LMFDB - Embedded newform 900.3.f.e.199.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,3,Mod(199,900)] 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("900.199"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,8,0,0,0,0,0,0,0,0,0,80,0,-32,0,0,0,0,0,0,0,0,0,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(26)] == traces)

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

Self dual:	no
Analytic conductor:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.5
Root			$-0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	900.199
Dual form			900.3.f.e.199.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.17557 - 1.61803i) q^{2} +(-1.23607 - 3.80423i) q^{4} +8.50651 q^{7} +(-7.60845 - 2.47214i) q^{8} +1.79611i q^{11} +0.472136i q^{13} +(10.0000 - 13.7638i) q^{14} +(-12.9443 + 9.40456i) q^{16} -23.8885i q^{17} -9.40456i q^{19} +(2.90617 + 2.11146i) q^{22} +16.1150 q^{23} +(0.763932 + 0.555029i) q^{26} +(-10.5146 - 32.3607i) q^{28} +6.94427 q^{29} -47.4468i q^{31} +32.0000i q^{32} +(-38.6525 - 28.0827i) q^{34} -26.3607i q^{37} +(-15.2169 - 11.0557i) q^{38} +41.4164 q^{41} -2.00811 q^{43} +(6.83282 - 2.22012i) q^{44} +(18.9443 - 26.0746i) q^{46} -35.3481 q^{47} +23.3607 q^{49} +(1.79611 - 0.583592i) q^{52} +21.6393i q^{53} +(-64.7214 - 21.0292i) q^{56} +(8.16348 - 11.2361i) q^{58} -73.8644i q^{59} -26.1378 q^{61} +(-76.7706 - 55.7771i) q^{62} +(51.7771 + 37.6183i) q^{64} -88.8693 q^{67} +(-90.8774 + 29.5279i) q^{68} -39.4144i q^{71} +137.554i q^{73} +(-42.6525 - 30.9888i) q^{74} +(-35.7771 + 11.6247i) q^{76} +15.2786i q^{77} -113.703i q^{79} +(48.6879 - 67.0132i) q^{82} -21.2412 q^{83} +(-2.36068 + 3.24920i) q^{86} +(4.44023 - 13.6656i) q^{88} +67.4427 q^{89} +4.01623i q^{91} +(-19.9192 - 61.3050i) q^{92} +(-41.5542 + 57.1944i) q^{94} +39.1672i q^{97} +(27.4621 - 37.7984i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} + 80 q^{14} - 32 q^{16} + 24 q^{26} - 16 q^{29} - 184 q^{34} + 224 q^{41} - 160 q^{44} + 80 q^{46} + 8 q^{49} - 160 q^{56} + 256 q^{61} + 128 q^{64} - 216 q^{74} + 160 q^{86} - 176 q^{89}+ \cdots + 240 q^{94}+O(q^{100}) $ 8 * q + 8 * q^4 + 80 * q^14 - 32 * q^16 + 24 * q^26 - 16 * q^29 - 184 * q^34 + 224 * q^41 - 160 * q^44 + 80 * q^46 + 8 * q^49 - 160 * q^56 + 256 * q^61 + 128 * q^64 - 216 * q^74 + 160 * q^86 - 176 * q^89 + 240 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	1.17557	−	1.61803i	0.587785	−	0.809017i
$2$	1.17557	−	1.61803i	0.587785	−	0.809017i
$3$		0			0
$3$		0			0
$4$	−1.23607	−	3.80423i	−0.309017	−	0.951057i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	8.50651			1.21522			0.607608	−	0.794237i	$-0.292129\pi$
$7$	8.50651			1.21522			0.607608	+	0.794237i	$0.292129\pi$
$8$	−7.60845	−	2.47214i	−0.951057	−	0.309017i
$9$		0			0
$10$		0			0
$11$			1.79611i			0.163283i	0.996662	+	0.0816415i	$0.0260162\pi$
$11$			1.79611i			0.163283i	−0.996662	+	0.0816415i	$0.973984\pi$
$12$		0			0
$13$			0.472136i			0.0363182i	0.999835	+	0.0181591i	$0.00578053\pi$
$13$			0.472136i			0.0363182i	−0.999835	+	0.0181591i	$0.994219\pi$
$14$	10.0000	−	13.7638i	0.714286	−	0.983130i
$15$		0			0
$16$	−12.9443	+	9.40456i	−0.809017	+	0.587785i
$17$		−	23.8885i		−	1.40521i	−0.711581	−	0.702604i	$-0.752020\pi$
$17$		−	23.8885i		−	1.40521i	0.711581	−	0.702604i	$-0.247980\pi$
$18$		0			0
$19$		−	9.40456i		−	0.494977i	−0.968891	−	0.247489i	$-0.920395\pi$
$19$		−	9.40456i		−	0.494977i	0.968891	−	0.247489i	$-0.0796053\pi$
$20$		0			0
$21$		0			0
$22$	2.90617	+	2.11146i	0.132099	+	0.0959753i
$23$	16.1150			0.700650			0.350325	−	0.936628i	$-0.386071\pi$
$23$	16.1150			0.700650			0.350325	+	0.936628i	$0.386071\pi$
$24$		0			0
$25$		0			0
$26$	0.763932	+	0.555029i	0.0293820	+	0.0213473i
$27$		0			0
$28$	−10.5146	−	32.3607i	−0.375522	−	1.15574i
$29$	6.94427			0.239458			0.119729	−	0.992807i	$-0.461797\pi$
$29$	6.94427			0.239458			0.119729	+	0.992807i	$0.461797\pi$
$30$		0			0
$31$		−	47.4468i		−	1.53054i	−0.643708	−	0.765271i	$-0.722605\pi$
$31$		−	47.4468i		−	1.53054i	0.643708	−	0.765271i	$-0.277395\pi$
$32$			32.0000i			1.00000i
$33$		0			0
$34$	−38.6525	−	28.0827i	−1.13684	−	0.825961i
$35$		0			0
$36$		0			0
$37$		−	26.3607i		−	0.712451i	−0.934400	−	0.356225i	$-0.884064\pi$
$37$		−	26.3607i		−	0.712451i	0.934400	−	0.356225i	$-0.115936\pi$
$38$	−15.2169	−	11.0557i	−0.400445	−	0.290940i
$39$		0			0
$40$		0			0
$41$	41.4164			1.01016			0.505078	−	0.863074i	$-0.331464\pi$
$41$	41.4164			1.01016			0.505078	+	0.863074i	$0.331464\pi$
$42$		0			0
$43$	−2.00811			−0.0467003			−0.0233502	−	0.999727i	$-0.507433\pi$
$43$	−2.00811			−0.0467003			−0.0233502	+	0.999727i	$0.507433\pi$
$44$	6.83282	−	2.22012i	0.155291	−	0.0504572i
$45$		0			0
$46$	18.9443	−	26.0746i	0.411832	−	0.566838i
$47$	−35.3481			−0.752087			−0.376044	−	0.926602i	$-0.622716\pi$
$47$	−35.3481			−0.752087			−0.376044	+	0.926602i	$0.622716\pi$
$48$		0			0
$49$	23.3607			0.476749
$50$		0			0
$51$		0			0
$52$	1.79611	−	0.583592i	0.0345406	−	0.0112229i
$53$			21.6393i			0.408289i	0.978941	+	0.204145i	$0.0654413\pi$
$53$			21.6393i			0.408289i	−0.978941	+	0.204145i	$0.934559\pi$
$54$		0			0
$55$		0			0
$56$	−64.7214	−	21.0292i	−1.15574	−	0.375522i
$57$		0			0
$58$	8.16348	−	11.2361i	0.140750	−	0.193725i
$59$		−	73.8644i		−	1.25194i	−0.779848	−	0.625970i	$-0.784703\pi$
$59$		−	73.8644i		−	1.25194i	0.779848	−	0.625970i	$-0.215297\pi$
$60$		0			0
$61$	−26.1378			−0.428488			−0.214244	−	0.976780i	$-0.568729\pi$
$61$	−26.1378			−0.428488			−0.214244	+	0.976780i	$0.568729\pi$
$62$	−76.7706	−	55.7771i	−1.23824	−	0.899630i
$63$		0			0
$64$	51.7771	+	37.6183i	0.809017	+	0.587785i
$65$		0			0
$66$		0			0
$67$	−88.8693			−1.32641			−0.663204	−	0.748439i	$-0.730804\pi$
$67$	−88.8693			−1.32641			−0.663204	+	0.748439i	$0.730804\pi$
$68$	−90.8774	+	29.5279i	−1.33643	+	0.434233i
$69$		0			0
$70$		0			0
$71$		−	39.4144i		−	0.555132i	−0.960707	−	0.277566i	$-0.910472\pi$
$71$		−	39.4144i		−	0.555132i	0.960707	−	0.277566i	$-0.0895277\pi$
$72$		0			0
$73$			137.554i			1.88430i	0.335186	+	0.942152i	$0.391201\pi$
$73$			137.554i			1.88430i	−0.335186	+	0.942152i	$0.608799\pi$
$74$	−42.6525	−	30.9888i	−0.576385	−	0.418768i
$75$		0			0
$76$	−35.7771	+	11.6247i	−0.470751	+	0.152956i
$77$			15.2786i			0.198424i
$78$		0			0
$79$		−	113.703i		−	1.43928i	−0.694350	−	0.719638i	$-0.744308\pi$
$79$		−	113.703i		−	1.43928i	0.694350	−	0.719638i	$-0.255692\pi$
$80$		0			0
$81$		0			0
$82$	48.6879	−	67.0132i	0.593755	−	0.817234i
$83$	−21.2412			−0.255919			−0.127959	−	0.991779i	$-0.540843\pi$
$83$	−21.2412			−0.255919			−0.127959	+	0.991779i	$0.540843\pi$
$84$		0			0
$85$		0			0
$86$	−2.36068	+	3.24920i	−0.0274498	+	0.0377814i
$87$		0			0
$88$	4.44023	−	13.6656i	0.0504572	−	0.155291i
$89$	67.4427			0.757783			0.378892	−	0.925441i	$-0.376305\pi$
$89$	67.4427			0.757783			0.378892	+	0.925441i	$0.376305\pi$
$90$		0			0
$91$			4.01623i			0.0441344i
$92$	−19.9192	−	61.3050i	−0.216513	−	0.666358i
$93$		0			0
$94$	−41.5542	+	57.1944i	−0.442066	+	0.608451i
$95$		0			0
$96$		0			0
$97$			39.1672i			0.403785i	0.979408	+	0.201893i	$0.0647092\pi$
$97$			39.1672i			0.403785i	−0.979408	+	0.201893i	$0.935291\pi$
$98$	27.4621	−	37.7984i	0.280226	−	0.385698i
$99$		0			0
$100$		0			0
$101$	−99.8885			−0.988995			−0.494498	−	0.869179i	$-0.664648\pi$
$101$	−99.8885			−0.988995			−0.494498	+	0.869179i	$0.664648\pi$
$102$		0			0
$103$	−35.7721			−0.347302			−0.173651	−	0.984807i	$-0.555556\pi$
$103$	−35.7721			−0.347302			−0.173651	+	0.984807i	$0.555556\pi$
$104$	1.16718	−	3.59222i	0.0112229	−	0.0345406i
$105$		0			0
$106$	35.0132	+	25.4385i	0.330313	+	0.239986i
$107$	−121.099			−1.13177			−0.565884	−	0.824485i	$-0.691465\pi$
$107$	−121.099			−1.13177			−0.565884	+	0.824485i	$0.691465\pi$
$108$		0			0
$109$	197.469			1.81164			0.905821	−	0.423660i	$-0.139255\pi$
$109$	197.469			1.81164			0.905821	+	0.423660i	$0.139255\pi$
$110$		0			0
$111$		0			0
$112$	−110.111	+	80.0000i	−0.983130	+	0.714286i
$113$		−	81.2786i		−	0.719280i	−0.933091	−	0.359640i	$-0.882900\pi$
$113$		−	81.2786i		−	0.719280i	0.933091	−	0.359640i	$-0.117100\pi$
$114$		0			0
$115$		0			0
$116$	−8.58359	−	26.4176i	−0.0739965	−	0.227738i
$117$		0			0
$118$	−119.515	−	86.8328i	−1.01284	−	0.735871i
$119$		−	203.208i		−	1.70763i
$120$		0			0
$121$	117.774			0.973339
$122$	−30.7268	+	42.2918i	−0.251859	+	0.346654i
$123$		0			0
$124$	−180.498	+	58.6475i	−1.45563	+	0.472964i
$125$		0			0
$126$		0			0
$127$	1.84616			0.0145367			0.00726834	−	0.999974i	$-0.497686\pi$
$127$	1.84616			0.0145367			0.00726834	+	0.999974i	$0.497686\pi$
$128$	121.735	−	39.5542i	0.951057	−	0.309017i
$129$		0			0
$130$		0			0
$131$			225.609i			1.72221i	0.508428	+	0.861105i	$0.330227\pi$
$131$			225.609i			1.72221i	−0.508428	+	0.861105i	$0.669773\pi$
$132$		0			0
$133$		−	80.0000i		−	0.601504i
$134$	−104.472	+	143.794i	−0.779643	+	1.07309i
$135$		0			0
$136$	−59.0557	+	181.755i	−0.434233	+	1.33643i
$137$		−	52.8328i		−	0.385641i	−0.981234	−	0.192820i	$-0.938236\pi$
$137$		−	52.8328i		−	0.385641i	0.981234	−	0.192820i	$-0.0617635\pi$
$138$		0			0
$139$		−	125.852i		−	0.905407i	−0.891661	−	0.452703i	$-0.850460\pi$
$139$		−	125.852i		−	0.905407i	0.891661	−	0.452703i	$-0.149540\pi$
$140$		0			0
$141$		0			0
$142$	−63.7738	−	46.3344i	−0.449111	−	0.326298i
$143$	−0.848009			−0.00593013
$144$		0			0
$145$		0			0
$146$	222.567	+	161.705i	1.52443	+	1.10757i
$147$		0			0
$148$	−100.282	+	32.5836i	−0.677581	+	0.220159i
$149$	132.971			0.892420			0.446210	−	0.894928i	$-0.352773\pi$
$149$	132.971			0.892420			0.446210	+	0.894928i	$0.352773\pi$
$150$		0			0
$151$			151.221i			1.00146i	0.865603	+	0.500732i	$0.166936\pi$
$151$			151.221i			1.00146i	−0.865603	+	0.500732i	$0.833064\pi$
$152$	−23.2494	+	71.5542i	−0.152956	+	0.470751i
$153$		0			0
$154$	24.7214	+	17.9611i	0.160528	+	0.116631i
$155$		0			0
$156$		0			0
$157$			36.7477i			0.234062i	0.993128	+	0.117031i	$0.0373376\pi$
$157$			36.7477i			0.234062i	−0.993128	+	0.117031i	$0.962662\pi$
$158$	−183.975	−	133.666i	−1.16440	−	0.845985i
$159$		0			0
$160$		0			0
$161$	137.082			0.851441
$162$		0			0
$163$	302.854			1.85800			0.929000	−	0.370079i	$-0.120669\pi$
$163$	302.854			1.85800			0.929000	+	0.370079i	$0.120669\pi$
$164$	−51.1935	−	157.557i	−0.312155	−	0.960716i
$165$		0			0
$166$	−24.9706	+	34.3691i	−0.150425	+	0.207043i
$167$	99.3839			0.595113			0.297557	−	0.954704i	$-0.403828\pi$
$167$	99.3839			0.595113			0.297557	+	0.954704i	$0.403828\pi$
$168$		0			0
$169$	168.777			0.998681
$170$		0			0
$171$		0			0
$172$	2.48217	+	7.63932i	0.0144312	+	0.0444147i
$173$			181.639i			1.04994i	0.851121	+	0.524969i	$0.175923\pi$
$173$			181.639i			1.04994i	−0.851121	+	0.524969i	$0.824077\pi$
$174$		0			0
$175$		0			0
$176$	−16.8916	−	23.2494i	−0.0959753	−	0.132099i
$177$		0			0
$178$	79.2837	−	109.125i	0.445414	−	0.613060i
$179$			260.907i			1.45758i	0.684735	+	0.728792i	$0.259918\pi$
$179$			260.907i			1.45758i	−0.684735	+	0.728792i	$0.740082\pi$
$180$		0			0
$181$	157.777			0.871697			0.435848	−	0.900020i	$-0.356448\pi$
$181$	157.777			0.871697			0.435848	+	0.900020i	$0.356448\pi$
$182$	6.49839	+	4.72136i	0.0357055	+	0.0259415i
$183$		0			0
$184$	−122.610	−	39.8384i	−0.666358	−	0.216513i
$185$		0			0
$186$		0			0
$187$	42.9065			0.229447
$188$	43.6926	+	134.472i	0.232408	+	0.715277i
$189$		0			0
$190$		0			0
$191$		−	324.095i		−	1.69683i	−0.529328	−	0.848417i	$-0.677556\pi$
$191$		−	324.095i		−	1.69683i	0.529328	−	0.848417i	$-0.322444\pi$
$192$		0			0
$193$			181.777i			0.941850i	0.882173	+	0.470925i	$0.156080\pi$
$193$			181.777i			0.941850i	−0.882173	+	0.470925i	$0.843920\pi$
$194$	63.3738	+	46.0438i	0.326669	+	0.237339i
$195$		0			0
$196$	−28.8754	−	88.8693i	−0.147323	−	0.453415i
$197$			140.525i			0.713324i	0.934234	+	0.356662i	$0.116085\pi$
$197$			140.525i			0.713324i	−0.934234	+	0.356662i	$0.883915\pi$
$198$		0			0
$199$			168.234i			0.845397i	0.906270	+	0.422698i	$0.138917\pi$
$199$			168.234i			0.845397i	−0.906270	+	0.422698i	$0.861083\pi$
$200$		0			0
$201$		0			0
$202$	−117.426	+	161.623i	−0.581317	+	0.800114i
$203$	59.0715			0.290993
$204$		0			0
$205$		0			0
$206$	−42.0526	+	57.8805i	−0.204139	+	0.280973i
$207$		0			0
$208$	−4.44023	−	6.11146i	−0.0213473	−	0.0293820i
$209$	16.8916			0.0808213
$210$		0			0
$211$		−	93.9455i		−	0.445240i	−0.974905	−	0.222620i	$-0.928539\pi$
$211$		−	93.9455i		−	0.445240i	0.974905	−	0.222620i	$-0.0714608\pi$
$212$	82.3209	−	26.7477i	0.388306	−	0.126168i
$213$		0			0
$214$	−142.361	+	195.943i	−0.665237	+	0.915620i
$215$		0			0
$216$		0			0
$217$		−	403.607i		−	1.85994i
$218$	232.139	−	319.512i	1.06486	−	1.46565i
$219$		0			0
$220$		0			0
$221$	11.2786			0.0510346
$222$		0			0
$223$	214.035			0.959797			0.479899	−	0.877324i	$-0.340673\pi$
$223$	214.035			0.959797			0.479899	+	0.877324i	$0.340673\pi$
$224$			272.208i			1.21522i
$225$		0			0
$226$	−131.512	−	95.5488i	−0.581910	−	0.422782i
$227$	−41.4225			−0.182478			−0.0912389	−	0.995829i	$-0.529083\pi$
$227$	−41.4225			−0.182478			−0.0912389	+	0.995829i	$0.529083\pi$
$228$		0			0
$229$	−73.2786			−0.319994			−0.159997	−	0.987117i	$-0.551148\pi$
$229$	−73.2786			−0.319994			−0.159997	+	0.987117i	$0.551148\pi$
$230$		0			0
$231$		0			0
$232$	−52.8352	−	17.1672i	−0.227738	−	0.0739965i
$233$			307.050i			1.31781i	0.752227	+	0.658905i	$0.228980\pi$
$233$			307.050i			1.31781i	−0.752227	+	0.658905i	$0.771020\pi$
$234$		0			0
$235$		0			0
$236$	−280.997	+	91.3014i	−1.19066	+	0.386870i
$237$		0			0
$238$	−328.798	−	238.885i	−1.38150	−	1.00372i
$239$			42.9065i			0.179525i	0.995963	+	0.0897625i	$0.0286108\pi$
$239$			42.9065i			0.179525i	−0.995963	+	0.0897625i	$0.971389\pi$
$240$		0			0
$241$	−135.082			−0.560506			−0.280253	−	0.959926i	$-0.590418\pi$
$241$	−135.082			−0.560506			−0.280253	+	0.959926i	$0.590418\pi$
$242$	138.452	−	190.562i	0.572114	−	0.787448i
$243$		0			0
$244$	32.3081	+	99.4340i	0.132410	+	0.407516i
$245$		0			0
$246$		0			0
$247$	4.44023			0.0179767
$248$	−117.295	+	360.997i	−0.472964	+	1.45563i
$249$		0			0
$250$		0			0
$251$		−	221.169i		−	0.881152i	−0.897715	−	0.440576i	$-0.854774\pi$
$251$		−	221.169i		−	0.881152i	0.897715	−	0.440576i	$-0.145226\pi$
$252$		0			0
$253$			28.9443i			0.114404i
$254$	2.17029	−	2.98715i	0.00854445	−	0.0117604i
$255$		0			0
$256$	79.1084	−	243.470i	0.309017	−	0.951057i
$257$		−	257.056i		−	1.00022i	−0.865963	−	0.500108i	$-0.833293\pi$
$257$		−	257.056i		−	1.00022i	0.865963	−	0.500108i	$-0.166707\pi$
$258$		0			0
$259$		−	224.237i		−	0.865781i
$260$		0			0
$261$		0			0
$262$	365.044	+	265.220i	1.39330	+	1.01229i
$263$	164.168			0.624212			0.312106	−	0.950047i	$-0.398966\pi$
$263$	164.168			0.624212			0.312106	+	0.950047i	$0.398966\pi$
$264$		0			0
$265$		0			0
$266$	−129.443	−	94.0456i	−0.486627	−	0.353555i
$267$		0			0
$268$	109.849	+	338.079i	0.409882	+	1.26149i
$269$	−35.4752			−0.131878			−0.0659391	−	0.997824i	$-0.521004\pi$
$269$	−35.4752			−0.131878			−0.0659391	+	0.997824i	$0.521004\pi$
$270$		0			0
$271$		−	298.950i		−	1.10314i	−0.834130	−	0.551568i	$-0.814030\pi$
$271$		−	298.950i		−	1.10314i	0.834130	−	0.551568i	$-0.185970\pi$
$272$	224.661	+	309.220i	0.825961	+	1.13684i
$273$		0			0
$274$	−85.4853	−	62.1087i	−0.311990	−	0.226674i
$275$		0			0
$276$		0			0
$277$			457.246i			1.65071i	0.564616	+	0.825354i	$0.309024\pi$
$277$			457.246i			1.65071i	−0.564616	+	0.825354i	$0.690976\pi$
$278$	−203.632	−	147.947i	−0.732490	−	0.532185i
$279$		0			0
$280$		0			0
$281$	5.63932			0.0200688			0.0100344	−	0.999950i	$-0.496806\pi$
$281$	5.63932			0.0200688			0.0100344	+	0.999950i	$0.496806\pi$
$282$		0			0
$283$	−169.918			−0.600418			−0.300209	−	0.953874i	$-0.597056\pi$
$283$	−169.918			−0.600418			−0.300209	+	0.953874i	$0.597056\pi$
$284$	−149.941	+	48.7188i	−0.527962	+	0.171545i
$285$		0			0
$286$	−0.996894	+	1.37211i	−0.00348564	+	0.00479758i
$287$	352.309			1.22756
$288$		0			0
$289$	−281.663			−0.974611
$290$		0			0
$291$		0			0
$292$	523.287	−	170.026i	1.79208	−	0.582282i
$293$			26.8591i			0.0916694i	0.998949	+	0.0458347i	$0.0145947\pi$
$293$			26.8591i			0.0916694i	−0.998949	+	0.0458347i	$0.985405\pi$
$294$		0			0
$295$		0			0
$296$	−65.1672	+	200.564i	−0.220159	+	0.677581i
$297$		0			0
$298$	156.316	−	215.151i	0.524551	−	0.721983i
$299$			7.60845i			0.0254463i
$300$		0			0
$301$	−17.0820			−0.0567510
$302$	244.681	+	177.771i	0.810201	+	0.588645i
$303$		0			0
$304$	88.4458	+	121.735i	0.290940	+	0.400445i
$305$		0			0
$306$		0			0
$307$	118.031			0.384466			0.192233	−	0.981349i	$-0.438427\pi$
$307$	118.031			0.384466			0.192233	+	0.981349i	$0.438427\pi$
$308$	58.1234	−	18.8854i	0.188712	−	0.0613164i
$309$		0			0
$310$		0			0
$311$			121.835i			0.391753i	0.980629	+	0.195877i	$0.0627552\pi$
$311$			121.835i			0.391753i	−0.980629	+	0.195877i	$0.937245\pi$
$312$		0			0
$313$			219.548i			0.701431i	0.936482	+	0.350716i	$0.114062\pi$
$313$			219.548i			0.701431i	−0.936482	+	0.350716i	$0.885938\pi$
$314$	59.4590	+	43.1995i	0.189360	+	0.137578i
$315$		0			0
$316$	−432.551	+	140.544i	−1.36883	+	0.444761i
$317$			366.859i			1.15728i	0.815582	+	0.578642i	$0.196417\pi$
$317$			366.859i			1.15728i	−0.815582	+	0.578642i	$0.803583\pi$
$318$		0			0
$319$			12.4727i			0.0390993i
$320$		0			0
$321$		0			0
$322$	161.150	−	221.803i	0.500465	−	0.688830i
$323$	−224.661			−0.695546
$324$		0			0
$325$		0			0
$326$	356.026	−	490.028i	1.09211	−	1.50315i
$327$		0			0
$328$	−315.115	−	102.387i	−0.960716	−	0.312155i
$329$	−300.689			−0.913948
$330$		0			0
$331$			162.846i			0.491981i	0.969272	+	0.245990i	$0.0791132\pi$
$331$			162.846i			0.491981i	−0.969272	+	0.245990i	$0.920887\pi$
$332$	26.2556	+	80.8065i	0.0790832	+	0.243393i
$333$		0			0
$334$	116.833	−	160.807i	0.349799	−	0.481457i
$335$		0			0
$336$		0			0
$337$		−	17.1084i		−	0.0507666i	−0.999678	−	0.0253833i	$-0.991919\pi$
$337$		−	17.1084i		−	0.0507666i	0.999678	−	0.0253833i	$-0.00808063\pi$
$338$	198.409	−	273.087i	0.587010	−	0.807950i
$339$		0			0
$340$		0			0
$341$	85.2198			0.249911
$342$		0			0
$343$	−218.101			−0.635863
$344$	15.2786	+	4.96433i	0.0444147	+	0.0144312i
$345$		0			0
$346$	293.899	+	213.530i	0.849418	+	0.617138i
$347$	167.498			0.482703			0.241351	−	0.970438i	$-0.422409\pi$
$347$	167.498			0.482703			0.241351	+	0.970438i	$0.422409\pi$
$348$		0			0
$349$	483.495			1.38537			0.692687	−	0.721239i	$-0.256427\pi$
$349$	483.495			1.38537			0.692687	+	0.721239i	$0.256427\pi$
$350$		0			0
$351$		0			0
$352$	−57.4756			−0.163283
$353$		−	307.994i		−	0.872504i	−0.899825	−	0.436252i	$-0.856306\pi$
$353$		−	307.994i		−	0.872504i	0.899825	−	0.436252i	$-0.143694\pi$
$354$		0			0
$355$		0			0
$356$	−83.3638	−	256.567i	−0.234168	−	0.720695i
$357$		0			0
$358$	422.157	+	306.715i	1.17921	+	0.856746i
$359$			23.2494i			0.0647615i	0.999476	+	0.0323807i	$0.0103089\pi$
$359$			23.2494i			0.0647615i	−0.999476	+	0.0323807i	$0.989691\pi$
$360$		0			0
$361$	272.554			0.754998
$362$	185.478	−	255.289i	0.512370	−	0.705217i
$363$		0			0
$364$	15.2786	−	4.96433i	0.0419743	−	0.0136383i
$365$		0			0
$366$		0			0
$367$	517.325			1.40960			0.704802	−	0.709404i	$-0.251036\pi$
$367$	517.325			1.40960			0.704802	+	0.709404i	$0.251036\pi$
$368$	−208.596	+	151.554i	−0.566838	+	0.411832i
$369$		0			0
$370$		0			0
$371$			184.075i			0.496159i
$372$		0			0
$373$		−	88.3545i		−	0.236875i	−0.992961	−	0.118438i	$-0.962211\pi$
$373$		−	88.3545i		−	0.236875i	0.992961	−	0.118438i	$-0.0377886\pi$
$374$	50.4396	−	69.4242i	0.134865	−	0.185626i
$375$		0			0
$376$	268.944	+	87.3853i	0.715277	+	0.232408i
$377$			3.27864i			0.00869666i
$378$		0			0
$379$			19.3332i			0.0510112i	0.999675	+	0.0255056i	$0.00811956\pi$
$379$			19.3332i			0.0510112i	−0.999675	+	0.0255056i	$0.991880\pi$
$380$		0			0
$381$		0			0
$382$	−524.397	−	380.997i	−1.37277	−	0.997374i
$383$	431.612			1.12692			0.563462	−	0.826142i	$-0.309469\pi$
$383$	431.612			1.12692			0.563462	+	0.826142i	$0.309469\pi$
$384$		0			0
$385$		0			0
$386$	294.122	+	213.692i	0.761973	+	0.553606i
$387$		0			0
$388$	149.001	−	48.4133i	0.384023	−	0.124777i
$389$	−296.354			−0.761837			−0.380918	−	0.924609i	$-0.624392\pi$
$389$	−296.354			−0.761837			−0.380918	+	0.924609i	$0.624392\pi$
$390$		0			0
$391$		−	384.963i		−	0.984560i
$392$	−177.739	−	57.7508i	−0.453415	−	0.147323i
$393$		0			0
$394$	227.374	+	165.197i	0.577091	+	0.419281i
$395$		0			0
$396$		0			0
$397$			86.1904i			0.217104i	0.994091	+	0.108552i	$0.0346214\pi$
$397$			86.1904i			0.217104i	−0.994091	+	0.108552i	$0.965379\pi$
$398$	272.208	+	197.771i	0.683940	+	0.496912i
$399$		0			0
$400$		0			0
$401$	−442.997			−1.10473			−0.552365	−	0.833602i	$-0.686275\pi$
$401$	−442.997			−1.10473			−0.552365	+	0.833602i	$0.686275\pi$
$402$		0			0
$403$	22.4014			0.0555865
$404$	123.469	+	379.999i	0.305616	+	0.940591i
$405$		0			0
$406$	69.4427	−	95.5797i	0.171041	−	0.235418i
$407$	47.3467			0.116331
$408$		0			0
$409$	−63.4102			−0.155037			−0.0775186	−	0.996991i	$-0.524700\pi$
$409$	−63.4102			−0.155037			−0.0775186	+	0.996991i	$0.524700\pi$
$410$		0			0
$411$		0			0
$412$	44.2167	+	136.085i	0.107322	+	0.330304i
$413$		−	628.328i		−	1.52138i
$414$		0			0
$415$		0			0
$416$	−15.1084			−0.0363182
$417$		0			0
$418$	19.8573	−	27.3313i	0.0475056	−	0.0653858i
$419$			435.678i			1.03980i	0.854226	+	0.519902i	$0.174032\pi$
$419$			435.678i			1.03980i	−0.854226	+	0.519902i	$0.825968\pi$
$420$		0			0
$421$	−582.912			−1.38459			−0.692294	−	0.721615i	$-0.743400\pi$
$421$	−582.912			−1.38459			−0.692294	+	0.721615i	$0.743400\pi$
$422$	−152.007	−	110.440i	−0.360206	−	0.261705i
$423$		0			0
$424$	53.4953	−	164.642i	0.126168	−	0.388306i
$425$		0			0
$426$		0			0
$427$	−222.341			−0.520705
$428$	149.687	+	460.689i	0.349736	+	1.07638i
$429$		0			0
$430$		0			0
$431$			375.882i			0.872117i	0.899918	+	0.436058i	$0.143626\pi$
$431$			375.882i			0.872117i	−0.899918	+	0.436058i	$0.856374\pi$
$432$		0			0
$433$		−	368.164i		−	0.850263i	−0.905131	−	0.425132i	$-0.860228\pi$
$433$		−	368.164i		−	0.850263i	0.905131	−	0.425132i	$-0.139772\pi$
$434$	−653.050	−	474.468i	−1.50472	−	1.09324i
$435$		0			0
$436$	−244.085	−	751.217i	−0.559828	−	1.72297i
$437$		−	151.554i		−	0.346806i
$438$		0			0
$439$			483.549i			1.10148i	0.834677	+	0.550739i	$0.185654\pi$
$439$			483.549i			1.10148i	−0.834677	+	0.550739i	$0.814346\pi$
$440$		0			0
$441$		0			0
$442$	13.2588	−	18.2492i	0.0299974	−	0.0412878i
$443$	279.181			0.630205			0.315102	−	0.949058i	$-0.397961\pi$
$443$	279.181			0.630205			0.315102	+	0.949058i	$0.397961\pi$
$444$		0			0
$445$		0			0
$446$	251.613	−	346.316i	0.564155	−	0.776492i
$447$		0			0
$448$	440.442	+	320.000i	0.983130	+	0.714286i
$449$	756.079			1.68392			0.841959	−	0.539542i	$-0.181403\pi$
$449$	756.079			1.68392			0.841959	+	0.539542i	$0.181403\pi$
$450$		0			0
$451$			74.3885i			0.164941i
$452$	−309.202	+	100.466i	−0.684076	+	0.222270i
$453$		0			0
$454$	−48.6950	+	67.0230i	−0.107258	+	0.147628i
$455$		0			0
$456$		0			0
$457$		−	285.672i		−	0.625103i	−0.949901	−	0.312551i	$-0.898816\pi$
$457$		−	285.672i		−	0.625103i	0.949901	−	0.312551i	$-0.101184\pi$
$458$	−86.1442	+	118.567i	−0.188088	+	0.258881i
$459$		0			0
$460$		0			0
$461$	99.1146			0.214999			0.107500	−	0.994205i	$-0.465716\pi$
$461$	99.1146			0.214999			0.107500	+	0.994205i	$0.465716\pi$
$462$		0			0
$463$	−630.603			−1.36199			−0.680997	−	0.732286i	$-0.738453\pi$
$463$	−630.603			−1.36199			−0.680997	+	0.732286i	$0.738453\pi$
$464$	−89.8885	+	65.3078i	−0.193725	+	0.140750i
$465$		0			0
$466$	496.817	+	360.958i	1.06613	+	0.774589i
$467$	496.010			1.06212			0.531060	−	0.847334i	$-0.321794\pi$
$467$	496.010			1.06212			0.531060	+	0.847334i	$0.321794\pi$
$468$		0			0
$469$	−755.967			−1.61187
$470$		0			0
$471$		0			0
$472$	−182.603	+	561.994i	−0.386870	+	1.19066i
$473$		−	3.60680i		−	0.00762537i
$474$		0			0
$475$		0			0
$476$	−773.050	+	251.179i	−1.62405	+	0.527687i
$477$		0			0
$478$	69.4242	+	50.4396i	0.145239	+	0.105522i
$479$		−	579.090i		−	1.20896i	−0.796621	−	0.604478i	$-0.793382\pi$
$479$		−	579.090i		−	1.20896i	0.796621	−	0.604478i	$-0.206618\pi$
$480$		0			0
$481$	12.4458			0.0258749
$482$	−158.798	+	218.567i	−0.329457	+	0.453459i
$483$		0			0
$484$	−145.577	−	448.039i	−0.300778	−	0.925700i
$485$		0			0
$486$		0			0
$487$	−626.363			−1.28617			−0.643084	−	0.765796i	$-0.722345\pi$
$487$	−626.363			−1.28617			−0.643084	+	0.765796i	$0.722345\pi$
$488$	198.868	+	64.6161i	0.407516	+	0.132410i
$489$		0			0
$490$		0			0
$491$			22.3013i			0.0454201i	0.999742	+	0.0227100i	$0.00722945\pi$
$491$			22.3013i			0.0454201i	−0.999742	+	0.0227100i	$0.992771\pi$
$492$		0			0
$493$		−	165.889i		−	0.336488i
$494$	5.21981	−	7.18445i	0.0105664	−	0.0145434i
$495$		0			0
$496$	446.217	+	614.165i	0.899630	+	1.23824i
$497$		−	335.279i		−	0.674605i
$498$		0			0
$499$			627.362i			1.25724i	0.777714	+	0.628619i	$0.216379\pi$
$499$			627.362i			1.25724i	−0.777714	+	0.628619i	$0.783621\pi$
$500$		0			0
$501$		0			0
$502$	−357.859	−	260.000i	−0.712867	−	0.517928i
$503$	−780.853			−1.55239			−0.776196	−	0.630492i	$-0.782853\pi$
$503$	−780.853			−1.55239			−0.776196	+	0.630492i	$0.782853\pi$
$504$		0			0
$505$		0			0
$506$	46.8328	+	34.0260i	0.0925550	+	0.0672451i
$507$		0			0
$508$	−2.28198	−	7.02321i	−0.00449208	−	0.0138252i
$509$	−288.950			−0.567683			−0.283841	−	0.958871i	$-0.591609\pi$
$509$	−288.950			−0.567683			−0.283841	+	0.958871i	$0.591609\pi$
$510$		0			0
$511$			1170.11i			2.28984i
$512$	−300.946	−	414.217i	−0.587785	−	0.809017i
$513$		0			0
$514$	−415.925	−	302.187i	−0.809192	−	0.587913i
$515$		0			0
$516$		0			0
$517$		−	63.4891i		−	0.122803i
$518$	−362.824	−	263.607i	−0.700432	−	0.508893i
$519$		0			0
$520$		0			0
$521$	602.984			1.15736			0.578680	−	0.815555i	$-0.303568\pi$
$521$	602.984			1.15736			0.578680	+	0.815555i	$0.303568\pi$
$522$		0			0
$523$	367.962			0.703560			0.351780	−	0.936083i	$-0.385577\pi$
$523$	367.962			0.703560			0.351780	+	0.936083i	$0.385577\pi$
$524$	858.269	−	278.869i	1.63792	−	0.532192i
$525$		0			0
$526$	192.991	−	265.629i	0.366902	−	0.504998i
$527$	−1133.44			−2.15073
$528$		0			0
$529$	−269.308			−0.509089
$530$		0			0
$531$		0			0
$532$	−304.338	+	98.8854i	−0.572064	+	0.185875i
$533$			19.5542i			0.0366870i
$534$		0			0
$535$		0			0
$536$	676.158	+	219.697i	1.26149	+	0.409882i
$537$		0			0
$538$	−41.7036	+	57.4001i	−0.0775161	+	0.106692i
$539$			41.9584i			0.0778449i
$540$		0			0
$541$	−616.885			−1.14027			−0.570134	−	0.821551i	$-0.693109\pi$
$541$	−616.885			−1.14027			−0.570134	+	0.821551i	$0.693109\pi$
$542$	−483.711	−	351.437i	−0.892455	−	0.648407i
$543$		0			0
$544$	764.433			1.40521
$545$		0			0
$546$		0			0
$547$	97.8499			0.178885			0.0894423	−	0.995992i	$-0.471492\pi$
$547$	97.8499			0.178885			0.0894423	+	0.995992i	$0.471492\pi$
$548$	−200.988	+	65.3050i	−0.366766	+	0.119170i
$549$		0			0
$550$		0			0
$551$		−	65.3078i		−	0.118526i
$552$		0			0
$553$		−	967.214i		−	1.74903i
$554$	739.840	+	537.525i	1.33545	+	0.970262i
$555$		0			0
$556$	−478.768	+	155.561i	−0.861093	+	0.279786i
$557$			896.302i			1.60916i	0.593845	+	0.804580i	$0.297609\pi$
$557$			896.302i			1.60916i	−0.593845	+	0.804580i	$0.702391\pi$
$558$		0			0
$559$		−	0.948103i		−	0.00169607i
$560$		0			0
$561$		0			0
$562$	6.62942	−	9.12461i	0.0117961	−	0.0162360i
$563$	−771.186			−1.36978			−0.684890	−	0.728647i	$-0.740150\pi$
$563$	−771.186			−1.36978			−0.684890	+	0.728647i	$0.740150\pi$
$564$		0			0
$565$		0			0
$566$	−199.751	+	274.933i	−0.352917	+	0.485748i
$567$		0			0
$568$	−97.4377	+	299.882i	−0.171545	+	0.527962i
$569$	8.74767			0.0153738			0.00768688	−	0.999970i	$-0.497553\pi$
$569$	8.74767			0.0153738			0.00768688	+	0.999970i	$0.497553\pi$
$570$		0			0
$571$		−	511.138i		−	0.895164i	−0.894243	−	0.447582i	$-0.852285\pi$
$571$		−	511.138i		−	0.895164i	0.894243	−	0.447582i	$-0.147715\pi$
$572$	1.04820	+	3.22602i	0.00183251	+	0.00563989i
$573$		0			0
$574$	414.164	−	570.048i	0.721540	−	0.993115i
$575$		0			0
$576$		0			0
$577$			713.712i			1.23694i	0.785810	+	0.618468i	$0.212246\pi$
$577$			713.712i			1.23694i	−0.785810	+	0.618468i	$0.787754\pi$
$578$	−331.114	+	455.740i	−0.572862	+	0.788477i
$579$		0			0
$580$		0			0
$581$	−180.689			−0.310996
$582$		0			0
$583$	−38.8666			−0.0666666
$584$	340.053	−	1046.57i	0.582282	−	1.79208i
$585$		0			0
$586$	43.4590	+	31.5748i	0.0741621	+	0.0538819i
$587$	−422.169			−0.719198			−0.359599	−	0.933107i	$-0.617086\pi$
$587$	−422.169			−0.719198			−0.359599	+	0.933107i	$0.617086\pi$
$588$		0			0
$589$	−446.217			−0.757584
$590$		0			0
$591$		0			0
$592$	247.911	+	341.220i	0.418768	+	0.576385i
$593$			308.663i			0.520510i	0.965540	+	0.260255i	$0.0838067\pi$
$593$			308.663i			0.520510i	−0.965540	+	0.260255i	$0.916193\pi$
$594$		0			0
$595$		0			0
$596$	−164.361	−	505.850i	−0.275773	−	0.848742i
$597$		0			0
$598$	12.3107	+	8.94427i	0.0205865	+	0.0149570i
$599$			462.196i			0.771612i	0.922580	+	0.385806i	$0.126077\pi$
$599$			462.196i			0.771612i	−0.922580	+	0.385806i	$0.873923\pi$
$600$		0			0
$601$	355.358			0.591277			0.295639	−	0.955300i	$-0.404468\pi$
$601$	355.358			0.591277			0.295639	+	0.955300i	$0.404468\pi$
$602$	−20.0811	+	27.6393i	−0.0333574	+	0.0459125i
$603$		0			0
$604$	575.279	−	186.919i	0.952448	−	0.309469i
$605$		0			0
$606$		0			0
$607$	−630.403			−1.03856			−0.519278	−	0.854605i	$-0.673799\pi$
$607$	−630.403			−1.03856			−0.519278	+	0.854605i	$0.673799\pi$
$608$	300.946			0.494977
$609$		0			0
$610$		0			0
$611$		−	16.6891i		−	0.0273144i
$612$		0			0
$613$			812.525i			1.32549i	0.748846	+	0.662745i	$0.230608\pi$
$613$			812.525i			1.32549i	−0.748846	+	0.662745i	$0.769392\pi$
$614$	138.754	−	190.978i	0.225984	−	0.311040i
$615$		0			0
$616$	37.7709	−	116.247i	0.0613164	−	0.188712i
$617$		−	437.935i		−	0.709781i	−0.934908	−	0.354891i	$-0.884518\pi$
$617$		−	437.935i		−	0.709781i	0.934908	−	0.354891i	$-0.115482\pi$
$618$		0			0
$619$		−	770.250i		−	1.24435i	−0.782880	−	0.622173i	$-0.786250\pi$
$619$		−	770.250i		−	1.24435i	0.782880	−	0.622173i	$-0.213750\pi$
$620$		0			0
$621$		0			0
$622$	197.134	+	143.226i	0.316935	+	0.230267i
$623$	573.702			0.920870
$624$		0			0
$625$		0			0
$626$	355.236	+	258.094i	0.567470	+	0.412291i
$627$		0			0
$628$	139.796	−	45.4226i	0.222606	−	0.0723290i
$629$	−629.718			−1.00114
$630$		0			0
$631$			875.496i			1.38747i	0.720228	+	0.693737i	$0.244037\pi$
$631$			875.496i			1.38747i	−0.720228	+	0.693737i	$0.755963\pi$
$632$	−281.089	+	865.102i	−0.444761	+	1.36883i
$633$		0			0
$634$	593.591	+	431.269i	0.936263	+	0.680235i
$635$		0			0
$636$		0			0
$637$			11.0294i			0.0173146i
$638$	20.1812	+	14.6625i	0.0316320	+	0.0229820i
$639$		0			0
$640$		0			0
$641$	−842.571			−1.31446			−0.657232	−	0.753689i	$-0.728273\pi$
$641$	−842.571			−1.31446			−0.657232	+	0.753689i	$0.728273\pi$
$642$		0			0
$643$	−1153.20			−1.79348			−0.896738	−	0.442563i	$-0.854069\pi$
$643$	−1153.20			−1.79348			−0.896738	+	0.442563i	$0.854069\pi$
$644$	−169.443	−	521.491i	−0.263110	−	0.809769i
$645$		0			0
$646$	−264.105	+	363.510i	−0.408832	+	0.562708i
$647$	−355.751			−0.549847			−0.274924	−	0.961466i	$-0.588653\pi$
$647$	−355.751			−0.549847			−0.274924	+	0.961466i	$0.588653\pi$
$648$		0			0
$649$	132.669			0.204420
$650$		0			0
$651$		0			0
$652$	−374.348	−	1152.13i	−0.574154	−	1.76706i
$653$			557.915i			0.854387i	0.904160	+	0.427194i	$0.140498\pi$
$653$			557.915i			0.854387i	−0.904160	+	0.427194i	$0.859502\pi$
$654$		0			0
$655$		0			0
$656$	−536.105	+	389.503i	−0.817234	+	0.593755i
$657$		0			0
$658$	−353.481	+	486.525i	−0.537205	+	0.739399i
$659$		−	284.157i		−	0.431194i	−0.976482	−	0.215597i	$-0.930830\pi$
$659$		−	284.157i		−	0.431194i	0.976482	−	0.215597i	$-0.0691697\pi$
$660$		0			0
$661$	716.735			1.08432			0.542160	−	0.840275i	$-0.317607\pi$
$661$	716.735			1.08432			0.542160	+	0.840275i	$0.317607\pi$
$662$	263.490	+	191.437i	0.398021	+	0.289179i
$663$		0			0
$664$	161.613	+	52.5112i	0.243393	+	0.0790832i
$665$		0			0
$666$		0			0
$667$	111.907			0.167776
$668$	−122.845	−	378.079i	−0.183900	−	0.565986i
$669$		0			0
$670$		0			0
$671$		−	46.9464i		−	0.0699648i
$672$		0			0
$673$		−	695.378i		−	1.03325i	−0.856212	−	0.516625i	$-0.827188\pi$
$673$		−	695.378i		−	1.03325i	0.856212	−	0.516625i	$-0.172812\pi$
$674$	−27.6819	−	20.1121i	−0.0410711	−	0.0298399i
$675$		0			0
$676$	−208.620	−	642.066i	−0.308609	−	0.949802i
$677$		−	820.237i		−	1.21158i	−0.795626	−	0.605788i	$-0.792858\pi$
$677$		−	820.237i		−	1.21158i	0.795626	−	0.605788i	$-0.207142\pi$
$678$		0			0
$679$			333.176i			0.490686i
$680$		0			0
$681$		0			0
$682$	100.182	−	137.889i	0.146894	−	0.202183i
$683$	−335.508			−0.491227			−0.245613	−	0.969368i	$-0.578989\pi$
$683$	−335.508			−0.491227			−0.245613	+	0.969368i	$0.578989\pi$
$684$		0			0
$685$		0			0
$686$	−256.393	+	352.895i	−0.373751	+	0.514424i
$687$		0			0
$688$	25.9936	−	18.8854i	0.0377814	−	0.0274498i
$689$	−10.2167			−0.0148283
$690$		0			0
$691$		−	336.568i		−	0.487074i	−0.969892	−	0.243537i	$-0.921692\pi$
$691$		−	336.568i		−	0.487074i	0.969892	−	0.243537i	$-0.0783077\pi$
$692$	690.997	−	224.519i	0.998551	−	0.324449i
$693$		0			0
$694$	196.906	−	271.017i	0.283726	−	0.390515i
$695$		0			0
$696$		0			0
$697$		−	989.378i		−	1.41948i
$698$	568.383	−	782.312i	0.814302	−	1.12079i
$699$		0			0
$700$		0			0
$701$	429.364			0.612502			0.306251	−	0.951951i	$-0.400925\pi$
$701$	429.364			0.612502			0.306251	+	0.951951i	$0.400925\pi$
$702$		0			0
$703$	−247.911			−0.352647
$704$	−67.5666	+	92.9974i	−0.0959753	+	0.132099i
$705$		0			0
$706$	−498.344	−	362.068i	−0.705870	−	0.512845i
$707$	−849.703			−1.20184
$708$		0			0
$709$	−1224.60			−1.72722			−0.863609	−	0.504162i	$-0.831801\pi$
$709$	−1224.60			−1.72722			−0.863609	+	0.504162i	$0.831801\pi$
$710$		0			0
$711$		0			0
$712$	−513.135	−	166.728i	−0.720695	−	0.234168i
$713$		−	764.604i		−	1.07238i
$714$		0			0
$715$		0			0
$716$	992.551	−	322.499i	1.38624	−	0.450418i
$717$		0			0
$718$	37.6183	+	27.3313i	0.0523931	+	0.0380658i
$719$		−	496.022i		−	0.689877i	−0.938625	−	0.344939i	$-0.887900\pi$
$719$		−	496.022i		−	0.689877i	0.938625	−	0.344939i	$-0.112100\pi$
$720$		0			0
$721$	−304.296			−0.422047
$722$	320.407	−	441.002i	0.443777	−	0.610806i
$723$		0			0
$724$	−195.023	−	600.220i	−0.269369	−	0.829033i
$725$		0			0
$726$		0			0
$727$	152.843			0.210238			0.105119	−	0.994460i	$-0.466478\pi$
$727$	152.843			0.210238			0.105119	+	0.994460i	$0.466478\pi$
$728$	9.92866	−	30.5573i	0.0136383	−	0.0419743i
$729$		0			0
$730$		0			0
$731$			47.9709i			0.0656237i
$732$		0			0
$733$		−	761.286i		−	1.03859i	−0.854595	−	0.519295i	$-0.826195\pi$
$733$		−	761.286i		−	1.03859i	0.854595	−	0.519295i	$-0.173805\pi$
$734$	608.152	−	837.049i	0.828544	−	1.14039i
$735$		0			0
$736$			515.679i			0.700650i
$737$		−	159.619i		−	0.216580i
$738$		0			0
$739$		−	183.975i		−	0.248951i	−0.992223	−	0.124476i	$-0.960275\pi$
$739$		−	183.975i		−	0.248951i	0.992223	−	0.124476i	$-0.0397249\pi$
$740$		0			0
$741$		0			0
$742$	297.840	+	216.393i	0.401401	+	0.291635i
$743$	−495.247			−0.666551			−0.333275	−	0.942830i	$-0.608154\pi$
$743$	−495.247			−0.666551			−0.333275	+	0.942830i	$0.608154\pi$
$744$		0			0
$745$		0			0
$746$	−142.961	−	103.867i	−0.191636	−	0.139232i
$747$		0			0
$748$	−53.0353	−	163.226i	−0.0709029	−	0.218217i
$749$	−1030.13			−1.37534
$750$		0			0
$751$		−	800.059i		−	1.06533i	−0.846328	−	0.532663i	$-0.821191\pi$
$751$		−	800.059i		−	1.06533i	0.846328	−	0.532663i	$-0.178809\pi$
$752$	457.555	−	332.433i	0.608451	−	0.442066i
$753$		0			0
$754$	5.30495	+	3.85427i	0.00703574	+	0.00511177i
$755$		0			0
$756$		0			0
$757$			276.367i			0.365082i	0.983198	+	0.182541i	$0.0584322\pi$
$757$			276.367i			0.365082i	−0.983198	+	0.182541i	$0.941568\pi$
$758$	31.2818	+	22.7276i	0.0412689	+	0.0299836i
$759$		0			0
$760$		0			0
$761$	−891.207			−1.17110			−0.585550	−	0.810636i	$-0.699121\pi$
$761$	−891.207			−1.17110			−0.585550	+	0.810636i	$0.699121\pi$
$762$		0			0
$763$	1679.77			2.20154
$764$	−1232.93	+	400.604i	−1.61379	+	0.524351i
$765$		0			0
$766$	507.390	−	698.363i	0.662389	−	0.911700i
$767$	34.8740			0.0454681
$768$		0			0
$769$	835.430			1.08639			0.543193	−	0.839608i	$-0.317215\pi$
$769$	835.430			1.08639			0.543193	+	0.839608i	$0.317215\pi$
$770$		0			0
$771$		0			0
$772$	691.521	−	224.689i	0.895753	−	0.291048i
$773$		−	213.522i		−	0.276225i	−0.990417	−	0.138112i	$-0.955897\pi$
$773$		−	213.522i		−	0.276225i	0.990417	−	0.138112i	$-0.0441035\pi$
$774$		0			0
$775$		0			0
$776$	96.8266	−	298.002i	0.124777	−	0.384023i
$777$		0			0
$778$	−348.386	+	479.512i	−0.447796	+	0.616339i
$779$		−	389.503i		−	0.500004i
$780$		0			0
$781$	70.7926			0.0906436
$782$	−622.883	−	452.551i	−0.796526	−	0.578710i
$783$		0			0
$784$	−302.387	+	219.697i	−0.385698	+	0.280226i
$785$		0			0
$786$		0			0
$787$	370.182			0.470371			0.235185	−	0.971951i	$-0.424430\pi$
$787$	370.182			0.470371			0.235185	+	0.971951i	$0.424430\pi$
$788$	534.588	−	173.698i	0.678411	−	0.220429i
$789$		0			0
$790$		0			0
$791$		−	691.397i		−	0.874080i
$792$		0			0
$793$		−	12.3406i		−	0.0155619i
$794$	139.459	+	101.323i	0.175641	+	0.127611i
$795$		0			0
$796$	640.000	−	207.949i	0.804020	−	0.261242i
$797$			274.426i			0.344323i	0.985069	+	0.172162i	$0.0550752\pi$
$797$			274.426i			0.344323i	−0.985069	+	0.172162i	$0.944925\pi$
$798$		0			0
$799$			844.414i			1.05684i
$800$		0			0
$801$		0			0
$802$	−520.774	+	716.784i	−0.649344	+	0.893746i
$803$	−247.063			−0.307675
$804$		0			0
$805$		0			0
$806$	26.3344	−	36.2461i	0.0326729	−	0.0449704i
$807$		0			0
$808$	759.997	+	246.938i	0.940591	+	0.305616i
$809$	665.214			0.822266			0.411133	−	0.911575i	$-0.365133\pi$
$809$	665.214			0.822266			0.411133	+	0.911575i	$0.365133\pi$
$810$		0			0
$811$			360.665i			0.444717i	0.974965	+	0.222358i	$0.0713755\pi$
$811$			360.665i			0.444717i	−0.974965	+	0.222358i	$0.928624\pi$
$812$	−73.0164	−	224.721i	−0.0899217	−	0.276750i
$813$		0			0
$814$	55.6594	−	76.6086i	0.0683777	−	0.0941138i
$815$		0			0
$816$		0			0
$817$			18.8854i			0.0231156i
$818$	−74.5432	+	102.600i	−0.0911286	+	0.125428i
$819$		0			0
$820$		0			0
$821$	666.899			0.812301			0.406151	−	0.913806i	$-0.366871\pi$
$821$	666.899			0.812301			0.406151	+	0.913806i	$0.366871\pi$
$822$		0			0
$823$	−122.433			−0.148764			−0.0743822	−	0.997230i	$-0.523698\pi$
$823$	−122.433			−0.148764			−0.0743822	+	0.997230i	$0.523698\pi$
$824$	272.170	+	88.4335i	0.330304	+	0.107322i
$825$		0			0
$826$	−1016.66	−	738.644i	−1.23082	−	0.894242i
$827$	1532.98			1.85366			0.926832	−	0.375477i	$-0.122521\pi$
$827$	1532.98			1.85366			0.926832	+	0.375477i	$0.122521\pi$
$828$		0			0
$829$	195.475			0.235796			0.117898	−	0.993026i	$-0.462384\pi$
$829$	195.475			0.235796			0.117898	+	0.993026i	$0.462384\pi$
$830$		0			0
$831$		0			0
$832$	−17.7609	+	24.4458i	−0.0213473	+	0.0293820i
$833$		−	558.053i		−	0.669931i
$834$		0			0
$835$		0			0
$836$	−20.8792	−	64.2597i	−0.0249752	−	0.0768656i
$837$		0			0
$838$	704.942	+	512.170i	0.841219	+	0.611182i
$839$			1325.97i			1.58041i	0.612840	+	0.790207i	$0.290027\pi$
$839$			1325.97i			1.58041i	−0.612840	+	0.790207i	$0.709973\pi$
$840$		0			0
$841$	−792.777			−0.942660
$842$	−685.254	+	943.171i	−0.813841	+	1.12016i
$843$		0			0
$844$	−357.390	+	116.123i	−0.423448	+	0.137587i
$845$		0			0
$846$		0			0
$847$	1001.85			1.18282
$848$	−203.508	−	280.105i	−0.239986	−	0.330313i
$849$		0			0
$850$		0			0
$851$		−	424.801i		−	0.499179i
$852$		0			0
$853$			1055.28i			1.23714i	0.785730	+	0.618570i	$0.212288\pi$
$853$			1055.28i			1.23714i	−0.785730	+	0.618570i	$0.787712\pi$
$854$	−261.378	+	359.756i	−0.306063	+	0.421259i
$855$		0			0
$856$	921.378	+	299.374i	1.07638	+	0.349736i
$857$			155.378i			0.181304i	0.995883	+	0.0906521i	$0.0288951\pi$
$857$			155.378i			0.181304i	−0.995883	+	0.0906521i	$0.971105\pi$
$858$		0			0
$859$			226.033i			0.263136i	0.991307	+	0.131568i	$0.0420011\pi$
$859$			226.033i			0.263136i	−0.991307	+	0.131568i	$0.957999\pi$
$860$		0			0
$861$		0			0
$862$	608.190	+	441.876i	0.705557	+	0.512617i
$863$	930.702			1.07845			0.539225	−	0.842162i	$-0.318717\pi$
$863$	930.702			1.07845			0.539225	+	0.842162i	$0.318717\pi$
$864$		0			0
$865$		0			0
$866$	−595.702	−	432.803i	−0.687878	−	0.499772i
$867$		0			0
$868$	−1535.41	+	498.885i	−1.76891	+	0.574753i
$869$	204.223			0.235009
$870$		0			0
$871$		−	41.9584i		−	0.0481727i
$872$	−1502.43	−	488.170i	−1.72297	−	0.559828i
$873$		0			0
$874$	−245.220	−	178.163i	−0.280572	−	0.203847i
$875$		0			0
$876$		0			0
$877$			33.5217i			0.0382231i	0.999817	+	0.0191115i	$0.00608376\pi$
$877$			33.5217i			0.0382231i	−0.999817	+	0.0191115i	$0.993916\pi$
$878$	782.399	+	568.446i	0.891115	+	0.647433i
$879$		0			0
$880$		0			0
$881$	933.850			1.05999			0.529994	−	0.848001i	$-0.322194\pi$
$881$	933.850			1.05999			0.529994	+	0.848001i	$0.322194\pi$
$882$		0			0
$883$	−542.308			−0.614166			−0.307083	−	0.951683i	$-0.599353\pi$
$883$	−542.308			−0.614166			−0.307083	+	0.951683i	$0.599353\pi$
$884$	−13.9412	−	42.9065i	−0.0157706	−	0.0485368i
$885$		0			0
$886$	328.197	−	451.724i	0.370425	−	0.509846i
$887$	714.720			0.805773			0.402886	−	0.915250i	$-0.368007\pi$
$887$	714.720			0.805773			0.402886	+	0.915250i	$0.368007\pi$
$888$		0			0
$889$	15.7044			0.0176652
$890$		0			0
$891$		0			0
$892$	−264.562	−	814.237i	−0.296594	−	0.912822i
$893$			332.433i			0.372266i
$894$		0			0
$895$		0			0
$896$	1035.54	−	336.468i	1.15574	−	0.375522i
$897$		0			0
$898$	888.824	−	1223.36i	0.989782	−	1.36232i
$899$		−	329.484i		−	0.366500i
$900$		0			0
$901$	516.932			0.573731
$902$	120.363	+	87.4489i	0.133440	+	0.0969500i
$903$		0			0
$904$	−200.932	+	618.405i	−0.222270	+	0.684076i
$905$		0			0
$906$		0			0
$907$	−347.233			−0.382837			−0.191418	−	0.981509i	$-0.561309\pi$
$907$	−347.233			−0.382837			−0.191418	+	0.981509i	$0.561309\pi$
$908$	51.2010	+	157.580i	0.0563888	+	0.173547i
$909$		0			0
$910$		0			0
$911$			1427.54i			1.56701i	0.621386	+	0.783504i	$0.286570\pi$
$911$			1427.54i			1.56701i	−0.621386	+	0.783504i	$0.713430\pi$
$912$		0			0
$913$		−	38.1517i		−	0.0417871i
$914$	−462.227	−	335.827i	−0.505719	−	0.367426i
$915$		0			0
$916$	90.5774	+	278.769i	0.0988836	+	0.304332i
$917$			1919.15i			2.09286i
$918$		0			0
$919$		−	569.162i		−	0.619327i	−0.950846	−	0.309664i	$-0.899784\pi$
$919$		−	569.162i		−	0.619327i	0.950846	−	0.309664i	$-0.100216\pi$
$920$		0			0
$921$		0			0
$922$	116.516	−	160.371i	0.126373	−	0.173938i
$923$	18.6089			0.0201614
$924$		0			0
$925$		0			0
$926$	−741.319	+	1020.34i	−0.800560	+	1.10188i
$927$		0			0
$928$			222.217i			0.239458i
$929$	1535.96			1.65335			0.826675	−	0.562680i	$-0.190230\pi$
$929$	1535.96			1.65335			0.826675	+	0.562680i	$0.190230\pi$
$930$		0			0
$931$		−	219.697i		−	0.235980i
$932$	1168.09	−	379.534i	1.25331	−	0.407225i
$933$		0			0
$934$	583.094	−	802.561i	0.624298	−	0.859273i
$935$		0			0
$936$		0			0
$937$		−	338.721i		−	0.361496i	−0.983529	−	0.180748i	$-0.942148\pi$
$937$		−	338.721i		−	0.361496i	0.983529	−	0.180748i	$-0.0578518\pi$
$938$	−888.693	+	1223.18i	−0.947434	+	1.30403i
$939$		0			0
$940$		0			0
$941$	−1439.77			−1.53004			−0.765022	−	0.644004i	$-0.777272\pi$
$941$	−1439.77			−1.53004			−0.765022	+	0.644004i	$0.777272\pi$
$942$		0			0
$943$	667.424			0.707766
$944$	694.663	+	956.121i	0.735871	+	1.01284i
$945$		0			0
$946$	−5.83592	−	4.24005i	−0.00616905	−	0.00448208i
$947$	656.135			0.692856			0.346428	−	0.938077i	$-0.387394\pi$
$947$	656.135			0.692856			0.346428	+	0.938077i	$0.387394\pi$
$948$		0			0
$949$	−64.9443			−0.0684344
$950$		0			0
$951$		0			0
$952$	−502.358	+	1546.10i	−0.527687	+	1.62405i
$953$		−	436.675i		−	0.458211i	−0.973402	−	0.229105i	$-0.926420\pi$
$953$		−	436.675i		−	0.458211i	0.973402	−	0.229105i	$-0.0735801\pi$
$954$		0			0
$955$		0			0
$956$	163.226	−	53.0353i	0.170739	−	0.0554763i
$957$		0			0
$958$	−936.988	−	680.762i	−0.978067	−	0.710607i
$959$		−	449.423i		−	0.468637i
$960$		0			0
$961$	−1290.20			−1.34256
$962$	14.6309	−	20.1378i	0.0152089	−	0.0209332i
$963$		0			0
$964$	166.971	+	513.883i	0.173206	+	0.533073i
$965$		0			0
$966$		0			0
$967$	903.436			0.934267			0.467133	−	0.884187i	$-0.345287\pi$
$967$	903.436			0.934267			0.467133	+	0.884187i	$0.345287\pi$
$968$	−896.078	−	291.153i	−0.925700	−	0.300778i
$969$		0			0
$970$		0			0
$971$		−	1866.89i		−	1.92265i	−0.275420	−	0.961324i	$-0.588817\pi$
$971$		−	1866.89i		−	1.92265i	0.275420	−	0.961324i	$-0.411183\pi$
$972$		0			0
$973$		−	1070.56i		−	1.10026i
$974$	−736.334	+	1013.48i	−0.755990	+	1.04053i
$975$		0			0
$976$	338.334	−	245.814i	0.346654	−	0.251859i
$977$		−	1073.95i		−	1.09923i	−0.835418	−	0.549615i	$-0.814774\pi$
$977$		−	1073.95i		−	1.09923i	0.835418	−	0.549615i	$-0.185226\pi$
$978$		0			0
$979$			121.135i			0.123733i
$980$		0			0
$981$		0			0
$982$	36.0842	+	26.2167i	0.0367456	+	0.0266973i
$983$	−534.114			−0.543351			−0.271675	−	0.962389i	$-0.587578\pi$
$983$	−534.114			−0.543351			−0.271675	+	0.962389i	$0.587578\pi$
$984$		0			0
$985$		0			0
$986$	−268.413	−	195.014i	−0.272224	−	0.197783i
$987$		0			0
$988$	−5.48843	−	16.8916i	−0.00555509	−	0.0170968i
$989$	−32.3607			−0.0327206
$990$		0			0
$991$		−	520.419i		−	0.525146i	−0.964912	−	0.262573i	$-0.915429\pi$
$991$		−	520.419i		−	0.525146i	0.964912	−	0.262573i	$-0.0845710\pi$
$992$	1518.30			1.53054
$993$		0			0
$994$	−542.492	−	394.144i	−0.545767	−	0.396523i
$995$		0			0
$996$		0			0
$997$		−	457.680i		−	0.459057i	−0.973302	−	0.229528i	$-0.926282\pi$
$997$		−	457.680i		−	0.459057i	0.973302	−	0.229528i	$-0.0737184\pi$
$998$	1015.09	+	737.508i	1.01713	+	0.738986i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.f.e.199.5		8
3.2	odd	2		100.3.d.b.99.4		8
4.3	odd	2	inner	900.3.f.e.199.3		8
5.2	odd	4		180.3.c.a.91.4		4
5.3	odd	4		900.3.c.k.451.1		4
5.4	even	2	inner	900.3.f.e.199.4		8
12.11	even	2		100.3.d.b.99.6		8
15.2	even	4		20.3.b.a.11.1	✓	4
15.8	even	4		100.3.b.f.51.4		4
15.14	odd	2		100.3.d.b.99.5		8
20.3	even	4		900.3.c.k.451.2		4
20.7	even	4		180.3.c.a.91.3		4
20.19	odd	2	inner	900.3.f.e.199.6		8
24.5	odd	2		1600.3.h.n.1599.2		8
24.11	even	2		1600.3.h.n.1599.7		8
40.27	even	4		2880.3.e.e.2431.3		4
40.37	odd	4		2880.3.e.e.2431.4		4
60.23	odd	4		100.3.b.f.51.3		4
60.47	odd	4		20.3.b.a.11.2	yes	4
60.59	even	2		100.3.d.b.99.3		8
120.29	odd	2		1600.3.h.n.1599.8		8
120.53	even	4		1600.3.b.s.1151.1		4
120.59	even	2		1600.3.h.n.1599.1		8
120.77	even	4		320.3.b.c.191.4		4
120.83	odd	4		1600.3.b.s.1151.4		4
120.107	odd	4		320.3.b.c.191.1		4
240.77	even	4		1280.3.g.e.1151.7		8
240.107	odd	4		1280.3.g.e.1151.8		8
240.197	even	4		1280.3.g.e.1151.2		8
240.227	odd	4		1280.3.g.e.1151.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.3.b.a.11.1	✓	4	15.2	even	4
20.3.b.a.11.2	yes	4	60.47	odd	4
100.3.b.f.51.3		4	60.23	odd	4
100.3.b.f.51.4		4	15.8	even	4
100.3.d.b.99.3		8	60.59	even	2
100.3.d.b.99.4		8	3.2	odd	2
100.3.d.b.99.5		8	15.14	odd	2
100.3.d.b.99.6		8	12.11	even	2
180.3.c.a.91.3		4	20.7	even	4
180.3.c.a.91.4		4	5.2	odd	4
320.3.b.c.191.1		4	120.107	odd	4
320.3.b.c.191.4		4	120.77	even	4
900.3.c.k.451.1		4	5.3	odd	4
900.3.c.k.451.2		4	20.3	even	4
900.3.f.e.199.3		8	4.3	odd	2	inner
900.3.f.e.199.4		8	5.4	even	2	inner
900.3.f.e.199.5		8	1.1	even	1	trivial
900.3.f.e.199.6		8	20.19	odd	2	inner
1280.3.g.e.1151.1		8	240.227	odd	4
1280.3.g.e.1151.2		8	240.197	even	4
1280.3.g.e.1151.7		8	240.77	even	4
1280.3.g.e.1151.8		8	240.107	odd	4
1600.3.b.s.1151.1		4	120.53	even	4
1600.3.b.s.1151.4		4	120.83	odd	4
1600.3.h.n.1599.1		8	120.59	even	2
1600.3.h.n.1599.2		8	24.5	odd	2
1600.3.h.n.1599.7		8	24.11	even	2
1600.3.h.n.1599.8		8	120.29	odd	2
2880.3.e.e.2431.3		4	40.27	even	4
2880.3.e.e.2431.4		4	40.37	odd	4

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.17557 - 1.61803i) q^{2} +(-1.23607 - 3.80423i) q^{4} +8.50651 q^{7} +(-7.60845 - 2.47214i) q^{8} +1.79611i q^{11} +0.472136i q^{13} +(10.0000 - 13.7638i) q^{14} +(-12.9443 + 9.40456i) q^{16} -23.8885i q^{17} -9.40456i q^{19} +(2.90617 + 2.11146i) q^{22} +16.1150 q^{23} +(0.763932 + 0.555029i) q^{26} +(-10.5146 - 32.3607i) q^{28} +6.94427 q^{29} -47.4468i q^{31} +32.0000i q^{32} +(-38.6525 - 28.0827i) q^{34} -26.3607i q^{37} +(-15.2169 - 11.0557i) q^{38} +41.4164 q^{41} -2.00811 q^{43} +(6.83282 - 2.22012i) q^{44} +(18.9443 - 26.0746i) q^{46} -35.3481 q^{47} +23.3607 q^{49} +(1.79611 - 0.583592i) q^{52} +21.6393i q^{53} +(-64.7214 - 21.0292i) q^{56} +(8.16348 - 11.2361i) q^{58} -73.8644i q^{59} -26.1378 q^{61} +(-76.7706 - 55.7771i) q^{62} +(51.7771 + 37.6183i) q^{64} -88.8693 q^{67} +(-90.8774 + 29.5279i) q^{68} -39.4144i q^{71} +137.554i q^{73} +(-42.6525 - 30.9888i) q^{74} +(-35.7771 + 11.6247i) q^{76} +15.2786i q^{77} -113.703i q^{79} +(48.6879 - 67.0132i) q^{82} -21.2412 q^{83} +(-2.36068 + 3.24920i) q^{86} +(4.44023 - 13.6656i) q^{88} +67.4427 q^{89} +4.01623i q^{91} +(-19.9192 - 61.3050i) q^{92} +(-41.5542 + 57.1944i) q^{94} +39.1672i q^{97} +(27.4621 - 37.7984i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} + 80 q^{14} - 32 q^{16} + 24 q^{26} - 16 q^{29} - 184 q^{34} + 224 q^{41} - 160 q^{44} + 80 q^{46} + 8 q^{49} - 160 q^{56} + 256 q^{61} + 128 q^{64} - 216 q^{74} + 160 q^{86} - 176 q^{89}+ \cdots + 240 q^{94}+O(q^{100}) \) 8 * q + 8 * q^4 + 80 * q^14 - 32 * q^16 + 24 * q^26 - 16 * q^29 - 184 * q^34 + 224 * q^41 - 160 * q^44 + 80 * q^46 + 8 * q^49 - 160 * q^56 + 256 * q^61 + 128 * q^64 - 216 * q^74 + 160 * q^86 - 176 * q^89 + 240 * q^94

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