LMFDB - Embedded newform 475.2.g.b.18.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(18,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("475.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.g (of order $4$, degree $2$, 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:	$3.79289409601$
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} + 35x^{8} + 223x^{4} + 289 $ x^12 + 35x^8 + 223x^4 + 289
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			18.6
Root			$1.61467 - 1.61467i$ of defining polynomial
Character	$\chi$	$=$	475.18
Dual form			475.2.g.b.132.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61467 + 1.61467i) q^{2} +(-1.11233 + 1.11233i) q^{3} +3.21432i q^{4} -3.59210 q^{6} +(-1.21432 + 1.21432i) q^{7} +(-1.96073 + 1.96073i) q^{8} +0.525428i q^{9} +O(q^{10})$	\(q+(1.61467 + 1.61467i) q^{2} +(-1.11233 + 1.11233i) q^{3} +3.21432i q^{4} -3.59210 q^{6} +(-1.21432 + 1.21432i) q^{7} +(-1.96073 + 1.96073i) q^{8} +0.525428i q^{9} -3.52543 q^{11} +(-3.57540 - 3.57540i) q^{12} +(1.11233 - 1.11233i) q^{13} -3.92145 q^{14} +0.0967881 q^{16} +(-3.90321 + 3.90321i) q^{17} +(-0.848392 + 0.848392i) q^{18} +(3.92145 + 1.90321i) q^{19} -2.70146i q^{21} +(-5.69240 - 5.69240i) q^{22} +(-1.21432 - 1.21432i) q^{23} -4.36196i q^{24} +3.59210 q^{26} +(-3.92145 - 3.92145i) q^{27} +(-3.90321 - 3.90321i) q^{28} +8.68335 q^{29} -5.14145i q^{31} +(4.07773 + 4.07773i) q^{32} +(3.92145 - 3.92145i) q^{33} -12.6048 q^{34} -1.68889 q^{36} +(2.11701 + 2.11701i) q^{37} +(3.25879 + 9.40491i) q^{38} +2.47457i q^{39} +11.3848i q^{41} +(4.36196 - 4.36196i) q^{42} +(1.96989 + 1.96989i) q^{43} -11.3319i q^{44} -3.92145i q^{46} +(5.83654 - 5.83654i) q^{47} +(-0.107661 + 0.107661i) q^{48} +4.05086i q^{49} -8.68335i q^{51} +(3.57540 + 3.57540i) q^{52} +(0.107661 - 0.107661i) q^{53} -12.6637i q^{54} -4.76190i q^{56} +(-6.47897 + 2.24496i) q^{57} +(14.0207 + 14.0207i) q^{58} -11.3848 q^{59} +9.13828 q^{61} +(8.30174 - 8.30174i) q^{62} +(-0.638037 - 0.638037i) q^{63} +12.9748i q^{64} +12.6637 q^{66} +(6.56634 + 6.56634i) q^{67} +(-12.5462 - 12.5462i) q^{68} +2.70146 q^{69} -2.70146i q^{71} +(-1.03022 - 1.03022i) q^{72} +(-4.65878 - 4.65878i) q^{73} +6.83654i q^{74} +(-6.11753 + 12.6048i) q^{76} +(4.28100 - 4.28100i) q^{77} +(-3.99562 + 3.99562i) q^{78} -3.54190 q^{79} +7.14764 q^{81} +(-18.3827 + 18.3827i) q^{82} +(3.06668 + 3.06668i) q^{83} +8.68335 q^{84} +6.36144i q^{86} +(-9.65878 + 9.65878i) q^{87} +(6.91240 - 6.91240i) q^{88} +6.24336 q^{89} +2.70146i q^{91} +(3.90321 - 3.90321i) q^{92} +(5.71900 + 5.71900i) q^{93} +18.8482 q^{94} -9.07160 q^{96} +(-1.42490 - 1.42490i) q^{97} +(-6.54080 + 6.54080i) q^{98} -1.85236i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 16 q^{6} + 12 q^{7}+O(q^{10}) $ 12 * q - 16 * q^6 + 12 * q^7	$ 12 q - 16 q^{6} + 12 q^{7} - 16 q^{11} + 28 q^{16} - 20 q^{17} + 12 q^{23} + 16 q^{26} - 20 q^{28} - 20 q^{36} - 4 q^{38} - 4 q^{43} + 44 q^{47} + 88 q^{58} - 24 q^{61} - 8 q^{62} - 60 q^{63} - 8 q^{66} - 44 q^{68} - 28 q^{73} - 20 q^{76} + 24 q^{77} + 60 q^{81} - 88 q^{82} + 36 q^{83} - 88 q^{87} + 20 q^{92} + 96 q^{93} + 24 q^{96}+O(q^{100}) $ 12 * q - 16 * q^6 + 12 * q^7 - 16 * q^11 + 28 * q^16 - 20 * q^17 + 12 * q^23 + 16 * q^26 - 20 * q^28 - 20 * q^36 - 4 * q^38 - 4 * q^43 + 44 * q^47 + 88 * q^58 - 24 * q^61 - 8 * q^62 - 60 * q^63 - 8 * q^66 - 44 * q^68 - 28 * q^73 - 20 * q^76 + 24 * q^77 + 60 * q^81 - 88 * q^82 + 36 * q^83 - 88 * q^87 + 20 * q^92 + 96 * q^93 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	1.61467	+	1.61467i	1.14174	+	1.14174i	0.988131	+	0.153613i	$0.0490910\pi$
$2$	1.61467	+	1.61467i	1.14174	+	1.14174i	0.153613	+	0.988131i	$0.450909\pi$
$3$	−1.11233	+	1.11233i	−0.642206	+	0.642206i	−0.951097	−	0.308891i	$-0.900042\pi$
$3$	−1.11233	+	1.11233i	−0.642206	+	0.642206i	0.308891	+	0.951097i	$0.400042\pi$
$4$			3.21432i			1.60716i
$5$		0			0
$5$		0			0
$6$	−3.59210			−1.46647
$7$	−1.21432	+	1.21432i	−0.458970	+	0.458970i	−0.898317	−	0.439347i	$-0.855210\pi$
$7$	−1.21432	+	1.21432i	−0.458970	+	0.458970i	0.439347	+	0.898317i	$0.355210\pi$
$8$	−1.96073	+	1.96073i	−0.693221	+	0.693221i
$9$			0.525428i			0.175143i
$10$		0			0
$11$	−3.52543			−1.06296			−0.531478	−	0.847072i	$-0.678363\pi$
$11$	−3.52543			−1.06296			−0.531478	+	0.847072i	$0.678363\pi$
$12$	−3.57540	−	3.57540i	−1.03213	−	1.03213i
$13$	1.11233	−	1.11233i	0.308506	−	0.308506i	−0.535824	−	0.844330i	$-0.679999\pi$
$13$	1.11233	−	1.11233i	0.308506	−	0.308506i	0.844330	+	0.535824i	$0.179999\pi$
$14$	−3.92145			−1.04805
$15$		0			0
$16$	0.0967881			0.0241970
$17$	−3.90321	+	3.90321i	−0.946668	+	0.946668i	−0.998648	−	0.0519802i	$-0.983447\pi$
$17$	−3.90321	+	3.90321i	−0.946668	+	0.946668i	0.0519802	+	0.998648i	$0.483447\pi$
$18$	−0.848392	+	0.848392i	−0.199968	+	0.199968i
$19$	3.92145	+	1.90321i	0.899643	+	0.436627i
$19$	3.92145	+	1.90321i	0.899643	+	0.436627i
$20$		0			0
$21$		−	2.70146i		−	0.589506i
$22$	−5.69240	−	5.69240i	−1.21362	−	1.21362i
$23$	−1.21432	−	1.21432i	−0.253203	−	0.253203i	0.569079	−	0.822283i	$-0.307300\pi$
$23$	−1.21432	−	1.21432i	−0.253203	−	0.253203i	−0.822283	+	0.569079i	$0.807300\pi$
$24$		−	4.36196i		−	0.890382i
$25$		0			0
$26$	3.59210			0.704470
$27$	−3.92145	−	3.92145i	−0.754684	−	0.754684i
$28$	−3.90321	−	3.90321i	−0.737638	−	0.737638i
$29$	8.68335			1.61246			0.806229	−	0.591604i	$-0.201505\pi$
$29$	8.68335			1.61246			0.806229	+	0.591604i	$0.201505\pi$
$30$		0			0
$31$		−	5.14145i		−	0.923431i	−0.887028	−	0.461715i	$-0.847234\pi$
$31$		−	5.14145i		−	0.923431i	0.887028	−	0.461715i	$-0.152766\pi$
$32$	4.07773	+	4.07773i	0.720848	+	0.720848i
$33$	3.92145	−	3.92145i	0.682637	−	0.682637i
$34$	−12.6048			−2.16171
$35$		0			0
$36$	−1.68889			−0.281482
$37$	2.11701	+	2.11701i	0.348034	+	0.348034i	0.859377	−	0.511343i	$-0.170852\pi$
$37$	2.11701	+	2.11701i	0.348034	+	0.348034i	−0.511343	+	0.859377i	$0.670852\pi$
$38$	3.25879	+	9.40491i	0.528646	+	1.52568i
$39$			2.47457i			0.396249i
$40$		0			0
$41$			11.3848i			1.77801i	0.457899	+	0.889004i	$0.348602\pi$
$41$			11.3848i			1.77801i	−0.457899	+	0.889004i	$0.651398\pi$
$42$	4.36196	−	4.36196i	0.673065	−	0.673065i
$43$	1.96989	+	1.96989i	0.300405	+	0.300405i	0.841172	−	0.540767i	$-0.181866\pi$
$43$	1.96989	+	1.96989i	0.300405	+	0.300405i	−0.540767	+	0.841172i	$0.681866\pi$
$44$		−	11.3319i		−	1.70834i
$45$		0			0
$46$		−	3.92145i		−	0.578187i
$47$	5.83654	−	5.83654i	0.851346	−	0.851346i	−0.138953	−	0.990299i	$-0.544374\pi$
$47$	5.83654	−	5.83654i	0.851346	−	0.851346i	0.990299	+	0.138953i	$0.0443736\pi$
$48$	−0.107661	+	0.107661i	−0.0155395	+	0.0155395i
$49$			4.05086i			0.578694i
$50$		0			0
$51$		−	8.68335i		−	1.21591i
$52$	3.57540	+	3.57540i	0.495818	+	0.495818i
$53$	0.107661	−	0.107661i	0.0147883	−	0.0147883i	−0.699674	−	0.714462i	$-0.746671\pi$
$53$	0.107661	−	0.107661i	0.0147883	−	0.0147883i	0.714462	+	0.699674i	$0.246671\pi$
$54$		−	12.6637i		−	1.72331i
$55$		0			0
$56$		−	4.76190i		−	0.636335i
$57$	−6.47897	+	2.24496i	−0.858160	+	0.297352i
$58$	14.0207	+	14.0207i	1.84101	+	1.84101i
$59$	−11.3848			−1.48218			−0.741088	−	0.671408i	$-0.765690\pi$
$59$	−11.3848			−1.48218			−0.741088	+	0.671408i	$0.765690\pi$
$60$		0			0
$61$	9.13828			1.17004			0.585018	−	0.811020i	$-0.301087\pi$
$61$	9.13828			1.17004			0.585018	+	0.811020i	$0.301087\pi$
$62$	8.30174	−	8.30174i	1.05432	−	1.05432i
$63$	−0.638037	−	0.638037i	−0.0803851	−	0.0803851i
$64$			12.9748i			1.62185i
$65$		0			0
$66$	12.6637			1.55879
$67$	6.56634	+	6.56634i	0.802206	+	0.802206i	0.983440	−	0.181234i	$-0.0580091\pi$
$67$	6.56634	+	6.56634i	0.802206	+	0.802206i	−0.181234	+	0.983440i	$0.558009\pi$
$68$	−12.5462	−	12.5462i	−1.52145	−	1.52145i
$69$	2.70146			0.325217
$70$		0			0
$71$		−	2.70146i		−	0.320604i	−0.987068	−	0.160302i	$-0.948753\pi$
$71$		−	2.70146i		−	0.320604i	0.987068	−	0.160302i	$-0.0512468\pi$
$72$	−1.03022	−	1.03022i	−0.121413	−	0.121413i
$73$	−4.65878	−	4.65878i	−0.545269	−	0.545269i	0.379800	−	0.925069i	$-0.375993\pi$
$73$	−4.65878	−	4.65878i	−0.545269	−	0.545269i	−0.925069	+	0.379800i	$0.875993\pi$
$74$			6.83654i			0.794731i
$75$		0			0
$76$	−6.11753	+	12.6048i	−0.701729	+	1.44587i
$77$	4.28100	−	4.28100i	0.487865	−	0.487865i
$78$	−3.99562	+	3.99562i	−0.452415	+	0.452415i
$79$	−3.54190			−0.398495			−0.199248	−	0.979949i	$-0.563850\pi$
$79$	−3.54190			−0.398495			−0.199248	+	0.979949i	$0.563850\pi$
$80$		0			0
$81$	7.14764			0.794183
$82$	−18.3827	+	18.3827i	−2.03003	+	2.03003i
$83$	3.06668	+	3.06668i	0.336611	+	0.336611i	0.855090	−	0.518479i	$-0.173502\pi$
$83$	3.06668	+	3.06668i	0.336611	+	0.336611i	−0.518479	+	0.855090i	$0.673502\pi$
$84$	8.68335			0.947431
$85$		0			0
$86$			6.36144i			0.685972i
$87$	−9.65878	+	9.65878i	−1.03553	+	1.03553i
$88$	6.91240	−	6.91240i	0.736864	−	0.736864i
$89$	6.24336			0.661795			0.330897	−	0.943667i	$-0.392649\pi$
$89$	6.24336			0.661795			0.330897	+	0.943667i	$0.392649\pi$
$90$		0			0
$91$			2.70146i			0.283190i
$92$	3.90321	−	3.90321i	0.406938	−	0.406938i
$93$	5.71900	+	5.71900i	0.593033	+	0.593033i
$94$	18.8482			1.94404
$95$		0			0
$96$	−9.07160			−0.925866
$97$	−1.42490	−	1.42490i	−0.144676	−	0.144676i	0.631059	−	0.775735i	$-0.282621\pi$
$97$	−1.42490	−	1.42490i	−0.144676	−	0.144676i	−0.775735	+	0.631059i	$0.782621\pi$
$98$	−6.54080	+	6.54080i	−0.660720	+	0.660720i
$99$		−	1.85236i		−	0.186169i
$100$		0			0
$101$	−4.28100			−0.425975			−0.212988	−	0.977055i	$-0.568319\pi$
$101$	−4.28100			−0.425975			−0.212988	+	0.977055i	$0.568319\pi$
$102$	14.0207	−	14.0207i	1.38826	−	1.38826i
$103$	7.73524	−	7.73524i	0.762176	−	0.762176i	−0.214539	−	0.976715i	$-0.568825\pi$
$103$	7.73524	−	7.73524i	0.762176	−	0.762176i	0.976715	+	0.214539i	$0.0688250\pi$
$104$			4.36196i			0.427726i
$105$		0			0
$106$	0.347673			0.0337690
$107$	0.584451	+	0.584451i	0.0565010	+	0.0565010i	0.734793	−	0.678292i	$-0.237279\pi$
$107$	0.584451	+	0.584451i	0.0565010	+	0.0565010i	−0.678292	+	0.734793i	$0.737279\pi$
$108$	12.6048	−	12.6048i	1.21290	−	1.21290i
$109$	5.14145			0.492461			0.246231	−	0.969211i	$-0.420808\pi$
$109$	5.14145			0.492461			0.246231	+	0.969211i	$0.420808\pi$
$110$		0			0
$111$	−4.70964			−0.447019
$112$	−0.117532	+	0.117532i	−0.0111057	+	0.0111057i
$113$	12.4971	−	12.4971i	1.17563	−	1.17563i	0.194786	−	0.980846i	$-0.437599\pi$
$113$	12.4971	−	12.4971i	1.17563	−	1.17563i	0.980846	−	0.194786i	$-0.0624013\pi$
$114$	−14.0863	−	6.83654i	−1.31930	−	0.640300i
$115$		0			0
$116$			27.9111i			2.59148i
$117$	0.584451	+	0.584451i	0.0540325	+	0.0540325i
$118$	−18.3827	−	18.3827i	−1.69227	−	1.69227i
$119$		−	9.47949i		−	0.868984i
$120$		0			0
$121$	1.42864			0.129876
$122$	14.7553	+	14.7553i	1.33588	+	1.33588i
$123$	−12.6637	−	12.6637i	−1.14185	−	1.14185i
$124$	16.5263			1.48410
$125$		0			0
$126$		−	2.06044i		−	0.183558i
$127$	−1.80445	−	1.80445i	−0.160119	−	0.160119i	0.622501	−	0.782619i	$-0.286117\pi$
$127$	−1.80445	−	1.80445i	−0.160119	−	0.160119i	−0.782619	+	0.622501i	$0.786117\pi$
$128$	−12.7946	+	12.7946i	−1.13089	+	1.13089i
$129$	−4.38235			−0.385844
$130$		0			0
$131$	−17.7146			−1.54773			−0.773864	−	0.633352i	$-0.781679\pi$
$131$	−17.7146			−1.54773			−0.773864	+	0.633352i	$0.781679\pi$
$132$	12.6048	+	12.6048i	1.09711	+	1.09711i
$133$	−7.07300	+	2.45079i	−0.613307	+	0.212510i
$134$			21.2050i			1.83183i
$135$		0			0
$136$		−	15.3063i		−	1.31250i
$137$	2.80642	−	2.80642i	0.239769	−	0.239769i	−0.576985	−	0.816754i	$-0.695771\pi$
$137$	2.80642	−	2.80642i	0.239769	−	0.239769i	0.816754	+	0.576985i	$0.195771\pi$
$138$	4.36196	+	4.36196i	0.371315	+	0.371315i
$139$		−	8.14764i		−	0.691074i	−0.938405	−	0.345537i	$-0.887697\pi$
$139$		−	8.14764i		−	0.691074i	0.938405	−	0.345537i	$-0.112303\pi$
$140$		0			0
$141$			12.9843i			1.09348i
$142$	4.36196	−	4.36196i	0.366048	−	0.366048i
$143$	−3.92145	+	3.92145i	−0.327928	+	0.327928i
$144$			0.0508551i			0.00423793i
$145$		0			0
$146$		−	15.0448i		−	1.24512i
$147$	−4.50590	−	4.50590i	−0.371641	−	0.371641i
$148$	−6.80474	+	6.80474i	−0.559346	+	0.559346i
$149$		−	3.52543i		−	0.288814i	−0.989518	−	0.144407i	$-0.953873\pi$
$149$		−	3.52543i		−	0.288814i	0.989518	−	0.144407i	$-0.0461275\pi$
$150$		0			0
$151$		−	8.68335i		−	0.706641i	−0.935502	−	0.353320i	$-0.885053\pi$
$151$		−	8.68335i		−	0.706641i	0.935502	−	0.353320i	$-0.114947\pi$
$152$	−11.4206	+	3.95722i	−0.926330	+	0.320973i
$153$	−2.05086	−	2.05086i	−0.165802	−	0.165802i
$154$	13.8248			1.11403
$155$		0			0
$156$	−7.95407			−0.636835
$157$	−1.70964	+	1.70964i	−0.136444	+	0.136444i	−0.772030	−	0.635586i	$-0.780758\pi$
$157$	−1.70964	+	1.70964i	−0.136444	+	0.136444i	0.635586	+	0.772030i	$0.280758\pi$
$158$	−5.71900	−	5.71900i	−0.454980	−	0.454980i
$159$			0.239509i			0.0189943i
$160$		0			0
$161$	2.94914			0.232425
$162$	11.5411	+	11.5411i	0.906753	+	0.906753i
$163$	7.16839	+	7.16839i	0.561471	+	0.561471i	0.929725	−	0.368254i	$-0.120044\pi$
$163$	7.16839	+	7.16839i	0.561471	+	0.561471i	−0.368254	+	0.929725i	$0.620044\pi$
$164$	−36.5944			−2.85754
$165$		0			0
$166$			9.90334i			0.768648i
$167$	−16.7312	−	16.7312i	−1.29470	−	1.29470i	−0.931849	−	0.362847i	$-0.881805\pi$
$167$	−16.7312	−	16.7312i	−1.29470	−	1.29470i	−0.362847	−	0.931849i	$-0.618195\pi$
$168$	5.29682	+	5.29682i	0.408658	+	0.408658i
$169$			10.5254i			0.809648i
$170$		0			0
$171$	−1.00000	+	2.06044i	−0.0764719	+	0.157566i
$172$	−6.33185	+	6.33185i	−0.482799	+	0.482799i
$173$	−1.32765	+	1.32765i	−0.100940	+	0.100940i	−0.755773	−	0.654833i	$-0.772739\pi$
$173$	−1.32765	+	1.32765i	−0.100940	+	0.100940i	0.654833	+	0.755773i	$0.272739\pi$
$174$	−31.1915			−2.36462
$175$		0			0
$176$	−0.341219			−0.0257204
$177$	12.6637	−	12.6637i	0.951862	−	0.951862i
$178$	10.0810	+	10.0810i	0.755600	+	0.755600i
$179$	3.54190			0.264734			0.132367	−	0.991201i	$-0.457742\pi$
$179$	3.54190			0.264734			0.132367	+	0.991201i	$0.457742\pi$
$180$		0			0
$181$		−	22.7696i		−	1.69245i	−0.532824	−	0.846226i	$-0.678869\pi$
$181$		−	22.7696i		−	1.69245i	0.532824	−	0.846226i	$-0.321131\pi$
$182$	−4.36196	+	4.36196i	−0.323330	+	0.323330i
$183$	−10.1648	+	10.1648i	−0.751404	+	0.751404i
$184$	4.76190			0.351052
$185$		0			0
$186$			18.4686i			1.35418i
$187$	13.7605	−	13.7605i	1.00627	−	1.00627i
$188$	18.7605	+	18.7605i	1.36825	+	1.36825i
$189$	9.52379			0.692754
$190$		0			0
$191$	23.0923			1.67090			0.835452	−	0.549564i	$-0.185206\pi$
$191$	23.0923			1.67090			0.835452	+	0.549564i	$0.185206\pi$
$192$	−14.4323	−	14.4323i	−1.04156	−	1.04156i
$193$	7.95056	−	7.95056i	0.572294	−	0.572294i	−0.360475	−	0.932769i	$-0.617385\pi$
$193$	7.95056	−	7.95056i	0.572294	−	0.572294i	0.932769	+	0.360475i	$0.117385\pi$
$194$		−	4.60147i		−	0.330366i
$195$		0			0
$196$	−13.0207			−0.930053
$197$	−12.4652	+	12.4652i	−0.888109	+	0.888109i	−0.994341	−	0.106232i	$-0.966121\pi$
$197$	−12.4652	+	12.4652i	−0.888109	+	0.888109i	0.106232	+	0.994341i	$0.466121\pi$
$198$	2.99095	−	2.99095i	0.212557	−	0.212557i
$199$		−	8.10171i		−	0.574315i	−0.957883	−	0.287158i	$-0.907290\pi$
$199$		−	8.10171i		−	0.574315i	0.957883	−	0.287158i	$-0.0927103\pi$
$200$		0			0
$201$	−14.6079			−1.03036
$202$	−6.91240	−	6.91240i	−0.486355	−	0.486355i
$203$	−10.5444	+	10.5444i	−0.740069	+	0.740069i
$204$	27.9111			1.95416
$205$		0			0
$206$	24.9797			1.74042
$207$	0.638037	−	0.638037i	0.0443466	−	0.0443466i
$208$	0.107661	−	0.107661i	0.00746492	−	0.00746492i
$209$	−13.8248	−	6.70964i	−0.956281	−	0.464115i
$210$		0			0
$211$			0.840445i			0.0578586i	0.999581	+	0.0289293i	$0.00920977\pi$
$211$			0.840445i			0.0578586i	−0.999581	+	0.0289293i	$0.990790\pi$
$212$	0.346056	+	0.346056i	0.0237672	+	0.0237672i
$213$	3.00492	+	3.00492i	0.205894	+	0.205894i
$214$			1.88739i			0.129019i
$215$		0			0
$216$	15.3778			1.04633
$217$	6.24336	+	6.24336i	0.423827	+	0.423827i
$218$	8.30174	+	8.30174i	0.562265	+	0.562265i
$219$	10.3642			0.700350
$220$		0			0
$221$			8.68335i			0.584105i
$222$	−7.60451	−	7.60451i	−0.510381	−	0.510381i
$223$	2.42957	−	2.42957i	0.162696	−	0.162696i	−0.621064	−	0.783760i	$-0.713299\pi$
$223$	2.42957	−	2.42957i	0.162696	−	0.162696i	0.783760	+	0.621064i	$0.213299\pi$
$224$	−9.90334			−0.661695
$225$		0			0
$226$	40.3575			2.68454
$227$	−3.71655	−	3.71655i	−0.246676	−	0.246676i	0.572929	−	0.819605i	$-0.305807\pi$
$227$	−3.71655	−	3.71655i	−0.246676	−	0.246676i	−0.819605	+	0.572929i	$0.805807\pi$
$228$	−7.21601	−	20.8255i	−0.477892	−	1.37920i
$229$		−	25.5067i		−	1.68553i	−0.538282	−	0.842765i	$-0.680926\pi$
$229$		−	25.5067i		−	1.68553i	0.538282	−	0.842765i	$-0.319074\pi$
$230$		0			0
$231$			9.52379i			0.626620i
$232$	−17.0257	+	17.0257i	−1.11779	+	1.11779i
$233$	−12.8064	−	12.8064i	−0.838977	−	0.838977i	0.149748	−	0.988724i	$-0.452154\pi$
$233$	−12.8064	−	12.8064i	−0.838977	−	0.838977i	−0.988724	+	0.149748i	$0.952154\pi$
$234$			1.88739i			0.123383i
$235$		0			0
$236$		−	36.5944i		−	2.38209i
$237$	3.93978	−	3.93978i	0.255916	−	0.255916i
$238$	15.3063	−	15.3063i	0.992157	−	0.992157i
$239$			2.04149i			0.132053i	0.997818	+	0.0660264i	$0.0210322\pi$
$239$			2.04149i			0.132053i	−0.997818	+	0.0660264i	$0.978968\pi$
$240$		0			0
$241$			1.86101i			0.119878i	0.998202	+	0.0599392i	$0.0190907\pi$
$241$			1.86101i			0.119878i	−0.998202	+	0.0599392i	$0.980909\pi$
$242$	2.30678	+	2.30678i	0.148286	+	0.148286i
$243$	3.81379	−	3.81379i	0.244655	−	0.244655i
$244$			29.3733i			1.88044i
$245$		0			0
$246$		−	40.8954i		−	2.60740i
$247$	6.47897	−	2.24496i	0.412247	−	0.142843i
$248$	10.0810	+	10.0810i	0.640142	+	0.640142i
$249$	−6.82234			−0.432348
$250$		0			0
$251$	−11.4795			−0.724579			−0.362290	−	0.932066i	$-0.618005\pi$
$251$	−11.4795			−0.724579			−0.362290	+	0.932066i	$0.618005\pi$
$252$	2.05086	−	2.05086i	0.129192	−	0.129192i
$253$	4.28100	+	4.28100i	0.269144	+	0.269144i
$254$		−	5.82717i		−	0.365629i
$255$		0			0
$256$	−15.3684			−0.960526
$257$	8.09890	+	8.09890i	0.505195	+	0.505195i	0.913048	−	0.407852i	$-0.133722\pi$
$257$	8.09890	+	8.09890i	0.505195	+	0.505195i	−0.407852	+	0.913048i	$0.633722\pi$
$258$	−7.07604	−	7.07604i	−0.440535	−	0.440535i
$259$	−5.14145			−0.319474
$260$		0			0
$261$			4.56247i			0.282410i
$262$	−28.6032	−	28.6032i	−1.76711	−	1.76711i
$263$	12.5462	+	12.5462i	0.773630	+	0.773630i	0.978739	−	0.205109i	$-0.0657549\pi$
$263$	12.5462	+	12.5462i	0.773630	+	0.773630i	−0.205109	+	0.978739i	$0.565755\pi$
$264$			15.3778i			0.946437i
$265$		0			0
$266$	−15.3778	−	7.46335i	−0.942872	−	0.457608i
$267$	−6.94470	+	6.94470i	−0.425009	+	0.425009i
$268$	−21.1063	+	21.1063i	−1.28927	+	1.28927i
$269$	−8.10437			−0.494132			−0.247066	−	0.968999i	$-0.579467\pi$
$269$	−8.10437			−0.494132			−0.247066	+	0.968999i	$0.579467\pi$
$270$		0			0
$271$	2.01429			0.122359			0.0611797	−	0.998127i	$-0.480514\pi$
$271$	2.01429			0.122359			0.0611797	+	0.998127i	$0.480514\pi$
$272$	−0.377784	+	0.377784i	−0.0229065	+	0.0229065i
$273$	−3.00492	−	3.00492i	−0.181866	−	0.181866i
$274$	9.06290			0.547510
$275$		0			0
$276$			8.68335i			0.522676i
$277$	4.13828	−	4.13828i	0.248645	−	0.248645i	−0.571769	−	0.820414i	$-0.693743\pi$
$277$	4.13828	−	4.13828i	0.248645	−	0.248645i	0.820414	+	0.571769i	$0.193743\pi$
$278$	13.1558	−	13.1558i	0.789030	−	0.789030i
$279$	2.70146			0.161732
$280$		0			0
$281$		−	21.6677i		−	1.29259i	−0.763089	−	0.646293i	$-0.776318\pi$
$281$		−	21.6677i		−	1.29259i	0.763089	−	0.646293i	$-0.223682\pi$
$282$	−20.9654	+	20.9654i	−1.24847	+	1.24847i
$283$	4.91903	+	4.91903i	0.292406	+	0.292406i	0.838030	−	0.545624i	$-0.183707\pi$
$283$	4.91903	+	4.91903i	0.292406	+	0.292406i	−0.545624	+	0.838030i	$0.683707\pi$
$284$	8.68335			0.515262
$285$		0			0
$286$	−12.6637			−0.748820
$287$	−13.8248	−	13.8248i	−0.816052	−	0.816052i
$288$	−2.14255	+	2.14255i	−0.126251	+	0.126251i
$289$		−	13.4701i		−	0.792360i
$290$		0			0
$291$	3.16992			0.185824
$292$	14.9748	−	14.9748i	0.876335	−	0.876335i
$293$	−15.5781	+	15.5781i	−0.910085	+	0.910085i	−0.996278	−	0.0861934i	$-0.972530\pi$
$293$	−15.5781	+	15.5781i	−0.910085	+	0.910085i	0.0861934	+	0.996278i	$0.472530\pi$
$294$		−	14.5511i		−	0.848637i
$295$		0			0
$296$	−8.30174			−0.482529
$297$	13.8248	+	13.8248i	0.802196	+	0.802196i
$298$	5.69240	−	5.69240i	0.329752	−	0.329752i
$299$	−2.70146			−0.156229
$300$		0			0
$301$	−4.78415			−0.275754
$302$	14.0207	−	14.0207i	0.806803	−	0.806803i
$303$	4.76190	−	4.76190i	0.273564	−	0.273564i
$304$	0.379550	+	0.184208i	0.0217687	+	0.0105651i
$305$		0			0
$306$		−	6.62291i		−	0.378607i
$307$	−4.81846	−	4.81846i	−0.275004	−	0.275004i	0.556107	−	0.831111i	$-0.312295\pi$
$307$	−4.81846	−	4.81846i	−0.275004	−	0.275004i	−0.831111	+	0.556107i	$0.812295\pi$
$308$	13.7605	+	13.7605i	0.784077	+	0.784077i
$309$			17.2083i			0.978948i
$310$		0			0
$311$	−11.4050			−0.646717			−0.323359	−	0.946277i	$-0.604812\pi$
$311$	−11.4050			−0.646717			−0.323359	+	0.946277i	$0.604812\pi$
$312$	−4.85196	−	4.85196i	−0.274688	−	0.274688i
$313$	15.2351	+	15.2351i	0.861137	+	0.861137i	0.991470	−	0.130334i	$-0.0416048\pi$
$313$	15.2351	+	15.2351i	0.861137	+	0.861137i	−0.130334	+	0.991470i	$0.541605\pi$
$314$	−5.52100			−0.311568
$315$		0			0
$316$		−	11.3848i		−	0.640445i
$317$	18.3307	+	18.3307i	1.02955	+	1.02955i	0.999550	+	0.0300048i	$0.00955224\pi$
$317$	18.3307	+	18.3307i	1.02955	+	1.02955i	0.0300048	+	0.999550i	$0.490448\pi$
$318$	−0.386728	+	0.386728i	−0.0216866	+	0.0216866i
$319$	−30.6125			−1.71397
$320$		0			0
$321$	−1.30021			−0.0725706
$322$	4.76190	+	4.76190i	0.265370	+	0.265370i
$323$	−22.7349	+	7.87762i	−1.26500	+	0.438322i
$324$			22.9748i			1.27638i
$325$		0			0
$326$			23.1492i			1.28211i
$327$	−5.71900	+	5.71900i	−0.316262	+	0.316262i
$328$	−22.3225	−	22.3225i	−1.23255	−	1.23255i
$329$			14.1748i			0.781484i
$330$		0			0
$331$			26.0500i			1.43184i	0.698182	+	0.715920i	$0.253992\pi$
$331$			26.0500i			1.43184i	−0.698182	+	0.715920i	$0.746008\pi$
$332$	−9.85728	+	9.85728i	−0.540988	+	0.540988i
$333$	−1.11233	+	1.11233i	−0.0609555	+	0.0609555i
$334$		−	54.0306i		−	2.95642i
$335$		0			0
$336$		−	0.261469i		−	0.0142643i
$337$	0.964001	+	0.964001i	0.0525125	+	0.0525125i	0.732875	−	0.680363i	$-0.238178\pi$
$337$	0.964001	+	0.964001i	0.0525125	+	0.0525125i	−0.680363	+	0.732875i	$0.738178\pi$
$338$	−16.9951	+	16.9951i	−0.924411	+	0.924411i
$339$			27.8020i			1.51000i
$340$		0			0
$341$			18.1258i			0.981567i
$342$	−4.94160	+	1.71226i	−0.267211	+	0.0925884i
$343$	−13.4193	−	13.4193i	−0.724573	−	0.724573i
$344$	−7.72482			−0.416495
$345$		0			0
$346$	−4.28745			−0.230495
$347$	−24.6336	+	24.6336i	−1.32240	+	1.32240i	−0.410573	+	0.911828i	$0.634671\pi$
$347$	−24.6336	+	24.6336i	−1.32240	+	1.32240i	−0.911828	+	0.410573i	$0.865329\pi$
$348$	−31.0464	−	31.0464i	−1.66426	−	1.66426i
$349$			7.27607i			0.389479i	0.980855	+	0.194740i	$0.0623862\pi$
$349$			7.27607i			0.389479i	−0.980855	+	0.194740i	$0.937614\pi$
$350$		0			0
$351$	−8.72393			−0.465649
$352$	−14.3758	−	14.3758i	−0.766230	−	0.766230i
$353$	−13.1476	−	13.1476i	−0.699778	−	0.699778i	0.264584	−	0.964363i	$-0.414765\pi$
$353$	−13.1476	−	13.1476i	−0.699778	−	0.699778i	−0.964363	+	0.264584i	$0.914765\pi$
$354$	40.8954			2.17357
$355$		0			0
$356$			20.0682i			1.06361i
$357$	10.5444	+	10.5444i	0.558067	+	0.558067i
$358$	5.71900	+	5.71900i	0.302259	+	0.302259i
$359$			8.97634i			0.473753i	0.971540	+	0.236877i	$0.0761237\pi$
$359$			8.97634i			0.473753i	−0.971540	+	0.236877i	$0.923876\pi$
$360$		0			0
$361$	11.7556	+	14.9267i	0.618714	+	0.785616i
$362$	36.7654	−	36.7654i	1.93235	−	1.93235i
$363$	−1.58912	+	1.58912i	−0.0834074	+	0.0834074i
$364$	−8.68335			−0.455131
$365$		0			0
$366$	−32.8256			−1.71582
$367$	4.73975	−	4.73975i	0.247413	−	0.247413i	−0.572495	−	0.819908i	$-0.694025\pi$
$367$	4.73975	−	4.73975i	0.247413	−	0.247413i	0.819908	+	0.572495i	$0.194025\pi$
$368$	−0.117532	−	0.117532i	−0.00612676	−	0.00612676i
$369$	−5.98189			−0.311405
$370$		0			0
$371$			0.261469i			0.0135748i
$372$	−18.3827	+	18.3827i	−0.953099	+	0.953099i
$373$	−13.7171	+	13.7171i	−0.710246	+	0.710246i	−0.966587	−	0.256340i	$-0.917483\pi$
$373$	−13.7171	+	13.7171i	−0.710246	+	0.710246i	0.256340	+	0.966587i	$0.417483\pi$
$374$	44.4373			2.29780
$375$		0			0
$376$			22.8877i			1.18034i
$377$	9.65878	−	9.65878i	0.497453	−	0.497453i
$378$	15.3778	+	15.3778i	0.790948	+	0.790948i
$379$	−4.87998			−0.250668			−0.125334	−	0.992115i	$-0.540000\pi$
$379$	−4.87998			−0.250668			−0.125334	+	0.992115i	$0.540000\pi$
$380$		0			0
$381$	4.01429			0.205658
$382$	37.2865	+	37.2865i	1.90774	+	1.90774i
$383$	−11.4925	+	11.4925i	−0.587238	+	0.587238i	−0.936882	−	0.349645i	$-0.886302\pi$
$383$	−11.4925	+	11.4925i	−0.587238	+	0.587238i	0.349645	+	0.936882i	$0.386302\pi$
$384$		−	28.4637i		−	1.45253i
$385$		0			0
$386$	25.6751			1.30683
$387$	−1.03503	+	1.03503i	−0.0526137	+	0.0526137i
$388$	4.58007	−	4.58007i	0.232518	−	0.232518i
$389$			17.4193i			0.883192i	0.897214	+	0.441596i	$0.145588\pi$
$389$			17.4193i			0.883192i	−0.897214	+	0.441596i	$0.854412\pi$
$390$		0			0
$391$	9.47949			0.479399
$392$	−7.94262	−	7.94262i	−0.401163	−	0.401163i
$393$	19.7045	−	19.7045i	0.993961	−	0.993961i
$394$	−40.2544			−2.02799
$395$		0			0
$396$	5.95407			0.299203
$397$	23.3827	−	23.3827i	1.17354	−	1.17354i	0.192186	−	0.981359i	$-0.438442\pi$
$397$	23.3827	−	23.3827i	1.17354	−	1.17354i	0.981359	−	0.192186i	$-0.0615576\pi$
$398$	13.0816	−	13.0816i	0.655721	−	0.655721i
$399$	5.14145	−	10.5936i	0.257394	−	0.530345i
$400$		0			0
$401$			0.759100i			0.0379076i	0.999820	+	0.0189538i	$0.00603355\pi$
$401$			0.759100i			0.0379076i	−0.999820	+	0.0189538i	$0.993966\pi$
$402$	−23.5870	−	23.5870i	−1.17641	−	1.17641i
$403$	−5.71900	−	5.71900i	−0.284884	−	0.284884i
$404$		−	13.7605i		−	0.684610i
$405$		0			0
$406$	−34.0513			−1.68994
$407$	−7.46335	−	7.46335i	−0.369945	−	0.369945i
$408$	17.0257	+	17.0257i	0.842896	+	0.842896i
$409$	20.8273			1.02984			0.514921	−	0.857238i	$-0.327821\pi$
$409$	20.8273			1.02984			0.514921	+	0.857238i	$0.327821\pi$
$410$		0			0
$411$			6.24336i			0.307962i
$412$	24.8635	+	24.8635i	1.22494	+	1.22494i
$413$	13.8248	−	13.8248i	0.680274	−	0.680274i
$414$	2.06044			0.101265
$415$		0			0
$416$	9.07160			0.444772
$417$	9.06290	+	9.06290i	0.443812	+	0.443812i
$418$	−11.4886	−	33.1563i	−0.561927	−	1.62173i
$419$			19.0192i			0.929149i	0.885534	+	0.464575i	$0.153793\pi$
$419$			19.0192i			0.929149i	−0.885534	+	0.464575i	$0.846207\pi$
$420$		0			0
$421$			16.7877i			0.818183i	0.912493	+	0.409092i	$0.134154\pi$
$421$			16.7877i			0.818183i	−0.912493	+	0.409092i	$0.865846\pi$
$422$	−1.35704	+	1.35704i	−0.0660597	+	0.0660597i
$423$	3.06668	+	3.06668i	0.149107	+	0.149107i
$424$			0.422186i			0.0205032i
$425$		0			0
$426$			9.70392i			0.470156i
$427$	−11.0968	+	11.0968i	−0.537011	+	0.537011i
$428$	−1.87861	+	1.87861i	−0.0908061	+	0.0908061i
$429$		−	8.72393i		−	0.421195i
$430$		0			0
$431$		−	19.4892i		−	0.938761i	−0.882996	−	0.469380i	$-0.844477\pi$
$431$		−	19.4892i		−	0.938761i	0.882996	−	0.469380i	$-0.155523\pi$
$432$	−0.379550	−	0.379550i	−0.0182611	−	0.0182611i
$433$	18.4790	−	18.4790i	0.888046	−	0.888046i	−0.106290	−	0.994335i	$-0.533897\pi$
$433$	18.4790	−	18.4790i	0.888046	−	0.888046i	0.994335	+	0.106290i	$0.0338971\pi$
$434$			20.1619i			0.967804i
$435$		0			0
$436$			16.5263i			0.791464i
$437$	−2.45079	−	7.07300i	−0.117237	−	0.338348i
$438$	16.7348	+	16.7348i	0.799621	+	0.799621i
$439$	−16.2648			−0.776276			−0.388138	−	0.921601i	$-0.626882\pi$
$439$	−16.2648			−0.776276			−0.388138	+	0.921601i	$0.626882\pi$
$440$		0			0
$441$	−2.12843			−0.101354
$442$	−14.0207	+	14.0207i	−0.666899	+	0.666899i
$443$	−7.45383	−	7.45383i	−0.354142	−	0.354142i	0.507506	−	0.861648i	$-0.330567\pi$
$443$	−7.45383	−	7.45383i	−0.354142	−	0.354142i	−0.861648	+	0.507506i	$0.830567\pi$
$444$		−	15.1383i		−	0.718431i
$445$		0			0
$446$	7.84590			0.371514
$447$	3.92145	+	3.92145i	0.185478	+	0.185478i
$448$	−15.7556	−	15.7556i	−0.744381	−	0.744381i
$449$	30.3510			1.43235			0.716177	−	0.697918i	$-0.245890\pi$
$449$	30.3510			1.43235			0.716177	+	0.697918i	$0.245890\pi$
$450$		0			0
$451$		−	40.1363i		−	1.88994i
$452$	40.1698	+	40.1698i	1.88943	+	1.88943i
$453$	9.65878	+	9.65878i	0.453809	+	0.453809i
$454$		−	12.0020i		−	0.563282i
$455$		0			0
$456$	8.30174	−	17.1052i	0.388765	−	0.801026i
$457$	10.6128	−	10.6128i	0.496448	−	0.496448i	−0.413882	−	0.910330i	$-0.635828\pi$
$457$	10.6128	−	10.6128i	0.496448	−	0.496448i	0.910330	+	0.413882i	$0.135828\pi$
$458$	41.1849	−	41.1849i	1.92444	−	1.92444i
$459$	30.6125			1.42887
$460$		0			0
$461$	−4.58073			−0.213346			−0.106673	−	0.994294i	$-0.534020\pi$
$461$	−4.58073			−0.213346			−0.106673	+	0.994294i	$0.534020\pi$
$462$	−15.3778	+	15.3778i	−0.715439	+	0.715439i
$463$	27.9797	+	27.9797i	1.30033	+	1.30033i	0.928169	+	0.372160i	$0.121383\pi$
$463$	27.9797	+	27.9797i	1.30033	+	1.30033i	0.372160	+	0.928169i	$0.378617\pi$
$464$	0.840445			0.0390167
$465$		0			0
$466$		−	41.3563i		−	1.91579i
$467$	−14.5605	+	14.5605i	−0.673778	+	0.673778i	−0.958585	−	0.284807i	$-0.908070\pi$
$467$	−14.5605	+	14.5605i	−0.673778	+	0.673778i	0.284807	+	0.958585i	$0.408070\pi$
$468$	−1.87861	+	1.87861i	−0.0868389	+	0.0868389i
$469$	−15.9473			−0.736377
$470$		0			0
$471$		−	3.80337i		−	0.175250i
$472$	22.3225	−	22.3225i	1.02748	−	1.02748i
$473$	−6.94470	−	6.94470i	−0.319318	−	0.319318i
$474$	12.7229			0.584381
$475$		0			0
$476$	30.4701			1.39660
$477$	0.0565679	+	0.0565679i	0.00259006	+	0.00259006i
$478$	−3.29633	+	3.29633i	−0.150771	+	0.150771i
$479$			21.5669i			0.985417i	0.870194	+	0.492709i	$0.163993\pi$
$479$			21.5669i			0.985417i	−0.870194	+	0.492709i	$0.836007\pi$
$480$		0			0
$481$	4.70964			0.214741
$482$	−3.00492	+	3.00492i	−0.136870	+	0.136870i
$483$	−3.28043	+	3.28043i	−0.149265	+	0.149265i
$484$			4.59210i			0.208732i
$485$		0			0
$486$	12.3160			0.558666
$487$	−12.6614	−	12.6614i	−0.573741	−	0.573741i	0.359431	−	0.933172i	$-0.382971\pi$
$487$	−12.6614	−	12.6614i	−0.573741	−	0.573741i	−0.933172	+	0.359431i	$0.882971\pi$
$488$	−17.9177	+	17.9177i	−0.811094	+	0.811094i
$489$	−15.9473			−0.721161
$490$		0			0
$491$	4.13335			0.186536			0.0932678	−	0.995641i	$-0.470269\pi$
$491$	4.13335			0.186536			0.0932678	+	0.995641i	$0.470269\pi$
$492$	40.7052	−	40.7052i	1.83513	−	1.83513i
$493$	−33.8929	+	33.8929i	−1.52646	+	1.52646i
$494$	14.0863	+	6.83654i	0.633771	+	0.307590i
$495$		0			0
$496$		−	0.497631i		−	0.0223443i
$497$	3.28043	+	3.28043i	0.147148	+	0.147148i
$498$	−11.0158	−	11.0158i	−0.493631	−	0.493631i
$499$		−	8.61777i		−	0.385784i	−0.981220	−	0.192892i	$-0.938213\pi$
$499$		−	8.61777i		−	0.385784i	0.981220	−	0.192892i	$-0.0617868\pi$
$500$		0			0
$501$	37.2212			1.66292
$502$	−18.5356	−	18.5356i	−0.827284	−	0.827284i
$503$	18.2652	+	18.2652i	0.814404	+	0.814404i	0.985291	−	0.170887i	$-0.0546632\pi$
$503$	18.2652	+	18.2652i	0.814404	+	0.814404i	−0.170887	+	0.985291i	$0.554663\pi$
$504$	2.50203			0.111449
$505$		0			0
$506$			13.8248i			0.614587i
$507$	−11.7078	−	11.7078i	−0.519961	−	0.519961i
$508$	5.80006	−	5.80006i	0.257336	−	0.257336i
$509$	−0.840445			−0.0372520			−0.0186260	−	0.999827i	$-0.505929\pi$
$509$	−0.840445			−0.0372520			−0.0186260	+	0.999827i	$0.505929\pi$
$510$		0			0
$511$	11.3145			0.500524
$512$	0.774226	+	0.774226i	0.0342163	+	0.0342163i
$513$	−7.91443	−	22.8411i	−0.349431	−	1.00846i
$514$			26.1541i			1.15361i
$515$		0			0
$516$		−	14.0863i		−	0.620113i
$517$	−20.5763	+	20.5763i	−0.904944	+	0.904944i
$518$	−8.30174	−	8.30174i	−0.364758	−	0.364758i
$519$		−	2.95359i		−	0.129648i
$520$		0			0
$521$		−	25.9687i		−	1.13771i	−0.822438	−	0.568855i	$-0.807387\pi$
$521$		−	25.9687i		−	1.13771i	0.822438	−	0.568855i	$-0.192613\pi$
$522$	−7.36689	+	7.36689i	−0.322440	+	0.322440i
$523$	18.6944	−	18.6944i	0.817447	−	0.817447i	−0.168291	−	0.985737i	$-0.553825\pi$
$523$	18.6944	−	18.6944i	0.817447	−	0.817447i	0.985737	+	0.168291i	$0.0538247\pi$
$524$		−	56.9403i		−	2.48745i
$525$		0			0
$526$			40.5159i			1.76658i
$527$	20.0682	+	20.0682i	0.874183	+	0.874183i
$528$	0.379550	−	0.379550i	0.0165178	−	0.0165178i
$529$		−	20.0509i		−	0.871776i
$530$		0			0
$531$		−	5.98189i		−	0.259592i
$532$	−7.87762	−	22.7349i	−0.341538	−	0.985683i
$533$	12.6637	+	12.6637i	0.548526	+	0.548526i
$534$	−22.4268			−0.970502
$535$		0			0
$536$	−25.7496			−1.11221
$537$	−3.93978	+	3.93978i	−0.170014	+	0.170014i
$538$	−13.0859	−	13.0859i	−0.564173	−	0.564173i
$539$		−	14.2810i		−	0.615126i
$540$		0			0
$541$	−29.1383			−1.25275			−0.626376	−	0.779521i	$-0.715463\pi$
$541$	−29.1383			−1.25275			−0.626376	+	0.779521i	$0.715463\pi$
$542$	3.25241	+	3.25241i	0.139703	+	0.139703i
$543$	25.3274	+	25.3274i	1.08690	+	1.08690i
$544$	−31.8325			−1.36481
$545$		0			0
$546$		−	9.70392i		−	0.415289i
$547$	13.8814	+	13.8814i	0.593524	+	0.593524i	0.938582	−	0.345057i	$-0.112141\pi$
$547$	13.8814	+	13.8814i	0.593524	+	0.593524i	−0.345057	+	0.938582i	$0.612141\pi$
$548$	9.02074	+	9.02074i	0.385347	+	0.385347i
$549$			4.80150i			0.204923i
$550$		0			0
$551$	34.0513	+	16.5263i	1.45064	+	0.704042i
$552$	−5.29682	+	5.29682i	−0.225448	+	0.225448i
$553$	4.30100	−	4.30100i	0.182897	−	0.182897i
$554$	13.3639			0.567778
$555$		0			0
$556$	26.1891			1.11067
$557$	22.1066	−	22.1066i	0.936688	−	0.936688i	−0.0614237	−	0.998112i	$-0.519564\pi$
$557$	22.1066	−	22.1066i	0.936688	−	0.936688i	0.998112	+	0.0614237i	$0.0195641\pi$
$558$	4.36196	+	4.36196i	0.184657	+	0.184657i
$559$	4.38235			0.185354
$560$		0			0
$561$			30.6125i			1.29246i
$562$	34.9862	−	34.9862i	1.47580	−	1.47580i
$563$	4.29058	−	4.29058i	0.180826	−	0.180826i	−0.610889	−	0.791716i	$-0.709188\pi$
$563$	4.29058	−	4.29058i	0.180826	−	0.180826i	0.791716	+	0.610889i	$0.209188\pi$
$564$	−41.7359			−1.75740
$565$		0			0
$566$			15.8852i			0.667706i
$567$	−8.67952	+	8.67952i	−0.364506	+	0.364506i
$568$	5.29682	+	5.29682i	0.222250	+	0.222250i
$569$	−12.2253			−0.512509			−0.256255	−	0.966609i	$-0.582489\pi$
$569$	−12.2253			−0.512509			−0.256255	+	0.966609i	$0.582489\pi$
$570$		0			0
$571$	29.2114			1.22246			0.611230	−	0.791453i	$-0.290675\pi$
$571$	29.2114			1.22246			0.611230	+	0.791453i	$0.290675\pi$
$572$	−12.6048	−	12.6048i	−0.527033	−	0.527033i
$573$	−25.6864	+	25.6864i	−1.07306	+	1.07306i
$574$		−	44.6450i		−	1.86344i
$575$		0			0
$576$	−6.81732			−0.284055
$577$	−5.75557	+	5.75557i	−0.239607	+	0.239607i	−0.816688	−	0.577080i	$-0.804192\pi$
$577$	−5.75557	+	5.75557i	−0.239607	+	0.239607i	0.577080	+	0.816688i	$0.304192\pi$
$578$	21.7498	−	21.7498i	0.904673	−	0.904673i
$579$			17.6874i			0.735062i
$580$		0			0
$581$	−7.44785			−0.308989
$582$	5.11837	+	5.11837i	0.212163	+	0.212163i
$583$	−0.379550	+	0.379550i	−0.0157193	+	0.0157193i
$584$	18.2692			0.755984
$585$		0			0
$586$	−50.3071			−2.07817
$587$	−8.44446	+	8.44446i	−0.348540	+	0.348540i	−0.859566	−	0.511025i	$-0.829266\pi$
$587$	−8.44446	+	8.44446i	−0.348540	+	0.348540i	0.511025	+	0.859566i	$0.329266\pi$
$588$	14.4834	−	14.4834i	0.597286	−	0.597286i
$589$	9.78526	−	20.1619i	0.403195	−	0.830758i
$590$		0			0
$591$		−	27.7309i		−	1.14070i
$592$	0.204901	+	0.204901i	0.00842138	+	0.00842138i
$593$	22.0509	+	22.0509i	0.905520	+	0.905520i	0.995907	−	0.0903867i	$-0.0288103\pi$
$593$	22.0509	+	22.0509i	0.905520	+	0.905520i	−0.0903867	+	0.995907i	$0.528810\pi$
$594$			44.6450i			1.83181i
$595$		0			0
$596$	11.3319			0.464171
$597$	9.01181	+	9.01181i	0.368829	+	0.368829i
$598$	−4.36196	−	4.36196i	−0.178374	−	0.178374i
$599$	−3.54190			−0.144718			−0.0723591	−	0.997379i	$-0.523053\pi$
$599$	−3.54190			−0.144718			−0.0723591	+	0.997379i	$0.523053\pi$
$600$		0			0
$601$			33.6315i			1.37186i	0.727669	+	0.685928i	$0.240604\pi$
$601$			33.6315i			1.37186i	−0.727669	+	0.685928i	$0.759396\pi$
$602$	−7.72482	−	7.72482i	−0.314840	−	0.314840i
$603$	−3.45014	+	3.45014i	−0.140500	+	0.140500i
$604$	27.9111			1.13568
$605$		0			0
$606$	15.3778			0.624680
$607$	−10.8004	−	10.8004i	−0.438373	−	0.438373i	0.453091	−	0.891464i	$-0.350321\pi$
$607$	−10.8004	−	10.8004i	−0.438373	−	0.438373i	−0.891464	+	0.453091i	$0.850321\pi$
$608$	8.22984	+	23.7514i	0.333764	+	0.963247i
$609$		−	23.4577i		−	0.950554i
$610$		0			0
$611$		−	12.9843i		−	0.525291i
$612$	6.59210	−	6.59210i	0.266470	−	0.266470i
$613$	1.88892	+	1.88892i	0.0762928	+	0.0762928i	0.744224	−	0.667931i	$-0.232820\pi$
$613$	1.88892	+	1.88892i	0.0762928	+	0.0762928i	−0.667931	+	0.744224i	$0.732820\pi$
$614$		−	15.5605i		−	0.627969i
$615$		0			0
$616$			16.7877i			0.676397i
$617$	−23.0973	+	23.0973i	−0.929861	+	0.929861i	−0.997697	−	0.0678357i	$-0.978391\pi$
$617$	−23.0973	+	23.0973i	−0.929861	+	0.929861i	0.0678357	+	0.997697i	$0.478391\pi$
$618$	−27.7858	+	27.7858i	−1.11771	+	1.11771i
$619$			32.3225i			1.29915i	0.760297	+	0.649575i	$0.225053\pi$
$619$			32.3225i			1.29915i	−0.760297	+	0.649575i	$0.774947\pi$
$620$		0			0
$621$			9.52379i			0.382177i
$622$	−18.4153	−	18.4153i	−0.738386	−	0.738386i
$623$	−7.58143	+	7.58143i	−0.303744	+	0.303744i
$624$			0.239509i			0.00958804i
$625$		0			0
$626$			49.1992i			1.96640i
$627$	22.8411	−	7.91443i	0.912187	−	0.316072i
$628$	−5.49532	−	5.49532i	−0.219287	−	0.219287i
$629$	−16.5263			−0.658945
$630$		0			0
$631$	3.99555			0.159061			0.0795303	−	0.996832i	$-0.474658\pi$
$631$	3.99555			0.159061			0.0795303	+	0.996832i	$0.474658\pi$
$632$	6.94470	−	6.94470i	0.276245	−	0.276245i
$633$	−0.934855	−	0.934855i	−0.0371571	−	0.0371571i
$634$			59.1961i			2.35098i
$635$		0			0
$636$	−0.769859			−0.0305269
$637$	4.50590	+	4.50590i	0.178530	+	0.178530i
$638$	−49.4291	−	49.4291i	−1.95692	−	1.95692i
$639$	1.41942			0.0561514
$640$		0			0
$641$		−	29.5106i		−	1.16560i	−0.812616	−	0.582799i	$-0.801957\pi$
$641$		−	29.5106i		−	1.16560i	0.812616	−	0.582799i	$-0.198043\pi$
$642$	−2.09941	−	2.09941i	−0.0828570	−	0.0828570i
$643$	−16.1447	−	16.1447i	−0.636686	−	0.636686i	0.313051	−	0.949736i	$-0.398649\pi$
$643$	−16.1447	−	16.1447i	−0.636686	−	0.636686i	−0.949736	+	0.313051i	$0.898649\pi$
$644$			9.47949i			0.373544i
$645$		0			0
$646$	−49.4291	−	23.9896i	−1.94476	−	0.943858i
$647$	15.2603	−	15.2603i	0.599942	−	0.599942i	−0.340355	−	0.940297i	$-0.610547\pi$
$647$	15.2603	−	15.2603i	0.599942	−	0.599942i	0.940297	+	0.340355i	$0.110547\pi$
$648$	−14.0146	+	14.0146i	−0.550544	+	0.550544i
$649$	40.1363			1.57549
$650$		0			0
$651$	−13.8894			−0.544368
$652$	−23.0415	+	23.0415i	−0.902374	+	0.902374i
$653$	−25.6321	−	25.6321i	−1.00306	−	1.00306i	−0.999995	−	0.00306471i	$-0.999024\pi$
$653$	−25.6321	−	25.6321i	−1.00306	−	1.00306i	−0.00306471	−	0.999995i	$-0.500976\pi$
$654$	−18.4686			−0.722180
$655$		0			0
$656$			1.10191i			0.0430225i
$657$	2.44785	−	2.44785i	0.0954998	−	0.0954998i
$658$	−22.8877	+	22.8877i	−0.892255	+	0.892255i
$659$	−23.8715			−0.929903			−0.464951	−	0.885336i	$-0.653928\pi$
$659$	−23.8715			−0.929903			−0.464951	+	0.885336i	$0.653928\pi$
$660$		0			0
$661$		−	27.9924i		−	1.08878i	−0.838833	−	0.544389i	$-0.816762\pi$
$661$		−	27.9924i		−	1.08878i	0.838833	−	0.544389i	$-0.183238\pi$
$662$	−42.0622	+	42.0622i	−1.63480	+	1.63480i
$663$	−9.65878	−	9.65878i	−0.375116	−	0.375116i
$664$	−12.0258			−0.466692
$665$		0			0
$666$	−3.59210			−0.139191
$667$	−10.5444	−	10.5444i	−0.408279	−	0.408279i
$668$	53.7793	−	53.7793i	2.08078	−	2.08078i
$669$			5.40498i			0.208969i
$670$		0			0
$671$	−32.2163			−1.24370
$672$	11.0158	−	11.0158i	0.424945	−	0.424945i
$673$	0.0104203	−	0.0104203i	0.000401672	−	0.000401672i	−0.706906	−	0.707308i	$-0.749910\pi$
$673$	0.0104203	−	0.0104203i	0.000401672	−	0.000401672i	0.707308	+	0.706906i	$0.249910\pi$
$674$			3.11309i			0.119912i
$675$		0			0
$676$	−33.8321			−1.30123
$677$	−2.18399	−	2.18399i	−0.0839377	−	0.0839377i	0.663891	−	0.747829i	$-0.268904\pi$
$677$	−2.18399	−	2.18399i	−0.0839377	−	0.0839377i	−0.747829	+	0.663891i	$0.768904\pi$
$678$	−44.8910	+	44.8910i	−1.72403	+	1.72403i
$679$	3.46056			0.132804
$680$		0			0
$681$	8.26809			0.316834
$682$	−29.2672	+	29.2672i	−1.12070	+	1.12070i
$683$	−12.4971	+	12.4971i	−0.478190	+	0.478190i	−0.904552	−	0.426363i	$-0.859795\pi$
$683$	−12.4971	+	12.4971i	−0.478190	+	0.478190i	0.426363	+	0.904552i	$0.359795\pi$
$684$	−6.62291	−	3.21432i	−0.253233	−	0.122903i
$685$		0			0
$686$		−	43.3354i		−	1.65455i
$687$	28.3720	+	28.3720i	1.08246	+	1.08246i
$688$	0.190662	+	0.190662i	0.00726891	+	0.00726891i
$689$		−	0.239509i		−	0.00912457i
$690$		0			0
$691$	−11.0464			−0.420225			−0.210113	−	0.977677i	$-0.567383\pi$
$691$	−11.0464			−0.420225			−0.210113	+	0.977677i	$0.567383\pi$
$692$	−4.26751	−	4.26751i	−0.162226	−	0.162226i
$693$	2.24935	+	2.24935i	0.0854459	+	0.0854459i
$694$	−79.5503			−3.01969
$695$		0			0
$696$		−	37.8764i		−	1.43570i
$697$	−44.4373	−	44.4373i	−1.68318	−	1.68318i
$698$	−11.7485	+	11.7485i	−0.444686	+	0.444686i
$699$	28.4900			1.07759
$700$		0			0
$701$	15.0366			0.567923			0.283962	−	0.958836i	$-0.408351\pi$
$701$	15.0366			0.567923			0.283962	+	0.958836i	$0.408351\pi$
$702$	−14.0863	−	14.0863i	−0.531652	−	0.531652i
$703$	4.27263	+	12.3309i	0.161145	+	0.465067i
$704$		−	45.7418i		−	1.72396i
$705$		0			0
$706$		−	42.4582i		−	1.59794i
$707$	5.19850	−	5.19850i	0.195510	−	0.195510i
$708$	40.7052	+	40.7052i	1.52979	+	1.52979i
$709$		−	1.64449i		−	0.0617601i	−0.999523	−	0.0308801i	$-0.990169\pi$
$709$		−	1.64449i		−	0.0617601i	0.999523	−	0.0308801i	$-0.00983099\pi$
$710$		0			0
$711$		−	1.86101i		−	0.0697934i
$712$	−12.2415	+	12.2415i	−0.458770	+	0.458770i
$713$	−6.24336	+	6.24336i	−0.233816	+	0.233816i
$714$			34.0513i			1.27434i
$715$		0			0
$716$			11.3848i			0.425470i
$717$	−2.27081	−	2.27081i	−0.0848051	−	0.0848051i
$718$	−14.4938	+	14.4938i	−0.540905	+	0.540905i
$719$		−	19.8435i		−	0.740036i	−0.929025	−	0.370018i	$-0.879351\pi$
$719$		−	19.8435i		−	0.740036i	0.929025	−	0.370018i	$-0.120649\pi$
$720$		0			0
$721$			18.7861i			0.699632i
$722$	−5.12034	+	43.0831i	−0.190559	+	1.60339i
$723$	−2.07007	−	2.07007i	−0.0769866	−	0.0769866i
$724$	73.1888			2.72004
$725$		0			0
$726$	−5.13182			−0.190460
$727$	20.1907	−	20.1907i	0.748830	−	0.748830i	−0.225429	−	0.974260i	$-0.572378\pi$
$727$	20.1907	−	20.1907i	0.748830	−	0.748830i	0.974260	+	0.225429i	$0.0723785\pi$
$728$	−5.29682	−	5.29682i	−0.196313	−	0.196313i
$729$			29.9273i			1.10842i
$730$		0			0
$731$	−15.3778			−0.568768
$732$	−32.6730	−	32.6730i	−1.20763	−	1.20763i
$733$	−6.22570	−	6.22570i	−0.229951	−	0.229951i	0.582721	−	0.812672i	$-0.301988\pi$
$733$	−6.22570	−	6.22570i	−0.229951	−	0.229951i	−0.812672	+	0.582721i	$0.801988\pi$
$734$	15.3063			0.564964
$735$		0			0
$736$		−	9.90334i		−	0.365042i
$737$	−23.1492	−	23.1492i	−0.852710	−	0.852710i
$738$	−9.65878	−	9.65878i	−0.355545	−	0.355545i
$739$		−	28.9304i		−	1.06422i	−0.846675	−	0.532111i	$-0.821399\pi$
$739$		−	28.9304i		−	1.06422i	0.846675	−	0.532111i	$-0.178601\pi$
$740$		0			0
$741$	−4.70964	+	9.70392i	−0.173013	+	0.356482i
$742$	−0.422186	+	0.422186i	−0.0154989	+	0.0154989i
$743$	31.1811	−	31.1811i	1.14392	−	1.14392i	0.156197	−	0.987726i	$-0.450077\pi$
$743$	31.1811	−	31.1811i	1.14392	−	1.14392i	0.987726	−	0.156197i	$-0.0499233\pi$
$744$	−22.4268			−0.822206
$745$		0			0
$746$	−44.2973			−1.62184
$747$	−1.61132	+	1.61132i	−0.0589550	+	0.0589550i
$748$	44.2306	+	44.2306i	1.61723	+	1.61723i
$749$	−1.41942			−0.0518645
$750$		0			0
$751$		−	5.72042i		−	0.208741i	−0.994538	−	0.104371i	$-0.966717\pi$
$751$		−	5.72042i		−	0.208741i	0.994538	−	0.104371i	$-0.0332828\pi$
$752$	0.564907	−	0.564907i	0.0206000	−	0.0206000i
$753$	12.7690	−	12.7690i	0.465329	−	0.465329i
$754$	31.1915			1.13593
$755$		0			0
$756$			30.6125i			1.11337i
$757$	6.85236	−	6.85236i	0.249053	−	0.249053i	−0.571529	−	0.820582i	$-0.693649\pi$
$757$	6.85236	−	6.85236i	0.249053	−	0.249053i	0.820582	+	0.571529i	$0.193649\pi$
$758$	−7.87955	−	7.87955i	−0.286198	−	0.286198i
$759$	−9.52379			−0.345692
$760$		0			0
$761$	−30.0785			−1.09035			−0.545173	−	0.838324i	$-0.683536\pi$
$761$	−30.0785			−1.09035			−0.545173	+	0.838324i	$0.683536\pi$
$762$	6.48175	+	6.48175i	0.234809	+	0.234809i
$763$	−6.24336	+	6.24336i	−0.226025	+	0.226025i
$764$			74.2262i			2.68541i
$765$		0			0
$766$	−37.1131			−1.34095
$767$	−12.6637	+	12.6637i	−0.457260	+	0.457260i
$768$	17.0948	−	17.0948i	0.616856	−	0.616856i
$769$		−	5.71900i		−	0.206233i	−0.994669	−	0.103116i	$-0.967119\pi$
$769$		−	5.71900i		−	0.206233i	0.994669	−	0.103116i	$-0.0328814\pi$
$770$		0			0
$771$	−18.0174			−0.648879
$772$	25.5557	+	25.5557i	0.919768	+	0.919768i
$773$	20.3400	−	20.3400i	0.731580	−	0.731580i	−0.239352	−	0.970933i	$-0.576935\pi$
$773$	20.3400	−	20.3400i	0.731580	−	0.731580i	0.970933	+	0.239352i	$0.0769351\pi$
$774$	−3.34248			−0.120143
$775$		0			0
$776$	5.58766			0.200585
$777$	5.71900	−	5.71900i	0.205168	−	0.205168i
$778$	−28.1264	+	28.1264i	−1.00838	+	1.00838i
$779$	−21.6677	+	44.6450i	−0.776326	+	1.59957i
$780$		0			0
$781$			9.52379i			0.340788i
$782$	15.3063	+	15.3063i	0.547351	+	0.547351i
$783$	−34.0513	−	34.0513i	−1.21690	−	1.21690i
$784$			0.392074i			0.0140027i
$785$		0			0
$786$	63.6325			2.26970
$787$	31.2481	+	31.2481i	1.11387	+	1.11387i	0.992622	+	0.121251i	$0.0386906\pi$
$787$	31.2481	+	31.2481i	1.11387	+	1.11387i	0.121251	+	0.992622i	$0.461309\pi$
$788$	−40.0672	−	40.0672i	−1.42733	−	1.42733i
$789$	−27.9111			−0.993660
$790$		0			0
$791$			30.3510i			1.07916i
$792$	3.63196	+	3.63196i	0.129056	+	0.129056i
$793$	10.1648	−	10.1648i	0.360963	−	0.360963i
$794$	75.5107			2.67978
$795$		0			0
$796$	26.0415			0.923016
$797$	−9.26780	−	9.26780i	−0.328282	−	0.328282i	0.523651	−	0.851933i	$-0.324570\pi$
$797$	−9.26780	−	9.26780i	−0.328282	−	0.328282i	−0.851933	+	0.523651i	$0.824570\pi$
$798$	25.4070	−	8.80349i	0.899397	−	0.311640i
$799$			45.5625i			1.61188i
$800$		0			0
$801$			3.28043i			0.115908i
$802$	−1.22570	+	1.22570i	−0.0432808	+	0.0432808i
$803$	16.4242	+	16.4242i	0.579597	+	0.579597i
$804$		−	46.9545i		−	1.65596i
$805$		0			0
$806$		−	18.4686i		−	0.650529i
$807$	9.01477	−	9.01477i	0.317335	−	0.317335i
$808$	8.39386	−	8.39386i	0.295295	−	0.295295i
$809$		−	37.7275i		−	1.32643i	−0.748430	−	0.663214i	$-0.769192\pi$
$809$		−	37.7275i		−	1.32643i	0.748430	−	0.663214i	$-0.230808\pi$
$810$		0			0
$811$			14.6652i			0.514966i	0.966283	+	0.257483i	$0.0828932\pi$
$811$			14.6652i			0.514966i	−0.966283	+	0.257483i	$0.917107\pi$
$812$	−33.8929	−	33.8929i	−1.18941	−	1.18941i
$813$	−2.24056	+	2.24056i	−0.0785800	+	0.0785800i
$814$		−	24.1017i		−	0.844765i
$815$		0			0
$816$		−	0.840445i		−	0.0294214i
$817$	3.97571	+	11.4739i	0.139092	+	0.401422i
$818$	33.6291	+	33.6291i	1.17582	+	1.17582i
$819$	−1.41942			−0.0495986
$820$		0			0
$821$	−11.4193			−0.398535			−0.199268	−	0.979945i	$-0.563856\pi$
$821$	−11.4193			−0.398535			−0.199268	+	0.979945i	$0.563856\pi$
$822$	−10.0810	+	10.0810i	−0.351614	+	0.351614i
$823$	−19.2000	−	19.2000i	−0.669271	−	0.669271i	0.288276	−	0.957547i	$-0.406918\pi$
$823$	−19.2000	−	19.2000i	−0.669271	−	0.669271i	−0.957547	+	0.288276i	$0.906918\pi$
$824$			30.3334i			1.05671i
$825$		0			0
$826$	44.6450			1.55340
$827$	−38.3989	−	38.3989i	−1.33526	−	1.33526i	−0.900591	−	0.434668i	$-0.856866\pi$
$827$	−38.3989	−	38.3989i	−1.33526	−	1.33526i	−0.434668	−	0.900591i	$-0.643134\pi$
$828$	2.05086	+	2.05086i	0.0712721	+	0.0712721i
$829$	−18.3873			−0.638616			−0.319308	−	0.947651i	$-0.603450\pi$
$829$	−18.3873			−0.638616			−0.319308	+	0.947651i	$0.603450\pi$
$830$		0			0
$831$			9.20629i			0.319363i
$832$	14.4323	+	14.4323i	0.500351	+	0.500351i
$833$	−15.8113	−	15.8113i	−0.547831	−	0.547831i
$834$			29.2672i			1.01344i
$835$		0			0
$836$	21.5669	−	44.4373i	0.745907	−	1.53690i
$837$	−20.1619	+	20.1619i	−0.696898	+	0.696898i
$838$	−30.7098	+	30.7098i	−1.06085	+	1.06085i
$839$	20.1495			0.695638			0.347819	−	0.937562i	$-0.386922\pi$
$839$	20.1495			0.695638			0.347819	+	0.937562i	$0.386922\pi$
$840$		0			0
$841$	46.4005			1.60002
$842$	−27.1066	+	27.1066i	−0.934156	+	0.934156i
$843$	24.1017	+	24.1017i	0.830107	+	0.830107i
$844$	−2.70146			−0.0929880
$845$		0			0
$846$			9.90334i			0.340484i
$847$	−1.73483	+	1.73483i	−0.0596093	+	0.0596093i
$848$	0.0104203	−	0.0104203i	0.000357833	−	0.000357833i
$849$	−10.9432			−0.375570
$850$		0			0
$851$		−	5.14145i		−	0.176247i
$852$	−9.65878	+	9.65878i	−0.330904	+	0.330904i
$853$	12.2859	+	12.2859i	0.420662	+	0.420662i	0.885432	−	0.464770i	$-0.153863\pi$
$853$	12.2859	+	12.2859i	0.420662	+	0.420662i	−0.464770	+	0.885432i	$0.653863\pi$
$854$	−35.8353			−1.22626
$855$		0			0
$856$	−2.29190			−0.0783354
$857$	−18.9717	−	18.9717i	−0.648061	−	0.648061i	0.304463	−	0.952524i	$-0.401523\pi$
$857$	−18.9717	−	18.9717i	−0.648061	−	0.648061i	−0.952524	+	0.304463i	$0.901523\pi$
$858$	14.0863	−	14.0863i	0.480897	−	0.480897i
$859$		−	10.6953i		−	0.364920i	−0.983213	−	0.182460i	$-0.941594\pi$
$859$		−	10.6953i		−	0.364920i	0.983213	−	0.182460i	$-0.0584061\pi$
$860$		0			0
$861$	30.7556			1.04815
$862$	31.4686	−	31.4686i	1.07182	−	1.07182i
$863$	−34.1648	+	34.1648i	−1.16298	+	1.16298i	−0.179166	+	0.983819i	$0.557340\pi$
$863$	−34.1648	+	34.1648i	−1.16298	+	1.16298i	−0.983819	+	0.179166i	$0.942660\pi$
$864$		−	31.9813i		−	1.08802i
$865$		0			0
$866$	59.6751			2.02784
$867$	14.9833	+	14.9833i	0.508859	+	0.508859i
$868$	−20.0682	+	20.0682i	−0.681158	+	0.681158i
$869$	12.4867			0.423583
$870$		0			0
$871$	14.6079			0.494971
$872$	−10.0810	+	10.0810i	−0.341385	+	0.341385i
$873$	0.748679	−	0.748679i	0.0253390	−	0.0253390i
$874$	7.46335	−	15.3778i	0.252452	−	0.520161i
$875$		0			0
$876$			33.3140i			1.12557i
$877$	33.4886	+	33.4886i	1.13083	+	1.13083i	0.990039	+	0.140791i	$0.0449646\pi$
$877$	33.4886	+	33.4886i	1.13083	+	1.13083i	0.140791	+	0.990039i	$0.455035\pi$
$878$	−26.2623	−	26.2623i	−0.886308	−	0.886308i
$879$		−	34.6562i		−	1.16892i
$880$		0			0
$881$	−45.4336			−1.53070			−0.765348	−	0.643617i	$-0.777433\pi$
$881$	−45.4336			−1.53070			−0.765348	+	0.643617i	$0.777433\pi$
$882$	−3.43671	−	3.43671i	−0.115720	−	0.115720i
$883$	−19.5970	−	19.5970i	−0.659492	−	0.659492i	0.295768	−	0.955260i	$-0.404425\pi$
$883$	−19.5970	−	19.5970i	−0.659492	−	0.659492i	−0.955260	+	0.295768i	$0.904425\pi$
$884$	−27.9111			−0.938750
$885$		0			0
$886$		−	24.0710i		−	0.808679i
$887$	20.3911	+	20.3911i	0.684667	+	0.684667i	0.961048	−	0.276381i	$-0.0891351\pi$
$887$	20.3911	+	20.3911i	0.684667	+	0.684667i	−0.276381	+	0.961048i	$0.589135\pi$
$888$	9.23430	−	9.23430i	0.309883	−	0.309883i
$889$	4.38235			0.146979
$890$		0			0
$891$	−25.1985			−0.844181
$892$	7.80941	+	7.80941i	0.261478	+	0.261478i
$893$	33.9959	−	11.7795i	1.13763	−	0.394187i
$894$			12.6637i			0.423538i
$895$		0			0
$896$		−	31.0734i		−	1.03809i
$897$	3.00492	−	3.00492i	0.100331	−	0.100331i
$898$	49.0069	+	49.0069i	1.63538	+	1.63538i
$899$		−	44.6450i		−	1.48899i
$900$		0			0
$901$			0.840445i			0.0279993i
$902$	64.8069	−	64.8069i	2.15783	−	2.15783i
$903$	5.32157	−	5.32157i	0.177091	−	0.177091i
$904$			49.0069i			1.62995i
$905$		0			0
$906$			31.1915i			1.03627i
$907$	−25.7271	−	25.7271i	−0.854253	−	0.854253i	0.136401	−	0.990654i	$-0.456447\pi$
$907$	−25.7271	−	25.7271i	−0.854253	−	0.854253i	−0.990654	+	0.136401i	$0.956447\pi$
$908$	11.9462	−	11.9462i	0.396448	−	0.396448i
$909$		−	2.24935i		−	0.0746063i
$910$		0			0
$911$		−	47.8979i		−	1.58693i	−0.608618	−	0.793464i	$-0.708276\pi$
$911$		−	47.8979i		−	1.58693i	0.608618	−	0.793464i	$-0.291724\pi$
$912$	−0.627087	+	0.217285i	−0.0207649	+	0.00719502i
$913$	−10.8113	−	10.8113i	−0.357803	−	0.357803i
$914$	34.2725			1.13363
$915$		0			0
$916$	81.9867			2.70892
$917$	21.5111	−	21.5111i	0.710360	−	0.710360i
$918$	49.4291	+	49.4291i	1.63140	+	1.63140i
$919$		−	35.1941i		−	1.16094i	−0.814280	−	0.580472i	$-0.802868\pi$
$919$		−	35.1941i		−	1.16094i	0.814280	−	0.580472i	$-0.197132\pi$
$920$		0			0
$921$	10.7195			0.353219
$922$	−7.39637	−	7.39637i	−0.243586	−	0.243586i
$923$	−3.00492	−	3.00492i	−0.0989082	−	0.0989082i
$924$	−30.6125			−1.00708
$925$		0			0
$926$			90.3561i			2.96929i
$927$	4.06431	+	4.06431i	0.133489	+	0.133489i
$928$	35.4084	+	35.4084i	1.16234	+	1.16234i
$929$			4.93624i			0.161953i	0.996716	+	0.0809764i	$0.0258038\pi$
$929$			4.93624i			0.161953i	−0.996716	+	0.0809764i	$0.974196\pi$
$930$		0			0
$931$	−7.70964	+	15.8852i	−0.252673	+	0.520617i
$932$	41.1639	−	41.1639i	1.34837	−	1.34837i
$933$	12.6861	−	12.6861i	0.415326	−	0.415326i
$934$	−47.0207			−1.53856
$935$		0			0
$936$	−2.29190			−0.0749129
$937$	−21.4242	+	21.4242i	−0.699898	+	0.699898i	−0.964388	−	0.264490i	$-0.914796\pi$
$937$	−21.4242	+	21.4242i	−0.699898	+	0.699898i	0.264490	+	0.964388i	$0.414796\pi$
$938$	−25.7496	−	25.7496i	−0.840754	−	0.840754i
$939$	−33.8929			−1.10605
$940$		0			0
$941$			39.3772i			1.28366i	0.766847	+	0.641830i	$0.221825\pi$
$941$			39.3772i			1.28366i	−0.766847	+	0.641830i	$0.778175\pi$
$942$	6.14119	−	6.14119i	0.200091	−	0.200091i
$943$	13.8248	−	13.8248i	0.450197	−	0.450197i
$944$	−1.10191			−0.0358642
$945$		0			0
$946$		−	22.4268i		−	0.729158i
$947$	14.4543	−	14.4543i	0.469702	−	0.469702i	−0.432116	−	0.901818i	$-0.642233\pi$
$947$	14.4543	−	14.4543i	0.469702	−	0.469702i	0.901818	+	0.432116i	$0.142233\pi$
$948$	12.6637	+	12.6637i	0.411298	+	0.411298i
$949$	−10.3642			−0.336437
$950$		0			0
$951$	−40.7797			−1.32237
$952$	18.5867	+	18.5867i	0.602398	+	0.602398i
$953$	−1.57323	+	1.57323i	−0.0509619	+	0.0509619i	−0.732128	−	0.681167i	$-0.761473\pi$
$953$	−1.57323	+	1.57323i	−0.0509619	+	0.0509619i	0.681167	+	0.732128i	$0.261473\pi$
$954$			0.182677i			0.00591438i
$955$		0			0
$956$	−6.56199			−0.212230
$957$	34.0513	−	34.0513i	1.10072	−	1.10072i
$958$	−34.8235	+	34.8235i	−1.12509	+	1.12509i
$959$			6.81579i			0.220093i
$960$		0			0
$961$	4.56553			0.147275
$962$	7.60451	+	7.60451i	0.245179	+	0.245179i
$963$	−0.307087	+	0.307087i	−0.00989573	+	0.00989573i
$964$	−5.98189			−0.192664
$965$		0			0
$966$	−10.5936			−0.340845
$967$	−15.3160	+	15.3160i	−0.492530	+	0.492530i	−0.909103	−	0.416572i	$-0.863231\pi$
$967$	−15.3160	+	15.3160i	−0.492530	+	0.492530i	0.416572	+	0.909103i	$0.363231\pi$
$968$	−2.80117	+	2.80117i	−0.0900330	+	0.0900330i
$969$	16.5263	−	34.0513i	0.530900	−	1.09389i
$970$		0			0
$971$		−	54.8015i		−	1.75867i	−0.476208	−	0.879333i	$-0.657989\pi$
$971$		−	54.8015i		−	1.75867i	0.476208	−	0.879333i	$-0.342011\pi$
$972$	12.2587	+	12.2587i	0.393199	+	0.393199i
$973$	9.89384	+	9.89384i	0.317182	+	0.317182i
$974$		−	40.8879i		−	1.31013i
$975$		0			0
$976$	0.884476			0.0283114
$977$	−38.2505	−	38.2505i	−1.22374	−	1.22374i	−0.966291	−	0.257451i	$-0.917117\pi$
$977$	−38.2505	−	38.2505i	−1.22374	−	1.22374i	−0.257451	−	0.966291i	$-0.582883\pi$
$978$	−25.7496	−	25.7496i	−0.823381	−	0.823381i
$979$	−22.0105			−0.703459
$980$		0			0
$981$			2.70146i			0.0862509i
$982$	6.67400	+	6.67400i	0.212976	+	0.212976i
$983$	−18.5763	+	18.5763i	−0.592491	+	0.592491i	−0.938304	−	0.345813i	$-0.887603\pi$
$983$	−18.5763	+	18.5763i	−0.592491	+	0.592491i	0.345813	+	0.938304i	$0.387603\pi$
$984$	49.6601			1.58311
$985$		0			0
$986$	−109.452			−3.48566
$987$	−15.7672	−	15.7672i	−0.501874	−	0.501874i
$988$	7.21601	+	20.8255i	0.229572	+	0.662547i
$989$		−	4.78415i		−	0.152127i
$990$		0			0
$991$		−	12.8042i		−	0.406740i	−0.979102	−	0.203370i	$-0.934811\pi$
$991$		−	12.8042i		−	0.406740i	0.979102	−	0.203370i	$-0.0651894\pi$
$992$	20.9654	−	20.9654i	0.665653	−	0.665653i
$993$	−28.9763	−	28.9763i	−0.919536	−	0.919536i
$994$			10.5936i			0.336010i
$995$		0			0
$996$		−	21.9292i		−	0.694852i
$997$	−14.4795	+	14.4795i	−0.458570	+	0.458570i	−0.898186	−	0.439616i	$-0.855115\pi$
$997$	−14.4795	+	14.4795i	−0.458570	+	0.458570i	0.439616	+	0.898186i	$0.355115\pi$
$998$	13.9149	−	13.9149i	0.440467	−	0.440467i
$999$		−	16.6035i		−	0.525311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.g.b.18.6		12
5.2	odd	4	inner	475.2.g.b.132.1		12
5.3	odd	4		95.2.g.b.37.6	yes	12
5.4	even	2		95.2.g.b.18.1	✓	12
15.8	even	4		855.2.p.f.37.1		12
15.14	odd	2		855.2.p.f.208.6		12
19.18	odd	2	inner	475.2.g.b.18.1		12
95.18	even	4		95.2.g.b.37.1	yes	12
95.37	even	4	inner	475.2.g.b.132.6		12
95.94	odd	2		95.2.g.b.18.6	yes	12
285.113	odd	4		855.2.p.f.37.6		12
285.284	even	2		855.2.p.f.208.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.g.b.18.1	✓	12	5.4	even	2
95.2.g.b.18.6	yes	12	95.94	odd	2
95.2.g.b.37.1	yes	12	95.18	even	4
95.2.g.b.37.6	yes	12	5.3	odd	4
475.2.g.b.18.1		12	19.18	odd	2	inner
475.2.g.b.18.6		12	1.1	even	1	trivial
475.2.g.b.132.1		12	5.2	odd	4	inner
475.2.g.b.132.6		12	95.37	even	4	inner
855.2.p.f.37.1		12	15.8	even	4
855.2.p.f.37.6		12	285.113	odd	4
855.2.p.f.208.1		12	285.284	even	2
855.2.p.f.208.6		12	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.61467 + 1.61467i) q^{2} +(-1.11233 + 1.11233i) q^{3} +3.21432i q^{4} -3.59210 q^{6} +(-1.21432 + 1.21432i) q^{7} +(-1.96073 + 1.96073i) q^{8} +0.525428i q^{9} +O(q^{10})\)	\(q+(1.61467 + 1.61467i) q^{2} +(-1.11233 + 1.11233i) q^{3} +3.21432i q^{4} -3.59210 q^{6} +(-1.21432 + 1.21432i) q^{7} +(-1.96073 + 1.96073i) q^{8} +0.525428i q^{9} -3.52543 q^{11} +(-3.57540 - 3.57540i) q^{12} +(1.11233 - 1.11233i) q^{13} -3.92145 q^{14} +0.0967881 q^{16} +(-3.90321 + 3.90321i) q^{17} +(-0.848392 + 0.848392i) q^{18} +(3.92145 + 1.90321i) q^{19} -2.70146i q^{21} +(-5.69240 - 5.69240i) q^{22} +(-1.21432 - 1.21432i) q^{23} -4.36196i q^{24} +3.59210 q^{26} +(-3.92145 - 3.92145i) q^{27} +(-3.90321 - 3.90321i) q^{28} +8.68335 q^{29} -5.14145i q^{31} +(4.07773 + 4.07773i) q^{32} +(3.92145 - 3.92145i) q^{33} -12.6048 q^{34} -1.68889 q^{36} +(2.11701 + 2.11701i) q^{37} +(3.25879 + 9.40491i) q^{38} +2.47457i q^{39} +11.3848i q^{41} +(4.36196 - 4.36196i) q^{42} +(1.96989 + 1.96989i) q^{43} -11.3319i q^{44} -3.92145i q^{46} +(5.83654 - 5.83654i) q^{47} +(-0.107661 + 0.107661i) q^{48} +4.05086i q^{49} -8.68335i q^{51} +(3.57540 + 3.57540i) q^{52} +(0.107661 - 0.107661i) q^{53} -12.6637i q^{54} -4.76190i q^{56} +(-6.47897 + 2.24496i) q^{57} +(14.0207 + 14.0207i) q^{58} -11.3848 q^{59} +9.13828 q^{61} +(8.30174 - 8.30174i) q^{62} +(-0.638037 - 0.638037i) q^{63} +12.9748i q^{64} +12.6637 q^{66} +(6.56634 + 6.56634i) q^{67} +(-12.5462 - 12.5462i) q^{68} +2.70146 q^{69} -2.70146i q^{71} +(-1.03022 - 1.03022i) q^{72} +(-4.65878 - 4.65878i) q^{73} +6.83654i q^{74} +(-6.11753 + 12.6048i) q^{76} +(4.28100 - 4.28100i) q^{77} +(-3.99562 + 3.99562i) q^{78} -3.54190 q^{79} +7.14764 q^{81} +(-18.3827 + 18.3827i) q^{82} +(3.06668 + 3.06668i) q^{83} +8.68335 q^{84} +6.36144i q^{86} +(-9.65878 + 9.65878i) q^{87} +(6.91240 - 6.91240i) q^{88} +6.24336 q^{89} +2.70146i q^{91} +(3.90321 - 3.90321i) q^{92} +(5.71900 + 5.71900i) q^{93} +18.8482 q^{94} -9.07160 q^{96} +(-1.42490 - 1.42490i) q^{97} +(-6.54080 + 6.54080i) q^{98} -1.85236i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 16 q^{6} + 12 q^{7}+O(q^{10}) \) 12 * q - 16 * q^6 + 12 * q^7	\( 12 q - 16 q^{6} + 12 q^{7} - 16 q^{11} + 28 q^{16} - 20 q^{17} + 12 q^{23} + 16 q^{26} - 20 q^{28} - 20 q^{36} - 4 q^{38} - 4 q^{43} + 44 q^{47} + 88 q^{58} - 24 q^{61} - 8 q^{62} - 60 q^{63} - 8 q^{66} - 44 q^{68} - 28 q^{73} - 20 q^{76} + 24 q^{77} + 60 q^{81} - 88 q^{82} + 36 q^{83} - 88 q^{87} + 20 q^{92} + 96 q^{93} + 24 q^{96}+O(q^{100}) \) 12 * q - 16 * q^6 + 12 * q^7 - 16 * q^11 + 28 * q^16 - 20 * q^17 + 12 * q^23 + 16 * q^26 - 20 * q^28 - 20 * q^36 - 4 * q^38 - 4 * q^43 + 44 * q^47 + 88 * q^58 - 24 * q^61 - 8 * q^62 - 60 * q^63 - 8 * q^66 - 44 * q^68 - 28 * q^73 - 20 * q^76 + 24 * q^77 + 60 * q^81 - 88 * q^82 + 36 * q^83 - 88 * q^87 + 20 * q^92 + 96 * q^93 + 24 * q^96

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