LMFDB - Embedded newform 432.7.q.b.17.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [432,7,Mod(17,432)] 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("432.17"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(432, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	432.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,-432] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$99.3833641238$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 370x^{10} + 51793x^{8} + 3491832x^{6} + 117603792x^{4} + 1832032512x^{2} + 10453017600 $ x^12 + 370x^10 + 51793x^8 + 3491832x^6 + 117603792x^4 + 1832032512*x^2 + 10453017600
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{20} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.2
Root			$4.28281i$ of defining polynomial
Character	$\chi$	$=$	432.17
Dual form			432.7.q.b.305.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-156.951 - 90.6160i) q^{5} +(-104.306 - 180.663i) q^{7} +(2301.99 - 1329.05i) q^{11} +(-438.599 + 759.676i) q^{13} -4428.53i q^{17} +4194.21 q^{19} +(10399.9 + 6004.40i) q^{23} +(8610.01 + 14913.0i) q^{25} +(-2288.79 + 1321.43i) q^{29} +(2902.50 - 5027.28i) q^{31} +37807.1i q^{35} +41579.5 q^{37} +(64721.2 + 37366.8i) q^{41} +(73052.9 + 126531. i) q^{43} +(-22319.7 + 12886.3i) q^{47} +(37065.1 - 64198.6i) q^{49} -197505. i q^{53} -481734. q^{55} +(-31321.5 - 18083.5i) q^{59} +(-11967.3 - 20728.0i) q^{61} +(137678. - 79488.2i) q^{65} +(176540. - 305776. i) q^{67} -496781. i q^{71} -382139. q^{73} +(-480222. - 277257. i) q^{77} +(193328. + 334855. i) q^{79} +(359691. - 207667. i) q^{83} +(-401295. + 695064. i) q^{85} -405654. i q^{89} +182994. q^{91} +(-658288. - 380063. i) q^{95} +(-178244. - 308727. i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 432 q^{5} - 240 q^{7} + 378 q^{11} + 1680 q^{13} + 2820 q^{19} - 76248 q^{23} + 8094 q^{25} - 97092 q^{29} - 21480 q^{31} - 25536 q^{37} + 410562 q^{41} - 71430 q^{43} + 347652 q^{47} - 135954 q^{49}+ \cdots - 38874 q^{97}+O(q^{100}) $ 12 * q - 432 * q^5 - 240 * q^7 + 378 * q^11 + 1680 * q^13 + 2820 * q^19 - 76248 * q^23 + 8094 * q^25 - 97092 * q^29 - 21480 * q^31 - 25536 * q^37 + 410562 * q^41 - 71430 * q^43 + 347652 * q^47 - 135954 * q^49 - 580392 * q^55 + 369738 * q^59 + 135744 * q^61 + 753840 * q^65 + 289938 * q^67 - 977700 * q^73 + 159192 * q^77 + 764796 * q^79 + 396900 * q^83 + 1619568 * q^85 - 355584 * q^91 - 2089260 * q^95 - 38874 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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
$5$	−156.951	−	90.6160i	−1.25561	−	0.724928i	−0.283394	−	0.959004i	$-0.591460\pi$
$5$	−156.951	−	90.6160i	−1.25561	−	0.724928i	−0.972218	+	0.234076i	$0.924794\pi$
$6$		0			0
$7$	−104.306	−	180.663i	−0.304099	−	0.526715i	0.672961	−	0.739678i	$-0.265022\pi$
$7$	−104.306	−	180.663i	−0.304099	−	0.526715i	−0.977060	+	0.212963i	$0.931689\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2301.99	−	1329.05i	1.72952	−	0.998538i	0.837737	−	0.546074i	$-0.183878\pi$
$11$	2301.99	−	1329.05i	1.72952	−	0.998538i	0.891782	−	0.452465i	$-0.149455\pi$
$12$		0			0
$13$	−438.599	+	759.676i	−0.199636	+	0.345779i	−0.948410	−	0.317046i	$-0.897309\pi$
$13$	−438.599	+	759.676i	−0.199636	+	0.345779i	0.748775	+	0.662825i	$0.230642\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	4428.53i		−	0.901389i	−0.892678	−	0.450695i	$-0.851176\pi$
$17$		−	4428.53i		−	0.901389i	0.892678	−	0.450695i	$-0.148824\pi$
$18$		0			0
$19$	4194.21			0.611491			0.305745	−	0.952113i	$-0.401094\pi$
$19$	4194.21			0.611491			0.305745	+	0.952113i	$0.401094\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	10399.9	+	6004.40i	0.854766	+	0.493499i	0.862256	−	0.506473i	$-0.169051\pi$
$23$	10399.9	+	6004.40i	0.854766	+	0.493499i	−0.00749035	+	0.999972i	$0.502384\pi$
$24$		0			0
$25$	8610.01	+	14913.0i	0.551041	+	0.954431i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2288.79	+	1321.43i	−0.0938450	+	0.0541815i	−0.546188	−	0.837663i	$-0.683922\pi$
$29$	−2288.79	+	1321.43i	−0.0938450	+	0.0541815i	0.452343	+	0.891844i	$0.350588\pi$
$30$		0			0
$31$	2902.50	−	5027.28i	0.0974289	−	0.168752i	−0.813191	−	0.581997i	$-0.802271\pi$
$31$	2902.50	−	5027.28i	0.0974289	−	0.168752i	0.910620	+	0.413245i	$0.135605\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			37807.1i			0.881799i
$36$		0			0
$37$	41579.5			0.820869			0.410435	−	0.911890i	$-0.365377\pi$
$37$	41579.5			0.820869			0.410435	+	0.911890i	$0.365377\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	64721.2	+	37366.8i	0.939063	+	0.542168i	0.889666	−	0.456611i	$-0.150937\pi$
$41$	64721.2	+	37366.8i	0.939063	+	0.542168i	0.0493965	+	0.998779i	$0.484270\pi$
$42$		0			0
$43$	73052.9	+	126531.i	0.918824	+	1.59145i	0.801204	+	0.598391i	$0.204193\pi$
$43$	73052.9	+	126531.i	0.918824	+	1.59145i	0.117620	+	0.993059i	$0.462474\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−22319.7	+	12886.3i	−0.214978	+	0.124118i	−0.603623	−	0.797270i	$-0.706277\pi$
$47$	−22319.7	+	12886.3i	−0.214978	+	0.124118i	0.388645	+	0.921388i	$0.372943\pi$
$48$		0			0
$49$	37065.1	−	64198.6i	0.315048	−	0.545679i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	197505.i		−	1.32663i	−0.748340	−	0.663316i	$-0.769149\pi$
$53$		−	197505.i		−	1.32663i	0.748340	−	0.663316i	$-0.230851\pi$
$54$		0			0
$55$	−481734.			−2.89547
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−31321.5	−	18083.5i	−0.152506	−	0.0880493i	0.421805	−	0.906687i	$-0.361397\pi$
$59$	−31321.5	−	18083.5i	−0.152506	−	0.0880493i	−0.574311	+	0.818637i	$0.694730\pi$
$60$		0			0
$61$	−11967.3	−	20728.0i	−0.0527239	−	0.0913204i	0.838459	−	0.544965i	$-0.183457\pi$
$61$	−11967.3	−	20728.0i	−0.0527239	−	0.0913204i	−0.891183	+	0.453644i	$0.850124\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	137678.	−	79488.2i	0.501330	−	0.289443i
$66$		0			0
$67$	176540.	−	305776.i	0.586973	−	1.01667i	−0.407653	−	0.913137i	$-0.633653\pi$
$67$	176540.	−	305776.i	0.586973	−	1.01667i	0.994626	−	0.103530i	$-0.0330138\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	496781.i		−	1.38800i	−0.719974	−	0.694001i	$-0.755846\pi$
$71$		−	496781.i		−	1.38800i	0.719974	−	0.694001i	$-0.244154\pi$
$72$		0			0
$73$	−382139.			−0.982319			−0.491160	−	0.871070i	$-0.663427\pi$
$73$	−382139.			−0.982319			−0.491160	+	0.871070i	$0.663427\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−480222.	−	277257.i	−1.05189	−	0.607309i
$78$		0			0
$79$	193328.	+	334855.i	0.392116	+	0.679165i	0.992728	−	0.120376i	$-0.0384099\pi$
$79$	193328.	+	334855.i	0.392116	+	0.679165i	−0.600613	+	0.799540i	$0.705077\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	359691.	−	207667.i	0.629064	−	0.363190i	−0.151326	−	0.988484i	$-0.548354\pi$
$83$	359691.	−	207667.i	0.629064	−	0.363190i	0.780389	+	0.625294i	$0.215021\pi$
$84$		0			0
$85$	−401295.	+	695064.i	−0.653442	+	1.13180i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	405654.i		−	0.575421i	−0.957717	−	0.287710i	$-0.907106\pi$
$89$		−	405654.i		−	0.575421i	0.957717	−	0.287710i	$-0.0928941\pi$
$90$		0			0
$91$	182994.			0.242836
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−658288.	−	380063.i	−0.767795	−	0.443287i
$96$		0			0
$97$	−178244.	−	308727.i	−0.195298	−	0.338267i	0.751700	−	0.659505i	$-0.229234\pi$
$97$	−178244.	−	308727.i	−0.195298	−	0.338267i	−0.946998	+	0.321239i	$0.895901\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.41963e6	+	819621.i	−1.37787	+	0.795516i	−0.991903	−	0.126995i	$-0.959467\pi$
$101$	−1.41963e6	+	819621.i	−1.37787	+	0.795516i	−0.385971	+	0.922511i	$0.626133\pi$
$102$		0			0
$103$	462737.	−	801484.i	0.423470	−	0.733472i	−0.572806	−	0.819691i	$-0.694145\pi$
$103$	462737.	−	801484.i	0.423470	−	0.733472i	0.996276	+	0.0862192i	$0.0274785\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			266819.i			0.217804i	0.994053	+	0.108902i	$0.0347334\pi$
$107$			266819.i			0.217804i	−0.994053	+	0.108902i	$0.965267\pi$
$108$		0			0
$109$	169960.			0.131240			0.0656200	−	0.997845i	$-0.479097\pi$
$109$	169960.			0.131240			0.0656200	+	0.997845i	$0.479097\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.65439e6	+	955161.i	1.14657	+	0.661974i	0.948050	−	0.318122i	$-0.103052\pi$
$113$	1.65439e6	+	955161.i	1.14657	+	0.661974i	0.198523	+	0.980096i	$0.436385\pi$
$114$		0			0
$115$	−1.08819e6	−	1.88480e6i	−0.715503	−	1.23929i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−800071.	+	461921.i	−0.474775	+	0.274111i
$120$		0			0
$121$	2.64699e6	−	4.58473e6i	1.49416	−	2.58796i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	289070.i		−	0.148004i
$126$		0			0
$127$	1.75663e6			0.857571			0.428786	−	0.903406i	$-0.358942\pi$
$127$	1.75663e6			0.857571			0.428786	+	0.903406i	$0.358942\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.07548e6	−	1.19828e6i	−0.923221	−	0.533022i	−0.0385598	−	0.999256i	$-0.512277\pi$
$131$	−2.07548e6	−	1.19828e6i	−0.923221	−	0.533022i	−0.884661	+	0.466234i	$0.845610\pi$
$132$		0			0
$133$	−437481.	−	757740.i	−0.185954	−	0.322081i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.15495e6	+	666808.i	−0.449159	+	0.259322i	−0.707475	−	0.706739i	$-0.750166\pi$
$137$	−1.15495e6	+	666808.i	−0.449159	+	0.259322i	0.258316	+	0.966060i	$0.416832\pi$
$138$		0			0
$139$	1.08878e6	−	1.88583e6i	0.405412	−	0.702194i	−0.588957	−	0.808164i	$-0.700461\pi$
$139$	1.08878e6	−	1.88583e6i	0.405412	−	0.702194i	0.994369	+	0.105970i	$0.0337948\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			2.33169e6i			0.797375i
$144$		0			0
$145$	478971.			0.157111
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.35022e6	−	1.93425e6i	−1.01278	−	0.584727i	−0.100774	−	0.994909i	$-0.532132\pi$
$149$	−3.35022e6	−	1.93425e6i	−1.01278	−	0.584727i	−0.912004	+	0.410182i	$0.865465\pi$
$150$		0			0
$151$	480879.	+	832907.i	0.139671	+	0.241917i	0.927372	−	0.374141i	$-0.122062\pi$
$151$	480879.	+	832907.i	0.139671	+	0.241917i	−0.787701	+	0.616057i	$0.788729\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−911105.	+	526027.i	−0.244666	+	0.141258i
$156$		0			0
$157$	796173.	−	1.37901e6i	0.205735	−	0.356344i	−0.744632	−	0.667476i	$-0.767375\pi$
$157$	796173.	−	1.37901e6i	0.205735	−	0.356344i	0.950367	+	0.311132i	$0.100708\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	2.50518e6i		−	0.600290i
$162$		0			0
$163$	−702280.			−0.162161			−0.0810807	−	0.996708i	$-0.525837\pi$
$163$	−702280.			−0.162161			−0.0810807	+	0.996708i	$0.525837\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.27789e6	−	1.89249e6i	−0.703794	−	0.406335i	0.104965	−	0.994476i	$-0.466527\pi$
$167$	−3.27789e6	−	1.89249e6i	−0.703794	−	0.406335i	−0.808759	+	0.588140i	$0.799860\pi$
$168$		0			0
$169$	2.02867e6	+	3.51375e6i	0.420291	+	0.727966i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.78706e6	+	2.18646e6i	−0.731416	+	0.422283i	−0.818940	−	0.573879i	$-0.805438\pi$
$173$	−3.78706e6	+	2.18646e6i	−0.731416	+	0.422283i	0.0875242	+	0.996162i	$0.472104\pi$
$174$		0			0
$175$	1.79615e6	−	3.11102e6i	0.335142	−	0.580483i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	49288.2i		−	0.00859377i	−0.999991	−	0.00429688i	$-0.998632\pi$
$179$		−	49288.2i		−	0.00859377i	0.999991	−	0.00429688i	$-0.00136775\pi$
$180$		0			0
$181$	−4.52205e6			−0.762605			−0.381303	−	0.924450i	$-0.624524\pi$
$181$	−4.52205e6			−0.762605			−0.381303	+	0.924450i	$0.624524\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.52596e6	−	3.76777e6i	−1.03069	−	0.595071i
$186$		0			0
$187$	−5.88575e6	−	1.01944e7i	−0.900072	−	1.55897i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.07831e6	−	622561.i	0.154754	−	0.0893473i	−0.420623	−	0.907235i	$-0.638189\pi$
$191$	1.07831e6	−	622561.i	0.154754	−	0.0893473i	0.575377	+	0.817888i	$0.304855\pi$
$192$		0			0
$193$	5.47671e6	−	9.48595e6i	0.761812	−	1.31950i	−0.180103	−	0.983648i	$-0.557643\pi$
$193$	5.47671e6	−	9.48595e6i	0.761812	−	1.31950i	0.941915	−	0.335850i	$-0.109024\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	1.07910e7i		−	1.41144i	−0.708492	−	0.705719i	$-0.750624\pi$
$197$		−	1.07910e7i		−	1.41144i	0.708492	−	0.705719i	$-0.249376\pi$
$198$		0			0
$199$	−5.05948e6			−0.642017			−0.321008	−	0.947076i	$-0.604022\pi$
$199$	−5.05948e6			−0.642017			−0.321008	+	0.947076i	$0.604022\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	477468.	+	275666.i	0.0570763	+	0.0329530i
$204$		0			0
$205$	−6.77205e6	−	1.17295e7i	−0.786066	−	1.36151i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	9.65504e6	−	5.57434e6i	1.05758	−	0.610597i
$210$		0			0
$211$	−1.72915e6	+	2.99498e6i	−0.184071	+	0.318821i	−0.943263	−	0.332046i	$-0.892261\pi$
$211$	−1.72915e6	+	2.99498e6i	−0.184071	+	0.318821i	0.759192	+	0.650867i	$0.225594\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	2.64791e7i		−	2.66432i
$216$		0			0
$217$	−1.21099e6			−0.118512
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.36425e6	+	1.94235e6i	0.311681	+	0.179949i
$222$		0			0
$223$	3.78005e6	+	6.54724e6i	0.340865	+	0.590396i	0.984594	−	0.174858i	$-0.0559467\pi$
$223$	3.78005e6	+	6.54724e6i	0.340865	+	0.590396i	−0.643728	+	0.765254i	$0.722613\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.44652e6	+	2.56720e6i	−0.380139	+	0.219473i	−0.677879	−	0.735174i	$-0.737101\pi$
$227$	−4.44652e6	+	2.56720e6i	−0.380139	+	0.219473i	0.297740	+	0.954647i	$0.403767\pi$
$228$		0			0
$229$	−9.32792e6	+	1.61564e7i	−0.776744	+	1.34536i	0.157064	+	0.987588i	$0.449797\pi$
$229$	−9.32792e6	+	1.61564e7i	−0.776744	+	1.34536i	−0.933809	+	0.357772i	$0.883536\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	421669.i		−	0.0333352i	−0.999861	−	0.0166676i	$-0.994694\pi$
$233$		−	421669.i		−	0.0333352i	0.999861	−	0.0166676i	$-0.00530571\pi$
$234$		0			0
$235$	4.67081e6			0.359905
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.93062e7	−	1.11465e7i	−1.41418	−	0.816475i	−0.418398	−	0.908264i	$-0.637408\pi$
$239$	−1.93062e7	−	1.11465e7i	−1.41418	−	0.816475i	−0.995779	+	0.0917886i	$0.970742\pi$
$240$		0			0
$241$	−4.91596e6	−	8.51470e6i	−0.351202	−	0.608300i	0.635258	−	0.772300i	$-0.280894\pi$
$241$	−4.91596e6	−	8.51470e6i	−0.351202	−	0.608300i	−0.986460	+	0.164000i	$0.947560\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.16348e7	+	6.71737e6i	−0.791155	+	0.456774i
$246$		0			0
$247$	−1.83958e6	+	3.18624e6i	−0.122075	+	0.211441i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			1.55511e7i			0.983422i	0.870759	+	0.491711i	$0.163628\pi$
$251$			1.55511e7i			0.983422i	−0.870759	+	0.491711i	$0.836372\pi$
$252$		0			0
$253$	3.19207e7			1.97111
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.84675e6	+	1.06622e6i	0.108795	+	0.0628128i	0.553410	−	0.832909i	$-0.313326\pi$
$257$	1.84675e6	+	1.06622e6i	0.108795	+	0.0628128i	−0.444615	+	0.895722i	$0.646660\pi$
$258$		0			0
$259$	−4.33699e6	−	7.51188e6i	−0.249625	−	0.432364i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−911256.	+	526114.i	−0.0500925	+	0.0289209i	−0.524837	−	0.851203i	$-0.675874\pi$
$263$	−911256.	+	526114.i	−0.0500925	+	0.0289209i	0.474745	+	0.880124i	$0.342540\pi$
$264$		0			0
$265$	−1.78971e7	+	3.09987e7i	−0.961712	+	1.66573i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			9.68762e6i			0.497692i	0.968543	+	0.248846i	$0.0800512\pi$
$269$			9.68762e6i			0.497692i	−0.968543	+	0.248846i	$0.919949\pi$
$270$		0			0
$271$	2.05637e7			1.03322			0.516610	−	0.856221i	$-0.327194\pi$
$271$	2.05637e7			1.03322			0.516610	+	0.856221i	$0.327194\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.96403e7	+	2.28864e7i	1.90607	+	1.10047i
$276$		0			0
$277$	−1.00696e7	−	1.74411e7i	−0.473776	−	0.820604i	0.525773	−	0.850625i	$-0.323776\pi$
$277$	−1.00696e7	−	1.74411e7i	−0.473776	−	0.820604i	−0.999549	+	0.0300208i	$0.990443\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.75923e7	+	1.01569e7i	−0.792873	+	0.457766i	−0.840973	−	0.541077i	$-0.818017\pi$
$281$	−1.75923e7	+	1.01569e7i	−0.792873	+	0.457766i	0.0480998	+	0.998843i	$0.484683\pi$
$282$		0			0
$283$	1.13075e7	−	1.95852e7i	0.498894	−	0.864110i	−0.501105	−	0.865387i	$-0.667073\pi$
$283$	1.13075e7	−	1.95852e7i	0.498894	−	0.864110i	0.999999	+	0.00127619i	$0.000406222\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	1.55903e7i		−	0.659491i
$288$		0			0
$289$	4.52573e6			0.187497
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.34647e6	+	1.93209e6i	0.133041	+	0.0768111i	0.565043	−	0.825061i	$-0.308859\pi$
$293$	3.34647e6	+	1.93209e6i	0.133041	+	0.0768111i	−0.432002	+	0.901872i	$0.642193\pi$
$294$		0			0
$295$	3.27730e6	+	5.67646e6i	0.127659	+	0.221111i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−9.12281e6	+	5.26705e6i	−0.341283	+	0.197040i
$300$		0			0
$301$	1.52397e7	−	2.63959e7i	0.558827	−	0.967916i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			4.33772e6i			0.152884i
$306$		0			0
$307$	3.02526e6			0.104556			0.0522779	−	0.998633i	$-0.483352\pi$
$307$	3.02526e6			0.104556			0.0522779	+	0.998633i	$0.483352\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.30190e7	+	1.90635e7i	1.09770	+	0.633755i	0.935615	−	0.353022i	$-0.114846\pi$
$311$	3.30190e7	+	1.90635e7i	1.09770	+	0.633755i	0.162081	+	0.986777i	$0.448179\pi$
$312$		0			0
$313$	1.13148e7	+	1.95979e7i	0.368990	+	0.639110i	0.989408	−	0.145161i	$-0.0463702\pi$
$313$	1.13148e7	+	1.95979e7i	0.368990	+	0.639110i	−0.620417	+	0.784272i	$0.713037\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.07004e7	−	1.19514e7i	0.649831	−	0.375180i	−0.138560	−	0.990354i	$-0.544247\pi$
$317$	2.07004e7	−	1.19514e7i	0.649831	−	0.375180i	0.788392	+	0.615174i	$0.210914\pi$
$318$		0			0
$319$	−3.51251e6	+	6.08385e6i	−0.108205	+	0.187416i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	1.85742e7i		−	0.551191i
$324$		0			0
$325$	−1.51054e7			−0.440029
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.65615e6	+	2.68823e6i	0.130749	+	0.0754881i
$330$		0			0
$331$	−1.41912e7	−	2.45799e7i	−0.391324	−	0.677792i	0.601301	−	0.799023i	$-0.294649\pi$
$331$	−1.41912e7	−	2.45799e7i	−0.391324	−	0.677792i	−0.992624	+	0.121230i	$0.961316\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.54164e7	+	3.19946e7i	−1.47402	+	0.851026i
$336$		0			0
$337$	1.56151e7	−	2.70461e7i	0.407994	−	0.706666i	−0.586671	−	0.809825i	$-0.699562\pi$
$337$	1.56151e7	−	2.70461e7i	0.407994	−	0.706666i	0.994665	+	0.103159i	$0.0328951\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	1.54303e7i		−	0.389146i
$342$		0			0
$343$	−4.00074e7			−0.991420
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.73955e7	−	1.00433e7i	−0.416340	−	0.240374i	0.277170	−	0.960821i	$-0.410603\pi$
$347$	−1.73955e7	−	1.00433e7i	−0.416340	−	0.240374i	−0.693510	+	0.720447i	$0.743937\pi$
$348$		0			0
$349$	1.84002e7	+	3.18701e7i	0.432859	+	0.749733i	0.997118	−	0.0758644i	$-0.0241716\pi$
$349$	1.84002e7	+	3.18701e7i	0.432859	+	0.749733i	−0.564260	+	0.825597i	$0.690838\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2.05019e7	−	1.18368e7i	0.466089	−	0.269097i	−0.248512	−	0.968629i	$-0.579942\pi$
$353$	2.05019e7	−	1.18368e7i	0.466089	−	0.269097i	0.714601	+	0.699532i	$0.246608\pi$
$354$		0			0
$355$	−4.50163e7	+	7.79705e7i	−1.00620	+	1.74279i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			3.67159e7i			0.793544i	0.917917	+	0.396772i	$0.129870\pi$
$359$			3.67159e7i			0.793544i	−0.917917	+	0.396772i	$0.870130\pi$
$360$		0			0
$361$	−2.94545e7			−0.626079
$362$		0			0
$363$		0			0
$364$		0			0
$365$	5.99773e7	+	3.46279e7i	1.23341	+	0.712111i
$366$		0			0
$367$	4.15020e7	+	7.18836e7i	0.839597	+	1.45422i	0.890232	+	0.455507i	$0.150542\pi$
$367$	4.15020e7	+	7.18836e7i	0.839597	+	1.45422i	−0.0506351	+	0.998717i	$0.516125\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−3.56819e7	+	2.06009e7i	−0.698756	+	0.403427i
$372$		0			0
$373$	3.06825e7	−	5.31436e7i	0.591241	−	1.02406i	−0.402825	−	0.915277i	$-0.631972\pi$
$373$	3.06825e7	−	5.31436e7i	0.591241	−	1.02406i	0.994066	−	0.108782i	$-0.0346950\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	2.31832e6i		−	0.0432662i
$378$		0			0
$379$	−8.94442e6			−0.164299			−0.0821495	−	0.996620i	$-0.526178\pi$
$379$	−8.94442e6			−0.164299			−0.0821495	+	0.996620i	$0.526178\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.60170e7	+	4.38884e7i	1.35305	+	0.781184i	0.988676	−	0.150068i	$-0.0479492\pi$
$383$	7.60170e7	+	4.38884e7i	1.35305	+	0.781184i	0.364375	+	0.931252i	$0.381283\pi$
$384$		0			0
$385$	5.02477e7	+	8.70317e7i	0.880510	+	1.52509i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.09387e7	+	4.67300e7i	−1.37501	+	0.793865i	−0.991554	−	0.129693i	$-0.958601\pi$
$389$	−8.09387e7	+	4.67300e7i	−1.37501	+	0.793865i	−0.383460	+	0.923558i	$0.625268\pi$
$390$		0			0
$391$	2.65907e7	−	4.60564e7i	0.444835	−	0.770477i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	7.00746e7i		−	1.13702i
$396$		0			0
$397$	−1.21583e8			−1.94313			−0.971566	−	0.236767i	$-0.923912\pi$
$397$	−1.21583e8			−1.94313			−0.971566	+	0.236767i	$0.923912\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.85999e7	−	1.07387e7i	−0.288455	−	0.166540i	0.348790	−	0.937201i	$-0.386593\pi$
$401$	−1.85999e7	−	1.07387e7i	−0.288455	−	0.166540i	−0.637245	+	0.770661i	$0.719926\pi$
$402$		0			0
$403$	2.54607e6	+	4.40993e6i	0.0389005	+	0.0673777i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	9.57156e7	−	5.52614e7i	1.41971	−	0.819670i
$408$		0			0
$409$	−5.80930e7	+	1.00620e8i	−0.849090	+	1.47067i	0.0329322	+	0.999458i	$0.489515\pi$
$409$	−5.80930e7	+	1.00620e8i	−0.849090	+	1.47067i	−0.882022	+	0.471209i	$0.843818\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			7.54485e6i			0.107103i
$414$		0			0
$415$	−7.52720e7			−1.05315
$416$		0			0
$417$		0			0
$418$		0			0
$419$	2.73269e7	+	1.57772e7i	0.371492	+	0.214481i	0.674110	−	0.738631i	$-0.264527\pi$
$419$	2.73269e7	+	1.57772e7i	0.371492	+	0.214481i	−0.302618	+	0.953112i	$0.597861\pi$
$420$		0			0
$421$	7.50313e6	+	1.29958e7i	0.100553	+	0.174163i	0.911913	−	0.410384i	$-0.134605\pi$
$421$	7.50313e6	+	1.29958e7i	0.100553	+	0.174163i	−0.811359	+	0.584548i	$0.801272\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.60425e7	−	3.81297e7i	0.860314	−	0.496702i
$426$		0			0
$427$	−2.49652e6	+	4.32411e6i	−0.0320665	+	0.0555409i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			6.49322e7i			0.811014i	0.914092	+	0.405507i	$0.132905\pi$
$431$			6.49322e7i			0.811014i	−0.914092	+	0.405507i	$0.867095\pi$
$432$		0			0
$433$	8.31669e7			1.02444			0.512220	−	0.858854i	$-0.328823\pi$
$433$	8.31669e7			1.02444			0.512220	+	0.858854i	$0.328823\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.36195e7	+	2.51838e7i	0.522681	+	0.301770i
$438$		0			0
$439$	1.63576e7	+	2.83321e7i	0.193341	+	0.334877i	0.946356	−	0.323127i	$-0.104734\pi$
$439$	1.63576e7	+	2.83321e7i	0.193341	+	0.334877i	−0.753014	+	0.658004i	$0.771401\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.29959e7	−	5.36912e7i	1.06968	−	0.617578i	0.141584	−	0.989926i	$-0.454781\pi$
$443$	9.29959e7	−	5.36912e7i	1.06968	−	0.617578i	0.928093	+	0.372348i	$0.121447\pi$
$444$		0			0
$445$	−3.67587e7	+	6.36680e7i	−0.417139	+	0.722505i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	3.79594e7i		−	0.419354i	−0.977771	−	0.209677i	$-0.932759\pi$
$449$		−	3.79594e7i		−	0.419354i	0.977771	−	0.209677i	$-0.0672413\pi$
$450$		0			0
$451$	1.98650e8			2.16550
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.87212e7	−	1.65822e7i	−0.304907	−	0.176038i
$456$		0			0
$457$	−1.27236e7	−	2.20379e7i	−0.133309	−	0.230898i	0.791641	−	0.610986i	$-0.209227\pi$
$457$	−1.27236e7	−	2.20379e7i	−0.133309	−	0.230898i	−0.924950	+	0.380088i	$0.875894\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−5.64160e7	+	3.25718e7i	−0.575837	+	0.332460i	−0.759477	−	0.650534i	$-0.774545\pi$
$461$	−5.64160e7	+	3.25718e7i	−0.575837	+	0.332460i	0.183640	+	0.982994i	$0.441212\pi$
$462$		0			0
$463$	1.44914e7	−	2.50999e7i	0.146005	−	0.252888i	−0.783742	−	0.621086i	$-0.786692\pi$
$463$	1.44914e7	−	2.50999e7i	0.146005	−	0.252888i	0.929747	+	0.368198i	$0.120025\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			6.09985e7i			0.598919i	0.954109	+	0.299460i	$0.0968064\pi$
$467$			6.09985e7i			0.598919i	−0.954109	+	0.299460i	$0.903194\pi$
$468$		0			0
$469$	−7.36566e7			−0.713991
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.36334e8	+	1.94183e8i	3.17825	+	1.83496i
$474$		0			0
$475$	3.61122e7	+	6.25482e7i	0.336956	+	0.583626i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−8.59855e7	+	4.96437e7i	−0.782381	+	0.451708i	−0.837274	−	0.546784i	$-0.815852\pi$
$479$	−8.59855e7	+	4.96437e7i	−0.782381	+	0.451708i	0.0548922	+	0.998492i	$0.482518\pi$
$480$		0			0
$481$	−1.82367e7	+	3.15870e7i	−0.163875	+	0.283839i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			6.46069e7i			0.566309i
$486$		0			0
$487$	−1.05049e8			−0.909504			−0.454752	−	0.890618i	$-0.650272\pi$
$487$	−1.05049e8			−0.909504			−0.454752	+	0.890618i	$0.650272\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.64341e8	+	9.48823e7i	1.38836	+	0.801569i	0.993130	−	0.117014i	$-0.0373323\pi$
$491$	1.64341e8	+	9.48823e7i	1.38836	+	0.801569i	0.395228	+	0.918583i	$0.370666\pi$
$492$		0			0
$493$	5.85199e6	+	1.01360e7i	0.0488386	+	0.0845909i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−8.97500e7	+	5.18172e7i	−0.731081	+	0.422090i
$498$		0			0
$499$	−1.01002e8	+	1.74941e8i	−0.812887	+	1.40796i	0.0979477	+	0.995192i	$0.468772\pi$
$499$	−1.01002e8	+	1.74941e8i	−0.812887	+	1.40796i	−0.910835	+	0.412771i	$0.864561\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	1.88347e8i		−	1.47998i	−0.672619	−	0.739989i	$-0.734831\pi$
$503$		−	1.88347e8i		−	1.47998i	0.672619	−	0.739989i	$-0.265169\pi$
$504$		0			0
$505$	2.97083e8			2.30677
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.43572e8	−	8.28912e7i	−1.08872	−	0.628572i	−0.155484	−	0.987838i	$-0.549694\pi$
$509$	−1.43572e8	−	8.28912e7i	−1.08872	−	0.628572i	−0.933235	+	0.359266i	$0.883027\pi$
$510$		0			0
$511$	3.98593e7	+	6.90384e7i	0.298722	+	0.517402i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.45255e8	+	8.38628e7i	−1.06343	+	0.613971i
$516$		0			0
$517$	−3.42531e7	+	5.93281e7i	−0.247873	+	0.429328i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	2.76446e8i		−	1.95478i	−0.211451	−	0.977389i	$-0.567819\pi$
$521$		−	2.76446e8i		−	1.95478i	0.211451	−	0.977389i	$-0.432181\pi$
$522$		0			0
$523$	−8.78008e7			−0.613753			−0.306876	−	0.951749i	$-0.599284\pi$
$523$	−8.78008e7			−0.613753			−0.306876	+	0.951749i	$0.599284\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.22635e7	−	1.28538e7i	−0.152111	−	0.0878214i
$528$		0			0
$529$	−1.91221e6	−	3.31204e6i	−0.0129172	−	0.0223732i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−5.67733e7	+	3.27781e7i	−0.374941	+	0.216472i
$534$		0			0
$535$	2.41780e7	−	4.18776e7i	0.157892	−	0.273477i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	1.97046e8i		−	1.25835i
$540$		0			0
$541$	−1.60020e8			−1.01061			−0.505305	−	0.862941i	$-0.668620\pi$
$541$	−1.60020e8			−1.01061			−0.505305	+	0.862941i	$0.668620\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.66754e7	−	1.54011e7i	−0.164787	−	0.0951395i
$546$		0			0
$547$	−1.10308e7	−	1.91059e7i	−0.0673977	−	0.116736i	0.830357	−	0.557231i	$-0.188136\pi$
$547$	−1.10308e7	−	1.91059e7i	−0.0673977	−	0.116736i	−0.897755	+	0.440495i	$0.854803\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−9.59966e6	+	5.54237e6i	−0.0573854	+	0.0331315i
$552$		0			0
$553$	4.03306e7	−	6.98546e7i	0.238484	−	0.413066i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	1.71224e8i		−	0.990830i	−0.868657	−	0.495415i	$-0.835016\pi$
$557$		−	1.71224e8i		−	0.990830i	0.868657	−	0.495415i	$-0.164984\pi$
$558$		0			0
$559$	−1.28164e8			−0.733720
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.92436e8	−	1.11103e8i	−1.07835	−	0.622586i	−0.147900	−	0.989002i	$-0.547251\pi$
$563$	−1.92436e8	−	1.11103e8i	−1.07835	−	0.622586i	−0.930451	+	0.366416i	$0.880585\pi$
$564$		0			0
$565$	−1.73106e8	−	2.99828e8i	−0.959767	−	1.66237i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2.25736e8	−	1.30329e8i	1.22536	−	0.707461i	0.259303	−	0.965796i	$-0.416507\pi$
$569$	2.25736e8	−	1.30329e8i	1.22536	−	0.707461i	0.966056	+	0.258335i	$0.0831737\pi$
$570$		0			0
$571$	6.09463e7	−	1.05562e8i	0.327370	−	0.567022i	−0.654619	−	0.755959i	$-0.727171\pi$
$571$	6.09463e7	−	1.05562e8i	0.327370	−	0.567022i	0.981989	+	0.188937i	$0.0605042\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			2.06792e8i			1.08775i
$576$		0			0
$577$	1.22005e8			0.635111			0.317555	−	0.948240i	$-0.397138\pi$
$577$	1.22005e8			0.635111			0.317555	+	0.948240i	$0.397138\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−7.50357e7	−	4.33219e7i	−0.382595	−	0.220891i
$582$		0			0
$583$	−2.62495e8	−	4.54654e8i	−1.32469	−	2.29444i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.15748e8	+	6.68273e7i	−0.572269	+	0.330400i	−0.758055	−	0.652191i	$-0.773850\pi$
$587$	−1.15748e8	+	6.68273e7i	−0.572269	+	0.330400i	0.185786	+	0.982590i	$0.440517\pi$
$588$		0			0
$589$	1.21737e7	−	2.10855e7i	0.0595768	−	0.103190i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	1.98748e7i		−	0.0953100i	−0.998864	−	0.0476550i	$-0.984825\pi$
$593$		−	1.98748e7i		−	0.0953100i	0.998864	−	0.0476550i	$-0.0151748\pi$
$594$		0			0
$595$	1.67430e8			0.794844
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.37964e8	+	1.95123e8i	1.57250	+	0.907881i	0.995862	+	0.0908789i	$0.0289676\pi$
$599$	3.37964e8	+	1.95123e8i	1.57250	+	0.907881i	0.576634	+	0.817002i	$0.304366\pi$
$600$		0			0
$601$	−7.89071e7	−	1.36671e8i	−0.363490	−	0.629583i	0.625043	−	0.780591i	$-0.285082\pi$
$601$	−7.89071e7	−	1.36671e8i	−0.363490	−	0.629583i	−0.988533	+	0.151007i	$0.951748\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−8.30899e8	+	4.79720e8i	−3.75217	+	2.16631i
$606$		0			0
$607$	1.74295e8	−	3.01887e8i	0.779325	−	1.34983i	−0.153007	−	0.988225i	$-0.548896\pi$
$607$	1.74295e8	−	3.01887e8i	0.779325	−	1.34983i	0.932332	−	0.361605i	$-0.117771\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	2.26076e7i		−	0.0991132i
$612$		0			0
$613$	1.41726e7			0.0615273			0.0307636	−	0.999527i	$-0.490206\pi$
$613$	1.41726e7			0.0615273			0.0307636	+	0.999527i	$0.490206\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.81599e8	+	1.04846e8i	0.773140	+	0.446373i	0.833994	−	0.551774i	$-0.186049\pi$
$617$	1.81599e8	+	1.04846e8i	0.773140	+	0.446373i	−0.0608535	+	0.998147i	$0.519382\pi$
$618$		0			0
$619$	−8.36020e7	−	1.44803e8i	−0.352488	−	0.610528i	0.634196	−	0.773172i	$-0.281331\pi$
$619$	−8.36020e7	−	1.44803e8i	−0.352488	−	0.610528i	−0.986685	+	0.162644i	$0.947998\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−7.32867e7	+	4.23121e7i	−0.303083	+	0.174985i
$624$		0			0
$625$	1.08337e8	−	1.87645e8i	0.443749	−	0.768595i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	1.84136e8i		−	0.739923i
$630$		0			0
$631$	3.36933e8			1.34108			0.670541	−	0.741872i	$-0.266062\pi$
$631$	3.36933e8			1.34108			0.670541	+	0.741872i	$0.266062\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.75706e8	−	1.59179e8i	−1.07678	−	0.621677i
$636$		0			0
$637$	3.25134e7	+	5.63149e7i	0.125789	+	0.217874i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	8.63536e7	−	4.98563e7i	0.327873	−	0.189298i	−0.327023	−	0.945016i	$-0.606046\pi$
$641$	8.63536e7	−	4.98563e7i	0.327873	−	0.189298i	0.654897	+	0.755719i	$0.272712\pi$
$642$		0			0
$643$	−1.34692e8	+	2.33294e8i	−0.506652	+	0.877547i	0.493318	+	0.869849i	$0.335784\pi$
$643$	−1.34692e8	+	2.33294e8i	−0.506652	+	0.877547i	−0.999970	+	0.00769844i	$0.997549\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	7.78039e7i		−	0.287269i	−0.989631	−	0.143634i	$-0.954121\pi$
$647$		−	7.78039e7i		−	0.287269i	0.989631	−	0.143634i	$-0.0458790\pi$
$648$		0			0
$649$	−9.61357e7			−0.351682
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.95063e8	−	1.12620e8i	−0.700543	−	0.404459i	0.107007	−	0.994258i	$-0.465873\pi$
$653$	−1.95063e8	−	1.12620e8i	−0.700543	−	0.404459i	−0.807550	+	0.589800i	$0.799207\pi$
$654$		0			0
$655$	2.17167e8	+	3.76144e8i	0.772805	+	1.33854i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.98537e8	+	1.14625e8i	−0.693722	+	0.400521i	−0.805005	−	0.593268i	$-0.797837\pi$
$659$	−1.98537e8	+	1.14625e8i	−0.693722	+	0.400521i	0.111283	+	0.993789i	$0.464504\pi$
$660$		0			0
$661$	1.05495e8	−	1.82722e8i	0.365280	−	0.632684i	−0.623541	−	0.781791i	$-0.714306\pi$
$661$	1.05495e8	−	1.82722e8i	0.365280	−	0.632684i	0.988821	+	0.149107i	$0.0476398\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			1.58571e8i			0.539212i
$666$		0			0
$667$	−3.17376e7			−0.106954
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−5.50973e7	−	3.18104e7i	−0.182374	−	0.105294i
$672$		0			0
$673$	2.87715e8	+	4.98336e8i	0.943880	+	1.63485i	0.757978	+	0.652280i	$0.226187\pi$
$673$	2.87715e8	+	4.98336e8i	0.943880	+	1.63485i	0.185901	+	0.982568i	$0.440479\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.05834e8	−	1.76573e8i	0.985644	−	0.569062i	0.0816747	−	0.996659i	$-0.473973\pi$
$677$	3.05834e8	−	1.76573e8i	0.985644	−	0.569062i	0.903969	+	0.427597i	$0.140640\pi$
$678$		0			0
$679$	−3.71837e7	+	6.44041e7i	−0.118780	+	0.205733i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	4.65139e8i		−	1.45989i	−0.683506	−	0.729945i	$-0.739546\pi$
$683$		−	4.65139e8i		−	1.45989i	0.683506	−	0.729945i	$-0.260454\pi$
$684$		0			0
$685$	2.41694e8			0.751959
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.50040e8	+	8.66255e7i	0.458721	+	0.264843i
$690$		0			0
$691$	−5.96318e7	−	1.03285e8i	−0.180736	−	0.313043i	0.761396	−	0.648288i	$-0.224515\pi$
$691$	−5.96318e7	−	1.03285e8i	−0.180736	−	0.313043i	−0.942131	+	0.335244i	$0.891181\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.41772e8	+	1.97322e8i	−1.01808	+	0.587789i
$696$		0			0
$697$	1.65480e8	−	2.86619e8i	0.488705	−	0.846461i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			3.55114e8i			1.03089i	0.856921	+	0.515447i	$0.172374\pi$
$701$			3.55114e8i			1.03089i	−0.856921	+	0.515447i	$0.827626\pi$
$702$		0			0
$703$	1.74393e8			0.501954
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.96151e8	+	1.70983e8i	0.838020	+	0.483831i
$708$		0			0
$709$	−3.01326e8	−	5.21912e8i	−0.845470	−	1.46440i	−0.885212	−	0.465187i	$-0.845987\pi$
$709$	−3.01326e8	−	5.21912e8i	−0.845470	−	1.46440i	0.0397425	−	0.999210i	$-0.487346\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	6.03717e7	−	3.48556e7i	0.166558	−	0.0961621i
$714$		0			0
$715$	2.11288e8	−	3.65962e8i	0.578039	−	1.00119i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	3.36046e8i		−	0.904092i	−0.891995	−	0.452046i	$-0.850694\pi$
$719$		−	3.36046e8i		−	0.904092i	0.891995	−	0.452046i	$-0.149306\pi$
$720$		0			0
$721$	−1.93065e8			−0.515107
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3.94130e7	−	2.27551e7i	−0.103425	−	0.0597124i
$726$		0			0
$727$	−2.56241e8	−	4.43823e8i	−0.666877	−	1.15507i	−0.978773	−	0.204949i	$-0.934297\pi$
$727$	−2.56241e8	−	4.43823e8i	−0.666877	−	1.15507i	0.311895	−	0.950116i	$-0.399036\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	5.60348e8	−	3.23517e8i	1.43452	−	0.828218i
$732$		0			0
$733$	1.79393e7	−	3.10717e7i	0.0455505	−	0.0788957i	−0.842351	−	0.538929i	$-0.818829\pi$
$733$	1.79393e7	−	3.10717e7i	0.0455505	−	0.0788957i	0.887902	+	0.460033i	$0.152162\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	9.38524e8i		−	2.34446i
$738$		0			0
$739$	3.58948e7			0.0889403			0.0444701	−	0.999011i	$-0.485840\pi$
$739$	3.58948e7			0.0889403			0.0444701	+	0.999011i	$0.485840\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−3.77466e8	−	2.17930e8i	−0.920261	−	0.531313i	−0.0365427	−	0.999332i	$-0.511634\pi$
$743$	−3.77466e8	−	2.17930e8i	−0.920261	−	0.531313i	−0.883718	+	0.468019i	$0.844968\pi$
$744$		0			0
$745$	3.50548e8	+	6.07166e8i	0.847771	+	1.46838i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	4.82043e7	−	2.78308e7i	0.114720	−	0.0662338i
$750$		0			0
$751$	−2.14559e8	+	3.71627e8i	−0.506556	+	0.877380i	0.493416	+	0.869794i	$0.335748\pi$
$751$	−2.14559e8	+	3.71627e8i	−0.506556	+	0.877380i	−0.999971	+	0.00758650i	$0.997585\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	1.74301e8i		−	0.405005i
$756$		0			0
$757$	−8.26773e8			−1.90589			−0.952947	−	0.303136i	$-0.901966\pi$
$757$	−8.26773e8			−1.90589			−0.952947	+	0.303136i	$0.901966\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−3.22643e8	−	1.86278e8i	−0.732097	−	0.422677i	0.0870916	−	0.996200i	$-0.472243\pi$
$761$	−3.22643e8	−	1.86278e8i	−0.732097	−	0.422677i	−0.819189	+	0.573524i	$0.805576\pi$
$762$		0			0
$763$	−1.77278e7	−	3.07054e7i	−0.0399099	−	0.0691260i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.74752e7	−	1.58628e7i	0.0608912	−	0.0351555i
$768$		0			0
$769$	−2.05010e8	+	3.55087e8i	−0.450812	+	0.780829i	−0.998437	−	0.0558948i	$-0.982199\pi$
$769$	−2.05010e8	+	3.55087e8i	−0.450812	+	0.780829i	0.547625	+	0.836724i	$0.315532\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			6.77485e8i			1.46677i	0.679815	+	0.733384i	$0.262060\pi$
$773$			6.77485e8i			1.46677i	−0.679815	+	0.733384i	$0.737940\pi$
$774$		0			0
$775$	9.99624e7			0.214749
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.71454e8	+	1.56724e8i	0.574228	+	0.331531i
$780$		0			0
$781$	−6.60249e8	−	1.14359e9i	−1.38597	−	2.40058i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.49921e8	+	1.44292e8i	−0.516647	+	0.298286i
$786$		0			0
$787$	2.70650e8	−	4.68779e8i	0.555244	−	0.961710i	−0.442641	−	0.896699i	$-0.645958\pi$
$787$	2.70650e8	−	4.68779e8i	0.555244	−	0.961710i	0.997885	−	0.0650114i	$-0.0207084\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	3.98516e8i		−	0.805222i
$792$		0			0
$793$	2.09954e7			0.0421022
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−5.31873e8	−	3.07077e8i	−1.05059	−	0.606557i	−0.127774	−	0.991803i	$-0.540783\pi$
$797$	−5.31873e8	−	3.07077e8i	−1.05059	−	0.606557i	−0.922814	+	0.385246i	$0.874117\pi$
$798$		0			0
$799$	5.70672e7	+	9.88432e7i	0.111878	+	0.193779i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−8.79680e8	+	5.07883e8i	−1.69894	+	0.980883i
$804$		0			0
$805$	−2.27009e8	+	3.93192e8i	−0.435167	+	0.753731i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	1.54965e8i		−	0.292677i	−0.989235	−	0.146338i	$-0.953251\pi$
$809$		−	1.54965e8i		−	0.292677i	0.989235	−	0.146338i	$-0.0467489\pi$
$810$		0			0
$811$	−8.47410e8			−1.58866			−0.794330	−	0.607487i	$-0.792178\pi$
$811$	−8.47410e8			−1.58866			−0.794330	+	0.607487i	$0.792178\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.10224e8	+	6.36378e7i	0.203612	+	0.117555i
$816$		0			0
$817$	3.06400e8	+	5.30700e8i	0.561852	+	0.973157i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	2.24729e8	−	1.29747e8i	0.406096	−	0.234460i	−0.283015	−	0.959116i	$-0.591335\pi$
$821$	2.24729e8	−	1.29747e8i	0.406096	−	0.234460i	0.689111	+	0.724656i	$0.258001\pi$
$822$		0			0
$823$	−1.94060e8	+	3.36121e8i	−0.348126	+	0.602971i	−0.985916	−	0.167238i	$-0.946515\pi$
$823$	−1.94060e8	+	3.36121e8i	−0.348126	+	0.602971i	0.637791	+	0.770210i	$0.279848\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			7.11216e8i			1.25743i	0.777635	+	0.628716i	$0.216419\pi$
$827$			7.11216e8i			1.25743i	−0.777635	+	0.628716i	$0.783581\pi$
$828$		0			0
$829$	9.26204e8			1.62571			0.812855	−	0.582466i	$-0.197912\pi$
$829$	9.26204e8			1.62571			0.812855	+	0.582466i	$0.197912\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.84305e8	−	1.64144e8i	−0.491869	−	0.283981i
$834$		0			0
$835$	3.42980e8	+	5.94059e8i	0.589128	+	1.02040i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	5.79914e8	−	3.34814e8i	0.981924	−	0.566914i	0.0790734	−	0.996869i	$-0.474804\pi$
$839$	5.79914e8	−	3.34814e8i	0.981924	−	0.566914i	0.902850	+	0.429955i	$0.141471\pi$
$840$		0			0
$841$	−2.93919e8	+	5.09083e8i	−0.494129	+	0.855856i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	7.35318e8i		−	1.21872i
$846$		0			0
$847$	−1.10439e9			−1.81749
$848$		0			0
$849$		0			0
$850$		0			0
$851$	4.32424e8	+	2.49660e8i	0.701651	+	0.405098i
$852$		0			0
$853$	1.01924e8	+	1.76538e8i	0.164221	+	0.284440i	0.936379	−	0.350992i	$-0.114156\pi$
$853$	1.01924e8	+	1.76538e8i	0.164221	+	0.284440i	−0.772157	+	0.635432i	$0.780822\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	3.04635e8	−	1.75881e8i	0.483992	−	0.279433i	−0.238087	−	0.971244i	$-0.576520\pi$
$857$	3.04635e8	−	1.75881e8i	0.483992	−	0.279433i	0.722079	+	0.691811i	$0.243187\pi$
$858$		0			0
$859$	1.89638e8	−	3.28462e8i	0.299189	−	0.518210i	−0.676762	−	0.736202i	$-0.736617\pi$
$859$	1.89638e8	−	3.28462e8i	0.299189	−	0.518210i	0.975951	+	0.217992i	$0.0699507\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	5.09276e7i		−	0.0792358i	−0.999215	−	0.0396179i	$-0.987386\pi$
$863$		−	5.09276e7i		−	0.0792358i	0.999215	−	0.0396179i	$-0.0126141\pi$
$864$		0			0
$865$	7.92514e8			1.22450
$866$		0			0
$867$		0			0
$868$		0			0
$869$	8.90080e8	+	5.13888e8i	1.35634	+	0.783086i
$870$		0			0
$871$	1.54860e8	+	2.68226e8i	0.234361	+	0.405926i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−5.22243e7	+	3.01517e7i	−0.0779559	+	0.0450078i
$876$		0			0
$877$	4.47593e8	−	7.75254e8i	0.663567	−	1.14933i	−0.316105	−	0.948724i	$-0.602375\pi$
$877$	4.47593e8	−	7.75254e8i	0.663567	−	1.14933i	0.979672	−	0.200608i	$-0.0642916\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			5.82577e8i			0.851973i	0.904730	+	0.425986i	$0.140073\pi$
$881$			5.82577e8i			0.851973i	−0.904730	+	0.425986i	$0.859927\pi$
$882$		0			0
$883$	2.10539e7			0.0305810			0.0152905	−	0.999883i	$-0.495133\pi$
$883$	2.10539e7			0.0305810			0.0152905	+	0.999883i	$0.495133\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−9.71754e8	−	5.61043e8i	−1.39247	−	0.803942i	−0.398881	−	0.917003i	$-0.630601\pi$
$887$	−9.71754e8	−	5.61043e8i	−1.39247	−	0.803942i	−0.993588	+	0.113060i	$0.963935\pi$
$888$		0			0
$889$	−1.83227e8	−	3.17359e8i	−0.260787	−	0.451695i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−9.36135e7	+	5.40478e7i	−0.131457	+	0.0758968i
$894$		0			0
$895$	−4.46630e6	+	7.73585e6i	−0.00622986	+	0.0107904i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			1.53418e7i			0.0211154i
$900$		0			0
$901$	−8.74656e8			−1.19581
$902$		0			0
$903$		0			0
$904$		0			0
$905$	7.09743e8	+	4.09770e8i	0.957536	+	0.552834i
$906$		0			0
$907$	3.15685e8	+	5.46783e8i	0.423089	+	0.732812i	0.996240	−	0.0866378i	$-0.0276123\pi$
$907$	3.15685e8	+	5.46783e8i	0.423089	+	0.732812i	−0.573150	+	0.819450i	$0.694279\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.13526e8	−	6.55445e7i	0.150156	−	0.0866924i	−0.423040	−	0.906111i	$-0.639037\pi$
$911$	1.13526e8	−	6.55445e7i	0.150156	−	0.0866924i	0.573195	+	0.819419i	$0.305704\pi$
$912$		0			0
$913$	5.52003e8	−	9.56097e8i	0.725319	−	1.25629i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			4.99951e8i			0.648365i
$918$		0			0
$919$	7.88351e8			1.01572			0.507859	−	0.861440i	$-0.330437\pi$
$919$	7.88351e8			1.01572			0.507859	+	0.861440i	$0.330437\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	3.77393e8	+	2.17888e8i	0.479942	+	0.277094i
$924$		0			0
$925$	3.58000e8	+	6.20074e8i	0.452333	+	0.783463i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	8.26532e8	−	4.77199e8i	1.03089	−	0.595185i	0.113651	−	0.993521i	$-0.463745\pi$
$929$	8.26532e8	−	4.77199e8i	1.03089	−	0.595185i	0.917240	+	0.398336i	$0.130412\pi$
$930$		0			0
$931$	1.55459e8	−	2.69262e8i	0.192649	−	0.333677i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			2.13337e9i			2.60995i
$936$		0			0
$937$	−4.59379e8			−0.558409			−0.279205	−	0.960232i	$-0.590071\pi$
$937$	−4.59379e8			−0.558409			−0.279205	+	0.960232i	$0.590071\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.27228e8	+	7.34552e7i	0.152691	+	0.0881563i	0.574399	−	0.818575i	$-0.305236\pi$
$941$	1.27228e8	+	7.34552e7i	0.152691	+	0.0881563i	−0.421708	+	0.906732i	$0.638569\pi$
$942$		0			0
$943$	4.48730e8	+	7.77224e8i	0.535119	+	0.926853i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.87438e8	−	2.23687e8i	0.456197	−	0.263385i	−0.254247	−	0.967139i	$-0.581828\pi$
$947$	3.87438e8	−	2.23687e8i	0.456197	−	0.263385i	0.710444	+	0.703754i	$0.248494\pi$
$948$		0			0
$949$	1.67606e8	−	2.90302e8i	0.196106	−	0.339665i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	1.69556e8i		−	0.195900i	−0.995191	−	0.0979500i	$-0.968771\pi$
$953$		−	1.69556e8i		−	0.195900i	0.995191	−	0.0979500i	$-0.0312285\pi$
$954$		0			0
$955$	−2.25656e8			−0.259081
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.40935e8	+	1.39104e8i	0.273177	+	0.157719i
$960$		0			0
$961$	4.26903e8	+	7.39417e8i	0.481015	+	0.833143i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.71916e9	+	9.92556e8i	−1.91308	+	1.10452i
$966$		0			0
$967$	−1.92132e8	+	3.32782e8i	−0.212481	+	0.368027i	−0.952490	−	0.304569i	$-0.901488\pi$
$967$	−1.92132e8	+	3.32782e8i	−0.212481	+	0.368027i	0.740010	+	0.672596i	$0.234821\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			3.23298e8i			0.353139i	0.984288	+	0.176569i	$0.0565000\pi$
$971$			3.23298e8i			0.353139i	−0.984288	+	0.176569i	$0.943500\pi$
$972$		0			0
$973$	−4.54265e8			−0.493141
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.07518e9	+	6.20753e8i	1.15291	+	0.665634i	0.949595	−	0.313479i	$-0.101495\pi$
$977$	1.07518e9	+	6.20753e8i	1.15291	+	0.665634i	0.203317	+	0.979113i	$0.434828\pi$
$978$		0			0
$979$	−5.39136e8	−	9.33811e8i	−0.574580	−	0.995202i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	5.98285e8	−	3.45420e8i	0.629866	−	0.363653i	−0.150834	−	0.988559i	$-0.548196\pi$
$983$	5.98285e8	−	3.45420e8i	0.629866	−	0.363653i	0.780700	+	0.624906i	$0.214863\pi$
$984$		0			0
$985$	−9.77835e8	+	1.69366e9i	−1.02319	+	1.77222i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			1.75456e9i			1.81376i
$990$		0			0
$991$	1.68628e9			1.73264			0.866321	−	0.499487i	$-0.166478\pi$
$991$	1.68628e9			1.73264			0.866321	+	0.499487i	$0.166478\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	7.94092e8	+	4.58469e8i	0.806124	+	0.465416i
$996$		0			0
$997$	7.84012e8	+	1.35795e9i	0.791110	+	1.37024i	0.925280	+	0.379285i	$0.123830\pi$
$997$	7.84012e8	+	1.35795e9i	0.791110	+	1.37024i	−0.134170	+	0.990958i	$0.542837\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.7.q.b.17.2		12
3.2	odd	2		144.7.q.c.113.5		12
4.3	odd	2		54.7.d.a.17.4		12
9.2	odd	6	inner	432.7.q.b.305.2		12
9.7	even	3		144.7.q.c.65.5		12
12.11	even	2		18.7.d.a.5.1	✓	12
36.7	odd	6		18.7.d.a.11.1	yes	12
36.11	even	6		54.7.d.a.35.4		12
36.23	even	6		162.7.b.c.161.1		12
36.31	odd	6		162.7.b.c.161.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.7.d.a.5.1	✓	12	12.11	even	2
18.7.d.a.11.1	yes	12	36.7	odd	6
54.7.d.a.17.4		12	4.3	odd	2
54.7.d.a.35.4		12	36.11	even	6
144.7.q.c.65.5		12	9.7	even	3
144.7.q.c.113.5		12	3.2	odd	2
162.7.b.c.161.1		12	36.23	even	6
162.7.b.c.161.12		12	36.31	odd	6
432.7.q.b.17.2		12	1.1	even	1	trivial
432.7.q.b.305.2		12	9.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	432.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-156.951 - 90.6160i) q^{5} +(-104.306 - 180.663i) q^{7} +(2301.99 - 1329.05i) q^{11} +(-438.599 + 759.676i) q^{13} -4428.53i q^{17} +4194.21 q^{19} +(10399.9 + 6004.40i) q^{23} +(8610.01 + 14913.0i) q^{25} +(-2288.79 + 1321.43i) q^{29} +(2902.50 - 5027.28i) q^{31} +37807.1i q^{35} +41579.5 q^{37} +(64721.2 + 37366.8i) q^{41} +(73052.9 + 126531. i) q^{43} +(-22319.7 + 12886.3i) q^{47} +(37065.1 - 64198.6i) q^{49} -197505. i q^{53} -481734. q^{55} +(-31321.5 - 18083.5i) q^{59} +(-11967.3 - 20728.0i) q^{61} +(137678. - 79488.2i) q^{65} +(176540. - 305776. i) q^{67} -496781. i q^{71} -382139. q^{73} +(-480222. - 277257. i) q^{77} +(193328. + 334855. i) q^{79} +(359691. - 207667. i) q^{83} +(-401295. + 695064. i) q^{85} -405654. i q^{89} +182994. q^{91} +(-658288. - 380063. i) q^{95} +(-178244. - 308727. i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 432 q^{5} - 240 q^{7} + 378 q^{11} + 1680 q^{13} + 2820 q^{19} - 76248 q^{23} + 8094 q^{25} - 97092 q^{29} - 21480 q^{31} - 25536 q^{37} + 410562 q^{41} - 71430 q^{43} + 347652 q^{47} - 135954 q^{49}+ \cdots - 38874 q^{97}+O(q^{100}) \) 12 * q - 432 * q^5 - 240 * q^7 + 378 * q^11 + 1680 * q^13 + 2820 * q^19 - 76248 * q^23 + 8094 * q^25 - 97092 * q^29 - 21480 * q^31 - 25536 * q^37 + 410562 * q^41 - 71430 * q^43 + 347652 * q^47 - 135954 * q^49 - 580392 * q^55 + 369738 * q^59 + 135744 * q^61 + 753840 * q^65 + 289938 * q^67 - 977700 * q^73 + 159192 * q^77 + 764796 * q^79 + 396900 * q^83 + 1619568 * q^85 - 355584 * q^91 - 2089260 * q^95 - 38874 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more