LMFDB - Embedded newform 207.2.o.a.11.21

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			11.21
Character	$\chi$	$=$	207.11
Dual form			207.2.o.a.113.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.25367 - 0.107356i) q^{2} +(0.597916 + 1.62558i) q^{3} +(3.07657 - 0.293777i) q^{4} +(-1.85967 - 1.77319i) q^{5} +(1.52202 + 3.59933i) q^{6} +(0.300622 + 1.55978i) q^{7} +(2.43553 - 0.350176i) q^{8} +(-2.28499 + 1.94391i) q^{9} +O(q^{10})$	\(q+(2.25367 - 0.107356i) q^{2} +(0.597916 + 1.62558i) q^{3} +(3.07657 - 0.293777i) q^{4} +(-1.85967 - 1.77319i) q^{5} +(1.52202 + 3.59933i) q^{6} +(0.300622 + 1.55978i) q^{7} +(2.43553 - 0.350176i) q^{8} +(-2.28499 + 1.94391i) q^{9} +(-4.38145 - 3.79655i) q^{10} +(5.28603 - 2.72514i) q^{11} +(2.31709 + 4.82555i) q^{12} +(-5.29081 - 1.01972i) q^{13} +(0.844955 + 3.48295i) q^{14} +(1.77053 - 4.08326i) q^{15} +(-0.618147 + 0.119138i) q^{16} +(-1.57778 - 3.45486i) q^{17} +(-4.94094 + 4.62625i) q^{18} +(-0.847774 - 0.387165i) q^{19} +(-6.24234 - 4.90903i) q^{20} +(-2.35579 + 1.42130i) q^{21} +(11.6204 - 6.70906i) q^{22} +(3.48037 + 3.29955i) q^{23} +(2.02548 + 3.74976i) q^{24} +(0.0762544 + 1.60078i) q^{25} +(-12.0332 - 1.73012i) q^{26} +(-4.52621 - 2.55213i) q^{27} +(1.38311 + 4.71045i) q^{28} +(-0.741129 + 7.76145i) q^{29} +(3.55184 - 9.39240i) q^{30} +(0.873833 - 0.687190i) q^{31} +(-6.16274 + 1.49506i) q^{32} +(7.59052 + 6.96344i) q^{33} +(-3.92671 - 7.61675i) q^{34} +(2.20673 - 3.43373i) q^{35} +(-6.45888 + 6.65188i) q^{36} +(-0.0220947 + 0.0752475i) q^{37} +(-1.95217 - 0.781531i) q^{38} +(-1.50583 - 9.21032i) q^{39} +(-5.15021 - 3.66745i) q^{40} +(5.40903 - 5.67283i) q^{41} +(-5.15659 + 3.45605i) q^{42} +(-2.17721 + 2.76855i) q^{43} +(15.4623 - 9.93701i) q^{44} +(7.69627 + 0.436694i) q^{45} +(8.19784 + 7.06247i) q^{46} +(3.45875 + 1.99691i) q^{47} +(-0.563267 - 0.933610i) q^{48} +(4.15605 - 1.66383i) q^{49} +(0.343705 + 3.59944i) q^{50} +(4.67276 - 4.63052i) q^{51} +(-16.5771 - 1.58293i) q^{52} +(0.295664 + 0.341214i) q^{53} +(-10.4746 - 5.26576i) q^{54} +(-14.6625 - 4.30529i) q^{55} +(1.27837 + 3.69361i) q^{56} +(0.122469 - 1.60961i) q^{57} +(-0.837026 + 17.5713i) q^{58} +(-1.51179 + 7.84393i) q^{59} +(4.24761 - 13.0826i) q^{60} +(0.808028 - 2.01836i) q^{61} +(1.89556 - 1.64251i) q^{62} +(-3.71899 - 2.97970i) q^{63} +(-12.5202 + 3.67628i) q^{64} +(8.03101 + 11.2780i) q^{65} +(17.8541 + 14.8784i) q^{66} +(-4.19450 + 8.13619i) q^{67} +(-5.86913 - 10.1656i) q^{68} +(-3.28270 + 7.63046i) q^{69} +(4.60461 - 7.97542i) q^{70} +(2.81080 + 4.37368i) q^{71} +(-4.88445 + 5.53461i) q^{72} +(-3.26377 + 7.14666i) q^{73} +(-0.0417159 + 0.171955i) q^{74} +(-2.55659 + 1.08109i) q^{75} +(-2.72198 - 0.942086i) q^{76} +(5.83971 + 7.42579i) q^{77} +(-4.38242 - 20.5954i) q^{78} +(3.40860 - 1.17973i) q^{79} +(1.36080 + 0.874536i) q^{80} +(1.44239 - 8.88366i) q^{81} +(11.5812 - 13.3654i) q^{82} +(10.3643 - 9.88236i) q^{83} +(-6.83021 + 5.06481i) q^{84} +(-3.19198 + 9.22263i) q^{85} +(-4.60951 + 6.47315i) q^{86} +(-13.0600 + 3.43593i) q^{87} +(11.9200 - 8.48819i) q^{88} +(-0.0508144 + 0.353422i) q^{89} +(17.3918 + 0.157926i) q^{90} -8.55903i q^{91} +(11.6770 + 9.12885i) q^{92} +(1.63956 + 1.00960i) q^{93} +(8.00928 + 4.12907i) q^{94} +(0.890062 + 2.22327i) q^{95} +(-6.11514 - 9.12407i) q^{96} +(6.82305 + 1.65525i) q^{97} +(9.18775 - 4.19590i) q^{98} +(-6.78111 + 16.5025i) 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 $

$2$	2.25367	−	0.107356i	1.59359	−	0.0759119i	0.768099	−	0.640331i	$-0.221203\pi$
$2$	2.25367	−	0.107356i	1.59359	−	0.0759119i	0.825488	+	0.564419i	$0.190900\pi$
$3$	0.597916	+	1.62558i	0.345207	+	0.938527i
$3$	0.597916	+	1.62558i	0.345207	+	0.938527i
$4$	3.07657	−	0.293777i	1.53829	−	0.146889i
$5$	−1.85967	−	1.77319i	−0.831670	−	0.792996i	0.148964	−	0.988843i	$-0.452406\pi$
$5$	−1.85967	−	1.77319i	−0.831670	−	0.792996i	−0.980635	+	0.195846i	$0.937255\pi$
$6$	1.52202	+	3.59933i	0.621363	+	1.46942i
$7$	0.300622	+	1.55978i	0.113625	+	0.589540i	0.993452	+	0.114247i	$0.0364457\pi$
$7$	0.300622	+	1.55978i	0.113625	+	0.589540i	−0.879828	+	0.475293i	$0.842342\pi$
$8$	2.43553	−	0.350176i	0.861089	−	0.123806i
$9$	−2.28499	+	1.94391i	−0.761665	+	0.647971i
$10$	−4.38145	−	3.79655i	−1.38554	−	1.20058i
$11$	5.28603	−	2.72514i	1.59380	−	0.821660i	0.593946	−	0.804505i	$-0.297569\pi$
$11$	5.28603	−	2.72514i	1.59380	−	0.821660i	0.999853	−	0.0171550i	$-0.00546089\pi$
$12$	2.31709	+	4.82555i	0.668886	+	1.39302i
$13$	−5.29081	−	1.01972i	−1.46741	−	0.282819i	−0.607929	−	0.793992i	$-0.707999\pi$
$13$	−5.29081	−	1.01972i	−1.46741	−	0.282819i	−0.859478	+	0.511172i	$0.829211\pi$
$14$	0.844955	+	3.48295i	0.225824	+	0.930858i
$15$	1.77053	−	4.08326i	0.457150	−	1.05429i
$16$	−0.618147	+	0.119138i	−0.154537	+	0.0297845i
$17$	−1.57778	−	3.45486i	−0.382669	−	0.837928i	−0.998737	−	0.0502352i	$-0.984003\pi$
$17$	−1.57778	−	3.45486i	−0.382669	−	0.837928i	0.616069	−	0.787692i	$-0.288724\pi$
$18$	−4.94094	+	4.62625i	−1.16459	+	1.09042i
$19$	−0.847774	−	0.387165i	−0.194493	−	0.0888218i	0.315788	−	0.948830i	$-0.397731\pi$
$19$	−0.847774	−	0.387165i	−0.194493	−	0.0888218i	−0.510281	+	0.860008i	$0.670458\pi$
$20$	−6.24234	−	4.90903i	−1.39583	−	1.09769i
$21$	−2.35579	+	1.42130i	−0.514075	+	0.310153i
$22$	11.6204	−	6.70906i	2.47748	−	1.43038i
$23$	3.48037	+	3.29955i	0.725708	+	0.688003i
$23$	3.48037	+	3.29955i	0.725708	+	0.688003i
$24$	2.02548	+	3.74976i	0.413449	+	0.765416i
$25$	0.0762544	+	1.60078i	0.0152509	+	0.320156i
$26$	−12.0332	−	1.73012i	−2.35991	−	0.339304i
$27$	−4.52621	−	2.55213i	−0.871070	−	0.491158i
$28$	1.38311	+	4.71045i	0.261384	+	0.890192i
$29$	−0.741129	+	7.76145i	−0.137624	+	1.44126i	0.617958	+	0.786211i	$0.287960\pi$
$29$	−0.741129	+	7.76145i	−0.137624	+	1.44126i	−0.755582	+	0.655054i	$0.772646\pi$
$30$	3.55184	−	9.39240i	0.648475	−	1.71481i
$31$	0.873833	−	0.687190i	0.156945	−	0.123423i	−0.536598	−	0.843838i	$-0.680291\pi$
$31$	0.873833	−	0.687190i	0.156945	−	0.123423i	0.693543	+	0.720415i	$0.256049\pi$
$32$	−6.16274	+	1.49506i	−1.08943	+	0.264292i
$33$	7.59052	+	6.96344i	1.32134	+	1.21218i
$34$	−3.92671	−	7.61675i	−0.673425	−	1.30626i
$35$	2.20673	−	3.43373i	0.373005	−	0.580407i
$36$	−6.45888	+	6.65188i	−1.07648	+	1.10865i
$37$	−0.0220947	+	0.0752475i	−0.00363234	+	0.0123706i	−0.961289	−	0.275541i	$-0.911143\pi$
$37$	−0.0220947	+	0.0752475i	−0.00363234	+	0.0123706i	0.957657	+	0.287912i	$0.0929611\pi$
$38$	−1.95217	−	0.781531i	−0.316684	−	0.126781i
$39$	−1.50583	−	9.21032i	−0.241125	−	1.47483i
$40$	−5.15021	−	3.66745i	−0.814320	−	0.579874i
$41$	5.40903	−	5.67283i	0.844748	−	0.885947i	−0.149959	−	0.988692i	$-0.547914\pi$
$41$	5.40903	−	5.67283i	0.844748	−	0.885947i	0.994708	+	0.102746i	$0.0327627\pi$
$42$	−5.15659	+	3.45605i	−0.795680	+	0.533280i
$43$	−2.17721	+	2.76855i	−0.332022	+	0.422200i	−0.923187	−	0.384350i	$-0.874426\pi$
$43$	−2.17721	+	2.76855i	−0.332022	+	0.422200i	0.591165	+	0.806550i	$0.298668\pi$
$44$	15.4623	−	9.93701i	2.33103	−	1.49806i
$45$	7.69627	+	0.436694i	1.14729	+	0.0650984i
$46$	8.19784	+	7.06247i	1.20871	+	1.04130i
$47$	3.45875	+	1.99691i	0.504511	+	0.291280i	0.730575	−	0.682833i	$-0.239252\pi$
$47$	3.45875	+	1.99691i	0.504511	+	0.291280i	−0.226063	+	0.974113i	$0.572586\pi$
$48$	−0.563267	−	0.933610i	−0.0813006	−	0.134755i
$49$	4.15605	−	1.66383i	0.593721	−	0.237690i
$50$	0.343705	+	3.59944i	0.0486073	+	0.509038i
$51$	4.67276	−	4.63052i	0.654318	−	0.648403i
$52$	−16.5771	−	1.58293i	−2.29884	−	0.219512i
$53$	0.295664	+	0.341214i	0.0406125	+	0.0468693i	0.775692	−	0.631111i	$-0.217401\pi$
$53$	0.295664	+	0.341214i	0.0406125	+	0.0468693i	−0.735080	+	0.677980i	$0.762855\pi$
$54$	−10.4746	−	5.26576i	−1.42541	−	0.716579i
$55$	−14.6625	−	4.30529i	−1.97709	−	0.580526i
$56$	1.27837	+	3.69361i	0.170829	+	0.493579i
$57$	0.122469	−	1.60961i	0.0162215	−	0.213198i
$58$	−0.837026	+	17.5713i	−0.109907	+	2.30723i
$59$	−1.51179	+	7.84393i	−0.196819	+	1.02119i	0.740325	+	0.672249i	$0.234672\pi$
$59$	−1.51179	+	7.84393i	−0.196819	+	1.02119i	−0.937144	+	0.348943i	$0.886541\pi$
$60$	4.24761	−	13.0826i	0.548364	−	1.68895i
$61$	0.808028	−	2.01836i	0.103457	−	0.258424i	−0.867603	−	0.497257i	$-0.834341\pi$
$61$	0.808028	−	2.01836i	0.103457	−	0.258424i	0.971061	+	0.238833i	$0.0767648\pi$
$62$	1.89556	−	1.64251i	0.240736	−	0.208599i
$63$	−3.71899	−	2.97970i	−0.468549	−	0.375406i
$64$	−12.5202	+	3.67628i	−1.56503	+	0.459534i
$65$	8.03101	+	11.2780i	0.996124	+	1.39886i
$66$	17.8541	+	14.8784i	2.19769	+	1.83141i
$67$	−4.19450	+	8.13619i	−0.512439	+	0.993993i	0.480681	+	0.876895i	$0.340389\pi$
$67$	−4.19450	+	8.13619i	−0.512439	+	0.993993i	−0.993120	+	0.117098i	$0.962641\pi$
$68$	−5.86913	−	10.1656i	−0.711736	−	1.23276i
$69$	−3.28270	+	7.63046i	−0.395190	+	0.918599i
$70$	4.60461	−	7.97542i	0.550356	−	0.953245i
$71$	2.81080	+	4.37368i	0.333580	+	0.519061i	0.967010	−	0.254740i	$-0.0819897\pi$
$71$	2.81080	+	4.37368i	0.333580	+	0.519061i	−0.633430	+	0.773800i	$0.718353\pi$
$72$	−4.88445	+	5.53461i	−0.575638	+	0.652260i
$73$	−3.26377	+	7.14666i	−0.381995	+	0.836453i	0.616787	+	0.787130i	$0.288434\pi$
$73$	−3.26377	+	7.14666i	−0.381995	+	0.836453i	−0.998783	+	0.0493235i	$0.984293\pi$
$74$	−0.0417159	+	0.171955i	−0.00484937	+	0.0199894i
$75$	−2.55659	+	1.08109i	−0.295210	+	0.124833i
$76$	−2.72198	−	0.942086i	−0.312232	−	0.108065i
$77$	5.83971	+	7.42579i	0.665496	+	0.846247i
$78$	−4.38242	−	20.5954i	−0.496211	−	2.33197i
$79$	3.40860	−	1.17973i	0.383498	−	0.132730i	−0.128515	−	0.991708i	$-0.541021\pi$
$79$	3.40860	−	1.17973i	0.383498	−	0.132730i	0.512013	+	0.858978i	$0.328900\pi$
$80$	1.36080	+	0.874536i	0.152143	+	0.0977761i
$81$	1.44239	−	8.88366i	0.160266	−	0.987074i
$82$	11.5812	−	13.3654i	1.27893	−	1.47596i
$83$	10.3643	−	9.88236i	1.13763	−	1.08473i	0.142144	−	0.989846i	$-0.454600\pi$
$83$	10.3643	−	9.88236i	1.13763	−	1.08473i	0.995488	−	0.0948845i	$-0.0302482\pi$
$84$	−6.83021	+	5.06481i	−0.745237	+	0.552616i
$85$	−3.19198	+	9.22263i	−0.346219	+	1.00033i
$86$	−4.60951	+	6.47315i	−0.497056	+	0.698018i
$87$	−13.0600	+	3.43593i	−1.40017	+	0.368370i
$88$	11.9200	−	8.48819i	1.27068	−	0.904844i
$89$	−0.0508144	+	0.353422i	−0.00538631	+	0.0374626i	−0.992337	−	0.123558i	$-0.960569\pi$
$89$	−0.0508144	+	0.353422i	−0.00538631	+	0.0374626i	0.986951	+	0.161021i	$0.0514786\pi$
$90$	17.3918	+	0.157926i	1.83325	+	0.0166468i
$91$		−	8.55903i		−	0.897230i
$92$	11.6770	+	9.12885i	1.21741	+	0.951749i
$93$	1.63956	+	1.00960i	0.170014	+	0.104691i
$94$	8.00928	+	4.12907i	0.826095	+	0.425881i
$95$	0.890062	+	2.22327i	0.0913184	+	0.228102i
$96$	−6.11514	−	9.12407i	−0.624123	−	0.931222i
$97$	6.82305	+	1.65525i	0.692775	+	0.168066i	0.566662	−	0.823950i	$-0.308235\pi$
$97$	6.82305	+	1.65525i	0.692775	+	0.168066i	0.126113	+	0.992016i	$0.459750\pi$
$98$	9.18775	−	4.19590i	0.928103	−	0.423850i
$99$	−6.78111	+	16.5025i	−0.681528	+	1.65857i
$100$	0.704875	+	4.90251i	0.0704875	+	0.490251i
$101$	−0.774806	−	0.812593i	−0.0770961	−	0.0808561i	0.684056	−	0.729430i	$-0.260214\pi$
$101$	−0.774806	−	0.812593i	−0.0770961	−	0.0808561i	−0.761152	+	0.648573i	$0.775366\pi$
$102$	10.0338	−	10.9373i	0.993491	−	1.08296i
$103$	−10.6569	−	0.507649i	−1.05005	−	0.0500202i	−0.484548	−	0.874765i	$-0.661016\pi$
$103$	−10.6569	−	0.507649i	−1.05005	−	0.0500202i	−0.565505	+	0.824745i	$0.691319\pi$
$104$	−13.2430	−	0.630842i	−1.29858	−	0.0618591i
$105$	6.90123	+	1.53412i	0.673491	+	0.149715i
$106$	0.702960	+	0.737244i	0.0682776	+	0.0716074i
$107$	−2.81855	−	19.6034i	−0.272480	−	1.89514i	−0.422353	−	0.906432i	$-0.638796\pi$
$107$	−2.81855	−	19.6034i	−0.272480	−	1.89514i	0.149873	−	0.988705i	$-0.452113\pi$
$108$	−14.6750	−	6.52213i	−1.41210	−	0.627592i
$109$	−7.15199	+	3.26621i	−0.685037	+	0.312846i	−0.727358	−	0.686258i	$-0.759252\pi$
$109$	−7.15199	+	3.26621i	−0.685037	+	0.312846i	0.0423212	+	0.999104i	$0.486525\pi$
$110$	−33.5066	−	8.12862i	−3.19473	−	0.775034i
$111$	−0.135531	+	0.00907511i	−0.0128641	+	0.000861371i
$112$	−0.371657	−	0.928355i	−0.0351183	−	0.0877213i
$113$	−12.9849	−	6.69418i	−1.22152	−	0.629735i	−0.277847	−	0.960625i	$-0.589621\pi$
$113$	−12.9849	−	6.69418i	−1.22152	−	0.629735i	−0.943669	+	0.330890i	$0.892651\pi$
$114$	0.103205	−	3.64069i	0.00966603	−	0.340982i
$115$	−0.621610	−	12.3074i	−0.0579655	−	1.14768i
$116$			24.0964i			2.23729i
$117$	14.0717	−	7.95483i	1.30093	−	0.735424i
$118$	−2.56500	+	17.8399i	−0.236127	+	1.64230i
$119$	4.91450	−	3.49960i	0.450511	−	0.320808i
$120$	2.88232	−	10.5649i	0.263119	−	0.964437i
$121$	14.1351	−	19.8500i	1.28501	−	1.80455i
$122$	1.60435	−	4.63546i	0.145251	−	0.419675i
$123$	12.4558	+	5.40092i	1.12310	+	0.486984i
$124$	2.48653	−	2.37090i	0.223297	−	0.212913i
$125$	−5.71681	+	6.59755i	−0.511327	+	0.590103i
$126$	−8.70128	−	6.31601i	−0.775172	−	0.562675i
$127$	4.86862	+	3.12887i	0.432021	+	0.277643i	0.738524	−	0.674227i	$-0.235523\pi$
$127$	4.86862	+	3.12887i	0.432021	+	0.277643i	−0.306504	+	0.951869i	$0.599159\pi$
$128$	−15.8364	+	5.48104i	−1.39976	+	0.484460i
$129$	−5.80228	−	1.88387i	−0.510862	−	0.165865i
$130$	19.3100	+	24.5547i	1.69360	+	2.15359i
$131$	16.5380	+	5.72385i	1.44493	+	0.500095i	0.933296	−	0.359109i	$-0.116919\pi$
$131$	16.5380	+	5.72385i	1.44493	+	0.500095i	0.511633	+	0.859204i	$0.329041\pi$
$132$	25.3985	+	19.1936i	2.21066	+	1.67059i
$133$	0.349032	−	1.43873i	0.0302649	−	0.124754i
$134$	−8.57956	+	18.7866i	−0.741161	+	1.62292i
$135$	3.89184	+	12.7720i	0.334957	+	1.09924i
$136$	−5.05255	−	7.86191i	−0.433252	−	0.674154i
$137$	6.44885	−	11.1697i	0.550962	−	0.954294i	−0.447243	−	0.894412i	$-0.647594\pi$
$137$	6.44885	−	11.1697i	0.550962	−	0.954294i	0.998205	−	0.0598820i	$-0.0190725\pi$
$138$	−6.57896	+	17.5490i	−0.560038	+	1.49387i
$139$	−1.07291	−	1.85834i	−0.0910034	−	0.157622i	0.816930	−	0.576737i	$-0.195674\pi$
$139$	−1.07291	−	1.85834i	−0.0910034	−	0.157622i	−0.907934	+	0.419114i	$0.862341\pi$
$140$	5.78041	−	11.2124i	0.488533	−	0.947623i
$141$	−1.17809	+	6.81645i	−0.0992131	+	0.574049i
$142$	6.80415	+	9.55510i	0.570992	+	0.801846i
$143$	−30.7463	+	9.02792i	−2.57113	+	0.754953i
$144$	1.18087	−	1.47385i	0.0984056	−	0.122821i
$145$	15.1408	−	13.1196i	1.25738	−	1.08952i
$146$	−6.58824	+	16.4566i	−0.545246	+	1.36196i
$147$	5.18965	+	5.76114i	0.428035	+	0.475171i
$148$	−0.0458698	+	0.237995i	−0.00377048	+	0.0195631i
$149$	0.686073	−	14.4024i	0.0562053	−	1.17989i	−0.777936	−	0.628344i	$-0.783733\pi$
$149$	0.686073	−	14.4024i	0.0562053	−	1.17989i	0.834141	−	0.551551i	$-0.185964\pi$
$150$	−5.64566	+	2.71088i	−0.460966	+	0.221343i
$151$	3.47617	+	10.0437i	0.282887	+	0.817348i	0.993507	+	0.113772i	$0.0362934\pi$
$151$	3.47617	+	10.0437i	0.282887	+	0.817348i	−0.710620	+	0.703576i	$0.751585\pi$
$152$	−2.20035	−	0.646082i	−0.178472	−	0.0524041i
$153$	10.3212	+	4.82727i	0.834418	+	0.390261i
$154$	13.9580	+	16.1084i	1.12477	+	1.29805i
$155$	−2.84356	−	0.271527i	−0.228401	−	0.0218096i
$156$	−7.33857	−	27.8939i	−0.587556	−	2.23330i
$157$	0.473155	+	4.95510i	0.0377619	+	0.395460i	0.994518	+	0.104568i	$0.0333460\pi$
$157$	0.473155	+	4.95510i	0.0377619	+	0.395460i	−0.956756	+	0.290892i	$0.906048\pi$
$158$	7.55523	−	3.02466i	0.601062	−	0.240629i
$159$	−0.377887	+	0.684641i	−0.0299684	+	0.0542955i
$160$	14.1117	+	8.14739i	1.11563	+	0.644108i
$161$	−4.10028	+	6.42052i	−0.323147	+	0.506008i
$162$	2.29697	−	20.1757i	0.180467	−	1.58515i
$163$	−12.0700	+	7.75693i	−0.945397	+	0.607570i	−0.919920	−	0.392105i	$-0.871747\pi$
$163$	−12.0700	+	7.75693i	−0.945397	+	0.607570i	−0.0254770	+	0.999675i	$0.508110\pi$
$164$	14.9747	−	19.0419i	1.16933	−	1.48692i
$165$	−1.76835	−	26.4092i	−0.137666	−	2.05595i
$166$	22.2969	−	23.3843i	1.73057	−	1.81497i
$167$	−14.3302	−	10.2045i	−1.10891	−	0.789648i	−0.129506	−	0.991579i	$-0.541339\pi$
$167$	−14.3302	−	10.2045i	−1.10891	−	0.789648i	−0.979400	+	0.201930i	$0.935279\pi$
$168$	−5.23988	+	4.28655i	−0.404266	+	0.330715i
$169$	14.8841	+	5.95868i	1.14493	+	0.458360i
$170$	−6.20358	+	21.1275i	−0.475793	+	1.62040i
$171$	2.68977	−	0.763329i	0.205692	−	0.0583733i
$172$	−5.88502	+	9.15727i	−0.448729	+	0.698236i
$173$	−0.155629	−	0.301879i	−0.0118323	−	0.0229514i	0.882845	−	0.469664i	$-0.155625\pi$
$173$	−0.155629	−	0.301879i	−0.0118323	−	0.0229514i	−0.894678	+	0.446713i	$0.852595\pi$
$174$	−29.0640	+	9.14553i	−2.20334	+	0.693321i
$175$	−2.47393	+	0.600169i	−0.187012	+	0.0453685i
$176$	−2.94288	+	2.31430i	−0.221828	+	0.174447i
$177$	−13.6548	+	2.23247i	−1.02636	+	0.167803i
$178$	−0.0765771	+	0.801952i	−0.00573970	+	0.0601088i
$179$	−2.22102	−	7.56409i	−0.166007	−	0.565367i	−0.999909	−	0.0134555i	$-0.995717\pi$
$179$	−2.22102	−	7.56409i	−0.166007	−	0.565367i	0.833903	−	0.551911i	$-0.186101\pi$
$180$	23.8064	−	0.917470i	1.77443	−	0.0683842i
$181$	−7.02665	−	1.01028i	−0.522287	−	0.0750935i	−0.123871	−	0.992298i	$-0.539531\pi$
$181$	−7.02665	−	1.01028i	−0.522287	−	0.0750935i	−0.398416	+	0.917205i	$0.630440\pi$
$182$	−0.918861	−	19.2893i	−0.0681105	−	1.42982i
$183$	3.76412	+	0.106704i	0.278252	+	0.00788779i
$184$	9.63196	+	6.81740i	0.710078	+	0.502585i
$185$	0.174517	−	0.100758i	0.0128308	−	0.00740784i
$186$	3.80341	+	2.09929i	0.278880	+	0.153928i
$187$	−17.7552	−	13.9628i	−1.29839	−	1.02106i
$188$	11.2278	+	5.12755i	0.818869	+	0.373965i
$189$	2.62008	−	7.82711i	0.190583	−	0.569338i
$190$	2.24459	+	4.91497i	0.162840	+	0.356569i
$191$	4.15739	−	0.801271i	0.300818	−	0.0579779i	−0.0366089	−	0.999330i	$-0.511656\pi$
$191$	4.15739	−	0.801271i	0.300818	−	0.0579779i	0.337427	+	0.941352i	$0.390443\pi$
$192$	−13.4621	−	18.1545i	−0.971544	−	1.31019i
$193$	−2.61515	−	10.7798i	−0.188243	−	0.775946i	−0.985129	−	0.171817i	$-0.945036\pi$
$193$	−2.61515	−	10.7798i	−0.188243	−	0.775946i	0.796886	−	0.604129i	$-0.206479\pi$
$194$	15.5546	+	2.99791i	1.11676	+	0.215237i
$195$	−13.5313	+	19.7983i	−0.968999	+	1.41779i
$196$	12.2976	−	6.33985i	0.878399	−	0.452846i
$197$	−4.72100	−	4.09077i	−0.336357	−	0.291455i	0.470262	−	0.882527i	$-0.344160\pi$
$197$	−4.72100	−	4.09077i	−0.336357	−	0.291455i	−0.806619	+	0.591072i	$0.798705\pi$
$198$	−13.5108	+	37.9193i	−0.960169	+	2.69481i
$199$	9.36666	−	1.34672i	0.663985	−	0.0954666i	0.197921	−	0.980218i	$-0.436581\pi$
$199$	9.36666	−	1.34672i	0.663985	−	0.0954666i	0.466064	+	0.884751i	$0.345672\pi$
$200$	0.746274	+	3.87204i	0.0527695	+	0.273794i
$201$	−15.7339	−	1.95372i	−1.10979	−	0.137805i
$202$	−1.83340	−	1.74814i	−0.128997	−	0.122999i
$203$	−12.3289	+	1.17727i	−0.865321	+	0.0826281i
$204$	13.0158	−	15.6189i	0.911285	−	1.09354i
$205$	−20.1180	+	0.958340i	−1.40510	+	0.0669334i
$206$	−24.0716			−1.67715
$207$	−14.3667	−	0.773904i	−0.998552	−	0.0537901i
$208$	3.39198			0.235192
$209$	−5.53644	+	0.263733i	−0.382963	+	0.0182428i
$210$	15.7178	+	2.71652i	1.08463	+	0.187457i
$211$	−8.54002	+	0.815473i	−0.587919	+	0.0561395i	−0.384777	−	0.923010i	$-0.625722\pi$
$211$	−8.54002	+	0.815473i	−0.587919	+	0.0561395i	−0.203142	+	0.979149i	$0.565115\pi$
$212$	1.00987	+	0.962911i	0.0693583	+	0.0661330i
$213$	−5.42914	+	7.18426i	−0.371998	+	0.492257i
$214$	−8.45663	−	43.8772i	−0.578084	−	2.99938i
$215$	8.95808	−	1.28798i	0.610936	−	0.0878394i
$216$	−11.9174	−	4.63082i	−0.810877	−	0.315087i
$217$	1.33456	+	1.15640i	0.0905956	+	0.0785015i
$218$	−15.7676	+	8.12877i	−1.06792	+	0.550550i
$219$	−13.5689	−	1.03241i	−0.916901	−	0.0697636i
$220$	−46.3750	−	8.93805i	−3.12660	−	0.602603i
$221$	4.82476	+	19.8879i	0.324548	+	1.33781i
$222$	−0.304469	+	0.0350024i	−0.0204346	+	0.00234921i
$223$	−16.3270	+	3.14676i	−1.09333	+	0.210723i	−0.703877	−	0.710322i	$-0.748549\pi$
$223$	−16.3270	+	3.14676i	−1.09333	+	0.210723i	−0.389457	+	0.921045i	$0.627337\pi$
$224$	−4.18462	−	9.16304i	−0.279597	−	0.612231i
$225$	−3.28602	−	3.50954i	−0.219068	−	0.233969i
$226$	−29.9824	−	13.6925i	−1.99440	−	0.910811i
$227$	−12.9830	−	10.2099i	−0.861710	−	0.677656i	0.0861713	−	0.996280i	$-0.472537\pi$
$227$	−12.9830	−	10.2099i	−0.861710	−	0.677656i	−0.947881	+	0.318624i	$0.896779\pi$
$228$	−0.0960813	−	4.98807i	−0.00636314	−	0.330343i
$229$	−8.58436	+	4.95618i	−0.567270	+	0.327514i	−0.756058	−	0.654504i	$-0.772877\pi$
$229$	−8.58436	+	4.95618i	−0.567270	+	0.327514i	0.188788	+	0.982018i	$0.439544\pi$
$230$	−2.72218	−	27.6702i	−0.179495	−	1.82452i
$231$	−8.57953	+	13.9329i	−0.564492	+	0.916716i
$232$	0.912834	+	19.1627i	0.0599305	+	1.25810i
$233$	24.3339	+	3.49868i	1.59416	+	0.229206i	0.881460	−	0.472259i	$-0.156561\pi$
$233$	24.3339	+	3.49868i	1.59416	+	0.229206i	0.712704	+	0.701465i	$0.247470\pi$
$234$	30.8591	−	19.4383i	2.01732	−	1.27072i
$235$	−2.89124	−	9.84664i	−0.188603	−	0.642324i
$236$	−2.34678	+	24.5766i	−0.152762	+	1.59980i
$237$	3.95580	+	4.83557i	0.256957	+	0.314104i
$238$	10.7000	−	8.41455i	0.693576	−	0.545434i
$239$	23.8379	−	5.78302i	1.54195	−	0.374072i	0.627448	−	0.778659i	$-0.284100\pi$
$239$	23.8379	−	5.78302i	1.54195	−	0.374072i	0.914500	+	0.404586i	$0.132584\pi$
$240$	−0.607978	+	2.73499i	−0.0392448	+	0.176543i
$241$	5.77330	+	11.1986i	0.371891	+	0.721368i	0.998310	−	0.0581186i	$-0.0185102\pi$
$241$	5.77330	+	11.1986i	0.371891	+	0.721368i	−0.626418	+	0.779487i	$0.715480\pi$
$242$	29.7249	−	46.2529i	1.91079	−	2.97325i
$243$	15.3035	−	2.96696i	0.981720	−	0.190331i
$244$	1.89301	−	6.44700i	0.121188	−	0.412727i
$245$	−10.6792	−	4.27530i	−0.682267	−	0.273139i
$246$	28.6510	+	10.8347i	1.82672	+	0.690795i
$247$	4.09061	+	2.91291i	0.260279	+	0.185344i
$248$	1.88761	−	1.97967i	0.119863	−	0.125709i
$249$	22.2615	+	10.9392i	1.41077	+	0.693242i
$250$	−12.1755	+	15.4825i	−0.770049	+	0.979197i
$251$	4.85798	−	3.12204i	0.306633	−	0.197061i	−0.378270	−	0.925695i	$-0.623481\pi$
$251$	4.85798	−	3.12204i	0.306633	−	0.197061i	0.684903	+	0.728634i	$0.259845\pi$
$252$	−12.3171	−	8.07470i	−0.775906	−	0.508658i
$253$	27.3891	+	7.95702i	1.72194	+	0.500254i
$254$	11.3082	+	6.52879i	0.709539	+	0.409653i
$255$	−16.9006	+	0.325543i	−1.05836	+	0.0203863i
$256$	−10.8735	+	4.35311i	−0.679596	+	0.272069i
$257$	0.405722	+	4.24892i	0.0253083	+	0.265040i	0.999266	+	0.0383101i	$0.0121975\pi$
$257$	0.405722	+	4.24892i	0.0253083	+	0.265040i	−0.973958	+	0.226730i	$0.927196\pi$
$258$	−13.2787	−	3.62271i	−0.826695	−	0.225540i
$259$	−0.124011	−	0.0118417i	−0.00770569	−	0.000735804i
$260$	28.0212	+	32.3382i	1.73780	+	2.00553i
$261$	−13.3941	−	19.1756i	−0.829075	−	1.18694i
$262$	37.8857	+	11.1242i	2.34058	+	0.687258i
$263$	−6.28580	−	18.1616i	−0.387599	−	1.11989i	−0.955039	−	0.296479i	$-0.904187\pi$
$263$	−6.28580	−	18.1616i	−0.387599	−	1.11989i	0.567440	−	0.823415i	$-0.307934\pi$
$264$	20.9253	+	14.3016i	1.28787	+	0.880205i
$265$	0.0552011	−	1.15881i	0.00339098	−	0.0711854i
$266$	0.632148	−	3.27989i	0.0387595	−	0.201103i
$267$	−0.604896	+	0.128714i	−0.0370191	+	0.00787715i
$268$	−10.5145	+	26.2638i	−0.642272	+	1.60432i
$269$	−17.3924	+	15.0706i	−1.06043	+	0.918868i	−0.996866	−	0.0791093i	$-0.974792\pi$
$269$	−17.3924	+	15.0706i	−1.06043	+	0.918868i	−0.0635648	+	0.997978i	$0.520247\pi$
$270$	10.1421	+	28.3661i	0.617228	+	1.72630i
$271$	−4.53996	+	1.33305i	−0.275783	+	0.0809771i	−0.416699	−	0.909044i	$-0.636813\pi$
$271$	−4.53996	+	1.33305i	−0.275783	+	0.0809771i	0.140917	+	0.990021i	$0.454995\pi$
$272$	1.38691	+	1.94764i	0.0840936	+	0.118093i
$273$	13.9134	−	5.11758i	0.842075	−	0.309730i
$274$	13.3345	−	25.8652i	0.805564	−	1.56258i
$275$	4.76543	+	8.25396i	0.287366	+	0.497732i
$276$	−7.85781	+	24.4401i	−0.472985	+	1.47112i
$277$	11.9060	−	20.6217i	0.715359	−	1.23904i	−0.247461	−	0.968898i	$-0.579596\pi$
$277$	11.9060	−	20.6217i	0.715359	−	1.23904i	0.962821	−	0.270141i	$-0.0870704\pi$
$278$	−2.61750	−	4.07291i	−0.156987	−	0.244277i
$279$	−0.660865	+	3.26888i	−0.0395649	+	0.195703i
$280$	4.17213	−	9.13569i	0.249333	−	0.545962i
$281$	−3.88651	+	16.0204i	−0.231850	+	0.955699i	0.730289	+	0.683139i	$0.239386\pi$
$281$	−3.88651	+	16.0204i	−0.231850	+	0.955699i	−0.962139	+	0.272560i	$0.912130\pi$
$282$	−1.92325	+	15.4885i	−0.114528	+	0.922329i
$283$	−29.8631	−	10.3357i	−1.77518	−	0.614396i	−0.775327	−	0.631560i	$-0.782415\pi$
$283$	−29.8631	−	10.3357i	−1.77518	−	0.614396i	−0.999853	+	0.0171641i	$0.994536\pi$
$284$	9.93251	+	12.6302i	0.589386	+	0.749465i
$285$	−3.08191	+	2.77619i	−0.182556	+	0.164447i
$286$	−68.3228	+	23.6468i	−4.04001	+	1.39826i
$287$	10.4744	+	6.73150i	0.618285	+	0.397348i
$288$	11.1755	−	15.3960i	0.658525	−	0.907220i
$289$	1.68595	−	1.94569i	0.0991733	−	0.114452i
$290$	32.7140	−	31.1927i	1.92103	−	1.83170i
$291$	1.38887	+	12.0811i	0.0814168	+	0.708206i
$292$	−7.94170	+	22.9460i	−0.464753	+	1.34282i
$293$	1.75095	−	2.45886i	0.102292	−	0.143648i	−0.760258	−	0.649622i	$-0.774927\pi$
$293$	1.75095	−	2.45886i	0.102292	−	0.143648i	0.862549	+	0.505973i	$0.168867\pi$
$294$	12.3143	+	12.4266i	0.718182	+	0.724733i
$295$	16.7202	−	11.9064i	0.973490	−	0.693219i
$296$	−0.0274623	+	0.191004i	−0.00159621	+	0.0111019i
$297$	−30.8806	−	1.15610i	−1.79188	−	0.0670838i
$298$		−	32.5321i		−	1.88453i
$299$	−15.0494	−	21.0063i	−0.870327	−	1.21483i
$300$	−7.54795	+	4.07711i	−0.435781	+	0.235392i
$301$	−4.97284	−	2.56368i	−0.286630	−	0.147768i
$302$	8.91241	+	22.2621i	0.512852	+	1.28104i
$303$	0.857664	−	1.74537i	0.0492715	−	0.100269i
$304$	0.570175	+	0.138323i	0.0327018	+	0.00793336i
$305$	−5.08160	+	2.32069i	−0.290972	+	0.132882i
$306$	23.7788	+	9.77105i	1.35934	+	0.558573i
$307$	0.222003	+	1.54407i	0.0126704	+	0.0881245i	0.995175	−	0.0981115i	$-0.0312802\pi$
$307$	0.222003	+	1.54407i	0.0126704	+	0.0881245i	−0.982505	+	0.186236i	$0.940371\pi$
$308$	20.1478	+	21.1304i	1.14803	+	1.20402i
$309$	−5.54669	−	17.6271i	−0.315540	−	1.00277i
$310$	−6.43761	−	0.306661i	−0.365632	−	0.0174172i
$311$	−25.3925	−	1.20959i	−1.43988	−	0.0685898i	−0.686955	−	0.726700i	$-0.741053\pi$
$311$	−25.3925	−	1.20959i	−1.43988	−	0.0685898i	−0.752922	+	0.658110i	$0.771356\pi$
$312$	−6.89271	−	21.9047i	−0.390223	−	1.24011i
$313$	18.2573	+	19.1477i	1.03197	+	1.08229i	0.996556	+	0.0829213i	$0.0264250\pi$
$313$	18.2573	+	19.1477i	1.03197	+	1.08229i	0.0354094	+	0.999373i	$0.488726\pi$
$314$	1.59829	+	11.1164i	0.0901970	+	0.627334i
$315$	1.63253	+	12.1357i	0.0919825	+	0.683772i
$316$	10.1402	−	4.63090i	0.570433	−	0.260508i
$317$	1.32575	+	0.321624i	0.0744617	+	0.0180642i	0.272817	−	0.962066i	$-0.412045\pi$
$317$	1.32575	+	0.321624i	0.0744617	+	0.0180642i	−0.198355	+	0.980130i	$0.563560\pi$
$318$	−0.778135	+	1.58353i	−0.0436356	+	0.0887997i
$319$	17.2334	+	43.0469i	0.964885	+	2.41017i
$320$	29.8023	+	15.3641i	1.66600	+	0.858882i
$321$	30.1816	−	16.3030i	1.68457	−	0.909943i
$322$	−8.55141	+	14.9099i	−0.476552	+	0.830898i
$323$			3.53981i			0.196960i
$324$	1.82781	−	27.7550i	0.101545	−	1.54194i
$325$	1.22890	−	8.54717i	0.0681670	−	0.474112i
$326$	−26.3691	+	18.7774i	−1.46045	+	1.03998i
$327$	−9.58576	−	9.67319i	−0.530093	−	0.534929i
$328$	11.1874	−	15.7104i	0.617718	−	0.867464i
$329$	−2.07496	+	5.99520i	−0.114396	+	0.330526i
$330$	−6.82045	−	59.3278i	−0.375453	−	3.26589i
$331$	17.6425	−	16.8221i	0.969722	−	0.924628i	−0.0274617	−	0.999623i	$-0.508742\pi$
$331$	17.6425	−	16.8221i	0.969722	−	0.924628i	0.997184	+	0.0749946i	$0.0238940\pi$
$332$	28.9834	−	33.4486i	1.59067	−	1.83573i
$333$	−0.0957885	−	0.214890i	−0.00524918	−	0.0117759i
$334$	−33.3912	−	21.4592i	−1.82708	−	1.17419i
$335$	22.2274	−	7.69298i	1.21441	−	0.420313i
$336$	1.28689	−	1.15924i	0.0702057	−	0.0632415i
$337$	4.84570	+	6.16180i	0.263962	+	0.335655i	0.899909	−	0.436078i	$-0.143633\pi$
$337$	4.84570	+	6.16180i	0.263962	+	0.335655i	−0.635947	+	0.771733i	$0.719390\pi$
$338$	34.1835	+	11.8310i	1.85934	+	0.643523i
$339$	3.11802	−	25.1105i	0.169348	−	1.36381i
$340$	−7.11097	+	29.3118i	−0.385647	+	1.58966i
$341$	2.74642	−	6.01382i	0.148727	−	0.325667i
$342$	5.97992	−	2.00906i	0.323357	−	0.108637i
$343$	9.85619	+	15.3365i	0.532184	+	0.828095i
$344$	−4.33318	+	7.50529i	−0.233630	+	0.404658i
$345$	19.6350	−	8.36929i	1.05711	−	0.450587i
$346$	−0.383146	−	0.663628i	−0.0205981	−	0.0356769i
$347$	−5.51250	+	10.6928i	−0.295926	+	0.574017i	−0.989185	−	0.146672i	$-0.953144\pi$
$347$	−5.51250	+	10.6928i	−0.295926	+	0.574017i	0.693259	+	0.720689i	$0.256174\pi$
$348$	−39.1705	+	14.4076i	−2.09976	+	0.772329i
$349$	16.6188	+	23.3378i	0.889583	+	1.24924i	0.967650	+	0.252297i	$0.0811858\pi$
$349$	16.6188	+	23.3378i	0.889583	+	1.24924i	−0.0780669	+	0.996948i	$0.524875\pi$
$350$	−5.51100	+	1.61818i	−0.294575	+	0.0864952i
$351$	21.3449	+	18.1183i	1.13931	+	0.967085i
$352$	−28.5022	+	24.6973i	−1.51917	+	1.31637i
$353$	−13.0113	+	32.5006i	−0.692521	+	1.72983i	−0.00893850	+	0.999960i	$0.502845\pi$
$353$	−13.0113	+	32.5006i	−0.692521	+	1.72983i	−0.683582	+	0.729873i	$0.739579\pi$
$354$	−30.5338	+	6.49719i	−1.62286	+	0.345322i
$355$	2.52823	−	13.1177i	0.134184	−	0.696215i
$356$	−0.0525069	+	1.10226i	−0.00278286	+	0.0584194i
$357$	8.62732	+	5.89643i	0.456606	+	0.312072i
$358$	−5.81750	−	16.8086i	−0.307464	−	0.888360i
$359$	9.64813	+	2.83295i	0.509209	+	0.149517i	0.526237	−	0.850338i	$-0.323602\pi$
$359$	9.64813	+	2.83295i	0.509209	+	0.149517i	−0.0170284	+	0.999855i	$0.505421\pi$
$360$	18.8974	−	1.63147i	0.995981	−	0.0859861i
$361$	−11.8735	−	13.7028i	−0.624923	−	0.721199i
$362$	−15.9442	−	1.52249i	−0.838011	−	0.0800203i
$363$	40.7193	+	11.1091i	2.13721	+	0.583076i
$364$	−2.51445	−	26.3325i	−0.131793	−	1.38020i
$365$	18.7419	−	7.50314i	0.980998	−	0.392733i
$366$	8.49456	−	0.163624i	0.444018	−	0.00855277i
$367$	18.9441	+	10.9374i	0.988875	+	0.570927i	0.904938	−	0.425544i	$-0.139917\pi$
$367$	18.9441	+	10.9374i	0.988875	+	0.570927i	0.0839370	+	0.996471i	$0.473251\pi$
$368$	−2.54448	−	1.62496i	−0.132640	−	0.0847069i
$369$	−1.33211	+	23.4771i	−0.0693469	+	1.22217i
$370$	0.382488	−	0.245810i	0.0198846	−	0.0127790i
$371$	−0.443335	+	0.563746i	−0.0230168	+	0.0292682i
$372$	5.34082	+	2.62445i	0.276909	+	0.136071i
$373$	−13.5758	+	14.2379i	−0.702930	+	0.737212i	−0.974298	−	0.225264i	$-0.927676\pi$
$373$	−13.5758	+	14.2379i	−0.702930	+	0.737212i	0.271368	+	0.962476i	$0.412524\pi$
$374$	−41.5134	−	29.5616i	−2.14661	−	1.52859i
$375$	−14.1430	−	5.34833i	−0.730341	−	0.276187i
$376$	9.12316	+	3.65236i	0.470491	+	0.188356i
$377$	11.8357	−	40.3086i	0.609568	−	2.07600i
$378$	5.06452	−	17.9210i	0.260491	−	0.921758i
$379$	8.30444	−	12.9220i	0.426570	−	0.663756i	−0.559738	−	0.828670i	$-0.689098\pi$
$379$	8.30444	−	12.9220i	0.426570	−	0.663756i	0.986308	+	0.164914i	$0.0527345\pi$
$380$	3.39149	+	6.57857i	0.173980	+	0.337473i
$381$	−2.17520	+	9.78512i	−0.111439	+	0.501307i
$382$	9.28337	−	2.25212i	0.474979	−	0.115229i
$383$	9.09354	−	7.15124i	0.464658	−	0.365411i	−0.358212	−	0.933640i	$-0.616614\pi$
$383$	9.09354	−	7.15124i	0.464658	−	0.365411i	0.822871	+	0.568229i	$0.192371\pi$
$384$	−18.3787	−	22.4661i	−0.937885	−	1.14647i
$385$	2.30743	−	24.1645i	0.117597	−	1.23153i
$386$	−7.05096	−	24.0134i	−0.358885	−	1.22225i
$387$	−0.406909	−	10.5584i	−0.0206843	−	0.536716i
$388$	21.4779	+	3.08805i	1.09037	+	0.156772i
$389$	−0.941011	−	19.7542i	−0.0477111	−	1.00158i	−0.888116	−	0.459620i	$-0.847986\pi$
$389$	−0.941011	−	19.7542i	−0.0477111	−	1.00158i	0.840404	−	0.541960i	$-0.182318\pi$
$390$	−28.3698	+	46.0715i	−1.43656	+	2.33292i
$391$	5.90822	−	17.2302i	0.298791	−	0.871368i
$392$	9.53953	−	5.50765i	0.481819	−	0.278178i
$393$	0.583762	+	30.3061i	0.0294469	+	1.52874i
$394$	−11.0788	−	8.71244i	−0.558140	−	0.438926i
$395$	−8.43077	−	3.85021i	−0.424198	−	0.193725i
$396$	−16.0145	+	52.7634i	−0.804761	+	2.65146i
$397$	0.490893	+	1.07491i	0.0246372	+	0.0539480i	0.921551	−	0.388258i	$-0.126923\pi$
$397$	0.490893	+	1.07491i	0.0246372	+	0.0539480i	−0.896913	+	0.442206i	$0.854196\pi$
$398$	20.9648	−	4.04064i	1.05087	−	0.202539i
$399$	2.54745	−	0.292861i	0.127532	−	0.0146614i
$400$	−0.237850	−	0.980431i	−0.0118925	−	0.0490215i
$401$	−8.84816	−	1.70534i	−0.441856	−	0.0851608i	−0.0365292	−	0.999333i	$-0.511630\pi$
$401$	−8.84816	−	1.70534i	−0.441856	−	0.0851608i	−0.405327	+	0.914172i	$0.632842\pi$
$402$	−35.6689	−	2.71391i	−1.77900	−	0.135358i
$403$	−5.32403	+	2.74473i	−0.265209	+	0.136725i
$404$	−2.62247	−	2.27238i	−0.130473	−	0.113055i
$405$	−18.4348	+	13.9631i	−0.916034	+	0.693830i
$406$	−27.6590	+	3.97676i	−1.37269	+	0.197363i
$407$	0.0882668	+	0.457972i	0.00437522	+	0.0227008i
$408$	9.75914	−	12.9141i	0.483150	−	0.639341i
$409$	17.6513	+	16.8304i	0.872799	+	0.832212i	0.986913	−	0.161256i	$-0.0515544\pi$
$409$	17.6513	+	16.8304i	0.872799	+	0.832212i	−0.114114	+	0.993468i	$0.536403\pi$
$410$	−45.2366	+	4.31957i	−2.23408	+	0.213328i
$411$	22.0131	+	3.80453i	1.08583	+	0.187664i
$412$	−32.9358	+	1.56893i	−1.62263	+	0.0772954i
$413$	−12.6893			−0.624397
$414$	−32.4609	−	0.201784i	−1.59536	−	0.00991716i
$415$	−36.7976			−1.80632
$416$	34.1304	−	1.62583i	1.67338	−	0.0797130i
$417$	2.37936	−	2.85523i	0.116518	−	0.139821i
$418$	−12.4490	+	1.18874i	−0.608901	+	0.0581430i
$419$	16.7897	+	16.0090i	0.820232	+	0.782090i	0.978705	−	0.205274i	$-0.0658084\pi$
$419$	16.7897	+	16.0090i	0.820232	+	0.782090i	−0.158473	+	0.987363i	$0.550657\pi$
$420$	21.6828	+	2.69241i	1.05801	+	0.131376i
$421$	−0.845603	−	4.38740i	−0.0412121	−	0.213829i	0.955485	−	0.295041i	$-0.0953332\pi$
$421$	−0.845603	−	4.38740i	−0.0412121	−	0.213829i	−0.996697	+	0.0812116i	$0.974121\pi$
$422$	−19.1589	+	2.75463i	−0.932639	+	0.134093i
$423$	−11.7851	+	2.16059i	−0.573009	+	0.105051i
$424$	0.839582	+	0.727502i	0.0407737	+	0.0353306i
$425$	5.41016	−	2.78913i	0.262431	−	0.135293i
$426$	−11.4642	+	16.7738i	−0.555444	+	0.812694i
$427$	3.39110	+	0.653580i	0.164107	+	0.0316290i
$428$	−14.4305	−	59.4834i	−0.697526	−	2.87524i
$429$	−33.0592	−	44.5825i	−1.59612	−	2.15246i
$430$	20.0503	−	3.86438i	0.966912	−	0.186357i
$431$	11.0276	+	24.1470i	0.531179	+	1.16312i	0.965031	+	0.262135i	$0.0844266\pi$
$431$	11.0276	+	24.1470i	0.531179	+	1.16312i	−0.433853	+	0.900984i	$0.642846\pi$
$432$	3.10192	+	1.03835i	0.149241	+	0.0499576i
$433$	5.36922	+	2.45204i	0.258028	+	0.117838i	0.540230	−	0.841518i	$-0.318337\pi$
$433$	5.36922	+	2.45204i	0.258028	+	0.117838i	−0.282201	+	0.959355i	$0.591065\pi$
$434$	3.13180	+	2.46288i	0.150331	+	0.118222i
$435$	30.3798	+	16.7681i	1.45660	+	0.803970i
$436$	−21.0441	+	12.1498i	−1.00783	+	0.581871i
$437$	−1.67310	−	4.14475i	−0.0800351	−	0.198270i
$438$	−30.6907	−	0.870009i	−1.46646	−	0.0415706i
$439$	−0.469659	−	9.85937i	−0.0224156	−	0.470562i	−0.981970	−	0.189038i	$-0.939463\pi$
$439$	−0.469659	−	9.85937i	−0.0224156	−	0.470562i	0.959554	−	0.281524i	$-0.0908399\pi$
$440$	−37.2185	−	5.35121i	−1.77432	−	0.255109i
$441$	−6.26220	+	11.8808i	−0.298200	+	0.565754i
$442$	13.0085	+	44.3029i	0.618752	+	2.10728i
$443$	−0.618218	+	6.47428i	−0.0293724	+	0.307602i	0.968833	+	0.247716i	$0.0796799\pi$
$443$	−0.618218	+	6.47428i	−0.0293724	+	0.307602i	−0.998205	+	0.0598864i	$0.980926\pi$
$444$	−0.414306	+	0.0677362i	−0.0196621	+	0.00321462i
$445$	0.721183	−	0.567144i	0.0341873	−	0.0268852i
$446$	−36.4578	+	8.84457i	−1.72633	+	0.418802i
$447$	23.8225	−	7.49619i	1.12677	−	0.354557i
$448$	−9.49803	−	18.4236i	−0.448740	−	0.870434i
$449$	1.78661	−	2.78001i	0.0843152	−	0.131197i	−0.796534	−	0.604593i	$-0.793336\pi$
$449$	1.78661	−	2.78001i	0.0843152	−	0.131197i	0.880850	+	0.473396i	$0.156972\pi$
$450$	−7.78238	−	7.55657i	−0.366865	−	0.356220i
$451$	13.1331	−	44.7271i	0.618412	−	2.10612i
$452$	−41.9156	−	16.7805i	−1.97154	−	0.789287i
$453$	−14.2484	+	11.6561i	−0.669449	+	0.547651i
$454$	−30.3555	−	21.6160i	−1.42465	−	1.01449i
$455$	−15.1768	+	15.9170i	−0.711500	+	0.746200i
$456$	−0.265370	−	3.96314i	−0.0124271	−	0.185591i
$457$	−18.6564	+	23.7235i	−0.872709	+	1.10974i	0.120421	+	0.992723i	$0.461575\pi$
$457$	−18.6564	+	23.7235i	−0.872709	+	1.10974i	−0.993130	+	0.117017i	$0.962667\pi$
$458$	−18.8143	+	12.0912i	−0.879133	+	0.564984i
$459$	−1.67589	+	19.6642i	−0.0782239	+	0.917845i
$460$	−5.52808	−	37.6822i	−0.257748	−	1.75694i
$461$	3.99820	+	2.30836i	0.186215	+	0.107511i	0.590209	−	0.807250i	$-0.299045\pi$
$461$	3.99820	+	2.30836i	0.186215	+	0.107511i	−0.403995	+	0.914761i	$0.632379\pi$
$462$	−17.8397	+	32.3212i	−0.829978	+	1.50372i
$463$	11.2827	−	4.51691i	0.524351	−	0.209919i	−0.0943584	−	0.995538i	$-0.530080\pi$
$463$	11.2827	−	4.51691i	0.524351	−	0.209919i	0.618710	+	0.785620i	$0.287656\pi$
$464$	−0.466557	−	4.88601i	−0.0216594	−	0.226827i
$465$	−1.25882	−	4.78478i	−0.0583765	−	0.221889i
$466$	55.2162	+	5.27250i	2.55784	+	0.244244i
$467$	11.4461	+	13.2095i	0.529664	+	0.611265i	0.956024	−	0.293289i	$-0.0947497\pi$
$467$	11.4461	+	13.2095i	0.529664	+	0.611265i	−0.426360	+	0.904554i	$0.640204\pi$
$468$	40.9557	−	28.6076i	1.89318	−	1.32239i
$469$	−13.9516	−	4.09656i	−0.644225	−	0.189161i
$470$	−7.57299	−	21.8807i	−0.349316	−	1.00928i
$471$	−7.77199	+	3.73188i	−0.358114	+	0.171956i
$472$	−0.935258	+	19.6335i	−0.0430488	+	0.903705i
$473$	−3.96413	+	20.5679i	−0.182271	+	0.945711i
$474$	9.43420	+	10.4731i	0.433327	+	0.481046i
$475$	0.555119	−	1.38662i	0.0254706	−	0.0636225i
$476$	14.0917	−	12.2105i	0.645893	−	0.559669i
$477$	−1.33888	−	0.204927i	−0.0613031	−	0.00938297i
$478$	53.1021	−	15.5922i	2.42883	−	0.713169i
$479$	−1.79337	−	2.51844i	−0.0819413	−	0.115070i	0.771571	−	0.636143i	$-0.219471\pi$
$479$	−1.79337	−	2.51844i	−0.0819413	−	0.115070i	−0.853512	+	0.521073i	$0.825532\pi$
$480$	−4.80660	+	27.8111i	−0.219390	+	1.26940i
$481$	0.193630	−	0.375590i	0.00882877	−	0.0171254i
$482$	14.2134	+	24.6183i	0.647402	+	1.12133i
$483$	−12.8887	−	2.82639i	−0.586454	−	0.128605i
$484$	37.6563	−	65.2226i	1.71165	−	2.96466i
$485$	−9.75354	−	15.1768i	−0.442886	−	0.689143i
$486$	34.1706	−	8.32948i	1.55001	−	0.377833i
$487$	−6.80280	+	14.8961i	−0.308264	+	0.675005i	−0.998835	−	0.0482604i	$-0.984632\pi$
$487$	−6.80280	+	14.8961i	−0.308264	+	0.675005i	0.690570	+	0.723265i	$0.257360\pi$
$488$	1.26119	−	5.19871i	0.0570916	−	0.235335i
$489$	−19.8263	−	14.9827i	−0.896578	−	0.677543i
$490$	−24.5263	−	8.48865i	−1.10799	−	0.383478i
$491$	−25.0612	−	31.8679i	−1.13099	−	1.43818i	−0.882974	−	0.469421i	$-0.844463\pi$
$491$	−25.0612	−	31.8679i	−1.13099	−	1.43818i	−0.248020	−	0.968755i	$-0.579780\pi$
$492$	39.9077	+	12.9571i	1.79918	+	0.584151i
$493$	27.9841	−	9.68539i	1.26034	−	0.436208i
$494$	9.53162	+	6.12560i	0.428848	+	0.275604i
$495$	41.8728	−	18.6650i	1.88204	−	0.838931i
$496$	−0.458287	+	0.528891i	−0.0205777	+	0.0237479i
$497$	−5.97698	+	5.69904i	−0.268104	+	0.255637i
$498$	51.3446	+	22.2634i	2.30081	+	0.997648i
$499$	2.65974	−	7.68481i	0.119066	−	0.344020i	−0.869681	−	0.493614i	$-0.835676\pi$
$499$	2.65974	−	7.68481i	0.119066	−	0.344020i	0.988747	+	0.149594i	$0.0477968\pi$
$500$	−15.6500	+	21.9773i	−0.699888	+	0.982856i
$501$	8.01993	−	29.3963i	0.358304	−	1.31333i
$502$	10.6131	−	7.55758i	0.473687	−	0.337311i
$503$	−2.27587	+	15.8290i	−0.101476	+	0.705781i	0.874040	+	0.485854i	$0.161491\pi$
$503$	−2.27587	+	15.8290i	−0.101476	+	0.705781i	−0.975516	+	0.219928i	$0.929418\pi$
$504$	−10.1011	−	5.95483i	−0.449940	−	0.265249i
$505$			2.88504i			0.128383i
$506$	62.5803	+	14.9922i	2.78203	+	0.666483i
$507$	−0.786873	+	27.7580i	−0.0349463	+	1.23277i
$508$	15.8979	+	8.19592i	0.705354	+	0.363635i
$509$	−10.2556	−	25.6173i	−0.454573	−	1.13547i	−0.961824	−	0.273670i	$-0.911762\pi$
$509$	−10.2556	−	25.6173i	−0.454573	−	1.13547i	0.507250	−	0.861799i	$-0.330662\pi$
$510$	−38.0535	+	2.54805i	−1.68504	+	0.112829i
$511$	−12.1284	−	2.94231i	−0.536527	−	0.130160i
$512$	6.44937	−	2.94533i	0.285025	−	0.130166i
$513$	2.84911	+	3.91603i	0.125791	+	0.172897i
$514$	1.37051	+	9.53211i	0.0604506	+	0.420443i
$515$	18.9181	+	19.8408i	0.833632	+	0.874288i
$516$	−18.4046	−	4.09127i	−0.810217	−	0.180108i
$517$	23.7250	+	1.13016i	1.04342	+	0.0497043i
$518$	−0.280752	−	0.0133739i	−0.0123356	−	0.000587615i
$519$	0.397673	−	0.433485i	0.0174559	−	0.0190279i
$520$	23.5090	+	24.6555i	1.03094	+	1.08122i
$521$	−0.612203	−	4.25796i	−0.0268211	−	0.186545i	0.972007	−	0.234954i	$-0.0754939\pi$
$521$	−0.612203	−	4.25796i	−0.0268211	−	0.186545i	−0.998828	+	0.0484092i	$0.984585\pi$
$522$	−32.2446	−	41.7775i	−1.41131	−	1.82855i
$523$	16.8247	−	7.68359i	0.735694	−	0.335980i	−0.0120860	−	0.999927i	$-0.503847\pi$
$523$	16.8247	−	7.68359i	0.735694	−	0.335980i	0.747780	+	0.663947i	$0.231120\pi$
$524$	52.5618	+	12.7514i	2.29617	+	0.557046i
$525$	−2.45482	−	3.66271i	−0.107137	−	0.159854i
$526$	−16.1159	−	40.2556i	−0.702686	−	1.75523i
$527$	−3.75287	−	1.93474i	−0.163477	−	0.0842785i
$528$	−5.52167	−	3.40011i	−0.240300	−	0.147971i
$529$	1.22596	+	22.9673i	0.0533028	+	0.998578i
$530$		−	2.61752i		−	0.113698i
$531$	−11.7935	−	20.8621i	−0.511794	−	0.905339i
$532$	0.651156	−	4.52889i	0.0282312	−	0.196352i
$533$	−34.4028	+	24.4982i	−1.49015	+	1.06113i
$534$	−1.34942	+	0.355018i	−0.0583951	+	0.0153631i
$535$	−29.5191	+	41.4538i	−1.27622	+	1.79220i
$536$	−7.36671	+	21.2847i	−0.318193	+	0.919360i
$537$	10.9680	−	8.13312i	0.473305	−	0.350970i
$538$	−37.5788	+	35.8313i	−1.62014	+	1.54480i
$539$	17.4348	−	20.1209i	0.750971	−	0.866667i
$540$	15.7257	+	38.1506i	0.676725	+	1.64174i
$541$	2.52797	+	1.62463i	0.108686	+	0.0698483i	0.593855	−	0.804572i	$-0.297605\pi$
$541$	2.52797	+	1.62463i	0.108686	+	0.0698483i	−0.485169	+	0.874421i	$0.661242\pi$
$542$	−10.0885	+	3.49165i	−0.433337	+	0.149979i
$543$	−2.55906	−	12.0264i	−0.109820	−	0.516103i
$544$	14.8887	+	18.9325i	0.638348	+	0.811725i
$545$	19.0920	+	6.60780i	0.817810	+	0.283047i
$546$	30.8068	−	13.0270i	1.31841	−	0.557505i
$547$	−6.19308	+	25.5282i	−0.264797	+	1.09151i	0.671697	+	0.740826i	$0.265566\pi$
$547$	−6.19308	+	25.5282i	−0.264797	+	1.09151i	−0.936494	+	0.350683i	$0.885950\pi$
$548$	16.5589	−	36.2590i	0.707363	−	1.54891i
$549$	2.07717	+	6.18267i	0.0886516	+	0.263870i
$550$	11.6258	+	18.0901i	0.495727	+	0.771366i
$551$	3.63327	−	6.29301i	0.154783	−	0.268091i
$552$	−5.32310	+	19.7337i	−0.226566	+	0.839923i
$553$	2.86482	+	4.96201i	0.121824	+	0.211006i
$554$	24.6183	−	47.7528i	1.04593	−	2.02882i
$555$	0.268135	+	0.223446i	0.0113817	+	0.00948477i
$556$	−3.84684	−	5.40213i	−0.163142	−	0.229101i
$557$	−33.6596	+	9.88336i	−1.42620	+	0.418771i	−0.901598	−	0.432574i	$-0.857605\pi$
$557$	−33.6596	+	9.88336i	−1.42620	+	0.418771i	−0.524606	+	0.851345i	$0.675787\pi$
$558$	−1.13844	+	7.43794i	−0.0481940	+	0.314873i
$559$	14.3424	−	12.4277i	0.606618	−	0.525637i
$560$	−0.954993	+	2.38546i	−0.0403558	+	0.100804i
$561$	12.0815	−	37.2110i	0.510083	−	1.57105i
$562$	−7.03905	+	36.5221i	−0.296924	+	1.54059i
$563$	−1.14919	+	24.1244i	−0.0484324	+	1.01672i	0.835612	+	0.549320i	$0.185113\pi$
$563$	−1.14919	+	24.1244i	−0.0484324	+	1.01672i	−0.884045	+	0.467402i	$0.845190\pi$
$564$	−1.62196	+	21.3174i	−0.0682970	+	0.897625i
$565$	12.2776	+	35.4737i	0.516521	+	1.49239i
$566$	−68.4114	−	20.0874i	−2.87554	−	0.844336i
$567$	14.2901	−	0.420815i	0.600130	−	0.0176726i
$568$	8.37733	+	9.66795i	0.351505	+	0.405658i
$569$	34.6897	+	3.31247i	1.45427	+	0.138866i	0.792055	−	0.610450i	$-0.209011\pi$
$569$	34.6897	+	3.31247i	1.45427	+	0.138866i	0.662213	+	0.749315i	$0.269617\pi$
$570$	−6.64757	+	6.58748i	−0.278436	+	0.275919i
$571$	0.00425220	+	0.0445310i	0.000177949	+	0.00186357i	0.995560	−	0.0941242i	$-0.0300051\pi$
$571$	0.00425220	+	0.0445310i	0.000177949	+	0.00186357i	−0.995383	+	0.0959878i	$0.969399\pi$
$572$	−91.9410	+	36.8076i	−3.84425	+	1.53900i
$573$	3.78829	+	6.27906i	0.158258	+	0.262311i
$574$	24.3286	+	14.0461i	1.01546	+	0.586273i
$575$	−5.01645	+	5.82291i	−0.209200	+	0.242832i
$576$	21.4623	−	32.7385i	0.894263	−	1.36411i
$577$	27.8213	−	17.8797i	1.15822	−	0.744341i	0.186959	−	0.982368i	$-0.440137\pi$
$577$	27.8213	−	17.8797i	1.15822	−	0.744341i	0.971259	+	0.238026i	$0.0765004\pi$
$578$	3.59069	−	4.56594i	0.149353	−	0.189918i
$579$	15.9597	−	10.6965i	0.663264	−	0.444533i
$580$	42.7276	−	44.8114i	1.77417	−	1.86069i
$581$	18.5300	+	13.1952i	0.768755	+	0.547428i
$582$	4.42702	+	27.0777i	0.183506	+	1.12241i
$583$	2.49274	+	0.997944i	0.103239	+	0.0413306i
$584$	−5.44641	+	18.5488i	−0.225374	+	0.767554i
$585$	−40.2742	−	10.1585i	−1.66513	−	0.420003i
$586$	3.68209	−	5.72945i	0.152106	−	0.236681i
$587$	7.43702	+	14.4258i	0.306959	+	0.595417i	0.990975	−	0.134050i	$-0.0427984\pi$
$587$	7.43702	+	14.4258i	0.306959	+	0.595417i	−0.684016	+	0.729467i	$0.739768\pi$
$588$	17.6588	+	16.2000i	0.728238	+	0.668076i
$589$	−1.00687	+	0.244264i	−0.0414873	+	0.0100647i
$590$	36.4037	−	28.6282i	1.49872	−	1.17860i
$591$	3.82710	−	10.1203i	0.157426	−	0.416293i
$592$	0.00469290	−	0.0491463i	0.000192877	−	0.00201990i
$593$	6.72727	+	22.9110i	0.276256	+	0.940841i	0.974388	+	0.224872i	$0.0721965\pi$
$593$	6.72727	+	22.9110i	0.276256	+	0.940841i	−0.698133	+	0.715969i	$0.745985\pi$
$594$	−69.7190	+	0.709735i	−2.86060	+	0.0291208i
$595$	−15.3448	−	2.20625i	−0.629076	−	0.0904475i
$596$	−2.12036	−	44.5118i	−0.0868532	−	1.82327i
$597$	7.78967	+	14.4210i	0.318810	+	0.590212i
$598$	−36.1715	−	45.7257i	−1.47916	−	1.86986i
$599$	−22.8221	+	13.1763i	−0.932484	+	0.538370i	−0.887596	−	0.460622i	$-0.847626\pi$
$599$	−22.8221	+	13.1763i	−0.932484	+	0.538370i	−0.0448876	+	0.998992i	$0.514293\pi$
$600$	−5.84808	+	3.52828i	−0.238747	+	0.144041i
$601$	3.32201	+	2.61246i	0.135508	+	0.106564i	0.683612	−	0.729845i	$-0.260408\pi$
$601$	3.32201	+	2.61246i	0.135508	+	0.106564i	−0.548105	+	0.836410i	$0.684650\pi$
$602$	−11.4824	−	5.24383i	−0.467987	−	0.213723i
$603$	−6.23165	−	26.7449i	−0.253773	−	1.08914i
$604$	13.6453	+	29.8791i	0.555221	+	1.21576i
$605$	−61.4846	+	11.8502i	−2.49970	+	0.481778i
$606$	1.74552	−	4.02557i	0.0709068	−	0.163527i
$607$	−2.32187	−	9.57086i	−0.0942416	−	0.388469i	0.905082	−	0.425237i	$-0.139809\pi$
$607$	−2.32187	−	9.57086i	−0.0942416	−	0.388469i	−0.999324	+	0.0367673i	$0.988294\pi$
$608$	5.80344	+	1.11852i	0.235361	+	0.0453621i
$609$	−9.28540	−	19.3377i	−0.376263	−	0.783603i
$610$	−11.2031	+	5.77562i	−0.453602	+	0.233848i
$611$	−16.2633	−	14.0923i	−0.657944	−	0.570111i
$612$	33.1720	+	11.8193i	1.34090	+	0.477768i
$613$	6.98799	−	1.00472i	0.282242	−	0.0405803i	0.000260120	−	1.00000i	$-0.499917\pi$
$613$	6.98799	−	1.00472i	0.282242	−	0.0405803i	0.281982	+	0.959420i	$0.409008\pi$
$614$	0.666087	+	3.45599i	0.0268811	+	0.139472i
$615$	−13.5867	−	32.1304i	−0.547870	−	1.29562i
$616$	16.8231	+	16.0408i	0.677822	+	0.646302i
$617$	−10.8623	+	1.03722i	−0.437300	+	0.0417571i	−0.311385	−	0.950284i	$-0.600793\pi$
$617$	−10.8623	+	1.03722i	−0.437300	+	0.0417571i	−0.125915	+	0.992041i	$0.540187\pi$
$618$	−14.3928	−	39.1302i	−0.578963	−	1.57405i
$619$	−12.6258	+	0.601439i	−0.507472	+	0.0241739i	−0.299757	−	0.954016i	$-0.596906\pi$
$619$	−12.6258	+	0.601439i	−0.507472	+	0.0241739i	−0.207715	+	0.978189i	$0.566603\pi$
$620$	−8.82820			−0.354549
$621$	−7.33201	−	23.8168i	−0.294224	−	0.955737i
$622$	−57.3562			−2.29978
$623$	−0.566535	+	0.0269874i	−0.0226977	+	0.00108123i
$624$	2.02812	+	5.51393i	0.0811898	+	0.220734i
$625$	30.3068	−	2.89395i	1.21227	−	0.115758i
$626$	43.2017	+	41.1927i	1.72669	+	1.64639i
$627$	−3.73904	−	8.84221i	−0.149323	−	0.353124i
$628$	2.91139	+	15.1057i	0.116177	+	0.602785i
$629$	0.294830	−	0.0423902i	0.0117557	−	0.00169021i
$630$	4.98202	+	27.1747i	0.198489	+	1.08267i
$631$	8.76130	+	7.59171i	0.348782	+	0.302221i	0.811579	−	0.584243i	$-0.198609\pi$
$631$	8.76130	+	7.59171i	0.348782	+	0.302221i	−0.462797	+	0.886464i	$0.653154\pi$
$632$	7.88864	−	4.06687i	0.313793	−	0.161772i
$633$	−6.43182	−	13.3949i	−0.255642	−	0.532398i
$634$	3.02234	+	0.582508i	0.120032	+	0.0231344i
$635$	−3.50594	−	14.4517i	−0.139129	−	0.573498i
$636$	−0.961467	+	2.21736i	−0.0381246	+	0.0879242i
$637$	−23.6855	+	4.56501i	−0.938453	+	0.180872i
$638$	43.4598	+	95.1636i	1.72059	+	3.76756i
$639$	−14.9247	−	4.52989i	−0.590413	−	0.179200i
$640$	39.1695	+	17.8881i	1.54831	+	0.707090i
$641$	−30.0913	−	23.6641i	−1.18854	−	0.934674i	−0.189649	−	0.981852i	$-0.560735\pi$
$641$	−30.0913	−	23.6641i	−1.18854	−	0.934674i	−0.998887	+	0.0471776i	$0.984977\pi$
$642$	66.2693	−	39.9817i	2.61544	−	1.57795i
$643$	−18.2600	+	10.5424i	−0.720103	+	0.415751i	−0.814790	−	0.579756i	$-0.803148\pi$
$643$	−18.2600	+	10.5424i	−0.720103	+	0.415751i	0.0946878	+	0.995507i	$0.469815\pi$
$644$	−10.7286	+	20.9578i	−0.422767	+	0.825852i
$645$	7.44988	+	13.7919i	0.293339	+	0.543057i
$646$	0.380018	+	7.97757i	0.0149516	+	0.313873i
$647$	21.1613	+	3.04253i	0.831935	+	0.119614i	0.545106	−	0.838367i	$-0.316490\pi$
$647$	21.1613	+	3.04253i	0.831935	+	0.119614i	0.286830	+	0.957982i	$0.407399\pi$
$648$	0.402144	−	22.1415i	0.0157977	−	0.869800i
$649$	13.3844	+	45.5831i	0.525384	+	1.78929i
$650$	1.85195	−	19.3945i	0.0726393	−	0.760713i
$651$	−1.08186	+	2.86085i	−0.0424016	+	0.112126i
$652$	−34.8555	+	27.4107i	−1.36505	+	1.07349i
$653$	15.3937	−	3.73446i	0.602401	−	0.146141i	0.0770508	−	0.997027i	$-0.475450\pi$
$653$	15.3937	−	3.73446i	0.602401	−	0.146141i	0.525350	+	0.850886i	$0.323934\pi$
$654$	−22.6416	−	20.7711i	−0.885358	−	0.812216i
$655$	−20.6057	−	39.9695i	−0.805131	−	1.56174i
$656$	−2.66772	+	4.15106i	−0.104157	+	0.162072i
$657$	−6.43480	−	22.6746i	−0.251045	−	0.884619i
$658$	−4.03266	+	13.7340i	−0.157210	+	0.535406i
$659$	35.3491	+	14.1517i	1.37701	+	0.551270i	0.937819	−	0.347125i	$-0.112842\pi$
$659$	35.3491	+	14.1517i	1.37701	+	0.551270i	0.439188	+	0.898395i	$0.355266\pi$
$660$	−13.1989	−	80.7303i	−0.513765	−	3.14242i
$661$	−37.9758	−	27.0425i	−1.47709	−	1.05183i	−0.983247	−	0.182278i	$-0.941653\pi$
$661$	−37.9758	−	27.0425i	−1.47709	−	1.05183i	−0.493841	−	0.869552i	$-0.664408\pi$
$662$	37.9546	−	39.8056i	1.47515	−	1.54709i
$663$	−29.4445	+	19.7343i	−1.14353	+	0.766417i
$664$	21.7820	−	27.6981i	0.845307	−	1.07489i
$665$	−3.20023	+	2.05666i	−0.124100	+	0.0797539i
$666$	−0.238946	−	0.474009i	−0.00925896	−	0.0183675i
$667$	−28.1887	+	24.5673i	−1.09147	+	0.951251i
$668$	−47.0858	−	27.1850i	−1.82181	−	1.05182i
$669$	−14.8774	−	24.6592i	−0.575195	−	0.953380i
$670$	49.2674	−	19.7237i	1.90337	−	0.761993i
$671$	−1.22904	−	12.8711i	−0.0474466	−	0.496883i
$672$	12.3932	−	12.2811i	0.478077	−	0.473755i
$673$	−31.2329	−	2.98238i	−1.20394	−	0.114962i	−0.526262	−	0.850322i	$-0.676407\pi$
$673$	−31.2329	−	2.98238i	−1.20394	−	0.114962i	−0.677677	+	0.735360i	$0.737013\pi$
$674$	11.5821	+	13.3665i	0.446127	+	0.514858i
$675$	3.74026	−	7.44007i	0.143963	−	0.286369i
$676$	47.5424	+	13.9597i	1.82856	+	0.536912i
$677$	3.05394	+	8.82378i	0.117372	+	0.339125i	0.988350	−	0.152197i	$-0.0486349\pi$
$677$	3.05394	+	8.82378i	0.117372	+	0.339125i	−0.870978	+	0.491322i	$0.836514\pi$
$678$	4.33125	−	56.9256i	0.166341	−	2.18621i
$679$	−0.530665	+	11.1400i	−0.0203651	+	0.427515i
$680$	−4.54462	+	23.5797i	−0.174278	+	0.904241i
$681$	8.83428	−	27.2095i	0.338530	−	1.04267i
$682$	5.54392	−	13.8480i	0.212288	−	0.530269i
$683$	9.11620	−	7.89923i	0.348822	−	0.302256i	−0.462773	−	0.886477i	$-0.653145\pi$
$683$	9.11620	−	7.89923i	0.348822	−	0.302256i	0.811594	+	0.584221i	$0.198600\pi$
$684$	8.05104	−	3.13863i	0.307839	−	0.120009i
$685$	−31.7988	+	9.33698i	−1.21497	+	0.356748i
$686$	23.8591	+	33.5054i	0.910945	+	1.27924i
$687$	−13.1894	−	10.9911i	−0.503206	−	0.419338i
$688$	1.01600	−	1.97076i	0.0387345	−	0.0751345i
$689$	−1.21636	−	2.10679i	−0.0463395	−	0.0802624i
$690$	43.3524	−	20.9696i	1.65040	−	0.798298i
$691$	2.21910	−	3.84359i	0.0844184	−	0.146217i	−0.820725	−	0.571324i	$-0.806430\pi$
$691$	2.21910	−	3.84359i	0.0844184	−	0.146217i	0.905143	+	0.425107i	$0.139763\pi$
$692$	−0.567490	−	0.883032i	−0.0215727	−	0.0335678i
$693$	−27.7788	−	5.61600i	−1.05523	−	0.213334i
$694$	−11.2754	+	24.6898i	−0.428010	+	0.937211i
$695$	−1.29993	+	5.35839i	−0.0493092	+	0.203255i
$696$	−30.6047	+	12.9416i	−1.16007	+	0.490550i
$697$	−28.1331	−	9.73697i	−1.06562	−	0.368814i
$698$	39.9588	+	50.8117i	1.51246	+	1.92325i
$699$	8.86222	+	41.6484i	0.335200	+	1.57529i
$700$	−7.43492	+	2.57325i	−0.281014	+	0.0972597i
$701$	9.43779	+	6.06530i	0.356460	+	0.229083i	0.706598	−	0.707615i	$-0.250229\pi$
$701$	9.43779	+	6.06530i	0.356460	+	0.229083i	−0.350138	+	0.936698i	$0.613865\pi$
$702$	50.0495	+	38.5413i	1.88900	+	1.45465i
$703$	0.0478645	−	0.0552386i	0.00180524	−	0.00208336i
$704$	−56.1640	+	53.5523i	−2.11676	+	2.01833i
$705$	14.2778	−	10.5874i	0.537731	−	0.398744i
$706$	−25.8341	+	74.6426i	−0.972278	+	2.80921i
$707$	1.03454	−	1.45281i	0.0389079	−	0.0546385i
$708$	−41.3542	+	10.8798i	−1.55419	+	0.408889i
$709$	−23.5502	+	16.7701i	−0.884448	+	0.629812i	−0.929358	−	0.369179i	$-0.879639\pi$
$709$	−23.5502	+	16.7701i	−0.884448	+	0.629812i	0.0449106	+	0.998991i	$0.485700\pi$
$710$	4.28954	−	29.8344i	0.160984	−	1.11967i
$711$	−5.49535	+	9.32171i	−0.206092	+	0.349591i
$712$			0.878562i			0.0329255i
$713$	5.30868	+	0.491579i	0.198812	+	0.0184098i
$714$	20.0762	+	12.3624i	0.751332	+	0.462652i
$715$	73.1862	+	37.7301i	2.73701	+	1.41103i
$716$	−9.05528	−	22.6190i	−0.338412	−	0.845312i
$717$	23.6538	+	35.2926i	0.883368	+	1.31803i
$718$	22.0479	+	5.34875i	0.822819	+	0.199614i
$719$	23.3671	−	10.6714i	0.871446	−	0.397976i	0.0710677	−	0.997471i	$-0.477359\pi$
$719$	23.3671	−	10.6714i	0.871446	−	0.397976i	0.800378	+	0.599496i	$0.204632\pi$
$720$	−4.80945	+	0.646978i	−0.179238	+	0.0241115i
$721$	−2.41187	−	16.7750i	−0.0898229	−	0.624732i
$722$	−28.2301	−	29.6069i	−1.05062	−	1.10186i
$723$	−14.7523	+	16.0808i	−0.548644	+	0.598051i
$724$	−21.9148	−	1.04393i	−0.814458	−	0.0387974i
$725$	−12.4809	−	0.594537i	−0.463528	−	0.0220806i
$726$	92.9606	+	20.6648i	3.45009	+	0.766943i
$727$	−18.0536	−	18.9340i	−0.669570	−	0.702225i	0.298074	−	0.954543i	$-0.403656\pi$
$727$	−18.0536	−	18.9340i	−0.669570	−	0.702225i	−0.967644	+	0.252318i	$0.918807\pi$
$728$	−2.99717	−	20.8458i	−0.111082	−	0.772595i
$729$	13.9732	+	23.1030i	0.517527	+	0.855667i
$730$	41.4327	−	18.9217i	1.53349	−	0.700323i
$731$	13.0001	+	3.15380i	0.480828	+	0.116648i
$732$	11.6120	−	0.777531i	0.429190	−	0.0287384i
$733$	−9.57014	−	23.9051i	−0.353481	−	0.882953i	−0.993420	−	0.114527i	$-0.963465\pi$
$733$	−9.57014	−	23.9051i	−0.353481	−	0.882953i	0.639939	−	0.768426i	$-0.278960\pi$
$734$	43.8680	+	22.6155i	1.61920	+	0.834755i
$735$	0.564574	−	19.9161i	0.0208246	−	0.734615i
$736$	−26.3816	−	15.1309i	−0.972440	−	0.557731i
$737$			54.4387i			2.00528i
$738$	−0.481744	+	53.0526i	−0.0177332	+	1.95289i
$739$	3.36236	−	23.3857i	0.123686	−	0.860257i	−0.829636	−	0.558304i	$-0.811452\pi$
$739$	3.36236	−	23.3857i	0.123686	−	0.860257i	0.953323	−	0.301953i	$-0.0976386\pi$
$740$	0.507315	−	0.361257i	0.0186493	−	0.0132801i
$741$	−2.28932	+	8.39127i	−0.0841002	+	0.308261i
$742$	−0.938610	+	1.31809i	−0.0344575	+	0.0483887i
$743$	17.1478	−	49.5453i	0.629092	−	1.81764i	0.0555640	−	0.998455i	$-0.482304\pi$
$743$	17.1478	−	49.5453i	0.629092	−	1.81764i	0.573528	−	0.819186i	$-0.305574\pi$
$744$	4.34673	+	1.88478i	0.159359	+	0.0690992i
$745$	−26.8142	+	25.5673i	−0.982396	+	0.936713i
$746$	−29.0670	+	33.5451i	−1.06422	+	1.22817i
$747$	−4.47195	+	42.7285i	−0.163620	+	1.56335i
$748$	−58.7272	−	37.7416i	−2.14728	−	1.37997i
$749$	29.7297	−	10.2895i	1.08630	−	0.375972i
$750$	−32.4479	−	10.5351i	−1.18483	−	0.384686i
$751$	−10.6684	−	13.5660i	−0.389295	−	0.495029i	0.551420	−	0.834228i	$-0.314086\pi$
$751$	−10.6684	−	13.5660i	−0.389295	−	0.495029i	−0.940715	+	0.339199i	$0.889844\pi$
$752$	−2.37593	−	0.822316i	−0.0866411	−	0.0299868i
$753$	7.97977	+	6.03030i	0.290799	+	0.219757i
$754$	22.3464	−	92.1131i	0.813807	−	3.35456i
$755$	11.3450	−	24.8420i	0.412885	−	0.904093i
$756$	5.76144	−	24.8504i	0.209541	−	0.903800i
$757$	−0.963644	−	1.49946i	−0.0350242	−	0.0544988i	0.823300	−	0.567606i	$-0.192130\pi$
$757$	−0.963644	−	1.49946i	−0.0350242	−	0.0544988i	−0.858324	+	0.513108i	$0.828494\pi$
$758$	17.3282	−	30.0134i	0.629390	−	1.09014i
$759$	3.44161	+	49.2807i	0.124923	+	1.78877i
$760$	2.94630	+	5.10315i	0.106874	+	0.185111i
$761$	−5.48790	+	10.6451i	−0.198936	+	0.385883i	−0.967110	−	0.254359i	$-0.918136\pi$
$761$	−5.48790	+	10.6451i	−0.198936	+	0.385883i	0.768173	+	0.640242i	$0.221166\pi$
$762$	−3.85170	+	22.2860i	−0.139532	+	0.807336i
$763$	−7.24460	−	10.1736i	−0.262272	−	0.368310i
$764$	12.5551	−	3.68651i	0.454228	−	0.133373i
$765$	−10.6343	−	27.2786i	−0.384485	−	0.986260i
$766$	19.7261	−	17.0928i	0.712734	−	0.617588i
$767$	15.9972	−	39.9591i	0.577626	−	1.44284i
$768$	−13.5778	−	15.0730i	−0.489945	−	0.543899i
$769$	−1.89638	+	9.83933i	−0.0683851	+	0.354815i	−0.999962	−	0.00872912i	$-0.997221\pi$
$769$	−1.89638	+	9.83933i	−0.0683851	+	0.354815i	0.931577	+	0.363544i	$0.118434\pi$
$770$	2.60599	−	54.7065i	0.0939134	−	1.97149i
$771$	−6.66435	+	3.20003i	−0.240011	+	0.115246i
$772$	−11.2126	−	32.3966i	−0.403549	−	1.16598i
$773$	31.5407	+	9.26117i	1.13444	+	0.333101i	0.794451	−	0.607328i	$-0.207759\pi$
$773$	31.5407	+	9.26117i	1.13444	+	0.333101i	0.339988	+	0.940430i	$0.389577\pi$
$774$	−2.05055	−	23.7516i	−0.0737054	−	0.853734i
$775$	1.16667	+	1.34641i	0.0419081	+	0.0483645i
$776$	17.1973	+	1.64215i	0.617349	+	0.0589497i
$777$	−0.0548988	−	0.208670i	−0.00196948	−	0.00748600i
$778$	−4.24146	−	44.4186i	−0.152064	−	1.59248i
$779$	−6.78196	+	2.71509i	−0.242989	+	0.0972780i
$780$	−35.8139	+	64.8861i	−1.28234	+	2.32330i
$781$	26.7768	+	15.4596i	0.958151	+	0.553189i
$782$	11.4654	−	39.4655i	0.410003	−	1.41128i
$783$	23.1628	−	33.2385i	0.827770	−	1.18785i
$784$	−2.37082	+	1.52363i	−0.0846722	+	0.0544155i
$785$	7.90644	−	10.0539i	0.282193	−	0.358838i
$786$	4.56914	+	68.2374i	0.162976	+	2.43395i
$787$	−12.5258	+	13.1367i	−0.446496	+	0.468272i	−0.908063	−	0.418834i	$-0.862439\pi$
$787$	−12.5258	+	13.1367i	−0.446496	+	0.468272i	0.461567	+	0.887105i	$0.347287\pi$
$788$	−15.7263	−	11.1986i	−0.560226	−	0.398935i
$789$	25.7647	−	21.0772i	0.917249	−	0.750367i
$790$	−19.4136	−	7.77201i	−0.690703	−	0.276516i
$791$	6.53787	−	22.2659i	0.232460	−	0.791686i
$792$	−10.7368	+	42.5669i	−0.381516	+	1.51255i
$793$	−6.33328	+	9.85478i	−0.224901	+	0.349954i
$794$	1.22171	+	2.36979i	0.0433569	+	0.0841006i
$795$	1.91675	−	0.603140i	0.0679800	−	0.0213912i
$796$	28.4216	−	6.89500i	1.00738	−	0.244387i
$797$	−33.3845	+	26.2539i	−1.18254	+	0.929959i	−0.998596	−	0.0529777i	$-0.983129\pi$
$797$	−33.3845	+	26.2539i	−1.18254	+	0.929959i	−0.183943	+	0.982937i	$0.558886\pi$
$798$	5.70969	−	0.933496i	0.202121	−	0.0330454i
$799$	1.44190	−	15.1002i	0.0510106	−	0.534208i
$800$	−2.86320	−	9.75117i	−0.101229	−	0.344756i
$801$	−0.570911	−	0.906345i	−0.0201721	−	0.0320241i
$802$	−20.1239	−	2.89339i	−0.710601	−	0.102169i
$803$	2.22325	+	46.6717i	0.0784567	+	1.64701i
$804$	−48.9806	−	1.38848i	−1.72741	−	0.0489681i
$805$	19.0100	−	4.66947i	0.670014	−	0.164577i
$806$	−11.7040	+	6.75728i	−0.412254	+	0.238015i
$807$	−34.8975	−	19.2617i	−1.22845	−	0.678043i
$808$	−2.17161	−	1.70778i	−0.0763971	−	0.0600793i
$809$	−45.1713	−	20.6290i	−1.58814	−	0.725278i	−0.591429	−	0.806357i	$-0.701436\pi$
$809$	−45.1713	−	20.6290i	−1.58814	−	0.725278i	−0.996708	+	0.0810794i	$0.974163\pi$
$810$	−40.0471	+	33.4473i	−1.40711	+	1.17522i
$811$	−1.18737	−	2.59998i	−0.0416942	−	0.0912977i	0.887639	−	0.460540i	$-0.152344\pi$
$811$	−1.18737	−	2.59998i	−0.0416942	−	0.0912977i	−0.929333	+	0.369243i	$0.879617\pi$
$812$	−37.5850	+	7.24392i	−1.31897	+	0.254212i
$813$	−4.88149	−	6.58299i	−0.171201	−	0.230876i
$814$	0.248090	+	1.02264i	0.00869556	+	0.0358436i
$815$	36.2008	+	6.97714i	1.26806	+	0.244398i
$816$	−2.33678	+	3.41905i	−0.0818037	+	0.119691i
$817$	2.91767	−	1.50416i	0.102076	−	0.0526241i
$818$	41.5870	+	36.0354i	1.45406	+	1.25995i
$819$	16.6380	+	19.5573i	0.581380	+	0.683389i
$820$	−61.6131	+	8.85863i	−2.15162	+	0.309357i
$821$	−0.700379	−	3.63391i	−0.0244434	−	0.126824i	0.967657	−	0.252268i	$-0.0811766\pi$
$821$	−0.700379	−	3.63391i	−0.0244434	−	0.126824i	−0.992101	+	0.125444i	$0.959964\pi$
$822$	50.0188	+	6.21094i	1.74461	+	0.216632i
$823$	6.96082	+	6.63713i	0.242639	+	0.231356i	0.801634	−	0.597815i	$-0.203964\pi$
$823$	6.96082	+	6.63713i	0.242639	+	0.231356i	−0.558995	+	0.829171i	$0.688813\pi$
$824$	−26.1329	+	2.49539i	−0.910382	+	0.0869309i
$825$	−10.5681	+	12.6817i	−0.367934	+	0.441521i
$826$	−28.5974	+	1.36226i	−0.995032	+	0.0473992i
$827$	1.39886			0.0486432			0.0243216	−	0.999704i	$-0.492257\pi$
$827$	1.39886			0.0486432			0.0243216	+	0.999704i	$0.492257\pi$
$828$	−44.4275	+	1.83962i	−1.54396	+	0.0639314i
$829$	13.3082			0.462211			0.231106	−	0.972929i	$-0.425766\pi$
$829$	13.3082			0.462211			0.231106	+	0.972929i	$0.425766\pi$
$830$	−82.9297	+	3.95043i	−2.87853	+	0.137121i
$831$	40.6409	+	7.02399i	1.40982	+	0.243659i
$832$	69.9910	−	6.68333i	2.42650	−	0.231703i
$833$	−12.3056	−	11.7334i	−0.426365	−	0.406539i
$834$	5.05578	−	6.69020i	0.175067	−	0.231663i
$835$	8.55495	+	44.3873i	0.296056	+	1.53609i
$836$	−16.9558	+	2.43787i	−0.586428	+	0.0843156i
$837$	−5.70896	+	0.880229i	−0.197330	+	0.0304252i
$838$	39.5572	+	34.2765i	1.36648	+	1.18406i
$839$	−12.6800	+	6.53702i	−0.437764	+	0.225683i	−0.662997	−	0.748622i	$-0.730716\pi$
$839$	−12.6800	+	6.53702i	−0.437764	+	0.225683i	0.225233	+	0.974305i	$0.427686\pi$
$840$	17.3453	+	1.31974i	0.598471	+	0.0455354i
$841$	−31.2149	−	6.01618i	−1.07638	−	0.207454i
$842$	−2.37672	−	9.79699i	−0.0819073	−	0.337627i
$843$	−28.3662	+	3.26104i	−0.976985	+	0.112316i
$844$	−26.0344	+	5.01773i	−0.896142	+	0.172717i
$845$	−17.1136	−	37.4735i	−0.588725	−	1.28913i
$846$	−26.3277	+	6.13446i	−0.905166	+	0.210907i
$847$	35.2109	+	16.0803i	1.20986	+	0.552525i
$848$	−0.223415	−	0.175696i	−0.00767210	−	0.00603341i
$849$	−1.05412	−	54.7247i	−0.0361773	−	1.87815i
$850$	11.8933	−	6.86660i	0.407937	−	0.235522i
$851$	−0.325180	+	0.188987i	−0.0111470	+	0.00647838i
$852$	−14.5926	+	23.6979i	−0.499933	+	0.811875i
$853$	−1.24650	−	26.1672i	−0.0426793	−	0.895949i	−0.914119	−	0.405446i	$-0.867116\pi$
$853$	−1.24650	−	26.1672i	−0.0426793	−	0.895949i	0.871440	−	0.490503i	$-0.163187\pi$
$854$	7.71259	+	1.10890i	0.263919	+	0.0379459i
$855$	−6.35563	−	3.34995i	−0.217358	−	0.114566i
$856$	−13.7293	−	46.7577i	−0.469258	−	1.59815i
$857$	−2.65845	+	27.8405i	−0.0908108	+	0.951014i	0.829156	+	0.559018i	$0.188822\pi$
$857$	−2.65845	+	27.8405i	−0.0908108	+	0.951014i	−0.919967	+	0.391997i	$0.871784\pi$
$858$	−79.2909	−	96.9252i	−2.70695	−	3.30897i
$859$	−16.6415	+	13.0870i	−0.567800	+	0.446523i	−0.860333	−	0.509732i	$-0.829744\pi$
$859$	−16.6415	+	13.0870i	−0.567800	+	0.446523i	0.292533	+	0.956256i	$0.405502\pi$
$860$	27.1818	−	6.59424i	0.926893	−	0.224862i
$861$	−4.67974	+	21.0518i	−0.159485	+	0.717444i
$862$	27.4448	+	53.2355i	0.934774	+	1.81321i
$863$	−8.92077	+	13.8810i	−0.303667	+	0.472514i	−0.959230	−	0.282625i	$-0.908795\pi$
$863$	−8.92077	+	13.8810i	−0.303667	+	0.472514i	0.655564	+	0.755140i	$0.272431\pi$
$864$	31.7095	+	8.96115i	1.07878	+	0.304865i
$865$	−0.245870	+	0.837356i	−0.00835983	+	0.0284710i
$866$	12.3637	+	4.94968i	0.420136	+	0.168197i
$867$	4.17091	+	1.57728i	0.141652	+	0.0535672i
$868$	4.44559	+	3.16569i	0.150893	+	0.107450i
$869$	14.8031	−	15.5250i	0.502160	−	0.526650i
$870$	70.2663	+	34.5284i	2.38225	+	1.17062i
$871$	30.4889	−	38.7698i	1.03308	−	1.31366i
$872$	−16.2751	+	10.4594i	−0.551145	+	0.354200i
$873$	−18.8083	+	9.48118i	−0.636564	+	0.320889i
$874$	−4.21558	−	9.16130i	−0.142594	−	0.309885i
$875$	−12.0093	−	6.93358i	−0.405989	−	0.234398i
$876$	−42.0490	+	0.809957i	−1.42070	+	0.0273659i
$877$	10.3513	−	4.14403i	0.349539	−	0.139934i	−0.190248	−	0.981736i	$-0.560929\pi$
$877$	10.3513	−	4.14403i	0.349539	−	0.139934i	0.539787	+	0.841802i	$0.318505\pi$
$878$	−2.11692	−	22.1694i	−0.0714425	−	0.748180i
$879$	5.04399	+	1.37611i	0.170130	+	0.0464149i
$880$	9.57649	+	0.914444i	0.322823	+	0.0308259i
$881$	20.2572	+	23.3781i	0.682484	+	0.787628i	0.986275	−	0.165111i	$-0.0527981\pi$
$881$	20.2572	+	23.3781i	0.682484	+	0.787628i	−0.303792	+	0.952739i	$0.598253\pi$
$882$	−12.8375	+	27.4478i	−0.432260	+	0.924216i
$883$	−24.1360	−	7.08698i	−0.812243	−	0.238496i	−0.150870	−	0.988554i	$-0.548208\pi$
$883$	−24.1360	−	7.08698i	−0.812243	−	0.238496i	−0.661373	+	0.750058i	$0.730026\pi$
$884$	20.6864	+	59.7693i	0.695757	+	2.01026i
$885$	29.3521	+	20.0610i	0.986660	+	0.674342i
$886$	−0.698212	+	14.6573i	−0.0234569	+	0.492421i
$887$	5.42019	−	28.1226i	0.181992	−	0.944264i	−0.769977	−	0.638071i	$-0.779733\pi$
$887$	5.42019	−	28.1226i	0.181992	−	0.944264i	0.951969	−	0.306193i	$-0.0990553\pi$
$888$	−0.326912	+	0.0695624i	−0.0109705	+	0.00233436i
$889$	−3.41673	+	8.53458i	−0.114593	+	0.286240i
$890$	1.56442	−	1.35558i	0.0524396	−	0.0454392i
$891$	−16.5847	−	50.8901i	−0.555608	−	1.70488i
$892$	−49.3066	+	14.4777i	−1.65091	+	0.484750i
$893$	−2.15911	−	3.03204i	−0.0722517	−	0.101463i
$894$	52.8833	−	19.4514i	1.76868	−	0.650553i
$895$	−9.28223	+	18.0050i	−0.310271	+	0.601841i
$896$	−13.3100	−	23.0536i	−0.444656	−	0.770166i
$897$	25.1491	−	37.0239i	0.839703	−	1.23619i
$898$	3.72798	−	6.45704i	0.124404	−	0.215474i
$899$	4.68597	+	7.29151i	0.156286	+	0.243185i
$900$	−11.1407	−	9.83199i	−0.371356	−	0.327733i
$901$	0.712355	−	1.55984i	0.0237320	−	0.0519658i
$902$	24.7959	−	102.210i	0.825614	−	3.40323i
$903$	1.19411	−	9.61660i	0.0397376	−	0.320020i
$904$	−33.9692	−	11.7569i	−1.12980	−	0.391027i
$905$	11.2758	+	14.3384i	0.374822	+	0.476625i
$906$	−30.8599	+	27.7987i	−1.02525	+	0.923549i
$907$	−1.54541	+	0.534873i	−0.0513146	+	0.0177602i	−0.352605	−	0.935772i	$-0.614704\pi$
$907$	−1.54541	+	0.534873i	−0.0513146	+	0.0177602i	0.301290	+	0.953533i	$0.402583\pi$
$908$	−42.9425	−	27.5975i	−1.42510	−	0.915854i
$909$	3.35004	+	0.350614i	0.111114	+	0.0116291i
$910$	−32.4948	+	37.5010i	−1.07719	+	1.24315i
$911$	−4.28606	+	4.08675i	−0.142004	+	0.135400i	−0.757752	−	0.652543i	$-0.773702\pi$
$911$	−4.28606	+	4.08675i	−0.142004	+	0.135400i	0.615748	+	0.787943i	$0.288854\pi$
$912$	0.116062	+	1.00957i	0.00384320	+	0.0334301i
$913$	27.8553	−	80.4827i	0.921877	−	2.66359i
$914$	−39.4985	+	55.4679i	−1.30650	+	1.83472i
$915$	−6.81083	−	6.87296i	−0.225159	−	0.227213i
$916$	−24.9544	+	17.7700i	−0.824517	+	0.587136i
$917$	−3.95624	+	27.5163i	−0.130647	+	0.908667i
$918$	−1.66585	+	44.4965i	−0.0549813	+	1.46860i
$919$		−	30.9710i		−	1.02164i	−0.859688	−	0.510819i	$-0.829342\pi$
$919$		−	30.9710i		−	1.02164i	0.859688	−	0.510819i	$-0.170658\pi$
$920$	−5.82372	−	29.7574i	−0.192002	−	0.981074i
$921$	−2.37726	+	1.28410i	−0.0783333	+	0.0423127i
$922$	9.25845	+	4.77306i	0.304911	+	0.157193i
$923$	−10.4115	−	26.0066i	−0.342697	−	0.856016i
$924$	−22.3024	+	45.3860i	−0.733695	+	1.49309i
$925$	−0.122139	−	0.0296307i	−0.00401592	−	0.000974251i
$926$	24.9426	−	11.3909i	0.819664	−	0.374328i
$927$	25.3377	−	19.5561i	0.832200	−	0.642306i
$928$	−7.03648	−	48.9398i	−0.230984	−	1.60653i
$929$	−7.10482	−	7.45132i	−0.233101	−	0.244470i	0.596786	−	0.802400i	$-0.296444\pi$
$929$	−7.10482	−	7.45132i	−0.233101	−	0.244470i	−0.829888	+	0.557930i	$0.811596\pi$
$930$	−3.35065	−	10.6482i	−0.109872	−	0.349168i
$931$	−4.16756	−	0.198526i	−0.136586	−	0.00650641i
$932$	75.8928	+	3.61522i	2.48595	+	0.118420i
$933$	−13.2163	−	42.0007i	−0.432682	−	1.37504i
$934$	27.2140	+	28.5412i	0.890468	+	0.933896i
$935$	8.26002	+	57.4497i	0.270132	+	1.87881i
$936$	31.4865	−	24.3018i	1.02917	−	0.794328i
$937$	−20.5544	+	9.38687i	−0.671482	+	0.306656i	−0.721824	−	0.692076i	$-0.756696\pi$
$937$	−20.5544	+	9.38687i	−0.671482	+	0.306656i	0.0503420	+	0.998732i	$0.483969\pi$
$938$	−31.8821	−	7.73452i	−1.04099	−	0.252541i
$939$	−20.2098	+	41.1274i	−0.659521	+	1.34214i
$940$	−11.7878	−	29.4446i	−0.384476	−	0.960375i
$941$	−38.9723	−	20.0916i	−1.27046	−	0.654968i	−0.314722	−	0.949184i	$-0.601911\pi$
$941$	−38.9723	−	20.0916i	−1.27046	−	0.654968i	−0.955739	+	0.294215i	$0.904942\pi$
$942$	−17.1149	+	9.24481i	−0.557633	+	0.301212i
$943$	37.5432	−	1.89619i	1.22257	−	0.0617484i
$944$		−	5.02881i		−	0.163674i
$945$	−18.7515	+	9.90995i	−0.609985	+	0.322371i
$946$	−6.72578	+	46.7788i	−0.218674	+	1.52091i
$947$	−6.48784	+	4.61997i	−0.210827	+	0.150129i	−0.680593	−	0.732662i	$-0.738278\pi$
$947$	−6.48784	+	4.61997i	−0.210827	+	0.150129i	0.469766	+	0.882791i	$0.344338\pi$
$948$	13.5909	+	13.7149i	0.441411	+	0.445438i
$949$	24.5556	−	34.4835i	0.797108	−	1.11938i
$950$	1.10220	−	3.18459i	0.0357600	−	0.103322i
$951$	0.269864	+	2.34741i	0.00875093	+	0.0761201i
$952$	10.7439	−	10.2443i	0.348212	−	0.332020i
$953$	29.1504	−	33.6413i	0.944274	−	1.08975i	−0.0515700	−	0.998669i	$-0.516423\pi$
$953$	29.1504	−	33.6413i	0.944274	−	1.08975i	0.995844	−	0.0910804i	$-0.0290320\pi$
$954$	−3.03940	−	0.318102i	−0.0984042	−	0.0102989i
$955$	−9.15218	−	5.88175i	−0.296158	−	0.190329i
$956$	71.6402	−	24.7949i	2.31701	−	0.801925i
$957$	−59.6720	+	53.7526i	−1.92892	+	1.73758i
$958$	−4.31204	−	5.48321i	−0.139316	−	0.177154i
$959$	19.3609	+	6.70089i	0.625198	+	0.216383i
$960$	−7.15633	+	57.6323i	−0.230970	+	1.86008i
$961$	−7.01717	+	28.9252i	−0.226360	+	0.933070i
$962$	0.396057	−	0.867244i	0.0127694	−	0.0279611i
$963$	44.5478	+	39.3147i	1.43553	+	1.26690i
$964$	21.0519	+	32.7574i	0.678036	+	1.05504i
$965$	−14.2513	+	24.6840i	−0.458767	+	0.794607i
$966$	−29.3503	−	4.98609i	−0.944329	−	0.160425i
$967$	25.8838	+	44.8320i	0.832366	+	1.44170i	0.896157	+	0.443737i	$0.146348\pi$
$967$	25.8838	+	44.8320i	0.832366	+	1.44170i	−0.0637911	+	0.997963i	$0.520319\pi$
$968$	27.4755	−	53.2950i	0.883095	−	1.71297i
$969$	−5.75422	+	2.11651i	−0.184852	+	0.0679920i
$970$	−23.6106	−	33.1565i	−0.758091	−	1.06459i
$971$	26.9508	−	7.91347i	0.864892	−	0.253955i	0.180951	−	0.983492i	$-0.442082\pi$
$971$	26.9508	−	7.91347i	0.864892	−	0.253955i	0.683942	+	0.729537i	$0.260264\pi$
$972$	46.2107	−	13.6239i	1.48221	−	0.436987i
$973$	2.57606	−	2.23216i	0.0825845	−	0.0715599i
$974$	−13.7321	+	34.3012i	−0.440005	+	1.09908i
$975$	14.6289	−	3.11282i	0.468498	−	0.0996900i
$976$	−0.259017	+	1.34391i	−0.00829093	+	0.0430174i
$977$	−0.873438	+	18.3357i	−0.0279438	+	0.586612i	0.940862	+	0.338790i	$0.110018\pi$
$977$	−0.873438	+	18.3357i	−0.0279438	+	0.586612i	−0.968806	+	0.247821i	$0.920285\pi$
$978$	−46.2906	−	31.6377i	−1.48021	−	1.01166i
$979$	0.694517	+	2.00667i	0.0221968	+	0.0641336i
$980$	−34.1113	−	10.0160i	−1.08964	−	0.319948i
$981$	9.99304	−	21.3661i	0.319053	−	0.682168i
$982$	−59.9009	−	69.1293i	−1.91151	−	2.20600i
$983$	−51.9847	−	4.96393i	−1.65805	−	0.158325i	−0.776406	−	0.630233i	$-0.782959\pi$
$983$	−51.9847	−	4.96393i	−1.65805	−	0.158325i	−0.881648	+	0.471908i	$0.843565\pi$
$984$	32.2276	+	8.79237i	1.02738	+	0.280291i
$985$	1.52578	+	15.9787i	0.0486155	+	0.509125i
$986$	62.0272	−	24.8320i	1.97535	−	0.790811i
$987$	−10.9863	+	0.211621i	−0.349698	+	0.00673596i
$988$	13.4408	+	7.76006i	0.427609	+	0.246880i
$989$	−16.7125	+	2.45177i	−0.531426	+	0.0779617i
$990$	92.3638	−	46.5602i	2.93551	−	1.47978i
$991$	13.9625	−	8.97314i	0.443533	−	0.285041i	−0.299751	−	0.954017i	$-0.596904\pi$
$991$	13.9625	−	8.97314i	0.443533	−	0.285041i	0.743284	+	0.668976i	$0.233267\pi$
$992$	−4.35781	+	5.54141i	−0.138361	+	0.175940i
$993$	37.8944	+	18.6211i	1.20254	+	0.590922i
$994$	−12.8583	+	13.4854i	−0.407842	+	0.427732i
$995$	−19.8069	−	14.1044i	−0.627921	−	0.447141i
$996$	71.7029	+	27.1153i	2.27199	+	0.859180i
$997$	36.7819	+	14.7253i	1.16490	+	0.466354i	0.871863	−	0.489749i	$-0.162912\pi$
$997$	36.7819	+	14.7253i	1.16490	+	0.466354i	0.293032	+	0.956103i	$0.405336\pi$
$998$	5.16918	−	17.6046i	0.163627	−	0.557264i
$999$	0.292047	−	0.284198i	0.00923995	−	0.00899162i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.11.21	✓	440
3.2	odd	2		621.2.s.a.494.2		440
9.4	even	3		621.2.s.a.287.2		440
9.5	odd	6	inner	207.2.o.a.149.21	yes	440
23.21	odd	22	inner	207.2.o.a.182.21	yes	440
69.44	even	22		621.2.s.a.251.2		440
207.67	odd	66		621.2.s.a.44.2		440
207.113	even	66	inner	207.2.o.a.113.21	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.21	✓	440	1.1	even	1	trivial
207.2.o.a.113.21	yes	440	207.113	even	66	inner
207.2.o.a.149.21	yes	440	9.5	odd	6	inner
207.2.o.a.182.21	yes	440	23.21	odd	22	inner
621.2.s.a.44.2		440	207.67	odd	66
621.2.s.a.251.2		440	69.44	even	22
621.2.s.a.287.2		440	9.4	even	3
621.2.s.a.494.2		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)

\(f(q)\)	\(=\)	\(q+(2.25367 - 0.107356i) q^{2} +(0.597916 + 1.62558i) q^{3} +(3.07657 - 0.293777i) q^{4} +(-1.85967 - 1.77319i) q^{5} +(1.52202 + 3.59933i) q^{6} +(0.300622 + 1.55978i) q^{7} +(2.43553 - 0.350176i) q^{8} +(-2.28499 + 1.94391i) q^{9} +O(q^{10})\)	\(q+(2.25367 - 0.107356i) q^{2} +(0.597916 + 1.62558i) q^{3} +(3.07657 - 0.293777i) q^{4} +(-1.85967 - 1.77319i) q^{5} +(1.52202 + 3.59933i) q^{6} +(0.300622 + 1.55978i) q^{7} +(2.43553 - 0.350176i) q^{8} +(-2.28499 + 1.94391i) q^{9} +(-4.38145 - 3.79655i) q^{10} +(5.28603 - 2.72514i) q^{11} +(2.31709 + 4.82555i) q^{12} +(-5.29081 - 1.01972i) q^{13} +(0.844955 + 3.48295i) q^{14} +(1.77053 - 4.08326i) q^{15} +(-0.618147 + 0.119138i) q^{16} +(-1.57778 - 3.45486i) q^{17} +(-4.94094 + 4.62625i) q^{18} +(-0.847774 - 0.387165i) q^{19} +(-6.24234 - 4.90903i) q^{20} +(-2.35579 + 1.42130i) q^{21} +(11.6204 - 6.70906i) q^{22} +(3.48037 + 3.29955i) q^{23} +(2.02548 + 3.74976i) q^{24} +(0.0762544 + 1.60078i) q^{25} +(-12.0332 - 1.73012i) q^{26} +(-4.52621 - 2.55213i) q^{27} +(1.38311 + 4.71045i) q^{28} +(-0.741129 + 7.76145i) q^{29} +(3.55184 - 9.39240i) q^{30} +(0.873833 - 0.687190i) q^{31} +(-6.16274 + 1.49506i) q^{32} +(7.59052 + 6.96344i) q^{33} +(-3.92671 - 7.61675i) q^{34} +(2.20673 - 3.43373i) q^{35} +(-6.45888 + 6.65188i) q^{36} +(-0.0220947 + 0.0752475i) q^{37} +(-1.95217 - 0.781531i) q^{38} +(-1.50583 - 9.21032i) q^{39} +(-5.15021 - 3.66745i) q^{40} +(5.40903 - 5.67283i) q^{41} +(-5.15659 + 3.45605i) q^{42} +(-2.17721 + 2.76855i) q^{43} +(15.4623 - 9.93701i) q^{44} +(7.69627 + 0.436694i) q^{45} +(8.19784 + 7.06247i) q^{46} +(3.45875 + 1.99691i) q^{47} +(-0.563267 - 0.933610i) q^{48} +(4.15605 - 1.66383i) q^{49} +(0.343705 + 3.59944i) q^{50} +(4.67276 - 4.63052i) q^{51} +(-16.5771 - 1.58293i) q^{52} +(0.295664 + 0.341214i) q^{53} +(-10.4746 - 5.26576i) q^{54} +(-14.6625 - 4.30529i) q^{55} +(1.27837 + 3.69361i) q^{56} +(0.122469 - 1.60961i) q^{57} +(-0.837026 + 17.5713i) q^{58} +(-1.51179 + 7.84393i) q^{59} +(4.24761 - 13.0826i) q^{60} +(0.808028 - 2.01836i) q^{61} +(1.89556 - 1.64251i) q^{62} +(-3.71899 - 2.97970i) q^{63} +(-12.5202 + 3.67628i) q^{64} +(8.03101 + 11.2780i) q^{65} +(17.8541 + 14.8784i) q^{66} +(-4.19450 + 8.13619i) q^{67} +(-5.86913 - 10.1656i) q^{68} +(-3.28270 + 7.63046i) q^{69} +(4.60461 - 7.97542i) q^{70} +(2.81080 + 4.37368i) q^{71} +(-4.88445 + 5.53461i) q^{72} +(-3.26377 + 7.14666i) q^{73} +(-0.0417159 + 0.171955i) q^{74} +(-2.55659 + 1.08109i) q^{75} +(-2.72198 - 0.942086i) q^{76} +(5.83971 + 7.42579i) q^{77} +(-4.38242 - 20.5954i) q^{78} +(3.40860 - 1.17973i) q^{79} +(1.36080 + 0.874536i) q^{80} +(1.44239 - 8.88366i) q^{81} +(11.5812 - 13.3654i) q^{82} +(10.3643 - 9.88236i) q^{83} +(-6.83021 + 5.06481i) q^{84} +(-3.19198 + 9.22263i) q^{85} +(-4.60951 + 6.47315i) q^{86} +(-13.0600 + 3.43593i) q^{87} +(11.9200 - 8.48819i) q^{88} +(-0.0508144 + 0.353422i) q^{89} +(17.3918 + 0.157926i) q^{90} -8.55903i q^{91} +(11.6770 + 9.12885i) q^{92} +(1.63956 + 1.00960i) q^{93} +(8.00928 + 4.12907i) q^{94} +(0.890062 + 2.22327i) q^{95} +(-6.11514 - 9.12407i) q^{96} +(6.82305 + 1.65525i) q^{97} +(9.18775 - 4.19590i) q^{98} +(-6.78111 + 16.5025i) 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

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