.106975			−0.0534876	−	0.998569i	$-0.517034\pi$
$479$	−2.34127			−0.106975			−0.0534876	+	0.998569i	$0.517034\pi$
$480$		0			0
$481$		−	2.15594i		−	0.0983026i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	16.6254	+	9.59871i	0.754923	+	0.435855i
$486$		0			0
$487$	8.83818	+	15.3082i	0.400496	+	0.693679i	0.993786	−	0.111310i	$-0.0355045\pi$
$487$	8.83818	+	15.3082i	0.400496	+	0.693679i	−0.593290	+	0.804989i	$0.702171\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	2.01875	−	1.16553i	0.0911051	−	0.0525995i	−0.453755	−	0.891126i	$-0.649916\pi$
$491$	2.01875	−	1.16553i	0.0911051	−	0.0525995i	0.544860	+	0.838527i	$0.316583\pi$
$492$		0			0
$493$		−	32.0424i		−	1.44312i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−23.3813	+	10.2736i	−1.04880	+	0.460832i
$498$		0			0
$499$	−31.6088			−1.41500			−0.707501	−	0.706712i	$-0.750178\pi$
$499$	−31.6088			−1.41500			−0.707501	+	0.706712i	$0.750178\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	38.9500			1.73670			0.868348	−	0.495956i	$-0.165182\pi$
$503$	38.9500			1.73670			0.868348	+	0.495956i	$0.165182\pi$
$504$		0			0
$505$	−0.0385567			−0.00171575
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−13.7956			−0.611477			−0.305739	−	0.952115i	$-0.598903\pi$
$509$	−13.7956			−0.611477			−0.305739	+	0.952115i	$0.598903\pi$
$510$		0			0
$511$	18.8328	+	13.8238i	0.833116	+	0.611530i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			2.26398i			0.0997629i
$516$		0			0
$517$	3.71928	−	2.14733i	0.163574	−	0.0944393i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−2.27458	−	3.93969i	−0.0996512	−	0.172601i	0.811889	−	0.583812i	$-0.198439\pi$
$521$	−2.27458	−	3.93969i	−0.0996512	−	0.172601i	−0.911540	+	0.411211i	$0.865106\pi$
$522$		0			0
$523$	−32.6301	−	18.8390i	−1.42681	−	0.823772i	−0.429946	−	0.902855i	$-0.641467\pi$
$523$	−32.6301	−	18.8390i	−1.42681	−	0.823772i	−0.996868	+	0.0790830i	$0.974801\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	6.31425i		−	0.275053i
$528$		0			0
$529$	17.0901			0.743050
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−56.8976	−	32.8498i	−2.46451	−	1.42288i
$534$		0			0
$535$	−17.3580	−	10.0216i	−0.750452	−	0.433274i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−20.3793	−	18.7131i	−0.877800	−	0.806031i
$540$		0			0
$541$	−1.53417	+	2.65727i	−0.0659593	+	0.114245i	−0.897119	−	0.441789i	$-0.854344\pi$
$541$	−1.53417	+	2.65727i	−0.0659593	+	0.114245i	0.831160	+	0.556034i	$0.187677\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.115148	+	0.199443i	0.00493241	+	0.00854319i
$546$		0			0
$547$	7.22022	−	12.5058i	0.308714	−	0.534709i	−0.669367	−	0.742932i	$-0.733435\pi$
$547$	7.22022	−	12.5058i	0.308714	−	0.534709i	0.978081	+	0.208223i	$0.0667679\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−18.4578	−	31.9698i	−0.786329	−	1.36196i
$552$		0			0
$553$	16.6155	−	22.6360i	0.706561	−	0.962581i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.14024	+	4.12242i	−0.302542	+	0.174672i	−0.643584	−	0.765375i	$-0.722553\pi$
$557$	−7.14024	+	4.12242i	−0.302542	+	0.174672i	0.341042	+	0.940048i	$0.389220\pi$
$558$		0			0
$559$			14.8982i			0.630128i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.68623	+	8.11678i	−0.197501	+	0.342082i	−0.947717	−	0.319111i	$-0.896616\pi$
$563$	−4.68623	+	8.11678i	−0.197501	+	0.342082i	0.750217	+	0.661192i	$0.229949\pi$
$564$		0			0
$565$	14.8429	−	8.56955i	0.624445	−	0.360524i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	16.5077	−	9.53072i	0.692039	−	0.399549i	−0.112337	−	0.993670i	$-0.535833\pi$
$569$	16.5077	−	9.53072i	0.692039	−	0.399549i	0.804375	+	0.594121i	$0.202500\pi$
$570$		0			0
$571$	−5.02208	+	8.69850i	−0.210167	+	0.364021i	−0.951767	−	0.306822i	$-0.900734\pi$
$571$	−5.02208	+	8.69850i	−0.210167	+	0.364021i	0.741599	+	0.670843i	$0.234068\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			6.04009i			0.251889i
$576$		0			0
$577$	−10.1403	+	5.85453i	−0.422148	+	0.243727i	−0.695996	−	0.718046i	$-0.745037\pi$
$577$	−10.1403	+	5.85453i	−0.422148	+	0.243727i	0.273848	+	0.961773i	$0.411704\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	15.6119	+	1.71797i	0.647692	+	0.0712735i
$582$		0			0
$583$	−15.7236	−	27.2340i	−0.651204	−	1.12792i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.476262	+	0.824911i	−0.0196575	+	0.0340477i	−0.875687	−	0.482880i	$-0.839591\pi$
$587$	−0.476262	+	0.824911i	−0.0196575	+	0.0340477i	0.856029	+	0.516927i	$0.172924\pi$
$588$		0			0
$589$	−3.63728	−	6.29996i	−0.149872	−	0.259585i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	15.4339	−	26.7323i	0.633794	−	1.09776i	−0.352976	−	0.935632i	$-0.614830\pi$
$593$	15.4339	−	26.7323i	0.633794	−	1.09776i	0.986769	−	0.162130i	$-0.0518365\pi$
$594$		0			0
$595$	−15.8738	+	21.6257i	−0.650764	+	0.886567i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	35.6899	+	20.6056i	1.45825	+	0.841921i	0.998925	−	0.0463468i	$-0.0147579\pi$
$599$	35.6899	+	20.6056i	1.45825	+	0.841921i	0.459325	+	0.888268i	$0.348091\pi$
$600$		0			0
$601$	−14.3592	−	8.29029i	−0.585724	−	0.338168i	0.177681	−	0.984088i	$-0.443141\pi$
$601$	−14.3592	−	8.29029i	−0.585724	−	0.338168i	−0.763405	+	0.645920i	$0.776474\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−7.33116			−0.298054
$606$		0			0
$607$		−	47.4652i		−	1.92655i	−0.268510	−	0.963277i	$-0.586531\pi$
$607$		−	47.4652i		−	1.92655i	0.268510	−	0.963277i	$-0.413469\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.53292	−	3.19443i	−0.223838	−	0.129233i
$612$		0			0
$613$	7.32074	+	12.6799i	0.295682	+	0.512136i	0.975143	−	0.221575i	$-0.0711199\pi$
$613$	7.32074	+	12.6799i	0.295682	+	0.512136i	−0.679462	+	0.733711i	$0.737787\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	40.1960	−	23.2072i	1.61823	−	0.934286i	0.630852	−	0.775903i	$-0.282705\pi$
$617$	40.1960	−	23.2072i	1.61823	−	0.934286i	0.987378	−	0.158383i	$-0.0506279\pi$
$618$		0			0
$619$			7.74450i			0.311278i	0.987814	+	0.155639i	$0.0497436\pi$
$619$			7.74450i			0.311278i	−0.987814	+	0.155639i	$0.950256\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−24.7709	−	2.72585i	−0.992425	−	0.109209i
$624$		0			0
$625$	−6.40386			−0.256154
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2.34409			0.0934651
$630$		0			0
$631$	−24.3088			−0.967718			−0.483859	−	0.875146i	$-0.660765\pi$
$631$	−24.3088			−0.967718			−0.483859	+	0.875146i	$0.660765\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	5.76746			0.228875
$636$		0			0
$637$	−8.95014	+	40.1744i	−0.354617	+	1.59177i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			17.5326i			0.692495i	0.938143	+	0.346248i	$0.112544\pi$
$641$			17.5326i			0.692495i	−0.938143	+	0.346248i	$0.887456\pi$
$642$		0			0
$643$	7.49992	−	4.33008i	0.295768	−	0.170762i	−0.344772	−	0.938686i	$-0.612044\pi$
$643$	7.49992	−	4.33008i	0.295768	−	0.170762i	0.640540	+	0.767925i	$0.278710\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.3349	−	23.0967i	−0.524249	−	0.908026i	−0.999601	−	0.0282305i	$-0.991013\pi$
$647$	−13.3349	−	23.0967i	−0.524249	−	0.908026i	0.475352	−	0.879796i	$-0.342321\pi$
$648$		0			0
$649$	−18.7182	−	10.8070i	−0.734755	−	0.424211i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	43.8362i		−	1.71544i	−0.514116	−	0.857721i	$-0.671880\pi$
$653$		−	43.8362i		−	1.71544i	0.514116	−	0.857721i	$-0.328120\pi$
$654$		0			0
$655$	7.96148			0.311081
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−39.3555	−	22.7219i	−1.53307	−	0.885120i	−0.999218	−	0.0395437i	$-0.987410\pi$
$659$	−39.3555	−	22.7219i	−1.53307	−	0.885120i	−0.533855	−	0.845576i	$-0.679257\pi$
$660$		0			0
$661$	−34.9261	−	20.1646i	−1.35847	−	0.784311i	−0.369050	−	0.929410i	$-0.620317\pi$
$661$	−34.9261	−	20.1646i	−1.35847	−	0.784311i	−0.989417	+	0.145098i	$0.953650\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.38058	+	30.7208i	−0.131093	+	1.19130i
$666$		0			0
$667$	−6.09223	+	10.5520i	−0.235892	+	0.408577i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	28.4712	+	49.3135i	1.09912	+	1.90373i
$672$		0			0
$673$	−3.85511	+	6.67724i	−0.148603	+	0.257389i	−0.930712	−	0.365754i	$-0.880811\pi$
$673$	−3.85511	+	6.67724i	−0.148603	+	0.257389i	0.782108	+	0.623143i	$0.214144\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−22.0288	−	38.1550i	−0.846635	−	1.46642i	−0.884194	−	0.467121i	$-0.845291\pi$
$677$	−22.0288	−	38.1550i	−0.846635	−	1.46642i	0.0375585	−	0.999294i	$-0.488042\pi$
$678$		0			0
$679$	−3.50294	+	31.8327i	−0.134431	+	1.22163i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−3.75165	+	2.16602i	−0.143553	+	0.0828804i	−0.570056	−	0.821606i	$-0.693079\pi$
$683$	−3.75165	+	2.16602i	−0.143553	+	0.0828804i	0.426503	+	0.904486i	$0.359745\pi$
$684$		0			0
$685$		−	14.7643i		−	0.564114i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−23.3909	+	40.5142i	−0.891123	+	1.54347i
$690$		0			0
$691$	−7.00301	+	4.04319i	−0.266407	+	0.153810i	−0.627254	−	0.778815i	$-0.715821\pi$
$691$	−7.00301	+	4.04319i	−0.266407	+	0.153810i	0.360847	+	0.932625i	$0.382488\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.06341	−	3.50071i	0.229998	−	0.132790i
$696$		0			0
$697$	35.7167	−	61.8631i	1.35286	−	2.34323i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			41.8099i			1.57914i	0.613662	+	0.789569i	$0.289696\pi$
$701$			41.8099i			1.57914i	−0.613662	+	0.789569i	$0.710304\pi$
$702$		0			0
$703$	2.33879	−	1.35030i	0.0882091	−	0.0509275i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.0258741	−	0.0588861i	−0.000973095	−	0.00221464i
$708$		0			0
$709$	22.6470	+	39.2257i	0.850526	+	1.47315i	0.880735	+	0.473610i	$0.157049\pi$
$709$	22.6470	+	39.2257i	0.850526	+	1.47315i	−0.0302091	+	0.999544i	$0.509617\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.20053	+	2.07938i	−0.0449602	+	0.0778734i
$714$		0			0
$715$	18.4297	+	31.9212i	0.689231	+	1.19378i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.73529	−	3.00561i	0.0647155	−	0.112090i	−0.831852	−	0.554997i	$-0.812719\pi$
$719$	1.73529	−	3.00561i	0.0647155	−	0.112090i	0.896568	+	0.442907i	$0.146053\pi$
$720$		0			0
$721$	−3.45768	+	1.51928i	−0.128771	+	0.0565809i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	10.7846	+	6.22648i	0.400529	+	0.231246i
$726$		0			0
$727$	37.7189	+	21.7770i	1.39892	+	0.807665i	0.994279	−	0.106811i	$-0.0340641\pi$
$727$	37.7189	+	21.7770i	1.39892	+	0.807665i	0.404638	+	0.914477i	$0.367397\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−16.1984			−0.599120
$732$		0			0
$733$		−	7.63755i		−	0.282099i	−0.990003	−	0.141050i	$-0.954952\pi$
$733$		−	7.63755i		−	0.282099i	0.990003	−	0.141050i	$-0.0450477\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−39.0563	−	22.5492i	−1.43866	−	0.830610i
$738$		0			0
$739$	−22.0809	−	38.2453i	−0.812260	−	1.40687i	−0.911279	−	0.411789i	$-0.864904\pi$
$739$	−22.0809	−	38.2453i	−0.812260	−	1.40687i	0.0990195	−	0.995085i	$-0.468429\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	10.8720	−	6.27693i	0.398853	−	0.230278i	−0.287136	−	0.957890i	$-0.592703\pi$
$743$	10.8720	−	6.27693i	0.398853	−	0.230278i	0.685989	+	0.727612i	$0.259370\pi$
$744$		0			0
$745$		−	4.59105i		−	0.168203i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.65729	−	33.2353i	0.133635	−	1.21439i
$750$		0			0
$751$	−18.1150			−0.661025			−0.330512	−	0.943802i	$-0.607222\pi$
$751$	−18.1150			−0.661025			−0.330512	+	0.943802i	$0.607222\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−4.39509			−0.159954
$756$		0			0
$757$	39.8682			1.44903			0.724517	−	0.689257i	$-0.242063\pi$
$757$	39.8682			1.44903			0.724517	+	0.689257i	$0.242063\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−15.0569			−0.545812			−0.272906	−	0.962041i	$-0.587985\pi$
$761$	−15.0569			−0.545812			−0.272906	+	0.962041i	$0.587985\pi$
$762$		0			0
$763$	−0.227328	+	0.309700i	−0.00822984	+	0.0112119i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			32.1536i			1.16100i
$768$		0			0
$769$	−0.522559	+	0.301700i	−0.0188440	+	0.0108796i	−0.509392	−	0.860534i	$-0.670130\pi$
$769$	−0.522559	+	0.301700i	−0.0188440	+	0.0108796i	0.490548	+	0.871414i	$0.336796\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−1.56956	−	2.71856i	−0.0564533	−	0.0977799i	0.836418	−	0.548093i	$-0.184646\pi$
$773$	−1.56956	−	2.71856i	−0.0564533	−	0.0977799i	−0.892871	+	0.450313i	$0.851313\pi$
$774$		0			0
$775$	2.12520	+	1.22699i	0.0763395	+	0.0440746i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	82.2974i		−	2.94861i
$780$		0			0
$781$	−38.1528			−1.36521
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.232137	+	0.134024i	0.00828532	+	0.00478353i
$786$		0			0
$787$	−15.9640	−	9.21682i	−0.569055	−	0.328544i	0.187717	−	0.982223i	$-0.439891\pi$
$787$	−15.9640	−	9.21682i	−0.569055	−	0.328544i	−0.756772	+	0.653679i	$0.773225\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	23.0485	+	16.9182i	0.819509	+	0.601542i
$792$		0			0
$793$	42.3547	−	73.3604i	1.50406	−	2.60510i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	17.1802	+	29.7570i	0.608554	+	1.05405i	0.991479	+	0.130267i	$0.0415833\pi$
$797$	17.1802	+	29.7570i	0.608554	+	1.05405i	−0.382925	+	0.923779i	$0.625083\pi$
$798$		0			0
$799$	3.47321	−	6.01578i	0.122873	−	0.212823i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	17.4502	+	30.2247i	0.615806	+	1.06661i
$804$		0			0
$805$	9.33920	−	4.10357i	0.329164	−	0.144632i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	44.3399	−	25.5996i	1.55891	−	0.900035i	0.561544	−	0.827447i	$-0.310207\pi$
$809$	44.3399	−	25.5996i	1.55891	−	0.900035i	0.997362	−	0.0725881i	$-0.0231258\pi$
$810$		0			0
$811$			46.2446i			1.62387i	0.583751	+	0.811933i	$0.301585\pi$
$811$			46.2446i			1.62387i	−0.583751	+	0.811933i	$0.698415\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	5.64505	−	9.77751i	0.197737	−	0.342491i
$816$		0			0
$817$	−16.1617	+	9.33099i	−0.565428	+	0.326450i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.33282	−	4.23361i	0.255917	−	0.147754i	−0.366553	−	0.930397i	$-0.619462\pi$
$821$	7.33282	−	4.23361i	0.255917	−	0.147754i	0.622471	+	0.782643i	$0.286129\pi$
$822$		0			0
$823$	−12.6623	+	21.9317i	−0.441380	+	0.764492i	−0.997792	−	0.0664144i	$-0.978844\pi$
$823$	−12.6623	+	21.9317i	−0.441380	+	0.764492i	0.556413	+	0.830906i	$0.312177\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	6.75531i		−	0.234905i	−0.993078	−	0.117453i	$-0.962527\pi$
$827$		−	6.75531i		−	0.234905i	0.993078	−	0.117453i	$-0.0374728\pi$
$828$		0			0
$829$	−17.0191	+	9.82599i	−0.591098	+	0.341271i	−0.765532	−	0.643398i	$-0.777524\pi$
$829$	−17.0191	+	9.82599i	−0.591098	+	0.341271i	0.174434	+	0.984669i	$0.444191\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−43.6804	−	9.73122i	−1.51344	−	0.337167i
$834$		0			0
$835$	1.89519	+	3.28256i	0.0655856	+	0.113598i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	16.6302	−	28.8044i	0.574140	−	0.994439i	−0.421995	−	0.906598i	$-0.638670\pi$
$839$	16.6302	−	28.8044i	0.574140	−	0.994439i	0.996135	−	0.0878410i	$-0.0279967\pi$
$840$		0			0
$841$	−1.93955	−	3.35940i	−0.0668811	−	0.115841i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	17.1076	−	29.6312i	0.588518	−	1.01934i
$846$		0			0
$847$	−4.91969	−	11.1966i	−0.169043	−	0.384719i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−0.771946	−	0.445683i	−0.0264620	−	0.0152778i
$852$		0			0
$853$	−25.0891	−	14.4852i	−0.859035	−	0.495964i	0.00465409	−	0.999989i	$-0.498519\pi$
$853$	−25.0891	−	14.4852i	−0.859035	−	0.495964i	−0.863689	+	0.504025i	$0.831852\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	46.6449			1.59336			0.796680	−	0.604401i	$-0.206588\pi$
$857$	46.6449			1.59336			0.796680	+	0.604401i	$0.206588\pi$
$858$		0			0
$859$			14.7329i			0.502680i	0.967899	+	0.251340i	$0.0808712\pi$
$859$			14.7329i			0.502680i	−0.967899	+	0.251340i	$0.919129\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	40.0533	+	23.1248i	1.36343	+	0.787177i	0.990079	−	0.140513i	$-0.0448751\pi$
$863$	40.0533	+	23.1248i	1.36343	+	0.787177i	0.373352	+	0.927690i	$0.378208\pi$
$864$		0			0
$865$	5.67743	+	9.83360i	0.193038	+	0.334352i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	36.3284	−	20.9742i	1.23236	−	0.711501i
$870$		0			0
$871$			67.0898i			2.27325i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−12.6340	−	28.7534i	−0.427108	−	0.972042i
$876$		0			0
$877$	−47.9408			−1.61884			−0.809422	−	0.587227i	$-0.800220\pi$
$877$	−47.9408			−1.61884			−0.809422	+	0.587227i	$0.800220\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−22.8464			−0.769715			−0.384857	−	0.922976i	$-0.625749\pi$
$881$	−22.8464			−0.769715			−0.384857	+	0.922976i	$0.625749\pi$
$882$		0			0
$883$	9.97054			0.335535			0.167768	−	0.985827i	$-0.446344\pi$
$883$	9.97054			0.335535			0.167768	+	0.985827i	$0.446344\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.5527			0.488633			0.244317	−	0.969696i	$-0.421436\pi$
$887$	14.5527			0.488633			0.244317	+	0.969696i	$0.421436\pi$
$888$		0			0
$889$	3.87034	+	8.80840i	0.129807	+	0.295424i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	8.00288i		−	0.267806i
$894$		0			0
$895$	−12.7243	+	7.34637i	−0.425326	+	0.245562i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.47516	+	4.28709i	0.0825510	+	0.142983i
$900$		0			0
$901$	−44.0499	−	25.4322i	−1.46752	−	0.847270i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	34.1849i		−	1.13634i
$906$		0			0
$907$	21.9091			0.727481			0.363740	−	0.931500i	$-0.381500\pi$
$907$	21.9091			0.727481			0.363740	+	0.931500i	$0.381500\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	44.3072	+	25.5808i	1.46796	+	0.847529i	0.999356	−	0.0358768i	$-0.0114224\pi$
$911$	44.3072	+	25.5808i	1.46796	+	0.847529i	0.468608	+	0.883406i	$0.344756\pi$
$912$		0			0
$913$	20.3201	+	11.7318i	0.672497	+	0.388266i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.34268	+	12.1592i	0.176431	+	0.401534i
$918$		0			0
$919$	28.4261	−	49.2355i	0.937691	−	1.62413i	0.167928	−	0.985799i	$-0.446293\pi$
$919$	28.4261	−	49.2355i	0.937691	−	1.62413i	0.769763	−	0.638329i	$-0.220374\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	28.3786	+	49.1533i	0.934094	+	1.61790i
$924$		0			0
$925$	−0.455505	+	0.788957i	−0.0149769	+	0.0259407i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−5.15562	−	8.92980i	−0.169151	−	0.292977i	0.768971	−	0.639284i	$-0.220769\pi$
$929$	−5.15562	−	8.92980i	−0.169151	−	0.292977i	−0.938121	+	0.346306i	$0.887436\pi$
$930$		0			0
$931$	−49.1871	+	15.4526i	−1.61204	+	0.506439i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−34.7069	+	20.0380i	−1.13504	+	0.655314i
$936$		0			0
$937$			2.65580i			0.0867614i	0.999059	+	0.0433807i	$0.0138128\pi$
$937$			2.65580i			0.0867614i	−0.999059	+	0.0433807i	$0.986187\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.43664	+	2.48834i	−0.0468333	+	0.0811176i	−0.888492	−	0.458893i	$-0.848246\pi$
$941$	−1.43664	+	2.48834i	−0.0468333	+	0.0811176i	0.841658	+	0.540010i	$0.181580\pi$
$942$		0			0
$943$	−23.5241	+	13.5816i	−0.766050	+	0.442279i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.03333	+	4.63804i	−0.261048	+	0.150716i	−0.624813	−	0.780775i	$-0.714825\pi$
$947$	−8.03333	+	4.63804i	−0.261048	+	0.150716i	0.363765	+	0.931491i	$0.381491\pi$
$948$		0			0
$949$	25.9595	−	44.9632i	0.842682	−	1.45957i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	52.9084i		−	1.71387i	−0.515425	−	0.856935i	$-0.672366\pi$
$953$		−	52.9084i		−	1.71387i	0.515425	−	0.856935i	$-0.327634\pi$
$954$		0			0
$955$	4.61686	−	2.66555i	0.149398	−	0.0862551i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	22.5489	−	9.90780i	0.728141	−	0.319940i
$960$		0			0
$961$	−15.0122	−	26.0020i	−0.484266	−	0.838773i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−6.62703	+	11.4784i	−0.213332	+	0.369501i
$966$		0			0
$967$	−5.65450	−	9.79388i	−0.181836	−	0.314950i	0.760669	−	0.649139i	$-0.224871\pi$
$967$	−5.65450	−	9.79388i	−0.181836	−	0.314950i	−0.942506	+	0.334189i	$0.891537\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	22.5860	−	39.1201i	0.724819	−	1.25542i	−0.234230	−	0.972181i	$-0.575257\pi$
$971$	22.5860	−	39.1201i	0.724819	−	1.25542i	0.959048	−	0.283242i	$-0.0914099\pi$
$972$		0			0
$973$	9.41544	+	6.91119i	0.301845	+	0.221563i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−15.2443	−	8.80132i	−0.487710	−	0.281579i	0.235914	−	0.971774i	$-0.424192\pi$
$977$	−15.2443	−	8.80132i	−0.487710	−	0.281579i	−0.723624	+	0.690195i	$0.757525\pi$
$978$		0			0
$979$	−32.2412	−	18.6145i	−1.03043	−	0.594921i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−35.0841			−1.11901			−0.559504	−	0.828827i	$-0.689008\pi$
$983$	−35.0841			−1.11901			−0.559504	+	0.828827i	$0.689008\pi$
$984$		0			0
$985$			8.83656i			0.281556i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	5.33438	+	3.07981i	0.169624	+	0.0979322i
$990$		0			0
$991$	−16.9731	−	29.3982i	−0.539167	−	0.933865i	−0.998949	−	0.0458331i	$-0.985406\pi$
$991$	−16.9731	−	29.3982i	−0.539167	−	0.933865i	0.459782	−	0.888032i	$-0.347928\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	18.4937	−	10.6773i	0.586289	−	0.338494i
$996$		0			0
$997$			25.5331i			0.808642i	0.914617	+	0.404321i	$0.132492\pi$
$997$			25.5331i			0.808642i	−0.914617	+	0.404321i	$0.867508\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.df.e.1601.18		48
3.2	odd	2		1008.2.df.e.929.7		48
4.3	odd	2		1512.2.cx.a.89.18		48
7.3	odd	6		3024.2.ca.e.2033.18		48
9.4	even	3		1008.2.ca.e.257.3		48
9.5	odd	6		3024.2.ca.e.2609.18		48
12.11	even	2		504.2.cx.a.425.18	yes	48
21.17	even	6		1008.2.ca.e.353.3		48
28.3	even	6		1512.2.bs.a.521.18		48
36.23	even	6		1512.2.bs.a.1097.18		48
36.31	odd	6		504.2.bs.a.257.22	✓	48
63.31	odd	6		1008.2.df.e.689.7		48
63.59	even	6	inner	3024.2.df.e.17.18		48
84.59	odd	6		504.2.bs.a.353.22	yes	48
252.31	even	6		504.2.cx.a.185.18	yes	48
252.59	odd	6		1512.2.cx.a.17.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.22	✓	48	36.31	odd	6
504.2.bs.a.353.22	yes	48	84.59	odd	6
504.2.cx.a.185.18	yes	48	252.31	even	6
504.2.cx.a.425.18	yes	48	12.11	even	2
1008.2.ca.e.257.3		48	9.4	even	3
1008.2.ca.e.353.3		48	21.17	even	6
1008.2.df.e.689.7		48	63.31	odd	6
1008.2.df.e.929.7		48	3.2	odd	2
1512.2.bs.a.521.18		48	28.3	even	6
1512.2.bs.a.1097.18		48	36.23	even	6
1512.2.cx.a.17.18		48	252.59	odd	6
1512.2.cx.a.89.18		48	4.3	odd	2
3024.2.ca.e.2033.18		48	7.3	odd	6
3024.2.ca.e.2609.18		48	9.5	odd	6
3024.2.df.e.17.18		48	63.59	even	6	inner
3024.2.df.e.1601.18		48	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.58600 q^{5} +(1.06431 + 2.42224i) q^{7} +3.95252i q^{11} +(5.09214 - 2.93995i) q^{13} +(3.19652 + 5.53653i) q^{17} +(6.37856 + 3.68267i) q^{19} -2.43102i q^{23} -2.48459 q^{25} +(-4.34058 - 2.50604i) q^{29} +(-0.855353 - 0.493838i) q^{31} +(1.68800 + 3.84168i) q^{35} +(0.183332 - 0.317540i) q^{37} +(-5.58681 - 9.67664i) q^{41} +(-1.26688 + 2.19430i) q^{43} +(-0.543280 - 0.940989i) q^{47} +(-4.73448 + 5.15604i) q^{49} +(-6.89030 + 3.97812i) q^{53} +6.26871i q^{55} +(-2.73420 + 4.73577i) q^{59} +(12.4765 - 7.20330i) q^{61} +(8.07615 - 4.66277i) q^{65} +(-5.70501 + 9.88137i) q^{67} +9.65277i q^{71} +(7.64694 - 4.41497i) q^{73} +(-9.57394 + 4.20672i) q^{77} +(-5.30654 - 9.19120i) q^{79} +(2.96819 - 5.14105i) q^{83} +(5.06969 + 8.78096i) q^{85} +(-4.70952 + 8.15712i) q^{89} +(12.5409 + 9.20535i) q^{91} +(10.1164 + 5.84072i) q^{95} +(10.4826 + 6.05213i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{25} - 18 q^{29} - 18 q^{31} + 6 q^{41} + 6 q^{43} + 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} - 6 q^{79} + 18 q^{89} - 6 q^{91} - 54 q^{95}+O(q^{100}) \) 48 * q + 48 * q^25 - 18 * q^29 - 18 * q^31 + 6 * q^41 + 6 * q^43 + 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 - 6 * q^79 + 18 * q^89 - 6 * q^91 - 54 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more