LMFDB - Embedded newform 1568.2.q.h.815.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1568,2,Mod(815,1568)] 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("1568.815"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1568, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1568 = 2^{5} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1568.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(23)] == traces)

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

Self dual:	no
Analytic conductor:	$12.5205430369$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.9640188644209402576896.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 4x^{14} + 6x^{12} + 8x^{10} + 20x^{8} + 32x^{6} + 96x^{4} + 256x^{2} + 256 $ x^16 + 4x^14 + 6x^12 + 8x^10 + 20x^8 + 32x^6 + 96x^4 + 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 392)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			815.5
Root			$-0.264742 - 1.38921i$ of defining polynomial
Character	$\chi$	$=$	1568.815
Dual form			1568.2.q.h.1391.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.662827 + 0.382683i) q^{3} +(-1.51423 - 2.62272i) q^{5} +(-1.20711 - 2.09077i) q^{9} +(2.12132 - 3.67423i) q^{11} -3.02846 q^{13} -2.31788i q^{15} +(3.86324 + 2.23044i) q^{17} +(-2.92586 + 1.68925i) q^{19} +(-4.84616 + 2.79793i) q^{23} +(-2.08579 + 3.61269i) q^{25} -4.14386i q^{27} -5.59587i q^{29} +(-5.16991 + 8.95454i) q^{31} +(2.81214 - 1.62359i) q^{33} +(-2.00735 + 1.15894i) q^{37} +(-2.00735 - 1.15894i) q^{39} +7.07401i q^{41} -2.58579 q^{43} +(-3.65568 + 6.33182i) q^{45} +(-3.02846 - 5.24545i) q^{47} +(1.70711 + 2.95680i) q^{51} +(2.83882 + 1.63899i) q^{53} -12.8487 q^{55} -2.58579 q^{57} +(-9.32669 - 5.38476i) q^{59} +(-3.65568 - 6.33182i) q^{61} +(4.58579 + 7.94282i) q^{65} +(-1.00000 + 1.73205i) q^{67} -4.28289 q^{69} -14.4697i q^{71} +(-2.92586 - 1.68925i) q^{73} +(-2.76503 + 1.59639i) q^{75} +(9.69232 - 5.59587i) q^{79} +(-2.03553 + 3.52565i) q^{81} +9.23880i q^{83} -13.5096i q^{85} +(2.14144 - 3.70909i) q^{87} +(2.14931 - 1.24090i) q^{89} +(-6.85351 + 3.95687i) q^{93} +(8.86085 + 5.11582i) q^{95} -6.88830i q^{97} -10.2426 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{9} - 56 q^{25} - 64 q^{43} + 16 q^{51} - 64 q^{57} + 96 q^{65} - 16 q^{67} + 24 q^{81} - 96 q^{99}+O(q^{100}) $ 16 * q - 8 * q^9 - 56 * q^25 - 64 * q^43 + 16 * q^51 - 64 * q^57 + 96 * q^65 - 16 * q^67 + 24 * q^81 - 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times$.

$n$	$197$	$1471$	$1473$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.662827	+	0.382683i	0.382683	+	0.220942i	0.678985	−	0.734152i	$-0.262420\pi$
$3$	0.662827	+	0.382683i	0.382683	+	0.220942i	−0.296302	+	0.955094i	$0.595753\pi$
$4$		0			0
$5$	−1.51423	−	2.62272i	−0.677184	−	1.17292i	−0.975825	−	0.218552i	$-0.929867\pi$
$5$	−1.51423	−	2.62272i	−0.677184	−	1.17292i	0.298641	−	0.954366i	$-0.403467\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.20711	−	2.09077i	−0.402369	−	0.696923i
$10$		0			0
$11$	2.12132	−	3.67423i	0.639602	−	1.10782i	−0.345918	−	0.938265i	$-0.612432\pi$
$11$	2.12132	−	3.67423i	0.639602	−	1.10782i	0.985520	−	0.169559i	$-0.0542342\pi$
$12$		0			0
$13$	−3.02846			−0.839944			−0.419972	−	0.907537i	$-0.637960\pi$
$13$	−3.02846			−0.839944			−0.419972	+	0.907537i	$0.637960\pi$
$14$		0			0
$15$		−	2.31788i		−	0.598475i
$16$		0			0
$17$	3.86324	+	2.23044i	0.936973	+	0.540962i	0.889010	−	0.457887i	$-0.151394\pi$
$17$	3.86324	+	2.23044i	0.936973	+	0.540962i	0.0479630	+	0.998849i	$0.484727\pi$
$18$		0			0
$19$	−2.92586	+	1.68925i	−0.671238	+	0.387540i	−0.796546	−	0.604578i	$-0.793342\pi$
$19$	−2.92586	+	1.68925i	−0.671238	+	0.387540i	0.125307	+	0.992118i	$0.460008\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.84616	+	2.79793i	−1.01049	+	0.583409i	−0.911336	−	0.411662i	$-0.864948\pi$
$23$	−4.84616	+	2.79793i	−1.01049	+	0.583409i	−0.0991581	+	0.995072i	$0.531615\pi$
$24$		0			0
$25$	−2.08579	+	3.61269i	−0.417157	+	0.722538i
$26$		0			0
$27$		−	4.14386i		−	0.797486i
$28$		0			0
$29$		−	5.59587i		−	1.03913i	−0.854432	−	0.519563i	$-0.826095\pi$
$29$		−	5.59587i		−	1.03913i	0.854432	−	0.519563i	$-0.173905\pi$
$30$		0			0
$31$	−5.16991	+	8.95454i	−0.928542	+	1.60828i	−0.142780	+	0.989754i	$0.545604\pi$
$31$	−5.16991	+	8.95454i	−0.928542	+	1.60828i	−0.785763	+	0.618528i	$0.787729\pi$
$32$		0			0
$33$	2.81214	−	1.62359i	0.489530	−	0.282630i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.00735	+	1.15894i	−0.330006	+	0.190529i	−0.655844	−	0.754897i	$-0.727687\pi$
$37$	−2.00735	+	1.15894i	−0.330006	+	0.190529i	0.325838	+	0.945426i	$0.394354\pi$
$38$		0			0
$39$	−2.00735	−	1.15894i	−0.321433	−	0.185579i
$40$		0			0
$41$			7.07401i			1.10477i	0.833587	+	0.552387i	$0.186283\pi$
$41$			7.07401i			1.10477i	−0.833587	+	0.552387i	$0.813717\pi$
$42$		0			0
$43$	−2.58579			−0.394329			−0.197164	−	0.980370i	$-0.563173\pi$
$43$	−2.58579			−0.394329			−0.197164	+	0.980370i	$0.563173\pi$
$44$		0			0
$45$	−3.65568	+	6.33182i	−0.544956	+	0.943891i
$46$		0			0
$47$	−3.02846	−	5.24545i	−0.441746	−	0.765127i	0.556073	−	0.831134i	$-0.312308\pi$
$47$	−3.02846	−	5.24545i	−0.441746	−	0.765127i	−0.997819	+	0.0660064i	$0.978974\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	1.70711	+	2.95680i	0.239043	+	0.414034i
$52$		0			0
$53$	2.83882	+	1.63899i	0.389941	+	0.225133i	0.682135	−	0.731227i	$-0.261052\pi$
$53$	2.83882	+	1.63899i	0.389941	+	0.225133i	−0.292193	+	0.956359i	$0.594385\pi$
$54$		0			0
$55$	−12.8487			−1.73251
$56$		0			0
$57$	−2.58579			−0.342496
$58$		0			0
$59$	−9.32669	−	5.38476i	−1.21423	−	0.701037i	−0.250553	−	0.968103i	$-0.580612\pi$
$59$	−9.32669	−	5.38476i	−1.21423	−	0.701037i	−0.963678	+	0.267066i	$0.913946\pi$
$60$		0			0
$61$	−3.65568	−	6.33182i	−0.468061	−	0.810706i	0.531273	−	0.847201i	$-0.321714\pi$
$61$	−3.65568	−	6.33182i	−0.468061	−	0.810706i	−0.999334	+	0.0364951i	$0.988381\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.58579	+	7.94282i	0.568797	+	0.985185i
$66$		0			0
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$		0			0
$69$	−4.28289			−0.515599
$70$		0			0
$71$		−	14.4697i		−	1.71724i	−0.512613	−	0.858619i	$-0.671323\pi$
$71$		−	14.4697i		−	1.71724i	0.512613	−	0.858619i	$-0.328677\pi$
$72$		0			0
$73$	−2.92586	−	1.68925i	−0.342446	−	0.197711i	0.318907	−	0.947786i	$-0.396684\pi$
$73$	−2.92586	−	1.68925i	−0.342446	−	0.197711i	−0.661353	+	0.750075i	$0.730018\pi$
$74$		0			0
$75$	−2.76503	+	1.59639i	−0.319278	+	0.184335i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	9.69232	−	5.59587i	1.09047	−	0.629584i	0.156770	−	0.987635i	$-0.449892\pi$
$79$	9.69232	−	5.59587i	1.09047	−	0.629584i	0.933702	+	0.358051i	$0.116559\pi$
$80$		0			0
$81$	−2.03553	+	3.52565i	−0.226170	+	0.391739i
$82$		0			0
$83$			9.23880i			1.01409i	0.861920	+	0.507045i	$0.169262\pi$
$83$			9.23880i			1.01409i	−0.861920	+	0.507045i	$0.830738\pi$
$84$		0			0
$85$		−	13.5096i		−	1.46532i
$86$		0			0
$87$	2.14144	−	3.70909i	0.229587	−	0.397656i
$88$		0			0
$89$	2.14931	−	1.24090i	0.227826	−	0.131536i	−0.381743	−	0.924269i	$-0.624676\pi$
$89$	2.14931	−	1.24090i	0.227826	−	0.131536i	0.609569	+	0.792733i	$0.291343\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−6.85351	+	3.95687i	−0.710676	+	0.410309i
$94$		0			0
$95$	8.86085	+	5.11582i	0.909104	+	0.524872i
$96$		0			0
$97$		−	6.88830i		−	0.699401i	−0.936862	−	0.349701i	$-0.886283\pi$
$97$		−	6.88830i		−	0.699401i	0.936862	−	0.349701i	$-0.113717\pi$
$98$		0			0
$99$	−10.2426			−1.02942
$100$		0			0
$101$	−5.79712	+	10.0409i	−0.576835	+	0.999108i	0.419005	+	0.907984i	$0.362379\pi$
$101$	−5.79712	+	10.0409i	−0.576835	+	0.999108i	−0.995840	+	0.0911234i	$0.970954\pi$
$102$		0			0
$103$	−2.14144	−	3.70909i	−0.211003	−	0.365468i	0.741026	−	0.671477i	$-0.234340\pi$
$103$	−2.14144	−	3.70909i	−0.211003	−	0.365468i	−0.952029	+	0.306009i	$0.901006\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.65685	−	2.86976i	−0.160174	−	0.277430i	0.774757	−	0.632259i	$-0.217872\pi$
$107$	−1.65685	−	2.86976i	−0.160174	−	0.277430i	−0.934931	+	0.354830i	$0.884539\pi$
$108$		0			0
$109$	4.84616	+	2.79793i	0.464178	+	0.267993i	0.713799	−	0.700350i	$-0.246973\pi$
$109$	4.84616	+	2.79793i	0.464178	+	0.267993i	−0.249621	+	0.968344i	$0.580306\pi$
$110$		0			0
$111$	−1.77403			−0.168384
$112$		0			0
$113$	−1.41421			−0.133038			−0.0665190	−	0.997785i	$-0.521189\pi$
$113$	−1.41421			−0.133038			−0.0665190	+	0.997785i	$0.521189\pi$
$114$		0			0
$115$	14.6764	+	8.47343i	1.36858	+	0.790151i
$116$		0			0
$117$	3.65568	+	6.33182i	0.337967	+	0.585377i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−3.50000	−	6.06218i	−0.318182	−	0.551107i
$122$		0			0
$123$	−2.70711	+	4.68885i	−0.244092	+	0.422779i
$124$		0			0
$125$	−2.50886			−0.224399
$126$		0			0
$127$			0.960099i			0.0851950i	0.999092	+	0.0425975i	$0.0135633\pi$
$127$			0.960099i			0.0851950i	−0.999092	+	0.0425975i	$0.986437\pi$
$128$		0			0
$129$	−1.71393	−	0.989538i	−0.150903	−	0.0871239i
$130$		0			0
$131$	5.96544	−	3.44415i	0.521203	−	0.300917i	−0.216224	−	0.976344i	$-0.569374\pi$
$131$	5.96544	−	3.44415i	0.521203	−	0.300917i	0.737427	+	0.675427i	$0.236041\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−10.8682	+	6.27476i	−0.935386	+	0.540045i
$136$		0			0
$137$	9.77817	−	16.9363i	0.835406	−	1.44697i	−0.0582937	−	0.998299i	$-0.518566\pi$
$137$	9.77817	−	16.9363i	0.835406	−	1.44697i	0.893700	−	0.448666i	$-0.148101\pi$
$138$		0			0
$139$		−	1.66205i		−	0.140973i	−0.997513	−	0.0704866i	$-0.977545\pi$
$139$		−	1.66205i		−	0.140973i	0.997513	−	0.0704866i	$-0.0224552\pi$
$140$		0			0
$141$		−	4.63577i		−	0.390402i
$142$		0			0
$143$	−6.42433	+	11.1273i	−0.537230	+	0.930509i
$144$		0			0
$145$	−14.6764	+	8.47343i	−1.21881	+	0.703680i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.01469	−	2.31788i	0.328896	−	0.189888i	−0.326455	−	0.945213i	$-0.605854\pi$
$149$	4.01469	−	2.31788i	0.328896	−	0.189888i	0.655351	+	0.755324i	$0.272521\pi$
$150$		0			0
$151$	−8.86085	−	5.11582i	−0.721086	−	0.416319i	0.0940663	−	0.995566i	$-0.470013\pi$
$151$	−8.86085	−	5.11582i	−0.721086	−	0.416319i	−0.815152	+	0.579247i	$0.803347\pi$
$152$		0			0
$153$		−	10.7695i		−	0.870665i
$154$		0			0
$155$	31.3137			2.51518
$156$		0			0
$157$	3.65568	−	6.33182i	0.291755	−	0.505334i	−0.682470	−	0.730914i	$-0.739094\pi$
$157$	3.65568	−	6.33182i	0.291755	−	0.505334i	0.974225	+	0.225580i	$0.0724276\pi$
$158$		0			0
$159$	1.25443	+	2.17274i	0.0994827	+	0.172309i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−2.70711	−	4.68885i	−0.212037	−	0.367259i	0.740315	−	0.672260i	$-0.234676\pi$
$163$	−2.70711	−	4.68885i	−0.212037	−	0.367259i	−0.952352	+	0.305001i	$0.901343\pi$
$164$		0			0
$165$	−8.51645	−	4.91697i	−0.663005	−	0.382786i
$166$		0			0
$167$	8.56578			0.662840			0.331420	−	0.943483i	$-0.392472\pi$
$167$	8.56578			0.662840			0.331420	+	0.943483i	$0.392472\pi$
$168$		0			0
$169$	−3.82843			−0.294494
$170$		0			0
$171$	7.06365	+	4.07820i	0.540171	+	0.311868i
$172$		0			0
$173$	4.91010	+	8.50455i	0.373308	+	0.646589i	0.990072	−	0.140559i	$-0.0448900\pi$
$173$	4.91010	+	8.50455i	0.373308	+	0.646589i	−0.616764	+	0.787148i	$0.711557\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.12132	−	7.13834i	−0.309777	−	0.536550i
$178$		0			0
$179$	1.17157	−	2.02922i	0.0875675	−	0.151671i	−0.818915	−	0.573915i	$-0.805424\pi$
$179$	1.17157	−	2.02922i	0.0875675	−	0.151671i	0.906482	+	0.422244i	$0.138757\pi$
$180$		0			0
$181$	−9.08538			−0.675311			−0.337656	−	0.941270i	$-0.609634\pi$
$181$	−9.08538			−0.675311			−0.337656	+	0.941270i	$0.609634\pi$
$182$		0			0
$183$		−	5.59587i		−	0.413658i
$184$		0			0
$185$	6.07917	+	3.50981i	0.446949	+	0.258046i
$186$		0			0
$187$	16.3903	−	9.46297i	1.19858	−	0.692001i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.83882	+	1.63899i	−0.205409	+	0.118593i	−0.599176	−	0.800617i	$-0.704505\pi$
$191$	−2.83882	+	1.63899i	−0.205409	+	0.118593i	0.393767	+	0.919210i	$0.371172\pi$
$192$		0			0
$193$	4.70711	−	8.15295i	0.338825	−	0.586862i	−0.645387	−	0.763856i	$-0.723304\pi$
$193$	4.70711	−	8.15295i	0.338825	−	0.586862i	0.984212	+	0.176994i	$0.0566372\pi$
$194$		0			0
$195$			7.01962i			0.502685i
$196$		0			0
$197$			19.1055i			1.36121i	0.732651	+	0.680605i	$0.238283\pi$
$197$			19.1055i			1.36121i	−0.732651	+	0.680605i	$0.761717\pi$
$198$		0			0
$199$	8.19837	−	14.2000i	0.581167	−	1.00661i	−0.414175	−	0.910197i	$-0.635930\pi$
$199$	8.19837	−	14.2000i	0.581167	−	1.00661i	0.995341	−	0.0964129i	$-0.0307369\pi$
$200$		0			0
$201$	−1.32565	+	0.765367i	−0.0935044	+	0.0539848i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	18.5532	−	10.7117i	1.29581	−	0.748136i
$206$		0			0
$207$	11.6997	+	6.75481i	0.813183	+	0.469492i
$208$		0			0
$209$			14.3337i			0.991485i
$210$		0			0
$211$	−18.9706			−1.30599			−0.652994	−	0.757363i	$-0.726487\pi$
$211$	−18.9706			−1.30599			−0.652994	+	0.757363i	$0.726487\pi$
$212$		0			0
$213$	5.53732	−	9.59092i	0.379411	−	0.657159i
$214$		0			0
$215$	3.91548	+	6.78180i	0.267033	+	0.462515i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1.29289	−	2.23936i	−0.0873656	−	0.151322i
$220$		0			0
$221$	−11.6997	−	6.75481i	−0.787005	−	0.454377i
$222$		0			0
$223$	4.28289			0.286804			0.143402	−	0.989665i	$-0.454196\pi$
$223$	4.28289			0.286804			0.143402	+	0.989665i	$0.454196\pi$
$224$		0			0
$225$	10.0711			0.671405
$226$		0			0
$227$	4.09069	+	2.36176i	0.271508	+	0.156755i	0.629573	−	0.776941i	$-0.283230\pi$
$227$	4.09069	+	2.36176i	0.271508	+	0.156755i	−0.358065	+	0.933697i	$0.616563\pi$
$228$		0			0
$229$	−12.2215	−	21.1682i	−0.807616	−	1.39883i	−0.914510	−	0.404562i	$-0.867424\pi$
$229$	−12.2215	−	21.1682i	−0.807616	−	1.39883i	0.106894	−	0.994270i	$-0.465909\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.94975	+	8.57321i	0.324269	+	0.561650i	0.981364	−	0.192158i	$-0.0615485\pi$
$233$	4.94975	+	8.57321i	0.324269	+	0.561650i	−0.657095	+	0.753807i	$0.728215\pi$
$234$		0			0
$235$	−9.17157	+	15.8856i	−0.598287	+	1.03626i
$236$		0			0
$237$	8.56578			0.556407
$238$		0			0
$239$			18.1454i			1.17373i	0.809686	+	0.586864i	$0.199638\pi$
$239$			18.1454i			1.17373i	−0.809686	+	0.586864i	$0.800362\pi$
$240$		0			0
$241$	−15.9550	−	9.21160i	−1.02775	−	0.593371i	−0.111410	−	0.993775i	$-0.535537\pi$
$241$	−15.9550	−	9.21160i	−1.02775	−	0.593371i	−0.916339	+	0.400403i	$0.868870\pi$
$242$		0			0
$243$	−13.4645	+	7.77372i	−0.863747	+	0.498684i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	8.86085	−	5.11582i	0.563803	−	0.325512i
$248$		0			0
$249$	−3.53553	+	6.12372i	−0.224055	+	0.388075i
$250$		0			0
$251$		−	21.4077i		−	1.35124i	−0.737248	−	0.675622i	$-0.763875\pi$
$251$		−	21.4077i		−	1.35124i	0.737248	−	0.675622i	$-0.236125\pi$
$252$		0			0
$253$			23.7412i			1.49260i
$254$		0			0
$255$	5.16991	−	8.95454i	0.323752	−	0.560755i
$256$		0			0
$257$	−9.48751	+	5.47762i	−0.591815	+	0.341684i	−0.765815	−	0.643061i	$-0.777664\pi$
$257$	−9.48751	+	5.47762i	−0.591815	+	0.341684i	0.174000	+	0.984746i	$0.444331\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−11.6997	+	6.75481i	−0.724191	+	0.418112i
$262$		0			0
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$		0			0
$265$		−	9.92724i		−	0.609825i
$266$		0			0
$267$	1.89949			0.116247
$268$		0			0
$269$	2.76866	−	4.79546i	0.168808	−	0.292384i	−0.769193	−	0.639017i	$-0.779341\pi$
$269$	2.76866	−	4.79546i	0.168808	−	0.292384i	0.938001	+	0.346632i	$0.112675\pi$
$270$		0			0
$271$	0.887016	+	1.53636i	0.0538824	+	0.0933270i	0.891708	−	0.452610i	$-0.149507\pi$
$271$	0.887016	+	1.53636i	0.0538824	+	0.0933270i	−0.837826	+	0.545937i	$0.816174\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.84924	+	15.3273i	0.533629	+	0.924273i
$276$		0			0
$277$	8.51645	+	4.91697i	0.511704	+	0.295432i	0.733534	−	0.679653i	$-0.237870\pi$
$277$	8.51645	+	4.91697i	0.511704	+	0.295432i	−0.221830	+	0.975085i	$0.571203\pi$
$278$		0			0
$279$	24.9625			1.49447
$280$		0			0
$281$	−11.0711			−0.660445			−0.330222	−	0.943903i	$-0.607124\pi$
$281$	−11.0711			−0.660445			−0.330222	+	0.943903i	$0.607124\pi$
$282$		0			0
$283$	−22.3558	−	12.9071i	−1.32891	−	0.767248i	−0.343782	−	0.939050i	$-0.611708\pi$
$283$	−22.3558	−	12.9071i	−1.32891	−	0.767248i	−0.985132	+	0.171801i	$0.945041\pi$
$284$		0			0
$285$	3.91548	+	6.78180i	0.231933	+	0.401719i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1.44975	+	2.51104i	0.0852793	+	0.147708i
$290$		0			0
$291$	2.63604	−	4.56575i	0.154527	−	0.267649i
$292$		0			0
$293$	29.7650			1.73889			0.869445	−	0.494030i	$-0.164477\pi$
$293$	29.7650			1.73889			0.869445	+	0.494030i	$0.164477\pi$
$294$		0			0
$295$			32.6151i			1.89892i
$296$		0			0
$297$	−15.2255	−	8.79045i	−0.883474	−	0.510074i
$298$		0			0
$299$	14.6764	−	8.47343i	0.848759	−	0.490031i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−7.68498	+	4.43692i	−0.441490	+	0.254895i
$304$		0			0
$305$	−11.0711	+	19.1757i	−0.633927	+	1.09799i
$306$		0			0
$307$			23.2011i			1.32416i	0.749434	+	0.662079i	$0.230326\pi$
$307$			23.2011i			1.32416i	−0.749434	+	0.662079i	$0.769674\pi$
$308$		0			0
$309$		−	3.27798i		−	0.186478i
$310$		0			0
$311$	−1.77403	+	3.07271i	−0.100596	+	0.174238i	−0.911930	−	0.410345i	$-0.865408\pi$
$311$	−1.77403	+	3.07271i	−0.100596	+	0.174238i	0.811334	+	0.584582i	$0.198742\pi$
$312$		0			0
$313$	30.0823	−	17.3680i	1.70035	−	0.981698i	0.754952	−	0.655781i	$-0.227660\pi$
$313$	30.0823	−	17.3680i	1.70035	−	0.981698i	0.945398	−	0.325917i	$-0.105673\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.7070	+	7.91375i	−0.769863	+	0.444480i	−0.832826	−	0.553535i	$-0.813278\pi$
$317$	−13.7070	+	7.91375i	−0.769863	+	0.444480i	0.0629630	+	0.998016i	$0.479945\pi$
$318$		0			0
$319$	−20.5605	−	11.8706i	−1.15117	−	0.664627i
$320$		0			0
$321$		−	2.53620i		−	0.141557i
$322$		0			0
$323$	−15.0711			−0.838577
$324$		0			0
$325$	6.31672	−	10.9409i	0.350389	−	0.606891i
$326$		0			0
$327$	2.14144	+	3.70909i	0.118422	+	0.205113i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.53553	−	2.65962i	−0.0844006	−	0.146186i	0.820735	−	0.571309i	$-0.193564\pi$
$331$	−1.53553	−	2.65962i	−0.0844006	−	0.146186i	−0.905136	+	0.425123i	$0.860231\pi$
$332$		0			0
$333$	4.84616	+	2.79793i	0.265568	+	0.153326i
$334$		0			0
$335$	6.05692			0.330925
$336$		0			0
$337$	14.1421			0.770371			0.385186	−	0.922839i	$-0.374137\pi$
$337$	14.1421			0.770371			0.385186	+	0.922839i	$0.374137\pi$
$338$		0			0
$339$	−0.937379	−	0.541196i	−0.0509114	−	0.0293937i
$340$		0			0
$341$	21.9341	+	37.9909i	1.18780	+	2.05732i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	6.48528	+	11.2328i	0.349156	+	0.604756i
$346$		0			0
$347$	1.87868	−	3.25397i	0.100853	−	0.174682i	−0.811183	−	0.584792i	$-0.801176\pi$
$347$	1.87868	−	3.25397i	0.100853	−	0.174682i	0.912036	+	0.410110i	$0.134510\pi$
$348$		0			0
$349$	5.53732			0.296406			0.148203	−	0.988957i	$-0.452651\pi$
$349$	5.53732			0.296406			0.148203	+	0.988957i	$0.452651\pi$
$350$		0			0
$351$			12.5495i			0.669844i
$352$		0			0
$353$	18.9279	+	10.9280i	1.00743	+	0.581641i	0.910439	−	0.413644i	$-0.135744\pi$
$353$	18.9279	+	10.9280i	1.00743	+	0.581641i	0.0969930	+	0.995285i	$0.469078\pi$
$354$		0			0
$355$	−37.9501	+	21.9105i	−2.01418	+	1.16289i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	15.7144	−	9.07269i	0.829372	−	0.478838i	−0.0242655	−	0.999706i	$-0.507725\pi$
$359$	15.7144	−	9.07269i	0.829372	−	0.478838i	0.853638	+	0.520867i	$0.174391\pi$
$360$		0			0
$361$	−3.79289	+	6.56948i	−0.199626	+	0.345762i
$362$		0			0
$363$		−	5.35757i		−	0.281199i
$364$		0			0
$365$			10.2316i			0.535548i
$366$		0			0
$367$	18.0186	−	31.2091i	0.940562	−	1.62910i	0.176160	−	0.984362i	$-0.443633\pi$
$367$	18.0186	−	31.2091i	0.940562	−	1.62910i	0.764402	−	0.644739i	$-0.223034\pi$
$368$		0			0
$369$	14.7901	−	8.53909i	0.769944	−	0.444527i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	27.4140	−	15.8275i	1.41944	−	0.819517i	0.423195	−	0.906039i	$-0.360909\pi$
$373$	27.4140	−	15.8275i	1.41944	−	0.819517i	0.996250	+	0.0865220i	$0.0275753\pi$
$374$		0			0
$375$	−1.66294	−	0.960099i	−0.0858738	−	0.0495793i
$376$		0			0
$377$			16.9469i			0.872808i
$378$		0			0
$379$	26.3848			1.35529			0.677647	−	0.735387i	$-0.263000\pi$
$379$	26.3848			1.35529			0.677647	+	0.735387i	$0.263000\pi$
$380$		0			0
$381$	−0.367414	+	0.636379i	−0.0188232	+	0.0326027i
$382$		0			0
$383$	4.80249	+	8.31816i	0.245396	+	0.425038i	0.962243	−	0.272192i	$-0.0877487\pi$
$383$	4.80249	+	8.31816i	0.245396	+	0.425038i	−0.716847	+	0.697231i	$0.754415\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	3.12132	+	5.40629i	0.158666	+	0.274817i
$388$		0			0
$389$	−0.831470	−	0.480049i	−0.0421572	−	0.0243395i	0.478773	−	0.877939i	$-0.341082\pi$
$389$	−0.831470	−	0.480049i	−0.0421572	−	0.0243395i	−0.520930	+	0.853599i	$0.674415\pi$
$390$		0			0
$391$	−24.9625			−1.26241
$392$		0			0
$393$	5.27208			0.265941
$394$		0			0
$395$	−29.3528	−	16.9469i	−1.47690	−	0.852689i
$396$		0			0
$397$	−1.88164	−	3.25910i	−0.0944370	−	0.163570i	0.814936	−	0.579550i	$-0.196772\pi$
$397$	−1.88164	−	3.25910i	−0.0944370	−	0.163570i	−0.909374	+	0.415981i	$0.863438\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.07107	−	13.9795i	−0.403050	−	0.698103i	0.591042	−	0.806640i	$-0.298717\pi$
$401$	−8.07107	−	13.9795i	−0.403050	−	0.698103i	−0.994092	+	0.108538i	$0.965383\pi$
$402$		0			0
$403$	15.6569	−	27.1185i	0.779923	−	1.35087i
$404$		0			0
$405$	12.3291			0.612636
$406$		0			0
$407$			9.83395i			0.487451i
$408$		0			0
$409$	22.2892	+	12.8687i	1.10213	+	0.636314i	0.936779	−	0.349921i	$-0.113792\pi$
$409$	22.2892	+	12.8687i	1.10213	+	0.636314i	0.165349	+	0.986235i	$0.447125\pi$
$410$		0			0
$411$	12.9625	−	7.48389i	0.639392	−	0.369153i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	24.2308	−	13.9897i	1.18944	−	0.686726i
$416$		0			0
$417$	0.636039	−	1.10165i	0.0311470	−	0.0539481i
$418$		0			0
$419$		−	24.0209i		−	1.17350i	−0.809770	−	0.586748i	$-0.800408\pi$
$419$		−	24.0209i		−	1.17350i	0.809770	−	0.586748i	$-0.199592\pi$
$420$		0			0
$421$			30.2972i			1.47660i	0.674475	+	0.738298i	$0.264370\pi$
$421$			30.2972i			1.47660i	−0.674475	+	0.738298i	$0.735630\pi$
$422$		0			0
$423$	−7.31135	+	12.6636i	−0.355490	+	0.615727i
$424$		0			0
$425$	−16.1158	+	9.30445i	−0.781730	+	0.451332i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−8.51645	+	4.91697i	−0.411178	+	0.237394i
$430$		0			0
$431$	−17.3773	−	10.0328i	−0.837035	−	0.483262i	0.0192202	−	0.999815i	$-0.493882\pi$
$431$	−17.3773	−	10.0328i	−0.837035	−	0.483262i	−0.856255	+	0.516553i	$0.827215\pi$
$432$		0			0
$433$		−	3.19278i		−	0.153435i	−0.997053	−	0.0767177i	$-0.975556\pi$
$433$		−	3.19278i		−	0.153435i	0.997053	−	0.0767177i	$-0.0244440\pi$
$434$		0			0
$435$	−12.9706			−0.621891
$436$		0			0
$437$	9.45280	−	16.3727i	0.452189	−	0.783213i
$438$		0			0
$439$	−2.66105	−	4.60907i	−0.127005	−	0.219979i	0.795510	−	0.605940i	$-0.207203\pi$
$439$	−2.66105	−	4.60907i	−0.127005	−	0.219979i	−0.922515	+	0.385962i	$0.873870\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−17.4853	−	30.2854i	−0.830751	−	1.43890i	−0.897444	−	0.441129i	$-0.854578\pi$
$443$	−17.4853	−	30.2854i	−0.830751	−	1.43890i	0.0666929	−	0.997774i	$-0.478755\pi$
$444$		0			0
$445$	−6.50910	−	3.75803i	−0.308561	−	0.178148i
$446$		0			0
$447$	3.54806			0.167818
$448$		0			0
$449$	−20.2843			−0.957274			−0.478637	−	0.878013i	$-0.658869\pi$
$449$	−20.2843			−0.957274			−0.478637	+	0.878013i	$0.658869\pi$
$450$		0			0
$451$	25.9916	+	15.0062i	1.22390	+	0.706616i
$452$		0			0
$453$	−3.91548	−	6.78180i	−0.183965	−	0.318637i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−12.0208	−	20.8207i	−0.562310	−	0.973950i	−0.997294	−	0.0735115i	$-0.976579\pi$
$457$	−12.0208	−	20.8207i	−0.562310	−	0.973950i	0.434984	−	0.900438i	$-0.356754\pi$
$458$		0			0
$459$	9.24264	−	16.0087i	0.431410	−	0.747223i
$460$		0			0
$461$	14.1031			0.656847			0.328423	−	0.944531i	$-0.393483\pi$
$461$	14.1031			0.656847			0.328423	+	0.944531i	$0.393483\pi$
$462$		0			0
$463$		−	23.7412i		−	1.10335i	−0.834059	−	0.551675i	$-0.813989\pi$
$463$		−	23.7412i		−	1.10335i	0.834059	−	0.551675i	$-0.186011\pi$
$464$		0			0
$465$	20.7556	+	11.9832i	0.962517	+	0.555709i
$466$		0			0
$467$	−4.57317	+	2.64032i	−0.211621	+	0.122180i	−0.602065	−	0.798447i	$-0.705655\pi$
$467$	−4.57317	+	2.64032i	−0.211621	+	0.122180i	0.390443	+	0.920627i	$0.372322\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	4.84616	−	2.79793i	0.223299	−	0.128922i
$472$		0			0
$473$	−5.48528	+	9.50079i	−0.252214	+	0.436847i
$474$		0			0
$475$		−	14.0936i		−	0.646660i
$476$		0			0
$477$		−	7.91375i		−	0.362346i
$478$		0			0
$479$	9.45280	−	16.3727i	0.431909	−	0.748089i	−0.565128	−	0.825003i	$-0.691173\pi$
$479$	9.45280	−	16.3727i	0.431909	−	0.748089i	0.997038	+	0.0769142i	$0.0245067\pi$
$480$		0			0
$481$	6.07917	−	3.50981i	0.277186	−	0.160034i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−18.0661	+	10.4305i	−0.820340	+	0.473623i
$486$		0			0
$487$	29.4214	+	16.9864i	1.33321	+	0.769729i	0.985790	−	0.167981i	$-0.0537247\pi$
$487$	29.4214	+	16.9864i	1.33321	+	0.769729i	0.347420	+	0.937710i	$0.387058\pi$
$488$		0			0
$489$		−	4.14386i		−	0.187392i
$490$		0			0
$491$	26.0000			1.17336			0.586682	−	0.809818i	$-0.300434\pi$
$491$	26.0000			1.17336			0.586682	+	0.809818i	$0.300434\pi$
$492$		0			0
$493$	12.4813	−	21.6182i	0.562127	−	0.973633i
$494$		0			0
$495$	15.5097	+	26.8636i	0.697110	+	1.20743i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	2.31371	+	4.00746i	0.103576	+	0.179399i	0.913155	−	0.407611i	$-0.133638\pi$
$499$	2.31371	+	4.00746i	0.103576	+	0.179399i	−0.809580	+	0.587010i	$0.800305\pi$
$500$		0			0
$501$	5.67763	+	3.27798i	0.253658	+	0.146449i
$502$		0			0
$503$	15.3575			0.684758			0.342379	−	0.939562i	$-0.388767\pi$
$503$	15.3575			0.684758			0.342379	+	0.939562i	$0.388767\pi$
$504$		0			0
$505$	35.1127			1.56249
$506$		0			0
$507$	−2.53759	−	1.46508i	−0.112698	−	0.0650663i
$508$		0			0
$509$	−6.68414	−	11.5773i	−0.296269	−	0.513153i	0.679010	−	0.734129i	$-0.262409\pi$
$509$	−6.68414	−	11.5773i	−0.296269	−	0.513153i	−0.975279	+	0.220976i	$0.929076\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	7.00000	+	12.1244i	0.309058	+	0.535303i
$514$		0			0
$515$	−6.48528	+	11.2328i	−0.285776	+	0.494978i
$516$		0			0
$517$	−25.6973			−1.13017
$518$		0			0
$519$			7.51606i			0.329919i
$520$		0			0
$521$	−8.84420	−	5.10620i	−0.387471	−	0.223707i	0.293593	−	0.955931i	$-0.405149\pi$
$521$	−8.84420	−	5.10620i	−0.387471	−	0.223707i	−0.681064	+	0.732224i	$0.738482\pi$
$522$		0			0
$523$	−5.18889	+	2.99581i	−0.226894	+	0.130998i	−0.609139	−	0.793064i	$-0.708485\pi$
$523$	−5.18889	+	2.99581i	−0.226894	+	0.130998i	0.382244	+	0.924061i	$0.375151\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−39.9452	+	23.0624i	−1.74004	+	1.00461i
$528$		0			0
$529$	4.15685	−	7.19988i	0.180733	−	0.313038i
$530$		0			0
$531$			25.9999i			1.12830i
$532$		0			0
$533$		−	21.4234i		−	0.927949i
$534$		0			0
$535$	−5.01772	+	8.69094i	−0.216935	+	0.375742i
$536$		0			0
$537$	1.55310	−	0.896683i	0.0670212	−	0.0386947i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	26.2382	−	15.1486i	1.12807	−	0.651289i	0.184618	−	0.982810i	$-0.440895\pi$
$541$	26.2382	−	15.1486i	1.12807	−	0.651289i	0.943448	+	0.331521i	$0.107562\pi$
$542$		0			0
$543$	−6.02204	−	3.47682i	−0.258430	−	0.149205i
$544$		0			0
$545$		−	16.9469i		−	0.725924i
$546$		0			0
$547$	−34.5858			−1.47878			−0.739391	−	0.673277i	$-0.764886\pi$
$547$	−34.5858			−1.47878			−0.739391	+	0.673277i	$0.764886\pi$
$548$		0			0
$549$	−8.82558	+	15.2864i	−0.376667	+	0.652406i
$550$		0			0
$551$	9.45280	+	16.3727i	0.402703	+	0.697501i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	2.68629	+	4.65279i	0.114027	+	0.197500i
$556$		0			0
$557$	26.2382	+	15.1486i	1.11175	+	0.641867i	0.939281	−	0.343149i	$-0.111493\pi$
$557$	26.2382	+	15.1486i	1.11175	+	0.641867i	0.172465	+	0.985016i	$0.444827\pi$
$558$		0			0
$559$	7.83095			0.331214
$560$		0			0
$561$	14.4853			0.611569
$562$		0			0
$563$	21.5126	+	12.4203i	0.906649	+	0.523454i	0.879351	−	0.476174i	$-0.157977\pi$
$563$	21.5126	+	12.4203i	0.906649	+	0.523454i	0.0272973	+	0.999627i	$0.491310\pi$
$564$		0			0
$565$	2.14144	+	3.70909i	0.0900913	+	0.156043i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.41421	−	16.3059i	−0.394664	−	0.683579i	0.598394	−	0.801202i	$-0.295806\pi$
$569$	−9.41421	−	16.3059i	−0.394664	−	0.683579i	−0.993058	+	0.117623i	$0.962472\pi$
$570$		0			0
$571$	1.19239	−	2.06528i	0.0498999	−	0.0864291i	−0.839997	−	0.542592i	$-0.817443\pi$
$571$	1.19239	−	2.06528i	0.0498999	−	0.0864291i	0.889896	+	0.456163i	$0.150776\pi$
$572$		0			0
$573$	−2.50886			−0.104809
$574$		0			0
$575$		−	23.3436i		−	0.973494i
$576$		0			0
$577$	−28.1409	−	16.2471i	−1.17152	−	0.676378i	−0.217483	−	0.976064i	$-0.569785\pi$
$577$	−28.1409	−	16.2471i	−1.17152	−	0.676378i	−0.954038	+	0.299687i	$0.903118\pi$
$578$		0			0
$579$	6.24000	−	3.60266i	0.259325	−	0.149722i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	12.0441	−	6.95365i	0.498815	−	0.287991i
$584$		0			0
$585$	11.0711	−	19.1757i	0.457732	−	0.792816i
$586$		0			0
$587$		−	38.8799i		−	1.60474i	−0.596824	−	0.802372i	$-0.703571\pi$
$587$		−	38.8799i		−	1.60474i	0.596824	−	0.802372i	$-0.296429\pi$
$588$		0			0
$589$		−	34.9330i		−	1.43939i
$590$		0			0
$591$	−7.31135	+	12.6636i	−0.300749	+	0.520912i
$592$		0			0
$593$	16.5983	−	9.58302i	0.681609	−	0.393527i	−0.118852	−	0.992912i	$-0.537921\pi$
$593$	16.5983	−	9.58302i	0.681609	−	0.393527i	0.800461	+	0.599385i	$0.204588\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	10.8682	−	6.27476i	0.444806	−	0.256809i
$598$		0			0
$599$	26.2382	+	15.1486i	1.07206	+	0.618955i	0.928744	−	0.370722i	$-0.120890\pi$
$599$	26.2382	+	15.1486i	1.07206	+	0.618955i	0.143318	+	0.989677i	$0.454223\pi$
$600$		0			0
$601$			43.5809i			1.77770i	0.458198	+	0.888850i	$0.348495\pi$
$601$			43.5809i			1.77770i	−0.458198	+	0.888850i	$0.651505\pi$
$602$		0			0
$603$	4.82843			0.196629
$604$		0			0
$605$	−10.5996	+	18.3591i	−0.430935	+	0.746402i
$606$		0			0
$607$	−20.1600	−	34.9182i	−0.818270	−	1.41729i	−0.906956	−	0.421226i	$-0.861600\pi$
$607$	−20.1600	−	34.9182i	−0.818270	−	1.41729i	0.0886860	−	0.996060i	$-0.471733\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	9.17157	+	15.8856i	0.371042	+	0.642664i
$612$		0			0
$613$	−36.7619	−	21.2245i	−1.48480	−	0.857250i	−0.484951	−	0.874542i	$-0.661162\pi$
$613$	−36.7619	−	21.2245i	−1.48480	−	0.857250i	−0.999850	+	0.0172913i	$0.994496\pi$
$614$		0			0
$615$	16.3967			0.661180
$616$		0			0
$617$	−28.8284			−1.16059			−0.580294	−	0.814407i	$-0.697063\pi$
$617$	−28.8284			−1.16059			−0.580294	+	0.814407i	$0.697063\pi$
$618$		0			0
$619$	−17.6689	−	10.2011i	−0.710173	−	0.410018i	0.100952	−	0.994891i	$-0.467811\pi$
$619$	−17.6689	−	10.2011i	−0.710173	−	0.410018i	−0.811125	+	0.584873i	$0.801144\pi$
$620$		0			0
$621$	11.5942	+	20.0818i	0.465261	+	0.805855i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	14.2279	+	24.6435i	0.569117	+	0.985739i
$626$		0			0
$627$	−5.48528	+	9.50079i	−0.219061	+	0.379425i
$628$		0			0
$629$	−10.3398			−0.412275
$630$		0			0
$631$			17.1853i			0.684135i	0.939675	+	0.342068i	$0.111127\pi$
$631$			17.1853i			0.684135i	−0.939675	+	0.342068i	$0.888873\pi$
$632$		0			0
$633$	−12.5742	−	7.25972i	−0.499780	−	0.288548i
$634$		0			0
$635$	2.51807	−	1.45381i	0.0999267	−	0.0576927i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−30.2528	+	17.4665i	−1.19678	+	0.690964i
$640$		0			0
$641$	3.07107	−	5.31925i	0.121300	−	0.210098i	−0.798981	−	0.601357i	$-0.794627\pi$
$641$	3.07107	−	5.31925i	0.121300	−	0.210098i	0.920281	+	0.391259i	$0.127960\pi$
$642$		0			0
$643$			49.3324i			1.94548i	0.231901	+	0.972739i	$0.425505\pi$
$643$			49.3324i			1.94548i	−0.231901	+	0.972739i	$0.574495\pi$
$644$		0			0
$645$			5.99355i			0.235996i
$646$		0			0
$647$	−17.2837	+	29.9363i	−0.679494	+	1.17692i	0.295639	+	0.955300i	$0.404467\pi$
$647$	−17.2837	+	29.9363i	−0.679494	+	1.17692i	−0.975133	+	0.221619i	$0.928866\pi$
$648$		0			0
$649$	−39.5698	+	22.8456i	−1.55325	+	0.896769i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.67029	−	2.11904i	0.143629	−	0.0829245i	−0.426463	−	0.904505i	$-0.640241\pi$
$653$	3.67029	−	2.11904i	0.143629	−	0.0829245i	0.570093	+	0.821580i	$0.306907\pi$
$654$		0			0
$655$	−18.0661	−	10.4305i	−0.705901	−	0.407552i
$656$		0			0
$657$			8.15640i			0.318212i
$658$		0			0
$659$	−25.6985			−1.00107			−0.500535	−	0.865716i	$-0.666863\pi$
$659$	−25.6985			−1.00107			−0.500535	+	0.865716i	$0.666863\pi$
$660$		0			0
$661$	−9.71260	+	16.8227i	−0.377776	+	0.654328i	−0.990738	−	0.135785i	$-0.956644\pi$
$661$	−9.71260	+	16.8227i	−0.377776	+	0.654328i	0.612962	+	0.790112i	$0.289978\pi$
$662$		0			0
$663$	−5.16991	−	8.95454i	−0.200782	−	0.347765i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	15.6569	+	27.1185i	0.606236	+	1.05003i
$668$		0			0
$669$	2.83882	+	1.63899i	0.109755	+	0.0633671i
$670$		0			0
$671$	−31.0194			−1.19749
$672$		0			0
$673$	−29.8995			−1.15254			−0.576270	−	0.817259i	$-0.695492\pi$
$673$	−29.8995			−1.15254			−0.576270	+	0.817259i	$0.695492\pi$
$674$		0			0
$675$	14.9705	+	8.64321i	0.576214	+	0.332677i
$676$		0			0
$677$	−21.6743	−	37.5409i	−0.833009	−	1.44281i	−0.895641	−	0.444777i	$-0.853283\pi$
$677$	−21.6743	−	37.5409i	−0.833009	−	1.44281i	0.0626320	−	0.998037i	$-0.480051\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	1.80761	+	3.13088i	0.0692678	+	0.119975i
$682$		0			0
$683$	−25.4853	+	44.1418i	−0.975167	+	1.68904i	−0.295785	+	0.955255i	$0.595581\pi$
$683$	−25.4853	+	44.1418i	−0.975167	+	1.68904i	−0.679382	+	0.733785i	$0.737752\pi$
$684$		0			0
$685$	−59.2256			−2.26290
$686$		0			0
$687$		−	18.7078i		−	0.713747i
$688$		0			0
$689$	−8.59724	−	4.96362i	−0.327529	−	0.189099i
$690$		0			0
$691$	26.0387	−	15.0334i	0.990558	−	0.571899i	0.0851170	−	0.996371i	$-0.472874\pi$
$691$	26.0387	−	15.0334i	0.990558	−	0.571899i	0.905441	+	0.424472i	$0.139540\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.35910	+	2.51673i	−0.165350	+	0.0954649i
$696$		0			0
$697$	−15.7782	+	27.3286i	−0.597641	+	1.03514i
$698$		0			0
$699$			7.57675i			0.286579i
$700$		0			0
$701$			16.7876i			0.634059i	0.948416	+	0.317029i	$0.102685\pi$
$701$			16.7876i			0.634059i	−0.948416	+	0.317029i	$0.897315\pi$
$702$		0			0
$703$	3.91548	−	6.78180i	0.147675	−	0.255781i
$704$		0			0
$705$	−12.1583	+	7.01962i	−0.457909	+	0.264374i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−9.34792	+	5.39702i	−0.351068	+	0.202689i	−0.665156	−	0.746705i	$-0.731635\pi$
$709$	−9.34792	+	5.39702i	−0.351068	+	0.202689i	0.314087	+	0.949394i	$0.398302\pi$
$710$		0			0
$711$	−23.3993	−	13.5096i	−0.877544	−	0.506650i
$712$		0			0
$713$		−	57.8602i		−	2.16688i
$714$		0			0
$715$	38.9117			1.45521
$716$		0			0
$717$	−6.94394	+	12.0273i	−0.259326	+	0.449166i
$718$		0			0
$719$	−6.05692	−	10.4909i	−0.225885	−	0.391244i	0.730700	−	0.682699i	$-0.239194\pi$
$719$	−6.05692	−	10.4909i	−0.225885	−	0.391244i	−0.956585	+	0.291455i	$0.905861\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−7.05025	−	12.2114i	−0.262202	−	0.454147i
$724$		0			0
$725$	20.2161	+	11.6718i	0.750808	+	0.433479i
$726$		0			0
$727$	−38.8504			−1.44088			−0.720441	−	0.693517i	$-0.756060\pi$
$727$	−38.8504			−1.44088			−0.720441	+	0.693517i	$0.756060\pi$
$728$		0			0
$729$	0.313708			0.0116188
$730$		0			0
$731$	−9.98951	−	5.76745i	−0.369475	−	0.213317i
$732$		0			0
$733$	−13.6281	−	23.6045i	−0.503364	−	0.871853i	−0.999992	−	0.00388916i	$-0.998762\pi$
$733$	−13.6281	−	23.6045i	−0.503364	−	0.871853i	0.496628	−	0.867963i	$-0.334571\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.24264	+	7.34847i	0.156280	+	0.270684i
$738$		0			0
$739$	−12.1213	+	20.9947i	−0.445890	+	0.772304i	−0.998114	−	0.0613918i	$-0.980446\pi$
$739$	−12.1213	+	20.9947i	−0.445890	+	0.772304i	0.552224	+	0.833696i	$0.313779\pi$
$740$		0			0
$741$	7.83095			0.287677
$742$		0			0
$743$		−	38.6086i		−	1.41641i	−0.706005	−	0.708207i	$-0.749504\pi$
$743$		−	38.6086i		−	1.41641i	0.706005	−	0.708207i	$-0.250496\pi$
$744$		0			0
$745$	−12.1583	−	7.01962i	−0.445447	−	0.257179i
$746$		0			0
$747$	19.3162	−	11.1522i	0.706743	−	0.408038i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	32.7473	−	18.9066i	1.19496	−	0.689913i	0.235536	−	0.971866i	$-0.424315\pi$
$751$	32.7473	−	18.9066i	1.19496	−	0.689913i	0.959428	+	0.281953i	$0.0909821\pi$
$752$		0			0
$753$	8.19239	−	14.1896i	0.298547	−	0.517099i
$754$		0			0
$755$			30.9861i			1.12770i
$756$		0			0
$757$		−	27.4169i		−	0.996485i	−0.867038	−	0.498242i	$-0.833979\pi$
$757$		−	27.4169i		−	0.996485i	0.867038	−	0.498242i	$-0.166021\pi$
$758$		0			0
$759$	−9.08538	+	15.7363i	−0.329778	+	0.571193i
$760$		0			0
$761$	−12.0446	+	6.95396i	−0.436617	+	0.252081i	−0.702162	−	0.712018i	$-0.747782\pi$
$761$	−12.0446	+	6.95396i	−0.436617	+	0.252081i	0.265545	+	0.964099i	$0.414448\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−28.2455	+	16.3075i	−1.02122	+	0.589601i
$766$		0			0
$767$	28.2455	+	16.3075i	1.01989	+	0.588831i
$768$		0			0
$769$		−	1.21371i		−	0.0437674i	−0.999761	−	0.0218837i	$-0.993034\pi$
$769$		−	1.21371i		−	0.0437674i	0.999761	−	0.0218837i	$-0.00696636\pi$
$770$		0			0
$771$	−8.38478			−0.301970
$772$		0			0
$773$	−8.82558	+	15.2864i	−0.317434	+	0.549812i	−0.979952	−	0.199234i	$-0.936155\pi$
$773$	−8.82558	+	15.2864i	−0.317434	+	0.549812i	0.662518	+	0.749046i	$0.269488\pi$
$774$		0			0
$775$	−21.5666	−	37.3545i	−0.774696	−	1.34181i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−11.9497	−	20.6976i	−0.428144	−	0.741567i
$780$		0			0
$781$	−53.1651	−	30.6949i	−1.90240	−	1.09835i
$782$		0			0
$783$	−23.1885			−0.828689
$784$		0			0
$785$	−22.1421			−0.790287
$786$		0			0
$787$	5.57717	+	3.21998i	0.198805	+	0.114780i	0.596098	−	0.802912i	$-0.296717\pi$
$787$	5.57717	+	3.21998i	0.198805	+	0.114780i	−0.397293	+	0.917692i	$0.630050\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	11.0711	+	19.1757i	0.393145	+	0.680947i
$794$		0			0
$795$	3.79899	−	6.58004i	0.134736	−	0.233370i
$796$		0			0
$797$	23.7081			0.839783			0.419892	−	0.907574i	$-0.362068\pi$
$797$	23.7081			0.839783			0.419892	+	0.907574i	$0.362068\pi$
$798$		0			0
$799$		−	27.0192i		−	0.955872i
$800$		0			0
$801$	−5.18889	−	2.99581i	−0.183341	−	0.105852i
$802$		0			0
$803$	−12.4134	+	7.16687i	−0.438058	+	0.252913i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	3.67029	−	2.11904i	0.129200	−	0.0745938i
$808$		0			0
$809$	17.5355	−	30.3724i	0.616517	−	1.06784i	−0.373600	−	0.927590i	$-0.621877\pi$
$809$	17.5355	−	30.3724i	0.616517	−	1.06784i	0.990116	−	0.140248i	$-0.0447900\pi$
$810$		0			0
$811$		−	32.6800i		−	1.14755i	−0.819013	−	0.573775i	$-0.805478\pi$
$811$		−	32.6800i		−	1.14755i	0.819013	−	0.573775i	$-0.194522\pi$
$812$		0			0
$813$			1.35778i			0.0476196i
$814$		0			0
$815$	−8.19837	+	14.2000i	−0.287176	+	0.497404i
$816$		0			0
$817$	7.56565	−	4.36803i	0.264689	−	0.152818i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−25.0623	+	14.4697i	−0.874680	+	0.504996i	−0.868900	−	0.494987i	$-0.835173\pi$
$821$	−25.0623	+	14.4697i	−0.874680	+	0.504996i	−0.00577905	+	0.999983i	$0.501840\pi$
$822$		0			0
$823$	22.2235	+	12.8307i	0.774661	+	0.447251i	0.834535	−	0.550955i	$-0.185736\pi$
$823$	22.2235	+	12.8307i	0.774661	+	0.447251i	−0.0598737	+	0.998206i	$0.519070\pi$
$824$		0			0
$825$			13.5458i			0.471605i
$826$		0			0
$827$	1.65685			0.0576145			0.0288072	−	0.999585i	$-0.490829\pi$
$827$	1.65685			0.0576145			0.0288072	+	0.999585i	$0.490829\pi$
$828$		0			0
$829$	−13.4759	+	23.3409i	−0.468037	+	0.810664i	−0.999333	−	0.0365227i	$-0.988372\pi$
$829$	−13.4759	+	23.3409i	−0.468037	+	0.810664i	0.531296	+	0.847186i	$0.321705\pi$
$830$		0			0
$831$	3.76329	+	6.51821i	0.130547	+	0.226114i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−12.9706	−	22.4657i	−0.448865	−	0.777457i
$836$		0			0
$837$	37.1064	+	21.4234i	1.28258	+	0.740500i
$838$		0			0
$839$	16.3967			0.566078			0.283039	−	0.959108i	$-0.408657\pi$
$839$	16.3967			0.566078			0.283039	+	0.959108i	$0.408657\pi$
$840$		0			0
$841$	−2.31371			−0.0797831
$842$		0			0
$843$	−7.33820	−	4.23671i	−0.252741	−	0.145920i
$844$		0			0
$845$	5.79712	+	10.0409i	0.199427	+	0.345418i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−9.87868	−	17.1104i	−0.339035	−	0.587227i
$850$		0			0
$851$	6.48528	−	11.2328i	0.222313	−	0.385057i
$852$		0			0
$853$	−19.4252			−0.665106			−0.332553	−	0.943085i	$-0.607910\pi$
$853$	−19.4252			−0.665106			−0.332553	+	0.943085i	$0.607910\pi$
$854$		0			0
$855$		−	24.7013i		−	0.844768i
$856$		0			0
$857$	33.5101	+	19.3471i	1.14468	+	0.660884i	0.947586	−	0.319500i	$-0.103515\pi$
$857$	33.5101	+	19.3471i	1.14468	+	0.660884i	0.197098	+	0.980384i	$0.436848\pi$
$858$		0			0
$859$	−2.60420	+	1.50354i	−0.0888543	+	0.0513000i	−0.543769	−	0.839235i	$-0.683003\pi$
$859$	−2.60420	+	1.50354i	−0.0888543	+	0.0513000i	0.454915	+	0.890535i	$0.349670\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−29.0770	+	16.7876i	−0.989792	+	0.571456i	−0.905212	−	0.424960i	$-0.860288\pi$
$863$	−29.0770	+	16.7876i	−0.989792	+	0.571456i	−0.0845796	+	0.996417i	$0.526955\pi$
$864$		0			0
$865$	14.8701	−	25.7557i	0.505597	−	0.875720i
$866$		0			0
$867$			2.21918i			0.0753672i
$868$		0			0
$869$		−	47.4825i		−	1.61073i
$870$		0			0
$871$	3.02846	−	5.24545i	0.102615	−	0.177735i
$872$		0			0
$873$	−14.4019	+	8.31492i	−0.487429	+	0.281417i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−24.2308	+	13.9897i	−0.818216	+	0.472397i	−0.849801	−	0.527104i	$-0.823278\pi$
$877$	−24.2308	+	13.9897i	−0.818216	+	0.472397i	0.0315847	+	0.999501i	$0.489945\pi$
$878$		0			0
$879$	19.7291	+	11.3906i	0.665444	+	0.384195i
$880$		0			0
$881$		−	4.19825i		−	0.141443i	−0.997496	−	0.0707214i	$-0.977470\pi$
$881$		−	4.19825i		−	0.141443i	0.997496	−	0.0707214i	$-0.0225301\pi$
$882$		0			0
$883$	13.6569			0.459590			0.229795	−	0.973239i	$-0.426194\pi$
$883$	13.6569			0.459590			0.229795	+	0.973239i	$0.426194\pi$
$884$		0			0
$885$	−12.4813	+	21.6182i	−0.419553	+	0.726687i
$886$		0			0
$887$	−13.3683	−	23.1545i	−0.448863	−	0.777453i	0.549450	−	0.835527i	$-0.314837\pi$
$887$	−13.3683	−	23.1545i	−0.448863	−	0.777453i	−0.998312	+	0.0580740i	$0.981504\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	8.63604	+	14.9581i	0.289318	+	0.501114i
$892$		0			0
$893$	17.7217	+	10.2316i	0.593034	+	0.342389i
$894$		0			0
$895$	−7.09612			−0.237197
$896$		0			0
$897$	12.9706			0.433074
$898$		0			0
$899$	50.1084	+	28.9301i	1.67121	+	0.964873i
$900$		0			0
$901$	7.31135	+	12.6636i	0.243576	+	0.421887i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	13.7574	+	23.8284i	0.457310	+	0.792084i
$906$		0			0
$907$	18.4853	−	32.0174i	0.613794	−	1.06312i	−0.376801	−	0.926294i	$-0.622976\pi$
$907$	18.4853	−	32.0174i	0.613794	−	1.06312i	0.990595	−	0.136828i	$-0.0436907\pi$
$908$		0			0
$909$	27.9910			0.928402
$910$		0			0
$911$			27.9793i			0.926996i	0.886098	+	0.463498i	$0.153406\pi$
$911$			27.9793i			0.926996i	−0.886098	+	0.463498i	$0.846594\pi$
$912$		0			0
$913$	33.9455	+	19.5984i	1.12343	+	0.648614i
$914$		0			0
$915$	−14.6764	+	8.47343i	−0.485187	+	0.280123i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−12.5311	+	7.23486i	−0.413364	+	0.238656i	−0.692234	−	0.721673i	$-0.743373\pi$
$919$	−12.5311	+	7.23486i	−0.413364	+	0.238656i	0.278870	+	0.960329i	$0.410040\pi$
$920$		0			0
$921$	−8.87868	+	15.3783i	−0.292562	+	0.506733i
$922$		0			0
$923$			43.8210i			1.44238i
$924$		0			0
$925$		−	9.66922i		−	0.317922i
$926$		0			0
$927$	−5.16991	+	8.95454i	−0.169802	+	0.294106i
$928$		0			0
$929$	−6.51455	+	3.76118i	−0.213735	+	0.123400i	−0.603046	−	0.797706i	$-0.706047\pi$
$929$	−6.51455	+	3.76118i	−0.213735	+	0.123400i	0.389311	+	0.921106i	$0.372713\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−2.35175	+	1.35778i	−0.0769929	+	0.0444519i
$934$		0			0
$935$	−49.6375	−	28.6582i	−1.62332	−	0.937224i
$936$		0			0
$937$		−	12.0376i		−	0.393252i	−0.980479	−	0.196626i	$-0.937001\pi$
$937$		−	12.0376i		−	0.393252i	0.980479	−	0.196626i	$-0.0629985\pi$
$938$		0			0
$939$	26.5858			0.867594
$940$		0			0
$941$	−8.30598	+	14.3864i	−0.270767	+	0.468983i	−0.969058	−	0.246831i	$-0.920611\pi$
$941$	−8.30598	+	14.3864i	−0.270767	+	0.468983i	0.698291	+	0.715814i	$0.253944\pi$
$942$		0			0
$943$	−19.7926	−	34.2818i	−0.644536	−	1.11637i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	8.60660	+	14.9071i	0.279677	+	0.484415i	0.971304	−	0.237840i	$-0.0764393\pi$
$947$	8.60660	+	14.9071i	0.279677	+	0.484415i	−0.691627	+	0.722254i	$0.743106\pi$
$948$		0			0
$949$	8.86085	+	5.11582i	0.287635	+	0.166066i
$950$		0			0
$951$	−12.1138			−0.392818
$952$		0			0
$953$	50.6274			1.63998			0.819991	−	0.572376i	$-0.193978\pi$
$953$	50.6274			1.63998			0.819991	+	0.572376i	$0.193978\pi$
$954$		0			0
$955$	8.59724	+	4.96362i	0.278200	+	0.160619i
$956$		0			0
$957$	−9.08538	−	15.7363i	−0.293689	−	0.508684i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−37.9558	−	65.7415i	−1.22438	−	2.12069i
$962$		0			0
$963$	−4.00000	+	6.92820i	−0.128898	+	0.223258i
$964$		0			0
$965$	−28.5106			−0.917788
$966$		0			0
$967$		−	16.7876i		−	0.539853i	−0.962881	−	0.269926i	$-0.913001\pi$
$967$		−	16.7876i		−	0.539853i	0.962881	−	0.269926i	$-0.0869994\pi$
$968$		0			0
$969$	−9.98951	−	5.76745i	−0.320909	−	0.185277i
$970$		0			0
$971$	−1.27855	+	0.738170i	−0.0410306	+	0.0236890i	−0.520375	−	0.853938i	$-0.674208\pi$
$971$	−1.27855	+	0.738170i	−0.0410306	+	0.0236890i	0.479344	+	0.877627i	$0.340874\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	8.37379	−	4.83461i	0.268176	−	0.154831i
$976$		0			0
$977$	−6.12132	+	10.6024i	−0.195838	+	0.339202i	−0.947175	−	0.320717i	$-0.896076\pi$
$977$	−6.12132	+	10.6024i	−0.195838	+	0.339202i	0.751337	+	0.659919i	$0.229409\pi$
$978$		0			0
$979$		−	10.5294i		−	0.336522i
$980$		0			0
$981$		−	13.5096i		−	0.431329i
$982$		0			0
$983$	5.16991	−	8.95454i	0.164894	−	0.285605i	−0.771723	−	0.635958i	$-0.780605\pi$
$983$	5.16991	−	8.95454i	0.164894	−	0.285605i	0.936618	+	0.350353i	$0.113938\pi$
$984$		0			0
$985$	50.1084	−	28.9301i	1.59659	−	0.921789i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	12.5311	−	7.23486i	0.398467	−	0.230055i
$990$		0			0
$991$	−18.2088	−	10.5128i	−0.578421	−	0.333951i	0.182085	−	0.983283i	$-0.441715\pi$
$991$	−18.2088	−	10.5128i	−0.578421	−	0.333951i	−0.760505	+	0.649332i	$0.775049\pi$
$992$		0			0
$993$		−	2.35049i		−	0.0745907i
$994$		0			0
$995$	−49.6569			−1.57423
$996$		0			0
$997$	13.1085	−	22.7045i	0.415149	−	0.719060i	−0.580295	−	0.814407i	$-0.697063\pi$
$997$	13.1085	−	22.7045i	0.415149	−	0.719060i	0.995444	+	0.0953467i	$0.0303960\pi$
$998$		0			0
$999$	4.80249	+	8.31816i	0.151944	+	0.263175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1568.2.q.h.815.5		16
4.3	odd	2		392.2.m.h.227.7		16
7.2	even	3	inner	1568.2.q.h.1391.3		16
7.3	odd	6		1568.2.e.d.783.5		8
7.4	even	3		1568.2.e.d.783.4		8
7.5	odd	6	inner	1568.2.q.h.1391.6		16
7.6	odd	2	inner	1568.2.q.h.815.4		16
8.3	odd	2	inner	1568.2.q.h.815.6		16
8.5	even	2		392.2.m.h.227.3		16
28.3	even	6		392.2.e.d.195.3	yes	8
28.11	odd	6		392.2.e.d.195.4	yes	8
28.19	even	6		392.2.m.h.19.3		16
28.23	odd	6		392.2.m.h.19.4		16
28.27	even	2		392.2.m.h.227.8		16
56.3	even	6		1568.2.e.d.783.6		8
56.5	odd	6		392.2.m.h.19.7		16
56.11	odd	6		1568.2.e.d.783.3		8
56.13	odd	2		392.2.m.h.227.4		16
56.19	even	6	inner	1568.2.q.h.1391.5		16
56.27	even	2	inner	1568.2.q.h.815.3		16
56.37	even	6		392.2.m.h.19.8		16
56.45	odd	6		392.2.e.d.195.1	✓	8
56.51	odd	6	inner	1568.2.q.h.1391.4		16
56.53	even	6		392.2.e.d.195.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.e.d.195.1	✓	8	56.45	odd	6
392.2.e.d.195.2	yes	8	56.53	even	6
392.2.e.d.195.3	yes	8	28.3	even	6
392.2.e.d.195.4	yes	8	28.11	odd	6
392.2.m.h.19.3		16	28.19	even	6
392.2.m.h.19.4		16	28.23	odd	6
392.2.m.h.19.7		16	56.5	odd	6
392.2.m.h.19.8		16	56.37	even	6
392.2.m.h.227.3		16	8.5	even	2
392.2.m.h.227.4		16	56.13	odd	2
392.2.m.h.227.7		16	4.3	odd	2
392.2.m.h.227.8		16	28.27	even	2
1568.2.e.d.783.3		8	56.11	odd	6
1568.2.e.d.783.4		8	7.4	even	3
1568.2.e.d.783.5		8	7.3	odd	6
1568.2.e.d.783.6		8	56.3	even	6
1568.2.q.h.815.3		16	56.27	even	2	inner
1568.2.q.h.815.4		16	7.6	odd	2	inner
1568.2.q.h.815.5		16	1.1	even	1	trivial
1568.2.q.h.815.6		16	8.3	odd	2	inner
1568.2.q.h.1391.3		16	7.2	even	3	inner
1568.2.q.h.1391.4		16	56.51	odd	6	inner
1568.2.q.h.1391.5		16	56.19	even	6	inner
1568.2.q.h.1391.6		16	7.5	odd	6	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:	\( N \)	\(=\)	\( 1568 = 2^{5} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1568.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.662827 + 0.382683i) q^{3} +(-1.51423 - 2.62272i) q^{5} +(-1.20711 - 2.09077i) q^{9} +(2.12132 - 3.67423i) q^{11} -3.02846 q^{13} -2.31788i q^{15} +(3.86324 + 2.23044i) q^{17} +(-2.92586 + 1.68925i) q^{19} +(-4.84616 + 2.79793i) q^{23} +(-2.08579 + 3.61269i) q^{25} -4.14386i q^{27} -5.59587i q^{29} +(-5.16991 + 8.95454i) q^{31} +(2.81214 - 1.62359i) q^{33} +(-2.00735 + 1.15894i) q^{37} +(-2.00735 - 1.15894i) q^{39} +7.07401i q^{41} -2.58579 q^{43} +(-3.65568 + 6.33182i) q^{45} +(-3.02846 - 5.24545i) q^{47} +(1.70711 + 2.95680i) q^{51} +(2.83882 + 1.63899i) q^{53} -12.8487 q^{55} -2.58579 q^{57} +(-9.32669 - 5.38476i) q^{59} +(-3.65568 - 6.33182i) q^{61} +(4.58579 + 7.94282i) q^{65} +(-1.00000 + 1.73205i) q^{67} -4.28289 q^{69} -14.4697i q^{71} +(-2.92586 - 1.68925i) q^{73} +(-2.76503 + 1.59639i) q^{75} +(9.69232 - 5.59587i) q^{79} +(-2.03553 + 3.52565i) q^{81} +9.23880i q^{83} -13.5096i q^{85} +(2.14144 - 3.70909i) q^{87} +(2.14931 - 1.24090i) q^{89} +(-6.85351 + 3.95687i) q^{93} +(8.86085 + 5.11582i) q^{95} -6.88830i q^{97} -10.2426 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{9} - 56 q^{25} - 64 q^{43} + 16 q^{51} - 64 q^{57} + 96 q^{65} - 16 q^{67} + 24 q^{81} - 96 q^{99}+O(q^{100}) \) 16 * q - 8 * q^9 - 56 * q^25 - 64 * q^43 + 16 * q^51 - 64 * q^57 + 96 * q^65 - 16 * q^67 + 24 * q^81 - 96 * q^99

Introduction

L-functions

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