LMFDB - Embedded newform 930.2.z.b.529.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(109,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 2]))

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

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

chi := DirichletCharacter("930.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.z (of order $10$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 44 x^{13} + 63 x^{12} - 46 x^{11} + 110 x^{10} - 120 x^{9} - 79 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 44x^13 + 63x^12 - 46x^11 + 110x^10 - 120x^9 - 79x^8 + 120x^7 + 110x^6 + 46x^5 + 63x^4 + 44x^3 + 18x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			529.2
Root			$2.63087 - 0.416689i$ of defining polynomial
Character	$\chi$	$=$	930.529
Dual form			930.2.z.b.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.71943 + 1.42953i) q^{5} -1.00000 q^{6} +(2.04378 - 0.664066i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.71943 + 1.42953i) q^{5} -1.00000 q^{6} +(2.04378 - 0.664066i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-2.16717 + 0.550794i) q^{10} +(-0.164066 - 0.504942i) q^{11} +(0.587785 - 0.809017i) q^{12} +(1.53884 + 2.11803i) q^{13} +(-0.664066 + 2.04378i) q^{14} +(-0.145857 + 2.23131i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.18545 + 0.710097i) q^{17} +(-0.587785 - 0.809017i) q^{18} +(-3.43106 - 2.49281i) q^{19} +(0.828229 - 2.07703i) q^{20} +(1.73855 + 1.26313i) q^{21} +(0.504942 + 0.164066i) q^{22} +(4.25325 + 1.38197i) q^{23} +(0.309017 + 0.951057i) q^{24} +(0.912893 + 4.91596i) q^{25} -2.61803 q^{26} +(-0.951057 + 0.309017i) q^{27} +(-1.26313 - 1.73855i) q^{28} +(3.97060 + 2.88481i) q^{29} +(-1.71943 - 1.42953i) q^{30} +(-0.566677 - 5.53885i) q^{31} -1.00000i q^{32} +(0.312071 - 0.429529i) q^{33} +(-1.85906 + 1.35068i) q^{34} +(4.46345 + 1.77983i) q^{35} +1.00000 q^{36} -2.67989i q^{37} +(4.03345 - 1.31055i) q^{38} +(-0.809017 + 2.48990i) q^{39} +(1.19353 + 1.89090i) q^{40} +(0.305007 + 0.221601i) q^{41} +(-2.04378 + 0.664066i) q^{42} +(-0.723629 + 0.995990i) q^{43} +(-0.429529 + 0.312071i) q^{44} +(-1.89090 + 1.19353i) q^{45} +(-3.61803 + 2.62866i) q^{46} +(1.80067 + 2.47841i) q^{47} +(-0.951057 - 0.309017i) q^{48} +(-1.92705 + 1.40008i) q^{49} +(-4.51368 - 2.15098i) q^{50} +(0.710097 + 2.18545i) q^{51} +(1.53884 - 2.11803i) q^{52} +(1.05637 + 0.343235i) q^{53} +(0.309017 - 0.951057i) q^{54} +(0.439729 - 1.10275i) q^{55} +2.14896 q^{56} -4.24102i q^{57} +(-4.66773 + 1.51664i) q^{58} +(-3.02312 + 2.19643i) q^{59} +(2.16717 - 0.550794i) q^{60} +1.98935 q^{61} +(4.81411 + 2.79720i) q^{62} +2.14896i q^{63} +(0.809017 + 0.587785i) q^{64} +(-0.381857 + 5.84163i) q^{65} +(0.164066 + 0.504942i) q^{66} -2.64824i q^{67} -2.29792i q^{68} +(1.38197 + 4.25325i) q^{69} +(-4.06346 + 2.56485i) q^{70} +(0.970604 - 2.98721i) q^{71} +(-0.587785 + 0.809017i) q^{72} +(-15.5573 + 5.05486i) q^{73} +(2.16808 + 1.57520i) q^{74} +(-3.44051 + 3.62807i) q^{75} +(-1.31055 + 4.03345i) q^{76} +(-0.670629 - 0.923041i) q^{77} +(-1.53884 - 2.11803i) q^{78} +(-1.41772 + 4.36328i) q^{79} +(-2.23131 - 0.145857i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.358558 + 0.116502i) q^{82} +(-2.23194 + 3.07200i) q^{83} +(0.664066 - 2.04378i) q^{84} +(2.74264 + 4.34513i) q^{85} +(-0.380434 - 1.17086i) q^{86} +4.90794i q^{87} -0.530927i q^{88} +(-0.173401 - 0.533672i) q^{89} +(0.145857 - 2.23131i) q^{90} +(4.55157 + 3.30691i) q^{91} -4.47214i q^{92} +(4.14794 - 3.71411i) q^{93} -3.06348 q^{94} +(-2.33593 - 9.19102i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-4.16458 + 1.35316i) q^{97} -2.38197i q^{98} +0.530927 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 12 q^{5} - 16 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 + 12 * q^5 - 16 * q^6 + 4 * q^9	$ 16 q + 4 q^{4} + 12 q^{5} - 16 q^{6} + 4 q^{9} + 4 q^{10} + 8 q^{11} + 4 q^{15} - 4 q^{16} + 8 q^{19} - 2 q^{20} - 4 q^{24} + 16 q^{25} - 24 q^{26} + 36 q^{29} - 12 q^{30} + 40 q^{31} + 8 q^{34} + 14 q^{35} + 16 q^{36} - 4 q^{39} + 6 q^{40} + 32 q^{41} + 12 q^{44} - 2 q^{45} - 40 q^{46} - 4 q^{49} - 8 q^{50} + 8 q^{51} - 4 q^{54} + 24 q^{55} - 4 q^{60} - 16 q^{61} + 4 q^{64} + 6 q^{65} - 8 q^{66} + 40 q^{69} + 18 q^{70} - 12 q^{71} - 12 q^{74} - 8 q^{75} + 32 q^{76} - 8 q^{79} - 8 q^{80} - 4 q^{81} - 40 q^{85} - 68 q^{86} + 20 q^{89} - 4 q^{90} - 56 q^{94} - 18 q^{95} + 4 q^{96} - 8 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 + 12 * q^5 - 16 * q^6 + 4 * q^9 + 4 * q^10 + 8 * q^11 + 4 * q^15 - 4 * q^16 + 8 * q^19 - 2 * q^20 - 4 * q^24 + 16 * q^25 - 24 * q^26 + 36 * q^29 - 12 * q^30 + 40 * q^31 + 8 * q^34 + 14 * q^35 + 16 * q^36 - 4 * q^39 + 6 * q^40 + 32 * q^41 + 12 * q^44 - 2 * q^45 - 40 * q^46 - 4 * q^49 - 8 * q^50 + 8 * q^51 - 4 * q^54 + 24 * q^55 - 4 * q^60 - 16 * q^61 + 4 * q^64 + 6 * q^65 - 8 * q^66 + 40 * q^69 + 18 * q^70 - 12 * q^71 - 12 * q^74 - 8 * q^75 + 32 * q^76 - 8 * q^79 - 8 * q^80 - 4 * q^81 - 40 * q^85 - 68 * q^86 + 20 * q^89 - 4 * q^90 - 56 * q^94 - 18 * q^95 + 4 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	1.71943	+	1.42953i	0.768953	+	0.639305i
$5$	1.71943	+	1.42953i	0.768953	+	0.639305i
$6$	−1.00000			−0.408248
$7$	2.04378	−	0.664066i	0.772478	−	0.250993i	0.103852	−	0.994593i	$-0.466883\pi$
$7$	2.04378	−	0.664066i	0.772478	−	0.250993i	0.668625	+	0.743600i	$0.266883\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	−2.16717	+	0.550794i	−0.685319	+	0.174176i
$11$	−0.164066	−	0.504942i	−0.0494676	−	0.152246i	0.923271	−	0.384148i	$-0.125505\pi$
$11$	−0.164066	−	0.504942i	−0.0494676	−	0.152246i	−0.972739	+	0.231903i	$0.925505\pi$
$12$	0.587785	−	0.809017i	0.169679	−	0.233543i
$13$	1.53884	+	2.11803i	0.426798	+	0.587437i	0.967215	−	0.253961i	$-0.0817334\pi$
$13$	1.53884	+	2.11803i	0.426798	+	0.587437i	−0.540417	+	0.841398i	$0.681733\pi$
$14$	−0.664066	+	2.04378i	−0.177479	+	0.546224i
$15$	−0.145857	+	2.23131i	−0.0376600	+	0.576121i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	2.18545	+	0.710097i	0.530050	+	0.172224i	0.561802	−	0.827272i	$-0.310108\pi$
$17$	2.18545	+	0.710097i	0.530050	+	0.172224i	−0.0317512	+	0.999496i	$0.510108\pi$
$18$	−0.587785	−	0.809017i	−0.138542	−	0.190687i
$19$	−3.43106	−	2.49281i	−0.787139	−	0.571890i	0.119974	−	0.992777i	$-0.461719\pi$
$19$	−3.43106	−	2.49281i	−0.787139	−	0.571890i	−0.907113	+	0.420887i	$0.861719\pi$
$20$	0.828229	−	2.07703i	0.185198	−	0.464437i
$21$	1.73855	+	1.26313i	0.379382	+	0.275637i
$22$	0.504942	+	0.164066i	0.107654	+	0.0349789i
$23$	4.25325	+	1.38197i	0.886865	+	0.288160i	0.716805	−	0.697274i	$-0.245604\pi$
$23$	4.25325	+	1.38197i	0.886865	+	0.288160i	0.170060	+	0.985434i	$0.445604\pi$
$24$	0.309017	+	0.951057i	0.0630778	+	0.194134i
$25$	0.912893	+	4.91596i	0.182579	+	0.983191i
$26$	−2.61803			−0.513439
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	−1.26313	−	1.73855i	−0.238709	−	0.328554i
$29$	3.97060	+	2.88481i	0.737323	+	0.535696i	0.891872	−	0.452289i	$-0.149392\pi$
$29$	3.97060	+	2.88481i	0.737323	+	0.535696i	−0.154549	+	0.987985i	$0.549392\pi$
$30$	−1.71943	−	1.42953i	−0.313924	−	0.260995i
$31$	−0.566677	−	5.53885i	−0.101778	−	0.994807i
$31$	−0.566677	−	5.53885i	−0.101778	−	0.994807i
$32$		−	1.00000i		−	0.176777i
$33$	0.312071	−	0.429529i	0.0543246	−	0.0747714i
$34$	−1.85906	+	1.35068i	−0.318826	+	0.231641i
$35$	4.46345	+	1.77983i	0.754460	+	0.300847i
$36$	1.00000			0.166667
$37$		−	2.67989i		−	0.440571i	−0.975435	−	0.220285i	$-0.929301\pi$
$37$		−	2.67989i		−	0.440571i	0.975435	−	0.220285i	$-0.0706989\pi$
$38$	4.03345	−	1.31055i	0.654313	−	0.212599i
$39$	−0.809017	+	2.48990i	−0.129546	+	0.398703i
$40$	1.19353	+	1.89090i	0.188713	+	0.298977i
$41$	0.305007	+	0.221601i	0.0476341	+	0.0346082i	0.611348	−	0.791362i	$-0.290628\pi$
$41$	0.305007	+	0.221601i	0.0476341	+	0.0346082i	−0.563713	+	0.825970i	$0.690628\pi$
$42$	−2.04378	+	0.664066i	−0.315363	+	0.102468i
$43$	−0.723629	+	0.995990i	−0.110352	+	0.151887i	−0.860621	−	0.509246i	$-0.829924\pi$
$43$	−0.723629	+	0.995990i	−0.110352	+	0.151887i	0.750268	+	0.661133i	$0.229924\pi$
$44$	−0.429529	+	0.312071i	−0.0647539	+	0.0470465i
$45$	−1.89090	+	1.19353i	−0.281878	+	0.177921i
$46$	−3.61803	+	2.62866i	−0.533450	+	0.387574i
$47$	1.80067	+	2.47841i	0.262655	+	0.361513i	0.919893	−	0.392170i	$-0.128275\pi$
$47$	1.80067	+	2.47841i	0.262655	+	0.361513i	−0.657238	+	0.753683i	$0.728275\pi$
$48$	−0.951057	−	0.309017i	−0.137273	−	0.0446028i
$49$	−1.92705	+	1.40008i	−0.275293	+	0.200012i
$50$	−4.51368	−	2.15098i	−0.638330	−	0.304195i
$51$	0.710097	+	2.18545i	0.0994335	+	0.306025i
$52$	1.53884	−	2.11803i	0.213399	−	0.293718i
$53$	1.05637	+	0.343235i	0.145104	+	0.0471470i	0.380668	−	0.924712i	$-0.375694\pi$
$53$	1.05637	+	0.343235i	0.145104	+	0.0471470i	−0.235565	+	0.971859i	$0.575694\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	0.439729	−	1.10275i	0.0592931	−	0.148695i
$56$	2.14896			0.287167
$57$		−	4.24102i		−	0.561737i
$58$	−4.66773	+	1.51664i	−0.612902	+	0.199144i
$59$	−3.02312	+	2.19643i	−0.393577	+	0.285951i	−0.766920	−	0.641743i	$-0.778212\pi$
$59$	−3.02312	+	2.19643i	−0.393577	+	0.285951i	0.373343	+	0.927694i	$0.378212\pi$
$60$	2.16717	−	0.550794i	0.279780	−	0.0711072i
$61$	1.98935			0.254710			0.127355	−	0.991857i	$-0.459351\pi$
$61$	1.98935			0.254710			0.127355	+	0.991857i	$0.459351\pi$
$62$	4.81411	+	2.79720i	0.611393	+	0.355245i
$63$			2.14896i			0.270744i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−0.381857	+	5.84163i	−0.0473636	+	0.724566i
$66$	0.164066	+	0.504942i	0.0201951	+	0.0621540i
$67$		−	2.64824i		−	0.323534i	−0.986829	−	0.161767i	$-0.948281\pi$
$67$		−	2.64824i		−	0.323534i	0.986829	−	0.161767i	$-0.0517194\pi$
$68$		−	2.29792i		−	0.278664i
$69$	1.38197	+	4.25325i	0.166369	+	0.512032i
$70$	−4.06346	+	2.56485i	−0.485677	+	0.306558i
$71$	0.970604	−	2.98721i	0.115190	−	0.354517i	−0.876797	−	0.480861i	$-0.840324\pi$
$71$	0.970604	−	2.98721i	0.115190	−	0.354517i	0.991987	+	0.126344i	$0.0403242\pi$
$72$	−0.587785	+	0.809017i	−0.0692712	+	0.0953436i
$73$	−15.5573	+	5.05486i	−1.82084	+	0.591627i	−0.821057	+	0.570846i	$0.806615\pi$
$73$	−15.5573	+	5.05486i	−1.82084	+	0.591627i	−0.999784	+	0.0207807i	$0.993385\pi$
$74$	2.16808	+	1.57520i	0.252034	+	0.183113i
$75$	−3.44051	+	3.62807i	−0.397276	+	0.418934i
$76$	−1.31055	+	4.03345i	−0.150330	+	0.462669i
$77$	−0.670629	−	0.923041i	−0.0764252	−	0.105190i
$78$	−1.53884	−	2.11803i	−0.174240	−	0.239820i
$79$	−1.41772	+	4.36328i	−0.159506	+	0.490907i	−0.998589	−	0.0530944i	$-0.983092\pi$
$79$	−1.41772	+	4.36328i	−0.159506	+	0.490907i	0.839084	+	0.544002i	$0.183092\pi$
$80$	−2.23131	−	0.145857i	−0.249468	−	0.0163073i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−0.358558	+	0.116502i	−0.0395961	+	0.0128655i
$83$	−2.23194	+	3.07200i	−0.244987	+	0.337196i	−0.913748	−	0.406282i	$-0.866825\pi$
$83$	−2.23194	+	3.07200i	−0.244987	+	0.337196i	0.668761	+	0.743478i	$0.266825\pi$
$84$	0.664066	−	2.04378i	0.0724555	−	0.222995i
$85$	2.74264	+	4.34513i	0.297481	+	0.471296i
$86$	−0.380434	−	1.17086i	−0.0410233	−	0.126257i
$87$			4.90794i			0.526186i
$88$		−	0.530927i		−	0.0565970i
$89$	−0.173401	−	0.533672i	−0.0183804	−	0.0565691i	0.941446	−	0.337165i	$-0.109468\pi$
$89$	−0.173401	−	0.533672i	−0.0183804	−	0.0565691i	−0.959826	+	0.280596i	$0.909468\pi$
$90$	0.145857	−	2.23131i	0.0153746	−	0.235200i
$91$	4.55157	+	3.30691i	0.477134	+	0.346658i
$92$		−	4.47214i		−	0.466252i
$93$	4.14794	−	3.71411i	0.430121	−	0.385135i
$94$	−3.06348			−0.315974
$95$	−2.33593	−	9.19102i	−0.239661	−	0.942979i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	−4.16458	+	1.35316i	−0.422849	+	0.137392i	−0.512709	−	0.858562i	$-0.671358\pi$
$97$	−4.16458	+	1.35316i	−0.422849	+	0.137392i	0.0898598	+	0.995954i	$0.471358\pi$
$98$		−	2.38197i		−	0.240615i
$99$	0.530927			0.0533602
$100$	4.39325	−	2.38733i	0.439325	−	0.238733i
$101$	2.87416	−	8.84576i	0.285990	−	0.880186i	−0.700110	−	0.714035i	$-0.746866\pi$
$101$	2.87416	−	8.84576i	0.285990	−	0.880186i	0.986100	−	0.166152i	$-0.0531341\pi$
$102$	−2.18545	−	0.710097i	−0.216392	−	0.0703101i
$103$	−4.66327	+	6.41843i	−0.459485	+	0.632427i	−0.974402	−	0.224813i	$-0.927823\pi$
$103$	−4.66327	+	6.41843i	−0.459485	+	0.632427i	0.514917	+	0.857240i	$0.327823\pi$
$104$	0.809017	+	2.48990i	0.0793306	+	0.244155i
$105$	1.18363	+	4.65716i	0.115511	+	0.454493i
$106$	−0.898602	+	0.652873i	−0.0872799	+	0.0634126i
$107$	14.8464	+	4.82389i	1.43526	+	0.466343i	0.920415	−	0.390942i	$-0.127851\pi$
$107$	14.8464	+	4.82389i	1.43526	+	0.466343i	0.514842	+	0.857285i	$0.327851\pi$
$108$	0.587785	+	0.809017i	0.0565597	+	0.0778477i
$109$	−2.47440	+	1.79776i	−0.237004	+	0.172194i	−0.699948	−	0.714194i	$-0.746793\pi$
$109$	−2.47440	+	1.79776i	−0.237004	+	0.172194i	0.462943	+	0.886388i	$0.346793\pi$
$110$	0.633677	+	1.00393i	0.0604187	+	0.0957208i
$111$	2.16808	−	1.57520i	0.205785	−	0.149511i
$112$	−1.26313	+	1.73855i	−0.119354	+	0.164277i
$113$	−4.01235	+	1.30369i	−0.377450	+	0.122641i	−0.491597	−	0.870823i	$-0.663587\pi$
$113$	−4.01235	+	1.30369i	−0.377450	+	0.122641i	0.114147	+	0.993464i	$0.463587\pi$
$114$	3.43106	+	2.49281i	0.321348	+	0.233473i
$115$	5.33762	+	8.45635i	0.497736	+	0.788558i
$116$	1.51664	−	4.66773i	0.140816	−	0.433387i
$117$	−2.48990	+	0.809017i	−0.230191	+	0.0747936i
$118$		−	3.73679i		−	0.343999i
$119$	4.93815			0.452679
$120$	−0.828229	+	2.07703i	−0.0756066	+	0.189606i
$121$	8.67114	−	6.29995i	0.788285	−	0.572723i
$122$	−1.16931	+	1.60942i	−0.105864	+	0.145710i
$123$			0.377010i			0.0339938i
$124$	−5.09265	+	2.25054i	−0.457333	+	0.202105i
$125$	−5.45784	+	9.75766i	−0.488164	+	0.872752i
$126$	−1.73855	−	1.26313i	−0.154882	−	0.112528i
$127$	−6.18881	−	8.51817i	−0.549168	−	0.755865i	0.440731	−	0.897639i	$-0.354719\pi$
$127$	−6.18881	−	8.51817i	−0.549168	−	0.755865i	−0.989899	+	0.141774i	$0.954719\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	−1.23111			−0.108393
$130$	−4.50153	−	3.74256i	−0.394810	−	0.328244i
$131$	−6.09513	−	18.7589i	−0.532534	−	1.63897i	−0.748919	−	0.662662i	$-0.769427\pi$
$131$	−6.09513	−	18.7589i	−0.532534	−	1.63897i	0.216385	−	0.976308i	$-0.430573\pi$
$132$	−0.504942	−	0.164066i	−0.0439495	−	0.0142801i
$133$	−8.66774	−	2.81632i	−0.751588	−	0.244206i
$134$	2.14247	+	1.55660i	0.185082	+	0.134470i
$135$	−2.07703	−	0.828229i	−0.178762	−	0.0712826i
$136$	1.85906	+	1.35068i	0.159413	+	0.115820i
$137$	−1.53317	−	2.11023i	−0.130988	−	0.180289i	0.738485	−	0.674270i	$-0.235541\pi$
$137$	−1.53317	−	2.11023i	−0.130988	−	0.180289i	−0.869473	+	0.493980i	$0.835541\pi$
$138$	−4.25325	−	1.38197i	−0.362061	−	0.117641i
$139$	−6.79544	+	4.93718i	−0.576382	+	0.418766i	−0.837418	−	0.546563i	$-0.815936\pi$
$139$	−6.79544	+	4.93718i	−0.576382	+	0.418766i	0.261036	+	0.965329i	$0.415936\pi$
$140$	0.313440	−	4.79499i	0.0264905	−	0.405251i
$141$	−0.946668	+	2.91354i	−0.0797238	+	0.245365i
$142$	1.84620	+	2.54108i	0.154930	+	0.213242i
$143$	0.817013	−	1.12452i	0.0683220	−	0.0940372i
$144$	−0.309017	−	0.951057i	−0.0257514	−	0.0792547i
$145$	2.70326	+	10.6363i	0.224494	+	0.883299i
$146$	5.05486	−	15.5573i	0.418344	−	1.28753i
$147$	−2.26538	−	0.736068i	−0.186846	−	0.0607099i
$148$	−2.54873	+	0.828131i	−0.209504	+	0.0680720i
$149$	0.898025			0.0735690			0.0367845	−	0.999323i	$-0.488288\pi$
$149$	0.898025			0.0735690			0.0367845	+	0.999323i	$0.488288\pi$
$150$	−0.912893	−	4.91596i	−0.0745374	−	0.401386i
$151$	−2.93003	−	9.01771i	−0.238443	−	0.733851i	−0.996646	−	0.0818328i	$-0.973923\pi$
$151$	−2.93003	−	9.01771i	−0.238443	−	0.733851i	0.758203	−	0.652018i	$-0.226077\pi$
$152$	−2.49281	−	3.43106i	−0.202194	−	0.278296i
$153$	−1.35068	+	1.85906i	−0.109196	+	0.150296i
$154$	1.14094			0.0919397
$155$	6.94359	−	10.3338i	0.557722	−	0.830028i
$156$	2.61803			0.209610
$157$	−1.61156	+	2.21812i	−0.128616	+	0.177025i	−0.868469	−	0.495744i	$-0.834895\pi$
$157$	−1.61156	+	2.21812i	−0.128616	+	0.177025i	0.739852	+	0.672769i	$0.234895\pi$
$158$	−2.69666	−	3.71163i	−0.214534	−	0.295281i
$159$	0.343235	+	1.05637i	0.0272203	+	0.0837756i
$160$	1.42953	−	1.71943i	0.113014	−	0.135933i
$161$	9.61045			0.757409
$162$	0.951057	−	0.309017i	0.0747221	−	0.0242787i
$163$	−14.7210	−	4.78313i	−1.15303	−	0.374644i	−0.330749	−	0.943719i	$-0.607301\pi$
$163$	−14.7210	−	4.78313i	−1.15303	−	0.374644i	−0.822285	+	0.569075i	$0.807301\pi$
$164$	0.116502	−	0.358558i	0.00909731	−	0.0279986i
$165$	1.15061	−	0.292431i	0.0895748	−	0.0227657i
$166$	−1.17340	−	3.61136i	−0.0910735	−	0.280296i
$167$	8.43129	−	11.6047i	0.652433	−	0.897997i	−0.346769	−	0.937951i	$-0.612721\pi$
$167$	8.43129	−	11.6047i	0.652433	−	0.897997i	0.999202	+	0.0399538i	$0.0127211\pi$
$168$	1.26313	+	1.73855i	0.0974524	+	0.134132i
$169$	1.89919	−	5.84510i	0.146091	−	0.449623i
$170$	−5.12737	−	0.335167i	−0.393251	−	0.0257061i
$171$	3.43106	−	2.49281i	0.262380	−	0.190630i
$172$	1.17086	+	0.380434i	0.0892770	+	0.0290079i
$173$	1.89378	+	2.60657i	0.143982	+	0.198174i	0.874917	−	0.484273i	$-0.160916\pi$
$173$	1.89378	+	2.60657i	0.143982	+	0.198174i	−0.730935	+	0.682447i	$0.760916\pi$
$174$	−3.97060	−	2.88481i	−0.301011	−	0.218697i
$175$	5.13027	+	9.44093i	0.387812	+	0.713667i
$176$	0.429529	+	0.312071i	0.0323770	+	0.0235232i
$177$	−3.55390	−	1.15473i	−0.267127	−	0.0867949i
$178$	0.533672	+	0.173401i	0.0400004	+	0.0129969i
$179$	−0.449590	−	1.38369i	−0.0336039	−	0.103422i	0.932848	−	0.360271i	$-0.117316\pi$
$179$	−0.449590	−	1.38369i	−0.0336039	−	0.103422i	−0.966452	+	0.256849i	$0.917316\pi$
$180$	1.71943	+	1.42953i	0.128159	+	0.106551i
$181$	23.3947			1.73891			0.869455	−	0.494012i	$-0.164470\pi$
$181$	23.3947			1.73891			0.869455	+	0.494012i	$0.164470\pi$
$182$	−5.35069	+	1.73855i	−0.396620	+	0.128870i
$183$	1.16931	+	1.60942i	0.0864379	+	0.118972i
$184$	3.61803	+	2.62866i	0.266725	+	0.193787i
$185$	3.83098	−	4.60789i	0.281659	−	0.338779i
$186$	0.566677	+	5.53885i	0.0415508	+	0.406128i
$187$		−	1.22003i		−	0.0892174i
$188$	1.80067	−	2.47841i	0.131327	−	0.180756i
$189$	−1.73855	+	1.26313i	−0.126461	+	0.0918790i
$190$	8.80872	+	3.51254i	0.639051	+	0.254826i
$191$	14.8526			1.07470			0.537350	−	0.843360i	$-0.319426\pi$
$191$	14.8526			1.07470			0.537350	+	0.843360i	$0.319426\pi$
$192$			1.00000i			0.0721688i
$193$	−10.2777	+	3.33944i	−0.739808	+	0.240378i	−0.654590	−	0.755984i	$-0.727159\pi$
$193$	−10.2777	+	3.33944i	−0.739808	+	0.240378i	−0.0852182	+	0.996362i	$0.527159\pi$
$194$	1.35316	−	4.16458i	0.0971509	−	0.299000i
$195$	−4.95043	+	3.12470i	−0.354508	+	0.223764i
$196$	1.92705	+	1.40008i	0.137646	+	0.100006i
$197$	−12.9333	+	4.20229i	−0.921462	+	0.299401i	−0.731066	−	0.682306i	$-0.760977\pi$
$197$	−12.9333	+	4.20229i	−0.921462	+	0.299401i	−0.190395	+	0.981707i	$0.560977\pi$
$198$	−0.312071	+	0.429529i	−0.0221779	+	0.0305253i
$199$	20.4303	−	14.8435i	1.44827	−	1.05223i	0.462036	−	0.886861i	$-0.347119\pi$
$199$	20.4303	−	14.8435i	1.44827	−	1.05223i	0.986232	−	0.165367i	$-0.0528807\pi$
$200$	−0.650901	+	4.95745i	−0.0460257	+	0.350545i
$201$	2.14247	−	1.55660i	0.151118	−	0.109794i
$202$	5.46698	+	7.52466i	0.384656	+	0.529433i
$203$	10.0308	+	3.25919i	0.704021	+	0.228750i
$204$	1.85906	−	1.35068i	0.130160	−	0.0945669i
$205$	0.207655	+	0.817044i	0.0145032	+	0.0570649i
$206$	−2.45162	−	7.54532i	−0.170813	−	0.525708i
$207$	−2.62866	+	3.61803i	−0.182704	+	0.251471i
$208$	−2.48990	−	0.809017i	−0.172643	−	0.0560952i
$209$	−0.695806	+	2.14147i	−0.0481299	+	0.148129i
$210$	−4.46345	−	1.77983i	−0.308007	−	0.122820i
$211$	22.1843			1.52723			0.763615	−	0.645672i	$-0.223423\pi$
$211$	22.1843			1.52723			0.763615	+	0.645672i	$0.223423\pi$
$212$		−	1.11073i		−	0.0762855i
$213$	2.98721	−	0.970604i	0.204680	−	0.0665047i
$214$	−12.6291	+	9.17559i	−0.863309	+	0.627230i
$215$	−2.66803	+	0.678089i	−0.181958	+	0.0462453i
$216$	−1.00000			−0.0680414
$217$	−4.83633	−	10.9439i	−0.328311	−	0.742921i
$218$		−	3.05852i		−	0.207149i
$219$	−13.2338	−	9.61492i	−0.894258	−	0.649716i
$220$	−1.18466	−	0.0774392i	−0.0798698	−	0.00522095i
$221$	1.85906	+	5.72159i	0.125054	+	0.384876i
$222$			2.67989i			0.179862i
$223$		−	18.3104i		−	1.22616i	−0.790022	−	0.613079i	$-0.789931\pi$
$223$		−	18.3104i		−	1.22616i	0.790022	−	0.613079i	$-0.210069\pi$
$224$	−0.664066	−	2.04378i	−0.0443697	−	0.136556i
$225$	−4.95745	−	0.650901i	−0.330497	−	0.0433934i
$226$	1.30369	−	4.01235i	0.0867203	−	0.266898i
$227$	10.8053	−	14.8723i	0.717175	−	0.987107i	−0.282438	−	0.959286i	$-0.591143\pi$
$227$	10.8053	−	14.8723i	0.717175	−	0.987107i	0.999613	−	0.0278215i	$-0.00885700\pi$
$228$	−4.03345	+	1.31055i	−0.267122	+	0.0867932i
$229$	−14.7917	−	10.7468i	−0.977460	−	0.710166i	−0.0203203	−	0.999794i	$-0.506469\pi$
$229$	−14.7917	−	10.7468i	−0.977460	−	0.710166i	−0.957139	+	0.289627i	$0.906469\pi$
$230$	−9.97870	−	0.652290i	−0.657976	−	0.0430107i
$231$	0.352570	−	1.08510i	0.0231974	−	0.0713943i
$232$	2.88481	+	3.97060i	0.189397	+	0.260683i
$233$	10.0427	+	13.8226i	0.657919	+	0.905547i	0.999410	−	0.0343376i	$-0.0109321\pi$
$233$	10.0427	+	13.8226i	0.657919	+	0.905547i	−0.341492	+	0.939885i	$0.610932\pi$
$234$	0.809017	−	2.48990i	0.0528871	−	0.162770i
$235$	−0.446829	+	6.83556i	−0.0291479	+	0.445903i
$236$	3.02312	+	2.19643i	0.196789	+	0.142975i
$237$	−4.36328	+	1.41772i	−0.283426	+	0.0920905i
$238$	−2.90257	+	3.99504i	−0.188146	+	0.258960i
$239$	3.72877	−	11.4760i	0.241194	−	0.742318i	−0.755045	−	0.655673i	$-0.772385\pi$
$239$	3.72877	−	11.4760i	0.241194	−	0.742318i	0.996239	−	0.0866458i	$-0.0276148\pi$
$240$	−1.19353	−	1.89090i	−0.0770419	−	0.122057i
$241$	−5.20280	−	16.0126i	−0.335142	−	1.03146i	−0.966652	−	0.256093i	$-0.917565\pi$
$241$	−5.20280	−	16.0126i	−0.335142	−	1.03146i	0.631511	−	0.775367i	$-0.282435\pi$
$242$			10.7181i			0.688987i
$243$		−	1.00000i		−	0.0641500i
$244$	−0.614743	−	1.89198i	−0.0393549	−	0.121122i
$245$	−5.31489	−	0.347425i	−0.339556	−	0.0221962i
$246$	−0.305007	−	0.221601i	−0.0194466	−	0.0141288i
$247$		−	11.1031i		−	0.706476i
$248$	1.17266	−	5.44287i	0.0744638	−	0.345623i
$249$	−3.79720			−0.240638
$250$	−4.68607	−	10.1509i	−0.296373	−	0.641999i
$251$	−2.98358	+	2.16770i	−0.188322	+	0.136824i	−0.677951	−	0.735107i	$-0.737132\pi$
$251$	−2.98358	+	2.16770i	−0.188322	+	0.136824i	0.489630	+	0.871931i	$0.337132\pi$
$252$	2.04378	−	0.664066i	0.128746	−	0.0418322i
$253$		−	2.37438i		−	0.149276i
$254$	10.5290			0.660650
$255$	−1.90321	+	4.77284i	−0.119183	+	0.298887i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−7.64051	−	2.48255i	−0.476602	−	0.154857i	0.0608585	−	0.998146i	$-0.480616\pi$
$257$	−7.64051	−	2.48255i	−0.476602	−	0.154857i	−0.537460	+	0.843289i	$0.680616\pi$
$258$	0.723629	−	0.995990i	0.0450512	−	0.0620077i
$259$	−1.77962	−	5.47711i	−0.110580	−	0.340331i
$260$	5.67373	−	1.44200i	0.351869	−	0.0894288i
$261$	−3.97060	+	2.88481i	−0.245774	+	0.178565i
$262$	18.7589	+	6.09513i	1.15893	+	0.376558i
$263$	−1.24983	−	1.72025i	−0.0770679	−	0.106075i	0.768743	−	0.639558i	$-0.220883\pi$
$263$	−1.24983	−	1.72025i	−0.0770679	−	0.106075i	−0.845811	+	0.533483i	$0.820883\pi$
$264$	0.429529	−	0.312071i	0.0264357	−	0.0192067i
$265$	1.32569	+	2.10028i	0.0814366	+	0.129019i
$266$	7.37322	−	5.35695i	0.452081	−	0.328456i
$267$	0.329827	−	0.453968i	0.0201851	−	0.0277824i
$268$	−2.51863	+	0.818352i	−0.153850	+	0.0499888i
$269$	−3.19916	−	2.32432i	−0.195056	−	0.141716i	0.485971	−	0.873975i	$-0.338466\pi$
$269$	−3.19916	−	2.32432i	−0.195056	−	0.141716i	−0.681027	+	0.732259i	$0.738466\pi$
$270$	1.89090	−	1.19353i	0.115076	−	0.0726358i
$271$	4.47367	−	13.7685i	0.271756	−	0.836379i	−0.718304	−	0.695730i	$-0.755081\pi$
$271$	4.47367	−	13.7685i	0.271756	−	0.836379i	0.990060	−	0.140649i	$-0.0449189\pi$
$272$	−2.18545	+	0.710097i	−0.132513	+	0.0430560i
$273$			5.62605i			0.340504i
$274$	2.60839			0.157579
$275$	2.33250	−	1.26750i	0.140655	−	0.0764329i
$276$	3.61803	−	2.62866i	0.217780	−	0.158226i
$277$	8.13380	−	11.1952i	0.488712	−	0.672655i	−0.491437	−	0.870913i	$-0.663528\pi$
$277$	8.13380	−	11.1952i	0.488712	−	0.672655i	0.980150	+	0.198258i	$0.0635284\pi$
$278$		−	8.39963i		−	0.503776i
$279$	5.44287	+	1.17266i	0.325856	+	0.0702052i
$280$	3.69499	+	3.07200i	0.220818	+	0.183587i
$281$	−9.22980	−	6.70584i	−0.550603	−	0.400037i	0.277404	−	0.960753i	$-0.410526\pi$
$281$	−9.22980	−	6.70584i	−0.550603	−	0.400037i	−0.828008	+	0.560716i	$0.810526\pi$
$282$	−1.80067	−	2.47841i	−0.107228	−	0.147587i
$283$	14.2750	−	4.63824i	0.848562	−	0.275714i	0.147718	−	0.989029i	$-0.452807\pi$
$283$	14.2750	−	4.63824i	0.848562	−	0.275714i	0.700844	+	0.713315i	$0.252807\pi$
$284$	−3.14094			−0.186381
$285$	6.06267	−	7.29215i	0.359121	−	0.431950i
$286$	0.429529	+	1.32195i	0.0253986	+	0.0781688i
$287$	0.770526	+	0.250359i	0.0454827	+	0.0147782i
$288$	0.951057	+	0.309017i	0.0560415	+	0.0182090i
$289$	−9.48132	−	6.88858i	−0.557725	−	0.405211i
$290$	−10.1939	−	4.06490i	−0.598607	−	0.238699i
$291$	−3.54261	−	2.57385i	−0.207671	−	0.150882i
$292$	9.61492	+	13.2338i	0.562671	+	0.774450i
$293$	26.5483	+	8.62605i	1.55097	+	0.503939i	0.954376	−	0.298607i	$-0.0965219\pi$
$293$	26.5483	+	8.62605i	1.55097	+	0.503939i	0.596590	+	0.802546i	$0.296522\pi$
$294$	1.92705	−	1.40008i	0.112388	−	0.0816546i
$295$	−8.33791	−	0.545035i	−0.485452	−	0.0317331i
$296$	0.828131	−	2.54873i	0.0481341	−	0.148142i
$297$	0.312071	+	0.429529i	0.0181082	+	0.0249238i
$298$	−0.527846	+	0.726517i	−0.0305773	+	0.0420860i
$299$	3.61803	+	11.1352i	0.209236	+	0.643963i
$300$	4.51368	+	2.15098i	0.260597	+	0.124187i
$301$	−0.817539	+	2.51613i	−0.0471222	+	0.145027i
$302$	9.01771	+	2.93003i	0.518911	+	0.168604i
$303$	8.84576	−	2.87416i	0.508176	−	0.165116i
$304$	4.24102			0.243239
$305$	3.42055	+	2.84383i	0.195860	+	0.162837i
$306$	−0.710097	−	2.18545i	−0.0405935	−	0.124934i
$307$	2.88894	+	3.97628i	0.164880	+	0.226938i	0.883460	−	0.468506i	$-0.155208\pi$
$307$	2.88894	+	3.97628i	0.164880	+	0.226938i	−0.718580	+	0.695444i	$0.755208\pi$
$308$	−0.670629	+	0.923041i	−0.0382126	+	0.0525952i
$309$	−7.93362			−0.451328
$310$	4.27885	+	11.6915i	0.243022	+	0.664033i
$311$	−16.2584			−0.921931			−0.460965	−	0.887418i	$-0.652497\pi$
$311$	−16.2584			−0.921931			−0.460965	+	0.887418i	$0.652497\pi$
$312$	−1.53884	+	2.11803i	−0.0871198	+	0.119910i
$313$	−14.9011	−	20.5095i	−0.842257	−	1.15927i	−0.985516	−	0.169582i	$-0.945758\pi$
$313$	−14.9011	−	20.5095i	−0.842257	−	1.15927i	0.143259	−	0.989685i	$-0.454242\pi$
$314$	−0.847245	−	2.60755i	−0.0478128	−	0.147153i
$315$	−3.07200	+	3.69499i	−0.173088	+	0.208189i
$316$	4.58783			0.258085
$317$	−23.8139	+	7.73760i	−1.33752	+	0.434587i	−0.888476	−	0.458922i	$-0.848236\pi$
$317$	−23.8139	+	7.73760i	−1.33752	+	0.434587i	−0.449045	+	0.893509i	$0.648236\pi$
$318$	−1.05637	−	0.343235i	−0.0592383	−	0.0192477i
$319$	0.805223	−	2.47822i	0.0450838	−	0.138754i
$320$	0.550794	+	2.16717i	0.0307903	+	0.121148i
$321$	4.82389	+	14.8464i	0.269243	+	0.828646i
$322$	−5.64888	+	7.77501i	−0.314800	+	0.433285i
$323$	−5.72829	−	7.88431i	−0.318730	−	0.438695i
$324$	−0.309017	+	0.951057i	−0.0171676	+	0.0528365i
$325$	−9.00736	+	9.49842i	−0.499639	+	0.526877i
$326$	12.5224	−	9.09805i	0.693551	−	0.503894i
$327$	−2.90883	−	0.945136i	−0.160859	−	0.0522661i
$328$	0.221601	+	0.305007i	0.0122359	+	0.0168412i
$329$	5.32600	+	3.86957i	0.293632	+	0.213336i
$330$	−0.439729	+	1.10275i	−0.0242063	+	0.0607044i
$331$	−5.40866	−	3.92962i	−0.297287	−	0.215991i	0.429136	−	0.903240i	$-0.358818\pi$
$331$	−5.40866	−	3.92962i	−0.297287	−	0.215991i	−0.726422	+	0.687249i	$0.758818\pi$
$332$	3.61136	+	1.17340i	0.198199	+	0.0643987i
$333$	2.54873	+	0.828131i	0.139669	+	0.0453813i
$334$	4.43259	+	13.6421i	0.242541	+	0.746463i
$335$	3.78574	−	4.55347i	0.206837	−	0.248783i
$336$	−2.14896			−0.117235
$337$	16.3096	−	5.29932i	0.888442	−	0.288672i	0.170984	−	0.985274i	$-0.445305\pi$
$337$	16.3096	−	5.29932i	0.888442	−	0.288672i	0.717458	+	0.696601i	$0.245305\pi$
$338$	3.61247	+	4.97214i	0.196492	+	0.270449i
$339$	−3.41311	−	2.47977i	−0.185375	−	0.134683i
$340$	3.28495	−	3.95112i	0.178151	−	0.214280i
$341$	−2.70383	+	1.19487i	−0.146420	+	0.0647060i
$342$			4.24102i			0.229328i
$343$	−11.8506	+	16.3110i	−0.639873	+	0.880710i
$344$	−0.995990	+	0.723629i	−0.0537002	+	0.0390155i
$345$	−3.70395	+	9.28874i	−0.199414	+	0.500089i
$346$	−3.22190			−0.173210
$347$		−	3.63012i		−	0.194875i	−0.995242	−	0.0974376i	$-0.968935\pi$
$347$		−	3.63012i		−	0.194875i	0.995242	−	0.0974376i	$-0.0310646\pi$
$348$	4.66773	−	1.51664i	0.250216	−	0.0813002i
$349$	−6.51240	+	20.0431i	−0.348601	+	1.07288i	0.611027	+	0.791610i	$0.290757\pi$
$349$	−6.51240	+	20.0431i	−0.348601	+	1.07288i	−0.959628	+	0.281273i	$0.909243\pi$
$350$	−10.6534	−	1.39876i	−0.569447	−	0.0747669i
$351$	−2.11803	−	1.53884i	−0.113052	−	0.0821373i
$352$	−0.504942	+	0.164066i	−0.0269135	+	0.00874472i
$353$	13.6886	−	18.8407i	0.728571	−	1.00279i	−0.270625	−	0.962685i	$-0.587230\pi$
$353$	13.6886	−	18.8407i	0.728571	−	1.00279i	0.999195	−	0.0401067i	$-0.0127698\pi$
$354$	3.02312	−	2.19643i	0.160677	−	0.116739i
$355$	5.93920	−	3.74880i	0.315220	−	0.198966i
$356$	−0.453968	+	0.329827i	−0.0240603	+	0.0174808i
$357$	2.90257	+	3.99504i	0.153620	+	0.211440i
$358$	1.38369	+	0.449590i	0.0731305	+	0.0237616i
$359$	−24.1711	+	17.5614i	−1.27570	+	0.926853i	−0.999414	−	0.0342220i	$-0.989105\pi$
$359$	−24.1711	+	17.5614i	−1.27570	+	0.926853i	−0.276289	+	0.961075i	$0.589105\pi$
$360$	−2.16717	+	0.550794i	−0.114220	+	0.0290294i
$361$	−0.313255	−	0.964099i	−0.0164871	−	0.0507421i
$362$	−13.7510	+	18.9267i	−0.722738	+	0.994764i
$363$	10.1935	+	3.31208i	0.535022	+	0.173839i
$364$	1.73855	−	5.35069i	0.0911246	−	0.280453i
$365$	−33.9757	−	13.5481i	−1.77837	−	0.709139i
$366$	−1.98935			−0.103985
$367$		−	36.6846i		−	1.91492i	−0.288569	−	0.957459i	$-0.593180\pi$
$367$		−	36.6846i		−	1.91492i	0.288569	−	0.957459i	$-0.406820\pi$
$368$	−4.25325	+	1.38197i	−0.221716	+	0.0720400i
$369$	−0.305007	+	0.221601i	−0.0158780	+	0.0115361i
$370$	1.47607	+	5.80777i	0.0767370	+	0.301932i
$371$	2.38692			0.123923
$372$	−4.81411	−	2.79720i	−0.249600	−	0.145028i
$373$			3.66006i			0.189511i	0.995501	+	0.0947555i	$0.0302069\pi$
$373$			3.66006i			0.189511i	−0.995501	+	0.0947555i	$0.969793\pi$
$374$	0.987024	+	0.717115i	0.0510378	+	0.0370811i
$375$	−11.1022	+	1.31992i	−0.573313	+	0.0681604i
$376$	0.946668	+	2.91354i	0.0488207	+	0.150255i
$377$			12.8491i			0.661765i
$378$		−	2.14896i		−	0.110531i
$379$	6.02749	+	18.5507i	0.309612	+	0.952887i	0.977916	+	0.208999i	$0.0670204\pi$
$379$	6.02749	+	18.5507i	0.309612	+	0.952887i	−0.668304	+	0.743888i	$0.732980\pi$
$380$	−8.01934	+	5.06178i	−0.411383	+	0.259664i
$381$	3.25365	−	10.0137i	0.166690	−	0.513018i
$382$	−8.73016	+	12.0160i	−0.446674	+	0.614794i
$383$	−21.8900	+	7.11248i	−1.11852	+	0.363431i	−0.809204	−	0.587527i	$-0.800102\pi$
$383$	−21.8900	+	7.11248i	−1.11852	+	0.363431i	−0.309320	+	0.950958i	$0.600102\pi$
$384$	−0.809017	−	0.587785i	−0.0412850	−	0.0299953i
$385$	0.166414	−	2.54579i	0.00848123	−	0.129745i
$386$	3.33944	−	10.2777i	0.169973	−	0.523123i
$387$	−0.723629	−	0.995990i	−0.0367841	−	0.0506290i
$388$	2.57385	+	3.54261i	0.130668	+	0.179849i
$389$	−11.0471	+	33.9995i	−0.560111	+	1.72384i	0.121940	+	0.992538i	$0.461089\pi$
$389$	−11.0471	+	33.9995i	−0.560111	+	1.72384i	−0.682050	+	0.731305i	$0.738911\pi$
$390$	0.381857	−	5.84163i	0.0193361	−	0.295803i
$391$	8.31396	+	6.04045i	0.420455	+	0.305478i
$392$	−2.26538	+	0.736068i	−0.114419	+	0.0371770i
$393$	11.5936	−	15.9572i	0.584821	−	0.804937i
$394$	4.20229	−	12.9333i	0.211708	−	0.651572i
$395$	−8.67510	+	5.47570i	−0.436492	+	0.275512i
$396$	−0.164066	−	0.504942i	−0.00824460	−	0.0253743i
$397$			29.5311i			1.48212i	0.671437	+	0.741062i	$0.265677\pi$
$397$			29.5311i			1.48212i	−0.671437	+	0.741062i	$0.734323\pi$
$398$			25.2533i			1.26583i
$399$	−2.81632	−	8.66774i	−0.140992	−	0.433930i
$400$	−3.62807	−	3.44051i	−0.181404	−	0.172025i
$401$	6.19346	+	4.49981i	0.309287	+	0.224710i	0.731590	−	0.681744i	$-0.238778\pi$
$401$	6.19346	+	4.49981i	0.309287	+	0.224710i	−0.422304	+	0.906454i	$0.638778\pi$
$402$			2.64824i			0.132082i
$403$	10.8594	−	9.72366i	0.540948	−	0.484370i
$404$	−9.30099			−0.462741
$405$	−0.550794	−	2.16717i	−0.0273692	−	0.107688i
$406$	−8.53267	+	6.19935i	−0.423470	+	0.307669i
$407$	−1.35319	+	0.439677i	−0.0670750	+	0.0217940i
$408$			2.29792i			0.113764i
$409$	17.4424			0.862469			0.431235	−	0.902240i	$-0.358078\pi$
$409$	17.4424			0.862469			0.431235	+	0.902240i	$0.358078\pi$
$410$	−0.783059	−	0.312251i	−0.0386725	−	0.0154210i
$411$	0.806036	−	2.48072i	0.0397588	−	0.122365i
$412$	7.54532	+	2.45162i	0.371731	+	0.120783i
$413$	−4.72004	+	6.49658i	−0.232258	+	0.319676i
$414$	−1.38197	−	4.25325i	−0.0679199	−	0.209036i
$415$	−8.22919	+	2.09148i	−0.403955	+	0.102667i
$416$	2.11803	−	1.53884i	0.103845	−	0.0754479i
$417$	−7.98852	−	2.59563i	−0.391200	−	0.127108i
$418$	−1.32350	−	1.82164i	−0.0647346	−	0.0890995i
$419$	−0.319299	+	0.231984i	−0.0155988	+	0.0113332i	−0.595557	−	0.803313i	$-0.703069\pi$
$419$	−0.319299	+	0.231984i	−0.0155988	+	0.0113332i	0.579959	+	0.814646i	$0.303069\pi$
$420$	4.06346	−	2.56485i	0.198277	−	0.125152i
$421$	−16.1295	+	11.7187i	−0.786102	+	0.571137i	−0.906804	−	0.421552i	$-0.861485\pi$
$421$	−16.1295	+	11.7187i	−0.786102	+	0.571137i	0.120702	+	0.992689i	$0.461485\pi$
$422$	−13.0396	+	17.9475i	−0.634758	+	0.873669i
$423$	−2.91354	+	0.946668i	−0.141661	+	0.0460286i
$424$	0.898602	+	0.652873i	0.0436400	+	0.0317063i
$425$	−1.49572	+	11.3918i	−0.0725531	+	0.552585i
$426$	−0.970604	+	2.98721i	−0.0470259	+	0.144731i
$427$	4.06580	−	1.32106i	0.196758	−	0.0639305i
$428$		−	15.6104i		−	0.754559i
$429$	1.38999			0.0671091
$430$	1.01964	−	2.55705i	0.0491715	−	0.123312i
$431$	−17.7078	+	12.8655i	−0.852956	+	0.619709i	−0.925959	−	0.377623i	$-0.876742\pi$
$431$	−17.7078	+	12.8655i	−0.852956	+	0.619709i	0.0730036	+	0.997332i	$0.476742\pi$
$432$	0.587785	−	0.809017i	0.0282798	−	0.0389238i
$433$			3.12560i			0.150207i	0.997176	+	0.0751034i	$0.0239287\pi$
$433$			3.12560i			0.150207i	−0.997176	+	0.0751034i	$0.976071\pi$
$434$	11.6965	+	2.52000i	0.561451	+	0.120964i
$435$	−7.01604	+	8.43886i	−0.336393	+	0.404613i
$436$	2.47440	+	1.79776i	0.118502	+	0.0860969i
$437$	−11.1482	−	15.3442i	−0.533290	−	0.734011i
$438$	15.5573	−	5.05486i	0.743355	−	0.241531i
$439$	−0.506296			−0.0241642			−0.0120821	−	0.999927i	$-0.503846\pi$
$439$	−0.506296			−0.0241642			−0.0120821	+	0.999927i	$0.503846\pi$
$440$	0.758976	−	0.912893i	0.0361828	−	0.0435205i
$441$	−0.736068	−	2.26538i	−0.0350509	−	0.107875i
$442$	−5.72159	−	1.85906i	−0.272148	−	0.0884264i
$443$	−5.23190	−	1.69995i	−0.248575	−	0.0807670i	0.182079	−	0.983284i	$-0.441717\pi$
$443$	−5.23190	−	1.69995i	−0.248575	−	0.0807670i	−0.430655	+	0.902517i	$0.641717\pi$
$444$	−2.16808	−	1.57520i	−0.102892	−	0.0747556i
$445$	0.464749	−	1.16549i	0.0220312	−	0.0552497i
$446$	14.8135	+	10.7626i	0.701438	+	0.509624i
$447$	0.527846	+	0.726517i	0.0249662	+	0.0343631i
$448$	2.04378	+	0.664066i	0.0965597	+	0.0313741i
$449$	−12.2378	+	8.89129i	−0.577538	+	0.419606i	−0.837836	−	0.545922i	$-0.816179\pi$
$449$	−12.2378	+	8.89129i	−0.577538	+	0.419606i	0.260298	+	0.965528i	$0.416179\pi$
$450$	3.44051	−	3.62807i	0.162187	−	0.171029i
$451$	0.0618543	−	0.190368i	0.00291261	−	0.00896408i
$452$	2.47977	+	3.41311i	0.116639	+	0.160539i
$453$	5.57325	−	7.67092i	0.261854	−	0.360411i
$454$	5.68070	+	17.4834i	0.266609	+	0.820537i
$455$	3.09879	+	12.1926i	0.145274	+	0.571599i
$456$	1.31055	−	4.03345i	0.0613721	−	0.188884i
$457$	−1.78086	−	0.578636i	−0.0833050	−	0.0270674i	0.267068	−	0.963678i	$-0.413945\pi$
$457$	−1.78086	−	0.578636i	−0.0833050	−	0.0270674i	−0.350373	+	0.936610i	$0.613945\pi$
$458$	17.3886	−	5.64991i	0.812517	−	0.264003i
$459$	−2.29792			−0.107258
$460$	6.39305	−	7.68953i	0.298077	−	0.358526i
$461$	11.5255	+	35.4717i	0.536795	+	1.65208i	0.739739	+	0.672894i	$0.234949\pi$
$461$	11.5255	+	35.4717i	0.536795	+	1.65208i	−0.202945	+	0.979190i	$0.565051\pi$
$462$	0.670629	+	0.923041i	0.0312005	+	0.0429438i
$463$	6.72221	−	9.25232i	0.312407	−	0.429992i	−0.623723	−	0.781646i	$-0.714381\pi$
$463$	6.72221	−	9.25232i	0.312407	−	0.429992i	0.936130	+	0.351654i	$0.114381\pi$
$464$	−4.90794			−0.227845
$465$	12.4415	−	0.456552i	0.576962	−	0.0211721i
$466$	−17.0856			−0.791477
$467$	−15.6482	+	21.5379i	−0.724111	+	0.996654i	0.275266	+	0.961368i	$0.411234\pi$
$467$	−15.6482	+	21.5379i	−0.724111	+	0.996654i	−0.999377	+	0.0352855i	$0.988766\pi$
$468$	1.53884	+	2.11803i	0.0711330	+	0.0979062i
$469$	−1.75861	−	5.41243i	−0.0812049	−	0.249923i
$470$	−5.26745	−	4.37933i	−0.242969	−	0.202004i
$471$	−2.74174			−0.126333
$472$	−3.55390	+	1.15473i	−0.163581	+	0.0531508i
$473$	0.621640	+	0.201983i	0.0285830	+	0.00928719i
$474$	1.41772	−	4.36328i	0.0651179	−	0.200412i
$475$	9.12236	−	19.1426i	0.418563	−	0.878323i
$476$	−1.52597	−	4.69646i	−0.0699428	−	0.215262i
$477$	−0.652873	+	0.898602i	−0.0298930	+	0.0411442i
$478$	7.09254	+	9.76204i	0.324405	+	0.446505i
$479$	2.16167	−	6.65294i	0.0987692	−	0.303980i	−0.889448	−	0.457036i	$-0.848911\pi$
$479$	2.16167	−	6.65294i	0.0987692	−	0.303980i	0.988218	+	0.153055i	$0.0489112\pi$
$480$	2.23131	+	0.145857i	0.101845	+	0.00665741i
$481$	5.67609	−	4.12392i	0.258808	−	0.188035i
$482$	16.0126	+	5.20280i	0.729352	+	0.236981i
$483$	5.64888	+	7.77501i	0.257033	+	0.353775i
$484$	−8.67114	−	6.29995i	−0.394143	−	0.286361i
$485$	−9.09509	−	3.62674i	−0.412987	−	0.164682i
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	20.2027	+	6.56425i	0.915471	+	0.297455i	0.728608	−	0.684931i	$-0.240168\pi$
$487$	20.2027	+	6.56425i	0.915471	+	0.297455i	0.186863	+	0.982386i	$0.440168\pi$
$488$	1.89198	+	0.614743i	0.0856461	+	0.0278281i
$489$	−4.78313	−	14.7210i	−0.216301	−	0.665705i
$490$	3.40509	−	4.09563i	0.153826	−	0.185022i
$491$	−25.7259			−1.16099			−0.580496	−	0.814263i	$-0.697141\pi$
$491$	−25.7259			−1.16099			−0.580496	+	0.814263i	$0.697141\pi$
$492$	0.358558	−	0.116502i	0.0161650	−	0.00525234i
$493$	6.62908	+	9.12414i	0.298559	+	0.410931i
$494$	8.98263	+	6.52627i	0.404148	+	0.293631i
$495$	0.912893	+	0.758976i	0.0410315	+	0.0341134i
$496$	3.71411	+	4.14794i	0.166768	+	0.186248i
$497$		−	6.74976i		−	0.302768i
$498$	2.23194	−	3.07200i	0.100016	−	0.137660i
$499$	12.1419	−	8.82160i	0.543546	−	0.394909i	−0.281854	−	0.959457i	$-0.590949\pi$
$499$	12.1419	−	8.82160i	0.543546	−	0.394909i	0.825400	+	0.564548i	$0.190949\pi$
$500$	10.9667	+	2.17544i	0.490444	+	0.0972885i
$501$	14.3442			0.640850
$502$		−	3.68791i		−	0.164599i
$503$	14.8379	−	4.82114i	0.661591	−	0.214964i	0.0410732	−	0.999156i	$-0.486922\pi$
$503$	14.8379	−	4.82114i	0.661591	−	0.214964i	0.620518	+	0.784192i	$0.286922\pi$
$504$	−0.664066	+	2.04378i	−0.0295798	+	0.0910374i
$505$	17.5872	−	11.1010i	0.782620	−	0.493988i
$506$	1.92091	+	1.39562i	0.0853950	+	0.0620431i
$507$	5.84510	−	1.89919i	0.259590	−	0.0843459i
$508$	−6.18881	+	8.51817i	−0.274584	+	0.377933i
$509$	22.2681	−	16.1788i	0.987018	−	0.717111i	0.0277521	−	0.999615i	$-0.491165\pi$
$509$	22.2681	−	16.1788i	0.987018	−	0.717111i	0.959266	+	0.282504i	$0.0911651\pi$
$510$	−2.74264	−	4.34513i	−0.121446	−	0.192406i
$511$	−28.4389	+	20.6621i	−1.25806	+	0.914037i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	4.03345	+	1.31055i	0.178081	+	0.0578621i
$514$	6.49940	−	4.72209i	0.286676	−	0.208283i
$515$	−17.1935	+	4.36979i	−0.757636	+	0.192556i
$516$	0.380434	+	1.17086i	0.0167477	+	0.0515441i
$517$	0.956024	−	1.31585i	0.0420459	−	0.0578712i
$518$	5.47711	+	1.77962i	0.240650	+	0.0781921i
$519$	−0.995621	+	3.06421i	−0.0437029	+	0.134504i
$520$	−2.16833	+	5.43772i	−0.0950877	+	0.238460i
$521$	5.00685			0.219354			0.109677	−	0.993967i	$-0.465018\pi$
$521$	5.00685			0.219354			0.109677	+	0.993967i	$0.465018\pi$
$522$		−	4.90794i		−	0.214815i
$523$	−27.4080	+	8.90540i	−1.19847	+	0.389406i	−0.839197	−	0.543827i	$-0.816975\pi$
$523$	−27.4080	+	8.90540i	−1.19847	+	0.389406i	−0.359271	+	0.933233i	$0.616975\pi$
$524$	−15.9572	+	11.5936i	−0.697096	+	0.506470i
$525$	−4.62237	+	9.69972i	−0.201737	+	0.423330i
$526$	2.12634			0.0927128
$527$	2.69468	−	12.5073i	0.117382	−	0.544827i
$528$			0.530927i			0.0231056i
$529$	−2.42705	−	1.76336i	−0.105524	−	0.0766676i
$530$	−2.47839	−	0.162008i	−0.107654	−	0.00703716i
$531$	−1.15473	−	3.55390i	−0.0501110	−	0.154226i
$532$			9.11380i			0.395133i
$533$			0.987024i			0.0427528i
$534$	0.173401	+	0.533672i	0.00750377	+	0.0230942i
$535$	18.6315	+	29.5177i	0.805510	+	1.27616i
$536$	0.818352	−	2.51863i	0.0353474	−	0.108788i
$537$	0.855170	−	1.17704i	0.0369033	−	0.0507931i
$538$	3.76083	−	1.22197i	0.162141	−	0.0526828i
$539$	1.02312	+	0.743343i	0.0440691	+	0.0320180i
$540$	−0.145857	+	2.23131i	−0.00627667	+	0.0960201i
$541$	−11.6577	+	35.8786i	−0.501202	+	1.54254i	0.305861	+	0.952076i	$0.401056\pi$
$541$	−11.6577	+	35.8786i	−0.501202	+	1.54254i	−0.807063	+	0.590465i	$0.798944\pi$
$542$	8.50942	+	11.7122i	0.365511	+	0.503083i
$543$	13.7510	+	18.9267i	0.590113	+	0.812221i
$544$	0.710097	−	2.18545i	0.0304452	−	0.0937006i
$545$	−6.82450	−	0.446106i	−0.292330	−	0.0191091i
$546$	−4.55157	−	3.30691i	−0.194789	−	0.141523i
$547$	15.9178	−	5.17200i	0.680595	−	0.221139i	0.0517394	−	0.998661i	$-0.483523\pi$
$547$	15.9178	−	5.17200i	0.680595	−	0.221139i	0.628856	+	0.777522i	$0.283523\pi$
$548$	−1.53317	+	2.11023i	−0.0654939	+	0.0901446i
$549$	−0.614743	+	1.89198i	−0.0262366	+	0.0807479i
$550$	−0.345581	+	2.63205i	−0.0147356	+	0.112231i
$551$	−6.43209	−	19.7959i	−0.274016	−	0.843335i
$552$			4.47214i			0.190347i
$553$			9.85906i			0.419250i
$554$	4.27619	+	13.1608i	0.181678	+	0.559147i
$555$	5.97965	+	0.390879i	0.253822	+	0.0165919i
$556$	6.79544	+	4.93718i	0.288191	+	0.209383i
$557$		−	25.4716i		−	1.07926i	−0.841901	−	0.539632i	$-0.818563\pi$
$557$		−	25.4716i		−	1.07926i	0.841901	−	0.539632i	$-0.181437\pi$
$558$	−4.14794	+	3.71411i	−0.175596	+	0.157231i
$559$	−3.22309			−0.136322
$560$	−4.65716	+	1.18363i	−0.196801	+	0.0500177i
$561$	0.987024	−	0.717115i	0.0416722	−	0.0302766i
$562$	10.8503	−	3.52547i	0.457691	−	0.148713i
$563$			23.4698i			0.989134i	0.869140	+	0.494567i	$0.164673\pi$
$563$			23.4698i			0.989134i	−0.869140	+	0.494567i	$0.835327\pi$
$564$	3.06348			0.128996
$565$	−8.76263	−	3.49416i	−0.368647	−	0.147001i
$566$	−4.63824	+	14.2750i	−0.194960	+	0.600024i
$567$	−2.04378	−	0.664066i	−0.0858308	−	0.0278881i
$568$	1.84620	−	2.54108i	0.0774648	−	0.106621i
$569$	12.7759	+	39.3201i	0.535592	+	1.64838i	0.742365	+	0.669995i	$0.233704\pi$
$569$	12.7759	+	39.3201i	0.535592	+	1.64838i	−0.206773	+	0.978389i	$0.566296\pi$
$570$	2.33593	+	9.19102i	0.0978413	+	0.384970i
$571$	21.2552	−	15.4428i	0.889501	−	0.646260i	−0.0462467	−	0.998930i	$-0.514726\pi$
$571$	21.2552	−	15.4428i	0.889501	−	0.646260i	0.935748	+	0.352670i	$0.114726\pi$
$572$	−1.32195	−	0.429529i	−0.0552737	−	0.0179595i
$573$	8.73016	+	12.0160i	0.364708	+	0.501977i
$574$	−0.655449	+	0.476212i	−0.0273579	+	0.0198767i
$575$	−2.91092	+	22.1704i	−0.121394	+	0.924570i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	−24.1955	+	33.3022i	−1.00727	+	1.38639i	−0.0865149	+	0.996251i	$0.527573\pi$
$577$	−24.1955	+	33.3022i	−1.00727	+	1.38639i	−0.920756	+	0.390139i	$0.872427\pi$
$578$	11.1460	−	3.62154i	0.463611	−	0.150636i
$579$	−8.74277	−	6.35200i	−0.363337	−	0.263980i
$580$	9.28040	−	5.85776i	0.385348	−	0.243230i
$581$	−2.52159	+	7.76066i	−0.104613	+	0.321967i
$582$	4.16458	−	1.35316i	0.172628	−	0.0560901i
$583$		−	0.589718i		−	0.0244236i
$584$	−16.3579			−0.676894
$585$	−5.43772	−	2.16833i	−0.224822	−	0.0896495i
$586$	−22.5833	+	16.4077i	−0.932908	+	0.677797i
$587$	16.4058	−	22.5807i	0.677141	−	0.932004i	−0.322755	−	0.946483i	$-0.604609\pi$
$587$	16.4058	−	22.5807i	0.677141	−	0.932004i	0.999895	+	0.0144787i	$0.00460887\pi$
$588$			2.38197i			0.0982306i
$589$	−11.8630	+	20.4168i	−0.488807	+	0.841258i
$590$	5.34184	−	6.42515i	0.219920	−	0.264519i
$591$	−11.0017	−	7.99324i	−0.452551	−	0.328798i
$592$	1.57520	+	2.16808i	0.0647403	+	0.0891073i
$593$	21.1530	−	6.87304i	0.868651	−	0.282242i	0.159414	−	0.987212i	$-0.449040\pi$
$593$	21.1530	−	6.87304i	0.868651	−	0.282242i	0.709237	+	0.704970i	$0.249040\pi$
$594$	−0.530927			−0.0217842
$595$	8.49081	+	7.05922i	0.348089	+	0.289400i
$596$	−0.277505	−	0.854072i	−0.0113670	−	0.0349842i
$597$	24.0173	+	7.80369i	0.982962	+	0.319384i
$598$	−11.1352	−	3.61803i	−0.455351	−	0.147952i
$599$	−4.80829	−	3.49342i	−0.196461	−	0.142737i	0.485206	−	0.874400i	$-0.338745\pi$
$599$	−4.80829	−	3.49342i	−0.196461	−	0.142737i	−0.681667	+	0.731663i	$0.738745\pi$
$600$	−4.39325	+	2.38733i	−0.179354	+	0.0974622i
$601$	−11.2280	−	8.15765i	−0.458001	−	0.332757i	0.334746	−	0.942309i	$-0.391350\pi$
$601$	−11.2280	−	8.15765i	−0.458001	−	0.332757i	−0.792747	+	0.609551i	$0.791350\pi$
$602$	−1.55505	−	2.14034i	−0.0633792	−	0.0872339i
$603$	2.51863	+	0.818352i	0.102566	+	0.0333259i
$604$	−7.67092	+	5.57325i	−0.312125	+	0.226772i
$605$	23.9154	+	1.56331i	0.972299	+	0.0635575i
$606$	−2.87416	+	8.84576i	−0.116755	+	0.359335i
$607$	−16.4204	−	22.6007i	−0.666484	−	0.917336i	0.333191	−	0.942860i	$-0.391875\pi$
$607$	−16.4204	−	22.6007i	−0.666484	−	0.917336i	−0.999674	+	0.0255234i	$0.991875\pi$
$608$	−2.49281	+	3.43106i	−0.101097	+	0.139148i
$609$	3.25919	+	10.0308i	0.132069	+	0.406467i
$610$	−4.31126	+	1.09572i	−0.174558	+	0.0443644i
$611$	−2.47841	+	7.62776i	−0.100266	+	0.308586i
$612$	2.18545	+	0.710097i	0.0883417	+	0.0287040i
$613$	−7.06201	+	2.29458i	−0.285232	+	0.0926774i	−0.448139	−	0.893964i	$-0.647913\pi$
$613$	−7.06201	+	2.29458i	−0.285232	+	0.0926774i	0.162907	+	0.986641i	$0.447913\pi$
$614$	−4.91495			−0.198351
$615$	−0.538946	+	0.648243i	−0.0217324	+	0.0261397i
$616$	−0.352570	−	1.08510i	−0.0142055	−	0.0437199i
$617$	−18.3960	−	25.3200i	−0.740596	−	1.01934i	−0.998584	−	0.0531953i	$-0.983059\pi$
$617$	−18.3960	−	25.3200i	−0.740596	−	1.01934i	0.257988	−	0.966148i	$-0.416941\pi$
$618$	4.66327	−	6.41843i	0.187584	−	0.258187i
$619$	13.2930			0.534289			0.267145	−	0.963656i	$-0.413920\pi$
$619$	13.2930			0.534289			0.267145	+	0.963656i	$0.413920\pi$
$620$	−11.9737	−	3.41044i	−0.480874	−	0.136966i
$621$	−4.47214			−0.179461
$622$	9.55646	−	13.1533i	0.383179	−	0.527401i
$623$	−0.708786	−	0.975561i	−0.0283969	−	0.0390850i
$624$	−0.809017	−	2.48990i	−0.0323866	−	0.0996757i
$625$	−23.3333	+	8.97549i	−0.933330	+	0.359019i
$626$	25.3512			1.01324
$627$	−2.14147	+	0.695806i	−0.0855221	+	0.0277878i
$628$	2.60755	+	0.847245i	0.104053	+	0.0338088i
$629$	1.90298	−	5.85677i	0.0758768	−	0.233525i
$630$	−1.18363	−	4.65716i	−0.0471571	−	0.185546i
$631$	−6.08362	−	18.7235i	−0.242185	−	0.745370i	−0.996087	−	0.0883820i	$-0.971830\pi$
$631$	−6.08362	−	18.7235i	−0.242185	−	0.745370i	0.753901	−	0.656988i	$-0.228170\pi$
$632$	−2.69666	+	3.71163i	−0.107267	+	0.147641i
$633$	13.0396	+	17.9475i	0.518278	+	0.713348i
$634$	7.73760	−	23.8139i	0.307299	−	0.945770i
$635$	1.53573	−	23.4935i	0.0609435	−	0.932311i
$636$	0.898602	−	0.652873i	0.0356319	−	0.0258881i
$637$	−5.93085	−	1.92705i	−0.234989	−	0.0763525i
$638$	1.53163	+	2.10810i	0.0606376	+	0.0834605i
$639$	2.54108	+	1.84620i	0.100523	+	0.0730345i
$640$	−2.07703	−	0.828229i	−0.0821017	−	0.0327386i
$641$	−2.61366	−	1.89893i	−0.103233	−	0.0750033i	0.534971	−	0.844870i	$-0.320322\pi$
$641$	−2.61366	−	1.89893i	−0.103233	−	0.0750033i	−0.638204	+	0.769867i	$0.720322\pi$
$642$	−14.8464	−	4.82389i	−0.585941	−	0.190384i
$643$	9.42353	+	3.06189i	0.371628	+	0.120749i	0.488876	−	0.872354i	$-0.337407\pi$
$643$	9.42353	+	3.06189i	0.371628	+	0.120749i	−0.117248	+	0.993103i	$0.537407\pi$
$644$	−2.96979	−	9.14008i	−0.117026	−	0.360170i
$645$	−2.11681	−	1.75991i	−0.0833494	−	0.0692964i
$646$	9.74554			0.383433
$647$	−25.0857	+	8.15085i	−0.986223	+	0.320443i	−0.757347	−	0.653013i	$-0.773505\pi$
$647$	−25.0857	+	8.15085i	−0.986223	+	0.320443i	−0.228876	+	0.973456i	$0.573505\pi$
$648$	−0.587785	−	0.809017i	−0.0230904	−	0.0317812i
$649$	1.60506	+	1.16614i	0.0630041	+	0.0457751i
$650$	−2.38999	−	12.8701i	−0.0937429	−	0.504808i
$651$	6.01108	−	10.3453i	0.235593	−	0.405466i
$652$			15.4785i			0.606186i
$653$	−4.12699	+	5.68032i	−0.161502	+	0.222288i	−0.882097	−	0.471068i	$-0.843869\pi$
$653$	−4.12699	+	5.68032i	−0.161502	+	0.222288i	0.720595	+	0.693356i	$0.243869\pi$
$654$	2.47440	−	1.79776i	0.0967566	−	0.0702978i
$655$	16.3362	−	40.9678i	0.638308	−	1.60074i
$656$	−0.377010			−0.0147198
$657$		−	16.3579i		−	0.638182i
$658$	−6.26109	+	2.03435i	−0.244083	+	0.0793073i
$659$	1.65301	−	5.08743i	0.0643920	−	0.198178i	−0.913684	−	0.406424i	$-0.866775\pi$
$659$	1.65301	−	5.08743i	0.0643920	−	0.198178i	0.978076	+	0.208246i	$0.0667755\pi$
$660$	−0.633677	−	1.00393i	−0.0246658	−	0.0390779i
$661$	−26.3882	−	19.1721i	−1.02638	−	0.745709i	−0.0587993	−	0.998270i	$-0.518727\pi$
$661$	−26.3882	−	19.1721i	−1.02638	−	0.745709i	−0.967581	+	0.252561i	$0.918727\pi$
$662$	6.35826	−	2.06592i	0.247121	−	0.0802944i
$663$	−3.53614	+	4.86708i	−0.137332	+	0.189022i
$664$	−3.07200	+	2.23194i	−0.119217	+	0.0866161i
$665$	−10.8776	−	17.2332i	−0.421814	−	0.668277i
$666$	−2.16808	+	1.57520i	−0.0840112	+	0.0610377i
$667$	12.9013	+	17.7571i	0.499539	+	0.687557i
$668$	−13.6421	−	4.43259i	−0.527829	−	0.171502i
$669$	14.8135	−	10.7626i	0.572721	−	0.416106i
$670$	1.45864	+	5.73919i	0.0563520	+	0.221724i
$671$	−0.326384	−	1.00451i	−0.0125999	−	0.0387785i
$672$	1.26313	−	1.73855i	0.0487262	−	0.0670659i
$673$	−18.7374	−	6.08814i	−0.722272	−	0.234680i	−0.0752640	−	0.997164i	$-0.523980\pi$
$673$	−18.7374	−	6.08814i	−0.722272	−	0.234680i	−0.647008	+	0.762483i	$0.723980\pi$
$674$	−5.29932	+	16.3096i	−0.204122	+	0.628224i
$675$	−2.38733	−	4.39325i	−0.0918883	−	0.169096i
$676$	−6.14590			−0.236381
$677$			0.342010i			0.0131445i	0.999978	+	0.00657225i	$0.00209203\pi$
$677$			0.342010i			0.0131445i	−0.999978	+	0.00657225i	$0.997908\pi$
$678$	4.01235	−	1.30369i	0.154093	−	0.0500680i
$679$	−7.61292	+	5.53111i	−0.292157	+	0.212265i
$680$	1.26568	+	4.97999i	0.0485366	+	0.190974i
$681$	18.3831			0.704443
$682$	0.622596	−	2.88977i	0.0238404	−	0.110655i
$683$			22.6935i			0.868341i	0.900831	+	0.434171i	$0.142958\pi$
$683$			22.6935i			0.868341i	−0.900831	+	0.434171i	$0.857042\pi$
$684$	−3.43106	−	2.49281i	−0.131190	−	0.0953150i
$685$	0.380450	−	5.82011i	0.0145363	−	0.222375i
$686$	−6.23024	−	19.1747i	−0.237872	−	0.732094i
$687$		−	18.2835i		−	0.697558i
$688$		−	1.23111i		−	0.0469357i
$689$	0.898602	+	2.76561i	0.0342340	+	0.105361i
$690$	−5.33762	−	8.45635i	−0.203200	−	0.321928i
$691$	15.8580	−	48.8058i	0.603266	−	1.85666i	0.0949658	−	0.995481i	$-0.469726\pi$
$691$	15.8580	−	48.8058i	0.603266	−	1.85666i	0.508300	−	0.861180i	$-0.330274\pi$
$692$	1.89378	−	2.60657i	0.0719909	−	0.0990869i
$693$	1.08510	−	0.352570i	0.0412195	−	0.0133930i
$694$	2.93683	+	2.13373i	0.111481	+	0.0809954i
$695$	−18.7421	−	1.22514i	−0.710930	−	0.0464722i
$696$	−1.51664	+	4.66773i	−0.0574879	+	0.176930i
$697$	0.509221	+	0.700883i	0.0192881	+	0.0265478i
$698$	−12.3873	−	17.0497i	−0.468867	−	0.645340i
$699$	−5.27975	+	16.2494i	−0.199699	+	0.614609i
$700$	7.39352	−	7.79659i	0.279449	−	0.294683i
$701$	5.95267	+	4.32487i	0.224829	+	0.163348i	0.694498	−	0.719495i	$-0.255627\pi$
$701$	5.95267	+	4.32487i	0.224829	+	0.163348i	−0.469669	+	0.882843i	$0.655627\pi$
$702$	2.48990	−	0.809017i	0.0939752	−	0.0305344i
$703$	−6.68046	+	9.19486i	−0.251958	+	0.346791i
$704$	0.164066	−	0.504942i	0.00618345	−	0.0190307i
$705$	−5.79273	+	3.65635i	−0.218167	+	0.137706i
$706$	7.19652	+	22.1486i	0.270845	+	0.833574i
$707$		−	19.9875i		−	0.751706i
$708$			3.73679i			0.140437i
$709$	−9.59379	−	29.5266i	−0.360302	−	1.10890i	−0.952871	−	0.303376i	$-0.901886\pi$
$709$	−9.59379	−	29.5266i	−0.360302	−	1.10890i	0.592569	−	0.805520i	$-0.298114\pi$
$710$	−0.458127	+	7.00840i	−0.0171932	+	0.263021i
$711$	−3.71163	−	2.69666i	−0.139197	−	0.101133i
$712$		−	0.561136i		−	0.0210295i
$713$	5.24428	−	24.3413i	0.196400	−	0.911588i
$714$	−4.93815			−0.184805
$715$	3.01233	−	0.765595i	0.112655	−	0.0286316i
$716$	−1.17704	+	0.855170i	−0.0439881	+	0.0319592i
$717$	11.4760	−	3.72877i	0.428578	−	0.139253i
$718$		−	29.8772i		−	1.11501i
$719$	10.5938			0.395083			0.197542	−	0.980294i	$-0.436704\pi$
$719$	10.5938			0.395083			0.197542	+	0.980294i	$0.436704\pi$
$720$	0.828229	−	2.07703i	0.0308663	−	0.0774062i
$721$	−5.26844	+	16.2146i	−0.196207	+	0.603863i
$722$	0.964099	+	0.313255i	0.0358801	+	0.0116581i
$723$	9.89631	−	13.6211i	0.368048	−	0.506574i
$724$	−7.22934	−	22.2496i	−0.268676	−	0.826901i
$725$	−10.5569	+	22.1528i	−0.392073	+	0.822736i
$726$	−8.67114	+	6.29995i	−0.321816	+	0.233813i
$727$	−15.5730	−	5.05996i	−0.577569	−	0.187664i	0.00564218	−	0.999984i	$-0.498204\pi$
$727$	−15.5730	−	5.05996i	−0.577569	−	0.187664i	−0.583211	+	0.812321i	$0.698204\pi$
$728$	3.30691	+	4.55157i	0.122562	+	0.168693i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	30.9311	−	19.5236i	1.14481	−	0.722601i
$731$	−2.28871	+	1.66284i	−0.0846509	+	0.0615025i
$732$	1.16931	−	1.60942i	0.0432189	−	0.0594858i
$733$	−12.2192	+	3.97025i	−0.451325	+	0.146644i	−0.525855	−	0.850574i	$-0.676254\pi$
$733$	−12.2192	+	3.97025i	−0.451325	+	0.146644i	0.0745296	+	0.997219i	$0.476254\pi$
$734$	29.6784	+	21.5626i	1.09545	+	0.795892i
$735$	−2.84294	−	4.50405i	−0.104864	−	0.166134i
$736$	1.38197	−	4.25325i	0.0509399	−	0.156777i
$737$	−1.33721	+	0.434485i	−0.0492567	+	0.0160045i
$738$		−	0.377010i		−	0.0138779i
$739$	−0.758402			−0.0278983			−0.0139491	−	0.999903i	$-0.504440\pi$
$739$	−0.758402			−0.0278983			−0.0139491	+	0.999903i	$0.504440\pi$
$740$	−5.56620	−	2.21956i	−0.204617	−	0.0815927i
$741$	8.98263	−	6.52627i	0.329985	−	0.239748i
$742$	−1.40300	+	1.93106i	−0.0515057	+	0.0708915i
$743$		−	10.2497i		−	0.376024i	−0.982167	−	0.188012i	$-0.939796\pi$
$743$		−	10.2497i		−	0.376024i	0.982167	−	0.188012i	$-0.0602043\pi$
$744$	5.09265	−	2.25054i	0.186706	−	0.0825088i
$745$	1.54409	+	1.28375i	0.0565712	+	0.0470330i
$746$	−2.96105	−	2.15133i	−0.108412	−	0.0787658i
$747$	−2.23194	−	3.07200i	−0.0816624	−	0.112399i
$748$	−1.16032	+	0.377010i	−0.0424254	+	0.0137848i
$749$	33.5462			1.22575
$750$	5.45784	−	9.75766i	0.199292	−	0.356299i
$751$	−1.27719	−	3.93080i	−0.0466055	−	0.143437i	0.925046	−	0.379856i	$-0.124026\pi$
$751$	−1.27719	−	3.93080i	−0.0466055	−	0.143437i	−0.971651	+	0.236419i	$0.924026\pi$
$752$	−2.91354	−	0.946668i	−0.106246	−	0.0345214i
$753$	−3.50741	−	1.13963i	−0.127817	−	0.0415303i
$754$	−10.3952	−	7.55254i	−0.378570	−	0.275047i
$755$	7.85309	−	19.6939i	0.285803	−	0.716735i
$756$	1.73855	+	1.26313i	0.0632303	+	0.0459395i
$757$	5.68851	+	7.82957i	0.206753	+	0.284570i	0.899783	−	0.436338i	$-0.143725\pi$
$757$	5.68851	+	7.82957i	0.206753	+	0.284570i	−0.693030	+	0.720908i	$0.743725\pi$
$758$	−18.5507	−	6.02749i	−0.673793	−	0.218928i
$759$	1.92091	−	1.39562i	0.0697247	−	0.0506580i
$760$	0.618581	−	9.46302i	0.0224383	−	0.343260i
$761$	−14.9136	+	45.8992i	−0.540616	+	1.66385i	0.190575	+	0.981673i	$0.438965\pi$
$761$	−14.9136	+	45.8992i	−0.540616	+	1.66385i	−0.731191	+	0.682173i	$0.761035\pi$
$762$	6.18881	+	8.51817i	0.224197	+	0.308581i
$763$	−3.86331	+	5.31739i	−0.139861	+	0.192502i
$764$	−4.58972	−	14.1257i	−0.166050	−	0.511050i
$765$	−4.97999	+	1.26568i	−0.180052	+	0.0457608i
$766$	7.11248	−	21.8900i	0.256984	−	0.790917i
$767$	−9.30422	−	3.02312i	−0.335956	−	0.109159i
$768$	0.951057	−	0.309017i	0.0343183	−	0.0111507i
$769$	27.2232			0.981694			0.490847	−	0.871246i	$-0.336687\pi$
$769$	27.2232			0.981694			0.490847	+	0.871246i	$0.336687\pi$
$770$	1.96177	+	1.63101i	0.0706974	+	0.0587775i
$771$	−2.48255	−	7.64051i	−0.0894069	−	0.275166i
$772$	6.35200	+	8.74277i	0.228613	+	0.314659i
$773$	27.7557	−	38.2024i	0.998302	−	1.37404i	0.0719399	−	0.997409i	$-0.477081\pi$
$773$	27.7557	−	38.2024i	0.998302	−	1.37404i	0.926362	−	0.376635i	$-0.122919\pi$
$774$	1.23111			0.0442514
$775$	26.7114	−	7.84214i	0.959503	−	0.281698i
$776$	−4.37890			−0.157193
$777$	3.38504	−	4.65911i	0.121438	−	0.167145i
$778$	−21.0128	−	28.9217i	−0.753347	−	1.03689i
$779$	−0.494090	−	1.52065i	−0.0177026	−	0.0544830i
$780$	4.50153	+	3.74256i	0.161181	+	0.134005i
$781$	−1.66761			−0.0596718
$782$	−9.77365	+	3.17565i	−0.349505	+	0.113561i
$783$	−4.66773	−	1.51664i	−0.166811	−	0.0542001i
$784$	0.736068	−	2.26538i	0.0262881	−	0.0809066i
$785$	−5.94182	+	1.51013i	−0.212073	+	0.0538990i
$786$	6.09513	+	18.7589i	0.217406	+	0.669107i
$787$	−11.2509	+	15.4855i	−0.401051	+	0.552000i	−0.961007	−	0.276522i	$-0.910818\pi$
$787$	−11.2509	+	15.4855i	−0.401051	+	0.552000i	0.559956	+	0.828522i	$0.310818\pi$
$788$	7.99324	+	11.0017i	0.284747	+	0.391921i
$789$	0.657075	−	2.02227i	0.0233925	−	0.0719947i
$790$	0.669164	−	10.2368i	0.0238078	−	0.364210i
$791$	−7.33464	+	5.32893i	−0.260790	+	0.189475i
$792$	0.504942	+	0.164066i	0.0179423	+	0.00582981i
$793$	3.06129	+	4.21351i	0.108710	+	0.149626i
$794$	−23.8912	−	17.3579i	−0.847865	−	0.616010i
$795$	−0.919942	+	2.30702i	−0.0326270	+	0.0818216i
$796$	−20.4303	−	14.8435i	−0.724134	−	0.526114i
$797$	−23.2719	−	7.56149i	−0.824332	−	0.267842i	−0.133676	−	0.991025i	$-0.542678\pi$
$797$	−23.2719	−	7.56149i	−0.824332	−	0.267842i	−0.690656	+	0.723183i	$0.742678\pi$
$798$	8.66774	+	2.81632i	0.306835	+	0.0996966i
$799$	2.17537	+	6.69510i	0.0769590	+	0.236855i
$800$	4.91596	−	0.912893i	0.173805	−	0.0322756i
$801$	0.561136			0.0198268
$802$	−7.28085	+	2.36569i	−0.257096	+	0.0835355i
$803$	5.10482	+	7.02619i	0.180145	+	0.247949i
$804$	−2.14247	−	1.55660i	−0.0755592	−	0.0548970i
$805$	16.5245	+	13.7384i	0.582412	+	0.484215i
$806$	1.48358	+	14.5009i	0.0522569	+	0.510772i
$807$		−	3.95437i		−	0.139201i
$808$	5.46698	−	7.52466i	0.192328	−	0.264716i
$809$	27.4642	−	19.9539i	0.965589	−	0.701541i	0.0111467	−	0.999938i	$-0.496452\pi$
$809$	27.4642	−	19.9539i	0.965589	−	0.701541i	0.954442	+	0.298397i	$0.0964518\pi$
$810$	2.07703	+	0.828229i	0.0729792	+	0.0291010i
$811$	32.9684			1.15768			0.578839	−	0.815442i	$-0.303506\pi$
$811$	32.9684			1.15768			0.578839	+	0.815442i	$0.303506\pi$
$812$		−	10.5470i		−	0.370126i
$813$	13.7685	−	4.47367i	0.482884	−	0.156898i
$814$	0.439677	−	1.35319i	0.0154107	−	0.0474292i
$815$	−18.4741	−	29.2683i	−0.647118	−	1.02522i
$816$	−1.85906	−	1.35068i	−0.0650801	−	0.0472834i
$817$	4.96563	−	1.61343i	0.173725	−	0.0564468i
$818$	−10.2524	+	14.1112i	−0.358465	+	0.493385i
$819$	−4.55157	+	3.30691i	−0.159045	+	0.115553i
$820$	0.712887	−	0.449972i	0.0248951	−	0.0157137i
$821$	−32.4374	+	23.5672i	−1.13207	+	0.822499i	−0.985995	−	0.166774i	$-0.946665\pi$
$821$	−32.4374	+	23.5672i	−1.13207	+	0.822499i	−0.146078	+	0.989273i	$0.546665\pi$
$822$	1.53317	+	2.11023i	0.0534755	+	0.0736027i
$823$	−50.2723	−	16.3345i	−1.75238	−	0.569384i	−0.756017	−	0.654552i	$-0.772857\pi$
$823$	−50.2723	−	16.3345i	−1.75238	−	0.569384i	−0.996367	+	0.0851681i	$0.972857\pi$
$824$	−6.41843	+	4.66327i	−0.223597	+	0.162453i
$825$	2.39643	+	1.14201i	0.0834331	+	0.0397598i
$826$	−2.48147	−	7.63718i	−0.0863414	−	0.265732i
$827$	−20.1199	+	27.6927i	−0.699639	+	0.962970i	0.300320	+	0.953839i	$0.402907\pi$
$827$	−20.1199	+	27.6927i	−0.699639	+	0.962970i	−0.999958	+	0.00913151i	$0.997093\pi$
$828$	4.25325	+	1.38197i	0.147811	+	0.0480266i
$829$	0.169296	−	0.521040i	0.00587990	−	0.0180965i	−0.948074	−	0.318051i	$-0.896972\pi$
$829$	0.169296	−	0.521040i	0.00587990	−	0.0180965i	0.953953	+	0.299955i	$0.0969716\pi$
$830$	3.14496	−	7.88689i	0.109163	−	0.273758i
$831$	13.8380			0.480036
$832$			2.61803i			0.0907640i
$833$	−5.20568	+	1.69143i	−0.180366	+	0.0586045i
$834$	6.79544	−	4.93718i	0.235307	−	0.170961i
$835$	31.0863	−	7.90068i	1.07578	−	0.273414i
$836$	2.25167			0.0778758
$837$	2.25054	+	5.09265i	0.0777901	+	0.176028i
$838$		−	0.394675i		−	0.0136338i
$839$	−24.9064	−	18.0955i	−0.859863	−	0.624727i	0.0679848	−	0.997686i	$-0.478343\pi$
$839$	−24.9064	−	18.0955i	−0.859863	−	0.624727i	−0.927848	+	0.372959i	$0.878343\pi$
$840$	−0.313440	+	4.79499i	−0.0108147	+	0.165443i
$841$	−1.51794	−	4.67174i	−0.0523427	−	0.161094i
$842$		−	19.9371i		−	0.687078i
$843$		−	11.4087i		−	0.392935i
$844$	−6.85532	−	21.0985i	−0.235970	−	0.726241i
$845$	11.6213	−	7.33530i	0.399783	−	0.252342i
$846$	0.946668	−	2.91354i	0.0325471	−	0.100170i
$847$	13.5383	−	18.6339i	0.465183	−	0.640270i
$848$	−1.05637	+	0.343235i	−0.0362759	+	0.0117868i
$849$	12.1431	+	8.82245i	0.416749	+	0.302786i
$850$	−8.33703	−	7.90602i	−0.285958	−	0.271174i
$851$	3.70351	−	11.3982i	0.126955	−	0.390727i
$852$	−1.84620	−	2.54108i	−0.0632497	−	0.0870558i
$853$	9.99629	+	13.7587i	0.342266	+	0.471089i	0.945102	−	0.326776i	$-0.105962\pi$
$853$	9.99629	+	13.7587i	0.342266	+	0.471089i	−0.602835	+	0.797866i	$0.705962\pi$
$854$	−1.32106	+	4.06580i	−0.0452057	+	0.139129i
$855$	9.46302	+	0.618581i	0.323629	+	0.0211550i
$856$	12.6291	+	9.17559i	0.431654	+	0.313615i
$857$	22.3995	−	7.27805i	0.765154	−	0.248614i	0.0996647	−	0.995021i	$-0.468223\pi$
$857$	22.3995	−	7.27805i	0.765154	−	0.248614i	0.665489	+	0.746407i	$0.268223\pi$
$858$	−0.817013	+	1.12452i	−0.0278924	+	0.0383905i
$859$	12.2872	−	37.8162i	0.419235	−	1.29027i	−0.489173	−	0.872187i	$-0.662701\pi$
$859$	12.2872	−	37.8162i	0.419235	−	1.29027i	0.908408	−	0.418085i	$-0.137299\pi$
$860$	1.46937	+	2.32791i	0.0501050	+	0.0793809i
$861$	0.250359	+	0.770526i	0.00853222	+	0.0262595i
$862$		−	21.8881i		−	0.745511i
$863$			54.9395i			1.87016i	0.354435	+	0.935081i	$0.384673\pi$
$863$			54.9395i			1.87016i	−0.354435	+	0.935081i	$0.615327\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	−0.469935	+	7.18904i	−0.0159783	+	0.244435i
$866$	−2.52866	−	1.83718i	−0.0859275	−	0.0624300i
$867$		−	11.7196i		−	0.398017i
$868$	−8.91376	+	7.98147i	−0.302553	+	0.270909i
$869$	2.43580			0.0826289
$870$	−2.70326	−	10.6363i	−0.0916491	−	0.360606i
$871$	5.60907	−	4.07523i	0.190056	−	0.138084i
$872$	−2.90883	+	0.945136i	−0.0985054	+	0.0320063i
$873$		−	4.37890i		−	0.148203i
$874$	18.9664			0.641549
$875$	−4.67493	+	23.5669i	−0.158041	+	0.796707i
$876$	−5.05486	+	15.5573i	−0.170788	+	0.525631i
$877$	28.0400	+	9.11073i	0.946842	+	0.307648i	0.741432	−	0.671028i	$-0.234147\pi$
$877$	28.0400	+	9.11073i	0.946842	+	0.307648i	0.205410	+	0.978676i	$0.434147\pi$
$878$	0.297593	−	0.409602i	0.0100433	−	0.0138234i
$879$	8.62605	+	26.5483i	0.290950	+	0.895451i
$880$	0.292431	+	1.15061i	0.00985786	+	0.0387870i
$881$	−29.5699	+	21.4838i	−0.996237	+	0.723808i	−0.961278	−	0.275580i	$-0.911130\pi$
$881$	−29.5699	+	21.4838i	−0.996237	+	0.723808i	−0.0349587	+	0.999389i	$0.511130\pi$
$882$	2.26538	+	0.736068i	0.0762795	+	0.0247847i
$883$	6.37920	+	8.78022i	0.214677	+	0.295478i	0.902752	−	0.430162i	$-0.141544\pi$
$883$	6.37920	+	8.78022i	0.214677	+	0.295478i	−0.688074	+	0.725640i	$0.741544\pi$
$884$	4.86708	−	3.53614i	0.163698	−	0.118933i
$885$	−4.45996	−	7.06588i	−0.149920	−	0.237517i
$886$	4.45052	−	3.23349i	0.149518	−	0.108631i
$887$	−11.3620	+	15.6385i	−0.381499	+	0.525088i	−0.955981	−	0.293429i	$-0.905203\pi$
$887$	−11.3620	+	15.6385i	−0.381499	+	0.525088i	0.574482	+	0.818517i	$0.305203\pi$
$888$	2.54873	−	0.828131i	0.0855296	−	0.0277903i
$889$	−18.3052	−	13.2995i	−0.613937	−	0.446051i
$890$	0.669732	+	1.06105i	0.0224495	+	0.0355665i
$891$	−0.164066	+	0.504942i	−0.00549640	+	0.0169162i
$892$	−17.4143	+	5.65824i	−0.583073	+	0.189452i
$893$		−	12.9923i		−	0.434771i
$894$	−0.898025			−0.0300344
$895$	1.20499	−	3.02187i	0.0402785	−	0.101010i
$896$	−1.73855	+	1.26313i	−0.0580807	+	0.0421981i
$897$	−6.88191	+	9.47214i	−0.229780	+	0.316265i
$898$		−	15.1268i		−	0.504787i
$899$	13.7285	−	23.6273i	0.457871	−	0.788016i
$900$	0.912893	+	4.91596i	0.0304298	+	0.163865i
$901$	2.06492	+	1.50025i	0.0687924	+	0.0499806i
$902$	0.117654	+	0.161937i	0.00391745	+	0.00539190i
$903$	−2.51613	+	0.817539i	−0.0837314	+	0.0272060i
$904$	−4.21883			−0.140316
$905$	40.2255	+	33.4433i	1.33714	+	1.11169i
$906$	2.93003	+	9.01771i	0.0973438	+	0.299593i
$907$	47.8388	+	15.5438i	1.58846	+	0.516122i	0.964219	−	0.265109i	$-0.0854078\pi$
$907$	47.8388	+	15.5438i	1.58846	+	0.516122i	0.624242	+	0.781231i	$0.285408\pi$
$908$	−17.4834	−	5.68070i	−0.580207	−	0.188521i
$909$	7.52466	+	5.46698i	0.249577	+	0.181328i
$910$	−11.6855	−	4.65966i	−0.387369	−	0.154466i
$911$	5.88505	+	4.27574i	0.194980	+	0.141662i	0.680992	−	0.732291i	$-0.261549\pi$
$911$	5.88505	+	4.27574i	0.194980	+	0.141662i	−0.486012	+	0.873952i	$0.661549\pi$
$912$	2.49281	+	3.43106i	0.0825452	+	0.113614i
$913$	1.91737	+	0.622990i	0.0634556	+	0.0206180i
$914$	1.51489	−	1.10063i	0.0501081	−	0.0364056i
$915$	−0.290160	+	4.43885i	−0.00959238	+	0.146744i
$916$	−5.64991	+	17.3886i	−0.186678	+	0.574536i
$917$	−24.9142	−	34.2915i	−0.822741	−	1.13241i
$918$	1.35068	−	1.85906i	0.0445792	−	0.0613581i
$919$	17.6825	+	54.4212i	0.583293	+	1.79519i	0.606020	+	0.795449i	$0.292765\pi$
$919$	17.6825	+	54.4212i	0.583293	+	1.79519i	−0.0227274	+	0.999742i	$0.507235\pi$
$920$	2.46322	+	9.69188i	0.0812101	+	0.319532i
$921$	−1.51880	+	4.67440i	−0.0500463	+	0.154027i
$922$	−35.4717	−	11.5255i	−1.16820	−	0.379571i
$923$	7.82063	−	2.54108i	0.257419	−	0.0836405i
$924$	−1.14094			−0.0375342
$925$	13.1742	−	2.44645i	0.433165	−	0.0804388i
$926$	3.53407	+	10.8768i	0.116137	+	0.357432i
$927$	−4.66327	−	6.41843i	−0.153162	−	0.210809i
$928$	2.88481	−	3.97060i	0.0946986	−	0.130341i
$929$	50.2070			1.64724			0.823619	−	0.567143i	$-0.191951\pi$
$929$	50.2070			1.64724			0.823619	+	0.567143i	$0.191951\pi$
$930$	−6.94359	+	10.3338i	−0.227689	+	0.338857i
$931$	10.1020			0.331079
$932$	10.0427	−	13.8226i	0.328959	−	0.452774i
$933$	−9.55646	−	13.1533i	−0.312864	−	0.430621i
$934$	−8.22673	−	25.3193i	−0.269187	−	0.828472i
$935$	1.74407	−	2.09776i	0.0570371	−	0.0686040i
$936$	−2.61803			−0.0855731
$937$	−33.2707	+	10.8103i	−1.08691	+	0.353158i	−0.797051	−	0.603912i	$-0.793608\pi$
$937$	−33.2707	+	10.8103i	−1.08691	+	0.353158i	−0.289857	+	0.957070i	$0.593608\pi$
$938$	5.41243	+	1.75861i	0.176722	+	0.0574205i
$939$	7.83395	−	24.1104i	0.255651	−	0.786813i
$940$	6.63908	−	1.68735i	0.216543	−	0.0550351i
$941$	−0.565680	−	1.74098i	−0.0184406	−	0.0567544i	0.941413	−	0.337257i	$-0.109499\pi$
$941$	−0.565680	−	1.74098i	−0.0184406	−	0.0567544i	−0.959853	+	0.280502i	$0.909499\pi$
$942$	1.61156	−	2.21812i	0.0525073	−	0.0722701i
$943$	0.991029	+	1.36403i	0.0322723	+	0.0444191i
$944$	1.15473	−	3.55390i	0.0375833	−	0.115669i
$945$	−4.79499	−	0.313440i	−0.155981	−	0.0101962i
$946$	−0.528798	+	0.384194i	−0.0171927	+	0.0124912i
$947$	31.1528	+	10.1222i	1.01233	+	0.328926i	0.767783	−	0.640711i	$-0.221360\pi$
$947$	31.1528	+	10.1222i	1.01233	+	0.328926i	0.244549	+	0.969637i	$0.421360\pi$
$948$	2.69666	+	3.71163i	0.0875833	+	0.120548i
$949$	−34.6466	−	25.1722i	−1.12467	−	0.817124i
$950$	10.1247	+	18.6319i	0.328489	+	0.604498i
$951$	−20.2573	−	14.7178i	−0.656888	−	0.477257i
$952$	4.69646	+	1.52597i	0.152213	+	0.0494570i
$953$	25.5390	+	8.29811i	0.827288	+	0.268802i	0.691903	−	0.721991i	$-0.256773\pi$
$953$	25.5390	+	8.29811i	0.827288	+	0.268802i	0.135386	+	0.990793i	$0.456773\pi$
$954$	−0.343235	−	1.05637i	−0.0111127	−	0.0342012i
$955$	25.5381	+	21.2323i	0.826394	+	0.687061i
$956$	−12.0665			−0.390260
$957$	2.47822	−	0.805223i	0.0801095	−	0.0260292i
$958$	4.11174	+	5.65933i	0.132844	+	0.182844i
$959$	−4.53480	−	3.29473i	−0.146436	−	0.106392i
$960$	−1.42953	+	1.71943i	−0.0461379	+	0.0554944i
$961$	−30.3578	+	6.27748i	−0.979282	+	0.202499i
$962$			7.01604i			0.226206i
$963$	−9.17559	+	12.6291i	−0.295679	+	0.406968i
$964$	−13.6211	+	9.89631i	−0.438706	+	0.318739i
$965$	−22.4457	−	8.95039i	−0.722553	−	0.288123i
$966$	−9.61045			−0.309211
$967$		−	18.1645i		−	0.584130i	−0.956398	−	0.292065i	$-0.905658\pi$
$967$		−	18.1645i		−	0.584130i	0.956398	−	0.292065i	$-0.0943423\pi$
$968$	10.1935	−	3.31208i	0.327633	−	0.106454i
$969$	3.01154	−	9.26856i	0.0967446	−	0.297749i
$970$	8.28005	−	5.22634i	0.265856	−	0.167808i
$971$	10.5792	+	7.68626i	0.339504	+	0.246664i	0.744452	−	0.667676i	$-0.232711\pi$
$971$	10.5792	+	7.68626i	0.339504	+	0.246664i	−0.404949	+	0.914339i	$0.632711\pi$
$972$	−0.951057	+	0.309017i	−0.0305052	+	0.00991172i
$973$	−10.6098	+	14.6031i	−0.340135	+	0.468155i
$974$	−17.1854	+	12.4859i	−0.550657	+	0.400075i
$975$	−12.9788	−	1.70408i	−0.415654	−	0.0545743i
$976$	−1.60942	+	1.16931i	−0.0515162	+	0.0374287i
$977$	14.7205	+	20.2611i	0.470951	+	0.648209i	0.976735	−	0.214452i	$-0.0687965\pi$
$977$	14.7205	+	20.2611i	0.470951	+	0.648209i	−0.505783	+	0.862661i	$0.668796\pi$
$978$	14.7210	+	4.78313i	0.470724	+	0.152948i
$979$	−0.241024	+	0.175114i	−0.00770317	+	0.00559668i
$980$	1.31197	+	5.16213i	0.0419094	+	0.164898i
$981$	−0.945136	−	2.90883i	−0.0301759	−	0.0928718i
$982$	15.1213	−	20.8127i	0.482540	−	0.664159i
$983$	−48.8349	−	15.8674i	−1.55759	−	0.506093i	−0.601429	−	0.798926i	$-0.705402\pi$
$983$	−48.8349	−	15.8674i	−1.55759	−	0.506093i	−0.956163	+	0.292833i	$0.905402\pi$
$984$	−0.116502	+	0.358558i	−0.00371396	+	0.0114304i
$985$	−28.2453	−	11.2630i	−0.899970	−	0.358869i
$986$	−11.2781			−0.359167
$987$			6.58330i			0.209549i
$988$	−10.5597	+	3.43106i	−0.335949	+	0.109157i
$989$	−4.45420	+	3.23617i	−0.141635	+	0.102904i
$990$	−1.15061	+	0.292431i	−0.0365688	+	0.00929408i
$991$	23.1615			0.735749			0.367875	−	0.929875i	$-0.380086\pi$
$991$	23.1615			0.735749			0.367875	+	0.929875i	$0.380086\pi$
$992$	−5.53885	+	0.566677i	−0.175859	+	0.0179920i
$993$		−	6.68547i		−	0.212157i
$994$	5.46067	+	3.96741i	0.173202	+	0.125839i
$995$	56.3478	+	3.68336i	1.78634	+	0.116770i
$996$	1.17340	+	3.61136i	0.0371806	+	0.114430i
$997$		−	33.4348i		−	1.05889i	−0.848344	−	0.529445i	$-0.822400\pi$
$997$		−	33.4348i		−	1.05889i	0.848344	−	0.529445i	$-0.177600\pi$
$998$			15.0082i			0.475077i
$999$	0.828131	+	2.54873i	0.0262009	+	0.0806381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.b.529.2	yes	16
5.4	even	2	inner	930.2.z.b.529.4	yes	16
31.16	even	5	inner	930.2.z.b.109.4	yes	16
155.109	even	10	inner	930.2.z.b.109.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.b.109.2	✓	16	155.109	even	10	inner
930.2.z.b.109.4	yes	16	31.16	even	5	inner
930.2.z.b.529.2	yes	16	1.1	even	1	trivial
930.2.z.b.529.4	yes	16	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.71943 + 1.42953i) q^{5} -1.00000 q^{6} +(2.04378 - 0.664066i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(0.587785 + 0.809017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.71943 + 1.42953i) q^{5} -1.00000 q^{6} +(2.04378 - 0.664066i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-2.16717 + 0.550794i) q^{10} +(-0.164066 - 0.504942i) q^{11} +(0.587785 - 0.809017i) q^{12} +(1.53884 + 2.11803i) q^{13} +(-0.664066 + 2.04378i) q^{14} +(-0.145857 + 2.23131i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.18545 + 0.710097i) q^{17} +(-0.587785 - 0.809017i) q^{18} +(-3.43106 - 2.49281i) q^{19} +(0.828229 - 2.07703i) q^{20} +(1.73855 + 1.26313i) q^{21} +(0.504942 + 0.164066i) q^{22} +(4.25325 + 1.38197i) q^{23} +(0.309017 + 0.951057i) q^{24} +(0.912893 + 4.91596i) q^{25} -2.61803 q^{26} +(-0.951057 + 0.309017i) q^{27} +(-1.26313 - 1.73855i) q^{28} +(3.97060 + 2.88481i) q^{29} +(-1.71943 - 1.42953i) q^{30} +(-0.566677 - 5.53885i) q^{31} -1.00000i q^{32} +(0.312071 - 0.429529i) q^{33} +(-1.85906 + 1.35068i) q^{34} +(4.46345 + 1.77983i) q^{35} +1.00000 q^{36} -2.67989i q^{37} +(4.03345 - 1.31055i) q^{38} +(-0.809017 + 2.48990i) q^{39} +(1.19353 + 1.89090i) q^{40} +(0.305007 + 0.221601i) q^{41} +(-2.04378 + 0.664066i) q^{42} +(-0.723629 + 0.995990i) q^{43} +(-0.429529 + 0.312071i) q^{44} +(-1.89090 + 1.19353i) q^{45} +(-3.61803 + 2.62866i) q^{46} +(1.80067 + 2.47841i) q^{47} +(-0.951057 - 0.309017i) q^{48} +(-1.92705 + 1.40008i) q^{49} +(-4.51368 - 2.15098i) q^{50} +(0.710097 + 2.18545i) q^{51} +(1.53884 - 2.11803i) q^{52} +(1.05637 + 0.343235i) q^{53} +(0.309017 - 0.951057i) q^{54} +(0.439729 - 1.10275i) q^{55} +2.14896 q^{56} -4.24102i q^{57} +(-4.66773 + 1.51664i) q^{58} +(-3.02312 + 2.19643i) q^{59} +(2.16717 - 0.550794i) q^{60} +1.98935 q^{61} +(4.81411 + 2.79720i) q^{62} +2.14896i q^{63} +(0.809017 + 0.587785i) q^{64} +(-0.381857 + 5.84163i) q^{65} +(0.164066 + 0.504942i) q^{66} -2.64824i q^{67} -2.29792i q^{68} +(1.38197 + 4.25325i) q^{69} +(-4.06346 + 2.56485i) q^{70} +(0.970604 - 2.98721i) q^{71} +(-0.587785 + 0.809017i) q^{72} +(-15.5573 + 5.05486i) q^{73} +(2.16808 + 1.57520i) q^{74} +(-3.44051 + 3.62807i) q^{75} +(-1.31055 + 4.03345i) q^{76} +(-0.670629 - 0.923041i) q^{77} +(-1.53884 - 2.11803i) q^{78} +(-1.41772 + 4.36328i) q^{79} +(-2.23131 - 0.145857i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.358558 + 0.116502i) q^{82} +(-2.23194 + 3.07200i) q^{83} +(0.664066 - 2.04378i) q^{84} +(2.74264 + 4.34513i) q^{85} +(-0.380434 - 1.17086i) q^{86} +4.90794i q^{87} -0.530927i q^{88} +(-0.173401 - 0.533672i) q^{89} +(0.145857 - 2.23131i) q^{90} +(4.55157 + 3.30691i) q^{91} -4.47214i q^{92} +(4.14794 - 3.71411i) q^{93} -3.06348 q^{94} +(-2.33593 - 9.19102i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-4.16458 + 1.35316i) q^{97} -2.38197i q^{98} +0.530927 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 12 q^{5} - 16 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 + 12 * q^5 - 16 * q^6 + 4 * q^9	\( 16 q + 4 q^{4} + 12 q^{5} - 16 q^{6} + 4 q^{9} + 4 q^{10} + 8 q^{11} + 4 q^{15} - 4 q^{16} + 8 q^{19} - 2 q^{20} - 4 q^{24} + 16 q^{25} - 24 q^{26} + 36 q^{29} - 12 q^{30} + 40 q^{31} + 8 q^{34} + 14 q^{35} + 16 q^{36} - 4 q^{39} + 6 q^{40} + 32 q^{41} + 12 q^{44} - 2 q^{45} - 40 q^{46} - 4 q^{49} - 8 q^{50} + 8 q^{51} - 4 q^{54} + 24 q^{55} - 4 q^{60} - 16 q^{61} + 4 q^{64} + 6 q^{65} - 8 q^{66} + 40 q^{69} + 18 q^{70} - 12 q^{71} - 12 q^{74} - 8 q^{75} + 32 q^{76} - 8 q^{79} - 8 q^{80} - 4 q^{81} - 40 q^{85} - 68 q^{86} + 20 q^{89} - 4 q^{90} - 56 q^{94} - 18 q^{95} + 4 q^{96} - 8 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 + 12 * q^5 - 16 * q^6 + 4 * q^9 + 4 * q^10 + 8 * q^11 + 4 * q^15 - 4 * q^16 + 8 * q^19 - 2 * q^20 - 4 * q^24 + 16 * q^25 - 24 * q^26 + 36 * q^29 - 12 * q^30 + 40 * q^31 + 8 * q^34 + 14 * q^35 + 16 * q^36 - 4 * q^39 + 6 * q^40 + 32 * q^41 + 12 * q^44 - 2 * q^45 - 40 * q^46 - 4 * q^49 - 8 * q^50 + 8 * q^51 - 4 * q^54 + 24 * q^55 - 4 * q^60 - 16 * q^61 + 4 * q^64 + 6 * q^65 - 8 * q^66 + 40 * q^69 + 18 * q^70 - 12 * q^71 - 12 * q^74 - 8 * q^75 + 32 * q^76 - 8 * q^79 - 8 * q^80 - 4 * q^81 - 40 * q^85 - 68 * q^86 + 20 * q^89 - 4 * q^90 - 56 * q^94 - 18 * q^95 + 4 * q^96 - 8 * q^99

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