LMFDB - Embedded newform 425.3.t.b.74.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,3,Mod(24,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 11])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.24"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	425.t (of order $16$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-8,-8,8,0,0,8,-8,-8,0,40,-32,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$11.5804112353$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			74.1
Root			$0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	425.74
Dual form			425.3.t.b.224.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.675577 + 1.63099i) q^{2} +(0.789499 + 3.96908i) q^{3} +(0.624715 + 0.624715i) q^{4} +(-7.00688 - 1.39376i) q^{6} +(-3.40262 + 2.27356i) q^{7} +(-7.96489 + 3.29916i) q^{8} +(-6.81537 + 2.82302i) q^{9} +(1.35387 - 6.80638i) q^{11} +(-1.98633 + 2.97275i) q^{12} +(2.37416 + 2.37416i) q^{13} +(-1.40941 - 7.08560i) q^{14} -11.6855i q^{16} +(-14.5645 + 8.76791i) q^{17} -13.0229i q^{18} +(-22.7712 - 9.43215i) q^{19} +(-11.7103 - 11.7103i) q^{21} +(10.1865 + 6.80638i) q^{22} +(2.24740 - 11.2984i) q^{23} +(-19.3829 - 29.0086i) q^{24} +(-5.47615 + 2.26829i) q^{26} +(3.64922 + 5.46144i) q^{27} +(-3.54600 - 0.705343i) q^{28} +(-9.98767 - 6.67355i) q^{29} +(7.38055 + 37.1045i) q^{31} +(-12.8006 - 5.30218i) q^{32} +28.0839 q^{33} +(-4.46094 - 29.6778i) q^{34} +(-6.02124 - 2.49408i) q^{36} +(6.29529 + 31.6486i) q^{37} +(30.7674 - 30.7674i) q^{38} +(-7.54883 + 11.2976i) q^{39} +(18.7852 + 28.1140i) q^{41} +(27.0106 - 11.1881i) q^{42} +(1.33189 + 3.21547i) q^{43} +(5.09783 - 3.40626i) q^{44} +(16.9093 + 11.2984i) q^{46} +(-3.16735 - 3.16735i) q^{47} +(46.3809 - 9.22573i) q^{48} +(-12.3427 + 29.7979i) q^{49} +(-46.2992 - 50.8853i) q^{51} +2.96634i q^{52} +(11.7603 - 28.3919i) q^{53} +(-11.3729 + 2.26220i) q^{54} +(19.6007 - 29.3345i) q^{56} +(19.4591 - 97.8275i) q^{57} +(17.6319 - 11.7813i) q^{58} +(4.49481 + 10.8514i) q^{59} +(58.9263 - 39.3733i) q^{61} +(-65.5031 - 13.0294i) q^{62} +(16.7718 - 25.1008i) q^{63} +(50.3473 - 50.3473i) q^{64} +(-18.9728 + 45.8045i) q^{66} +28.5842 q^{67} +(-14.5761 - 3.62119i) q^{68} +46.6187 q^{69} +(-33.7056 + 6.70446i) q^{71} +(44.9700 - 44.9700i) q^{72} +(-77.8880 - 52.0431i) q^{73} +(-55.8713 - 11.1135i) q^{74} +(-8.33312 - 20.1179i) q^{76} +(10.8680 + 26.2377i) q^{77} +(-13.3265 - 19.9444i) q^{78} +(-4.18708 + 21.0499i) q^{79} +(-65.7422 + 65.7422i) q^{81} +(-58.5443 + 11.6452i) q^{82} +(104.903 + 43.4522i) q^{83} -14.6312i q^{84} -6.14419 q^{86} +(18.6026 - 44.9106i) q^{87} +(11.6719 + 58.6787i) q^{88} +(28.3238 + 28.3238i) q^{89} +(-13.4762 - 2.68058i) q^{91} +(8.46229 - 5.65432i) q^{92} +(-141.444 + 58.5880i) q^{93} +(7.30570 - 3.02612i) q^{94} +(10.9387 - 54.9926i) q^{96} +(-92.4136 + 138.307i) q^{97} +(-40.2616 - 40.2616i) q^{98} +(9.98738 + 50.2100i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{7} - 8 q^{8} - 8 q^{9} + 40 q^{11} - 32 q^{12} - 16 q^{14} - 64 q^{17} + 32 q^{19} - 64 q^{21} + 8 q^{22} - 32 q^{23} - 24 q^{24} + 112 q^{27} - 8 q^{28} - 24 q^{29}+ \cdots - 136 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^7 - 8 * q^8 - 8 * q^9 + 40 * q^11 - 32 * q^12 - 16 * q^14 - 64 * q^17 + 32 * q^19 - 64 * q^21 + 8 * q^22 - 32 * q^23 - 24 * q^24 + 112 * q^27 - 8 * q^28 - 24 * q^29 + 32 * q^31 - 16 * q^32 + 16 * q^33 - 64 * q^34 - 104 * q^36 + 56 * q^37 - 8 * q^38 + 72 * q^39 + 88 * q^42 - 48 * q^43 + 96 * q^44 + 80 * q^47 + 16 * q^48 - 8 * q^49 - 176 * q^51 + 88 * q^53 - 208 * q^54 + 72 * q^56 - 168 * q^57 - 96 * q^58 - 8 * q^59 + 264 * q^61 - 96 * q^62 - 16 * q^63 + 120 * q^64 + 8 * q^66 - 32 * q^67 + 120 * q^68 + 208 * q^69 + 32 * q^71 + 24 * q^72 - 240 * q^73 - 176 * q^74 - 80 * q^76 + 120 * q^77 + 96 * q^79 - 224 * q^81 - 352 * q^82 + 504 * q^83 + 288 * q^86 - 216 * q^87 + 24 * q^88 - 288 * q^89 - 24 * q^91 - 72 * q^92 - 248 * q^93 + 8 * q^94 + 328 * q^96 + 280 * q^97 + 16 * q^98 - 136 * q^99

Character values

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

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{15}{16}\right)$

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 $

$2$	−0.675577	+	1.63099i	−0.337788	+	0.815493i	0.660139	+	0.751143i	$0.270497\pi$
$2$	−0.675577	+	1.63099i	−0.337788	+	0.815493i	−0.997927	+	0.0643498i	$0.979503\pi$
$3$	0.789499	+	3.96908i	0.263166	+	1.32303i	0.855696	+	0.517478i	$0.173129\pi$
$3$	0.789499	+	3.96908i	0.263166	+	1.32303i	−0.592530	+	0.805548i	$0.701871\pi$
$4$	0.624715	+	0.624715i	0.156179	+	0.156179i
$5$		0			0
$5$		0			0
$6$	−7.00688	−	1.39376i	−1.16781	−	0.232293i
$7$	−3.40262	+	2.27356i	−0.486089	+	0.324794i	−0.774350	−	0.632757i	$-0.781923\pi$
$7$	−3.40262	+	2.27356i	−0.486089	+	0.324794i	0.288261	+	0.957552i	$0.406923\pi$
$8$	−7.96489	+	3.29916i	−0.995611	+	0.412396i
$9$	−6.81537	+	2.82302i	−0.757263	+	0.313669i
$10$		0			0
$11$	1.35387	−	6.80638i	0.123079	−	0.618761i	−0.869172	−	0.494511i	$-0.835347\pi$
$11$	1.35387	−	6.80638i	0.123079	−	0.618761i	0.992251	−	0.124251i	$-0.0396527\pi$
$12$	−1.98633	+	2.97275i	−0.165528	+	0.247729i
$13$	2.37416	+	2.37416i	0.182628	+	0.182628i	0.792500	−	0.609872i	$-0.208779\pi$
$13$	2.37416	+	2.37416i	0.182628	+	0.182628i	−0.609872	+	0.792500i	$0.708779\pi$
$14$	−1.40941	−	7.08560i	−0.100672	−	0.506114i
$15$		0			0
$16$		−	11.6855i		−	0.730347i
$17$	−14.5645	+	8.76791i	−0.856733	+	0.515760i
$17$	−14.5645	+	8.76791i	−0.856733	+	0.515760i
$18$		−	13.0229i		−	0.723496i
$19$	−22.7712	−	9.43215i	−1.19849	−	0.496429i	−0.307977	−	0.951394i	$-0.599652\pi$
$19$	−22.7712	−	9.43215i	−1.19849	−	0.496429i	−0.890509	+	0.454965i	$0.849652\pi$
$20$		0			0
$21$	−11.7103	−	11.7103i	−0.557634	−	0.557634i
$22$	10.1865	+	6.80638i	0.463021	+	0.309381i
$23$	2.24740	−	11.2984i	0.0977131	−	0.491237i	−0.900676	−	0.434492i	$-0.856928\pi$
$23$	2.24740	−	11.2984i	0.0977131	−	0.491237i	0.998389	−	0.0567447i	$-0.0180721\pi$
$24$	−19.3829	−	29.0086i	−0.807622	−	1.20869i
$25$		0			0
$26$	−5.47615	+	2.26829i	−0.210621	+	0.0872421i
$27$	3.64922	+	5.46144i	0.135156	+	0.202276i
$28$	−3.54600	−	0.705343i	−0.126643	−	0.0251908i
$29$	−9.98767	−	6.67355i	−0.344402	−	0.230122i	0.371324	−	0.928504i	$-0.378904\pi$
$29$	−9.98767	−	6.67355i	−0.344402	−	0.230122i	−0.715726	+	0.698381i	$0.753904\pi$
$30$		0			0
$31$	7.38055	+	37.1045i	0.238082	+	1.19692i	0.896077	+	0.443898i	$0.146405\pi$
$31$	7.38055	+	37.1045i	0.238082	+	1.19692i	−0.657995	+	0.753022i	$0.728595\pi$
$32$	−12.8006	−	5.30218i	−0.400019	−	0.165693i
$33$	28.0839			0.851028
$34$	−4.46094	−	29.6778i	−0.131204	−	0.872878i
$35$		0			0
$36$	−6.02124	−	2.49408i	−0.167257	−	0.0692800i
$37$	6.29529	+	31.6486i	0.170143	+	0.855366i	0.967696	+	0.252118i	$0.0811272\pi$
$37$	6.29529	+	31.6486i	0.170143	+	0.855366i	−0.797554	+	0.603248i	$0.793873\pi$
$38$	30.7674	−	30.7674i	0.809669	−	0.809669i
$39$	−7.54883	+	11.2976i	−0.193560	+	0.289683i
$40$		0			0
$41$	18.7852	+	28.1140i	0.458175	+	0.685707i	0.986579	−	0.163286i	$-0.0522094\pi$
$41$	18.7852	+	28.1140i	0.458175	+	0.685707i	−0.528404	+	0.848993i	$0.677209\pi$
$42$	27.0106	−	11.1881i	0.643109	−	0.266384i
$43$	1.33189	+	3.21547i	0.0309742	+	0.0747784i	0.938610	−	0.344981i	$-0.112115\pi$
$43$	1.33189	+	3.21547i	0.0309742	+	0.0747784i	−0.907636	+	0.419759i	$0.862115\pi$
$44$	5.09783	−	3.40626i	0.115860	−	0.0774150i
$45$		0			0
$46$	16.9093	+	11.2984i	0.367594	+	0.245618i
$47$	−3.16735	−	3.16735i	−0.0673905	−	0.0673905i	0.672608	−	0.739999i	$-0.265174\pi$
$47$	−3.16735	−	3.16735i	−0.0673905	−	0.0673905i	−0.739999	+	0.672608i	$0.765174\pi$
$48$	46.3809	−	9.22573i	0.966268	−	0.192203i
$49$	−12.3427	+	29.7979i	−0.251892	+	0.608121i
$50$		0			0
$51$	−46.2992	−	50.8853i	−0.907827	−	0.997750i
$52$			2.96634i			0.0570451i
$53$	11.7603	−	28.3919i	0.221893	−	0.535697i	−0.773254	−	0.634096i	$-0.781372\pi$
$53$	11.7603	−	28.3919i	0.221893	−	0.535697i	0.995147	+	0.0983994i	$0.0313723\pi$
$54$	−11.3729	+	2.26220i	−0.210609	+	0.0418927i
$55$		0			0
$56$	19.6007	−	29.3345i	0.350012	−	0.523830i
$57$	19.4591	−	97.8275i	0.341388	−	1.71627i
$58$	17.6319	−	11.7813i	0.303998	−	0.203125i
$59$	4.49481	+	10.8514i	0.0761832	+	0.183923i	0.957383	−	0.288822i	$-0.0932635\pi$
$59$	4.49481	+	10.8514i	0.0761832	+	0.183923i	−0.881200	+	0.472744i	$0.843263\pi$
$60$		0			0
$61$	58.9263	−	39.3733i	0.966006	−	0.645464i	0.0307835	−	0.999526i	$-0.490200\pi$
$61$	58.9263	−	39.3733i	0.966006	−	0.645464i	0.935222	+	0.354062i	$0.115200\pi$
$62$	−65.5031	−	13.0294i	−1.05650	−	0.210151i
$63$	16.7718	−	25.1008i	0.266220	−	0.398426i
$64$	50.3473	−	50.3473i	0.786676	−	0.786676i
$65$		0			0
$66$	−18.9728	+	45.8045i	−0.287467	+	0.694008i
$67$	28.5842			0.426629			0.213315	−	0.976984i	$-0.431574\pi$
$67$	28.5842			0.426629			0.213315	+	0.976984i	$0.431574\pi$
$68$	−14.5761	−	3.62119i	−0.214354	−	0.0532528i
$69$	46.6187			0.675634
$70$		0			0
$71$	−33.7056	+	6.70446i	−0.474726	+	0.0944290i	−0.426654	−	0.904415i	$-0.640308\pi$
$71$	−33.7056	+	6.70446i	−0.474726	+	0.0944290i	−0.0480724	+	0.998844i	$0.515308\pi$
$72$	44.9700	−	44.9700i	0.624584	−	0.624584i
$73$	−77.8880	−	52.0431i	−1.06696	−	0.712919i	−0.107340	−	0.994222i	$-0.534233\pi$
$73$	−77.8880	−	52.0431i	−1.06696	−	0.712919i	−0.959619	+	0.281303i	$0.909233\pi$
$74$	−55.8713	−	11.1135i	−0.755018	−	0.150182i
$75$		0			0
$76$	−8.33312	−	20.1179i	−0.109646	−	0.264710i
$77$	10.8680	+	26.2377i	0.141143	+	0.340749i
$78$	−13.3265	−	19.9444i	−0.170852	−	0.255698i
$79$	−4.18708	+	21.0499i	−0.0530011	+	0.266454i	−0.998195	−	0.0600549i	$-0.980872\pi$
$79$	−4.18708	+	21.0499i	−0.0530011	+	0.266454i	0.945194	+	0.326509i	$0.105872\pi$
$80$		0			0
$81$	−65.7422	+	65.7422i	−0.811632	+	0.811632i
$82$	−58.5443	+	11.6452i	−0.713955	+	0.142015i
$83$	104.903	+	43.4522i	1.26389	+	0.523521i	0.911102	−	0.412182i	$-0.135233\pi$
$83$	104.903	+	43.4522i	1.26389	+	0.523521i	0.352789	+	0.935703i	$0.385233\pi$
$84$		−	14.6312i		−	0.174181i
$85$		0			0
$86$	−6.14419			−0.0714440
$87$	18.6026	−	44.9106i	0.213823	−	0.516214i
$88$	11.6719	+	58.6787i	0.132635	+	0.666803i
$89$	28.3238	+	28.3238i	0.318245	+	0.318245i	0.848093	−	0.529848i	$-0.177751\pi$
$89$	28.3238	+	28.3238i	0.318245	+	0.318245i	−0.529848	+	0.848093i	$0.677751\pi$
$90$		0			0
$91$	−13.4762	−	2.68058i	−0.148090	−	0.0294569i
$92$	8.46229	−	5.65432i	0.0919814	−	0.0614600i
$93$	−141.444	+	58.5880i	−1.52090	+	0.629978i
$94$	7.30570	−	3.02612i	0.0777202	−	0.0321928i
$95$		0			0
$96$	10.9387	−	54.9926i	0.113945	−	0.572840i
$97$	−92.4136	+	138.307i	−0.952718	+	1.42584i	−0.0484747	+	0.998824i	$0.515436\pi$
$97$	−92.4136	+	138.307i	−0.952718	+	1.42584i	−0.904243	+	0.427018i	$0.859564\pi$
$98$	−40.2616	−	40.2616i	−0.410833	−	0.410833i
$99$	9.98738	+	50.2100i	0.100883	+	0.507171i
$100$		0			0
$101$		−	124.444i		−	1.23211i	−0.787701	−	0.616057i	$-0.788729\pi$
$101$		−	124.444i		−	1.23211i	0.787701	−	0.616057i	$-0.211271\pi$
$102$	114.272	−	41.1364i	1.12031	−	0.403298i
$103$			175.084i			1.69984i	0.526908	+	0.849922i	$0.323351\pi$
$103$			175.084i			1.69984i	−0.526908	+	0.849922i	$0.676649\pi$
$104$	−26.7427	−	11.0772i	−0.257141	−	0.106511i
$105$		0			0
$106$	38.3619	+	38.3619i	0.361904	+	0.361904i
$107$	−33.1477	−	22.1486i	−0.309791	−	0.206996i	0.390949	−	0.920412i	$-0.372147\pi$
$107$	−33.1477	−	22.1486i	−0.309791	−	0.206996i	−0.700740	+	0.713416i	$0.747147\pi$
$108$	−1.13212	+	5.69157i	−0.0104826	+	0.0526997i
$109$	25.4604	+	38.1042i	0.233582	+	0.349580i	0.929681	−	0.368366i	$-0.120083\pi$
$109$	25.4604	+	38.1042i	0.233582	+	0.349580i	−0.696099	+	0.717946i	$0.745083\pi$
$110$		0			0
$111$	−120.645	+	49.9730i	−1.08690	+	0.450207i
$112$	26.5678	+	39.7615i	0.237213	+	0.355014i
$113$	−183.644	−	36.5291i	−1.62517	−	0.323267i	−0.703338	−	0.710855i	$-0.748308\pi$
$113$	−183.644	−	36.5291i	−1.62517	−	0.323267i	−0.921832	+	0.387589i	$0.873308\pi$
$114$	146.409	+	97.8275i	1.28429	+	0.858136i
$115$		0			0
$116$	−2.07038	−	10.4085i	−0.0178481	−	0.0897285i
$117$	−22.8831	−	9.47847i	−0.195582	−	0.0810126i
$118$	−20.7351			−0.175721
$119$	29.6230	−	62.9471i	0.248933	−	0.528967i
$120$		0			0
$121$	67.2956	+	27.8748i	0.556162	+	0.230370i
$122$	24.4081	+	122.708i	0.200066	+	1.00580i
$123$	−96.7557	+	96.7557i	−0.786632	+	0.786632i
$124$	−18.5690	+	27.7905i	−0.149750	+	0.224117i
$125$		0			0
$126$	29.6084	+	44.3122i	0.234988	+	0.351684i
$127$	−37.9454	+	15.7175i	−0.298783	+	0.123760i	−0.527039	−	0.849841i	$-0.676698\pi$
$127$	−37.9454	+	15.7175i	−0.298783	+	0.123760i	0.228256	+	0.973601i	$0.426698\pi$
$128$	26.8936	+	64.9268i	0.210106	+	0.507241i
$129$	−11.7109	+	7.82500i	−0.0907825	+	0.0606589i
$130$		0			0
$131$	160.044	+	106.938i	1.22171	+	0.816323i	0.987769	−	0.155927i	$-0.0498366\pi$
$131$	160.044	+	106.938i	1.22171	+	0.816323i	0.233944	+	0.972250i	$0.424837\pi$
$132$	17.5444	+	17.5444i	0.132912	+	0.132912i
$133$	98.9266	−	19.6777i	0.743809	−	0.147953i
$134$	−19.3108	+	46.6204i	−0.144110	+	0.347913i
$135$		0			0
$136$	87.0776	−	117.886i	0.640276	−	0.866809i
$137$		−	52.8361i		−	0.385665i	−0.981232	−	0.192832i	$-0.938233\pi$
$137$		−	52.8361i		−	0.385665i	0.981232	−	0.192832i	$-0.0617674\pi$
$138$	−31.4945	+	76.0345i	−0.228221	+	0.550975i
$139$	51.4676	−	10.2376i	0.370271	−	0.0736514i	−0.00644773	−	0.999979i	$-0.502052\pi$
$139$	51.4676	−	10.2376i	0.370271	−	0.0736514i	0.376719	+	0.926328i	$0.377052\pi$
$140$		0			0
$141$	10.0709	−	15.0721i	0.0714245	−	0.106894i
$142$	11.8358	−	59.5027i	0.0833509	−	0.419033i
$143$	19.3737	−	12.9451i	0.135481	−	0.0905253i
$144$	32.9885	+	79.6413i	0.229087	+	0.553064i
$145$		0			0
$146$	137.501	−	91.8752i	0.941787	−	0.629282i
$147$	−128.015	−	25.4638i	−0.870850	−	0.173223i
$148$	−15.8386	+	23.7041i	−0.107017	+	0.160163i
$149$	−36.5973	+	36.5973i	−0.245620	+	0.245620i	−0.819170	−	0.573551i	$-0.805566\pi$
$149$	−36.5973	+	36.5973i	−0.245620	+	0.245620i	0.573551	+	0.819170i	$0.305566\pi$
$150$		0			0
$151$	−91.9670	+	222.028i	−0.609053	+	1.47038i	0.254979	+	0.966947i	$0.417931\pi$
$151$	−91.9670	+	222.028i	−0.609053	+	1.47038i	−0.864032	+	0.503437i	$0.832069\pi$
$152$	212.489			1.39795
$153$	74.5102	−	100.872i	0.486995	−	0.659296i
$154$	−50.1354			−0.325555
$155$		0			0
$156$	−11.7737	+	2.34193i	−0.0754721	+	0.0150123i
$157$	−190.153	+	190.153i	−1.21117	+	1.21117i	−0.240522	+	0.970644i	$0.577319\pi$
$157$	−190.153	+	190.153i	−1.21117	+	1.21117i	−0.970644	+	0.240522i	$0.922681\pi$
$158$	−31.5034	−	21.0499i	−0.199389	−	0.133227i
$159$	121.975	+	24.2623i	0.767136	+	0.152593i
$160$		0			0
$161$	18.0406	+	43.5540i	0.112054	+	0.270522i
$162$	−62.8107	−	151.638i	−0.387720	−	0.936040i
$163$	21.5571	+	32.2626i	0.132252	+	0.197930i	0.891685	−	0.452656i	$-0.149523\pi$
$163$	21.5571	+	32.2626i	0.132252	+	0.197930i	−0.759433	+	0.650586i	$0.774523\pi$
$164$	−5.82785	+	29.2986i	−0.0355357	+	0.178650i
$165$		0			0
$166$	−141.740	+	141.740i	−0.853855	+	0.853855i
$167$	35.3355	−	7.02867i	0.211590	−	0.0420878i	−0.0881571	−	0.996107i	$-0.528098\pi$
$167$	35.3355	−	7.02867i	0.211590	−	0.0420878i	0.299747	+	0.954019i	$0.403098\pi$
$168$	131.906	+	54.6371i	0.785152	+	0.325221i
$169$		−	157.727i		−	0.933294i
$170$		0			0
$171$	181.821			1.06328
$172$	−1.17670	+	2.84081i	−0.00684128	+	0.0165163i
$173$	−37.6555	−	189.307i	−0.217662	−	1.09426i	−0.922827	−	0.385215i	$-0.874127\pi$
$173$	−37.6555	−	189.307i	−0.217662	−	1.09426i	0.705165	−	0.709043i	$-0.250873\pi$
$174$	60.6811	+	60.6811i	0.348742	+	0.348742i
$175$		0			0
$176$	−79.5362	−	15.8207i	−0.451910	−	0.0898905i
$177$	−39.5216	+	26.4075i	−0.223286	+	0.149195i
$178$	−65.3307	+	27.0608i	−0.367026	+	0.152027i
$179$	−223.947	+	92.7619i	−1.25110	+	0.518223i	−0.907167	−	0.420771i	$-0.861759\pi$
$179$	−223.947	+	92.7619i	−1.25110	+	0.518223i	−0.343933	+	0.938994i	$0.611759\pi$
$180$		0			0
$181$	−26.6333	+	133.895i	−0.147146	+	0.739750i	0.834795	+	0.550561i	$0.185586\pi$
$181$	−26.6333	+	133.895i	−0.147146	+	0.739750i	−0.981941	+	0.189190i	$0.939414\pi$
$182$	13.4762	−	20.1685i	0.0740449	−	0.110816i
$183$	202.798	+	202.798i	1.10819	+	1.10819i
$184$	19.3751	+	97.4054i	0.105300	+	0.529377i
$185$		0			0
$186$		−	270.274i		−	1.45308i
$187$	39.9593	+	111.002i	0.213686	+	0.593593i
$188$		−	3.95738i		−	0.0210499i
$189$	−24.8339	−	10.2865i	−0.131396	−	0.0544260i
$190$		0			0
$191$	123.244	+	123.244i	0.645254	+	0.645254i	0.951842	−	0.306588i	$-0.0991874\pi$
$191$	123.244	+	123.244i	0.645254	+	0.645254i	−0.306588	+	0.951842i	$0.599187\pi$
$192$	239.581	+	160.083i	1.24782	+	0.833767i
$193$	36.6126	−	184.064i	0.189703	−	0.953700i	−0.762210	−	0.647330i	$-0.775886\pi$
$193$	36.6126	−	184.064i	0.189703	−	0.953700i	0.951913	−	0.306370i	$-0.0991144\pi$
$194$	−163.144	−	244.162i	−0.840948	−	1.25857i
$195$		0			0
$196$	−26.3259	+	10.9045i	−0.134316	+	0.0556354i
$197$	−159.522	−	238.742i	−0.809759	−	1.21189i	−0.974241	−	0.225509i	$-0.927595\pi$
$197$	−159.522	−	238.742i	−0.809759	−	1.21189i	0.164482	−	0.986380i	$-0.447405\pi$
$198$	−88.6390	−	17.6314i	−0.447672	−	0.0890474i
$199$	76.1598	+	50.8883i	0.382712	+	0.255720i	0.732013	−	0.681290i	$-0.238581\pi$
$199$	76.1598	+	50.8883i	0.382712	+	0.255720i	−0.349301	+	0.937011i	$0.613581\pi$
$200$		0			0
$201$	22.5672	+	113.453i	0.112274	+	0.564442i
$202$	202.966	+	84.0712i	1.00478	+	0.416194i
$203$	49.1570			0.242153
$204$	2.86499	−	60.7125i	0.0140441	−	0.297610i
$205$		0			0
$206$	−285.560	−	118.283i	−1.38621	−	0.574188i
$207$	16.5788	+	83.3475i	0.0800911	+	0.402645i
$208$	27.7433	−	27.7433i	0.133381	−	0.133381i
$209$	−95.0281	+	142.220i	−0.454680	+	0.680477i
$210$		0			0
$211$	20.0890	+	30.0653i	0.0952086	+	0.142490i	0.876016	−	0.482282i	$-0.160192\pi$
$211$	20.0890	+	30.0653i	0.0952086	+	0.142490i	−0.780807	+	0.624772i	$0.785192\pi$
$212$	25.0837	−	10.3900i	0.118319	−	0.0490095i
$213$	−53.2210	−	128.487i	−0.249864	−	0.603225i
$214$	58.5178	−	39.1003i	0.273448	−	0.182712i
$215$		0			0
$216$	−47.0838	−	31.4604i	−0.217981	−	0.145650i
$217$	−109.473	−	109.473i	−0.504482	−	0.504482i
$218$	−79.3479	+	15.7833i	−0.363981	+	0.0724004i
$219$	145.071	−	350.232i	0.662423	−	1.59923i
$220$		0			0
$221$	−55.3948	−	13.7619i	−0.250655	−	0.0622712i
$222$		−	230.532i		−	1.03843i
$223$	−154.260	+	372.417i	−0.691750	+	1.67003i	0.0494759	+	0.998775i	$0.484245\pi$
$223$	−154.260	+	372.417i	−0.691750	+	1.67003i	−0.741226	+	0.671256i	$0.765755\pi$
$224$	55.6104	−	11.0616i	0.248261	−	0.0493822i
$225$		0			0
$226$	183.644	−	274.843i	0.812585	−	1.21612i
$227$	24.6288	−	123.817i	0.108497	−	0.545450i	−0.887856	−	0.460121i	$-0.847806\pi$
$227$	24.6288	−	123.817i	0.108497	−	0.545450i	0.996353	−	0.0853288i	$-0.0271941\pi$
$228$	73.2707	−	48.9579i	0.321363	−	0.214728i
$229$	47.0477	+	113.583i	0.205449	+	0.495997i	0.992696	−	0.120640i	$-0.0384947\pi$
$229$	47.0477	+	113.583i	0.205449	+	0.495997i	−0.787248	+	0.616637i	$0.788495\pi$
$230$		0			0
$231$	−95.5591	+	63.8505i	−0.413676	+	0.276409i
$232$	101.568	+	20.2031i	0.437792	+	0.0870823i
$233$	−33.4139	+	50.0074i	−0.143407	+	0.214624i	−0.896219	−	0.443612i	$-0.853697\pi$
$233$	−33.4139	+	50.0074i	−0.143407	+	0.214624i	0.752812	+	0.658236i	$0.228697\pi$
$234$	30.9185	−	30.9185i	0.132130	−	0.132130i
$235$		0			0
$236$	−3.97107	+	9.58702i	−0.0168266	+	0.0406230i
$237$	−86.8544			−0.366474
$238$	82.6533	+	90.8404i	0.347283	+	0.381682i
$239$	285.920			1.19632			0.598160	−	0.801377i	$-0.295899\pi$
$239$	285.920			1.19632			0.598160	+	0.801377i	$0.295899\pi$
$240$		0			0
$241$	121.946	−	24.2566i	0.506002	−	0.100650i	0.0645131	−	0.997917i	$-0.479451\pi$
$241$	121.946	−	24.2566i	0.506002	−	0.100650i	0.441489	+	0.897267i	$0.354451\pi$
$242$	−90.9267	+	90.9267i	−0.375730	+	0.375730i
$243$	−263.686	−	176.189i	−1.08513	−	0.725060i
$244$	61.4092	+	12.2151i	0.251677	+	0.0500617i
$245$		0			0
$246$	−92.4414	−	223.173i	−0.375778	−	0.907208i
$247$	−31.6691	−	76.4560i	−0.128215	−	0.309538i
$248$	−181.199	−	271.184i	−0.730642	−	1.09348i
$249$	−89.6446	+	450.674i	−0.360018	+	1.80993i
$250$		0			0
$251$	−99.6747	+	99.6747i	−0.397110	+	0.397110i	−0.877213	−	0.480102i	$-0.840600\pi$
$251$	−99.6747	+	99.6747i	−0.397110	+	0.397110i	0.480102	+	0.877213i	$0.340600\pi$
$252$	26.1585	−	5.20324i	0.103803	−	0.0206478i
$253$	−73.8588	−	30.5933i	−0.291932	−	0.120922i
$254$		−	72.5069i		−	0.285460i
$255$		0			0
$256$	160.744			0.627906
$257$	150.400	−	363.098i	0.585214	−	1.41283i	−0.302818	−	0.953048i	$-0.597927\pi$
$257$	150.400	−	363.098i	0.585214	−	1.41283i	0.888032	−	0.459783i	$-0.152073\pi$
$258$	−4.85083	−	24.3868i	−0.0188017	−	0.0945224i
$259$	−93.3754	−	93.3754i	−0.360523	−	0.360523i
$260$		0			0
$261$	86.9092	+	17.2873i	0.332985	+	0.0662349i
$262$	−282.537	+	188.785i	−1.07839	+	0.720554i
$263$	269.286	−	111.542i	1.02390	−	0.424113i	0.193393	−	0.981121i	$-0.438051\pi$
$263$	269.286	−	111.542i	1.02390	−	0.424113i	0.830507	+	0.557008i	$0.188051\pi$
$264$	−223.685	+	92.6535i	−0.847293	+	0.350960i
$265$		0			0
$266$	−34.7384	+	174.642i	−0.130595	+	0.656548i
$267$	−90.0578	+	134.781i	−0.337295	+	0.504798i
$268$	17.8569	+	17.8569i	0.0666304	+	0.0666304i
$269$	−19.8781	−	99.9342i	−0.0738965	−	0.371503i	0.926087	−	0.377311i	$-0.123151\pi$
$269$	−19.8781	−	99.9342i	−0.0738965	−	0.371503i	−0.999983	+	0.00580827i	$0.998151\pi$
$270$		0			0
$271$		−	381.059i		−	1.40612i	−0.711129	−	0.703061i	$-0.751816\pi$
$271$		−	381.059i		−	1.40612i	0.711129	−	0.703061i	$-0.248184\pi$
$272$	102.458	+	170.194i	0.376683	+	0.625712i
$273$		−	55.6043i		−	0.203679i
$274$	86.1749	+	35.6948i	0.314507	+	0.130273i
$275$		0			0
$276$	29.1234	+	29.1234i	0.105520	+	0.105520i
$277$	55.8881	+	37.3432i	0.201762	+	0.134813i	0.652347	−	0.757920i	$-0.273785\pi$
$277$	55.8881	+	37.3432i	0.201762	+	0.134813i	−0.450585	+	0.892734i	$0.648785\pi$
$278$	−18.0730	+	90.8593i	−0.0650109	+	0.326832i
$279$	−155.048	−	232.046i	−0.555727	−	0.831705i
$280$		0			0
$281$	−348.356	+	144.294i	−1.23970	+	0.513501i	−0.903621	−	0.428333i	$-0.859101\pi$
$281$	−348.356	+	144.294i	−1.23970	+	0.513501i	−0.336079	+	0.941834i	$0.609101\pi$
$282$	17.7788	+	26.6078i	0.0630452	+	0.0943539i
$283$	291.125	+	57.9083i	1.02871	+	0.204623i	0.680465	−	0.732781i	$-0.261778\pi$
$283$	291.125	+	57.9083i	1.02871	+	0.204623i	0.348245	+	0.937404i	$0.386778\pi$
$284$	−25.2447	−	16.8680i	−0.0888899	−	0.0593944i
$285$		0			0
$286$	8.02486	+	40.3437i	0.0280590	+	0.141062i
$287$	−127.838	−	52.9521i	−0.445428	−	0.184502i
$288$	102.209			0.354892
$289$	135.247	−	255.400i	0.467984	−	0.883737i
$290$		0			0
$291$	−621.911	−	257.604i	−2.13715	−	0.885237i
$292$	−16.1457	−	81.1699i	−0.0552935	−	0.277979i
$293$	−99.8472	+	99.8472i	−0.340776	+	0.340776i	−0.856659	−	0.515883i	$-0.827464\pi$
$293$	−99.8472	+	99.8472i	−0.340776	+	0.340776i	0.515883	+	0.856659i	$0.327464\pi$
$294$	128.015	−	191.588i	0.435425	−	0.651660i
$295$		0			0
$296$	−154.555	−	231.308i	−0.522146	−	0.781446i
$297$	42.1132	−	17.4439i	0.141795	−	0.0587336i
$298$	−34.9654	−	84.4140i	−0.117334	−	0.283269i
$299$	32.1600	−	21.4886i	0.107559	−	0.0718683i
$300$		0			0
$301$	−11.8425	−	7.91291i	−0.0393439	−	0.0262887i
$302$	−299.994	−	299.994i	−0.993357	−	0.993357i
$303$	493.926	−	98.2481i	1.63012	−	0.324251i
$304$	−110.220	+	266.094i	−0.362565	+	0.875310i
$305$		0			0
$306$	114.184	+	189.672i	0.373150	+	0.619843i
$307$			259.641i			0.845735i	0.906192	+	0.422868i	$0.138976\pi$
$307$			259.641i			0.845735i	−0.906192	+	0.422868i	$0.861024\pi$
$308$	−9.60165	+	23.1804i	−0.0311742	+	0.0752612i
$309$	−694.922	+	138.229i	−2.24894	+	0.447342i
$310$		0			0
$311$	313.413	−	469.055i	1.00776	−	1.50822i	0.153646	−	0.988126i	$-0.450898\pi$
$311$	313.413	−	469.055i	1.00776	−	1.50822i	0.854112	−	0.520090i	$-0.174102\pi$
$312$	22.8529	−	114.889i	0.0732464	−	0.368234i
$313$	378.950	−	253.206i	1.21070	−	0.808966i	0.224495	−	0.974475i	$-0.427927\pi$
$313$	378.950	−	253.206i	1.21070	−	0.808966i	0.986208	+	0.165509i	$0.0529267\pi$
$314$	−181.674	−	438.600i	−0.578580	−	1.39681i
$315$		0			0
$316$	−15.7659	+	10.5344i	−0.0498921	+	0.0333368i
$317$	325.560	+	64.7580i	1.02700	+	0.204284i	0.679717	−	0.733475i	$-0.262103\pi$
$317$	325.560	+	64.7580i	1.02700	+	0.204284i	0.347288	+	0.937759i	$0.387103\pi$
$318$	−121.975	+	182.548i	−0.383568	+	0.574050i
$319$	−58.9447	+	58.9447i	−0.184780	+	0.184780i
$320$		0			0
$321$	61.7394	−	149.052i	0.192334	−	0.464336i
$322$	−83.2238			−0.258459
$323$	414.351	−	62.2820i	1.28282	−	0.192823i
$324$	−82.1402			−0.253519
$325$		0			0
$326$	−67.1833	+	13.3636i	−0.206084	+	0.0409926i
$327$	−131.138	+	131.138i	−0.401033	+	0.401033i
$328$	−242.374	−	161.949i	−0.738946	−	0.493748i
$329$	17.9785	+	3.57614i	0.0546459	+	0.0108697i
$330$		0			0
$331$	225.594	+	544.633i	0.681554	+	1.64542i	0.761139	+	0.648588i	$0.224640\pi$
$331$	225.594	+	544.633i	0.681554	+	1.64542i	−0.0795855	+	0.996828i	$0.525360\pi$
$332$	38.3892	+	92.6796i	0.115630	+	0.279156i
$333$	−132.249	−	197.925i	−0.397145	−	0.594369i
$334$	−12.4082	+	62.3801i	−0.0371502	+	0.186767i
$335$		0			0
$336$	−136.841	+	136.841i	−0.407266	+	0.407266i
$337$	321.295	−	63.9095i	0.953397	−	0.189642i	0.306202	−	0.951967i	$-0.400942\pi$
$337$	321.295	−	63.9095i	0.953397	−	0.189642i	0.647195	+	0.762324i	$0.275942\pi$
$338$	257.250	+	106.557i	0.761095	+	0.315256i
$339$		−	757.738i		−	2.23522i
$340$		0			0
$341$	262.540			0.769911
$342$	−122.834	+	296.548i	−0.359165	+	0.867100i
$343$	−64.8699	−	326.123i	−0.189125	−	0.950796i
$344$	−21.2167	−	21.2167i	−0.0616766	−	0.0616766i
$345$		0			0
$346$	334.196	+	66.4757i	0.965884	+	0.192126i
$347$	201.268	−	134.483i	0.580024	−	0.387560i	−0.230668	−	0.973033i	$-0.574091\pi$
$347$	201.268	−	134.483i	0.580024	−	0.387560i	0.810692	+	0.585473i	$0.199091\pi$
$348$	39.6776	−	16.4350i	0.114016	−	0.0472270i
$349$	−464.685	+	192.479i	−1.33148	+	0.551515i	−0.931076	−	0.364826i	$-0.881129\pi$
$349$	−464.685	+	192.479i	−1.33148	+	0.551515i	−0.400399	+	0.916341i	$0.631129\pi$
$350$		0			0
$351$	−4.30251	+	21.6302i	−0.0122579	+	0.0616244i
$352$	−53.4190	+	79.9472i	−0.151759	+	0.227123i
$353$	−231.294	−	231.294i	−0.655223	−	0.655223i	0.299023	−	0.954246i	$-0.403339\pi$
$353$	−231.294	−	231.294i	−0.655223	−	0.655223i	−0.954246	+	0.299023i	$0.903339\pi$
$354$	−16.3704	−	82.2994i	−0.0462440	−	0.232484i
$355$		0			0
$356$			35.3886i			0.0994062i
$357$	273.230	+	67.8794i	0.765349	+	0.190138i
$358$		−	427.922i		−	1.19531i
$359$	490.942	+	203.355i	1.36753	+	0.566448i	0.941117	−	0.338082i	$-0.109778\pi$
$359$	490.942	+	203.355i	1.36753	+	0.566448i	0.426410	+	0.904530i	$0.359778\pi$
$360$		0			0
$361$	174.298	+	174.298i	0.482820	+	0.482820i
$362$	−200.388	−	133.895i	−0.553557	−	0.369875i
$363$	−57.5073	+	289.109i	−0.158422	+	0.796443i
$364$	−6.74416	−	10.0934i	−0.0185279	−	0.0277290i
$365$		0			0
$366$	−467.767	+	193.755i	−1.27805	+	0.529386i
$367$	183.923	+	275.260i	0.501152	+	0.750026i	0.992672	−	0.120840i	$-0.0385587\pi$
$367$	183.923	+	275.260i	0.501152	+	0.750026i	−0.491520	+	0.870866i	$0.663559\pi$
$368$	−132.028	−	26.2621i	−0.358773	−	0.0713644i
$369$	−207.394	−	138.576i	−0.562043	−	0.375545i
$370$		0			0
$371$	24.5348	+	123.345i	0.0661316	+	0.332466i
$372$	−124.963	−	51.7613i	−0.335922	−	0.139143i
$373$	147.856			0.396396			0.198198	−	0.980162i	$-0.436491\pi$
$373$	147.856			0.396396			0.198198	+	0.980162i	$0.436491\pi$
$374$	−208.038	−	9.81721i	−0.556252	−	0.0262492i
$375$		0			0
$376$	35.6772	+	14.7780i	0.0948863	+	0.0393032i
$377$	−7.86825	−	39.5564i	−0.0208707	−	0.104924i
$378$	33.5543	−	33.5543i	0.0887681	−	0.0887681i
$379$	−24.2695	+	36.3219i	−0.0640357	+	0.0958362i	−0.862106	−	0.506729i	$-0.830855\pi$
$379$	−24.2695	+	36.3219i	−0.0640357	+	0.0958362i	0.798070	+	0.602565i	$0.205855\pi$
$380$		0			0
$381$	−92.3419	−	138.199i	−0.242367	−	0.362728i
$382$	−284.269	+	117.748i	−0.744160	+	0.308241i
$383$	75.6230	+	182.570i	0.197449	+	0.476684i	0.991331	−	0.131387i	$-0.0419432\pi$
$383$	75.6230	+	182.570i	0.197449	+	0.476684i	−0.793882	+	0.608072i	$0.791943\pi$
$384$	−236.467	+	158.002i	−0.615800	+	0.411464i
$385$		0			0
$386$	275.471	+	184.064i	0.713656	+	0.476850i
$387$	−18.1547	−	18.1547i	−0.0469113	−	0.0469113i
$388$	−144.134	+	28.6701i	−0.371480	+	0.0738920i
$389$	−8.22534	+	19.8577i	−0.0211448	+	0.0510481i	−0.934099	−	0.357013i	$-0.883795\pi$
$389$	−8.22534	+	19.8577i	−0.0211448	+	0.0510481i	0.912954	+	0.408061i	$0.133795\pi$
$390$		0			0
$391$	66.3316	+	184.261i	0.169646	+	0.471255i
$392$		−	278.058i		−	0.709332i
$393$	−298.092	+	719.657i	−0.758503	+	1.83119i
$394$	497.155	−	98.8903i	1.26181	−	0.250991i
$395$		0			0
$396$	−25.1276	+	37.6062i	−0.0634536	+	0.0949650i
$397$	−6.92123	+	34.7954i	−0.0174338	+	0.0876457i	−0.988523	−	0.151073i	$-0.951727\pi$
$397$	−6.92123	+	34.7954i	−0.0174338	+	0.0876457i	0.971089	+	0.238718i	$0.0767273\pi$
$398$	−134.450	+	89.8366i	−0.337814	+	0.225720i
$399$	156.205	+	377.112i	0.391491	+	0.945142i
$400$		0			0
$401$	−124.358	+	83.0937i	−0.310121	+	0.207216i	−0.700884	−	0.713275i	$-0.747211\pi$
$401$	−124.358	+	83.0937i	−0.310121	+	0.207216i	0.390763	+	0.920491i	$0.372211\pi$
$402$	−200.286	−	39.8393i	−0.498224	−	0.0991028i
$403$	−70.5695	+	105.615i	−0.175110	+	0.262071i
$404$	77.7417	−	77.7417i	0.192430	−	0.192430i
$405$		0			0
$406$	−33.2093	+	80.1744i	−0.0817964	+	0.197474i
$407$	223.935			0.550209
$408$	536.647	+	252.547i	1.31531	+	0.618987i
$409$	398.892			0.975287			0.487643	−	0.873043i	$-0.337857\pi$
$409$	398.892			0.975287			0.487643	+	0.873043i	$0.337857\pi$
$410$		0			0
$411$	209.711	−	41.7140i	0.510245	−	0.101494i
$412$	−109.378	+	109.378i	−0.265479	+	0.265479i
$413$	−39.9656	−	26.7041i	−0.0967689	−	0.0646589i
$414$	−147.139	−	29.2678i	−0.355408	−	0.0706951i
$415$		0			0
$416$	−17.8024	−	42.9789i	−0.0427943	−	0.103315i
$417$	81.2673	+	196.197i	0.194886	+	0.470496i
$418$	−167.760	−	251.070i	−0.401339	−	0.600646i
$419$	−7.29632	+	36.6811i	−0.0174137	+	0.0875444i	−0.988515	−	0.151124i	$-0.951711\pi$
$419$	−7.29632	+	36.6811i	−0.0174137	+	0.0875444i	0.971101	+	0.238668i	$0.0767108\pi$
$420$		0			0
$421$	312.706	−	312.706i	0.742769	−	0.742769i	−0.230341	−	0.973110i	$-0.573984\pi$
$421$	312.706	−	312.706i	0.742769	−	0.742769i	0.973110	+	0.230341i	$0.0739841\pi$
$422$	−62.6078	+	12.4535i	−0.148360	+	0.0295106i
$423$	30.5282	+	12.6452i	0.0721706	+	0.0298941i
$424$			264.938i			0.624853i
$425$		0			0
$426$	245.515			0.576327
$427$	−110.987	+	267.945i	−0.259922	+	0.627507i
$428$	−6.87130	−	34.5444i	−0.0160544	−	0.0807111i
$429$	66.6757	+	66.6757i	0.155421	+	0.155421i
$430$		0			0
$431$	−340.230	−	67.6760i	−0.789397	−	0.157021i	−0.216103	−	0.976371i	$-0.569335\pi$
$431$	−340.230	−	67.6760i	−0.789397	−	0.157021i	−0.573294	+	0.819350i	$0.694335\pi$
$432$	63.8199	−	42.6431i	0.147731	−	0.0987109i
$433$	49.6556	−	20.5680i	0.114678	−	0.0475012i	−0.324607	−	0.945849i	$-0.605232\pi$
$433$	49.6556	−	20.5680i	0.114678	−	0.0475012i	0.439285	+	0.898348i	$0.355232\pi$
$434$	252.506	−	104.591i	0.581810	−	0.240994i
$435$		0			0
$436$	−7.89876	+	39.7098i	−0.0181164	+	0.0910774i
$437$	−157.745	+	236.082i	−0.360972	+	0.540233i
$438$	473.217	+	473.217i	1.08040	+	1.08040i
$439$	−47.4571	−	238.583i	−0.108103	−	0.543469i	−0.996442	−	0.0842815i	$-0.973140\pi$
$439$	−47.4571	−	238.583i	−0.108103	−	0.543469i	0.888339	−	0.459188i	$-0.151860\pi$
$440$		0			0
$441$		−	237.928i		−	0.539518i
$442$	59.8690	−	81.0509i	0.135450	−	0.183373i
$443$		−	114.592i		−	0.258673i	−0.991601	−	0.129336i	$-0.958715\pi$
$443$		−	114.592i		−	0.258673i	0.991601	−	0.129336i	$-0.0412847\pi$
$444$	−106.588	−	44.1501i	−0.240063	−	0.0994373i
$445$		0			0
$446$	−503.192	−	503.192i	−1.12823	−	1.12823i
$447$	−174.151	−	116.364i	−0.389600	−	0.260322i
$448$	−56.8453	+	285.780i	−0.126887	+	0.637903i
$449$	301.785	+	451.653i	0.672127	+	1.00591i	0.998165	+	0.0605527i	$0.0192863\pi$
$449$	301.785	+	451.653i	0.672127	+	1.00591i	−0.326038	+	0.945357i	$0.605714\pi$
$450$		0			0
$451$	216.787	−	89.7961i	0.480681	−	0.199104i
$452$	−91.9050	−	137.546i	−0.203330	−	0.304304i
$453$	−953.854	−	189.733i	−2.10564	−	0.418838i
$454$	185.305	+	123.817i	0.408162	+	0.272725i
$455$		0			0
$456$	167.760	+	843.384i	0.367894	+	1.84953i
$457$	207.434	+	85.9222i	0.453905	+	0.188014i	0.597910	−	0.801563i	$-0.295998\pi$
$457$	207.434	+	85.9222i	0.453905	+	0.188014i	−0.144005	+	0.989577i	$0.545998\pi$
$458$	−217.037			−0.473880
$459$	−101.034	−	47.5470i	−0.220119	−	0.103588i
$460$		0			0
$461$	−233.070	−	96.5408i	−0.505575	−	0.209416i	0.115292	−	0.993332i	$-0.463219\pi$
$461$	−233.070	−	96.5408i	−0.505575	−	0.209416i	−0.620867	+	0.783916i	$0.713219\pi$
$462$	−39.5819	−	198.991i	−0.0856750	−	0.430717i
$463$	−88.6506	+	88.6506i	−0.191470	+	0.191470i	−0.796331	−	0.604861i	$-0.793229\pi$
$463$	−88.6506	+	88.6506i	−0.191470	+	0.191470i	0.604861	+	0.796331i	$0.293229\pi$
$464$	−77.9840	+	116.711i	−0.168069	+	0.251533i
$465$		0			0
$466$	−58.9878	−	88.2815i	−0.126583	−	0.189445i
$467$	640.133	−	265.152i	1.37074	−	0.567777i	0.428748	−	0.903424i	$-0.358955\pi$
$467$	640.133	−	265.152i	1.37074	−	0.567777i	0.941988	+	0.335647i	$0.108955\pi$
$468$	−8.37404	−	20.2167i	−0.0178932	−	0.0431981i
$469$	−97.2612	+	64.9879i	−0.207380	+	0.138567i
$470$		0			0
$471$	−904.858	−	604.607i	−1.92114	−	1.28367i
$472$	−71.6013	−	71.6013i	−0.151698	−	0.151698i
$473$	23.6889	−	4.71202i	0.0500823	−	0.00996199i
$474$	58.6768	−	141.658i	0.123791	−	0.298857i
$475$		0			0
$476$	57.8299	−	20.8181i	0.121491	−	0.0437354i
$477$			226.701i			0.475264i
$478$	−193.161	+	466.332i	−0.404103	+	0.975591i
$479$	−469.496	+	93.3885i	−0.980158	+	0.194965i	−0.659068	−	0.752083i	$-0.729049\pi$
$479$	−469.496	+	93.3885i	−0.980158	+	0.194965i	−0.321090	+	0.947049i	$0.604049\pi$
$480$		0			0
$481$	−60.1927	+	90.0847i	−0.125141	+	0.187286i
$482$	−42.8219	+	215.280i	−0.0888421	+	0.446639i
$483$	−158.626	+	105.991i	−0.328418	+	0.219442i
$484$	24.6268	+	59.4543i	0.0508818	+	0.122840i
$485$		0			0
$486$	465.503	−	311.039i	0.957825	−	0.639998i
$487$	−397.869	−	79.1411i	−0.816980	−	0.162507i	−0.231126	−	0.972924i	$-0.574241\pi$
$487$	−397.869	−	79.1411i	−0.816980	−	0.162507i	−0.585854	+	0.810417i	$0.699241\pi$
$488$	−339.443	+	508.012i	−0.695579	+	1.04101i
$489$	−111.033	+	111.033i	−0.227062	+	0.227062i
$490$		0			0
$491$	−23.7416	+	57.3172i	−0.0483535	+	0.116736i	−0.946211	−	0.323551i	$-0.895123\pi$
$491$	−23.7416	+	57.3172i	−0.0483535	+	0.116736i	0.897857	+	0.440287i	$0.145123\pi$
$492$	−120.889			−0.245710
$493$	203.978	+	9.62562i	0.413749	+	0.0195246i
$494$	146.094			0.295736
$495$		0			0
$496$	433.587	−	86.2458i	0.874167	−	0.173883i
$497$	99.4445	−	99.4445i	0.200089	−	0.200089i
$498$	−674.481	−	450.674i	−1.35438	−	0.904967i
$499$	503.379	+	100.128i	1.00878	+	0.200658i	0.671703	−	0.740821i	$-0.265563\pi$
$499$	503.379	+	100.128i	1.00878	+	0.200658i	0.337073	+	0.941479i	$0.390563\pi$
$500$		0			0
$501$	55.7947	+	134.700i	0.111367	+	0.268863i
$502$	−95.2302	−	229.906i	−0.189702	−	0.457980i
$503$	183.828	+	275.118i	0.365463	+	0.546954i	0.967940	−	0.251182i	$-0.0808194\pi$
$503$	183.828	+	275.118i	0.365463	+	0.546954i	−0.602477	+	0.798136i	$0.705819\pi$
$504$	−50.7740	+	255.258i	−0.100742	+	0.506465i
$505$		0			0
$506$	99.7945	−	99.7945i	0.197222	−	0.197222i
$507$	626.030	−	124.525i	1.23477	−	0.245612i
$508$	−33.5240	−	13.8861i	−0.0659922	−	0.0273349i
$509$			343.247i			0.674355i	0.941441	+	0.337178i	$0.109472\pi$
$509$			343.247i			0.674355i	−0.941441	+	0.337178i	$0.890528\pi$
$510$		0			0
$511$	383.347			0.750190
$512$	−216.169	+	521.878i	−0.422205	+	1.01929i
$513$	−31.5841	−	158.784i	−0.0615674	−	0.309520i
$514$	490.601	+	490.601i	0.954476	+	0.954476i
$515$		0			0
$516$	−12.2044	−	2.42760i	−0.0236519	−	0.00470466i
$517$	−25.8464	+	17.2700i	−0.0499930	+	0.0334043i
$518$	215.376	−	89.2118i	0.415784	−	0.172224i
$519$	721.645	−	298.915i	1.39045	−	0.575944i
$520$		0			0
$521$	62.1355	−	312.376i	0.119262	−	0.599570i	−0.874215	−	0.485539i	$-0.838623\pi$
$521$	62.1355	−	312.376i	0.119262	−	0.599570i	0.993477	−	0.114032i	$-0.0363765\pi$
$522$	−86.9092	+	130.069i	−0.166493	+	0.249174i
$523$	−167.575	−	167.575i	−0.320410	−	0.320410i	0.528514	−	0.848924i	$-0.322749\pi$
$523$	−167.575	−	167.575i	−0.320410	−	0.320410i	−0.848924	+	0.528514i	$0.822749\pi$
$524$	33.1762	+	166.788i	0.0633133	+	0.318298i
$525$		0			0
$526$			514.556i			0.978244i
$527$	−432.823	−	475.696i	−0.821296	−	0.902649i
$528$		−	328.176i		−	0.621545i
$529$	366.128	+	151.655i	0.692114	+	0.286683i
$530$		0			0
$531$	−61.2676	−	61.2676i	−0.115381	−	0.115381i
$532$	74.0938	+	49.5079i	0.139274	+	0.0930600i
$533$	−22.1481	+	111.346i	−0.0415537	+	0.208904i
$534$	−158.985	−	237.938i	−0.297725	−	0.445577i
$535$		0			0
$536$	−227.670	+	94.3039i	−0.424757	+	0.175940i
$537$	−544.985	−	815.628i	−1.01487	−	1.51886i
$538$	176.421	+	35.0922i	0.327919	+	0.0652272i
$539$	186.106	+	124.352i	0.345279	+	0.230708i
$540$		0			0
$541$	51.6826	+	259.826i	0.0955316	+	0.480270i	0.998700	+	0.0509824i	$0.0162352\pi$
$541$	51.6826	+	259.826i	0.0955316	+	0.480270i	−0.903168	+	0.429287i	$0.858765\pi$
$542$	621.502	+	257.435i	1.14668	+	0.474972i
$543$	−552.466			−1.01743
$544$	232.923	−	35.0111i	0.428167	−	0.0643586i
$545$		0			0
$546$	90.6899	+	37.5650i	0.166099	+	0.0688003i
$547$	−70.3869	−	353.859i	−0.128678	−	0.646909i	−0.990253	−	0.139278i	$-0.955522\pi$
$547$	−70.3869	−	353.859i	−0.128678	−	0.646909i	0.861575	−	0.507630i	$-0.169478\pi$
$548$	33.0075	−	33.0075i	0.0602326	−	0.0602326i
$549$	−290.453	+	434.694i	−0.529058	+	0.791792i
$550$		0			0
$551$	164.486	+	246.170i	0.298522	+	0.446770i
$552$	−371.313	+	153.803i	−0.672669	+	0.278629i
$553$	−33.6111	−	81.1445i	−0.0607797	−	0.146735i
$554$	−98.6630	+	65.9245i	−0.178092	+	0.118997i
$555$		0			0
$556$	38.5481	+	25.7570i	0.0693312	+	0.0463256i
$557$	367.145	+	367.145i	0.659147	+	0.659147i	0.955178	−	0.296031i	$-0.0956632\pi$
$557$	367.145	+	367.145i	0.659147	+	0.659147i	−0.296031	+	0.955178i	$0.595663\pi$
$558$	483.210	−	96.1164i	0.865968	−	0.172252i
$559$	−4.47192	+	10.7962i	−0.00799986	+	0.0193134i
$560$		0			0
$561$	−409.027	+	246.237i	−0.729104	+	0.438926i
$562$		−	665.645i		−	1.18442i
$563$	−168.267	+	406.232i	−0.298875	+	0.721549i	0.701089	+	0.713074i	$0.252698\pi$
$563$	−168.267	+	406.232i	−0.298875	+	0.721549i	−0.999964	+	0.00847487i	$0.997302\pi$
$564$	15.7072	−	3.12435i	0.0278496	−	0.00553963i
$565$		0			0
$566$	−291.125	+	435.699i	−0.514355	+	0.769786i
$567$	74.2271	−	373.165i	0.130912	−	0.658139i
$568$	246.342	−	164.601i	0.433701	−	0.289790i
$569$	183.595	+	443.238i	0.322663	+	0.778977i	0.999098	+	0.0424747i	$0.0135242\pi$
$569$	183.595	+	443.238i	0.322663	+	0.778977i	−0.676435	+	0.736503i	$0.736476\pi$
$570$		0			0
$571$	452.464	−	302.327i	0.792406	−	0.529469i	−0.0922371	−	0.995737i	$-0.529402\pi$
$571$	452.464	−	302.327i	0.792406	−	0.529469i	0.884643	+	0.466268i	$0.154402\pi$
$572$	20.1901	+	4.01605i	0.0352973	+	0.00702107i
$573$	−391.863	+	586.464i	−0.683879	+	1.02350i
$574$	172.728	−	172.728i	0.300920	−	0.300920i
$575$		0			0
$576$	−201.004	+	485.266i	−0.348965	+	0.842476i
$577$	304.419			0.527589			0.263795	−	0.964579i	$-0.415026\pi$
$577$	304.419			0.527589			0.263795	+	0.964579i	$0.415026\pi$
$578$	325.184	+	393.129i	0.562602	+	0.680154i
$579$	759.470			1.31169
$580$		0			0
$581$	−455.737	+	90.6517i	−0.784400	+	0.156027i
$582$	840.297	−	840.297i	1.44381	−	1.44381i
$583$	−177.324	−	118.484i	−0.304158	−	0.203232i
$584$	792.068	+	157.552i	1.35628	+	0.269781i
$585$		0			0
$586$	−95.3950	−	230.304i	−0.162790	−	0.393010i
$587$	244.317	+	589.834i	0.416213	+	1.00483i	0.983435	+	0.181263i	$0.0580184\pi$
$587$	244.317	+	589.834i	0.416213	+	1.00483i	−0.567221	+	0.823565i	$0.691982\pi$
$588$	−64.0652	−	95.8804i	−0.108954	−	0.163062i
$589$	181.911	−	914.531i	0.308848	−	1.55268i
$590$		0			0
$591$	821.644	−	821.644i	1.39026	−	1.39026i
$592$	369.831	−	73.5639i	0.624714	−	0.124263i
$593$	594.149	+	246.104i	1.00194	+	0.415016i	0.822507	−	0.568755i	$-0.192575\pi$
$593$	594.149	+	246.104i	1.00194	+	0.415016i	0.179430	+	0.983771i	$0.442575\pi$
$594$			80.4708i			0.135473i
$595$		0			0
$596$	−45.7258			−0.0767211
$597$	−141.852	+	342.460i	−0.237608	+	0.573636i
$598$	13.3211	+	66.9697i	0.0222761	+	0.111990i
$599$	−354.327	−	354.327i	−0.591530	−	0.591530i	0.346514	−	0.938045i	$-0.387365\pi$
$599$	−354.327	−	354.327i	−0.591530	−	0.591530i	−0.938045	+	0.346514i	$0.887365\pi$
$600$		0			0
$601$	558.804	+	111.153i	0.929791	+	0.184947i	0.636677	−	0.771131i	$-0.280309\pi$
$601$	558.804	+	111.153i	0.929791	+	0.184947i	0.293114	+	0.956078i	$0.405309\pi$
$602$	20.9064	−	13.9692i	0.0347282	−	0.0232046i
$603$	−194.812	+	80.6936i	−0.323071	+	0.133820i
$604$	−196.157	+	81.2510i	−0.324764	+	0.134521i
$605$		0			0
$606$	−173.444	+	871.961i	−0.286211	+	1.43888i
$607$	100.769	−	150.811i	0.166011	−	0.248454i	−0.739131	−	0.673561i	$-0.764764\pi$
$607$	100.769	−	150.811i	0.166011	−	0.248454i	0.905143	+	0.425108i	$0.139764\pi$
$608$	241.474	+	241.474i	0.397162	+	0.397162i
$609$	38.8094	+	195.108i	0.0637265	+	0.320375i
$610$		0			0
$611$		−	15.0396i		−	0.0246147i
$612$	109.564	−	16.4688i	0.179026	−	0.0269098i
$613$		−	155.196i		−	0.253174i	−0.991956	−	0.126587i	$-0.959598\pi$
$613$		−	155.196i		−	0.253174i	0.991956	−	0.126587i	$-0.0404023\pi$
$614$	−423.470	−	175.407i	−0.689691	−	0.285679i
$615$		0			0
$616$	−173.125	−	173.125i	−0.281047	−	0.281047i
$617$	−388.627	−	259.673i	−0.629866	−	0.420863i	0.199243	−	0.979950i	$-0.436152\pi$
$617$	−388.627	−	259.673i	−0.629866	−	0.420863i	−0.829109	+	0.559087i	$0.811152\pi$
$618$	244.024	−	1226.79i	0.394861	−	1.98510i
$619$	−213.158	−	319.014i	−0.344359	−	0.515370i	0.618352	−	0.785901i	$-0.287801\pi$
$619$	−213.158	−	319.014i	−0.344359	−	0.515370i	−0.962711	+	0.270531i	$0.912801\pi$
$620$		0			0
$621$	69.9071	−	28.9565i	0.112572	−	0.0466288i
$622$	553.288	+	828.054i	0.889531	+	1.33128i
$623$	−160.771	−	31.9794i	−0.258060	−	0.0513313i
$624$	132.019	+	88.2122i	0.211569	+	0.141366i
$625$		0			0
$626$	156.966	+	789.123i	0.250745	+	1.26058i
$627$	−639.506	−	264.892i	−1.01995	−	0.422475i
$628$	−237.583			−0.378316
$629$	−369.179	−	405.748i	−0.586931	−	0.645068i
$630$		0			0
$631$	−308.547	−	127.804i	−0.488980	−	0.202542i	0.124550	−	0.992213i	$-0.460251\pi$
$631$	−308.547	−	127.804i	−0.488980	−	0.202542i	−0.613531	+	0.789671i	$0.710251\pi$
$632$	−36.0974	−	181.474i	−0.0571162	−	0.287142i
$633$	−103.471	+	103.471i	−0.163462	+	0.163462i
$634$	−325.560	+	487.236i	−0.513502	+	0.768511i
$635$		0			0
$636$	61.0423	+	91.3563i	0.0959785	+	0.143642i
$637$	−100.049	+	41.4415i	−0.157062	+	0.0650573i
$638$	−56.3163	−	135.960i	−0.0882701	−	0.213103i
$639$	210.789	−	140.845i	0.329873	−	0.220414i
$640$		0			0
$641$	−798.746	−	533.705i	−1.24609	−	0.832613i	−0.255151	−	0.966901i	$-0.582125\pi$
$641$	−798.746	−	533.705i	−1.24609	−	0.832613i	−0.990942	+	0.134289i	$0.957125\pi$
$642$	201.392	+	201.392i	0.313695	+	0.313695i
$643$	1027.11	−	204.305i	1.59737	−	0.317737i	0.685457	−	0.728113i	$-0.259602\pi$
$643$	1027.11	−	204.305i	1.59737	−	0.317737i	0.911917	+	0.410376i	$0.134602\pi$
$644$	−15.9385	+	38.4791i	−0.0247493	+	0.0597501i
$645$		0			0
$646$	−178.345	+	717.877i	−0.276076	+	1.11127i
$647$		−	328.253i		−	0.507346i	−0.967290	−	0.253673i	$-0.918361\pi$
$647$		−	328.253i		−	0.507346i	0.967290	−	0.253673i	$-0.0816388\pi$
$648$	306.735	−	740.523i	0.473356	−	1.14278i
$649$	79.9443	−	15.9019i	0.123181	−	0.0245022i
$650$		0			0
$651$	348.077	−	520.934i	0.534681	−	0.800206i
$652$	−6.68782	+	33.6220i	−0.0102574	+	0.0515674i
$653$	41.4569	−	27.7006i	0.0634869	−	0.0424206i	−0.523422	−	0.852074i	$-0.675345\pi$
$653$	41.4569	−	27.7006i	0.0634869	−	0.0424206i	0.586909	+	0.809653i	$0.300345\pi$
$654$	−125.290	−	302.477i	−0.191575	−	0.462504i
$655$		0			0
$656$	328.527	−	219.515i	0.500804	−	0.334626i
$657$	677.754	+	134.814i	1.03159	+	0.205196i
$658$	−17.9785	+	26.9067i	−0.0273229	+	0.0408917i
$659$	−61.2456	+	61.2456i	−0.0929371	+	0.0929371i	−0.752047	−	0.659110i	$-0.770933\pi$
$659$	−61.2456	+	61.2456i	−0.0929371	+	0.0929371i	0.659110	+	0.752047i	$0.270933\pi$
$660$		0			0
$661$	−314.044	+	758.170i	−0.475105	+	1.14700i	0.486774	+	0.873528i	$0.338173\pi$
$661$	−314.044	+	758.170i	−0.475105	+	1.14700i	−0.961879	+	0.273476i	$0.911827\pi$
$662$	−1040.69			−1.57205
$663$	10.8881	−	230.731i	0.0164225	−	0.348011i
$664$	−978.896			−1.47424
$665$		0			0
$666$	412.157	−	81.9831i	0.618854	−	0.123098i
$667$	−97.8470	+	97.8470i	−0.146697	+	0.146697i
$668$	26.4655	+	17.6837i	0.0396190	+	0.0264726i
$669$	−1599.94	−	318.248i	−2.39154	−	0.475707i
$670$		0			0
$671$	−188.211	−	454.381i	−0.280493	−	0.677170i
$672$	87.8088	+	211.989i	0.130668	+	0.315460i
$673$	−305.467	−	457.164i	−0.453889	−	0.679293i	0.531990	−	0.846751i	$-0.321444\pi$
$673$	−305.467	−	457.164i	−0.453889	−	0.679293i	−0.985879	+	0.167457i	$0.946444\pi$
$674$	−112.824	+	567.203i	−0.167394	+	0.841548i
$675$		0			0
$676$	98.5342	−	98.5342i	0.145761	−	0.145761i
$677$	−531.400	+	105.702i	−0.784933	+	0.156133i	−0.571257	−	0.820772i	$-0.693544\pi$
$677$	−531.400	+	105.702i	−0.784933	+	0.156133i	−0.213677	+	0.976904i	$0.568544\pi$
$678$	1235.86	+	511.910i	1.82280	+	0.755030i
$679$		−	680.714i		−	1.00252i
$680$		0			0
$681$	510.884			0.750197
$682$	−177.366	+	428.199i	−0.260067	+	0.627857i
$683$	77.2580	+	388.402i	0.113116	+	0.568671i	0.995223	+	0.0976233i	$0.0311240\pi$
$683$	77.2580	+	388.402i	0.113116	+	0.568671i	−0.882108	+	0.471048i	$0.843876\pi$
$684$	113.587	+	113.587i	0.166062	+	0.166062i
$685$		0			0
$686$	575.727	+	114.519i	0.839252	+	0.166938i
$687$	−413.677	+	276.410i	−0.602150	+	0.402344i
$688$	37.5745	−	15.5639i	0.0546142	−	0.0226219i
$689$	95.3279	−	39.4861i	0.138357	−	0.0573093i
$690$		0			0
$691$	182.146	−	915.708i	0.263597	−	1.32519i	−0.591324	−	0.806434i	$-0.701395\pi$
$691$	182.146	−	915.708i	0.263597	−	1.32519i	0.854921	−	0.518758i	$-0.173605\pi$
$692$	94.7388	−	141.787i	0.136906	−	0.204894i
$693$	−148.139	−	148.139i	−0.213764	−	0.213764i
$694$	83.3681	+	419.120i	0.120127	+	0.603919i
$695$		0			0
$696$			419.081i			0.602128i
$697$	−520.097	−	244.758i	−0.746193	−	0.351160i
$698$		−	887.929i		−	1.27210i
$699$	−224.864	−	93.1416i	−0.321693	−	0.133250i
$700$		0			0
$701$	−411.177	−	411.177i	−0.586558	−	0.586558i	0.350140	−	0.936697i	$-0.386134\pi$
$701$	−411.177	−	411.177i	−0.586558	−	0.586558i	−0.936697	+	0.350140i	$0.886134\pi$
$702$	−32.3718	−	21.6302i	−0.0461137	−	0.0308122i
$703$	155.163	−	780.055i	0.220715	−	1.10961i
$704$	−274.519	−	410.846i	−0.389941	−	0.583588i
$705$		0			0
$706$	533.494	−	220.980i	0.755657	−	0.313003i
$707$	282.930	+	423.435i	0.400184	+	0.598918i
$708$	−41.1868	−	8.19257i	−0.0581735	−	0.0115714i
$709$	−967.198	−	646.261i	−1.36417	−	0.911511i	−0.364367	−	0.931255i	$-0.618715\pi$
$709$	−967.198	−	646.261i	−1.36417	−	0.911511i	−0.999805	+	0.0197449i	$0.993715\pi$
$710$		0			0
$711$	−30.8877	−	155.283i	−0.0434426	−	0.218401i
$712$	−319.041	−	132.151i	−0.448091	−	0.185605i
$713$	435.811			0.611235
$714$	−295.298	+	399.776i	−0.413583	+	0.559910i
$715$		0			0
$716$	−197.853	−	81.9532i	−0.276330	−	0.114460i
$717$	225.734	+	1134.84i	0.314831	+	1.58276i
$718$	−663.338	+	663.338i	−0.923869	+	0.923869i
$719$	8.24905	−	12.3456i	0.0114729	−	0.0171705i	−0.825689	−	0.564126i	$-0.809213\pi$
$719$	8.24905	−	12.3456i	0.0114729	−	0.0171705i	0.837162	+	0.546955i	$0.184213\pi$
$720$		0			0
$721$	−398.064	−	595.745i	−0.552100	−	0.826276i
$722$	−402.030	+	166.526i	−0.556828	+	0.230646i
$723$	192.553	+	464.864i	0.266325	+	0.642966i
$724$	−100.284	+	67.0078i	−0.138514	+	0.0925522i
$725$		0			0
$726$	−432.682	−	289.109i	−0.595981	−	0.398222i
$727$	880.136	+	880.136i	1.21064	+	1.21064i	0.970816	+	0.239825i	$0.0770901\pi$
$727$	880.136	+	880.136i	1.21064	+	1.21064i	0.239825	+	0.970816i	$0.422910\pi$
$728$	116.180	−	23.1096i	0.159588	−	0.0317440i
$729$	170.915	−	412.626i	0.234452	−	0.566017i
$730$		0			0
$731$	−47.5913	−	35.1537i	−0.0651044	−	0.0480899i
$732$			253.382i			0.346150i
$733$	−208.728	+	503.915i	−0.284759	+	0.687469i	−0.999934	−	0.0114762i	$-0.996347\pi$
$733$	−208.728	+	503.915i	−0.284759	+	0.687469i	0.715175	+	0.698945i	$0.246347\pi$
$734$	−573.199	+	114.016i	−0.780925	+	0.155336i
$735$		0			0
$736$	−88.6744	+	132.711i	−0.120482	+	0.180313i
$737$	38.6993	−	194.555i	0.0525092	−	0.263982i
$738$	366.126	−	244.638i	0.496106	−	0.331488i
$739$	63.1371	+	152.427i	0.0854359	+	0.206261i	0.960823	−	0.277161i	$-0.0893937\pi$
$739$	63.1371	+	152.427i	0.0854359	+	0.206261i	−0.875387	+	0.483422i	$0.839394\pi$
$740$		0			0
$741$	278.457	−	186.059i	0.375786	−	0.251092i
$742$	−217.749	−	43.3130i	−0.293462	−	0.0583733i
$743$	−1.28081	+	1.91687i	−0.00172384	+	0.00257991i	−0.832331	−	0.554280i	$-0.812994\pi$
$743$	−1.28081	+	1.91687i	−0.00172384	+	0.00257991i	0.830607	+	0.556860i	$0.187994\pi$
$744$	933.294	−	933.294i	1.25443	−	1.25443i
$745$		0			0
$746$	−99.8879	+	241.151i	−0.133898	+	0.323258i
$747$	−837.618			−1.12131
$748$	−44.3813	+	94.3076i	−0.0593333	+	0.126080i
$749$	163.145			0.217817
$750$		0			0
$751$	−1414.78	+	281.416i	−1.88386	+	0.374722i	−0.996298	−	0.0859723i	$-0.972600\pi$
$751$	−1414.78	+	281.416i	−1.88386	+	0.374722i	−0.887559	+	0.460695i	$0.847600\pi$
$752$	−37.0123	+	37.0123i	−0.0492184	+	0.0492184i
$753$	−474.310	−	316.924i	−0.629894	−	0.420881i
$754$	69.8315	+	13.8904i	0.0926148	+	0.0184222i
$755$		0			0
$756$	−9.08793	−	21.9402i	−0.0120211	−	0.0290214i
$757$	115.414	+	278.634i	0.152463	+	0.368077i	0.981595	−	0.190975i	$-0.0611651\pi$
$757$	115.414	+	278.634i	0.152463	+	0.368077i	−0.829132	+	0.559052i	$0.811165\pi$
$758$	−42.8446	−	64.1215i	−0.0565233	−	0.0845931i
$759$	63.1158	−	317.305i	0.0831566	−	0.418056i
$760$		0			0
$761$	−811.549	+	811.549i	−1.06642	+	1.06642i	−0.0687929	+	0.997631i	$0.521915\pi$
$761$	−811.549	+	811.549i	−1.06642	+	1.06642i	−0.997631	+	0.0687929i	$0.978085\pi$
$762$	287.786	−	57.2441i	0.377671	−	0.0751235i
$763$	−173.265	−	71.7685i	−0.227083	−	0.0940610i
$764$			153.984i			0.201550i
$765$		0			0
$766$	−348.859			−0.455429
$767$	−15.0916	+	36.4344i	−0.0196762	+	0.0475025i
$768$	126.907	+	638.005i	0.165244	+	0.830736i
$769$	−870.130	−	870.130i	−1.13151	−	1.13151i	−0.989927	−	0.141582i	$-0.954781\pi$
$769$	−870.130	−	870.130i	−1.13151	−	1.13151i	−0.141582	−	0.989927i	$-0.545219\pi$
$770$		0			0
$771$	1559.90	+	310.284i	2.02322	+	0.402444i
$772$	137.860	−	92.1150i	0.178575	−	0.119320i
$773$	−1306.77	+	541.282i	−1.69052	+	0.700235i	−0.999739	−	0.0228308i	$-0.992732\pi$
$773$	−1306.77	+	541.282i	−1.69052	+	0.700235i	−0.690779	+	0.723066i	$0.742732\pi$
$774$	41.8749	−	17.3451i	0.0541019	−	0.0224098i
$775$		0			0
$776$	279.767	−	1406.49i	0.360525	−	1.81248i
$777$	296.895	−	444.334i	0.382104	−	0.571859i
$778$	−26.8308	−	26.8308i	−0.0344869	−	0.0344869i
$779$	−162.586	−	817.375i	−0.208711	−	1.04926i
$780$		0			0
$781$			238.490i			0.305365i
$782$	−345.339	−	16.2964i	−0.441610	−	0.0208393i
$783$		−	78.9004i		−	0.100767i
$784$	348.205	+	144.231i	0.444139	+	0.183969i
$785$		0			0
$786$	−972.366	−	972.366i	−1.23711	−	1.23711i
$787$	−1282.76	−	857.112i	−1.62994	−	1.08909i	−0.925104	−	0.379713i	$-0.876023\pi$
$787$	−1282.76	−	857.112i	−1.62994	−	1.08909i	−0.704831	−	0.709375i	$-0.748977\pi$
$788$	49.4897	−	248.802i	0.0628042	−	0.315738i
$789$	655.319	+	980.754i	0.830569	+	1.24303i
$790$		0			0
$791$	707.924	−	293.232i	0.894973	−	0.370710i
$792$	−245.199	−	366.967i	−0.309595	−	0.463342i
$793$	233.379	+	46.4220i	0.294299	+	0.0585397i
$794$	−52.0749	−	34.7954i	−0.0655856	−	0.0438229i
$795$		0			0
$796$	15.7874	+	79.3688i	0.0198335	+	0.0997095i
$797$	1040.17	+	430.853i	1.30511	+	0.540593i	0.923453	−	0.383712i	$-0.125355\pi$
$797$	1040.17	+	430.853i	1.30511	+	0.540593i	0.381654	+	0.924305i	$0.375355\pi$
$798$	−720.593			−0.902998
$799$	73.9019	+	18.3597i	0.0924930	+	0.0229784i
$800$		0			0
$801$	−272.996	−	113.079i	−0.340819	−	0.141172i
$802$	−51.5110	−	258.963i	−0.0642281	−	0.322897i
$803$	−459.675	+	459.675i	−0.572448	+	0.572448i
$804$	−56.7776	+	84.9737i	−0.0706189	+	0.105689i
$805$		0			0
$806$	−124.581	−	186.449i	−0.154567	−	0.231326i
$807$	380.953	−	157.796i	0.472061	−	0.195534i
$808$	410.560	+	991.179i	0.508119	+	1.22671i
$809$	273.249	−	182.579i	0.337761	−	0.225685i	−0.375109	−	0.926981i	$-0.622395\pi$
$809$	273.249	−	182.579i	0.337761	−	0.225685i	0.712870	+	0.701296i	$0.247395\pi$
$810$		0			0
$811$	−242.645	−	162.131i	−0.299193	−	0.199914i	0.396908	−	0.917859i	$-0.370083\pi$
$811$	−242.645	−	162.131i	−0.299193	−	0.199914i	−0.696101	+	0.717944i	$0.745083\pi$
$812$	30.7091	+	30.7091i	0.0378191	+	0.0378191i
$813$	1512.45	−	300.846i	1.86034	−	0.370044i
$814$	−151.285	+	365.235i	−0.185854	+	0.448692i
$815$		0			0
$816$	−594.622	+	541.031i	−0.728703	+	0.663028i
$817$		−	85.7829i		−	0.104997i
$818$	−269.482	+	650.588i	−0.329441	+	0.795340i
$819$	99.4124	−	19.7743i	0.121383	−	0.0241445i
$820$		0			0
$821$	−600.209	+	898.276i	−0.731070	+	1.09412i	0.260616	+	0.965443i	$0.416074\pi$
$821$	−600.209	+	898.276i	−0.731070	+	1.09412i	−0.991686	+	0.128681i	$0.958926\pi$
$822$	−73.6406	+	370.216i	−0.0895871	+	0.450385i
$823$	−75.4620	+	50.4221i	−0.0916914	+	0.0612662i	−0.600571	−	0.799572i	$-0.705060\pi$
$823$	−75.4620	+	50.4221i	−0.0916914	+	0.0612662i	0.508879	+	0.860838i	$0.330060\pi$
$824$	−577.631	−	1394.52i	−0.701008	−	1.69238i
$825$		0			0
$826$	70.5539	−	47.1426i	0.0854163	−	0.0570733i
$827$	476.748	+	94.8310i	0.576479	+	0.114669i	0.474715	−	0.880140i	$-0.342551\pi$
$827$	476.748	+	94.8310i	0.576479	+	0.114669i	0.101764	+	0.994809i	$0.467551\pi$
$828$	−41.7114	+	62.4255i	−0.0503760	+	0.0753931i
$829$	−743.445	+	743.445i	−0.896797	+	0.896797i	−0.995151	−	0.0983544i	$-0.968642\pi$
$829$	−743.445	+	743.445i	−0.896797	+	0.896797i	0.0983544	+	0.995151i	$0.468642\pi$
$830$		0			0
$831$	−104.095	+	251.307i	−0.125264	+	0.302415i
$832$	239.065			0.287338
$833$	−81.5008	−	542.211i	−0.0978401	−	0.650914i
$834$	−374.896			−0.449516
$835$		0			0
$836$	−148.212	+	29.4812i	−0.177287	+	0.0352646i
$837$	−175.711	+	175.711i	−0.209930	+	0.209930i
$838$	−54.8971	−	36.6811i	−0.0655097	−	0.0437722i
$839$	449.855	+	89.4817i	0.536180	+	0.106653i	0.455751	−	0.890108i	$-0.349371\pi$
$839$	449.855	+	89.4817i	0.536180	+	0.106653i	0.0804292	+	0.996760i	$0.474371\pi$
$840$		0			0
$841$	−266.619	−	643.676i	−0.317027	−	0.765370i
$842$	298.762	+	721.276i	0.354824	+	0.856622i
$843$	−847.739	−	1268.73i	−1.00562	−	1.50502i
$844$	−6.23235	+	31.3321i	−0.00738430	+	0.0371234i
$845$		0			0
$846$	−41.2482	+	41.2482i	−0.0487568	+	0.0487568i
$847$	−292.357	+	58.1534i	−0.345167	+	0.0686581i
$848$	−331.775	−	137.426i	−0.391244	−	0.162059i
$849$			1201.22i			1.41486i
$850$		0			0
$851$	371.728			0.436813
$852$	47.0197	−	113.516i	0.0551875	−	0.133234i
$853$	1.46888	+	7.38457i	0.00172202	+	0.00865717i	0.981637	−	0.190760i	$-0.0610952\pi$
$853$	1.46888	+	7.38457i	0.00172202	+	0.00865717i	−0.979915	+	0.199417i	$0.936095\pi$
$854$	−362.035	−	362.035i	−0.423929	−	0.423929i
$855$		0			0
$856$	337.089	+	67.0512i	0.393796	+	0.0783309i
$857$	−42.1566	+	28.1682i	−0.0491910	+	0.0328683i	−0.579923	−	0.814672i	$-0.696917\pi$
$857$	−42.1566	+	28.1682i	−0.0491910	+	0.0328683i	0.530732	+	0.847540i	$0.321917\pi$
$858$	−153.792	+	63.7026i	−0.179244	+	0.0742455i
$859$	464.849	−	192.547i	0.541151	−	0.224152i	−0.0953281	−	0.995446i	$-0.530390\pi$
$859$	464.849	−	192.547i	0.541151	−	0.224152i	0.636479	+	0.771294i	$0.280390\pi$
$860$		0			0
$861$	109.243	−	549.204i	0.126880	−	0.637867i
$862$	340.230	−	509.190i	0.394698	−	0.590708i
$863$	−98.9573	−	98.9573i	−0.114667	−	0.114667i	0.647445	−	0.762112i	$-0.275837\pi$
$863$	−98.9573	−	98.9573i	−0.114667	−	0.114667i	−0.762112	+	0.647445i	$0.775837\pi$
$864$	−17.7546	−	89.2585i	−0.0205493	−	0.103309i
$865$		0			0
$866$			94.8830i			0.109565i
$867$	1120.48	+	335.169i	1.29237	+	0.386585i
$868$		−	136.778i		−	0.157579i
$869$	137.605	+	56.9977i	0.158348	+	0.0655900i
$870$		0			0
$871$	67.8634	+	67.8634i	0.0779143	+	0.0779143i
$872$	−328.502	−	219.498i	−0.376722	−	0.251718i
$873$	239.390	−	1203.50i	0.274216	−	1.37858i
$874$	−278.477	−	416.771i	−0.318624	−	0.476855i
$875$		0			0
$876$	309.423	−	128.167i	0.353222	−	0.146309i
$877$	−527.563	−	789.554i	−0.601554	−	0.900289i	0.398302	−	0.917254i	$-0.369600\pi$
$877$	−527.563	−	789.554i	−0.601554	−	0.900289i	−0.999856	+	0.0169652i	$0.994600\pi$
$878$	421.187	+	83.7792i	0.479711	+	0.0954205i
$879$	−475.131	−	317.472i	−0.540536	−	0.361174i
$880$		0			0
$881$	204.085	+	1026.00i	0.231651	+	1.16459i	0.905049	+	0.425308i	$0.139834\pi$
$881$	204.085	+	1026.00i	0.231651	+	1.16459i	−0.673398	+	0.739280i	$0.735166\pi$
$882$	388.057	+	160.738i	0.439974	+	0.182243i
$883$	1264.99			1.43261			0.716303	−	0.697789i	$-0.245833\pi$
$883$	1264.99			1.43261			0.716303	+	0.697789i	$0.245833\pi$
$884$	−26.0086	−	43.2032i	−0.0294215	−	0.0488724i
$885$		0			0
$886$	186.898	+	77.4157i	0.210946	+	0.0873766i
$887$	−152.500	−	766.671i	−0.171928	−	0.864341i	−0.966401	−	0.257041i	$-0.917253\pi$
$887$	−152.500	−	766.671i	−0.171928	−	0.864341i	0.794472	−	0.607300i	$-0.207747\pi$
$888$	796.059	−	796.059i	0.896463	−	0.896463i
$889$	93.3794	−	139.752i	0.105039	−	0.157201i
$890$		0			0
$891$	358.459	+	536.472i	0.402311	+	0.602101i
$892$	−329.023	+	136.286i	−0.368860	+	0.152787i
$893$	42.2496	+	102.000i	0.0473120	+	0.114221i
$894$	307.441	−	205.425i	0.343894	−	0.229782i
$895$		0			0
$896$	−239.124	−	159.777i	−0.266879	−	0.178323i
$897$	110.680	+	110.680i	0.123389	+	0.123389i
$898$	−940.519	+	187.081i	−1.04735	+	0.208331i
$899$	173.904	−	419.842i	0.193442	−	0.467010i
$900$		0			0
$901$	77.6552	+	516.627i	0.0861878	+	0.573393i
$902$			414.241i			0.459247i
$903$	22.0573	−	53.2511i	0.0244267	−	0.0589713i
$904$	1583.22	−	314.922i	1.75135	−	0.348365i
$905$		0			0
$906$	953.854	−	1427.54i	1.05282	−	1.57566i
$907$	−72.9154	+	366.570i	−0.0803918	+	0.404157i	0.919546	+	0.392983i	$0.128557\pi$
$907$	−72.9154	+	366.570i	−0.0803918	+	0.404157i	−0.999938	+	0.0111739i	$0.996443\pi$
$908$	92.7363	−	61.9644i	0.102133	−	0.0682428i
$909$	351.306	+	848.129i	0.386476	+	0.933035i
$910$		0			0
$911$	−101.362	+	67.7280i	−0.111265	+	0.0743447i	−0.609958	−	0.792434i	$-0.708814\pi$
$911$	−101.362	+	67.7280i	−0.111265	+	0.0743447i	0.498693	+	0.866779i	$0.333814\pi$
$912$	−1143.17	−	227.390i	−1.25347	−	0.249331i
$913$	437.777	−	655.180i	0.479493	−	0.717612i
$914$	−280.276	+	280.276i	−0.306647	+	0.306647i
$915$		0			0
$916$	−41.5657	+	100.349i	−0.0453774	+	0.109551i
$917$	−787.702			−0.858999
$918$	145.805	−	132.664i	0.158829	−	0.144514i
$919$	−1592.00			−1.73232			−0.866158	−	0.499770i	$-0.833418\pi$
$919$	−1592.00			−1.73232			−0.866158	+	0.499770i	$0.833418\pi$
$920$		0			0
$921$	−1030.53	+	204.986i	−1.11893	+	0.222569i
$922$	314.913	−	314.913i	0.341555	−	0.341555i
$923$	−95.9399	−	64.1050i	−0.103944	−	0.0694528i
$924$	−99.5855	−	19.8088i	−0.107777	−	0.0214381i
$925$		0			0
$926$	−84.6976	−	204.478i	−0.0914661	−	0.220819i
$927$	−494.265	−	1193.26i	−0.533188	−	1.28723i
$928$	92.4638	+	138.382i	0.0996377	+	0.149118i
$929$	132.478	−	666.010i	0.142602	−	0.716910i	−0.841633	−	0.540049i	$-0.818406\pi$
$929$	132.478	−	666.010i	0.142602	−	0.716910i	0.984236	−	0.176861i	$-0.0565944\pi$
$930$		0			0
$931$	562.118	−	562.118i	0.603778	−	0.603778i
$932$	−52.1145	+	10.3662i	−0.0559169	+	0.0111226i
$933$	2109.16	+	873.641i	2.26062	+	0.936378i
$934$			1223.18i			1.30961i
$935$		0			0
$936$	213.532			0.228133
$937$	112.652	−	271.967i	0.120227	−	0.290253i	−0.852296	−	0.523059i	$-0.824791\pi$
$937$	112.652	−	271.967i	0.120227	−	0.290253i	0.972523	+	0.232806i	$0.0747907\pi$
$938$	−40.2869	−	202.536i	−0.0429498	−	0.215923i
$939$	1304.18	+	1304.18i	1.38890	+	1.38890i
$940$		0			0
$941$	819.035	+	162.916i	0.870388	+	0.173131i	0.610027	−	0.792381i	$-0.291159\pi$
$941$	819.035	+	162.916i	0.870388	+	0.173131i	0.260361	+	0.965511i	$0.416159\pi$
$942$	1597.41	−	1067.35i	1.69576	−	1.13307i
$943$	359.862	−	149.060i	0.381614	−	0.158070i
$944$	126.805	−	52.5243i	0.134327	−	0.0556402i
$945$		0			0
$946$	−8.31845	+	41.8196i	−0.00879328	+	0.0442068i
$947$	346.036	−	517.880i	0.365403	−	0.546864i	−0.602523	−	0.798102i	$-0.705838\pi$
$947$	346.036	−	517.880i	0.365403	−	0.546864i	0.967925	+	0.251238i	$0.0808376\pi$
$948$	−54.2592	−	54.2592i	−0.0572355	−	0.0572355i
$949$	−61.3599	−	308.477i	−0.0646575	−	0.325055i
$950$		0			0
$951$			1343.30i			1.41252i
$952$	−28.2711	+	599.098i	−0.0296966	+	0.629305i
$953$		−	373.214i		−	0.391620i	−0.980642	−	0.195810i	$-0.937266\pi$
$953$		−	373.214i		−	0.391620i	0.980642	−	0.195810i	$-0.0627335\pi$
$954$	−369.746	−	153.154i	−0.387575	−	0.160539i
$955$		0			0
$956$	178.619	+	178.619i	0.186840	+	0.186840i
$957$	−280.493	−	187.419i	−0.293096	−	0.195841i
$958$	164.865	−	828.832i	0.172093	−	0.865169i
$959$	120.126	+	179.781i	0.125262	+	0.187468i
$960$		0			0
$961$	−434.426	+	179.945i	−0.452056	+	0.187248i
$962$	−106.262	−	159.033i	−0.110460	−	0.165315i
$963$	288.439	+	57.3741i	0.299522	+	0.0595786i
$964$	91.3352	+	61.0282i	0.0947460	+	0.0633073i
$965$		0			0
$966$	−65.7051	−	330.322i	−0.0680177	−	0.341948i
$967$	947.512	+	392.472i	0.979847	+	0.405866i	0.814369	−	0.580348i	$-0.197083\pi$
$967$	947.512	+	392.472i	0.979847	+	0.405866i	0.165478	+	0.986213i	$0.447083\pi$
$968$	−627.966			−0.648725
$969$	574.332	+	1595.42i	0.592706	+	1.64646i
$970$		0			0
$971$	909.171	+	376.591i	0.936325	+	0.387838i	0.798074	−	0.602559i	$-0.205852\pi$
$971$	909.171	+	376.591i	0.936325	+	0.387838i	0.138250	+	0.990397i	$0.455852\pi$
$972$	−54.6605	−	274.797i	−0.0562351	−	0.282713i
$973$	−151.849	+	151.849i	−0.156063	+	0.156063i
$974$	397.869	−	595.453i	0.408490	−	0.611348i
$975$		0			0
$976$	−460.099	−	688.586i	−0.471413	−	0.705519i
$977$	525.837	−	217.809i	0.538216	−	0.222936i	−0.0969814	−	0.995286i	$-0.530919\pi$
$977$	525.837	−	217.809i	0.538216	−	0.222936i	0.635197	+	0.772350i	$0.280919\pi$
$978$	−106.082	−	256.105i	−0.108469	−	0.261866i
$979$	231.129	−	154.436i	0.236087	−	0.157748i
$980$		0			0
$981$	−281.091	−	187.819i	−0.286535	−	0.191457i
$982$	−77.4444	−	77.4444i	−0.0788639	−	0.0788639i
$983$	1410.25	−	280.516i	1.43464	−	0.285368i	0.584272	−	0.811558i	$-0.301380\pi$
$983$	1410.25	−	280.516i	1.43464	−	0.285368i	0.850367	+	0.526190i	$0.176380\pi$
$984$	451.436	−	1089.86i	0.458776	−	1.10758i
$985$		0			0
$986$	−153.502	+	326.183i	−0.155682	+	0.330814i
$987$			74.1814i			0.0751585i
$988$	27.9790	−	67.5473i	0.0283188	−	0.0683677i
$989$	39.3231	−	7.82186i	0.0397605	−	0.00790886i
$990$		0			0
$991$	46.6472	−	69.8125i	0.0470709	−	0.0704465i	−0.807188	−	0.590295i	$-0.799012\pi$
$991$	46.6472	−	69.8125i	0.0470709	−	0.0704465i	0.854259	+	0.519848i	$0.174012\pi$
$992$	102.259	−	514.093i	0.103084	−	0.518239i
$993$	−1983.58	+	1325.39i	−1.99757	+	1.33473i
$994$	95.0102	+	229.375i	0.0955837	+	0.230759i
$995$		0			0
$996$	−337.545	+	225.540i	−0.338900	+	0.226446i
$997$	738.843	+	146.965i	0.741066	+	0.147407i	0.551165	−	0.834396i	$-0.314183\pi$
$997$	738.843	+	146.965i	0.741066	+	0.147407i	0.189901	+	0.981803i	$0.439183\pi$
$998$	−503.379	+	753.360i	−0.504388	+	0.754870i
$999$	−149.874	+	149.874i	−0.150024	+	0.150024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.3.t.b.74.1		8
5.2	odd	4		17.3.e.b.6.1	yes	8
5.3	odd	4		425.3.u.a.176.1		8
5.4	even	2		425.3.t.d.74.1		8
15.2	even	4		153.3.p.a.91.1		8
17.3	odd	16		425.3.t.d.224.1		8
20.7	even	4		272.3.bh.b.193.1		8
85.2	odd	8		289.3.e.n.75.1		8
85.3	even	16		425.3.u.a.326.1		8
85.7	even	16		289.3.e.j.158.1		8
85.12	even	16		289.3.e.f.65.1		8
85.22	even	16		289.3.e.h.65.1		8
85.27	even	16		289.3.e.n.158.1		8
85.32	odd	8		289.3.e.j.75.1		8
85.37	even	16		17.3.e.b.3.1	✓	8
85.42	odd	8		289.3.e.a.214.1		8
85.47	odd	4		289.3.e.f.249.1		8
85.54	odd	16	inner	425.3.t.b.224.1		8
85.57	even	16		289.3.e.e.131.1		8
85.62	even	16		289.3.e.a.131.1		8
85.67	odd	4		289.3.e.g.40.1		8
85.72	odd	4		289.3.e.h.249.1		8
85.77	odd	8		289.3.e.e.214.1		8
85.82	even	16		289.3.e.g.224.1		8
255.122	odd	16		153.3.p.a.37.1		8
340.207	odd	16		272.3.bh.b.241.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.b.3.1	✓	8	85.37	even	16
17.3.e.b.6.1	yes	8	5.2	odd	4
153.3.p.a.37.1		8	255.122	odd	16
153.3.p.a.91.1		8	15.2	even	4
272.3.bh.b.193.1		8	20.7	even	4
272.3.bh.b.241.1		8	340.207	odd	16
289.3.e.a.131.1		8	85.62	even	16
289.3.e.a.214.1		8	85.42	odd	8
289.3.e.e.131.1		8	85.57	even	16
289.3.e.e.214.1		8	85.77	odd	8
289.3.e.f.65.1		8	85.12	even	16
289.3.e.f.249.1		8	85.47	odd	4
289.3.e.g.40.1		8	85.67	odd	4
289.3.e.g.224.1		8	85.82	even	16
289.3.e.h.65.1		8	85.22	even	16
289.3.e.h.249.1		8	85.72	odd	4
289.3.e.j.75.1		8	85.32	odd	8
289.3.e.j.158.1		8	85.7	even	16
289.3.e.n.75.1		8	85.2	odd	8
289.3.e.n.158.1		8	85.27	even	16
425.3.t.b.74.1		8	1.1	even	1	trivial
425.3.t.b.224.1		8	85.54	odd	16	inner
425.3.t.d.74.1		8	5.4	even	2
425.3.t.d.224.1		8	17.3	odd	16
425.3.u.a.176.1		8	5.3	odd	4
425.3.u.a.326.1		8	85.3	even	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	425.t (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.675577 + 1.63099i) q^{2} +(0.789499 + 3.96908i) q^{3} +(0.624715 + 0.624715i) q^{4} +(-7.00688 - 1.39376i) q^{6} +(-3.40262 + 2.27356i) q^{7} +(-7.96489 + 3.29916i) q^{8} +(-6.81537 + 2.82302i) q^{9} +(1.35387 - 6.80638i) q^{11} +(-1.98633 + 2.97275i) q^{12} +(2.37416 + 2.37416i) q^{13} +(-1.40941 - 7.08560i) q^{14} -11.6855i q^{16} +(-14.5645 + 8.76791i) q^{17} -13.0229i q^{18} +(-22.7712 - 9.43215i) q^{19} +(-11.7103 - 11.7103i) q^{21} +(10.1865 + 6.80638i) q^{22} +(2.24740 - 11.2984i) q^{23} +(-19.3829 - 29.0086i) q^{24} +(-5.47615 + 2.26829i) q^{26} +(3.64922 + 5.46144i) q^{27} +(-3.54600 - 0.705343i) q^{28} +(-9.98767 - 6.67355i) q^{29} +(7.38055 + 37.1045i) q^{31} +(-12.8006 - 5.30218i) q^{32} +28.0839 q^{33} +(-4.46094 - 29.6778i) q^{34} +(-6.02124 - 2.49408i) q^{36} +(6.29529 + 31.6486i) q^{37} +(30.7674 - 30.7674i) q^{38} +(-7.54883 + 11.2976i) q^{39} +(18.7852 + 28.1140i) q^{41} +(27.0106 - 11.1881i) q^{42} +(1.33189 + 3.21547i) q^{43} +(5.09783 - 3.40626i) q^{44} +(16.9093 + 11.2984i) q^{46} +(-3.16735 - 3.16735i) q^{47} +(46.3809 - 9.22573i) q^{48} +(-12.3427 + 29.7979i) q^{49} +(-46.2992 - 50.8853i) q^{51} +2.96634i q^{52} +(11.7603 - 28.3919i) q^{53} +(-11.3729 + 2.26220i) q^{54} +(19.6007 - 29.3345i) q^{56} +(19.4591 - 97.8275i) q^{57} +(17.6319 - 11.7813i) q^{58} +(4.49481 + 10.8514i) q^{59} +(58.9263 - 39.3733i) q^{61} +(-65.5031 - 13.0294i) q^{62} +(16.7718 - 25.1008i) q^{63} +(50.3473 - 50.3473i) q^{64} +(-18.9728 + 45.8045i) q^{66} +28.5842 q^{67} +(-14.5761 - 3.62119i) q^{68} +46.6187 q^{69} +(-33.7056 + 6.70446i) q^{71} +(44.9700 - 44.9700i) q^{72} +(-77.8880 - 52.0431i) q^{73} +(-55.8713 - 11.1135i) q^{74} +(-8.33312 - 20.1179i) q^{76} +(10.8680 + 26.2377i) q^{77} +(-13.3265 - 19.9444i) q^{78} +(-4.18708 + 21.0499i) q^{79} +(-65.7422 + 65.7422i) q^{81} +(-58.5443 + 11.6452i) q^{82} +(104.903 + 43.4522i) q^{83} -14.6312i q^{84} -6.14419 q^{86} +(18.6026 - 44.9106i) q^{87} +(11.6719 + 58.6787i) q^{88} +(28.3238 + 28.3238i) q^{89} +(-13.4762 - 2.68058i) q^{91} +(8.46229 - 5.65432i) q^{92} +(-141.444 + 58.5880i) q^{93} +(7.30570 - 3.02612i) q^{94} +(10.9387 - 54.9926i) q^{96} +(-92.4136 + 138.307i) q^{97} +(-40.2616 - 40.2616i) q^{98} +(9.98738 + 50.2100i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{7} - 8 q^{8} - 8 q^{9} + 40 q^{11} - 32 q^{12} - 16 q^{14} - 64 q^{17} + 32 q^{19} - 64 q^{21} + 8 q^{22} - 32 q^{23} - 24 q^{24} + 112 q^{27} - 8 q^{28} - 24 q^{29}+ \cdots - 136 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^7 - 8 * q^8 - 8 * q^9 + 40 * q^11 - 32 * q^12 - 16 * q^14 - 64 * q^17 + 32 * q^19 - 64 * q^21 + 8 * q^22 - 32 * q^23 - 24 * q^24 + 112 * q^27 - 8 * q^28 - 24 * q^29 + 32 * q^31 - 16 * q^32 + 16 * q^33 - 64 * q^34 - 104 * q^36 + 56 * q^37 - 8 * q^38 + 72 * q^39 + 88 * q^42 - 48 * q^43 + 96 * q^44 + 80 * q^47 + 16 * q^48 - 8 * q^49 - 176 * q^51 + 88 * q^53 - 208 * q^54 + 72 * q^56 - 168 * q^57 - 96 * q^58 - 8 * q^59 + 264 * q^61 - 96 * q^62 - 16 * q^63 + 120 * q^64 + 8 * q^66 - 32 * q^67 + 120 * q^68 + 208 * q^69 + 32 * q^71 + 24 * q^72 - 240 * q^73 - 176 * q^74 - 80 * q^76 + 120 * q^77 + 96 * q^79 - 224 * q^81 - 352 * q^82 + 504 * q^83 + 288 * q^86 - 216 * q^87 + 24 * q^88 - 288 * q^89 - 24 * q^91 - 72 * q^92 - 248 * q^93 + 8 * q^94 + 328 * q^96 + 280 * q^97 + 16 * q^98 - 136 * q^99

Introduction

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