LMFDB - Embedded newform 425.2.e.d.251.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(251,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.251"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.e (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 24x^{10} + 188x^{8} + 572x^{6} + 776x^{4} + 464x^{2} + 100 $ x^12 + 24x^10 + 188x^8 + 572x^6 + 776x^4 + 464*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.2
Root			$-0.803330i$ of defining polynomial
Character	$\chi$	$=$	425.251
Dual form			425.2.e.d.276.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.80333i q^{2} +(0.397180 + 0.397180i) q^{3} -1.25200 q^{4} +(0.716248 - 0.716248i) q^{6} +(-2.20051 + 2.20051i) q^{7} -1.34889i q^{8} -2.68450i q^{9} +(3.96825 - 3.96825i) q^{11} +(-0.497270 - 0.497270i) q^{12} -1.24880 q^{13} +(3.96825 + 3.96825i) q^{14} -4.93650 q^{16} +(0.397180 - 4.10393i) q^{17} -4.84103 q^{18} -4.00000i q^{19} -1.74800 q^{21} +(-7.15606 - 7.15606i) q^{22} +(1.64598 - 1.64598i) q^{23} +(0.535753 - 0.535753i) q^{24} +2.25200i q^{26} +(2.25777 - 2.25777i) q^{27} +(2.75504 - 2.75504i) q^{28} +(4.68450 + 4.68450i) q^{29} +(3.22025 + 3.22025i) q^{31} +6.20435i q^{32} +3.15222 q^{33} +(-7.40074 - 0.716248i) q^{34} +3.36099i q^{36} +(1.34889 + 1.34889i) q^{37} -7.21332 q^{38} +(-0.495999 - 0.495999i) q^{39} +(-4.18850 + 4.18850i) q^{41} +3.15222i q^{42} +2.04316i q^{43} +(-4.96825 + 4.96825i) q^{44} +(-2.96825 - 2.96825i) q^{46} -4.85546 q^{47} +(-1.96068 - 1.96068i) q^{48} -2.68450i q^{49} +(1.78775 - 1.47225i) q^{51} +1.56350 q^{52} +9.11674i q^{53} +(-4.07151 - 4.07151i) q^{54} +(2.96825 + 2.96825i) q^{56} +(1.58872 - 1.58872i) q^{57} +(8.44769 - 8.44769i) q^{58} +6.00000i q^{59} +(-4.00000 + 4.00000i) q^{61} +(5.80717 - 5.80717i) q^{62} +(5.90726 + 5.90726i) q^{63} +1.31550 q^{64} -5.68450i q^{66} +8.46212 q^{67} +(-0.497270 + 5.13812i) q^{68} +1.30750 q^{69} +(-6.22025 - 6.22025i) q^{71} -3.62109 q^{72} +(1.10906 + 1.10906i) q^{73} +(2.43250 - 2.43250i) q^{74} +5.00800i q^{76} +17.4643i q^{77} +(-0.894450 + 0.894450i) q^{78} +(3.47225 - 3.47225i) q^{79} -6.26000 q^{81} +(7.55324 + 7.55324i) q^{82} -3.94658i q^{83} +2.18850 q^{84} +3.68450 q^{86} +3.72118i q^{87} +(-5.35273 - 5.35273i) q^{88} +10.6130 q^{89} +(2.74800 - 2.74800i) q^{91} +(-2.06077 + 2.06077i) q^{92} +2.55804i q^{93} +8.75600i q^{94} +(-2.46425 + 2.46425i) q^{96} +(8.76239 + 8.76239i) q^{97} -4.84103 q^{98} +(-10.6527 - 10.6527i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 20 q^{6} + 16 q^{11} + 16 q^{14} + 4 q^{16} - 24 q^{21} + 32 q^{24} - 4 q^{29} + 4 q^{31} - 12 q^{39} + 16 q^{41} - 28 q^{44} - 4 q^{46} + 44 q^{51} - 100 q^{54} + 4 q^{56} - 48 q^{61}+ \cdots - 36 q^{99}+O(q^{100}) $ 12 * q - 12 * q^4 - 20 * q^6 + 16 * q^11 + 16 * q^14 + 4 * q^16 - 24 * q^21 + 32 * q^24 - 4 * q^29 + 4 * q^31 - 12 * q^39 + 16 * q^41 - 28 * q^44 - 4 * q^46 + 44 * q^51 - 100 * q^54 + 4 * q^56 - 48 * q^61 + 76 * q^64 + 88 * q^69 - 40 * q^71 - 28 * q^74 + 4 * q^79 - 60 * q^81 - 40 * q^84 - 16 * q^86 + 16 * q^89 + 36 * q^91 - 4 * q^96 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	1.80333i		−	1.27515i	−0.770389	−	0.637574i	$-0.779938\pi$
$2$		−	1.80333i		−	1.27515i	0.770389	−	0.637574i	$-0.220062\pi$
$3$	0.397180	+	0.397180i	0.229312	+	0.229312i	0.812405	−	0.583093i	$-0.198158\pi$
$3$	0.397180	+	0.397180i	0.229312	+	0.229312i	−0.583093	+	0.812405i	$0.698158\pi$
$4$	−1.25200			−0.626000
$5$		0			0
$5$		0			0
$6$	0.716248	−	0.716248i	0.292407	−	0.292407i
$7$	−2.20051	+	2.20051i	−0.831715	+	0.831715i	−0.987751	−	0.156036i	$-0.950128\pi$
$7$	−2.20051	+	2.20051i	−0.831715	+	0.831715i	0.156036	+	0.987751i	$0.450128\pi$
$8$		−	1.34889i		−	0.476905i
$9$		−	2.68450i		−	0.894832i
$10$		0			0
$11$	3.96825	−	3.96825i	1.19647	−	1.19647i	0.221256	−	0.975216i	$-0.428984\pi$
$11$	3.96825	−	3.96825i	1.19647	−	1.19647i	0.975216	−	0.221256i	$-0.0710156\pi$
$12$	−0.497270	−	0.497270i	−0.143549	−	0.143549i
$13$	−1.24880			−0.346355			−0.173178	−	0.984891i	$-0.555403\pi$
$13$	−1.24880			−0.346355			−0.173178	+	0.984891i	$0.555403\pi$
$14$	3.96825	+	3.96825i	1.06056	+	1.06056i
$15$		0			0
$16$	−4.93650			−1.23412
$17$	0.397180	−	4.10393i	0.0963304	−	0.995349i
$17$	0.397180	−	4.10393i	0.0963304	−	0.995349i
$18$	−4.84103			−1.14104
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$		0			0
$21$	−1.74800			−0.381445
$22$	−7.15606	−	7.15606i	−1.52568	−	1.52568i
$23$	1.64598	−	1.64598i	0.343211	−	0.343211i	−0.514362	−	0.857573i	$-0.671971\pi$
$23$	1.64598	−	1.64598i	0.343211	−	0.343211i	0.857573	+	0.514362i	$0.171971\pi$
$24$	0.535753	−	0.535753i	0.109360	−	0.109360i
$25$		0			0
$26$			2.25200i			0.441654i
$27$	2.25777	−	2.25777i	0.434508	−	0.434508i
$28$	2.75504	−	2.75504i	0.520654	−	0.520654i
$29$	4.68450	+	4.68450i	0.869889	+	0.869889i	0.992460	−	0.122571i	$-0.0391139\pi$
$29$	4.68450	+	4.68450i	0.869889	+	0.869889i	−0.122571	+	0.992460i	$0.539114\pi$
$30$		0			0
$31$	3.22025	+	3.22025i	0.578374	+	0.578374i	0.934455	−	0.356081i	$-0.115887\pi$
$31$	3.22025	+	3.22025i	0.578374	+	0.578374i	−0.356081	+	0.934455i	$0.615887\pi$
$32$			6.20435i			1.09678i
$33$	3.15222			0.548731
$34$	−7.40074	−	0.716248i	−1.26922	−	0.122835i
$35$		0			0
$36$			3.36099i			0.560165i
$37$	1.34889	+	1.34889i	0.221756	+	0.221756i	0.809238	−	0.587481i	$-0.199880\pi$
$37$	1.34889	+	1.34889i	0.221756	+	0.221756i	−0.587481	+	0.809238i	$0.699880\pi$
$38$	−7.21332			−1.17016
$39$	−0.495999	−	0.495999i	−0.0794234	−	0.0794234i
$40$		0			0
$41$	−4.18850	+	4.18850i	−0.654133	+	0.654133i	−0.953986	−	0.299852i	$-0.903063\pi$
$41$	−4.18850	+	4.18850i	−0.654133	+	0.654133i	0.299852	+	0.953986i	$0.403063\pi$
$42$			3.15222i			0.486398i
$43$			2.04316i			0.311579i	0.987790	+	0.155790i	$0.0497922\pi$
$43$			2.04316i			0.311579i	−0.987790	+	0.155790i	$0.950208\pi$
$44$	−4.96825	+	4.96825i	−0.748992	+	0.748992i
$45$		0			0
$46$	−2.96825	−	2.96825i	−0.437644	−	0.437644i
$47$	−4.85546			−0.708242			−0.354121	−	0.935200i	$-0.615220\pi$
$47$	−4.85546			−0.708242			−0.354121	+	0.935200i	$0.615220\pi$
$48$	−1.96068	−	1.96068i	−0.283000	−	0.283000i
$49$		−	2.68450i		−	0.383499i
$50$		0			0
$51$	1.78775	−	1.47225i	0.250336	−	0.206156i
$52$	1.56350			0.216818
$53$			9.11674i			1.25228i	0.779710	+	0.626140i	$0.215366\pi$
$53$			9.11674i			1.25228i	−0.779710	+	0.626140i	$0.784634\pi$
$54$	−4.07151	−	4.07151i	−0.554062	−	0.554062i
$55$		0			0
$56$	2.96825	+	2.96825i	0.396649	+	0.396649i
$57$	1.58872	−	1.58872i	0.210431	−	0.210431i
$58$	8.44769	−	8.44769i	1.10924	−	1.10924i
$59$			6.00000i			0.781133i	0.920575	+	0.390567i	$0.127721\pi$
$59$			6.00000i			0.781133i	−0.920575	+	0.390567i	$0.872279\pi$
$60$		0			0
$61$	−4.00000	+	4.00000i	−0.512148	+	0.512148i	−0.915184	−	0.403036i	$-0.867955\pi$
$61$	−4.00000	+	4.00000i	−0.512148	+	0.512148i	0.403036	+	0.915184i	$0.367955\pi$
$62$	5.80717	−	5.80717i	0.737512	−	0.737512i
$63$	5.90726	+	5.90726i	0.744245	+	0.744245i
$64$	1.31550			0.164438
$65$		0			0
$66$		−	5.68450i		−	0.699713i
$67$	8.46212			1.03381			0.516906	−	0.856042i	$-0.327084\pi$
$67$	8.46212			1.03381			0.516906	+	0.856042i	$0.327084\pi$
$68$	−0.497270	+	5.13812i	−0.0603029	+	0.623089i
$69$	1.30750			0.157405
$70$		0			0
$71$	−6.22025	−	6.22025i	−0.738208	−	0.738208i	0.234023	−	0.972231i	$-0.424811\pi$
$71$	−6.22025	−	6.22025i	−0.738208	−	0.738208i	−0.972231	+	0.234023i	$0.924811\pi$
$72$	−3.62109			−0.426750
$73$	1.10906	+	1.10906i	0.129806	+	0.129806i	0.769025	−	0.639219i	$-0.220742\pi$
$73$	1.10906	+	1.10906i	0.129806	+	0.129806i	−0.639219	+	0.769025i	$0.720742\pi$
$74$	2.43250	−	2.43250i	0.282772	−	0.282772i
$75$		0			0
$76$			5.00800i			0.574457i
$77$			17.4643i			1.99025i
$78$	−0.894450	+	0.894450i	−0.101277	+	0.101277i
$79$	3.47225	−	3.47225i	0.390658	−	0.390658i	−0.484264	−	0.874922i	$-0.660912\pi$
$79$	3.47225	−	3.47225i	0.390658	−	0.390658i	0.874922	+	0.484264i	$0.160912\pi$
$80$		0			0
$81$	−6.26000			−0.695556
$82$	7.55324	+	7.55324i	0.834116	+	0.834116i
$83$		−	3.94658i		−	0.433194i	−0.976261	−	0.216597i	$-0.930504\pi$
$83$		−	3.94658i		−	0.433194i	0.976261	−	0.216597i	$-0.0694957\pi$
$84$	2.18850			0.238785
$85$		0			0
$86$	3.68450			0.397309
$87$			3.72118i			0.398952i
$88$	−5.35273	−	5.35273i	−0.570603	−	0.570603i
$89$	10.6130			1.12497			0.562487	−	0.826806i	$-0.309845\pi$
$89$	10.6130			1.12497			0.562487	+	0.826806i	$0.309845\pi$
$90$		0			0
$91$	2.74800	−	2.74800i	0.288069	−	0.288069i
$92$	−2.06077	+	2.06077i	−0.214850	+	0.214850i
$93$			2.55804i			0.265256i
$94$			8.75600i			0.903113i
$95$		0			0
$96$	−2.46425	+	2.46425i	−0.251506	+	0.251506i
$97$	8.76239	+	8.76239i	0.889686	+	0.889686i	0.994493	−	0.104807i	$-0.0334224\pi$
$97$	8.76239	+	8.76239i	0.889686	+	0.889686i	−0.104807	+	0.994493i	$0.533422\pi$
$98$	−4.84103			−0.489018
$99$	−10.6527	−	10.6527i	−1.07064	−	1.07064i
$100$		0			0
$101$	9.62099			0.957324			0.478662	−	0.877999i	$-0.341122\pi$
$101$	9.62099			0.957324			0.478662	+	0.877999i	$0.341122\pi$
$102$	−2.65495	−	3.22391i	−0.262879	−	0.319215i
$103$	−1.84298			−0.181594			−0.0907972	−	0.995869i	$-0.528942\pi$
$103$	−1.84298			−0.181594			−0.0907972	+	0.995869i	$0.528942\pi$
$104$			1.68450i			0.165178i
$105$		0			0
$106$	16.4405			1.59684
$107$	−12.0115	−	12.0115i	−1.16120	−	1.16120i	−0.984214	−	0.176984i	$-0.943366\pi$
$107$	−12.0115	−	12.0115i	−1.16120	−	1.16120i	−0.176984	−	0.984214i	$-0.556634\pi$
$108$	−2.82673	+	2.82673i	−0.272002	+	0.272002i
$109$	0.315505	−	0.315505i	0.0302199	−	0.0302199i	−0.691835	−	0.722055i	$-0.743198\pi$
$109$	0.315505	−	0.315505i	0.0302199	−	0.0302199i	0.722055	+	0.691835i	$0.243198\pi$
$110$		0			0
$111$			1.07151i			0.101703i
$112$	10.8628	−	10.8628i	1.02644	−	1.02644i
$113$	8.00768	−	8.00768i	0.753299	−	0.753299i	−0.221794	−	0.975094i	$-0.571191\pi$
$113$	8.00768	−	8.00768i	0.753299	−	0.753299i	0.975094	+	0.221794i	$0.0711913\pi$
$114$	−2.86499	−	2.86499i	−0.268331	−	0.268331i
$115$		0			0
$116$	−5.86499	−	5.86499i	−0.544551	−	0.544551i
$117$			3.35240i			0.309929i
$118$	10.8200			0.996060
$119$	8.15674	+	9.90474i	0.747728	+	0.907966i
$120$		0			0
$121$		−	20.4940i		−	1.86309i
$122$	7.21332	+	7.21332i	0.653063	+	0.653063i
$123$	−3.32718			−0.300001
$124$	−4.03175	−	4.03175i	−0.362062	−	0.362062i
$125$		0			0
$126$	10.6527	−	10.6527i	0.949022	−	0.949022i
$127$		−	5.85000i		−	0.519104i	−0.965729	−	0.259552i	$-0.916425\pi$
$127$		−	5.85000i		−	0.519104i	0.965729	−	0.259552i	$-0.0835748\pi$
$128$			10.0364i			0.887102i
$129$	−0.811504	+	0.811504i	−0.0714489	+	0.0714489i
$130$		0			0
$131$	13.8332	+	13.8332i	1.20862	+	1.20862i	0.971475	+	0.237140i	$0.0762101\pi$
$131$	13.8332	+	13.8332i	1.20862	+	1.20862i	0.237140	+	0.971475i	$0.423790\pi$
$132$	−3.94658			−0.343506
$133$	8.80204	+	8.80204i	0.763234	+	0.763234i
$134$		−	15.2600i		−	1.31826i
$135$		0			0
$136$	−5.53575	−	0.535753i	−0.474687	−	0.0459404i
$137$	13.8577			1.18394			0.591971	−	0.805959i	$-0.298350\pi$
$137$	13.8577			1.18394			0.591971	+	0.805959i	$0.298350\pi$
$138$		−	2.35786i		−	0.200714i
$139$	−7.21225	−	7.21225i	−0.611735	−	0.611735i	0.331663	−	0.943398i	$-0.392390\pi$
$139$	−7.21225	−	7.21225i	−0.611735	−	0.611735i	−0.943398	+	0.331663i	$0.892390\pi$
$140$		0			0
$141$	−1.92849	−	1.92849i	−0.162409	−	0.162409i
$142$	−11.2172	+	11.2172i	−0.941323	+	0.941323i
$143$	−4.95555	+	4.95555i	−0.414404	+	0.414404i
$144$			13.2520i			1.10433i
$145$		0			0
$146$	2.00000	−	2.00000i	0.165521	−	0.165521i
$147$	1.06623	−	1.06623i	0.0879411	−	0.0879411i
$148$	−1.68881	−	1.68881i	−0.138819	−	0.138819i
$149$	−15.9365			−1.30557			−0.652784	−	0.757544i	$-0.726399\pi$
$149$	−15.9365			−1.30557			−0.652784	+	0.757544i	$0.726399\pi$
$150$		0			0
$151$			3.36899i			0.274165i	0.990560	+	0.137082i	$0.0437725\pi$
$151$			3.36899i			0.274165i	−0.990560	+	0.137082i	$0.956228\pi$
$152$	−5.39556			−0.437638
$153$	−11.0170	−	1.06623i	−0.890670	−	0.0861995i
$154$	31.4940			2.53786
$155$		0			0
$156$	0.620991	+	0.620991i	0.0497191	+	0.0497191i
$157$	−3.92136			−0.312959			−0.156479	−	0.987681i	$-0.550014\pi$
$157$	−3.92136			−0.312959			−0.156479	+	0.987681i	$0.550014\pi$
$158$	−6.26161	−	6.26161i	−0.498147	−	0.498147i
$159$	−3.62099	+	3.62099i	−0.287163	+	0.287163i
$160$		0			0
$161$			7.24400i			0.570907i
$162$			11.2889i			0.886936i
$163$	10.4084	−	10.4084i	0.815247	−	0.815247i	−0.170168	−	0.985415i	$-0.554431\pi$
$163$	10.4084	−	10.4084i	0.815247	−	0.815247i	0.985415	+	0.170168i	$0.0544312\pi$
$164$	5.24400	−	5.24400i	0.409488	−	0.409488i
$165$		0			0
$166$	−7.11699			−0.552386
$167$	0.297091	+	0.297091i	0.0229896	+	0.0229896i	0.718508	−	0.695519i	$-0.244825\pi$
$167$	0.297091	+	0.297091i	0.0229896	+	0.0229896i	−0.695519	+	0.718508i	$0.744825\pi$
$168$			2.35786i			0.181913i
$169$	−11.4405			−0.880038
$170$		0			0
$171$	−10.7380			−0.821154
$172$		−	2.55804i		−	0.195049i
$173$	11.7397	+	11.7397i	0.892549	+	0.892549i	0.994763	−	0.102213i	$-0.0325924\pi$
$173$	11.7397	+	11.7397i	0.892549	+	0.892549i	−0.102213	+	0.994763i	$0.532592\pi$
$174$	6.71052			0.508723
$175$		0			0
$176$	−19.5892	+	19.5892i	−1.47659	+	1.47659i
$177$	−2.38308	+	2.38308i	−0.179123	+	0.179123i
$178$		−	19.1387i		−	1.43451i
$179$			19.7935i			1.47943i	0.672918	+	0.739717i	$0.265041\pi$
$179$			19.7935i			1.47943i	−0.672918	+	0.739717i	$0.734959\pi$
$180$		0			0
$181$	−6.62099	+	6.62099i	−0.492134	+	0.492134i	−0.908978	−	0.416844i	$-0.863136\pi$
$181$	−6.62099	+	6.62099i	−0.492134	+	0.492134i	0.416844	+	0.908978i	$0.363136\pi$
$182$	−4.95555	−	4.95555i	−0.367330	−	0.367330i
$183$	−3.17744			−0.234883
$184$	−2.22025	−	2.22025i	−0.163679	−	0.163679i
$185$		0			0
$186$	4.61299			0.338241
$187$	−14.7093	−	17.8615i	−1.07565	−	1.30616i
$188$	6.07904			0.443360
$189$			9.93650i			0.722774i
$190$		0			0
$191$	−13.9365			−1.00841			−0.504205	−	0.863584i	$-0.668214\pi$
$191$	−13.9365			−1.00841			−0.504205	+	0.863584i	$0.668214\pi$
$192$	0.522493	+	0.522493i	0.0377077	+	0.0377077i
$193$	2.95204	−	2.95204i	0.212493	−	0.212493i	−0.592833	−	0.805325i	$-0.701991\pi$
$193$	2.95204	−	2.95204i	0.212493	−	0.212493i	0.805325	+	0.592833i	$0.201991\pi$
$194$	15.8015	−	15.8015i	1.13448	−	1.13448i
$195$		0			0
$196$			3.36099i			0.240071i
$197$	12.5088	−	12.5088i	0.891215	−	0.891215i	−0.103423	−	0.994637i	$-0.532979\pi$
$197$	12.5088	−	12.5088i	0.891215	−	0.891215i	0.994637	+	0.103423i	$0.0329795\pi$
$198$	−19.2104	+	19.2104i	−1.36522	+	1.36522i
$199$	3.96025	+	3.96025i	0.280734	+	0.280734i	0.833402	−	0.552667i	$-0.186390\pi$
$199$	3.96025	+	3.96025i	0.280734	+	0.280734i	−0.552667	+	0.833402i	$0.686390\pi$
$200$		0			0
$201$	3.36099	+	3.36099i	0.237066	+	0.237066i
$202$		−	17.3498i		−	1.22073i
$203$	−20.6166			−1.44700
$204$	−2.23827	+	1.84326i	−0.156710	+	0.129054i
$205$		0			0
$206$			3.32351i			0.231560i
$207$	−4.41863	−	4.41863i	−0.307116	−	0.307116i
$208$	6.16470			0.427445
$209$	−15.8730	−	15.8730i	−1.09796	−	1.09796i
$210$		0			0
$211$	0.652743	−	0.652743i	0.0449367	−	0.0449367i	−0.684281	−	0.729218i	$-0.739884\pi$
$211$	0.652743	−	0.652743i	0.0449367	−	0.0449367i	0.729218	+	0.684281i	$0.239884\pi$
$212$		−	11.4142i		−	0.783928i
$213$		−	4.94112i		−	0.338560i
$214$	−21.6607	+	21.6607i	−1.48070	+	1.48070i
$215$		0			0
$216$	−3.04548	−	3.04548i	−0.207219	−	0.207219i
$217$	−14.1724			−0.962084
$218$	−0.568959	−	0.568959i	−0.0385348	−	0.0385348i
$219$			0.880993i			0.0595320i
$220$		0			0
$221$	−0.495999	+	5.12499i	−0.0333645	+	0.344744i
$222$	1.93228			0.129686
$223$		−	1.24880i		−	0.0836259i	−0.999125	−	0.0418129i	$-0.986687\pi$
$223$		−	1.24880i		−	0.0836259i	0.999125	−	0.0418129i	$-0.0133134\pi$
$224$	−13.6527	−	13.6527i	−0.912212	−	0.912212i
$225$		0			0
$226$	−14.4405	−	14.4405i	−0.960568	−	0.960568i
$227$	−8.19025	+	8.19025i	−0.543606	+	0.543606i	−0.924584	−	0.380978i	$-0.875587\pi$
$227$	−8.19025	+	8.19025i	−0.543606	+	0.543606i	0.380978	+	0.924584i	$0.375587\pi$
$228$	−1.98908	+	1.98908i	−0.131730	+	0.131730i
$229$			11.7480i			0.776330i	0.921590	+	0.388165i	$0.126891\pi$
$229$			11.7480i			0.776330i	−0.921590	+	0.388165i	$0.873109\pi$
$230$		0			0
$231$	−6.93650	+	6.93650i	−0.456388	+	0.456388i
$232$	6.31887	−	6.31887i	0.414854	−	0.414854i
$233$	−7.99325	−	7.99325i	−0.523655	−	0.523655i	0.395018	−	0.918673i	$-0.370738\pi$
$233$	−7.99325	−	7.99325i	−0.523655	−	0.523655i	−0.918673	+	0.395018i	$0.870738\pi$
$234$	6.04548			0.395206
$235$		0			0
$236$		−	7.51200i		−	0.488990i
$237$	2.75822			0.179166
$238$	17.8615	−	14.7093i	1.15779	−	0.953463i
$239$	5.13501			0.332156			0.166078	−	0.986113i	$-0.446890\pi$
$239$	5.13501			0.332156			0.166078	+	0.986113i	$0.446890\pi$
$240$		0			0
$241$	6.00000	+	6.00000i	0.386494	+	0.386494i	0.873435	−	0.486941i	$-0.161887\pi$
$241$	6.00000	+	6.00000i	0.386494	+	0.386494i	−0.486941	+	0.873435i	$0.661887\pi$
$242$	−36.9574			−2.37571
$243$	−9.25966	−	9.25966i	−0.594008	−	0.594008i
$244$	5.00800	−	5.00800i	0.320604	−	0.320604i
$245$		0			0
$246$			6.00000i			0.382546i
$247$			4.99520i			0.317837i
$248$	4.34376	−	4.34376i	0.275829	−	0.275829i
$249$	1.56750	−	1.56750i	0.0993366	−	0.0993366i
$250$		0			0
$251$	19.8095			1.25036			0.625182	−	0.780479i	$-0.285025\pi$
$251$	19.8095			1.25036			0.625182	+	0.780479i	$0.285025\pi$
$252$	−7.39589	−	7.39589i	−0.465897	−	0.465897i
$253$		−	13.0633i		−	0.821284i
$254$	−10.5495			−0.661934
$255$		0			0
$256$	20.7300			1.29562
$257$			24.3982i			1.52192i	0.648801	+	0.760958i	$0.275271\pi$
$257$			24.3982i			1.52192i	−0.648801	+	0.760958i	$0.724729\pi$
$258$	1.46341	+	1.46341i	0.0911079	+	0.0911079i
$259$	−5.93650			−0.368876
$260$		0			0
$261$	12.5755	−	12.5755i	0.778404	−	0.778404i
$262$	24.9459	−	24.9459i	1.54116	−	1.54116i
$263$			18.0585i			1.11354i	0.830668	+	0.556768i	$0.187959\pi$
$263$			18.0585i			1.11354i	−0.830668	+	0.556768i	$0.812041\pi$
$264$		−	4.25200i		−	0.261693i
$265$		0			0
$266$	15.8730	−	15.8730i	0.973236	−	0.973236i
$267$	4.21527	+	4.21527i	0.257970	+	0.257970i
$268$	−10.5946			−0.647167
$269$	12.6290	+	12.6290i	0.770003	+	0.770003i	0.978107	−	0.208104i	$-0.0667291\pi$
$269$	12.6290	+	12.6290i	0.770003	+	0.770003i	−0.208104	+	0.978107i	$0.566729\pi$
$270$		0			0
$271$	−15.8570			−0.963243			−0.481622	−	0.876379i	$-0.659952\pi$
$271$	−15.8570			−0.963243			−0.481622	+	0.876379i	$0.659952\pi$
$272$	−1.96068	+	20.2590i	−0.118884	+	1.22838i
$273$	2.18290			0.132115
$274$		−	24.9900i		−	1.50970i
$275$		0			0
$276$	−1.63699			−0.0985355
$277$	10.0256	+	10.0256i	0.602381	+	0.602381i	0.940944	−	0.338563i	$-0.109941\pi$
$277$	10.0256	+	10.0256i	0.602381	+	0.602381i	−0.338563	+	0.940944i	$0.609941\pi$
$278$	−13.0061	+	13.0061i	−0.780052	+	0.780052i
$279$	8.64474	−	8.64474i	0.517547	−	0.517547i
$280$		0			0
$281$		−	7.80949i		−	0.465875i	−0.972492	−	0.232937i	$-0.925166\pi$
$281$		−	7.80949i		−	0.465875i	0.972492	−	0.232937i	$-0.0748338\pi$
$282$	−3.47771	+	3.47771i	−0.207095	+	0.207095i
$283$	14.7842	−	14.7842i	0.878828	−	0.878828i	−0.114586	−	0.993413i	$-0.536554\pi$
$283$	14.7842	−	14.7842i	0.878828	−	0.878828i	0.993413	+	0.114586i	$0.0365540\pi$
$284$	7.78775	+	7.78775i	0.462118	+	0.462118i
$285$		0			0
$286$	8.93650	+	8.93650i	0.528426	+	0.528426i
$287$		−	18.4337i		−	1.08810i
$288$	16.6556			0.981438
$289$	−16.6845	−	3.26000i	−0.981441	−	0.191765i
$290$		0			0
$291$			6.96050i			0.408032i
$292$	−1.38854	−	1.38854i	−0.0812583	−	0.0812583i
$293$	−4.79502			−0.280128			−0.140064	−	0.990142i	$-0.544731\pi$
$293$	−4.79502			−0.280128			−0.140064	+	0.990142i	$0.544731\pi$
$294$	−1.92276	−	1.92276i	−0.112138	−	0.112138i
$295$		0			0
$296$	1.81951	−	1.81951i	0.105757	−	0.105757i
$297$		−	17.9188i		−	1.03975i
$298$			28.7388i			1.66479i
$299$	−2.05550	+	2.05550i	−0.118873	+	0.118873i
$300$		0			0
$301$	−4.49600	−	4.49600i	−0.259145	−	0.259145i
$302$	6.07540			0.349600
$303$	3.82127	+	3.82127i	0.219526	+	0.219526i
$304$			19.7460i			1.13251i
$305$		0			0
$306$	−1.92276	+	19.8673i	−0.109917	+	1.13574i
$307$	−24.9924			−1.42639			−0.713195	−	0.700966i	$-0.752753\pi$
$307$	−24.9924			−1.42639			−0.713195	+	0.700966i	$0.752753\pi$
$308$		−	21.8654i		−	1.24589i
$309$	−0.731997	−	0.731997i	−0.0416418	−	0.0416418i
$310$		0			0
$311$	−2.85126	−	2.85126i	−0.161680	−	0.161680i	0.621631	−	0.783311i	$-0.286471\pi$
$311$	−2.85126	−	2.85126i	−0.161680	−	0.161680i	−0.783311	+	0.621631i	$0.786471\pi$
$312$	−0.669049	+	0.669049i	−0.0378774	+	0.0378774i
$313$	−16.0154	+	16.0154i	−0.905242	+	0.905242i	−0.995884	−	0.0906416i	$-0.971108\pi$
$313$	−16.0154	+	16.0154i	−0.905242	+	0.905242i	0.0906416	+	0.995884i	$0.471108\pi$
$314$			7.07151i			0.399068i
$315$		0			0
$316$	−4.34726	+	4.34726i	−0.244552	+	0.244552i
$317$	5.85000	−	5.85000i	0.328569	−	0.328569i	−0.523473	−	0.852042i	$-0.675364\pi$
$317$	5.85000	−	5.85000i	0.328569	−	0.328569i	0.852042	+	0.523473i	$0.175364\pi$
$318$	6.52984	+	6.52984i	0.366175	+	0.366175i
$319$	37.1785			2.08160
$320$		0			0
$321$		−	9.54148i		−	0.532554i
$322$	13.0633			0.727991
$323$	−16.4157	−	1.58872i	−0.913395	−	0.0883988i
$324$	7.83752			0.435418
$325$		0			0
$326$	−18.7697	−	18.7697i	−1.03956	−	1.03956i
$327$	0.250624			0.0138596
$328$	5.64982	+	5.64982i	0.311959	+	0.311959i
$329$	10.6845	−	10.6845i	0.589055	−	0.589055i
$330$		0			0
$331$		−	5.51200i		−	0.302967i	−0.988460	−	0.151484i	$-0.951595\pi$
$331$		−	5.51200i		−	0.302967i	0.988460	−	0.151484i	$-0.0484050\pi$
$332$			4.94112i			0.271179i
$333$	3.62109	−	3.62109i	0.198435	−	0.198435i
$334$	0.535753	−	0.535753i	0.0293151	−	0.0293151i
$335$		0			0
$336$	8.62899			0.470750
$337$	6.74445	+	6.74445i	0.367394	+	0.367394i	0.866526	−	0.499132i	$-0.166348\pi$
$337$	6.74445	+	6.74445i	0.367394	+	0.367394i	−0.499132	+	0.866526i	$0.666348\pi$
$338$			20.6310i			1.12218i
$339$	6.36099			0.345482
$340$		0			0
$341$	25.5575			1.38402
$342$			19.3641i			1.04709i
$343$	−9.49631	−	9.49631i	−0.512753	−	0.512753i
$344$	2.75600			0.148594
$345$		0			0
$346$	21.1705	−	21.1705i	1.13813	−	1.13813i
$347$	8.16503	−	8.16503i	0.438322	−	0.438322i	−0.453125	−	0.891447i	$-0.649691\pi$
$347$	8.16503	−	8.16503i	0.438322	−	0.438322i	0.891447	+	0.453125i	$0.149691\pi$
$348$		−	4.65892i		−	0.249744i
$349$		−	11.4325i		−	0.611967i	−0.952037	−	0.305984i	$-0.901015\pi$
$349$		−	11.4325i		−	0.611967i	0.952037	−	0.305984i	$-0.0989853\pi$
$350$		0			0
$351$	−2.81951	+	2.81951i	−0.150494	+	0.150494i
$352$	24.6204	+	24.6204i	1.31227	+	1.31227i
$353$	31.8017			1.69263			0.846317	−	0.532680i	$-0.178815\pi$
$353$	31.8017			1.69263			0.846317	+	0.532680i	$0.178815\pi$
$354$	4.29749	+	4.29749i	0.228409	+	0.228409i
$355$		0			0
$356$	−13.2875			−0.704234
$357$	−0.694271	+	7.17367i	−0.0367447	+	0.379671i
$358$	35.6942			1.88650
$359$		−	25.1785i		−	1.32887i	−0.747346	−	0.664435i	$-0.768672\pi$
$359$		−	25.1785i		−	1.32887i	0.747346	−	0.664435i	$-0.231328\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	11.9398	+	11.9398i	0.627544	+	0.627544i
$363$	8.13981	−	8.13981i	0.427229	−	0.427229i
$364$	−3.44050	+	3.44050i	−0.180331	+	0.180331i
$365$		0			0
$366$			5.72998i			0.299511i
$367$	−4.30411	+	4.30411i	−0.224673	+	0.224673i	−0.810463	−	0.585790i	$-0.800784\pi$
$367$	−4.30411	+	4.30411i	−0.224673	+	0.224673i	0.585790	+	0.810463i	$0.300784\pi$
$368$	−8.12538	+	8.12538i	−0.423565	+	0.423565i
$369$	11.2440	+	11.2440i	0.585339	+	0.585339i
$370$		0			0
$371$	−20.0615	−	20.0615i	−1.04154	−	1.04154i
$372$		−	3.20267i		−	0.166050i
$373$	−30.0732			−1.55713			−0.778566	−	0.627562i	$-0.784053\pi$
$373$	−30.0732			−1.55713			−0.778566	+	0.627562i	$0.784053\pi$
$374$	−32.2102	+	26.5257i	−1.66555	+	1.37161i
$375$		0			0
$376$			6.54949i			0.337764i
$377$	−5.85000	−	5.85000i	−0.301290	−	0.301290i
$378$	17.9188			0.921643
$379$	−0.716248	−	0.716248i	−0.0367912	−	0.0367912i	0.688472	−	0.725263i	$-0.258282\pi$
$379$	−0.716248	−	0.716248i	−0.0367912	−	0.0367912i	−0.725263	+	0.688472i	$0.758282\pi$
$380$		0			0
$381$	2.32351	−	2.32351i	0.119037	−	0.119037i
$382$			25.1321i			1.28587i
$383$		−	25.8660i		−	1.32169i	−0.750521	−	0.660846i	$-0.770198\pi$
$383$		−	25.8660i		−	1.32169i	0.750521	−	0.660846i	$-0.229802\pi$
$384$	−3.98627	+	3.98627i	−0.203423	+	0.203423i
$385$		0			0
$386$	−5.32351	−	5.32351i	−0.270959	−	0.270959i
$387$	5.48486			0.278811
$388$	−10.9705	−	10.9705i	−0.556944	−	0.556944i
$389$		−	33.0695i		−	1.67669i	−0.545140	−	0.838345i	$-0.683524\pi$
$389$		−	33.0695i		−	1.67669i	0.545140	−	0.838345i	$-0.316476\pi$
$390$		0			0
$391$	−6.10124	−	7.40874i	−0.308553	−	0.374676i
$392$	−3.62109			−0.182893
$393$			10.9886i			0.554301i
$394$	−22.5575	−	22.5575i	−1.13643	−	1.13643i
$395$		0			0
$396$	13.3372	+	13.3372i	0.670221	+	0.670221i
$397$	5.76434	−	5.76434i	0.289304	−	0.289304i	−0.547501	−	0.836805i	$-0.684421\pi$
$397$	5.76434	−	5.76434i	0.289304	−	0.289304i	0.836805	+	0.547501i	$0.184421\pi$
$398$	7.14163	−	7.14163i	0.357978	−	0.357978i
$399$			6.99200i			0.350038i
$400$		0			0
$401$	0.116990	−	0.116990i	0.00584222	−	0.00584222i	−0.704180	−	0.710022i	$-0.748685\pi$
$401$	0.116990	−	0.116990i	0.00584222	−	0.00584222i	0.710022	+	0.704180i	$0.248685\pi$
$402$	6.06097	−	6.06097i	0.302294	−	0.302294i
$403$	−4.02145	−	4.02145i	−0.200323	−	0.200323i
$404$	−12.0455			−0.599285
$405$		0			0
$406$			37.1785i			1.84514i
$407$	10.7055			0.530650
$408$	−1.98590	−	2.41148i	−0.0983168	−	0.119386i
$409$	13.3690			0.661054			0.330527	−	0.943797i	$-0.392774\pi$
$409$	13.3690			0.661054			0.330527	+	0.943797i	$0.392774\pi$
$410$		0			0
$411$	5.50400	+	5.50400i	0.271492	+	0.271492i
$412$	2.30741			0.113678
$413$	−13.2031	−	13.2031i	−0.649680	−	0.649680i
$414$	−7.96825	+	7.96825i	−0.391618	+	0.391618i
$415$		0			0
$416$		−	7.74800i		−	0.379877i
$417$		−	5.72913i		−	0.280557i
$418$	−28.6242	+	28.6242i	−1.40006	+	1.40006i
$419$	−16.6687	+	16.6687i	−0.814322	+	0.814322i	−0.985278	−	0.170957i	$-0.945314\pi$
$419$	−16.6687	+	16.6687i	−0.814322	+	0.814322i	0.170957	+	0.985278i	$0.445314\pi$
$420$		0			0
$421$	5.82751			0.284015			0.142008	−	0.989866i	$-0.454644\pi$
$421$	5.82751			0.284015			0.142008	+	0.989866i	$0.454644\pi$
$422$	−1.17711	−	1.17711i	−0.0573009	−	0.0573009i
$423$			13.0345i			0.633757i
$424$	12.2975			0.597219
$425$		0			0
$426$	−8.91047			−0.431714
$427$		−	17.6041i		−	0.851921i
$428$	15.0384	+	15.0384i	0.726910	+	0.726910i
$429$	−3.93650			−0.190056
$430$		0			0
$431$	4.90474	−	4.90474i	0.236253	−	0.236253i	−0.579043	−	0.815297i	$-0.696574\pi$
$431$	4.90474	−	4.90474i	0.236253	−	0.236253i	0.815297	+	0.579043i	$0.196574\pi$
$432$	−11.1455	+	11.1455i	−0.536237	+	0.536237i
$433$			15.4464i			0.742307i	0.928572	+	0.371153i	$0.121038\pi$
$433$			15.4464i			0.742307i	−0.928572	+	0.371153i	$0.878962\pi$
$434$			25.5575i			1.22680i
$435$		0			0
$436$	−0.395012	+	0.395012i	−0.0189176	+	0.0189176i
$437$	−6.58392	−	6.58392i	−0.314952	−	0.314952i
$438$	1.58872			0.0759121
$439$	−1.03975	−	1.03975i	−0.0496247	−	0.0496247i	0.681859	−	0.731484i	$-0.261172\pi$
$439$	−1.03975	−	1.03975i	−0.0496247	−	0.0496247i	−0.731484	+	0.681859i	$0.761172\pi$
$440$		0			0
$441$	−7.20652			−0.343167
$442$	9.24205	+	0.894450i	0.439600	+	0.0425447i
$443$	−12.7838			−0.607379			−0.303689	−	0.952771i	$-0.598218\pi$
$443$	−12.7838			−0.607379			−0.303689	+	0.952771i	$0.598218\pi$
$444$		−	1.34153i		−	0.0636660i
$445$		0			0
$446$	−2.25200			−0.106635
$447$	−6.32966	−	6.32966i	−0.299383	−	0.299383i
$448$	−2.89478	+	2.89478i	−0.136766	+	0.136766i
$449$	−6.88099	+	6.88099i	−0.324734	+	0.324734i	−0.850580	−	0.525846i	$-0.823749\pi$
$449$	−6.88099	+	6.88099i	−0.324734	+	0.324734i	0.525846	+	0.850580i	$0.323749\pi$
$450$		0			0
$451$			33.2420i			1.56530i
$452$	−10.0256	+	10.0256i	−0.471566	+	0.471566i
$453$	−1.33810	+	1.33810i	−0.0628693	+	0.0628693i
$454$	14.7697	+	14.7697i	0.693178	+	0.693178i
$455$		0			0
$456$	−2.14301	−	2.14301i	−0.100356	−	0.100356i
$457$			36.2279i			1.69467i	0.531058	+	0.847336i	$0.321795\pi$
$457$			36.2279i			1.69467i	−0.531058	+	0.847336i	$0.678205\pi$
$458$	21.1855			0.989935
$459$	−8.36899	−	10.1625i	−0.390631	−	0.474344i
$460$		0			0
$461$			40.0595i			1.86576i	0.360193	+	0.932878i	$0.382711\pi$
$461$			40.0595i			1.86576i	−0.360193	+	0.932878i	$0.617289\pi$
$462$	12.5088	+	12.5088i	0.581962	+	0.581962i
$463$	15.3607			0.713874			0.356937	−	0.934128i	$-0.383821\pi$
$463$	15.3607			0.713874			0.356937	+	0.934128i	$0.383821\pi$
$464$	−23.1250	−	23.1250i	−1.07355	−	1.07355i
$465$		0			0
$466$	−14.4145	+	14.4145i	−0.667738	+	0.667738i
$467$			19.4471i			0.899903i	0.893053	+	0.449952i	$0.148559\pi$
$467$			19.4471i			0.899903i	−0.893053	+	0.449952i	$0.851441\pi$
$468$		−	4.19721i		−	0.194016i
$469$	−18.6210	+	18.6210i	−0.859837	+	0.859837i
$470$		0			0
$471$	−1.55749	−	1.55749i	−0.0717652	−	0.0717652i
$472$	8.09334			0.372526
$473$	8.10777	+	8.10777i	0.372796	+	0.372796i
$474$		−	4.97398i		−	0.228462i
$475$		0			0
$476$	−10.2122	−	12.4007i	−0.468078	−	0.568387i
$477$	24.4739			1.12058
$478$		−	9.26012i		−	0.423548i
$479$	−10.2918	−	10.2918i	−0.470242	−	0.470242i	0.431751	−	0.901993i	$-0.357896\pi$
$479$	−10.2918	−	10.2918i	−0.470242	−	0.470242i	−0.901993	+	0.431751i	$0.857896\pi$
$480$		0			0
$481$	−1.68450	−	1.68450i	−0.0768064	−	0.0768064i
$482$	10.8200	−	10.8200i	0.492837	−	0.492837i
$483$	−2.87717	+	2.87717i	−0.130916	+	0.130916i
$484$			25.6585i			1.16629i
$485$		0			0
$486$	−16.6982	+	16.6982i	−0.757447	+	0.757447i
$487$	−20.9993	+	20.9993i	−0.951570	+	0.951570i	−0.998880	−	0.0473104i	$-0.984935\pi$
$487$	−20.9993	+	20.9993i	−0.951570	+	0.951570i	0.0473104	+	0.998880i	$0.484935\pi$
$488$	5.39556	+	5.39556i	0.244246	+	0.244246i
$489$	8.26800			0.373892
$490$		0			0
$491$		−	21.0715i		−	0.950944i	−0.879731	−	0.475472i	$-0.842277\pi$
$491$		−	21.0715i		−	0.950944i	0.879731	−	0.475472i	$-0.157723\pi$
$492$	4.16563			0.187801
$493$	21.0854	−	17.3643i	0.949640	−	0.782047i
$494$	9.00800			0.405289
$495$		0			0
$496$	−15.8967	−	15.8967i	−0.713785	−	0.713785i
$497$	27.3754			1.22796
$498$	−2.82673	−	2.82673i	−0.126669	−	0.126669i
$499$	6.65274	−	6.65274i	0.297818	−	0.297818i	−0.542341	−	0.840159i	$-0.682462\pi$
$499$	6.65274	−	6.65274i	0.297818	−	0.297818i	0.840159	+	0.542341i	$0.182462\pi$
$500$		0			0
$501$			0.235997i			0.0105436i
$502$		−	35.7231i		−	1.59440i
$503$	20.7739	−	20.7739i	0.926263	−	0.926263i	−0.0711991	−	0.997462i	$-0.522683\pi$
$503$	20.7739	−	20.7739i	0.926263	−	0.926263i	0.997462	+	0.0711991i	$0.0226826\pi$
$504$	7.96825	−	7.96825i	0.354934	−	0.354934i
$505$		0			0
$506$	−23.5575			−1.04726
$507$	−4.54394	−	4.54394i	−0.201804	−	0.201804i
$508$			7.32420i			0.324959i
$509$	14.3930			0.637958			0.318979	−	0.947762i	$-0.396660\pi$
$509$	14.3930			0.637958			0.318979	+	0.947762i	$0.396660\pi$
$510$		0			0
$511$	−4.88099			−0.215922
$512$		−	17.3102i		−	0.765009i
$513$	−9.03108	−	9.03108i	−0.398732	−	0.398732i
$514$	43.9980			1.94067
$515$		0			0
$516$	1.01600	−	1.01600i	0.0447270	−	0.0447270i
$517$	−19.2677	+	19.2677i	−0.847391	+	0.847391i
$518$			10.7055i			0.470371i
$519$			9.32552i			0.409345i
$520$		0			0
$521$	−19.5655	+	19.5655i	−0.857180	+	0.857180i	−0.991005	−	0.133825i	$-0.957274\pi$
$521$	−19.5655	+	19.5655i	−0.857180	+	0.857180i	0.133825	+	0.991005i	$0.457274\pi$
$522$	−22.6778	−	22.6778i	−0.992580	−	0.992580i
$523$	−37.4867			−1.63918			−0.819590	−	0.572950i	$-0.805799\pi$
$523$	−37.4867			−1.63918			−0.819590	+	0.572950i	$0.805799\pi$
$524$	−17.3192	−	17.3192i	−0.756594	−	0.756594i
$525$		0			0
$526$	32.5655			1.41992
$527$	14.4947	−	11.9367i	0.631399	−	0.519969i
$528$	−15.5609			−0.677202
$529$			17.5815i			0.764413i
$530$		0			0
$531$	16.1070			0.698983
$532$	−11.0202	−	11.0202i	−0.477785	−	0.477785i
$533$	5.23060	−	5.23060i	0.226562	−	0.226562i
$534$	7.60153	−	7.60153i	0.328950	−	0.328950i
$535$		0			0
$536$		−	11.4145i		−	0.493030i
$537$	−7.86158	+	7.86158i	−0.339252	+	0.339252i
$538$	22.7742	−	22.7742i	0.981867	−	0.981867i
$539$	−10.6527	−	10.6527i	−0.458846	−	0.458846i
$540$		0			0
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	0.486654	−	0.873595i	$-0.338217\pi$
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	−0.873595	+	0.486654i	$0.838217\pi$
$542$			28.5954i			1.22828i
$543$	−5.25946			−0.225705
$544$	25.4622	+	2.46425i	1.09168	+	0.105654i
$545$		0			0
$546$		−	3.93650i		−	0.168466i
$547$	−20.3591	−	20.3591i	−0.870493	−	0.870493i	0.122033	−	0.992526i	$-0.461059\pi$
$547$	−20.3591	−	20.3591i	−0.870493	−	0.870493i	−0.992526	+	0.122033i	$0.961059\pi$
$548$	−17.3498			−0.741148
$549$	10.7380	+	10.7380i	0.458286	+	0.458286i
$550$		0			0
$551$	18.7380	−	18.7380i	0.798265	−	0.798265i
$552$		−	1.76368i		−	0.0750671i
$553$			15.2814i			0.649833i
$554$	18.0795	−	18.0795i	0.768125	−	0.768125i
$555$		0			0
$556$	9.02974	+	9.02974i	0.382946	+	0.382946i
$557$	4.93477			0.209093			0.104546	−	0.994520i	$-0.466661\pi$
$557$	4.93477			0.209093			0.104546	+	0.994520i	$0.466661\pi$
$558$	−15.5893	−	15.5893i	−0.659949	−	0.659949i
$559$		−	2.55150i		−	0.107917i
$560$		0			0
$561$	1.25200	−	12.9365i	0.0528595	−	0.546179i
$562$	−14.0831			−0.594059
$563$			3.97544i			0.167545i	0.996485	+	0.0837724i	$0.0266969\pi$
$563$			3.97544i			0.167545i	−0.996485	+	0.0837724i	$0.973303\pi$
$564$	2.41448	+	2.41448i	0.101668	+	0.101668i
$565$		0			0
$566$	−26.6607	−	26.6607i	−1.12063	−	1.12063i
$567$	13.7752	−	13.7752i	0.578504	−	0.578504i
$568$	−8.39043	+	8.39043i	−0.352055	+	0.352055i
$569$		−	5.49600i		−	0.230404i	−0.993342	−	0.115202i	$-0.963248\pi$
$569$		−	5.49600i		−	0.230404i	0.993342	−	0.115202i	$-0.0367516\pi$
$570$		0			0
$571$	12.3372	−	12.3372i	0.516297	−	0.516297i	−0.400152	−	0.916449i	$-0.631043\pi$
$571$	12.3372	−	12.3372i	0.516297	−	0.516297i	0.916449	+	0.400152i	$0.131043\pi$
$572$	6.20435	−	6.20435i	0.259417	−	0.259417i
$573$	−5.53530	−	5.53530i	−0.231241	−	0.231241i
$574$	−33.2420			−1.38749
$575$		0			0
$576$		−	3.53147i		−	0.147144i
$577$	−32.3418			−1.34641			−0.673203	−	0.739458i	$-0.735082\pi$
$577$	−32.3418			−1.34641			−0.673203	+	0.739458i	$0.735082\pi$
$578$	−5.87886	+	30.0877i	−0.244528	+	1.25148i
$579$	2.34499			0.0974543
$580$		0			0
$581$	8.68450	+	8.68450i	0.360294	+	0.360294i
$582$	12.5521			0.520301
$583$	36.1775	+	36.1775i	1.49832	+	1.49832i
$584$	1.49600	−	1.49600i	0.0619049	−	0.0619049i
$585$		0			0
$586$			8.64701i			0.357205i
$587$		−	28.6847i		−	1.18394i	−0.805959	−	0.591972i	$-0.798350\pi$
$587$		−	28.6847i		−	1.18394i	0.805959	−	0.591972i	$-0.201650\pi$
$588$	−1.33492	+	1.33492i	−0.0550511	+	0.0550511i
$589$	12.8810	−	12.8810i	0.530752	−	0.530752i
$590$		0			0
$591$	9.93650			0.408733
$592$	−6.65879	−	6.65879i	−0.273675	−	0.273675i
$593$		−	9.74614i		−	0.400226i	−0.979773	−	0.200113i	$-0.935869\pi$
$593$		−	9.74614i		−	0.400226i	0.979773	−	0.200113i	$-0.0641309\pi$
$594$	−32.3135			−1.32584
$595$		0			0
$596$	19.9525			0.817286
$597$			3.14586i			0.128752i
$598$	3.70675	+	3.70675i	0.151580	+	0.151580i
$599$	−8.07951			−0.330120			−0.165060	−	0.986284i	$-0.552782\pi$
$599$	−8.07951			−0.330120			−0.165060	+	0.986284i	$0.552782\pi$
$600$		0			0
$601$	−12.8810	+	12.8810i	−0.525427	+	0.525427i	−0.919205	−	0.393779i	$-0.871168\pi$
$601$	−12.8810	+	12.8810i	−0.525427	+	0.525427i	0.393779	+	0.919205i	$0.371168\pi$
$602$	−8.10777	+	8.10777i	−0.330448	+	0.330448i
$603$		−	22.7165i		−	0.925089i
$604$		−	4.21798i		−	0.171627i
$605$		0			0
$606$	6.89101	−	6.89101i	0.279928	−	0.279928i
$607$	−8.37964	−	8.37964i	−0.340119	−	0.340119i	0.516293	−	0.856412i	$-0.327312\pi$
$607$	−8.37964	−	8.37964i	−0.340119	−	0.340119i	−0.856412	+	0.516293i	$0.827312\pi$
$608$	24.8174			1.00648
$609$	−8.18850	−	8.18850i	−0.331815	−	0.331815i
$610$		0			0
$611$	6.06350			0.245303
$612$	13.7933	+	1.33492i	0.557560	+	0.0539609i
$613$	−23.1494			−0.934995			−0.467497	−	0.883994i	$-0.654844\pi$
$613$	−23.1494			−0.934995			−0.467497	+	0.883994i	$0.654844\pi$
$614$			45.0695i			1.81886i
$615$		0			0
$616$	23.5575			0.949158
$617$	7.41350	+	7.41350i	0.298456	+	0.298456i	0.840409	−	0.541953i	$-0.182315\pi$
$617$	7.41350	+	7.41350i	0.298456	+	0.298456i	−0.541953	+	0.840409i	$0.682315\pi$
$618$	−1.32003	+	1.32003i	−0.0530995	+	0.0530995i
$619$	16.4702	−	16.4702i	0.661995	−	0.661995i	−0.293855	−	0.955850i	$-0.594938\pi$
$619$	16.4702	−	16.4702i	0.661995	−	0.661995i	0.955850	+	0.293855i	$0.0949384\pi$
$620$		0			0
$621$		−	7.43250i		−	0.298256i
$622$	−5.14176	+	5.14176i	−0.206166	+	0.206166i
$623$	−23.3540	+	23.3540i	−0.935658	+	0.935658i
$624$	2.44850	+	2.44850i	0.0980184	+	0.0980184i
$625$		0			0
$626$	28.8810	+	28.8810i	1.15432	+	1.15432i
$627$		−	12.6089i		−	0.503550i
$628$	4.90954			0.195912
$629$	6.07151	−	5.00000i	0.242087	−	0.199363i
$630$		0			0
$631$		−	41.1310i		−	1.63740i	−0.574223	−	0.818699i	$-0.694696\pi$
$631$		−	41.1310i		−	1.63740i	0.574223	−	0.818699i	$-0.305304\pi$
$632$	−4.68368	−	4.68368i	−0.186307	−	0.186307i
$633$	0.518514			0.0206091
$634$	−10.5495	−	10.5495i	−0.418974	−	0.418974i
$635$		0			0
$636$	4.53348	−	4.53348i	0.179764	−	0.179764i
$637$			3.35240i			0.132827i
$638$		−	67.0451i		−	2.65434i
$639$	−16.6982	+	16.6982i	−0.660572	+	0.660572i
$640$		0			0
$641$	33.4325	+	33.4325i	1.32050	+	1.32050i	0.913367	+	0.407137i	$0.133473\pi$
$641$	33.4325	+	33.4325i	1.32050	+	1.32050i	0.407137	+	0.913367i	$0.366527\pi$
$642$	−17.2064			−0.679084
$643$	−4.99838	−	4.99838i	−0.197117	−	0.197117i	0.601646	−	0.798763i	$-0.294512\pi$
$643$	−4.99838	−	4.99838i	−0.197117	−	0.197117i	−0.798763	+	0.601646i	$0.794512\pi$
$644$		−	9.06949i		−	0.357388i
$645$		0			0
$646$	−2.86499	+	29.6030i	−0.112722	+	1.16471i
$647$	−26.9462			−1.05937			−0.529683	−	0.848196i	$-0.677689\pi$
$647$	−26.9462			−1.05937			−0.529683	+	0.848196i	$0.677689\pi$
$648$			8.44406i			0.331714i
$649$	23.8095	+	23.8095i	0.934604	+	0.934604i
$650$		0			0
$651$	−5.62899	−	5.62899i	−0.220618	−	0.220618i
$652$	−13.0313	+	13.0313i	−0.510345	+	0.510345i
$653$	19.9764	−	19.9764i	0.781736	−	0.781736i	−0.198388	−	0.980124i	$-0.563570\pi$
$653$	19.9764	−	19.9764i	0.781736	−	0.781736i	0.980124	+	0.198388i	$0.0635705\pi$
$654$		−	0.451959i		−	0.0176730i
$655$		0			0
$656$	20.6765	−	20.6765i	0.807281	−	0.807281i
$657$	2.97726	−	2.97726i	0.116154	−	0.116154i
$658$	−19.2677	−	19.2677i	−0.751132	−	0.751132i
$659$	−14.1230			−0.550153			−0.275077	−	0.961422i	$-0.588703\pi$
$659$	−14.1230			−0.550153			−0.275077	+	0.961422i	$0.588703\pi$
$660$		0			0
$661$		−	49.0355i		−	1.90726i	−0.300984	−	0.953629i	$-0.597315\pi$
$661$		−	49.0355i		−	1.90726i	0.300984	−	0.953629i	$-0.402685\pi$
$662$	−9.93996			−0.386328
$663$	−2.23255	+	1.83855i	−0.0867050	+	0.0714032i
$664$	−5.32351			−0.206592
$665$		0			0
$666$	−6.53002	−	6.53002i	−0.253033	−	0.253033i
$667$	15.4212			0.597111
$668$	−0.371958	−	0.371958i	−0.0143915	−	0.0143915i
$669$	0.495999	−	0.495999i	0.0191764	−	0.0191764i
$670$		0			0
$671$			31.7460i			1.22554i
$672$		−	10.8452i		−	0.418363i
$673$	−22.2405	+	22.2405i	−0.857308	+	0.857308i	−0.991020	−	0.133712i	$-0.957310\pi$
$673$	−22.2405	+	22.2405i	−0.857308	+	0.857308i	0.133712	+	0.991020i	$0.457310\pi$
$674$	12.1625	−	12.1625i	0.468481	−	0.468481i
$675$		0			0
$676$	14.3235			0.550904
$677$	−21.4109	−	21.4109i	−0.822889	−	0.822889i	0.163633	−	0.986521i	$-0.447679\pi$
$677$	−21.4109	−	21.4109i	−0.822889	−	0.822889i	−0.986521	+	0.163633i	$0.947679\pi$
$678$		−	11.4710i		−	0.440540i
$679$	−38.5635			−1.47993
$680$		0			0
$681$	−6.50602			−0.249311
$682$		−	46.0886i		−	1.76482i
$683$	−32.6533	−	32.6533i	−1.24944	−	1.24944i	−0.955966	−	0.293479i	$-0.905187\pi$
$683$	−32.6533	−	32.6533i	−1.24944	−	1.24944i	−0.293479	−	0.955966i	$-0.594813\pi$
$684$	13.4440			0.514043
$685$		0			0
$686$	−17.1250	+	17.1250i	−0.653835	+	0.653835i
$687$	−4.66608	+	4.66608i	−0.178022	+	0.178022i
$688$		−	10.0861i		−	0.384527i
$689$		−	11.3850i		−	0.433734i
$690$		0			0
$691$	−7.52775	+	7.52775i	−0.286369	+	0.286369i	−0.835643	−	0.549273i	$-0.814905\pi$
$691$	−7.52775	+	7.52775i	−0.286369	+	0.286369i	0.549273	+	0.835643i	$0.314905\pi$
$692$	−14.6981	−	14.6981i	−0.558736	−	0.558736i
$693$	46.8830			1.78094
$694$	−14.7242	−	14.7242i	−0.558925	−	0.558925i
$695$		0			0
$696$	5.01946			0.190262
$697$	15.5257	+	18.8529i	0.588078	+	0.714104i
$698$	−20.6166			−0.780349
$699$		−	6.34953i		−	0.240161i
$700$		0			0
$701$	−39.4145			−1.48866			−0.744332	−	0.667810i	$-0.767232\pi$
$701$	−39.4145			−1.48866			−0.744332	+	0.667810i	$0.767232\pi$
$702$	5.08450	+	5.08450i	0.191902	+	0.191902i
$703$	5.39556	−	5.39556i	0.203497	−	0.203497i
$704$	5.22025	−	5.22025i	0.196746	−	0.196746i
$705$		0			0
$706$		−	57.3490i		−	2.15836i
$707$	−21.1711	+	21.1711i	−0.796221	+	0.796221i
$708$	2.98362	−	2.98362i	0.112131	−	0.112131i
$709$	−10.7460	−	10.7460i	−0.403574	−	0.403574i	0.475917	−	0.879490i	$-0.342116\pi$
$709$	−10.7460	−	10.7460i	−0.403574	−	0.403574i	−0.879490	+	0.475917i	$0.842116\pi$
$710$		0			0
$711$	−9.32124	−	9.32124i	−0.349574	−	0.349574i
$712$		−	14.3158i		−	0.536506i
$713$	10.6009			0.397008
$714$	12.9365	+	1.25200i	0.484136	+	0.0468549i
$715$		0			0
$716$		−	24.7815i		−	0.926126i
$717$	2.03953	+	2.03953i	0.0761675	+	0.0761675i
$718$	−45.4051			−1.69450
$719$	4.84924	+	4.84924i	0.180846	+	0.180846i	0.791724	−	0.610878i	$-0.209184\pi$
$719$	4.84924	+	4.84924i	0.180846	+	0.180846i	−0.610878	+	0.791724i	$0.709184\pi$
$720$		0			0
$721$	4.05550	−	4.05550i	0.151035	−	0.151035i
$722$		−	5.40999i		−	0.201339i
$723$			4.76617i			0.177256i
$724$	8.28948	−	8.28948i	0.308076	−	0.308076i
$725$		0			0
$726$	−14.6788	−	14.6788i	−0.544780	−	0.544780i
$727$	38.5606			1.43013			0.715066	−	0.699057i	$-0.246397\pi$
$727$	38.5606			1.43013			0.715066	+	0.699057i	$0.246397\pi$
$728$	−3.70675	−	3.70675i	−0.137381	−	0.137381i
$729$			11.4245i			0.423129i
$730$		0			0
$731$	8.38499	+	0.811504i	0.310130	+	0.0300146i
$732$	3.97816			0.147037
$733$			42.7425i			1.57873i	0.613923	+	0.789366i	$0.289591\pi$
$733$			42.7425i			1.57873i	−0.613923	+	0.789366i	$0.710409\pi$
$734$	7.76173	+	7.76173i	0.286491	+	0.286491i
$735$		0			0
$736$	10.2122	+	10.2122i	0.376428	+	0.376428i
$737$	33.5798	−	33.5798i	1.23693	−	1.23693i
$738$	20.2766	−	20.2766i	0.746394	−	0.746394i
$739$			6.00000i			0.220714i	0.993892	+	0.110357i	$0.0351994\pi$
$739$			6.00000i			0.220714i	−0.993892	+	0.110357i	$0.964801\pi$
$740$		0			0
$741$	−1.98400	+	1.98400i	−0.0728839	+	0.0728839i
$742$	−36.1775	+	36.1775i	−1.32812	+	1.32812i
$743$	36.9750	+	36.9750i	1.35648	+	1.35648i	0.878214	+	0.478269i	$0.158735\pi$
$743$	36.9750	+	36.9750i	1.35648	+	1.35648i	0.478269	+	0.878214i	$0.341265\pi$
$744$	3.45051			0.126502
$745$		0			0
$746$			54.2320i			1.98557i
$747$	−10.5946			−0.387635
$748$	18.4161	+	22.3626i	0.673358	+	0.817659i
$749$	52.8630			1.93157
$750$		0			0
$751$	27.9027	+	27.9027i	1.01818	+	1.01818i	0.999832	+	0.0183534i	$0.00584240\pi$
$751$	27.9027	+	27.9027i	1.01818	+	1.01818i	0.0183534	+	0.999832i	$0.494158\pi$
$752$	23.9690			0.874058
$753$	7.86794	+	7.86794i	0.286724	+	0.286724i
$754$	−10.5495	+	10.5495i	−0.384190	+	0.384190i
$755$		0			0
$756$		−	12.4405i		−	0.452456i
$757$		−	8.61186i		−	0.313003i	−0.987678	−	0.156502i	$-0.949978\pi$
$757$		−	8.61186i		−	0.313003i	0.987678	−	0.156502i	$-0.0500216\pi$
$758$	−1.29163	+	1.29163i	−0.0469141	+	0.0469141i
$759$	5.18850	−	5.18850i	0.188330	−	0.188330i
$760$		0			0
$761$	−41.2400			−1.49495			−0.747474	−	0.664291i	$-0.768733\pi$
$761$	−41.2400			−1.49495			−0.747474	+	0.664291i	$0.768733\pi$
$762$	−4.19005	−	4.19005i	−0.151789	−	0.151789i
$763$			1.38854i			0.0502686i
$764$	17.4485			0.631265
$765$		0			0
$766$	−46.6450			−1.68535
$767$		−	7.49280i		−	0.270549i
$768$	8.23354	+	8.23354i	0.297102	+	0.297102i
$769$	−17.3510			−0.625692			−0.312846	−	0.949804i	$-0.601282\pi$
$769$	−17.3510			−0.625692			−0.312846	+	0.949804i	$0.601282\pi$
$770$		0			0
$771$	−9.69048	+	9.69048i	−0.348994	+	0.348994i
$772$	−3.69596	+	3.69596i	−0.133020	+	0.133020i
$773$			20.0124i			0.719796i	0.932992	+	0.359898i	$0.117188\pi$
$773$			20.0124i			0.719796i	−0.932992	+	0.359898i	$0.882812\pi$
$774$		−	9.89101i		−	0.355525i
$775$		0			0
$776$	11.8195	−	11.8195i	0.424296	−	0.424296i
$777$	−2.35786	−	2.35786i	−0.0845878	−	0.0845878i
$778$	−59.6352			−2.13803
$779$	16.7540	+	16.7540i	0.600274	+	0.600274i
$780$		0			0
$781$	−49.3670			−1.76649
$782$	−13.3604	+	11.0026i	−0.477767	+	0.393451i
$783$	21.1530			0.755948
$784$			13.2520i			0.473286i
$785$		0			0
$786$	19.8160			0.706815
$787$	23.9802	+	23.9802i	0.854802	+	0.854802i	0.990720	−	0.135918i	$-0.0433983\pi$
$787$	23.9802	+	23.9802i	0.854802	+	0.854802i	−0.135918	+	0.990720i	$0.543398\pi$
$788$	−15.6610	+	15.6610i	−0.557901	+	0.557901i
$789$	−7.17249	+	7.17249i	−0.255348	+	0.255348i
$790$		0			0
$791$			35.2420i			1.25306i
$792$	−14.3694	+	14.3694i	−0.510594	+	0.510594i
$793$	4.99520	−	4.99520i	0.177385	−	0.177385i
$794$	−10.3950	−	10.3950i	−0.368905	−	0.368905i
$795$		0			0
$796$	−4.95823	−	4.95823i	−0.175740	−	0.175740i
$797$		−	0.730287i		−	0.0258681i	−0.999916	−	0.0129340i	$-0.995883\pi$
$797$		−	0.730287i		−	0.0258681i	0.999916	−	0.0129340i	$-0.00411715\pi$
$798$	12.6089			0.446350
$799$	−1.92849	+	19.9265i	−0.0682252	+	0.704948i
$800$		0			0
$801$		−	28.4905i		−	1.00666i
$802$	−0.210972	−	0.210972i	−0.00744970	−	0.00744970i
$803$	8.80204			0.310617
$804$	−4.20796	−	4.20796i	−0.148403	−	0.148403i
$805$		0			0
$806$	−7.25200	+	7.25200i	−0.255441	+	0.255441i
$807$			10.0320i			0.353142i
$808$		−	12.9777i		−	0.456553i
$809$	−14.4485	+	14.4485i	−0.507982	+	0.507982i	−0.913907	−	0.405924i	$-0.866950\pi$
$809$	−14.4485	+	14.4485i	−0.507982	+	0.507982i	0.405924	+	0.913907i	$0.366950\pi$
$810$		0			0
$811$	−1.77975	−	1.77975i	−0.0624955	−	0.0624955i	0.675168	−	0.737664i	$-0.264071\pi$
$811$	−1.77975	−	1.77975i	−0.0624955	−	0.0624955i	−0.737664	+	0.675168i	$0.764071\pi$
$812$	25.8119			0.905822
$813$	−6.29809	−	6.29809i	−0.220883	−	0.220883i
$814$		−	19.3055i		−	0.676657i
$815$		0			0
$816$	−8.82524	+	7.26775i	−0.308945	+	0.254422i
$817$	8.17265			0.285925
$818$		−	24.1087i		−	0.842941i
$819$	−7.37699	−	7.37699i	−0.257773	−	0.257773i
$820$		0			0
$821$	10.8175	+	10.8175i	0.377533	+	0.377533i	0.870211	−	0.492678i	$-0.163982\pi$
$821$	10.8175	+	10.8175i	0.377533	+	0.377533i	−0.492678	+	0.870211i	$0.663982\pi$
$822$	9.92553	−	9.92553i	0.346193	−	0.346193i
$823$	−10.1433	+	10.1433i	−0.353574	+	0.353574i	−0.861437	−	0.507864i	$-0.830435\pi$
$823$	−10.1433	+	10.1433i	−0.353574	+	0.353574i	0.507864	+	0.861437i	$0.330435\pi$
$824$			2.48598i			0.0866033i
$825$		0			0
$826$	−23.8095	+	23.8095i	−0.828438	+	0.828438i
$827$	−28.5066	+	28.5066i	−0.991270	+	0.991270i	−0.999962	−	0.00869233i	$-0.997233\pi$
$827$	−28.5066	+	28.5066i	−0.991270	+	0.991270i	0.00869233	+	0.999962i	$0.497233\pi$
$828$	5.53213	+	5.53213i	0.192255	+	0.192255i
$829$	−37.1150			−1.28906			−0.644528	−	0.764581i	$-0.722946\pi$
$829$	−37.1150			−1.28906			−0.644528	+	0.764581i	$0.722946\pi$
$830$		0			0
$831$			7.96396i			0.276267i
$832$	−1.64280			−0.0569540
$833$	−11.0170	−	1.06623i	−0.381716	−	0.0369426i
$834$	−10.3315			−0.357751
$835$		0			0
$836$	19.8730	+	19.8730i	0.687322	+	0.687322i
$837$	14.5412			0.502616
$838$	30.0593	+	30.0593i	1.03838	+	1.03838i
$839$	5.02173	−	5.02173i	0.173370	−	0.173370i	−0.615089	−	0.788458i	$-0.710880\pi$
$839$	5.02173	−	5.02173i	0.173370	−	0.173370i	0.788458	+	0.615089i	$0.210880\pi$
$840$		0			0
$841$			14.8890i			0.513414i
$842$		−	10.5089i		−	0.362161i
$843$	3.10178	−	3.10178i	0.106831	−	0.106831i
$844$	−0.817235	+	0.817235i	−0.0281304	+	0.0281304i
$845$		0			0
$846$	23.5054			0.808134
$847$	45.0972	+	45.0972i	1.54956	+	1.54956i
$848$		−	45.0048i		−	1.54547i
$849$	11.7440			0.403052
$850$		0			0
$851$	4.44050			0.152218
$852$			6.18629i			0.211939i
$853$	−27.1104	−	27.1104i	−0.928242	−	0.928242i	0.0693502	−	0.997592i	$-0.477907\pi$
$853$	−27.1104	−	27.1104i	−0.928242	−	0.928242i	−0.997592	+	0.0693502i	$0.977907\pi$
$854$	−31.7460			−1.08633
$855$		0			0
$856$	−16.2022	+	16.2022i	−0.553781	+	0.553781i
$857$	−1.22358	+	1.22358i	−0.0417966	+	0.0417966i	−0.727696	−	0.685900i	$-0.759409\pi$
$857$	−1.22358	+	1.22358i	−0.0417966	+	0.0417966i	0.685900	+	0.727696i	$0.259409\pi$
$858$			7.09880i			0.242349i
$859$			30.9245i			1.05513i	0.849515	+	0.527565i	$0.176895\pi$
$859$			30.9245i			1.05513i	−0.849515	+	0.527565i	$0.823105\pi$
$860$		0			0
$861$	7.32149	−	7.32149i	0.249516	−	0.249516i
$862$	−8.84487	−	8.84487i	−0.301258	−	0.301258i
$863$	40.2134			1.36888			0.684439	−	0.729070i	$-0.260047\pi$
$863$	40.2134			1.36888			0.684439	+	0.729070i	$0.260047\pi$
$864$	14.0080	+	14.0080i	0.476562	+	0.476562i
$865$		0			0
$866$	27.8550			0.946550
$867$	−5.33195	−	7.92156i	−0.181082	−	0.269030i
$868$	17.7438			0.602265
$869$		−	27.5575i		−	0.934824i
$870$		0			0
$871$	−10.5675			−0.358066
$872$	−0.425581	−	0.425581i	−0.0144120	−	0.0144120i
$873$	23.5226	−	23.5226i	0.796119	−	0.796119i
$874$	−11.8730	+	11.8730i	−0.401610	+	0.401610i
$875$		0			0
$876$		−	1.10300i		−	0.0372670i
$877$	−0.715057	+	0.715057i	−0.0241458	+	0.0241458i	−0.719077	−	0.694931i	$-0.755435\pi$
$877$	−0.715057	+	0.715057i	−0.0241458	+	0.0241458i	0.694931	+	0.719077i	$0.255435\pi$
$878$	−1.87502	+	1.87502i	−0.0632788	+	0.0632788i
$879$	−1.90449	−	1.90449i	−0.0642368	−	0.0642368i
$880$		0			0
$881$	13.8095	+	13.8095i	0.465253	+	0.465253i	0.900373	−	0.435119i	$-0.143294\pi$
$881$	13.8095	+	13.8095i	0.465253	+	0.465253i	−0.435119	+	0.900373i	$0.643294\pi$
$882$			12.9957i			0.437589i
$883$	−12.6125			−0.424445			−0.212223	−	0.977221i	$-0.568070\pi$
$883$	−12.6125			−0.424445			−0.212223	+	0.977221i	$0.568070\pi$
$884$	0.620991	−	6.41649i	0.0208862	−	0.215810i
$885$		0			0
$886$			23.0535i			0.774497i
$887$	26.2443	+	26.2443i	0.881199	+	0.881199i	0.993657	−	0.112458i	$-0.0358723\pi$
$887$	26.2443	+	26.2443i	0.881199	+	0.881199i	−0.112458	+	0.993657i	$0.535872\pi$
$888$	1.44534			0.0485026
$889$	12.8730	+	12.8730i	0.431746	+	0.431746i
$890$		0			0
$891$	−24.8412	+	24.8412i	−0.832213	+	0.832213i
$892$			1.56350i			0.0523498i
$893$			19.4218i			0.649927i
$894$	−11.4145	+	11.4145i	−0.381757	+	0.381757i
$895$		0			0
$896$	−22.0852	−	22.0852i	−0.737816	−	0.737816i
$897$	−1.63281			−0.0545180
$898$	12.4087	+	12.4087i	0.414084	+	0.414084i
$899$			30.1705i			1.00624i
$900$		0			0
$901$	37.4145	+	3.62099i	1.24646	+	0.120633i
$902$	59.9463			1.99599
$903$		−	3.57145i		−	0.118850i
$904$	−10.8015	−	10.8015i	−0.359252	−	0.359252i
$905$		0			0
$906$	2.41303	+	2.41303i	0.0801676	+	0.0801676i
$907$	−24.3554	+	24.3554i	−0.808706	+	0.808706i	−0.984438	−	0.175732i	$-0.943771\pi$
$907$	−24.3554	+	24.3554i	−0.808706	+	0.808706i	0.175732	+	0.984438i	$0.443771\pi$
$908$	10.2542	−	10.2542i	0.340298	−	0.340298i
$909$		−	25.8275i		−	0.856644i
$910$		0			0
$911$	−7.21023	+	7.21023i	−0.238886	+	0.238886i	−0.816389	−	0.577503i	$-0.804027\pi$
$911$	−7.21023	+	7.21023i	−0.238886	+	0.238886i	0.577503	+	0.816389i	$0.304027\pi$
$912$	−7.84272	+	7.84272i	−0.259698	+	0.259698i
$913$	−15.6610	−	15.6610i	−0.518304	−	0.518304i
$914$	65.3309			2.16096
$915$		0			0
$916$		−	14.7085i		−	0.485983i
$917$	−60.8804			−2.01045
$918$	−18.3263	+	15.0921i	−0.604858	+	0.498112i
$919$	−50.5315			−1.66688			−0.833440	−	0.552611i	$-0.813632\pi$
$919$	−50.5315			−1.66688			−0.833440	+	0.552611i	$0.813632\pi$
$920$		0			0
$921$	−9.92648	−	9.92648i	−0.327089	−	0.327089i
$922$	72.2405			2.37911
$923$	7.76785	+	7.76785i	0.255682	+	0.255682i
$924$	8.68450	−	8.68450i	0.285699	−	0.285699i
$925$		0			0
$926$		−	27.7005i		−	0.910295i
$927$			4.94748i			0.162496i
$928$	−29.0643	+	29.0643i	−0.954081	+	0.954081i
$929$	−20.0615	+	20.0615i	−0.658196	+	0.658196i	−0.954953	−	0.296757i	$-0.904095\pi$
$929$	−20.0615	+	20.0615i	−0.658196	+	0.658196i	0.296757	+	0.954953i	$0.404095\pi$
$930$		0			0
$931$	−10.7380			−0.351923
$932$	10.0076	+	10.0076i	0.327808	+	0.327808i
$933$		−	2.26493i		−	0.0741504i
$934$	35.0695			1.14751
$935$		0			0
$936$	4.52202			0.147807
$937$		−	47.5024i		−	1.55183i	−0.630835	−	0.775917i	$-0.717287\pi$
$937$		−	47.5024i		−	1.55183i	0.630835	−	0.775917i	$-0.282713\pi$
$938$	33.5798	+	33.5798i	1.09642	+	1.09642i
$939$	−12.7220			−0.415166
$940$		0			0
$941$	32.5555	−	32.5555i	1.06128	−	1.06128i	0.0632823	−	0.997996i	$-0.479843\pi$
$941$	32.5555	−	32.5555i	1.06128	−	1.06128i	0.997996	−	0.0632823i	$-0.0201569\pi$
$942$	−2.80866	+	2.80866i	−0.0915112	+	0.0915112i
$943$			13.7884i			0.449011i
$944$		−	29.6190i		−	0.964016i
$945$		0			0
$946$	14.6210	−	14.6210i	0.475369	−	0.475369i
$947$	−21.0282	−	21.0282i	−0.683324	−	0.683324i	0.277424	−	0.960748i	$-0.410519\pi$
$947$	−21.0282	−	21.0282i	−0.683324	−	0.683324i	−0.960748	+	0.277424i	$0.910519\pi$
$948$	−3.45329			−0.112158
$949$	−1.38499	−	1.38499i	−0.0449588	−	0.0449588i
$950$		0			0
$951$	4.64701			0.150690
$952$	13.3604	−	11.0026i	0.433014	−	0.356595i
$953$	−9.02109			−0.292222			−0.146111	−	0.989268i	$-0.546676\pi$
$953$	−9.02109			−0.292222			−0.146111	+	0.989268i	$0.546676\pi$
$954$		−	44.1344i		−	1.42891i
$955$		0			0
$956$	−6.42903			−0.207930
$957$	14.7666	+	14.7666i	0.477335	+	0.477335i
$958$	−18.5594	+	18.5594i	−0.599628	+	0.599628i
$959$	−30.4940	+	30.4940i	−0.984702	+	0.984702i
$960$		0			0
$961$		−	10.2600i		−	0.330968i
$962$	−3.03770	+	3.03770i	−0.0979394	+	0.0979394i
$963$	−32.2449	+	32.2449i	−1.03908	+	1.03908i
$964$	−7.51200	−	7.51200i	−0.241945	−	0.241945i
$965$		0			0
$966$	5.18850	+	5.18850i	0.166937	+	0.166937i
$967$		−	11.7541i		−	0.377986i	−0.981978	−	0.188993i	$-0.939478\pi$
$967$		−	11.7541i		−	0.377986i	0.981978	−	0.188993i	$-0.0605223\pi$
$968$	−27.6441			−0.888516
$969$	−5.88899	−	7.15101i	−0.189182	−	0.229724i
$970$		0			0
$971$		−	19.9525i		−	0.640306i	−0.947366	−	0.320153i	$-0.896266\pi$
$971$		−	19.9525i		−	0.640306i	0.947366	−	0.320153i	$-0.103734\pi$
$972$	11.5931	+	11.5931i	0.371849	+	0.371849i
$973$	31.7413			1.01758
$974$	37.8687	+	37.8687i	1.21339	+	1.21339i
$975$		0			0
$976$	19.7460	−	19.7460i	0.632054	−	0.632054i
$977$			27.2005i			0.870221i	0.900377	+	0.435110i	$0.143291\pi$
$977$			27.2005i			0.870221i	−0.900377	+	0.435110i	$0.856709\pi$
$978$		−	14.9099i		−	0.476767i
$979$	42.1150	−	42.1150i	1.34600	−	1.34600i
$980$		0			0
$981$	−0.846971	−	0.846971i	−0.0270417	−	0.0270417i
$982$	−37.9989			−1.21259
$983$	5.03803	+	5.03803i	0.160688	+	0.160688i	0.782872	−	0.622183i	$-0.213754\pi$
$983$	5.03803	+	5.03803i	0.160688	+	0.160688i	−0.622183	+	0.782872i	$0.713754\pi$
$984$			4.48800i			0.143072i
$985$		0			0
$986$	−31.3135	−	38.0240i	−0.997225	−	1.21093i
$987$	8.48734			0.270155
$988$		−	6.25400i		−	0.198966i
$989$	3.36301	+	3.36301i	0.106937	+	0.106937i
$990$		0			0
$991$	40.2817	+	40.2817i	1.27959	+	1.27959i	0.940896	+	0.338695i	$0.109986\pi$
$991$	40.2817	+	40.2817i	1.27959	+	1.27959i	0.338695	+	0.940896i	$0.390014\pi$
$992$	−19.9796	+	19.9796i	−0.634351	+	0.634351i
$993$	2.18926	−	2.18926i	0.0694740	−	0.0694740i
$994$		−	49.3670i		−	1.56583i
$995$		0			0
$996$	−1.96252	+	1.96252i	−0.0621847	+	0.0621847i
$997$	3.56701	−	3.56701i	0.112968	−	0.112968i	−0.648363	−	0.761331i	$-0.724546\pi$
$997$	3.56701	−	3.56701i	0.112968	−	0.112968i	0.761331	+	0.648363i	$0.224546\pi$
$998$	−11.9971	−	11.9971i	−0.379761	−	0.379761i
$999$	6.09097			0.192710

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.e.d.251.2		12
5.2	odd	4		85.2.j.c.64.5	yes	12
5.3	odd	4		85.2.j.c.64.2	yes	12
5.4	even	2	inner	425.2.e.d.251.5		12
15.2	even	4		765.2.t.e.64.2		12
15.8	even	4		765.2.t.e.64.5		12
17.2	even	8		7225.2.a.bp.1.10		12
17.4	even	4	inner	425.2.e.d.276.5		12
17.15	even	8		7225.2.a.bp.1.9		12
85.2	odd	8		1445.2.b.f.579.9		12
85.4	even	4	inner	425.2.e.d.276.2		12
85.19	even	8		7225.2.a.bp.1.3		12
85.32	odd	8		1445.2.b.f.579.10		12
85.38	odd	4		85.2.j.c.4.5	yes	12
85.49	even	8		7225.2.a.bp.1.4		12
85.53	odd	8		1445.2.b.f.579.4		12
85.72	odd	4		85.2.j.c.4.2	✓	12
85.83	odd	8		1445.2.b.f.579.3		12
255.38	even	4		765.2.t.e.514.2		12
255.242	even	4		765.2.t.e.514.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.j.c.4.2	✓	12	85.72	odd	4
85.2.j.c.4.5	yes	12	85.38	odd	4
85.2.j.c.64.2	yes	12	5.3	odd	4
85.2.j.c.64.5	yes	12	5.2	odd	4
425.2.e.d.251.2		12	1.1	even	1	trivial
425.2.e.d.251.5		12	5.4	even	2	inner
425.2.e.d.276.2		12	85.4	even	4	inner
425.2.e.d.276.5		12	17.4	even	4	inner
765.2.t.e.64.2		12	15.2	even	4
765.2.t.e.64.5		12	15.8	even	4
765.2.t.e.514.2		12	255.38	even	4
765.2.t.e.514.5		12	255.242	even	4
1445.2.b.f.579.3		12	85.83	odd	8
1445.2.b.f.579.4		12	85.53	odd	8
1445.2.b.f.579.9		12	85.2	odd	8
1445.2.b.f.579.10		12	85.32	odd	8
7225.2.a.bp.1.3		12	85.19	even	8
7225.2.a.bp.1.4		12	85.49	even	8
7225.2.a.bp.1.9		12	17.15	even	8
7225.2.a.bp.1.10		12	17.2	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.80333i q^{2} +(0.397180 + 0.397180i) q^{3} -1.25200 q^{4} +(0.716248 - 0.716248i) q^{6} +(-2.20051 + 2.20051i) q^{7} -1.34889i q^{8} -2.68450i q^{9} +(3.96825 - 3.96825i) q^{11} +(-0.497270 - 0.497270i) q^{12} -1.24880 q^{13} +(3.96825 + 3.96825i) q^{14} -4.93650 q^{16} +(0.397180 - 4.10393i) q^{17} -4.84103 q^{18} -4.00000i q^{19} -1.74800 q^{21} +(-7.15606 - 7.15606i) q^{22} +(1.64598 - 1.64598i) q^{23} +(0.535753 - 0.535753i) q^{24} +2.25200i q^{26} +(2.25777 - 2.25777i) q^{27} +(2.75504 - 2.75504i) q^{28} +(4.68450 + 4.68450i) q^{29} +(3.22025 + 3.22025i) q^{31} +6.20435i q^{32} +3.15222 q^{33} +(-7.40074 - 0.716248i) q^{34} +3.36099i q^{36} +(1.34889 + 1.34889i) q^{37} -7.21332 q^{38} +(-0.495999 - 0.495999i) q^{39} +(-4.18850 + 4.18850i) q^{41} +3.15222i q^{42} +2.04316i q^{43} +(-4.96825 + 4.96825i) q^{44} +(-2.96825 - 2.96825i) q^{46} -4.85546 q^{47} +(-1.96068 - 1.96068i) q^{48} -2.68450i q^{49} +(1.78775 - 1.47225i) q^{51} +1.56350 q^{52} +9.11674i q^{53} +(-4.07151 - 4.07151i) q^{54} +(2.96825 + 2.96825i) q^{56} +(1.58872 - 1.58872i) q^{57} +(8.44769 - 8.44769i) q^{58} +6.00000i q^{59} +(-4.00000 + 4.00000i) q^{61} +(5.80717 - 5.80717i) q^{62} +(5.90726 + 5.90726i) q^{63} +1.31550 q^{64} -5.68450i q^{66} +8.46212 q^{67} +(-0.497270 + 5.13812i) q^{68} +1.30750 q^{69} +(-6.22025 - 6.22025i) q^{71} -3.62109 q^{72} +(1.10906 + 1.10906i) q^{73} +(2.43250 - 2.43250i) q^{74} +5.00800i q^{76} +17.4643i q^{77} +(-0.894450 + 0.894450i) q^{78} +(3.47225 - 3.47225i) q^{79} -6.26000 q^{81} +(7.55324 + 7.55324i) q^{82} -3.94658i q^{83} +2.18850 q^{84} +3.68450 q^{86} +3.72118i q^{87} +(-5.35273 - 5.35273i) q^{88} +10.6130 q^{89} +(2.74800 - 2.74800i) q^{91} +(-2.06077 + 2.06077i) q^{92} +2.55804i q^{93} +8.75600i q^{94} +(-2.46425 + 2.46425i) q^{96} +(8.76239 + 8.76239i) q^{97} -4.84103 q^{98} +(-10.6527 - 10.6527i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 20 q^{6} + 16 q^{11} + 16 q^{14} + 4 q^{16} - 24 q^{21} + 32 q^{24} - 4 q^{29} + 4 q^{31} - 12 q^{39} + 16 q^{41} - 28 q^{44} - 4 q^{46} + 44 q^{51} - 100 q^{54} + 4 q^{56} - 48 q^{61}+ \cdots - 36 q^{99}+O(q^{100}) \) 12 * q - 12 * q^4 - 20 * q^6 + 16 * q^11 + 16 * q^14 + 4 * q^16 - 24 * q^21 + 32 * q^24 - 4 * q^29 + 4 * q^31 - 12 * q^39 + 16 * q^41 - 28 * q^44 - 4 * q^46 + 44 * q^51 - 100 * q^54 + 4 * q^56 - 48 * q^61 + 76 * q^64 + 88 * q^69 - 40 * q^71 - 28 * q^74 + 4 * q^79 - 60 * q^81 - 40 * q^84 - 16 * q^86 + 16 * q^89 + 36 * q^91 - 4 * q^96 - 36 * q^99

Introduction

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