LMFDB - Embedded newform 845.2.t.e.657.4

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			657.4
Root			$1.58474i$ of defining polynomial
Character	$\chi$	$=$	845.657
Dual form			845.2.t.e.418.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.37242 + 0.792369i) q^{2} +(-0.0510678 - 0.190588i) q^{3} +(0.255697 + 0.442881i) q^{4} +(2.23506 - 0.0672627i) q^{5} +(0.0809291 - 0.302032i) q^{6} +(-0.274164 - 0.474866i) q^{7} -2.35905i q^{8} +(2.56436 - 1.48053i) q^{9} +(3.12074 + 1.67868i) q^{10} +(0.0396372 + 0.147928i) q^{11} +(0.0713497 - 0.0713497i) q^{12} -0.868956i q^{14} +(-0.126959 - 0.422539i) q^{15} +(2.38063 - 4.12338i) q^{16} +(-3.03602 - 0.813499i) q^{17} +4.69252 q^{18} +(-4.40678 - 1.18079i) q^{19} +(0.601287 + 0.972665i) q^{20} +(-0.0765027 + 0.0765027i) q^{21} +(-0.0628146 + 0.234427i) q^{22} +(3.41860 - 0.916011i) q^{23} +(-0.449606 + 0.120472i) 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} +(0.160566 - 0.680501i) 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} +(-0.644713 - 1.04291i) 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} +(3.45612 - 0.926064i) q^{41} +(-0.165612 + 0.0443757i) q^{42} +(-1.84023 + 6.86784i) q^{43} +(-0.0553794 + 0.0553794i) q^{44} +(5.63190 - 3.48156i) q^{45} +(5.41759 + 1.45164i) q^{46} +9.13956 q^{47} +(-0.907439 - 0.243147i) q^{48} +(3.34967 - 5.80180i) q^{49} +(7.08794 + 3.54203i) q^{50} +0.620172i q^{51} +(-3.70952 + 3.70952i) q^{53} +(-0.482424 - 1.80043i) q^{54} +(0.0985415 + 0.327962i) q^{55} +(-1.12023 + 0.646766i) q^{56} +0.900179i q^{57} +(-1.85623 - 3.21508i) q^{58} +(-0.985325 + 3.67728i) q^{59} +(0.154672 - 0.164270i) q^{60} +(-3.92486 - 6.79805i) q^{61} +(3.83416 + 14.3093i) q^{62} +(-1.40611 - 0.811818i) q^{63} -5.04207 q^{64} +0.0478868 q^{66} +(4.23514 + 2.44516i) q^{67} +(-0.416019 - 1.55261i) q^{68} +(-0.349161 - 0.604765i) q^{69} +(-0.0584483 - 1.94217i) q^{70} +(-4.04725 + 15.1045i) q^{71} +(-3.49265 - 6.04945i) q^{72} +3.91807i q^{73} +(-9.34119 + 5.39314i) q^{74} +(-0.312181 - 0.935860i) q^{75} +(-0.603851 - 2.25360i) q^{76} +(0.0593789 - 0.0593789i) q^{77} +11.1394i q^{79} +(5.04350 - 9.37611i) q^{80} +(4.32557 - 7.49210i) q^{81} +(5.47704 + 1.46757i) q^{82} -13.4251 q^{83} +(-0.0534431 - 0.0143200i) q^{84} +(-6.84039 - 1.61401i) q^{85} +(-7.96744 + 7.96744i) q^{86} +(-0.119633 + 0.446477i) q^{87} +(0.348970 - 0.0935062i) q^{88} +(8.78419 - 2.35372i) 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} +(-9.92882 - 2.34273i) 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} - 4 q^{6} + 2 q^{7} - 12 q^{9} + 10 q^{10} - 8 q^{11} - 24 q^{12} + 8 q^{15} - 2 q^{16} + 10 q^{17} - 16 q^{19} - 12 q^{20} - 4 q^{21} + 16 q^{22} + 2 q^{23} + 28 q^{24}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 4 * q^6 + 2 * q^7 - 12 * q^9 + 10 * q^10 - 8 * q^11 - 24 * q^12 + 8 * q^15 - 2 * q^16 + 10 * q^17 - 16 * q^19 - 12 * q^20 - 4 * q^21 + 16 * q^22 + 2 * q^23 + 28 * q^24 + 18 * q^25 + 4 * q^27 - 18 * q^28 - 14 * q^30 + 48 * q^32 + 18 * q^33 - 2 * q^34 - 20 * q^35 - 36 * q^36 + 4 * q^37 - 8 * q^38 - 16 * q^40 - 28 * q^41 - 56 * q^42 + 22 * q^43 + 36 * q^44 - 6 * q^45 + 8 * q^46 + 40 * q^47 + 28 * q^48 + 18 * q^49 + 78 * q^50 - 10 * q^53 - 12 * q^54 + 26 * q^55 - 8 * q^59 - 28 * q^60 - 16 * q^61 + 40 * q^62 - 36 * q^63 + 20 * q^64 - 32 * q^66 + 18 * q^67 + 28 * q^68 - 16 * q^69 + 12 * q^70 - 56 * q^71 - 4 * q^72 - 18 * q^74 + 34 * q^75 - 80 * q^76 - 28 * q^77 + 110 * q^80 - 14 * q^81 - 22 * q^82 - 48 * q^83 - 32 * q^84 - 28 * q^85 - 60 * q^86 + 62 * q^87 - 50 * q^88 + 6 * q^89 + 46 * q^90 - 8 * q^92 - 32 * q^93 + 48 * q^94 - 14 * 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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{4}\right)$

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	$-0.144023\pi$
$2$	1.37242	+	0.792369i	0.970450	+	0.560290i	0.0710765	+	0.997471i	$0.477357\pi$
$3$	−0.0510678	−	0.190588i	−0.0294840	−	0.110036i	0.949616	−	0.313417i	$-0.101474\pi$
$3$	−0.0510678	−	0.190588i	−0.0294840	−	0.110036i	−0.979100	+	0.203381i	$0.934807\pi$
$4$	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
$6$	0.0809291	−	0.302032i	0.0330392	−	0.123304i
$7$	−0.274164	−	0.474866i	−0.103624	−	0.179482i	0.809551	−	0.587049i	$-0.199711\pi$
$7$	−0.274164	−	0.474866i	−0.103624	−	0.179482i	−0.913175	+	0.407567i	$0.866377\pi$
$8$		−	2.35905i		−	0.834050i
$9$	2.56436	−	1.48053i	0.854787	−	0.493511i
$10$	3.12074	+	1.67868i	0.986865	+	0.530844i
$11$	0.0396372	+	0.147928i	0.0119511	+	0.0446020i	0.971644	−	0.236449i	$-0.0759836\pi$
$11$	0.0396372	+	0.147928i	0.0119511	+	0.0446020i	−0.959693	+	0.281051i	$0.909317\pi$
$12$	0.0713497	−	0.0713497i	0.0205969	−	0.0205969i
$13$		0			0
$13$		0			0
$14$		−	0.868956i		−	0.232238i
$15$	−0.126959	−	0.422539i	−0.0327807	−	0.109099i
$16$	2.38063	−	4.12338i	0.595158	−	1.03084i
$17$	−3.03602	−	0.813499i	−0.736343	−	0.197303i	−0.128891	−	0.991659i	$-0.541142\pi$
$17$	−3.03602	−	0.813499i	−0.736343	−	0.197303i	−0.607452	+	0.794356i	$0.707808\pi$
$18$	4.69252			1.10604
$19$	−4.40678	−	1.18079i	−1.01098	−	0.270893i	−0.284944	−	0.958544i	$-0.591975\pi$
$19$	−4.40678	−	1.18079i	−1.01098	−	0.270893i	−0.726041	+	0.687652i	$0.758642\pi$
$20$	0.601287	+	0.972665i	0.134452	+	0.217494i
$21$	−0.0765027	+	0.0765027i	−0.0166942	+	0.0166942i
$22$	−0.0628146	+	0.234427i	−0.0133921	+	0.0499801i
$23$	3.41860	−	0.916011i	0.712828	−	0.191002i	0.115858	−	0.993266i	$-0.463038\pi$
$23$	3.41860	−	0.916011i	0.712828	−	0.191002i	0.596969	+	0.802264i	$0.296371\pi$
$24$	−0.449606	+	0.120472i	−0.0917754	+	0.0245912i
$25$	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	$-0.403126\pi$
$29$	−2.02878	−	1.17132i	−0.376735	−	0.217508i	−0.676397	+	0.736538i	$0.736459\pi$
$30$	0.160566	−	0.680501i	0.0293152	−	0.124242i
$31$	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
$35$	−0.644713	−	1.04291i	−0.108976	−	0.176284i
$36$	1.31140	+	0.757137i	0.218567	+	0.126190i
$37$	−3.40317	+	5.89447i	−0.559478	+	0.969045i	0.438062	+	0.898945i	$0.355665\pi$
$37$	−3.40317	+	5.89447i	−0.559478	+	0.969045i	−0.997540	+	0.0700997i	$0.977668\pi$
$38$	−5.11234	−	5.11234i	−0.829332	−	0.829332i
$39$		0			0
$40$	−0.158676	−	5.27261i	−0.0250889	−	0.833672i
$41$	3.45612	−	0.926064i	0.539755	−	0.144627i	0.0213659	−	0.999772i	$-0.493199\pi$
$41$	3.45612	−	0.926064i	0.539755	−	0.144627i	0.518389	+	0.855145i	$0.326532\pi$
$42$	−0.165612	+	0.0443757i	−0.0255545	+	0.00684732i
$43$	−1.84023	+	6.86784i	−0.280633	+	1.04734i	0.671339	+	0.741150i	$0.265719\pi$
$43$	−1.84023	+	6.86784i	−0.280633	+	1.04734i	−0.951972	+	0.306185i	$0.900947\pi$
$44$	−0.0553794	+	0.0553794i	−0.00834876	+	0.00834876i
$45$	5.63190	−	3.48156i	0.839555	−	0.519001i
$46$	5.41759	+	1.45164i	0.798780	+	0.214032i
$47$	9.13956			1.33314			0.666571	−	0.745442i	$-0.267761\pi$
$47$	9.13956			1.33314			0.666571	+	0.745442i	$0.267761\pi$
$48$	−0.907439	−	0.243147i	−0.130978	−	0.0350953i
$49$	3.34967	−	5.80180i	0.478524	−	0.828828i
$50$	7.08794	+	3.54203i	1.00239	+	0.500918i
$51$			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	$0.367326\pi$
$54$	−0.482424	−	1.80043i	−0.0656496	−	0.245008i
$55$	0.0985415	+	0.327962i	0.0132873	+	0.0442223i
$56$	−1.12023	+	0.646766i	−0.149697	+	0.0864278i
$57$			0.900179i			0.119232i
$58$	−1.85623	−	3.21508i	−0.243735	−	0.422161i
$59$	−0.985325	+	3.67728i	−0.128278	+	0.478742i	−0.999935	−	0.0113750i	$-0.996379\pi$
$59$	−0.985325	+	3.67728i	−0.128278	+	0.478742i	0.871657	+	0.490117i	$0.163046\pi$
$60$	0.154672	−	0.164270i	0.0199680	−	0.0212071i
$61$	−3.92486	−	6.79805i	−0.502526	−	0.870401i	−0.999996	−	0.00291945i	$-0.999071\pi$
$61$	−3.92486	−	6.79805i	−0.502526	−	0.870401i	0.497470	−	0.867481i	$-0.334263\pi$
$62$	3.83416	+	14.3093i	0.486939	+	1.81728i
$63$	−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	$-0.236772\pi$
$67$	4.23514	+	2.44516i	0.517405	+	0.298724i	−0.218467	+	0.975844i	$0.570106\pi$
$68$	−0.416019	−	1.55261i	−0.0504497	−	0.188281i
$69$	−0.349161	−	0.604765i	−0.0420341	−	0.0728051i
$70$	−0.0584483	−	1.94217i	−0.00698591	−	0.232133i
$71$	−4.04725	+	15.1045i	−0.480320	+	1.79258i	0.119947	+	0.992780i	$0.461727\pi$
$71$	−4.04725	+	15.1045i	−0.480320	+	1.79258i	−0.600267	+	0.799799i	$0.704939\pi$
$72$	−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
$75$	−0.312181	−	0.935860i	−0.0360476	−	0.108064i
$76$	−0.603851	−	2.25360i	−0.0692665	−	0.258506i
$77$	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	$0.784430\pi$
$80$	5.04350	−	9.37611i	0.563880	−	1.04828i
$81$	4.32557	−	7.49210i	0.480618	−	0.832455i
$82$	5.47704	+	1.46757i	0.604838	+	0.162066i
$83$	−13.4251			−1.47360			−0.736798	−	0.676113i	$-0.763663\pi$
$83$	−13.4251			−1.47360			−0.736798	+	0.676113i	$0.763663\pi$
$84$	−0.0534431	−	0.0143200i	−0.00583112	−	0.00156244i
$85$	−6.84039	−	1.61401i	−0.741945	−	0.175063i
$86$	−7.96744	+	7.96744i	−0.859151	+	0.859151i
$87$	−0.119633	+	0.446477i	−0.0128260	+	0.0478673i
$88$	0.348970	−	0.0935062i	0.0372003	−	0.00996779i
$89$	8.78419	−	2.35372i	0.931122	−	0.249493i	0.238789	−	0.971071i	$-0.423250\pi$
$89$	8.78419	−	2.35372i	0.931122	−	0.249493i	0.692333	+	0.721578i	$0.256583\pi$
$90$	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
$95$	−9.92882	−	2.34273i	−1.01868	−	0.240359i
$96$	−0.394459	−	0.394459i	−0.0402593	−	0.0402593i
$97$	6.55668	−	3.78550i	0.665730	−	0.384360i	−0.128727	−	0.991680i	$-0.541089\pi$
$97$	6.55668	−	3.78550i	0.665730	−	0.384360i	0.794457	+	0.607321i	$0.207756\pi$
$98$	9.19433	−	5.30835i	0.928767	−	0.536224i
$99$	0.320657	+	0.320657i	0.0322272	+	0.0322272i
$100$	1.40933	+	2.13352i	0.140933	+	0.213352i
$101$	−11.7218	−	6.76758i	−1.16636	−	0.673400i	−0.213542	−	0.976934i	$-0.568500\pi$
$101$	−11.7218	−	6.76758i	−1.16636	−	0.673400i	−0.952821	+	0.303534i	$0.901833\pi$
$102$	−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
$106$	−8.03034	+	2.15172i	−0.779975	+	0.208994i
$107$	−15.5283	+	4.16078i	−1.50117	+	0.402238i	−0.913493	−	0.406855i	$-0.866625\pi$
$107$	−15.5283	+	4.16078i	−1.50117	+	0.402238i	−0.587680	+	0.809093i	$0.699959\pi$
$108$	0.155678	−	0.580999i	0.0149801	−	0.0559066i
$109$	−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	$0.437638\pi$
$110$	−0.124626	+	0.528183i	−0.0118826	+	0.0503603i
$111$	1.29721	+	0.347585i	0.123125	+	0.0329913i
$112$	−2.61073			−0.246691
$113$	−4.40249	−	1.17964i	−0.414151	−	0.110972i	0.0457259	−	0.998954i	$-0.485440\pi$
$113$	−4.40249	−	1.17964i	−0.414151	−	0.110972i	−0.459877	+	0.887982i	$0.652107\pi$
$114$	−0.713274	+	1.23543i	−0.0668042	+	0.115708i
$115$	7.57915	−	2.27728i	0.706760	−	0.212358i
$116$		−	1.19801i		−	0.111232i
$117$		0			0
$118$	−4.26605	+	4.26605i	−0.392722	+	0.392722i
$119$	0.446064	+	1.66473i	0.0408907	+	0.152606i
$120$	−0.996791	+	0.299502i	−0.0909942	+	0.0273407i
$121$	9.50597	−	5.48827i	0.864179	−	0.498934i
$122$		−	12.4397i		−	1.12624i
$123$	−0.352993	−	0.611402i	−0.0318283	−	0.0551283i
$124$	−1.23728	+	4.61760i	−0.111111	+	0.414673i
$125$	11.1348	−	1.00772i	0.995930	−	0.0901335i
$126$	−1.28652	−	2.22832i	−0.114612	−	0.198514i
$127$	−0.629533	−	2.34945i	−0.0558620	−	0.208480i	0.932354	−	0.361547i	$-0.117751\pi$
$127$	−0.629533	−	2.34945i	−0.0558620	−	0.208480i	−0.988216	+	0.153068i	$0.951085\pi$
$128$	−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
$133$	0.647462	+	2.41636i	0.0561421	+	0.209525i
$134$	3.87494	+	6.71159i	0.334744	+	0.579793i
$135$	−1.91481	−	1.80293i	−0.164801	−	0.155171i
$136$	−1.91909	+	7.16212i	−0.164560	+	0.614147i
$137$	2.02775	+	3.51216i	0.173242	+	0.300064i	0.939552	−	0.342408i	$-0.111242\pi$
$137$	2.02775	+	3.51216i	0.173242	+	0.300064i	−0.766309	+	0.642472i	$0.777909\pi$
$138$		−	1.10666i		−	0.0942050i
$139$	11.1052	−	6.41160i	0.941932	−	0.543825i	0.0513668	−	0.998680i	$-0.483642\pi$
$139$	11.1052	−	6.41160i	0.941932	−	0.543825i	0.890566	+	0.454855i	$0.150309\pi$
$140$	0.297034	−	0.552200i	0.0251039	−	0.0466695i
$141$	−0.466737	−	1.74189i	−0.0393064	−	0.146693i
$142$	−17.5229	+	17.5229i	−1.47049	+	1.47049i
$143$		0			0
$144$		−	14.0984i		−	1.17487i
$145$	−4.61322	−	2.48149i	−0.383107	−	0.206077i
$146$	−3.10455	+	5.37725i	−0.256935	+	0.445024i
$147$	−1.27681	−	0.342121i	−0.105310	−	0.0282176i
$148$	−3.48073			−0.286114
$149$	−4.10983	−	1.10123i	−0.336690	−	0.0902159i	0.0865128	−	0.996251i	$-0.472428\pi$
$149$	−4.10983	−	1.10123i	−0.336690	−	0.0902159i	−0.423203	+	0.906035i	$0.639094\pi$
$150$	0.313101	−	1.53176i	0.0255646	−	0.125068i
$151$	−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	$0.340877\pi$
$152$	−2.78555	+	10.3958i	−0.225938	+	0.843212i
$153$	−8.98987	+	2.40883i	−0.726788	+	0.194742i
$154$	0.128543	−	0.0344430i	0.0103583	−	0.00277550i
$155$	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
$160$	5.37740	−	3.32423i	0.425121	−	0.262804i
$161$	−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	$-0.806618\pi$
$163$	−9.41236	+	5.43423i	−0.737233	+	0.425642i	0.0838295	+	0.996480i	$0.473285\pi$
$164$	1.29386	+	1.29386i	0.101033	+	0.101033i
$165$	0.0574732	−	0.0355291i	0.00447428	−	0.00276594i
$166$	−18.4249	−	10.6376i	−1.43005	−	0.825640i
$167$	−8.17941	+	14.1672i	−0.632942	+	1.09629i	0.354005	+	0.935243i	$0.384819\pi$
$167$	−8.17941	+	14.1672i	−0.632942	+	1.09629i	−0.986947	+	0.161044i	$0.948514\pi$
$168$	0.180474	+	0.180474i	0.0139238	+	0.0139238i
$169$		0			0
$170$	−8.10903	−	7.63522i	−0.621934	−	0.585594i
$171$	−13.0488	+	3.49641i	−0.997865	+	0.267377i
$172$	−3.51218	+	0.941085i	−0.267801	+	0.0717570i
$173$	1.76871	−	6.60091i	0.134472	−	0.501858i	−0.865527	−	0.500862i	$-0.833016\pi$
$173$	1.76871	−	6.60091i	0.134472	−	0.501858i	1.00000		0.000995657i	$-0.000316928\pi$
$174$	−0.517961	+	0.517961i	−0.0392666	+	0.0392666i
$175$	−1.51112	−	2.28760i	−0.114230	−	0.172926i
$176$	0.704325	+	0.188723i	0.0530905	+	0.0142256i
$177$	0.751164			0.0564609
$178$	13.9206	+	3.73002i	1.04340	+	0.279577i
$179$	2.83696	−	4.91376i	0.212044	−	0.367272i	−0.740310	−	0.672266i	$-0.765321\pi$
$179$	2.83696	−	4.91376i	0.212044	−	0.367272i	0.952354	+	0.304994i	$0.0986545\pi$
$180$	2.98198	+	1.60404i	0.222264	+	0.119558i
$181$			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
$184$	−2.16092	−	8.06465i	−0.159305	−	0.594534i
$185$	−7.20980	+	13.4034i	−0.530075	+	0.985436i
$186$	2.53137	−	1.46149i	0.185609	−	0.107161i
$187$		−	0.481358i		−	0.0352004i
$188$	2.33696	+	4.04773i	0.170440	+	0.295211i
$189$	−0.166921	+	0.622959i	−0.0121417	+	0.0453136i
$190$	−11.7702	−	11.0825i	−0.853903	−	0.804009i
$191$	11.7411	+	20.3361i	0.849553	+	1.47147i	0.881608	+	0.471982i	$0.156461\pi$
$191$	11.7411	+	20.3361i	0.849553	+	1.47147i	−0.0320553	+	0.999486i	$0.510205\pi$
$192$	0.257487	+	0.960956i	0.0185825	+	0.0693510i
$193$	−13.7160	−	7.91891i	−0.987296	−	0.570016i	−0.0828311	−	0.996564i	$-0.526396\pi$
$193$	−13.7160	−	7.91891i	−0.987296	−	0.570016i	−0.904465	+	0.426548i	$0.859730\pi$
$194$	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	$-0.268099\pi$
$197$	4.94741	+	2.85639i	0.352488	+	0.203509i	−0.313292	+	0.949657i	$0.601432\pi$
$198$	0.185998	+	0.694156i	0.0132183	+	0.0493315i
$199$	−4.65156	−	8.05674i	−0.329740	−	0.571127i	0.652720	−	0.757599i	$-0.273628\pi$
$199$	−4.65156	−	8.05674i	−0.329740	−	0.571127i	−0.982460	+	0.186472i	$0.940295\pi$
$200$	−0.709299	−	11.7739i	−0.0501550	−	0.832541i
$201$	0.249738	−	0.932035i	0.0176152	−	0.0657407i
$202$	−10.7248	−	18.5760i	−0.754597	−	1.30700i
$203$			1.28453i			0.0901563i
$204$	−0.274662	+	0.158576i	−0.0192302	+	0.0111026i
$205$	7.66233	−	2.30227i	0.535160	−	0.160798i
$206$	−6.00737	−	22.4198i	−0.418553	−	1.56206i
$207$	7.41034	−	7.41034i	0.515054	−	0.515054i
$208$		0			0
$209$		−	0.698690i		−	0.0483294i
$210$	−0.367168	+	0.110322i	−0.0253370	+	0.00761292i
$211$	2.73779	−	4.74199i	0.188477	−	0.326452i	−0.756265	−	0.654265i	$-0.772978\pi$
$211$	2.73779	−	4.74199i	0.188477	−	0.326452i	0.944743	+	0.327813i	$0.106311\pi$
$212$	−2.59139	−	0.694360i	−0.177977	−	0.0476889i
$213$	3.08543			0.211410
$214$	−24.6082	−	6.59375i	−1.68218	−	0.450739i
$215$	−3.65107	+	15.4738i	−0.249001	+	1.05530i
$216$	−1.96199	+	1.96199i	−0.133497	+	0.133497i
$217$	1.32664	−	4.95108i	0.0900581	−	0.336102i
$218$	−17.7691	+	4.76121i	−1.20347	+	0.322470i
$219$	0.746736	−	0.200087i	0.0504597	−	0.0135206i
$220$	−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	0.367460	+	0.930039i	$0.380227\pi$
$223$	−9.28408	+	16.0805i	−0.621708	+	1.07683i	−0.989168	+	0.146790i	$0.953106\pi$
$224$	−1.34257	−	0.775132i	−0.0897041	−	0.0517907i
$225$	12.3534	−	8.16030i	0.823563	−	0.544020i
$226$	−5.10737	−	5.10737i	−0.339737	−	0.339737i
$227$	−5.53101	+	3.19333i	−0.367106	+	0.211949i	−0.672193	−	0.740376i	$-0.734648\pi$
$227$	−5.53101	+	3.19333i	−0.367106	+	0.211949i	0.305087	+	0.952324i	$0.401314\pi$
$228$	−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	$0.923831\pi$
$230$	12.2063	+	2.88009i	0.804857	+	0.189908i
$231$	−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
$236$	−1.88054	+	0.503890i	−0.122413	+	0.0328004i
$237$	2.12303	−	0.568865i	0.137906	−	0.0369517i
$238$	−0.706895	+	2.63817i	−0.0458212	+	0.171007i
$239$	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	$0.0324123\pi$
$240$	−2.04453	−	0.482411i	−0.131974	−	0.0311395i
$241$	16.5493	+	4.43437i	1.06603	+	0.285643i	0.748863	−	0.662725i	$-0.230600\pi$
$241$	16.5493	+	4.43437i	1.06603	+	0.285643i	0.317172	+	0.948368i	$0.397267\pi$
$242$	17.3950			1.11819
$243$	−5.05712	−	1.35505i	−0.324414	−	0.0869266i
$244$	2.00715	−	3.47649i	0.128495	−	0.222559i
$245$	7.09645	−	13.1926i	0.453376	−	0.842847i
$246$		−	1.11880i		−	0.0713323i
$247$		0			0
$248$	15.5933	−	15.5933i	0.990176	−	0.990176i
$249$	0.685590	+	2.55866i	0.0434475	+	0.162148i
$250$	16.0802	+	7.43987i	1.01700	+	0.470539i
$251$	−8.61959	+	4.97652i	−0.544063	+	0.314115i	−0.746724	−	0.665134i	$-0.768374\pi$
$251$	−8.61959	+	4.97652i	−0.544063	+	0.314115i	0.202661	+	0.979249i	$0.435041\pi$
$252$		−	0.830319i		−	0.0523052i
$253$	0.271008	+	0.469399i	0.0170381	+	0.0295109i
$254$	0.997644	−	3.72326i	0.0625978	−	0.233618i
$255$	0.0417144	+	1.38612i	0.00261226	+	0.0868022i
$256$	−5.76971	−	9.99343i	−0.360607	−	0.624589i
$257$	0.712105	+	2.65761i	0.0444199	+	0.165777i	0.984573	−	0.174976i	$-0.0559847\pi$
$257$	0.712105	+	2.65761i	0.0444199	+	0.165777i	−0.940153	+	0.340753i	$0.889318\pi$
$258$	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
$263$	−1.59881	−	5.96686i	−0.0985871	−	0.367932i	0.898952	−	0.438048i	$-0.144330\pi$
$263$	−1.59881	−	5.96686i	−0.0985871	−	0.367932i	−0.997539	+	0.0701155i	$0.977663\pi$
$264$	−0.0356423	−	0.0617342i	−0.00219363	−	0.00379948i
$265$	−8.04147	+	8.54049i	−0.493983	+	0.524638i
$266$	−1.02606	+	3.82930i	−0.0629116	+	0.234789i
$267$	−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	$-0.442692\pi$
$269$	18.3796	−	10.6115i	1.12063	−	0.646994i	0.941561	+	0.336843i	$0.109359\pi$
$270$	−1.19935	−	3.99162i	−0.0729899	−	0.242922i
$271$	−3.33484	−	12.4458i	−0.202577	−	0.756027i	−0.990174	−	0.139837i	$-0.955342\pi$
$271$	−3.33484	−	12.4458i	−0.202577	−	0.756027i	0.787598	−	0.616190i	$-0.211325\pi$
$272$	−10.5820	+	10.5820i	−0.641629	+	0.641629i
$273$		0			0
$274$			6.42690i			0.388263i
$275$	0.242305	+	0.726385i	0.0146116	+	0.0438026i
$276$	0.178559	−	0.309274i	0.0107480	−	0.0186161i
$277$	20.5514	+	5.50674i	1.23482	+	0.330868i	0.816453	−	0.577412i	$-0.195937\pi$
$277$	20.5514	+	5.50674i	1.23482	+	0.330868i	0.418363	+	0.908280i	$0.362604\pi$
$278$	20.3214			1.21880
$279$	26.7367	+	7.16409i	1.60069	+	0.428903i
$280$	−2.46028	+	1.52091i	−0.147030	+	0.0908917i
$281$	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	$0.192945\pi$
$282$	0.739656	−	2.76044i	0.0440459	−	0.164382i
$283$	1.48552	−	0.398044i	0.0883050	−	0.0236613i	−0.214396	−	0.976747i	$-0.568778\pi$
$283$	1.48552	−	0.398044i	0.0883050	−	0.0236613i	0.302701	+	0.953086i	$0.402112\pi$
$284$	−7.72438	+	2.06974i	−0.458358	+	0.122817i
$285$	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
$290$	−4.36503	−	7.06103i	−0.256323	−	0.414638i
$291$	−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	$-0.640679\pi$
$293$	2.41782	−	1.39593i	0.141251	−	0.0815512i	0.568960	+	0.822365i	$0.307346\pi$
$294$	−1.48124	−	1.48124i	−0.0863877	−	0.0863877i
$295$	−1.95491	+	8.28521i	−0.113819	+	0.482384i
$296$	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
$301$	3.76583	−	1.00905i	0.217059	−	0.0581607i
$302$	−10.5951	+	2.83896i	−0.609682	+	0.163364i
$303$	−0.691212	+	2.57964i	−0.0397091	+	0.148196i
$304$	−15.3598	+	15.3598i	−0.880944	+	0.880944i
$305$	−9.22953	−	14.9300i	−0.528481	−	0.854891i
$306$	−14.2466	−	3.81736i	−0.814423	−	0.218224i
$307$	−2.12112			−0.121058			−0.0605292	−	0.998166i	$-0.519279\pi$
$307$	−2.12112			−0.121058			−0.0605292	+	0.998166i	$0.519279\pi$
$308$	0.0414808	+	0.0111148i	0.00236359	+	0.000633322i
$309$	−1.44495	+	2.50272i	−0.0822001	+	0.142375i
$310$	9.53204	+	31.7241i	0.541383	+	1.80181i
$311$		−	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	$0.444689\pi$
$314$	1.33347	+	4.97657i	0.0752519	+	0.280844i
$315$	−3.19734	−	1.71988i	−0.180150	−	0.0969043i
$316$	−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
$319$	0.0928554	−	0.346541i	0.00519890	−	0.0194026i
$320$	−11.2693	+	0.339143i	−0.629973	+	0.0189587i
$321$	1.58599	+	2.74701i	0.0885212	+	0.153323i
$322$	−0.795974	−	2.97061i	−0.0443579	−	0.165546i
$323$	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
$328$	−2.18463	−	8.15316i	−0.120626	−	0.450183i
$329$	−2.50574	−	4.34006i	−0.138146	−	0.239275i
$330$	0.107030	−	0.00322099i	0.00589179	−	0.000177310i
$331$	4.70310	−	17.5522i	0.258506	−	0.964756i	−0.707601	−	0.706612i	$-0.750223\pi$
$331$	4.70310	−	17.5522i	0.258506	−	0.964756i	0.966107	−	0.258144i	$-0.0831108\pi$
$332$	−3.43276	−	5.94572i	−0.188397	−	0.326314i
$333$			20.1541i			1.10444i
$334$	−22.4512	+	12.9622i	−1.22848	+	0.709261i
$335$	9.63025	+	5.18020i	0.526157	+	0.283025i
$336$	0.133325	+	0.497574i	0.00727345	+	0.0271449i
$337$	−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
$340$	−1.03426	−	3.44218i	−0.0560906	−	0.186678i
$341$	−0.715803	+	1.23981i	−0.0387629	+	0.0671393i
$342$	−20.6789	−	5.54089i	−1.11819	−	0.299617i
$343$	−7.51173			−0.405595
$344$	16.2016	+	4.34120i	0.873530	+	0.234062i
$345$	−0.821073	−	1.32820i	−0.0442051	−	0.0715078i
$346$	7.65777	−	7.65777i	0.411684	−	0.411684i
$347$	−2.01142	+	7.50674i	−0.107979	+	0.402983i	−0.998666	−	0.0516340i	$-0.983557\pi$
$347$	−2.01142	+	7.50674i	−0.107979	+	0.402983i	0.890687	+	0.454617i	$0.150224\pi$
$348$	−0.228326	+	0.0611797i	−0.0122395	+	0.00327958i
$349$	4.89796	−	1.31241i	0.262182	−	0.0702515i	−0.125333	−	0.992115i	$-0.540000\pi$
$349$	4.89796	−	1.31241i	0.262182	−	0.0702515i	0.387515	+	0.921863i	$0.373333\pi$
$350$	−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	−0.292698	−	0.956205i	$-0.594553\pi$
$353$	12.8089	−	22.1857i	0.681749	−	1.18082i	0.974447	−	0.224618i	$-0.0721136\pi$
$354$	1.03091	+	0.595199i	0.0547925	+	0.0316345i
$355$	−8.02986	+	34.0317i	−0.426181	+	1.80622i
$356$	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	$0.627694\pi$
$360$	−8.21318	−	13.2859i	−0.432873	−	0.700231i
$361$	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
$366$	−2.37086	+	0.635270i	−0.123927	+	0.0332061i
$367$	19.4366	−	5.20802i	1.01458	−	0.271857i	0.287040	−	0.957919i	$-0.407329\pi$
$367$	19.4366	−	5.20802i	1.01458	−	0.271857i	0.727543	+	0.686062i	$0.240662\pi$
$368$	4.36137	−	16.2769i	0.227352	−	0.848490i
$369$	7.49167	−	7.49167i	0.390001	−	0.390001i
$370$	−20.5153	+	12.6823i	−1.06654	+	0.659320i
$371$	2.77854	+	0.744507i	0.144255	+	0.0386529i
$372$	0.943243			0.0489049
$373$	−25.3125	−	6.78245i	−1.31063	−	0.351182i	−0.465170	−	0.885221i	$-0.654007\pi$
$373$	−25.3125	−	6.78245i	−1.31063	−	0.351182i	−0.845460	+	0.534039i	$0.820673\pi$
$374$	0.381413	−	0.660627i	0.0197224	−	0.0341602i
$375$	−0.760691	−	2.07070i	−0.0392819	−	0.106931i
$376$		−	21.5607i		−	1.11191i
$377$		0			0
$378$	−0.722700	+	0.722700i	−0.0371717	+	0.0371717i
$379$	−5.83130	−	21.7627i	−0.299534	−	1.11787i	−0.937550	−	0.347852i	$-0.886911\pi$
$379$	−5.83130	−	21.7627i	−0.299534	−	1.11787i	0.638016	−	0.770023i	$-0.279755\pi$
$380$	−1.50123	−	4.99631i	−0.0770112	−	0.256306i
$381$	−0.415627	+	0.239962i	−0.0212932	+	0.0122936i
$382$			37.2130i			1.90398i
$383$	12.0630	+	20.8938i	0.616392	+	1.06762i	0.990139	+	0.140091i	$0.0447396\pi$
$383$	12.0630	+	20.8938i	0.616392	+	1.06762i	−0.373747	+	0.927531i	$0.621927\pi$
$384$	−0.696814	+	2.60055i	−0.0355591	+	0.132709i
$385$	0.128721	−	0.136709i	0.00656024	−	0.00696735i
$386$	−12.5494	−	21.7362i	−0.638748	−	1.10634i
$387$	5.44905	+	20.3361i	0.276991	+	1.03374i
$388$	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
$393$	−0.337408	−	1.25922i	−0.0170200	−	0.0635194i
$394$	4.52662	+	7.84034i	0.228048	+	0.394991i
$395$	0.749265	+	24.8972i	0.0376996	+	1.25271i
$396$	−0.0600217	+	0.224004i	−0.00301620	+	0.0112566i
$397$	16.7465	+	29.0058i	0.840484	+	1.45576i	0.889486	+	0.456963i	$0.151063\pi$
$397$	16.7465	+	29.0058i	0.840484	+	1.45576i	−0.0490017	+	0.998799i	$0.515604\pi$
$398$		−	14.7430i		−	0.739000i
$399$	0.427464	−	0.246797i	0.0214000	−	0.0123553i
$400$	10.6418	−	21.2954i	0.532092	−	1.06477i
$401$	4.80084	+	17.9170i	0.239743	+	0.894731i	0.975953	+	0.217979i	$0.0699465\pi$
$401$	4.80084	+	17.9170i	0.239743	+	0.894731i	−0.736211	+	0.676752i	$0.763387\pi$
$402$	1.08126	−	1.08126i	0.0539285	−	0.0539285i
$403$		0			0
$404$		−	6.92181i		−	0.344373i
$405$	9.16394	−	17.0362i	0.455360	−	0.846536i
$406$	−1.01782	+	1.76292i	−0.0505136	+	0.0874922i
$407$	−1.00685	−	0.269785i	−0.0499077	−	0.0133727i
$408$	1.46302			0.0724301
$409$	−4.99622	−	1.33873i	−0.247047	−	0.0661960i	0.133171	−	0.991093i	$-0.457484\pi$
$409$	−4.99622	−	1.33873i	−0.247047	−	0.0661960i	−0.380218	+	0.924897i	$0.624151\pi$
$410$	12.3402	+	2.91170i	0.609440	+	0.143799i
$411$	0.565822	−	0.565822i	0.0279099	−	0.0279099i
$412$	1.93858	−	7.23487i	0.0955068	−	0.356436i
$413$	2.01636	−	0.540281i	0.0992184	−	0.0265855i
$414$	16.0418	−	4.29840i	0.788414	−	0.211255i
$415$	−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	$-0.325503\pi$
$419$	0.872048	+	0.503477i	0.0426023	+	0.0245965i	−0.478548	+	0.878062i	$0.658837\pi$
$420$	−0.120412	−	0.0284114i	−0.00587548	−	0.00138633i
$421$	−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
$425$	−15.3972	−	3.14729i	−0.746875	−	0.152666i
$426$	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
$431$	−4.01004	+	1.07449i	−0.193157	+	0.0517562i	−0.354100	−	0.935207i	$-0.615213\pi$
$431$	−4.01004	+	1.07449i	−0.193157	+	0.0517562i	0.160944	+	0.986964i	$0.448546\pi$
$432$	−5.40930	+	1.44942i	−0.260255	+	0.0697352i
$433$	−3.88103	+	14.4842i	−0.186511	+	0.696067i	0.807792	+	0.589468i	$0.200663\pi$
$433$	−3.88103	+	14.4842i	−0.186511	+	0.696067i	−0.994302	+	0.106599i	$0.966004\pi$
$434$	5.74380	−	5.74380i	0.275711	−	0.275711i
$435$	−0.237355	+	1.00595i	−0.0113803	+	0.0482315i
$436$	−5.73407	−	1.53644i	−0.274612	−	0.0735821i
$437$	−16.1466			−0.772399
$438$	1.18338	+	0.317086i	0.0565441	+	0.0151509i
$439$	−6.94098	+	12.0221i	−0.331275	+	0.573785i	−0.982762	−	0.184875i	$-0.940812\pi$
$439$	−6.94098	+	12.0221i	−0.331275	+	0.573785i	0.651487	+	0.758660i	$0.274145\pi$
$440$	0.773678	−	0.232464i	0.0368836	−	0.0110823i
$441$		−	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	$0.140265\pi$
$444$	0.177753	+	0.663384i	0.00843580	+	0.0314828i
$445$	19.4748	−	5.85154i	0.923196	−	0.277389i
$446$	−25.4834	+	14.7128i	−1.20667	+	0.696673i
$447$			0.839520i			0.0397079i
$448$	1.38235	+	2.39430i	0.0653100	+	0.113120i
$449$	1.72277	−	6.42946i	0.0813024	−	0.303425i	−0.913286	−	0.407319i	$-0.866464\pi$
$449$	1.72277	−	6.42946i	0.0813024	−	0.303425i	0.994588	+	0.103894i	$0.0331304\pi$
$450$	23.4201	−	1.41091i	1.10404	−	0.0665108i
$451$	0.273982	+	0.474551i	0.0129013	+	0.0223457i
$452$	−0.603263	−	2.25141i	−0.0283751	−	0.105897i
$453$	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	$-0.00101514\pi$
$457$	32.0071	+	18.4793i	1.49723	+	0.864426i	0.497236	+	0.867616i	$0.334348\pi$
$458$	−6.44722	−	24.0614i	−0.301259	−	1.12431i
$459$	1.84844	+	3.20160i	0.0862780	+	0.149438i
$460$	2.94653	+	2.77437i	0.137383	+	0.129355i
$461$	6.65860	−	24.8502i	0.310122	−	1.15739i	−0.618324	−	0.785923i	$-0.712188\pi$
$461$	6.65860	−	24.8502i	0.310122	−	1.15739i	0.928446	−	0.371468i	$-0.121145\pi$
$462$	−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
$465$	1.95379	−	3.63218i	0.0906046	−	0.168438i
$466$	3.39887	+	12.6847i	0.157449	+	0.587609i
$467$	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
$470$	28.5222	+	15.3424i	1.31563	+	0.707690i
$471$	0.320738	−	0.555534i	0.0147788	−	0.0255976i
$472$	8.67489	+	2.32443i	0.399294	+	0.106991i
$473$	−1.08889			−0.0500671
$474$	3.36445	+	0.901501i	0.154534	+	0.0414073i
$475$	−22.3491	−	4.56829i	−1.02544	−	0.209607i
$476$	−0.623222	+	0.623222i	−0.0285653	+	0.0285653i
$477$	−4.02047	+	15.0046i	−0.184085	+	0.687014i
$478$	29.8916	−	8.00943i	1.36721	−	0.366343i
$479$	16.0343	−	4.29638i	0.732627	−	0.196307i	0.126828	−	0.991925i	$-0.459520\pi$
$479$	16.0343	−	4.29638i	0.732627	−	0.196307i	0.605799	+	0.795618i	$0.292854\pi$
$480$	−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
$485$	14.3999	−	8.90183i	0.653867	−	0.404211i
$486$	−5.86681	−	5.86681i	−0.266124	−	0.266124i
$487$	−22.7590	+	13.1399i	−1.03131	+	0.595425i	−0.917359	−	0.398062i	$-0.869683\pi$
$487$	−22.7590	+	13.1399i	−1.03131	+	0.595425i	−0.113948	+	0.993487i	$0.536350\pi$
$488$	−16.0369	+	9.25893i	−0.725958	+	0.419132i
$489$	1.51637	+	1.51637i	0.0685724	+	0.0685724i
$490$	20.1928	−	12.4829i	0.912217	−	0.563919i
$491$	36.0301	+	20.8020i	1.62602	+	0.938781i	0.985265	+	0.171034i	$0.0547107\pi$
$491$	36.0301	+	20.8020i	1.62602	+	0.938781i	0.640752	+	0.767748i	$0.278623\pi$
$492$	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
$496$	42.9915	−	11.5195i	1.93037	−	0.517242i
$497$	8.28224	−	2.21922i	0.371509	−	0.0995456i
$498$	−1.08648	+	4.05480i	−0.0486864	+	0.181700i
$499$	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	$0.165204\pi$
$500$	3.29345	+	4.67373i	0.147287	+	0.209016i
$501$	3.11779	+	0.835410i	0.139293	+	0.0373234i
$502$	−15.7730			−0.703982
$503$	−10.3108	−	2.76277i	−0.459736	−	0.123186i	0.0215156	−	0.999769i	$-0.493151\pi$
$503$	−10.3108	−	2.76277i	−0.459736	−	0.123186i	−0.481251	+	0.876583i	$0.659818\pi$
$504$	−1.91512	+	3.31708i	−0.0853062	+	0.147755i
$505$	−26.6541	−	14.3375i	−1.18609	−	0.638010i
$506$			0.858953i			0.0381851i
$507$		0			0
$508$	0.879556	−	0.879556i	0.0390240	−	0.0390240i
$509$	0.780260	+	2.91197i	0.0345844	+	0.129071i	0.981060	−	0.193705i	$-0.0620506\pi$
$509$	0.780260	+	2.91197i	0.0345844	+	0.129071i	−0.946475	+	0.322776i	$0.895384\pi$
$510$	−1.04107	+	1.93540i	−0.0460993	+	0.0857008i
$511$	1.86056	−	1.07419i	0.0823062	−	0.0475195i
$512$			9.00279i			0.397871i
$513$	2.68301	+	4.64712i	0.118458	+	0.205175i
$514$	−1.12850	+	4.21162i	−0.0497760	+	0.185767i
$515$	−23.8441	−	22.4509i	−1.05070	−	0.989304i
$516$	0.358718	+	0.621318i	0.0157917	+	0.0273520i
$517$	0.362267	+	1.35200i	0.0159325	+	0.0594608i
$518$	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
$523$	0.767497	+	2.86434i	0.0335603	+	0.125249i	0.980674	−	0.195650i	$-0.0626817\pi$
$523$	0.767497	+	2.86434i	0.0335603	+	0.125249i	−0.947113	+	0.320899i	$0.896015\pi$
$524$	1.68940	+	2.92613i	0.0738020	+	0.127829i
$525$	−0.358819	+	0.404823i	−0.0156601	+	0.0176679i
$526$	2.53370	−	9.45590i	0.110475	−	0.412297i
$527$	−14.6909	−	25.4453i	−0.639944	−	1.10842i
$528$		−	0.143873i		−	0.00626129i
$529$	−9.07083	+	5.23704i	−0.394384	+	0.227698i
$530$	−17.8035	+	5.34936i	−0.773336	+	0.232361i
$531$	2.91762	+	10.8887i	0.126614	+	0.472529i
$532$	−0.904605	+	0.904605i	−0.0392196	+	0.0392196i
$533$		0			0
$534$		−	2.84359i		−	0.123054i
$535$	−34.4266	+	10.3441i	−1.48839	+	0.447212i
$536$	5.76825	−	9.99091i	0.249151	−	0.431542i
$537$	−1.08138	−	0.289755i	−0.0466650	−	0.0125038i
$538$	33.6329			1.45002
$539$	0.991021	+	0.265543i	0.0426863	+	0.0114378i
$540$	0.308870	−	1.30904i	0.0132916	−	0.0563320i
$541$	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	$0.0941691\pi$
$542$	5.28484	−	19.7233i	0.227003	−	0.847188i
$543$	0.684429	−	0.183392i	0.0293717	−	0.00787011i
$544$	−8.58362	+	2.29997i	−0.368020	+	0.0986105i
$545$	−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
$550$	−0.243019	+	1.18890i	−0.0103624	+	0.0506950i
$551$	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
$555$	2.92271	+	0.689619i	0.124062	+	0.0292727i
$556$	5.67915	+	3.27886i	0.240850	+	0.139055i
$557$	−4.71734	+	8.17068i	−0.199880	+	0.346203i	−0.948489	−	0.316809i	$-0.897389\pi$
$557$	−4.71734	+	8.17068i	−0.199880	+	0.346203i	0.748609	+	0.663012i	$0.230722\pi$
$558$	31.0175	+	31.0175i	1.31308	+	1.31308i
$559$		0			0
$560$	−5.83514	+	0.175605i	−0.246580	+	0.00742067i
$561$	−0.0917409	+	0.0245819i	−0.00387330	+	0.00103785i
$562$	9.14960	−	2.45163i	0.385953	−	0.103416i
$563$	2.53443	−	9.45863i	0.106814	−	0.398634i	−0.891731	−	0.452566i	$-0.850509\pi$
$563$	2.53443	−	9.45863i	0.106814	−	0.398634i	0.998545	+	0.0539320i	$0.0171754\pi$
$564$	0.652105	−	0.652105i	0.0274586	−	0.0274586i
$565$	−9.91916	−	2.34045i	−0.417302	−	0.0984633i
$566$	2.35416	+	0.630795i	0.0989527	+	0.0265143i
$567$	−4.74366			−0.199215
$568$	35.6324	+	9.54766i	1.49510	+	0.400611i
$569$	−3.20931	+	5.55868i	−0.134541	+	0.233032i	−0.925422	−	0.378938i	$-0.876289\pi$
$569$	−3.20931	+	5.55868i	−0.134541	+	0.233032i	0.790881	+	0.611970i	$0.209623\pi$
$570$	−1.51111	+	2.80922i	−0.0632934	+	0.117665i
$571$		−	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
$574$	−0.804709	−	3.00322i	−0.0335879	−	0.125352i
$575$	16.7867	−	5.59965i	0.700052	−	0.233521i
$576$	−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
$579$	−0.808803	+	3.01849i	−0.0336127	+	0.125444i
$580$	−0.0805813	−	2.67762i	−0.00334596	−	0.111182i
$581$	3.68068	+	6.37512i	0.152700	+	0.264484i
$582$	−0.612715	−	2.28668i	−0.0253979	−	0.0947861i
$583$	−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	$-0.519621\pi$
$587$	−23.1811	−	13.3836i	−0.956785	−	0.552400i	−0.895182	+	0.445701i	$0.852955\pi$
$588$	−0.174959	−	0.652955i	−0.00721517	−	0.0269274i
$589$	−21.3238	−	36.9338i	−0.878630	−	1.52183i
$590$	−9.24791	+	9.82180i	−0.380731	+	0.404357i
$591$	0.291739	−	1.08878i	0.0120005	−	0.0447866i
$592$	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
$595$	1.10895	+	3.69077i	0.0454627	+	0.151307i
$596$	−0.563161	−	2.10174i	−0.0230680	−	0.0860908i
$597$	−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	$-0.268151\pi$
$600$	−2.20774	+	0.736451i	−0.0901306	+	0.0300655i
$601$	−14.9478	+	25.8903i	−0.609732	+	1.05609i	0.381552	+	0.924347i	$0.375390\pi$
$601$	−14.9478	+	25.8903i	−0.609732	+	1.05609i	−0.991284	+	0.131740i	$0.957944\pi$
$602$	5.96785	+	1.59908i	0.243231	+	0.0651736i
$603$	14.4806			0.589695
$604$	−3.41905	−	0.916132i	−0.139119	−	0.0372769i
$605$	20.8772	−	12.9060i	0.848780	−	0.524703i
$606$	−2.99266	+	2.99266i	−0.121568	+	0.121568i
$607$	4.62475	−	17.2598i	0.187713	−	0.700553i	−0.806321	−	0.591478i	$-0.798544\pi$
$607$	4.62475	−	17.2598i	0.187713	−	0.700553i	0.994034	−	0.109075i	$-0.0347888\pi$
$608$	−12.4591	+	3.33841i	−0.505283	+	0.135390i
$609$	0.244816	−	0.0655981i	0.00992043	−	0.00265817i
$610$	−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	−0.667981	−	0.744178i	$-0.732841\pi$
$613$	7.68729	−	13.3148i	0.310487	−	0.537779i	0.978468	+	0.206399i	$0.0661746\pi$
$614$	−2.91107	−	1.68071i	−0.117481	−	0.0678278i
$615$	−0.830084	−	1.34277i	−0.0334722	−	0.0541459i
$616$	−0.140078	−	0.140078i	−0.00564390	−	0.00564390i
$617$	−1.07707	+	0.621849i	−0.0433614	+	0.0250347i	−0.521524	−	0.853237i	$-0.674636\pi$
$617$	−1.07707	+	0.621849i	−0.0433614	+	0.0250347i	0.478163	+	0.878271i	$0.341303\pi$
$618$	−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	$-0.554995\pi$
$620$	−2.45480	+	10.4038i	−0.0985872	+	0.417827i
$621$	−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
$626$	−31.1008	+	8.33343i	−1.24304	+	0.333071i
$627$	−0.133162	+	0.0356806i	−0.00531797	+	0.00142495i
$628$	−0.430310	+	1.60594i	−0.0171712	+	0.0640839i
$629$	15.1272	−	15.1272i	0.603163	−	0.603163i
$630$	−3.02533	−	4.89388i	−0.120532	−	0.194977i
$631$	−20.0180	−	5.36381i	−0.796904	−	0.213530i	−0.162680	−	0.986679i	$-0.552014\pi$
$631$	−20.0180	−	5.36381i	−0.796904	−	0.213530i	−0.634224	+	0.773149i	$0.718680\pi$
$632$	26.2784			1.04530
$633$	−1.04358	−	0.279626i	−0.0414785	−	0.0111141i
$634$	6.96483	−	12.0634i	0.276609	−	0.479101i
$635$	−1.56507	−	5.20880i	−0.0621080	−	0.206705i
$636$			0.529346i			0.0209899i
$637$		0			0
$638$	0.402025	−	0.402025i	0.0159163	−	0.0159163i
$639$	11.9842	+	44.7256i	0.474087	+	1.76932i
$640$	−26.8701	−	14.4537i	−1.06213	−	0.571332i
$641$	15.3071	−	8.83753i	0.604592	−	0.349061i	−0.166254	−	0.986083i	$-0.553167\pi$
$641$	15.3071	−	8.83753i	0.604592	−	0.349061i	0.770846	+	0.637022i	$0.219834\pi$
$642$			5.02675i			0.198390i
$643$	−1.33452	−	2.31145i	−0.0526282	−	0.0911547i	0.838511	−	0.544884i	$-0.183426\pi$
$643$	−1.33452	−	2.31145i	−0.0526282	−	0.0911547i	−0.891139	+	0.453730i	$0.850093\pi$
$644$	0.256861	−	0.958617i	0.0101217	−	0.0377748i
$645$	3.13556	−	0.0943630i	0.123463	−	0.00371554i
$646$	11.3623	+	19.6801i	0.447043	+	0.774302i
$647$	−10.9143	−	40.7326i	−0.429084	−	1.60136i	−0.754839	−	0.655910i	$-0.772285\pi$
$647$	−10.9143	−	40.7326i	−0.429084	−	1.60136i	0.325755	−	0.945454i	$-0.394381\pi$
$648$	−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
$653$	6.53917	+	24.4045i	0.255898	+	0.955023i	0.967589	+	0.252531i	$0.0812629\pi$
$653$	6.53917	+	24.4045i	0.255898	+	0.955023i	−0.711691	+	0.702492i	$0.752070\pi$
$654$	1.81485	+	3.14342i	0.0709664	+	0.122917i
$655$	14.7671	−	0.444408i	0.576999	−	0.0173644i
$656$	4.40924	−	16.4555i	0.172152	−	0.642479i
$657$	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	$-0.403061\pi$
$659$	32.7551	−	18.9112i	1.27596	−	0.736675i	0.976103	+	0.217310i	$0.0697281\pi$
$660$	0.0304309	+	0.0163691i	0.00118452	+	0.000637165i
$661$	−4.45346	−	16.6205i	−0.173219	−	0.646463i	−0.996848	−	0.0793341i	$-0.974721\pi$
$661$	−4.45346	−	16.6205i	−0.173219	−	0.646463i	0.823629	−	0.567129i	$-0.191946\pi$
$662$	20.3625	−	20.3625i	0.791409	−	0.791409i
$663$		0			0
$664$			31.6705i			1.22905i
$665$	1.60964	+	5.35715i	0.0624193	+	0.207741i
$666$	−15.9694	+	27.6599i	−0.618804	+	1.07180i
$667$	−8.00852	−	2.14588i	−0.310091	−	0.0830887i
$668$	−8.36582			−0.323683
$669$	3.53886	+	0.948235i	0.136820	+	0.0366609i
$670$	9.11214	+	14.7401i	0.352033	+	0.569461i
$671$	0.850052	−	0.850052i	0.0328159	−	0.0328159i
$672$	−0.0791687	+	0.295461i	−0.00305400	+	0.0113977i
$673$	−30.3909	+	8.14322i	−1.17148	+	0.313898i	−0.791543	−	0.611113i	$-0.790722\pi$
$673$	−30.3909	+	8.14322i	−1.17148	+	0.313898i	−0.379940	+	0.925011i	$0.624055\pi$
$674$	−37.3474	+	10.0072i	−1.43857	+	0.385464i
$675$	−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
$680$	−3.80752	+	16.1368i	−0.146012	+	0.618819i
$681$	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	$-0.874694\pi$
$683$	−27.5215	+	15.8896i	−1.05308	+	0.607998i	−0.129572	+	0.991570i	$0.541360\pi$
$684$	−4.88503	−	4.88503i	−0.186784	−	0.186784i
$685$	4.76837	+	7.71348i	0.182190	+	0.294717i
$686$	−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
$691$	−25.9278	+	6.94735i	−0.986342	+	0.264289i	−0.715713	−	0.698394i	$-0.753898\pi$
$691$	−25.9278	+	6.94735i	−0.986342	+	0.264289i	−0.270629	+	0.962684i	$0.587232\pi$
$692$	3.37567	−	0.904508i	0.128324	−	0.0343842i
$693$	0.0643565	−	0.240182i	0.00244470	−	0.00912374i
$694$	−8.70863	+	8.70863i	−0.330575	+	0.330575i
$695$	24.3895	−	15.0773i	0.925147	−	0.571913i
$696$	1.05326	+	0.282220i	0.0399237	+	0.0106975i
$697$	−11.2462			−0.425980
$698$	7.76199	+	2.07982i	0.293796	+	0.0787223i
$699$	0.817526	−	1.41600i	0.0309217	−	0.0535579i
$700$	0.626745	−	1.25418i	0.0236887	−	0.0474035i
$701$			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
$704$	−0.199854	−	0.745863i	−0.00753226	−	0.0281108i
$705$	−1.16035	−	3.86182i	−0.0437012	−	0.145445i
$706$	35.1585	−	20.2987i	1.32321	−	0.763953i
$707$			7.42171i			0.279122i
$708$	0.192071	+	0.332676i	0.00721845	+	0.0125027i
$709$	9.70804	−	36.2309i	0.364593	−	1.36068i	−0.503378	−	0.864066i	$-0.667910\pi$
$709$	9.70804	−	36.2309i	0.364593	−	1.36068i	0.867972	−	0.496614i	$-0.165424\pi$
$710$	−37.9861	+	40.3433i	−1.42559	+	1.51406i
$711$	16.4923	+	28.5654i	0.618508	+	1.07129i
$712$	−5.55253	−	20.7223i	−0.208090	−	0.776602i
$713$	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
$718$	5.82623	+	21.7438i	0.217433	+	0.811471i
$719$	14.5578	+	25.2148i	0.542913	+	0.940353i	0.998735	+	0.0502820i	$0.0160120\pi$
$719$	14.5578	+	25.2148i	0.542913	+	0.940353i	−0.455822	+	0.890071i	$0.650655\pi$
$720$	−0.948298	−	31.5108i	−0.0353410	−	1.17434i
$721$	−2.07858	+	7.75737i	−0.0774104	+	0.288900i
$722$	1.43734	+	2.48955i	0.0534923	+	0.0926514i
$723$		−	3.38055i		−	0.125724i
$724$	−1.59045	+	0.918247i	−0.0591086	+	0.0341264i
$725$	−10.4777	−	5.23598i	−0.389132	−	0.194459i
$726$	−0.888322	−	3.31526i	−0.0329687	−	0.123041i
$727$	−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
$730$	−6.57717	+	12.2273i	−0.243432	+	0.452552i
$731$	11.1740	−	19.3539i	0.413284	−	0.715829i
$732$	−0.765076	−	0.205002i	−0.0282780	−	0.00757708i
$733$	−34.8651			−1.28777			−0.643886	−	0.765121i	$-0.722679\pi$
$733$	−34.8651			−1.28777			−0.643886	+	0.765121i	$0.722679\pi$
$734$	30.8019	+	8.25335i	1.13692	+	0.304637i
$735$	−2.87676	−	0.678777i	−0.106111	−	0.0250371i
$736$	7.07547	−	7.07547i	0.260805	−	0.260805i
$737$	−0.193839	+	0.723416i	−0.00714014	+	0.0266474i
$738$	16.2179	−	4.34557i	0.596989	−	0.159963i
$739$	−33.0522	+	8.85631i	−1.21584	+	0.325785i	−0.809053	−	0.587736i	$-0.800019\pi$
$739$	−33.0522	+	8.85631i	−1.21584	+	0.325785i	−0.406792	+	0.913521i	$0.633353\pi$
$740$	−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	−0.893297	−	0.449468i	$-0.851614\pi$
$743$	−1.56456	+	2.70989i	−0.0573980	+	0.0994162i	0.835899	+	0.548884i	$0.184947\pi$
$744$	−3.76821	−	2.17558i	−0.138149	−	0.0797605i
$745$	−9.25977	−	2.18486i	−0.339252	−	0.0800472i
$746$	−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
$750$	0.596768	−	3.44463i	0.0217909	−	0.125780i
$751$	−6.28199	−	3.62691i	−0.229233	−	0.132348i	0.380985	−	0.924581i	$-0.375585\pi$
$751$	−6.28199	−	3.62691i	−0.229233	−	0.132348i	−0.610218	+	0.792233i	$0.708918\pi$
$752$	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
$756$	−0.318578	+	0.0853627i	−0.0115866	+	0.00310461i
$757$	−15.9782	+	4.28134i	−0.580737	+	0.155608i	−0.537216	−	0.843445i	$-0.680524\pi$
$757$	−15.9782	+	4.28134i	−0.580737	+	0.155608i	−0.0435205	+	0.999053i	$0.513857\pi$
$758$	9.24108	−	34.4882i	0.335651	−	1.25267i
$759$	0.0756220	−	0.0756220i	0.00274490	−	0.00274490i
$760$	−5.52661	+	23.4226i	−0.200471	+	0.849626i
$761$	−22.3674	−	5.99332i	−0.810817	−	0.217258i	−0.170489	−	0.985360i	$-0.554535\pi$
$761$	−22.3674	−	5.99332i	−0.810817	−	0.217258i	−0.640328	+	0.768102i	$0.721201\pi$
$762$	−0.760555			−0.0275520
$763$	6.14819	+	1.64740i	0.222579	+	0.0596400i
$764$	−6.00431	+	10.3998i	−0.217228	+	0.376251i
$765$	−19.9308	+	5.98855i	−0.720601	+	0.216516i
$766$			38.2335i			1.38143i
$767$		0			0
$768$	−1.60998	+	1.60998i	−0.0580951	+	0.0580951i
$769$	−1.52511	−	5.69177i	−0.0549967	−	0.205251i	0.932960	−	0.359979i	$-0.117216\pi$
$769$	−1.52511	−	5.69177i	−0.0549967	−	0.205251i	−0.987957	+	0.154729i	$0.950550\pi$
$770$	0.284984	−	0.0856282i	0.0102701	−	0.00308583i
$771$	0.470143	−	0.271437i	0.0169318	−	0.00977557i
$772$		−	8.09938i		−	0.291503i
$773$	−4.04499	−	7.00612i	−0.145488	−	0.251993i	0.784067	−	0.620676i	$-0.213142\pi$
$773$	−4.04499	−	7.00612i	−0.145488	−	0.251993i	−0.929555	+	0.368684i	$0.879809\pi$
$774$	−8.63532	+	32.2274i	−0.310390	+	1.15839i
$775$	34.9776	+	31.0027i	1.25643	+	1.11365i
$776$	−8.93019	−	15.4675i	−0.320575	−	0.555252i
$777$	−0.190591	−	0.711294i	−0.00683740	−	0.0255175i
$778$	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
$783$	0.713141	+	2.66148i	0.0254856	+	0.0951135i
$784$	−15.9487	−	27.6239i	−0.569595	−	0.986567i
$785$	5.29272	+	4.98347i	0.188905	+	0.177868i
$786$	0.534703	−	1.99554i	0.0190722	−	0.0711785i
$787$	−8.10582	−	14.0397i	−0.288941	−	0.500461i	0.684616	−	0.728904i	$-0.259970\pi$
$787$	−8.10582	−	14.0397i	−0.288941	−	0.500461i	−0.973557	+	0.228443i	$0.926637\pi$
$788$			2.92148i			0.104073i
$789$	−1.05556	+	0.609429i	−0.0375790	+	0.0216962i
$790$	−18.6994	+	34.7632i	−0.665296	+	1.23682i
$791$	0.646831	+	2.41401i	0.0229987	+	0.0858322i
$792$	0.756445	−	0.756445i	0.0268791	−	0.0268791i
$793$		0			0
$794$			53.0777i			1.88366i
$795$	2.03837	+	1.09646i	0.0722937	+	0.0388875i
$796$	2.37878	−	4.12017i	0.0843137	−	0.146036i
$797$	16.1019	+	4.31449i	0.570358	+	0.152827i	0.532461	−	0.846455i	$-0.321267\pi$
$797$	16.1019	+	4.31449i	0.570358	+	0.152827i	0.0378972	+	0.999282i	$0.487934\pi$
$798$	0.782216			0.0276901
$799$	−27.7479	−	7.43502i	−0.981649	−	0.263032i
$800$	11.7952	−	7.79154i	0.417023	−	0.275473i
$801$	19.0411	−	19.0411i	0.672783	−	0.672783i
$802$	−7.60807	+	28.3937i	−0.268650	+	1.00262i
$803$	−0.579592	+	0.155301i	−0.0204534	+	0.00548047i
$804$	0.476638	−	0.127715i	0.0168097	−	0.00450415i
$805$	−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	$-0.193916\pi$
$809$	20.8943	+	12.0633i	0.734603	+	0.424123i	−0.0855005	+	0.996338i	$0.527249\pi$
$810$	26.0758	−	16.1197i	0.916209	−	0.566388i
$811$	−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
$815$	−20.6716	+	12.7789i	−0.724096	+	0.447625i
$816$	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
$821$	38.2768	−	10.2562i	1.33587	−	0.357945i	0.480970	−	0.876737i	$-0.340285\pi$
$821$	38.2768	−	10.2562i	1.33587	−	0.357945i	0.854901	+	0.518792i	$0.173618\pi$
$822$	1.22489	−	0.328208i	0.0427229	−	0.0114476i
$823$	−10.3383	+	38.5831i	−0.360371	+	1.34492i	0.513219	+	0.858258i	$0.328453\pi$
$823$	−10.3383	+	38.5831i	−0.360371	+	1.34492i	−0.873589	+	0.486664i	$0.838214\pi$
$824$	−24.4316	+	24.4316i	−0.851116	+	0.851116i
$825$	0.126066	−	0.0832753i	0.00438905	−	0.00289927i
$826$	3.19540	+	0.856204i	0.111182	+	0.0297912i
$827$	−25.6019			−0.890264			−0.445132	−	0.895465i	$-0.646843\pi$
$827$	−25.6019			−0.890264			−0.445132	+	0.895465i	$0.646843\pi$
$828$	5.17670	+	1.38709i	0.179903	+	0.0482048i
$829$	−9.41684	+	16.3104i	−0.327060	+	0.566485i	−0.981927	−	0.189259i	$-0.939391\pi$
$829$	−9.41684	+	16.3104i	−0.327060	+	0.566485i	0.654867	+	0.755744i	$0.272725\pi$
$830$	−41.8962	−	22.5364i	−1.45424	−	0.782249i
$831$		−	4.19807i		−	0.145629i
$832$		0			0
$833$	−14.8894	+	14.8894i	−0.515888	+	0.515888i
$834$	−1.03777	−	3.87301i	−0.0359351	−	0.134111i
$835$	−17.3285	+	32.2146i	−0.599678	+	1.11483i
$836$	0.309436	−	0.178653i	0.0107021	−	0.00617885i
$837$		−	10.9949i		−	0.380040i
$838$	0.797879	+	1.38197i	0.0275623	+	0.0477393i
$839$	6.45374	−	24.0857i	0.222808	−	0.831530i	−0.760463	−	0.649381i	$-0.775028\pi$
$839$	6.45374	−	24.0857i	0.222808	−	0.831530i	0.983271	−	0.182149i	$-0.0583054\pi$
$840$	0.415508	+	0.391229i	0.0143364	+	0.0134987i
$841$	−11.7560	−	20.3621i	−0.405381	−	0.702140i
$842$	−0.170969	−	0.638063i	−0.00589196	−	0.0219891i
$843$	−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
$848$	6.46474	+	24.1267i	0.222000	+	0.828516i
$849$	−0.151725	−	0.262795i	−0.00520717	−	0.00901909i
$850$	−18.6377	−	16.5197i	−0.639268	−	0.566621i
$851$	−6.23469	+	23.2682i	−0.213722	+	0.797623i
$852$	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
$855$	−28.9296	+	8.69237i	−0.989370	+	0.297273i
$856$	9.81549	+	36.6319i	0.335487	+	1.25205i
$857$	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	$0.976045\pi$
$860$	−7.78661	+	2.33962i	−0.265521	+	0.0797802i
$861$	−0.193556	+	0.335249i	−0.00659637	+	0.0114252i
$862$	−6.35486	−	1.70278i	−0.216447	−	0.0579969i
$863$	−53.8912			−1.83448			−0.917239	−	0.398338i	$-0.869587\pi$
$863$	−53.8912			−1.83448			−0.917239	+	0.398338i	$0.869587\pi$
$864$	−3.21207	−	0.860671i	−0.109277	−	0.0292806i
$865$	3.50917	−	14.8724i	0.119315	−	0.505676i
$866$	−16.8033	+	16.8033i	−0.570998	+	0.570998i
$867$	−0.363644	+	1.35714i	−0.0123500	+	0.0460908i
$868$	2.53196	−	0.678436i	0.0859403	−	0.0230276i
$869$	−1.64783	+	0.441535i	−0.0558988	+	0.0149780i
$870$	−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
$875$	−3.53130	−	5.01127i	−0.119380	−	0.169412i
$876$	0.279553	+	0.279553i	0.00944522	+	0.00944522i
$877$	11.3743	−	6.56696i	0.384083	−	0.221750i	−0.295510	−	0.955340i	$-0.595490\pi$
$877$	11.3743	−	6.56696i	0.384083	−	0.221750i	0.679593	+	0.733589i	$0.262156\pi$
$878$	−19.0519	+	10.9996i	−0.642971	+	0.371220i
$879$	−0.389521	−	0.389521i	−0.0131382	−	0.0131382i
$880$	1.58690	+	0.374433i	0.0534944	+	0.0126221i
$881$	−31.7049	−	18.3049i	−1.06817	−	0.616706i	−0.140486	−	0.990083i	$-0.544867\pi$
$881$	−31.7049	−	18.3049i	−1.06817	−	0.616706i	−0.927680	+	0.373376i	$0.878200\pi$
$882$	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
$886$	21.7766	−	5.83502i	0.731599	−	0.196031i
$887$	52.7370	−	14.1308i	1.77074	−	0.474467i	0.781891	−	0.623416i	$-0.214255\pi$
$887$	52.7370	−	14.1308i	1.77074	−	0.474467i	0.988845	+	0.148948i	$0.0475888\pi$
$888$	0.819971	−	3.06017i	0.0275164	−	0.102693i
$889$	−0.943078	+	0.943078i	−0.0316298	+	0.0316298i
$890$	31.3643	+	7.40047i	1.05133	+	0.248064i
$891$	1.27975	+	0.342907i	0.0428731	+	0.0114878i
$892$	−9.49566			−0.317938
$893$	−40.2760	−	10.7919i	−1.34779	−	0.361138i
$894$	−0.665210	+	1.15218i	−0.0222479	+	0.0385346i
$895$	6.01025	−	11.1734i	0.200901	−	0.373484i
$896$			7.48186i			0.249951i
$897$		0			0
$898$	7.45887	−	7.45887i	0.248906	−	0.248906i
$899$	−5.66782	−	21.1526i	−0.189032	−	0.705479i
$900$	6.77279	+	3.38453i	0.225760	+	0.112818i
$901$	14.2799	−	8.24448i	0.475731	−	0.274664i
$902$			0.868379i			0.0289139i
$903$	−0.384625	−	0.666190i	−0.0127995	−	0.0221694i
$904$	−2.78284	+	10.3857i	−0.0925558	+	0.345423i
$905$	0.241550	+	8.02642i	0.00802940	+	0.266807i
$906$	1.08214	+	1.87433i	0.0359518	+	0.0622703i
$907$	−10.6057	−	39.5809i	−0.352155	−	1.31426i	−0.884027	−	0.467437i	$-0.845178\pi$
$907$	−10.6057	−	39.5809i	−0.352155	−	1.31426i	0.531871	−	0.846825i	$-0.321489\pi$
$908$	−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
$913$	−0.532133	−	1.98595i	−0.0176110	−	0.0657253i
$914$	29.2849	+	50.7229i	0.968658	+	1.67777i
$915$	−2.37415	+	2.52148i	−0.0784869	+	0.0833575i
$916$	2.08052	−	7.76460i	0.0687423	−	0.256550i
$917$	−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	$-0.861784\pi$
$919$	−30.2077	+	17.4404i	−0.996460	+	0.575307i	−0.0892612	+	0.996008i	$0.528451\pi$
$920$	−5.37222	−	17.8796i	−0.177117	−	0.589473i
$921$	0.108321	+	0.404259i	0.00356929	+	0.0133208i
$922$	28.8290	−	28.8290i	0.949432	−	0.949432i
$923$		0			0
$924$		−	0.00847334i		−	0.000278753i
$925$	−15.2128	+	30.4422i	−0.500193	+	1.00093i
$926$	−12.6446	+	21.9012i	−0.415529	+	0.719717i
$927$	−41.8912	−	11.2247i	−1.37589	−	0.368668i
$928$	−6.62322			−0.217418
$929$	−8.38235	−	2.24604i	−0.275016	−	0.0736903i	0.118675	−	0.992933i	$-0.462135\pi$
$929$	−8.38235	−	2.24604i	−0.275016	−	0.0736903i	−0.393691	+	0.919243i	$0.628802\pi$
$930$	5.55945	−	3.43677i	0.182302	−	0.112696i
$931$	−21.6120	+	21.6120i	−0.708304	+	0.708304i
$932$	−1.09681	+	4.09336i	−0.0359273	+	0.134083i
$933$	−4.05296	+	1.08599i	−0.132688	+	0.0355536i
$934$	40.3211	−	10.8040i	1.31935	−	0.353518i
$935$	−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
$940$	5.49550	+	8.88972i	0.179243	+	0.289951i
$941$	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
$945$	−0.331177	+	1.40358i	−0.0107732	+	0.0456583i
$946$	−1.49442	−	0.862801i	−0.0485876	−	0.0280521i
$947$	−13.8023	+	23.9064i	−0.448516	+	0.776852i	−0.998290	−	0.0584612i	$-0.981381\pi$
$947$	−13.8023	+	23.9064i	−0.448516	+	0.776852i	0.549774	+	0.835314i	$0.314714\pi$
$948$	0.794793	+	0.794793i	0.0258137	+	0.0258137i
$949$		0			0
$950$	−27.0526	−	23.9783i	−0.877702	−	0.777960i
$951$	−1.67524	+	0.448880i	−0.0543235	+	0.0145559i
$952$	3.92719	−	1.05229i	0.127281	−	0.0341048i
$953$	7.47941	−	27.9135i	0.242282	−	0.904208i	−0.732448	−	0.680822i	$-0.761623\pi$
$953$	7.47941	−	27.9135i	0.242282	−	0.904208i	0.974730	−	0.223385i	$-0.0717108\pi$
$954$	−17.4070	+	17.4070i	−0.563572	+	0.563572i
$955$	27.6098	+	44.6626i	0.893431	+	1.44525i
$956$	9.64602	+	2.58464i	0.311974	+	0.0835933i
$957$	−0.0707884			−0.00228826
$958$	25.4102	+	6.80864i	0.820966	+	0.219977i
$959$	1.11187	−	1.92582i	0.0359042	−	0.0621878i
$960$	0.640135	+	2.13047i	0.0206603	+	0.0687607i
$961$			56.3841i			1.81884i
$962$		0			0
$963$	−33.6599	+	33.6599i	−1.08467	+	1.08467i
$964$	2.26771	+	8.46323i	0.0730382	+	0.272582i
$965$	−31.1886	−	16.7766i	−1.00400	−	0.540059i
$966$	−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
$969$	0.732295	−	2.73296i	0.0235247	−	0.0877954i
$970$	26.8163	−	0.807022i	0.861021	−	0.0259119i
$971$	6.77930	+	11.7421i	0.217558	+	0.376822i	0.954061	−	0.299613i	$-0.0968575\pi$
$971$	6.77930	+	11.7421i	0.217558	+	0.376822i	−0.736503	+	0.676435i	$0.763524\pi$
$972$	−0.692966	−	2.58618i	−0.0222269	−	0.0829519i
$973$	−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	$-0.609235\pi$
$977$	−41.2668	−	23.8254i	−1.32024	−	0.762242i	−0.983767	+	0.179450i	$0.942568\pi$
$978$	0.879575	+	3.28262i	0.0281257	+	0.104967i
$979$	0.696362	+	1.20613i	0.0222558	+	0.0385482i
$980$	7.65731	−	0.230442i	0.244604	−	0.00736121i
$981$	−8.89627	+	33.2013i	−0.284036	+	1.06004i
$982$	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
$985$	11.2499	+	6.05141i	0.358450	+	0.192814i
$986$	3.02008	+	11.2711i	0.0961789	+	0.358945i
$987$	−0.699200	+	0.699200i	−0.0222558	+	0.0222558i
$988$		0			0
$989$			25.1641i			0.800171i
$990$	0.462408	+	1.53897i	0.0146963	+	0.0489115i
$991$	−10.0052	+	17.3296i	−0.317827	+	0.550493i	−0.980034	−	0.198828i	$-0.936287\pi$
$991$	−10.0052	+	17.3296i	−0.317827	+	0.550493i	0.662207	+	0.749321i	$0.269620\pi$
$992$	25.5285	+	6.84035i	0.810531	+	0.217181i
$993$	−3.58541			−0.113780
$994$	13.1252	+	3.51688i	0.416306	+	0.111549i
$995$	−10.9384	−	17.6944i	−0.346771	−	0.560950i
$996$	−0.957877	+	0.957877i	−0.0303515	+	0.0303515i
$997$	8.75402	−	32.6705i	0.277243	−	1.03468i	−0.677081	−	0.735909i	$-0.736755\pi$
$997$	8.75402	−	32.6705i	0.277243	−	1.03468i	0.954324	−	0.298775i	$-0.0965781\pi$
$998$	18.0035	−	4.82403i	0.569892	−	0.152702i
$999$	7.73273	−	2.07198i	0.244653	−	0.0655545i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.2	✓	20	13.8	odd	4
65.2.o.a.63.2	yes	20	65.23	odd	12
65.2.t.a.37.4	yes	20	13.10	even	6
65.2.t.a.58.4	yes	20	65.8	even	4
325.2.s.b.32.4		20	65.34	odd	4
325.2.s.b.193.4		20	65.62	odd	12
325.2.x.b.232.2		20	65.49	even	6
325.2.x.b.318.2		20	65.47	even	4
585.2.cf.a.388.4		20	195.23	even	12
585.2.cf.a.487.4		20	39.8	even	4
585.2.dp.a.37.2		20	39.23	odd	6
585.2.dp.a.253.2		20	195.8	odd	4
845.2.f.d.408.7		20	65.58	even	12
845.2.f.d.437.4		20	13.9	even	3
845.2.f.e.408.4		20	65.33	even	12
845.2.f.e.437.7		20	13.4	even	6
845.2.k.d.268.4		20	65.48	odd	12
845.2.k.d.577.4		20	13.6	odd	12
845.2.k.e.268.7		20	65.43	odd	12
845.2.k.e.577.7		20	13.7	odd	12
845.2.o.e.488.2		20	65.38	odd	4
845.2.o.e.587.2		20	13.11	odd	12
845.2.o.f.488.4		20	5.3	odd	4
845.2.o.f.587.4		20	13.2	odd	12
845.2.o.g.258.4		20	65.3	odd	12
845.2.o.g.357.4		20	13.5	odd	4
845.2.t.e.418.4		20	65.28	even	12	inner
845.2.t.e.657.4		20	1.1	even	1	trivial
845.2.t.f.418.2		20	65.63	even	12
845.2.t.f.657.2		20	13.12	even	2
845.2.t.g.188.2		20	65.18	even	4
845.2.t.g.427.2		20	13.3	even	3

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} +(-0.0510678 - 0.190588i) q^{3} +(0.255697 + 0.442881i) q^{4} +(2.23506 - 0.0672627i) q^{5} +(0.0809291 - 0.302032i) q^{6} +(-0.274164 - 0.474866i) q^{7} -2.35905i q^{8} +(2.56436 - 1.48053i) q^{9} +(3.12074 + 1.67868i) q^{10} +(0.0396372 + 0.147928i) q^{11} +(0.0713497 - 0.0713497i) q^{12} -0.868956i q^{14} +(-0.126959 - 0.422539i) q^{15} +(2.38063 - 4.12338i) q^{16} +(-3.03602 - 0.813499i) q^{17} +4.69252 q^{18} +(-4.40678 - 1.18079i) q^{19} +(0.601287 + 0.972665i) q^{20} +(-0.0765027 + 0.0765027i) q^{21} +(-0.0628146 + 0.234427i) q^{22} +(3.41860 - 0.916011i) q^{23} +(-0.449606 + 0.120472i) 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} +(0.160566 - 0.680501i) 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} +(-0.644713 - 1.04291i) 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} +(3.45612 - 0.926064i) q^{41} +(-0.165612 + 0.0443757i) q^{42} +(-1.84023 + 6.86784i) q^{43} +(-0.0553794 + 0.0553794i) q^{44} +(5.63190 - 3.48156i) q^{45} +(5.41759 + 1.45164i) q^{46} +9.13956 q^{47} +(-0.907439 - 0.243147i) q^{48} +(3.34967 - 5.80180i) q^{49} +(7.08794 + 3.54203i) q^{50} +0.620172i q^{51} +(-3.70952 + 3.70952i) q^{53} +(-0.482424 - 1.80043i) q^{54} +(0.0985415 + 0.327962i) q^{55} +(-1.12023 + 0.646766i) q^{56} +0.900179i q^{57} +(-1.85623 - 3.21508i) q^{58} +(-0.985325 + 3.67728i) q^{59} +(0.154672 - 0.164270i) q^{60} +(-3.92486 - 6.79805i) q^{61} +(3.83416 + 14.3093i) q^{62} +(-1.40611 - 0.811818i) q^{63} -5.04207 q^{64} +0.0478868 q^{66} +(4.23514 + 2.44516i) q^{67} +(-0.416019 - 1.55261i) q^{68} +(-0.349161 - 0.604765i) q^{69} +(-0.0584483 - 1.94217i) q^{70} +(-4.04725 + 15.1045i) q^{71} +(-3.49265 - 6.04945i) q^{72} +3.91807i q^{73} +(-9.34119 + 5.39314i) q^{74} +(-0.312181 - 0.935860i) q^{75} +(-0.603851 - 2.25360i) q^{76} +(0.0593789 - 0.0593789i) q^{77} +11.1394i q^{79} +(5.04350 - 9.37611i) q^{80} +(4.32557 - 7.49210i) q^{81} +(5.47704 + 1.46757i) q^{82} -13.4251 q^{83} +(-0.0534431 - 0.0143200i) q^{84} +(-6.84039 - 1.61401i) q^{85} +(-7.96744 + 7.96744i) q^{86} +(-0.119633 + 0.446477i) q^{87} +(0.348970 - 0.0935062i) q^{88} +(8.78419 - 2.35372i) 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} +(-9.92882 - 2.34273i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 4 q^{6} + 2 q^{7} - 12 q^{9} + 10 q^{10} - 8 q^{11} - 24 q^{12} + 8 q^{15} - 2 q^{16} + 10 q^{17} - 16 q^{19} - 12 q^{20} - 4 q^{21} + 16 q^{22} + 2 q^{23} + 28 q^{24}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 4 * q^6 + 2 * q^7 - 12 * q^9 + 10 * q^10 - 8 * q^11 - 24 * q^12 + 8 * q^15 - 2 * q^16 + 10 * q^17 - 16 * q^19 - 12 * q^20 - 4 * q^21 + 16 * q^22 + 2 * q^23 + 28 * q^24 + 18 * q^25 + 4 * q^27 - 18 * q^28 - 14 * q^30 + 48 * q^32 + 18 * q^33 - 2 * q^34 - 20 * q^35 - 36 * q^36 + 4 * q^37 - 8 * q^38 - 16 * q^40 - 28 * q^41 - 56 * q^42 + 22 * q^43 + 36 * q^44 - 6 * q^45 + 8 * q^46 + 40 * q^47 + 28 * q^48 + 18 * q^49 + 78 * q^50 - 10 * q^53 - 12 * q^54 + 26 * q^55 - 8 * q^59 - 28 * q^60 - 16 * q^61 + 40 * q^62 - 36 * q^63 + 20 * q^64 - 32 * q^66 + 18 * q^67 + 28 * q^68 - 16 * q^69 + 12 * q^70 - 56 * q^71 - 4 * q^72 - 18 * q^74 + 34 * q^75 - 80 * q^76 - 28 * q^77 + 110 * q^80 - 14 * q^81 - 22 * q^82 - 48 * q^83 - 32 * q^84 - 28 * q^85 - 60 * q^86 + 62 * q^87 - 50 * q^88 + 6 * q^89 + 46 * q^90 - 8 * q^92 - 32 * q^93 + 48 * q^94 - 14 * q^95 - 56 * q^96 + 66 * q^97 - 30 * q^98 - 60 * q^99

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