LMFDB - Embedded newform 475.2.g.b.132.2

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			132.2
Root			$-1.10924 - 1.10924i$ of defining polynomial
Character	$\chi$	$=$	475.132
Dual form			475.2.g.b.18.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10924 + 1.10924i) q^{2} +(-1.29790 - 1.29790i) q^{3} -0.460811i q^{4} +2.87936 q^{6} +(1.53919 + 1.53919i) q^{7} +(-1.70732 - 1.70732i) q^{8} +0.369102i q^{9} +O(q^{10})$	\(q+(-1.10924 + 1.10924i) q^{2} +(-1.29790 - 1.29790i) q^{3} -0.460811i q^{4} +2.87936 q^{6} +(1.53919 + 1.53919i) q^{7} +(-1.70732 - 1.70732i) q^{8} +0.369102i q^{9} -2.63090 q^{11} +(-0.598088 + 0.598088i) q^{12} +(1.29790 + 1.29790i) q^{13} -3.41465 q^{14} +4.70928 q^{16} +(0.709275 + 0.709275i) q^{17} +(-0.409422 - 0.409422i) q^{18} +(3.41465 + 2.70928i) q^{19} -3.99543i q^{21} +(2.91829 - 2.91829i) q^{22} +(1.53919 - 1.53919i) q^{23} +4.43188i q^{24} -2.87936 q^{26} +(-3.41465 + 3.41465i) q^{27} +(0.709275 - 0.709275i) q^{28} -1.84114 q^{29} +10.8247i q^{31} +(-1.80905 + 1.80905i) q^{32} +(3.41465 + 3.41465i) q^{33} -1.57351 q^{34} +0.170086 q^{36} +(-3.51638 + 3.51638i) q^{37} +(-6.79288 + 0.782426i) q^{38} -3.36910i q^{39} +5.83658i q^{41} +(4.43188 + 4.43188i) q^{42} +(-8.21953 + 8.21953i) q^{43} +1.21235i q^{44} +3.41465i q^{46} +(6.80098 + 6.80098i) q^{47} +(-6.11218 - 6.11218i) q^{48} -2.26180i q^{49} -1.84114i q^{51} +(0.598088 - 0.598088i) q^{52} +(6.11218 + 6.11218i) q^{53} -7.57531i q^{54} -5.25579i q^{56} +(-0.915506 - 7.94826i) q^{57} +(2.04226 - 2.04226i) q^{58} +5.83658 q^{59} -10.2062 q^{61} +(-12.0072 - 12.0072i) q^{62} +(-0.568118 + 0.568118i) q^{63} +5.40522i q^{64} -7.57531 q^{66} +(1.67523 - 1.67523i) q^{67} +(0.326842 - 0.326842i) q^{68} -3.99543 q^{69} -3.99543i q^{71} +(0.630178 - 0.630178i) q^{72} +(7.38962 - 7.38962i) q^{73} -7.80098i q^{74} +(1.24846 - 1.57351i) q^{76} +(-4.04945 - 4.04945i) q^{77} +(3.73713 + 3.73713i) q^{78} +12.6659 q^{79} +9.97107 q^{81} +(-6.47414 - 6.47414i) q^{82} +(-2.51026 + 2.51026i) q^{83} -1.84114 q^{84} -18.2348i q^{86} +(2.38962 + 2.38962i) q^{87} +(4.49180 + 4.49180i) q^{88} -16.6613 q^{89} +3.99543i q^{91} +(-0.709275 - 0.709275i) q^{92} +(14.0494 - 14.0494i) q^{93} -15.0878 q^{94} +4.69594 q^{96} +(9.14950 - 9.14950i) q^{97} +(2.50887 + 2.50887i) q^{98} -0.971071i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.10924	+	1.10924i	−0.784349	+	0.784349i	−0.980561	−	0.196213i	$-0.937136\pi$
$2$	−1.10924	+	1.10924i	−0.784349	+	0.784349i	0.196213	+	0.980561i	$0.437136\pi$
$3$	−1.29790	−	1.29790i	−0.749344	−	0.749344i	0.225012	−	0.974356i	$-0.427758\pi$
$3$	−1.29790	−	1.29790i	−0.749344	−	0.749344i	−0.974356	+	0.225012i	$0.927758\pi$
$4$		−	0.460811i		−	0.230406i
$5$		0			0
$5$		0			0
$6$	2.87936			1.17549
$7$	1.53919	+	1.53919i	0.581759	+	0.581759i	0.935386	−	0.353628i	$-0.115052\pi$
$7$	1.53919	+	1.53919i	0.581759	+	0.581759i	−0.353628	+	0.935386i	$0.615052\pi$
$8$	−1.70732	−	1.70732i	−0.603630	−	0.603630i
$9$			0.369102i			0.123034i
$10$		0			0
$11$	−2.63090			−0.793245			−0.396623	−	0.917982i	$-0.629818\pi$
$11$	−2.63090			−0.793245			−0.396623	+	0.917982i	$0.629818\pi$
$12$	−0.598088	+	0.598088i	−0.172653	+	0.172653i
$13$	1.29790	+	1.29790i	0.359973	+	0.359973i	0.863803	−	0.503830i	$-0.168076\pi$
$13$	1.29790	+	1.29790i	0.359973	+	0.359973i	−0.503830	+	0.863803i	$0.668076\pi$
$14$	−3.41465			−0.912603
$15$		0			0
$16$	4.70928			1.17732
$17$	0.709275	+	0.709275i	0.172025	+	0.172025i	0.787868	−	0.615844i	$-0.211185\pi$
$17$	0.709275	+	0.709275i	0.172025	+	0.172025i	−0.615844	+	0.787868i	$0.711185\pi$
$18$	−0.409422	−	0.409422i	−0.0965017	−	0.0965017i
$19$	3.41465	+	2.70928i	0.783374	+	0.621550i
$19$	3.41465	+	2.70928i	0.783374	+	0.621550i
$20$		0			0
$21$		−	3.99543i		−	0.871875i
$22$	2.91829	−	2.91829i	0.622181	−	0.622181i
$23$	1.53919	−	1.53919i	0.320943	−	0.320943i	−0.528186	−	0.849129i	$-0.677128\pi$
$23$	1.53919	−	1.53919i	0.320943	−	0.320943i	0.849129	+	0.528186i	$0.177128\pi$
$24$			4.43188i			0.904654i
$25$		0			0
$26$	−2.87936			−0.564689
$27$	−3.41465	+	3.41465i	−0.657149	+	0.657149i
$28$	0.709275	−	0.709275i	0.134040	−	0.134040i
$29$	−1.84114			−0.341891			−0.170946	−	0.985280i	$-0.554682\pi$
$29$	−1.84114			−0.341891			−0.170946	+	0.985280i	$0.554682\pi$
$30$		0			0
$31$			10.8247i			1.94418i	0.234610	+	0.972090i	$0.424619\pi$
$31$			10.8247i			1.94418i	−0.234610	+	0.972090i	$0.575381\pi$
$32$	−1.80905	+	1.80905i	−0.319798	+	0.319798i
$33$	3.41465	+	3.41465i	0.594414	+	0.594414i
$34$	−1.57351			−0.269854
$35$		0			0
$36$	0.170086			0.0283477
$37$	−3.51638	+	3.51638i	−0.578089	+	0.578089i	−0.934376	−	0.356288i	$-0.884042\pi$
$37$	−3.51638	+	3.51638i	−0.578089	+	0.578089i	0.356288	+	0.934376i	$0.384042\pi$
$38$	−6.79288	+	0.782426i	−1.10195	+	0.126926i
$39$		−	3.36910i		−	0.539488i
$40$		0			0
$41$			5.83658i			0.911520i	0.890103	+	0.455760i	$0.150632\pi$
$41$			5.83658i			0.911520i	−0.890103	+	0.455760i	$0.849368\pi$
$42$	4.43188	+	4.43188i	0.683854	+	0.683854i
$43$	−8.21953	+	8.21953i	−1.25347	+	1.25347i	−0.299312	+	0.954155i	$0.596757\pi$
$43$	−8.21953	+	8.21953i	−1.25347	+	1.25347i	−0.954155	+	0.299312i	$0.903243\pi$
$44$			1.21235i			0.182768i
$45$		0			0
$46$			3.41465i			0.503463i
$47$	6.80098	+	6.80098i	0.992025	+	0.992025i	0.999968	−	0.00794297i	$-0.00252835\pi$
$47$	6.80098	+	6.80098i	0.992025	+	0.992025i	−0.00794297	+	0.999968i	$0.502528\pi$
$48$	−6.11218	−	6.11218i	−0.882217	−	0.882217i
$49$		−	2.26180i		−	0.323114i
$50$		0			0
$51$		−	1.84114i		−	0.257811i
$52$	0.598088	−	0.598088i	0.0829399	−	0.0829399i
$53$	6.11218	+	6.11218i	0.839573	+	0.839573i	0.988803	−	0.149230i	$-0.0476795\pi$
$53$	6.11218	+	6.11218i	0.839573	+	0.839573i	−0.149230	+	0.988803i	$0.547679\pi$
$54$		−	7.57531i		−	1.03087i
$55$		0			0
$56$		−	5.25579i		−	0.702334i
$57$	−0.915506	−	7.94826i	−0.121262	−	1.05277i
$58$	2.04226	−	2.04226i	0.268162	−	0.268162i
$59$	5.83658			0.759857			0.379929	−	0.925016i	$-0.375949\pi$
$59$	5.83658			0.759857			0.379929	+	0.925016i	$0.375949\pi$
$60$		0			0
$61$	−10.2062			−1.30677			−0.653385	−	0.757026i	$-0.726652\pi$
$61$	−10.2062			−1.30677			−0.653385	+	0.757026i	$0.726652\pi$
$62$	−12.0072	−	12.0072i	−1.52491	−	1.52491i
$63$	−0.568118	+	0.568118i	−0.0715762	+	0.0715762i
$64$			5.40522i			0.675652i
$65$		0			0
$66$	−7.57531			−0.932456
$67$	1.67523	−	1.67523i	0.204663	−	0.204663i	−0.597332	−	0.801994i	$-0.703772\pi$
$67$	1.67523	−	1.67523i	0.204663	−	0.204663i	0.801994	+	0.597332i	$0.203772\pi$
$68$	0.326842	−	0.326842i	0.0396354	−	0.0396354i
$69$	−3.99543			−0.480994
$70$		0			0
$71$		−	3.99543i		−	0.474171i	−0.971489	−	0.237085i	$-0.923808\pi$
$71$		−	3.99543i		−	0.474171i	0.971489	−	0.237085i	$-0.0761921\pi$
$72$	0.630178	−	0.630178i	0.0742671	−	0.0742671i
$73$	7.38962	−	7.38962i	0.864890	−	0.864890i	−0.127011	−	0.991901i	$-0.540539\pi$
$73$	7.38962	−	7.38962i	0.864890	−	0.864890i	0.991901	+	0.127011i	$0.0405385\pi$
$74$		−	7.80098i		−	0.906846i
$75$		0			0
$76$	1.24846	−	1.57351i	0.143209	−	0.180494i
$77$	−4.04945	−	4.04945i	−0.461477	−	0.461477i
$78$	3.73713	+	3.73713i	0.423147	+	0.423147i
$79$	12.6659			1.42502			0.712511	−	0.701661i	$-0.247558\pi$
$79$	12.6659			1.42502			0.712511	+	0.701661i	$0.247558\pi$
$80$		0			0
$81$	9.97107			1.10790
$82$	−6.47414	−	6.47414i	−0.714949	−	0.714949i
$83$	−2.51026	+	2.51026i	−0.275537	+	0.275537i	−0.831324	−	0.555788i	$-0.812417\pi$
$83$	−2.51026	+	2.51026i	−0.275537	+	0.275537i	0.555788	+	0.831324i	$0.312417\pi$
$84$	−1.84114			−0.200885
$85$		0			0
$86$		−	18.2348i		−	1.96631i
$87$	2.38962	+	2.38962i	0.256194	+	0.256194i
$88$	4.49180	+	4.49180i	0.478827	+	0.478827i
$89$	−16.6613			−1.76610			−0.883048	−	0.469284i	$-0.844512\pi$
$89$	−16.6613			−1.76610			−0.883048	+	0.469284i	$0.844512\pi$
$90$		0			0
$91$			3.99543i			0.418835i
$92$	−0.709275	−	0.709275i	−0.0739471	−	0.0739471i
$93$	14.0494	−	14.0494i	1.45686	−	1.45686i
$94$	−15.0878			−1.55619
$95$		0			0
$96$	4.69594			0.479278
$97$	9.14950	−	9.14950i	0.928991	−	0.928991i	−0.0686501	−	0.997641i	$-0.521869\pi$
$97$	9.14950	−	9.14950i	0.928991	−	0.928991i	0.997641	+	0.0686501i	$0.0218692\pi$
$98$	2.50887	+	2.50887i	0.253434	+	0.253434i
$99$		−	0.971071i		−	0.0975963i
$100$		0			0
$101$	4.04945			0.402935			0.201468	−	0.979495i	$-0.435429\pi$
$101$	4.04945			0.402935			0.201468	+	0.979495i	$0.435429\pi$
$102$	2.04226	+	2.04226i	0.202214	+	0.202214i
$103$	0.717117	+	0.717117i	0.0706596	+	0.0706596i	0.741553	−	0.670894i	$-0.234089\pi$
$103$	0.717117	+	0.717117i	0.0706596	+	0.0706596i	−0.670894	+	0.741553i	$0.734089\pi$
$104$		−	4.43188i		−	0.434582i
$105$		0			0
$106$	−13.5597			−1.31704
$107$	−0.479059	+	0.479059i	−0.0463124	+	0.0463124i	−0.729884	−	0.683571i	$-0.760426\pi$
$107$	−0.479059	+	0.479059i	−0.0463124	+	0.0463124i	0.683571	+	0.729884i	$0.260426\pi$
$108$	1.57351	+	1.57351i	0.151411	+	0.151411i
$109$	10.8247			1.03682			0.518411	−	0.855132i	$-0.326524\pi$
$109$	10.8247			1.03682			0.518411	+	0.855132i	$0.326524\pi$
$110$		0			0
$111$	9.12783			0.866375
$112$	7.24846	+	7.24846i	0.684915	+	0.684915i
$113$	−4.53867	−	4.53867i	−0.426962	−	0.426962i	0.460630	−	0.887592i	$-0.347624\pi$
$113$	−4.53867	−	4.53867i	−0.426962	−	0.426962i	−0.887592	+	0.460630i	$0.847624\pi$
$114$	9.83201	+	7.80098i	0.920852	+	0.730629i
$115$		0			0
$116$			0.848418i			0.0787736i
$117$	−0.479059	+	0.479059i	−0.0442890	+	0.0442890i
$118$	−6.47414	+	6.47414i	−0.595993	+	0.595993i
$119$			2.18342i			0.200154i
$120$		0			0
$121$	−4.07838			−0.370762
$122$	11.3211	−	11.3211i	1.02496	−	1.02496i
$123$	7.57531	−	7.57531i	0.683042	−	0.683042i
$124$	4.98816			0.447950
$125$		0			0
$126$		−	1.26036i		−	0.112281i
$127$	−6.93102	+	6.93102i	−0.615029	+	0.615029i	−0.944252	−	0.329223i	$-0.893213\pi$
$127$	−6.93102	+	6.93102i	−0.615029	+	0.615029i	0.329223	+	0.944252i	$0.393213\pi$
$128$	−9.61377	−	9.61377i	−0.849745	−	0.849745i
$129$	21.3363			1.87856
$130$		0			0
$131$	4.31351			0.376873			0.188437	−	0.982085i	$-0.439658\pi$
$131$	4.31351			0.376873			0.188437	+	0.982085i	$0.439658\pi$
$132$	1.57351	−	1.57351i	0.136956	−	0.136956i
$133$	1.08570	+	9.42588i	0.0941424	+	0.817327i
$134$			3.71646i			0.321054i
$135$		0			0
$136$		−	2.42193i		−	0.207678i
$137$	−6.41855	−	6.41855i	−0.548374	−	0.548374i	0.377596	−	0.925970i	$-0.376751\pi$
$137$	−6.41855	−	6.41855i	−0.548374	−	0.548374i	−0.925970	+	0.377596i	$0.876751\pi$
$138$	4.43188	−	4.43188i	0.377267	−	0.377267i
$139$			10.9711i			0.930554i	0.885165	+	0.465277i	$0.154045\pi$
$139$			10.9711i			0.930554i	−0.885165	+	0.465277i	$0.845955\pi$
$140$		0			0
$141$		−	17.6540i		−	1.48674i
$142$	4.43188	+	4.43188i	0.371915	+	0.371915i
$143$	−3.41465	−	3.41465i	−0.285547	−	0.285547i
$144$			1.73820i			0.144850i
$145$		0			0
$146$			16.3937i			1.35675i
$147$	−2.93559	+	2.93559i	−0.242123	+	0.242123i
$148$	1.62038	+	1.62038i	0.133195	+	0.133195i
$149$			2.63090i			0.215532i	0.994176	+	0.107766i	$0.0343697\pi$
$149$			2.63090i			0.215532i	−0.994176	+	0.107766i	$0.965630\pi$
$150$		0			0
$151$		−	1.84114i		−	0.149830i	−0.997190	−	0.0749150i	$-0.976131\pi$
$151$		−	1.84114i		−	0.149830i	0.997190	−	0.0749150i	$-0.0238685\pi$
$152$	−1.20430	−	10.4555i	−0.0976817	−	0.848055i
$153$	−0.261795	+	0.261795i	−0.0211649	+	0.0211649i
$154$	8.98359			0.723918
$155$		0			0
$156$	−1.55252			−0.124301
$157$	12.1278	+	12.1278i	0.967906	+	0.967906i	0.999501	−	0.0315949i	$-0.0100586\pi$
$157$	12.1278	+	12.1278i	0.967906	+	0.967906i	−0.0315949	+	0.999501i	$0.510059\pi$
$158$	−14.0494	+	14.0494i	−1.11771	+	1.11771i
$159$		−	15.8660i		−	1.25826i
$160$		0			0
$161$	4.73820			0.373423
$162$	−11.0603	+	11.0603i	−0.868977	+	0.868977i
$163$	−1.98667	+	1.98667i	−0.155608	+	0.155608i	−0.780617	−	0.625009i	$-0.785095\pi$
$163$	−1.98667	+	1.98667i	−0.155608	+	0.155608i	0.625009	+	0.780617i	$0.285095\pi$
$164$	2.68956			0.210019
$165$		0			0
$166$		−	5.56894i		−	0.432234i
$167$	11.5714	−	11.5714i	0.895424	−	0.895424i	−0.0996036	−	0.995027i	$-0.531757\pi$
$167$	11.5714	−	11.5714i	0.895424	−	0.895424i	0.995027	+	0.0996036i	$0.0317575\pi$
$168$	−6.82150	+	6.82150i	−0.526290	+	0.526290i
$169$		−	9.63090i		−	0.740838i
$170$		0			0
$171$	−1.00000	+	1.26036i	−0.0764719	+	0.0963818i
$172$	3.78765	+	3.78765i	0.288806	+	0.288806i
$173$	−13.5223	−	13.5223i	−1.02808	−	1.02808i	−0.999594	−	0.0284845i	$-0.990932\pi$
$173$	−13.5223	−	13.5223i	−1.02808	−	1.02808i	−0.0284845	−	0.999594i	$-0.509068\pi$
$174$	−5.30131			−0.401891
$175$		0			0
$176$	−12.3896			−0.933903
$177$	−7.57531	−	7.57531i	−0.569395	−	0.569395i
$178$	18.4813	−	18.4813i	1.38523	−	1.38523i
$179$	−12.6659			−0.946692			−0.473346	−	0.880877i	$-0.656954\pi$
$179$	−12.6659			−0.946692			−0.473346	+	0.880877i	$0.656954\pi$
$180$		0			0
$181$		−	11.6732i		−	0.867658i	−0.900995	−	0.433829i	$-0.857162\pi$
$181$		−	11.6732i		−	0.867658i	0.900995	−	0.433829i	$-0.142838\pi$
$182$	−4.43188	−	4.43188i	−0.328513	−	0.328513i
$183$	13.2467	+	13.2467i	0.979221	+	0.979221i
$184$	−5.25579			−0.387462
$185$		0			0
$186$			31.1683i			2.28537i
$187$	−1.86603	−	1.86603i	−0.136458	−	0.136458i
$188$	3.13397	−	3.13397i	0.228568	−	0.228568i
$189$	−10.5116			−0.764605
$190$		0			0
$191$	−2.65368			−0.192014			−0.0960069	−	0.995381i	$-0.530607\pi$
$191$	−2.65368			−0.192014			−0.0960069	+	0.995381i	$0.530607\pi$
$192$	7.01545	−	7.01545i	0.506296	−	0.506296i
$193$	12.9415	+	12.9415i	0.931548	+	0.931548i	0.997803	−	0.0662547i	$-0.0211050\pi$
$193$	12.9415	+	12.9415i	0.931548	+	0.931548i	−0.0662547	+	0.997803i	$0.521105\pi$
$194$			20.2979i			1.45731i
$195$		0			0
$196$	−1.04226			−0.0744472
$197$	8.80817	+	8.80817i	0.627556	+	0.627556i	0.947453	−	0.319896i	$-0.103648\pi$
$197$	8.80817	+	8.80817i	0.627556	+	0.627556i	−0.319896	+	0.947453i	$0.603648\pi$
$198$	1.07715	+	1.07715i	0.0765495	+	0.0765495i
$199$			4.52359i			0.320669i	0.987063	+	0.160334i	$0.0512573\pi$
$199$			4.52359i			0.320669i	−0.987063	+	0.160334i	$0.948743\pi$
$200$		0			0
$201$	−4.34858			−0.306725
$202$	−4.49180	+	4.49180i	−0.316042	+	0.316042i
$203$	−2.83386	−	2.83386i	−0.198898	−	0.198898i
$204$	−0.848418			−0.0594011
$205$		0			0
$206$	−1.59090			−0.110844
$207$	0.568118	+	0.568118i	0.0394870	+	0.0394870i
$208$	6.11218	+	6.11218i	0.423803	+	0.423803i
$209$	−8.98359	−	7.12783i	−0.621408	−	0.493042i
$210$		0			0
$211$			8.67044i			0.596898i	0.954426	+	0.298449i	$0.0964692\pi$
$211$			8.67044i			0.596898i	−0.954426	+	0.298449i	$0.903531\pi$
$212$	2.81656	−	2.81656i	0.193442	−	0.193442i
$213$	−5.18568	+	5.18568i	−0.355317	+	0.355317i
$214$		−	1.06278i		−	0.0726501i
$215$		0			0
$216$	11.6598			0.793351
$217$	−16.6613	+	16.6613i	−1.13104	+	1.13104i
$218$	−12.0072	+	12.0072i	−0.813229	+	0.813229i
$219$	−19.1820			−1.29620
$220$		0			0
$221$			1.84114i			0.123849i
$222$	−10.1249	+	10.1249i	−0.679540	+	0.679540i
$223$	−13.9638	−	13.9638i	−0.935084	−	0.935084i	0.0629341	−	0.998018i	$-0.479954\pi$
$223$	−13.9638	−	13.9638i	−0.935084	−	0.935084i	−0.998018	+	0.0629341i	$0.979954\pi$
$224$	−5.56894			−0.372091
$225$		0			0
$226$	10.0689			0.669775
$227$	−19.9742	+	19.9742i	−1.32574	+	1.32574i	−0.416685	+	0.909051i	$0.636808\pi$
$227$	−19.9742	+	19.9742i	−1.32574	+	1.32574i	−0.909051	+	0.416685i	$0.863192\pi$
$228$	−3.66265	+	0.421875i	−0.242565	+	0.0279394i
$229$		−	19.7237i		−	1.30338i	−0.758487	−	0.651688i	$-0.774061\pi$
$229$		−	19.7237i		−	1.30338i	0.758487	−	0.651688i	$-0.225939\pi$
$230$		0			0
$231$			10.5116i			0.691611i
$232$	3.14342	+	3.14342i	0.206376	+	0.206376i
$233$	−3.58145	+	3.58145i	−0.234629	+	0.234629i	−0.814621	−	0.579993i	$-0.803055\pi$
$233$	−3.58145	+	3.58145i	−0.234629	+	0.234629i	0.579993	+	0.814621i	$0.303055\pi$
$234$		−	1.06278i		−	0.0694761i
$235$		0			0
$236$		−	2.68956i		−	0.175075i
$237$	−16.4391	−	16.4391i	−1.06783	−	1.06783i
$238$	−2.42193	−	2.42193i	−0.156990	−	0.156990i
$239$			21.9155i			1.41759i	0.705412	+	0.708797i	$0.250762\pi$
$239$			21.9155i			1.41759i	−0.705412	+	0.708797i	$0.749238\pi$
$240$		0			0
$241$		−	4.67500i		−	0.301143i	−0.988599	−	0.150572i	$-0.951889\pi$
$241$		−	4.67500i		−	0.301143i	0.988599	−	0.150572i	$-0.0481115\pi$
$242$	4.52389	−	4.52389i	0.290806	−	0.290806i
$243$	−2.69753	−	2.69753i	−0.173047	−	0.173047i
$244$			4.70313i			0.301087i
$245$		0			0
$246$			16.8056i			1.07149i
$247$	0.915506	+	7.94826i	0.0582523	+	0.505736i
$248$	18.4813	−	18.4813i	1.17357	−	1.17357i
$249$	6.51614			0.412944
$250$		0			0
$251$	−4.18342			−0.264055			−0.132027	−	0.991246i	$-0.542149\pi$
$251$	−4.18342			−0.264055			−0.132027	+	0.991246i	$0.542149\pi$
$252$	0.261795	+	0.261795i	0.0164915	+	0.0164915i
$253$	−4.04945	+	4.04945i	−0.254587	+	0.254587i
$254$		−	15.3763i		−	0.964794i
$255$		0			0
$256$	10.5174			0.657340
$257$	−1.36208	+	1.36208i	−0.0849643	+	0.0849643i	−0.748312	−	0.663347i	$-0.769135\pi$
$257$	−1.36208	+	1.36208i	−0.0849643	+	0.0849643i	0.663347	+	0.748312i	$0.269135\pi$
$258$	−23.6670	+	23.6670i	−1.47344	+	1.47344i
$259$	−10.8247			−0.672616
$260$		0			0
$261$		−	0.679569i		−	0.0420643i
$262$	−4.78470	+	4.78470i	−0.295600	+	0.295600i
$263$	−0.326842	+	0.326842i	−0.0201539	+	0.0201539i	−0.717112	−	0.696958i	$-0.754536\pi$
$263$	−0.326842	+	0.326842i	−0.0201539	+	0.0201539i	0.696958	+	0.717112i	$0.254536\pi$
$264$		−	11.6598i		−	0.717613i
$265$		0			0
$266$	−11.6598	−	9.25122i	−0.714910	−	0.567229i
$267$	21.6248	+	21.6248i	1.32341	+	1.32341i
$268$	−0.771967	−	0.771967i	−0.0471554	−	0.0471554i
$269$	11.9863			0.730818			0.365409	−	0.930847i	$-0.380929\pi$
$269$	11.9863			0.730818			0.365409	+	0.930847i	$0.380929\pi$
$270$		0			0
$271$	15.9916			0.971420			0.485710	−	0.874120i	$-0.338561\pi$
$271$	15.9916			0.971420			0.485710	+	0.874120i	$0.338561\pi$
$272$	3.34017	+	3.34017i	0.202528	+	0.202528i
$273$	5.18568	−	5.18568i	0.313852	−	0.313852i
$274$	14.2394			0.860232
$275$		0			0
$276$			1.84114i			0.110824i
$277$	−15.2062	−	15.2062i	−0.913652	−	0.913652i	0.0829052	−	0.996557i	$-0.473580\pi$
$277$	−15.2062	−	15.2062i	−0.913652	−	0.913652i	−0.996557	+	0.0829052i	$0.973580\pi$
$278$	−12.1695	−	12.1695i	−0.729879	−	0.729879i
$279$	−3.99543			−0.239200
$280$		0			0
$281$			15.8129i			0.943318i	0.881781	+	0.471659i	$0.156345\pi$
$281$			15.8129i			0.943318i	−0.881781	+	0.471659i	$0.843655\pi$
$282$	19.5825	+	19.5825i	1.16612	+	1.16612i
$283$	−3.48133	+	3.48133i	−0.206944	+	0.206944i	−0.802967	−	0.596023i	$-0.796747\pi$
$283$	−3.48133	+	3.48133i	−0.206944	+	0.206944i	0.596023	+	0.802967i	$0.296747\pi$
$284$	−1.84114			−0.109252
$285$		0			0
$286$	7.57531			0.447937
$287$	−8.98359	+	8.98359i	−0.530285	+	0.530285i
$288$	−0.667725	−	0.667725i	−0.0393461	−	0.0393461i
$289$		−	15.9939i		−	0.940815i
$290$		0			0
$291$	−23.7503			−1.39227
$292$	−3.40522	−	3.40522i	−0.199275	−	0.199275i
$293$	−7.54641	−	7.54641i	−0.440866	−	0.440866i	0.451437	−	0.892303i	$-0.350912\pi$
$293$	−7.54641	−	7.54641i	−0.440866	−	0.440866i	−0.892303	+	0.451437i	$0.850912\pi$
$294$		−	6.51253i		−	0.379818i
$295$		0			0
$296$	12.0072			0.697904
$297$	8.98359	−	8.98359i	0.521281	−	0.521281i
$298$	−2.91829	−	2.91829i	−0.169052	−	0.169052i
$299$	3.99543			0.231062
$300$		0			0
$301$	−25.3028			−1.45843
$302$	2.04226	+	2.04226i	0.117519	+	0.117519i
$303$	−5.25579	−	5.25579i	−0.301937	−	0.301937i
$304$	16.0805	+	12.7587i	0.922281	+	0.731763i
$305$		0			0
$306$		−	0.580786i		−	0.0332013i
$307$	7.51181	−	7.51181i	0.428722	−	0.428722i	−0.459471	−	0.888193i	$-0.651961\pi$
$307$	7.51181	−	7.51181i	0.428722	−	0.428722i	0.888193	+	0.459471i	$0.151961\pi$
$308$	−1.86603	+	1.86603i	−0.106327	+	0.106327i
$309$		−	1.86150i		−	0.105897i
$310$		0			0
$311$	30.2472			1.71516			0.857582	−	0.514348i	$-0.171966\pi$
$311$	30.2472			1.71516			0.857582	+	0.514348i	$0.171966\pi$
$312$	−5.75215	+	5.75215i	−0.325651	+	0.325651i
$313$	0.503072	−	0.503072i	0.0284353	−	0.0284353i	−0.692746	−	0.721181i	$-0.743599\pi$
$313$	0.503072	−	0.503072i	0.0284353	−	0.0284353i	0.721181	+	0.692746i	$0.243599\pi$
$314$	−26.9053			−1.51835
$315$		0			0
$316$		−	5.83658i		−	0.328333i
$317$	11.9192	−	11.9192i	0.669448	−	0.669448i	−0.288140	−	0.957588i	$-0.593037\pi$
$317$	11.9192	−	11.9192i	0.669448	−	0.669448i	0.957588	+	0.288140i	$0.0930369\pi$
$318$	17.5992	+	17.5992i	0.986913	+	0.986913i
$319$	4.84385			0.271204
$320$		0			0
$321$	1.24354			0.0694078
$322$	−5.25579	+	5.25579i	−0.292894	+	0.292894i
$323$	0.500304	+	4.34355i	0.0278377	+	0.241682i
$324$		−	4.59478i		−	0.255266i
$325$		0			0
$326$		−	4.40737i		−	0.244102i
$327$	−14.0494	−	14.0494i	−0.776936	−	0.776936i
$328$	9.96493	−	9.96493i	0.550221	−	0.550221i
$329$			20.9360i			1.15424i
$330$		0			0
$331$			5.52342i			0.303595i	0.988412	+	0.151797i	$0.0485061\pi$
$331$			5.52342i			0.303595i	−0.988412	+	0.151797i	$0.951494\pi$
$332$	1.15676	+	1.15676i	0.0634852	+	0.0634852i
$333$	−1.29790	−	1.29790i	−0.0711246	−	0.0711246i
$334$			25.6709i			1.40465i
$335$		0			0
$336$		−	18.8156i		−	1.02648i
$337$	15.6015	−	15.6015i	0.849866	−	0.849866i	−0.140250	−	0.990116i	$-0.544791\pi$
$337$	15.6015	−	15.6015i	0.849866	−	0.849866i	0.990116	+	0.140250i	$0.0447907\pi$
$338$	10.6829	+	10.6829i	0.581075	+	0.581075i
$339$			11.7815i			0.639884i
$340$		0			0
$341$		−	28.4788i		−	1.54221i
$342$	−0.288795	−	2.50727i	−0.0156163	−	0.135578i
$343$	14.2557	−	14.2557i	0.769733	−	0.769733i
$344$	28.0668			1.51326
$345$		0			0
$346$	29.9988			1.61274
$347$	5.79484	+	5.79484i	0.311083	+	0.311083i	0.845329	−	0.534246i	$-0.179404\pi$
$347$	5.79484	+	5.79484i	0.311083	+	0.311083i	−0.534246	+	0.845329i	$0.679404\pi$
$348$	1.10116	−	1.10116i	0.0590286	−	0.0590286i
$349$		−	7.13624i		−	0.381994i	−0.981591	−	0.190997i	$-0.938828\pi$
$349$		−	7.13624i		−	0.381994i	0.981591	−	0.190997i	$-0.0611721\pi$
$350$		0			0
$351$	−8.86376			−0.473113
$352$	4.75943	−	4.75943i	0.253678	−	0.253678i
$353$	−15.9711	+	15.9711i	−0.850054	+	0.850054i	−0.990139	−	0.140085i	$-0.955262\pi$
$353$	−15.9711	+	15.9711i	−0.850054	+	0.850054i	0.140085	+	0.990139i	$0.455262\pi$
$354$	16.8056			0.893208
$355$		0			0
$356$			7.67772i			0.406918i
$357$	2.83386	−	2.83386i	0.149984	−	0.149984i
$358$	14.0494	−	14.0494i	0.742536	−	0.742536i
$359$			27.1689i			1.43392i	0.697115	+	0.716959i	$0.254466\pi$
$359$			27.1689i			1.43392i	−0.697115	+	0.716959i	$0.745534\pi$
$360$		0			0
$361$	4.31965	+	18.5024i	0.227350	+	0.973813i
$362$	12.9483	+	12.9483i	0.680547	+	0.680547i
$363$	5.29334	+	5.29334i	0.277828	+	0.277828i
$364$	1.84114			0.0965020
$365$		0			0
$366$	−29.3874			−1.53610
$367$	1.09171	+	1.09171i	0.0569867	+	0.0569867i	0.735026	−	0.678039i	$-0.237170\pi$
$367$	1.09171	+	1.09171i	0.0569867	+	0.0569867i	−0.678039	+	0.735026i	$0.737170\pi$
$368$	7.24846	−	7.24846i	0.377852	−	0.377852i
$369$	−2.15429			−0.112148
$370$		0			0
$371$			18.8156i			0.976857i
$372$	−6.47414	−	6.47414i	−0.335669	−	0.335669i
$373$	−2.87141	−	2.87141i	−0.148676	−	0.148676i	0.628850	−	0.777526i	$-0.283526\pi$
$373$	−2.87141	−	2.87141i	−0.148676	−	0.148676i	−0.777526	+	0.628850i	$0.783526\pi$
$374$	4.13974			0.214061
$375$		0			0
$376$		−	23.2230i		−	1.19763i
$377$	−2.38962	−	2.38962i	−0.123072	−	0.123072i
$378$	11.6598	−	11.6598i	0.599717	−	0.599717i
$379$	−29.6403			−1.52252			−0.761261	−	0.648446i	$-0.775419\pi$
$379$	−29.6403			−1.52252			−0.761261	+	0.648446i	$0.775419\pi$
$380$		0			0
$381$	17.9916			0.921737
$382$	2.94356	−	2.94356i	0.150606	−	0.150606i
$383$	−0.275606	−	0.275606i	−0.0140828	−	0.0140828i	0.700030	−	0.714113i	$-0.253170\pi$
$383$	−0.275606	−	0.275606i	−0.0140828	−	0.0140828i	−0.714113	+	0.700030i	$0.753170\pi$
$384$			24.9555i			1.27350i
$385$		0			0
$386$	−28.7103			−1.46132
$387$	−3.03385	−	3.03385i	−0.154219	−	0.154219i
$388$	−4.21619	−	4.21619i	−0.214045	−	0.214045i
$389$			10.2557i			0.519982i	0.965611	+	0.259991i	$0.0837196\pi$
$389$			10.2557i			0.519982i	−0.965611	+	0.259991i	$0.916280\pi$
$390$		0			0
$391$	2.18342			0.110420
$392$	−3.86162	+	3.86162i	−0.195041	+	0.195041i
$393$	−5.59852	−	5.59852i	−0.282408	−	0.282408i
$394$	−19.5407			−0.984446
$395$		0			0
$396$	−0.447480			−0.0224867
$397$	11.4741	+	11.4741i	0.575871	+	0.575871i	0.933763	−	0.357892i	$-0.116504\pi$
$397$	11.4741	+	11.4741i	0.575871	+	0.575871i	−0.357892	+	0.933763i	$0.616504\pi$
$398$	−5.01773	−	5.01773i	−0.251516	−	0.251516i
$399$	10.8247	−	13.6430i	0.541914	−	0.683005i
$400$		0			0
$401$		−	32.1610i		−	1.60605i	−0.595948	−	0.803023i	$-0.703224\pi$
$401$		−	32.1610i		−	1.60605i	0.595948	−	0.803023i	$-0.296776\pi$
$402$	4.82361	−	4.82361i	0.240580	−	0.240580i
$403$	−14.0494	+	14.0494i	−0.699853	+	0.699853i
$404$		−	1.86603i		−	0.0928385i
$405$		0			0
$406$	6.28685			0.312011
$407$	9.25122	−	9.25122i	0.458566	−	0.458566i
$408$	−3.14342	+	3.14342i	−0.155623	+	0.155623i
$409$	24.4833			1.21062			0.605311	−	0.795989i	$-0.293049\pi$
$409$	24.4833			1.21062			0.605311	+	0.795989i	$0.293049\pi$
$410$		0			0
$411$			16.6613i			0.821842i
$412$	0.330455	−	0.330455i	0.0162804	−	0.0162804i
$413$	8.98359	+	8.98359i	0.442054	+	0.442054i
$414$	−1.26036			−0.0619431
$415$		0			0
$416$	−4.69594			−0.230238
$417$	14.2394	−	14.2394i	0.697305	−	0.697305i
$418$	17.8714	−	2.05848i	0.874117	−	0.100684i
$419$		−	24.8059i		−	1.21185i	−0.795523	−	0.605924i	$-0.792804\pi$
$419$		−	24.8059i		−	1.21185i	0.795523	−	0.605924i	$-0.207196\pi$
$420$		0			0
$421$			13.8274i			0.673908i	0.941521	+	0.336954i	$0.109397\pi$
$421$			13.8274i			0.673908i	−0.941521	+	0.336954i	$0.890603\pi$
$422$	−9.61757	−	9.61757i	−0.468176	−	0.468176i
$423$	−2.51026	+	2.51026i	−0.122053	+	0.122053i
$424$		−	20.8710i		−	1.01358i
$425$		0			0
$426$		−	11.5043i		−	0.557385i
$427$	−15.7093	−	15.7093i	−0.760225	−	0.760225i
$428$	0.220756	+	0.220756i	0.0106706	+	0.0106706i
$429$			8.86376i			0.427947i
$430$		0			0
$431$		−	17.8229i		−	0.858498i	−0.903186	−	0.429249i	$-0.858778\pi$
$431$		−	17.8229i		−	0.858498i	0.903186	−	0.429249i	$-0.141222\pi$
$432$	−16.0805	+	16.0805i	−0.773674	+	0.773674i
$433$	−2.38438	−	2.38438i	−0.114586	−	0.114586i	0.647489	−	0.762075i	$-0.275819\pi$
$433$	−2.38438	−	2.38438i	−0.114586	−	0.114586i	−0.762075	+	0.647489i	$0.775819\pi$
$434$		−	36.9627i		−	1.77426i
$435$		0			0
$436$		−	4.98816i		−	0.238889i
$437$	9.42588	−	1.08570i	0.450901	−	0.0519362i
$438$	21.2774	−	21.2774i	1.01667	−	1.01667i
$439$	−23.8038			−1.13609			−0.568046	−	0.822997i	$-0.692300\pi$
$439$	−23.8038			−1.13609			−0.568046	+	0.822997i	$0.692300\pi$
$440$		0			0
$441$	0.834834			0.0397540
$442$	−2.04226	−	2.04226i	−0.0971404	−	0.0971404i
$443$	−20.3268	+	20.3268i	−0.965757	+	0.965757i	−0.999433	−	0.0336754i	$-0.989279\pi$
$443$	−20.3268	+	20.3268i	−0.965757	+	0.965757i	0.0336754	+	0.999433i	$0.489279\pi$
$444$		−	4.20620i		−	0.199618i
$445$		0			0
$446$	30.9783			1.46686
$447$	3.41465	−	3.41465i	0.161507	−	0.161507i
$448$	−8.31965	+	8.31965i	−0.393067	+	0.393067i
$449$	13.9717			0.659368			0.329684	−	0.944091i	$-0.393058\pi$
$449$	13.9717			0.659368			0.329684	+	0.944091i	$0.393058\pi$
$450$		0			0
$451$		−	15.3554i		−	0.723059i
$452$	−2.09147	+	2.09147i	−0.0983745	+	0.0983745i
$453$	−2.38962	+	2.38962i	−0.112274	+	0.112274i
$454$		−	44.3123i		−	2.07968i
$455$		0			0
$456$	−12.0072	+	15.1333i	−0.562288	+	0.708683i
$457$	−7.83710	−	7.83710i	−0.366604	−	0.366604i	0.499633	−	0.866237i	$-0.333468\pi$
$457$	−7.83710	−	7.83710i	−0.366604	−	0.366604i	−0.866237	+	0.499633i	$0.833468\pi$
$458$	21.8782	+	21.8782i	1.02230	+	1.02230i
$459$	−4.84385			−0.226092
$460$		0			0
$461$	−32.2557			−1.50230			−0.751148	−	0.660134i	$-0.770499\pi$
$461$	−32.2557			−1.50230			−0.751148	+	0.660134i	$0.770499\pi$
$462$	−11.6598	−	11.6598i	−0.542464	−	0.542464i
$463$	1.40910	−	1.40910i	0.0654862	−	0.0654862i	−0.673605	−	0.739091i	$-0.735255\pi$
$463$	1.40910	−	1.40910i	0.0654862	−	0.0654862i	0.739091	+	0.673605i	$0.235255\pi$
$464$	−8.67044			−0.402515
$465$		0			0
$466$		−	7.94535i		−	0.368061i
$467$	−15.6647	−	15.6647i	−0.724878	−	0.724878i	0.244717	−	0.969595i	$-0.421305\pi$
$467$	−15.6647	−	15.6647i	−0.724878	−	0.724878i	−0.969595	+	0.244717i	$0.921305\pi$
$468$	0.220756	+	0.220756i	0.0102044	+	0.0102044i
$469$	5.15701			0.238128
$470$		0			0
$471$		−	31.4815i		−	1.45059i
$472$	−9.96493	−	9.96493i	−0.458673	−	0.458673i
$473$	21.6248	−	21.6248i	0.994307	−	0.994307i
$474$	36.4696			1.67511
$475$		0			0
$476$	1.00614			0.0461165
$477$	−2.25602	+	2.25602i	−0.103296	+	0.103296i
$478$	−24.3094	−	24.3094i	−1.11189	−	1.11189i
$479$			3.28458i			0.150076i	0.997181	+	0.0750382i	$0.0239079\pi$
$479$			3.28458i			0.150076i	−0.997181	+	0.0750382i	$0.976092\pi$
$480$		0			0
$481$	−9.12783			−0.416193
$482$	5.18568	+	5.18568i	0.236201	+	0.236201i
$483$	−6.14973	−	6.14973i	−0.279822	−	0.279822i
$484$			1.87936i			0.0854255i
$485$		0			0
$486$	5.98440			0.271458
$487$	0.682512	−	0.682512i	0.0309276	−	0.0309276i	−0.691474	−	0.722401i	$-0.743038\pi$
$487$	0.682512	−	0.682512i	0.0309276	−	0.0309276i	0.722401	+	0.691474i	$0.243038\pi$
$488$	17.4253	+	17.4253i	0.788806	+	0.788806i
$489$	5.15701			0.233208
$490$		0			0
$491$	−7.02052			−0.316832			−0.158416	−	0.987372i	$-0.550639\pi$
$491$	−7.02052			−0.316832			−0.158416	+	0.987372i	$0.550639\pi$
$492$	−3.49079	−	3.49079i	−0.157377	−	0.157377i
$493$	−1.30588	−	1.30588i	−0.0588137	−	0.0588137i
$494$	−9.83201	−	7.80098i	−0.442363	−	0.350983i
$495$		0			0
$496$			50.9766i			2.28892i
$497$	6.14973	−	6.14973i	0.275853	−	0.275853i
$498$	−7.22795	+	7.22795i	−0.323892	+	0.323892i
$499$		−	18.0228i		−	0.806811i	−0.915021	−	0.403405i	$-0.867826\pi$
$499$		−	18.0228i		−	0.806811i	0.915021	−	0.403405i	$-0.132174\pi$
$500$		0			0
$501$	−30.0372			−1.34196
$502$	4.64040	−	4.64040i	0.207111	−	0.207111i
$503$	13.7226	−	13.7226i	0.611861	−	0.611861i	−0.331570	−	0.943431i	$-0.607578\pi$
$503$	13.7226	−	13.7226i	0.611861	−	0.611861i	0.943431	+	0.331570i	$0.107578\pi$
$504$	1.93992			0.0864111
$505$		0			0
$506$		−	8.98359i		−	0.399369i
$507$	−12.5000	+	12.5000i	−0.555143	+	0.555143i
$508$	3.19389	+	3.19389i	0.141706	+	0.141706i
$509$	8.67044			0.384310			0.192155	−	0.981365i	$-0.438452\pi$
$509$	8.67044			0.384310			0.192155	+	0.981365i	$0.438452\pi$
$510$		0			0
$511$	22.7480			1.00631
$512$	7.56120	−	7.56120i	0.334161	−	0.334161i
$513$	−20.9111	+	2.40860i	−0.923245	+	0.106342i
$514$		−	3.02174i		−	0.133283i
$515$		0			0
$516$		−	9.83201i		−	0.432830i
$517$	−17.8927	−	17.8927i	−0.786920	−	0.786920i
$518$	12.0072	−	12.0072i	0.527566	−	0.527566i
$519$			35.1012i			1.54077i
$520$		0			0
$521$			35.3081i			1.54687i	0.633873	+	0.773437i	$0.281464\pi$
$521$			35.3081i			1.54687i	−0.633873	+	0.773437i	$0.718536\pi$
$522$	0.753803	+	0.753803i	0.0329931	+	0.0329931i
$523$	9.83998	+	9.83998i	0.430272	+	0.430272i	0.888721	−	0.458449i	$-0.151595\pi$
$523$	9.83998	+	9.83998i	0.430272	+	0.430272i	−0.458449	+	0.888721i	$0.651595\pi$
$524$		−	1.98771i		−	0.0868337i
$525$		0			0
$526$		−	0.725090i		−	0.0316154i
$527$	−7.67772	+	7.67772i	−0.334447	+	0.334447i
$528$	16.0805	+	16.0805i	0.699815	+	0.699815i
$529$			18.2618i			0.793991i
$530$		0			0
$531$			2.15429i			0.0934884i
$532$	4.34355	−	0.500304i	0.188317	−	0.0216909i
$533$	−7.57531	+	7.57531i	−0.328123	+	0.328123i
$534$	−47.9739			−2.07604
$535$		0			0
$536$	−5.72034			−0.247081
$537$	16.4391	+	16.4391i	0.709398	+	0.709398i
$538$	−13.2956	+	13.2956i	−0.573216	+	0.573216i
$539$			5.95055i			0.256308i
$540$		0			0
$541$	−9.79380			−0.421068			−0.210534	−	0.977587i	$-0.567520\pi$
$541$	−9.79380			−0.421068			−0.210534	+	0.977587i	$0.567520\pi$
$542$	−17.7385	+	17.7385i	−0.761932	+	0.761932i
$543$	−15.1506	+	15.1506i	−0.650175	+	0.650175i
$544$	−2.56623			−0.110026
$545$		0			0
$546$			11.5043i			0.492339i
$547$	6.72757	−	6.72757i	0.287650	−	0.287650i	−0.548500	−	0.836150i	$-0.684801\pi$
$547$	6.72757	−	6.72757i	0.287650	−	0.287650i	0.836150	+	0.548500i	$0.184801\pi$
$548$	−2.95774	+	2.95774i	−0.126348	+	0.126348i
$549$		−	3.76713i		−	0.160777i
$550$		0			0
$551$	−6.28685	−	4.98816i	−0.267829	−	0.212503i
$552$	6.82150	+	6.82150i	0.290342	+	0.290342i
$553$	19.4952	+	19.4952i	0.829019	+	0.829019i
$554$	33.7346			1.43324
$555$		0			0
$556$	5.05559			0.214405
$557$	10.3379	+	10.3379i	0.438031	+	0.438031i	0.891349	−	0.453318i	$-0.149760\pi$
$557$	10.3379	+	10.3379i	0.438031	+	0.438031i	−0.453318	+	0.891349i	$0.649760\pi$
$558$	4.43188	−	4.43188i	0.187617	−	0.187617i
$559$	−21.3363			−0.902430
$560$		0			0
$561$			4.84385i			0.204508i
$562$	−17.5402	−	17.5402i	−0.739890	−	0.739890i
$563$	−9.28877	−	9.28877i	−0.391475	−	0.391475i	0.483738	−	0.875213i	$-0.339279\pi$
$563$	−9.28877	−	9.28877i	−0.391475	−	0.391475i	−0.875213	+	0.483738i	$0.839279\pi$
$564$	−8.13517			−0.342553
$565$		0			0
$566$		−	7.72324i		−	0.324632i
$567$	15.3474	+	15.3474i	0.644529	+	0.644529i
$568$	−6.82150	+	6.82150i	−0.286224	+	0.286224i
$569$	14.5070			0.608166			0.304083	−	0.952646i	$-0.401650\pi$
$569$	14.5070			0.608166			0.304083	+	0.952646i	$0.401650\pi$
$570$		0			0
$571$	−21.6658			−0.906685			−0.453343	−	0.891336i	$-0.649769\pi$
$571$	−21.6658			−0.906685			−0.453343	+	0.891336i	$0.649769\pi$
$572$	−1.57351	+	1.57351i	−0.0657917	+	0.0657917i
$573$	3.44422	+	3.44422i	0.143884	+	0.143884i
$574$		−	19.9299i		−	0.831856i
$575$		0			0
$576$	−1.99508			−0.0831283
$577$	1.68035	+	1.68035i	0.0699537	+	0.0699537i	0.741218	−	0.671264i	$-0.234248\pi$
$577$	1.68035	+	1.68035i	0.0699537	+	0.0699537i	−0.671264	+	0.741218i	$0.734248\pi$
$578$	17.7410	+	17.7410i	0.737927	+	0.737927i
$579$		−	33.5936i		−	1.39610i
$580$		0			0
$581$	−7.72753			−0.320592
$582$	26.3447	−	26.3447i	1.09202	−	1.09202i
$583$	−16.0805	−	16.0805i	−0.665987	−	0.665987i
$584$	−25.2330			−1.04415
$585$		0			0
$586$	16.7415			0.691586
$587$	0.850432	+	0.850432i	0.0351011	+	0.0351011i	0.724439	−	0.689338i	$-0.242099\pi$
$587$	0.850432	+	0.850432i	0.0351011	+	0.0351011i	−0.689338	+	0.724439i	$0.742099\pi$
$588$	1.35275	+	1.35275i	0.0557866	+	0.0557866i
$589$	−29.3272	+	36.9627i	−1.20841	+	1.52302i
$590$		0			0
$591$		−	22.8643i		−	0.940512i
$592$	−16.5596	+	16.5596i	−0.680595	+	0.680595i
$593$	20.2618	−	20.2618i	0.832052	−	0.832052i	−0.155745	−	0.987797i	$-0.549778\pi$
$593$	20.2618	−	20.2618i	0.832052	−	0.832052i	0.987797	+	0.155745i	$0.0497778\pi$
$594$			19.9299i			0.817732i
$595$		0			0
$596$	1.21235			0.0496597
$597$	5.87118	−	5.87118i	0.240291	−	0.240291i
$598$	−4.43188	+	4.43188i	−0.181233	+	0.181233i
$599$	12.6659			0.517514			0.258757	−	0.965943i	$-0.416687\pi$
$599$	12.6659			0.517514			0.258757	+	0.965943i	$0.416687\pi$
$600$		0			0
$601$		−	20.1215i		−	0.820772i	−0.911912	−	0.410386i	$-0.865394\pi$
$601$		−	20.1215i		−	0.820772i	0.911912	−	0.410386i	$-0.134606\pi$
$602$	28.0668	−	28.0668i	1.14392	−	1.14392i
$603$	0.618333	+	0.618333i	0.0251805	+	0.0251805i
$604$	−0.848418			−0.0345216
$605$		0			0
$606$	11.6598			0.473648
$607$	5.35752	−	5.35752i	0.217455	−	0.217455i	−0.589970	−	0.807425i	$-0.700861\pi$
$607$	5.35752	−	5.35752i	0.217455	−	0.217455i	0.807425	+	0.589970i	$0.200861\pi$
$608$	−11.0785	+	1.27606i	−0.449292	+	0.0517509i
$609$			7.35616i			0.298087i
$610$		0			0
$611$			17.6540i			0.714206i
$612$	0.120638	+	0.120638i	0.00487651	+	0.00487651i
$613$	−16.7009	+	16.7009i	−0.674542	+	0.674542i	−0.958760	−	0.284218i	$-0.908266\pi$
$613$	−16.7009	+	16.7009i	−0.674542	+	0.674542i	0.284218	+	0.958760i	$0.408266\pi$
$614$			16.6647i			0.672534i
$615$		0			0
$616$			13.8274i			0.557124i
$617$	10.8394	+	10.8394i	0.436377	+	0.436377i	0.890791	−	0.454414i	$-0.150151\pi$
$617$	10.8394	+	10.8394i	0.436377	+	0.436377i	−0.454414	+	0.890791i	$0.650151\pi$
$618$	2.06484	+	2.06484i	0.0830600	+	0.0830600i
$619$		−	0.0350725i		−	0.00140968i	−1.00000		0.000704841i	$-0.999776\pi$
$619$		−	0.0350725i		−	0.00140968i	1.00000		0.000704841i	$-0.000224358\pi$
$620$		0			0
$621$			10.5116i			0.421815i
$622$	−33.5513	+	33.5513i	−1.34529	+	1.34529i
$623$	−25.6449	−	25.6449i	−1.02744	−	1.02744i
$624$		−	15.8660i		−	0.635150i
$625$		0			0
$626$			1.11605i			0.0446064i
$627$	2.40860	+	20.9111i	0.0961903	+	0.835107i
$628$	5.58864	−	5.58864i	0.223011	−	0.223011i
$629$	−4.98816			−0.198891
$630$		0			0
$631$	−26.3630			−1.04949			−0.524746	−	0.851259i	$-0.675840\pi$
$631$	−26.3630			−1.04949			−0.524746	+	0.851259i	$0.675840\pi$
$632$	−21.6248	−	21.6248i	−0.860187	−	0.860187i
$633$	11.2534	−	11.2534i	0.447282	−	0.447282i
$634$			26.4424i			1.05016i
$635$		0			0
$636$	−7.31124			−0.289910
$637$	2.93559	−	2.93559i	0.116312	−	0.116312i
$638$	−5.37298	+	5.37298i	−0.212718	+	0.212718i
$639$	1.47472			0.0583392
$640$		0			0
$641$			22.6422i			0.894313i	0.894456	+	0.447156i	$0.147563\pi$
$641$			22.6422i			0.894313i	−0.894456	+	0.447156i	$0.852437\pi$
$642$	−1.37938	+	1.37938i	−0.0544399	+	0.0544399i
$643$	29.1555	−	29.1555i	1.14978	−	1.14978i	0.163187	−	0.986595i	$-0.447823\pi$
$643$	29.1555	−	29.1555i	1.14978	−	1.14978i	0.986595	−	0.163187i	$-0.0521773\pi$
$644$		−	2.18342i		−	0.0860387i
$645$		0			0
$646$	−5.37298	−	4.26307i	−0.211397	−	0.167728i
$647$	18.9083	+	18.9083i	0.743362	+	0.743362i	0.973223	−	0.229862i	$-0.0738274\pi$
$647$	18.9083	+	18.9083i	0.743362	+	0.743362i	−0.229862	+	0.973223i	$0.573827\pi$
$648$	−17.0239	−	17.0239i	−0.668760	−	0.668760i
$649$	−15.3554			−0.602753
$650$		0			0
$651$	43.2495			1.69508
$652$	0.915479	+	0.915479i	0.0358529	+	0.0358529i
$653$	−12.9688	+	12.9688i	−0.507508	+	0.507508i	−0.913761	−	0.406252i	$-0.866835\pi$
$653$	−12.9688	+	12.9688i	−0.507508	+	0.507508i	0.406252	+	0.913761i	$0.366835\pi$
$654$	31.1683			1.21878
$655$		0			0
$656$			27.4860i			1.07315i
$657$	2.72753	+	2.72753i	0.106411	+	0.106411i
$658$	−23.2230	−	23.2230i	−0.905326	−	0.905326i
$659$	39.1592			1.52543			0.762713	−	0.646737i	$-0.223867\pi$
$659$	39.1592			1.52543			0.762713	+	0.646737i	$0.223867\pi$
$660$		0			0
$661$		−	41.6799i		−	1.62116i	−0.585628	−	0.810580i	$-0.699152\pi$
$661$		−	41.6799i		−	1.62116i	0.585628	−	0.810580i	$-0.300848\pi$
$662$	−6.12678	−	6.12678i	−0.238124	−	0.238124i
$663$	2.38962	−	2.38962i	0.0928052	−	0.0928052i
$664$	8.57165			0.332645
$665$		0			0
$666$	2.87936			0.111573
$667$	−2.83386	+	2.83386i	−0.109728	+	0.109728i
$668$	−5.33224	−	5.33224i	−0.206311	−	0.206311i
$669$			36.2472i			1.40140i
$670$		0			0
$671$	26.8515			1.03659
$672$	7.22795	+	7.22795i	0.278824	+	0.278824i
$673$	28.7839	+	28.7839i	1.10954	+	1.10954i	0.993211	+	0.116329i	$0.0371126\pi$
$673$	28.7839	+	28.7839i	1.10954	+	1.10954i	0.116329	+	0.993211i	$0.462887\pi$
$674$			34.6114i			1.33318i
$675$		0			0
$676$	−4.43802			−0.170693
$677$	−23.0115	+	23.0115i	−0.884406	+	0.884406i	−0.993979	−	0.109573i	$-0.965052\pi$
$677$	−23.0115	+	23.0115i	−0.884406	+	0.884406i	0.109573	+	0.993979i	$0.465052\pi$
$678$	−13.0685	−	13.0685i	−0.501892	−	0.501892i
$679$	28.1656			1.08090
$680$		0			0
$681$	51.8492			1.98687
$682$	31.5897	+	31.5897i	1.20963	+	1.20963i
$683$	4.53867	+	4.53867i	0.173667	+	0.173667i	0.788589	−	0.614921i	$-0.210812\pi$
$683$	4.53867	+	4.53867i	0.173667	+	0.173667i	−0.614921	+	0.788589i	$0.710812\pi$
$684$	0.580786	+	0.460811i	0.0222069	+	0.0176196i
$685$		0			0
$686$			31.6258i			1.20748i
$687$	−25.5994	+	25.5994i	−0.976677	+	0.976677i
$688$	−38.7081	+	38.7081i	−1.47573	+	1.47573i
$689$			15.8660i			0.604448i
$690$		0			0
$691$	21.1012			0.802726			0.401363	−	0.915919i	$-0.368537\pi$
$691$	21.1012			0.802726			0.401363	+	0.915919i	$0.368537\pi$
$692$	−6.23121	+	6.23121i	−0.236875	+	0.236875i
$693$	1.49466	−	1.49466i	0.0567775	−	0.0567775i
$694$	−12.8557			−0.487996
$695$		0			0
$696$		−	8.15972i		−	0.309293i
$697$	−4.13974	+	4.13974i	−0.156804	+	0.156804i
$698$	7.91577	+	7.91577i	0.299616	+	0.299616i
$699$	9.29674			0.351635
$700$		0			0
$701$	−0.729794			−0.0275639			−0.0137820	−	0.999905i	$-0.504387\pi$
$701$	−0.729794			−0.0275639			−0.0137820	+	0.999905i	$0.504387\pi$
$702$	9.83201	−	9.83201i	0.371085	−	0.371085i
$703$	−21.5340	+	2.48036i	−0.812171	+	0.0935485i
$704$		−	14.2206i		−	0.535958i
$705$		0			0
$706$		−	35.4314i		−	1.33348i
$707$	6.23287	+	6.23287i	0.234411	+	0.234411i
$708$	−3.49079	+	3.49079i	−0.131192	+	0.131192i
$709$		−	24.3812i		−	0.915656i	−0.889041	−	0.457828i	$-0.848628\pi$
$709$		−	24.3812i		−	0.915656i	0.889041	−	0.457828i	$-0.151372\pi$
$710$		0			0
$711$			4.67500i			0.175326i
$712$	28.4463	+	28.4463i	1.06607	+	1.06607i
$713$	16.6613	+	16.6613i	0.623971	+	0.623971i
$714$			6.28685i			0.235279i
$715$		0			0
$716$			5.83658i			0.218123i
$717$	28.4442	−	28.4442i	1.06227	−	1.06227i
$718$	−30.1367	−	30.1367i	−1.12469	−	1.12469i
$719$		−	43.6970i		−	1.62962i	−0.579726	−	0.814811i	$-0.696840\pi$
$719$		−	43.6970i		−	1.62962i	0.579726	−	0.814811i	$-0.303160\pi$
$720$		0			0
$721$			2.20756i			0.0822137i
$722$	−25.3151	−	15.7321i	−0.942131	−	0.585487i
$723$	−6.06770	+	6.06770i	−0.225660	+	0.225660i
$724$	−5.37912			−0.199913
$725$		0			0
$726$	−11.7431			−0.435828
$727$	−18.7081	−	18.7081i	−0.693843	−	0.693843i	0.269232	−	0.963075i	$-0.413230\pi$
$727$	−18.7081	−	18.7081i	−0.693843	−	0.693843i	−0.963075	+	0.269232i	$0.913230\pi$
$728$	6.82150	−	6.82150i	0.252822	−	0.252822i
$729$		−	22.9109i		−	0.848553i
$730$		0			0
$731$	−11.6598			−0.431254
$732$	6.10421	−	6.10421i	0.225618	−	0.225618i
$733$	30.6742	−	30.6742i	1.13298	−	1.13298i	0.143298	−	0.989680i	$-0.454229\pi$
$733$	30.6742	−	30.6742i	1.13298	−	1.13298i	0.989680	−	0.143298i	$-0.0457707\pi$
$734$	−2.42193			−0.0893949
$735$		0			0
$736$			5.56894i			0.205274i
$737$	−4.40737	+	4.40737i	−0.162348	+	0.162348i
$738$	2.38962	−	2.38962i	0.0879632	−	0.0879632i
$739$		−	13.6163i		−	0.500885i	−0.968131	−	0.250443i	$-0.919424\pi$
$739$		−	13.6163i		−	0.500885i	0.968131	−	0.250443i	$-0.0805762\pi$
$740$		0			0
$741$	9.12783	−	11.5043i	0.335319	−	0.422621i
$742$	−20.8710	−	20.8710i	−0.766197	−	0.766197i
$743$	−23.4826	−	23.4826i	−0.861494	−	0.861494i	0.130017	−	0.991512i	$-0.458497\pi$
$743$	−23.4826	−	23.4826i	−0.861494	−	0.861494i	−0.991512	+	0.130017i	$0.958497\pi$
$744$	−47.9739			−1.75881
$745$		0			0
$746$	6.37015			0.233228
$747$	−0.926543	−	0.926543i	−0.0339004	−	0.0339004i
$748$	−0.859888	+	0.859888i	−0.0314406	+	0.0314406i
$749$	−1.47472			−0.0538853
$750$		0			0
$751$			20.9699i			0.765202i	0.923914	+	0.382601i	$0.124972\pi$
$751$			20.9699i			0.765202i	−0.923914	+	0.382601i	$0.875028\pi$
$752$	32.0277	+	32.0277i	1.16793	+	1.16793i
$753$	5.42967	+	5.42967i	0.197868	+	0.197868i
$754$	5.30131			0.193062
$755$		0			0
$756$			4.84385i			0.176169i
$757$	4.02893	+	4.02893i	0.146434	+	0.146434i	0.776523	−	0.630089i	$-0.216982\pi$
$757$	4.02893	+	4.02893i	0.146434	+	0.146434i	−0.630089	+	0.776523i	$0.716982\pi$
$758$	32.8781	−	32.8781i	1.19419	−	1.19419i
$759$	10.5116			0.381546
$760$		0			0
$761$	48.1939			1.74703			0.873514	−	0.486799i	$-0.161836\pi$
$761$	48.1939			1.74703			0.873514	+	0.486799i	$0.161836\pi$
$762$	−19.9569	+	19.9569i	−0.722963	+	0.722963i
$763$	16.6613	+	16.6613i	0.603180	+	0.603180i
$764$			1.22285i			0.0442411i
$765$		0			0
$766$	0.611424			0.0220916
$767$	7.57531	+	7.57531i	0.273528	+	0.273528i
$768$	−13.6506	−	13.6506i	−0.492574	−	0.492574i
$769$			14.0494i			0.506636i	0.967383	+	0.253318i	$0.0815219\pi$
$769$			14.0494i			0.506636i	−0.967383	+	0.253318i	$0.918478\pi$
$770$		0			0
$771$	3.53570			0.127335
$772$	5.96358	−	5.96358i	0.214634	−	0.214634i
$773$	2.29063	+	2.29063i	0.0823881	+	0.0823881i	0.747100	−	0.664712i	$-0.231446\pi$
$773$	2.29063	+	2.29063i	0.0823881	+	0.0823881i	−0.664712	+	0.747100i	$0.731446\pi$
$774$	6.73051			0.241923
$775$		0			0
$776$	−31.2423			−1.12153
$777$	14.0494	+	14.0494i	0.504021	+	0.504021i
$778$	−11.3759	−	11.3759i	−0.407847	−	0.407847i
$779$	−15.8129	+	19.9299i	−0.566556	+	0.714061i
$780$		0			0
$781$			10.5116i			0.376134i
$782$	−2.42193	+	2.42193i	−0.0866079	+	0.0866079i
$783$	6.28685	−	6.28685i	0.224674	−	0.224674i
$784$		−	10.6514i		−	0.380408i
$785$		0			0
$786$	12.4202			0.443012
$787$	3.04529	−	3.04529i	0.108553	−	0.108553i	−0.650744	−	0.759297i	$-0.725543\pi$
$787$	3.04529	−	3.04529i	0.108553	−	0.108553i	0.759297	+	0.650744i	$0.225543\pi$
$788$	4.05890	−	4.05890i	0.144592	−	0.144592i
$789$	0.848418			0.0302045
$790$		0			0
$791$		−	13.9717i		−	0.496778i
$792$	−1.65793	+	1.65793i	−0.0589121	+	0.0589121i
$793$	−13.2467	−	13.2467i	−0.470403	−	0.470403i
$794$	−25.4551			−0.903367
$795$		0			0
$796$	2.08452			0.0738839
$797$	2.32020	−	2.32020i	0.0821857	−	0.0821857i	−0.664819	−	0.747005i	$-0.731491\pi$
$797$	2.32020	−	2.32020i	0.0821857	−	0.0821857i	0.747005	+	0.664819i	$0.231491\pi$
$798$	3.12613	+	27.1405i	0.110664	+	0.960764i
$799$			9.64754i			0.341305i
$800$		0			0
$801$		−	6.14973i		−	0.217290i
$802$	35.6742	+	35.6742i	1.25970	+	1.25970i
$803$	−19.4413	+	19.4413i	−0.686070	+	0.686070i
$804$			2.00388i			0.0706712i
$805$		0			0
$806$		−	31.1683i		−	1.09786i
$807$	−15.5571	−	15.5571i	−0.547634	−	0.547634i
$808$	−6.91372	−	6.91372i	−0.243224	−	0.243224i
$809$		−	36.2122i		−	1.27315i	−0.771214	−	0.636576i	$-0.780350\pi$
$809$		−	36.2122i		−	1.27315i	0.771214	−	0.636576i	$-0.219650\pi$
$810$		0			0
$811$		−	0.313153i		−	0.0109963i	−0.999985	−	0.00549815i	$-0.998250\pi$
$811$		−	0.313153i		−	0.0109963i	0.999985	−	0.00549815i	$-0.00175012\pi$
$812$	−1.30588	+	1.30588i	−0.0458273	+	0.0458273i
$813$	−20.7555	−	20.7555i	−0.727928	−	0.727928i
$814$			20.5236i			0.719351i
$815$		0			0
$816$		−	8.67044i		−	0.303526i
$817$	−50.3358	+	5.79784i	−1.76103	+	0.202841i
$818$	−27.1578	+	27.1578i	−0.949550	+	0.949550i
$819$	−1.47472			−0.0515310
$820$		0			0
$821$	16.2557			0.567326			0.283663	−	0.958924i	$-0.408450\pi$
$821$	16.2557			0.567326			0.283663	+	0.958924i	$0.408450\pi$
$822$	−18.4813	−	18.4813i	−0.644610	−	0.644610i
$823$	−2.46922	+	2.46922i	−0.0860717	+	0.0860717i	−0.748832	−	0.662760i	$-0.769385\pi$
$823$	−2.46922	+	2.46922i	−0.0860717	+	0.0860717i	0.662760	+	0.748832i	$0.269385\pi$
$824$		−	2.44870i		−	0.0853046i
$825$		0			0
$826$	−19.9299			−0.693448
$827$	−4.24147	+	4.24147i	−0.147490	+	0.147490i	−0.776996	−	0.629506i	$-0.783257\pi$
$827$	−4.24147	+	4.24147i	−0.147490	+	0.147490i	0.629506	+	0.776996i	$0.283257\pi$
$828$	0.261795	−	0.261795i	0.00909801	−	0.00909801i
$829$	−9.66316			−0.335615			−0.167808	−	0.985820i	$-0.553669\pi$
$829$	−9.66316			−0.335615			−0.167808	+	0.985820i	$0.553669\pi$
$830$		0			0
$831$			39.4723i			1.36928i
$832$	−7.01545	+	7.01545i	−0.243217	+	0.243217i
$833$	1.60424	−	1.60424i	0.0555835	−	0.0555835i
$834$			31.5897i			1.09386i
$835$		0			0
$836$	−3.28458	+	4.13974i	−0.113600	+	0.143176i
$837$	−36.9627	−	36.9627i	−1.27762	−	1.27762i
$838$	27.5156	+	27.5156i	0.950511	+	0.950511i
$839$	−48.5092			−1.67472			−0.837362	−	0.546649i	$-0.815903\pi$
$839$	−48.5092			−1.67472			−0.837362	+	0.546649i	$0.815903\pi$
$840$		0			0
$841$	−25.6102			−0.883110
$842$	−15.3379	−	15.3379i	−0.528579	−	0.528579i
$843$	20.5236	−	20.5236i	0.706870	−	0.706870i
$844$	3.99543			0.137529
$845$		0			0
$846$		−	5.56894i		−	0.191464i
$847$	−6.27739	−	6.27739i	−0.215694	−	0.215694i
$848$	28.7839	+	28.7839i	0.988445	+	0.988445i
$849$	9.03685			0.310144
$850$		0			0
$851$			10.8247i			0.371067i
$852$	2.38962	+	2.38962i	0.0818671	+	0.0818671i
$853$	−4.23513	+	4.23513i	−0.145008	+	0.145008i	−0.775884	−	0.630876i	$-0.782696\pi$
$853$	−4.23513	+	4.23513i	−0.145008	+	0.145008i	0.630876	+	0.775884i	$0.282696\pi$
$854$	34.8506			1.19256
$855$		0			0
$856$	1.63582			0.0559111
$857$	−9.18410	+	9.18410i	−0.313723	+	0.313723i	−0.846350	−	0.532627i	$-0.821205\pi$
$857$	−9.18410	+	9.18410i	−0.313723	+	0.313723i	0.532627	+	0.846350i	$0.321205\pi$
$858$	−9.83201	−	9.83201i	−0.335659	−	0.335659i
$859$		−	17.1194i		−	0.584107i	−0.956402	−	0.292053i	$-0.905661\pi$
$859$		−	17.1194i		−	0.584107i	0.956402	−	0.292053i	$-0.0943385\pi$
$860$		0			0
$861$	23.3197			0.794732
$862$	19.7698	+	19.7698i	0.673362	+	0.673362i
$863$	−11.2742	−	11.2742i	−0.383779	−	0.383779i	0.488683	−	0.872462i	$-0.337478\pi$
$863$	−11.2742	−	11.2742i	−0.383779	−	0.383779i	−0.872462	+	0.488683i	$0.837478\pi$
$864$		−	12.3545i		−	0.420310i
$865$		0			0
$866$	5.28968			0.179751
$867$	−20.7585	+	20.7585i	−0.704995	+	0.704995i
$868$	7.67772	+	7.67772i	0.260599	+	0.260599i
$869$	−33.3226			−1.13039
$870$		0			0
$871$	4.34858			0.147346
$872$	−18.4813	−	18.4813i	−0.625857	−	0.625857i
$873$	3.37710	+	3.37710i	0.114298	+	0.114298i
$874$	−9.25122	+	11.6598i	−0.312927	+	0.394400i
$875$		0			0
$876$			8.83929i			0.298652i
$877$	23.8008	−	23.8008i	0.803696	−	0.803696i	−0.179975	−	0.983671i	$-0.557602\pi$
$877$	23.8008	−	23.8008i	0.803696	−	0.803696i	0.983671	+	0.179975i	$0.0576016\pi$
$878$	26.4040	−	26.4040i	0.891092	−	0.891092i
$879$			19.5890i			0.660721i
$880$		0			0
$881$	−31.7359			−1.06921			−0.534605	−	0.845102i	$-0.679540\pi$
$881$	−31.7359			−1.06921			−0.534605	+	0.845102i	$0.679540\pi$
$882$	−0.926028	+	0.926028i	−0.0311810	+	0.0311810i
$883$	−4.93495	+	4.93495i	−0.166074	+	0.166074i	−0.785251	−	0.619177i	$-0.787466\pi$
$883$	−4.93495	+	4.93495i	−0.166074	+	0.166074i	0.619177	+	0.785251i	$0.287466\pi$
$884$	0.848418			0.0285354
$885$		0			0
$886$		−	45.0945i		−	1.51498i
$887$	10.6588	−	10.6588i	0.357888	−	0.357888i	−0.505146	−	0.863034i	$-0.668561\pi$
$887$	10.6588	−	10.6588i	0.357888	−	0.357888i	0.863034	+	0.505146i	$0.168561\pi$
$888$	−15.5842	−	15.5842i	−0.522970	−	0.522970i
$889$	−21.3363			−0.715597
$890$		0			0
$891$	−26.2329			−0.878834
$892$	−6.43466	+	6.43466i	−0.215448	+	0.215448i
$893$	4.79723	+	41.6487i	0.160533	+	1.39372i
$894$			7.57531i			0.253356i
$895$		0			0
$896$		−	29.5948i		−	0.988693i
$897$	−5.18568	−	5.18568i	−0.173145	−	0.173145i
$898$	−15.4980	+	15.4980i	−0.517174	+	0.517174i
$899$		−	19.9299i		−	0.664698i
$900$		0			0
$901$			8.67044i			0.288854i
$902$	17.0328	+	17.0328i	0.567130	+	0.567130i
$903$	32.8406	+	32.8406i	1.09287	+	1.09287i
$904$			15.4980i			0.515455i
$905$		0			0
$906$		−	5.30131i		−	0.176124i
$907$	23.8600	−	23.8600i	0.792257	−	0.792257i	−0.189604	−	0.981861i	$-0.560720\pi$
$907$	23.8600	−	23.8600i	0.792257	−	0.792257i	0.981861	+	0.189604i	$0.0607203\pi$
$908$	9.20435	+	9.20435i	0.305457	+	0.305457i
$909$			1.49466i			0.0495748i
$910$		0			0
$911$			32.3053i			1.07032i	0.844749	+	0.535162i	$0.179749\pi$
$911$			32.3053i			1.07032i	−0.844749	+	0.535162i	$0.820251\pi$
$912$	−4.31137	−	37.4305i	−0.142764	−	1.23945i
$913$	6.60424	−	6.60424i	0.218568	−	0.218568i
$914$	17.3864			0.575091
$915$		0			0
$916$	−9.08888			−0.300305
$917$	6.63931	+	6.63931i	0.219249	+	0.219249i
$918$	5.37298	−	5.37298i	0.177335	−	0.177335i
$919$			5.86991i			0.193630i	0.995302	+	0.0968152i	$0.0308656\pi$
$919$			5.86991i			0.193630i	−0.995302	+	0.0968152i	$0.969134\pi$
$920$		0			0
$921$	−19.4992			−0.642520
$922$	35.7791	−	35.7791i	1.17832	−	1.17832i
$923$	5.18568	−	5.18568i	0.170689	−	0.170689i
$924$	4.84385			0.159351
$925$		0			0
$926$			3.12604i			0.102728i
$927$	−0.264690	+	0.264690i	−0.00869355	+	0.00869355i
$928$	3.33072	−	3.33072i	0.109336	−	0.109336i
$929$		−	58.6369i		−	1.92381i	−0.273379	−	0.961907i	$-0.588141\pi$
$929$		−	58.6369i		−	1.92381i	0.273379	−	0.961907i	$-0.411859\pi$
$930$		0			0
$931$	6.12783	−	7.72324i	0.200831	−	0.253119i
$932$	1.65037	+	1.65037i	0.0540597	+	0.0540597i
$933$	−39.2580	−	39.2580i	−1.28525	−	1.28525i
$934$	34.7518			1.13711
$935$		0			0
$936$	1.63582			0.0534684
$937$	14.4413	+	14.4413i	0.471778	+	0.471778i	0.902490	−	0.430712i	$-0.141737\pi$
$937$	14.4413	+	14.4413i	0.471778	+	0.471778i	−0.430712	+	0.902490i	$0.641737\pi$
$938$	−5.72034	+	5.72034i	−0.186776	+	0.186776i
$939$	−1.30588			−0.0426156
$940$		0			0
$941$			47.5165i			1.54899i	0.632578	+	0.774496i	$0.281997\pi$
$941$			47.5165i			1.54899i	−0.632578	+	0.774496i	$0.718003\pi$
$942$	34.9204	+	34.9204i	1.13777	+	1.13777i
$943$	8.98359	+	8.98359i	0.292546	+	0.292546i
$944$	27.4860			0.894594
$945$		0			0
$946$			47.9739i			1.55977i
$947$	−11.2218	−	11.2218i	−0.364660	−	0.364660i	0.500866	−	0.865525i	$-0.333015\pi$
$947$	−11.2218	−	11.2218i	−0.364660	−	0.364660i	−0.865525	+	0.500866i	$0.833015\pi$
$948$	−7.57531	+	7.57531i	−0.246035	+	0.246035i
$949$	19.1820			0.622675
$950$		0			0
$951$	−30.9399			−1.00329
$952$	3.72780	−	3.72780i	0.120819	−	0.120819i
$953$	23.4531	+	23.4531i	0.759719	+	0.759719i	0.976271	−	0.216552i	$-0.0694811\pi$
$953$	23.4531	+	23.4531i	0.759719	+	0.759719i	−0.216552	+	0.976271i	$0.569481\pi$
$954$		−	5.00492i		−	0.162040i
$955$		0			0
$956$	10.0989			0.326622
$957$	−6.28685	−	6.28685i	−0.203225	−	0.203225i
$958$	−3.64338	−	3.64338i	−0.117712	−	0.117712i
$959$		−	19.7587i		−	0.638042i
$960$		0			0
$961$	−86.1748			−2.77983
$962$	10.1249	−	10.1249i	0.326440	−	0.326440i
$963$	−0.176822	−	0.176822i	−0.00569800	−	0.00569800i
$964$	−2.15429			−0.0693851
$965$		0			0
$966$	13.6430			0.438957
$967$	−8.98440	−	8.98440i	−0.288919	−	0.288919i	0.547734	−	0.836653i	$-0.315491\pi$
$967$	−8.98440	−	8.98440i	−0.288919	−	0.288919i	−0.836653	+	0.547734i	$0.815491\pi$
$968$	6.96311	+	6.96311i	0.223803	+	0.223803i
$969$	4.98816	−	6.28685i	0.160243	−	0.201963i
$970$		0			0
$971$		−	15.0423i		−	0.482730i	−0.970434	−	0.241365i	$-0.922405\pi$
$971$		−	15.0423i		−	0.482730i	0.970434	−	0.241365i	$-0.0775950\pi$
$972$	−1.24305	+	1.24305i	−0.0398709	+	0.0398709i
$973$	−16.8865	+	16.8865i	−0.541358	+	0.541358i
$974$			1.51414i			0.0485160i
$975$		0			0
$976$	−48.0638			−1.53849
$977$	−18.5450	+	18.5450i	−0.593308	+	0.593308i	−0.938523	−	0.345216i	$-0.887806\pi$
$977$	−18.5450	+	18.5450i	−0.593308	+	0.593308i	0.345216	+	0.938523i	$0.387806\pi$
$978$	−5.72034	+	5.72034i	−0.182916	+	0.182916i
$979$	43.8342			1.40095
$980$		0			0
$981$			3.99543i			0.127564i
$982$	7.78742	−	7.78742i	0.248506	−	0.248506i
$983$	25.0561	+	25.0561i	0.799167	+	0.799167i	0.982964	−	0.183797i	$-0.0588390\pi$
$983$	25.0561	+	25.0561i	0.799167	+	0.799167i	−0.183797	+	0.982964i	$0.558839\pi$
$984$	−25.8670			−0.824610
$985$		0			0
$986$	2.89705			0.0922609
$987$	27.1729	−	27.1729i	0.864923	−	0.864923i
$988$	3.66265	−	0.421875i	0.116524	−	0.0134216i
$989$			25.3028i			0.804583i
$990$		0			0
$991$		−	4.36185i		−	0.138559i	−0.997597	−	0.0692794i	$-0.977930\pi$
$991$		−	4.36185i		−	0.138559i	0.997597	−	0.0692794i	$-0.0220700\pi$
$992$	−19.5825	−	19.5825i	−0.621745	−	0.621745i
$993$	7.16886	−	7.16886i	0.227497	−	0.227497i
$994$			13.6430i			0.432730i
$995$		0			0
$996$		−	3.00271i		−	0.0951446i
$997$	−7.18342	−	7.18342i	−0.227501	−	0.227501i	0.584147	−	0.811648i	$-0.301429\pi$
$997$	−7.18342	−	7.18342i	−0.227501	−	0.227501i	−0.811648	+	0.584147i	$0.801429\pi$
$998$	19.9915	+	19.9915i	0.632821	+	0.632821i
$999$		−	24.0144i		−	0.759781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.g.b.132.2		12
5.2	odd	4		95.2.g.b.18.2	✓	12
5.3	odd	4	inner	475.2.g.b.18.5		12
5.4	even	2		95.2.g.b.37.5	yes	12
15.2	even	4		855.2.p.f.208.5		12
15.14	odd	2		855.2.p.f.37.2		12
19.18	odd	2	inner	475.2.g.b.132.5		12
95.18	even	4	inner	475.2.g.b.18.2		12
95.37	even	4		95.2.g.b.18.5	yes	12
95.94	odd	2		95.2.g.b.37.2	yes	12
285.227	odd	4		855.2.p.f.208.2		12
285.284	even	2		855.2.p.f.37.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.g.b.18.2	✓	12	5.2	odd	4
95.2.g.b.18.5	yes	12	95.37	even	4
95.2.g.b.37.2	yes	12	95.94	odd	2
95.2.g.b.37.5	yes	12	5.4	even	2
475.2.g.b.18.2		12	95.18	even	4	inner
475.2.g.b.18.5		12	5.3	odd	4	inner
475.2.g.b.132.2		12	1.1	even	1	trivial
475.2.g.b.132.5		12	19.18	odd	2	inner
855.2.p.f.37.2		12	15.14	odd	2
855.2.p.f.37.5		12	285.284	even	2
855.2.p.f.208.2		12	285.227	odd	4
855.2.p.f.208.5		12	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.10924 + 1.10924i) q^{2} +(-1.29790 - 1.29790i) q^{3} -0.460811i q^{4} +2.87936 q^{6} +(1.53919 + 1.53919i) q^{7} +(-1.70732 - 1.70732i) q^{8} +0.369102i q^{9} +O(q^{10})\)	\(q+(-1.10924 + 1.10924i) q^{2} +(-1.29790 - 1.29790i) q^{3} -0.460811i q^{4} +2.87936 q^{6} +(1.53919 + 1.53919i) q^{7} +(-1.70732 - 1.70732i) q^{8} +0.369102i q^{9} -2.63090 q^{11} +(-0.598088 + 0.598088i) q^{12} +(1.29790 + 1.29790i) q^{13} -3.41465 q^{14} +4.70928 q^{16} +(0.709275 + 0.709275i) q^{17} +(-0.409422 - 0.409422i) q^{18} +(3.41465 + 2.70928i) q^{19} -3.99543i q^{21} +(2.91829 - 2.91829i) q^{22} +(1.53919 - 1.53919i) q^{23} +4.43188i q^{24} -2.87936 q^{26} +(-3.41465 + 3.41465i) q^{27} +(0.709275 - 0.709275i) q^{28} -1.84114 q^{29} +10.8247i q^{31} +(-1.80905 + 1.80905i) q^{32} +(3.41465 + 3.41465i) q^{33} -1.57351 q^{34} +0.170086 q^{36} +(-3.51638 + 3.51638i) q^{37} +(-6.79288 + 0.782426i) q^{38} -3.36910i q^{39} +5.83658i q^{41} +(4.43188 + 4.43188i) q^{42} +(-8.21953 + 8.21953i) q^{43} +1.21235i q^{44} +3.41465i q^{46} +(6.80098 + 6.80098i) q^{47} +(-6.11218 - 6.11218i) q^{48} -2.26180i q^{49} -1.84114i q^{51} +(0.598088 - 0.598088i) q^{52} +(6.11218 + 6.11218i) q^{53} -7.57531i q^{54} -5.25579i q^{56} +(-0.915506 - 7.94826i) q^{57} +(2.04226 - 2.04226i) q^{58} +5.83658 q^{59} -10.2062 q^{61} +(-12.0072 - 12.0072i) q^{62} +(-0.568118 + 0.568118i) q^{63} +5.40522i q^{64} -7.57531 q^{66} +(1.67523 - 1.67523i) q^{67} +(0.326842 - 0.326842i) q^{68} -3.99543 q^{69} -3.99543i q^{71} +(0.630178 - 0.630178i) q^{72} +(7.38962 - 7.38962i) q^{73} -7.80098i q^{74} +(1.24846 - 1.57351i) q^{76} +(-4.04945 - 4.04945i) q^{77} +(3.73713 + 3.73713i) q^{78} +12.6659 q^{79} +9.97107 q^{81} +(-6.47414 - 6.47414i) q^{82} +(-2.51026 + 2.51026i) q^{83} -1.84114 q^{84} -18.2348i q^{86} +(2.38962 + 2.38962i) q^{87} +(4.49180 + 4.49180i) q^{88} -16.6613 q^{89} +3.99543i q^{91} +(-0.709275 - 0.709275i) q^{92} +(14.0494 - 14.0494i) q^{93} -15.0878 q^{94} +4.69594 q^{96} +(9.14950 - 9.14950i) q^{97} +(2.50887 + 2.50887i) q^{98} -0.971071i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 16 q^{6} + 12 q^{7}+O(q^{10}) \) 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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