LMFDB - Embedded newform 475.3.d.c.474.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,3,Mod(474,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("475.474");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	475.d (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:	$12.9428125571$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			474.17
Character	$\chi$	$=$	475.474
Dual form			475.3.d.c.474.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.88109 q^{2} +0.840697 q^{3} -0.461500 q^{4} +1.58143 q^{6} +2.31342i q^{7} -8.39248 q^{8} -8.29323 q^{9} +O(q^{10})$	\(q+1.88109 q^{2} +0.840697 q^{3} -0.461500 q^{4} +1.58143 q^{6} +2.31342i q^{7} -8.39248 q^{8} -8.29323 q^{9} -8.28979 q^{11} -0.387981 q^{12} -7.20783 q^{13} +4.35174i q^{14} -13.9410 q^{16} -6.37730i q^{17} -15.6003 q^{18} +(-8.31075 - 17.0860i) q^{19} +1.94488i q^{21} -15.5938 q^{22} +14.5958i q^{23} -7.05554 q^{24} -13.5586 q^{26} -14.5384 q^{27} -1.06764i q^{28} -16.9209i q^{29} +39.5651i q^{31} +7.34562 q^{32} -6.96920 q^{33} -11.9963i q^{34} +3.82732 q^{36} -8.68586 q^{37} +(-15.6333 - 32.1403i) q^{38} -6.05960 q^{39} +41.6193i q^{41} +3.65850i q^{42} +3.51015i q^{43} +3.82573 q^{44} +27.4560i q^{46} -68.8086i q^{47} -11.7202 q^{48} +43.6481 q^{49} -5.36138i q^{51} +3.32641 q^{52} -89.1014 q^{53} -27.3480 q^{54} -19.4153i q^{56} +(-6.98682 - 14.3642i) q^{57} -31.8297i q^{58} +95.2910i q^{59} -12.8583 q^{61} +74.4255i q^{62} -19.1857i q^{63} +69.5818 q^{64} -13.1097 q^{66} -65.8457 q^{67} +2.94312i q^{68} +12.2707i q^{69} -2.56645i q^{71} +69.6008 q^{72} -98.0969i q^{73} -16.3389 q^{74} +(3.83541 + 7.88518i) q^{76} -19.1777i q^{77} -11.3987 q^{78} -27.1569i q^{79} +62.4167 q^{81} +78.2896i q^{82} -12.4242i q^{83} -0.897562i q^{84} +6.60290i q^{86} -14.2253i q^{87} +69.5719 q^{88} +25.1923i q^{89} -16.6747i q^{91} -6.73596i q^{92} +33.2623i q^{93} -129.435i q^{94} +6.17544 q^{96} +62.6956 q^{97} +82.1060 q^{98} +68.7491 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} - 56 q^{6} + 96 q^{9}+O(q^{10}) $ 24 * q + 24 * q^4 - 56 * q^6 + 96 * q^9	$ 24 q + 24 q^{4} - 56 q^{6} + 96 q^{9} + 64 q^{11} - 88 q^{16} - 16 q^{19} - 200 q^{24} + 216 q^{26} - 160 q^{36} - 152 q^{39} + 512 q^{44} - 144 q^{49} + 152 q^{54} - 592 q^{61} - 376 q^{64} + 304 q^{66} - 272 q^{74} + 496 q^{76} - 744 q^{81} - 88 q^{96} + 624 q^{99}+O(q^{100}) $ 24 * q + 24 * q^4 - 56 * q^6 + 96 * q^9 + 64 * q^11 - 88 * q^16 - 16 * q^19 - 200 * q^24 + 216 * q^26 - 160 * q^36 - 152 * q^39 + 512 * q^44 - 144 * q^49 + 152 * q^54 - 592 * q^61 - 376 * q^64 + 304 * q^66 - 272 * q^74 + 496 * q^76 - 744 * q^81 - 88 * q^96 + 624 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.88109			0.940545			0.470273	−	0.882521i	$-0.344156\pi$
$2$	1.88109			0.940545			0.470273	+	0.882521i	$0.344156\pi$
$3$	0.840697			0.280232			0.140116	−	0.990135i	$-0.455252\pi$
$3$	0.840697			0.280232			0.140116	+	0.990135i	$0.455252\pi$
$4$	−0.461500			−0.115375
$5$		0			0
$5$		0			0
$6$	1.58143			0.263571
$7$			2.31342i			0.330488i	0.986253	+	0.165244i	$0.0528411\pi$
$7$			2.31342i			0.330488i	−0.986253	+	0.165244i	$0.947159\pi$
$8$	−8.39248			−1.04906
$9$	−8.29323			−0.921470
$10$		0			0
$11$	−8.28979			−0.753617			−0.376808	−	0.926291i	$-0.622979\pi$
$11$	−8.28979			−0.753617			−0.376808	+	0.926291i	$0.622979\pi$
$12$	−0.387981			−0.0323318
$13$	−7.20783			−0.554448			−0.277224	−	0.960805i	$-0.589414\pi$
$13$	−7.20783			−0.554448			−0.277224	+	0.960805i	$0.589414\pi$
$14$			4.35174i			0.310839i
$15$		0			0
$16$	−13.9410			−0.871314
$17$		−	6.37730i		−	0.375136i	−0.982252	−	0.187568i	$-0.939940\pi$
$17$		−	6.37730i		−	0.375136i	0.982252	−	0.187568i	$-0.0600604\pi$
$18$	−15.6003			−0.866684
$19$	−8.31075	−	17.0860i	−0.437408	−	0.899263i
$19$	−8.31075	−	17.0860i	−0.437408	−	0.899263i
$20$		0			0
$21$			1.94488i			0.0926134i
$22$	−15.5938			−0.708811
$23$			14.5958i			0.634601i	0.948325	+	0.317300i	$0.102776\pi$
$23$			14.5958i			0.634601i	−0.948325	+	0.317300i	$0.897224\pi$
$24$	−7.05554			−0.293981
$25$		0			0
$26$	−13.5586			−0.521484
$27$	−14.5384			−0.538458
$28$		−	1.06764i		−	0.0381300i
$29$		−	16.9209i		−	0.583478i	−0.956498	−	0.291739i	$-0.905766\pi$
$29$		−	16.9209i		−	0.583478i	0.956498	−	0.291739i	$-0.0942339\pi$
$30$		0			0
$31$			39.5651i			1.27629i	0.769915	+	0.638146i	$0.220299\pi$
$31$			39.5651i			1.27629i	−0.769915	+	0.638146i	$0.779701\pi$
$32$	7.34562			0.229551
$33$	−6.96920			−0.211188
$34$		−	11.9963i		−	0.352832i
$35$		0			0
$36$	3.82732			0.106314
$37$	−8.68586			−0.234753			−0.117377	−	0.993087i	$-0.537448\pi$
$37$	−8.68586			−0.234753			−0.117377	+	0.993087i	$0.537448\pi$
$38$	−15.6333	−	32.1403i	−0.411402	−	0.845798i
$39$	−6.05960			−0.155374
$40$		0			0
$41$			41.6193i			1.01510i	0.861621	+	0.507552i	$0.169450\pi$
$41$			41.6193i			1.01510i	−0.861621	+	0.507552i	$0.830550\pi$
$42$			3.65850i			0.0871071i
$43$			3.51015i			0.0816313i	0.999167	+	0.0408157i	$0.0129956\pi$
$43$			3.51015i			0.0816313i	−0.999167	+	0.0408157i	$0.987004\pi$
$44$	3.82573			0.0869485
$45$		0			0
$46$			27.4560i			0.596871i
$47$		−	68.8086i		−	1.46401i	−0.681298	−	0.732006i	$-0.738584\pi$
$47$		−	68.8086i		−	1.46401i	0.681298	−	0.732006i	$-0.261416\pi$
$48$	−11.7202			−0.244170
$49$	43.6481			0.890778
$50$		0			0
$51$		−	5.36138i		−	0.105125i
$52$	3.32641			0.0639694
$53$	−89.1014			−1.68116			−0.840579	−	0.541688i	$-0.817785\pi$
$53$	−89.1014			−1.68116			−0.840579	+	0.541688i	$0.817785\pi$
$54$	−27.3480			−0.506444
$55$		0			0
$56$		−	19.4153i		−	0.346702i
$57$	−6.98682	−	14.3642i	−0.122576	−	0.252003i
$58$		−	31.8297i		−	0.548788i
$59$			95.2910i			1.61510i	0.589798	+	0.807551i	$0.299207\pi$
$59$			95.2910i			1.61510i	−0.589798	+	0.807551i	$0.700793\pi$
$60$		0			0
$61$	−12.8583			−0.210792			−0.105396	−	0.994430i	$-0.533611\pi$
$61$	−12.8583			−0.210792			−0.105396	+	0.994430i	$0.533611\pi$
$62$			74.4255i			1.20041i
$63$		−	19.1857i		−	0.304535i
$64$	69.5818			1.08722
$65$		0			0
$66$	−13.1097			−0.198632
$67$	−65.8457			−0.982772			−0.491386	−	0.870942i	$-0.663510\pi$
$67$	−65.8457			−0.982772			−0.491386	+	0.870942i	$0.663510\pi$
$68$			2.94312i			0.0432812i
$69$			12.2707i			0.177836i
$70$		0			0
$71$		−	2.56645i		−	0.0361471i	−0.999837	−	0.0180736i	$-0.994247\pi$
$71$		−	2.56645i		−	0.0361471i	0.999837	−	0.0180736i	$-0.00575331\pi$
$72$	69.6008			0.966677
$73$		−	98.0969i		−	1.34379i	−0.740645	−	0.671897i	$-0.765480\pi$
$73$		−	98.0969i		−	1.34379i	0.740645	−	0.671897i	$-0.234520\pi$
$74$	−16.3389			−0.220796
$75$		0			0
$76$	3.83541	+	7.88518i	0.0504659	+	0.103752i
$77$		−	19.1777i		−	0.249061i
$78$	−11.3987			−0.146137
$79$		−	27.1569i		−	0.343758i	−0.985118	−	0.171879i	$-0.945016\pi$
$79$		−	27.1569i		−	0.343758i	0.985118	−	0.171879i	$-0.0549838\pi$
$80$		0			0
$81$	62.4167			0.770576
$82$			78.2896i			0.954751i
$83$		−	12.4242i		−	0.149689i	−0.997195	−	0.0748445i	$-0.976154\pi$
$83$		−	12.4242i		−	0.149689i	0.997195	−	0.0748445i	$-0.0238460\pi$
$84$		−	0.897562i		−	0.0106853i
$85$		0			0
$86$			6.60290i			0.0767780i
$87$		−	14.2253i		−	0.163510i
$88$	69.5719			0.790590
$89$			25.1923i			0.283060i	0.989934	+	0.141530i	$0.0452022\pi$
$89$			25.1923i			0.283060i	−0.989934	+	0.141530i	$0.954798\pi$
$90$		0			0
$91$		−	16.6747i		−	0.183238i
$92$		−	6.73596i		−	0.0732170i
$93$			33.2623i			0.357659i
$94$		−	129.435i		−	1.37697i
$95$		0			0
$96$	6.17544			0.0643275
$97$	62.6956			0.646346			0.323173	−	0.946340i	$-0.395250\pi$
$97$	62.6956			0.646346			0.323173	+	0.946340i	$0.395250\pi$
$98$	82.1060			0.837817
$99$	68.7491			0.694435
$100$		0			0
$101$	138.987			1.37611			0.688055	−	0.725658i	$-0.258465\pi$
$101$	138.987			1.37611			0.688055	+	0.725658i	$0.258465\pi$
$102$		−	10.0852i		−	0.0988749i
$103$	97.7629			0.949155			0.474577	−	0.880214i	$-0.342601\pi$
$103$	97.7629			0.949155			0.474577	+	0.880214i	$0.342601\pi$
$104$	60.4916			0.581650
$105$		0			0
$106$	−167.608			−1.58121
$107$	−88.3158			−0.825381			−0.412691	−	0.910871i	$-0.635411\pi$
$107$	−88.3158			−0.825381			−0.412691	+	0.910871i	$0.635411\pi$
$108$	6.70945			0.0621245
$109$			130.713i			1.19920i	0.800301	+	0.599599i	$0.204673\pi$
$109$			130.713i			1.19920i	−0.800301	+	0.599599i	$0.795327\pi$
$110$		0			0
$111$	−7.30218			−0.0657854
$112$		−	32.2514i		−	0.287959i
$113$	−74.9095			−0.662916			−0.331458	−	0.943470i	$-0.607541\pi$
$113$	−74.9095			−0.662916			−0.331458	+	0.943470i	$0.607541\pi$
$114$	−13.1428	−	27.0203i	−0.115288	−	0.237020i
$115$		0			0
$116$			7.80897i			0.0673187i
$117$	59.7762			0.510907
$118$			179.251i			1.51908i
$119$	14.7534			0.123978
$120$		0			0
$121$	−52.2794			−0.432062
$122$	−24.1876			−0.198259
$123$			34.9892i			0.284465i
$124$		−	18.2593i		−	0.147252i
$125$		0			0
$126$		−	36.0900i		−	0.286429i
$127$	−67.5562			−0.531938			−0.265969	−	0.963982i	$-0.585692\pi$
$127$	−67.5562			−0.531938			−0.265969	+	0.963982i	$0.585692\pi$
$128$	101.507			0.793026
$129$			2.95097i			0.0228758i
$130$		0			0
$131$	87.9131			0.671093			0.335546	−	0.942024i	$-0.391079\pi$
$131$	87.9131			0.671093			0.335546	+	0.942024i	$0.391079\pi$
$132$	3.21628			0.0243658
$133$	39.5270	−	19.2262i	0.297196	−	0.144558i
$134$	−123.862			−0.924342
$135$		0			0
$136$			53.5214i			0.393540i
$137$		−	112.209i		−	0.819040i	−0.912301	−	0.409520i	$-0.865696\pi$
$137$		−	112.209i		−	0.819040i	0.912301	−	0.409520i	$-0.134304\pi$
$138$			23.0822i			0.167263i
$139$	−162.255			−1.16731			−0.583653	−	0.812003i	$-0.698377\pi$
$139$	−162.255			−1.16731			−0.583653	+	0.812003i	$0.698377\pi$
$140$		0			0
$141$		−	57.8472i		−	0.410264i
$142$		−	4.82772i		−	0.0339980i
$143$	59.7513			0.417842
$144$	115.616			0.802889
$145$		0			0
$146$		−	184.529i		−	1.26390i
$147$	36.6948			0.249625
$148$	4.00852			0.0270846
$149$	−142.097			−0.953671			−0.476836	−	0.878992i	$-0.658216\pi$
$149$	−142.097			−0.953671			−0.476836	+	0.878992i	$0.658216\pi$
$150$		0			0
$151$		−	258.564i		−	1.71234i	−0.516692	−	0.856172i	$-0.672837\pi$
$151$		−	258.564i		−	1.71234i	0.516692	−	0.856172i	$-0.327163\pi$
$152$	69.7478	+	143.394i	0.458867	+	0.943381i
$153$			52.8884i			0.345676i
$154$		−	36.0750i		−	0.234253i
$155$		0			0
$156$	2.79650			0.0179263
$157$			179.201i			1.14141i	0.821155	+	0.570705i	$0.193330\pi$
$157$			179.201i			1.14141i	−0.821155	+	0.570705i	$0.806670\pi$
$158$		−	51.0846i		−	0.323320i
$159$	−74.9073			−0.471115
$160$		0			0
$161$	−33.7662			−0.209728
$162$	117.411			0.724762
$163$			207.556i			1.27335i	0.771132	+	0.636675i	$0.219691\pi$
$163$			207.556i			1.27335i	−0.771132	+	0.636675i	$0.780309\pi$
$164$		−	19.2073i		−	0.117118i
$165$		0			0
$166$		−	23.3710i		−	0.140789i
$167$	65.8665			0.394410			0.197205	−	0.980362i	$-0.436814\pi$
$167$	65.8665			0.394410			0.197205	+	0.980362i	$0.436814\pi$
$168$		−	16.3224i		−	0.0971571i
$169$	−117.047			−0.692587
$170$		0			0
$171$	68.9229	+	141.698i	0.403058	+	0.828644i
$172$		−	1.61993i		−	0.00941821i
$173$	75.7872			0.438076			0.219038	−	0.975716i	$-0.429708\pi$
$173$	75.7872			0.438076			0.219038	+	0.975716i	$0.429708\pi$
$174$		−	26.7591i		−	0.153788i
$175$		0			0
$176$	115.568			0.656637
$177$			80.1109i			0.452604i
$178$			47.3890i			0.266231i
$179$			148.451i			0.829338i	0.909972	+	0.414669i	$0.136103\pi$
$179$			148.451i			0.829338i	−0.909972	+	0.414669i	$0.863897\pi$
$180$		0			0
$181$		−	293.213i		−	1.61996i	−0.586455	−	0.809981i	$-0.699477\pi$
$181$		−	293.213i		−	1.61996i	0.586455	−	0.809981i	$-0.300523\pi$
$182$		−	31.3666i		−	0.172344i
$183$	−10.8099			−0.0590707
$184$		−	122.495i		−	0.665735i
$185$		0			0
$186$			62.5693i			0.336394i
$187$			52.8665i			0.282708i
$188$			31.7551i			0.168910i
$189$		−	33.6333i		−	0.177954i
$190$		0			0
$191$	−17.0781			−0.0894139			−0.0447070	−	0.999000i	$-0.514235\pi$
$191$	−17.0781			−0.0894139			−0.0447070	+	0.999000i	$0.514235\pi$
$192$	58.4973			0.304673
$193$	−227.915			−1.18091			−0.590453	−	0.807072i	$-0.701051\pi$
$193$	−227.915			−1.18091			−0.590453	+	0.807072i	$0.701051\pi$
$194$	117.936			0.607918
$195$		0			0
$196$	−20.1436			−0.102773
$197$		−	364.907i		−	1.85232i	−0.377130	−	0.926160i	$-0.623089\pi$
$197$		−	364.907i		−	1.85232i	0.377130	−	0.926160i	$-0.376911\pi$
$198$	129.323			0.653148
$199$	76.8411			0.386136			0.193068	−	0.981185i	$-0.438156\pi$
$199$	76.8411			0.386136			0.193068	+	0.981185i	$0.438156\pi$
$200$		0			0
$201$	−55.3563			−0.275405
$202$	261.447			1.29429
$203$	39.1450			0.192833
$204$			2.47428i			0.0121288i
$205$		0			0
$206$	183.901			0.892723
$207$		−	121.046i		−	0.584765i
$208$	100.484			0.483098
$209$	68.8943	+	141.639i	0.329638	+	0.677700i
$210$		0			0
$211$			178.990i			0.848293i	0.905594	+	0.424146i	$0.139426\pi$
$211$			178.990i			0.848293i	−0.905594	+	0.424146i	$0.860574\pi$
$212$	41.1203			0.193964
$213$		−	2.15761i		−	0.0101296i
$214$	−166.130			−0.776308
$215$		0			0
$216$	122.013			0.564875
$217$	−91.5305			−0.421799
$218$			245.882i			1.12790i
$219$		−	82.4698i		−	0.376575i
$220$		0			0
$221$			45.9665i			0.207993i
$222$	−13.7361			−0.0618742
$223$	46.2665			0.207473			0.103736	−	0.994605i	$-0.466920\pi$
$223$	46.2665			0.207473			0.103736	+	0.994605i	$0.466920\pi$
$224$			16.9935i			0.0758637i
$225$		0			0
$226$	−140.912			−0.623502
$227$	−353.533			−1.55741			−0.778707	−	0.627388i	$-0.784124\pi$
$227$	−353.533			−1.55741			−0.778707	+	0.627388i	$0.784124\pi$
$228$	3.22442	+	6.62905i	0.0141422	+	0.0290748i
$229$	−15.5586			−0.0679415			−0.0339707	−	0.999423i	$-0.510815\pi$
$229$	−15.5586			−0.0679415			−0.0339707	+	0.999423i	$0.510815\pi$
$230$		0			0
$231$		−	16.1227i		−	0.0697950i
$232$			142.008i			0.612104i
$233$		−	110.847i		−	0.475738i	−0.971297	−	0.237869i	$-0.923551\pi$
$233$		−	110.847i		−	0.475738i	0.971297	−	0.237869i	$-0.0764489\pi$
$234$	112.444			0.480531
$235$		0			0
$236$		−	43.9767i		−	0.186342i
$237$		−	22.8307i		−	0.0963322i
$238$	27.7524			0.116607
$239$	231.840			0.970040			0.485020	−	0.874503i	$-0.338812\pi$
$239$	231.840			0.970040			0.485020	+	0.874503i	$0.338812\pi$
$240$		0			0
$241$			25.2261i			0.104673i	0.998630	+	0.0523364i	$0.0166668\pi$
$241$			25.2261i			0.104673i	−0.998630	+	0.0523364i	$0.983333\pi$
$242$	−98.3423			−0.406373
$243$	183.319			0.754399
$244$	5.93410			0.0243201
$245$		0			0
$246$			65.8179i			0.267552i
$247$	59.9024	+	123.153i	0.242520	+	0.498595i
$248$		−	332.049i		−	1.33891i
$249$		−	10.4450i		−	0.0419477i
$250$		0			0
$251$	−302.298			−1.20438			−0.602188	−	0.798355i	$-0.705704\pi$
$251$	−302.298			−1.20438			−0.602188	+	0.798355i	$0.705704\pi$
$252$			8.85418i			0.0351356i
$253$		−	120.996i		−	0.478246i
$254$	−127.079			−0.500312
$255$		0			0
$256$	−87.3831			−0.341340
$257$	−482.042			−1.87565			−0.937826	−	0.347107i	$-0.887164\pi$
$257$	−482.042			−1.87565			−0.937826	+	0.347107i	$0.887164\pi$
$258$			5.55104i			0.0215157i
$259$		−	20.0940i		−	0.0775830i
$260$		0			0
$261$			140.329i			0.537658i
$262$	165.373			0.631193
$263$			14.9627i			0.0568925i	0.999595	+	0.0284462i	$0.00905594\pi$
$263$			14.9627i			0.0568925i	−0.999595	+	0.0284462i	$0.990944\pi$
$264$	58.4889			0.221549
$265$		0			0
$266$	74.3539	−	36.1662i	0.279526	−	0.135963i
$267$			21.1791i			0.0793226i
$268$	30.3878			0.113387
$269$			333.769i			1.24078i	0.784294	+	0.620389i	$0.213025\pi$
$269$			333.769i			1.24078i	−0.784294	+	0.620389i	$0.786975\pi$
$270$		0			0
$271$	−111.309			−0.410735			−0.205368	−	0.978685i	$-0.565839\pi$
$271$	−111.309			−0.410735			−0.205368	+	0.978685i	$0.565839\pi$
$272$			88.9061i			0.326861i
$273$		−	14.0184i		−	0.0513494i
$274$		−	211.074i		−	0.770345i
$275$		0			0
$276$		−	5.66291i		−	0.0205178i
$277$			245.520i			0.886355i	0.896434	+	0.443178i	$0.146149\pi$
$277$			245.520i			0.886355i	−0.896434	+	0.443178i	$0.853851\pi$
$278$	−305.217			−1.09790
$279$		−	328.122i		−	1.17607i
$280$		0			0
$281$			483.657i			1.72120i	0.509281	+	0.860600i	$0.329911\pi$
$281$			483.657i			1.72120i	−0.509281	+	0.860600i	$0.670089\pi$
$282$		−	108.816i		−	0.385872i
$283$		−	510.891i		−	1.80527i	−0.430407	−	0.902635i	$-0.641630\pi$
$283$		−	510.891i		−	1.80527i	0.430407	−	0.902635i	$-0.358370\pi$
$284$			1.18441i			0.00417047i
$285$		0			0
$286$	112.398			0.392999
$287$	−96.2827			−0.335480
$288$	−60.9189			−0.211524
$289$	248.330			0.859273
$290$		0			0
$291$	52.7080			0.181127
$292$			45.2717i			0.155040i
$293$	−459.172			−1.56714			−0.783570	−	0.621303i	$-0.786603\pi$
$293$	−459.172			−1.56714			−0.783570	+	0.621303i	$0.786603\pi$
$294$	69.0263			0.234783
$295$		0			0
$296$	72.8960			0.246270
$297$	120.520			0.405791
$298$	−267.297			−0.896971
$299$		−	105.204i		−	0.351853i
$300$		0			0
$301$	−8.12043			−0.0269782
$302$		−	486.382i		−	1.61054i
$303$	116.846			0.385631
$304$	115.860	+	238.196i	0.381119	+	0.783540i
$305$		0			0
$306$			99.4879i			0.325124i
$307$	560.721			1.82645			0.913227	−	0.407452i	$-0.133583\pi$
$307$	560.721			1.82645			0.913227	+	0.407452i	$0.133583\pi$
$308$			8.85051i			0.0287354i
$309$	82.1890			0.265984
$310$		0			0
$311$	−63.4058			−0.203877			−0.101939	−	0.994791i	$-0.532505\pi$
$311$	−63.4058			−0.203877			−0.101939	+	0.994791i	$0.532505\pi$
$312$	50.8551			0.162997
$313$		−	185.259i		−	0.591881i	−0.955206	−	0.295940i	$-0.904367\pi$
$313$		−	185.259i		−	0.591881i	0.955206	−	0.295940i	$-0.0956330\pi$
$314$			337.094i			1.07355i
$315$		0			0
$316$			12.5329i			0.0396611i
$317$	−362.734			−1.14427			−0.572135	−	0.820159i	$-0.693885\pi$
$317$	−362.734			−1.14427			−0.572135	+	0.820159i	$0.693885\pi$
$318$	−140.907			−0.443105
$319$			140.270i			0.439719i
$320$		0			0
$321$	−74.2469			−0.231299
$322$	−63.5172			−0.197259
$323$	−108.963	+	53.0002i	−0.337346	+	0.164087i
$324$	−28.8053			−0.0889052
$325$		0			0
$326$			390.432i			1.19764i
$327$			109.890i			0.336054i
$328$		−	349.289i		−	1.06491i
$329$	159.183			0.483838
$330$		0			0
$331$		−	368.904i		−	1.11451i	−0.830341	−	0.557256i	$-0.811854\pi$
$331$		−	368.904i		−	1.11451i	0.830341	−	0.557256i	$-0.188146\pi$
$332$			5.73375i			0.0172703i
$333$	72.0338			0.216318
$334$	123.901			0.370961
$335$		0			0
$336$		−	27.1136i		−	0.0806954i
$337$	−233.994			−0.694345			−0.347173	−	0.937801i	$-0.612858\pi$
$337$	−233.994			−0.694345			−0.347173	+	0.937801i	$0.612858\pi$
$338$	−220.176			−0.651409
$339$	−62.9762			−0.185771
$340$		0			0
$341$		−	327.986i		−	0.961836i
$342$	129.650	+	266.547i	0.379094	+	0.779377i
$343$			214.334i			0.624879i
$344$		−	29.4589i		−	0.0856362i
$345$		0			0
$346$	142.563			0.412031
$347$		−	377.811i		−	1.08879i	−0.838828	−	0.544396i	$-0.816759\pi$
$347$		−	377.811i		−	1.08879i	0.838828	−	0.544396i	$-0.183241\pi$
$348$			6.56498i			0.0188649i
$349$	−281.791			−0.807425			−0.403712	−	0.914886i	$-0.632280\pi$
$349$	−281.791			−0.807425			−0.403712	+	0.914886i	$0.632280\pi$
$350$		0			0
$351$	104.790			0.298547
$352$	−60.8936			−0.172993
$353$			92.5752i			0.262253i	0.991366	+	0.131126i	$0.0418593\pi$
$353$			92.5752i			0.262253i	−0.991366	+	0.131126i	$0.958141\pi$
$354$			150.696i			0.425694i
$355$		0			0
$356$		−	11.6262i		−	0.0326580i
$357$	12.4031			0.0347426
$358$			279.251i			0.780030i
$359$	−443.170			−1.23446			−0.617228	−	0.786785i	$-0.711744\pi$
$359$	−443.170			−1.23446			−0.617228	+	0.786785i	$0.711744\pi$
$360$		0			0
$361$	−222.863	+	283.995i	−0.617349	+	0.786690i
$362$		−	551.561i		−	1.52365i
$363$	−43.9512			−0.121078
$364$			7.69536i			0.0211411i
$365$		0			0
$366$	−20.3345			−0.0555587
$367$			576.621i			1.57117i	0.618751	+	0.785587i	$0.287639\pi$
$367$			576.621i			1.57117i	−0.618751	+	0.785587i	$0.712361\pi$
$368$		−	203.481i		−	0.552936i
$369$		−	345.158i		−	0.935388i
$370$		0			0
$371$		−	206.129i		−	0.555603i
$372$		−	15.3505i		−	0.0412648i
$373$	−291.370			−0.781153			−0.390577	−	0.920570i	$-0.627724\pi$
$373$	−291.370			−0.781153			−0.390577	+	0.920570i	$0.627724\pi$
$374$			99.4466i			0.265900i
$375$		0			0
$376$			577.475i			1.53584i
$377$			121.963i			0.323509i
$378$		−	63.2672i		−	0.167374i
$379$			208.089i			0.549048i	0.961580	+	0.274524i	$0.0885204\pi$
$379$			208.089i			0.549048i	−0.961580	+	0.274524i	$0.911480\pi$
$380$		0			0
$381$	−56.7943			−0.149066
$382$	−32.1254			−0.0840978
$383$	−19.9700			−0.0521410			−0.0260705	−	0.999660i	$-0.508299\pi$
$383$	−19.9700			−0.0521410			−0.0260705	+	0.999660i	$0.508299\pi$
$384$	85.3369			0.222231
$385$		0			0
$386$	−428.729			−1.11070
$387$		−	29.1105i		−	0.0752208i
$388$	−28.9340			−0.0745721
$389$	−389.050			−1.00013			−0.500065	−	0.865988i	$-0.666690\pi$
$389$	−389.050			−1.00013			−0.500065	+	0.865988i	$0.666690\pi$
$390$		0			0
$391$	93.0820			0.238061
$392$	−366.316			−0.934480
$393$	73.9083			0.188062
$394$		−	686.423i		−	1.74219i
$395$		0			0
$396$	−31.7277			−0.0801204
$397$		−	292.277i		−	0.736213i	−0.929784	−	0.368107i	$-0.880006\pi$
$397$		−	292.277i		−	0.736213i	0.929784	−	0.368107i	$-0.119994\pi$
$398$	144.545			0.363178
$399$	33.2303	−	16.1634i	0.0832839	−	0.0405098i
$400$		0			0
$401$			720.767i			1.79742i	0.438540	+	0.898712i	$0.355496\pi$
$401$			720.767i			1.79742i	−0.438540	+	0.898712i	$0.644504\pi$
$402$	−104.130			−0.259031
$403$		−	285.178i		−	0.707638i
$404$	−64.1425			−0.158769
$405$		0			0
$406$	73.6353			0.181368
$407$	72.0039			0.176914
$408$			44.9953i			0.110283i
$409$		−	310.253i		−	0.758564i	−0.925281	−	0.379282i	$-0.876171\pi$
$409$		−	310.253i		−	0.758564i	0.925281	−	0.379282i	$-0.123829\pi$
$410$		0			0
$411$		−	94.3334i		−	0.229522i
$412$	−45.1175			−0.109509
$413$	−220.448			−0.533772
$414$		−	227.699i		−	0.549998i
$415$		0			0
$416$	−52.9459			−0.127274
$417$	−136.408			−0.327117
$418$	129.596	+	266.436i	0.310039	+	0.637407i
$419$	−251.699			−0.600713			−0.300357	−	0.953827i	$-0.597106\pi$
$419$	−251.699			−0.600713			−0.300357	+	0.953827i	$0.597106\pi$
$420$		0			0
$421$			256.848i			0.610090i	0.952338	+	0.305045i	$0.0986715\pi$
$421$			256.848i			0.610090i	−0.952338	+	0.305045i	$0.901328\pi$
$422$			336.696i			0.797858i
$423$			570.645i			1.34904i
$424$	747.782			1.76364
$425$		0			0
$426$		−	4.05865i		−	0.00952735i
$427$		−	29.7466i		−	0.0696641i
$428$	40.7577			0.0952283
$429$	50.2328			0.117093
$430$		0			0
$431$		−	734.747i		−	1.70475i	−0.522931	−	0.852375i	$-0.675161\pi$
$431$		−	734.747i		−	1.70475i	0.522931	−	0.852375i	$-0.324839\pi$
$432$	202.680			0.469166
$433$	87.4830			0.202039			0.101020	−	0.994884i	$-0.467790\pi$
$433$	87.4830			0.202039			0.101020	+	0.994884i	$0.467790\pi$
$434$	−172.177			−0.396721
$435$		0			0
$436$		−	60.3238i		−	0.138357i
$437$	249.384	−	121.302i	0.570673	−	0.277579i
$438$		−	155.133i		−	0.354185i
$439$			340.926i			0.776598i	0.921534	+	0.388299i	$0.126937\pi$
$439$			340.926i			0.776598i	−0.921534	+	0.388299i	$0.873063\pi$
$440$		0			0
$441$	−361.984			−0.820825
$442$			86.4671i			0.195627i
$443$			573.891i			1.29546i	0.761868	+	0.647732i	$0.224282\pi$
$443$			573.891i			1.29546i	−0.761868	+	0.647732i	$0.775718\pi$
$444$	3.36995			0.00758999
$445$		0			0
$446$	87.0314			0.195138
$447$	−119.461			−0.267250
$448$			160.972i			0.359312i
$449$		−	650.271i		−	1.44826i	−0.689661	−	0.724132i	$-0.742240\pi$
$449$		−	650.271i		−	1.44826i	0.689661	−	0.724132i	$-0.257760\pi$
$450$		0			0
$451$		−	345.015i		−	0.765000i
$452$	34.5707			0.0764838
$453$		−	217.374i		−	0.479854i
$454$	−665.027			−1.46482
$455$		0			0
$456$	58.6368	+	120.551i	0.128589	+	0.264366i
$457$		−	743.048i		−	1.62593i	−0.582315	−	0.812963i	$-0.697853\pi$
$457$		−	743.048i		−	1.62593i	0.582315	−	0.812963i	$-0.302147\pi$
$458$	−29.2671			−0.0639020
$459$			92.7156i			0.201995i
$460$		0			0
$461$	−279.048			−0.605310			−0.302655	−	0.953100i	$-0.597873\pi$
$461$	−279.048			−0.605310			−0.302655	+	0.953100i	$0.597873\pi$
$462$		−	30.3282i		−	0.0656454i
$463$			399.848i			0.863603i	0.901969	+	0.431801i	$0.142122\pi$
$463$			399.848i			0.863603i	−0.901969	+	0.431801i	$0.857878\pi$
$464$			235.894i			0.508393i
$465$		0			0
$466$		−	208.513i		−	0.447453i
$467$			902.196i			1.93190i	0.258733	+	0.965949i	$0.416695\pi$
$467$			902.196i			1.93190i	−0.258733	+	0.965949i	$0.583305\pi$
$468$	−27.5867			−0.0589459
$469$		−	152.329i		−	0.324794i
$470$		0			0
$471$			150.654i			0.319860i
$472$		−	799.728i		−	1.69434i
$473$		−	29.0984i		−	0.0615188i
$474$		−	42.9467i		−	0.0906048i
$475$		0			0
$476$	−6.80867			−0.0143039
$477$	738.938			1.54914
$478$	436.111			0.912367
$479$	−138.417			−0.288971			−0.144485	−	0.989507i	$-0.546153\pi$
$479$	−138.417			−0.288971			−0.144485	+	0.989507i	$0.546153\pi$
$480$		0			0
$481$	62.6062			0.130158
$482$			47.4527i			0.0984495i
$483$	−28.3871			−0.0587725
$484$	24.1269			0.0498490
$485$		0			0
$486$	344.839			0.709546
$487$	533.362			1.09520			0.547600	−	0.836740i	$-0.315542\pi$
$487$	533.362			1.09520			0.547600	+	0.836740i	$0.315542\pi$
$488$	107.913			0.221133
$489$			174.492i			0.356834i
$490$		0			0
$491$	538.259			1.09625			0.548125	−	0.836396i	$-0.315342\pi$
$491$	538.259			1.09625			0.548125	+	0.836396i	$0.315342\pi$
$492$		−	16.1475i		−	0.0328201i
$493$	−107.910			−0.218883
$494$	112.682	+	231.662i	0.228101	+	0.468951i
$495$		0			0
$496$		−	551.578i		−	1.11205i
$497$	5.93726			0.0119462
$498$		−	19.6479i		−	0.0394537i
$499$	714.752			1.43237			0.716184	−	0.697911i	$-0.245887\pi$
$499$	714.752			1.43237			0.716184	+	0.697911i	$0.245887\pi$
$500$		0			0
$501$	55.3738			0.110527
$502$	−568.650			−1.13277
$503$		−	475.580i		−	0.945487i	−0.881200	−	0.472744i	$-0.843264\pi$
$503$		−	475.580i		−	0.945487i	0.881200	−	0.472744i	$-0.156736\pi$
$504$			161.015i			0.319475i
$505$		0			0
$506$		−	227.605i		−	0.449812i
$507$	−98.4013			−0.194085
$508$	31.1771			0.0613723
$509$			817.149i			1.60540i	0.596382	+	0.802701i	$0.296604\pi$
$509$			817.149i			1.60540i	−0.596382	+	0.802701i	$0.703396\pi$
$510$		0			0
$511$	226.939			0.444107
$512$	−570.404			−1.11407
$513$	120.825	+	248.403i	0.235526	+	0.484216i
$514$	−906.765			−1.76413
$515$		0			0
$516$		−	1.36187i		−	0.00263929i
$517$			570.409i			1.10330i
$518$		−	37.7986i		−	0.0729704i
$519$	63.7141			0.122763
$520$		0			0
$521$		−	56.3140i		−	0.108088i	−0.998539	−	0.0540441i	$-0.982789\pi$
$521$		−	56.3140i		−	0.108088i	0.998539	−	0.0540441i	$-0.0172112\pi$
$522$			263.971i			0.505691i
$523$	419.732			0.802547			0.401274	−	0.915958i	$-0.368568\pi$
$523$	419.732			0.802547			0.401274	+	0.915958i	$0.368568\pi$
$524$	−40.5719			−0.0774272
$525$		0			0
$526$			28.1462i			0.0535099i
$527$	252.319			0.478783
$528$	97.1578			0.184011
$529$	315.962			0.597282
$530$		0			0
$531$		−	790.270i		−	1.48827i
$532$	−18.2417	+	8.87289i	−0.0342889	+	0.0166784i
$533$		−	299.985i		−	0.562823i
$534$			39.8398i			0.0746065i
$535$		0			0
$536$	552.609			1.03099
$537$			124.803i			0.232407i
$538$			627.850i			1.16701i
$539$	−361.834			−0.671305
$540$		0			0
$541$	168.063			0.310652			0.155326	−	0.987863i	$-0.450357\pi$
$541$	168.063			0.310652			0.155326	+	0.987863i	$0.450357\pi$
$542$	−209.383			−0.386315
$543$		−	246.504i		−	0.453966i
$544$		−	46.8452i		−	0.0861125i
$545$		0			0
$546$		−	26.3698i		−	0.0482964i
$547$	974.400			1.78135			0.890676	−	0.454638i	$-0.150232\pi$
$547$	974.400			1.78135			0.890676	+	0.454638i	$0.150232\pi$
$548$			51.7842i			0.0944967i
$549$	106.637			0.194238
$550$		0			0
$551$	−289.110	+	140.625i	−0.524701	+	0.255218i
$552$		−	102.981i		−	0.186560i
$553$	62.8252			0.113608
$554$			461.846i			0.833657i
$555$		0			0
$556$	74.8808			0.134678
$557$			497.467i			0.893119i	0.894754	+	0.446560i	$0.147351\pi$
$557$			497.467i			0.893119i	−0.894754	+	0.446560i	$0.852649\pi$
$558$		−	617.228i		−	1.10614i
$559$		−	25.3005i		−	0.0452604i
$560$		0			0
$561$			44.4447i			0.0792241i
$562$			909.803i			1.61887i
$563$	550.233			0.977323			0.488661	−	0.872473i	$-0.337485\pi$
$563$	550.233			0.977323			0.488661	+	0.872473i	$0.337485\pi$
$564$			26.6965i			0.0473341i
$565$		0			0
$566$		−	961.033i		−	1.69794i
$567$			144.396i			0.254666i
$568$			21.5389i			0.0379205i
$569$		−	862.576i		−	1.51595i	−0.652283	−	0.757975i	$-0.726189\pi$
$569$		−	862.576i		−	1.51595i	0.652283	−	0.757975i	$-0.273811\pi$
$570$		0			0
$571$	372.995			0.653230			0.326615	−	0.945157i	$-0.394092\pi$
$571$	372.995			0.653230			0.326615	+	0.945157i	$0.394092\pi$
$572$	−27.5752			−0.0482084
$573$	−14.3575			−0.0250567
$574$	−181.116			−0.315534
$575$		0			0
$576$	−577.058			−1.00184
$577$		−	796.258i		−	1.38000i	−0.723811	−	0.689999i	$-0.757611\pi$
$577$		−	796.258i		−	1.38000i	0.723811	−	0.689999i	$-0.242389\pi$
$578$	467.131			0.808185
$579$	−191.608			−0.330928
$580$		0			0
$581$	28.7423			0.0494704
$582$	99.1486			0.170358
$583$	738.632			1.26695
$584$			823.277i			1.40972i
$585$		0			0
$586$	−863.744			−1.47397
$587$		−	469.946i		−	0.800590i	−0.916386	−	0.400295i	$-0.868908\pi$
$587$		−	469.946i		−	0.800590i	0.916386	−	0.400295i	$-0.131092\pi$
$588$	−16.9347			−0.0288004
$589$	676.009	−	328.815i	1.14772	−	0.558260i
$590$		0			0
$591$		−	306.777i		−	0.519080i
$592$	121.090			0.204544
$593$			242.100i			0.408263i	0.978943	+	0.204131i	$0.0654370\pi$
$593$			242.100i			0.408263i	−0.978943	+	0.204131i	$0.934563\pi$
$594$	226.709			0.381665
$595$		0			0
$596$	65.5777			0.110030
$597$	64.6001			0.108208
$598$		−	197.898i		−	0.330934i
$599$		−	209.810i		−	0.350268i	−0.984545	−	0.175134i	$-0.943964\pi$
$599$		−	209.810i		−	0.350268i	0.984545	−	0.175134i	$-0.0560358\pi$
$600$		0			0
$601$			782.856i			1.30259i	0.758825	+	0.651294i	$0.225774\pi$
$601$			782.856i			1.30259i	−0.758825	+	0.651294i	$0.774226\pi$
$602$	−15.2753			−0.0253742
$603$	546.074			0.905595
$604$			119.327i			0.197561i
$605$		0			0
$606$	219.798			0.362703
$607$	110.135			0.181442			0.0907210	−	0.995876i	$-0.471083\pi$
$607$	110.135			0.181442			0.0907210	+	0.995876i	$0.471083\pi$
$608$	−61.0476	−	125.507i	−0.100407	−	0.206426i
$609$	32.9091			0.0540379
$610$		0			0
$611$			495.960i			0.811719i
$612$		−	24.4080i		−	0.0398823i
$613$			793.645i			1.29469i	0.762197	+	0.647345i	$0.224121\pi$
$613$			793.645i			1.29469i	−0.762197	+	0.647345i	$0.775879\pi$
$614$	1054.77			1.71786
$615$		0			0
$616$			160.949i			0.261280i
$617$			243.961i			0.395398i	0.980263	+	0.197699i	$0.0633469\pi$
$617$			243.961i			0.395398i	−0.980263	+	0.197699i	$0.936653\pi$
$618$	154.605			0.250170
$619$	1163.97			1.88041			0.940205	−	0.340610i	$-0.110633\pi$
$619$	1163.97			1.88041			0.940205	+	0.340610i	$0.110633\pi$
$620$		0			0
$621$		−	212.199i		−	0.341706i
$622$	−119.272			−0.191756
$623$	−58.2803			−0.0935479
$624$	84.4770			0.135380
$625$		0			0
$626$		−	348.488i		−	0.556691i
$627$	57.9193	+	119.076i	0.0923752	+	0.189914i
$628$		−	82.7014i		−	0.131690i
$629$			55.3924i			0.0880642i
$630$		0			0
$631$	1244.64			1.97249			0.986244	−	0.165297i	$-0.0528581\pi$
$631$	1244.64			1.97249			0.986244	+	0.165297i	$0.0528581\pi$
$632$			227.914i			0.360623i
$633$			150.476i			0.237719i
$634$	−682.335			−1.07624
$635$		0			0
$636$	34.5697			0.0543549
$637$	−314.608			−0.493890
$638$			263.861i			0.413576i
$639$			21.2841i			0.0333085i
$640$		0			0
$641$		−	123.441i		−	0.192575i	−0.995354	−	0.0962877i	$-0.969303\pi$
$641$		−	123.441i		−	0.192575i	0.995354	−	0.0962877i	$-0.0306969\pi$
$642$	−139.665			−0.217547
$643$			97.0311i			0.150904i	0.997149	+	0.0754519i	$0.0240399\pi$
$643$			97.0311i			0.150904i	−0.997149	+	0.0754519i	$0.975960\pi$
$644$	15.5831			0.0241973
$645$		0			0
$646$	−204.969	+	99.6981i	−0.317289	+	0.154331i
$647$		−	988.138i		−	1.52726i	−0.645653	−	0.763631i	$-0.723415\pi$
$647$		−	988.138i		−	1.52726i	0.645653	−	0.763631i	$-0.276585\pi$
$648$	−523.831			−0.808381
$649$		−	789.942i		−	1.21717i
$650$		0			0
$651$	−76.9494			−0.118202
$652$		−	95.7871i		−	0.146913i
$653$		−	1068.01i		−	1.63554i	−0.575546	−	0.817770i	$-0.695210\pi$
$653$		−	1068.01i		−	1.63554i	0.575546	−	0.817770i	$-0.304790\pi$
$654$			206.712i			0.316074i
$655$		0			0
$656$		−	580.215i		−	0.884474i
$657$			813.540i			1.23827i
$658$	299.437			0.455072
$659$			515.122i			0.781672i	0.920460	+	0.390836i	$0.127814\pi$
$659$			515.122i			0.781672i	−0.920460	+	0.390836i	$0.872186\pi$
$660$		0			0
$661$			778.350i			1.17753i	0.808303	+	0.588767i	$0.200387\pi$
$661$			778.350i			1.17753i	−0.808303	+	0.588767i	$0.799613\pi$
$662$		−	693.941i		−	1.04825i
$663$			38.6439i			0.0582864i
$664$			104.270i			0.157033i
$665$		0			0
$666$	135.502			0.203457
$667$	246.974			0.370276
$668$	−30.3974			−0.0455050
$669$	38.8961			0.0581406
$670$		0			0
$671$	106.593			0.158856
$672$			14.2864i			0.0212595i
$673$	781.412			1.16109			0.580544	−	0.814229i	$-0.302840\pi$
$673$	781.412			1.16109			0.580544	+	0.814229i	$0.302840\pi$
$674$	−440.164			−0.653063
$675$		0			0
$676$	54.0172			0.0799072
$677$	−848.810			−1.25378			−0.626891	−	0.779107i	$-0.715673\pi$
$677$	−848.810			−1.25378			−0.626891	+	0.779107i	$0.715673\pi$
$678$	−118.464			−0.174726
$679$			145.041i			0.213610i
$680$		0			0
$681$	−297.214			−0.436438
$682$		−	616.971i		−	0.904650i
$683$	238.270			0.348859			0.174429	−	0.984670i	$-0.444192\pi$
$683$	238.270			0.348859			0.174429	+	0.984670i	$0.444192\pi$
$684$	−31.8079	−	65.3936i	−0.0465028	−	0.0956047i
$685$		0			0
$686$			403.181i			0.587727i
$687$	−13.0801			−0.0190394
$688$		−	48.9350i		−	0.0711265i
$689$	642.228			0.932116
$690$		0			0
$691$	147.763			0.213840			0.106920	−	0.994268i	$-0.465901\pi$
$691$	147.763			0.213840			0.106920	+	0.994268i	$0.465901\pi$
$692$	−34.9758			−0.0505430
$693$			159.045i			0.229502i
$694$		−	710.696i		−	1.02406i
$695$		0			0
$696$			119.386i			0.171531i
$697$	265.419			0.380802
$698$	−530.075			−0.759419
$699$		−	93.1887i		−	0.133317i
$700$		0			0
$701$	742.215			1.05879			0.529397	−	0.848374i	$-0.322418\pi$
$701$	742.215			1.05879			0.529397	+	0.848374i	$0.322418\pi$
$702$	197.120			0.280797
$703$	72.1860	+	148.407i	0.102683	+	0.211105i
$704$	−576.819			−0.819345
$705$		0			0
$706$			174.142i			0.246660i
$707$			321.535i			0.454788i
$708$		−	36.9711i		−	0.0522191i
$709$	233.821			0.329790			0.164895	−	0.986311i	$-0.447271\pi$
$709$	233.821			0.329790			0.164895	+	0.986311i	$0.447271\pi$
$710$		0			0
$711$			225.218i			0.316763i
$712$		−	211.426i		−	0.296947i
$713$	−577.485			−0.809936
$714$	23.3314			0.0326770
$715$		0			0
$716$		−	68.5103i		−	0.0956848i
$717$	194.907			0.271837
$718$	−833.642			−1.16106
$719$	−544.422			−0.757193			−0.378596	−	0.925562i	$-0.623593\pi$
$719$	−544.422			−0.757193			−0.378596	+	0.925562i	$0.623593\pi$
$720$		0			0
$721$			226.166i			0.313684i
$722$	−419.225	+	534.220i	−0.580644	+	0.739917i
$723$			21.2076i			0.0293327i
$724$			135.318i			0.186903i
$725$		0			0
$726$	−82.6762			−0.113879
$727$			239.420i			0.329326i	0.986350	+	0.164663i	$0.0526537\pi$
$727$			239.420i			0.329326i	−0.986350	+	0.164663i	$0.947346\pi$
$728$			139.942i			0.192228i
$729$	−407.634			−0.559169
$730$		0			0
$731$	22.3853			0.0306228
$732$	4.98878			0.00681528
$733$		−	322.159i		−	0.439507i	−0.975555	−	0.219754i	$-0.929475\pi$
$733$		−	322.159i		−	0.439507i	0.975555	−	0.219754i	$-0.0705253\pi$
$734$			1084.68i			1.47776i
$735$		0			0
$736$			107.215i			0.145673i
$737$	545.847			0.740634
$738$		−	649.274i		−	0.879775i
$739$	−1055.17			−1.42784			−0.713921	−	0.700227i	$-0.753082\pi$
$739$	−1055.17			−1.42784			−0.713921	+	0.700227i	$0.753082\pi$
$740$		0			0
$741$	50.3598	+	103.534i	0.0679620	+	0.139722i
$742$		−	387.746i		−	0.522569i
$743$	485.597			0.653562			0.326781	−	0.945100i	$-0.394036\pi$
$743$	485.597			0.653562			0.326781	+	0.945100i	$0.394036\pi$
$744$		−	279.153i		−	0.375206i
$745$		0			0
$746$	−548.094			−0.734710
$747$			103.037i			0.137934i
$748$		−	24.3979i		−	0.0326175i
$749$		−	204.311i		−	0.272779i
$750$		0			0
$751$		−	912.769i		−	1.21540i	−0.794165	−	0.607702i	$-0.792091\pi$
$751$		−	912.769i		−	1.21540i	0.794165	−	0.607702i	$-0.207909\pi$
$752$			959.262i			1.27561i
$753$	−254.141			−0.337505
$754$			229.423i			0.304274i
$755$		0			0
$756$			15.5217i			0.0205314i
$757$		−	737.208i		−	0.973855i	−0.873442	−	0.486928i	$-0.838118\pi$
$757$		−	737.208i		−	0.973855i	0.873442	−	0.486928i	$-0.161882\pi$
$758$			391.435i			0.516405i
$759$		−	101.721i		−	0.134020i
$760$		0			0
$761$	−990.845			−1.30203			−0.651015	−	0.759065i	$-0.725656\pi$
$761$	−990.845			−1.30203			−0.651015	+	0.759065i	$0.725656\pi$
$762$	−106.835			−0.140204
$763$	−302.392			−0.396320
$764$	7.88152			0.0103161
$765$		0			0
$766$	−37.5654			−0.0490410
$767$		−	686.841i		−	0.895490i
$768$	−73.4627			−0.0956546
$769$	331.509			0.431091			0.215545	−	0.976494i	$-0.430847\pi$
$769$	331.509			0.431091			0.215545	+	0.976494i	$0.430847\pi$
$770$		0			0
$771$	−405.252			−0.525618
$772$	105.183			0.136247
$773$	−1418.41			−1.83494			−0.917468	−	0.397809i	$-0.869771\pi$
$773$	−1418.41			−1.83494			−0.917468	+	0.397809i	$0.869771\pi$
$774$		−	54.7594i		−	0.0707486i
$775$		0			0
$776$	−526.172			−0.678056
$777$		−	16.8930i		−	0.0217413i
$778$	−731.839			−0.940667
$779$	711.107	−	345.887i	0.912846	−	0.444015i
$780$		0			0
$781$			21.2753i			0.0272411i
$782$	175.096			0.223907
$783$			246.002i			0.314179i
$784$	−608.499			−0.776147
$785$		0			0
$786$	139.028			0.176881
$787$	268.008			0.340543			0.170272	−	0.985397i	$-0.445535\pi$
$787$	268.008			0.340543			0.170272	+	0.985397i	$0.445535\pi$
$788$			168.405i			0.213711i
$789$			12.5791i			0.0159431i
$790$		0			0
$791$		−	173.297i		−	0.219086i
$792$	−576.976			−0.728505
$793$	92.6804			0.116873
$794$		−	549.799i		−	0.692442i
$795$		0			0
$796$	−35.4621			−0.0445504
$797$	−106.821			−0.134029			−0.0670147	−	0.997752i	$-0.521347\pi$
$797$	−106.821			−0.134029			−0.0670147	+	0.997752i	$0.521347\pi$
$798$	62.5091	−	30.4049i	0.0783322	−	0.0381013i
$799$	−438.813			−0.549203
$800$		0			0
$801$		−	208.926i		−	0.260831i
$802$			1355.83i			1.69056i
$803$			813.203i			1.01271i
$804$	25.5469			0.0317748
$805$		0			0
$806$		−	536.446i		−	0.665566i
$807$			280.599i			0.347706i
$808$	−1166.45			−1.44362
$809$	−235.725			−0.291378			−0.145689	−	0.989330i	$-0.546540\pi$
$809$	−235.725			−0.291378			−0.145689	+	0.989330i	$0.546540\pi$
$810$		0			0
$811$			953.232i			1.17538i	0.809087	+	0.587689i	$0.199962\pi$
$811$			953.232i			1.17538i	−0.809087	+	0.587689i	$0.800038\pi$
$812$	−18.0654			−0.0222480
$813$	−93.5774			−0.115101
$814$	135.446			0.166395
$815$		0			0
$816$			74.7431i			0.0915970i
$817$	59.9744	−	29.1720i	0.0734081	−	0.0357062i
$818$		−	583.614i		−	0.713464i
$819$			138.287i			0.168849i
$820$		0			0
$821$	−1229.40			−1.49745			−0.748723	−	0.662883i	$-0.769333\pi$
$821$	−1229.40			−1.49745			−0.748723	+	0.662883i	$0.769333\pi$
$822$		−	177.450i		−	0.215876i
$823$			625.946i			0.760566i	0.924870	+	0.380283i	$0.124173\pi$
$823$			625.946i			0.760566i	−0.924870	+	0.380283i	$0.875827\pi$
$824$	−820.474			−0.995721
$825$		0			0
$826$	−414.682			−0.502036
$827$	573.760			0.693785			0.346892	−	0.937905i	$-0.387237\pi$
$827$	573.760			0.693785			0.346892	+	0.937905i	$0.387237\pi$
$828$			55.8629i			0.0674672i
$829$			651.345i			0.785700i	0.919603	+	0.392850i	$0.128511\pi$
$829$			651.345i			0.785700i	−0.919603	+	0.392850i	$0.871489\pi$
$830$		0			0
$831$			206.408i			0.248385i
$832$	−501.534			−0.602805
$833$		−	278.357i		−	0.334162i
$834$	−256.595			−0.307668
$835$		0			0
$836$	−31.7947	−	65.3665i	−0.0380319	−	0.0781896i
$837$		−	575.212i		−	0.687230i
$838$	−473.468			−0.564998
$839$		−	737.524i		−	0.879051i	−0.898230	−	0.439525i	$-0.855147\pi$
$839$		−	737.524i		−	0.879051i	0.898230	−	0.439525i	$-0.144853\pi$
$840$		0			0
$841$	554.684			0.659553
$842$			483.154i			0.573817i
$843$			406.610i			0.482336i
$844$		−	82.6037i		−	0.0978717i
$845$		0			0
$846$			1073.44i			1.26884i
$847$		−	120.944i		−	0.142791i
$848$	1242.16			1.46482
$849$		−	429.505i		−	0.505895i
$850$		0			0
$851$		−	126.777i		−	0.148974i
$852$			0.995734i			0.00116870i
$853$		−	1181.14i		−	1.38469i	−0.721567	−	0.692345i	$-0.756578\pi$
$853$		−	1181.14i		−	1.38469i	0.721567	−	0.692345i	$-0.243422\pi$
$854$		−	55.9560i		−	0.0655223i
$855$		0			0
$856$	741.189			0.865875
$857$	−626.333			−0.730844			−0.365422	−	0.930842i	$-0.619075\pi$
$857$	−626.333			−0.730844			−0.365422	+	0.930842i	$0.619075\pi$
$858$	94.4924			0.110131
$859$	191.158			0.222536			0.111268	−	0.993790i	$-0.464509\pi$
$859$	191.158			0.222536			0.111268	+	0.993790i	$0.464509\pi$
$860$		0			0
$861$	−80.9446			−0.0940123
$862$		−	1382.13i		−	1.60339i
$863$	−831.146			−0.963089			−0.481544	−	0.876422i	$-0.659924\pi$
$863$	−831.146			−0.963089			−0.481544	+	0.876422i	$0.659924\pi$
$864$	−106.793			−0.123603
$865$		0			0
$866$	164.563			0.190027
$867$	208.770			0.240796
$868$	42.2413			0.0486651
$869$			225.125i			0.259062i
$870$		0			0
$871$	474.605			0.544896
$872$		−	1097.00i		−	1.25803i
$873$	−519.949			−0.595589
$874$	469.114	−	228.180i	0.536744	−	0.261076i
$875$		0			0
$876$			38.0598i			0.0434472i
$877$	−185.869			−0.211937			−0.105968	−	0.994369i	$-0.533794\pi$
$877$	−185.869			−0.211937			−0.105968	+	0.994369i	$0.533794\pi$
$878$			641.313i			0.730425i
$879$	−386.025			−0.439163
$880$		0			0
$881$	−397.804			−0.451537			−0.225768	−	0.974181i	$-0.572489\pi$
$881$	−397.804			−0.451537			−0.225768	+	0.974181i	$0.572489\pi$
$882$	−680.924			−0.772023
$883$		−	978.520i		−	1.10818i	−0.832458	−	0.554088i	$-0.813067\pi$
$883$		−	978.520i		−	1.10818i	0.832458	−	0.554088i	$-0.186933\pi$
$884$		−	21.2135i		−	0.0239972i
$885$		0			0
$886$			1079.54i			1.21844i
$887$	−128.464			−0.144830			−0.0724151	−	0.997375i	$-0.523071\pi$
$887$	−128.464			−0.144830			−0.0724151	+	0.997375i	$0.523071\pi$
$888$	61.2834			0.0690129
$889$		−	156.285i		−	0.175799i
$890$		0			0
$891$	−517.421			−0.580719
$892$	−21.3519			−0.0239372
$893$	−1175.66	+	571.851i	−1.31653	+	0.640371i
$894$	−224.716			−0.251360
$895$		0			0
$896$			234.828i			0.262085i
$897$		−	88.4448i		−	0.0986007i
$898$		−	1223.22i		−	1.36216i
$899$	669.476			0.744689
$900$		0			0
$901$			568.227i			0.630662i
$902$		−	649.004i		−	0.719517i
$903$	−6.82682			−0.00756016
$904$	628.677			0.695439
$905$		0			0
$906$		−	408.900i		−	0.451324i
$907$	−885.139			−0.975897			−0.487949	−	0.872872i	$-0.662255\pi$
$907$	−885.139			−0.975897			−0.487949	+	0.872872i	$0.662255\pi$
$908$	163.155			0.179686
$909$	−1152.65			−1.26804
$910$		0			0
$911$			1542.51i			1.69320i	0.532228	+	0.846601i	$0.321355\pi$
$911$			1542.51i			1.69320i	−0.532228	+	0.846601i	$0.678645\pi$
$912$	97.4034	+	200.251i	0.106802	+	0.219573i
$913$			102.994i			0.112808i
$914$		−	1397.74i		−	1.52926i
$915$		0			0
$916$	7.18028			0.00783874
$917$			203.380i			0.221788i
$918$			174.406i			0.189985i
$919$	1242.28			1.35178			0.675889	−	0.737003i	$-0.263760\pi$
$919$	1242.28			1.35178			0.675889	+	0.737003i	$0.263760\pi$
$920$		0			0
$921$	471.397			0.511831
$922$	−524.915			−0.569322
$923$			18.4985i			0.0200417i
$924$			7.44060i			0.00805260i
$925$		0			0
$926$			752.151i			0.812258i
$927$	−810.770			−0.874617
$928$		−	124.294i		−	0.133938i
$929$	−1276.20			−1.37373			−0.686866	−	0.726785i	$-0.741014\pi$
$929$	−1276.20			−1.37373			−0.686866	+	0.726785i	$0.741014\pi$
$930$		0			0
$931$	−362.748	−	745.772i	−0.389633	−	0.801044i
$932$			51.1558i			0.0548882i
$933$	−53.3051			−0.0571330
$934$			1697.11i			1.81704i
$935$		0			0
$936$	−501.670			−0.535973
$937$			1537.08i			1.64042i	0.572060	+	0.820212i	$0.306145\pi$
$937$			1537.08i			1.64042i	−0.572060	+	0.820212i	$0.693855\pi$
$938$		−	286.544i		−	0.305484i
$939$		−	155.747i		−	0.165864i
$940$		0			0
$941$			571.078i			0.606884i	0.952850	+	0.303442i	$0.0981359\pi$
$941$			571.078i			0.606884i	−0.952850	+	0.303442i	$0.901864\pi$
$942$			283.394i			0.300843i
$943$	−607.467			−0.644186
$944$		−	1328.45i		−	1.40726i
$945$		0			0
$946$		−	54.7367i		−	0.0578612i
$947$			578.957i			0.611359i	0.952135	+	0.305679i	$0.0988836\pi$
$947$			578.957i			0.611359i	−0.952135	+	0.305679i	$0.901116\pi$
$948$			10.5364i			0.0111143i
$949$			707.066i			0.745064i
$950$		0			0
$951$	−304.949			−0.320662
$952$	−123.817			−0.130060
$953$	−621.530			−0.652182			−0.326091	−	0.945338i	$-0.605732\pi$
$953$	−621.530			−0.652182			−0.326091	+	0.945338i	$0.605732\pi$
$954$	1390.01			1.45703
$955$		0			0
$956$	−106.994			−0.111918
$957$			117.925i			0.123224i
$958$	−260.375			−0.271790
$959$	259.585			0.270683
$960$		0			0
$961$	−604.396			−0.628924
$962$	117.768			0.122420
$963$	732.423			0.760564
$964$		−	11.6419i		−	0.0120766i
$965$		0			0
$966$	−53.3988			−0.0552782
$967$		−	1198.21i		−	1.23910i	−0.784955	−	0.619552i	$-0.787314\pi$
$967$		−	1198.21i		−	1.23910i	0.784955	−	0.619552i	$-0.212686\pi$
$968$	438.754			0.453259
$969$	−91.6046	+	44.5571i	−0.0945352	+	0.0459826i
$970$		0			0
$971$			448.776i			0.462179i	0.972932	+	0.231090i	$0.0742290\pi$
$971$			448.776i			0.462179i	−0.972932	+	0.231090i	$0.925771\pi$
$972$	−84.6016			−0.0870387
$973$		−	375.364i		−	0.385780i
$974$	1003.30			1.03008
$975$		0			0
$976$	179.258			0.183666
$977$	369.963			0.378673			0.189336	−	0.981912i	$-0.439366\pi$
$977$	369.963			0.378673			0.189336	+	0.981912i	$0.439366\pi$
$978$			328.235i			0.335619i
$979$		−	208.839i		−	0.213319i
$980$		0			0
$981$		−	1084.03i		−	1.10502i
$982$	1012.51			1.03107
$983$	972.897			0.989723			0.494861	−	0.868972i	$-0.335219\pi$
$983$	972.897			0.989723			0.494861	+	0.868972i	$0.335219\pi$
$984$		−	293.646i		−	0.298421i
$985$		0			0
$986$	−202.988			−0.205870
$987$	133.825			0.135587
$988$	−27.6449	−	56.8350i	−0.0279807	−	0.0575253i
$989$	−51.2335			−0.0518033
$990$		0			0
$991$		−	1332.05i		−	1.34415i	−0.740485	−	0.672073i	$-0.765404\pi$
$991$		−	1332.05i		−	1.34415i	0.740485	−	0.672073i	$-0.234596\pi$
$992$			290.630i			0.292974i
$993$		−	310.136i		−	0.312323i
$994$	11.1685			0.0112359
$995$		0			0
$996$			4.82035i			0.00483971i
$997$		−	719.460i		−	0.721625i	−0.932638	−	0.360813i	$-0.882499\pi$
$997$		−	719.460i		−	0.721625i	0.932638	−	0.360813i	$-0.117501\pi$
$998$	1344.51			1.34721
$999$	126.278			0.126405

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.3.d.c.474.17		24
5.2	odd	4		475.3.c.g.151.9		12
5.3	odd	4		95.3.c.a.56.4	✓	12
5.4	even	2	inner	475.3.d.c.474.8		24
15.8	even	4		855.3.e.a.721.9		12
19.18	odd	2	inner	475.3.d.c.474.7		24
20.3	even	4		1520.3.h.a.721.6		12
95.18	even	4		95.3.c.a.56.9	yes	12
95.37	even	4		475.3.c.g.151.4		12
95.94	odd	2	inner	475.3.d.c.474.18		24
285.113	odd	4		855.3.e.a.721.4		12
380.303	odd	4		1520.3.h.a.721.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.3.c.a.56.4	✓	12	5.3	odd	4
95.3.c.a.56.9	yes	12	95.18	even	4
475.3.c.g.151.4		12	95.37	even	4
475.3.c.g.151.9		12	5.2	odd	4
475.3.d.c.474.7		24	19.18	odd	2	inner
475.3.d.c.474.8		24	5.4	even	2	inner
475.3.d.c.474.17		24	1.1	even	1	trivial
475.3.d.c.474.18		24	95.94	odd	2	inner
855.3.e.a.721.4		12	285.113	odd	4
855.3.e.a.721.9		12	15.8	even	4
1520.3.h.a.721.6		12	20.3	even	4
1520.3.h.a.721.7		12	380.303	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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	475.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.88109 q^{2} +0.840697 q^{3} -0.461500 q^{4} +1.58143 q^{6} +2.31342i q^{7} -8.39248 q^{8} -8.29323 q^{9} +O(q^{10})\)	\(q+1.88109 q^{2} +0.840697 q^{3} -0.461500 q^{4} +1.58143 q^{6} +2.31342i q^{7} -8.39248 q^{8} -8.29323 q^{9} -8.28979 q^{11} -0.387981 q^{12} -7.20783 q^{13} +4.35174i q^{14} -13.9410 q^{16} -6.37730i q^{17} -15.6003 q^{18} +(-8.31075 - 17.0860i) q^{19} +1.94488i q^{21} -15.5938 q^{22} +14.5958i q^{23} -7.05554 q^{24} -13.5586 q^{26} -14.5384 q^{27} -1.06764i q^{28} -16.9209i q^{29} +39.5651i q^{31} +7.34562 q^{32} -6.96920 q^{33} -11.9963i q^{34} +3.82732 q^{36} -8.68586 q^{37} +(-15.6333 - 32.1403i) q^{38} -6.05960 q^{39} +41.6193i q^{41} +3.65850i q^{42} +3.51015i q^{43} +3.82573 q^{44} +27.4560i q^{46} -68.8086i q^{47} -11.7202 q^{48} +43.6481 q^{49} -5.36138i q^{51} +3.32641 q^{52} -89.1014 q^{53} -27.3480 q^{54} -19.4153i q^{56} +(-6.98682 - 14.3642i) q^{57} -31.8297i q^{58} +95.2910i q^{59} -12.8583 q^{61} +74.4255i q^{62} -19.1857i q^{63} +69.5818 q^{64} -13.1097 q^{66} -65.8457 q^{67} +2.94312i q^{68} +12.2707i q^{69} -2.56645i q^{71} +69.6008 q^{72} -98.0969i q^{73} -16.3389 q^{74} +(3.83541 + 7.88518i) q^{76} -19.1777i q^{77} -11.3987 q^{78} -27.1569i q^{79} +62.4167 q^{81} +78.2896i q^{82} -12.4242i q^{83} -0.897562i q^{84} +6.60290i q^{86} -14.2253i q^{87} +69.5719 q^{88} +25.1923i q^{89} -16.6747i q^{91} -6.73596i q^{92} +33.2623i q^{93} -129.435i q^{94} +6.17544 q^{96} +62.6956 q^{97} +82.1060 q^{98} +68.7491 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} - 56 q^{6} + 96 q^{9}+O(q^{10}) \) 24 * q + 24 * q^4 - 56 * q^6 + 96 * q^9	\( 24 q + 24 q^{4} - 56 q^{6} + 96 q^{9} + 64 q^{11} - 88 q^{16} - 16 q^{19} - 200 q^{24} + 216 q^{26} - 160 q^{36} - 152 q^{39} + 512 q^{44} - 144 q^{49} + 152 q^{54} - 592 q^{61} - 376 q^{64} + 304 q^{66} - 272 q^{74} + 496 q^{76} - 744 q^{81} - 88 q^{96} + 624 q^{99}+O(q^{100}) \) 24 * q + 24 * q^4 - 56 * q^6 + 96 * q^9 + 64 * q^11 - 88 * q^16 - 16 * q^19 - 200 * q^24 + 216 * q^26 - 160 * q^36 - 152 * q^39 + 512 * q^44 - 144 * q^49 + 152 * q^54 - 592 * q^61 - 376 * q^64 + 304 * q^66 - 272 * q^74 + 496 * q^76 - 744 * q^81 - 88 * q^96 + 624 * q^99

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