LMFDB - Embedded newform 845.2.t.f.418.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(188,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.188"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 5])) N = Newforms(chi, 2, names="a")

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:traces = [20,6,-2,6,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

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

Embedding invariants

Embedding label			418.3
Root			$-0.131303i$ of defining polynomial
Character	$\chi$	$=$	845.418
Dual form			845.2.t.f.657.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.113711 - 0.0656513i) q^{2} +(-0.0890070 + 0.332179i) q^{3} +(-0.991380 + 1.71712i) q^{4} +(2.08297 - 0.813169i) q^{5} +(0.0116869 + 0.0436159i) q^{6} +(1.39069 - 2.40874i) q^{7} +0.522947i q^{8} +(2.49566 + 1.44087i) q^{9} +(0.183472 - 0.229216i) q^{10} +(1.04957 - 3.91706i) q^{11} +(-0.482151 - 0.482151i) q^{12} -0.365201i q^{14} +(0.0847187 + 0.764295i) q^{15} +(-1.94843 - 3.37478i) q^{16} +(2.34186 - 0.627499i) q^{17} +0.378379 q^{18} +(-1.83459 + 0.491577i) q^{19} +(-0.668703 + 4.38287i) q^{20} +(0.676351 + 0.676351i) q^{21} +(-0.137812 - 0.514321i) q^{22} +(-7.70544 - 2.06467i) q^{23} +(-0.173712 - 0.0465459i) q^{24} +(3.67751 - 3.38761i) q^{25} +(-1.43027 + 1.43027i) q^{27} +(2.75740 + 4.77595i) q^{28} +(3.96565 - 2.28957i) q^{29} +(0.0598105 + 0.0813472i) q^{30} +(3.87352 - 3.87352i) q^{31} +(-1.34889 - 0.778780i) q^{32} +(1.20775 + 0.697292i) q^{33} +(0.225100 - 0.225100i) q^{34} +(0.938043 - 6.14819i) q^{35} +(-4.94829 + 2.85689i) q^{36} +(3.50510 + 6.07101i) q^{37} +(-0.176341 + 0.176341i) q^{38} +(0.425244 + 1.08928i) q^{40} +(6.20184 + 1.66178i) q^{41} +(0.121312 + 0.0325055i) q^{42} +(1.67299 + 6.24368i) q^{43} +(5.68554 + 5.68554i) q^{44} +(6.37004 + 0.971891i) q^{45} +(-1.01174 + 0.271096i) q^{46} -0.512375 q^{47} +(1.29445 - 0.346847i) q^{48} +(-0.368015 - 0.637420i) q^{49} +(0.195774 - 0.626643i) q^{50} +0.833767i q^{51} +(-1.32662 - 1.32662i) q^{53} +(-0.0687390 + 0.256537i) q^{54} +(-0.999006 - 9.01260i) q^{55} +(1.25964 + 0.727255i) q^{56} -0.653165i q^{57} +(0.300626 - 0.520700i) q^{58} +(-0.679700 - 2.53667i) q^{59} +(-1.39638 - 0.612235i) q^{60} +(0.641767 - 1.11157i) q^{61} +(0.186162 - 0.694764i) q^{62} +(6.94135 - 4.00759i) q^{63} +7.58920 q^{64} +0.183113 q^{66} +(-3.13180 + 1.80814i) q^{67} +(-1.24418 + 4.64334i) q^{68} +(1.37168 - 2.37581i) q^{69} +(-0.296970 - 0.760703i) q^{70} +(1.66343 + 6.20800i) q^{71} +(-0.753497 + 1.30509i) q^{72} +9.93250i q^{73} +(0.797139 + 0.460228i) q^{74} +(0.797968 + 1.52311i) q^{75} +(0.974678 - 3.63755i) q^{76} +(-7.97556 - 7.97556i) q^{77} +8.37577i q^{79} +(-6.80278 - 5.44515i) q^{80} +(3.97480 + 6.88456i) q^{81} +(0.814318 - 0.218196i) q^{82} +3.17194 q^{83} +(-1.83190 + 0.490855i) q^{84} +(4.36775 - 3.21139i) q^{85} +(0.600143 + 0.600143i) q^{86} +(0.407576 + 1.52109i) q^{87} +(2.04842 + 0.548871i) q^{88} +(-6.01705 - 1.61226i) q^{89} +(0.788152 - 0.307686i) q^{90} +(11.1843 - 11.1843i) q^{92} +(0.941930 + 1.63147i) q^{93} +(-0.0582629 + 0.0336381i) q^{94} +(-3.42165 + 2.51577i) q^{95} +(0.378755 - 0.378755i) q^{96} +(-10.1931 - 5.88500i) q^{97} +(-0.0836950 - 0.0483213i) q^{98} +(8.26335 - 8.26335i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 4 q^{6} - 2 q^{7} - 12 q^{9} + 10 q^{10} + 8 q^{11} - 24 q^{12} - 8 q^{15} - 2 q^{16} + 10 q^{17} + 16 q^{19} + 12 q^{20} + 4 q^{21} + 16 q^{22} + 2 q^{23} - 28 q^{24}+ \cdots + 60 q^{99}+O(q^{100}) $ 20 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 4 * q^6 - 2 * q^7 - 12 * q^9 + 10 * q^10 + 8 * q^11 - 24 * q^12 - 8 * q^15 - 2 * q^16 + 10 * q^17 + 16 * q^19 + 12 * q^20 + 4 * q^21 + 16 * q^22 + 2 * q^23 - 28 * q^24 + 18 * q^25 + 4 * q^27 + 18 * q^28 - 14 * q^30 - 48 * q^32 - 18 * q^33 + 2 * q^34 - 20 * q^35 - 36 * q^36 - 4 * q^37 - 8 * q^38 - 16 * q^40 + 28 * q^41 - 56 * q^42 + 22 * q^43 - 36 * q^44 + 6 * q^45 - 8 * q^46 - 40 * q^47 + 28 * q^48 + 18 * q^49 - 78 * q^50 - 10 * q^53 + 12 * q^54 + 26 * q^55 + 8 * q^59 + 28 * q^60 - 16 * q^61 + 40 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 + 28 * q^68 - 16 * q^69 - 12 * q^70 + 56 * q^71 + 4 * q^72 - 18 * q^74 + 34 * q^75 + 80 * q^76 - 28 * q^77 - 110 * q^80 - 14 * q^81 - 22 * q^82 + 48 * q^83 + 32 * q^84 + 28 * q^85 + 60 * q^86 + 62 * q^87 - 50 * q^88 - 6 * q^89 + 46 * q^90 - 8 * q^92 + 32 * q^93 + 48 * q^94 - 14 * q^95 + 56 * q^96 - 66 * q^97 + 30 * q^98 + 60 * q^99

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.113711	−	0.0656513i	0.0804061	−	0.0464225i	−0.459258	−	0.888303i	$-0.651885\pi$
$2$	0.113711	−	0.0656513i	0.0804061	−	0.0464225i	0.539664	+	0.841881i	$0.318551\pi$
$3$	−0.0890070	+	0.332179i	−0.0513882	+	0.191783i	−0.986848	−	0.161649i	$-0.948319\pi$
$3$	−0.0890070	+	0.332179i	−0.0513882	+	0.191783i	0.935460	+	0.353432i	$0.114985\pi$
$4$	−0.991380	+	1.71712i	−0.495690	+	0.858560i
$5$	2.08297	−	0.813169i	0.931532	−	0.363660i
$5$	2.08297	−	0.813169i	0.931532	−	0.363660i
$6$	0.0116869	+	0.0436159i	0.00477114	+	0.0178061i
$7$	1.39069	−	2.40874i	0.525630	−	0.910418i	−0.473924	−	0.880566i	$-0.657163\pi$
$7$	1.39069	−	2.40874i	0.525630	−	0.910418i	0.999554	−	0.0298522i	$-0.00950365\pi$
$8$			0.522947i			0.184890i
$9$	2.49566	+	1.44087i	0.831885	+	0.480289i
$10$	0.183472	−	0.229216i	0.0580188	−	0.0724845i
$11$	1.04957	−	3.91706i	0.316459	−	1.18104i	−0.606165	−	0.795339i	$-0.707293\pi$
$11$	1.04957	−	3.91706i	0.316459	−	1.18104i	0.922624	−	0.385701i	$-0.126040\pi$
$12$	−0.482151	−	0.482151i	−0.139185	−	0.139185i
$13$		0			0
$13$		0			0
$14$		−	0.365201i		−	0.0976042i
$15$	0.0847187	+	0.764295i	0.0218743	+	0.197340i
$16$	−1.94843	−	3.37478i	−0.487107	−	0.843694i
$17$	2.34186	−	0.627499i	0.567984	−	0.152191i	0.0366120	−	0.999330i	$-0.488343\pi$
$17$	2.34186	−	0.627499i	0.567984	−	0.152191i	0.531372	+	0.847139i	$0.321677\pi$
$18$	0.378379			0.0891849
$19$	−1.83459	+	0.491577i	−0.420883	+	0.112775i	−0.463044	−	0.886335i	$-0.653243\pi$
$19$	−1.83459	+	0.491577i	−0.420883	+	0.112775i	0.0421602	+	0.999111i	$0.486576\pi$
$20$	−0.668703	+	4.38287i	−0.149527	+	0.980039i
$21$	0.676351	+	0.676351i	0.147592	+	0.147592i
$22$	−0.137812	−	0.514321i	−0.0293816	−	0.109654i
$23$	−7.70544	−	2.06467i	−1.60670	−	0.430513i	−0.659640	−	0.751582i	$-0.729291\pi$
$23$	−7.70544	−	2.06467i	−1.60670	−	0.430513i	−0.947056	+	0.321069i	$0.895958\pi$
$24$	−0.173712	−	0.0465459i	−0.0354588	−	0.00950115i
$25$	3.67751	−	3.38761i	0.735502	−	0.677522i
$26$		0			0
$27$	−1.43027	+	1.43027i	−0.275256	+	0.275256i
$28$	2.75740	+	4.77595i	0.521099	+	0.902570i
$29$	3.96565	−	2.28957i	0.736403	−	0.425162i	−0.0843571	−	0.996436i	$-0.526884\pi$
$29$	3.96565	−	2.28957i	0.736403	−	0.425162i	0.820760	+	0.571273i	$0.193550\pi$
$30$	0.0598105	+	0.0813472i	0.0109198	+	0.0148519i
$31$	3.87352	−	3.87352i	0.695704	−	0.695704i	−0.267777	−	0.963481i	$-0.586289\pi$
$31$	3.87352	−	3.87352i	0.695704	−	0.695704i	0.963481	+	0.267777i	$0.0862890\pi$
$32$	−1.34889	−	0.778780i	−0.238452	−	0.137670i
$33$	1.20775	+	0.697292i	0.210242	+	0.121383i
$34$	0.225100	−	0.225100i	0.0386043	−	0.0386043i
$35$	0.938043	−	6.14819i	0.158558	−	1.03923i
$36$	−4.94829	+	2.85689i	−0.824714	+	0.476149i
$37$	3.50510	+	6.07101i	0.576234	+	0.998067i	0.995906	+	0.0903914i	$0.0288118\pi$
$37$	3.50510	+	6.07101i	0.576234	+	0.998067i	−0.419672	+	0.907676i	$0.637855\pi$
$38$	−0.176341	+	0.176341i	−0.0286063	+	0.0286063i
$39$		0			0
$40$	0.425244	+	1.08928i	0.0672370	+	0.172230i
$41$	6.20184	+	1.66178i	0.968565	+	0.259526i	0.708222	−	0.705990i	$-0.249498\pi$
$41$	6.20184	+	1.66178i	0.968565	+	0.259526i	0.260343	+	0.965516i	$0.416164\pi$
$42$	0.121312	+	0.0325055i	0.0187189	+	0.00501570i
$43$	1.67299	+	6.24368i	0.255128	+	0.952152i	0.968019	+	0.250877i	$0.0807189\pi$
$43$	1.67299	+	6.24368i	0.255128	+	0.952152i	−0.712891	+	0.701275i	$0.752614\pi$
$44$	5.68554	+	5.68554i	0.857128	+	0.857128i
$45$	6.37004	+	0.971891i	0.949590	+	0.144881i
$46$	−1.01174	+	0.271096i	−0.149174	+	0.0399709i
$47$	−0.512375			−0.0747376			−0.0373688	−	0.999302i	$-0.511898\pi$
$47$	−0.512375			−0.0747376			−0.0373688	+	0.999302i	$0.511898\pi$
$48$	1.29445	−	0.346847i	0.186838	−	0.0500631i
$49$	−0.368015	−	0.637420i	−0.0525736	−	0.0910601i
$50$	0.195774	−	0.626643i	0.0276866	−	0.0886207i
$51$			0.833767i			0.116751i
$52$		0			0
$53$	−1.32662	−	1.32662i	−0.182225	−	0.182225i	0.610100	−	0.792325i	$-0.291129\pi$
$53$	−1.32662	−	1.32662i	−0.182225	−	0.182225i	−0.792325	+	0.610100i	$0.791129\pi$
$54$	−0.0687390	+	0.256537i	−0.00935419	+	0.0349103i
$55$	−0.999006	−	9.01260i	−0.134706	−	1.21526i
$56$	1.25964	+	0.727255i	0.168327	+	0.0971835i
$57$		−	0.653165i		−	0.0865138i
$58$	0.300626	−	0.520700i	0.0394742	−	0.0683713i
$59$	−0.679700	−	2.53667i	−0.0884894	−	0.330247i	0.907463	−	0.420133i	$-0.138016\pi$
$59$	−0.679700	−	2.53667i	−0.0884894	−	0.330247i	−0.995952	+	0.0898858i	$0.971350\pi$
$60$	−1.39638	−	0.612235i	−0.180271	−	0.0790392i
$61$	0.641767	−	1.11157i	0.0821698	−	0.142322i	−0.822012	−	0.569470i	$-0.807148\pi$
$61$	0.641767	−	1.11157i	0.0821698	−	0.142322i	0.904182	+	0.427148i	$0.140482\pi$
$62$	0.186162	−	0.694764i	0.0236425	−	0.0882352i
$63$	6.94135	−	4.00759i	0.874528	−	0.504909i
$64$	7.58920			0.948650
$65$		0			0
$66$	0.183113			0.0225396
$67$	−3.13180	+	1.80814i	−0.382610	+	0.220900i	−0.678953	−	0.734181i	$-0.737566\pi$
$67$	−3.13180	+	1.80814i	−0.382610	+	0.220900i	0.296343	+	0.955082i	$0.404233\pi$
$68$	−1.24418	+	4.64334i	−0.150879	+	0.563088i
$69$	1.37168	−	2.37581i	0.165130	−	0.286014i
$70$	−0.296970	−	0.760703i	−0.0354948	−	0.0909214i
$71$	1.66343	+	6.20800i	0.197413	+	0.736754i	0.991629	+	0.129119i	$0.0412150\pi$
$71$	1.66343	+	6.20800i	0.197413	+	0.736754i	−0.794216	+	0.607635i	$0.792118\pi$
$72$	−0.753497	+	1.30509i	−0.0888005	+	0.153807i
$73$			9.93250i			1.16251i	0.813721	+	0.581256i	$0.197438\pi$
$73$			9.93250i			1.16251i	−0.813721	+	0.581256i	$0.802562\pi$
$74$	0.797139	+	0.460228i	0.0926655	+	0.0535005i
$75$	0.797968	+	1.52311i	0.0921414	+	0.175874i
$76$	0.974678	−	3.63755i	0.111803	−	0.417255i
$77$	−7.97556	−	7.97556i	−0.908899	−	0.908899i
$78$		0			0
$79$			8.37577i			0.942347i	0.882040	+	0.471174i	$0.156169\pi$
$79$			8.37577i			0.942347i	−0.882040	+	0.471174i	$0.843831\pi$
$80$	−6.80278	−	5.44515i	−0.760573	−	0.608786i
$81$	3.97480	+	6.88456i	0.441645	+	0.764951i
$82$	0.814318	−	0.218196i	0.0899264	−	0.0240957i
$83$	3.17194			0.348166			0.174083	−	0.984731i	$-0.444304\pi$
$83$	3.17194			0.348166			0.174083	+	0.984731i	$0.444304\pi$
$84$	−1.83190	+	0.490855i	−0.199876	+	0.0535567i
$85$	4.36775	−	3.21139i	0.473749	−	0.348324i
$86$	0.600143	+	0.600143i	0.0647151	+	0.0647151i
$87$	0.407576	+	1.52109i	0.0436967	+	0.163078i
$88$	2.04842	+	0.548871i	0.218362	+	0.0585099i
$89$	−6.01705	−	1.61226i	−0.637806	−	0.170900i	−0.0745967	−	0.997214i	$-0.523767\pi$
$89$	−6.01705	−	1.61226i	−0.637806	−	0.170900i	−0.563210	+	0.826314i	$0.690434\pi$
$90$	0.788152	−	0.307686i	0.0830785	−	0.0324330i
$91$		0			0
$92$	11.1843	−	11.1843i	1.16604	−	1.16604i
$93$	0.941930	+	1.63147i	0.0976736	+	0.169176i
$94$	−0.0582629	+	0.0336381i	−0.00600936	+	0.00346951i
$95$	−3.42165	+	2.51577i	−0.351054	+	0.258112i
$96$	0.378755	−	0.378755i	0.0386565	−	0.0386565i
$97$	−10.1931	−	5.88500i	−1.03495	−	0.597531i	−0.116554	−	0.993184i	$-0.537185\pi$
$97$	−10.1931	−	5.88500i	−1.03495	−	0.597531i	−0.918400	+	0.395654i	$0.870518\pi$
$98$	−0.0836950	−	0.0483213i	−0.00845447	−	0.00488119i
$99$	8.26335	−	8.26335i	0.830498	−	0.830498i
$100$	2.17112	+	9.67314i	0.217112	+	0.967314i
$101$	−0.873807	+	0.504493i	−0.0869471	+	0.0501989i	−0.542843	−	0.839834i	$-0.682652\pi$
$101$	−0.873807	+	0.504493i	−0.0869471	+	0.0501989i	0.455896	+	0.890033i	$0.349319\pi$
$102$	0.0547379	+	0.0948088i	0.00541986	+	0.00938747i
$103$	−6.00002	+	6.00002i	−0.591200	+	0.591200i	−0.937955	−	0.346756i	$-0.887283\pi$
$103$	−6.00002	+	6.00002i	−0.591200	+	0.591200i	0.346756	+	0.937955i	$0.387283\pi$
$104$		0			0
$105$	1.95880	+	0.858830i	0.191160	+	0.0838132i
$106$	−0.237946	−	0.0637574i	−0.0231113	−	0.00619267i
$107$	−4.78678	−	1.28261i	−0.462755	−	0.123995i	0.0199063	−	0.999802i	$-0.493663\pi$
$107$	−4.78678	−	1.28261i	−0.462755	−	0.123995i	−0.482662	+	0.875807i	$0.660330\pi$
$108$	−1.03801	−	3.87389i	−0.0998821	−	0.372765i
$109$	−6.51002	−	6.51002i	−0.623546	−	0.623546i	0.322890	−	0.946436i	$-0.395346\pi$
$109$	−6.51002	−	6.51002i	−0.623546	−	0.623546i	−0.946436	+	0.322890i	$0.895346\pi$
$110$	−0.705287	−	0.959249i	−0.0672465	−	0.0914608i
$111$	−2.32864	+	0.623956i	−0.221024	+	0.0592233i
$112$	−10.8386			−1.02415
$113$	−7.24731	+	1.94191i	−0.681769	+	0.182680i	−0.583051	−	0.812436i	$-0.698141\pi$
$113$	−7.24731	+	1.94191i	−0.681769	+	0.182680i	−0.0987188	+	0.995115i	$0.531474\pi$
$114$	−0.0428811	−	0.0742723i	−0.00401619	−	0.00695624i
$115$	−17.7291	+	1.96519i	−1.65325	+	0.183255i
$116$			9.07933i			0.842995i
$117$		0			0
$118$	−0.243826	−	0.243826i	−0.0224460	−	0.0224460i
$119$	1.74531	−	6.51358i	0.159992	−	0.597099i
$120$	−0.399686	+	0.0443033i	−0.0364861	+	0.00404432i
$121$	−4.71551	−	2.72250i	−0.428683	−	0.247500i
$122$		−	0.168531i		−	0.0152581i
$123$	−1.10402	+	1.91221i	−0.0995457	+	0.172418i
$124$	2.81117	+	10.4914i	0.252450	+	0.942157i
$125$	4.90544	−	10.0467i	0.438756	−	0.898606i
$126$	0.526207	−	0.911417i	0.0468782	−	0.0811955i
$127$	4.28310	−	15.9847i	0.380064	−	1.41842i	−0.465739	−	0.884922i	$-0.654212\pi$
$127$	4.28310	−	15.9847i	0.380064	−	1.41842i	0.845803	−	0.533495i	$-0.179122\pi$
$128$	3.56075	−	2.05580i	0.314729	−	0.181709i
$129$	−2.22292			−0.195718
$130$		0			0
$131$	−12.6880			−1.10856			−0.554278	−	0.832332i	$-0.687006\pi$
$131$	−12.6880			−1.10856			−0.554278	+	0.832332i	$0.687006\pi$
$132$	−2.39467	+	1.38256i	−0.208429	+	0.120337i
$133$	−1.36726	+	5.10267i	−0.118556	+	0.442458i
$134$	−0.237414	+	0.411213i	−0.0205095	+	0.0355234i
$135$	−1.81616	+	4.14226i	−0.156310	+	0.356509i
$136$	0.328148	+	1.22467i	0.0281385	+	0.105014i
$137$	7.47254	−	12.9428i	0.638422	−	1.10578i	−0.347357	−	0.937733i	$-0.612921\pi$
$137$	7.47254	−	12.9428i	0.638422	−	1.10578i	0.985779	−	0.168046i	$-0.0537458\pi$
$138$		−	0.360209i		−	0.0306631i
$139$	−7.42380	−	4.28613i	−0.629679	−	0.363545i	0.150949	−	0.988542i	$-0.451767\pi$
$139$	−7.42380	−	4.28613i	−0.629679	−	0.363545i	−0.780628	+	0.624996i	$0.785100\pi$
$140$	9.62722	+	7.70592i	0.813649	+	0.651269i
$141$	0.0456050	−	0.170200i	0.00384063	−	0.0143334i
$142$	0.596714	+	0.596714i	0.0500751	+	0.0500751i
$143$		0			0
$144$		−	11.2297i		−	0.935809i
$145$	6.39852	−	7.99385i	0.531368	−	0.663853i
$146$	0.652082	+	1.12944i	0.0539666	+	0.0934730i
$147$	0.244493	−	0.0655118i	0.0201655	−	0.00540332i
$148$	−13.8995			−1.14253
$149$	11.7276	−	3.14239i	0.960759	−	0.257435i	0.255837	−	0.966720i	$-0.417649\pi$
$149$	11.7276	−	3.14239i	0.960759	−	0.257435i	0.704922	+	0.709285i	$0.250982\pi$
$150$	0.190732	+	0.120808i	0.0155732	+	0.00986390i
$151$	1.86999	+	1.86999i	0.152177	+	0.152177i	0.779090	−	0.626912i	$-0.215682\pi$
$151$	1.86999	+	1.86999i	0.152177	+	0.152177i	−0.626912	+	0.779090i	$0.715682\pi$
$152$	−0.257068	−	0.959392i	−0.0208510	−	0.0778170i
$153$	6.74861	+	1.80829i	0.545593	+	0.146191i
$154$	−1.43052	−	0.383306i	−0.115274	−	0.0308877i
$155$	4.91859	−	11.2182i	0.395071	−	0.901071i
$156$		0			0
$157$	−10.3194	+	10.3194i	−0.823581	+	0.823581i	−0.986620	−	0.163039i	$-0.947870\pi$
$157$	−10.3194	+	10.3194i	−0.823581	+	0.823581i	0.163039	+	0.986620i	$0.447870\pi$
$158$	0.549880	+	0.952420i	0.0437461	+	0.0757705i
$159$	0.558753	−	0.322596i	0.0443120	−	0.0255835i
$160$	−3.44297	−	0.525301i	−0.272191	−	0.0415287i
$161$	−15.6891	+	15.6891i	−1.23647	+	1.23647i
$162$	0.903960	+	0.521902i	0.0710218	+	0.0410045i
$163$	−16.1907	−	9.34772i	−1.26815	−	0.732170i	−0.293516	−	0.955954i	$-0.594826\pi$
$163$	−16.1907	−	9.34772i	−1.26815	−	0.732170i	−0.974639	+	0.223784i	$0.928159\pi$
$164$	−9.00186	+	9.00186i	−0.702927	+	0.702927i
$165$	3.08271	+	0.470336i	0.239989	+	0.0366156i
$166$	0.360686	−	0.208242i	0.0279947	−	0.0161627i
$167$	10.3389	+	17.9075i	0.800049	+	1.38572i	0.919583	+	0.392895i	$0.128526\pi$
$167$	10.3389	+	17.9075i	0.800049	+	1.38572i	−0.119535	+	0.992830i	$0.538140\pi$
$168$	−0.353695	+	0.353695i	−0.0272882	+	0.0272882i
$169$		0			0
$170$	0.285831	−	0.651920i	0.0219223	−	0.0500000i
$171$	−5.28680	−	1.41659i	−0.404292	−	0.108330i
$172$	−12.3797	−	3.31713i	−0.943944	−	0.252929i
$173$	−4.69655	−	17.5278i	−0.357072	−	1.33261i	−0.877856	−	0.478924i	$-0.841027\pi$
$173$	−4.69655	−	17.5278i	−0.357072	−	1.33261i	0.520784	−	0.853688i	$-0.325640\pi$
$174$	0.146208	+	0.146208i	0.0110840	+	0.0110840i
$175$	−3.04560	−	13.5693i	−0.230226	−	1.02574i
$176$	−15.2642	+	4.09004i	−1.15058	+	0.308298i
$177$	0.903127			0.0678832
$178$	−0.790055	+	0.211694i	−0.0592171	+	0.0158672i
$179$	8.68110	+	15.0361i	0.648856	+	1.12385i	0.983396	+	0.181470i	$0.0580857\pi$
$179$	8.68110	+	15.0361i	0.648856	+	1.12385i	−0.334540	+	0.942382i	$0.608581\pi$
$180$	−7.98398	+	9.97461i	−0.595091	+	0.743464i
$181$			24.9284i			1.85291i	0.376406	+	0.926455i	$0.377160\pi$
$181$			24.9284i			1.85291i	−0.376406	+	0.926455i	$0.622840\pi$
$182$		0			0
$183$	0.312119	+	0.312119i	0.0230725	+	0.0230725i
$184$	1.07971	−	4.02953i	0.0795973	−	0.297061i
$185$	12.2378	+	9.79548i	0.899738	+	0.720178i
$186$	0.214216	+	0.123678i	0.0157071	+	0.00906850i
$187$		−	9.83181i		−	0.718973i
$188$	0.507958	−	0.879810i	0.0370467	−	0.0641667i
$189$	1.45609	+	5.43421i	0.105915	+	0.395280i
$190$	−0.223918	+	0.510708i	−0.0162447	+	0.0370506i
$191$	−3.39354	+	5.87779i	−0.245548	+	0.425302i	−0.962286	−	0.272041i	$-0.912301\pi$
$191$	−3.39354	+	5.87779i	−0.245548	+	0.425302i	0.716737	+	0.697343i	$0.245635\pi$
$192$	−0.675492	+	2.52097i	−0.0487494	+	0.181935i
$193$	1.03504	−	0.597582i	0.0745040	−	0.0430149i	−0.462285	−	0.886731i	$-0.652970\pi$
$193$	1.03504	−	0.597582i	0.0745040	−	0.0430149i	0.536789	+	0.843716i	$0.319637\pi$
$194$	−1.54543			−0.110955
$195$		0			0
$196$	1.45937			0.104241
$197$	−17.4253	+	10.0605i	−1.24150	+	0.716780i	−0.969399	−	0.245489i	$-0.921051\pi$
$197$	−17.4253	+	10.0605i	−1.24150	+	0.716780i	−0.272100	+	0.962269i	$0.587718\pi$
$198$	0.397137	−	1.48214i	0.0282233	−	0.105331i
$199$	−1.08885	+	1.88594i	−0.0771862	+	0.133690i	−0.902035	−	0.431663i	$-0.857927\pi$
$199$	−1.08885	+	1.88594i	−0.0771862	+	0.133690i	0.824849	+	0.565354i	$0.191260\pi$
$200$	1.77154	+	1.92314i	0.125267	+	0.135987i
$201$	−0.321875	−	1.20125i	−0.0227033	−	0.0847299i
$202$	−0.0662412	+	0.114733i	−0.00466071	+	0.00807259i
$203$		−	12.7363i		−	0.893912i
$204$	−1.43168	−	0.826580i	−0.100237	−	0.0578721i
$205$	14.2695	−	1.58171i	0.996629	−	0.110472i
$206$	−0.288362	+	1.07618i	−0.0200911	+	0.0749810i
$207$	−16.2552	−	16.2552i	−1.12982	−	1.12982i
$208$		0			0
$209$			7.70215i			0.532769i
$210$	0.279122	−	0.0309394i	0.0192612	−	0.00213502i
$211$	9.97642	+	17.2797i	0.686805	+	1.18958i	0.972866	+	0.231370i	$0.0743208\pi$
$211$	9.97642	+	17.2797i	0.686805	+	1.18958i	−0.286061	+	0.958211i	$0.592346\pi$
$212$	3.59315	−	0.962781i	0.246778	−	0.0661240i
$213$	−2.21022			−0.151442
$214$	−0.628516	+	0.168410i	−0.0429645	+	0.0115123i
$215$	8.56195	+	11.6450i	0.583920	+	0.794179i
$216$	−0.747956	−	0.747956i	−0.0508919	−	0.0508919i
$217$	−3.94345	−	14.7171i	−0.267698	−	0.999064i
$218$	−1.16765	−	0.312872i	−0.0790835	−	0.0211904i
$219$	−3.29936	−	0.884062i	−0.222950	−	0.0597394i
$220$	16.4661	+	7.21950i	1.11015	+	0.486738i
$221$		0			0
$222$	−0.223829	+	0.223829i	−0.0150224	+	0.0150224i
$223$	−6.70672	−	11.6164i	−0.449115	−	0.777891i	0.549213	−	0.835682i	$-0.314927\pi$
$223$	−6.70672	−	11.6164i	−0.449115	−	0.777891i	−0.998329	+	0.0577915i	$0.981594\pi$
$224$	−3.75176	+	2.16608i	−0.250675	+	0.144727i
$225$	14.0589	−	3.15550i	0.937260	−	0.210367i
$226$	−0.696612	+	0.696612i	−0.0463380	+	0.0463380i
$227$	12.7144	+	7.34064i	0.843882	+	0.487215i	0.858582	−	0.512677i	$-0.171346\pi$
$227$	12.7144	+	7.34064i	0.843882	+	0.487215i	−0.0147000	+	0.999892i	$0.504679\pi$
$228$	1.12156	+	0.647535i	0.0742773	+	0.0428840i
$229$	2.65280	−	2.65280i	0.175302	−	0.175302i	−0.614002	−	0.789304i	$-0.710442\pi$
$229$	2.65280	−	2.65280i	0.175302	−	0.175302i	0.789304	+	0.614002i	$0.210442\pi$
$230$	−1.88698	+	1.38740i	−0.124424	+	0.0914827i
$231$	3.35919	−	1.93943i	0.221018	−	0.127605i
$232$	1.19732	+	2.07382i	0.0786081	+	0.136153i
$233$	−13.9459	+	13.9459i	−0.913629	+	0.913629i	−0.996556	−	0.0829267i	$-0.973573\pi$
$233$	−13.9459	+	13.9459i	−0.913629	+	0.913629i	0.0829267	+	0.996556i	$0.473573\pi$
$234$		0			0
$235$	−1.06726	+	0.416648i	−0.0696205	+	0.0271791i
$236$	5.02962	+	1.34768i	0.327400	+	0.0877266i
$237$	−2.78225	−	0.745502i	−0.180727	−	0.0484256i
$238$	−0.229163	−	0.855249i	−0.0148545	−	0.0554376i
$239$	−10.1890	−	10.1890i	−0.659074	−	0.659074i	0.296087	−	0.955161i	$-0.404318\pi$
$239$	−10.1890	−	10.1890i	−0.659074	−	0.659074i	−0.955161	+	0.296087i	$0.904318\pi$
$240$	2.41426	−	1.77508i	0.155840	−	0.114581i
$241$	7.82799	−	2.09750i	0.504245	−	0.135112i	0.00227574	−	0.999997i	$-0.499276\pi$
$241$	7.82799	−	2.09750i	0.504245	−	0.135112i	0.501970	+	0.864885i	$0.332609\pi$
$242$	−0.714943			−0.0459582
$243$	−8.50205	+	2.27812i	−0.545407	+	0.146141i
$244$	1.27247	+	2.20398i	0.0814615	+	0.141095i
$245$	−1.28489	−	1.02847i	−0.0820889	−	0.0657064i
$246$			0.289920i			0.0184846i
$247$		0			0
$248$	2.02564	+	2.02564i	0.128628	+	0.128628i
$249$	−0.282325	+	1.05365i	−0.0178916	+	0.0667725i
$250$	−0.101776	−	1.46448i	−0.00643688	−	0.0926215i
$251$	4.04904	+	2.33771i	0.255573	+	0.147555i	0.622313	−	0.782768i	$-0.286193\pi$
$251$	4.04904	+	2.33771i	0.255573	+	0.147555i	−0.366740	+	0.930323i	$0.619526\pi$
$252$			15.8922i			1.00111i
$253$	−16.1749	+	28.0157i	−1.01690	+	1.76133i
$254$	−0.562382	−	2.09884i	−0.0352870	−	0.131693i
$255$	0.677993	+	1.73671i	0.0424576	+	0.108757i
$256$	−7.31927	+	12.6773i	−0.457454	+	0.792334i
$257$	4.49187	−	16.7639i	0.280195	−	1.04570i	−0.672085	−	0.740474i	$-0.734601\pi$
$257$	4.49187	−	16.7639i	0.280195	−	1.04570i	0.952280	−	0.305227i	$-0.0987324\pi$
$258$	−0.252772	+	0.145938i	−0.0157369	+	0.00908569i
$259$	19.4980			1.21154
$260$		0			0
$261$	13.1959			0.816804
$262$	−1.44277	+	0.832984i	−0.0891346	+	0.0514619i
$263$	0.626777	−	2.33916i	0.0386487	−	0.144239i	−0.943905	−	0.330216i	$-0.892878\pi$
$263$	0.626777	−	2.33916i	0.0386487	−	0.144239i	0.982554	+	0.185977i	$0.0595450\pi$
$264$	−0.364647	+	0.631587i	−0.0224425	+	0.0388715i
$265$	−3.84207	−	1.68454i	−0.236016	−	0.103480i
$266$	0.179524	+	0.669994i	0.0110073	+	0.0410800i
$267$	1.07112	−	1.85523i	0.0655515	−	0.113538i
$268$		−	7.17023i		−	0.437992i
$269$	8.42829	+	4.86608i	0.513882	+	0.296690i	0.734428	−	0.678687i	$-0.237451\pi$
$269$	8.42829	+	4.86608i	0.513882	+	0.296690i	−0.220546	+	0.975377i	$0.570784\pi$
$270$	0.0654271	+	0.590255i	0.00398177	+	0.0359218i
$271$	5.67269	−	21.1708i	0.344591	−	1.28603i	−0.548498	−	0.836152i	$-0.684800\pi$
$271$	5.67269	−	21.1708i	0.344591	−	1.28603i	0.893089	−	0.449880i	$-0.148533\pi$
$272$	−6.68061	−	6.68061i	−0.405071	−	0.405071i
$273$		0			0
$274$		−	1.96233i		−	0.118548i
$275$	−9.40967	−	17.9606i	−0.567424	−	1.08306i
$276$	2.71970	+	4.71067i	0.163707	+	0.283549i
$277$	−17.4408	+	4.67325i	−1.04792	+	0.280788i	−0.741390	−	0.671074i	$-0.765833\pi$
$277$	−17.4408	+	4.67325i	−1.04792	+	0.280788i	−0.306526	+	0.951862i	$0.599167\pi$
$278$	−1.12556			−0.0675067
$279$	15.2482	−	4.08574i	0.912885	−	0.244607i
$280$	3.21517	+	0.490546i	0.192143	+	0.0293157i
$281$	11.3739	+	11.3739i	0.678510	+	0.678510i	0.959663	−	0.281153i	$-0.0907168\pi$
$281$	11.3739	+	11.3739i	0.678510	+	0.678510i	−0.281153	+	0.959663i	$0.590717\pi$
$282$	−0.00598805	−	0.0223477i	−0.000356583	−	0.00133079i
$283$	−10.9682	−	2.93892i	−0.651991	−	0.174700i	−0.0823620	−	0.996602i	$-0.526246\pi$
$283$	−10.9682	−	2.93892i	−0.651991	−	0.174700i	−0.569629	+	0.821902i	$0.692913\pi$
$284$	−12.3090	−	3.29818i	−0.730403	−	0.195711i
$285$	−0.531134	−	1.36052i	−0.0314616	−	0.0805904i
$286$		0			0
$287$	12.6276	−	12.6276i	0.745384	−	0.745384i
$288$	−2.24424	−	3.88713i	−0.132243	−	0.229052i
$289$	−9.63189	+	5.56098i	−0.566582	+	0.327116i
$290$	0.202778	−	1.32906i	0.0119075	−	0.0780452i
$291$	2.86213	−	2.86213i	0.167781	−	0.167781i
$292$	−17.0553	−	9.84688i	−0.998086	−	0.576245i
$293$	−0.605883	−	0.349807i	−0.0353961	−	0.0204359i	0.482198	−	0.876063i	$-0.339839\pi$
$293$	−0.605883	−	0.349807i	−0.0353961	−	0.0204359i	−0.517594	+	0.855627i	$0.673172\pi$
$294$	0.0235007	−	0.0235007i	0.00137059	−	0.00137059i
$295$	−3.47854	−	4.73110i	−0.202528	−	0.275455i
$296$	−3.17481	+	1.83298i	−0.184532	+	0.106540i
$297$	4.10129	+	7.10364i	0.237981	+	0.412195i
$298$	1.12725	−	1.12725i	0.0653001	−	0.0653001i
$299$		0			0
$300$	−3.40646	−	0.139776i	−0.196672	−	0.00806999i
$301$	17.3660	+	4.65320i	1.00096	+	0.268206i
$302$	0.335406	+	0.0898718i	0.0193004	+	0.00517154i
$303$	−0.0898068	−	0.335163i	−0.00515926	−	0.0192546i
$304$	5.23352	+	5.23352i	0.300163	+	0.300163i
$305$	0.432883	−	2.83724i	0.0247868	−	0.162460i
$306$	0.886110	−	0.237433i	0.0506555	−	0.0135731i
$307$	−14.2048			−0.810709			−0.405355	−	0.914159i	$-0.632852\pi$
$307$	−14.2048			−0.810709			−0.405355	+	0.914159i	$0.632852\pi$
$308$	21.6018	−	5.78818i	1.23088	−	0.329812i
$309$	−1.45904	−	2.52712i	−0.0830016	−	0.143763i
$310$	−0.177192	−	1.59855i	−0.0100638	−	0.0907917i
$311$		−	21.4961i		−	1.21893i	−0.792812	−	0.609466i	$-0.791384\pi$
$311$		−	21.4961i		−	1.21893i	0.792812	−	0.609466i	$-0.208616\pi$
$312$		0			0
$313$	−9.36303	−	9.36303i	−0.529230	−	0.529230i	0.391113	−	0.920343i	$-0.372090\pi$
$313$	−9.36303	−	9.36303i	−0.529230	−	0.529230i	−0.920343	+	0.391113i	$0.872090\pi$
$314$	−0.495953	+	1.85092i	−0.0279882	+	0.104454i
$315$	11.1998	−	13.9922i	0.631035	−	0.788369i
$316$	−14.3822	−	8.30357i	−0.809062	−	0.467112i
$317$		−	17.3024i		−	0.971798i	−0.874015	−	0.485899i	$-0.838492\pi$
$317$		−	17.3024i		−	0.971798i	0.874015	−	0.485899i	$-0.161508\pi$
$318$	0.0423577	−	0.0733657i	0.00237530	−	0.00411414i
$319$	−4.80615	−	17.9368i	−0.269093	−	1.00427i
$320$	15.8081	−	6.17130i	0.883697	−	0.344986i
$321$	0.852114	−	1.47590i	0.0475603	−	0.0823769i
$322$	−0.754019	+	2.81404i	−0.0420198	+	0.156820i
$323$	−3.98788	+	2.30240i	−0.221892	+	0.128109i
$324$	−15.7622			−0.875675
$325$		0			0
$326$	−2.45476			−0.135957
$327$	2.74193	−	1.58305i	0.151629	−	0.0875429i
$328$	−0.869022	+	3.24323i	−0.0479837	+	0.179078i
$329$	−0.712553	+	1.23418i	−0.0392843	+	0.0680424i
$330$	0.381418	−	0.148901i	0.0209964	−	0.00819676i
$331$	−4.65090	−	17.3574i	−0.255637	−	0.954049i	−0.967735	−	0.251969i	$-0.918922\pi$
$331$	−4.65090	−	17.3574i	−0.255637	−	0.954049i	0.712099	−	0.702079i	$-0.247745\pi$
$332$	−3.14460	+	5.44661i	−0.172582	+	0.298921i
$333$			20.2015i			1.10704i
$334$	2.35130	+	1.35753i	0.128658	+	0.0742805i
$335$	−5.05311	+	6.31299i	−0.276081	+	0.344915i
$336$	0.964712	−	3.60035i	0.0526293	−	0.196415i
$337$	4.83668	+	4.83668i	0.263471	+	0.263471i	0.826462	−	0.562992i	$-0.190350\pi$
$337$	4.83668	+	4.83668i	0.263471	+	0.263471i	−0.562992	+	0.826462i	$0.690350\pi$
$338$		0			0
$339$		−	2.58024i		−	0.140140i
$340$	1.18423	+	10.6837i	0.0642242	+	0.579403i
$341$	−11.1073	−	19.2384i	−0.601493	−	1.04182i
$342$	−0.694170	+	0.186002i	−0.0375364	+	0.0100579i
$343$	17.4224			0.940723
$344$	−3.26511	+	0.874884i	−0.176043	+	0.0471706i
$345$	0.925220	−	6.06415i	0.0498122	−	0.326483i
$346$	−1.68477	−	1.68477i	−0.0905740	−	0.0905740i
$347$	4.81456	+	17.9682i	0.258459	+	0.964582i	0.966133	+	0.258043i	$0.0830778\pi$
$347$	4.81456	+	17.9682i	0.258459	+	0.964582i	−0.707674	+	0.706539i	$0.750256\pi$
$348$	−3.01596	−	0.808124i	−0.161672	−	0.0433200i
$349$	−2.43126	−	0.651455i	−0.130143	−	0.0348716i	0.193160	−	0.981167i	$-0.438126\pi$
$349$	−2.43126	−	0.651455i	−0.130143	−	0.0348716i	−0.323302	+	0.946296i	$0.604793\pi$
$350$	−1.23716	−	1.34303i	−0.0661290	−	0.0717881i
$351$		0			0
$352$	−4.46629	+	4.46629i	−0.238054	+	0.238054i
$353$	16.3608	+	28.3377i	0.870795	+	1.50826i	0.861175	+	0.508308i	$0.169729\pi$
$353$	16.3608	+	28.3377i	0.870795	+	1.50826i	0.00962005	+	0.999954i	$0.496938\pi$
$354$	0.102696	−	0.0592915i	0.00545822	−	0.00315131i
$355$	8.51302	+	11.5784i	0.451824	+	0.614519i
$356$	8.73364	−	8.73364i	0.462882	−	0.462882i
$357$	2.00833	+	1.15951i	0.106292	+	0.0613677i
$358$	1.97428	+	1.13985i	0.104344	+	0.0602430i
$359$	−0.699684	+	0.699684i	−0.0369279	+	0.0369279i	−0.725330	−	0.688402i	$-0.758313\pi$
$359$	−0.699684	+	0.699684i	−0.0369279	+	0.0369279i	0.688402	+	0.725330i	$0.258313\pi$
$360$	−0.508247	+	3.33119i	−0.0267870	+	0.175569i
$361$	−13.3304	+	7.69632i	−0.701601	+	0.405069i
$362$	1.63658	+	2.83464i	0.0860167	+	0.148985i
$363$	1.32407	−	1.32407i	0.0694956	−	0.0694956i
$364$		0			0
$365$	8.07680	+	20.6891i	0.422759	+	1.08292i
$366$	0.0559825	+	0.0150005i	0.00292625	+	0.000784087i
$367$	−13.9803	−	3.74601i	−0.729767	−	0.195540i	−0.125241	−	0.992126i	$-0.539971\pi$
$367$	−13.9803	−	3.74601i	−0.729767	−	0.195540i	−0.604525	+	0.796586i	$0.706637\pi$
$368$	8.04571	+	30.0270i	0.419411	+	1.56526i
$369$	13.0833	+	13.0833i	0.681087	+	0.681087i
$370$	2.03466	+	0.310432i	0.105777	+	0.0161386i
$371$	−5.04039	+	1.35057i	−0.261684	+	0.0701180i
$372$	−3.73524			−0.193663
$373$	9.79493	−	2.62454i	0.507162	−	0.135894i	0.00384023	−	0.999993i	$-0.498778\pi$
$373$	9.79493	−	2.62454i	0.507162	−	0.135894i	0.503322	+	0.864099i	$0.332111\pi$
$374$	−0.645471	−	1.11799i	−0.0333765	−	0.0578098i
$375$	2.90069	+	2.52371i	0.149791	+	0.130324i
$376$		−	0.267945i		−	0.0138182i
$377$		0			0
$378$	0.522337	+	0.522337i	0.0268661	+	0.0268661i
$379$	−0.271887	+	1.01470i	−0.0139659	+	0.0521215i	−0.972557	−	0.232664i	$-0.925256\pi$
$379$	−0.271887	+	1.01470i	−0.0139659	+	0.0521215i	0.958591	+	0.284786i	$0.0919224\pi$
$380$	−0.927718	−	8.36948i	−0.0475909	−	0.429345i
$381$	4.92857	+	2.84551i	0.252498	+	0.145780i
$382$			0.891162i			0.0455958i
$383$	6.00353	−	10.3984i	0.306766	−	0.531334i	−0.670887	−	0.741560i	$-0.734086\pi$
$383$	6.00353	−	10.3984i	0.306766	−	0.531334i	0.977653	+	0.210225i	$0.0674198\pi$
$384$	0.365961	+	1.36579i	0.0186754	+	0.0696975i
$385$	−23.0983	−	10.1274i	−1.17720	−	0.516138i
$386$	0.0784640	−	0.135904i	0.00399371	−	0.00691732i
$387$	−4.82111	+	17.9926i	−0.245071	+	0.914616i
$388$	20.2105	−	11.6685i	1.02603	−	0.592380i
$389$	7.37166			0.373758			0.186879	−	0.982383i	$-0.440163\pi$
$389$	7.37166			0.373758			0.186879	+	0.982383i	$0.440163\pi$
$390$		0			0
$391$	−19.3406			−0.978097
$392$	0.333337	−	0.192452i	0.0168361	−	0.00972030i
$393$	1.12932	−	4.21468i	0.0569667	−	0.212603i
$394$	−1.32097	+	2.28798i	−0.0665494	+	0.115267i
$395$	6.81091	+	17.4465i	0.342694	+	0.877826i
$396$	5.99704	+	22.3813i	0.301363	+	1.12470i
$397$	−3.02739	+	5.24359i	−0.151940	+	0.263168i	−0.931941	−	0.362611i	$-0.881885\pi$
$397$	−3.02739	+	5.24359i	−0.151940	+	0.263168i	0.780001	+	0.625779i	$0.215219\pi$
$398$			0.285937i			0.0143327i
$399$	−1.57330	−	0.908347i	−0.0787637	−	0.0454742i
$400$	−18.5978	−	5.81026i	−0.929890	−	0.290513i
$401$	0.624928	−	2.33226i	0.0312074	−	0.116468i	−0.948565	−	0.316582i	$-0.897465\pi$
$401$	0.624928	−	2.33226i	0.0312074	−	0.116468i	0.979773	+	0.200114i	$0.0641314\pi$
$402$	−0.115465	−	0.115465i	−0.00575886	−	0.00575886i
$403$		0			0
$404$		−	2.00058i		−	0.0995324i
$405$	13.8777	+	11.1081i	0.689588	+	0.551967i
$406$	−0.836154	−	1.44826i	−0.0414976	−	0.0718760i
$407$	27.4594	−	7.35772i	1.36111	−	0.364709i
$408$	−0.436016			−0.0215860
$409$	−19.4510	+	5.21187i	−0.961788	+	0.257710i	−0.705357	−	0.708852i	$-0.749213\pi$
$409$	−19.4510	+	5.21187i	−0.961788	+	0.257710i	−0.256431	+	0.966563i	$0.582547\pi$
$410$	1.51877	−	1.11667i	0.0750066	−	0.0551486i
$411$	3.63422	+	3.63422i	0.179263	+	0.179263i
$412$	−4.35446	−	16.2511i	−0.214529	−	0.800632i
$413$	−7.05543	−	1.89050i	−0.347175	−	0.0930253i
$414$	−2.91558	−	0.781227i	−0.143293	−	0.0383952i
$415$	6.60706	−	2.57933i	0.324328	−	0.126614i
$416$		0			0
$417$	2.08453	−	2.08453i	0.102080	−	0.102080i
$418$	0.505656	+	0.875822i	0.0247324	+	0.0428378i
$419$	26.0503	−	15.0401i	1.27264	−	0.734759i	0.297156	−	0.954829i	$-0.403962\pi$
$419$	26.0503	−	15.0401i	1.27264	−	0.734759i	0.975484	+	0.220070i	$0.0706287\pi$
$420$	−3.41663	+	2.51208i	−0.166715	+	0.122577i
$421$	9.24685	−	9.24685i	0.450664	−	0.450664i	−0.444911	−	0.895575i	$-0.646765\pi$
$421$	9.24685	−	9.24685i	0.450664	−	0.450664i	0.895575	+	0.444911i	$0.146765\pi$
$422$	2.26887	+	1.30993i	0.110447	+	0.0637664i
$423$	−1.27871	−	0.738265i	−0.0621731	−	0.0358957i
$424$	0.693751	−	0.693751i	0.0336915	−	0.0336915i
$425$	6.48649	−	10.2409i	0.314641	−	0.496758i
$426$	−0.251327	+	0.145104i	−0.0121769	+	0.00703031i
$427$	−1.78499	−	3.09170i	−0.0863818	−	0.149618i
$428$	6.94792	−	6.94792i	0.335840	−	0.335840i
$429$		0			0
$430$	1.73810	+	0.762061i	0.0838185	+	0.0367499i
$431$	6.09624	+	1.63348i	0.293646	+	0.0786821i	0.402634	−	0.915361i	$-0.368095\pi$
$431$	6.09624	+	1.63348i	0.293646	+	0.0786821i	−0.108989	+	0.994043i	$0.534761\pi$
$432$	7.61362	+	2.04006i	0.366311	+	0.0981527i
$433$	−3.18071	−	11.8706i	−0.152855	−	0.570463i	−0.999279	−	0.0379543i	$-0.987916\pi$
$433$	−3.18071	−	11.8706i	−0.152855	−	0.570463i	0.846424	−	0.532509i	$-0.178751\pi$
$434$	−1.41461	−	1.41461i	−0.0679036	−	0.0679036i
$435$	2.08587	+	2.83696i	0.100010	+	0.136022i
$436$	17.6324	−	4.72458i	0.844438	−	0.226266i
$437$	15.1513			0.724783
$438$	−0.433215	+	0.116080i	−0.0206998	+	0.00554650i
$439$	−17.2223	−	29.8300i	−0.821977	−	1.42371i	−0.904208	−	0.427093i	$-0.859538\pi$
$439$	−17.2223	−	29.8300i	−0.821977	−	1.42371i	0.0822306	−	0.996613i	$-0.473796\pi$
$440$	4.71311	−	0.522427i	0.224689	−	0.0249057i
$441$		−	2.12104i		−	0.101002i
$442$		0			0
$443$	−5.39452	−	5.39452i	−0.256301	−	0.256301i	0.567247	−	0.823548i	$-0.308009\pi$
$443$	−5.39452	−	5.39452i	−0.256301	−	0.256301i	−0.823548	+	0.567247i	$0.808009\pi$
$444$	1.23716	−	4.61713i	0.0587128	−	0.219119i
$445$	−13.8444	+	1.53459i	−0.656286	+	0.0727463i
$446$	−1.52526	−	0.880610i	−0.0722232	−	0.0416981i
$447$			4.17534i			0.197487i
$448$	10.5542	−	18.2804i	0.498639	−	0.863668i
$449$	8.05832	+	30.0741i	0.380296	+	1.41928i	0.845451	+	0.534053i	$0.179332\pi$
$449$	8.05832	+	30.0741i	0.380296	+	1.41928i	−0.465155	+	0.885229i	$0.654002\pi$
$450$	1.39149	−	1.28180i	0.0655957	−	0.0604247i
$451$	13.0186	−	22.5489i	0.613021	−	1.06178i
$452$	3.85034	−	14.3697i	0.181105	−	0.675892i
$453$	−0.787612	+	0.454728i	−0.0370053	+	0.0213650i
$454$	1.92769			0.0904710
$455$		0			0
$456$	0.341570			0.0159955
$457$	2.69118	−	1.55375i	0.125888	−	0.0726814i	−0.435734	−	0.900076i	$-0.643511\pi$
$457$	2.69118	−	1.55375i	0.125888	−	0.0726814i	0.561622	+	0.827394i	$0.310178\pi$
$458$	0.127494	−	0.475812i	0.00595738	−	0.0222333i
$459$	−2.45200	+	4.24698i	−0.114449	+	0.198232i
$460$	14.2018	−	32.3913i	0.662163	−	1.51025i
$461$	4.32132	+	16.1274i	0.201264	+	0.751126i	0.990556	+	0.137109i	$0.0437810\pi$
$461$	4.32132	+	16.1274i	0.201264	+	0.751126i	−0.789292	+	0.614018i	$0.789552\pi$
$462$	0.254652	−	0.441070i	0.0118475	−	0.0205205i
$463$			15.6396i			0.726832i	0.931627	+	0.363416i	$0.118390\pi$
$463$			15.6396i			0.726832i	−0.931627	+	0.363416i	$0.881610\pi$
$464$	−15.4536	−	8.92212i	−0.717414	−	0.414199i
$465$	3.28867	+	2.63235i	0.152508	+	0.122072i
$466$	−0.670243	+	2.50138i	−0.0310484	+	0.115874i
$467$	15.0821	+	15.0821i	0.697916	+	0.697916i	0.963961	−	0.266045i	$-0.0857169\pi$
$467$	15.0821	+	15.0821i	0.697916	+	0.697916i	−0.266045	+	0.963961i	$0.585717\pi$
$468$		0			0
$469$			10.0582i			0.464447i
$470$	−0.0940063	+	0.117445i	−0.00433619	+	0.00541732i
$471$	−2.50939	−	4.34640i	−0.115627	−	0.200272i
$472$	1.32655	−	0.355447i	0.0610592	−	0.0163608i
$473$	26.2128			1.20527
$474$	−0.365317	+	0.0978863i	−0.0167796	+	0.00449607i
$475$	−5.08145	+	8.02265i	−0.233153	+	0.368104i
$476$	9.45433	+	9.45433i	0.433339	+	0.433339i
$477$	−1.39930	−	5.22226i	−0.0640696	−	0.239111i
$478$	−1.82753	−	0.489686i	−0.0835894	−	0.0223977i
$479$	41.1964	+	11.0386i	1.88231	+	0.504364i	0.999393	+	0.0348421i	$0.0110928\pi$
$479$	41.1964	+	11.0386i	1.88231	+	0.504364i	0.882921	+	0.469522i	$0.155574\pi$
$480$	0.480942	−	1.09693i	0.0219519	−	0.0500676i
$481$		0			0
$482$	0.752428	−	0.752428i	0.0342722	−	0.0342722i
$483$	−3.81514	−	6.60802i	−0.173595	−	0.300675i
$484$	9.34972	−	5.39806i	0.424987	−	0.245366i
$485$	−26.0174	−	3.96953i	−1.18139	−	0.180247i
$486$	−0.817218	+	0.817218i	−0.0370698	+	0.0370698i
$487$	−13.1780	−	7.60834i	−0.597154	−	0.344767i	0.170767	−	0.985311i	$-0.445375\pi$
$487$	−13.1780	−	7.60834i	−0.597154	−	0.344767i	−0.767921	+	0.640545i	$0.778709\pi$
$488$	0.581293	+	0.335610i	0.0263139	+	0.0151923i
$489$	4.54620	−	4.54620i	0.205586	−	0.205586i
$490$	−0.213627	−	0.0325936i	−0.00965070	−	0.00147243i
$491$	−24.2273	+	13.9876i	−1.09336	+	0.631254i	−0.934470	−	0.356042i	$-0.884126\pi$
$491$	−24.2273	+	13.9876i	−1.09336	+	0.631254i	−0.158894	+	0.987296i	$0.550793\pi$
$492$	−2.18900	−	3.79145i	−0.0986876	−	0.170932i
$493$	7.85029	−	7.85029i	0.353559	−	0.353559i
$494$		0			0
$495$	10.4928	−	23.9318i	0.471616	−	1.07565i
$496$	−20.6195	−	5.52498i	−0.925844	−	0.248079i
$497$	17.2668	+	4.62661i	0.774520	+	0.207532i
$498$	0.0370700	+	0.138347i	0.00166115	+	0.00619949i
$499$	−1.67479	−	1.67479i	−0.0749740	−	0.0749740i	0.668625	−	0.743599i	$-0.266883\pi$
$499$	−1.67479	−	1.67479i	−0.0749740	−	0.0749740i	−0.743599	+	0.668625i	$0.766883\pi$
$500$	12.3883	+	18.3833i	0.554021	+	0.822128i
$501$	−6.86873	+	1.84047i	−0.306872	+	0.0822261i
$502$	0.613896			0.0273995
$503$	−22.3705	+	5.99415i	−0.997451	+	0.267266i	−0.720377	−	0.693583i	$-0.756031\pi$
$503$	−22.3705	+	5.99415i	−0.997451	+	0.267266i	−0.277073	+	0.960849i	$0.589365\pi$
$504$	2.09575	+	3.62995i	0.0933523	+	0.161691i
$505$	−1.40987	+	1.76140i	−0.0627386	+	0.0783811i
$506$			4.24760i			0.188829i
$507$		0			0
$508$	23.2016	+	23.2016i	1.02940	+	1.02940i
$509$	−1.55965	+	5.82068i	−0.0691301	+	0.257997i	−0.991838	−	0.127502i	$-0.959304\pi$
$509$	−1.55965	+	5.82068i	−0.0691301	+	0.257997i	0.922708	+	0.385499i	$0.125971\pi$
$510$	0.191113	+	0.152973i	0.00846262	+	0.00677374i
$511$	23.9248	+	13.8130i	1.05837	+	0.611051i
$512$			10.1453i			0.448362i
$513$	1.92087	−	3.32705i	0.0848086	−	0.146893i
$514$	−0.589794	−	2.20114i	−0.0260147	−	0.0970881i
$515$	−7.61882	+	17.3769i	−0.335725	+	0.765717i
$516$	2.20376	−	3.81703i	0.0970152	−	0.168035i
$517$	−0.537776	+	2.00701i	−0.0236514	+	0.0882681i
$518$	2.21714	−	1.28007i	0.0974155	−	0.0562429i
$519$	6.24038			0.273922
$520$		0			0
$521$	27.8183			1.21874			0.609371	−	0.792886i	$-0.291422\pi$
$521$	27.8183			1.21874			0.609371	+	0.792886i	$0.291422\pi$
$522$	1.50052	−	0.866326i	0.0656760	−	0.0379180i
$523$	−0.141761	+	0.529059i	−0.00619877	+	0.0231341i	−0.968956	−	0.247233i	$-0.920479\pi$
$523$	−0.141761	+	0.529059i	−0.00619877	+	0.0231341i	0.962757	+	0.270368i	$0.0871452\pi$
$524$	12.5786	−	21.7868i	0.549500	−	0.951762i
$525$	4.77850	+	0.196075i	0.208551	+	0.00855742i
$526$	−0.0822974	−	0.307138i	−0.00358834	−	0.0133919i
$527$	6.64060	−	11.5019i	0.289269	−	0.501029i
$528$		−	5.43449i		−	0.236506i
$529$	35.1924	+	20.3183i	1.53010	+	0.883406i
$530$	−0.547479	+	0.0606856i	−0.0237810	+	0.00263601i
$531$	1.95871	−	7.31002i	0.0850010	−	0.317228i
$532$	−7.40643	−	7.40643i	−0.321110	−	0.321110i
$533$		0			0
$534$		−	0.281282i		−	0.0121722i
$535$	−11.0137	+	1.22082i	−0.476163	+	0.0527805i
$536$	−0.945563	−	1.63776i	−0.0408421	−	0.0707406i
$537$	−5.76736	+	1.54536i	−0.248880	+	0.0666871i
$538$	1.27786			0.0550923
$539$	−2.88308	+	0.772518i	−0.124183	+	0.0332747i
$540$	−5.31226	−	7.22512i	−0.228603	−	0.310919i
$541$	−29.7507	−	29.7507i	−1.27908	−	1.27908i	−0.941182	−	0.337899i	$-0.890284\pi$
$541$	−29.7507	−	29.7507i	−1.27908	−	1.27908i	−0.337899	−	0.941182i	$-0.609716\pi$
$542$	−0.744839	−	2.77978i	−0.0319936	−	0.119402i
$543$	−8.28067	−	2.21880i	−0.355357	−	0.0952177i
$544$	−3.64758	−	0.977367i	−0.156389	−	0.0419043i
$545$	−18.8539	−	8.26641i	−0.807612	−	0.354094i
$546$		0			0
$547$	−14.2594	+	14.2594i	−0.609688	+	0.609688i	−0.942864	−	0.333176i	$-0.891880\pi$
$547$	−14.2594	+	14.2594i	−0.609688	+	0.609688i	0.333176	+	0.942864i	$0.391880\pi$
$548$	14.8162	+	25.6625i	0.632919	+	1.09625i
$549$	3.20326	−	1.84940i	0.136712	−	0.0789306i
$550$	−2.24912	−	1.42457i	−0.0959029	−	0.0607438i
$551$	−6.14984	+	6.14984i	−0.261992	+	0.261992i
$552$	1.24242	+	0.717314i	0.0528811	+	0.0305309i
$553$	20.1750	+	11.6481i	0.857930	+	0.495326i
$554$	−1.67641	+	1.67641i	−0.0712240	+	0.0712240i
$555$	−4.34309	+	3.19326i	−0.184354	+	0.135546i
$556$	14.7196	−	8.49837i	0.624251	−	0.360411i
$557$	−17.5886	−	30.4644i	−0.745254	−	1.29082i	−0.950076	−	0.312018i	$-0.898995\pi$
$557$	−17.5886	−	30.4644i	−0.745254	−	1.29082i	0.204822	−	0.978799i	$-0.434338\pi$
$558$	1.46566	−	1.46566i	0.0620463	−	0.0620463i
$559$		0			0
$560$	−22.5765	+	8.81362i	−0.954030	+	0.372443i
$561$	3.26592	+	0.875100i	0.137887	+	0.0369468i
$562$	2.04005	+	0.546631i	0.0860545	+	0.0230582i
$563$	10.8527	+	40.5028i	0.457387	+	1.70699i	0.680975	+	0.732306i	$0.261556\pi$
$563$	10.8527	+	40.5028i	0.457387	+	1.70699i	−0.223589	+	0.974684i	$0.571777\pi$
$564$	0.247042	+	0.247042i	0.0104024	+	0.0104024i
$565$	−13.5168	+	9.93822i	−0.568656	+	0.418104i
$566$	−1.44015	+	0.385887i	−0.0605341	+	0.0162201i
$567$	22.1108			0.928566
$568$	−3.24645	+	0.869884i	−0.136218	+	0.0364995i
$569$	13.7741	+	23.8575i	0.577441	+	1.00016i	0.995772	+	0.0918621i	$0.0292819\pi$
$569$	13.7741	+	23.8575i	0.577441	+	1.00016i	−0.418331	+	0.908295i	$0.637385\pi$
$570$	−0.149716	−	0.119837i	−0.00627091	−	0.00501943i
$571$		−	4.72029i		−	0.197538i	−0.995110	−	0.0987690i	$-0.968510\pi$
$571$		−	4.72029i		−	0.197538i	0.995110	−	0.0987690i	$-0.0314905\pi$
$572$		0			0
$573$	−1.65043	−	1.65043i	−0.0689476	−	0.0689476i
$574$	0.606884	−	2.26492i	0.0253308	−	0.0945360i
$575$	−35.3311	+	18.5102i	−1.47341	+	0.771928i
$576$	18.9400	+	10.9350i	0.789168	+	0.455626i
$577$		−	6.73701i		−	0.280465i	−0.990119	−	0.140233i	$-0.955215\pi$
$577$		−	6.73701i		−	0.280465i	0.990119	−	0.140233i	$-0.0447851\pi$
$578$	−0.730170	+	1.26469i	−0.0303711	+	0.0526043i
$579$	0.106378	+	0.397008i	0.00442092	+	0.0164991i
$580$	7.38303	+	18.9120i	0.306564	+	0.785276i
$581$	4.41118	−	7.64038i	0.183006	−	0.316977i
$582$	0.137554	−	0.513359i	0.00570180	−	0.0212794i
$583$	−6.58884	+	3.80407i	−0.272882	+	0.157548i
$584$	−5.19417			−0.214936
$585$		0			0
$586$	−0.0918611			−0.00379475
$587$	4.49847	−	2.59719i	0.185672	−	0.107198i	−0.404283	−	0.914634i	$-0.632479\pi$
$587$	4.49847	−	2.59719i	0.185672	−	0.107198i	0.589955	+	0.807436i	$0.299146\pi$
$588$	−0.129894	+	0.484772i	−0.00535674	+	0.0199916i
$589$	−5.20218	+	9.01044i	−0.214352	+	0.371269i
$590$	−0.706152	−	0.309609i	−0.0290718	−	0.0127464i
$591$	−1.79091	−	6.68376i	−0.0736681	−	0.274933i
$592$	13.6589	−	23.6578i	0.561375	−	0.972331i
$593$		−	12.9267i		−	0.530836i	−0.964133	−	0.265418i	$-0.914490\pi$
$593$		−	12.9267i		−	0.530836i	0.964133	−	0.265418i	$-0.0855100\pi$
$594$	0.932726	+	0.538510i	0.0382702	+	0.0220953i
$595$	−1.66122	−	14.9868i	−0.0681033	−	0.614399i
$596$	−6.23060	+	23.2529i	−0.255215	+	0.952477i
$597$	−0.529553	−	0.529553i	−0.0216732	−	0.0216732i
$598$		0			0
$599$		−	16.7523i		−	0.684481i	−0.939612	−	0.342241i	$-0.888814\pi$
$599$		−	16.7523i		−	0.684481i	0.939612	−	0.342241i	$-0.111186\pi$
$600$	−0.796506	+	0.417294i	−0.0325172	+	0.0170360i
$601$	−6.28803	−	10.8912i	−0.256494	−	0.444261i	0.708806	−	0.705403i	$-0.249234\pi$
$601$	−6.28803	−	10.8912i	−0.256494	−	0.444261i	−0.965300	+	0.261142i	$0.915901\pi$
$602$	2.28020	−	0.610977i	0.0929340	−	0.0249016i
$603$	−10.4212			−0.424384
$604$	−5.06486	+	1.35713i	−0.206086	+	0.0552207i
$605$	−12.0361	−	1.83638i	−0.489337	−	0.0746593i
$606$	−0.0322160	−	0.0322160i	−0.00130868	−	0.00130868i
$607$	9.69731	+	36.1909i	0.393602	+	1.46894i	0.824149	+	0.566374i	$0.191654\pi$
$607$	9.69731	+	36.1909i	0.393602	+	1.46894i	−0.430547	+	0.902568i	$0.641679\pi$
$608$	2.85748	+	0.765660i	0.115886	+	0.0310516i
$609$	4.23072	+	1.13362i	0.171438	+	0.0459366i
$610$	−0.137044	−	0.351045i	−0.00554877	−	0.0142134i
$611$		0			0
$612$	−9.79548	+	9.79548i	−0.395959	+	0.395959i
$613$	−8.64732	−	14.9776i	−0.349262	−	0.604940i	0.636856	−	0.770982i	$-0.280234\pi$
$613$	−8.64732	−	14.9776i	−0.349262	−	0.604940i	−0.986119	+	0.166043i	$0.946901\pi$
$614$	−1.61524	+	0.932562i	−0.0651860	+	0.0376351i
$615$	−0.744678	+	4.88082i	−0.0300283	+	0.196814i
$616$	4.17079	−	4.17079i	0.168046	−	0.168046i
$617$	10.5136	+	6.07005i	0.423263	+	0.244371i	0.696472	−	0.717584i	$-0.254752\pi$
$617$	10.5136	+	6.07005i	0.423263	+	0.244371i	−0.273210	+	0.961955i	$0.588085\pi$
$618$	−0.331818	−	0.191575i	−0.0133477	−	0.00770628i
$619$	−2.99993	+	2.99993i	−0.120577	+	0.120577i	−0.764821	−	0.644243i	$-0.777172\pi$
$619$	−2.99993	+	2.99993i	−0.120577	+	0.120577i	0.644243	+	0.764821i	$0.277172\pi$
$620$	14.3869	+	19.5673i	0.577791	+	0.785843i
$621$	13.9739	−	8.06784i	0.560753	−	0.323751i
$622$	−1.41125	−	2.44435i	−0.0565858	−	0.0980095i
$623$	−12.2514	+	12.2514i	−0.490840	+	0.490840i
$624$		0			0
$625$	2.04819	−	24.9160i	0.0819276	−	0.996638i
$626$	−1.67938	−	0.449988i	−0.0671215	−	0.0179851i
$627$	−2.55849	−	0.685545i	−0.102176	−	0.0273780i
$628$	−7.48923	−	27.9502i	−0.298853	−	1.11533i
$629$	12.0180	+	12.0180i	0.479188	+	0.479188i
$630$	0.354936	−	2.32635i	0.0141410	−	0.0926839i
$631$	−20.9006	+	5.60031i	−0.832041	+	0.222945i	−0.649604	−	0.760273i	$-0.725065\pi$
$631$	−20.9006	+	5.60031i	−0.832041	+	0.222945i	−0.182437	+	0.983218i	$0.558399\pi$
$632$	−4.38008			−0.174230
$633$	−6.62791	+	1.77594i	−0.263436	+	0.0705874i
$634$	−1.13592	−	1.96748i	−0.0451133	−	0.0781385i
$635$	−4.07674	−	36.7786i	−0.161781	−	1.45951i
$636$			1.27926i			0.0507260i
$637$		0			0
$638$	−1.72409	−	1.72409i	−0.0682572	−	0.0682572i
$639$	−4.79356	+	17.8898i	−0.189630	+	0.707710i
$640$	5.74522	−	7.17766i	0.227100	−	0.283722i
$641$	−39.2467	−	22.6591i	−1.55015	−	0.894980i	−0.998129	−	0.0611509i	$-0.980523\pi$
$641$	−39.2467	−	22.6591i	−1.55015	−	0.894980i	−0.552022	−	0.833829i	$-0.686144\pi$
$642$		−	0.223769i		−	0.00883148i
$643$	15.8249	−	27.4095i	0.624072	−	1.08092i	−0.364647	−	0.931146i	$-0.618810\pi$
$643$	15.8249	−	27.4095i	0.624072	−	1.08092i	0.988719	−	0.149779i	$-0.0478562\pi$
$644$	−11.3862	−	42.4939i	−0.448679	−	1.67449i
$645$	−4.63028	+	1.80761i	−0.182317	+	0.0711747i
$646$	−0.302312	+	0.523619i	−0.0118943	+	0.0206015i
$647$	−9.83169	+	36.6924i	−0.386524	+	1.44253i	0.449227	+	0.893418i	$0.351699\pi$
$647$	−9.83169	+	36.6924i	−0.386524	+	1.44253i	−0.835751	+	0.549109i	$0.814967\pi$
$648$	−3.60026	+	2.07861i	−0.141431	+	0.0816555i
$649$	−10.6497			−0.418038
$650$		0			0
$651$	5.23971			0.205361
$652$	32.1023	−	18.5343i	1.25722	−	0.725858i
$653$	0.713775	−	2.66385i	0.0279322	−	0.104244i	−0.950552	−	0.310564i	$-0.899482\pi$
$653$	0.713775	−	2.66385i	0.0279322	−	0.104244i	0.978485	+	0.206320i	$0.0661487\pi$
$654$	0.207859	−	0.360022i	0.00812792	−	0.0140780i
$655$	−26.4287	+	10.3175i	−1.03265	+	0.403138i
$656$	−6.47571	−	24.1677i	−0.252834	−	0.943590i
$657$	−14.3114	+	24.7881i	−0.558342	+	0.967076i
$658$			0.187120i			0.00729470i
$659$	−1.80219	−	1.04050i	−0.0702034	−	0.0405320i	0.464487	−	0.885580i	$-0.346239\pi$
$659$	−1.80219	−	1.04050i	−0.0702034	−	0.0405320i	−0.534691	+	0.845048i	$0.679572\pi$
$660$	−3.86376	+	4.82711i	−0.150397	+	0.187895i
$661$	−9.72683	+	36.3010i	−0.378330	+	1.41195i	0.470089	+	0.882619i	$0.344222\pi$
$661$	−9.72683	+	36.3010i	−0.378330	+	1.41195i	−0.848418	+	0.529326i	$0.822445\pi$
$662$	−1.66840	−	1.66840i	−0.0648440	−	0.0648440i
$663$		0			0
$664$			1.65876i			0.0643723i
$665$	1.30138	+	11.7405i	0.0504655	+	0.455278i
$666$	1.32626	+	2.29714i	0.0513914	+	0.0890125i
$667$	−35.2843	+	9.45440i	−1.36621	+	0.366076i
$668$	−40.9991			−1.58630
$669$	4.45566	−	1.19389i	0.172266	−	0.0461585i
$670$	−0.160140	+	1.04960i	−0.00618675	+	0.0405497i
$671$	−3.68052	−	3.68052i	−0.142085	−	0.142085i
$672$	−0.385592	−	1.43905i	−0.0148745	−	0.0555125i
$673$	17.3908	+	4.65984i	0.670364	+	0.179624i	0.577919	−	0.816094i	$-0.303865\pi$
$673$	17.3908	+	4.65984i	0.670364	+	0.179624i	0.0924454	+	0.995718i	$0.470532\pi$
$674$	0.867519	+	0.232451i	0.0334156	+	0.00895368i
$675$	−0.414638	+	10.1050i	−0.0159594	+	0.388943i
$676$		0			0
$677$	15.4021	−	15.4021i	0.591952	−	0.591952i	−0.346206	−	0.938158i	$-0.612530\pi$
$677$	15.4021	−	15.4021i	0.591952	−	0.591952i	0.938158	+	0.346206i	$0.112530\pi$
$678$	−0.169396	−	0.293403i	−0.00650563	−	0.0112681i
$679$	−28.3508	+	16.3684i	−1.08801	+	0.628160i
$680$	1.67938	+	2.28410i	0.0644014	+	0.0875913i
$681$	−3.57007	+	3.57007i	−0.136805	+	0.136805i
$682$	−2.52605	−	1.45841i	−0.0967273	−	0.0558455i
$683$	5.34122	+	3.08376i	0.204376	+	0.117997i	0.598695	−	0.800977i	$-0.295686\pi$
$683$	5.34122	+	3.08376i	0.204376	+	0.117997i	−0.394319	+	0.918974i	$0.629019\pi$
$684$	7.67369	−	7.67369i	0.293411	−	0.293411i
$685$	5.04036	−	33.0359i	0.192582	−	1.26224i
$686$	1.98113	−	1.14381i	0.0756398	−	0.0436707i
$687$	0.645085	+	1.11732i	0.0246115	+	0.0426284i
$688$	17.8113	−	17.8113i	0.679050	−	0.679050i
$689$		0			0
$690$	−0.292911	−	0.750304i	−0.0111509	−	0.0285636i
$691$	−12.6830	−	3.39841i	−0.482486	−	0.129282i	0.00937405	−	0.999956i	$-0.497016\pi$
$691$	−12.6830	−	3.39841i	−0.482486	−	0.129282i	−0.491860	+	0.870674i	$0.663683\pi$
$692$	34.7534	+	9.31214i	1.32112	+	0.353994i
$693$	−8.41252	−	31.3960i	−0.319565	−	1.19263i
$694$	1.72710	+	1.72710i	0.0655600	+	0.0655600i
$695$	−18.9489	−	2.89107i	−0.718773	−	0.109665i
$696$	−0.795450	+	0.213140i	−0.0301515	+	0.00807906i
$697$	15.5666			0.589627
$698$	−0.319231	+	0.0855377i	−0.0120831	+	0.00323765i
$699$	−3.39126	−	5.87383i	−0.128269	−	0.222169i
$700$	26.3194	+	8.22263i	0.994780	+	0.310786i
$701$		−	23.2292i		−	0.877354i	−0.898645	−	0.438677i	$-0.855447\pi$
$701$		−	23.2292i		−	0.877354i	0.898645	−	0.438677i	$-0.144553\pi$
$702$		0			0
$703$	−9.41478	−	9.41478i	−0.355085	−	0.355085i
$704$	7.96543	−	29.7274i	0.300208	−	1.12039i
$705$	−0.0434078	−	0.391606i	−0.00163483	−	0.0147487i
$706$	3.72081	+	2.14821i	0.140034	+	0.0808490i
$707$			2.80636i			0.105544i
$708$	−0.895342	+	1.55078i	−0.0336490	+	0.0582818i
$709$	−0.537189	−	2.00482i	−0.0201746	−	0.0752925i	0.955105	−	0.296269i	$-0.0957424\pi$
$709$	−0.537189	−	2.00482i	−0.0201746	−	0.0752925i	−0.975279	+	0.220976i	$0.929076\pi$
$710$	1.72817	+	0.757707i	0.0648569	+	0.0284362i
$711$	−12.0684	+	20.9030i	−0.452599	+	0.783925i
$712$	0.843128	−	3.14660i	0.0315976	−	0.117924i
$713$	−37.8447	+	21.8496i	−1.41729	+	0.818275i
$714$	0.304493			0.0113954
$715$		0			0
$716$	−34.4251			−1.28653
$717$	4.29148	−	2.47769i	0.160268	−	0.0925309i
$718$	−0.0336269	+	0.125497i	−0.00125494	+	0.00468351i
$719$	3.36848	−	5.83438i	0.125623	−	0.217586i	−0.796353	−	0.604832i	$-0.793240\pi$
$719$	3.36848	−	5.83438i	0.125623	−	0.217586i	0.921976	+	0.387246i	$0.126574\pi$
$720$	−9.13165	−	23.3911i	−0.340316	−	0.871735i
$721$	6.10834	+	22.7966i	0.227486	+	0.848991i
$722$	−1.01055	+	1.75032i	−0.0376086	+	0.0651401i
$723$			2.78698i			0.103649i
$724$	−42.8050	−	24.7135i	−1.59083	−	0.918469i
$725$	6.82756	−	21.8540i	0.253569	−	0.811637i
$726$	0.0636349	−	0.237489i	0.00236171	−	0.00881403i
$727$	34.4733	+	34.4733i	1.27854	+	1.27854i	0.941483	+	0.337062i	$0.109433\pi$
$727$	34.4733	+	34.4733i	1.27854	+	1.27854i	0.337062	+	0.941483i	$0.390567\pi$
$728$		0			0
$729$			20.8218i			0.771179i
$730$	2.27669	+	1.82233i	0.0842641	+	0.0674475i
$731$	7.83580	+	13.5720i	0.289817	+	0.501979i
$732$	−0.845374	+	0.226517i	−0.0312459	+	0.00837232i
$733$	−28.7555			−1.06211			−0.531054	−	0.847338i	$-0.678204\pi$
$733$	−28.7555			−1.06211			−0.531054	+	0.847338i	$0.678204\pi$
$734$	−1.83565	+	0.491861i	−0.0677551	+	0.0181549i
$735$	0.456000	−	0.335273i	0.0168198	−	0.0123667i
$736$	8.78585	+	8.78585i	0.323851	+	0.323851i
$737$	3.79556	+	14.1652i	0.139811	+	0.521783i
$738$	2.34665	+	0.628783i	0.0863813	+	0.0231458i
$739$	−29.6373	−	7.94129i	−1.09023	−	0.292125i	−0.331447	−	0.943474i	$-0.607537\pi$
$739$	−29.6373	−	7.94129i	−1.09023	−	0.292125i	−0.758778	+	0.651349i	$0.774203\pi$
$740$	−28.9523	+	11.3027i	−1.06431	+	0.415494i
$741$		0			0
$742$	−0.484483	+	0.484483i	−0.0177859	+	0.0177859i
$743$	−26.4817	−	45.8676i	−0.971519	−	1.68272i	−0.690976	−	0.722878i	$-0.742819\pi$
$743$	−26.4817	−	45.8676i	−0.971519	−	1.68272i	−0.280543	−	0.959841i	$-0.590515\pi$
$744$	−0.853172	+	0.492579i	−0.0312788	+	0.0180588i
$745$	21.8728	−	16.0820i	0.801359	−	0.589198i
$746$	0.941490	−	0.941490i	0.0344704	−	0.0344704i
$747$	7.91608	+	4.57035i	0.289634	+	0.167220i
$748$	16.8824	+	9.74706i	0.617282	+	0.356388i
$749$	−9.74639	+	9.74639i	−0.356125	+	0.356125i
$750$	0.495526	+	0.0965407i	0.0180941	+	0.00352517i
$751$	40.3780	−	23.3123i	1.47341	−	0.850676i	0.473862	−	0.880599i	$-0.342860\pi$
$751$	40.3780	−	23.3123i	1.47341	−	0.850676i	0.999552	+	0.0299230i	$0.00952620\pi$
$752$	0.998326	+	1.72915i	0.0364052	+	0.0630557i
$753$	−1.13693	+	1.13693i	−0.0414321	+	0.0414321i
$754$		0			0
$755$	5.41574	+	2.37451i	0.197099	+	0.0864172i
$756$	−10.7747	−	2.88708i	−0.391873	−	0.105002i
$757$	1.20667	+	0.323327i	0.0438572	+	0.0117515i	0.280681	−	0.959801i	$-0.409440\pi$
$757$	1.20667	+	0.323327i	0.0438572	+	0.0117515i	−0.236824	+	0.971553i	$0.576106\pi$
$758$	0.0356995	+	0.133232i	0.00129666	+	0.00483922i
$759$	−7.86654	−	7.86654i	−0.285537	−	0.285537i
$760$	−1.31561	−	1.78934i	−0.0477223	−	0.0649063i
$761$	19.7156	−	5.28278i	0.714690	−	0.191501i	0.116889	−	0.993145i	$-0.462708\pi$
$761$	19.7156	−	5.28278i	0.714690	−	0.191501i	0.597801	+	0.801644i	$0.296041\pi$
$762$	0.747246			0.0270698
$763$	−24.7343	+	6.62754i	−0.895442	+	0.239933i
$764$	−6.72858	−	11.6542i	−0.243432	−	0.421636i
$765$	15.5276	−	1.72116i	0.561401	−	0.0622288i
$766$		−	1.57656i		−	0.0569633i
$767$		0			0
$768$	−3.55968	−	3.55968i	−0.128449	−	0.128449i
$769$	−9.55609	+	35.6638i	−0.344602	+	1.28607i	0.548476	+	0.836167i	$0.315208\pi$
$769$	−9.55609	+	35.6638i	−0.344602	+	1.28607i	−0.893077	+	0.449904i	$0.851458\pi$
$770$	−3.29141	+	0.364838i	−0.118614	+	0.0131479i
$771$	5.16879	+	2.98420i	0.186150	+	0.107473i
$772$			2.36972i			0.0852882i
$773$	−10.6918	+	18.5187i	−0.384557	+	0.666072i	−0.991708	−	0.128515i	$-0.958979\pi$
$773$	−10.6918	+	18.5187i	−0.384557	+	0.666072i	0.607151	+	0.794587i	$0.292312\pi$
$774$	0.633024	+	2.36248i	0.0227536	+	0.0849175i
$775$	1.12294	−	27.3669i	0.0403372	−	0.983047i
$776$	3.07754	−	5.33045i	0.110477	−	0.191352i
$777$	−1.73545	+	6.47681i	−0.0622591	+	0.232354i
$778$	0.838242	−	0.483959i	0.0300524	−	0.0173508i
$779$	−12.1947			−0.436921
$780$		0			0
$781$	26.0630			0.932608
$782$	−2.19925	+	1.26974i	−0.0786449	+	0.0454057i
$783$	−2.39725	+	8.94666i	−0.0856708	+	0.319728i
$784$	−1.43410	+	2.48393i	−0.0512179	+	0.0887120i
$785$	−13.1036	+	29.8865i	−0.467688	+	1.06670i
$786$	−0.148283	−	0.553399i	−0.00528907	−	0.0197391i
$787$	−19.6914	+	34.1065i	−0.701923	+	1.21577i	0.265867	+	0.964010i	$0.414342\pi$
$787$	−19.6914	+	34.1065i	−0.701923	+	1.21577i	−0.967790	+	0.251757i	$0.918992\pi$
$788$		−	39.8950i		−	1.42120i
$789$	0.721232	+	0.416404i	0.0256766	+	0.0148244i
$790$	1.91986	+	1.53672i	0.0683056	+	0.0546739i
$791$	−5.40118	+	20.1575i	−0.192044	+	0.716717i
$792$	4.32129	+	4.32129i	0.153550	+	0.153550i
$793$		0			0
$794$			0.795007i			0.0282138i
$795$	0.901539	−	1.12632i	0.0319743	−	0.0399464i
$796$	−2.15892	−	3.73936i	−0.0765209	−	0.132538i
$797$	37.8319	−	10.1370i	1.34007	−	0.359072i	0.483612	−	0.875282i	$-0.339324\pi$
$797$	37.8319	−	10.1370i	1.34007	−	0.359072i	0.856462	+	0.516210i	$0.172658\pi$
$798$	−0.238537			−0.00844411
$799$	−1.19991	+	0.321515i	−0.0424498	+	0.0113744i
$800$	−7.59875	+	1.70553i	−0.268656	+	0.0602996i
$801$	−12.6934	−	12.6934i	−0.448500	−	0.448500i
$802$	−0.0820546	−	0.306232i	−0.00289745	−	0.0108134i
$803$	38.9062	+	10.4249i	1.37297	+	0.367887i
$804$	2.38180	+	0.638201i	0.0839996	+	0.0225076i
$805$	−19.9220	+	45.4378i	−0.702158	+	1.60147i
$806$		0			0
$807$	−2.36658	+	2.36658i	−0.0833077	+	0.0833077i
$808$	−0.263823	−	0.456954i	−0.00928125	−	0.0160756i
$809$	−23.1644	+	13.3740i	−0.814416	+	0.470203i	−0.848487	−	0.529216i	$-0.822486\pi$
$809$	−23.1644	+	13.3740i	−0.814416	+	0.470203i	0.0340712	+	0.999419i	$0.489153\pi$
$810$	2.30731	+	0.352032i	0.0810708	+	0.0123691i
$811$	−7.93739	+	7.93739i	−0.278720	+	0.278720i	−0.832598	−	0.553878i	$-0.813147\pi$
$811$	−7.93739	+	7.93739i	−0.278720	+	0.278720i	0.553878	+	0.832598i	$0.313147\pi$
$812$	21.8697	+	12.6265i	0.767477	+	0.443103i
$813$	6.52757	+	3.76869i	0.228932	+	0.132174i
$814$	2.63940	−	2.63940i	0.0925109	−	0.0925109i
$815$	−41.3260	−	6.30520i	−1.44759	−	0.220862i
$816$	2.81378	−	1.62453i	0.0985019	−	0.0568701i
$817$	−6.13849	−	10.6322i	−0.214759	−	0.371973i
$818$	−1.86963	+	1.86963i	−0.0653700	+	0.0653700i
$819$		0			0
$820$	−11.4305	+	26.0706i	−0.399172	+	0.910425i
$821$	−26.0924	−	6.99144i	−0.910632	−	0.244003i	−0.227055	−	0.973882i	$-0.572910\pi$
$821$	−26.0924	−	6.99144i	−0.910632	−	0.244003i	−0.683577	+	0.729879i	$0.739576\pi$
$822$	0.651843	+	0.174661i	0.0227356	+	0.00609200i
$823$	2.42695	+	9.05749i	0.0845980	+	0.315724i	0.995238	−	0.0974771i	$-0.0310773\pi$
$823$	2.42695	+	9.05749i	0.0845980	+	0.315724i	−0.910640	+	0.413201i	$0.864411\pi$
$824$	−3.13769	−	3.13769i	−0.109307	−	0.109307i
$825$	6.80365	−	1.52707i	0.236873	−	0.0531658i
$826$	−0.926397	+	0.248227i	−0.0322335	+	0.00863693i
$827$	−45.0330			−1.56595			−0.782976	−	0.622052i	$-0.786299\pi$
$827$	−45.0330			−1.56595			−0.782976	+	0.622052i	$0.786299\pi$
$828$	44.0273	−	11.7971i	1.53005	−	0.409976i
$829$	21.0075	+	36.3861i	0.729622	+	1.26374i	0.957043	+	0.289946i	$0.0936372\pi$
$829$	21.0075	+	36.3861i	0.729622	+	1.26374i	−0.227421	+	0.973796i	$0.573029\pi$
$830$	0.581961	−	0.727061i	0.0202002	−	0.0252366i
$831$		−	6.20942i		−	0.215402i
$832$		0			0
$833$	−1.26182	−	1.26182i	−0.0437194	−	0.0437194i
$834$	0.100183	−	0.373887i	0.00346905	−	0.0129467i
$835$	36.0974	+	28.8935i	1.24920	+	0.999901i
$836$	−13.2255	−	7.63575i	−0.457414	−	0.264088i
$837$			11.0804i			0.382993i
$838$	1.97481	−	3.42047i	0.0682186	−	0.118158i
$839$	1.40586	+	5.24673i	0.0485356	+	0.181137i	0.985938	−	0.167110i	$-0.0534436\pi$
$839$	1.40586	+	5.24673i	0.0485356	+	0.181137i	−0.937403	+	0.348247i	$0.886777\pi$
$840$	−0.449122	+	1.02435i	−0.0154962	+	0.0353434i
$841$	−4.01574	+	6.95547i	−0.138474	+	0.239844i
$842$	0.444405	−	1.65854i	0.0153152	−	0.0571571i
$843$	−4.79053	+	2.76581i	−0.164994	+	0.0952596i
$844$	−39.5617			−1.36177
$845$		0			0
$846$	−0.193872			−0.00666546
$847$	−13.1156	+	7.57228i	−0.450657	+	0.260187i
$848$	−1.89222	+	7.06186i	−0.0649791	+	0.242505i
$849$	1.95249	−	3.38181i	0.0670093	−	0.116063i
$850$	0.0652568	−	1.59036i	0.00223829	−	0.0545488i
$851$	−14.4737	−	54.0166i	−0.496152	−	1.85167i
$852$	2.19117	−	3.79522i	0.0750682	−	0.130022i
$853$			23.0805i			0.790260i	0.918625	+	0.395130i	$0.129300\pi$
$853$			23.0805i			0.790260i	−0.918625	+	0.395130i	$0.870700\pi$
$854$	−0.405948	−	0.234374i	−0.0138912	−	0.00802012i
$855$	−12.1642	+	1.34834i	−0.416006	+	0.0461123i
$856$	0.670738	−	2.50323i	0.0229254	−	0.0855586i
$857$	37.6679	+	37.6679i	1.28671	+	1.28671i	0.936772	+	0.349940i	$0.113798\pi$
$857$	37.6679	+	37.6679i	1.28671	+	1.28671i	0.349940	+	0.936772i	$0.386202\pi$
$858$		0			0
$859$		−	5.08674i		−	0.173557i	−0.996228	−	0.0867787i	$-0.972343\pi$
$859$		−	5.08674i		−	0.173557i	0.996228	−	0.0867787i	$-0.0276573\pi$
$860$	−28.4839	+	3.15731i	−0.971294	+	0.107664i
$861$	3.07068	+	5.31857i	0.104648	+	0.181256i
$862$	0.800452	−	0.214481i	0.0272635	−	0.00730524i
$863$	45.1879			1.53821			0.769107	−	0.639120i	$-0.220701\pi$
$863$	45.1879			1.53821			0.769107	+	0.639120i	$0.220701\pi$
$864$	3.04314	−	0.815407i	0.103530	−	0.0277407i
$865$	−24.0358	−	32.6907i	−0.817242	−	1.11152i
$866$	−1.14100	−	1.14100i	−0.0387728	−	0.0387728i
$867$	−0.989932	−	3.69447i	−0.0336198	−	0.125471i
$868$	29.1805	+	7.81890i	0.990452	+	0.265391i
$869$	32.8084	+	8.79099i	1.11295	+	0.298214i
$870$	0.423437	+	0.185654i	0.0143559	+	0.00629427i
$871$		0			0
$872$	3.40439	−	3.40439i	0.115287	−	0.115287i
$873$	−16.9590	−	29.3738i	−0.573975	−	0.994154i
$874$	1.72287	−	0.994699i	0.0582769	−	0.0336462i
$875$	−17.3780	−	25.7878i	−0.587484	−	0.871785i
$876$	4.78896	−	4.78896i	0.161804	−	0.161804i
$877$	17.6048	+	10.1641i	0.594471	+	0.343218i	0.766863	−	0.641810i	$-0.221816\pi$
$877$	17.6048	+	10.1641i	0.594471	+	0.343218i	−0.172392	+	0.985028i	$0.555150\pi$
$878$	−3.91675	−	2.26134i	−0.132184	−	0.0763164i
$879$	0.170126	−	0.170126i	0.00573821	−	0.00573821i
$880$	−28.4690	+	20.9318i	−0.959690	+	0.705612i
$881$	28.5961	−	16.5100i	0.963428	−	0.556236i	0.0662019	−	0.997806i	$-0.478912\pi$
$881$	28.5961	−	16.5100i	0.963428	−	0.556236i	0.897227	+	0.441571i	$0.145579\pi$
$882$	−0.139249	−	0.241187i	−0.00468876	−	0.00812118i
$883$	15.9555	−	15.9555i	0.536944	−	0.536944i	−0.385686	−	0.922630i	$-0.626035\pi$
$883$	15.9555	−	15.9555i	0.536944	−	0.536944i	0.922630	+	0.385686i	$0.126035\pi$
$884$		0			0
$885$	1.88119	−	0.734395i	0.0632353	−	0.0246864i
$886$	−0.967576	−	0.259261i	−0.0325063	−	0.00871005i
$887$	0.609784	+	0.163391i	0.0204745	+	0.00548614i	0.269042	−	0.963129i	$-0.413293\pi$
$887$	0.609784	+	0.163391i	0.0204745	+	0.00548614i	−0.248567	+	0.968615i	$0.579960\pi$
$888$	−0.326296	−	1.21775i	−0.0109498	−	0.0408651i
$889$	−32.5466	−	32.5466i	−1.09158	−	1.09158i
$890$	−1.47351	+	1.08340i	−0.0493923	+	0.0363157i
$891$	31.1391	−	8.34370i	1.04320	−	0.279524i
$892$	26.5956			0.890488
$893$	0.939998	−	0.251872i	0.0314558	−	0.00842856i
$894$	0.274116	+	0.474784i	0.00916782	+	0.0158791i
$895$	30.3094	+	24.2605i	1.01313	+	0.810940i
$896$		−	11.4359i		−	0.382046i
$897$		0			0
$898$	2.89072	+	2.89072i	0.0964647	+	0.0964647i
$899$	6.49233	−	24.2297i	0.216531	−	0.808106i
$900$	−8.51934	+	27.2691i	−0.283978	+	0.908971i
$901$	−3.93920	−	2.27430i	−0.131234	−	0.0757679i
$902$		−	3.41875i		−	0.113832i
$903$	−3.09139	+	5.35444i	−0.102875	+	0.178185i
$904$	−1.01552	−	3.78996i	−0.0337755	−	0.126052i
$905$	20.2710	+	51.9250i	0.673830	+	1.72604i
$906$	−0.0597070	+	0.103416i	−0.00198363	+	0.00343575i
$907$	−10.1387	+	37.8383i	−0.336651	+	1.25640i	0.565417	+	0.824805i	$0.308715\pi$
$907$	−10.1387	+	37.8383i	−0.336651	+	1.25640i	−0.902068	+	0.431594i	$0.857951\pi$
$908$	−25.2095	+	14.5547i	−0.836607	+	0.483015i
$909$	−2.90763			−0.0964400
$910$		0			0
$911$	6.21630			0.205955			0.102978	−	0.994684i	$-0.467163\pi$
$911$	6.21630			0.205955			0.102978	+	0.994684i	$0.467163\pi$
$912$	−2.20429	+	1.27264i	−0.0729912	+	0.0421415i
$913$	3.32919	−	12.4247i	0.110180	−	0.411198i
$914$	0.204012	−	0.353358i	0.00674810	−	0.0116881i
$915$	0.903940	+	0.396328i	0.0298833	+	0.0131022i
$916$	1.92524	+	7.18510i	0.0636117	+	0.237402i
$917$	−17.6450	+	30.5621i	−0.582690	+	1.00925i
$918$			0.643907i			0.0212521i
$919$	19.9013	+	11.4900i	0.656485	+	0.379022i	0.790936	−	0.611899i	$-0.209594\pi$
$919$	19.9013	+	11.4900i	0.656485	+	0.379022i	−0.134452	+	0.990920i	$0.542927\pi$
$920$	−1.02769	−	9.27138i	−0.0338819	−	0.305668i
$921$	1.26432	−	4.71852i	0.0416609	−	0.155481i
$922$	1.55017	+	1.55017i	0.0510520	+	0.0510520i
$923$		0			0
$924$			7.69084i			0.253010i
$925$	33.4562	+	10.4523i	1.10003	+	0.343669i
$926$	1.02676	+	1.77840i	0.0337413	+	0.0584417i
$927$	−23.6192	+	6.32875i	−0.775757	+	0.207863i
$928$	−7.13229			−0.234129
$929$	−1.04756	+	0.280692i	−0.0343692	+	0.00920921i	−0.275963	−	0.961168i	$-0.588997\pi$
$929$	−1.04756	+	0.280692i	−0.0343692	+	0.00920921i	0.241593	+	0.970378i	$0.422330\pi$
$930$	0.546777	+	0.0834229i	0.0179295	+	0.00273554i
$931$	0.988497	+	0.988497i	0.0323967	+	0.0323967i
$932$	−10.1211	−	37.7726i	−0.331529	−	1.23728i
$933$	7.14054	+	1.91330i	0.233771	+	0.0626387i
$934$	2.70516	+	0.724846i	0.0885157	+	0.0237177i
$935$	−7.99493	−	20.4794i	−0.261462	−	0.669746i
$936$		0			0
$937$	−2.17699	+	2.17699i	−0.0711191	+	0.0711191i	−0.741772	−	0.670653i	$-0.766014\pi$
$937$	−2.17699	+	2.17699i	−0.0711191	+	0.0711191i	0.670653	+	0.741772i	$0.266014\pi$
$938$	0.660337	+	1.14374i	0.0215608	+	0.0373443i
$939$	3.94358	−	2.27682i	0.128694	−	0.0743014i
$940$	0.342627	−	2.24567i	0.0111753	−	0.0732457i
$941$	−22.9413	+	22.9413i	−0.747866	+	0.747866i	−0.974078	−	0.226212i	$-0.927366\pi$
$941$	−22.9413	+	22.9413i	−0.747866	+	0.747866i	0.226212	+	0.974078i	$0.427366\pi$
$942$	−0.570694	−	0.329490i	−0.0185942	−	0.0107354i
$943$	−44.3569	−	25.6095i	−1.44446	−	0.833959i
$944$	−7.23636	+	7.23636i	−0.235523	+	0.235523i
$945$	7.45192	+	10.1352i	0.242411	+	0.329699i
$946$	2.98069	−	1.72090i	0.0969107	−	0.0559514i
$947$	−13.6493	−	23.6413i	−0.443543	−	0.768239i	0.554406	−	0.832246i	$-0.312945\pi$
$947$	−13.6493	−	23.6413i	−0.443543	−	0.768239i	−0.997949	+	0.0640069i	$0.979612\pi$
$948$	4.03838	−	4.03838i	0.131161	−	0.131161i
$949$		0			0
$950$	−0.0511215	+	1.24587i	−0.00165860	+	0.0404214i
$951$	5.74748	+	1.54003i	0.186375	+	0.0499390i
$952$	3.40625	+	0.912703i	0.110397	+	0.0295809i
$953$	−1.65546	−	6.17827i	−0.0536257	−	0.200134i	0.933916	−	0.357493i	$-0.116369\pi$
$953$	−1.65546	−	6.17827i	−0.0536257	−	0.200134i	−0.987541	+	0.157360i	$0.949702\pi$
$954$	−0.501965	−	0.501965i	−0.0162517	−	0.0162517i
$955$	−2.28901	+	15.0028i	−0.0740705	+	0.485478i
$956$	27.5970	−	7.39460i	0.892551	−	0.239158i
$957$	6.38600			0.206430
$958$	5.40920	−	1.44939i	0.174763	−	0.0468277i
$959$	−20.7839	−	35.9988i	−0.671147	−	1.16246i
$960$	0.642947	+	5.80039i	0.0207510	+	0.187207i
$961$			0.991728i			0.0319912i
$962$		0			0
$963$	−10.0981	−	10.0981i	−0.325406	−	0.325406i
$964$	−4.15885	+	15.5210i	−0.133947	+	0.499899i
$965$	1.67002	−	2.08641i	0.0537600	−	0.0671638i
$966$	−0.867650	−	0.500938i	−0.0279162	−	0.0161174i
$967$			28.4424i			0.914647i	0.889300	+	0.457324i	$0.151192\pi$
$967$			28.4424i			0.914647i	−0.889300	+	0.457324i	$0.848808\pi$
$968$	1.42372	−	2.46596i	0.0457602	−	0.0792589i
$969$	−0.409860	−	1.52962i	−0.0131666	−	0.0491384i
$970$	−3.21908	+	1.25670i	−0.103358	+	0.0403501i
$971$	0.619921	−	1.07374i	0.0198942	−	0.0344578i	−0.855907	−	0.517130i	$-0.827000\pi$
$971$	0.619921	−	1.07374i	0.0198942	−	0.0344578i	0.875801	+	0.482672i	$0.160334\pi$
$972$	4.51696	−	16.8575i	0.144882	−	0.540705i
$973$	−20.6484	+	11.9213i	−0.661956	+	0.382180i
$974$	−1.99799			−0.0640197
$975$		0			0
$976$	−5.00174			−0.160102
$977$	32.9480	−	19.0226i	1.05410	−	0.608586i	0.130307	−	0.991474i	$-0.458404\pi$
$977$	32.9480	−	19.0226i	1.05410	−	0.608586i	0.923795	+	0.382888i	$0.125071\pi$
$978$	0.218491	−	0.815418i	0.00698656	−	0.0260742i
$979$	−12.6307	+	21.8770i	−0.403678	+	0.699192i
$980$	3.03982	−	1.18671i	0.0971035	−	0.0379082i
$981$	−6.86669	−	25.6268i	−0.219236	−	0.818202i
$982$	−1.83661	+	3.18111i	−0.0586087	+	0.101513i
$983$		−	34.5934i		−	1.10336i	−0.834056	−	0.551679i	$-0.813987\pi$
$983$		−	34.5934i		−	1.10336i	0.834056	−	0.551679i	$-0.186013\pi$
$984$	−0.999984	−	0.577341i	−0.0318783	−	0.0184050i
$985$	−28.1154	+	35.1254i	−0.895831	+	1.11919i
$986$	0.377285	−	1.40805i	0.0120152	−	0.0448414i
$987$	−0.346545	−	0.346545i	−0.0110307	−	0.0110307i
$988$		0			0
$989$		−	51.5644i		−	1.63965i
$990$	−0.378003	−	3.41018i	−0.0120137	−	0.108383i
$991$	−19.7486	−	34.2056i	−0.627335	−	1.08658i	−0.988084	−	0.153913i	$-0.950813\pi$
$991$	−19.7486	−	34.2056i	−0.627335	−	1.08658i	0.360750	−	0.932663i	$-0.382521\pi$
$992$	−8.24156	+	2.20832i	−0.261670	+	0.0701142i
$993$	6.17972			0.196107
$994$	2.26717	−	0.607486i	0.0719103	−	0.0192683i
$995$	−0.734446	+	4.81376i	−0.0232835	+	0.152606i
$996$	−1.52936	−	1.52936i	−0.0484595	−	0.0484595i
$997$	1.90378	+	7.10500i	0.0602933	+	0.225018i	0.989498	−	0.144549i	$-0.0461730\pi$
$997$	1.90378	+	7.10500i	0.0602933	+	0.225018i	−0.929204	+	0.369566i	$0.879506\pi$
$998$	−0.300395	−	0.0804906i	−0.00950884	−	0.00254789i
$999$	−13.6964	−	3.66995i	−0.433336	−	0.116112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.t.f.418.3		20
5.2	odd	4		845.2.o.e.587.3		20
13.2	odd	12		845.2.k.d.268.7		20
13.3	even	3		845.2.f.e.408.7		20
13.4	even	6		845.2.t.g.188.3		20
13.5	odd	4		845.2.o.g.258.3		20
13.6	odd	12		845.2.o.f.488.3		20
13.7	odd	12		845.2.o.e.488.3		20
13.8	odd	4		65.2.o.a.63.3	yes	20
13.9	even	3		65.2.t.a.58.3	yes	20
13.10	even	6		845.2.f.d.408.4		20
13.11	odd	12		845.2.k.e.268.4		20
13.12	even	2		845.2.t.e.418.3		20
39.8	even	4		585.2.cf.a.388.3		20
39.35	odd	6		585.2.dp.a.253.3		20
65.2	even	12		845.2.f.d.437.7		20
65.7	even	12	inner	845.2.t.f.657.3		20
65.8	even	4		325.2.x.b.232.3		20
65.9	even	6		325.2.x.b.318.3		20
65.12	odd	4		845.2.o.f.587.3		20
65.17	odd	12		845.2.o.g.357.3		20
65.22	odd	12		65.2.o.a.32.3	✓	20
65.32	even	12		845.2.t.e.657.3		20
65.34	odd	4		325.2.s.b.193.3		20
65.37	even	12		845.2.f.e.437.4		20
65.42	odd	12		845.2.k.e.577.4		20
65.47	even	4		65.2.t.a.37.3	yes	20
65.48	odd	12		325.2.s.b.32.3		20
65.57	even	4		845.2.t.g.427.3		20
65.62	odd	12		845.2.k.d.577.7		20
195.47	odd	4		585.2.dp.a.37.3		20
195.152	even	12		585.2.cf.a.487.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.3	✓	20	65.22	odd	12
65.2.o.a.63.3	yes	20	13.8	odd	4
65.2.t.a.37.3	yes	20	65.47	even	4
65.2.t.a.58.3	yes	20	13.9	even	3
325.2.s.b.32.3		20	65.48	odd	12
325.2.s.b.193.3		20	65.34	odd	4
325.2.x.b.232.3		20	65.8	even	4
325.2.x.b.318.3		20	65.9	even	6
585.2.cf.a.388.3		20	39.8	even	4
585.2.cf.a.487.3		20	195.152	even	12
585.2.dp.a.37.3		20	195.47	odd	4
585.2.dp.a.253.3		20	39.35	odd	6
845.2.f.d.408.4		20	13.10	even	6
845.2.f.d.437.7		20	65.2	even	12
845.2.f.e.408.7		20	13.3	even	3
845.2.f.e.437.4		20	65.37	even	12
845.2.k.d.268.7		20	13.2	odd	12
845.2.k.d.577.7		20	65.62	odd	12
845.2.k.e.268.4		20	13.11	odd	12
845.2.k.e.577.4		20	65.42	odd	12
845.2.o.e.488.3		20	13.7	odd	12
845.2.o.e.587.3		20	5.2	odd	4
845.2.o.f.488.3		20	13.6	odd	12
845.2.o.f.587.3		20	65.12	odd	4
845.2.o.g.258.3		20	13.5	odd	4
845.2.o.g.357.3		20	65.17	odd	12
845.2.t.e.418.3		20	13.12	even	2
845.2.t.e.657.3		20	65.32	even	12
845.2.t.f.418.3		20	1.1	even	1	trivial
845.2.t.f.657.3		20	65.7	even	12	inner
845.2.t.g.188.3		20	13.4	even	6
845.2.t.g.427.3		20	65.57	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.113711 - 0.0656513i) q^{2} +(-0.0890070 + 0.332179i) q^{3} +(-0.991380 + 1.71712i) q^{4} +(2.08297 - 0.813169i) q^{5} +(0.0116869 + 0.0436159i) q^{6} +(1.39069 - 2.40874i) q^{7} +0.522947i q^{8} +(2.49566 + 1.44087i) q^{9} +(0.183472 - 0.229216i) q^{10} +(1.04957 - 3.91706i) q^{11} +(-0.482151 - 0.482151i) q^{12} -0.365201i q^{14} +(0.0847187 + 0.764295i) q^{15} +(-1.94843 - 3.37478i) q^{16} +(2.34186 - 0.627499i) q^{17} +0.378379 q^{18} +(-1.83459 + 0.491577i) q^{19} +(-0.668703 + 4.38287i) q^{20} +(0.676351 + 0.676351i) q^{21} +(-0.137812 - 0.514321i) q^{22} +(-7.70544 - 2.06467i) q^{23} +(-0.173712 - 0.0465459i) q^{24} +(3.67751 - 3.38761i) q^{25} +(-1.43027 + 1.43027i) q^{27} +(2.75740 + 4.77595i) q^{28} +(3.96565 - 2.28957i) q^{29} +(0.0598105 + 0.0813472i) q^{30} +(3.87352 - 3.87352i) q^{31} +(-1.34889 - 0.778780i) q^{32} +(1.20775 + 0.697292i) q^{33} +(0.225100 - 0.225100i) q^{34} +(0.938043 - 6.14819i) q^{35} +(-4.94829 + 2.85689i) q^{36} +(3.50510 + 6.07101i) q^{37} +(-0.176341 + 0.176341i) q^{38} +(0.425244 + 1.08928i) q^{40} +(6.20184 + 1.66178i) q^{41} +(0.121312 + 0.0325055i) q^{42} +(1.67299 + 6.24368i) q^{43} +(5.68554 + 5.68554i) q^{44} +(6.37004 + 0.971891i) q^{45} +(-1.01174 + 0.271096i) q^{46} -0.512375 q^{47} +(1.29445 - 0.346847i) q^{48} +(-0.368015 - 0.637420i) q^{49} +(0.195774 - 0.626643i) q^{50} +0.833767i q^{51} +(-1.32662 - 1.32662i) q^{53} +(-0.0687390 + 0.256537i) q^{54} +(-0.999006 - 9.01260i) q^{55} +(1.25964 + 0.727255i) q^{56} -0.653165i q^{57} +(0.300626 - 0.520700i) q^{58} +(-0.679700 - 2.53667i) q^{59} +(-1.39638 - 0.612235i) q^{60} +(0.641767 - 1.11157i) q^{61} +(0.186162 - 0.694764i) q^{62} +(6.94135 - 4.00759i) q^{63} +7.58920 q^{64} +0.183113 q^{66} +(-3.13180 + 1.80814i) q^{67} +(-1.24418 + 4.64334i) q^{68} +(1.37168 - 2.37581i) q^{69} +(-0.296970 - 0.760703i) q^{70} +(1.66343 + 6.20800i) q^{71} +(-0.753497 + 1.30509i) q^{72} +9.93250i q^{73} +(0.797139 + 0.460228i) q^{74} +(0.797968 + 1.52311i) q^{75} +(0.974678 - 3.63755i) q^{76} +(-7.97556 - 7.97556i) q^{77} +8.37577i q^{79} +(-6.80278 - 5.44515i) q^{80} +(3.97480 + 6.88456i) q^{81} +(0.814318 - 0.218196i) q^{82} +3.17194 q^{83} +(-1.83190 + 0.490855i) q^{84} +(4.36775 - 3.21139i) q^{85} +(0.600143 + 0.600143i) q^{86} +(0.407576 + 1.52109i) q^{87} +(2.04842 + 0.548871i) q^{88} +(-6.01705 - 1.61226i) q^{89} +(0.788152 - 0.307686i) q^{90} +(11.1843 - 11.1843i) q^{92} +(0.941930 + 1.63147i) q^{93} +(-0.0582629 + 0.0336381i) q^{94} +(-3.42165 + 2.51577i) q^{95} +(0.378755 - 0.378755i) q^{96} +(-10.1931 - 5.88500i) q^{97} +(-0.0836950 - 0.0483213i) q^{98} +(8.26335 - 8.26335i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 4 q^{6} - 2 q^{7} - 12 q^{9} + 10 q^{10} + 8 q^{11} - 24 q^{12} - 8 q^{15} - 2 q^{16} + 10 q^{17} + 16 q^{19} + 12 q^{20} + 4 q^{21} + 16 q^{22} + 2 q^{23} - 28 q^{24}+ \cdots + 60 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 4 * q^6 - 2 * q^7 - 12 * q^9 + 10 * q^10 + 8 * q^11 - 24 * q^12 - 8 * q^15 - 2 * q^16 + 10 * q^17 + 16 * q^19 + 12 * q^20 + 4 * q^21 + 16 * q^22 + 2 * q^23 - 28 * q^24 + 18 * q^25 + 4 * q^27 + 18 * q^28 - 14 * q^30 - 48 * q^32 - 18 * q^33 + 2 * q^34 - 20 * q^35 - 36 * q^36 - 4 * q^37 - 8 * q^38 - 16 * q^40 + 28 * q^41 - 56 * q^42 + 22 * q^43 - 36 * q^44 + 6 * q^45 - 8 * q^46 - 40 * q^47 + 28 * q^48 + 18 * q^49 - 78 * q^50 - 10 * q^53 + 12 * q^54 + 26 * q^55 + 8 * q^59 + 28 * q^60 - 16 * q^61 + 40 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 + 28 * q^68 - 16 * q^69 - 12 * q^70 + 56 * q^71 + 4 * q^72 - 18 * q^74 + 34 * q^75 + 80 * q^76 - 28 * q^77 - 110 * q^80 - 14 * q^81 - 22 * q^82 + 48 * q^83 + 32 * q^84 + 28 * q^85 + 60 * q^86 + 62 * q^87 - 50 * q^88 - 6 * q^89 + 46 * q^90 - 8 * q^92 + 32 * q^93 + 48 * q^94 - 14 * q^95 + 56 * q^96 - 66 * q^97 + 30 * q^98 + 60 * q^99

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