LMFDB - Embedded newform 2548.2.u.f.589.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2548,2,Mod(589,2548)] 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("2548.589"); 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, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.u (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0,0,-8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == 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			589.6
Character	$\chi$	$=$	2548.589
Dual form			2548.2.u.f.1765.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.307410 + 0.532450i) q^{3} -2.84979i q^{5} +(1.31100 + 2.27072i) q^{9} +(-1.56065 - 0.901040i) q^{11} +(3.01398 + 1.97887i) q^{13} +(1.51737 + 0.876054i) q^{15} +(0.806891 + 1.39758i) q^{17} +(4.64909 - 2.68415i) q^{19} +(-0.575859 + 0.997417i) q^{23} -3.12129 q^{25} -3.45652 q^{27} +(-1.88686 + 3.26813i) q^{29} +0.375670i q^{31} +(0.959517 - 0.553978i) q^{33} +(1.96662 + 1.13543i) q^{37} +(-1.98018 + 0.996468i) q^{39} +(5.59731 + 3.23161i) q^{41} +(-0.235139 - 0.407272i) q^{43} +(6.47106 - 3.73607i) q^{45} -1.43923i q^{47} -0.992186 q^{51} -12.1308 q^{53} +(-2.56777 + 4.44751i) q^{55} +3.30054i q^{57} +(6.17352 - 3.56428i) q^{59} +(2.80721 + 4.86224i) q^{61} +(5.63937 - 8.58920i) q^{65} +(-1.40482 - 0.811071i) q^{67} +(-0.354050 - 0.613233i) q^{69} +(8.79759 - 5.07929i) q^{71} +5.62031i q^{73} +(0.959517 - 1.66193i) q^{75} +14.3724 q^{79} +(-2.87043 + 4.97172i) q^{81} -2.93485i q^{83} +(3.98279 - 2.29947i) q^{85} +(-1.16008 - 2.00931i) q^{87} +(11.1754 + 6.45210i) q^{89} +(-0.200026 - 0.115485i) q^{93} +(-7.64927 - 13.2489i) q^{95} +(10.4934 - 6.05837i) q^{97} -4.72505i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{9} - 12 q^{15} + 16 q^{23} + 24 q^{29} + 8 q^{39} + 4 q^{43} + 80 q^{51} - 48 q^{53} + 8 q^{65} - 24 q^{71} - 48 q^{79} + 4 q^{81} + 12 q^{85} + 48 q^{93} - 20 q^{95}+O(q^{100}) $ 24 * q - 8 * q^9 - 12 * q^15 + 16 * q^23 + 24 * q^29 + 8 * q^39 + 4 * q^43 + 80 * q^51 - 48 * q^53 + 8 * q^65 - 24 * q^71 - 48 * q^79 + 4 * q^81 + 12 * q^85 + 48 * q^93 - 20 * q^95

Character values

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

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

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
$3$	−0.307410	+	0.532450i	−0.177483	+	0.307410i	−0.941018	−	0.338357i	$-0.890129\pi$
$3$	−0.307410	+	0.532450i	−0.177483	+	0.307410i	0.763535	+	0.645767i	$0.223462\pi$
$4$		0			0
$5$		−	2.84979i		−	1.27446i	−0.770672	−	0.637232i	$-0.780079\pi$
$5$		−	2.84979i		−	1.27446i	0.770672	−	0.637232i	$-0.219921\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.31100	+	2.27072i	0.436999	+	0.756905i
$10$		0			0
$11$	−1.56065	−	0.901040i	−0.470553	−	0.271674i	0.245918	−	0.969291i	$-0.420910\pi$
$11$	−1.56065	−	0.901040i	−0.470553	−	0.271674i	−0.716471	+	0.697617i	$0.754244\pi$
$12$		0			0
$13$	3.01398	+	1.97887i	0.835927	+	0.548840i
$13$	3.01398	+	1.97887i	0.835927	+	0.548840i
$14$		0			0
$15$	1.51737	+	0.876054i	0.391783	+	0.226196i
$16$		0			0
$17$	0.806891	+	1.39758i	0.195700	+	0.338962i	0.947130	−	0.320851i	$-0.103969\pi$
$17$	0.806891	+	1.39758i	0.195700	+	0.338962i	−0.751430	+	0.659813i	$0.770636\pi$
$18$		0			0
$19$	4.64909	−	2.68415i	1.06657	−	0.615787i	0.139331	−	0.990246i	$-0.455505\pi$
$19$	4.64909	−	2.68415i	1.06657	−	0.615787i	0.927243	+	0.374459i	$0.122172\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.575859	+	0.997417i	−0.120075	+	0.207976i	−0.919797	−	0.392394i	$-0.871647\pi$
$23$	−0.575859	+	0.997417i	−0.120075	+	0.207976i	0.799722	+	0.600370i	$0.204980\pi$
$24$		0			0
$25$	−3.12129			−0.624259
$26$		0			0
$27$	−3.45652			−0.665207
$28$		0			0
$29$	−1.88686	+	3.26813i	−0.350381	+	0.606877i	−0.986316	−	0.164865i	$-0.947281\pi$
$29$	−1.88686	+	3.26813i	−0.350381	+	0.606877i	0.635936	+	0.771742i	$0.280614\pi$
$30$		0			0
$31$			0.375670i			0.0674724i	0.999431	+	0.0337362i	$0.0107406\pi$
$31$			0.375670i			0.0674724i	−0.999431	+	0.0337362i	$0.989259\pi$
$32$		0			0
$33$	0.959517	−	0.553978i	0.167031	−	0.0964351i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.96662	+	1.13543i	0.323311	+	0.186664i	0.652867	−	0.757472i	$-0.273566\pi$
$37$	1.96662	+	1.13543i	0.323311	+	0.186664i	−0.329556	+	0.944136i	$0.606899\pi$
$38$		0			0
$39$	−1.98018	+	0.996468i	−0.317082	+	0.159563i
$40$		0			0
$41$	5.59731	+	3.23161i	0.874153	+	0.504692i	0.868726	−	0.495293i	$-0.164939\pi$
$41$	5.59731	+	3.23161i	0.874153	+	0.504692i	0.00542662	+	0.999985i	$0.498273\pi$
$42$		0			0
$43$	−0.235139	−	0.407272i	−0.0358583	−	0.0621084i	0.847539	−	0.530733i	$-0.178083\pi$
$43$	−0.235139	−	0.407272i	−0.0358583	−	0.0621084i	−0.883398	+	0.468624i	$0.844750\pi$
$44$		0			0
$45$	6.47106	−	3.73607i	0.964648	−	0.556940i
$46$		0			0
$47$		−	1.43923i		−	0.209933i	−0.994476	−	0.104966i	$-0.966526\pi$
$47$		−	1.43923i		−	0.209933i	0.994476	−	0.104966i	$-0.0334735\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−0.992186			−0.138934
$52$		0			0
$53$	−12.1308			−1.66630			−0.833150	−	0.553048i	$-0.813465\pi$
$53$	−12.1308			−1.66630			−0.833150	+	0.553048i	$0.813465\pi$
$54$		0			0
$55$	−2.56777	+	4.44751i	−0.346238	+	0.599703i
$56$		0			0
$57$			3.30054i			0.437168i
$58$		0			0
$59$	6.17352	−	3.56428i	0.803724	−	0.464030i	−0.0410479	−	0.999157i	$-0.513070\pi$
$59$	6.17352	−	3.56428i	0.803724	−	0.464030i	0.844772	+	0.535127i	$0.179736\pi$
$60$		0			0
$61$	2.80721	+	4.86224i	0.359427	+	0.622546i	0.987865	−	0.155314i	$-0.0496388\pi$
$61$	2.80721	+	4.86224i	0.359427	+	0.622546i	−0.628438	+	0.777860i	$0.716306\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.63937	−	8.58920i	0.699477	−	1.06536i
$66$		0			0
$67$	−1.40482	−	0.811071i	−0.171626	−	0.0990881i	0.411727	−	0.911307i	$-0.364926\pi$
$67$	−1.40482	−	0.811071i	−0.171626	−	0.0990881i	−0.583352	+	0.812219i	$0.698259\pi$
$68$		0			0
$69$	−0.354050	−	0.613233i	−0.0426226	−	0.0738245i
$70$		0			0
$71$	8.79759	−	5.07929i	1.04408	−	0.602801i	0.123095	−	0.992395i	$-0.460718\pi$
$71$	8.79759	−	5.07929i	1.04408	−	0.602801i	0.920987	+	0.389594i	$0.127385\pi$
$72$		0			0
$73$			5.62031i			0.657808i	0.944363	+	0.328904i	$0.106679\pi$
$73$			5.62031i			0.657808i	−0.944363	+	0.328904i	$0.893321\pi$
$74$		0			0
$75$	0.959517	−	1.66193i	0.110796	−	0.191903i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	14.3724			1.61702			0.808510	−	0.588482i	$-0.200274\pi$
$79$	14.3724			1.61702			0.808510	+	0.588482i	$0.200274\pi$
$80$		0			0
$81$	−2.87043	+	4.97172i	−0.318936	+	0.552414i
$82$		0			0
$83$		−	2.93485i		−	0.322141i	−0.986943	−	0.161071i	$-0.948505\pi$
$83$		−	2.93485i		−	0.322141i	0.986943	−	0.161071i	$-0.0514947\pi$
$84$		0			0
$85$	3.98279	−	2.29947i	0.431995	−	0.249412i
$86$		0			0
$87$	−1.16008	−	2.00931i	−0.124373	−	0.215421i
$88$		0			0
$89$	11.1754	+	6.45210i	1.18459	+	0.683921i	0.957071	−	0.289854i	$-0.0936067\pi$
$89$	11.1754	+	6.45210i	1.18459	+	0.683921i	0.227515	+	0.973775i	$0.426940\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−0.200026	−	0.115485i	−0.0207417	−	0.0119752i
$94$		0			0
$95$	−7.64927	−	13.2489i	−0.784798	−	1.35931i
$96$		0			0
$97$	10.4934	−	6.05837i	1.06544	−	0.615135i	0.138511	−	0.990361i	$-0.455768\pi$
$97$	10.4934	−	6.05837i	1.06544	−	0.615135i	0.926933	+	0.375226i	$0.122435\pi$
$98$		0			0
$99$		−	4.72505i		−	0.474885i
$100$		0			0
$101$	2.03122	−	3.51818i	0.202114	−	0.350072i	−0.747095	−	0.664717i	$-0.768552\pi$
$101$	2.03122	−	3.51818i	0.202114	−	0.350072i	0.949209	+	0.314645i	$0.101885\pi$
$102$		0			0
$103$	19.1795			1.88981			0.944904	−	0.327348i	$-0.106155\pi$
$103$	19.1795			1.88981			0.944904	+	0.327348i	$0.106155\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.59081	−	7.95152i	0.443810	−	0.768702i	−0.554158	−	0.832411i	$-0.686960\pi$
$107$	4.59081	−	7.95152i	0.443810	−	0.768702i	0.997968	+	0.0637093i	$0.0202930\pi$
$108$		0			0
$109$			5.05828i			0.484496i	0.970214	+	0.242248i	$0.0778847\pi$
$109$			5.05828i			0.484496i	−0.970214	+	0.242248i	$0.922115\pi$
$110$		0			0
$111$	−1.20912	+	0.698086i	−0.114765	+	0.0662594i
$112$		0			0
$113$	−2.21934	−	3.84401i	−0.208778	−	0.361614i	0.742552	−	0.669788i	$-0.233615\pi$
$113$	−2.21934	−	3.84401i	−0.208778	−	0.361614i	−0.951330	+	0.308175i	$0.900282\pi$
$114$		0			0
$115$	2.84243	+	1.64108i	0.265058	+	0.153031i
$116$		0			0
$117$	−0.542134	+	9.43818i	−0.0501203	+	0.872560i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−3.87625	−	6.71387i	−0.352387	−	0.610352i
$122$		0			0
$123$	−3.44134	+	1.98686i	−0.310295	+	0.179149i
$124$		0			0
$125$		−	5.35392i		−	0.478869i
$126$		0			0
$127$	8.68065	−	15.0353i	0.770283	−	1.33417i	−0.167125	−	0.985936i	$-0.553448\pi$
$127$	8.68065	−	15.0353i	0.770283	−	1.33417i	0.937408	−	0.348234i	$-0.113218\pi$
$128$		0			0
$129$	0.289136			0.0254570
$130$		0			0
$131$	−5.25994			−0.459563			−0.229781	−	0.973242i	$-0.573801\pi$
$131$	−5.25994			−0.459563			−0.229781	+	0.973242i	$0.573801\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$			9.85034i			0.847783i
$136$		0			0
$137$	−15.7804	+	9.11081i	−1.34821	+	0.778389i	−0.987996	−	0.154481i	$-0.950629\pi$
$137$	−15.7804	+	9.11081i	−1.34821	+	0.778389i	−0.360213	+	0.932870i	$0.617296\pi$
$138$		0			0
$139$	−10.0434	−	17.3956i	−0.851868	−	1.47548i	−0.879520	−	0.475861i	$-0.842137\pi$
$139$	−10.0434	−	17.3956i	−0.851868	−	1.47548i	0.0276525	−	0.999618i	$-0.491197\pi$
$140$		0			0
$141$	0.766317	+	0.442433i	0.0645355	+	0.0372596i
$142$		0			0
$143$	−2.92071	−	5.80403i	−0.244242	−	0.485358i
$144$		0			0
$145$	9.31349	+	5.37714i	0.773443	+	0.446547i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−12.9068	+	7.45173i	−1.05736	+	0.610469i	−0.924702	−	0.380692i	$-0.875686\pi$
$149$	−12.9068	+	7.45173i	−1.05736	+	0.610469i	−0.132662	+	0.991161i	$0.542352\pi$
$150$		0			0
$151$		−	6.95740i		−	0.566185i	−0.959093	−	0.283093i	$-0.908640\pi$
$151$		−	6.95740i		−	0.566185i	0.959093	−	0.283093i	$-0.0913604\pi$
$152$		0			0
$153$	−2.11566	+	3.66444i	−0.171041	+	0.296252i
$154$		0			0
$155$	1.07058			0.0859911
$156$		0			0
$157$	6.21365			0.495903			0.247952	−	0.968772i	$-0.420243\pi$
$157$	6.21365			0.495903			0.247952	+	0.968772i	$0.420243\pi$
$158$		0			0
$159$	3.72914	−	6.45907i	0.295740	−	0.512237i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	7.94888	−	4.58929i	0.622605	−	0.359461i	−0.155278	−	0.987871i	$-0.549627\pi$
$163$	7.94888	−	4.58929i	0.622605	−	0.359461i	0.777882	+	0.628410i	$0.216294\pi$
$164$		0			0
$165$	−1.57872	−	2.73442i	−0.122903	−	0.212874i
$166$		0			0
$167$	−0.810372	−	0.467869i	−0.0627085	−	0.0362048i	0.468318	−	0.883560i	$-0.344860\pi$
$167$	−0.810372	−	0.467869i	−0.0627085	−	0.0362048i	−0.531026	+	0.847355i	$0.678194\pi$
$168$		0			0
$169$	5.16813	+	11.9286i	0.397549	+	0.917581i
$170$		0			0
$171$	12.1899	+	7.03784i	0.932184	+	0.538197i
$172$		0			0
$173$	1.73303	+	3.00170i	0.131760	+	0.228215i	0.924355	−	0.381533i	$-0.124604\pi$
$173$	1.73303	+	3.00170i	0.131760	+	0.228215i	−0.792595	+	0.609748i	$0.791270\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			4.38279i			0.329430i
$178$		0			0
$179$	−1.28051	+	2.21792i	−0.0957102	+	0.165775i	−0.909905	−	0.414817i	$-0.863846\pi$
$179$	−1.28051	+	2.21792i	−0.0957102	+	0.165775i	0.814195	+	0.580592i	$0.197179\pi$
$180$		0			0
$181$	12.9745			0.964389			0.482194	−	0.876064i	$-0.339840\pi$
$181$	12.9745			0.964389			0.482194	+	0.876064i	$0.339840\pi$
$182$		0			0
$183$	−3.45187			−0.255169
$184$		0			0
$185$	3.23574	−	5.60446i	0.237896	−	0.412048i
$186$		0			0
$187$		−	2.90816i		−	0.212666i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.9853	+	22.4912i	0.939583	+	1.62741i	0.766250	+	0.642543i	$0.222121\pi$
$191$	12.9853	+	22.4912i	0.939583	+	1.62741i	0.173334	+	0.984863i	$0.444546\pi$
$192$		0			0
$193$	5.94916	+	3.43475i	0.428230	+	0.247239i	0.698592	−	0.715520i	$-0.253810\pi$
$193$	5.94916	+	3.43475i	0.428230	+	0.247239i	−0.270362	+	0.962759i	$0.587143\pi$
$194$		0			0
$195$	2.83972	+	5.64309i	0.203357	+	0.404110i
$196$		0			0
$197$	12.9358	+	7.46849i	0.921638	+	0.532108i	0.884157	−	0.467189i	$-0.154733\pi$
$197$	12.9358	+	7.46849i	0.921638	+	0.532108i	0.0374808	+	0.999297i	$0.488067\pi$
$198$		0			0
$199$	2.69895	+	4.67473i	0.191324	+	0.331383i	0.945689	−	0.325072i	$-0.105389\pi$
$199$	2.69895	+	4.67473i	0.191324	+	0.331383i	−0.754365	+	0.656455i	$0.772055\pi$
$200$		0			0
$201$	0.863709	−	0.498663i	0.0609214	−	0.0351730i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	9.20940	−	15.9511i	0.643212	−	1.11408i
$206$		0			0
$207$	−3.01980			−0.209891
$208$		0			0
$209$	−9.67411			−0.669172
$210$		0			0
$211$	−4.46899	+	7.74051i	−0.307658	+	0.532879i	−0.977850	−	0.209309i	$-0.932879\pi$
$211$	−4.46899	+	7.74051i	−0.307658	+	0.532879i	0.670192	+	0.742188i	$0.266212\pi$
$212$		0			0
$213$			6.24570i			0.427949i
$214$		0			0
$215$	−1.16064	+	0.670096i	−0.0791550	+	0.0457001i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−2.99253	−	1.72774i	−0.202217	−	0.116750i
$220$		0			0
$221$	−0.333672	+	5.80900i	−0.0224452	+	0.390755i
$222$		0			0
$223$	12.8537	+	7.42106i	0.860744	+	0.496951i	0.864262	−	0.503043i	$-0.167786\pi$
$223$	12.8537	+	7.42106i	0.860744	+	0.496951i	−0.00351707	+	0.999994i	$0.501120\pi$
$224$		0			0
$225$	−4.09201	−	7.08757i	−0.272801	−	0.472505i
$226$		0			0
$227$	19.6000	−	11.3160i	1.30089	−	0.751072i	0.320337	−	0.947304i	$-0.396204\pi$
$227$	19.6000	−	11.3160i	1.30089	−	0.751072i	0.980558	+	0.196232i	$0.0628705\pi$
$228$		0			0
$229$		−	16.4717i		−	1.08848i	−0.838930	−	0.544240i	$-0.816818\pi$
$229$		−	16.4717i		−	1.08848i	0.838930	−	0.544240i	$-0.183182\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−14.2544			−0.933838			−0.466919	−	0.884300i	$-0.654636\pi$
$233$	−14.2544			−0.933838			−0.466919	+	0.884300i	$0.654636\pi$
$234$		0			0
$235$	−4.10149			−0.267552
$236$		0			0
$237$	−4.41822	+	7.65258i	−0.286994	+	0.497089i
$238$		0			0
$239$			25.1730i			1.62831i	0.580650	+	0.814154i	$0.302799\pi$
$239$			25.1730i			1.62831i	−0.580650	+	0.814154i	$0.697201\pi$
$240$		0			0
$241$	−12.0781	+	6.97331i	−0.778021	+	0.449191i	−0.835728	−	0.549143i	$-0.814954\pi$
$241$	−12.0781	+	6.97331i	−0.778021	+	0.449191i	0.0577074	+	0.998334i	$0.481621\pi$
$242$		0			0
$243$	−6.94957	−	12.0370i	−0.445815	−	0.772175i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	19.3238	+	1.10997i	1.22955	+	0.0706258i
$248$		0			0
$249$	1.56266	+	0.902202i	0.0990296	+	0.0571748i
$250$		0			0
$251$	−9.08534	−	15.7363i	−0.573462	−	0.993265i	−0.996207	−	0.0870160i	$-0.972267\pi$
$251$	−9.08534	−	15.7363i	−0.573462	−	0.993265i	0.422745	−	0.906248i	$-0.361066\pi$
$252$		0			0
$253$	1.79743	−	1.03774i	0.113003	−	0.0652424i
$254$		0			0
$255$			2.82752i			0.177066i
$256$		0			0
$257$	2.52851	−	4.37952i	0.157724	−	0.273187i	−0.776323	−	0.630335i	$-0.782918\pi$
$257$	2.52851	−	4.37952i	0.157724	−	0.273187i	0.934048	+	0.357148i	$0.116251\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−9.89466			−0.612464
$262$		0			0
$263$	−2.60888	+	4.51872i	−0.160871	+	0.278636i	−0.935181	−	0.354170i	$-0.884764\pi$
$263$	−2.60888	+	4.51872i	−0.160871	+	0.278636i	0.774311	+	0.632806i	$0.218097\pi$
$264$		0			0
$265$			34.5703i			2.12364i
$266$		0			0
$267$	−6.87084	+	3.96688i	−0.420488	+	0.242769i
$268$		0			0
$269$	−2.10274	−	3.64206i	−0.128206	−	0.222060i	0.794775	−	0.606904i	$-0.207589\pi$
$269$	−2.10274	−	3.64206i	−0.128206	−	0.222060i	−0.922982	+	0.384844i	$0.874255\pi$
$270$		0			0
$271$	8.34869	+	4.82012i	0.507147	+	0.292801i	0.731660	−	0.681670i	$-0.238746\pi$
$271$	8.34869	+	4.82012i	0.507147	+	0.292801i	−0.224513	+	0.974471i	$0.572079\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.87124	+	2.81241i	0.293747	+	0.169595i
$276$		0			0
$277$	2.47816	+	4.29231i	0.148898	+	0.257900i	0.930821	−	0.365476i	$-0.119094\pi$
$277$	2.47816	+	4.29231i	0.148898	+	0.257900i	−0.781922	+	0.623376i	$0.785761\pi$
$278$		0			0
$279$	−0.853040	+	0.492503i	−0.0510702	+	0.0294854i
$280$		0			0
$281$			9.93319i			0.592564i	0.955100	+	0.296282i	$0.0957469\pi$
$281$			9.93319i			0.592564i	−0.955100	+	0.296282i	$0.904253\pi$
$282$		0			0
$283$	−12.8921	+	22.3298i	−0.766356	+	1.32737i	0.173170	+	0.984892i	$0.444599\pi$
$283$	−12.8921	+	22.3298i	−0.766356	+	1.32737i	−0.939527	+	0.342476i	$0.888734\pi$
$284$		0			0
$285$	9.40585			0.557154
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.19786	−	12.4671i	0.423403	−	0.733356i
$290$		0			0
$291$			7.44962i			0.436705i
$292$		0			0
$293$	−8.82379	+	5.09442i	−0.515492	+	0.297619i	−0.735088	−	0.677972i	$-0.762859\pi$
$293$	−8.82379	+	5.09442i	−0.515492	+	0.297619i	0.219597	+	0.975591i	$0.429526\pi$
$294$		0			0
$295$	−10.1575	−	17.5932i	−0.591390	−	1.02432i
$296$		0			0
$297$	5.39440	+	3.11446i	0.313015	+	0.180719i
$298$		0			0
$299$	−3.70939	+	1.86664i	−0.214519	+	0.107951i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	1.24884	+	2.16305i	0.0717438	+	0.124264i
$304$		0			0
$305$	13.8563	−	7.99997i	0.793412	−	0.458077i
$306$		0			0
$307$		−	30.2516i		−	1.72655i	−0.504734	−	0.863275i	$-0.668409\pi$
$307$		−	30.2516i		−	1.72655i	0.504734	−	0.863275i	$-0.331591\pi$
$308$		0			0
$309$	−5.89596	+	10.2121i	−0.335409	+	0.580946i
$310$		0			0
$311$	−20.7199			−1.17492			−0.587459	−	0.809254i	$-0.699872\pi$
$311$	−20.7199			−1.17492			−0.587459	+	0.809254i	$0.699872\pi$
$312$		0			0
$313$	−11.3628			−0.642266			−0.321133	−	0.947034i	$-0.604064\pi$
$313$	−11.3628			−0.642266			−0.321133	+	0.947034i	$0.604064\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	15.7291i		−	0.883433i	−0.897155	−	0.441717i	$-0.854370\pi$
$317$		−	15.7291i		−	0.883433i	0.897155	−	0.441717i	$-0.145630\pi$
$318$		0			0
$319$	5.88944	−	3.40027i	0.329745	−	0.190378i
$320$		0			0
$321$	2.82252	+	4.88875i	0.157538	+	0.272864i
$322$		0			0
$323$	7.50261	+	4.33163i	0.417456	+	0.241019i
$324$		0			0
$325$	−9.40751	−	6.17664i	−0.521835	−	0.342618i
$326$		0			0
$327$	−2.69328	−	1.55497i	−0.148939	−	0.0859899i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−30.1029	+	17.3799i	−1.65461	+	0.955288i	−0.679464	+	0.733709i	$0.737788\pi$
$331$	−30.1029	+	17.3799i	−1.65461	+	0.955288i	−0.975142	+	0.221579i	$0.928879\pi$
$332$		0			0
$333$			5.95419i			0.326288i
$334$		0			0
$335$	−2.31138	+	4.00343i	−0.126284	+	0.218731i
$336$		0			0
$337$	15.4211			0.840042			0.420021	−	0.907514i	$-0.362023\pi$
$337$	15.4211			0.840042			0.420021	+	0.907514i	$0.362023\pi$
$338$		0			0
$339$	2.72899			0.148218
$340$		0			0
$341$	0.338494	−	0.586289i	0.0183305	−	0.0317493i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−1.74758	+	1.00897i	−0.0940867	+	0.0543210i
$346$		0			0
$347$	−9.17454	−	15.8908i	−0.492515	−	0.853061i	0.507448	−	0.861683i	$-0.330589\pi$
$347$	−9.17454	−	15.8908i	−0.492515	−	0.853061i	−0.999963	+	0.00862142i	$0.997256\pi$
$348$		0			0
$349$	10.9773	+	6.33774i	0.587600	+	0.339251i	0.764148	−	0.645041i	$-0.223160\pi$
$349$	10.9773	+	6.33774i	0.587600	+	0.339251i	−0.176548	+	0.984292i	$0.556493\pi$
$350$		0			0
$351$	−10.4179	−	6.84001i	−0.556065	−	0.365092i
$352$		0			0
$353$	−10.2825	−	5.93658i	−0.547280	−	0.315972i	0.200744	−	0.979644i	$-0.435664\pi$
$353$	−10.2825	−	5.93658i	−0.547280	−	0.315972i	−0.748024	+	0.663671i	$0.768997\pi$
$354$		0			0
$355$	−14.4749	−	25.0713i	−0.768248	−	1.33064i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			7.06966i			0.373122i	0.982443	+	0.186561i	$0.0597342\pi$
$359$			7.06966i			0.373122i	−0.982443	+	0.186561i	$0.940266\pi$
$360$		0			0
$361$	4.90935	−	8.50324i	0.258387	−	0.447539i
$362$		0			0
$363$	4.76640			0.250171
$364$		0			0
$365$	16.0167			0.838352
$366$		0			0
$367$	−13.8085	+	23.9169i	−0.720795	+	1.24845i	0.239886	+	0.970801i	$0.422890\pi$
$367$	−13.8085	+	23.9169i	−0.720795	+	1.24845i	−0.960681	+	0.277653i	$0.910443\pi$
$368$		0			0
$369$			16.9465i			0.882201i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	14.3110	+	24.7874i	0.740996	+	1.28344i	0.952042	+	0.305967i	$0.0989797\pi$
$373$	14.3110	+	24.7874i	0.740996	+	1.28344i	−0.211046	+	0.977476i	$0.567687\pi$
$374$		0			0
$375$	2.85069	+	1.64585i	0.147209	+	0.0849912i
$376$		0			0
$377$	−12.1542	+	6.11623i	−0.625971	+	0.315002i
$378$		0			0
$379$	−27.8128	−	16.0577i	−1.42865	−	0.824830i	−0.431634	−	0.902049i	$-0.642063\pi$
$379$	−27.8128	−	16.0577i	−1.42865	−	0.824830i	−0.997014	+	0.0772189i	$0.975396\pi$
$380$		0			0
$381$	5.33704	+	9.24402i	0.273425	+	0.473586i
$382$		0			0
$383$	−19.1914	+	11.0801i	−0.980633	+	0.566169i	−0.902461	−	0.430771i	$-0.858242\pi$
$383$	−19.1914	+	11.0801i	−0.980633	+	0.566169i	−0.0781720	+	0.996940i	$0.524908\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.616533	−	1.06787i	0.0313401	−	0.0542827i
$388$		0			0
$389$	15.9099			0.806666			0.403333	−	0.915053i	$-0.367852\pi$
$389$	15.9099			0.806666			0.403333	+	0.915053i	$0.367852\pi$
$390$		0			0
$391$	−1.85862			−0.0939945
$392$		0			0
$393$	1.61696	−	2.80065i	0.0815648	−	0.141274i
$394$		0			0
$395$		−	40.9583i		−	2.06083i
$396$		0			0
$397$	−26.1161	+	15.0781i	−1.31073	+	0.756750i	−0.982217	−	0.187750i	$-0.939880\pi$
$397$	−26.1161	+	15.0781i	−1.31073	+	0.756750i	−0.328512	+	0.944500i	$0.606547\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−29.9226	−	17.2758i	−1.49426	−	0.862712i	−0.494283	−	0.869301i	$-0.664569\pi$
$401$	−29.9226	−	17.2758i	−1.49426	−	0.862712i	−0.999978	+	0.00658877i	$0.997903\pi$
$402$		0			0
$403$	−0.743403	+	1.13226i	−0.0370316	+	0.0564020i
$404$		0			0
$405$	14.1684	+	8.18010i	0.704031	+	0.406473i
$406$		0			0
$407$	−2.04614	−	3.54401i	−0.101423	−	0.175670i
$408$		0			0
$409$	24.5091	−	14.1504i	1.21190	−	0.699690i	0.248726	−	0.968574i	$-0.419988\pi$
$409$	24.5091	−	14.1504i	1.21190	−	0.699690i	0.963173	+	0.268884i	$0.0866547\pi$
$410$		0			0
$411$		−	11.2030i		−	0.552604i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−8.36370			−0.410558
$416$		0			0
$417$	12.3497			0.604770
$418$		0			0
$419$	6.75416	−	11.6985i	0.329962	−	0.571511i	−0.652542	−	0.757753i	$-0.726297\pi$
$419$	6.75416	−	11.6985i	0.329962	−	0.571511i	0.982504	+	0.186241i	$0.0596307\pi$
$420$		0			0
$421$		−	1.45597i		−	0.0709594i	−0.999370	−	0.0354797i	$-0.988704\pi$
$421$		−	1.45597i		−	0.0709594i	0.999370	−	0.0354797i	$-0.0112959\pi$
$422$		0			0
$423$	3.26807	−	1.88682i	0.158899	−	0.0917405i
$424$		0			0
$425$	−2.51854	−	4.36224i	−0.122167	−	0.211600i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	3.98822	+	0.229085i	0.192553	+	0.0110603i
$430$		0			0
$431$	31.8357	+	18.3804i	1.53347	+	0.885352i	0.999198	+	0.0400414i	$0.0127490\pi$
$431$	31.8357	+	18.3804i	1.53347	+	0.885352i	0.534276	+	0.845310i	$0.320584\pi$
$432$		0			0
$433$	−7.33480	−	12.7043i	−0.352488	−	0.610527i	0.634197	−	0.773172i	$-0.281331\pi$
$433$	−7.33480	−	12.7043i	−0.352488	−	0.610527i	−0.986685	+	0.162644i	$0.947998\pi$
$434$		0			0
$435$	−5.72612	+	3.30598i	−0.274546	+	0.158509i
$436$		0			0
$437$			6.18278i			0.295762i
$438$		0			0
$439$	−8.23925	+	14.2708i	−0.393238	+	0.681108i	−0.992875	−	0.119164i	$-0.961979\pi$
$439$	−8.23925	+	14.2708i	−0.393238	+	0.681108i	0.599637	+	0.800272i	$0.295312\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−18.0424			−0.857221			−0.428610	−	0.903489i	$-0.640997\pi$
$443$	−18.0424			−0.857221			−0.428610	+	0.903489i	$0.640997\pi$
$444$		0			0
$445$	18.3871	−	31.8474i	0.871633	−	1.50971i
$446$		0			0
$447$		−	9.16294i		−	0.433392i
$448$		0			0
$449$	−5.28375	+	3.05058i	−0.249356	+	0.143966i	−0.619469	−	0.785021i	$-0.712652\pi$
$449$	−5.28375	+	3.05058i	−0.249356	+	0.143966i	0.370113	+	0.928987i	$0.379319\pi$
$450$		0			0
$451$	−5.82361	−	10.0868i	−0.274223	−	0.474969i
$452$		0			0
$453$	3.70447	+	2.13878i	0.174051	+	0.100488i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.23542	+	0.713269i	0.0577904	+	0.0333653i	0.528617	−	0.848861i	$-0.322711\pi$
$457$	1.23542	+	0.713269i	0.0577904	+	0.0333653i	−0.470826	+	0.882226i	$0.656044\pi$
$458$		0			0
$459$	−2.78903	−	4.83074i	−0.130181	−	0.225480i
$460$		0			0
$461$	3.67565	−	2.12213i	0.171192	−	0.0988377i	−0.411956	−	0.911204i	$-0.635154\pi$
$461$	3.67565	−	2.12213i	0.171192	−	0.0988377i	0.583148	+	0.812366i	$0.301821\pi$
$462$		0			0
$463$		−	31.0675i		−	1.44383i	−0.691982	−	0.721915i	$-0.743262\pi$
$463$		−	31.0675i		−	1.44383i	0.691982	−	0.721915i	$-0.256738\pi$
$464$		0			0
$465$	−0.329107	+	0.570031i	−0.0152620	+	0.0264345i
$466$		0			0
$467$	−15.8029			−0.731272			−0.365636	−	0.930758i	$-0.619149\pi$
$467$	−15.8029			−0.731272			−0.365636	+	0.930758i	$0.619149\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−1.91014	+	3.30846i	−0.0880146	+	0.152446i
$472$		0			0
$473$			0.847477i			0.0389671i
$474$		0			0
$475$	−14.5112	+	8.37803i	−0.665818	+	0.384410i
$476$		0			0
$477$	−15.9035	−	27.5457i	−0.728172	−	1.26123i
$478$		0			0
$479$	−31.4478	−	18.1564i	−1.43689	−	0.829586i	−0.439253	−	0.898363i	$-0.644757\pi$
$479$	−31.4478	−	18.1564i	−1.43689	−	0.829586i	−0.997632	+	0.0687771i	$0.978090\pi$
$480$		0			0
$481$	3.68049	+	7.31386i	0.167816	+	0.333483i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−17.2651	−	29.9040i	−0.783967	−	1.35787i
$486$		0			0
$487$	−19.5839	+	11.3068i	−0.887432	+	0.512359i	−0.873102	−	0.487538i	$-0.837895\pi$
$487$	−19.5839	+	11.3068i	−0.887432	+	0.512359i	−0.0143304	+	0.999897i	$0.504562\pi$
$488$		0			0
$489$			5.64318i			0.255193i
$490$		0			0
$491$	0.687916	−	1.19151i	0.0310452	−	0.0537719i	−0.850085	−	0.526645i	$-0.823450\pi$
$491$	0.687916	−	1.19151i	0.0310452	−	0.0537719i	0.881131	+	0.472873i	$0.156783\pi$
$492$		0			0
$493$	−6.08995			−0.274278
$494$		0			0
$495$	−13.4654			−0.605224
$496$		0			0
$497$		0			0
$498$		0			0
$499$		−	0.717661i		−	0.0321269i	−0.999871	−	0.0160635i	$-0.994887\pi$
$499$		−	0.717661i		−	0.0321269i	0.999871	−	0.0160635i	$-0.00511338\pi$
$500$		0			0
$501$	0.498233	−	0.287655i	0.0222594	−	0.0128515i
$502$		0			0
$503$	−16.5915	−	28.7373i	−0.739777	−	1.28133i	−0.952596	−	0.304239i	$-0.901598\pi$
$503$	−16.5915	−	28.7373i	−0.739777	−	1.28133i	0.212819	−	0.977092i	$-0.431736\pi$
$504$		0			0
$505$	−10.0261	−	5.78855i	−0.446154	−	0.257587i
$506$		0			0
$507$	−7.94010	−	0.915187i	−0.352632	−	0.0406449i
$508$		0			0
$509$	10.8310	+	6.25329i	0.480077	+	0.277172i	0.720448	−	0.693509i	$-0.243936\pi$
$509$	10.8310	+	6.25329i	0.480077	+	0.277172i	−0.240372	+	0.970681i	$0.577269\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−16.0697	+	9.27782i	−0.709493	+	0.409626i
$514$		0			0
$515$		−	54.6574i		−	2.40849i
$516$		0			0
$517$	−1.29680	+	2.24613i	−0.0570332	+	0.0987845i
$518$		0			0
$519$	−2.13101			−0.0935410
$520$		0			0
$521$	9.75115			0.427206			0.213603	−	0.976921i	$-0.431480\pi$
$521$	9.75115			0.427206			0.213603	+	0.976921i	$0.431480\pi$
$522$		0			0
$523$	−8.78204	+	15.2109i	−0.384012	+	0.665128i	−0.991632	−	0.129100i	$-0.958791\pi$
$523$	−8.78204	+	15.2109i	−0.384012	+	0.665128i	0.607620	+	0.794228i	$0.292124\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.525027	+	0.303125i	−0.0228706	+	0.0132043i
$528$		0			0
$529$	10.8368	+	18.7698i	0.471164	+	0.816080i
$530$		0			0
$531$	16.1869	+	9.34553i	0.702453	+	0.405562i
$532$		0			0
$533$	10.4752	+	20.8163i	0.453733	+	0.901656i
$534$		0			0
$535$	−22.6601	−	13.0828i	−0.979683	−	0.565620i
$536$		0			0
$537$	−0.787286	−	1.36362i	−0.0339739	−	0.0588446i
$538$		0			0
$539$		0			0
$540$		0			0
$541$		−	23.0805i		−	0.992306i	−0.868235	−	0.496153i	$-0.834745\pi$
$541$		−	23.0805i		−	0.992306i	0.868235	−	0.496153i	$-0.165255\pi$
$542$		0			0
$543$	−3.98850	+	6.90829i	−0.171163	+	0.296463i
$544$		0			0
$545$	14.4150			0.617472
$546$		0			0
$547$	−40.2760			−1.72208			−0.861039	−	0.508538i	$-0.830186\pi$
$547$	−40.2760			−1.72208			−0.861039	+	0.508538i	$0.830186\pi$
$548$		0			0
$549$	−7.36050	+	12.7488i	−0.314139	+	0.544104i
$550$		0			0
$551$			20.2584i			0.863039i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	1.98940	+	3.44574i	0.0844452	+	0.146263i
$556$		0			0
$557$	21.2364	+	12.2609i	0.899817	+	0.519510i	0.877141	−	0.480233i	$-0.159448\pi$
$557$	21.2364	+	12.2609i	0.899817	+	0.519510i	0.0226763	+	0.999743i	$0.492781\pi$
$558$		0			0
$559$	0.0972365	−	1.69282i	0.00411266	−	0.0715986i
$560$		0			0
$561$	1.54845	+	0.893999i	0.0653757	+	0.0377447i
$562$		0			0
$563$	6.01842	+	10.4242i	0.253646	+	0.439328i	0.964527	−	0.263985i	$-0.0850368\pi$
$563$	6.01842	+	10.4242i	0.253646	+	0.439328i	−0.710881	+	0.703312i	$0.751704\pi$
$564$		0			0
$565$	−10.9546	+	6.32464i	−0.460864	+	0.266080i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.72129	−	16.8378i	0.407538	−	0.705876i	−0.587076	−	0.809532i	$-0.699721\pi$
$569$	9.72129	−	16.8378i	0.407538	−	0.705876i	0.994613	+	0.103656i	$0.0330542\pi$
$570$		0			0
$571$	35.4836			1.48494			0.742470	−	0.669879i	$-0.233654\pi$
$571$	35.4836			1.48494			0.742470	+	0.669879i	$0.233654\pi$
$572$		0			0
$573$	−15.9673			−0.667042
$574$		0			0
$575$	1.79743	−	3.11323i	0.0749578	−	0.129831i
$576$		0			0
$577$		−	5.57375i		−	0.232038i	−0.993247	−	0.116019i	$-0.962987\pi$
$577$		−	5.57375i		−	0.232038i	0.993247	−	0.116019i	$-0.0370134\pi$
$578$		0			0
$579$	−3.65767	+	2.11176i	−0.152007	+	0.0877616i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	18.9320	+	10.9304i	0.784082	+	0.452690i
$584$		0			0
$585$	26.8968	+	1.54497i	1.11205	+	0.0638766i
$586$		0			0
$587$	−8.01798	−	4.62918i	−0.330938	−	0.191067i	0.325320	−	0.945604i	$-0.394528\pi$
$587$	−8.01798	−	4.62918i	−0.330938	−	0.191067i	−0.656257	+	0.754537i	$0.727861\pi$
$588$		0			0
$589$	1.00836	+	1.74652i	0.0415486	+	0.0719643i
$590$		0			0
$591$	−7.95320	+	4.59178i	−0.327151	+	0.188881i
$592$		0			0
$593$		−	5.14329i		−	0.211209i	−0.994408	−	0.105605i	$-0.966322\pi$
$593$		−	5.14329i		−	0.211209i	0.994408	−	0.105605i	$-0.0336778\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−3.31874			−0.135827
$598$		0			0
$599$	−16.0525			−0.655886			−0.327943	−	0.944697i	$-0.606355\pi$
$599$	−16.0525			−0.655886			−0.327943	+	0.944697i	$0.606355\pi$
$600$		0			0
$601$	2.32115	−	4.02035i	0.0946816	−	0.163993i	−0.814794	−	0.579750i	$-0.803150\pi$
$601$	2.32115	−	4.02035i	0.0946816	−	0.163993i	0.909476	+	0.415757i	$0.136483\pi$
$602$		0			0
$603$		−	4.25325i		−	0.173206i
$604$		0			0
$605$	−19.1331	+	11.0465i	−0.777871	+	0.449104i
$606$		0			0
$607$	−4.37417	−	7.57629i	−0.177542	−	0.307512i	0.763496	−	0.645813i	$-0.223481\pi$
$607$	−4.37417	−	7.57629i	−0.177542	−	0.307512i	−0.941038	+	0.338301i	$0.890148\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.84805	−	4.33780i	0.115220	−	0.175489i
$612$		0			0
$613$	40.2324	+	23.2282i	1.62497	+	0.938179i	0.985562	+	0.169313i	$0.0541549\pi$
$613$	40.2324	+	23.2282i	1.62497	+	0.938179i	0.639411	+	0.768865i	$0.279178\pi$
$614$		0			0
$615$	5.66212	+	9.80709i	0.228319	+	0.395460i
$616$		0			0
$617$	−29.0761	+	16.7871i	−1.17056	+	0.675822i	−0.953812	−	0.300406i	$-0.902878\pi$
$617$	−29.0761	+	16.7871i	−1.17056	+	0.675822i	−0.216747	+	0.976228i	$0.569545\pi$
$618$		0			0
$619$			2.42868i			0.0976169i	0.998808	+	0.0488085i	$0.0155424\pi$
$619$			2.42868i			0.0976169i	−0.998808	+	0.0488085i	$0.984458\pi$
$620$		0			0
$621$	1.99047	−	3.44759i	0.0798747	−	0.138347i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−30.8640			−1.23456
$626$		0			0
$627$	2.97392	−	5.15098i	0.118767	−	0.205710i
$628$		0			0
$629$			3.66467i			0.146120i
$630$		0			0
$631$	13.2815	−	7.66809i	0.528729	−	0.305262i	−0.211770	−	0.977320i	$-0.567923\pi$
$631$	13.2815	−	7.66809i	0.528729	−	0.305262i	0.740499	+	0.672058i	$0.234589\pi$
$632$		0			0
$633$	−2.74762	−	4.75902i	−0.109208	−	0.189154i
$634$		0			0
$635$	−42.8475	−	24.7380i	−1.70035	−	0.981698i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	23.0672	+	13.3179i	0.912526	+	0.526847i
$640$		0			0
$641$	−16.5124	−	28.6003i	−0.652199	−	1.12964i	−0.982588	−	0.185797i	$-0.940513\pi$
$641$	−16.5124	−	28.6003i	−0.652199	−	1.12964i	0.330389	−	0.943845i	$-0.392820\pi$
$642$		0			0
$643$	−14.5972	+	8.42772i	−0.575659	+	0.332357i	−0.759406	−	0.650617i	$-0.774510\pi$
$643$	−14.5972	+	8.42772i	−0.575659	+	0.332357i	0.183747	+	0.982973i	$0.441177\pi$
$644$		0			0
$645$		−	0.823977i		−	0.0324441i
$646$		0			0
$647$	−22.7037	+	39.3240i	−0.892576	+	1.54599i	−0.0557999	+	0.998442i	$0.517771\pi$
$647$	−22.7037	+	39.3240i	−0.892576	+	1.54599i	−0.836776	+	0.547545i	$0.815562\pi$
$648$		0			0
$649$	−12.8462			−0.504259
$650$		0			0
$651$		0			0
$652$		0			0
$653$	20.1975	−	34.9831i	0.790389	−	1.36899i	−0.135338	−	0.990800i	$-0.543212\pi$
$653$	20.1975	−	34.9831i	0.790389	−	1.36899i	0.925726	−	0.378194i	$-0.123455\pi$
$654$		0			0
$655$			14.9897i			0.585696i
$656$		0			0
$657$	−12.7621	+	7.36822i	−0.497898	+	0.287461i
$658$		0			0
$659$	18.2656	+	31.6369i	0.711526	+	1.23240i	0.964284	+	0.264870i	$0.0853292\pi$
$659$	18.2656	+	31.6369i	0.711526	+	1.23240i	−0.252758	+	0.967530i	$0.581338\pi$
$660$		0			0
$661$	17.4301	+	10.0633i	0.677951	+	0.391415i	0.799083	−	0.601221i	$-0.205319\pi$
$661$	17.4301	+	10.0633i	0.677951	+	0.391415i	−0.121131	+	0.992636i	$0.538652\pi$
$662$		0			0
$663$	−2.99043	−	1.96341i	−0.116139	−	0.0762524i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−2.17313	−	3.76397i	−0.0841439	−	0.145741i
$668$		0			0
$669$	−7.90269	+	4.56262i	−0.305536	+	0.176401i
$670$		0			0
$671$		−	10.1176i		−	0.390587i
$672$		0			0
$673$	−7.89716	+	13.6783i	−0.304413	+	0.527259i	−0.977131	−	0.212641i	$-0.931794\pi$
$673$	−7.89716	+	13.6783i	−0.304413	+	0.527259i	0.672717	+	0.739900i	$0.265127\pi$
$674$		0			0
$675$	10.7888			0.415261
$676$		0			0
$677$	−25.7439			−0.989419			−0.494710	−	0.869058i	$-0.664726\pi$
$677$	−25.7439			−0.989419			−0.494710	+	0.869058i	$0.664726\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$			13.9147i			0.533211i
$682$		0			0
$683$	5.63910	−	3.25573i	0.215774	−	0.124577i	−0.388218	−	0.921568i	$-0.626909\pi$
$683$	5.63910	−	3.25573i	0.215774	−	0.124577i	0.603992	+	0.796990i	$0.293576\pi$
$684$		0			0
$685$	25.9639	+	44.9708i	0.992029	+	1.71824i
$686$		0			0
$687$	8.77035	+	5.06357i	0.334610	+	0.193187i
$688$		0			0
$689$	−36.5621	−	24.0054i	−1.39290	−	0.914532i
$690$		0			0
$691$	0.965340	+	0.557340i	0.0367233	+	0.0212022i	0.518249	−	0.855230i	$-0.326584\pi$
$691$	0.965340	+	0.557340i	0.0367233	+	0.0212022i	−0.481526	+	0.876432i	$0.659917\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−49.5739	+	28.6215i	−1.88044	+	1.08568i
$696$		0			0
$697$			10.4302i			0.395072i
$698$		0			0
$699$	4.38195	−	7.58977i	0.165741	−	0.287071i
$700$		0			0
$701$	29.3444			1.10832			0.554161	−	0.832410i	$-0.313039\pi$
$701$	29.3444			1.10832			0.554161	+	0.832410i	$0.313039\pi$
$702$		0			0
$703$	12.1907			0.459780
$704$		0			0
$705$	1.26084	−	2.18384i	0.0474860	−	0.0822482i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−34.9489	+	20.1778i	−1.31253	+	0.757792i	−0.982515	−	0.186183i	$-0.940388\pi$
$709$	−34.9489	+	20.1778i	−1.31253	+	0.757792i	−0.330018	+	0.943975i	$0.607055\pi$
$710$		0			0
$711$	18.8422	+	32.6356i	0.706637	+	1.22393i
$712$		0			0
$713$	−0.374700	−	0.216333i	−0.0140326	−	0.00810174i
$714$		0			0
$715$	−16.5403	+	8.32342i	−0.618571	+	0.311278i
$716$		0			0
$717$	−13.4034	−	7.73844i	−0.500558	−	0.288997i
$718$		0			0
$719$	−15.0163	−	26.0090i	−0.560013	−	0.969972i	−0.997494	−	0.0707441i	$-0.977463\pi$
$719$	−15.0163	−	26.0090i	−0.560013	−	0.969972i	0.437481	−	0.899228i	$-0.355871\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		−	8.57467i		−	0.318895i
$724$		0			0
$725$	5.88944	−	10.2008i	0.218728	−	0.378848i
$726$		0			0
$727$	−30.7097			−1.13896			−0.569479	−	0.822006i	$-0.692855\pi$
$727$	−30.7097			−1.13896			−0.569479	+	0.822006i	$0.692855\pi$
$728$		0			0
$729$	−8.67707			−0.321373
$730$		0			0
$731$	0.379462	−	0.657248i	0.0140349	−	0.0243092i
$732$		0			0
$733$			11.6482i			0.430238i	0.976588	+	0.215119i	$0.0690139\pi$
$733$			11.6482i			0.430238i	−0.976588	+	0.215119i	$0.930986\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.46161	+	2.53159i	0.0538393	+	0.0932523i
$738$		0			0
$739$	−11.8399	−	6.83578i	−0.435539	−	0.251458i	0.266165	−	0.963928i	$-0.414243\pi$
$739$	−11.8399	−	6.83578i	−0.435539	−	0.251458i	−0.701703	+	0.712469i	$0.747577\pi$
$740$		0			0
$741$	−6.53135	+	9.94777i	−0.239935	+	0.365440i
$742$		0			0
$743$	3.73344	+	2.15550i	0.136966	+	0.0790776i	0.566917	−	0.823775i	$-0.308136\pi$
$743$	3.73344	+	2.15550i	0.136966	+	0.0790776i	−0.429951	+	0.902852i	$0.641469\pi$
$744$		0			0
$745$	21.2358	+	36.7816i	0.778021	+	1.34757i
$746$		0			0
$747$	6.66421	−	3.84758i	0.243831	−	0.140776i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−21.3882	+	37.0454i	−0.780466	+	1.35181i	0.151204	+	0.988503i	$0.451685\pi$
$751$	−21.3882	+	37.0454i	−0.780466	+	1.35181i	−0.931670	+	0.363305i	$0.881648\pi$
$752$		0			0
$753$	11.1717			0.407119
$754$		0			0
$755$	−19.8271			−0.721583
$756$		0			0
$757$	−8.90718	+	15.4277i	−0.323737	+	0.560729i	−0.981256	−	0.192709i	$-0.938273\pi$
$757$	−8.90718	+	15.4277i	−0.323737	+	0.560729i	0.657519	+	0.753438i	$0.271606\pi$
$758$		0			0
$759$			1.27605i			0.0463178i
$760$		0			0
$761$	18.5610	−	10.7162i	0.672837	−	0.388463i	−0.124314	−	0.992243i	$-0.539673\pi$
$761$	18.5610	−	10.7162i	0.672837	−	0.388463i	0.797151	+	0.603780i	$0.206340\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	10.4429	+	6.02919i	0.377563	+	0.217986i
$766$		0			0
$767$	25.6601	+	1.47393i	0.926533	+	0.0532206i
$768$		0			0
$769$	9.01602	+	5.20540i	0.325126	+	0.187712i	0.653675	−	0.756775i	$-0.273226\pi$
$769$	9.01602	+	5.20540i	0.325126	+	0.187712i	−0.328549	+	0.944487i	$0.606560\pi$
$770$		0			0
$771$	1.55458	+	2.69262i	0.0559869	+	0.0969722i
$772$		0			0
$773$	30.4896	−	17.6032i	1.09663	−	0.633142i	0.161300	−	0.986905i	$-0.448431\pi$
$773$	30.4896	−	17.6032i	1.09663	−	0.633142i	0.935335	+	0.353763i	$0.115098\pi$
$774$		0			0
$775$		−	1.17258i		−	0.0421202i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	34.6965			1.24313
$780$		0			0
$781$	−18.3066			−0.655061
$782$		0			0
$783$	6.52196	−	11.2964i	0.233076	−	0.403699i
$784$		0			0
$785$		−	17.7076i		−	0.632011i
$786$		0			0
$787$	35.5200	−	20.5075i	1.26615	−	0.731014i	0.291895	−	0.956450i	$-0.405714\pi$
$787$	35.5200	−	20.5075i	1.26615	−	0.731014i	0.974258	+	0.225437i	$0.0723809\pi$
$788$		0			0
$789$	−1.60399	−	2.77820i	−0.0571037	−	0.0989065i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−1.16086	+	20.2098i	−0.0412234	+	0.717671i
$794$		0			0
$795$	−18.4070	−	10.6273i	−0.652828	−	0.376910i
$796$		0			0
$797$	−12.1708	−	21.0805i	−0.431113	−	0.746710i	0.565856	−	0.824504i	$-0.308546\pi$
$797$	−12.1708	−	21.0805i	−0.431113	−	0.746710i	−0.996969	+	0.0777940i	$0.975212\pi$
$798$		0			0
$799$	2.01143	−	1.16130i	0.0711592	−	0.0410838i
$800$		0			0
$801$			33.8347i			1.19549i
$802$		0			0
$803$	5.06412	−	8.77132i	0.178709	−	0.309533i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.58562			0.0910180
$808$		0			0
$809$	−6.50727	+	11.2709i	−0.228784	+	0.396265i	−0.957448	−	0.288606i	$-0.906808\pi$
$809$	−6.50727	+	11.2709i	−0.228784	+	0.396265i	0.728664	+	0.684871i	$0.240141\pi$
$810$		0			0
$811$		−	14.5520i		−	0.510988i	−0.966811	−	0.255494i	$-0.917762\pi$
$811$		−	14.5520i		−	0.510988i	0.966811	−	0.255494i	$-0.0822382\pi$
$812$		0			0
$813$	−5.13294	+	2.96351i	−0.180020	+	0.103935i
$814$		0			0
$815$	−13.0785	−	22.6526i	−0.458120	−	0.793487i
$816$		0			0
$817$	−2.18636	−	1.26230i	−0.0764911	−	0.0441622i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.27293	−	4.77638i	−0.288727	−	0.166697i	0.348641	−	0.937257i	$-0.386643\pi$
$821$	−8.27293	−	4.77638i	−0.288727	−	0.166697i	−0.637368	+	0.770560i	$0.719977\pi$
$822$		0			0
$823$	5.31638	+	9.20824i	0.185317	+	0.320979i	0.943683	−	0.330850i	$-0.107335\pi$
$823$	5.31638	+	9.20824i	0.185317	+	0.320979i	−0.758366	+	0.651829i	$0.774002\pi$
$824$		0			0
$825$	−2.99494	+	1.72913i	−0.104270	+	0.0602005i
$826$		0			0
$827$			44.7329i			1.55552i	0.628564	+	0.777758i	$0.283643\pi$
$827$			44.7329i			1.55552i	−0.628564	+	0.777758i	$0.716357\pi$
$828$		0			0
$829$	−11.1854	+	19.3737i	−0.388484	+	0.672875i	−0.992246	−	0.124290i	$-0.960335\pi$
$829$	−11.1854	+	19.3737i	−0.388484	+	0.672875i	0.603761	+	0.797165i	$0.293668\pi$
$830$		0			0
$831$	−3.04725			−0.105708
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.33333	+	2.30939i	−0.0461417	+	0.0799197i
$836$		0			0
$837$		−	1.29851i		−	0.0448831i
$838$		0			0
$839$	−4.05352	+	2.34030i	−0.139943	+	0.0807961i	−0.568337	−	0.822796i	$-0.692413\pi$
$839$	−4.05352	+	2.34030i	−0.139943	+	0.0807961i	0.428394	+	0.903592i	$0.359080\pi$
$840$		0			0
$841$	7.37954	+	12.7817i	0.254467	+	0.440750i
$842$		0			0
$843$	−5.28893	−	3.05356i	−0.182160	−	0.105170i
$844$		0			0
$845$	33.9939	−	14.7281i	1.16942	−	0.506661i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−7.92633	−	13.7288i	−0.272031	−	0.471171i
$850$		0			0
$851$	−2.26500	+	1.30770i	−0.0776431	+	0.0448273i
$852$		0			0
$853$			10.1857i			0.348753i	0.984679	+	0.174376i	$0.0557910\pi$
$853$			10.1857i			0.348753i	−0.984679	+	0.174376i	$0.944209\pi$
$854$		0			0
$855$	20.0563	−	34.7386i	0.685913	−	1.18804i
$856$		0			0
$857$	−48.8600			−1.66903			−0.834513	−	0.550988i	$-0.814251\pi$
$857$	−48.8600			−1.66903			−0.834513	+	0.550988i	$0.814251\pi$
$858$		0			0
$859$	4.96639			0.169451			0.0847256	−	0.996404i	$-0.472999\pi$
$859$	4.96639			0.169451			0.0847256	+	0.996404i	$0.472999\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			29.6673i			1.00989i	0.863153	+	0.504943i	$0.168486\pi$
$863$			29.6673i			1.00989i	−0.863153	+	0.504943i	$0.831514\pi$
$864$		0			0
$865$	8.55422	−	4.93878i	0.290852	−	0.167924i
$866$		0			0
$867$	4.42539	+	7.66500i	0.150294	+	0.260317i
$868$		0			0
$869$	−22.4302	−	12.9501i	−0.760893	−	0.439302i
$870$		0			0
$871$	−2.62908	−	5.22450i	−0.0890830	−	0.177025i
$872$		0			0
$873$	27.5137	+	15.8850i	0.931197	+	0.537627i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−6.70755	+	3.87261i	−0.226498	+	0.130769i	−0.608955	−	0.793204i	$-0.708411\pi$
$877$	−6.70755	+	3.87261i	−0.226498	+	0.130769i	0.382458	+	0.923973i	$0.375078\pi$
$878$		0			0
$879$		−	6.26431i		−	0.211290i
$880$		0			0
$881$	26.5762	−	46.0313i	0.895375	−	1.55083i	0.0620348	−	0.998074i	$-0.480241\pi$
$881$	26.5762	−	46.0313i	0.895375	−	1.55083i	0.833340	−	0.552761i	$-0.186426\pi$
$882$		0			0
$883$	−19.7373			−0.664214			−0.332107	−	0.943242i	$-0.607760\pi$
$883$	−19.7373			−0.664214			−0.332107	+	0.943242i	$0.607760\pi$
$884$		0			0
$885$	12.4900			0.419847
$886$		0			0
$887$	20.4840	−	35.4793i	0.687785	−	1.19128i	−0.284768	−	0.958596i	$-0.591917\pi$
$887$	20.4840	−	35.4793i	0.687785	−	1.19128i	0.972553	−	0.232682i	$-0.0747501\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	8.95944	−	5.17274i	0.300153	−	0.173293i
$892$		0			0
$893$	−3.86310	−	6.69109i	−0.129274	−	0.223909i
$894$		0			0
$895$	6.32059	+	3.64920i	0.211274	+	0.121979i
$896$		0			0
$897$	0.146410	−	2.54889i	0.00488847	−	0.0851049i
$898$		0			0
$899$	−1.22774	−	0.708836i	−0.0409474	−	0.0236410i
$900$		0			0
$901$	−9.78826	−	16.9538i	−0.326094	−	0.564812i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	36.9747i		−	1.22908i
$906$		0			0
$907$	−2.35224	+	4.07421i	−0.0781050	+	0.135282i	−0.902432	−	0.430832i	$-0.858220\pi$
$907$	−2.35224	+	4.07421i	−0.0781050	+	0.135282i	0.824327	+	0.566113i	$0.191554\pi$
$908$		0			0
$909$	10.6517			0.353295
$910$		0			0
$911$	7.33499			0.243019			0.121509	−	0.992590i	$-0.461227\pi$
$911$	7.33499			0.243019			0.121509	+	0.992590i	$0.461227\pi$
$912$		0			0
$913$	−2.64442	+	4.58026i	−0.0875174	+	0.151585i
$914$		0			0
$915$			9.83709i			0.325204i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−3.13488	−	5.42976i	−0.103410	−	0.179111i	0.809677	−	0.586875i	$-0.199642\pi$
$919$	−3.13488	−	5.42976i	−0.103410	−	0.179111i	−0.913087	+	0.407764i	$0.866309\pi$
$920$		0			0
$921$	16.1075	+	9.29965i	0.530759	+	0.306434i
$922$		0			0
$923$	36.5670	+	2.10043i	1.20362	+	0.0691365i
$924$		0			0
$925$	−6.13841	−	3.54401i	−0.201830	−	0.116526i
$926$		0			0
$927$	25.1442	+	43.5511i	0.825845	+	1.43040i
$928$		0			0
$929$	−39.7459	+	22.9473i	−1.30402	+	0.752877i	−0.981091	−	0.193546i	$-0.938001\pi$
$929$	−39.7459	+	22.9473i	−1.30402	+	0.752877i	−0.322930	+	0.946423i	$0.604668\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	6.36951	−	11.0323i	0.208528	−	0.361182i
$934$		0			0
$935$	−8.28765			−0.271035
$936$		0			0
$937$	−19.9322			−0.651155			−0.325578	−	0.945515i	$-0.605559\pi$
$937$	−19.9322			−0.651155			−0.325578	+	0.945515i	$0.605559\pi$
$938$		0			0
$939$	3.49305	−	6.05014i	0.113991	−	0.197439i
$940$		0			0
$941$		−	49.0230i		−	1.59810i	−0.601262	−	0.799052i	$-0.705335\pi$
$941$		−	49.0230i		−	1.59810i	0.601262	−	0.799052i	$-0.294665\pi$
$942$		0			0
$943$	−6.44652	+	3.72190i	−0.209928	+	0.121202i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	31.4093	+	18.1342i	1.02067	+	0.589282i	0.914297	−	0.405045i	$-0.132744\pi$
$947$	31.4093	+	18.1342i	1.02067	+	0.589282i	0.106369	+	0.994327i	$0.466078\pi$
$948$		0			0
$949$	−11.1219	+	16.9395i	−0.361031	+	0.549879i
$950$		0			0
$951$	8.37495	+	4.83528i	0.271576	+	0.156795i
$952$		0			0
$953$	26.4115	+	45.7461i	0.855554	+	1.48186i	0.876130	+	0.482074i	$0.160116\pi$
$953$	26.4115	+	45.7461i	0.855554	+	1.48186i	−0.0205766	+	0.999788i	$0.506550\pi$
$954$		0			0
$955$	64.0952	−	37.0054i	2.07407	−	1.19747i
$956$		0			0
$957$			4.18111i			0.135156i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	30.8589			0.995447
$962$		0			0
$963$	24.0742			0.775779
$964$		0			0
$965$	9.78832	−	16.9539i	0.315097	−	0.545764i
$966$		0			0
$967$		−	21.0424i		−	0.676679i	−0.941024	−	0.338340i	$-0.890135\pi$
$967$		−	21.0424i		−	0.676679i	0.941024	−	0.338340i	$-0.109865\pi$
$968$		0			0
$969$	−4.61276	+	2.66318i	−0.148183	+	0.0855536i
$970$		0			0
$971$	22.3678	+	38.7421i	0.717816	+	1.24329i	0.961864	+	0.273530i	$0.0881912\pi$
$971$	22.3678	+	38.7421i	0.717816	+	1.24329i	−0.244048	+	0.969763i	$0.578475\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	6.18072	−	3.11027i	0.197941	−	0.0996083i
$976$		0			0
$977$	−28.6223	−	16.5251i	−0.915709	−	0.528685i	−0.0334455	−	0.999441i	$-0.510648\pi$
$977$	−28.6223	−	16.5251i	−0.915709	−	0.528685i	−0.882264	+	0.470756i	$0.843981\pi$
$978$		0			0
$979$	−11.6272	−	20.1389i	−0.371607	−	0.643642i
$980$		0			0
$981$	−11.4859	+	6.63140i	−0.366717	+	0.211724i
$982$		0			0
$983$			24.8221i			0.791703i	0.918315	+	0.395852i	$0.129551\pi$
$983$			24.8221i			0.791703i	−0.918315	+	0.395852i	$0.870449\pi$
$984$		0			0
$985$	21.2836	−	36.8643i	0.678153	−	1.17459i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.541627			0.0172227
$990$		0			0
$991$	3.37733	−	5.84970i	0.107284	−	0.185822i	−0.807385	−	0.590025i	$-0.799118\pi$
$991$	3.37733	−	5.84970i	0.107284	−	0.185822i	0.914669	+	0.404203i	$0.132451\pi$
$992$		0			0
$993$		−	21.3711i		−	0.678191i
$994$		0			0
$995$	13.3220	−	7.69145i	0.422335	−	0.243835i
$996$		0			0
$997$	11.5038	+	19.9252i	0.364330	+	0.631037i	0.988668	−	0.150116i	$-0.0479649\pi$
$997$	11.5038	+	19.9252i	0.364330	+	0.631037i	−0.624339	+	0.781154i	$0.714632\pi$
$998$		0			0
$999$	−6.79767	−	3.92464i	−0.215069	−	0.124170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.u.f.589.6	✓	24
7.2	even	3		2548.2.bb.g.1733.6		24
7.3	odd	6		2548.2.bq.g.1941.6		24
7.4	even	3		2548.2.bq.g.1941.7		24
7.5	odd	6		2548.2.bb.g.1733.7		24
7.6	odd	2	inner	2548.2.u.f.589.7	yes	24
13.10	even	6	inner	2548.2.u.f.1765.6	yes	24
91.10	odd	6		2548.2.bb.g.569.7		24
91.23	even	6		2548.2.bq.g.361.7		24
91.62	odd	6	inner	2548.2.u.f.1765.7	yes	24
91.75	odd	6		2548.2.bq.g.361.6		24
91.88	even	6		2548.2.bb.g.569.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2548.2.u.f.589.6	✓	24	1.1	even	1	trivial
2548.2.u.f.589.7	yes	24	7.6	odd	2	inner
2548.2.u.f.1765.6	yes	24	13.10	even	6	inner
2548.2.u.f.1765.7	yes	24	91.62	odd	6	inner
2548.2.bb.g.569.6		24	91.88	even	6
2548.2.bb.g.569.7		24	91.10	odd	6
2548.2.bb.g.1733.6		24	7.2	even	3
2548.2.bb.g.1733.7		24	7.5	odd	6
2548.2.bq.g.361.6		24	91.75	odd	6
2548.2.bq.g.361.7		24	91.23	even	6
2548.2.bq.g.1941.6		24	7.3	odd	6
2548.2.bq.g.1941.7		24	7.4	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.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.307410 + 0.532450i) q^{3} -2.84979i q^{5} +(1.31100 + 2.27072i) q^{9} +(-1.56065 - 0.901040i) q^{11} +(3.01398 + 1.97887i) q^{13} +(1.51737 + 0.876054i) q^{15} +(0.806891 + 1.39758i) q^{17} +(4.64909 - 2.68415i) q^{19} +(-0.575859 + 0.997417i) q^{23} -3.12129 q^{25} -3.45652 q^{27} +(-1.88686 + 3.26813i) q^{29} +0.375670i q^{31} +(0.959517 - 0.553978i) q^{33} +(1.96662 + 1.13543i) q^{37} +(-1.98018 + 0.996468i) q^{39} +(5.59731 + 3.23161i) q^{41} +(-0.235139 - 0.407272i) q^{43} +(6.47106 - 3.73607i) q^{45} -1.43923i q^{47} -0.992186 q^{51} -12.1308 q^{53} +(-2.56777 + 4.44751i) q^{55} +3.30054i q^{57} +(6.17352 - 3.56428i) q^{59} +(2.80721 + 4.86224i) q^{61} +(5.63937 - 8.58920i) q^{65} +(-1.40482 - 0.811071i) q^{67} +(-0.354050 - 0.613233i) q^{69} +(8.79759 - 5.07929i) q^{71} +5.62031i q^{73} +(0.959517 - 1.66193i) q^{75} +14.3724 q^{79} +(-2.87043 + 4.97172i) q^{81} -2.93485i q^{83} +(3.98279 - 2.29947i) q^{85} +(-1.16008 - 2.00931i) q^{87} +(11.1754 + 6.45210i) q^{89} +(-0.200026 - 0.115485i) q^{93} +(-7.64927 - 13.2489i) q^{95} +(10.4934 - 6.05837i) q^{97} -4.72505i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{9} - 12 q^{15} + 16 q^{23} + 24 q^{29} + 8 q^{39} + 4 q^{43} + 80 q^{51} - 48 q^{53} + 8 q^{65} - 24 q^{71} - 48 q^{79} + 4 q^{81} + 12 q^{85} + 48 q^{93} - 20 q^{95}+O(q^{100}) \) 24 * q - 8 * q^9 - 12 * q^15 + 16 * q^23 + 24 * q^29 + 8 * q^39 + 4 * q^43 + 80 * q^51 - 48 * q^53 + 8 * q^65 - 24 * q^71 - 48 * q^79 + 4 * q^81 + 12 * q^85 + 48 * q^93 - 20 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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