LMFDB - Embedded newform 845.2.o.e.587.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(258,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.258"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 7])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [20,-4,-2,-6,-6,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			587.4
Root			$1.02262i$ of defining polynomial
Character	$\chi$	$=$	845.587
Dual form			845.2.o.e.488.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.511309 + 0.885613i) q^{2} +(2.69193 + 0.721300i) q^{3} +(0.477126 - 0.826407i) q^{4} +(-1.69584 + 1.45744i) q^{5} +(0.737614 + 2.75281i) q^{6} +(-0.834479 - 0.481787i) q^{7} +3.02107 q^{8} +(4.12812 + 2.38337i) q^{9} +(-2.15782 - 0.756660i) q^{10} +(-0.430490 + 1.60661i) q^{11} +(1.88048 - 1.88048i) q^{12} -0.985368i q^{14} +(-5.61633 + 2.70010i) q^{15} +(0.590448 + 1.02269i) q^{16} +(1.87656 + 7.00342i) q^{17} +4.87456i q^{18} +(2.64041 - 0.707496i) q^{19} +(0.395304 + 2.09684i) q^{20} +(-1.89884 - 1.89884i) q^{21} +(-1.64295 + 0.440226i) q^{22} +(0.997344 - 3.72214i) q^{23} +(8.13250 + 2.17910i) q^{24} +(0.751762 - 4.94316i) q^{25} +(3.48159 + 3.48159i) q^{27} +(-0.796304 + 0.459747i) q^{28} +(-0.253107 + 0.146132i) q^{29} +(-5.26292 - 3.59331i) q^{30} +(-0.125649 + 0.125649i) q^{31} +(2.41727 - 4.18683i) q^{32} +(-2.31769 + 4.01436i) q^{33} +(-5.24282 + 5.24282i) q^{34} +(2.11732 - 0.399166i) q^{35} +(3.93927 - 2.27434i) q^{36} +(-3.53443 + 2.04061i) q^{37} +(1.97663 + 1.97663i) q^{38} +(-5.12326 + 4.40302i) q^{40} +(6.69071 + 1.79277i) q^{41} +(0.710745 - 2.65254i) q^{42} +(-7.67707 + 2.05706i) q^{43} +(1.12232 + 1.12232i) q^{44} +(-10.4743 + 1.97465i) q^{45} +(3.80633 - 1.01990i) q^{46} -7.84582i q^{47} +(0.851780 + 3.17888i) q^{48} +(-3.03576 - 5.25810i) q^{49} +(4.76211 - 1.86171i) q^{50} +20.2063i q^{51} +(-1.99855 + 1.99855i) q^{53} +(-1.30317 + 4.86351i) q^{54} +(-1.61149 - 3.35197i) q^{55} +(-2.52102 - 1.45551i) q^{56} +7.61811 q^{57} +(-0.258832 - 0.149437i) q^{58} +(-1.30739 - 4.87924i) q^{59} +(-0.448318 + 5.92967i) q^{60} +(-1.04169 + 1.80425i) q^{61} +(-0.175522 - 0.0470311i) q^{62} +(-2.29655 - 3.97775i) q^{63} +7.30568 q^{64} -4.74023 q^{66} +(-3.64915 - 6.32050i) q^{67} +(6.68304 + 1.79071i) q^{68} +(5.36956 - 9.30034i) q^{69} +(1.43611 + 1.67103i) q^{70} +(-3.37837 - 12.6082i) q^{71} +(12.4713 + 7.20034i) q^{72} +3.22747 q^{73} +(-3.61437 - 2.08676i) q^{74} +(5.58919 - 12.7644i) q^{75} +(0.675130 - 2.51962i) q^{76} +(1.13328 - 1.13328i) q^{77} -13.5845i q^{79} +(-2.49180 - 0.873774i) q^{80} +(-0.289196 - 0.500902i) q^{81} +(1.83332 + 6.84204i) q^{82} +8.56854i q^{83} +(-2.47521 + 0.663230i) q^{84} +(-13.3894 - 9.14173i) q^{85} +(-5.74712 - 5.74712i) q^{86} +(-0.786751 + 0.210809i) q^{87} +(-1.30054 + 4.85368i) q^{88} +(-0.500868 - 0.134207i) q^{89} +(-7.10435 - 8.26648i) q^{90} +(-2.60014 - 2.60014i) q^{92} +(-0.428870 + 0.247608i) q^{93} +(6.94836 - 4.01164i) q^{94} +(-3.44659 + 5.04803i) q^{95} +(9.52707 - 9.52707i) q^{96} +(-3.75660 + 6.50662i) q^{97} +(3.10442 - 5.37702i) q^{98} +(-5.60626 + 5.60626i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 4 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9} + 2 q^{10} + 8 q^{11} + 24 q^{12} + 12 q^{15} - 2 q^{16} - 4 q^{17} - 16 q^{19} + 8 q^{20} + 4 q^{21} + 16 q^{22} + 10 q^{23}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 4 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9 + 2 * q^10 + 8 * q^11 + 24 * q^12 + 12 * q^15 - 2 * q^16 - 4 * q^17 - 16 * q^19 + 8 * q^20 + 4 * q^21 + 16 * q^22 + 10 * q^23 + 28 * q^24 - 18 * q^25 + 4 * q^27 - 6 * q^28 + 26 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 + 40 * q^35 - 36 * q^36 - 42 * q^37 + 8 * q^38 - 16 * q^40 + 28 * q^41 + 40 * q^42 - 10 * q^43 + 36 * q^44 - 32 * q^45 - 8 * q^46 - 56 * q^48 - 18 * q^49 + 8 * q^50 - 10 * q^53 - 12 * q^54 - 10 * q^55 - 12 * q^57 + 90 * q^58 - 8 * q^59 - 92 * q^60 - 16 * q^61 + 44 * q^62 - 32 * q^63 - 20 * q^64 - 32 * q^66 - 58 * q^67 + 22 * q^68 + 16 * q^69 + 32 * q^70 + 56 * q^71 + 66 * q^72 + 72 * q^73 + 18 * q^74 + 38 * q^75 + 80 * q^76 + 28 * q^77 + 68 * q^80 - 14 * q^81 - 56 * q^82 - 32 * q^84 + 6 * q^85 + 60 * q^86 - 34 * q^87 - 82 * q^88 + 6 * q^89 - 46 * q^90 - 8 * q^92 - 48 * q^93 - 48 * q^94 + 26 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * q^99

Character values

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

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

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 $

$2$	0.511309	+	0.885613i	0.361550	+	0.626223i	0.988216	−	0.153065i	$-0.0489144\pi$
$2$	0.511309	+	0.885613i	0.361550	+	0.626223i	−0.626666	+	0.779288i	$0.715581\pi$
$3$	2.69193	+	0.721300i	1.55418	+	0.416443i	0.930817	−	0.365486i	$-0.119097\pi$
$3$	2.69193	+	0.721300i	1.55418	+	0.416443i	0.623368	+	0.781929i	$0.285764\pi$
$4$	0.477126	−	0.826407i	0.238563	−	0.413204i
$5$	−1.69584	+	1.45744i	−0.758404	+	0.651785i
$5$	−1.69584	+	1.45744i	−0.758404	+	0.651785i
$6$	0.737614	+	2.75281i	0.301130	+	1.12383i
$7$	−0.834479	−	0.481787i	−0.315404	−	0.182098i	0.333938	−	0.942595i	$-0.391622\pi$
$7$	−0.834479	−	0.481787i	−0.315404	−	0.182098i	−0.649342	+	0.760497i	$0.724956\pi$
$8$	3.02107			1.06811
$9$	4.12812	+	2.38337i	1.37604	+	0.794457i
$10$	−2.15782	−	0.756660i	−0.682364	−	0.239277i
$11$	−0.430490	+	1.60661i	−0.129797	+	0.484411i	−0.999965	−	0.00834492i	$-0.997344\pi$
$11$	−0.430490	+	1.60661i	−0.129797	+	0.484411i	0.870168	+	0.492756i	$0.164010\pi$
$12$	1.88048	−	1.88048i	0.542847	−	0.542847i
$13$		0			0
$13$		0			0
$14$		−	0.985368i		−	0.263351i
$15$	−5.61633	+	2.70010i	−1.45013	+	0.697163i
$16$	0.590448	+	1.02269i	0.147612	+	0.255671i
$17$	1.87656	+	7.00342i	0.455133	+	1.69858i	0.687697	+	0.725998i	$0.258622\pi$
$17$	1.87656	+	7.00342i	0.455133	+	1.69858i	−0.232564	+	0.972581i	$0.574711\pi$
$18$			4.87456i			1.14894i
$19$	2.64041	−	0.707496i	0.605752	−	0.162311i	0.0571095	−	0.998368i	$-0.481812\pi$
$19$	2.64041	−	0.707496i	0.605752	−	0.162311i	0.548642	+	0.836057i	$0.315145\pi$
$20$	0.395304	+	2.09684i	0.0883927	+	0.468867i
$21$	−1.89884	−	1.89884i	−0.414362	−	0.414362i
$22$	−1.64295	+	0.440226i	−0.350277	+	0.0938565i
$23$	0.997344	−	3.72214i	0.207961	−	0.776120i	−0.780566	−	0.625073i	$-0.785069\pi$
$23$	0.997344	−	3.72214i	0.207961	−	0.776120i	0.988527	−	0.151046i	$-0.0482643\pi$
$24$	8.13250	+	2.17910i	1.66004	+	0.444806i
$25$	0.751762	−	4.94316i	0.150352	−	0.988632i
$26$		0			0
$27$	3.48159	+	3.48159i	0.670033	+	0.670033i
$28$	−0.796304	+	0.459747i	−0.150487	+	0.0868839i
$29$	−0.253107	+	0.146132i	−0.0470008	+	0.0271360i	−0.523316	−	0.852139i	$-0.675305\pi$
$29$	−0.253107	+	0.146132i	−0.0470008	+	0.0271360i	0.476315	+	0.879274i	$0.341972\pi$
$30$	−5.26292	−	3.59331i	−0.960874	−	0.656046i
$31$	−0.125649	+	0.125649i	−0.0225673	+	0.0225673i	−0.718300	−	0.695733i	$-0.755080\pi$
$31$	−0.125649	+	0.125649i	−0.0225673	+	0.0225673i	0.695733	+	0.718300i	$0.255080\pi$
$32$	2.41727	−	4.18683i	0.427317	−	0.740134i
$33$	−2.31769	+	4.01436i	−0.403458	+	0.698811i
$34$	−5.24282	+	5.24282i	−0.899136	+	0.899136i
$35$	2.11732	−	0.399166i	0.357892	−	0.0674713i
$36$	3.93927	−	2.27434i	0.656545	−	0.379057i
$37$	−3.53443	+	2.04061i	−0.581057	+	0.335474i	−0.761553	−	0.648102i	$-0.775563\pi$
$37$	−3.53443	+	2.04061i	−0.581057	+	0.335474i	0.180496	+	0.983576i	$0.442230\pi$
$38$	1.97663	+	1.97663i	0.320652	+	0.320652i
$39$		0			0
$40$	−5.12326	+	4.40302i	−0.810059	+	0.696178i
$41$	6.69071	+	1.79277i	1.04491	+	0.279984i	0.740148	−	0.672444i	$-0.234755\pi$
$41$	6.69071	+	1.79277i	1.04491	+	0.279984i	0.304765	+	0.952427i	$0.401422\pi$
$42$	0.710745	−	2.65254i	0.109670	−	0.409295i
$43$	−7.67707	+	2.05706i	−1.17074	+	0.313699i	−0.791248	−	0.611495i	$-0.790568\pi$
$43$	−7.67707	+	2.05706i	−1.17074	+	0.313699i	−0.379494	+	0.925194i	$0.623902\pi$
$44$	1.12232	+	1.12232i	0.169195	+	0.169195i
$45$	−10.4743	+	1.97465i	−1.56141	+	0.294363i
$46$	3.80633	−	1.01990i	0.561212	−	0.150376i
$47$		−	7.84582i		−	1.14443i	−0.820103	−	0.572215i	$-0.806084\pi$
$47$		−	7.84582i		−	1.14443i	0.820103	−	0.572215i	$-0.193916\pi$
$48$	0.851780	+	3.17888i	0.122944	+	0.458832i
$49$	−3.03576	−	5.25810i	−0.433680	−	0.751156i
$50$	4.76211	−	1.86171i	0.673464	−	0.263286i
$51$			20.2063i			2.82944i
$52$		0			0
$53$	−1.99855	+	1.99855i	−0.274522	+	0.274522i	−0.830918	−	0.556395i	$-0.812184\pi$
$53$	−1.99855	+	1.99855i	−0.274522	+	0.274522i	0.556395	+	0.830918i	$0.312184\pi$
$54$	−1.30317	+	4.86351i	−0.177339	+	0.661840i
$55$	−1.61149	−	3.35197i	−0.217293	−	0.451979i
$56$	−2.52102	−	1.45551i	−0.336886	−	0.194501i
$57$	7.61811			1.00904
$58$	−0.258832	−	0.149437i	−0.0339863	−	0.0196220i
$59$	−1.30739	−	4.87924i	−0.170207	−	0.635223i	−0.997318	−	0.0731843i	$-0.976684\pi$
$59$	−1.30739	−	4.87924i	−0.170207	−	0.635223i	0.827111	−	0.562039i	$-0.189983\pi$
$60$	−0.448318	+	5.92967i	−0.0578776	+	0.765517i
$61$	−1.04169	+	1.80425i	−0.133374	+	0.231011i	−0.924975	−	0.380027i	$-0.875915\pi$
$61$	−1.04169	+	1.80425i	−0.133374	+	0.231011i	0.791601	+	0.611038i	$0.209248\pi$
$62$	−0.175522	−	0.0470311i	−0.0222914	−	0.00597296i
$63$	−2.29655	−	3.97775i	−0.289339	−	0.501149i
$64$	7.30568			0.913209
$65$		0			0
$66$	−4.74023			−0.583482
$67$	−3.64915	−	6.32050i	−0.445814	−	0.772173i	0.552294	−	0.833649i	$-0.313752\pi$
$67$	−3.64915	−	6.32050i	−0.445814	−	0.772173i	−0.998109	+	0.0614765i	$0.980419\pi$
$68$	6.68304	+	1.79071i	0.810437	+	0.217156i
$69$	5.36956	−	9.30034i	0.646419	−	1.11963i
$70$	1.43611	+	1.67103i	0.171648	+	0.199726i
$71$	−3.37837	−	12.6082i	−0.400939	−	1.49632i	−0.811425	−	0.584457i	$-0.801308\pi$
$71$	−3.37837	−	12.6082i	−0.400939	−	1.49632i	0.410486	−	0.911867i	$-0.365359\pi$
$72$	12.4713	+	7.20034i	1.46976	+	0.848568i
$73$	3.22747			0.377746			0.188873	−	0.982001i	$-0.439517\pi$
$73$	3.22747			0.377746			0.188873	+	0.982001i	$0.439517\pi$
$74$	−3.61437	−	2.08676i	−0.420163	−	0.242581i
$75$	5.58919	−	12.7644i	0.645384	−	1.47390i
$76$	0.675130	−	2.51962i	0.0774427	−	0.289020i
$77$	1.13328	−	1.13328i	0.129149	−	0.129149i
$78$		0			0
$79$		−	13.5845i		−	1.52838i	−0.644992	−	0.764190i	$-0.723139\pi$
$79$		−	13.5845i		−	1.52838i	0.644992	−	0.764190i	$-0.276861\pi$
$80$	−2.49180	−	0.873774i	−0.278592	−	0.0976909i
$81$	−0.289196	−	0.500902i	−0.0321329	−	0.0556558i
$82$	1.83332	+	6.84204i	0.202456	+	0.755577i
$83$			8.56854i			0.940519i	0.882528	+	0.470260i	$0.155840\pi$
$83$			8.56854i			0.940519i	−0.882528	+	0.470260i	$0.844160\pi$
$84$	−2.47521	+	0.663230i	−0.270067	+	0.0723643i
$85$	−13.3894	−	9.14173i	−1.45228	−	0.991560i
$86$	−5.74712	−	5.74712i	−0.619728	−	0.619728i
$87$	−0.786751	+	0.210809i	−0.0843486	+	0.0226011i
$88$	−1.30054	+	4.85368i	−0.138638	+	0.517404i
$89$	−0.500868	−	0.134207i	−0.0530919	−	0.0142259i	0.232175	−	0.972674i	$-0.425416\pi$
$89$	−0.500868	−	0.134207i	−0.0530919	−	0.0142259i	−0.285267	+	0.958448i	$0.592082\pi$
$90$	−7.10435	−	8.26648i	−0.748864	−	0.871363i
$91$		0			0
$92$	−2.60014	−	2.60014i	−0.271084	−	0.271084i
$93$	−0.428870	+	0.247608i	−0.0444718	+	0.0256758i
$94$	6.94836	−	4.01164i	0.716669	−	0.413769i
$95$	−3.44659	+	5.04803i	−0.353613	+	0.517917i
$96$	9.52707	−	9.52707i	0.972353	−	0.972353i
$97$	−3.75660	+	6.50662i	−0.381425	+	0.660648i	−0.991266	−	0.131876i	$-0.957900\pi$
$97$	−3.75660	+	6.50662i	−0.381425	+	0.660648i	0.609841	+	0.792524i	$0.291233\pi$
$98$	3.10442	−	5.37702i	0.313594	−	0.543161i
$99$	−5.60626	+	5.60626i	−0.563450	+	0.563450i
$100$	−3.72638	−	2.97978i	−0.372638	−	0.297978i
$101$	−8.44685	+	4.87679i	−0.840493	+	0.485259i	−0.857432	−	0.514598i	$-0.827941\pi$
$101$	−8.44685	+	4.87679i	−0.840493	+	0.485259i	0.0169388	+	0.999857i	$0.494608\pi$
$102$	−17.8949	+	10.3316i	−1.77186	+	1.02298i
$103$	−2.52321	−	2.52321i	−0.248619	−	0.248619i	0.571784	−	0.820404i	$-0.306251\pi$
$103$	−2.52321	−	2.52321i	−0.248619	−	0.248619i	−0.820404	+	0.571784i	$0.806251\pi$
$104$		0			0
$105$	5.98759	+	0.452697i	0.584329	+	0.0441787i
$106$	−2.79182	−	0.748066i	−0.271166	−	0.0726586i
$107$	−0.115046	+	0.429359i	−0.0111220	+	0.0415077i	−0.971264	−	0.238005i	$-0.923506\pi$
$107$	−0.115046	+	0.429359i	−0.0111220	+	0.0415077i	0.960142	+	0.279513i	$0.0901731\pi$
$108$	4.53837	−	1.21605i	0.436705	−	0.117015i
$109$	−6.42134	−	6.42134i	−0.615053	−	0.615053i	0.329206	−	0.944258i	$-0.393219\pi$
$109$	−6.42134	−	6.42134i	−0.615053	−	0.615053i	−0.944258	+	0.329206i	$0.893219\pi$
$110$	2.14458	−	3.14104i	0.204477	−	0.299487i
$111$	−10.9863	+	2.94378i	−1.04278	+	0.279411i
$112$		−	1.13788i		−	0.107520i
$113$	0.500704	+	1.86865i	0.0471023	+	0.175788i	0.985470	−	0.169851i	$-0.0543287\pi$
$113$	0.500704	+	1.86865i	0.0471023	+	0.175788i	−0.938367	+	0.345639i	$0.887662\pi$
$114$	3.89521	+	6.74670i	0.364820	+	0.631886i
$115$	3.73344	+	7.76573i	0.348145	+	0.724158i
$116$			0.278893i			0.0258946i
$117$		0			0
$118$	3.65264	−	3.65264i	0.336253	−	0.336253i
$119$	1.80821	−	6.74831i	0.165758	−	0.618617i
$120$	−16.9673	+	8.15720i	−1.54890	+	0.744647i
$121$	7.13041	+	4.11674i	0.648219	+	0.374249i
$122$	−2.13050			−0.192886
$123$	16.7178	+	9.65202i	1.50739	+	0.870293i
$124$	0.0438869	+	0.163788i	0.00394116	+	0.0147086i
$125$	5.92947	+	9.47847i	0.530348	+	0.847780i
$126$	2.34850	−	4.06772i	0.209221	−	0.362381i
$127$	2.10102	+	0.562967i	0.186436	+	0.0499553i	0.350829	−	0.936440i	$-0.385900\pi$
$127$	2.10102	+	0.562967i	0.186436	+	0.0499553i	−0.164393	+	0.986395i	$0.552567\pi$
$128$	−1.09908	−	1.90366i	−0.0971460	−	0.168262i
$129$	−22.1499			−1.95019
$130$		0			0
$131$	−0.0622493			−0.00543874			−0.00271937	−	0.999996i	$-0.500866\pi$
$131$	−0.0622493			−0.00543874			−0.00271937	+	0.999996i	$0.500866\pi$
$132$	2.21166	+	3.83072i	0.192501	+	0.333421i
$133$	−2.54423	−	0.681725i	−0.220613	−	0.0591130i
$134$	3.73168	−	6.46346i	0.322368	−	0.558358i
$135$	−10.9784	−	0.830034i	−0.944872	−	0.0714380i
$136$	5.66923	+	21.1578i	0.486132	+	1.81427i
$137$	3.82564	+	2.20873i	0.326846	+	0.188705i	0.654440	−	0.756114i	$-0.272904\pi$
$137$	3.82564	+	2.20873i	0.326846	+	0.188705i	−0.327594	+	0.944819i	$0.606238\pi$
$138$	10.9820			0.934850
$139$	−11.9066	−	6.87430i	−1.00991	−	0.583070i	−0.0987430	−	0.995113i	$-0.531482\pi$
$139$	−11.9066	−	6.87430i	−1.00991	−	0.583070i	−0.911165	+	0.412043i	$0.864816\pi$
$140$	0.680356	−	1.94022i	0.0575005	−	0.163979i
$141$	5.65919	−	21.1204i	0.476590	−	1.77866i
$142$	9.43864	−	9.43864i	0.792073	−	0.792073i
$143$		0			0
$144$			5.62903i			0.469085i
$145$	0.216253	−	0.616704i	0.0179588	−	0.0512145i
$146$	1.65023	+	2.85829i	0.136574	+	0.236553i
$147$	−4.37939	−	16.3441i	−0.361206	−	1.34804i
$148$			3.89451i			0.320127i
$149$	4.18471	−	1.12129i	0.342825	−	0.0918596i	−0.0832987	−	0.996525i	$-0.526546\pi$
$149$	4.18471	−	1.12129i	0.342825	−	0.0918596i	0.426124	+	0.904665i	$0.359879\pi$
$150$	14.1621	−	1.57669i	1.15633	−	0.128736i
$151$	4.74990	+	4.74990i	0.386542	+	0.386542i	0.873452	−	0.486910i	$-0.161876\pi$
$151$	4.74990	+	4.74990i	0.386542	+	0.386542i	−0.486910	+	0.873452i	$0.661876\pi$
$152$	7.97687	−	2.13740i	0.647010	−	0.173366i
$153$	−8.94508	+	33.3835i	−0.723167	+	2.69890i
$154$	1.58310	+	0.424190i	0.127570	+	0.0341822i
$155$	0.0299556	−	0.396208i	0.00240610	−	0.0318242i
$156$		0			0
$157$	14.4488	+	14.4488i	1.15314	+	1.15314i	0.985920	+	0.167218i	$0.0534784\pi$
$157$	14.4488	+	14.4488i	1.15314	+	1.15314i	0.167218	+	0.985920i	$0.446522\pi$
$158$	12.0306	−	6.94589i	0.957106	−	0.552586i
$159$	−6.82151	+	3.93840i	−0.540981	+	0.312336i
$160$	2.00273	+	10.6232i	0.158330	+	0.839839i
$161$	−2.62554	+	2.62554i	−0.206922	+	0.206922i
$162$	0.295737	−	0.512231i	0.0232353	−	0.0402447i
$163$	−10.6926	+	18.5201i	−0.837508	+	1.45061i	0.0544633	+	0.998516i	$0.482655\pi$
$163$	−10.6926	+	18.5201i	−0.837508	+	1.45061i	−0.891972	+	0.452091i	$0.850678\pi$
$164$	4.67387	−	4.67387i	0.364968	−	0.364968i
$165$	−1.92023	−	10.1856i	−0.149490	−	0.792949i
$166$	−7.58841	+	4.38117i	−0.588975	+	0.340045i
$167$	−1.48475	+	0.857220i	−0.114893	+	0.0663337i	−0.556345	−	0.830951i	$-0.687797\pi$
$167$	−1.48475	+	0.857220i	−0.114893	+	0.0663337i	0.441452	+	0.897285i	$0.354464\pi$
$168$	−5.73655	−	5.73655i	−0.442584	−	0.442584i
$169$		0			0
$170$	1.24992	−	16.5321i	0.0958646	−	1.26795i
$171$	12.5862	+	3.37245i	0.962488	+	0.257898i
$172$	−1.96296	+	7.32587i	−0.149674	+	0.558592i
$173$	14.6596	−	3.92804i	1.11455	−	0.298643i	0.345875	−	0.938281i	$-0.387582\pi$
$173$	14.6596	−	3.92804i	1.11455	−	0.298643i	0.768677	+	0.639638i	$0.220916\pi$
$174$	−0.588968	−	0.588968i	−0.0446496	−	0.0446496i
$175$	−3.00888	+	3.76278i	−0.227450	+	0.284439i
$176$	−1.89724	+	0.508363i	−0.143010	+	0.0383193i
$177$		−	14.0776i		−	1.05814i
$178$	−0.137243	−	0.512196i	−0.0102868	−	0.0383907i
$179$	1.37961	+	2.38956i	0.103117	+	0.178604i	0.912967	−	0.408033i	$-0.133785\pi$
$179$	1.37961	+	2.38956i	0.103117	+	0.178604i	−0.809850	+	0.586637i	$0.800452\pi$
$180$	−3.36568	+	9.59815i	−0.250863	+	0.715404i
$181$		−	10.3568i		−	0.769818i	−0.922954	−	0.384909i	$-0.874233\pi$
$181$		−	10.3568i		−	0.769818i	0.922954	−	0.384909i	$-0.125767\pi$
$182$		0			0
$183$	−4.10555	+	4.10555i	−0.303491	+	0.303491i
$184$	3.01305	−	11.2449i	0.222125	−	0.828981i
$185$	3.01979	−	8.61176i	0.222019	−	0.633149i
$186$	−0.438570	−	0.253209i	−0.0321575	−	0.0185662i
$187$	−12.0596			−0.881885
$188$	−6.48384	−	3.74345i	−0.472883	−	0.273019i
$189$	−1.22793	−	4.58270i	−0.0893188	−	0.333342i
$190$	−6.23287	−	0.471242i	−0.452180	−	0.0341875i
$191$	−9.28983	+	16.0905i	−0.672189	+	1.16427i	0.305093	+	0.952322i	$0.401312\pi$
$191$	−9.28983	+	16.0905i	−0.672189	+	1.16427i	−0.977282	+	0.211943i	$0.932021\pi$
$192$	19.6663	+	5.26958i	1.41930	+	0.380299i
$193$	−6.28576	−	10.8872i	−0.452459	−	0.783681i	0.546079	−	0.837733i	$-0.316120\pi$
$193$	−6.28576	−	10.8872i	−0.452459	−	0.783681i	−0.998538	+	0.0540520i	$0.982786\pi$
$194$	−7.68313			−0.551617
$195$		0			0
$196$	−5.79377			−0.413841
$197$	−7.14308	−	12.3722i	−0.508924	−	0.881481i	−0.999947	−	0.0103349i	$-0.996710\pi$
$197$	−7.14308	−	12.3722i	−0.508924	−	0.881481i	0.491023	−	0.871147i	$-0.336623\pi$
$198$	−7.83150	−	2.09845i	−0.556561	−	0.149130i
$199$	−7.36781	+	12.7614i	−0.522291	+	0.904634i	0.477373	+	0.878701i	$0.341589\pi$
$199$	−7.36781	+	12.7614i	−0.522291	+	0.904634i	−0.999664	+	0.0259331i	$0.991744\pi$
$200$	2.27113	−	14.9336i	0.160593	−	1.05597i
$201$	−5.26425	−	19.6465i	−0.371312	−	1.38575i
$202$	−8.63790	−	4.98709i	−0.607760	−	0.350891i
$203$	0.281617			0.0197656
$204$	16.6986	+	9.64094i	1.16914	+	0.675001i
$205$	−13.9592	+	6.71103i	−0.974956	+	0.468718i
$206$	0.944449	−	3.52473i	0.0658029	−	0.245580i
$207$	12.9884	−	12.9884i	0.902756	−	0.902756i
$208$		0			0
$209$			4.54668i			0.314500i
$210$	2.66059	+	5.53415i	0.183598	+	0.381893i
$211$	4.26604	+	7.38900i	0.293686	+	0.508680i	0.974678	−	0.223611i	$-0.0717845\pi$
$211$	4.26604	+	7.38900i	0.293686	+	0.508680i	−0.680992	+	0.732291i	$0.738451\pi$
$212$	0.698056	+	2.60518i	0.0479427	+	0.178925i
$213$		−	36.3773i		−	2.49253i
$214$	−0.439070	+	0.117649i	−0.0300142	+	0.00804229i
$215$	10.0211	−	14.6773i	0.683431	−	1.00098i
$216$	10.5181	+	10.5181i	0.715669	+	0.715669i
$217$	0.165388	−	0.0443156i	0.0112273	−	0.00300834i
$218$	2.40353	−	8.97011i	0.162788	−	0.607532i
$219$	8.68810	+	2.32797i	0.587087	+	0.157310i
$220$	−3.53897	−	0.267567i	−0.238597	−	0.0180394i
$221$		0			0
$222$	−8.22445	−	8.22445i	−0.551989	−	0.551989i
$223$	−6.11483	+	3.53040i	−0.409479	+	0.236413i	−0.690566	−	0.723269i	$-0.742638\pi$
$223$	−6.11483	+	3.53040i	−0.409479	+	0.236413i	0.281087	+	0.959682i	$0.409305\pi$
$224$	−4.03432	+	2.32922i	−0.269555	+	0.155627i
$225$	14.8848	−	18.6142i	0.992317	−	1.24095i
$226$	−1.39889	+	1.39889i	−0.0930527	+	0.0930527i
$227$	8.58775	−	14.8744i	0.569989	−	0.987249i	−0.426578	−	0.904451i	$-0.640281\pi$
$227$	8.58775	−	14.8744i	0.569989	−	0.987249i	0.996566	−	0.0827985i	$-0.0263858\pi$
$228$	3.63480	−	6.29566i	0.240721	−	0.416940i
$229$	8.90647	−	8.90647i	0.588556	−	0.588556i	−0.348684	−	0.937240i	$-0.613371\pi$
$229$	8.90647	−	8.90647i	0.588556	−	0.588556i	0.937240	+	0.348684i	$0.113371\pi$
$230$	−4.96849	+	7.27707i	−0.327612	+	0.479836i
$231$	3.86813	−	2.23327i	0.254504	−	0.146938i
$232$	−0.764655	+	0.441474i	−0.0502021	+	0.0289842i
$233$	17.5822	+	17.5822i	1.15185	+	1.15185i	0.986182	+	0.165666i	$0.0529773\pi$
$233$	17.5822	+	17.5822i	1.15185	+	1.15185i	0.165666	+	0.986182i	$0.447023\pi$
$234$		0			0
$235$	11.4348	+	13.3053i	0.745923	+	0.867940i
$236$	−4.65603	−	1.24758i	−0.303082	−	0.0812105i
$237$	9.79852	−	36.5686i	0.636482	−	2.37538i
$238$	6.90095	−	1.84910i	0.447322	−	0.119860i
$239$	2.23488	+	2.23488i	0.144562	+	0.144562i	0.775684	−	0.631122i	$-0.217405\pi$
$239$	2.23488	+	2.23488i	0.144562	+	0.144562i	−0.631122	+	0.775684i	$0.717405\pi$
$240$	−6.07750	−	4.14947i	−0.392301	−	0.267847i
$241$	17.4048	−	4.66361i	1.12114	−	0.300409i	0.349797	−	0.936825i	$-0.386250\pi$
$241$	17.4048	−	4.66361i	1.12114	−	0.300409i	0.771346	+	0.636416i	$0.219584\pi$
$242$			8.41971i			0.541239i
$243$	−4.24025	−	15.8248i	−0.272012	−	1.01516i
$244$	0.994033	+	1.72172i	0.0636364	+	0.110222i
$245$	12.8115	+	4.49247i	0.818497	+	0.287013i
$246$			19.7406i			1.25862i
$247$		0			0
$248$	−0.379596	+	0.379596i	−0.0241044	+	0.0241044i
$249$	−6.18048	+	23.0659i	−0.391672	+	1.46174i
$250$	−5.36246	+	10.0976i	−0.339152	+	0.638631i
$251$	−12.1009	−	6.98644i	−0.763800	−	0.440980i	0.0668586	−	0.997762i	$-0.478702\pi$
$251$	−12.1009	−	6.98644i	−0.763800	−	0.440980i	−0.830658	+	0.556782i	$0.812036\pi$
$252$	−4.38299			−0.276102
$253$	5.55068	+	3.20468i	0.348968	+	0.201477i
$254$	0.575700	+	2.14854i	0.0361227	+	0.134812i
$255$	−29.4493	−	34.2666i	−1.84419	−	2.14586i
$256$	8.42962	−	14.6005i	0.526851	−	0.912533i
$257$	22.3881	+	5.99887i	1.39653	+	0.374199i	0.877098	−	0.480312i	$-0.159476\pi$
$257$	22.3881	+	5.99887i	1.39653	+	0.374199i	0.519433	+	0.854511i	$0.326143\pi$
$258$	−11.3254	−	19.6162i	−0.705090	−	1.22125i
$259$	3.93255			0.244357
$260$		0			0
$261$	−1.39314			−0.0862334
$262$	−0.0318286	−	0.0551288i	−0.00196638	−	0.00340587i
$263$	−1.25672	−	0.336737i	−0.0774926	−	0.0207641i	0.219864	−	0.975530i	$-0.429438\pi$
$263$	−1.25672	−	0.336737i	−0.0774926	−	0.0207641i	−0.297357	+	0.954766i	$0.596105\pi$
$264$	−7.00191	+	12.1277i	−0.430938	+	0.746407i
$265$	0.476468	−	6.30199i	0.0292692	−	0.387128i
$266$	−0.697144	−	2.60178i	−0.0427446	−	0.159525i
$267$	−1.25150	−	0.722551i	−0.0765903	−	0.0442194i
$268$	−6.96441			−0.425419
$269$	−6.87429	−	3.96887i	−0.419133	−	0.241986i	0.275574	−	0.961280i	$-0.411132\pi$
$269$	−6.87429	−	3.96887i	−0.419133	−	0.241986i	−0.694706	+	0.719294i	$0.744466\pi$
$270$	−4.87828	−	10.1470i	−0.296883	−	0.617529i
$271$	0.231787	−	0.865041i	0.0140801	−	0.0525475i	−0.958528	−	0.284997i	$-0.908007\pi$
$271$	0.231787	−	0.865041i	0.0140801	−	0.0525475i	0.972608	+	0.232450i	$0.0746741\pi$
$272$	−6.05429	+	6.05429i	−0.367095	+	0.367095i
$273$		0			0
$274$			4.51738i			0.272905i
$275$	7.61810	+	3.33577i	0.459389	+	0.201154i
$276$	−5.12391	−	8.87488i	−0.308423	−	0.534205i
$277$	−2.47298	−	9.22930i	−0.148587	−	0.554535i	−0.999569	−	0.0293404i	$-0.990659\pi$
$277$	−2.47298	−	9.22930i	−0.148587	−	0.554535i	0.850982	−	0.525194i	$-0.176007\pi$
$278$		−	14.0596i		−	0.843236i
$279$	−0.818165	+	0.219227i	−0.0489823	+	0.0131248i
$280$	6.39657	−	1.20591i	0.382268	−	0.0720668i
$281$	5.58408	+	5.58408i	0.333118	+	0.333118i	0.853769	−	0.520651i	$-0.174311\pi$
$281$	5.58408	+	5.58408i	0.333118	+	0.333118i	−0.520651	+	0.853769i	$0.674311\pi$
$282$	21.5981	−	5.78719i	1.28615	−	0.344622i
$283$	5.46218	−	20.3851i	0.324693	−	1.21177i	−0.589927	−	0.807457i	$-0.700843\pi$
$283$	5.46218	−	20.3851i	0.324693	−	1.21177i	0.914620	−	0.404314i	$-0.132490\pi$
$284$	−12.0315	−	3.22382i	−0.713936	−	0.191298i
$285$	−12.9191	+	11.1029i	−0.765262	+	0.657679i
$286$		0			0
$287$	−4.71953	−	4.71953i	−0.278585	−	0.278585i
$288$	19.9576	−	11.5225i	1.17601	−	0.678970i
$289$	−30.8040	+	17.7847i	−1.81200	+	1.04616i
$290$	0.656733	−	0.123810i	0.0385647	−	0.00727037i
$291$	−14.8057	+	14.8057i	−0.867927	+	0.867927i
$292$	1.53991	−	2.66720i	0.0901164	−	0.156086i
$293$	−2.01079	+	3.48280i	−0.117472	+	0.203467i	−0.918765	−	0.394805i	$-0.870812\pi$
$293$	−2.01079	+	3.48280i	−0.117472	+	0.203467i	0.801293	+	0.598272i	$0.204146\pi$
$294$	12.2353	−	12.2353i	0.713579	−	0.713579i
$295$	9.32830	+	6.36899i	0.543115	+	0.370817i
$296$	−10.6778	+	6.16482i	−0.620633	+	0.358323i
$297$	−7.09234	+	4.09477i	−0.411539	+	0.237602i
$298$	3.13271	+	3.13271i	0.181473	+	0.181473i
$299$		0			0
$300$	−7.88183	−	10.7092i	−0.455058	−	0.618294i
$301$	7.39742	+	1.98213i	0.426380	+	0.114248i
$302$	−1.77791	+	6.63524i	−0.102307	+	0.381815i
$303$	−26.2559	+	7.03525i	−1.50836	+	0.404165i
$304$	2.28257	+	2.28257i	0.130914	+	0.130914i
$305$	−0.863049	−	4.57792i	−0.0494180	−	0.262131i
$306$	−34.1386	+	9.14740i	−1.95157	+	0.522922i
$307$			24.2191i			1.38226i	0.722732	+	0.691128i	$0.242886\pi$
$307$			24.2191i			1.38226i	−0.722732	+	0.691128i	$0.757114\pi$
$308$	−0.395832	−	1.47727i	−0.0225546	−	0.0841750i
$309$	−4.97231	−	8.61229i	−0.282865	−	0.489936i
$310$	0.366203	−	0.176055i	0.0207989	−	0.00999927i
$311$			7.87243i			0.446405i	0.974772	+	0.223202i	$0.0716511\pi$
$311$			7.87243i			0.446405i	−0.974772	+	0.223202i	$0.928349\pi$
$312$		0			0
$313$	3.39121	−	3.39121i	0.191683	−	0.191683i	−0.604740	−	0.796423i	$-0.706723\pi$
$313$	3.39121	−	3.39121i	0.191683	−	0.191683i	0.796423	+	0.604740i	$0.206723\pi$
$314$	−5.40824	+	20.1838i	−0.305204	+	1.13904i
$315$	9.69191	+	3.39855i	0.546077	+	0.191487i
$316$	−11.2264	−	6.48154i	−0.631532	−	0.364615i
$317$	22.9255			1.28762			0.643812	−	0.765184i	$-0.277352\pi$
$317$	22.9255			1.28762			0.643812	+	0.765184i	$0.277352\pi$
$318$	−6.97580	−	4.02748i	−0.391183	−	0.225850i
$319$	−0.125816	−	0.469553i	−0.00704436	−	0.0262899i
$320$	−12.3893	+	10.6476i	−0.692581	+	0.595216i
$321$	−0.619393	+	1.07282i	−0.0345712	+	0.0598790i
$322$	−3.66768	−	0.982751i	−0.204392	−	0.0547666i
$323$	9.90979	+	17.1643i	0.551395	+	0.955044i
$324$	−0.551932			−0.0306629
$325$		0			0
$326$	−21.8689			−1.21120
$327$	−12.6541	−	21.9175i	−0.699771	−	1.21204i
$328$	20.2131	+	5.41609i	1.11608	+	0.299053i
$329$	−3.78001	+	6.54718i	−0.208399	+	0.360958i
$330$	8.03868	−	6.90858i	0.442515	−	0.380305i
$331$	8.68470	+	32.4118i	0.477354	+	1.78151i	0.612264	+	0.790653i	$0.290259\pi$
$331$	8.68470	+	32.4118i	0.477354	+	1.78151i	−0.134910	+	0.990858i	$0.543075\pi$
$332$	7.08110	+	4.08828i	0.388626	+	0.224373i
$333$	−19.4541			−1.06608
$334$	−1.51833	−	0.876609i	−0.0830794	−	0.0479659i
$335$	15.4001	+	5.40018i	0.841398	+	0.295044i
$336$	0.820752	−	3.06309i	0.0447757	−	0.167105i
$337$	14.5544	−	14.5544i	0.792826	−	0.792826i	−0.189126	−	0.981953i	$-0.560566\pi$
$337$	14.5544	−	14.5544i	0.792826	−	0.792826i	0.981953	+	0.189126i	$0.0605656\pi$
$338$		0			0
$339$			5.39143i			0.292822i
$340$	−13.9432	+	6.70333i	−0.756178	+	0.363539i
$341$	−0.147779	−	0.255960i	−0.00800267	−	0.0138610i
$342$	3.44873	+	12.8708i	0.186486	+	0.695975i
$343$			12.5954i			0.680087i
$344$	−23.1930	+	6.21454i	−1.25048	+	0.335065i
$345$	4.44873	+	23.5977i	0.239512	+	1.27046i
$346$	10.9743	+	10.9743i	0.589983	+	0.589983i
$347$	−22.0356	+	5.90442i	−1.18293	+	0.316966i	−0.796089	−	0.605179i	$-0.793101\pi$
$347$	−22.0356	+	5.90442i	−1.18293	+	0.316966i	−0.386844	+	0.922145i	$0.626435\pi$
$348$	−0.201165	+	0.750759i	−0.0107836	+	0.0402449i
$349$	−10.0317	−	2.68798i	−0.536983	−	0.143884i	−0.0198718	−	0.999803i	$-0.506326\pi$
$349$	−10.0317	−	2.68798i	−0.536983	−	0.143884i	−0.517111	+	0.855918i	$0.672992\pi$
$350$	−4.87083	−	0.740762i	−0.260357	−	0.0395954i
$351$		0			0
$352$	5.68599	+	5.68599i	0.303064	+	0.303064i
$353$	−3.72420	+	2.15017i	−0.198219	+	0.114442i	−0.595825	−	0.803115i	$-0.703175\pi$
$353$	−3.72420	+	2.15017i	−0.198219	+	0.114442i	0.397605	+	0.917556i	$0.369841\pi$
$354$	12.4673	−	7.19799i	0.662629	−	0.382569i
$355$	24.1049	+	16.4578i	1.27935	+	0.873491i
$356$	−0.349887	+	0.349887i	−0.0185440	+	0.0185440i
$357$	9.73511	−	16.8617i	0.515237	−	0.892416i
$358$	−1.41082	+	2.44361i	−0.0745640	+	0.129149i
$359$	10.4273	−	10.4273i	0.550333	−	0.550333i	−0.376204	−	0.926537i	$-0.622771\pi$
$359$	10.4273	−	10.4273i	0.550333	−	0.550333i	0.926537	+	0.376204i	$0.122771\pi$
$360$	−31.6435	+	5.96555i	−1.66776	+	0.314412i
$361$	−9.98326	+	5.76384i	−0.525435	+	0.303360i
$362$	9.17216	−	5.29555i	0.482078	−	0.278328i
$363$	16.2251	+	16.2251i	0.851599	+	0.851599i
$364$		0			0
$365$	−5.47327	+	4.70382i	−0.286484	+	0.246209i
$366$	−5.73514	−	1.53673i	−0.299780	−	0.0803259i
$367$	2.95657	−	11.0341i	0.154331	−	0.575973i	−0.844830	−	0.535034i	$-0.820299\pi$
$367$	2.95657	−	11.0341i	0.154331	−	0.575973i	0.999162	−	0.0409383i	$-0.0130347\pi$
$368$	4.39546	−	1.17776i	0.229129	−	0.0613950i
$369$	23.3472	+	23.3472i	1.21541	+	1.21541i
$370$	9.17073	−	1.72890i	0.476763	−	0.0898814i
$371$	2.63063	−	0.704874i	0.136575	−	0.0365953i
$372$			0.472562i			0.0245012i
$373$	7.28755	+	27.1975i	0.377335	+	1.40823i	0.849903	+	0.526939i	$0.176661\pi$
$373$	7.28755	+	27.1975i	0.377335	+	1.40823i	−0.472568	+	0.881294i	$0.656673\pi$
$374$	−6.16618	−	10.6801i	−0.318846	−	0.552257i
$375$	9.12489	+	29.7923i	0.471207	+	1.53847i
$376$		−	23.7028i		−	1.22238i
$377$		0			0
$378$	3.43065	−	3.43065i	0.176453	−	0.176453i
$379$	4.38232	−	16.3551i	0.225105	−	0.840103i	−0.757258	−	0.653116i	$-0.773461\pi$
$379$	4.38232	−	16.3551i	0.225105	−	0.840103i	0.982362	−	0.186987i	$-0.0598721\pi$
$380$	2.52727	+	5.25684i	0.129646	+	0.269670i
$381$	5.24973	+	3.03093i	0.268952	+	0.155279i
$382$	−18.9999			−0.972119
$383$	5.71918	+	3.30197i	0.292236	+	0.168723i	0.638950	−	0.769248i	$-0.279369\pi$
$383$	5.71918	+	3.30197i	0.292236	+	0.168723i	−0.346714	+	0.937971i	$0.612702\pi$
$384$	−1.58553	−	5.91729i	−0.0809114	−	0.301966i
$385$	−0.270181	+	3.57354i	−0.0137697	+	0.182124i
$386$	6.42793	−	11.1335i	0.327173	−	0.566680i
$387$	−36.5946	−	9.80550i	−1.86021	−	0.498441i
$388$	3.58475	+	6.20897i	0.181988	+	0.315212i
$389$	−33.6949			−1.70840			−0.854199	−	0.519946i	$-0.825952\pi$
$389$	−33.6949			−1.70840			−0.854199	+	0.519946i	$0.825952\pi$
$390$		0			0
$391$	27.9393			1.41295
$392$	−9.17126	−	15.8851i	−0.463218	−	0.802318i
$393$	−0.167570	−	0.0449004i	−0.00845281	−	0.00226492i
$394$	7.30464	−	12.6520i	0.368003	−	0.637399i
$395$	19.7986	+	23.0372i	0.996175	+	1.15913i
$396$	1.95816	+	7.30795i	0.0984012	+	0.367238i
$397$	−5.04104	−	2.91045i	−0.253002	−	0.146071i	0.368136	−	0.929772i	$-0.379996\pi$
$397$	−5.04104	−	2.91045i	−0.253002	−	0.146071i	−0.621138	+	0.783701i	$0.713329\pi$
$398$	−15.0689			−0.755337
$399$	−6.35716	−	3.67031i	−0.318256	−	0.183745i
$400$	5.49918	−	2.14986i	0.274959	−	0.107493i
$401$	−0.0683280	+	0.255004i	−0.00341214	+	0.0127343i	−0.967611	−	0.252446i	$-0.918765\pi$
$401$	−0.0683280	+	0.255004i	−0.00341214	+	0.0127343i	0.964199	+	0.265181i	$0.0854316\pi$
$402$	14.7075	−	14.7075i	0.733544	−	0.733544i
$403$		0			0
$404$			9.30738i			0.463060i
$405$	1.22046	+	0.427966i	0.0606453	+	0.0212658i
$406$	0.143993	+	0.249404i	0.00714627	+	0.0123777i
$407$	−1.75692	−	6.55691i	−0.0870872	−	0.325014i
$408$			61.0446i			3.02216i
$409$	−35.8975	+	9.61872i	−1.77502	+	0.475615i	−0.989661	−	0.143427i	$-0.954188\pi$
$409$	−35.8975	+	9.61872i	−1.77502	+	0.475615i	−0.785358	+	0.619042i	$0.787521\pi$
$410$	−13.0809	−	8.93108i	−0.646017	−	0.441074i
$411$	8.70518	+	8.70518i	0.429395	+	0.429395i
$412$	−3.28909	+	0.881310i	−0.162042	+	0.0434190i
$413$	−1.25977	+	4.70151i	−0.0619890	+	0.231346i
$414$	18.1438	+	4.86161i	0.891718	+	0.238935i
$415$	−12.4881	−	14.5309i	−0.613016	−	0.713293i
$416$		0			0
$417$	−27.0934	−	27.0934i	−1.32677	−	1.32677i
$418$	−4.02660	+	2.32476i	−0.196947	+	0.113708i
$419$	29.3721	−	16.9580i	1.43492	−	0.828451i	0.437428	−	0.899253i	$-0.355889\pi$
$419$	29.3721	−	16.9580i	1.43492	−	0.828451i	0.997490	+	0.0708027i	$0.0225561\pi$
$420$	3.23095	−	4.73219i	0.157654	−	0.230907i
$421$	−21.5599	+	21.5599i	−1.05076	+	1.05076i	−0.0521230	+	0.998641i	$0.516599\pi$
$421$	−21.5599	+	21.5599i	−1.05076	+	1.05076i	−0.998641	+	0.0521230i	$0.983401\pi$
$422$	−4.36253	+	7.55613i	−0.212365	+	0.367826i
$423$	18.6995	−	32.3885i	0.909201	−	1.57478i
$424$	−6.03777	+	6.03777i	−0.293220	+	0.293220i
$425$	36.0298	−	4.01124i	1.74770	−	0.194574i
$426$	32.2162	−	18.6000i	1.56088	−	0.901175i
$427$	1.73853	−	1.00374i	0.0841335	−	0.0485745i
$428$	0.299934	+	0.299934i	0.0144979	+	0.0144979i
$429$		0			0
$430$	18.1223	+	1.37015i	0.873933	+	0.0660745i
$431$	−4.44167	−	1.19014i	−0.213948	−	0.0573271i	0.150253	−	0.988648i	$-0.451991\pi$
$431$	−4.44167	−	1.19014i	−0.213948	−	0.0573271i	−0.364201	+	0.931320i	$0.618658\pi$
$432$	−1.50488	+	5.61627i	−0.0724033	+	0.270213i
$433$	3.86627	−	1.03596i	0.185801	−	0.0497853i	−0.164719	−	0.986341i	$-0.552672\pi$
$433$	3.86627	−	1.03596i	0.185801	−	0.0497853i	0.350520	+	0.936555i	$0.386005\pi$
$434$	0.123811	+	0.123811i	0.00594311	+	0.00594311i
$435$	1.02696	−	1.50414i	0.0492392	−	0.0721179i
$436$	−8.37043	+	2.24285i	−0.400871	+	0.107413i
$437$		−	10.5336i		−	0.503890i
$438$	2.38062	+	8.88461i	0.113751	+	0.424523i
$439$	−11.3618	−	19.6793i	−0.542271	−	0.939242i	−0.998773	−	0.0495192i	$-0.984231\pi$
$439$	−11.3618	−	19.6793i	−0.542271	−	0.939242i	0.456502	−	0.889723i	$-0.349102\pi$
$440$	−4.86842	−	10.1265i	−0.232093	−	0.482763i
$441$		−	28.9414i		−	1.37816i
$442$		0			0
$443$	1.84874	−	1.84874i	0.0878361	−	0.0878361i	−0.661824	−	0.749660i	$-0.730217\pi$
$443$	1.84874	−	1.84874i	0.0878361	−	0.0878361i	0.749660	+	0.661824i	$0.230217\pi$
$444$	−2.80911	+	10.4837i	−0.133314	+	0.497536i
$445$	1.04499	−	0.502388i	0.0495373	−	0.0238155i
$446$	−6.25313	−	3.61025i	−0.296094	−	0.170950i
$447$	12.0737			0.571067
$448$	−6.09644	−	3.51978i	−0.288030	−	0.166294i
$449$	8.32705	+	31.0770i	0.392978	+	1.46661i	0.825197	+	0.564845i	$0.191064\pi$
$449$	8.32705	+	31.0770i	0.392978	+	1.46661i	−0.432219	+	0.901769i	$0.642269\pi$
$450$	24.0957	+	3.66451i	1.13588	+	0.172746i
$451$	−5.76056	+	9.97759i	−0.271254	+	0.469826i
$452$	1.78317	+	0.477798i	0.0838731	+	0.0224737i
$453$	9.36029	+	16.2125i	0.439785	+	0.761729i
$454$	17.5640			0.824318
$455$		0			0
$456$	23.0149			1.07777
$457$	14.1837	+	24.5669i	0.663486	+	1.14919i	0.979693	+	0.200501i	$0.0642571\pi$
$457$	14.1837	+	24.5669i	0.663486	+	1.14919i	−0.316208	+	0.948690i	$0.602410\pi$
$458$	12.4416	+	3.33373i	0.581360	+	0.155775i
$459$	−17.8496	+	30.9165i	−0.833149	+	1.44306i
$460$	8.19898	+	0.619891i	0.382279	+	0.0289026i
$461$	2.97890	+	11.1174i	0.138741	+	0.517790i	0.999954	+	0.00954570i	$0.00303854\pi$
$461$	2.97890	+	11.1174i	0.138741	+	0.517790i	−0.861213	+	0.508244i	$0.830295\pi$
$462$	3.95562	+	2.28378i	0.184032	+	0.106251i
$463$	29.9456			1.39169			0.695845	−	0.718192i	$-0.255030\pi$
$463$	29.9456			1.39169			0.695845	+	0.718192i	$0.255030\pi$
$464$	−0.298893	−	0.172566i	−0.0138758	−	0.00801118i
$465$	0.366423	−	1.04496i	0.0169925	−	0.0484586i
$466$	−6.58109	+	24.5609i	−0.304863	+	1.13776i
$467$	−16.1332	+	16.1332i	−0.746557	+	0.746557i	−0.973831	−	0.227274i	$-0.927019\pi$
$467$	−16.1332	+	16.1332i	−0.746557	+	0.746557i	0.227274	+	0.973831i	$0.427019\pi$
$468$		0			0
$469$			7.03244i			0.324728i
$470$	−5.93662	+	16.9299i	−0.273836	+	0.780918i
$471$	28.4732	+	49.3170i	1.31197	+	2.27241i
$472$	−3.94971	−	14.7405i	−0.181800	−	0.678488i
$473$		−	13.2196i		−	0.607837i
$474$	37.3957	−	10.0201i	1.71764	−	0.460240i
$475$	−1.51231	−	13.5838i	−0.0693894	−	0.623270i
$476$	−4.71411	−	4.71411i	−0.216071	−	0.216071i
$477$	−13.0136	+	3.48697i	−0.595850	+	0.159657i
$478$	−0.836524	+	3.12195i	−0.0382617	+	0.142795i
$479$	−37.5043	−	10.0493i	−1.71362	−	0.459162i	−0.737309	−	0.675555i	$-0.763904\pi$
$479$	−37.5043	−	10.0493i	−1.71362	−	0.459162i	−0.976306	+	0.216393i	$0.930571\pi$
$480$	−2.27132	+	30.0415i	−0.103671	+	1.37120i
$481$		0			0
$482$	13.0294	+	13.0294i	0.593473	+	0.593473i
$483$	−8.96157	+	5.17396i	−0.407765	+	0.235424i
$484$	6.80421	−	3.92841i	0.309282	−	0.178564i
$485$	−3.11238	−	16.5092i	−0.141326	−	0.749645i
$486$	11.8466	−	11.8466i	0.537372	−	0.537372i
$487$	−14.4718	+	25.0660i	−0.655782	+	1.13585i	0.325916	+	0.945399i	$0.394327\pi$
$487$	−14.4718	+	25.0660i	−0.655782	+	1.13585i	−0.981697	+	0.190448i	$0.939006\pi$
$488$	−3.14701	+	5.45078i	−0.142458	+	0.246745i
$489$	−42.1422	+	42.1422i	−1.90574	+	1.90574i
$490$	2.57205	+	13.6431i	0.116193	+	0.616332i
$491$	−6.30003	+	3.63733i	−0.284317	+	0.164150i	−0.635376	−	0.772203i	$-0.719155\pi$
$491$	−6.30003	+	3.63733i	−0.284317	+	0.164150i	0.351059	+	0.936353i	$0.385822\pi$
$492$	15.9530	−	9.21046i	0.719216	−	0.415240i
$493$	−1.49839	−	1.49839i	−0.0674842	−	0.0674842i
$494$		0			0
$495$	1.33657	−	17.6781i	0.0600743	−	0.794571i
$496$	−0.202689	−	0.0543104i	−0.00910102	−	0.00243861i
$497$	−3.25531	+	12.1490i	−0.146021	+	0.544956i
$498$	−23.5876	+	6.32027i	−1.05698	+	0.283218i
$499$	−4.24201	−	4.24201i	−0.189899	−	0.189899i	0.605754	−	0.795652i	$-0.292872\pi$
$499$	−4.24201	−	4.24201i	−0.189899	−	0.189899i	−0.795652	+	0.605754i	$0.792872\pi$
$500$	10.6622	−	0.377731i	0.476827	−	0.0168926i
$501$	−4.61515	+	1.23663i	−0.206190	+	0.0552483i
$502$		−	14.2889i		−	0.637745i
$503$	0.939636	+	3.50677i	0.0418963	+	0.156359i	0.983705	−	0.179790i	$-0.0575419\pi$
$503$	0.939636	+	3.50677i	0.0418963	+	0.156359i	−0.941809	+	0.336149i	$0.890875\pi$
$504$	−6.93805	−	12.0171i	−0.309046	−	0.535283i
$505$	7.21692	−	20.5810i	0.321149	−	0.915843i
$506$			6.55433i			0.291376i
$507$		0			0
$508$	1.46769	−	1.46769i	0.0651184	−	0.0651184i
$509$	−6.02986	+	22.5037i	−0.267269	+	0.997460i	0.693578	+	0.720381i	$0.256033\pi$
$509$	−6.02986	+	22.5037i	−0.267269	+	0.997460i	−0.960847	+	0.277079i	$0.910634\pi$
$510$	15.2893	−	43.6015i	0.677020	−	1.93071i
$511$	−2.69325	−	1.55495i	−0.119143	−	0.0687870i
$512$	12.8442			0.567640
$513$	11.6560	+	6.72962i	0.514627	+	0.297120i
$514$	6.13455	+	22.8945i	0.270584	+	1.00983i
$515$	7.95639	+	0.601550i	0.350600	+	0.0265075i
$516$	−10.5683	+	18.3048i	−0.465243	+	0.805824i
$517$	12.6052	+	3.37754i	0.554375	+	0.148544i
$518$	2.01075	+	3.48272i	0.0883472	+	0.153022i
$519$	42.2960			1.85659
$520$		0			0
$521$	−13.0530			−0.571862			−0.285931	−	0.958250i	$-0.592303\pi$
$521$	−13.0530			−0.571862			−0.285931	+	0.958250i	$0.592303\pi$
$522$	−0.712327	−	1.23379i	−0.0311777	−	0.0540013i
$523$	−16.4404	−	4.40520i	−0.718890	−	0.192626i	−0.119214	−	0.992869i	$-0.538037\pi$
$523$	−16.4404	−	4.40520i	−0.718890	−	0.192626i	−0.599677	+	0.800243i	$0.704704\pi$
$524$	−0.0297008	+	0.0514432i	−0.00129748	+	0.00224731i
$525$	−10.8138	+	7.95882i	−0.471952	+	0.347351i
$526$	−0.344353	−	1.28514i	−0.0150145	−	0.0560349i
$527$	−1.11577	−	0.644187i	−0.0486035	−	0.0280612i
$528$	−5.47391			−0.238221
$529$	7.05896	+	4.07549i	0.306911	+	0.177195i
$530$	5.82475	−	2.80030i	0.253011	−	0.121637i
$531$	6.23198	−	23.2581i	0.270445	−	1.00931i
$532$	−1.77730	+	1.77730i	−0.0770558	+	0.0770558i
$533$		0			0
$534$		−	1.47779i		−	0.0639501i
$535$	−0.430663	−	0.895798i	−0.0186192	−	0.0387287i
$536$	−11.0243	−	19.0947i	−0.476178	−	0.824765i
$537$	1.99023	+	7.42764i	0.0858847	+	0.320526i
$538$		−	8.11728i		−	0.349961i
$539$	9.75457	−	2.61373i	0.420159	−	0.112581i
$540$	−5.92404	+	8.67662i	−0.254930	+	0.373382i
$541$	−10.9728	−	10.9728i	−0.471756	−	0.471756i	0.430727	−	0.902483i	$-0.358257\pi$
$541$	−10.9728	−	10.9728i	−0.471756	−	0.471756i	−0.902483	+	0.430727i	$0.858257\pi$
$542$	0.884606	−	0.237029i	0.0379971	−	0.0101813i
$543$	7.47039	−	27.8799i	0.320585	−	1.19644i
$544$	33.8583	+	9.07231i	1.45166	+	0.388972i
$545$	20.2483	+	1.53089i	0.867340	+	0.0655761i
$546$		0			0
$547$	−20.4450	−	20.4450i	−0.874167	−	0.874167i	0.118756	−	0.992923i	$-0.462109\pi$
$547$	−20.4450	−	20.4450i	−0.874167	−	0.874167i	−0.992923	+	0.118756i	$0.962109\pi$
$548$	3.65063	−	2.10769i	0.155947	−	0.0900361i
$549$	−8.60042	+	4.96545i	−0.367057	+	0.211920i
$550$	0.941005	+	8.45230i	0.0401246	+	0.360407i
$551$	−0.564920	+	0.564920i	−0.0240664	+	0.0240664i
$552$	16.2218	−	28.0970i	0.690446	−	1.19589i
$553$	−6.54485	+	11.3360i	−0.278315	+	0.482056i
$554$	6.90913	−	6.90913i	0.293541	−	0.293541i
$555$	14.3407	−	21.0040i	0.608729	−	0.891572i
$556$	−11.3619	+	6.55982i	−0.481854	+	0.278198i
$557$	−11.7609	+	6.79015i	−0.498324	+	0.287708i	−0.728021	−	0.685555i	$-0.759560\pi$
$557$	−11.7609	+	6.79015i	−0.498324	+	0.287708i	0.229697	+	0.973262i	$0.426226\pi$
$558$	−0.612485	−	0.612485i	−0.0259286	−	0.0259286i
$559$		0			0
$560$	1.65839	+	1.92967i	0.0700797	+	0.0815432i
$561$	−32.4636	−	8.69858i	−1.37061	−	0.367254i
$562$	−2.09014	+	7.80052i	−0.0881673	+	0.329045i
$563$	−4.68514	+	1.25538i	−0.197455	+	0.0529080i	−0.356191	−	0.934413i	$-0.615925\pi$
$563$	−4.68514	+	1.25538i	−0.197455	+	0.0529080i	0.158736	+	0.987321i	$0.449258\pi$
$564$	−14.7539	−	14.7539i	−0.621251	−	0.621251i
$565$	−3.57256	−	2.43920i	−0.150299	−	0.102618i
$566$	20.8462	−	5.58573i	0.876232	−	0.234786i
$567$			0.557323i			0.0234054i
$568$	−10.2063	−	38.0904i	−0.428247	−	1.59824i
$569$	−0.124396	−	0.215461i	−0.00521497	−	0.00903259i	0.863406	−	0.504509i	$-0.168327\pi$
$569$	−0.124396	−	0.215461i	−0.00521497	−	0.00903259i	−0.868621	+	0.495477i	$0.834993\pi$
$570$	−16.4385	−	5.76432i	−0.688534	−	0.241441i
$571$			7.72842i			0.323424i	0.986838	+	0.161712i	$0.0517016\pi$
$571$			7.72842i			0.323424i	−0.986838	+	0.161712i	$0.948298\pi$
$572$		0			0
$573$	−36.6136	+	36.6136i	−1.52955	+	1.52955i
$574$	1.76654	−	6.59281i	0.0737339	−	0.275179i
$575$	−17.6494	−	7.72820i	−0.736030	−	0.322288i
$576$	30.1587	+	17.4121i	1.25661	+	0.725506i
$577$	−12.1339			−0.505141			−0.252570	−	0.967578i	$-0.581276\pi$
$577$	−12.1339			−0.505141			−0.252570	+	0.967578i	$0.581276\pi$
$578$	−31.5007	−	18.1869i	−1.31026	−	0.756477i
$579$	−9.06783	−	33.8416i	−0.376846	−	1.40641i
$580$	−0.406469	−	0.472958i	−0.0168777	−	0.0196385i
$581$	4.12821	−	7.15027i	0.171267	−	0.296643i
$582$	−20.6824	−	5.54184i	−0.857315	−	0.229717i
$583$	−2.35054	−	4.07125i	−0.0973492	−	0.168614i
$584$	9.75040			0.403475
$585$		0			0
$586$	−4.11255			−0.169888
$587$	18.2647	+	31.6354i	0.753865	+	1.30573i	0.945937	+	0.324351i	$0.105146\pi$
$587$	18.2647	+	31.6354i	0.753865	+	1.30573i	−0.192072	+	0.981381i	$0.561521\pi$
$588$	−15.5964	−	4.17904i	−0.643185	−	0.172341i
$589$	−0.242870	+	0.420663i	−0.0100073	+	0.0173331i
$590$	−0.870813	+	11.5178i	−0.0358508	+	0.474180i
$591$	−10.3046	−	38.4573i	−0.423875	−	1.58192i
$592$	−4.17380	−	2.40974i	−0.171542	−	0.0990398i
$593$	−16.6936			−0.685525			−0.342762	−	0.939422i	$-0.611363\pi$
$593$	−16.6936			−0.685525			−0.342762	+	0.939422i	$0.611363\pi$
$594$	−7.25276	−	4.18738i	−0.297584	−	0.171810i
$595$	6.76880	+	14.0794i	0.277494	+	0.577200i
$596$	1.06999	−	3.99327i	0.0438287	−	0.163571i
$597$	−29.0384	+	29.0384i	−1.18846	+	1.18846i
$598$		0			0
$599$		−	13.2549i		−	0.541579i	−0.962639	−	0.270789i	$-0.912715\pi$
$599$		−	13.2549i		−	0.541579i	0.962639	−	0.270789i	$-0.0872847\pi$
$600$	16.8853	−	38.5621i	0.689341	−	1.57429i
$601$	−0.546605	−	0.946748i	−0.0222965	−	0.0386187i	0.854662	−	0.519185i	$-0.173764\pi$
$601$	−0.546605	−	0.946748i	−0.0222965	−	0.0386187i	−0.876958	+	0.480566i	$0.840431\pi$
$602$	2.02696	+	7.56474i	0.0826129	+	0.308316i
$603$		−	34.7891i		−	1.41672i
$604$	6.19166	−	1.65905i	0.251935	−	0.0675058i
$605$	−18.0919	+	3.41077i	−0.735542	+	0.138667i
$606$	−19.6554	−	19.6554i	−0.798446	−	0.798446i
$607$	40.4361	−	10.8348i	1.64125	−	0.439771i	0.684105	−	0.729384i	$-0.260193\pi$
$607$	40.4361	−	10.8348i	1.64125	−	0.439771i	0.957144	+	0.289612i	$0.0935263\pi$
$608$	3.42042	−	12.7652i	0.138716	−	0.517696i
$609$	0.758093	+	0.203130i	0.0307195	+	0.00823126i
$610$	3.61298	−	3.10506i	0.146285	−	0.125720i
$611$		0			0
$612$	23.3204	+	23.3204i	0.942673	+	0.942673i
$613$	−24.1705	+	13.9548i	−0.976235	+	0.563630i	−0.901131	−	0.433546i	$-0.857262\pi$
$613$	−24.1705	+	13.9548i	−0.976235	+	0.563630i	−0.0751039	+	0.997176i	$0.523929\pi$
$614$	−21.4487	+	12.3834i	−0.865601	+	0.499755i
$615$	−42.4179	+	7.99680i	−1.71046	+	0.322462i
$616$	3.42371	−	3.42371i	0.137945	−	0.137945i
$617$	−2.19132	+	3.79548i	−0.0882193	+	0.152800i	−0.906758	−	0.421650i	$-0.861451\pi$
$617$	−2.19132	+	3.79548i	−0.0882193	+	0.152800i	0.818539	+	0.574451i	$0.194784\pi$
$618$	5.08477	−	8.80708i	0.204540	−	0.354273i
$619$	−8.67268	+	8.67268i	−0.348584	+	0.348584i	−0.859582	−	0.510998i	$-0.829276\pi$
$619$	−8.67268	+	8.67268i	−0.348584	+	0.348584i	0.510998	+	0.859582i	$0.329276\pi$
$620$	−0.313136	−	0.213797i	−0.0125759	−	0.00858628i
$621$	16.4313	−	9.48662i	0.659366	−	0.380685i
$622$	−6.97193	+	4.02525i	−0.279549	+	0.161398i
$623$	0.353304	+	0.353304i	0.0141548	+	0.0141548i
$624$		0			0
$625$	−23.8697	−	7.43216i	−0.954788	−	0.297287i
$626$	4.73726	+	1.26934i	0.189339	+	0.0507332i
$627$	−3.27952	+	12.2393i	−0.130971	+	0.488791i
$628$	18.8345	−	5.04668i	0.751577	−	0.201385i
$629$	−20.9238	−	20.9238i	−0.834287	−	0.834287i
$630$	1.94575	+	10.3210i	0.0775207	+	0.411198i
$631$	24.4748	−	6.55800i	0.974326	−	0.261070i	0.263673	−	0.964612i	$-0.415066\pi$
$631$	24.4748	−	6.55800i	0.974326	−	0.261070i	0.710653	+	0.703542i	$0.248399\pi$
$632$		−	41.0398i		−	1.63248i
$633$	6.15419	+	22.9677i	0.244607	+	0.912886i
$634$	11.7220	+	20.3031i	0.465540	+	0.806340i
$635$	−4.38349	+	2.10740i	−0.173954	+	0.0836297i
$636$			7.51646i			0.298047i
$637$		0			0
$638$	0.351511	−	0.351511i	0.0139164	−	0.0139164i
$639$	16.1038	−	60.1003i	0.637057	−	2.37753i
$640$	4.63834	+	1.62647i	0.183346	+	0.0642920i
$641$	1.41675	+	0.817961i	0.0559582	+	0.0323075i	0.527718	−	0.849420i	$-0.323048\pi$
$641$	1.41675	+	0.817961i	0.0559582	+	0.0323075i	−0.471760	+	0.881727i	$0.656381\pi$
$642$	−1.26681			−0.0499968
$643$	−34.3541	−	19.8344i	−1.35479	−	0.782191i	−0.365878	−	0.930663i	$-0.619231\pi$
$643$	−34.3541	−	19.8344i	−1.35479	−	0.782191i	−0.988917	+	0.148472i	$0.952565\pi$
$644$	0.917051	+	3.42248i	0.0361369	+	0.134865i
$645$	37.5627	−	32.2820i	1.47903	−	1.27110i
$646$	−10.1339	+	17.5525i	−0.398714	+	0.690593i
$647$	14.3588	+	3.84742i	0.564501	+	0.151258i	0.529773	−	0.848139i	$-0.322277\pi$
$647$	14.3588	+	3.84742i	0.564501	+	0.151258i	0.0347277	+	0.999397i	$0.488944\pi$
$648$	−0.873682	−	1.51326i	−0.0343215	−	0.0594465i
$649$	8.40185			0.329801
$650$		0			0
$651$	0.477178			0.0187021
$652$	10.2034	+	17.6729i	0.399597	+	0.692123i
$653$	−12.4172	−	3.32718i	−0.485922	−	0.130203i	0.00753655	−	0.999972i	$-0.497601\pi$
$653$	−12.4172	−	3.32718i	−0.485922	−	0.130203i	−0.493459	+	0.869769i	$0.664268\pi$
$654$	12.9403	−	22.4132i	0.506005	−	0.876426i
$655$	0.105565	−	0.0907243i	0.00412476	−	0.00354489i
$656$	2.11708	+	7.90103i	0.0826579	+	0.308483i
$657$	13.3234	+	7.69225i	0.519794	+	0.300103i
$658$	−7.73102			−0.301387
$659$	20.8742	+	12.0517i	0.813144	+	0.469469i	0.848047	−	0.529922i	$-0.177779\pi$
$659$	20.8742	+	12.0517i	0.813144	+	0.469469i	−0.0349025	+	0.999391i	$0.511112\pi$
$660$	−9.33366	−	3.27293i	−0.363312	−	0.127399i
$661$	−10.1325	+	37.8150i	−0.394108	+	1.47083i	0.429185	+	0.903217i	$0.358801\pi$
$661$	−10.1325	+	37.8150i	−0.394108	+	1.47083i	−0.823293	+	0.567616i	$0.807866\pi$
$662$	−24.2637	+	24.2637i	−0.943036	+	0.943036i
$663$		0			0
$664$			25.8862i			1.00458i
$665$	5.30818	−	2.55196i	0.205843	−	0.0989606i
$666$	−9.94705	−	17.2288i	−0.385440	−	0.667602i
$667$	0.291487	+	1.08784i	0.0112864	+	0.0421215i
$668$			1.63601i			0.0632991i
$669$	−19.0071	+	5.09295i	−0.734858	+	0.196905i
$670$	3.09174	+	16.3997i	0.119444	+	0.633575i
$671$	−2.45030	−	2.45030i	−0.0945926	−	0.0945926i
$672$	−12.5402	+	3.36013i	−0.483747	+	0.129620i
$673$	2.64660	−	9.87723i	0.102019	−	0.380739i	−0.895971	−	0.444112i	$-0.853519\pi$
$673$	2.64660	−	9.87723i	0.102019	−	0.380739i	0.997990	+	0.0633730i	$0.0201858\pi$
$674$	20.3313	+	5.44776i	0.783132	+	0.209840i
$675$	19.8274	−	14.5927i	0.763157	−	0.561675i
$676$		0			0
$677$	29.8933	+	29.8933i	1.14889	+	1.14889i	0.986771	+	0.162121i	$0.0518333\pi$
$677$	29.8933	+	29.8933i	1.14889	+	1.14889i	0.162121	+	0.986771i	$0.448167\pi$
$678$	−4.77472	+	2.75669i	−0.183372	+	0.105870i
$679$	6.26961	−	3.61976i	0.240606	−	0.138914i
$680$	−40.4503	−	27.6178i	−1.55120	−	1.05910i
$681$	33.8465	−	33.8465i	1.29700	−	1.29700i
$682$	0.151121	−	0.261750i	0.00578673	−	0.0100229i
$683$	−10.0103	+	17.3384i	−0.383035	+	0.663436i	−0.991494	−	0.130149i	$-0.958455\pi$
$683$	−10.0103	+	17.3384i	−0.383035	+	0.663436i	0.608459	+	0.793585i	$0.291788\pi$
$684$	8.79221	−	8.79221i	0.336178	−	0.336178i
$685$	−9.70677	+	1.82996i	−0.370876	+	0.0699191i
$686$	−11.1546	+	6.44013i	−0.425886	+	0.245885i
$687$	30.3998	−	17.5513i	1.15983	−	0.669625i
$688$	−6.63664	−	6.63664i	−0.253019	−	0.253019i
$689$		0			0
$690$	−18.6238	+	16.0056i	−0.708994	+	0.609322i
$691$	34.1813	+	9.15886i	1.30032	+	0.348420i	0.841571	−	0.540147i	$-0.181631\pi$
$691$	34.1813	+	9.15886i	1.30032	+	0.348420i	0.458749	+	0.888566i	$0.348298\pi$
$692$	3.74834	−	13.9890i	0.142491	−	0.531782i
$693$	7.37933	−	1.97729i	0.280318	−	0.0751109i
$694$	−16.4960	−	16.4960i	−0.626181	−	0.626181i
$695$	30.2106	−	5.69543i	1.14595	−	0.216040i
$696$	−2.37683	+	0.636870i	−0.0900935	+	0.0241405i
$697$			50.2221i			1.90230i
$698$	−2.74877	−	10.2586i	−0.104043	−	0.388292i
$699$	34.6479	+	60.0120i	1.31051	+	2.26986i
$700$	1.67397	+	4.28188i	0.0632701	+	0.161840i
$701$		−	37.1781i		−	1.40420i	−0.712080	−	0.702098i	$-0.752247\pi$
$701$		−	37.1781i		−	1.40420i	0.712080	−	0.702098i	$-0.247753\pi$
$702$		0			0
$703$	−7.88864	+	7.88864i	−0.297526	+	0.297526i
$704$	−3.14502	+	11.7374i	−0.118532	+	0.442368i
$705$	21.1845	+	44.0647i	0.797854	+	1.65957i
$706$	−3.80843	−	2.19880i	−0.143332	−	0.0827529i
$707$	9.39830			0.353459
$708$	−11.6338	−	6.71678i	−0.437225	−	0.252432i
$709$	−12.4732	−	46.5506i	−0.468440	−	1.74824i	−0.645224	−	0.763994i	$-0.723236\pi$
$709$	−12.4732	−	46.5506i	−0.468440	−	1.74824i	0.176783	−	0.984250i	$-0.443431\pi$
$710$	−2.25023	+	29.7626i	−0.0844497	+	1.11697i
$711$	32.3770	−	56.0786i	1.21423	−	2.10311i
$712$	−1.51316	−	0.405449i	−0.0567079	−	0.0151948i
$713$	0.342369	+	0.593001i	0.0128218	+	0.0222080i
$714$	19.9106			0.745135
$715$		0			0
$716$	2.63300			0.0983998
$717$	4.40411	+	7.62814i	0.164474	+	0.284878i
$718$	14.5662	+	3.90299i	0.543604	+	0.145658i
$719$	16.6992	−	28.9239i	0.622777	−	1.07868i	−0.366190	−	0.930540i	$-0.619338\pi$
$719$	16.6992	−	28.9239i	0.622777	−	1.07868i	0.988966	−	0.148141i	$-0.0473288\pi$
$720$	−8.20394	−	9.54594i	−0.305743	−	0.355756i
$721$	0.889918	+	3.32122i	0.0331423	+	0.123689i
$722$	−10.2091	−	5.89421i	−0.379942	−	0.219360i
$723$	50.2164			1.86757
$724$	−8.55897	−	4.94153i	−0.318092	−	0.183650i
$725$	0.532076	+	1.36101i	0.0197608	+	0.0505465i
$726$	−6.07313	+	22.6652i	−0.225395	+	0.841186i
$727$	−23.6487	+	23.6487i	−0.877083	+	0.877083i	−0.993232	−	0.116149i	$-0.962945\pi$
$727$	−23.6487	+	23.6487i	−0.877083	+	0.877083i	0.116149	+	0.993232i	$0.462945\pi$
$728$		0			0
$729$		−	43.9226i		−	1.62676i
$730$	−6.96430	−	2.44209i	−0.257760	−	0.0903860i
$731$	−28.8130	−	49.9055i	−1.06569	−	1.84582i
$732$	1.43399	+	5.35173i	0.0530018	+	0.197806i
$733$			14.7049i			0.543138i	0.962419	+	0.271569i	$0.0875424\pi$
$733$			14.7049i			0.543138i	−0.962419	+	0.271569i	$0.912458\pi$
$734$	11.2836	−	3.02344i	0.416486	−	0.111597i
$735$	31.2472	+	21.3343i	1.15257	+	0.786929i
$736$	−13.1731	−	13.1731i	−0.485568	−	0.485568i
$737$	11.7255	−	3.14184i	0.431914	−	0.115731i
$738$	−8.73896	+	32.6142i	−0.321686	+	1.20055i
$739$	−19.8706	−	5.32432i	−0.730953	−	0.195858i	−0.125900	−	0.992043i	$-0.540182\pi$
$739$	−19.8706	−	5.32432i	−0.730953	−	0.195858i	−0.605054	+	0.796185i	$0.706848\pi$
$740$	−5.67600	−	6.60447i	−0.208654	−	0.242785i
$741$		0			0
$742$	1.96931	+	1.96931i	0.0722956	+	0.0722956i
$743$	38.6601	−	22.3204i	1.41830	−	0.818856i	0.422151	−	0.906526i	$-0.361275\pi$
$743$	38.6601	−	22.3204i	1.41830	−	0.818856i	0.996150	+	0.0876692i	$0.0279419\pi$
$744$	−1.29565	+	0.748042i	−0.0475007	+	0.0274246i
$745$	−5.46240	+	8.00048i	−0.200127	+	0.293115i
$746$	−20.3603	+	20.3603i	−0.745443	+	0.745443i
$747$	−20.4220	+	35.3720i	−0.747202	+	1.29419i
$748$	−5.75395	+	9.96614i	−0.210385	+	0.364398i
$749$	0.302864	−	0.302864i	0.0110664	−	0.0110664i
$750$	−21.7188	+	23.3142i	−0.793058	+	0.851313i
$751$	−15.2247	+	8.78996i	−0.555555	+	0.320750i	−0.751360	−	0.659893i	$-0.770602\pi$
$751$	−15.2247	+	8.78996i	−0.555555	+	0.320750i	0.195804	+	0.980643i	$0.437268\pi$
$752$	8.02381	−	4.63255i	0.292598	−	0.168932i
$753$	−27.5353	−	27.5353i	−1.00344	−	1.00344i
$754$		0			0
$755$	−14.9778	−	1.13241i	−0.545097	−	0.0412125i
$756$	−4.37306	−	1.17176i	−0.159047	−	0.0426164i
$757$	−9.10848	+	33.9933i	−0.331053	+	1.23551i	0.577032	+	0.816722i	$0.304211\pi$
$757$	−9.10848	+	33.9933i	−0.331053	+	1.23551i	−0.908085	+	0.418786i	$0.862456\pi$
$758$	16.7250	−	4.48144i	0.607478	−	0.162773i
$759$	12.6305	+	12.6305i	0.458457	+	0.458457i
$760$	−10.4124	+	15.2505i	−0.377697	+	0.553192i
$761$	11.3127	−	3.03122i	0.410084	−	0.109882i	−0.0478787	−	0.998853i	$-0.515246\pi$
$761$	11.3127	−	3.03122i	0.410084	−	0.109882i	0.457962	+	0.888972i	$0.348579\pi$
$762$			6.19897i			0.224565i
$763$	2.26476	+	8.45219i	0.0819897	+	0.305990i
$764$	8.86485	+	15.3544i	0.320719	+	0.555502i
$765$	−33.4849	−	69.6501i	−1.21065	−	2.51820i
$766$			6.75331i			0.244007i
$767$		0			0
$768$	33.2233	−	33.2233i	1.19884	−	1.19884i
$769$	4.90954	−	18.3227i	0.177043	−	0.660732i	−0.819152	−	0.573576i	$-0.805556\pi$
$769$	4.90954	−	18.3227i	0.177043	−	0.660732i	0.996195	−	0.0871555i	$-0.0277777\pi$
$770$	−3.30292	+	1.58791i	−0.119029	+	0.0572242i
$771$	55.9401	+	32.2971i	2.01463	+	1.16315i
$772$	−11.9964			−0.431760
$773$	14.2114	+	8.20497i	0.511149	+	0.295112i	0.733306	−	0.679899i	$-0.237976\pi$
$773$	14.2114	+	8.20497i	0.511149	+	0.295112i	−0.222157	+	0.975011i	$0.571310\pi$
$774$	−10.0273	−	37.4223i	−0.360423	−	1.34512i
$775$	0.526647	+	0.715564i	0.0189177	+	0.0257038i
$776$	−11.3490	+	19.6570i	−0.407404	+	0.705644i
$777$	10.5861	+	2.83655i	0.379775	+	0.101761i
$778$	−17.2285	−	29.8406i	−0.617671	−	1.06984i
$779$	18.9346			0.678403
$780$		0			0
$781$	21.7109			0.776876
$782$	14.2856	+	24.7434i	0.510852	+	0.884822i
$783$	−1.38999	−	0.372446i	−0.0496741	−	0.0133101i
$784$	3.58492	−	6.20926i	0.128033	−	0.221759i
$785$	−45.5610	−	3.44468i	−1.62614	−	0.122946i
$786$	−0.0459159	−	0.171361i	−0.00163777	−	0.00611223i
$787$	11.7781	+	6.80008i	0.419844	+	0.242397i	0.695010	−	0.719000i	$-0.255400\pi$
$787$	11.7781	+	6.80008i	0.419844	+	0.242397i	−0.275167	+	0.961396i	$0.588733\pi$
$788$	−13.6326			−0.485642
$789$	−3.14011	−	1.81294i	−0.111791	−	0.0645424i
$790$	−10.2789	+	29.3130i	−0.365706	+	1.04291i
$791$	0.482465	−	1.80058i	0.0171545	−	0.0640214i
$792$	−16.9369	+	16.9369i	−0.601827	+	0.601827i
$793$		0			0
$794$		−	5.95255i		−	0.211248i
$795$	5.82824	−	16.6208i	0.206706	−	0.589480i
$796$	7.03076	+	12.1776i	0.249199	+	0.431625i
$797$	7.74769	+	28.9148i	0.274437	+	1.02421i	0.956218	+	0.292657i	$0.0945393\pi$
$797$	7.74769	+	28.9148i	0.274437	+	1.02421i	−0.681780	+	0.731557i	$0.738794\pi$
$798$		−	7.50664i		−	0.265732i
$799$	54.9476	−	14.7232i	1.94391	−	0.520868i
$800$	−18.8790	−	15.0965i	−0.667473	−	0.533740i
$801$	−1.74778	−	1.74778i	−0.0617546	−	0.0617546i
$802$	−0.260771	+	0.0698734i	−0.00920815	+	0.00246732i
$803$	−1.38939	+	5.18527i	−0.0490305	+	0.182984i
$804$	−18.7477	−	5.02343i	−0.661180	−	0.177163i
$805$	0.625946	−	8.27906i	0.0220617	−	0.291799i
$806$		0			0
$807$	−15.6423	−	15.6423i	−0.550636	−	0.550636i
$808$	−25.5185	+	14.7331i	−0.897739	+	0.518310i
$809$	−2.54661	+	1.47029i	−0.0895342	+	0.0516926i	−0.544099	−	0.839021i	$-0.683128\pi$
$809$	−2.54661	+	1.47029i	−0.0895342	+	0.0516926i	0.454564	+	0.890714i	$0.349795\pi$
$810$	0.245021	+	1.29968i	0.00860916	+	0.0456661i
$811$	16.3366	−	16.3366i	0.573657	−	0.573657i	−0.359492	−	0.933148i	$-0.617050\pi$
$811$	16.3366	−	16.3366i	0.573657	−	0.573657i	0.933148	+	0.359492i	$0.117050\pi$
$812$	0.134367	−	0.232730i	0.00471536	−	0.00816724i
$813$	1.24791	−	2.16144i	0.0437660	−	0.0758050i
$814$	4.90856	−	4.90856i	0.172045	−	0.172045i
$815$	−8.85892	−	46.9910i	−0.310315	−	1.64602i
$816$	−20.6647	+	11.9307i	−0.723408	+	0.417660i
$817$	−18.8153	+	10.8630i	−0.658262	+	0.380048i
$818$	−26.8732	−	26.8732i	−0.939599	−	0.939599i
$819$		0			0
$820$	−1.11428	+	14.7380i	−0.0389124	+	0.514674i
$821$	−44.3125	−	11.8735i	−1.54652	−	0.414388i	−0.618151	−	0.786059i	$-0.712118\pi$
$821$	−44.3125	−	11.8735i	−1.54652	−	0.414388i	−0.928364	+	0.371672i	$0.878785\pi$
$822$	−3.25838	+	12.1605i	−0.113649	+	0.424145i
$823$	17.1209	−	4.58752i	0.596796	−	0.159911i	0.0522385	−	0.998635i	$-0.483364\pi$
$823$	17.1209	−	4.58752i	0.596796	−	0.159911i	0.544557	+	0.838724i	$0.316698\pi$
$824$	−7.62280	−	7.62280i	−0.265553	−	0.265553i
$825$	18.1013	+	14.4746i	0.630206	+	0.503940i
$826$	−4.80785	+	1.28826i	−0.167286	+	0.0448242i
$827$			5.79276i			0.201434i	0.994915	+	0.100717i	$0.0321137\pi$
$827$			5.79276i			0.201434i	−0.994915	+	0.100717i	$0.967886\pi$
$828$	−4.53660	−	16.9308i	−0.157658	−	0.588387i
$829$	−16.8799	−	29.2368i	−0.586262	−	1.01544i	−0.994717	−	0.102657i	$-0.967265\pi$
$829$	−16.8799	−	29.2368i	−0.586262	−	1.01544i	0.408454	−	0.912779i	$-0.366068\pi$
$830$	6.48347	−	18.4894i	0.225045	−	0.641776i
$831$		−	26.6284i		−	0.923727i
$832$		0			0
$833$	31.1279	−	31.1279i	1.07852	−	1.07852i
$834$	10.1412	−	37.8473i	0.351160	−	1.31055i
$835$	1.26856	−	3.61764i	0.0439002	−	0.125193i
$836$	3.75741	+	2.16934i	0.129953	+	0.0750282i
$837$	−0.874920			−0.0302417
$838$	30.0364	+	17.3415i	1.03759	+	0.599053i
$839$	10.1452	+	37.8626i	0.350253	+	1.30716i	0.886354	+	0.463008i	$0.153230\pi$
$839$	10.1452	+	37.8626i	0.350253	+	1.30716i	−0.536101	+	0.844154i	$0.680103\pi$
$840$	18.0889	+	1.36763i	0.624127	+	0.0471877i
$841$	−14.4573	+	25.0408i	−0.498527	+	0.863475i
$842$	−30.1175	−	8.06995i	−1.03792	−	0.278109i
$843$	11.0041	+	19.0597i	0.379002	+	0.656451i
$844$	8.14177			0.280251
$845$		0			0
$846$	38.2449			1.31489
$847$	−3.96679	−	6.87068i	−0.136300	−	0.236079i
$848$	−3.22393	−	0.863850i	−0.110710	−	0.0296647i
$849$	29.4076	−	50.9354i	1.00927	−	1.74810i
$850$	21.9748	+	29.8575i	0.753728	+	1.02410i
$851$	4.07037	+	15.1908i	0.139531	+	0.520735i
$852$	−30.0625	−	17.3566i	−1.02992	−	0.594626i
$853$	40.6417			1.39154			0.695772	−	0.718262i	$-0.255062\pi$
$853$	40.6417			1.39154			0.695772	+	0.718262i	$0.255062\pi$
$854$	1.77785	+	1.02644i	0.0608369	+	0.0351242i
$855$	−26.2593	+	12.6244i	−0.898048	+	0.431744i
$856$	−0.347564	+	1.29713i	−0.0118795	+	0.0443348i
$857$	27.2327	−	27.2327i	0.930252	−	0.930252i	−0.0674695	−	0.997721i	$-0.521493\pi$
$857$	27.2327	−	27.2327i	0.930252	−	0.930252i	0.997721	+	0.0674695i	$0.0214925\pi$
$858$		0			0
$859$		−	44.5502i		−	1.52003i	−0.649904	−	0.760016i	$-0.725191\pi$
$859$		−	44.5502i		−	1.52003i	0.649904	−	0.760016i	$-0.274809\pi$
$860$	−7.34811	−	15.2844i	−0.250568	−	0.521194i
$861$	−9.30043	−	16.1088i	−0.316958	−	0.548987i
$862$	−1.21706	−	4.54213i	−0.0414532	−	0.154706i
$863$		−	55.4497i		−	1.88753i	−0.330615	−	0.943766i	$-0.607256\pi$
$863$		−	55.4497i		−	1.88753i	0.330615	−	0.943766i	$-0.392744\pi$
$864$	22.9928	−	6.16090i	0.782230	−	0.209598i
$865$	−19.1356	+	28.0268i	−0.650629	+	0.952940i
$866$	2.89432	+	2.89432i	0.0983531	+	0.0983531i
$867$	−95.7502	+	25.6562i	−3.25185	+	0.871330i
$868$	0.0422883	−	0.157822i	0.00143536	−	0.00535683i
$869$	21.8250	+	5.84800i	0.740363	+	0.198380i
$870$	1.85718	+	0.140414i	0.0629643	+	0.00476048i
$871$		0			0
$872$	−19.3993	−	19.3993i	−0.656944	−	0.656944i
$873$	−31.0154	+	17.9068i	−1.04971	+	0.606052i
$874$	9.32869	−	5.38592i	0.315548	−	0.182181i
$875$	−0.381420	−	10.7663i	−0.0128944	−	0.363968i
$876$	6.06917	−	6.06917i	0.205058	−	0.205058i
$877$	−2.68849	+	4.65661i	−0.0907839	+	0.157242i	−0.907841	−	0.419314i	$-0.862271\pi$
$877$	−2.68849	+	4.65661i	−0.0907839	+	0.157242i	0.817057	+	0.576557i	$0.195604\pi$
$878$	11.6188	−	20.1244i	0.392116	−	0.679166i
$879$	−7.92505	+	7.92505i	−0.267305	+	0.267305i
$880$	2.47651	−	3.62721i	0.0834831	−	0.122273i
$881$	37.0890	−	21.4133i	1.24956	−	0.721434i	0.278538	−	0.960425i	$-0.410150\pi$
$881$	37.0890	−	21.4133i	1.24956	−	0.721434i	0.971022	+	0.238992i	$0.0768169\pi$
$882$	25.6309	−	14.7980i	0.863037	−	0.498274i
$883$	−32.9568	−	32.9568i	−1.10908	−	1.10908i	−0.993271	−	0.115813i	$-0.963053\pi$
$883$	−32.9568	−	32.9568i	−1.10908	−	1.10908i	−0.115813	−	0.993271i	$-0.536947\pi$
$884$		0			0
$885$	20.5172	+	23.8733i	0.689677	+	0.802494i
$886$	2.58254	+	0.691990i	0.0867622	+	0.0232478i
$887$	−5.47136	+	20.4194i	−0.183710	+	0.685616i	0.811193	+	0.584779i	$0.198819\pi$
$887$	−5.47136	+	20.4194i	−0.183710	+	0.685616i	−0.994903	+	0.100837i	$0.967848\pi$
$888$	−33.1905	+	8.89336i	−1.11380	+	0.298442i
$889$	−1.48203	−	1.48203i	−0.0497057	−	0.0497057i
$890$	0.979235	+	0.668582i	0.0328240	+	0.0224109i
$891$	0.929249	−	0.248992i	0.0311310	−	0.00834153i
$892$			6.73778i			0.225598i
$893$	−5.55089	−	20.7162i	−0.185753	−	0.693241i
$894$	6.17340	+	10.6926i	0.206469	+	0.357616i
$895$	−5.82224	−	2.04162i	−0.194616	−	0.0682438i
$896$			2.11809i			0.0707605i
$897$		0			0
$898$	−23.2645	+	23.2645i	−0.776346	+	0.776346i
$899$	0.0134414	−	0.0501642i	0.000448297	−	0.00167307i
$900$	−8.28103	−	21.1822i	−0.276034	−	0.706074i
$901$	−17.7471	−	10.2463i	−0.591242	−	0.341354i
$902$	−11.7817			−0.392288
$903$	18.4836	+	10.6715i	0.615096	+	0.355126i
$904$	1.51266	+	5.64533i	0.0503104	+	0.187761i
$905$	15.0944	+	17.5636i	0.501756	+	0.583833i
$906$	−9.57200	+	16.5792i	−0.318008	+	0.550807i
$907$	−10.6869	−	2.86355i	−0.354853	−	0.0950825i	0.0769889	−	0.997032i	$-0.475469\pi$
$907$	−10.6869	−	2.86355i	−0.354853	−	0.0950825i	−0.431842	+	0.901949i	$0.642136\pi$
$908$	−8.19488	−	14.1940i	−0.271957	−	0.471043i
$909$	−46.4928			−1.54207
$910$		0			0
$911$	−15.0479			−0.498560			−0.249280	−	0.968431i	$-0.580194\pi$
$911$	−15.0479			−0.498560			−0.249280	+	0.968431i	$0.580194\pi$
$912$	4.49810	+	7.79093i	0.148947	+	0.257983i
$913$	−13.7663	−	3.68867i	−0.455598	−	0.122077i
$914$	−14.5045	+	25.1226i	−0.479767	+	0.830980i
$915$	0.978791	−	12.9459i	0.0323578	−	0.427980i
$916$	−3.11086	−	11.6099i	−0.102786	−	0.383602i
$917$	0.0519457	+	0.0299909i	0.00171540	+	0.000990386i
$918$	−36.5067			−1.20490
$919$	−10.8342	−	6.25513i	−0.357388	−	0.206338i	0.310547	−	0.950558i	$-0.399488\pi$
$919$	−10.8342	−	6.25513i	−0.357388	−	0.206338i	−0.667934	+	0.744220i	$0.732821\pi$
$920$	11.2790	+	23.4608i	0.371857	+	0.773480i
$921$	−17.4692	+	65.1960i	−0.575630	+	2.14828i
$922$	−8.32259	+	8.32259i	−0.274090	+	0.274090i
$923$		0			0
$924$		−	4.26220i		−	0.140216i
$925$	7.42999	+	19.0053i	0.244297	+	0.624891i
$926$	15.3114	+	26.5202i	0.503165	+	0.871508i
$927$	−4.40237	−	16.4299i	−0.144593	−	0.539628i
$928$			1.41296i			0.0463826i
$929$	−47.0874	+	12.6170i	−1.54489	+	0.413952i	−0.927841	−	0.372975i	$-0.878338\pi$
$929$	−47.0874	+	12.6170i	−1.54489	+	0.413952i	−0.617047	+	0.786926i	$0.711671\pi$
$930$	1.11278	−	0.209786i	0.0364895	−	0.00687915i
$931$	−11.7357	−	11.7357i	−0.384623	−	0.384623i
$932$	22.9190	−	6.14112i	0.750736	−	0.201159i
$933$	−5.67838	+	21.1920i	−0.185902	+	0.693795i
$934$	−22.5369	−	6.03874i	−0.737429	−	0.197594i
$935$	20.4512	−	17.5761i	0.668825	−	0.574800i
$936$		0			0
$937$	7.38027	+	7.38027i	0.241103	+	0.241103i	0.817306	−	0.576203i	$-0.195466\pi$
$937$	7.38027	+	7.38027i	0.241103	+	0.241103i	−0.576203	+	0.817306i	$0.695466\pi$
$938$	−6.22802	+	3.59575i	−0.203352	+	0.117405i
$939$	11.5750	−	6.68281i	0.377735	−	0.218085i
$940$	16.4514	−	3.10149i	0.536586	−	0.101159i
$941$	−1.54410	+	1.54410i	−0.0503363	+	0.0503363i	−0.731827	−	0.681491i	$-0.761332\pi$
$941$	−1.54410	+	1.54410i	−0.0503363	+	0.0503363i	0.681491	+	0.731827i	$0.261332\pi$
$942$	−29.1172	+	50.4324i	−0.948688	+	1.64318i
$943$	13.3459	−	23.1158i	0.434602	−	0.752753i
$944$	4.21798	−	4.21798i	0.137284	−	0.137284i
$945$	8.76137	+	5.98191i	0.285007	+	0.194591i
$946$	11.7074	−	6.75929i	0.380642	−	0.219764i
$947$	−5.81670	+	3.35827i	−0.189017	+	0.109129i	−0.591522	−	0.806289i	$-0.701473\pi$
$947$	−5.81670	+	3.35827i	−0.189017	+	0.109129i	0.402505	+	0.915418i	$0.368140\pi$
$948$	−25.5454	−	25.5454i	−0.829676	−	0.829676i
$949$		0			0
$950$	11.2568	−	8.28486i	0.365218	−	0.268796i
$951$	61.7137	+	16.5361i	2.00121	+	0.536221i
$952$	5.46272	−	20.3871i	0.177048	−	0.660751i
$953$	17.4402	−	4.67309i	0.564944	−	0.151376i	0.0349673	−	0.999388i	$-0.488867\pi$
$953$	17.4402	−	4.67309i	0.564944	−	0.151376i	0.529977	+	0.848012i	$0.322201\pi$
$954$	−9.74205	−	9.74205i	−0.315411	−	0.315411i
$955$	−7.69672	−	40.8262i	−0.249060	−	1.32111i
$956$	2.91324	−	0.780600i	0.0942208	−	0.0252464i
$957$		−	1.35475i		−	0.0437929i
$958$	−10.2765	−	38.3526i	−0.332020	−	1.23912i
$959$	−2.12828	−	3.68629i	−0.0687257	−	0.119036i
$960$	−41.0311	+	19.7261i	−1.32427	+	0.636656i
$961$			30.9684i			0.998981i
$962$		0			0
$963$	−1.49825	+	1.49825i	−0.0482804	+	0.0482804i
$964$	4.45026	−	16.6086i	0.143333	−	0.534927i
$965$	26.5271	+	9.30197i	0.853938	+	0.299441i
$966$	−9.16426	−	5.29099i	−0.294855	−	0.170235i
$967$	60.0570			1.93130			0.965651	−	0.259841i	$-0.0836701\pi$
$967$	60.0570			1.93130			0.965651	+	0.259841i	$0.0836701\pi$
$968$	21.5415	+	12.4370i	0.692369	+	0.399740i
$969$	14.2958	+	53.3528i	0.459249	+	1.71394i
$970$	13.0294	−	11.1977i	0.418348	−	0.359536i
$971$	20.4589	−	35.4359i	0.656558	−	1.13719i	−0.324942	−	0.945734i	$-0.605345\pi$
$971$	20.4589	−	35.4359i	0.656558	−	1.13719i	0.981501	−	0.191459i	$-0.0613218\pi$
$972$	−15.1009	−	4.04627i	−0.484361	−	0.129784i
$973$	6.62390	+	11.4729i	0.212352	+	0.367805i
$974$	−29.5983			−0.948391
$975$		0			0
$976$	−2.46025			−0.0787506
$977$	−18.7479	−	32.4724i	−0.599800	−	1.03888i	−0.992850	−	0.119367i	$-0.961913\pi$
$977$	−18.7479	−	32.4724i	−0.599800	−	1.03888i	0.393050	−	0.919517i	$-0.371420\pi$
$978$	−58.8694	−	15.7740i	−1.88244	−	0.504397i
$979$	0.431236	−	0.746923i	0.0137824	−	0.0238718i
$980$	9.82532	−	8.44405i	0.313858	−	0.269735i
$981$	−11.2036	−	41.8125i	−0.357704	−	1.33497i
$982$	−6.44253	−	3.71959i	−0.205589	−	0.118697i
$983$	−46.1176			−1.47092			−0.735461	−	0.677567i	$-0.763034\pi$
$983$	−46.1176			−1.47092			−0.735461	+	0.677567i	$0.763034\pi$
$984$	50.5056	+	29.1594i	1.61006	+	0.929569i
$985$	30.1452	+	10.5707i	0.960506	+	0.336810i
$986$	0.560854	−	2.09314i	0.0178612	−	0.0666591i
$987$	−14.8980	+	14.8980i	−0.474208	+	0.474208i
$988$		0			0
$989$			30.6267i			0.973873i
$990$	16.3393	−	7.85528i	0.519298	−	0.249657i
$991$	−0.401099	−	0.694724i	−0.0127413	−	0.0220686i	0.859584	−	0.510994i	$-0.170722\pi$
$991$	−0.401099	−	0.694724i	−0.0127413	−	0.0220686i	−0.872326	+	0.488925i	$0.837389\pi$
$992$	0.222345	+	0.829802i	0.00705945	+	0.0263462i
$993$			93.5143i			2.96759i
$994$	−12.4238	+	3.32894i	−0.394058	+	0.105587i
$995$	−6.10431	−	32.3795i	−0.193520	−	1.02650i
$996$	16.1129	+	16.1129i	0.510558	+	0.510558i
$997$	−15.0779	+	4.04012i	−0.477522	+	0.127952i	−0.489549	−	0.871976i	$-0.662838\pi$
$997$	−15.0779	+	4.04012i	−0.477522	+	0.127952i	0.0120264	+	0.999928i	$0.496172\pi$
$998$	1.58780	−	5.92576i	0.0502610	−	0.187577i
$999$	−19.4100	−	5.20090i	−0.614106	−	0.164549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.o.e.587.4		20
5.3	odd	4		845.2.t.f.418.4		20
13.2	odd	12		845.2.f.d.437.8		20
13.3	even	3		845.2.k.e.577.3		20
13.4	even	6		845.2.o.g.357.2		20
13.5	odd	4		845.2.t.g.427.4		20
13.6	odd	12		845.2.t.e.657.2		20
13.7	odd	12		845.2.t.f.657.4		20
13.8	odd	4		65.2.t.a.37.2	yes	20
13.9	even	3		65.2.o.a.32.4	✓	20
13.10	even	6		845.2.k.d.577.8		20
13.11	odd	12		845.2.f.e.437.3		20
13.12	even	2		845.2.o.f.587.2		20
39.8	even	4		585.2.dp.a.37.4		20
39.35	odd	6		585.2.cf.a.487.2		20
65.3	odd	12		845.2.f.e.408.8		20
65.8	even	4		65.2.o.a.63.4	yes	20
65.9	even	6		325.2.s.b.32.2		20
65.18	even	4		845.2.o.g.258.2		20
65.22	odd	12		325.2.x.b.318.4		20
65.23	odd	12		845.2.f.d.408.3		20
65.28	even	12		845.2.k.d.268.8		20
65.33	even	12	inner	845.2.o.e.488.4		20
65.34	odd	4		325.2.x.b.232.4		20
65.38	odd	4		845.2.t.e.418.2		20
65.43	odd	12		845.2.t.g.188.4		20
65.47	even	4		325.2.s.b.193.2		20
65.48	odd	12		65.2.t.a.58.2	yes	20
65.58	even	12		845.2.o.f.488.2		20
65.63	even	12		845.2.k.e.268.3		20
195.8	odd	4		585.2.cf.a.388.2		20
195.113	even	12		585.2.dp.a.253.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.4	✓	20	13.9	even	3
65.2.o.a.63.4	yes	20	65.8	even	4
65.2.t.a.37.2	yes	20	13.8	odd	4
65.2.t.a.58.2	yes	20	65.48	odd	12
325.2.s.b.32.2		20	65.9	even	6
325.2.s.b.193.2		20	65.47	even	4
325.2.x.b.232.4		20	65.34	odd	4
325.2.x.b.318.4		20	65.22	odd	12
585.2.cf.a.388.2		20	195.8	odd	4
585.2.cf.a.487.2		20	39.35	odd	6
585.2.dp.a.37.4		20	39.8	even	4
585.2.dp.a.253.4		20	195.113	even	12
845.2.f.d.408.3		20	65.23	odd	12
845.2.f.d.437.8		20	13.2	odd	12
845.2.f.e.408.8		20	65.3	odd	12
845.2.f.e.437.3		20	13.11	odd	12
845.2.k.d.268.8		20	65.28	even	12
845.2.k.d.577.8		20	13.10	even	6
845.2.k.e.268.3		20	65.63	even	12
845.2.k.e.577.3		20	13.3	even	3
845.2.o.e.488.4		20	65.33	even	12	inner
845.2.o.e.587.4		20	1.1	even	1	trivial
845.2.o.f.488.2		20	65.58	even	12
845.2.o.f.587.2		20	13.12	even	2
845.2.o.g.258.2		20	65.18	even	4
845.2.o.g.357.2		20	13.4	even	6
845.2.t.e.418.2		20	65.38	odd	4
845.2.t.e.657.2		20	13.6	odd	12
845.2.t.f.418.4		20	5.3	odd	4
845.2.t.f.657.4		20	13.7	odd	12
845.2.t.g.188.4		20	65.43	odd	12
845.2.t.g.427.4		20	13.5	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.511309 + 0.885613i) q^{2} +(2.69193 + 0.721300i) q^{3} +(0.477126 - 0.826407i) q^{4} +(-1.69584 + 1.45744i) q^{5} +(0.737614 + 2.75281i) q^{6} +(-0.834479 - 0.481787i) q^{7} +3.02107 q^{8} +(4.12812 + 2.38337i) q^{9} +(-2.15782 - 0.756660i) q^{10} +(-0.430490 + 1.60661i) q^{11} +(1.88048 - 1.88048i) q^{12} -0.985368i q^{14} +(-5.61633 + 2.70010i) q^{15} +(0.590448 + 1.02269i) q^{16} +(1.87656 + 7.00342i) q^{17} +4.87456i q^{18} +(2.64041 - 0.707496i) q^{19} +(0.395304 + 2.09684i) q^{20} +(-1.89884 - 1.89884i) q^{21} +(-1.64295 + 0.440226i) q^{22} +(0.997344 - 3.72214i) q^{23} +(8.13250 + 2.17910i) q^{24} +(0.751762 - 4.94316i) q^{25} +(3.48159 + 3.48159i) q^{27} +(-0.796304 + 0.459747i) q^{28} +(-0.253107 + 0.146132i) q^{29} +(-5.26292 - 3.59331i) q^{30} +(-0.125649 + 0.125649i) q^{31} +(2.41727 - 4.18683i) q^{32} +(-2.31769 + 4.01436i) q^{33} +(-5.24282 + 5.24282i) q^{34} +(2.11732 - 0.399166i) q^{35} +(3.93927 - 2.27434i) q^{36} +(-3.53443 + 2.04061i) q^{37} +(1.97663 + 1.97663i) q^{38} +(-5.12326 + 4.40302i) q^{40} +(6.69071 + 1.79277i) q^{41} +(0.710745 - 2.65254i) q^{42} +(-7.67707 + 2.05706i) q^{43} +(1.12232 + 1.12232i) q^{44} +(-10.4743 + 1.97465i) q^{45} +(3.80633 - 1.01990i) q^{46} -7.84582i q^{47} +(0.851780 + 3.17888i) q^{48} +(-3.03576 - 5.25810i) q^{49} +(4.76211 - 1.86171i) q^{50} +20.2063i q^{51} +(-1.99855 + 1.99855i) q^{53} +(-1.30317 + 4.86351i) q^{54} +(-1.61149 - 3.35197i) q^{55} +(-2.52102 - 1.45551i) q^{56} +7.61811 q^{57} +(-0.258832 - 0.149437i) q^{58} +(-1.30739 - 4.87924i) q^{59} +(-0.448318 + 5.92967i) q^{60} +(-1.04169 + 1.80425i) q^{61} +(-0.175522 - 0.0470311i) q^{62} +(-2.29655 - 3.97775i) q^{63} +7.30568 q^{64} -4.74023 q^{66} +(-3.64915 - 6.32050i) q^{67} +(6.68304 + 1.79071i) q^{68} +(5.36956 - 9.30034i) q^{69} +(1.43611 + 1.67103i) q^{70} +(-3.37837 - 12.6082i) q^{71} +(12.4713 + 7.20034i) q^{72} +3.22747 q^{73} +(-3.61437 - 2.08676i) q^{74} +(5.58919 - 12.7644i) q^{75} +(0.675130 - 2.51962i) q^{76} +(1.13328 - 1.13328i) q^{77} -13.5845i q^{79} +(-2.49180 - 0.873774i) q^{80} +(-0.289196 - 0.500902i) q^{81} +(1.83332 + 6.84204i) q^{82} +8.56854i q^{83} +(-2.47521 + 0.663230i) q^{84} +(-13.3894 - 9.14173i) q^{85} +(-5.74712 - 5.74712i) q^{86} +(-0.786751 + 0.210809i) q^{87} +(-1.30054 + 4.85368i) q^{88} +(-0.500868 - 0.134207i) q^{89} +(-7.10435 - 8.26648i) q^{90} +(-2.60014 - 2.60014i) q^{92} +(-0.428870 + 0.247608i) q^{93} +(6.94836 - 4.01164i) q^{94} +(-3.44659 + 5.04803i) q^{95} +(9.52707 - 9.52707i) q^{96} +(-3.75660 + 6.50662i) q^{97} +(3.10442 - 5.37702i) q^{98} +(-5.60626 + 5.60626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 4 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9} + 2 q^{10} + 8 q^{11} + 24 q^{12} + 12 q^{15} - 2 q^{16} - 4 q^{17} - 16 q^{19} + 8 q^{20} + 4 q^{21} + 16 q^{22} + 10 q^{23}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 4 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9 + 2 * q^10 + 8 * q^11 + 24 * q^12 + 12 * q^15 - 2 * q^16 - 4 * q^17 - 16 * q^19 + 8 * q^20 + 4 * q^21 + 16 * q^22 + 10 * q^23 + 28 * q^24 - 18 * q^25 + 4 * q^27 - 6 * q^28 + 26 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 + 40 * q^35 - 36 * q^36 - 42 * q^37 + 8 * q^38 - 16 * q^40 + 28 * q^41 + 40 * q^42 - 10 * q^43 + 36 * q^44 - 32 * q^45 - 8 * q^46 - 56 * q^48 - 18 * q^49 + 8 * q^50 - 10 * q^53 - 12 * q^54 - 10 * q^55 - 12 * q^57 + 90 * q^58 - 8 * q^59 - 92 * q^60 - 16 * q^61 + 44 * q^62 - 32 * q^63 - 20 * q^64 - 32 * q^66 - 58 * q^67 + 22 * q^68 + 16 * q^69 + 32 * q^70 + 56 * q^71 + 66 * q^72 + 72 * q^73 + 18 * q^74 + 38 * q^75 + 80 * q^76 + 28 * q^77 + 68 * q^80 - 14 * q^81 - 56 * q^82 - 32 * q^84 + 6 * q^85 + 60 * q^86 - 34 * q^87 - 82 * q^88 + 6 * q^89 - 46 * q^90 - 8 * q^92 - 48 * q^93 - 48 * q^94 + 26 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more