LMFDB - Embedded newform 475.2.g.b.18.2

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			18.2
Root			$-1.10924 + 1.10924i$ of defining polynomial
Character	$\chi$	$=$	475.18
Dual form			475.2.g.b.132.2

$q$-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 $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.10924	−	1.10924i	−0.784349	−	0.784349i	0.196213	−	0.980561i	$-0.437136\pi$
$2$	−1.10924	−	1.10924i	−0.784349	−	0.784349i	−0.980561	+	0.196213i	$0.937136\pi$
$3$	−1.29790	+	1.29790i	−0.749344	+	0.749344i	−0.974356	−	0.225012i	$-0.927758\pi$
$3$	−1.29790	+	1.29790i	−0.749344	+	0.749344i	0.225012	+	0.974356i	$0.427758\pi$
$4$			0.460811i			0.230406i
$5$		0			0
$5$		0			0
$6$	2.87936			1.17549
$7$	1.53919	−	1.53919i	0.581759	−	0.581759i	−0.353628	−	0.935386i	$-0.615052\pi$
$7$	1.53919	−	1.53919i	0.581759	−	0.581759i	0.935386	+	0.353628i	$0.115052\pi$
$8$	−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	−0.503830	−	0.863803i	$-0.668076\pi$
$13$	1.29790	−	1.29790i	0.359973	−	0.359973i	0.863803	+	0.503830i	$0.168076\pi$
$14$	−3.41465			−0.912603
$15$		0			0
$16$	4.70928			1.17732
$17$	0.709275	−	0.709275i	0.172025	−	0.172025i	−0.615844	−	0.787868i	$-0.711185\pi$
$17$	0.709275	−	0.709275i	0.172025	−	0.172025i	0.787868	+	0.615844i	$0.211185\pi$
$18$	−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	0.849129	−	0.528186i	$-0.177128\pi$
$23$	1.53919	+	1.53919i	0.320943	+	0.320943i	−0.528186	+	0.849129i	$0.677128\pi$
$24$		−	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	$-0.575381\pi$
$31$		−	10.8247i		−	1.94418i	0.234610	−	0.972090i	$-0.424619\pi$
$32$	−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	0.356288	−	0.934376i	$-0.384042\pi$
$37$	−3.51638	−	3.51638i	−0.578089	−	0.578089i	−0.934376	+	0.356288i	$0.884042\pi$
$38$	−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	$-0.849368\pi$
$41$		−	5.83658i		−	0.911520i	0.890103	−	0.455760i	$-0.150632\pi$
$42$	4.43188	−	4.43188i	0.683854	−	0.683854i
$43$	−8.21953	−	8.21953i	−1.25347	−	1.25347i	−0.954155	−	0.299312i	$-0.903243\pi$
$43$	−8.21953	−	8.21953i	−1.25347	−	1.25347i	−0.299312	−	0.954155i	$-0.596757\pi$
$44$		−	1.21235i		−	0.182768i
$45$		0			0
$46$		−	3.41465i		−	0.503463i
$47$	6.80098	−	6.80098i	0.992025	−	0.992025i	−0.00794297	−	0.999968i	$-0.502528\pi$
$47$	6.80098	−	6.80098i	0.992025	−	0.992025i	0.999968	+	0.00794297i	$0.00252835\pi$
$48$	−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	−0.149230	−	0.988803i	$-0.547679\pi$
$53$	6.11218	−	6.11218i	0.839573	−	0.839573i	0.988803	+	0.149230i	$0.0476795\pi$
$54$			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	0.801994	−	0.597332i	$-0.203772\pi$
$67$	1.67523	+	1.67523i	0.204663	+	0.204663i	−0.597332	+	0.801994i	$0.703772\pi$
$68$	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	$0.0761921\pi$
$71$			3.99543i			0.474171i	−0.971489	+	0.237085i	$0.923808\pi$
$72$	0.630178	+	0.630178i	0.0742671	+	0.0742671i
$73$	7.38962	+	7.38962i	0.864890	+	0.864890i	0.991901	−	0.127011i	$-0.0405385\pi$
$73$	7.38962	+	7.38962i	0.864890	+	0.864890i	−0.127011	+	0.991901i	$0.540539\pi$
$74$			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	0.555788	−	0.831324i	$-0.312417\pi$
$83$	−2.51026	−	2.51026i	−0.275537	−	0.275537i	−0.831324	+	0.555788i	$0.812417\pi$
$84$	−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	0.997641	−	0.0686501i	$-0.0218692\pi$
$97$	9.14950	+	9.14950i	0.928991	+	0.928991i	−0.0686501	+	0.997641i	$0.521869\pi$
$98$	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	−0.670894	−	0.741553i	$-0.734089\pi$
$103$	0.717117	−	0.717117i	0.0706596	−	0.0706596i	0.741553	+	0.670894i	$0.234089\pi$
$104$			4.43188i			0.434582i
$105$		0			0
$106$	−13.5597			−1.31704
$107$	−0.479059	−	0.479059i	−0.0463124	−	0.0463124i	0.683571	−	0.729884i	$-0.260426\pi$
$107$	−0.479059	−	0.479059i	−0.0463124	−	0.0463124i	−0.729884	+	0.683571i	$0.760426\pi$
$108$	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	−0.887592	−	0.460630i	$-0.847624\pi$
$113$	−4.53867	+	4.53867i	−0.426962	+	0.426962i	0.460630	+	0.887592i	$0.347624\pi$
$114$	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	0.329223	−	0.944252i	$-0.393213\pi$
$127$	−6.93102	−	6.93102i	−0.615029	−	0.615029i	−0.944252	+	0.329223i	$0.893213\pi$
$128$	−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	−0.925970	−	0.377596i	$-0.876751\pi$
$137$	−6.41855	+	6.41855i	−0.548374	+	0.548374i	0.377596	+	0.925970i	$0.376751\pi$
$138$	4.43188	+	4.43188i	0.377267	+	0.377267i
$139$		−	10.9711i		−	0.930554i	−0.885165	−	0.465277i	$-0.845955\pi$
$139$		−	10.9711i		−	0.930554i	0.885165	−	0.465277i	$-0.154045\pi$
$140$		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	$-0.965630\pi$
$149$		−	2.63090i		−	0.215532i	0.994176	−	0.107766i	$-0.0343697\pi$
$150$		0			0
$151$			1.84114i			0.149830i	0.997190	+	0.0749150i	$0.0238685\pi$
$151$			1.84114i			0.149830i	−0.997190	+	0.0749150i	$0.976131\pi$
$152$	−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	−0.0315949	−	0.999501i	$-0.510059\pi$
$157$	12.1278	−	12.1278i	0.967906	−	0.967906i	0.999501	+	0.0315949i	$0.0100586\pi$
$158$	−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	0.625009	−	0.780617i	$-0.285095\pi$
$163$	−1.98667	−	1.98667i	−0.155608	−	0.155608i	−0.780617	+	0.625009i	$0.785095\pi$
$164$	2.68956			0.210019
$165$		0			0
$166$			5.56894i			0.432234i
$167$	11.5714	+	11.5714i	0.895424	+	0.895424i	0.995027	−	0.0996036i	$-0.0317575\pi$
$167$	11.5714	+	11.5714i	0.895424	+	0.895424i	−0.0996036	+	0.995027i	$0.531757\pi$
$168$	−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	−0.0284845	+	0.999594i	$0.509068\pi$
$173$	−13.5223	+	13.5223i	−1.02808	+	1.02808i	−0.999594	+	0.0284845i	$0.990932\pi$
$174$	−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	$0.142838\pi$
$181$			11.6732i			0.867658i	−0.900995	+	0.433829i	$0.857162\pi$
$182$	−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	−0.0662547	−	0.997803i	$-0.521105\pi$
$193$	12.9415	−	12.9415i	0.931548	−	0.931548i	0.997803	+	0.0662547i	$0.0211050\pi$
$194$		−	20.2979i		−	1.45731i
$195$		0			0
$196$	−1.04226			−0.0744472
$197$	8.80817	−	8.80817i	0.627556	−	0.627556i	−0.319896	−	0.947453i	$-0.603648\pi$
$197$	8.80817	−	8.80817i	0.627556	−	0.627556i	0.947453	+	0.319896i	$0.103648\pi$
$198$	1.07715	−	1.07715i	0.0765495	−	0.0765495i
$199$		−	4.52359i		−	0.320669i	−0.987063	−	0.160334i	$-0.948743\pi$
$199$		−	4.52359i		−	0.320669i	0.987063	−	0.160334i	$-0.0512573\pi$
$200$		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	$-0.903531\pi$
$211$		−	8.67044i		−	0.596898i	0.954426	−	0.298449i	$-0.0964692\pi$
$212$	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	−0.998018	−	0.0629341i	$-0.979954\pi$
$223$	−13.9638	+	13.9638i	−0.935084	+	0.935084i	0.0629341	+	0.998018i	$0.479954\pi$
$224$	−5.56894			−0.372091
$225$		0			0
$226$	10.0689			0.669775
$227$	−19.9742	−	19.9742i	−1.32574	−	1.32574i	−0.909051	−	0.416685i	$-0.863192\pi$
$227$	−19.9742	−	19.9742i	−1.32574	−	1.32574i	−0.416685	−	0.909051i	$-0.636808\pi$
$228$	−3.66265	−	0.421875i	−0.242565	−	0.0279394i
$229$			19.7237i			1.30338i	0.758487	+	0.651688i	$0.225939\pi$
$229$			19.7237i			1.30338i	−0.758487	+	0.651688i	$0.774061\pi$
$230$		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	0.579993	−	0.814621i	$-0.303055\pi$
$233$	−3.58145	−	3.58145i	−0.234629	−	0.234629i	−0.814621	+	0.579993i	$0.803055\pi$
$234$			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	$-0.749238\pi$
$239$		−	21.9155i		−	1.41759i	0.705412	−	0.708797i	$-0.250762\pi$
$240$		0			0
$241$			4.67500i			0.301143i	0.988599	+	0.150572i	$0.0481115\pi$
$241$			4.67500i			0.301143i	−0.988599	+	0.150572i	$0.951889\pi$
$242$	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	0.663347	−	0.748312i	$-0.269135\pi$
$257$	−1.36208	−	1.36208i	−0.0849643	−	0.0849643i	−0.748312	+	0.663347i	$0.769135\pi$
$258$	−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	0.696958	−	0.717112i	$-0.254536\pi$
$263$	−0.326842	−	0.326842i	−0.0201539	−	0.0201539i	−0.717112	+	0.696958i	$0.754536\pi$
$264$			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	−0.996557	−	0.0829052i	$-0.973580\pi$
$277$	−15.2062	+	15.2062i	−0.913652	+	0.913652i	0.0829052	+	0.996557i	$0.473580\pi$
$278$	−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	$-0.843655\pi$
$281$		−	15.8129i		−	0.943318i	0.881781	−	0.471659i	$-0.156345\pi$
$282$	19.5825	−	19.5825i	1.16612	−	1.16612i
$283$	−3.48133	−	3.48133i	−0.206944	−	0.206944i	0.596023	−	0.802967i	$-0.296747\pi$
$283$	−3.48133	−	3.48133i	−0.206944	−	0.206944i	−0.802967	+	0.596023i	$0.796747\pi$
$284$	−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	−0.892303	−	0.451437i	$-0.850912\pi$
$293$	−7.54641	+	7.54641i	−0.440866	+	0.440866i	0.451437	+	0.892303i	$0.350912\pi$
$294$			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	0.888193	−	0.459471i	$-0.151961\pi$
$307$	7.51181	+	7.51181i	0.428722	+	0.428722i	−0.459471	+	0.888193i	$0.651961\pi$
$308$	−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	0.721181	−	0.692746i	$-0.243599\pi$
$313$	0.503072	+	0.503072i	0.0284353	+	0.0284353i	−0.692746	+	0.721181i	$0.743599\pi$
$314$	−26.9053			−1.51835
$315$		0			0
$316$			5.83658i			0.328333i
$317$	11.9192	+	11.9192i	0.669448	+	0.669448i	0.957588	−	0.288140i	$-0.0930369\pi$
$317$	11.9192	+	11.9192i	0.669448	+	0.669448i	−0.288140	+	0.957588i	$0.593037\pi$
$318$	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	$-0.951494\pi$
$331$		−	5.52342i		−	0.303595i	0.988412	−	0.151797i	$-0.0485061\pi$
$332$	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	0.990116	−	0.140250i	$-0.0447907\pi$
$337$	15.6015	+	15.6015i	0.849866	+	0.849866i	−0.140250	+	0.990116i	$0.544791\pi$
$338$	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	−0.534246	−	0.845329i	$-0.679404\pi$
$347$	5.79484	−	5.79484i	0.311083	−	0.311083i	0.845329	+	0.534246i	$0.179404\pi$
$348$	1.10116	+	1.10116i	0.0590286	+	0.0590286i
$349$			7.13624i			0.381994i	0.981591	+	0.190997i	$0.0611721\pi$
$349$			7.13624i			0.381994i	−0.981591	+	0.190997i	$0.938828\pi$
$350$		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	0.140085	−	0.990139i	$-0.455262\pi$
$353$	−15.9711	−	15.9711i	−0.850054	−	0.850054i	−0.990139	+	0.140085i	$0.955262\pi$
$354$	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	$-0.745534\pi$
$359$		−	27.1689i		−	1.43392i	0.697115	−	0.716959i	$-0.254466\pi$
$360$		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	−0.678039	−	0.735026i	$-0.737170\pi$
$367$	1.09171	−	1.09171i	0.0569867	−	0.0569867i	0.735026	+	0.678039i	$0.237170\pi$
$368$	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	−0.777526	−	0.628850i	$-0.783526\pi$
$373$	−2.87141	+	2.87141i	−0.148676	+	0.148676i	0.628850	+	0.777526i	$0.283526\pi$
$374$	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	−0.714113	−	0.700030i	$-0.753170\pi$
$383$	−0.275606	+	0.275606i	−0.0140828	+	0.0140828i	0.700030	+	0.714113i	$0.253170\pi$
$384$		−	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	$-0.916280\pi$
$389$		−	10.2557i		−	0.519982i	0.965611	−	0.259991i	$-0.0837196\pi$
$390$		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	−0.357892	−	0.933763i	$-0.616504\pi$
$397$	11.4741	−	11.4741i	0.575871	−	0.575871i	0.933763	+	0.357892i	$0.116504\pi$
$398$	−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	$0.296776\pi$
$401$			32.1610i			1.60605i	−0.595948	+	0.803023i	$0.703224\pi$
$402$	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	$0.207196\pi$
$419$			24.8059i			1.21185i	−0.795523	+	0.605924i	$0.792804\pi$
$420$		0			0
$421$		−	13.8274i		−	0.673908i	−0.941521	−	0.336954i	$-0.890603\pi$
$421$		−	13.8274i		−	0.673908i	0.941521	−	0.336954i	$-0.109397\pi$
$422$	−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	$0.141222\pi$
$431$			17.8229i			0.858498i	−0.903186	+	0.429249i	$0.858778\pi$
$432$	−16.0805	−	16.0805i	−0.773674	−	0.773674i
$433$	−2.38438	+	2.38438i	−0.114586	+	0.114586i	−0.762075	−	0.647489i	$-0.775819\pi$
$433$	−2.38438	+	2.38438i	−0.114586	+	0.114586i	0.647489	+	0.762075i	$0.275819\pi$
$434$			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	0.0336754	−	0.999433i	$-0.489279\pi$
$443$	−20.3268	−	20.3268i	−0.965757	−	0.965757i	−0.999433	+	0.0336754i	$0.989279\pi$
$444$			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	−0.866237	−	0.499633i	$-0.833468\pi$
$457$	−7.83710	+	7.83710i	−0.366604	+	0.366604i	0.499633	+	0.866237i	$0.333468\pi$
$458$	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	0.739091	−	0.673605i	$-0.235255\pi$
$463$	1.40910	+	1.40910i	0.0654862	+	0.0654862i	−0.673605	+	0.739091i	$0.735255\pi$
$464$	−8.67044			−0.402515
$465$		0			0
$466$			7.94535i			0.368061i
$467$	−15.6647	+	15.6647i	−0.724878	+	0.724878i	−0.969595	−	0.244717i	$-0.921305\pi$
$467$	−15.6647	+	15.6647i	−0.724878	+	0.724878i	0.244717	+	0.969595i	$0.421305\pi$
$468$	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	$-0.976092\pi$
$479$		−	3.28458i		−	0.150076i	0.997181	−	0.0750382i	$-0.0239079\pi$
$480$		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	0.722401	−	0.691474i	$-0.243038\pi$
$487$	0.682512	+	0.682512i	0.0309276	+	0.0309276i	−0.691474	+	0.722401i	$0.743038\pi$
$488$	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	$0.132174\pi$
$499$			18.0228i			0.806811i	−0.915021	+	0.403405i	$0.867826\pi$
$500$		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	0.943431	−	0.331570i	$-0.107578\pi$
$503$	13.7226	+	13.7226i	0.611861	+	0.611861i	−0.331570	+	0.943431i	$0.607578\pi$
$504$	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	$-0.718536\pi$
$521$		−	35.3081i		−	1.54687i	0.633873	−	0.773437i	$-0.281464\pi$
$522$	0.753803	−	0.753803i	0.0329931	−	0.0329931i
$523$	9.83998	−	9.83998i	0.430272	−	0.430272i	−0.458449	−	0.888721i	$-0.651595\pi$
$523$	9.83998	−	9.83998i	0.430272	−	0.430272i	0.888721	+	0.458449i	$0.151595\pi$
$524$			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	0.836150	−	0.548500i	$-0.184801\pi$
$547$	6.72757	+	6.72757i	0.287650	+	0.287650i	−0.548500	+	0.836150i	$0.684801\pi$
$548$	−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	−0.453318	−	0.891349i	$-0.649760\pi$
$557$	10.3379	−	10.3379i	0.438031	−	0.438031i	0.891349	+	0.453318i	$0.149760\pi$
$558$	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	−0.875213	−	0.483738i	$-0.839279\pi$
$563$	−9.28877	+	9.28877i	−0.391475	+	0.391475i	0.483738	+	0.875213i	$0.339279\pi$
$564$	−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	−0.671264	−	0.741218i	$-0.734248\pi$
$577$	1.68035	−	1.68035i	0.0699537	−	0.0699537i	0.741218	+	0.671264i	$0.234248\pi$
$578$	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	−0.689338	−	0.724439i	$-0.742099\pi$
$587$	0.850432	−	0.850432i	0.0351011	−	0.0351011i	0.724439	+	0.689338i	$0.242099\pi$
$588$	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	0.987797	−	0.155745i	$-0.0497778\pi$
$593$	20.2618	+	20.2618i	0.832052	+	0.832052i	−0.155745	+	0.987797i	$0.549778\pi$
$594$		−	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	$0.134606\pi$
$601$			20.1215i			0.820772i	−0.911912	+	0.410386i	$0.865394\pi$
$602$	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	0.807425	−	0.589970i	$-0.200861\pi$
$607$	5.35752	+	5.35752i	0.217455	+	0.217455i	−0.589970	+	0.807425i	$0.700861\pi$
$608$	−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	0.284218	−	0.958760i	$-0.408266\pi$
$613$	−16.7009	−	16.7009i	−0.674542	−	0.674542i	−0.958760	+	0.284218i	$0.908266\pi$
$614$		−	16.6647i		−	0.672534i
$615$		0			0
$616$		−	13.8274i		−	0.557124i
$617$	10.8394	−	10.8394i	0.436377	−	0.436377i	−0.454414	−	0.890791i	$-0.650151\pi$
$617$	10.8394	−	10.8394i	0.436377	−	0.436377i	0.890791	+	0.454414i	$0.150151\pi$
$618$	2.06484	−	2.06484i	0.0830600	−	0.0830600i
$619$			0.0350725i			0.00140968i	1.00000		0.000704841i	$0.000224358\pi$
$619$			0.0350725i			0.00140968i	−1.00000		0.000704841i	$0.999776\pi$
$620$		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	$-0.852437\pi$
$641$		−	22.6422i		−	0.894313i	0.894456	−	0.447156i	$-0.147563\pi$
$642$	−1.37938	−	1.37938i	−0.0544399	−	0.0544399i
$643$	29.1555	+	29.1555i	1.14978	+	1.14978i	0.986595	+	0.163187i	$0.0521773\pi$
$643$	29.1555	+	29.1555i	1.14978	+	1.14978i	0.163187	+	0.986595i	$0.447823\pi$
$644$			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	−0.229862	−	0.973223i	$-0.573827\pi$
$647$	18.9083	−	18.9083i	0.743362	−	0.743362i	0.973223	+	0.229862i	$0.0738274\pi$
$648$	−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	0.406252	−	0.913761i	$-0.366835\pi$
$653$	−12.9688	−	12.9688i	−0.507508	−	0.507508i	−0.913761	+	0.406252i	$0.866835\pi$
$654$	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	$0.300848\pi$
$661$			41.6799i			1.62116i	−0.585628	+	0.810580i	$0.699152\pi$
$662$	−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	0.116329	−	0.993211i	$-0.462887\pi$
$673$	28.7839	−	28.7839i	1.10954	−	1.10954i	0.993211	−	0.116329i	$-0.0371126\pi$
$674$		−	34.6114i		−	1.33318i
$675$		0			0
$676$	−4.43802			−0.170693
$677$	−23.0115	−	23.0115i	−0.884406	−	0.884406i	0.109573	−	0.993979i	$-0.465052\pi$
$677$	−23.0115	−	23.0115i	−0.884406	−	0.884406i	−0.993979	+	0.109573i	$0.965052\pi$
$678$	−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	−0.614921	−	0.788589i	$-0.710812\pi$
$683$	4.53867	−	4.53867i	0.173667	−	0.173667i	0.788589	+	0.614921i	$0.210812\pi$
$684$	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	$0.151372\pi$
$709$			24.3812i			0.915656i	−0.889041	+	0.457828i	$0.848628\pi$
$710$		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	$0.303160\pi$
$719$			43.6970i			1.62962i	−0.579726	+	0.814811i	$0.696840\pi$
$720$		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	−0.963075	−	0.269232i	$-0.913230\pi$
$727$	−18.7081	+	18.7081i	−0.693843	+	0.693843i	0.269232	+	0.963075i	$0.413230\pi$
$728$	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	0.989680	+	0.143298i	$0.0457707\pi$
$733$	30.6742	+	30.6742i	1.13298	+	1.13298i	0.143298	+	0.989680i	$0.454229\pi$
$734$	−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	$0.0805762\pi$
$739$			13.6163i			0.500885i	−0.968131	+	0.250443i	$0.919424\pi$
$740$		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	−0.991512	−	0.130017i	$-0.958497\pi$
$743$	−23.4826	+	23.4826i	−0.861494	+	0.861494i	0.130017	+	0.991512i	$0.458497\pi$
$744$	−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	$-0.875028\pi$
$751$		−	20.9699i		−	0.765202i	0.923914	−	0.382601i	$-0.124972\pi$
$752$	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	−0.630089	−	0.776523i	$-0.716982\pi$
$757$	4.02893	−	4.02893i	0.146434	−	0.146434i	0.776523	+	0.630089i	$0.216982\pi$
$758$	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	$-0.918478\pi$
$769$		−	14.0494i		−	0.506636i	0.967383	−	0.253318i	$-0.0815219\pi$
$770$		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	−0.664712	−	0.747100i	$-0.731446\pi$
$773$	2.29063	−	2.29063i	0.0823881	−	0.0823881i	0.747100	+	0.664712i	$0.231446\pi$
$774$	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	0.759297	−	0.650744i	$-0.225543\pi$
$787$	3.04529	+	3.04529i	0.108553	+	0.108553i	−0.650744	+	0.759297i	$0.725543\pi$
$788$	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	0.747005	−	0.664819i	$-0.231491\pi$
$797$	2.32020	+	2.32020i	0.0821857	+	0.0821857i	−0.664819	+	0.747005i	$0.731491\pi$
$798$	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	$0.219650\pi$
$809$			36.2122i			1.27315i	−0.771214	+	0.636576i	$0.780350\pi$
$810$		0			0
$811$			0.313153i			0.0109963i	0.999985	+	0.00549815i	$0.00175012\pi$
$811$			0.313153i			0.0109963i	−0.999985	+	0.00549815i	$0.998250\pi$
$812$	−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	0.662760	−	0.748832i	$-0.269385\pi$
$823$	−2.46922	−	2.46922i	−0.0860717	−	0.0860717i	−0.748832	+	0.662760i	$0.769385\pi$
$824$			2.44870i			0.0853046i
$825$		0			0
$826$	−19.9299			−0.693448
$827$	−4.24147	−	4.24147i	−0.147490	−	0.147490i	0.629506	−	0.776996i	$-0.283257\pi$
$827$	−4.24147	−	4.24147i	−0.147490	−	0.147490i	−0.776996	+	0.629506i	$0.783257\pi$
$828$	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	0.630876	−	0.775884i	$-0.282696\pi$
$853$	−4.23513	−	4.23513i	−0.145008	−	0.145008i	−0.775884	+	0.630876i	$0.782696\pi$
$854$	34.8506			1.19256
$855$		0			0
$856$	1.63582			0.0559111
$857$	−9.18410	−	9.18410i	−0.313723	−	0.313723i	0.532627	−	0.846350i	$-0.321205\pi$
$857$	−9.18410	−	9.18410i	−0.313723	−	0.313723i	−0.846350	+	0.532627i	$0.821205\pi$
$858$	−9.83201	+	9.83201i	−0.335659	+	0.335659i
$859$			17.1194i			0.584107i	0.956402	+	0.292053i	$0.0943385\pi$
$859$			17.1194i			0.584107i	−0.956402	+	0.292053i	$0.905661\pi$
$860$		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	−0.872462	−	0.488683i	$-0.837478\pi$
$863$	−11.2742	+	11.2742i	−0.383779	+	0.383779i	0.488683	+	0.872462i	$0.337478\pi$
$864$			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	0.983671	−	0.179975i	$-0.0576016\pi$
$877$	23.8008	+	23.8008i	0.803696	+	0.803696i	−0.179975	+	0.983671i	$0.557602\pi$
$878$	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	0.619177	−	0.785251i	$-0.287466\pi$
$883$	−4.93495	−	4.93495i	−0.166074	−	0.166074i	−0.785251	+	0.619177i	$0.787466\pi$
$884$	0.848418			0.0285354
$885$		0			0
$886$			45.0945i			1.51498i
$887$	10.6588	+	10.6588i	0.357888	+	0.357888i	0.863034	−	0.505146i	$-0.168561\pi$
$887$	10.6588	+	10.6588i	0.357888	+	0.357888i	−0.505146	+	0.863034i	$0.668561\pi$
$888$	−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	0.981861	−	0.189604i	$-0.0607203\pi$
$907$	23.8600	+	23.8600i	0.792257	+	0.792257i	−0.189604	+	0.981861i	$0.560720\pi$
$908$	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	$-0.820251\pi$
$911$		−	32.3053i		−	1.07032i	0.844749	−	0.535162i	$-0.179749\pi$
$912$	−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	$-0.969134\pi$
$919$		−	5.86991i		−	0.193630i	0.995302	−	0.0968152i	$-0.0308656\pi$
$920$		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	$0.411859\pi$
$929$			58.6369i			1.92381i	−0.273379	+	0.961907i	$0.588141\pi$
$930$		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	−0.430712	−	0.902490i	$-0.641737\pi$
$937$	14.4413	−	14.4413i	0.471778	−	0.471778i	0.902490	+	0.430712i	$0.141737\pi$
$938$	−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	$-0.718003\pi$
$941$		−	47.5165i		−	1.54899i	0.632578	−	0.774496i	$-0.281997\pi$
$942$	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	−0.865525	−	0.500866i	$-0.833015\pi$
$947$	−11.2218	+	11.2218i	−0.364660	+	0.364660i	0.500866	+	0.865525i	$0.333015\pi$
$948$	−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	−0.216552	−	0.976271i	$-0.569481\pi$
$953$	23.4531	−	23.4531i	0.759719	−	0.759719i	0.976271	+	0.216552i	$0.0694811\pi$
$954$			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	−0.836653	−	0.547734i	$-0.815491\pi$
$967$	−8.98440	+	8.98440i	−0.288919	+	0.288919i	0.547734	+	0.836653i	$0.315491\pi$
$968$	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	$0.0775950\pi$
$971$			15.0423i			0.482730i	−0.970434	+	0.241365i	$0.922405\pi$
$972$	−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	0.345216	−	0.938523i	$-0.387806\pi$
$977$	−18.5450	−	18.5450i	−0.593308	−	0.593308i	−0.938523	+	0.345216i	$0.887806\pi$
$978$	−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	−0.183797	−	0.982964i	$-0.558839\pi$
$983$	25.0561	−	25.0561i	0.799167	−	0.799167i	0.982964	+	0.183797i	$0.0588390\pi$
$984$	−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	$0.0220700\pi$
$991$			4.36185i			0.138559i	−0.997597	+	0.0692794i	$0.977930\pi$
$992$	−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	−0.811648	−	0.584147i	$-0.801429\pi$
$997$	−7.18342	+	7.18342i	−0.227501	+	0.227501i	0.584147	+	0.811648i	$0.301429\pi$
$998$	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.18.2		12
5.2	odd	4	inner	475.2.g.b.132.5		12
5.3	odd	4		95.2.g.b.37.2	yes	12
5.4	even	2		95.2.g.b.18.5	yes	12
15.8	even	4		855.2.p.f.37.5		12
15.14	odd	2		855.2.p.f.208.2		12
19.18	odd	2	inner	475.2.g.b.18.5		12
95.18	even	4		95.2.g.b.37.5	yes	12
95.37	even	4	inner	475.2.g.b.132.2		12
95.94	odd	2		95.2.g.b.18.2	✓	12
285.113	odd	4		855.2.p.f.37.2		12
285.284	even	2		855.2.p.f.208.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.g.b.18.2	✓	12	95.94	odd	2
95.2.g.b.18.5	yes	12	5.4	even	2
95.2.g.b.37.2	yes	12	5.3	odd	4
95.2.g.b.37.5	yes	12	95.18	even	4
475.2.g.b.18.2		12	1.1	even	1	trivial
475.2.g.b.18.5		12	19.18	odd	2	inner
475.2.g.b.132.2		12	95.37	even	4	inner
475.2.g.b.132.5		12	5.2	odd	4	inner
855.2.p.f.37.2		12	285.113	odd	4
855.2.p.f.37.5		12	15.8	even	4
855.2.p.f.208.2		12	15.14	odd	2
855.2.p.f.208.5		12	285.284	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
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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