LMFDB - Embedded newform 900.2.n.c.721.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(181,900)] 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("900.181"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.n (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 24 x^{9} + 93 x^{8} - 6 x^{7} + 342 x^{6} + 786 x^{5} + 1473 x^{4} + \cdots + 16 $ x^12 - 3x^11 + 13x^10 - 24x^9 + 93x^8 - 6x^7 + 342x^6 + 786x^5 + 1473x^4 + 84x^3 + 688x^2 + 168*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 100)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			721.1
Root			$0.838695 + 2.58124i$ of defining polynomial
Character	$\chi$	$=$	900.721
Dual form			900.2.n.c.181.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.548020 + 2.16787i) q^{5} -4.40288 q^{7} +(0.516162 - 1.58858i) q^{11} +(-0.795501 - 2.44830i) q^{13} +(0.239003 - 0.173646i) q^{17} +(3.13970 - 2.28113i) q^{19} +(2.71760 - 8.36392i) q^{23} +(-4.39935 - 2.37607i) q^{25} +(0.177592 + 0.129028i) q^{29} +(5.90981 - 4.29372i) q^{31} +(2.41286 - 9.54488i) q^{35} +(-0.231242 - 0.711690i) q^{37} +(0.947030 + 2.91466i) q^{41} -0.913208 q^{43} +(0.00570791 + 0.00414704i) q^{47} +12.3853 q^{49} +(-9.20313 - 6.68646i) q^{53} +(3.16098 + 1.98955i) q^{55} +(-0.635908 - 1.95712i) q^{59} +(-3.52338 + 10.8438i) q^{61} +(5.74355 - 0.382828i) q^{65} +(-4.94968 + 3.59615i) q^{67} +(-6.51168 - 4.73101i) q^{71} +(1.08475 - 3.33853i) q^{73} +(-2.27260 + 6.99434i) q^{77} +(-9.42807 - 6.84989i) q^{79} +(2.30779 - 1.67671i) q^{83} +(0.245464 + 0.613289i) q^{85} +(1.02955 - 3.16864i) q^{89} +(3.50249 + 10.7796i) q^{91} +(3.22458 + 8.05658i) q^{95} +(-8.73973 - 6.34979i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{5} - 2 q^{7} + 5 q^{11} - 2 q^{13} - q^{17} - 8 q^{19} + 6 q^{23} - 26 q^{25} + 18 q^{29} + 12 q^{31} + 3 q^{35} + 13 q^{37} + 23 q^{41} + 50 q^{43} - q^{47} + 34 q^{49} - 21 q^{53} + 5 q^{55}+ \cdots - 7 q^{97}+O(q^{100}) $ 12 * q + 4 * q^5 - 2 * q^7 + 5 * q^11 - 2 * q^13 - q^17 - 8 * q^19 + 6 * q^23 - 26 * q^25 + 18 * q^29 + 12 * q^31 + 3 * q^35 + 13 * q^37 + 23 * q^41 + 50 * q^43 - q^47 + 34 * q^49 - 21 * q^53 + 5 * q^55 - 9 * q^59 - 26 * q^61 + 18 * q^65 - 37 * q^67 - 21 * q^71 + 18 * q^73 + 60 * q^77 - 24 * q^79 + 46 * q^83 - 16 * q^85 + 2 * q^89 - 32 * q^91 - 6 * q^95 - 7 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$5$	−0.548020	+	2.16787i	−0.245082	+	0.969502i
$5$	−0.548020	+	2.16787i	−0.245082	+	0.969502i
$6$		0			0
$7$	−4.40288			−1.66413			−0.832066	−	0.554677i	$-0.812842\pi$
$7$	−4.40288			−1.66413			−0.832066	+	0.554677i	$0.812842\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.516162	−	1.58858i	0.155629	−	0.478976i	−0.842595	−	0.538547i	$-0.818973\pi$
$11$	0.516162	−	1.58858i	0.155629	−	0.478976i	0.998224	+	0.0595715i	$0.0189734\pi$
$12$		0			0
$13$	−0.795501	−	2.44830i	−0.220632	−	0.679036i	−0.998706	−	0.0508628i	$-0.983803\pi$
$13$	−0.795501	−	2.44830i	−0.220632	−	0.679036i	0.778073	−	0.628173i	$-0.216197\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.239003	−	0.173646i	0.0579667	−	0.0421153i	−0.558425	−	0.829555i	$-0.688594\pi$
$17$	0.239003	−	0.173646i	0.0579667	−	0.0421153i	0.616391	+	0.787440i	$0.288594\pi$
$18$		0			0
$19$	3.13970	−	2.28113i	0.720297	−	0.523326i	−0.166182	−	0.986095i	$-0.553144\pi$
$19$	3.13970	−	2.28113i	0.720297	−	0.523326i	0.886479	+	0.462769i	$0.153144\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.71760	−	8.36392i	0.566659	−	1.74400i	−0.0963111	−	0.995351i	$-0.530704\pi$
$23$	2.71760	−	8.36392i	0.566659	−	1.74400i	0.662970	−	0.748646i	$-0.269296\pi$
$24$		0			0
$25$	−4.39935	−	2.37607i	−0.879870	−	0.475215i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.177592	+	0.129028i	0.0329779	+	0.0239599i	0.604152	−	0.796869i	$-0.293512\pi$
$29$	0.177592	+	0.129028i	0.0329779	+	0.0239599i	−0.571174	+	0.820829i	$0.693512\pi$
$30$		0			0
$31$	5.90981	−	4.29372i	1.06143	−	0.771176i	0.0870795	−	0.996201i	$-0.472247\pi$
$31$	5.90981	−	4.29372i	1.06143	−	0.771176i	0.974353	+	0.225026i	$0.0722466\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.41286	−	9.54488i	0.407849	−	1.61338i
$36$		0			0
$37$	−0.231242	−	0.711690i	−0.0380160	−	0.117001i	0.930248	−	0.366932i	$-0.119592\pi$
$37$	−0.231242	−	0.711690i	−0.0380160	−	0.117001i	−0.968264	+	0.249931i	$0.919592\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.947030	+	2.91466i	0.147901	+	0.455193i	0.997373	−	0.0724415i	$-0.0230791\pi$
$41$	0.947030	+	2.91466i	0.147901	+	0.455193i	−0.849471	+	0.527635i	$0.823079\pi$
$42$		0			0
$43$	−0.913208			−0.139263			−0.0696315	−	0.997573i	$-0.522182\pi$
$43$	−0.913208			−0.139263			−0.0696315	+	0.997573i	$0.522182\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.00570791	+	0.00414704i	0.000832584	+	0.000604907i	0.588201	−	0.808714i	$-0.299836\pi$
$47$	0.00570791	+	0.00414704i	0.000832584	+	0.000604907i	−0.587369	+	0.809319i	$0.699836\pi$
$48$		0			0
$49$	12.3853			1.76933
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−9.20313	−	6.68646i	−1.26415	−	0.918457i	−0.265193	−	0.964195i	$-0.585436\pi$
$53$	−9.20313	−	6.68646i	−1.26415	−	0.918457i	−0.998953	+	0.0457387i	$0.985436\pi$
$54$		0			0
$55$	3.16098	+	1.98955i	0.426226	+	0.268271i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.635908	−	1.95712i	−0.0827882	−	0.254796i	0.901091	−	0.433630i	$-0.142767\pi$
$59$	−0.635908	−	1.95712i	−0.0827882	−	0.254796i	−0.983879	+	0.178834i	$0.942767\pi$
$60$		0			0
$61$	−3.52338	+	10.8438i	−0.451123	+	1.38841i	0.424505	+	0.905426i	$0.360448\pi$
$61$	−3.52338	+	10.8438i	−0.451123	+	1.38841i	−0.875628	+	0.482987i	$0.839552\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.74355	−	0.382828i	0.712400	−	0.0474840i
$66$		0			0
$67$	−4.94968	+	3.59615i	−0.604699	+	0.439340i	−0.847544	−	0.530725i	$-0.821920\pi$
$67$	−4.94968	+	3.59615i	−0.604699	+	0.439340i	0.242844	+	0.970065i	$0.421920\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.51168	−	4.73101i	−0.772794	−	0.561468i	0.130013	−	0.991512i	$-0.458498\pi$
$71$	−6.51168	−	4.73101i	−0.772794	−	0.561468i	−0.902808	+	0.430044i	$0.858498\pi$
$72$		0			0
$73$	1.08475	−	3.33853i	0.126961	−	0.390745i	−0.867292	−	0.497799i	$-0.834142\pi$
$73$	1.08475	−	3.33853i	0.126961	−	0.390745i	0.994253	+	0.107054i	$0.0341418\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.27260	+	6.99434i	−0.258987	+	0.797079i
$78$		0			0
$79$	−9.42807	−	6.84989i	−1.06074	−	0.770673i	−0.0865155	−	0.996251i	$-0.527573\pi$
$79$	−9.42807	−	6.84989i	−1.06074	−	0.770673i	−0.974225	+	0.225577i	$0.927573\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.30779	−	1.67671i	0.253313	−	0.184043i	−0.453881	−	0.891062i	$-0.649961\pi$
$83$	2.30779	−	1.67671i	0.253313	−	0.184043i	0.707194	+	0.707020i	$0.249961\pi$
$84$		0			0
$85$	0.245464	+	0.613289i	0.0266243	+	0.0665205i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.02955	−	3.16864i	0.109132	−	0.335875i	−0.881546	−	0.472099i	$-0.843497\pi$
$89$	1.02955	−	3.16864i	0.109132	−	0.335875i	0.990678	+	0.136224i	$0.0434966\pi$
$90$		0			0
$91$	3.50249	+	10.7796i	0.367161	+	1.13001i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.22458	+	8.05658i	0.330834	+	0.826587i
$96$		0			0
$97$	−8.73973	−	6.34979i	−0.887385	−	0.644723i	0.0478096	−	0.998856i	$-0.484776\pi$
$97$	−8.73973	−	6.34979i	−0.887385	−	0.644723i	−0.935195	+	0.354133i	$0.884776\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−11.0970			−1.10419			−0.552095	−	0.833781i	$-0.686171\pi$
$101$	−11.0970			−1.10419			−0.552095	+	0.833781i	$0.686171\pi$
$102$		0			0
$103$	−6.12368	−	4.44911i	−0.603384	−	0.438384i	0.243694	−	0.969852i	$-0.421641\pi$
$103$	−6.12368	−	4.44911i	−0.603384	−	0.438384i	−0.847078	+	0.531468i	$0.821641\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.82026			0.175972			0.0879858	−	0.996122i	$-0.471957\pi$
$107$	1.82026			0.175972			0.0879858	+	0.996122i	$0.471957\pi$
$108$		0			0
$109$	−3.69779	−	11.3806i	−0.354184	−	1.09007i	−0.956481	−	0.291794i	$-0.905748\pi$
$109$	−3.69779	−	11.3806i	−0.354184	−	1.09007i	0.602297	−	0.798272i	$-0.294252\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.70798	+	11.4120i	0.348817	+	1.07355i	0.959508	+	0.281680i	$0.0908917\pi$
$113$	3.70798	+	11.4120i	0.348817	+	1.07355i	−0.610691	+	0.791869i	$0.709108\pi$
$114$		0			0
$115$	16.6426	+	10.4750i	1.55193	+	0.976799i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.05230	+	0.764541i	−0.0964642	+	0.0700854i
$120$		0			0
$121$	6.64202	+	4.82571i	0.603820	+	0.438701i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	7.56196	−	8.23509i	0.676362	−	0.736569i
$126$		0			0
$127$	1.53732	−	4.73140i	0.136415	−	0.419844i	−0.859392	−	0.511317i	$-0.829158\pi$
$127$	1.53732	−	4.73140i	0.136415	−	0.419844i	0.995808	+	0.0914736i	$0.0291577\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	15.4346	−	11.2139i	1.34853	−	0.979765i	0.349447	−	0.936956i	$-0.386369\pi$
$131$	15.4346	−	11.2139i	1.34853	−	0.979765i	0.999083	−	0.0428087i	$-0.0136306\pi$
$132$		0			0
$133$	−13.8237	+	10.0435i	−1.19867	+	0.870884i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.80931	−	8.64616i	−0.240015	−	0.738691i	−0.996416	−	0.0845830i	$-0.973044\pi$
$137$	−2.80931	−	8.64616i	−0.240015	−	0.738691i	0.756401	−	0.654108i	$-0.226956\pi$
$138$		0			0
$139$	4.12063	−	12.6820i	0.349508	−	1.07567i	−0.609618	−	0.792695i	$-0.708677\pi$
$139$	4.12063	−	12.6820i	0.349508	−	1.07567i	0.959126	−	0.282979i	$-0.0913227\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.29993			−0.359578
$144$		0			0
$145$	−0.377040	+	0.314286i	−0.0313115	+	0.0261001i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.47079			−0.530108			−0.265054	−	0.964234i	$-0.585390\pi$
$149$	−6.47079			−0.530108			−0.265054	+	0.964234i	$0.585390\pi$
$150$		0			0
$151$	−11.0604			−0.900086			−0.450043	−	0.893007i	$-0.648591\pi$
$151$	−11.0604			−0.900086			−0.450043	+	0.893007i	$0.648591\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	6.06956	+	15.1648i	0.487519	+	1.21806i
$156$		0			0
$157$	6.26300			0.499842			0.249921	−	0.968266i	$-0.419595\pi$
$157$	6.26300			0.499842			0.249921	+	0.968266i	$0.419595\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−11.9653	+	36.8253i	−0.942995	+	2.90224i
$162$		0			0
$163$	−1.25630	−	3.86650i	−0.0984012	−	0.302848i	0.889724	−	0.456499i	$-0.150897\pi$
$163$	−1.25630	−	3.86650i	−0.0984012	−	0.302848i	−0.988125	+	0.153651i	$0.950897\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−16.0147	+	11.6354i	−1.23926	+	0.900372i	−0.997549	−	0.0699770i	$-0.977707\pi$
$167$	−16.0147	+	11.6354i	−1.23926	+	0.900372i	−0.241707	+	0.970349i	$0.577707\pi$
$168$		0			0
$169$	5.15587	−	3.74596i	0.396605	−	0.288151i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.402408	+	1.23849i	−0.0305945	+	0.0941603i	−0.965188	−	0.261558i	$-0.915764\pi$
$173$	−0.402408	+	1.23849i	−0.0305945	+	0.0941603i	0.934593	+	0.355718i	$0.115764\pi$
$174$		0			0
$175$	19.3698	+	10.4616i	1.46422	+	0.790820i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	17.2951	+	12.5657i	1.29270	+	0.939202i	0.999856	−	0.0169586i	$-0.00539836\pi$
$179$	17.2951	+	12.5657i	1.29270	+	0.939202i	0.292844	+	0.956160i	$0.405398\pi$
$180$		0			0
$181$	−12.3017	+	8.93773i	−0.914381	+	0.664337i	−0.942119	−	0.335279i	$-0.891170\pi$
$181$	−12.3017	+	8.93773i	−0.914381	+	0.664337i	0.0277381	+	0.999615i	$0.491170\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.66958	−	0.111283i	0.122750	−	0.00818172i
$186$		0			0
$187$	−0.152486	−	0.469305i	−0.0111509	−	0.0343190i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.98276	+	15.3353i	0.360540	+	1.10963i	0.952727	+	0.303827i	$0.0982644\pi$
$191$	4.98276	+	15.3353i	0.360540	+	1.10963i	−0.592188	+	0.805800i	$0.701736\pi$
$192$		0			0
$193$	10.3557			0.745420			0.372710	−	0.927948i	$-0.378429\pi$
$193$	10.3557			0.745420			0.372710	+	0.927948i	$0.378429\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	16.2595	+	11.8133i	1.15844	+	0.841659i	0.989581	−	0.143980i	$-0.0459901\pi$
$197$	16.2595	+	11.8133i	1.15844	+	0.841659i	0.168864	+	0.985639i	$0.445990\pi$
$198$		0			0
$199$	2.82095			0.199972			0.0999859	−	0.994989i	$-0.468120\pi$
$199$	2.82095			0.199972			0.0999859	+	0.994989i	$0.468120\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.781915	−	0.568094i	−0.0548797	−	0.0398724i
$204$		0			0
$205$	−6.83760	+	0.455750i	−0.477559	+	0.0318310i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.00316	−	6.16510i	−0.138562	−	0.426449i
$210$		0			0
$211$	−2.68797	+	8.27273i	−0.185048	+	0.569518i	−0.999949	−	0.0100813i	$-0.996791\pi$
$211$	−2.68797	+	8.27273i	−0.185048	+	0.569518i	0.814902	+	0.579599i	$0.196791\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.500456	−	1.97972i	0.0341308	−	0.135016i
$216$		0			0
$217$	−26.0202	+	18.9048i	−1.76636	+	1.28334i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.615264	−	0.447015i	−0.0413871	−	0.0300695i
$222$		0			0
$223$	3.00568	−	9.25053i	0.201275	−	0.619461i	−0.798571	−	0.601901i	$-0.794410\pi$
$223$	3.00568	−	9.25053i	0.201275	−	0.619461i	0.999846	−	0.0175601i	$-0.00558984\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.68733	−	8.27076i	0.178365	−	0.548950i	−0.821407	−	0.570343i	$-0.806810\pi$
$227$	2.68733	−	8.27076i	0.178365	−	0.548950i	0.999771	+	0.0213934i	$0.00681025\pi$
$228$		0			0
$229$	10.9755	+	7.97420i	0.725284	+	0.526950i	0.888068	−	0.459712i	$-0.152047\pi$
$229$	10.9755	+	7.97420i	0.725284	+	0.526950i	−0.162784	+	0.986662i	$0.552047\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.7120	+	9.23583i	−0.832793	+	0.605060i	−0.920348	−	0.391100i	$-0.872095\pi$
$233$	−12.7120	+	9.23583i	−0.832793	+	0.605060i	0.0875552	+	0.996160i	$0.472095\pi$
$234$		0			0
$235$	−0.0121183	+	0.0101014i	−0.000790510	+	0.000658940i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.67480	−	20.5429i	0.431757	−	1.32881i	−0.464617	−	0.885512i	$-0.653808\pi$
$239$	6.67480	−	20.5429i	0.431757	−	1.32881i	0.896374	−	0.443299i	$-0.146192\pi$
$240$		0			0
$241$	2.47318	+	7.61166i	0.159312	+	0.490310i	0.998572	−	0.0534188i	$-0.0170118\pi$
$241$	2.47318	+	7.61166i	0.159312	+	0.490310i	−0.839261	+	0.543729i	$0.817012\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−6.78741	+	26.8499i	−0.433632	+	1.71537i
$246$		0			0
$247$	−8.08252	−	5.87229i	−0.514278	−	0.373645i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.26202			0.0796582			0.0398291	−	0.999207i	$-0.487319\pi$
$251$	1.26202			0.0796582			0.0398291	+	0.999207i	$0.487319\pi$
$252$		0			0
$253$	−11.8840	−	8.63427i	−0.747144	−	0.542832i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−27.8198			−1.73535			−0.867676	−	0.497130i	$-0.834387\pi$
$257$	−27.8198			−1.73535			−0.867676	+	0.497130i	$0.834387\pi$
$258$		0			0
$259$	1.01813	+	3.13349i	0.0632636	+	0.194705i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.58904	−	17.2013i	−0.344635	−	1.06068i	−0.961779	−	0.273827i	$-0.911710\pi$
$263$	−5.58904	−	17.2013i	−0.344635	−	1.06068i	0.617144	−	0.786850i	$-0.288290\pi$
$264$		0			0
$265$	19.5389	−	16.2869i	1.20027	−	1.00050i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	9.88615	−	7.18271i	0.602769	−	0.437937i	−0.244092	−	0.969752i	$-0.578490\pi$
$269$	9.88615	−	7.18271i	0.602769	−	0.437937i	0.846861	+	0.531815i	$0.178490\pi$
$270$		0			0
$271$	−0.642434	−	0.466756i	−0.0390251	−	0.0283534i	0.568102	−	0.822958i	$-0.307678\pi$
$271$	−0.642434	−	0.466756i	−0.0390251	−	0.0283534i	−0.607127	+	0.794605i	$0.707678\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−6.04537	+	5.76229i	−0.364549	+	0.347479i
$276$		0			0
$277$	−7.98890	+	24.5873i	−0.480007	+	1.47731i	0.359078	+	0.933307i	$0.383091\pi$
$277$	−7.98890	+	24.5873i	−0.480007	+	1.47731i	−0.839085	+	0.544001i	$0.816909\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	14.1996	−	10.3166i	0.847080	−	0.615440i	−0.0772594	−	0.997011i	$-0.524617\pi$
$281$	14.1996	−	10.3166i	0.847080	−	0.615440i	0.924339	+	0.381571i	$0.124617\pi$
$282$		0			0
$283$	6.73824	−	4.89562i	0.400547	−	0.291014i	−0.369217	−	0.929343i	$-0.620374\pi$
$283$	6.73824	−	4.89562i	0.400547	−	0.291014i	0.769764	+	0.638329i	$0.220374\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.16966	−	12.8329i	−0.246127	−	0.757501i
$288$		0			0
$289$	−5.22632	+	16.0850i	−0.307431	+	0.946174i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	18.5010			1.08084			0.540421	−	0.841395i	$-0.318265\pi$
$293$	18.5010			1.08084			0.540421	+	0.841395i	$0.318265\pi$
$294$		0			0
$295$	4.59129	−	0.306025i	0.267315	−	0.0178175i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−22.6392			−1.30926
$300$		0			0
$301$	4.02074			0.231752
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−21.5772	−	13.5809i	−1.23551	−	0.777639i
$306$		0			0
$307$	2.36704			0.135094			0.0675469	−	0.997716i	$-0.478483\pi$
$307$	2.36704			0.135094			0.0675469	+	0.997716i	$0.478483\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.86977	−	5.75455i	0.106025	−	0.326311i	−0.883945	−	0.467591i	$-0.845122\pi$
$311$	1.86977	−	5.75455i	0.106025	−	0.326311i	0.989970	+	0.141281i	$0.0451220\pi$
$312$		0			0
$313$	−7.58326	−	23.3389i	−0.428631	−	1.31919i	−0.899474	−	0.436974i	$-0.856050\pi$
$313$	−7.58326	−	23.3389i	−0.428631	−	1.31919i	0.470843	−	0.882217i	$-0.343950\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.96032	+	1.42425i	−0.110102	+	0.0799941i	−0.641474	−	0.767145i	$-0.721677\pi$
$317$	−1.96032	+	1.42425i	−0.110102	+	0.0799941i	0.531372	+	0.847139i	$0.321677\pi$
$318$		0			0
$319$	0.296637	−	0.215520i	0.0166085	−	0.0120668i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	0.354290	−	1.09039i	0.0197132	−	0.0606710i
$324$		0			0
$325$	−2.31766	+	12.6611i	−0.128561	+	0.702311i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.0251312	−	0.0182589i	−0.00138553	−	0.00100665i
$330$		0			0
$331$	12.3919	−	9.00326i	0.681122	−	0.494864i	−0.192608	−	0.981276i	$-0.561695\pi$
$331$	12.3919	−	9.00326i	0.681122	−	0.494864i	0.873730	+	0.486412i	$0.161695\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.08348	−	12.7010i	−0.277740	−	0.693932i
$336$		0			0
$337$	7.00754	+	21.5670i	0.381725	+	1.17483i	0.938828	+	0.344385i	$0.111913\pi$
$337$	7.00754	+	21.5670i	0.381725	+	1.17483i	−0.557104	+	0.830443i	$0.688087\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−3.77052	−	11.6045i	−0.204185	−	0.628417i
$342$		0			0
$343$	−23.7110			−1.28027
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.88365	+	5.00126i	0.369534	+	0.268482i	0.757017	−	0.653395i	$-0.226656\pi$
$347$	6.88365	+	5.00126i	0.369534	+	0.268482i	−0.387484	+	0.921876i	$0.626656\pi$
$348$		0			0
$349$	23.5983			1.26319			0.631594	−	0.775300i	$-0.282401\pi$
$349$	23.5983			1.26319			0.631594	+	0.775300i	$0.282401\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.14507	−	3.73811i	−0.273845	−	0.198960i	0.442384	−	0.896826i	$-0.354133\pi$
$353$	−5.14507	−	3.73811i	−0.273845	−	0.198960i	−0.716228	+	0.697866i	$0.754133\pi$
$354$		0			0
$355$	13.8248	−	11.5238i	0.733743	−	0.611620i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.07611	+	27.9334i	0.479019	+	1.47427i	0.840460	+	0.541873i	$0.182285\pi$
$359$	9.07611	+	27.9334i	0.479019	+	1.47427i	−0.361441	+	0.932395i	$0.617715\pi$
$360$		0			0
$361$	−1.21714	+	3.74596i	−0.0640598	+	0.197156i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	6.64304	+	4.18119i	0.347712	+	0.218853i
$366$		0			0
$367$	−11.0641	+	8.03852i	−0.577540	+	0.419607i	−0.837836	−	0.545921i	$-0.816180\pi$
$367$	−11.0641	+	8.03852i	−0.577540	+	0.419607i	0.260296	+	0.965529i	$0.416180\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	40.5203	+	29.4397i	2.10371	+	1.52843i
$372$		0			0
$373$	4.60333	−	14.1676i	0.238352	−	0.733571i	−0.758307	−	0.651897i	$-0.773973\pi$
$373$	4.60333	−	14.1676i	0.238352	−	0.733571i	0.996659	−	0.0816739i	$-0.0260266\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.174625	−	0.537439i	0.00899363	−	0.0276795i
$378$		0			0
$379$	−10.5189	−	7.64241i	−0.540318	−	0.392564i	0.283885	−	0.958858i	$-0.408377\pi$
$379$	−10.5189	−	7.64241i	−0.540318	−	0.392564i	−0.824203	+	0.566294i	$0.808377\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.04621	−	0.760113i	0.0534586	−	0.0388400i	−0.560735	−	0.827995i	$-0.689481\pi$
$383$	1.04621	−	0.760113i	0.0534586	−	0.0388400i	0.614194	+	0.789155i	$0.289481\pi$
$384$		0			0
$385$	−13.9174	−	8.75974i	−0.709297	−	0.446438i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	5.35538	−	16.4822i	0.271529	−	0.835679i	−0.718588	−	0.695436i	$-0.755211\pi$
$389$	5.35538	−	16.4822i	0.271529	−	0.835679i	0.990117	−	0.140244i	$-0.0447886\pi$
$390$		0			0
$391$	−0.802844	−	2.47090i	−0.0406016	−	0.124959i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	20.0165	−	16.6850i	1.00714	−	0.839513i
$396$		0			0
$397$	21.6576	+	15.7352i	1.08696	+	0.789726i	0.978884	−	0.204416i	$-0.0655296\pi$
$397$	21.6576	+	15.7352i	1.08696	+	0.789726i	0.108080	+	0.994142i	$0.465530\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.50607			−0.274960			−0.137480	−	0.990505i	$-0.543900\pi$
$401$	−5.50607			−0.274960			−0.137480	+	0.990505i	$0.543900\pi$
$402$		0			0
$403$	−15.2136	−	11.0533i	−0.757842	−	0.550605i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.24994			−0.0619571
$408$		0			0
$409$	−4.32386	−	13.3075i	−0.213801	−	0.658012i	−0.999237	−	0.0390683i	$-0.987561\pi$
$409$	−4.32386	−	13.3075i	−0.213801	−	0.658012i	0.785436	−	0.618943i	$-0.212439\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	2.79983	+	8.61698i	0.137770	+	0.424014i
$414$		0			0
$415$	2.37018	+	5.92187i	0.116347	+	0.290693i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	13.7294	−	9.97500i	0.670726	−	0.487311i	−0.199542	−	0.979889i	$-0.563946\pi$
$419$	13.7294	−	9.97500i	0.670726	−	0.487311i	0.870268	+	0.492578i	$0.163946\pi$
$420$		0			0
$421$	−10.9487	−	7.95470i	−0.533607	−	0.387688i	0.288098	−	0.957601i	$-0.406977\pi$
$421$	−10.9487	−	7.95470i	−0.533607	−	0.387688i	−0.821705	+	0.569912i	$0.806977\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.46405	+	0.196039i	−0.0710169	+	0.00950931i
$426$		0			0
$427$	15.5130	−	47.7442i	0.750727	−	2.31050i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−18.7825	+	13.6463i	−0.904721	+	0.657318i	−0.939674	−	0.342071i	$-0.888872\pi$
$431$	−18.7825	+	13.6463i	−0.904721	+	0.657318i	0.0349532	+	0.999389i	$0.488872\pi$
$432$		0			0
$433$	30.7134	−	22.3146i	1.47599	−	1.07237i	0.497168	−	0.867654i	$-0.334373\pi$
$433$	30.7134	−	22.3146i	1.47599	−	1.07237i	0.978822	−	0.204715i	$-0.0656268\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.5467	−	32.4594i	−0.504517	−	1.55274i
$438$		0			0
$439$	−11.9315	+	36.7213i	−0.569458	+	1.75261i	0.0848602	+	0.996393i	$0.472956\pi$
$439$	−11.9315	+	36.7213i	−0.569458	+	1.75261i	−0.654318	+	0.756219i	$0.727044\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−22.5688			−1.07228			−0.536138	−	0.844130i	$-0.680117\pi$
$443$	−22.5688			−1.07228			−0.536138	+	0.844130i	$0.680117\pi$
$444$		0			0
$445$	6.30499	+	3.96842i	0.298885	+	0.188121i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	29.2091			1.37846			0.689232	−	0.724541i	$-0.257948\pi$
$449$	29.2091			1.37846			0.689232	+	0.724541i	$0.257948\pi$
$450$		0			0
$451$	5.11899			0.241044
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−25.2882	+	1.68555i	−1.18553	+	0.0790196i
$456$		0			0
$457$	−21.4154			−1.00177			−0.500885	−	0.865514i	$-0.666992\pi$
$457$	−21.4154			−1.00177			−0.500885	+	0.865514i	$0.666992\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	7.46239	−	22.9669i	0.347558	−	1.06967i	−0.612642	−	0.790361i	$-0.709893\pi$
$461$	7.46239	−	22.9669i	0.347558	−	1.06967i	0.960200	−	0.279313i	$-0.0901069\pi$
$462$		0			0
$463$	1.28333	+	3.94968i	0.0596414	+	0.183557i	0.976438	−	0.215796i	$-0.0692347\pi$
$463$	1.28333	+	3.94968i	0.0596414	+	0.183557i	−0.916797	+	0.399353i	$0.869235\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−14.5240	+	10.5523i	−0.672092	+	0.488304i	−0.870725	−	0.491770i	$-0.836350\pi$
$467$	−14.5240	+	10.5523i	−0.672092	+	0.488304i	0.198633	+	0.980074i	$0.436350\pi$
$468$		0			0
$469$	21.7928	−	15.8334i	1.00630	−	0.731119i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.471363	+	1.45071i	−0.0216733	+	0.0667035i
$474$		0			0
$475$	−19.2328	+	2.57531i	−0.882460	+	0.118163i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−15.2189	−	11.0571i	−0.695367	−	0.505214i	0.183053	−	0.983103i	$-0.441402\pi$
$479$	−15.2189	−	11.0571i	−0.695367	−	0.505214i	−0.878420	+	0.477889i	$0.841402\pi$
$480$		0			0
$481$	−1.55848	+	1.13230i	−0.0710605	+	0.0516285i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	18.5551	−	15.4668i	0.842543	−	0.702312i
$486$		0			0
$487$	−10.1834	−	31.3412i	−0.461452	−	1.42020i	−0.863390	−	0.504537i	$-0.831663\pi$
$487$	−10.1834	−	31.3412i	−0.461452	−	1.42020i	0.401937	−	0.915667i	$-0.368337\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−10.3651	−	31.9005i	−0.467771	−	1.43965i	−0.855464	−	0.517862i	$-0.826728\pi$
$491$	−10.3651	−	31.9005i	−0.467771	−	1.43965i	0.387693	−	0.921789i	$-0.373272\pi$
$492$		0			0
$493$	0.0648500			0.00292070
$494$		0			0
$495$		0			0
$496$		0			0
$497$	28.6701	+	20.8301i	1.28603	+	0.934357i
$498$		0			0
$499$	−13.4640			−0.602732			−0.301366	−	0.953509i	$-0.597443\pi$
$499$	−13.4640			−0.602732			−0.301366	+	0.953509i	$0.597443\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	3.84374	+	2.79264i	0.171384	+	0.124518i	0.670171	−	0.742207i	$-0.266221\pi$
$503$	3.84374	+	2.79264i	0.171384	+	0.124518i	−0.498787	+	0.866725i	$0.666221\pi$
$504$		0			0
$505$	6.08136	−	24.0568i	0.270617	−	1.07052i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−6.63417	−	20.4179i	−0.294055	−	0.905007i	−0.983537	−	0.180705i	$-0.942162\pi$
$509$	−6.63417	−	20.4179i	−0.294055	−	0.905007i	0.689483	−	0.724302i	$-0.257838\pi$
$510$		0			0
$511$	−4.77604	+	14.6991i	−0.211279	+	0.650251i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	13.0010	−	10.8372i	0.572893	−	0.477542i
$516$		0			0
$517$	0.00953411	−	0.00692694i	0.000419310	−	0.000304646i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−10.4542	−	7.59539i	−0.458005	−	0.332760i	0.334743	−	0.942309i	$-0.391350\pi$
$521$	−10.4542	−	7.59539i	−0.458005	−	0.332760i	−0.792748	+	0.609549i	$0.791350\pi$
$522$		0			0
$523$	−6.29759	+	19.3820i	−0.275374	+	0.847515i	0.713746	+	0.700405i	$0.246997\pi$
$523$	−6.29759	+	19.3820i	−0.275374	+	0.847515i	−0.989120	+	0.147110i	$0.953003\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.666873	−	2.05242i	0.0290494	−	0.0894050i
$528$		0			0
$529$	−43.9624	−	31.9405i	−1.91141	−	1.38872i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.38259	−	4.63722i	0.276461	−	0.200861i
$534$		0			0
$535$	−0.997541	+	3.94610i	−0.0431274	+	0.170605i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	6.39284	−	19.6751i	0.275359	−	0.847468i
$540$		0			0
$541$	−9.79560	−	30.1478i	−0.421146	−	1.29615i	−0.906637	−	0.421912i	$-0.861359\pi$
$541$	−9.79560	−	30.1478i	−0.421146	−	1.29615i	0.485491	−	0.874242i	$-0.338641\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	26.6982	−	1.77953i	1.14363	−	0.0762267i
$546$		0			0
$547$	24.9414	+	18.1210i	1.06642	+	0.774798i	0.975265	−	0.221039i	$-0.0709449\pi$
$547$	24.9414	+	18.1210i	1.06642	+	0.774798i	0.0911524	+	0.995837i	$0.470945\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.851914			0.0362928
$552$		0			0
$553$	41.5107	+	30.1593i	1.76521	+	1.28250i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	5.19763			0.220231			0.110115	−	0.993919i	$-0.464878\pi$
$557$	5.19763			0.220231			0.110115	+	0.993919i	$0.464878\pi$
$558$		0			0
$559$	0.726458	+	2.23581i	0.0307259	+	0.0945646i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.93482	−	5.95477i	−0.0815430	−	0.250964i	0.901971	−	0.431797i	$-0.142120\pi$
$563$	−1.93482	−	5.95477i	−0.0815430	−	0.250964i	−0.983514	+	0.180834i	$0.942120\pi$
$564$		0			0
$565$	−26.7718	+	1.78443i	−1.12630	+	0.0750717i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−24.8382	+	18.0460i	−1.04127	+	0.756528i	−0.970533	−	0.240967i	$-0.922536\pi$
$569$	−24.8382	+	18.0460i	−1.04127	+	0.756528i	−0.0707384	+	0.997495i	$0.522536\pi$
$570$		0			0
$571$	21.2560	+	15.4434i	0.889537	+	0.646287i	0.935757	−	0.352645i	$-0.114718\pi$
$571$	21.2560	+	15.4434i	0.889537	+	0.646287i	−0.0462202	+	0.998931i	$0.514718\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−31.8290	+	30.3386i	−1.32736	+	1.26521i
$576$		0			0
$577$	−0.565447	+	1.74027i	−0.0235399	+	0.0724483i	−0.962136	−	0.272569i	$-0.912127\pi$
$577$	−0.565447	+	1.74027i	−0.0235399	+	0.0724483i	0.938596	+	0.345017i	$0.112127\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−10.1609	+	7.38235i	−0.421546	+	0.306271i
$582$		0			0
$583$	−15.3723	+	11.1686i	−0.636656	+	0.462557i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−13.8225	−	42.5413i	−0.570516	−	1.75587i	−0.650965	−	0.759108i	$-0.725635\pi$
$587$	−13.8225	−	42.5413i	−0.570516	−	1.75587i	0.0804491	−	0.996759i	$-0.474365\pi$
$588$		0			0
$589$	8.76049	−	26.9620i	0.360970	−	1.11095i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	24.9335			1.02390			0.511948	−	0.859017i	$-0.328924\pi$
$593$	24.9335			1.02390			0.511948	+	0.859017i	$0.328924\pi$
$594$		0			0
$595$	−1.08075	−	2.70024i	−0.0443063	−	0.110699i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−24.4375			−0.998490			−0.499245	−	0.866461i	$-0.666389\pi$
$599$	−24.4375			−0.998490			−0.499245	+	0.866461i	$0.666389\pi$
$600$		0			0
$601$	−27.3066			−1.11386			−0.556930	−	0.830559i	$-0.688021\pi$
$601$	−27.3066			−1.11386			−0.556930	+	0.830559i	$0.688021\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−14.1015	+	11.7545i	−0.573307	+	0.477887i
$606$		0			0
$607$	24.4802			0.993620			0.496810	−	0.867859i	$-0.334505\pi$
$607$	24.4802			0.993620			0.496810	+	0.867859i	$0.334505\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.00561254	−	0.0172736i	0.000227059	−	0.000698816i
$612$		0			0
$613$	9.33170	+	28.7200i	0.376904	+	1.15999i	0.942185	+	0.335092i	$0.108768\pi$
$613$	9.33170	+	28.7200i	0.376904	+	1.15999i	−0.565282	+	0.824898i	$0.691232\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−8.16876	+	5.93495i	−0.328862	+	0.238932i	−0.739948	−	0.672665i	$-0.765150\pi$
$617$	−8.16876	+	5.93495i	−0.328862	+	0.238932i	0.411086	+	0.911597i	$0.365150\pi$
$618$		0			0
$619$	−1.85616	+	1.34858i	−0.0746056	+	0.0542041i	−0.624463	−	0.781054i	$-0.714682\pi$
$619$	−1.85616	+	1.34858i	−0.0746056	+	0.0542041i	0.549857	+	0.835259i	$0.314682\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−4.53300	+	13.9511i	−0.181611	+	0.558940i
$624$		0			0
$625$	13.7085	+	20.9064i	0.548341	+	0.836255i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−0.178849	−	0.129942i	−0.00713120	−	0.00518112i
$630$		0			0
$631$	−0.984245	+	0.715096i	−0.0391822	+	0.0284675i	−0.607204	−	0.794546i	$-0.707709\pi$
$631$	−0.984245	+	0.715096i	−0.0391822	+	0.0284675i	0.568022	+	0.823014i	$0.307709\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	9.41459	+	5.92562i	0.373606	+	0.235151i
$636$		0			0
$637$	−9.85255	−	30.3230i	−0.390372	−	1.20144i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−5.20042	−	16.0053i	−0.205404	−	0.632170i	−0.999697	−	0.0246337i	$-0.992158\pi$
$641$	−5.20042	−	16.0053i	−0.205404	−	0.632170i	0.794292	−	0.607536i	$-0.207842\pi$
$642$		0			0
$643$	−23.4446			−0.924566			−0.462283	−	0.886732i	$-0.652970\pi$
$643$	−23.4446			−0.924566			−0.462283	+	0.886732i	$0.652970\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.72470	+	6.33886i	0.343003	+	0.249206i	0.745928	−	0.666027i	$-0.232006\pi$
$647$	8.72470	+	6.33886i	0.343003	+	0.249206i	−0.402925	+	0.915233i	$0.632006\pi$
$648$		0			0
$649$	−3.43728			−0.134925
$650$		0			0
$651$		0			0
$652$		0			0
$653$	39.3900	+	28.6185i	1.54145	+	1.11993i	0.949419	+	0.314011i	$0.101673\pi$
$653$	39.3900	+	28.6185i	1.54145	+	1.11993i	0.592029	+	0.805917i	$0.298327\pi$
$654$		0			0
$655$	15.8519	+	39.6058i	0.619384	+	1.54753i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	12.2847	+	37.8085i	0.478545	+	1.47281i	0.841116	+	0.540855i	$0.181899\pi$
$659$	12.2847	+	37.8085i	0.478545	+	1.47281i	−0.362571	+	0.931956i	$0.618101\pi$
$660$		0			0
$661$	5.40244	−	16.6270i	0.210131	−	0.646716i	−0.789333	−	0.613965i	$-0.789573\pi$
$661$	5.40244	−	16.6270i	0.210131	−	0.646716i	0.999464	−	0.0327502i	$-0.0104266\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−14.1974	−	35.4721i	−0.550552	−	1.37555i
$666$		0			0
$667$	1.56180	−	1.13472i	0.0604732	−	0.0439364i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	15.4077	+	11.1944i	0.594808	+	0.432153i
$672$		0			0
$673$	−8.60639	+	26.4878i	−0.331752	+	1.02103i	0.636548	+	0.771237i	$0.280362\pi$
$673$	−8.60639	+	26.4878i	−0.331752	+	1.02103i	−0.968300	+	0.249791i	$0.919638\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.01733	−	9.28639i	0.115965	−	0.356905i	−0.876182	−	0.481981i	$-0.839917\pi$
$677$	3.01733	−	9.28639i	0.115965	−	0.356905i	0.992147	+	0.125076i	$0.0399175\pi$
$678$		0			0
$679$	38.4800	+	27.9573i	1.47673	+	1.07290i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	9.72632	−	7.06659i	0.372167	−	0.270395i	−0.385942	−	0.922523i	$-0.626123\pi$
$683$	9.72632	−	7.06659i	0.372167	−	0.270395i	0.758109	+	0.652128i	$0.226123\pi$
$684$		0			0
$685$	20.2833	−	1.35196i	0.774986	−	0.0516556i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−9.04937	+	27.8511i	−0.344754	+	1.06104i
$690$		0			0
$691$	−5.57282	−	17.1514i	−0.212000	−	0.652469i	−0.999353	−	0.0359667i	$-0.988549\pi$
$691$	−5.57282	−	17.1514i	−0.212000	−	0.652469i	0.787353	−	0.616503i	$-0.211451\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	25.2348	+	15.8830i	0.957210	+	0.602477i
$696$		0			0
$697$	0.732460	+	0.532164i	0.0277439	+	0.0201571i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−39.2938			−1.48411			−0.742053	−	0.670341i	$-0.766148\pi$
$701$	−39.2938			−1.48411			−0.742053	+	0.670341i	$0.766148\pi$
$702$		0			0
$703$	−2.34949	−	1.70700i	−0.0886126	−	0.0643808i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	48.8586			1.83752
$708$		0			0
$709$	−1.15852	−	3.56557i	−0.0435093	−	0.133908i	0.926942	−	0.375204i	$-0.122427\pi$
$709$	−1.15852	−	3.56557i	−0.0435093	−	0.133908i	−0.970451	+	0.241296i	$0.922427\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−19.8519	−	61.0977i	−0.743458	−	2.28813i
$714$		0			0
$715$	2.35645	−	9.32171i	0.0881262	−	0.348612i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−14.5857	+	10.5971i	−0.543954	+	0.395206i	−0.825551	−	0.564327i	$-0.809136\pi$
$719$	−14.5857	+	10.5971i	−0.543954	+	0.395206i	0.281597	+	0.959533i	$0.409136\pi$
$720$		0			0
$721$	26.9618	+	19.5889i	1.00411	+	0.729529i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.474708	−	0.989610i	−0.0176302	−	0.0367532i
$726$		0			0
$727$	10.9245	−	33.6221i	0.405167	−	1.24697i	−0.515589	−	0.856836i	$-0.672427\pi$
$727$	10.9245	−	33.6221i	0.405167	−	1.24697i	0.920756	−	0.390139i	$-0.127573\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.218259	+	0.158575i	−0.00807261	+	0.00586509i
$732$		0			0
$733$	2.82540	−	2.05278i	0.104359	−	0.0758210i	−0.534382	−	0.845243i	$-0.679456\pi$
$733$	2.82540	−	2.05278i	0.104359	−	0.0758210i	0.638741	+	0.769422i	$0.279456\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.15795	+	9.71917i	0.116325	+	0.358010i
$738$		0			0
$739$	−7.31335	+	22.5082i	−0.269026	+	0.827976i	0.721713	+	0.692193i	$0.243355\pi$
$739$	−7.31335	+	22.5082i	−0.269026	+	0.827976i	−0.990739	+	0.135784i	$0.956645\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−50.0459			−1.83601			−0.918003	−	0.396574i	$-0.870199\pi$
$743$	−50.0459			−1.83601			−0.918003	+	0.396574i	$0.870199\pi$
$744$		0			0
$745$	3.54612	−	14.0279i	0.129920	−	0.513941i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−8.01440			−0.292840
$750$		0			0
$751$	−1.64636			−0.0600765			−0.0300383	−	0.999549i	$-0.509563\pi$
$751$	−1.64636			−0.0600765			−0.0300383	+	0.999549i	$0.509563\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	6.06134	−	23.9776i	0.220595	−	0.872636i
$756$		0			0
$757$	23.4001			0.850493			0.425246	−	0.905078i	$-0.360187\pi$
$757$	23.4001			0.850493			0.425246	+	0.905078i	$0.360187\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−15.2003	+	46.7816i	−0.551010	+	1.69583i	0.155246	+	0.987876i	$0.450383\pi$
$761$	−15.2003	+	46.7816i	−0.551010	+	1.69583i	−0.706255	+	0.707957i	$0.749617\pi$
$762$		0			0
$763$	16.2809	+	50.1075i	0.589408	+	1.81401i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.28576	+	3.11379i	−0.154750	+	0.112432i
$768$		0			0
$769$	−26.0912	+	18.9564i	−0.940872	+	0.683584i	−0.948630	−	0.316386i	$-0.897530\pi$
$769$	−26.0912	+	18.9564i	−0.940872	+	0.683584i	0.00775840	+	0.999970i	$0.497530\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−2.46824	+	7.59646i	−0.0887764	+	0.273226i	−0.985582	−	0.169200i	$-0.945882\pi$
$773$	−2.46824	+	7.59646i	−0.0887764	+	0.273226i	0.896805	+	0.442425i	$0.145882\pi$
$774$		0			0
$775$	−36.2015	+	4.84745i	−1.30040	+	0.174126i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	9.62209	+	6.99086i	0.344747	+	0.250474i
$780$		0			0
$781$	−10.8767	+	7.90237i	−0.389198	+	0.282769i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.43225	+	13.5774i	−0.122502	+	0.484598i
$786$		0			0
$787$	10.0798	+	31.0225i	0.359307	+	1.10583i	0.953470	+	0.301489i	$0.0974835\pi$
$787$	10.0798	+	31.0225i	0.359307	+	1.10583i	−0.594163	+	0.804345i	$0.702516\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−16.3258	−	50.2456i	−0.580478	−	1.78653i
$792$		0			0
$793$	29.3518			1.04231
$794$		0			0
$795$		0			0
$796$		0			0
$797$	39.2425	+	28.5113i	1.39004	+	1.00992i	0.995861	+	0.0908891i	$0.0289709\pi$
$797$	39.2425	+	28.5113i	1.39004	+	1.00992i	0.394179	+	0.919034i	$0.371029\pi$
$798$		0			0
$799$	0.00208432			7.37379e−5
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−4.74362	−	3.44644i	−0.167399	−	0.121622i
$804$		0			0
$805$	−73.2754	−	46.1202i	−2.58262	−	1.62552i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−9.07658	−	27.9348i	−0.319116	−	0.982137i	−0.974027	−	0.226431i	$-0.927294\pi$
$809$	−9.07658	−	27.9348i	−0.319116	−	0.982137i	0.654912	−	0.755706i	$-0.272706\pi$
$810$		0			0
$811$	9.70579	−	29.8713i	0.340816	−	1.04892i	−0.622969	−	0.782246i	$-0.714074\pi$
$811$	9.70579	−	29.8713i	0.340816	−	1.04892i	0.963786	−	0.266678i	$-0.0859261\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	9.07056	−	0.604585i	0.317728	−	0.0211777i
$816$		0			0
$817$	−2.86720	+	2.08314i	−0.100311	+	0.0728800i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	34.0816	+	24.7617i	1.18946	+	0.864190i	0.993207	−	0.116364i	$-0.0371240\pi$
$821$	34.0816	+	24.7617i	1.18946	+	0.864190i	0.196249	+	0.980554i	$0.437124\pi$
$822$		0			0
$823$	6.16667	−	18.9791i	0.214957	−	0.661569i	−0.784200	−	0.620508i	$-0.786926\pi$
$823$	6.16667	−	18.9791i	0.214957	−	0.661569i	0.999157	−	0.0410605i	$-0.0130737\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.30442	+	13.2476i	−0.149679	+	0.460666i	−0.997583	−	0.0694845i	$-0.977865\pi$
$827$	−4.30442	+	13.2476i	−0.149679	+	0.460666i	0.847904	+	0.530150i	$0.177865\pi$
$828$		0			0
$829$	21.5627	+	15.6662i	0.748902	+	0.544109i	0.895486	−	0.445089i	$-0.146828\pi$
$829$	21.5627	+	15.6662i	0.748902	+	0.544109i	−0.146584	+	0.989198i	$0.546828\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	2.96013	−	2.15066i	0.102562	−	0.0745160i
$834$		0			0
$835$	−16.4476	−	41.0943i	−0.569194	−	1.42213i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−10.2268	+	31.4748i	−0.353067	+	1.08663i	0.604054	+	0.796943i	$0.293551\pi$
$839$	−10.2268	+	31.4748i	−0.353067	+	1.08663i	−0.957122	+	0.289686i	$0.906449\pi$
$840$		0			0
$841$	−8.94660	−	27.5348i	−0.308504	−	0.949476i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.29525	+	13.2301i	0.182162	+	0.455130i
$846$		0			0
$847$	−29.2440	−	21.2470i	−1.00484	−	0.730056i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−6.58094			−0.225592
$852$		0			0
$853$	13.9610	+	10.1433i	0.478017	+	0.347300i	0.800557	−	0.599256i	$-0.204537\pi$
$853$	13.9610	+	10.1433i	0.478017	+	0.347300i	−0.322541	+	0.946556i	$0.604537\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	33.6214			1.14849			0.574243	−	0.818685i	$-0.305296\pi$
$857$	33.6214			1.14849			0.574243	+	0.818685i	$0.305296\pi$
$858$		0			0
$859$	3.08649	+	9.49923i	0.105310	+	0.324110i	0.989803	−	0.142443i	$-0.0454958\pi$
$859$	3.08649	+	9.49923i	0.105310	+	0.324110i	−0.884493	+	0.466553i	$0.845496\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	15.2688	+	46.9925i	0.519756	+	1.59964i	0.774459	+	0.632625i	$0.218022\pi$
$863$	15.2688	+	46.9925i	0.519756	+	1.59964i	−0.254703	+	0.967019i	$0.581978\pi$
$864$		0			0
$865$	−2.46435	−	1.55108i	−0.0837905	−	0.0527385i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−15.7480	+	11.4416i	−0.534215	+	0.388130i
$870$		0			0
$871$	12.7419	+	9.25755i	0.431744	+	0.313680i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−33.2944	+	36.2581i	−1.12556	+	1.22575i
$876$		0			0
$877$	−0.0171184	+	0.0526851i	−0.000578048	+	0.00177905i	−0.951345	−	0.308127i	$-0.900298\pi$
$877$	−0.0171184	+	0.0526851i	−0.000578048	+	0.00177905i	0.950767	+	0.309906i	$0.100298\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	34.5433	−	25.0972i	1.16379	−	0.845546i	0.173541	−	0.984827i	$-0.444479\pi$
$881$	34.5433	−	25.0972i	1.16379	−	0.845546i	0.990253	+	0.139281i	$0.0444791\pi$
$882$		0			0
$883$	−19.2078	+	13.9553i	−0.646394	+	0.469633i	−0.862041	−	0.506839i	$-0.830814\pi$
$883$	−19.2078	+	13.9553i	−0.646394	+	0.469633i	0.215647	+	0.976471i	$0.430814\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.1905	+	31.3633i	0.342165	+	1.05308i	0.963084	+	0.269201i	$0.0867596\pi$
$887$	10.1905	+	31.3633i	0.342165	+	1.05308i	−0.620919	+	0.783875i	$0.713240\pi$
$888$		0			0
$889$	−6.76865	+	20.8318i	−0.227013	+	0.698675i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.0273810			0.000916271
$894$		0			0
$895$	−36.7188	+	30.6075i	−1.22738	+	1.02309i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.60354			0.0534811
$900$		0			0
$901$	−3.36065			−0.111959
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−12.6343	−	31.5667i	−0.419978	−	1.04931i
$906$		0			0
$907$	7.31372			0.242848			0.121424	−	0.992601i	$-0.461254\pi$
$907$	7.31372			0.242848			0.121424	+	0.992601i	$0.461254\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−5.68376	+	17.4928i	−0.188311	+	0.579563i	−0.999990	−	0.00454173i	$-0.998554\pi$
$911$	−5.68376	+	17.4928i	−0.188311	+	0.579563i	0.811678	+	0.584105i	$0.198554\pi$
$912$		0			0
$913$	−1.47240	−	4.53157i	−0.0487292	−	0.149973i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−67.9568	+	49.3735i	−2.24413	+	1.63046i
$918$		0			0
$919$	−28.3447	+	20.5936i	−0.935004	+	0.679320i	−0.947213	−	0.320605i	$-0.896114\pi$
$919$	−28.3447	+	20.5936i	−0.935004	+	0.679320i	0.0122089	+	0.999925i	$0.496114\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6.40289	+	19.7061i	−0.210754	+	0.648633i
$924$		0			0
$925$	−0.673714	+	3.68042i	−0.0221516	+	0.121012i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	12.3232	+	8.95336i	0.404312	+	0.293750i	0.771295	−	0.636478i	$-0.219609\pi$
$929$	12.3232	+	8.95336i	0.404312	+	0.293750i	−0.366983	+	0.930228i	$0.619609\pi$
$930$		0			0
$931$	38.8863	−	28.2525i	1.27445	−	0.925940i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.10096	−	0.0733828i	0.0360052	−	0.00239987i
$936$		0			0
$937$	−1.33342	−	4.10386i	−0.0435611	−	0.134067i	0.926911	−	0.375282i	$-0.122454\pi$
$937$	−1.33342	−	4.10386i	−0.0435611	−	0.134067i	−0.970472	+	0.241215i	$0.922454\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−5.84704	−	17.9953i	−0.190608	−	0.586631i	0.809392	−	0.587269i	$-0.199797\pi$
$941$	−5.84704	−	17.9953i	−0.190608	−	0.586631i	−1.00000		0.000637969i	$0.999797\pi$
$942$		0			0
$943$	26.9516			0.877665
$944$		0			0
$945$		0			0
$946$		0			0
$947$	14.1171	+	10.2567i	0.458745	+	0.333298i	0.793039	−	0.609171i	$-0.208498\pi$
$947$	14.1171	+	10.2567i	0.458745	+	0.333298i	−0.334293	+	0.942469i	$0.608498\pi$
$948$		0			0
$949$	−9.03664			−0.293342
$950$		0			0
$951$		0			0
$952$		0			0
$953$	29.3862	+	21.3503i	0.951912	+	0.691605i	0.951258	−	0.308395i	$-0.0997919\pi$
$953$	29.3862	+	21.3503i	0.951912	+	0.691605i	0.000653920		1.00000i	$0.499792\pi$
$954$		0			0
$955$	−35.9757	+	2.39791i	−1.16415	+	0.0775946i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	12.3690	+	38.0680i	0.399417	+	1.22928i
$960$		0			0
$961$	6.91020	−	21.2674i	0.222910	−	0.686045i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−5.67514	+	22.4499i	−0.182689	+	0.722687i
$966$		0			0
$967$	−29.1294	+	21.1638i	−0.936740	+	0.680581i	−0.947634	−	0.319359i	$-0.896532\pi$
$967$	−29.1294	+	21.1638i	−0.936740	+	0.680581i	0.0108940	+	0.999941i	$0.496532\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	3.15763	+	2.29415i	0.101333	+	0.0736229i	0.637298	−	0.770617i	$-0.280052\pi$
$971$	3.15763	+	2.29415i	0.101333	+	0.0736229i	−0.535965	+	0.844240i	$0.680052\pi$
$972$		0			0
$973$	−18.1427	+	55.8374i	−0.581627	+	1.79006i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	13.6318	−	41.9543i	0.436119	−	1.34224i	−0.455817	−	0.890074i	$-0.650653\pi$
$977$	13.6318	−	41.9543i	0.436119	−	1.34224i	0.891936	−	0.452162i	$-0.149347\pi$
$978$		0			0
$979$	−4.50223	−	3.27106i	−0.143892	−	0.104544i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	27.2785	−	19.8190i	0.870048	−	0.632127i	−0.0605518	−	0.998165i	$-0.519286\pi$
$983$	27.2785	−	19.8190i	0.870048	−	0.632127i	0.930600	+	0.366038i	$0.119286\pi$
$984$		0			0
$985$	−34.5202	+	28.7747i	−1.09990	+	0.916839i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.48174	+	7.63800i	−0.0789146	+	0.242874i
$990$		0			0
$991$	−5.66357	−	17.4307i	−0.179909	−	0.553704i	0.819914	−	0.572486i	$-0.194021\pi$
$991$	−5.66357	−	17.4307i	−0.179909	−	0.553704i	−0.999824	+	0.0187824i	$0.994021\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.54594	+	6.11546i	−0.0490095	+	0.193873i
$996$		0			0
$997$	40.7197	+	29.5846i	1.28961	+	0.936954i	0.999797	−	0.0201300i	$-0.00640800\pi$
$997$	40.7197	+	29.5846i	1.28961	+	0.936954i	0.289810	+	0.957084i	$0.406408\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.n.c.721.1		12
3.2	odd	2		100.2.g.a.21.3	✓	12
12.11	even	2		400.2.u.f.321.1		12
15.2	even	4		500.2.i.b.149.5		24
15.8	even	4		500.2.i.b.149.2		24
15.14	odd	2		500.2.g.a.101.1		12
25.6	even	5	inner	900.2.n.c.181.1		12
75.8	even	20		500.2.i.b.349.5		24
75.17	even	20		500.2.i.b.349.2		24
75.38	even	20		2500.2.c.c.1249.3		12
75.41	odd	10		2500.2.a.d.1.1		6
75.44	odd	10		500.2.g.a.401.1		12
75.56	odd	10		100.2.g.a.81.3	yes	12
75.59	odd	10		2500.2.a.c.1.6		6
75.62	even	20		2500.2.c.c.1249.10		12
300.59	even	10		10000.2.a.bd.1.1		6
300.131	even	10		400.2.u.f.81.1		12
300.191	even	10		10000.2.a.bc.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.g.a.21.3	✓	12	3.2	odd	2
100.2.g.a.81.3	yes	12	75.56	odd	10
400.2.u.f.81.1		12	300.131	even	10
400.2.u.f.321.1		12	12.11	even	2
500.2.g.a.101.1		12	15.14	odd	2
500.2.g.a.401.1		12	75.44	odd	10
500.2.i.b.149.2		24	15.8	even	4
500.2.i.b.149.5		24	15.2	even	4
500.2.i.b.349.2		24	75.17	even	20
500.2.i.b.349.5		24	75.8	even	20
900.2.n.c.181.1		12	25.6	even	5	inner
900.2.n.c.721.1		12	1.1	even	1	trivial
2500.2.a.c.1.6		6	75.59	odd	10
2500.2.a.d.1.1		6	75.41	odd	10
2500.2.c.c.1249.3		12	75.38	even	20
2500.2.c.c.1249.10		12	75.62	even	20
10000.2.a.bc.1.6		6	300.191	even	10
10000.2.a.bd.1.1		6	300.59	even	10

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.548020 + 2.16787i) q^{5} -4.40288 q^{7} +(0.516162 - 1.58858i) q^{11} +(-0.795501 - 2.44830i) q^{13} +(0.239003 - 0.173646i) q^{17} +(3.13970 - 2.28113i) q^{19} +(2.71760 - 8.36392i) q^{23} +(-4.39935 - 2.37607i) q^{25} +(0.177592 + 0.129028i) q^{29} +(5.90981 - 4.29372i) q^{31} +(2.41286 - 9.54488i) q^{35} +(-0.231242 - 0.711690i) q^{37} +(0.947030 + 2.91466i) q^{41} -0.913208 q^{43} +(0.00570791 + 0.00414704i) q^{47} +12.3853 q^{49} +(-9.20313 - 6.68646i) q^{53} +(3.16098 + 1.98955i) q^{55} +(-0.635908 - 1.95712i) q^{59} +(-3.52338 + 10.8438i) q^{61} +(5.74355 - 0.382828i) q^{65} +(-4.94968 + 3.59615i) q^{67} +(-6.51168 - 4.73101i) q^{71} +(1.08475 - 3.33853i) q^{73} +(-2.27260 + 6.99434i) q^{77} +(-9.42807 - 6.84989i) q^{79} +(2.30779 - 1.67671i) q^{83} +(0.245464 + 0.613289i) q^{85} +(1.02955 - 3.16864i) q^{89} +(3.50249 + 10.7796i) q^{91} +(3.22458 + 8.05658i) q^{95} +(-8.73973 - 6.34979i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{5} - 2 q^{7} + 5 q^{11} - 2 q^{13} - q^{17} - 8 q^{19} + 6 q^{23} - 26 q^{25} + 18 q^{29} + 12 q^{31} + 3 q^{35} + 13 q^{37} + 23 q^{41} + 50 q^{43} - q^{47} + 34 q^{49} - 21 q^{53} + 5 q^{55}+ \cdots - 7 q^{97}+O(q^{100}) \) 12 * q + 4 * q^5 - 2 * q^7 + 5 * q^11 - 2 * q^13 - q^17 - 8 * q^19 + 6 * q^23 - 26 * q^25 + 18 * q^29 + 12 * q^31 + 3 * q^35 + 13 * q^37 + 23 * q^41 + 50 * q^43 - q^47 + 34 * q^49 - 21 * q^53 + 5 * q^55 - 9 * q^59 - 26 * q^61 + 18 * q^65 - 37 * q^67 - 21 * q^71 + 18 * q^73 + 60 * q^77 - 24 * q^79 + 46 * q^83 - 16 * q^85 + 2 * q^89 - 32 * q^91 - 6 * q^95 - 7 * q^97

Introduction

L-functions

Modular forms

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Database

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