LMFDB - Embedded newform 1404.2.cc.a.305.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1404,2,Mod(305,1404)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1404.305"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1404, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1404 = 2^{2} \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1404.cc (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$11.2109964438$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 468)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			305.14
Character	$\chi$	$=$	1404.305
Dual form			1404.2.cc.a.557.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.01961 - 3.80525i) q^{5} +(-1.33162 - 1.33162i) q^{7} +(-4.35045 - 1.16570i) q^{11} +(3.41964 + 1.14283i) q^{13} +(-2.31976 - 4.01793i) q^{17} +(7.37291 + 1.97557i) q^{19} +0.999222 q^{23} +(-9.11020 - 5.25978i) q^{25} +(-0.0144776 + 0.00835862i) q^{29} +(-3.02992 - 0.811864i) q^{31} +(-6.42489 + 3.70941i) q^{35} +(-5.97798 + 1.60179i) q^{37} +(-8.54895 - 8.54895i) q^{41} +2.30282i q^{43} +(0.0107778 + 0.0402231i) q^{47} -3.45357i q^{49} +1.73858i q^{53} +(-8.87157 + 15.3660i) q^{55} +(2.25516 + 8.41636i) q^{59} -5.22569 q^{61} +(7.83547 - 11.8473i) q^{65} +(-0.0524121 + 0.0524121i) q^{67} +(-1.28159 + 4.78296i) q^{71} +(-0.0292789 - 0.0292789i) q^{73} +(4.24088 + 7.34542i) q^{77} +(-1.17774 + 2.03990i) q^{79} +(4.57822 - 1.22673i) q^{83} +(-17.6545 + 4.73051i) q^{85} +(3.20395 + 11.9573i) q^{89} +(-3.03185 - 6.07548i) q^{91} +(15.0350 - 26.0415i) q^{95} +(6.01956 - 6.01956i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} - 12 q^{11} + 4 q^{19} - 4 q^{31} - 66 q^{35} + 2 q^{37} - 24 q^{41} + 36 q^{47} + 36 q^{65} - 14 q^{67} + 24 q^{71} - 14 q^{73} - 24 q^{77} + 12 q^{79} + 42 q^{83} - 36 q^{85} + 4 q^{91}+ \cdots - 46 q^{97}+O(q^{100}) $ 56 * q + 4 * q^7 - 12 * q^11 + 4 * q^19 - 4 * q^31 - 66 * q^35 + 2 * q^37 - 24 * q^41 + 36 * q^47 + 36 * q^65 - 14 * q^67 + 24 * q^71 - 14 * q^73 - 24 * q^77 + 12 * q^79 + 42 * q^83 - 36 * q^85 + 4 * q^91 - 46 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1404\mathbb{Z}\right)^\times$.

$n$	$677$	$703$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{12}\right)$

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
$5$	1.01961	−	3.80525i	0.455985	−	1.70176i	−0.229189	−	0.973382i	$-0.573608\pi$
$5$	1.01961	−	3.80525i	0.455985	−	1.70176i	0.685175	−	0.728379i	$-0.259726\pi$
$6$		0			0
$7$	−1.33162	−	1.33162i	−0.503305	−	0.503305i	0.409158	−	0.912463i	$-0.365822\pi$
$7$	−1.33162	−	1.33162i	−0.503305	−	0.503305i	−0.912463	+	0.409158i	$0.865822\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.35045	−	1.16570i	−1.31171	−	0.351472i	−0.465844	−	0.884867i	$-0.654249\pi$
$11$	−4.35045	−	1.16570i	−1.31171	−	0.351472i	−0.845866	+	0.533395i	$0.820916\pi$
$12$		0			0
$13$	3.41964	+	1.14283i	0.948438	+	0.316964i
$13$	3.41964	+	1.14283i	0.948438	+	0.316964i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.31976	−	4.01793i	−0.562623	−	0.974492i	−0.997266	−	0.0738894i	$-0.976459\pi$
$17$	−2.31976	−	4.01793i	−0.562623	−	0.974492i	0.434643	−	0.900603i	$-0.356875\pi$
$18$		0			0
$19$	7.37291	+	1.97557i	1.69146	+	0.453226i	0.970766	−	0.240026i	$-0.0771561\pi$
$19$	7.37291	+	1.97557i	1.69146	+	0.453226i	0.720695	+	0.693252i	$0.243823\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.999222			0.208352			0.104176	−	0.994559i	$-0.466779\pi$
$23$	0.999222			0.208352			0.104176	+	0.994559i	$0.466779\pi$
$24$		0			0
$25$	−9.11020	−	5.25978i	−1.82204	−	1.05196i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.0144776	+	0.00835862i	−0.00268841	+	0.00155216i	−0.501344	−	0.865248i	$-0.667161\pi$
$29$	−0.0144776	+	0.00835862i	−0.00268841	+	0.00155216i	0.498655	+	0.866800i	$0.333827\pi$
$30$		0			0
$31$	−3.02992	−	0.811864i	−0.544189	−	0.145815i	−0.0237564	−	0.999718i	$-0.507563\pi$
$31$	−3.02992	−	0.811864i	−0.544189	−	0.145815i	−0.520433	+	0.853903i	$0.674229\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.42489	+	3.70941i	−1.08601	+	0.627005i
$36$		0			0
$37$	−5.97798	+	1.60179i	−0.982774	+	0.263333i	−0.714212	−	0.699929i	$-0.753215\pi$
$37$	−5.97798	+	1.60179i	−0.982774	+	0.263333i	−0.268561	+	0.963263i	$0.586548\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−8.54895	−	8.54895i	−1.33512	−	1.33512i	−0.900719	−	0.434403i	$-0.856960\pi$
$41$	−8.54895	−	8.54895i	−1.33512	−	1.33512i	−0.434403	−	0.900719i	$-0.643040\pi$
$42$		0			0
$43$			2.30282i			0.351177i	0.984464	+	0.175588i	$0.0561828\pi$
$43$			2.30282i			0.351177i	−0.984464	+	0.175588i	$0.943817\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.0107778	+	0.0402231i	0.00157210	+	0.00586715i	0.966707	−	0.255884i	$-0.0823666\pi$
$47$	0.0107778	+	0.0402231i	0.00157210	+	0.00586715i	−0.965135	+	0.261751i	$0.915700\pi$
$48$		0			0
$49$		−	3.45357i		−	0.493367i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			1.73858i			0.238812i	0.992845	+	0.119406i	$0.0380991\pi$
$53$			1.73858i			0.238812i	−0.992845	+	0.119406i	$0.961901\pi$
$54$		0			0
$55$	−8.87157	+	15.3660i	−1.19624	+	2.07195i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.25516	+	8.41636i	0.293596	+	1.09572i	0.942326	+	0.334697i	$0.108634\pi$
$59$	2.25516	+	8.41636i	0.293596	+	1.09572i	−0.648729	+	0.761019i	$0.724699\pi$
$60$		0			0
$61$	−5.22569			−0.669082			−0.334541	−	0.942381i	$-0.608581\pi$
$61$	−5.22569			−0.669082			−0.334541	+	0.942381i	$0.608581\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	7.83547	−	11.8473i	0.971870	−	1.46948i
$66$		0			0
$67$	−0.0524121	+	0.0524121i	−0.00640316	+	0.00640316i	−0.710301	−	0.703898i	$-0.751441\pi$
$67$	−0.0524121	+	0.0524121i	−0.00640316	+	0.00640316i	0.703898	+	0.710301i	$0.251441\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.28159	+	4.78296i	−0.152097	+	0.567633i	0.847240	+	0.531211i	$0.178263\pi$
$71$	−1.28159	+	4.78296i	−0.152097	+	0.567633i	−0.999336	+	0.0364221i	$0.988404\pi$
$72$		0			0
$73$	−0.0292789	−	0.0292789i	−0.00342684	−	0.00342684i	0.705391	−	0.708818i	$-0.250771\pi$
$73$	−0.0292789	−	0.0292789i	−0.00342684	−	0.00342684i	−0.708818	+	0.705391i	$0.750771\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.24088	+	7.34542i	0.483293	+	0.837089i
$78$		0			0
$79$	−1.17774	+	2.03990i	−0.132506	+	0.229507i	−0.924642	−	0.380837i	$-0.875636\pi$
$79$	−1.17774	+	2.03990i	−0.132506	+	0.229507i	0.792136	+	0.610345i	$0.208969\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.57822	−	1.22673i	0.502525	−	0.134651i	0.00135341	−	0.999999i	$-0.499569\pi$
$83$	4.57822	−	1.22673i	0.502525	−	0.134651i	0.501172	+	0.865348i	$0.332903\pi$
$84$		0			0
$85$	−17.6545	+	4.73051i	−1.91490	+	0.513096i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.20395	+	11.9573i	0.339618	+	1.26747i	0.898776	+	0.438409i	$0.144458\pi$
$89$	3.20395	+	11.9573i	0.339618	+	1.26747i	−0.559158	+	0.829061i	$0.688875\pi$
$90$		0			0
$91$	−3.03185	−	6.07548i	−0.317824	−	0.636883i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	15.0350	−	26.0415i	1.54256	−	2.67180i
$96$		0			0
$97$	6.01956	−	6.01956i	0.611194	−	0.611194i	−0.332063	−	0.943257i	$-0.607745\pi$
$97$	6.01956	−	6.01956i	0.611194	−	0.611194i	0.943257	+	0.332063i	$0.107745\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.89315	−	11.9393i	−0.685894	−	1.18800i	−0.973155	−	0.230151i	$-0.926078\pi$
$101$	−6.89315	−	11.9393i	−0.685894	−	1.18800i	0.287261	−	0.957852i	$-0.407255\pi$
$102$		0			0
$103$	−14.2999	+	8.25605i	−1.40901	+	0.813493i	−0.995293	−	0.0969123i	$-0.969103\pi$
$103$	−14.2999	+	8.25605i	−1.40901	+	0.813493i	−0.413718	+	0.910405i	$0.635770\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.79512	−	5.07786i	−0.850256	−	0.490896i	0.0104810	−	0.999945i	$-0.496664\pi$
$107$	−8.79512	−	5.07786i	−0.850256	−	0.490896i	−0.860737	+	0.509049i	$0.829997\pi$
$108$		0			0
$109$	11.2739	−	11.2739i	1.07985	−	1.07985i	0.0833248	−	0.996522i	$-0.473446\pi$
$109$	11.2739	−	11.2739i	1.07985	−	1.07985i	0.996522	−	0.0833248i	$-0.0265539\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.07280	+	1.77408i	0.289065	+	0.166892i	0.637520	−	0.770434i	$-0.279960\pi$
$113$	3.07280	+	1.77408i	0.289065	+	0.166892i	−0.348455	+	0.937325i	$0.613294\pi$
$114$		0			0
$115$	1.01882	−	3.80229i	0.0950056	−	0.354566i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.26133	+	8.43940i	−0.207296	+	0.773638i
$120$		0			0
$121$	8.04130	+	4.64265i	0.731027	+	0.422059i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−15.3755	+	15.3755i	−1.37523	+	1.37523i
$126$		0			0
$127$	−7.78898	−	4.49697i	−0.691160	−	0.399042i	0.112886	−	0.993608i	$-0.463990\pi$
$127$	−7.78898	−	4.49697i	−0.691160	−	0.399042i	−0.804047	+	0.594566i	$0.797324\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.85588	+	5.11294i	−0.773742	+	0.446720i	−0.834208	−	0.551450i	$-0.814075\pi$
$131$	−8.85588	+	5.11294i	−0.773742	+	0.446720i	0.0604660	+	0.998170i	$0.480741\pi$
$132$		0			0
$133$	−7.18722	−	12.4486i	−0.623211	−	1.07943i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	12.5721	−	12.5721i	1.07411	−	1.07411i	0.0770844	−	0.997025i	$-0.475439\pi$
$137$	12.5721	−	12.5721i	1.07411	−	1.07411i	0.997025	−	0.0770844i	$-0.0245611\pi$
$138$		0			0
$139$	5.49827	−	9.52329i	0.466358	−	0.807755i	−0.532904	−	0.846176i	$-0.678899\pi$
$139$	5.49827	−	9.52329i	0.466358	−	0.807755i	0.999262	+	0.0384207i	$0.0122327\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−13.5448	−	8.95810i	−1.13267	−	0.749114i
$144$		0			0
$145$	0.0170451	+	0.0636133i	0.00141552	+	0.00528280i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	21.3835	−	5.72969i	1.75181	−	0.469395i	0.766795	−	0.641892i	$-0.221850\pi$
$149$	21.3835	−	5.72969i	1.75181	−	0.469395i	0.985010	+	0.172497i	$0.0551835\pi$
$150$		0			0
$151$	22.9143	−	6.13987i	1.86474	−	0.499655i	0.864742	−	0.502216i	$-0.167482\pi$
$151$	22.9143	−	6.13987i	1.86474	−	0.499655i	0.999997	+	0.00256111i	$0.000815229\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.17869	+	10.7018i	−0.496284	+	0.859590i
$156$		0			0
$157$	−11.3850	−	19.7195i	−0.908626	−	1.57379i	−0.815975	−	0.578087i	$-0.803799\pi$
$157$	−11.3850	−	19.7195i	−0.908626	−	1.57379i	−0.0926507	−	0.995699i	$-0.529534\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.33058	−	1.33058i	−0.104865	−	0.104865i
$162$		0			0
$163$	3.35459	−	12.5195i	0.262752	−	0.980604i	−0.700860	−	0.713299i	$-0.747200\pi$
$163$	3.35459	−	12.5195i	0.262752	−	0.980604i	0.963612	−	0.267305i	$-0.0861330\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.28123	+	4.28123i	−0.331292	+	0.331292i	−0.853077	−	0.521785i	$-0.825266\pi$
$167$	−4.28123	+	4.28123i	−0.331292	+	0.331292i	0.521785	+	0.853077i	$0.325266\pi$
$168$		0			0
$169$	10.3879	+	7.81613i	0.799068	+	0.601241i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.119661			−0.00909766			−0.00454883	−	0.999990i	$-0.501448\pi$
$173$	−0.119661			−0.00909766			−0.00454883	+	0.999990i	$0.501448\pi$
$174$		0			0
$175$	5.12731	+	19.1354i	0.387588	+	1.44650i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.04673	−	12.2053i	0.526698	−	0.912267i	−0.472819	−	0.881160i	$-0.656763\pi$
$179$	7.04673	−	12.2053i	0.526698	−	0.912267i	0.999516	−	0.0311070i	$-0.00990327\pi$
$180$		0			0
$181$			5.37997i			0.399890i	0.979807	+	0.199945i	$0.0640764\pi$
$181$			5.37997i			0.399890i	−0.979807	+	0.199945i	$0.935924\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$			24.3809i			1.79252i
$186$		0			0
$187$	5.40828	+	20.1840i	0.395492	+	1.47600i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	10.3416i		−	0.748291i	−0.927370	−	0.374146i	$-0.877936\pi$
$191$		−	10.3416i		−	0.748291i	0.927370	−	0.374146i	$-0.122064\pi$
$192$		0			0
$193$	11.2662	+	11.2662i	0.810960	+	0.810960i	0.984778	−	0.173818i	$-0.0556105\pi$
$193$	11.2662	+	11.2662i	0.810960	+	0.810960i	−0.173818	+	0.984778i	$0.555610\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.40291	−	2.25155i	0.598683	−	0.160417i	0.0532643	−	0.998580i	$-0.483037\pi$
$197$	8.40291	−	2.25155i	0.598683	−	0.160417i	0.545418	+	0.838164i	$0.316371\pi$
$198$		0			0
$199$	12.1832	−	7.03398i	0.863645	−	0.498626i	−0.00158596	−	0.999999i	$-0.500505\pi$
$199$	12.1832	−	7.03398i	0.863645	−	0.498626i	0.865231	+	0.501373i	$0.167171\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.0304091	+	0.00814810i	0.00213430	+	0.000571884i
$204$		0			0
$205$	−41.2475	+	23.8143i	−2.88085	+	1.66326i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−29.7726	−	17.1892i	−2.05941	−	1.18900i
$210$		0			0
$211$	−1.89164			−0.130226			−0.0651131	−	0.997878i	$-0.520741\pi$
$211$	−1.89164			−0.130226			−0.0651131	+	0.997878i	$0.520741\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.76281	+	2.34799i	0.597619	+	0.160131i
$216$		0			0
$217$	2.95360	+	5.11579i	0.200504	+	0.347283i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.34091	−	16.3910i	−0.224734	−	1.10258i
$222$		0			0
$223$	18.4580	+	4.94580i	1.23604	+	0.331195i	0.816928	−	0.576740i	$-0.195675\pi$
$223$	18.4580	+	4.94580i	1.23604	+	0.331195i	0.419110	+	0.907935i	$0.362342\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.53495	+	9.53495i	0.632857	+	0.632857i	0.948784	−	0.315927i	$-0.102315\pi$
$227$	9.53495	+	9.53495i	0.632857	+	0.632857i	−0.315927	+	0.948784i	$0.602315\pi$
$228$		0			0
$229$	2.94216	−	10.9803i	0.194424	−	0.725599i	−0.797992	−	0.602669i	$-0.794104\pi$
$229$	2.94216	−	10.9803i	0.194424	−	0.725599i	0.992415	−	0.122930i	$-0.0392292\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.36969			0.548316			0.274158	−	0.961685i	$-0.411601\pi$
$233$	8.36969			0.548316			0.274158	+	0.961685i	$0.411601\pi$
$234$		0			0
$235$	0.164048			0.0107013
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4.29278	+	16.0209i	−0.277677	+	1.03630i	0.676349	+	0.736581i	$0.263561\pi$
$239$	−4.29278	+	16.0209i	−0.277677	+	1.03630i	−0.954026	+	0.299724i	$0.903106\pi$
$240$		0			0
$241$	0.480854	+	0.480854i	0.0309745	+	0.0309745i	0.722424	−	0.691450i	$-0.243028\pi$
$241$	0.480854	+	0.480854i	0.0309745	+	0.0309745i	−0.691450	+	0.722424i	$0.743028\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−13.1417	−	3.52131i	−0.839593	−	0.224968i
$246$		0			0
$247$	22.9550	+	15.1817i	1.46059	+	0.965989i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	14.0317	+	24.3035i	0.885670	+	1.53403i	0.844944	+	0.534855i	$0.179634\pi$
$251$	14.0317	+	24.3035i	0.885670	+	1.53403i	0.0407262	+	0.999170i	$0.487033\pi$
$252$		0			0
$253$	−4.34707	−	1.16479i	−0.273298	−	0.0732299i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.89235			0.492311			0.246155	−	0.969230i	$-0.420833\pi$
$257$	7.89235			0.492311			0.246155	+	0.969230i	$0.420833\pi$
$258$		0			0
$259$	10.0934	+	5.82742i	0.627172	+	0.362098i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.14048	+	2.96786i	−0.316976	+	0.183006i	−0.650044	−	0.759897i	$-0.725249\pi$
$263$	−5.14048	+	2.96786i	−0.316976	+	0.183006i	0.333068	+	0.942903i	$0.391916\pi$
$264$		0			0
$265$	6.61574	+	1.77268i	0.406401	+	0.108895i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.40210	+	4.27360i	−0.451314	+	0.260566i	−0.708385	−	0.705826i	$-0.750576\pi$
$269$	−7.40210	+	4.27360i	−0.451314	+	0.260566i	0.257071	+	0.966392i	$0.417243\pi$
$270$		0			0
$271$	−5.18870	+	1.39031i	−0.315191	+	0.0844552i	−0.412946	−	0.910755i	$-0.635500\pi$
$271$	−5.18870	+	1.39031i	−0.315191	+	0.0844552i	0.0977555	+	0.995210i	$0.468834\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	33.5022	+	33.5022i	2.02026	+	2.02026i
$276$		0			0
$277$		−	23.1882i		−	1.39324i	−0.717439	−	0.696621i	$-0.754686\pi$
$277$		−	23.1882i		−	1.39324i	0.717439	−	0.696621i	$-0.245314\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.981285	+	3.66221i	0.0585386	+	0.218469i	0.988999	−	0.147924i	$-0.0472592\pi$
$281$	0.981285	+	3.66221i	0.0585386	+	0.218469i	−0.930460	+	0.366393i	$0.880593\pi$
$282$		0			0
$283$		−	28.0666i		−	1.66838i	−0.551474	−	0.834192i	$-0.685934\pi$
$283$		−	28.0666i		−	1.66838i	0.551474	−	0.834192i	$-0.314066\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			22.7679i			1.34395i
$288$		0			0
$289$	−2.26253	+	3.91882i	−0.133090	+	0.230519i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.45012	+	12.8760i	0.201558	+	0.752225i	0.990471	+	0.137720i	$0.0439775\pi$
$293$	3.45012	+	12.8760i	0.201558	+	0.752225i	−0.788913	+	0.614505i	$0.789356\pi$
$294$		0			0
$295$	34.3258			1.99852
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.41698	+	1.14194i	0.197609	+	0.0660401i
$300$		0			0
$301$	3.06648	−	3.06648i	0.176749	−	0.176749i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−5.32819	+	19.8851i	−0.305091	+	1.13862i
$306$		0			0
$307$	9.09884	+	9.09884i	0.519298	+	0.519298i	0.917359	−	0.398061i	$-0.130317\pi$
$307$	9.09884	+	9.09884i	0.519298	+	0.519298i	−0.398061	+	0.917359i	$0.630317\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.39052	−	2.40845i	−0.0788492	−	0.136571i	0.823904	−	0.566729i	$-0.191791\pi$
$311$	−1.39052	−	2.40845i	−0.0788492	−	0.136571i	−0.902754	+	0.430158i	$0.858458\pi$
$312$		0			0
$313$	−8.75421	+	15.1627i	−0.494817	+	0.857049i	−0.999982	−	0.00597416i	$-0.998098\pi$
$313$	−8.75421	+	15.1627i	−0.494817	+	0.857049i	0.505165	+	0.863023i	$0.331432\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−20.3076	+	5.44141i	−1.14059	+	0.305620i	−0.779188	−	0.626790i	$-0.784368\pi$
$317$	−20.3076	+	5.44141i	−1.14059	+	0.305620i	−0.361402	+	0.932410i	$0.617702\pi$
$318$		0			0
$319$	0.0727275	−	0.0194873i	0.00407196	−	0.00109108i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−9.16566	−	34.2067i	−0.509991	−	1.90331i
$324$		0			0
$325$	−25.1426	−	28.3980i	−1.39466	−	1.57524i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.0392101	−	0.0679138i	0.00216172	−	0.00374421i
$330$		0			0
$331$	0.792923	−	0.792923i	0.0435830	−	0.0435830i	−0.684979	−	0.728562i	$-0.740189\pi$
$331$	0.792923	−	0.792923i	0.0435830	−	0.0435830i	0.728562	+	0.684979i	$0.240189\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.146001	+	0.252882i	0.00797690	+	0.0138164i
$336$		0			0
$337$	−1.39429	+	0.804994i	−0.0759519	+	0.0438508i	−0.537495	−	0.843267i	$-0.680629\pi$
$337$	−1.39429	+	0.804994i	−0.0759519	+	0.0438508i	0.461543	+	0.887118i	$0.347296\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	12.2351	+	7.06395i	0.662569	+	0.382534i
$342$		0			0
$343$	−13.9202	+	13.9202i	−0.751620	+	0.751620i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.60090	+	1.50163i	0.139624	+	0.0806119i	0.568185	−	0.822901i	$-0.307646\pi$
$347$	2.60090	+	1.50163i	0.139624	+	0.0806119i	−0.428561	+	0.903513i	$0.640979\pi$
$348$		0			0
$349$	−6.17845	+	23.0583i	−0.330725	+	1.23428i	0.577706	+	0.816245i	$0.303948\pi$
$349$	−6.17845	+	23.0583i	−0.330725	+	1.23428i	−0.908430	+	0.418036i	$0.862718\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	4.88095	−	18.2159i	0.259787	−	0.969537i	−0.705578	−	0.708632i	$-0.749313\pi$
$353$	4.88095	−	18.2159i	0.259787	−	0.969537i	0.965365	−	0.260904i	$-0.0840208\pi$
$354$		0			0
$355$	16.8936	+	9.75355i	0.896621	+	0.517664i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.19442	−	1.19442i	0.0630389	−	0.0630389i	−0.674885	−	0.737923i	$-0.735807\pi$
$359$	1.19442	−	1.19442i	0.0630389	−	0.0630389i	0.737923	+	0.674885i	$0.235807\pi$
$360$		0			0
$361$	34.0025	+	19.6313i	1.78960	+	1.03323i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.141267	+	0.0815605i	−0.00739425	+	0.00426907i
$366$		0			0
$367$	−10.1517	−	17.5832i	−0.529913	−	0.917836i	−0.999391	−	0.0348923i	$-0.988891\pi$
$367$	−10.1517	−	17.5832i	−0.529913	−	0.917836i	0.469478	−	0.882944i	$-0.344442\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.31513	−	2.31513i	0.120196	−	0.120196i
$372$		0			0
$373$	−1.06229	+	1.83995i	−0.0550034	+	0.0952688i	−0.892216	−	0.451609i	$-0.850850\pi$
$373$	−1.06229	+	1.83995i	−0.0550034	+	0.0952688i	0.837213	+	0.546877i	$0.184184\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.0590605	+	0.0120381i	−0.00304177	+	0.000619993i
$378$		0			0
$379$	−4.82922	−	18.0229i	−0.248060	−	0.925774i	−0.971820	−	0.235722i	$-0.924254\pi$
$379$	−4.82922	−	18.0229i	−0.248060	−	0.925774i	0.723760	−	0.690052i	$-0.242412\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.642392	−	0.172129i	0.0328247	−	0.00879536i	−0.242369	−	0.970184i	$-0.577925\pi$
$383$	0.642392	−	0.172129i	0.0328247	−	0.00879536i	0.275194	+	0.961389i	$0.411258\pi$
$384$		0			0
$385$	32.2753	−	8.64813i	1.64490	−	0.440749i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	11.6152	−	20.1182i	0.588916	−	1.02003i	−0.405458	−	0.914113i	$-0.632888\pi$
$389$	11.6152	−	20.1182i	0.588916	−	1.02003i	0.994375	−	0.105919i	$-0.0337785\pi$
$390$		0			0
$391$	−2.31795	−	4.01481i	−0.117224	−	0.203038i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	6.56151	+	6.56151i	0.330145	+	0.330145i
$396$		0			0
$397$	4.19965	−	15.6733i	0.210774	−	0.786621i	−0.776837	−	0.629702i	$-0.783177\pi$
$397$	4.19965	−	15.6733i	0.210774	−	0.786621i	0.987611	−	0.156919i	$-0.0501562\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	20.0928	−	20.0928i	1.00339	−	1.00339i	0.00339153	−	0.999994i	$-0.498920\pi$
$401$	20.0928	−	20.0928i	1.00339	−	1.00339i	0.999994	−	0.00339153i	$-0.00107956\pi$
$402$		0			0
$403$	−9.43340	−	6.23896i	−0.469911	−	0.310785i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	27.8741			1.38167
$408$		0			0
$409$	−3.16669	−	11.8182i	−0.156583	−	0.584375i	−0.998965	−	0.0454938i	$-0.985514\pi$
$409$	−3.16669	−	11.8182i	−0.156583	−	0.584375i	0.842382	−	0.538881i	$-0.181153\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	8.20438	−	14.2104i	0.403711	−	0.699249i
$414$		0			0
$415$		−	18.6721i		−	0.916576i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	0.438006i		−	0.0213980i	−0.999943	−	0.0106990i	$-0.996594\pi$
$419$		−	0.438006i		−	0.0213980i	0.999943	−	0.0106990i	$-0.00340566\pi$
$420$		0			0
$421$	1.63663	+	6.10799i	0.0797645	+	0.297685i	0.994271	−	0.106885i	$-0.0340877\pi$
$421$	1.63663	+	6.10799i	0.0797645	+	0.297685i	−0.914507	+	0.404570i	$0.867421\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$			48.8056i			2.36742i
$426$		0			0
$427$	6.95864	+	6.95864i	0.336752	+	0.336752i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−22.5907	+	6.05315i	−1.08815	+	0.291570i	−0.757932	−	0.652333i	$-0.773790\pi$
$431$	−22.5907	+	6.05315i	−1.08815	+	0.291570i	−0.330222	+	0.943903i	$0.607124\pi$
$432$		0			0
$433$	−7.49672	+	4.32823i	−0.360269	+	0.208002i	−0.669199	−	0.743083i	$-0.733363\pi$
$433$	−7.49672	+	4.32823i	−0.360269	+	0.208002i	0.308930	+	0.951085i	$0.400029\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	7.36717	+	1.97403i	0.352420	+	0.0944306i
$438$		0			0
$439$	−1.49405	+	0.862589i	−0.0713070	+	0.0411691i	−0.535230	−	0.844707i	$-0.679775\pi$
$439$	−1.49405	+	0.862589i	−0.0713070	+	0.0411691i	0.463923	+	0.885876i	$0.346442\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.81328	−	1.62425i	−0.133663	−	0.0771704i	0.431677	−	0.902028i	$-0.357922\pi$
$443$	−2.81328	−	1.62425i	−0.133663	−	0.0771704i	−0.565340	+	0.824858i	$0.691255\pi$
$444$		0			0
$445$	48.7673			2.31179
$446$		0			0
$447$		0			0
$448$		0			0
$449$	4.05170	+	1.08565i	0.191212	+	0.0512350i	0.353154	−	0.935565i	$-0.385109\pi$
$449$	4.05170	+	1.08565i	0.191212	+	0.0512350i	−0.161942	+	0.986800i	$0.551776\pi$
$450$		0			0
$451$	27.2263	+	47.1573i	1.28204	+	2.22055i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−26.2101	+	5.34230i	−1.22875	+	0.250451i
$456$		0			0
$457$	1.25001	+	0.334939i	0.0584730	+	0.0156678i	0.287937	−	0.957649i	$-0.407031\pi$
$457$	1.25001	+	0.334939i	0.0584730	+	0.0156678i	−0.229464	+	0.973317i	$0.573697\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−9.85374	−	9.85374i	−0.458934	−	0.458934i	0.439371	−	0.898306i	$-0.355201\pi$
$461$	−9.85374	−	9.85374i	−0.458934	−	0.458934i	−0.898306	+	0.439371i	$0.855201\pi$
$462$		0			0
$463$	9.59936	−	35.8253i	0.446120	−	1.66494i	−0.266842	−	0.963740i	$-0.585980\pi$
$463$	9.59936	−	35.8253i	0.446120	−	1.66494i	0.712962	−	0.701203i	$-0.247353\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	20.2780			0.938353			0.469176	−	0.883104i	$-0.344551\pi$
$467$	20.2780			0.938353			0.469176	+	0.883104i	$0.344551\pi$
$468$		0			0
$469$	0.139586			0.00644549
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.68440	−	10.0183i	0.123429	−	0.460642i
$474$		0			0
$475$	−56.7777	−	56.7777i	−2.60514	−	2.60514i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−19.6844	−	5.27443i	−0.899405	−	0.240995i	−0.220644	−	0.975354i	$-0.570816\pi$
$479$	−19.6844	−	5.27443i	−0.899405	−	0.240995i	−0.678761	+	0.734360i	$0.737483\pi$
$480$		0			0
$481$	−22.2731	−	1.35425i	−1.01557	−	0.0617485i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−16.7683	−	29.0436i	−0.761411	−	1.31880i
$486$		0			0
$487$	−5.24083	−	1.40428i	−0.237485	−	0.0636338i	0.138114	−	0.990416i	$-0.455896\pi$
$487$	−5.24083	−	1.40428i	−0.237485	−	0.0636338i	−0.375598	+	0.926783i	$0.622563\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−23.2041			−1.04719			−0.523594	−	0.851968i	$-0.675409\pi$
$491$	−23.2041			−1.04719			−0.523594	+	0.851968i	$0.675409\pi$
$492$		0			0
$493$	0.0671688	+	0.0387799i	0.00302513	+	0.00174656i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	8.07568	−	4.66250i	0.362244	−	0.209142i
$498$		0			0
$499$	−30.6811	−	8.22097i	−1.37347	−	0.368021i	−0.504728	−	0.863279i	$-0.668407\pi$
$499$	−30.6811	−	8.22097i	−1.37347	−	0.368021i	−0.868746	+	0.495257i	$0.835074\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	23.3710	−	13.4932i	1.04206	−	0.601634i	0.121644	−	0.992574i	$-0.461183\pi$
$503$	23.3710	−	13.4932i	1.04206	−	0.601634i	0.920416	+	0.390940i	$0.127850\pi$
$504$		0			0
$505$	−52.4603	+	14.0567i	−2.33445	+	0.625515i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7.32135	+	7.32135i	0.324513	+	0.324513i	0.850495	−	0.525982i	$-0.176302\pi$
$509$	7.32135	+	7.32135i	0.324513	+	0.324513i	−0.525982	+	0.850495i	$0.676302\pi$
$510$		0			0
$511$			0.0779769i			0.00344949i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	16.8360	+	62.8327i	0.741882	+	2.76874i
$516$		0			0
$517$		−	0.187552i		−	0.00824855i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			13.8080i			0.604939i	0.953159	+	0.302469i	$0.0978110\pi$
$521$			13.8080i			0.604939i	−0.953159	+	0.302469i	$0.902189\pi$
$522$		0			0
$523$	−4.75258	+	8.23170i	−0.207816	+	0.359947i	−0.951026	−	0.309110i	$-0.899969\pi$
$523$	−4.75258	+	8.23170i	−0.207816	+	0.359947i	0.743211	+	0.669058i	$0.233302\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.76665	+	14.0573i	0.164078	+	0.612347i
$528$		0			0
$529$	−22.0016			−0.956589
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−19.4643	−	39.0043i	−0.843094	−	1.68946i
$534$		0			0
$535$	−28.2902	+	28.2902i	−1.22309	+	1.22309i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−4.02583	+	15.0246i	−0.173405	+	0.647155i
$540$		0			0
$541$	19.2507	+	19.2507i	0.827651	+	0.827651i	0.987191	−	0.159540i	$-0.0510012\pi$
$541$	19.2507	+	19.2507i	0.827651	+	0.827651i	−0.159540	+	0.987191i	$0.551001\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−31.4051	−	54.3952i	−1.34525	−	2.33004i
$546$		0			0
$547$	−20.0559	+	34.7379i	−0.857530	+	1.48529i	0.0167471	+	0.999860i	$0.494669\pi$
$547$	−20.0559	+	34.7379i	−0.857530	+	1.48529i	−0.874277	+	0.485426i	$0.838664\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.123255	+	0.0330260i	−0.00525083	+	0.00140695i
$552$		0			0
$553$	4.28468	−	1.14808i	0.182203	−	0.0488212i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.96905	−	7.34860i	−0.0834313	−	0.311370i	0.911581	−	0.411120i	$-0.134862\pi$
$557$	−1.96905	−	7.34860i	−0.0834313	−	0.311370i	−0.995013	+	0.0997501i	$0.968196\pi$
$558$		0			0
$559$	−2.63173	+	7.87481i	−0.111310	+	0.333069i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.29228	+	7.43445i	−0.180898	+	0.313325i	−0.942187	−	0.335089i	$-0.891234\pi$
$563$	−4.29228	+	7.43445i	−0.180898	+	0.313325i	0.761289	+	0.648413i	$0.224567\pi$
$564$		0			0
$565$	9.88390	−	9.88390i	0.415819	−	0.415819i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	17.9702	+	31.1253i	0.753351	+	1.30484i	0.946190	+	0.323611i	$0.104897\pi$
$569$	17.9702	+	31.1253i	0.753351	+	1.30484i	−0.192839	+	0.981230i	$0.561770\pi$
$570$		0			0
$571$	9.68042	−	5.58899i	0.405113	−	0.233892i	−0.283575	−	0.958950i	$-0.591520\pi$
$571$	9.68042	−	5.58899i	0.405113	−	0.233892i	0.688688	+	0.725058i	$0.258187\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−9.10312	−	5.25569i	−0.379626	−	0.219177i
$576$		0			0
$577$	12.4732	−	12.4732i	0.519266	−	0.519266i	−0.398083	−	0.917349i	$-0.630325\pi$
$577$	12.4732	−	12.4732i	0.519266	−	0.519266i	0.917349	+	0.398083i	$0.130325\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−7.72999	−	4.46291i	−0.320694	−	0.185153i
$582$		0			0
$583$	2.02666	−	7.56361i	0.0839358	−	0.313253i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−3.48074	+	12.9903i	−0.143666	+	0.536167i	0.856146	+	0.516735i	$0.172853\pi$
$587$	−3.48074	+	12.9903i	−0.143666	+	0.536167i	−0.999811	+	0.0194325i	$0.993814\pi$
$588$		0			0
$589$	−20.7354	−	11.9716i	−0.854388	−	0.493281i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	4.12229	−	4.12229i	0.169282	−	0.169282i	−0.617382	−	0.786664i	$-0.711807\pi$
$593$	4.12229	−	4.12229i	0.169282	−	0.169282i	0.786664	+	0.617382i	$0.211807\pi$
$594$		0			0
$595$	29.8084	+	17.2099i	1.22202	+	0.705536i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	26.3160	−	15.1935i	1.07524	−	0.620791i	0.145633	−	0.989339i	$-0.453478\pi$
$599$	26.3160	−	15.1935i	1.07524	−	0.620791i	0.929609	+	0.368547i	$0.120145\pi$
$600$		0			0
$601$	8.54362	+	14.7980i	0.348502	+	0.603622i	0.985983	−	0.166843i	$-0.0533573\pi$
$601$	8.54362	+	14.7980i	0.348502	+	0.603622i	−0.637482	+	0.770465i	$0.720024\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	25.8655	−	25.8655i	1.05158	−	1.05158i
$606$		0			0
$607$	14.2310	−	24.6488i	0.577619	−	1.00047i	−0.418133	−	0.908386i	$-0.637315\pi$
$607$	14.2310	−	24.6488i	0.577619	−	1.00047i	0.995752	−	0.0920795i	$-0.0293514\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.00911214	+	0.149866i	−0.000368638	+	0.00606292i
$612$		0			0
$613$	8.00452	+	29.8733i	0.323299	+	1.20657i	0.916010	+	0.401155i	$0.131391\pi$
$613$	8.00452	+	29.8733i	0.323299	+	1.20657i	−0.592711	+	0.805415i	$0.701942\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−26.9588	+	7.22358i	−1.08532	+	0.290810i	−0.756773	−	0.653677i	$-0.773225\pi$
$617$	−26.9588	+	7.22358i	−1.08532	+	0.290810i	−0.328546	+	0.944488i	$0.606559\pi$
$618$		0			0
$619$	−13.2777	+	3.55774i	−0.533674	+	0.142998i	−0.515584	−	0.856839i	$-0.672425\pi$
$619$	−13.2777	+	3.55774i	−0.533674	+	0.142998i	−0.0180898	+	0.999836i	$0.505758\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	11.6561	−	20.1890i	0.466993	−	0.808856i
$624$		0			0
$625$	16.5317	+	28.6337i	0.661266	+	1.14535i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	20.3034	+	20.3034i	0.809548	+	0.809548i
$630$		0			0
$631$	−2.32391	+	8.67295i	−0.0925133	+	0.345265i	−0.996631	−	0.0820197i	$-0.973863\pi$
$631$	−2.32391	+	8.67295i	−0.0925133	+	0.345265i	0.904117	+	0.427284i	$0.140530\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−25.0539	+	25.0539i	−0.994232	+	0.994232i
$636$		0			0
$637$	3.94684	−	11.8100i	0.156380	−	0.467928i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	41.4190			1.63595			0.817976	−	0.575253i	$-0.195096\pi$
$641$	41.4190			1.63595			0.817976	+	0.575253i	$0.195096\pi$
$642$		0			0
$643$	−12.7764	−	47.6823i	−0.503854	−	1.88041i	−0.473352	−	0.880874i	$-0.656956\pi$
$643$	−12.7764	−	47.6823i	−0.503854	−	1.88041i	−0.0305022	−	0.999535i	$-0.509711\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.03827	−	1.79833i	0.0408184	−	0.0706996i	−0.844894	−	0.534933i	$-0.820337\pi$
$647$	1.03827	−	1.79833i	0.0408184	−	0.0706996i	0.885713	+	0.464233i	$0.153670\pi$
$648$		0			0
$649$		−	39.2438i		−	1.54045i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			5.31179i			0.207867i	0.994584	+	0.103933i	$0.0331428\pi$
$653$			5.31179i			0.207867i	−0.994584	+	0.103933i	$0.966857\pi$
$654$		0			0
$655$	10.4265	+	38.9121i	0.407396	+	1.52042i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		−	7.00574i		−	0.272905i	−0.990647	−	0.136452i	$-0.956430\pi$
$659$		−	7.00574i		−	0.272905i	0.990647	−	0.136452i	$-0.0435701\pi$
$660$		0			0
$661$	23.2482	+	23.2482i	0.904249	+	0.904249i	0.995800	−	0.0915510i	$-0.0291824\pi$
$661$	23.2482	+	23.2482i	0.904249	+	0.904249i	−0.0915510	+	0.995800i	$0.529182\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−54.6983	+	14.6564i	−2.12111	+	0.568350i
$666$		0			0
$667$	−0.0144663	+	0.00835212i	−0.000560137	+	0.000323395i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	22.7341	+	6.09159i	0.877641	+	0.235163i
$672$		0			0
$673$	−1.68972	+	0.975559i	−0.0651338	+	0.0376050i	−0.532213	−	0.846610i	$-0.678640\pi$
$673$	−1.68972	+	0.975559i	−0.0651338	+	0.0376050i	0.467079	+	0.884215i	$0.345306\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−13.1079	−	7.56783i	−0.503776	−	0.290855i	0.226495	−	0.974012i	$-0.427273\pi$
$677$	−13.1079	−	7.56783i	−0.503776	−	0.290855i	−0.730272	+	0.683157i	$0.760607\pi$
$678$		0			0
$679$	−16.0316			−0.615235
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−26.1296	−	7.00141i	−0.999822	−	0.267901i	−0.278451	−	0.960450i	$-0.589821\pi$
$683$	−26.1296	−	7.00141i	−0.999822	−	0.267901i	−0.721371	+	0.692549i	$0.756488\pi$
$684$		0			0
$685$	−35.0214	−	60.6588i	−1.33810	−	2.31765i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.98690	+	5.94532i	−0.0756949	+	0.226499i
$690$		0			0
$691$	35.8188	+	9.59761i	1.36261	+	0.365110i	0.864774	−	0.502161i	$-0.167462\pi$
$691$	35.8188	+	9.59761i	1.36261	+	0.365110i	0.497836	+	0.867271i	$0.334128\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−30.6324	−	30.6324i	−1.16195	−	1.16195i
$696$		0			0
$697$	−14.5176	+	54.1806i	−0.549895	+	2.05224i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−7.64065			−0.288583			−0.144292	−	0.989535i	$-0.546090\pi$
$701$	−7.64065			−0.288583			−0.144292	+	0.989535i	$0.546090\pi$
$702$		0			0
$703$	−47.2395			−1.78167
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−6.71954	+	25.0777i	−0.252714	+	0.943142i
$708$		0			0
$709$	24.1779	+	24.1779i	0.908021	+	0.908021i	0.996112	−	0.0880916i	$-0.0280768\pi$
$709$	24.1779	+	24.1779i	0.908021	+	0.908021i	−0.0880916	+	0.996112i	$0.528077\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.02756	−	0.811232i	−0.113383	−	0.0303809i
$714$		0			0
$715$	−47.8983	+	42.4075i	−1.79129	+	1.58595i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−2.01084	−	3.48288i	−0.0749917	−	0.129889i	0.826091	−	0.563537i	$-0.190560\pi$
$719$	−2.01084	−	3.48288i	−0.0749917	−	0.129889i	−0.901083	+	0.433647i	$0.857226\pi$
$720$		0			0
$721$	30.0360	+	8.04811i	1.11860	+	0.299727i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.175858			0.00653120
$726$		0			0
$727$	−31.9389	−	18.4399i	−1.18455	−	0.683900i	−0.227486	−	0.973781i	$-0.573051\pi$
$727$	−31.9389	−	18.4399i	−1.18455	−	0.683900i	−0.957062	+	0.289882i	$0.906384\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	9.25258	−	5.34198i	0.342219	−	0.197580i
$732$		0			0
$733$	−38.9036	−	10.4242i	−1.43694	−	0.385026i	−0.545478	−	0.838125i	$-0.683652\pi$
$733$	−38.9036	−	10.4242i	−1.43694	−	0.385026i	−0.891460	+	0.453099i	$0.850318\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.289113	−	0.166920i	0.0106496	−	0.00614857i
$738$		0			0
$739$	10.9711	−	2.93969i	0.403578	−	0.108138i	−0.0513194	−	0.998682i	$-0.516343\pi$
$739$	10.9711	−	2.93969i	0.403578	−	0.108138i	0.454897	+	0.890544i	$0.349676\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−4.17617	−	4.17617i	−0.153209	−	0.153209i	0.626341	−	0.779549i	$-0.284552\pi$
$743$	−4.17617	−	4.17617i	−0.153209	−	0.153209i	−0.779549	+	0.626341i	$0.784552\pi$
$744$		0			0
$745$		−	87.2117i		−	3.19519i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	4.94997	+	18.4736i	0.180868	+	0.675009i
$750$		0			0
$751$			44.7900i			1.63441i	0.576348	+	0.817205i	$0.304477\pi$
$751$			44.7900i			1.63441i	−0.576348	+	0.817205i	$0.695523\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	93.4550i		−	3.40117i
$756$		0			0
$757$	13.4400	−	23.2787i	0.488484	−	0.846079i	−0.511428	−	0.859326i	$-0.670883\pi$
$757$	13.4400	−	23.2787i	0.488484	−	0.846079i	0.999912	+	0.0132468i	$0.00421670\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−9.52394	−	35.5438i	−0.345242	−	1.28846i	−0.892329	−	0.451386i	$-0.850930\pi$
$761$	−9.52394	−	35.5438i	−0.345242	−	1.28846i	0.547086	−	0.837076i	$-0.315737\pi$
$762$		0			0
$763$	−30.0252			−1.08699
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.90664	+	31.3582i	−0.0688448	+	1.13228i
$768$		0			0
$769$	−20.8065	+	20.8065i	−0.750300	+	0.750300i	−0.974535	−	0.224235i	$-0.928012\pi$
$769$	−20.8065	+	20.8065i	−0.750300	+	0.750300i	0.224235	+	0.974535i	$0.428012\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.62390	−	13.5246i	0.130343	−	0.486445i	−0.869631	−	0.493702i	$-0.835643\pi$
$773$	3.62390	−	13.5246i	0.130343	−	0.486445i	0.999974	+	0.00725702i	$0.00231000\pi$
$774$		0			0
$775$	23.3329	+	23.3329i	0.838144	+	0.838144i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−46.1416	−	79.9196i	−1.65319	−	2.86342i
$780$		0			0
$781$	11.1510	−	19.3141i	0.399014	−	0.691112i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−86.6460	+	23.2167i	−3.09253	+	0.828640i
$786$		0			0
$787$	9.08397	−	2.43404i	0.323809	−	0.0867643i	−0.0932530	−	0.995642i	$-0.529727\pi$
$787$	9.08397	−	2.43404i	0.323809	−	0.0867643i	0.417062	+	0.908878i	$0.363060\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.72940	−	6.45421i	−0.0614904	−	0.229485i
$792$		0			0
$793$	−17.8700	−	5.97208i	−0.634582	−	0.212075i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	19.9237	−	34.5089i	0.705735	−	1.22237i	−0.260690	−	0.965423i	$-0.583950\pi$
$797$	19.9237	−	34.5089i	0.705735	−	1.22237i	0.966426	−	0.256947i	$-0.0827166\pi$
$798$		0			0
$799$	0.136612	−	0.136612i	0.00483299	−	0.00483299i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.0932461	+	0.161507i	0.00329058	+	0.00569946i
$804$		0			0
$805$	−6.41989	+	3.70653i	−0.226272	+	0.130638i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−3.19032	−	1.84193i	−0.112166	−	0.0647588i	0.442868	−	0.896587i	$-0.353961\pi$
$809$	−3.19032	−	1.84193i	−0.112166	−	0.0647588i	−0.555033	+	0.831828i	$0.687294\pi$
$810$		0			0
$811$	23.1531	−	23.1531i	0.813016	−	0.813016i	−0.172069	−	0.985085i	$-0.555045\pi$
$811$	23.1531	−	23.1531i	0.813016	−	0.813016i	0.985085	+	0.172069i	$0.0550453\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−44.2195	−	25.5301i	−1.54894	−	0.894282i
$816$		0			0
$817$	−4.54937	+	16.9785i	−0.159162	+	0.594002i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3.35025	+	12.5033i	−0.116924	+	0.436368i	−0.999424	−	0.0339458i	$-0.989193\pi$
$821$	−3.35025	+	12.5033i	−0.116924	+	0.436368i	0.882499	+	0.470314i	$0.155859\pi$
$822$		0			0
$823$	18.9105	+	10.9180i	0.659178	+	0.380577i	0.791964	−	0.610568i	$-0.209059\pi$
$823$	18.9105	+	10.9180i	0.659178	+	0.380577i	−0.132785	+	0.991145i	$0.542392\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	16.4531	−	16.4531i	0.572131	−	0.572131i	−0.360592	−	0.932724i	$-0.617425\pi$
$827$	16.4531	−	16.4531i	0.572131	−	0.572131i	0.932724	+	0.360592i	$0.117425\pi$
$828$		0			0
$829$	−21.9234	−	12.6575i	−0.761432	−	0.439613i	0.0683775	−	0.997660i	$-0.478218\pi$
$829$	−21.9234	−	12.6575i	−0.761432	−	0.439613i	−0.829810	+	0.558046i	$0.811551\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−13.8762	+	8.01144i	−0.480783	+	0.277580i
$834$		0			0
$835$	11.9260	+	20.6564i	0.412715	+	0.714843i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	15.3174	−	15.3174i	0.528814	−	0.528814i	−0.391404	−	0.920219i	$-0.628011\pi$
$839$	15.3174	−	15.3174i	0.528814	−	0.528814i	0.920219	+	0.391404i	$0.128011\pi$
$840$		0			0
$841$	−14.4999	+	25.1145i	−0.499995	+	0.866017i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	40.3340	−	31.5591i	1.38753	−	1.08566i
$846$		0			0
$847$	−4.52572	−	16.8902i	−0.155505	−	0.580354i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−5.97333	+	1.60055i	−0.204763	+	0.0548661i
$852$		0			0
$853$	12.3890	−	3.31961i	0.424190	−	0.113661i	−0.0404076	−	0.999183i	$-0.512866\pi$
$853$	12.3890	−	3.31961i	0.424190	−	0.113661i	0.464598	+	0.885522i	$0.346199\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−24.4649	+	42.3745i	−0.835705	+	1.44748i	0.0577497	+	0.998331i	$0.481607\pi$
$857$	−24.4649	+	42.3745i	−0.835705	+	1.44748i	−0.893455	+	0.449153i	$0.851726\pi$
$858$		0			0
$859$	18.1131	+	31.3727i	0.618010	+	1.07042i	0.989848	+	0.142127i	$0.0453941\pi$
$859$	18.1131	+	31.3727i	0.618010	+	1.07042i	−0.371839	+	0.928297i	$0.621273\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−25.6667	−	25.6667i	−0.873704	−	0.873704i	0.119170	−	0.992874i	$-0.461977\pi$
$863$	−25.6667	−	25.6667i	−0.873704	−	0.873704i	−0.992874	+	0.119170i	$0.961977\pi$
$864$		0			0
$865$	−0.122008	+	0.455341i	−0.00414840	+	0.0154820i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	7.50162	−	7.50162i	0.254475	−	0.254475i
$870$		0			0
$871$	−0.239129	+	0.119333i	−0.00810257	+	0.00404343i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	40.9486			1.38432
$876$		0			0
$877$	−7.39964	−	27.6158i	−0.249868	−	0.932521i	−0.970874	−	0.239592i	$-0.922986\pi$
$877$	−7.39964	−	27.6158i	−0.249868	−	0.932521i	0.721006	−	0.692929i	$-0.243680\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−10.2203	+	17.7021i	−0.344331	+	0.596399i	−0.985232	−	0.171225i	$-0.945228\pi$
$881$	−10.2203	+	17.7021i	−0.344331	+	0.596399i	0.640901	+	0.767624i	$0.278561\pi$
$882$		0			0
$883$		−	59.1925i		−	1.99199i	−0.0894367	−	0.995993i	$-0.528507\pi$
$883$		−	59.1925i		−	1.99199i	0.0894367	−	0.995993i	$-0.471493\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		−	44.9612i		−	1.50965i	−0.655927	−	0.754825i	$-0.727722\pi$
$887$		−	44.9612i		−	1.50965i	0.655927	−	0.754825i	$-0.272278\pi$
$888$		0			0
$889$	4.38371	+	16.3602i	0.147025	+	0.548705i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			0.317854i			0.0106366i
$894$		0			0
$895$	−39.2593	−	39.2593i	−1.31229	−	1.31229i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.0506518	−	0.0135721i	0.00168933	−	0.000452655i
$900$		0			0
$901$	6.98550	−	4.03308i	0.232721	−	0.134361i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	20.4721	+	5.48550i	0.680517	+	0.182344i
$906$		0			0
$907$	−16.8952	+	9.75445i	−0.560996	+	0.323891i	−0.753545	−	0.657396i	$-0.771658\pi$
$907$	−16.8952	+	9.75445i	−0.560996	+	0.323891i	0.192549	+	0.981287i	$0.438325\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	51.3564	+	29.6506i	1.70151	+	0.982370i	0.944231	+	0.329283i	$0.106807\pi$
$911$	51.3564	+	29.6506i	1.70151	+	0.982370i	0.757283	+	0.653087i	$0.226526\pi$
$912$		0			0
$913$	−21.3473			−0.706494
$914$		0			0
$915$		0			0
$916$		0			0
$917$	18.6012	+	4.98417i	0.614265	+	0.164592i
$918$		0			0
$919$	21.8304	+	37.8114i	0.720119	+	1.24728i	0.960952	+	0.276716i	$0.0892463\pi$
$919$	21.8304	+	37.8114i	0.720119	+	1.24728i	−0.240832	+	0.970567i	$0.577420\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−9.84868	+	14.8914i	−0.324173	+	0.490155i
$924$		0			0
$925$	62.8857	+	16.8502i	2.06767	+	0.554030i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	12.0748	+	12.0748i	0.396160	+	0.396160i	0.876876	−	0.480716i	$-0.159623\pi$
$929$	12.0748	+	12.0748i	0.396160	+	0.396160i	−0.480716	+	0.876876i	$0.659623\pi$
$930$		0			0
$931$	6.82276	−	25.4629i	0.223607	−	0.834512i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	82.3195			2.69213
$936$		0			0
$937$	41.1938			1.34574			0.672871	−	0.739759i	$-0.265061\pi$
$937$	41.1938			1.34574			0.672871	+	0.739759i	$0.265061\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−10.3736	+	38.7147i	−0.338169	+	1.26206i	0.562224	+	0.826985i	$0.309946\pi$
$941$	−10.3736	+	38.7147i	−0.338169	+	1.26206i	−0.900393	+	0.435078i	$0.856721\pi$
$942$		0			0
$943$	−8.54230	−	8.54230i	−0.278175	−	0.278175i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−24.5842	−	6.58731i	−0.798879	−	0.214059i	−0.163787	−	0.986496i	$-0.552371\pi$
$947$	−24.5842	−	6.58731i	−0.798879	−	0.214059i	−0.635092	+	0.772437i	$0.719038\pi$
$948$		0			0
$949$	−0.0666626	−	0.133584i	−0.00216396	−	0.00433633i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	11.7501	+	20.3518i	0.380624	+	0.659260i	0.991152	−	0.132735i	$-0.0423758\pi$
$953$	11.7501	+	20.3518i	0.380624	+	0.659260i	−0.610527	+	0.791995i	$0.709043\pi$
$954$		0			0
$955$	−39.3524	−	10.5444i	−1.27341	−	0.341210i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−33.4826			−1.08121
$960$		0			0
$961$	−18.3255	−	10.5802i	−0.591146	−	0.341298i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	54.3580	−	31.3836i	1.74984	−	1.01027i
$966$		0			0
$967$	−0.799247	−	0.214158i	−0.0257021	−	0.00688685i	0.245945	−	0.969284i	$-0.420902\pi$
$967$	−0.799247	−	0.214158i	−0.0257021	−	0.00688685i	−0.271647	+	0.962397i	$0.587568\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−41.6673	+	24.0566i	−1.33717	+	0.772013i	−0.986386	−	0.164444i	$-0.947417\pi$
$971$	−41.6673	+	24.0566i	−1.33717	+	0.772013i	−0.350780	+	0.936458i	$0.614084\pi$
$972$		0			0
$973$	−20.0030	+	5.35980i	−0.641268	+	0.171827i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.77017	+	8.77017i	0.280583	+	0.280583i	0.833341	−	0.552759i	$-0.186425\pi$
$977$	8.77017	+	8.77017i	0.280583	+	0.280583i	−0.552759	+	0.833341i	$0.686425\pi$
$978$		0			0
$979$		−	55.7545i		−	1.78192i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	11.2667	+	42.0477i	0.359350	+	1.34111i	0.874920	+	0.484267i	$0.160914\pi$
$983$	11.2667	+	42.0477i	0.359350	+	1.34111i	−0.515570	+	0.856847i	$0.672420\pi$
$984$		0			0
$985$		−	34.2709i		−	1.09196i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			2.30103i			0.0731684i
$990$		0			0
$991$	2.07400	−	3.59227i	0.0658826	−	0.114112i	−0.831203	−	0.555970i	$-0.812347\pi$
$991$	2.07400	−	3.59227i	0.0658826	−	0.114112i	0.897085	+	0.441858i	$0.145680\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−14.3439	−	53.5322i	−0.454732	−	1.69708i
$996$		0			0
$997$	25.4139			0.804868			0.402434	−	0.915449i	$-0.368164\pi$
$997$	25.4139			0.804868			0.402434	+	0.915449i	$0.368164\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1404.2.cc.a.305.14		56
3.2	odd	2		468.2.bz.a.461.7	yes	56
9.4	even	3		468.2.bw.a.149.12	✓	56
9.5	odd	6		1404.2.bz.a.773.14		56
13.11	odd	12		1404.2.bz.a.89.14		56
39.11	even	12		468.2.bw.a.245.12	yes	56
117.50	even	12	inner	1404.2.cc.a.557.14		56
117.76	odd	12		468.2.bz.a.401.7	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.bw.a.149.12	✓	56	9.4	even	3
468.2.bw.a.245.12	yes	56	39.11	even	12
468.2.bz.a.401.7	yes	56	117.76	odd	12
468.2.bz.a.461.7	yes	56	3.2	odd	2
1404.2.bz.a.89.14		56	13.11	odd	12
1404.2.bz.a.773.14		56	9.5	odd	6
1404.2.cc.a.305.14		56	1.1	even	1	trivial
1404.2.cc.a.557.14		56	117.50	even	12	inner

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:	\( N \)	\(=\)	\( 1404 = 2^{2} \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1404.cc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.01961 - 3.80525i) q^{5} +(-1.33162 - 1.33162i) q^{7} +(-4.35045 - 1.16570i) q^{11} +(3.41964 + 1.14283i) q^{13} +(-2.31976 - 4.01793i) q^{17} +(7.37291 + 1.97557i) q^{19} +0.999222 q^{23} +(-9.11020 - 5.25978i) q^{25} +(-0.0144776 + 0.00835862i) q^{29} +(-3.02992 - 0.811864i) q^{31} +(-6.42489 + 3.70941i) q^{35} +(-5.97798 + 1.60179i) q^{37} +(-8.54895 - 8.54895i) q^{41} +2.30282i q^{43} +(0.0107778 + 0.0402231i) q^{47} -3.45357i q^{49} +1.73858i q^{53} +(-8.87157 + 15.3660i) q^{55} +(2.25516 + 8.41636i) q^{59} -5.22569 q^{61} +(7.83547 - 11.8473i) q^{65} +(-0.0524121 + 0.0524121i) q^{67} +(-1.28159 + 4.78296i) q^{71} +(-0.0292789 - 0.0292789i) q^{73} +(4.24088 + 7.34542i) q^{77} +(-1.17774 + 2.03990i) q^{79} +(4.57822 - 1.22673i) q^{83} +(-17.6545 + 4.73051i) q^{85} +(3.20395 + 11.9573i) q^{89} +(-3.03185 - 6.07548i) q^{91} +(15.0350 - 26.0415i) q^{95} +(6.01956 - 6.01956i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} - 12 q^{11} + 4 q^{19} - 4 q^{31} - 66 q^{35} + 2 q^{37} - 24 q^{41} + 36 q^{47} + 36 q^{65} - 14 q^{67} + 24 q^{71} - 14 q^{73} - 24 q^{77} + 12 q^{79} + 42 q^{83} - 36 q^{85} + 4 q^{91}+ \cdots - 46 q^{97}+O(q^{100}) \) 56 * q + 4 * q^7 - 12 * q^11 + 4 * q^19 - 4 * q^31 - 66 * q^35 + 2 * q^37 - 24 * q^41 + 36 * q^47 + 36 * q^65 - 14 * q^67 + 24 * q^71 - 14 * q^73 - 24 * q^77 + 12 * q^79 + 42 * q^83 - 36 * q^85 + 4 * q^91 - 46 * q^97

Introduction

L-functions

Modular forms

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Database

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