LMFDB - Embedded newform 930.2.z.b.109.4

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			109.4
Root			$0.416689 - 2.63087i$ of defining polynomial
Character	$\chi$	$=$	930.109
Dual form			930.2.z.b.529.4

$q$-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} +(-0.145857 + 2.23131i) 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} +(-2.16717 + 0.550794i) 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} +(-1.89090 + 1.19353i) 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} +(-2.56485 - 4.06346i) q^{35} +1.00000 q^{36} -2.67989i q^{37} +(-4.03345 - 1.31055i) q^{38} +(-0.809017 - 2.48990i) q^{39} +(-2.07703 - 0.828229i) 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} +(0.828229 - 2.07703i) 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} +(-3.44051 + 3.62807i) 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} +(-1.00393 + 0.633677i) q^{55} +2.14896 q^{56} -4.24102i q^{57} +(4.66773 + 1.51664i) q^{58} +(-3.02312 - 2.19643i) q^{59} +(0.145857 - 2.23131i) q^{60} +1.98935 q^{61} +(-4.81411 + 2.79720i) q^{62} +2.14896i q^{63} +(0.809017 - 0.587785i) q^{64} +(-5.67373 + 1.44200i) q^{65} +(0.164066 - 0.504942i) q^{66} -2.64824i q^{67} -2.29792i q^{68} +(1.38197 - 4.25325i) q^{69} +(1.77983 - 4.46345i) 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} +(-4.51368 - 2.15098i) 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} +(-0.550794 - 2.16717i) 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} +(-4.77284 - 1.90321i) q^{85} +(-0.380434 + 1.17086i) q^{86} +4.90794i q^{87} -0.530927i q^{88} +(-0.173401 + 0.533672i) q^{89} +(2.16717 - 0.550794i) q^{90} +(4.55157 - 3.30691i) q^{91} -4.47214i q^{92} +(-4.14794 - 3.71411i) q^{93} -3.06348 q^{94} +(-9.46302 - 0.618581i) 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

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

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	$-0.533117\pi$
$7$	−2.04378	−	0.664066i	−0.772478	−	0.250993i	−0.668625	+	0.743600i	$0.733117\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$	−0.145857	+	2.23131i	−0.0461239	+	0.705601i
$11$	−0.164066	+	0.504942i	−0.0494676	+	0.152246i	−0.972739	−	0.231903i	$-0.925505\pi$
$11$	−0.164066	+	0.504942i	−0.0494676	+	0.152246i	0.923271	+	0.384148i	$0.125505\pi$
$12$	−0.587785	−	0.809017i	−0.169679	−	0.233543i
$13$	−1.53884	+	2.11803i	−0.426798	+	0.587437i	−0.967215	−	0.253961i	$-0.918267\pi$
$13$	−1.53884	+	2.11803i	−0.426798	+	0.587437i	0.540417	+	0.841398i	$0.318267\pi$
$14$	−0.664066	−	2.04378i	−0.177479	−	0.546224i
$15$	−2.16717	+	0.550794i	−0.559561	+	0.142214i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−2.18545	+	0.710097i	−0.530050	+	0.172224i	−0.561802	−	0.827272i	$-0.689892\pi$
$17$	−2.18545	+	0.710097i	−0.530050	+	0.172224i	0.0317512	+	0.999496i	$0.489892\pi$
$18$	0.587785	−	0.809017i	0.138542	−	0.190687i
$19$	−3.43106	+	2.49281i	−0.787139	+	0.571890i	−0.907113	−	0.420887i	$-0.861719\pi$
$19$	−3.43106	+	2.49281i	−0.787139	+	0.571890i	0.119974	+	0.992777i	$0.461719\pi$
$20$	−1.89090	+	1.19353i	−0.422817	+	0.266881i
$21$	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	$-0.754396\pi$
$23$	−4.25325	+	1.38197i	−0.886865	+	0.288160i	−0.170060	+	0.985434i	$0.554396\pi$
$24$	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	−0.154549	−	0.987985i	$-0.549392\pi$
$29$	3.97060	−	2.88481i	0.737323	−	0.535696i	0.891872	+	0.452289i	$0.149392\pi$
$30$	−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
$35$	−2.56485	−	4.06346i	−0.433538	−	0.686851i
$36$	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
$40$	−2.07703	−	0.828229i	−0.328407	−	0.130955i
$41$	0.305007	−	0.221601i	0.0476341	−	0.0346082i	−0.563713	−	0.825970i	$-0.690628\pi$
$41$	0.305007	−	0.221601i	0.0476341	−	0.0346082i	0.611348	+	0.791362i	$0.290628\pi$
$42$	2.04378	+	0.664066i	0.315363	+	0.102468i
$43$	0.723629	+	0.995990i	0.110352	+	0.151887i	0.860621	−	0.509246i	$-0.170076\pi$
$43$	0.723629	+	0.995990i	0.110352	+	0.151887i	−0.750268	+	0.661133i	$0.770076\pi$
$44$	−0.429529	−	0.312071i	−0.0647539	−	0.0470465i
$45$	0.828229	−	2.07703i	0.123465	−	0.309625i
$46$	−3.61803	−	2.62866i	−0.533450	−	0.387574i
$47$	−1.80067	+	2.47841i	−0.262655	+	0.361513i	−0.919893	−	0.392170i	$-0.871725\pi$
$47$	−1.80067	+	2.47841i	−0.262655	+	0.361513i	0.657238	+	0.753683i	$0.271725\pi$
$48$	0.951057	−	0.309017i	0.137273	−	0.0446028i
$49$	−1.92705	−	1.40008i	−0.275293	−	0.200012i
$50$	−3.44051	+	3.62807i	−0.486561	+	0.513087i
$51$	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	$-0.624306\pi$
$53$	−1.05637	+	0.343235i	−0.145104	+	0.0471470i	0.235565	+	0.971859i	$0.424306\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$	−1.00393	+	0.633677i	−0.135370	+	0.0854449i
$56$	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	0.373343	−	0.927694i	$-0.378212\pi$
$59$	−3.02312	−	2.19643i	−0.393577	−	0.285951i	−0.766920	+	0.641743i	$0.778212\pi$
$60$	0.145857	−	2.23131i	0.0188300	−	0.288060i
$61$	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
$65$	−5.67373	+	1.44200i	−0.703739	+	0.178858i
$66$	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
$70$	1.77983	−	4.46345i	0.212731	−	0.533484i
$71$	0.970604	+	2.98721i	0.115190	+	0.354517i	0.991987	−	0.126344i	$-0.0403242\pi$
$71$	0.970604	+	2.98721i	0.115190	+	0.354517i	−0.876797	+	0.480861i	$0.840324\pi$
$72$	0.587785	+	0.809017i	0.0692712	+	0.0953436i
$73$	15.5573	+	5.05486i	1.82084	+	0.591627i	0.999784	+	0.0207807i	$0.00661517\pi$
$73$	15.5573	+	5.05486i	1.82084	+	0.591627i	0.821057	+	0.570846i	$0.193385\pi$
$74$	2.16808	−	1.57520i	0.252034	−	0.183113i
$75$	−4.51368	−	2.15098i	−0.521195	−	0.248374i
$76$	−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	0.839084	−	0.544002i	$-0.183092\pi$
$79$	−1.41772	−	4.36328i	−0.159506	−	0.490907i	−0.998589	+	0.0530944i	$0.983092\pi$
$80$	−0.550794	−	2.16717i	−0.0615806	−	0.242297i
$81$	−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	$-0.133175\pi$
$83$	2.23194	+	3.07200i	0.244987	+	0.337196i	−0.668761	+	0.743478i	$0.733175\pi$
$84$	0.664066	+	2.04378i	0.0724555	+	0.222995i
$85$	−4.77284	−	1.90321i	−0.517688	−	0.206432i
$86$	−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	−0.959826	−	0.280596i	$-0.909468\pi$
$89$	−0.173401	+	0.533672i	−0.0183804	+	0.0565691i	0.941446	+	0.337165i	$0.109468\pi$
$90$	2.16717	−	0.550794i	0.228440	−	0.0580587i
$91$	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
$95$	−9.46302	−	0.618581i	−0.970886	−	0.0634651i
$96$	0.809017	+	0.587785i	0.0825700	+	0.0599906i
$97$	4.16458	+	1.35316i	0.422849	+	0.137392i	0.512709	−	0.858562i	$-0.328642\pi$
$97$	4.16458	+	1.35316i	0.422849	+	0.137392i	−0.0898598	+	0.995954i	$0.528642\pi$
$98$		−	2.38197i		−	0.240615i
$99$	0.530927			0.0533602
$100$	−4.95745	−	0.650901i	−0.495745	−	0.0650901i
$101$	2.87416	+	8.84576i	0.285990	+	0.880186i	0.986100	+	0.166152i	$0.0531341\pi$
$101$	2.87416	+	8.84576i	0.285990	+	0.880186i	−0.700110	+	0.714035i	$0.746866\pi$
$102$	2.18545	−	0.710097i	0.216392	−	0.0703101i
$103$	4.66327	+	6.41843i	0.459485	+	0.632427i	0.974402	−	0.224813i	$-0.0721772\pi$
$103$	4.66327	+	6.41843i	0.459485	+	0.632427i	−0.514917	+	0.857240i	$0.672177\pi$
$104$	0.809017	−	2.48990i	0.0793306	−	0.244155i
$105$	4.79499	+	0.313440i	0.467943	+	0.0305886i
$106$	−0.898602	−	0.652873i	−0.0872799	−	0.0634126i
$107$	−14.8464	+	4.82389i	−1.43526	+	0.466343i	−0.920415	−	0.390942i	$-0.872149\pi$
$107$	−14.8464	+	4.82389i	−1.43526	+	0.466343i	−0.514842	+	0.857285i	$0.672149\pi$
$108$	−0.587785	+	0.809017i	−0.0565597	+	0.0778477i
$109$	−2.47440	−	1.79776i	−0.237004	−	0.172194i	0.462943	−	0.886388i	$-0.346793\pi$
$109$	−2.47440	−	1.79776i	−0.237004	−	0.172194i	−0.699948	+	0.714194i	$0.746793\pi$
$110$	−1.10275	−	0.439729i	−0.105143	−	0.0419266i
$111$	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	$-0.336413\pi$
$113$	4.01235	+	1.30369i	0.377450	+	0.122641i	−0.114147	+	0.993464i	$0.536413\pi$
$114$	3.43106	−	2.49281i	0.321348	−	0.233473i
$115$	−9.28874	−	3.70395i	−0.866180	−	0.345395i
$116$	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
$120$	1.89090	−	1.19353i	0.172614	−	0.108954i
$121$	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	$-0.645281\pi$
$127$	6.18881	−	8.51817i	0.549168	−	0.755865i	0.989899	+	0.141774i	$0.0452807\pi$
$128$	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	0.216385	+	0.976308i	$0.430573\pi$
$131$	−6.09513	+	18.7589i	−0.532534	+	1.63897i	−0.748919	+	0.662662i	$0.769427\pi$
$132$	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
$135$	1.19353	+	1.89090i	0.102723	+	0.162742i
$136$	1.85906	−	1.35068i	0.159413	−	0.115820i
$137$	1.53317	−	2.11023i	0.130988	−	0.180289i	−0.738485	−	0.674270i	$-0.764459\pi$
$137$	1.53317	−	2.11023i	0.130988	−	0.180289i	0.869473	+	0.493980i	$0.164459\pi$
$138$	4.25325	−	1.38197i	0.362061	−	0.117641i
$139$	−6.79544	−	4.93718i	−0.576382	−	0.418766i	0.261036	−	0.965329i	$-0.415936\pi$
$139$	−6.79544	−	4.93718i	−0.576382	−	0.418766i	−0.837418	+	0.546563i	$0.815936\pi$
$140$	4.65716	−	1.18363i	0.393602	−	0.100035i
$141$	−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
$145$	10.9511	+	0.715855i	0.909440	+	0.0594485i
$146$	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	0.758203	+	0.652018i	$0.226077\pi$
$151$	−2.93003	+	9.01771i	−0.238443	+	0.733851i	−0.996646	+	0.0818328i	$0.973923\pi$
$152$	2.49281	−	3.43106i	0.202194	−	0.278296i
$153$	1.35068	+	1.85906i	0.109196	+	0.150296i
$154$	1.14094			0.0919397
$155$	−8.89231	+	8.71360i	−0.714248	+	0.699893i
$156$	2.61803			0.209610
$157$	1.61156	+	2.21812i	0.128616	+	0.177025i	0.868469	−	0.495744i	$-0.165105\pi$
$157$	1.61156	+	2.21812i	0.128616	+	0.177025i	−0.739852	+	0.672769i	$0.765105\pi$
$158$	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	$-0.392699\pi$
$163$	14.7210	−	4.78313i	1.15303	−	0.374644i	0.822285	+	0.569075i	$0.192699\pi$
$164$	0.116502	+	0.358558i	0.00909731	+	0.0279986i
$165$	0.0774392	−	1.18466i	0.00602863	−	0.0922257i
$166$	−1.17340	+	3.61136i	−0.0910735	+	0.280296i
$167$	−8.43129	−	11.6047i	−0.652433	−	0.897997i	0.346769	−	0.937951i	$-0.387279\pi$
$167$	−8.43129	−	11.6047i	−0.652433	−	0.897997i	−0.999202	+	0.0399538i	$0.987279\pi$
$168$	−1.26313	+	1.73855i	−0.0974524	+	0.134132i
$169$	1.89919	+	5.84510i	0.146091	+	0.449623i
$170$	−1.26568	−	4.97999i	−0.0970733	−	0.381948i
$171$	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	$-0.839084\pi$
$173$	−1.89378	+	2.60657i	−0.143982	+	0.198174i	0.730935	+	0.682447i	$0.239084\pi$
$174$	−3.97060	+	2.88481i	−0.301011	+	0.218697i
$175$	1.39876	−	10.6534i	0.105736	−	0.805319i
$176$	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	−0.966452	−	0.256849i	$-0.917316\pi$
$179$	−0.449590	+	1.38369i	−0.0336039	+	0.103422i	0.932848	+	0.360271i	$0.117316\pi$
$180$	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
$190$	−5.06178	−	8.01934i	−0.367220	−	0.581784i
$191$	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	$-0.272841\pi$
$193$	10.2777	+	3.33944i	0.739808	+	0.240378i	0.0852182	+	0.996362i	$0.472841\pi$
$194$	1.35316	+	4.16458i	0.0971509	+	0.299000i
$195$	2.16833	−	5.43772i	0.155277	−	0.389404i
$196$	1.92705	−	1.40008i	0.137646	−	0.100006i
$197$	12.9333	+	4.20229i	0.921462	+	0.299401i	0.731066	−	0.682306i	$-0.239023\pi$
$197$	12.9333	+	4.20229i	0.921462	+	0.299401i	0.190395	+	0.981707i	$0.439023\pi$
$198$	0.312071	+	0.429529i	0.0221779	+	0.0305253i
$199$	20.4303	+	14.8435i	1.44827	+	1.05223i	0.986232	+	0.165367i	$0.0528807\pi$
$199$	20.4303	+	14.8435i	1.44827	+	1.05223i	0.462036	+	0.886861i	$0.347119\pi$
$200$	−2.38733	−	4.39325i	−0.168810	−	0.310650i
$201$	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
$205$	0.841224	+	0.0549893i	0.0587536	+	0.00384062i
$206$	−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
$210$	2.56485	+	4.06346i	0.176991	+	0.280406i
$211$	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
$215$	−0.179566	+	2.74699i	−0.0122463	+	0.187343i
$216$	−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
$220$	−0.292431	−	1.15061i	−0.0197157	−	0.0775741i
$221$	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
$225$	4.39325	−	2.38733i	0.292884	−	0.159155i
$226$	1.30369	+	4.01235i	0.0867203	+	0.266898i
$227$	−10.8053	−	14.8723i	−0.717175	−	0.987107i	−0.999613	−	0.0278215i	$-0.991143\pi$
$227$	−10.8053	−	14.8723i	−0.717175	−	0.987107i	0.282438	−	0.959286i	$-0.408857\pi$
$228$	4.03345	+	1.31055i	0.267122	+	0.0867932i
$229$	−14.7917	+	10.7468i	−0.977460	+	0.710166i	−0.957139	−	0.289627i	$-0.906469\pi$
$229$	−14.7917	+	10.7468i	−0.977460	+	0.710166i	−0.0203203	+	0.999794i	$0.506469\pi$
$230$	−2.46322	−	9.69188i	−0.162420	−	0.639064i
$231$	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	$-0.989068\pi$
$233$	−10.0427	+	13.8226i	−0.657919	+	0.905547i	0.341492	+	0.939885i	$0.389068\pi$
$234$	0.809017	+	2.48990i	0.0528871	+	0.162770i
$235$	−6.63908	+	1.68735i	−0.433086	+	0.110070i
$236$	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	0.996239	+	0.0866458i	$0.0276148\pi$
$239$	3.72877	+	11.4760i	0.241194	+	0.742318i	−0.755045	+	0.655673i	$0.772385\pi$
$240$	2.07703	+	0.828229i	0.134071	+	0.0534620i
$241$	−5.20280	+	16.0126i	−0.335142	+	1.03146i	0.631511	+	0.775367i	$0.282435\pi$
$241$	−5.20280	+	16.0126i	−0.335142	+	1.03146i	−0.966652	+	0.256093i	$0.917565\pi$
$242$			10.7181i			0.688987i
$243$		−	1.00000i		−	0.0641500i
$244$	−0.614743	+	1.89198i	−0.0393549	+	0.121122i
$245$	−1.31197	−	5.16213i	−0.0838188	−	0.329796i
$246$	−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
$250$	−11.1022	+	1.31992i	−0.702162	+	0.0834790i
$251$	−2.98358	−	2.16770i	−0.188322	−	0.136824i	0.489630	−	0.871931i	$-0.337132\pi$
$251$	−2.98358	−	2.16770i	−0.188322	−	0.136824i	−0.677951	+	0.735107i	$0.737132\pi$
$252$	−2.04378	−	0.664066i	−0.128746	−	0.0418322i
$253$		−	2.37438i		−	0.149276i
$254$	10.5290			0.660650
$255$	4.34513	−	2.74264i	0.272103	−	0.171750i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	7.64051	−	2.48255i	0.476602	−	0.154857i	−0.0608585	−	0.998146i	$-0.519384\pi$
$257$	7.64051	−	2.48255i	0.476602	−	0.154857i	0.537460	+	0.843289i	$0.319384\pi$
$258$	−0.723629	−	0.995990i	−0.0450512	−	0.0620077i
$259$	−1.77962	+	5.47711i	−0.110580	+	0.340331i
$260$	0.381857	−	5.84163i	0.0236818	−	0.362283i
$261$	−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	$-0.779117\pi$
$263$	1.24983	−	1.72025i	0.0770679	−	0.106075i	0.845811	+	0.533483i	$0.179117\pi$
$264$	0.429529	+	0.312071i	0.0264357	+	0.0192067i
$265$	−2.30702	−	0.919942i	−0.141719	−	0.0565116i
$266$	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	−0.681027	−	0.732259i	$-0.738466\pi$
$269$	−3.19916	+	2.32432i	−0.195056	+	0.141716i	0.485971	+	0.873975i	$0.338466\pi$
$270$	−0.828229	+	2.07703i	−0.0504044	+	0.126404i
$271$	4.47367	+	13.7685i	0.271756	+	0.836379i	0.990060	+	0.140649i	$0.0449189\pi$
$271$	4.47367	+	13.7685i	0.271756	+	0.836379i	−0.718304	+	0.695730i	$0.755081\pi$
$272$	2.18545	+	0.710097i	0.132513	+	0.0430560i
$273$			5.62605i			0.340504i
$274$	2.60839			0.157579
$275$	−2.63205	−	0.345581i	−0.158718	−	0.0208393i
$276$	3.61803	+	2.62866i	0.217780	+	0.158226i
$277$	−8.13380	−	11.1952i	−0.488712	−	0.672655i	0.491437	−	0.870913i	$-0.336472\pi$
$277$	−8.13380	−	11.1952i	−0.488712	−	0.672655i	−0.980150	+	0.198258i	$0.936472\pi$
$278$		−	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	−0.828008	−	0.560716i	$-0.810526\pi$
$281$	−9.22980	+	6.70584i	−0.550603	+	0.400037i	0.277404	+	0.960753i	$0.410526\pi$
$282$	1.80067	−	2.47841i	0.107228	−	0.147587i
$283$	−14.2750	−	4.63824i	−0.848562	−	0.275714i	−0.147718	−	0.989029i	$-0.547193\pi$
$283$	−14.2750	−	4.63824i	−0.848562	−	0.275714i	−0.700844	+	0.713315i	$0.747193\pi$
$284$	−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
$290$	5.85776	+	9.28040i	0.343980	+	0.544964i
$291$	−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	$-0.903478\pi$
$293$	−26.5483	+	8.62605i	−1.55097	+	0.503939i	−0.596590	+	0.802546i	$0.703478\pi$
$294$	1.92705	+	1.40008i	0.112388	+	0.0816546i
$295$	−2.05820	−	8.09825i	−0.119833	−	0.471498i
$296$	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
$300$	3.44051	−	3.62807i	0.198638	−	0.209467i
$301$	−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	$-0.844792\pi$
$307$	−2.88894	+	3.97628i	−0.164880	+	0.226938i	0.718580	+	0.695444i	$0.244792\pi$
$308$	0.670629	+	0.923041i	0.0382126	+	0.0525952i
$309$	−7.93362			−0.451328
$310$	−12.2762	−	2.07231i	−0.697242	−	0.117699i
$311$	−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	−0.143259	−	0.989685i	$-0.545758\pi$
$313$	14.9011	−	20.5095i	0.842257	−	1.15927i	0.985516	−	0.169582i	$-0.0542419\pi$
$314$	−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	$-0.151764\pi$
$317$	23.8139	+	7.73760i	1.33752	+	0.434587i	0.449045	+	0.893509i	$0.351764\pi$
$318$	1.05637	−	0.343235i	0.0592383	−	0.0192477i
$319$	0.805223	+	2.47822i	0.0450838	+	0.138754i
$320$	2.23131	+	0.145857i	0.124734	+	0.00815363i
$321$	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
$325$	−11.8170	−	5.63134i	−0.655487	−	0.312371i
$326$	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
$330$	1.00393	−	0.633677i	0.0552644	−	0.0348827i
$331$	−5.40866	+	3.92962i	−0.297287	+	0.215991i	−0.726422	−	0.687249i	$-0.758818\pi$
$331$	−5.40866	+	3.92962i	−0.297287	+	0.215991i	0.429136	+	0.903240i	$0.358818\pi$
$332$	−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	$-0.554695\pi$
$337$	−16.3096	−	5.29932i	−0.888442	−	0.288672i	−0.717458	+	0.696601i	$0.754695\pi$
$338$	−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
$345$	8.45635	−	5.33762i	0.455274	−	0.287368i
$346$	−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	−0.959628	−	0.281273i	$-0.909243\pi$
$349$	−6.51240	−	20.0431i	−0.348601	−	1.07288i	0.611027	−	0.791610i	$-0.290757\pi$
$350$	9.44093	−	5.13027i	0.504639	−	0.274225i
$351$	−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	−0.999195	−	0.0401067i	$-0.987230\pi$
$353$	−13.6886	−	18.8407i	−0.728571	−	1.00279i	0.270625	−	0.962685i	$-0.412770\pi$
$354$	3.02312	+	2.19643i	0.160677	+	0.116739i
$355$	−2.60142	+	6.52382i	−0.138069	+	0.346248i
$356$	−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	−0.276289	−	0.961075i	$-0.589105\pi$
$359$	−24.1711	−	17.5614i	−1.27570	−	0.926853i	−0.999414	+	0.0342220i	$0.989105\pi$
$360$	−0.145857	+	2.23131i	−0.00768731	+	0.117600i
$361$	−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
$365$	19.5236	+	30.9311i	1.02191	+	1.61901i
$366$	−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
$370$	5.97965	+	0.390879i	0.310867	+	0.0203208i
$371$	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
$375$	−4.68607	−	10.1509i	−0.241988	−	0.524190i
$376$	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	−0.668304	−	0.743888i	$-0.732980\pi$
$379$	6.02749	−	18.5507i	0.309612	−	0.952887i	0.977916	−	0.208999i	$-0.0670204\pi$
$380$	3.51254	−	8.80872i	0.180190	−	0.451878i
$381$	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	$-0.199898\pi$
$383$	21.8900	+	7.11248i	1.11852	+	0.363431i	0.309320	+	0.950958i	$0.399898\pi$
$384$	−0.809017	+	0.587785i	−0.0412850	+	0.0299953i
$385$	2.47262	−	0.628423i	0.126016	−	0.0320274i
$386$	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	−0.682050	−	0.731305i	$-0.738911\pi$
$389$	−11.0471	−	33.9995i	−0.560111	−	1.72384i	0.121940	−	0.992538i	$-0.461089\pi$
$390$	5.67373	−	1.44200i	0.287300	−	0.0730183i
$391$	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
$395$	3.79977	−	9.52903i	0.191187	−	0.479458i
$396$	−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
$400$	2.15098	−	4.51368i	0.107549	−	0.225684i
$401$	6.19346	−	4.49981i	0.309287	−	0.224710i	−0.422304	−	0.906454i	$-0.638778\pi$
$401$	6.19346	−	4.49981i	0.309287	−	0.224710i	0.731590	+	0.681744i	$0.238778\pi$
$402$			2.64824i			0.132082i
$403$	−10.8594	−	9.72366i	−0.540948	−	0.484370i
$404$	−9.30099			−0.462741
$405$	−2.23131	−	0.145857i	−0.110874	−	0.00724767i
$406$	−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	$0.358078\pi$
$410$	0.449972	+	0.712887i	0.0222225	+	0.0352070i
$411$	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
$415$	−0.553847	+	8.47272i	−0.0271873	+	0.415910i
$416$	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	0.579959	−	0.814646i	$-0.303069\pi$
$419$	−0.319299	−	0.231984i	−0.0155988	−	0.0113332i	−0.595557	+	0.803313i	$0.703069\pi$
$420$	−1.77983	+	4.46345i	−0.0868469	+	0.217794i
$421$	−16.1295	−	11.7187i	−0.786102	−	0.571137i	0.120702	−	0.992689i	$-0.461485\pi$
$421$	−16.1295	−	11.7187i	−0.786102	−	0.571137i	−0.906804	+	0.421552i	$0.861485\pi$
$422$	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
$425$	−5.48589	−	10.0954i	−0.266105	−	0.489697i
$426$	−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
$430$	−2.32791	+	1.46937i	−0.112262	+	0.0708592i
$431$	−17.7078	−	12.8655i	−0.852956	−	0.619709i	0.0730036	−	0.997332i	$-0.476742\pi$
$431$	−17.7078	−	12.8655i	−0.852956	−	0.619709i	−0.925959	+	0.377623i	$0.876742\pi$
$432$	−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	$-0.558283\pi$
$443$	5.23190	−	1.69995i	0.248575	−	0.0807670i	0.430655	+	0.902517i	$0.358283\pi$
$444$	−2.16808	+	1.57520i	−0.102892	+	0.0747556i
$445$	−1.06105	+	0.669732i	−0.0502986	+	0.0317483i
$446$	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	0.260298	−	0.965528i	$-0.416179\pi$
$449$	−12.2378	−	8.89129i	−0.577538	−	0.419606i	−0.837836	+	0.545922i	$0.816179\pi$
$450$	4.51368	+	2.15098i	0.212777	+	0.101398i
$451$	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
$455$	12.5534	+	0.820597i	0.588515	+	0.0384702i
$456$	1.31055	+	4.03345i	0.0613721	+	0.188884i
$457$	1.78086	−	0.578636i	0.0833050	−	0.0270674i	−0.267068	−	0.963678i	$-0.586055\pi$
$457$	1.78086	−	0.578636i	0.0833050	−	0.0270674i	0.350373	+	0.936610i	$0.386055\pi$
$458$	−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	−0.202945	−	0.979190i	$-0.565051\pi$
$461$	11.5255	−	35.4717i	0.536795	−	1.65208i	0.739739	−	0.672894i	$-0.234949\pi$
$462$	−0.670629	+	0.923041i	−0.0312005	+	0.0429438i
$463$	−6.72221	−	9.25232i	−0.312407	−	0.429992i	0.623723	−	0.781646i	$-0.285619\pi$
$463$	−6.72221	−	9.25232i	−0.312407	−	0.429992i	−0.936130	+	0.351654i	$0.885619\pi$
$464$	−4.90794			−0.227845
$465$	−1.82268	−	12.3158i	−0.0845247	−	0.571130i
$466$	−17.0856			−0.791477
$467$	15.6482	+	21.5379i	0.724111	+	0.996654i	0.999377	+	0.0352855i	$0.0112341\pi$
$467$	15.6482	+	21.5379i	0.724111	+	0.996654i	−0.275266	+	0.961368i	$0.588766\pi$
$468$	−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
$475$	−15.3867	−	14.5913i	−0.705992	−	0.669494i
$476$	−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	0.988218	−	0.153055i	$-0.0489112\pi$
$479$	2.16167	+	6.65294i	0.0987692	+	0.303980i	−0.889448	+	0.457036i	$0.848911\pi$
$480$	0.550794	+	2.16717i	0.0251402	+	0.0989173i
$481$	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
$485$	5.22634	+	8.28005i	0.237316	+	0.375978i
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	−20.2027	+	6.56425i	−0.915471	+	0.297455i	−0.728608	−	0.684931i	$-0.759832\pi$
$487$	−20.2027	+	6.56425i	−0.915471	+	0.297455i	−0.186863	+	0.982386i	$0.559832\pi$
$488$	−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	0.825400	−	0.564548i	$-0.190949\pi$
$499$	12.1419	+	8.82160i	0.543546	+	0.394909i	−0.281854	+	0.959457i	$0.590949\pi$
$500$	−7.59352	−	8.20600i	−0.339593	−	0.366984i
$501$	14.3442			0.640850
$502$		−	3.68791i		−	0.164599i
$503$	−14.8379	−	4.82114i	−0.661591	−	0.214964i	−0.0410732	−	0.999156i	$-0.513078\pi$
$503$	−14.8379	−	4.82114i	−0.661591	−	0.214964i	−0.620518	+	0.784192i	$0.713078\pi$
$504$	−0.664066	−	2.04378i	−0.0295798	−	0.0910374i
$505$	−7.70335	+	19.3184i	−0.342794	+	0.859657i
$506$	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	0.959266	−	0.282504i	$-0.0911651\pi$
$509$	22.2681	+	16.1788i	0.987018	+	0.717111i	0.0277521	+	0.999615i	$0.491165\pi$
$510$	4.77284	+	1.90321i	0.211345	+	0.0842754i
$511$	−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
$515$	−1.15717	+	17.7023i	−0.0509910	+	0.780058i
$516$	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
$520$	4.95043	−	3.12470i	0.217091	−	0.137027i
$521$	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	$-0.183025\pi$
$523$	27.4080	+	8.90540i	1.19847	+	0.389406i	0.359271	+	0.933233i	$0.383025\pi$
$524$	−15.9572	−	11.5936i	−0.697096	−	0.506470i
$525$	7.79659	+	7.39352i	0.340271	+	0.322679i
$526$	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
$530$	−0.611785	−	2.40715i	−0.0265742	−	0.104560i
$531$	−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
$535$	−32.4233	−	12.9290i	−1.40178	−	0.558971i
$536$	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
$540$	−2.16717	+	0.550794i	−0.0932602	+	0.0237024i
$541$	−11.6577	−	35.8786i	−0.501202	−	1.54254i	−0.807063	−	0.590465i	$-0.798944\pi$
$541$	−11.6577	−	35.8786i	−0.501202	−	1.54254i	0.305861	−	0.952076i	$-0.401056\pi$
$542$	−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
$545$	−1.68462	−	6.62834i	−0.0721610	−	0.283927i
$546$	−4.55157	+	3.30691i	−0.194789	+	0.141523i
$547$	−15.9178	−	5.17200i	−0.680595	−	0.221139i	−0.0517394	−	0.998661i	$-0.516477\pi$
$547$	−15.9178	−	5.17200i	−0.680595	−	0.221139i	−0.628856	+	0.777522i	$0.716477\pi$
$548$	1.53317	+	2.11023i	0.0654939	+	0.0901446i
$549$	−0.614743	−	1.89198i	−0.0262366	−	0.0807479i
$550$	−1.26750	−	2.33250i	−0.0540462	−	0.0994580i
$551$	−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
$555$	1.47607	+	5.80777i	0.0626555	+	0.246526i
$556$	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
$560$	−0.313440	+	4.79499i	−0.0132453	+	0.202625i
$561$	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
$565$	5.03530	+	7.97738i	0.211837	+	0.335611i
$566$	−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	−0.206773	−	0.978389i	$-0.566296\pi$
$569$	12.7759	−	39.3201i	0.535592	−	1.64838i	0.742365	−	0.669995i	$-0.233704\pi$
$570$	9.46302	+	0.618581i	0.396362	+	0.0259095i
$571$	21.2552	+	15.4428i	0.889501	+	0.646260i	0.935748	−	0.352670i	$-0.114726\pi$
$571$	21.2552	+	15.4428i	0.889501	+	0.646260i	−0.0462467	+	0.998930i	$0.514726\pi$
$572$	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
$575$	−10.6765	−	19.6472i	−0.445239	−	0.819346i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	24.1955	+	33.3022i	1.00727	+	1.38639i	0.920756	+	0.390139i	$0.127573\pi$
$577$	24.1955	+	33.3022i	1.00727	+	1.38639i	0.0865149	+	0.996251i	$0.472427\pi$
$578$	−11.1460	−	3.62154i	−0.463611	−	0.150636i
$579$	−8.74277	+	6.35200i	−0.363337	+	0.263980i
$580$	−4.06490	+	10.1939i	−0.168786	+	0.423279i
$581$	−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
$585$	3.12470	+	4.95043i	0.129190	+	0.204675i
$586$	−22.5833	−	16.4077i	−0.932908	−	0.677797i
$587$	−16.4058	−	22.5807i	−0.677141	−	0.932004i	0.322755	−	0.946483i	$-0.395391\pi$
$587$	−16.4058	−	22.5807i	−0.677141	−	0.932004i	−0.999895	+	0.0144787i	$0.995391\pi$
$588$			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	$-0.550960\pi$
$593$	−21.1530	−	6.87304i	−0.868651	−	0.282242i	−0.709237	+	0.704970i	$0.750960\pi$
$594$	−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	−0.681667	−	0.731663i	$-0.738745\pi$
$599$	−4.80829	+	3.49342i	−0.196461	+	0.142737i	0.485206	+	0.874400i	$0.338745\pi$
$600$	4.95745	+	0.650901i	0.202387	+	0.0265729i
$601$	−11.2280	+	8.15765i	−0.458001	+	0.332757i	−0.792747	−	0.609551i	$-0.791350\pi$
$601$	−11.2280	+	8.15765i	−0.458001	+	0.332757i	0.334746	+	0.942309i	$0.391350\pi$
$602$	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
$605$	5.90347	+	23.2280i	0.240010	+	0.944352i
$606$	−2.87416	−	8.84576i	−0.116755	−	0.359335i
$607$	16.4204	−	22.6007i	0.666484	−	0.917336i	−0.333191	−	0.942860i	$-0.608125\pi$
$607$	16.4204	−	22.6007i	0.666484	−	0.917336i	0.999674	+	0.0255234i	$0.00812523\pi$
$608$	2.49281	+	3.43106i	0.101097	+	0.139148i
$609$	3.25919	−	10.0308i	0.132069	−	0.406467i
$610$	−0.290160	+	4.43885i	−0.0117482	+	0.179724i
$611$	−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	$-0.352087\pi$
$613$	7.06201	+	2.29458i	0.285232	+	0.0926774i	−0.162907	+	0.986641i	$0.552087\pi$
$614$	−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	−0.257988	−	0.966148i	$-0.583059\pi$
$617$	18.3960	−	25.3200i	0.740596	−	1.01934i	0.998584	−	0.0531953i	$-0.0169406\pi$
$618$	−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	$0.413920\pi$
$620$	−5.53925	−	11.1497i	−0.222462	−	0.447784i
$621$	−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
$630$	−4.79499	−	0.313440i	−0.191037	−	0.0124877i
$631$	−6.08362	+	18.7235i	−0.242185	+	0.745370i	0.753901	+	0.656988i	$0.228170\pi$
$631$	−6.08362	+	18.7235i	−0.242185	+	0.745370i	−0.996087	+	0.0883820i	$0.971830\pi$
$632$	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
$635$	22.8182	−	5.79932i	0.905513	−	0.230139i
$636$	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
$640$	1.19353	+	1.89090i	0.0471783	+	0.0747443i
$641$	−2.61366	+	1.89893i	−0.103233	+	0.0750033i	−0.638204	−	0.769867i	$-0.720322\pi$
$641$	−2.61366	+	1.89893i	−0.103233	+	0.0750033i	0.534971	+	0.844870i	$0.320322\pi$
$642$	14.8464	−	4.82389i	0.585941	−	0.190384i
$643$	−9.42353	+	3.06189i	−0.371628	+	0.120749i	−0.488876	−	0.872354i	$-0.662593\pi$
$643$	−9.42353	+	3.06189i	−0.371628	+	0.120749i	0.117248	+	0.993103i	$0.462593\pi$
$644$	−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	$-0.226495\pi$
$647$	25.0857	+	8.15085i	0.986223	+	0.320443i	0.228876	+	0.973456i	$0.426495\pi$
$648$	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	$-0.156131\pi$
$653$	4.12699	+	5.68032i	0.161502	+	0.222288i	−0.720595	+	0.693356i	$0.756131\pi$
$654$	2.47440	+	1.79776i	0.0967566	+	0.0702978i
$655$	−37.2965	+	23.5414i	−1.45730	+	0.919840i
$656$	−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	0.978076	−	0.208246i	$-0.0667755\pi$
$659$	1.65301	+	5.08743i	0.0643920	+	0.198178i	−0.913684	+	0.406424i	$0.866775\pi$
$660$	1.10275	+	0.439729i	0.0429245	+	0.0171164i
$661$	−26.3882	+	19.1721i	−1.02638	+	0.745709i	−0.967581	−	0.252561i	$-0.918727\pi$
$661$	−26.3882	+	19.1721i	−1.02638	+	0.745709i	−0.0587993	+	0.998270i	$0.518727\pi$
$662$	−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
$665$	18.9296	+	7.54831i	0.734058	+	0.292711i
$666$	−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
$670$	5.90904	+	0.386263i	0.228286	+	0.0149227i
$671$	−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	$-0.476020\pi$
$673$	18.7374	−	6.08814i	0.722272	−	0.234680i	0.647008	+	0.762483i	$0.276020\pi$
$674$	−5.29932	−	16.3096i	−0.204122	−	0.628224i
$675$	−0.650901	+	4.95745i	−0.0250532	+	0.190812i
$676$	−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
$680$	5.12737	+	0.335167i	0.196626	+	0.0128531i
$681$	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
$685$	5.65282	−	1.43668i	0.215983	−	0.0548929i
$686$	−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
$690$	9.28874	+	3.70395i	0.353616	+	0.141007i
$691$	15.8580	+	48.8058i	0.603266	+	1.85666i	0.508300	+	0.861180i	$0.330274\pi$
$691$	15.8580	+	48.8058i	0.603266	+	1.85666i	0.0949658	+	0.995481i	$0.469726\pi$
$692$	−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
$695$	−4.62646	−	18.2034i	−0.175492	−	0.690495i
$696$	−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
$700$	9.69972	+	4.62237i	0.366615	+	0.174709i
$701$	5.95267	−	4.32487i	0.224829	−	0.163348i	−0.469669	−	0.882843i	$-0.655627\pi$
$701$	5.95267	−	4.32487i	0.224829	−	0.163348i	0.694498	+	0.719495i	$0.255627\pi$
$702$	−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
$705$	2.53726	−	6.36293i	0.0955589	−	0.239642i
$706$	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	0.592569	+	0.805520i	$0.298114\pi$
$709$	−9.59379	+	29.5266i	−0.360302	+	1.10890i	−0.952871	+	0.303376i	$0.901886\pi$
$710$	−6.80696	+	1.73001i	−0.255460	+	0.0649261i
$711$	−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
$715$	0.202738	−	3.10148i	0.00758199	−	0.115989i
$716$	−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	$0.436704\pi$
$720$	−1.89090	+	1.19353i	−0.0704696	+	0.0444802i
$721$	−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
$725$	17.8064	+	16.8858i	0.661311	+	0.627123i
$726$	−8.67114	−	6.29995i	−0.321816	−	0.233813i
$727$	15.5730	−	5.05996i	0.577569	−	0.187664i	−0.00564218	−	0.999984i	$-0.501796\pi$
$727$	15.5730	−	5.05996i	0.577569	−	0.187664i	0.583211	+	0.812321i	$0.301796\pi$
$728$	−3.30691	+	4.55157i	−0.122562	+	0.168693i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	−13.5481	+	33.9757i	−0.501437	+	1.25750i
$731$	−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	$-0.323746\pi$
$733$	12.2192	+	3.97025i	0.451325	+	0.146644i	−0.0745296	+	0.997219i	$0.523746\pi$
$734$	29.6784	−	21.5626i	1.09545	−	0.795892i
$735$	4.94740	+	1.97281i	0.182488	+	0.0727683i
$736$	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	$0.504440\pi$
$740$	3.19852	+	5.06739i	0.117580	+	0.186281i
$741$	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	−0.971651	−	0.236419i	$-0.924026\pi$
$751$	−1.27719	+	3.93080i	−0.0466055	+	0.143437i	0.925046	+	0.379856i	$0.124026\pi$
$752$	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
$755$	−17.9291	+	11.3168i	−0.652506	+	0.411860i
$756$	1.73855	−	1.26313i	0.0632303	−	0.0459395i
$757$	−5.68851	+	7.82957i	−0.206753	+	0.284570i	−0.899783	−	0.436338i	$-0.856275\pi$
$757$	−5.68851	+	7.82957i	−0.206753	+	0.284570i	0.693030	+	0.720908i	$0.256275\pi$
$758$	18.5507	−	6.02749i	0.673793	−	0.218928i
$759$	1.92091	+	1.39562i	0.0697247	+	0.0506580i
$760$	9.19102	−	2.33593i	0.333393	−	0.0847331i
$761$	−14.9136	−	45.8992i	−0.540616	−	1.66385i	−0.731191	−	0.682173i	$-0.761035\pi$
$761$	−14.9136	−	45.8992i	−0.540616	−	1.66385i	0.190575	−	0.981673i	$-0.438965\pi$
$762$	−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
$765$	−0.335167	+	5.12737i	−0.0121180	+	0.185380i
$766$	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	−0.926362	−	0.376635i	$-0.877081\pi$
$773$	−27.7557	−	38.2024i	−0.998302	−	1.37404i	−0.0719399	−	0.997409i	$-0.522919\pi$
$774$	1.23111			0.0442514
$775$	−27.7461	+	2.27062i	−0.996668	+	0.0815631i
$776$	−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
$785$	−0.399901	+	6.11767i	−0.0142731	+	0.218349i
$786$	6.09513	−	18.7589i	0.217406	−	0.669107i
$787$	11.2509	+	15.4855i	0.401051	+	0.552000i	0.961007	−	0.276522i	$-0.0891820\pi$
$787$	11.2509	+	15.4855i	0.401051	+	0.552000i	−0.559956	+	0.828522i	$0.689182\pi$
$788$	−7.99324	+	11.0017i	−0.284747	+	0.391921i
$789$	0.657075	+	2.02227i	0.0233925	+	0.0719947i
$790$	9.94260	−	2.52694i	0.353742	−	0.0899047i
$791$	−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
$795$	2.10028	−	1.32569i	0.0744893	−	0.0470174i
$796$	−20.4303	+	14.8435i	−0.724134	+	0.526114i
$797$	23.2719	−	7.56149i	0.824332	−	0.267842i	0.133676	−	0.991025i	$-0.457322\pi$
$797$	23.2719	−	7.56149i	0.824332	−	0.267842i	0.690656	+	0.723183i	$0.257322\pi$
$798$	−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	0.954442	−	0.298397i	$-0.0964518\pi$
$809$	27.4642	+	19.9539i	0.965589	+	0.701541i	0.0111467	+	0.999938i	$0.496452\pi$
$810$	−1.19353	−	1.89090i	−0.0419363	−	0.0664393i
$811$	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
$815$	32.1493	+	12.8198i	1.12614	+	0.449057i
$816$	−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
$820$	−0.312251	+	0.783059i	−0.0109043	+	0.0273456i
$821$	−32.4374	−	23.5672i	−1.13207	−	0.822499i	−0.146078	−	0.989273i	$-0.546665\pi$
$821$	−32.4374	−	23.5672i	−1.13207	−	0.822499i	−0.985995	+	0.166774i	$0.946665\pi$
$822$	−1.53317	+	2.11023i	−0.0534755	+	0.0736027i
$823$	50.2723	−	16.3345i	1.75238	−	0.569384i	0.756017	−	0.654552i	$-0.227143\pi$
$823$	50.2723	−	16.3345i	1.75238	−	0.569384i	0.996367	+	0.0851681i	$0.0271427\pi$
$824$	−6.41843	−	4.66327i	−0.223597	−	0.162453i
$825$	1.82666	−	1.92624i	0.0635961	−	0.0670631i
$826$	−2.48147	+	7.63718i	−0.0863414	+	0.265732i
$827$	20.1199	+	27.6927i	0.699639	+	0.962970i	0.999958	+	0.00913151i	$0.00290669\pi$
$827$	20.1199	+	27.6927i	0.699639	+	0.962970i	−0.300320	+	0.953839i	$0.597093\pi$
$828$	−4.25325	+	1.38197i	−0.147811	+	0.0480266i
$829$	0.169296	+	0.521040i	0.00587990	+	0.0180965i	0.953953	−	0.299955i	$-0.0969716\pi$
$829$	0.169296	+	0.521040i	0.00587990	+	0.0180965i	−0.948074	+	0.318051i	$0.896972\pi$
$830$	−7.18012	+	4.53207i	−0.249226	+	0.157310i
$831$	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
$835$	2.09219	−	32.0062i	0.0724032	−	1.10762i
$836$	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	−0.927848	−	0.372959i	$-0.878343\pi$
$839$	−24.9064	+	18.0955i	−0.859863	+	0.624727i	0.0679848	+	0.997686i	$0.478343\pi$
$840$	−4.65716	+	1.18363i	−0.160687	+	0.0408393i
$841$	−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
$845$	−5.09021	+	12.7652i	−0.175109	+	0.439136i
$846$	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
$850$	4.94279	−	10.3721i	0.169536	−	0.355759i
$851$	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	$-0.894038\pi$
$853$	−9.99629	+	13.7587i	−0.342266	+	0.471089i	0.602835	+	0.797866i	$0.294038\pi$
$854$	−1.32106	−	4.06580i	−0.0452057	−	0.139129i
$855$	2.33593	+	9.19102i	0.0798871	+	0.314326i
$856$	12.6291	−	9.17559i	0.431654	−	0.313615i
$857$	−22.3995	−	7.27805i	−0.765154	−	0.248614i	−0.0996647	−	0.995021i	$-0.531777\pi$
$857$	−22.3995	−	7.27805i	−0.765154	−	0.248614i	−0.665489	+	0.746407i	$0.731777\pi$
$858$	0.817013	+	1.12452i	0.0278924	+	0.0383905i
$859$	12.2872	+	37.8162i	0.419235	+	1.29027i	0.908408	+	0.418085i	$0.137299\pi$
$859$	12.2872	+	37.8162i	0.419235	+	1.29027i	−0.489173	+	0.872187i	$0.662701\pi$
$860$	−2.55705	−	1.01964i	−0.0871947	−	0.0347695i
$861$	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
$865$	−6.98240	+	1.77460i	−0.237409	+	0.0603382i
$866$	−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
$870$	−10.9511	−	0.715855i	−0.371277	−	0.0242697i
$871$	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
$875$	17.6344	−	16.3182i	0.596151	−	0.551655i
$876$	−5.05486	−	15.5573i	−0.170788	−	0.525631i
$877$	−28.0400	+	9.11073i	−0.946842	+	0.307648i	−0.741432	−	0.671028i	$-0.765853\pi$
$877$	−28.0400	+	9.11073i	−0.946842	+	0.307648i	−0.205410	+	0.978676i	$0.565853\pi$
$878$	−0.297593	−	0.409602i	−0.0100433	−	0.0138234i
$879$	8.62605	−	26.5483i	0.290950	−	0.895451i
$880$	1.18466	+	0.0774392i	0.0399349	+	0.00261047i
$881$	−29.5699	−	21.4838i	−0.996237	−	0.723808i	−0.0349587	−	0.999389i	$-0.511130\pi$
$881$	−29.5699	−	21.4838i	−0.996237	−	0.723808i	−0.961278	+	0.275580i	$0.911130\pi$
$882$	−2.26538	+	0.736068i	−0.0762795	+	0.0247847i
$883$	−6.37920	+	8.78022i	−0.214677	+	0.295478i	−0.902752	−	0.430162i	$-0.858456\pi$
$883$	−6.37920	+	8.78022i	−0.214677	+	0.295478i	0.688074	+	0.725640i	$0.258456\pi$
$884$	4.86708	+	3.53614i	0.163698	+	0.118933i
$885$	7.76140	+	3.09492i	0.260897	+	0.104034i
$886$	4.45052	+	3.23349i	0.149518	+	0.108631i
$887$	11.3620	+	15.6385i	0.381499	+	0.525088i	0.955981	−	0.293429i	$-0.0947965\pi$
$887$	11.3620	+	15.6385i	0.381499	+	0.525088i	−0.574482	+	0.818517i	$0.694797\pi$
$888$	−2.54873	−	0.828131i	−0.0855296	−	0.0277903i
$889$	−18.3052	+	13.2995i	−0.613937	+	0.446051i
$890$	−1.16549	−	0.464749i	−0.0390674	−	0.0155784i
$891$	−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
$895$	−2.75107	+	1.73647i	−0.0919582	+	0.0580437i
$896$	−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	$-0.914592\pi$
$907$	−47.8388	+	15.5438i	−1.58846	+	0.516122i	−0.624242	+	0.781231i	$0.714592\pi$
$908$	17.4834	−	5.68070i	0.580207	−	0.188521i
$909$	7.52466	−	5.46698i	0.249577	−	0.181328i
$910$	6.71485	+	10.6383i	0.222595	+	0.352656i
$911$	5.88505	−	4.27574i	0.194980	−	0.141662i	−0.486012	−	0.873952i	$-0.661549\pi$
$911$	5.88505	−	4.27574i	0.194980	−	0.141662i	0.680992	+	0.732291i	$0.261549\pi$
$912$	−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
$915$	−4.31126	+	1.09572i	−0.142526	+	0.0362234i
$916$	−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	−0.0227274	−	0.999742i	$-0.507235\pi$
$919$	17.6825	−	54.4212i	0.583293	−	1.79519i	0.606020	−	0.795449i	$-0.292765\pi$
$920$	9.97870	+	0.652290i	0.328988	+	0.0215054i
$921$	−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	$0.191951\pi$
$930$	8.89231	−	8.71360i	0.291590	−	0.285730i
$931$	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	$-0.206392\pi$
$937$	33.2707	+	10.8103i	1.08691	+	0.353158i	0.289857	+	0.957070i	$0.406392\pi$
$938$	−5.41243	+	1.75861i	−0.176722	+	0.0574205i
$939$	7.83395	+	24.1104i	0.255651	+	0.786813i
$940$	0.446829	−	6.83556i	0.0145739	−	0.222951i
$941$	−0.565680	+	1.74098i	−0.0184406	+	0.0567544i	−0.959853	−	0.280502i	$-0.909499\pi$
$941$	−0.565680	+	1.74098i	−0.0184406	+	0.0567544i	0.941413	+	0.337257i	$0.109499\pi$
$942$	−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
$945$	−1.18363	−	4.65716i	−0.0385036	−	0.151498i
$946$	−0.528798	−	0.384194i	−0.0171927	−	0.0124912i
$947$	−31.1528	+	10.1222i	−1.01233	+	0.328926i	−0.767783	−	0.640711i	$-0.778640\pi$
$947$	−31.1528	+	10.1222i	−1.01233	+	0.328926i	−0.244549	+	0.969637i	$0.578640\pi$
$948$	−2.69666	+	3.71163i	−0.0875833	+	0.120548i
$949$	−34.6466	+	25.1722i	−1.12467	+	0.817124i
$950$	2.76049	−	21.0247i	0.0895620	−	0.682130i
$951$	−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	$-0.743227\pi$
$953$	−25.5390	+	8.29811i	−0.827288	+	0.268802i	−0.135386	+	0.990793i	$0.543227\pi$
$954$	−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
$965$	12.8981	+	20.4343i	0.415203	+	0.657803i
$966$	−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
$970$	−3.62674	+	9.09509i	−0.116447	+	0.292026i
$971$	10.5792	−	7.68626i	0.339504	−	0.246664i	−0.404949	−	0.914339i	$-0.632711\pi$
$971$	10.5792	−	7.68626i	0.339504	−	0.246664i	0.744452	+	0.667676i	$0.232711\pi$
$972$	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
$975$	11.5017	−	6.25010i	0.368349	−	0.200164i
$976$	−1.60942	−	1.16931i	−0.0515162	−	0.0374287i
$977$	−14.7205	+	20.2611i	−0.470951	+	0.648209i	−0.976735	−	0.214452i	$-0.931204\pi$
$977$	−14.7205	+	20.2611i	−0.470951	+	0.648209i	0.505783	+	0.862661i	$0.331204\pi$
$978$	−14.7210	+	4.78313i	−0.470724	+	0.152948i
$979$	−0.241024	−	0.175114i	−0.00770317	−	0.00559668i
$980$	5.31489	+	0.347425i	0.169778	+	0.0110981i
$981$	−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	$-0.294598\pi$
$983$	48.8349	−	15.8674i	1.55759	−	0.506093i	0.956163	+	0.292833i	$0.0945982\pi$
$984$	−0.116502	−	0.358558i	−0.00371396	−	0.0114304i
$985$	16.2307	+	25.7141i	0.517152	+	0.819320i
$986$	−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
$990$	−0.0774392	+	1.18466i	−0.00246118	+	0.0376510i
$991$	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
$995$	13.9093	+	54.7281i	0.440956	+	1.73500i
$996$	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.109.4	yes	16
5.4	even	2	inner	930.2.z.b.109.2	✓	16
31.2	even	5	inner	930.2.z.b.529.2	yes	16
155.64	even	10	inner	930.2.z.b.529.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.b.109.2	✓	16	5.4	even	2	inner
930.2.z.b.109.4	yes	16	1.1	even	1	trivial
930.2.z.b.529.2	yes	16	31.2	even	5	inner
930.2.z.b.529.4	yes	16	155.64	even	10	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} +(-0.145857 + 2.23131i) 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} +(-2.16717 + 0.550794i) 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} +(-1.89090 + 1.19353i) 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} +(-2.56485 - 4.06346i) q^{35} +1.00000 q^{36} -2.67989i q^{37} +(-4.03345 - 1.31055i) q^{38} +(-0.809017 - 2.48990i) q^{39} +(-2.07703 - 0.828229i) 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} +(0.828229 - 2.07703i) 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} +(-3.44051 + 3.62807i) 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} +(-1.00393 + 0.633677i) q^{55} +2.14896 q^{56} -4.24102i q^{57} +(4.66773 + 1.51664i) q^{58} +(-3.02312 - 2.19643i) q^{59} +(0.145857 - 2.23131i) q^{60} +1.98935 q^{61} +(-4.81411 + 2.79720i) q^{62} +2.14896i q^{63} +(0.809017 - 0.587785i) q^{64} +(-5.67373 + 1.44200i) q^{65} +(0.164066 - 0.504942i) q^{66} -2.64824i q^{67} -2.29792i q^{68} +(1.38197 - 4.25325i) q^{69} +(1.77983 - 4.46345i) 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} +(-4.51368 - 2.15098i) 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} +(-0.550794 - 2.16717i) 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} +(-4.77284 - 1.90321i) q^{85} +(-0.380434 + 1.17086i) q^{86} +4.90794i q^{87} -0.530927i q^{88} +(-0.173401 + 0.533672i) q^{89} +(2.16717 - 0.550794i) q^{90} +(4.55157 - 3.30691i) q^{91} -4.47214i q^{92} +(-4.14794 - 3.71411i) q^{93} -3.06348 q^{94} +(-9.46302 - 0.618581i) 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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