LMFDB - Embedded newform 845.2.t.g.427.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(188,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("845.188");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.t (of order $12$, degree $4$, not 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			427.2
Root			$1.58474i$ of defining polynomial
Character	$\chi$	$=$	845.427
Dual form			845.2.t.g.188.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37242 + 0.792369i) q^{2} +(0.190588 + 0.0510678i) q^{3} +(0.255697 - 0.442881i) q^{4} +(2.23506 - 0.0672627i) q^{5} +(-0.302032 + 0.0809291i) q^{6} +(-0.274164 + 0.474866i) q^{7} -2.35905i q^{8} +(-2.56436 - 1.48053i) q^{9} +(-3.01415 + 1.86330i) q^{10} +(-0.147928 - 0.0396372i) q^{11} +(0.0713497 - 0.0713497i) q^{12} -0.868956i q^{14} +(0.429409 + 0.101320i) q^{15} +(2.38063 + 4.12338i) q^{16} +(0.813499 + 3.03602i) q^{17} +4.69252 q^{18} +(1.18079 + 4.40678i) q^{19} +(0.541709 - 1.00706i) q^{20} +(-0.0765027 + 0.0765027i) q^{21} +(0.234427 - 0.0628146i) q^{22} +(-0.916011 + 3.41860i) q^{23} +(0.120472 - 0.449606i) q^{24} +(4.99095 - 0.300672i) q^{25} +(-0.831688 - 0.831688i) q^{27} +(0.140206 + 0.242844i) q^{28} +(2.02878 - 1.17132i) q^{29} +(-0.669614 + 0.201197i) q^{30} +(6.61000 + 6.61000i) q^{31} +(-2.44848 - 1.41363i) q^{32} +(-0.0261691 - 0.0151087i) q^{33} +(-3.52211 - 3.52211i) q^{34} +(-0.580831 + 1.07979i) q^{35} +(-1.31140 + 0.757137i) q^{36} +(-3.40317 - 5.89447i) q^{37} +(-5.11234 - 5.11234i) q^{38} +(-0.158676 - 5.27261i) q^{40} +(-0.926064 + 3.45612i) q^{41} +(0.0443757 - 0.165612i) q^{42} +(6.86784 - 1.84023i) q^{43} +(-0.0553794 + 0.0553794i) q^{44} +(-5.83107 - 3.13659i) q^{45} +(-1.45164 - 5.41759i) q^{46} +9.13956 q^{47} +(0.243147 + 0.907439i) q^{48} +(3.34967 + 5.80180i) q^{49} +(-6.61146 + 4.36732i) q^{50} +0.620172i q^{51} +(-3.70952 + 3.70952i) q^{53} +(1.80043 + 0.482424i) q^{54} +(-0.333294 - 0.0786414i) q^{55} +(1.12023 + 0.646766i) q^{56} +0.900179i q^{57} +(-1.85623 + 3.21508i) q^{58} +(3.67728 - 0.985325i) q^{59} +(0.154672 - 0.164270i) q^{60} +(-3.92486 + 6.79805i) q^{61} +(-14.3093 - 3.83416i) q^{62} +(1.40611 - 0.811818i) q^{63} -5.04207 q^{64} +0.0478868 q^{66} +(-4.23514 + 2.44516i) q^{67} +(1.55261 + 0.416019i) q^{68} +(-0.349161 + 0.604765i) q^{69} +(-0.0584483 - 1.94217i) q^{70} +(15.1045 - 4.04725i) q^{71} +(-3.49265 + 6.04945i) q^{72} +3.91807i q^{73} +(9.34119 + 5.39314i) q^{74} +(0.966569 + 0.197573i) q^{75} +(2.25360 + 0.603851i) q^{76} +(0.0593789 - 0.0593789i) q^{77} +11.1394i q^{79} +(5.59820 + 9.05585i) q^{80} +(4.32557 + 7.49210i) q^{81} +(-1.46757 - 5.47704i) q^{82} -13.4251 q^{83} +(0.0143200 + 0.0534431i) q^{84} +(2.02243 + 6.73096i) q^{85} +(-7.96744 + 7.96744i) q^{86} +(0.446477 - 0.119633i) q^{87} +(-0.0935062 + 0.348970i) q^{88} +(-2.35372 + 8.78419i) q^{89} +(10.4880 - 0.315631i) q^{90} +(1.27981 + 1.27981i) q^{92} +(0.922226 + 1.59734i) q^{93} +(-12.5433 + 7.24190i) q^{94} +(2.93555 + 9.76998i) q^{95} +(-0.394459 - 0.394459i) q^{96} +(-6.55668 - 3.78550i) q^{97} +(-9.19433 - 5.30835i) q^{98} +(0.320657 + 0.320657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 8 q^{6} + 2 q^{7} + 12 q^{9} - 2 q^{10} + 16 q^{11} - 24 q^{12} + 20 q^{15} - 2 q^{16} + 4 q^{17} + 20 q^{19} - 4 q^{21} + 16 q^{22} - 10 q^{23} - 32 q^{24} + 18 q^{25}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 8 * q^6 + 2 * q^7 + 12 * q^9 - 2 * q^10 + 16 * q^11 - 24 * q^12 + 20 * q^15 - 2 * q^16 + 4 * q^17 + 20 * q^19 - 4 * q^21 + 16 * q^22 - 10 * q^23 - 32 * q^24 + 18 * q^25 + 4 * q^27 - 18 * q^28 - 26 * q^30 - 48 * q^32 - 18 * q^33 - 2 * q^34 + 40 * q^35 + 36 * q^36 + 4 * q^37 - 8 * q^38 - 16 * q^40 - 10 * q^41 + 40 * q^42 + 10 * q^43 + 36 * q^44 - 4 * q^46 + 40 * q^47 - 56 * q^48 + 18 * q^49 - 36 * q^50 - 10 * q^53 + 48 * q^54 - 10 * q^55 + 16 * q^59 - 28 * q^60 - 16 * q^61 - 44 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 + 22 * q^68 - 16 * q^69 + 12 * q^70 + 16 * q^71 - 4 * q^72 + 18 * q^74 - 38 * q^75 + 64 * q^76 - 28 * q^77 + 2 * q^80 - 14 * q^81 + 56 * q^82 - 48 * q^83 + 40 * q^84 + 26 * q^85 - 60 * q^86 - 34 * q^87 + 82 * q^88 + 6 * q^89 + 46 * q^90 - 8 * q^92 - 32 * q^93 - 48 * q^94 - 26 * q^95 - 56 * q^96 - 66 * q^97 + 30 * q^98 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.37242	+	0.792369i	−0.970450	+	0.560290i	−0.899373	−	0.437181i	$-0.855977\pi$
$2$	−1.37242	+	0.792369i	−0.970450	+	0.560290i	−0.0710765	+	0.997471i	$0.522643\pi$
$3$	0.190588	+	0.0510678i	0.110036	+	0.0294840i	0.313417	−	0.949616i	$-0.398526\pi$
$3$	0.190588	+	0.0510678i	0.110036	+	0.0294840i	−0.203381	+	0.979100i	$0.565193\pi$
$4$	0.255697	−	0.442881i	0.127849	−	0.221440i
$5$	2.23506	−	0.0672627i	0.999547	−	0.0300808i
$5$	2.23506	−	0.0672627i	0.999547	−	0.0300808i
$6$	−0.302032	+	0.0809291i	−0.123304	+	0.0330392i
$7$	−0.274164	+	0.474866i	−0.103624	+	0.179482i	−0.913175	−	0.407567i	$-0.866377\pi$
$7$	−0.274164	+	0.474866i	−0.103624	+	0.179482i	0.809551	+	0.587049i	$0.199711\pi$
$8$		−	2.35905i		−	0.834050i
$9$	−2.56436	−	1.48053i	−0.854787	−	0.493511i
$10$	−3.01415	+	1.86330i	−0.953157	+	0.589228i
$11$	−0.147928	−	0.0396372i	−0.0446020	−	0.0119511i	0.236449	−	0.971644i	$-0.424016\pi$
$11$	−0.147928	−	0.0396372i	−0.0446020	−	0.0119511i	−0.281051	+	0.959693i	$0.590683\pi$
$12$	0.0713497	−	0.0713497i	0.0205969	−	0.0205969i
$13$		0			0
$13$		0			0
$14$		−	0.868956i		−	0.232238i
$15$	0.429409	+	0.101320i	0.110873	+	0.0261607i
$16$	2.38063	+	4.12338i	0.595158	+	1.03084i
$17$	0.813499	+	3.03602i	0.197303	+	0.736343i	0.991659	+	0.128891i	$0.0411417\pi$
$17$	0.813499	+	3.03602i	0.197303	+	0.736343i	−0.794356	+	0.607452i	$0.792192\pi$
$18$	4.69252			1.10604
$19$	1.18079	+	4.40678i	0.270893	+	1.01098i	0.958544	+	0.284944i	$0.0919750\pi$
$19$	1.18079	+	4.40678i	0.270893	+	1.01098i	−0.687652	+	0.726041i	$0.741358\pi$
$20$	0.541709	−	1.00706i	0.121130	−	0.225186i
$21$	−0.0765027	+	0.0765027i	−0.0166942	+	0.0166942i
$22$	0.234427	−	0.0628146i	0.0499801	−	0.0133921i
$23$	−0.916011	+	3.41860i	−0.191002	+	0.712828i	0.802264	+	0.596969i	$0.203629\pi$
$23$	−0.916011	+	3.41860i	−0.191002	+	0.712828i	−0.993266	+	0.115858i	$0.963038\pi$
$24$	0.120472	−	0.449606i	0.0245912	−	0.0917754i
$25$	4.99095	−	0.300672i	0.998190	−	0.0601343i
$26$		0			0
$27$	−0.831688	−	0.831688i	−0.160058	−	0.160058i
$28$	0.140206	+	0.242844i	0.0264964	+	0.0458932i
$29$	2.02878	−	1.17132i	0.376735	−	0.217508i	−0.299662	−	0.954045i	$-0.596874\pi$
$29$	2.02878	−	1.17132i	0.376735	−	0.217508i	0.676397	+	0.736538i	$0.263541\pi$
$30$	−0.669614	+	0.201197i	−0.122254	+	0.0367333i
$31$	6.61000	+	6.61000i	1.18719	+	1.18719i	0.977841	+	0.209350i	$0.0671347\pi$
$31$	6.61000	+	6.61000i	1.18719	+	1.18719i	0.209350	+	0.977841i	$0.432865\pi$
$32$	−2.44848	−	1.41363i	−0.432834	−	0.249897i
$33$	−0.0261691	−	0.0151087i	−0.00455546	−	0.00263009i
$34$	−3.52211	−	3.52211i	−0.604038	−	0.604038i
$35$	−0.580831	+	1.07979i	−0.0981784	+	0.182518i
$36$	−1.31140	+	0.757137i	−0.218567	+	0.126190i
$37$	−3.40317	−	5.89447i	−0.559478	−	0.969045i	−0.997540	−	0.0700997i	$-0.977668\pi$
$37$	−3.40317	−	5.89447i	−0.559478	−	0.969045i	0.438062	−	0.898945i	$-0.355665\pi$
$38$	−5.11234	−	5.11234i	−0.829332	−	0.829332i
$39$		0			0
$40$	−0.158676	−	5.27261i	−0.0250889	−	0.833672i
$41$	−0.926064	+	3.45612i	−0.144627	+	0.539755i	0.855145	+	0.518389i	$0.173468\pi$
$41$	−0.926064	+	3.45612i	−0.144627	+	0.539755i	−0.999772	+	0.0213659i	$0.993199\pi$
$42$	0.0443757	−	0.165612i	0.00684732	−	0.0255545i
$43$	6.86784	−	1.84023i	1.04734	−	0.280633i	0.306185	−	0.951972i	$-0.400947\pi$
$43$	6.86784	−	1.84023i	1.04734	−	0.280633i	0.741150	+	0.671339i	$0.234281\pi$
$44$	−0.0553794	+	0.0553794i	−0.00834876	+	0.00834876i
$45$	−5.83107	−	3.13659i	−0.869245	−	0.467575i
$46$	−1.45164	−	5.41759i	−0.214032	−	0.798780i
$47$	9.13956			1.33314			0.666571	−	0.745442i	$-0.267761\pi$
$47$	9.13956			1.33314			0.666571	+	0.745442i	$0.267761\pi$
$48$	0.243147	+	0.907439i	0.0350953	+	0.130978i
$49$	3.34967	+	5.80180i	0.478524	+	0.828828i
$50$	−6.61146	+	4.36732i	−0.935001	+	0.617633i
$51$			0.620172i			0.0868415i
$52$		0			0
$53$	−3.70952	+	3.70952i	−0.509541	+	0.509541i	−0.914386	−	0.404844i	$-0.867326\pi$
$53$	−3.70952	+	3.70952i	−0.509541	+	0.509541i	0.404844	+	0.914386i	$0.367326\pi$
$54$	1.80043	+	0.482424i	0.245008	+	0.0656496i
$55$	−0.333294	−	0.0786414i	−0.0449413	−	0.0106040i
$56$	1.12023	+	0.646766i	0.149697	+	0.0864278i
$57$			0.900179i			0.119232i
$58$	−1.85623	+	3.21508i	−0.243735	+	0.422161i
$59$	3.67728	−	0.985325i	0.478742	−	0.128278i	−0.0113750	−	0.999935i	$-0.503621\pi$
$59$	3.67728	−	0.985325i	0.478742	−	0.128278i	0.490117	+	0.871657i	$0.336954\pi$
$60$	0.154672	−	0.164270i	0.0199680	−	0.0212071i
$61$	−3.92486	+	6.79805i	−0.502526	+	0.870401i	0.497470	+	0.867481i	$0.334263\pi$
$61$	−3.92486	+	6.79805i	−0.502526	+	0.870401i	−0.999996	+	0.00291945i	$0.999071\pi$
$62$	−14.3093	−	3.83416i	−1.81728	−	0.486939i
$63$	1.40611	−	0.811818i	0.177153	−	0.102279i
$64$	−5.04207			−0.630258
$65$		0			0
$66$	0.0478868			0.00589446
$67$	−4.23514	+	2.44516i	−0.517405	+	0.298724i	−0.735872	−	0.677120i	$-0.763228\pi$
$67$	−4.23514	+	2.44516i	−0.517405	+	0.298724i	0.218467	+	0.975844i	$0.429894\pi$
$68$	1.55261	+	0.416019i	0.188281	+	0.0504497i
$69$	−0.349161	+	0.604765i	−0.0420341	+	0.0728051i
$70$	−0.0584483	−	1.94217i	−0.00698591	−	0.232133i
$71$	15.1045	−	4.04725i	1.79258	−	0.480320i	0.799799	−	0.600267i	$-0.204939\pi$
$71$	15.1045	−	4.04725i	1.79258	−	0.480320i	0.992780	+	0.119947i	$0.0382725\pi$
$72$	−3.49265	+	6.04945i	−0.411613	+	0.712935i
$73$			3.91807i			0.458575i	0.973359	+	0.229288i	$0.0736396\pi$
$73$			3.91807i			0.458575i	−0.973359	+	0.229288i	$0.926360\pi$
$74$	9.34119	+	5.39314i	1.08589	+	0.626939i
$75$	0.966569	+	0.197573i	0.111610	+	0.0228137i
$76$	2.25360	+	0.603851i	0.258506	+	0.0692665i
$77$	0.0593789	−	0.0593789i	0.00676686	−	0.00676686i
$78$		0			0
$79$			11.1394i			1.25328i	0.779309	+	0.626640i	$0.215570\pi$
$79$			11.1394i			1.25328i	−0.779309	+	0.626640i	$0.784430\pi$
$80$	5.59820	+	9.05585i	0.625897	+	1.01247i
$81$	4.32557	+	7.49210i	0.480618	+	0.832455i
$82$	−1.46757	−	5.47704i	−0.162066	−	0.604838i
$83$	−13.4251			−1.47360			−0.736798	−	0.676113i	$-0.763663\pi$
$83$	−13.4251			−1.47360			−0.736798	+	0.676113i	$0.763663\pi$
$84$	0.0143200	+	0.0534431i	0.00156244	+	0.00583112i
$85$	2.02243	+	6.73096i	0.219363	+	0.730075i
$86$	−7.96744	+	7.96744i	−0.859151	+	0.859151i
$87$	0.446477	−	0.119633i	0.0478673	−	0.0128260i
$88$	−0.0935062	+	0.348970i	−0.00996779	+	0.0372003i
$89$	−2.35372	+	8.78419i	−0.249493	+	0.931122i	0.721578	+	0.692333i	$0.243417\pi$
$89$	−2.35372	+	8.78419i	−0.249493	+	0.931122i	−0.971071	+	0.238789i	$0.923250\pi$
$90$	10.4880	−	0.315631i	1.10554	−	0.0332705i
$91$		0			0
$92$	1.27981	+	1.27981i	0.133430	+	0.133430i
$93$	0.922226	+	1.59734i	0.0956304	+	0.165637i
$94$	−12.5433	+	7.24190i	−1.29375	+	0.746945i
$95$	2.93555	+	9.76998i	0.301181	+	1.00238i
$96$	−0.394459	−	0.394459i	−0.0402593	−	0.0402593i
$97$	−6.55668	−	3.78550i	−0.665730	−	0.384360i	0.128727	−	0.991680i	$-0.458911\pi$
$97$	−6.55668	−	3.78550i	−0.665730	−	0.384360i	−0.794457	+	0.607321i	$0.792244\pi$
$98$	−9.19433	−	5.30835i	−0.928767	−	0.536224i
$99$	0.320657	+	0.320657i	0.0322272	+	0.0322272i
$100$	1.14301	−	2.28728i	0.114301	−	0.228728i
$101$	11.7218	−	6.76758i	1.16636	−	0.673400i	0.213542	−	0.976934i	$-0.431500\pi$
$101$	11.7218	−	6.76758i	1.16636	−	0.673400i	0.952821	+	0.303534i	$0.0981667\pi$
$102$	−0.491405	−	0.851139i	−0.0486564	−	0.0842753i
$103$	−10.3566	−	10.3566i	−1.02046	−	1.02046i	−0.999786	−	0.0206759i	$-0.993418\pi$
$103$	−10.3566	−	10.3566i	−1.02046	−	1.02046i	−0.0206759	−	0.999786i	$-0.506582\pi$
$104$		0			0
$105$	−0.165842	+	0.176134i	−0.0161845	+	0.0171889i
$106$	2.15172	−	8.03034i	0.208994	−	0.779975i
$107$	4.16078	−	15.5283i	0.402238	−	1.50117i	−0.406855	−	0.913493i	$-0.633375\pi$
$107$	4.16078	−	15.5283i	0.402238	−	1.50117i	0.809093	−	0.587680i	$-0.199959\pi$
$108$	−0.580999	+	0.155678i	−0.0559066	+	0.0149801i
$109$	−8.20821	+	8.20821i	−0.786203	+	0.786203i	−0.980870	−	0.194666i	$-0.937638\pi$
$109$	−8.20821	+	8.20821i	−0.786203	+	0.786203i	0.194666	+	0.980870i	$0.437638\pi$
$110$	0.519733	−	0.156162i	0.0495546	−	0.0148895i
$111$	−0.347585	−	1.29721i	−0.0329913	−	0.123125i
$112$	−2.61073			−0.246691
$113$	1.17964	+	4.40249i	0.110972	+	0.414151i	0.998954	−	0.0457259i	$-0.0145601\pi$
$113$	1.17964	+	4.40249i	0.110972	+	0.414151i	−0.887982	+	0.459877i	$0.847893\pi$
$114$	−0.713274	−	1.23543i	−0.0668042	−	0.115708i
$115$	−1.81739	+	7.70238i	−0.169473	+	0.718251i
$116$		−	1.19801i		−	0.111232i
$117$		0			0
$118$	−4.26605	+	4.26605i	−0.392722	+	0.392722i
$119$	−1.66473	−	0.446064i	−0.152606	−	0.0408907i
$120$	0.239019	−	1.01300i	0.0218193	−	0.0924736i
$121$	−9.50597	−	5.48827i	−0.864179	−	0.498934i
$122$		−	12.4397i		−	1.12624i
$123$	−0.352993	+	0.611402i	−0.0318283	+	0.0551283i
$124$	4.61760	−	1.23728i	0.414673	−	0.111111i
$125$	11.1348	−	1.00772i	0.995930	−	0.0901335i
$126$	−1.28652	+	2.22832i	−0.114612	+	0.198514i
$127$	2.34945	+	0.629533i	0.208480	+	0.0558620i	0.361547	−	0.932354i	$-0.382249\pi$
$127$	2.34945	+	0.629533i	0.208480	+	0.0558620i	−0.153068	+	0.988216i	$0.548915\pi$
$128$	11.8168	−	6.82244i	1.04447	−	0.603024i
$129$	1.40290			0.123519
$130$		0			0
$131$	6.60705			0.577260			0.288630	−	0.957441i	$-0.406800\pi$
$131$	6.60705			0.577260			0.288630	+	0.957441i	$0.406800\pi$
$132$	−0.0133827	+	0.00772653i	−0.00116482	+	0.000672508i
$133$	−2.41636	−	0.647462i	−0.209525	−	0.0561421i
$134$	3.87494	−	6.71159i	0.334744	−	0.579793i
$135$	−1.91481	−	1.80293i	−0.164801	−	0.155171i
$136$	7.16212	−	1.91909i	0.614147	−	0.164560i
$137$	2.02775	−	3.51216i	0.173242	−	0.300064i	−0.766309	−	0.642472i	$-0.777909\pi$
$137$	2.02775	−	3.51216i	0.173242	−	0.300064i	0.939552	+	0.342408i	$0.111242\pi$
$138$		−	1.10666i		−	0.0942050i
$139$	−11.1052	−	6.41160i	−0.941932	−	0.543825i	−0.0513668	−	0.998680i	$-0.516358\pi$
$139$	−11.1052	−	6.41160i	−0.941932	−	0.543825i	−0.890566	+	0.454855i	$0.849691\pi$
$140$	0.329703	+	0.533339i	0.0278650	+	0.0450754i
$141$	1.74189	+	0.466737i	0.146693	+	0.0393064i
$142$	−17.5229	+	17.5229i	−1.47049	+	1.47049i
$143$		0			0
$144$		−	14.0984i		−	1.17487i
$145$	4.45565	−	2.75442i	0.370021	−	0.228742i
$146$	−3.10455	−	5.37725i	−0.256935	−	0.445024i
$147$	0.342121	+	1.27681i	0.0282176	+	0.105310i
$148$	−3.48073			−0.286114
$149$	1.10123	+	4.10983i	0.0902159	+	0.336690i	0.996251	−	0.0865128i	$-0.0275723\pi$
$149$	1.10123	+	4.10983i	0.0902159	+	0.336690i	−0.906035	+	0.423203i	$0.860906\pi$
$150$	−1.48309	+	0.494726i	−0.121094	+	0.0403942i
$151$	−4.89430	+	4.89430i	−0.398293	+	0.398293i	−0.877630	−	0.479338i	$-0.840877\pi$
$151$	−4.89430	+	4.89430i	−0.398293	+	0.398293i	0.479338	+	0.877630i	$0.340877\pi$
$152$	10.3958	−	2.78555i	0.843212	−	0.225938i
$153$	2.40883	−	8.98987i	0.194742	−	0.726788i
$154$	−0.0344430	+	0.128543i	−0.00277550	+	0.0103583i
$155$	15.2183	+	14.3291i	1.22236	+	1.15094i
$156$		0			0
$157$	2.29887	+	2.29887i	0.183470	+	0.183470i	0.792866	−	0.609396i	$-0.208588\pi$
$157$	2.29887	+	2.29887i	0.183470	+	0.183470i	−0.609396	+	0.792866i	$0.708588\pi$
$158$	−8.82651	−	15.2880i	−0.702199	−	1.21625i
$159$	−0.896426	+	0.517552i	−0.0710912	+	0.0410445i
$160$	−5.56757	−	2.99485i	−0.440155	−	0.236764i
$161$	−1.37224	−	1.37224i	−0.108148	−	0.108148i
$162$	−11.8730	−	6.85489i	−0.932832	−	0.538571i
$163$	9.41236	+	5.43423i	0.737233	+	0.425642i	0.821062	−	0.570839i	$-0.193382\pi$
$163$	9.41236	+	5.43423i	0.737233	+	0.425642i	−0.0838295	+	0.996480i	$0.526715\pi$
$164$	1.29386	+	1.29386i	0.101033	+	0.101033i
$165$	−0.0595057	−	0.0320087i	−0.00463251	−	0.00249187i
$166$	18.4249	−	10.6376i	1.43005	−	0.825640i
$167$	−8.17941	−	14.1672i	−0.632942	−	1.09629i	−0.986947	−	0.161044i	$-0.948514\pi$
$167$	−8.17941	−	14.1672i	−0.632942	−	1.09629i	0.354005	−	0.935243i	$-0.384819\pi$
$168$	0.180474	+	0.180474i	0.0139238	+	0.0139238i
$169$		0			0
$170$	−8.10903	−	7.63522i	−0.621934	−	0.585594i
$171$	3.49641	−	13.0488i	0.267377	−	0.997865i
$172$	0.941085	−	3.51218i	0.0717570	−	0.267801i
$173$	−6.60091	+	1.76871i	−0.501858	+	0.134472i	−0.500862	−	0.865527i	$-0.666984\pi$
$173$	−6.60091	+	1.76871i	−0.501858	+	0.134472i	−0.000995657		1.00000i	$0.500317\pi$
$174$	−0.517961	+	0.517961i	−0.0392666	+	0.0392666i
$175$	−1.22556	+	2.45247i	−0.0926436	+	0.185389i
$176$	−0.188723	−	0.704325i	−0.0142256	−	0.0530905i
$177$	0.751164			0.0564609
$178$	−3.73002	−	13.9206i	−0.279577	−	1.04340i
$179$	2.83696	+	4.91376i	0.212044	+	0.367272i	0.952354	−	0.304994i	$-0.0986545\pi$
$179$	2.83696	+	4.91376i	0.212044	+	0.367272i	−0.740310	+	0.672266i	$0.765321\pi$
$180$	−2.88013	+	1.78045i	−0.214672	+	0.132707i
$181$			3.59115i			0.266928i	0.991054	+	0.133464i	$0.0426101\pi$
$181$			3.59115i			0.266928i	−0.991054	+	0.133464i	$0.957390\pi$
$182$		0			0
$183$	−1.09519	+	1.09519i	−0.0809588	+	0.0809588i
$184$	8.06465	+	2.16092i	0.594534	+	0.159305i
$185$	−8.00276	−	12.9456i	−0.588375	−	0.951777i
$186$	−2.53137	−	1.46149i	−0.185609	−	0.107161i
$187$		−	0.481358i		−	0.0352004i
$188$	2.33696	−	4.04773i	0.170440	−	0.295211i
$189$	0.622959	−	0.166921i	0.0453136	−	0.0121417i
$190$	−11.7702	−	11.0825i	−0.853903	−	0.804009i
$191$	11.7411	−	20.3361i	0.849553	−	1.47147i	−0.0320553	−	0.999486i	$-0.510205\pi$
$191$	11.7411	−	20.3361i	0.849553	−	1.47147i	0.881608	−	0.471982i	$-0.156461\pi$
$192$	−0.960956	−	0.257487i	−0.0693510	−	0.0185825i
$193$	13.7160	−	7.91891i	0.987296	−	0.570016i	0.0828311	−	0.996564i	$-0.473604\pi$
$193$	13.7160	−	7.91891i	0.987296	−	0.570016i	0.904465	+	0.426548i	$0.140270\pi$
$194$	11.9981			0.861411
$195$		0			0
$196$	3.42601			0.244715
$197$	−4.94741	+	2.85639i	−0.352488	+	0.203509i	−0.665781	−	0.746148i	$-0.731901\pi$
$197$	−4.94741	+	2.85639i	−0.352488	+	0.203509i	0.313292	+	0.949657i	$0.398568\pi$
$198$	−0.694156	−	0.185998i	−0.0493315	−	0.0132183i
$199$	−4.65156	+	8.05674i	−0.329740	+	0.571127i	−0.982460	−	0.186472i	$-0.940295\pi$
$199$	−4.65156	+	8.05674i	−0.329740	+	0.571127i	0.652720	+	0.757599i	$0.273628\pi$
$200$	−0.709299	−	11.7739i	−0.0501550	−	0.832541i
$201$	−0.932035	+	0.249738i	−0.0657407	+	0.0176152i
$202$	−10.7248	+	18.5760i	−0.754597	+	1.30700i
$203$			1.28453i			0.0901563i
$204$	0.274662	+	0.158576i	0.0192302	+	0.0111026i
$205$	−1.83734	+	7.78691i	−0.128325	+	0.543861i
$206$	22.4198	+	6.00737i	1.56206	+	0.418553i
$207$	7.41034	−	7.41034i	0.515054	−	0.515054i
$208$		0			0
$209$		−	0.698690i		−	0.0483294i
$210$	0.0880427	−	0.373138i	0.00607552	−	0.0257490i
$211$	2.73779	+	4.74199i	0.188477	+	0.326452i	0.944743	−	0.327813i	$-0.106311\pi$
$211$	2.73779	+	4.74199i	0.188477	+	0.326452i	−0.756265	+	0.654265i	$0.772978\pi$
$212$	0.694360	+	2.59139i	0.0476889	+	0.177977i
$213$	3.08543			0.211410
$214$	6.59375	+	24.6082i	0.450739	+	1.68218i
$215$	15.2262	−	4.57497i	1.03842	−	0.312010i
$216$	−1.96199	+	1.96199i	−0.133497	+	0.133497i
$217$	−4.95108	+	1.32664i	−0.336102	+	0.0900581i
$218$	4.76121	−	17.7691i	0.322470	−	1.20347i
$219$	−0.200087	+	0.746736i	−0.0135206	+	0.0504597i
$220$	−0.120051	+	0.127501i	−0.00809385	+	0.00859612i
$221$		0			0
$222$	1.50490	+	1.50490i	0.101002	+	0.101002i
$223$	−9.28408	−	16.0805i	−0.621708	−	1.07683i	−0.989168	−	0.146790i	$-0.953106\pi$
$223$	−9.28408	−	16.0805i	−0.621708	−	1.07683i	0.367460	−	0.930039i	$-0.380227\pi$
$224$	1.34257	−	0.775132i	0.0897041	−	0.0517907i
$225$	−13.2438	−	6.61824i	−0.882917	−	0.441216i
$226$	−5.10737	−	5.10737i	−0.339737	−	0.339737i
$227$	5.53101	+	3.19333i	0.367106	+	0.211949i	0.672193	−	0.740376i	$-0.265352\pi$
$227$	5.53101	+	3.19333i	0.367106	+	0.211949i	−0.305087	+	0.952324i	$0.598686\pi$
$228$	0.398672	+	0.230173i	0.0264027	+	0.0152436i
$229$	−11.1149	−	11.1149i	−0.734491	−	0.734491i	0.237015	−	0.971506i	$-0.423831\pi$
$229$	−11.1149	−	11.1149i	−0.734491	−	0.734491i	−0.971506	+	0.237015i	$0.923831\pi$
$230$	−3.60889	−	12.0110i	−0.237963	−	0.791980i
$231$	0.0143493	−	0.00828454i	0.000944111	−	0.000545083i
$232$	−2.76319	−	4.78599i	−0.181412	−	0.314215i
$233$	5.85956	+	5.85956i	0.383873	+	0.383873i	0.872495	−	0.488623i	$-0.162500\pi$
$233$	5.85956	+	5.85956i	0.383873	+	0.383873i	−0.488623	+	0.872495i	$0.662500\pi$
$234$		0			0
$235$	20.4274	−	0.614751i	1.33254	−	0.0401019i
$236$	0.503890	−	1.88054i	0.0328004	−	0.122413i
$237$	−0.568865	+	2.12303i	−0.0369517	+	0.137906i
$238$	2.63817	−	0.706895i	0.171007	−	0.0458212i
$239$	13.8081	−	13.8081i	0.893170	−	0.893170i	−0.101650	−	0.994820i	$-0.532412\pi$
$239$	13.8081	−	13.8081i	0.893170	−	0.893170i	0.994820	+	0.101650i	$0.0324123\pi$
$240$	0.604485	+	2.01182i	0.0390193	+	0.129863i
$241$	−4.43437	−	16.5493i	−0.285643	−	1.06603i	−0.948368	−	0.317172i	$-0.897267\pi$
$241$	−4.43437	−	16.5493i	−0.285643	−	1.06603i	0.662725	−	0.748863i	$-0.269400\pi$
$242$	17.3950			1.11819
$243$	1.35505	+	5.05712i	0.0869266	+	0.324414i
$244$	2.00715	+	3.47649i	0.128495	+	0.222559i
$245$	7.87694	+	12.7420i	0.503239	+	0.814058i
$246$		−	1.11880i		−	0.0713323i
$247$		0			0
$248$	15.5933	−	15.5933i	0.990176	−	0.990176i
$249$	−2.55866	−	0.685590i	−0.162148	−	0.0434475i
$250$	−14.4832	+	10.2059i	−0.915999	+	0.645479i
$251$	8.61959	+	4.97652i	0.544063	+	0.314115i	0.746724	−	0.665134i	$-0.231626\pi$
$251$	8.61959	+	4.97652i	0.544063	+	0.314115i	−0.202661	+	0.979249i	$0.564959\pi$
$252$		−	0.830319i		−	0.0523052i
$253$	0.271008	−	0.469399i	0.0170381	−	0.0295109i
$254$	−3.72326	+	0.997644i	−0.233618	+	0.0625978i
$255$	0.0417144	+	1.38612i	0.00261226	+	0.0868022i
$256$	−5.76971	+	9.99343i	−0.360607	+	0.624589i
$257$	−2.65761	−	0.712105i	−0.165777	−	0.0444199i	0.174976	−	0.984573i	$-0.444015\pi$
$257$	−2.65761	−	0.712105i	−0.165777	−	0.0444199i	−0.340753	+	0.940153i	$0.610682\pi$
$258$	−1.92538	+	1.11162i	−0.119869	+	0.0692062i
$259$	3.73211			0.231902
$260$		0			0
$261$	−6.93669			−0.429370
$262$	−9.06767	+	5.23522i	−0.560202	+	0.323433i
$263$	5.96686	+	1.59881i	0.367932	+	0.0985871i	0.438048	−	0.898952i	$-0.355670\pi$
$263$	5.96686	+	1.59881i	0.367932	+	0.0985871i	−0.0701155	+	0.997539i	$0.522337\pi$
$264$	−0.0356423	+	0.0617342i	−0.00219363	+	0.00379948i
$265$	−8.04147	+	8.54049i	−0.493983	+	0.524638i
$266$	3.82930	−	1.02606i	0.234789	−	0.0629116i
$267$	−0.897179	+	1.55396i	−0.0549065	+	0.0951008i
$268$			2.50088i			0.152766i
$269$	−18.3796	−	10.6115i	−1.12063	−	0.646994i	−0.179066	−	0.983837i	$-0.557308\pi$
$269$	−18.3796	−	10.6115i	−1.12063	−	0.646994i	−0.941561	+	0.336843i	$0.890641\pi$
$270$	4.05651	+	0.957143i	0.246872	+	0.0582499i
$271$	12.4458	+	3.33484i	0.756027	+	0.202577i	0.616190	−	0.787598i	$-0.288675\pi$
$271$	12.4458	+	3.33484i	0.756027	+	0.202577i	0.139837	+	0.990174i	$0.455342\pi$
$272$	−10.5820	+	10.5820i	−0.641629	+	0.641629i
$273$		0			0
$274$			6.42690i			0.388263i
$275$	−0.750220	−	0.153350i	−0.0452400	−	0.00924733i
$276$	0.178559	+	0.309274i	0.0107480	+	0.0186161i
$277$	−5.50674	−	20.5514i	−0.330868	−	1.23482i	−0.908280	−	0.418363i	$-0.862604\pi$
$277$	−5.50674	−	20.5514i	−0.330868	−	1.23482i	0.577412	−	0.816453i	$-0.304063\pi$
$278$	20.3214			1.21880
$279$	−7.16409	−	26.7367i	−0.428903	−	1.60069i
$280$	2.54728	+	1.37021i	0.152229	+	0.0818857i
$281$	4.22655	−	4.22655i	0.252135	−	0.252135i	−0.569711	−	0.821845i	$-0.692945\pi$
$281$	4.22655	−	4.22655i	0.252135	−	0.252135i	0.821845	+	0.569711i	$0.192945\pi$
$282$	−2.76044	+	0.739656i	−0.164382	+	0.0440459i
$283$	−0.398044	+	1.48552i	−0.0236613	+	0.0883050i	−0.976747	−	0.214396i	$-0.931222\pi$
$283$	−0.398044	+	1.48552i	−0.0236613	+	0.0883050i	0.953086	+	0.302701i	$0.0978884\pi$
$284$	2.06974	−	7.72438i	0.122817	−	0.458358i
$285$	0.0605484	+	2.01195i	0.00358658	+	0.119178i
$286$		0			0
$287$	−1.38730	−	1.38730i	−0.0818897	−	0.0818897i
$288$	4.18585	+	7.25011i	0.246654	+	0.427217i
$289$	6.16679	−	3.56040i	0.362752	−	0.209435i
$290$	−3.93252	+	7.31074i	−0.230925	+	0.429301i
$291$	−1.05631	−	1.05631i	−0.0619218	−	0.0619218i
$292$	1.73524	+	1.00184i	0.101547	+	0.0586282i
$293$	−2.41782	−	1.39593i	−0.141251	−	0.0815512i	0.427709	−	0.903916i	$-0.359321\pi$
$293$	−2.41782	−	1.39593i	−0.141251	−	0.0815512i	−0.568960	+	0.822365i	$0.692654\pi$
$294$	−1.48124	−	1.48124i	−0.0863877	−	0.0863877i
$295$	8.15266	−	2.44960i	0.474666	−	0.142621i
$296$	−13.9053	+	8.02825i	−0.808232	+	0.466633i
$297$	0.0900642	+	0.155996i	0.00522606	+	0.00905180i
$298$	−4.76785	−	4.76785i	−0.276194	−	0.276194i
$299$		0			0
$300$	0.334650	−	0.377556i	0.0193210	−	0.0217982i
$301$	−1.00905	+	3.76583i	−0.0581607	+	0.217059i
$302$	2.83896	−	10.5951i	0.163364	−	0.609682i
$303$	2.57964	−	0.691212i	0.148196	−	0.0397091i
$304$	−15.3598	+	15.3598i	−0.880944	+	0.880944i
$305$	−8.31502	+	15.4580i	−0.476116	+	0.885123i
$306$	3.81736	+	14.2466i	0.218224	+	0.814423i
$307$	−2.12112			−0.121058			−0.0605292	−	0.998166i	$-0.519279\pi$
$307$	−2.12112			−0.121058			−0.0605292	+	0.998166i	$0.519279\pi$
$308$	−0.0111148	−	0.0414808i	−0.000633322	−	0.00236359i
$309$	−1.44495	−	2.50272i	−0.0822001	−	0.142375i
$310$	−32.2399	−	7.60708i	−1.83110	−	0.432053i
$311$		−	21.2656i		−	1.20586i	−0.797794	−	0.602931i	$-0.794000\pi$
$311$		−	21.2656i		−	1.20586i	0.797794	−	0.602931i	$-0.206000\pi$
$312$		0			0
$313$	−14.3666	+	14.3666i	−0.812050	+	0.812050i	−0.984941	−	0.172891i	$-0.944689\pi$
$313$	−14.3666	+	14.3666i	−0.812050	+	0.812050i	0.172891	+	0.984941i	$0.444689\pi$
$314$	−4.97657	−	1.33347i	−0.280844	−	0.0752519i
$315$	3.08813	−	1.90904i	0.173996	−	0.107562i
$316$	4.93342	+	2.84831i	0.277527	+	0.160230i
$317$		−	8.78989i		−	0.493689i	−0.969055	−	0.246845i	$-0.920606\pi$
$317$		−	8.78989i		−	0.493689i	0.969055	−	0.246845i	$-0.0793937\pi$
$318$	0.820184	−	1.42060i	0.0459936	−	0.0796633i
$319$	−0.346541	+	0.0928554i	−0.0194026	+	0.00519890i
$320$	−11.2693	+	0.339143i	−0.629973	+	0.0189587i
$321$	1.58599	−	2.74701i	0.0885212	−	0.153323i
$322$	2.97061	+	0.795974i	0.165546	+	0.0443579i
$323$	−12.4185	+	7.16982i	−0.690984	+	0.398940i
$324$	4.42414			0.245786
$325$		0			0
$326$	−17.2237			−0.953930
$327$	−1.98356	+	1.14521i	−0.109691	+	0.0633302i
$328$	8.15316	+	2.18463i	0.450183	+	0.120626i
$329$	−2.50574	+	4.34006i	−0.138146	+	0.239275i
$330$	0.107030	−	0.00322099i	0.00589179	−	0.000177310i
$331$	−17.5522	+	4.70310i	−0.964756	+	0.258506i	−0.706612	−	0.707601i	$-0.749777\pi$
$331$	−17.5522	+	4.70310i	−0.964756	+	0.258506i	−0.258144	+	0.966107i	$0.583111\pi$
$332$	−3.43276	+	5.94572i	−0.188397	+	0.326314i
$333$			20.1541i			1.10444i
$334$	22.4512	+	12.9622i	1.22848	+	0.709261i
$335$	−9.30131	+	5.74994i	−0.508185	+	0.314153i
$336$	−0.497574	−	0.133325i	−0.0271449	−	0.00727345i
$337$	−17.2522	+	17.2522i	−0.939788	+	0.939788i	−0.998287	−	0.0584999i	$-0.981368\pi$
$337$	−17.2522	+	17.2522i	−0.939788	+	0.939788i	0.0584999	+	0.998287i	$0.481368\pi$
$338$		0			0
$339$			0.899302i			0.0488434i
$340$	3.49814	+	0.825394i	0.189713	+	0.0447633i
$341$	−0.715803	−	1.23981i	−0.0387629	−	0.0671393i
$342$	5.54089	+	20.6789i	0.299617	+	1.11819i
$343$	−7.51173			−0.405595
$344$	−4.34120	−	16.2016i	−0.234062	−	0.873530i
$345$	−0.739717	+	1.37517i	−0.0398250	+	0.0740366i
$346$	7.65777	−	7.65777i	0.411684	−	0.411684i
$347$	7.50674	−	2.01142i	0.402983	−	0.107979i	−0.0516340	−	0.998666i	$-0.516443\pi$
$347$	7.50674	−	2.01142i	0.402983	−	0.107979i	0.454617	+	0.890687i	$0.349776\pi$
$348$	0.0611797	−	0.228326i	0.00327958	−	0.0122395i
$349$	−1.31241	+	4.89796i	−0.0702515	+	0.262182i	−0.992115	−	0.125333i	$-0.960000\pi$
$349$	−1.31241	+	4.89796i	−0.0702515	+	0.262182i	0.921863	+	0.387515i	$0.126667\pi$
$350$	−0.261271	−	4.33692i	−0.0139655	−	0.231818i
$351$		0			0
$352$	0.306166	+	0.306166i	0.0163187	+	0.0163187i
$353$	12.8089	+	22.1857i	0.681749	+	1.18082i	0.974447	+	0.224618i	$0.0721136\pi$
$353$	12.8089	+	22.1857i	0.681749	+	1.18082i	−0.292698	+	0.956205i	$0.594553\pi$
$354$	−1.03091	+	0.595199i	−0.0547925	+	0.0316345i
$355$	33.4873	−	10.0618i	1.77732	−	0.534025i
$356$	3.28851	+	3.28851i	0.174291	+	0.174291i
$357$	−0.294499	−	0.170029i	−0.0155865	−	0.00899888i
$358$	−7.78702	−	4.49584i	−0.411557	−	0.237613i
$359$	10.0443	+	10.0443i	0.530117	+	0.530117i	0.920607	−	0.390490i	$-0.127694\pi$
$359$	10.0443	+	10.0443i	0.530117	+	0.530117i	−0.390490	+	0.920607i	$0.627694\pi$
$360$	−7.39937	+	13.7558i	−0.389981	+	0.724994i
$361$	−1.57095	+	0.906990i	−0.0826817	+	0.0477363i
$362$	−2.84552	−	4.92858i	−0.149557	−	0.259040i
$363$	−1.53145	−	1.53145i	−0.0803801	−	0.0803801i
$364$		0			0
$365$	0.263540	+	8.75710i	0.0137943	+	0.458368i
$366$	0.635270	−	2.37086i	0.0332061	−	0.123927i
$367$	−5.20802	+	19.4366i	−0.271857	+	1.01458i	0.686062	+	0.727543i	$0.259338\pi$
$367$	−5.20802	+	19.4366i	−0.271857	+	1.01458i	−0.957919	+	0.287040i	$0.907329\pi$
$368$	−16.2769	+	4.36137i	−0.848490	+	0.227352i
$369$	7.49167	−	7.49167i	0.390001	−	0.390001i
$370$	21.2408	+	11.4257i	1.10426	+	0.593991i
$371$	−0.744507	−	2.77854i	−0.0386529	−	0.144255i
$372$	0.943243			0.0489049
$373$	6.78245	+	25.3125i	0.351182	+	1.31063i	0.885221	+	0.465170i	$0.154007\pi$
$373$	6.78245	+	25.3125i	0.351182	+	1.31063i	−0.534039	+	0.845460i	$0.679327\pi$
$374$	0.381413	+	0.660627i	0.0197224	+	0.0341602i
$375$	2.17362	+	0.376572i	0.112246	+	0.0194461i
$376$		−	21.5607i		−	1.11191i
$377$		0			0
$378$	−0.722700	+	0.722700i	−0.0371717	+	0.0371717i
$379$	21.7627	+	5.83130i	1.11787	+	0.299534i	0.770023	−	0.638016i	$-0.220245\pi$
$379$	21.7627	+	5.83130i	1.11787	+	0.299534i	0.347852	+	0.937550i	$0.386911\pi$
$380$	5.07755	+	1.19806i	0.260473	+	0.0614591i
$381$	0.415627	+	0.239962i	0.0212932	+	0.0122936i
$382$			37.2130i			1.90398i
$383$	12.0630	−	20.8938i	0.616392	−	1.06762i	−0.373747	−	0.927531i	$-0.621927\pi$
$383$	12.0630	−	20.8938i	0.616392	−	1.06762i	0.990139	−	0.140091i	$-0.0447396\pi$
$384$	2.60055	−	0.696814i	0.132709	−	0.0355591i
$385$	0.128721	−	0.136709i	0.00656024	−	0.00696735i
$386$	−12.5494	+	21.7362i	−0.638748	+	1.10634i
$387$	−20.3361	−	5.44905i	−1.03374	−	0.276991i
$388$	−3.35305	+	1.93589i	−0.170225	+	0.0982797i
$389$	14.3262			0.726365			0.363183	−	0.931718i	$-0.381690\pi$
$389$	14.3262			0.726365			0.363183	+	0.931718i	$0.381690\pi$
$390$		0			0
$391$	−11.1241			−0.562571
$392$	13.6867	−	7.90203i	0.691284	−	0.399113i
$393$	1.25922	+	0.337408i	0.0635194	+	0.0170200i
$394$	4.52662	−	7.84034i	0.228048	−	0.394991i
$395$	0.749265	+	24.8972i	0.0376996	+	1.25271i
$396$	0.224004	−	0.0600217i	0.0112566	−	0.00301620i
$397$	16.7465	−	29.0058i	0.840484	−	1.45576i	−0.0490017	−	0.998799i	$-0.515604\pi$
$397$	16.7465	−	29.0058i	0.840484	−	1.45576i	0.889486	−	0.456963i	$-0.151063\pi$
$398$		−	14.7430i		−	0.739000i
$399$	−0.427464	−	0.246797i	−0.0214000	−	0.0123553i
$400$	13.1214	+	19.8638i	0.656070	+	0.993189i
$401$	−17.9170	−	4.80084i	−0.894731	−	0.239743i	−0.217979	−	0.975953i	$-0.569946\pi$
$401$	−17.9170	−	4.80084i	−0.894731	−	0.239743i	−0.676752	+	0.736211i	$0.736613\pi$
$402$	1.08126	−	1.08126i	0.0539285	−	0.0539285i
$403$		0			0
$404$		−	6.92181i		−	0.344373i
$405$	10.1718	+	16.4543i	0.505442	+	0.817621i
$406$	−1.01782	−	1.76292i	−0.0505136	−	0.0874922i
$407$	0.269785	+	1.00685i	0.0133727	+	0.0499077i
$408$	1.46302			0.0724301
$409$	1.33873	+	4.99622i	0.0661960	+	0.247047i	0.991093	−	0.133171i	$-0.0425158\pi$
$409$	1.33873	+	4.99622i	0.0661960	+	0.247047i	−0.924897	+	0.380218i	$0.875849\pi$
$410$	−3.64850	−	12.1428i	−0.180187	−	0.599690i
$411$	0.565822	−	0.565822i	0.0279099	−	0.0279099i
$412$	−7.23487	+	1.93858i	−0.356436	+	0.0955068i
$413$	−0.540281	+	2.01636i	−0.0265855	+	0.0992184i
$414$	−4.29840	+	16.0418i	−0.211255	+	0.788414i
$415$	−30.0058	+	0.903008i	−1.47293	+	0.0443269i
$416$		0			0
$417$	−1.78909	−	1.78909i	−0.0876122	−	0.0876122i
$418$	0.553620	+	0.958899i	0.0270785	+	0.0469013i
$419$	−0.872048	+	0.503477i	−0.0426023	+	0.0245965i	−0.521150	−	0.853465i	$-0.674497\pi$
$419$	−0.872048	+	0.503477i	−0.0426023	+	0.0245965i	0.478548	+	0.878062i	$0.341163\pi$
$420$	0.0356008	+	0.118485i	0.00173714	+	0.00578148i
$421$	−0.294746	−	0.294746i	−0.0143650	−	0.0143650i	0.699888	−	0.714253i	$-0.253233\pi$
$421$	−0.294746	−	0.294746i	−0.0143650	−	0.0143650i	−0.714253	+	0.699888i	$0.753233\pi$
$422$	−7.51482	−	4.33868i	−0.365816	−	0.211204i
$423$	−23.4371	−	13.5314i	−1.13955	−	0.657920i
$424$	8.75094	+	8.75094i	0.424983	+	0.424983i
$425$	4.97298	+	14.9080i	0.241225	+	0.723146i
$426$	−4.23451	+	2.44480i	−0.205163	+	0.118451i
$427$	−2.15211	−	3.72756i	−0.104148	−	0.180389i
$428$	−5.81326	−	5.81326i	−0.280995	−	0.280995i
$429$		0			0
$430$	−17.2718	+	18.3436i	−0.832918	+	0.884606i
$431$	1.07449	−	4.01004i	0.0517562	−	0.193157i	−0.935207	−	0.354100i	$-0.884787\pi$
$431$	1.07449	−	4.01004i	0.0517562	−	0.193157i	0.986964	+	0.160944i	$0.0514538\pi$
$432$	1.44942	−	5.40930i	0.0697352	−	0.260255i
$433$	14.4842	−	3.88103i	0.696067	−	0.186511i	0.106599	−	0.994302i	$-0.466004\pi$
$433$	14.4842	−	3.88103i	0.696067	−	0.186511i	0.589468	+	0.807792i	$0.299337\pi$
$434$	5.74380	−	5.74380i	0.275711	−	0.275711i
$435$	0.989854	−	0.297418i	0.0474598	−	0.0142601i
$436$	1.53644	+	5.73407i	0.0735821	+	0.274612i
$437$	−16.1466			−0.772399
$438$	−0.317086	−	1.18338i	−0.0151509	−	0.0565441i
$439$	−6.94098	−	12.0221i	−0.331275	−	0.573785i	0.651487	−	0.758660i	$-0.274145\pi$
$439$	−6.94098	−	12.0221i	−0.331275	−	0.573785i	−0.982762	+	0.184875i	$0.940812\pi$
$440$	−0.185519	+	0.786257i	−0.00884427	+	0.0374833i
$441$		−	19.8372i		−	0.944628i
$442$		0			0
$443$	10.0594	−	10.0594i	0.477938	−	0.477938i	−0.426533	−	0.904472i	$-0.640265\pi$
$443$	10.0594	−	10.0594i	0.477938	−	0.477938i	0.904472	+	0.426533i	$0.140265\pi$
$444$	−0.663384	−	0.177753i	−0.0314828	−	0.00843580i
$445$	−4.66984	+	19.7915i	−0.221372	+	0.938206i
$446$	25.4834	+	14.7128i	1.20667	+	0.696673i
$447$			0.839520i			0.0397079i
$448$	1.38235	−	2.39430i	0.0653100	−	0.113120i
$449$	−6.42946	+	1.72277i	−0.303425	+	0.0813024i	−0.407319	−	0.913286i	$-0.633536\pi$
$449$	−6.42946	+	1.72277i	−0.303425	+	0.0813024i	0.103894	+	0.994588i	$0.466870\pi$
$450$	23.4201	−	1.41091i	1.10404	−	0.0665108i
$451$	0.273982	−	0.474551i	0.0129013	−	0.0223457i
$452$	2.25141	+	0.603263i	0.105897	+	0.0283751i
$453$	−1.18274	+	0.682853i	−0.0555698	+	0.0320832i
$454$	−10.1212			−0.475011
$455$		0			0
$456$	2.12357			0.0994451
$457$	−32.0071	+	18.4793i	−1.49723	+	0.864426i	−0.999995	−	0.00318917i	$-0.998985\pi$
$457$	−32.0071	+	18.4793i	−1.49723	+	0.864426i	−0.497236	+	0.867616i	$0.665652\pi$
$458$	24.0614	+	6.44722i	1.12431	+	0.301259i
$459$	1.84844	−	3.20160i	0.0862780	−	0.149438i
$460$	2.94653	+	2.77437i	0.137383	+	0.129355i
$461$	−24.8502	+	6.65860i	−1.15739	+	0.310122i	−0.785923	−	0.618324i	$-0.787812\pi$
$461$	−24.8502	+	6.65860i	−1.15739	+	0.310122i	−0.371468	+	0.928446i	$0.621145\pi$
$462$	−0.0131288	+	0.0227398i	−0.000610809	+	0.00105795i
$463$			15.9580i			0.741632i	0.928706	+	0.370816i	$0.120922\pi$
$463$			15.9580i			0.741632i	−0.928706	+	0.370816i	$0.879078\pi$
$464$	9.65955	+	5.57694i	0.448433	+	0.258903i
$465$	2.16867	+	3.50812i	0.100570	+	0.162685i
$466$	−12.6847	−	3.39887i	−0.587609	−	0.157449i
$467$	18.6259	−	18.6259i	0.861902	−	0.861902i	−0.129657	−	0.991559i	$-0.541388\pi$
$467$	18.6259	−	18.6259i	0.861902	−	0.861902i	0.991559	+	0.129657i	$0.0413877\pi$
$468$		0			0
$469$		−	2.68150i		−	0.123820i
$470$	−27.5480	+	17.0298i	−1.27069	+	0.785524i
$471$	0.320738	+	0.555534i	0.0147788	+	0.0255976i
$472$	−2.32443	−	8.67489i	−0.106991	−	0.399294i
$473$	−1.08889			−0.0500671
$474$	−0.901501	−	3.36445i	−0.0414073	−	0.154534i
$475$	7.21827	+	21.6390i	0.331197	+	0.992865i
$476$	−0.623222	+	0.623222i	−0.0285653	+	0.0285653i
$477$	15.0046	−	4.02047i	0.687014	−	0.184085i
$478$	−8.00943	+	29.8916i	−0.366343	+	1.36721i
$479$	−4.29638	+	16.0343i	−0.196307	+	0.732627i	0.795618	+	0.605799i	$0.207146\pi$
$479$	−4.29638	+	16.0343i	−0.196307	+	0.732627i	−0.991925	+	0.126828i	$0.959520\pi$
$480$	−0.908170	−	0.855105i	−0.0414521	−	0.0390300i
$481$		0			0
$482$	19.1990	+	19.1990i	0.874490	+	0.874490i
$483$	−0.191455	−	0.331609i	−0.00871149	−	0.0150888i
$484$	−4.86130	+	2.80667i	−0.220968	+	0.127576i
$485$	−14.9092	−	8.01979i	−0.676991	−	0.364160i
$486$	−5.86681	−	5.86681i	−0.266124	−	0.266124i
$487$	22.7590	+	13.1399i	1.03131	+	0.595425i	0.917359	−	0.398062i	$-0.130317\pi$
$487$	22.7590	+	13.1399i	1.03131	+	0.595425i	0.113948	+	0.993487i	$0.463650\pi$
$488$	16.0369	+	9.25893i	0.725958	+	0.419132i
$489$	1.51637	+	1.51637i	0.0685724	+	0.0685724i
$490$	−20.9069	−	11.2460i	−0.944477	−	0.508043i
$491$	−36.0301	+	20.8020i	−1.62602	+	0.938781i	−0.640752	+	0.767748i	$0.721377\pi$
$491$	−36.0301	+	20.8020i	−1.62602	+	0.938781i	−0.985265	+	0.171034i	$0.945289\pi$
$492$	0.180519	+	0.312668i	0.00813842	+	0.0140961i
$493$	5.20655	+	5.20655i	0.234491	+	0.234491i
$494$		0			0
$495$	0.738254	+	0.695118i	0.0331821	+	0.0312432i
$496$	−11.5195	+	42.9915i	−0.517242	+	1.93037i
$497$	−2.21922	+	8.28224i	−0.0995456	+	0.371509i
$498$	4.05480	−	1.08648i	0.181700	−	0.0486864i
$499$	8.31651	−	8.31651i	0.372298	−	0.372298i	−0.496015	−	0.868314i	$-0.665204\pi$
$499$	8.31651	−	8.31651i	0.372298	−	0.372298i	0.868314	+	0.496015i	$0.165204\pi$
$500$	2.40085	−	5.18908i	0.107369	−	0.232063i
$501$	−0.835410	−	3.11779i	−0.0373234	−	0.139293i
$502$	−15.7730			−0.703982
$503$	2.76277	+	10.3108i	0.123186	+	0.459736i	0.999769	−	0.0215156i	$-0.00684916\pi$
$503$	2.76277	+	10.3108i	0.123186	+	0.459736i	−0.876583	+	0.481251i	$0.840182\pi$
$504$	−1.91512	−	3.31708i	−0.0853062	−	0.147755i
$505$	25.7437	−	15.9144i	1.14558	−	0.708180i
$506$			0.858953i			0.0381851i
$507$		0			0
$508$	0.879556	−	0.879556i	0.0390240	−	0.0390240i
$509$	−2.91197	−	0.780260i	−0.129071	−	0.0345844i	0.193705	−	0.981060i	$-0.437949\pi$
$509$	−2.91197	−	0.780260i	−0.129071	−	0.0345844i	−0.322776	+	0.946475i	$0.604616\pi$
$510$	−1.15557	−	1.86929i	−0.0511694	−	0.0827735i
$511$	−1.86056	−	1.07419i	−0.0823062	−	0.0475195i
$512$			9.00279i			0.397871i
$513$	2.68301	−	4.64712i	0.118458	−	0.205175i
$514$	4.21162	−	1.12850i	0.185767	−	0.0497760i
$515$	−23.8441	−	22.4509i	−1.05070	−	0.989304i
$516$	0.358718	−	0.621318i	0.0157917	−	0.0273520i
$517$	−1.35200	−	0.362267i	−0.0594608	−	0.0159325i
$518$	−5.12203	+	2.95721i	−0.225049	+	0.129932i
$519$	−1.34838			−0.0591871
$520$		0			0
$521$	−5.84796			−0.256204			−0.128102	−	0.991761i	$-0.540888\pi$
$521$	−5.84796			−0.256204			−0.128102	+	0.991761i	$0.540888\pi$
$522$	9.52007	−	5.49642i	0.416682	−	0.240572i
$523$	−2.86434	−	0.767497i	−0.125249	−	0.0335603i	0.195650	−	0.980674i	$-0.437318\pi$
$523$	−2.86434	−	0.767497i	−0.125249	−	0.0335603i	−0.320899	+	0.947113i	$0.603985\pi$
$524$	1.68940	−	2.92613i	0.0738020	−	0.127829i
$525$	−0.358819	+	0.404823i	−0.0156601	+	0.0176679i
$526$	−9.45590	+	2.53370i	−0.412297	+	0.110475i
$527$	−14.6909	+	25.4453i	−0.639944	+	1.10842i
$528$		−	0.143873i		−	0.00626129i
$529$	9.07083	+	5.23704i	0.394384	+	0.227698i
$530$	4.26908	−	18.0930i	0.185437	−	0.785909i
$531$	−10.8887	−	2.91762i	−0.472529	−	0.126614i
$532$	−0.904605	+	0.904605i	−0.0392196	+	0.0392196i
$533$		0			0
$534$		−	2.84359i		−	0.123054i
$535$	8.25511	−	34.9864i	0.356900	−	1.51259i
$536$	5.76825	+	9.99091i	0.249151	+	0.431542i
$537$	0.289755	+	1.08138i	0.0125038	+	0.0466650i
$538$	33.6329			1.45002
$539$	−0.265543	−	0.991021i	−0.0114378	−	0.0426863i
$540$	−1.28809	+	0.387029i	−0.0554307	+	0.0166551i
$541$	15.4678	−	15.4678i	0.665013	−	0.665013i	−0.291544	−	0.956557i	$-0.594169\pi$
$541$	15.4678	−	15.4678i	0.665013	−	0.665013i	0.956557	+	0.291544i	$0.0941691\pi$
$542$	−19.7233	+	5.28484i	−0.847188	+	0.227003i
$543$	−0.183392	+	0.684429i	−0.00787011	+	0.0293717i
$544$	2.29997	−	8.58362i	0.0986105	−	0.368020i
$545$	−17.7937	+	18.8979i	−0.762198	+	0.809497i
$546$		0			0
$547$	1.76989	+	1.76989i	0.0756751	+	0.0756751i	0.743931	−	0.668256i	$-0.232959\pi$
$547$	1.76989	+	1.76989i	0.0756751	+	0.0756751i	−0.668256	+	0.743931i	$0.732959\pi$
$548$	−1.03698	−	1.79610i	−0.0442976	−	0.0767256i
$549$	20.1295	−	11.6218i	0.859106	−	0.496005i
$550$	1.15113	−	0.383990i	0.0490843	−	0.0163734i
$551$	7.55729	+	7.55729i	0.321952	+	0.321952i
$552$	1.42667	+	0.823688i	0.0607231	+	0.0350585i
$553$	−5.28972	−	3.05402i	−0.224942	−	0.129870i
$554$	23.8419	+	23.8419i	1.01295	+	1.01295i
$555$	−0.864126	−	2.87595i	−0.0366801	−	0.122077i
$556$	−5.67915	+	3.27886i	−0.240850	+	0.139055i
$557$	−4.71734	−	8.17068i	−0.199880	−	0.346203i	0.748609	−	0.663012i	$-0.230722\pi$
$557$	−4.71734	−	8.17068i	−0.199880	−	0.346203i	−0.948489	+	0.316809i	$0.897389\pi$
$558$	31.0175	+	31.0175i	1.31308	+	1.31308i
$559$		0			0
$560$	−5.83514	+	0.175605i	−0.246580	+	0.00742067i
$561$	0.0245819	−	0.0917409i	0.00103785	−	0.00387330i
$562$	−2.45163	+	9.14960i	−0.103416	+	0.385953i
$563$	−9.45863	+	2.53443i	−0.398634	+	0.106814i	−0.452566	−	0.891731i	$-0.649491\pi$
$563$	−9.45863	+	2.53443i	−0.398634	+	0.106814i	0.0539320	+	0.998545i	$0.482825\pi$
$564$	0.652105	−	0.652105i	0.0274586	−	0.0274586i
$565$	2.93269	+	9.76047i	0.123379	+	0.410626i
$566$	−0.630795	−	2.35416i	−0.0265143	−	0.0989527i
$567$	−4.74366			−0.199215
$568$	−9.54766	−	35.6324i	−0.400611	−	1.49510i
$569$	−3.20931	−	5.55868i	−0.134541	−	0.233032i	0.790881	−	0.611970i	$-0.209623\pi$
$569$	−3.20931	−	5.55868i	−0.134541	−	0.233032i	−0.925422	+	0.378938i	$0.876289\pi$
$570$	−1.67731	−	2.71327i	−0.0702546	−	0.113646i
$571$		−	1.72174i		−	0.0720527i	−0.999351	−	0.0360264i	$-0.988530\pi$
$571$		−	1.72174i		−	0.0720527i	0.999351	−	0.0360264i	$-0.0114700\pi$
$572$		0			0
$573$	3.27622	−	3.27622i	0.136866	−	0.136866i
$574$	3.00322	+	0.804709i	0.125352	+	0.0335879i
$575$	−3.54389	+	17.3375i	−0.147791	+	0.723023i
$576$	12.9297	+	7.46495i	0.538736	+	0.311040i
$577$		−	24.8642i		−	1.03511i	−0.855650	−	0.517554i	$-0.826843\pi$
$577$		−	24.8642i		−	1.03511i	0.855650	−	0.517554i	$-0.173157\pi$
$578$	−5.64230	+	9.77275i	−0.234689	+	0.406493i
$579$	3.01849	−	0.808803i	0.125444	−	0.0336127i
$580$	−0.0805813	−	2.67762i	−0.00334596	−	0.111182i
$581$	3.68068	−	6.37512i	0.152700	−	0.264484i
$582$	2.28668	+	0.612715i	0.0947861	+	0.0253979i
$583$	0.695777	−	0.401707i	0.0288161	−	0.0166370i
$584$	9.24291			0.382474
$585$		0			0
$586$	4.42437			0.182769
$587$	23.1811	−	13.3836i	0.956785	−	0.552400i	0.0616029	−	0.998101i	$-0.480379\pi$
$587$	23.1811	−	13.3836i	0.956785	−	0.552400i	0.895182	+	0.445701i	$0.147045\pi$
$588$	0.652955	+	0.174959i	0.0269274	+	0.00721517i
$589$	−21.3238	+	36.9338i	−0.878630	+	1.52183i
$590$	−9.24791	+	9.82180i	−0.380731	+	0.404357i
$591$	−1.08878	+	0.291739i	−0.0447866	+	0.0120005i
$592$	16.2034	−	28.0651i	0.665956	−	1.15347i
$593$		−	19.8452i		−	0.814944i	−0.913218	−	0.407472i	$-0.866410\pi$
$593$		−	19.8452i		−	0.814944i	0.913218	−	0.407472i	$-0.133590\pi$
$594$	−0.247213	−	0.142728i	−0.0101433	−	0.00585621i
$595$	−3.75078	−	0.885004i	−0.153767	−	0.0362816i
$596$	2.10174	+	0.563161i	0.0860908	+	0.0230680i
$597$	−1.29797	+	1.29797i	−0.0531224	+	0.0531224i
$598$		0			0
$599$		−	36.5285i		−	1.49252i	−0.665657	−	0.746258i	$-0.731849\pi$
$599$		−	36.5285i		−	1.49252i	0.665657	−	0.746258i	$-0.268151\pi$
$600$	0.466084	−	2.28018i	0.0190278	−	0.0930881i
$601$	−14.9478	−	25.8903i	−0.609732	−	1.05609i	−0.991284	−	0.131740i	$-0.957944\pi$
$601$	−14.9478	−	25.8903i	−0.609732	−	1.05609i	0.381552	−	0.924347i	$-0.375390\pi$
$602$	−1.59908	−	5.96785i	−0.0651736	−	0.243231i
$603$	14.4806			0.589695
$604$	0.916132	+	3.41905i	0.0372769	+	0.139119i
$605$	−21.6155	−	11.6272i	−0.878796	−	0.472713i
$606$	−2.99266	+	2.99266i	−0.121568	+	0.121568i
$607$	−17.2598	+	4.62475i	−0.700553	+	0.187713i	−0.591478	−	0.806321i	$-0.701456\pi$
$607$	−17.2598	+	4.62475i	−0.700553	+	0.187713i	−0.109075	+	0.994034i	$0.534789\pi$
$608$	3.33841	−	12.4591i	0.135390	−	0.505283i
$609$	−0.0655981	+	0.244816i	−0.00265817	+	0.00992043i
$610$	−0.836730	−	27.8035i	−0.0338782	−	1.12573i
$611$		0			0
$612$	−3.36551	−	3.36551i	−0.136043	−	0.136043i
$613$	7.68729	+	13.3148i	0.310487	+	0.537779i	0.978468	−	0.206399i	$-0.0661746\pi$
$613$	7.68729	+	13.3148i	0.310487	+	0.537779i	−0.667981	+	0.744178i	$0.732841\pi$
$614$	2.91107	−	1.68071i	0.117481	−	0.0678278i
$615$	−0.747835	+	1.39026i	−0.0301556	+	0.0560607i
$616$	−0.140078	−	0.140078i	−0.00564390	−	0.00564390i
$617$	1.07707	+	0.621849i	0.0433614	+	0.0250347i	0.521524	−	0.853237i	$-0.325364\pi$
$617$	1.07707	+	0.621849i	0.0433614	+	0.0250347i	−0.478163	+	0.878271i	$0.658697\pi$
$618$	3.96616	+	2.28986i	0.159542	+	0.0921117i
$619$	−28.7865	−	28.7865i	−1.15703	−	1.15703i	−0.985112	−	0.171915i	$-0.945005\pi$
$619$	−28.7865	−	28.7865i	−1.15703	−	1.15703i	−0.171915	−	0.985112i	$-0.554995\pi$
$620$	10.2374	−	3.07599i	0.411143	−	0.123535i
$621$	3.60504	−	2.08137i	0.144665	−	0.0835226i
$622$	16.8502	+	29.1854i	0.675631	+	1.17023i
$623$	−3.52601	−	3.52601i	−0.141266	−	0.141266i
$624$		0			0
$625$	24.8192	−	3.00128i	0.992768	−	0.120051i
$626$	8.33343	−	31.1008i	0.333071	−	1.24304i
$627$	0.0356806	−	0.133162i	0.00142495	−	0.00531797i
$628$	1.60594	−	0.430310i	0.0640839	−	0.0171712i
$629$	15.1272	−	15.1272i	0.603163	−	0.603163i
$630$	−2.72556	+	5.06695i	−0.108589	+	0.201872i
$631$	5.36381	+	20.0180i	0.213530	+	0.796904i	0.986679	+	0.162680i	$0.0520137\pi$
$631$	5.36381	+	20.0180i	0.213530	+	0.796904i	−0.773149	+	0.634224i	$0.781320\pi$
$632$	26.2784			1.04530
$633$	0.279626	+	1.04358i	0.0111141	+	0.0414785i
$634$	6.96483	+	12.0634i	0.276609	+	0.479101i
$635$	5.29349	+	1.24901i	0.210066	+	0.0495655i
$636$			0.529346i			0.0209899i
$637$		0			0
$638$	0.402025	−	0.402025i	0.0159163	−	0.0159163i
$639$	−44.7256	−	11.9842i	−1.76932	−	0.474087i
$640$	25.9523	−	16.0434i	1.02586	−	0.634169i
$641$	−15.3071	−	8.83753i	−0.604592	−	0.349061i	0.166254	−	0.986083i	$-0.446833\pi$
$641$	−15.3071	−	8.83753i	−0.604592	−	0.349061i	−0.770846	+	0.637022i	$0.780166\pi$
$642$			5.02675i			0.198390i
$643$	−1.33452	+	2.31145i	−0.0526282	+	0.0911547i	−0.891139	−	0.453730i	$-0.850093\pi$
$643$	−1.33452	+	2.31145i	−0.0526282	+	0.0911547i	0.838511	+	0.544884i	$0.183426\pi$
$644$	−0.958617	+	0.256861i	−0.0377748	+	0.0101217i
$645$	3.13556	−	0.0943630i	0.123463	−	0.00371554i
$646$	11.3623	−	19.6801i	0.447043	−	0.774302i
$647$	40.7326	+	10.9143i	1.60136	+	0.429084i	0.945454	−	0.325755i	$-0.105619\pi$
$647$	40.7326	+	10.9143i	1.60136	+	0.429084i	0.655910	+	0.754839i	$0.272285\pi$
$648$	17.6742	−	10.2042i	0.694309	−	0.400860i
$649$	−0.583029			−0.0228859
$650$		0			0
$651$	−1.01136			−0.0396385
$652$	4.81343	−	2.77904i	0.188508	−	0.108835i
$653$	−24.4045	−	6.53917i	−0.955023	−	0.255898i	−0.252531	−	0.967589i	$-0.581263\pi$
$653$	−24.4045	−	6.53917i	−0.955023	−	0.255898i	−0.702492	+	0.711691i	$0.747930\pi$
$654$	1.81485	−	3.14342i	0.0709664	−	0.122917i
$655$	14.7671	−	0.444408i	0.576999	−	0.0173644i
$656$	−16.4555	+	4.40924i	−0.642479	+	0.172152i
$657$	5.80083	−	10.0473i	0.226312	−	0.391984i
$658$		−	7.94187i		−	0.309606i
$659$	−32.7551	−	18.9112i	−1.27596	−	0.736675i	−0.299856	−	0.953985i	$-0.596939\pi$
$659$	−32.7551	−	18.9112i	−1.27596	−	0.736675i	−0.976103	+	0.217310i	$0.930272\pi$
$660$	−0.0293915	+	0.0181694i	−0.00114406	+	0.000707243i
$661$	16.6205	+	4.45346i	0.646463	+	0.173219i	0.567129	−	0.823629i	$-0.308054\pi$
$661$	16.6205	+	4.45346i	0.646463	+	0.173219i	0.0793341	+	0.996848i	$0.474721\pi$
$662$	20.3625	−	20.3625i	0.791409	−	0.791409i
$663$		0			0
$664$			31.6705i			1.22905i
$665$	−5.44425	−	1.28458i	−0.211119	−	0.0498140i
$666$	−15.9694	−	27.6599i	−0.618804	−	1.07180i
$667$	2.14588	+	8.00852i	0.0830887	+	0.310091i
$668$	−8.36582			−0.323683
$669$	−0.948235	−	3.53886i	−0.0366609	−	0.136820i
$670$	8.20927	−	15.2614i	0.317152	−	0.589600i
$671$	0.850052	−	0.850052i	0.0328159	−	0.0328159i
$672$	0.295461	−	0.0791687i	0.0113977	−	0.00305400i
$673$	8.14322	−	30.3909i	0.313898	−	1.17148i	−0.611113	−	0.791543i	$-0.709278\pi$
$673$	8.14322	−	30.3909i	0.313898	−	1.17148i	0.925011	−	0.379940i	$-0.124055\pi$
$674$	10.0072	−	37.3474i	0.385464	−	1.43857i
$675$	−4.40098	−	3.90085i	−0.169394	−	0.150144i
$676$		0			0
$677$	−28.8731	−	28.8731i	−1.10968	−	1.10968i	−0.993191	−	0.116494i	$-0.962835\pi$
$677$	−28.8731	−	28.8731i	−1.10968	−	1.10968i	−0.116494	−	0.993191i	$-0.537165\pi$
$678$	−0.712579	−	1.23422i	−0.0273664	−	0.0474001i
$679$	3.59521	−	2.07570i	0.137972	−	0.0796579i
$680$	15.8787	−	4.77101i	0.608919	−	0.182960i
$681$	0.891066	+	0.891066i	0.0341457	+	0.0341457i
$682$	1.96477	+	1.13436i	0.0752349	+	0.0434369i
$683$	27.5215	+	15.8896i	1.05308	+	0.607998i	0.923511	−	0.383572i	$-0.125306\pi$
$683$	27.5215	+	15.8896i	1.05308	+	0.607998i	0.129572	+	0.991570i	$0.458640\pi$
$684$	−4.88503	−	4.88503i	−0.186784	−	0.186784i
$685$	4.29589	−	7.98627i	0.164138	−	0.305140i
$686$	10.3093	−	5.95206i	0.393610	−	0.227251i
$687$	−1.55074	−	2.68597i	−0.0591646	−	0.102476i
$688$	23.9378	+	23.9378i	0.912619	+	0.912619i
$689$		0			0
$690$	−0.0744368	−	2.47344i	−0.00283376	−	0.0941623i
$691$	6.94735	−	25.9278i	0.264289	−	0.986342i	−0.698394	−	0.715713i	$-0.746102\pi$
$691$	6.94735	−	25.9278i	0.264289	−	0.986342i	0.962684	−	0.270629i	$-0.0872315\pi$
$692$	−0.904508	+	3.37567i	−0.0343842	+	0.128324i
$693$	−0.240182	+	0.0643565i	−0.00912374	+	0.00244470i
$694$	−8.70863	+	8.70863i	−0.330575	+	0.330575i
$695$	−25.2520	−	13.5833i	−0.957865	−	0.515245i
$696$	−0.282220	−	1.05326i	−0.0106975	−	0.0399237i
$697$	−11.2462			−0.425980
$698$	−2.07982	−	7.76199i	−0.0787223	−	0.293796i
$699$	0.817526	+	1.41600i	0.0309217	+	0.0535579i
$700$	0.772778	+	1.16987i	0.0292082	+	0.0442168i
$701$			39.3253i			1.48530i	0.669681	+	0.742649i	$0.266431\pi$
$701$			39.3253i			1.48530i	−0.669681	+	0.742649i	$0.733569\pi$
$702$		0			0
$703$	21.9572	−	21.9572i	0.828131	−	0.828131i
$704$	0.745863	+	0.199854i	0.0281108	+	0.00753226i
$705$	3.92461	+	0.926020i	0.147809	+	0.0348759i
$706$	−35.1585	−	20.2987i	−1.32321	−	0.763953i
$707$			7.42171i			0.279122i
$708$	0.192071	−	0.332676i	0.00721845	−	0.0125027i
$709$	−36.2309	+	9.70804i	−1.36068	+	0.364593i	−0.864066	−	0.503378i	$-0.832090\pi$
$709$	−36.2309	+	9.70804i	−1.36068	+	0.364593i	−0.496614	+	0.867972i	$0.665424\pi$
$710$	−37.9861	+	40.3433i	−1.42559	+	1.51406i
$711$	16.4923	−	28.5654i	0.618508	−	1.07129i
$712$	20.7223	+	5.55253i	0.776602	+	0.208090i
$713$	−28.6518	+	16.5421i	−1.07302	+	0.619507i
$714$	0.538902			0.0201679
$715$		0			0
$716$	2.90161			0.108438
$717$	3.33680	−	1.92650i	0.124615	−	0.0719465i
$718$	−21.7438	−	5.82623i	−0.811471	−	0.217433i
$719$	14.5578	−	25.2148i	0.542913	−	0.940353i	−0.455822	−	0.890071i	$-0.650655\pi$
$719$	14.5578	−	25.2148i	0.542913	−	0.940353i	0.998735	−	0.0502820i	$-0.0160120\pi$
$720$	−0.948298	−	31.5108i	−0.0353410	−	1.17434i
$721$	7.75737	−	2.07858i	0.288900	−	0.0774104i
$722$	1.43734	−	2.48955i	0.0534923	−	0.0926514i
$723$		−	3.38055i		−	0.125724i
$724$	1.59045	+	0.918247i	0.0591086	+	0.0341264i
$725$	9.77335	−	6.45597i	0.362973	−	0.239769i
$726$	3.31526	+	0.888322i	0.123041	+	0.0329687i
$727$	−15.6053	+	15.6053i	−0.578768	+	0.578768i	−0.934564	−	0.355796i	$-0.884210\pi$
$727$	−15.6053	+	15.6053i	−0.578768	+	0.578768i	0.355796	+	0.934564i	$0.384210\pi$
$728$		0			0
$729$		−	24.9204i		−	0.922977i
$730$	−7.30054	−	11.8096i	−0.270205	−	0.437094i
$731$	11.1740	+	19.3539i	0.413284	+	0.715829i
$732$	0.205002	+	0.765076i	0.00757708	+	0.0282780i
$733$	−34.8651			−1.28777			−0.643886	−	0.765121i	$-0.722679\pi$
$733$	−34.8651			−1.28777			−0.643886	+	0.765121i	$0.722679\pi$
$734$	−8.25335	−	30.8019i	−0.304637	−	1.13692i
$735$	0.850540	+	2.83073i	0.0313727	+	0.104413i
$736$	7.07547	−	7.07547i	0.260805	−	0.260805i
$737$	0.723416	−	0.193839i	0.0266474	−	0.00714014i
$738$	−4.34557	+	16.2179i	−0.159963	+	0.596989i
$739$	8.85631	−	33.0522i	0.325785	−	1.21584i	−0.587736	−	0.809053i	$-0.699981\pi$
$739$	8.85631	−	33.0522i	0.325785	−	1.21584i	0.913521	−	0.406792i	$-0.133353\pi$
$740$	−7.77962	+	0.234123i	−0.285985	+	0.00860654i
$741$		0			0
$742$	3.22341	+	3.22341i	0.118335	+	0.118335i
$743$	−1.56456	−	2.70989i	−0.0573980	−	0.0994162i	0.835899	−	0.548884i	$-0.184947\pi$
$743$	−1.56456	−	2.70989i	−0.0573980	−	0.0994162i	−0.893297	+	0.449468i	$0.851614\pi$
$744$	3.76821	−	2.17558i	0.138149	−	0.0797605i
$745$	2.73774	+	9.11163i	0.100303	+	0.333824i
$746$	−29.3652	−	29.3652i	−1.07514	−	1.07514i
$747$	34.4268	+	19.8763i	1.25961	+	0.727236i
$748$	−0.213184	−	0.123082i	−0.00779478	−	0.00450032i
$749$	6.23310	+	6.23310i	0.227753	+	0.227753i
$750$	−3.28152	+	1.20550i	−0.119824	+	0.0440185i
$751$	6.28199	−	3.62691i	0.229233	−	0.132348i	−0.380985	−	0.924581i	$-0.624415\pi$
$751$	6.28199	−	3.62691i	0.229233	−	0.132348i	0.610218	+	0.792233i	$0.291082\pi$
$752$	21.7579	+	37.6858i	0.793430	+	1.37426i
$753$	1.38865	+	1.38865i	0.0506051	+	0.0506051i
$754$		0			0
$755$	−10.6098	+	11.2682i	−0.386131	+	0.410093i
$756$	0.0853627	−	0.318578i	0.00310461	−	0.0115866i
$757$	4.28134	−	15.9782i	0.155608	−	0.580737i	−0.843445	−	0.537216i	$-0.819476\pi$
$757$	4.28134	−	15.9782i	0.155608	−	0.580737i	0.999053	−	0.0435205i	$-0.0138574\pi$
$758$	−34.4882	+	9.24108i	−1.25267	+	0.335651i
$759$	0.0756220	−	0.0756220i	0.00274490	−	0.00274490i
$760$	23.0479	−	6.92511i	0.836034	−	0.251200i
$761$	5.99332	+	22.3674i	0.217258	+	0.810817i	0.985360	+	0.170489i	$0.0545348\pi$
$761$	5.99332	+	22.3674i	0.217258	+	0.810817i	−0.768102	+	0.640328i	$0.778799\pi$
$762$	−0.760555			−0.0275520
$763$	−1.64740	−	6.14819i	−0.0596400	−	0.222579i
$764$	−6.00431	−	10.3998i	−0.217228	−	0.376251i
$765$	4.77918	−	20.2549i	0.172792	−	0.732317i
$766$			38.2335i			1.38143i
$767$		0			0
$768$	−1.60998	+	1.60998i	−0.0580951	+	0.0580951i
$769$	5.69177	+	1.52511i	0.205251	+	0.0549967i	0.359979	−	0.932960i	$-0.382784\pi$
$769$	5.69177	+	1.52511i	0.205251	+	0.0549967i	−0.154729	+	0.987957i	$0.549450\pi$
$770$	−0.0683359	+	0.289618i	−0.00246266	+	0.0104371i
$771$	−0.470143	−	0.271437i	−0.0169318	−	0.00977557i
$772$		−	8.09938i		−	0.291503i
$773$	−4.04499	+	7.00612i	−0.145488	+	0.251993i	−0.929555	−	0.368684i	$-0.879809\pi$
$773$	−4.04499	+	7.00612i	−0.145488	+	0.251993i	0.784067	+	0.620676i	$0.213142\pi$
$774$	32.2274	−	8.63532i	1.15839	−	0.310390i
$775$	34.9776	+	31.0027i	1.25643	+	1.11365i
$776$	−8.93019	+	15.4675i	−0.320575	+	0.555252i
$777$	0.711294	+	0.190591i	0.0255175	+	0.00683740i
$778$	−19.6616	+	11.3516i	−0.704901	+	0.406975i
$779$	−16.3238			−0.584863
$780$		0			0
$781$	−2.39481			−0.0856930
$782$	15.2670	−	8.81441i	0.545947	−	0.315203i
$783$	−2.66148	−	0.713141i	−0.0951135	−	0.0254856i
$784$	−15.9487	+	27.6239i	−0.569595	+	0.986567i
$785$	5.29272	+	4.98347i	0.188905	+	0.177868i
$786$	−1.99554	+	0.534703i	−0.0711785	+	0.0190722i
$787$	−8.10582	+	14.0397i	−0.288941	+	0.500461i	−0.973557	−	0.228443i	$-0.926637\pi$
$787$	−8.10582	+	14.0397i	−0.288941	+	0.500461i	0.684616	+	0.728904i	$0.259970\pi$
$788$			2.92148i			0.104073i
$789$	1.05556	+	0.609429i	0.0375790	+	0.0216962i
$790$	−20.7561	−	33.5758i	−0.738467	−	1.19457i
$791$	−2.41401	−	0.646831i	−0.0858322	−	0.0229987i
$792$	0.756445	−	0.756445i	0.0268791	−	0.0268791i
$793$		0			0
$794$			53.0777i			1.88366i
$795$	−1.96875	+	1.21705i	−0.0698244	+	0.0431644i
$796$	2.37878	+	4.12017i	0.0843137	+	0.146036i
$797$	−4.31449	−	16.1019i	−0.152827	−	0.570358i	−0.999282	−	0.0378972i	$-0.987934\pi$
$797$	−4.31449	−	16.1019i	−0.152827	−	0.570358i	0.846455	−	0.532461i	$-0.178733\pi$
$798$	0.782216			0.0276901
$799$	7.43502	+	27.7479i	0.263032	+	0.981649i
$800$	−12.6453	−	6.31917i	−0.447078	−	0.223416i
$801$	19.0411	−	19.0411i	0.672783	−	0.672783i
$802$	28.3937	−	7.60807i	1.00262	−	0.268650i
$803$	0.155301	−	0.579592i	0.00548047	−	0.0204534i
$804$	−0.127715	+	0.476638i	−0.00450415	+	0.0168097i
$805$	−3.15933	−	2.97473i	−0.111352	−	0.104846i
$806$		0			0
$807$	−2.96103	−	2.96103i	−0.104233	−	0.104233i
$808$	−15.9651	−	27.6523i	−0.561649	−	0.972804i
$809$	−20.8943	+	12.0633i	−0.734603	+	0.424123i	−0.820104	−	0.572215i	$-0.806084\pi$
$809$	−20.8943	+	12.0633i	−0.734603	+	0.424123i	0.0855005	+	0.996338i	$0.472751\pi$
$810$	−26.9979	−	14.5224i	−0.948611	−	0.510267i
$811$	−17.7808	−	17.7808i	−0.624369	−	0.624369i	0.322276	−	0.946646i	$-0.395552\pi$
$811$	−17.7808	−	17.7808i	−0.624369	−	0.624369i	−0.946646	+	0.322276i	$0.895552\pi$
$812$	0.568894	+	0.328451i	0.0199642	+	0.0115264i
$813$	2.20171	+	1.27116i	0.0772173	+	0.0445815i
$814$	−1.16806	−	1.16806i	−0.0409403	−	0.0409403i
$815$	21.4027	+	11.5127i	0.749703	+	0.403272i
$816$	−2.55720	+	1.47640i	−0.0895200	+	0.0516844i
$817$	16.2190	+	28.0921i	0.567431	+	0.982819i
$818$	−5.79615	−	5.79615i	−0.202658	−	0.202658i
$819$		0			0
$820$	2.97887	+	2.80481i	0.104027	+	0.0979484i
$821$	−10.2562	+	38.2768i	−0.357945	+	1.33587i	0.518792	+	0.854901i	$0.326382\pi$
$821$	−10.2562	+	38.2768i	−0.357945	+	1.33587i	−0.876737	+	0.480970i	$0.840285\pi$
$822$	−0.328208	+	1.22489i	−0.0114476	+	0.0427229i
$823$	38.5831	−	10.3383i	1.34492	−	0.360371i	0.486664	−	0.873589i	$-0.338214\pi$
$823$	38.5831	−	10.3383i	1.34492	−	0.360371i	0.858258	+	0.513219i	$0.171547\pi$
$824$	−24.4316	+	24.4316i	−0.851116	+	0.851116i
$825$	−0.135152	−	0.0675387i	−0.00470537	−	0.00235140i
$826$	−0.856204	−	3.19540i	−0.0297912	−	0.111182i
$827$	−25.6019			−0.890264			−0.445132	−	0.895465i	$-0.646843\pi$
$827$	−25.6019			−0.890264			−0.445132	+	0.895465i	$0.646843\pi$
$828$	−1.38709	−	5.17670i	−0.0482048	−	0.179903i
$829$	−9.41684	−	16.3104i	−0.327060	−	0.566485i	0.654867	−	0.755744i	$-0.272725\pi$
$829$	−9.41684	−	16.3104i	−0.327060	−	0.566485i	−0.981927	+	0.189259i	$0.939391\pi$
$830$	40.4652	−	25.0150i	1.40457	−	0.868283i
$831$		−	4.19807i		−	0.145629i
$832$		0			0
$833$	−14.8894	+	14.8894i	−0.515888	+	0.515888i
$834$	3.87301	+	1.03777i	0.134111	+	0.0359351i
$835$	−19.2344	−	31.1142i	−0.665633	−	1.07675i
$836$	−0.309436	−	0.178653i	−0.0107021	−	0.00617885i
$837$		−	10.9949i		−	0.380040i
$838$	0.797879	−	1.38197i	0.0275623	−	0.0477393i
$839$	−24.0857	+	6.45374i	−0.831530	+	0.222808i	−0.649381	−	0.760463i	$-0.724972\pi$
$839$	−24.0857	+	6.45374i	−0.831530	+	0.222808i	−0.182149	+	0.983271i	$0.558305\pi$
$840$	0.415508	+	0.391229i	0.0143364	+	0.0134987i
$841$	−11.7560	+	20.3621i	−0.405381	+	0.702140i
$842$	0.638063	+	0.170969i	0.0219891	+	0.00589196i
$843$	1.02137	−	0.589688i	0.0351778	−	0.0203099i
$844$	2.80018			0.0963863
$845$		0			0
$846$	42.8875			1.47450
$847$	5.21239	−	3.00937i	0.179100	−	0.103403i
$848$	−24.1267	−	6.46474i	−0.828516	−	0.222000i
$849$	−0.151725	+	0.262795i	−0.00520717	+	0.00901909i
$850$	−18.6377	−	16.5197i	−0.639268	−	0.566621i
$851$	23.2682	−	6.23469i	0.797623	−	0.213722i
$852$	0.788935	−	1.36648i	0.0270285	−	0.0468147i
$853$			2.14143i			0.0733210i	0.999328	+	0.0366605i	$0.0116720\pi$
$853$			2.14143i			0.0733210i	−0.999328	+	0.0366605i	$0.988328\pi$
$854$	5.90721	+	3.41053i	0.202140	+	0.116706i
$855$	6.93697	−	29.3999i	0.237240	−	1.00546i
$856$	−36.6319	−	9.81549i	−1.25205	−	0.335487i
$857$	36.4384	−	36.4384i	1.24471	−	1.24471i	0.286686	−	0.958025i	$-0.407446\pi$
$857$	36.4384	−	36.4384i	1.24471	−	1.24471i	0.958025	−	0.286686i	$-0.0925537\pi$
$858$		0			0
$859$			4.40721i			0.150372i	0.997170	+	0.0751861i	$0.0239551\pi$
$859$			4.40721i			0.150372i	−0.997170	+	0.0751861i	$0.976045\pi$
$860$	1.86714	−	7.91321i	0.0636689	−	0.269838i
$861$	−0.193556	−	0.335249i	−0.00659637	−	0.0114252i
$862$	1.70278	+	6.35486i	0.0579969	+	0.216447i
$863$	−53.8912			−1.83448			−0.917239	−	0.398338i	$-0.869587\pi$
$863$	−53.8912			−1.83448			−0.917239	+	0.398338i	$0.869587\pi$
$864$	0.860671	+	3.21207i	0.0292806	+	0.109277i
$865$	−14.6344	+	4.39716i	−0.497586	+	0.149508i
$866$	−16.8033	+	16.8033i	−0.570998	+	0.570998i
$867$	1.35714	−	0.363644i	0.0460908	−	0.0123500i
$868$	−0.678436	+	2.53196i	−0.0230276	+	0.0859403i
$869$	0.441535	−	1.64783i	0.0149780	−	0.0558988i
$870$	−1.12283	+	1.19251i	−0.0380676	+	0.0404300i
$871$		0			0
$872$	19.3636	+	19.3636i	0.655733	+	0.655733i
$873$	11.2091	+	19.4148i	0.379372	+	0.657091i
$874$	22.1600	−	12.7941i	0.749574	−	0.432767i
$875$	−2.57424	+	5.56383i	−0.0870251	+	0.188092i
$876$	0.279553	+	0.279553i	0.00944522	+	0.00944522i
$877$	−11.3743	−	6.56696i	−0.384083	−	0.221750i	0.295510	−	0.955340i	$-0.404510\pi$
$877$	−11.3743	−	6.56696i	−0.384083	−	0.221750i	−0.679593	+	0.733589i	$0.737844\pi$
$878$	19.0519	+	10.9996i	0.642971	+	0.371220i
$879$	−0.389521	−	0.389521i	−0.0131382	−	0.0131382i
$880$	−0.469182	−	1.56151i	−0.0158161	−	0.0526386i
$881$	31.7049	−	18.3049i	1.06817	−	0.616706i	0.140486	−	0.990083i	$-0.455133\pi$
$881$	31.7049	−	18.3049i	1.06817	−	0.616706i	0.927680	+	0.373376i	$0.121800\pi$
$882$	15.7184	+	27.2250i	0.529265	+	0.916714i
$883$	−7.40474	−	7.40474i	−0.249189	−	0.249189i	0.571449	−	0.820638i	$-0.306382\pi$
$883$	−7.40474	−	7.40474i	−0.249189	−	0.249189i	−0.820638	+	0.571449i	$0.806382\pi$
$884$		0			0
$885$	1.67889	−	0.0505253i	0.0564354	−	0.00169839i
$886$	−5.83502	+	21.7766i	−0.196031	+	0.731599i
$887$	−14.1308	+	52.7370i	−0.474467	+	1.77074i	0.148948	+	0.988845i	$0.452411\pi$
$887$	−14.1308	+	52.7370i	−0.474467	+	1.77074i	−0.623416	+	0.781891i	$0.714255\pi$
$888$	−3.06017	+	0.819971i	−0.102693	+	0.0275164i
$889$	−0.943078	+	0.943078i	−0.0316298	+	0.0316298i
$890$	−9.27315	−	30.8625i	−0.310837	−	1.03451i
$891$	−0.342907	−	1.27975i	−0.0114878	−	0.0428731i
$892$	−9.49566			−0.317938
$893$	10.7919	+	40.2760i	0.361138	+	1.34779i
$894$	−0.665210	−	1.15218i	−0.0222479	−	0.0385346i
$895$	6.67128	+	10.7917i	0.222996	+	0.360727i
$896$			7.48186i			0.249951i
$897$		0			0
$898$	7.45887	−	7.45887i	0.248906	−	0.248906i
$899$	21.1526	+	5.66782i	0.705479	+	0.189032i
$900$	−6.31749	+	4.17314i	−0.210583	+	0.139105i
$901$	−14.2799	−	8.24448i	−0.475731	−	0.274664i
$902$			0.868379i			0.0289139i
$903$	−0.384625	+	0.666190i	−0.0127995	+	0.0221694i
$904$	10.3857	−	2.78284i	0.345423	−	0.0925558i
$905$	0.241550	+	8.02642i	0.00802940	+	0.266807i
$906$	1.08214	−	1.87433i	0.0359518	−	0.0622703i
$907$	39.5809	+	10.6057i	1.31426	+	0.352155i	0.846825	−	0.531871i	$-0.178511\pi$
$907$	39.5809	+	10.6057i	1.31426	+	0.352155i	0.467437	+	0.884027i	$0.345178\pi$
$908$	2.82853	−	1.63305i	0.0938680	−	0.0541947i
$909$	−40.0785			−1.32932
$910$		0			0
$911$	24.2232			0.802551			0.401276	−	0.915957i	$-0.368567\pi$
$911$	24.2232			0.802551			0.401276	+	0.915957i	$0.368567\pi$
$912$	−3.71178	+	2.14299i	−0.122909	+	0.0709616i
$913$	1.98595	+	0.532133i	0.0657253	+	0.0176110i
$914$	29.2849	−	50.7229i	0.968658	−	1.67777i
$915$	−2.37415	+	2.52148i	−0.0784869	+	0.0833575i
$916$	−7.76460	+	2.08052i	−0.256550	+	0.0687423i
$917$	−1.81141	+	3.13746i	−0.0598182	+	0.103608i
$918$			5.85860i			0.193363i
$919$	30.2077	+	17.4404i	0.996460	+	0.575307i	0.907199	−	0.420702i	$-0.138216\pi$
$919$	30.2077	+	17.4404i	0.996460	+	0.575307i	0.0892612	+	0.996008i	$0.471549\pi$
$920$	18.1703	+	4.28732i	0.599057	+	0.141349i
$921$	−0.404259	−	0.108321i	−0.0133208	−	0.00356929i
$922$	28.8290	−	28.8290i	0.949432	−	0.949432i
$923$		0			0
$924$		−	0.00847334i		−	0.000278753i
$925$	−18.7574	−	28.3958i	−0.616739	−	0.933647i
$926$	−12.6446	−	21.9012i	−0.415529	−	0.719717i
$927$	11.2247	+	41.8912i	0.368668	+	1.37589i
$928$	−6.62322			−0.217418
$929$	2.24604	+	8.38235i	0.0736903	+	0.275016i	0.992933	−	0.118675i	$-0.0378647\pi$
$929$	2.24604	+	8.38235i	0.0736903	+	0.275016i	−0.919243	+	0.393691i	$0.871198\pi$
$930$	−5.75606	−	3.09624i	−0.188749	−	0.101530i
$931$	−21.6120	+	21.6120i	−0.708304	+	0.708304i
$932$	4.09336	−	1.09681i	0.134083	−	0.0359273i
$933$	1.08599	−	4.05296i	0.0355536	−	0.132688i
$934$	−10.8040	+	40.3211i	−0.353518	+	1.31935i
$935$	−0.0323774	−	1.07586i	−0.00105885	−	0.0351844i
$936$		0			0
$937$	−25.8920	−	25.8920i	−0.845856	−	0.845856i	0.143757	−	0.989613i	$-0.454082\pi$
$937$	−25.8920	−	25.8920i	−0.845856	−	0.845856i	−0.989613	+	0.143757i	$0.954082\pi$
$938$	2.12474	+	3.68015i	0.0693751	+	0.120161i
$939$	−3.47178	+	2.00443i	−0.113297	+	0.0654122i
$940$	4.95098	−	9.20410i	0.161483	−	0.300205i
$941$	20.9205	+	20.9205i	0.681989	+	0.681989i	0.960448	−	0.278459i	$-0.0898236\pi$
$941$	20.9205	+	20.9205i	0.681989	+	0.681989i	−0.278459	+	0.960448i	$0.589824\pi$
$942$	−0.880376	−	0.508285i	−0.0286842	−	0.0165608i
$943$	−10.9668	−	6.33169i	−0.357128	−	0.206188i
$944$	12.8171	+	12.8171i	0.417162	+	0.417162i
$945$	1.38112	−	0.414980i	0.0449279	−	0.0134993i
$946$	1.49442	−	0.862801i	0.0485876	−	0.0280521i
$947$	−13.8023	−	23.9064i	−0.448516	−	0.776852i	0.549774	−	0.835314i	$-0.314714\pi$
$947$	−13.8023	−	23.9064i	−0.448516	−	0.776852i	−0.998290	+	0.0584612i	$0.981381\pi$
$948$	0.794793	+	0.794793i	0.0258137	+	0.0258137i
$949$		0			0
$950$	−27.0526	−	23.9783i	−0.877702	−	0.777960i
$951$	0.448880	−	1.67524i	0.0145559	−	0.0543235i
$952$	−1.05229	+	3.92719i	−0.0341048	+	0.127281i
$953$	−27.9135	+	7.47941i	−0.904208	+	0.242282i	−0.680822	−	0.732448i	$-0.738377\pi$
$953$	−27.9135	+	7.47941i	−0.904208	+	0.242282i	−0.223385	+	0.974730i	$0.571711\pi$
$954$	−17.4070	+	17.4070i	−0.563572	+	0.563572i
$955$	24.8740	−	46.2421i	0.804905	−	1.49636i
$956$	−2.58464	−	9.64602i	−0.0835933	−	0.311974i
$957$	−0.0707884			−0.00228826
$958$	−6.80864	−	25.4102i	−0.219977	−	0.820966i
$959$	1.11187	+	1.92582i	0.0359042	+	0.0621878i
$960$	−2.16511	−	0.510862i	−0.0698786	−	0.0164880i
$961$			56.3841i			1.81884i
$962$		0			0
$963$	−33.6599	+	33.6599i	−1.08467	+	1.08467i
$964$	−8.46323	−	2.26771i	−0.272582	−	0.0730382i
$965$	30.1233	−	18.6218i	0.969703	−	0.599456i
$966$	0.525514	+	0.303406i	0.0169081	+	0.00976192i
$967$		−	4.31688i		−	0.138822i	−0.997588	−	0.0694108i	$-0.977888\pi$
$967$		−	4.31688i		−	0.138822i	0.997588	−	0.0694108i	$-0.0221119\pi$
$968$	−12.9471	+	22.4250i	−0.416136	+	0.720768i
$969$	−2.73296	+	0.732295i	−0.0877954	+	0.0235247i
$970$	26.8163	−	0.807022i	0.861021	−	0.0259119i
$971$	6.77930	−	11.7421i	0.217558	−	0.376822i	−0.736503	−	0.676435i	$-0.763524\pi$
$971$	6.77930	−	11.7421i	0.217558	−	0.376822i	0.954061	+	0.299613i	$0.0968575\pi$
$972$	2.58618	+	0.692966i	0.0829519	+	0.0222269i
$973$	6.08930	−	3.51566i	0.195214	−	0.112707i
$974$	−41.6466			−1.33444
$975$		0			0
$976$	−37.3745			−1.19633
$977$	41.2668	−	23.8254i	1.32024	−	0.762242i	0.336475	−	0.941692i	$-0.390765\pi$
$977$	41.2668	−	23.8254i	1.32024	−	0.762242i	0.983767	+	0.179450i	$0.0574318\pi$
$978$	−3.28262	−	0.879575i	−0.104967	−	0.0281257i
$979$	0.696362	−	1.20613i	0.0222558	−	0.0385482i
$980$	7.65731	−	0.230442i	0.244604	−	0.00736121i
$981$	33.2013	−	8.89627i	1.06004	−	0.284036i
$982$	32.9657	−	57.0983i	1.05198	−	1.82208i
$983$			7.39039i			0.235717i	0.993030	+	0.117858i	$0.0376029\pi$
$983$			7.39039i			0.235717i	−0.993030	+	0.117858i	$0.962397\pi$
$984$	1.44233	+	0.832728i	0.0459797	+	0.0265464i
$985$	−10.8656	+	6.71696i	−0.346207	+	0.214020i
$986$	−11.2711	−	3.02008i	−0.358945	−	0.0961789i
$987$	−0.699200	+	0.699200i	−0.0222558	+	0.0222558i
$988$		0			0
$989$			25.1641i			0.800171i
$990$	−1.56399	−	0.369026i	−0.0497068	−	0.0117284i
$991$	−10.0052	−	17.3296i	−0.317827	−	0.550493i	0.662207	−	0.749321i	$-0.269620\pi$
$991$	−10.0052	−	17.3296i	−0.317827	−	0.550493i	−0.980034	+	0.198828i	$0.936287\pi$
$992$	−6.84035	−	25.5285i	−0.217181	−	0.810531i
$993$	−3.58541			−0.113780
$994$	−3.51688	−	13.1252i	−0.111549	−	0.416306i
$995$	−9.85458	+	18.3201i	−0.312411	+	0.580787i
$996$	−0.957877	+	0.957877i	−0.0303515	+	0.0303515i
$997$	−32.6705	+	8.75402i	−1.03468	+	0.277243i	−0.735909	−	0.677081i	$-0.763245\pi$
$997$	−32.6705	+	8.75402i	−1.03468	+	0.277243i	−0.298775	+	0.954324i	$0.596578\pi$
$998$	−4.82403	+	18.0035i	−0.152702	+	0.569892i
$999$	−2.07198	+	7.73273i	−0.0655545	+	0.244653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.t.g.427.2		20
5.3	odd	4		845.2.o.g.258.4		20
13.2	odd	12		845.2.k.d.577.4		20
13.3	even	3		845.2.f.d.437.4		20
13.4	even	6		845.2.t.f.657.2		20
13.5	odd	4		845.2.o.f.587.4		20
13.6	odd	12		845.2.o.g.357.4		20
13.7	odd	12		65.2.o.a.32.2	✓	20
13.8	odd	4		845.2.o.e.587.2		20
13.9	even	3		845.2.t.e.657.4		20
13.10	even	6		845.2.f.e.437.7		20
13.11	odd	12		845.2.k.e.577.7		20
13.12	even	2		65.2.t.a.37.4	yes	20
39.20	even	12		585.2.cf.a.487.4		20
39.38	odd	2		585.2.dp.a.37.2		20
65.3	odd	12		845.2.k.d.268.4		20
65.7	even	12		325.2.x.b.318.2		20
65.8	even	4		845.2.t.f.418.2		20
65.12	odd	4		325.2.s.b.193.4		20
65.18	even	4		845.2.t.e.418.4		20
65.23	odd	12		845.2.k.e.268.7		20
65.28	even	12		845.2.f.d.408.7		20
65.33	even	12		65.2.t.a.58.4	yes	20
65.38	odd	4		65.2.o.a.63.2	yes	20
65.43	odd	12		845.2.o.e.488.2		20
65.48	odd	12		845.2.o.f.488.4		20
65.58	even	12	inner	845.2.t.g.188.2		20
65.59	odd	12		325.2.s.b.32.4		20
65.63	even	12		845.2.f.e.408.4		20
65.64	even	2		325.2.x.b.232.2		20
195.38	even	4		585.2.cf.a.388.4		20
195.98	odd	12		585.2.dp.a.253.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.2	✓	20	13.7	odd	12
65.2.o.a.63.2	yes	20	65.38	odd	4
65.2.t.a.37.4	yes	20	13.12	even	2
65.2.t.a.58.4	yes	20	65.33	even	12
325.2.s.b.32.4		20	65.59	odd	12
325.2.s.b.193.4		20	65.12	odd	4
325.2.x.b.232.2		20	65.64	even	2
325.2.x.b.318.2		20	65.7	even	12
585.2.cf.a.388.4		20	195.38	even	4
585.2.cf.a.487.4		20	39.20	even	12
585.2.dp.a.37.2		20	39.38	odd	2
585.2.dp.a.253.2		20	195.98	odd	12
845.2.f.d.408.7		20	65.28	even	12
845.2.f.d.437.4		20	13.3	even	3
845.2.f.e.408.4		20	65.63	even	12
845.2.f.e.437.7		20	13.10	even	6
845.2.k.d.268.4		20	65.3	odd	12
845.2.k.d.577.4		20	13.2	odd	12
845.2.k.e.268.7		20	65.23	odd	12
845.2.k.e.577.7		20	13.11	odd	12
845.2.o.e.488.2		20	65.43	odd	12
845.2.o.e.587.2		20	13.8	odd	4
845.2.o.f.488.4		20	65.48	odd	12
845.2.o.f.587.4		20	13.5	odd	4
845.2.o.g.258.4		20	5.3	odd	4
845.2.o.g.357.4		20	13.6	odd	12
845.2.t.e.418.4		20	65.18	even	4
845.2.t.e.657.4		20	13.9	even	3
845.2.t.f.418.2		20	65.8	even	4
845.2.t.f.657.2		20	13.4	even	6
845.2.t.g.188.2		20	65.58	even	12	inner
845.2.t.g.427.2		20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.t (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.37242 + 0.792369i) q^{2} +(0.190588 + 0.0510678i) q^{3} +(0.255697 - 0.442881i) q^{4} +(2.23506 - 0.0672627i) q^{5} +(-0.302032 + 0.0809291i) q^{6} +(-0.274164 + 0.474866i) q^{7} -2.35905i q^{8} +(-2.56436 - 1.48053i) q^{9} +(-3.01415 + 1.86330i) q^{10} +(-0.147928 - 0.0396372i) q^{11} +(0.0713497 - 0.0713497i) q^{12} -0.868956i q^{14} +(0.429409 + 0.101320i) q^{15} +(2.38063 + 4.12338i) q^{16} +(0.813499 + 3.03602i) q^{17} +4.69252 q^{18} +(1.18079 + 4.40678i) q^{19} +(0.541709 - 1.00706i) q^{20} +(-0.0765027 + 0.0765027i) q^{21} +(0.234427 - 0.0628146i) q^{22} +(-0.916011 + 3.41860i) q^{23} +(0.120472 - 0.449606i) q^{24} +(4.99095 - 0.300672i) q^{25} +(-0.831688 - 0.831688i) q^{27} +(0.140206 + 0.242844i) q^{28} +(2.02878 - 1.17132i) q^{29} +(-0.669614 + 0.201197i) q^{30} +(6.61000 + 6.61000i) q^{31} +(-2.44848 - 1.41363i) q^{32} +(-0.0261691 - 0.0151087i) q^{33} +(-3.52211 - 3.52211i) q^{34} +(-0.580831 + 1.07979i) q^{35} +(-1.31140 + 0.757137i) q^{36} +(-3.40317 - 5.89447i) q^{37} +(-5.11234 - 5.11234i) q^{38} +(-0.158676 - 5.27261i) q^{40} +(-0.926064 + 3.45612i) q^{41} +(0.0443757 - 0.165612i) q^{42} +(6.86784 - 1.84023i) q^{43} +(-0.0553794 + 0.0553794i) q^{44} +(-5.83107 - 3.13659i) q^{45} +(-1.45164 - 5.41759i) q^{46} +9.13956 q^{47} +(0.243147 + 0.907439i) q^{48} +(3.34967 + 5.80180i) q^{49} +(-6.61146 + 4.36732i) q^{50} +0.620172i q^{51} +(-3.70952 + 3.70952i) q^{53} +(1.80043 + 0.482424i) q^{54} +(-0.333294 - 0.0786414i) q^{55} +(1.12023 + 0.646766i) q^{56} +0.900179i q^{57} +(-1.85623 + 3.21508i) q^{58} +(3.67728 - 0.985325i) q^{59} +(0.154672 - 0.164270i) q^{60} +(-3.92486 + 6.79805i) q^{61} +(-14.3093 - 3.83416i) q^{62} +(1.40611 - 0.811818i) q^{63} -5.04207 q^{64} +0.0478868 q^{66} +(-4.23514 + 2.44516i) q^{67} +(1.55261 + 0.416019i) q^{68} +(-0.349161 + 0.604765i) q^{69} +(-0.0584483 - 1.94217i) q^{70} +(15.1045 - 4.04725i) q^{71} +(-3.49265 + 6.04945i) q^{72} +3.91807i q^{73} +(9.34119 + 5.39314i) q^{74} +(0.966569 + 0.197573i) q^{75} +(2.25360 + 0.603851i) q^{76} +(0.0593789 - 0.0593789i) q^{77} +11.1394i q^{79} +(5.59820 + 9.05585i) q^{80} +(4.32557 + 7.49210i) q^{81} +(-1.46757 - 5.47704i) q^{82} -13.4251 q^{83} +(0.0143200 + 0.0534431i) q^{84} +(2.02243 + 6.73096i) q^{85} +(-7.96744 + 7.96744i) q^{86} +(0.446477 - 0.119633i) q^{87} +(-0.0935062 + 0.348970i) q^{88} +(-2.35372 + 8.78419i) q^{89} +(10.4880 - 0.315631i) q^{90} +(1.27981 + 1.27981i) q^{92} +(0.922226 + 1.59734i) q^{93} +(-12.5433 + 7.24190i) q^{94} +(2.93555 + 9.76998i) q^{95} +(-0.394459 - 0.394459i) q^{96} +(-6.55668 - 3.78550i) q^{97} +(-9.19433 - 5.30835i) q^{98} +(0.320657 + 0.320657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 8 q^{6} + 2 q^{7} + 12 q^{9} - 2 q^{10} + 16 q^{11} - 24 q^{12} + 20 q^{15} - 2 q^{16} + 4 q^{17} + 20 q^{19} - 4 q^{21} + 16 q^{22} - 10 q^{23} - 32 q^{24} + 18 q^{25}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 8 * q^6 + 2 * q^7 + 12 * q^9 - 2 * q^10 + 16 * q^11 - 24 * q^12 + 20 * q^15 - 2 * q^16 + 4 * q^17 + 20 * q^19 - 4 * q^21 + 16 * q^22 - 10 * q^23 - 32 * q^24 + 18 * q^25 + 4 * q^27 - 18 * q^28 - 26 * q^30 - 48 * q^32 - 18 * q^33 - 2 * q^34 + 40 * q^35 + 36 * q^36 + 4 * q^37 - 8 * q^38 - 16 * q^40 - 10 * q^41 + 40 * q^42 + 10 * q^43 + 36 * q^44 - 4 * q^46 + 40 * q^47 - 56 * q^48 + 18 * q^49 - 36 * q^50 - 10 * q^53 + 48 * q^54 - 10 * q^55 + 16 * q^59 - 28 * q^60 - 16 * q^61 - 44 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 + 22 * q^68 - 16 * q^69 + 12 * q^70 + 16 * q^71 - 4 * q^72 + 18 * q^74 - 38 * q^75 + 64 * q^76 - 28 * q^77 + 2 * q^80 - 14 * q^81 + 56 * q^82 - 48 * q^83 + 40 * q^84 + 26 * q^85 - 60 * q^86 - 34 * q^87 + 82 * q^88 + 6 * q^89 + 46 * q^90 - 8 * q^92 - 32 * q^93 - 48 * q^94 - 26 * q^95 - 56 * q^96 - 66 * q^97 + 30 * q^98 - 60 * q^99

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