LMFDB - Embedded newform 845.2.t.g.427.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("845.188");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			427.4
Root			$-1.02262i$ of defining polynomial
Character	$\chi$	$=$	845.427
Dual form			845.2.t.g.188.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

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

Coefficient data

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

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

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

$2$	0.885613	−	0.511309i	0.626223	−	0.361550i	−0.153065	−	0.988216i	$-0.548914\pi$
$2$	0.885613	−	0.511309i	0.626223	−	0.361550i	0.779288	+	0.626666i	$0.215581\pi$
$3$	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
$5$	1.45744	+	1.69584i	0.651785	+	0.758404i
$5$	1.45744	+	1.69584i	0.651785	+	0.758404i
$6$	2.75281	−	0.737614i	1.12383	−	0.301130i
$7$	0.481787	−	0.834479i	0.182098	−	0.315404i	−0.760497	−	0.649342i	$-0.775044\pi$
$7$	0.481787	−	0.834479i	0.182098	−	0.315404i	0.942595	+	0.333938i	$0.108378\pi$
$8$			3.02107i			1.06811i
$9$	4.12812	+	2.38337i	1.37604	+	0.794457i
$10$	2.15782	+	0.756660i	0.682364	+	0.239277i
$11$	−1.60661	−	0.430490i	−0.484411	−	0.129797i	0.00834492	−	0.999965i	$-0.497344\pi$
$11$	−1.60661	−	0.430490i	−0.484411	−	0.129797i	−0.492756	+	0.870168i	$0.664010\pi$
$12$	−1.88048	+	1.88048i	−0.542847	+	0.542847i
$13$		0			0
$13$		0			0
$14$		−	0.985368i		−	0.263351i
$15$	2.70010	+	5.61633i	0.697163	+	1.45013i
$16$	0.590448	+	1.02269i	0.147612	+	0.255671i
$17$	−1.87656	−	7.00342i	−0.455133	−	1.69858i	−0.687697	−	0.725998i	$-0.741378\pi$
$17$	−1.87656	−	7.00342i	−0.455133	−	1.69858i	0.232564	−	0.972581i	$-0.425289\pi$
$18$	4.87456			1.14894
$19$	−0.707496	−	2.64041i	−0.162311	−	0.605752i	−0.998368	−	0.0571095i	$-0.981812\pi$
$19$	−0.707496	−	2.64041i	−0.162311	−	0.605752i	0.836057	−	0.548642i	$-0.184855\pi$
$20$	−2.09684	+	0.395304i	−0.468867	+	0.0883927i
$21$	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	$0.214931\pi$
$23$	−0.997344	+	3.72214i	−0.207961	+	0.776120i	−0.988527	+	0.151046i	$0.951736\pi$
$24$	−2.17910	+	8.13250i	−0.444806	+	1.66004i
$25$	−0.751762	+	4.94316i	−0.150352	+	0.988632i
$26$		0			0
$27$	3.48159	+	3.48159i	0.670033	+	0.670033i
$28$	0.459747	+	0.796304i	0.0868839	+	0.150487i
$29$	−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	$-0.244920\pi$
$31$	0.125649	+	0.125649i	0.0225673	+	0.0225673i	−0.695733	+	0.718300i	$0.744920\pi$
$32$	−4.18683	−	2.41727i	−0.740134	−	0.427317i
$33$	−4.01436	−	2.31769i	−0.698811	−	0.403458i
$34$	−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
$37$	−2.04061	−	3.53443i	−0.335474	−	0.581057i	0.648102	−	0.761553i	$-0.275563\pi$
$37$	−2.04061	−	3.53443i	−0.335474	−	0.581057i	−0.983576	+	0.180496i	$0.942230\pi$
$38$	−1.97663	−	1.97663i	−0.320652	−	0.320652i
$39$		0			0
$40$	−5.12326	+	4.40302i	−0.810059	+	0.696178i
$41$	1.79277	−	6.69071i	0.279984	−	1.04491i	−0.672444	−	0.740148i	$-0.734755\pi$
$41$	1.79277	−	6.69071i	0.279984	−	1.04491i	0.952427	−	0.304765i	$-0.0985780\pi$
$42$	0.710745	−	2.65254i	0.109670	−	0.409295i
$43$	7.67707	−	2.05706i	1.17074	−	0.313699i	0.379494	−	0.925194i	$-0.376098\pi$
$43$	7.67707	−	2.05706i	1.17074	−	0.313699i	0.791248	+	0.611495i	$0.209432\pi$
$44$	1.12232	−	1.12232i	0.169195	−	0.169195i
$45$	1.97465	+	10.4743i	0.294363	+	1.56141i
$46$	1.01990	+	3.80633i	0.150376	+	0.561212i
$47$	7.84582			1.14443			0.572215	−	0.820103i	$-0.306084\pi$
$47$	7.84582			1.14443			0.572215	+	0.820103i	$0.306084\pi$
$48$	0.851780	+	3.17888i	0.122944	+	0.458832i
$49$	3.03576	+	5.25810i	0.433680	+	0.751156i
$50$	1.86171	+	4.76211i	0.263286	+	0.673464i
$51$		−	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	$0.312184\pi$
$54$	4.86351	+	1.30317i	0.661840	+	0.177339i
$55$	−1.61149	−	3.35197i	−0.217293	−	0.451979i
$56$	2.52102	+	1.45551i	0.336886	+	0.194501i
$57$		−	7.61811i		−	1.00904i
$58$	−0.149437	+	0.258832i	−0.0196220	+	0.0339863i
$59$	4.87924	−	1.30739i	0.635223	−	0.170207i	0.0731843	−	0.997318i	$-0.476684\pi$
$59$	4.87924	−	1.30739i	0.635223	−	0.170207i	0.562039	+	0.827111i	$0.310017\pi$
$60$	−5.92967	−	0.448318i	−0.765517	−	0.0578776i
$61$	−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
$63$	3.97775	−	2.29655i	0.501149	−	0.289339i
$64$	−7.30568			−0.913209
$65$		0			0
$66$	−4.74023			−0.583482
$67$	−6.32050	+	3.64915i	−0.772173	+	0.445814i	−0.833649	−	0.552294i	$-0.813752\pi$
$67$	−6.32050	+	3.64915i	−0.772173	+	0.445814i	0.0614765	+	0.998109i	$0.480419\pi$
$68$	6.68304	+	1.79071i	0.810437	+	0.217156i
$69$	−5.36956	+	9.30034i	−0.646419	+	1.11963i
$70$	1.67103	−	1.43611i	0.199726	−	0.171648i
$71$	−12.6082	+	3.37837i	−1.49632	+	0.400939i	−0.911867	−	0.410486i	$-0.865359\pi$
$71$	−12.6082	+	3.37837i	−1.49632	+	0.400939i	−0.584457	+	0.811425i	$0.698692\pi$
$72$	−7.20034	+	12.4713i	−0.848568	+	1.46976i
$73$			3.22747i			0.377746i	0.982001	+	0.188873i	$0.0604835\pi$
$73$			3.22747i			0.377746i	−0.982001	+	0.188873i	$0.939517\pi$
$74$	−3.61437	−	2.08676i	−0.420163	−	0.242581i
$75$	−5.58919	+	12.7644i	−0.645384	+	1.47390i
$76$	2.51962	+	0.675130i	0.289020	+	0.0774427i
$77$	−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	$-0.276861\pi$
$80$	−0.873774	+	2.49180i	−0.0976909	+	0.278592i
$81$	−0.289196	−	0.500902i	−0.0321329	−	0.0556558i
$82$	−1.83332	−	6.84204i	−0.202456	−	0.755577i
$83$	8.56854			0.940519			0.470260	−	0.882528i	$-0.344160\pi$
$83$	8.56854			0.940519			0.470260	+	0.882528i	$0.344160\pi$
$84$	0.663230	+	2.47521i	0.0723643	+	0.270067i
$85$	9.14173	−	13.3894i	0.991560	−	1.45228i
$86$	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
$89$	0.134207	−	0.500868i	0.0142259	−	0.0530919i	−0.958448	−	0.285267i	$-0.907918\pi$
$89$	0.134207	−	0.500868i	0.0142259	−	0.0530919i	0.972674	+	0.232175i	$0.0745843\pi$
$90$	7.10435	+	8.26648i	0.748864	+	0.871363i
$91$		0			0
$92$	−2.60014	−	2.60014i	−0.271084	−	0.271084i
$93$	0.247608	+	0.428870i	0.0256758	+	0.0444718i
$94$	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
$97$	6.50662	+	3.75660i	0.660648	+	0.381425i	0.792524	−	0.609841i	$-0.208767\pi$
$97$	6.50662	+	3.75660i	0.660648	+	0.381425i	−0.131876	+	0.991266i	$0.542100\pi$
$98$	5.37702	+	3.10442i	0.543161	+	0.313594i
$99$	−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	$-0.505392\pi$
$101$	8.44685	−	4.87679i	0.840493	−	0.485259i	0.857432	+	0.514598i	$0.172059\pi$
$102$	−10.3316	−	17.8949i	−1.02298	−	1.77186i
$103$	2.52321	+	2.52321i	0.248619	+	0.248619i	0.820404	−	0.571784i	$-0.193749\pi$
$103$	2.52321	+	2.52321i	0.248619	+	0.248619i	−0.571784	+	0.820404i	$0.693749\pi$
$104$		0			0
$105$	5.98759	+	0.452697i	0.584329	+	0.0441787i
$106$	−0.748066	+	2.79182i	−0.0726586	+	0.271166i
$107$	−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	−0.944258	−	0.329206i	$-0.893219\pi$
$109$	−6.42134	+	6.42134i	−0.615053	+	0.615053i	0.329206	+	0.944258i	$0.393219\pi$
$110$	−3.14104	−	2.14458i	−0.299487	−	0.204477i
$111$	−2.94378	−	10.9863i	−0.279411	−	1.04278i
$112$	1.13788			0.107520
$113$	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
$115$	−7.76573	+	3.73344i	−0.724158	+	0.348145i
$116$		−	0.278893i		−	0.0258946i
$117$		0			0
$118$	3.65264	−	3.65264i	0.336253	−	0.336253i
$119$	−6.74831	−	1.80821i	−0.618617	−	0.165758i
$120$	−16.9673	+	8.15720i	−1.54890	+	0.744647i
$121$	−7.13041	−	4.11674i	−0.648219	−	0.374249i
$122$			2.13050i			0.192886i
$123$	9.65202	−	16.7178i	0.870293	−	1.50739i
$124$	−0.163788	+	0.0438869i	−0.0147086	+	0.00394116i
$125$	−9.47847	+	5.92947i	−0.847780	+	0.530348i
$126$	2.34850	−	4.06772i	0.209221	−	0.362381i
$127$	−2.10102	−	0.562967i	−0.186436	−	0.0499553i	0.164393	−	0.986395i	$-0.447433\pi$
$127$	−2.10102	−	0.562967i	−0.186436	−	0.0499553i	−0.350829	+	0.936440i	$0.614100\pi$
$128$	1.90366	−	1.09908i	0.168262	−	0.0971460i
$129$	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	$0.500866\pi$
$132$	3.83072	−	2.21166i	0.333421	−	0.192501i
$133$	−2.54423	−	0.681725i	−0.220613	−	0.0591130i
$134$	−3.73168	+	6.46346i	−0.322368	+	0.558358i
$135$	−0.830034	+	10.9784i	−0.0714380	+	0.944872i
$136$	21.1578	−	5.66923i	1.81427	−	0.486132i
$137$	−2.20873	+	3.82564i	−0.188705	+	0.326846i	−0.944819	−	0.327594i	$-0.893762\pi$
$137$	−2.20873	+	3.82564i	−0.188705	+	0.326846i	0.756114	+	0.654440i	$0.227096\pi$
$138$			10.9820i			0.934850i
$139$	−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
$141$	21.1204	+	5.65919i	1.77866	+	0.476590i
$142$	−9.43864	+	9.43864i	−0.792073	+	0.792073i
$143$		0			0
$144$			5.62903i			0.469085i
$145$	−0.616704	−	0.216253i	−0.0512145	−	0.0179588i
$146$	1.65023	+	2.85829i	0.136574	+	0.236553i
$147$	4.37939	+	16.3441i	0.361206	+	1.34804i
$148$	3.89451			0.320127
$149$	−1.12129	−	4.18471i	−0.0918596	−	0.342825i	0.904665	−	0.426124i	$-0.140121\pi$
$149$	−1.12129	−	4.18471i	−0.0918596	−	0.342825i	−0.996525	+	0.0832987i	$0.973454\pi$
$150$	1.57669	+	14.1621i	0.128736	+	1.15633i
$151$	−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
$154$	−0.424190	+	1.58310i	−0.0341822	+	0.127570i
$155$	−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	$0.446522\pi$
$158$	−6.94589	−	12.0306i	−0.552586	−	0.957106i
$159$	−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
$162$	−0.512231	−	0.295737i	−0.0402447	−	0.0232353i
$163$	−18.5201	−	10.6926i	−1.45061	−	0.837508i	−0.452091	−	0.891972i	$-0.649322\pi$
$163$	−18.5201	−	10.6926i	−1.45061	−	0.837508i	−0.998516	+	0.0544633i	$0.982655\pi$
$164$	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
$167$	−0.857220	−	1.48475i	−0.0663337	−	0.114893i	0.830951	−	0.556345i	$-0.187797\pi$
$167$	−0.857220	−	1.48475i	−0.0663337	−	0.114893i	−0.897285	+	0.441452i	$0.854464\pi$
$168$	5.73655	+	5.73655i	0.442584	+	0.442584i
$169$		0			0
$170$	1.24992	−	16.5321i	0.0958646	−	1.26795i
$171$	3.37245	−	12.5862i	0.257898	−	0.962488i
$172$	−1.96296	+	7.32587i	−0.149674	+	0.558592i
$173$	−14.6596	+	3.92804i	−1.11455	+	0.298643i	−0.768677	−	0.639638i	$-0.779084\pi$
$173$	−14.6596	+	3.92804i	−1.11455	+	0.298643i	−0.345875	+	0.938281i	$0.612418\pi$
$174$	−0.588968	+	0.588968i	−0.0446496	+	0.0446496i
$175$	3.76278	+	3.00888i	0.284439	+	0.227450i
$176$	−0.508363	−	1.89724i	−0.0383193	−	0.143010i
$177$	14.0776			1.05814
$178$	−0.137243	−	0.512196i	−0.0102868	−	0.0383907i
$179$	−1.37961	−	2.38956i	−0.103117	−	0.178604i	0.809850	−	0.586637i	$-0.199548\pi$
$179$	−1.37961	−	2.38956i	−0.103117	−	0.178604i	−0.912967	+	0.408033i	$0.866215\pi$
$180$	−9.59815	−	3.36568i	−0.715404	−	0.250863i
$181$			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
$184$	−11.2449	−	3.01305i	−0.828981	−	0.222125i
$185$	3.01979	−	8.61176i	0.222019	−	0.633149i
$186$	0.438570	+	0.253209i	0.0321575	+	0.0185662i
$187$			12.0596i			0.881885i
$188$	−3.74345	+	6.48384i	−0.273019	+	0.472883i
$189$	4.58270	−	1.22793i	0.333342	−	0.0893188i
$190$	0.471242	−	6.23287i	0.0341875	−	0.452180i
$191$	−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
$193$	10.8872	−	6.28576i	0.783681	−	0.452459i	−0.0540520	−	0.998538i	$-0.517214\pi$
$193$	10.8872	−	6.28576i	0.783681	−	0.452459i	0.837733	+	0.546079i	$0.183880\pi$
$194$	7.68313			0.551617
$195$		0			0
$196$	−5.79377			−0.413841
$197$	−12.3722	+	7.14308i	−0.881481	+	0.508924i	−0.871147	−	0.491023i	$-0.836623\pi$
$197$	−12.3722	+	7.14308i	−0.881481	+	0.508924i	−0.0103349	+	0.999947i	$0.503290\pi$
$198$	−7.83150	−	2.09845i	−0.556561	−	0.149130i
$199$	7.36781	−	12.7614i	0.522291	−	0.904634i	−0.477373	−	0.878701i	$-0.658411\pi$
$199$	7.36781	−	12.7614i	0.522291	−	0.904634i	0.999664	−	0.0259331i	$-0.00825568\pi$
$200$	−14.9336	−	2.27113i	−1.05597	−	0.160593i
$201$	−19.6465	+	5.26425i	−1.38575	+	0.371312i
$202$	4.98709	−	8.63790i	0.350891	−	0.607760i
$203$			0.281617i			0.0197656i
$204$	16.6986	+	9.64094i	1.16914	+	0.675001i
$205$	13.9592	−	6.71103i	0.974956	−	0.468718i
$206$	3.52473	+	0.944449i	0.245580	+	0.0658029i
$207$	−12.9884	+	12.9884i	−0.902756	+	0.902756i
$208$		0			0
$209$			4.54668i			0.314500i
$210$	5.53415	−	2.66059i	0.381893	−	0.183598i
$211$	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
$213$	−36.3773			−2.49253
$214$	0.117649	+	0.439070i	0.00804229	+	0.0300142i
$215$	14.6773	+	10.0211i	1.00098	+	0.683431i
$216$	−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
$219$	−2.32797	+	8.68810i	−0.157310	+	0.587087i
$220$	3.53897	+	0.267567i	0.238597	+	0.0180394i
$221$		0			0
$222$	−8.22445	−	8.22445i	−0.551989	−	0.551989i
$223$	3.53040	+	6.11483i	0.236413	+	0.409479i	0.959682	−	0.281087i	$-0.0906949\pi$
$223$	3.53040	+	6.11483i	0.236413	+	0.409479i	−0.723269	+	0.690566i	$0.757362\pi$
$224$	−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
$227$	−14.8744	−	8.58775i	−0.987249	−	0.569989i	−0.0827985	−	0.996566i	$-0.526386\pi$
$227$	−14.8744	−	8.58775i	−0.987249	−	0.569989i	−0.904451	+	0.426578i	$0.859719\pi$
$228$	6.29566	+	3.63480i	0.416940	+	0.240721i
$229$	8.90647	+	8.90647i	0.588556	+	0.588556i	0.937240	−	0.348684i	$-0.113371\pi$
$229$	8.90647	+	8.90647i	0.588556	+	0.588556i	−0.348684	+	0.937240i	$0.613371\pi$
$230$	−4.96849	+	7.27707i	−0.327612	+	0.479836i
$231$	−3.86813	+	2.23327i	−0.254504	+	0.146938i
$232$	−0.441474	−	0.764655i	−0.0289842	−	0.0502021i
$233$	−17.5822	−	17.5822i	−1.15185	−	1.15185i	−0.986182	−	0.165666i	$-0.947023\pi$
$233$	−17.5822	−	17.5822i	−1.15185	−	1.15185i	−0.165666	−	0.986182i	$-0.552977\pi$
$234$		0			0
$235$	11.4348	+	13.3053i	0.745923	+	0.867940i
$236$	−1.24758	+	4.65603i	−0.0812105	+	0.303082i
$237$	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	−0.631122	−	0.775684i	$-0.717405\pi$
$239$	2.23488	−	2.23488i	0.144562	−	0.144562i	0.775684	+	0.631122i	$0.217405\pi$
$240$	−4.14947	+	6.07750i	−0.267847	+	0.392301i
$241$	4.66361	+	17.4048i	0.300409	+	1.12114i	0.936825	+	0.349797i	$0.113750\pi$
$241$	4.66361	+	17.4048i	0.300409	+	1.12114i	−0.636416	+	0.771346i	$0.719584\pi$
$242$	−8.41971			−0.541239
$243$	−4.24025	−	15.8248i	−0.272012	−	1.01516i
$244$	−0.994033	−	1.72172i	−0.0636364	−	0.110222i
$245$	−4.49247	+	12.8115i	−0.287013	+	0.818497i
$246$		−	19.7406i		−	1.25862i
$247$		0			0
$248$	−0.379596	+	0.379596i	−0.0241044	+	0.0241044i
$249$	23.0659	+	6.18048i	1.46174	+	0.391672i
$250$	−5.36246	+	10.0976i	−0.339152	+	0.638631i
$251$	12.1009	+	6.98644i	0.763800	+	0.440980i	0.830658	−	0.556782i	$-0.187964\pi$
$251$	12.1009	+	6.98644i	0.763800	+	0.440980i	−0.0668586	+	0.997762i	$0.521298\pi$
$252$			4.38299i			0.276102i
$253$	3.20468	−	5.55068i	0.201477	−	0.348968i
$254$	−2.14854	+	0.575700i	−0.134812	+	0.0361227i
$255$	34.2666	−	29.4493i	2.14586	−	1.84419i
$256$	8.42962	−	14.6005i	0.526851	−	0.912533i
$257$	−22.3881	−	5.99887i	−1.39653	−	0.374199i	−0.519433	−	0.854511i	$-0.673857\pi$
$257$	−22.3881	−	5.99887i	−1.39653	−	0.374199i	−0.877098	+	0.480312i	$0.840524\pi$
$258$	19.6162	−	11.3254i	1.22125	−	0.705090i
$259$	−3.93255			−0.244357
$260$		0			0
$261$	−1.39314			−0.0862334
$262$	−0.0551288	+	0.0318286i	−0.00340587	+	0.00196638i
$263$	−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
$265$	−6.30199	−	0.476468i	−0.387128	−	0.0292692i
$266$	−2.60178	+	0.697144i	−0.159525	+	0.0427446i
$267$	0.722551	−	1.25150i	0.0442194	−	0.0765903i
$268$		−	6.96441i		−	0.425419i
$269$	−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
$271$	0.865041	+	0.231787i	0.0525475	+	0.0140801i	0.284997	−	0.958528i	$-0.408007\pi$
$271$	0.865041	+	0.231787i	0.0525475	+	0.0140801i	−0.232450	+	0.972608i	$0.574674\pi$
$272$	6.05429	−	6.05429i	0.367095	−	0.367095i
$273$		0			0
$274$			4.51738i			0.272905i
$275$	3.33577	−	7.61810i	0.201154	−	0.459389i
$276$	−5.12391	−	8.87488i	−0.308423	−	0.534205i
$277$	2.47298	+	9.22930i	0.148587	+	0.554535i	0.999569	+	0.0293404i	$0.00934068\pi$
$277$	2.47298	+	9.22930i	0.148587	+	0.554535i	−0.850982	+	0.525194i	$0.823993\pi$
$278$	−14.0596			−0.843236
$279$	0.219227	+	0.818165i	0.0131248	+	0.0489823i
$280$	1.20591	+	6.39657i	0.0720668	+	0.382268i
$281$	−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	0.589927	+	0.807457i	$0.299157\pi$
$283$	−5.46218	+	20.3851i	−0.324693	+	1.21177i	−0.914620	+	0.404314i	$0.867510\pi$
$284$	3.22382	−	12.0315i	0.191298	−	0.713936i
$285$	12.9191	−	11.1029i	0.765262	−	0.657679i
$286$		0			0
$287$	−4.71953	−	4.71953i	−0.278585	−	0.278585i
$288$	−11.5225	−	19.9576i	−0.678970	−	1.17601i
$289$	−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
$292$	−2.66720	−	1.53991i	−0.156086	−	0.0901164i
$293$	−3.48280	−	2.01079i	−0.203467	−	0.117472i	0.394805	−	0.918765i	$-0.370812\pi$
$293$	−3.48280	−	2.01079i	−0.203467	−	0.117472i	−0.598272	+	0.801293i	$0.704146\pi$
$294$	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
$297$	−4.09477	−	7.09234i	−0.237602	−	0.411539i
$298$	−3.13271	−	3.13271i	−0.181473	−	0.181473i
$299$		0			0
$300$	−7.88183	−	10.7092i	−0.455058	−	0.618294i
$301$	1.98213	−	7.39742i	0.114248	−	0.426380i
$302$	−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
$305$	−4.57792	+	0.863049i	−0.262131	+	0.0494180i
$306$	−9.14740	−	34.1386i	−0.522922	−	1.95157i
$307$	−24.2191			−1.38226			−0.691128	−	0.722732i	$-0.742886\pi$
$307$	−24.2191			−1.38226			−0.691128	+	0.722732i	$0.742886\pi$
$308$	−0.395832	−	1.47727i	−0.0225546	−	0.0841750i
$309$	4.97231	+	8.61229i	0.282865	+	0.489936i
$310$	0.176055	+	0.366203i	0.00999927	+	0.0207989i
$311$		−	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	−0.604740	−	0.796423i	$-0.706723\pi$
$313$	3.39121	−	3.39121i	0.191683	−	0.191683i	0.796423	+	0.604740i	$0.206723\pi$
$314$	20.1838	+	5.40824i	1.13904	+	0.305204i
$315$	9.69191	+	3.39855i	0.546077	+	0.191487i
$316$	11.2264	+	6.48154i	0.631532	+	0.364615i
$317$		−	22.9255i		−	1.28762i	−0.765184	−	0.643812i	$-0.777352\pi$
$317$		−	22.9255i		−	1.28762i	0.765184	−	0.643812i	$-0.222648\pi$
$318$	−4.02748	+	6.97580i	−0.225850	+	0.391183i
$319$	0.469553	−	0.125816i	0.0262899	−	0.00704436i
$320$	−10.6476	−	12.3893i	−0.595216	−	0.692581i
$321$	−0.619393	+	1.07282i	−0.0345712	+	0.0598790i
$322$	3.66768	+	0.982751i	0.204392	+	0.0547666i
$323$	−17.1643	+	9.90979i	−0.955044	+	0.551395i
$324$	0.551932			0.0306629
$325$		0			0
$326$	−21.8689			−1.21120
$327$	−21.9175	+	12.6541i	−1.21204	+	0.699771i
$328$	20.2131	+	5.41609i	1.11608	+	0.299053i
$329$	3.78001	−	6.54718i	0.208399	−	0.360958i
$330$	−6.90858	−	8.03868i	−0.380305	−	0.442515i
$331$	32.4118	−	8.68470i	1.78151	−	0.477354i	0.790653	−	0.612264i	$-0.209741\pi$
$331$	32.4118	−	8.68470i	1.78151	−	0.477354i	0.990858	+	0.134910i	$0.0430745\pi$
$332$	−4.08828	+	7.08110i	−0.224373	+	0.388626i
$333$		−	19.4541i		−	1.06608i
$334$	−1.51833	−	0.876609i	−0.0830794	−	0.0479659i
$335$	−15.4001	−	5.40018i	−0.841398	−	0.295044i
$336$	3.06309	+	0.820752i	0.167105	+	0.0447757i
$337$	−14.5544	+	14.5544i	−0.792826	+	0.792826i	−0.981953	−	0.189126i	$-0.939434\pi$
$337$	−14.5544	+	14.5544i	−0.792826	+	0.792826i	0.189126	+	0.981953i	$0.439434\pi$
$338$		0			0
$339$			5.39143i			0.292822i
$340$	6.70333	+	13.9432i	0.363539	+	0.756178i
$341$	−0.147779	−	0.255960i	−0.00800267	−	0.0138610i
$342$	−3.44873	−	12.8708i	−0.186486	−	0.695975i
$343$	12.5954			0.680087
$344$	6.21454	+	23.1930i	0.335065	+	1.25048i
$345$	−23.5977	+	4.44873i	−1.27046	+	0.239512i
$346$	−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
$349$	2.68798	−	10.0317i	0.143884	−	0.536983i	−0.855918	−	0.517111i	$-0.827008\pi$
$349$	2.68798	−	10.0317i	0.143884	−	0.536983i	0.999803	−	0.0198718i	$-0.00632581\pi$
$350$	4.87083	+	0.740762i	0.260357	+	0.0395954i
$351$		0			0
$352$	5.68599	+	5.68599i	0.303064	+	0.303064i
$353$	2.15017	+	3.72420i	0.114442	+	0.198219i	0.917556	−	0.397605i	$-0.130159\pi$
$353$	2.15017	+	3.72420i	0.114442	+	0.198219i	−0.803115	+	0.595825i	$0.796825\pi$
$354$	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
$357$	−16.8617	−	9.73511i	−0.892416	−	0.515237i
$358$	−2.44361	−	1.41082i	−0.129149	−	0.0745640i
$359$	10.4273	+	10.4273i	0.550333	+	0.550333i	0.926537	−	0.376204i	$-0.122771\pi$
$359$	10.4273	+	10.4273i	0.550333	+	0.550333i	−0.376204	+	0.926537i	$0.622771\pi$
$360$	−31.6435	+	5.96555i	−1.66776	+	0.314412i
$361$	9.98326	−	5.76384i	0.525435	−	0.303360i
$362$	5.29555	+	9.17216i	0.278328	+	0.482078i
$363$	−16.2251	−	16.2251i	−0.851599	−	0.851599i
$364$		0			0
$365$	−5.47327	+	4.70382i	−0.286484	+	0.246209i
$366$	−1.53673	+	5.73514i	−0.0803259	+	0.299780i
$367$	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
$370$	−1.72890	−	9.17073i	−0.0898814	−	0.476763i
$371$	0.704874	+	2.63063i	0.0365953	+	0.136575i
$372$	−0.472562			−0.0245012
$373$	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
$375$	−29.7923	+	9.12489i	−1.53847	+	0.471207i
$376$			23.7028i			1.22238i
$377$		0			0
$378$	3.43065	−	3.43065i	0.176453	−	0.176453i
$379$	−16.3551	−	4.38232i	−0.840103	−	0.225105i	−0.186987	−	0.982362i	$-0.559872\pi$
$379$	−16.3551	−	4.38232i	−0.840103	−	0.225105i	−0.653116	+	0.757258i	$0.726539\pi$
$380$	2.52727	+	5.25684i	0.129646	+	0.269670i
$381$	−5.24973	−	3.03093i	−0.268952	−	0.155279i
$382$			18.9999i			0.972119i
$383$	3.30197	−	5.71918i	0.168723	−	0.292236i	−0.769248	−	0.638950i	$-0.779369\pi$
$383$	3.30197	−	5.71918i	0.168723	−	0.292236i	0.937971	+	0.346714i	$0.112702\pi$
$384$	5.91729	−	1.58553i	0.301966	−	0.0809114i
$385$	−3.57354	−	0.270181i	−0.182124	−	0.0137697i
$386$	6.42793	−	11.1335i	0.327173	−	0.566680i
$387$	36.5946	+	9.80550i	1.86021	+	0.498441i
$388$	−6.20897	+	3.58475i	−0.315212	+	0.181988i
$389$	33.6949			1.70840			0.854199	−	0.519946i	$-0.174048\pi$
$389$	33.6949			1.70840			0.854199	+	0.519946i	$0.174048\pi$
$390$		0			0
$391$	27.9393			1.41295
$392$	−15.8851	+	9.17126i	−0.802318	+	0.463218i
$393$	−0.167570	−	0.0449004i	−0.00845281	−	0.00226492i
$394$	−7.30464	+	12.6520i	−0.368003	+	0.637399i
$395$	23.0372	−	19.7986i	1.15913	−	0.996175i
$396$	7.30795	−	1.95816i	0.367238	−	0.0984012i
$397$	2.91045	−	5.04104i	0.146071	−	0.253002i	−0.783701	−	0.621138i	$-0.786671\pi$
$397$	2.91045	−	5.04104i	0.146071	−	0.253002i	0.929772	+	0.368136i	$0.120004\pi$
$398$		−	15.0689i		−	0.755337i
$399$	−6.35716	−	3.67031i	−0.318256	−	0.183745i
$400$	−5.49918	+	2.14986i	−0.274959	+	0.107493i
$401$	−0.255004	−	0.0683280i	−0.0127343	−	0.00341214i	0.252446	−	0.967611i	$-0.418765\pi$
$401$	−0.255004	−	0.0683280i	−0.0127343	−	0.00341214i	−0.265181	+	0.964199i	$0.585432\pi$
$402$	−14.7075	+	14.7075i	−0.733544	+	0.733544i
$403$		0			0
$404$			9.30738i			0.463060i
$405$	0.427966	−	1.22046i	0.0212658	−	0.0606453i
$406$	0.143993	+	0.249404i	0.00714627	+	0.0123777i
$407$	1.75692	+	6.55691i	0.0870872	+	0.325014i
$408$	61.0446			3.02216
$409$	9.61872	+	35.8975i	0.475615	+	1.77502i	0.619042	+	0.785358i	$0.287521\pi$
$409$	9.61872	+	35.8975i	0.475615	+	1.77502i	−0.143427	+	0.989661i	$0.545812\pi$
$410$	8.93108	−	13.0809i	0.441074	−	0.646017i
$411$	−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
$414$	−4.86161	+	18.1438i	−0.238935	+	0.891718i
$415$	12.4881	+	14.5309i	0.613016	+	0.713293i
$416$		0			0
$417$	−27.0934	−	27.0934i	−1.32677	−	1.32677i
$418$	2.32476	+	4.02660i	0.113708	+	0.196947i
$419$	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	0.998641	+	0.0521230i	$0.0165988\pi$
$421$	21.5599	+	21.5599i	1.05076	+	1.05076i	0.0521230	+	0.998641i	$0.483401\pi$
$422$	7.55613	+	4.36253i	0.367826	+	0.212365i
$423$	32.3885	+	18.6995i	1.57478	+	0.909201i
$424$	−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
$427$	1.00374	+	1.73853i	0.0485745	+	0.0841335i
$428$	−0.299934	−	0.299934i	−0.0144979	−	0.0144979i
$429$		0			0
$430$	18.1223	+	1.37015i	0.873933	+	0.0660745i
$431$	−1.19014	+	4.44167i	−0.0573271	+	0.213948i	−0.988648	−	0.150253i	$-0.951991\pi$
$431$	−1.19014	+	4.44167i	−0.0573271	+	0.213948i	0.931320	+	0.364201i	$0.118658\pi$
$432$	−1.50488	+	5.61627i	−0.0724033	+	0.270213i
$433$	−3.86627	+	1.03596i	−0.185801	+	0.0497853i	−0.350520	−	0.936555i	$-0.613995\pi$
$433$	−3.86627	+	1.03596i	−0.185801	+	0.0497853i	0.164719	+	0.986341i	$0.447328\pi$
$434$	0.123811	−	0.123811i	0.00594311	−	0.00594311i
$435$	−1.50414	−	1.02696i	−0.0721179	−	0.0492392i
$436$	−2.24285	−	8.37043i	−0.107413	−	0.400871i
$437$	10.5336			0.503890
$438$	2.38062	+	8.88461i	0.113751	+	0.424523i
$439$	11.3618	+	19.6793i	0.542271	+	0.939242i	0.998773	+	0.0495192i	$0.0157689\pi$
$439$	11.3618	+	19.6793i	0.542271	+	0.939242i	−0.456502	+	0.889723i	$0.650898\pi$
$440$	10.1265	−	4.86842i	0.482763	−	0.232093i
$441$			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	$0.230217\pi$
$444$	10.4837	+	2.80911i	0.497536	+	0.133314i
$445$	1.04499	−	0.502388i	0.0495373	−	0.0238155i
$446$	6.25313	+	3.61025i	0.296094	+	0.170950i
$447$		−	12.0737i		−	0.571067i
$448$	−3.51978	+	6.09644i	−0.166294	+	0.288030i
$449$	−31.0770	+	8.32705i	−1.46661	+	0.392978i	−0.901769	−	0.432219i	$-0.857731\pi$
$449$	−31.0770	+	8.32705i	−1.46661	+	0.392978i	−0.564845	+	0.825197i	$0.691064\pi$
$450$	−3.66451	+	24.0957i	−0.172746	+	1.13588i
$451$	−5.76056	+	9.97759i	−0.271254	+	0.469826i
$452$	−1.78317	−	0.477798i	−0.0838731	−	0.0224737i
$453$	−16.2125	+	9.36029i	−0.761729	+	0.439785i
$454$	−17.5640			−0.824318
$455$		0			0
$456$	23.0149			1.07777
$457$	24.5669	−	14.1837i	1.14919	−	0.663486i	0.200501	−	0.979693i	$-0.435743\pi$
$457$	24.5669	−	14.1837i	1.14919	−	0.663486i	0.948690	+	0.316208i	$0.102410\pi$
$458$	12.4416	+	3.33373i	0.581360	+	0.155775i
$459$	17.8496	−	30.9165i	0.833149	−	1.44306i
$460$	0.619891	−	8.19898i	0.0289026	−	0.382279i
$461$	11.1174	−	2.97890i	0.517790	−	0.138741i	0.00954570	−	0.999954i	$-0.496961\pi$
$461$	11.1174	−	2.97890i	0.517790	−	0.138741i	0.508244	+	0.861213i	$0.330295\pi$
$462$	−2.28378	+	3.95562i	−0.106251	+	0.184032i
$463$			29.9456i			1.39169i	0.718192	+	0.695845i	$0.244970\pi$
$463$			29.9456i			1.39169i	−0.718192	+	0.695845i	$0.755030\pi$
$464$	−0.298893	−	0.172566i	−0.0138758	−	0.00801118i
$465$	−0.366423	+	1.04496i	−0.0169925	+	0.0484586i
$466$	−24.5609	−	6.58109i	−1.13776	−	0.304863i
$467$	16.1332	−	16.1332i	0.746557	−	0.746557i	−0.227274	−	0.973831i	$-0.572981\pi$
$467$	16.1332	−	16.1332i	0.746557	−	0.746557i	0.973831	+	0.227274i	$0.0729812\pi$
$468$		0			0
$469$			7.03244i			0.324728i
$470$	16.9299	+	5.93662i	0.780918	+	0.273836i
$471$	28.4732	+	49.3170i	1.31197	+	2.27241i
$472$	3.94971	+	14.7405i	0.181800	+	0.678488i
$473$	−13.2196			−0.607837
$474$	−10.0201	−	37.3957i	−0.460240	−	1.71764i
$475$	13.5838	−	1.51231i	0.623270	−	0.0693894i
$476$	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
$479$	10.0493	−	37.5043i	0.459162	−	1.71362i	−0.216393	−	0.976306i	$-0.569429\pi$
$479$	10.0493	−	37.5043i	0.459162	−	1.71362i	0.675555	−	0.737309i	$-0.263904\pi$
$480$	2.27132	−	30.0415i	0.103671	−	1.37120i
$481$		0			0
$482$	13.0294	+	13.0294i	0.593473	+	0.593473i
$483$	5.17396	+	8.96157i	0.235424	+	0.407765i
$484$	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
$487$	25.0660	+	14.4718i	1.13585	+	0.655782i	0.945399	−	0.325916i	$-0.105673\pi$
$487$	25.0660	+	14.4718i	1.13585	+	0.655782i	0.190448	+	0.981697i	$0.439006\pi$
$488$	−5.45078	−	3.14701i	−0.246745	−	0.142458i
$489$	−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	$-0.614178\pi$
$491$	6.30003	−	3.63733i	0.284317	−	0.164150i	0.635376	+	0.772203i	$0.280845\pi$
$492$	9.21046	+	15.9530i	0.415240	+	0.719216i
$493$	1.49839	+	1.49839i	0.0674842	+	0.0674842i
$494$		0			0
$495$	1.33657	−	17.6781i	0.0600743	−	0.794571i
$496$	−0.0543104	+	0.202689i	−0.00243861	+	0.00910102i
$497$	−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	−0.795652	−	0.605754i	$-0.792872\pi$
$499$	−4.24201	+	4.24201i	−0.189899	+	0.189899i	0.605754	+	0.795652i	$0.292872\pi$
$500$	−0.377731	−	10.6622i	−0.0168926	−	0.476827i
$501$	−1.23663	−	4.61515i	−0.0552483	−	0.206190i
$502$	14.2889			0.637745
$503$	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
$505$	20.5810	+	7.21692i	0.915843	+	0.321149i
$506$		−	6.55433i		−	0.291376i
$507$		0			0
$508$	1.46769	−	1.46769i	0.0651184	−	0.0651184i
$509$	22.5037	+	6.02986i	0.997460	+	0.267269i	0.720381	−	0.693578i	$-0.243967\pi$
$509$	22.5037	+	6.02986i	0.997460	+	0.267269i	0.277079	+	0.960847i	$0.410634\pi$
$510$	15.2893	−	43.6015i	0.677020	−	1.93071i
$511$	2.69325	+	1.55495i	0.119143	+	0.0687870i
$512$		−	12.8442i		−	0.567640i
$513$	6.72962	−	11.6560i	0.297120	−	0.514627i
$514$	−22.8945	+	6.13455i	−1.00983	+	0.270584i
$515$	−0.601550	+	7.95639i	−0.0265075	+	0.350600i
$516$	−10.5683	+	18.3048i	−0.465243	+	0.805824i
$517$	−12.6052	−	3.37754i	−0.554375	−	0.148544i
$518$	−3.48272	+	2.01075i	−0.153022	+	0.0883472i
$519$	−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	$0.592303\pi$
$522$	−1.23379	+	0.712327i	−0.0540013	+	0.0311777i
$523$	−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
$525$	7.95882	+	10.8138i	0.347351	+	0.471952i
$526$	−1.28514	+	0.344353i	−0.0560349	+	0.0150145i
$527$	0.644187	−	1.11577i	0.0280612	−	0.0486035i
$528$		−	5.47391i		−	0.238221i
$529$	7.05896	+	4.07549i	0.306911	+	0.177195i
$530$	−5.82475	+	2.80030i	−0.253011	+	0.121637i
$531$	23.2581	+	6.23198i	1.00931	+	0.270445i
$532$	1.77730	−	1.77730i	0.0770558	−	0.0770558i
$533$		0			0
$534$		−	1.47779i		−	0.0639501i
$535$	−0.895798	+	0.430663i	−0.0387287	+	0.0186192i
$536$	−11.0243	−	19.0947i	−0.476178	−	0.824765i
$537$	−1.99023	−	7.42764i	−0.0858847	−	0.320526i
$538$	−8.11728			−0.349961
$539$	−2.61373	−	9.75457i	−0.112581	−	0.420159i
$540$	−8.67662	−	5.92404i	−0.373382	−	0.254930i
$541$	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
$544$	−9.07231	+	33.8583i	−0.388972	+	1.45166i
$545$	−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	$0.962109\pi$
$548$	−2.10769	−	3.65063i	−0.0900361	−	0.155947i
$549$	−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
$552$	−28.0970	−	16.2218i	−1.19589	−	0.690446i
$553$	−11.3360	−	6.54485i	−0.482056	−	0.278315i
$554$	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
$557$	−6.79015	−	11.7609i	−0.287708	−	0.498324i	0.685555	−	0.728021i	$-0.259560\pi$
$557$	−6.79015	−	11.7609i	−0.287708	−	0.498324i	−0.973262	+	0.229697i	$0.926226\pi$
$558$	0.612485	+	0.612485i	0.0259286	+	0.0259286i
$559$		0			0
$560$	1.65839	+	1.92967i	0.0700797	+	0.0815432i
$561$	−8.69858	+	32.4636i	−0.367254	+	1.37061i
$562$	−2.09014	+	7.80052i	−0.0881673	+	0.329045i
$563$	4.68514	−	1.25538i	0.197455	−	0.0529080i	−0.158736	−	0.987321i	$-0.550742\pi$
$563$	4.68514	−	1.25538i	0.197455	−	0.0529080i	0.356191	+	0.934413i	$0.384075\pi$
$564$	−14.7539	+	14.7539i	−0.621251	+	0.621251i
$565$	−2.43920	+	3.57256i	−0.102618	+	0.150299i
$566$	5.58573	+	20.8462i	0.234786	+	0.876232i
$567$	−0.557323			−0.0234054
$568$	−10.2063	−	38.0904i	−0.428247	−	1.59824i
$569$	0.124396	+	0.215461i	0.00521497	+	0.00903259i	0.868621	−	0.495477i	$-0.165007\pi$
$569$	0.124396	+	0.215461i	0.00521497	+	0.00903259i	−0.863406	+	0.504509i	$0.831673\pi$
$570$	5.76432	−	16.4385i	0.241441	−	0.688534i
$571$		−	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
$574$	−6.59281	−	1.76654i	−0.275179	−	0.0737339i
$575$	−17.6494	−	7.72820i	−0.736030	−	0.322288i
$576$	−30.1587	−	17.4121i	−1.25661	−	0.725506i
$577$			12.1339i			0.505141i	0.967578	+	0.252570i	$0.0812760\pi$
$577$			12.1339i			0.505141i	−0.967578	+	0.252570i	$0.918724\pi$
$578$	−18.1869	+	31.5007i	−0.756477	+	1.31026i
$579$	33.8416	−	9.06783i	1.40641	−	0.376846i
$580$	0.472958	−	0.406469i	0.0196385	−	0.0168777i
$581$	4.12821	−	7.15027i	0.171267	−	0.296643i
$582$	20.6824	+	5.54184i	0.857315	+	0.229717i
$583$	4.07125	−	2.35054i	0.168614	−	0.0973492i
$584$	−9.75040			−0.403475
$585$		0			0
$586$	−4.11255			−0.169888
$587$	31.6354	−	18.2647i	1.30573	−	0.753865i	0.324351	−	0.945937i	$-0.394854\pi$
$587$	31.6354	−	18.2647i	1.30573	−	0.753865i	0.981381	+	0.192072i	$0.0615207\pi$
$588$	−15.5964	−	4.17904i	−0.643185	−	0.172341i
$589$	0.242870	−	0.420663i	0.0100073	−	0.0173331i
$590$	11.5178	+	0.870813i	0.474180	+	0.0358508i
$591$	−38.4573	+	10.3046i	−1.58192	+	0.423875i
$592$	2.40974	−	4.17380i	0.0990398	−	0.171542i
$593$		−	16.6936i		−	0.685525i	−0.939422	−	0.342762i	$-0.888637\pi$
$593$		−	16.6936i		−	0.685525i	0.939422	−	0.342762i	$-0.111363\pi$
$594$	−7.25276	−	4.18738i	−0.297584	−	0.171810i
$595$	−6.76880	−	14.0794i	−0.277494	−	0.577200i
$596$	3.99327	+	1.06999i	0.163571	+	0.0438287i
$597$	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	$-0.0872847\pi$
$600$	−38.5621	−	16.8853i	−1.57429	−	0.689341i
$601$	−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
$603$	−34.7891			−1.41672
$604$	−1.65905	−	6.19166i	−0.0675058	−	0.251935i
$605$	−3.41077	−	18.0919i	−0.138667	−	0.735542i
$606$	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
$609$	−0.203130	+	0.758093i	−0.00823126	+	0.0307195i
$610$	−3.61298	+	3.10506i	−0.146285	+	0.125720i
$611$		0			0
$612$	23.3204	+	23.3204i	0.942673	+	0.942673i
$613$	13.9548	+	24.1705i	0.563630	+	0.976235i	0.997176	+	0.0751039i	$0.0239288\pi$
$613$	13.9548	+	24.1705i	0.563630	+	0.976235i	−0.433546	+	0.901131i	$0.642738\pi$
$614$	−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
$617$	3.79548	+	2.19132i	0.152800	+	0.0882193i	0.574451	−	0.818539i	$-0.305216\pi$
$617$	3.79548	+	2.19132i	0.152800	+	0.0882193i	−0.421650	+	0.906758i	$0.638549\pi$
$618$	8.80708	+	5.08477i	0.354273	+	0.204540i
$619$	−8.67268	−	8.67268i	−0.348584	−	0.348584i	0.510998	−	0.859582i	$-0.329276\pi$
$619$	−8.67268	−	8.67268i	−0.348584	−	0.348584i	−0.859582	+	0.510998i	$0.829276\pi$
$620$	−0.313136	−	0.213797i	−0.0125759	−	0.00858628i
$621$	−16.4313	+	9.48662i	−0.659366	+	0.380685i
$622$	−4.02525	−	6.97193i	−0.161398	−	0.279549i
$623$	−0.353304	−	0.353304i	−0.0141548	−	0.0141548i
$624$		0			0
$625$	−23.8697	−	7.43216i	−0.954788	−	0.297287i
$626$	1.26934	−	4.73726i	0.0507332	−	0.189339i
$627$	−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
$630$	10.3210	−	1.94575i	0.411198	−	0.0775207i
$631$	6.55800	+	24.4748i	0.261070	+	0.974326i	0.964612	+	0.263673i	$0.0849339\pi$
$631$	6.55800	+	24.4748i	0.261070	+	0.974326i	−0.703542	+	0.710653i	$0.748399\pi$
$632$	41.0398			1.63248
$633$	6.15419	+	22.9677i	0.244607	+	0.912886i
$634$	−11.7220	−	20.3031i	−0.465540	−	0.806340i
$635$	−2.10740	−	4.38349i	−0.0836297	−	0.173954i
$636$		−	7.51646i		−	0.298047i
$637$		0			0
$638$	0.351511	−	0.351511i	0.0139164	−	0.0139164i
$639$	−60.1003	−	16.1038i	−2.37753	−	0.637057i
$640$	4.63834	+	1.62647i	0.183346	+	0.0642920i
$641$	−1.41675	−	0.817961i	−0.0559582	−	0.0323075i	0.471760	−	0.881727i	$-0.343619\pi$
$641$	−1.41675	−	0.817961i	−0.0559582	−	0.0323075i	−0.527718	+	0.849420i	$0.676952\pi$
$642$			1.26681i			0.0499968i
$643$	−19.8344	+	34.3541i	−0.782191	+	1.35479i	0.148472	+	0.988917i	$0.452565\pi$
$643$	−19.8344	+	34.3541i	−0.782191	+	1.35479i	−0.930663	+	0.365878i	$0.880769\pi$
$644$	−3.42248	+	0.917051i	−0.134865	+	0.0361369i
$645$	32.2820	+	37.5627i	1.27110	+	1.47903i
$646$	−10.1339	+	17.5525i	−0.398714	+	0.690593i
$647$	−14.3588	−	3.84742i	−0.564501	−	0.151258i	−0.0347277	−	0.999397i	$-0.511056\pi$
$647$	−14.3588	−	3.84742i	−0.564501	−	0.151258i	−0.529773	+	0.848139i	$0.677723\pi$
$648$	1.51326	−	0.873682i	0.0594465	−	0.0343215i
$649$	−8.40185			−0.329801
$650$		0			0
$651$	0.477178			0.0187021
$652$	17.6729	−	10.2034i	0.692123	−	0.399597i
$653$	−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
$655$	−0.0907243	−	0.105565i	−0.00354489	−	0.00412476i
$656$	7.90103	−	2.11708i	0.308483	−	0.0826579i
$657$	−7.69225	+	13.3234i	−0.300103	+	0.519794i
$658$		−	7.73102i		−	0.301387i
$659$	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
$661$	−37.8150	−	10.1325i	−1.47083	−	0.394108i	−0.567616	−	0.823293i	$-0.692134\pi$
$661$	−37.8150	−	10.1325i	−1.47083	−	0.394108i	−0.903217	+	0.429185i	$0.858801\pi$
$662$	24.2637	−	24.2637i	0.943036	−	0.943036i
$663$		0			0
$664$			25.8862i			1.00458i
$665$	−2.55196	−	5.30818i	−0.0989606	−	0.205843i
$666$	−9.94705	−	17.2288i	−0.385440	−	0.667602i
$667$	−0.291487	−	1.08784i	−0.0112864	−	0.0421215i
$668$	1.63601			0.0632991
$669$	5.09295	+	19.0071i	0.196905	+	0.734858i
$670$	−16.3997	+	3.09174i	−0.633575	+	0.119444i
$671$	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	$-0.979814\pi$
$673$	−2.64660	+	9.87723i	−0.102019	+	0.380739i	0.895971	+	0.444112i	$0.146481\pi$
$674$	−5.44776	+	20.3313i	−0.209840	+	0.783132i
$675$	−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	$0.448167\pi$
$678$	2.75669	+	4.77472i	0.105870	+	0.183372i
$679$	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
$682$	−0.261750	−	0.151121i	−0.0100229	−	0.00578673i
$683$	−17.3384	−	10.0103i	−0.663436	−	0.383035i	0.130149	−	0.991494i	$-0.458455\pi$
$683$	−17.3384	−	10.0103i	−0.663436	−	0.383035i	−0.793585	+	0.608459i	$0.791788\pi$
$684$	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
$687$	17.5513	+	30.3998i	0.669625	+	1.15983i
$688$	6.63664	+	6.63664i	0.253019	+	0.253019i
$689$		0			0
$690$	−18.6238	+	16.0056i	−0.708994	+	0.609322i
$691$	9.15886	−	34.1813i	0.348420	−	1.30032i	−0.540147	−	0.841571i	$-0.681631\pi$
$691$	9.15886	−	34.1813i	0.348420	−	1.30032i	0.888566	−	0.458749i	$-0.151702\pi$
$692$	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
$695$	−5.69543	−	30.2106i	−0.216040	−	1.14595i
$696$	−0.636870	−	2.37683i	−0.0241405	−	0.0900935i
$697$	−50.2221			−1.90230
$698$	−2.74877	−	10.2586i	−0.104043	−	0.388292i
$699$	−34.6479	−	60.0120i	−1.31051	−	2.26986i
$700$	−4.28188	+	1.67397i	−0.161840	+	0.0632701i
$701$			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
$704$	11.7374	+	3.14502i	0.442368	+	0.118532i
$705$	21.1845	+	44.0647i	0.797854	+	1.65957i
$706$	3.80843	+	2.19880i	0.143332	+	0.0827529i
$707$		−	9.39830i		−	0.353459i
$708$	−6.71678	+	11.6338i	−0.252432	+	0.437225i
$709$	46.5506	−	12.4732i	1.74824	−	0.468440i	0.763994	−	0.645224i	$-0.223236\pi$
$709$	46.5506	−	12.4732i	1.74824	−	0.468440i	0.984250	+	0.176783i	$0.0565692\pi$
$710$	−29.7626	−	2.25023i	−1.11697	−	0.0844497i
$711$	32.3770	−	56.0786i	1.21423	−	2.10311i
$712$	1.51316	+	0.405449i	0.0567079	+	0.0151948i
$713$	−0.593001	+	0.342369i	−0.0222080	+	0.0128218i
$714$	−19.9106			−0.745135
$715$		0			0
$716$	2.63300			0.0983998
$717$	7.62814	−	4.40411i	0.284878	−	0.164474i
$718$	14.5662	+	3.90299i	0.543604	+	0.145658i
$719$	−16.6992	+	28.9239i	−0.622777	+	1.07868i	0.366190	+	0.930540i	$0.380662\pi$
$719$	−16.6992	+	28.9239i	−0.622777	+	1.07868i	−0.988966	+	0.148141i	$0.952671\pi$
$720$	−9.54594	+	8.20394i	−0.355756	+	0.305743i
$721$	3.32122	−	0.889918i	0.123689	−	0.0331423i
$722$	5.89421	−	10.2091i	0.219360	−	0.379942i
$723$			50.2164i			1.86757i
$724$	−8.55897	−	4.94153i	−0.318092	−	0.183650i
$725$	−0.532076	−	1.36101i	−0.0197608	−	0.0505465i
$726$	−22.6652	−	6.07313i	−0.841186	−	0.225395i
$727$	23.6487	−	23.6487i	0.877083	−	0.877083i	−0.116149	−	0.993232i	$-0.537055\pi$
$727$	23.6487	−	23.6487i	0.877083	−	0.877083i	0.993232	+	0.116149i	$0.0370549\pi$
$728$		0			0
$729$		−	43.9226i		−	1.62676i
$730$	−2.44209	+	6.96430i	−0.0903860	+	0.257760i
$731$	−28.8130	−	49.9055i	−1.06569	−	1.84582i
$732$	−1.43399	−	5.35173i	−0.0530018	−	0.197806i
$733$	14.7049			0.543138			0.271569	−	0.962419i	$-0.412458\pi$
$733$	14.7049			0.543138			0.271569	+	0.962419i	$0.412458\pi$
$734$	−3.02344	−	11.2836i	−0.111597	−	0.416486i
$735$	−21.3343	+	31.2472i	−0.786929	+	1.15257i
$736$	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
$739$	5.32432	−	19.8706i	0.195858	−	0.730953i	−0.796185	−	0.605054i	$-0.793152\pi$
$739$	5.32432	−	19.8706i	0.195858	−	0.730953i	0.992043	−	0.125900i	$-0.0401817\pi$
$740$	5.67600	+	6.60447i	0.208654	+	0.242785i
$741$		0			0
$742$	1.96931	+	1.96931i	0.0722956	+	0.0722956i
$743$	−22.3204	−	38.6601i	−0.818856	−	1.41830i	−0.906526	−	0.422151i	$-0.861275\pi$
$743$	−22.3204	−	38.6601i	−0.818856	−	1.41830i	0.0876692	−	0.996150i	$-0.472058\pi$
$744$	−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
$747$	35.3720	+	20.4220i	1.29419	+	0.747202i
$748$	−9.96614	−	5.75395i	−0.364398	−	0.210385i
$749$	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	$-0.562732\pi$
$751$	15.2247	−	8.78996i	0.555555	−	0.320750i	0.751360	+	0.659893i	$0.229398\pi$
$752$	4.63255	+	8.02381i	0.168932	+	0.292598i
$753$	27.5353	+	27.5353i	1.00344	+	1.00344i
$754$		0			0
$755$	−14.9778	−	1.13241i	−0.545097	−	0.0412125i
$756$	−1.17176	+	4.37306i	−0.0426164	+	0.159047i
$757$	−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
$760$	15.2505	+	10.4124i	0.553192	+	0.377697i
$761$	3.03122	+	11.3127i	0.109882	+	0.410084i	0.998853	−	0.0478787i	$-0.0152461\pi$
$761$	3.03122	+	11.3127i	0.109882	+	0.410084i	−0.888972	+	0.457962i	$0.848579\pi$
$762$	−6.19897			−0.224565
$763$	2.26476	+	8.45219i	0.0819897	+	0.305990i
$764$	−8.86485	−	15.3544i	−0.320719	−	0.555502i
$765$	69.6501	−	33.4849i	2.51820	−	1.21065i
$766$		−	6.75331i		−	0.244007i
$767$		0			0
$768$	33.2233	−	33.2233i	1.19884	−	1.19884i
$769$	−18.3227	−	4.90954i	−0.660732	−	0.177043i	−0.0871555	−	0.996195i	$-0.527778\pi$
$769$	−18.3227	−	4.90954i	−0.660732	−	0.177043i	−0.573576	+	0.819152i	$0.694444\pi$
$770$	−3.30292	+	1.58791i	−0.119029	+	0.0572242i
$771$	−55.9401	−	32.2971i	−2.01463	−	1.16315i
$772$			11.9964i			0.431760i
$773$	8.20497	−	14.2114i	0.295112	−	0.511149i	−0.679899	−	0.733306i	$-0.737976\pi$
$773$	8.20497	−	14.2114i	0.295112	−	0.511149i	0.975011	+	0.222157i	$0.0713096\pi$
$774$	37.4223	−	10.0273i	1.34512	−	0.360423i
$775$	−0.715564	+	0.526647i	−0.0257038	+	0.0189177i
$776$	−11.3490	+	19.6570i	−0.407404	+	0.705644i
$777$	−10.5861	−	2.83655i	−0.379775	−	0.101761i
$778$	29.8406	−	17.2285i	1.06984	−	0.617671i
$779$	−18.9346			−0.678403
$780$		0			0
$781$	21.7109			0.776876
$782$	24.7434	−	14.2856i	0.884822	−	0.510852i
$783$	−1.38999	−	0.372446i	−0.0496741	−	0.0133101i
$784$	−3.58492	+	6.20926i	−0.128033	+	0.221759i
$785$	−3.44468	+	45.5610i	−0.122946	+	1.62614i
$786$	−0.171361	+	0.0459159i	−0.00611223	+	0.00163777i
$787$	−6.80008	+	11.7781i	−0.242397	+	0.419844i	−0.961396	−	0.275167i	$-0.911267\pi$
$787$	−6.80008	+	11.7781i	−0.242397	+	0.419844i	0.719000	+	0.695010i	$0.244600\pi$
$788$		−	13.6326i		−	0.485642i
$789$	−3.14011	−	1.81294i	−0.111791	−	0.0645424i
$790$	10.2789	−	29.3130i	0.365706	−	1.04291i
$791$	1.80058	+	0.482465i	0.0640214	+	0.0171545i
$792$	16.9369	−	16.9369i	0.601827	−	0.601827i
$793$		0			0
$794$		−	5.95255i		−	0.211248i
$795$	−16.6208	−	5.82824i	−0.589480	−	0.206706i
$796$	7.03076	+	12.1776i	0.249199	+	0.431625i
$797$	−7.74769	−	28.9148i	−0.274437	−	1.02421i	−0.956218	−	0.292657i	$-0.905461\pi$
$797$	−7.74769	−	28.9148i	−0.274437	−	1.02421i	0.681780	−	0.731557i	$-0.261206\pi$
$798$	−7.50664			−0.265732
$799$	−14.7232	−	54.9476i	−0.520868	−	1.94391i
$800$	15.0965	−	18.8790i	0.533740	−	0.667473i
$801$	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
$804$	5.02343	−	18.7477i	0.177163	−	0.661180i
$805$	−0.625946	+	8.27906i	−0.0220617	+	0.291799i
$806$		0			0
$807$	−15.6423	−	15.6423i	−0.550636	−	0.550636i
$808$	14.7331	+	25.5185i	0.518310	+	0.897739i
$809$	−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	$-0.382950\pi$
$811$	−16.3366	−	16.3366i	−0.573657	−	0.573657i	−0.933148	+	0.359492i	$0.882950\pi$
$812$	−0.232730	−	0.134367i	−0.00816724	−	0.00471536i
$813$	2.16144	+	1.24791i	0.0758050	+	0.0437660i
$814$	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
$817$	−10.8630	−	18.8153i	−0.380048	−	0.658262i
$818$	26.8732	+	26.8732i	0.939599	+	0.939599i
$819$		0			0
$820$	−1.11428	+	14.7380i	−0.0389124	+	0.514674i
$821$	−11.8735	+	44.3125i	−0.414388	+	1.54652i	0.371672	+	0.928364i	$0.378785\pi$
$821$	−11.8735	+	44.3125i	−0.414388	+	1.54652i	−0.786059	+	0.618151i	$0.787882\pi$
$822$	−3.25838	+	12.1605i	−0.113649	+	0.424145i
$823$	−17.1209	+	4.58752i	−0.596796	+	0.159911i	−0.544557	−	0.838724i	$-0.683302\pi$
$823$	−17.1209	+	4.58752i	−0.596796	+	0.159911i	−0.0522385	+	0.998635i	$0.516636\pi$
$824$	−7.62280	+	7.62280i	−0.265553	+	0.265553i
$825$	14.4746	−	18.1013i	0.503940	−	0.630206i
$826$	−1.28826	−	4.80785i	−0.0448242	−	0.167286i
$827$	−5.79276			−0.201434			−0.100717	−	0.994915i	$-0.532114\pi$
$827$	−5.79276			−0.201434			−0.100717	+	0.994915i	$0.532114\pi$
$828$	−4.53660	−	16.9308i	−0.157658	−	0.588387i
$829$	16.8799	+	29.2368i	0.586262	+	1.01544i	0.994717	+	0.102657i	$0.0327346\pi$
$829$	16.8799	+	29.2368i	0.586262	+	1.01544i	−0.408454	+	0.912779i	$0.633932\pi$
$830$	18.4894	+	6.48347i	0.641776	+	0.225045i
$831$			26.6284i			0.923727i
$832$		0			0
$833$	31.1279	−	31.1279i	1.07852	−	1.07852i
$834$	−37.8473	−	10.1412i	−1.31055	−	0.351160i
$835$	1.26856	−	3.61764i	0.0439002	−	0.125193i
$836$	−3.75741	−	2.16934i	−0.129953	−	0.0750282i
$837$			0.874920i			0.0302417i
$838$	17.3415	−	30.0364i	0.599053	−	1.03759i
$839$	−37.8626	+	10.1452i	−1.30716	+	0.350253i	−0.844154	−	0.536101i	$-0.819897\pi$
$839$	−37.8626	+	10.1452i	−1.30716	+	0.350253i	−0.463008	+	0.886354i	$0.653230\pi$
$840$	−1.36763	+	18.0889i	−0.0471877	+	0.624127i
$841$	−14.4573	+	25.0408i	−0.498527	+	0.863475i
$842$	30.1175	+	8.06995i	1.03792	+	0.278109i
$843$	−19.0597	+	11.0041i	−0.656451	+	0.379002i
$844$	−8.14177			−0.280251
$845$		0			0
$846$	38.2449			1.31489
$847$	−6.87068	+	3.96679i	−0.236079	+	0.136300i
$848$	−3.22393	−	0.863850i	−0.110710	−	0.0296647i
$849$	−29.4076	+	50.9354i	−1.00927	+	1.74810i
$850$	29.8575	−	21.9748i	1.02410	−	0.753728i
$851$	15.1908	−	4.07037i	0.520735	−	0.139531i
$852$	17.3566	−	30.0625i	0.594626	−	1.02992i
$853$			40.6417i			1.39154i	0.718262	+	0.695772i	$0.244938\pi$
$853$			40.6417i			1.39154i	−0.718262	+	0.695772i	$0.755062\pi$
$854$	1.77785	+	1.02644i	0.0608369	+	0.0351242i
$855$	26.2593	−	12.6244i	0.898048	−	0.431744i
$856$	−1.29713	−	0.347564i	−0.0443348	−	0.0118795i
$857$	−27.2327	+	27.2327i	−0.930252	+	0.930252i	−0.997721	−	0.0674695i	$-0.978507\pi$
$857$	−27.2327	+	27.2327i	−0.930252	+	0.930252i	0.0674695	+	0.997721i	$0.478507\pi$
$858$		0			0
$859$		−	44.5502i		−	1.52003i	−0.649904	−	0.760016i	$-0.725191\pi$
$859$		−	44.5502i		−	1.52003i	0.649904	−	0.760016i	$-0.274809\pi$
$860$	−15.2844	+	7.34811i	−0.521194	+	0.250568i
$861$	−9.30043	−	16.1088i	−0.316958	−	0.548987i
$862$	1.21706	+	4.54213i	0.0414532	+	0.154706i
$863$	−55.4497			−1.88753			−0.943766	−	0.330615i	$-0.892744\pi$
$863$	−55.4497			−1.88753			−0.943766	+	0.330615i	$0.892744\pi$
$864$	−6.16090	−	22.9928i	−0.209598	−	0.782230i
$865$	−28.0268	−	19.1356i	−0.952940	−	0.650629i
$866$	−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
$869$	−5.84800	+	21.8250i	−0.198380	+	0.740363i
$870$	−1.85718	−	0.140414i	−0.0629643	−	0.00476048i
$871$		0			0
$872$	−19.3993	−	19.3993i	−0.656944	−	0.656944i
$873$	17.9068	+	31.0154i	0.606052	+	1.04971i
$874$	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
$877$	4.65661	+	2.68849i	0.157242	+	0.0907839i	0.576557	−	0.817057i	$-0.304396\pi$
$877$	4.65661	+	2.68849i	0.157242	+	0.0907839i	−0.419314	+	0.907841i	$0.637729\pi$
$878$	20.1244	+	11.6188i	0.679166	+	0.392116i
$879$	−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	$-0.923183\pi$
$881$	−37.0890	+	21.4133i	−1.24956	+	0.721434i	−0.278538	+	0.960425i	$0.589850\pi$
$882$	14.7980	+	25.6309i	0.498274	+	0.863037i
$883$	32.9568	+	32.9568i	1.10908	+	1.10908i	0.993271	+	0.115813i	$0.0369473\pi$
$883$	32.9568	+	32.9568i	1.10908	+	1.10908i	0.115813	+	0.993271i	$0.463053\pi$
$884$		0			0
$885$	20.5172	+	23.8733i	0.689677	+	0.802494i
$886$	0.691990	−	2.58254i	0.0232478	−	0.0867622i
$887$	−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
$890$	0.668582	−	0.979235i	0.0224109	−	0.0328240i
$891$	0.248992	+	0.929249i	0.00834153	+	0.0311310i
$892$	−6.73778			−0.225598
$893$	−5.55089	−	20.7162i	−0.185753	−	0.693241i
$894$	−6.17340	−	10.6926i	−0.206469	−	0.357616i
$895$	2.04162	−	5.82224i	0.0682438	−	0.194616i
$896$		−	2.11809i		−	0.0707605i
$897$		0			0
$898$	−23.2645	+	23.2645i	−0.776346	+	0.776346i
$899$	−0.0501642	−	0.0134414i	−0.00167307	−	0.000448297i
$900$	−8.28103	−	21.1822i	−0.276034	−	0.706074i
$901$	17.7471	+	10.2463i	0.591242	+	0.341354i
$902$			11.7817i			0.392288i
$903$	10.6715	−	18.4836i	0.355126	−	0.615096i
$904$	−5.64533	+	1.51266i	−0.187761	+	0.0503104i
$905$	−17.5636	+	15.0944i	−0.583833	+	0.501756i
$906$	−9.57200	+	16.5792i	−0.318008	+	0.550807i
$907$	10.6869	+	2.86355i	0.354853	+	0.0950825i	0.431842	−	0.901949i	$-0.357864\pi$
$907$	10.6869	+	2.86355i	0.354853	+	0.0950825i	−0.0769889	+	0.997032i	$0.524531\pi$
$908$	14.1940	−	8.19488i	0.471043	−	0.271957i
$909$	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	$0.580194\pi$
$912$	7.79093	−	4.49810i	0.257983	−	0.148947i
$913$	−13.7663	−	3.68867i	−0.455598	−	0.122077i
$914$	14.5045	−	25.1226i	0.479767	−	0.830980i
$915$	−12.9459	−	0.978791i	−0.427980	−	0.0323578i
$916$	−11.6099	+	3.11086i	−0.383602	+	0.102786i
$917$	−0.0299909	+	0.0519457i	−0.000990386	+	0.00171540i
$918$		−	36.5067i		−	1.20490i
$919$	−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
$921$	−65.1960	−	17.4692i	−2.14828	−	0.575630i
$922$	8.32259	−	8.32259i	0.274090	−	0.274090i
$923$		0			0
$924$		−	4.26220i		−	0.140216i
$925$	19.0053	−	7.42999i	0.624891	−	0.244297i
$926$	15.3114	+	26.5202i	0.503165	+	0.871508i
$927$	4.40237	+	16.4299i	0.144593	+	0.539628i
$928$	1.41296			0.0463826
$929$	12.6170	+	47.0874i	0.413952	+	1.54489i	0.786926	+	0.617047i	$0.211671\pi$
$929$	12.6170	+	47.0874i	0.413952	+	1.54489i	−0.372975	+	0.927841i	$0.621662\pi$
$930$	0.209786	+	1.11278i	0.00687915	+	0.0364895i
$931$	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
$934$	6.03874	−	22.5369i	0.197594	−	0.737429i
$935$	−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	$0.695466\pi$
$938$	3.59575	+	6.22802i	0.117405	+	0.203352i
$939$	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	$0.738668\pi$
$942$	50.4324	+	29.1172i	1.64318	+	0.948688i
$943$	23.1158	+	13.3459i	0.752753	+	0.434602i
$944$	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
$947$	−3.35827	−	5.81670i	−0.109129	−	0.189017i	0.806289	−	0.591522i	$-0.201473\pi$
$947$	−3.35827	−	5.81670i	−0.109129	−	0.189017i	−0.915418	+	0.402505i	$0.868140\pi$
$948$	25.5454	+	25.5454i	0.829676	+	0.829676i
$949$		0			0
$950$	11.2568	−	8.28486i	0.365218	−	0.268796i
$951$	16.5361	−	61.7137i	0.536221	−	2.00121i
$952$	5.46272	−	20.3871i	0.177048	−	0.660751i
$953$	−17.4402	+	4.67309i	−0.564944	+	0.151376i	−0.529977	−	0.848012i	$-0.677799\pi$
$953$	−17.4402	+	4.67309i	−0.564944	+	0.151376i	−0.0349673	+	0.999388i	$0.511133\pi$
$954$	−9.74205	+	9.74205i	−0.315411	+	0.315411i
$955$	−40.8262	+	7.69672i	−1.32111	+	0.249060i
$956$	0.780600	+	2.91324i	0.0252464	+	0.0942208i
$957$	1.35475			0.0437929
$958$	−10.2765	−	38.3526i	−0.332020	−	1.23912i
$959$	2.12828	+	3.68629i	0.0687257	+	0.119036i
$960$	−19.7261	−	41.0311i	−0.636656	−	1.32427i
$961$		−	30.9684i		−	0.998981i
$962$		0			0
$963$	−1.49825	+	1.49825i	−0.0482804	+	0.0482804i
$964$	−16.6086	−	4.45026i	−0.534927	−	0.143333i
$965$	26.5271	+	9.30197i	0.853938	+	0.299441i
$966$	9.16426	+	5.29099i	0.294855	+	0.170235i
$967$		−	60.0570i		−	1.93130i	−0.259841	−	0.965651i	$-0.583670\pi$
$967$		−	60.0570i		−	1.93130i	0.259841	−	0.965651i	$-0.416330\pi$
$968$	12.4370	−	21.5415i	0.399740	−	0.692369i
$969$	−53.3528	+	14.2958i	−1.71394	+	0.459249i
$970$	11.1977	+	13.0294i	0.359536	+	0.418348i
$971$	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
$973$	−11.4729	+	6.62390i	−0.367805	+	0.212352i
$974$	29.5983			0.948391
$975$		0			0
$976$	−2.46025			−0.0787506
$977$	−32.4724	+	18.7479i	−1.03888	+	0.599800i	−0.919517	−	0.393050i	$-0.871420\pi$
$977$	−32.4724	+	18.7479i	−1.03888	+	0.599800i	−0.119367	+	0.992850i	$0.538087\pi$
$978$	−58.8694	−	15.7740i	−1.88244	−	0.504397i
$979$	−0.431236	+	0.746923i	−0.0137824	+	0.0238718i
$980$	−8.44405	−	9.82532i	−0.269735	−	0.313858i
$981$	−41.8125	+	11.2036i	−1.33497	+	0.357704i
$982$	3.71959	−	6.44253i	0.118697	−	0.205589i
$983$		−	46.1176i		−	1.47092i	−0.677567	−	0.735461i	$-0.736966\pi$
$983$		−	46.1176i		−	1.47092i	0.677567	−	0.735461i	$-0.263034\pi$
$984$	50.5056	+	29.1594i	1.61006	+	0.929569i
$985$	−30.1452	−	10.5707i	−0.960506	−	0.336810i
$986$	2.09314	+	0.560854i	0.0666591	+	0.0178612i
$987$	14.8980	−	14.8980i	0.474208	−	0.474208i
$988$		0			0
$989$			30.6267i			0.973873i
$990$	−7.85528	−	16.3393i	−0.249657	−	0.519298i
$991$	−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
$993$	93.5143			2.96759
$994$	3.32894	+	12.4238i	0.105587	+	0.394058i
$995$	32.3795	−	6.10431i	1.02650	−	0.193520i
$996$	−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
$999$	5.20090	−	19.4100i	0.164549	−	0.614106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.t.g.427.4		20
5.3	odd	4		845.2.o.g.258.2		20
13.2	odd	12		845.2.k.d.577.8		20
13.3	even	3		845.2.f.d.437.8		20
13.4	even	6		845.2.t.f.657.4		20
13.5	odd	4		845.2.o.f.587.2		20
13.6	odd	12		845.2.o.g.357.2		20
13.7	odd	12		65.2.o.a.32.4	✓	20
13.8	odd	4		845.2.o.e.587.4		20
13.9	even	3		845.2.t.e.657.2		20
13.10	even	6		845.2.f.e.437.3		20
13.11	odd	12		845.2.k.e.577.3		20
13.12	even	2		65.2.t.a.37.2	yes	20
39.20	even	12		585.2.cf.a.487.2		20
39.38	odd	2		585.2.dp.a.37.4		20
65.3	odd	12		845.2.k.d.268.8		20
65.7	even	12		325.2.x.b.318.4		20
65.8	even	4		845.2.t.f.418.4		20
65.12	odd	4		325.2.s.b.193.2		20
65.18	even	4		845.2.t.e.418.2		20
65.23	odd	12		845.2.k.e.268.3		20
65.28	even	12		845.2.f.d.408.3		20
65.33	even	12		65.2.t.a.58.2	yes	20
65.38	odd	4		65.2.o.a.63.4	yes	20
65.43	odd	12		845.2.o.e.488.4		20
65.48	odd	12		845.2.o.f.488.2		20
65.58	even	12	inner	845.2.t.g.188.4		20
65.59	odd	12		325.2.s.b.32.2		20
65.63	even	12		845.2.f.e.408.8		20
65.64	even	2		325.2.x.b.232.4		20
195.38	even	4		585.2.cf.a.388.2		20
195.98	odd	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	13.7	odd	12
65.2.o.a.63.4	yes	20	65.38	odd	4
65.2.t.a.37.2	yes	20	13.12	even	2
65.2.t.a.58.2	yes	20	65.33	even	12
325.2.s.b.32.2		20	65.59	odd	12
325.2.s.b.193.2		20	65.12	odd	4
325.2.x.b.232.4		20	65.64	even	2
325.2.x.b.318.4		20	65.7	even	12
585.2.cf.a.388.2		20	195.38	even	4
585.2.cf.a.487.2		20	39.20	even	12
585.2.dp.a.37.4		20	39.38	odd	2
585.2.dp.a.253.4		20	195.98	odd	12
845.2.f.d.408.3		20	65.28	even	12
845.2.f.d.437.8		20	13.3	even	3
845.2.f.e.408.8		20	65.63	even	12
845.2.f.e.437.3		20	13.10	even	6
845.2.k.d.268.8		20	65.3	odd	12
845.2.k.d.577.8		20	13.2	odd	12
845.2.k.e.268.3		20	65.23	odd	12
845.2.k.e.577.3		20	13.11	odd	12
845.2.o.e.488.4		20	65.43	odd	12
845.2.o.e.587.4		20	13.8	odd	4
845.2.o.f.488.2		20	65.48	odd	12
845.2.o.f.587.2		20	13.5	odd	4
845.2.o.g.258.2		20	5.3	odd	4
845.2.o.g.357.2		20	13.6	odd	12
845.2.t.e.418.2		20	65.18	even	4
845.2.t.e.657.2		20	13.9	even	3
845.2.t.f.418.4		20	65.8	even	4
845.2.t.f.657.4		20	13.4	even	6
845.2.t.g.188.4		20	65.58	even	12	inner
845.2.t.g.427.4		20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

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