LMFDB - Embedded newform 1620.2.x.c.593.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1620,2,Mod(53,1620)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1620, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 10, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1620.53"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.162447943996702457856.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} - 15x^{8} - 16x^{4} + 256 $ x^16 - x^12 - 15x^8 - 16x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 540)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			593.3
Root			$-1.40721 - 0.140577i$ of defining polynomial
Character	$\chi$	$=$	1620.593
Dual form			1620.2.x.c.377.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.125246 - 2.23256i) q^{5} +(-0.655657 - 2.44694i) q^{7} +(-0.559525 - 0.323042i) q^{11} +(1.38771 - 5.17900i) q^{13} +(-4.96640 - 4.96640i) q^{17} +6.58258i q^{19} +(2.55560 + 0.684771i) q^{23} +(-4.96863 - 0.559237i) q^{25} +(-3.99728 + 6.92349i) q^{29} +(0.291288 + 0.504525i) q^{31} +(-5.54506 + 1.15732i) q^{35} +(3.00000 - 3.00000i) q^{37} +(-3.68312 + 2.12645i) q^{41} +(1.08092 - 0.289631i) q^{43} +(-2.64770 + 0.709449i) q^{47} +(0.504525 - 0.291288i) q^{49} +(-5.47764 + 5.47764i) q^{53} +(-0.791288 + 1.20871i) q^{55} +(-6.44677 - 11.1661i) q^{59} +(-3.08258 + 5.33918i) q^{61} +(-11.3886 - 3.74678i) q^{65} +(9.56218 + 2.56218i) q^{67} -14.3205i q^{71} +(-1.20871 - 1.20871i) q^{73} +(-0.423609 + 1.58093i) q^{77} +(5.33918 + 3.08258i) q^{79} +(0.448288 + 1.67303i) q^{83} +(-11.7098 + 10.4658i) q^{85} -9.42157 q^{89} -13.5826 q^{91} +(14.6960 + 0.824440i) q^{95} +(2.77542 + 10.3580i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{7} - 12 q^{13} - 16 q^{25} - 32 q^{31} + 48 q^{37} - 12 q^{43} + 24 q^{55} + 24 q^{61} + 56 q^{67} - 56 q^{73} + 44 q^{85} - 144 q^{91} - 24 q^{97}+O(q^{100}) $ 16 * q - 4 * q^7 - 12 * q^13 - 16 * q^25 - 32 * q^31 + 48 * q^37 - 12 * q^43 + 24 * q^55 + 24 * q^61 + 56 * q^67 - 56 * q^73 + 44 * q^85 - 144 * q^91 - 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.125246	−	2.23256i	0.0560116	−	0.998430i
$5$	0.125246	−	2.23256i	0.0560116	−	0.998430i
$6$		0			0
$7$	−0.655657	−	2.44694i	−0.247815	−	0.924858i	−0.971948	−	0.235197i	$-0.924426\pi$
$7$	−0.655657	−	2.44694i	−0.247815	−	0.924858i	0.724133	−	0.689661i	$-0.242240\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.559525	−	0.323042i	−0.168703	−	0.0974008i	0.413271	−	0.910608i	$-0.364386\pi$
$11$	−0.559525	−	0.323042i	−0.168703	−	0.0974008i	−0.581974	+	0.813207i	$0.697720\pi$
$12$		0			0
$13$	1.38771	−	5.17900i	0.384881	−	1.43639i	−0.453474	−	0.891270i	$-0.649815\pi$
$13$	1.38771	−	5.17900i	0.384881	−	1.43639i	0.838355	−	0.545125i	$-0.183518\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.96640	−	4.96640i	−1.20453	−	1.20453i	−0.972774	−	0.231755i	$-0.925553\pi$
$17$	−4.96640	−	4.96640i	−1.20453	−	1.20453i	−0.231755	−	0.972774i	$-0.574447\pi$
$18$		0			0
$19$			6.58258i			1.51015i	0.655640	+	0.755073i	$0.272399\pi$
$19$			6.58258i			1.51015i	−0.655640	+	0.755073i	$0.727601\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.55560	+	0.684771i	0.532879	+	0.142785i	0.515218	−	0.857059i	$-0.327711\pi$
$23$	2.55560	+	0.684771i	0.532879	+	0.142785i	0.0176618	+	0.999844i	$0.494378\pi$
$24$		0			0
$25$	−4.96863	−	0.559237i	−0.993725	−	0.111847i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.99728	+	6.92349i	−0.742276	+	1.28566i	0.209181	+	0.977877i	$0.432920\pi$
$29$	−3.99728	+	6.92349i	−0.742276	+	1.28566i	−0.951457	+	0.307782i	$0.900413\pi$
$30$		0			0
$31$	0.291288	+	0.504525i	0.0523168	+	0.0906154i	0.890998	−	0.454008i	$-0.150006\pi$
$31$	0.291288	+	0.504525i	0.0523168	+	0.0906154i	−0.838681	+	0.544623i	$0.816673\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.54506	+	1.15732i	−0.937287	+	0.195623i
$36$		0			0
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	−0.416115	−	0.909312i	$-0.636609\pi$
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	0.909312	+	0.416115i	$0.136609\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.68312	+	2.12645i	−0.575206	+	0.332095i	−0.759226	−	0.650827i	$-0.774422\pi$
$41$	−3.68312	+	2.12645i	−0.575206	+	0.332095i	0.184020	+	0.982923i	$0.441089\pi$
$42$		0			0
$43$	1.08092	−	0.289631i	0.164839	−	0.0441684i	−0.175456	−	0.984487i	$-0.556140\pi$
$43$	1.08092	−	0.289631i	0.164839	−	0.0441684i	0.340294	+	0.940319i	$0.389473\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.64770	+	0.709449i	−0.386207	+	0.103484i	−0.446698	−	0.894685i	$-0.647400\pi$
$47$	−2.64770	+	0.709449i	−0.386207	+	0.103484i	0.0604909	+	0.998169i	$0.480733\pi$
$48$		0			0
$49$	0.504525	−	0.291288i	0.0720751	−	0.0416125i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.47764	+	5.47764i	−0.752412	+	0.752412i	−0.974929	−	0.222517i	$-0.928573\pi$
$53$	−5.47764	+	5.47764i	−0.752412	+	0.752412i	0.222517	+	0.974929i	$0.428573\pi$
$54$		0			0
$55$	−0.791288	+	1.20871i	−0.106697	+	0.162983i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.44677	−	11.1661i	−0.839297	−	1.45371i	−0.890483	−	0.455017i	$-0.849633\pi$
$59$	−6.44677	−	11.1661i	−0.839297	−	1.45371i	0.0511854	−	0.998689i	$-0.483700\pi$
$60$		0			0
$61$	−3.08258	+	5.33918i	−0.394683	+	0.683612i	−0.993061	−	0.117603i	$-0.962479\pi$
$61$	−3.08258	+	5.33918i	−0.394683	+	0.683612i	0.598377	+	0.801214i	$0.295812\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−11.3886	−	3.74678i	−1.41258	−	0.464731i
$66$		0			0
$67$	9.56218	+	2.56218i	1.16821	+	0.313020i	0.790239	−	0.612799i	$-0.209957\pi$
$67$	9.56218	+	2.56218i	1.16821	+	0.313020i	0.377967	+	0.925819i	$0.376623\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	14.3205i		−	1.69954i	−0.527157	−	0.849768i	$-0.676742\pi$
$71$		−	14.3205i		−	1.69954i	0.527157	−	0.849768i	$-0.323258\pi$
$72$		0			0
$73$	−1.20871	−	1.20871i	−0.141469	−	0.141469i	0.632825	−	0.774294i	$-0.281895\pi$
$73$	−1.20871	−	1.20871i	−0.141469	−	0.141469i	−0.774294	+	0.632825i	$0.781895\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.423609	+	1.58093i	−0.0482748	+	0.180164i
$78$		0			0
$79$	5.33918	+	3.08258i	0.600704	+	0.346817i	0.769319	−	0.638865i	$-0.220596\pi$
$79$	5.33918	+	3.08258i	0.600704	+	0.346817i	−0.168614	+	0.985682i	$0.553929\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.448288	+	1.67303i	0.0492060	+	0.183639i	0.986155	−	0.165827i	$-0.0530295\pi$
$83$	0.448288	+	1.67303i	0.0492060	+	0.183639i	−0.936949	+	0.349467i	$0.886363\pi$
$84$		0			0
$85$	−11.7098	+	10.4658i	−1.27011	+	1.13517i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−9.42157			−0.998684			−0.499342	−	0.866405i	$-0.666425\pi$
$89$	−9.42157			−0.998684			−0.499342	+	0.866405i	$0.666425\pi$
$90$		0			0
$91$	−13.5826			−1.42384
$92$		0			0
$93$		0			0
$94$		0			0
$95$	14.6960	+	0.824440i	1.50778	+	0.0845858i
$96$		0			0
$97$	2.77542	+	10.3580i	0.281801	+	1.05169i	0.951146	+	0.308743i	$0.0999082\pi$
$97$	2.77542	+	10.3580i	0.281801	+	1.05169i	−0.669345	+	0.742952i	$0.733425\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.36623	+	4.25290i	0.732967	+	0.423179i	0.819507	−	0.573069i	$-0.194247\pi$
$101$	7.36623	+	4.25290i	0.732967	+	0.423179i	−0.0865394	+	0.996248i	$0.527581\pi$
$102$		0			0
$103$	−1.31131	+	4.89389i	−0.129208	+	0.482209i	−0.999955	−	0.00952189i	$-0.996969\pi$
$103$	−1.31131	+	4.89389i	−0.129208	+	0.482209i	0.870747	+	0.491731i	$0.163636\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−13.5396	−	13.5396i	−1.30892	−	1.30892i	−0.922192	−	0.386732i	$-0.873604\pi$
$107$	−13.5396	−	13.5396i	−1.30892	−	1.30892i	−0.386732	−	0.922192i	$-0.626396\pi$
$108$		0			0
$109$		−	15.7477i		−	1.50836i	−0.656668	−	0.754179i	$-0.728035\pi$
$109$		−	15.7477i		−	1.50836i	0.656668	−	0.754179i	$-0.271965\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6.87633	−	1.84251i	−0.646871	−	0.173329i	−0.0795572	−	0.996830i	$-0.525351\pi$
$113$	−6.87633	−	1.84251i	−0.646871	−	0.173329i	−0.567314	+	0.823502i	$0.692017\pi$
$114$		0			0
$115$	1.84887	−	5.61976i	0.172408	−	0.524045i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−8.89626	+	15.4088i	−0.815518	+	1.41252i
$120$		0			0
$121$	−5.29129	−	9.16478i	−0.481026	−	0.833162i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.87083	+	11.0227i	−0.167332	+	0.985901i
$126$		0			0
$127$	6.58258	−	6.58258i	0.584109	−	0.584109i	−0.351921	−	0.936030i	$-0.614471\pi$
$127$	6.58258	−	6.58258i	0.584109	−	0.584109i	0.936030	+	0.351921i	$0.114471\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.60206	−	4.96640i	0.751566	−	0.433917i	−0.0746937	−	0.997207i	$-0.523798\pi$
$131$	8.60206	−	4.96640i	0.751566	−	0.433917i	0.826259	+	0.563290i	$0.190465\pi$
$132$		0			0
$133$	16.1072	−	4.31591i	1.39667	−	0.374237i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.67303	−	0.448288i	0.142937	−	0.0382998i	−0.186641	−	0.982428i	$-0.559760\pi$
$137$	1.67303	−	0.448288i	0.142937	−	0.0382998i	0.329578	+	0.944128i	$0.393094\pi$
$138$		0			0
$139$	−9.66930	+	5.58258i	−0.820140	+	0.473508i	−0.850465	−	0.526032i	$-0.823679\pi$
$139$	−9.66930	+	5.58258i	−0.820140	+	0.473508i	0.0303249	+	0.999540i	$0.490346\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.44949	+	2.44949i	−0.204837	+	0.204837i
$144$		0			0
$145$	14.9564	+	9.79129i	1.24206	+	0.813122i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.86811	−	10.1639i	−0.480734	−	0.832656i	0.519022	−	0.854761i	$-0.326296\pi$
$149$	−5.86811	−	10.1639i	−0.480734	−	0.832656i	−0.999756	+	0.0221055i	$0.992963\pi$
$150$		0			0
$151$	8.58258	−	14.8655i	0.698440	−	1.20973i	−0.270567	−	0.962701i	$-0.587211\pi$
$151$	8.58258	−	14.8655i	0.698440	−	1.20973i	0.969007	−	0.247033i	$-0.0794555\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.16286	−	0.587127i	0.0934035	−	0.0471592i
$156$		0			0
$157$	4.95339	+	1.32726i	0.395324	+	0.105927i	0.451004	−	0.892522i	$-0.351066\pi$
$157$	4.95339	+	1.32726i	0.395324	+	0.105927i	−0.0556801	+	0.998449i	$0.517733\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	6.70239i		−	0.528222i
$162$		0			0
$163$	−8.58258	−	8.58258i	−0.672239	−	0.672239i	0.285993	−	0.958232i	$-0.407677\pi$
$163$	−8.58258	−	8.58258i	−0.672239	−	0.672239i	−0.958232	+	0.285993i	$0.907677\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.47792	+	9.24773i	−0.191747	+	0.715611i	0.801338	+	0.598212i	$0.204122\pi$
$167$	−2.47792	+	9.24773i	−0.191747	+	0.715611i	−0.993085	+	0.117398i	$0.962545\pi$
$168$		0			0
$169$	−13.6379	−	7.87386i	−1.04907	−	0.605682i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−4.98052	−	18.5876i	−0.378662	−	1.41319i	−0.847920	−	0.530125i	$-0.822145\pi$
$173$	−4.98052	−	18.5876i	−0.378662	−	1.41319i	0.469258	−	0.883061i	$-0.344522\pi$
$174$		0			0
$175$	1.88929	+	12.5246i	0.142817	+	0.946773i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	24.7646			1.85099			0.925496	−	0.378757i	$-0.123648\pi$
$179$	24.7646			1.85099			0.925496	+	0.378757i	$0.123648\pi$
$180$		0			0
$181$	−5.41742			−0.402674			−0.201337	−	0.979522i	$-0.564529\pi$
$181$	−5.41742			−0.402674			−0.201337	+	0.979522i	$0.564529\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.32194	−	7.07341i	−0.464798	−	0.520047i
$186$		0			0
$187$	1.17447	+	4.38318i	0.0858858	+	0.320530i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.24037	−	1.87083i	−0.234465	−	0.135368i	0.378165	−	0.925738i	$-0.376555\pi$
$191$	−3.24037	−	1.87083i	−0.234465	−	0.135368i	−0.612630	+	0.790370i	$0.709888\pi$
$192$		0			0
$193$	5.78001	−	21.5713i	0.416054	−	1.55274i	−0.366660	−	0.930355i	$-0.619499\pi$
$193$	5.78001	−	21.5713i	0.416054	−	1.55274i	0.782714	−	0.622381i	$-0.213835\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.12372	+	6.12372i	0.436297	+	0.436297i	0.890764	−	0.454467i	$-0.150170\pi$
$197$	6.12372	+	6.12372i	0.436297	+	0.436297i	−0.454467	+	0.890764i	$0.650170\pi$
$198$		0			0
$199$			13.5826i			0.962843i	0.876489	+	0.481422i	$0.159879\pi$
$199$			13.5826i			0.962843i	−0.876489	+	0.481422i	$0.840121\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	19.5622	+	5.24168i	1.37300	+	0.367894i
$204$		0			0
$205$	4.28612	+	8.48910i	0.299356	+	0.592904i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.12645	−	3.68312i	0.147089	−	0.254766i
$210$		0			0
$211$	−13.0826	−	22.6597i	−0.900642	−	1.55996i	−0.826663	−	0.562697i	$-0.809764\pi$
$211$	−13.0826	−	22.6597i	−0.900642	−	1.55996i	−0.0739786	−	0.997260i	$-0.523570\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.511238	−	2.44949i	−0.0348662	−	0.167054i
$216$		0			0
$217$	1.04356	−	1.04356i	0.0708415	−	0.0708415i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−32.6129	+	18.8291i	−2.19378	+	1.26658i
$222$		0			0
$223$	−16.6179	+	4.45275i	−1.11282	+	0.298178i	−0.767974	−	0.640482i	$-0.778735\pi$
$223$	−16.6179	+	4.45275i	−1.11282	+	0.298178i	−0.344844	+	0.938660i	$0.612068\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	21.2353	−	5.68997i	1.40943	−	0.377657i	0.527711	−	0.849424i	$-0.323050\pi$
$227$	21.2353	−	5.68997i	1.40943	−	0.377657i	0.881723	+	0.471767i	$0.156384\pi$
$228$		0			0
$229$	−12.9904	+	7.50000i	−0.858429	+	0.495614i	−0.863486	−	0.504373i	$-0.831724\pi$
$229$	−12.9904	+	7.50000i	−0.858429	+	0.495614i	0.00505719	+	0.999987i	$0.498390\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.38774	+	4.38774i	−0.287450	+	0.287450i	−0.836071	−	0.548621i	$-0.815153\pi$
$233$	−4.38774	+	4.38774i	−0.287450	+	0.287450i	0.548621	+	0.836071i	$0.315153\pi$
$234$		0			0
$235$	1.25227	+	6.00000i	0.0816893	+	0.391397i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.55074	+	13.0783i	0.488417	+	0.845962i	0.999911	−	0.0133241i	$-0.00424132\pi$
$239$	7.55074	+	13.0783i	0.488417	+	0.845962i	−0.511495	+	0.859286i	$0.670908\pi$
$240$		0			0
$241$	1.87386	−	3.24563i	0.120706	−	0.209069i	−0.799340	−	0.600879i	$-0.794817\pi$
$241$	1.87386	−	3.24563i	0.120706	−	0.209069i	0.920046	+	0.391810i	$0.128151\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.587127	−	1.16286i	−0.0375102	−	0.0742927i
$246$		0			0
$247$	34.0911	+	9.13469i	2.16917	+	0.581226i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			27.3489i			1.72625i	0.504991	+	0.863124i	$0.331496\pi$
$251$			27.3489i			1.72625i	−0.504991	+	0.863124i	$0.668504\pi$
$252$		0			0
$253$	−1.20871	−	1.20871i	−0.0759911	−	0.0759911i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.684771	+	2.55560i	−0.0427148	+	0.159414i	−0.983989	−	0.178229i	$-0.942963\pi$
$257$	−0.684771	+	2.55560i	−0.0427148	+	0.159414i	0.941274	+	0.337643i	$0.109630\pi$
$258$		0			0
$259$	−9.30780	−	5.37386i	−0.578359	−	0.333916i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	6.13826	+	22.9083i	0.378501	+	1.41259i	0.848161	+	0.529738i	$0.177710\pi$
$263$	6.13826	+	22.9083i	0.378501	+	1.41259i	−0.469660	+	0.882847i	$0.655623\pi$
$264$		0			0
$265$	11.5431	+	12.9152i	0.709087	+	0.793374i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	14.8318			0.904310			0.452155	−	0.891939i	$-0.350655\pi$
$269$	14.8318			0.904310			0.452155	+	0.891939i	$0.350655\pi$
$270$		0			0
$271$	13.7477			0.835115			0.417557	−	0.908651i	$-0.362886\pi$
$271$	13.7477			0.835115			0.417557	+	0.908651i	$0.362886\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.59941	+	1.91798i	0.156751	+	0.115659i
$276$		0			0
$277$	0.289631	+	1.08092i	0.0174023	+	0.0649461i	0.974081	−	0.226200i	$-0.0726302\pi$
$277$	0.289631	+	1.08092i	0.0174023	+	0.0649461i	−0.956679	+	0.291146i	$0.905964\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.442745	−	0.255619i	−0.0264120	−	0.0152490i	0.486736	−	0.873549i	$-0.338187\pi$
$281$	−0.442745	−	0.255619i	−0.0264120	−	0.0152490i	−0.513148	+	0.858300i	$0.671521\pi$
$282$		0			0
$283$	5.41399	−	20.2053i	0.321828	−	1.20108i	−0.595634	−	0.803256i	$-0.703099\pi$
$283$	5.41399	−	20.2053i	0.321828	−	1.20108i	0.917462	−	0.397823i	$-0.130234\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7.61816	+	7.61816i	0.449686	+	0.449686i
$288$		0			0
$289$			32.3303i			1.90178i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.37140	+	0.635414i	0.138538	+	0.0371213i	0.327422	−	0.944878i	$-0.393820\pi$
$293$	2.37140	+	0.635414i	0.138538	+	0.0371213i	−0.188883	+	0.982000i	$0.560487\pi$
$294$		0			0
$295$	−25.7365	+	12.9943i	−1.49843	+	0.756555i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	7.09285	−	12.2852i	0.410190	−	0.710470i
$300$		0			0
$301$	−1.41742	−	2.45505i	−0.0816990	−	0.141507i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	11.5339	+	7.55074i	0.660432	+	0.432354i
$306$		0			0
$307$	15.0000	−	15.0000i	0.856095	−	0.856095i	−0.134780	−	0.990876i	$-0.543033\pi$
$307$	15.0000	−	15.0000i	0.856095	−	0.856095i	0.990876	+	0.134780i	$0.0430329\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	22.7750	−	13.1492i	1.29145	−	0.745620i	0.312540	−	0.949905i	$-0.398820\pi$
$311$	22.7750	−	13.1492i	1.29145	−	0.745620i	0.978912	+	0.204285i	$0.0654868\pi$
$312$		0			0
$313$	−12.5198	+	3.35468i	−0.707663	+	0.189618i	−0.594660	−	0.803977i	$-0.702713\pi$
$313$	−12.5198	+	3.35468i	−0.707663	+	0.189618i	−0.113002	+	0.993595i	$0.536047\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.67303	−	0.448288i	0.0939669	−	0.0251783i	−0.211529	−	0.977372i	$-0.567844\pi$
$317$	1.67303	−	0.448288i	0.0939669	−	0.0251783i	0.305496	+	0.952193i	$0.401178\pi$
$318$		0			0
$319$	4.47315	−	2.58258i	0.250448	−	0.144596i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	32.6917	−	32.6917i	1.81902	−	1.81902i
$324$		0			0
$325$	−9.79129	+	24.9564i	−0.543123	+	1.38433i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3.47197	+	6.01362i	0.191416	+	0.331542i
$330$		0			0
$331$	4.79129	−	8.29875i	0.263353	−	0.456141i	−0.703778	−	0.710420i	$-0.748505\pi$
$331$	4.79129	−	8.29875i	0.263353	−	0.456141i	0.967131	+	0.254279i	$0.0818383\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	6.91783	−	21.0272i	0.377962	−	1.14884i
$336$		0			0
$337$	25.8950	+	6.93854i	1.41059	+	0.377966i	0.882135	−	0.470996i	$-0.156105\pi$
$337$	25.8950	+	6.93854i	1.41059	+	0.377966i	0.528454	+	0.848962i	$0.322772\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	0.376393i		−	0.0203828i
$342$		0			0
$343$	−13.5826	−	13.5826i	−0.733390	−	0.733390i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3.11334	−	11.6191i	0.167133	−	0.623747i	−0.830626	−	0.556831i	$-0.812017\pi$
$347$	3.11334	−	11.6191i	0.167133	−	0.623747i	0.997759	−	0.0669166i	$-0.0213162\pi$
$348$		0			0
$349$	−0.218475	−	0.126136i	−0.0116947	−	0.00675193i	0.494141	−	0.869382i	$-0.335483\pi$
$349$	−0.218475	−	0.126136i	−0.0116947	−	0.00675193i	−0.505836	+	0.862630i	$0.668816\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.58630	−	13.3843i	−0.190880	−	0.712372i	−0.993295	−	0.115607i	$-0.963119\pi$
$353$	−3.58630	−	13.3843i	−0.190880	−	0.712372i	0.802415	−	0.596766i	$-0.203548\pi$
$354$		0			0
$355$	−31.9714	−	1.79359i	−1.69687	−	0.0951938i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.134846			−0.00711688			−0.00355844	−	0.999994i	$-0.501133\pi$
$359$	−0.134846			−0.00711688			−0.00355844	+	0.999994i	$0.501133\pi$
$360$		0			0
$361$	−24.3303			−1.28054
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.84991	+	2.54713i	−0.149171	+	0.133323i
$366$		0			0
$367$	6.51206	+	24.3034i	0.339927	+	1.26862i	0.898428	+	0.439121i	$0.144710\pi$
$367$	6.51206	+	24.3034i	0.339927	+	1.26862i	−0.558501	+	0.829504i	$0.688623\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	16.9949	+	9.81203i	0.882333	+	0.509415i
$372$		0			0
$373$	−2.46984	+	9.21757i	−0.127883	+	0.477268i	−0.999926	−	0.0121625i	$-0.996128\pi$
$373$	−2.46984	+	9.21757i	−0.127883	+	0.477268i	0.872043	+	0.489430i	$0.162795\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	30.3097	+	30.3097i	1.56103	+	1.56103i
$378$		0			0
$379$		−	1.00000i		−	0.0513665i	−0.999670	−	0.0256833i	$-0.991824\pi$
$379$		−	1.00000i		−	0.0513665i	0.999670	−	0.0256833i	$-0.00817614\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−23.6988	−	6.35006i	−1.21095	−	0.324473i	−0.403815	−	0.914840i	$-0.632316\pi$
$383$	−23.6988	−	6.35006i	−1.21095	−	0.324473i	−0.807135	+	0.590367i	$0.798983\pi$
$384$		0			0
$385$	3.47647	+	1.14374i	0.177177	+	0.0582902i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	19.5426	−	33.8487i	0.990847	−	1.71620i	0.378522	−	0.925592i	$-0.376432\pi$
$389$	19.5426	−	33.8487i	0.990847	−	1.71620i	0.612325	−	0.790606i	$-0.290234\pi$
$390$		0			0
$391$	−9.29129	−	16.0930i	−0.469881	−	0.813857i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	7.55074	−	11.5339i	0.379919	−	0.580336i
$396$		0			0
$397$	16.9564	−	16.9564i	0.851019	−	0.851019i	−0.139239	−	0.990259i	$-0.544466\pi$
$397$	16.9564	−	16.9564i	0.851019	−	0.851019i	0.990259	+	0.139239i	$0.0444658\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.12132	+	1.22474i	−0.105934	+	0.0611608i	−0.552031	−	0.833824i	$-0.686147\pi$
$401$	−2.12132	+	1.22474i	−0.105934	+	0.0611608i	0.446097	+	0.894985i	$0.352814\pi$
$402$		0			0
$403$	3.01716	−	0.808445i	0.150295	−	0.0402715i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.64770	+	0.709449i	−0.131242	+	0.0351661i
$408$		0			0
$409$	−10.5353	+	6.08258i	−0.520939	+	0.300764i	−0.737319	−	0.675545i	$-0.763908\pi$
$409$	−10.5353	+	6.08258i	−0.520939	+	0.300764i	0.216380	+	0.976309i	$0.430575\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−23.0960	+	23.0960i	−1.13648	+	1.13648i
$414$		0			0
$415$	3.79129	−	0.791288i	0.186107	−	0.0388428i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	7.80636	+	13.5210i	0.381365	+	0.660544i	0.991258	−	0.131940i	$-0.0421206\pi$
$419$	7.80636	+	13.5210i	0.381365	+	0.660544i	−0.609892	+	0.792484i	$0.708787\pi$
$420$		0			0
$421$	5.70871	−	9.88778i	0.278226	−	0.481901i	−0.692718	−	0.721208i	$-0.743587\pi$
$421$	5.70871	−	9.88778i	0.278226	−	0.481901i	0.970944	+	0.239307i	$0.0769204\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	21.8988	+	27.4536i	1.06225	+	1.33170i
$426$		0			0
$427$	15.0858	+	4.04222i	0.730052	+	0.195617i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	5.67991i		−	0.273592i	−0.990599	−	0.136796i	$-0.956320\pi$
$431$		−	5.67991i		−	0.273592i	0.990599	−	0.136796i	$-0.0436804\pi$
$432$		0			0
$433$	5.79129	+	5.79129i	0.278312	+	0.278312i	0.832435	−	0.554123i	$-0.186946\pi$
$433$	5.79129	+	5.79129i	0.278312	+	0.278312i	−0.554123	+	0.832435i	$0.686946\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.50756	+	16.8224i	−0.215626	+	0.804726i
$438$		0			0
$439$	22.6597	+	13.0826i	1.08149	+	0.624397i	0.931297	−	0.364260i	$-0.118678\pi$
$439$	22.6597	+	13.0826i	1.08149	+	0.624397i	0.150190	+	0.988657i	$0.452011\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.84746	−	14.3589i	−0.182799	−	0.682213i	−0.995091	−	0.0989632i	$-0.968447\pi$
$443$	−3.84746	−	14.3589i	−0.182799	−	0.682213i	0.812293	−	0.583250i	$-0.198219\pi$
$444$		0			0
$445$	−1.18001	+	21.0342i	−0.0559379	+	0.997116i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−12.6238			−0.595756			−0.297878	−	0.954604i	$-0.596279\pi$
$449$	−12.6238			−0.595756			−0.297878	+	0.954604i	$0.596279\pi$
$450$		0			0
$451$	2.74773			0.129385
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.70116	+	30.3239i	−0.0797517	+	1.42161i
$456$		0			0
$457$	−8.32625	−	31.0740i	−0.389485	−	1.45358i	−0.830973	−	0.556312i	$-0.812216\pi$
$457$	−8.32625	−	31.0740i	−0.389485	−	1.45358i	0.441488	−	0.897267i	$-0.354451\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.24037	+	1.87083i	0.150919	+	0.0871332i	0.573558	−	0.819165i	$-0.305563\pi$
$461$	3.24037	+	1.87083i	0.150919	+	0.0871332i	−0.422639	+	0.906298i	$0.638896\pi$
$462$		0			0
$463$	1.37176	−	5.11949i	0.0637512	−	0.237923i	−0.926697	−	0.375810i	$-0.877364\pi$
$463$	1.37176	−	5.11949i	0.0637512	−	0.237923i	0.990448	+	0.137887i	$0.0440312\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	16.5678	+	16.5678i	0.766665	+	0.766665i	0.977518	−	0.210853i	$-0.0676241\pi$
$467$	16.5678	+	16.5678i	0.766665	+	0.766665i	−0.210853	+	0.977518i	$0.567624\pi$
$468$		0			0
$469$		−	25.0780i		−	1.15800i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.698364	−	0.187126i	−0.0321108	−	0.00860407i
$474$		0			0
$475$	3.68122	−	32.7064i	0.168906	−	1.50067i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−6.64903	+	11.5165i	−0.303802	+	0.526201i	−0.976994	−	0.213267i	$-0.931590\pi$
$479$	−6.64903	+	11.5165i	−0.303802	+	0.526201i	0.673192	+	0.739468i	$0.264923\pi$
$480$		0			0
$481$	−11.3739	−	19.7001i	−0.518604	−	0.898248i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	23.4724	−	4.89898i	1.06583	−	0.222451i
$486$		0			0
$487$	8.37386	−	8.37386i	0.379456	−	0.379456i	−0.491450	−	0.870906i	$-0.663533\pi$
$487$	8.37386	−	8.37386i	0.379456	−	0.379456i	0.870906	+	0.491450i	$0.163533\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	23.5681	−	13.6070i	1.06361	−	0.614077i	0.137183	−	0.990546i	$-0.456195\pi$
$491$	23.5681	−	13.6070i	1.06361	−	0.614077i	0.926429	+	0.376469i	$0.122862\pi$
$492$		0			0
$493$	54.2369	−	14.5327i	2.44271	−	0.654521i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−35.0416	+	9.38936i	−1.57183	+	0.421171i
$498$		0			0
$499$	−16.0930	+	9.29129i	−0.720421	+	0.415935i	−0.814908	−	0.579591i	$-0.803212\pi$
$499$	−16.0930	+	9.29129i	−0.720421	+	0.415935i	0.0944867	+	0.995526i	$0.469879\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	12.9610	−	12.9610i	0.577900	−	0.577900i	−0.356424	−	0.934324i	$-0.616004\pi$
$503$	12.9610	−	12.9610i	0.577900	−	0.577900i	0.934324	+	0.356424i	$0.116004\pi$
$504$		0			0
$505$	10.4174	−	15.9129i	0.463569	−	0.708114i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.60681	+	6.24718i	0.159869	+	0.276901i	0.934821	−	0.355118i	$-0.115559\pi$
$509$	3.60681	+	6.24718i	0.159869	+	0.276901i	−0.774952	+	0.632020i	$0.782226\pi$
$510$		0			0
$511$	−2.16515	+	3.75015i	−0.0957807	+	0.165897i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	10.7617	+	3.54052i	0.474215	+	0.156014i
$516$		0			0
$517$	1.71064	+	0.458364i	0.0752337	+	0.0201588i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			26.4331i			1.15806i	0.815307	+	0.579029i	$0.196568\pi$
$521$			26.4331i			1.15806i	−0.815307	+	0.579029i	$0.803432\pi$
$522$		0			0
$523$	−5.04356	−	5.04356i	−0.220540	−	0.220540i	0.588186	−	0.808726i	$-0.299842\pi$
$523$	−5.04356	−	5.04356i	−0.220540	−	0.220540i	−0.808726	+	0.588186i	$0.799842\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.05902	−	3.95233i	0.0461318	−	0.172166i
$528$		0			0
$529$	−13.8564	−	8.00000i	−0.602452	−	0.347826i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	5.90178	+	22.0257i	0.255634	+	0.954040i
$534$		0			0
$535$	−31.9238	+	28.5322i	−1.38018	+	1.23355i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.376393			−0.0162124
$540$		0			0
$541$	−41.1652			−1.76983			−0.884914	−	0.465754i	$-0.845783\pi$
$541$	−41.1652			−1.76983			−0.884914	+	0.465754i	$0.845783\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−35.1577	−	1.97234i	−1.50599	−	0.0844856i
$546$		0			0
$547$	10.8120	+	40.3510i	0.462289	+	1.72529i	0.665724	+	0.746198i	$0.268123\pi$
$547$	10.8120	+	40.3510i	0.462289	+	1.72529i	−0.203435	+	0.979088i	$0.565211\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−45.5744	−	26.3124i	−1.94153	−	1.12094i
$552$		0			0
$553$	4.04222	−	15.0858i	0.171893	−	0.641513i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−13.6745	−	13.6745i	−0.579406	−	0.579406i	0.355334	−	0.934739i	$-0.384367\pi$
$557$	−13.6745	−	13.6745i	−0.579406	−	0.579406i	−0.934739	+	0.355334i	$0.884367\pi$
$558$		0			0
$559$		−	6.00000i		−	0.253773i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.74279	−	1.27083i	−0.199885	−	0.0535590i	0.157487	−	0.987521i	$-0.449661\pi$
$563$	−4.74279	−	1.27083i	−0.199885	−	0.0535590i	−0.357372	+	0.933962i	$0.616327\pi$
$564$		0			0
$565$	−4.97474	+	15.1210i	−0.209289	+	0.636147i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	16.2447	−	28.1367i	0.681014	−	1.17955i	−0.293657	−	0.955911i	$-0.594872\pi$
$569$	16.2447	−	28.1367i	0.681014	−	1.17955i	0.974672	−	0.223641i	$-0.0717942\pi$
$570$		0			0
$571$	7.45644	+	12.9149i	0.312042	+	0.540473i	0.978804	−	0.204798i	$-0.0656536\pi$
$571$	7.45644	+	12.9149i	0.312042	+	0.540473i	−0.666762	+	0.745271i	$0.732320\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−12.3149	−	4.83156i	−0.513566	−	0.201490i
$576$		0			0
$577$	−4.37386	+	4.37386i	−0.182086	+	0.182086i	−0.792264	−	0.610178i	$-0.791098\pi$
$577$	−4.37386	+	4.37386i	−0.182086	+	0.182086i	0.610178	+	0.792264i	$0.291098\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3.79990	−	2.19387i	0.157646	−	0.0910171i
$582$		0			0
$583$	4.83438	−	1.29537i	0.200220	−	0.0536487i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	30.3909	−	8.14321i	1.25437	−	0.336106i	0.430345	−	0.902665i	$-0.358392\pi$
$587$	30.3909	−	8.14321i	1.25437	−	0.336106i	0.824022	+	0.566558i	$0.191725\pi$
$588$		0			0
$589$	−3.32108	+	1.91742i	−0.136843	+	0.0790061i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	4.45516	−	4.45516i	0.182952	−	0.182952i	−0.609689	−	0.792641i	$-0.708706\pi$
$593$	4.45516	−	4.45516i	0.182952	−	0.182952i	0.792641	+	0.609689i	$0.208706\pi$
$594$		0			0
$595$	33.2867	+	21.7913i	1.36462	+	0.893356i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.41294	+	2.44729i	0.0577312	+	0.0999934i	0.893447	−	0.449169i	$-0.148280\pi$
$599$	1.41294	+	2.44729i	0.0577312	+	0.0999934i	−0.835715	+	0.549163i	$0.814947\pi$
$600$		0			0
$601$	−7.87386	+	13.6379i	−0.321182	+	0.556303i	−0.980732	−	0.195357i	$-0.937413\pi$
$601$	−7.87386	+	13.6379i	−0.321182	+	0.556303i	0.659551	+	0.751660i	$0.270747\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−21.1236	+	10.6653i	−0.858797	+	0.433604i
$606$		0			0
$607$	−34.3167	−	9.19514i	−1.39287	−	0.373219i	−0.517093	−	0.855929i	$-0.672986\pi$
$607$	−34.3167	−	9.19514i	−1.39287	−	0.373219i	−0.875780	+	0.482710i	$0.839653\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			14.6969i			0.594574i
$612$		0			0
$613$	−24.3303	−	24.3303i	−0.982692	−	0.982692i	0.0171611	−	0.999853i	$-0.494537\pi$
$613$	−24.3303	−	24.3303i	−0.982692	−	0.982692i	−0.999853	+	0.0171611i	$0.994537\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	8.51747	−	31.7876i	0.342900	−	1.27972i	−0.552146	−	0.833748i	$-0.686191\pi$
$617$	8.51747	−	31.7876i	0.342900	−	1.27972i	0.895046	−	0.445974i	$-0.147143\pi$
$618$		0			0
$619$	9.30780	+	5.37386i	0.374112	+	0.215994i	0.675253	−	0.737586i	$-0.264034\pi$
$619$	9.30780	+	5.37386i	0.374112	+	0.215994i	−0.301141	+	0.953580i	$0.597368\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	6.17731	+	23.0541i	0.247489	+	0.923641i
$624$		0			0
$625$	24.3745	+	5.55728i	0.974980	+	0.222291i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−29.7984			−1.18814
$630$		0			0
$631$	−2.16515			−0.0861933			−0.0430967	−	0.999071i	$-0.513722\pi$
$631$	−2.16515			−0.0861933			−0.0430967	+	0.999071i	$0.513722\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−13.8715	−	15.5204i	−0.550475	−	0.615909i
$636$		0			0
$637$	−0.808445	−	3.01716i	−0.0320317	−	0.119544i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.233559	−	0.134846i	−0.00922504	−	0.00532608i	0.495380	−	0.868676i	$-0.335029\pi$
$641$	−0.233559	−	0.134846i	−0.00922504	−	0.00532608i	−0.504605	+	0.863350i	$0.668362\pi$
$642$		0			0
$643$	3.12550	−	11.6645i	0.123258	−	0.460003i	−0.876514	−	0.481376i	$-0.840137\pi$
$643$	3.12550	−	11.6645i	0.123258	−	0.460003i	0.999772	+	0.0213729i	$0.00680372\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−17.4835	−	17.4835i	−0.687349	−	0.687349i	0.274296	−	0.961645i	$-0.411555\pi$
$647$	−17.4835	−	17.4835i	−0.687349	−	0.687349i	−0.961645	+	0.274296i	$0.911555\pi$
$648$		0			0
$649$			8.33030i			0.326993i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−6.27007	−	1.68006i	−0.245367	−	0.0657458i	0.134040	−	0.990976i	$-0.457205\pi$
$653$	−6.27007	−	1.68006i	−0.245367	−	0.0657458i	−0.379406	+	0.925230i	$0.623872\pi$
$654$		0			0
$655$	−10.0104	−	19.8266i	−0.391139	−	0.774690i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	8.38502	−	14.5233i	0.326634	−	0.565747i	−0.655208	−	0.755449i	$-0.727419\pi$
$659$	8.38502	−	14.5233i	0.326634	−	0.565747i	0.981842	+	0.189702i	$0.0607523\pi$
$660$		0			0
$661$	15.7477	+	27.2759i	0.612516	+	1.06091i	0.990815	+	0.135225i	$0.0431757\pi$
$661$	15.7477	+	27.2759i	0.612516	+	1.06091i	−0.378299	+	0.925683i	$0.623491\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−7.61816	−	36.5008i	−0.295420	−	1.41544i
$666$		0			0
$667$	−14.9564	+	14.9564i	−0.579116	+	0.579116i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3.44956	−	1.99160i	0.133169	−	0.0768850i
$672$		0			0
$673$	9.62168	−	2.57812i	0.370889	−	0.0993793i	−0.0685601	−	0.997647i	$-0.521840\pi$
$673$	9.62168	−	2.57812i	0.370889	−	0.0993793i	0.439449	+	0.898268i	$0.355174\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.27306	+	2.21676i	−0.317960	+	0.0851970i	−0.414269	−	0.910154i	$-0.635963\pi$
$677$	−8.27306	+	2.21676i	−0.317960	+	0.0851970i	0.0963096	+	0.995351i	$0.469296\pi$
$678$		0			0
$679$	23.5257	−	13.5826i	0.902834	−	0.521251i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−12.4497	+	12.4497i	−0.476375	+	0.476375i	−0.903970	−	0.427595i	$-0.859361\pi$
$683$	−12.4497	+	12.4497i	−0.476375	+	0.476375i	0.427595	+	0.903970i	$0.359361\pi$
$684$		0			0
$685$	−0.791288	−	3.79129i	−0.0302336	−	0.144858i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	20.7673	+	35.9700i	0.791172	+	1.37035i
$690$		0			0
$691$	−19.8303	+	34.3471i	−0.754380	+	1.30662i	0.191302	+	0.981531i	$0.438729\pi$
$691$	−19.8303	+	34.3471i	−0.754380	+	1.30662i	−0.945682	+	0.325094i	$0.894604\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	11.2524	+	22.2865i	0.426827	+	0.845374i
$696$		0			0
$697$	28.8526	+	7.73104i	1.09287	+	0.292834i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	27.2141i		−	1.02786i	−0.857832	−	0.513931i	$-0.828189\pi$
$701$		−	27.2141i		−	1.02786i	0.857832	−	0.513931i	$-0.171811\pi$
$702$		0			0
$703$	19.7477	+	19.7477i	0.744800	+	0.744800i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.57688	−	20.8132i	0.209740	−	0.782761i
$708$		0			0
$709$	−22.5167	−	13.0000i	−0.845631	−	0.488225i	0.0135434	−	0.999908i	$-0.495689\pi$
$709$	−22.5167	−	13.0000i	−0.845631	−	0.488225i	−0.859174	+	0.511683i	$0.829022\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.398931	+	1.48883i	0.0149401	+	0.0557571i
$714$		0			0
$715$	5.16184	+	5.77542i	0.193042	+	0.215988i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−37.0120			−1.38032			−0.690158	−	0.723659i	$-0.742459\pi$
$719$	−37.0120			−1.38032			−0.690158	+	0.723659i	$0.742459\pi$
$720$		0			0
$721$	12.8348			0.477995
$722$		0			0
$723$		0			0
$724$		0			0
$725$	23.7328	−	32.1648i	0.881416	−	1.19457i
$726$		0			0
$727$	−4.51320	−	16.8435i	−0.167385	−	0.624691i	−0.997724	−	0.0674316i	$-0.978520\pi$
$727$	−4.51320	−	16.8435i	−0.167385	−	0.624691i	0.830338	−	0.557259i	$-0.188147\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−6.80671	−	3.92985i	−0.251755	−	0.145351i
$732$		0			0
$733$	8.75272	−	32.6656i	0.323289	−	1.20653i	−0.592731	−	0.805400i	$-0.701950\pi$
$733$	8.75272	−	32.6656i	0.323289	−	1.20653i	0.916021	−	0.401131i	$-0.131383\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.52259	−	4.52259i	−0.166592	−	0.166592i
$738$		0			0
$739$			11.4174i			0.419997i	0.977702	+	0.209998i	$0.0673459\pi$
$739$			11.4174i			0.419997i	−0.977702	+	0.209998i	$0.932654\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	27.1369	+	7.27132i	0.995557	+	0.266759i	0.719583	−	0.694406i	$-0.244333\pi$
$743$	27.1369	+	7.27132i	0.995557	+	0.266759i	0.275974	+	0.961165i	$0.411000\pi$
$744$		0			0
$745$	−23.4264	+	11.8279i	−0.858275	+	0.433341i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−24.2534	+	42.0080i	−0.886198	+	1.53494i
$750$		0			0
$751$	−7.50000	−	12.9904i	−0.273679	−	0.474026i	0.696122	−	0.717923i	$-0.254907\pi$
$751$	−7.50000	−	12.9904i	−0.273679	−	0.474026i	−0.969801	+	0.243898i	$0.921574\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−32.1131	−	21.0229i	−1.16871	−	0.765103i
$756$		0			0
$757$	15.0000	−	15.0000i	0.545184	−	0.545184i	−0.379860	−	0.925044i	$-0.624028\pi$
$757$	15.0000	−	15.0000i	0.545184	−	0.545184i	0.925044	+	0.379860i	$0.124028\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−25.2467	+	14.5762i	−0.915191	+	0.528386i	−0.882098	−	0.471067i	$-0.843869\pi$
$761$	−25.2467	+	14.5762i	−0.915191	+	0.528386i	−0.0330931	+	0.999452i	$0.510536\pi$
$762$		0			0
$763$	−38.5338	+	10.3251i	−1.39502	+	0.373794i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−66.7755	+	17.8925i	−2.41113	+	0.646059i
$768$		0			0
$769$	−19.9186	+	11.5000i	−0.718283	+	0.414701i	−0.814120	−	0.580696i	$-0.802780\pi$
$769$	−19.9186	+	11.5000i	−0.718283	+	0.414701i	0.0958377	+	0.995397i	$0.469447\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	25.6129	−	25.6129i	0.921233	−	0.921233i	−0.0758833	−	0.997117i	$-0.524178\pi$
$773$	25.6129	−	25.6129i	0.921233	−	0.921233i	0.997117	+	0.0758833i	$0.0241776\pi$
$774$		0			0
$775$	−1.16515	−	2.66970i	−0.0418535	−	0.0958984i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−13.9975	−	24.2444i	−0.501513	−	0.868645i
$780$		0			0
$781$	−4.62614	+	8.01270i	−0.165536	+	0.286717i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	3.58357	−	10.8925i	0.127903	−	0.388770i
$786$		0			0
$787$	39.2106	+	10.5065i	1.39771	+	0.374515i	0.877521	−	0.479538i	$-0.159196\pi$
$787$	39.2106	+	10.5065i	1.39771	+	0.374515i	0.520187	+	0.854053i	$0.325862\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			18.0341i			0.641217i
$792$		0			0
$793$	23.3739	+	23.3739i	0.830030	+	0.830030i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	10.6458	−	39.7307i	0.377094	−	1.40733i	−0.473167	−	0.880973i	$-0.656889\pi$
$797$	10.6458	−	39.7307i	0.377094	−	1.40733i	0.850261	−	0.526361i	$-0.176444\pi$
$798$		0			0
$799$	16.6730	+	9.62614i	0.589847	+	0.340548i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.285840	+	1.06677i	0.0100871	+	0.0376455i
$804$		0			0
$805$	−14.9635	−	0.839446i	−0.527393	−	0.0295866i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−39.8379			−1.40063			−0.700313	−	0.713836i	$-0.746956\pi$
$809$	−39.8379			−1.40063			−0.700313	+	0.713836i	$0.746956\pi$
$810$		0			0
$811$	−16.3303			−0.573434			−0.286717	−	0.958015i	$-0.592564\pi$
$811$	−16.3303			−0.573434			−0.286717	+	0.958015i	$0.592564\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−20.2360	+	18.0862i	−0.708837	+	0.633531i
$816$		0			0
$817$	1.90652	+	7.11523i	0.0667007	+	0.248930i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−7.71657	−	4.45516i	−0.269310	−	0.155486i	0.359264	−	0.933236i	$-0.383028\pi$
$821$	−7.71657	−	4.45516i	−0.269310	−	0.155486i	−0.628574	+	0.777750i	$0.716361\pi$
$822$		0			0
$823$	−4.07078	+	15.1924i	−0.141899	+	0.529573i	0.857975	+	0.513691i	$0.171722\pi$
$823$	−4.07078	+	15.1924i	−0.141899	+	0.529573i	−0.999874	+	0.0158819i	$0.994944\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	3.16300	+	3.16300i	0.109988	+	0.109988i	0.759959	−	0.649971i	$-0.225219\pi$
$827$	3.16300	+	3.16300i	0.109988	+	0.109988i	−0.649971	+	0.759959i	$0.725219\pi$
$828$		0			0
$829$			33.0780i			1.14885i	0.818558	+	0.574424i	$0.194774\pi$
$829$			33.0780i			1.14885i	−0.818558	+	0.574424i	$0.805226\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.95233	−	1.05902i	−0.136940	−	0.0366930i
$834$		0			0
$835$	20.3357	+	6.69034i	0.703747	+	0.231529i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−22.1803	+	38.4173i	−0.765747	+	1.32631i	0.174103	+	0.984727i	$0.444297\pi$
$839$	−22.1803	+	38.4173i	−0.765747	+	1.32631i	−0.939851	+	0.341586i	$0.889036\pi$
$840$		0			0
$841$	−17.4564	−	30.2354i	−0.601946	−	1.04260i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−19.2869	+	29.4613i	−0.663491	+	1.01350i
$846$		0			0
$847$	−18.9564	+	18.9564i	−0.651351	+	0.651351i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	9.72111	−	5.61249i	0.333235	−	0.192394i
$852$		0			0
$853$	−22.3076	+	5.97731i	−0.763798	+	0.204659i	−0.619630	−	0.784894i	$-0.712717\pi$
$853$	−22.3076	+	5.97731i	−0.763798	+	0.204659i	−0.144168	+	0.989553i	$0.546051\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−6.27007	+	1.68006i	−0.214181	+	0.0573898i	−0.364314	−	0.931276i	$-0.618697\pi$
$857$	−6.27007	+	1.68006i	−0.214181	+	0.0573898i	0.150133	+	0.988666i	$0.452030\pi$
$858$		0			0
$859$	38.8957	−	22.4564i	1.32710	−	0.766204i	0.342253	−	0.939608i	$-0.388810\pi$
$859$	38.8957	−	22.4564i	1.32710	−	0.766204i	0.984851	+	0.173404i	$0.0554766\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−12.1800	+	12.1800i	−0.414613	+	0.414613i	−0.883342	−	0.468729i	$-0.844712\pi$
$863$	−12.1800	+	12.1800i	−0.414613	+	0.414613i	0.468729	+	0.883342i	$0.344712\pi$
$864$		0			0
$865$	−42.1216	+	8.79129i	−1.43218	+	0.298913i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.99160	−	3.44956i	−0.0675605	−	0.117018i
$870$		0			0
$871$	26.5390	−	45.9669i	0.899240	−	1.55753i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	28.1986	−	2.64930i	0.953286	−	0.0895626i
$876$		0			0
$877$	−23.5075	−	6.29883i	−0.793793	−	0.212696i	−0.160936	−	0.986965i	$-0.551451\pi$
$877$	−23.5075	−	6.29883i	−0.793793	−	0.212696i	−0.632857	+	0.774269i	$0.718118\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	18.3319i		−	0.617617i	−0.951124	−	0.308809i	$-0.900070\pi$
$881$		−	18.3319i		−	0.617617i	0.951124	−	0.308809i	$-0.0999303\pi$
$882$		0			0
$883$	−17.7913	−	17.7913i	−0.598725	−	0.598725i	0.341249	−	0.939973i	$-0.389150\pi$
$883$	−17.7913	−	17.7913i	−0.598725	−	0.598725i	−0.939973	+	0.341249i	$0.889150\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−11.7295	+	43.7752i	−0.393839	+	1.46983i	0.429911	+	0.902871i	$0.358545\pi$
$887$	−11.7295	+	43.7752i	−0.393839	+	1.46983i	−0.823749	+	0.566954i	$0.808122\pi$
$888$		0			0
$889$	−20.4231	−	11.7913i	−0.684969	−	0.395467i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.67000	−	17.4287i	−0.156276	−	0.583229i
$894$		0			0
$895$	3.10166	−	55.2884i	0.103677	−	1.84809i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.65743			−0.155334
$900$		0			0
$901$	54.4083			1.81260
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.678510	+	12.0947i	−0.0225544	+	0.402042i
$906$		0			0
$907$	−6.86214	−	25.6099i	−0.227854	−	0.850362i	−0.981241	−	0.192785i	$-0.938248\pi$
$907$	−6.86214	−	25.6099i	−0.227854	−	0.850362i	0.753387	−	0.657577i	$-0.228419\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	7.80898	+	4.50851i	0.258723	+	0.149374i	0.623752	−	0.781622i	$-0.285608\pi$
$911$	7.80898	+	4.50851i	0.258723	+	0.149374i	−0.365029	+	0.930996i	$0.618941\pi$
$912$		0			0
$913$	0.289631	−	1.08092i	0.00958540	−	0.0357732i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−17.7925	−	17.7925i	−0.587561	−	0.587561i
$918$		0			0
$919$			16.0000i			0.527791i	0.964551	+	0.263896i	$0.0850075\pi$
$919$			16.0000i			0.527791i	−0.964551	+	0.263896i	$0.914993\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−74.1660	−	19.8727i	−2.44121	−	0.654119i
$924$		0			0
$925$	−16.5836	+	13.2282i	−0.545265	+	0.434940i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	10.9019	−	18.8827i	0.357681	−	0.619521i	−0.629892	−	0.776683i	$-0.716901\pi$
$929$	10.9019	−	18.8827i	0.357681	−	0.619521i	0.987573	+	0.157161i	$0.0502343\pi$
$930$		0			0
$931$	1.91742	+	3.32108i	0.0628410	+	0.108844i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	9.93280	−	2.07310i	0.324837	−	0.0677975i
$936$		0			0
$937$	27.0780	−	27.0780i	0.884601	−	0.884601i	−0.109397	−	0.993998i	$-0.534892\pi$
$937$	27.0780	−	27.0780i	0.884601	−	0.884601i	0.993998	+	0.109397i	$0.0348921\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	24.9207	−	14.3880i	0.812391	−	0.469034i	−0.0353943	−	0.999373i	$-0.511269\pi$
$941$	24.9207	−	14.3880i	0.812391	−	0.469034i	0.847786	+	0.530339i	$0.177935\pi$
$942$		0			0
$943$	−10.8687	+	2.91226i	−0.353934	+	0.0948362i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−20.1685	+	5.40413i	−0.655388	+	0.175611i	−0.571164	−	0.820836i	$-0.693508\pi$
$947$	−20.1685	+	5.40413i	−0.655388	+	0.175611i	−0.0842242	+	0.996447i	$0.526841\pi$
$948$		0			0
$949$	−7.93725	+	4.58258i	−0.257654	+	0.148757i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−21.5342	+	21.5342i	−0.697560	+	0.697560i	−0.963884	−	0.266324i	$-0.914191\pi$
$953$	−21.5342	+	21.5342i	−0.697560	+	0.697560i	0.266324	+	0.963884i	$0.414191\pi$
$954$		0			0
$955$	−4.58258	+	7.00000i	−0.148289	+	0.226515i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.19387	−	3.79990i	−0.0708438	−	0.122705i
$960$		0			0
$961$	15.3303	−	26.5529i	0.494526	−	0.856544i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−47.4352	−	15.6059i	−1.52699	−	0.502373i
$966$		0			0
$967$	0.344611	+	0.0923383i	0.0110819	+	0.00296940i	0.264356	−	0.964425i	$-0.414841\pi$
$967$	0.344611	+	0.0923383i	0.0110819	+	0.00296940i	−0.253274	+	0.967395i	$0.581507\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	23.6073i		−	0.757593i	−0.925480	−	0.378797i	$-0.876338\pi$
$971$		−	23.6073i		−	0.757593i	0.925480	−	0.378797i	$-0.123662\pi$
$972$		0			0
$973$	20.0000	+	20.0000i	0.641171	+	0.641171i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.374252	−	1.39673i	0.0119734	−	0.0446853i	−0.959681	−	0.281092i	$-0.909303\pi$
$977$	0.374252	−	1.39673i	0.0119734	−	0.0446853i	0.971654	+	0.236407i	$0.0759699\pi$
$978$		0			0
$979$	5.27160	+	3.04356i	0.168481	+	0.0972726i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	3.03930	+	11.3428i	0.0969386	+	0.361780i	0.997306	−	0.0733502i	$-0.0233691\pi$
$983$	3.03930	+	11.3428i	0.0969386	+	0.361780i	−0.900368	+	0.435130i	$0.856702\pi$
$984$		0			0
$985$	14.4385	−	12.9046i	0.460050	−	0.411175i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.96073			0.0941457
$990$		0			0
$991$	13.0000			0.412959			0.206479	−	0.978451i	$-0.433799\pi$
$991$	13.0000			0.412959			0.206479	+	0.978451i	$0.433799\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	30.3239	+	1.70116i	0.961332	+	0.0539304i
$996$		0			0
$997$	−3.67620	−	13.7198i	−0.116426	−	0.434509i	0.882963	−	0.469442i	$-0.155545\pi$
$997$	−3.67620	−	13.7198i	−0.116426	−	0.434509i	−0.999390	+	0.0349329i	$0.988878\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.x.c.593.3		16
3.2	odd	2	inner	1620.2.x.c.593.2		16
5.2	odd	4	inner	1620.2.x.c.917.4		16
9.2	odd	6		540.2.j.b.53.1	✓	8
9.4	even	3	inner	1620.2.x.c.53.1		16
9.5	odd	6	inner	1620.2.x.c.53.4		16
9.7	even	3		540.2.j.b.53.4	yes	8
15.2	even	4	inner	1620.2.x.c.917.1		16
36.7	odd	6		2160.2.w.c.593.4		8
36.11	even	6		2160.2.w.c.593.1		8
45.2	even	12		540.2.j.b.377.3	yes	8
45.7	odd	12		540.2.j.b.377.2	yes	8
45.22	odd	12	inner	1620.2.x.c.377.2		16
45.29	odd	6		2700.2.j.i.593.3		8
45.32	even	12	inner	1620.2.x.c.377.3		16
45.34	even	6		2700.2.j.i.593.4		8
45.38	even	12		2700.2.j.i.1457.3		8
45.43	odd	12		2700.2.j.i.1457.4		8
180.7	even	12		2160.2.w.c.1457.2		8
180.47	odd	12		2160.2.w.c.1457.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.j.b.53.1	✓	8	9.2	odd	6
540.2.j.b.53.4	yes	8	9.7	even	3
540.2.j.b.377.2	yes	8	45.7	odd	12
540.2.j.b.377.3	yes	8	45.2	even	12
1620.2.x.c.53.1		16	9.4	even	3	inner
1620.2.x.c.53.4		16	9.5	odd	6	inner
1620.2.x.c.377.2		16	45.22	odd	12	inner
1620.2.x.c.377.3		16	45.32	even	12	inner
1620.2.x.c.593.2		16	3.2	odd	2	inner
1620.2.x.c.593.3		16	1.1	even	1	trivial
1620.2.x.c.917.1		16	15.2	even	4	inner
1620.2.x.c.917.4		16	5.2	odd	4	inner
2160.2.w.c.593.1		8	36.11	even	6
2160.2.w.c.593.4		8	36.7	odd	6
2160.2.w.c.1457.2		8	180.7	even	12
2160.2.w.c.1457.3		8	180.47	odd	12
2700.2.j.i.593.3		8	45.29	odd	6
2700.2.j.i.593.4		8	45.34	even	6
2700.2.j.i.1457.3		8	45.38	even	12
2700.2.j.i.1457.4		8	45.43	odd	12

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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.125246 - 2.23256i) q^{5} +(-0.655657 - 2.44694i) q^{7} +(-0.559525 - 0.323042i) q^{11} +(1.38771 - 5.17900i) q^{13} +(-4.96640 - 4.96640i) q^{17} +6.58258i q^{19} +(2.55560 + 0.684771i) q^{23} +(-4.96863 - 0.559237i) q^{25} +(-3.99728 + 6.92349i) q^{29} +(0.291288 + 0.504525i) q^{31} +(-5.54506 + 1.15732i) q^{35} +(3.00000 - 3.00000i) q^{37} +(-3.68312 + 2.12645i) q^{41} +(1.08092 - 0.289631i) q^{43} +(-2.64770 + 0.709449i) q^{47} +(0.504525 - 0.291288i) q^{49} +(-5.47764 + 5.47764i) q^{53} +(-0.791288 + 1.20871i) q^{55} +(-6.44677 - 11.1661i) q^{59} +(-3.08258 + 5.33918i) q^{61} +(-11.3886 - 3.74678i) q^{65} +(9.56218 + 2.56218i) q^{67} -14.3205i q^{71} +(-1.20871 - 1.20871i) q^{73} +(-0.423609 + 1.58093i) q^{77} +(5.33918 + 3.08258i) q^{79} +(0.448288 + 1.67303i) q^{83} +(-11.7098 + 10.4658i) q^{85} -9.42157 q^{89} -13.5826 q^{91} +(14.6960 + 0.824440i) q^{95} +(2.77542 + 10.3580i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{7} - 12 q^{13} - 16 q^{25} - 32 q^{31} + 48 q^{37} - 12 q^{43} + 24 q^{55} + 24 q^{61} + 56 q^{67} - 56 q^{73} + 44 q^{85} - 144 q^{91} - 24 q^{97}+O(q^{100}) \) 16 * q - 4 * q^7 - 12 * q^13 - 16 * q^25 - 32 * q^31 + 48 * q^37 - 12 * q^43 + 24 * q^55 + 24 * q^61 + 56 * q^67 - 56 * q^73 + 44 * q^85 - 144 * q^91 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more