LMFDB - Embedded newform 2548.2.bb.g.1733.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2548,2,Mod(569,2548)] 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("2548.569"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2548, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0,0,-8,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1733.1
Character	$\chi$	$=$	2548.1733
Dual form			2548.2.bb.g.569.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.49140 - 2.58319i) q^{3} +(-0.626773 + 0.361868i) q^{5} +(-2.94857 + 5.10707i) q^{9} +(-2.23810 + 1.29217i) q^{11} +(0.896087 - 3.49242i) q^{13} +(1.86954 + 1.07938i) q^{15} +4.53814 q^{17} +(6.26073 + 3.61464i) q^{19} +0.199571 q^{23} +(-2.23810 + 3.87651i) q^{25} +8.64159 q^{27} +(2.84878 - 4.93424i) q^{29} +(-5.36678 - 3.09851i) q^{31} +(6.67583 + 3.85429i) q^{33} -4.64097i q^{37} +(-10.3580 + 2.89385i) q^{39} +(8.26614 + 4.77246i) q^{41} +(3.54835 + 6.14593i) q^{43} -4.26797i q^{45} +(-0.838451 + 0.484080i) q^{47} +(-6.76819 - 11.7229i) q^{51} +(2.13432 - 3.69675i) q^{53} +(0.935189 - 1.61979i) q^{55} -21.5635i q^{57} -8.64812i q^{59} +(4.36866 - 7.56674i) q^{61} +(0.702152 + 2.51322i) q^{65} +(2.36911 - 1.36781i) q^{67} +(-0.297641 - 0.515530i) q^{69} +(0.0784987 - 0.0453212i) q^{71} +(3.56175 + 2.05638i) q^{73} +13.3517 q^{75} +(-3.96626 - 6.86976i) q^{79} +(-4.04240 - 7.00164i) q^{81} +6.65604i q^{83} +(-2.84438 + 1.64221i) q^{85} -16.9947 q^{87} -14.1387i q^{89} +18.4845i q^{93} -5.23208 q^{95} +(1.09191 - 0.630417i) q^{97} -15.2402i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{9} - 12 q^{15} - 32 q^{23} + 24 q^{29} - 28 q^{39} + 4 q^{43} - 40 q^{51} + 24 q^{53} + 32 q^{65} - 24 q^{71} + 24 q^{79} + 4 q^{81} + 12 q^{85} + 40 q^{95}+O(q^{100}) $ 24 * q - 8 * q^9 - 12 * q^15 - 32 * q^23 + 24 * q^29 - 28 * q^39 + 4 * q^43 - 40 * q^51 + 24 * q^53 + 32 * q^65 - 24 * q^71 + 24 * q^79 + 4 * q^81 + 12 * q^85 + 40 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−1.49140	−	2.58319i	−0.861062	−	1.49140i	−0.870905	−	0.491452i	$-0.836466\pi$
$3$	−1.49140	−	2.58319i	−0.861062	−	1.49140i	0.00984273	−	0.999952i	$-0.496867\pi$
$4$		0			0
$5$	−0.626773	+	0.361868i	−0.280302	+	0.161832i	−0.633560	−	0.773694i	$-0.718407\pi$
$5$	−0.626773	+	0.361868i	−0.280302	+	0.161832i	0.353258	+	0.935526i	$0.385074\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.94857	+	5.10707i	−0.982856	+	1.70236i
$10$		0			0
$11$	−2.23810	+	1.29217i	−0.674814	+	0.389604i	−0.797898	−	0.602792i	$-0.794055\pi$
$11$	−2.23810	+	1.29217i	−0.674814	+	0.389604i	0.123084	+	0.992396i	$0.460721\pi$
$12$		0			0
$13$	0.896087	−	3.49242i	0.248530	−	0.968624i
$13$	0.896087	−	3.49242i	0.248530	−	0.968624i
$14$		0			0
$15$	1.86954	+	1.07938i	0.482714	+	0.278695i
$16$		0			0
$17$	4.53814			1.10066			0.550330	−	0.834947i	$-0.314502\pi$
$17$	4.53814			1.10066			0.550330	+	0.834947i	$0.314502\pi$
$18$		0			0
$19$	6.26073	+	3.61464i	1.43631	+	0.829254i	0.997591	−	0.0693695i	$-0.0220987\pi$
$19$	6.26073	+	3.61464i	1.43631	+	0.829254i	0.438720	+	0.898624i	$0.355432\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.199571			0.0416135			0.0208067	−	0.999784i	$-0.493377\pi$
$23$	0.199571			0.0416135			0.0208067	+	0.999784i	$0.493377\pi$
$24$		0			0
$25$	−2.23810	+	3.87651i	−0.447621	+	0.775302i
$26$		0			0
$27$	8.64159			1.66308
$28$		0			0
$29$	2.84878	−	4.93424i	0.529006	−	0.916264i	−0.470422	−	0.882441i	$-0.655898\pi$
$29$	2.84878	−	4.93424i	0.529006	−	0.916264i	0.999428	−	0.0338230i	$-0.0107683\pi$
$30$		0			0
$31$	−5.36678	−	3.09851i	−0.963901	−	0.556509i	−0.0665299	−	0.997784i	$-0.521193\pi$
$31$	−5.36678	−	3.09851i	−0.963901	−	0.556509i	−0.897372	+	0.441276i	$0.854526\pi$
$32$		0			0
$33$	6.67583	+	3.85429i	1.16211	+	0.670946i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	4.64097i		−	0.762971i	−0.924375	−	0.381485i	$-0.875413\pi$
$37$		−	4.64097i		−	0.762971i	0.924375	−	0.381485i	$-0.124587\pi$
$38$		0			0
$39$	−10.3580	+	2.89385i	−1.65861	+	0.463387i
$40$		0			0
$41$	8.26614	+	4.77246i	1.29095	+	0.745333i	0.978823	−	0.204706i	$-0.0656240\pi$
$41$	8.26614	+	4.77246i	1.29095	+	0.745333i	0.312131	+	0.950039i	$0.398957\pi$
$42$		0			0
$43$	3.54835	+	6.14593i	0.541119	+	0.937245i	0.998840	+	0.0481495i	$0.0153324\pi$
$43$	3.54835	+	6.14593i	0.541119	+	0.937245i	−0.457721	+	0.889096i	$0.651334\pi$
$44$		0			0
$45$		−	4.26797i		−	0.636231i
$46$		0			0
$47$	−0.838451	+	0.484080i	−0.122301	+	0.0706103i	−0.559902	−	0.828559i	$-0.689161\pi$
$47$	−0.838451	+	0.484080i	−0.122301	+	0.0706103i	0.437602	+	0.899169i	$0.355828\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−6.76819	−	11.7229i	−0.947737	−	1.64153i
$52$		0			0
$53$	2.13432	−	3.69675i	0.293172	−	0.507788i	−0.681386	−	0.731924i	$-0.738623\pi$
$53$	2.13432	−	3.69675i	0.293172	−	0.507788i	0.974558	+	0.224136i	$0.0719559\pi$
$54$		0			0
$55$	0.935189	−	1.61979i	0.126101	−	0.218413i
$56$		0			0
$57$		−	21.5635i		−	2.85616i
$58$		0			0
$59$		−	8.64812i		−	1.12589i	−0.826495	−	0.562944i	$-0.809669\pi$
$59$		−	8.64812i		−	1.12589i	0.826495	−	0.562944i	$-0.190331\pi$
$60$		0			0
$61$	4.36866	−	7.56674i	0.559349	−	0.968822i	−0.438201	−	0.898877i	$-0.644384\pi$
$61$	4.36866	−	7.56674i	0.559349	−	0.968822i	0.997551	−	0.0699449i	$-0.0222823\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.702152	+	2.51322i	0.0870913	+	0.311727i
$66$		0			0
$67$	2.36911	−	1.36781i	0.289433	−	0.167104i	−0.348253	−	0.937401i	$-0.613225\pi$
$67$	2.36911	−	1.36781i	0.289433	−	0.167104i	0.637686	+	0.770296i	$0.279892\pi$
$68$		0			0
$69$	−0.297641	−	0.515530i	−0.0358318	−	0.0620625i
$70$		0			0
$71$	0.0784987	−	0.0453212i	0.00931608	−	0.00537864i	−0.495335	−	0.868702i	$-0.664955\pi$
$71$	0.0784987	−	0.0453212i	0.00931608	−	0.00537864i	0.504651	+	0.863324i	$0.331621\pi$
$72$		0			0
$73$	3.56175	+	2.05638i	0.416871	+	0.240681i	0.693738	−	0.720228i	$-0.255963\pi$
$73$	3.56175	+	2.05638i	0.416871	+	0.240681i	−0.276866	+	0.960908i	$0.589296\pi$
$74$		0			0
$75$	13.3517			1.54172
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−3.96626	−	6.86976i	−0.446239	−	0.772908i	0.551899	−	0.833911i	$-0.313903\pi$
$79$	−3.96626	−	6.86976i	−0.446239	−	0.772908i	−0.998138	+	0.0610029i	$0.980570\pi$
$80$		0			0
$81$	−4.04240	−	7.00164i	−0.449155	−	0.777960i
$82$		0			0
$83$			6.65604i			0.730596i	0.930891	+	0.365298i	$0.119033\pi$
$83$			6.65604i			0.730596i	−0.930891	+	0.365298i	$0.880967\pi$
$84$		0			0
$85$	−2.84438	+	1.64221i	−0.308517	+	0.178122i
$86$		0			0
$87$	−16.9947			−1.82203
$88$		0			0
$89$		−	14.1387i		−	1.49870i	−0.662173	−	0.749351i	$-0.730366\pi$
$89$		−	14.1387i		−	1.49870i	0.662173	−	0.749351i	$-0.269634\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$			18.4845i			1.91675i
$94$		0			0
$95$	−5.23208			−0.536800
$96$		0			0
$97$	1.09191	−	0.630417i	0.110867	−	0.0640091i	−0.443541	−	0.896254i	$-0.646278\pi$
$97$	1.09191	−	0.630417i	0.110867	−	0.0640091i	0.554408	+	0.832245i	$0.312945\pi$
$98$		0			0
$99$		−	15.2402i		−	1.53170i
$100$		0			0
$101$	−0.759470	−	1.31544i	−0.0755701	−	0.130891i	0.825764	−	0.564016i	$-0.190744\pi$
$101$	−0.759470	−	1.31544i	−0.0755701	−	0.130891i	−0.901334	+	0.433125i	$0.857411\pi$
$102$		0			0
$103$	−7.66416	−	13.2747i	−0.755172	−	1.30800i	−0.945289	−	0.326235i	$-0.894220\pi$
$103$	−7.66416	−	13.2747i	−0.755172	−	1.30800i	0.190117	−	0.981761i	$-0.439113\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.93055			−0.863348			−0.431674	−	0.902030i	$-0.642077\pi$
$107$	−8.93055			−0.863348			−0.431674	+	0.902030i	$0.642077\pi$
$108$		0			0
$109$	−6.03546	−	3.48457i	−0.578092	−	0.333762i	0.182283	−	0.983246i	$-0.441651\pi$
$109$	−6.03546	−	3.48457i	−0.578092	−	0.333762i	−0.760375	+	0.649484i	$0.774985\pi$
$110$		0			0
$111$	−11.9885	+	6.92156i	−1.13790	+	0.656965i
$112$		0			0
$113$	10.2346	+	17.7268i	0.962790	+	1.66760i	0.715440	+	0.698674i	$0.246226\pi$
$113$	10.2346	+	17.7268i	0.962790	+	1.66760i	0.247349	+	0.968926i	$0.420440\pi$
$114$		0			0
$115$	−0.125086	+	0.0722184i	−0.0116643	+	0.00673440i
$116$		0			0
$117$	15.1939	+	14.8740i	1.40467	+	1.37510i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.16060	+	3.74226i	−0.196418	+	0.340206i
$122$		0			0
$123$		−	28.4706i		−	2.56711i
$124$		0			0
$125$		−	6.85827i		−	0.613422i
$126$		0			0
$127$	−7.14173	+	12.3698i	−0.633726	+	1.09765i	0.353057	+	0.935602i	$0.385142\pi$
$127$	−7.14173	+	12.3698i	−0.633726	+	1.09765i	−0.986783	+	0.162044i	$0.948191\pi$
$128$		0			0
$129$	10.5841	−	18.3321i	0.931874	−	1.61405i
$130$		0			0
$131$	6.17629	+	10.6976i	0.539625	+	0.934658i	0.998924	+	0.0463762i	$0.0147673\pi$
$131$	6.17629	+	10.6976i	0.539625	+	0.934658i	−0.459299	+	0.888282i	$0.651899\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−5.41632	+	3.12711i	−0.466163	+	0.269139i
$136$		0			0
$137$		−	0.270332i		−	0.0230960i	−0.999933	−	0.0115480i	$-0.996324\pi$
$137$		−	0.270332i		−	0.0230960i	0.999933	−	0.0115480i	$-0.00367593\pi$
$138$		0			0
$139$	−8.50164	−	14.7253i	−0.721100	−	1.24898i	−0.960559	−	0.278075i	$-0.910304\pi$
$139$	−8.50164	−	14.7253i	−0.721100	−	1.24898i	0.239459	−	0.970906i	$-0.423030\pi$
$140$		0			0
$141$	2.50094	+	1.44392i	0.210617	+	0.121600i
$142$		0			0
$143$	2.50727	+	8.97430i	0.209668	+	0.750469i
$144$		0			0
$145$			4.12353i			0.342440i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	15.7763	+	9.10848i	1.29245	+	0.746195i	0.979088	−	0.203439i	$-0.0652118\pi$
$149$	15.7763	+	9.10848i	1.29245	+	0.746195i	0.313361	+	0.949634i	$0.398545\pi$
$150$		0			0
$151$	−13.1371	−	7.58471i	−1.06908	−	0.617235i	−0.141151	−	0.989988i	$-0.545080\pi$
$151$	−13.1371	−	7.58471i	−1.06908	−	0.617235i	−0.927930	+	0.372753i	$0.878414\pi$
$152$		0			0
$153$	−13.3810	+	23.1766i	−1.08179	+	1.87372i
$154$		0			0
$155$	4.48500			0.360244
$156$		0			0
$157$	−1.25551	+	2.17461i	−0.100201	+	0.173553i	−0.911767	−	0.410707i	$-0.865282\pi$
$157$	−1.25551	+	2.17461i	−0.100201	+	0.173553i	0.811566	+	0.584260i	$0.198615\pi$
$158$		0			0
$159$	−12.7325			−1.00976
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1.78051	−	1.02798i	−0.139460	−	0.0805174i	0.428647	−	0.903472i	$-0.358991\pi$
$163$	−1.78051	−	1.02798i	−0.139460	−	0.0805174i	−0.568107	+	0.822955i	$0.692324\pi$
$164$		0			0
$165$	−5.57898			−0.434323
$166$		0			0
$167$	−11.2017	−	6.46730i	−0.866813	−	0.500455i	−0.000525166	−	1.00000i	$-0.500167\pi$
$167$	−11.2017	−	6.46730i	−0.866813	−	0.500455i	−0.866288	+	0.499545i	$0.833500\pi$
$168$		0			0
$169$	−11.3941	−	6.25903i	−0.876466	−	0.481464i
$170$		0			0
$171$	−36.9204	+	21.3160i	−2.82337	+	1.63008i
$172$		0			0
$173$	12.9290	−	22.3936i	0.982970	−	1.70255i	0.332339	−	0.943160i	$-0.392162\pi$
$173$	12.9290	−	22.3936i	0.982970	−	1.70255i	0.650631	−	0.759394i	$-0.274505\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−22.3397	+	12.8978i	−1.67915	+	0.969460i
$178$		0			0
$179$	−4.49291	−	7.78195i	−0.335816	−	0.581650i	0.647825	−	0.761789i	$-0.275679\pi$
$179$	−4.49291	−	7.78195i	−0.335816	−	0.581650i	−0.983641	+	0.180139i	$0.942345\pi$
$180$		0			0
$181$	−25.7453			−1.91364			−0.956818	−	0.290688i	$-0.906116\pi$
$181$	−25.7453			−1.91364			−0.956818	+	0.290688i	$0.906116\pi$
$182$		0			0
$183$	−26.0617			−1.92654
$184$		0			0
$185$	1.67942	+	2.90884i	0.123473	+	0.213862i
$186$		0			0
$187$	−10.1568	+	5.86404i	−0.742740	+	0.428821i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.09964	−	7.10079i	0.296640	−	0.513795i	−0.678725	−	0.734392i	$-0.737467\pi$
$191$	4.09964	−	7.10079i	0.296640	−	0.513795i	0.975365	+	0.220597i	$0.0708006\pi$
$192$		0			0
$193$	15.7093	−	9.06976i	1.13078	−	0.652856i	0.186648	−	0.982427i	$-0.440238\pi$
$193$	15.7093	−	9.06976i	1.13078	−	0.652856i	0.944131	+	0.329571i	$0.106904\pi$
$194$		0			0
$195$	5.44493	−	5.56202i	0.389920	−	0.398304i
$196$		0			0
$197$	18.9365	+	10.9330i	1.34917	+	0.778942i	0.988132	−	0.153610i	$-0.0490898\pi$
$197$	18.9365	+	10.9330i	1.34917	+	0.778942i	0.361036	+	0.932552i	$0.382423\pi$
$198$		0			0
$199$	14.6033			1.03520			0.517602	−	0.855622i	$-0.326825\pi$
$199$	14.6033			1.03520			0.517602	+	0.855622i	$0.326825\pi$
$200$		0			0
$201$	−7.06661	−	4.07991i	−0.498440	−	0.287774i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−6.90799			−0.482475
$206$		0			0
$207$	−0.588449	+	1.01922i	−0.0409000	+	0.0708409i
$208$		0			0
$209$	−18.6829			−1.29232
$210$		0			0
$211$	7.52413	−	13.0322i	0.517982	−	0.897172i	−0.481799	−	0.876282i	$-0.660017\pi$
$211$	7.52413	−	13.0322i	0.517982	−	0.897172i	0.999782	−	0.0208903i	$-0.00665007\pi$
$212$		0			0
$213$	−0.234146	−	0.135184i	−0.0160434	−	0.00926268i
$214$		0			0
$215$	−4.44803	−	2.56807i	−0.303353	−	0.175141i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		−	12.2676i		−	0.828965i
$220$		0			0
$221$	4.06657	−	15.8491i	0.273547	−	1.06613i
$222$		0			0
$223$	16.5326	+	9.54512i	1.10711	+	0.639189i	0.938079	−	0.346423i	$-0.112604\pi$
$223$	16.5326	+	9.54512i	1.10711	+	0.639189i	0.169029	+	0.985611i	$0.445937\pi$
$224$		0			0
$225$	−13.1984	−	22.8603i	−0.879893	−	1.52402i
$226$		0			0
$227$			28.2144i			1.87266i	0.351126	+	0.936328i	$0.385799\pi$
$227$			28.2144i			1.87266i	−0.351126	+	0.936328i	$0.614201\pi$
$228$		0			0
$229$	10.6105	−	6.12600i	0.701164	−	0.404817i	−0.106617	−	0.994300i	$-0.534002\pi$
$229$	10.6105	−	6.12600i	0.701164	−	0.404817i	0.807781	+	0.589483i	$0.200669\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.41804	−	9.38432i	−0.354948	−	0.614787i	0.632161	−	0.774837i	$-0.282168\pi$
$233$	−5.41804	−	9.38432i	−0.354948	−	0.614787i	−0.987109	+	0.160050i	$0.948835\pi$
$234$		0			0
$235$	0.350346	−	0.606816i	0.0228540	−	0.0395843i
$236$		0			0
$237$	−11.8306	+	20.4912i	−0.768478	+	1.33104i
$238$		0			0
$239$		−	28.4040i		−	1.83730i	−0.395069	−	0.918652i	$-0.629279\pi$
$239$		−	28.4040i		−	1.83730i	0.395069	−	0.918652i	$-0.370721\pi$
$240$		0			0
$241$		−	24.9199i		−	1.60523i	−0.596497	−	0.802615i	$-0.703441\pi$
$241$		−	24.9199i		−	1.60523i	0.596497	−	0.802615i	$-0.296559\pi$
$242$		0			0
$243$	0.904698	−	1.56698i	0.0580364	−	0.100522i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	18.2340	−	18.6261i	1.16020	−	1.18515i
$248$		0			0
$249$	17.1938	−	9.92685i	1.08961	−	0.629088i
$250$		0			0
$251$	0.601570	+	1.04195i	0.0379707	+	0.0657673i	0.884386	−	0.466756i	$-0.154577\pi$
$251$	0.601570	+	1.04195i	0.0379707	+	0.0657673i	−0.846415	+	0.532523i	$0.821244\pi$
$252$		0			0
$253$	−0.446661	+	0.257880i	−0.0280813	+	0.0162128i
$254$		0			0
$255$	8.48425	+	4.89838i	0.531304	+	0.306749i
$256$		0			0
$257$	4.38376			0.273451			0.136726	−	0.990609i	$-0.456342\pi$
$257$	4.38376			0.273451			0.136726	+	0.990609i	$0.456342\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	16.7997	+	29.0979i	1.03987	+	1.80111i
$262$		0			0
$263$	−1.91389	−	3.31495i	−0.118015	−	0.204409i	0.800966	−	0.598710i	$-0.204320\pi$
$263$	−1.91389	−	3.31495i	−0.118015	−	0.204409i	−0.918981	+	0.394302i	$0.870987\pi$
$264$		0			0
$265$			3.08937i			0.189778i
$266$		0			0
$267$	−36.5230	+	21.0865i	−2.23517	+	1.29048i
$268$		0			0
$269$	4.43728			0.270546			0.135273	−	0.990808i	$-0.456809\pi$
$269$	4.43728			0.270546			0.135273	+	0.990808i	$0.456809\pi$
$270$		0			0
$271$		−	14.7090i		−	0.893509i	−0.894657	−	0.446755i	$-0.852580\pi$
$271$		−	14.7090i		−	0.893509i	0.894657	−	0.446755i	$-0.147420\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	11.5680i		−	0.697579i
$276$		0			0
$277$	−15.5411			−0.933774			−0.466887	−	0.884317i	$-0.654624\pi$
$277$	−15.5411			−0.933774			−0.466887	+	0.884317i	$0.654624\pi$
$278$		0			0
$279$	31.6486	−	18.2723i	1.89475	−	1.09394i
$280$		0			0
$281$		−	2.32066i		−	0.138439i	−0.997601	−	0.0692194i	$-0.977949\pi$
$281$		−	2.32066i		−	0.138439i	0.997601	−	0.0692194i	$-0.0220508\pi$
$282$		0			0
$283$	−14.3851	−	24.9158i	−0.855107	−	1.48109i	−0.876545	−	0.481319i	$-0.840158\pi$
$283$	−14.3851	−	24.9158i	−0.855107	−	1.48109i	0.0214381	−	0.999770i	$-0.493176\pi$
$284$		0			0
$285$	7.80314	+	13.5154i	0.462218	+	0.800586i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	3.59470			0.211453
$290$		0			0
$291$	−3.25697	−	1.88041i	−0.190927	−	0.110232i
$292$		0			0
$293$	22.0773	−	12.7464i	1.28977	−	0.744650i	0.311159	−	0.950358i	$-0.399283\pi$
$293$	22.0773	−	12.7464i	1.28977	−	0.744650i	0.978613	+	0.205708i	$0.0659496\pi$
$294$		0			0
$295$	3.12947	+	5.42041i	0.182205	+	0.315588i
$296$		0			0
$297$	−19.3408	+	11.1664i	−1.12227	+	0.647941i
$298$		0			0
$299$	0.178833	−	0.696987i	0.0103422	−	0.0403078i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−2.26535	+	3.92370i	−0.130141	+	0.225411i
$304$		0			0
$305$			6.32351i			0.362083i
$306$		0			0
$307$			8.39430i			0.479088i	0.970886	+	0.239544i	$0.0769979\pi$
$307$			8.39430i			0.479088i	−0.970886	+	0.239544i	$0.923002\pi$
$308$		0			0
$309$	−22.8607	+	39.5959i	−1.30050	+	2.25253i
$310$		0			0
$311$	−5.75985	+	9.97635i	−0.326611	+	0.565707i	−0.981837	−	0.189726i	$-0.939240\pi$
$311$	−5.75985	+	9.97635i	−0.326611	+	0.565707i	0.655226	+	0.755433i	$0.272573\pi$
$312$		0			0
$313$	−6.17947	−	10.7032i	−0.349284	−	0.604978i	0.636838	−	0.770997i	$-0.280242\pi$
$313$	−6.17947	−	10.7032i	−0.349284	−	0.604978i	−0.986122	+	0.166019i	$0.946909\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	13.4007	−	7.73691i	0.752660	−	0.434548i	−0.0739943	−	0.997259i	$-0.523575\pi$
$317$	13.4007	−	7.73691i	0.752660	−	0.434548i	0.826654	+	0.562710i	$0.190241\pi$
$318$		0			0
$319$			14.7244i			0.824410i
$320$		0			0
$321$	13.3190	+	23.0693i	0.743397	+	1.28760i
$322$		0			0
$323$	28.4121	+	16.4037i	1.58089	+	0.912727i
$324$		0			0
$325$	11.5329	+	11.2901i	0.639729	+	0.626262i
$326$		0			0
$327$			20.7876i			1.14956i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.374803	−	0.216393i	−0.0206010	−	0.0118940i	0.489664	−	0.871911i	$-0.337119\pi$
$331$	−0.374803	−	0.216393i	−0.0206010	−	0.0118940i	−0.510265	+	0.860017i	$0.670453\pi$
$332$		0			0
$333$	23.7018	+	13.6842i	1.29885	+	0.749890i
$334$		0			0
$335$	−0.989931	+	1.71461i	−0.0540857	+	0.0936792i
$336$		0			0
$337$	13.6844			0.745435			0.372718	−	0.927945i	$-0.378426\pi$
$337$	13.6844			0.745435			0.372718	+	0.927945i	$0.378426\pi$
$338$		0			0
$339$	30.5278	−	52.8757i	1.65804	−	2.87181i
$340$		0			0
$341$	16.0152			0.867272
$342$		0			0
$343$		0			0
$344$		0			0
$345$	0.373107	+	0.215413i	0.0200874	+	0.0115975i
$346$		0			0
$347$	23.4597			1.25938			0.629692	−	0.776845i	$-0.283181\pi$
$347$	23.4597			1.25938			0.629692	+	0.776845i	$0.283181\pi$
$348$		0			0
$349$	−2.07571	−	1.19841i	−0.111110	−	0.0641494i	0.443415	−	0.896316i	$-0.353767\pi$
$349$	−2.07571	−	1.19841i	−0.111110	−	0.0641494i	−0.554525	+	0.832167i	$0.687100\pi$
$350$		0			0
$351$	7.74362	−	30.1801i	0.413324	−	1.61090i
$352$		0			0
$353$	−28.8702	+	16.6682i	−1.53661	+	0.887161i	−0.537574	+	0.843217i	$0.680659\pi$
$353$	−28.8702	+	16.6682i	−1.53661	+	0.887161i	−0.999034	+	0.0439444i	$0.986008\pi$
$354$		0			0
$355$	−0.0328006	+	0.0568123i	−0.00174087	+	0.00301528i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.95209	−	3.43644i	0.314139	−	0.181369i	−0.334638	−	0.942347i	$-0.608614\pi$
$359$	5.95209	−	3.43644i	0.314139	−	0.181369i	0.648777	+	0.760978i	$0.275281\pi$
$360$		0			0
$361$	16.6312	+	28.8061i	0.875326	+	1.51611i
$362$		0			0
$363$	12.8893			0.676512
$364$		0			0
$365$	−2.97655			−0.155800
$366$		0			0
$367$	13.5376	+	23.4478i	0.706658	+	1.22397i	0.966090	+	0.258206i	$0.0831312\pi$
$367$	13.5376	+	23.4478i	0.706658	+	1.22397i	−0.259432	+	0.965761i	$0.583535\pi$
$368$		0			0
$369$	−48.7465	+	28.1438i	−2.53764	+	1.46511i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−5.66509	+	9.81222i	−0.293327	+	0.508058i	−0.974594	−	0.223977i	$-0.928096\pi$
$373$	−5.66509	+	9.81222i	−0.293327	+	0.508058i	0.681267	+	0.732035i	$0.261429\pi$
$374$		0			0
$375$	−17.7162	+	10.2284i	−0.914860	+	0.528194i
$376$		0			0
$377$	−14.6797	−	14.3707i	−0.756042	−	0.740127i
$378$		0			0
$379$	25.2335	+	14.5686i	1.29616	+	0.748337i	0.979738	−	0.200283i	$-0.0641861\pi$
$379$	25.2335	+	14.5686i	1.29616	+	0.748337i	0.316419	+	0.948619i	$0.397519\pi$
$380$		0			0
$381$	42.6048			2.18271
$382$		0			0
$383$	−28.1794	−	16.2694i	−1.43990	−	0.831326i	−0.442056	−	0.896987i	$-0.645751\pi$
$383$	−28.1794	−	16.2694i	−1.43990	−	0.831326i	−0.997842	+	0.0656616i	$0.979084\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−41.8502			−2.12737
$388$		0			0
$389$	−15.7828	+	27.3366i	−0.800220	+	1.38602i	0.119251	+	0.992864i	$0.461951\pi$
$389$	−15.7828	+	27.3366i	−0.800220	+	1.38602i	−0.919471	+	0.393157i	$0.871383\pi$
$390$		0			0
$391$	0.905682			0.0458023
$392$		0			0
$393$	18.4227	−	31.9090i	0.929301	−	1.60960i
$394$		0			0
$395$	4.97189	+	2.87052i	0.250163	+	0.144432i
$396$		0			0
$397$	22.3296	+	12.8920i	1.12069	+	0.647031i	0.941577	−	0.336797i	$-0.109344\pi$
$397$	22.3296	+	12.8920i	1.12069	+	0.647031i	0.179114	+	0.983828i	$0.442677\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			24.0514i			1.20107i	0.799599	+	0.600534i	$0.205045\pi$
$401$			24.0514i			1.20107i	−0.799599	+	0.600534i	$0.794955\pi$
$402$		0			0
$403$	−15.6304	+	15.9665i	−0.778606	+	0.795349i
$404$		0			0
$405$	5.06733	+	2.92563i	0.251798	+	0.145376i
$406$		0			0
$407$	5.99692	+	10.3870i	0.297256	+	0.514863i
$408$		0			0
$409$		−	16.0055i		−	0.791419i	−0.918376	−	0.395709i	$-0.870499\pi$
$409$		−	16.0055i		−	0.791419i	0.918376	−	0.395709i	$-0.129501\pi$
$410$		0			0
$411$	−0.698319	+	0.403175i	−0.0344455	+	0.0198871i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.40861	−	4.17183i	−0.118234	−	0.204787i
$416$		0			0
$417$	−25.3588	+	43.9227i	−1.24182	+	2.15090i
$418$		0			0
$419$	13.9630	−	24.1846i	0.682136	−	1.18149i	−0.292192	−	0.956360i	$-0.594385\pi$
$419$	13.9630	−	24.1846i	0.682136	−	1.18149i	0.974328	−	0.225134i	$-0.0722821\pi$
$420$		0			0
$421$			24.5187i			1.19497i	0.801880	+	0.597485i	$0.203833\pi$
$421$			24.5187i			1.19497i	−0.801880	+	0.597485i	$0.796167\pi$
$422$		0			0
$423$		−	5.70937i		−	0.277599i
$424$		0			0
$425$	−10.1568	+	17.5921i	−0.492678	+	0.853344i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	19.4429	−	19.8610i	0.938714	−	0.958900i
$430$		0			0
$431$	12.4652	−	7.19679i	0.600428	−	0.346657i	−0.168782	−	0.985653i	$-0.553983\pi$
$431$	12.4652	−	7.19679i	0.600428	−	0.346657i	0.769210	+	0.638996i	$0.220650\pi$
$432$		0			0
$433$	−9.32322	−	16.1483i	−0.448045	−	0.776037i	0.550214	−	0.835024i	$-0.314546\pi$
$433$	−9.32322	−	16.1483i	−0.448045	−	0.776037i	−0.998259	+	0.0589869i	$0.981213\pi$
$434$		0			0
$435$	10.6518	−	6.14984i	0.510717	−	0.294862i
$436$		0			0
$437$	1.24946	+	0.721377i	0.0597699	+	0.0345082i
$438$		0			0
$439$	3.73494			0.178259			0.0891295	−	0.996020i	$-0.471592\pi$
$439$	3.73494			0.178259			0.0891295	+	0.996020i	$0.471592\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.98125	+	5.16367i	0.141643	+	0.245333i	0.928116	−	0.372292i	$-0.121428\pi$
$443$	2.98125	+	5.16367i	0.141643	+	0.245333i	−0.786472	+	0.617626i	$0.788095\pi$
$444$		0			0
$445$	5.11635	+	8.86178i	0.242538	+	0.420088i
$446$		0			0
$447$		−	54.3376i		−	2.57008i
$448$		0			0
$449$	20.6585	−	11.9272i	0.974934	−	0.562878i	0.0741970	−	0.997244i	$-0.476361\pi$
$449$	20.6585	−	11.9272i	0.974934	−	0.562878i	0.900737	+	0.434365i	$0.143027\pi$
$450$		0			0
$451$	−24.6673			−1.16154
$452$		0			0
$453$			45.2474i			2.12591i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	11.6931i		−	0.546979i	−0.961875	−	0.273489i	$-0.911822\pi$
$457$		−	11.6931i		−	0.546979i	0.961875	−	0.273489i	$-0.0881778\pi$
$458$		0			0
$459$	39.2167			1.83048
$460$		0			0
$461$	34.8297	−	20.1089i	1.62218	−	0.936566i	0.635844	−	0.771817i	$-0.280652\pi$
$461$	34.8297	−	20.1089i	1.62218	−	0.936566i	0.986336	−	0.164749i	$-0.0526814\pi$
$462$		0			0
$463$			12.2045i			0.567191i	0.958944	+	0.283596i	$0.0915274\pi$
$463$			12.2045i			0.567191i	−0.958944	+	0.283596i	$0.908473\pi$
$464$		0			0
$465$	−6.68895	−	11.5856i	−0.310193	−	0.537269i
$466$		0			0
$467$	−4.48493	−	7.76813i	−0.207538	−	0.359466i	0.743401	−	0.668847i	$-0.233212\pi$
$467$	−4.48493	−	7.76813i	−0.207538	−	0.359466i	−0.950938	+	0.309380i	$0.899878\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	7.48991			0.345117
$472$		0			0
$473$	−15.8832	−	9.17015i	−0.730309	−	0.421644i
$474$		0			0
$475$	−28.0243	+	16.1799i	−1.28584	+	0.742383i
$476$		0			0
$477$	12.5864	+	21.8003i	0.576291	+	0.998165i
$478$		0			0
$479$	9.73972	−	5.62323i	0.445019	−	0.256932i	−0.260705	−	0.965418i	$-0.583955\pi$
$479$	9.73972	−	5.62323i	0.445019	−	0.256932i	0.705724	+	0.708487i	$0.250622\pi$
$480$		0			0
$481$	−16.2082	−	4.15871i	−0.739032	−	0.189621i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.456255	+	0.790257i	−0.0207175	+	0.0358837i
$486$		0			0
$487$		−	13.3720i		−	0.605944i	−0.953000	−	0.302972i	$-0.902021\pi$
$487$		−	13.3720i		−	0.605944i	0.953000	−	0.302972i	$-0.0979788\pi$
$488$		0			0
$489$			6.13251i			0.277322i
$490$		0			0
$491$	−10.5538	+	18.2798i	−0.476288	+	0.824955i	−0.999631	−	0.0271672i	$-0.991351\pi$
$491$	−10.5538	+	18.2798i	−0.476288	+	0.824955i	0.523343	+	0.852122i	$0.324685\pi$
$492$		0			0
$493$	12.9282	−	22.3922i	0.582255	−	1.00850i
$494$		0			0
$495$	5.51494	+	9.55215i	0.247878	+	0.429337i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	5.60307	−	3.23493i	0.250828	−	0.144815i	−0.369315	−	0.929304i	$-0.620408\pi$
$499$	5.60307	−	3.23493i	0.250828	−	0.144815i	0.620143	+	0.784489i	$0.287074\pi$
$500$		0			0
$501$			38.5814i			1.72369i
$502$		0			0
$503$	4.71308	+	8.16329i	0.210146	+	0.363983i	0.951760	−	0.306843i	$-0.0992728\pi$
$503$	4.71308	+	8.16329i	0.210146	+	0.363983i	−0.741614	+	0.670827i	$0.765939\pi$
$504$		0			0
$505$	0.952031	+	0.549655i	0.0423648	+	0.0244593i
$506$		0			0
$507$	0.824884	+	38.7677i	0.0366344	+	1.72173i
$508$		0			0
$509$		−	35.6633i		−	1.58075i	−0.612625	−	0.790374i	$-0.709886\pi$
$509$		−	35.6633i		−	1.58075i	0.612625	−	0.790374i	$-0.290114\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	54.1027	+	31.2362i	2.38869	+	1.37911i
$514$		0			0
$515$	9.60738	+	5.54682i	0.423352	+	0.244422i
$516$		0			0
$517$	1.25103	−	2.16684i	0.0550201	−	0.0952975i
$518$		0			0
$519$	−77.1291			−3.38559
$520$		0			0
$521$	−0.513733	+	0.889812i	−0.0225071	+	0.0389834i	−0.877060	−	0.480382i	$-0.840498\pi$
$521$	−0.513733	+	0.889812i	−0.0225071	+	0.0389834i	0.854552	+	0.519365i	$0.173831\pi$
$522$		0			0
$523$	9.72790			0.425371			0.212686	−	0.977121i	$-0.431779\pi$
$523$	9.72790			0.425371			0.212686	+	0.977121i	$0.431779\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−24.3552	−	14.0615i	−1.06093	−	0.612527i
$528$		0			0
$529$	−22.9602			−0.998268
$530$		0			0
$531$	44.1665	+	25.4996i	1.91666	+	1.10659i
$532$		0			0
$533$	24.0746	−	24.5923i	1.04279	−	1.06521i
$534$		0			0
$535$	5.59743	−	3.23168i	0.241998	−	0.139718i
$536$		0			0
$537$	−13.4015	+	23.2121i	−0.578317	+	1.00167i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	33.7379	−	19.4786i	1.45051	−	0.837451i	0.451997	−	0.892019i	$-0.350712\pi$
$541$	33.7379	−	19.4786i	1.45051	−	0.837451i	0.998510	+	0.0545685i	$0.0173783\pi$
$542$		0			0
$543$	38.3967	+	66.5050i	1.64776	+	2.85400i
$544$		0			0
$545$	5.04382			0.216054
$546$		0			0
$547$	−4.88536			−0.208883			−0.104441	−	0.994531i	$-0.533305\pi$
$547$	−4.88536			−0.208883			−0.104441	+	0.994531i	$0.533305\pi$
$548$		0			0
$549$	25.7626	+	44.6221i	1.09952	+	1.90442i
$550$		0			0
$551$	35.6709	−	20.5946i	1.51963	−	0.877360i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	5.00938	−	8.67650i	0.212636	−	0.368297i
$556$		0			0
$557$	9.16308	−	5.29031i	0.388252	−	0.224158i	−0.293150	−	0.956066i	$-0.594704\pi$
$557$	9.16308	−	5.29031i	0.388252	−	0.224158i	0.681403	+	0.731909i	$0.261370\pi$
$558$		0			0
$559$	24.6438	−	6.88507i	1.04232	−	0.291207i
$560$		0			0
$561$	30.2958	+	17.4913i	1.27909	+	0.738484i
$562$		0			0
$563$	26.0664			1.09857			0.549284	−	0.835635i	$-0.314900\pi$
$563$	26.0664			1.09857			0.549284	+	0.835635i	$0.314900\pi$
$564$		0			0
$565$	−12.8295	−	7.40714i	−0.539743	−	0.311621i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−10.7441			−0.450416			−0.225208	−	0.974311i	$-0.572306\pi$
$569$	−10.7441			−0.450416			−0.225208	+	0.974311i	$0.572306\pi$
$570$		0			0
$571$	1.42823	−	2.47377i	0.0597696	−	0.103524i	−0.834592	−	0.550868i	$-0.814297\pi$
$571$	1.42823	−	2.47377i	0.0597696	−	0.103524i	0.894362	+	0.447344i	$0.147630\pi$
$572$		0			0
$573$	−24.4569			−1.02170
$574$		0			0
$575$	−0.446661	+	0.773639i	−0.0186270	+	0.0322630i
$576$		0			0
$577$	23.0645	+	13.3163i	0.960189	+	0.554365i	0.896231	−	0.443587i	$-0.146294\pi$
$577$	23.0645	+	13.3163i	0.960189	+	0.554365i	0.0639576	+	0.997953i	$0.479628\pi$
$578$		0			0
$579$	−46.8578	−	27.0533i	−1.94734	−	1.12430i
$580$		0			0
$581$		0			0
$582$		0			0
$583$			11.0316i			0.456883i
$584$		0			0
$585$	−14.9055	−	3.82447i	−0.616269	−	0.158122i
$586$		0			0
$587$	25.2637	+	14.5860i	1.04274	+	0.602029i	0.920609	−	0.390485i	$-0.127693\pi$
$587$	25.2637	+	14.5860i	1.04274	+	0.602029i	0.122135	+	0.992513i	$0.461026\pi$
$588$		0			0
$589$	−22.4000	−	38.7979i	−0.922975	−	1.59864i
$590$		0			0
$591$		−	65.2219i		−	2.68287i
$592$		0			0
$593$	−27.5072	+	15.8813i	−1.12958	+	0.652165i	−0.943830	−	0.330431i	$-0.892806\pi$
$593$	−27.5072	+	15.8813i	−1.12958	+	0.652165i	−0.185753	+	0.982596i	$0.559473\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−21.7795	−	37.7232i	−0.891374	−	1.54391i
$598$		0			0
$599$	22.8974	−	39.6594i	0.935561	−	1.62044i	0.161932	−	0.986802i	$-0.448228\pi$
$599$	22.8974	−	39.6594i	0.935561	−	1.62044i	0.773630	−	0.633638i	$-0.218439\pi$
$600$		0			0
$601$	−3.67250	+	6.36096i	−0.149805	+	0.259469i	−0.931155	−	0.364623i	$-0.881198\pi$
$601$	−3.67250	+	6.36096i	−0.149805	+	0.259469i	0.781351	+	0.624092i	$0.214531\pi$
$602$		0			0
$603$			16.1323i			0.656958i
$604$		0			0
$605$		−	3.12740i		−	0.127147i
$606$		0			0
$607$	−3.12609	+	5.41454i	−0.126884	+	0.219770i	−0.922468	−	0.386074i	$-0.873831\pi$
$607$	−3.12609	+	5.41454i	−0.126884	+	0.219770i	0.795584	+	0.605844i	$0.207164\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.939287	+	3.36200i	0.0379995	+	0.136012i
$612$		0			0
$613$	−2.06656	+	1.19313i	−0.0834676	+	0.0481900i	−0.541153	−	0.840924i	$-0.682012\pi$
$613$	−2.06656	+	1.19313i	−0.0834676	+	0.0481900i	0.457685	+	0.889114i	$0.348679\pi$
$614$		0			0
$615$	10.3026	+	17.8446i	0.415441	+	0.719565i
$616$		0			0
$617$	32.3460	−	18.6750i	1.30220	−	0.751827i	0.321420	−	0.946937i	$-0.395840\pi$
$617$	32.3460	−	18.6750i	1.30220	−	0.751827i	0.980781	+	0.195110i	$0.0625064\pi$
$618$		0			0
$619$	24.2964	+	14.0275i	0.976556	+	0.563815i	0.901229	−	0.433344i	$-0.142666\pi$
$619$	24.2964	+	14.0275i	0.976556	+	0.563815i	0.0753273	+	0.997159i	$0.476000\pi$
$620$		0			0
$621$	1.72461			0.0692063
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−8.70873	−	15.0840i	−0.348349	−	0.603359i
$626$		0			0
$627$	27.8637	+	48.2614i	1.11277	+	1.92737i
$628$		0			0
$629$		−	21.0614i		−	0.839772i
$630$		0			0
$631$	−27.5062	+	15.8807i	−1.09501	+	0.632202i	−0.934905	−	0.354899i	$-0.884515\pi$
$631$	−27.5062	+	15.8807i	−1.09501	+	0.632202i	−0.160101	+	0.987101i	$0.551182\pi$
$632$		0			0
$633$	−44.8860			−1.78406
$634$		0			0
$635$		−	10.3375i		−	0.410229i
$636$		0			0
$637$		0			0
$638$		0			0
$639$			0.534531i			0.0211457i
$640$		0			0
$641$	16.0213			0.632803			0.316401	−	0.948625i	$-0.397525\pi$
$641$	16.0213			0.632803			0.316401	+	0.948625i	$0.397525\pi$
$642$		0			0
$643$	−2.09386	+	1.20889i	−0.0825739	+	0.0476740i	−0.540718	−	0.841204i	$-0.681848\pi$
$643$	−2.09386	+	1.20889i	−0.0825739	+	0.0476740i	0.458145	+	0.888878i	$0.348514\pi$
$644$		0			0
$645$			15.3201i			0.603229i
$646$		0			0
$647$	9.64910	+	16.7127i	0.379345	+	0.657046i	0.990967	−	0.134105i	$-0.0428159\pi$
$647$	9.64910	+	16.7127i	0.379345	+	0.657046i	−0.611622	+	0.791150i	$0.709483\pi$
$648$		0			0
$649$	11.1748	+	19.3554i	0.438651	+	0.759765i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	29.4756			1.15347			0.576735	−	0.816932i	$-0.304327\pi$
$653$	29.4756			1.15347			0.576735	+	0.816932i	$0.304327\pi$
$654$		0			0
$655$	−7.74227	−	4.47000i	−0.302515	−	0.174657i
$656$		0			0
$657$	−21.0041	+	12.1267i	−0.819449	+	0.473109i
$658$		0			0
$659$	13.9651	+	24.1882i	0.544003	+	0.942240i	0.998669	+	0.0515784i	$0.0164252\pi$
$659$	13.9651	+	24.1882i	0.544003	+	0.942240i	−0.454666	+	0.890662i	$0.650241\pi$
$660$		0			0
$661$	−12.9164	+	7.45731i	−0.502392	+	0.290056i	−0.729701	−	0.683767i	$-0.760341\pi$
$661$	−12.9164	+	7.45731i	−0.502392	+	0.290056i	0.227309	+	0.973823i	$0.427007\pi$
$662$		0			0
$663$	−47.0061	+	13.1327i	−1.82556	+	0.510032i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.568535	−	0.984731i	0.0220138	−	0.0381289i
$668$		0			0
$669$		−	56.9425i		−	2.20152i
$670$		0			0
$671$			22.5802i			0.871699i
$672$		0			0
$673$	−5.92919	+	10.2697i	−0.228553	+	0.395866i	−0.957380	−	0.288833i	$-0.906733\pi$
$673$	−5.92919	+	10.2697i	−0.228553	+	0.395866i	0.728826	+	0.684699i	$0.240066\pi$
$674$		0			0
$675$	−19.3408	+	33.4992i	−0.744427	+	1.28939i
$676$		0			0
$677$	−10.5182	−	18.2181i	−0.404249	−	0.700179i	0.589985	−	0.807414i	$-0.299134\pi$
$677$	−10.5182	−	18.2181i	−0.404249	−	0.700179i	−0.994234	+	0.107235i	$0.965800\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	72.8831	−	42.0791i	2.79289	−	1.61247i
$682$		0			0
$683$		−	44.1562i		−	1.68959i	−0.535091	−	0.844794i	$-0.679723\pi$
$683$		−	44.1562i		−	1.68959i	0.535091	−	0.844794i	$-0.320277\pi$
$684$		0			0
$685$	0.0978246	+	0.169437i	0.00373768	+	0.00647386i
$686$		0			0
$687$	−31.6492	−	18.2727i	−1.20749	−	0.697145i
$688$		0			0
$689$	−10.9981	−	10.7666i	−0.418994	−	0.410174i
$690$		0			0
$691$		−	17.3183i		−	0.658818i	−0.944187	−	0.329409i	$-0.893151\pi$
$691$		−	17.3183i		−	0.658818i	0.944187	−	0.329409i	$-0.106849\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	10.6572	+	6.15294i	0.404251	+	0.233394i
$696$		0			0
$697$	37.5129	+	21.6581i	1.42090	+	0.820358i
$698$		0			0
$699$	−16.1610	+	27.9916i	−0.611264	+	1.05874i
$700$		0			0
$701$	−21.6063			−0.816059			−0.408029	−	0.912969i	$-0.633784\pi$
$701$	−21.6063			−0.816059			−0.408029	+	0.912969i	$0.633784\pi$
$702$		0			0
$703$	16.7754	−	29.0559i	0.632697	−	1.09586i
$704$		0			0
$705$	−2.09003			−0.0787149
$706$		0			0
$707$		0			0
$708$		0			0
$709$	25.9030	+	14.9551i	0.972808	+	0.561651i	0.900091	−	0.435702i	$-0.143500\pi$
$709$	25.9030	+	14.9551i	0.972808	+	0.561651i	0.0727165	+	0.997353i	$0.476833\pi$
$710$		0			0
$711$	46.7791			1.75435
$712$		0			0
$713$	−1.07105	−	0.618373i	−0.0401113	−	0.0231583i
$714$		0			0
$715$	−4.81900	−	4.71755i	−0.180220	−	0.176427i
$716$		0			0
$717$	−73.3729	+	42.3618i	−2.74016	+	1.58203i
$718$		0			0
$719$	−10.4266	+	18.0594i	−0.388847	+	0.673503i	−0.992295	−	0.123899i	$-0.960460\pi$
$719$	−10.4266	+	18.0594i	−0.388847	+	0.673503i	0.603447	+	0.797403i	$0.293793\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−64.3727	+	37.1656i	−2.39405	+	1.38220i
$724$		0			0
$725$	12.7517	+	22.0867i	0.473588	+	0.820278i
$726$		0			0
$727$	−46.9592			−1.74162			−0.870810	−	0.491620i	$-0.836405\pi$
$727$	−46.9592			−1.74162			−0.870810	+	0.491620i	$0.836405\pi$
$728$		0			0
$729$	−29.6515			−1.09820
$730$		0			0
$731$	16.1029	+	27.8911i	0.595588	+	1.03159i
$732$		0			0
$733$	20.4440	−	11.8033i	0.755115	−	0.435966i	−0.0724243	−	0.997374i	$-0.523074\pi$
$733$	20.4440	−	11.8033i	0.755115	−	0.435966i	0.827539	+	0.561408i	$0.189740\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.53488	+	6.12259i	−0.130209	+	0.225529i
$738$		0			0
$739$	−4.54420	+	2.62359i	−0.167161	+	0.0965105i	−0.581247	−	0.813728i	$-0.697435\pi$
$739$	−4.54420	+	2.62359i	−0.167161	+	0.0965105i	0.414085	+	0.910238i	$0.364101\pi$
$740$		0			0
$741$	−75.3090	−	19.3228i	−2.76654	−	0.709841i
$742$		0			0
$743$	32.9998	+	19.0525i	1.21065	+	0.698967i	0.962900	−	0.269858i	$-0.0869769\pi$
$743$	32.9998	+	19.0525i	1.21065	+	0.698967i	0.247746	+	0.968825i	$0.420310\pi$
$744$		0			0
$745$	−13.1843			−0.483034
$746$		0			0
$747$	−33.9929	−	19.6258i	−1.24373	−	0.718070i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−39.7430			−1.45024			−0.725122	−	0.688620i	$-0.758217\pi$
$751$	−39.7430			−1.45024			−0.725122	+	0.688620i	$0.758217\pi$
$752$		0			0
$753$	1.79437	−	3.10793i	0.0653903	−	0.113259i
$754$		0			0
$755$	10.9786			0.399554
$756$		0			0
$757$	−22.1856	+	38.4266i	−0.806349	+	1.39664i	0.109027	+	0.994039i	$0.465227\pi$
$757$	−22.1856	+	38.4266i	−0.806349	+	1.39664i	−0.915376	+	0.402599i	$0.868107\pi$
$758$		0			0
$759$	1.33230	+	0.769206i	0.0483595	+	0.0279204i
$760$		0			0
$761$	−1.26726	−	0.731654i	−0.0459382	−	0.0265224i	0.476855	−	0.878982i	$-0.341777\pi$
$761$	−1.26726	−	0.731654i	−0.0459382	−	0.0265224i	−0.522793	+	0.852460i	$0.675110\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		−	19.3686i		−	0.700274i
$766$		0			0
$767$	−30.2029	−	7.74947i	−1.09056	−	0.279817i
$768$		0			0
$769$	−34.2543	−	19.7767i	−1.23524	−	0.713166i	−0.267123	−	0.963663i	$-0.586073\pi$
$769$	−34.2543	−	19.7767i	−1.23524	−	0.713166i	−0.968118	+	0.250496i	$0.919406\pi$
$770$		0			0
$771$	−6.53795	−	11.3241i	−0.235459	−	0.407826i
$772$		0			0
$773$			4.54728i			0.163554i	0.996651	+	0.0817771i	$0.0260596\pi$
$773$			4.54728i			0.163554i	−0.996651	+	0.0817771i	$0.973940\pi$
$774$		0			0
$775$	24.0228	−	13.8696i	0.862924	−	0.498210i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	34.5014	+	59.7582i	1.23614	+	2.14106i
$780$		0			0
$781$	−0.117125	+	0.202867i	−0.00419108	+	0.00725916i
$782$		0			0
$783$	24.6180	−	42.6397i	0.879776	−	1.52382i
$784$		0			0
$785$		−	1.81732i		−	0.0648629i
$786$		0			0
$787$			4.53412i			0.161624i	0.996729	+	0.0808119i	$0.0257513\pi$
$787$			4.53412i			0.161624i	−0.996729	+	0.0808119i	$0.974249\pi$
$788$		0			0
$789$	−5.70876	+	9.88786i	−0.203237	+	0.352017i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−22.5116	−	22.0377i	−0.799409	−	0.782581i
$794$		0			0
$795$	7.98042	−	4.60750i	0.283036	−	0.163411i
$796$		0			0
$797$	−3.27263	−	5.66835i	−0.115922	−	0.200783i	0.802226	−	0.597021i	$-0.203649\pi$
$797$	−3.27263	−	5.66835i	−0.115922	−	0.200783i	−0.918148	+	0.396237i	$0.870316\pi$
$798$		0			0
$799$	−3.80500	+	2.19682i	−0.134611	+	0.0777179i
$800$		0			0
$801$	72.2074	+	41.6890i	2.55132	+	1.47301i
$802$		0			0
$803$	−10.6288			−0.375081
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−6.61777	−	11.4623i	−0.232957	−	0.403493i
$808$		0			0
$809$	−18.2281	−	31.5721i	−0.640868	−	1.11002i	−0.985239	−	0.171182i	$-0.945241\pi$
$809$	−18.2281	−	31.5721i	−0.640868	−	1.11002i	0.344372	−	0.938833i	$-0.388092\pi$
$810$		0			0
$811$			0.00642760i			0.000225703i	1.00000		0.000112852i	$3.59218e-5\pi$
$811$			0.00642760i			0.000225703i	−1.00000		0.000112852i	$0.999964\pi$
$812$		0			0
$813$	−37.9961	+	21.9371i	−1.33258	+	0.769367i
$814$		0			0
$815$	1.48797			0.0521212
$816$		0			0
$817$			51.3040i			1.79490i
$818$		0			0
$819$		0			0
$820$		0			0
$821$			31.1711i			1.08788i	0.839125	+	0.543939i	$0.183068\pi$
$821$			31.1711i			1.08788i	−0.839125	+	0.543939i	$0.816932\pi$
$822$		0			0
$823$	18.8886			0.658416			0.329208	−	0.944257i	$-0.393218\pi$
$823$	18.8886			0.658416			0.329208	+	0.944257i	$0.393218\pi$
$824$		0			0
$825$	−29.8824	+	17.2526i	−1.04037	+	0.600659i
$826$		0			0
$827$		−	12.6707i		−	0.440605i	−0.975432	−	0.220302i	$-0.929296\pi$
$827$		−	12.6707i		−	0.440605i	0.975432	−	0.220302i	$-0.0707044\pi$
$828$		0			0
$829$	−3.01754	−	5.22652i	−0.104803	−	0.181525i	0.808855	−	0.588009i	$-0.200088\pi$
$829$	−3.01754	−	5.22652i	−0.104803	−	0.181525i	−0.913658	+	0.406484i	$0.866755\pi$
$830$		0			0
$831$	23.1780	+	40.1455i	0.804037	+	1.39263i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	9.36123			0.323959
$836$		0			0
$837$	−46.3775	−	26.7761i	−1.60304	−	0.925516i
$838$		0			0
$839$	−27.2737	+	15.7465i	−0.941594	+	0.543629i	−0.890460	−	0.455062i	$-0.849617\pi$
$839$	−27.2737	+	15.7465i	−0.941594	+	0.543629i	−0.0511342	+	0.998692i	$0.516284\pi$
$840$		0			0
$841$	−1.73112	−	2.99838i	−0.0596937	−	0.103392i
$842$		0			0
$843$	−5.99469	+	3.46103i	−0.206468	+	0.119204i
$844$		0			0
$845$	9.40643	−	0.200146i	0.323591	−	0.00688524i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−42.9081	+	74.3189i	−1.47260	+	2.55062i
$850$		0			0
$851$		−	0.926204i		−	0.0317499i
$852$		0			0
$853$		−	22.6189i		−	0.774456i	−0.921984	−	0.387228i	$-0.873433\pi$
$853$		−	22.6189i		−	0.774456i	0.921984	−	0.387228i	$-0.126567\pi$
$854$		0			0
$855$	15.4271	−	26.7206i	0.527597	−	0.913825i
$856$		0			0
$857$	−28.5945	+	49.5272i	−0.976770	+	1.69182i	−0.302804	+	0.953053i	$0.597923\pi$
$857$	−28.5945	+	49.5272i	−0.976770	+	1.69182i	−0.673966	+	0.738763i	$0.735410\pi$
$858$		0			0
$859$	−19.6239	−	33.9897i	−0.669560	−	1.15971i	−0.978027	−	0.208477i	$-0.933149\pi$
$859$	−19.6239	−	33.9897i	−0.669560	−	1.15971i	0.308467	−	0.951235i	$-0.400184\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	41.5902	−	24.0121i	1.41575	−	0.817381i	0.419825	−	0.907605i	$-0.362092\pi$
$863$	41.5902	−	24.0121i	1.41575	−	0.817381i	0.995922	+	0.0902240i	$0.0287583\pi$
$864$		0			0
$865$			18.7143i			0.636305i
$866$		0			0
$867$	−5.36115	−	9.28578i	−0.182074	−	0.315362i
$868$		0			0
$869$	17.7538	+	10.2502i	0.602256	+	0.347713i
$870$		0			0
$871$	−2.65403	−	9.49962i	−0.0899285	−	0.321882i
$872$		0			0
$873$			7.43530i			0.251647i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−18.5224	−	10.6939i	−0.625456	−	0.361107i	0.153534	−	0.988143i	$-0.450935\pi$
$877$	−18.5224	−	10.6939i	−0.625456	−	0.361107i	−0.778990	+	0.627036i	$0.784268\pi$
$878$		0			0
$879$	−65.8524	−	38.0199i	−2.22115	−	1.28238i
$880$		0			0
$881$	−16.7420	+	28.9980i	−0.564053	+	0.976968i	0.433084	+	0.901353i	$0.357425\pi$
$881$	−16.7420	+	28.9980i	−0.564053	+	0.976968i	−0.997137	+	0.0756147i	$0.975908\pi$
$882$		0			0
$883$	−29.4351			−0.990570			−0.495285	−	0.868730i	$-0.664936\pi$
$883$	−29.4351			−0.990570			−0.495285	+	0.868730i	$0.664936\pi$
$884$		0			0
$885$	9.33462	−	16.1680i	0.313780	−	0.543482i
$886$		0			0
$887$	−1.86982			−0.0627824			−0.0313912	−	0.999507i	$-0.509994\pi$
$887$	−1.86982			−0.0627824			−0.0313912	+	0.999507i	$0.509994\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	18.0946	+	10.4469i	0.606192	+	0.349985i
$892$		0			0
$893$	−6.99909			−0.234216
$894$		0			0
$895$	5.63208	+	3.25168i	0.188260	+	0.108692i
$896$		0			0
$897$	−2.06716	+	0.577530i	−0.0690205	+	0.0192832i
$898$		0			0
$899$	−30.5775	+	17.6540i	−1.01982	+	0.588792i
$900$		0			0
$901$	9.68585	−	16.7764i	0.322682	−	0.558902i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	16.1365	−	9.31641i	0.536395	−	0.309688i
$906$		0			0
$907$	0.802961	+	1.39077i	0.0266619	+	0.0461798i	0.879048	−	0.476732i	$-0.158179\pi$
$907$	0.802961	+	1.39077i	0.0266619	+	0.0461798i	−0.852387	+	0.522912i	$0.824846\pi$
$908$		0			0
$909$	8.95739			0.297098
$910$		0			0
$911$	31.1901			1.03337			0.516687	−	0.856174i	$-0.327165\pi$
$911$	31.1901			1.03337			0.516687	+	0.856174i	$0.327165\pi$
$912$		0			0
$913$	−8.60074	−	14.8969i	−0.284643	−	0.493016i
$914$		0			0
$915$	16.3348	−	9.43090i	0.540012	−	0.311776i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−24.0413	+	41.6408i	−0.793050	+	1.37360i	0.131021	+	0.991380i	$0.458175\pi$
$919$	−24.0413	+	41.6408i	−0.793050	+	1.37360i	−0.924070	+	0.382223i	$0.875159\pi$
$920$		0			0
$921$	21.6840	−	12.5193i	0.714513	−	0.412524i
$922$		0			0
$923$	−0.0879393	−	0.314762i	−0.00289456	−	0.0103605i
$924$		0			0
$925$	17.9908	+	10.3870i	0.591533	+	0.341522i
$926$		0			0
$927$	90.3932			2.96890
$928$		0			0
$929$	−21.2810	−	12.2866i	−0.698208	−	0.403111i	0.108471	−	0.994100i	$-0.465404\pi$
$929$	−21.2810	−	12.2866i	−0.698208	−	0.403111i	−0.806680	+	0.590989i	$0.798738\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	34.3610			1.12493
$934$		0			0
$935$	4.24402	−	7.35085i	0.138794	−	0.240399i
$936$		0			0
$937$	22.7270			0.742460			0.371230	−	0.928541i	$-0.378936\pi$
$937$	22.7270			0.742460			0.371230	+	0.928541i	$0.378936\pi$
$938$		0			0
$939$	−18.4322	+	31.9254i	−0.601511	+	1.04185i
$940$		0			0
$941$	−11.8098	−	6.81838i	−0.384988	−	0.222273i	0.294998	−	0.955498i	$-0.404681\pi$
$941$	−11.8098	−	6.81838i	−0.384988	−	0.222273i	−0.679986	+	0.733225i	$0.738014\pi$
$942$		0			0
$943$	1.64968	+	0.952445i	0.0537211	+	0.0310159i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	16.5519i		−	0.537866i	−0.963159	−	0.268933i	$-0.913329\pi$
$947$		−	16.5519i		−	0.537866i	0.963159	−	0.268933i	$-0.0866710\pi$
$948$		0			0
$949$	10.3734	−	10.5965i	0.336734	−	0.343975i
$950$		0			0
$951$	−39.9718	−	23.0777i	−1.29617	−	0.748346i
$952$		0			0
$953$	−5.39642	−	9.34688i	−0.174807	−	0.302775i	0.765287	−	0.643689i	$-0.222597\pi$
$953$	−5.39642	−	9.34688i	−0.174807	−	0.302775i	−0.940095	+	0.340914i	$0.889264\pi$
$954$		0			0
$955$			5.93411i			0.192023i
$956$		0			0
$957$	38.0360	−	21.9601i	1.22953	−	0.709868i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	3.70152	+	6.41123i	0.119404	+	0.206814i
$962$		0			0
$963$	26.3323	−	45.6089i	0.848547	−	1.46973i
$964$		0			0
$965$	−6.56411	+	11.3694i	−0.211306	+	0.365993i
$966$		0			0
$967$		−	28.3119i		−	0.910448i	−0.890377	−	0.455224i	$-0.849559\pi$
$967$		−	28.3119i		−	0.910448i	0.890377	−	0.455224i	$-0.150441\pi$
$968$		0			0
$969$		−	97.8582i		−	3.14366i
$970$		0			0
$971$	−24.4807	+	42.4018i	−0.785623	+	1.36074i	0.143003	+	0.989722i	$0.454324\pi$
$971$	−24.4807	+	42.4018i	−0.785623	+	1.36074i	−0.928626	+	0.371017i	$0.879009\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	11.9643	−	46.6297i	0.383163	−	1.49334i
$976$		0			0
$977$	−24.6463	+	14.2296i	−0.788506	+	0.455244i	−0.839436	−	0.543458i	$-0.817115\pi$
$977$	−24.6463	+	14.2296i	−0.788506	+	0.455244i	0.0509302	+	0.998702i	$0.483781\pi$
$978$		0			0
$979$	18.2696	+	31.6439i	0.583900	+	1.01134i
$980$		0			0
$981$	35.5919	−	20.5490i	1.13636	−	0.656079i
$982$		0			0
$983$	17.3677	+	10.0273i	0.553945	+	0.319820i	0.750711	−	0.660630i	$-0.229711\pi$
$983$	17.3677	+	10.0273i	0.553945	+	0.319820i	−0.196767	+	0.980450i	$0.563044\pi$
$984$		0			0
$985$	−15.8252			−0.504232
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.708149	+	1.22655i	0.0225178	+	0.0390020i
$990$		0			0
$991$	−16.8102	−	29.1160i	−0.533992	−	0.924902i	−0.999211	−	0.0397061i	$-0.987358\pi$
$991$	−16.8102	−	29.1160i	−0.533992	−	0.924902i	0.465219	−	0.885195i	$-0.345975\pi$
$992$		0			0
$993$			1.29091i			0.0409659i
$994$		0			0
$995$	−9.15298	+	5.28448i	−0.290169	+	0.167529i
$996$		0			0
$997$	−6.11231			−0.193579			−0.0967894	−	0.995305i	$-0.530857\pi$
$997$	−6.11231			−0.193579			−0.0967894	+	0.995305i	$0.530857\pi$
$998$		0			0
$999$		−	40.1054i		−	1.26888i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.bb.g.1733.1		24
7.2	even	3		2548.2.bq.g.1941.12		24
7.3	odd	6		2548.2.u.f.589.12	yes	24
7.4	even	3		2548.2.u.f.589.1	✓	24
7.5	odd	6		2548.2.bq.g.1941.1		24
7.6	odd	2	inner	2548.2.bb.g.1733.12		24
13.10	even	6		2548.2.bq.g.361.12		24
91.10	odd	6		2548.2.u.f.1765.12	yes	24
91.23	even	6	inner	2548.2.bb.g.569.1		24
91.62	odd	6		2548.2.bq.g.361.1		24
91.75	odd	6	inner	2548.2.bb.g.569.12		24
91.88	even	6		2548.2.u.f.1765.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2548.2.u.f.589.1	✓	24	7.4	even	3
2548.2.u.f.589.12	yes	24	7.3	odd	6
2548.2.u.f.1765.1	yes	24	91.88	even	6
2548.2.u.f.1765.12	yes	24	91.10	odd	6
2548.2.bb.g.569.1		24	91.23	even	6	inner
2548.2.bb.g.569.12		24	91.75	odd	6	inner
2548.2.bb.g.1733.1		24	1.1	even	1	trivial
2548.2.bb.g.1733.12		24	7.6	odd	2	inner
2548.2.bq.g.361.1		24	91.62	odd	6
2548.2.bq.g.361.12		24	13.10	even	6
2548.2.bq.g.1941.1		24	7.5	odd	6
2548.2.bq.g.1941.12		24	7.2	even	3

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:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.49140 - 2.58319i) q^{3} +(-0.626773 + 0.361868i) q^{5} +(-2.94857 + 5.10707i) q^{9} +(-2.23810 + 1.29217i) q^{11} +(0.896087 - 3.49242i) q^{13} +(1.86954 + 1.07938i) q^{15} +4.53814 q^{17} +(6.26073 + 3.61464i) q^{19} +0.199571 q^{23} +(-2.23810 + 3.87651i) q^{25} +8.64159 q^{27} +(2.84878 - 4.93424i) q^{29} +(-5.36678 - 3.09851i) q^{31} +(6.67583 + 3.85429i) q^{33} -4.64097i q^{37} +(-10.3580 + 2.89385i) q^{39} +(8.26614 + 4.77246i) q^{41} +(3.54835 + 6.14593i) q^{43} -4.26797i q^{45} +(-0.838451 + 0.484080i) q^{47} +(-6.76819 - 11.7229i) q^{51} +(2.13432 - 3.69675i) q^{53} +(0.935189 - 1.61979i) q^{55} -21.5635i q^{57} -8.64812i q^{59} +(4.36866 - 7.56674i) q^{61} +(0.702152 + 2.51322i) q^{65} +(2.36911 - 1.36781i) q^{67} +(-0.297641 - 0.515530i) q^{69} +(0.0784987 - 0.0453212i) q^{71} +(3.56175 + 2.05638i) q^{73} +13.3517 q^{75} +(-3.96626 - 6.86976i) q^{79} +(-4.04240 - 7.00164i) q^{81} +6.65604i q^{83} +(-2.84438 + 1.64221i) q^{85} -16.9947 q^{87} -14.1387i q^{89} +18.4845i q^{93} -5.23208 q^{95} +(1.09191 - 0.630417i) q^{97} -15.2402i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{9} - 12 q^{15} - 32 q^{23} + 24 q^{29} - 28 q^{39} + 4 q^{43} - 40 q^{51} + 24 q^{53} + 32 q^{65} - 24 q^{71} + 24 q^{79} + 4 q^{81} + 12 q^{85} + 40 q^{95}+O(q^{100}) \) 24 * q - 8 * q^9 - 12 * q^15 - 32 * q^23 + 24 * q^29 - 28 * q^39 + 4 * q^43 - 40 * q^51 + 24 * q^53 + 32 * q^65 - 24 * q^71 + 24 * q^79 + 4 * q^81 + 12 * q^85 + 40 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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