LMFDB - Embedded newform 207.2.o.a.11.17

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			11.17
Character	$\chi$	$=$	207.11
Dual form			207.2.o.a.113.17

$q$-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 $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$

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	0.447671	−	0.894198i	$-0.352253\pi$
$2$	1.38355	−	0.0659064i	0.978314	−	0.0466029i	0.530643	+	0.847595i	$0.321950\pi$
$3$	−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	0.999385	+	0.0350567i	$0.0111612\pi$
$5$	2.41932	+	2.30682i	1.08195	+	1.03164i	0.0825697	+	0.996585i	$0.473687\pi$
$6$	−2.39899	−	0.0219866i	−0.979383	−	0.00897599i
$7$	0.529794	+	2.74883i	0.200243	+	1.03896i	0.933383	+	0.358883i	$0.116842\pi$
$7$	0.529794	+	2.74883i	0.200243	+	1.03896i	−0.733139	+	0.680079i	$0.761946\pi$
$8$	−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	0.136714	−	0.990611i	$-0.456346\pi$
$11$	3.39272	−	1.74907i	1.02294	−	0.527364i	0.886229	+	0.463247i	$0.153316\pi$
$12$	0.140985	−	0.00542146i	0.0406989	−	0.00156504i
$13$	2.52392	+	0.486446i	0.700010	+	0.134916i	0.526825	−	0.849974i	$-0.323382\pi$
$13$	2.52392	+	0.486446i	0.700010	+	0.134916i	0.173184	+	0.984889i	$0.444594\pi$
$14$	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	0.694020	−	0.719956i	$-0.255838\pi$
$17$	−1.25579	−	2.74979i	−0.304573	−	0.666921i	−0.998593	+	0.0530345i	$0.983111\pi$
$18$	4.14632	+	0.273760i	0.977296	+	0.0645259i
$19$	−4.61501	−	2.10760i	−1.05876	−	0.483517i	−0.191557	−	0.981481i	$-0.561354\pi$
$19$	−4.61501	−	2.10760i	−1.05876	−	0.483517i	−0.867198	+	0.497964i	$0.834081\pi$
$20$	−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	0.654933	+	0.755687i	$0.272697\pi$
$29$	−0.706422	+	7.39798i	−0.131179	+	1.37377i	−0.786112	+	0.618084i	$0.787909\pi$
$30$	−5.75321	−	5.58723i	−1.05039	−	1.02008i
$31$	7.49075	−	5.89079i	1.34538	−	1.05802i	0.352893	−	0.935664i	$-0.385198\pi$
$31$	7.49075	−	5.89079i	1.34538	−	1.05802i	0.992487	−	0.122354i	$-0.0390443\pi$
$32$	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	−0.649930	−	0.759994i	$-0.725202\pi$
$37$	1.87173	−	6.37451i	0.307710	−	1.04796i	0.957640	−	0.287969i	$-0.0929801\pi$
$38$	−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	−0.278649	−	0.960393i	$-0.589886\pi$
$41$	4.44323	−	4.65992i	0.693915	−	0.727758i	0.972564	+	0.232636i	$0.0747350\pi$
$42$	−1.21053	−	6.60607i	−0.186789	−	1.01934i
$43$	4.08330	−	5.19234i	0.622698	−	0.791824i	−0.367719	−	0.929937i	$-0.619861\pi$
$43$	4.08330	−	5.19234i	0.622698	−	0.791824i	0.990417	+	0.138113i	$0.0441036\pi$
$44$	−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	−0.426107	−	0.904673i	$-0.640115\pi$
$47$	−9.75306	−	5.63093i	−1.42263	−	0.821356i	−0.996523	+	0.0833165i	$0.973449\pi$
$48$	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	0.748748	−	0.662855i	$-0.230655\pi$
$53$	−0.101320	−	0.116930i	−0.0139174	−	0.0160616i	−0.762666	+	0.646793i	$0.776110\pi$
$54$	−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	−0.977468	−	0.211083i	$-0.932301\pi$
$59$	0.0647809	−	0.336115i	0.00843375	−	0.0437585i	0.985902	+	0.167325i	$0.0535129\pi$
$60$	0.353595	+	0.312111i	0.0456489	+	0.0402934i
$61$	2.27908	−	5.69286i	0.291806	−	0.728896i	−0.707938	−	0.706274i	$-0.750374\pi$
$61$	2.27908	−	5.69286i	0.291806	−	0.728896i	0.999744	−	0.0226216i	$-0.00720130\pi$
$62$	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	−0.937236	−	0.348695i	$-0.886625\pi$
$67$	−0.896686	+	1.73933i	−0.109548	+	0.212493i	0.827689	+	0.561187i	$0.189655\pi$
$68$	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	0.867468	−	0.497493i	$-0.165746\pi$
$71$	0.459839	+	0.715523i	0.0545728	+	0.0849170i	−0.812895	+	0.582410i	$0.802110\pi$
$72$	−8.64547	+	0.253130i	−1.01888	+	0.0298316i
$73$	−1.68321	+	3.68571i	−0.197005	+	0.431380i	−0.982192	−	0.187878i	$-0.939839\pi$
$73$	−1.68321	+	3.68571i	−0.197005	+	0.431380i	0.785188	+	0.619258i	$0.212566\pi$
$74$	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	−0.197466	−	0.980310i	$-0.563271\pi$
$79$	2.25140	−	0.779217i	0.253302	−	0.0876687i	0.450768	+	0.892641i	$0.351150\pi$
$80$	−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	−0.0958640	+	0.995394i	$0.530561\pi$
$83$	−9.97312	+	9.50935i	−1.09469	+	1.04379i	−0.998828	+	0.0483926i	$0.984590\pi$
$84$	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	0.632582	+	0.774493i	$0.281995\pi$
$89$	−1.81676	+	12.6358i	−0.192576	+	1.33939i	−0.825158	+	0.564901i	$0.808914\pi$
$90$	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	0.116958	−	0.993137i	$-0.462686\pi$
$97$	−2.30629	−	0.559499i	−0.234168	−	0.0568085i	−0.351126	+	0.936328i	$0.614201\pi$
$98$	−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	0.496026	−	0.868308i	$-0.334792\pi$
$101$	−3.96870	−	4.16225i	−0.394900	−	0.414159i	−0.890926	+	0.454148i	$0.849944\pi$
$102$	2.95216	+	6.62432i	0.292307	+	0.655905i
$103$	−2.00436	−	0.0954793i	−0.197495	−	0.00940786i	−0.0513988	−	0.998678i	$-0.516368\pi$
$103$	−2.00436	−	0.0954793i	−0.197495	−	0.00940786i	−0.146096	+	0.989270i	$0.546671\pi$
$104$	−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	0.975296	+	0.220900i	$0.0708994\pi$
$107$	1.05242	+	7.31973i	0.101741	+	0.707625i	−0.873555	+	0.486725i	$0.838191\pi$
$108$	0.422075	+	0.0317550i	0.0406142	+	0.00305562i
$109$	−1.13579	+	0.518696i	−0.108789	+	0.0496821i	−0.469066	−	0.883163i	$-0.655409\pi$
$109$	−1.13579	+	0.518696i	−0.108789	+	0.0496821i	0.360277	+	0.932845i	$0.382682\pi$
$110$	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	0.584848	−	0.811143i	$-0.301154\pi$
$113$	2.79951	+	1.44325i	0.263356	+	0.135770i	−0.321492	+	0.946912i	$0.604184\pi$
$114$	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	0.827617	−	0.561294i	$-0.189696\pi$
$127$	7.44740	+	4.78616i	0.660850	+	0.424703i	−0.166766	+	0.985996i	$0.553333\pi$
$128$	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	−0.444163	−	0.895946i	$-0.646499\pi$
$131$	−15.4187	−	5.33645i	−1.34714	−	0.466248i	−0.902973	+	0.429698i	$0.858620\pi$
$132$	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	−0.989754	−	0.142780i	$-0.954396\pi$
$137$	−4.34509	+	7.52592i	−0.371226	+	0.642983i	0.618528	+	0.785763i	$0.287729\pi$
$138$	10.4491	−	4.81615i	0.889488	−	0.409978i
$139$	−1.00358	−	1.73825i	−0.0851225	−	0.147437i	0.820321	−	0.571904i	$-0.193795\pi$
$139$	−1.00358	−	1.73825i	−0.0851225	−	0.147437i	−0.905443	+	0.424467i	$0.860462\pi$
$140$	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	−0.928019	−	0.372532i	$-0.878490\pi$
$149$	0.380957	−	7.99728i	0.0312092	−	0.655163i	0.959229	−	0.282631i	$-0.0912072\pi$
$150$	−0.569213	−	14.8024i	−0.0464760	−	1.20861i
$151$	4.29323	+	12.4045i	0.349378	+	1.00946i	0.973609	+	0.228222i	$0.0732911\pi$
$151$	4.29323	+	12.4045i	0.349378	+	1.00946i	−0.624231	+	0.781240i	$0.714588\pi$
$152$	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	−0.995826	−	0.0912743i	$-0.970906\pi$
$157$	−0.441927	−	4.62807i	−0.0352697	−	0.369361i	0.960556	−	0.278086i	$-0.0897001\pi$
$158$	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	−0.770700	−	0.637198i	$-0.780093\pi$
$163$	−6.52714	+	4.19474i	−0.511245	+	0.328557i	0.259455	+	0.965755i	$0.416457\pi$
$164$	−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	0.854878	−	0.518828i	$-0.173632\pi$
$167$	8.32475	+	5.92803i	0.644189	+	0.458725i	−0.210690	+	0.977553i	$0.567571\pi$
$168$	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	0.608701	−	0.793400i	$-0.291691\pi$
$173$	−5.13839	−	9.96709i	−0.390665	−	0.757784i	−0.999366	+	0.0356160i	$0.988661\pi$
$174$	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	−0.943022	−	0.332730i	$-0.892030\pi$
$179$	−4.40960	−	15.0177i	−0.329589	−	1.12248i	0.613433	−	0.789747i	$-0.289788\pi$
$180$	−0.580788	−	0.574468i	−0.0432894	−	0.0428183i
$181$	−20.7287	−	2.98033i	−1.54075	−	0.221526i	−0.681015	−	0.732269i	$-0.738461\pi$
$181$	−20.7287	−	2.98033i	−1.54075	−	0.221526i	−0.859733	+	0.510743i	$0.829370\pi$
$182$	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	−0.128161	−	0.991753i	$-0.540908\pi$
$191$	1.67854	−	0.323513i	0.121455	−	0.0234086i	0.249617	+	0.968345i	$0.419695\pi$
$192$	−13.9991	+	3.26061i	−1.01030	+	0.235314i
$193$	1.41196	+	5.82017i	0.101635	+	0.418945i	0.999785	−	0.0207444i	$-0.00660363\pi$
$193$	1.41196	+	5.82017i	0.101635	+	0.418945i	−0.898150	+	0.439690i	$0.855088\pi$
$194$	−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	0.768946	−	0.639314i	$-0.220782\pi$
$197$	3.44676	+	2.98663i	0.245571	+	0.212789i	−0.523374	+	0.852103i	$0.675327\pi$
$198$	14.5461	−	6.32340i	1.03375	−	0.449384i
$199$	14.6209	−	2.10216i	1.03645	−	0.149018i	0.396972	−	0.917831i	$-0.370061\pi$
$199$	14.6209	−	2.10216i	1.03645	−	0.149018i	0.639474	+	0.768812i	$0.279152\pi$
$200$	−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	0.983619	−	0.180259i	$-0.0576936\pi$
$211$	28.8131	−	2.75132i	1.98358	−	0.189409i	0.999958	−	0.00914953i	$-0.00291243\pi$
$212$	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	−0.222335	−	0.974970i	$-0.571368\pi$
$223$	−0.991326	+	0.191062i	−0.0663841	+	0.0127945i	0.155951	+	0.987765i	$0.450156\pi$
$224$	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	0.312987	−	0.949757i	$-0.398670\pi$
$227$	−8.07879	−	6.35323i	−0.536208	−	0.421679i	−0.849196	+	0.528078i	$0.822913\pi$
$228$	−0.662073	−	0.272120i	−0.0438469	−	0.0180216i
$229$	−14.6939	+	8.48352i	−0.971000	+	0.560607i	−0.899541	−	0.436837i	$-0.856099\pi$
$229$	−14.6939	+	8.48352i	−0.971000	+	0.560607i	−0.0714589	+	0.997444i	$0.522765\pi$
$230$	−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	−0.263439	−	0.964676i	$-0.584857\pi$
$233$	−12.0281	−	1.72938i	−0.787987	−	0.113295i	−0.524548	+	0.851381i	$0.675766\pi$
$234$	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	0.0532265	−	0.998582i	$-0.483049\pi$
$239$	8.62822	−	2.09318i	0.558113	−	0.135397i	0.504887	+	0.863186i	$0.331534\pi$
$240$	17.9471	+	13.0296i	1.15848	+	0.841058i
$241$	−6.36132	−	12.3392i	−0.409769	−	0.794840i	0.590154	−	0.807291i	$-0.299067\pi$
$241$	−6.36132	−	12.3392i	−0.409769	−	0.794840i	−0.999922	+	0.0124504i	$0.996037\pi$
$242$	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	−0.992075	−	0.125645i	$-0.959900\pi$
$251$	−20.4360	+	13.1334i	−1.28991	+	0.828974i	−0.297833	+	0.954618i	$0.596264\pi$
$252$	−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	0.723745	+	0.690067i	$0.242419\pi$
$257$	2.30329	+	24.1211i	0.143675	+	1.50463i	−0.580070	+	0.814567i	$0.696975\pi$
$258$	−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	0.848393	+	0.529367i	$0.177571\pi$
$263$	8.25044	+	23.8381i	0.508744	+	1.46992i	−0.339648	+	0.940552i	$0.610308\pi$
$264$	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	−0.756012	−	0.654558i	$-0.772855\pi$
$269$	−3.53786	+	3.06558i	−0.215707	+	0.186912i	0.540304	+	0.841470i	$0.318309\pi$
$270$	−15.2497	−	18.6091i	−0.928065	−	1.13251i
$271$	27.5252	−	8.08213i	1.67204	−	0.490955i	0.697765	−	0.716326i	$-0.254178\pi$
$271$	27.5252	−	8.08213i	1.67204	−	0.490955i	0.974273	+	0.225372i	$0.0723597\pi$
$272$	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	−0.958650	−	0.284588i	$-0.908143\pi$
$277$	−3.87565	+	6.71282i	−0.232865	+	0.403334i	0.725785	+	0.687922i	$0.241477\pi$
$278$	−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	−0.960912	−	0.276855i	$-0.910708\pi$
$281$	0.335980	−	1.38493i	0.0200429	−	0.0826179i	0.980955	+	0.194237i	$0.0622230\pi$
$282$	23.2737	+	13.7230i	1.38593	+	0.817191i
$283$	−4.72974	−	1.63698i	−0.281154	−	0.0973083i	0.182852	−	0.983140i	$-0.441467\pi$
$283$	−4.72974	−	1.63698i	−0.281154	−	0.0973083i	−0.464006	+	0.885832i	$0.653588\pi$
$284$	−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	−0.649177	−	0.760637i	$-0.724887\pi$
$293$	4.82621	−	6.77746i	0.281950	−	0.395944i	0.931128	+	0.364693i	$0.118826\pi$
$294$	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	−0.967265	−	0.253767i	$-0.918330\pi$
$307$	−1.93919	−	13.4874i	−0.110675	−	0.769765i	0.856590	−	0.515998i	$-0.172579\pi$
$308$	−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	0.296057	−	0.955170i	$-0.404328\pi$
$311$	8.81721	+	0.420015i	0.499978	+	0.0238169i	0.203921	+	0.978987i	$0.434631\pi$
$312$	12.7656	+	1.33713i	0.722708	+	0.0757001i
$313$	20.2699	+	21.2585i	1.14572	+	1.20160i	0.976384	+	0.216041i	$0.0693144\pi$
$313$	20.2699	+	21.2585i	1.14572	+	1.20160i	0.169338	+	0.985558i	$0.445837\pi$
$314$	−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	−0.0129076	−	0.999917i	$-0.504109\pi$
$317$	−8.59189	−	2.08437i	−0.482569	−	0.117070i	−0.469661	+	0.882847i	$0.655624\pi$
$318$	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	−0.726371	−	0.687303i	$-0.758795\pi$
$331$	−1.35376	+	1.29081i	−0.0744093	+	0.0709491i	0.651962	+	0.758252i	$0.273946\pi$
$332$	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	0.830384	−	0.557192i	$-0.188121\pi$
$337$	1.70960	+	2.17394i	0.0931279	+	0.118422i	−0.737256	+	0.675614i	$0.763879\pi$
$338$	−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	0.494949	+	0.868922i	$0.335187\pi$
$347$	−9.31309	+	18.0649i	−0.499953	+	0.969773i	−0.994902	+	0.100851i	$0.967844\pi$
$348$	−0.0594870	+	1.04683i	−0.00318884	+	0.0561162i
$349$	−18.9035	−	26.5463i	−1.01188	−	1.42099i	−0.904351	−	0.426789i	$-0.859645\pi$
$349$	−18.9035	−	26.5463i	−1.01188	−	1.42099i	−0.107532	−	0.994202i	$-0.534295\pi$
$350$	−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	−0.597905	−	0.801567i	$-0.704000\pi$
$353$	7.28918	−	18.2075i	0.387964	−	0.969086i	0.985869	−	0.167519i	$-0.0535757\pi$
$354$	−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	−0.454079	−	0.890961i	$-0.650032\pi$
$359$	−24.9681	−	7.33129i	−1.31777	−	0.386931i	−0.863686	+	0.504030i	$0.831850\pi$
$360$	−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	−0.998435	−	0.0559244i	$-0.982189\pi$
$367$	−29.6187	−	17.1004i	−1.54608	−	0.892632i	−0.547649	−	0.836708i	$-0.684477\pi$
$368$	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	−0.541072	−	0.840976i	$-0.681981\pi$
$373$	6.27095	−	6.57678i	0.324698	−	0.340533i	0.865769	+	0.500444i	$0.166830\pi$
$374$	−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	−0.110453	+	0.993881i	$0.535230\pi$
$379$	−18.8573	+	29.3426i	−0.968635	+	1.50723i	−0.858183	+	0.513345i	$0.828406\pi$
$380$	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	−0.934046	−	0.357152i	$-0.883748\pi$
$383$	−15.7967	+	12.4226i	−0.807171	+	0.634767i	0.126875	+	0.991919i	$0.459505\pi$
$384$	−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	−0.560662	−	0.828045i	$-0.689453\pi$
$389$	−1.60249	−	33.6404i	−0.0812494	−	1.70563i	0.479413	−	0.877590i	$-0.340850\pi$
$390$	−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	−0.942375	−	0.334560i	$-0.891412\pi$
$397$	−11.5184	−	25.2219i	−0.578094	−	1.26585i	0.364281	−	0.931289i	$-0.381315\pi$
$398$	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	0.0737394	−	0.997278i	$-0.476507\pi$
$401$	−4.57479	−	0.881718i	−0.228454	−	0.0440309i	−0.302193	+	0.953247i	$0.597719\pi$
$402$	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	0.999849	+	0.0173804i	$0.00553264\pi$
$409$	21.5339	+	20.5326i	1.06478	+	1.01527i	0.0649355	+	0.997889i	$0.479316\pi$
$410$	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	0.920960	−	0.389657i	$-0.127406\pi$
$419$	11.7815	+	11.2337i	0.575565	+	0.548800i	−0.345395	+	0.938458i	$0.612255\pi$
$420$	−0.670609	+	1.13733i	−0.0327224	+	0.0554960i
$421$	5.62362	+	29.1781i	0.274079	+	1.42205i	0.814257	+	0.580504i	$0.197145\pi$
$421$	5.62362	+	29.1781i	0.274079	+	1.42205i	−0.540179	+	0.841550i	$0.681643\pi$
$422$	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	0.996058	+	0.0887017i	$0.0282718\pi$
$431$	8.52874	+	18.6753i	0.410815	+	0.899560i	−0.585243	+	0.810858i	$0.699001\pi$
$432$	19.8996	−	0.400151i	0.957419	−	0.0192523i
$433$	−26.3539	−	12.0354i	−1.26649	−	0.578385i	−0.335020	−	0.942211i	$-0.608743\pi$
$433$	−26.3539	−	12.0354i	−1.26649	−	0.578385i	−0.931467	+	0.363826i	$0.881470\pi$
$434$	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	−0.650867	−	0.759192i	$-0.725594\pi$
$439$	−1.57379	−	33.0379i	−0.0751129	−	1.57681i	0.575754	−	0.817623i	$-0.304709\pi$
$440$	−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	0.979903	+	0.199473i	$0.0639229\pi$
$443$	−0.421842	+	4.41773i	−0.0200423	+	0.209893i	−0.999946	+	0.0104200i	$0.996683\pi$
$444$	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	−0.897242	−	0.441539i	$-0.854433\pi$
$449$	−2.60371	+	4.05145i	−0.122877	+	0.191200i	0.774366	+	0.632738i	$0.218069\pi$
$450$	−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	−0.966596	−	0.256306i	$-0.917495\pi$
$457$	−10.4671	+	13.3100i	−0.489632	+	0.622617i	0.476964	+	0.878923i	$0.341737\pi$
$458$	−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	0.771468	−	0.636268i	$-0.219523\pi$
$461$	13.0152	+	7.51432i	0.606178	+	0.349977i	−0.165290	+	0.986245i	$0.552856\pi$
$462$	−15.6615	−	20.2952i	−0.728637	−	0.944220i
$463$	17.7730	−	7.11524i	0.825982	−	0.330673i	0.0801296	−	0.996784i	$-0.474467\pi$
$463$	17.7730	−	7.11524i	0.825982	−	0.330673i	0.745853	+	0.666111i	$0.232042\pi$
$464$	−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	0.837670	−	0.546177i	$-0.183917\pi$
$467$	3.84314	+	4.43522i	0.177839	+	0.205238i	−0.659830	+	0.751415i	$0.729372\pi$
$468$	−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	0.946380	−	0.323055i	$-0.104710\pi$
$479$	7.25659	+	10.1905i	0.331562	+	0.465614i	−0.614818	+	0.788669i	$0.710771\pi$
$480$	−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	0.510086	+	0.860123i	$0.329614\pi$
$487$	−10.4600	+	22.9042i	−0.473987	+	1.03789i	−0.984073	+	0.177764i	$0.943114\pi$
$488$	−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	0.943743	−	0.330680i	$-0.107278\pi$
$491$	8.86093	+	11.2676i	0.399888	+	0.508499i	−0.543855	+	0.839179i	$0.683036\pi$
$492$	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	−0.699336	−	0.714793i	$-0.746521\pi$
$499$	6.52803	−	18.8615i	0.292235	−	0.844357i	0.991571	−	0.129564i	$-0.0413578\pi$
$500$	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	−0.902698	−	0.430276i	$-0.858416\pi$
$503$	1.89866	−	13.2055i	0.0846570	−	0.588803i	0.987355	−	0.158527i	$-0.0506745\pi$
$504$	−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	0.906258	+	0.422724i	$0.138926\pi$
$509$	12.2299	+	30.5488i	0.542081	+	1.35405i	−0.364177	+	0.931330i	$0.618650\pi$
$510$	−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	0.877025	+	0.480445i	$0.159525\pi$
$521$	3.90047	+	27.1283i	0.170883	+	1.18851i	−0.706143	+	0.708070i	$0.749566\pi$
$522$	−4.95432	+	30.4810i	−0.216845	+	1.33412i
$523$	0.563832	−	0.257494i	0.0246547	−	0.0112594i	−0.403050	−	0.915178i	$-0.632050\pi$
$523$	0.563832	−	0.257494i	0.0246547	−	0.0112594i	0.427704	+	0.903919i	$0.359322\pi$
$524$	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	−0.0865625	−	0.996246i	$-0.527588\pi$
$541$	−23.9279	−	15.3775i	−1.02874	−	0.661131i	−0.942177	+	0.335116i	$0.891225\pi$
$542$	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	0.787148	+	0.616764i	$0.211557\pi$
$547$	−4.56335	+	18.8104i	−0.195115	+	0.804274i	−0.982263	+	0.187510i	$0.939958\pi$
$548$	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	−0.179073	−	0.983836i	$-0.557310\pi$
$557$	4.77170	−	1.40110i	0.202183	−	0.0593663i	0.381256	+	0.924469i	$0.375492\pi$
$558$	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	−0.972689	−	0.232111i	$-0.925437\pi$
$563$	0.419009	−	8.79608i	0.0176591	−	0.370711i	0.990348	−	0.138600i	$-0.0442602\pi$
$564$	−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	0.0457018	−	0.998955i	$-0.485448\pi$
$569$	−2.34901	−	0.224304i	−0.0984758	−	0.00940330i	−0.144178	+	0.989552i	$0.546054\pi$
$570$	14.7754	+	37.9106i	0.618875	+	1.58790i
$571$	−0.669639	−	7.01277i	−0.0280235	−	0.293475i	−0.998609	−	0.0527201i	$-0.983211\pi$
$571$	−0.669639	−	7.01277i	−0.0280235	−	0.293475i	0.970586	−	0.240755i	$-0.0773952\pi$
$572$	−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	−0.436793	−	0.899562i	$-0.643886\pi$
$577$	4.80479	−	3.08785i	0.200026	−	0.128549i	0.636820	+	0.771013i	$0.280250\pi$
$578$	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	0.824535	+	0.565812i	$0.191437\pi$
$587$	19.5558	+	37.9330i	0.807154	+	1.56566i	−0.0173805	+	0.999849i	$0.505533\pi$
$588$	−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	−0.997827	−	0.0658873i	$-0.979012\pi$
$593$	−4.72477	−	16.0911i	−0.194023	−	0.660781i	0.803804	−	0.594894i	$-0.202806\pi$
$594$	−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	0.0141345	−	0.999900i	$-0.495501\pi$
$599$	21.7123	−	12.5356i	0.887141	−	0.512191i	0.873006	+	0.487709i	$0.162167\pi$
$600$	4.10815	+	30.5584i	0.167715	+	1.24754i
$601$	−4.24411	−	3.33760i	−0.173121	−	0.136144i	0.527839	−	0.849344i	$-0.323002\pi$
$601$	−4.24411	−	3.33760i	−0.173121	−	0.136144i	−0.700960	+	0.713201i	$0.747245\pi$
$602$	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	0.999725	+	0.0234524i	$0.00746581\pi$
$607$	3.00281	+	12.3778i	0.121880	+	0.502398i	−0.877844	+	0.478946i	$0.841019\pi$
$608$	−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	−0.175984	−	0.984393i	$-0.556311\pi$
$613$	−1.67134	+	0.240302i	−0.0675046	+	0.00970570i	0.108480	+	0.994099i	$0.465402\pi$
$614$	−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	0.141669	−	0.989914i	$-0.454753\pi$
$617$	11.6279	−	1.11033i	0.468120	−	0.0447000i	0.326451	+	0.945214i	$0.394147\pi$
$618$	4.80633	+	0.273123i	0.193339	+	0.0109866i
$619$	−24.3449	+	1.15969i	−0.978505	+	0.0466119i	−0.530736	−	0.847537i	$-0.678084\pi$
$619$	−24.3449	+	1.15969i	−0.978505	+	0.0466119i	−0.447769	+	0.894149i	$0.647781\pi$
$620$	−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	0.999989	+	0.00460175i	$0.00146479\pi$
$631$	28.8087	+	24.9629i	1.14686	+	0.993758i	0.146868	+	0.989156i	$0.453081\pi$
$632$	−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	0.121027	−	0.992649i	$-0.461381\pi$
$641$	−20.6369	−	16.2290i	−0.815108	−	0.641008i	−0.936135	+	0.351641i	$0.885624\pi$
$642$	−2.36380	−	17.5831i	−0.0932918	−	0.693949i
$643$	−0.914500	+	0.527987i	−0.0360644	+	0.0208218i	−0.517924	−	0.855427i	$-0.673295\pi$
$643$	−0.914500	+	0.527987i	−0.0360644	+	0.0208218i	0.481859	+	0.876249i	$0.339962\pi$
$644$	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	0.199216	−	0.979956i	$-0.436160\pi$
$647$	2.90679	+	0.417933i	0.114278	+	0.0164306i	−0.0849387	+	0.996386i	$0.527069\pi$
$648$	−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	−0.542401	−	0.840119i	$-0.682485\pi$
$653$	−16.3428	+	3.96471i	−0.639542	+	0.155151i	−0.0971406	+	0.995271i	$0.530970\pi$
$654$	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	0.771056	−	0.636768i	$-0.219729\pi$
$659$	22.8388	+	9.14329i	0.889675	+	0.356172i	0.118619	+	0.992940i	$0.462153\pi$
$660$	1.74555	+	0.440443i	0.0679455	+	0.0171442i
$661$	26.1321	+	18.6086i	1.01642	+	0.723791i	0.961530	−	0.274701i	$-0.0885790\pi$
$661$	26.1321	+	18.6086i	1.01642	+	0.723791i	0.0548924	+	0.998492i	$0.482518\pi$
$662$	−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	0.0364345	−	0.999336i	$-0.488400\pi$
$673$	−3.03304	−	0.289620i	−0.116915	−	0.0111640i	−0.153350	+	0.988172i	$0.549006\pi$
$674$	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	0.859821	−	0.510595i	$-0.170575\pi$
$677$	−3.42602	−	9.89884i	−0.131673	−	0.380443i	−0.991494	+	0.130152i	$0.958454\pi$
$678$	−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	−0.0323912	−	0.999475i	$-0.510312\pi$
$683$	24.8877	−	21.5653i	0.952301	−	0.825174i	0.984692	+	0.174302i	$0.0557668\pi$
$684$	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	−0.685687	−	0.727896i	$-0.740498\pi$
$691$	7.55835	−	13.0914i	0.287533	−	0.498022i	0.973220	+	0.229874i	$0.0738316\pi$
$692$	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	−0.210416	−	0.977612i	$-0.567482\pi$
$701$	−31.4299	−	20.1988i	−1.18709	−	0.762898i	−0.976677	+	0.214714i	$0.931118\pi$
$702$	−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	−0.999327	−	0.0366810i	$-0.988321\pi$
$709$	−34.3891	+	24.4884i	−1.29151	+	0.919681i	−0.292184	+	0.956362i	$0.594382\pi$
$710$	−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	−0.246709	−	0.969090i	$-0.579349\pi$
$719$	8.69101	−	3.96905i	0.324120	−	0.148021i	0.570829	+	0.821069i	$0.306622\pi$
$720$	−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	0.521714	−	0.853120i	$-0.325293\pi$
$727$	−9.57897	−	10.0461i	−0.355264	−	0.372590i	−0.876978	+	0.480530i	$0.840444\pi$
$728$	−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	0.849392	−	0.527762i	$-0.176969\pi$
$733$	−3.50715	−	8.76043i	−0.129539	−	0.323574i	−0.978932	+	0.204188i	$0.934545\pi$
$734$	−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	0.921190	+	0.389114i	$0.127219\pi$
$739$	−1.96575	+	13.6721i	−0.0723113	+	0.502936i	−0.993501	+	0.113823i	$0.963690\pi$
$740$	−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	−0.945669	−	0.325130i	$-0.894592\pi$
$743$	−0.0365457	+	0.105592i	−0.00134073	+	0.00387379i	0.944328	+	0.329004i	$0.106713\pi$
$744$	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	0.994636	+	0.103439i	$0.0329846\pi$
$751$	23.5860	+	29.9920i	0.860665	+	1.09442i	−0.133971	+	0.990985i	$0.542773\pi$
$752$	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	0.610810	−	0.791777i	$-0.290844\pi$
$757$	−9.99173	−	15.5474i	−0.363156	−	0.565081i	−0.973966	+	0.226696i	$0.927208\pi$
$758$	−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	0.0566750	−	0.998393i	$-0.481950\pi$
$761$	23.0915	−	44.7913i	0.837067	−	1.62368i	0.780392	−	0.625291i	$-0.215020\pi$
$762$	−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	−0.559219	−	0.829020i	$-0.688899\pi$
$769$	7.43347	−	38.5685i	0.268058	−	1.39082i	0.827276	−	0.561795i	$-0.189889\pi$
$770$	−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	−0.351981	−	0.936007i	$-0.614492\pi$
$773$	−32.0881	−	9.42193i	−1.15413	−	0.338883i	−0.802149	+	0.597124i	$0.796310\pi$
$774$	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	−0.332441	−	0.943124i	$-0.607872\pi$
$787$	17.5456	−	18.4013i	0.625432	−	0.655935i	0.957874	+	0.287189i	$0.0927209\pi$
$788$	−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	−0.250408	−	0.968140i	$-0.580565\pi$
$797$	17.8253	−	14.0180i	0.631406	−	0.496543i	0.881814	+	0.471597i	$0.156322\pi$
$798$	−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	0.432171	−	0.901792i	$-0.357748\pi$
$809$	0.957217	+	0.437147i	0.0336540	+	0.0153693i	−0.398517	+	0.917161i	$0.630475\pi$
$810$	24.5420	+	33.6784i	0.862319	+	1.18334i
$811$	0.948148	+	2.07616i	0.0332940	+	0.0729037i	0.925548	−	0.378629i	$-0.123605\pi$
$811$	0.948148	+	2.07616i	0.0332940	+	0.0729037i	−0.892254	+	0.451533i	$0.850877\pi$
$812$	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	−0.999880	−	0.0155003i	$-0.995066\pi$
$821$	−2.21730	−	11.5045i	−0.0773843	−	0.401508i	0.922496	−	0.386008i	$-0.126146\pi$
$822$	10.5893	−	17.9591i	0.369344	−	0.626394i
$823$	−22.8599	−	21.7968i	−0.796844	−	0.759790i	0.177676	−	0.984089i	$-0.443142\pi$
$823$	−22.8599	−	21.7968i	−0.796844	−	0.759790i	−0.974520	+	0.224300i	$0.927991\pi$
$824$	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	−0.802369	−	0.596828i	$-0.796427\pi$
$839$	−22.6402	+	11.6718i	−0.781627	+	0.402957i	0.0207421	+	0.999785i	$0.493397\pi$
$840$	−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	−0.997698	−	0.0678069i	$-0.978400\pi$
$853$	−0.320190	−	6.72162i	−0.0109631	−	0.230144i	0.986735	−	0.162337i	$-0.0519032\pi$
$854$	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	0.557316	+	0.830300i	$0.311831\pi$
$857$	−4.30523	+	45.0864i	−0.147064	+	1.54012i	−0.704380	+	0.709823i	$0.748775\pi$
$858$	−22.6443	+	6.42415i	−0.773064	+	0.219317i
$859$	−5.66463	+	4.45472i	−0.193275	+	0.151993i	−0.710107	−	0.704094i	$-0.751353\pi$
$859$	−5.66463	+	4.45472i	−0.193275	+	0.151993i	0.516832	+	0.856087i	$0.327111\pi$
$860$	−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	−0.0371784	−	0.999309i	$-0.511837\pi$
$863$	26.0652	−	40.5582i	0.887269	−	1.38062i	0.924448	−	0.381309i	$-0.124527\pi$
$864$	−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	0.238440	−	0.971157i	$-0.423364\pi$
$877$	32.0183	−	12.8182i	1.08118	−	0.432840i	0.842742	+	0.538317i	$0.180940\pi$
$878$	−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	0.990216	−	0.139544i	$-0.0445635\pi$
$881$	21.1087	+	24.3607i	0.711170	+	0.820734i	−0.279046	+	0.960278i	$0.590018\pi$
$882$	−3.30614	+	1.07683i	−0.111323	+	0.0362586i
$883$	49.7483	+	14.6074i	1.67416	+	0.491579i	0.974780	−	0.223168i	$-0.0716398\pi$
$883$	49.7483	+	14.6074i	1.67416	+	0.491579i	0.699384	+	0.714747i	$0.253458\pi$
$884$	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	−0.963743	−	0.266832i	$-0.914023\pi$
$887$	0.897548	−	4.65692i	0.0301367	−	0.156364i	0.993880	+	0.110468i	$0.0352351\pi$
$888$	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	−0.761689	−	0.647943i	$-0.775630\pi$
$907$	−28.9083	+	10.0053i	−0.959886	+	0.332220i	−0.198197	+	0.980162i	$0.563508\pi$
$908$	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	−0.0740357	−	0.997256i	$-0.523588\pi$
$911$	27.7249	−	26.4357i	0.918568	−	0.875852i	0.992603	+	0.121403i	$0.0387394\pi$
$912$	−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	$0.0647708\pi$
$919$			12.2522i			0.404164i	−0.979369	+	0.202082i	$0.935229\pi$
$920$	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	0.768873	−	0.639401i	$-0.220818\pi$
$929$	2.85326	+	2.99241i	0.0936123	+	0.0981777i	−0.675261	+	0.737579i	$0.735969\pi$
$930$	−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	0.234150	−	0.972201i	$-0.424769\pi$
$937$	34.3518	−	15.6880i	1.12223	−	0.512503i	0.888076	+	0.459698i	$0.152042\pi$
$938$	−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	0.815877	−	0.578225i	$-0.196254\pi$
$941$	25.0966	+	12.9382i	0.818124	+	0.421772i	0.00224712	+	0.999997i	$0.499285\pi$
$942$	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	−0.708774	−	0.705435i	$-0.750751\pi$
$947$	−8.43050	+	6.00333i	−0.273954	+	0.195082i	0.434820	+	0.900517i	$0.356812\pi$
$948$	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	−0.754918	−	0.655819i	$-0.772324\pi$
$953$	0.0512838	−	0.0591847i	0.00166125	−	0.00191718i	0.756580	+	0.653902i	$0.226869\pi$
$954$	−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	0.533901	−	0.845547i	$-0.320726\pi$
$967$	−14.4697	−	25.0623i	−0.465315	−	0.805949i	−0.999216	+	0.0395982i	$0.987392\pi$
$968$	−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	−0.0754778	−	0.997147i	$-0.524048\pi$
$971$	12.4682	−	3.66101i	0.400125	−	0.117487i	0.475603	+	0.879660i	$0.342230\pi$
$972$	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	0.879690	+	0.475548i	$0.157750\pi$
$977$	−1.28843	+	27.0474i	−0.0412204	+	0.865323i	−0.920910	+	0.389775i	$0.872553\pi$
$978$	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	0.705633	−	0.708578i	$-0.250663\pi$
$983$	39.6430	+	3.78545i	1.26442	+	0.120737i	0.558782	+	0.829315i	$0.311269\pi$
$984$	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	−0.899808	−	0.436287i	$-0.856293\pi$
$991$	−27.5999	+	17.7374i	−0.876740	+	0.563447i	0.0230671	+	0.999734i	$0.492657\pi$
$992$	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	0.877601	−	0.479392i	$-0.159143\pi$
$997$	37.3199	+	14.9406i	1.18193	+	0.473174i	0.304331	+	0.952566i	$0.401567\pi$
$998$	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.11.17	✓	440
3.2	odd	2		621.2.s.a.494.6		440
9.4	even	3		621.2.s.a.287.6		440
9.5	odd	6	inner	207.2.o.a.149.17	yes	440
23.21	odd	22	inner	207.2.o.a.182.17	yes	440
69.44	even	22		621.2.s.a.251.6		440
207.67	odd	66		621.2.s.a.44.6		440
207.113	even	66	inner	207.2.o.a.113.17	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.17	✓	440	1.1	even	1	trivial
207.2.o.a.113.17	yes	440	207.113	even	66	inner
207.2.o.a.149.17	yes	440	9.5	odd	6	inner
207.2.o.a.182.17	yes	440	23.21	odd	22	inner
621.2.s.a.44.6		440	207.67	odd	66
621.2.s.a.251.6		440	69.44	even	22
621.2.s.a.287.6		440	9.4	even	3
621.2.s.a.494.6		440	3.2	odd	2

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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Groups

Database

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