LMFDB - Embedded newform 189.2.w.a.25.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(25,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 12]))

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

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

chi := DirichletCharacter("189.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.w (of order $9$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.7
Character	$\chi$	$=$	189.25
Dual form			189.2.w.a.121.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30907 + 0.476464i) q^{2} +(-1.39125 - 1.03171i) q^{3} +(-0.0454330 + 0.0381228i) q^{4} +(1.40139 + 0.510065i) q^{5} +(2.31282 + 0.687701i) q^{6} +(-2.64009 - 0.173054i) q^{7} +(1.43440 - 2.48445i) q^{8} +(0.871157 + 2.87073i) q^{9} +O(q^{10})$	\(q+(-1.30907 + 0.476464i) q^{2} +(-1.39125 - 1.03171i) q^{3} +(-0.0454330 + 0.0381228i) q^{4} +(1.40139 + 0.510065i) q^{5} +(2.31282 + 0.687701i) q^{6} +(-2.64009 - 0.173054i) q^{7} +(1.43440 - 2.48445i) q^{8} +(0.871157 + 2.87073i) q^{9} -2.07755 q^{10} +(4.49413 - 1.63573i) q^{11} +(0.102540 - 0.00616480i) q^{12} +(0.371663 + 2.10780i) q^{13} +(3.53852 - 1.03137i) q^{14} +(-1.42345 - 2.15546i) q^{15} +(-0.673384 + 3.81895i) q^{16} +5.84823 q^{17} +(-2.50821 - 3.34292i) q^{18} +7.81006 q^{19} +(-0.0831146 + 0.0302512i) q^{20} +(3.49448 + 2.96456i) q^{21} +(-5.10378 + 4.28258i) q^{22} +(-0.451305 - 2.55948i) q^{23} +(-4.55883 + 1.97661i) q^{24} +(-2.12649 - 1.78433i) q^{25} +(-1.49083 - 2.58219i) q^{26} +(1.74976 - 4.89268i) q^{27} +(0.126544 - 0.0927851i) q^{28} +(-1.22445 + 6.94422i) q^{29} +(2.89040 + 2.14343i) q^{30} +(1.19198 - 1.00019i) q^{31} +(0.0582395 + 0.330293i) q^{32} +(-7.94006 - 2.36092i) q^{33} +(-7.65576 + 2.78647i) q^{34} +(-3.61153 - 1.58913i) q^{35} +(-0.149019 - 0.0972148i) q^{36} +(-3.52981 + 6.11382i) q^{37} +(-10.2239 + 3.72121i) q^{38} +(1.65756 - 3.31593i) q^{39} +(3.27739 - 2.75005i) q^{40} +(-1.33423 - 7.56680i) q^{41} +(-5.98704 - 2.21583i) q^{42} +(-6.86262 - 5.75842i) q^{43} +(-0.141823 + 0.245645i) q^{44} +(-0.243426 + 4.46737i) q^{45} +(1.81029 + 3.13551i) q^{46} +(4.90812 + 4.11840i) q^{47} +(4.87689 - 4.61838i) q^{48} +(6.94010 + 0.913753i) q^{49} +(3.63390 + 1.32263i) q^{50} +(-8.13636 - 6.03367i) q^{51} +(-0.0972411 - 0.0815949i) q^{52} +(3.57502 - 6.19211i) q^{53} +(0.0406280 + 7.23858i) q^{54} +7.13238 q^{55} +(-4.21688 + 6.31093i) q^{56} +(-10.8658 - 8.05770i) q^{57} +(-1.70577 - 9.67390i) q^{58} +(0.143277 + 0.812567i) q^{59} +(0.146844 + 0.0436629i) q^{60} +(6.10769 + 5.12496i) q^{61} +(-1.08383 + 1.87725i) q^{62} +(-1.80314 - 7.72973i) q^{63} +(-4.11148 - 7.12129i) q^{64} +(-0.554272 + 3.14343i) q^{65} +(11.5190 - 0.692533i) q^{66} +(0.431518 + 0.157060i) q^{67} +(-0.265703 + 0.222951i) q^{68} +(-2.01275 + 4.02649i) q^{69} +(5.48492 + 0.359528i) q^{70} +(2.15632 + 3.73486i) q^{71} +(8.38177 + 1.95342i) q^{72} +(2.27530 + 3.94093i) q^{73} +(1.70777 - 9.68527i) q^{74} +(1.11756 + 4.67637i) q^{75} +(-0.354834 + 0.297741i) q^{76} +(-12.1480 + 3.54074i) q^{77} +(-0.589949 + 5.13056i) q^{78} +(-5.54499 + 2.01821i) q^{79} +(-2.89159 + 5.00838i) q^{80} +(-7.48217 + 5.00171i) q^{81} +(5.35191 + 9.26979i) q^{82} +(-0.177225 + 1.00509i) q^{83} +(-0.271782 - 0.00146936i) q^{84} +(8.19567 + 2.98298i) q^{85} +(11.7274 + 4.26841i) q^{86} +(8.86793 - 8.39787i) q^{87} +(2.38248 - 13.5117i) q^{88} -1.93404 q^{89} +(-1.80988 - 5.96410i) q^{90} +(-0.616458 - 5.62910i) q^{91} +(0.118079 + 0.0990797i) q^{92} +(-2.69024 + 0.161739i) q^{93} +(-8.38736 - 3.05275i) q^{94} +(10.9450 + 3.98364i) q^{95} +(0.259740 - 0.519606i) q^{96} +(8.10490 + 6.80081i) q^{97} +(-9.52048 + 2.11054i) q^{98} +(8.61084 + 11.4765i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.30907	+	0.476464i	−0.925655	+	0.336911i	−0.760486	−	0.649354i	$-0.775039\pi$
$2$	−1.30907	+	0.476464i	−0.925655	+	0.336911i	−0.165169	+	0.986265i	$0.552817\pi$
$3$	−1.39125	−	1.03171i	−0.803239	−	0.595657i
$3$	−1.39125	−	1.03171i	−0.803239	−	0.595657i
$4$	−0.0454330	+	0.0381228i	−0.0227165	+	0.0190614i
$5$	1.40139	+	0.510065i	0.626722	+	0.228108i	0.635804	−	0.771851i	$-0.280669\pi$
$5$	1.40139	+	0.510065i	0.626722	+	0.228108i	−0.00908190	+	0.999959i	$0.502891\pi$
$6$	2.31282	+	0.687701i	0.944205	+	0.280753i
$7$	−2.64009	−	0.173054i	−0.997859	−	0.0654081i
$7$	−2.64009	−	0.173054i	−0.997859	−	0.0654081i
$8$	1.43440	−	2.48445i	0.507136	−	0.878386i
$9$	0.871157	+	2.87073i	0.290386	+	0.956910i
$10$	−2.07755			−0.656980
$11$	4.49413	−	1.63573i	1.35503	−	0.493191i	0.440518	−	0.897744i	$-0.354795\pi$
$11$	4.49413	−	1.63573i	1.35503	−	0.493191i	0.914515	+	0.404553i	$0.132573\pi$
$12$	0.102540	−	0.00616480i	0.0296008	−	0.00177963i
$13$	0.371663	+	2.10780i	0.103081	+	0.584599i	0.991970	+	0.126477i	$0.0403669\pi$
$13$	0.371663	+	2.10780i	0.103081	+	0.584599i	−0.888889	+	0.458123i	$0.848522\pi$
$14$	3.53852	−	1.03137i	0.945709	−	0.275644i
$15$	−1.42345	−	2.15546i	−0.367533	−	0.556537i
$16$	−0.673384	+	3.81895i	−0.168346	+	0.954738i
$17$	5.84823			1.41840			0.709202	−	0.705005i	$-0.249055\pi$
$17$	5.84823			1.41840			0.709202	+	0.705005i	$0.249055\pi$
$18$	−2.50821	−	3.34292i	−0.591190	−	0.787934i
$19$	7.81006			1.79175			0.895875	−	0.444306i	$-0.146550\pi$
$19$	7.81006			1.79175			0.895875	+	0.444306i	$0.146550\pi$
$20$	−0.0831146	+	0.0302512i	−0.0185850	+	0.00676438i
$21$	3.49448	+	2.96456i	0.762558	+	0.646920i
$22$	−5.10378	+	4.28258i	−1.08813	+	0.913050i
$23$	−0.451305	−	2.55948i	−0.0941036	−	0.533688i	−0.995018	−	0.0996919i	$-0.968214\pi$
$23$	−0.451305	−	2.55948i	−0.0941036	−	0.533688i	0.900915	−	0.433996i	$-0.142897\pi$
$24$	−4.55883	+	1.97661i	−0.930568	+	0.403475i
$25$	−2.12649	−	1.78433i	−0.425297	−	0.356867i
$26$	−1.49083	−	2.58219i	−0.292375	−	0.506408i
$27$	1.74976	−	4.89268i	0.336741	−	0.941597i
$28$	0.126544	−	0.0927851i	0.0239146	−	0.0175347i
$29$	−1.22445	+	6.94422i	−0.227375	+	1.28951i	0.630717	+	0.776013i	$0.282761\pi$
$29$	−1.22445	+	6.94422i	−0.227375	+	1.28951i	−0.858092	+	0.513496i	$0.828350\pi$
$30$	2.89040	+	2.14343i	0.527712	+	0.391335i
$31$	1.19198	−	1.00019i	0.214085	−	0.179639i	−0.529439	−	0.848348i	$-0.677597\pi$
$31$	1.19198	−	1.00019i	0.214085	−	0.179639i	0.743524	+	0.668709i	$0.233153\pi$
$32$	0.0582395	+	0.330293i	0.0102954	+	0.0583881i
$33$	−7.94006	−	2.36092i	−1.38219	−	0.410984i
$34$	−7.65576	+	2.78647i	−1.31295	+	0.477876i
$35$	−3.61153	−	1.58913i	−0.610460	−	0.268612i
$36$	−0.149019	−	0.0972148i	−0.0248366	−	0.0162025i
$37$	−3.52981	+	6.11382i	−0.580298	+	1.00511i	0.415146	+	0.909755i	$0.363731\pi$
$37$	−3.52981	+	6.11382i	−0.580298	+	1.00511i	−0.995444	+	0.0953507i	$0.969603\pi$
$38$	−10.2239	+	3.72121i	−1.65854	+	0.603660i
$39$	1.65756	−	3.31593i	0.265422	−	0.530974i
$40$	3.27739	−	2.75005i	0.518200	−	0.434822i
$41$	−1.33423	−	7.56680i	−0.208372	−	1.18174i	−0.892045	−	0.451947i	$-0.850730\pi$
$41$	−1.33423	−	7.56680i	−0.208372	−	1.18174i	0.683673	−	0.729789i	$-0.260382\pi$
$42$	−5.98704	−	2.21583i	−0.923820	−	0.341910i
$43$	−6.86262	−	5.75842i	−1.04654	−	0.878152i	−0.0538147	−	0.998551i	$-0.517138\pi$
$43$	−6.86262	−	5.75842i	−1.04654	−	0.878152i	−0.992726	+	0.120399i	$0.961582\pi$
$44$	−0.141823	+	0.245645i	−0.0213807	+	0.0370324i
$45$	−0.243426	+	4.46737i	−0.0362877	+	0.665956i
$46$	1.81029	+	3.13551i	0.266913	+	0.462306i
$47$	4.90812	+	4.11840i	0.715923	+	0.600730i	0.926254	−	0.376900i	$-0.123010\pi$
$47$	4.90812	+	4.11840i	0.715923	+	0.600730i	−0.210332	+	0.977630i	$0.567454\pi$
$48$	4.87689	−	4.61838i	0.703918	−	0.666606i
$49$	6.94010	+	0.913753i	0.991444	+	0.130536i
$50$	3.63390	+	1.32263i	0.513911	+	0.187048i
$51$	−8.13636	−	6.03367i	−1.13932	−	0.844882i
$52$	−0.0972411	−	0.0815949i	−0.0134849	−	0.0113152i
$53$	3.57502	−	6.19211i	0.491066	−	0.850552i	−0.508881	−	0.860837i	$-0.669941\pi$
$53$	3.57502	−	6.19211i	0.491066	−	0.850552i	0.999947	+	0.0102850i	$0.00327388\pi$
$54$	0.0406280	+	7.23858i	0.00552877	+	0.985046i
$55$	7.13238			0.961730
$56$	−4.21688	+	6.31093i	−0.563504	+	0.843334i
$57$	−10.8658	−	8.05770i	−1.43920	−	1.06727i
$58$	−1.70577	−	9.67390i	−0.223978	−	1.27025i
$59$	0.143277	+	0.812567i	0.0186531	+	0.105787i	0.992713	−	0.120504i	$-0.0384510\pi$
$59$	0.143277	+	0.812567i	0.0186531	+	0.105787i	−0.974060	+	0.226291i	$0.927340\pi$
$60$	0.146844	+	0.0436629i	0.0189574	+	0.00563686i
$61$	6.10769	+	5.12496i	0.782010	+	0.656184i	0.943754	−	0.330649i	$-0.107267\pi$
$61$	6.10769	+	5.12496i	0.782010	+	0.656184i	−0.161744	+	0.986833i	$0.551712\pi$
$62$	−1.08383	+	1.87725i	−0.137647	+	0.238411i
$63$	−1.80314	−	7.72973i	−0.227174	−	0.973854i
$64$	−4.11148	−	7.12129i	−0.513935	−	0.890161i
$65$	−0.554272	+	3.14343i	−0.0687490	+	0.389895i
$66$	11.5190	−	0.692533i	1.41789	−	0.0852449i
$67$	0.431518	+	0.157060i	0.0527183	+	0.0191879i	0.368245	−	0.929729i	$-0.379959\pi$
$67$	0.431518	+	0.157060i	0.0527183	+	0.0191879i	−0.315526	+	0.948917i	$0.602181\pi$
$68$	−0.265703	+	0.222951i	−0.0322212	+	0.0270368i
$69$	−2.01275	+	4.02649i	−0.242307	+	0.484732i
$70$	5.48492	+	0.359528i	0.655574	+	0.0429719i
$71$	2.15632	+	3.73486i	0.255909	+	0.443247i	0.965142	−	0.261727i	$-0.0842921\pi$
$71$	2.15632	+	3.73486i	0.255909	+	0.443247i	−0.709233	+	0.704974i	$0.750959\pi$
$72$	8.38177	+	1.95342i	0.987801	+	0.230213i
$73$	2.27530	+	3.94093i	0.266304	+	0.461251i	0.967904	−	0.251319i	$-0.0808643\pi$
$73$	2.27530	+	3.94093i	0.266304	+	0.461251i	−0.701601	+	0.712570i	$0.747531\pi$
$74$	1.70777	−	9.68527i	0.198525	−	1.12589i
$75$	1.11756	+	4.67637i	0.129045	+	0.539981i
$76$	−0.354834	+	0.297741i	−0.0407023	+	0.0341533i
$77$	−12.1480	+	3.54074i	−1.38439	+	0.403505i
$78$	−0.589949	+	5.13056i	−0.0667986	+	0.580922i
$79$	−5.54499	+	2.01821i	−0.623860	+	0.227067i	−0.634557	−	0.772876i	$-0.718817\pi$
$79$	−5.54499	+	2.01821i	−0.623860	+	0.227067i	0.0106965	+	0.999943i	$0.496595\pi$
$80$	−2.89159	+	5.00838i	−0.323290	+	0.559954i
$81$	−7.48217	+	5.00171i	−0.831352	+	0.555746i
$82$	5.35191	+	9.26979i	0.591020	+	1.02368i
$83$	−0.177225	+	1.00509i	−0.0194529	+	0.110323i	−0.992988	−	0.118214i	$-0.962283\pi$
$83$	−0.177225	+	1.00509i	−0.0194529	+	0.110323i	0.973535	+	0.228537i	$0.0733942\pi$
$84$	−0.271782	−	0.00146936i	−0.0296538	−	0.000160320i
$85$	8.19567	+	2.98298i	0.888945	+	0.323550i
$86$	11.7274	+	4.26841i	1.26459	+	0.460274i
$87$	8.86793	−	8.39787i	0.950741	−	0.900346i
$88$	2.38248	−	13.5117i	0.253974	−	1.44036i
$89$	−1.93404			−0.205007			−0.102504	−	0.994733i	$-0.532685\pi$
$89$	−1.93404			−0.205007			−0.102504	+	0.994733i	$0.532685\pi$
$90$	−1.80988	−	5.96410i	−0.190778	−	0.628671i
$91$	−0.616458	−	5.62910i	−0.0646224	−	0.590090i
$92$	0.118079	+	0.0990797i	0.0123105	+	0.0103298i
$93$	−2.69024	+	0.161739i	−0.278965	+	0.0167716i
$94$	−8.38736	−	3.05275i	−0.865090	−	0.314867i
$95$	10.9450	+	3.98364i	1.12293	+	0.408713i
$96$	0.259740	−	0.519606i	0.0265096	−	0.0530321i
$97$	8.10490	+	6.80081i	0.822927	+	0.690518i	0.953656	−	0.300900i	$-0.0972871\pi$
$97$	8.10490	+	6.80081i	0.822927	+	0.690518i	−0.130728	+	0.991418i	$0.541732\pi$
$98$	−9.52048	+	2.11054i	−0.961714	+	0.213197i
$99$	8.61084	+	11.4765i	0.865422	+	1.15343i
$100$	0.164636			0.0164636
$101$	0.439689	−	2.49360i	0.0437507	−	0.248123i	−0.955087	−	0.296326i	$-0.904238\pi$
$101$	0.439689	−	2.49360i	0.0437507	−	0.248123i	0.998838	+	0.0482035i	$0.0153496\pi$
$102$	13.5259	+	4.02183i	1.33926	+	0.398221i
$103$	−1.88418	−	0.685784i	−0.185653	−	0.0675723i	0.247521	−	0.968883i	$-0.420384\pi$
$103$	−1.88418	−	0.685784i	−0.185653	−	0.0675723i	−0.433174	+	0.901310i	$0.642606\pi$
$104$	5.76984	+	2.10005i	0.565780	+	0.205927i
$105$	3.38502	+	5.93693i	0.330344	+	0.579385i
$106$	−1.72964	+	9.80930i	−0.167998	+	0.952763i
$107$	−5.24178	−	9.07903i	−0.506742	−	0.877703i	−0.999970	−	0.00780249i	$-0.997516\pi$
$107$	−5.24178	−	9.07903i	−0.506742	−	0.877703i	0.493228	−	0.869900i	$-0.335817\pi$
$108$	0.107026	+	0.288995i	0.0102986	+	0.0278085i
$109$	2.80584	−	4.85985i	0.268750	−	0.465489i	−0.699789	−	0.714350i	$-0.746723\pi$
$109$	2.80584	−	4.85985i	0.268750	−	0.465489i	0.968539	+	0.248860i	$0.0800560\pi$
$110$	−9.33681	+	3.39832i	−0.890230	+	0.324017i
$111$	11.2185	−	4.86412i	1.06482	−	0.461682i
$112$	2.43868	−	9.96583i	0.230433	−	0.941682i
$113$	8.41891	−	7.06430i	0.791984	−	0.664553i	−0.154252	−	0.988032i	$-0.549297\pi$
$113$	8.41891	−	7.06430i	0.791984	−	0.664553i	0.946236	+	0.323478i	$0.104852\pi$
$114$	18.0633	+	5.37099i	1.69178	+	0.503039i
$115$	0.673045	−	3.81703i	0.0627618	−	0.355940i
$116$	−0.209102	−	0.362176i	−0.0194147	−	0.0336272i
$117$	−5.72715	+	2.90317i	−0.529476	+	0.268398i
$118$	−0.574719	−	0.995443i	−0.0529072	−	0.0916380i
$119$	−15.4398	−	1.01206i	−1.41537	−	0.0927752i
$120$	−7.39692	+	0.444709i	−0.675243	+	0.0405962i
$121$	9.09513	−	7.63172i	0.826830	−	0.693793i
$122$	−10.4373	−	3.79886i	−0.944947	−	0.343932i
$123$	−5.95048	+	11.9039i	−0.536537	+	1.07333i
$124$	−0.0160251	+	0.0908829i	−0.00143910	+	0.00816153i
$125$	−5.79824	−	10.0429i	−0.518611	−	0.898260i
$126$	6.04338	+	9.25965i	0.538387	+	0.824915i
$127$	−4.39951	+	7.62018i	−0.390394	+	0.676182i	−0.992501	−	0.122233i	$-0.960994\pi$
$127$	−4.39951	+	7.62018i	−0.390394	+	0.676182i	0.602108	+	0.798415i	$0.294328\pi$
$128$	8.26142	+	6.93215i	0.730213	+	0.612722i
$129$	3.60662	+	15.0916i	0.317545	+	1.32874i
$130$	−0.772149	−	4.37908i	−0.0677220	−	0.384070i
$131$	0.191855	+	1.08806i	0.0167624	+	0.0950644i	0.992041	−	0.125914i	$-0.0401862\pi$
$131$	0.191855	+	1.08806i	0.0167624	+	0.0950644i	−0.975279	+	0.220978i	$0.929075\pi$
$132$	0.450746	−	0.195434i	0.0392324	−	0.0170103i
$133$	−20.6192	−	1.35156i	−1.78791	−	0.117195i
$134$	−0.639722			−0.0552636
$135$	4.94768	−	5.96408i	0.425829	−	0.513307i
$136$	8.38869	−	14.5296i	0.719324	−	1.24591i
$137$	−0.723085	−	0.606740i	−0.0617773	−	0.0518373i	0.611376	−	0.791340i	$-0.290616\pi$
$137$	−0.723085	−	0.606740i	−0.0617773	−	0.0518373i	−0.673153	+	0.739503i	$0.735061\pi$
$138$	0.716368	−	6.22998i	0.0609813	−	0.530331i
$139$	−8.90721	−	3.24196i	−0.755499	−	0.274979i	−0.0645814	−	0.997912i	$-0.520571\pi$
$139$	−8.90721	−	3.24196i	−0.755499	−	0.274979i	−0.690918	+	0.722933i	$0.742793\pi$
$140$	0.224665	−	0.0654826i	0.0189876	−	0.00553429i
$141$	−2.57944	−	10.7935i	−0.217228	−	0.908974i
$142$	−4.60231	−	3.86180i	−0.386218	−	0.324075i
$143$	5.11810	+	8.86481i	0.427997	+	0.741312i
$144$	−11.5498	+	1.39380i	−0.962483	+	0.116150i
$145$	−5.25794	+	9.10703i	−0.436649	+	0.756297i
$146$	−4.85625	−	4.07487i	−0.401906	−	0.337239i
$147$	−8.71270	−	8.43142i	−0.718611	−	0.695412i
$148$	−0.0727059	−	0.412335i	−0.00597638	−	0.0338938i
$149$	0.0332949	−	0.0279377i	0.00272763	−	0.00228875i	−0.641423	−	0.767188i	$-0.721656\pi$
$149$	0.0332949	−	0.0279377i	0.00272763	−	0.00228875i	0.644150	+	0.764899i	$0.277211\pi$
$150$	−3.69109	−	5.58923i	−0.301377	−	0.456359i
$151$	−17.4552	+	6.35317i	−1.42048	+	0.517014i	−0.934188	−	0.356781i	$-0.883874\pi$
$151$	−17.4552	+	6.35317i	−1.42048	+	0.517014i	−0.486295	+	0.873795i	$0.661652\pi$
$152$	11.2027	−	19.4037i	0.908662	−	1.57385i
$153$	5.09473	+	16.7887i	0.411884	+	1.35728i
$154$	14.2155	−	10.4232i	1.14552	−	0.839922i
$155$	2.18059	−	0.793669i	0.175149	−	0.0637490i
$156$	0.0511046	+	0.213843i	0.00409164	+	0.0171212i
$157$	−2.20209	−	12.4887i	−0.175746	−	0.996704i	−0.937279	−	0.348579i	$-0.886664\pi$
$157$	−2.20209	−	12.4887i	−0.175746	−	0.996704i	0.761534	−	0.648125i	$-0.224447\pi$
$158$	6.29720	−	5.28398i	0.500978	−	0.420371i
$159$	−11.3622	+	4.92641i	−0.901081	+	0.390689i
$160$	−0.0868544	+	0.492576i	−0.00686645	+	0.0389415i
$161$	0.748557	+	6.83534i	0.0589945	+	0.538700i
$162$	7.41158	−	10.1126i	0.582308	−	0.794520i
$163$	−1.63127	−	2.82544i	−0.127771	−	0.221306i	0.795042	−	0.606555i	$-0.207449\pi$
$163$	−1.63127	−	2.82544i	−0.127771	−	0.221306i	−0.922813	+	0.385249i	$0.874116\pi$
$164$	0.349086	+	0.292918i	0.0272590	+	0.0228730i
$165$	−9.92293	−	7.35853i	−0.772499	−	0.572861i
$166$	−0.246889	−	1.40018i	−0.0191623	−	0.108675i
$167$	−13.5065	+	11.3333i	−1.04516	+	0.876996i	−0.992577	−	0.121620i	$-0.961191\pi$
$167$	−13.5065	+	11.3333i	−1.04516	+	0.876996i	−0.0525869	+	0.998616i	$0.516747\pi$
$168$	12.3778	−	4.42951i	0.954966	−	0.341744i
$169$	7.91130	−	2.87948i	0.608562	−	0.221498i
$170$	−12.1500			−0.931864
$171$	6.80379	+	22.4206i	0.520299	+	1.71454i
$172$	0.531317			0.0405125
$173$	2.07208	−	11.7513i	0.157537	−	0.893438i	−0.798892	−	0.601474i	$-0.794580\pi$
$173$	2.07208	−	11.7513i	0.157537	−	0.893438i	0.956429	−	0.291964i	$-0.0943086\pi$
$174$	−7.60749	+	15.2187i	−0.576722	+	1.15372i
$175$	5.30532	+	5.07879i	0.401045	+	0.383920i
$176$	3.22050	+	18.2644i	0.242754	+	1.37673i
$177$	0.638997	−	1.27830i	0.0480299	−	0.0960832i
$178$	2.53179	−	0.921498i	0.189766	−	0.0690692i
$179$	−9.92811			−0.742062			−0.371031	−	0.928620i	$-0.620996\pi$
$179$	−9.92811			−0.742062			−0.371031	+	0.928620i	$0.620996\pi$
$180$	−0.159249	−	0.212246i	−0.0118697	−	0.0158199i
$181$	−11.0205	+	19.0880i	−0.819146	+	1.41880i	0.0871660	+	0.996194i	$0.472219\pi$
$181$	−11.0205	+	19.0880i	−0.819146	+	1.41880i	−0.906312	+	0.422609i	$0.861114\pi$
$182$	3.48905	+	7.07518i	0.258626	+	0.524447i
$183$	−3.20987	−	13.4315i	−0.237280	−	0.992882i
$184$	−7.00624	−	2.55006i	−0.516507	−	0.187993i
$185$	−8.06511	+	6.76743i	−0.592958	+	0.497551i
$186$	3.44466	−	1.49353i	0.252575	−	0.109511i
$187$	26.2827	−	9.56613i	1.92198	−	0.699545i
$188$	−0.379995			−0.0277140
$189$	−5.46620	+	12.6143i	−0.397608	+	0.917556i
$190$	−16.2258			−1.17714
$191$	4.40924	−	1.60483i	0.319042	−	0.116122i	−0.177535	−	0.984114i	$-0.556812\pi$
$191$	4.40924	−	1.60483i	0.319042	−	0.116122i	0.496577	+	0.867993i	$0.334590\pi$
$192$	−1.62699	+	14.1493i	−0.117418	+	1.02114i
$193$	−16.7099	+	14.0213i	−1.20281	+	1.00928i	−0.203262	+	0.979124i	$0.565154\pi$
$193$	−16.7099	+	14.0213i	−1.20281	+	1.00928i	−0.999545	+	0.0301510i	$0.990401\pi$
$194$	−13.8502	−	5.04108i	−0.994390	−	0.361928i
$195$	4.01424	−	3.80146i	0.287465	−	0.272228i
$196$	−0.350144	+	0.223062i	−0.0250103	+	0.0159330i
$197$	1.13500	−	1.96587i	0.0808651	−	0.140063i	−0.822757	−	0.568394i	$-0.807565\pi$
$197$	1.13500	−	1.96587i	0.0808651	−	0.140063i	0.903622	+	0.428331i	$0.140898\pi$
$198$	−16.7403	−	10.9208i	−1.18968	−	0.776106i
$199$	−0.0489016			−0.00346655			−0.00173327	−	0.999998i	$-0.500552\pi$
$199$	−0.0489016			−0.00346655			−0.00173327	+	0.999998i	$0.500552\pi$
$200$	−7.48332	+	2.72370i	−0.529150	+	0.192595i
$201$	−0.438310	−	0.663710i	−0.0309160	−	0.0468145i
$202$	0.612525	+	3.47380i	0.0430971	+	0.244416i
$203$	4.43438	−	18.1214i	0.311233	−	1.27188i
$204$	0.599679	−	0.0360532i	0.0419859	−	0.00252423i
$205$	1.98978	−	11.2846i	0.138972	−	0.788151i
$206$	2.79328			0.194617
$207$	6.95441	−	3.52528i	0.483365	−	0.245024i
$208$	−8.29987			−0.575492
$209$	35.0994	−	12.7752i	2.42788	−	0.883676i
$210$	−7.25997	−	6.15903i	−0.500986	−	0.425014i
$211$	−6.37793	+	5.35172i	−0.439075	+	0.368428i	−0.835363	−	0.549698i	$-0.814743\pi$
$211$	−6.37793	+	5.35172i	−0.439075	+	0.368428i	0.396288	+	0.918126i	$0.370298\pi$
$212$	0.0736369	+	0.417616i	0.00505741	+	0.0286820i
$213$	0.853300	−	7.42083i	0.0584672	−	0.508467i
$214$	11.1877	+	9.38760i	0.764776	+	0.641723i
$215$	−6.68006	−	11.5702i	−0.455576	−	0.789081i
$216$	−9.64578	−	11.3652i	−0.656312	−	0.773306i
$217$	−3.32001	+	2.43430i	−0.225377	+	0.165251i
$218$	−1.35750	+	7.69878i	−0.0919417	+	0.521427i
$219$	0.900381	−	7.83027i	0.0608421	−	0.529121i
$220$	−0.324045	+	0.271906i	−0.0218471	+	0.0183319i
$221$	2.17357	+	12.3269i	0.146210	+	0.829198i
$222$	−12.3683	+	11.7127i	−0.830107	+	0.786106i
$223$	3.41124	−	1.24159i	0.228434	−	0.0831431i	−0.225267	−	0.974297i	$-0.572326\pi$
$223$	3.41124	−	1.24159i	0.228434	−	0.0831431i	0.453701	+	0.891154i	$0.350103\pi$
$224$	−0.0965990	−	0.882080i	−0.00645429	−	0.0589364i
$225$	3.26983	−	7.65900i	0.217989	−	0.510600i
$226$	−7.65508	+	13.2590i	−0.509209	+	0.881975i
$227$	8.50651	−	3.09612i	0.564597	−	0.205496i	−0.0439233	−	0.999035i	$-0.513986\pi$
$227$	8.50651	−	3.09612i	0.564597	−	0.205496i	0.608520	+	0.793538i	$0.291763\pi$
$228$	0.800845	−	0.0481475i	0.0530373	−	0.00318864i
$229$	7.84521	−	6.58291i	0.518426	−	0.435011i	−0.345656	−	0.938361i	$-0.612344\pi$
$229$	7.84521	−	6.58291i	0.518426	−	0.435011i	0.864083	+	0.503350i	$0.167899\pi$
$230$	0.937610	+	5.31745i	0.0618242	+	0.350622i
$231$	20.5539	+	7.60709i	1.35235	+	0.500510i
$232$	15.4962	+	13.0029i	1.01738	+	0.853680i
$233$	−6.85759	+	11.8777i	−0.449256	+	0.778133i	−0.998338	−	0.0576349i	$-0.981644\pi$
$233$	−6.85759	+	11.8777i	−0.449256	+	0.778133i	0.549082	+	0.835768i	$0.314977\pi$
$234$	6.11401	−	6.52925i	0.399685	−	0.426830i
$235$	4.77755	+	8.27496i	0.311653	+	0.539799i
$236$	−0.0374868	−	0.0314552i	−0.00244018	−	0.00204756i
$237$	9.79668	+	2.91297i	0.636363	+	0.189218i
$238$	20.6941	−	6.03166i	1.34140	−	0.390975i
$239$	9.66912	+	3.51927i	0.625444	+	0.227643i	0.635247	−	0.772309i	$-0.280898\pi$
$239$	9.66912	+	3.51927i	0.625444	+	0.227643i	−0.00980329	+	0.999952i	$0.503121\pi$
$240$	9.19012	−	3.98464i	0.593220	−	0.257207i
$241$	−3.78789	−	3.17842i	−0.244000	−	0.204740i	0.512584	−	0.858637i	$-0.328688\pi$
$241$	−3.78789	−	3.17842i	−0.244000	−	0.204740i	−0.756583	+	0.653897i	$0.773133\pi$
$242$	−8.26996	+	14.3240i	−0.531613	+	0.920781i
$243$	15.5699	+	0.760777i	0.998808	+	0.0488038i
$244$	−0.472868			−0.0302723
$245$	9.25974	+	4.82043i	0.591583	+	0.307966i
$246$	2.11786	−	18.4182i	0.135030	−	1.17430i
$247$	2.90271	+	16.4621i	0.184695	+	1.04746i
$248$	−0.775146	−	4.39607i	−0.0492218	−	0.279151i
$249$	1.28352	−	1.21549i	0.0813401	−	0.0770285i
$250$	12.3754	+	10.3842i	0.782688	+	0.656753i
$251$	−2.29292	+	3.97146i	−0.144728	+	0.250676i	−0.929271	−	0.369398i	$-0.879564\pi$
$251$	−2.29292	+	3.97146i	−0.144728	+	0.250676i	0.784543	+	0.620074i	$0.212897\pi$
$252$	0.376601	+	0.282444i	0.0237236	+	0.0177923i
$253$	−6.21484	−	10.7644i	−0.390724	−	0.676753i
$254$	2.12855	−	12.0716i	0.133557	−	0.757439i
$255$	−8.32467	−	12.6056i	−0.521311	−	0.789394i
$256$	1.33638	+	0.486401i	0.0835235	+	0.0304001i
$257$	−15.9125	+	13.3522i	−0.992596	+	0.832887i	−0.985941	−	0.167091i	$-0.946563\pi$
$257$	−15.9125	+	13.3522i	−0.992596	+	0.832887i	−0.00665437	+	0.999978i	$0.502118\pi$
$258$	−11.9119	−	18.0376i	−0.741605	−	1.12297i
$259$	10.3770	−	15.5302i	0.644797	−	0.964997i
$260$	−0.0946542	−	0.163946i	−0.00587021	−	0.0101675i
$261$	−21.0017	+	2.53443i	−1.29997	+	0.156878i
$262$	−0.769574	−	1.33294i	−0.0475444	−	0.0823494i
$263$	3.49710	−	19.8330i	0.215640	−	1.22296i	−0.664152	−	0.747598i	$-0.731207\pi$
$263$	3.49710	−	19.8330i	0.215640	−	1.22296i	0.879792	−	0.475359i	$-0.157682\pi$
$264$	−17.2548	+	16.3402i	−1.06196	+	1.00567i
$265$	8.16839	−	6.85409i	0.501780	−	0.421043i
$266$	27.6361	−	8.05502i	1.69448	−	0.493885i
$267$	2.69073	+	1.99536i	0.164670	+	0.122114i
$268$	−0.0255927	+	0.00931498i	−0.00156332	+	0.000569003i
$269$	3.35015	−	5.80263i	0.204262	−	0.353792i	−0.745635	−	0.666354i	$-0.767854\pi$
$269$	3.35015	−	5.80263i	0.204262	−	0.353792i	0.949897	+	0.312562i	$0.101187\pi$
$270$	−3.63521	+	10.1648i	−0.221232	+	0.618611i
$271$	−7.25281	−	12.5622i	−0.440577	−	0.763102i	0.557155	−	0.830408i	$-0.311893\pi$
$271$	−7.25281	−	12.5622i	−0.440577	−	0.763102i	−0.997732	+	0.0673067i	$0.978559\pi$
$272$	−3.93811	+	22.3341i	−0.238783	+	1.35420i
$273$	−4.94994	+	8.46749i	−0.299584	+	0.512476i
$274$	1.23566	+	0.449744i	0.0746490	+	0.0271700i
$275$	−12.4754	−	4.54068i	−0.752295	−	0.273813i
$276$	−0.0620556	−	0.259667i	−0.00373531	−	0.0156301i
$277$	−2.02300	+	11.4730i	−0.121550	+	0.689344i	0.861747	+	0.507338i	$0.169370\pi$
$277$	−2.02300	+	11.4730i	−0.121550	+	0.689344i	−0.983297	+	0.182007i	$0.941741\pi$
$278$	13.2049			0.791975
$279$	3.90966	+	2.55052i	0.234066	+	0.152696i
$280$	−9.12849	+	6.69322i	−0.545532	+	0.399996i
$281$	−23.3996	−	19.6346i	−1.39590	−	1.17130i	−0.962883	−	0.269920i	$-0.913003\pi$
$281$	−23.3996	−	19.6346i	−1.39590	−	1.17130i	−0.433022	−	0.901383i	$-0.642553\pi$
$282$	8.51937	+	12.9004i	0.507321	+	0.768210i
$283$	−19.8751	−	7.23396i	−1.18145	−	0.430014i	−0.324739	−	0.945804i	$-0.605276\pi$
$283$	−19.8751	−	7.23396i	−1.18145	−	0.430014i	−0.856715	+	0.515789i	$0.827499\pi$
$284$	−0.240352	−	0.0874808i	−0.0142622	−	0.00519103i
$285$	−11.1172	−	16.8342i	−0.658528	−	0.997175i
$286$	−10.9237	−	9.16610i	−0.645934	−	0.542003i
$287$	2.21302	+	20.2079i	0.130631	+	1.19283i
$288$	−0.897445	+	0.454927i	−0.0528825	+	0.0268068i
$289$	17.2018			1.01187
$290$	2.54387	−	14.4270i	0.149381	−	0.847182i
$291$	−4.25949	−	17.8235i	−0.249696	−	1.04483i
$292$	−0.253613	−	0.0923076i	−0.0148416	−	0.00540189i
$293$	−10.3694	−	3.77415i	−0.605787	−	0.220488i	0.0208719	−	0.999782i	$-0.493356\pi$
$293$	−10.3694	−	3.77415i	−0.605787	−	0.220488i	−0.626659	+	0.779294i	$0.715578\pi$
$294$	15.4228	+	6.88606i	0.899478	+	0.401603i
$295$	−0.213674	+	1.21181i	−0.0124406	+	0.0705541i
$296$	10.1263	+	17.5393i	0.588580	+	1.01945i
$297$	−0.139479	−	24.8505i	−0.00809337	−	1.44197i
$298$	−0.0302742	+	0.0524364i	−0.00175374	+	0.00303756i
$299$	5.22714	−	1.90252i	0.302293	−	0.110026i
$300$	−0.229051	−	0.169857i	−0.0132242	−	0.00980668i
$301$	17.1214	+	16.3903i	0.986861	+	0.944723i
$302$	19.8231	−	16.6335i	1.14069	−	0.957152i
$303$	−3.18439	+	3.01559i	−0.182938	+	0.173241i
$304$	−5.25917	+	29.8262i	−0.301634	+	1.71065i
$305$	5.94521	+	10.2974i	0.340422	+	0.589628i
$306$	−14.6686	−	19.5502i	−0.838547	−	1.11761i
$307$	2.00598	+	3.47446i	0.114487	+	0.198298i	0.917575	−	0.397563i	$-0.130144\pi$
$307$	2.00598	+	3.47446i	0.114487	+	0.198298i	−0.803087	+	0.595861i	$0.796811\pi$
$308$	0.416935	−	0.623981i	0.0237571	−	0.0355546i
$309$	1.91383	+	2.89802i	0.108874	+	0.164862i
$310$	−2.47640	+	2.07794i	−0.140650	+	0.118019i
$311$	5.86732	+	2.13553i	0.332705	+	0.121095i	0.502971	−	0.864303i	$-0.332240\pi$
$311$	5.86732	+	2.13553i	0.332705	+	0.121095i	−0.170265	+	0.985398i	$0.554463\pi$
$312$	−5.86066	−	8.87449i	−0.331794	−	0.502419i
$313$	−3.63982	+	20.6424i	−0.205735	+	1.16678i	0.690545	+	0.723290i	$0.257371\pi$
$313$	−3.63982	+	20.6424i	−0.205735	+	1.16678i	−0.896279	+	0.443490i	$0.853740\pi$
$314$	8.83310	+	15.2994i	0.498480	+	0.863393i
$315$	1.41576	−	11.7521i	0.0797689	−	0.662156i
$316$	0.174986	−	0.303084i	0.00984371	−	0.0170498i
$317$	14.2672	+	11.9716i	0.801324	+	0.672391i	0.948520	−	0.316716i	$-0.102580\pi$
$317$	14.2672	+	11.9716i	0.801324	+	0.672391i	−0.147196	+	0.989107i	$0.547025\pi$
$318$	12.5267	−	11.8627i	0.702462	−	0.665228i
$319$	5.85602	+	33.2111i	0.327874	+	1.85947i
$320$	−2.12947	−	12.0768i	−0.119041	−	0.675116i
$321$	−2.07428	+	18.0392i	−0.115775	+	1.00685i
$322$	−4.23671	−	8.59130i	−0.236102	−	0.478775i
$323$	45.6750			2.54143
$324$	0.149258	−	0.512484i	0.00829211	−	0.0284713i
$325$	2.97069	−	5.14538i	0.164784	−	0.285415i
$326$	3.48167	+	2.92147i	0.192832	+	0.161805i
$327$	−8.91757	+	3.86647i	−0.493143	+	0.213816i
$328$	−20.7132	−	7.53897i	−1.14369	−	0.416270i
$329$	−12.2451	−	11.7223i	−0.675097	−	0.646271i
$330$	16.4959	+	4.90494i	0.908070	+	0.270008i
$331$	−8.87008	−	7.44288i	−0.487544	−	0.409098i	0.365601	−	0.930772i	$-0.380863\pi$
$331$	−8.87008	−	7.44288i	−0.487544	−	0.409098i	−0.853145	+	0.521674i	$0.825308\pi$
$332$	−0.0302650	−	0.0524206i	−0.00166101	−	0.00287695i
$333$	−20.6261	−	4.80704i	−1.13031	−	0.263424i
$334$	12.2811	−	21.2715i	0.671991	−	1.16392i
$335$	0.524616	+	0.440205i	0.0286628	+	0.0240510i
$336$	−13.6746	+	11.3490i	−0.746012	+	0.619137i
$337$	4.85745	+	27.5479i	0.264602	+	1.50063i	0.770166	+	0.637843i	$0.220173\pi$
$337$	4.85745	+	27.5479i	0.264602	+	1.50063i	−0.505564	+	0.862789i	$0.668716\pi$
$338$	−8.98451	+	7.53890i	−0.488693	+	0.410062i
$339$	−19.0011	+	1.14236i	−1.03200	+	0.0620446i
$340$	−0.486073	+	0.176916i	−0.0263610	+	0.00959463i
$341$	3.72086	−	6.44473i	0.201496	−	0.349002i
$342$	−19.5892	−	26.1084i	−1.05927	−	1.41178i
$343$	−18.1643	−	3.61340i	−0.980782	−	0.195105i
$344$	−24.1503	+	8.78997i	−1.30209	+	0.473924i
$345$	−4.87443	+	4.61606i	−0.262431	+	0.248520i
$346$	2.88659	+	16.3706i	0.155184	+	0.880091i
$347$	−2.45931	+	2.06361i	−0.132023	+	0.110780i	−0.706408	−	0.707805i	$-0.749686\pi$
$347$	−2.45931	+	2.06361i	−0.132023	+	0.110780i	0.574385	+	0.818585i	$0.305241\pi$
$348$	−0.0827460	+	0.719610i	−0.00443565	+	0.0385752i
$349$	2.39501	−	13.5828i	0.128202	−	0.727068i	−0.851153	−	0.524918i	$-0.824096\pi$
$349$	2.39501	−	13.5828i	0.128202	−	0.727068i	0.979355	−	0.202150i	$-0.0647929\pi$
$350$	−9.36491	−	4.12072i	−0.500576	−	0.220262i
$351$	10.9631	+	1.86971i	0.585169	+	0.0997979i
$352$	0.802006	+	1.38912i	0.0427471	+	0.0740401i
$353$	−1.64539	−	1.38064i	−0.0875751	−	0.0734843i	0.597949	−	0.801534i	$-0.295982\pi$
$353$	−1.64539	−	1.38064i	−0.0875751	−	0.0734843i	−0.685524	+	0.728050i	$0.740427\pi$
$354$	−0.227428	+	1.97785i	−0.0120877	+	0.105122i
$355$	1.11683	+	6.33388i	0.0592754	+	0.336167i
$356$	0.0878690	−	0.0737308i	0.00465705	−	0.00390773i
$357$	20.4365	+	17.3374i	1.08162	+	0.917594i
$358$	12.9966	−	4.73039i	0.686893	−	0.250009i
$359$	−0.544651			−0.0287456			−0.0143728	−	0.999897i	$-0.504575\pi$
$359$	−0.544651			−0.0287456			−0.0143728	+	0.999897i	$0.504575\pi$
$360$	10.7498	+	7.01276i	0.566563	+	0.369605i
$361$	41.9970			2.21037
$362$	5.33186	−	30.2385i	0.280237	−	1.58930i
$363$	−20.5273	+	1.23412i	−1.07740	+	0.0647744i
$364$	0.242604	+	0.232246i	0.0127159	+	0.0121730i
$365$	1.17845	+	6.68335i	0.0616831	+	0.349822i
$366$	10.6016	+	16.0534i	0.554152	+	0.839124i
$367$	14.1305	−	5.14307i	0.737605	−	0.268466i	0.0542245	−	0.998529i	$-0.482731\pi$
$367$	14.1305	−	5.14307i	0.737605	−	0.268466i	0.683380	+	0.730063i	$0.260509\pi$
$368$	10.0784			0.525374
$369$	20.5599	−	10.4221i	1.07031	−	0.542552i
$370$	7.33338	−	12.7018i	0.381244	−	0.660335i
$371$	−10.5099	+	15.7290i	−0.545648	+	0.816611i
$372$	0.116060	−	0.109908i	0.00601741	−	0.00569845i
$373$	−16.2540	−	5.91597i	−0.841600	−	0.306317i	−0.114989	−	0.993367i	$-0.536683\pi$
$373$	−16.2540	−	5.91597i	−0.841600	−	0.306317i	−0.726611	+	0.687049i	$0.758906\pi$
$374$	−29.8481	+	25.0455i	−1.54341	+	1.29507i
$375$	−2.29448	+	19.9542i	−0.118486	+	1.03043i
$376$	17.2722	−	6.28655i	0.890743	−	0.324204i
$377$	−15.0921			−0.777284
$378$	1.14540	−	19.1175i	0.0589131	−	0.983298i
$379$	−32.3988			−1.66421			−0.832107	−	0.554615i	$-0.812866\pi$
$379$	−32.3988			−1.66421			−0.832107	+	0.554615i	$0.812866\pi$
$380$	−0.649130	+	0.236264i	−0.0332997	+	0.0121201i
$381$	13.9826	−	6.06257i	0.716352	−	0.310595i
$382$	−5.00738	+	4.20169i	−0.256200	+	0.214977i
$383$	8.46130	+	3.07966i	0.432352	+	0.157363i	0.549023	−	0.835807i	$-0.315000\pi$
$383$	8.46130	+	3.07966i	0.432352	+	0.157363i	−0.116671	+	0.993171i	$0.537222\pi$
$384$	−4.34175	−	18.1677i	−0.221564	−	0.927118i
$385$	−18.8301	−	1.23428i	−0.959670	−	0.0629049i
$386$	15.1939	−	26.3166i	0.773349	−	1.33948i
$387$	10.5525	−	24.7172i	0.536411	−	1.25645i
$388$	−0.627496			−0.0318563
$389$	21.8477	−	7.95190i	1.10772	−	0.403177i	0.277564	−	0.960707i	$-0.410473\pi$
$389$	21.8477	−	7.95190i	1.10772	−	0.403177i	0.830157	+	0.557530i	$0.188251\pi$
$390$	−3.44367	+	6.88902i	−0.174377	+	0.348839i
$391$	−2.63934	−	14.9684i	−0.133477	−	0.756985i
$392$	12.2250	−	15.9317i	0.617458	−	0.804670i
$393$	0.855644	−	1.71170i	0.0431615	−	0.0863441i
$394$	−0.549127	+	3.11425i	−0.0276646	+	0.156894i
$395$	−8.80013			−0.442783
$396$	−0.828731	−	0.193141i	−0.0416453	−	0.00970568i
$397$	−29.1889			−1.46495			−0.732475	−	0.680794i	$-0.761635\pi$
$397$	−29.1889			−1.46495			−0.732475	+	0.680794i	$0.761635\pi$
$398$	0.0640158	−	0.0232999i	0.00320882	−	0.00116792i
$399$	27.2921	+	23.1534i	1.36631	+	1.15912i
$400$	8.24623	−	6.91941i	0.412311	−	0.345970i
$401$	−5.16132	−	29.2713i	−0.257744	−	1.46174i	−0.788930	−	0.614484i	$-0.789364\pi$
$401$	−5.16132	−	29.2713i	−0.257744	−	1.46174i	0.531186	−	0.847255i	$-0.321747\pi$
$402$	0.890014	+	0.660006i	0.0443899	+	0.0329181i
$403$	2.55121	+	2.14072i	0.127085	+	0.106637i
$404$	0.0750867	+	0.130054i	0.00373570	+	0.00647042i
$405$	−13.0367	+	3.19297i	−0.647797	+	0.158660i
$406$	2.82927	+	25.8351i	0.140415	+	1.28218i
$407$	−5.86290	+	33.2501i	−0.290613	+	1.64815i
$408$	−26.6611	+	11.5597i	−1.31992	+	0.572290i
$409$	16.8366	−	14.1276i	0.832516	−	0.698564i	−0.123351	−	0.992363i	$-0.539364\pi$
$409$	16.8366	−	14.1276i	0.832516	−	0.698564i	0.955867	+	0.293799i	$0.0949196\pi$
$410$	2.77194	+	15.7204i	0.136896	+	0.776377i
$411$	0.380014	+	1.59014i	0.0187447	+	0.0784358i
$412$	0.111748	−	0.0406729i	0.00550542	−	0.00200381i
$413$	−0.237647	−	2.17004i	−0.0116938	−	0.106781i
$414$	−7.42416	+	7.92838i	−0.364878	+	0.389658i
$415$	−0.761024	+	1.31813i	−0.0373572	+	0.0647045i
$416$	−0.674547	+	0.245515i	−0.0330724	+	0.0120374i
$417$	9.04740	+	13.7000i	0.443053	+	0.670892i
$418$	−39.8609	+	33.4472i	−1.94966	+	1.63596i
$419$	−0.0110791	−	0.0628327i	−0.000541250	−	0.00306958i	0.984536	−	0.175183i	$-0.0560516\pi$
$419$	−0.0110791	−	0.0628327i	−0.000541250	−	0.00306958i	−0.985077	+	0.172113i	$0.944941\pi$
$420$	−0.380124	−	0.140686i	−0.0185481	−	0.00686476i
$421$	−29.7483	−	24.9618i	−1.44984	−	1.21656i	−0.932694	−	0.360669i	$-0.882548\pi$
$421$	−29.7483	−	24.9618i	−1.44984	−	1.21656i	−0.517150	−	0.855895i	$-0.673007\pi$
$422$	5.79928	−	10.0447i	0.282305	−	0.488966i
$423$	−7.54707	+	17.6776i	−0.366951	+	0.859517i
$424$	−10.2560	−	17.7639i	−0.498075	−	0.862692i
$425$	−12.4362	−	10.4352i	−0.603243	−	0.506181i
$426$	2.41872	+	10.1210i	0.117187	+	0.490363i
$427$	−15.2379	−	14.5873i	−0.737415	−	0.705929i
$428$	0.584268	+	0.212656i	0.0282416	+	0.0102791i
$429$	2.02533	−	17.6136i	0.0977840	−	0.850390i
$430$	14.2575	+	11.9634i	0.687556	+	0.576928i
$431$	−11.4662	+	19.8600i	−0.552306	+	0.956623i	0.445801	+	0.895132i	$0.352919\pi$
$431$	−11.4662	+	19.8600i	−0.552306	+	0.956623i	−0.998108	+	0.0614907i	$0.980415\pi$
$432$	17.5067	+	9.97689i	0.842290	+	0.480013i
$433$	24.7963			1.19163			0.595816	−	0.803121i	$-0.296829\pi$
$433$	24.7963			1.19163			0.595816	+	0.803121i	$0.296829\pi$
$434$	3.18627	−	4.76855i	0.152946	−	0.228897i
$435$	16.7109	−	7.24550i	0.801227	−	0.347395i
$436$	0.0577936	+	0.327764i	0.00276781	+	0.0156970i
$437$	−3.52472	−	19.9897i	−0.168610	−	0.956235i
$438$	2.55218	+	10.6794i	0.121948	+	0.510281i
$439$	−22.8844	−	19.2023i	−1.09221	−	0.916474i	−0.0953345	−	0.995445i	$-0.530392\pi$
$439$	−22.8844	−	19.2023i	−1.09221	−	0.916474i	−0.996877	+	0.0789711i	$0.974837\pi$
$440$	10.2307	−	17.7200i	0.487728	−	0.844770i
$441$	3.42279	+	20.7192i	0.162990	+	0.986628i
$442$	−8.71869	−	15.1012i	−0.414706	−	0.718292i
$443$	−2.31611	+	13.1353i	−0.110042	+	0.624077i	0.879045	+	0.476739i	$0.158181\pi$
$443$	−2.31611	+	13.1353i	−0.110042	+	0.624077i	−0.989086	+	0.147337i	$0.952930\pi$
$444$	−0.324258	+	0.648673i	−0.0153886	+	0.0307847i
$445$	−2.71034	−	0.986484i	−0.128483	−	0.0467638i
$446$	−3.87399	+	3.25067i	−0.183439	+	0.153924i
$447$	−0.0751452	+	0.00451779i	−0.00355424	+	0.000213684i
$448$	9.62229	+	19.5123i	0.454610	+	0.921870i
$449$	0.345536	+	0.598487i	0.0163069	+	0.0282443i	0.874064	−	0.485811i	$-0.161476\pi$
$449$	0.345536	+	0.598487i	0.0163069	+	0.0282443i	−0.857757	+	0.514056i	$0.828142\pi$
$450$	−0.631217	+	11.5842i	−0.0297559	+	0.546082i
$451$	−18.3735	−	31.8238i	−0.865173	−	1.49852i
$452$	−0.113185	+	0.641904i	−0.00532378	+	0.0301926i
$453$	30.8392	+	9.16981i	1.44895	+	0.430835i
$454$	−9.66046	+	8.10609i	−0.453388	+	0.380438i
$455$	2.00731	−	8.20301i	0.0941040	−	0.384563i
$456$	−35.6048	+	15.4375i	−1.66735	+	0.722926i
$457$	12.0285	−	4.37800i	0.562668	−	0.204794i	−0.0449982	−	0.998987i	$-0.514328\pi$
$457$	12.0285	−	4.37800i	0.562668	−	0.204794i	0.607666	+	0.794193i	$0.292106\pi$
$458$	−7.13344	+	12.3555i	−0.333324	+	0.577334i
$459$	10.2330	−	28.6135i	0.477634	−	1.33557i
$460$	0.114937	+	0.199077i	0.00535898	+	0.00928203i
$461$	4.76655	−	27.0325i	0.222000	−	1.25903i	−0.646337	−	0.763052i	$-0.723700\pi$
$461$	4.76655	−	27.0325i	0.222000	−	1.25903i	0.868337	−	0.495974i	$-0.165189\pi$
$462$	−30.5310	−	0.165062i	−1.42043	−	0.00767939i
$463$	23.7421	+	8.64141i	1.10339	+	0.401600i	0.828564	−	0.559894i	$-0.189158\pi$
$463$	23.7421	+	8.64141i	1.10339	+	0.401600i	0.274824	+	0.961495i	$0.411380\pi$
$464$	−25.6951	−	9.35225i	−1.19287	−	0.434167i
$465$	−3.85258	−	1.14554i	−0.178659	−	0.0531230i
$466$	3.31780	−	18.8162i	0.153694	−	0.871642i
$467$	−2.41125			−0.111579			−0.0557897	−	0.998443i	$-0.517768\pi$
$467$	−2.41125			−0.111579			−0.0557897	+	0.998443i	$0.517768\pi$
$468$	0.149525	−	0.350235i	0.00691178	−	0.0161896i
$469$	−1.11206	−	0.489327i	−0.0513504	−	0.0225950i
$470$	−10.1969	−	8.55620i	−0.470347	−	0.394668i
$471$	−9.82100	+	19.6468i	−0.452528	+	0.905276i
$472$	2.22430	+	0.809578i	0.102382	+	0.0372639i
$473$	−40.2608	−	14.6537i	−1.85119	−	0.673779i
$474$	−14.2125	+	0.854467i	−0.652802	+	0.0392470i
$475$	−16.6080	−	13.9358i	−0.762026	−	0.639416i
$476$	0.740060	−	0.542629i	0.0339206	−	0.0248713i
$477$	20.8903	+	4.86860i	0.956500	+	0.222918i
$478$	−14.3344			−0.655640
$479$	1.30209	−	7.38454i	0.0594941	−	0.337408i	−0.940503	−	0.339785i	$-0.889646\pi$
$479$	1.30209	−	7.38454i	0.0594941	−	0.337408i	0.999997	+	0.00237724i	$0.000756698\pi$
$480$	0.629031	−	0.595688i	0.0287112	−	0.0271893i
$481$	−14.1986	−	5.16788i	−0.647402	−	0.235635i
$482$	6.47303	+	2.35599i	0.294838	+	0.107312i
$483$	6.01064	−	10.2820i	0.273494	−	0.467845i
$484$	−0.122276	+	0.693464i	−0.00555802	+	0.0315211i
$485$	7.88928	+	13.6646i	0.358234	+	0.620479i
$486$	−20.7446	+	6.42257i	−0.940994	+	0.291334i
$487$	−6.59719	+	11.4267i	−0.298947	+	0.517792i	−0.975895	−	0.218239i	$-0.929969\pi$
$487$	−6.59719	+	11.4267i	−0.298947	+	0.517792i	0.676948	+	0.736031i	$0.263302\pi$
$488$	21.4936	−	7.82302i	0.972968	−	0.354131i
$489$	−0.645525	+	5.61389i	−0.0291917	+	0.253869i
$490$	−14.4184	−	1.89837i	−0.651359	−	0.0857597i
$491$	−17.6183	+	14.7835i	−0.795104	+	0.667171i	−0.947003	−	0.321225i	$-0.895905\pi$
$491$	−17.6183	+	14.7835i	−0.795104	+	0.667171i	0.151899	+	0.988396i	$0.451461\pi$
$492$	−0.183460	−	0.767676i	−0.00827103	−	0.0346095i
$493$	−7.16088	+	40.6114i	−0.322510	+	1.82904i
$494$	−11.6434	−	20.1670i	−0.523863	−	0.907357i
$495$	6.21342	+	20.4751i	0.279273	+	0.920288i
$496$	3.01701	+	5.22561i	0.135468	+	0.234637i
$497$	−5.04655	−	10.2335i	−0.226369	−	0.459036i
$498$	−1.10109	+	2.20272i	−0.0493411	+	0.0987062i
$499$	14.3591	−	12.0488i	0.642803	−	0.539376i	−0.262074	−	0.965048i	$-0.584407\pi$
$499$	14.3591	−	12.0488i	0.642803	−	0.539376i	0.904878	+	0.425672i	$0.139962\pi$
$500$	0.646293	+	0.235231i	0.0289031	+	0.0105199i
$501$	30.4836	−	1.83270i	1.36191	−	0.0818788i
$502$	1.10935	−	6.29143i	0.0495127	−	0.280800i
$503$	9.60239	+	16.6318i	0.428149	+	0.741576i	0.996709	−	0.0810660i	$-0.0258324\pi$
$503$	9.60239	+	16.6318i	0.428149	+	0.741576i	−0.568560	+	0.822642i	$0.692499\pi$
$504$	−21.7905	−	6.60769i	−0.970628	−	0.294330i
$505$	1.88808	−	3.27025i	0.0840183	−	0.145524i
$506$	13.2645	+	11.1303i	0.589681	+	0.494801i
$507$	−13.9774	−	4.15608i	−0.620758	−	0.184578i
$508$	−0.0906196	−	0.513929i	−0.00402059	−	0.0228019i
$509$	0.475326	+	2.69571i	0.0210685	+	0.119485i	0.993528	−	0.113586i	$-0.0362337\pi$
$509$	0.475326	+	2.69571i	0.0210685	+	0.119485i	−0.972460	+	0.233071i	$0.925123\pi$
$510$	16.9037	+	12.5353i	0.748509	+	0.555071i
$511$	−5.32499	−	10.7981i	−0.235564	−	0.477682i
$512$	−23.5502			−1.04078
$513$	13.6657	−	38.2121i	0.603355	−	1.68711i
$514$	14.4688	−	25.0607i	0.638193	−	1.10538i
$515$	−2.29068	−	1.92211i	−0.100939	−	0.0846981i
$516$	−0.739195	−	0.548164i	−0.0325412	−	0.0241316i
$517$	28.7943	+	10.4803i	1.26637	+	0.460922i
$518$	−6.18474	+	25.2744i	−0.271742	+	1.11049i
$519$	−15.0067	+	14.2113i	−0.658722	+	0.623806i
$520$	7.01466	+	5.88599i	0.307613	+	0.258118i
$521$	15.5604	+	26.9514i	0.681714	+	1.18076i	0.974457	+	0.224573i	$0.0720986\pi$
$521$	15.5604	+	26.9514i	0.681714	+	1.18076i	−0.292743	+	0.956191i	$0.594568\pi$
$522$	26.2851	−	13.3243i	1.15047	−	0.583188i
$523$	−5.71752	+	9.90304i	−0.250010	+	0.433030i	−0.963528	−	0.267607i	$-0.913767\pi$
$523$	−5.71752	+	9.90304i	−0.250010	+	0.433030i	0.713518	+	0.700637i	$0.247101\pi$
$524$	−0.0501965	−	0.0421199i	−0.00219284	−	0.00184001i
$525$	−2.14120	−	12.5394i	−0.0934497	−	0.547265i
$526$	4.87176	+	27.6291i	0.212419	+	1.20469i
$527$	6.97095	−	5.84932i	0.303660	−	0.254801i
$528$	14.3630	−	28.7329i	0.625068	−	1.25044i
$529$	15.2657	−	5.55625i	0.663725	−	0.241576i
$530$	−7.42729	+	12.8645i	−0.322621	+	0.558796i
$531$	−2.20784	+	1.11918i	−0.0958122	+	0.0485685i
$532$	0.988318	−	0.724657i	0.0428490	−	0.0314179i
$533$	15.4534	−	5.62459i	0.669363	−	0.243628i
$534$	−4.47308	−	1.33004i	−0.193569	−	0.0575564i
$535$	−2.71490	−	15.3969i	−0.117375	−	0.665668i
$536$	1.00918	−	0.846799i	0.0435898	−	0.0365761i
$537$	13.8125	+	10.2429i	0.596053	+	0.442014i
$538$	−1.62085	+	9.19229i	−0.0698797	+	0.396308i
$539$	32.6844	−	7.24562i	1.40782	−	0.312091i
$540$	0.00257952	+	0.459586i	0.000111005	+	0.0197774i
$541$	7.51932	+	13.0238i	0.323281	+	0.559939i	0.981163	−	0.193182i	$-0.0618808\pi$
$541$	7.51932	+	13.0238i	0.323281	+	0.559939i	−0.657882	+	0.753121i	$0.728547\pi$
$542$	15.4799	+	12.9892i	0.664919	+	0.557934i
$543$	35.0255	−	15.1863i	1.50309	−	0.651708i
$544$	0.340598	+	1.93163i	0.0146030	+	0.0828179i
$545$	6.41092	−	5.37940i	0.274614	−	0.230428i
$546$	2.44538	−	13.4430i	0.104653	−	0.575309i
$547$	39.8368	−	14.4994i	1.70330	−	0.619950i	0.707105	−	0.707109i	$-0.250001\pi$
$547$	39.8368	−	14.4994i	1.70330	−	0.619950i	0.996194	+	0.0871585i	$0.0277787\pi$
$548$	0.0559825			0.00239145
$549$	−9.39162	+	21.9982i	−0.400824	+	0.938859i
$550$	18.4947			0.788616
$551$	−9.56305	+	54.2347i	−0.407400	+	2.31048i
$552$	7.11652	+	10.7762i	0.302899	+	0.458665i
$553$	14.9885	−	4.36867i	0.637376	−	0.185775i
$554$	−2.81821	−	15.9829i	−0.119734	−	0.679046i
$555$	18.2026	−	1.09435i	0.772657	−	0.0464528i
$556$	0.528273	−	0.192276i	0.0224038	−	0.00815431i
$557$	−30.2590			−1.28211			−0.641056	−	0.767494i	$-0.721504\pi$
$557$	−30.2590			−1.28211			−0.641056	+	0.767494i	$0.721504\pi$
$558$	−6.33327	−	1.47601i	−0.268109	−	0.0624843i
$559$	9.58704	−	16.6052i	0.405489	−	0.702327i
$560$	8.50077	−	12.7222i	0.359223	−	0.537609i
$561$	−46.4353	−	13.8072i	−1.96050	−	0.582941i
$562$	39.9870	+	14.5541i	1.68675	+	0.613927i
$563$	−26.0504	+	21.8589i	−1.09789	+	0.921242i	−0.997282	−	0.0736839i	$-0.976524\pi$
$563$	−26.0504	+	21.8589i	−1.09789	+	0.921242i	−0.100612	+	0.994926i	$0.532080\pi$
$564$	0.528669	+	0.392044i	0.0222610	+	0.0165080i
$565$	15.4015	−	5.60567i	0.647944	−	0.235832i
$566$	29.4647			1.23850
$567$	20.6191	−	11.9101i	0.865922	−	0.500179i
$568$	12.3721			0.519122
$569$	−22.0584	+	8.02861i	−0.924737	+	0.336577i	−0.760122	−	0.649781i	$-0.774861\pi$
$569$	−22.0584	+	8.02861i	−0.924737	+	0.336577i	−0.164616	+	0.986358i	$0.552638\pi$
$570$	22.5742	+	16.7403i	0.945529	+	0.701174i
$571$	2.82552	−	2.37090i	0.118244	−	0.0992189i	−0.581748	−	0.813369i	$-0.697631\pi$
$571$	2.82552	−	2.37090i	0.118244	−	0.0992189i	0.699993	+	0.714150i	$0.253187\pi$
$572$	−0.570482	−	0.207638i	−0.0238530	−	0.00868180i
$573$	−7.79008	−	2.31632i	−0.325435	−	0.0967659i
$574$	−12.5253	−	25.3992i	−0.522798	−	1.06014i
$575$	−3.60727	+	6.24797i	−0.150433	+	0.260558i
$576$	16.8615	−	18.0067i	0.702564	−	0.750279i
$577$	35.8996			1.49452			0.747259	−	0.664533i	$-0.231369\pi$
$577$	35.8996			1.49452			0.747259	+	0.664533i	$0.231369\pi$
$578$	−22.5184	+	8.19604i	−0.936643	+	0.340910i
$579$	37.7136	−	2.26737i	1.56732	−	0.0942288i
$580$	−0.108301	−	0.614207i	−0.00449696	−	0.0255036i
$581$	0.641823	−	2.62286i	0.0266273	−	0.108814i
$582$	14.0682	+	21.3028i	0.583148	+	0.883030i
$583$	5.93798	−	33.6759i	0.245926	−	1.39472i
$584$	13.0547			0.540209
$585$	−9.50680	+	1.14726i	−0.393058	+	0.0474334i
$586$	15.3726			0.635034
$587$	−23.9743	+	8.72592i	−0.989524	+	0.360157i	−0.785536	−	0.618816i	$-0.787613\pi$
$587$	−23.9743	+	8.72592i	−0.989524	+	0.360157i	−0.203988	+	0.978973i	$0.565390\pi$
$588$	0.717273	+	0.0509121i	0.0295799	+	0.00209958i
$589$	9.30941	−	7.81152i	0.383587	−	0.321868i
$590$	−0.297667	−	1.68815i	−0.0122547	−	0.0695001i
$591$	−3.60727	+	1.56404i	−0.148383	+	0.0643358i
$592$	−20.9715	−	17.5971i	−0.861922	−	0.723238i
$593$	7.52044	+	13.0258i	0.308828	+	0.534905i	0.978106	−	0.208106i	$-0.0667301\pi$
$593$	7.52044	+	13.0258i	0.308828	+	0.534905i	−0.669279	+	0.743012i	$0.733397\pi$
$594$	12.0230	+	32.4647i	0.493308	+	1.33204i
$595$	−21.1211	−	9.29361i	−0.865879	−	0.381001i
$596$	−0.000447622		0.00253859i	−1.83353e−5		0.000103985i
$597$	0.0680344	+	0.0504522i	0.00278446	+	0.00206487i
$598$	−5.93623	+	4.98109i	−0.242750	+	0.203692i
$599$	0.386535	+	2.19215i	0.0157934	+	0.0895688i	0.991686	−	0.128684i	$-0.0410753\pi$
$599$	0.386535	+	2.19215i	0.0157934	+	0.0895688i	−0.975892	+	0.218253i	$0.929964\pi$
$600$	13.2212	+	3.93124i	0.539755	+	0.160492i
$601$	19.6594	−	7.15543i	0.801923	−	0.291876i	0.0916402	−	0.995792i	$-0.470789\pi$
$601$	19.6594	−	7.15543i	0.801923	−	0.291876i	0.710283	+	0.703916i	$0.248567\pi$
$602$	−30.2226	−	13.2984i	−1.23178	−	0.542004i
$603$	−0.0749558	+	1.37560i	−0.00305244	+	0.0560186i
$604$	0.550841	−	0.954084i	0.0224134	−	0.0388211i
$605$	16.6385	−	6.05593i	0.676453	−	0.246209i
$606$	2.73177	−	5.46488i	0.110971	−	0.221996i
$607$	9.78791	−	8.21303i	0.397279	−	0.333357i	−0.422162	−	0.906521i	$-0.638729\pi$
$607$	9.78791	−	8.21303i	0.397279	−	0.333357i	0.819441	+	0.573164i	$0.194284\pi$
$608$	0.454854	+	2.57961i	0.0184468	+	0.104617i
$609$	−24.8654	+	20.6365i	−1.00760	+	0.836232i
$610$	−12.6891	−	10.6474i	−0.513765	−	0.431100i
$611$	−6.85661	+	11.8760i	−0.277389	+	0.480451i
$612$	−0.871500	−	0.568535i	−0.0352283	−	0.0229817i
$613$	−7.87511	−	13.6401i	−0.318073	−	0.550918i	0.662013	−	0.749492i	$-0.269702\pi$
$613$	−7.87511	−	13.6401i	−0.318073	−	0.550918i	−0.980086	+	0.198574i	$0.936369\pi$
$614$	−4.28144	−	3.59255i	−0.172785	−	0.144984i
$615$	−14.4107	+	13.6468i	−0.581096	+	0.550294i
$616$	−8.62822	+	35.2599i	−0.347641	+	1.42066i
$617$	1.10667	+	0.402796i	0.0445529	+	0.0162159i	0.364200	−	0.931321i	$-0.381342\pi$
$617$	1.10667	+	0.402796i	0.0445529	+	0.0162159i	−0.319648	+	0.947537i	$0.603565\pi$
$618$	−3.88615	−	2.88185i	−0.156324	−	0.115925i
$619$	3.45184	+	2.89643i	0.138741	+	0.116418i	0.709517	−	0.704688i	$-0.248913\pi$
$619$	3.45184	+	2.89643i	0.138741	+	0.116418i	−0.570776	+	0.821106i	$0.693358\pi$
$620$	−0.0688137	+	0.119189i	−0.00276363	+	0.00478674i
$621$	−13.3124	−	2.27037i	−0.534208	−	0.0911067i
$622$	−8.69826			−0.348769
$623$	5.10602	+	0.334692i	0.204568	+	0.0134091i
$624$	11.5472	+	8.56304i	0.462258	+	0.342796i
$625$	−0.592932	−	3.36268i	−0.0237173	−	0.134507i
$626$	−5.07058	−	28.7567i	−0.202661	−	1.14935i
$627$	−62.0124	−	18.4389i	−2.47654	−	0.736380i
$628$	0.576150	+	0.483448i	0.0229909	+	0.0192917i
$629$	−20.6432	+	35.7550i	−0.823097	+	1.42565i
$630$	3.74612	+	16.0589i	0.149249	+	0.639803i
$631$	−1.35722	−	2.35078i	−0.0540302	−	0.0935831i	0.837745	−	0.546061i	$-0.183873\pi$
$631$	−1.35722	−	2.35078i	−0.0540302	−	0.0935831i	−0.891776	+	0.452478i	$0.850540\pi$
$632$	−2.93958	+	16.6712i	−0.116930	+	0.663144i
$633$	14.3947	−	0.865422i	0.572139	−	0.0343974i
$634$	−24.3808	−	8.87389i	−0.968285	−	0.352427i
$635$	−10.0522	+	8.43483i	−0.398911	+	0.334726i
$636$	0.328410	−	0.656980i	0.0130223	−	0.0260510i
$637$	0.653366	+	14.9680i	0.0258873	+	0.593053i
$638$	−23.4899	−	40.6856i	−0.929972	−	1.61076i
$639$	−8.84328	+	9.44387i	−0.349835	+	0.373594i
$640$	8.04164	+	13.9285i	0.317874	+	0.550574i
$641$	−0.956914	+	5.42693i	−0.0377958	+	0.214351i	−0.997856	−	0.0654414i	$-0.979154\pi$
$641$	−0.956914	+	5.42693i	−0.0377958	+	0.214351i	0.960061	+	0.279792i	$0.0902656\pi$
$642$	−5.87964	−	24.6029i	−0.232051	−	0.971001i
$643$	−1.96919	+	1.65235i	−0.0776575	+	0.0651623i	−0.680790	−	0.732479i	$-0.738363\pi$
$643$	−1.96919	+	1.65235i	−0.0776575	+	0.0651623i	0.603133	+	0.797641i	$0.293919\pi$
$644$	−0.294591	−	0.282013i	−0.0116085	−	0.0111129i
$645$	−2.64343	+	22.9889i	−0.104085	+	0.905188i
$646$	−59.7920	+	21.7625i	−2.35248	+	0.856234i
$647$	15.2410	−	26.3983i	0.599187	−	1.03782i	−0.393754	−	0.919216i	$-0.628824\pi$
$647$	15.2410	−	26.3983i	0.599187	−	1.03782i	0.992941	−	0.118607i	$-0.0378429\pi$
$648$	1.69410	+	25.7635i	0.0665505	+	1.01209i
$649$	1.97305	+	3.41742i	0.0774489	+	0.134145i
$650$	−1.43726	+	8.15111i	−0.0563740	+	0.319713i
$651$	7.13045	+	0.0385499i	0.279464	+	0.00151089i
$652$	0.181827	+	0.0661796i	0.00712090	+	0.00259179i
$653$	44.3248	+	16.1329i	1.73456	+	0.631330i	0.998939	−	0.0460589i	$-0.0146662\pi$
$653$	44.3248	+	16.1329i	1.73456	+	0.631330i	0.735625	+	0.677389i	$0.236888\pi$
$654$	9.83152	−	9.31039i	0.384443	−	0.364065i
$655$	−0.286119	+	1.62266i	−0.0111796	+	0.0634026i
$656$	29.7957			1.16333
$657$	−9.33121	+	9.96494i	−0.364045	+	0.388769i
$658$	21.6150	+	9.51098i	0.842642	+	0.370777i
$659$	−8.99638	−	7.54886i	−0.350449	−	0.294062i	0.450521	−	0.892766i	$-0.351238\pi$
$659$	−8.99638	−	7.54886i	−0.350449	−	0.294062i	−0.800970	+	0.598704i	$0.795683\pi$
$660$	0.731356	−	0.0439697i	0.0284680	−	0.00171152i
$661$	−25.1459	−	9.15236i	−0.978062	−	0.355986i	−0.196976	−	0.980408i	$-0.563112\pi$
$661$	−25.1459	−	9.15236i	−0.978062	−	0.355986i	−0.781087	+	0.624423i	$0.785334\pi$
$662$	15.1579	+	5.51701i	0.589127	+	0.214425i
$663$	9.69380	−	19.3923i	0.376476	−	0.753135i
$664$	2.24289	+	1.88201i	0.0870409	+	0.0730360i
$665$	−28.2063	−	12.4112i	−1.09379	−	0.481286i
$666$	29.2915	−	3.53484i	1.13502	−	0.136972i
$667$	18.3262			0.709592
$668$	0.181583	−	1.02981i	0.00702567	−	0.0398446i
$669$	−6.02685	−	1.79204i	−0.233012	−	0.0692844i
$670$	−0.896502	−	0.326300i	−0.0346349	−	0.0126061i
$671$	35.8318	+	13.0417i	1.38327	+	0.503470i
$672$	−0.775655	+	1.32686i	−0.0299215	+	0.0511846i
$673$	−1.93416	+	10.9692i	−0.0745564	+	0.422830i	0.924569	+	0.381015i	$0.124425\pi$
$673$	−1.93416	+	10.9692i	−0.0745564	+	0.422830i	−0.999125	+	0.0418154i	$0.986686\pi$
$674$	−19.4844	−	33.7479i	−0.750509	−	1.29992i
$675$	−12.4510	+	7.28208i	−0.479240	+	0.280287i
$676$	−0.249660	+	0.432424i	−0.00960232	+	0.0166317i
$677$	−10.3039	+	3.75031i	−0.396011	+	0.144136i	−0.532347	−	0.846526i	$-0.678690\pi$
$677$	−10.3039	+	3.75031i	−0.396011	+	0.144136i	0.136336	+	0.990663i	$0.456467\pi$
$678$	24.3295	−	10.5488i	0.934371	−	0.405123i
$679$	−20.2207	−	19.3573i	−0.776000	−	0.742866i
$680$	19.1669	−	16.0830i	0.735018	−	0.616753i
$681$	−15.0290	−	4.46876i	−0.575912	−	0.171243i
$682$	−1.80021	+	10.2095i	−0.0689335	+	0.390941i
$683$	7.29090	+	12.6282i	0.278978	+	0.483205i	0.971131	−	0.238546i	$-0.0766708\pi$
$683$	7.29090	+	12.6282i	0.278978	+	0.483205i	−0.692153	+	0.721751i	$0.743338\pi$
$684$	−1.16385	−	0.759253i	−0.0445010	−	0.0290308i
$685$	−0.703849	−	1.21910i	−0.0268927	−	0.0465795i
$686$	25.5001	−	3.92445i	0.973599	−	0.149836i
$687$	−17.7063	+	1.06452i	−0.675538	+	0.0406139i
$688$	26.6123	−	22.3304i	1.01459	−	0.851338i
$689$	14.3805	+	5.23406i	0.547852	+	0.199402i
$690$	4.18161	−	8.36525i	0.159191	−	0.318460i
$691$	−8.20271	+	46.5199i	−0.312046	+	1.76970i	0.276282	+	0.961077i	$0.410898\pi$
$691$	−8.20271	+	46.5199i	−0.312046	+	1.76970i	−0.588328	+	0.808623i	$0.700213\pi$
$692$	0.353853	+	0.612892i	0.0134515	+	0.0232986i
$693$	−20.7473	−	31.7890i	−0.788125	−	1.20756i
$694$	2.23619	−	3.87319i	0.0848845	−	0.147024i
$695$	−10.8289	−	9.08651i	−0.410763	−	0.344671i
$696$	−8.14396	−	34.0778i	−0.308696	−	1.29172i
$697$	−7.80289	−	44.2524i	−0.295556	−	1.67618i
$698$	3.33645	+	18.9220i	0.126287	+	0.716207i
$699$	21.7949	−	9.44982i	0.824360	−	0.357425i
$700$	−0.434654	−	0.0284909i	−0.0164284	−	0.00107686i
$701$	−36.9374			−1.39511			−0.697553	−	0.716533i	$-0.745728\pi$
$701$	−36.9374			−1.39511			−0.697553	+	0.716533i	$0.745728\pi$
$702$	−15.2424	+	2.77594i	−0.575287	+	0.104771i
$703$	−27.5681	+	47.7493i	−1.03975	+	1.80090i
$704$	−30.1260	−	25.2787i	−1.13542	−	0.952729i
$705$	1.89057	−	16.4416i	0.0712030	−	0.619226i
$706$	2.81176	+	1.02340i	0.105822	+	0.0385161i
$707$	−1.59234	+	6.50723i	−0.0598862	+	0.244730i
$708$	0.0197010	+	0.0824375i	0.000740410	+	0.00309819i
$709$	20.5181	+	17.2167i	0.770573	+	0.646587i	0.940856	−	0.338808i	$-0.110024\pi$
$709$	20.5181	+	17.2167i	0.770573	+	0.646587i	−0.170283	+	0.985395i	$0.554468\pi$
$710$	−4.47988	−	7.75938i	−0.168127	−	0.291204i
$711$	−10.6243	−	14.1600i	−0.398442	−	0.531041i
$712$	−2.77418	+	4.80501i	−0.103967	+	0.180076i
$713$	−3.09790	−	2.59945i	−0.116017	−	0.0973501i
$714$	−35.0136	−	12.9587i	−1.31035	−	0.484967i
$715$	2.65084	+	15.0336i	0.0991357	+	0.562226i
$716$	0.451064	−	0.378487i	0.0168570	−	0.0141447i
$717$	−9.82131	−	14.8719i	−0.366784	−	0.555401i
$718$	0.712989	−	0.259507i	0.0266085	−	0.00968470i
$719$	0.376366	−	0.651884i	0.0140361	−	0.0243112i	−0.858922	−	0.512106i	$-0.828865\pi$
$719$	0.376366	−	0.651884i	0.0140361	−	0.0243112i	0.872958	+	0.487795i	$0.162199\pi$
$720$	−16.8967	−	3.93789i	−0.629704	−	0.146756i
$721$	4.85571	+	2.13659i	0.180836	+	0.0795709i
$722$	−54.9772	+	20.0101i	−2.04604	+	0.744697i
$723$	1.99071	+	8.32997i	0.0740352	+	0.309795i
$724$	−0.226996	−	1.28736i	−0.00843624	−	0.0478443i
$725$	14.9946	−	12.5819i	0.556885	−	0.467282i
$726$	26.2838	−	11.3961i	0.975482	−	0.422948i
$727$	−7.84405	+	44.4858i	−0.290920	+	1.64989i	0.392419	+	0.919786i	$0.371638\pi$
$727$	−7.84405	+	44.4858i	−0.290920	+	1.64989i	−0.683339	+	0.730101i	$0.739473\pi$
$728$	−14.8695	−	6.54281i	−0.551099	−	0.242493i
$729$	−20.8767	−	17.1220i	−0.773212	−	0.634148i
$730$	−4.72706	−	8.18750i	−0.174956	−	0.303033i
$731$	−40.1342	−	33.6766i	−1.48442	−	1.24557i
$732$	0.657879	+	0.487862i	0.0243159	+	0.0180319i
$733$	−6.07259	−	34.4394i	−0.224296	−	1.27205i	−0.864026	−	0.503447i	$-0.832065\pi$
$733$	−6.07259	−	34.4394i	−0.224296	−	1.27205i	0.639730	−	0.768600i	$-0.279046\pi$
$734$	−16.0473	+	13.4653i	−0.592318	+	0.497014i
$735$	−7.90934	−	16.2598i	−0.291740	−	0.599751i
$736$	0.819093	−	0.298125i	0.0301922	−	0.0109890i
$737$	2.19621			0.0808983
$738$	−21.9487	+	23.4393i	−0.807942	+	0.862814i
$739$	−31.2474			−1.14945			−0.574727	−	0.818345i	$-0.694892\pi$
$739$	−31.2474			−1.14945			−0.574727	+	0.818345i	$0.694892\pi$
$740$	0.108429	−	0.614929i	0.00398591	−	0.0226052i
$741$	12.9457	−	25.8976i	0.475570	−	0.951372i
$742$	6.26394	−	25.5981i	0.229957	−	0.939735i
$743$	9.21125	+	52.2396i	0.337928	+	1.91649i	0.396159	+	0.918182i	$0.370343\pi$
$743$	9.21125	+	52.2396i	0.337928	+	1.91649i	−0.0582305	+	0.998303i	$0.518546\pi$
$744$	−3.45704	+	6.91576i	−0.126741	+	0.253544i
$745$	0.0609093	−	0.0221692i	0.00223155	−	0.000812216i
$746$	24.0964			0.882233
$747$	−3.03973	+	0.366828i	−0.111218	+	0.0134216i
$748$	−0.829415	+	1.43659i	−0.0303264	+	0.0525269i
$749$	12.2676	+	24.8765i	0.448248	+	0.908968i
$750$	−6.50382	−	27.2148i	−0.237486	−	0.993743i
$751$	23.0941	+	8.40556i	0.842715	+	0.306723i	0.727067	−	0.686567i	$-0.240883\pi$
$751$	23.0941	+	8.40556i	0.842715	+	0.306723i	0.115649	+	0.993290i	$0.463105\pi$
$752$	−19.0330	+	15.9706i	−0.694063	+	0.582388i
$753$	7.28742	−	3.15967i	0.265568	−	0.115145i
$754$	19.7567	−	7.19085i	0.719497	−	0.261875i
$755$	−27.7021			−1.00818
$756$	−0.232547	−	0.781492i	−0.00845764	−	0.0284226i
$757$	−36.7061			−1.33411			−0.667054	−	0.745010i	$-0.732445\pi$
$757$	−36.7061			−1.33411			−0.667054	+	0.745010i	$0.732445\pi$
$758$	42.4124	−	15.4369i	1.54049	−	0.560692i
$759$	−2.45934	+	21.3879i	−0.0892682	+	0.776332i
$760$	25.5966	−	21.4781i	0.928486	−	0.779092i
$761$	11.5697	+	4.21104i	0.419403	+	0.152650i	0.543096	−	0.839670i	$-0.317252\pi$
$761$	11.5697	+	4.21104i	0.419403	+	0.152650i	−0.123694	+	0.992320i	$0.539474\pi$
$762$	−15.4157	+	14.5986i	−0.558452	+	0.528850i
$763$	−8.24866	+	12.3449i	−0.298622	+	0.446914i
$764$	−0.139144	+	0.241005i	−0.00503406	+	0.00871925i
$765$	−1.42361	+	26.1262i	−0.0514707	+	0.944595i
$766$	−12.5438			−0.453226
$767$	−1.65948	+	0.604001i	−0.0599203	+	0.0218092i
$768$	−1.35741	−	2.05545i	−0.0489813	−	0.0741698i
$769$	−6.86231	−	38.9181i	−0.247461	−	1.40342i	−0.814707	−	0.579873i	$-0.803102\pi$
$769$	−6.86231	−	38.9181i	−0.247461	−	1.40342i	0.567245	−	0.823549i	$-0.308009\pi$
$770$	25.2381	−	7.35609i	0.909517	−	0.265095i
$771$	35.9139	−	2.15917i	1.29341	−	0.0777606i
$772$	0.224651	−	1.27406i	0.00808537	−	0.0458544i
$773$	46.3334			1.66650			0.833248	−	0.552900i	$-0.186479\pi$
$773$	46.3334			1.66650			0.833248	+	0.552900i	$0.186479\pi$
$774$	−2.03707	+	37.3845i	−0.0732210	+	1.34376i
$775$	−4.31939			−0.155157
$776$	28.5219	−	10.3811i	1.02388	−	0.372661i
$777$	−30.4596	+	10.9003i	−1.09273	+	0.391045i
$778$	−24.8114	+	20.8193i	−0.889532	+	0.746406i
$779$	−10.4204	−	59.0972i	−0.373350	−	2.11738i
$780$	−0.0374566	+	0.325745i	−0.00134116	+	0.0116636i
$781$	15.8000	+	13.2578i	0.565370	+	0.474402i
$782$	10.5870	+	18.3372i	0.378590	+	0.655737i
$783$	31.8334	+	18.1415i	1.13763	+	0.648326i
$784$	−8.16294	+	25.8886i	−0.291533	+	0.924594i
$785$	3.28404	−	18.6247i	0.117213	−	0.664746i
$786$	−0.304536	+	2.64843i	−0.0108624	+	0.0944664i
$787$	−35.4621	+	29.7563i	−1.26409	+	1.06070i	−0.268855	+	0.963181i	$0.586645\pi$
$787$	−35.4621	+	29.7563i	−1.26409	+	1.06070i	−0.995234	+	0.0975158i	$0.968910\pi$
$788$	0.0233782	+	0.132585i	0.000832816	+	0.00472313i
$789$	−25.3272	+	23.9847i	−0.901673	+	0.853879i
$790$	11.5200	−	4.19295i	0.409864	−	0.149178i
$791$	−23.4491	+	17.1934i	−0.833755	+	0.611328i
$792$	40.8641	−	4.93139i	1.45204	−	0.175229i
$793$	−8.53241	+	14.7786i	−0.302995	+	0.524802i
$794$	38.2105	−	13.9075i	1.35604	−	0.493558i
$795$	−18.4357	+	1.10837i	−0.653847	+	0.0393098i
$796$	0.00222175	−	0.00186427i	7.87477e−5	−	6.60772e-5i
$797$	−8.63136	−	48.9509i	−0.305739	−	1.73393i	−0.620008	−	0.784596i	$-0.712871\pi$
$797$	−8.63136	−	48.9509i	−0.305739	−	1.73393i	0.314269	−	0.949334i	$-0.398241\pi$
$798$	−46.7591	−	17.3058i	−1.65525	−	0.612618i
$799$	28.7038	+	24.0854i	1.01547	+	0.852079i
$800$	0.465507	−	0.806282i	0.0164582	−	0.0285064i
$801$	−1.68485	−	5.55209i	−0.0595312	−	0.196173i
$802$	20.7033	+	35.8591i	0.731058	+	1.26623i
$803$	16.6718	+	13.9893i	0.588335	+	0.493672i
$804$	0.0452162	+	0.0134447i	0.00159465	+	0.000474159i
$805$	−2.43745	+	9.96081i	−0.0859087	+	0.351072i
$806$	−4.35970	−	1.58680i	−0.153564	−	0.0558926i
$807$	−10.6475	+	4.61653i	−0.374810	+	0.162510i
$808$	−5.56454	−	4.66920i	−0.195760	−	0.164262i
$809$	24.2528	−	42.0071i	0.852683	−	1.47689i	−0.0260950	−	0.999659i	$-0.508307\pi$
$809$	24.2528	−	42.0071i	0.852683	−	1.47689i	0.878778	−	0.477231i	$-0.158359\pi$
$810$	15.5446	−	10.3913i	0.546182	−	0.365114i
$811$	4.01228			0.140890			0.0704450	−	0.997516i	$-0.477558\pi$
$811$	4.01228			0.140890			0.0704450	+	0.997516i	$0.477558\pi$
$812$	0.489372	+	0.992362i	0.0171736	+	0.0348251i
$813$	−2.87008	+	24.9600i	−0.100658	+	0.875386i
$814$	−8.16753	−	46.3203i	−0.286272	−	1.62353i
$815$	−0.844889	−	4.79161i	−0.0295952	−	0.167843i
$816$	28.5212	−	27.0094i	0.998441	−	0.945517i
$817$	−53.5975	−	44.9736i	−1.87514	−	1.57343i
$818$	−15.3091	+	26.5161i	−0.535269	+	0.927113i
$819$	15.6226	−	6.67351i	0.545897	−	0.233191i
$820$	0.339799	+	0.588549i	0.0118663	+	0.0205530i
$821$	−0.673656	+	3.82049i	−0.0235107	+	0.133336i	−0.994304	−	0.106582i	$-0.966009\pi$
$821$	−0.673656	+	3.82049i	−0.0235107	+	0.133336i	0.970793	+	0.239918i	$0.0771205\pi$
$822$	−1.25511	−	1.90055i	−0.0437770	−	0.0662892i
$823$	13.3158	+	4.84655i	0.464159	+	0.168940i	0.563505	−	0.826113i	$-0.309453\pi$
$823$	13.3158	+	4.84655i	0.464159	+	0.168940i	−0.0993457	+	0.995053i	$0.531675\pi$
$824$	−4.40646	+	3.69746i	−0.153506	+	0.128807i
$825$	12.6718	+	19.1882i	0.441174	+	0.668047i
$826$	1.34504	+	2.72751i	0.0468000	+	0.0949023i
$827$	−19.5216	−	33.8124i	−0.678833	−	1.17577i	−0.975333	−	0.220741i	$-0.929153\pi$
$827$	−19.5216	−	33.8124i	−0.678833	−	1.17577i	0.296499	−	0.955033i	$-0.404181\pi$
$828$	−0.181566	+	0.425285i	−0.00630985	+	0.0147797i
$829$	13.1944	+	22.8534i	0.458262	+	0.793733i	0.998869	−	0.0475421i	$-0.0151388\pi$
$829$	13.1944	+	22.8534i	0.458262	+	0.793733i	−0.540607	+	0.841275i	$0.681806\pi$
$830$	0.368194	−	2.08813i	0.0127802	−	0.0724801i
$831$	14.6513	−	13.8746i	0.508246	−	0.481306i
$832$	13.4822	−	11.3129i	0.467411	−	0.392204i
$833$	40.5873	+	5.34384i	1.40627	+	0.185153i
$834$	−18.3713	−	13.6236i	−0.636145	−	0.471745i
$835$	−24.7086	+	8.99320i	−0.855077	+	0.311223i
$836$	−1.10765	+	1.91850i	−0.0383088	+	0.0663528i
$837$	−2.80793	−	7.58205i	−0.0970563	−	0.262074i
$838$	0.0444409	+	0.0769738i	0.00153518	+	0.00265902i
$839$	6.79475	−	38.5349i	0.234581	−	1.33037i	−0.608914	−	0.793236i	$-0.708394\pi$
$839$	6.79475	−	38.5349i	0.234581	−	1.33037i	0.843495	−	0.537138i	$-0.180494\pi$
$840$	19.6055	+	0.105995i	0.676453	+	0.00365716i
$841$	−19.4718	−	7.08715i	−0.671441	−	0.244384i
$842$	50.8361	+	18.5028i	1.75193	+	0.637650i
$843$	12.2976	+	51.4583i	0.423550	+	1.77232i
$844$	0.0857459	−	0.486289i	0.00295150	−	0.0167388i
$845$	12.5556			0.431925
$846$	1.45690	−	26.7372i	0.0500894	−	0.919246i
$847$	−25.3326	+	18.5745i	−0.870439	+	0.638226i
$848$	21.2400	+	17.8225i	0.729385	+	0.612027i
$849$	20.1880	+	30.5696i	0.692849	+	1.04915i
$850$	21.2519	+	7.73505i	0.728933	+	0.265310i
$851$	17.2412	+	6.27528i	0.591021	+	0.215114i
$852$	0.244135	+	0.369680i	0.00836392	+	0.0126650i
$853$	11.8999	+	9.98516i	0.407443	+	0.341885i	0.823362	−	0.567516i	$-0.192096\pi$
$853$	11.8999	+	9.98516i	0.407443	+	0.341885i	−0.415919	+	0.909402i	$0.636540\pi$
$854$	26.8979	+	11.8355i	0.920427	+	0.405003i
$855$	−1.90117	+	34.8904i	−0.0650186	+	1.19323i
$856$	−30.0752			−1.02795
$857$	2.37480	−	13.4682i	0.0811217	−	0.460064i	−0.917005	−	0.398877i	$-0.869400\pi$
$857$	2.37480	−	13.4682i	0.0811217	−	0.460064i	0.998126	−	0.0611875i	$-0.0194888\pi$
$858$	5.74091	+	24.0224i	0.195991	+	0.820112i
$859$	−10.8343	−	3.94335i	−0.369661	−	0.134545i	0.150509	−	0.988609i	$-0.451909\pi$
$859$	−10.8343	−	3.94335i	−0.369661	−	0.134545i	−0.520169	+	0.854063i	$0.674131\pi$
$860$	0.744584	+	0.271006i	0.0253901	+	0.00924124i
$861$	17.7698	−	30.3974i	0.605592	−	1.03594i
$862$	5.54750	−	31.4614i	0.188949	−	1.07158i
$863$	−14.3054	−	24.7776i	−0.486960	−	0.843439i	0.512928	−	0.858432i	$-0.328561\pi$
$863$	−14.3054	−	24.7776i	−0.486960	−	0.843439i	−0.999888	+	0.0149927i	$0.995228\pi$
$864$	1.71792	+	0.292984i	0.0584449	+	0.00996752i
$865$	8.89775	−	15.4114i	0.302533	−	0.524002i
$866$	−32.4601	+	11.8145i	−1.10304	+	0.401474i
$867$	−23.9320	−	17.7472i	−0.812774	−	0.602728i
$868$	0.0580353	−	0.237166i	0.00196985	−	0.00804992i
$869$	−21.6187	+	18.1402i	−0.733364	+	0.615365i
$870$	−18.4236	+	17.4470i	−0.624618	+	0.591510i
$871$	−0.170672	+	0.967928i	−0.00578300	+	0.0327970i
$872$	−8.04937	−	13.9419i	−0.272586	−	0.472133i
$873$	−12.4627	+	29.1915i	−0.421797	+	0.987984i
$874$	14.1385	+	24.4885i	0.478241	+	0.828337i
$875$	13.5699	+	27.5174i	0.458747	+	0.930258i
$876$	0.257605	+	0.390078i	0.00870366	+	0.0131795i
$877$	−28.2263	+	23.6847i	−0.953134	+	0.799775i	−0.979823	−	0.199869i	$-0.935948\pi$
$877$	−28.2263	+	23.6847i	−0.953134	+	0.799775i	0.0266883	+	0.999644i	$0.491504\pi$
$878$	39.1065	+	14.2336i	1.31978	+	0.480361i
$879$	10.5326	+	15.9490i	0.355256	+	0.537946i
$880$	−4.80283	+	27.2382i	−0.161903	+	0.918200i
$881$	−25.2138	−	43.6715i	−0.849473	−	1.47133i	−0.881679	−	0.471850i	$-0.843587\pi$
$881$	−25.2138	−	43.6715i	−0.849473	−	1.47133i	0.0322059	−	0.999481i	$-0.489747\pi$
$882$	−14.3526	−	25.4921i	−0.483278	−	0.858364i
$883$	11.5513	−	20.0075i	0.388732	−	0.673304i	−0.603547	−	0.797328i	$-0.706246\pi$
$883$	11.5513	−	20.0075i	0.388732	−	0.673304i	0.992279	+	0.124023i	$0.0395797\pi$
$884$	−0.568688	−	0.477186i	−0.0191271	−	0.0160495i
$885$	1.54750	−	1.46548i	0.0520188	−	0.0492615i
$886$	−3.22654	−	18.2986i	−0.108398	−	0.614754i
$887$	8.58117	+	48.6662i	0.288127	+	1.63405i	0.693895	+	0.720076i	$0.255893\pi$
$887$	8.58117	+	48.6662i	0.288127	+	1.63405i	−0.405768	+	0.913976i	$0.632996\pi$
$888$	4.00719	−	34.8490i	0.134472	−	1.16945i
$889$	12.9338	−	19.3566i	0.433785	−	0.649199i
$890$	4.01806			0.134686
$891$	−25.4444	+	34.7172i	−0.852420	+	1.16307i
$892$	−0.107650	+	0.186455i	−0.00360439	+	0.00624298i
$893$	38.3327	+	32.1649i	1.28275	+	1.07636i
$894$	0.0962180	−	0.0417181i	0.00321801	−	0.00139526i
$895$	−13.9132	−	5.06399i	−0.465067	−	0.169270i
$896$	−20.6112	−	19.7311i	−0.688573	−	0.659171i
$897$	−9.23511	−	2.74599i	−0.308351	−	0.0916861i
$898$	−0.737490	−	0.618828i	−0.0246104	−	0.0206505i
$899$	5.48600	+	9.50202i	0.182968	+	0.316910i
$900$	0.143424	+	0.472626i	0.00478081	+	0.0157542i
$901$	20.9075	−	36.2129i	0.696531	−	1.20643i
$902$	39.2151	+	32.9054i	1.30572	+	1.09563i
$903$	−6.91012	−	40.4673i	−0.229954	−	1.34667i
$904$	−5.47484	−	31.0494i	−0.182091	−	1.03269i
$905$	−25.1802	+	21.1287i	−0.837017	+	0.702341i
$906$	−44.7398	+	2.68979i	−1.48638	+	0.0893624i
$907$	−11.6001	+	4.22210i	−0.385175	+	0.140192i	−0.527348	−	0.849650i	$-0.676813\pi$
$907$	−11.6001	+	4.22210i	−0.385175	+	0.140192i	0.142172	+	0.989842i	$0.454591\pi$
$908$	−0.268443	+	0.464958i	−0.00890861	+	0.0154302i
$909$	7.54149	−	0.910091i	0.250135	−	0.0301858i
$910$	1.28073	+	11.6948i	0.0424556	+	0.387677i
$911$	−8.77906	+	3.19532i	−0.290863	+	0.105866i	−0.483331	−	0.875438i	$-0.660573\pi$
$911$	−8.77906	+	3.19532i	−0.290863	+	0.105866i	0.192468	+	0.981303i	$0.438351\pi$
$912$	38.0888	−	36.0699i	1.26125	−	1.19439i
$913$	0.847587	+	4.80691i	0.0280510	+	0.159085i
$914$	−13.6602	+	11.4623i	−0.451839	+	0.379138i
$915$	2.35264	−	20.4600i	0.0777758	−	0.676387i
$916$	−0.105472	+	0.598163i	−0.00348490	+	0.0197639i
$917$	−0.318220	−	2.90578i	−0.0105085	−	0.0959572i
$918$	0.237602	+	42.3329i	0.00784203	+	1.39719i
$919$	27.2566	+	47.2098i	0.899112	+	1.55731i	0.828631	+	0.559795i	$0.189120\pi$
$919$	27.2566	+	47.2098i	0.899112	+	1.55731i	0.0704812	+	0.997513i	$0.477547\pi$
$920$	−8.51780	−	7.14729i	−0.280824	−	0.235639i
$921$	0.793807	−	6.90344i	0.0261568	−	0.227476i
$922$	6.64022	+	37.6586i	0.218684	+	1.24022i
$923$	−7.07093	+	5.93321i	−0.232742	+	0.195294i
$924$	−1.22383	+	0.437959i	−0.0402610	+	0.0144078i
$925$	18.4152	−	6.70258i	0.605488	−	0.220380i
$926$	−35.1975			−1.15666
$927$	0.327286	−	6.00639i	0.0107495	−	0.197276i
$928$	−2.36494			−0.0776328
$929$	−0.563662	+	3.19669i	−0.0184932	+	0.104880i	−0.992657	−	0.120962i	$-0.961402\pi$
$929$	−0.563662	+	3.19669i	−0.0184932	+	0.104880i	0.974164	+	0.225842i	$0.0725132\pi$
$930$	5.58912	−	0.336022i	0.183274	−	0.0110186i
$931$	54.2026	+	7.13646i	1.77642	+	0.233888i
$932$	−0.141250	−	0.801069i	−0.00462680	−	0.0262399i
$933$	−5.95967	−	9.02442i	−0.195111	−	0.295446i
$934$	3.15651	−	1.14887i	0.103284	−	0.0375923i
$935$	41.7118			1.36412
$936$	−1.00224	+	18.3931i	−0.0327591	+	0.601198i
$937$	−27.2712	+	47.2351i	−0.890911	+	1.54310i	−0.0521269	+	0.998640i	$0.516600\pi$
$937$	−27.2712	+	47.2351i	−0.890911	+	1.54310i	−0.838785	+	0.544463i	$0.816733\pi$
$938$	1.68892	+	0.110706i	0.0551452	+	0.00361469i
$939$	26.3609	−	24.9636i	0.860254	−	0.814655i
$940$	−0.532523	−	0.193822i	−0.0173690	−	0.00632179i
$941$	26.1250	−	21.9215i	0.851652	−	0.714621i	−0.108501	−	0.994096i	$-0.534605\pi$
$941$	26.1250	−	21.9215i	0.851652	−	0.714621i	0.960153	+	0.279475i	$0.0901605\pi$
$942$	3.49543	−	30.3984i	0.113887	−	0.990435i
$943$	−18.7649	+	6.82987i	−0.611069	+	0.222411i
$944$	−3.19963			−0.104139
$945$	−14.0944	+	14.8895i	−0.458491	+	0.484355i
$946$	59.6863			1.94057
$947$	19.0899	−	6.94816i	0.620339	−	0.225785i	−0.0126819	−	0.999920i	$-0.504037\pi$
$947$	19.0899	−	6.94816i	0.620339	−	0.225785i	0.633021	+	0.774135i	$0.281815\pi$
$948$	−0.556143	+	0.241132i	−0.0180627	+	0.00783160i
$949$	−7.46107	+	6.26058i	−0.242196	+	0.203227i
$950$	28.3810	+	10.3298i	0.920800	+	0.335144i
$951$	−7.49804	−	31.3750i	−0.243141	−	1.01740i
$952$	−24.6613	+	36.9078i	−0.799276	+	1.19619i
$953$	18.1140	−	31.3745i	0.586772	−	1.01632i	−0.407880	−	0.913035i	$-0.633732\pi$
$953$	18.1140	−	31.3745i	0.586772	−	1.01632i	0.994652	−	0.103283i	$-0.0329347\pi$
$954$	−29.6666	+	3.58010i	−0.960493	+	0.115910i
$955$	6.99765			0.226439
$956$	−0.573462	+	0.208723i	−0.0185471	+	0.00675058i
$957$	26.1170	−	52.2467i	0.844242	−	1.68890i
$958$	1.81393	+	10.2873i	0.0586054	+	0.332368i
$959$	1.80401	+	1.72698i	0.0582544	+	0.0557670i
$960$	−9.49715	+	18.9989i	−0.306519	+	0.613187i
$961$	−4.96266	+	28.1446i	−0.160086	+	0.907892i
$962$	21.0494			0.678658
$963$	21.4970	−	22.9570i	0.692732	−	0.739779i
$964$	0.293265			0.00944544
$965$	−30.5690	+	11.1262i	−0.984050	+	0.358165i
$966$	−2.96939	+	16.3237i	−0.0955386	+	0.525206i
$967$	5.45475	−	4.57708i	0.175413	−	0.147189i	−0.550854	−	0.834601i	$-0.685698\pi$
$967$	5.45475	−	4.57708i	0.175413	−	0.147189i	0.726267	+	0.687413i	$0.241254\pi$
$968$	−5.91459	−	33.5433i	−0.190102	−	1.07812i
$969$	−63.5454	−	47.1233i	−2.04137	−	1.51382i
$970$	−16.8384	−	14.1291i	−0.540647	−	0.453657i
$971$	−17.5786	−	30.4471i	−0.564125	−	0.977093i	−0.997130	−	0.0757020i	$-0.975880\pi$
$971$	−17.5786	−	30.4471i	−0.564125	−	0.977093i	0.433005	−	0.901391i	$-0.357453\pi$
$972$	−0.736389	+	0.559003i	−0.0236197	+	0.0179300i
$973$	22.9548	+	10.1005i	0.735896	+	0.323806i
$974$	3.19181	−	18.1017i	0.102272	−	0.580015i
$975$	−9.44151	+	4.09364i	−0.302370	+	0.131101i
$976$	−23.6848	+	19.8739i	−0.758132	+	0.636148i
$977$	−7.76765	−	44.0525i	−0.248509	−	1.40936i	−0.812200	−	0.583379i	$-0.801730\pi$
$977$	−7.76765	−	44.0525i	−0.248509	−	1.40936i	0.563691	−	0.825986i	$-0.309381\pi$
$978$	−1.82977	−	7.65656i	−0.0585097	−	0.244830i
$979$	−8.69181	+	3.16356i	−0.277792	+	0.101108i
$980$	−0.604466	+	0.134001i	−0.0193090	+	0.00428049i
$981$	16.3956	+	3.82110i	0.523473	+	0.121998i
$982$	16.0199	−	27.7472i	0.511214	−	0.885449i
$983$	−38.6428	+	14.0648i	−1.23251	+	0.448598i	−0.874458	−	0.485102i	$-0.838783\pi$
$983$	−38.6428	+	14.0648i	−1.23251	+	0.448598i	−0.358056	+	0.933700i	$0.616560\pi$
$984$	21.0392	+	31.8585i	0.670704	+	1.01561i
$985$	2.59330	−	2.17604i	0.0826294	−	0.0693343i
$986$	−9.97573	−	56.5752i	−0.317692	−	1.80172i
$987$	4.94208	+	28.9421i	0.157308	+	0.921236i
$988$	−0.759459	−	0.637261i	−0.0241616	−	0.0202740i
$989$	−11.6414	+	20.1635i	−0.370176	+	0.641163i
$990$	−17.8895	−	23.8430i	−0.568565	−	0.757779i
$991$	−26.7637	−	46.3561i	−0.850177	−	1.47255i	−0.881048	−	0.473027i	$-0.843161\pi$
$991$	−26.7637	−	46.3561i	−0.850177	−	1.47255i	0.0308709	−	0.999523i	$-0.490172\pi$
$992$	0.399775	+	0.335451i	0.0126929	+	0.0106506i
$993$	4.66163	+	19.5062i	0.147932	+	0.619012i
$994$	11.4822	+	10.9919i	0.364193	+	0.348643i
$995$	−0.0685304	−	0.0249430i	−0.00217256	−	0.000790747i
$996$	−0.0119765	+	0.104155i	−0.000379489	+	0.00330027i
$997$	−12.6320	−	10.5995i	−0.400058	−	0.335689i	0.420458	−	0.907312i	$-0.361869\pi$
$997$	−12.6320	−	10.5995i	−0.400058	−	0.335689i	−0.820516	+	0.571623i	$0.806314\pi$
$998$	−13.0564	+	22.6143i	−0.413292	+	0.715844i
$999$	23.7367	+	27.9680i	0.750995	+	0.884867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.25.7	yes	132
3.2	odd	2		567.2.w.a.235.16		132
7.2	even	3		189.2.u.a.79.16	yes	132
21.2	odd	6		567.2.u.a.478.7		132
27.13	even	9		189.2.u.a.67.16	✓	132
27.14	odd	18		567.2.u.a.172.7		132
189.121	even	9	inner	189.2.w.a.121.7	yes	132
189.149	odd	18		567.2.w.a.415.16		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.67.16	✓	132	27.13	even	9
189.2.u.a.79.16	yes	132	7.2	even	3
189.2.w.a.25.7	yes	132	1.1	even	1	trivial
189.2.w.a.121.7	yes	132	189.121	even	9	inner
567.2.u.a.172.7		132	27.14	odd	18
567.2.u.a.478.7		132	21.2	odd	6
567.2.w.a.235.16		132	3.2	odd	2
567.2.w.a.415.16		132	189.149	odd	18

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30907 + 0.476464i) q^{2} +(-1.39125 - 1.03171i) q^{3} +(-0.0454330 + 0.0381228i) q^{4} +(1.40139 + 0.510065i) q^{5} +(2.31282 + 0.687701i) q^{6} +(-2.64009 - 0.173054i) q^{7} +(1.43440 - 2.48445i) q^{8} +(0.871157 + 2.87073i) q^{9} +O(q^{10})\)	\(q+(-1.30907 + 0.476464i) q^{2} +(-1.39125 - 1.03171i) q^{3} +(-0.0454330 + 0.0381228i) q^{4} +(1.40139 + 0.510065i) q^{5} +(2.31282 + 0.687701i) q^{6} +(-2.64009 - 0.173054i) q^{7} +(1.43440 - 2.48445i) q^{8} +(0.871157 + 2.87073i) q^{9} -2.07755 q^{10} +(4.49413 - 1.63573i) q^{11} +(0.102540 - 0.00616480i) q^{12} +(0.371663 + 2.10780i) q^{13} +(3.53852 - 1.03137i) q^{14} +(-1.42345 - 2.15546i) q^{15} +(-0.673384 + 3.81895i) q^{16} +5.84823 q^{17} +(-2.50821 - 3.34292i) q^{18} +7.81006 q^{19} +(-0.0831146 + 0.0302512i) q^{20} +(3.49448 + 2.96456i) q^{21} +(-5.10378 + 4.28258i) q^{22} +(-0.451305 - 2.55948i) q^{23} +(-4.55883 + 1.97661i) q^{24} +(-2.12649 - 1.78433i) q^{25} +(-1.49083 - 2.58219i) q^{26} +(1.74976 - 4.89268i) q^{27} +(0.126544 - 0.0927851i) q^{28} +(-1.22445 + 6.94422i) q^{29} +(2.89040 + 2.14343i) q^{30} +(1.19198 - 1.00019i) q^{31} +(0.0582395 + 0.330293i) q^{32} +(-7.94006 - 2.36092i) q^{33} +(-7.65576 + 2.78647i) q^{34} +(-3.61153 - 1.58913i) q^{35} +(-0.149019 - 0.0972148i) q^{36} +(-3.52981 + 6.11382i) q^{37} +(-10.2239 + 3.72121i) q^{38} +(1.65756 - 3.31593i) q^{39} +(3.27739 - 2.75005i) q^{40} +(-1.33423 - 7.56680i) q^{41} +(-5.98704 - 2.21583i) q^{42} +(-6.86262 - 5.75842i) q^{43} +(-0.141823 + 0.245645i) q^{44} +(-0.243426 + 4.46737i) q^{45} +(1.81029 + 3.13551i) q^{46} +(4.90812 + 4.11840i) q^{47} +(4.87689 - 4.61838i) q^{48} +(6.94010 + 0.913753i) q^{49} +(3.63390 + 1.32263i) q^{50} +(-8.13636 - 6.03367i) q^{51} +(-0.0972411 - 0.0815949i) q^{52} +(3.57502 - 6.19211i) q^{53} +(0.0406280 + 7.23858i) q^{54} +7.13238 q^{55} +(-4.21688 + 6.31093i) q^{56} +(-10.8658 - 8.05770i) q^{57} +(-1.70577 - 9.67390i) q^{58} +(0.143277 + 0.812567i) q^{59} +(0.146844 + 0.0436629i) q^{60} +(6.10769 + 5.12496i) q^{61} +(-1.08383 + 1.87725i) q^{62} +(-1.80314 - 7.72973i) q^{63} +(-4.11148 - 7.12129i) q^{64} +(-0.554272 + 3.14343i) q^{65} +(11.5190 - 0.692533i) q^{66} +(0.431518 + 0.157060i) q^{67} +(-0.265703 + 0.222951i) q^{68} +(-2.01275 + 4.02649i) q^{69} +(5.48492 + 0.359528i) q^{70} +(2.15632 + 3.73486i) q^{71} +(8.38177 + 1.95342i) q^{72} +(2.27530 + 3.94093i) q^{73} +(1.70777 - 9.68527i) q^{74} +(1.11756 + 4.67637i) q^{75} +(-0.354834 + 0.297741i) q^{76} +(-12.1480 + 3.54074i) q^{77} +(-0.589949 + 5.13056i) q^{78} +(-5.54499 + 2.01821i) q^{79} +(-2.89159 + 5.00838i) q^{80} +(-7.48217 + 5.00171i) q^{81} +(5.35191 + 9.26979i) q^{82} +(-0.177225 + 1.00509i) q^{83} +(-0.271782 - 0.00146936i) q^{84} +(8.19567 + 2.98298i) q^{85} +(11.7274 + 4.26841i) q^{86} +(8.86793 - 8.39787i) q^{87} +(2.38248 - 13.5117i) q^{88} -1.93404 q^{89} +(-1.80988 - 5.96410i) q^{90} +(-0.616458 - 5.62910i) q^{91} +(0.118079 + 0.0990797i) q^{92} +(-2.69024 + 0.161739i) q^{93} +(-8.38736 - 3.05275i) q^{94} +(10.9450 + 3.98364i) q^{95} +(0.259740 - 0.519606i) q^{96} +(8.10490 + 6.80081i) q^{97} +(-9.52048 + 2.11054i) q^{98} +(8.61084 + 11.4765i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Introduction

L-functions

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