LMFDB - Embedded newform 900.3.c.l.451.3

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:	$4$
Coefficient field:	4.0.8405.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} + 8x^{2} - 7x + 2 $ x^4 - 2x^3 + 8x^2 - 7*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 100)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			451.3
Root			$0.500000 - 0.220086i$ of defining polynomial
Character	$\chi$	$=$	900.451
Dual form			900.3.c.l.451.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35078 - 1.47492i) q^{2} +(-0.350781 - 3.98459i) q^{4} +10.9190i q^{7} +(-6.35078 - 4.86493i) q^{8} +O(q^{10})$	\(q+(1.35078 - 1.47492i) q^{2} +(-0.350781 - 3.98459i) q^{4} +10.9190i q^{7} +(-6.35078 - 4.86493i) q^{8} -11.3592i q^{11} -10.8062 q^{13} +(16.1047 + 14.7492i) q^{14} +(-15.7539 + 2.79544i) q^{16} -15.8062 q^{17} +24.9192i q^{19} +(-16.7539 - 15.3438i) q^{22} +20.9577i q^{23} +(-14.5969 + 15.9384i) q^{26} +(43.5078 - 3.83019i) q^{28} -22.8062 q^{29} -22.7184i q^{31} +(-17.1570 + 27.0118i) q^{32} +(-21.3508 + 23.3130i) q^{34} -19.1938 q^{37} +(36.7539 + 33.6604i) q^{38} -17.0000 q^{41} +6.51730i q^{43} +(-45.2617 + 3.98459i) q^{44} +(30.9109 + 28.3093i) q^{46} +38.9195i q^{47} -70.2250 q^{49} +(3.79063 + 43.0585i) q^{52} -13.2250 q^{53} +(53.1203 - 69.3443i) q^{56} +(-30.8062 + 33.6374i) q^{58} +95.6301i q^{59} -92.0312 q^{61} +(-33.5078 - 30.6876i) q^{62} +(16.6648 + 61.7923i) q^{64} +54.1549i q^{67} +(5.54453 + 62.9814i) q^{68} -68.5100i q^{71} +44.1938 q^{73} +(-25.9266 + 28.3093i) q^{74} +(99.2930 - 8.74120i) q^{76} +124.031 q^{77} -81.7152i q^{79} +(-22.9633 + 25.0736i) q^{82} +27.9152i q^{83} +(9.61250 + 8.80344i) q^{86} +(-55.2617 + 72.1397i) q^{88} +42.1938 q^{89} -117.994i q^{91} +(83.5078 - 7.35156i) q^{92} +(57.4031 + 52.5717i) q^{94} +154.837 q^{97} +(-94.8586 + 103.576i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 5 q^{4} - 19 q^{8}+O(q^{10}) $ 4 * q - q^2 + 5 * q^4 - 19 * q^8	$ 4 q - q^{2} + 5 q^{4} - 19 q^{8} + 8 q^{13} + 26 q^{14} - 31 q^{16} - 12 q^{17} - 35 q^{22} - 84 q^{26} + 110 q^{28} - 40 q^{29} - 11 q^{32} - 79 q^{34} - 128 q^{37} + 115 q^{38} - 68 q^{41} - 85 q^{44} + 34 q^{46} - 76 q^{49} + 92 q^{52} + 152 q^{53} + 46 q^{56} - 72 q^{58} - 112 q^{61} - 70 q^{62} - 55 q^{64} + 67 q^{68} + 228 q^{73} + 114 q^{74} + 45 q^{76} + 240 q^{77} + 17 q^{82} - 64 q^{86} - 125 q^{88} + 220 q^{89} + 270 q^{92} + 204 q^{94} + 312 q^{97} - 309 q^{98}+O(q^{100}) $ 4 * q - q^2 + 5 * q^4 - 19 * q^8 + 8 * q^13 + 26 * q^14 - 31 * q^16 - 12 * q^17 - 35 * q^22 - 84 * q^26 + 110 * q^28 - 40 * q^29 - 11 * q^32 - 79 * q^34 - 128 * q^37 + 115 * q^38 - 68 * q^41 - 85 * q^44 + 34 * q^46 - 76 * q^49 + 92 * q^52 + 152 * q^53 + 46 * q^56 - 72 * q^58 - 112 * q^61 - 70 * q^62 - 55 * q^64 + 67 * q^68 + 228 * q^73 + 114 * q^74 + 45 * q^76 + 240 * q^77 + 17 * q^82 - 64 * q^86 - 125 * q^88 + 220 * q^89 + 270 * q^92 + 204 * q^94 + 312 * q^97 - 309 * 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 $

$2$	1.35078	−	1.47492i	0.675391	−	0.737460i
$2$	1.35078	−	1.47492i	0.675391	−	0.737460i
$3$		0			0
$3$		0			0
$4$	−0.350781	−	3.98459i	−0.0876953	−	0.996147i
$5$		0			0
$5$		0			0
$6$		0			0
$7$			10.9190i			1.55986i	0.625867	+	0.779930i	$0.284745\pi$
$7$			10.9190i			1.55986i	−0.625867	+	0.779930i	$0.715255\pi$
$8$	−6.35078	−	4.86493i	−0.793848	−	0.608117i
$9$		0			0
$10$		0			0
$11$		−	11.3592i		−	1.03265i	−0.856392	−	0.516327i	$-0.827299\pi$
$11$		−	11.3592i		−	1.03265i	0.856392	−	0.516327i	$-0.172701\pi$
$12$		0			0
$13$	−10.8062			−0.831250			−0.415625	−	0.909536i	$-0.636437\pi$
$13$	−10.8062			−0.831250			−0.415625	+	0.909536i	$0.636437\pi$
$14$	16.1047	+	14.7492i	1.15033	+	1.05351i
$15$		0			0
$16$	−15.7539	+	2.79544i	−0.984619	+	0.174715i
$17$	−15.8062			−0.929779			−0.464890	−	0.885369i	$-0.653906\pi$
$17$	−15.8062			−0.929779			−0.464890	+	0.885369i	$0.653906\pi$
$18$		0			0
$19$			24.9192i			1.31154i	0.754961	+	0.655770i	$0.227656\pi$
$19$			24.9192i			1.31154i	−0.754961	+	0.655770i	$0.772344\pi$
$20$		0			0
$21$		0			0
$22$	−16.7539	−	15.3438i	−0.761541	−	0.697445i
$23$			20.9577i			0.911204i	0.890184	+	0.455602i	$0.150576\pi$
$23$			20.9577i			0.911204i	−0.890184	+	0.455602i	$0.849424\pi$
$24$		0			0
$25$		0			0
$26$	−14.5969	+	15.9384i	−0.561418	+	0.613014i
$27$		0			0
$28$	43.5078	−	3.83019i	1.55385	−	0.136792i
$29$	−22.8062			−0.786422			−0.393211	−	0.919448i	$-0.628636\pi$
$29$	−22.8062			−0.786422			−0.393211	+	0.919448i	$0.628636\pi$
$30$		0			0
$31$		−	22.7184i		−	0.732851i	−0.930447	−	0.366426i	$-0.880581\pi$
$31$		−	22.7184i		−	0.732851i	0.930447	−	0.366426i	$-0.119419\pi$
$32$	−17.1570	+	27.0118i	−0.536157	+	0.844118i
$33$		0			0
$34$	−21.3508	+	23.3130i	−0.627964	+	0.685675i
$35$		0			0
$36$		0			0
$37$	−19.1938			−0.518750			−0.259375	−	0.965777i	$-0.583517\pi$
$37$	−19.1938			−0.518750			−0.259375	+	0.965777i	$0.583517\pi$
$38$	36.7539	+	33.6604i	0.967208	+	0.885801i
$39$		0			0
$40$		0			0
$41$	−17.0000			−0.414634			−0.207317	−	0.978274i	$-0.566473\pi$
$41$	−17.0000			−0.414634			−0.207317	+	0.978274i	$0.566473\pi$
$42$		0			0
$43$			6.51730i			0.151565i	0.997124	+	0.0757825i	$0.0241455\pi$
$43$			6.51730i			0.151565i	−0.997124	+	0.0757825i	$0.975855\pi$
$44$	−45.2617	+	3.98459i	−1.02868	+	0.0905588i
$45$		0			0
$46$	30.9109	+	28.3093i	0.671977	+	0.615419i
$47$			38.9195i			0.828074i	0.910260	+	0.414037i	$0.135882\pi$
$47$			38.9195i			0.828074i	−0.910260	+	0.414037i	$0.864118\pi$
$48$		0			0
$49$	−70.2250			−1.43316
$50$		0			0
$51$		0			0
$52$	3.79063	+	43.0585i	0.0728967	+	0.828047i
$53$	−13.2250			−0.249528			−0.124764	−	0.992186i	$-0.539817\pi$
$53$	−13.2250			−0.249528			−0.124764	+	0.992186i	$0.539817\pi$
$54$		0			0
$55$		0			0
$56$	53.1203	−	69.3443i	0.948577	−	1.23829i
$57$		0			0
$58$	−30.8062	+	33.6374i	−0.531142	+	0.579955i
$59$			95.6301i			1.62085i	0.585842	+	0.810425i	$0.300764\pi$
$59$			95.6301i			1.62085i	−0.585842	+	0.810425i	$0.699236\pi$
$60$		0			0
$61$	−92.0312			−1.50871			−0.754354	−	0.656467i	$-0.772050\pi$
$61$	−92.0312			−1.50871			−0.754354	+	0.656467i	$0.772050\pi$
$62$	−33.5078	−	30.6876i	−0.540449	−	0.494961i
$63$		0			0
$64$	16.6648	+	61.7923i	0.260388	+	0.965504i
$65$		0			0
$66$		0			0
$67$			54.1549i			0.808282i	0.914697	+	0.404141i	$0.132430\pi$
$67$			54.1549i			0.808282i	−0.914697	+	0.404141i	$0.867570\pi$
$68$	5.54453	+	62.9814i	0.0815372	+	0.926197i
$69$		0			0
$70$		0			0
$71$		−	68.5100i		−	0.964930i	−0.875915	−	0.482465i	$-0.839742\pi$
$71$		−	68.5100i		−	0.964930i	0.875915	−	0.482465i	$-0.160258\pi$
$72$		0			0
$73$	44.1938			0.605394			0.302697	−	0.953087i	$-0.402113\pi$
$73$	44.1938			0.605394			0.302697	+	0.953087i	$0.402113\pi$
$74$	−25.9266	+	28.3093i	−0.350359	+	0.382558i
$75$		0			0
$76$	99.2930	−	8.74120i	1.30649	−	0.115016i
$77$	124.031			1.61080
$78$		0			0
$79$		−	81.7152i		−	1.03437i	−0.855874	−	0.517185i	$-0.826980\pi$
$79$		−	81.7152i		−	1.03437i	0.855874	−	0.517185i	$-0.173020\pi$
$80$		0			0
$81$		0			0
$82$	−22.9633	+	25.0736i	−0.280040	+	0.305776i
$83$			27.9152i			0.336327i	0.985759	+	0.168164i	$0.0537837\pi$
$83$			27.9152i			0.336327i	−0.985759	+	0.168164i	$0.946216\pi$
$84$		0			0
$85$		0			0
$86$	9.61250	+	8.80344i	0.111773	+	0.102366i
$87$		0			0
$88$	−55.2617	+	72.1397i	−0.627974	+	0.819770i
$89$	42.1938			0.474087			0.237044	−	0.971499i	$-0.423822\pi$
$89$	42.1938			0.474087			0.237044	+	0.971499i	$0.423822\pi$
$90$		0			0
$91$		−	117.994i		−	1.29663i
$92$	83.5078	−	7.35156i	0.907694	−	0.0799083i
$93$		0			0
$94$	57.4031	+	52.5717i	0.610672	+	0.559273i
$95$		0			0
$96$		0			0
$97$	154.837			1.59626			0.798131	−	0.602483i	$-0.205822\pi$
$97$	154.837			1.59626			0.798131	+	0.602483i	$0.205822\pi$
$98$	−94.8586	+	103.576i	−0.967945	+	1.05690i
$99$		0			0
$100$		0			0
$101$	3.96876			0.0392946			0.0196473	−	0.999807i	$-0.493746\pi$
$101$	3.96876			0.0392946			0.0196473	+	0.999807i	$0.493746\pi$
$102$		0			0
$103$		−	66.0396i		−	0.641161i	−0.947221	−	0.320580i	$-0.896122\pi$
$103$		−	66.0396i		−	0.641161i	0.947221	−	0.320580i	$-0.103878\pi$
$104$	68.6281	+	52.5717i	0.659886	+	0.505497i
$105$		0			0
$106$	−17.8641	+	19.5058i	−0.168529	+	0.184017i
$107$			96.0703i			0.897853i	0.893569	+	0.448927i	$0.148194\pi$
$107$			96.0703i			0.897853i	−0.893569	+	0.448927i	$0.851806\pi$
$108$		0			0
$109$	112.806			1.03492			0.517460	−	0.855707i	$-0.326878\pi$
$109$	112.806			1.03492			0.517460	+	0.855707i	$0.326878\pi$
$110$		0			0
$111$		0			0
$112$	−30.5234	−	172.017i	−0.272531	−	1.53587i
$113$	−18.2250			−0.161283			−0.0806416	−	0.996743i	$-0.525697\pi$
$113$	−18.2250			−0.161283			−0.0806416	+	0.996743i	$0.525697\pi$
$114$		0			0
$115$		0			0
$116$	8.00000	+	90.8735i	0.0689655	+	0.783393i
$117$		0			0
$118$	141.047	+	129.175i	1.19531	+	1.09471i
$119$		−	172.589i		−	1.45033i
$120$		0			0
$121$	−8.03124			−0.0663739
$122$	−124.314	+	135.739i	−1.01897	+	1.11261i
$123$		0			0
$124$	−90.5234	+	7.96918i	−0.730028	+	0.0642676i
$125$		0			0
$126$		0			0
$127$			51.5992i			0.406293i	0.979148	+	0.203146i	$0.0651167\pi$
$127$			51.5992i			0.406293i	−0.979148	+	0.203146i	$0.934883\pi$
$128$	113.649	+	58.8885i	0.887885	+	0.460066i
$129$		0			0
$130$		0			0
$131$		−	158.674i		−	1.21125i	−0.795750	−	0.605625i	$-0.792923\pi$
$131$		−	158.674i		−	1.21125i	0.795750	−	0.605625i	$-0.207077\pi$
$132$		0			0
$133$	−272.094			−2.04582
$134$	79.8742	+	73.1514i	0.596076	+	0.545906i
$135$		0			0
$136$	100.382	+	76.8964i	0.738103	+	0.565414i
$137$	−209.837			−1.53166			−0.765830	−	0.643043i	$-0.777672\pi$
$137$	−209.837			−1.53166			−0.765830	+	0.643043i	$0.777672\pi$
$138$		0			0
$139$			84.6258i			0.608819i	0.952541	+	0.304410i	$0.0984591\pi$
$139$			84.6258i			0.608819i	−0.952541	+	0.304410i	$0.901541\pi$
$140$		0			0
$141$		0			0
$142$	−101.047	−	92.5421i	−0.711598	−	0.651705i
$143$			122.750i			0.858393i
$144$		0			0
$145$		0			0
$146$	59.6961	−	65.1823i	0.408877	−	0.446454i
$147$		0			0
$148$	6.73280	+	76.4792i	0.0454919	+	0.516751i
$149$	−170.869			−1.14677			−0.573385	−	0.819286i	$-0.694370\pi$
$149$	−170.869			−1.14677			−0.573385	+	0.819286i	$0.694370\pi$
$150$		0			0
$151$		−	181.392i		−	1.20127i	−0.799522	−	0.600636i	$-0.794914\pi$
$151$		−	181.392i		−	1.20127i	0.799522	−	0.600636i	$-0.205086\pi$
$152$	121.230	−	158.257i	0.797569	−	1.04116i
$153$		0			0
$154$	167.539	−	182.936i	1.08792	−	1.18790i
$155$		0			0
$156$		0			0
$157$	−25.1625			−0.160271			−0.0801354	−	0.996784i	$-0.525535\pi$
$157$	−25.1625			−0.160271			−0.0801354	+	0.996784i	$0.525535\pi$
$158$	−120.523	−	110.379i	−0.762807	−	0.698603i
$159$		0			0
$160$		0			0
$161$	−228.837			−1.42135
$162$		0			0
$163$			8.00838i			0.0491312i	0.999698	+	0.0245656i	$0.00782026\pi$
$163$			8.00838i			0.0491312i	−0.999698	+	0.0245656i	$0.992180\pi$
$164$	5.96328	+	67.7380i	0.0363615	+	0.413037i
$165$		0			0
$166$	41.1727	+	37.7073i	0.248028	+	0.227152i
$167$		−	187.555i		−	1.12308i	−0.827449	−	0.561541i	$-0.810209\pi$
$167$		−	187.555i		−	1.12308i	0.827449	−	0.561541i	$-0.189791\pi$
$168$		0			0
$169$	−52.2250			−0.309024
$170$		0			0
$171$		0			0
$172$	25.9688	−	2.28614i	0.150981	−	0.0132915i
$173$	−123.225			−0.712283			−0.356142	−	0.934432i	$-0.615908\pi$
$173$	−123.225			−0.712283			−0.356142	+	0.934432i	$0.615908\pi$
$174$		0			0
$175$		0			0
$176$	31.7539	+	178.952i	0.180420	+	1.01677i
$177$		0			0
$178$	56.9945	−	62.2324i	0.320194	−	0.349620i
$179$			138.511i			0.773805i	0.922121	+	0.386903i	$0.126455\pi$
$179$			138.511i			0.773805i	−0.922121	+	0.386903i	$0.873545\pi$
$180$		0			0
$181$	−194.125			−1.07251			−0.536257	−	0.844055i	$-0.680162\pi$
$181$	−194.125			−1.07251			−0.536257	+	0.844055i	$0.680162\pi$
$182$	−174.031	−	159.384i	−0.956216	−	0.875734i
$183$		0			0
$184$	101.958	−	133.098i	0.554118	−	0.723357i
$185$		0			0
$186$		0			0
$187$			179.546i			0.960140i
$188$	155.078	−	13.6522i	0.824884	−	0.0726182i
$189$		0			0
$190$		0			0
$191$		−	67.4454i		−	0.353117i	−0.984290	−	0.176559i	$-0.943503\pi$
$191$		−	67.4454i		−	0.353117i	0.984290	−	0.176559i	$-0.0564965\pi$
$192$		0			0
$193$	−153.869			−0.797247			−0.398624	−	0.917115i	$-0.630512\pi$
$193$	−153.869			−0.797247			−0.398624	+	0.917115i	$0.630512\pi$
$194$	209.152	−	228.373i	1.07810	−	1.17718i
$195$		0			0
$196$	24.6336	+	279.818i	0.125682	+	1.42764i
$197$	261.287			1.32633			0.663166	−	0.748472i	$-0.269212\pi$
$197$	261.287			1.32633			0.663166	+	0.748472i	$0.269212\pi$
$198$		0			0
$199$		−	227.184i		−	1.14163i	−0.821080	−	0.570814i	$-0.806628\pi$
$199$		−	227.184i		−	1.14163i	0.821080	−	0.570814i	$-0.193372\pi$
$200$		0			0
$201$		0			0
$202$	5.36092	−	5.85360i	0.0265392	−	0.0289782i
$203$		−	249.022i		−	1.22671i
$204$		0			0
$205$		0			0
$206$	−97.4031	−	89.2050i	−0.472831	−	0.433034i
$207$		0			0
$208$	170.241	−	30.2082i	0.818464	−	0.145232i
$209$	283.062			1.35437
$210$		0			0
$211$		−	193.816i		−	0.918559i	−0.888292	−	0.459280i	$-0.848108\pi$
$211$		−	193.816i		−	0.918559i	0.888292	−	0.459280i	$-0.151892\pi$
$212$	4.63908	+	52.6962i	0.0218824	+	0.248567i
$213$		0			0
$214$	141.696	+	129.770i	0.662131	+	0.606402i
$215$		0			0
$216$		0			0
$217$	248.062			1.14315
$218$	152.377	−	166.380i	0.698975	−	0.763212i
$219$		0			0
$220$		0			0
$221$	170.806			0.772879
$222$		0			0
$223$		−	25.3594i		−	0.113719i	−0.998382	−	0.0568597i	$-0.981891\pi$
$223$		−	25.3594i		−	0.113719i	0.998382	−	0.0568597i	$-0.0181088\pi$
$224$	−294.942	−	187.338i	−1.31671	−	0.836330i
$225$		0			0
$226$	−24.6180	+	26.8804i	−0.108929	+	0.118940i
$227$			374.584i			1.65015i	0.565024	+	0.825074i	$0.308867\pi$
$227$			374.584i			1.65015i	−0.565024	+	0.825074i	$0.691133\pi$
$228$		0			0
$229$	−259.287			−1.13226			−0.566130	−	0.824316i	$-0.691560\pi$
$229$	−259.287			−1.13226			−0.566130	+	0.824316i	$0.691560\pi$
$230$		0			0
$231$		0			0
$232$	144.837	+	110.951i	0.624300	+	0.478237i
$233$	−153.225			−0.657618			−0.328809	−	0.944396i	$-0.606647\pi$
$233$	−153.225			−0.657618			−0.328809	+	0.944396i	$0.606647\pi$
$234$		0			0
$235$		0			0
$236$	381.047	−	33.5452i	1.61461	−	0.142141i
$237$		0			0
$238$	−254.555	−	233.130i	−1.06956	−	0.979536i
$239$		−	187.213i		−	0.783320i	−0.920110	−	0.391660i	$-0.871901\pi$
$239$		−	187.213i		−	0.783320i	0.920110	−	0.391660i	$-0.128099\pi$
$240$		0			0
$241$	−65.0937			−0.270098			−0.135049	−	0.990839i	$-0.543119\pi$
$241$	−65.0937			−0.270098			−0.135049	+	0.990839i	$0.543119\pi$
$242$	−10.8485	+	11.8454i	−0.0448283	+	0.0489481i
$243$		0			0
$244$	32.2828	+	366.707i	0.132307	+	1.50290i
$245$		0			0
$246$		0			0
$247$		−	269.284i		−	1.09022i
$248$	−110.523	+	144.279i	−0.445659	+	0.581772i
$249$		0			0
$250$		0			0
$251$			443.363i			1.76639i	0.469008	+	0.883194i	$0.344612\pi$
$251$			443.363i			1.76639i	−0.469008	+	0.883194i	$0.655388\pi$
$252$		0			0
$253$	238.062			0.940958
$254$	76.1047	+	69.6992i	0.299625	+	0.274406i
$255$		0			0
$256$	240.371	−	88.0781i	0.938949	−	0.344055i
$257$	241.287			0.938862			0.469431	−	0.882969i	$-0.344459\pi$
$257$	241.287			0.938862			0.469431	+	0.882969i	$0.344459\pi$
$258$		0			0
$259$		−	209.577i		−	0.809177i
$260$		0			0
$261$		0			0
$262$	−234.031	−	214.334i	−0.893249	−	0.818067i
$263$		−	379.170i		−	1.44171i	−0.693086	−	0.720855i	$-0.743749\pi$
$263$		−	379.170i		−	1.44171i	0.693086	−	0.720855i	$-0.256251\pi$
$264$		0			0
$265$		0			0
$266$	−367.539	+	401.317i	−1.38173	+	1.50871i
$267$		0			0
$268$	215.785	−	18.9965i	0.805168	−	0.0708825i
$269$	−120.713			−0.448745			−0.224373	−	0.974503i	$-0.572033\pi$
$269$	−120.713			−0.448745			−0.224373	+	0.974503i	$0.572033\pi$
$270$		0			0
$271$			114.302i			0.421777i	0.977510	+	0.210889i	$0.0676358\pi$
$271$			114.302i			0.421777i	−0.977510	+	0.210889i	$0.932364\pi$
$272$	249.010	−	44.1854i	0.915478	−	0.162446i
$273$		0			0
$274$	−283.445	+	309.494i	−1.03447	+	1.12954i
$275$		0			0
$276$		0			0
$277$	−197.256			−0.712116			−0.356058	−	0.934464i	$-0.615880\pi$
$277$	−197.256			−0.712116			−0.356058	+	0.934464i	$0.615880\pi$
$278$	124.816	+	114.311i	0.448980	+	0.411191i
$279$		0			0
$280$		0			0
$281$	−10.0625			−0.0358096			−0.0179048	−	0.999840i	$-0.505700\pi$
$281$	−10.0625			−0.0358096			−0.0179048	+	0.999840i	$0.505700\pi$
$282$		0			0
$283$		−	541.280i		−	1.91265i	−0.292307	−	0.956324i	$-0.594423\pi$
$283$		−	541.280i		−	1.91265i	0.292307	−	0.956324i	$-0.405577\pi$
$284$	−272.984	+	24.0320i	−0.961213	+	0.0846198i
$285$		0			0
$286$	181.047	+	165.809i	0.633031	+	0.579751i
$287$		−	185.623i		−	0.646771i
$288$		0			0
$289$	−39.1625			−0.135510
$290$		0			0
$291$		0			0
$292$	−15.5023	−	176.094i	−0.0530902	−	0.603061i
$293$	344.994			1.17745			0.588726	−	0.808332i	$-0.299630\pi$
$293$	344.994			1.17745			0.588726	+	0.808332i	$0.299630\pi$
$294$		0			0
$295$		0			0
$296$	121.895	+	93.3763i	0.411808	+	0.315461i
$297$		0			0
$298$	−230.806	+	252.018i	−0.774518	+	0.845697i
$299$		−	226.474i		−	0.757438i
$300$		0			0
$301$	−71.1625			−0.236420
$302$	−267.539	−	245.021i	−0.885891	−	0.811328i
$303$		0			0
$304$	−69.6602	−	392.575i	−0.229145	−	1.29137i
$305$		0			0
$306$		0			0
$307$			181.307i			0.590576i	0.955408	+	0.295288i	$0.0954156\pi$
$307$			181.307i			0.590576i	−0.955408	+	0.295288i	$0.904584\pi$
$308$	−43.5078	−	494.214i	−0.141259	−	1.60459i
$309$		0			0
$310$		0			0
$311$		−	91.9382i		−	0.295621i	−0.989016	−	0.147811i	$-0.952777\pi$
$311$		−	91.9382i		−	0.295621i	0.989016	−	0.147811i	$-0.0472226\pi$
$312$		0			0
$313$	401.287			1.28207			0.641034	−	0.767512i	$-0.278506\pi$
$313$	401.287			1.28207			0.641034	+	0.767512i	$0.278506\pi$
$314$	−33.9890	+	37.1127i	−0.108245	+	0.118193i
$315$		0			0
$316$	−325.602	+	28.6641i	−1.03038	+	0.0907093i
$317$	−552.900			−1.74416			−0.872082	−	0.489360i	$-0.837230\pi$
$317$	−552.900			−1.74416			−0.872082	+	0.489360i	$0.837230\pi$
$318$		0			0
$319$			259.061i			0.812102i
$320$		0			0
$321$		0			0
$322$	−309.109	+	337.517i	−0.959967	+	1.04819i
$323$		−	393.880i		−	1.21944i
$324$		0			0
$325$		0			0
$326$	11.8117	+	10.8176i	0.0362323	+	0.0331827i
$327$		0			0
$328$	107.963	+	82.7039i	0.329156	+	0.252146i
$329$	−424.962			−1.29168
$330$		0			0
$331$			602.037i			1.81884i	0.415875	+	0.909422i	$0.363475\pi$
$331$			602.037i			1.81884i	−0.415875	+	0.909422i	$0.636525\pi$
$332$	111.230	−	9.79211i	0.335032	−	0.0294943i
$333$		0			0
$334$	−276.628	−	253.345i	−0.828228	−	0.758519i
$335$		0			0
$336$		0			0
$337$	−32.1000			−0.0952523			−0.0476261	−	0.998865i	$-0.515166\pi$
$337$	−32.1000			−0.0952523			−0.0476261	+	0.998865i	$0.515166\pi$
$338$	−70.5445	+	77.0277i	−0.208712	+	0.227893i
$339$		0			0
$340$		0			0
$341$	−258.062			−0.756781
$342$		0			0
$343$		−	231.756i		−	0.675674i
$344$	31.7062	−	41.3899i	0.0921693	−	0.120320i
$345$		0			0
$346$	−166.450	+	181.747i	−0.481069	+	0.525281i
$347$		−	522.438i		−	1.50558i	−0.658259	−	0.752792i	$-0.728707\pi$
$347$		−	522.438i		−	1.50558i	0.658259	−	0.752792i	$-0.271293\pi$
$348$		0			0
$349$	128.931			0.369430			0.184715	−	0.982792i	$-0.440864\pi$
$349$	128.931			0.369430			0.184715	+	0.982792i	$0.440864\pi$
$350$		0			0
$351$		0			0
$352$	306.832	+	194.890i	0.871682	+	0.553665i
$353$	594.837			1.68509			0.842546	−	0.538624i	$-0.181056\pi$
$353$	594.837			1.68509			0.842546	+	0.538624i	$0.181056\pi$
$354$		0			0
$355$		0			0
$356$	−14.8008	−	168.125i	−0.0415752	−	0.472261i
$357$		0			0
$358$	204.293	+	187.098i	0.570651	+	0.522621i
$359$			26.0554i			0.0725778i	0.999341	+	0.0362889i	$0.0115537\pi$
$359$			26.0554i			0.0725778i	−0.999341	+	0.0362889i	$0.988446\pi$
$360$		0			0
$361$	−259.969			−0.720135
$362$	−262.220	+	286.319i	−0.724366	+	0.790936i
$363$		0			0
$364$	−470.156	+	41.3899i	−1.29164	+	0.113709i
$365$		0			0
$366$		0			0
$367$			420.915i			1.14691i	0.819238	+	0.573453i	$0.194397\pi$
$367$			420.915i			1.14691i	−0.819238	+	0.573453i	$0.805603\pi$
$368$	−58.5859	−	330.166i	−0.159201	−	0.897189i
$369$		0			0
$370$		0			0
$371$		−	144.404i		−	0.389229i
$372$		0			0
$373$	−218.713			−0.586361			−0.293180	−	0.956057i	$-0.594714\pi$
$373$	−218.713			−0.586361			−0.293180	+	0.956057i	$0.594714\pi$
$374$	264.816	+	242.528i	0.708065	+	0.648470i
$375$		0			0
$376$	189.341	−	247.169i	0.503566	−	0.657364i
$377$	246.450			0.653713
$378$		0			0
$379$			246.282i			0.649820i	0.945745	+	0.324910i	$0.105334\pi$
$379$			246.282i			0.649820i	−0.945745	+	0.324910i	$0.894666\pi$
$380$		0			0
$381$		0			0
$382$	−99.4766	−	91.1039i	−0.260410	−	0.238492i
$383$			406.106i			1.06033i	0.847895	+	0.530164i	$0.177870\pi$
$383$			406.106i			1.06033i	−0.847895	+	0.530164i	$0.822130\pi$
$384$		0			0
$385$		0			0
$386$	−207.843	+	226.944i	−0.538453	+	0.587938i
$387$		0			0
$388$	−54.3141	−	616.964i	−0.139985	−	1.59011i
$389$	201.225			0.517288			0.258644	−	0.965973i	$-0.416724\pi$
$389$	201.225			0.517288			0.258644	+	0.965973i	$0.416724\pi$
$390$		0			0
$391$		−	331.263i		−	0.847219i
$392$	445.984	+	341.640i	1.13771	+	0.871530i
$393$		0			0
$394$	352.942	−	385.378i	0.895792	−	0.978117i
$395$		0			0
$396$		0			0
$397$	96.7750			0.243766			0.121883	−	0.992544i	$-0.461107\pi$
$397$	96.7750			0.243766			0.121883	+	0.992544i	$0.461107\pi$
$398$	−335.078	−	306.876i	−0.841905	−	0.771044i
$399$		0			0
$400$		0			0
$401$	−279.094			−0.695994			−0.347997	−	0.937496i	$-0.613138\pi$
$401$	−279.094			−0.695994			−0.347997	+	0.937496i	$0.613138\pi$
$402$		0			0
$403$			245.501i			0.609182i
$404$	−1.39217	−	15.8139i	−0.00344595	−	0.0391432i
$405$		0			0
$406$	−367.287	−	336.374i	−0.904649	−	0.828507i
$407$			218.026i			0.535689i
$408$		0			0
$409$	521.837			1.27589			0.637943	−	0.770083i	$-0.279785\pi$
$409$	521.837			1.27589			0.637943	+	0.770083i	$0.279785\pi$
$410$		0			0
$411$		0			0
$412$	−263.141	+	23.1654i	−0.638691	+	0.0562268i
$413$	−1044.19			−2.52830
$414$		0			0
$415$		0			0
$416$	185.403	−	291.896i	0.445681	−	0.701673i
$417$		0			0
$418$	382.355	−	417.495i	0.914726	−	0.998791i
$419$		−	252.103i		−	0.601678i	−0.953675	−	0.300839i	$-0.902733\pi$
$419$		−	252.103i		−	0.601678i	0.953675	−	0.300839i	$-0.0972667\pi$
$420$		0			0
$421$	776.187			1.84368			0.921838	−	0.387576i	$-0.126687\pi$
$421$	776.187			1.84368			0.921838	+	0.387576i	$0.126687\pi$
$422$	−285.863	−	261.803i	−0.677401	−	0.620386i
$423$		0			0
$424$	83.9890	+	64.3387i	0.198087	+	0.151742i
$425$		0			0
$426$		0			0
$427$		−	1004.89i		−	2.35337i
$428$	382.801	−	33.6996i	0.894394	−	0.0787375i
$429$		0			0
$430$		0			0
$431$			588.904i			1.36637i	0.730247	+	0.683183i	$0.239405\pi$
$431$			588.904i			1.36637i	−0.730247	+	0.683183i	$0.760595\pi$
$432$		0			0
$433$	−541.931			−1.25157			−0.625787	−	0.779994i	$-0.715222\pi$
$433$	−541.931			−1.25157			−0.625787	+	0.779994i	$0.715222\pi$
$434$	335.078	−	365.872i	0.772069	−	0.843024i
$435$		0			0
$436$	−39.5703	−	449.487i	−0.0907576	−	1.03093i
$437$	−522.250			−1.19508
$438$		0			0
$439$			4.04683i			0.00921830i	0.999989	+	0.00460915i	$0.00146714\pi$
$439$			4.04683i			0.00921830i	−0.999989	+	0.00460915i	$0.998533\pi$
$440$		0			0
$441$		0			0
$442$	230.722	−	251.926i	0.521995	−	0.569968i
$443$			342.635i			0.773444i	0.922196	+	0.386722i	$0.126393\pi$
$443$			342.635i			0.773444i	−0.922196	+	0.386722i	$0.873607\pi$
$444$		0			0
$445$		0			0
$446$	−37.4031	−	34.2550i	−0.0838635	−	0.0768050i
$447$		0			0
$448$	−674.711	+	181.964i	−1.50605	+	0.406169i
$449$	484.444			1.07894			0.539470	−	0.842005i	$-0.318625\pi$
$449$	484.444			1.07894			0.539470	+	0.842005i	$0.318625\pi$
$450$		0			0
$451$			193.106i			0.428174i
$452$	6.39298	+	72.6191i	0.0141438	+	0.160662i
$453$		0			0
$454$	552.481	+	505.981i	1.21692	+	1.11449i
$455$		0			0
$456$		0			0
$457$	−698.537			−1.52853			−0.764264	−	0.644903i	$-0.776898\pi$
$457$	−698.537			−1.52853			−0.764264	+	0.644903i	$0.776898\pi$
$458$	−350.241	+	382.428i	−0.764718	+	0.834997i
$459$		0			0
$460$		0			0
$461$	820.250			1.77928			0.889642	−	0.456659i	$-0.150954\pi$
$461$	820.250			1.77928			0.889642	+	0.456659i	$0.150954\pi$
$462$		0			0
$463$			881.956i			1.90487i	0.304736	+	0.952437i	$0.401432\pi$
$463$			881.956i			1.90487i	−0.304736	+	0.952437i	$0.598568\pi$
$464$	359.287	−	63.7534i	0.774326	−	0.137400i
$465$		0			0
$466$	−206.973	+	225.995i	−0.444149	+	0.484967i
$467$			57.2361i			0.122561i	0.998121	+	0.0612807i	$0.0195185\pi$
$467$			57.2361i			0.122561i	−0.998121	+	0.0612807i	$0.980482\pi$
$468$		0			0
$469$	−591.319			−1.26081
$470$		0			0
$471$		0			0
$472$	465.234	−	607.326i	0.985666	−	1.28671i
$473$	74.0312			0.156514
$474$		0			0
$475$		0			0
$476$	−687.695	+	60.5409i	−1.44474	+	0.127187i
$477$		0			0
$478$	−276.125	−	252.884i	−0.577667	−	0.529047i
$479$			651.449i			1.36002i	0.733203	+	0.680010i	$0.238024\pi$
$479$			651.449i			1.36002i	−0.733203	+	0.680010i	$0.761976\pi$
$480$		0			0
$481$	207.412			0.431211
$482$	−87.9274	+	96.0081i	−0.182422	+	0.199187i
$483$		0			0
$484$	2.81721	+	32.0012i	0.00582068	+	0.0661182i
$485$		0			0
$486$		0			0
$487$			53.0187i			0.108868i	0.998517	+	0.0544340i	$0.0173355\pi$
$487$			53.0187i			0.108868i	−0.998517	+	0.0544340i	$0.982665\pi$
$488$	584.470	+	447.726i	1.19768	+	0.917471i
$489$		0			0
$490$		0			0
$491$		−	21.6537i		−	0.0441013i	−0.999757	−	0.0220506i	$-0.992980\pi$
$491$		−	21.6537i		−	0.0441013i	0.999757	−	0.0220506i	$-0.00701950\pi$
$492$		0			0
$493$	360.481			0.731199
$494$	−397.172	−	363.743i	−0.803992	−	0.736322i
$495$		0			0
$496$	63.5078	+	357.903i	0.128040	+	0.721579i
$497$	748.062			1.50516
$498$		0			0
$499$		−	203.401i		−	0.407617i	−0.979011	−	0.203808i	$-0.934668\pi$
$499$		−	203.401i		−	0.407617i	0.979011	−	0.203808i	$-0.0653320\pi$
$500$		0			0
$501$		0			0
$502$	653.926	+	598.887i	1.30264	+	1.19300i
$503$		−	84.5406i		−	0.168073i	−0.996463	−	0.0840363i	$-0.973219\pi$
$503$		−	84.5406i		−	0.168073i	0.996463	−	0.0840363i	$-0.0267812\pi$
$504$		0			0
$505$		0			0
$506$	321.570	−	351.123i	0.635514	−	0.693919i
$507$		0			0
$508$	205.602	−	18.1000i	0.404727	−	0.0356299i
$509$	101.225			0.198870			0.0994352	−	0.995044i	$-0.468296\pi$
$509$	101.225			0.198870			0.0994352	+	0.995044i	$0.468296\pi$
$510$		0			0
$511$			482.552i			0.944330i
$512$	194.780	−	473.502i	0.380431	−	0.924809i
$513$		0			0
$514$	325.927	−	355.880i	0.634098	−	0.692373i
$515$		0			0
$516$		0			0
$517$	442.094			0.855114
$518$	−309.109	−	283.093i	−0.596736	−	0.546511i
$519$		0			0
$520$		0			0
$521$	671.375			1.28863			0.644314	−	0.764761i	$-0.277143\pi$
$521$	671.375			1.28863			0.644314	+	0.764761i	$0.277143\pi$
$522$		0			0
$523$			848.589i			1.62254i	0.584671	+	0.811270i	$0.301223\pi$
$523$			848.589i			1.62254i	−0.584671	+	0.811270i	$0.698777\pi$
$524$	−632.250	+	55.6598i	−1.20658	+	0.106221i
$525$		0			0
$526$	−559.245	−	512.175i	−1.06320	−	0.973717i
$527$			359.092i			0.681390i
$528$		0			0
$529$	89.7750			0.169707
$530$		0			0
$531$		0			0
$532$	95.4453	+	1084.18i	0.179409	+	2.03794i
$533$	183.706			0.344665
$534$		0			0
$535$		0			0
$536$	263.460	−	343.926i	0.491530	−	0.641653i
$537$		0			0
$538$	−163.056	+	178.041i	−0.303078	+	0.330932i
$539$			797.699i			1.47996i
$540$		0			0
$541$	824.250			1.52357			0.761784	−	0.647831i	$-0.224324\pi$
$541$	824.250			1.52357			0.761784	+	0.647831i	$0.224324\pi$
$542$	168.586	+	154.397i	0.311044	+	0.284865i
$543$		0			0
$544$	271.188	−	426.955i	0.498508	−	0.784844i
$545$		0			0
$546$		0			0
$547$			275.020i			0.502778i	0.967886	+	0.251389i	$0.0808873\pi$
$547$			275.020i			0.502778i	−0.967886	+	0.251389i	$0.919113\pi$
$548$	73.6070	+	836.116i	0.134319	+	1.52576i
$549$		0			0
$550$		0			0
$551$		−	568.314i		−	1.03142i
$552$		0			0
$553$	892.250			1.61347
$554$	−266.450	+	290.937i	−0.480957	+	0.525158i
$555$		0			0
$556$	337.199	−	29.6851i	0.606473	−	0.0533905i
$557$	−154.681			−0.277704			−0.138852	−	0.990313i	$-0.544341\pi$
$557$	−154.681			−0.277704			−0.138852	+	0.990313i	$0.544341\pi$
$558$		0			0
$559$		−	70.4275i		−	0.125988i
$560$		0			0
$561$		0			0
$562$	−13.5922	+	14.8414i	−0.0241854	+	0.0264081i
$563$			767.327i			1.36293i	0.731853	+	0.681463i	$0.238656\pi$
$563$			767.327i			1.36293i	−0.731853	+	0.681463i	$0.761344\pi$
$564$		0			0
$565$		0			0
$566$	−798.344	−	731.150i	−1.41050	−	1.29179i
$567$		0			0
$568$	−333.297	+	435.092i	−0.586790	+	0.766008i
$569$	−346.025			−0.608128			−0.304064	−	0.952652i	$-0.598344\pi$
$569$	−346.025			−0.608128			−0.304064	+	0.952652i	$0.598344\pi$
$570$		0			0
$571$		−	389.407i		−	0.681973i	−0.940068	−	0.340986i	$-0.889239\pi$
$571$		−	389.407i		−	0.681973i	0.940068	−	0.340986i	$-0.110761\pi$
$572$	489.109	−	43.0585i	0.855086	−	0.0752770i
$573$		0			0
$574$	−273.780	−	250.736i	−0.476968	−	0.436823i
$575$		0			0
$576$		0			0
$577$	−800.475			−1.38730			−0.693652	−	0.720310i	$-0.744000\pi$
$577$	−800.475			−1.38730			−0.693652	+	0.720310i	$0.744000\pi$
$578$	−52.9000	+	57.7616i	−0.0915224	+	0.0999335i
$579$		0			0
$580$		0			0
$581$	−304.806			−0.524623
$582$		0			0
$583$			150.225i			0.257676i
$584$	−280.665	−	215.000i	−0.480590	−	0.368150i
$585$		0			0
$586$	466.011	−	508.838i	0.795241	−	0.868325i
$587$		−	758.780i		−	1.29264i	−0.763066	−	0.646320i	$-0.776307\pi$
$587$		−	758.780i		−	1.29264i	0.763066	−	0.646320i	$-0.223693\pi$
$588$		0			0
$589$	566.125			0.961163
$590$		0			0
$591$		0			0
$592$	302.377	−	53.6549i	0.510771	−	0.0906333i
$593$	1049.84			1.77038			0.885192	−	0.465226i	$-0.154027\pi$
$593$	1049.84			1.77038			0.885192	+	0.465226i	$0.154027\pi$
$594$		0			0
$595$		0			0
$596$	59.9375	+	680.842i	0.100566	+	1.14235i
$597$		0			0
$598$	−334.031	−	305.917i	−0.558581	−	0.511567i
$599$		−	269.427i		−	0.449794i	−0.974383	−	0.224897i	$-0.927795\pi$
$599$		−	269.427i		−	0.449794i	0.974383	−	0.224897i	$-0.0722046\pi$
$600$		0			0
$601$	−567.031			−0.943480			−0.471740	−	0.881738i	$-0.656374\pi$
$601$	−567.031			−0.943480			−0.471740	+	0.881738i	$0.656374\pi$
$602$	−96.1250	+	104.959i	−0.159676	+	0.174351i
$603$		0			0
$604$	−722.773	+	63.6289i	−1.19664	+	0.105346i
$605$		0			0
$606$		0			0
$607$		−	846.770i		−	1.39501i	−0.716581	−	0.697504i	$-0.754294\pi$
$607$		−	846.770i		−	1.39501i	0.716581	−	0.697504i	$-0.245706\pi$
$608$	−673.113	−	427.540i	−1.10709	−	0.703191i
$609$		0			0
$610$		0			0
$611$		−	420.573i		−	0.688336i
$612$		0			0
$613$	−306.775			−0.500449			−0.250224	−	0.968188i	$-0.580504\pi$
$613$	−306.775			−0.500449			−0.250224	+	0.968188i	$0.580504\pi$
$614$	267.413	+	244.906i	0.435526	+	0.398870i
$615$		0			0
$616$	−787.695	−	603.404i	−1.27873	−	0.979552i
$617$	−435.150			−0.705267			−0.352634	−	0.935761i	$-0.614714\pi$
$617$	−435.150			−0.705267			−0.352634	+	0.935761i	$0.614714\pi$
$618$		0			0
$619$		−	123.460i		−	0.199451i	−0.995015	−	0.0997254i	$-0.968204\pi$
$619$		−	123.460i		−	0.199451i	0.995015	−	0.0997254i	$-0.0317964\pi$
$620$		0			0
$621$		0			0
$622$	−135.602	−	124.188i	−0.218009	−	0.199660i
$623$			460.714i			0.739509i
$624$		0			0
$625$		0			0
$626$	542.052	−	591.867i	0.865897	−	0.945475i
$627$		0			0
$628$	8.82653	+	100.262i	0.0140550	+	0.159653i
$629$	303.381			0.482323
$630$		0			0
$631$			519.684i			0.823588i	0.911277	+	0.411794i	$0.135098\pi$
$631$			519.684i			0.823588i	−0.911277	+	0.411794i	$0.864902\pi$
$632$	−397.539	+	518.955i	−0.629017	+	0.821132i
$633$		0			0
$634$	−746.847	+	815.484i	−1.17799	+	1.28625i
$635$		0			0
$636$		0			0
$637$	758.869			1.19132
$638$	382.094	+	349.934i	0.598893	+	0.548486i
$639$		0			0
$640$		0			0
$641$	82.1875			0.128218			0.0641088	−	0.997943i	$-0.479580\pi$
$641$	82.1875			0.128218			0.0641088	+	0.997943i	$0.479580\pi$
$642$		0			0
$643$		−	513.023i		−	0.797859i	−0.916982	−	0.398930i	$-0.869382\pi$
$643$		−	513.023i		−	0.797859i	0.916982	−	0.398930i	$-0.130618\pi$
$644$	80.2719	+	911.823i	0.124646	+	1.41587i
$645$		0			0
$646$	−580.941	−	532.045i	−0.899290	−	0.823600i
$647$			573.440i			0.886306i	0.896446	+	0.443153i	$0.146140\pi$
$647$			573.440i			0.886306i	−0.896446	+	0.443153i	$0.853860\pi$
$648$		0			0
$649$	1086.28			1.67378
$650$		0			0
$651$		0			0
$652$	31.9101	−	2.80919i	0.0489419	−	0.00430857i
$653$	−767.256			−1.17497			−0.587486	−	0.809235i	$-0.699882\pi$
$653$	−767.256			−1.17497			−0.587486	+	0.809235i	$0.699882\pi$
$654$		0			0
$655$		0			0
$656$	267.816	−	47.5224i	0.408257	−	0.0724427i
$657$		0			0
$658$	−574.031	+	626.786i	−0.872388	+	0.952562i
$659$		−	1054.84i		−	1.60067i	−0.599552	−	0.800336i	$-0.704655\pi$
$659$		−	1054.84i		−	1.60067i	0.599552	−	0.800336i	$-0.295345\pi$
$660$		0			0
$661$	618.281			0.935372			0.467686	−	0.883895i	$-0.345088\pi$
$661$	618.281			0.935372			0.467686	+	0.883895i	$0.345088\pi$
$662$	887.957	+	813.220i	1.34132	+	1.22843i
$663$		0			0
$664$	135.805	−	177.283i	0.204526	−	0.266993i
$665$		0			0
$666$		0			0
$667$		−	477.966i		−	0.716591i
$668$	−747.328	+	65.7906i	−1.11875	+	0.0984889i
$669$		0			0
$670$		0			0
$671$			1045.40i			1.55797i
$672$		0			0
$673$	−26.7750			−0.0397846			−0.0198923	−	0.999802i	$-0.506332\pi$
$673$	−26.7750			−0.0397846			−0.0198923	+	0.999802i	$0.506332\pi$
$674$	−43.3601	+	47.3450i	−0.0643325	+	0.0702448i
$675$		0			0
$676$	18.3195	+	208.095i	0.0270999	+	0.307833i
$677$	−264.837			−0.391193			−0.195596	−	0.980684i	$-0.562664\pi$
$677$	−264.837			−0.391193			−0.195596	+	0.980684i	$0.562664\pi$
$678$		0			0
$679$			1690.67i			2.48995i
$680$		0			0
$681$		0			0
$682$	−348.586	+	380.622i	−0.511123	+	0.558096i
$683$			761.435i			1.11484i	0.830231	+	0.557419i	$0.188208\pi$
$683$			761.435i			1.11484i	−0.830231	+	0.557419i	$0.811792\pi$
$684$		0			0
$685$		0			0
$686$	−341.822	−	313.052i	−0.498283	−	0.456344i
$687$		0			0
$688$	−18.2187	−	102.673i	−0.0264807	−	0.149234i
$689$	142.913			0.207420
$690$		0			0
$691$			715.984i			1.03616i	0.855333	+	0.518078i	$0.173352\pi$
$691$			715.984i			1.03616i	−0.855333	+	0.518078i	$0.826648\pi$
$692$	43.2250	+	491.001i	0.0624639	+	0.709539i
$693$		0			0
$694$	−770.554	−	705.699i	−1.11031	−	1.01686i
$695$		0			0
$696$		0			0
$697$	268.706			0.385518
$698$	174.158	−	190.163i	0.249510	−	0.272440i
$699$		0			0
$700$		0			0
$701$	−6.03124			−0.00860377			−0.00430188	−	0.999991i	$-0.501369\pi$
$701$	−6.03124			−0.00860377			−0.00430188	+	0.999991i	$0.501369\pi$
$702$		0			0
$703$		−	478.294i		−	0.680361i
$704$	701.910	−	189.299i	0.997031	−	0.268891i
$705$		0			0
$706$	803.495	−	877.338i	1.13810	−	1.24269i
$707$			43.3349i			0.0612941i
$708$		0			0
$709$	−170.913			−0.241061			−0.120531	−	0.992710i	$-0.538460\pi$
$709$	−170.913			−0.241061			−0.120531	+	0.992710i	$0.538460\pi$
$710$		0			0
$711$		0			0
$712$	−267.963	−	205.270i	−0.376353	−	0.288300i
$713$	476.125			0.667777
$714$		0			0
$715$		0			0
$716$	551.910	−	48.5871i	0.770824	−	0.0678591i
$717$		0			0
$718$	38.4297	+	35.1952i	0.0535233	+	0.0490184i
$719$			1369.42i			1.90462i	0.305131	+	0.952310i	$0.401300\pi$
$719$			1369.42i			1.90462i	−0.305131	+	0.952310i	$0.598700\pi$
$720$		0			0
$721$	721.087			1.00012
$722$	−351.161	+	383.433i	−0.486372	+	0.531071i
$723$		0			0
$724$	68.0954	+	773.508i	0.0940544	+	1.06838i
$725$		0			0
$726$		0			0
$727$			1006.13i			1.38394i	0.721925	+	0.691971i	$0.243258\pi$
$727$			1006.13i			1.38394i	−0.721925	+	0.691971i	$0.756742\pi$
$728$	−574.031	+	749.352i	−0.788504	+	1.02933i
$729$		0			0
$730$		0			0
$731$		−	103.014i		−	0.140922i
$732$		0			0
$733$	365.319			0.498388			0.249194	−	0.968454i	$-0.419834\pi$
$733$	365.319			0.498388			0.249194	+	0.968454i	$0.419834\pi$
$734$	620.816	+	568.563i	0.845798	+	0.774610i
$735$		0			0
$736$	−566.105	−	359.572i	−0.769164	−	0.488549i
$737$	615.156			0.834676
$738$		0			0
$739$			187.213i			0.253334i	0.991945	+	0.126667i	$0.0404279\pi$
$739$			187.213i			0.253334i	−0.991945	+	0.126667i	$0.959572\pi$
$740$		0			0
$741$		0			0
$742$	−212.984	−	195.058i	−0.287041	−	0.262882i
$743$			183.678i			0.247212i	0.992331	+	0.123606i	$0.0394459\pi$
$743$			183.678i			0.247212i	−0.992331	+	0.123606i	$0.960554\pi$
$744$		0			0
$745$		0			0
$746$	−295.433	+	322.584i	−0.396022	+	0.432418i
$747$		0			0
$748$	715.418	−	62.9814i	0.956441	−	0.0841997i
$749$	−1048.99			−1.40053
$750$		0			0
$751$			569.734i			0.758634i	0.925267	+	0.379317i	$0.123841\pi$
$751$			569.734i			0.758634i	−0.925267	+	0.379317i	$0.876159\pi$
$752$	−108.797	−	613.134i	−0.144677	−	0.815337i
$753$		0			0
$754$	332.900	−	363.494i	0.441512	−	0.482088i
$755$		0			0
$756$		0			0
$757$	−1131.60			−1.49485			−0.747424	−	0.664347i	$-0.768710\pi$
$757$	−1131.60			−1.49485			−0.747424	+	0.664347i	$0.768710\pi$
$758$	363.246	+	332.673i	0.479216	+	0.438882i
$759$		0			0
$760$		0			0
$761$	−753.125			−0.989652			−0.494826	−	0.868992i	$-0.664768\pi$
$761$	−753.125			−0.989652			−0.494826	+	0.868992i	$0.664768\pi$
$762$		0			0
$763$			1231.73i			1.61433i
$764$	−268.742	+	23.6586i	−0.351757	+	0.0309667i
$765$		0			0
$766$	598.973	+	548.560i	0.781950	+	0.716135i
$767$		−	1033.40i		−	1.34733i
$768$		0			0
$769$	−648.319			−0.843067			−0.421534	−	0.906813i	$-0.638508\pi$
$769$	−648.319			−0.843067			−0.421534	+	0.906813i	$0.638508\pi$
$770$		0			0
$771$		0			0
$772$	53.9742	+	613.104i	0.0699148	+	0.794176i
$773$	−709.506			−0.917861			−0.458930	−	0.888472i	$-0.651767\pi$
$773$	−709.506			−0.917861			−0.458930	+	0.888472i	$0.651767\pi$
$774$		0			0
$775$		0			0
$776$	−983.339	−	753.274i	−1.26719	−	0.970714i
$777$		0			0
$778$	271.811	−	296.791i	0.349371	−	0.381479i
$779$		−	423.627i		−	0.543809i
$780$		0			0
$781$	−778.219			−0.996439
$782$	−488.586	−	447.463i	−0.624790	−	0.572204i
$783$		0			0
$784$	1106.32	−	196.310i	1.41112	−	0.250395i
$785$		0			0
$786$		0			0
$787$			3.67819i			0.00467369i	0.999997	+	0.00233684i	$0.000743841\pi$
$787$			3.67819i			0.00467369i	−0.999997	+	0.00233684i	$0.999256\pi$
$788$	−91.6547	−	1041.12i	−0.116313	−	1.32122i
$789$		0			0
$790$		0			0
$791$		−	198.999i		−	0.251579i
$792$		0			0
$793$	994.512			1.25411
$794$	130.722	−	142.735i	0.164637	−	0.179768i
$795$		0			0
$796$	−905.234	+	79.6918i	−1.13723	+	0.100115i
$797$	−1379.02			−1.73027			−0.865135	−	0.501539i	$-0.832767\pi$
$797$	−1379.02			−1.73027			−0.865135	+	0.501539i	$0.832767\pi$
$798$		0			0
$799$		−	615.171i		−	0.769926i
$800$		0			0
$801$		0			0
$802$	−376.995	+	411.641i	−0.470068	+	0.513268i
$803$		−	502.005i		−	0.625162i
$804$		0			0
$805$		0			0
$806$	362.094	+	331.617i	0.449248	+	0.411436i
$807$		0			0
$808$	−25.2047	−	19.3077i	−0.0311939	−	0.0238957i
$809$	1333.79			1.64869			0.824343	−	0.566090i	$-0.191545\pi$
$809$	1333.79			1.64869			0.824343	+	0.566090i	$0.191545\pi$
$810$		0			0
$811$		−	204.820i		−	0.252553i	−0.991995	−	0.126276i	$-0.959697\pi$
$811$		−	204.820i		−	0.252553i	0.991995	−	0.126276i	$-0.0403026\pi$
$812$	−992.250	+	87.3522i	−1.22198	+	0.107577i
$813$		0			0
$814$	321.570	+	294.505i	0.395050	+	0.361799i
$815$		0			0
$816$		0			0
$817$	−162.406			−0.198784
$818$	704.888	−	769.669i	0.861722	−	0.940915i
$819$		0			0
$820$		0			0
$821$	493.813			0.601477			0.300738	−	0.953707i	$-0.402767\pi$
$821$	493.813			0.601477			0.300738	+	0.953707i	$0.402767\pi$
$822$		0			0
$823$		−	173.312i		−	0.210586i	−0.994441	−	0.105293i	$-0.966422\pi$
$823$		−	173.312i		−	0.210586i	0.994441	−	0.105293i	$-0.0335780\pi$
$824$	−321.278	+	419.403i	−0.389901	+	0.508984i
$825$		0			0
$826$	−1410.47	+	1540.09i	−1.70759	+	1.86452i
$827$			693.777i			0.838908i	0.907776	+	0.419454i	$0.137779\pi$
$827$			693.777i			0.838908i	−0.907776	+	0.419454i	$0.862221\pi$
$828$		0			0
$829$	−1125.57			−1.35774			−0.678871	−	0.734257i	$-0.737531\pi$
$829$	−1125.57			−1.35774			−0.678871	+	0.734257i	$0.737531\pi$
$830$		0			0
$831$		0			0
$832$	−180.084	−	667.742i	−0.216448	−	0.802575i
$833$	1109.99			1.33253
$834$		0			0
$835$		0			0
$836$	−99.2930	−	1127.89i	−0.118771	−	1.34915i
$837$		0			0
$838$	−371.832	−	340.536i	−0.443714	−	0.406368i
$839$			1243.69i			1.48235i	0.671313	+	0.741174i	$0.265731\pi$
$839$			1243.69i			1.48235i	−0.671313	+	0.741174i	$0.734269\pi$
$840$		0			0
$841$	−320.875			−0.381540
$842$	1048.46	−	1144.81i	1.24520	−	1.35964i
$843$		0			0
$844$	−772.277	+	67.9870i	−0.915021	+	0.0805533i
$845$		0			0
$846$		0			0
$847$		−	87.6933i		−	0.103534i
$848$	208.345	−	36.9696i	0.245690	−	0.0435963i
$849$		0			0
$850$		0			0
$851$		−	402.257i		−	0.472687i
$852$		0			0
$853$	−1027.09			−1.20409			−0.602044	−	0.798463i	$-0.705647\pi$
$853$	−1027.09			−1.20409			−0.602044	+	0.798463i	$0.705647\pi$
$854$	−1482.13	−	1357.39i	−1.73552	−	1.58945i
$855$		0			0
$856$	467.376	−	610.122i	0.546000	−	0.712759i
$857$	−341.775			−0.398804			−0.199402	−	0.979918i	$-0.563900\pi$
$857$	−341.775			−0.398804			−0.199402	+	0.979918i	$0.563900\pi$
$858$		0			0
$859$			300.167i			0.349438i	0.984618	+	0.174719i	$0.0559017\pi$
$859$			300.167i			0.349438i	−0.984618	+	0.174719i	$0.944098\pi$
$860$		0			0
$861$		0			0
$862$	868.586	+	795.480i	1.00764	+	0.922830i
$863$		−	1312.54i		−	1.52091i	−0.649394	−	0.760453i	$-0.724977\pi$
$863$		−	1312.54i		−	1.52091i	0.649394	−	0.760453i	$-0.275023\pi$
$864$		0			0
$865$		0			0
$866$	−732.030	+	799.305i	−0.845301	+	0.922986i
$867$		0			0
$868$	−87.0156	−	988.427i	−0.100248	−	1.13874i
$869$	−928.219			−1.06815
$870$		0			0
$871$		−	585.212i		−	0.671885i
$872$	−716.408	−	548.795i	−0.821569	−	0.629352i
$873$		0			0
$874$	−705.445	+	770.277i	−0.807146	+	0.881324i
$875$		0			0
$876$		0			0
$877$	−1543.22			−1.75966			−0.879832	−	0.475285i	$-0.842345\pi$
$877$	−1543.22			−1.75966			−0.879832	+	0.475285i	$0.842345\pi$
$878$	5.96876	+	5.46639i	0.00679813	+	0.00622595i
$879$		0			0
$880$		0			0
$881$	254.437			0.288805			0.144403	−	0.989519i	$-0.453874\pi$
$881$	254.437			0.288805			0.144403	+	0.989519i	$0.453874\pi$
$882$		0			0
$883$			380.661i			0.431099i	0.976493	+	0.215550i	$0.0691543\pi$
$883$			380.661i			0.431099i	−0.976493	+	0.215550i	$0.930846\pi$
$884$	−59.9156	−	680.593i	−0.0677778	−	0.769901i
$885$		0			0
$886$	505.360	+	462.826i	0.570384	+	0.522376i
$887$			851.315i			0.959769i	0.877332	+	0.479884i	$0.159321\pi$
$887$			851.315i			0.959769i	−0.877332	+	0.479884i	$0.840679\pi$
$888$		0			0
$889$	−563.412			−0.633760
$890$		0			0
$891$		0			0
$892$	−101.047	+	8.89560i	−0.113281	+	0.00997265i
$893$	−969.844			−1.08605
$894$		0			0
$895$		0			0
$896$	−643.005	+	1240.94i	−0.717639	+	1.38498i
$897$		0			0
$898$	654.377	−	714.516i	0.728705	−	0.795675i
$899$			518.121i			0.576330i
$900$		0			0
$901$	209.038			0.232006
$902$	284.816	+	260.844i	0.315761	+	0.289184i
$903$		0			0
$904$	115.743	+	88.6634i	0.128034	+	0.0980790i
$905$		0			0
$906$		0			0
$907$			531.313i			0.585791i	0.956144	+	0.292896i	$0.0946188\pi$
$907$			531.313i			0.585791i	−0.956144	+	0.292896i	$0.905381\pi$
$908$	1492.56	−	131.397i	1.64379	−	0.144710i
$909$		0			0
$910$		0			0
$911$			316.638i			0.347572i	0.984783	+	0.173786i	$0.0556001\pi$
$911$			316.638i			0.347572i	−0.984783	+	0.173786i	$0.944400\pi$
$912$		0			0
$913$	317.094			0.347310
$914$	−943.571	+	1030.29i	−1.03235	+	1.12723i
$915$		0			0
$916$	90.9531	+	1033.15i	0.0992938	+	1.12790i
$917$	1732.56			1.88938
$918$		0			0
$919$		−	715.203i		−	0.778240i	−0.921187	−	0.389120i	$-0.872779\pi$
$919$		−	715.203i		−	0.778240i	0.921187	−	0.389120i	$-0.127221\pi$
$920$		0			0
$921$		0			0
$922$	1107.98	−	1209.80i	1.20171	−	1.31215i
$923$			740.337i			0.802098i
$924$		0			0
$925$		0			0
$926$	1300.82	+	1191.33i	1.40477	+	1.28653i
$927$		0			0
$928$	391.287	−	616.037i	0.421646	−	0.663833i
$929$	301.225			0.324246			0.162123	−	0.986771i	$-0.448166\pi$
$929$	301.225			0.324246			0.162123	+	0.986771i	$0.448166\pi$
$930$		0			0
$931$		−	1749.95i		−	1.87965i
$932$	53.7484	+	610.539i	0.0576700	+	0.655084i
$933$		0			0
$934$	84.4187	+	77.3135i	0.0903841	+	0.0827767i
$935$		0			0
$936$		0			0
$937$	1386.43			1.47965			0.739824	−	0.672800i	$-0.234909\pi$
$937$	1386.43			1.47965			0.739824	+	0.672800i	$0.234909\pi$
$938$	−798.742	+	872.148i	−0.851537	+	0.929795i
$939$		0			0
$940$		0			0
$941$	697.844			0.741598			0.370799	−	0.928713i	$-0.379084\pi$
$941$	697.844			0.741598			0.370799	+	0.928713i	$0.379084\pi$
$942$		0			0
$943$		−	356.281i		−	0.377816i
$944$	−267.328	−	1506.55i	−0.283186	−	1.59592i
$945$		0			0
$946$	100.000	−	109.190i	0.105708	−	0.115423i
$947$			310.121i			0.327477i	0.986504	+	0.163738i	$0.0523553\pi$
$947$			310.121i			0.327477i	−0.986504	+	0.163738i	$0.947645\pi$
$948$		0			0
$949$	−477.569			−0.503234
$950$		0			0
$951$		0			0
$952$	−839.633	+	1096.07i	−0.881967	+	1.15134i
$953$	−552.725			−0.579984			−0.289992	−	0.957029i	$-0.593653\pi$
$953$	−552.725			−0.579984			−0.289992	+	0.957029i	$0.593653\pi$
$954$		0			0
$955$		0			0
$956$	−745.969	+	65.6709i	−0.780302	+	0.0686934i
$957$		0			0
$958$	960.836	+	879.965i	1.00296	+	0.918544i
$959$		−	2291.22i		−	2.38918i
$960$		0			0
$961$	444.875			0.462929
$962$	280.169	−	305.917i	0.291236	−	0.318001i
$963$		0			0
$964$	22.8336	+	259.372i	0.0236864	+	0.269058i
$965$		0			0
$966$		0			0
$967$		−	1606.13i		−	1.66094i	−0.557060	−	0.830472i	$-0.688071\pi$
$967$		−	1606.13i		−	1.66094i	0.557060	−	0.830472i	$-0.311929\pi$
$968$	51.0047	+	39.0715i	0.0526908	+	0.0403631i
$969$		0			0
$970$		0			0
$971$			1265.13i			1.30291i	0.758686	+	0.651457i	$0.225842\pi$
$971$			1265.13i			1.30291i	−0.758686	+	0.651457i	$0.774158\pi$
$972$		0			0
$973$	−924.031			−0.949672
$974$	78.1984	+	71.6167i	0.0802858	+	0.0735284i
$975$		0			0
$976$	1449.85	−	257.268i	1.48550	−	0.263594i
$977$	−592.244			−0.606186			−0.303093	−	0.952961i	$-0.598019\pi$
$977$	−592.244			−0.606186			−0.303093	+	0.952961i	$0.598019\pi$
$978$		0			0
$979$		−	479.287i		−	0.489568i
$980$		0			0
$981$		0			0
$982$	−31.9375	−	29.2494i	−0.0325229	−	0.0297856i
$983$		−	1087.34i		−	1.10615i	−0.833132	−	0.553074i	$-0.813455\pi$
$983$		−	1087.34i		−	1.10615i	0.833132	−	0.553074i	$-0.186545\pi$
$984$		0			0
$985$		0			0
$986$	486.931	−	531.681i	0.493845	−	0.539230i
$987$		0			0
$988$	−1072.98	+	94.4596i	−1.08602	+	0.0956069i
$989$	−136.588			−0.138107
$990$		0			0
$991$			182.812i			0.184472i	0.995737	+	0.0922360i	$0.0294014\pi$
$991$			182.812i			0.184472i	−0.995737	+	0.0922360i	$0.970599\pi$
$992$	613.664	+	389.780i	0.618613	+	0.392923i
$993$		0			0
$994$	1010.47	−	1103.33i	1.01657	−	1.10999i
$995$		0			0
$996$		0			0
$997$	237.087			0.237801			0.118900	−	0.992906i	$-0.462063\pi$
$997$	237.087			0.237801			0.118900	+	0.992906i	$0.462063\pi$
$998$	−300.000	−	274.750i	−0.300601	−	0.275301i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.c.l.451.3		4
3.2	odd	2		100.3.b.e.51.2	yes	4
4.3	odd	2	inner	900.3.c.l.451.4		4
5.2	odd	4		900.3.f.d.199.8		8
5.3	odd	4		900.3.f.d.199.1		8
5.4	even	2		900.3.c.m.451.2		4
12.11	even	2		100.3.b.e.51.1	yes	4
15.2	even	4		100.3.d.a.99.1		8
15.8	even	4		100.3.d.a.99.8		8
15.14	odd	2		100.3.b.d.51.3	✓	4
20.3	even	4		900.3.f.d.199.7		8
20.7	even	4		900.3.f.d.199.2		8
20.19	odd	2		900.3.c.m.451.1		4
24.5	odd	2		1600.3.b.o.1151.3		4
24.11	even	2		1600.3.b.o.1151.2		4
60.23	odd	4		100.3.d.a.99.2		8
60.47	odd	4		100.3.d.a.99.7		8
60.59	even	2		100.3.b.d.51.4	yes	4
120.29	odd	2		1600.3.b.p.1151.2		4
120.53	even	4		1600.3.h.o.1599.3		8
120.59	even	2		1600.3.b.p.1151.3		4
120.77	even	4		1600.3.h.o.1599.5		8
120.83	odd	4		1600.3.h.o.1599.6		8
120.107	odd	4		1600.3.h.o.1599.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.3.b.d.51.3	✓	4	15.14	odd	2
100.3.b.d.51.4	yes	4	60.59	even	2
100.3.b.e.51.1	yes	4	12.11	even	2
100.3.b.e.51.2	yes	4	3.2	odd	2
100.3.d.a.99.1		8	15.2	even	4
100.3.d.a.99.2		8	60.23	odd	4
100.3.d.a.99.7		8	60.47	odd	4
100.3.d.a.99.8		8	15.8	even	4
900.3.c.l.451.3		4	1.1	even	1	trivial
900.3.c.l.451.4		4	4.3	odd	2	inner
900.3.c.m.451.1		4	20.19	odd	2
900.3.c.m.451.2		4	5.4	even	2
900.3.f.d.199.1		8	5.3	odd	4
900.3.f.d.199.2		8	20.7	even	4
900.3.f.d.199.7		8	20.3	even	4
900.3.f.d.199.8		8	5.2	odd	4
1600.3.b.o.1151.2		4	24.11	even	2
1600.3.b.o.1151.3		4	24.5	odd	2
1600.3.b.p.1151.2		4	120.29	odd	2
1600.3.b.p.1151.3		4	120.59	even	2
1600.3.h.o.1599.3		8	120.53	even	4
1600.3.h.o.1599.4		8	120.107	odd	4
1600.3.h.o.1599.5		8	120.77	even	4
1600.3.h.o.1599.6		8	120.83	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 $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q+(1.35078 - 1.47492i) q^{2} +(-0.350781 - 3.98459i) q^{4} +10.9190i q^{7} +(-6.35078 - 4.86493i) q^{8} +O(q^{10})\)	\(q+(1.35078 - 1.47492i) q^{2} +(-0.350781 - 3.98459i) q^{4} +10.9190i q^{7} +(-6.35078 - 4.86493i) q^{8} -11.3592i q^{11} -10.8062 q^{13} +(16.1047 + 14.7492i) q^{14} +(-15.7539 + 2.79544i) q^{16} -15.8062 q^{17} +24.9192i q^{19} +(-16.7539 - 15.3438i) q^{22} +20.9577i q^{23} +(-14.5969 + 15.9384i) q^{26} +(43.5078 - 3.83019i) q^{28} -22.8062 q^{29} -22.7184i q^{31} +(-17.1570 + 27.0118i) q^{32} +(-21.3508 + 23.3130i) q^{34} -19.1938 q^{37} +(36.7539 + 33.6604i) q^{38} -17.0000 q^{41} +6.51730i q^{43} +(-45.2617 + 3.98459i) q^{44} +(30.9109 + 28.3093i) q^{46} +38.9195i q^{47} -70.2250 q^{49} +(3.79063 + 43.0585i) q^{52} -13.2250 q^{53} +(53.1203 - 69.3443i) q^{56} +(-30.8062 + 33.6374i) q^{58} +95.6301i q^{59} -92.0312 q^{61} +(-33.5078 - 30.6876i) q^{62} +(16.6648 + 61.7923i) q^{64} +54.1549i q^{67} +(5.54453 + 62.9814i) q^{68} -68.5100i q^{71} +44.1938 q^{73} +(-25.9266 + 28.3093i) q^{74} +(99.2930 - 8.74120i) q^{76} +124.031 q^{77} -81.7152i q^{79} +(-22.9633 + 25.0736i) q^{82} +27.9152i q^{83} +(9.61250 + 8.80344i) q^{86} +(-55.2617 + 72.1397i) q^{88} +42.1938 q^{89} -117.994i q^{91} +(83.5078 - 7.35156i) q^{92} +(57.4031 + 52.5717i) q^{94} +154.837 q^{97} +(-94.8586 + 103.576i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 5 q^{4} - 19 q^{8}+O(q^{10}) \) 4 * q - q^2 + 5 * q^4 - 19 * q^8	\( 4 q - q^{2} + 5 q^{4} - 19 q^{8} + 8 q^{13} + 26 q^{14} - 31 q^{16} - 12 q^{17} - 35 q^{22} - 84 q^{26} + 110 q^{28} - 40 q^{29} - 11 q^{32} - 79 q^{34} - 128 q^{37} + 115 q^{38} - 68 q^{41} - 85 q^{44} + 34 q^{46} - 76 q^{49} + 92 q^{52} + 152 q^{53} + 46 q^{56} - 72 q^{58} - 112 q^{61} - 70 q^{62} - 55 q^{64} + 67 q^{68} + 228 q^{73} + 114 q^{74} + 45 q^{76} + 240 q^{77} + 17 q^{82} - 64 q^{86} - 125 q^{88} + 220 q^{89} + 270 q^{92} + 204 q^{94} + 312 q^{97} - 309 q^{98}+O(q^{100}) \) 4 * q - q^2 + 5 * q^4 - 19 * q^8 + 8 * q^13 + 26 * q^14 - 31 * q^16 - 12 * q^17 - 35 * q^22 - 84 * q^26 + 110 * q^28 - 40 * q^29 - 11 * q^32 - 79 * q^34 - 128 * q^37 + 115 * q^38 - 68 * q^41 - 85 * q^44 + 34 * q^46 - 76 * q^49 + 92 * q^52 + 152 * q^53 + 46 * q^56 - 72 * q^58 - 112 * q^61 - 70 * q^62 - 55 * q^64 + 67 * q^68 + 228 * q^73 + 114 * q^74 + 45 * q^76 + 240 * q^77 + 17 * q^82 - 64 * q^86 - 125 * q^88 + 220 * q^89 + 270 * q^92 + 204 * q^94 + 312 * q^97 - 309 * q^98

Introduction

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