LMFDB - Embedded newform 845.2.o.f.488.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(258,845)]

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, 7]))

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

//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);

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

Embedding invariants

Embedding label			488.2
Root			$-1.02262i$ of defining polynomial
Character	$\chi$	$=$	845.488
Dual form			845.2.o.f.587.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.511309 + 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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{4}\right)$

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	$-0.951086\pi$
$2$	−0.511309	+	0.885613i	−0.361550	+	0.626223i	0.626666	+	0.779288i	$0.284419\pi$
$3$	2.69193	−	0.721300i	1.55418	−	0.416443i	0.623368	−	0.781929i	$-0.285764\pi$
$3$	2.69193	−	0.721300i	1.55418	−	0.416443i	0.930817	+	0.365486i	$0.119097\pi$
$4$	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	$-0.608378\pi$
$7$	0.834479	−	0.481787i	0.315404	−	0.182098i	0.649342	+	0.760497i	$0.275044\pi$
$8$	−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	$-0.00265630\pi$
$11$	0.430490	+	1.60661i	0.129797	+	0.484411i	−0.870168	+	0.492756i	$0.835990\pi$
$12$	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	−0.232564	−	0.972581i	$-0.574711\pi$
$17$	1.87656	−	7.00342i	0.455133	−	1.69858i	0.687697	−	0.725998i	$-0.258622\pi$
$18$			4.87456i			1.14894i
$19$	−2.64041	−	0.707496i	−0.605752	−	0.162311i	−0.0571095	−	0.998368i	$-0.518188\pi$
$19$	−2.64041	−	0.707496i	−0.605752	−	0.162311i	−0.548642	+	0.836057i	$0.684855\pi$
$20$	−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	0.988527	+	0.151046i	$0.0482643\pi$
$23$	0.997344	+	3.72214i	0.207961	+	0.776120i	−0.780566	+	0.625073i	$0.785069\pi$
$24$	−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	0.476315	−	0.879274i	$-0.341972\pi$
$29$	−0.253107	−	0.146132i	−0.0470008	−	0.0271360i	−0.523316	+	0.852139i	$0.675305\pi$
$30$	−5.26292	+	3.59331i	−0.960874	+	0.656046i
$31$	0.125649	+	0.125649i	0.0225673	+	0.0225673i	0.718300	−	0.695733i	$-0.244920\pi$
$31$	0.125649	+	0.125649i	0.0225673	+	0.0225673i	−0.695733	+	0.718300i	$0.744920\pi$
$32$	−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	$-0.224437\pi$
$37$	3.53443	+	2.04061i	0.581057	+	0.335474i	−0.180496	+	0.983576i	$0.557770\pi$
$38$	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	$-0.765245\pi$
$41$	−6.69071	+	1.79277i	−1.04491	+	0.279984i	−0.304765	+	0.952427i	$0.598578\pi$
$42$	0.710745	+	2.65254i	0.109670	+	0.409295i
$43$	−7.67707	−	2.05706i	−1.17074	−	0.313699i	−0.379494	−	0.925194i	$-0.623902\pi$
$43$	−7.67707	−	2.05706i	−1.17074	−	0.313699i	−0.791248	+	0.611495i	$0.790568\pi$
$44$	−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	0.556395	−	0.830918i	$-0.312184\pi$
$53$	−1.99855	−	1.99855i	−0.274522	−	0.274522i	−0.830918	+	0.556395i	$0.812184\pi$
$54$	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	−0.827111	−	0.562039i	$-0.810017\pi$
$59$	1.30739	−	4.87924i	0.170207	−	0.635223i	0.997318	−	0.0731843i	$-0.0233161\pi$
$60$	0.448318	+	5.92967i	0.0578776	+	0.765517i
$61$	−1.04169	−	1.80425i	−0.133374	−	0.231011i	0.791601	−	0.611038i	$-0.209248\pi$
$61$	−1.04169	−	1.80425i	−0.133374	−	0.231011i	−0.924975	+	0.380027i	$0.875915\pi$
$62$	−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	$-0.686248\pi$
$67$	3.64915	−	6.32050i	0.445814	−	0.772173i	0.998109	+	0.0614765i	$0.0195809\pi$
$68$	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	−0.410486	−	0.911867i	$-0.634641\pi$
$71$	3.37837	−	12.6082i	0.400939	−	1.49632i	0.811425	−	0.584457i	$-0.198692\pi$
$72$	−12.4713	+	7.20034i	−1.46976	+	0.848568i
$73$	−3.22747			−0.377746			−0.188873	−	0.982001i	$-0.560483\pi$
$73$	−3.22747			−0.377746			−0.188873	+	0.982001i	$0.560483\pi$
$74$	−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	$0.276861\pi$
$79$			13.5845i			1.52838i	−0.644992	+	0.764190i	$0.723139\pi$
$80$	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	$-0.574584\pi$
$89$	0.500868	−	0.134207i	0.0530919	−	0.0142259i	0.285267	+	0.958448i	$0.407918\pi$
$90$	−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	$-0.0421001\pi$
$97$	3.75660	+	6.50662i	0.381425	+	0.660648i	−0.609841	+	0.792524i	$0.708767\pi$
$98$	−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	0.0169388	−	0.999857i	$-0.494608\pi$
$101$	−8.44685	−	4.87679i	−0.840493	−	0.485259i	−0.857432	+	0.514598i	$0.827941\pi$
$102$	17.8949	+	10.3316i	1.77186	+	1.02298i
$103$	−2.52321	+	2.52321i	−0.248619	+	0.248619i	−0.820404	−	0.571784i	$-0.806251\pi$
$103$	−2.52321	+	2.52321i	−0.248619	+	0.248619i	0.571784	+	0.820404i	$0.306251\pi$
$104$		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	0.960142	−	0.279513i	$-0.0901731\pi$
$107$	−0.115046	−	0.429359i	−0.0111220	−	0.0415077i	−0.971264	+	0.238005i	$0.923506\pi$
$108$	4.53837	+	1.21605i	0.436705	+	0.117015i
$109$	6.42134	−	6.42134i	0.615053	−	0.615053i	−0.329206	−	0.944258i	$-0.606781\pi$
$109$	6.42134	−	6.42134i	0.615053	−	0.615053i	0.944258	+	0.329206i	$0.106781\pi$
$110$	−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	−0.938367	−	0.345639i	$-0.887662\pi$
$113$	0.500704	−	1.86865i	0.0471023	−	0.175788i	0.985470	+	0.169851i	$0.0543287\pi$
$114$	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	−0.164393	−	0.986395i	$-0.552567\pi$
$127$	2.10102	−	0.562967i	0.186436	−	0.0499553i	0.350829	+	0.936440i	$0.385900\pi$
$128$	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	$-0.727096\pi$
$137$	−3.82564	+	2.20873i	−0.326846	+	0.188705i	0.327594	+	0.944819i	$0.393762\pi$
$138$	−10.9820			−0.934850
$139$	−11.9066	+	6.87430i	−1.00991	+	0.583070i	−0.911165	−	0.412043i	$-0.864816\pi$
$139$	−11.9066	+	6.87430i	−1.00991	+	0.583070i	−0.0987430	+	0.995113i	$0.531482\pi$
$140$	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	$-0.473454\pi$
$149$	−4.18471	−	1.12129i	−0.342825	−	0.0918596i	−0.426124	+	0.904665i	$0.640121\pi$
$150$	−14.1621	−	1.57669i	−1.15633	−	0.128736i
$151$	−4.74990	+	4.74990i	−0.386542	+	0.386542i	−0.873452	−	0.486910i	$-0.838124\pi$
$151$	−4.74990	+	4.74990i	−0.386542	+	0.386542i	0.486910	+	0.873452i	$0.338124\pi$
$152$	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	0.167218	−	0.985920i	$-0.446522\pi$
$157$	14.4488	−	14.4488i	1.15314	−	1.15314i	0.985920	−	0.167218i	$-0.0534784\pi$
$158$	−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	0.891972	+	0.452091i	$0.149322\pi$
$163$	10.6926	+	18.5201i	0.837508	+	1.45061i	−0.0544633	+	0.998516i	$0.517345\pi$
$164$	−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	$-0.312203\pi$
$167$	1.48475	+	0.857220i	0.114893	+	0.0663337i	−0.441452	+	0.897285i	$0.645536\pi$
$168$	−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	0.768677	−	0.639638i	$-0.220916\pi$
$173$	14.6596	+	3.92804i	1.11455	+	0.298643i	0.345875	+	0.938281i	$0.387582\pi$
$174$	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	−0.809850	−	0.586637i	$-0.800452\pi$
$179$	1.37961	−	2.38956i	0.103117	−	0.178604i	0.912967	+	0.408033i	$0.133785\pi$
$180$	3.36568	+	9.59815i	0.250863	+	0.715404i
$181$			10.3568i			0.769818i	0.922954	+	0.384909i	$0.125767\pi$
$181$			10.3568i			0.769818i	−0.922954	+	0.384909i	$0.874233\pi$
$182$		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	−0.977282	−	0.211943i	$-0.932021\pi$
$191$	−9.28983	−	16.0905i	−0.672189	−	1.16427i	0.305093	−	0.952322i	$-0.401312\pi$
$192$	19.6663	−	5.26958i	1.41930	−	0.380299i
$193$	6.28576	−	10.8872i	0.452459	−	0.783681i	−0.546079	−	0.837733i	$-0.683880\pi$
$193$	6.28576	−	10.8872i	0.452459	−	0.783681i	0.998538	+	0.0540520i	$0.0172137\pi$
$194$	−7.68313			−0.551617
$195$		0			0
$196$	−5.79377			−0.413841
$197$	7.14308	−	12.3722i	0.508924	−	0.881481i	−0.491023	−	0.871147i	$-0.663377\pi$
$197$	7.14308	−	12.3722i	0.508924	−	0.881481i	0.999947	−	0.0103349i	$-0.00328975\pi$
$198$	−7.83150	+	2.09845i	−0.556561	+	0.149130i
$199$	−7.36781	−	12.7614i	−0.522291	−	0.904634i	−0.999664	−	0.0259331i	$-0.991744\pi$
$199$	−7.36781	−	12.7614i	−0.522291	−	0.904634i	0.477373	−	0.878701i	$-0.341589\pi$
$200$	−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	−0.680992	−	0.732291i	$-0.738451\pi$
$211$	4.26604	−	7.38900i	0.293686	−	0.508680i	0.974678	+	0.223611i	$0.0717845\pi$
$212$	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	$-0.257362\pi$
$223$	6.11483	+	3.53040i	0.409479	+	0.236413i	−0.281087	+	0.959682i	$0.590695\pi$
$224$	−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	−0.996566	−	0.0827985i	$-0.973614\pi$
$227$	−8.58775	−	14.8744i	−0.569989	−	0.987249i	0.426578	−	0.904451i	$-0.359719\pi$
$228$	−3.63480	−	6.29566i	−0.240721	−	0.416940i
$229$	−8.90647	−	8.90647i	−0.588556	−	0.588556i	0.348684	−	0.937240i	$-0.386629\pi$
$229$	−8.90647	−	8.90647i	−0.588556	−	0.588556i	−0.937240	+	0.348684i	$0.886629\pi$
$230$	−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	0.165666	−	0.986182i	$-0.447023\pi$
$233$	17.5822	−	17.5822i	1.15185	−	1.15185i	0.986182	−	0.165666i	$-0.0529773\pi$
$234$		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	$-0.782595\pi$
$239$	−2.23488	+	2.23488i	−0.144562	+	0.144562i	0.631122	+	0.775684i	$0.282595\pi$
$240$	6.07750	−	4.14947i	0.392301	−	0.267847i
$241$	−17.4048	−	4.66361i	−1.12114	−	0.300409i	−0.349797	−	0.936825i	$-0.613750\pi$
$241$	−17.4048	−	4.66361i	−1.12114	−	0.300409i	−0.771346	+	0.636416i	$0.780416\pi$
$242$			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	−0.830658	−	0.556782i	$-0.812036\pi$
$251$	−12.1009	+	6.98644i	−0.763800	+	0.440980i	0.0668586	+	0.997762i	$0.478702\pi$
$252$	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	0.519433	−	0.854511i	$-0.326143\pi$
$257$	22.3881	−	5.99887i	1.39653	−	0.374199i	0.877098	+	0.480312i	$0.159476\pi$
$258$	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	−0.297357	−	0.954766i	$-0.596105\pi$
$263$	−1.25672	+	0.336737i	−0.0774926	+	0.0207641i	0.219864	+	0.975530i	$0.429438\pi$
$264$	−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	−0.694706	−	0.719294i	$-0.744466\pi$
$269$	−6.87429	+	3.96887i	−0.419133	+	0.241986i	0.275574	+	0.961280i	$0.411132\pi$
$270$	−4.87828	+	10.1470i	−0.296883	+	0.617529i
$271$	−0.231787	−	0.865041i	−0.0140801	−	0.0525475i	0.958528	−	0.284997i	$-0.0919926\pi$
$271$	−0.231787	−	0.865041i	−0.0140801	−	0.0525475i	−0.972608	+	0.232450i	$0.925326\pi$
$272$	−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	0.850982	+	0.525194i	$0.176007\pi$
$277$	−2.47298	+	9.22930i	−0.148587	+	0.554535i	−0.999569	+	0.0293404i	$0.990659\pi$
$278$		−	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	$-0.825689\pi$
$281$	−5.58408	+	5.58408i	−0.333118	+	0.333118i	0.520651	+	0.853769i	$0.325689\pi$
$282$	21.5981	+	5.78719i	1.28615	+	0.344622i
$283$	5.46218	+	20.3851i	0.324693	+	1.21177i	0.914620	+	0.404314i	$0.132490\pi$
$283$	5.46218	+	20.3851i	0.324693	+	1.21177i	−0.589927	+	0.807457i	$0.700843\pi$
$284$	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	$-0.129188\pi$
$293$	2.01079	+	3.48280i	0.117472	+	0.203467i	−0.801293	+	0.598272i	$0.795854\pi$
$294$	−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	$-0.928349\pi$
$311$		−	7.87243i		−	0.446405i	0.974772	−	0.223202i	$-0.0716511\pi$
$312$		0			0
$313$	3.39121	+	3.39121i	0.191683	+	0.191683i	0.796423	−	0.604740i	$-0.206723\pi$
$313$	3.39121	+	3.39121i	0.191683	+	0.191683i	−0.604740	+	0.796423i	$0.706723\pi$
$314$	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	$-0.722648\pi$
$317$	−22.9255			−1.28762			−0.643812	+	0.765184i	$0.722648\pi$
$318$	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	0.134910	+	0.990858i	$0.456925\pi$
$331$	−8.68470	+	32.4118i	−0.477354	+	1.78151i	−0.612264	+	0.790653i	$0.709741\pi$
$332$	−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	0.981953	−	0.189126i	$-0.0605656\pi$
$337$	14.5544	+	14.5544i	0.792826	+	0.792826i	−0.189126	+	0.981953i	$0.560566\pi$
$338$		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	−0.386844	−	0.922145i	$-0.626435\pi$
$347$	−22.0356	−	5.90442i	−1.18293	−	0.316966i	−0.796089	+	0.605179i	$0.793101\pi$
$348$	−0.201165	−	0.750759i	−0.0107836	−	0.0402449i
$349$	10.0317	−	2.68798i	0.536983	−	0.143884i	0.0198718	−	0.999803i	$-0.493674\pi$
$349$	10.0317	−	2.68798i	0.536983	−	0.143884i	0.517111	+	0.855918i	$0.327008\pi$
$350$	−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	$-0.296825\pi$
$353$	3.72420	+	2.15017i	0.198219	+	0.114442i	−0.397605	+	0.917556i	$0.630159\pi$
$354$	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	$-0.377229\pi$
$359$	−10.4273	−	10.4273i	−0.550333	−	0.550333i	−0.926537	+	0.376204i	$0.877229\pi$
$360$	−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	0.999162	+	0.0409383i	$0.0130347\pi$
$367$	2.95657	+	11.0341i	0.154331	+	0.575973i	−0.844830	+	0.535034i	$0.820299\pi$
$368$	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	−0.472568	−	0.881294i	$-0.656673\pi$
$373$	7.28755	−	27.1975i	0.377335	−	1.40823i	0.849903	−	0.526939i	$-0.176661\pi$
$374$	−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	−0.982362	−	0.186987i	$-0.940128\pi$
$379$	−4.38232	−	16.3551i	−0.225105	−	0.840103i	0.757258	−	0.653116i	$-0.226539\pi$
$380$	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	$-0.720631\pi$
$383$	−5.71918	+	3.30197i	−0.292236	+	0.168723i	0.346714	+	0.937971i	$0.387298\pi$
$384$	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	$-0.620004\pi$
$397$	5.04104	−	2.91045i	0.253002	−	0.146071i	0.621138	+	0.783701i	$0.286671\pi$
$398$	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	$-0.0812351\pi$
$401$	0.0683280	+	0.255004i	0.00341214	+	0.0127343i	−0.964199	+	0.265181i	$0.914568\pi$
$402$	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	$-0.0458121\pi$
$409$	35.8975	+	9.61872i	1.77502	+	0.475615i	0.785358	+	0.619042i	$0.212479\pi$
$410$	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	0.997490	−	0.0708027i	$-0.0225561\pi$
$419$	29.3721	+	16.9580i	1.43492	+	0.828451i	0.437428	+	0.899253i	$0.355889\pi$
$420$	3.23095	+	4.73219i	0.157654	+	0.230907i
$421$	21.5599	+	21.5599i	1.05076	+	1.05076i	0.998641	+	0.0521230i	$0.0165988\pi$
$421$	21.5599	+	21.5599i	1.05076	+	1.05076i	0.0521230	+	0.998641i	$0.483401\pi$
$422$	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	$-0.548009\pi$
$431$	4.44167	−	1.19014i	0.213948	−	0.0573271i	0.364201	+	0.931320i	$0.381342\pi$
$432$	−1.50488	−	5.61627i	−0.0724033	−	0.270213i
$433$	3.86627	+	1.03596i	0.185801	+	0.0497853i	0.350520	−	0.936555i	$-0.386005\pi$
$433$	3.86627	+	1.03596i	0.185801	+	0.0497853i	−0.164719	+	0.986341i	$0.552672\pi$
$434$	−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	0.456502	+	0.889723i	$0.349102\pi$
$439$	−11.3618	+	19.6793i	−0.542271	+	0.939242i	−0.998773	+	0.0495192i	$0.984231\pi$
$440$	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	0.749660	−	0.661824i	$-0.230217\pi$
$443$	1.84874	+	1.84874i	0.0878361	+	0.0878361i	−0.661824	+	0.749660i	$0.730217\pi$
$444$	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	0.432219	+	0.901769i	$0.357731\pi$
$449$	−8.32705	+	31.0770i	−0.392978	+	1.46661i	−0.825197	+	0.564845i	$0.808936\pi$
$450$	−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	0.316208	+	0.948690i	$0.397590\pi$
$457$	−14.1837	+	24.5669i	−0.663486	+	1.14919i	−0.979693	+	0.200501i	$0.935743\pi$
$458$	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	0.861213	+	0.508244i	$0.169705\pi$
$461$	−2.97890	+	11.1174i	−0.138741	+	0.517790i	−0.999954	+	0.00954570i	$0.996961\pi$
$462$	−3.95562	+	2.28378i	−0.184032	+	0.106251i
$463$	−29.9456			−1.39169			−0.695845	−	0.718192i	$-0.744970\pi$
$463$	−29.9456			−1.39169			−0.695845	+	0.718192i	$0.744970\pi$
$464$	−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	0.227274	−	0.973831i	$-0.427019\pi$
$467$	−16.1332	−	16.1332i	−0.746557	−	0.746557i	−0.973831	+	0.227274i	$0.927019\pi$
$468$		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	$-0.236096\pi$
$479$	37.5043	−	10.0493i	1.71362	−	0.459162i	0.976306	+	0.216393i	$0.0694293\pi$
$480$	−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	0.981697	+	0.190448i	$0.0609941\pi$
$487$	14.4718	+	25.0660i	0.655782	+	1.13585i	−0.325916	+	0.945399i	$0.605673\pi$
$488$	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	0.351059	−	0.936353i	$-0.385822\pi$
$491$	−6.30003	−	3.63733i	−0.284317	−	0.164150i	−0.635376	+	0.772203i	$0.719155\pi$
$492$	−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	$-0.707128\pi$
$499$	4.24201	−	4.24201i	0.189899	−	0.189899i	0.795652	+	0.605754i	$0.207128\pi$
$500$	−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	−0.941809	−	0.336149i	$-0.890875\pi$
$503$	0.939636	−	3.50677i	0.0418963	−	0.156359i	0.983705	+	0.179790i	$0.0575419\pi$
$504$	−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	0.960847	+	0.277079i	$0.0893664\pi$
$509$	6.02986	+	22.5037i	0.267269	+	0.997460i	−0.693578	+	0.720381i	$0.743967\pi$
$510$	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	−0.599677	−	0.800243i	$-0.704704\pi$
$523$	−16.4404	+	4.40520i	−0.718890	+	0.192626i	−0.119214	+	0.992869i	$0.538037\pi$
$524$	−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	$-0.641743\pi$
$541$	10.9728	−	10.9728i	0.471756	−	0.471756i	0.902483	+	0.430727i	$0.141743\pi$
$542$	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	−0.992923	−	0.118756i	$-0.962109\pi$
$547$	−20.4450	+	20.4450i	−0.874167	+	0.874167i	0.118756	+	0.992923i	$0.462109\pi$
$548$	−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	$-0.240440\pi$
$557$	11.7609	+	6.79015i	0.498324	+	0.287708i	−0.229697	+	0.973262i	$0.573774\pi$
$558$	−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	0.158736	−	0.987321i	$-0.449258\pi$
$563$	−4.68514	−	1.25538i	−0.197455	−	0.0529080i	−0.356191	+	0.934413i	$0.615925\pi$
$564$	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	−0.868621	−	0.495477i	$-0.834993\pi$
$569$	−0.124396	+	0.215461i	−0.00521497	+	0.00903259i	0.863406	+	0.504509i	$0.168327\pi$
$570$	16.4385	−	5.76432i	0.688534	−	0.241441i
$571$		−	7.72842i		−	0.323424i	−0.986838	−	0.161712i	$-0.948298\pi$
$571$		−	7.72842i		−	0.323424i	0.986838	−	0.161712i	$-0.0517016\pi$
$572$		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	$-0.418724\pi$
$577$	12.1339			0.505141			0.252570	+	0.967578i	$0.418724\pi$
$578$	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	0.192072	+	0.981381i	$0.438479\pi$
$587$	−18.2647	+	31.6354i	−0.753865	+	1.30573i	−0.945937	+	0.324351i	$0.894854\pi$
$588$	−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	$-0.388637\pi$
$593$	16.6936			0.685525			0.342762	+	0.939422i	$0.388637\pi$
$594$	−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	$0.0872847\pi$
$599$			13.2549i			0.541579i	−0.962639	+	0.270789i	$0.912715\pi$
$600$	−16.8853	−	38.5621i	−0.689341	−	1.57429i
$601$	−0.546605	+	0.946748i	−0.0222965	+	0.0386187i	−0.876958	−	0.480566i	$-0.840431\pi$
$601$	−0.546605	+	0.946748i	−0.0222965	+	0.0386187i	0.854662	+	0.519185i	$0.173764\pi$
$602$	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	0.957144	−	0.289612i	$-0.0935263\pi$
$607$	40.4361	+	10.8348i	1.64125	+	0.439771i	0.684105	+	0.729384i	$0.260193\pi$
$608$	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	$-0.142738\pi$
$613$	24.1705	+	13.9548i	0.976235	+	0.563630i	0.0751039	+	0.997176i	$0.476071\pi$
$614$	−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	$-0.138549\pi$
$617$	2.19132	+	3.79548i	0.0882193	+	0.152800i	−0.818539	+	0.574451i	$0.805216\pi$
$618$	−5.08477	−	8.80708i	−0.204540	−	0.354273i
$619$	8.67268	+	8.67268i	0.348584	+	0.348584i	0.859582	−	0.510998i	$-0.170724\pi$
$619$	8.67268	+	8.67268i	0.348584	+	0.348584i	−0.510998	+	0.859582i	$0.670724\pi$
$620$	−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	$-0.584934\pi$
$631$	−24.4748	−	6.55800i	−0.974326	−	0.261070i	−0.710653	+	0.703542i	$0.751601\pi$
$632$		−	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	−0.471760	−	0.881727i	$-0.656381\pi$
$641$	1.41675	−	0.817961i	0.0559582	−	0.0323075i	0.527718	+	0.849420i	$0.323048\pi$
$642$	1.26681			0.0499968
$643$	34.3541	−	19.8344i	1.35479	−	0.782191i	0.365878	−	0.930663i	$-0.380769\pi$
$643$	34.3541	−	19.8344i	1.35479	−	0.782191i	0.988917	+	0.148472i	$0.0474354\pi$
$644$	−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	0.0347277	−	0.999397i	$-0.488944\pi$
$647$	14.3588	−	3.84742i	0.564501	−	0.151258i	0.529773	+	0.848139i	$0.322277\pi$
$648$	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	−0.493459	−	0.869769i	$-0.664268\pi$
$653$	−12.4172	+	3.32718i	−0.485922	+	0.130203i	0.00753655	+	0.999972i	$0.497601\pi$
$654$	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	−0.0349025	−	0.999391i	$-0.511112\pi$
$659$	20.8742	−	12.0517i	0.813144	−	0.469469i	0.848047	+	0.529922i	$0.177779\pi$
$660$	−9.33366	+	3.27293i	−0.363312	+	0.127399i
$661$	10.1325	+	37.8150i	0.394108	+	1.47083i	0.823293	+	0.567616i	$0.192134\pi$
$661$	10.1325	+	37.8150i	0.394108	+	1.47083i	−0.429185	+	0.903217i	$0.641199\pi$
$662$	−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	0.997990	−	0.0633730i	$-0.0201858\pi$
$673$	2.64660	+	9.87723i	0.102019	+	0.380739i	−0.895971	+	0.444112i	$0.853519\pi$
$674$	−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	0.162121	−	0.986771i	$-0.448167\pi$
$677$	29.8933	−	29.8933i	1.14889	−	1.14889i	0.986771	−	0.162121i	$-0.0518333\pi$
$678$	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	$-0.0415455\pi$
$683$	10.0103	+	17.3384i	0.383035	+	0.663436i	−0.608459	+	0.793585i	$0.708212\pi$
$684$	−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	$-0.818369\pi$
$691$	−34.1813	+	9.15886i	−1.30032	+	0.348420i	−0.458749	+	0.888566i	$0.651702\pi$
$692$	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	$0.247753\pi$
$701$			37.1781i			1.40420i	−0.712080	+	0.702098i	$0.752247\pi$
$702$		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	−0.176783	−	0.984250i	$-0.556569\pi$
$709$	12.4732	−	46.5506i	0.468440	−	1.74824i	0.645224	−	0.763994i	$-0.276764\pi$
$710$	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	0.988966	+	0.148141i	$0.0473288\pi$
$719$	16.6992	+	28.9239i	0.622777	+	1.07868i	−0.366190	+	0.930540i	$0.619338\pi$
$720$	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	0.116149	−	0.993232i	$-0.462945\pi$
$727$	−23.6487	−	23.6487i	−0.877083	−	0.877083i	−0.993232	+	0.116149i	$0.962945\pi$
$728$		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	$-0.459818\pi$
$739$	19.8706	−	5.32432i	0.730953	−	0.195858i	0.605054	+	0.796185i	$0.293152\pi$
$740$	−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	$-0.638725\pi$
$743$	−38.6601	−	22.3204i	−1.41830	−	0.818856i	−0.996150	+	0.0876692i	$0.972058\pi$
$744$	−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	0.195804	−	0.980643i	$-0.437268\pi$
$751$	−15.2247	−	8.78996i	−0.555555	−	0.320750i	−0.751360	+	0.659893i	$0.770602\pi$
$752$	−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	−0.908085	−	0.418786i	$-0.862456\pi$
$757$	−9.10848	−	33.9933i	−0.331053	−	1.23551i	0.577032	−	0.816722i	$-0.304211\pi$
$758$	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	$-0.484754\pi$
$761$	−11.3127	−	3.03122i	−0.410084	−	0.109882i	−0.457962	+	0.888972i	$0.651421\pi$
$762$			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	−0.996195	−	0.0871555i	$-0.972222\pi$
$769$	−4.90954	−	18.3227i	−0.177043	−	0.660732i	0.819152	−	0.573576i	$-0.194444\pi$
$770$	−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	$-0.762024\pi$
$773$	−14.2114	+	8.20497i	−0.511149	+	0.295112i	0.222157	+	0.975011i	$0.428690\pi$
$774$	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	$-0.744600\pi$
$787$	−11.7781	+	6.80008i	−0.419844	+	0.242397i	0.275167	+	0.961396i	$0.411267\pi$
$788$	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	−0.681780	−	0.731557i	$-0.738794\pi$
$797$	7.74769	−	28.9148i	0.274437	−	1.02421i	0.956218	−	0.292657i	$-0.0945393\pi$
$798$		−	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	0.454564	−	0.890714i	$-0.349795\pi$
$809$	−2.54661	−	1.47029i	−0.0895342	−	0.0516926i	−0.544099	+	0.839021i	$0.683128\pi$
$810$	0.245021	−	1.29968i	0.00860916	−	0.0456661i
$811$	−16.3366	−	16.3366i	−0.573657	−	0.573657i	0.359492	−	0.933148i	$-0.382950\pi$
$811$	−16.3366	−	16.3366i	−0.573657	−	0.573657i	−0.933148	+	0.359492i	$0.882950\pi$
$812$	−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	$-0.287882\pi$
$821$	44.3125	−	11.8735i	1.54652	−	0.414388i	0.928364	+	0.371672i	$0.121215\pi$
$822$	−3.25838	−	12.1605i	−0.113649	−	0.424145i
$823$	17.1209	+	4.58752i	0.596796	+	0.159911i	0.544557	−	0.838724i	$-0.316698\pi$
$823$	17.1209	+	4.58752i	0.596796	+	0.159911i	0.0522385	+	0.998635i	$0.483364\pi$
$824$	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	0.408454	+	0.912779i	$0.366068\pi$
$829$	−16.8799	+	29.2368i	−0.586262	+	1.01544i	−0.994717	+	0.102657i	$0.967265\pi$
$830$	−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	0.536101	+	0.844154i	$0.319897\pi$
$839$	−10.1452	+	37.8626i	−0.350253	+	1.30716i	−0.886354	+	0.463008i	$0.846770\pi$
$840$	−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	$-0.744938\pi$
$853$	−40.6417			−1.39154			−0.695772	+	0.718262i	$0.744938\pi$
$854$	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	0.997721	−	0.0674695i	$-0.0214925\pi$
$857$	27.2327	+	27.2327i	0.930252	+	0.930252i	−0.0674695	+	0.997721i	$0.521493\pi$
$858$		0			0
$859$			44.5502i			1.52003i	0.649904	+	0.760016i	$0.274809\pi$
$859$			44.5502i			1.52003i	−0.649904	+	0.760016i	$0.725191\pi$
$860$	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	$-0.137729\pi$
$877$	2.68849	+	4.65661i	0.0907839	+	0.157242i	−0.817057	+	0.576557i	$0.804396\pi$
$878$	−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	0.971022	−	0.238992i	$-0.0768169\pi$
$881$	37.0890	+	21.4133i	1.24956	+	0.721434i	0.278538	+	0.960425i	$0.410150\pi$
$882$	−25.6309	−	14.7980i	−0.863037	−	0.498274i
$883$	−32.9568	+	32.9568i	−1.10908	+	1.10908i	−0.115813	+	0.993271i	$0.536947\pi$
$883$	−32.9568	+	32.9568i	−1.10908	+	1.10908i	−0.993271	+	0.115813i	$0.963053\pi$
$884$		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	−0.994903	−	0.100837i	$-0.967848\pi$
$887$	−5.47136	−	20.4194i	−0.183710	−	0.685616i	0.811193	−	0.584779i	$-0.198819\pi$
$888$	−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	−0.431842	−	0.901949i	$-0.642136\pi$
$907$	−10.6869	+	2.86355i	−0.354853	+	0.0950825i	0.0769889	+	0.997032i	$0.475469\pi$
$908$	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	−0.667934	−	0.744220i	$-0.732821\pi$
$919$	−10.8342	+	6.25513i	−0.357388	+	0.206338i	0.310547	+	0.950558i	$0.399488\pi$
$920$	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	$-0.121662\pi$
$929$	47.0874	+	12.6170i	1.54489	+	0.413952i	0.617047	+	0.786926i	$0.288329\pi$
$930$	−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	−0.576203	−	0.817306i	$-0.695466\pi$
$937$	7.38027	−	7.38027i	0.241103	−	0.241103i	0.817306	+	0.576203i	$0.195466\pi$
$938$	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	$-0.238668\pi$
$941$	1.54410	+	1.54410i	0.0503363	+	0.0503363i	−0.681491	+	0.731827i	$0.738668\pi$
$942$	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	$-0.298527\pi$
$947$	5.81670	+	3.35827i	0.189017	+	0.109129i	−0.402505	+	0.915418i	$0.631860\pi$
$948$	−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	0.529977	−	0.848012i	$-0.322201\pi$
$953$	17.4402	+	4.67309i	0.564944	+	0.151376i	0.0349673	+	0.999388i	$0.488867\pi$
$954$	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	$-0.916330\pi$
$967$	−60.0570			−1.93130			−0.965651	+	0.259841i	$0.916330\pi$
$968$	−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	0.981501	+	0.191459i	$0.0613218\pi$
$971$	20.4589	+	35.4359i	0.656558	+	1.13719i	−0.324942	+	0.945734i	$0.605345\pi$
$972$	−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	−0.393050	−	0.919517i	$-0.628580\pi$
$977$	18.7479	−	32.4724i	0.599800	−	1.03888i	0.992850	−	0.119367i	$-0.0380865\pi$
$978$	−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	$-0.236966\pi$
$983$	46.1176			1.47092			0.735461	+	0.677567i	$0.236966\pi$
$984$	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	−0.872326	−	0.488925i	$-0.837389\pi$
$991$	−0.401099	+	0.694724i	−0.0127413	+	0.0220686i	0.859584	+	0.510994i	$0.170722\pi$
$992$	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	0.0120264	−	0.999928i	$-0.496172\pi$
$997$	−15.0779	−	4.04012i	−0.477522	−	0.127952i	−0.489549	+	0.871976i	$0.662838\pi$
$998$	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.f.488.2		20
5.2	odd	4		845.2.t.e.657.2		20
13.2	odd	12		845.2.t.e.418.2		20
13.3	even	3		845.2.o.g.258.2		20
13.4	even	6		845.2.k.e.268.3		20
13.5	odd	4		845.2.t.g.188.4		20
13.6	odd	12		845.2.f.d.408.3		20
13.7	odd	12		845.2.f.e.408.8		20
13.8	odd	4		65.2.t.a.58.2	yes	20
13.9	even	3		845.2.k.d.268.8		20
13.10	even	6		65.2.o.a.63.4	yes	20
13.11	odd	12		845.2.t.f.418.4		20
13.12	even	2		845.2.o.e.488.4		20
39.8	even	4		585.2.dp.a.253.4		20
39.23	odd	6		585.2.cf.a.388.2		20
65.2	even	12	inner	845.2.o.f.587.2		20
65.7	even	12		845.2.k.e.577.3		20
65.8	even	4		325.2.s.b.32.2		20
65.12	odd	4		845.2.t.f.657.4		20
65.17	odd	12		845.2.f.e.437.3		20
65.22	odd	12		845.2.f.d.437.8		20
65.23	odd	12		325.2.x.b.232.4		20
65.32	even	12		845.2.k.d.577.8		20
65.34	odd	4		325.2.x.b.318.4		20
65.37	even	12		845.2.o.e.587.4		20
65.42	odd	12		845.2.t.g.427.4		20
65.47	even	4		65.2.o.a.32.4	✓	20
65.49	even	6		325.2.s.b.193.2		20
65.57	even	4		845.2.o.g.357.2		20
65.62	odd	12		65.2.t.a.37.2	yes	20
195.47	odd	4		585.2.cf.a.487.2		20
195.62	even	12		585.2.dp.a.37.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.4	✓	20	65.47	even	4
65.2.o.a.63.4	yes	20	13.10	even	6
65.2.t.a.37.2	yes	20	65.62	odd	12
65.2.t.a.58.2	yes	20	13.8	odd	4
325.2.s.b.32.2		20	65.8	even	4
325.2.s.b.193.2		20	65.49	even	6
325.2.x.b.232.4		20	65.23	odd	12
325.2.x.b.318.4		20	65.34	odd	4
585.2.cf.a.388.2		20	39.23	odd	6
585.2.cf.a.487.2		20	195.47	odd	4
585.2.dp.a.37.4		20	195.62	even	12
585.2.dp.a.253.4		20	39.8	even	4
845.2.f.d.408.3		20	13.6	odd	12
845.2.f.d.437.8		20	65.22	odd	12
845.2.f.e.408.8		20	13.7	odd	12
845.2.f.e.437.3		20	65.17	odd	12
845.2.k.d.268.8		20	13.9	even	3
845.2.k.d.577.8		20	65.32	even	12
845.2.k.e.268.3		20	13.4	even	6
845.2.k.e.577.3		20	65.7	even	12
845.2.o.e.488.4		20	13.12	even	2
845.2.o.e.587.4		20	65.37	even	12
845.2.o.f.488.2		20	1.1	even	1	trivial
845.2.o.f.587.2		20	65.2	even	12	inner
845.2.o.g.258.2		20	13.3	even	3
845.2.o.g.357.2		20	65.57	even	4
845.2.t.e.418.2		20	13.2	odd	12
845.2.t.e.657.2		20	5.2	odd	4
845.2.t.f.418.4		20	13.11	odd	12
845.2.t.f.657.4		20	65.12	odd	4
845.2.t.g.188.4		20	13.5	odd	4
845.2.t.g.427.4		20	65.42	odd	12

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.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

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