LMFDB - Embedded newform 207.2.o.a.113.5

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			113.5
Character	$\chi$	$=$	207.113
Dual form			207.2.o.a.11.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.82640 - 0.0870020i) q^{2} +(-0.662869 - 1.60019i) q^{3} +(1.33722 + 0.127689i) q^{4} +(-0.497778 + 0.474630i) q^{5} +(1.07144 + 2.98025i) q^{6} +(0.727727 - 3.77580i) q^{7} +(1.18854 + 0.170886i) q^{8} +(-2.12121 + 2.12143i) q^{9} +O(q^{10})$	\(q+(-1.82640 - 0.0870020i) q^{2} +(-0.662869 - 1.60019i) q^{3} +(1.33722 + 0.127689i) q^{4} +(-0.497778 + 0.474630i) q^{5} +(1.07144 + 2.98025i) q^{6} +(0.727727 - 3.77580i) q^{7} +(1.18854 + 0.170886i) q^{8} +(-2.12121 + 2.12143i) q^{9} +(0.950434 - 0.823555i) q^{10} +(-3.80876 - 1.96355i) q^{11} +(-0.682073 - 2.22444i) q^{12} +(0.691689 - 0.133312i) q^{13} +(-1.65762 + 6.83281i) q^{14} +(1.08946 + 0.481921i) q^{15} +(-4.79392 - 0.923952i) q^{16} +(-3.30816 + 7.24386i) q^{17} +(4.05874 - 3.69003i) q^{18} +(-1.89153 + 0.863831i) q^{19} +(-0.726241 + 0.571122i) q^{20} +(-6.52439 + 1.33836i) q^{21} +(6.78547 + 3.91760i) q^{22} +(-4.04740 - 2.57265i) q^{23} +(-0.514395 - 2.01516i) q^{24} +(-0.215401 + 4.52182i) q^{25} +(-1.27490 + 0.183303i) q^{26} +(4.80078 + 1.98810i) q^{27} +(1.45525 - 4.95614i) q^{28} +(-0.711492 - 7.45108i) q^{29} +(-1.94786 - 0.974964i) q^{30} +(-3.93002 - 3.09060i) q^{31} +(6.34139 + 1.53841i) q^{32} +(-0.617345 + 7.39631i) q^{33} +(6.67225 - 12.9424i) q^{34} +(1.42986 + 2.22491i) q^{35} +(-3.10740 + 2.56596i) q^{36} +(-0.969499 - 3.30181i) q^{37} +(3.52983 - 1.41313i) q^{38} +(-0.671824 - 1.01846i) q^{39} +(-0.672735 + 0.479052i) q^{40} +(0.863301 + 0.905404i) q^{41} +(12.0326 - 1.87675i) q^{42} +(1.04122 + 1.32402i) q^{43} +(-4.84241 - 3.11203i) q^{44} +(0.0489951 - 2.06279i) q^{45} +(7.16834 + 5.05081i) q^{46} +(0.172200 - 0.0994197i) q^{47} +(1.69924 + 8.28364i) q^{48} +(-7.22854 - 2.89387i) q^{49} +(0.786815 - 8.23989i) q^{50} +(13.7844 + 0.491949i) q^{51} +(0.941960 - 0.0899462i) q^{52} +(7.10983 - 8.20518i) q^{53} +(-8.59516 - 4.04874i) q^{54} +(2.82787 - 0.830339i) q^{55} +(1.51016 - 4.36333i) q^{56} +(2.63613 + 2.45419i) q^{57} +(0.651208 + 13.6705i) q^{58} +(-1.40276 - 7.27823i) q^{59} +(1.39531 + 0.783543i) q^{60} +(3.81925 + 9.54002i) q^{61} +(6.90889 + 5.98659i) q^{62} +(6.46645 + 9.55309i) q^{63} +(-2.07929 - 0.610536i) q^{64} +(-0.281033 + 0.394656i) q^{65} +(1.77101 - 13.4549i) q^{66} +(1.99939 + 3.87827i) q^{67} +(-5.34868 + 9.26419i) q^{68} +(-1.43383 + 8.18194i) q^{69} +(-2.41793 - 4.18797i) q^{70} +(0.172587 - 0.268551i) q^{71} +(-2.88366 + 2.15892i) q^{72} +(-4.97498 - 10.8937i) q^{73} +(1.48343 + 6.11477i) q^{74} +(7.37854 - 2.65269i) q^{75} +(-2.63968 + 0.913602i) q^{76} +(-10.1857 + 12.9522i) q^{77} +(1.13841 + 1.91857i) q^{78} +(-15.2755 - 5.28691i) q^{79} +(2.82484 - 1.81542i) q^{80} +(-0.000945804 - 9.00000i) q^{81} +(-1.49796 - 1.72874i) q^{82} +(-2.43239 - 2.31928i) q^{83} +(-8.89541 + 0.956591i) q^{84} +(-1.79143 - 5.17599i) q^{85} +(-1.78649 - 2.50877i) q^{86} +(-11.4515 + 6.07761i) q^{87} +(-4.19131 - 2.98462i) q^{88} +(-1.65318 - 11.4981i) q^{89} +(-0.268952 + 3.76321i) q^{90} -2.70870i q^{91} +(-5.08375 - 3.95699i) q^{92} +(-2.34046 + 8.33744i) q^{93} +(-0.323155 + 0.166598i) q^{94} +(0.531559 - 1.32777i) q^{95} +(-1.74178 - 11.1672i) q^{96} +(-4.69126 + 1.13809i) q^{97} +(12.9504 + 5.91426i) q^{98} +(12.2447 - 3.91492i) 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 $

$2$	−1.82640	−	0.0870020i	−1.29146	−	0.0615197i	−0.609427	−	0.792842i	$-0.708600\pi$
$2$	−1.82640	−	0.0870020i	−1.29146	−	0.0615197i	−0.682032	+	0.731323i	$0.738903\pi$
$3$	−0.662869	−	1.60019i	−0.382708	−	0.923869i
$3$	−0.662869	−	1.60019i	−0.382708	−	0.923869i
$4$	1.33722	+	0.127689i	0.668608	+	0.0638443i
$5$	−0.497778	+	0.474630i	−0.222613	+	0.212261i	−0.793175	−	0.608993i	$-0.791574\pi$
$5$	−0.497778	+	0.474630i	−0.222613	+	0.212261i	0.570563	+	0.821254i	$0.306725\pi$
$6$	1.07144	+	2.98025i	0.437415	+	1.21668i
$7$	0.727727	−	3.77580i	0.275055	−	1.42712i	−0.537021	−	0.843569i	$-0.680451\pi$
$7$	0.727727	−	3.77580i	0.275055	−	1.42712i	0.812076	−	0.583551i	$-0.198337\pi$
$8$	1.18854	+	0.170886i	0.420211	+	0.0604173i
$9$	−2.12121	+	2.12143i	−0.707070	+	0.707144i
$10$	0.950434	−	0.823555i	0.300553	−	0.260431i
$11$	−3.80876	−	1.96355i	−1.14838	−	0.592033i	−0.224412	−	0.974494i	$-0.572046\pi$
$11$	−3.80876	−	1.96355i	−1.14838	−	0.592033i	−0.923972	+	0.382461i	$0.875077\pi$
$12$	−0.682073	−	2.22444i	−0.196898	−	0.642140i
$13$	0.691689	−	0.133312i	0.191840	−	0.0369741i	−0.0924261	−	0.995720i	$-0.529462\pi$
$13$	0.691689	−	0.133312i	0.191840	−	0.0369741i	0.284266	+	0.958745i	$0.408250\pi$
$14$	−1.65762	+	6.83281i	−0.443018	+	1.82614i
$15$	1.08946	+	0.481921i	0.281297	+	0.124431i
$16$	−4.79392	−	0.923952i	−1.19848	−	0.230988i
$17$	−3.30816	+	7.24386i	−0.802347	+	1.75689i	−0.165037	+	0.986287i	$0.552774\pi$
$17$	−3.30816	+	7.24386i	−0.802347	+	1.75689i	−0.637310	+	0.770607i	$0.719953\pi$
$18$	4.05874	−	3.69003i	0.956654	−	0.869748i
$19$	−1.89153	+	0.863831i	−0.433946	+	0.198176i	−0.620397	−	0.784288i	$-0.713029\pi$
$19$	−1.89153	+	0.863831i	−0.433946	+	0.198176i	0.186451	+	0.982464i	$0.440301\pi$
$20$	−0.726241	+	0.571122i	−0.162392	+	0.127707i
$21$	−6.52439	+	1.33836i	−1.42374	+	0.292055i
$22$	6.78547	+	3.91760i	1.44667	+	0.835234i
$23$	−4.04740	−	2.57265i	−0.843942	−	0.536434i
$23$	−4.04740	−	2.57265i	−0.843942	−	0.536434i
$24$	−0.514395	−	2.01516i	−0.105000	−	0.411343i
$25$	−0.215401	+	4.52182i	−0.0430801	+	0.904363i
$26$	−1.27490	+	0.183303i	−0.250028	+	0.0359486i
$27$	4.80078	+	1.98810i	0.923910	+	0.382611i
$28$	1.45525	−	4.95614i	0.275017	−	0.936623i
$29$	−0.711492	−	7.45108i	−0.132121	−	1.38363i	−0.781851	−	0.623465i	$-0.785724\pi$
$29$	−0.711492	−	7.45108i	−0.132121	−	1.38363i	0.649730	−	0.760165i	$-0.274882\pi$
$30$	−1.94786	−	0.974964i	−0.355628	−	0.178003i
$31$	−3.93002	−	3.09060i	−0.705853	−	0.555089i	0.199423	−	0.979914i	$-0.436093\pi$
$31$	−3.93002	−	3.09060i	−0.705853	−	0.555089i	−0.905276	+	0.424825i	$0.860336\pi$
$32$	6.34139	+	1.53841i	1.12101	+	0.271954i
$33$	−0.617345	+	7.39631i	−0.107466	+	1.28753i
$34$	6.67225	−	12.9424i	1.14428	−	2.21960i
$35$	1.42986	+	2.22491i	0.241691	+	0.376079i
$36$	−3.10740	+	2.56596i	−0.517899	+	0.427659i
$37$	−0.969499	−	3.30181i	−0.159385	−	0.542814i	−0.999999	−	0.00118053i	$-0.999624\pi$
$37$	−0.969499	−	3.30181i	−0.159385	−	0.542814i	0.840615	−	0.541634i	$-0.182194\pi$
$38$	3.52983	−	1.41313i	0.572615	−	0.229240i
$39$	−0.671824	−	1.01846i	−0.107578	−	0.163085i
$40$	−0.672735	+	0.479052i	−0.106369	+	0.0757448i
$41$	0.863301	+	0.905404i	0.134825	+	0.141400i	0.787685	−	0.616078i	$-0.211280\pi$
$41$	0.863301	+	0.905404i	0.134825	+	0.141400i	−0.652860	+	0.757479i	$0.726431\pi$
$42$	12.0326	−	1.87675i	1.85667	−	0.289589i
$43$	1.04122	+	1.32402i	0.158785	+	0.201911i	0.858935	−	0.512084i	$-0.171126\pi$
$43$	1.04122	+	1.32402i	0.158785	+	0.201911i	−0.700151	+	0.713995i	$0.746884\pi$
$44$	−4.84241	−	3.11203i	−0.730020	−	0.469156i
$45$	0.0489951	−	2.06279i	0.00730376	−	0.307503i
$46$	7.16834	+	5.05081i	1.05691	+	0.744702i
$47$	0.172200	−	0.0994197i	0.0251179	−	0.0145018i	−0.487388	−	0.873185i	$-0.662050\pi$
$47$	0.172200	−	0.0994197i	0.0251179	−	0.0145018i	0.512506	+	0.858683i	$0.328717\pi$
$48$	1.69924	+	8.28364i	0.245265	+	1.19564i
$49$	−7.22854	−	2.89387i	−1.03265	−	0.413410i
$50$	0.786815	−	8.23989i	0.111272	−	1.16530i
$51$	13.7844	+	0.491949i	1.93021	+	0.0688867i
$52$	0.941960	−	0.0899462i	0.130626	−	0.0124733i
$53$	7.10983	−	8.20518i	0.976610	−	1.12707i	−0.0152691	−	0.999883i	$-0.504861\pi$
$53$	7.10983	−	8.20518i	0.976610	−	1.12707i	0.991879	−	0.127185i	$-0.0405940\pi$
$54$	−8.59516	−	4.04874i	−1.16965	−	0.550964i
$55$	2.82787	−	0.830339i	0.381311	−	0.111963i
$56$	1.51016	−	4.36333i	0.201804	−	0.583074i
$57$	2.63613	+	2.45419i	0.349164	+	0.325066i
$58$	0.651208	+	13.6705i	0.0855078	+	1.79503i
$59$	−1.40276	−	7.27823i	−0.182624	−	0.947545i	−0.951384	−	0.308007i	$-0.900338\pi$
$59$	−1.40276	−	7.27823i	−0.182624	−	0.947545i	0.768760	−	0.639538i	$-0.220874\pi$
$60$	1.39531	+	0.783543i	0.180133	+	0.101155i
$61$	3.81925	+	9.54002i	0.489005	+	1.22147i	0.943693	+	0.330824i	$0.107327\pi$
$61$	3.81925	+	9.54002i	0.489005	+	1.22147i	−0.454688	+	0.890651i	$0.650249\pi$
$62$	6.90889	+	5.98659i	0.877430	+	0.760298i
$63$	6.46645	+	9.55309i	0.814696	+	1.20358i
$64$	−2.07929	−	0.610536i	−0.259912	−	0.0763170i
$65$	−0.281033	+	0.394656i	−0.0348579	+	0.0489511i
$66$	1.77101	−	13.4549i	0.217996	−	1.65618i
$67$	1.99939	+	3.87827i	0.244264	+	0.473807i	0.978815	−	0.204747i	$-0.0656373\pi$
$67$	1.99939	+	3.87827i	0.244264	+	0.473807i	−0.734551	+	0.678554i	$0.762607\pi$
$68$	−5.34868	+	9.26419i	−0.648623	+	1.12345i
$69$	−1.43383	+	8.18194i	−0.172612	+	0.984990i
$70$	−2.41793	−	4.18797i	−0.288998	−	0.500559i
$71$	0.172587	−	0.268551i	0.0204823	−	0.0318711i	−0.830861	−	0.556479i	$-0.812152\pi$
$71$	0.172587	−	0.268551i	0.0204823	−	0.0318711i	0.851344	+	0.524608i	$0.175788\pi$
$72$	−2.88366	+	2.15892i	−0.339842	+	0.254431i
$73$	−4.97498	−	10.8937i	−0.582277	−	1.27501i	−0.939998	−	0.341181i	$-0.889173\pi$
$73$	−4.97498	−	10.8937i	−0.582277	−	1.27501i	0.357721	−	0.933829i	$-0.383554\pi$
$74$	1.48343	+	6.11477i	0.172445	+	0.710827i
$75$	7.37854	−	2.65269i	0.852001	−	0.306306i
$76$	−2.63968	+	0.913602i	−0.302792	+	0.104797i
$77$	−10.1857	+	12.9522i	−1.16077	+	1.47604i
$78$	1.13841	+	1.91857i	0.128899	+	0.217235i
$79$	−15.2755	−	5.28691i	−1.71863	−	0.594823i	−0.723228	−	0.690610i	$-0.757342\pi$
$79$	−15.2755	−	5.28691i	−1.71863	−	0.594823i	−0.995402	+	0.0957862i	$0.969463\pi$
$80$	2.82484	−	1.81542i	0.315827	−	0.202970i
$81$	−0.000945804	−	9.00000i	−0.000105089	−	1.00000i
$82$	−1.49796	−	1.72874i	−0.165422	−	0.190907i
$83$	−2.43239	−	2.31928i	−0.266990	−	0.254574i	0.544743	−	0.838603i	$-0.316627\pi$
$83$	−2.43239	−	2.31928i	−0.266990	−	0.254574i	−0.811733	+	0.584029i	$0.801476\pi$
$84$	−8.89541	+	0.956591i	−0.970568	+	0.104373i
$85$	−1.79143	−	5.17599i	−0.194307	−	0.561414i
$86$	−1.78649	−	2.50877i	−0.192642	−	0.270528i
$87$	−11.4515	+	6.07761i	−1.22773	+	0.651588i
$88$	−4.19131	−	2.98462i	−0.446795	−	0.318161i
$89$	−1.65318	−	11.4981i	−0.175237	−	1.21880i	−0.867604	−	0.497256i	$-0.834341\pi$
$89$	−1.65318	−	11.4981i	−0.175237	−	1.21880i	0.692367	−	0.721546i	$-0.256568\pi$
$90$	−0.268952	+	3.76321i	−0.0283500	+	0.396677i
$91$		−	2.70870i		−	0.283949i
$92$	−5.08375	−	3.95699i	−0.530018	−	0.412545i
$93$	−2.34046	+	8.33744i	−0.242694	+	0.864553i
$94$	−0.323155	+	0.166598i	−0.0333309	+	0.0171833i
$95$	0.531559	−	1.32777i	0.0545368	−	0.136226i
$96$	−1.74178	−	11.1672i	−0.177769	−	1.13975i
$97$	−4.69126	+	1.13809i	−0.476326	+	0.115555i	−0.466732	−	0.884399i	$-0.654569\pi$
$97$	−4.69126	+	1.13809i	−0.476326	+	0.115555i	−0.00959340	+	0.999954i	$0.503054\pi$
$98$	12.9504	+	5.91426i	1.30819	+	0.597430i
$99$	12.2447	−	3.91492i	1.23064	−	0.393464i
$100$	−0.865421	+	6.01914i	−0.0865421	+	0.601914i
$101$	1.99639	−	2.09375i	0.198648	−	0.208336i	−0.616874	−	0.787062i	$-0.711601\pi$
$101$	1.99639	−	2.09375i	0.198648	−	0.208336i	0.815522	+	0.578726i	$0.196450\pi$
$102$	−25.1330	−	2.09777i	−2.48854	−	0.207710i
$103$	6.92991	−	0.330112i	0.682824	−	0.0325269i	0.296696	−	0.954972i	$-0.404115\pi$
$103$	6.92991	−	0.330112i	0.682824	−	0.0325269i	0.386128	+	0.922445i	$0.373812\pi$
$104$	0.844880	−	0.0402466i	0.0828473	−	0.00394650i
$105$	2.61247	−	3.76288i	0.254951	−	0.367219i
$106$	−13.6992	+	14.3673i	−1.33059	+	1.39548i
$107$	−1.45241	+	10.1017i	−0.140410	+	0.976572i	0.790796	+	0.612079i	$0.209667\pi$
$107$	−1.45241	+	10.1017i	−0.140410	+	0.976572i	−0.931206	+	0.364493i	$0.881242\pi$
$108$	6.16581	+	3.27153i	0.593306	+	0.314803i
$109$	−2.47709	−	1.13125i	−0.237262	−	0.108354i	0.293236	−	0.956040i	$-0.405268\pi$
$109$	−2.47709	−	1.13125i	−0.237262	−	0.108354i	−0.530498	+	0.847686i	$0.677995\pi$
$110$	−5.23706	+	1.27050i	−0.499335	+	0.121137i
$111$	−4.64087	+	3.74005i	−0.440492	+	0.354990i
$112$	−6.97733	+	17.4285i	−0.659295	+	1.64684i
$113$	0.523879	−	0.270079i	0.0492824	−	0.0254069i	−0.433409	−	0.901197i	$-0.642690\pi$
$113$	0.523879	−	0.270079i	0.0492824	−	0.0254069i	0.482692	+	0.875790i	$0.339659\pi$
$114$	−4.60110	−	4.71168i	−0.430932	−	0.441289i
$115$	3.23576	−	0.640412i	0.301736	−	0.0597187i
$116$		−	10.0545i		−	0.933541i
$117$	−1.18440	+	1.75015i	−0.109498	+	0.161802i
$118$	1.92878	+	13.4150i	0.177559	+	1.23495i
$119$	24.9440	+	17.7625i	2.28661	+	1.62829i
$120$	1.21251	+	0.758954i	0.110686	+	0.0692827i
$121$	4.27048	+	5.99705i	0.388225	+	0.545186i
$122$	−6.14547	−	17.7562i	−0.556384	−	1.60757i
$123$	0.876562	−	1.98161i	0.0790369	−	0.178676i
$124$	−4.86065	−	4.63462i	−0.436499	−	0.416201i
$125$	−4.29100	−	4.95208i	−0.383799	−	0.442928i
$126$	−10.9792	−	18.0103i	−0.978103	−	1.60449i
$127$	13.9757	−	8.98161i	1.24014	−	0.796989i	0.254701	−	0.967020i	$-0.418023\pi$
$127$	13.9757	−	8.98161i	1.24014	−	0.796989i	0.985439	+	0.170031i	$0.0543866\pi$
$128$	−8.58839	−	2.97247i	−0.759114	−	0.262732i
$129$	1.42849	−	2.54380i	0.125771	−	0.223969i
$130$	0.547615	−	0.696349i	0.0480290	−	0.0610738i
$131$	5.39981	−	1.86889i	0.471783	−	0.163286i	−0.0808225	−	0.996729i	$-0.525755\pi$
$131$	5.39981	−	1.86889i	0.471783	−	0.163286i	0.552606	+	0.833443i	$0.313633\pi$
$132$	−1.76995	+	9.81163i	−0.154054	+	0.853993i
$133$	1.88514	+	7.77066i	0.163463	+	0.673802i
$134$	−3.31426	−	7.25722i	−0.286309	−	0.626929i
$135$	−3.33333	+	1.28896i	−0.286888	+	0.110936i
$136$	−5.16975	+	8.04428i	−0.443302	+	0.689792i
$137$	0.705864	+	1.22259i	0.0603060	+	0.104453i	0.894602	−	0.446863i	$-0.147459\pi$
$137$	0.705864	+	1.22259i	0.0603060	+	0.104453i	−0.834296	+	0.551317i	$0.814126\pi$
$138$	3.33058	−	14.8187i	0.283518	−	1.26145i
$139$	7.64739	−	13.2457i	0.648643	−	1.12348i	−0.334804	−	0.942288i	$-0.608670\pi$
$139$	7.64739	−	13.2457i	0.648643	−	1.12348i	0.983447	−	0.181196i	$-0.0579967\pi$
$140$	1.62794	+	3.15776i	0.137586	+	0.266880i
$141$	−0.273236	−	0.209650i	−0.0230106	−	0.0176557i
$142$	−0.338577	+	0.475466i	−0.0284128	+	0.0399002i
$143$	−2.89624	−	0.850413i	−0.242196	−	0.0711151i
$144$	12.1290	−	8.21008i	1.01075	−	0.684173i
$145$	3.89067	+	3.37128i	0.323102	+	0.279970i
$146$	8.13852	+	20.3290i	0.673548	+	1.68244i
$147$	0.160836	+	13.4853i	0.0132656	+	1.11225i
$148$	−0.874825	−	4.53902i	−0.0719102	−	0.373105i
$149$	−0.364633	−	7.65459i	−0.0298719	−	0.627089i	−0.963317	−	0.268367i	$-0.913516\pi$
$149$	−0.364633	−	7.65459i	−0.0298719	−	0.627089i	0.933445	−	0.358721i	$-0.116787\pi$
$150$	−13.7069	+	4.20292i	−1.11917	+	0.343167i
$151$	−3.21483	+	9.28863i	−0.261619	+	0.755898i	0.735320	+	0.677720i	$0.237032\pi$
$151$	−3.21483	+	9.28863i	−0.261619	+	0.755898i	−0.996939	+	0.0781786i	$0.975090\pi$
$152$	−2.39577	+	0.703460i	−0.194322	+	0.0570582i
$153$	−8.35006	−	22.3838i	−0.675062	−	1.80962i
$154$	19.7300	−	22.7697i	1.58989	−	1.83483i
$155$	3.42317	−	0.326873i	0.274956	−	0.0262551i
$156$	−0.768327	−	1.44769i	−0.0615154	−	0.115908i
$157$	−0.657534	+	6.88601i	−0.0524770	+	0.549564i	0.930558	+	0.366145i	$0.119322\pi$
$157$	−0.657534	+	6.88601i	−0.0524770	+	0.549564i	−0.983035	+	0.183419i	$0.941284\pi$
$158$	27.4392	+	10.9850i	2.18294	+	0.873919i
$159$	−17.8427	−	5.93811i	−1.41502	−	0.470923i
$160$	−3.88678	+	2.24403i	−0.307277	+	0.177406i
$161$	−12.6592	+	13.4100i	−0.997687	+	1.05686i
$162$	−0.781291	+	16.4377i	−0.0613840	+	1.29146i
$163$	7.94124	+	5.10352i	0.622006	+	0.399739i	0.813342	−	0.581786i	$-0.197646\pi$
$163$	7.94124	+	5.10352i	0.622006	+	0.399739i	−0.191336	+	0.981525i	$0.561282\pi$
$164$	1.03881	+	1.32095i	0.0811174	+	0.103149i
$165$	−3.20321	−	3.97473i	−0.249370	−	0.309432i
$166$	4.24073	+	4.44755i	0.329145	+	0.345197i
$167$	6.05282	−	4.31020i	0.468382	−	0.333533i	−0.321376	−	0.946952i	$-0.604145\pi$
$167$	6.05282	−	4.31020i	0.468382	−	0.333533i	0.789758	+	0.613419i	$0.210206\pi$
$168$	−7.98319	+	0.475770i	−0.615916	+	0.0367065i
$169$	−11.6081	+	4.64719i	−0.892932	+	0.357476i
$170$	2.82153	+	9.60926i	0.216402	+	0.736997i
$171$	2.17976	−	5.84511i	0.166691	−	0.446987i
$172$	1.22327	+	1.90345i	0.0932737	+	0.145137i
$173$	4.76457	−	9.24197i	0.362243	−	0.702654i	−0.635333	−	0.772239i	$-0.719137\pi$
$173$	4.76457	−	9.24197i	0.362243	−	0.702654i	0.997576	+	0.0695845i	$0.0221673\pi$
$174$	21.4438	−	10.1038i	1.62565	−	0.765969i
$175$	16.9167	+	4.10396i	1.27879	+	0.310230i
$176$	16.4447	+	12.9322i	1.23956	+	0.974803i
$177$	−10.7167	+	7.06920i	−0.805516	+	0.531354i
$178$	2.01901	+	21.1440i	0.151331	+	1.58481i
$179$	−2.75416	+	9.37982i	−0.205856	+	0.701080i	0.790240	+	0.612798i	$0.209956\pi$
$179$	−2.75416	+	9.37982i	−0.205856	+	0.701080i	−0.996095	+	0.0882825i	$0.971862\pi$
$180$	0.328912	−	2.75214i	0.0245156	−	0.205132i
$181$	4.57265	−	0.657447i	0.339882	−	0.0488677i	0.0297394	−	0.999558i	$-0.490532\pi$
$181$	4.57265	−	0.657447i	0.339882	−	0.0488677i	0.310143	+	0.950690i	$0.399623\pi$
$182$	−0.235662	+	4.94716i	−0.0174684	+	0.366708i
$183$	12.7342	−	12.4353i	0.941337	−	0.919244i
$184$	−4.37086	−	3.74933i	−0.322224	−	0.276405i
$185$	2.04973	+	1.18341i	0.150699	+	0.0870063i
$186$	4.99998	−	15.0239i	0.366617	−	1.10160i
$187$	26.8237	−	21.0944i	1.96154	−	1.54257i
$188$	0.242963	−	0.110958i	0.0177199	−	0.00809241i
$189$	11.0003	−	16.6800i	0.800157	−	1.21329i
$190$	−1.08636	+	2.37879i	−0.0788126	+	0.172576i
$191$	−20.6911	−	3.98788i	−1.49715	−	0.288553i	−0.626101	−	0.779742i	$-0.715350\pi$
$191$	−20.6911	−	3.98788i	−1.49715	−	0.288553i	−0.871053	+	0.491189i	$0.836562\pi$
$192$	0.401327	+	3.73197i	0.0289633	+	0.269332i
$193$	3.01877	−	12.4435i	0.217296	−	0.895706i	−0.753817	−	0.657084i	$-0.771789\pi$
$193$	3.01877	−	12.4435i	0.217296	−	0.895706i	0.971113	−	0.238621i	$-0.0766954\pi$
$194$	8.66713	−	1.67045i	0.622264	−	0.119932i
$195$	0.817813	+	0.188101i	0.0585648	+	0.0134702i
$196$	−9.29660	−	4.79273i	−0.664043	−	0.342338i
$197$	12.7308	−	11.0313i	0.907034	−	0.785950i	−0.0703277	−	0.997524i	$-0.522404\pi$
$197$	12.7308	−	11.0313i	0.907034	−	0.785950i	0.977362	+	0.211574i	$0.0678590\pi$
$198$	−22.7043	+	6.08488i	−1.61353	+	0.432434i
$199$	−4.85097	−	0.697464i	−0.343876	−	0.0494419i	−0.0317868	−	0.999495i	$-0.510120\pi$
$199$	−4.85097	−	0.697464i	−0.343876	−	0.0494419i	−0.312089	+	0.950053i	$0.601029\pi$
$200$	−1.02873	+	5.33754i	−0.0727419	+	0.377421i
$201$	4.88064	−	5.77019i	0.344254	−	0.406998i
$202$	−3.82836	+	3.65033i	−0.269362	+	0.256836i
$203$	−28.6516	−	2.73589i	−2.01095	−	0.192022i
$204$	18.3699	+	2.41796i	1.28615	+	0.169291i
$205$	−0.859464	−	0.0409413i	−0.0600275	−	0.00285946i
$206$	−12.6855			−0.883840
$207$	14.0431	−	3.12916i	0.976062	−	0.217492i
$208$	−3.43908			−0.238457
$209$	8.90054	+	0.423985i	0.615663	+	0.0293277i
$210$	−5.09878	+	6.64522i	−0.351849	+	0.458564i
$211$	−21.0335	−	2.00845i	−1.44800	−	0.138268i	−0.658763	−	0.752351i	$-0.728920\pi$
$211$	−21.0335	−	2.00845i	−1.44800	−	0.138268i	−0.789241	+	0.614083i	$0.789526\pi$
$212$	10.5551	−	10.0642i	0.724926	−	0.691215i
$213$	−0.544135	−	0.0981580i	−0.0372835	−	0.00672568i
$214$	3.53155	−	18.3234i	0.241412	−	1.25256i
$215$	−1.14672	−	0.164873i	−0.0782053	−	0.0112442i
$216$	5.36616	+	3.18332i	0.365121	+	0.216597i
$217$	−14.5295	+	12.5899i	−0.986326	+	0.854657i
$218$	4.42573	+	2.28162i	0.299749	+	0.154531i
$219$	−14.1342	+	15.1820i	−0.955100	+	1.02590i
$220$	3.88750	−	0.749255i	0.262095	−	0.0505147i
$221$	−1.32252	+	5.45152i	−0.0889626	+	0.366709i
$222$	8.80146	−	6.42705i	0.590715	−	0.431355i
$223$	20.0900	+	3.87204i	1.34533	+	0.259291i	0.810534	−	0.585691i	$-0.199177\pi$
$223$	20.0900	+	3.87204i	1.34533	+	0.259291i	0.534794	+	0.844982i	$0.320389\pi$
$224$	10.4235	−	22.8243i	0.696451	−	1.52501i
$225$	−9.13582	−	10.0487i	−0.609054	−	0.669912i
$226$	−0.980310	+	0.447692i	−0.0652092	+	0.0297801i
$227$	−2.07842	+	1.63448i	−0.137949	+	0.108485i	−0.684749	−	0.728779i	$-0.740088\pi$
$227$	−2.07842	+	1.63448i	−0.137949	+	0.108485i	0.546800	+	0.837263i	$0.315846\pi$
$228$	3.21170	+	3.61839i	0.212700	+	0.239633i
$229$	5.44939	+	3.14621i	0.360106	+	0.207907i	0.669127	−	0.743148i	$-0.266668\pi$
$229$	5.44939	+	3.14621i	0.360106	+	0.207907i	−0.309021	+	0.951055i	$0.600001\pi$
$230$	−5.96551	+	0.888129i	−0.393354	+	0.0585615i
$231$	27.4778	+	7.71346i	1.80790	+	0.507509i
$232$	0.427649	−	8.97747i	0.0280766	−	0.589400i
$233$	−15.1039	+	2.17161i	−0.989488	+	0.142267i	−0.618006	−	0.786173i	$-0.712059\pi$
$233$	−15.1039	+	2.17161i	−0.989488	+	0.142267i	−0.371482	+	0.928440i	$0.621150\pi$
$234$	2.31546	−	3.09343i	0.151366	−	0.202224i
$235$	−0.0385297	+	0.131220i	−0.00251340	+	0.00855986i
$236$	−0.946450	−	9.91167i	−0.0616087	−	0.645195i
$237$	1.66562	+	27.9482i	0.108194	+	1.81543i
$238$	−44.0122	−	34.6116i	−2.85289	−	2.24354i
$239$	−10.1974	−	2.47386i	−0.659614	−	0.160021i	−0.108040	−	0.994147i	$-0.534457\pi$
$239$	−10.1974	−	2.47386i	−0.659614	−	0.160021i	−0.551574	+	0.834126i	$0.685973\pi$
$240$	−4.77751	−	3.31690i	−0.308387	−	0.214105i
$241$	3.34809	−	6.49439i	0.215669	−	0.418340i	−0.756038	−	0.654527i	$-0.772868\pi$
$241$	3.34809	−	6.49439i	0.215669	−	0.418340i	0.971708	+	0.236187i	$0.0758979\pi$
$242$	−7.27784	−	11.3245i	−0.467837	−	0.727969i
$243$	−14.4011	+	5.96734i	−0.923829	+	0.382805i
$244$	3.88901	+	13.2447i	0.248968	+	0.847907i
$245$	4.97172	−	1.99038i	0.317632	−	0.127161i
$246$	−1.77335	+	3.54294i	−0.113065	+	0.225890i
$247$	−1.19319	+	0.849666i	−0.0759208	+	0.0540629i
$248$	−4.14284	−	4.34488i	−0.263070	−	0.275900i
$249$	−2.09893	+	5.42966i	−0.133014	+	0.344091i
$250$	7.40624	+	9.41780i	0.468412	+	0.595634i
$251$	2.09511	+	1.34645i	0.132242	+	0.0849871i	0.605089	−	0.796157i	$-0.293137\pi$
$251$	2.09511	+	1.34645i	0.132242	+	0.0849871i	−0.472847	+	0.881145i	$0.656774\pi$
$252$	7.42722	+	13.6002i	0.467871	+	0.856734i
$253$	10.3641	+	17.7459i	0.651582	+	1.11567i
$254$	−26.3065	+	15.1881i	−1.65062	+	0.952985i
$255$	−7.09507	+	6.29762i	−0.444311	+	0.394372i
$256$	19.4509	+	7.78696i	1.21568	+	0.486685i
$257$	−1.93438	+	20.2578i	−0.120663	+	1.26364i	0.708931	+	0.705278i	$0.249178\pi$
$257$	−1.93438	+	20.2578i	−0.120663	+	1.26364i	−0.829594	+	0.558366i	$0.811428\pi$
$258$	−2.83030	+	4.52171i	−0.176207	+	0.281509i
$259$	−13.1725	+	1.25782i	−0.818500	+	0.0781573i
$260$	−0.426195	+	0.491856i	−0.0264315	+	0.0305036i
$261$	17.3162	+	14.2959i	1.07184	+	0.884895i
$262$	−10.0248	+	2.94354i	−0.619334	+	0.181853i
$263$	−3.97236	+	11.4774i	−0.244946	+	0.707726i	0.753773	+	0.657135i	$0.228232\pi$
$263$	−3.97236	+	11.4774i	−0.244946	+	0.707726i	−0.998719	+	0.0505910i	$0.983890\pi$
$264$	−1.99766	+	8.68529i	−0.122948	+	0.534543i
$265$	0.355311	+	7.45889i	0.0218266	+	0.458196i
$266$	−2.76696	−	14.3563i	−0.169653	−	0.880243i
$267$	−17.3034	+	10.2672i	−1.05895	+	0.628341i
$268$	2.17840	+	5.44139i	0.133067	+	0.332386i
$269$	9.86711	+	8.54990i	0.601609	+	0.521297i	0.901558	−	0.432658i	$-0.142424\pi$
$269$	9.86711	+	8.54990i	0.601609	+	0.521297i	−0.299949	+	0.953955i	$0.596970\pi$
$270$	6.20013	−	2.06414i	0.377328	−	0.125620i
$271$	−9.43054	−	2.76906i	−0.572864	−	0.168208i	−0.0175461	−	0.999846i	$-0.505585\pi$
$271$	−9.43054	−	2.76906i	−0.572864	−	0.168208i	−0.555318	+	0.831638i	$0.687404\pi$
$272$	22.5520	−	31.6699i	1.36742	−	1.92027i
$273$	−4.33443	+	1.79551i	−0.262332	+	0.108669i
$274$	−1.18282	−	2.29435i	−0.0714568	−	0.138607i
$275$	9.69923	−	16.7996i	0.584885	−	1.01305i
$276$	−2.96207	+	10.7579i	−0.178296	+	0.647551i
$277$	−4.91170	−	8.50732i	−0.295116	−	0.511155i	0.679896	−	0.733308i	$-0.262025\pi$
$277$	−4.91170	−	8.50732i	−0.295116	−	0.511155i	−0.975012	+	0.222153i	$0.928692\pi$
$278$	−15.1196	+	23.5265i	−0.906812	+	1.41103i
$279$	14.8929	−	1.78146i	0.891615	−	0.106653i
$280$	1.31924	+	2.88873i	0.0788397	+	0.172635i
$281$	3.71993	+	15.3338i	0.221912	+	0.914735i	0.968413	+	0.249351i	$0.0802172\pi$
$281$	3.71993	+	15.3338i	0.221912	+	0.914735i	−0.746501	+	0.665384i	$0.768268\pi$
$282$	0.480798	+	0.406677i	0.0286311	+	0.0242172i
$283$	18.8674	−	6.53008i	1.12155	−	0.388173i	0.297520	−	0.954716i	$-0.403840\pi$
$283$	18.8674	−	6.53008i	1.12155	−	0.388173i	0.824033	+	0.566542i	$0.191719\pi$
$284$	0.265077	−	0.337073i	0.0157294	−	0.0200016i
$285$	−2.47704	+	0.0295432i	−0.146727	+	0.00174999i
$286$	5.21570	+	1.80517i	0.308411	+	0.106742i
$287$	4.04687	−	2.60077i	0.238879	−	0.153519i
$288$	−16.7150	+	10.1896i	−0.984944	+	0.600425i
$289$	−30.3970	−	35.0800i	−1.78806	−	2.06353i
$290$	−6.81260	−	6.49580i	−0.400050	−	0.381447i
$291$	4.93085	+	6.75251i	0.289052	+	0.395839i
$292$	−5.26162	−	15.2024i	−0.307913	−	0.889656i
$293$	−2.67432	−	3.75555i	−0.156235	−	0.219402i	0.729038	−	0.684474i	$-0.239968\pi$
$293$	−2.67432	−	3.75555i	−0.156235	−	0.219402i	−0.885273	+	0.465072i	$0.846028\pi$
$294$	0.879496	−	24.6435i	0.0512933	−	1.43724i
$295$	4.15273	+	2.95715i	0.241781	+	0.172172i
$296$	−0.588053	−	4.09000i	−0.0341799	−	0.237726i
$297$	−14.3813	−	16.9988i	−0.834485	−	0.986369i
$298$			14.0121i			0.811696i
$299$	−3.14251	−	1.23991i	−0.181736	−	0.0717056i
$300$	10.2054	−	2.60506i	0.589210	−	0.150403i
$301$	5.75696	−	2.96792i	0.331826	−	0.171068i
$302$	6.67968	−	16.6850i	0.384373	−	0.960116i
$303$	−4.67374	−	1.80671i	−0.268499	−	0.103793i
$304$	9.86596	−	2.39346i	0.565852	−	0.137274i
$305$	−6.42912	−	2.93608i	−0.368130	−	0.168119i
$306$	13.3031	+	41.6082i	0.760487	+	2.37858i
$307$	3.22232	−	22.4117i	0.183908	−	1.27910i	−0.663506	−	0.748171i	$-0.730932\pi$
$307$	3.22232	−	22.4117i	0.183908	−	1.27910i	0.847413	−	0.530934i	$-0.178159\pi$
$308$	−15.2743	+	16.0193i	−0.870337	+	0.912783i
$309$	−5.12186	−	10.8703i	−0.291373	−	0.618392i
$310$	−6.28051	+	0.299177i	−0.356709	+	0.0169921i
$311$	−21.5965	+	1.02877i	−1.22462	+	0.0583361i	−0.649906	−	0.760015i	$-0.725192\pi$
$311$	−21.5965	+	1.02877i	−1.22462	+	0.0583361i	−0.574719	+	0.818351i	$0.694889\pi$
$312$	−0.624447	−	1.32529i	−0.0353523	−	0.0750297i
$313$	12.9438	−	13.5750i	0.731624	−	0.767305i	−0.247867	−	0.968794i	$-0.579730\pi$
$313$	12.9438	−	13.5750i	0.731624	−	0.767305i	0.979491	+	0.201489i	$0.0645780\pi$
$314$	1.80002	−	12.5194i	0.101581	−	0.706510i
$315$	−7.75304	−	1.68614i	−0.436834	−	0.0950034i
$316$	−19.7516	−	9.02024i	−1.11111	−	0.507428i
$317$	27.7410	−	6.72988i	1.55809	−	0.377988i	0.638106	−	0.769949i	$-0.279718\pi$
$317$	27.7410	−	6.72988i	1.55809	−	0.377988i	0.919982	+	0.391961i	$0.128203\pi$
$318$	32.0713	+	12.3977i	1.79847	+	0.695228i
$319$	−11.9207	+	29.7764i	−0.667430	+	1.66716i
$320$	1.32480	−	0.682984i	0.0740588	−	0.0381800i
$321$	17.1274	−	4.37200i	0.955961	−	0.244021i
$322$	24.2875	−	23.3907i	1.35349	−	1.30351i
$323$		−	16.5596i		−	0.921403i
$324$	1.14793	−	12.0351i	0.0637740	−	0.668614i
$325$	0.453823	+	3.15641i	0.0251736	+	0.175086i
$326$	−14.0598	−	10.0120i	−0.778703	−	0.554512i
$327$	−0.168226	+	4.71369i	−0.00930290	+	0.260667i
$328$	0.871344	+	1.22363i	0.0481119	+	0.0675638i
$329$	−0.250075	−	0.722544i	−0.0137871	−	0.0398351i
$330$	5.50453	+	7.53812i	0.303014	+	0.414960i
$331$	14.8418	+	14.1516i	0.815779	+	0.777844i	0.977932	−	0.208922i	$-0.0669955\pi$
$331$	14.8418	+	14.1516i	0.815779	+	0.777844i	−0.162153	+	0.986766i	$0.551844\pi$
$332$	−2.95648	−	3.41197i	−0.162258	−	0.187256i
$333$	9.06107	+	4.94710i	0.496544	+	0.271100i
$334$	−11.4299	+	7.34552i	−0.625414	+	0.401929i
$335$	−2.83600	−	0.981548i	−0.154947	−	0.0536277i
$336$	32.5140	−	0.387788i	1.77378	−	0.0211556i
$337$	−15.5934	+	19.8286i	−0.849424	+	1.08013i	0.146435	+	0.989220i	$0.453220\pi$
$337$	−15.5934	+	19.8286i	−0.849424	+	1.08013i	−0.995859	+	0.0909103i	$0.971022\pi$
$338$	21.6054	−	7.47769i	1.17518	−	0.406733i
$339$	−0.779440	−	0.659279i	−0.0423334	−	0.0358071i
$340$	−1.73461	−	7.15015i	−0.0940723	−	0.387771i
$341$	8.89994	+	19.4882i	0.481959	+	1.05534i
$342$	−4.48965	+	10.4858i	−0.242772	+	0.567010i
$343$	−1.63463	+	2.54353i	−0.0882617	+	0.137338i
$344$	1.01127	+	1.75158i	0.0545242	+	0.0944387i
$345$	−3.16967	−	4.75332i	−0.170649	−	0.255910i
$346$	−9.50607	+	16.4650i	−0.511049	+	0.885163i
$347$	10.3882	+	20.1503i	0.557669	+	1.08173i	0.984168	+	0.177238i	$0.0567163\pi$
$347$	10.3882	+	20.1503i	0.557669	+	1.08173i	−0.426499	+	0.904488i	$0.640253\pi$
$348$	−16.0892	+	6.66485i	−0.862470	+	0.357273i
$349$	−5.02038	+	7.05014i	−0.268735	+	0.377386i	−0.926787	−	0.375587i	$-0.877441\pi$
$349$	−5.02038	+	7.05014i	−0.268735	+	0.377386i	0.658052	+	0.752972i	$0.271381\pi$
$350$	−30.5396	−	8.96725i	−1.63241	−	0.479320i
$351$	3.58568	+	0.735148i	0.191390	+	0.0392393i
$352$	−21.1321	−	18.3111i	−1.12634	−	0.975983i
$353$	8.65884	+	21.6287i	0.460864	+	1.15118i	0.958829	+	0.283985i	$0.0916566\pi$
$353$	8.65884	+	21.6287i	0.460864	+	1.15118i	−0.497965	+	0.867197i	$0.665919\pi$
$354$	20.1880	−	11.9788i	1.07298	−	0.636666i
$355$	0.0415523	+	0.215594i	0.00220537	+	0.0114425i
$356$	−0.742481	−	15.5866i	−0.0393514	−	0.826088i
$357$	11.8888	−	51.6893i	0.629222	−	2.73569i
$358$	5.84626	−	16.8917i	0.308984	−	0.892752i
$359$	−11.1076	+	3.26148i	−0.586235	+	0.172134i	−0.561382	−	0.827557i	$-0.689730\pi$
$359$	−11.1076	+	3.26148i	−0.586235	+	0.172134i	−0.0248533	+	0.999691i	$0.507912\pi$
$360$	0.410734	−	2.44333i	0.0216476	−	0.128775i
$361$	−9.61069	+	11.0913i	−0.505826	+	0.583754i
$362$	−8.40867	+	0.802930i	−0.441950	+	0.0422011i
$363$	6.76564	−	10.8088i	0.355104	−	0.567316i
$364$	0.345870	−	3.62211i	0.0181285	−	0.189850i
$365$	7.64690	+	3.06136i	0.400257	+	0.160239i
$366$	−24.3396	+	21.6039i	−1.27225	+	1.12925i
$367$	−18.6842	+	10.7873i	−0.975308	+	0.563094i	−0.900850	−	0.434130i	$-0.857056\pi$
$367$	−18.6842	+	10.7873i	−0.975308	+	0.563094i	−0.0744577	+	0.997224i	$0.523723\pi$
$368$	17.0259	+	16.0727i	0.887538	+	0.837846i
$369$	−3.75199	−	0.0891168i	−0.195321	−	0.00463924i
$370$	−3.64067	−	2.33971i	−0.189269	−	0.121636i
$371$	−25.8071	−	32.8164i	−1.33984	−	1.70375i
$372$	−4.19429	+	10.8501i	−0.217464	+	0.562552i
$373$	−24.2002	−	25.3805i	−1.25304	−	1.31415i	−0.929905	−	0.367799i	$-0.880111\pi$
$373$	−24.2002	−	25.3805i	−1.25304	−	1.31415i	−0.323136	−	0.946352i	$-0.604737\pi$
$374$	−50.8260	+	36.1930i	−2.62815	+	1.87150i
$375$	−5.07989	+	10.1490i	−0.262325	+	0.524092i
$376$	0.221655	−	0.0887374i	0.0114310	−	0.00457628i
$377$	−1.48545	−	5.05898i	−0.0765046	−	0.260551i
$378$	−21.5422	+	29.5073i	−1.10801	+	1.51769i
$379$	6.54282	+	10.1808i	0.336082	+	0.522954i	0.967627	−	0.252386i	$-0.0812152\pi$
$379$	6.54282	+	10.1808i	0.336082	+	0.522954i	−0.631545	+	0.775339i	$0.717579\pi$
$380$	0.880350	−	1.70764i	0.0451610	−	0.0876001i
$381$	−23.6363	−	16.4101i	−1.21093	−	0.840713i
$382$	37.4432	+	9.08362i	1.91576	+	0.464758i
$383$	12.6744	+	9.96723i	0.647630	+	0.509302i	0.887085	−	0.461606i	$-0.152726\pi$
$383$	12.6744	+	9.96723i	0.647630	+	0.509302i	−0.239455	+	0.970907i	$0.576969\pi$
$384$	0.936465	+	15.7134i	0.0477888	+	0.801872i
$385$	−1.07728	−	11.2818i	−0.0549032	−	0.574972i
$386$	−6.59609	+	22.4642i	−0.335732	+	1.14340i
$387$	−5.01746	−	0.599644i	−0.255052	−	0.0304816i
$388$	−6.41855	+	0.922848i	−0.325853	+	0.0468505i
$389$	0.533965	−	11.2093i	0.0270731	−	0.568335i	−0.944057	−	0.329783i	$-0.893024\pi$
$389$	0.533965	−	11.2093i	0.0270731	−	0.568335i	0.971130	−	0.238551i	$-0.0766726\pi$
$390$	−1.47729	−	0.414699i	−0.0748053	−	0.0209991i
$391$	32.0254	−	20.8081i	1.61959	−	1.05231i
$392$	−8.09687	−	4.67473i	−0.408954	−	0.236109i
$393$	−6.56995	−	7.40188i	−0.331410	−	0.373376i
$394$	−24.2113	+	19.0400i	−1.21975	+	0.959221i
$395$	10.1131	−	4.61851i	0.508847	−	0.232383i
$396$	16.8737	−	3.67158i	0.847936	−	0.184504i
$397$	0.386564	−	0.846457i	0.0194011	−	0.0424825i	−0.899683	−	0.436543i	$-0.856203\pi$
$397$	0.386564	−	0.846457i	0.0194011	−	0.0424825i	0.919085	+	0.394060i	$0.128930\pi$
$398$	8.79912	+	1.69589i	0.441060	+	0.0850074i
$399$	11.1849	−	8.16752i	0.559947	−	0.408887i
$400$	5.21056	−	21.4782i	0.260528	−	1.07391i
$401$	23.7964	−	4.58639i	1.18834	−	0.229033i	0.443497	−	0.896276i	$-0.353738\pi$
$401$	23.7964	−	4.58639i	1.18834	−	0.229033i	0.744841	+	0.667243i	$0.232526\pi$
$402$	−9.41601	+	10.1140i	−0.469628	+	0.504442i
$403$	−3.13037	−	1.61382i	−0.155935	−	0.0803899i
$404$	2.93695	−	2.54488i	0.146119	−	0.126613i
$405$	4.27214	+	4.47955i	0.212284	+	0.222591i
$406$	52.0912	+	7.48958i	2.58524	+	0.371702i
$407$	−2.79069	+	14.4795i	−0.138329	+	0.717720i
$408$	16.2992	+	2.94026i	0.806933	+	0.145565i
$409$	16.3095	−	15.5511i	0.806453	−	0.768952i	−0.169824	−	0.985474i	$-0.554320\pi$
$409$	16.3095	−	15.5511i	0.806453	−	0.768952i	0.976278	+	0.216523i	$0.0694715\pi$
$410$	1.56616	+	0.149550i	0.0773471	+	0.00738576i
$411$	1.48848	−	1.93993i	0.0734214	−	0.0956899i
$412$	9.30893	+	0.443439i	0.458618	+	0.0218467i
$413$	−28.5020			−1.40249
$414$	−25.9205	+	4.49332i	−1.27392	+	0.220835i
$415$	2.31159			0.113471
$416$	4.59136	+	0.218714i	0.225110	+	0.0107233i
$417$	−26.2648	−	3.45712i	−1.28619	−	0.169296i
$418$	−16.2190	−	1.54873i	−0.793299	−	0.0757509i
$419$	−12.3790	+	11.8033i	−0.604752	+	0.576630i	−0.929340	−	0.369226i	$-0.879623\pi$
$419$	−12.3790	+	11.8033i	−0.604752	+	0.576630i	0.324588	+	0.945856i	$0.394774\pi$
$420$	3.97391	−	4.69820i	0.193907	−	0.229248i
$421$	−6.89914	+	35.7961i	−0.336243	+	1.74460i	0.282744	+	0.959196i	$0.408755\pi$
$421$	−6.89914	+	35.7961i	−0.336243	+	1.74460i	−0.618987	+	0.785401i	$0.712457\pi$
$422$	38.2407	+	5.49819i	1.86153	+	0.267648i
$423$	−0.154360	+	0.576200i	−0.00750524	+	0.0280158i
$424$	9.85244	−	8.53719i	0.478477	−	0.414603i
$425$	−32.0428	−	16.5192i	−1.55431	−	0.801300i
$426$	0.985267	+	0.226616i	0.0477364	+	0.0109796i
$427$	38.8006	−	7.47821i	1.87769	−	0.361896i
$428$	−3.23206	+	13.3227i	−0.156228	+	0.643979i
$429$	0.559008	+	5.19825i	0.0269891	+	0.250974i
$430$	2.08001	+	0.400890i	0.100307	+	0.0193326i
$431$	1.29293	−	2.83113i	0.0622783	−	0.136371i	−0.875934	−	0.482432i	$-0.839754\pi$
$431$	1.29293	−	2.83113i	0.0622783	−	0.136371i	0.938212	+	0.346061i	$0.112481\pi$
$432$	−21.1776	−	13.9665i	−1.01891	−	0.671963i
$433$	−28.0657	+	12.8172i	−1.34875	+	0.615954i	−0.953158	−	0.302471i	$-0.902188\pi$
$433$	−28.0657	+	12.8172i	−1.34875	+	0.615954i	−0.395593	+	0.918426i	$0.629461\pi$
$434$	27.6320	−	21.7300i	1.32638	−	1.04307i
$435$	2.81569	−	8.46053i	0.135002	−	0.405651i
$436$	−3.16796	−	1.82902i	−0.151718	−	0.0875942i
$437$	9.87810	+	1.36996i	0.472534	+	0.0655341i
$438$	27.1355	−	26.4987i	1.29659	−	1.26615i
$439$	0.407501	−	8.55450i	0.0194490	−	0.408284i	−0.968060	−	0.250720i	$-0.919333\pi$
$439$	0.407501	−	8.55450i	0.0194490	−	0.408284i	0.987509	−	0.157564i	$-0.0503642\pi$
$440$	3.50293	−	0.503645i	0.166996	−	0.0240103i
$441$	21.4724	−	9.19635i	1.02249	−	0.437921i
$442$	2.88975	−	9.84158i	0.137451	−	0.468116i
$443$	−1.77405	−	18.5787i	−0.0842877	−	0.882701i	−0.934430	−	0.356148i	$-0.884090\pi$
$443$	−1.77405	−	18.5787i	−0.0842877	−	0.882701i	0.850142	−	0.526554i	$-0.176516\pi$
$444$	−6.68340	+	4.40866i	−0.317180	+	0.209226i
$445$	6.28028	+	4.93887i	0.297714	+	0.234125i
$446$	−36.3555	−	8.81976i	−1.72148	−	0.417628i
$447$	−12.0071	+	5.65747i	−0.567916	+	0.267589i
$448$	−3.81842	+	7.40670i	−0.180403	+	0.349934i
$449$	21.5862	+	33.5888i	1.01872	+	1.58515i	0.791370	+	0.611338i	$0.209368\pi$
$449$	21.5862	+	33.5888i	1.01872	+	1.58515i	0.227346	+	0.973814i	$0.426995\pi$
$450$	15.8114	+	19.1477i	0.745355	+	0.902632i
$451$	−1.51030	−	5.14360i	−0.0711171	−	0.242203i
$452$	0.735026	−	0.294260i	0.0345727	−	0.0138408i
$453$	16.9946	−	1.01282i	0.798475	−	0.0475863i
$454$	3.93822	−	2.80439i	0.184830	−	0.131617i
$455$	1.28563	+	1.34833i	0.0602712	+	0.0632106i
$456$	2.71375	+	3.36738i	0.127083	+	0.157692i
$457$	7.10588	+	9.03586i	0.332399	+	0.422680i	0.923309	−	0.384058i	$-0.125474\pi$
$457$	7.10588	+	9.03586i	0.332399	+	0.422680i	−0.590910	+	0.806737i	$0.701231\pi$
$458$	−9.67902	−	6.22033i	−0.452271	−	0.290657i
$459$	−30.2833	+	28.1992i	−1.41350	+	1.31623i
$460$	4.40869	−	0.443199i	0.205556	−	0.0206642i
$461$	−1.94634	+	1.12372i	−0.0906502	+	0.0523369i	−0.544640	−	0.838670i	$-0.683334\pi$
$461$	−1.94634	+	1.12372i	−0.0906502	+	0.0523369i	0.453990	+	0.891007i	$0.350000\pi$
$462$	−49.5142	−	16.4785i	−2.30361	−	0.766648i
$463$	−3.53910	−	1.41684i	−0.164476	−	0.0658462i	0.287963	−	0.957641i	$-0.407022\pi$
$463$	−3.53910	−	1.41684i	−0.164476	−	0.0658462i	−0.452439	+	0.891795i	$0.649446\pi$
$464$	−3.47361	+	36.3773i	−0.161258	+	1.68877i
$465$	−2.79217	−	5.26104i	−0.129484	−	0.243975i
$466$	27.7746	−	2.65215i	1.28663	−	0.122859i
$467$	5.27043	−	6.08240i	0.243886	−	0.281460i	−0.620588	−	0.784137i	$-0.713106\pi$
$467$	5.27043	−	6.08240i	0.243886	−	0.281460i	0.864474	+	0.502677i	$0.167651\pi$
$468$	−1.80728	+	2.18910i	−0.0835415	+	0.101191i
$469$	16.0986	−	4.72698i	0.743365	−	0.218272i
$470$	0.0817870	−	0.236308i	0.00377255	−	0.0109001i
$471$	11.4548	−	3.51235i	0.527808	−	0.161840i
$472$	−0.423490	−	8.89016i	−0.0194927	−	0.409203i
$473$	−1.36598	−	7.08736i	−0.0628077	−	0.325877i
$474$	−0.610527	−	51.1895i	−0.0280425	−	2.35121i
$475$	−3.49865	−	8.73920i	−0.160529	−	0.400982i
$476$	31.0874	+	26.9374i	1.42489	+	1.23467i
$477$	2.32530	+	32.4879i	0.106468	+	1.48752i
$478$	18.4092	+	5.40544i	0.842019	+	0.247239i
$479$	−6.51917	+	9.15489i	−0.297868	+	0.418298i	−0.936202	−	0.351462i	$-0.885685\pi$
$479$	−6.51917	+	9.15489i	−0.297868	+	0.418298i	0.638334	+	0.769760i	$0.279624\pi$
$480$	6.16730	+	4.73208i	0.281497	+	0.215989i
$481$	−1.11076	−	2.15458i	−0.0506464	−	0.0982404i
$482$	−6.67997	+	11.5700i	−0.304264	+	0.527001i
$483$	29.8500	+	11.3681i	1.35822	+	0.517265i
$484$	4.94479	+	8.56464i	0.224763	+	0.389302i
$485$	1.79504	−	2.79313i	0.0815084	−	0.126829i
$486$	26.8213	−	9.64581i	1.21664	−	0.437543i
$487$	11.1988	+	24.5219i	0.507466	+	1.11119i	0.973970	+	0.226676i	$0.0727858\pi$
$487$	11.1988	+	24.5219i	0.507466	+	1.11119i	−0.466505	+	0.884519i	$0.654487\pi$
$488$	2.90906	+	11.9913i	0.131687	+	0.542822i
$489$	2.90260	−	16.0905i	0.131260	−	0.727635i
$490$	−9.25351	+	3.20267i	−0.418031	+	0.144682i
$491$	1.80173	−	2.29108i	0.0813108	−	0.103395i	−0.743696	−	0.668518i	$-0.766929\pi$
$491$	1.80173	−	2.29108i	0.0813108	−	0.103395i	0.825007	+	0.565123i	$0.191171\pi$
$492$	1.42518	−	2.53791i	0.0642521	−	0.114418i
$493$	56.3283	+	19.4954i	2.53690	+	0.878029i
$494$	2.25316	−	1.44802i	0.101374	−	0.0651494i
$495$	−4.23701	+	7.76047i	−0.190439	+	0.348807i
$496$	15.9846	+	18.4473i	0.717731	+	0.828306i
$497$	−0.888400	−	0.847088i	−0.0398502	−	0.0379971i
$498$	4.30587	−	9.73412i	0.192951	−	0.436196i
$499$	−13.2568	−	38.3030i	−0.593456	−	1.71468i	−0.694215	−	0.719768i	$-0.744248\pi$
$499$	−13.2568	−	38.3030i	−0.593456	−	1.71468i	0.100759	−	0.994911i	$-0.467873\pi$
$500$	−5.10567	−	7.16991i	−0.228333	−	0.320648i
$501$	−10.9094	−	6.82856i	−0.487394	−	0.305078i
$502$	−3.70937	−	2.64143i	−0.165557	−	0.117893i
$503$	−1.21107	−	8.42315i	−0.0539988	−	0.375570i	−0.998845	−	0.0480546i	$-0.984698\pi$
$503$	−1.21107	−	8.42315i	−0.0539988	−	0.375570i	0.944846	−	0.327515i	$-0.106211\pi$
$504$	6.05313	+	12.4592i	0.269628	+	0.554978i
$505$			1.98977i			0.0885435i
$506$	−17.3850	−	33.3127i	−0.772855	−	1.48093i
$507$	15.1310	+	15.4947i	0.671993	+	0.688144i
$508$	19.8353	−	10.2258i	0.880050	−	0.453697i
$509$	9.97524	−	24.9169i	0.442145	−	1.10442i	−0.525205	−	0.850976i	$-0.676011\pi$
$509$	9.97524	−	24.9169i	0.442145	−	1.10442i	0.967349	−	0.253448i	$-0.0815646\pi$
$510$	13.5063	−	10.8847i	0.598070	−	0.481981i
$511$	−44.7528	+	10.8569i	−1.97975	+	0.480282i
$512$	−18.3137	−	8.36358i	−0.809358	−	0.369621i
$513$	−10.7982	+	0.386510i	−0.476751	+	0.0170648i
$514$	5.29542	−	36.8304i	0.233571	−	1.62452i
$515$	−3.29287	+	3.45346i	−0.145101	+	0.152178i
$516$	2.23501	−	3.21921i	0.0983908	−	0.141718i
$517$	−0.851083	+	0.0405421i	−0.0374306	+	0.00178304i
$518$	24.1677	−	1.15125i	1.06187	−	0.0505830i
$519$	−17.9472	−	1.49799i	−0.787794	−	0.0657544i
$520$	−0.401460	+	0.421039i	−0.0176052	+	0.0184638i
$521$	−0.983411	+	6.83977i	−0.0430840	+	0.299656i	0.956874	+	0.290503i	$0.0938226\pi$
$521$	−0.983411	+	6.83977i	−0.0430840	+	0.299656i	−0.999958	+	0.00915296i	$0.997086\pi$
$522$	−30.3824	−	27.6166i	−1.32980	−	1.20874i
$523$	−39.2907	−	17.9435i	−1.71806	−	0.784613i	−0.995652	−	0.0931477i	$-0.970307\pi$
$523$	−39.2907	−	17.9435i	−1.71806	−	0.784613i	−0.722410	−	0.691465i	$-0.756966\pi$
$524$	7.45934	−	1.80962i	0.325863	−	0.0790535i
$525$	−4.64648	−	29.7904i	−0.202789	−	1.30016i
$526$	8.25366	−	20.6167i	0.359877	−	0.898929i
$527$	35.3891	−	18.2443i	1.54157	−	0.794735i
$528$	9.79334	−	34.8869i	0.426200	−	1.51826i
$529$	9.76295	+	20.8251i	0.424476	+	0.905439i
$530$		−	13.6538i		−	0.593084i
$531$	18.4158	+	12.4628i	0.799178	+	0.540838i
$532$	1.52862	+	10.6318i	0.0662739	+	0.460945i
$533$	0.717837	+	0.511169i	0.0310930	+	0.0221412i
$534$	32.4961	−	17.2465i	1.40624	−	0.746330i
$535$	−4.07161	−	5.71778i	−0.176031	−	0.247201i
$536$	1.71361	+	4.95114i	0.0740165	+	0.213857i
$537$	16.8351	−	1.81041i	0.726489	−	0.0781250i
$538$	−17.2774	−	16.4740i	−0.744882	−	0.710244i
$539$	21.8495	+	25.2157i	0.941124	+	1.08612i
$540$	−4.62197	+	1.29799i	−0.198898	+	0.0558565i
$541$	−24.4970	+	15.7433i	−1.05321	+	0.676855i	−0.948219	−	0.317618i	$-0.897117\pi$
$541$	−24.4970	+	15.7433i	−1.05321	+	0.676855i	−0.104989	+	0.994473i	$0.533481\pi$
$542$	16.9830	+	5.87787i	0.729482	+	0.252476i
$543$	−4.08311	−	6.88129i	−0.175223	−	0.295305i
$544$	−32.1224	+	40.8469i	−1.37723	+	1.75130i
$545$	1.76997	−	0.612591i	0.0758170	−	0.0262405i
$546$	8.07260	−	2.90222i	0.345476	−	0.124203i
$547$	−5.67335	−	23.3859i	−0.242575	−	0.999907i	−0.954633	−	0.297786i	$-0.903752\pi$
$547$	−5.67335	−	23.3859i	−0.242575	−	0.999907i	0.712058	−	0.702121i	$-0.247763\pi$
$548$	0.787781	+	1.72500i	0.0336523	+	0.0736883i
$549$	−28.3399	−	12.1341i	−1.20952	−	0.517871i
$550$	−19.1762	+	29.8388i	−0.817678	+	1.27233i
$551$	7.78228	+	13.4793i	0.331536	+	0.574237i
$552$	−3.10233	+	9.47952i	−0.132044	+	0.403475i
$553$	−31.0787	+	53.8299i	−1.32160	+	2.28908i
$554$	8.23057	+	15.9651i	0.349683	+	0.678291i
$555$	0.534981	−	4.06441i	0.0227087	−	0.172524i
$556$	11.9175	−	16.7358i	0.505416	−	0.709757i
$557$	30.6458	+	8.99841i	1.29850	+	0.381275i	0.856689	−	0.515833i	$-0.172517\pi$
$557$	30.6458	+	8.99841i	1.29850	+	0.381275i	0.441813	+	0.897107i	$0.354336\pi$
$558$	−27.3553	+	1.95794i	−1.15804	+	0.0828861i
$559$	0.896709	+	0.777002i	0.0379267	+	0.0328637i
$560$	−4.79894	−	11.9872i	−0.202792	−	0.506551i
$561$	−51.5356	−	28.9401i	−2.17583	−	1.22185i
$562$	−5.46000	−	28.3292i	−0.230316	−	1.19499i
$563$	0.520129	+	10.9188i	0.0219208	+	0.460175i	0.982966	+	0.183785i	$0.0588350\pi$
$563$	0.520129	+	10.9188i	0.0219208	+	0.460175i	−0.961046	+	0.276390i	$0.910862\pi$
$564$	−0.338606	−	0.315237i	−0.0142579	−	0.0132739i
$565$	−0.132588	+	0.383088i	−0.00557802	+	0.0161166i
$566$	−35.0276	+	10.2850i	−1.47232	+	0.432312i
$567$	−33.9829	−	6.54597i	−1.42715	−	0.274905i
$568$	0.251018	−	0.289690i	0.0105325	−	0.0121551i
$569$	16.2143	−	1.54828i	0.679738	−	0.0649071i	0.250525	−	0.968110i	$-0.419397\pi$
$569$	16.2143	−	1.54828i	0.679738	−	0.0649071i	0.429213	+	0.903203i	$0.358791\pi$
$570$	4.52663	+	0.161550i	0.189600	+	0.00676658i
$571$	0.370369	−	3.87867i	0.0154994	−	0.162317i	−0.984408	−	0.175898i	$-0.943717\pi$
$571$	0.370369	−	3.87867i	0.0154994	−	0.162317i	0.999908	+	0.0135809i	$0.00432306\pi$
$572$	−3.76431	−	1.50700i	−0.157394	−	0.0630109i
$573$	7.33412	+	35.7531i	0.306387	+	1.49361i
$574$	−7.61747	+	4.39795i	−0.317947	+	0.183567i
$575$	12.5049	−	17.7475i	0.521489	−	0.740120i
$576$	5.70583	−	3.11601i	0.237743	−	0.129834i
$577$	23.9241	+	15.3751i	0.995972	+	0.640072i	0.933726	−	0.357989i	$-0.116537\pi$
$577$	23.9241	+	15.3751i	0.995972	+	0.640072i	0.0622458	+	0.998061i	$0.480174\pi$
$578$	52.4650	+	66.7146i	2.18225	+	2.77496i
$579$	−21.9131	+	3.41784i	−0.910676	+	0.142040i
$580$	4.77219	+	5.00493i	0.198154	+	0.207818i
$581$	−10.5273	+	7.49643i	−0.436745	+	0.311004i
$582$	−8.41821	−	12.7618i	−0.348946	−	0.528992i
$583$	−43.1909	+	17.2910i	−1.78878	+	0.716121i
$584$	−4.05137	−	13.7977i	−0.167647	−	0.570953i
$585$	−0.241106	−	1.43334i	−0.00996849	−	0.0592614i
$586$	4.55762	+	7.09180i	0.188274	+	0.292960i
$587$	12.1250	−	23.5191i	0.500451	−	0.970739i	−0.494385	−	0.869243i	$-0.664607\pi$
$587$	12.1250	−	23.5191i	0.500451	−	0.970739i	0.994836	−	0.101496i	$-0.0323628\pi$
$588$	−1.50684	+	18.0533i	−0.0621412	+	0.744504i
$589$	10.1035	+	2.45108i	0.416307	+	0.100995i
$590$	−7.32726	−	5.76222i	−0.301658	−	0.237227i
$591$	−26.0911	−	13.0594i	−1.07324	−	0.537192i
$592$	1.59698	+	16.7244i	0.0656357	+	0.687368i
$593$	10.3740	−	35.3306i	0.426009	−	1.45085i	−0.414995	−	0.909824i	$-0.636217\pi$
$593$	10.3740	−	35.3306i	0.426009	−	1.45085i	0.841004	−	0.541029i	$-0.181965\pi$
$594$	24.7870	+	32.2977i	1.01702	+	1.32519i
$595$	−20.8472	+	2.99737i	−0.854651	+	0.122880i
$596$	0.489811	−	10.2824i	0.0200634	−	0.421183i
$597$	2.09948	+	8.22480i	0.0859262	+	0.336619i
$598$	5.63160	+	2.53797i	0.230293	+	0.103785i
$599$	−16.3246	−	9.42499i	−0.667004	−	0.385095i	0.127937	−	0.991782i	$-0.459165\pi$
$599$	−16.3246	−	9.42499i	−0.667004	−	0.385095i	−0.794940	+	0.606688i	$0.792498\pi$
$600$	9.22298	−	1.89193i	0.376527	−	0.0772379i
$601$	13.5827	−	10.6816i	0.554051	−	0.435711i	−0.301472	−	0.953475i	$-0.597478\pi$
$601$	13.5827	−	10.6816i	0.554051	−	0.435711i	0.855523	+	0.517764i	$0.173236\pi$
$602$	−10.7727	+	4.91973i	−0.439063	+	0.200513i
$603$	−12.4686	−	3.98506i	−0.507761	−	0.162284i
$604$	−5.48497	+	12.0104i	−0.223180	+	0.488696i
$605$	−4.97213	−	0.958299i	−0.202146	−	0.0389604i
$606$	8.37892	+	3.70640i	0.340370	+	0.150562i
$607$	−1.99971	+	8.24293i	−0.0811658	+	0.334570i	−0.997888	−	0.0649547i	$-0.979310\pi$
$607$	−1.99971	+	8.24293i	−0.0811658	+	0.334570i	0.916722	+	0.399525i	$0.130825\pi$
$608$	−13.3238	+	2.56796i	−0.540353	+	0.104144i
$609$	14.6143	+	47.6615i	0.592202	+	1.93134i
$610$	11.4867	+	5.92179i	0.465082	+	0.239766i
$611$	0.105855	−	0.0917238i	0.00428243	−	0.00371075i
$612$	−8.30767	−	30.9981i	−0.335818	−	1.25303i
$613$	−16.6964	−	2.40059i	−0.674363	−	0.0969587i	−0.203378	−	0.979100i	$-0.565192\pi$
$613$	−16.6964	−	2.40059i	−0.674363	−	0.0969587i	−0.470985	+	0.882141i	$0.656101\pi$
$614$	−7.83510	+	40.6524i	−0.316199	+	1.64060i
$615$	0.504198	+	1.40244i	0.0203312	+	0.0565519i
$616$	−14.3195	+	13.6536i	−0.576947	+	0.550118i
$617$	−45.2101	−	4.31704i	−1.82009	−	0.173798i	−0.871520	−	0.490361i	$-0.836865\pi$
$617$	−45.2101	−	4.31704i	−1.82009	−	0.173798i	−0.948571	+	0.316563i	$0.897471\pi$
$618$	8.40882	+	20.2992i	0.338252	+	0.816552i
$619$	17.0176	+	0.810648i	0.683995	+	0.0325827i	0.386703	−	0.922204i	$-0.373614\pi$
$619$	17.0176	+	0.810648i	0.683995	+	0.0325827i	0.297291	+	0.954787i	$0.403917\pi$
$620$	4.61925			0.185514
$621$	−14.3160	−	20.3974i	−0.574481	−	0.818518i
$622$	39.5333			1.58514
$623$	−44.6178	−	2.12541i	−1.78758	−	0.0851527i
$624$	2.27966	+	5.50317i	0.0912593	+	0.220303i
$625$	−18.0459	−	1.72317i	−0.721834	−	0.0689268i
$626$	−24.8215	+	23.6672i	−0.992066	+	0.945933i
$627$	−5.22144	−	14.5236i	−0.208524	−	0.580016i
$628$	−1.75853	+	9.12412i	−0.0701730	+	0.364092i
$629$	27.1251	+	3.90000i	1.08155	+	0.155503i
$630$	14.0134	+	3.75410i	0.558309	+	0.149567i
$631$	−0.534040	+	0.462748i	−0.0212598	+	0.0184217i	−0.665426	−	0.746464i	$-0.731750\pi$
$631$	−0.534040	+	0.462748i	−0.0212598	+	0.0184217i	0.644166	+	0.764886i	$0.277205\pi$
$632$	−17.2521	−	8.89406i	−0.686250	−	0.353787i
$633$	10.7285	+	34.9889i	0.426421	+	1.39068i
$634$	−51.2515	+	9.87793i	−2.03546	+	0.392303i
$635$	−2.69383	+	11.1041i	−0.106901	+	0.440653i
$636$	−23.1013	−	10.2188i	−0.916027	−	0.405203i
$637$	−5.38569	−	1.03801i	−0.213389	−	0.0411273i
$638$	24.3625	−	53.3464i	0.964521	−	2.11201i
$639$	0.203619	+	0.935785i	0.00805505	+	0.0370191i
$640$	5.68593	−	2.59668i	0.224756	−	0.102643i
$641$	25.7812	−	20.2746i	1.01830	−	0.800797i	0.0381900	−	0.999270i	$-0.487841\pi$
$641$	25.7812	−	20.2746i	1.01830	−	0.800797i	0.980106	+	0.198473i	$0.0635984\pi$
$642$	−31.6619	+	6.49489i	−1.24960	+	0.256333i
$643$	−14.4108	−	8.32011i	−0.568308	−	0.328113i	0.188165	−	0.982137i	$-0.439746\pi$
$643$	−14.4108	−	8.32011i	−0.568308	−	0.328113i	−0.756473	+	0.654024i	$0.773079\pi$
$644$	−18.6404	+	16.3156i	−0.734535	+	0.642927i
$645$	0.496295	+	1.94425i	0.0195416	+	0.0765548i
$646$	−1.44072	+	30.2445i	−0.0566845	+	1.18995i
$647$	4.37389	−	0.628871i	0.171955	−	0.0247235i	−0.0557992	−	0.998442i	$-0.517771\pi$
$647$	4.37389	−	0.628871i	0.171955	−	0.0247235i	0.227755	+	0.973719i	$0.426862\pi$
$648$	1.53685	−	10.6970i	0.0603731	−	0.420218i
$649$	−8.94839	+	30.4754i	−0.351255	+	1.19626i
$650$	−0.554247	−	5.80434i	−0.0217394	−	0.227665i
$651$	29.7773	+	14.9045i	1.16707	+	0.584153i
$652$	9.96749	+	7.83852i	0.390357	+	0.306980i
$653$	39.2063	+	9.51134i	1.53426	+	0.372208i	0.911863	−	0.410494i	$-0.134644\pi$
$653$	39.2063	+	9.51134i	1.53426	+	0.372208i	0.622397	+	0.782701i	$0.286159\pi$
$654$	0.717347	−	8.59443i	0.0280505	−	0.336069i
$655$	−1.80087	+	3.49320i	−0.0703659	+	0.136491i
$656$	−3.30204	−	5.13808i	−0.128923	−	0.200608i
$657$	33.6632	+	12.5537i	1.31333	+	0.489766i
$658$	0.393873	+	1.34141i	0.0153548	+	0.0522936i
$659$	−15.6766	+	6.27595i	−0.610672	+	0.244476i	−0.656321	−	0.754481i	$-0.727888\pi$
$659$	−15.6766	+	6.27595i	−0.610672	+	0.244476i	0.0456496	+	0.998958i	$0.485464\pi$
$660$	−3.77585	−	5.72408i	−0.146975	−	0.222810i
$661$	4.72808	−	3.36685i	0.183901	−	0.130955i	−0.484399	−	0.874847i	$-0.660962\pi$
$661$	4.72808	−	3.36685i	0.183901	−	0.130955i	0.668300	+	0.743892i	$0.267022\pi$
$662$	−25.8758	−	27.1378i	−1.00569	−	1.05474i
$663$	9.60012	−	1.49736i	0.372838	−	0.0581525i
$664$	−2.49466	−	3.17221i	−0.0968114	−	0.123106i
$665$	−4.62657	−	2.97332i	−0.179411	−	0.115300i
$666$	−16.1187	−	9.82371i	−0.624587	−	0.380661i
$667$	−16.2893	+	31.9879i	−0.630725	+	1.23858i
$668$	8.64429	−	4.99078i	0.334458	−	0.193099i
$669$	−7.12108	−	34.7145i	−0.275317	−	1.34214i
$670$	5.09426	+	2.03943i	0.196808	+	0.0787902i
$671$	4.18573	−	43.8349i	0.161588	−	1.69223i
$672$	−43.4327	−	1.55006i	−1.67545	−	0.0597948i
$673$	−8.70790	+	0.831504i	−0.335665	+	0.0320521i	−0.261528	−	0.965196i	$-0.584226\pi$
$673$	−8.70790	+	0.831504i	−0.335665	+	0.0320521i	−0.0741371	+	0.997248i	$0.523620\pi$
$674$	30.2048	−	34.8582i	1.16345	−	1.34269i
$675$	−10.0239	+	21.2800i	−0.385821	+	0.819067i
$676$	−16.1160	+	4.73207i	−0.619844	+	0.182003i
$677$	0.831292	−	2.40186i	0.0319491	−	0.0923110i	−0.927898	−	0.372833i	$-0.878386\pi$
$677$	0.831292	−	2.40186i	0.0319491	−	0.0923110i	0.959848	+	0.280522i	$0.0905076\pi$
$678$	1.36621	+	1.27192i	0.0524690	+	0.0488478i
$679$	0.883241	+	18.5415i	0.0338957	+	0.711558i
$680$	−1.24467	−	6.45798i	−0.0477311	−	0.247652i
$681$	3.99320	+	2.24241i	0.153020	+	0.0859293i
$682$	−14.5593	−	36.3674i	−0.557505	−	1.39258i
$683$	−24.5834	−	21.3017i	−0.940659	−	0.815086i	0.0422633	−	0.999107i	$-0.486543\pi$
$683$	−24.5834	−	21.3017i	−0.940659	−	0.815086i	−0.982922	+	0.184021i	$0.941089\pi$
$684$	3.66117	−	7.53784i	0.139988	−	0.288216i
$685$	−0.931642	−	0.273555i	−0.0355962	−	0.0104520i
$686$	3.20678	−	4.50329i	0.122435	−	0.171936i
$687$	1.42229	−	10.8056i	0.0542638	−	0.412258i
$688$	−3.76820	−	7.30928i	−0.143661	−	0.278664i
$689$	3.82394	−	6.62326i	0.145681	−	0.252326i
$690$	5.37553	+	8.95723i	0.204643	+	0.340996i
$691$	−16.1522	−	27.9765i	−0.614460	−	1.06428i	−0.990479	−	0.137663i	$-0.956041\pi$
$691$	−16.1522	−	27.9765i	−0.614460	−	1.06428i	0.376019	−	0.926612i	$-0.377293\pi$
$692$	7.55135	−	11.7501i	0.287059	−	0.446673i
$693$	−5.87116	−	49.0826i	−0.223027	−	1.86449i
$694$	−17.2199	−	37.7063i	−0.653658	−	1.43131i
$695$	2.48009	+	10.2231i	0.0940753	+	0.387784i
$696$	−14.6491	+	5.26657i	−0.555273	+	0.199629i
$697$	−9.41456	+	3.25841i	−0.356602	+	0.123421i
$698$	9.78260	−	12.4396i	0.370277	−	0.470845i
$699$	13.4869	+	22.7296i	0.510121	+	0.859711i
$700$	22.0973	+	7.64795i	0.835199	+	0.289065i
$701$	−29.4895	+	18.9518i	−1.11380	+	0.715798i	−0.962119	−	0.272630i	$-0.912106\pi$
$701$	−29.4895	+	18.9518i	−1.11380	+	0.715798i	−0.151685	+	0.988429i	$0.548470\pi$
$702$	−6.48492	−	1.65463i	−0.244758	−	0.0624501i
$703$	4.68604	+	5.40797i	0.176737	+	0.203966i
$704$	6.72071	+	6.40818i	0.253296	+	0.241517i
$705$	0.235517	−	0.0253270i	0.00887009	−	0.000953869i
$706$	−13.9327	−	40.2560i	−0.524366	−	1.51506i
$707$	−6.45277	−	9.06165i	−0.242681	−	0.340798i
$708$	−15.2332	+	8.08464i	−0.572498	+	0.303839i
$709$	17.9176	+	12.7591i	0.672911	+	0.479178i	0.864720	−	0.502255i	$-0.167496\pi$
$709$	17.9176	+	12.7591i	0.672911	+	0.479178i	−0.191809	+	0.981432i	$0.561435\pi$
$710$	−0.0571339	−	0.397375i	−0.00214420	−	0.0149132i
$711$	43.6184	−	21.1913i	1.63582	−	0.794737i
$712$		−	13.9485i		−	0.522741i
$713$	7.95535	+	22.6195i	0.297930	+	0.847106i
$714$	−26.2108	+	93.3709i	−0.980913	+	3.49432i
$715$	1.84532	−	0.951326i	0.0690109	−	0.0355776i
$716$	−4.88060	+	12.1912i	−0.182397	+	0.455605i
$717$	2.80089	+	17.9576i	0.104601	+	0.670638i
$718$	20.5706	−	4.99037i	0.767688	−	0.186239i
$719$	34.9109	+	15.9433i	1.30196	+	0.594583i	0.941128	−	0.338050i	$-0.109767\pi$
$719$	34.9109	+	15.9433i	1.30196	+	0.594583i	0.360827	+	0.932633i	$0.382495\pi$
$720$	−2.14080	+	9.84358i	−0.0797829	+	0.366849i
$721$	3.79664	−	26.4062i	0.141394	−	0.983418i
$722$	18.5179	−	19.4210i	0.689165	−	0.722776i
$723$	−12.6116	−	1.05265i	−0.469030	−	0.0391483i
$724$	6.19856	−	0.295274i	0.230368	−	0.0109738i
$725$	33.8457	−	1.61227i	1.25700	−	0.0598781i
$726$	−13.2971	+	19.1526i	−0.493503	+	0.710820i
$727$	−28.4361	+	29.8230i	−1.05464	+	1.10607i	−0.0604761	+	0.998170i	$0.519262\pi$
$727$	−28.4361	+	29.8230i	−1.05464	+	1.10607i	−0.994161	+	0.107902i	$0.965587\pi$
$728$	0.462878	−	3.21939i	0.0171554	−	0.119318i
$729$	19.0949	+	19.0889i	0.707218	+	0.706995i
$730$	−13.6999	−	6.25655i	−0.507057	−	0.231565i
$731$	−13.0355	+	3.16239i	−0.482137	+	0.116965i
$732$	18.6162	−	15.0027i	0.688074	−	0.554515i
$733$	−5.53644	+	13.8294i	−0.204493	+	0.510799i	−0.994792	−	0.101922i	$-0.967501\pi$
$733$	−5.53644	+	13.8294i	−0.204493	+	0.510799i	0.790299	+	0.612721i	$0.209925\pi$
$734$	35.0633	−	18.0764i	1.29421	−	0.667212i
$735$	−6.48058	−	6.63634i	−0.239040	−	0.244785i
$736$	−21.7084	−	22.5407i	−0.800182	−	0.830862i
$737$		−	18.6973i		−	0.688724i
$738$	6.84488	+	0.489194i	0.251963	+	0.0180075i
$739$	−1.85257	−	12.8849i	−0.0681480	−	0.473979i	−0.995106	−	0.0988142i	$-0.968495\pi$
$739$	−1.85257	−	12.8849i	−0.0681480	−	0.473979i	0.926958	−	0.375165i	$-0.122414\pi$
$740$	2.58983	+	1.84421i	0.0952039	+	0.0677944i
$741$	2.15055	+	1.34611i	0.0790026	+	0.0494506i
$742$	44.2790	+	62.1812i	1.62553	+	2.28274i
$743$	4.62943	+	13.3759i	0.169837	+	0.490713i	0.997512	−	0.0704953i	$-0.0224580\pi$
$743$	4.62943	+	13.3759i	0.169837	+	0.490713i	−0.827675	+	0.561208i	$0.810337\pi$
$744$	−4.20647	+	9.50941i	−0.154217	+	0.348632i
$745$	3.81460	+	3.63722i	0.139756	+	0.133257i
$746$	41.9911	+	48.4603i	1.53740	+	1.77426i
$747$	10.0798	−	0.240474i	0.368801	−	0.00879848i
$748$	38.5625	−	24.7826i	1.40999	−	0.906143i
$749$	37.0852	+	12.8353i	1.35506	+	0.468992i
$750$	10.1609	−	18.0941i	0.371023	−	0.660705i
$751$	18.1504	−	23.0801i	0.662318	−	0.842206i	−0.332581	−	0.943075i	$-0.607920\pi$
$751$	18.1504	−	23.0801i	0.662318	−	0.842206i	0.994900	+	0.100868i	$0.0321620\pi$
$752$	−0.917372	+	0.317505i	−0.0334531	+	0.0115782i
$753$	0.765785	−	4.24510i	0.0279067	−	0.154700i
$754$	2.27288	+	9.36894i	0.0827735	+	0.341197i
$755$	−2.80839	−	6.14953i	−0.102208	−	0.223804i
$756$	16.8397	−	20.9001i	0.612453	−	0.760130i
$757$	13.7741	−	21.4329i	0.500628	−	0.778993i	−0.495340	−	0.868699i	$-0.664957\pi$
$757$	13.7741	−	21.4329i	0.500628	−	0.778993i	0.995968	+	0.0897066i	$0.0285929\pi$
$758$	−11.0640	−	19.1635i	−0.401864	−	0.696049i
$759$	21.5268	−	28.3476i	0.781372	−	1.02895i
$760$	0.858675	−	1.48727i	0.0311474	−	0.0539489i
$761$	−0.503166	−	0.976006i	−0.0182398	−	0.0353802i	0.879540	−	0.475826i	$-0.157851\pi$
$761$	−0.503166	−	0.976006i	−0.0182398	−	0.0353802i	−0.897779	+	0.440446i	$0.854820\pi$
$762$	41.7416	+	32.0277i	1.51214	+	1.16024i
$763$	−6.07402	+	8.52977i	−0.219894	+	0.308799i
$764$	−27.1592	−	7.97467i	−0.982586	−	0.288513i
$765$	14.7805	+	7.17896i	0.534390	+	0.259556i
$766$	−22.2813	−	19.3068i	−0.805055	−	0.697584i
$767$	−1.94055	−	4.84727i	−0.0700693	−	0.175025i
$768$	−0.432786	−	36.2868i	−0.0156168	−	1.30939i
$769$	−4.25832	−	22.0942i	−0.153559	−	0.796739i	−0.974268	−	0.225393i	$-0.927633\pi$
$769$	−4.25832	−	22.0942i	−0.153559	−	0.796739i	0.820709	−	0.571346i	$-0.193579\pi$
$770$	0.986001	+	20.6987i	0.0355330	+	0.745930i
$771$	33.6985	−	10.3329i	1.21362	−	0.372129i
$772$	5.62564	−	16.2542i	0.202471	−	0.585002i
$773$	−21.4593	+	6.30101i	−0.771836	+	0.226632i	−0.643858	−	0.765145i	$-0.722667\pi$
$773$	−21.4593	+	6.30101i	−0.771836	+	0.226632i	−0.127979	+	0.991777i	$0.540849\pi$
$774$	9.11171	+	1.53172i	0.327514	+	0.0550564i
$775$	14.8217	−	17.1051i	0.532410	−	0.614434i
$776$	−5.77023	+	0.550990i	−0.207139	+	0.0197794i
$777$	10.7444	+	20.2447i	0.385454	+	0.726276i
$778$	−1.95047	+	20.4262i	−0.0699276	+	0.732315i
$779$	−2.41507	−	0.966849i	−0.0865289	−	0.0346410i
$780$	1.06957	+	0.355957i	0.0382969	+	0.0127453i
$781$	−1.18466	+	0.683962i	−0.0423904	+	0.0244741i
$782$	−60.3014	+	35.2176i	−2.15637	+	1.25938i
$783$	11.3978	−	37.1855i	0.407324	−	1.32890i
$784$	31.9792	+	20.5518i	1.14212	+	0.733993i
$785$	−2.94100	−	3.73979i	−0.104969	−	0.133479i
$786$	11.3554	+	14.0904i	0.405032	+	0.502587i
$787$	8.31925	+	8.72498i	0.296549	+	0.311012i	0.855105	−	0.518455i	$-0.173493\pi$
$787$	8.31925	+	8.72498i	0.296549	+	0.311012i	−0.558556	+	0.829467i	$0.688644\pi$
$788$	18.4324	−	13.1257i	0.656628	−	0.467583i
$789$	20.9991	−	1.25148i	0.747589	−	0.0445537i
$790$	−18.8724	+	7.55538i	−0.671451	+	0.268808i
$791$	−0.638523	−	2.17461i	−0.0227033	−	0.0773202i
$792$	15.2223	−	2.56058i	0.540901	−	0.0909862i
$793$	3.91353	+	6.08958i	0.138974	+	0.216247i
$794$	−0.779663	+	1.51234i	−0.0276692	+	0.0536708i
$795$	11.7001	−	5.51283i	0.414960	−	0.195520i
$796$	−6.39774	−	1.55207i	−0.226762	−	0.0550118i
$797$	−7.37897	−	5.80289i	−0.261377	−	0.205549i	0.478867	−	0.877887i	$-0.341048\pi$
$797$	−7.37897	−	5.80289i	−0.261377	−	0.205549i	−0.740244	+	0.672338i	$0.765290\pi$
$798$	−21.1387	+	13.9440i	−0.748303	+	0.493613i
$799$	0.150517	+	1.57629i	0.00532492	+	0.0557651i
$800$	−8.32233	+	28.3432i	−0.294239	+	1.00209i
$801$	27.8993	+	20.8829i	0.985773	+	0.737859i
$802$	−43.8608	+	6.30623i	−1.54878	+	0.222681i
$803$	−2.44182	+	51.2600i	−0.0861698	+	1.80893i
$804$	7.26325	−	7.09278i	0.256155	−	0.250143i
$805$	−0.0633193	−	12.6837i	−0.00223171	−	0.447040i
$806$	5.57689	+	3.21982i	0.196438	+	0.113413i
$807$	7.14085	−	21.4567i	0.251370	−	0.755312i
$808$	2.73057	−	2.14735i	0.0960612	−	0.0755434i
$809$	−7.44835	+	3.40155i	−0.261870	+	0.119592i	−0.542024	−	0.840363i	$-0.682342\pi$
$809$	−7.44835	+	3.40155i	−0.261870	+	0.119592i	0.280154	+	0.959955i	$0.409615\pi$
$810$	−7.41290	−	8.55312i	−0.260463	−	0.300526i
$811$	12.1769	−	26.6638i	0.427590	−	0.936291i	−0.566122	−	0.824322i	$-0.691557\pi$
$811$	12.1769	−	26.6638i	0.427590	−	0.936291i	0.993712	−	0.111970i	$-0.0357159\pi$
$812$	−37.9640	−	7.31696i	−1.33228	−	0.256775i
$813$	1.82020	+	16.9262i	0.0638372	+	0.593627i
$814$	6.35664	−	26.2024i	0.222800	−	0.918395i
$815$	−6.37526	+	1.22873i	−0.223316	+	0.0430405i
$816$	−65.6269	−	15.0945i	−2.29740	−	0.528414i
$817$	−3.11322	−	1.60498i	−0.108918	−	0.0561511i
$818$	−31.1406	+	26.9835i	−1.08881	+	0.943456i
$819$	5.74632	+	5.74571i	0.200793	+	0.200771i
$820$	−1.14406	−	0.164491i	−0.0399523	−	0.00574427i
$821$	6.03426	−	31.3087i	0.210597	−	1.09268i	−0.710603	−	0.703593i	$-0.751578\pi$
$821$	6.03426	−	31.3087i	0.210597	−	1.09268i	0.921200	−	0.389088i	$-0.127210\pi$
$822$	−2.88734	+	3.41359i	−0.100708	+	0.119063i
$823$	18.2680	−	17.4185i	0.636783	−	0.607171i	−0.301322	−	0.953522i	$-0.597428\pi$
$823$	18.2680	−	17.4185i	0.636783	−	0.607171i	0.938105	+	0.346351i	$0.112579\pi$
$824$	8.29286	+	0.791872i	0.288896	+	0.0275862i
$825$	−33.3118	−	4.38469i	−1.15977	−	0.152655i
$826$	52.0560	+	2.47973i	1.81126	+	0.0862809i
$827$	−11.5329			−0.401037			−0.200518	−	0.979690i	$-0.564263\pi$
$827$	−11.5329			−0.401037			−0.200518	+	0.979690i	$0.564263\pi$
$828$	19.1782	−	2.39122i	0.666488	−	0.0831008i
$829$	27.0765			0.940405			0.470203	−	0.882558i	$-0.344181\pi$
$829$	27.0765			0.940405			0.470203	+	0.882558i	$0.344181\pi$
$830$	−4.22188	−	0.201113i	−0.146544	−	0.00698073i
$831$	−10.3575	+	13.4989i	−0.359298	+	0.468271i
$832$	−1.51962	−	0.145106i	−0.0526832	−	0.00503064i
$833$	44.8760	−	42.7892i	1.55486	−	1.48256i
$834$	47.6692	+	8.59918i	1.65065	+	0.297765i
$835$	−0.967212	+	5.01837i	−0.0334717	+	0.173668i
$836$	11.8478	+	1.70346i	0.409765	+	0.0589153i
$837$	−12.7227	−	22.6506i	−0.439761	−	0.782919i
$838$	23.6358	−	20.4805i	0.816486	−	0.707489i
$839$	34.8493	+	17.9661i	1.20313	+	0.620257i	0.938896	−	0.344201i	$-0.111850\pi$
$839$	34.8493	+	17.9661i	1.20313	+	0.620257i	0.264235	+	0.964458i	$0.414881\pi$
$840$	3.74804	−	4.02589i	0.129320	−	0.138906i
$841$	−26.5364	+	5.11447i	−0.915048	+	0.176361i
$842$	15.7149	−	64.7777i	0.541571	−	2.23239i
$843$	22.0711	−	16.1169i	0.760168	−	0.555094i
$844$	−27.8698	−	5.37147i	−0.959319	−	0.184894i
$845$	3.57257	−	7.82283i	0.122900	−	0.269114i
$846$	0.332053	−	1.03894i	0.0114162	−	0.0357195i
$847$	25.7514	−	11.7603i	0.884829	−	0.404088i
$848$	−41.6651	+	32.7658i	−1.43079	+	1.12518i
$849$	−22.9560	−	25.8629i	−0.787848	−	0.887612i
$850$	57.0858	+	32.9585i	1.95803	+	1.13047i
$851$	−4.57044	+	15.8579i	−0.156673	+	0.543603i
$852$	−0.715092	−	0.200738i	−0.0244987	−	0.00687718i
$853$	2.21807	−	46.5631i	0.0759454	−	1.59429i	−0.563937	−	0.825817i	$-0.690714\pi$
$853$	2.21807	−	46.5631i	0.0759454	−	1.59429i	0.639883	−	0.768472i	$-0.278983\pi$
$854$	−71.5160	+	10.2824i	−2.44723	+	0.351858i
$855$	1.68923	+	3.94415i	0.0577703	+	0.134887i
$856$	−3.45249	+	11.7581i	−0.118004	+	0.401883i
$857$	−1.70902	−	17.8977i	−0.0583790	−	0.611372i	−0.976565	−	0.215223i	$-0.930952\pi$
$857$	−1.70902	−	17.8977i	−0.0583790	−	0.611372i	0.918186	−	0.396150i	$-0.129654\pi$
$858$	−0.568712	−	9.54270i	−0.0194155	−	0.325782i
$859$	42.3897	+	33.3357i	1.44632	+	1.13740i	0.965444	+	0.260609i	$0.0839233\pi$
$859$	42.3897	+	33.3357i	1.44632	+	1.13740i	0.480875	+	0.876789i	$0.340319\pi$
$860$	−1.51235	−	0.366893i	−0.0515708	−	0.0125109i
$861$	−6.84427	−	4.75179i	−0.233252	−	0.161941i
$862$	−2.60772	+	5.05827i	−0.0888193	+	0.172285i
$863$	−11.8456	−	18.4322i	−0.403230	−	0.627438i	0.578954	−	0.815360i	$-0.303461\pi$
$863$	−11.8456	−	18.4322i	−0.403230	−	0.627438i	−0.982184	+	0.187922i	$0.939825\pi$
$864$	27.3851	+	19.9929i	0.931660	+	0.680172i
$865$	2.01482	+	6.86185i	0.0685060	+	0.233310i
$866$	52.3743	−	20.9675i	1.77975	−	0.712504i
$867$	−35.9854	+	71.8944i	−1.22213	+	2.44166i
$868$	−21.0366	+	14.9801i	−0.714030	+	0.508459i
$869$	47.7996	+	50.1308i	1.62149	+	1.70057i
$870$	−5.87865	+	15.2073i	−0.199305	+	0.515576i
$871$	1.89998	+	2.41602i	0.0643783	+	0.0818636i
$872$	−2.75080	−	1.76783i	−0.0931539	−	0.0598664i
$873$	7.53678	−	12.3663i	0.255081	−	0.418537i
$874$	−17.9222	−	3.36151i	−0.606226	−	0.113705i
$875$	−21.8208	+	12.5982i	−0.737677	+	0.425898i
$876$	−20.8390	+	18.4968i	−0.704085	+	0.624950i
$877$	−11.9736	−	4.79350i	−0.404319	−	0.161865i	0.160584	−	0.987022i	$-0.448662\pi$
$877$	−11.9736	−	4.79350i	−0.404319	−	0.161865i	−0.564903	+	0.825157i	$0.691086\pi$
$878$	−1.48852	+	15.5885i	−0.0502351	+	0.526085i
$879$	−4.23687	+	6.76885i	−0.142906	+	0.228308i
$880$	−14.3238	+	1.36776i	−0.482855	+	0.0461071i
$881$	33.9904	−	39.2270i	1.14516	−	1.32159i	0.205831	−	0.978588i	$-0.434010\pi$
$881$	33.9904	−	39.2270i	1.14516	−	1.32159i	0.939334	−	0.343003i	$-0.111444\pi$
$882$	−40.0172	+	14.9280i	−1.34745	+	0.502654i
$883$	5.75369	−	1.68944i	0.193627	−	0.0568540i	−0.183481	−	0.983023i	$-0.558737\pi$
$883$	5.75369	−	1.68944i	0.193627	−	0.0568540i	0.377108	+	0.926169i	$0.376918\pi$
$884$	−2.46460	+	7.12098i	−0.0828933	+	0.239505i
$885$	1.97927	−	8.60535i	0.0665326	−	0.289266i
$886$	1.62374	+	34.0865i	0.0545505	+	1.14516i
$887$	2.04269	+	10.5985i	0.0685870	+	0.355863i	0.999966	−	0.00818669i	$-0.00260593\pi$
$887$	2.04269	+	10.5985i	0.0685870	+	0.355863i	−0.931380	+	0.364050i	$0.881394\pi$
$888$	−6.15497	+	3.65213i	−0.206547	+	0.122557i
$889$	−23.7424	−	59.3055i	−0.796293	−	1.98904i
$890$	−11.0406	−	9.56674i	−0.370082	−	0.320678i
$891$	−17.6684	+	34.2807i	−0.591912	+	1.14845i
$892$	26.3703	+	7.74302i	0.882943	+	0.259255i
$893$	−0.239839	+	0.336806i	−0.00802590	+	0.0112708i
$894$	22.4219	−	9.28816i	0.749901	−	0.310642i
$895$	−3.08098	−	5.97627i	−0.102986	−	0.199765i
$896$	−17.4735	+	30.2649i	−0.583748	+	1.01108i
$897$	0.0989907	+	5.85051i	0.00330520	+	0.195343i
$898$	−36.5027	−	63.2245i	−1.21811	−	2.10983i
$899$	−20.2321	+	31.4818i	−0.674780	+	1.04998i
$900$	−10.9335	−	14.6038i	−0.364448	−	0.486793i
$901$	35.9167	+	78.6467i	1.19656	+	2.62010i
$902$	2.31090	+	9.52566i	0.0769445	+	0.317170i
$903$	−8.56534	−	7.24488i	−0.285037	−	0.241095i
$904$	0.668803	−	0.231475i	0.0222441	−	0.00769874i
$905$	−1.96412	+	2.49758i	−0.0652894	+	0.0830223i
$906$	−31.1270	+	0.371245i	−1.03412	+	0.0123338i
$907$	−15.2489	−	5.27770i	−0.506332	−	0.175243i	0.0619466	−	0.998079i	$-0.480269\pi$
$907$	−15.2489	−	5.27770i	−0.506332	−	0.175243i	−0.568278	+	0.822836i	$0.692390\pi$
$908$	−2.98799	+	1.92027i	−0.0991601	+	0.0637263i
$909$	0.206995	+	8.67648i	0.00686559	+	0.287781i
$910$	−2.23076	−	2.57444i	−0.0739491	−	0.0853418i
$911$	−12.3736	−	11.7982i	−0.409956	−	0.390892i	0.456845	−	0.889546i	$-0.348979\pi$
$911$	−12.3736	−	11.7982i	−0.409956	−	0.390892i	−0.866801	+	0.498654i	$0.833828\pi$
$912$	−10.3698	−	14.2009i	−0.343379	−	0.470237i
$913$	4.71036	+	13.6097i	0.155890	+	0.450415i
$914$	−12.1920	−	17.1213i	−0.403276	−	0.566322i
$915$	−0.436618	+	12.2340i	−0.0144341	+	0.404445i
$916$	6.88527	+	4.90298i	0.227496	+	0.161999i
$917$	−3.12699	−	21.7487i	−0.103262	−	0.718204i
$918$	57.7627	−	48.8682i	1.90645	−	1.61289i
$919$		−	32.0171i		−	1.05615i	−0.849198	−	0.528074i	$-0.822914\pi$
$919$		−	32.0171i		−	1.05615i	0.849198	−	0.528074i	$-0.177086\pi$
$920$	3.95526	−	0.208207i	0.130401	−	0.00686439i
$921$	−37.9990	+	9.69972i	−1.25211	+	0.319617i
$922$	3.65256	−	1.88303i	0.120291	−	0.0620142i
$923$	0.0835756	−	0.208762i	0.00275093	−	0.00687148i
$924$	35.7588	+	13.8232i	1.17638	+	0.454749i
$925$	15.1390	−	3.67268i	0.497767	−	0.120757i
$926$	6.34054	+	2.89563i	0.208363	+	0.0951562i
$927$	−13.9995	+	15.4016i	−0.459803	+	0.505854i
$928$	6.95093	−	48.3448i	0.228175	−	1.58700i
$929$	−23.6958	+	24.8515i	−0.777435	+	0.815351i	−0.986707	−	0.162507i	$-0.948042\pi$
$929$	−23.6958	+	24.8515i	−0.777435	+	0.815351i	0.209272	+	0.977857i	$0.432891\pi$
$930$	4.64190	+	9.85168i	0.152214	+	0.323049i
$931$	16.1728	−	0.770405i	0.530042	−	0.0252490i
$932$	−20.4744	+	0.975317i	−0.670662	+	0.0319476i
$933$	15.9619	+	33.8765i	0.522568	+	1.10907i
$934$	−10.1551	+	10.6503i	−0.332284	+	0.348490i
$935$	−3.34020	+	23.2316i	−0.109236	+	0.759756i
$936$	−1.70679	+	1.87773i	−0.0557880	+	0.0613754i
$937$	16.6128	+	7.58683i	0.542718	+	0.247851i	0.667859	−	0.744288i	$-0.267211\pi$
$937$	16.6128	+	7.58683i	0.542718	+	0.247851i	−0.125141	+	0.992139i	$0.539938\pi$
$938$	−29.8137	+	7.23273i	−0.973453	+	0.236157i
$939$	−30.3026	−	11.7140i	−0.988888	−	0.382272i
$940$	−0.0682778	+	0.170550i	−0.00222698	+	0.00556272i
$941$	−37.7729	+	19.4733i	−1.23136	+	0.634811i	−0.946173	−	0.323660i	$-0.895086\pi$
$941$	−37.7729	+	19.4733i	−1.23136	+	0.634811i	−0.285188	+	0.958471i	$0.592056\pi$
$942$	−21.2266	+	5.41835i	−0.691599	+	0.176539i
$943$	−1.16484	−	5.88550i	−0.0379324	−	0.191658i
$944$			36.1873i			1.17780i
$945$	2.44110	+	13.5240i	0.0794091	+	0.439936i
$946$	1.87820	+	13.0632i	0.0610656	+	0.424721i
$947$	−18.0529	−	12.8554i	−0.586640	−	0.417744i	0.247826	−	0.968805i	$-0.420284\pi$
$947$	−18.0529	−	12.8554i	−0.586640	−	0.417744i	−0.834465	+	0.551060i	$0.814223\pi$
$948$	−1.34138	+	37.5855i	−0.0435660	+	1.22072i
$949$	−4.89340	−	6.87182i	−0.158846	−	0.223069i
$950$	5.62960	+	16.2656i	0.182648	+	0.527727i
$951$	−29.1577	−	39.9297i	−0.945504	−	1.29481i
$952$	26.6115	+	25.3740i	0.862483	+	0.822376i
$953$	−12.7163	−	14.6754i	−0.411921	−	0.475382i	0.511438	−	0.859320i	$-0.329113\pi$
$953$	−12.7163	−	14.6754i	−0.411921	−	0.475382i	−0.923359	+	0.383938i	$0.874567\pi$
$954$	−1.42040	−	59.5382i	−0.0459872	−	1.92762i
$955$	12.1923	−	7.83553i	0.394534	−	0.253552i
$956$	−13.3202	−	4.61017i	−0.430806	−	0.149104i
$957$	55.5497	−	0.662531i	1.79567	−	0.0214166i
$958$	12.7031	−	16.1533i	0.410418	−	0.521889i
$959$	5.12994	−	1.77549i	0.165655	−	0.0573336i
$960$	−1.97108	−	1.66721i	−0.0636162	−	0.0538089i
$961$	−1.41529	−	5.83388i	−0.0456544	−	0.188190i
$962$	1.84124	+	4.03176i	0.0593640	+	0.129989i
$963$	−18.3493	−	24.5091i	−0.591297	−	0.789794i
$964$	5.30637	−	8.25688i	0.170907	−	0.265936i
$965$	4.40340	+	7.62691i	0.141750	+	0.245519i
$966$	−53.5289	−	23.3596i	−1.72226	−	0.751583i
$967$	−3.78066	+	6.54830i	−0.121578	+	0.210579i	−0.920390	−	0.391001i	$-0.872129\pi$
$967$	−3.78066	+	6.54830i	−0.121578	+	0.210579i	0.798812	+	0.601581i	$0.205462\pi$
$968$	4.05081	+	7.85748i	0.130198	+	0.252549i
$969$	−26.4986	+	10.9769i	−0.851256	+	0.352628i
$970$	−3.52146	+	4.94519i	−0.113067	+	0.158781i
$971$	−47.2669	−	13.8788i	−1.51687	−	0.445392i	−0.585866	−	0.810408i	$-0.699245\pi$
$971$	−47.2669	−	13.8788i	−1.51687	−	0.445392i	−0.931001	+	0.365016i	$0.881064\pi$
$972$	−20.0193	+	6.14076i	−0.642119	+	0.196965i
$973$	−44.4479	−	38.5143i	−1.42493	−	1.23471i
$974$	−18.3200	−	45.7611i	−0.587010	−	1.46628i
$975$	4.75002	−	2.81849i	0.152122	−	0.0902638i
$976$	−9.49465	−	49.2629i	−0.303916	−	1.57687i
$977$	−0.427563	−	8.97565i	−0.0136789	−	0.287156i	−0.995334	−	0.0964904i	$-0.969238\pi$
$977$	−0.427563	−	8.97565i	−0.0136789	−	0.287156i	0.981655	−	0.190666i	$-0.0610647\pi$
$978$	−6.70121	+	29.1350i	−0.214281	+	0.931636i
$979$	−16.2806	+	47.0398i	−0.520331	+	1.50340i
$980$	6.90241	−	2.02673i	0.220489	−	0.0647415i
$981$	7.65430	−	2.85536i	0.244383	−	0.0911648i
$982$	−3.49000	+	4.02767i	−0.111370	+	0.128528i
$983$	29.9087	−	2.85594i	0.953940	−	0.0910902i	0.393536	−	0.919309i	$-0.371252\pi$
$983$	29.9087	−	2.85594i	0.953940	−	0.0910902i	0.560404	+	0.828219i	$0.310646\pi$
$984$	1.38045	−	2.20542i	0.0440073	−	0.0703063i
$985$	−1.10132	+	11.5336i	−0.0350911	+	0.367490i
$986$	−101.182	−	40.5071i	−3.22228	−	1.29001i
$987$	−0.990439	+	0.879119i	−0.0315260	+	0.0279827i
$988$	−1.70404	+	0.983830i	−0.0542128	+	0.0312998i
$989$	−0.808002	−	8.03753i	−0.0256930	−	0.255579i
$990$	8.41363	−	13.8051i	0.267403	−	0.438754i
$991$	−18.6828	−	12.0067i	−0.593478	−	0.381405i	0.209151	−	0.977883i	$-0.432930\pi$
$991$	−18.6828	−	12.0067i	−0.593478	−	0.381405i	−0.802629	+	0.596478i	$0.796566\pi$
$992$	−20.1672	−	25.6447i	−0.640310	−	0.814220i
$993$	12.8071	−	33.1304i	0.406421	−	1.05136i
$994$	1.54887	+	1.62441i	0.0491273	+	0.0515232i
$995$	2.74574	−	1.95523i	0.0870459	−	0.0619851i
$996$	−3.50003	+	6.99262i	−0.110903	+	0.221570i
$997$	45.0476	−	18.0343i	1.42667	−	0.571153i	0.475472	−	0.879731i	$-0.342277\pi$
$997$	45.0476	−	18.0343i	1.42667	−	0.571153i	0.951199	+	0.308578i	$0.0998532\pi$
$998$	20.8798	+	71.1099i	0.660937	+	2.25094i
$999$	1.90999	−	17.7787i	0.0604295	−	0.562493i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.113.5	yes	440
3.2	odd	2		621.2.s.a.44.18		440
9.2	odd	6	inner	207.2.o.a.182.5	yes	440
9.7	even	3		621.2.s.a.251.18		440
23.11	odd	22	inner	207.2.o.a.149.5	yes	440
69.11	even	22		621.2.s.a.287.18		440
207.11	even	66	inner	207.2.o.a.11.5	✓	440
207.34	odd	66		621.2.s.a.494.18		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.5	✓	440	207.11	even	66	inner
207.2.o.a.113.5	yes	440	1.1	even	1	trivial
207.2.o.a.149.5	yes	440	23.11	odd	22	inner
207.2.o.a.182.5	yes	440	9.2	odd	6	inner
621.2.s.a.44.18		440	3.2	odd	2
621.2.s.a.251.18		440	9.7	even	3
621.2.s.a.287.18		440	69.11	even	22
621.2.s.a.494.18		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)

\(f(q)\)	\(=\)	\(q+(-1.82640 - 0.0870020i) q^{2} +(-0.662869 - 1.60019i) q^{3} +(1.33722 + 0.127689i) q^{4} +(-0.497778 + 0.474630i) q^{5} +(1.07144 + 2.98025i) q^{6} +(0.727727 - 3.77580i) q^{7} +(1.18854 + 0.170886i) q^{8} +(-2.12121 + 2.12143i) q^{9} +O(q^{10})\)	\(q+(-1.82640 - 0.0870020i) q^{2} +(-0.662869 - 1.60019i) q^{3} +(1.33722 + 0.127689i) q^{4} +(-0.497778 + 0.474630i) q^{5} +(1.07144 + 2.98025i) q^{6} +(0.727727 - 3.77580i) q^{7} +(1.18854 + 0.170886i) q^{8} +(-2.12121 + 2.12143i) q^{9} +(0.950434 - 0.823555i) q^{10} +(-3.80876 - 1.96355i) q^{11} +(-0.682073 - 2.22444i) q^{12} +(0.691689 - 0.133312i) q^{13} +(-1.65762 + 6.83281i) q^{14} +(1.08946 + 0.481921i) q^{15} +(-4.79392 - 0.923952i) q^{16} +(-3.30816 + 7.24386i) q^{17} +(4.05874 - 3.69003i) q^{18} +(-1.89153 + 0.863831i) q^{19} +(-0.726241 + 0.571122i) q^{20} +(-6.52439 + 1.33836i) q^{21} +(6.78547 + 3.91760i) q^{22} +(-4.04740 - 2.57265i) q^{23} +(-0.514395 - 2.01516i) q^{24} +(-0.215401 + 4.52182i) q^{25} +(-1.27490 + 0.183303i) q^{26} +(4.80078 + 1.98810i) q^{27} +(1.45525 - 4.95614i) q^{28} +(-0.711492 - 7.45108i) q^{29} +(-1.94786 - 0.974964i) q^{30} +(-3.93002 - 3.09060i) q^{31} +(6.34139 + 1.53841i) q^{32} +(-0.617345 + 7.39631i) q^{33} +(6.67225 - 12.9424i) q^{34} +(1.42986 + 2.22491i) q^{35} +(-3.10740 + 2.56596i) q^{36} +(-0.969499 - 3.30181i) q^{37} +(3.52983 - 1.41313i) q^{38} +(-0.671824 - 1.01846i) q^{39} +(-0.672735 + 0.479052i) q^{40} +(0.863301 + 0.905404i) q^{41} +(12.0326 - 1.87675i) q^{42} +(1.04122 + 1.32402i) q^{43} +(-4.84241 - 3.11203i) q^{44} +(0.0489951 - 2.06279i) q^{45} +(7.16834 + 5.05081i) q^{46} +(0.172200 - 0.0994197i) q^{47} +(1.69924 + 8.28364i) q^{48} +(-7.22854 - 2.89387i) q^{49} +(0.786815 - 8.23989i) q^{50} +(13.7844 + 0.491949i) q^{51} +(0.941960 - 0.0899462i) q^{52} +(7.10983 - 8.20518i) q^{53} +(-8.59516 - 4.04874i) q^{54} +(2.82787 - 0.830339i) q^{55} +(1.51016 - 4.36333i) q^{56} +(2.63613 + 2.45419i) q^{57} +(0.651208 + 13.6705i) q^{58} +(-1.40276 - 7.27823i) q^{59} +(1.39531 + 0.783543i) q^{60} +(3.81925 + 9.54002i) q^{61} +(6.90889 + 5.98659i) q^{62} +(6.46645 + 9.55309i) q^{63} +(-2.07929 - 0.610536i) q^{64} +(-0.281033 + 0.394656i) q^{65} +(1.77101 - 13.4549i) q^{66} +(1.99939 + 3.87827i) q^{67} +(-5.34868 + 9.26419i) q^{68} +(-1.43383 + 8.18194i) q^{69} +(-2.41793 - 4.18797i) q^{70} +(0.172587 - 0.268551i) q^{71} +(-2.88366 + 2.15892i) q^{72} +(-4.97498 - 10.8937i) q^{73} +(1.48343 + 6.11477i) q^{74} +(7.37854 - 2.65269i) q^{75} +(-2.63968 + 0.913602i) q^{76} +(-10.1857 + 12.9522i) q^{77} +(1.13841 + 1.91857i) q^{78} +(-15.2755 - 5.28691i) q^{79} +(2.82484 - 1.81542i) q^{80} +(-0.000945804 - 9.00000i) q^{81} +(-1.49796 - 1.72874i) q^{82} +(-2.43239 - 2.31928i) q^{83} +(-8.89541 + 0.956591i) q^{84} +(-1.79143 - 5.17599i) q^{85} +(-1.78649 - 2.50877i) q^{86} +(-11.4515 + 6.07761i) q^{87} +(-4.19131 - 2.98462i) q^{88} +(-1.65318 - 11.4981i) q^{89} +(-0.268952 + 3.76321i) q^{90} -2.70870i q^{91} +(-5.08375 - 3.95699i) q^{92} +(-2.34046 + 8.33744i) q^{93} +(-0.323155 + 0.166598i) q^{94} +(0.531559 - 1.32777i) q^{95} +(-1.74178 - 11.1672i) q^{96} +(-4.69126 + 1.13809i) q^{97} +(12.9504 + 5.91426i) q^{98} +(12.2447 - 3.91492i) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more