LMFDB - Embedded newform 207.2.o.a.113.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(5,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("207.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, degree $20$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			113.17
Character	$\chi$	$=$	207.113
Dual form			207.2.o.a.11.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38355 + 0.0659064i) q^{2} +(-1.72926 + 0.0982663i) q^{3} +(-0.0810891 - 0.00774307i) q^{4} +(2.41932 - 2.30682i) q^{5} +(-2.39899 + 0.0219866i) q^{6} +(0.529794 - 2.74883i) q^{7} +(-2.85371 - 0.410302i) q^{8} +(2.98069 - 0.339856i) q^{9} +O(q^{10})$	\(q+(1.38355 + 0.0659064i) q^{2} +(-1.72926 + 0.0982663i) q^{3} +(-0.0810891 - 0.00774307i) q^{4} +(2.41932 - 2.30682i) q^{5} +(-2.39899 + 0.0219866i) q^{6} +(0.529794 - 2.74883i) q^{7} +(-2.85371 - 0.410302i) q^{8} +(2.98069 - 0.339856i) q^{9} +(3.49928 - 3.03214i) q^{10} +(3.39272 + 1.74907i) q^{11} +(0.140985 + 0.00542146i) q^{12} +(2.52392 - 0.486446i) q^{13} +(0.914161 - 3.76822i) q^{14} +(-3.95696 + 4.22684i) q^{15} +(-3.76123 - 0.724917i) q^{16} +(-1.25579 + 2.74979i) q^{17} +(4.14632 - 0.273760i) q^{18} +(-4.61501 + 2.10760i) q^{19} +(-0.214043 + 0.168325i) q^{20} +(-0.646035 + 4.80551i) q^{21} +(4.57871 + 2.64352i) q^{22} +(-4.33687 - 2.04732i) q^{23} +(4.97513 + 0.429095i) q^{24} +(0.293797 - 6.16757i) q^{25} +(3.52402 - 0.506677i) q^{26} +(-5.12099 + 0.880602i) q^{27} +(-0.0642449 + 0.218798i) q^{28} +(-0.706422 - 7.39798i) q^{29} +(-5.75321 + 5.58723i) q^{30} +(7.49075 + 5.89079i) q^{31} +(0.447524 + 0.108568i) q^{32} +(-6.03877 - 2.69121i) q^{33} +(-1.91867 + 3.72169i) q^{34} +(-5.05933 - 7.87247i) q^{35} +(-0.244333 + 0.00447897i) q^{36} +(1.87173 + 6.37451i) q^{37} +(-6.52398 + 2.61181i) q^{38} +(-4.31672 + 1.08921i) q^{39} +(-7.85055 + 5.59035i) q^{40} +(4.44323 + 4.65992i) q^{41} +(-1.21053 + 6.60607i) q^{42} +(4.08330 + 5.19234i) q^{43} +(-0.261569 - 0.168100i) q^{44} +(6.42726 - 7.69814i) q^{45} +(-5.86533 - 3.11839i) q^{46} +(-9.75306 + 5.63093i) q^{47} +(6.57538 + 0.883969i) q^{48} +(-0.776834 - 0.310997i) q^{49} +(0.812964 - 8.51375i) q^{50} +(1.90137 - 4.87850i) q^{51} +(-0.208429 + 0.0199025i) q^{52} +(-0.101320 + 0.116930i) q^{53} +(-7.14316 + 0.880846i) q^{54} +(12.2429 - 3.59483i) q^{55} +(-2.63973 + 7.62701i) q^{56} +(7.77344 - 4.09810i) q^{57} +(-0.489792 - 10.2820i) q^{58} +(0.0647809 + 0.336115i) q^{59} +(0.353595 - 0.312111i) q^{60} +(2.27908 + 5.69286i) q^{61} +(9.97556 + 8.64387i) q^{62} +(0.644943 - 8.37347i) q^{63} +(7.96259 + 2.33803i) q^{64} +(4.98404 - 6.99910i) q^{65} +(-8.17755 - 4.12140i) q^{66} +(-0.896686 - 1.73933i) q^{67} +(0.123122 - 0.213254i) q^{68} +(7.70077 + 3.11419i) q^{69} +(-6.48096 - 11.2254i) q^{70} +(0.459839 - 0.715523i) q^{71} +(-8.64547 - 0.253130i) q^{72} +(-1.68321 - 3.68571i) q^{73} +(2.16950 + 8.94279i) q^{74} +(0.0980118 + 10.6942i) q^{75} +(0.390546 - 0.135169i) q^{76} +(6.60534 - 8.39938i) q^{77} +(-6.04416 + 1.22247i) q^{78} +(2.25140 + 0.779217i) q^{79} +(-10.7719 + 6.92267i) q^{80} +(8.76900 - 2.02601i) q^{81} +(5.84029 + 6.74005i) q^{82} +(-9.97312 - 9.50935i) q^{83} +(0.0895958 - 0.384672i) q^{84} +(3.30511 + 9.54950i) q^{85} +(5.30723 + 7.45296i) q^{86} +(1.94856 + 12.7236i) q^{87} +(-8.96420 - 6.38338i) q^{88} +(-1.81676 - 12.6358i) q^{89} +(9.39977 - 10.2271i) q^{90} -7.19556i q^{91} +(0.335820 + 0.199596i) q^{92} +(-13.5323 - 9.45063i) q^{93} +(-13.8649 + 7.14786i) q^{94} +(-6.30334 + 15.7450i) q^{95} +(-0.784554 - 0.143766i) q^{96} +(-2.30629 + 0.559499i) q^{97} +(-1.05429 - 0.481477i) q^{98} +(10.7071 + 4.06039i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.38355	+	0.0659064i	0.978314	+	0.0466029i	0.530643	−	0.847595i	$-0.321950\pi$
$2$	1.38355	+	0.0659064i	0.978314	+	0.0466029i	0.447671	+	0.894198i	$0.352253\pi$
$3$	−1.72926	+	0.0982663i	−0.998389	+	0.0567341i
$3$	−1.72926	+	0.0982663i	−0.998389	+	0.0567341i
$4$	−0.0810891	−	0.00774307i	−0.0405445	−	0.00387153i
$5$	2.41932	−	2.30682i	1.08195	−	1.03164i	0.0825697	−	0.996585i	$-0.473687\pi$
$5$	2.41932	−	2.30682i	1.08195	−	1.03164i	0.999385	−	0.0350567i	$-0.0111612\pi$
$6$	−2.39899	+	0.0219866i	−0.979383	+	0.00897599i
$7$	0.529794	−	2.74883i	0.200243	−	1.03896i	−0.733139	−	0.680079i	$-0.761946\pi$
$7$	0.529794	−	2.74883i	0.200243	−	1.03896i	0.933383	−	0.358883i	$-0.116842\pi$
$8$	−2.85371	−	0.410302i	−1.00894	−	0.145064i
$9$	2.98069	−	0.339856i	0.993562	−	0.113285i
$10$	3.49928	−	3.03214i	1.10657	−	0.958848i
$11$	3.39272	+	1.74907i	1.02294	+	0.527364i	0.886229	−	0.463247i	$-0.153316\pi$
$11$	3.39272	+	1.74907i	1.02294	+	0.527364i	0.136714	+	0.990611i	$0.456346\pi$
$12$	0.140985	+	0.00542146i	0.0406989	+	0.00156504i
$13$	2.52392	−	0.486446i	0.700010	−	0.134916i	0.173184	−	0.984889i	$-0.444594\pi$
$13$	2.52392	−	0.486446i	0.700010	−	0.134916i	0.526825	+	0.849974i	$0.323382\pi$
$14$	0.914161	−	3.76822i	0.244320	−	1.00710i
$15$	−3.95696	+	4.22684i	−1.02168	+	1.09136i
$16$	−3.76123	−	0.724917i	−0.940307	−	0.181229i
$17$	−1.25579	+	2.74979i	−0.304573	+	0.666921i	−0.998593	−	0.0530345i	$-0.983111\pi$
$17$	−1.25579	+	2.74979i	−0.304573	+	0.666921i	0.694020	+	0.719956i	$0.255838\pi$
$18$	4.14632	−	0.273760i	0.977296	−	0.0645259i
$19$	−4.61501	+	2.10760i	−1.05876	+	0.483517i	−0.867198	−	0.497964i	$-0.834081\pi$
$19$	−4.61501	+	2.10760i	−1.05876	+	0.483517i	−0.191557	+	0.981481i	$0.561354\pi$
$20$	−0.214043	+	0.168325i	−0.0478614	+	0.0376386i
$21$	−0.646035	+	4.80551i	−0.140976	+	1.04865i
$22$	4.57871	+	2.64352i	0.976183	+	0.563600i
$23$	−4.33687	−	2.04732i	−0.904301	−	0.426896i
$23$	−4.33687	−	2.04732i	−0.904301	−	0.426896i
$24$	4.97513	+	0.429095i	1.01554	+	0.0875887i
$25$	0.293797	−	6.16757i	0.0587595	−	1.23351i
$26$	3.52402	−	0.506677i	0.691117	−	0.0993676i
$27$	−5.12099	+	0.880602i	−0.985535	+	0.169472i
$28$	−0.0642449	+	0.218798i	−0.0121412	+	0.0413490i
$29$	−0.706422	−	7.39798i	−0.131179	−	1.37377i	−0.786112	−	0.618084i	$-0.787909\pi$
$29$	−0.706422	−	7.39798i	−0.131179	−	1.37377i	0.654933	−	0.755687i	$-0.272697\pi$
$30$	−5.75321	+	5.58723i	−1.05039	+	1.02008i
$31$	7.49075	+	5.89079i	1.34538	+	1.05802i	0.992487	+	0.122354i	$0.0390443\pi$
$31$	7.49075	+	5.89079i	1.34538	+	1.05802i	0.352893	+	0.935664i	$0.385198\pi$
$32$	0.447524	+	0.108568i	0.0791118	+	0.0191923i
$33$	−6.03877	−	2.69121i	−1.05122	−	0.468479i
$34$	−1.91867	+	3.72169i	−0.329048	+	0.638265i
$35$	−5.05933	−	7.87247i	−0.855182	−	1.33069i
$36$	−0.244333	+	0.00447897i	−0.0407221	+	0.000746495i
$37$	1.87173	+	6.37451i	0.307710	+	1.04796i	0.957640	+	0.287969i	$0.0929801\pi$
$37$	1.87173	+	6.37451i	0.307710	+	1.04796i	−0.649930	+	0.759994i	$0.725202\pi$
$38$	−6.52398	+	2.61181i	−1.05833	+	0.423691i
$39$	−4.31672	+	1.08921i	−0.691228	+	0.174413i
$40$	−7.85055	+	5.59035i	−1.24128	+	0.883912i
$41$	4.44323	+	4.65992i	0.693915	+	0.727758i	0.972564	−	0.232636i	$-0.0747350\pi$
$41$	4.44323	+	4.65992i	0.693915	+	0.727758i	−0.278649	+	0.960393i	$0.589886\pi$
$42$	−1.21053	+	6.60607i	−0.186789	+	1.01934i
$43$	4.08330	+	5.19234i	0.622698	+	0.791824i	0.990417	−	0.138113i	$-0.0441036\pi$
$43$	4.08330	+	5.19234i	0.622698	+	0.791824i	−0.367719	+	0.929937i	$0.619861\pi$
$44$	−0.261569	−	0.168100i	−0.0394330	−	0.0253421i
$45$	6.42726	−	7.69814i	0.958120	−	1.14757i
$46$	−5.86533	−	3.11839i	−0.864796	−	0.459782i
$47$	−9.75306	+	5.63093i	−1.42263	+	0.821356i	−0.996523	−	0.0833165i	$-0.973449\pi$
$47$	−9.75306	+	5.63093i	−1.42263	+	0.821356i	−0.426107	+	0.904673i	$0.640115\pi$
$48$	6.57538	+	0.883969i	0.949074	+	0.127590i
$49$	−0.776834	−	0.310997i	−0.110976	−	0.0444282i
$50$	0.812964	−	8.51375i	0.114970	−	1.20403i
$51$	1.90137	−	4.87850i	0.266245	−	0.683127i
$52$	−0.208429	+	0.0199025i	−0.0289039	+	0.00275999i
$53$	−0.101320	+	0.116930i	−0.0139174	+	0.0160616i	−0.762666	−	0.646793i	$-0.776110\pi$
$53$	−0.101320	+	0.116930i	−0.0139174	+	0.0160616i	0.748748	+	0.662855i	$0.230655\pi$
$54$	−7.14316	+	0.880846i	−0.972061	+	0.119868i
$55$	12.2429	−	3.59483i	1.65083	−	0.484727i
$56$	−2.63973	+	7.62701i	−0.352749	+	1.01920i
$57$	7.77344	−	4.09810i	1.02962	−	0.542806i
$58$	−0.489792	−	10.2820i	−0.0643129	−	1.35009i
$59$	0.0647809	+	0.336115i	0.00843375	+	0.0437585i	0.985902	−	0.167325i	$-0.0535129\pi$
$59$	0.0647809	+	0.336115i	0.00843375	+	0.0437585i	−0.977468	+	0.211083i	$0.932301\pi$
$60$	0.353595	−	0.312111i	0.0456489	−	0.0402934i
$61$	2.27908	+	5.69286i	0.291806	+	0.728896i	0.999744	+	0.0226216i	$0.00720130\pi$
$61$	2.27908	+	5.69286i	0.291806	+	0.728896i	−0.707938	+	0.706274i	$0.750374\pi$
$62$	9.97556	+	8.64387i	1.26690	+	1.09777i
$63$	0.644943	−	8.37347i	0.0812552	−	1.05496i
$64$	7.96259	+	2.33803i	0.995324	+	0.292253i
$65$	4.98404	−	6.99910i	0.618194	−	0.868132i
$66$	−8.17755	−	4.12140i	−1.00659	−	0.507309i
$67$	−0.896686	−	1.73933i	−0.109548	−	0.212493i	0.827689	−	0.561187i	$-0.189655\pi$
$67$	−0.896686	−	1.73933i	−0.109548	−	0.212493i	−0.937236	+	0.348695i	$0.886625\pi$
$68$	0.123122	−	0.213254i	0.0149308	−	0.0258608i
$69$	7.70077	+	3.11419i	0.927064	+	0.374904i
$70$	−6.48096	−	11.2254i	−0.774623	−	1.34169i
$71$	0.459839	−	0.715523i	0.0545728	−	0.0849170i	−0.812895	−	0.582410i	$-0.802110\pi$
$71$	0.459839	−	0.715523i	0.0545728	−	0.0849170i	0.867468	+	0.497493i	$0.165746\pi$
$72$	−8.64547	−	0.253130i	−1.01888	−	0.0298316i
$73$	−1.68321	−	3.68571i	−0.197005	−	0.431380i	0.785188	−	0.619258i	$-0.212566\pi$
$73$	−1.68321	−	3.68571i	−0.197005	−	0.431380i	−0.982192	+	0.187878i	$0.939839\pi$
$74$	2.16950	+	8.94279i	0.252199	+	1.03958i
$75$	0.0980118	+	10.6942i	0.0113174	+	1.23486i
$76$	0.390546	−	0.135169i	0.0447987	−	0.0155050i
$77$	6.60534	−	8.39938i	0.752749	−	0.957198i
$78$	−6.04416	+	1.22247i	−0.684366	+	0.138417i
$79$	2.25140	+	0.779217i	0.253302	+	0.0876687i	0.450768	−	0.892641i	$-0.351150\pi$
$79$	2.25140	+	0.779217i	0.253302	+	0.0876687i	−0.197466	+	0.980310i	$0.563271\pi$
$80$	−10.7719	+	6.92267i	−1.20433	+	0.773978i
$81$	8.76900	−	2.02601i	0.974333	−	0.225112i
$82$	5.84029	+	6.74005i	0.644952	+	0.744314i
$83$	−9.97312	−	9.50935i	−1.09469	−	1.04379i	−0.998828	−	0.0483926i	$-0.984590\pi$
$83$	−9.97312	−	9.50935i	−1.09469	−	1.04379i	−0.0958640	−	0.995394i	$-0.530561\pi$
$84$	0.0895958	−	0.384672i	0.00977570	−	0.0419712i
$85$	3.30511	+	9.54950i	0.358490	+	1.03579i
$86$	5.30723	+	7.45296i	0.572293	+	0.803673i
$87$	1.94856	+	12.7236i	0.208908	+	1.36412i
$88$	−8.96420	−	6.38338i	−0.955587	−	0.680470i
$89$	−1.81676	−	12.6358i	−0.192576	−	1.33939i	−0.825158	−	0.564901i	$-0.808914\pi$
$89$	−1.81676	−	12.6358i	−0.192576	−	1.33939i	0.632582	−	0.774493i	$-0.281995\pi$
$90$	9.39977	−	10.2271i	0.990823	−	1.07803i
$91$		−	7.19556i		−	0.754299i
$92$	0.335820	+	0.199596i	0.0350117	+	0.0208093i
$93$	−13.5323	−	9.45063i	−1.40324	−	0.979985i
$94$	−13.8649	+	7.14786i	−1.43006	+	0.737246i
$95$	−6.30334	+	15.7450i	−0.646709	+	1.61540i
$96$	−0.784554	−	0.143766i	−0.0800732	−	0.0146731i
$97$	−2.30629	+	0.559499i	−0.234168	+	0.0568085i	−0.351126	−	0.936328i	$-0.614201\pi$
$97$	−2.30629	+	0.559499i	−0.234168	+	0.0568085i	0.116958	+	0.993137i	$0.462686\pi$
$98$	−1.05429	−	0.481477i	−0.106499	−	0.0486365i
$99$	10.7071	+	4.06039i	1.07610	+	0.408084i
$100$	−0.0715796	+	0.497847i	−0.00715796	+	0.0497847i
$101$	−3.96870	+	4.16225i	−0.394900	+	0.414159i	−0.890926	−	0.454148i	$-0.849944\pi$
$101$	−3.96870	+	4.16225i	−0.394900	+	0.414159i	0.496026	+	0.868308i	$0.334792\pi$
$102$	2.95216	−	6.62432i	0.292307	−	0.655905i
$103$	−2.00436	+	0.0954793i	−0.197495	+	0.00940786i	−0.146096	−	0.989270i	$-0.546671\pi$
$103$	−2.00436	+	0.0954793i	−0.197495	+	0.00940786i	−0.0513988	+	0.998678i	$0.516368\pi$
$104$	−7.40213	+	0.352607i	−0.725839	+	0.0345760i
$105$	9.52249	+	13.1164i	0.929300	+	1.28003i
$106$	−0.147888	+	0.155100i	−0.0143641	+	0.0150647i
$107$	1.05242	−	7.31973i	0.101741	−	0.707625i	−0.873555	−	0.486725i	$-0.838191\pi$
$107$	1.05242	−	7.31973i	0.101741	−	0.707625i	0.975296	−	0.220900i	$-0.0708994\pi$
$108$	0.422075	−	0.0317550i	0.0406142	−	0.00305562i
$109$	−1.13579	−	0.518696i	−0.108789	−	0.0496821i	0.360277	−	0.932845i	$-0.382682\pi$
$109$	−1.13579	−	0.518696i	−0.108789	−	0.0496821i	−0.469066	+	0.883163i	$0.655409\pi$
$110$	17.1755	−	4.16673i	1.63762	−	0.397282i
$111$	−3.86310	−	10.8393i	−0.366669	−	1.02882i
$112$	−3.98535	+	9.95494i	−0.376581	+	0.940653i
$113$	2.79951	−	1.44325i	0.263356	−	0.135770i	−0.321492	−	0.946912i	$-0.604184\pi$
$113$	2.79951	−	1.44325i	0.263356	−	0.135770i	0.584848	+	0.811143i	$0.301154\pi$
$114$	11.0250	−	5.15758i	1.03259	−	0.483052i
$115$	−15.2151	+	5.05125i	−1.41882	+	0.471032i
$116$			0.605365i			0.0562068i
$117$	7.35770	−	2.30771i	0.680219	−	0.213348i
$118$	0.0674752	+	0.469300i	0.00621159	+	0.0432026i
$119$	6.89340	+	4.90877i	0.631917	+	0.449986i
$120$	13.0263	−	10.4386i	1.18913	−	0.952911i
$121$	2.07068	+	2.90786i	0.188243	+	0.264351i
$122$	2.77801	+	8.02654i	0.251509	+	0.726689i
$123$	−8.14141	−	7.62160i	−0.734086	−	0.687217i
$124$	−0.561805	−	0.535680i	−0.0504516	−	0.0481055i
$125$	−2.57122	−	2.96734i	−0.229977	−	0.265407i
$126$	1.44417	−	11.5426i	0.128657	−	1.02829i
$127$	7.44740	−	4.78616i	0.660850	−	0.424703i	−0.166766	−	0.985996i	$-0.553333\pi$
$127$	7.44740	−	4.78616i	0.660850	−	0.424703i	0.827617	+	0.561294i	$0.189696\pi$
$128$	9.99216	+	3.45832i	0.883191	+	0.305675i
$129$	−7.57133	−	8.57766i	−0.666618	−	0.755221i
$130$	7.35693	−	9.35510i	0.645246	−	0.820497i
$131$	−15.4187	+	5.33645i	−1.34714	+	0.466248i	−0.902973	−	0.429698i	$-0.858620\pi$
$131$	−15.4187	+	5.33645i	−1.34714	+	0.466248i	−0.444163	+	0.895946i	$0.646499\pi$
$132$	0.468840	+	0.264986i	0.0408073	+	0.0230641i
$133$	3.34845	+	13.8025i	0.290347	+	1.19683i
$134$	−1.12597	−	2.46554i	−0.0972692	−	0.212990i
$135$	−10.3579	+	13.9437i	−0.891470	+	1.20008i
$136$	4.71189	−	7.33185i	0.404041	−	0.628701i
$137$	−4.34509	−	7.52592i	−0.371226	−	0.642983i	0.618528	−	0.785763i	$-0.287729\pi$
$137$	−4.34509	−	7.52592i	−0.371226	−	0.642983i	−0.989754	+	0.142780i	$0.954396\pi$
$138$	10.4491	+	4.81615i	0.889488	+	0.409978i
$139$	−1.00358	+	1.73825i	−0.0851225	+	0.147437i	−0.905443	−	0.424467i	$-0.860462\pi$
$139$	−1.00358	+	1.73825i	−0.0851225	+	0.147437i	0.820321	+	0.571904i	$0.193795\pi$
$140$	0.349299	+	0.677545i	0.0295212	+	0.0572630i
$141$	16.3123	−	10.6958i	1.37374	−	0.900745i
$142$	0.683366	−	0.959653i	0.0573468	−	0.0805323i
$143$	9.41378	+	2.76413i	0.787220	+	0.231149i
$144$	−11.4574	−	0.882475i	−0.954784	−	0.0735396i
$145$	−18.7749	−	16.2685i	−1.55917	−	1.35103i
$146$	−2.08588	−	5.21028i	−0.172629	−	0.431206i
$147$	1.37391	+	0.461459i	0.113318	+	0.0380605i
$148$	−0.102418	−	0.531396i	−0.00841872	−	0.0436805i
$149$	0.380957	+	7.99728i	0.0312092	+	0.655163i	0.959229	+	0.282631i	$0.0912072\pi$
$149$	0.380957	+	7.99728i	0.0312092	+	0.655163i	−0.928019	+	0.372532i	$0.878490\pi$
$150$	−0.569213	+	14.8024i	−0.0464760	+	1.20861i
$151$	4.29323	−	12.4045i	0.349378	−	1.00946i	−0.624231	−	0.781240i	$-0.714588\pi$
$151$	4.29323	−	12.4045i	0.349378	−	1.00946i	0.973609	−	0.228222i	$-0.0732911\pi$
$152$	14.0347	−	4.12095i	1.13836	−	0.334253i
$153$	−2.80857	+	8.62304i	−0.227060	+	0.697132i
$154$	9.69236	−	11.1856i	0.781033	−	0.901360i
$155$	31.7116	−	3.02809i	2.54714	−	0.243222i
$156$	0.358472	−	0.0548982i	0.0287007	−	0.00439538i
$157$	−0.441927	+	4.62807i	−0.0352697	+	0.369361i	0.960556	+	0.278086i	$0.0897001\pi$
$157$	−0.441927	+	4.62807i	−0.0352697	+	0.369361i	−0.995826	+	0.0912743i	$0.970906\pi$
$158$	3.06356	+	1.22646i	0.243724	+	0.0975722i
$159$	0.163719	−	0.212159i	0.0129838	−	0.0168253i
$160$	1.33315	−	0.769696i	0.105395	−	0.0608498i
$161$	−7.92540	+	10.8367i	−0.624609	+	0.854050i
$162$	12.2658	−	2.22515i	0.963695	−	0.174824i
$163$	−6.52714	−	4.19474i	−0.511245	−	0.328557i	0.259455	−	0.965755i	$-0.416457\pi$
$163$	−6.52714	−	4.19474i	−0.511245	−	0.328557i	−0.770700	+	0.637198i	$0.780093\pi$
$164$	−0.324215	−	0.412273i	−0.0253169	−	0.0321931i
$165$	−20.8179	+	7.41947i	−1.62067	+	0.577605i
$166$	−13.1715	−	13.8139i	−1.02231	−	1.07217i
$167$	8.32475	−	5.92803i	0.644189	−	0.458725i	−0.210690	−	0.977553i	$-0.567571\pi$
$167$	8.32475	−	5.92803i	0.644189	−	0.458725i	0.854878	+	0.518828i	$0.173632\pi$
$168$	3.81531	−	13.4485i	0.294357	−	1.03757i
$169$	−5.93524	+	2.37611i	−0.456557	+	0.182778i
$170$	3.94340	+	13.4300i	0.302445	+	1.03003i
$171$	−13.0396	+	7.85054i	−0.997164	+	0.600346i
$172$	−0.290906	−	0.452659i	−0.0221814	−	0.0345149i
$173$	−5.13839	+	9.96709i	−0.390665	+	0.757784i	−0.999366	−	0.0356160i	$-0.988661\pi$
$173$	−5.13839	+	9.96709i	−0.390665	+	0.757784i	0.608701	+	0.793400i	$0.291691\pi$
$174$	1.85735	+	17.7321i	0.140806	+	1.34427i
$175$	−16.7980	−	4.07514i	−1.26981	−	0.308052i
$176$	−11.4929	−	9.03808i	−0.866307	−	0.681271i
$177$	−0.145052	−	0.574865i	−0.0109028	−	0.0432095i
$178$	−1.68078	−	17.6020i	−0.125980	−	1.31932i
$179$	−4.40960	+	15.0177i	−0.329589	+	1.12248i	0.613433	+	0.789747i	$0.289788\pi$
$179$	−4.40960	+	15.0177i	−0.329589	+	1.12248i	−0.943022	+	0.332730i	$0.892030\pi$
$180$	−0.580788	+	0.574468i	−0.0432894	+	0.0428183i
$181$	−20.7287	+	2.98033i	−1.54075	+	0.221526i	−0.859733	−	0.510743i	$-0.829370\pi$
$181$	−20.7287	+	2.98033i	−1.54075	+	0.221526i	−0.681015	+	0.732269i	$0.738461\pi$
$182$	0.474233	−	9.95538i	0.0351525	−	0.737942i
$183$	−4.50054	−	9.62048i	−0.332689	−	0.711167i
$184$	11.5362	+	7.62190i	0.850457	+	0.561894i
$185$	19.2332	+	11.1043i	1.41405	+	0.816403i
$186$	−18.0997	−	13.9672i	−1.32714	−	1.02413i
$187$	−9.07009	+	7.13280i	−0.663271	+	0.521602i
$188$	0.834467	−	0.381089i	0.0608598	−	0.0277937i
$189$	−0.292444	+	14.5433i	−0.0212722	+	1.05787i
$190$	−9.75865	+	21.3685i	−0.707967	+	1.55023i
$191$	1.67854	+	0.323513i	0.121455	+	0.0234086i	0.249617	−	0.968345i	$-0.419695\pi$
$191$	1.67854	+	0.323513i	0.121455	+	0.0234086i	−0.128161	+	0.991753i	$0.540908\pi$
$192$	−13.9991	−	3.26061i	−1.01030	−	0.235314i
$193$	1.41196	−	5.82017i	0.101635	−	0.418945i	−0.898150	−	0.439690i	$-0.855088\pi$
$193$	1.41196	−	5.82017i	0.101635	−	0.418945i	0.999785	+	0.0207444i	$0.00660363\pi$
$194$	−3.22773	+	0.622093i	−0.231737	+	0.0446637i
$195$	−7.93093	+	12.5930i	−0.567946	+	0.901807i
$196$	0.0605846	+	0.0312336i	0.00432747	+	0.00223097i
$197$	3.44676	−	2.98663i	0.245571	−	0.212789i	−0.523374	−	0.852103i	$-0.675327\pi$
$197$	3.44676	−	2.98663i	0.245571	−	0.212789i	0.768946	+	0.639314i	$0.220782\pi$
$198$	14.5461	+	6.32340i	1.03375	+	0.449384i
$199$	14.6209	+	2.10216i	1.03645	+	0.149018i	0.639474	−	0.768812i	$-0.279152\pi$
$199$	14.6209	+	2.10216i	1.03645	+	0.149018i	0.396972	+	0.917831i	$0.370061\pi$
$200$	−3.36898	+	17.4799i	−0.238223	+	1.23602i
$201$	1.72152	+	2.91964i	0.121427	+	0.205935i
$202$	−5.76519	+	5.49710i	−0.405638	+	0.386775i
$203$	−20.7101	−	1.97757i	−1.45356	−	0.138798i
$204$	−0.191955	+	0.380871i	−0.0134395	+	0.0266663i
$205$	21.4992	+	1.02413i	1.50157	+	0.0715286i
$206$	−2.77941			−0.193651
$207$	−13.6227	−	4.62852i	−0.946840	−	0.321704i
$208$	−9.84567			−0.682675
$209$	−19.3438	−	0.921457i	−1.33804	−	0.0637385i
$210$	12.3104	+	18.7747i	0.849495	+	1.29558i
$211$	28.8131	+	2.75132i	1.98358	+	0.189409i	0.999958	+	0.00914953i	$0.00291243\pi$
$211$	28.8131	+	2.75132i	1.98358	+	0.189409i	0.983619	+	0.180259i	$0.0576936\pi$
$212$	0.00912138	−	0.00869722i	0.000626459	−	0.000597327i
$213$	−0.724870	+	1.28251i	−0.0496672	+	0.0878764i
$214$	1.93848	−	10.0578i	0.132512	−	0.687538i
$215$	21.8566	+	3.14251i	1.49061	+	0.214317i
$216$	14.9751	−	0.411831i	1.01893	−	0.0280216i
$217$	20.1614	−	17.4699i	1.36864	−	1.18594i
$218$	−1.53723	−	0.792496i	−0.104114	−	0.0536746i
$219$	3.27289	+	6.20815i	0.221161	+	0.419508i
$220$	−1.02060	+	0.196704i	−0.0688087	+	0.0132618i
$221$	−1.83188	+	7.55111i	−0.123226	+	0.507943i
$222$	−4.63040	−	15.2512i	−0.310772	−	1.02360i
$223$	−0.991326	−	0.191062i	−0.0663841	−	0.0127945i	0.155951	−	0.987765i	$-0.450156\pi$
$223$	−0.991326	−	0.191062i	−0.0663841	−	0.0127945i	−0.222335	+	0.974970i	$0.571368\pi$
$224$	0.535532	−	1.17265i	0.0357817	−	0.0783510i
$225$	−1.22037	−	18.4834i	−0.0813579	−	1.23223i
$226$	3.96837	−	1.81230i	0.263972	−	0.120552i
$227$	−8.07879	+	6.35323i	−0.536208	+	0.421679i	−0.849196	−	0.528078i	$-0.822913\pi$
$227$	−8.07879	+	6.35323i	−0.536208	+	0.421679i	0.312987	+	0.949757i	$0.398670\pi$
$228$	−0.662073	+	0.272120i	−0.0438469	+	0.0180216i
$229$	−14.6939	−	8.48352i	−0.971000	−	0.560607i	−0.0714589	−	0.997444i	$-0.522765\pi$
$229$	−14.6939	−	8.48352i	−0.971000	−	0.560607i	−0.899541	+	0.436837i	$0.856099\pi$
$230$	−21.3837	+	5.98586i	−1.41000	+	0.394696i
$231$	−10.5970	+	15.1738i	−0.697230	+	0.998362i
$232$	−1.01948	+	21.4016i	−0.0669323	+	1.40508i
$233$	−12.0281	+	1.72938i	−0.787987	+	0.113295i	−0.524548	−	0.851381i	$-0.675766\pi$
$233$	−12.0281	+	1.72938i	−0.787987	+	0.113295i	−0.263439	+	0.964676i	$0.584857\pi$
$234$	10.3318	−	2.70791i	0.675411	−	0.177021i
$235$	−10.6063	+	36.1216i	−0.691877	+	2.35632i
$236$	−0.00265046	−	0.0277569i	−0.000172530	−	0.00180682i
$237$	−3.96983	−	1.12623i	−0.257868	−	0.0731567i
$238$	9.21381	+	7.24582i	0.597243	+	0.469677i
$239$	8.62822	+	2.09318i	0.558113	+	0.135397i	0.504887	−	0.863186i	$-0.331534\pi$
$239$	8.62822	+	2.09318i	0.558113	+	0.135397i	0.0532265	+	0.998582i	$0.483049\pi$
$240$	17.9471	−	13.0296i	1.15848	−	0.841058i
$241$	−6.36132	+	12.3392i	−0.409769	+	0.794840i	−0.999922	−	0.0124504i	$-0.996037\pi$
$241$	−6.36132	+	12.3392i	−0.409769	+	0.794840i	0.590154	+	0.807291i	$0.299067\pi$
$242$	2.67323	+	4.15962i	0.171842	+	0.267391i
$243$	−14.9648	+	4.36520i	−0.959992	+	0.280028i
$244$	−0.140728	−	0.479276i	−0.00900919	−	0.0306825i
$245$	−2.59683	+	1.03961i	−0.165905	+	0.0664185i
$246$	−10.7617	−	11.0814i	−0.686141	−	0.706525i
$247$	−10.6227	+	7.56437i	−0.675905	+	0.481309i
$248$	−18.9595	−	19.8841i	−1.20393	−	1.26264i
$249$	18.1806	+	15.4641i	1.15215	+	0.979999i
$250$	−3.36183	−	4.27492i	−0.212621	−	0.270369i
$251$	−20.4360	−	13.1334i	−1.28991	−	0.828974i	−0.297833	−	0.954618i	$-0.596264\pi$
$251$	−20.4360	−	13.1334i	−1.28991	−	0.828974i	−0.992075	+	0.125645i	$0.959900\pi$
$252$	−0.117134	+	0.674003i	−0.00737876	+	0.0424582i
$253$	−11.1329	−	14.5315i	−0.699918	−	0.913586i
$254$	10.6193	−	6.13103i	0.666312	−	0.384695i
$255$	−6.65380	−	16.1888i	−0.416677	−	1.01378i
$256$	−1.81190	−	0.725375i	−0.113244	−	0.0453359i
$257$	2.30329	−	24.1211i	0.143675	−	1.50463i	−0.580070	−	0.814567i	$-0.696975\pi$
$257$	2.30329	−	24.1211i	0.143675	−	1.50463i	0.723745	−	0.690067i	$-0.242419\pi$
$258$	−9.90995	−	12.3666i	−0.616967	−	0.769910i
$259$	18.5141	−	1.76788i	1.15041	−	0.109851i
$260$	−0.458346	+	0.528959i	−0.0284254	+	0.0328046i
$261$	−4.61987	−	21.8110i	−0.285963	−	1.35007i
$262$	−21.6841	+	6.36704i	−1.33965	+	0.393357i
$263$	8.25044	−	23.8381i	0.508744	−	1.46992i	−0.339648	−	0.940552i	$-0.610308\pi$
$263$	8.25044	−	23.8381i	0.508744	−	1.46992i	0.848393	−	0.529367i	$-0.177571\pi$
$264$	16.1287	+	10.1576i	0.992653	+	0.625160i
$265$	0.0246096	+	0.516620i	0.00151176	+	0.0317357i
$266$	3.72306	+	19.3171i	0.228275	+	1.18440i
$267$	4.38332	+	21.6721i	0.268255	+	1.32631i
$268$	0.0592437	+	0.147984i	0.00361888	+	0.00903953i
$269$	−3.53786	−	3.06558i	−0.215707	−	0.186912i	0.540304	−	0.841470i	$-0.318309\pi$
$269$	−3.53786	−	3.06558i	−0.215707	−	0.186912i	−0.756012	+	0.654558i	$0.772855\pi$
$270$	−15.2497	+	18.6091i	−0.928065	+	1.13251i
$271$	27.5252	+	8.08213i	1.67204	+	0.490955i	0.974273	−	0.225372i	$-0.0723597\pi$
$271$	27.5252	+	8.08213i	1.67204	+	0.490955i	0.697765	+	0.716326i	$0.254178\pi$
$272$	6.71666	−	9.43223i	0.407258	−	0.571913i
$273$	0.707081	+	12.4430i	0.0427945	+	0.753084i
$274$	−5.51562	−	10.6988i	−0.333211	−	0.646339i
$275$	11.7843	−	20.4109i	0.710618	−	1.23083i
$276$	−0.600335	−	0.312154i	−0.0361359	−	0.0187895i
$277$	−3.87565	−	6.71282i	−0.232865	−	0.403334i	0.725785	−	0.687922i	$-0.241477\pi$
$277$	−3.87565	−	6.71282i	−0.232865	−	0.403334i	−0.958650	+	0.284588i	$0.908143\pi$
$278$	−1.50306	+	2.33881i	−0.0901476	+	0.140272i
$279$	24.3296	+	15.0128i	1.45658	+	0.898795i
$280$	11.2078	+	24.5416i	0.669793	+	1.46664i
$281$	0.335980	+	1.38493i	0.0200429	+	0.0826179i	0.980955	−	0.194237i	$-0.0622230\pi$
$281$	0.335980	+	1.38493i	0.0200429	+	0.0826179i	−0.960912	+	0.276855i	$0.910708\pi$
$282$	23.2737	−	13.7230i	1.38593	−	0.817191i
$283$	−4.72974	+	1.63698i	−0.281154	+	0.0973083i	−0.464006	−	0.885832i	$-0.653588\pi$
$283$	−4.72974	+	1.63698i	−0.281154	+	0.0973083i	0.182852	+	0.983140i	$0.441467\pi$
$284$	−0.0428282	+	0.0544605i	−0.00254139	+	0.00323164i
$285$	9.35291	−	27.8466i	0.554019	−	1.64949i
$286$	12.8422	+	4.44474i	0.759376	+	0.262823i
$287$	15.1634	−	9.74489i	0.895064	−	0.575223i
$288$	1.37083	+	0.171514i	0.0807767	+	0.0101066i
$289$	5.14830	+	5.94146i	0.302841	+	0.349498i
$290$	−24.9037	−	23.7456i	−1.46240	−	1.39439i
$291$	3.93319	−	1.19415i	0.230568	−	0.0700023i
$292$	0.107951	+	0.311904i	0.00631736	+	0.0182528i
$293$	4.82621	+	6.77746i	0.281950	+	0.395944i	0.931128	−	0.364693i	$-0.118826\pi$
$293$	4.82621	+	6.77746i	0.281950	+	0.395944i	−0.649177	+	0.760637i	$0.724887\pi$
$294$	1.87045	+	0.728999i	0.109087	+	0.0425161i
$295$	0.932084	+	0.663734i	0.0542680	+	0.0386441i
$296$	−2.72589	−	18.9590i	−0.158439	−	1.10197i
$297$	−18.9143	−	5.96933i	−1.09752	−	0.346375i
$298$			11.0897i			0.642410i
$299$	−11.9418	−	3.05763i	−0.690614	−	0.176827i
$300$	0.0748582	−	0.867942i	0.00432194	−	0.0501106i
$301$	16.4362	−	8.47345i	0.947366	−	0.488401i
$302$	6.75741	−	16.8792i	0.388845	−	0.971289i
$303$	6.45390	−	7.58761i	0.370767	−	0.435897i
$304$	18.8859	−	4.58168i	1.08318	−	0.262777i
$305$	18.6462	+	8.51545i	1.06768	+	0.487593i
$306$	−4.45410	+	11.7453i	−0.254624	+	0.671432i
$307$	−1.93919	+	13.4874i	−0.110675	+	0.769765i	0.856590	+	0.515998i	$0.172579\pi$
$307$	−1.93919	+	13.4874i	−0.110675	+	0.769765i	−0.967265	+	0.253767i	$0.918330\pi$
$308$	−0.600658	+	0.629952i	−0.0342257	+	0.0358948i
$309$	3.45667	−	0.362070i	0.196643	−	0.0205974i
$310$	44.0740	−	2.09950i	2.50323	−	0.119244i
$311$	8.81721	−	0.420015i	0.499978	−	0.0238169i	0.203921	−	0.978987i	$-0.434631\pi$
$311$	8.81721	−	0.420015i	0.499978	−	0.0238169i	0.296057	+	0.955170i	$0.404328\pi$
$312$	12.7656	−	1.33713i	0.722708	−	0.0757001i
$313$	20.2699	−	21.2585i	1.14572	−	1.20160i	0.169338	−	0.985558i	$-0.445837\pi$
$313$	20.2699	−	21.2585i	1.14572	−	1.20160i	0.976384	−	0.216041i	$-0.0693144\pi$
$314$	−0.916447	+	6.37403i	−0.0517181	+	0.359707i
$315$	−17.7558	−	21.7459i	−1.00042	−	1.22524i
$316$	−0.176530	−	0.0806187i	−0.00993061	−	0.00453516i
$317$	−8.59189	+	2.08437i	−0.482569	+	0.117070i	−0.469661	−	0.882847i	$-0.655624\pi$
$317$	−8.59189	+	2.08437i	−0.482569	+	0.117070i	−0.0129076	+	0.999917i	$0.504109\pi$
$318$	0.240496	−	0.282741i	0.0134863	−	0.0158554i
$319$	10.5429	−	26.3349i	0.590288	−	1.47447i
$320$	24.6575	−	12.7118i	1.37840	−	0.710613i
$321$	−1.10062	+	12.7611i	−0.0614307	+	0.712257i
$322$	−11.6794	+	14.4707i	−0.650866	+	0.806421i
$323$		−	15.3370i		−	0.853372i
$324$	−0.726757	+	0.0963884i	−0.0403754	+	0.00535491i
$325$	−2.25867	−	15.7094i	−0.125288	−	0.871399i
$326$	−8.75413	−	6.23379i	−0.484847	−	0.345258i
$327$	2.01504	+	0.785352i	0.111432	+	0.0434300i
$328$	−10.7677	−	15.1211i	−0.594548	−	0.834925i
$329$	10.3114	+	29.7928i	0.568485	+	1.64253i
$330$	−29.2915	+	8.89314i	−1.61244	+	0.489551i
$331$	−1.35376	−	1.29081i	−0.0744093	−	0.0709491i	0.651962	−	0.758252i	$-0.273946\pi$
$331$	−1.35376	−	1.29081i	−0.0744093	−	0.0709491i	−0.726371	+	0.687303i	$0.758795\pi$
$332$	0.735080	+	0.848327i	0.0403427	+	0.0465580i
$333$	7.74545	+	18.3643i	0.424448	+	1.00636i
$334$	11.9084	−	7.65304i	0.651597	−	0.418756i
$335$	−6.18169	−	2.13950i	−0.337742	−	0.116894i
$336$	5.91348	−	17.6063i	0.322607	−	0.960503i
$337$	1.70960	−	2.17394i	0.0931279	−	0.118422i	−0.737256	−	0.675614i	$-0.763879\pi$
$337$	1.70960	−	2.17394i	0.0931279	−	0.118422i	0.830384	+	0.557192i	$0.188121\pi$
$338$	−8.36827	+	2.89629i	−0.455174	+	0.157537i
$339$	−4.69927	+	2.77085i	−0.255229	+	0.150492i
$340$	−0.194066	−	0.799952i	−0.0105247	−	0.0433835i
$341$	15.1106	+	33.0876i	0.818286	+	1.79180i
$342$	−18.5583	+	10.0022i	−1.00352	+	0.540857i
$343$	9.32794	−	14.5146i	0.503661	−	0.783712i
$344$	−9.52214	−	16.4928i	−0.513399	−	0.889234i
$345$	25.8145	−	10.2301i	1.38981	−	0.550768i
$346$	−7.76609	+	13.4513i	−0.417508	+	0.723145i
$347$	−9.31309	−	18.0649i	−0.499953	−	0.969773i	−0.994902	−	0.100851i	$-0.967844\pi$
$347$	−9.31309	−	18.0649i	−0.499953	−	0.969773i	0.494949	−	0.868922i	$-0.335187\pi$
$348$	−0.0594870	−	1.04683i	−0.00318884	−	0.0561162i
$349$	−18.9035	+	26.5463i	−1.01188	+	1.42099i	−0.107532	+	0.994202i	$0.534295\pi$
$349$	−18.9035	+	26.5463i	−1.01188	+	1.42099i	−0.904351	+	0.426789i	$0.859645\pi$
$350$	−22.9722	−	6.74524i	−1.22791	−	0.360548i
$351$	−12.4966	+	4.71365i	−0.667020	+	0.251596i
$352$	1.32843	+	1.15109i	0.0708055	+	0.0613534i
$353$	7.28918	+	18.2075i	0.387964	+	0.969086i	0.985869	+	0.167519i	$0.0535757\pi$
$353$	7.28918	+	18.2075i	0.387964	+	0.969086i	−0.597905	+	0.801567i	$0.704000\pi$
$354$	−0.162799	−	0.804912i	−0.00865265	−	0.0427806i
$355$	−0.538085	−	2.79185i	−0.0285586	−	0.148176i
$356$	0.0494791	+	1.03869i	0.00262239	+	0.0550507i
$357$	−12.4029	−	7.81115i	−0.656429	−	0.413410i
$358$	−7.09065	+	20.4871i	−0.374752	+	1.08278i
$359$	−24.9681	+	7.33129i	−1.31777	+	0.386931i	−0.863686	−	0.504030i	$-0.831850\pi$
$359$	−24.9681	+	7.33129i	−1.31777	+	0.386931i	−0.454079	+	0.890961i	$0.650032\pi$
$360$	−21.5001	+	19.3311i	−1.13316	+	1.01884i
$361$	4.41394	−	5.09396i	0.232313	−	0.268103i
$362$	−28.8755	+	2.75727i	−1.51766	+	0.144919i
$363$	−3.86648	−	4.82497i	−0.202938	−	0.253245i
$364$	−0.0557157	+	0.583481i	−0.00292029	+	0.0305827i
$365$	−12.5745	−	5.03407i	−0.658180	−	0.263495i
$366$	−5.59265	−	13.6070i	−0.292332	−	0.711249i
$367$	−29.6187	+	17.1004i	−1.54608	+	0.892632i	−0.547649	+	0.836708i	$0.684477\pi$
$367$	−29.6187	+	17.1004i	−1.54608	+	0.892632i	−0.998435	+	0.0559244i	$0.982189\pi$
$368$	14.8278	+	10.8443i	0.772954	+	0.565299i
$369$	14.8276	+	12.3797i	0.771893	+	0.644462i
$370$	25.8781	+	16.6309i	1.34534	+	0.864598i
$371$	0.267742	+	0.340462i	0.0139005	+	0.0176759i
$372$	1.02415	+	0.871125i	0.0530996	+	0.0451657i
$373$	6.27095	+	6.57678i	0.324698	+	0.340533i	0.865769	−	0.500444i	$-0.166830\pi$
$373$	6.27095	+	6.57678i	0.324698	+	0.340533i	−0.541072	+	0.840976i	$0.681981\pi$
$374$	−13.0190	+	9.27078i	−0.673196	+	0.479380i
$375$	4.73790	+	4.87865i	0.244664	+	0.251932i
$376$	30.1428	−	12.0674i	1.55450	−	0.622327i
$377$	−5.38167	−	18.3283i	−0.277170	−	0.943955i
$378$	−1.36311	+	20.1020i	−0.0701106	+	1.03394i
$379$	−18.8573	−	29.3426i	−0.968635	−	1.50723i	−0.858183	−	0.513345i	$-0.828406\pi$
$379$	−18.8573	−	29.3426i	−0.968635	−	1.50723i	−0.110453	−	0.993881i	$-0.535230\pi$
$380$	0.633046	−	1.22794i	0.0324746	−	0.0629919i
$381$	−12.4082	+	9.00834i	−0.635691	+	0.461511i
$382$	2.30102	+	0.558221i	0.117730	+	0.0285611i
$383$	−15.7967	−	12.4226i	−0.807171	−	0.634767i	0.126875	−	0.991919i	$-0.459505\pi$
$383$	−15.7967	−	12.4226i	−0.807171	−	0.634767i	−0.934046	+	0.357152i	$0.883748\pi$
$384$	−17.6189	−	4.99845i	−0.899110	−	0.255076i
$385$	−3.39539	−	35.5582i	−0.173045	−	1.81221i
$386$	2.33710	−	7.95942i	0.118955	−	0.405124i
$387$	13.9357	+	14.0890i	0.708391	+	0.716184i
$388$	0.191347	−	0.0275115i	0.00971416	−	0.00139669i
$389$	−1.60249	+	33.6404i	−0.0812494	+	1.70563i	0.479413	+	0.877590i	$0.340850\pi$
$389$	−1.60249	+	33.6404i	−0.0812494	+	1.70563i	−0.560662	+	0.828045i	$0.689453\pi$
$390$	−11.8028	+	16.9003i	−0.597656	+	0.855782i
$391$	11.0759	−	9.35448i	0.560132	−	0.473076i
$392$	2.08926	+	1.20623i	0.105523	+	0.0609240i
$393$	26.1385	−	10.7433i	1.31851	−	0.541926i
$394$	4.96558	−	3.90498i	0.250162	−	0.196730i
$395$	7.24438	−	3.30840i	0.364504	−	0.166464i
$396$	−0.836786	−	0.412159i	−0.0420501	−	0.0207117i
$397$	−11.5184	+	25.2219i	−0.578094	+	1.26585i	0.364281	+	0.931289i	$0.381315\pi$
$397$	−11.5184	+	25.2219i	−0.578094	+	1.26585i	−0.942375	+	0.334560i	$0.891412\pi$
$398$	20.0901	+	3.87205i	1.00703	+	0.194088i
$399$	−7.14666	−	23.5391i	−0.357780	−	1.17843i
$400$	−5.57601	+	22.9846i	−0.278801	+	1.14923i
$401$	−4.57479	+	0.881718i	−0.228454	+	0.0440309i	−0.302193	−	0.953247i	$-0.597719\pi$
$401$	−4.57479	+	0.881718i	−0.228454	+	0.0440309i	0.0737394	+	0.997278i	$0.476507\pi$
$402$	2.18938	+	4.15291i	0.109196	+	0.207128i
$403$	21.7716	+	11.2240i	1.08452	+	0.559110i
$404$	0.354047	−	0.306783i	0.0176145	−	0.0152630i
$405$	16.5414	−	25.1301i	0.821949	−	1.24872i
$406$	−28.5230	−	4.10099i	−1.41557	−	0.203529i
$407$	−4.79922	+	24.9007i	−0.237888	+	1.23428i
$408$	−7.42762	+	13.1417i	−0.367722	+	0.650611i
$409$	21.5339	−	20.5326i	1.06478	−	1.01527i	0.0649355	−	0.997889i	$-0.479316\pi$
$409$	21.5339	−	20.5326i	1.06478	−	1.01527i	0.999849	−	0.0173804i	$-0.00553264\pi$
$410$	29.6777	+	2.83387i	1.46567	+	0.139955i
$411$	8.25334	+	12.5873i	0.407107	+	0.620886i
$412$	0.163271	+	0.00777754i	0.00804377	+	0.000383172i
$413$	0.958245			0.0471522
$414$	−18.5425	−	7.30159i	−0.911315	−	0.358853i
$415$	−46.0646			−2.26122
$416$	1.18233	+	0.0563212i	0.0579684	+	0.00276137i
$417$	1.56464	−	3.10451i	0.0766207	−	0.152028i
$418$	−26.7022	−	2.54976i	−1.30605	−	0.124713i
$419$	11.7815	−	11.2337i	0.575565	−	0.548800i	−0.345395	−	0.938458i	$-0.612255\pi$
$419$	11.7815	−	11.2337i	0.575565	−	0.548800i	0.920960	+	0.389657i	$0.127406\pi$
$420$	−0.670609	−	1.13733i	−0.0327224	−	0.0554960i
$421$	5.62362	−	29.1781i	0.274079	−	1.42205i	−0.540179	−	0.841550i	$-0.681643\pi$
$421$	5.62362	−	29.1781i	0.274079	−	1.42205i	0.814257	−	0.580504i	$-0.197145\pi$
$422$	39.6829	+	5.70555i	1.93174	+	0.277742i
$423$	−27.1571	+	20.0987i	−1.32042	+	0.977232i
$424$	0.337116	−	0.292113i	0.0163718	−	0.0141862i
$425$	16.5905	+	8.55302i	0.804760	+	0.414882i
$426$	−1.08742	+	1.72664i	−0.0526855	+	0.0836561i
$427$	16.8562	−	3.24876i	0.815727	−	0.157219i
$428$	−0.142017	+	0.585401i	−0.00686464	+	0.0282964i
$429$	−16.5505	−	3.85485i	−0.799066	−	0.186114i
$430$	30.0325	+	5.78830i	1.44830	+	0.279137i
$431$	8.52874	−	18.6753i	0.410815	−	0.899560i	−0.585243	−	0.810858i	$-0.699001\pi$
$431$	8.52874	−	18.6753i	0.410815	−	0.899560i	0.996058	−	0.0887017i	$-0.0282718\pi$
$432$	19.8996	+	0.400151i	0.957419	+	0.0192523i
$433$	−26.3539	+	12.0354i	−1.26649	+	0.578385i	−0.931467	−	0.363826i	$-0.881470\pi$
$433$	−26.3539	+	12.0354i	−1.26649	+	0.578385i	−0.335020	+	0.942211i	$0.608743\pi$
$434$	29.0456	−	22.8417i	1.39423	−	1.09644i
$435$	34.0653	+	26.2876i	1.63331	+	1.26039i
$436$	0.0880836	+	0.0508551i	0.00421844	+	0.00243552i
$437$	24.3296	+	0.308006i	1.16384	+	0.0147339i
$438$	4.11903	+	8.80497i	0.196815	+	0.420718i
$439$	−1.57379	+	33.0379i	−0.0751129	+	1.57681i	0.575754	+	0.817623i	$0.304709\pi$
$439$	−1.57379	+	33.0379i	−0.0751129	+	1.57681i	−0.650867	+	0.759192i	$0.725594\pi$
$440$	−36.4126	+	5.23534i	−1.73590	+	0.249585i
$441$	−2.42119	−	0.662974i	−0.115295	−	0.0315702i
$442$	−3.03216	+	10.3266i	−0.144225	+	0.491185i
$443$	−0.421842	−	4.41773i	−0.0200423	−	0.209893i	−0.999946	−	0.0104200i	$-0.996683\pi$
$443$	−0.421842	−	4.41773i	−0.0200423	−	0.209893i	0.979903	−	0.199473i	$-0.0639229\pi$
$444$	0.229326	+	0.908858i	0.0108833	+	0.0431325i
$445$	−33.5439	−	26.3792i	−1.59013	−	1.25050i
$446$	−1.35895	−	0.329678i	−0.0643483	−	0.0156107i
$447$	−1.44464	−	13.7920i	−0.0683290	−	0.652337i
$448$	10.6454	−	20.6492i	0.502947	−	0.975582i
$449$	−2.60371	−	4.05145i	−0.122877	−	0.191200i	0.774366	−	0.632738i	$-0.218069\pi$
$449$	−2.60371	−	4.05145i	−0.122877	−	0.191200i	−0.897242	+	0.441539i	$0.854433\pi$
$450$	−0.470258	−	25.6531i	−0.0221682	−	1.20930i
$451$	6.92410	+	23.5813i	0.326043	+	1.11040i
$452$	−0.238185	+	0.0953549i	−0.0112033	+	0.00448512i
$453$	−6.20517	+	21.8724i	−0.291544	+	1.02766i
$454$	−11.5961	+	8.25754i	−0.544232	+	0.387546i
$455$	−16.5989	−	17.4084i	−0.778167	−	0.816118i
$456$	−23.8646	+	8.50532i	−1.11756	+	0.398298i
$457$	−10.4671	−	13.3100i	−0.489632	−	0.622617i	0.476964	−	0.878923i	$-0.341737\pi$
$457$	−10.4671	−	13.3100i	−0.489632	−	0.622617i	−0.966596	+	0.256306i	$0.917495\pi$
$458$	−19.7706	−	12.7058i	−0.923817	−	0.593701i
$459$	4.00940	−	15.1875i	0.187143	−	0.708891i
$460$	1.27289	−	0.291790i	0.0593489	−	0.0136048i
$461$	13.0152	−	7.51432i	0.606178	−	0.349977i	−0.165290	−	0.986245i	$-0.552856\pi$
$461$	13.0152	−	7.51432i	0.606178	−	0.349977i	0.771468	+	0.636268i	$0.219523\pi$
$462$	−15.6615	+	20.2952i	−0.728637	+	0.944220i
$463$	17.7730	+	7.11524i	0.825982	+	0.330673i	0.745853	−	0.666111i	$-0.232042\pi$
$463$	17.7730	+	7.11524i	0.825982	+	0.330673i	0.0801296	+	0.996784i	$0.474467\pi$
$464$	−2.70591	+	28.3376i	−0.125619	+	1.31554i
$465$	−54.5400	+	8.35254i	−2.52923	+	0.387340i
$466$	−16.7554	+	1.59995i	−0.776179	+	0.0741161i
$467$	3.84314	−	4.43522i	0.177839	−	0.205238i	−0.659830	−	0.751415i	$-0.729372\pi$
$467$	3.84314	−	4.43522i	0.177839	−	0.205238i	0.837670	+	0.546177i	$0.183917\pi$
$468$	−0.614497	+	0.130159i	−0.0284052	+	0.00601661i
$469$	−5.25618	+	1.54335i	−0.242708	+	0.0712655i
$470$	−17.0549	+	49.2769i	−0.786684	+	2.27297i
$471$	0.309424	−	8.04657i	0.0142575	−	0.370767i
$472$	−0.0469573	−	0.985755i	−0.00216139	−	0.0453731i
$473$	4.77174	+	24.7581i	0.219405	+	1.13838i
$474$	−5.41821	−	1.81983i	−0.248867	−	0.0835876i
$475$	11.6429	+	29.0826i	0.534213	+	1.33440i
$476$	−0.520970	−	0.451423i	−0.0238786	−	0.0206910i
$477$	−0.262265	+	0.382966i	−0.0120083	+	0.0175348i
$478$	11.7996	+	3.46467i	0.539700	+	0.158470i
$479$	7.25659	−	10.1905i	0.331562	−	0.465614i	−0.614818	−	0.788669i	$-0.710771\pi$
$479$	7.25659	−	10.1905i	0.331562	−	0.465614i	0.946380	+	0.323055i	$0.104710\pi$
$480$	−2.22973	+	1.46201i	−0.101773	+	0.0667313i
$481$	7.82494	+	15.1783i	0.356787	+	0.692069i
$482$	−9.61441	+	16.6527i	−0.437924	+	0.758507i
$483$	12.6402	−	19.5183i	0.575150	−	0.888111i
$484$	−0.145393	−	0.251829i	−0.00660879	−	0.0114468i
$485$	−4.28899	+	6.67380i	−0.194753	+	0.303042i
$486$	−20.9922	+	5.05318i	−0.952224	+	0.229217i
$487$	−10.4600	−	22.9042i	−0.473987	−	1.03789i	−0.984073	−	0.177764i	$-0.943114\pi$
$487$	−10.4600	−	22.9042i	−0.473987	−	1.03789i	0.510086	−	0.860123i	$-0.329614\pi$
$488$	−4.16804	−	17.1809i	−0.188678	−	0.777743i
$489$	11.6993	+	6.61240i	0.529062	+	0.299023i
$490$	−3.66135	+	1.26720i	−0.165403	+	0.0572465i
$491$	8.86093	−	11.2676i	0.399888	−	0.508499i	−0.543855	−	0.839179i	$-0.683036\pi$
$491$	8.86093	−	11.2676i	0.399888	−	0.508499i	0.943743	+	0.330680i	$0.107278\pi$
$492$	0.601165	+	0.681068i	0.0271026	+	0.0307049i
$493$	21.2300	+	7.34777i	0.956151	+	0.330927i
$494$	−15.1955	+	9.76555i	−0.683678	+	0.439373i
$495$	35.2705	−	14.8759i	1.58529	−	0.668622i
$496$	−23.9041	−	27.5868i	−1.07333	−	1.23868i
$497$	−1.72324	−	1.64310i	−0.0772977	−	0.0737032i
$498$	24.1345	+	22.5935i	1.08149	+	1.01244i
$499$	6.52803	+	18.8615i	0.292235	+	0.844357i	0.991571	+	0.129564i	$0.0413578\pi$
$499$	6.52803	+	18.8615i	0.292235	+	0.844357i	−0.699336	+	0.714793i	$0.746521\pi$
$500$	0.185521	+	0.260528i	0.00829677	+	0.0116512i
$501$	−13.8131	+	11.0692i	−0.617126	+	0.494533i
$502$	−27.4085	−	19.5175i	−1.22330	−	0.871110i
$503$	1.89866	+	13.2055i	0.0846570	+	0.588803i	0.987355	+	0.158527i	$0.0506745\pi$
$503$	1.89866	+	13.2055i	0.0846570	+	0.588803i	−0.902698	+	0.430276i	$0.858416\pi$
$504$	−5.27613	+	23.6309i	−0.235018	+	1.05260i
$505$			19.2249i			0.855497i
$506$	−14.4451	−	20.8387i	−0.642164	−	0.926393i
$507$	10.0301	−	4.69215i	0.445452	−	0.208386i
$508$	−0.640962	+	0.330439i	−0.0284381	+	0.0146609i
$509$	12.2299	−	30.5488i	0.542081	−	1.35405i	−0.364177	−	0.931330i	$-0.618650\pi$
$509$	12.2299	−	30.5488i	0.542081	−	1.35405i	0.906258	−	0.422724i	$-0.138926\pi$
$510$	−8.13889	−	22.8365i	−0.360396	−	1.01122i
$511$	−11.0232	+	2.67419i	−0.487636	+	0.118299i
$512$	−21.6954	−	9.90796i	−0.958810	−	0.437874i
$513$	21.7774	−	14.8570i	0.961498	−	0.655952i
$514$	4.77644	−	33.2209i	0.210680	−	1.46531i
$515$	−4.62894	+	4.85469i	−0.203975	+	0.213923i
$516$	0.547534	+	0.754180i	0.0241039	+	0.0332009i
$517$	−42.9383	+	2.04540i	−1.88842	+	0.0899567i
$518$	25.7316	−	1.22575i	1.13058	−	0.0538563i
$519$	7.90619	−	17.7406i	0.347043	−	0.778727i
$520$	−17.0948	+	17.9285i	−0.749655	+	0.786215i
$521$	3.90047	−	27.1283i	0.170883	−	1.18851i	−0.706143	−	0.708070i	$-0.749566\pi$
$521$	3.90047	−	27.1283i	0.170883	−	1.18851i	0.877025	−	0.480445i	$-0.159525\pi$
$522$	−4.95432	−	30.4810i	−0.216845	−	1.33412i
$523$	0.563832	+	0.257494i	0.0246547	+	0.0112594i	0.427704	−	0.903919i	$-0.359322\pi$
$523$	0.563832	+	0.257494i	0.0246547	+	0.0112594i	−0.403050	+	0.915178i	$0.632050\pi$
$524$	1.29161	−	0.313340i	0.0564241	−	0.0136883i
$525$	29.4485	+	5.39631i	1.28524	+	0.235514i
$526$	12.9859	−	32.4373i	0.566214	−	1.41433i
$527$	−25.6052	+	13.2004i	−1.11538	+	0.575019i
$528$	20.7623	+	14.4998i	0.903563	+	0.631025i
$529$	14.6169	+	17.7580i	0.635519	+	0.772085i
$530$			0.716389i			0.0311180i
$531$	0.307322	+	0.979838i	0.0133367	+	0.0425213i
$532$	−0.164649	−	1.14516i	−0.00713843	−	0.0496489i
$533$	13.4811	+	9.59988i	0.583933	+	0.415817i
$534$	4.63620	+	30.2732i	0.200628	+	1.31005i
$535$	−14.3392	−	20.1365i	−0.619936	−	0.870578i
$536$	1.84523	+	5.33145i	0.0797019	+	0.230284i
$537$	6.14961	−	26.4029i	0.265375	−	1.13937i
$538$	−4.69276	−	4.47453i	−0.202319	−	0.192911i
$539$	−2.09162	−	2.41386i	−0.0900926	−	0.103972i
$540$	0.947883	−	1.05048i	0.0407904	−	0.0452053i
$541$	−23.9279	+	15.3775i	−1.02874	+	0.661131i	−0.942177	−	0.335116i	$-0.891225\pi$
$541$	−23.9279	+	15.3775i	−1.02874	+	0.661131i	−0.0865625	+	0.996246i	$0.527588\pi$
$542$	37.5497	+	12.9961i	1.61290	+	0.558230i
$543$	35.5524	−	7.19070i	1.52570	−	0.308582i
$544$	−0.860533	+	1.09426i	−0.0368951	+	0.0469159i
$545$	−3.94438	+	1.36516i	−0.168959	+	0.0584771i
$546$	0.158206	+	17.2621i	0.00677058	+	0.738748i
$547$	−4.56335	−	18.8104i	−0.195115	−	0.804274i	−0.982263	−	0.187510i	$-0.939958\pi$
$547$	−4.56335	−	18.8104i	−0.195115	−	0.804274i	0.787148	−	0.616764i	$-0.211557\pi$
$548$	0.294066	+	0.643914i	0.0125619	+	0.0275066i
$549$	8.72797	+	16.1941i	0.372501	+	0.691146i
$550$	17.6493	−	27.4628i	0.752568	−	1.17102i
$551$	18.8521	+	32.6529i	0.803129	+	1.39106i
$552$	−20.6980	−	12.0466i	−0.880966	−	0.512739i
$553$	3.33472	−	5.77590i	0.141807	−	0.245616i
$554$	−4.91972	−	9.54292i	−0.209019	−	0.405440i
$555$	−34.3504	−	17.3122i	−1.45809	−	0.734863i
$556$	0.0948387	−	0.133182i	0.00402206	−	0.00564819i
$557$	4.77170	+	1.40110i	0.202183	+	0.0593663i	0.381256	−	0.924469i	$-0.375492\pi$
$557$	4.77170	+	1.40110i	0.202183	+	0.0593663i	−0.179073	+	0.983836i	$0.557310\pi$
$558$	32.6717	+	22.3744i	1.38310	+	0.947185i
$559$	12.8317	+	11.1187i	0.542724	+	0.470273i
$560$	13.3224	+	33.2777i	0.562974	+	1.40624i
$561$	14.9836	−	13.2258i	0.632610	−	0.558392i
$562$	0.373568	+	1.93825i	0.0157580	+	0.0817603i
$563$	0.419009	+	8.79608i	0.0176591	+	0.370711i	0.990348	+	0.138600i	$0.0442602\pi$
$563$	0.419009	+	8.79608i	0.0176591	+	0.370711i	−0.972689	+	0.232111i	$0.925437\pi$
$564$	−1.40556	+	0.741002i	−0.0591849	+	0.0312018i
$565$	3.44361	−	9.94967i	0.144874	−	0.418586i
$566$	−6.65170	+	1.95312i	−0.279592	+	0.0820956i
$567$	−0.923404	−	25.1779i	−0.0387793	−	1.05737i
$568$	−1.60583	+	1.85322i	−0.0673791	+	0.0777596i
$569$	−2.34901	+	0.224304i	−0.0984758	+	0.00940330i	−0.144178	−	0.989552i	$-0.546054\pi$
$569$	−2.34901	+	0.224304i	−0.0984758	+	0.00940330i	0.0457018	+	0.998955i	$0.485448\pi$
$570$	14.7754	−	37.9106i	0.618875	−	1.58790i
$571$	−0.669639	+	7.01277i	−0.0280235	+	0.293475i	0.970586	+	0.240755i	$0.0773952\pi$
$571$	−0.669639	+	7.01277i	−0.0280235	+	0.293475i	−0.998609	+	0.0527201i	$0.983211\pi$
$572$	−0.741952	−	0.297033i	−0.0310226	−	0.0124196i
$573$	−2.93443	−	0.394494i	−0.122588	−	0.0164802i
$574$	21.6214	−	12.4831i	0.902461	−	0.521036i
$575$	−13.9012	+	26.1464i	−0.579719	+	1.09038i
$576$	24.5286	+	4.26279i	1.02202	+	0.177616i
$577$	4.80479	+	3.08785i	0.200026	+	0.128549i	0.636820	−	0.771013i	$-0.280250\pi$
$577$	4.80479	+	3.08785i	0.200026	+	0.128549i	−0.436793	+	0.899562i	$0.643886\pi$
$578$	6.73133	+	8.55958i	0.279986	+	0.356032i
$579$	−1.86972	+	10.2033i	−0.0777028	+	0.424036i
$580$	1.39647	+	1.46458i	0.0579853	+	0.0608132i
$581$	−31.4233	+	22.3765i	−1.30366	+	0.928332i
$582$	5.52045	−	1.39294i	0.228830	−	0.0577391i
$583$	−0.548270	+	0.219494i	−0.0227070	+	0.00909053i
$584$	3.29114	+	11.2086i	0.136188	+	0.463814i
$585$	12.4772	−	22.5560i	0.515868	−	0.932576i
$586$	6.23060	+	9.69501i	0.257384	+	0.400497i
$587$	19.5558	−	37.9330i	0.807154	−	1.56566i	−0.0173805	−	0.999849i	$-0.505533\pi$
$587$	19.5558	−	37.9330i	0.807154	−	1.56566i	0.824535	−	0.565812i	$-0.191437\pi$
$588$	−0.107836	−	0.0480575i	−0.00444708	−	0.00198186i
$589$	−46.9853	−	11.3985i	−1.93600	−	0.469668i
$590$	1.24584	+	0.979736i	0.0512903	+	0.0403351i
$591$	−5.66685	+	5.50336i	−0.233103	+	0.226378i
$592$	−2.41899	−	25.3328i	−0.0994200	−	1.04117i
$593$	−4.72477	+	16.0911i	−0.194023	+	0.660781i	0.803804	+	0.594894i	$0.202806\pi$
$593$	−4.72477	+	16.0911i	−0.194023	+	0.660781i	−0.997827	+	0.0658873i	$0.979012\pi$
$594$	−25.7754	−	9.50541i	−1.05758	−	0.390012i
$595$	28.0010	−	4.02594i	1.14793	−	0.165047i
$596$	0.0310320	−	0.651442i	0.00127112	−	0.0266841i
$597$	−25.4899	−	2.19845i	−1.04323	−	0.0899766i
$598$	−16.3206	−	5.01741i	−0.667397	−	0.205177i
$599$	21.7123	+	12.5356i	0.887141	+	0.512191i	0.873006	−	0.487709i	$-0.162167\pi$
$599$	21.7123	+	12.5356i	0.887141	+	0.512191i	0.0141345	+	0.999900i	$0.495501\pi$
$600$	4.10815	−	30.5584i	0.167715	−	1.24754i
$601$	−4.24411	+	3.33760i	−0.173121	+	0.136144i	−0.700960	−	0.713201i	$-0.747245\pi$
$601$	−4.24411	+	3.33760i	−0.173121	+	0.136144i	0.527839	+	0.849344i	$0.323002\pi$
$602$	23.2987	−	10.6402i	0.949583	−	0.433660i
$603$	−3.26386	−	4.87965i	−0.132915	−	0.198715i
$604$	−0.444182	+	0.972624i	−0.0180735	+	0.0395755i
$605$	11.7175	+	2.25837i	0.476386	+	0.0918158i
$606$	9.42934	−	10.0724i	0.383041	−	0.409165i
$607$	3.00281	−	12.3778i	0.121880	−	0.502398i	−0.877844	−	0.478946i	$-0.841019\pi$
$607$	3.00281	−	12.3778i	0.121880	−	0.502398i	0.999725	−	0.0234524i	$-0.00746581\pi$
$608$	−2.29414	+	0.442160i	−0.0930398	+	0.0179320i
$609$	36.0075	+	1.38464i	1.45910	+	0.0561083i
$610$	25.2367	+	13.0104i	1.02180	+	0.526777i
$611$	−21.8768	+	18.9564i	−0.885041	+	0.766892i
$612$	0.294513	−	0.677487i	0.0119050	−	0.0273858i
$613$	−1.67134	−	0.240302i	−0.0675046	−	0.00970570i	0.108480	−	0.994099i	$-0.465402\pi$
$613$	−1.67134	−	0.240302i	−0.0675046	−	0.00970570i	−0.175984	+	0.984393i	$0.556311\pi$
$614$	−3.57186	+	18.5326i	−0.144149	+	0.747914i
$615$	−37.2784	+	0.341655i	−1.50321	+	0.0137768i
$616$	−22.2960	+	21.2592i	−0.898332	+	0.856558i
$617$	11.6279	+	1.11033i	0.468120	+	0.0447000i	0.326451	−	0.945214i	$-0.394147\pi$
$617$	11.6279	+	1.11033i	0.468120	+	0.0447000i	0.141669	+	0.989914i	$0.454753\pi$
$618$	4.80633	−	0.273123i	0.193339	−	0.0109866i
$619$	−24.3449	−	1.15969i	−0.978505	−	0.0466119i	−0.447769	−	0.894149i	$-0.647781\pi$
$619$	−24.3449	−	1.15969i	−0.978505	−	0.0466119i	−0.530736	+	0.847537i	$0.678084\pi$
$620$	−2.59491			−0.104214
$621$	24.0120	+	6.66527i	0.963567	+	0.267468i
$622$	12.2267			0.490246
$623$	−35.6963	−	1.70042i	−1.43014	−	0.0681260i
$624$	17.0257	−	0.967498i	0.681575	−	0.0387309i
$625$	17.6673	+	1.68702i	0.706690	+	0.0674807i
$626$	29.4454	−	28.0761i	1.17687	−	1.12215i
$627$	33.5410	−	0.307401i	1.33950	−	0.0122764i
$628$	0.0716710	−	0.371864i	0.00285998	−	0.0148390i
$629$	−19.8790	−	2.85817i	−0.792629	−	0.113963i
$630$	−23.1327	−	31.2567i	−0.921630	−	1.24530i
$631$	28.8087	−	24.9629i	1.14686	−	0.993758i	0.146868	−	0.989156i	$-0.453081\pi$
$631$	28.8087	−	24.9629i	1.14686	−	0.993758i	0.999989	−	0.00460175i	$-0.00146479\pi$
$632$	−6.10513	−	3.14741i	−0.242849	−	0.125197i
$633$	−50.0958	−	1.92639i	−1.99113	−	0.0765671i
$634$	−12.0246	+	2.31756i	−0.477560	+	0.0920421i
$635$	6.97688	−	28.7591i	0.276869	−	1.14127i
$636$	−0.0149186	+	0.0159361i	−0.000591561	+	0.000631907i
$637$	−2.11195	−	0.407045i	−0.0836785	−	0.0161277i
$638$	16.3222	−	35.7406i	0.646202	−	1.41499i
$639$	1.12746	−	2.28903i	0.0446017	−	0.0905526i
$640$	32.1520	−	14.6833i	1.27092	−	0.580410i
$641$	−20.6369	+	16.2290i	−0.815108	+	0.641008i	−0.936135	−	0.351641i	$-0.885624\pi$
$641$	−20.6369	+	16.2290i	−0.815108	+	0.641008i	0.121027	+	0.992649i	$0.461381\pi$
$642$	−2.36380	+	17.5831i	−0.0932918	+	0.693949i
$643$	−0.914500	−	0.527987i	−0.0360644	−	0.0208218i	0.481859	−	0.876249i	$-0.339962\pi$
$643$	−0.914500	−	0.527987i	−0.0360644	−	0.0208218i	−0.517924	+	0.855427i	$0.673295\pi$
$644$	0.726573	−	0.817370i	0.0286310	−	0.0322089i
$645$	−38.1046	−	3.28645i	−1.50037	−	0.129404i
$646$	1.01081	−	21.2194i	0.0397696	−	0.834867i
$647$	2.90679	−	0.417933i	0.114278	−	0.0164306i	−0.0849387	−	0.996386i	$-0.527069\pi$
$647$	2.90679	−	0.417933i	0.114278	−	0.0164306i	0.199216	+	0.979956i	$0.436160\pi$
$648$	−25.8555	+	2.18372i	−1.01570	+	0.0857845i
$649$	−0.368105	+	1.25365i	−0.0144494	+	0.0492101i
$650$	−2.08962	−	21.8835i	−0.0819616	−	0.858341i
$651$	−33.1476	+	32.1913i	−1.29916	+	1.26167i
$652$	0.496799	+	0.390687i	0.0194562	+	0.0153005i
$653$	−16.3428	−	3.96471i	−0.639542	−	0.155151i	−0.0971406	−	0.995271i	$-0.530970\pi$
$653$	−16.3428	−	3.96471i	−0.639542	−	0.155151i	−0.542401	+	0.840119i	$0.682485\pi$
$654$	2.73614	+	1.21937i	0.106992	+	0.0476813i
$655$	−24.9925	+	48.4787i	−0.976539	+	1.89422i
$656$	−13.3339	−	20.7480i	−0.520602	−	0.810073i
$657$	−6.26973	−	10.4139i	−0.244605	−	0.406285i
$658$	12.3027	+	41.8993i	0.479611	+	1.63340i
$659$	22.8388	−	9.14329i	0.889675	−	0.356172i	0.118619	−	0.992940i	$-0.462153\pi$
$659$	22.8388	−	9.14329i	0.889675	−	0.356172i	0.771056	+	0.636768i	$0.219729\pi$
$660$	1.74555	−	0.440443i	0.0679455	−	0.0171442i
$661$	26.1321	−	18.6086i	1.01642	−	0.723791i	0.0548924	−	0.998492i	$-0.482518\pi$
$661$	26.1321	−	18.6086i	1.01642	−	0.723791i	0.961530	+	0.274701i	$0.0885790\pi$
$662$	−1.78791	−	1.87511i	−0.0694892	−	0.0728782i
$663$	2.42578	−	13.2379i	0.0942095	−	0.514116i
$664$	24.5587	+	31.2289i	0.953063	+	1.21192i
$665$	39.9409	+	25.6684i	1.54884	+	0.995379i
$666$	9.50585	+	25.9183i	0.368344	+	1.00432i
$667$	−12.0824	+	33.5304i	−0.467833	+	1.29830i
$668$	−0.720947	+	0.416239i	−0.0278943	+	0.0161048i
$669$	1.73304	+	0.232983i	0.0670031	+	0.00900764i
$670$	−8.41165	−	3.36751i	−0.324970	−	0.130098i
$671$	−2.22493	+	23.3005i	−0.0858925	+	0.899507i
$672$	−0.810842	+	2.08044i	−0.0312789	+	0.0802549i
$673$	−3.03304	+	0.289620i	−0.116915	+	0.0111640i	−0.153350	−	0.988172i	$-0.549006\pi$
$673$	−3.03304	+	0.289620i	−0.116915	+	0.0111640i	0.0364345	+	0.999336i	$0.488400\pi$
$674$	2.50859	−	2.89506i	0.0966272	−	0.111514i
$675$	3.92663	+	31.8428i	0.151136	+	1.22563i
$676$	0.499681	−	0.146720i	0.0192185	−	0.00564306i
$677$	−3.42602	+	9.89884i	−0.131673	+	0.380443i	−0.991494	−	0.130152i	$-0.958454\pi$
$677$	−3.42602	+	9.89884i	−0.131673	+	0.380443i	0.859821	+	0.510595i	$0.170575\pi$
$678$	−6.68427	+	3.52389i	−0.256708	+	0.135334i
$679$	0.316112	+	6.63602i	0.0121313	+	0.254667i
$680$	−5.51367	−	28.6076i	−0.211439	−	1.09705i
$681$	13.3460	−	11.7803i	0.511421	−	0.451421i
$682$	18.7255	+	46.7742i	0.717038	+	1.79107i
$683$	24.8877	+	21.5653i	0.952301	+	0.825174i	0.984692	−	0.174302i	$-0.0557668\pi$
$683$	24.8877	+	21.5653i	0.952301	+	0.825174i	−0.0323912	+	0.999475i	$0.510312\pi$
$684$	1.11816	−	0.535627i	0.0427538	−	0.0204802i
$685$	−27.8731	−	8.18429i	−1.06498	−	0.312706i
$686$	13.8622	−	19.4668i	0.529262	−	0.743245i
$687$	26.2432	+	13.2263i	1.00124	+	0.504615i
$688$	−11.5942	−	22.4896i	−0.442025	−	0.857409i
$689$	−0.198845	+	0.344409i	−0.00757538	+	0.0131209i
$690$	36.3898	−	12.4524i	1.38534	−	0.474055i
$691$	7.55835	+	13.0914i	0.287533	+	0.498022i	0.973220	−	0.229874i	$-0.0738316\pi$
$691$	7.55835	+	13.0914i	0.287533	+	0.498022i	−0.685687	+	0.727896i	$0.740498\pi$
$692$	0.493843	−	0.768435i	0.0187731	−	0.0292115i
$693$	16.8339	−	27.2808i	0.639466	−	1.03631i
$694$	−11.6945	−	25.6074i	−0.443917	−	0.972042i
$695$	1.58185	+	6.52047i	0.0600030	+	0.247336i
$696$	−0.340103	−	37.1091i	−0.0128916	−	1.40662i
$697$	−18.3935	+	6.36606i	−0.696705	+	0.241132i
$698$	−27.9035	+	35.4822i	−1.05616	+	1.34302i
$699$	20.6298	−	4.17250i	0.780290	−	0.157819i
$700$	1.33058	+	0.460517i	0.0502911	+	0.0174059i
$701$	−31.4299	+	20.1988i	−1.18709	+	0.762898i	−0.976677	−	0.214714i	$-0.931118\pi$
$701$	−31.4299	+	20.1988i	−1.18709	+	0.762898i	−0.210416	+	0.977612i	$0.567482\pi$
$702$	−17.6003	+	5.69795i	−0.664280	+	0.215055i
$703$	−22.0730	−	25.4736i	−0.832498	−	0.960754i
$704$	22.9255	+	21.8594i	0.864036	+	0.823857i
$705$	14.7915	−	63.5060i	0.557079	−	2.39177i
$706$	8.88492	+	25.6713i	0.334388	+	0.966151i
$707$	9.33874	+	13.1144i	0.351220	+	0.493219i
$708$	0.00731090	+	0.0477384i	0.000274760	+	0.00179412i
$709$	−34.3891	−	24.4884i	−1.29151	−	0.919681i	−0.292184	−	0.956362i	$-0.594382\pi$
$709$	−34.3891	−	24.4884i	−1.29151	−	0.919681i	−0.999327	+	0.0366810i	$0.988321\pi$
$710$	−0.560464	−	3.89811i	−0.0210338	−	0.146294i
$711$	6.97554	+	1.55745i	0.261603	+	0.0584089i
$712$			36.8044i			1.37930i
$713$	−20.4261	−	40.8836i	−0.764963	−	1.53110i
$714$	−16.6451	−	11.6245i	−0.622928	−	0.435036i
$715$	29.1514	−	15.0286i	1.09020	−	0.562037i
$716$	0.473853	−	1.18363i	0.0177087	−	0.0442343i
$717$	−15.1261	−	2.77180i	−0.564896	−	0.103515i
$718$	−35.0277	+	8.49762i	−1.30722	+	0.317128i
$719$	8.69101	+	3.96905i	0.324120	+	0.148021i	0.570829	−	0.821069i	$-0.306622\pi$
$719$	8.69101	+	3.96905i	0.324120	+	0.148021i	−0.246709	+	0.969090i	$0.579349\pi$
$720$	−29.7549	+	24.2952i	−1.10890	+	0.905429i
$721$	−0.799441	+	5.56023i	−0.0297727	+	0.207074i
$722$	6.44261	−	6.75682i	0.239769	−	0.251463i
$723$	9.78785	−	21.9629i	0.364014	−	0.816808i
$724$	1.70394	−	0.0811689i	0.0633266	−	0.00301662i
$725$	−45.8351	+	2.18339i	−1.70227	+	0.0810892i
$726$	−5.03146	−	6.93039i	−0.186735	−	0.257211i
$727$	−9.57897	+	10.0461i	−0.355264	+	0.372590i	−0.876978	−	0.480530i	$-0.840444\pi$
$727$	−9.57897	+	10.0461i	−0.355264	+	0.372590i	0.521714	+	0.853120i	$0.325293\pi$
$728$	−2.95235	+	20.5340i	−0.109421	+	0.761042i
$729$	25.4491	−	9.01910i	0.942559	−	0.334041i
$730$	−17.0656	−	7.79361i	−0.631627	−	0.288454i
$731$	−19.4056	+	4.70774i	−0.717741	+	0.174122i
$732$	0.290452	+	0.814964i	0.0107354	+	0.0301219i
$733$	−3.50715	+	8.76043i	−0.129539	+	0.323574i	−0.978932	−	0.204188i	$-0.934545\pi$
$733$	−3.50715	+	8.76043i	−0.129539	+	0.323574i	0.849392	+	0.527762i	$0.176969\pi$
$734$	−42.1059	+	21.7071i	−1.55416	+	0.801223i
$735$	4.38843	−	2.05294i	0.161870	−	0.0757240i
$736$	−1.71858	−	1.38707i	−0.0633477	−	0.0511282i
$737$		−	7.46941i		−	0.275139i
$738$	19.6987	+	18.1051i	0.725120	+	0.666459i
$739$	−1.96575	−	13.6721i	−0.0723113	−	0.502936i	−0.993501	−	0.113823i	$-0.963690\pi$
$739$	−1.96575	−	13.6721i	−0.0723113	−	0.502936i	0.921190	−	0.389114i	$-0.127219\pi$
$740$	−1.47362	−	1.04936i	−0.0541713	−	0.0385752i
$741$	17.6261	−	14.1246i	0.647509	−	0.518881i
$742$	0.347995	+	0.488691i	0.0127753	+	0.0179404i
$743$	−0.0365457	−	0.105592i	−0.00134073	−	0.00387379i	0.944328	−	0.329004i	$-0.106713\pi$
$743$	−0.0365457	−	0.105592i	−0.00134073	−	0.00387379i	−0.945669	+	0.325130i	$0.894592\pi$
$744$	34.7398	+	32.5217i	1.27362	+	1.19230i
$745$	19.3700	+	18.4692i	0.709660	+	0.676660i
$746$	8.24269	+	9.51258i	0.301786	+	0.348280i
$747$	−32.9586	−	24.9550i	−1.20589	−	0.913055i
$748$	0.790715	−	0.508162i	0.0289114	−	0.0185802i
$749$	−19.5632	−	6.77087i	−0.714822	−	0.247402i
$750$	6.23357	+	7.06209i	0.227618	+	0.257871i
$751$	23.5860	−	29.9920i	0.860665	−	1.09442i	−0.133971	−	0.990985i	$-0.542773\pi$
$751$	23.5860	−	29.9920i	0.860665	−	1.09442i	0.994636	−	0.103439i	$-0.0329846\pi$
$752$	40.7655	−	14.1091i	1.48656	−	0.514504i
$753$	36.6297	+	20.7029i	1.33486	+	0.754457i
$754$	−6.23783	−	25.7127i	−0.227169	−	0.936401i
$755$	−18.2282	−	39.9142i	−0.663391	−	1.45262i
$756$	0.136324	−	1.17704i	0.00495805	−	0.0428084i
$757$	−9.99173	+	15.5474i	−0.363156	+	0.565081i	−0.973966	−	0.226696i	$-0.927208\pi$
$757$	−9.99173	+	15.5474i	−0.363156	+	0.565081i	0.610810	+	0.791777i	$0.290844\pi$
$758$	−24.1561	−	41.8396i	−0.877389	−	1.51968i
$759$	20.6796	+	24.0347i	0.750622	+	0.872406i
$760$	24.4481	−	42.3453i	0.886826	−	1.53603i
$761$	23.0915	+	44.7913i	0.837067	+	1.62368i	0.780392	+	0.625291i	$0.215020\pi$
$761$	23.0915	+	44.7913i	0.837067	+	1.62368i	0.0566750	+	0.998393i	$0.481950\pi$
$762$	−17.7610	+	11.6457i	−0.643413	+	0.421878i
$763$	−2.02754	+	2.84729i	−0.0734020	+	0.103079i
$764$	−0.133607	−	0.0392304i	−0.00483371	−	0.00141931i
$765$	13.0970	+	27.3408i	0.473522	+	0.988509i
$766$	−21.0367	−	18.2284i	−0.760085	−	0.658618i
$767$	0.327004	+	0.816815i	0.0118074	+	0.0294935i
$768$	3.20452	+	1.07631i	0.115633	+	0.0388381i
$769$	7.43347	+	38.5685i	0.268058	+	1.39082i	0.827276	+	0.561795i	$0.189889\pi$
$769$	7.43347	+	38.5685i	0.268058	+	1.39082i	−0.559219	+	0.829020i	$0.688899\pi$
$770$	−2.35417	−	49.4201i	−0.0848384	−	1.78098i
$771$	−1.61269	+	41.9380i	−0.0580797	+	1.51036i
$772$	−0.159560	+	0.461019i	−0.00574270	+	0.0165924i
$773$	−32.0881	+	9.42193i	−1.15413	+	0.338883i	−0.802149	−	0.597124i	$-0.796310\pi$
$773$	−32.0881	+	9.42193i	−1.15413	+	0.338883i	−0.351981	+	0.936007i	$0.614492\pi$
$774$	18.3521	+	20.4112i	0.659653	+	0.733667i
$775$	38.5326	−	44.4690i	1.38413	−	1.59737i
$776$	6.81104	−	0.650375i	0.244502	−	0.0233471i
$777$	−31.8420	+	4.87645i	−1.14233	+	0.174941i
$778$	−4.43423	+	46.4374i	−0.158975	+	1.66486i
$779$	−30.3268	−	12.1410i	−1.08657	−	0.434997i
$780$	0.740620	−	0.959748i	0.0265185	−	0.0343645i
$781$	2.81160	−	1.62328i	0.100607	−	0.0580855i
$782$	15.9405	−	12.2124i	0.570032	−	0.436714i
$783$	10.1323	+	37.2629i	0.362097	+	1.33167i
$784$	2.69640	+	1.73287i	0.0963000	+	0.0618883i
$785$	9.60698	+	12.2163i	0.342888	+	0.436017i
$786$	36.8719	−	13.1411i	1.31518	−	0.468727i
$787$	17.5456	+	18.4013i	0.625432	+	0.655935i	0.957874	−	0.287189i	$-0.0927209\pi$
$787$	17.5456	+	18.4013i	0.625432	+	0.655935i	−0.332441	+	0.943124i	$0.607872\pi$
$788$	−0.302620	+	0.215495i	−0.0107804	+	0.00767668i
$789$	−11.9247	+	42.0330i	−0.424530	+	1.49642i
$790$	10.2410	−	4.09987i	0.364358	−	0.145867i
$791$	−2.48409	−	8.46003i	−0.0883240	−	0.300804i
$792$	−28.8889	−	15.9803i	−1.02652	−	0.567836i
$793$	8.52148	+	13.2597i	0.302607	+	0.470865i
$794$	−17.5986	+	34.1365i	−0.624550	+	1.21146i
$795$	−0.0933228	−	0.890952i	−0.00330982	−	0.0315988i
$796$	−1.16932	−	0.283673i	−0.0414453	−	0.0100545i
$797$	17.8253	+	14.0180i	0.631406	+	0.496543i	0.881814	−	0.471597i	$-0.156322\pi$
$797$	17.8253	+	14.0180i	0.631406	+	0.496543i	−0.250408	+	0.968140i	$0.580565\pi$
$798$	−8.33635	−	33.0384i	−0.295104	−	1.16955i
$799$	−3.23611	−	33.8901i	−0.114485	−	1.19895i
$800$	0.801082	−	2.72824i	0.0283225	−	0.0964577i
$801$	−9.70955	−	37.0460i	−0.343070	−	1.30896i
$802$	−6.38754	+	0.918389i	−0.225552	+	0.0324295i
$803$	0.735909	−	15.4486i	0.0259697	−	0.545170i
$804$	−0.116990	−	0.250080i	−0.00412590	−	0.00881966i
$805$	5.82417	+	44.5000i	0.205275	+	1.56842i
$806$	29.3823	+	16.9639i	1.03495	+	0.597527i
$807$	6.41913	+	4.95353i	0.225964	+	0.174373i
$808$	13.0333	−	10.2495i	0.458510	−	0.360576i
$809$	0.957217	−	0.437147i	0.0336540	−	0.0153693i	−0.398517	−	0.917161i	$-0.630475\pi$
$809$	0.957217	−	0.437147i	0.0336540	−	0.0153693i	0.432171	+	0.901792i	$0.357748\pi$
$810$	24.5420	−	33.6784i	0.862319	−	1.18334i
$811$	0.948148	−	2.07616i	0.0332940	−	0.0729037i	−0.892254	−	0.451533i	$-0.850877\pi$
$811$	0.948148	−	2.07616i	0.0332940	−	0.0729037i	0.925548	+	0.378629i	$0.123605\pi$
$812$	1.66405	+	0.320719i	0.0583967	+	0.0112550i
$813$	−48.3925	−	11.2713i	−1.69720	−	0.395302i
$814$	−8.28105	+	34.1350i	−0.290251	+	1.19643i
$815$	−25.4678	+	4.90851i	−0.892097	+	0.171938i
$816$	−10.6880	+	16.9708i	−0.374155	+	0.594097i
$817$	−29.7879	−	15.3567i	−1.04215	−	0.537263i
$818$	31.1464	−	26.9885i	1.08901	−	0.943631i
$819$	−2.44546	−	21.4477i	−0.0854511	−	0.749443i
$820$	−1.73542	−	0.249516i	−0.0606035	−	0.00871347i
$821$	−2.21730	+	11.5045i	−0.0773843	+	0.401508i	0.922496	+	0.386008i	$0.126146\pi$
$821$	−2.21730	+	11.5045i	−0.0773843	+	0.401508i	−0.999880	+	0.0155003i	$0.995066\pi$
$822$	10.5893	+	17.9591i	0.369344	+	0.626394i
$823$	−22.8599	+	21.7968i	−0.796844	+	0.759790i	−0.974520	−	0.224300i	$-0.927991\pi$
$823$	−22.8599	+	21.7968i	−0.796844	+	0.759790i	0.177676	+	0.984089i	$0.443142\pi$
$824$	5.75903	+	0.549921i	0.200625	+	0.0191574i
$825$	−18.3724	+	36.4538i	−0.639643	+	1.26916i
$826$	1.32578	+	0.0631545i	0.0461297	+	0.00219743i
$827$	28.6891			0.997616			0.498808	−	0.866712i	$-0.333771\pi$
$827$	28.6891			0.997616			0.498808	+	0.866712i	$0.333771\pi$
$828$	1.06881	+	0.480803i	0.0371437	+	0.0167091i
$829$	−19.6459			−0.682329			−0.341165	−	0.940004i	$-0.610821\pi$
$829$	−19.6459			−0.682329			−0.341165	+	0.940004i	$0.610821\pi$
$830$	−63.7325	−	3.03595i	−2.21219	−	0.105379i
$831$	7.36165	+	11.2274i	0.255373	+	0.389473i
$832$	21.2343	+	2.02763i	0.736166	+	0.0702953i
$833$	1.83071	−	1.74558i	0.0634304	−	0.0604808i
$834$	2.36936	−	4.19211i	0.0820441	−	0.145161i
$835$	6.46537	−	33.5455i	0.223744	−	1.16089i
$836$	1.56143	+	0.224500i	0.0540033	+	0.00776450i
$837$	−43.5475	−	23.5703i	−1.50522	−	0.814710i
$838$	17.0407	−	14.7658i	0.588660	−	0.510076i
$839$	−22.6402	−	11.6718i	−0.781627	−	0.402957i	0.0207421	−	0.999785i	$-0.493397\pi$
$839$	−22.6402	−	11.6718i	−0.781627	−	0.402957i	−0.802369	+	0.596828i	$0.796427\pi$
$840$	−21.7928	−	41.3375i	−0.751922	−	1.42628i
$841$	−25.7552	+	4.96391i	−0.888110	+	0.171169i
$842$	9.70356	−	39.9986i	0.334407	−	1.37844i
$843$	−0.717089	−	2.36189i	−0.0246979	−	0.0813477i
$844$	−2.31513	−	0.446204i	−0.0796899	−	0.0153590i
$845$	−8.87801	+	19.4401i	−0.305413	+	0.668760i
$846$	−38.8978	+	26.0176i	−1.33733	+	0.894505i
$847$	9.09025	−	4.15138i	0.312345	−	0.142643i
$848$	0.465854	−	0.366352i	0.0159975	−	0.0125806i
$849$	8.01810	−	3.29554i	0.275180	−	0.113103i
$850$	22.3901	+	12.9269i	0.767973	+	0.443390i
$851$	4.93325	−	31.4775i	0.169110	−	1.07903i
$852$	0.0687096	−	0.0983851i	0.00235395	−	0.00337062i
$853$	−0.320190	+	6.72162i	−0.0109631	+	0.230144i	0.986735	+	0.162337i	$0.0519032\pi$
$853$	−0.320190	+	6.72162i	−0.0109631	+	0.230144i	−0.997698	+	0.0678069i	$0.978400\pi$
$854$	23.5354	−	3.38388i	0.805365	−	0.115794i
$855$	−13.4372	+	49.0731i	−0.459544	+	1.67826i
$856$	−6.00659	+	20.4566i	−0.205301	+	0.699192i
$857$	−4.30523	−	45.0864i	−0.147064	−	1.54012i	−0.704380	−	0.709823i	$-0.748775\pi$
$857$	−4.30523	−	45.0864i	−0.147064	−	1.54012i	0.557316	−	0.830300i	$-0.311831\pi$
$858$	−22.6443	−	6.42415i	−0.773064	−	0.219317i
$859$	−5.66463	−	4.45472i	−0.193275	−	0.151993i	0.516832	−	0.856087i	$-0.327111\pi$
$859$	−5.66463	−	4.45472i	−0.193275	−	0.151993i	−0.710107	+	0.704094i	$0.751353\pi$
$860$	−1.74800	−	0.424061i	−0.0596064	−	0.0144603i
$861$	−25.2638	+	18.3415i	−0.860988	+	0.625077i
$862$	13.0307	−	25.2761i	0.443828	−	0.860907i
$863$	26.0652	+	40.5582i	0.887269	+	1.38062i	0.924448	+	0.381309i	$0.124527\pi$
$863$	26.0652	+	40.5582i	0.887269	+	1.38062i	−0.0371784	+	0.999309i	$0.511837\pi$
$864$	−2.38737	−	0.161886i	−0.0812200	−	0.00550748i
$865$	10.5609	+	35.9670i	0.359080	+	1.22291i
$866$	−37.2550	+	14.9147i	−1.26598	+	0.506820i
$867$	−9.48660	−	9.76843i	−0.322182	−	0.331753i
$868$	−1.77014	+	1.26051i	−0.0600824	+	0.0427845i
$869$	6.27546	+	6.58151i	0.212880	+	0.223263i
$870$	45.3984	+	38.6152i	1.53915	+	1.30918i
$871$	−3.10925	−	3.95374i	−0.105353	−	0.133967i
$872$	3.02839	+	1.94623i	0.102554	+	0.0659075i
$873$	−6.68417	+	2.45150i	−0.226225	+	0.0829706i
$874$	33.6409	+	2.02962i	1.13792	+	0.0686529i
$875$	−9.51896	+	5.49577i	−0.321800	+	0.185791i
$876$	−0.217325	−	0.528755i	−0.00734274	−	0.0178650i
$877$	32.0183	+	12.8182i	1.08118	+	0.432840i	0.842742	−	0.538317i	$-0.180940\pi$
$877$	32.0183	+	12.8182i	1.08118	+	0.432840i	0.238440	+	0.971157i	$0.423364\pi$
$878$	−4.35482	+	45.6058i	−0.146968	+	1.53912i
$879$	−9.01177	−	11.2458i	−0.303960	−	0.379310i
$880$	−48.6542	+	4.64591i	−1.64013	+	0.156614i
$881$	21.1087	−	24.3607i	0.711170	−	0.820734i	−0.279046	−	0.960278i	$-0.590018\pi$
$881$	21.1087	−	24.3607i	0.711170	−	0.820734i	0.990216	+	0.139544i	$0.0445635\pi$
$882$	−3.30614	−	1.07683i	−0.111323	−	0.0362586i
$883$	49.7483	−	14.6074i	1.67416	−	0.491579i	0.699384	−	0.714747i	$-0.253458\pi$
$883$	49.7483	−	14.6074i	1.67416	−	0.491579i	0.974780	+	0.223168i	$0.0716398\pi$
$884$	0.207014	−	0.598128i	0.00696264	−	0.0201172i
$885$	−1.67704	−	1.05618i	−0.0563730	−	0.0355030i
$886$	−0.292481	−	6.13993i	−0.00982609	−	0.206275i
$887$	0.897548	+	4.65692i	0.0301367	+	0.156364i	0.993880	−	0.110468i	$-0.0352351\pi$
$887$	0.897548	+	4.65692i	0.0301367	+	0.156364i	−0.963743	+	0.266832i	$0.914023\pi$
$888$	6.57681	+	32.5172i	0.220703	+	1.09121i
$889$	−9.21076	−	23.0074i	−0.308919	−	0.771642i
$890$	−44.6710	−	38.7076i	−1.49737	−	1.29748i
$891$	33.2944	+	8.46388i	1.11540	+	0.283551i
$892$	0.0789063	+	0.0231690i	0.00264198	+	0.000775755i
$893$	33.1427	−	46.5424i	1.10908	−	1.55748i
$894$	−1.08975	−	19.1770i	−0.0364465	−	0.641375i
$895$	23.9749	+	46.5049i	0.801394	+	1.55449i
$896$	14.8001	−	25.6346i	0.494438	−	0.856392i
$897$	20.9510	+	4.11396i	0.699534	+	0.137361i
$898$	−3.33533	−	5.77696i	−0.111301	−	0.192780i
$899$	38.2884	−	59.5779i	1.27699	−	1.98703i
$900$	−0.0441600	+	1.50825i	−0.00147200	+	0.0502751i
$901$	−0.194296	−	0.425449i	−0.00647293	−	0.0141738i
$902$	8.02565	+	33.0822i	0.267225	+	1.10152i
$903$	−27.5898	+	16.2679i	−0.918132	+	0.541363i
$904$	−8.58117	+	2.96997i	−0.285406	+	0.0987799i
$905$	−43.2743	+	55.0277i	−1.43849	+	1.82918i
$906$	−10.0267	+	29.8526i	−0.333114	+	0.991785i
$907$	−28.9083	−	10.0053i	−0.959886	−	0.332220i	−0.198197	−	0.980162i	$-0.563508\pi$
$907$	−28.9083	−	10.0053i	−0.959886	−	0.332220i	−0.761689	+	0.647943i	$0.775630\pi$
$908$	0.704295	−	0.452623i	0.0233729	−	0.0150208i
$909$	−10.4149	+	13.7552i	−0.345440	+	0.456230i
$910$	−21.8180	−	25.1793i	−0.723258	−	0.834685i
$911$	27.7249	+	26.4357i	0.918568	+	0.875852i	0.992603	−	0.121403i	$-0.0387394\pi$
$911$	27.7249	+	26.4357i	0.918568	+	0.875852i	−0.0740357	+	0.997256i	$0.523588\pi$
$912$	−32.2085	+	9.77877i	−1.06653	+	0.323807i
$913$	−17.2035	−	49.7062i	−0.569353	−	1.64504i
$914$	−13.6045	−	19.1049i	−0.449998	−	0.631934i
$915$	−33.0810	−	12.8931i	−1.09362	−	0.426234i
$916$	1.12583	+	0.801697i	0.0371983	+	0.0264888i
$917$	6.50030	+	45.2106i	0.214659	+	1.49299i
$918$	6.54814	−	20.7483i	0.216121	−	0.684797i
$919$		−	12.2522i		−	0.404164i	−0.979369	−	0.202082i	$-0.935229\pi$
$919$		−	12.2522i		−	0.404164i	0.979369	−	0.202082i	$-0.0647708\pi$
$920$	45.4921	−	8.17203i	1.49983	−	0.269424i
$921$	2.02801	−	23.5137i	0.0668253	−	0.774804i
$922$	18.5024	−	9.53863i	0.609343	−	0.314138i
$923$	0.812534	−	2.02961i	0.0267449	−	0.0668054i
$924$	0.976791	−	1.14838i	0.0321341	−	0.0377788i
$925$	39.8651	−	9.67118i	1.31076	−	0.317986i
$926$	24.1208	+	11.0156i	0.792660	+	0.361996i
$927$	−5.94191	+	0.965788i	−0.195158	+	0.0317206i
$928$	0.487045	−	3.38747i	0.0159880	−	0.111199i
$929$	2.85326	−	2.99241i	0.0936123	−	0.0981777i	−0.675261	−	0.737579i	$-0.735969\pi$
$929$	2.85326	−	2.99241i	0.0936123	−	0.0981777i	0.768873	+	0.639401i	$0.220818\pi$
$930$	−76.0091	+	7.96158i	−2.49244	+	0.261070i
$931$	4.24055	−	0.202002i	0.138978	−	0.00662036i
$932$	0.988738	−	0.0470994i	0.0323872	−	0.00154279i
$933$	−15.2060	+	1.59275i	−0.497822	+	0.0521443i
$934$	5.60947	−	5.88304i	0.183548	−	0.192499i
$935$	−5.48940	+	38.1796i	−0.179523	+	1.24861i
$936$	−21.9436	+	3.56667i	−0.717249	+	0.116580i
$937$	34.3518	+	15.6880i	1.12223	+	0.512503i	0.888076	−	0.459698i	$-0.152042\pi$
$937$	34.3518	+	15.6880i	1.12223	+	0.512503i	0.234150	+	0.972201i	$0.424769\pi$
$938$	−7.37388	+	1.78889i	−0.240766	+	0.0584092i
$939$	−32.9629	+	38.7533i	−1.07571	+	1.26466i
$940$	1.13974	−	2.84694i	0.0371744	−	0.0928571i
$941$	25.0966	−	12.9382i	0.818124	−	0.421772i	0.00224712	−	0.999997i	$-0.499285\pi$
$941$	25.0966	−	12.9382i	0.818124	−	0.421772i	0.815877	+	0.578225i	$0.196254\pi$
$942$	0.958423	−	11.1124i	0.0312271	−	0.362062i
$943$	−9.72934	−	29.3062i	−0.316831	−	0.954342i
$944$		−	1.31117i		−	0.0426748i
$945$	32.8413	+	35.8596i	1.06833	+	1.16651i
$946$	4.97020	+	34.5685i	0.161595	+	1.12392i
$947$	−8.43050	−	6.00333i	−0.273954	−	0.195082i	0.434820	−	0.900517i	$-0.356812\pi$
$947$	−8.43050	−	6.00333i	−0.273954	−	0.195082i	−0.708774	+	0.705435i	$0.750751\pi$
$948$	0.313189	+	0.122064i	0.0101719	+	0.00396445i
$949$	−6.04118	−	8.48365i	−0.196105	−	0.275391i
$950$	14.1918	+	41.0044i	0.460441	+	1.33036i
$951$	14.6528	−	4.44871i	0.475149	−	0.144259i
$952$	−17.6577	−	16.8366i	−0.572289	−	0.545677i
$953$	0.0512838	+	0.0591847i	0.00166125	+	0.00191718i	0.756580	−	0.653902i	$-0.226869\pi$
$953$	0.0512838	+	0.0591847i	0.00166125	+	0.00191718i	−0.754918	+	0.655819i	$0.772324\pi$
$954$	−0.388096	+	0.512566i	−0.0125651	+	0.0165949i
$955$	4.80723	−	3.08942i	0.155558	−	0.0999712i
$956$	−0.683446	−	0.236543i	−0.0221042	−	0.00765035i
$957$	−15.6436	+	46.5758i	−0.505685	+	1.50558i
$958$	10.7114	−	13.6207i	0.346071	−	0.440065i
$959$	−22.9895	+	7.95675i	−0.742370	+	0.256937i
$960$	−41.3901	+	24.4051i	−1.33586	+	0.787670i
$961$	14.1014	+	58.1268i	0.454884	+	1.87506i
$962$	9.82582	+	21.5155i	0.316797	+	0.693689i
$963$	0.649273	−	22.1755i	0.0209225	−	0.714595i
$964$	0.611377	−	0.951321i	0.0196911	−	0.0306400i
$965$	−10.0101	−	17.3380i	−0.322237	−	0.558131i
$966$	18.7747	−	26.1713i	0.604066	−	0.842049i
$967$	−14.4697	+	25.0623i	−0.465315	+	0.805949i	−0.999216	−	0.0395982i	$-0.987392\pi$
$967$	−14.4697	+	25.0623i	−0.465315	+	0.805949i	0.533901	+	0.845547i	$0.320726\pi$
$968$	−4.71601	−	9.14779i	−0.151578	−	0.294021i
$969$	1.50711	+	26.5216i	0.0484153	+	0.851998i
$970$	−6.37386	+	8.95083i	−0.204652	+	0.287394i
$971$	12.4682	+	3.66101i	0.400125	+	0.117487i	0.475603	−	0.879660i	$-0.342230\pi$
$971$	12.4682	+	3.66101i	0.400125	+	0.117487i	−0.0754778	+	0.997147i	$0.524048\pi$
$972$	1.24728	−	0.238096i	0.0400066	−	0.00763695i
$973$	4.24647	+	3.67959i	0.136136	+	0.117962i
$974$	−12.9623	−	32.3783i	−0.415340	−	1.03747i
$975$	5.44952	+	26.9436i	0.174524	+	0.862887i
$976$	−4.44528	−	23.0643i	−0.142290	−	0.738270i
$977$	−1.28843	−	27.0474i	−0.0412204	−	0.865323i	−0.920910	−	0.389775i	$-0.872553\pi$
$977$	−1.28843	−	27.0474i	−0.0412204	−	0.865323i	0.879690	−	0.475548i	$-0.157750\pi$
$978$	15.7508	+	9.91961i	0.503654	+	0.317194i
$979$	15.9372	−	46.0474i	0.509354	−	1.47168i
$980$	0.218624	−	0.0641938i	0.00698369	−	0.00205060i
$981$	−3.56171	−	1.16007i	−0.113717	−	0.0370381i
$982$	13.0021	−	15.0052i	0.414914	−	0.478836i
$983$	39.6430	−	3.78545i	1.26442	−	0.120737i	0.558782	−	0.829315i	$-0.311269\pi$
$983$	39.6430	−	3.78545i	1.26442	−	0.120737i	0.705633	+	0.708578i	$0.250663\pi$
$984$	20.1061	+	25.0903i	0.640959	+	0.799849i
$985$	1.44920	−	15.1767i	0.0461753	−	0.483569i
$986$	28.8884	+	11.5652i	0.919994	+	0.368310i
$987$	−20.7587	−	50.5063i	−0.660757	−	1.60763i
$988$	0.919954	−	0.531136i	0.0292676	−	0.0168977i
$989$	−7.07836	−	30.8784i	−0.225079	−	0.981875i
$990$	49.7787	−	18.2569i	1.58207	−	0.580243i
$991$	−27.5999	−	17.7374i	−0.876740	−	0.563447i	0.0230671	−	0.999734i	$-0.492657\pi$
$991$	−27.5999	−	17.7374i	−0.876740	−	0.563447i	−0.899808	+	0.436287i	$0.856293\pi$
$992$	2.71274	+	3.44953i	0.0861296	+	0.109523i
$993$	2.46784	+	2.09911i	0.0783147	+	0.0666133i
$994$	−2.27588	−	2.38688i	−0.0721866	−	0.0757072i
$995$	40.2220	−	28.6419i	1.27512	−	0.908010i
$996$	−1.35451	−	1.39475i	−0.0429192	−	0.0441942i
$997$	37.3199	−	14.9406i	1.18193	−	0.473174i	0.304331	−	0.952566i	$-0.401567\pi$
$997$	37.3199	−	14.9406i	1.18193	−	0.473174i	0.877601	+	0.479392i	$0.159143\pi$
$998$	7.78873	+	26.5260i	0.246548	+	0.839665i
$999$	−15.1985	−	30.9956i	−0.480859	−	0.980656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.113.17	yes	440
3.2	odd	2		621.2.s.a.44.6		440
9.2	odd	6	inner	207.2.o.a.182.17	yes	440
9.7	even	3		621.2.s.a.251.6		440
23.11	odd	22	inner	207.2.o.a.149.17	yes	440
69.11	even	22		621.2.s.a.287.6		440
207.11	even	66	inner	207.2.o.a.11.17	✓	440
207.34	odd	66		621.2.s.a.494.6		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.17	✓	440	207.11	even	66	inner
207.2.o.a.113.17	yes	440	1.1	even	1	trivial
207.2.o.a.149.17	yes	440	23.11	odd	22	inner
207.2.o.a.182.17	yes	440	9.2	odd	6	inner
621.2.s.a.44.6		440	3.2	odd	2
621.2.s.a.251.6		440	9.7	even	3
621.2.s.a.287.6		440	69.11	even	22
621.2.s.a.494.6		440	207.34	odd	66

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38355 + 0.0659064i) q^{2} +(-1.72926 + 0.0982663i) q^{3} +(-0.0810891 - 0.00774307i) q^{4} +(2.41932 - 2.30682i) q^{5} +(-2.39899 + 0.0219866i) q^{6} +(0.529794 - 2.74883i) q^{7} +(-2.85371 - 0.410302i) q^{8} +(2.98069 - 0.339856i) q^{9} +O(q^{10})\)	\(q+(1.38355 + 0.0659064i) q^{2} +(-1.72926 + 0.0982663i) q^{3} +(-0.0810891 - 0.00774307i) q^{4} +(2.41932 - 2.30682i) q^{5} +(-2.39899 + 0.0219866i) q^{6} +(0.529794 - 2.74883i) q^{7} +(-2.85371 - 0.410302i) q^{8} +(2.98069 - 0.339856i) q^{9} +(3.49928 - 3.03214i) q^{10} +(3.39272 + 1.74907i) q^{11} +(0.140985 + 0.00542146i) q^{12} +(2.52392 - 0.486446i) q^{13} +(0.914161 - 3.76822i) q^{14} +(-3.95696 + 4.22684i) q^{15} +(-3.76123 - 0.724917i) q^{16} +(-1.25579 + 2.74979i) q^{17} +(4.14632 - 0.273760i) q^{18} +(-4.61501 + 2.10760i) q^{19} +(-0.214043 + 0.168325i) q^{20} +(-0.646035 + 4.80551i) q^{21} +(4.57871 + 2.64352i) q^{22} +(-4.33687 - 2.04732i) q^{23} +(4.97513 + 0.429095i) q^{24} +(0.293797 - 6.16757i) q^{25} +(3.52402 - 0.506677i) q^{26} +(-5.12099 + 0.880602i) q^{27} +(-0.0642449 + 0.218798i) q^{28} +(-0.706422 - 7.39798i) q^{29} +(-5.75321 + 5.58723i) q^{30} +(7.49075 + 5.89079i) q^{31} +(0.447524 + 0.108568i) q^{32} +(-6.03877 - 2.69121i) q^{33} +(-1.91867 + 3.72169i) q^{34} +(-5.05933 - 7.87247i) q^{35} +(-0.244333 + 0.00447897i) q^{36} +(1.87173 + 6.37451i) q^{37} +(-6.52398 + 2.61181i) q^{38} +(-4.31672 + 1.08921i) q^{39} +(-7.85055 + 5.59035i) q^{40} +(4.44323 + 4.65992i) q^{41} +(-1.21053 + 6.60607i) q^{42} +(4.08330 + 5.19234i) q^{43} +(-0.261569 - 0.168100i) q^{44} +(6.42726 - 7.69814i) q^{45} +(-5.86533 - 3.11839i) q^{46} +(-9.75306 + 5.63093i) q^{47} +(6.57538 + 0.883969i) q^{48} +(-0.776834 - 0.310997i) q^{49} +(0.812964 - 8.51375i) q^{50} +(1.90137 - 4.87850i) q^{51} +(-0.208429 + 0.0199025i) q^{52} +(-0.101320 + 0.116930i) q^{53} +(-7.14316 + 0.880846i) q^{54} +(12.2429 - 3.59483i) q^{55} +(-2.63973 + 7.62701i) q^{56} +(7.77344 - 4.09810i) q^{57} +(-0.489792 - 10.2820i) q^{58} +(0.0647809 + 0.336115i) q^{59} +(0.353595 - 0.312111i) q^{60} +(2.27908 + 5.69286i) q^{61} +(9.97556 + 8.64387i) q^{62} +(0.644943 - 8.37347i) q^{63} +(7.96259 + 2.33803i) q^{64} +(4.98404 - 6.99910i) q^{65} +(-8.17755 - 4.12140i) q^{66} +(-0.896686 - 1.73933i) q^{67} +(0.123122 - 0.213254i) q^{68} +(7.70077 + 3.11419i) q^{69} +(-6.48096 - 11.2254i) q^{70} +(0.459839 - 0.715523i) q^{71} +(-8.64547 - 0.253130i) q^{72} +(-1.68321 - 3.68571i) q^{73} +(2.16950 + 8.94279i) q^{74} +(0.0980118 + 10.6942i) q^{75} +(0.390546 - 0.135169i) q^{76} +(6.60534 - 8.39938i) q^{77} +(-6.04416 + 1.22247i) q^{78} +(2.25140 + 0.779217i) q^{79} +(-10.7719 + 6.92267i) q^{80} +(8.76900 - 2.02601i) q^{81} +(5.84029 + 6.74005i) q^{82} +(-9.97312 - 9.50935i) q^{83} +(0.0895958 - 0.384672i) q^{84} +(3.30511 + 9.54950i) q^{85} +(5.30723 + 7.45296i) q^{86} +(1.94856 + 12.7236i) q^{87} +(-8.96420 - 6.38338i) q^{88} +(-1.81676 - 12.6358i) q^{89} +(9.39977 - 10.2271i) q^{90} -7.19556i q^{91} +(0.335820 + 0.199596i) q^{92} +(-13.5323 - 9.45063i) q^{93} +(-13.8649 + 7.14786i) q^{94} +(-6.30334 + 15.7450i) q^{95} +(-0.784554 - 0.143766i) q^{96} +(-2.30629 + 0.559499i) q^{97} +(-1.05429 - 0.481477i) q^{98} +(10.7071 + 4.06039i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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