LMFDB - Embedded newform 1260.2.ej.a.737.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(53,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 9, 8]))

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

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

chi := DirichletCharacter("1260.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.ej (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			737.10
Character	$\chi$	$=$	1260.737
Dual form			1260.2.ej.a.53.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.832439 - 2.07534i) q^{5} +(-0.0650831 - 2.64495i) q^{7} +(1.79266 - 1.03499i) q^{11} +(-0.920307 + 0.920307i) q^{13} +(1.55253 + 0.416000i) q^{17} +(1.78623 + 1.03128i) q^{19} +(4.89140 - 1.31065i) q^{23} +(-3.61409 - 3.45519i) q^{25} -1.58666 q^{29} +(-4.97330 - 8.61402i) q^{31} +(-5.54336 - 2.06669i) q^{35} +(-4.52881 + 1.21349i) q^{37} -11.8345i q^{41} +(-6.62285 + 6.62285i) q^{43} +(2.65657 + 9.91444i) q^{47} +(-6.99153 + 0.344283i) q^{49} +(1.55788 - 5.81410i) q^{53} +(-0.655686 - 4.58196i) q^{55} +(4.46092 + 7.72654i) q^{59} +(4.41894 - 7.65383i) q^{61} +(1.14385 + 2.67605i) q^{65} +(1.99667 - 7.45169i) q^{67} -1.25658i q^{71} +(-8.38264 - 2.24612i) q^{73} +(-2.85418 - 4.67414i) q^{77} +(2.95983 + 1.70886i) q^{79} +(0.626045 + 0.626045i) q^{83} +(2.15573 - 2.87575i) q^{85} +(2.79258 - 4.83689i) q^{89} +(2.49406 + 2.37427i) q^{91} +(3.62718 - 2.84855i) q^{95} +(-8.71944 - 8.71944i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7} + 16 q^{25} + 32 q^{31} + 16 q^{37} - 16 q^{43} + 32 q^{55} + 48 q^{61} + 32 q^{67} + 40 q^{73} + 80 q^{85} + 96 q^{91} + 80 q^{97}+O(q^{100}) $ 64 * q - 8 * q^7 + 16 * q^25 + 32 * q^31 + 16 * q^37 - 16 * q^43 + 32 * q^55 + 48 * q^61 + 32 * q^67 + 40 * q^73 + 80 * q^85 + 96 * q^91 + 80 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$

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
$5$	0.832439	−	2.07534i	0.372278	−	0.928121i
$5$	0.832439	−	2.07534i	0.372278	−	0.928121i
$6$		0			0
$7$	−0.0650831	−	2.64495i	−0.0245991	−	0.999697i
$7$	−0.0650831	−	2.64495i	−0.0245991	−	0.999697i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.79266	−	1.03499i	0.540508	−	0.312062i	−0.204777	−	0.978809i	$-0.565647\pi$
$11$	1.79266	−	1.03499i	0.540508	−	0.312062i	0.745285	+	0.666746i	$0.232314\pi$
$12$		0			0
$13$	−0.920307	+	0.920307i	−0.255247	+	0.255247i	−0.823118	−	0.567871i	$-0.807767\pi$
$13$	−0.920307	+	0.920307i	−0.255247	+	0.255247i	0.567871	+	0.823118i	$0.307767\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.55253	+	0.416000i	0.376545	+	0.100895i	0.442127	−	0.896952i	$-0.354224\pi$
$17$	1.55253	+	0.416000i	0.376545	+	0.100895i	−0.0655826	+	0.997847i	$0.520891\pi$
$18$		0			0
$19$	1.78623	+	1.03128i	0.409788	+	0.236591i	0.690699	−	0.723143i	$-0.257303\pi$
$19$	1.78623	+	1.03128i	0.409788	+	0.236591i	−0.280910	+	0.959734i	$0.590636\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.89140	−	1.31065i	1.01993	−	0.273289i	0.290156	−	0.956979i	$-0.406293\pi$
$23$	4.89140	−	1.31065i	1.01993	−	0.273289i	0.729772	+	0.683691i	$0.239626\pi$
$24$		0			0
$25$	−3.61409	−	3.45519i	−0.722818	−	0.691038i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.58666			−0.294636			−0.147318	−	0.989089i	$-0.547064\pi$
$29$	−1.58666			−0.294636			−0.147318	+	0.989089i	$0.547064\pi$
$30$		0			0
$31$	−4.97330	−	8.61402i	−0.893232	−	1.54712i	−0.835978	−	0.548763i	$-0.815099\pi$
$31$	−4.97330	−	8.61402i	−0.893232	−	1.54712i	−0.0572541	−	0.998360i	$-0.518235\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.54336	−	2.06669i	−0.936998	−	0.349334i
$36$		0			0
$37$	−4.52881	+	1.21349i	−0.744531	+	0.199497i	−0.611091	−	0.791560i	$-0.709269\pi$
$37$	−4.52881	+	1.21349i	−0.744531	+	0.199497i	−0.133440	+	0.991057i	$0.542602\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	11.8345i		−	1.84824i	−0.382101	−	0.924120i	$-0.624799\pi$
$41$		−	11.8345i		−	1.84824i	0.382101	−	0.924120i	$-0.375201\pi$
$42$		0			0
$43$	−6.62285	+	6.62285i	−1.00998	+	1.00998i	−0.0100260	+	0.999950i	$0.503191\pi$
$43$	−6.62285	+	6.62285i	−1.00998	+	1.00998i	−0.999950	+	0.0100260i	$0.996809\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.65657	+	9.91444i	0.387500	+	1.44617i	0.834188	+	0.551480i	$0.185937\pi$
$47$	2.65657	+	9.91444i	0.387500	+	1.44617i	−0.446688	+	0.894690i	$0.647397\pi$
$48$		0			0
$49$	−6.99153	+	0.344283i	−0.998790	+	0.0491833i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.55788	−	5.81410i	0.213992	−	0.798629i	−0.772527	−	0.634982i	$-0.781008\pi$
$53$	1.55788	−	5.81410i	0.213992	−	0.798629i	0.986519	−	0.163647i	$-0.0523258\pi$
$54$		0			0
$55$	−0.655686	−	4.58196i	−0.0884126	−	0.617831i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.46092	+	7.72654i	0.580762	+	1.00591i	0.995389	+	0.0959185i	$0.0305788\pi$
$59$	4.46092	+	7.72654i	0.580762	+	1.00591i	−0.414627	+	0.909992i	$0.636088\pi$
$60$		0			0
$61$	4.41894	−	7.65383i	0.565787	−	0.979972i	−0.431189	−	0.902262i	$-0.641906\pi$
$61$	4.41894	−	7.65383i	0.565787	−	0.979972i	0.996976	−	0.0777106i	$-0.0247610\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.14385	+	2.67605i	0.141878	+	0.331923i
$66$		0			0
$67$	1.99667	−	7.45169i	0.243933	−	0.910369i	−0.729984	−	0.683464i	$-0.760473\pi$
$67$	1.99667	−	7.45169i	0.243933	−	0.910369i	0.973917	−	0.226905i	$-0.0728606\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	1.25658i		−	0.149128i	−0.997216	−	0.0745641i	$-0.976243\pi$
$71$		−	1.25658i		−	0.149128i	0.997216	−	0.0745641i	$-0.0237565\pi$
$72$		0			0
$73$	−8.38264	−	2.24612i	−0.981114	−	0.262889i	−0.267600	−	0.963530i	$-0.586231\pi$
$73$	−8.38264	−	2.24612i	−0.981114	−	0.262889i	−0.713514	+	0.700641i	$0.752897\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.85418	−	4.67414i	−0.325264	−	0.532668i
$78$		0			0
$79$	2.95983	+	1.70886i	0.333007	+	0.192262i	0.657175	−	0.753738i	$-0.271751\pi$
$79$	2.95983	+	1.70886i	0.333007	+	0.192262i	−0.324168	+	0.945999i	$0.605084\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.626045	+	0.626045i	0.0687173	+	0.0687173i	0.740630	−	0.671913i	$-0.234527\pi$
$83$	0.626045	+	0.626045i	0.0687173	+	0.0687173i	−0.671913	+	0.740630i	$0.734527\pi$
$84$		0			0
$85$	2.15573	−	2.87575i	0.233822	−	0.311918i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.79258	−	4.83689i	0.296013	−	0.512709i	−0.679207	−	0.733946i	$-0.737676\pi$
$89$	2.79258	−	4.83689i	0.296013	−	0.512709i	0.975220	+	0.221238i	$0.0710096\pi$
$90$		0			0
$91$	2.49406	+	2.37427i	0.261449	+	0.248891i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.62718	−	2.84855i	0.372141	−	0.292256i
$96$		0			0
$97$	−8.71944	−	8.71944i	−0.885325	−	0.885325i	0.108744	−	0.994070i	$-0.465317\pi$
$97$	−8.71944	−	8.71944i	−0.885325	−	0.885325i	−0.994070	+	0.108744i	$0.965317\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.95466	−	4.59263i	0.791518	−	0.456983i	−0.0489784	−	0.998800i	$-0.515597\pi$
$101$	7.95466	−	4.59263i	0.791518	−	0.456983i	0.840497	+	0.541816i	$0.182263\pi$
$102$		0			0
$103$	0.554208	+	2.06833i	0.0546078	+	0.203799i	0.987840	−	0.155475i	$-0.0496909\pi$
$103$	0.554208	+	2.06833i	0.0546078	+	0.203799i	−0.933232	+	0.359274i	$0.883024\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.170615	−	0.636744i	−0.0164940	−	0.0615564i	0.957188	−	0.289466i	$-0.0934777\pi$
$107$	−0.170615	−	0.636744i	−0.0164940	−	0.0615564i	−0.973682	+	0.227909i	$0.926811\pi$
$108$		0			0
$109$	0.650545	−	0.375592i	0.0623109	−	0.0359752i	−0.468521	−	0.883452i	$-0.655213\pi$
$109$	0.650545	−	0.375592i	0.0623109	−	0.0359752i	0.530832	+	0.847477i	$0.321880\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	11.6139	+	11.6139i	1.09255	+	1.09255i	0.995256	+	0.0972906i	$0.0310176\pi$
$113$	11.6139	+	11.6139i	1.09255	+	1.09255i	0.0972906	+	0.995256i	$0.468982\pi$
$114$		0			0
$115$	1.35175	−	11.2424i	0.126051	−	1.04836i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.999256	−	4.13345i	0.0916017	−	0.378913i
$120$		0			0
$121$	−3.35757	+	5.81549i	−0.305234	+	0.528681i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−10.1792	+	4.62424i	−0.910456	+	0.413605i
$126$		0			0
$127$	12.6012	+	12.6012i	1.11818	+	1.11818i	0.992008	+	0.126171i	$0.0402689\pi$
$127$	12.6012	+	12.6012i	1.11818	+	1.11818i	0.126171	+	0.992008i	$0.459731\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.77300	−	3.33304i	−0.504389	−	0.291209i	0.226135	−	0.974096i	$-0.427391\pi$
$131$	−5.77300	−	3.33304i	−0.504389	−	0.291209i	−0.730524	+	0.682887i	$0.760724\pi$
$132$		0			0
$133$	2.61143	−	4.79160i	0.226439	−	0.415484i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.417488	+	0.111865i	0.0356684	+	0.00955731i	0.276609	−	0.960983i	$-0.410789\pi$
$137$	0.417488	+	0.111865i	0.0356684	+	0.00955731i	−0.240941	+	0.970540i	$0.577456\pi$
$138$		0			0
$139$			7.96116i			0.675257i	0.941280	+	0.337628i	$0.109625\pi$
$139$			7.96116i			0.675257i	−0.941280	+	0.337628i	$0.890375\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.697287	+	2.60231i	−0.0583101	+	0.217616i
$144$		0			0
$145$	−1.32080	+	3.29287i	−0.109686	+	0.273458i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	11.1655	−	19.3392i	0.914714	−	1.58433i	0.107394	−	0.994217i	$-0.465749\pi$
$149$	11.1655	−	19.3392i	0.914714	−	1.58433i	0.807320	−	0.590114i	$-0.200917\pi$
$150$		0			0
$151$	3.77742	+	6.54268i	0.307402	+	0.532436i	0.977793	−	0.209572i	$-0.0672071\pi$
$151$	3.77742	+	6.54268i	0.307402	+	0.532436i	−0.670391	+	0.742008i	$0.733874\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−22.0170	+	3.15067i	−1.76845	+	0.253068i
$156$		0			0
$157$	2.87299	−	10.7222i	0.229290	−	0.855722i	−0.751350	−	0.659904i	$-0.770597\pi$
$157$	2.87299	−	10.7222i	0.229290	−	0.855722i	0.980640	−	0.195818i	$-0.0627362\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.78494	−	12.8522i	−0.298295	−	1.01290i
$162$		0			0
$163$	3.02412	+	11.2862i	0.236868	+	0.884002i	0.977298	+	0.211869i	$0.0679550\pi$
$163$	3.02412	+	11.2862i	0.236868	+	0.884002i	−0.740431	+	0.672133i	$0.765378\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.35971	−	5.35971i	0.414747	−	0.414747i	−0.468641	−	0.883388i	$-0.655256\pi$
$167$	5.35971	−	5.35971i	0.414747	−	0.414747i	0.883388	+	0.468641i	$0.155256\pi$
$168$		0			0
$169$			11.3061i			0.869698i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.61430	−	0.700500i	0.198762	−	0.0532580i	−0.158065	−	0.987429i	$-0.550525\pi$
$173$	2.61430	−	0.700500i	0.198762	−	0.0532580i	0.356826	+	0.934171i	$0.383859\pi$
$174$		0			0
$175$	−8.90359	+	9.78397i	−0.673048	+	0.739599i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	5.82071	+	10.0818i	0.435061	+	0.753547i	0.997301	−	0.0734271i	$-0.0233936\pi$
$179$	5.82071	+	10.0818i	0.435061	+	0.753547i	−0.562240	+	0.826974i	$0.690060\pi$
$180$		0			0
$181$	11.1684			0.830138			0.415069	−	0.909790i	$-0.363757\pi$
$181$	11.1684			0.830138			0.415069	+	0.909790i	$0.363757\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.25155	+	10.4090i	−0.0920155	+	0.765283i
$186$		0			0
$187$	3.21373	−	0.861116i	0.235011	−	0.0629710i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−15.0042	−	8.66268i	−1.08567	−	0.626810i	−0.153247	−	0.988188i	$-0.548973\pi$
$191$	−15.0042	−	8.66268i	−1.08567	−	0.626810i	−0.932419	+	0.361378i	$0.882306\pi$
$192$		0			0
$193$	−8.17275	−	2.18988i	−0.588287	−	0.157631i	−0.0476170	−	0.998866i	$-0.515163\pi$
$193$	−8.17275	−	2.18988i	−0.588287	−	0.157631i	−0.540670	+	0.841235i	$0.681829\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−18.1277	+	18.1277i	−1.29155	+	1.29155i	−0.357714	+	0.933831i	$0.616444\pi$
$197$	−18.1277	+	18.1277i	−1.29155	+	1.29155i	−0.933831	+	0.357714i	$0.883556\pi$
$198$		0			0
$199$	9.74552	−	5.62658i	0.690842	−	0.398858i	−0.113086	−	0.993585i	$-0.536073\pi$
$199$	9.74552	−	5.62658i	0.690842	−	0.398858i	0.803927	+	0.594728i	$0.202740\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.103265	+	4.19664i	0.00724778	+	0.294547i
$204$		0			0
$205$	−24.5607	−	9.85151i	−1.71539	−	0.688059i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.26947			0.295325
$210$		0			0
$211$	24.3671			1.67750			0.838750	−	0.544517i	$-0.183287\pi$
$211$	24.3671			1.67750			0.838750	+	0.544517i	$0.183287\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.23157	+	19.2578i	0.561388	+	1.31337i
$216$		0			0
$217$	−22.4600	+	13.7148i	−1.52468	+	0.931019i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.81166	+	1.04596i	−0.121865	+	0.0703589i
$222$		0			0
$223$	0.214929	−	0.214929i	0.0143927	−	0.0143927i	−0.699874	−	0.714267i	$-0.746760\pi$
$223$	0.214929	−	0.214929i	0.0143927	−	0.0143927i	0.714267	+	0.699874i	$0.246760\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.78960	−	1.28337i	−0.317897	−	0.0851802i	0.0963423	−	0.995348i	$-0.469286\pi$
$227$	−4.78960	−	1.28337i	−0.317897	−	0.0851802i	−0.414239	+	0.910168i	$0.635952\pi$
$228$		0			0
$229$	8.46578	+	4.88772i	0.559434	+	0.322990i	0.752918	−	0.658114i	$-0.228645\pi$
$229$	8.46578	+	4.88772i	0.559434	+	0.322990i	−0.193484	+	0.981103i	$0.561979\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−11.5972	+	3.10745i	−0.759756	+	0.203576i	−0.617841	−	0.786303i	$-0.711992\pi$
$233$	−11.5972	+	3.10745i	−0.759756	+	0.203576i	−0.141915	+	0.989879i	$0.545326\pi$
$234$		0			0
$235$	22.7873	+	2.73988i	1.48648	+	0.178730i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	9.70299			0.627634			0.313817	−	0.949483i	$-0.398392\pi$
$239$	9.70299			0.627634			0.313817	+	0.949483i	$0.398392\pi$
$240$		0			0
$241$	8.24473	+	14.2803i	0.531090	+	0.919874i	0.999342	+	0.0362795i	$0.0115506\pi$
$241$	8.24473	+	14.2803i	0.531090	+	0.919874i	−0.468252	+	0.883595i	$0.655116\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−5.10551	+	14.7964i	−0.326179	+	0.945308i
$246$		0			0
$247$	−2.59297	+	0.694784i	−0.164987	+	0.0442080i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			4.05492i			0.255944i	0.991778	+	0.127972i	$0.0408468\pi$
$251$			4.05492i			0.255944i	−0.991778	+	0.127972i	$0.959153\pi$
$252$		0			0
$253$	7.41212	−	7.41212i	0.465996	−	0.465996i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	0.832881	+	3.10835i	0.0519537	+	0.193894i	0.987025	−	0.160565i	$-0.0513317\pi$
$257$	0.832881	+	3.10835i	0.0519537	+	0.193894i	−0.935072	+	0.354459i	$0.884665\pi$
$258$		0			0
$259$	3.50437	+	11.8995i	0.217751	+	0.739398i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.70445	+	25.0214i	−0.413414	+	1.54288i	0.374576	+	0.927196i	$0.377788\pi$
$263$	−6.70445	+	25.0214i	−0.413414	+	1.54288i	−0.787991	+	0.615687i	$0.788878\pi$
$264$		0			0
$265$	−10.7694	−	8.07303i	−0.661560	−	0.495922i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.19919	+	5.54115i	0.195058	+	0.337850i	0.946919	−	0.321471i	$-0.104177\pi$
$269$	3.19919	+	5.54115i	0.195058	+	0.337850i	−0.751862	+	0.659321i	$0.770844\pi$
$270$		0			0
$271$	9.68721	−	16.7787i	0.588456	−	1.01924i	−0.405979	−	0.913882i	$-0.633069\pi$
$271$	9.68721	−	16.7787i	0.588456	−	1.01924i	0.994435	−	0.105353i	$-0.0335973\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−10.0549	−	2.45343i	−0.606336	−	0.147947i
$276$		0			0
$277$	−4.41024	+	16.4593i	−0.264986	+	0.988941i	0.697273	+	0.716806i	$0.254396\pi$
$277$	−4.41024	+	16.4593i	−0.264986	+	0.988941i	−0.962259	+	0.272135i	$0.912270\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	0.136136i		−	0.00812121i	−0.999992	−	0.00406060i	$-0.998707\pi$
$281$		−	0.136136i		−	0.00812121i	0.999992	−	0.00406060i	$-0.00129253\pi$
$282$		0			0
$283$	15.4069	+	4.12826i	0.915843	+	0.245399i	0.685807	−	0.727783i	$-0.259449\pi$
$283$	15.4069	+	4.12826i	0.915843	+	0.245399i	0.230035	+	0.973182i	$0.426116\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−31.3017	+	0.770228i	−1.84768	+	0.0454651i
$288$		0			0
$289$	−12.4851	−	7.20829i	−0.734419	−	0.424017i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	21.9866	+	21.9866i	1.28447	+	1.28447i	0.938096	+	0.346375i	$0.112588\pi$
$293$	21.9866	+	21.9866i	1.28447	+	1.28447i	0.346375	+	0.938096i	$0.387412\pi$
$294$		0			0
$295$	19.7487	−	2.82607i	1.14981	−	0.164540i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.29539	+	5.70779i	−0.190577	+	0.330090i
$300$		0			0
$301$	17.9482	+	17.0861i	1.03451	+	0.984826i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−12.2058	−	15.5422i	−0.698903	−	0.889941i
$306$		0			0
$307$	−4.51324	−	4.51324i	−0.257584	−	0.257584i	0.566487	−	0.824071i	$-0.308302\pi$
$307$	−4.51324	−	4.51324i	−0.257584	−	0.257584i	−0.824071	+	0.566487i	$0.808302\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	20.3653	−	11.7579i	1.15481	−	0.666730i	0.204756	−	0.978813i	$-0.434360\pi$
$311$	20.3653	−	11.7579i	1.15481	−	0.666730i	0.950055	+	0.312083i	$0.101027\pi$
$312$		0			0
$313$	2.33358	+	8.70905i	0.131902	+	0.492264i	0.999991	−	0.00414319i	$-0.00131882\pi$
$313$	2.33358	+	8.70905i	0.131902	+	0.492264i	−0.868090	+	0.496408i	$0.834652\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.32976	−	8.69480i	−0.130853	−	0.488349i	0.869128	−	0.494587i	$-0.164681\pi$
$317$	−2.32976	−	8.69480i	−0.130853	−	0.488349i	−0.999981	+	0.00623873i	$0.998014\pi$
$318$		0			0
$319$	−2.84435	+	1.64219i	−0.159253	+	0.0919448i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.34417	+	2.34417i	0.130433	+	0.130433i
$324$		0			0
$325$	6.50591	−	0.146238i	0.360883	−	0.00811183i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	26.0503	−	7.67175i	1.43620	−	0.422957i
$330$		0			0
$331$	−7.59294	+	13.1514i	−0.417346	+	0.722864i	−0.995672	−	0.0929421i	$-0.970373\pi$
$331$	−7.59294	+	13.1514i	−0.417346	+	0.722864i	0.578326	+	0.815806i	$0.303706\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−13.8027	−	10.3469i	−0.754122	−	0.565309i
$336$		0			0
$337$	15.2449	+	15.2449i	0.830442	+	0.830442i	0.987577	−	0.157135i	$-0.0502259\pi$
$337$	15.2449	+	15.2449i	0.830442	+	0.830442i	−0.157135	+	0.987577i	$0.550226\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−17.8309	−	10.2947i	−0.965598	−	0.557488i
$342$		0			0
$343$	1.36564	+	18.4698i	0.0737378	+	0.997278i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.5534	+	2.82777i	0.566535	+	0.151803i	0.530707	−	0.847555i	$-0.321926\pi$
$347$	10.5534	+	2.82777i	0.566535	+	0.151803i	0.0358281	+	0.999358i	$0.488593\pi$
$348$		0			0
$349$		−	12.4107i		−	0.664328i	−0.943222	−	0.332164i	$-0.892221\pi$
$349$		−	12.4107i		−	0.664328i	0.943222	−	0.332164i	$-0.107779\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	3.18153	−	11.8736i	0.169336	−	0.631970i	−0.828111	−	0.560563i	$-0.810585\pi$
$353$	3.18153	−	11.8736i	0.169336	−	0.631970i	0.997447	−	0.0714065i	$-0.0227488\pi$
$354$		0			0
$355$	−2.60782	−	1.04602i	−0.138409	−	0.0555171i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−6.91881	+	11.9837i	−0.365161	+	0.632477i	−0.988802	−	0.149233i	$-0.952319\pi$
$359$	−6.91881	+	11.9837i	−0.365161	+	0.632477i	0.623641	+	0.781711i	$0.285653\pi$
$360$		0			0
$361$	−7.37293	−	12.7703i	−0.388049	−	0.672121i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−11.6395	+	15.5271i	−0.609240	+	0.812725i
$366$		0			0
$367$	6.40699	−	23.9112i	0.334442	−	1.24816i	−0.570030	−	0.821624i	$-0.693068\pi$
$367$	6.40699	−	23.9112i	0.334442	−	1.24816i	0.904472	−	0.426532i	$-0.140265\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−15.4794	−	3.74213i	−0.803651	−	0.194282i
$372$		0			0
$373$	1.56110	+	5.82609i	0.0808306	+	0.301664i	0.994492	−	0.104812i	$-0.0334242\pi$
$373$	1.56110	+	5.82609i	0.0808306	+	0.301664i	−0.913661	+	0.406476i	$0.866757\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.46022	−	1.46022i	0.0752050	−	0.0752050i
$378$		0			0
$379$			35.4262i			1.81972i	0.414912	+	0.909862i	$0.363813\pi$
$379$			35.4262i			1.81972i	−0.414912	+	0.909862i	$0.636187\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.88073	−	1.30779i	0.249394	−	0.0668248i	−0.131956	−	0.991256i	$-0.542126\pi$
$383$	4.88073	−	1.30779i	0.249394	−	0.0668248i	0.381350	+	0.924431i	$0.375459\pi$
$384$		0			0
$385$	−12.0764	+	2.03246i	−0.615469	+	0.103584i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−12.0642	−	20.8959i	−0.611680	−	1.05946i	−0.990957	−	0.134178i	$-0.957160\pi$
$389$	−12.0642	−	20.8959i	−0.611680	−	1.05946i	0.379277	−	0.925283i	$-0.376173\pi$
$390$		0			0
$391$	8.13930			0.411622
$392$		0			0
$393$		0			0
$394$		0			0
$395$	6.01035	−	4.72014i	0.302413	−	0.237496i
$396$		0			0
$397$	−6.30707	+	1.68997i	−0.316543	+	0.0848174i	−0.413592	−	0.910462i	$-0.635726\pi$
$397$	−6.30707	+	1.68997i	−0.316543	+	0.0848174i	0.0970495	+	0.995280i	$0.469059\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−12.5981	−	7.27351i	−0.629119	−	0.363222i	0.151292	−	0.988489i	$-0.451657\pi$
$401$	−12.5981	−	7.27351i	−0.629119	−	0.363222i	−0.780411	+	0.625267i	$0.784990\pi$
$402$		0			0
$403$	12.5045	+	3.35057i	0.622894	+	0.166904i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.86267	+	6.86267i	−0.340170	+	0.340170i
$408$		0			0
$409$	10.8306	−	6.25305i	0.535539	−	0.309194i	−0.207730	−	0.978186i	$-0.566608\pi$
$409$	10.8306	−	6.25305i	0.535539	−	0.309194i	0.743269	+	0.668993i	$0.233274\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	20.1460	−	12.3018i	0.991319	−	0.605331i
$414$		0			0
$415$	1.82040	−	0.778113i	0.0893599	−	0.0381961i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	33.7945			1.65097			0.825485	−	0.564425i	$-0.190902\pi$
$419$	33.7945			1.65097			0.825485	+	0.564425i	$0.190902\pi$
$420$		0			0
$421$	38.7453			1.88833			0.944165	−	0.329472i	$-0.106871\pi$
$421$	38.7453			1.88833			0.944165	+	0.329472i	$0.106871\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.17364	−	6.86776i	−0.202451	−	0.333136i
$426$		0			0
$427$	−20.5316	−	11.1897i	−0.993594	−	0.541510i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−9.40066	+	5.42747i	−0.452814	+	0.261432i	−0.709018	−	0.705191i	$-0.750861\pi$
$431$	−9.40066	+	5.42747i	−0.452814	+	0.261432i	0.256204	+	0.966623i	$0.417528\pi$
$432$		0			0
$433$	−20.6363	+	20.6363i	−0.991719	+	0.991719i	−0.999966	−	0.00824728i	$-0.997375\pi$
$433$	−20.6363	+	20.6363i	−0.991719	+	0.991719i	0.00824728	+	0.999966i	$0.497375\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	10.0888	+	2.70328i	0.482612	+	0.129316i
$438$		0			0
$439$	19.7818	+	11.4210i	0.944132	+	0.545095i	0.891253	−	0.453506i	$-0.149827\pi$
$439$	19.7818	+	11.4210i	0.944132	+	0.545095i	0.0528790	+	0.998601i	$0.483160\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	25.0024	−	6.69937i	1.18790	−	0.318297i	0.389844	−	0.920881i	$-0.372529\pi$
$443$	25.0024	−	6.69937i	1.18790	−	0.318297i	0.798055	+	0.602584i	$0.205862\pi$
$444$		0			0
$445$	−7.71355	−	9.82197i	−0.365657	−	0.465606i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−36.9105			−1.74191			−0.870957	−	0.491358i	$-0.836501\pi$
$449$	−36.9105			−1.74191			−0.870957	+	0.491358i	$0.836501\pi$
$450$		0			0
$451$	−12.2487	−	21.2153i	−0.576767	−	0.998989i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	7.00358	−	3.19960i	0.328333	−	0.150000i
$456$		0			0
$457$	−24.6338	+	6.60060i	−1.15232	+	0.308763i	−0.783894	−	0.620894i	$-0.786770\pi$
$457$	−24.6338	+	6.60060i	−1.15232	+	0.308763i	−0.368425	+	0.929657i	$0.620103\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	22.7818i		−	1.06105i	−0.847669	−	0.530526i	$-0.821994\pi$
$461$		−	22.7818i		−	1.06105i	0.847669	−	0.530526i	$-0.178006\pi$
$462$		0			0
$463$	−16.8483	+	16.8483i	−0.783005	+	0.783005i	−0.980337	−	0.197332i	$-0.936772\pi$
$463$	−16.8483	+	16.8483i	−0.783005	+	0.783005i	0.197332	+	0.980337i	$0.436772\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.1911	+	38.0338i	0.471589	+	1.75999i	0.634065	+	0.773280i	$0.281385\pi$
$467$	10.1911	+	38.0338i	0.471589	+	1.75999i	−0.162476	+	0.986712i	$0.551948\pi$
$468$		0			0
$469$	−19.8393	−	4.79612i	−0.916094	−	0.221464i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−5.01793	+	18.7272i	−0.230724	+	0.861075i
$474$		0			0
$475$	−2.89232	−	9.89888i	−0.132709	−	0.454192i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	6.97178	+	12.0755i	0.318549	+	0.551743i	0.980186	−	0.198082i	$-0.0634711\pi$
$479$	6.97178	+	12.0755i	0.318549	+	0.551743i	−0.661637	+	0.749825i	$0.730138\pi$
$480$		0			0
$481$	3.05111	−	5.28468i	0.139119	−	0.240961i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−25.3542	+	10.8374i	−1.15128	+	0.492102i
$486$		0			0
$487$	4.71318	−	17.5898i	0.213575	−	0.797072i	−0.773089	−	0.634298i	$-0.781289\pi$
$487$	4.71318	−	17.5898i	0.213575	−	0.797072i	0.986663	−	0.162774i	$-0.0520441\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			4.91225i			0.221687i	0.993838	+	0.110843i	$0.0353552\pi$
$491$			4.91225i			0.221687i	−0.993838	+	0.110843i	$0.964645\pi$
$492$		0			0
$493$	−2.46335	−	0.660052i	−0.110944	−	0.0297272i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.32358	+	0.0817819i	−0.149083	+	0.00366842i
$498$		0			0
$499$	−26.6432	−	15.3825i	−1.19272	−	0.688615i	−0.233794	−	0.972286i	$-0.575114\pi$
$499$	−26.6432	−	15.3825i	−1.19272	−	0.688615i	−0.958922	+	0.283672i	$0.908447\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	6.44578	+	6.44578i	0.287403	+	0.287403i	0.836053	−	0.548649i	$-0.184858\pi$
$503$	6.44578	+	6.44578i	0.287403	+	0.287403i	−0.548649	+	0.836053i	$0.684858\pi$
$504$		0			0
$505$	−2.90950	−	20.3317i	−0.129471	−	0.904750i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6.58314	−	11.4023i	0.291793	−	0.505400i	−0.682441	−	0.730941i	$-0.739082\pi$
$509$	6.58314	−	11.4023i	0.291793	−	0.505400i	0.974234	+	0.225541i	$0.0724149\pi$
$510$		0			0
$511$	−5.39531	+	22.3179i	−0.238675	+	0.987284i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	4.75384	+	0.571589i	0.209479	+	0.0251872i
$516$		0			0
$517$	15.0237	+	15.0237i	0.660742	+	0.660742i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	36.0893	−	20.8362i	1.58110	−	0.912850i	0.586404	−	0.810019i	$-0.300543\pi$
$521$	36.0893	−	20.8362i	1.58110	−	0.912850i	0.994699	−	0.102831i	$-0.0327901\pi$
$522$		0			0
$523$	−9.24821	−	34.5148i	−0.404396	−	1.50923i	−0.805167	−	0.593048i	$-0.797925\pi$
$523$	−9.24821	−	34.5148i	−0.404396	−	1.50923i	0.400772	−	0.916178i	$-0.368742\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.13779	−	15.4425i	−0.180245	−	0.672684i
$528$		0			0
$529$	2.28942	−	1.32180i	0.0995398	−	0.0574694i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	10.8914	+	10.8914i	0.471758	+	0.471758i
$534$		0			0
$535$	−1.46349	−	0.175966i	−0.0632721	−	0.00760766i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−12.1771	+	7.85337i	−0.524506	+	0.338269i
$540$		0			0
$541$	6.20634	−	10.7497i	0.266831	−	0.462166i	−0.701210	−	0.712954i	$-0.747357\pi$
$541$	6.20634	−	10.7497i	0.266831	−	0.462166i	0.968042	+	0.250789i	$0.0806900\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.237944	−	1.66276i	−0.0101924	−	0.0712249i
$546$		0			0
$547$	14.4711	+	14.4711i	0.618741	+	0.618741i	0.945209	−	0.326467i	$-0.105858\pi$
$547$	14.4711	+	14.4711i	0.618741	+	0.618741i	−0.326467	+	0.945209i	$0.605858\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.83414	−	1.63629i	−0.120738	−	0.0697083i
$552$		0			0
$553$	4.32721	−	7.93983i	0.184012	−	0.337636i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	26.0216	+	6.97246i	1.10257	+	0.295432i	0.763810	−	0.645441i	$-0.223326\pi$
$557$	26.0216	+	6.97246i	1.10257	+	0.295432i	0.338759	+	0.940873i	$0.389993\pi$
$558$		0			0
$559$		−	12.1901i		−	0.515587i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	6.78697	−	25.3293i	0.286037	−	1.06750i	−0.662042	−	0.749467i	$-0.730310\pi$
$563$	6.78697	−	25.3293i	0.286037	−	1.06750i	0.948078	−	0.318037i	$-0.103024\pi$
$564$		0			0
$565$	33.7708	−	14.4350i	1.42075	−	0.607285i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−0.374804	+	0.649179i	−0.0157126	+	0.0272150i	−0.873775	−	0.486331i	$-0.838335\pi$
$569$	−0.374804	+	0.649179i	−0.0157126	+	0.0272150i	0.858062	+	0.513546i	$0.171668\pi$
$570$		0			0
$571$	−10.0179	−	17.3516i	−0.419237	−	0.726140i	0.576626	−	0.817009i	$-0.304369\pi$
$571$	−10.0179	−	17.3516i	−0.419237	−	0.726140i	−0.995863	+	0.0908682i	$0.971036\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−22.2065	−	12.1639i	−0.926075	−	0.507271i
$576$		0			0
$577$	9.06892	−	33.8457i	0.377544	−	1.40901i	−0.472048	−	0.881573i	$-0.656485\pi$
$577$	9.06892	−	33.8457i	0.377544	−	1.40901i	0.849592	−	0.527441i	$-0.176848\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.61511	−	1.69660i	0.0670061	−	0.0703869i
$582$		0			0
$583$	−3.22480	−	12.0351i	−0.133558	−	0.498444i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−17.2300	+	17.2300i	−0.711156	+	0.711156i	−0.966777	−	0.255621i	$-0.917720\pi$
$587$	−17.2300	+	17.2300i	−0.711156	+	0.711156i	0.255621	+	0.966777i	$0.417720\pi$
$588$		0			0
$589$		−	20.5154i		−	0.845324i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−26.8397	+	7.19168i	−1.10217	+	0.295327i	−0.763650	−	0.645631i	$-0.776595\pi$
$593$	−26.8397	+	7.19168i	−1.10217	+	0.295327i	−0.338525	+	0.940958i	$0.609928\pi$
$594$		0			0
$595$	−7.74651	−	5.51464i	−0.317576	−	0.226078i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	15.7938	+	27.3557i	0.645318	+	1.11772i	0.984228	+	0.176905i	$0.0566086\pi$
$599$	15.7938	+	27.3557i	0.645318	+	1.11772i	−0.338909	+	0.940819i	$0.610058\pi$
$600$		0			0
$601$	−45.0704			−1.83846			−0.919231	−	0.393720i	$-0.871188\pi$
$601$	−45.0704			−1.83846			−0.919231	+	0.393720i	$0.871188\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.27416	+	11.8092i	0.377048	+	0.480110i
$606$		0			0
$607$	−9.12618	+	2.44535i	−0.370420	+	0.0992538i	−0.439227	−	0.898376i	$-0.644748\pi$
$607$	−9.12618	+	2.44535i	−0.370420	+	0.0992538i	0.0688065	+	0.997630i	$0.478081\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−11.5692	−	6.67947i	−0.468039	−	0.270223i
$612$		0			0
$613$	−33.6467	−	9.01561i	−1.35898	−	0.364137i	−0.495537	−	0.868587i	$-0.665029\pi$
$613$	−33.6467	−	9.01561i	−1.35898	−	0.364137i	−0.863441	+	0.504450i	$0.831695\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	32.6321	−	32.6321i	1.31372	−	1.31372i	0.395065	−	0.918653i	$-0.370722\pi$
$617$	32.6321	−	32.6321i	1.31372	−	1.31372i	0.918653	−	0.395065i	$-0.129278\pi$
$618$		0			0
$619$	−13.8691	+	8.00732i	−0.557446	+	0.321842i	−0.752120	−	0.659027i	$-0.770968\pi$
$619$	−13.8691	+	8.00732i	−0.557446	+	0.321842i	0.194674	+	0.980868i	$0.437635\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−12.9751	−	7.07143i	−0.519835	−	0.283311i
$624$		0			0
$625$	1.12332	+	24.9748i	0.0449328	+	0.998990i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−7.53594			−0.300478
$630$		0			0
$631$	−32.7818			−1.30502			−0.652511	−	0.757779i	$-0.726284\pi$
$631$	−32.7818			−1.30502			−0.652511	+	0.757779i	$0.726284\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	36.6417	−	15.6621i	1.45408	−	0.621533i
$636$		0			0
$637$	6.11751	−	6.75120i	0.242384	−	0.267492i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	35.6286	−	20.5702i	1.40725	−	0.812473i	0.412124	−	0.911128i	$-0.364787\pi$
$641$	35.6286	−	20.5702i	1.40725	−	0.812473i	0.995122	+	0.0986545i	$0.0314539\pi$
$642$		0			0
$643$	−7.21487	+	7.21487i	−0.284527	+	0.284527i	−0.834911	−	0.550385i	$-0.814481\pi$
$643$	−7.21487	+	7.21487i	−0.284527	+	0.284527i	0.550385	+	0.834911i	$0.314481\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−19.1136	−	5.12148i	−0.751434	−	0.201346i	−0.137280	−	0.990532i	$-0.543836\pi$
$647$	−19.1136	−	5.12148i	−0.751434	−	0.201346i	−0.614154	+	0.789186i	$0.710503\pi$
$648$		0			0
$649$	15.9938	+	9.23405i	0.627814	+	0.362468i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	23.4535	−	6.28434i	0.917806	−	0.245925i	0.231159	−	0.972916i	$-0.425748\pi$
$653$	23.4535	−	6.28434i	0.917806	−	0.245925i	0.686647	+	0.726991i	$0.259082\pi$
$654$		0			0
$655$	−11.7229	+	9.20640i	−0.458051	+	0.359724i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−10.3433			−0.402918			−0.201459	−	0.979497i	$-0.564568\pi$
$659$	−10.3433			−0.402918			−0.201459	+	0.979497i	$0.564568\pi$
$660$		0			0
$661$	−5.25115	−	9.09526i	−0.204246	−	0.353765i	0.745646	−	0.666342i	$-0.232141\pi$
$661$	−5.25115	−	9.09526i	−0.204246	−	0.353765i	−0.949892	+	0.312578i	$0.898808\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−7.77035	−	9.40832i	−0.301321	−	0.364839i
$666$		0			0
$667$	−7.76100	+	2.07955i	−0.300507	+	0.0805206i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	18.2943i		−	0.706244i
$672$		0			0
$673$	−10.2728	+	10.2728i	−0.395989	+	0.395989i	−0.876816	−	0.480827i	$-0.840337\pi$
$673$	−10.2728	+	10.2728i	−0.395989	+	0.395989i	0.480827	+	0.876816i	$0.340337\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	11.5277	+	43.0220i	0.443046	+	1.65347i	0.721044	+	0.692889i	$0.243662\pi$
$677$	11.5277	+	43.0220i	0.443046	+	1.65347i	−0.277998	+	0.960582i	$0.589671\pi$
$678$		0			0
$679$	−22.4950	+	23.6300i	−0.863279	+	0.906836i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	13.1876	−	49.2166i	0.504608	−	1.88322i	0.0369388	−	0.999318i	$-0.488239\pi$
$683$	13.1876	−	49.2166i	0.504608	−	1.88322i	0.467669	−	0.883904i	$-0.345094\pi$
$684$		0			0
$685$	0.579692	−	0.773309i	0.0221489	−	0.0295466i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.91703	+	6.78449i	0.149227	+	0.258469i
$690$		0			0
$691$	10.3933	−	18.0017i	0.395379	−	0.684816i	−0.597771	−	0.801667i	$-0.703947\pi$
$691$	10.3933	−	18.0017i	0.395379	−	0.684816i	0.993149	+	0.116851i	$0.0372800\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	16.5221	+	6.62718i	0.626720	+	0.251383i
$696$		0			0
$697$	4.92316	−	18.3735i	0.186478	−	0.695946i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			47.5242i			1.79497i	0.441049	+	0.897483i	$0.354606\pi$
$701$			47.5242i			1.79497i	−0.441049	+	0.897483i	$0.645394\pi$
$702$		0			0
$703$	−9.34092	−	2.50289i	−0.352299	−	0.0943983i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−12.6650	−	20.7408i	−0.476316	−	0.780037i
$708$		0			0
$709$	28.7512	+	16.5995i	1.07977	+	0.623407i	0.930835	−	0.365440i	$-0.119081\pi$
$709$	28.7512	+	16.5995i	1.07977	+	0.623407i	0.148937	+	0.988847i	$0.452415\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−35.6164	−	35.6164i	−1.33384	−	1.33384i
$714$		0			0
$715$	4.82024	+	3.61338i	0.180267	+	0.135133i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	18.5069	−	32.0549i	0.690190	−	1.19544i	−0.281585	−	0.959536i	$-0.590860\pi$
$719$	18.5069	−	32.0549i	0.690190	−	1.19544i	0.971775	−	0.235909i	$-0.0758066\pi$
$720$		0			0
$721$	5.43457	−	1.60047i	0.202394	−	0.0596045i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	5.73434	+	5.48222i	0.212968	+	0.203605i
$726$		0			0
$727$	−30.2950	−	30.2950i	−1.12358	−	1.12358i	−0.991199	−	0.132381i	$-0.957738\pi$
$727$	−30.2950	−	30.2950i	−1.12358	−	1.12358i	−0.132381	−	0.991199i	$-0.542262\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−13.0373	+	7.52710i	−0.482203	+	0.278400i
$732$		0			0
$733$	1.64638	+	6.14436i	0.0608103	+	0.226947i	0.989643	−	0.143553i	$-0.0458529\pi$
$733$	1.64638	+	6.14436i	0.0608103	+	0.226947i	−0.928832	+	0.370500i	$0.879186\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.13309	−	15.4249i	−0.152244	−	0.568184i
$738$		0			0
$739$	16.3934	−	9.46473i	0.603041	−	0.348166i	−0.167196	−	0.985924i	$-0.553471\pi$
$739$	16.3934	−	9.46473i	0.603041	−	0.348166i	0.770237	+	0.637758i	$0.220138\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	2.95638	+	2.95638i	0.108459	+	0.108459i	0.759254	−	0.650795i	$-0.225564\pi$
$743$	2.95638	+	2.95638i	0.108459	+	0.108459i	−0.650795	+	0.759254i	$0.725564\pi$
$744$		0			0
$745$	−30.8409	−	39.2710i	−1.12992	−	1.43878i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.67305	+	0.492710i	−0.0611320	+	0.0180032i
$750$		0			0
$751$	11.3918	−	19.7312i	0.415692	−	0.720000i	−0.579809	−	0.814753i	$-0.696873\pi$
$751$	11.3918	−	19.7312i	0.415692	−	0.720000i	0.995501	+	0.0947527i	$0.0302060\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	16.7228	−	2.39306i	0.608604	−	0.0870922i
$756$		0			0
$757$	26.8834	+	26.8834i	0.977092	+	0.977092i	0.999743	−	0.0226513i	$-0.00721076\pi$
$757$	26.8834	+	26.8834i	0.977092	+	0.977092i	−0.0226513	+	0.999743i	$0.507211\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−5.63819	−	3.25521i	−0.204384	−	0.118001i	0.394315	−	0.918976i	$-0.370982\pi$
$761$	−5.63819	−	3.25521i	−0.204384	−	0.118001i	−0.598699	+	0.800974i	$0.704315\pi$
$762$		0			0
$763$	−1.03576	−	1.69622i	−0.0374971	−	0.0614071i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−11.2162	−	3.00537i	−0.404994	−	0.108518i
$768$		0			0
$769$			16.1605i			0.582762i	0.956607	+	0.291381i	$0.0941147\pi$
$769$			16.1605i			0.582762i	−0.956607	+	0.291381i	$0.905885\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−9.39756	+	35.0722i	−0.338007	+	1.26146i	0.562566	+	0.826752i	$0.309814\pi$
$773$	−9.39756	+	35.0722i	−0.338007	+	1.26146i	−0.900573	+	0.434706i	$0.856852\pi$
$774$		0			0
$775$	−11.7891	+	48.3156i	−0.423476	+	1.73555i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.2047	−	21.1391i	0.437278	−	0.757388i
$780$		0			0
$781$	−1.30055	−	2.25262i	−0.0465373	−	0.0806049i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−19.8606	−	14.8880i	−0.708854	−	0.531375i
$786$		0			0
$787$	9.76500	−	36.4435i	0.348085	−	1.29907i	−0.540882	−	0.841099i	$-0.681909\pi$
$787$	9.76500	−	36.4435i	0.348085	−	1.29907i	0.888967	−	0.457972i	$-0.151424\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	29.9624	−	31.4741i	1.06534	−	1.11909i
$792$		0			0
$793$	2.97709	+	11.1107i	0.105720	+	0.394551i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	20.2855	−	20.2855i	0.718549	−	0.718549i	−0.249759	−	0.968308i	$-0.580351\pi$
$797$	20.2855	−	20.2855i	0.718549	−	0.718549i	0.968308	+	0.249759i	$0.0803514\pi$
$798$		0			0
$799$			16.4976i			0.583645i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−17.3520	+	4.64945i	−0.612338	+	0.164075i
$804$		0			0
$805$	−29.8235	−	2.84362i	−1.05114	−	0.100225i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−23.5077	−	40.7166i	−0.826488	−	1.43152i	−0.900777	−	0.434283i	$-0.857002\pi$
$809$	−23.5077	−	40.7166i	−0.826488	−	1.43152i	0.0742885	−	0.997237i	$-0.476331\pi$
$810$		0			0
$811$	8.24816			0.289632			0.144816	−	0.989459i	$-0.453741\pi$
$811$	8.24816			0.289632			0.144816	+	0.989459i	$0.453741\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	25.9401	+	3.11896i	0.908641	+	0.109252i
$816$		0			0
$817$	−18.6599	+	4.99991i	−0.652828	+	0.174925i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	38.8132	+	22.4088i	1.35459	+	0.782072i	0.988888	−	0.148660i	$-0.0474961\pi$
$821$	38.8132	+	22.4088i	1.35459	+	0.782072i	0.365701	+	0.930733i	$0.380829\pi$
$822$		0			0
$823$	27.7357	+	7.43176i	0.966805	+	0.259055i	0.707479	−	0.706735i	$-0.249833\pi$
$823$	27.7357	+	7.43176i	0.966805	+	0.259055i	0.259327	+	0.965790i	$0.416499\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	14.1240	−	14.1240i	0.491138	−	0.491138i	−0.417526	−	0.908665i	$-0.637103\pi$
$827$	14.1240	−	14.1240i	0.491138	−	0.491138i	0.908665	+	0.417526i	$0.137103\pi$
$828$		0			0
$829$	11.4383	−	6.60390i	0.397268	−	0.229363i	−0.288036	−	0.957619i	$-0.593002\pi$
$829$	11.4383	−	6.60390i	0.397268	−	0.229363i	0.685305	+	0.728256i	$0.259669\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−10.9978	−	2.37397i	−0.381052	−	0.0822530i
$834$		0			0
$835$	−6.66161	−	15.5849i	−0.230534	−	0.539337i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−12.3640			−0.426854			−0.213427	−	0.976959i	$-0.568463\pi$
$839$	−12.3640			−0.426854			−0.213427	+	0.976959i	$0.568463\pi$
$840$		0			0
$841$	−26.4825			−0.913190
$842$		0			0
$843$		0			0
$844$		0			0
$845$	23.4640	+	9.41161i	0.807185	+	0.323769i
$846$		0			0
$847$	15.6002	+	8.50213i	0.536029	+	0.292137i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−20.5617	+	11.8713i	−0.704848	+	0.406944i
$852$		0			0
$853$	23.3128	−	23.3128i	0.798215	−	0.798215i	−0.184599	−	0.982814i	$-0.559099\pi$
$853$	23.3128	−	23.3128i	0.798215	−	0.798215i	0.982814	+	0.184599i	$0.0590985\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	14.3629	+	3.84853i	0.490627	+	0.131463i	0.495647	−	0.868524i	$-0.334931\pi$
$857$	14.3629	+	3.84853i	0.490627	+	0.131463i	−0.00501942	+	0.999987i	$0.501598\pi$
$858$		0			0
$859$	−34.8177	−	20.1020i	−1.18797	−	0.685873i	−0.230122	−	0.973162i	$-0.573913\pi$
$859$	−34.8177	−	20.1020i	−1.18797	−	0.685873i	−0.957844	+	0.287289i	$0.907246\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−31.6775	+	8.48797i	−1.07832	+	0.288934i	−0.753906	−	0.656983i	$-0.771832\pi$
$863$	−31.6775	+	8.48797i	−1.07832	+	0.288934i	−0.324410	+	0.945917i	$0.605166\pi$
$864$		0			0
$865$	0.722468	−	6.00869i	0.0245647	−	0.204302i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	7.07464			0.239991
$870$		0			0
$871$	5.02029	+	8.69539i	0.170106	+	0.294632i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	12.8934	+	26.6226i	0.435876	+	0.900007i
$876$		0			0
$877$	32.0189	−	8.57943i	1.08120	−	0.289707i	0.326113	−	0.945331i	$-0.394261\pi$
$877$	32.0189	−	8.57943i	1.08120	−	0.289707i	0.755087	+	0.655624i	$0.227594\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			25.6978i			0.865780i	0.901447	+	0.432890i	$0.142506\pi$
$881$			25.6978i			0.865780i	−0.901447	+	0.432890i	$0.857494\pi$
$882$		0			0
$883$	9.70034	−	9.70034i	0.326442	−	0.326442i	−0.524790	−	0.851232i	$-0.675856\pi$
$883$	9.70034	−	9.70034i	0.326442	−	0.326442i	0.851232	+	0.524790i	$0.175856\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−0.341110	−	1.27304i	−0.0114534	−	0.0427445i	0.959963	−	0.280128i	$-0.0903769\pi$
$887$	−0.341110	−	1.27304i	−0.0114534	−	0.0427445i	−0.971416	+	0.237383i	$0.923710\pi$
$888$		0			0
$889$	32.5095	−	34.1498i	1.09034	−	1.14535i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−5.47932	+	20.4491i	−0.183358	+	0.684303i
$894$		0			0
$895$	25.7685	−	3.68752i	0.861346	−	0.123260i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	7.89095	+	13.6675i	0.263178	+	0.455838i
$900$		0			0
$901$	4.83734	−	8.37852i	0.161155	−	0.279129i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	9.29698	−	23.1782i	0.309042	−	0.770469i
$906$		0			0
$907$	−11.7355	+	43.7974i	−0.389670	+	1.45427i	0.441002	+	0.897506i	$0.354623\pi$
$907$	−11.7355	+	43.7974i	−0.389670	+	1.45427i	−0.830672	+	0.556762i	$0.812044\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			40.1728i			1.33098i	0.746405	+	0.665492i	$0.231778\pi$
$911$			40.1728i			1.33098i	−0.746405	+	0.665492i	$0.768222\pi$
$912$		0			0
$913$	1.77024	+	0.474334i	0.0585864	+	0.0156982i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−8.44001	+	15.4862i	−0.278714	+	0.511400i
$918$		0			0
$919$	−12.1328	−	7.00488i	−0.400224	−	0.231070i	0.286356	−	0.958123i	$-0.407556\pi$
$919$	−12.1328	−	7.00488i	−0.400224	−	0.231070i	−0.686581	+	0.727053i	$0.740889\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.15644	+	1.15644i	0.0380645	+	0.0380645i
$924$		0			0
$925$	20.5604	+	11.2622i	0.676021	+	0.370300i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−13.8950	+	24.0668i	−0.455879	+	0.789605i	−0.998738	−	0.0502183i	$-0.984008\pi$
$929$	−13.8950	+	24.0668i	−0.455879	+	0.789605i	0.542859	+	0.839824i	$0.317342\pi$
$930$		0			0
$931$	−12.8435	−	6.59524i	−0.420929	−	0.216150i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.888121	−	7.38641i	0.0290447	−	0.241561i
$936$		0			0
$937$	8.75138	+	8.75138i	0.285895	+	0.285895i	0.835455	−	0.549559i	$-0.185204\pi$
$937$	8.75138	+	8.75138i	0.285895	+	0.285895i	−0.549559	+	0.835455i	$0.685204\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−26.7152	+	15.4240i	−0.870890	+	0.502808i	−0.867644	−	0.497186i	$-0.834367\pi$
$941$	−26.7152	+	15.4240i	−0.870890	+	0.502808i	−0.00324585	+	0.999995i	$0.501033\pi$
$942$		0			0
$943$	−15.5109	−	57.8874i	−0.505103	−	1.88507i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.60409	−	35.8430i	−0.312091	−	1.16474i	−0.926667	−	0.375882i	$-0.877340\pi$
$947$	−9.60409	−	35.8430i	−0.312091	−	1.16474i	0.614576	−	0.788857i	$-0.289327\pi$
$948$		0			0
$949$	9.78173	−	5.64748i	0.317528	−	0.183325i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	12.4853	+	12.4853i	0.404440	+	0.404440i	0.879794	−	0.475355i	$-0.157680\pi$
$953$	12.4853	+	12.4853i	0.404440	+	0.404440i	−0.475355	+	0.879794i	$0.657680\pi$
$954$		0			0
$955$	−30.4681	+	23.9277i	−0.985925	+	0.774283i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	0.268707	−	1.11152i	0.00867701	−	0.0358927i
$960$		0			0
$961$	−33.9675	+	58.8335i	−1.09573	+	1.89785i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−11.3481	+	15.1383i	−0.365307	+	0.487319i
$966$		0			0
$967$	−3.52371	−	3.52371i	−0.113315	−	0.113315i	0.648176	−	0.761491i	$-0.275532\pi$
$967$	−3.52371	−	3.52371i	−0.113315	−	0.113315i	−0.761491	+	0.648176i	$0.775532\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−7.39965	−	4.27219i	−0.237466	−	0.137101i	0.376546	−	0.926398i	$-0.377112\pi$
$971$	−7.39965	−	4.27219i	−0.237466	−	0.137101i	−0.614011	+	0.789297i	$0.710445\pi$
$972$		0			0
$973$	21.0569	−	0.518137i	0.675052	−	0.0166107i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.913421	+	0.244750i	0.0292229	+	0.00783026i	0.273401	−	0.961900i	$-0.411851\pi$
$977$	0.913421	+	0.244750i	0.0292229	+	0.00783026i	−0.244178	+	0.969730i	$0.578518\pi$
$978$		0			0
$979$		−	11.5612i		−	0.369498i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	6.66846	−	24.8870i	0.212691	−	0.793773i	−0.774276	−	0.632848i	$-0.781886\pi$
$983$	6.66846	−	24.8870i	0.212691	−	0.793773i	0.986967	−	0.160925i	$-0.0514476\pi$
$984$		0			0
$985$	22.5310	+	52.7114i	0.717897	+	1.67952i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−23.7148	+	41.0752i	−0.754087	+	1.30612i
$990$		0			0
$991$	9.19441	+	15.9252i	0.292070	+	0.505880i	0.974299	−	0.225258i	$-0.0723226\pi$
$991$	9.19441	+	15.9252i	0.292070	+	0.505880i	−0.682229	+	0.731139i	$0.738989\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−3.56453	−	24.9091i	−0.113003	−	0.789671i
$996$		0			0
$997$	−8.31060	+	31.0156i	−0.263199	+	0.982273i	0.700144	+	0.714002i	$0.253119\pi$
$997$	−8.31060	+	31.0156i	−0.263199	+	0.982273i	−0.963343	+	0.268272i	$0.913548\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.ej.a.737.10	yes	64
3.2	odd	2	inner	1260.2.ej.a.737.7	yes	64
5.3	odd	4	inner	1260.2.ej.a.233.5	yes	64
7.4	even	3	inner	1260.2.ej.a.557.12	yes	64
15.8	even	4	inner	1260.2.ej.a.233.12	yes	64
21.11	odd	6	inner	1260.2.ej.a.557.5	yes	64
35.18	odd	12	inner	1260.2.ej.a.53.7	✓	64
105.53	even	12	inner	1260.2.ej.a.53.10	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.ej.a.53.7	✓	64	35.18	odd	12	inner
1260.2.ej.a.53.10	yes	64	105.53	even	12	inner
1260.2.ej.a.233.5	yes	64	5.3	odd	4	inner
1260.2.ej.a.233.12	yes	64	15.8	even	4	inner
1260.2.ej.a.557.5	yes	64	21.11	odd	6	inner
1260.2.ej.a.557.12	yes	64	7.4	even	3	inner
1260.2.ej.a.737.7	yes	64	3.2	odd	2	inner
1260.2.ej.a.737.10	yes	64	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.ej (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.832439 - 2.07534i) q^{5} +(-0.0650831 - 2.64495i) q^{7} +(1.79266 - 1.03499i) q^{11} +(-0.920307 + 0.920307i) q^{13} +(1.55253 + 0.416000i) q^{17} +(1.78623 + 1.03128i) q^{19} +(4.89140 - 1.31065i) q^{23} +(-3.61409 - 3.45519i) q^{25} -1.58666 q^{29} +(-4.97330 - 8.61402i) q^{31} +(-5.54336 - 2.06669i) q^{35} +(-4.52881 + 1.21349i) q^{37} -11.8345i q^{41} +(-6.62285 + 6.62285i) q^{43} +(2.65657 + 9.91444i) q^{47} +(-6.99153 + 0.344283i) q^{49} +(1.55788 - 5.81410i) q^{53} +(-0.655686 - 4.58196i) q^{55} +(4.46092 + 7.72654i) q^{59} +(4.41894 - 7.65383i) q^{61} +(1.14385 + 2.67605i) q^{65} +(1.99667 - 7.45169i) q^{67} -1.25658i q^{71} +(-8.38264 - 2.24612i) q^{73} +(-2.85418 - 4.67414i) q^{77} +(2.95983 + 1.70886i) q^{79} +(0.626045 + 0.626045i) q^{83} +(2.15573 - 2.87575i) q^{85} +(2.79258 - 4.83689i) q^{89} +(2.49406 + 2.37427i) q^{91} +(3.62718 - 2.84855i) q^{95} +(-8.71944 - 8.71944i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7} + 16 q^{25} + 32 q^{31} + 16 q^{37} - 16 q^{43} + 32 q^{55} + 48 q^{61} + 32 q^{67} + 40 q^{73} + 80 q^{85} + 96 q^{91} + 80 q^{97}+O(q^{100}) \) 64 * q - 8 * q^7 + 16 * q^25 + 32 * q^31 + 16 * q^37 - 16 * q^43 + 32 * q^55 + 48 * q^61 + 32 * q^67 + 40 * q^73 + 80 * q^85 + 96 * q^91 + 80 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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