LMFDB - Embedded newform 845.2.t.g.188.3

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			188.3
Root			$0.131303i$ of defining polynomial
Character	$\chi$	$=$	845.188
Dual form			845.2.t.g.427.3

$q$-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} +(0.332179 - 0.0890070i) q^{3} +(-0.991380 - 1.71712i) q^{4} +(-2.08297 + 0.813169i) q^{5} +(0.0436159 + 0.0116869i) q^{6} +(-1.39069 - 2.40874i) q^{7} -0.522947i q^{8} +(-2.49566 + 1.44087i) q^{9} +(-0.290243 - 0.0442830i) q^{10} +(3.91706 - 1.04957i) q^{11} +(-0.482151 - 0.482151i) q^{12} -0.365201i q^{14} +(-0.619540 + 0.455516i) q^{15} +(-1.94843 + 3.37478i) q^{16} +(-0.627499 + 2.34186i) q^{17} -0.378379 q^{18} +(-0.491577 + 1.83459i) q^{19} +(3.46132 + 2.77055i) q^{20} +(-0.676351 - 0.676351i) q^{21} +(0.514321 + 0.137812i) q^{22} +(2.06467 + 7.70544i) q^{23} +(-0.0465459 - 0.173712i) 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} +(-0.100354 + 0.0111238i) 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} +(4.85547 + 3.88646i) 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} +(1.66178 + 6.20184i) q^{41} +(-0.0325055 - 0.121312i) q^{42} +(-6.24368 - 1.67299i) q^{43} +(-5.68554 - 5.68554i) q^{44} +(4.02670 - 5.03067i) q^{45} +(-0.271096 + 1.01174i) q^{46} +0.512375 q^{47} +(-0.346847 + 1.29445i) q^{48} +(-0.368015 + 0.637420i) q^{49} +(0.640576 - 0.143776i) q^{50} +0.833767i q^{51} +(-1.32662 - 1.32662i) q^{53} +(-0.256537 + 0.0687390i) q^{54} +(-7.30564 + 5.37147i) q^{55} +(-1.25964 + 0.727255i) q^{56} +0.653165i q^{57} +(-0.300626 - 0.520700i) q^{58} +(-2.53667 - 0.679700i) q^{59} +(1.39638 + 0.612235i) q^{60} +(0.641767 + 1.11157i) q^{61} +(-0.694764 + 0.186162i) q^{62} +(6.94135 + 4.00759i) q^{63} +7.58920 q^{64} +0.183113 q^{66} +(-3.13180 - 1.80814i) q^{67} +(4.64334 - 1.24418i) q^{68} +(1.37168 + 2.37581i) q^{69} +(0.296970 + 0.760703i) q^{70} +(6.20800 + 1.66343i) q^{71} +(0.753497 + 1.30509i) q^{72} -9.93250i q^{73} +(-0.797139 + 0.460228i) q^{74} +(0.920070 - 1.45262i) q^{75} +(3.63755 - 0.974678i) q^{76} +(-7.97556 - 7.97556i) q^{77} +8.37577i q^{79} +(1.31425 - 8.61395i) q^{80} +(3.97480 - 6.88456i) q^{81} +(-0.218196 + 0.814318i) q^{82} -3.17194 q^{83} +(-0.490855 + 1.83190i) q^{84} +(-0.597266 - 5.38828i) q^{85} +(-0.600143 - 0.600143i) q^{86} +(-1.52109 - 0.407576i) q^{87} +(-0.548871 - 2.04842i) q^{88} +(-1.61226 - 6.01705i) 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} +(-0.467892 - 4.22112i) 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} + 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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

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	0.539664	−	0.841881i	$-0.318551\pi$
$2$	0.113711	+	0.0656513i	0.0804061	+	0.0464225i	−0.459258	+	0.888303i	$0.651885\pi$
$3$	0.332179	−	0.0890070i	0.191783	−	0.0513882i	−0.161649	−	0.986848i	$-0.551681\pi$
$3$	0.332179	−	0.0890070i	0.191783	−	0.0513882i	0.353432	+	0.935460i	$0.385015\pi$
$4$	−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
$6$	0.0436159	+	0.0116869i	0.0178061	+	0.00477114i
$7$	−1.39069	−	2.40874i	−0.525630	−	0.910418i	−0.999554	−	0.0298522i	$-0.990496\pi$
$7$	−1.39069	−	2.40874i	−0.525630	−	0.910418i	0.473924	−	0.880566i	$-0.342837\pi$
$8$		−	0.522947i		−	0.184890i
$9$	−2.49566	+	1.44087i	−0.831885	+	0.480289i
$10$	−0.290243	−	0.0442830i	−0.0917828	−	0.0140035i
$11$	3.91706	−	1.04957i	1.18104	−	0.316459i	0.385701	−	0.922624i	$-0.373960\pi$
$11$	3.91706	−	1.04957i	1.18104	−	0.316459i	0.795339	+	0.606165i	$0.207293\pi$
$12$	−0.482151	−	0.482151i	−0.139185	−	0.139185i
$13$		0			0
$13$		0			0
$14$		−	0.365201i		−	0.0976042i
$15$	−0.619540	+	0.455516i	−0.159965	+	0.117614i
$16$	−1.94843	+	3.37478i	−0.487107	+	0.843694i
$17$	−0.627499	+	2.34186i	−0.152191	+	0.567984i	0.847139	+	0.531372i	$0.178323\pi$
$17$	−0.627499	+	2.34186i	−0.152191	+	0.567984i	−0.999330	+	0.0366120i	$0.988343\pi$
$18$	−0.378379			−0.0891849
$19$	−0.491577	+	1.83459i	−0.112775	+	0.420883i	−0.999111	−	0.0421602i	$-0.986576\pi$
$19$	−0.491577	+	1.83459i	−0.112775	+	0.420883i	0.886335	+	0.463044i	$0.153243\pi$
$20$	3.46132	+	2.77055i	0.773975	+	0.619513i
$21$	−0.676351	−	0.676351i	−0.147592	−	0.147592i
$22$	0.514321	+	0.137812i	0.109654	+	0.0293816i
$23$	2.06467	+	7.70544i	0.430513	+	1.60670i	0.751582	+	0.659640i	$0.229291\pi$
$23$	2.06467	+	7.70544i	0.430513	+	1.60670i	−0.321069	+	0.947056i	$0.604042\pi$
$24$	−0.0465459	−	0.173712i	−0.00950115	−	0.0354588i
$25$	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	$-0.473116\pi$
$29$	−3.96565	−	2.28957i	−0.736403	−	0.425162i	−0.820760	+	0.571273i	$0.806450\pi$
$30$	−0.100354	+	0.0111238i	−0.0183220	+	0.00203092i
$31$	−3.87352	+	3.87352i	−0.695704	+	0.695704i	−0.963481	−	0.267777i	$-0.913711\pi$
$31$	−3.87352	+	3.87352i	−0.695704	+	0.695704i	0.267777	+	0.963481i	$0.413711\pi$
$32$	−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
$35$	4.85547	+	3.88646i	0.820724	+	0.656932i
$36$	4.94829	+	2.85689i	0.824714	+	0.476149i
$37$	−3.50510	+	6.07101i	−0.576234	+	0.998067i	0.419672	+	0.907676i	$0.362145\pi$
$37$	−3.50510	+	6.07101i	−0.576234	+	0.998067i	−0.995906	+	0.0903914i	$0.971188\pi$
$38$	−0.176341	+	0.176341i	−0.0286063	+	0.0286063i
$39$		0			0
$40$	0.425244	+	1.08928i	0.0672370	+	0.172230i
$41$	1.66178	+	6.20184i	0.259526	+	0.968565i	0.965516	+	0.260343i	$0.0838357\pi$
$41$	1.66178	+	6.20184i	0.259526	+	0.968565i	−0.705990	+	0.708222i	$0.749498\pi$
$42$	−0.0325055	−	0.121312i	−0.00501570	−	0.0187189i
$43$	−6.24368	−	1.67299i	−0.952152	−	0.255128i	−0.250877	−	0.968019i	$-0.580719\pi$
$43$	−6.24368	−	1.67299i	−0.952152	−	0.255128i	−0.701275	+	0.712891i	$0.747386\pi$
$44$	−5.68554	−	5.68554i	−0.857128	−	0.857128i
$45$	4.02670	−	5.03067i	0.600265	−	0.749928i
$46$	−0.271096	+	1.01174i	−0.0399709	+	0.149174i
$47$	0.512375			0.0747376			0.0373688	−	0.999302i	$-0.488102\pi$
$47$	0.512375			0.0747376			0.0373688	+	0.999302i	$0.488102\pi$
$48$	−0.346847	+	1.29445i	−0.0500631	+	0.186838i
$49$	−0.368015	+	0.637420i	−0.0525736	+	0.0910601i
$50$	0.640576	−	0.143776i	0.0905911	−	0.0203331i
$51$			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	$0.791129\pi$
$54$	−0.256537	+	0.0687390i	−0.0349103	+	0.00935419i
$55$	−7.30564	+	5.37147i	−0.985092	+	0.724288i
$56$	−1.25964	+	0.727255i	−0.168327	+	0.0971835i
$57$			0.653165i			0.0865138i
$58$	−0.300626	−	0.520700i	−0.0394742	−	0.0683713i
$59$	−2.53667	−	0.679700i	−0.330247	−	0.0884894i	0.0898858	−	0.995952i	$-0.471350\pi$
$59$	−2.53667	−	0.679700i	−0.330247	−	0.0884894i	−0.420133	+	0.907463i	$0.638016\pi$
$60$	1.39638	+	0.612235i	0.180271	+	0.0790392i
$61$	0.641767	+	1.11157i	0.0821698	+	0.142322i	0.904182	−	0.427148i	$-0.140482\pi$
$61$	0.641767	+	1.11157i	0.0821698	+	0.142322i	−0.822012	+	0.569470i	$0.807148\pi$
$62$	−0.694764	+	0.186162i	−0.0882352	+	0.0236425i
$63$	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	0.296343	−	0.955082i	$-0.404233\pi$
$67$	−3.13180	−	1.80814i	−0.382610	−	0.220900i	−0.678953	+	0.734181i	$0.737566\pi$
$68$	4.64334	−	1.24418i	0.563088	−	0.150879i
$69$	1.37168	+	2.37581i	0.165130	+	0.286014i
$70$	0.296970	+	0.760703i	0.0354948	+	0.0909214i
$71$	6.20800	+	1.66343i	0.736754	+	0.197413i	0.607635	−	0.794216i	$-0.292118\pi$
$71$	6.20800	+	1.66343i	0.736754	+	0.197413i	0.129119	+	0.991629i	$0.458785\pi$
$72$	0.753497	+	1.30509i	0.0888005	+	0.153807i
$73$		−	9.93250i		−	1.16251i	−0.813721	−	0.581256i	$-0.802562\pi$
$73$		−	9.93250i		−	1.16251i	0.813721	−	0.581256i	$-0.197438\pi$
$74$	−0.797139	+	0.460228i	−0.0926655	+	0.0535005i
$75$	0.920070	−	1.45262i	0.106241	−	0.167734i
$76$	3.63755	−	0.974678i	0.417255	−	0.111803i
$77$	−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	$0.843831\pi$
$80$	1.31425	−	8.61395i	0.146938	−	0.963069i
$81$	3.97480	−	6.88456i	0.441645	−	0.764951i
$82$	−0.218196	+	0.814318i	−0.0240957	+	0.0899264i
$83$	−3.17194			−0.348166			−0.174083	−	0.984731i	$-0.555696\pi$
$83$	−3.17194			−0.348166			−0.174083	+	0.984731i	$0.555696\pi$
$84$	−0.490855	+	1.83190i	−0.0535567	+	0.199876i
$85$	−0.597266	−	5.38828i	−0.0647826	−	0.584441i
$86$	−0.600143	−	0.600143i	−0.0647151	−	0.0647151i
$87$	−1.52109	−	0.407576i	−0.163078	−	0.0436967i
$88$	−0.548871	−	2.04842i	−0.0585099	−	0.218362i
$89$	−1.61226	−	6.01705i	−0.170900	−	0.637806i	−0.997214	−	0.0745967i	$-0.976233\pi$
$89$	−1.61226	−	6.01705i	−0.170900	−	0.637806i	0.826314	−	0.563210i	$-0.190434\pi$
$90$	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
$95$	−0.467892	−	4.22112i	−0.0480048	−	0.433078i
$96$	−0.378755	+	0.378755i	−0.0386565	+	0.0386565i
$97$	−10.1931	+	5.88500i	−1.03495	+	0.597531i	−0.918400	−	0.395654i	$-0.870518\pi$
$97$	−10.1931	+	5.88500i	−1.03495	+	0.597531i	−0.116554	+	0.993184i	$0.537185\pi$
$98$	−0.0836950	+	0.0483213i	−0.00845447	+	0.00488119i
$99$	−8.26335	+	8.26335i	−0.830498	+	0.830498i
$100$	−9.46275	−	2.95632i	−0.946275	−	0.295632i
$101$	0.873807	+	0.504493i	0.0869471	+	0.0501989i	0.542843	−	0.839834i	$-0.317348\pi$
$101$	0.873807	+	0.504493i	0.0869471	+	0.0501989i	−0.455896	+	0.890033i	$0.650681\pi$
$102$	−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
$106$	−0.0637574	−	0.237946i	−0.00619267	−	0.0231113i
$107$	1.28261	+	4.78678i	0.123995	+	0.462755i	0.999802	−	0.0199063i	$-0.00633678\pi$
$107$	1.28261	+	4.78678i	0.123995	+	0.462755i	−0.875807	+	0.482662i	$0.839670\pi$
$108$	3.87389	+	1.03801i	0.372765	+	0.0998821i
$109$	6.51002	+	6.51002i	0.623546	+	0.623546i	0.946436	−	0.322890i	$-0.104654\pi$
$109$	6.51002	+	6.51002i	0.623546	+	0.623546i	−0.322890	+	0.946436i	$0.604654\pi$
$110$	−1.18338	+	0.131172i	−0.112831	+	0.0125068i
$111$	−0.623956	+	2.32864i	−0.0592233	+	0.221024i
$112$	10.8386			1.02415
$113$	1.94191	−	7.24731i	0.182680	−	0.681769i	−0.812436	−	0.583051i	$-0.801859\pi$
$113$	1.94191	−	7.24731i	0.182680	−	0.681769i	0.995115	−	0.0987188i	$-0.0314744\pi$
$114$	−0.0428811	+	0.0742723i	−0.00401619	+	0.00695624i
$115$	−10.5665	−	14.3713i	−0.985327	−	1.34013i
$116$			9.07933i			0.842995i
$117$		0			0
$118$	−0.243826	−	0.243826i	−0.0224460	−	0.0224460i
$119$	6.51358	−	1.74531i	0.597099	−	0.159992i
$120$	0.238211	+	0.323986i	0.0217456	+	0.0295758i
$121$	4.71551	−	2.72250i	0.428683	−	0.247500i
$122$			0.168531i			0.0152581i
$123$	1.10402	+	1.91221i	0.0995457	+	0.172418i
$124$	10.4914	+	2.81117i	0.942157	+	0.252450i
$125$	−4.90544	+	10.0467i	−0.438756	+	0.898606i
$126$	0.526207	+	0.911417i	0.0468782	+	0.0811955i
$127$	−15.9847	+	4.28310i	−1.41842	+	0.380064i	−0.884922	−	0.465739i	$-0.845788\pi$
$127$	−15.9847	+	4.28310i	−1.41842	+	0.380064i	−0.533495	+	0.845803i	$0.679122\pi$
$128$	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
$133$	5.10267	−	1.36726i	0.442458	−	0.118556i
$134$	−0.237414	−	0.411213i	−0.0205095	−	0.0355234i
$135$	1.81616	−	4.14226i	0.156310	−	0.356509i
$136$	1.22467	+	0.328148i	0.105014	+	0.0281385i
$137$	−7.47254	−	12.9428i	−0.638422	−	1.10578i	−0.985779	−	0.168046i	$-0.946254\pi$
$137$	−7.47254	−	12.9428i	−0.638422	−	1.10578i	0.347357	−	0.937733i	$-0.387079\pi$
$138$			0.360209i			0.0306631i
$139$	7.42380	−	4.28613i	0.629679	−	0.363545i	−0.150949	−	0.988542i	$-0.548233\pi$
$139$	7.42380	−	4.28613i	0.629679	−	0.363545i	0.780628	+	0.624996i	$0.214900\pi$
$140$	1.85991	−	12.1904i	0.157191	−	1.03028i
$141$	0.170200	−	0.0456050i	0.0143334	−	0.00384063i
$142$	0.596714	+	0.596714i	0.0500751	+	0.0500751i
$143$		0			0
$144$		−	11.2297i		−	0.935809i
$145$	10.1221	+	1.54436i	0.840597	+	0.128252i
$146$	0.652082	−	1.12944i	0.0539666	−	0.0934730i
$147$	−0.0655118	+	0.244493i	−0.00540332	+	0.0201655i
$148$	13.8995			1.14253
$149$	3.14239	−	11.7276i	0.257435	−	0.960759i	−0.709285	−	0.704922i	$-0.750982\pi$
$149$	3.14239	−	11.7276i	0.257435	−	0.960759i	0.966720	−	0.255837i	$-0.0823511\pi$
$150$	0.199989	−	0.104775i	0.0163290	−	0.00855486i
$151$	−1.86999	−	1.86999i	−0.152177	−	0.152177i	0.626912	−	0.779090i	$-0.284318\pi$
$151$	−1.86999	−	1.86999i	−0.152177	−	0.152177i	−0.779090	+	0.626912i	$0.784318\pi$
$152$	0.959392	+	0.257068i	0.0778170	+	0.0208510i
$153$	−1.80829	−	6.74861i	−0.146191	−	0.545593i
$154$	−0.383306	−	1.43052i	−0.0308877	−	0.115274i
$155$	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
$160$	2.17641	−	2.71905i	0.172060	−	0.214960i
$161$	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	−0.974639	−	0.223784i	$-0.928159\pi$
$163$	−16.1907	+	9.34772i	−1.26815	+	0.732170i	−0.293516	+	0.955954i	$0.594826\pi$
$164$	9.00186	−	9.00186i	0.702927	−	0.702927i
$165$	−1.94868	+	2.43454i	−0.151704	+	0.189529i
$166$	−0.360686	−	0.208242i	−0.0279947	−	0.0161627i
$167$	−10.3389	+	17.9075i	−0.800049	+	1.38572i	0.119535	+	0.992830i	$0.461860\pi$
$167$	−10.3389	+	17.9075i	−0.800049	+	1.38572i	−0.919583	+	0.392895i	$0.871474\pi$
$168$	−0.353695	+	0.353695i	−0.0272882	+	0.0272882i
$169$		0			0
$170$	0.285831	−	0.651920i	0.0219223	−	0.0500000i
$171$	−1.41659	−	5.28680i	−0.108330	−	0.404292i
$172$	3.31713	+	12.3797i	0.252929	+	0.943944i
$173$	17.5278	+	4.69655i	1.33261	+	0.357072i	0.853688	−	0.520784i	$-0.174360\pi$
$173$	17.5278	+	4.69655i	1.33261	+	0.357072i	0.478924	+	0.877856i	$0.341027\pi$
$174$	−0.146208	−	0.146208i	−0.0110840	−	0.0110840i
$175$	−13.2741	−	4.14706i	−1.00343	−	0.313489i
$176$	−4.09004	+	15.2642i	−0.308298	+	1.15058i
$177$	−0.903127			−0.0678832
$178$	0.211694	−	0.790055i	0.0158672	−	0.0592171i
$179$	8.68110	−	15.0361i	0.648856	−	1.12385i	−0.334540	−	0.942382i	$-0.608581\pi$
$179$	8.68110	−	15.0361i	0.648856	−	1.12385i	0.983396	−	0.181470i	$-0.0580857\pi$
$180$	−12.6303	−	1.92703i	−0.941404	−	0.143632i
$181$			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
$184$	4.02953	−	1.07971i	0.297061	−	0.0795973i
$185$	2.36425	−	15.4959i	0.173823	−	1.13928i
$186$	−0.214216	+	0.123678i	−0.0157071	+	0.00906850i
$187$			9.83181i			0.718973i
$188$	−0.507958	−	0.879810i	−0.0370467	−	0.0641667i
$189$	5.43421	+	1.45609i	0.395280	+	0.105915i
$190$	0.223918	−	0.510708i	0.0162447	−	0.0370506i
$191$	−3.39354	−	5.87779i	−0.245548	−	0.425302i	0.716737	−	0.697343i	$-0.245635\pi$
$191$	−3.39354	−	5.87779i	−0.245548	−	0.425302i	−0.962286	+	0.272041i	$0.912301\pi$
$192$	2.52097	−	0.675492i	0.181935	−	0.0487494i
$193$	1.03504	+	0.597582i	0.0745040	+	0.0430149i	0.536789	−	0.843716i	$-0.319637\pi$
$193$	1.03504	+	0.597582i	0.0745040	+	0.0430149i	−0.462285	+	0.886731i	$0.652970\pi$
$194$	−1.54543			−0.110955
$195$		0			0
$196$	1.45937			0.104241
$197$	−17.4253	−	10.0605i	−1.24150	−	0.716780i	−0.272100	−	0.962269i	$-0.587718\pi$
$197$	−17.4253	−	10.0605i	−1.24150	−	0.716780i	−0.969399	+	0.245489i	$0.921051\pi$
$198$	−1.48214	+	0.397137i	−0.105331	+	0.0282233i
$199$	−1.08885	−	1.88594i	−0.0771862	−	0.133690i	0.824849	−	0.565354i	$-0.191260\pi$
$199$	−1.08885	−	1.88594i	−0.0771862	−	0.133690i	−0.902035	+	0.431663i	$0.857927\pi$
$200$	−1.77154	−	1.92314i	−0.125267	−	0.135987i
$201$	−1.20125	−	0.321875i	−0.0847299	−	0.0227033i
$202$	0.0662412	+	0.114733i	0.00466071	+	0.00807259i
$203$			12.7363i			0.893912i
$204$	1.43168	−	0.826580i	0.100237	−	0.0578721i
$205$	−8.50458	−	11.5669i	−0.593986	−	0.807870i
$206$	−1.07618	+	0.288362i	−0.0749810	+	0.0200911i
$207$	−16.2552	−	16.2552i	−1.12982	−	1.12982i
$208$		0			0
$209$			7.70215i			0.532769i
$210$	0.166355	+	0.226257i	0.0114796	+	0.0156132i
$211$	9.97642	−	17.2797i	0.686805	−	1.18958i	−0.286061	−	0.958211i	$-0.592346\pi$
$211$	9.97642	−	17.2797i	0.686805	−	1.18958i	0.972866	−	0.231370i	$-0.0743208\pi$
$212$	−0.962781	+	3.59315i	−0.0661240	+	0.246778i
$213$	2.21022			0.151442
$214$	−0.168410	+	0.628516i	−0.0115123	+	0.0429645i
$215$	14.3658	−	1.59238i	0.979740	−	0.108600i
$216$	0.747956	+	0.747956i	0.0508919	+	0.0508919i
$217$	14.7171	+	3.94345i	0.999064	+	0.267698i
$218$	0.312872	+	1.16765i	0.0211904	+	0.0790835i
$219$	−0.884062	−	3.29936i	−0.0597394	−	0.222950i
$220$	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	$-0.685073\pi$
$223$	6.70672	−	11.6164i	0.449115	−	0.777891i	0.998329	+	0.0577915i	$0.0184059\pi$
$224$	3.75176	+	2.16608i	0.250675	+	0.144727i
$225$	−4.29671	+	13.7531i	−0.286447	+	0.916874i
$226$	0.696612	−	0.696612i	0.0463380	−	0.0463380i
$227$	12.7144	−	7.34064i	0.843882	−	0.487215i	−0.0147000	−	0.999892i	$-0.504679\pi$
$227$	12.7144	−	7.34064i	0.843882	−	0.487215i	0.858582	+	0.512677i	$0.171346\pi$
$228$	1.12156	−	0.647535i	0.0742773	−	0.0428840i
$229$	−2.65280	+	2.65280i	−0.175302	+	0.175302i	−0.789304	−	0.614002i	$-0.789558\pi$
$229$	−2.65280	+	2.65280i	−0.175302	+	0.175302i	0.614002	+	0.789304i	$0.289558\pi$
$230$	−0.258035	−	2.32788i	−0.0170143	−	0.153496i
$231$	−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
$236$	1.34768	+	5.02962i	0.0877266	+	0.327400i
$237$	0.745502	+	2.78225i	0.0484256	+	0.180727i
$238$	0.855249	+	0.229163i	0.0554376	+	0.0148545i
$239$	10.1890	+	10.1890i	0.659074	+	0.659074i	0.955161	−	0.296087i	$-0.0956818\pi$
$239$	10.1890	+	10.1890i	0.659074	+	0.659074i	−0.296087	+	0.955161i	$0.595682\pi$
$240$	−0.330136	−	2.97835i	−0.0213102	−	0.192252i
$241$	2.09750	−	7.82799i	0.135112	−	0.504245i	−0.864885	−	0.501970i	$-0.832609\pi$
$241$	2.09750	−	7.82799i	0.135112	−	0.504245i	0.999997	−	0.00227574i	$-0.000724392\pi$
$242$	0.714943			0.0459582
$243$	2.27812	−	8.50205i	0.146141	−	0.545407i
$244$	1.27247	−	2.20398i	0.0814615	−	0.141095i
$245$	0.248233	−	1.62698i	0.0158590	−	0.103944i
$246$			0.289920i			0.0184846i
$247$		0			0
$248$	2.02564	+	2.02564i	0.128628	+	0.128628i
$249$	−1.05365	+	0.282325i	−0.0667725	+	0.0178916i
$250$	−1.21738	+	0.820378i	−0.0769942	+	0.0518853i
$251$	−4.04904	+	2.33771i	−0.255573	+	0.147555i	−0.622313	−	0.782768i	$-0.713807\pi$
$251$	−4.04904	+	2.33771i	−0.255573	+	0.147555i	0.366740	+	0.930323i	$0.380474\pi$
$252$		−	15.8922i		−	1.00111i
$253$	16.1749	+	28.0157i	1.01690	+	1.76133i
$254$	−2.09884	−	0.562382i	−0.131693	−	0.0352870i
$255$	−0.677993	−	1.73671i	−0.0424576	−	0.108757i
$256$	−7.31927	−	12.6773i	−0.457454	−	0.792334i
$257$	−16.7639	+	4.49187i	−1.04570	+	0.280195i	−0.740474	−	0.672085i	$-0.765399\pi$
$257$	−16.7639	+	4.49187i	−1.04570	+	0.280195i	−0.305227	+	0.952280i	$0.598732\pi$
$258$	−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
$263$	−2.33916	+	0.626777i	−0.144239	+	0.0386487i	−0.330216	−	0.943905i	$-0.607122\pi$
$263$	−2.33916	+	0.626777i	−0.144239	+	0.0386487i	0.185977	+	0.982554i	$0.440455\pi$
$264$	−0.364647	−	0.631587i	−0.0224425	−	0.0388715i
$265$	3.84207	+	1.68454i	0.236016	+	0.103480i
$266$	0.669994	+	0.179524i	0.0410800	+	0.0110073i
$267$	−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	$-0.762549\pi$
$269$	−8.42829	+	4.86608i	−0.513882	+	0.296690i	0.220546	+	0.975377i	$0.429216\pi$
$270$	0.478463	−	0.351789i	0.0291183	−	0.0214092i
$271$	21.1708	−	5.67269i	1.28603	−	0.344591i	0.449880	−	0.893089i	$-0.351467\pi$
$271$	21.1708	−	5.67269i	1.28603	−	0.344591i	0.836152	+	0.548498i	$0.184800\pi$
$272$	−6.68061	−	6.68061i	−0.405071	−	0.405071i
$273$		0			0
$274$		−	1.96233i		−	0.118548i
$275$	10.8495	−	17.1293i	0.654250	−	1.03294i
$276$	2.71970	−	4.71067i	0.163707	−	0.283549i
$277$	4.67325	−	17.4408i	0.280788	−	1.04792i	−0.671074	−	0.741390i	$-0.734167\pi$
$277$	4.67325	−	17.4408i	0.280788	−	1.04792i	0.951862	−	0.306526i	$-0.0991666\pi$
$278$	1.12556			0.0675067
$279$	4.08574	−	15.2482i	0.244607	−	0.912885i
$280$	2.03241	−	2.53915i	0.121460	−	0.151743i
$281$	−11.3739	−	11.3739i	−0.678510	−	0.678510i	0.281153	−	0.959663i	$-0.409283\pi$
$281$	−11.3739	−	11.3739i	−0.678510	−	0.678510i	−0.959663	+	0.281153i	$0.909283\pi$
$282$	0.0223477	+	0.00598805i	0.00133079	+	0.000356583i
$283$	2.93892	+	10.9682i	0.174700	+	0.651991i	0.996602	+	0.0823620i	$0.0262464\pi$
$283$	2.93892	+	10.9682i	0.174700	+	0.651991i	−0.821902	+	0.569629i	$0.807087\pi$
$284$	−3.29818	−	12.3090i	−0.195711	−	0.730403i
$285$	−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
$290$	1.04961	+	0.840142i	0.0616354	+	0.0493348i
$291$	−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	−0.517594	−	0.855627i	$-0.673172\pi$
$293$	−0.605883	+	0.349807i	−0.0353961	+	0.0204359i	0.482198	+	0.876063i	$0.339839\pi$
$294$	−0.0235007	+	0.0235007i	−0.00137059	+	0.00137059i
$295$	5.83652	−	0.646952i	0.339815	−	0.0376670i
$296$	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
$301$	4.65320	+	17.3660i	0.268206	+	1.00096i
$302$	−0.0898718	−	0.335406i	−0.00517154	−	0.0193004i
$303$	0.335163	+	0.0898068i	0.0192546	+	0.00515926i
$304$	−5.23352	−	5.23352i	−0.300163	−	0.300163i
$305$	−2.24068	−	1.79351i	−0.128301	−	0.102696i
$306$	0.237433	−	0.886110i	0.0135731	−	0.0506555i
$307$	14.2048			0.810709			0.405355	−	0.914159i	$-0.367148\pi$
$307$	14.2048			0.810709			0.405355	+	0.914159i	$0.367148\pi$
$308$	−5.78818	+	21.6018i	−0.329812	+	1.23088i
$309$	−1.45904	+	2.52712i	−0.0830016	+	0.143763i
$310$	1.29579	−	0.952730i	0.0735960	−	0.0541114i
$311$		−	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	$0.872090\pi$
$314$	−1.85092	+	0.495953i	−0.104454	+	0.0279882i
$315$	−17.7175	−	2.70319i	−0.998265	−	0.152308i
$316$	14.3822	−	8.30357i	0.809062	−	0.467112i
$317$			17.3024i			0.971798i	0.874015	+	0.485899i	$0.161508\pi$
$317$			17.3024i			0.971798i	−0.874015	+	0.485899i	$0.838492\pi$
$318$	−0.0423577	−	0.0733657i	−0.00237530	−	0.00411414i
$319$	−17.9368	−	4.80615i	−1.00427	−	0.269093i
$320$	−15.8081	+	6.17130i	−0.883697	+	0.344986i
$321$	0.852114	+	1.47590i	0.0475603	+	0.0823769i
$322$	2.81404	−	0.754019i	0.156820	−	0.0420198i
$323$	−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
$328$	3.24323	−	0.869022i	0.179078	−	0.0479837i
$329$	−0.712553	−	1.23418i	−0.0392843	−	0.0680424i
$330$	−0.381418	+	0.148901i	−0.0209964	+	0.00819676i
$331$	−17.3574	−	4.65090i	−0.954049	−	0.255637i	−0.251969	−	0.967735i	$-0.581078\pi$
$331$	−17.3574	−	4.65090i	−0.954049	−	0.255637i	−0.702079	+	0.712099i	$0.747745\pi$
$332$	3.14460	+	5.44661i	0.172582	+	0.298921i
$333$		−	20.2015i		−	1.10704i
$334$	−2.35130	+	1.35753i	−0.128658	+	0.0742805i
$335$	7.99376	+	1.21963i	0.436746	+	0.0666353i
$336$	3.60035	−	0.964712i	0.196415	−	0.0526293i
$337$	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
$340$	−8.66020	+	6.36741i	−0.469665	+	0.345321i
$341$	−11.1073	+	19.2384i	−0.601493	+	1.04182i
$342$	0.186002	−	0.694170i	0.0100579	−	0.0375364i
$343$	−17.4224			−0.940723
$344$	−0.874884	+	3.26511i	−0.0471706	+	0.176043i
$345$	−4.78910	−	3.83334i	−0.257836	−	0.206380i
$346$	1.68477	+	1.68477i	0.0905740	+	0.0905740i
$347$	−17.9682	−	4.81456i	−0.964582	−	0.258459i	−0.258043	−	0.966133i	$-0.583078\pi$
$347$	−17.9682	−	4.81456i	−0.964582	−	0.258459i	−0.706539	+	0.707674i	$0.749744\pi$
$348$	0.808124	+	3.01596i	0.0433200	+	0.161672i
$349$	−0.651455	−	2.43126i	−0.0348716	−	0.130143i	0.946296	−	0.323302i	$-0.104793\pi$
$349$	−0.651455	−	2.43126i	−0.0348716	−	0.130143i	−0.981167	+	0.193160i	$0.938126\pi$
$350$	−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	−0.00962005	+	0.999954i	$0.503062\pi$
$353$	−16.3608	+	28.3377i	−0.870795	+	1.50826i	−0.861175	+	0.508308i	$0.830271\pi$
$354$	−0.102696	−	0.0592915i	−0.00545822	−	0.00315131i
$355$	−14.2837	+	1.58329i	−0.758101	+	0.0840320i
$356$	−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	−0.688402	−	0.725330i	$-0.741687\pi$
$359$	0.699684	−	0.699684i	0.0369279	−	0.0369279i	0.725330	+	0.688402i	$0.241687\pi$
$360$	−2.63077	−	2.10575i	−0.138654	−	0.110983i
$361$	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
$366$	0.0150005	+	0.0559825i	0.000784087	+	0.00292625i
$367$	3.74601	+	13.9803i	0.195540	+	0.729767i	0.992126	+	0.125241i	$0.0399705\pi$
$367$	3.74601	+	13.9803i	0.195540	+	0.729767i	−0.796586	+	0.604525i	$0.793363\pi$
$368$	−30.0270	−	8.04571i	−1.56526	−	0.419411i
$369$	−13.0833	−	13.0833i	−0.681087	−	0.681087i
$370$	1.28617	−	1.60685i	0.0668649	−	0.0835361i
$371$	−1.35057	+	5.04039i	−0.0701180	+	0.261684i
$372$	3.73524			0.193663
$373$	−2.62454	+	9.79493i	−0.135894	+	0.507162i	0.864099	+	0.503322i	$0.167889\pi$
$373$	−2.62454	+	9.79493i	−0.135894	+	0.507162i	−0.999993	+	0.00384023i	$0.998778\pi$
$374$	−0.645471	+	1.11799i	−0.0333765	+	0.0578098i
$375$	−0.735254	+	3.77393i	−0.0379683	+	0.194885i
$376$		−	0.267945i		−	0.0138182i
$377$		0			0
$378$	0.522337	+	0.522337i	0.0268661	+	0.0268661i
$379$	−1.01470	+	0.271887i	−0.0521215	+	0.0139659i	−0.284786	−	0.958591i	$-0.591922\pi$
$379$	−1.01470	+	0.271887i	−0.0521215	+	0.0139659i	0.232664	+	0.972557i	$0.425256\pi$
$380$	−6.78432	+	4.98817i	−0.348028	+	0.255887i
$381$	−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	$-0.265914\pi$
$383$	−6.00353	−	10.3984i	−0.306766	−	0.531334i	−0.977653	+	0.210225i	$0.932580\pi$
$384$	1.36579	+	0.365961i	0.0696975	+	0.0186754i
$385$	23.0983	+	10.1274i	1.17720	+	0.516138i
$386$	0.0784640	+	0.135904i	0.00399371	+	0.00691732i
$387$	17.9926	−	4.82111i	0.914616	−	0.245071i
$388$	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
$393$	−4.21468	+	1.12932i	−0.212603	+	0.0569667i
$394$	−1.32097	−	2.28798i	−0.0665494	−	0.115267i
$395$	−6.81091	−	17.4465i	−0.342694	−	0.877826i
$396$	22.3813	+	5.99704i	1.12470	+	0.301363i
$397$	3.02739	+	5.24359i	0.151940	+	0.263168i	0.931941	−	0.362611i	$-0.118115\pi$
$397$	3.02739	+	5.24359i	0.151940	+	0.263168i	−0.780001	+	0.625779i	$0.784781\pi$
$398$		−	0.285937i		−	0.0143327i
$399$	1.57330	−	0.908347i	0.0787637	−	0.0454742i
$400$	4.26706	+	19.0113i	0.213353	+	0.950565i
$401$	2.33226	−	0.624928i	0.116468	−	0.0312074i	−0.200114	−	0.979773i	$-0.564131\pi$
$401$	2.33226	−	0.624928i	0.116468	−	0.0312074i	0.316582	+	0.948565i	$0.397465\pi$
$402$	−0.115465	−	0.115465i	−0.00575886	−	0.00575886i
$403$		0			0
$404$		−	2.00058i		−	0.0995324i
$405$	−2.68107	+	17.5725i	−0.133224	+	0.873184i
$406$	−0.836154	+	1.44826i	−0.0414976	+	0.0718760i
$407$	−7.35772	+	27.4594i	−0.364709	+	1.36111i
$408$	0.436016			0.0215860
$409$	−5.21187	+	19.4510i	−0.257710	+	0.961788i	0.708852	+	0.705357i	$0.249213\pi$
$409$	−5.21187	+	19.4510i	−0.257710	+	0.961788i	−0.966563	+	0.256431i	$0.917453\pi$
$410$	−0.207683	−	1.87363i	−0.0102567	−	0.0925319i
$411$	−3.63422	−	3.63422i	−0.179263	−	0.179263i
$412$	16.2511	+	4.35446i	0.800632	+	0.214529i
$413$	1.89050	+	7.05543i	0.0930253	+	0.347175i
$414$	−0.781227	−	2.91558i	−0.0383952	−	0.143293i
$415$	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	$-0.596038\pi$
$419$	−26.0503	−	15.0401i	−1.27264	−	0.734759i	−0.975484	+	0.220070i	$0.929371\pi$
$420$	−0.467206	−	4.21493i	−0.0227973	−	0.205668i
$421$	−9.24685	+	9.24685i	−0.450664	+	0.450664i	−0.895575	−	0.444911i	$-0.853235\pi$
$421$	−9.24685	+	9.24685i	−0.450664	+	0.450664i	0.444911	+	0.895575i	$0.353235\pi$
$422$	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
$425$	5.62567	+	10.7379i	0.272885	+	0.520866i
$426$	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
$431$	1.63348	+	6.09624i	0.0786821	+	0.293646i	0.994043	−	0.108989i	$-0.0347613\pi$
$431$	1.63348	+	6.09624i	0.0786821	+	0.293646i	−0.915361	+	0.402634i	$0.868095\pi$
$432$	−2.04006	−	7.61362i	−0.0981527	−	0.366311i
$433$	11.8706	+	3.18071i	0.570463	+	0.152855i	0.532509	−	0.846424i	$-0.321249\pi$
$433$	11.8706	+	3.18071i	0.570463	+	0.152855i	0.0379543	+	0.999279i	$0.487916\pi$
$434$	1.41461	+	1.41461i	0.0679036	+	0.0679036i
$435$	3.49982	−	0.387939i	0.167803	−	0.0186002i
$436$	4.72458	−	17.6324i	0.226266	−	0.844438i
$437$	−15.1513			−0.724783
$438$	0.116080	−	0.433215i	0.00554650	−	0.0206998i
$439$	−17.2223	+	29.8300i	−0.821977	+	1.42371i	0.0822306	+	0.996613i	$0.473796\pi$
$439$	−17.2223	+	29.8300i	−0.821977	+	1.42371i	−0.904208	+	0.427093i	$0.859538\pi$
$440$	2.80899	+	3.82046i	0.133913	+	0.182133i
$441$		−	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	$0.808009\pi$
$444$	4.61713	−	1.23716i	0.219119	−	0.0587128i
$445$	8.25118	+	11.2223i	0.391143	+	0.531987i
$446$	1.52526	−	0.880610i	0.0722232	−	0.0416981i
$447$		−	4.17534i		−	0.197487i
$448$	−10.5542	−	18.2804i	−0.498639	−	0.863668i
$449$	30.0741	+	8.05832i	1.41928	+	0.380296i	0.885229	−	0.465155i	$-0.154002\pi$
$449$	30.0741	+	8.05832i	1.41928	+	0.380296i	0.534053	+	0.845451i	$0.320668\pi$
$450$	−1.39149	+	1.28180i	−0.0655957	+	0.0604247i
$451$	13.0186	+	22.5489i	0.613021	+	1.06178i
$452$	−14.3697	+	3.85034i	−0.675892	+	0.181105i
$453$	−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	0.561622	−	0.827394i	$-0.310178\pi$
$457$	2.69118	+	1.55375i	0.125888	+	0.0726814i	−0.435734	+	0.900076i	$0.643511\pi$
$458$	−0.475812	+	0.127494i	−0.0222333	+	0.00595738i
$459$	−2.45200	−	4.24698i	−0.114449	−	0.198232i
$460$	−14.2018	+	32.3913i	−0.662163	+	1.51025i
$461$	16.1274	+	4.32132i	0.751126	+	0.201264i	0.614018	−	0.789292i	$-0.289552\pi$
$461$	16.1274	+	4.32132i	0.751126	+	0.201264i	0.137109	+	0.990556i	$0.456219\pi$
$462$	−0.254652	−	0.441070i	−0.0118475	−	0.0205205i
$463$		−	15.6396i		−	0.726832i	−0.931627	−	0.363416i	$-0.881610\pi$
$463$		−	15.6396i		−	0.726832i	0.931627	−	0.363416i	$-0.118390\pi$
$464$	15.4536	−	8.92212i	0.717414	−	0.414199i
$465$	0.635348	−	4.16425i	0.0294636	−	0.193112i
$466$	−2.50138	+	0.670243i	−0.115874	+	0.0310484i
$467$	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
$470$	−0.148713	−	0.0226895i	−0.00685963	−	0.00104659i
$471$	−2.50939	+	4.34640i	−0.115627	+	0.200272i
$472$	−0.355447	+	1.32655i	−0.0163608	+	0.0610592i
$473$	−26.2128			−1.20527
$474$	−0.0978863	+	0.365317i	−0.00449607	+	0.0167796i
$475$	4.40709	+	8.41199i	0.202211	+	0.385969i
$476$	−9.45433	−	9.45433i	−0.433339	−	0.433339i
$477$	5.22226	+	1.39930i	0.239111	+	0.0640696i
$478$	0.489686	+	1.82753i	0.0223977	+	0.0835894i
$479$	11.0386	+	41.1964i	0.504364	+	1.88231i	0.469522	+	0.882921i	$0.344426\pi$
$479$	11.0386	+	41.1964i	0.504364	+	1.88231i	0.0348421	+	0.999393i	$0.488907\pi$
$480$	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
$485$	16.4464	−	20.5470i	0.746794	−	0.932990i
$486$	0.817218	−	0.817218i	0.0370698	−	0.0370698i
$487$	−13.1780	+	7.60834i	−0.597154	+	0.344767i	−0.767921	−	0.640545i	$-0.778709\pi$
$487$	−13.1780	+	7.60834i	−0.597154	+	0.344767i	0.170767	+	0.985311i	$0.445375\pi$
$488$	0.581293	−	0.335610i	0.0263139	−	0.0151923i
$489$	−4.54620	+	4.54620i	−0.205586	+	0.205586i
$490$	0.135041	−	0.168710i	0.00610051	−	0.00762154i
$491$	24.2273	+	13.9876i	1.09336	+	0.631254i	0.934470	−	0.356042i	$-0.115874\pi$
$491$	24.2273	+	13.9876i	1.09336	+	0.631254i	0.158894	+	0.987296i	$0.449207\pi$
$492$	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
$496$	−5.52498	−	20.6195i	−0.248079	−	0.925844i
$497$	−4.62661	−	17.2668i	−0.207532	−	0.774520i
$498$	−0.138347	−	0.0370700i	−0.00619949	−	0.00166115i
$499$	1.67479	+	1.67479i	0.0749740	+	0.0749740i	0.743599	−	0.668625i	$-0.233117\pi$
$499$	1.67479	+	1.67479i	0.0749740	+	0.0749740i	−0.668625	+	0.743599i	$0.733117\pi$
$500$	22.1146	−	1.53689i	0.988994	−	0.0687317i
$501$	−1.84047	+	6.86873i	−0.0822261	+	0.306872i
$502$	−0.613896			−0.0273995
$503$	5.99415	−	22.3705i	0.267266	−	0.997451i	−0.693583	−	0.720377i	$-0.743969\pi$
$503$	5.99415	−	22.3705i	0.267266	−	0.997451i	0.960849	−	0.277073i	$-0.0893645\pi$
$504$	2.09575	−	3.62995i	0.0933523	−	0.161691i
$505$	−2.23035	−	0.340289i	−0.0992493	−	0.0151427i
$506$			4.24760i			0.188829i
$507$		0			0
$508$	23.2016	+	23.2016i	1.02940	+	1.02940i
$509$	−5.82068	+	1.55965i	−0.257997	+	0.0691301i	−0.385499	−	0.922708i	$-0.625971\pi$
$509$	−5.82068	+	1.55965i	−0.257997	+	0.0691301i	0.127502	+	0.991838i	$0.459304\pi$
$510$	0.0369217	−	0.241995i	0.00163492	−	0.0107157i
$511$	−23.9248	+	13.8130i	−1.05837	+	0.611051i
$512$		−	10.1453i		−	0.448362i
$513$	−1.92087	−	3.32705i	−0.0848086	−	0.146893i
$514$	−2.20114	−	0.589794i	−0.0970881	−	0.0260147i
$515$	7.61882	−	17.3769i	0.335725	−	0.765717i
$516$	2.20376	+	3.81703i	0.0970152	+	0.168035i
$517$	2.00701	−	0.537776i	0.0882681	−	0.0236514i
$518$	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
$523$	0.529059	−	0.141761i	0.0231341	−	0.00619877i	−0.247233	−	0.968956i	$-0.579521\pi$
$523$	0.529059	−	0.141761i	0.0231341	−	0.00619877i	0.270368	+	0.962757i	$0.412855\pi$
$524$	12.5786	+	21.7868i	0.549500	+	0.951762i
$525$	−4.77850	−	0.196075i	−0.208551	−	0.00855742i
$526$	−0.307138	−	0.0822974i	−0.0133919	−	0.00358834i
$527$	−6.64060	−	11.5019i	−0.289269	−	0.501029i
$528$			5.43449i			0.236506i
$529$	−35.1924	+	20.3183i	−1.53010	+	0.883406i
$530$	0.326295	+	0.443788i	0.0141733	+	0.0192769i
$531$	7.31002	−	1.95871i	0.317228	−	0.0850010i
$532$	−7.40643	−	7.40643i	−0.321110	−	0.321110i
$533$		0			0
$534$		−	0.281282i		−	0.0121722i
$535$	−6.56410	−	8.92772i	−0.283791	−	0.385979i
$536$	−0.945563	+	1.63776i	−0.0408421	+	0.0707406i
$537$	1.54536	−	5.76736i	0.0666871	−	0.248880i
$538$	−1.27786			−0.0550923
$539$	−0.772518	+	2.88308i	−0.0332747	+	0.124183i
$540$	−8.91326	+	0.987995i	−0.383566	+	0.0425165i
$541$	29.7507	+	29.7507i	1.27908	+	1.27908i	0.941182	+	0.337899i	$0.109716\pi$
$541$	29.7507	+	29.7507i	1.27908	+	1.27908i	0.337899	+	0.941182i	$0.390284\pi$
$542$	2.77978	+	0.744839i	0.119402	+	0.0319936i
$543$	2.21880	+	8.28067i	0.0952177	+	0.355357i
$544$	−0.977367	−	3.64758i	−0.0419043	−	0.156389i
$545$	−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
$550$	2.35827	−	1.23551i	0.100557	−	0.0526825i
$551$	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
$555$	−0.593894	−	5.35786i	−0.0252094	−	0.227428i
$556$	−14.7196	−	8.49837i	−0.624251	−	0.360411i
$557$	17.5886	−	30.4644i	0.745254	−	1.29082i	−0.204822	−	0.978799i	$-0.565662\pi$
$557$	17.5886	−	30.4644i	0.745254	−	1.29082i	0.950076	−	0.312018i	$-0.101005\pi$
$558$	1.46566	−	1.46566i	0.0620463	−	0.0620463i
$559$		0			0
$560$	−22.5765	+	8.81362i	−0.954030	+	0.372443i
$561$	0.875100	+	3.26592i	0.0369468	+	0.137887i
$562$	−0.546631	−	2.04005i	−0.0230582	−	0.0860545i
$563$	−40.5028	−	10.8527i	−1.70699	−	0.457387i	−0.732306	−	0.680975i	$-0.761556\pi$
$563$	−40.5028	−	10.8527i	−1.70699	−	0.457387i	−0.974684	+	0.223589i	$0.928223\pi$
$564$	−0.247042	−	0.247042i	−0.0104024	−	0.0104024i
$565$	1.84835	+	16.6750i	0.0777607	+	0.701523i
$566$	−0.385887	+	1.44015i	−0.0162201	+	0.0605341i
$567$	−22.1108			−0.928566
$568$	0.869884	−	3.24645i	0.0364995	−	0.136218i
$569$	13.7741	−	23.8575i	0.577441	−	1.00016i	−0.418331	−	0.908295i	$-0.637385\pi$
$569$	13.7741	−	23.8575i	0.577441	−	1.00016i	0.995772	−	0.0918621i	$-0.0292819\pi$
$570$	0.0289241	−	0.189576i	0.00121150	−	0.00794048i
$571$		−	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
$574$	2.26492	−	0.606884i	0.0945360	−	0.0253308i
$575$	33.6959	+	21.3426i	1.40521	+	0.890046i
$576$	−18.9400	+	10.9350i	−0.789168	+	0.455626i
$577$			6.73701i			0.280465i	0.990119	+	0.140233i	$0.0447851\pi$
$577$			6.73701i			0.280465i	−0.990119	+	0.140233i	$0.955215\pi$
$578$	0.730170	+	1.26469i	0.0303711	+	0.0526043i
$579$	0.397008	+	0.106378i	0.0164991	+	0.00442092i
$580$	−7.38303	−	18.9120i	−0.306564	−	0.785276i
$581$	4.41118	+	7.64038i	0.183006	+	0.316977i
$582$	−0.513359	+	0.137554i	−0.0212794	+	0.00570180i
$583$	−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	0.589955	−	0.807436i	$-0.299146\pi$
$587$	4.49847	+	2.59719i	0.185672	+	0.107198i	−0.404283	+	0.914634i	$0.632479\pi$
$588$	0.484772	−	0.129894i	0.0199916	−	0.00535674i
$589$	−5.20218	−	9.01044i	−0.214352	−	0.371269i
$590$	0.706152	+	0.309609i	0.0290718	+	0.0127464i
$591$	−6.68376	−	1.79091i	−0.274933	−	0.0736681i
$592$	−13.6589	−	23.6578i	−0.561375	−	0.972331i
$593$			12.9267i			0.530836i	0.964133	+	0.265418i	$0.0855100\pi$
$593$			12.9267i			0.530836i	−0.964133	+	0.265418i	$0.914490\pi$
$594$	−0.932726	+	0.538510i	−0.0382702	+	0.0220953i
$595$	−12.1483	+	8.93206i	−0.498033	+	0.366179i
$596$	−23.2529	+	6.23060i	−0.952477	+	0.255215i
$597$	−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	$-0.111186\pi$
$600$	−0.759641	−	0.481148i	−0.0310122	−	0.0196428i
$601$	−6.28803	+	10.8912i	−0.256494	+	0.444261i	−0.965300	−	0.261142i	$-0.915901\pi$
$601$	−6.28803	+	10.8912i	−0.256494	+	0.444261i	0.708806	+	0.705403i	$0.249234\pi$
$602$	−0.610977	+	2.28020i	−0.0249016	+	0.0929340i
$603$	10.4212			0.424384
$604$	−1.35713	+	5.06486i	−0.0552207	+	0.206086i
$605$	−7.60840	+	9.50539i	−0.309325	+	0.386449i
$606$	0.0322160	+	0.0322160i	0.00130868	+	0.00130868i
$607$	−36.1909	−	9.69731i	−1.46894	−	0.393602i	−0.566374	−	0.824149i	$-0.691654\pi$
$607$	−36.1909	−	9.69731i	−1.46894	−	0.393602i	−0.902568	+	0.430547i	$0.858321\pi$
$608$	−0.765660	−	2.85748i	−0.0310516	−	0.115886i
$609$	1.13362	+	4.23072i	0.0459366	+	0.171438i
$610$	−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	$-0.719766\pi$
$613$	8.64732	−	14.9776i	0.349262	−	0.604940i	0.986119	+	0.166043i	$0.0530990\pi$
$614$	1.61524	+	0.932562i	0.0651860	+	0.0376351i
$615$	−3.85458	−	3.08532i	−0.155432	−	0.124412i
$616$	−4.17079	+	4.17079i	−0.168046	+	0.168046i
$617$	10.5136	−	6.07005i	0.423263	−	0.244371i	−0.273210	−	0.961955i	$-0.588085\pi$
$617$	10.5136	−	6.07005i	0.423263	−	0.244371i	0.696472	+	0.717584i	$0.254752\pi$
$618$	−0.331818	+	0.191575i	−0.0133477	+	0.00770628i
$619$	2.99993	−	2.99993i	0.120577	−	0.120577i	−0.644243	−	0.764821i	$-0.722828\pi$
$619$	2.99993	−	2.99993i	0.120577	−	0.120577i	0.764821	+	0.644243i	$0.222828\pi$
$620$	−24.1393	+	2.67573i	−0.969456	+	0.107460i
$621$	−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
$626$	−0.449988	−	1.67938i	−0.0179851	−	0.0671215i
$627$	0.685545	+	2.55849i	0.0273780	+	0.102176i
$628$	27.9502	+	7.48923i	1.11533	+	0.298853i
$629$	−12.0180	−	12.0180i	−0.479188	−	0.479188i
$630$	−1.83721	−	1.47056i	−0.0731961	−	0.0585884i
$631$	−5.60031	+	20.9006i	−0.222945	+	0.832041i	0.760273	+	0.649604i	$0.225065\pi$
$631$	−5.60031	+	20.9006i	−0.222945	+	0.832041i	−0.983218	+	0.182437i	$0.941601\pi$
$632$	4.38008			0.174230
$633$	1.77594	−	6.62791i	0.0705874	−	0.263436i
$634$	−1.13592	+	1.96748i	−0.0451133	+	0.0781385i
$635$	29.8128	−	21.9199i	1.18309	−	0.869863i
$636$			1.27926i			0.0507260i
$637$		0			0
$638$	−1.72409	−	1.72409i	−0.0682572	−	0.0682572i
$639$	−17.8898	+	4.79356i	−0.707710	+	0.189630i
$640$	−9.08865	−	1.38667i	−0.359260	−	0.0548131i
$641$	39.2467	−	22.6591i	1.55015	−	0.894980i	0.552022	−	0.833829i	$-0.313856\pi$
$641$	39.2467	−	22.6591i	1.55015	−	0.894980i	0.998129	−	0.0611509i	$-0.0194771\pi$
$642$			0.223769i			0.00883148i
$643$	−15.8249	−	27.4095i	−0.624072	−	1.08092i	−0.988719	−	0.149779i	$-0.952144\pi$
$643$	−15.8249	−	27.4095i	−0.624072	−	1.08092i	0.364647	−	0.931146i	$-0.381190\pi$
$644$	−42.4939	−	11.3862i	−1.67449	−	0.448679i
$645$	4.63028	−	1.80761i	0.182317	−	0.0711747i
$646$	−0.302312	−	0.523619i	−0.0118943	−	0.0206015i
$647$	36.6924	−	9.83169i	1.44253	−	0.386524i	0.549109	−	0.835751i	$-0.314967\pi$
$647$	36.6924	−	9.83169i	1.44253	−	0.386524i	0.893418	+	0.449227i	$0.148301\pi$
$648$	−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
$653$	−2.66385	+	0.713775i	−0.104244	+	0.0279322i	−0.310564	−	0.950552i	$-0.600518\pi$
$653$	−2.66385	+	0.713775i	−0.104244	+	0.0279322i	0.206320	+	0.978485i	$0.433851\pi$
$654$	0.207859	+	0.360022i	0.00812792	+	0.0140780i
$655$	26.4287	−	10.3175i	1.03265	−	0.403138i
$656$	−24.1677	−	6.47571i	−0.943590	−	0.252834i
$657$	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	$-0.653761\pi$
$659$	1.80219	−	1.04050i	0.0702034	−	0.0405320i	0.534691	+	0.845048i	$0.320428\pi$
$660$	6.11228	+	0.932564i	0.237920	+	0.0363000i
$661$	−36.3010	+	9.72683i	−1.41195	+	0.378330i	−0.882619	−	0.470089i	$-0.844222\pi$
$661$	−36.3010	+	9.72683i	−1.41195	+	0.378330i	−0.529326	+	0.848418i	$0.677555\pi$
$662$	−1.66840	−	1.66840i	−0.0648440	−	0.0648440i
$663$		0			0
$664$			1.65876i			0.0643723i
$665$	−9.51689	+	6.99729i	−0.369049	+	0.271343i
$666$	1.32626	−	2.29714i	0.0513914	−	0.0890125i
$667$	9.45440	−	35.2843i	0.366076	−	1.36621i
$668$	40.9991			1.58630
$669$	1.19389	−	4.45566i	0.0461585	−	0.172266i
$670$	0.828912	+	0.663486i	0.0320237	+	0.0256327i
$671$	3.68052	+	3.68052i	0.142085	+	0.142085i
$672$	1.43905	+	0.385592i	0.0555125	+	0.0148745i
$673$	−4.65984	−	17.3908i	−0.179624	−	0.670364i	−0.995718	−	0.0924454i	$-0.970532\pi$
$673$	−4.65984	−	17.3908i	−0.179624	−	0.670364i	0.816094	−	0.577919i	$-0.196135\pi$
$674$	0.232451	+	0.867519i	0.00895368	+	0.0334156i
$675$	−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
$680$	−2.81778	+	0.312338i	−0.108057	+	0.0119776i
$681$	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	−0.394319	−	0.918974i	$-0.629019\pi$
$683$	5.34122	−	3.08376i	0.204376	−	0.117997i	0.598695	+	0.800977i	$0.295686\pi$
$684$	−7.67369	+	7.67369i	−0.293411	+	0.293411i
$685$	26.0897	+	20.8830i	0.996838	+	0.797900i
$686$	−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
$691$	−3.39841	−	12.6830i	−0.129282	−	0.482486i	0.870674	−	0.491860i	$-0.163683\pi$
$691$	−3.39841	−	12.6830i	−0.129282	−	0.482486i	−0.999956	+	0.00937405i	$0.997016\pi$
$692$	−9.31214	−	34.7534i	−0.353994	−	1.32112i
$693$	31.3960	+	8.41252i	1.19263	+	0.319565i
$694$	−1.72710	−	1.72710i	−0.0655600	−	0.0655600i
$695$	−11.9782	+	14.9647i	−0.454359	+	0.567643i
$696$	−0.213140	+	0.795450i	−0.00807906	+	0.0301515i
$697$	−15.5666			−0.589627
$698$	0.0855377	−	0.319231i	0.00323765	−	0.0120831i
$699$	−3.39126	+	5.87383i	−0.128269	+	0.222169i
$700$	6.03870	+	26.9046i	0.228241	+	1.01690i
$701$		−	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
$704$	29.7274	−	7.96543i	1.12039	−	0.300208i
$705$	−0.317437	+	0.233395i	−0.0119554	+	0.00879017i
$706$	−3.72081	+	2.14821i	−0.140034	+	0.0808490i
$707$		−	2.80636i		−	0.105544i
$708$	0.895342	+	1.55078i	0.0336490	+	0.0582818i
$709$	−2.00482	−	0.537189i	−0.0752925	−	0.0201746i	0.220976	−	0.975279i	$-0.429076\pi$
$709$	−2.00482	−	0.537189i	−0.0752925	−	0.0201746i	−0.296269	+	0.955105i	$0.595742\pi$
$710$	−1.72817	−	0.757707i	−0.0648569	−	0.0284362i
$711$	−12.0684	−	20.9030i	−0.452599	−	0.783925i
$712$	−3.14660	+	0.843128i	−0.117924	+	0.0315976i
$713$	−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
$718$	0.125497	−	0.0336269i	0.00468351	−	0.00125494i
$719$	3.36848	+	5.83438i	0.125623	+	0.217586i	0.921976	−	0.387246i	$-0.126574\pi$
$719$	3.36848	+	5.83438i	0.125623	+	0.217586i	−0.796353	+	0.604832i	$0.793240\pi$
$720$	9.13165	+	23.3911i	0.340316	+	0.871735i
$721$	22.7966	+	6.10834i	0.848991	+	0.227486i
$722$	1.01055	+	1.75032i	0.0376086	+	0.0651401i
$723$		−	2.78698i		−	0.103649i
$724$	42.8050	−	24.7135i	1.59083	−	0.918469i
$725$	−22.3399	+	5.01416i	−0.829683	+	0.186221i
$726$	0.237489	−	0.0636349i	0.00881403	−	0.00236171i
$727$	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
$730$	−0.439841	+	2.88284i	−0.0162792	+	0.106699i
$731$	7.83580	−	13.5720i	0.289817	−	0.501979i
$732$	0.226517	−	0.845374i	0.00837232	−	0.0312459i
$733$	28.7555			1.06211			0.531054	−	0.847338i	$-0.321796\pi$
$733$	28.7555			1.06211			0.531054	+	0.847338i	$0.321796\pi$
$734$	−0.491861	+	1.83565i	−0.0181549	+	0.0677551i
$735$	−0.0623555	−	0.562544i	−0.00230002	−	0.0207498i
$736$	−8.78585	−	8.78585i	−0.323851	−	0.323851i
$737$	−14.1652	−	3.79556i	−0.521783	−	0.139811i
$738$	−0.628783	−	2.34665i	−0.0231458	−	0.0863813i
$739$	−7.94129	−	29.6373i	−0.292125	−	1.09023i	−0.943474	−	0.331447i	$-0.892463\pi$
$739$	−7.94129	−	29.6373i	−0.292125	−	1.09023i	0.651349	−	0.758778i	$-0.274203\pi$
$740$	−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	0.280543	−	0.959841i	$-0.409485\pi$
$743$	26.4817	−	45.8676i	0.971519	−	1.68272i	0.690976	−	0.722878i	$-0.257181\pi$
$744$	0.853172	+	0.492579i	0.0312788	+	0.0180588i
$745$	2.99099	+	26.9834i	0.109581	+	0.988596i
$746$	−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
$750$	−0.331370	+	0.380868i	−0.0120999	+	0.0139073i
$751$	−40.3780	−	23.3123i	−1.47341	−	0.850676i	−0.473862	−	0.880599i	$-0.657140\pi$
$751$	−40.3780	−	23.3123i	−1.47341	−	0.850676i	−0.999552	+	0.0299230i	$0.990474\pi$
$752$	−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
$756$	−2.88708	−	10.7747i	−0.105002	−	0.391873i
$757$	−0.323327	−	1.20667i	−0.0117515	−	0.0438572i	0.959801	−	0.280681i	$-0.0905603\pi$
$757$	−0.323327	−	1.20667i	−0.0117515	−	0.0438572i	−0.971553	+	0.236824i	$0.923894\pi$
$758$	−0.133232	−	0.0356995i	−0.00483922	−	0.00129666i
$759$	7.86654	+	7.86654i	0.285537	+	0.285537i
$760$	−2.20742	+	0.244683i	−0.0800716	+	0.00887558i
$761$	5.28278	−	19.7156i	0.191501	−	0.714690i	−0.801644	−	0.597801i	$-0.796041\pi$
$761$	5.28278	−	19.7156i	0.191501	−	0.714690i	0.993145	−	0.116889i	$-0.0372921\pi$
$762$	−0.747246			−0.0270698
$763$	6.62754	−	24.7343i	0.239933	−	0.895442i
$764$	−6.72858	+	11.6542i	−0.243432	+	0.421636i
$765$	9.25436	+	12.5867i	0.334592	+	0.455073i
$766$		−	1.57656i		−	0.0569633i
$767$		0			0
$768$	−3.55968	−	3.55968i	−0.128449	−	0.128449i
$769$	−35.6638	+	9.55609i	−1.28607	+	0.344602i	−0.836167	−	0.548476i	$-0.815208\pi$
$769$	−35.6638	+	9.55609i	−1.28607	+	0.344602i	−0.449904	+	0.893077i	$0.648542\pi$
$770$	1.96167	+	2.66803i	0.0706935	+	0.0961491i
$771$	−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	$-0.0410209\pi$
$773$	10.6918	+	18.5187i	0.384557	+	0.666072i	−0.607151	+	0.794587i	$0.707688\pi$
$774$	2.36248	+	0.633024i	0.0849175	+	0.0227536i
$775$	−1.12294	+	27.3669i	−0.0403372	+	0.983047i
$776$	3.07754	+	5.33045i	0.110477	+	0.191352i
$777$	6.47681	−	1.73545i	0.232354	−	0.0622591i
$778$	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
$783$	8.94666	−	2.39725i	0.319728	−	0.0856708i
$784$	−1.43410	−	2.48393i	−0.0512179	−	0.0887120i
$785$	13.1036	−	29.8865i	0.467688	−	1.06670i
$786$	−0.553399	−	0.148283i	−0.0197391	−	0.00528907i
$787$	19.6914	+	34.1065i	0.701923	+	1.21577i	0.967790	+	0.251757i	$0.0810085\pi$
$787$	19.6914	+	34.1065i	0.701923	+	1.21577i	−0.265867	+	0.964010i	$0.585658\pi$
$788$			39.8950i			1.42120i
$789$	−0.721232	+	0.416404i	−0.0256766	+	0.0148244i
$790$	0.370904	−	2.43101i	0.0131962	−	0.0864913i
$791$	−20.1575	+	5.40118i	−0.716717	+	0.192044i
$792$	4.32129	+	4.32129i	0.153550	+	0.153550i
$793$		0			0
$794$			0.795007i			0.0282138i
$795$	1.42619	+	0.217597i	0.0505817	+	0.00771736i
$796$	−2.15892	+	3.73936i	−0.0765209	+	0.132538i
$797$	−10.1370	+	37.8319i	−0.359072	+	1.34007i	0.516210	+	0.856462i	$0.327342\pi$
$797$	−10.1370	+	37.8319i	−0.359072	+	1.34007i	−0.875282	+	0.483612i	$0.839324\pi$
$798$	0.238537			0.00844411
$799$	−0.321515	+	1.19991i	−0.0113744	+	0.0424498i
$800$	−2.32234	+	7.43348i	−0.0821073	+	0.262813i
$801$	12.6934	+	12.6934i	0.448500	+	0.448500i
$802$	0.306232	+	0.0820546i	0.0108134	+	0.00289745i
$803$	−10.4249	−	38.9062i	−0.367887	−	1.37297i
$804$	0.638201	+	2.38180i	0.0225076	+	0.0839996i
$805$	−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	$-0.177514\pi$
$809$	23.1644	+	13.3740i	0.814416	+	0.470203i	−0.0340712	+	0.999419i	$0.510847\pi$
$810$	−1.45853	+	1.82218i	−0.0512474	+	0.0640248i
$811$	7.93739	−	7.93739i	0.278720	−	0.278720i	−0.553878	−	0.832598i	$-0.686853\pi$
$811$	7.93739	−	7.93739i	0.278720	−	0.278720i	0.832598	+	0.553878i	$0.186853\pi$
$812$	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
$815$	26.1235	−	32.6368i	0.915065	−	1.14322i
$816$	−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
$821$	−6.99144	−	26.0924i	−0.244003	−	0.910632i	−0.973882	−	0.227055i	$-0.927090\pi$
$821$	−6.99144	−	26.0924i	−0.244003	−	0.910632i	0.729879	−	0.683577i	$-0.239576\pi$
$822$	−0.174661	−	0.651843i	−0.00609200	−	0.0227356i
$823$	−9.05749	−	2.42695i	−0.315724	−	0.0845980i	0.0974771	−	0.995238i	$-0.468923\pi$
$823$	−9.05749	−	2.42695i	−0.315724	−	0.0845980i	−0.413201	+	0.910640i	$0.635589\pi$
$824$	3.13769	+	3.13769i	0.109307	+	0.109307i
$825$	2.07934	−	6.65567i	0.0723935	−	0.231721i
$826$	−0.248227	+	0.926397i	−0.00863693	+	0.0322335i
$827$	45.0330			1.56595			0.782976	−	0.622052i	$-0.213701\pi$
$827$	45.0330			1.56595			0.782976	+	0.622052i	$0.213701\pi$
$828$	−11.7971	+	44.0273i	−0.409976	+	1.53005i
$829$	21.0075	−	36.3861i	0.729622	−	1.26374i	−0.227421	−	0.973796i	$-0.573029\pi$
$829$	21.0075	−	36.3861i	0.729622	−	1.26374i	0.957043	−	0.289946i	$-0.0936372\pi$
$830$	0.920634	+	0.140463i	0.0319557	+	0.00487555i
$831$		−	6.20942i		−	0.215402i
$832$		0			0
$833$	−1.26182	−	1.26182i	−0.0437194	−	0.0437194i
$834$	0.373887	−	0.100183i	0.0129467	−	0.00346905i
$835$	6.97378	−	45.7081i	0.241338	−	1.58179i
$836$	13.2255	−	7.63575i	0.457414	−	0.264088i
$837$		−	11.0804i		−	0.382993i
$838$	−1.97481	−	3.42047i	−0.0682186	−	0.118158i
$839$	5.24673	+	1.40586i	0.181137	+	0.0485356i	0.348247	−	0.937403i	$-0.386777\pi$
$839$	5.24673	+	1.40586i	0.181137	+	0.0485356i	−0.167110	+	0.985938i	$0.553444\pi$
$840$	0.449122	−	1.02435i	0.0154962	−	0.0353434i
$841$	−4.01574	−	6.95547i	−0.138474	−	0.239844i
$842$	−1.65854	+	0.444405i	−0.0571571	+	0.0153152i
$843$	−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
$848$	7.06186	−	1.89222i	0.242505	−	0.0649791i
$849$	1.95249	+	3.38181i	0.0670093	+	0.116063i
$850$	−0.0652568	+	1.59036i	−0.00223829	+	0.0545488i
$851$	−54.0166	−	14.4737i	−1.85167	−	0.496152i
$852$	−2.19117	−	3.79522i	−0.0750682	−	0.130022i
$853$		−	23.0805i		−	0.790260i	−0.918625	−	0.395130i	$-0.870700\pi$
$853$		−	23.0805i		−	0.790260i	0.918625	−	0.395130i	$-0.129300\pi$
$854$	0.405948	−	0.234374i	0.0138912	−	0.00802012i
$855$	7.24978	+	9.86030i	0.247937	+	0.337215i
$856$	2.50323	−	0.670738i	0.0855586	−	0.0229254i
$857$	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	$-0.0276573\pi$
$860$	−16.9763	−	23.0892i	−0.578886	−	0.787333i
$861$	3.07068	−	5.31857i	0.104648	−	0.181256i
$862$	−0.214481	+	0.800452i	−0.00730524	+	0.0272635i
$863$	−45.1879			−1.53821			−0.769107	−	0.639120i	$-0.779299\pi$
$863$	−45.1879			−1.53821			−0.769107	+	0.639120i	$0.779299\pi$
$864$	0.815407	−	3.04314i	0.0277407	−	0.103530i
$865$	−40.3289	+	4.47028i	−1.37122	+	0.151994i
$866$	1.14100	+	1.14100i	0.0387728	+	0.0387728i
$867$	3.69447	+	0.989932i	0.125471	+	0.0336198i
$868$	−7.81890	−	29.1805i	−0.265391	−	0.990452i
$869$	8.79099	+	32.8084i	0.298214	+	1.11295i
$870$	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
$875$	31.0219	−	2.15591i	1.04873	−	0.0728832i
$876$	−4.78896	+	4.78896i	−0.161804	+	0.161804i
$877$	17.6048	−	10.1641i	0.594471	−	0.343218i	−0.172392	−	0.985028i	$-0.555150\pi$
$877$	17.6048	−	10.1641i	0.594471	−	0.343218i	0.766863	+	0.641810i	$0.221816\pi$
$878$	−3.91675	+	2.26134i	−0.132184	+	0.0763164i
$879$	−0.170126	+	0.170126i	−0.00573821	+	0.00573821i
$880$	−3.89298	−	35.1208i	−0.131232	−	1.18392i
$881$	−28.5961	−	16.5100i	−0.963428	−	0.556236i	−0.0662019	−	0.997806i	$-0.521088\pi$
$881$	−28.5961	−	16.5100i	−0.963428	−	0.556236i	−0.897227	+	0.441571i	$0.854421\pi$
$882$	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
$886$	−0.259261	−	0.967576i	−0.00871005	−	0.0325063i
$887$	−0.163391	−	0.609784i	−0.00548614	−	0.0204745i	0.963129	−	0.269042i	$-0.0867070\pi$
$887$	−0.163391	−	0.609784i	−0.00548614	−	0.0204745i	−0.968615	+	0.248567i	$0.920040\pi$
$888$	1.21775	+	0.326296i	0.0408651	+	0.0109498i
$889$	32.5466	+	32.5466i	1.09158	+	1.09158i
$890$	0.201495	+	1.81780i	0.00675413	+	0.0609329i
$891$	8.34370	−	31.1391i	0.279524	−	1.04320i
$892$	−26.5956			−0.890488
$893$	−0.251872	+	0.939998i	−0.00842856	+	0.0314558i
$894$	0.274116	−	0.474784i	0.00916782	−	0.0158791i
$895$	−5.85556	+	38.3790i	−0.195730	+	1.28287i
$896$		−	11.4359i		−	0.382046i
$897$		0			0
$898$	2.89072	+	2.89072i	0.0964647	+	0.0964647i
$899$	24.2297	−	6.49233i	0.808106	−	0.216531i
$900$	27.8754	−	6.25660i	0.929181	−	0.208553i
$901$	3.93920	−	2.27430i	0.131234	−	0.0757679i
$902$			3.41875i			0.113832i
$903$	3.09139	+	5.35444i	0.102875	+	0.178185i
$904$	−3.78996	−	1.01552i	−0.126052	−	0.0337755i
$905$	−20.2710	−	51.9250i	−0.673830	−	1.72604i
$906$	−0.0597070	−	0.103416i	−0.00198363	−	0.00343575i
$907$	37.8383	−	10.1387i	1.25640	−	0.336651i	0.431594	−	0.902068i	$-0.357951\pi$
$907$	37.8383	−	10.1387i	1.25640	−	0.336651i	0.824805	+	0.565417i	$0.191285\pi$
$908$	−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
$913$	−12.4247	+	3.32919i	−0.411198	+	0.110180i
$914$	0.204012	+	0.353358i	0.00674810	+	0.0116881i
$915$	−0.903940	−	0.396328i	−0.0298833	−	0.0131022i
$916$	7.18510	+	1.92524i	0.237402	+	0.0636117i
$917$	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	$-0.790406\pi$
$919$	−19.9013	+	11.4900i	−0.656485	+	0.379022i	0.134452	+	0.990920i	$0.457073\pi$
$920$	−7.51540	+	5.52569i	−0.247776	+	0.182177i
$921$	4.71852	−	1.26432i	0.155481	−	0.0416609i
$922$	1.55017	+	1.55017i	0.0510520	+	0.0510520i
$923$		0			0
$924$			7.69084i			0.253010i
$925$	7.67617	+	34.2001i	0.252391	+	1.12449i
$926$	1.02676	−	1.77840i	0.0337413	−	0.0584417i
$927$	6.32875	−	23.6192i	0.207863	−	0.775757i
$928$	7.13229			0.234129
$929$	−0.280692	+	1.04756i	−0.00920921	+	0.0343692i	−0.970378	−	0.241593i	$-0.922330\pi$
$929$	−0.280692	+	1.04756i	−0.00920921	+	0.0343692i	0.961168	+	0.275963i	$0.0889966\pi$
$930$	0.345635	−	0.431811i	0.0113338	−	0.0141596i
$931$	−0.988497	−	0.988497i	−0.0323967	−	0.0323967i
$932$	37.7726	+	10.1211i	1.23728	+	0.331529i
$933$	−1.91330	−	7.14054i	−0.0626387	−	0.233771i
$934$	0.724846	+	2.70516i	0.0237177	+	0.0885157i
$935$	−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
$940$	1.77350	+	1.41956i	0.0578450	+	0.0463009i
$941$	22.9413	−	22.9413i	0.747866	−	0.747866i	−0.226212	−	0.974078i	$-0.572634\pi$
$941$	22.9413	−	22.9413i	0.747866	−	0.747866i	0.974078	+	0.226212i	$0.0726342\pi$
$942$	−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
$945$	−12.5033	+	1.38594i	−0.406733	+	0.0450846i
$946$	−2.98069	−	1.72090i	−0.0969107	−	0.0559514i
$947$	13.6493	−	23.6413i	0.443543	−	0.768239i	−0.554406	−	0.832246i	$-0.687055\pi$
$947$	13.6493	−	23.6413i	0.443543	−	0.768239i	0.997949	+	0.0640069i	$0.0203880\pi$
$948$	4.03838	−	4.03838i	0.131161	−	0.131161i
$949$		0			0
$950$	−0.0511215	+	1.24587i	−0.00165860	+	0.0404214i
$951$	1.54003	+	5.74748i	0.0499390	+	0.186375i
$952$	−0.912703	−	3.40625i	−0.0295809	−	0.110397i
$953$	6.17827	+	1.65546i	0.200134	+	0.0536257i	0.357493	−	0.933916i	$-0.383631\pi$
$953$	6.17827	+	1.65546i	0.200134	+	0.0536257i	−0.157360	+	0.987541i	$0.550298\pi$
$954$	0.501965	+	0.501965i	0.0162517	+	0.0162517i
$955$	11.8483	+	9.48372i	0.383401	+	0.306886i
$956$	7.39460	−	27.5970i	0.239158	−	0.892551i
$957$	−6.38600			−0.206430
$958$	−1.44939	+	5.40920i	−0.0468277	+	0.174763i
$959$	−20.7839	+	35.9988i	−0.671147	+	1.16246i
$960$	−4.70181	+	3.45700i	−0.151750	+	0.111574i
$961$			0.991728i			0.0319912i
$962$		0			0
$963$	−10.0981	−	10.0981i	−0.325406	−	0.325406i
$964$	−15.5210	+	4.15885i	−0.499899	+	0.133947i
$965$	−2.64189	−	0.403080i	−0.0850456	−	0.0129756i
$966$	0.867650	−	0.500938i	0.0279162	−	0.0161174i
$967$		−	28.4424i		−	0.914647i	−0.889300	−	0.457324i	$-0.848808\pi$
$967$		−	28.4424i		−	0.914647i	0.889300	−	0.457324i	$-0.151192\pi$
$968$	−1.42372	−	2.46596i	−0.0457602	−	0.0792589i
$969$	−1.52962	−	0.409860i	−0.0491384	−	0.0131666i
$970$	3.21908	−	1.25670i	0.103358	−	0.0403501i
$971$	0.619921	+	1.07374i	0.0198942	+	0.0344578i	0.875801	−	0.482672i	$-0.160334\pi$
$971$	0.619921	+	1.07374i	0.0198942	+	0.0344578i	−0.855907	+	0.517130i	$0.827000\pi$
$972$	−16.8575	+	4.51696i	−0.540705	+	0.144882i
$973$	−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	0.923795	−	0.382888i	$-0.125071\pi$
$977$	32.9480	+	19.0226i	1.05410	+	0.608586i	0.130307	+	0.991474i	$0.458404\pi$
$978$	−0.815418	+	0.218491i	−0.0260742	+	0.00698656i
$979$	−12.6307	−	21.8770i	−0.403678	−	0.699192i
$980$	−3.03982	+	1.18671i	−0.0971035	+	0.0379082i
$981$	−25.6268	−	6.86669i	−0.818202	−	0.219236i
$982$	1.83661	+	3.18111i	0.0586087	+	0.101513i
$983$			34.5934i			1.10336i	0.834056	+	0.551679i	$0.186013\pi$
$983$			34.5934i			1.10336i	−0.834056	+	0.551679i	$0.813987\pi$
$984$	0.999984	−	0.577341i	0.0318783	−	0.0184050i
$985$	44.4772	+	6.78598i	1.41716	+	0.216219i
$986$	1.40805	−	0.377285i	0.0448414	−	0.0120152i
$987$	−0.346545	−	0.346545i	−0.0110307	−	0.0110307i
$988$		0			0
$989$		−	51.5644i		−	1.63965i
$990$	2.76430	−	2.03245i	0.0878553	−	0.0645955i
$991$	−19.7486	+	34.2056i	−0.627335	+	1.08658i	0.360750	+	0.932663i	$0.382521\pi$
$991$	−19.7486	+	34.2056i	−0.627335	+	1.08658i	−0.988084	+	0.153913i	$0.950813\pi$
$992$	2.20832	−	8.24156i	0.0701142	−	0.261670i
$993$	−6.17972			−0.196107
$994$	0.607486	−	2.26717i	0.0192683	−	0.0719103i
$995$	3.80162	+	3.04293i	0.120519	+	0.0964673i
$996$	1.52936	+	1.52936i	0.0484595	+	0.0484595i
$997$	−7.10500	−	1.90378i	−0.225018	−	0.0602933i	0.144549	−	0.989498i	$-0.453827\pi$
$997$	−7.10500	−	1.90378i	−0.225018	−	0.0602933i	−0.369566	+	0.929204i	$0.620494\pi$
$998$	0.0804906	+	0.300395i	0.00254789	+	0.00950884i
$999$	−3.66995	−	13.6964i	−0.116112	−	0.433336i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.3	✓	20	65.12	odd	4
65.2.o.a.63.3	yes	20	13.2	odd	12
65.2.t.a.37.3	yes	20	65.2	even	12
65.2.t.a.58.3	yes	20	13.12	even	2
325.2.s.b.32.3		20	65.38	odd	4
325.2.s.b.193.3		20	65.54	odd	12
325.2.x.b.232.3		20	65.28	even	12
325.2.x.b.318.3		20	65.64	even	2
585.2.cf.a.388.3		20	39.2	even	12
585.2.cf.a.487.3		20	195.77	even	4
585.2.dp.a.37.3		20	195.2	odd	12
585.2.dp.a.253.3		20	39.38	odd	2
845.2.f.d.408.4		20	13.9	even	3
845.2.f.d.437.7		20	65.7	even	12
845.2.f.e.408.7		20	13.4	even	6
845.2.f.e.437.4		20	65.32	even	12
845.2.k.d.268.7		20	13.7	odd	12
845.2.k.d.577.7		20	65.22	odd	12
845.2.k.e.268.4		20	13.6	odd	12
845.2.k.e.577.4		20	65.17	odd	12
845.2.o.e.488.3		20	13.5	odd	4
845.2.o.e.587.3		20	65.62	odd	12
845.2.o.f.488.3		20	13.8	odd	4
845.2.o.f.587.3		20	65.42	odd	12
845.2.o.g.258.3		20	13.11	odd	12
845.2.o.g.357.3		20	5.2	odd	4
845.2.t.e.418.3		20	13.3	even	3
845.2.t.e.657.3		20	65.47	even	4
845.2.t.f.418.3		20	13.10	even	6
845.2.t.f.657.3		20	65.57	even	4
845.2.t.g.188.3		20	1.1	even	1	trivial
845.2.t.g.427.3		20	65.37	even	12	inner

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+(0.113711 + 0.0656513i) q^{2} +(0.332179 - 0.0890070i) q^{3} +(-0.991380 - 1.71712i) q^{4} +(-2.08297 + 0.813169i) q^{5} +(0.0436159 + 0.0116869i) q^{6} +(-1.39069 - 2.40874i) q^{7} -0.522947i q^{8} +(-2.49566 + 1.44087i) q^{9} +(-0.290243 - 0.0442830i) q^{10} +(3.91706 - 1.04957i) q^{11} +(-0.482151 - 0.482151i) q^{12} -0.365201i q^{14} +(-0.619540 + 0.455516i) q^{15} +(-1.94843 + 3.37478i) q^{16} +(-0.627499 + 2.34186i) q^{17} -0.378379 q^{18} +(-0.491577 + 1.83459i) q^{19} +(3.46132 + 2.77055i) q^{20} +(-0.676351 - 0.676351i) q^{21} +(0.514321 + 0.137812i) q^{22} +(2.06467 + 7.70544i) q^{23} +(-0.0465459 - 0.173712i) 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} +(-0.100354 + 0.0111238i) 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} +(4.85547 + 3.88646i) 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} +(1.66178 + 6.20184i) q^{41} +(-0.0325055 - 0.121312i) q^{42} +(-6.24368 - 1.67299i) q^{43} +(-5.68554 - 5.68554i) q^{44} +(4.02670 - 5.03067i) q^{45} +(-0.271096 + 1.01174i) q^{46} +0.512375 q^{47} +(-0.346847 + 1.29445i) q^{48} +(-0.368015 + 0.637420i) q^{49} +(0.640576 - 0.143776i) q^{50} +0.833767i q^{51} +(-1.32662 - 1.32662i) q^{53} +(-0.256537 + 0.0687390i) q^{54} +(-7.30564 + 5.37147i) q^{55} +(-1.25964 + 0.727255i) q^{56} +0.653165i q^{57} +(-0.300626 - 0.520700i) q^{58} +(-2.53667 - 0.679700i) q^{59} +(1.39638 + 0.612235i) q^{60} +(0.641767 + 1.11157i) q^{61} +(-0.694764 + 0.186162i) q^{62} +(6.94135 + 4.00759i) q^{63} +7.58920 q^{64} +0.183113 q^{66} +(-3.13180 - 1.80814i) q^{67} +(4.64334 - 1.24418i) q^{68} +(1.37168 + 2.37581i) q^{69} +(0.296970 + 0.760703i) q^{70} +(6.20800 + 1.66343i) q^{71} +(0.753497 + 1.30509i) q^{72} -9.93250i q^{73} +(-0.797139 + 0.460228i) q^{74} +(0.920070 - 1.45262i) q^{75} +(3.63755 - 0.974678i) q^{76} +(-7.97556 - 7.97556i) q^{77} +8.37577i q^{79} +(1.31425 - 8.61395i) q^{80} +(3.97480 - 6.88456i) q^{81} +(-0.218196 + 0.814318i) q^{82} -3.17194 q^{83} +(-0.490855 + 1.83190i) q^{84} +(-0.597266 - 5.38828i) q^{85} +(-0.600143 - 0.600143i) q^{86} +(-1.52109 - 0.407576i) q^{87} +(-0.548871 - 2.04842i) q^{88} +(-1.61226 - 6.01705i) 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} +(-0.467892 - 4.22112i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 8 q^{6} + 2 q^{7} + 12 q^{9} - 2 q^{10} + 16 q^{11} - 24 q^{12} + 20 q^{15} - 2 q^{16} + 4 q^{17} + 20 q^{19} - 4 q^{21} + 16 q^{22} - 10 q^{23} - 32 q^{24} + 18 q^{25}+ \cdots - 60 q^{99}+O(q^{100}) \) 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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