LMFDB - Embedded newform 900.3.c.u.451.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(451,900)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("900.451");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.85100625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + x^{5} + 3x^{4} + 2x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + x^5 + 3x^4 + 2x^3 - 8x^2 - 8*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			451.6
Root			$-0.600040 + 1.28061i$ of defining polynomial
Character	$\chi$	$=$	900.451
Dual form			900.3.c.u.451.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.67986 + 1.08539i) q^{2} +(1.64388 + 3.64660i) q^{4} +0.596540i q^{7} +(-1.19648 + 7.91002i) q^{8} +O(q^{10})$	\(q+(1.67986 + 1.08539i) q^{2} +(1.64388 + 3.64660i) q^{4} +0.596540i q^{7} +(-1.19648 + 7.91002i) q^{8} +9.27963i q^{11} +23.5117 q^{13} +(-0.647476 + 1.00210i) q^{14} +(-10.5953 + 11.9891i) q^{16} +3.97751 q^{17} +7.04756i q^{19} +(-10.0720 + 15.5885i) q^{22} -32.0793i q^{23} +(39.4964 + 25.5192i) q^{26} +(-2.17534 + 0.980637i) q^{28} -35.6734 q^{29} +59.2585i q^{31} +(-30.8115 + 8.64000i) q^{32} +(6.68167 + 4.31713i) q^{34} +5.38761 q^{37} +(-7.64932 + 11.8389i) q^{38} -40.0791 q^{41} +36.1157i q^{43} +(-33.8391 + 15.2545i) q^{44} +(34.8184 - 53.8888i) q^{46} +74.0131i q^{47} +48.6441 q^{49} +(38.6503 + 85.7376i) q^{52} -2.55123 q^{53} +(-4.71864 - 0.713748i) q^{56} +(-59.9265 - 38.7194i) q^{58} +36.4026i q^{59} -8.73223 q^{61} +(-64.3183 + 99.5461i) q^{62} +(-61.1369 - 18.9284i) q^{64} +69.7379i q^{67} +(6.53853 + 14.5044i) q^{68} -59.2170i q^{71} +83.0019 q^{73} +(9.05044 + 5.84763i) q^{74} +(-25.6996 + 11.5853i) q^{76} -5.53566 q^{77} -65.8705i q^{79} +(-67.3274 - 43.5013i) q^{82} -129.909i q^{83} +(-39.1995 + 60.6695i) q^{86} +(-73.4020 - 11.1029i) q^{88} +130.466 q^{89} +14.0256i q^{91} +(116.980 - 52.7344i) q^{92} +(-80.3327 + 124.332i) q^{94} -93.1113 q^{97} +(81.7155 + 52.7977i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 10 q^{4} - 20 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 + 10 * q^4 - 20 * q^8	$ 8 q + 4 q^{2} + 10 q^{4} - 20 q^{8} - 16 q^{13} + 20 q^{14} + 34 q^{16} - 68 q^{22} + 36 q^{26} - 28 q^{28} - 64 q^{29} - 76 q^{32} - 92 q^{34} + 112 q^{37} - 40 q^{38} + 16 q^{41} - 172 q^{44} + 152 q^{46} - 56 q^{49} + 128 q^{52} + 352 q^{53} - 116 q^{56} + 204 q^{58} - 176 q^{61} - 56 q^{62} - 110 q^{64} - 184 q^{68} + 240 q^{73} - 132 q^{74} - 24 q^{76} - 288 q^{77} - 40 q^{82} + 200 q^{86} - 140 q^{88} - 80 q^{89} + 144 q^{92} - 96 q^{94} - 432 q^{97} + 660 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 + 10 * q^4 - 20 * q^8 - 16 * q^13 + 20 * q^14 + 34 * q^16 - 68 * q^22 + 36 * q^26 - 28 * q^28 - 64 * q^29 - 76 * q^32 - 92 * q^34 + 112 * q^37 - 40 * q^38 + 16 * q^41 - 172 * q^44 + 152 * q^46 - 56 * q^49 + 128 * q^52 + 352 * q^53 - 116 * q^56 + 204 * q^58 - 176 * q^61 - 56 * q^62 - 110 * q^64 - 184 * q^68 + 240 * q^73 - 132 * q^74 - 24 * q^76 - 288 * q^77 - 40 * q^82 + 200 * q^86 - 140 * q^88 - 80 * q^89 + 144 * q^92 - 96 * q^94 - 432 * q^97 + 660 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	1.67986	+	1.08539i	0.839931	+	0.542693i
$2$	1.67986	+	1.08539i	0.839931	+	0.542693i
$3$		0			0
$3$		0			0
$4$	1.64388	+	3.64660i	0.410969	+	0.911649i
$5$		0			0
$5$		0			0
$6$		0			0
$7$			0.596540i			0.0852199i	0.999092	+	0.0426100i	$0.0135673\pi$
$7$			0.596540i			0.0852199i	−0.999092	+	0.0426100i	$0.986433\pi$
$8$	−1.19648	+	7.91002i	−0.149560	+	0.988753i
$9$		0			0
$10$		0			0
$11$			9.27963i			0.843602i	0.906688	+	0.421801i	$0.138602\pi$
$11$			9.27963i			0.843602i	−0.906688	+	0.421801i	$0.861398\pi$
$12$		0			0
$13$	23.5117			1.80859			0.904295	−	0.426907i	$-0.140397\pi$
$13$	23.5117			1.80859			0.904295	+	0.426907i	$0.140397\pi$
$14$	−0.647476	+	1.00210i	−0.0462483	+	0.0715789i
$15$		0			0
$16$	−10.5953	+	11.9891i	−0.662209	+	0.749319i
$17$	3.97751			0.233971			0.116986	−	0.993134i	$-0.462677\pi$
$17$	3.97751			0.233971			0.116986	+	0.993134i	$0.462677\pi$
$18$		0			0
$19$			7.04756i			0.370924i	0.982651	+	0.185462i	$0.0593782\pi$
$19$			7.04756i			0.370924i	−0.982651	+	0.185462i	$0.940622\pi$
$20$		0			0
$21$		0			0
$22$	−10.0720	+	15.5885i	−0.457817	+	0.708568i
$23$		−	32.0793i		−	1.39475i	−0.716705	−	0.697376i	$-0.754351\pi$
$23$		−	32.0793i		−	1.39475i	0.716705	−	0.697376i	$-0.245649\pi$
$24$		0			0
$25$		0			0
$26$	39.4964	+	25.5192i	1.51909	+	0.981509i
$27$		0			0
$28$	−2.17534	+	0.980637i	−0.0776907	+	0.0350227i
$29$	−35.6734			−1.23012			−0.615059	−	0.788481i	$-0.710868\pi$
$29$	−35.6734			−1.23012			−0.615059	+	0.788481i	$0.710868\pi$
$30$		0			0
$31$			59.2585i			1.91156i	0.294076	+	0.955782i	$0.404988\pi$
$31$			59.2585i			1.91156i	−0.294076	+	0.955782i	$0.595012\pi$
$32$	−30.8115	+	8.64000i	−0.962860	+	0.270000i
$33$		0			0
$34$	6.68167	+	4.31713i	0.196520	+	0.126974i
$35$		0			0
$36$		0			0
$37$	5.38761			0.145611			0.0728055	−	0.997346i	$-0.476805\pi$
$37$	5.38761			0.145611			0.0728055	+	0.997346i	$0.476805\pi$
$38$	−7.64932	+	11.8389i	−0.201298	+	0.311551i
$39$		0			0
$40$		0			0
$41$	−40.0791			−0.977539			−0.488769	−	0.872413i	$-0.662554\pi$
$41$	−40.0791			−0.977539			−0.488769	+	0.872413i	$0.662554\pi$
$42$		0			0
$43$			36.1157i			0.839901i	0.907547	+	0.419950i	$0.137953\pi$
$43$			36.1157i			0.839901i	−0.907547	+	0.419950i	$0.862047\pi$
$44$	−33.8391	+	15.2545i	−0.769070	+	0.346694i
$45$		0			0
$46$	34.8184	−	53.8888i	0.756922	−	1.17150i
$47$			74.0131i			1.57475i	0.616477	+	0.787373i	$0.288559\pi$
$47$			74.0131i			1.57475i	−0.616477	+	0.787373i	$0.711441\pi$
$48$		0			0
$49$	48.6441			0.992738
$50$		0			0
$51$		0			0
$52$	38.6503	+	85.7376i	0.743275	+	1.64880i
$53$	−2.55123			−0.0481364			−0.0240682	−	0.999710i	$-0.507662\pi$
$53$	−2.55123			−0.0481364			−0.0240682	+	0.999710i	$0.507662\pi$
$54$		0			0
$55$		0			0
$56$	−4.71864	−	0.713748i	−0.0842614	−	0.0127455i
$57$		0			0
$58$	−59.9265	−	38.7194i	−1.03321	−	0.667576i
$59$			36.4026i			0.616993i	0.951225	+	0.308497i	$0.0998259\pi$
$59$			36.4026i			0.616993i	−0.951225	+	0.308497i	$0.900174\pi$
$60$		0			0
$61$	−8.73223			−0.143151			−0.0715757	−	0.997435i	$-0.522803\pi$
$61$	−8.73223			−0.143151			−0.0715757	+	0.997435i	$0.522803\pi$
$62$	−64.3183	+	99.5461i	−1.03739	+	1.60558i
$63$		0			0
$64$	−61.1369	−	18.9284i	−0.955264	−	0.295756i
$65$		0			0
$66$		0			0
$67$			69.7379i			1.04086i	0.853903	+	0.520432i	$0.174229\pi$
$67$			69.7379i			1.04086i	−0.853903	+	0.520432i	$0.825771\pi$
$68$	6.53853	+	14.5044i	0.0961548	+	0.213300i
$69$		0			0
$70$		0			0
$71$		−	59.2170i		−	0.834043i	−0.908897	−	0.417021i	$-0.863074\pi$
$71$		−	59.2170i		−	0.834043i	0.908897	−	0.417021i	$-0.136926\pi$
$72$		0			0
$73$	83.0019			1.13701			0.568506	−	0.822679i	$-0.307522\pi$
$73$	83.0019			1.13701			0.568506	+	0.822679i	$0.307522\pi$
$74$	9.05044	+	5.84763i	0.122303	+	0.0790220i
$75$		0			0
$76$	−25.6996	+	11.5853i	−0.338153	+	0.152438i
$77$	−5.53566			−0.0718917
$78$		0			0
$79$		−	65.8705i		−	0.833804i	−0.908951	−	0.416902i	$-0.863116\pi$
$79$		−	65.8705i		−	0.833804i	0.908951	−	0.416902i	$-0.136884\pi$
$80$		0			0
$81$		0			0
$82$	−67.3274	−	43.5013i	−0.821065	−	0.530503i
$83$		−	129.909i		−	1.56517i	−0.622542	−	0.782586i	$-0.713900\pi$
$83$		−	129.909i		−	1.56517i	0.622542	−	0.782586i	$-0.286100\pi$
$84$		0			0
$85$		0			0
$86$	−39.1995	+	60.6695i	−0.455808	+	0.705459i
$87$		0			0
$88$	−73.4020	−	11.1029i	−0.834114	−	0.126169i
$89$	130.466			1.46591			0.732956	−	0.680277i	$-0.238140\pi$
$89$	130.466			1.46591			0.732956	+	0.680277i	$0.238140\pi$
$90$		0			0
$91$			14.0256i			0.154128i
$92$	116.980	−	52.7344i	1.27152	−	0.573200i
$93$		0			0
$94$	−80.3327	+	124.332i	−0.854603	+	1.32268i
$95$		0			0
$96$		0			0
$97$	−93.1113			−0.959911			−0.479955	−	0.877293i	$-0.659347\pi$
$97$	−93.1113			−0.959911			−0.479955	+	0.877293i	$0.659347\pi$
$98$	81.7155	+	52.7977i	0.833831	+	0.538752i
$99$		0			0
$100$		0			0
$101$	3.66081			0.0362457			0.0181228	−	0.999836i	$-0.494231\pi$
$101$	3.66081			0.0362457			0.0181228	+	0.999836i	$0.494231\pi$
$102$		0			0
$103$		−	151.417i		−	1.47007i	−0.678032	−	0.735033i	$-0.737167\pi$
$103$		−	151.417i		−	1.47007i	0.678032	−	0.735033i	$-0.262833\pi$
$104$	−28.1313	+	185.978i	−0.270493	+	1.78825i
$105$		0			0
$106$	−4.28571	−	2.76907i	−0.0404313	−	0.0261233i
$107$			82.8092i			0.773918i	0.922097	+	0.386959i	$0.126474\pi$
$107$			82.8092i			0.773918i	−0.922097	+	0.386959i	$0.873526\pi$
$108$		0			0
$109$	−7.36835			−0.0675996			−0.0337998	−	0.999429i	$-0.510761\pi$
$109$	−7.36835			−0.0675996			−0.0337998	+	0.999429i	$0.510761\pi$
$110$		0			0
$111$		0			0
$112$	−7.15197	−	6.32054i	−0.0638569	−	0.0564334i
$113$	65.0370			0.575549			0.287774	−	0.957698i	$-0.407085\pi$
$113$	65.0370			0.575549			0.287774	+	0.957698i	$0.407085\pi$
$114$		0			0
$115$		0			0
$116$	−58.6427	−	130.087i	−0.505540	−	1.12144i
$117$		0			0
$118$	−39.5109	+	61.1514i	−0.334838	+	0.518232i
$119$			2.37274i			0.0199390i
$120$		0			0
$121$	34.8885			0.288335
$122$	−14.6689	−	9.47784i	−0.120237	−	0.0776872i
$123$		0			0
$124$	−216.092	+	97.4136i	−1.74268	+	0.785593i
$125$		0			0
$126$		0			0
$127$		−	139.469i		−	1.09818i	−0.835763	−	0.549091i	$-0.814974\pi$
$127$		−	139.469i		−	1.09818i	0.835763	−	0.549091i	$-0.185026\pi$
$128$	−82.1569	−	98.1542i	−0.641851	−	0.766829i
$129$		0			0
$130$		0			0
$131$			63.4856i			0.484623i	0.970198	+	0.242312i	$0.0779056\pi$
$131$			63.4856i			0.484623i	−0.970198	+	0.242312i	$0.922094\pi$
$132$		0			0
$133$	−4.20415			−0.0316101
$134$	−75.6925	+	117.150i	−0.564870	+	0.874254i
$135$		0			0
$136$	−4.75901	+	31.4622i	−0.0349927	+	0.231340i
$137$	−138.157			−1.00845			−0.504223	−	0.863573i	$-0.668221\pi$
$137$	−138.157			−1.00845			−0.504223	+	0.863573i	$0.668221\pi$
$138$		0			0
$139$			29.9578i			0.215523i	0.994177	+	0.107762i	$0.0343684\pi$
$139$			29.9578i			0.215523i	−0.994177	+	0.107762i	$0.965632\pi$
$140$		0			0
$141$		0			0
$142$	64.2733	−	99.4765i	0.452629	−	0.700539i
$143$			218.180i			1.52573i
$144$		0			0
$145$		0			0
$146$	139.432	+	90.0891i	0.955012	+	0.617048i
$147$		0			0
$148$	8.85655	+	19.6464i	0.0598416	+	0.132746i
$149$	47.3823			0.318002			0.159001	−	0.987278i	$-0.449173\pi$
$149$	47.3823			0.318002			0.159001	+	0.987278i	$0.449173\pi$
$150$		0			0
$151$		−	109.604i		−	0.725852i	−0.931818	−	0.362926i	$-0.881778\pi$
$151$		−	109.604i		−	0.725852i	0.931818	−	0.362926i	$-0.118222\pi$
$152$	−55.7463	−	8.43227i	−0.366752	−	0.0554755i
$153$		0			0
$154$	−9.29915	−	6.00833i	−0.0603841	−	0.0390151i
$155$		0			0
$156$		0			0
$157$	177.588			1.13113			0.565566	−	0.824703i	$-0.308658\pi$
$157$	177.588			1.13113			0.565566	+	0.824703i	$0.308658\pi$
$158$	71.4950	−	110.653i	0.452500	−	0.700338i
$159$		0			0
$160$		0			0
$161$	19.1366			0.118861
$162$		0			0
$163$		−	96.8778i		−	0.594342i	−0.954824	−	0.297171i	$-0.903957\pi$
$163$		−	96.8778i		−	0.594342i	0.954824	−	0.297171i	$-0.0960432\pi$
$164$	−65.8850	−	146.152i	−0.401738	−	0.891173i
$165$		0			0
$166$	141.002	−	218.230i	0.849408	−	1.31464i
$167$		−	152.605i		−	0.913801i	−0.889518	−	0.456901i	$-0.848960\pi$
$167$		−	152.605i		−	0.913801i	0.889518	−	0.456901i	$-0.151040\pi$
$168$		0			0
$169$	383.799			2.27100
$170$		0			0
$171$		0			0
$172$	−131.700	+	59.3698i	−0.765695	+	0.345173i
$173$	155.773			0.900422			0.450211	−	0.892922i	$-0.351349\pi$
$173$	155.773			0.900422			0.450211	+	0.892922i	$0.351349\pi$
$174$		0			0
$175$		0			0
$176$	−111.254	−	98.3209i	−0.632127	−	0.558641i
$177$		0			0
$178$	219.165	+	141.606i	1.23126	+	0.795540i
$179$		−	126.001i		−	0.703915i	−0.936016	−	0.351957i	$-0.885516\pi$
$179$		−	126.001i		−	0.703915i	0.936016	−	0.351957i	$-0.114484\pi$
$180$		0			0
$181$	−346.725			−1.91561			−0.957803	−	0.287424i	$-0.907201\pi$
$181$	−346.725			−1.91561			−0.957803	+	0.287424i	$0.907201\pi$
$182$	−15.2232	+	23.5612i	−0.0836442	+	0.129457i
$183$		0			0
$184$	253.748	+	38.3823i	1.37906	+	0.208599i
$185$		0			0
$186$		0			0
$187$			36.9098i			0.197379i
$188$	−269.896	+	121.668i	−1.43562	+	0.647171i
$189$		0			0
$190$		0			0
$191$			133.159i			0.697167i	0.937278	+	0.348584i	$0.113337\pi$
$191$			133.159i			0.697167i	−0.937278	+	0.348584i	$0.886663\pi$
$192$		0			0
$193$	136.246			0.705940			0.352970	−	0.935635i	$-0.385172\pi$
$193$	136.246			0.705940			0.352970	+	0.935635i	$0.385172\pi$
$194$	−156.414	−	101.062i	−0.806259	−	0.520937i
$195$		0			0
$196$	79.9649	+	177.386i	0.407984	+	0.905029i
$197$	74.8945			0.380175			0.190087	−	0.981767i	$-0.439123\pi$
$197$	74.8945			0.380175			0.190087	+	0.981767i	$0.439123\pi$
$198$		0			0
$199$		−	251.605i		−	1.26434i	−0.774828	−	0.632172i	$-0.782164\pi$
$199$		−	251.605i		−	1.26434i	0.774828	−	0.632172i	$-0.217836\pi$
$200$		0			0
$201$		0			0
$202$	6.14966	+	3.97339i	0.0304439	+	0.0196703i
$203$		−	21.2806i		−	0.104831i
$204$		0			0
$205$		0			0
$206$	164.346	−	254.359i	0.797794	−	1.23475i
$207$		0			0
$208$	−249.114	+	281.884i	−1.19767	+	1.35521i
$209$	−65.3987			−0.312913
$210$		0			0
$211$		−	228.203i		−	1.08153i	−0.841173	−	0.540766i	$-0.818135\pi$
$211$		−	228.203i		−	1.08153i	0.841173	−	0.540766i	$-0.181865\pi$
$212$	−4.19390	−	9.30331i	−0.0197826	−	0.0438835i
$213$		0			0
$214$	−89.8799	+	139.108i	−0.420000	+	0.650038i
$215$		0			0
$216$		0			0
$217$	−35.3500			−0.162903
$218$	−12.3778	−	7.99751i	−0.0567790	−	0.0366858i
$219$		0			0
$220$		0			0
$221$	93.5179			0.423158
$222$		0			0
$223$		−	85.9549i		−	0.385448i	−0.981253	−	0.192724i	$-0.938268\pi$
$223$		−	85.9549i		−	0.385448i	0.981253	−	0.192724i	$-0.0617322\pi$
$224$	−5.15410	−	18.3803i	−0.0230094	−	0.0820549i
$225$		0			0
$226$	109.253	+	70.5902i	0.483421	+	0.312346i
$227$		−	282.357i		−	1.24386i	−0.783071	−	0.621932i	$-0.786348\pi$
$227$		−	282.357i		−	1.24386i	0.783071	−	0.621932i	$-0.213652\pi$
$228$		0			0
$229$	138.263			0.603768			0.301884	−	0.953345i	$-0.402385\pi$
$229$	138.263			0.603768			0.301884	+	0.953345i	$0.402385\pi$
$230$		0			0
$231$		0			0
$232$	42.6826	−	282.178i	0.183977	−	1.21628i
$233$	−0.522939			−0.00224438			−0.00112219	−	0.999999i	$-0.500357\pi$
$233$	−0.522939			−0.00224438			−0.00112219	+	0.999999i	$0.500357\pi$
$234$		0			0
$235$		0			0
$236$	−132.746	+	59.8413i	−0.562482	+	0.253565i
$237$		0			0
$238$	−2.57534	+	3.98588i	−0.0108208	+	0.0167474i
$239$			73.6928i			0.308338i	0.988044	+	0.154169i	$0.0492700\pi$
$239$			73.6928i			0.308338i	−0.988044	+	0.154169i	$0.950730\pi$
$240$		0			0
$241$	31.3705			0.130168			0.0650840	−	0.997880i	$-0.479268\pi$
$241$	31.3705			0.130168			0.0650840	+	0.997880i	$0.479268\pi$
$242$	58.6080	+	37.8675i	0.242182	+	0.156477i
$243$		0			0
$244$	−14.3547	−	31.8429i	−0.0588307	−	0.130504i
$245$		0			0
$246$		0			0
$247$			165.700i			0.670850i
$248$	−468.736	−	70.9016i	−1.89006	−	0.285894i
$249$		0			0
$250$		0			0
$251$			78.7478i			0.313736i	0.987620	+	0.156868i	$0.0501398\pi$
$251$			78.7478i			0.313736i	−0.987620	+	0.156868i	$0.949860\pi$
$252$		0			0
$253$	297.684			1.17662
$254$	151.378	−	234.289i	0.595975	−	0.922397i
$255$		0			0
$256$	−31.4772	−	254.057i	−0.122958	−	0.992412i
$257$	243.954			0.949236			0.474618	−	0.880192i	$-0.342586\pi$
$257$	243.954			0.949236			0.474618	+	0.880192i	$0.342586\pi$
$258$		0			0
$259$			3.21392i			0.0124090i
$260$		0			0
$261$		0			0
$262$	−68.9064	+	106.647i	−0.263002	+	0.407050i
$263$		−	102.737i		−	0.390635i	−0.980740	−	0.195317i	$-0.937426\pi$
$263$		−	102.737i		−	0.390635i	0.980740	−	0.195317i	$-0.0625737\pi$
$264$		0			0
$265$		0			0
$266$	−7.06239	−	4.56312i	−0.0265503	−	0.0171546i
$267$		0			0
$268$	−254.306	+	114.640i	−0.948903	+	0.427763i
$269$	123.646			0.459651			0.229825	−	0.973232i	$-0.426184\pi$
$269$	123.646			0.459651			0.229825	+	0.973232i	$0.426184\pi$
$270$		0			0
$271$			332.371i			1.22646i	0.789904	+	0.613230i	$0.210130\pi$
$271$			332.371i			1.22646i	−0.789904	+	0.613230i	$0.789870\pi$
$272$	−42.1431	+	47.6868i	−0.154938	+	0.175319i
$273$		0			0
$274$	−232.085	−	149.954i	−0.847026	−	0.547277i
$275$		0			0
$276$		0			0
$277$	125.916			0.454571			0.227286	−	0.973828i	$-0.427015\pi$
$277$	125.916			0.454571			0.227286	+	0.973828i	$0.427015\pi$
$278$	−32.5157	+	50.3249i	−0.116963	+	0.181025i
$279$		0			0
$280$		0			0
$281$	−52.5628			−0.187056			−0.0935281	−	0.995617i	$-0.529814\pi$
$281$	−52.5628			−0.187056			−0.0935281	+	0.995617i	$0.529814\pi$
$282$		0			0
$283$		−	199.288i		−	0.704199i	−0.935963	−	0.352100i	$-0.885468\pi$
$283$		−	199.288i		−	0.704199i	0.935963	−	0.352100i	$-0.114532\pi$
$284$	215.941	−	97.3454i	0.760355	−	0.342766i
$285$		0			0
$286$	−236.809	+	366.512i	−0.828004	+	1.28151i
$287$		−	23.9088i		−	0.0833058i
$288$		0			0
$289$	−273.179			−0.945258
$290$		0			0
$291$		0			0
$292$	136.445	+	302.674i	0.467276	+	1.03656i
$293$	102.161			0.348672			0.174336	−	0.984686i	$-0.444222\pi$
$293$	102.161			0.348672			0.174336	+	0.984686i	$0.444222\pi$
$294$		0			0
$295$		0			0
$296$	−6.44617	+	42.6161i	−0.0217776	+	0.143973i
$297$		0			0
$298$	79.5957	+	51.4281i	0.267100	+	0.172577i
$299$		−	754.238i		−	2.52254i
$300$		0			0
$301$	−21.5445			−0.0715763
$302$	118.962	−	184.119i	0.393915	−	0.609666i
$303$		0			0
$304$	−84.4939	−	74.6713i	−0.277941	−	0.245629i
$305$		0			0
$306$		0			0
$307$		−	328.391i		−	1.06968i	−0.844954	−	0.534839i	$-0.820372\pi$
$307$		−	328.391i		−	1.06968i	0.844954	−	0.534839i	$-0.179628\pi$
$308$	−9.09994	−	20.1863i	−0.0295453	−	0.0655401i
$309$		0			0
$310$		0			0
$311$		−	95.4377i		−	0.306874i	−0.988158	−	0.153437i	$-0.950966\pi$
$311$		−	95.4377i		−	0.306874i	0.988158	−	0.153437i	$-0.0490342\pi$
$312$		0			0
$313$	−550.408			−1.75849			−0.879246	−	0.476368i	$-0.841953\pi$
$313$	−550.408			−1.75849			−0.879246	+	0.476368i	$0.841953\pi$
$314$	298.323	+	192.751i	0.950073	+	0.613858i
$315$		0			0
$316$	240.203	−	108.283i	0.760137	−	0.342668i
$317$	439.394			1.38610			0.693051	−	0.720889i	$-0.256266\pi$
$317$	439.394			1.38610			0.693051	+	0.720889i	$0.256266\pi$
$318$		0			0
$319$		−	331.036i		−	1.03773i
$320$		0			0
$321$		0			0
$322$	32.1468	+	20.7706i	0.0998348	+	0.0645048i
$323$			28.0317i			0.0867855i
$324$		0			0
$325$		0			0
$326$	105.150	−	162.741i	0.322545	−	0.499206i
$327$		0			0
$328$	47.9539	−	317.026i	0.146201	−	0.966544i
$329$	−44.1517			−0.134200
$330$		0			0
$331$			479.922i			1.44992i	0.688794	+	0.724958i	$0.258141\pi$
$331$			479.922i			1.44992i	−0.688794	+	0.724958i	$0.741859\pi$
$332$	473.727	−	213.555i	1.42689	−	0.643237i
$333$		0			0
$334$	165.635	−	256.355i	0.495913	−	0.767530i
$335$		0			0
$336$		0			0
$337$	−58.8437			−0.174610			−0.0873052	−	0.996182i	$-0.527826\pi$
$337$	−58.8437			−0.174610			−0.0873052	+	0.996182i	$0.527826\pi$
$338$	644.730	+	416.570i	1.90748	+	1.23246i
$339$		0			0
$340$		0			0
$341$	−549.897			−1.61260
$342$		0			0
$343$			58.2486i			0.169821i
$344$	−285.676	−	43.2118i	−0.830454	−	0.125616i
$345$		0			0
$346$	261.677	+	169.074i	0.756293	+	0.488653i
$347$		−	12.1484i		−	0.0350099i	−0.999847	−	0.0175049i	$-0.994428\pi$
$347$		−	12.1484i		−	0.0350099i	0.999847	−	0.0175049i	$-0.00557228\pi$
$348$		0			0
$349$	−30.9277			−0.0886180			−0.0443090	−	0.999018i	$-0.514109\pi$
$349$	−30.9277			−0.0886180			−0.0443090	+	0.999018i	$0.514109\pi$
$350$		0			0
$351$		0			0
$352$	−80.1760	−	285.919i	−0.227773	−	0.812271i
$353$	−288.065			−0.816048			−0.408024	−	0.912971i	$-0.633782\pi$
$353$	−288.065			−0.816048			−0.408024	+	0.912971i	$0.633782\pi$
$354$		0			0
$355$		0			0
$356$	214.470	+	475.757i	0.602444	+	1.33640i
$357$		0			0
$358$	136.759	−	211.664i	0.382010	−	0.591240i
$359$			663.911i			1.84933i	0.380776	+	0.924667i	$0.375657\pi$
$359$			663.911i			1.84933i	−0.380776	+	0.924667i	$0.624343\pi$
$360$		0			0
$361$	311.332			0.862415
$362$	−582.450	−	376.330i	−1.60898	−	1.03959i
$363$		0			0
$364$	−51.1459	+	23.0564i	−0.140511	+	0.0633418i
$365$		0			0
$366$		0			0
$367$			6.08529i			0.0165812i	0.999966	+	0.00829059i	$0.00263901\pi$
$367$			6.08529i			0.0165812i	−0.999966	+	0.00829059i	$0.997361\pi$
$368$	384.602	+	339.891i	1.04511	+	0.923618i
$369$		0			0
$370$		0			0
$371$		−	1.52191i		−	0.00410218i
$372$		0			0
$373$	204.741			0.548903			0.274451	−	0.961601i	$-0.411504\pi$
$373$	204.741			0.548903			0.274451	+	0.961601i	$0.411504\pi$
$374$	−40.0614	+	62.0034i	−0.107116	+	0.165784i
$375$		0			0
$376$	−585.445	−	88.5552i	−1.55703	−	0.235519i
$377$	−838.742			−2.22478
$378$		0			0
$379$			402.331i			1.06156i	0.847510	+	0.530780i	$0.178101\pi$
$379$			402.331i			1.06156i	−0.847510	+	0.530780i	$0.821899\pi$
$380$		0			0
$381$		0			0
$382$	−144.529	+	223.689i	−0.378348	+	0.585573i
$383$			331.751i			0.866191i	0.901348	+	0.433096i	$0.142579\pi$
$383$			331.751i			0.866191i	−0.901348	+	0.433096i	$0.857421\pi$
$384$		0			0
$385$		0			0
$386$	228.875	+	147.880i	0.592941	+	0.383109i
$387$		0			0
$388$	−153.063	−	339.540i	−0.394493	−	0.875102i
$389$	623.310			1.60234			0.801169	−	0.598438i	$-0.204212\pi$
$389$	623.310			1.60234			0.801169	+	0.598438i	$0.204212\pi$
$390$		0			0
$391$		−	127.596i		−	0.326332i
$392$	−58.2018	+	384.776i	−0.148474	+	0.981572i
$393$		0			0
$394$	125.812	+	81.2894i	0.319321	+	0.206318i
$395$		0			0
$396$		0			0
$397$	355.449			0.895338			0.447669	−	0.894199i	$-0.352254\pi$
$397$	355.449			0.895338			0.447669	+	0.894199i	$0.352254\pi$
$398$	273.088	−	422.661i	0.686151	−	1.06196i
$399$		0			0
$400$		0			0
$401$	542.927			1.35393			0.676966	−	0.736014i	$-0.263294\pi$
$401$	542.927			1.35393			0.676966	+	0.736014i	$0.263294\pi$
$402$		0			0
$403$			1393.27i			3.45724i
$404$	6.01792	+	13.3495i	0.0148958	+	0.0330433i
$405$		0			0
$406$	23.0977	−	35.7485i	0.0568908	−	0.0880505i
$407$			49.9950i			0.122838i
$408$		0			0
$409$	−108.497			−0.265273			−0.132636	−	0.991165i	$-0.542344\pi$
$409$	−108.497			−0.265273			−0.132636	+	0.991165i	$0.542344\pi$
$410$		0			0
$411$		0			0
$412$	552.156	−	248.910i	1.34018	−	0.604151i
$413$	−21.7156			−0.0525801
$414$		0			0
$415$		0			0
$416$	−724.431	+	203.141i	−1.74142	+	0.488320i
$417$		0			0
$418$	−109.861	−	70.9828i	−0.262825	−	0.169815i
$419$		−	172.176i		−	0.410921i	−0.978665	−	0.205460i	$-0.934131\pi$
$419$		−	172.176i		−	0.410921i	0.978665	−	0.205460i	$-0.0658691\pi$
$420$		0			0
$421$	478.522			1.13663			0.568316	−	0.822810i	$-0.307595\pi$
$421$	478.522			1.13663			0.568316	+	0.822810i	$0.307595\pi$
$422$	247.688	−	383.350i	0.586940	−	0.908412i
$423$		0			0
$424$	3.05250	−	20.1803i	0.00719929	−	0.0475950i
$425$		0			0
$426$		0			0
$427$		−	5.20912i		−	0.0121993i
$428$	−301.972	+	136.128i	−0.705541	+	0.318056i
$429$		0			0
$430$		0			0
$431$		−	290.722i		−	0.674530i	−0.941410	−	0.337265i	$-0.890498\pi$
$431$		−	290.722i		−	0.674530i	0.941410	−	0.337265i	$-0.109502\pi$
$432$		0			0
$433$	−53.7726			−0.124186			−0.0620931	−	0.998070i	$-0.519778\pi$
$433$	−53.7726			−0.124186			−0.0620931	+	0.998070i	$0.519778\pi$
$434$	−59.3832	−	38.3684i	−0.136828	−	0.0884065i
$435$		0			0
$436$	−12.1127	−	26.8694i	−0.0277813	−	0.0616271i
$437$	226.081			0.517347
$438$		0			0
$439$		−	328.657i		−	0.748650i	−0.927298	−	0.374325i	$-0.877874\pi$
$439$		−	328.657i		−	0.748650i	0.927298	−	0.374325i	$-0.122126\pi$
$440$		0			0
$441$		0			0
$442$	157.097	+	101.503i	0.355424	+	0.229645i
$443$		−	428.910i		−	0.968194i	−0.875014	−	0.484097i	$-0.839148\pi$
$443$		−	428.910i		−	0.968194i	0.875014	−	0.484097i	$-0.160852\pi$
$444$		0			0
$445$		0			0
$446$	93.2942	−	144.392i	0.209180	−	0.323750i
$447$		0			0
$448$	11.2915	−	36.4706i	0.0252043	−	0.0814075i
$449$	−409.229			−0.911423			−0.455711	−	0.890128i	$-0.650615\pi$
$449$	−409.229			−0.911423			−0.455711	+	0.890128i	$0.650615\pi$
$450$		0			0
$451$		−	371.919i		−	0.824654i
$452$	106.913	+	237.164i	0.236533	+	0.524698i
$453$		0			0
$454$	306.466	−	474.321i	0.675036	−	1.04476i
$455$		0			0
$456$		0			0
$457$	−768.561			−1.68175			−0.840876	−	0.541228i	$-0.817960\pi$
$457$	−768.561			−1.68175			−0.840876	+	0.541228i	$0.817960\pi$
$458$	232.262	+	150.068i	0.507123	+	0.327660i
$459$		0			0
$460$		0			0
$461$	316.563			0.686687			0.343343	−	0.939210i	$-0.388441\pi$
$461$	316.563			0.686687			0.343343	+	0.939210i	$0.388441\pi$
$462$		0			0
$463$		−	491.208i		−	1.06093i	−0.847708	−	0.530463i	$-0.822018\pi$
$463$		−	491.208i		−	1.06093i	0.847708	−	0.530463i	$-0.177982\pi$
$464$	377.972	−	427.692i	0.814596	−	0.921751i
$465$		0			0
$466$	−0.878466	−	0.567591i	−0.00188512	−	0.00121801i
$467$			410.393i			0.878785i	0.898295	+	0.439393i	$0.144806\pi$
$467$			410.393i			0.878785i	−0.898295	+	0.439393i	$0.855194\pi$
$468$		0			0
$469$	−41.6014			−0.0887024
$470$		0			0
$471$		0			0
$472$	−287.945	−	43.5550i	−0.610054	−	0.0922776i
$473$	−335.141			−0.708542
$474$		0			0
$475$		0			0
$476$	−8.65243	+	3.90049i	−0.0181774	+	0.00819431i
$477$		0			0
$478$	−79.9851	+	123.794i	−0.167333	+	0.258983i
$479$		−	198.918i		−	0.415277i	−0.978206	−	0.207638i	$-0.933422\pi$
$479$		−	198.918i		−	0.415277i	0.978206	−	0.207638i	$-0.0665778\pi$
$480$		0			0
$481$	126.672			0.263351
$482$	52.6981	+	34.0491i	0.109332	+	0.0706413i
$483$		0			0
$484$	57.3524	+	127.224i	0.118497	+	0.262860i
$485$		0			0
$486$		0			0
$487$			204.762i			0.420456i	0.977652	+	0.210228i	$0.0674206\pi$
$487$			204.762i			0.420456i	−0.977652	+	0.210228i	$0.932579\pi$
$488$	10.4479	−	69.0721i	0.0214097	−	0.141541i
$489$		0			0
$490$		0			0
$491$		−	788.598i		−	1.60611i	−0.595908	−	0.803053i	$-0.703208\pi$
$491$		−	788.598i		−	1.60611i	0.595908	−	0.803053i	$-0.296792\pi$
$492$		0			0
$493$	−141.891			−0.287812
$494$	−179.848	+	278.353i	−0.364066	+	0.563468i
$495$		0			0
$496$	−710.456	−	627.864i	−1.43237	−	1.26586i
$497$	35.3253			0.0710771
$498$		0			0
$499$			740.385i			1.48374i	0.670545	+	0.741869i	$0.266060\pi$
$499$			740.385i			1.48374i	−0.670545	+	0.741869i	$0.733940\pi$
$500$		0			0
$501$		0			0
$502$	−85.4717	+	132.285i	−0.170262	+	0.263517i
$503$			70.8800i			0.140914i	0.997515	+	0.0704572i	$0.0224458\pi$
$503$			70.8800i			0.140914i	−0.997515	+	0.0704572i	$0.977554\pi$
$504$		0			0
$505$		0			0
$506$	500.068	+	323.102i	0.988277	+	0.638541i
$507$		0			0
$508$	508.588	−	229.270i	1.00116	−	0.451318i
$509$	−522.642			−1.02680			−0.513400	−	0.858149i	$-0.671614\pi$
$509$	−522.642			−1.02680			−0.513400	+	0.858149i	$0.671614\pi$
$510$		0			0
$511$			49.5139i			0.0968961i
$512$	222.873	−	460.946i	0.435299	−	0.900286i
$513$		0			0
$514$	409.809	+	264.784i	0.797293	+	0.515144i
$515$		0			0
$516$		0			0
$517$	−686.813			−1.32846
$518$	−3.48834	+	5.39894i	−0.00673425	+	0.0104227i
$519$		0			0
$520$		0			0
$521$	−304.082			−0.583650			−0.291825	−	0.956472i	$-0.594262\pi$
$521$	−304.082			−0.583650			−0.291825	+	0.956472i	$0.594262\pi$
$522$		0			0
$523$			174.416i			0.333491i	0.986000	+	0.166746i	$0.0533259\pi$
$523$			174.416i			0.333491i	−0.986000	+	0.166746i	$0.946674\pi$
$524$	−231.507	+	104.362i	−0.441806	+	0.199165i
$525$		0			0
$526$	111.509	−	172.584i	0.211995	−	0.328106i
$527$			235.701i			0.447251i
$528$		0			0
$529$	−500.081			−0.945333
$530$		0			0
$531$		0			0
$532$	−6.91109	−	15.3308i	−0.0129908	−	0.0288174i
$533$	−942.327			−1.76797
$534$		0			0
$535$		0			0
$536$	−551.628	−	83.4401i	−1.02916	−	0.155672i
$537$		0			0
$538$	207.708	+	134.204i	0.386075	+	0.249449i
$539$			451.399i			0.837476i
$540$		0			0
$541$	−262.199			−0.484655			−0.242328	−	0.970194i	$-0.577911\pi$
$541$	−262.199			−0.484655			−0.242328	+	0.970194i	$0.577911\pi$
$542$	−360.750	+	558.337i	−0.665591	+	1.03014i
$543$		0			0
$544$	−122.553	+	34.3657i	−0.225281	+	0.0631722i
$545$		0			0
$546$		0			0
$547$		−	146.179i		−	0.267237i	−0.991033	−	0.133619i	$-0.957340\pi$
$547$		−	146.179i		−	0.267237i	0.991033	−	0.133619i	$-0.0426598\pi$
$548$	−227.113	−	503.804i	−0.414440	−	0.919350i
$549$		0			0
$550$		0			0
$551$		−	251.411i		−	0.456281i
$552$		0			0
$553$	39.2944			0.0710568
$554$	211.522	+	136.668i	0.381809	+	0.246693i
$555$		0			0
$556$	−109.244	+	49.2468i	−0.196482	+	0.0885734i
$557$	187.700			0.336984			0.168492	−	0.985703i	$-0.446110\pi$
$557$	187.700			0.336984			0.168492	+	0.985703i	$0.446110\pi$
$558$		0			0
$559$			849.142i			1.51904i
$560$		0			0
$561$		0			0
$562$	−88.2982	−	57.0509i	−0.157114	−	0.101514i
$563$		−	447.848i		−	0.795467i	−0.917501	−	0.397734i	$-0.869797\pi$
$563$		−	447.848i		−	0.795467i	0.917501	−	0.397734i	$-0.130203\pi$
$564$		0			0
$565$		0			0
$566$	216.305	−	334.777i	0.382164	−	0.591479i
$567$		0			0
$568$	468.408	+	70.8520i	0.824662	+	0.124740i
$569$	−1078.91			−1.89615			−0.948077	−	0.318042i	$-0.896975\pi$
$569$	−1078.91			−1.89615			−0.948077	+	0.318042i	$0.896975\pi$
$570$		0			0
$571$		−	936.324i		−	1.63980i	−0.572509	−	0.819899i	$-0.694030\pi$
$571$		−	936.324i		−	1.63980i	0.572509	−	0.819899i	$-0.305970\pi$
$572$	−795.613	+	358.660i	−1.39093	+	0.627028i
$573$		0			0
$574$	25.9502	−	40.1634i	0.0452095	−	0.0699711i
$575$		0			0
$576$		0			0
$577$	544.832			0.944250			0.472125	−	0.881532i	$-0.343487\pi$
$577$	544.832			0.944250			0.472125	+	0.881532i	$0.343487\pi$
$578$	−458.904	−	296.505i	−0.793951	−	0.512985i
$579$		0			0
$580$		0			0
$581$	77.4960			0.133384
$582$		0			0
$583$		−	23.6745i		−	0.0406080i
$584$	−99.3101	+	656.547i	−0.170052	+	1.12422i
$585$		0			0
$586$	171.616	+	110.884i	0.292861	+	0.189222i
$587$		−	337.889i		−	0.575619i	−0.957688	−	0.287810i	$-0.907073\pi$
$587$		−	337.889i		−	0.575619i	0.957688	−	0.287810i	$-0.0929271\pi$
$588$		0			0
$589$	−417.628			−0.709045
$590$		0			0
$591$		0			0
$592$	−57.0836	+	64.5926i	−0.0964249	+	0.109109i
$593$	567.269			0.956608			0.478304	−	0.878194i	$-0.341252\pi$
$593$	567.269			0.956608			0.478304	+	0.878194i	$0.341252\pi$
$594$		0			0
$595$		0			0
$596$	77.8906	+	172.784i	0.130689	+	0.289906i
$597$		0			0
$598$	818.640	−	1267.02i	1.36896	−	2.11876i
$599$			762.966i			1.27373i	0.770974	+	0.636867i	$0.219770\pi$
$599$			762.966i			1.27373i	−0.770974	+	0.636867i	$0.780230\pi$
$600$		0			0
$601$	−790.102			−1.31464			−0.657322	−	0.753609i	$-0.728311\pi$
$601$	−790.102			−1.31464			−0.657322	+	0.753609i	$0.728311\pi$
$602$	−36.1917	−	23.3841i	−0.0601192	−	0.0388440i
$603$		0			0
$604$	399.680	−	180.175i	0.661722	−	0.298302i
$605$		0			0
$606$		0			0
$607$		−	522.994i		−	0.861605i	−0.902446	−	0.430802i	$-0.858231\pi$
$607$		−	522.994i		−	0.861605i	0.902446	−	0.430802i	$-0.141769\pi$
$608$	−60.8909	−	217.146i	−0.100150	−	0.357148i
$609$		0			0
$610$		0			0
$611$			1740.17i			2.84807i
$612$		0			0
$613$	−1026.91			−1.67522			−0.837609	−	0.546270i	$-0.816047\pi$
$613$	−1026.91			−1.67522			−0.837609	+	0.546270i	$0.816047\pi$
$614$	356.431	−	551.652i	0.580506	−	0.898455i
$615$		0			0
$616$	6.62332	−	43.7872i	0.0107521	−	0.0710831i
$617$	−479.223			−0.776698			−0.388349	−	0.921512i	$-0.626954\pi$
$617$	−479.223			−0.776698			−0.388349	+	0.921512i	$0.626954\pi$
$618$		0			0
$619$			507.654i			0.820119i	0.912059	+	0.410059i	$0.134492\pi$
$619$			507.654i			0.820119i	−0.912059	+	0.410059i	$0.865508\pi$
$620$		0			0
$621$		0			0
$622$	103.587	−	160.322i	0.166538	−	0.257753i
$623$			77.8282i			0.124925i
$624$		0			0
$625$		0			0
$626$	−924.609	−	597.405i	−1.47701	−	0.954321i
$627$		0			0
$628$	291.932	+	647.591i	0.464860	+	1.03120i
$629$	21.4293			0.0340688
$630$		0			0
$631$			460.186i			0.729297i	0.931145	+	0.364648i	$0.118811\pi$
$631$			460.186i			0.729297i	−0.931145	+	0.364648i	$0.881189\pi$
$632$	521.037	+	78.8128i	0.824426	+	0.124704i
$633$		0			0
$634$	738.122	+	476.912i	1.16423	+	0.752228i
$635$		0			0
$636$		0			0
$637$	1143.71			1.79546
$638$	359.302	−	556.095i	0.563169	−	0.871622i
$639$		0			0
$640$		0			0
$641$	−250.774			−0.391223			−0.195612	−	0.980681i	$-0.562669\pi$
$641$	−250.774			−0.391223			−0.195612	+	0.980681i	$0.562669\pi$
$642$		0			0
$643$		−	590.355i		−	0.918126i	−0.888404	−	0.459063i	$-0.848185\pi$
$643$		−	590.355i		−	0.918126i	0.888404	−	0.459063i	$-0.151815\pi$
$644$	31.4581	+	69.7834i	0.0488480	+	0.108359i
$645$		0			0
$646$	−30.4252	+	47.0894i	−0.0470979	+	0.0728939i
$647$			319.341i			0.493572i	0.969070	+	0.246786i	$0.0793744\pi$
$647$			319.341i			0.493572i	−0.969070	+	0.246786i	$0.920626\pi$
$648$		0			0
$649$	−337.803			−0.520497
$650$		0			0
$651$		0			0
$652$	353.274	−	159.255i	0.541832	−	0.244256i
$653$	88.5949			0.135674			0.0678369	−	0.997696i	$-0.478390\pi$
$653$	88.5949			0.135674			0.0678369	+	0.997696i	$0.478390\pi$
$654$		0			0
$655$		0			0
$656$	424.652	−	480.512i	0.647335	−	0.732488i
$657$		0			0
$658$	−74.1688	−	47.9216i	−0.112719	−	0.0728292i
$659$			758.423i			1.15087i	0.817847	+	0.575435i	$0.195167\pi$
$659$			758.423i			1.15087i	−0.817847	+	0.575435i	$0.804833\pi$
$660$		0			0
$661$	527.327			0.797771			0.398885	−	0.917001i	$-0.369397\pi$
$661$	527.327			0.797771			0.398885	+	0.917001i	$0.369397\pi$
$662$	−520.900	+	806.203i	−0.786859	+	1.21783i
$663$		0			0
$664$	1027.59	+	155.434i	1.54757	+	0.234087i
$665$		0			0
$666$		0			0
$667$			1144.38i			1.71571i
$668$	556.488	−	250.863i	0.833066	−	0.375544i
$669$		0			0
$670$		0			0
$671$		−	81.0318i		−	0.120763i
$672$		0			0
$673$	−120.657			−0.179283			−0.0896415	−	0.995974i	$-0.528572\pi$
$673$	−120.657			−0.179283			−0.0896415	+	0.995974i	$0.528572\pi$
$674$	−98.8493	−	63.8681i	−0.146661	−	0.0947598i
$675$		0			0
$676$	630.918	+	1399.56i	0.933311	+	2.07036i
$677$	−219.196			−0.323776			−0.161888	−	0.986809i	$-0.551758\pi$
$677$	−219.196			−0.323776			−0.161888	+	0.986809i	$0.551758\pi$
$678$		0			0
$679$		−	55.5446i		−	0.0818035i
$680$		0			0
$681$		0			0
$682$	−923.751	−	596.850i	−1.35447	−	0.875146i
$683$			205.502i			0.300881i	0.988619	+	0.150441i	$0.0480693\pi$
$683$			205.502i			0.300881i	−0.988619	+	0.150441i	$0.951931\pi$
$684$		0			0
$685$		0			0
$686$	−63.2222	+	97.8496i	−0.0921606	+	0.142638i
$687$		0			0
$688$	−432.995	−	382.659i	−0.629354	−	0.556190i
$689$	−59.9837			−0.0870591
$690$		0			0
$691$			109.536i			0.158519i	0.996854	+	0.0792593i	$0.0252555\pi$
$691$			109.536i			0.158519i	−0.996854	+	0.0792593i	$0.974744\pi$
$692$	256.071	+	568.042i	0.370045	+	0.820869i
$693$		0			0
$694$	13.1857	−	20.4077i	0.0189996	−	0.0294059i
$695$		0			0
$696$		0			0
$697$	−159.415			−0.228716
$698$	−51.9543	−	33.5685i	−0.0744331	−	0.0480924i
$699$		0			0
$700$		0			0
$701$	−168.847			−0.240865			−0.120433	−	0.992721i	$-0.538428\pi$
$701$	−168.847			−0.240865			−0.120433	+	0.992721i	$0.538428\pi$
$702$		0			0
$703$			37.9695i			0.0540106i
$704$	175.648	−	567.327i	0.249500	−	0.805863i
$705$		0			0
$706$	−483.909	−	312.661i	−0.685424	−	0.442863i
$707$			2.18382i			0.00308885i
$708$		0			0
$709$	−554.846			−0.782576			−0.391288	−	0.920268i	$-0.627970\pi$
$709$	−554.846			−0.782576			−0.391288	+	0.920268i	$0.627970\pi$
$710$		0			0
$711$		0			0
$712$	−156.100	+	1031.99i	−0.219242	+	1.44942i
$713$	1900.97			2.66616
$714$		0			0
$715$		0			0
$716$	459.474	−	207.130i	0.641723	−	0.289287i
$717$		0			0
$718$	−720.600	+	1115.28i	−1.00362	+	1.55331i
$719$			377.485i			0.525014i	0.964930	+	0.262507i	$0.0845494\pi$
$719$			377.485i			0.525014i	−0.964930	+	0.262507i	$0.915451\pi$
$720$		0			0
$721$	90.3261			0.125279
$722$	522.995	+	337.915i	0.724369	+	0.468027i
$723$		0			0
$724$	−569.972	−	1264.37i	−0.787255	−	1.74636i
$725$		0			0
$726$		0			0
$727$			173.183i			0.238216i	0.992881	+	0.119108i	$0.0380035\pi$
$727$			173.183i			0.238216i	−0.992881	+	0.119108i	$0.961997\pi$
$728$	−110.943	−	16.7814i	−0.152394	−	0.0230514i
$729$		0			0
$730$		0			0
$731$			143.651i			0.196513i
$732$		0			0
$733$	−278.722			−0.380249			−0.190124	−	0.981760i	$-0.560889\pi$
$733$	−278.722			−0.380249			−0.190124	+	0.981760i	$0.560889\pi$
$734$	−6.60489	+	10.2225i	−0.00899849	+	0.0139270i
$735$		0			0
$736$	277.165	+	988.412i	0.376583	+	1.34295i
$737$	−647.142			−0.878075
$738$		0			0
$739$		−	521.363i		−	0.705498i	−0.935718	−	0.352749i	$-0.885247\pi$
$739$		−	521.363i		−	0.705498i	0.935718	−	0.352749i	$-0.114753\pi$
$740$		0			0
$741$		0			0
$742$	1.65186	−	2.55660i	0.00222622	−	0.00344555i
$743$			1277.93i			1.71996i	0.510326	+	0.859981i	$0.329525\pi$
$743$			1277.93i			1.71996i	−0.510326	+	0.859981i	$0.670475\pi$
$744$		0			0
$745$		0			0
$746$	343.936	+	222.223i	0.461041	+	0.297886i
$747$		0			0
$748$	−134.595	+	60.6751i	−0.179940	+	0.0811164i
$749$	−49.3989			−0.0659532
$750$		0			0
$751$		−	1165.31i		−	1.55168i	−0.630930	−	0.775840i	$-0.717327\pi$
$751$		−	1165.31i		−	1.55168i	0.630930	−	0.775840i	$-0.282673\pi$
$752$	−887.350	−	784.194i	−1.17999	−	1.04281i
$753$		0			0
$754$	−1408.97	−	910.359i	−1.86866	−	1.20737i
$755$		0			0
$756$		0			0
$757$	−1063.75			−1.40522			−0.702611	−	0.711574i	$-0.747983\pi$
$757$	−1063.75			−1.40522			−0.702611	+	0.711574i	$0.747983\pi$
$758$	−436.685	+	675.861i	−0.576101	+	0.891638i
$759$		0			0
$760$		0			0
$761$	677.847			0.890732			0.445366	−	0.895349i	$-0.353074\pi$
$761$	677.847			0.890732			0.445366	+	0.895349i	$0.353074\pi$
$762$		0			0
$763$		−	4.39551i		−	0.00576083i
$764$	−485.577	+	218.897i	−0.635572	+	0.286514i
$765$		0			0
$766$	−360.078	+	557.296i	−0.470076	+	0.727541i
$767$			855.887i			1.11589i
$768$		0			0
$769$	−1289.59			−1.67697			−0.838486	−	0.544922i	$-0.816559\pi$
$769$	−1289.59			−1.67697			−0.838486	+	0.544922i	$0.816559\pi$
$770$		0			0
$771$		0			0
$772$	223.972	+	496.836i	0.290119	+	0.643570i
$773$	−750.339			−0.970684			−0.485342	−	0.874324i	$-0.661305\pi$
$773$	−750.339			−0.970684			−0.485342	+	0.874324i	$0.661305\pi$
$774$		0			0
$775$		0			0
$776$	111.406	−	736.513i	0.143564	−	0.949114i
$777$		0			0
$778$	1047.07	+	676.532i	1.34585	+	0.869578i
$779$		−	282.460i		−	0.362593i
$780$		0			0
$781$	549.512			0.703600
$782$	138.491	−	214.343i	0.177098	−	0.274096i
$783$		0			0
$784$	−515.402	+	583.200i	−0.657400	+	0.743877i
$785$		0			0
$786$		0			0
$787$			825.185i			1.04852i	0.851558	+	0.524260i	$0.175658\pi$
$787$			825.185i			1.04852i	−0.851558	+	0.524260i	$0.824342\pi$
$788$	123.117	+	273.110i	0.156240	+	0.346586i
$789$		0			0
$790$		0			0
$791$			38.7971i			0.0490482i
$792$		0			0
$793$	−205.309			−0.258902
$794$	597.106	+	385.799i	0.752022	+	0.485893i
$795$		0			0
$796$	917.500	−	413.606i	1.15264	−	0.519606i
$797$	1113.70			1.39737			0.698684	−	0.715430i	$-0.253769\pi$
$797$	1113.70			1.39737			0.698684	+	0.715430i	$0.253769\pi$
$798$		0			0
$799$			294.388i			0.368445i
$800$		0			0
$801$		0			0
$802$	912.043	+	589.285i	1.13721	+	0.734770i
$803$			770.226i			0.959186i
$804$		0			0
$805$		0			0
$806$	−1512.23	+	2340.50i	−1.87622	+	2.90384i
$807$		0			0
$808$	−4.38009	+	28.9571i	−0.00542090	+	0.0358380i
$809$	1049.54			1.29733			0.648664	−	0.761075i	$-0.275328\pi$
$809$	1049.54			1.29733			0.648664	+	0.761075i	$0.275328\pi$
$810$		0			0
$811$			424.482i			0.523406i	0.965148	+	0.261703i	$0.0842841\pi$
$811$			424.482i			0.523406i	−0.965148	+	0.261703i	$0.915716\pi$
$812$	77.6018	−	34.9827i	0.0955688	−	0.0430821i
$813$		0			0
$814$	−54.2638	+	83.9847i	−0.0666632	+	0.103175i
$815$		0			0
$816$		0			0
$817$	−254.528			−0.311540
$818$	−182.259	−	117.761i	−0.222811	−	0.143962i
$819$		0			0
$820$		0			0
$821$	1257.98			1.53225			0.766126	−	0.642690i	$-0.222182\pi$
$821$	1257.98			1.53225			0.766126	+	0.642690i	$0.222182\pi$
$822$		0			0
$823$		−	729.181i		−	0.886004i	−0.896521	−	0.443002i	$-0.853913\pi$
$823$		−	729.181i		−	0.886004i	0.896521	−	0.443002i	$-0.146087\pi$
$824$	1197.71	+	181.167i	1.45353	+	0.219863i
$825$		0			0
$826$	−36.4792	−	23.5698i	−0.0441637	−	0.0285349i
$827$		−	72.5882i		−	0.0877729i	−0.999037	−	0.0438865i	$-0.986026\pi$
$827$		−	72.5882i		−	0.0877729i	0.999037	−	0.0438865i	$-0.0139740\pi$
$828$		0			0
$829$	900.257			1.08596			0.542978	−	0.839747i	$-0.317297\pi$
$829$	900.257			1.08596			0.542978	+	0.839747i	$0.317297\pi$
$830$		0			0
$831$		0			0
$832$	−1437.43	−	445.038i	−1.72768	−	0.534901i
$833$	193.482			0.232272
$834$		0			0
$835$		0			0
$836$	−107.507	−	238.483i	−0.128597	−	0.285266i
$837$		0			0
$838$	186.877	−	289.232i	0.223004	−	0.345145i
$839$		−	71.4721i		−	0.0851872i	−0.999092	−	0.0425936i	$-0.986438\pi$
$839$		−	71.4721i		−	0.0851872i	0.999092	−	0.0425936i	$-0.0135621\pi$
$840$		0			0
$841$	431.594			0.513191
$842$	803.851	+	519.381i	0.954693	+	0.616842i
$843$		0			0
$844$	832.165	−	375.138i	0.985978	−	0.444476i
$845$		0			0
$846$		0			0
$847$			20.8124i			0.0245719i
$848$	27.0312	−	30.5870i	0.0318764	−	0.0360695i
$849$		0			0
$850$		0			0
$851$		−	172.831i		−	0.203091i
$852$		0			0
$853$	−882.349			−1.03441			−0.517203	−	0.855862i	$-0.673027\pi$
$853$	−882.349			−1.03441			−0.517203	+	0.855862i	$0.673027\pi$
$854$	5.65391	−	8.75061i	0.00662050	−	0.0102466i
$855$		0			0
$856$	−655.022	−	99.0796i	−0.765213	−	0.115747i
$857$	−370.111			−0.431868			−0.215934	−	0.976408i	$-0.569280\pi$
$857$	−370.111			−0.431868			−0.215934	+	0.976408i	$0.569280\pi$
$858$		0			0
$859$		−	1039.00i		−	1.20955i	−0.796397	−	0.604774i	$-0.793264\pi$
$859$		−	1039.00i		−	1.20955i	0.796397	−	0.604774i	$-0.206736\pi$
$860$		0			0
$861$		0			0
$862$	315.546	−	488.373i	0.366062	−	0.566558i
$863$			72.0666i			0.0835071i	0.999128	+	0.0417535i	$0.0132944\pi$
$863$			72.0666i			0.0835071i	−0.999128	+	0.0417535i	$0.986706\pi$
$864$		0			0
$865$		0			0
$866$	−90.3306	−	58.3640i	−0.104308	−	0.0673950i
$867$		0			0
$868$	−58.1110	−	128.907i	−0.0669482	−	0.148511i
$869$	611.254			0.703399
$870$		0			0
$871$			1639.66i			1.88250i
$872$	8.81609	−	58.2838i	0.0101102	−	0.0668393i
$873$		0			0
$874$	379.785	+	245.385i	0.434536	+	0.280761i
$875$		0			0
$876$		0			0
$877$	−14.4444			−0.0164703			−0.00823514	−	0.999966i	$-0.502621\pi$
$877$	−14.4444			−0.0164703			−0.00823514	+	0.999966i	$0.502621\pi$
$878$	356.720	−	552.099i	0.406287	−	0.628815i
$879$		0			0
$880$		0			0
$881$	−1589.22			−1.80388			−0.901942	−	0.431858i	$-0.857858\pi$
$881$	−1589.22			−1.80388			−0.901942	+	0.431858i	$0.857858\pi$
$882$		0			0
$883$			495.149i			0.560758i	0.959889	+	0.280379i	$0.0904601\pi$
$883$			495.149i			0.560758i	−0.959889	+	0.280379i	$0.909540\pi$
$884$	153.732	+	341.022i	0.173905	+	0.385772i
$885$		0			0
$886$	465.533	−	720.510i	0.525432	−	0.813216i
$887$		−	1384.20i		−	1.56054i	−0.625440	−	0.780272i	$-0.715081\pi$
$887$		−	1384.20i		−	1.56054i	0.625440	−	0.780272i	$-0.284919\pi$
$888$		0			0
$889$	83.1988			0.0935870
$890$		0			0
$891$		0			0
$892$	313.443	−	141.299i	0.351393	−	0.158407i
$893$	−521.611			−0.584111
$894$		0			0
$895$		0			0
$896$	58.5528	−	49.0099i	0.0653491	−	0.0546985i
$897$		0			0
$898$	−687.448	−	444.171i	−0.765533	−	0.494623i
$899$		−	2113.95i		−	2.35145i
$900$		0			0
$901$	−10.1475			−0.0112625
$902$	403.676	−	624.773i	0.447534	−	0.692653i
$903$		0			0
$904$	−77.8155	+	514.444i	−0.0860791	+	0.569075i
$905$		0			0
$906$		0			0
$907$		−	957.750i		−	1.05595i	−0.849259	−	0.527977i	$-0.822951\pi$
$907$		−	957.750i		−	1.05595i	0.849259	−	0.527977i	$-0.177049\pi$
$908$	1029.64	−	464.160i	1.13397	−	0.511189i
$909$		0			0
$910$		0			0
$911$			704.979i			0.773852i	0.922111	+	0.386926i	$0.126463\pi$
$911$			704.979i			0.773852i	−0.922111	+	0.386926i	$0.873537\pi$
$912$		0			0
$913$	1205.51			1.32038
$914$	−1291.08	−	834.185i	−1.41256	−	0.912675i
$915$		0			0
$916$	227.287	+	504.189i	0.248130	+	0.550424i
$917$	−37.8717			−0.0412996
$918$		0			0
$919$		−	607.048i		−	0.660553i	−0.943884	−	0.330277i	$-0.892858\pi$
$919$		−	607.048i		−	0.660553i	0.943884	−	0.330277i	$-0.107142\pi$
$920$		0			0
$921$		0			0
$922$	531.782	+	343.593i	0.576770	+	0.372660i
$923$		−	1392.29i		−	1.50844i
$924$		0			0
$925$		0			0
$926$	533.151	−	825.163i	0.575757	−	0.891104i
$927$		0			0
$928$	1099.15	−	308.219i	1.18443	−	0.332132i
$929$	−1011.21			−1.08849			−0.544247	−	0.838925i	$-0.683185\pi$
$929$	−1011.21			−1.08849			−0.544247	+	0.838925i	$0.683185\pi$
$930$		0			0
$931$			342.822i			0.368230i
$932$	−0.859647	−	1.90695i	−0.000922368	−	0.00204608i
$933$		0			0
$934$	−445.434	+	689.403i	−0.476910	+	0.738119i
$935$		0			0
$936$		0			0
$937$	363.105			0.387519			0.193760	−	0.981049i	$-0.437932\pi$
$937$	363.105			0.387519			0.193760	+	0.981049i	$0.437932\pi$
$938$	−69.8846	−	45.1536i	−0.0745039	−	0.0481381i
$939$		0			0
$940$		0			0
$941$	1106.51			1.17588			0.587942	−	0.808903i	$-0.299939\pi$
$941$	1106.51			1.17588			0.587942	+	0.808903i	$0.299939\pi$
$942$		0			0
$943$			1285.71i			1.36342i
$944$	−436.435	−	385.698i	−0.462325	−	0.408579i
$945$		0			0
$946$	−562.990	−	363.757i	−0.595127	−	0.384521i
$947$			553.561i			0.584541i	0.956336	+	0.292271i	$0.0944108\pi$
$947$			553.561i			0.584541i	−0.956336	+	0.292271i	$0.905589\pi$
$948$		0			0
$949$	1951.51			2.05639
$950$		0			0
$951$		0			0
$952$	−18.7684	−	2.83894i	−0.0197147	−	0.00298208i
$953$	−1674.84			−1.75744			−0.878718	−	0.477342i	$-0.841600\pi$
$953$	−1674.84			−1.75744			−0.878718	+	0.477342i	$0.841600\pi$
$954$		0			0
$955$		0			0
$956$	−268.728	+	121.142i	−0.281096	+	0.126717i
$957$		0			0
$958$	215.902	−	334.154i	0.225368	−	0.348804i
$959$		−	82.4162i		−	0.0859398i
$960$		0			0
$961$	−2550.57			−2.65408
$962$	212.791	+	137.488i	0.221196	+	0.142919i
$963$		0			0
$964$	51.5692	+	114.396i	0.0534950	+	0.118668i
$965$		0			0
$966$		0			0
$967$			786.720i			0.813568i	0.913524	+	0.406784i	$0.133350\pi$
$967$			786.720i			0.813568i	−0.913524	+	0.406784i	$0.866650\pi$
$968$	−41.7435	+	275.969i	−0.0431234	+	0.285092i
$969$		0			0
$970$		0			0
$971$		−	1289.75i		−	1.32827i	−0.747612	−	0.664135i	$-0.768800\pi$
$971$		−	1289.75i		−	1.32827i	0.747612	−	0.664135i	$-0.231200\pi$
$972$		0			0
$973$	−17.8710			−0.0183669
$974$	−222.246	+	343.972i	−0.228178	+	0.353154i
$975$		0			0
$976$	92.5210	−	104.692i	0.0947961	−	0.107266i
$977$	495.847			0.507520			0.253760	−	0.967267i	$-0.418333\pi$
$977$	495.847			0.507520			0.253760	+	0.967267i	$0.418333\pi$
$978$		0			0
$979$			1210.68i			1.23665i
$980$		0			0
$981$		0			0
$982$	855.933	−	1324.74i	0.871622	−	1.34902i
$983$		−	967.035i		−	0.983759i	−0.870663	−	0.491880i	$-0.836310\pi$
$983$		−	967.035i		−	0.983759i	0.870663	−	0.491880i	$-0.163690\pi$
$984$		0			0
$985$		0			0
$986$	−238.358	−	154.007i	−0.241742	−	0.156194i
$987$		0			0
$988$	−604.241	+	272.390i	−0.611580	+	0.275698i
$989$	1158.57			1.17145
$990$		0			0
$991$		−	1203.68i		−	1.21461i	−0.794469	−	0.607305i	$-0.792251\pi$
$991$		−	1203.68i		−	1.21461i	0.794469	−	0.607305i	$-0.207749\pi$
$992$	−511.994	−	1825.84i	−0.516123	−	1.84057i
$993$		0			0
$994$	59.3417	+	38.3416i	0.0596999	+	0.0385730i
$995$		0			0
$996$		0			0
$997$	1274.55			1.27838			0.639192	−	0.769047i	$-0.279269\pi$
$997$	1274.55			1.27838			0.639192	+	0.769047i	$0.279269\pi$
$998$	−803.603	+	1243.74i	−0.805214	+	1.24624i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.c.u.451.6		8
3.2	odd	2		300.3.c.d.151.3		8
4.3	odd	2	inner	900.3.c.u.451.5		8
5.2	odd	4		900.3.f.f.199.4		16
5.3	odd	4		900.3.f.f.199.13		16
5.4	even	2		180.3.c.b.91.3		8
12.11	even	2		300.3.c.d.151.4		8
15.2	even	4		300.3.f.b.199.13		16
15.8	even	4		300.3.f.b.199.4		16
15.14	odd	2		60.3.c.a.31.6	yes	8
20.3	even	4		900.3.f.f.199.3		16
20.7	even	4		900.3.f.f.199.14		16
20.19	odd	2		180.3.c.b.91.4		8
40.19	odd	2		2880.3.e.j.2431.7		8
40.29	even	2		2880.3.e.j.2431.6		8
60.23	odd	4		300.3.f.b.199.14		16
60.47	odd	4		300.3.f.b.199.3		16
60.59	even	2		60.3.c.a.31.5	✓	8
120.29	odd	2		960.3.e.c.511.6		8
120.59	even	2		960.3.e.c.511.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.c.a.31.5	✓	8	60.59	even	2
60.3.c.a.31.6	yes	8	15.14	odd	2
180.3.c.b.91.3		8	5.4	even	2
180.3.c.b.91.4		8	20.19	odd	2
300.3.c.d.151.3		8	3.2	odd	2
300.3.c.d.151.4		8	12.11	even	2
300.3.f.b.199.3		16	60.47	odd	4
300.3.f.b.199.4		16	15.8	even	4
300.3.f.b.199.13		16	15.2	even	4
300.3.f.b.199.14		16	60.23	odd	4
900.3.c.u.451.5		8	4.3	odd	2	inner
900.3.c.u.451.6		8	1.1	even	1	trivial
900.3.f.f.199.3		16	20.3	even	4
900.3.f.f.199.4		16	5.2	odd	4
900.3.f.f.199.13		16	5.3	odd	4
900.3.f.f.199.14		16	20.7	even	4
960.3.e.c.511.1		8	120.59	even	2
960.3.e.c.511.6		8	120.29	odd	2
2880.3.e.j.2431.6		8	40.29	even	2
2880.3.e.j.2431.7		8	40.19	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.67986 + 1.08539i) q^{2} +(1.64388 + 3.64660i) q^{4} +0.596540i q^{7} +(-1.19648 + 7.91002i) q^{8} +O(q^{10})\)	\(q+(1.67986 + 1.08539i) q^{2} +(1.64388 + 3.64660i) q^{4} +0.596540i q^{7} +(-1.19648 + 7.91002i) q^{8} +9.27963i q^{11} +23.5117 q^{13} +(-0.647476 + 1.00210i) q^{14} +(-10.5953 + 11.9891i) q^{16} +3.97751 q^{17} +7.04756i q^{19} +(-10.0720 + 15.5885i) q^{22} -32.0793i q^{23} +(39.4964 + 25.5192i) q^{26} +(-2.17534 + 0.980637i) q^{28} -35.6734 q^{29} +59.2585i q^{31} +(-30.8115 + 8.64000i) q^{32} +(6.68167 + 4.31713i) q^{34} +5.38761 q^{37} +(-7.64932 + 11.8389i) q^{38} -40.0791 q^{41} +36.1157i q^{43} +(-33.8391 + 15.2545i) q^{44} +(34.8184 - 53.8888i) q^{46} +74.0131i q^{47} +48.6441 q^{49} +(38.6503 + 85.7376i) q^{52} -2.55123 q^{53} +(-4.71864 - 0.713748i) q^{56} +(-59.9265 - 38.7194i) q^{58} +36.4026i q^{59} -8.73223 q^{61} +(-64.3183 + 99.5461i) q^{62} +(-61.1369 - 18.9284i) q^{64} +69.7379i q^{67} +(6.53853 + 14.5044i) q^{68} -59.2170i q^{71} +83.0019 q^{73} +(9.05044 + 5.84763i) q^{74} +(-25.6996 + 11.5853i) q^{76} -5.53566 q^{77} -65.8705i q^{79} +(-67.3274 - 43.5013i) q^{82} -129.909i q^{83} +(-39.1995 + 60.6695i) q^{86} +(-73.4020 - 11.1029i) q^{88} +130.466 q^{89} +14.0256i q^{91} +(116.980 - 52.7344i) q^{92} +(-80.3327 + 124.332i) q^{94} -93.1113 q^{97} +(81.7155 + 52.7977i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 10 q^{4} - 20 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 + 10 * q^4 - 20 * q^8	\( 8 q + 4 q^{2} + 10 q^{4} - 20 q^{8} - 16 q^{13} + 20 q^{14} + 34 q^{16} - 68 q^{22} + 36 q^{26} - 28 q^{28} - 64 q^{29} - 76 q^{32} - 92 q^{34} + 112 q^{37} - 40 q^{38} + 16 q^{41} - 172 q^{44} + 152 q^{46} - 56 q^{49} + 128 q^{52} + 352 q^{53} - 116 q^{56} + 204 q^{58} - 176 q^{61} - 56 q^{62} - 110 q^{64} - 184 q^{68} + 240 q^{73} - 132 q^{74} - 24 q^{76} - 288 q^{77} - 40 q^{82} + 200 q^{86} - 140 q^{88} - 80 q^{89} + 144 q^{92} - 96 q^{94} - 432 q^{97} + 660 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 + 10 * q^4 - 20 * q^8 - 16 * q^13 + 20 * q^14 + 34 * q^16 - 68 * q^22 + 36 * q^26 - 28 * q^28 - 64 * q^29 - 76 * q^32 - 92 * q^34 + 112 * q^37 - 40 * q^38 + 16 * q^41 - 172 * q^44 + 152 * q^46 - 56 * q^49 + 128 * q^52 + 352 * q^53 - 116 * q^56 + 204 * q^58 - 176 * q^61 - 56 * q^62 - 110 * q^64 - 184 * q^68 + 240 * q^73 - 132 * q^74 - 24 * q^76 - 288 * q^77 - 40 * q^82 + 200 * q^86 - 140 * q^88 - 80 * q^89 + 144 * q^92 - 96 * q^94 - 432 * q^97 + 660 * q^98

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