LMFDB - Embedded newform 1800.2.b.g.251.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1800,2,Mod(251,1800)] 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("1800.251"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1800, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1800.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,-12,0,0,0,0,0,0,0,0,0,0,0,-12,0,0,-16,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(22)] == traces)

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

Self dual:	no
Analytic conductor:	$14.3730723638$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 28x^{12} + 16x^{10} - 40x^{8} + 610x^{6} + 1625x^{4} - 524x^{2} + 1444 $ x^16 - 6x^14 + 28x^12 + 16x^10 - 40x^8 + 610x^6 + 1625x^4 - 524*x^2 + 1444
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.9
Root			$-0.328458 - 1.49331i$ of defining polynomial
Character	$\chi$	$=$	1800.251
Dual form			1800.2.b.g.251.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.331077 - 1.37491i) q^{2} +(-1.78078 - 0.910404i) q^{4} -0.936426i q^{7} +(-1.84130 + 2.14700i) q^{8} +2.20837i q^{11} +3.33513i q^{13} +(-1.28751 - 0.310029i) q^{14} +(2.34233 + 3.24245i) q^{16} -1.54417i q^{17} +3.12311 q^{19} +(3.03632 + 0.731140i) q^{22} +3.39228 q^{23} +(4.58552 + 1.10418i) q^{26} +(-0.852526 + 1.66757i) q^{28} +8.44804 q^{29} -8.30571i q^{31} +(5.23358 - 2.14700i) q^{32} +(-2.12311 - 0.511240i) q^{34} -7.60669i q^{37} +(1.03399 - 4.29400i) q^{38} +5.83095i q^{41} +7.77769 q^{43} +(2.01051 - 3.93261i) q^{44} +(1.12311 - 4.66410i) q^{46} -10.7575 q^{47} +6.12311 q^{49} +(3.03632 - 5.93912i) q^{52} -5.08842 q^{53} +(2.01051 + 1.72424i) q^{56} +(2.79695 - 11.6153i) q^{58} +10.6937i q^{59} +(-11.4196 - 2.74983i) q^{62} +(-1.21922 - 7.90655i) q^{64} +12.1453 q^{67} +(-1.40582 + 2.74983i) q^{68} +11.7460 q^{71} -5.59390 q^{73} +(-10.4585 - 2.51840i) q^{74} +(-5.56155 - 2.84329i) q^{76} +2.06798 q^{77} +1.02248i q^{79} +(8.01706 + 1.93049i) q^{82} -14.0877i q^{83} +(2.57501 - 10.6937i) q^{86} +(-4.74137 - 4.06627i) q^{88} +13.0761i q^{89} +3.12311 q^{91} +(-6.04090 - 3.08835i) q^{92} +(-3.56155 + 14.7906i) q^{94} +2.18379 q^{97} +(2.02722 - 8.41874i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{4} - 12 q^{16} - 16 q^{19} + 32 q^{34} - 48 q^{46} + 32 q^{49} - 36 q^{64} - 56 q^{76} - 16 q^{91} - 24 q^{94}+O(q^{100}) $ 16 * q - 12 * q^4 - 12 * q^16 - 16 * q^19 + 32 * q^34 - 48 * q^46 + 32 * q^49 - 36 * q^64 - 56 * q^76 - 16 * q^91 - 24 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1001$	$1351$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.331077	−	1.37491i	0.234107	−	0.972211i
$2$	0.331077	−	1.37491i	0.234107	−	0.972211i
$3$		0			0
$3$		0			0
$4$	−1.78078	−	0.910404i	−0.890388	−	0.455202i
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	0.936426i		−	0.353936i	−0.984217	−	0.176968i	$-0.943371\pi$
$7$		−	0.936426i		−	0.353936i	0.984217	−	0.176968i	$-0.0566289\pi$
$8$	−1.84130	+	2.14700i	−0.650998	+	0.759079i
$9$		0			0
$10$		0			0
$11$			2.20837i			0.665848i	0.942954	+	0.332924i	$0.108035\pi$
$11$			2.20837i			0.665848i	−0.942954	+	0.332924i	$0.891965\pi$
$12$		0			0
$13$			3.33513i			0.924999i	0.886619	+	0.462500i	$0.153047\pi$
$13$			3.33513i			0.924999i	−0.886619	+	0.462500i	$0.846953\pi$
$14$	−1.28751	−	0.310029i	−0.344100	−	0.0828587i
$15$		0			0
$16$	2.34233	+	3.24245i	0.585582	+	0.810613i
$17$		−	1.54417i		−	0.374517i	−0.982311	−	0.187259i	$-0.940040\pi$
$17$		−	1.54417i		−	0.374517i	0.982311	−	0.187259i	$-0.0599602\pi$
$18$		0			0
$19$	3.12311			0.716490			0.358245	−	0.933628i	$-0.383375\pi$
$19$	3.12311			0.716490			0.358245	+	0.933628i	$0.383375\pi$
$20$		0			0
$21$		0			0
$22$	3.03632	+	0.731140i	0.647345	+	0.155879i
$23$	3.39228			0.707340			0.353670	−	0.935370i	$-0.384934\pi$
$23$	3.39228			0.707340			0.353670	+	0.935370i	$0.384934\pi$
$24$		0			0
$25$		0			0
$26$	4.58552	+	1.10418i	0.899294	+	0.216548i
$27$		0			0
$28$	−0.852526	+	1.66757i	−0.161112	+	0.315140i
$29$	8.44804			1.56876			0.784380	−	0.620280i	$-0.212981\pi$
$29$	8.44804			1.56876			0.784380	+	0.620280i	$0.212981\pi$
$30$		0			0
$31$		−	8.30571i		−	1.49175i	−0.666086	−	0.745875i	$-0.732032\pi$
$31$		−	8.30571i		−	1.49175i	0.666086	−	0.745875i	$-0.267968\pi$
$32$	5.23358	−	2.14700i	0.925175	−	0.379540i
$33$		0			0
$34$	−2.12311	−	0.511240i	−0.364110	−	0.0876769i
$35$		0			0
$36$		0			0
$37$		−	7.60669i		−	1.25053i	−0.780412	−	0.625266i	$-0.784990\pi$
$37$		−	7.60669i		−	1.25053i	0.780412	−	0.625266i	$-0.215010\pi$
$38$	1.03399	−	4.29400i	0.167735	−	0.696579i
$39$		0			0
$40$		0			0
$41$			5.83095i			0.910642i	0.890327	+	0.455321i	$0.150475\pi$
$41$			5.83095i			0.910642i	−0.890327	+	0.455321i	$0.849525\pi$
$42$		0			0
$43$	7.77769			1.18609			0.593043	−	0.805171i	$-0.297926\pi$
$43$	7.77769			1.18609			0.593043	+	0.805171i	$0.297926\pi$
$44$	2.01051	−	3.93261i	0.303095	−	0.592864i
$45$		0			0
$46$	1.12311	−	4.66410i	0.165593	−	0.687683i
$47$	−10.7575			−1.56914			−0.784570	−	0.620040i	$-0.787116\pi$
$47$	−10.7575			−1.56914			−0.784570	+	0.620040i	$0.787116\pi$
$48$		0			0
$49$	6.12311			0.874729
$50$		0			0
$51$		0			0
$52$	3.03632	−	5.93912i	0.421061	−	0.823608i
$53$	−5.08842			−0.698949			−0.349474	−	0.936946i	$-0.613640\pi$
$53$	−5.08842			−0.698949			−0.349474	+	0.936946i	$0.613640\pi$
$54$		0			0
$55$		0			0
$56$	2.01051	+	1.72424i	0.268665	+	0.230412i
$57$		0			0
$58$	2.79695	−	11.6153i	0.367257	−	1.52517i
$59$			10.6937i			1.39219i	0.717947	+	0.696097i	$0.245082\pi$
$59$			10.6937i			1.39219i	−0.717947	+	0.696097i	$0.754918\pi$
$60$		0			0
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$	−11.4196	−	2.74983i	−1.45030	−	0.349228i
$63$		0			0
$64$	−1.21922	−	7.90655i	−0.152403	−	0.988318i
$65$		0			0
$66$		0			0
$67$	12.1453			1.48378			0.741890	−	0.670521i	$-0.233929\pi$
$67$	12.1453			1.48378			0.741890	+	0.670521i	$0.233929\pi$
$68$	−1.40582	+	2.74983i	−0.170481	+	0.333466i
$69$		0			0
$70$		0			0
$71$	11.7460			1.39400			0.697000	−	0.717071i	$-0.254518\pi$
$71$	11.7460			1.39400			0.697000	+	0.717071i	$0.254518\pi$
$72$		0			0
$73$	−5.59390			−0.654716			−0.327358	−	0.944900i	$-0.606158\pi$
$73$	−5.59390			−0.654716			−0.327358	+	0.944900i	$0.606158\pi$
$74$	−10.4585	−	2.51840i	−1.21578	−	0.292758i
$75$		0			0
$76$	−5.56155	−	2.84329i	−0.637954	−	0.326147i
$77$	2.06798			0.235668
$78$		0			0
$79$			1.02248i			0.115038i	0.998344	+	0.0575190i	$0.0183190\pi$
$79$			1.02248i			0.115038i	−0.998344	+	0.0575190i	$0.981681\pi$
$80$		0			0
$81$		0			0
$82$	8.01706	+	1.93049i	0.885336	+	0.213187i
$83$		−	14.0877i		−	1.54632i	−0.634210	−	0.773161i	$-0.718675\pi$
$83$		−	14.0877i		−	1.54632i	0.634210	−	0.773161i	$-0.281325\pi$
$84$		0			0
$85$		0			0
$86$	2.57501	−	10.6937i	0.277671	−	1.15313i
$87$		0			0
$88$	−4.74137	−	4.06627i	−0.505432	−	0.433466i
$89$			13.0761i			1.38607i	0.720906	+	0.693033i	$0.243726\pi$
$89$			13.0761i			1.38607i	−0.720906	+	0.693033i	$0.756274\pi$
$90$		0			0
$91$	3.12311			0.327390
$92$	−6.04090	−	3.08835i	−0.629807	−	0.321982i
$93$		0			0
$94$	−3.56155	+	14.7906i	−0.367346	+	1.52554i
$95$		0			0
$96$		0			0
$97$	2.18379			0.221730			0.110865	−	0.993835i	$-0.464638\pi$
$97$	2.18379			0.221730			0.110865	+	0.993835i	$0.464638\pi$
$98$	2.02722	−	8.41874i	0.204780	−	0.850421i
$99$		0			0
$100$		0			0
$101$	−3.29801			−0.328165			−0.164082	−	0.986447i	$-0.552466\pi$
$101$	−3.29801			−0.328165			−0.164082	+	0.986447i	$0.552466\pi$
$102$		0			0
$103$		−	18.0227i		−	1.77583i	−0.460012	−	0.887913i	$-0.652155\pi$
$103$		−	18.0227i		−	1.77583i	0.460012	−	0.887913i	$-0.347845\pi$
$104$	−7.16053	−	6.14098i	−0.702148	−	0.602173i
$105$		0			0
$106$	−1.68466	+	6.99614i	−0.163628	+	0.679526i
$107$		−	10.9993i		−	1.06334i	−0.846950	−	0.531672i	$-0.821564\pi$
$107$		−	10.9993i		−	1.06334i	0.846950	−	0.531672i	$-0.178436\pi$
$108$		0			0
$109$		−	11.9473i		−	1.14435i	−0.820133	−	0.572173i	$-0.806100\pi$
$109$		−	11.9473i		−	1.14435i	0.820133	−	0.572173i	$-0.193900\pi$
$110$		0			0
$111$		0			0
$112$	3.03632	−	2.19342i	0.286905	−	0.207259i
$113$			12.5435i			1.17999i	0.807406	+	0.589996i	$0.200871\pi$
$113$			12.5435i			1.17999i	−0.807406	+	0.589996i	$0.799129\pi$
$114$		0			0
$115$		0			0
$116$	−15.0441	−	7.69113i	−1.39681	−	0.714103i
$117$		0			0
$118$	14.7028	+	3.54042i	1.35351	+	0.325922i
$119$	−1.44600			−0.132555
$120$		0			0
$121$	6.12311			0.556646
$122$		0			0
$123$		0			0
$124$	−7.56155	+	14.7906i	−0.679047	+	1.32824i
$125$		0			0
$126$		0			0
$127$		−	4.68213i		−	0.415472i	−0.978185	−	0.207736i	$-0.933391\pi$
$127$		−	4.68213i		−	0.415472i	0.978185	−	0.207736i	$-0.0666095\pi$
$128$	−11.2745	−	0.941346i	−0.996533	−	0.0832041i
$129$		0			0
$130$		0			0
$131$			0.620058i			0.0541747i	0.999633	+	0.0270874i	$0.00862323\pi$
$131$			0.620058i			0.0541747i	−0.999633	+	0.0270874i	$0.991377\pi$
$132$		0			0
$133$		−	2.92456i		−	0.253591i
$134$	4.02102	−	16.6987i	0.347363	−	1.44255i
$135$		0			0
$136$	3.31534	+	2.84329i	0.284288	+	0.243810i
$137$		−	1.54417i		−	0.131928i	−0.997822	−	0.0659638i	$-0.978988\pi$
$137$		−	1.54417i		−	0.131928i	0.997822	−	0.0659638i	$-0.0210122\pi$
$138$		0			0
$139$	12.0000			1.01783			0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000			1.01783			0.508913	+	0.860818i	$0.330047\pi$
$140$		0			0
$141$		0			0
$142$	3.88884	−	16.1498i	0.326345	−	1.35526i
$143$	−7.36520			−0.615909
$144$		0			0
$145$		0			0
$146$	−1.85201	+	7.69113i	−0.153273	+	0.636522i
$147$		0			0
$148$	−6.92516	+	13.5458i	−0.569245	+	1.11346i
$149$	1.85201			0.151722			0.0758612	−	0.997118i	$-0.475829\pi$
$149$	1.85201			0.151722			0.0758612	+	0.997118i	$0.475829\pi$
$150$		0			0
$151$			17.6339i			1.43503i	0.696545	+	0.717513i	$0.254720\pi$
$151$			17.6339i			1.43503i	−0.696545	+	0.717513i	$0.745280\pi$
$152$	−5.75058	+	6.70531i	−0.466433	+	0.543872i
$153$		0			0
$154$	0.684658	−	2.84329i	0.0551713	−	0.229119i
$155$		0			0
$156$		0			0
$157$			2.80928i			0.224205i	0.993697	+	0.112102i	$0.0357585\pi$
$157$			2.80928i			0.224205i	−0.993697	+	0.112102i	$0.964242\pi$
$158$	1.40582	+	0.338519i	0.111841	+	0.0269311i
$159$		0			0
$160$		0			0
$161$		−	3.17662i		−	0.250353i
$162$		0			0
$163$	15.5554			1.21839			0.609195	−	0.793020i	$-0.291492\pi$
$163$	15.5554			1.21839			0.609195	+	0.793020i	$0.291492\pi$
$164$	5.30852	−	10.3836i	0.414526	−	0.810825i
$165$		0			0
$166$	−19.3693	−	4.66410i	−1.50335	−	0.362004i
$167$	9.43318			0.729961			0.364981	−	0.931015i	$-0.381076\pi$
$167$	9.43318			0.729961			0.364981	+	0.931015i	$0.381076\pi$
$168$		0			0
$169$	1.87689			0.144376
$170$		0			0
$171$		0			0
$172$	−13.8503	−	7.08084i	−1.05608	−	0.539909i
$173$	1.69614			0.128955			0.0644776	−	0.997919i	$-0.479462\pi$
$173$	1.69614			0.128955			0.0644776	+	0.997919i	$0.479462\pi$
$174$		0			0
$175$		0			0
$176$	−7.16053	+	5.17273i	−0.539745	+	0.389909i
$177$		0			0
$178$	17.9785	+	4.32920i	1.34755	+	0.324487i
$179$			8.21342i			0.613900i	0.951726	+	0.306950i	$0.0993084\pi$
$179$			8.21342i			0.613900i	−0.951726	+	0.306950i	$0.900692\pi$
$180$		0			0
$181$			4.66410i			0.346680i	0.984862	+	0.173340i	$0.0554559\pi$
$181$			4.66410i			0.346680i	−0.984862	+	0.173340i	$0.944544\pi$
$182$	1.03399	−	4.29400i	0.0766443	−	0.318293i
$183$		0			0
$184$	−6.24621	+	7.28323i	−0.460477	+	0.536927i
$185$		0			0
$186$		0			0
$187$	3.41011			0.249372
$188$	19.1567	+	9.79366i	1.39714	+	0.714276i
$189$		0			0
$190$		0			0
$191$	−13.1921			−0.954544			−0.477272	−	0.878756i	$-0.658374\pi$
$191$	−13.1921			−0.954544			−0.477272	+	0.878756i	$0.658374\pi$
$192$		0			0
$193$	−23.3331			−1.67955			−0.839775	−	0.542934i	$-0.817313\pi$
$193$	−23.3331			−1.67955			−0.839775	+	0.542934i	$0.817313\pi$
$194$	0.723002	−	3.00252i	0.0519085	−	0.215569i
$195$		0			0
$196$	−10.9039	−	5.57450i	−0.778849	−	0.398179i
$197$	4.92539			0.350920			0.175460	−	0.984487i	$-0.443859\pi$
$197$	4.92539			0.350920			0.175460	+	0.984487i	$0.443859\pi$
$198$		0			0
$199$		−	17.6339i		−	1.25003i	−0.780611	−	0.625017i	$-0.785092\pi$
$199$		−	17.6339i		−	1.25003i	0.780611	−	0.625017i	$-0.214908\pi$
$200$		0			0
$201$		0			0
$202$	−1.09190	+	4.53448i	−0.0768255	+	0.319045i
$203$		−	7.91096i		−	0.555241i
$204$		0			0
$205$		0			0
$206$	−24.7796	−	5.96688i	−1.72648	−	0.415732i
$207$		0			0
$208$	−10.8140	+	7.81198i	−0.749816	+	0.541663i
$209$			6.89697i			0.477073i
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	9.06134	+	4.63252i	0.622336	+	0.318163i
$213$		0			0
$214$	−15.1231	−	3.64162i	−1.03379	−	0.248936i
$215$		0			0
$216$		0			0
$217$	−7.77769			−0.527984
$218$	−16.4265	−	3.95548i	−1.11255	−	0.267899i
$219$		0			0
$220$		0			0
$221$	5.15002			0.346428
$222$		0			0
$223$			21.9989i			1.47316i	0.676352	+	0.736578i	$0.263560\pi$
$223$			21.9989i			1.47316i	−0.676352	+	0.736578i	$0.736440\pi$
$224$	−2.01051	−	4.90086i	−0.134333	−	0.327453i
$225$		0			0
$226$	17.2462	+	4.15286i	1.14720	+	0.276244i
$227$		−	3.08835i		−	0.204981i	−0.994734	−	0.102490i	$-0.967319\pi$
$227$		−	3.08835i		−	0.204981i	0.994734	−	0.102490i	$-0.0326811\pi$
$228$		0			0
$229$		−	2.61914i		−	0.173077i	−0.996248	−	0.0865387i	$-0.972419\pi$
$229$		−	2.61914i		−	0.173077i	0.996248	−	0.0865387i	$-0.0275806\pi$
$230$		0			0
$231$		0			0
$232$	−15.5554	+	18.1379i	−1.02126	+	1.19081i
$233$			20.4544i			1.34002i	0.742354	+	0.670008i	$0.233709\pi$
$233$			20.4544i			1.34002i	−0.742354	+	0.670008i	$0.766291\pi$
$234$		0			0
$235$		0			0
$236$	9.73554	−	19.0430i	0.633730	−	1.23959i
$237$		0			0
$238$	−0.478739	+	1.98813i	−0.0310320	+	0.128871i
$239$	23.4921			1.51958			0.759789	−	0.650170i	$-0.225302\pi$
$239$	23.4921			1.51958			0.759789	+	0.650170i	$0.225302\pi$
$240$		0			0
$241$	−4.00000			−0.257663			−0.128831	−	0.991667i	$-0.541123\pi$
$241$	−4.00000			−0.257663			−0.128831	+	0.991667i	$0.541123\pi$
$242$	2.02722	−	8.41874i	0.130314	−	0.541177i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$			10.4160i			0.662752i
$248$	17.8324	+	15.2933i	1.13236	+	0.971126i
$249$		0			0
$250$		0			0
$251$			3.44849i			0.217666i	0.994060	+	0.108833i	$0.0347114\pi$
$251$			3.44849i			0.217666i	−0.994060	+	0.108833i	$0.965289\pi$
$252$		0			0
$253$			7.49141i			0.470981i
$254$	−6.43753	−	1.55014i	−0.403926	−	0.0972647i
$255$		0			0
$256$	−5.02699	+	15.1898i	−0.314187	+	0.949361i
$257$			15.6318i			0.975087i	0.873099	+	0.487543i	$0.162107\pi$
$257$			15.6318i			0.975087i	−0.873099	+	0.487543i	$0.837893\pi$
$258$		0			0
$259$	−7.12311			−0.442608
$260$		0			0
$261$		0			0
$262$	0.852526	+	0.205287i	0.0526693	+	0.0126827i
$263$	−14.7304			−0.908316			−0.454158	−	0.890921i	$-0.650060\pi$
$263$	−14.7304			−0.908316			−0.454158	+	0.890921i	$0.650060\pi$
$264$		0			0
$265$		0			0
$266$	−4.02102	−	0.968253i	−0.246544	−	0.0593674i
$267$		0			0
$268$	−21.6280	−	11.0571i	−1.32114	−	0.675420i
$269$	−15.0441			−0.917253			−0.458626	−	0.888629i	$-0.651658\pi$
$269$	−15.0441			−0.917253			−0.458626	+	0.888629i	$0.651658\pi$
$270$		0			0
$271$		−	10.3507i		−	0.628758i	−0.949297	−	0.314379i	$-0.898204\pi$
$271$		−	10.3507i		−	0.628758i	0.949297	−	0.314379i	$-0.101796\pi$
$272$	5.00691	−	3.61696i	0.303588	−	0.219311i
$273$		0			0
$274$	−2.12311	−	0.511240i	−0.128262	−	0.0308851i
$275$		0			0
$276$		0			0
$277$			23.3459i			1.40272i	0.712807	+	0.701360i	$0.247424\pi$
$277$			23.3459i			1.40272i	−0.712807	+	0.701360i	$0.752576\pi$
$278$	3.97292	−	16.4990i	0.238280	−	0.989542i
$279$		0			0
$280$		0			0
$281$			3.00252i			0.179116i	0.995982	+	0.0895578i	$0.0285454\pi$
$281$			3.00252i			0.179116i	−0.995982	+	0.0895578i	$0.971455\pi$
$282$		0			0
$283$	23.3331			1.38701			0.693503	−	0.720453i	$-0.256066\pi$
$283$	23.3331			1.38701			0.693503	+	0.720453i	$0.256066\pi$
$284$	−20.9171	−	10.6937i	−1.24120	−	0.634551i
$285$		0			0
$286$	−2.43845	+	10.1265i	−0.144188	+	0.598794i
$287$	5.46026			0.322309
$288$		0			0
$289$	14.6155			0.859737
$290$		0			0
$291$		0			0
$292$	9.96148	+	5.09271i	0.582951	+	0.298028i
$293$	29.8326			1.74284			0.871421	−	0.490536i	$-0.163199\pi$
$293$	29.8326			1.74284			0.871421	+	0.490536i	$0.163199\pi$
$294$		0			0
$295$		0			0
$296$	16.3316	+	14.0062i	0.949253	+	0.814094i
$297$		0			0
$298$	0.613157	−	2.54635i	0.0355192	−	0.147506i
$299$			11.3137i			0.654289i
$300$		0			0
$301$		−	7.28323i		−	0.419799i
$302$	24.2451	+	5.83817i	1.39515	+	0.335949i
$303$		0			0
$304$	7.31534	+	10.1265i	0.419564	+	0.580796i
$305$		0			0
$306$		0			0
$307$	−4.36758			−0.249271			−0.124636	−	0.992203i	$-0.539776\pi$
$307$	−4.36758			−0.249271			−0.124636	+	0.992203i	$0.539776\pi$
$308$	−3.68260	−	1.88269i	−0.209836	−	0.107276i
$309$		0			0
$310$		0			0
$311$	−10.3000			−0.584062			−0.292031	−	0.956409i	$-0.594331\pi$
$311$	−10.3000			−0.584062			−0.292031	+	0.956409i	$0.594331\pi$
$312$		0			0
$313$	−32.0682			−1.81260			−0.906302	−	0.422631i	$-0.861107\pi$
$313$	−32.0682			−1.81260			−0.906302	+	0.422631i	$0.861107\pi$
$314$	3.86252	+	0.930087i	0.217974	+	0.0524878i
$315$		0			0
$316$	0.930870	−	1.82081i	0.0523655	−	0.102428i
$317$	−24.5354			−1.37805			−0.689023	−	0.724739i	$-0.741960\pi$
$317$	−24.5354			−1.37805			−0.689023	+	0.724739i	$0.741960\pi$
$318$		0			0
$319$			18.6564i			1.04456i
$320$		0			0
$321$		0			0
$322$	−4.36758	−	1.05171i	−0.243396	−	0.0586093i
$323$		−	4.82262i		−	0.268338i
$324$		0			0
$325$		0			0
$326$	5.15002	−	21.3873i	0.285233	−	1.18453i
$327$		0			0
$328$	−12.5191	−	10.7365i	−0.691249	−	0.592826i
$329$			10.0736i			0.555375i
$330$		0			0
$331$	−1.36932			−0.0752645			−0.0376322	−	0.999292i	$-0.511982\pi$
$331$	−1.36932			−0.0752645			−0.0376322	+	0.999292i	$0.511982\pi$
$332$	−12.8255	+	25.0870i	−0.703889	+	1.37683i
$333$		0			0
$334$	3.12311	−	12.9698i	0.170889	−	0.709676i
$335$		0			0
$336$		0			0
$337$	−29.8844			−1.62791			−0.813954	−	0.580929i	$-0.802690\pi$
$337$	−29.8844			−1.62791			−0.813954	+	0.580929i	$0.802690\pi$
$338$	0.621396	−	2.58057i	0.0337995	−	0.140364i
$339$		0			0
$340$		0			0
$341$	18.3421			0.993279
$342$		0			0
$343$		−	12.2888i		−	0.663534i
$344$	−14.3211	+	16.6987i	−0.772140	+	0.900334i
$345$		0			0
$346$	0.561553	−	2.33205i	0.0301893	−	0.125372i
$347$			14.0877i			0.756265i	0.925751	+	0.378133i	$0.123434\pi$
$347$			14.0877i			0.756265i	−0.925751	+	0.378133i	$0.876566\pi$
$348$		0			0
$349$			33.2228i			1.77838i	0.457540	+	0.889189i	$0.348731\pi$
$349$			33.2228i			1.77838i	−0.457540	+	0.889189i	$0.651269\pi$
$350$		0			0
$351$		0			0
$352$	4.74137	+	11.5577i	0.252716	+	0.616027i
$353$		−	7.72087i		−	0.410940i	−0.978663	−	0.205470i	$-0.934128\pi$
$353$		−	7.72087i		−	0.410940i	0.978663	−	0.205470i	$-0.0658724\pi$
$354$		0			0
$355$		0			0
$356$	11.9045	−	23.2856i	0.630940	−	1.23414i
$357$		0			0
$358$	11.2927	+	2.71927i	0.596840	+	0.143718i
$359$	−1.44600			−0.0763172			−0.0381586	−	0.999272i	$-0.512149\pi$
$359$	−1.44600			−0.0763172			−0.0381586	+	0.999272i	$0.512149\pi$
$360$		0			0
$361$	−9.24621			−0.486643
$362$	6.41273	+	1.54417i	0.337046	+	0.0811600i
$363$		0			0
$364$	−5.56155	−	2.84329i	−0.291505	−	0.149029i
$365$		0			0
$366$		0			0
$367$		−	32.4149i		−	1.69204i	−0.533148	−	0.846022i	$-0.678991\pi$
$367$		−	32.4149i		−	1.69204i	0.533148	−	0.846022i	$-0.321009\pi$
$368$	7.94584	+	10.9993i	0.414206	+	0.573379i
$369$		0			0
$370$		0			0
$371$			4.76493i			0.247383i
$372$		0			0
$373$			9.47954i			0.490832i	0.969418	+	0.245416i	$0.0789246\pi$
$373$			9.47954i			0.490832i	−0.969418	+	0.245416i	$0.921075\pi$
$374$	1.12901	−	4.68860i	0.0583795	−	0.242442i
$375$		0			0
$376$	19.8078	−	23.0963i	1.02151	−	1.19110i
$377$			28.1753i			1.45110i
$378$		0			0
$379$	16.4924			0.847159			0.423579	−	0.905859i	$-0.360773\pi$
$379$	16.4924			0.847159			0.423579	+	0.905859i	$0.360773\pi$
$380$		0			0
$381$		0			0
$382$	−4.36758	+	18.1379i	−0.223465	+	0.928018i
$383$	10.0138			0.511682			0.255841	−	0.966719i	$-0.417648\pi$
$383$	10.0138			0.511682			0.255841	+	0.966719i	$0.417648\pi$
$384$		0			0
$385$		0			0
$386$	−7.72503	+	32.0810i	−0.393194	+	1.63288i
$387$		0			0
$388$	−3.88884	−	1.98813i	−0.197426	−	0.100932i
$389$	9.89404			0.501648			0.250824	−	0.968033i	$-0.419298\pi$
$389$	9.89404			0.501648			0.250824	+	0.968033i	$0.419298\pi$
$390$		0			0
$391$		−	5.23827i		−	0.264911i
$392$	−11.2745	+	13.1463i	−0.569447	+	0.663989i
$393$		0			0
$394$	1.63068	−	6.77199i	0.0821526	−	0.341168i
$395$		0			0
$396$		0			0
$397$			10.3007i			0.516977i	0.966014	+	0.258488i	$0.0832244\pi$
$397$			10.3007i			0.516977i	−0.966014	+	0.258488i	$0.916776\pi$
$398$	−24.2451	−	5.83817i	−1.21530	−	0.292641i
$399$		0			0
$400$		0			0
$401$			0.522293i			0.0260821i	0.999915	+	0.0130410i	$0.00415121\pi$
$401$			0.522293i			0.0260821i	−0.999915	+	0.0130410i	$0.995849\pi$
$402$		0			0
$403$	27.7006			1.37987
$404$	5.87302	+	3.00252i	0.292194	+	0.149381i
$405$		0			0
$406$	−10.8769	−	2.61914i	−0.539811	−	0.129986i
$407$	16.7984			0.832665
$408$		0			0
$409$	−3.12311			−0.154428			−0.0772138	−	0.997015i	$-0.524602\pi$
$409$	−3.12311			−0.154428			−0.0772138	+	0.997015i	$0.524602\pi$
$410$		0			0
$411$		0			0
$412$	−16.4079	+	32.0943i	−0.808359	+	1.58117i
$413$	10.0138			0.492748
$414$		0			0
$415$		0			0
$416$	7.16053	+	17.4547i	0.351074	+	0.855787i
$417$		0			0
$418$	9.48274	+	2.28343i	0.463816	+	0.111686i
$419$		−	32.4291i		−	1.58427i	−0.610348	−	0.792134i	$-0.708970\pi$
$419$		−	32.4291i		−	1.58427i	0.610348	−	0.792134i	$-0.291030\pi$
$420$		0			0
$421$		−	30.6037i		−	1.49153i	−0.666207	−	0.745767i	$-0.732083\pi$
$421$		−	30.6037i		−	1.49153i	0.666207	−	0.745767i	$-0.267917\pi$
$422$	1.32431	−	5.49966i	0.0644663	−	0.267719i
$423$		0			0
$424$	9.36932	−	10.9248i	0.455014	−	0.530558i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−10.0138	+	19.5873i	−0.484036	+	0.946789i
$429$		0			0
$430$		0			0
$431$	−1.44600			−0.0696516			−0.0348258	−	0.999393i	$-0.511088\pi$
$431$	−1.44600			−0.0696516			−0.0348258	+	0.999393i	$0.511088\pi$
$432$		0			0
$433$	−15.5554			−0.747544			−0.373772	−	0.927521i	$-0.621936\pi$
$433$	−15.5554			−0.747544			−0.373772	+	0.927521i	$0.621936\pi$
$434$	−2.57501	+	10.6937i	−0.123604	+	0.513312i
$435$		0			0
$436$	−10.8769	+	21.2755i	−0.520909	+	1.01891i
$437$	10.5945			0.506802
$438$		0			0
$439$		−	26.9621i		−	1.28683i	−0.765517	−	0.643415i	$-0.777517\pi$
$439$		−	26.9621i		−	1.28683i	0.765517	−	0.643415i	$-0.222483\pi$
$440$		0			0
$441$		0			0
$442$	1.70505	−	7.08084i	0.0811011	−	0.336801i
$443$		−	25.0870i		−	1.19192i	−0.803015	−	0.595959i	$-0.796772\pi$
$443$		−	25.0870i		−	1.19192i	0.803015	−	0.595959i	$-0.203228\pi$
$444$		0			0
$445$		0			0
$446$	30.2466	+	7.28333i	1.43222	+	0.344876i
$447$		0			0
$448$	−7.40390	+	1.14171i	−0.349801	+	0.0539409i
$449$		−	9.89949i		−	0.467186i	−0.972334	−	0.233593i	$-0.924952\pi$
$449$		−	9.89949i		−	0.467186i	0.972334	−	0.233593i	$-0.0750483\pi$
$450$		0			0
$451$	−12.8769			−0.606349
$452$	11.4196	−	22.3371i	0.537135	−	1.05065i
$453$		0			0
$454$	−4.24621	−	1.02248i	−0.199285	−	0.0479874i
$455$		0			0
$456$		0			0
$457$	−13.3716			−0.625496			−0.312748	−	0.949836i	$-0.601250\pi$
$457$	−13.3716			−0.625496			−0.312748	+	0.949836i	$0.601250\pi$
$458$	−3.60109	−	0.867135i	−0.168268	−	0.0405186i
$459$		0			0
$460$		0			0
$461$	−1.85201			−0.0862567			−0.0431283	−	0.999070i	$-0.513732\pi$
$461$	−1.85201			−0.0862567			−0.0431283	+	0.999070i	$0.513732\pi$
$462$		0			0
$463$			13.2252i			0.614629i	0.951608	+	0.307315i	$0.0994304\pi$
$463$			13.2252i			0.614629i	−0.951608	+	0.307315i	$0.900570\pi$
$464$	19.7881	+	27.3924i	0.918639	+	1.27166i
$465$		0			0
$466$	28.1231	+	6.77199i	1.30278	+	0.313706i
$467$		−	18.9103i		−	0.875063i	−0.899203	−	0.437532i	$-0.855853\pi$
$467$		−	18.9103i		−	0.875063i	0.899203	−	0.437532i	$-0.144147\pi$
$468$		0			0
$469$		−	11.3732i		−	0.525163i
$470$		0			0
$471$		0			0
$472$	−22.9593	−	19.6902i	−1.05679	−	0.906316i
$473$			17.1760i			0.789754i
$474$		0			0
$475$		0			0
$476$	2.57501	+	1.31645i	0.118025	+	0.0603393i
$477$		0			0
$478$	7.77769	−	32.2996i	0.355743	−	1.47735i
$479$	14.6381			0.668830			0.334415	−	0.942426i	$-0.391461\pi$
$479$	14.6381			0.668830			0.334415	+	0.942426i	$0.391461\pi$
$480$		0			0
$481$	25.3693			1.15674
$482$	−1.32431	+	5.49966i	−0.0603205	+	0.250502i
$483$		0			0
$484$	−10.9039	−	5.57450i	−0.495631	−	0.253386i
$485$		0			0
$486$		0			0
$487$			29.4903i			1.33633i	0.744011	+	0.668167i	$0.232921\pi$
$487$			29.4903i			1.33633i	−0.744011	+	0.668167i	$0.767079\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			16.3505i			0.737888i	0.929452	+	0.368944i	$0.120281\pi$
$491$			16.3505i			0.737888i	−0.929452	+	0.368944i	$0.879719\pi$
$492$		0			0
$493$		−	13.0452i		−	0.587528i
$494$	14.3211	+	3.44849i	0.644335	+	0.155155i
$495$		0			0
$496$	26.9309	−	19.4547i	1.20923	−	0.873542i
$497$		−	10.9993i		−	0.493387i
$498$		0			0
$499$	−16.8769			−0.755514			−0.377757	−	0.925905i	$-0.623304\pi$
$499$	−16.8769			−0.755514			−0.377757	+	0.925905i	$0.623304\pi$
$500$		0			0
$501$		0			0
$502$	4.74137	+	1.14171i	0.211618	+	0.0509572i
$503$	−16.0547			−0.715844			−0.357922	−	0.933751i	$-0.616515\pi$
$503$	−16.0547			−0.715844			−0.357922	+	0.933751i	$0.616515\pi$
$504$		0			0
$505$		0			0
$506$	10.3000	+	2.48023i	0.457893	+	0.110260i
$507$		0			0
$508$	−4.26263	+	8.33783i	−0.189124	+	0.369931i
$509$	3.29801			0.146182			0.0730909	−	0.997325i	$-0.476714\pi$
$509$	3.29801			0.146182			0.0730909	+	0.997325i	$0.476714\pi$
$510$		0			0
$511$			5.23827i			0.231728i
$512$	19.2203	+	11.9407i	0.849426	+	0.527707i
$513$		0			0
$514$	21.4924	+	5.17534i	0.947990	+	0.228274i
$515$		0			0
$516$		0			0
$517$		−	23.7565i		−	1.04481i
$518$	−2.35829	+	9.79366i	−0.103618	+	0.430309i
$519$		0			0
$520$		0			0
$521$			2.65433i			0.116288i	0.998308	+	0.0581441i	$0.0185183\pi$
$521$			2.65433i			0.116288i	−0.998308	+	0.0581441i	$0.981482\pi$
$522$		0			0
$523$	−4.36758			−0.190981			−0.0954905	−	0.995430i	$-0.530442\pi$
$523$	−4.36758			−0.190981			−0.0954905	+	0.995430i	$0.530442\pi$
$524$	0.564503	−	1.10418i	0.0246604	−	0.0482365i
$525$		0			0
$526$	−4.87689	+	20.2530i	−0.212643	+	0.883074i
$527$	−12.8255			−0.558686
$528$		0			0
$529$	−11.4924			−0.499671
$530$		0			0
$531$		0			0
$532$	−2.66253	+	5.20798i	−0.115435	+	0.225795i
$533$	−19.4470			−0.842343
$534$		0			0
$535$		0			0
$536$	−22.3631	+	26.0759i	−0.965939	+	1.12631i
$537$		0			0
$538$	−4.98074	+	20.6843i	−0.214735	+	0.891763i
$539$			13.5221i			0.582437i
$540$		0			0
$541$			9.90237i			0.425736i	0.977081	+	0.212868i	$0.0682804\pi$
$541$			9.90237i			0.425736i	−0.977081	+	0.212868i	$0.931720\pi$
$542$	−14.2313	−	3.42687i	−0.611286	−	0.147197i
$543$		0			0
$544$	−3.31534	−	8.08156i	−0.142144	−	0.346494i
$545$		0			0
$546$		0			0
$547$	−16.5129			−0.706039			−0.353019	−	0.935616i	$-0.614845\pi$
$547$	−16.5129			−0.706039			−0.353019	+	0.935616i	$0.614845\pi$
$548$	−1.40582	+	2.74983i	−0.0600537	+	0.117467i
$549$		0			0
$550$		0			0
$551$	26.3841			1.12400
$552$		0			0
$553$	0.957477			0.0407161
$554$	32.0986	+	7.72929i	1.36374	+	0.328386i
$555$		0			0
$556$	−21.3693	−	10.9248i	−0.906261	−	0.463317i
$557$	32.6443			1.38318			0.691591	−	0.722289i	$-0.256910\pi$
$557$	32.6443			1.38318			0.691591	+	0.722289i	$0.256910\pi$
$558$		0			0
$559$			25.9396i			1.09713i
$560$		0			0
$561$		0			0
$562$	4.12821	+	0.994066i	0.174138	+	0.0419321i
$563$			14.0877i			0.593724i	0.954920	+	0.296862i	$0.0959401\pi$
$563$			14.0877i			0.593724i	−0.954920	+	0.296862i	$0.904060\pi$
$564$		0			0
$565$		0			0
$566$	7.72503	−	32.0810i	0.324707	−	1.34846i
$567$		0			0
$568$	−21.6280	+	25.2188i	−0.907491	+	1.05816i
$569$		−	30.0467i		−	1.25962i	−0.776748	−	0.629811i	$-0.783132\pi$
$569$		−	30.0467i		−	1.25962i	0.776748	−	0.629811i	$-0.216868\pi$
$570$		0			0
$571$	33.8617			1.41707			0.708535	−	0.705676i	$-0.249356\pi$
$571$	33.8617			1.41707			0.708535	+	0.705676i	$0.249356\pi$
$572$	13.1158	+	6.70531i	0.548398	+	0.280363i
$573$		0			0
$574$	1.80776	−	7.50738i	0.0754546	−	0.313352i
$575$		0			0
$576$		0			0
$577$	7.77769			0.323789			0.161895	−	0.986808i	$-0.448240\pi$
$577$	7.77769			0.323789			0.161895	+	0.986808i	$0.448240\pi$
$578$	4.83886	−	20.0951i	0.201270	−	0.835846i
$579$		0			0
$580$		0			0
$581$	−13.1921			−0.547299
$582$		0			0
$583$		−	11.2371i		−	0.465394i
$584$	10.3000	−	12.0101i	0.426219	−	0.496981i
$585$		0			0
$586$	9.87689	−	41.0173i	0.408011	−	1.69441i
$587$			10.9993i			0.453990i	0.973896	+	0.226995i	$0.0728901\pi$
$587$			10.9993i			0.453990i	−0.973896	+	0.226995i	$0.927110\pi$
$588$		0			0
$589$		−	25.9396i		−	1.06882i
$590$		0			0
$591$		0			0
$592$	24.6643	−	17.8174i	1.01370	−	0.732290i
$593$			43.8071i			1.79894i	0.436978	+	0.899472i	$0.356049\pi$
$593$			43.8071i			1.79894i	−0.436978	+	0.899472i	$0.643951\pi$
$594$		0			0
$595$		0			0
$596$	−3.29801	−	1.68608i	−0.135092	−	0.0690644i
$597$		0			0
$598$	15.5554	+	3.74571i	0.636107	+	0.153173i
$599$	−45.5382			−1.86064			−0.930320	−	0.366749i	$-0.880471\pi$
$599$	−45.5382			−1.86064			−0.930320	+	0.366749i	$0.880471\pi$
$600$		0			0
$601$	−23.3693			−0.953254			−0.476627	−	0.879106i	$-0.658141\pi$
$601$	−23.3693			−0.953254			−0.476627	+	0.879106i	$0.658141\pi$
$602$	−10.0138	−	2.41131i	−0.408133	−	0.0982776i
$603$		0			0
$604$	16.0540	−	31.4020i	0.653227	−	1.27773i
$605$		0			0
$606$		0			0
$607$			9.71010i			0.394121i	0.980391	+	0.197060i	$0.0631395\pi$
$607$			9.71010i			0.394121i	−0.980391	+	0.197060i	$0.936860\pi$
$608$	16.3450	−	6.70531i	0.662879	−	0.271936i
$609$		0			0
$610$		0			0
$611$		−	35.8776i		−	1.45145i
$612$		0			0
$613$			23.8718i			0.964172i	0.876124	+	0.482086i	$0.160121\pi$
$613$			23.8718i			0.964172i	−0.876124	+	0.482086i	$0.839879\pi$
$614$	−1.44600	+	6.00505i	−0.0583560	+	0.242344i
$615$		0			0
$616$	−3.80776	+	4.43994i	−0.153419	+	0.178890i
$617$		−	15.6318i		−	0.629314i	−0.949205	−	0.314657i	$-0.898111\pi$
$617$		−	15.6318i		−	0.629314i	0.949205	−	0.314657i	$-0.101889\pi$
$618$		0			0
$619$	−18.7386			−0.753169			−0.376585	−	0.926382i	$-0.622902\pi$
$619$	−18.7386			−0.753169			−0.376585	+	0.926382i	$0.622902\pi$
$620$		0			0
$621$		0			0
$622$	−3.41011	+	14.1617i	−0.136733	+	0.567831i
$623$	12.2448			0.490578
$624$		0			0
$625$		0			0
$626$	−10.6170	+	44.0911i	−0.424342	+	1.76223i
$627$		0			0
$628$	2.55758	−	5.00270i	0.102059	−	0.199629i
$629$	−11.7460			−0.468346
$630$		0			0
$631$			17.6339i			0.701995i	0.936376	+	0.350997i	$0.114157\pi$
$631$			17.6339i			0.701995i	−0.936376	+	0.350997i	$0.885843\pi$
$632$	−2.19526	−	1.88269i	−0.0873229	−	0.0748895i
$633$		0			0
$634$	−8.12311	+	33.7341i	−0.322610	+	1.33975i
$635$		0			0
$636$		0			0
$637$			20.4214i			0.809124i
$638$	25.6509	+	6.17669i	1.01553	+	0.244538i
$639$		0			0
$640$		0			0
$641$			7.07107i			0.279290i	0.990202	+	0.139645i	$0.0445962\pi$
$641$			7.07107i			0.279290i	−0.990202	+	0.139645i	$0.955404\pi$
$642$		0			0
$643$	−8.73516			−0.344481			−0.172241	−	0.985055i	$-0.555101\pi$
$643$	−8.73516			−0.344481			−0.172241	+	0.985055i	$0.555101\pi$
$644$	−2.89201	+	5.65685i	−0.113961	+	0.222911i
$645$		0			0
$646$	−6.63068	−	1.59666i	−0.260881	−	0.0628196i
$647$	1.32431			0.0520639			0.0260319	−	0.999661i	$-0.491713\pi$
$647$	1.32431			0.0520639			0.0260319	+	0.999661i	$0.491713\pi$
$648$		0			0
$649$	−23.6155			−0.926991
$650$		0			0
$651$		0			0
$652$	−27.7006	−	14.1617i	−1.08484	−	0.554614i
$653$	−15.8459			−0.620098			−0.310049	−	0.950721i	$-0.600346\pi$
$653$	−15.8459			−0.620098			−0.310049	+	0.950721i	$0.600346\pi$
$654$		0			0
$655$		0			0
$656$	−18.9066	+	13.6580i	−0.738178	+	0.533256i
$657$		0			0
$658$	13.8503	+	3.33513i	0.539942	+	0.130017i
$659$		−	33.3211i		−	1.29800i	−0.760786	−	0.649002i	$-0.775187\pi$
$659$		−	33.3211i		−	1.29800i	0.760786	−	0.649002i	$-0.224813\pi$
$660$		0			0
$661$			44.5960i			1.73458i	0.497800	+	0.867292i	$0.334141\pi$
$661$			44.5960i			1.73458i	−0.497800	+	0.867292i	$0.665859\pi$
$662$	−0.453349	+	1.88269i	−0.0176199	+	0.0731729i
$663$		0			0
$664$	30.2462	+	25.9396i	1.17378	+	1.00665i
$665$		0			0
$666$		0			0
$667$	28.6581			1.10965
$668$	−16.7984	−	8.58800i	−0.649949	−	0.332280i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0			−	1.00000i	$-0.5\pi$
$673$		0			0				1.00000i	$0.5\pi$
$674$	−9.89404	+	41.0885i	−0.381104	+	1.58267i
$675$		0			0
$676$	−3.34233	−	1.70873i	−0.128551	−	0.0657205i
$677$	5.25145			0.201830			0.100915	−	0.994895i	$-0.467823\pi$
$677$	5.25145			0.201830			0.100915	+	0.994895i	$0.467823\pi$
$678$		0			0
$679$		−	2.04496i		−	0.0784783i
$680$		0			0
$681$		0			0
$682$	6.07263	−	25.2188i	0.232533	−	0.965677i
$683$		−	20.2644i		−	0.775394i	−0.921787	−	0.387697i	$-0.873271\pi$
$683$		−	20.2644i		−	0.775394i	0.921787	−	0.387697i	$-0.126729\pi$
$684$		0			0
$685$		0			0
$686$	−16.8961	−	4.06854i	−0.645095	−	0.155338i
$687$		0			0
$688$	18.2179	+	25.2188i	0.694551	+	0.961457i
$689$		−	16.9706i		−	0.646527i
$690$		0			0
$691$	−23.1231			−0.879644			−0.439822	−	0.898085i	$-0.644959\pi$
$691$	−23.1231			−0.879644			−0.439822	+	0.898085i	$0.644959\pi$
$692$	−3.02045	−	1.54417i	−0.114820	−	0.0587007i
$693$		0			0
$694$	19.3693	+	4.66410i	0.735249	+	0.177047i
$695$		0			0
$696$		0			0
$697$	9.00400			0.341051
$698$	45.6786	+	10.9993i	1.72896	+	0.416330i
$699$		0			0
$700$		0			0
$701$	−20.1941			−0.762720			−0.381360	−	0.924427i	$-0.624544\pi$
$701$	−20.1941			−0.762720			−0.381360	+	0.924427i	$0.624544\pi$
$702$		0			0
$703$		−	23.7565i		−	0.895993i
$704$	17.4606	−	2.69250i	0.658070	−	0.101477i
$705$		0			0
$706$	−10.6155	−	2.55620i	−0.399521	−	0.0962038i
$707$			3.08835i			0.116149i
$708$		0			0
$709$			30.6037i			1.14935i	0.818383	+	0.574673i	$0.194871\pi$
$709$			30.6037i			1.14935i	−0.818383	+	0.574673i	$0.805129\pi$
$710$		0			0
$711$		0			0
$712$	−28.0744	−	24.0771i	−1.05213	−	0.902326i
$713$		−	28.1753i		−	1.05517i
$714$		0			0
$715$		0			0
$716$	7.47753	−	14.6263i	0.279448	−	0.546609i
$717$		0			0
$718$	−0.478739	+	1.98813i	−0.0178664	+	0.0741964i
$719$	−32.3461			−1.20631			−0.603154	−	0.797625i	$-0.706089\pi$
$719$	−32.3461			−1.20631			−0.603154	+	0.797625i	$0.706089\pi$
$720$		0			0
$721$	−16.8769			−0.628528
$722$	−3.06121	+	12.7127i	−0.113926	+	0.473119i
$723$		0			0
$724$	4.24621	−	8.30571i	0.157809	−	0.308679i
$725$		0			0
$726$		0			0
$727$			9.47954i			0.351577i	0.984428	+	0.175788i	$0.0562475\pi$
$727$			9.47954i			0.351577i	−0.984428	+	0.175788i	$0.943753\pi$
$728$	−5.75058	+	6.70531i	−0.213131	+	0.248515i
$729$		0			0
$730$		0			0
$731$		−	12.0101i		−	0.444210i
$732$		0			0
$733$			19.6002i			0.723951i	0.932188	+	0.361975i	$0.117898\pi$
$733$			19.6002i			0.723951i	−0.932188	+	0.361975i	$0.882102\pi$
$734$	−44.5677	−	10.7318i	−1.64502	−	0.396119i
$735$		0			0
$736$	17.7538	−	7.28323i	0.654413	−	0.268463i
$737$			26.8212i			0.987973i
$738$		0			0
$739$	−35.6155			−1.31014			−0.655069	−	0.755569i	$-0.727361\pi$
$739$	−35.6155			−1.31014			−0.655069	+	0.755569i	$0.727361\pi$
$740$		0			0
$741$		0			0
$742$	6.55137	+	1.57756i	0.240508	+	0.0579140i
$743$	10.0138			0.367371			0.183686	−	0.982985i	$-0.441197\pi$
$743$	10.0138			0.367371			0.183686	+	0.982985i	$0.441197\pi$
$744$		0			0
$745$		0			0
$746$	13.0336	+	3.13846i	0.477192	+	0.114907i
$747$		0			0
$748$	−6.07263	−	3.10457i	−0.222038	−	0.113514i
$749$	−10.3000			−0.376355
$750$		0			0
$751$		−	41.5286i		−	1.51540i	−0.652604	−	0.757699i	$-0.726323\pi$
$751$		−	41.5286i		−	1.51540i	0.652604	−	0.757699i	$-0.273677\pi$
$752$	−25.1976	−	34.8806i	−0.918861	−	1.27197i
$753$		0			0
$754$	38.7386	+	9.32819i	1.41078	+	0.339713i
$755$		0			0
$756$		0			0
$757$		−	3.33513i		−	0.121217i	−0.998162	−	0.0606087i	$-0.980696\pi$
$757$		−	3.33513i		−	0.121217i	0.998162	−	0.0606087i	$-0.0193042\pi$
$758$	5.46026	−	22.6757i	0.198325	−	0.823617i
$759$		0			0
$760$		0			0
$761$		−	49.3019i		−	1.78719i	−0.448870	−	0.893597i	$-0.648173\pi$
$761$		−	49.3019i		−	1.78719i	0.448870	−	0.893597i	$-0.351827\pi$
$762$		0			0
$763$	−11.1878			−0.405025
$764$	23.4921	+	12.0101i	0.849914	+	0.434510i
$765$		0			0
$766$	3.31534	−	13.7681i	0.119788	−	0.497463i
$767$	−35.6647			−1.28778
$768$		0			0
$769$	−25.6155			−0.923720			−0.461860	−	0.886953i	$-0.652818\pi$
$769$	−25.6155			−0.923720			−0.461860	+	0.886953i	$0.652818\pi$
$770$		0			0
$771$		0			0
$772$	41.5510	+	21.2425i	1.49545	+	0.764535i
$773$	2.27678			0.0818901			0.0409450	−	0.999161i	$-0.486963\pi$
$773$	2.27678			0.0818901			0.0409450	+	0.999161i	$0.486963\pi$
$774$		0			0
$775$		0			0
$776$	−4.02102	+	4.68860i	−0.144346	+	0.168311i
$777$		0			0
$778$	3.27569	−	13.6035i	0.117439	−	0.487707i
$779$			18.2107i			0.652465i
$780$		0			0
$781$			25.9396i			0.928192i
$782$	−7.20217	−	1.73427i	−0.257549	−	0.0620174i
$783$		0			0
$784$	14.3423	+	19.8539i	0.512226	+	0.709067i
$785$		0			0
$786$		0			0
$787$	19.9230			0.710177			0.355088	−	0.934833i	$-0.384451\pi$
$787$	19.9230			0.710177			0.355088	+	0.934833i	$0.384451\pi$
$788$	−8.77102	−	4.48410i	−0.312455	−	0.159739i
$789$		0			0
$790$		0			0
$791$	11.7460			0.417641
$792$		0			0
$793$		0			0
$794$	14.1626	+	3.41032i	0.502611	+	0.121028i
$795$		0			0
$796$	−16.0540	+	31.4020i	−0.569018	+	1.11302i
$797$	−15.6829			−0.555516			−0.277758	−	0.960651i	$-0.589591\pi$
$797$	−15.6829			−0.555516			−0.277758	+	0.960651i	$0.589591\pi$
$798$		0			0
$799$			16.6114i			0.587670i
$800$		0			0
$801$		0			0
$802$	0.718108	+	0.172919i	0.0253573	+	0.00610598i
$803$		−	12.3534i		−	0.435942i
$804$		0			0
$805$		0			0
$806$	9.17104	−	38.0860i	0.323036	−	1.34152i
$807$		0			0
$808$	6.07263	−	7.08084i	0.213635	−	0.249103i
$809$		−	20.6695i		−	0.726700i	−0.931653	−	0.363350i	$-0.881633\pi$
$809$		−	20.6695i		−	0.726700i	0.931653	−	0.363350i	$-0.118367\pi$
$810$		0			0
$811$	−49.4773			−1.73738			−0.868691	−	0.495354i	$-0.835038\pi$
$811$	−49.4773			−1.73738			−0.868691	+	0.495354i	$0.835038\pi$
$812$	−7.20217	+	14.0877i	−0.252747	+	0.494380i
$813$		0			0
$814$	5.56155	−	23.0963i	0.194932	−	0.809526i
$815$		0			0
$816$		0			0
$817$	24.2905			0.849818
$818$	−1.03399	+	4.29400i	−0.0361525	+	0.150136i
$819$		0			0
$820$		0			0
$821$	−12.1521			−0.424110			−0.212055	−	0.977258i	$-0.568016\pi$
$821$	−12.1521			−0.424110			−0.212055	+	0.977258i	$0.568016\pi$
$822$		0			0
$823$		−	28.6692i		−	0.999345i	−0.866214	−	0.499673i	$-0.833454\pi$
$823$		−	28.6692i		−	0.999345i	0.866214	−	0.499673i	$-0.166546\pi$
$824$	38.6947	+	33.1851i	1.34799	+	1.15606i
$825$		0			0
$826$	3.31534	−	13.7681i	0.115355	−	0.479055i
$827$		−	39.1746i		−	1.36224i	−0.732174	−	0.681118i	$-0.761494\pi$
$827$		−	39.1746i		−	1.36224i	0.732174	−	0.681118i	$-0.238506\pi$
$828$		0			0
$829$		−	4.66410i		−	0.161991i	−0.996714	−	0.0809954i	$-0.974190\pi$
$829$		−	4.66410i		−	0.161991i	0.996714	−	0.0809954i	$-0.0258099\pi$
$830$		0			0
$831$		0			0
$832$	26.3694	−	4.06627i	0.914194	−	0.140973i
$833$		−	9.45514i		−	0.327601i
$834$		0			0
$835$		0			0
$836$	6.27903	−	12.2820i	0.217165	−	0.424781i
$837$		0			0
$838$	−44.5873	−	10.7365i	−1.54024	−	0.370887i
$839$	−24.9381			−0.860959			−0.430479	−	0.902600i	$-0.641656\pi$
$839$	−24.9381			−0.860959			−0.430479	+	0.902600i	$0.641656\pi$
$840$		0			0
$841$	42.3693			1.46101
$842$	−42.0775	−	10.1322i	−1.45009	−	0.349178i
$843$		0			0
$844$	−7.12311	−	3.64162i	−0.245187	−	0.125350i
$845$		0			0
$846$		0			0
$847$		−	5.73384i		−	0.197017i
$848$	−11.9188	−	16.4990i	−0.409292	−	0.566577i
$849$		0			0
$850$		0			0
$851$		−	25.8040i		−	0.884551i
$852$		0			0
$853$		−	45.5249i		−	1.55874i	−0.626563	−	0.779371i	$-0.715539\pi$
$853$		−	45.5249i		−	1.55874i	0.626563	−	0.779371i	$-0.284461\pi$
$854$		0			0
$855$		0			0
$856$	23.6155	+	20.2530i	0.807162	+	0.692235i
$857$		−	40.7188i		−	1.39093i	−0.718561	−	0.695464i	$-0.755199\pi$
$857$		−	40.7188i		−	1.39093i	0.718561	−	0.695464i	$-0.244801\pi$
$858$		0			0
$859$	33.7538			1.15166			0.575832	−	0.817568i	$-0.304678\pi$
$859$	33.7538			1.15166			0.575832	+	0.817568i	$0.304678\pi$
$860$		0			0
$861$		0			0
$862$	−0.478739	+	1.98813i	−0.0163059	+	0.0677160i
$863$	45.6786			1.55492			0.777458	−	0.628935i	$-0.216509\pi$
$863$	45.6786			1.55492			0.777458	+	0.628935i	$0.216509\pi$
$864$		0			0
$865$		0			0
$866$	−5.15002	+	21.3873i	−0.175005	+	0.726770i
$867$		0			0
$868$	13.8503	+	7.08084i	0.470111	+	0.240339i
$869$	−2.25801			−0.0765978
$870$		0			0
$871$			40.5061i			1.37250i
$872$	25.6509	+	21.9986i	0.868650	+	0.744967i
$873$		0			0
$874$	3.50758	−	14.5665i	0.118646	−	0.492718i
$875$		0			0
$876$		0			0
$877$		−	46.5766i		−	1.57278i	−0.617731	−	0.786389i	$-0.711948\pi$
$877$		−	46.5766i		−	1.57278i	0.617731	−	0.786389i	$-0.288052\pi$
$878$	−37.0706	−	8.92652i	−1.25107	−	0.301256i
$879$		0			0
$880$		0			0
$881$		−	5.83095i		−	0.196450i	−0.995164	−	0.0982249i	$-0.968684\pi$
$881$		−	5.83095i		−	0.196450i	0.995164	−	0.0982249i	$-0.0313164\pi$
$882$		0			0
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$	−9.17104	−	4.68860i	−0.308455	−	0.157695i
$885$		0			0
$886$	−34.4924	−	8.30571i	−1.15880	−	0.279036i
$887$	−16.2177			−0.544538			−0.272269	−	0.962221i	$-0.587774\pi$
$887$	−16.2177			−0.544538			−0.272269	+	0.962221i	$0.587774\pi$
$888$		0			0
$889$	−4.38447			−0.147050
$890$		0			0
$891$		0			0
$892$	20.0279	−	39.1752i	0.670584	−	1.31168i
$893$	−33.5968			−1.12427
$894$		0			0
$895$		0			0
$896$	−0.881502	+	10.5577i	−0.0294489	+	0.352709i
$897$		0			0
$898$	−13.6110	−	3.27749i	−0.454203	−	0.109371i
$899$		−	70.1670i		−	2.34020i
$900$		0			0
$901$			7.85741i			0.261768i
$902$	−4.26324	+	17.7046i	−0.141950	+	0.589499i
$903$		0			0
$904$	−26.9309	−	23.0963i	−0.895707	−	0.768172i
$905$		0			0
$906$		0			0
$907$	16.5129			0.548300			0.274150	−	0.961687i	$-0.411603\pi$
$907$	16.5129			0.548300			0.274150	+	0.961687i	$0.411603\pi$
$908$	−2.81164	+	5.49966i	−0.0933077	+	0.182512i
$909$		0			0
$910$		0			0
$911$	−36.6842			−1.21540			−0.607700	−	0.794167i	$-0.707908\pi$
$911$	−36.6842			−1.21540			−0.607700	+	0.794167i	$0.707908\pi$
$912$		0			0
$913$	31.1107			1.02962
$914$	−4.42702	+	18.3848i	−0.146433	+	0.608114i
$915$		0			0
$916$	−2.38447	+	4.66410i	−0.0787852	+	0.154106i
$917$	0.580639			0.0191744
$918$		0			0
$919$			30.1554i			0.994735i	0.867540	+	0.497368i	$0.165700\pi$
$919$			30.1554i			0.994735i	−0.867540	+	0.497368i	$0.834300\pi$
$920$		0			0
$921$		0			0
$922$	−0.613157	+	2.54635i	−0.0201933	+	0.0838597i
$923$			39.1746i			1.28945i
$924$		0			0
$925$		0			0
$926$	18.1836	+	4.37857i	0.597549	+	0.143889i
$927$		0			0
$928$	44.2135	−	18.1379i	1.45138	−	0.595407i
$929$			3.00252i			0.0985096i	0.998786	+	0.0492548i	$0.0156846\pi$
$929$			3.00252i			0.0985096i	−0.998786	+	0.0492548i	$0.984315\pi$
$930$		0			0
$931$	19.1231			0.626734
$932$	18.6218	−	36.4248i	0.609978	−	1.19313i
$933$		0			0
$934$	−26.0000	−	6.26075i	−0.850746	−	0.204858i
$935$		0			0
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$	−15.6371	−	3.76539i	−0.510570	−	0.122944i
$939$		0			0
$940$		0			0
$941$	3.29801			0.107512			0.0537561	−	0.998554i	$-0.482881\pi$
$941$	3.29801			0.107512			0.0537561	+	0.998554i	$0.482881\pi$
$942$		0			0
$943$			19.7802i			0.644133i
$944$	−34.6736	+	25.0481i	−1.12853	+	0.815245i
$945$		0			0
$946$	23.6155	+	5.68658i	0.767807	+	0.184887i
$947$			32.9979i			1.07229i	0.844126	+	0.536144i	$0.180120\pi$
$947$			32.9979i			1.07229i	−0.844126	+	0.536144i	$0.819880\pi$
$948$		0			0
$949$		−	18.6564i		−	0.605612i
$950$		0			0
$951$		0			0
$952$	2.66253	−	3.10457i	0.0862931	−	0.100620i
$953$		−	12.5435i		−	0.406323i	−0.979145	−	0.203162i	$-0.934878\pi$
$953$		−	12.5435i		−	0.406323i	0.979145	−	0.203162i	$-0.0651217\pi$
$954$		0			0
$955$		0			0
$956$	−41.8342	−	21.3873i	−1.35301	−	0.691715i
$957$		0			0
$958$	4.84632	−	20.1261i	0.156578	−	0.650244i
$959$	−1.44600			−0.0466939
$960$		0			0
$961$	−37.9848			−1.22532
$962$	8.39919	−	34.8806i	0.270801	−	1.12460i
$963$		0			0
$964$	7.12311	+	3.64162i	0.229420	+	0.117289i
$965$		0			0
$966$		0			0
$967$		−	15.0981i		−	0.485522i	−0.970086	−	0.242761i	$-0.921947\pi$
$967$		−	15.0981i		−	0.485522i	0.970086	−	0.242761i	$-0.0780531\pi$
$968$	−11.2745	+	13.1463i	−0.362375	+	0.422538i
$969$		0			0
$970$		0			0
$971$			19.8753i			0.637829i	0.947783	+	0.318915i	$0.103318\pi$
$971$			19.8753i			0.637829i	−0.947783	+	0.318915i	$0.896682\pi$
$972$		0			0
$973$		−	11.2371i		−	0.360245i
$974$	40.5467	+	9.76356i	1.29920	+	0.312845i
$975$		0			0
$976$		0			0
$977$		−	37.6305i		−	1.20390i	−0.798532	−	0.601952i	$-0.794390\pi$
$977$		−	37.6305i		−	1.20390i	0.798532	−	0.601952i	$-0.205610\pi$
$978$		0			0
$979$	−28.8769			−0.922910
$980$		0			0
$981$		0			0
$982$	22.4805	+	5.41327i	0.717383	+	0.172744i
$983$	−53.0438			−1.69183			−0.845917	−	0.533315i	$-0.820946\pi$
$983$	−53.0438			−1.69183			−0.845917	+	0.533315i	$0.820946\pi$
$984$		0			0
$985$		0			0
$986$	−17.9361	−	4.31897i	−0.571201	−	0.137544i
$987$		0			0
$988$	9.48274	−	18.5485i	0.301686	−	0.590107i
$989$	26.3841			0.838966
$990$		0			0
$991$		−	17.6339i		−	0.560159i	−0.959977	−	0.280080i	$-0.909639\pi$
$991$		−	17.6339i		−	0.560159i	0.959977	−	0.280080i	$-0.0903609\pi$
$992$	−17.8324	−	43.4686i	−0.566178	−	1.38013i
$993$		0			0
$994$	−15.1231	−	3.64162i	−0.479676	−	0.115505i
$995$		0			0
$996$		0			0
$997$		−	25.5141i		−	0.808039i	−0.914750	−	0.404019i	$-0.867613\pi$
$997$		−	25.5141i		−	0.808039i	0.914750	−	0.404019i	$-0.132387\pi$
$998$	−5.58755	+	23.2043i	−0.176871	+	0.734519i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.b.g.251.9		16
3.2	odd	2	inner	1800.2.b.g.251.7		16
4.3	odd	2		7200.2.b.i.4751.9		16
5.2	odd	4		360.2.m.c.179.15	yes	16
5.3	odd	4		360.2.m.c.179.1	✓	16
5.4	even	2	inner	1800.2.b.g.251.8		16
8.3	odd	2	inner	1800.2.b.g.251.6		16
8.5	even	2		7200.2.b.i.4751.5		16
12.11	even	2		7200.2.b.i.4751.12		16
15.2	even	4		360.2.m.c.179.2	yes	16
15.8	even	4		360.2.m.c.179.16	yes	16
15.14	odd	2	inner	1800.2.b.g.251.10		16
20.3	even	4		1440.2.m.c.719.6		16
20.7	even	4		1440.2.m.c.719.7		16
20.19	odd	2		7200.2.b.i.4751.6		16
24.5	odd	2		7200.2.b.i.4751.8		16
24.11	even	2	inner	1800.2.b.g.251.12		16
40.3	even	4		360.2.m.c.179.4	yes	16
40.13	odd	4		1440.2.m.c.719.11		16
40.19	odd	2	inner	1800.2.b.g.251.11		16
40.27	even	4		360.2.m.c.179.14	yes	16
40.29	even	2		7200.2.b.i.4751.10		16
40.37	odd	4		1440.2.m.c.719.10		16
60.23	odd	4		1440.2.m.c.719.12		16
60.47	odd	4		1440.2.m.c.719.9		16
60.59	even	2		7200.2.b.i.4751.7		16
120.29	odd	2		7200.2.b.i.4751.11		16
120.53	even	4		1440.2.m.c.719.5		16
120.59	even	2	inner	1800.2.b.g.251.5		16
120.77	even	4		1440.2.m.c.719.8		16
120.83	odd	4		360.2.m.c.179.13	yes	16
120.107	odd	4		360.2.m.c.179.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.m.c.179.1	✓	16	5.3	odd	4
360.2.m.c.179.2	yes	16	15.2	even	4
360.2.m.c.179.3	yes	16	120.107	odd	4
360.2.m.c.179.4	yes	16	40.3	even	4
360.2.m.c.179.13	yes	16	120.83	odd	4
360.2.m.c.179.14	yes	16	40.27	even	4
360.2.m.c.179.15	yes	16	5.2	odd	4
360.2.m.c.179.16	yes	16	15.8	even	4
1440.2.m.c.719.5		16	120.53	even	4
1440.2.m.c.719.6		16	20.3	even	4
1440.2.m.c.719.7		16	20.7	even	4
1440.2.m.c.719.8		16	120.77	even	4
1440.2.m.c.719.9		16	60.47	odd	4
1440.2.m.c.719.10		16	40.37	odd	4
1440.2.m.c.719.11		16	40.13	odd	4
1440.2.m.c.719.12		16	60.23	odd	4
1800.2.b.g.251.5		16	120.59	even	2	inner
1800.2.b.g.251.6		16	8.3	odd	2	inner
1800.2.b.g.251.7		16	3.2	odd	2	inner
1800.2.b.g.251.8		16	5.4	even	2	inner
1800.2.b.g.251.9		16	1.1	even	1	trivial
1800.2.b.g.251.10		16	15.14	odd	2	inner
1800.2.b.g.251.11		16	40.19	odd	2	inner
1800.2.b.g.251.12		16	24.11	even	2	inner
7200.2.b.i.4751.5		16	8.5	even	2
7200.2.b.i.4751.6		16	20.19	odd	2
7200.2.b.i.4751.7		16	60.59	even	2
7200.2.b.i.4751.8		16	24.5	odd	2
7200.2.b.i.4751.9		16	4.3	odd	2
7200.2.b.i.4751.10		16	40.29	even	2
7200.2.b.i.4751.11		16	120.29	odd	2
7200.2.b.i.4751.12		16	12.11	even	2

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:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1800.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.331077 - 1.37491i) q^{2} +(-1.78078 - 0.910404i) q^{4} -0.936426i q^{7} +(-1.84130 + 2.14700i) q^{8} +2.20837i q^{11} +3.33513i q^{13} +(-1.28751 - 0.310029i) q^{14} +(2.34233 + 3.24245i) q^{16} -1.54417i q^{17} +3.12311 q^{19} +(3.03632 + 0.731140i) q^{22} +3.39228 q^{23} +(4.58552 + 1.10418i) q^{26} +(-0.852526 + 1.66757i) q^{28} +8.44804 q^{29} -8.30571i q^{31} +(5.23358 - 2.14700i) q^{32} +(-2.12311 - 0.511240i) q^{34} -7.60669i q^{37} +(1.03399 - 4.29400i) q^{38} +5.83095i q^{41} +7.77769 q^{43} +(2.01051 - 3.93261i) q^{44} +(1.12311 - 4.66410i) q^{46} -10.7575 q^{47} +6.12311 q^{49} +(3.03632 - 5.93912i) q^{52} -5.08842 q^{53} +(2.01051 + 1.72424i) q^{56} +(2.79695 - 11.6153i) q^{58} +10.6937i q^{59} +(-11.4196 - 2.74983i) q^{62} +(-1.21922 - 7.90655i) q^{64} +12.1453 q^{67} +(-1.40582 + 2.74983i) q^{68} +11.7460 q^{71} -5.59390 q^{73} +(-10.4585 - 2.51840i) q^{74} +(-5.56155 - 2.84329i) q^{76} +2.06798 q^{77} +1.02248i q^{79} +(8.01706 + 1.93049i) q^{82} -14.0877i q^{83} +(2.57501 - 10.6937i) q^{86} +(-4.74137 - 4.06627i) q^{88} +13.0761i q^{89} +3.12311 q^{91} +(-6.04090 - 3.08835i) q^{92} +(-3.56155 + 14.7906i) q^{94} +2.18379 q^{97} +(2.02722 - 8.41874i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4} - 12 q^{16} - 16 q^{19} + 32 q^{34} - 48 q^{46} + 32 q^{49} - 36 q^{64} - 56 q^{76} - 16 q^{91} - 24 q^{94}+O(q^{100}) \) 16 * q - 12 * q^4 - 12 * q^16 - 16 * q^19 + 32 * q^34 - 48 * q^46 + 32 * q^49 - 36 * q^64 - 56 * q^76 - 16 * q^91 - 24 * q^94

Introduction

L-functions

Modular forms

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Database

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