LMFDB - Embedded newform 95.2.g.b.18.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,2,Mod(18,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, 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("95.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.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:	$0.758578819202$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			18.2
Root			$-1.10924 + 1.10924i$ of defining polynomial
Character	$\chi$	$=$	95.18
Dual form			95.2.g.b.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10924 - 1.10924i) q^{2} +(-1.29790 + 1.29790i) q^{3} +0.460811i q^{4} +(-2.17009 + 0.539189i) q^{5} +2.87936 q^{6} +(-1.53919 + 1.53919i) q^{7} +(-1.70732 + 1.70732i) q^{8} -0.369102i q^{9} +O(q^{10})$	\(q+(-1.10924 - 1.10924i) q^{2} +(-1.29790 + 1.29790i) q^{3} +0.460811i q^{4} +(-2.17009 + 0.539189i) q^{5} +2.87936 q^{6} +(-1.53919 + 1.53919i) q^{7} +(-1.70732 + 1.70732i) q^{8} -0.369102i q^{9} +(3.00523 + 1.80905i) q^{10} -2.63090 q^{11} +(-0.598088 - 0.598088i) q^{12} +(1.29790 - 1.29790i) q^{13} +3.41465 q^{14} +(2.11675 - 3.51638i) q^{15} +4.70928 q^{16} +(-0.709275 + 0.709275i) q^{17} +(-0.409422 + 0.409422i) q^{18} +(-3.41465 - 2.70928i) q^{19} +(-0.248464 - 1.00000i) q^{20} -3.99543i q^{21} +(2.91829 + 2.91829i) q^{22} +(-1.53919 - 1.53919i) q^{23} -4.43188i q^{24} +(4.41855 - 2.34017i) q^{25} -2.87936 q^{26} +(-3.41465 - 3.41465i) q^{27} +(-0.709275 - 0.709275i) q^{28} +1.84114 q^{29} +(-6.24846 + 1.55252i) q^{30} +10.8247i q^{31} +(-1.80905 - 1.80905i) q^{32} +(3.41465 - 3.41465i) q^{33} +1.57351 q^{34} +(2.51026 - 4.17009i) q^{35} +0.170086 q^{36} +(-3.51638 - 3.51638i) q^{37} +(0.782426 + 6.79288i) q^{38} +3.36910i q^{39} +(2.78447 - 4.62561i) q^{40} +5.83658i q^{41} +(-4.43188 + 4.43188i) q^{42} +(8.21953 + 8.21953i) q^{43} -1.21235i q^{44} +(0.199016 + 0.800984i) q^{45} +3.41465i q^{46} +(-6.80098 + 6.80098i) q^{47} +(-6.11218 + 6.11218i) q^{48} +2.26180i q^{49} +(-7.49702 - 2.30541i) q^{50} -1.84114i q^{51} +(0.598088 + 0.598088i) q^{52} +(6.11218 - 6.11218i) q^{53} +7.57531i q^{54} +(5.70928 - 1.41855i) q^{55} -5.25579i q^{56} +(7.94826 - 0.915506i) q^{57} +(-2.04226 - 2.04226i) q^{58} -5.83658 q^{59} +(1.62038 + 0.975420i) q^{60} -10.2062 q^{61} +(12.0072 - 12.0072i) q^{62} +(0.568118 + 0.568118i) q^{63} -5.40522i q^{64} +(-2.11675 + 3.51638i) q^{65} -7.57531 q^{66} +(1.67523 + 1.67523i) q^{67} +(-0.326842 - 0.326842i) q^{68} +3.99543 q^{69} +(-7.41008 + 1.84114i) q^{70} -3.99543i q^{71} +(0.630178 + 0.630178i) q^{72} +(-7.38962 - 7.38962i) q^{73} +7.80098i q^{74} +(-2.69753 + 8.77217i) q^{75} +(1.24846 - 1.57351i) q^{76} +(4.04945 - 4.04945i) q^{77} +(3.73713 - 3.73713i) q^{78} -12.6659 q^{79} +(-10.2195 + 2.53919i) q^{80} +9.97107 q^{81} +(6.47414 - 6.47414i) q^{82} +(2.51026 + 2.51026i) q^{83} +1.84114 q^{84} +(1.15676 - 1.92162i) q^{85} -18.2348i q^{86} +(-2.38962 + 2.38962i) q^{87} +(4.49180 - 4.49180i) q^{88} +16.6613 q^{89} +(0.667725 - 1.10924i) q^{90} +3.99543i q^{91} +(0.709275 - 0.709275i) q^{92} +(-14.0494 - 14.0494i) q^{93} +15.0878 q^{94} +(8.87089 + 4.03822i) q^{95} +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 - 4 q^{5} - 16 q^{6} - 12 q^{7}+O(q^{10}) $ 12 * q - 4 * q^5 - 16 * q^6 - 12 * q^7	$ 12 q - 4 q^{5} - 16 q^{6} - 12 q^{7} - 16 q^{11} + 28 q^{16} + 20 q^{17} + 32 q^{20} - 12 q^{23} - 4 q^{25} + 16 q^{26} + 20 q^{28} - 40 q^{30} - 36 q^{35} - 20 q^{36} + 4 q^{38} + 4 q^{43} + 40 q^{45} - 44 q^{47} + 40 q^{55} - 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} - 28 q^{80} + 60 q^{81} + 88 q^{82} - 36 q^{83} - 12 q^{85} + 88 q^{87} - 20 q^{92} - 96 q^{93} + 24 q^{95} + 24 q^{96}+O(q^{100}) $ 12 * q - 4 * q^5 - 16 * q^6 - 12 * q^7 - 16 * q^11 + 28 * q^16 + 20 * q^17 + 32 * q^20 - 12 * q^23 - 4 * q^25 + 16 * q^26 + 20 * q^28 - 40 * q^30 - 36 * q^35 - 20 * q^36 + 4 * q^38 + 4 * q^43 + 40 * q^45 - 44 * q^47 + 40 * q^55 - 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 - 28 * q^80 + 60 * q^81 + 88 * q^82 - 36 * q^83 - 12 * q^85 + 88 * q^87 - 20 * q^92 - 96 * q^93 + 24 * q^95 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.10924	−	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
$5$	−2.17009	+	0.539189i	−0.970492	+	0.241133i
$5$	−2.17009	+	0.539189i	−0.970492	+	0.241133i
$6$	2.87936			1.17549
$7$	−1.53919	+	1.53919i	−0.581759	+	0.581759i	−0.935386	−	0.353628i	$-0.884948\pi$
$7$	−1.53919	+	1.53919i	−0.581759	+	0.581759i	0.353628	+	0.935386i	$0.384948\pi$
$8$	−1.70732	+	1.70732i	−0.603630	+	0.603630i
$9$		−	0.369102i		−	0.123034i
$10$	3.00523	+	1.80905i	0.950336	+	0.572072i
$11$	−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
$15$	2.11675	−	3.51638i	0.546542	−	0.907924i
$16$	4.70928			1.17732
$17$	−0.709275	+	0.709275i	−0.172025	+	0.172025i	−0.787868	−	0.615844i	$-0.788815\pi$
$17$	−0.709275	+	0.709275i	−0.172025	+	0.172025i	0.615844	+	0.787868i	$0.288815\pi$
$18$	−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
$20$	−0.248464	−	1.00000i	−0.0555583	−	0.223607i
$21$		−	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	$-0.322872\pi$
$23$	−1.53919	−	1.53919i	−0.320943	−	0.320943i	−0.849129	+	0.528186i	$0.822872\pi$
$24$		−	4.43188i		−	0.904654i
$25$	4.41855	−	2.34017i	0.883710	−	0.468035i
$26$	−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	$-0.445318\pi$
$29$	1.84114			0.341891			0.170946	+	0.985280i	$0.445318\pi$
$30$	−6.24846	+	1.55252i	−1.14081	+	0.283450i
$31$			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
$35$	2.51026	−	4.17009i	0.424311	−	0.704873i
$36$	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	$0.884042\pi$
$38$	0.782426	+	6.79288i	0.126926	+	1.10195i
$39$			3.36910i			0.539488i
$40$	2.78447	−	4.62561i	0.440264	−	0.731373i
$41$			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	0.954155	+	0.299312i	$0.0967571\pi$
$43$	8.21953	+	8.21953i	1.25347	+	1.25347i	0.299312	+	0.954155i	$0.403243\pi$
$44$		−	1.21235i		−	0.182768i
$45$	0.199016	+	0.800984i	0.0296675	+	0.119404i
$46$			3.41465i			0.503463i
$47$	−6.80098	+	6.80098i	−0.992025	+	0.992025i	−0.999968	−	0.00794297i	$-0.997472\pi$
$47$	−6.80098	+	6.80098i	−0.992025	+	0.992025i	0.00794297	+	0.999968i	$0.497472\pi$
$48$	−6.11218	+	6.11218i	−0.882217	+	0.882217i
$49$			2.26180i			0.323114i
$50$	−7.49702	−	2.30541i	−1.06024	−	0.326035i
$51$		−	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
$55$	5.70928	−	1.41855i	0.769839	−	0.191277i
$56$		−	5.25579i		−	0.702334i
$57$	7.94826	−	0.915506i	1.05277	−	0.121262i
$58$	−2.04226	−	2.04226i	−0.268162	−	0.268162i
$59$	−5.83658			−0.759857			−0.379929	−	0.925016i	$-0.624051\pi$
$59$	−5.83658			−0.759857			−0.379929	+	0.925016i	$0.624051\pi$
$60$	1.62038	+	0.975420i	0.209191	+	0.125926i
$61$	−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
$65$	−2.11675	+	3.51638i	−0.262550	+	0.436153i
$66$	−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
$70$	−7.41008	+	1.84114i	−0.885674	+	0.220058i
$71$		−	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	$-0.459461\pi$
$73$	−7.38962	−	7.38962i	−0.864890	−	0.864890i	−0.991901	+	0.127011i	$0.959461\pi$
$74$			7.80098i			0.906846i
$75$	−2.69753	+	8.77217i	−0.311484	+	1.01292i
$76$	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	$-0.752442\pi$
$79$	−12.6659			−1.42502			−0.712511	+	0.701661i	$0.752442\pi$
$80$	−10.2195	+	2.53919i	−1.14258	+	0.283890i
$81$	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	$-0.187583\pi$
$83$	2.51026	+	2.51026i	0.275537	+	0.275537i	−0.555788	+	0.831324i	$0.687583\pi$
$84$	1.84114			0.200885
$85$	1.15676	−	1.92162i	0.125468	−	0.208429i
$86$		−	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	$-0.155488\pi$
$89$	16.6613			1.76610			0.883048	+	0.469284i	$0.155488\pi$
$90$	0.667725	−	1.10924i	0.0703844	−	0.116924i
$91$			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
$95$	8.87089	+	4.03822i	0.910135	+	0.414313i
$96$	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
$100$	1.07838	+	2.03612i	0.107838	+	0.203612i
$101$	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
$105$	2.15429	+	8.67044i	0.210238	+	0.846148i
$106$	−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	$-0.673476\pi$
$109$	−10.8247			−1.03682			−0.518411	+	0.855132i	$0.673476\pi$
$110$	−7.90644	−	4.75943i	−0.753850	−	0.453794i
$111$	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
$115$	4.17009	+	2.51026i	0.388863	+	0.234083i
$116$			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
$120$	2.38962	+	9.61757i	0.218142	+	0.877960i
$121$	−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
$125$	−8.32684	+	7.46081i	−0.744775	+	0.667315i
$126$		−	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
$130$	6.24846	−	1.55252i	0.548027	−	0.136165i
$131$	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
$133$	9.42588	−	1.08570i	0.817327	−	0.0941424i
$134$		−	3.71646i		−	0.321054i
$135$	9.25122	+	5.56894i	0.796219	+	0.479298i
$136$		−	2.42193i		−	0.207678i
$137$	6.41855	−	6.41855i	0.548374	−	0.548374i	−0.377596	−	0.925970i	$-0.623249\pi$
$137$	6.41855	−	6.41855i	0.548374	−	0.548374i	0.925970	+	0.377596i	$0.123249\pi$
$138$	−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	$-0.154045\pi$
$140$	1.92162	+	1.15676i	0.162407	+	0.0977637i
$141$		−	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
$145$	−3.99543	+	0.992723i	−0.331803	+	0.0824411i
$146$			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	$-0.0343697\pi$
$150$	12.7226	−	6.73820i	1.03880	−	0.550172i
$151$		−	1.84114i		−	0.149830i	−0.997190	−	0.0749150i	$-0.976131\pi$
$151$		−	1.84114i		−	0.149830i	0.997190	−	0.0749150i	$-0.0238685\pi$
$152$	10.4555	−	1.20430i	0.848055	−	0.0976817i
$153$	0.261795	+	0.261795i	0.0211649	+	0.0211649i
$154$	−8.98359			−0.723918
$155$	−5.83658	−	23.4906i	−0.468805	−	1.88681i
$156$	−1.55252			−0.124301
$157$	−12.1278	+	12.1278i	−0.967906	+	0.967906i	−0.999501	−	0.0315949i	$-0.989941\pi$
$157$	−12.1278	+	12.1278i	−0.967906	+	0.967906i	0.0315949	+	0.999501i	$0.489941\pi$
$158$	14.0494	+	14.0494i	1.11771	+	1.11771i
$159$			15.8660i			1.25826i
$160$	4.90122	+	2.95038i	0.387475	+	0.233248i
$161$	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	$-0.214905\pi$
$163$	1.98667	+	1.98667i	0.155608	+	0.155608i	−0.625009	+	0.780617i	$0.714905\pi$
$164$	−2.68956			−0.210019
$165$	−5.56894	+	9.25122i	−0.433542	+	0.720207i
$166$		−	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
$170$	−3.41465	+	0.848418i	−0.261892	+	0.0650707i
$171$	−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
$175$	−3.19902	+	10.4030i	−0.241823	+	0.786389i
$176$	−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	$-0.343046\pi$
$179$	12.6659			0.946692			0.473346	+	0.880877i	$0.343046\pi$
$180$	−0.369102	+	0.0917087i	−0.0275113	+	0.00683557i
$181$		−	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
$185$	9.52683	+	5.73485i	0.700426	+	0.421634i
$186$			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
$190$	−5.36058	−	14.3193i	−0.388897	−	1.03883i
$191$	−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
$195$	−1.81658	−	7.31124i	−0.130088	−	0.523569i
$196$	−1.04226			−0.0744472
$197$	−8.80817	+	8.80817i	−0.627556	+	0.627556i	−0.947453	−	0.319896i	$-0.896352\pi$
$197$	−8.80817	+	8.80817i	−0.627556	+	0.627556i	0.319896	+	0.947453i	$0.396352\pi$
$198$	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	$-0.0512573\pi$
$200$	−3.54847	+	11.5393i	−0.250914	+	0.815954i
$201$	−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
$205$	−3.14702	−	12.6659i	−0.219797	−	0.884623i
$206$	−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
$210$	7.22795	−	12.0072i	0.498776	−	0.828575i
$211$			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
$215$	−22.2690	−	13.4052i	−1.51873	−	0.914228i
$216$	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
$220$	0.653684	+	2.63090i	0.0440714	+	0.177375i
$221$			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
$225$	−0.863763	−	1.63090i	−0.0575842	−	0.108727i
$226$	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	$-0.636808\pi$
$228$	0.421875	+	3.66265i	0.0279394	+	0.242565i
$229$			19.7237i			1.30338i	0.758487	+	0.651688i	$0.225939\pi$
$229$			19.7237i			1.30338i	−0.758487	+	0.651688i	$0.774061\pi$
$230$	−1.84114	−	7.41008i	−0.121401	−	0.488606i
$231$			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	$-0.196945\pi$
$233$	3.58145	+	3.58145i	0.234629	+	0.234629i	−0.579993	+	0.814621i	$0.696945\pi$
$234$			1.06278i			0.0694761i
$235$	11.0917	−	18.4257i	0.723543	−	1.20196i
$236$		−	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	$-0.250762\pi$
$240$	9.96834	−	16.5596i	0.643454	−	1.06892i
$241$		−	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
$245$	−1.21953	−	4.90829i	−0.0779132	−	0.313579i
$246$			16.8056i			1.07149i
$247$	−7.94826	+	0.915506i	−0.505736	+	0.0582523i
$248$	−18.4813	−	18.4813i	−1.17357	−	1.17357i
$249$	−6.51614			−0.412944
$250$	17.5122	+	0.960633i	1.10757	+	0.0607558i
$251$	−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
$255$	0.992723	+	3.99543i	0.0621667	+	0.250204i
$256$	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
$260$	−1.62038	−	0.975420i	−0.100492	−	0.0604930i
$261$		−	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	$-0.245464\pi$
$263$	0.326842	+	0.326842i	0.0201539	+	0.0201539i	−0.696958	+	0.717112i	$0.745464\pi$
$264$			11.6598i			0.717613i
$265$	−9.96834	+	16.5596i	−0.612350	+	1.01725i
$266$	−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	$-0.619071\pi$
$269$	−11.9863			−0.730818			−0.365409	+	0.930847i	$0.619071\pi$
$270$	−4.08452	−	16.4391i	−0.248576	−	1.00045i
$271$	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
$275$	−11.6248	+	6.15676i	−0.700999	+	0.371266i
$276$			1.84114i			0.110824i
$277$	15.2062	−	15.2062i	0.913652	−	0.913652i	−0.0829052	−	0.996557i	$-0.526420\pi$
$277$	15.2062	−	15.2062i	0.913652	−	0.913652i	0.996557	+	0.0829052i	$0.0264199\pi$
$278$	−12.1695	+	12.1695i	−0.729879	+	0.729879i
$279$	3.99543			0.239200
$280$	2.83386	+	11.4055i	0.169356	+	0.681610i
$281$			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	$-0.203253\pi$
$283$	3.48133	+	3.48133i	0.206944	+	0.206944i	−0.596023	+	0.802967i	$0.703253\pi$
$284$	1.84114			0.109252
$285$	−16.7548	+	6.27234i	−0.992467	+	0.371541i
$286$	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
$290$	5.53305	+	3.33072i	0.324912	+	0.195586i
$291$	−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
$295$	12.6659	−	3.14702i	0.737436	−	0.183226i
$296$	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
$300$	−4.04231	−	1.24305i	−0.233383	−	0.0717677i
$301$	−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
$305$	22.1483	−	5.50307i	1.26821	−	0.315105i
$306$		−	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
$310$	−19.5825	+	32.5308i	−1.11221	+	1.84762i
$311$	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	$-0.256401\pi$
$313$	−0.503072	−	0.503072i	−0.0284353	−	0.0284353i	−0.721181	+	0.692746i	$0.756401\pi$
$314$	26.9053			1.51835
$315$	−1.53919	−	0.926543i	−0.0867235	−	0.0522048i
$316$		−	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
$320$	2.91443	+	11.7298i	0.162922	+	0.655715i
$321$	1.24354			0.0694078
$322$	−5.25579	−	5.25579i	−0.292894	−	0.292894i
$323$	4.34355	−	0.500304i	0.241682	−	0.0278377i
$324$			4.59478i			0.255266i
$325$	2.69753	−	8.77217i	0.149632	−	0.486592i
$326$		−	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
$330$	16.4391	−	4.08452i	0.904941	−	0.224845i
$331$			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
$335$	−4.53867	−	2.73214i	−0.247974	−	0.149273i
$336$		−	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
$340$	0.885505	+	0.533046i	0.0480232	+	0.0289085i
$341$		−	28.4788i		−	1.54221i
$342$	2.50727	−	0.288795i	0.135578	−	0.0156163i
$343$	−14.2557	−	14.2557i	−0.769733	−	0.769733i
$344$	−28.0668			−1.51326
$345$	−8.67044	+	2.15429i	−0.466801	+	0.115983i
$346$	29.9988			1.61274
$347$	−5.79484	+	5.79484i	−0.311083	+	0.311083i	−0.845329	−	0.534246i	$-0.820596\pi$
$347$	−5.79484	+	5.79484i	−0.311083	+	0.311083i	0.534246	+	0.845329i	$0.320596\pi$
$348$	−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	$0.938828\pi$
$350$	15.0878	−	7.99087i	0.806477	−	0.427130i
$351$	−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	$-0.0447376\pi$
$353$	15.9711	+	15.9711i	0.850054	+	0.850054i	−0.140085	+	0.990139i	$0.544738\pi$
$354$	−16.8056			−0.893208
$355$	2.15429	+	8.67044i	0.114338	+	0.460179i
$356$			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	$-0.254466\pi$
$360$	−1.70732	−	1.02776i	−0.0899839	−	0.0541674i
$361$	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
$365$	20.0205	+	12.0517i	1.04792	+	0.630816i
$366$	−29.3874			−1.53610
$367$	−1.09171	+	1.09171i	−0.0569867	+	0.0569867i	−0.735026	−	0.678039i	$-0.762830\pi$
$367$	−1.09171	+	1.09171i	−0.0569867	+	0.0569867i	0.678039	+	0.735026i	$0.262830\pi$
$368$	−7.24846	−	7.24846i	−0.377852	−	0.377852i
$369$	2.15429			0.112148
$370$	−4.20620	−	16.9288i	−0.218670	−	0.880087i
$371$			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
$375$	1.12402	−	20.4908i	0.0580443	−	1.05814i
$376$		−	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	$-0.224581\pi$
$379$	29.6403			1.52252			0.761261	+	0.648446i	$0.224581\pi$
$380$	−1.86086	+	4.08781i	−0.0954600	+	0.209700i
$381$	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
$385$	−6.60424	+	10.9711i	−0.336583	+	0.559138i
$386$	−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	$-0.0837196\pi$
$390$	−6.09488	+	10.1249i	−0.308626	+	0.512695i
$391$	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
$395$	27.4860	−	6.82930i	1.38297	−	0.343619i
$396$	−0.447480			−0.0224867
$397$	−11.4741	+	11.4741i	−0.575871	+	0.575871i	−0.933763	−	0.357892i	$-0.883496\pi$
$397$	−11.4741	+	11.4741i	−0.575871	+	0.575871i	0.357892	+	0.933763i	$0.383496\pi$
$398$	−5.01773	+	5.01773i	−0.251516	+	0.251516i
$399$	−10.8247	+	13.6430i	−0.541914	+	0.683005i
$400$	20.8082	−	11.0205i	1.04041	−	0.551026i
$401$		−	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
$405$	−21.6381	+	5.37629i	−1.07521	+	0.267150i
$406$	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	$-0.706951\pi$
$409$	−24.4833			−1.21062			−0.605311	+	0.795989i	$0.706951\pi$
$410$	−10.5587	+	17.5402i	−0.521455	+	0.866250i
$411$			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
$415$	−6.80098	−	4.09398i	−0.333847	−	0.200965i
$416$	−4.69594			−0.230238
$417$	14.2394	+	14.2394i	0.697305	+	0.697305i
$418$	−2.05848	−	17.8714i	−0.100684	−	0.874117i
$419$			24.8059i			1.21185i	0.795523	+	0.605924i	$0.207196\pi$
$419$			24.8059i			1.21185i	−0.795523	+	0.605924i	$0.792804\pi$
$420$	−3.99543	+	0.992723i	−0.194957	+	0.0484399i
$421$			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
$425$	−1.47414	+	4.79380i	−0.0715064	+	0.232533i
$426$		−	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
$430$	9.83201	+	39.5711i	0.474142	+	1.90829i
$431$		−	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	−0.762075	−	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
$435$	3.89723	−	6.47414i	0.186858	−	0.310411i
$436$		−	4.98816i		−	0.238889i
$437$	1.08570	+	9.42588i	0.0519362	+	0.450901i
$438$	−21.2774	−	21.2774i	−1.01667	−	1.01667i
$439$	23.8038			1.13609			0.568046	−	0.822997i	$-0.307700\pi$
$439$	23.8038			1.13609			0.568046	+	0.822997i	$0.307700\pi$
$440$	−7.32566	+	12.1695i	−0.349237	+	0.580159i
$441$	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	$-0.0107212\pi$
$443$	20.3268	+	20.3268i	0.965757	+	0.965757i	−0.0336754	+	0.999433i	$0.510721\pi$
$444$			4.20620i			0.199618i
$445$	−36.1565	+	8.98359i	−1.71398	+	0.425863i
$446$	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	$-0.606942\pi$
$449$	−13.9717			−0.659368			−0.329684	+	0.944091i	$0.606942\pi$
$450$	−0.850933	+	2.76717i	−0.0401134	+	0.130446i
$451$		−	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
$455$	−2.15429	−	8.67044i	−0.100995	−	0.406476i
$456$	−12.0072	+	15.1333i	−0.562288	+	0.708683i
$457$	7.83710	−	7.83710i	0.366604	−	0.366604i	−0.499633	−	0.866237i	$-0.666532\pi$
$457$	7.83710	−	7.83710i	0.366604	−	0.366604i	0.866237	+	0.499633i	$0.166532\pi$
$458$	21.8782	−	21.8782i	1.02230	−	1.02230i
$459$	4.84385			0.226092
$460$	−1.15676	+	1.92162i	−0.0539340	+	0.0895961i
$461$	−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	$-0.264745\pi$
$463$	−1.40910	−	1.40910i	−0.0654862	−	0.0654862i	−0.739091	+	0.673605i	$0.764745\pi$
$464$	8.67044			0.402515
$465$	38.0638	+	22.9132i	1.76517	+	1.06257i
$466$		−	7.94535i		−	0.368061i
$467$	15.6647	−	15.6647i	0.724878	−	0.724878i	−0.244717	−	0.969595i	$-0.578695\pi$
$467$	15.6647	−	15.6647i	0.724878	−	0.724878i	0.969595	+	0.244717i	$0.0786949\pi$
$468$	0.220756	−	0.220756i	0.0102044	−	0.0102044i
$469$	−5.15701			−0.238128
$470$	−32.7418	+	8.13517i	−1.51027	+	0.375248i
$471$		−	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
$475$	−21.4280	−	3.98020i	−0.983183	−	0.182624i
$476$	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	$-0.0239079\pi$
$480$	−10.1906	+	2.53200i	−0.465135	+	0.115570i
$481$	−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
$485$	−24.7885	−	14.9219i	−1.12559	−	0.677568i
$486$	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
$490$	−4.09170	+	6.79721i	−0.184844	+	0.307067i
$491$	−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
$495$	−0.523590	−	2.10731i	−0.0235336	−	0.0947164i
$496$			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	$0.867826\pi$
$500$	−3.43802	−	3.83710i	−0.153753	−	0.171600i
$501$	−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	$-0.392422\pi$
$503$	−13.7226	−	13.7226i	−0.611861	−	0.611861i	−0.943431	+	0.331570i	$0.892422\pi$
$504$	−1.93992			−0.0864111
$505$	−8.78765	+	2.18342i	−0.391045	+	0.0971608i
$506$		−	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	$-0.561548\pi$
$509$	−8.67044			−0.384310			−0.192155	+	0.981365i	$0.561548\pi$
$510$	3.33072	−	5.53305i	0.147487	−	0.245007i
$511$	22.7480			1.00631
$512$	7.56120	+	7.56120i	0.334161	+	0.334161i
$513$	2.40860	+	20.9111i	0.106342	+	0.923245i
$514$			3.02174i			0.133283i
$515$	−1.16954	+	1.94287i	−0.0515363	+	0.0856130i
$516$		−	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
$520$	−2.38962	−	9.61757i	−0.104792	−	0.421758i
$521$			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	−0.458449	−	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
$525$	−9.35001	−	17.6540i	−0.408068	−	0.770485i
$526$		−	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
$530$	29.4257	−	7.31124i	1.27817	−	0.317580i
$531$			2.15429i			0.0934884i
$532$	0.500304	+	4.34355i	0.0216909	+	0.188317i
$533$	7.57531	+	7.57531i	0.328123	+	0.328123i
$534$	47.9739			2.07604
$535$	1.29790	+	0.781296i	0.0561132	+	0.0337784i
$536$	−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
$540$	−2.56623	+	4.26307i	−0.110433	+	0.183453i
$541$	−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
$545$	23.4906	−	5.83658i	1.00623	−	0.250011i
$546$			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
$550$	19.7239	+	6.06530i	0.841030	+	0.258625i
$551$	−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
$555$	−19.8082	+	4.92162i	−0.840810	+	0.208911i
$556$	5.05559			0.214405
$557$	−10.3379	+	10.3379i	−0.438031	+	0.438031i	−0.891349	−	0.453318i	$-0.850240\pi$
$557$	−10.3379	+	10.3379i	−0.438031	+	0.438031i	0.453318	+	0.891349i	$0.350240\pi$
$558$	−4.43188	−	4.43188i	−0.187617	−	0.187617i
$559$	21.3363			0.902430
$560$	11.8215	−	19.6381i	0.499550	−	0.829861i
$561$			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
$565$	7.40211	−	12.2965i	0.311409	−	0.517318i
$566$		−	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	$-0.598350\pi$
$569$	−14.5070			−0.608166			−0.304083	+	0.952646i	$0.598350\pi$
$570$	25.5425	+	11.6275i	1.06986	+	0.487022i
$571$	−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
$575$	−10.4030	−	3.19902i	−0.433833	−	0.133408i
$576$	−1.99508			−0.0831283
$577$	−1.68035	+	1.68035i	−0.0699537	+	0.0699537i	−0.741218	−	0.671264i	$-0.765752\pi$
$577$	−1.68035	+	1.68035i	−0.0699537	+	0.0699537i	0.671264	+	0.741218i	$0.265752\pi$
$578$	17.7410	−	17.7410i	0.737927	−	0.737927i
$579$			33.5936i			1.39610i
$580$	−0.457458	−	1.84114i	−0.0189949	−	0.0764492i
$581$	−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
$585$	1.29790	+	0.781296i	0.0536617	+	0.0323026i
$586$	16.7415			0.691586
$587$	−0.850432	+	0.850432i	−0.0351011	+	0.0351011i	−0.724439	−	0.689338i	$-0.757901\pi$
$587$	−0.850432	+	0.850432i	−0.0351011	+	0.0351011i	0.689338	+	0.724439i	$0.257901\pi$
$588$	1.35275	−	1.35275i	0.0557866	−	0.0557866i
$589$	29.3272	−	36.9627i	1.20841	−	1.52302i
$590$	−17.5402	−	10.5587i	−0.722120	−	0.434693i
$591$		−	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	$-0.450222\pi$
$593$	−20.2618	−	20.2618i	−0.832052	−	0.832052i	−0.987797	+	0.155745i	$0.950222\pi$
$594$		−	19.9299i		−	0.817732i
$595$	1.17727	+	4.73820i	0.0482635	+	0.194247i
$596$	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	$-0.583313\pi$
$599$	−12.6659			−0.517514			−0.258757	+	0.965943i	$0.583313\pi$
$600$	−10.3714	−	19.5825i	−0.423409	−	0.799452i
$601$		−	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
$605$	8.85043	−	2.19902i	0.359821	−	0.0894027i
$606$	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	$0.700861\pi$
$608$	1.27606	+	11.0785i	0.0517509	+	0.449292i
$609$		−	7.35616i		−	0.298087i
$610$	−30.6720	−	18.4635i	−1.24187	−	0.747567i
$611$			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	$-0.0917340\pi$
$613$	16.7009	+	16.7009i	0.674542	+	0.674542i	−0.284218	+	0.958760i	$0.591734\pi$
$614$		−	16.6647i		−	0.672534i
$615$	20.5236	+	12.3545i	0.827591	+	0.498183i
$616$			13.8274i			0.557124i
$617$	−10.8394	+	10.8394i	−0.436377	+	0.436377i	−0.890791	−	0.454414i	$-0.849849\pi$
$617$	−10.8394	+	10.8394i	−0.436377	+	0.436377i	0.454414	+	0.890791i	$0.349849\pi$
$618$	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	$0.999776\pi$
$620$	10.8247	−	2.68956i	0.434732	−	0.108015i
$621$			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
$625$	14.0472	−	20.6803i	0.561887	−	0.827214i
$626$			1.11605i			0.0446064i
$627$	−20.9111	+	2.40860i	−0.835107	+	0.0961903i
$628$	−5.58864	−	5.58864i	−0.223011	−	0.223011i
$629$	4.98816			0.198891
$630$	0.679569	+	2.73508i	0.0270747	+	0.108968i
$631$	−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
$635$	18.7781	+	11.3038i	0.745184	+	0.448577i
$636$	−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
$640$	15.6791	−	26.0463i	0.619770	−	1.02957i
$641$			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	−0.986595	−	0.163187i	$-0.947823\pi$
$643$	−29.1555	−	29.1555i	−1.14978	−	1.14978i	−0.163187	−	0.986595i	$-0.552177\pi$
$644$			2.18342i			0.0860387i
$645$	46.3016	−	11.5043i	1.82313	−	0.452981i
$646$	−5.37298	−	4.26307i	−0.211397	−	0.167728i
$647$	−18.9083	+	18.9083i	−0.743362	+	0.743362i	−0.973223	−	0.229862i	$-0.926173\pi$
$647$	−18.9083	+	18.9083i	−0.743362	+	0.743362i	0.229862	+	0.973223i	$0.426173\pi$
$648$	−17.0239	+	17.0239i	−0.668760	+	0.668760i
$649$	15.3554			0.602753
$650$	−12.7226	+	6.73820i	−0.499022	+	0.264294i
$651$	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	$-0.133165\pi$
$653$	12.9688	+	12.9688i	0.507508	+	0.507508i	−0.406252	+	0.913761i	$0.633165\pi$
$654$	−31.1683			−1.21878
$655$	−9.36069	+	2.32580i	−0.365752	+	0.0908764i
$656$			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	$-0.776133\pi$
$659$	−39.1592			−1.52543			−0.762713	+	0.646737i	$0.776133\pi$
$660$	−4.26307	−	2.56623i	−0.165940	−	0.0998904i
$661$		−	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
$665$	−19.8696	+	7.43840i	−0.770509	+	0.288449i
$666$	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
$670$	2.00388	+	8.06505i	0.0774165	+	0.311580i
$671$	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
$675$	−23.0787	−	7.09693i	−0.888298	−	0.273161i
$676$	−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
$680$	1.30588	+	5.25579i	0.0500780	+	0.201550i
$681$	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
$685$	−10.4680	+	17.3896i	−0.399962	+	0.664423i
$686$			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
$690$	12.0072	+	7.22795i	0.457106	+	0.275163i
$691$	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
$695$	5.91548	+	23.8082i	0.224387	+	0.903095i
$696$		−	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
$700$	−4.79380	−	1.47414i	−0.181188	−	0.0557173i
$701$	−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
$703$	2.48036	+	21.5340i	0.0935485	+	0.812171i
$704$			14.2206i			0.535958i
$705$	9.51886	+	38.3108i	0.358501	+	1.44287i
$706$		−	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	$0.848628\pi$
$710$	7.22795	−	12.0072i	0.271260	−	0.450622i
$711$			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
$715$	5.56894	−	9.25122i	0.208267	−	0.345976i
$716$			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	$0.696840\pi$
$720$	0.937221	+	3.77205i	0.0349282	+	0.140576i
$721$			2.20756i			0.0822137i
$722$	15.7321	−	25.3151i	0.585487	−	0.942131i
$723$	6.06770	+	6.06770i	0.225660	+	0.225660i
$724$	5.37912			0.199913
$725$	8.13517	−	4.30859i	0.302133	−	0.160017i
$726$	−11.7431			−0.435828
$727$	18.7081	−	18.7081i	0.693843	−	0.693843i	−0.269232	−	0.963075i	$-0.586770\pi$
$727$	18.7081	−	18.7081i	0.693843	−	0.693843i	0.963075	+	0.269232i	$0.0867699\pi$
$728$	−6.82150	−	6.82150i	−0.252822	−	0.252822i
$729$			22.9109i			0.848553i
$730$	−8.83929	−	35.5757i	−0.327157	−	1.31672i
$731$	−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	$-0.954229\pi$
$733$	−30.6742	−	30.6742i	−1.13298	−	1.13298i	−0.143298	−	0.989680i	$-0.545771\pi$
$734$	2.42193			0.0893949
$735$	7.95332	+	4.78765i	0.293363	+	0.176595i
$736$			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	$0.919424\pi$
$740$	−2.64268	+	4.39007i	−0.0971469	+	0.161382i
$741$	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
$745$	1.41855	+	5.70928i	0.0519717	+	0.209172i
$746$	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
$750$	−23.9760	+	21.4824i	−0.875479	+	0.784425i
$751$			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
$755$	0.992723	+	3.99543i	0.0361289	+	0.145409i
$756$			4.84385i			0.176169i
$757$	−4.02893	+	4.02893i	−0.146434	+	0.146434i	−0.776523	−	0.630089i	$-0.783018\pi$
$757$	−4.02893	+	4.02893i	−0.146434	+	0.146434i	0.630089	+	0.776523i	$0.283018\pi$
$758$	−32.8781	−	32.8781i	−1.19419	−	1.19419i
$759$	−10.5116			−0.381546
$760$	−22.0400	+	8.25094i	−0.799477	+	0.299293i
$761$	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
$765$	−0.709275	−	0.426961i	−0.0256439	−	0.0154368i
$766$	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	$-0.0815219\pi$
$770$	19.4952	−	4.84385i	0.702557	−	0.174560i
$771$	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
$775$	25.3317	+	47.8296i	0.909943	+	1.71809i
$776$	−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
$780$	3.36910	−	0.837101i	0.120633	−	0.0299730i
$781$			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
$785$	19.7792	−	32.8576i	0.705951	−	1.17274i
$786$	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
$790$	−38.0638	−	22.9132i	−1.35425	−	0.815215i
$791$		−	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
$795$	−8.55479	−	34.4307i	−0.303407	−	1.22113i
$796$	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	$0.731491\pi$
$798$	27.1405	−	3.12613i	0.960764	−	0.110664i
$799$		−	9.64754i		−	0.341305i
$800$	−12.2269	−	3.75989i	−0.432285	−	0.132932i
$801$		−	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
$805$	−10.2823	+	2.55479i	−0.362404	+	0.0900444i
$806$		−	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	$0.780350\pi$
$810$	29.9653	+	18.0382i	1.05287	+	0.633797i
$811$		−	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
$815$	−5.38243	−	3.24005i	−0.188538	−	0.113494i
$816$		−	8.67044i		−	0.303526i
$817$	−5.79784	−	50.3358i	−0.202841	−	1.76103i
$818$	27.1578	+	27.1578i	0.949550	+	0.949550i
$819$	1.47472			0.0515310
$820$	5.83658	−	1.45018i	0.203822	−	0.0506425i
$821$	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	$-0.230615\pi$
$823$	2.46922	+	2.46922i	0.0860717	+	0.0860717i	−0.662760	+	0.748832i	$0.730615\pi$
$824$			2.44870i			0.0853046i
$825$	7.09693	−	23.0787i	0.247083	−	0.803496i
$826$	−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	$-0.446331\pi$
$829$	9.66316			0.335615			0.167808	+	0.985820i	$0.446331\pi$
$830$	3.00271	+	12.0851i	0.104226	+	0.419480i
$831$			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
$835$	−31.3502	−	18.8718i	−1.08492	−	0.653086i
$836$	−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	$-0.184097\pi$
$839$	48.5092			1.67472			0.837362	+	0.546649i	$0.184097\pi$
$840$	−18.4813	−	11.1252i	−0.637666	−	0.383855i
$841$	−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
$845$	−5.19287	−	20.8999i	−0.178640	−	0.718978i
$846$		−	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
$850$	6.95263	−	3.68228i	0.238473	−	0.126301i
$851$			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	$-0.217304\pi$
$853$	4.23513	+	4.23513i	0.145008	+	0.145008i	−0.630876	+	0.775884i	$0.717304\pi$
$854$	−34.8506			−1.19256
$855$	1.49052	−	3.27427i	0.0509746	−	0.111978i
$856$	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	$0.905661\pi$
$860$	6.17727	−	10.2618i	0.210643	−	0.349924i
$861$	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
$865$	22.0534	−	36.6355i	0.749839	−	1.24565i
$866$	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
$870$	−11.5043	+	2.85841i	−0.390032	+	0.0969091i
$871$	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
$875$	1.33299	−	24.3002i	0.0450631	−	0.821496i
$876$			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
$880$	26.8865	−	6.68035i	0.906345	−	0.225194i
$881$	−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	$-0.212534\pi$
$883$	4.93495	+	4.93495i	0.166074	+	0.166074i	−0.619177	+	0.785251i	$0.712534\pi$
$884$	−0.848418			−0.0285354
$885$	−12.3545	+	20.5236i	−0.415294	+	0.689893i
$886$		−	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
$890$	50.0710	+	30.1412i	1.67838	+	1.01033i
$891$	−26.2329			−0.878834
$892$	−6.43466	−	6.43466i	−0.215448	−	0.215448i
$893$	41.6487	−	4.79723i	1.39372	−	0.160533i
$894$		−	7.57531i		−	0.253356i
$895$	−27.4860	+	6.82930i	−0.918757	+	0.228278i
$896$		−	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
$900$	0.751536	−	0.398032i	0.0250512	−	0.0132677i
$901$			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
$905$	6.29403	+	25.3317i	0.209221	+	0.842056i
$906$		−	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
$910$	−7.22795	+	12.0072i	−0.239604	+	0.398034i
$911$			32.3053i			1.07032i	0.844749	+	0.535162i	$0.179749\pi$
$911$			32.3053i			1.07032i	−0.844749	+	0.535162i	$0.820251\pi$
$912$	37.4305	−	4.31137i	1.23945	−	0.142764i
$913$	−6.60424	−	6.60424i	−0.218568	−	0.218568i
$914$	−17.3864			−0.575091
$915$	−21.6039	+	35.8888i	−0.714204	+	1.18645i
$916$	−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	$-0.0308656\pi$
$920$	−11.4055	+	2.83386i	−0.376029	+	0.0934297i
$921$	−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
$925$	−23.7662	−	7.30836i	−0.781428	−	0.240297i
$926$			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	$0.588141\pi$
$930$	−16.8056	−	67.6380i	−0.551078	−	2.21794i
$931$	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
$935$	−3.04331	+	5.05559i	−0.0995267	+	0.165336i
$936$	1.63582			0.0534684
$937$	−14.4413	+	14.4413i	−0.471778	+	0.471778i	−0.902490	−	0.430712i	$-0.858263\pi$
$937$	−14.4413	+	14.4413i	−0.471778	+	0.471778i	0.430712	+	0.902490i	$0.358263\pi$
$938$	5.72034	+	5.72034i	0.186776	+	0.186776i
$939$	1.30588			0.0426156
$940$	8.49079	+	5.11118i	0.276939	+	0.166708i
$941$			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
$945$	−22.8110	+	5.66773i	−0.742043	+	0.184371i
$946$			47.9739i			1.55977i
$947$	11.2218	−	11.2218i	0.364660	−	0.364660i	−0.500866	−	0.865525i	$-0.666985\pi$
$947$	11.2218	−	11.2218i	0.364660	−	0.364660i	0.865525	+	0.500866i	$0.166985\pi$
$948$	7.57531	+	7.57531i	0.246035	+	0.246035i
$949$	−19.1820			−0.622675
$950$	19.3537	+	28.1837i	0.627917	+	0.914399i
$951$	−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
$955$	5.75872	−	1.43084i	0.186348	−	0.0463008i
$956$	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
$960$	−19.0068	−	11.4415i	−0.613441	−	0.369272i
$961$	−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
$965$	−21.1062	+	35.0620i	−0.679433	+	1.12869i
$966$	13.6430			0.438957
$967$	8.98440	−	8.98440i	0.288919	−	0.288919i	−0.547734	−	0.836653i	$-0.684509\pi$
$967$	8.98440	−	8.98440i	0.288919	−	0.288919i	0.836653	+	0.547734i	$0.184509\pi$
$968$	6.96311	−	6.96311i	0.223803	−	0.223803i
$969$	−4.98816	+	6.28685i	−0.160243	+	0.201963i
$970$	10.9444	+	44.0482i	0.351404	+	1.41430i
$971$		−	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
$975$	7.88428	+	14.8865i	0.252499	+	0.476751i
$976$	−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
$980$	2.26180	−	0.561975i	0.0722504	−	0.0179516i
$981$			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
$985$	14.3652	−	23.8638i	0.457714	−	0.760363i
$986$	2.89705			0.0922609
$987$	27.1729	+	27.1729i	0.864923	+	0.864923i
$988$	−0.421875	−	3.66265i	−0.0134216	−	0.116524i
$989$		−	25.3028i		−	0.804583i
$990$	−1.75672	+	2.91829i	−0.0558321	+	0.0927493i
$991$		−	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
$995$	2.43907	+	9.81658i	0.0773237	+	0.311207i
$996$		−	3.00271i		−	0.0951446i
$997$	7.18342	−	7.18342i	0.227501	−	0.227501i	−0.584147	−	0.811648i	$-0.698571\pi$
$997$	7.18342	−	7.18342i	0.227501	−	0.227501i	0.811648	+	0.584147i	$0.198571\pi$
$998$	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	95.2.g.b.18.2	✓	12
3.2	odd	2		855.2.p.f.208.5		12
5.2	odd	4	inner	95.2.g.b.37.5	yes	12
5.3	odd	4		475.2.g.b.132.2		12
5.4	even	2		475.2.g.b.18.5		12
15.2	even	4		855.2.p.f.37.2		12
19.18	odd	2	inner	95.2.g.b.18.5	yes	12
57.56	even	2		855.2.p.f.208.2		12
95.18	even	4		475.2.g.b.132.5		12
95.37	even	4	inner	95.2.g.b.37.2	yes	12
95.94	odd	2		475.2.g.b.18.2		12
285.227	odd	4		855.2.p.f.37.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.g.b.18.2	✓	12	1.1	even	1	trivial
95.2.g.b.18.5	yes	12	19.18	odd	2	inner
95.2.g.b.37.2	yes	12	95.37	even	4	inner
95.2.g.b.37.5	yes	12	5.2	odd	4	inner
475.2.g.b.18.2		12	95.94	odd	2
475.2.g.b.18.5		12	5.4	even	2
475.2.g.b.132.2		12	5.3	odd	4
475.2.g.b.132.5		12	95.18	even	4
855.2.p.f.37.2		12	15.2	even	4
855.2.p.f.37.5		12	285.227	odd	4
855.2.p.f.208.2		12	57.56	even	2
855.2.p.f.208.5		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.10924 - 1.10924i) q^{2} +(-1.29790 + 1.29790i) q^{3} +0.460811i q^{4} +(-2.17009 + 0.539189i) q^{5} +2.87936 q^{6} +(-1.53919 + 1.53919i) q^{7} +(-1.70732 + 1.70732i) q^{8} -0.369102i q^{9} +O(q^{10})\)	\(q+(-1.10924 - 1.10924i) q^{2} +(-1.29790 + 1.29790i) q^{3} +0.460811i q^{4} +(-2.17009 + 0.539189i) q^{5} +2.87936 q^{6} +(-1.53919 + 1.53919i) q^{7} +(-1.70732 + 1.70732i) q^{8} -0.369102i q^{9} +(3.00523 + 1.80905i) q^{10} -2.63090 q^{11} +(-0.598088 - 0.598088i) q^{12} +(1.29790 - 1.29790i) q^{13} +3.41465 q^{14} +(2.11675 - 3.51638i) q^{15} +4.70928 q^{16} +(-0.709275 + 0.709275i) q^{17} +(-0.409422 + 0.409422i) q^{18} +(-3.41465 - 2.70928i) q^{19} +(-0.248464 - 1.00000i) q^{20} -3.99543i q^{21} +(2.91829 + 2.91829i) q^{22} +(-1.53919 - 1.53919i) q^{23} -4.43188i q^{24} +(4.41855 - 2.34017i) q^{25} -2.87936 q^{26} +(-3.41465 - 3.41465i) q^{27} +(-0.709275 - 0.709275i) q^{28} +1.84114 q^{29} +(-6.24846 + 1.55252i) q^{30} +10.8247i q^{31} +(-1.80905 - 1.80905i) q^{32} +(3.41465 - 3.41465i) q^{33} +1.57351 q^{34} +(2.51026 - 4.17009i) q^{35} +0.170086 q^{36} +(-3.51638 - 3.51638i) q^{37} +(0.782426 + 6.79288i) q^{38} +3.36910i q^{39} +(2.78447 - 4.62561i) q^{40} +5.83658i q^{41} +(-4.43188 + 4.43188i) q^{42} +(8.21953 + 8.21953i) q^{43} -1.21235i q^{44} +(0.199016 + 0.800984i) q^{45} +3.41465i q^{46} +(-6.80098 + 6.80098i) q^{47} +(-6.11218 + 6.11218i) q^{48} +2.26180i q^{49} +(-7.49702 - 2.30541i) q^{50} -1.84114i q^{51} +(0.598088 + 0.598088i) q^{52} +(6.11218 - 6.11218i) q^{53} +7.57531i q^{54} +(5.70928 - 1.41855i) q^{55} -5.25579i q^{56} +(7.94826 - 0.915506i) q^{57} +(-2.04226 - 2.04226i) q^{58} -5.83658 q^{59} +(1.62038 + 0.975420i) q^{60} -10.2062 q^{61} +(12.0072 - 12.0072i) q^{62} +(0.568118 + 0.568118i) q^{63} -5.40522i q^{64} +(-2.11675 + 3.51638i) q^{65} -7.57531 q^{66} +(1.67523 + 1.67523i) q^{67} +(-0.326842 - 0.326842i) q^{68} +3.99543 q^{69} +(-7.41008 + 1.84114i) q^{70} -3.99543i q^{71} +(0.630178 + 0.630178i) q^{72} +(-7.38962 - 7.38962i) q^{73} +7.80098i q^{74} +(-2.69753 + 8.77217i) q^{75} +(1.24846 - 1.57351i) q^{76} +(4.04945 - 4.04945i) q^{77} +(3.73713 - 3.73713i) q^{78} -12.6659 q^{79} +(-10.2195 + 2.53919i) q^{80} +9.97107 q^{81} +(6.47414 - 6.47414i) q^{82} +(2.51026 + 2.51026i) q^{83} +1.84114 q^{84} +(1.15676 - 1.92162i) q^{85} -18.2348i q^{86} +(-2.38962 + 2.38962i) q^{87} +(4.49180 - 4.49180i) q^{88} +16.6613 q^{89} +(0.667725 - 1.10924i) q^{90} +3.99543i q^{91} +(0.709275 - 0.709275i) q^{92} +(-14.0494 - 14.0494i) q^{93} +15.0878 q^{94} +(8.87089 + 4.03822i) q^{95} +4.69594 q^{96} +(9.14950 + 9.14950i) q^{97} +(2.50887 - 2.50887i) q^{98} +0.971071i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{5} - 16 q^{6} - 12 q^{7}+O(q^{10}) \) 12 * q - 4 * q^5 - 16 * q^6 - 12 * q^7	\( 12 q - 4 q^{5} - 16 q^{6} - 12 q^{7} - 16 q^{11} + 28 q^{16} + 20 q^{17} + 32 q^{20} - 12 q^{23} - 4 q^{25} + 16 q^{26} + 20 q^{28} - 40 q^{30} - 36 q^{35} - 20 q^{36} + 4 q^{38} + 4 q^{43} + 40 q^{45} - 44 q^{47} + 40 q^{55} - 88 q^{58} - 24 q^{61} + 8 q^{62} + 60 q^{63} - 8 q^{66} + 44 q^{68} + 28 q^{73} - 20 q^{76} - 24 q^{77} - 28 q^{80} + 60 q^{81} + 88 q^{82} - 36 q^{83} - 12 q^{85} + 88 q^{87} - 20 q^{92} - 96 q^{93} + 24 q^{95} + 24 q^{96}+O(q^{100}) \) 12 * q - 4 * q^5 - 16 * q^6 - 12 * q^7 - 16 * q^11 + 28 * q^16 + 20 * q^17 + 32 * q^20 - 12 * q^23 - 4 * q^25 + 16 * q^26 + 20 * q^28 - 40 * q^30 - 36 * q^35 - 20 * q^36 + 4 * q^38 + 4 * q^43 + 40 * q^45 - 44 * q^47 + 40 * q^55 - 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 - 28 * q^80 + 60 * q^81 + 88 * q^82 - 36 * q^83 - 12 * q^85 + 88 * q^87 - 20 * q^92 - 96 * q^93 + 24 * q^95 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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