LMFDB - Embedded newform 900.3.f.d.199.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(199,900)]

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, 1]))

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

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

chi := DirichletCharacter("900.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: 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:	8.0.18084870400.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 12x^{6} + 40x^{4} + 17x^{2} + 4 $ x^8 - 12x^6 + 40x^4 + 17*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{4}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 100)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.8
Root			$-0.220086 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	900.199
Dual form			900.3.f.d.199.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.47492 + 1.35078i) q^{2} +(0.350781 + 3.98459i) q^{4} -10.9190 q^{7} +(-4.86493 + 6.35078i) q^{8} +O(q^{10})$	\(q+(1.47492 + 1.35078i) q^{2} +(0.350781 + 3.98459i) q^{4} -10.9190 q^{7} +(-4.86493 + 6.35078i) q^{8} -11.3592i q^{11} +10.8062i q^{13} +(-16.1047 - 14.7492i) q^{14} +(-15.7539 + 2.79544i) q^{16} -15.8062i q^{17} -24.9192i q^{19} +(15.3438 - 16.7539i) q^{22} +20.9577 q^{23} +(-14.5969 + 15.9384i) q^{26} +(-3.83019 - 43.5078i) q^{28} +22.8062 q^{29} -22.7184i q^{31} +(-27.0118 - 17.1570i) q^{32} +(21.3508 - 23.3130i) q^{34} -19.1938i q^{37} +(33.6604 - 36.7539i) q^{38} -17.0000 q^{41} +6.51730 q^{43} +(45.2617 - 3.98459i) q^{44} +(30.9109 + 28.3093i) q^{46} -38.9195 q^{47} +70.2250 q^{49} +(-43.0585 + 3.79063i) q^{52} +13.2250i q^{53} +(53.1203 - 69.3443i) q^{56} +(33.6374 + 30.8062i) q^{58} -95.6301i q^{59} -92.0312 q^{61} +(30.6876 - 33.5078i) q^{62} +(-16.6648 - 61.7923i) q^{64} -54.1549 q^{67} +(62.9814 - 5.54453i) q^{68} -68.5100i q^{71} -44.1938i q^{73} +(25.9266 - 28.3093i) q^{74} +(99.2930 - 8.74120i) q^{76} +124.031i q^{77} +81.7152i q^{79} +(-25.0736 - 22.9633i) q^{82} +27.9152 q^{83} +(9.61250 + 8.80344i) q^{86} +(72.1397 + 55.2617i) q^{88} -42.1938 q^{89} -117.994i q^{91} +(7.35156 + 83.5078i) q^{92} +(-57.4031 - 52.5717i) q^{94} +154.837i q^{97} +(103.576 + 94.8586i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 10 q^{4}+O(q^{10}) $ 8 * q - 10 * q^4	$ 8 q - 10 q^{4} - 52 q^{14} - 62 q^{16} - 168 q^{26} + 80 q^{29} + 158 q^{34} - 136 q^{41} + 170 q^{44} + 68 q^{46} + 152 q^{49} + 92 q^{56} - 224 q^{61} + 110 q^{64} - 228 q^{74} + 90 q^{76} - 128 q^{86} - 440 q^{89} - 408 q^{94}+O(q^{100}) $ 8 * q - 10 * q^4 - 52 * q^14 - 62 * q^16 - 168 * q^26 + 80 * q^29 + 158 * q^34 - 136 * q^41 + 170 * q^44 + 68 * q^46 + 152 * q^49 + 92 * q^56 - 224 * q^61 + 110 * q^64 - 228 * q^74 + 90 * q^76 - 128 * q^86 - 440 * q^89 - 408 * q^94

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 $

$2$	1.47492	+	1.35078i	0.737460	+	0.675391i
$2$	1.47492	+	1.35078i	0.737460	+	0.675391i
$3$		0			0
$3$		0			0
$4$	0.350781	+	3.98459i	0.0876953	+	0.996147i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−10.9190			−1.55986			−0.779930	−	0.625867i	$-0.784745\pi$
$7$	−10.9190			−1.55986			−0.779930	+	0.625867i	$0.784745\pi$
$8$	−4.86493	+	6.35078i	−0.608117	+	0.793848i
$9$		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
$13$			10.8062i			0.831250i	0.909536	+	0.415625i	$0.136437\pi$
$13$			10.8062i			0.831250i	−0.909536	+	0.415625i	$0.863563\pi$
$14$	−16.1047	−	14.7492i	−1.15033	−	1.05351i
$15$		0			0
$16$	−15.7539	+	2.79544i	−0.984619	+	0.174715i
$17$		−	15.8062i		−	0.929779i	−0.885369	−	0.464890i	$-0.846094\pi$
$17$		−	15.8062i		−	0.929779i	0.885369	−	0.464890i	$-0.153906\pi$
$18$		0			0
$19$		−	24.9192i		−	1.31154i	−0.754961	−	0.655770i	$-0.772344\pi$
$19$		−	24.9192i		−	1.31154i	0.754961	−	0.655770i	$-0.227656\pi$
$20$		0			0
$21$		0			0
$22$	15.3438	−	16.7539i	0.697445	−	0.761541i
$23$	20.9577			0.911204			0.455602	−	0.890184i	$-0.349424\pi$
$23$	20.9577			0.911204			0.455602	+	0.890184i	$0.349424\pi$
$24$		0			0
$25$		0			0
$26$	−14.5969	+	15.9384i	−0.561418	+	0.613014i
$27$		0			0
$28$	−3.83019	−	43.5078i	−0.136792	−	1.55385i
$29$	22.8062			0.786422			0.393211	−	0.919448i	$-0.371364\pi$
$29$	22.8062			0.786422			0.393211	+	0.919448i	$0.371364\pi$
$30$		0			0
$31$		−	22.7184i		−	0.732851i	−0.930447	−	0.366426i	$-0.880581\pi$
$31$		−	22.7184i		−	0.732851i	0.930447	−	0.366426i	$-0.119419\pi$
$32$	−27.0118	−	17.1570i	−0.844118	−	0.536157i
$33$		0			0
$34$	21.3508	−	23.3130i	0.627964	−	0.685675i
$35$		0			0
$36$		0			0
$37$		−	19.1938i		−	0.518750i	−0.965777	−	0.259375i	$-0.916483\pi$
$37$		−	19.1938i		−	0.518750i	0.965777	−	0.259375i	$-0.0835166\pi$
$38$	33.6604	−	36.7539i	0.885801	−	0.967208i
$39$		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
$43$	6.51730			0.151565			0.0757825	−	0.997124i	$-0.475855\pi$
$43$	6.51730			0.151565			0.0757825	+	0.997124i	$0.475855\pi$
$44$	45.2617	−	3.98459i	1.02868	−	0.0905588i
$45$		0			0
$46$	30.9109	+	28.3093i	0.671977	+	0.615419i
$47$	−38.9195			−0.828074			−0.414037	−	0.910260i	$-0.635882\pi$
$47$	−38.9195			−0.828074			−0.414037	+	0.910260i	$0.635882\pi$
$48$		0			0
$49$	70.2250			1.43316
$50$		0			0
$51$		0			0
$52$	−43.0585	+	3.79063i	−0.828047	+	0.0728967i
$53$			13.2250i			0.249528i	0.992186	+	0.124764i	$0.0398174\pi$
$53$			13.2250i			0.249528i	−0.992186	+	0.124764i	$0.960183\pi$
$54$		0			0
$55$		0			0
$56$	53.1203	−	69.3443i	0.948577	−	1.23829i
$57$		0			0
$58$	33.6374	+	30.8062i	0.579955	+	0.531142i
$59$		−	95.6301i		−	1.62085i	−0.585842	−	0.810425i	$-0.699236\pi$
$59$		−	95.6301i		−	1.62085i	0.585842	−	0.810425i	$-0.300764\pi$
$60$		0			0
$61$	−92.0312			−1.50871			−0.754354	−	0.656467i	$-0.772050\pi$
$61$	−92.0312			−1.50871			−0.754354	+	0.656467i	$0.772050\pi$
$62$	30.6876	−	33.5078i	0.494961	−	0.540449i
$63$		0			0
$64$	−16.6648	−	61.7923i	−0.260388	−	0.965504i
$65$		0			0
$66$		0			0
$67$	−54.1549			−0.808282			−0.404141	−	0.914697i	$-0.632430\pi$
$67$	−54.1549			−0.808282			−0.404141	+	0.914697i	$0.632430\pi$
$68$	62.9814	−	5.54453i	0.926197	−	0.0815372i
$69$		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
$73$		−	44.1938i		−	0.605394i	−0.953087	−	0.302697i	$-0.902113\pi$
$73$		−	44.1938i		−	0.605394i	0.953087	−	0.302697i	$-0.0978870\pi$
$74$	25.9266	−	28.3093i	0.350359	−	0.382558i
$75$		0			0
$76$	99.2930	−	8.74120i	1.30649	−	0.115016i
$77$			124.031i			1.61080i
$78$		0			0
$79$			81.7152i			1.03437i	0.855874	+	0.517185i	$0.173020\pi$
$79$			81.7152i			1.03437i	−0.855874	+	0.517185i	$0.826980\pi$
$80$		0			0
$81$		0			0
$82$	−25.0736	−	22.9633i	−0.305776	−	0.280040i
$83$	27.9152			0.336327			0.168164	−	0.985759i	$-0.446216\pi$
$83$	27.9152			0.336327			0.168164	+	0.985759i	$0.446216\pi$
$84$		0			0
$85$		0			0
$86$	9.61250	+	8.80344i	0.111773	+	0.102366i
$87$		0			0
$88$	72.1397	+	55.2617i	0.819770	+	0.627974i
$89$	−42.1938			−0.474087			−0.237044	−	0.971499i	$-0.576178\pi$
$89$	−42.1938			−0.474087			−0.237044	+	0.971499i	$0.576178\pi$
$90$		0			0
$91$		−	117.994i		−	1.29663i
$92$	7.35156	+	83.5078i	0.0799083	+	0.907694i
$93$		0			0
$94$	−57.4031	−	52.5717i	−0.610672	−	0.559273i
$95$		0			0
$96$		0			0
$97$			154.837i			1.59626i	0.602483	+	0.798131i	$0.294178\pi$
$97$			154.837i			1.59626i	−0.602483	+	0.798131i	$0.705822\pi$
$98$	103.576	+	94.8586i	1.05690	+	0.967945i
$99$		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
$103$	−66.0396			−0.641161			−0.320580	−	0.947221i	$-0.603878\pi$
$103$	−66.0396			−0.641161			−0.320580	+	0.947221i	$0.603878\pi$
$104$	−68.6281	−	52.5717i	−0.659886	−	0.505497i
$105$		0			0
$106$	−17.8641	+	19.5058i	−0.168529	+	0.184017i
$107$	−96.0703			−0.897853			−0.448927	−	0.893569i	$-0.648194\pi$
$107$	−96.0703			−0.897853			−0.448927	+	0.893569i	$0.648194\pi$
$108$		0			0
$109$	−112.806			−1.03492			−0.517460	−	0.855707i	$-0.673122\pi$
$109$	−112.806			−1.03492			−0.517460	+	0.855707i	$0.673122\pi$
$110$		0			0
$111$		0			0
$112$	172.017	−	30.5234i	1.53587	−	0.272531i
$113$			18.2250i			0.161283i	0.996743	+	0.0806416i	$0.0256969\pi$
$113$			18.2250i			0.161283i	−0.996743	+	0.0806416i	$0.974303\pi$
$114$		0			0
$115$		0			0
$116$	8.00000	+	90.8735i	0.0689655	+	0.783393i
$117$		0			0
$118$	129.175	−	141.047i	1.09471	−	1.19531i
$119$			172.589i			1.45033i
$120$		0			0
$121$	−8.03124			−0.0663739
$122$	−135.739	−	124.314i	−1.11261	−	1.01897i
$123$		0			0
$124$	90.5234	−	7.96918i	0.730028	−	0.0642676i
$125$		0			0
$126$		0			0
$127$	−51.5992			−0.406293			−0.203146	−	0.979148i	$-0.565117\pi$
$127$	−51.5992			−0.406293			−0.203146	+	0.979148i	$0.565117\pi$
$128$	58.8885	−	113.649i	0.460066	−	0.887885i
$129$		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
$133$			272.094i			2.04582i
$134$	−79.8742	−	73.1514i	−0.596076	−	0.545906i
$135$		0			0
$136$	100.382	+	76.8964i	0.738103	+	0.565414i
$137$		−	209.837i		−	1.53166i	−0.643043	−	0.765830i	$-0.722328\pi$
$137$		−	209.837i		−	1.53166i	0.643043	−	0.765830i	$-0.277672\pi$
$138$		0			0
$139$		−	84.6258i		−	0.608819i	−0.952541	−	0.304410i	$-0.901541\pi$
$139$		−	84.6258i		−	0.608819i	0.952541	−	0.304410i	$-0.0984591\pi$
$140$		0			0
$141$		0			0
$142$	92.5421	−	101.047i	0.651705	−	0.711598i
$143$	122.750			0.858393
$144$		0			0
$145$		0			0
$146$	59.6961	−	65.1823i	0.408877	−	0.446454i
$147$		0			0
$148$	76.4792	−	6.73280i	0.516751	−	0.0454919i
$149$	170.869			1.14677			0.573385	−	0.819286i	$-0.305630\pi$
$149$	170.869			1.14677			0.573385	+	0.819286i	$0.305630\pi$
$150$		0			0
$151$		−	181.392i		−	1.20127i	−0.799522	−	0.600636i	$-0.794914\pi$
$151$		−	181.392i		−	1.20127i	0.799522	−	0.600636i	$-0.205086\pi$
$152$	158.257	+	121.230i	1.04116	+	0.797569i
$153$		0			0
$154$	−167.539	+	182.936i	−1.08792	+	1.18790i
$155$		0			0
$156$		0			0
$157$		−	25.1625i		−	0.160271i	−0.996784	−	0.0801354i	$-0.974465\pi$
$157$		−	25.1625i		−	0.160271i	0.996784	−	0.0801354i	$-0.0255353\pi$
$158$	−110.379	+	120.523i	−0.698603	+	0.762807i
$159$		0			0
$160$		0			0
$161$	−228.837			−1.42135
$162$		0			0
$163$	8.00838			0.0491312			0.0245656	−	0.999698i	$-0.492180\pi$
$163$	8.00838			0.0491312			0.0245656	+	0.999698i	$0.492180\pi$
$164$	−5.96328	−	67.7380i	−0.0363615	−	0.413037i
$165$		0			0
$166$	41.1727	+	37.7073i	0.248028	+	0.227152i
$167$	187.555			1.12308			0.561541	−	0.827449i	$-0.310209\pi$
$167$	187.555			1.12308			0.561541	+	0.827449i	$0.310209\pi$
$168$		0			0
$169$	52.2250			0.309024
$170$		0			0
$171$		0			0
$172$	2.28614	+	25.9688i	0.0132915	+	0.150981i
$173$			123.225i			0.712283i	0.934432	+	0.356142i	$0.115908\pi$
$173$			123.225i			0.712283i	−0.934432	+	0.356142i	$0.884092\pi$
$174$		0			0
$175$		0			0
$176$	31.7539	+	178.952i	0.180420	+	1.01677i
$177$		0			0
$178$	−62.2324	−	56.9945i	−0.349620	−	0.320194i
$179$		−	138.511i		−	0.773805i	−0.922121	−	0.386903i	$-0.873545\pi$
$179$		−	138.511i		−	0.773805i	0.922121	−	0.386903i	$-0.126455\pi$
$180$		0			0
$181$	−194.125			−1.07251			−0.536257	−	0.844055i	$-0.680162\pi$
$181$	−194.125			−1.07251			−0.536257	+	0.844055i	$0.680162\pi$
$182$	159.384	−	174.031i	0.875734	−	0.956216i
$183$		0			0
$184$	−101.958	+	133.098i	−0.554118	+	0.723357i
$185$		0			0
$186$		0			0
$187$	−179.546			−0.960140
$188$	−13.6522	−	155.078i	−0.0726182	−	0.824884i
$189$		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
$193$			153.869i			0.797247i	0.917115	+	0.398624i	$0.130512\pi$
$193$			153.869i			0.797247i	−0.917115	+	0.398624i	$0.869488\pi$
$194$	−209.152	+	228.373i	−1.07810	+	1.17718i
$195$		0			0
$196$	24.6336	+	279.818i	0.125682	+	1.42764i
$197$			261.287i			1.32633i	0.748472	+	0.663166i	$0.230788\pi$
$197$			261.287i			1.32633i	−0.748472	+	0.663166i	$0.769212\pi$
$198$		0			0
$199$			227.184i			1.14163i	0.821080	+	0.570814i	$0.193372\pi$
$199$			227.184i			1.14163i	−0.821080	+	0.570814i	$0.806628\pi$
$200$		0			0
$201$		0			0
$202$	5.85360	+	5.36092i	0.0289782	+	0.0265392i
$203$	−249.022			−1.22671
$204$		0			0
$205$		0			0
$206$	−97.4031	−	89.2050i	−0.472831	−	0.433034i
$207$		0			0
$208$	−30.2082	−	170.241i	−0.145232	−	0.818464i
$209$	−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	$-0.151892\pi$
$212$	−52.6962	+	4.63908i	−0.248567	+	0.0218824i
$213$		0			0
$214$	−141.696	−	129.770i	−0.662131	−	0.606402i
$215$		0			0
$216$		0			0
$217$			248.062i			1.14315i
$218$	−166.380	−	152.377i	−0.763212	−	0.698975i
$219$		0			0
$220$		0			0
$221$	170.806			0.772879
$222$		0			0
$223$	−25.3594			−0.113719			−0.0568597	−	0.998382i	$-0.518109\pi$
$223$	−25.3594			−0.113719			−0.0568597	+	0.998382i	$0.518109\pi$
$224$	294.942	+	187.338i	1.31671	+	0.836330i
$225$		0			0
$226$	−24.6180	+	26.8804i	−0.108929	+	0.118940i
$227$	−374.584			−1.65015			−0.825074	−	0.565024i	$-0.808867\pi$
$227$	−374.584			−1.65015			−0.825074	+	0.565024i	$0.808867\pi$
$228$		0			0
$229$	259.287			1.13226			0.566130	−	0.824316i	$-0.308440\pi$
$229$	259.287			1.13226			0.566130	+	0.824316i	$0.308440\pi$
$230$		0			0
$231$		0			0
$232$	−110.951	+	144.837i	−0.478237	+	0.624300i
$233$			153.225i			0.657618i	0.944396	+	0.328809i	$0.106647\pi$
$233$			153.225i			0.657618i	−0.944396	+	0.328809i	$0.893353\pi$
$234$		0			0
$235$		0			0
$236$	381.047	−	33.5452i	1.61461	−	0.142141i
$237$		0			0
$238$	−233.130	+	254.555i	−0.979536	+	1.06956i
$239$			187.213i			0.783320i	0.920110	+	0.391660i	$0.128099\pi$
$239$			187.213i			0.783320i	−0.920110	+	0.391660i	$0.871901\pi$
$240$		0			0
$241$	−65.0937			−0.270098			−0.135049	−	0.990839i	$-0.543119\pi$
$241$	−65.0937			−0.270098			−0.135049	+	0.990839i	$0.543119\pi$
$242$	−11.8454	−	10.8485i	−0.0489481	−	0.0448283i
$243$		0			0
$244$	−32.2828	−	366.707i	−0.132307	−	1.50290i
$245$		0			0
$246$		0			0
$247$	269.284			1.09022
$248$	144.279	+	110.523i	0.581772	+	0.445659i
$249$		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
$253$		−	238.062i		−	0.940958i
$254$	−76.1047	−	69.6992i	−0.299625	−	0.274406i
$255$		0			0
$256$	240.371	−	88.0781i	0.938949	−	0.344055i
$257$			241.287i			0.938862i	0.882969	+	0.469431i	$0.155541\pi$
$257$			241.287i			0.938862i	−0.882969	+	0.469431i	$0.844459\pi$
$258$		0			0
$259$			209.577i			0.809177i
$260$		0			0
$261$		0			0
$262$	214.334	−	234.031i	0.818067	−	0.893249i
$263$	−379.170			−1.44171			−0.720855	−	0.693086i	$-0.756251\pi$
$263$	−379.170			−1.44171			−0.720855	+	0.693086i	$0.756251\pi$
$264$		0			0
$265$		0			0
$266$	−367.539	+	401.317i	−1.38173	+	1.50871i
$267$		0			0
$268$	−18.9965	−	215.785i	−0.0708825	−	0.805168i
$269$	120.713			0.448745			0.224373	−	0.974503i	$-0.427967\pi$
$269$	120.713			0.448745			0.224373	+	0.974503i	$0.427967\pi$
$270$		0			0
$271$			114.302i			0.421777i	0.977510	+	0.210889i	$0.0676358\pi$
$271$			114.302i			0.421777i	−0.977510	+	0.210889i	$0.932364\pi$
$272$	44.1854	+	249.010i	0.162446	+	0.915478i
$273$		0			0
$274$	283.445	−	309.494i	1.03447	−	1.12954i
$275$		0			0
$276$		0			0
$277$		−	197.256i		−	0.712116i	−0.934464	−	0.356058i	$-0.884120\pi$
$277$		−	197.256i		−	0.712116i	0.934464	−	0.356058i	$-0.115880\pi$
$278$	114.311	−	124.816i	0.411191	−	0.448980i
$279$		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
$283$	−541.280			−1.91265			−0.956324	−	0.292307i	$-0.905577\pi$
$283$	−541.280			−1.91265			−0.956324	+	0.292307i	$0.905577\pi$
$284$	272.984	−	24.0320i	0.961213	−	0.0846198i
$285$		0			0
$286$	181.047	+	165.809i	0.633031	+	0.579751i
$287$	185.623			0.646771
$288$		0			0
$289$	39.1625			0.135510
$290$		0			0
$291$		0			0
$292$	176.094	−	15.5023i	0.603061	−	0.0530902i
$293$		−	344.994i		−	1.17745i	−0.808332	−	0.588726i	$-0.799630\pi$
$293$		−	344.994i		−	1.17745i	0.808332	−	0.588726i	$-0.200370\pi$
$294$		0			0
$295$		0			0
$296$	121.895	+	93.3763i	0.411808	+	0.315461i
$297$		0			0
$298$	252.018	+	230.806i	0.845697	+	0.774518i
$299$			226.474i			0.757438i
$300$		0			0
$301$	−71.1625			−0.236420
$302$	245.021	−	267.539i	0.811328	−	0.885891i
$303$		0			0
$304$	69.6602	+	392.575i	0.229145	+	1.29137i
$305$		0			0
$306$		0			0
$307$	−181.307			−0.590576			−0.295288	−	0.955408i	$-0.595416\pi$
$307$	−181.307			−0.590576			−0.295288	+	0.955408i	$0.595416\pi$
$308$	−494.214	+	43.5078i	−1.60459	+	0.141259i
$309$		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
$313$		−	401.287i		−	1.28207i	−0.767512	−	0.641034i	$-0.778506\pi$
$313$		−	401.287i		−	1.28207i	0.767512	−	0.641034i	$-0.221494\pi$
$314$	33.9890	−	37.1127i	0.108245	−	0.118193i
$315$		0			0
$316$	−325.602	+	28.6641i	−1.03038	+	0.0907093i
$317$		−	552.900i		−	1.74416i	−0.489360	−	0.872082i	$-0.662770\pi$
$317$		−	552.900i		−	1.74416i	0.489360	−	0.872082i	$-0.337230\pi$
$318$		0			0
$319$		−	259.061i		−	0.812102i
$320$		0			0
$321$		0			0
$322$	−337.517	−	309.109i	−1.04819	−	0.959967i
$323$	−393.880			−1.21944
$324$		0			0
$325$		0			0
$326$	11.8117	+	10.8176i	0.0362323	+	0.0331827i
$327$		0			0
$328$	82.7039	−	107.963i	0.252146	−	0.329156i
$329$	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	$0.636525\pi$
$332$	9.79211	+	111.230i	0.0294943	+	0.335032i
$333$		0			0
$334$	276.628	+	253.345i	0.828228	+	0.758519i
$335$		0			0
$336$		0			0
$337$		−	32.1000i		−	0.0952523i	−0.998865	−	0.0476261i	$-0.984834\pi$
$337$		−	32.1000i		−	0.0952523i	0.998865	−	0.0476261i	$-0.0151656\pi$
$338$	77.0277	+	70.5445i	0.227893	+	0.208712i
$339$		0			0
$340$		0			0
$341$	−258.062			−0.756781
$342$		0			0
$343$	−231.756			−0.675674
$344$	−31.7062	+	41.3899i	−0.0921693	+	0.120320i
$345$		0			0
$346$	−166.450	+	181.747i	−0.481069	+	0.525281i
$347$	522.438			1.50558			0.752792	−	0.658259i	$-0.228707\pi$
$347$	522.438			1.50558			0.752792	+	0.658259i	$0.228707\pi$
$348$		0			0
$349$	−128.931			−0.369430			−0.184715	−	0.982792i	$-0.559136\pi$
$349$	−128.931			−0.369430			−0.184715	+	0.982792i	$0.559136\pi$
$350$		0			0
$351$		0			0
$352$	−194.890	+	306.832i	−0.553665	+	0.871682i
$353$		−	594.837i		−	1.68509i	−0.538624	−	0.842546i	$-0.681056\pi$
$353$		−	594.837i		−	1.68509i	0.538624	−	0.842546i	$-0.318944\pi$
$354$		0			0
$355$		0			0
$356$	−14.8008	−	168.125i	−0.0415752	−	0.472261i
$357$		0			0
$358$	187.098	−	204.293i	0.522621	−	0.570651i
$359$		−	26.0554i		−	0.0725778i	−0.999341	−	0.0362889i	$-0.988446\pi$
$359$		−	26.0554i		−	0.0725778i	0.999341	−	0.0362889i	$-0.0115537\pi$
$360$		0			0
$361$	−259.969			−0.720135
$362$	−286.319	−	262.220i	−0.790936	−	0.724366i
$363$		0			0
$364$	470.156	−	41.3899i	1.29164	−	0.113709i
$365$		0			0
$366$		0			0
$367$	−420.915			−1.14691			−0.573453	−	0.819238i	$-0.694397\pi$
$367$	−420.915			−1.14691			−0.573453	+	0.819238i	$0.694397\pi$
$368$	−330.166	+	58.5859i	−0.897189	+	0.159201i
$369$		0			0
$370$		0			0
$371$		−	144.404i		−	0.389229i
$372$		0			0
$373$			218.713i			0.586361i	0.956057	+	0.293180i	$0.0947136\pi$
$373$			218.713i			0.586361i	−0.956057	+	0.293180i	$0.905286\pi$
$374$	−264.816	−	242.528i	−0.708065	−	0.648470i
$375$		0			0
$376$	189.341	−	247.169i	0.503566	−	0.657364i
$377$			246.450i			0.653713i
$378$		0			0
$379$		−	246.282i		−	0.649820i	−0.945745	−	0.324910i	$-0.894666\pi$
$379$		−	246.282i		−	0.649820i	0.945745	−	0.324910i	$-0.105334\pi$
$380$		0			0
$381$		0			0
$382$	91.1039	−	99.4766i	0.238492	−	0.260410i
$383$	406.106			1.06033			0.530164	−	0.847895i	$-0.322130\pi$
$383$	406.106			1.06033			0.530164	+	0.847895i	$0.322130\pi$
$384$		0			0
$385$		0			0
$386$	−207.843	+	226.944i	−0.538453	+	0.587938i
$387$		0			0
$388$	−616.964	+	54.3141i	−1.59011	+	0.139985i
$389$	−201.225			−0.517288			−0.258644	−	0.965973i	$-0.583276\pi$
$389$	−201.225			−0.517288			−0.258644	+	0.965973i	$0.583276\pi$
$390$		0			0
$391$		−	331.263i		−	0.847219i
$392$	−341.640	+	445.984i	−0.871530	+	1.13771i
$393$		0			0
$394$	−352.942	+	385.378i	−0.895792	+	0.978117i
$395$		0			0
$396$		0			0
$397$			96.7750i			0.243766i	0.992544	+	0.121883i	$0.0388932\pi$
$397$			96.7750i			0.243766i	−0.992544	+	0.121883i	$0.961107\pi$
$398$	−306.876	+	335.078i	−0.771044	+	0.841905i
$399$		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
$403$	245.501			0.609182
$404$	1.39217	+	15.8139i	0.00344595	+	0.0391432i
$405$		0			0
$406$	−367.287	−	336.374i	−0.904649	−	0.828507i
$407$	−218.026			−0.535689
$408$		0			0
$409$	−521.837			−1.27589			−0.637943	−	0.770083i	$-0.720215\pi$
$409$	−521.837			−1.27589			−0.637943	+	0.770083i	$0.720215\pi$
$410$		0			0
$411$		0			0
$412$	−23.1654	−	263.141i	−0.0562268	−	0.638691i
$413$			1044.19i			2.52830i
$414$		0			0
$415$		0			0
$416$	185.403	−	291.896i	0.445681	−	0.701673i
$417$		0			0
$418$	−417.495	−	382.355i	−0.998791	−	0.914726i
$419$			252.103i			0.601678i	0.953675	+	0.300839i	$0.0972667\pi$
$419$			252.103i			0.601678i	−0.953675	+	0.300839i	$0.902733\pi$
$420$		0			0
$421$	776.187			1.84368			0.921838	−	0.387576i	$-0.126687\pi$
$421$	776.187			1.84368			0.921838	+	0.387576i	$0.126687\pi$
$422$	261.803	−	285.863i	0.620386	−	0.677401i
$423$		0			0
$424$	−83.9890	−	64.3387i	−0.198087	−	0.151742i
$425$		0			0
$426$		0			0
$427$	1004.89			2.35337
$428$	−33.6996	−	382.801i	−0.0787375	−	0.894394i
$429$		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
$433$			541.931i			1.25157i	0.779994	+	0.625787i	$0.215222\pi$
$433$			541.931i			1.25157i	−0.779994	+	0.625787i	$0.784778\pi$
$434$	−335.078	+	365.872i	−0.772069	+	0.843024i
$435$		0			0
$436$	−39.5703	−	449.487i	−0.0907576	−	1.03093i
$437$		−	522.250i		−	1.19508i
$438$		0			0
$439$		−	4.04683i		−	0.00921830i	−0.999989	−	0.00460915i	$-0.998533\pi$
$439$		−	4.04683i		−	0.00921830i	0.999989	−	0.00460915i	$-0.00146714\pi$
$440$		0			0
$441$		0			0
$442$	251.926	+	230.722i	0.569968	+	0.521995i
$443$	342.635			0.773444			0.386722	−	0.922196i	$-0.373607\pi$
$443$	342.635			0.773444			0.386722	+	0.922196i	$0.373607\pi$
$444$		0			0
$445$		0			0
$446$	−37.4031	−	34.2550i	−0.0838635	−	0.0768050i
$447$		0			0
$448$	181.964	+	674.711i	0.406169	+	1.50605i
$449$	−484.444			−1.07894			−0.539470	−	0.842005i	$-0.681375\pi$
$449$	−484.444			−1.07894			−0.539470	+	0.842005i	$0.681375\pi$
$450$		0			0
$451$			193.106i			0.428174i
$452$	−72.6191	+	6.39298i	−0.160662	+	0.0141438i
$453$		0			0
$454$	−552.481	−	505.981i	−1.21692	−	1.11449i
$455$		0			0
$456$		0			0
$457$		−	698.537i		−	1.52853i	−0.644903	−	0.764264i	$-0.723102\pi$
$457$		−	698.537i		−	1.52853i	0.644903	−	0.764264i	$-0.276898\pi$
$458$	382.428	+	350.241i	0.834997	+	0.764718i
$459$		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
$463$	881.956			1.90487			0.952437	−	0.304736i	$-0.0985684\pi$
$463$	881.956			1.90487			0.952437	+	0.304736i	$0.0985684\pi$
$464$	−359.287	+	63.7534i	−0.774326	+	0.137400i
$465$		0			0
$466$	−206.973	+	225.995i	−0.444149	+	0.484967i
$467$	−57.2361			−0.122561			−0.0612807	−	0.998121i	$-0.519518\pi$
$467$	−57.2361			−0.122561			−0.0612807	+	0.998121i	$0.519518\pi$
$468$		0			0
$469$	591.319			1.26081
$470$		0			0
$471$		0			0
$472$	607.326	+	465.234i	1.28671	+	0.985666i
$473$		−	74.0312i		−	0.156514i
$474$		0			0
$475$		0			0
$476$	−687.695	+	60.5409i	−1.44474	+	0.127187i
$477$		0			0
$478$	−252.884	+	276.125i	−0.529047	+	0.577667i
$479$		−	651.449i		−	1.36002i	−0.733203	−	0.680010i	$-0.761976\pi$
$479$		−	651.449i		−	1.36002i	0.733203	−	0.680010i	$-0.238024\pi$
$480$		0			0
$481$	207.412			0.431211
$482$	−96.0081	−	87.9274i	−0.199187	−	0.182422i
$483$		0			0
$484$	−2.81721	−	32.0012i	−0.00582068	−	0.0661182i
$485$		0			0
$486$		0			0
$487$	−53.0187			−0.108868			−0.0544340	−	0.998517i	$-0.517335\pi$
$487$	−53.0187			−0.108868			−0.0544340	+	0.998517i	$0.517335\pi$
$488$	447.726	−	584.470i	0.917471	−	1.19768i
$489$		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
$493$		−	360.481i		−	0.731199i
$494$	397.172	+	363.743i	0.803992	+	0.736322i
$495$		0			0
$496$	63.5078	+	357.903i	0.128040	+	0.721579i
$497$			748.062i			1.50516i
$498$		0			0
$499$			203.401i			0.407617i	0.979011	+	0.203808i	$0.0653320\pi$
$499$			203.401i			0.407617i	−0.979011	+	0.203808i	$0.934668\pi$
$500$		0			0
$501$		0			0
$502$	−598.887	+	653.926i	−1.19300	+	1.30264i
$503$	−84.5406			−0.168073			−0.0840363	−	0.996463i	$-0.526781\pi$
$503$	−84.5406			−0.168073			−0.0840363	+	0.996463i	$0.526781\pi$
$504$		0			0
$505$		0			0
$506$	321.570	−	351.123i	0.635514	−	0.693919i
$507$		0			0
$508$	−18.1000	−	205.602i	−0.0356299	−	0.404727i
$509$	−101.225			−0.198870			−0.0994352	−	0.995044i	$-0.531704\pi$
$509$	−101.225			−0.198870			−0.0994352	+	0.995044i	$0.531704\pi$
$510$		0			0
$511$			482.552i			0.944330i
$512$	473.502	+	194.780i	0.924809	+	0.380431i
$513$		0			0
$514$	−325.927	+	355.880i	−0.634098	+	0.692373i
$515$		0			0
$516$		0			0
$517$			442.094i			0.855114i
$518$	−283.093	+	309.109i	−0.546511	+	0.596736i
$519$		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
$523$	848.589			1.62254			0.811270	−	0.584671i	$-0.198777\pi$
$523$	848.589			1.62254			0.811270	+	0.584671i	$0.198777\pi$
$524$	632.250	−	55.6598i	1.20658	−	0.106221i
$525$		0			0
$526$	−559.245	−	512.175i	−1.06320	−	0.973717i
$527$	−359.092			−0.681390
$528$		0			0
$529$	−89.7750			−0.169707
$530$		0			0
$531$		0			0
$532$	−1084.18	+	95.4453i	−2.03794	+	0.179409i
$533$		−	183.706i		−	0.344665i
$534$		0			0
$535$		0			0
$536$	263.460	−	343.926i	0.491530	−	0.641653i
$537$		0			0
$538$	178.041	+	163.056i	0.330932	+	0.303078i
$539$		−	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	$0.224324\pi$
$542$	−154.397	+	168.586i	−0.284865	+	0.311044i
$543$		0			0
$544$	−271.188	+	426.955i	−0.498508	+	0.784844i
$545$		0			0
$546$		0			0
$547$	−275.020			−0.502778			−0.251389	−	0.967886i	$-0.580887\pi$
$547$	−275.020			−0.502778			−0.251389	+	0.967886i	$0.580887\pi$
$548$	836.116	−	73.6070i	1.52576	−	0.134319i
$549$		0			0
$550$		0			0
$551$		−	568.314i		−	1.03142i
$552$		0			0
$553$		−	892.250i		−	1.61347i
$554$	266.450	−	290.937i	0.480957	−	0.525158i
$555$		0			0
$556$	337.199	−	29.6851i	0.606473	−	0.0533905i
$557$		−	154.681i		−	0.277704i	−0.990313	−	0.138852i	$-0.955659\pi$
$557$		−	154.681i		−	0.277704i	0.990313	−	0.138852i	$-0.0443413\pi$
$558$		0			0
$559$			70.4275i			0.125988i
$560$		0			0
$561$		0			0
$562$	−14.8414	−	13.5922i	−0.0264081	−	0.0241854i
$563$	767.327			1.36293			0.681463	−	0.731853i	$-0.261344\pi$
$563$	767.327			1.36293			0.681463	+	0.731853i	$0.261344\pi$
$564$		0			0
$565$		0			0
$566$	−798.344	−	731.150i	−1.41050	−	1.29179i
$567$		0			0
$568$	435.092	+	333.297i	0.766008	+	0.586790i
$569$	346.025			0.608128			0.304064	−	0.952652i	$-0.401656\pi$
$569$	346.025			0.608128			0.304064	+	0.952652i	$0.401656\pi$
$570$		0			0
$571$		−	389.407i		−	0.681973i	−0.940068	−	0.340986i	$-0.889239\pi$
$571$		−	389.407i		−	0.681973i	0.940068	−	0.340986i	$-0.110761\pi$
$572$	43.0585	+	489.109i	0.0752770	+	0.855086i
$573$		0			0
$574$	273.780	+	250.736i	0.476968	+	0.436823i
$575$		0			0
$576$		0			0
$577$		−	800.475i		−	1.38730i	−0.720310	−	0.693652i	$-0.756000\pi$
$577$		−	800.475i		−	1.38730i	0.720310	−	0.693652i	$-0.244000\pi$
$578$	57.7616	+	52.9000i	0.0999335	+	0.0915224i
$579$		0			0
$580$		0			0
$581$	−304.806			−0.524623
$582$		0			0
$583$	150.225			0.257676
$584$	280.665	+	215.000i	0.480590	+	0.368150i
$585$		0			0
$586$	466.011	−	508.838i	0.795241	−	0.868325i
$587$	758.780			1.29264			0.646320	−	0.763066i	$-0.276307\pi$
$587$	758.780			1.29264			0.646320	+	0.763066i	$0.276307\pi$
$588$		0			0
$589$	−566.125			−0.961163
$590$		0			0
$591$		0			0
$592$	53.6549	+	302.377i	0.0906333	+	0.510771i
$593$		−	1049.84i		−	1.77038i	−0.465226	−	0.885192i	$-0.654027\pi$
$593$		−	1049.84i		−	1.77038i	0.465226	−	0.885192i	$-0.345973\pi$
$594$		0			0
$595$		0			0
$596$	59.9375	+	680.842i	0.100566	+	1.14235i
$597$		0			0
$598$	−305.917	+	334.031i	−0.511567	+	0.558581i
$599$			269.427i			0.449794i	0.974383	+	0.224897i	$0.0722046\pi$
$599$			269.427i			0.449794i	−0.974383	+	0.224897i	$0.927795\pi$
$600$		0			0
$601$	−567.031			−0.943480			−0.471740	−	0.881738i	$-0.656374\pi$
$601$	−567.031			−0.943480			−0.471740	+	0.881738i	$0.656374\pi$
$602$	−104.959	−	96.1250i	−0.174351	−	0.159676i
$603$		0			0
$604$	722.773	−	63.6289i	1.19664	−	0.105346i
$605$		0			0
$606$		0			0
$607$	846.770			1.39501			0.697504	−	0.716581i	$-0.254294\pi$
$607$	846.770			1.39501			0.697504	+	0.716581i	$0.254294\pi$
$608$	−427.540	+	673.113i	−0.703191	+	1.10709i
$609$		0			0
$610$		0			0
$611$		−	420.573i		−	0.688336i
$612$		0			0
$613$			306.775i			0.500449i	0.968188	+	0.250224i	$0.0805044\pi$
$613$			306.775i			0.500449i	−0.968188	+	0.250224i	$0.919496\pi$
$614$	−267.413	−	244.906i	−0.435526	−	0.398870i
$615$		0			0
$616$	−787.695	−	603.404i	−1.27873	−	0.979552i
$617$		−	435.150i		−	0.705267i	−0.935761	−	0.352634i	$-0.885286\pi$
$617$		−	435.150i		−	0.705267i	0.935761	−	0.352634i	$-0.114714\pi$
$618$		0			0
$619$			123.460i			0.199451i	0.995015	+	0.0997254i	$0.0317964\pi$
$619$			123.460i			0.199451i	−0.995015	+	0.0997254i	$0.968204\pi$
$620$		0			0
$621$		0			0
$622$	124.188	−	135.602i	0.199660	−	0.218009i
$623$	460.714			0.739509
$624$		0			0
$625$		0			0
$626$	542.052	−	591.867i	0.865897	−	0.945475i
$627$		0			0
$628$	100.262	−	8.82653i	0.159653	−	0.0140550i
$629$	−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	$0.864902\pi$
$632$	−518.955	−	397.539i	−0.821132	−	0.629017i
$633$		0			0
$634$	746.847	−	815.484i	1.17799	−	1.28625i
$635$		0			0
$636$		0			0
$637$			758.869i			1.19132i
$638$	349.934	−	382.094i	0.548486	−	0.598893i
$639$		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
$643$	−513.023			−0.797859			−0.398930	−	0.916982i	$-0.630618\pi$
$643$	−513.023			−0.797859			−0.398930	+	0.916982i	$0.630618\pi$
$644$	−80.2719	−	911.823i	−0.124646	−	1.41587i
$645$		0			0
$646$	−580.941	−	532.045i	−0.899290	−	0.823600i
$647$	−573.440			−0.886306			−0.443153	−	0.896446i	$-0.646140\pi$
$647$	−573.440			−0.886306			−0.443153	+	0.896446i	$0.646140\pi$
$648$		0			0
$649$	−1086.28			−1.67378
$650$		0			0
$651$		0			0
$652$	2.80919	+	31.9101i	0.00430857	+	0.0489419i
$653$			767.256i			1.17497i	0.809235	+	0.587486i	$0.199882\pi$
$653$			767.256i			1.17497i	−0.809235	+	0.587486i	$0.800118\pi$
$654$		0			0
$655$		0			0
$656$	267.816	−	47.5224i	0.408257	−	0.0724427i
$657$		0			0
$658$	626.786	+	574.031i	0.952562	+	0.872388i
$659$			1054.84i			1.60067i	0.599552	+	0.800336i	$0.295345\pi$
$659$			1054.84i			1.60067i	−0.599552	+	0.800336i	$0.704655\pi$
$660$		0			0
$661$	618.281			0.935372			0.467686	−	0.883895i	$-0.345088\pi$
$661$	618.281			0.935372			0.467686	+	0.883895i	$0.345088\pi$
$662$	−813.220	+	887.957i	−1.22843	+	1.34132i
$663$		0			0
$664$	−135.805	+	177.283i	−0.204526	+	0.266993i
$665$		0			0
$666$		0			0
$667$	477.966			0.716591
$668$	65.7906	+	747.328i	0.0984889	+	1.11875i
$669$		0			0
$670$		0			0
$671$			1045.40i			1.55797i
$672$		0			0
$673$			26.7750i			0.0397846i	0.999802	+	0.0198923i	$0.00633233\pi$
$673$			26.7750i			0.0397846i	−0.999802	+	0.0198923i	$0.993668\pi$
$674$	43.3601	−	47.3450i	0.0643325	−	0.0702448i
$675$		0			0
$676$	18.3195	+	208.095i	0.0270999	+	0.307833i
$677$		−	264.837i		−	0.391193i	−0.980684	−	0.195596i	$-0.937336\pi$
$677$		−	264.837i		−	0.391193i	0.980684	−	0.195596i	$-0.0626642\pi$
$678$		0			0
$679$		−	1690.67i		−	2.48995i
$680$		0			0
$681$		0			0
$682$	−380.622	−	348.586i	−0.558096	−	0.511123i
$683$	761.435			1.11484			0.557419	−	0.830231i	$-0.311792\pi$
$683$	761.435			1.11484			0.557419	+	0.830231i	$0.311792\pi$
$684$		0			0
$685$		0			0
$686$	−341.822	−	313.052i	−0.498283	−	0.456344i
$687$		0			0
$688$	−102.673	+	18.2187i	−0.149234	+	0.0264807i
$689$	−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	$0.826648\pi$
$692$	−491.001	+	43.2250i	−0.709539	+	0.0624639i
$693$		0			0
$694$	770.554	+	705.699i	1.11031	+	1.01686i
$695$		0			0
$696$		0			0
$697$			268.706i			0.385518i
$698$	−190.163	−	174.158i	−0.272440	−	0.249510i
$699$		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
$703$	−478.294			−0.680361
$704$	−701.910	+	189.299i	−0.997031	+	0.268891i
$705$		0			0
$706$	803.495	−	877.338i	1.13810	−	1.24269i
$707$	−43.3349			−0.0612941
$708$		0			0
$709$	170.913			0.241061			0.120531	−	0.992710i	$-0.461540\pi$
$709$	170.913			0.241061			0.120531	+	0.992710i	$0.461540\pi$
$710$		0			0
$711$		0			0
$712$	205.270	−	267.963i	0.288300	−	0.376353i
$713$		−	476.125i		−	0.667777i
$714$		0			0
$715$		0			0
$716$	551.910	−	48.5871i	0.770824	−	0.0678591i
$717$		0			0
$718$	35.1952	−	38.4297i	0.0490184	−	0.0535233i
$719$		−	1369.42i		−	1.90462i	−0.305131	−	0.952310i	$-0.598700\pi$
$719$		−	1369.42i		−	1.90462i	0.305131	−	0.952310i	$-0.401300\pi$
$720$		0			0
$721$	721.087			1.00012
$722$	−383.433	−	351.161i	−0.531071	−	0.486372i
$723$		0			0
$724$	−68.0954	−	773.508i	−0.0940544	−	1.06838i
$725$		0			0
$726$		0			0
$727$	−1006.13			−1.38394			−0.691971	−	0.721925i	$-0.743258\pi$
$727$	−1006.13			−1.38394			−0.691971	+	0.721925i	$0.743258\pi$
$728$	749.352	+	574.031i	1.02933	+	0.788504i
$729$		0			0
$730$		0			0
$731$		−	103.014i		−	0.140922i
$732$		0			0
$733$		−	365.319i		−	0.498388i	−0.968454	−	0.249194i	$-0.919834\pi$
$733$		−	365.319i		−	0.498388i	0.968454	−	0.249194i	$-0.0801658\pi$
$734$	−620.816	−	568.563i	−0.845798	−	0.774610i
$735$		0			0
$736$	−566.105	−	359.572i	−0.769164	−	0.488549i
$737$			615.156i			0.834676i
$738$		0			0
$739$		−	187.213i		−	0.253334i	−0.991945	−	0.126667i	$-0.959572\pi$
$739$		−	187.213i		−	0.253334i	0.991945	−	0.126667i	$-0.0404279\pi$
$740$		0			0
$741$		0			0
$742$	195.058	−	212.984i	0.262882	−	0.287041i
$743$	183.678			0.247212			0.123606	−	0.992331i	$-0.460554\pi$
$743$	183.678			0.247212			0.123606	+	0.992331i	$0.460554\pi$
$744$		0			0
$745$		0			0
$746$	−295.433	+	322.584i	−0.396022	+	0.432418i
$747$		0			0
$748$	−62.9814	−	715.418i	−0.0841997	−	0.956441i
$749$	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	$0.876159\pi$
$752$	613.134	−	108.797i	0.815337	−	0.144677i
$753$		0			0
$754$	−332.900	+	363.494i	−0.441512	+	0.482088i
$755$		0			0
$756$		0			0
$757$		−	1131.60i		−	1.49485i	−0.664347	−	0.747424i	$-0.731290\pi$
$757$		−	1131.60i		−	1.49485i	0.664347	−	0.747424i	$-0.268710\pi$
$758$	332.673	−	363.246i	0.438882	−	0.479216i
$759$		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
$763$	1231.73			1.61433
$764$	268.742	−	23.6586i	0.351757	−	0.0309667i
$765$		0			0
$766$	598.973	+	548.560i	0.781950	+	0.716135i
$767$	1033.40			1.34733
$768$		0			0
$769$	648.319			0.843067			0.421534	−	0.906813i	$-0.361492\pi$
$769$	648.319			0.843067			0.421534	+	0.906813i	$0.361492\pi$
$770$		0			0
$771$		0			0
$772$	−613.104	+	53.9742i	−0.794176	+	0.0699148i
$773$			709.506i			0.917861i	0.888472	+	0.458930i	$0.151767\pi$
$773$			709.506i			0.917861i	−0.888472	+	0.458930i	$0.848233\pi$
$774$		0			0
$775$		0			0
$776$	−983.339	−	753.274i	−1.26719	−	0.970714i
$777$		0			0
$778$	−296.791	−	271.811i	−0.381479	−	0.349371i
$779$			423.627i			0.543809i
$780$		0			0
$781$	−778.219			−0.996439
$782$	447.463	−	488.586i	0.572204	−	0.624790i
$783$		0			0
$784$	−1106.32	+	196.310i	−1.41112	+	0.250395i
$785$		0			0
$786$		0			0
$787$	−3.67819			−0.00467369			−0.00233684	−	0.999997i	$-0.500744\pi$
$787$	−3.67819			−0.00467369			−0.00233684	+	0.999997i	$0.500744\pi$
$788$	−1041.12	+	91.6547i	−1.32122	+	0.116313i
$789$		0			0
$790$		0			0
$791$		−	198.999i		−	0.251579i
$792$		0			0
$793$		−	994.512i		−	1.25411i
$794$	−130.722	+	142.735i	−0.164637	+	0.179768i
$795$		0			0
$796$	−905.234	+	79.6918i	−1.13723	+	0.100115i
$797$		−	1379.02i		−	1.73027i	−0.501539	−	0.865135i	$-0.667233\pi$
$797$		−	1379.02i		−	1.73027i	0.501539	−	0.865135i	$-0.332767\pi$
$798$		0			0
$799$			615.171i			0.769926i
$800$		0			0
$801$		0			0
$802$	−411.641	−	376.995i	−0.513268	−	0.470068i
$803$	−502.005			−0.625162
$804$		0			0
$805$		0			0
$806$	362.094	+	331.617i	0.449248	+	0.411436i
$807$		0			0
$808$	−19.3077	+	25.2047i	−0.0238957	+	0.0311939i
$809$	−1333.79			−1.64869			−0.824343	−	0.566090i	$-0.808455\pi$
$809$	−1333.79			−1.64869			−0.824343	+	0.566090i	$0.808455\pi$
$810$		0			0
$811$		−	204.820i		−	0.252553i	−0.991995	−	0.126276i	$-0.959697\pi$
$811$		−	204.820i		−	0.252553i	0.991995	−	0.126276i	$-0.0403026\pi$
$812$	−87.3522	−	992.250i	−0.107577	−	1.22198i
$813$		0			0
$814$	−321.570	−	294.505i	−0.395050	−	0.361799i
$815$		0			0
$816$		0			0
$817$		−	162.406i		−	0.198784i
$818$	−769.669	−	704.888i	−0.940915	−	0.861722i
$819$		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
$823$	−173.312			−0.210586			−0.105293	−	0.994441i	$-0.533578\pi$
$823$	−173.312			−0.210586			−0.105293	+	0.994441i	$0.533578\pi$
$824$	321.278	−	419.403i	0.389901	−	0.508984i
$825$		0			0
$826$	−1410.47	+	1540.09i	−1.70759	+	1.86452i
$827$	−693.777			−0.838908			−0.419454	−	0.907776i	$-0.637779\pi$
$827$	−693.777			−0.838908			−0.419454	+	0.907776i	$0.637779\pi$
$828$		0			0
$829$	1125.57			1.35774			0.678871	−	0.734257i	$-0.262469\pi$
$829$	1125.57			1.35774			0.678871	+	0.734257i	$0.262469\pi$
$830$		0			0
$831$		0			0
$832$	667.742	−	180.084i	0.802575	−	0.216448i
$833$		−	1109.99i		−	1.33253i
$834$		0			0
$835$		0			0
$836$	−99.2930	−	1127.89i	−0.118771	−	1.34915i
$837$		0			0
$838$	−340.536	+	371.832i	−0.406368	+	0.443714i
$839$		−	1243.69i		−	1.48235i	−0.671313	−	0.741174i	$-0.734269\pi$
$839$		−	1243.69i		−	1.48235i	0.671313	−	0.741174i	$-0.265731\pi$
$840$		0			0
$841$	−320.875			−0.381540
$842$	1144.81	+	1048.46i	1.35964	+	1.24520i
$843$		0			0
$844$	772.277	−	67.9870i	0.915021	−	0.0805533i
$845$		0			0
$846$		0			0
$847$	87.6933			0.103534
$848$	−36.9696	−	208.345i	−0.0435963	−	0.245690i
$849$		0			0
$850$		0			0
$851$		−	402.257i		−	0.472687i
$852$		0			0
$853$			1027.09i			1.20409i	0.798463	+	0.602044i	$0.205647\pi$
$853$			1027.09i			1.20409i	−0.798463	+	0.602044i	$0.794353\pi$
$854$	1482.13	+	1357.39i	1.73552	+	1.58945i
$855$		0			0
$856$	467.376	−	610.122i	0.546000	−	0.712759i
$857$		−	341.775i		−	0.398804i	−0.979918	−	0.199402i	$-0.936100\pi$
$857$		−	341.775i		−	0.398804i	0.979918	−	0.199402i	$-0.0639000\pi$
$858$		0			0
$859$		−	300.167i		−	0.349438i	−0.984618	−	0.174719i	$-0.944098\pi$
$859$		−	300.167i		−	0.349438i	0.984618	−	0.174719i	$-0.0559017\pi$
$860$		0			0
$861$		0			0
$862$	−795.480	+	868.586i	−0.922830	+	1.00764i
$863$	−1312.54			−1.52091			−0.760453	−	0.649394i	$-0.775023\pi$
$863$	−1312.54			−1.52091			−0.760453	+	0.649394i	$0.775023\pi$
$864$		0			0
$865$		0			0
$866$	−732.030	+	799.305i	−0.845301	+	0.922986i
$867$		0			0
$868$	−988.427	+	87.0156i	−1.13874	+	0.100248i
$869$	928.219			1.06815
$870$		0			0
$871$		−	585.212i		−	0.671885i
$872$	548.795	−	716.408i	0.629352	−	0.821569i
$873$		0			0
$874$	705.445	−	770.277i	0.807146	−	0.881324i
$875$		0			0
$876$		0			0
$877$		−	1543.22i		−	1.75966i	−0.475285	−	0.879832i	$-0.657655\pi$
$877$		−	1543.22i		−	1.75966i	0.475285	−	0.879832i	$-0.342345\pi$
$878$	5.46639	−	5.96876i	0.00622595	−	0.00679813i
$879$		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
$883$	380.661			0.431099			0.215550	−	0.976493i	$-0.430846\pi$
$883$	380.661			0.431099			0.215550	+	0.976493i	$0.430846\pi$
$884$	59.9156	+	680.593i	0.0677778	+	0.769901i
$885$		0			0
$886$	505.360	+	462.826i	0.570384	+	0.522376i
$887$	−851.315			−0.959769			−0.479884	−	0.877332i	$-0.659321\pi$
$887$	−851.315			−0.959769			−0.479884	+	0.877332i	$0.659321\pi$
$888$		0			0
$889$	563.412			0.633760
$890$		0			0
$891$		0			0
$892$	−8.89560	−	101.047i	−0.00997265	−	0.113281i
$893$			969.844i			1.08605i
$894$		0			0
$895$		0			0
$896$	−643.005	+	1240.94i	−0.717639	+	1.38498i
$897$		0			0
$898$	−714.516	−	654.377i	−0.795675	−	0.728705i
$899$		−	518.121i		−	0.576330i
$900$		0			0
$901$	209.038			0.232006
$902$	−260.844	+	284.816i	−0.289184	+	0.315761i
$903$		0			0
$904$	−115.743	−	88.6634i	−0.128034	−	0.0980790i
$905$		0			0
$906$		0			0
$907$	−531.313			−0.585791			−0.292896	−	0.956144i	$-0.594619\pi$
$907$	−531.313			−0.585791			−0.292896	+	0.956144i	$0.594619\pi$
$908$	−131.397	−	1492.56i	−0.144710	−	1.64379i
$909$		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
$913$		−	317.094i		−	0.347310i
$914$	943.571	−	1030.29i	1.03235	−	1.12723i
$915$		0			0
$916$	90.9531	+	1033.15i	0.0992938	+	1.12790i
$917$			1732.56i			1.88938i
$918$		0			0
$919$			715.203i			0.778240i	0.921187	+	0.389120i	$0.127221\pi$
$919$			715.203i			0.778240i	−0.921187	+	0.389120i	$0.872779\pi$
$920$		0			0
$921$		0			0
$922$	1209.80	+	1107.98i	1.31215	+	1.20171i
$923$	740.337			0.802098
$924$		0			0
$925$		0			0
$926$	1300.82	+	1191.33i	1.40477	+	1.28653i
$927$		0			0
$928$	−616.037	−	391.287i	−0.663833	−	0.421646i
$929$	−301.225			−0.324246			−0.162123	−	0.986771i	$-0.551834\pi$
$929$	−301.225			−0.324246			−0.162123	+	0.986771i	$0.551834\pi$
$930$		0			0
$931$		−	1749.95i		−	1.87965i
$932$	−610.539	+	53.7484i	−0.655084	+	0.0576700i
$933$		0			0
$934$	−84.4187	−	77.3135i	−0.0903841	−	0.0827767i
$935$		0			0
$936$		0			0
$937$			1386.43i			1.47965i	0.672800	+	0.739824i	$0.265091\pi$
$937$			1386.43i			1.47965i	−0.672800	+	0.739824i	$0.734909\pi$
$938$	872.148	+	798.742i	0.929795	+	0.851537i
$939$		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
$943$	−356.281			−0.377816
$944$	267.328	+	1506.55i	0.283186	+	1.59592i
$945$		0			0
$946$	100.000	−	109.190i	0.105708	−	0.115423i
$947$	−310.121			−0.327477			−0.163738	−	0.986504i	$-0.552355\pi$
$947$	−310.121			−0.327477			−0.163738	+	0.986504i	$0.552355\pi$
$948$		0			0
$949$	477.569			0.503234
$950$		0			0
$951$		0			0
$952$	−1096.07	−	839.633i	−1.15134	−	0.881967i
$953$			552.725i			0.579984i	0.957029	+	0.289992i	$0.0936527\pi$
$953$			552.725i			0.579984i	−0.957029	+	0.289992i	$0.906347\pi$
$954$		0			0
$955$		0			0
$956$	−745.969	+	65.6709i	−0.780302	+	0.0686934i
$957$		0			0
$958$	879.965	−	960.836i	0.918544	−	1.00296i
$959$			2291.22i			2.38918i
$960$		0			0
$961$	444.875			0.462929
$962$	305.917	+	280.169i	0.318001	+	0.291236i
$963$		0			0
$964$	−22.8336	−	259.372i	−0.0236864	−	0.269058i
$965$		0			0
$966$		0			0
$967$	1606.13			1.66094			0.830472	−	0.557060i	$-0.188071\pi$
$967$	1606.13			1.66094			0.830472	+	0.557060i	$0.188071\pi$
$968$	39.0715	−	51.0047i	0.0403631	−	0.0526908i
$969$		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
$973$			924.031i			0.949672i
$974$	−78.1984	−	71.6167i	−0.0802858	−	0.0735284i
$975$		0			0
$976$	1449.85	−	257.268i	1.48550	−	0.263594i
$977$		−	592.244i		−	0.606186i	−0.952961	−	0.303093i	$-0.901981\pi$
$977$		−	592.244i		−	0.606186i	0.952961	−	0.303093i	$-0.0980193\pi$
$978$		0			0
$979$			479.287i			0.489568i
$980$		0			0
$981$		0			0
$982$	29.2494	−	31.9375i	0.0297856	−	0.0325229i
$983$	−1087.34			−1.10615			−0.553074	−	0.833132i	$-0.686545\pi$
$983$	−1087.34			−1.10615			−0.553074	+	0.833132i	$0.686545\pi$
$984$		0			0
$985$		0			0
$986$	486.931	−	531.681i	0.493845	−	0.539230i
$987$		0			0
$988$	94.4596	+	1072.98i	0.0956069	+	1.08602i
$989$	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	$0.970599\pi$
$992$	−389.780	+	613.664i	−0.392923	+	0.618613i
$993$		0			0
$994$	−1010.47	+	1103.33i	−1.01657	+	1.10999i
$995$		0			0
$996$		0			0
$997$			237.087i			0.237801i	0.992906	+	0.118900i	$0.0379369\pi$
$997$			237.087i			0.237801i	−0.992906	+	0.118900i	$0.962063\pi$
$998$	−274.750	+	300.000i	−0.275301	+	0.300601i
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.47492 + 1.35078i) q^{2} +(0.350781 + 3.98459i) q^{4} -10.9190 q^{7} +(-4.86493 + 6.35078i) q^{8} +O(q^{10})\)	\(q+(1.47492 + 1.35078i) q^{2} +(0.350781 + 3.98459i) q^{4} -10.9190 q^{7} +(-4.86493 + 6.35078i) q^{8} -11.3592i q^{11} +10.8062i q^{13} +(-16.1047 - 14.7492i) q^{14} +(-15.7539 + 2.79544i) q^{16} -15.8062i q^{17} -24.9192i q^{19} +(15.3438 - 16.7539i) q^{22} +20.9577 q^{23} +(-14.5969 + 15.9384i) q^{26} +(-3.83019 - 43.5078i) q^{28} +22.8062 q^{29} -22.7184i q^{31} +(-27.0118 - 17.1570i) q^{32} +(21.3508 - 23.3130i) q^{34} -19.1938i q^{37} +(33.6604 - 36.7539i) q^{38} -17.0000 q^{41} +6.51730 q^{43} +(45.2617 - 3.98459i) q^{44} +(30.9109 + 28.3093i) q^{46} -38.9195 q^{47} +70.2250 q^{49} +(-43.0585 + 3.79063i) q^{52} +13.2250i q^{53} +(53.1203 - 69.3443i) q^{56} +(33.6374 + 30.8062i) q^{58} -95.6301i q^{59} -92.0312 q^{61} +(30.6876 - 33.5078i) q^{62} +(-16.6648 - 61.7923i) q^{64} -54.1549 q^{67} +(62.9814 - 5.54453i) q^{68} -68.5100i q^{71} -44.1938i q^{73} +(25.9266 - 28.3093i) q^{74} +(99.2930 - 8.74120i) q^{76} +124.031i q^{77} +81.7152i q^{79} +(-25.0736 - 22.9633i) q^{82} +27.9152 q^{83} +(9.61250 + 8.80344i) q^{86} +(72.1397 + 55.2617i) q^{88} -42.1938 q^{89} -117.994i q^{91} +(7.35156 + 83.5078i) q^{92} +(-57.4031 - 52.5717i) q^{94} +154.837i q^{97} +(103.576 + 94.8586i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 10 q^{4}+O(q^{10}) \) 8 * q - 10 * q^4	\( 8 q - 10 q^{4} - 52 q^{14} - 62 q^{16} - 168 q^{26} + 80 q^{29} + 158 q^{34} - 136 q^{41} + 170 q^{44} + 68 q^{46} + 152 q^{49} + 92 q^{56} - 224 q^{61} + 110 q^{64} - 228 q^{74} + 90 q^{76} - 128 q^{86} - 440 q^{89} - 408 q^{94}+O(q^{100}) \) 8 * q - 10 * q^4 - 52 * q^14 - 62 * q^16 - 168 * q^26 + 80 * q^29 + 158 * q^34 - 136 * q^41 + 170 * q^44 + 68 * q^46 + 152 * q^49 + 92 * q^56 - 224 * q^61 + 110 * q^64 - 228 * q^74 + 90 * q^76 - 128 * q^86 - 440 * q^89 - 408 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more