LMFDB - Embedded newform 729.2.k.a.4.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(4,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(486))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("729.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.k (of order $243$, degree $162$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12960$
Relative dimension:	$80$ over $\Q(\zeta_{243})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{243}]$

Embedding invariants

Embedding label			4.9
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.38009 - 0.0307723i) q^{2} +(-1.09995 + 1.33795i) q^{3} +(3.66453 + 0.0947738i) q^{4} +(2.99225 + 0.916937i) q^{5} +(2.65915 - 3.15058i) q^{6} +(-0.120994 + 0.301715i) q^{7} +(-3.96199 - 0.153743i) q^{8} +(-0.580208 - 2.94336i) q^{9} +O(q^{10})$	\(q+(-2.38009 - 0.0307723i) q^{2} +(-1.09995 + 1.33795i) q^{3} +(3.66453 + 0.0947738i) q^{4} +(2.99225 + 0.916937i) q^{5} +(2.65915 - 3.15058i) q^{6} +(-0.120994 + 0.301715i) q^{7} +(-3.96199 - 0.153743i) q^{8} +(-0.580208 - 2.94336i) q^{9} +(-7.09359 - 2.27447i) q^{10} +(-2.57335 - 1.46363i) q^{11} +(-4.15761 + 4.79870i) q^{12} +(2.35060 + 5.26122i) q^{13} +(0.297261 - 0.714385i) q^{14} +(-4.51815 + 2.99488i) q^{15} +(2.10343 + 0.108873i) q^{16} +(-6.15139 - 2.79615i) q^{17} +(1.29037 + 7.02330i) q^{18} +(-0.549676 - 0.801448i) q^{19} +(10.8783 + 3.64373i) q^{20} +(-0.270591 - 0.493757i) q^{21} +(6.07976 + 3.56275i) q^{22} +(-1.84006 + 5.61370i) q^{23} +(4.56370 - 5.13182i) q^{24} +(3.97120 + 2.68609i) q^{25} +(-5.43273 - 12.5945i) q^{26} +(4.57626 + 2.46127i) q^{27} +(-0.471982 + 1.09418i) q^{28} +(-3.83899 + 2.45443i) q^{29} +(10.8457 - 6.98905i) q^{30} +(-0.244785 - 0.901881i) q^{31} +(2.91038 + 0.188395i) q^{32} +(4.78883 - 1.83309i) q^{33} +(14.5548 + 6.84437i) q^{34} +(-0.638699 + 0.791863i) q^{35} +(-1.84724 - 10.8410i) q^{36} +(10.3658 + 2.03577i) q^{37} +(1.28361 + 1.92443i) q^{38} +(-9.62478 - 2.64211i) q^{39} +(-11.7143 - 4.09293i) q^{40} +(-0.489437 + 0.185341i) q^{41} +(0.628836 + 1.18351i) q^{42} +(-8.37284 + 3.67607i) q^{43} +(-9.29141 - 5.60740i) q^{44} +(0.962748 - 9.33927i) q^{45} +(4.55226 - 13.3045i) q^{46} +(2.08127 - 7.66820i) q^{47} +(-2.45934 + 2.69452i) q^{48} +(4.98406 + 4.76349i) q^{49} +(-9.36915 - 6.51532i) q^{50} +(10.5073 - 5.15460i) q^{51} +(8.11521 + 19.5026i) q^{52} +(-8.14164 + 8.62964i) q^{53} +(-10.8162 - 5.99885i) q^{54} +(-6.35805 - 6.73914i) q^{55} +(0.525765 - 1.17679i) q^{56} +(1.67691 + 0.146116i) q^{57} +(9.21264 - 5.72363i) q^{58} +(-9.23154 + 1.56631i) q^{59} +(-16.8407 + 10.5466i) q^{60} +(-5.54009 + 10.1957i) q^{61} +(0.554857 + 2.15409i) q^{62} +(0.958258 + 0.181072i) q^{63} +(-11.1210 - 0.864392i) q^{64} +(2.20937 + 17.8982i) q^{65} +(-11.4542 + 4.21555i) q^{66} +(-10.7198 + 5.55835i) q^{67} +(-22.2769 - 10.8296i) q^{68} +(-5.48686 - 8.63672i) q^{69} +(1.54453 - 1.86505i) q^{70} +(1.85510 + 1.43781i) q^{71} +(1.84626 + 11.7507i) q^{72} +(6.09372 - 1.95387i) q^{73} +(-24.6088 - 5.16429i) q^{74} +(-7.96198 + 2.35869i) q^{75} +(-1.93835 - 2.98902i) q^{76} +(0.752960 - 0.599329i) q^{77} +(22.8265 + 6.58462i) q^{78} +(-0.343987 + 1.81343i) q^{79} +(6.19415 + 2.25449i) q^{80} +(-8.32672 + 3.41552i) q^{81} +(1.17061 - 0.426066i) q^{82} +(0.252678 + 1.54992i) q^{83} +(-0.944794 - 1.83503i) q^{84} +(-15.8426 - 14.0072i) q^{85} +(20.0412 - 8.49170i) q^{86} +(0.938797 - 7.83613i) q^{87} +(9.97057 + 6.19451i) q^{88} +(-0.100757 - 0.0411636i) q^{89} +(-2.57881 + 22.1986i) q^{90} +(-1.87180 + 0.0726343i) q^{91} +(-7.27500 + 20.3972i) q^{92} +(1.47592 + 0.664517i) q^{93} +(-5.18958 + 18.1869i) q^{94} +(-0.909891 - 2.90215i) q^{95} +(-3.45335 + 3.68672i) q^{96} +(2.87978 - 12.5106i) q^{97} +(-11.7159 - 11.4909i) q^{98} +(-2.81490 + 8.42351i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) $ 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{243}\right)$

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 $

$2$	−2.38009	−	0.0307723i	−1.68297	−	0.0217593i	−0.834504	−	0.551002i	$-0.814246\pi$
$2$	−2.38009	−	0.0307723i	−1.68297	−	0.0217593i	−0.848471	+	0.529243i	$0.822476\pi$
$3$	−1.09995	+	1.33795i	−0.635058	+	0.772464i
$3$	−1.09995	+	1.33795i	−0.635058	+	0.772464i
$4$	3.66453	+	0.0947738i	1.83226	+	0.0473869i
$5$	2.99225	+	0.916937i	1.33817	+	0.410067i	0.878382	−	0.477960i	$-0.158623\pi$
$5$	2.99225	+	0.916937i	1.33817	+	0.410067i	0.459792	+	0.888027i	$0.347924\pi$
$6$	2.65915	−	3.15058i	1.08559	−	1.28622i
$7$	−0.120994	+	0.301715i	−0.0457316	+	0.114038i	−0.949262	−	0.314486i	$-0.898168\pi$
$7$	−0.120994	+	0.301715i	−0.0457316	+	0.114038i	0.903531	+	0.428524i	$0.140966\pi$
$8$	−3.96199	−	0.153743i	−1.40077	−	0.0543564i
$9$	−0.580208	−	2.94336i	−0.193403	−	0.981119i
$10$	−7.09359	−	2.27447i	−2.24319	−	0.719250i
$11$	−2.57335	−	1.46363i	−0.775895	−	0.441301i	0.0544734	−	0.998515i	$-0.482652\pi$
$11$	−2.57335	−	1.46363i	−0.775895	−	0.441301i	−0.830369	+	0.557215i	$0.811870\pi$
$12$	−4.15761	+	4.79870i	−1.20020	+	1.38527i
$13$	2.35060	+	5.26122i	0.651939	+	1.45920i	0.874867	+	0.484364i	$0.160949\pi$
$13$	2.35060	+	5.26122i	0.651939	+	1.45920i	−0.222928	+	0.974835i	$0.571561\pi$
$14$	0.297261	−	0.714385i	0.0794465	−	0.190927i
$15$	−4.51815	+	2.99488i	−1.16658	+	0.773276i
$16$	2.10343	+	0.108873i	0.525857	+	0.0272182i
$17$	−6.15139	−	2.79615i	−1.49193	−	0.678166i	−0.508769	−	0.860903i	$-0.669899\pi$
$17$	−6.15139	−	2.79615i	−1.49193	−	0.678166i	−0.983162	+	0.182737i	$0.941504\pi$
$18$	1.29037	+	7.02330i	0.304143	+	1.65541i
$19$	−0.549676	−	0.801448i	−0.126104	−	0.183865i	0.756483	−	0.654014i	$-0.226916\pi$
$19$	−0.549676	−	0.801448i	−0.126104	−	0.183865i	−0.882587	+	0.470149i	$0.844200\pi$
$20$	10.8783	+	3.64373i	2.43246	+	0.814763i
$21$	−0.270591	−	0.493757i	−0.0590479	−	0.107747i
$22$	6.07976	+	3.56275i	1.29621	+	0.759581i
$23$	−1.84006	+	5.61370i	−0.383680	+	1.17054i	0.556788	+	0.830655i	$0.312034\pi$
$23$	−1.84006	+	5.61370i	−0.383680	+	1.17054i	−0.940468	+	0.339883i	$0.889612\pi$
$24$	4.56370	−	5.13182i	0.931561	−	1.04753i
$25$	3.97120	+	2.68609i	0.794241	+	0.537217i
$26$	−5.43273	−	12.5945i	−1.06545	−	2.46998i
$27$	4.57626	+	2.46127i	0.880702	+	0.473671i
$28$	−0.471982	+	1.09418i	−0.0891962	+	0.206780i
$29$	−3.83899	+	2.45443i	−0.712882	+	0.455777i	−0.844522	−	0.535520i	$-0.820115\pi$
$29$	−3.83899	+	2.45443i	−0.712882	+	0.455777i	0.131640	+	0.991298i	$0.457976\pi$
$30$	10.8457	−	6.98905i	1.98015	−	1.27602i
$31$	−0.244785	−	0.901881i	−0.0439647	−	0.161983i	0.939697	−	0.342007i	$-0.111107\pi$
$31$	−0.244785	−	0.901881i	−0.0439647	−	0.161983i	−0.983662	+	0.180024i	$0.942382\pi$
$32$	2.91038	+	0.188395i	0.514488	+	0.0333039i
$33$	4.78883	−	1.83309i	0.833627	−	0.319100i
$34$	14.5548	+	6.84437i	2.49613	+	1.17380i
$35$	−0.638699	+	0.791863i	−0.107960	+	0.133849i
$36$	−1.84724	−	10.8410i	−0.307873	−	1.80683i
$37$	10.3658	+	2.03577i	1.70412	+	0.334679i	0.947641	−	0.319338i	$-0.103460\pi$
$37$	10.3658	+	2.03577i	1.70412	+	0.334679i	0.756481	+	0.654016i	$0.226917\pi$
$38$	1.28361	+	1.92443i	0.208230	+	0.312184i
$39$	−9.62478	−	2.64211i	−1.54120	−	0.423076i
$40$	−11.7143	−	4.09293i	−1.85219	−	0.647149i
$41$	−0.489437	+	0.185341i	−0.0764372	+	0.0289454i	−0.392063	−	0.919939i	$-0.628238\pi$
$41$	−0.489437	+	0.185341i	−0.0764372	+	0.0289454i	0.315625	+	0.948884i	$0.397786\pi$
$42$	0.628836	+	1.18351i	0.0970316	+	0.182620i
$43$	−8.37284	+	3.67607i	−1.27685	+	0.560595i	−0.926595	−	0.376061i	$-0.877278\pi$
$43$	−8.37284	+	3.67607i	−1.27685	+	0.560595i	−0.350252	+	0.936656i	$0.613904\pi$
$44$	−9.29141	−	5.60740i	−1.40073	−	0.845347i
$45$	0.962748	−	9.33927i	0.143518	−	1.39222i
$46$	4.55226	−	13.3045i	0.671193	−	1.96164i
$47$	2.08127	−	7.66820i	0.303585	−	1.11852i	−0.634728	−	0.772735i	$-0.718888\pi$
$47$	2.08127	−	7.66820i	0.303585	−	1.11852i	0.938313	−	0.345786i	$-0.112388\pi$
$48$	−2.45934	+	2.69452i	−0.354975	+	0.388921i
$49$	4.98406	+	4.76349i	0.712009	+	0.680499i
$50$	−9.36915	−	6.51532i	−1.32500	−	0.921405i
$51$	10.5073	−	5.15460i	1.47132	−	0.721789i
$52$	8.11521	+	19.5026i	1.12538	+	2.70453i
$53$	−8.14164	+	8.62964i	−1.11834	+	1.18537i	−0.137512	+	0.990500i	$0.543911\pi$
$53$	−8.14164	+	8.62964i	−1.11834	+	1.18537i	−0.980829	+	0.194872i	$0.937571\pi$
$54$	−10.8162	−	5.99885i	−1.47189	−	0.816340i
$55$	−6.35805	−	6.73914i	−0.857320	−	0.908706i
$56$	0.525765	−	1.17679i	0.0702583	−	0.157255i
$57$	1.67691	+	0.146116i	0.222113	+	0.0193536i
$58$	9.21264	−	5.72363i	1.20968	−	0.751550i
$59$	−9.23154	+	1.56631i	−1.20184	+	0.203916i	−0.733537	−	0.679650i	$-0.762132\pi$
$59$	−9.23154	+	1.56631i	−1.20184	+	0.203916i	−0.468307	+	0.883566i	$0.655136\pi$
$60$	−16.8407	+	10.5466i	−2.17413	+	1.36156i
$61$	−5.54009	+	10.1957i	−0.709335	+	1.30543i	0.233561	+	0.972342i	$0.424962\pi$
$61$	−5.54009	+	10.1957i	−0.709335	+	1.30543i	−0.942897	+	0.333085i	$0.891910\pi$
$62$	0.554857	+	2.15409i	0.0704669	+	0.273569i
$63$	0.958258	+	0.181072i	0.120729	+	0.0228129i
$64$	−11.1210	−	0.864392i	−1.39012	−	0.108049i
$65$	2.20937	+	17.8982i	0.274039	+	2.22000i
$66$	−11.4542	+	4.21555i	−1.40992	+	0.518898i
$67$	−10.7198	+	5.55835i	−1.30963	+	0.679061i	−0.965633	−	0.259911i	$-0.916307\pi$
$67$	−10.7198	+	5.55835i	−1.30963	+	0.679061i	−0.343995	+	0.938972i	$0.611780\pi$
$68$	−22.2769	−	10.8296i	−2.70148	−	1.31328i
$69$	−5.48686	−	8.63672i	−0.660540	−	1.03974i
$70$	1.54453	−	1.86505i	0.184606	−	0.222916i
$71$	1.85510	+	1.43781i	0.220160	+	0.170637i	0.716710	−	0.697371i	$-0.245647\pi$
$71$	1.85510	+	1.43781i	0.220160	+	0.170637i	−0.496550	+	0.868008i	$0.665400\pi$
$72$	1.84626	+	11.7507i	0.217583	+	1.38484i
$73$	6.09372	−	1.95387i	0.713216	−	0.228684i	0.0735004	−	0.997295i	$-0.476583\pi$
$73$	6.09372	−	1.95387i	0.713216	−	0.228684i	0.639716	+	0.768612i	$0.279052\pi$
$74$	−24.6088	−	5.16429i	−2.86071	−	0.600336i
$75$	−7.96198	+	2.35869i	−0.919370	+	0.272359i
$76$	−1.93835	−	2.98902i	−0.222344	−	0.342865i
$77$	0.752960	−	0.599329i	0.0858078	−	0.0682999i
$78$	22.8265	+	6.58462i	2.58459	+	0.745562i
$79$	−0.343987	+	1.81343i	−0.0387015	+	0.204027i	−0.996521	−	0.0833446i	$-0.973440\pi$
$79$	−0.343987	+	1.81343i	−0.0387015	+	0.204027i	0.957819	+	0.287371i	$0.0927814\pi$
$80$	6.19415	+	2.25449i	0.692527	+	0.252059i
$81$	−8.32672	+	3.41552i	−0.925191	+	0.379502i
$82$	1.17061	−	0.426066i	0.129272	−	0.0470511i
$83$	0.252678	+	1.54992i	0.0277350	+	0.170126i	0.997165	−	0.0752402i	$-0.0239724\pi$
$83$	0.252678	+	1.54992i	0.0277350	+	0.170126i	−0.969430	+	0.245366i	$0.921092\pi$
$84$	−0.944794	−	1.83503i	−0.103086	−	0.200218i
$85$	−15.8426	−	14.0072i	−1.71837	−	1.51930i
$86$	20.0412	−	8.49170i	2.16110	−	0.915684i
$87$	0.938797	−	7.83613i	0.100650	−	0.840121i
$88$	9.97057	+	6.19451i	1.06287	+	0.660337i
$89$	−0.100757	−	0.0411636i	−0.0106802	−	0.00436334i	0.372853	−	0.927890i	$-0.378379\pi$
$89$	−0.100757	−	0.0411636i	−0.0106802	−	0.00436334i	−0.383534	+	0.923527i	$0.625293\pi$
$90$	−2.57881	+	22.1986i	−0.271831	+	2.33994i
$91$	−1.87180	+	0.0726343i	−0.196218	+	0.00761414i
$92$	−7.27500	+	20.3972i	−0.758471	+	2.12655i
$93$	1.47592	+	0.664517i	0.153046	+	0.0689072i
$94$	−5.18958	+	18.1869i	−0.535264	+	1.87584i
$95$	−0.909891	−	2.90215i	−0.0933528	−	0.297754i
$96$	−3.45335	+	3.68672i	−0.352456	+	0.376274i
$97$	2.87978	−	12.5106i	0.292397	−	1.27026i	−0.592917	−	0.805264i	$-0.702024\pi$
$97$	2.87978	−	12.5106i	0.292397	−	1.27026i	0.885314	−	0.464993i	$-0.153943\pi$
$98$	−11.7159	−	11.4909i	−1.18349	−	1.16076i
$99$	−2.81490	+	8.42351i	−0.282908	+	0.846595i
$100$	14.2980	+	10.2196i	1.42980	+	1.02196i
$101$	0.404776	−	2.70244i	0.0402767	−	0.268903i	−0.959648	−	0.281205i	$-0.909266\pi$
$101$	0.404776	−	2.70244i	0.0402767	−	0.268903i	0.999924	+	0.0123021i	$0.00391599\pi$
$102$	−25.1670	+	11.9451i	−2.49190	+	1.18274i
$103$	−0.619527	−	1.73699i	−0.0610439	−	0.171151i	0.907466	−	0.420125i	$-0.138014\pi$
$103$	−0.619527	−	1.73699i	−0.0610439	−	0.171151i	−0.968510	+	0.248974i	$0.919907\pi$
$104$	−8.50417	−	21.2063i	−0.833902	−	2.07944i
$105$	−0.356932	−	1.72556i	−0.0348330	−	0.168397i
$106$	19.6434	−	20.2887i	1.90793	−	1.97062i
$107$	0.424397	+	7.28661i	0.0410280	+	0.704423i	0.954626	+	0.297806i	$0.0962548\pi$
$107$	0.424397	+	7.28661i	0.0410280	+	0.704423i	−0.913598	+	0.406618i	$0.866708\pi$
$108$	16.5366	+	9.45309i	1.59123	+	0.909624i
$109$	0.413161	−	7.09369i	0.0395736	−	0.679453i	−0.918939	−	0.394401i	$-0.870952\pi$
$109$	0.413161	−	7.09369i	0.0395736	−	0.679453i	0.958512	−	0.285052i	$-0.0920108\pi$
$110$	14.9253	+	16.2354i	1.42307	+	1.54798i
$111$	−14.1256	+	11.6296i	−1.34074	+	1.10383i
$112$	−0.287352	+	0.621464i	−0.0271522	+	0.0587228i
$113$	5.23657	−	3.84612i	0.492615	−	0.361813i	−0.317333	−	0.948314i	$-0.602787\pi$
$113$	5.23657	−	3.84612i	0.492615	−	0.361813i	0.809948	+	0.586502i	$0.199495\pi$
$114$	−3.98670	−	0.399372i	−0.373389	−	0.0374046i
$115$	−10.6533	+	15.1104i	−0.993429	+	1.40905i
$116$	−14.3007	+	8.63051i	−1.32779	+	0.801323i
$117$	14.1218	−	9.97126i	1.30556	−	0.921843i
$118$	22.0201	−	3.44387i	2.02711	−	0.317034i
$119$	1.58792	−	1.51765i	0.145565	−	0.139123i
$120$	18.3613	−	11.1711i	1.67615	−	1.01977i
$121$	−1.14276	−	1.92151i	−0.103887	−	0.174683i
$122$	13.4996	−	24.0962i	1.22220	−	2.18157i
$123$	0.290382	−	0.858707i	0.0261828	−	0.0774270i
$124$	−0.811548	−	3.32817i	−0.0728792	−	0.298878i
$125$	−0.404115	−	0.501025i	−0.0361452	−	0.0448130i
$126$	−2.27516	−	0.460455i	−0.202688	−	0.0410206i
$127$	−0.0419081	−	2.16077i	−0.00371874	−	0.191737i	−0.997064	−	0.0765666i	$-0.975604\pi$
$127$	−0.0419081	−	2.16077i	−0.00371874	−	0.191737i	0.993346	−	0.115171i	$-0.0367415\pi$
$128$	20.6332	+	1.87239i	1.82374	+	0.165498i
$129$	4.29135	−	15.2459i	0.377832	−	1.34233i
$130$	−4.70772	−	42.6673i	−0.412894	−	3.74217i
$131$	−7.44479	+	0.675588i	−0.650454	+	0.0590264i	−0.410647	−	0.911794i	$-0.634697\pi$
$131$	−7.44479	+	0.675588i	−0.650454	+	0.0590264i	−0.239807	+	0.970821i	$0.577084\pi$
$132$	17.7225	−	6.26355i	1.54255	−	0.545172i
$133$	0.308317	−	0.0688751i	0.0267345	−	0.00597223i
$134$	25.6850	−	12.8995i	2.21885	−	1.11435i
$135$	11.4365	+	11.5609i	0.984296	+	0.995001i
$136$	23.9418	+	12.0240i	2.05299	+	1.03105i
$137$	22.1677	+	5.55748i	1.89392	+	0.474808i	0.999627	+	0.0273177i	$0.00869656\pi$
$137$	22.1677	+	5.55748i	1.89392	+	0.474808i	0.894289	+	0.447490i	$0.147682\pi$
$138$	12.7934	+	20.7250i	1.08905	+	1.76423i
$139$	−8.50557	−	1.21781i	−0.721433	−	0.103294i	−0.228728	−	0.973490i	$-0.573457\pi$
$139$	−8.50557	−	1.21781i	−0.721433	−	0.103294i	−0.492705	+	0.870197i	$0.663992\pi$
$140$	−2.41558	+	2.84127i	−0.204154	+	0.240131i
$141$	7.97034	+	11.2193i	0.671224	+	0.944834i
$142$	−4.37105	−	3.47920i	−0.366810	−	0.291968i
$143$	1.65155	−	16.9794i	0.138109	−	1.41989i
$144$	−0.899976	−	6.25431i	−0.0749980	−	0.521193i
$145$	−13.7378	+	3.82417i	−1.14086	+	0.317580i
$146$	−14.5637	+	4.46287i	−1.20530	+	0.369349i
$147$	−11.8555	+	1.42880i	−0.977828	+	0.117846i
$148$	37.7927	+	8.44254i	3.10654	+	0.693973i
$149$	0.156888	−	0.0393321i	0.0128528	−	0.00322221i	−0.236744	−	0.971572i	$-0.576080\pi$
$149$	0.156888	−	0.0393321i	0.0128528	−	0.00322221i	0.249597	+	0.968350i	$0.419702\pi$
$150$	19.0228	−	5.36889i	1.55320	−	0.438368i
$151$	−10.5874	−	12.4532i	−0.861591	−	1.01343i	−0.999735	−	0.0230153i	$-0.992673\pi$
$151$	−10.5874	−	12.4532i	−0.861591	−	1.01343i	0.138144	−	0.990412i	$-0.455886\pi$
$152$	2.05459	+	3.25983i	0.166650	+	0.264408i
$153$	−4.66098	+	19.7281i	−0.376818	+	1.59492i
$154$	−1.81055	+	1.40328i	−0.145899	+	0.113080i
$155$	0.0945103	−	2.92311i	0.00759125	−	0.234789i
$156$	−35.0199	−	10.5943i	−2.80383	−	0.848220i
$157$	−1.34820	+	10.9218i	−0.107598	+	0.871657i	0.837854	+	0.545895i	$0.183810\pi$
$157$	−1.34820	+	10.9218i	−0.107598	+	0.871657i	−0.945452	+	0.325762i	$0.894379\pi$
$158$	0.874521	−	4.30553i	0.0695732	−	0.342530i
$159$	−2.59058	−	20.3853i	−0.205447	−	1.61666i
$160$	8.53585	+	3.23237i	0.674818	+	0.255541i
$161$	−1.47110	−	1.23440i	−0.115939	−	0.0972845i
$162$	19.9234	−	7.87300i	1.56533	−	0.618562i
$163$	−17.1777	+	14.4138i	−1.34546	+	1.12898i	−0.365274	+	0.930900i	$0.619025\pi$
$163$	−17.1777	+	14.4138i	−1.34546	+	1.12898i	−0.980187	+	0.198076i	$0.936531\pi$
$164$	−1.81112	+	0.632801i	−0.141425	+	0.0494134i
$165$	16.0102	−	1.09401i	1.24639	−	0.0851682i
$166$	−0.553701	−	3.69673i	−0.0429755	−	0.286922i
$167$	0.250920	−	0.491673i	0.0194168	−	0.0380468i	−0.880801	−	0.473486i	$-0.842995\pi$
$167$	0.250920	−	0.491673i	0.0194168	−	0.0380468i	0.900218	+	0.435439i	$0.143407\pi$
$168$	0.996167	+	1.99786i	0.0768560	+	0.154138i
$169$	−13.4814	+	15.0507i	−1.03703	+	1.15774i
$170$	37.2757	+	33.8259i	2.85891	+	2.59433i
$171$	−2.04002	+	2.08290i	−0.156004	+	0.159283i
$172$	−31.0309	+	12.6775i	−2.36609	+	0.966652i
$173$	3.41279	+	0.579045i	0.259469	+	0.0440240i	0.295559	−	0.955325i	$-0.404494\pi$
$173$	3.41279	+	0.579045i	0.259469	+	0.0440240i	−0.0360893	+	0.999349i	$0.511490\pi$
$174$	−2.47555	+	18.6218i	−0.187671	+	1.41171i
$175$	−1.29093	+	0.873172i	−0.0975849	+	0.0660056i
$176$	−5.25352	−	3.35881i	−0.395999	−	0.253180i
$177$	8.05862	−	14.0742i	0.605723	−	1.05788i
$178$	0.238543	+	0.101074i	0.0178795	+	0.00757578i
$179$	6.18100	+	12.9265i	0.461990	+	0.966170i	0.992923	+	0.118757i	$0.0378908\pi$
$179$	6.18100	+	12.9265i	0.461990	+	0.966170i	−0.530933	+	0.847414i	$0.678159\pi$
$180$	4.41314	−	34.1328i	0.328936	−	2.54411i
$181$	3.99185	+	1.11121i	0.296712	+	0.0825953i	0.413329	−	0.910582i	$-0.364366\pi$
$181$	3.99185	+	1.11121i	0.296712	+	0.0825953i	−0.116618	+	0.993177i	$0.537205\pi$
$182$	4.45728	−	0.115276i	0.330395	−	0.00854485i
$183$	−7.54750	−	18.6271i	−0.557927	−	1.37696i
$184$	8.15338	−	21.9585i	0.601075	−	1.61880i
$185$	29.1503	+	15.5963i	2.14317	+	1.14666i
$186$	−3.49237	−	1.62702i	−0.256073	−	0.119299i
$187$	11.7372	+	16.1988i	0.858307	+	1.18458i
$188$	8.35363	−	27.9031i	0.609251	−	2.03504i
$189$	−1.29630	+	1.08293i	−0.0942922	+	0.0787715i
$190$	2.07631	+	6.93536i	0.150631	+	0.503144i
$191$	8.09050	−	10.5791i	0.585408	−	0.765477i	−0.403343	−	0.915049i	$-0.632152\pi$
$191$	8.09050	−	10.5791i	0.585408	−	0.765477i	0.988751	+	0.149572i	$0.0477896\pi$
$192$	13.3891	−	13.9285i	0.966273	−	1.00520i
$193$	−14.8294	+	6.97349i	−1.06744	+	0.501963i	−0.877374	−	0.479808i	$-0.840706\pi$
$193$	−14.8294	+	6.97349i	−1.06744	+	0.501963i	−0.190069	+	0.981771i	$0.560871\pi$
$194$	−7.23910	+	29.6876i	−0.519737	+	2.13145i
$195$	−26.3771	−	16.7312i	−1.88890	−	1.19814i
$196$	17.8128	+	17.9283i	1.27234	+	1.28059i
$197$	−10.8778	+	2.13633i	−0.775012	+	0.152207i	−0.564555	−	0.825396i	$-0.690952\pi$
$197$	−10.8778	+	2.13633i	−0.775012	+	0.152207i	−0.210458	+	0.977603i	$0.567495\pi$
$198$	6.95892	−	19.9621i	0.494549	−	1.41864i
$199$	17.5179	−	9.66594i	1.24181	−	0.685201i	0.280283	−	0.959917i	$-0.409572\pi$
$199$	17.5179	−	9.66594i	1.24181	−	0.685201i	0.961525	+	0.274717i	$0.0885841\pi$
$200$	−15.3209	−	11.2528i	−1.08335	−	0.795692i
$201$	4.35444	−	20.4564i	0.307139	−	1.44288i
$202$	−1.04656	+	6.41959i	−0.0736358	+	0.451681i
$203$	−0.276045	−	1.45525i	−0.0193746	−	0.102139i
$204$	38.9930	−	17.8934i	2.73005	−	1.25279i
$205$	−1.63446	+	0.105802i	−0.114156	+	0.00738954i
$206$	1.42108	+	4.15325i	0.0990111	+	0.289371i
$207$	17.5908	+	2.15885i	1.22264	+	0.150050i
$208$	4.37151	+	11.3225i	0.303110	+	0.785075i
$209$	0.241489	+	2.86693i	0.0167042	+	0.198310i
$210$	0.796430	+	4.11796i	0.0549589	+	0.284166i
$211$	−0.657517	+	0.985767i	−0.0452653	+	0.0678630i	−0.853859	−	0.520505i	$-0.825744\pi$
$211$	−0.657517	+	0.985767i	−0.0452653	+	0.0678630i	0.808593	+	0.588368i	$0.200229\pi$
$212$	−30.6532	+	30.8519i	−2.10527	+	2.11892i
$213$	−3.96424	+	0.900502i	−0.271625	+	0.0617014i
$214$	−0.785875	−	17.3558i	−0.0537213	−	1.18642i
$215$	−28.4243	+	3.32233i	−1.93852	+	0.226581i
$216$	−17.7527	−	10.4551i	−1.20792	−	0.711378i
$217$	0.301729	+	0.0352671i	0.0204827	+	0.00239408i
$218$	−1.20165	+	16.8709i	−0.0813858	+	1.14264i
$219$	−4.08862	+	10.3022i	−0.276284	+	0.696161i
$220$	−22.6606	−	25.2984i	−1.52778	−	1.70562i
$221$	0.251696	−	38.9364i	0.0169309	−	2.61915i
$222$	33.9780	−	27.2448i	2.28046	−	1.82855i
$223$	8.29216	−	7.33151i	0.555284	−	0.490954i	−0.337570	−	0.941301i	$-0.609605\pi$
$223$	8.29216	−	7.33151i	0.555284	−	0.490954i	0.892854	+	0.450346i	$0.148699\pi$
$224$	−0.408982	+	0.855313i	−0.0273262	+	0.0571480i
$225$	5.60199	−	13.2472i	0.373466	−	0.883144i
$226$	−12.5818	+	8.99295i	−0.836931	+	0.598202i
$227$	−1.37309	−	2.69054i	−0.0911353	−	0.178578i	0.840659	−	0.541565i	$-0.182168\pi$
$227$	−1.37309	−	2.69054i	−0.0911353	−	0.178578i	−0.931794	+	0.362988i	$0.881757\pi$
$228$	6.13125	+	0.694375i	0.406052	+	0.0459861i
$229$	−5.40306	−	7.06502i	−0.357045	−	0.466870i	0.580739	−	0.814090i	$-0.302764\pi$
$229$	−5.40306	−	7.06502i	−0.357045	−	0.466870i	−0.937784	+	0.347220i	$0.887126\pi$
$230$	25.8208	−	35.6361i	1.70258	−	2.34978i
$231$	−0.0263496	+	1.66666i	−0.00173368	+	0.109658i
$232$	15.5874	−	9.13422i	1.02336	−	0.599691i
$233$	4.28021	+	19.7597i	0.280406	+	1.29450i	0.872494	+	0.488625i	$0.162501\pi$
$233$	4.28021	+	19.7597i	0.280406	+	1.29450i	−0.592088	+	0.805873i	$0.701696\pi$
$234$	−33.9179	+	23.2979i	−2.21729	+	1.52303i
$235$	13.2589	−	21.0367i	0.864918	−	1.37229i
$236$	−33.9777	+	4.86488i	−2.21176	+	0.316676i
$237$	−2.04790	−	2.45492i	−0.133026	−	0.159464i
$238$	−3.82610	+	3.56327i	−0.248009	+	0.230973i
$239$	−4.92680	−	9.06705i	−0.318688	−	0.586499i	0.668939	−	0.743317i	$-0.266749\pi$
$239$	−4.92680	−	9.06705i	−0.318688	−	0.586499i	−0.987627	+	0.156819i	$0.949876\pi$
$240$	−9.82966	+	5.80762i	−0.634502	+	0.374880i
$241$	4.70376	−	7.90922i	0.302996	−	0.509478i	−0.669373	−	0.742926i	$-0.733437\pi$
$241$	4.70376	−	7.90922i	0.302996	−	0.509478i	0.972369	+	0.233449i	$0.0750011\pi$
$242$	2.66074	+	4.60853i	0.171039	+	0.296248i
$243$	4.58920	−	14.8976i	0.294398	−	0.955683i
$244$	−21.2681	+	36.8374i	−1.36155	+	2.35827i
$245$	10.5457	+	18.8236i	0.673742	+	1.20260i
$246$	−0.717557	+	2.03486i	−0.0457498	+	0.129738i
$247$	2.92452	−	4.77585i	0.186083	−	0.303880i
$248$	0.831178	+	3.61088i	0.0527799	+	0.229291i
$249$	−2.35165	−	1.36677i	−0.149030	−	0.0866157i
$250$	0.946412	+	1.20492i	0.0598563	+	0.0762056i
$251$	11.7073	+	22.2258i	0.738961	+	1.40288i	0.908724	+	0.417398i	$0.137058\pi$
$251$	11.7073	+	22.2258i	0.738961	+	1.40288i	−0.169763	+	0.985485i	$0.554300\pi$
$252$	3.49440	+	0.754361i	0.220127	+	0.0475203i
$253$	12.9515	−	11.7529i	0.814254	−	0.738896i
$254$	0.0332529	+	5.14410i	0.00208647	+	0.322770i
$255$	36.1670	−	5.78928i	2.26487	−	0.362539i
$256$	−26.8614	−	2.78814i	−1.67884	−	0.174259i
$257$	−2.41698	+	0.314228i	−0.150767	+	0.0196010i	−0.203934	−	0.978985i	$-0.565373\pi$
$257$	−2.41698	+	0.314228i	−0.150767	+	0.0196010i	0.0531673	+	0.998586i	$0.483068\pi$
$258$	−10.6829	+	36.1546i	−0.665090	+	2.25088i
$259$	−1.86842	+	2.88119i	−0.116098	+	0.179029i
$260$	6.40001	+	65.7979i	0.396912	+	4.08061i
$261$	9.45169	+	9.87543i	0.585045	+	0.611274i
$262$	17.7400	−	1.37886i	1.09598	−	0.0851865i
$263$	0.609281	+	2.99967i	0.0375699	+	0.184968i	0.994400	−	0.105679i	$-0.0337016\pi$
$263$	0.609281	+	2.99967i	0.0375699	+	0.184968i	−0.956830	+	0.290647i	$0.906130\pi$
$264$	−19.2551	+	6.52643i	−1.18507	+	0.401674i
$265$	−32.2747	+	18.3566i	−1.98262	+	1.12764i
$266$	−0.735940	+	0.154441i	−0.0451234	+	0.00946939i
$267$	0.165902	−	0.0895291i	0.0101531	−	0.00547909i
$268$	−39.8097	+	19.3528i	−2.43176	+	1.18216i
$269$	12.5663	−	16.8794i	0.766178	−	1.02916i	−0.232225	−	0.972662i	$-0.574600\pi$
$269$	12.5663	−	16.8794i	0.766178	−	1.02916i	0.998403	−	0.0564938i	$-0.0179921\pi$
$270$	−26.8640	−	27.8678i	−1.63489	−	1.69598i
$271$	8.23962	+	11.0677i	0.500521	+	0.672317i	0.978546	−	0.206030i	$-0.0660543\pi$
$271$	8.23962	+	11.0677i	0.500521	+	0.672317i	−0.478024	+	0.878347i	$0.658647\pi$
$272$	−12.6346	−	6.55122i	−0.766084	−	0.397226i
$273$	1.96171	−	2.58426i	0.118728	−	0.156407i
$274$	−52.5900	−	13.9094i	−3.17708	−	0.840300i
$275$	−6.28787	−	12.7246i	−0.379173	−	0.767323i
$276$	−19.2882	−	32.1695i	−1.16101	−	1.93638i
$277$	10.4992	−	7.30117i	0.630837	−	0.438685i	−0.211692	−	0.977336i	$-0.567897\pi$
$277$	10.4992	−	7.30117i	0.630837	−	0.438685i	0.842529	+	0.538651i	$0.181066\pi$
$278$	20.2065	+	3.16024i	1.21191	+	0.189539i
$279$	−2.51253	+	1.24377i	−0.150421	+	0.0744626i
$280$	2.65226	−	3.03915i	0.158503	−	0.181624i
$281$	2.51728	−	5.09416i	0.150168	−	0.303892i	−0.808461	−	0.588550i	$-0.799699\pi$
$281$	2.51728	−	5.09416i	0.150168	−	0.303892i	0.958629	+	0.284658i	$0.0918801\pi$
$282$	−18.6249	−	26.9481i	−1.10909	−	1.60474i
$283$	−16.2103	+	13.9631i	−0.963600	+	0.830020i	−0.985489	−	0.169741i	$-0.945707\pi$
$283$	−16.2103	+	13.9631i	−0.963600	+	0.830020i	0.0218885	+	0.999760i	$0.493032\pi$
$284$	6.66180	+	5.44471i	0.395305	+	0.323084i
$285$	4.88376	+	1.97484i	0.289289	+	0.116979i
$286$	−4.45331	+	40.3615i	−0.263330	+	2.38663i
$287$	0.00329901	−	0.170096i	0.000194734	−	0.0100404i
$288$	−1.13412	−	8.67561i	−0.0668284	−	0.511215i
$289$	18.8433	+	21.5920i	1.10843	+	1.27012i
$290$	32.8147	−	8.67910i	1.92695	−	0.509654i
$291$	13.5709	+	17.6140i	0.795539	+	1.03255i
$292$	22.5158	−	6.58250i	1.31764	−	0.385212i
$293$	−1.98261	+	23.5372i	−0.115825	+	1.37506i	0.663376	+	0.748286i	$0.269123\pi$
$293$	−1.98261	+	23.5372i	−0.115825	+	1.37506i	−0.779201	+	0.626774i	$0.784375\pi$
$294$	28.2612	−	3.03585i	1.64822	−	0.177054i
$295$	−29.0593	−	3.77796i	−1.69190	−	0.219961i
$296$	−40.7560	−	9.65936i	−2.36890	−	0.561439i
$297$	−8.17396	−	13.0317i	−0.474301	−	0.756173i
$298$	−0.374618	+	0.0887860i	−0.0217010	+	0.00514324i
$299$	−33.8601	+	3.51459i	−1.95818	+	0.203254i
$300$	−29.4004	+	7.88892i	−1.69744	+	0.455467i
$301$	−0.0960588	−	2.97100i	−0.00553674	−	0.171246i
$302$	24.8157	+	29.9655i	1.42798	+	1.72432i
$303$	3.17049	+	3.51413i	0.182140	+	0.201881i
$304$	−1.06895	−	1.74563i	−0.0613085	−	0.100119i
$305$	−25.9261	+	25.4282i	−1.48453	+	1.45601i
$306$	11.7006	−	46.8111i	0.668880	−	2.67601i
$307$	12.3451	−	17.9996i	0.704574	−	1.02729i	−0.292892	−	0.956145i	$-0.594618\pi$
$307$	12.3451	−	17.9996i	0.704574	−	1.02729i	0.997466	−	0.0711480i	$-0.0226663\pi$
$308$	2.81605	−	2.12490i	0.160459	−	0.121077i
$309$	3.00546	+	1.08171i	0.170974	+	0.0615366i
$310$	−0.314893	+	6.95433i	−0.0178847	+	0.394979i
$311$	1.39858	+	19.6357i	0.0793059	+	1.11344i	0.867310	+	0.497769i	$0.165847\pi$
$311$	1.39858	+	19.6357i	0.0793059	+	1.11344i	−0.788004	+	0.615671i	$0.788885\pi$
$312$	37.7270	+	11.9477i	2.13587	+	0.676408i
$313$	8.56302	+	23.0618i	0.484010	+	1.30353i	0.915830	+	0.401567i	$0.131534\pi$
$313$	8.56302	+	23.0618i	0.484010	+	1.30353i	−0.431819	+	0.901960i	$0.642128\pi$
$314$	3.54492	−	25.9534i	0.200051	−	1.46464i
$315$	2.70131	+	1.42048i	0.152202	+	0.0800347i
$316$	−1.43241	+	6.61276i	−0.0805796	+	0.371997i
$317$	4.87091	+	14.8603i	0.273577	+	0.834635i	0.990504	+	0.137486i	$0.0439023\pi$
$317$	4.87091	+	14.8603i	0.273577	+	0.834635i	−0.716926	+	0.697149i	$0.754452\pi$
$318$	5.53851	+	48.5984i	0.310584	+	2.72527i
$319$	13.4714	−	0.697277i	0.754256	−	0.0390400i
$320$	−32.4842	−	12.7837i	−1.81592	−	0.714632i
$321$	−10.2159	−	7.44711i	−0.570197	−	0.415657i
$322$	3.46336	+	2.98325i	0.193006	+	0.166250i
$323$	1.14031	+	6.46699i	0.0634483	+	0.359833i
$324$	−30.8372	+	11.7271i	−1.71318	+	0.651507i
$325$	−4.79738	+	27.2073i	−0.266111	+	1.50919i
$326$	41.3279	−	33.7775i	2.28894	−	1.87076i
$327$	9.03653	+	8.35551i	0.499721	+	0.462061i
$328$	1.96764	−	0.659070i	0.108645	−	0.0363910i
$329$	2.06179	+	1.55576i	0.113670	+	0.0857719i
$330$	−38.1393	+	2.11116i	−2.09950	+	0.116215i
$331$	28.7234	−	15.3679i	1.57878	−	0.844697i	0.579217	−	0.815173i	$-0.303358\pi$
$331$	28.7234	−	15.3679i	1.57878	−	0.844697i	0.999564	−	0.0295235i	$-0.00939900\pi$
$332$	0.779054	+	5.70369i	0.0427562	+	0.313031i
$333$	−0.0223034	−	31.6913i	−0.00122222	−	1.73667i
$334$	−0.612342	+	1.16250i	−0.0335059	+	0.0636093i
$335$	−37.1728	+	6.80262i	−2.03097	+	0.371667i
$336$	−0.515413	−	1.06804i	−0.0281181	−	0.0582665i
$337$	−7.80144	−	8.05775i	−0.424971	−	0.438934i	0.471614	−	0.881805i	$-0.343672\pi$
$337$	−7.80144	−	8.05775i	−0.424971	−	0.438934i	−0.896585	+	0.442872i	$0.853960\pi$
$338$	32.5500	−	35.4070i	1.77049	−	1.92589i
$339$	−0.614068	+	11.2368i	−0.0333516	+	0.610299i
$340$	−56.7281	−	52.8313i	−3.07651	−	2.86518i
$341$	−0.690100	+	2.67913i	−0.0373710	+	0.145083i
$342$	4.91952	−	4.89471i	0.266017	−	0.264675i
$343$	−4.11180	+	1.86904i	−0.222016	+	0.100919i
$344$	33.7383	−	13.2773i	1.81905	−	0.715862i
$345$	−8.49871	−	30.8743i	−0.457555	−	1.66222i
$346$	−8.10491	−	1.48320i	−0.435722	−	0.0797371i
$347$	10.7516	−	13.6883i	0.577174	−	0.734825i	−0.406725	−	0.913551i	$-0.633329\pi$
$347$	10.7516	−	13.6883i	0.577174	−	0.734825i	0.983899	+	0.178726i	$0.0571975\pi$
$348$	4.18291	−	28.6267i	0.224228	−	1.53455i
$349$	6.05277	+	21.2120i	0.323998	+	1.13545i	0.938140	+	0.346257i	$0.112547\pi$
$349$	6.05277	+	21.2120i	0.323998	+	1.13545i	−0.614142	+	0.789195i	$0.710498\pi$
$350$	3.09939	−	2.03850i	0.165669	−	0.108962i
$351$	−2.19230	+	29.8621i	−0.117016	+	1.59392i
$352$	−7.21371	−	4.74453i	−0.384492	−	0.252884i
$353$	−0.501127	+	1.59837i	−0.0266723	+	0.0850729i	−0.966589	−	0.256330i	$-0.917487\pi$
$353$	−0.501127	+	1.59837i	−0.0266723	+	0.0850729i	0.939917	+	0.341403i	$0.110902\pi$
$354$	−19.6133	+	33.2498i	−1.04243	+	1.76721i
$355$	4.23253	+	6.00330i	0.224640	+	0.318622i
$356$	−0.365325	−	0.160394i	−0.0193622	−	0.00850089i
$357$	0.283895	+	3.79390i	0.0150253	+	0.200795i
$358$	−14.3135	−	30.9563i	−0.756494	−	1.63609i
$359$	−0.293604	−	0.162004i	−0.0154958	−	0.00855023i	0.475346	−	0.879799i	$-0.342323\pi$
$359$	−0.293604	−	0.162004i	−0.0154958	−	0.00855023i	−0.490842	+	0.871249i	$0.663311\pi$
$360$	−5.25024	+	36.8541i	−0.276712	+	1.94238i
$361$	6.50320	−	16.8437i	0.342274	−	0.886511i
$362$	−9.46674	−	2.76760i	−0.497561	−	0.145462i
$363$	3.82786	+	0.584620i	0.200911	+	0.0306846i
$364$	−6.86614	+	0.0887730i	−0.359884	+	0.00465297i
$365$	20.0255	−	0.258911i	1.04818	−	0.0135520i
$366$	17.3905	+	44.5665i	0.909015	+	2.32953i
$367$	−31.1389	−	9.10347i	−1.62544	−	0.475197i	−0.663434	−	0.748234i	$-0.730902\pi$
$367$	−31.1389	−	9.10347i	−1.62544	−	0.475197i	−0.962004	+	0.273037i	$0.911972\pi$
$368$	−4.48162	+	11.6077i	−0.233621	+	0.605093i
$369$	0.829500	+	1.33305i	0.0431820	+	0.0693960i
$370$	−68.9002	−	38.0175i	−3.58195	−	1.97644i
$371$	−1.61860	−	3.50060i	−0.0840336	−	0.181742i
$372$	5.34558	+	2.57502i	0.277155	+	0.133509i
$373$	11.7085	+	5.14059i	0.606245	+	0.266170i	0.682462	−	0.730921i	$-0.260909\pi$
$373$	11.7085	+	5.14059i	0.606245	+	0.266170i	−0.0762162	+	0.997091i	$0.524284\pi$
$374$	−27.4370	−	38.9158i	−1.41873	−	2.01229i
$375$	1.11485	+	0.0104179i	0.0575707	+	0.000537979i
$376$	−9.42491	+	30.0613i	−0.486053	+	1.55029i
$377$	−21.9372	−	14.4283i	−1.12982	−	0.743097i
$378$	3.11864	−	2.53757i	0.160405	−	0.130519i
$379$	−1.35827	+	0.893347i	−0.0697695	+	0.0458882i	−0.583915	−	0.811815i	$-0.698480\pi$
$379$	−1.35827	+	0.893347i	−0.0697695	+	0.0458882i	0.514145	+	0.857703i	$0.328109\pi$
$380$	−3.05927	−	10.7212i	−0.156937	−	0.549988i
$381$	2.93709	+	2.32067i	0.150472	+	0.118892i
$382$	−19.5816	+	24.9302i	−1.00188	+	1.27554i
$383$	18.9338	+	3.46488i	0.967471	+	0.177047i	0.640475	−	0.767979i	$-0.278737\pi$
$383$	18.9338	+	3.46488i	0.967471	+	0.177047i	0.326996	+	0.945026i	$0.393964\pi$
$384$	−25.2007	+	25.5466i	−1.28602	+	1.30367i
$385$	2.80259	−	1.10292i	0.142833	−	0.0562102i
$386$	35.5098	−	16.1412i	1.80740	−	0.821564i
$387$	15.6780	+	22.5114i	0.796956	+	1.14432i
$388$	11.7387	−	45.5724i	0.595942	−	2.31359i
$389$	−12.1495	−	11.3149i	−0.616003	−	0.573688i	0.310219	−	0.950665i	$-0.399597\pi$
$389$	−12.1495	−	11.3149i	−0.616003	−	0.573688i	−0.926223	+	0.376977i	$0.876964\pi$
$390$	62.2648	+	40.6333i	3.15290	+	2.05755i
$391$	27.0157	−	29.3870i	1.36624	−	1.48616i
$392$	−19.0144	−	19.6392i	−0.960374	−	0.991927i
$393$	7.28501	−	10.7039i	0.367480	−	0.539938i
$394$	25.9559	−	4.74992i	1.30764	−	0.239298i
$395$	−2.69209	+	5.11082i	−0.135454	+	0.257153i
$396$	−11.1136	+	30.6014i	−0.558480	+	1.53778i
$397$	1.45201	+	10.6306i	0.0728742	+	0.533534i	0.990649	+	0.136433i	$0.0435638\pi$
$397$	1.45201	+	10.6306i	0.0728742	+	0.533534i	−0.917775	+	0.397101i	$0.870016\pi$
$398$	−41.9914	+	22.4667i	−2.10484	+	1.12615i
$399$	−0.246983	+	0.488271i	−0.0123646	+	0.0244441i
$400$	8.06070	+	6.08235i	0.403035	+	0.304117i
$401$	−19.3852	+	6.49317i	−0.968052	+	0.324254i	−0.757141	−	0.653252i	$-0.773404\pi$
$401$	−19.3852	+	6.49317i	−0.968052	+	0.324254i	−0.210911	+	0.977505i	$0.567643\pi$
$402$	−10.9934	+	48.5540i	−0.548303	+	2.42165i
$403$	4.16960	−	3.40783i	0.207703	−	0.169756i
$404$	1.73943	−	9.86482i	0.0865401	−	0.490793i
$405$	−28.0474	+	2.58501i	−1.39369	+	0.128450i
$406$	0.612229	+	3.47212i	0.0303844	+	0.172319i
$407$	−23.6952	−	20.4104i	−1.17453	−	1.01171i
$408$	−42.4224	+	18.8070i	−2.10022	+	0.931087i
$409$	20.8322	+	8.19824i	1.03009	+	0.405377i	0.820035	−	0.572314i	$-0.193954\pi$
$409$	20.8322	+	8.19824i	1.03009	+	0.405377i	0.210051	+	0.977691i	$0.432637\pi$
$410$	3.89342	−	0.201522i	0.192282	−	0.00995245i
$411$	−31.8191	+	23.5463i	−1.56952	+	1.16145i
$412$	−2.10565	−	6.42397i	−0.103738	−	0.316486i
$413$	0.644385	−	2.97481i	0.0317081	−	0.146381i
$414$	−41.8011	−	5.67955i	−2.05441	−	0.279135i
$415$	−0.665107	+	4.86945i	−0.0326488	+	0.239032i
$416$	5.84996	+	15.7550i	0.286818	+	0.772453i
$417$	10.9851	−	10.0405i	0.537942	−	0.491684i
$418$	−0.486543	−	6.83097i	−0.0237976	−	0.334114i
$419$	0.488498	−	10.7883i	0.0238647	−	0.527045i	−0.951660	−	0.307154i	$-0.900623\pi$
$419$	0.488498	−	10.7883i	0.0238647	−	0.527045i	0.975524	−	0.219891i	$-0.0705701\pi$
$420$	−1.14445	−	6.35718i	−0.0558435	−	0.310199i
$421$	28.6893	−	21.6480i	1.39823	−	1.05506i	0.408400	−	0.912803i	$-0.366087\pi$
$421$	28.6893	−	21.6480i	1.39823	−	1.05506i	0.989830	−	0.142256i	$-0.0454357\pi$
$422$	1.59528	−	2.32598i	0.0776571	−	0.113227i
$423$	−23.7778	−	1.67678i	−1.15612	−	0.0815280i
$424$	33.5838	−	32.9388i	1.63097	−	1.59965i
$425$	−16.9177	−	27.6272i	−0.820630	−	1.34012i
$426$	9.46293	−	2.02128i	0.458481	−	0.0979315i
$427$	−2.40588	−	2.90515i	−0.116429	−	0.140590i
$428$	0.864634	+	26.7422i	0.0417937	+	1.29263i
$429$	20.9009	+	20.8862i	1.00910	+	1.00839i
$430$	67.7546	−	7.03275i	3.26742	−	0.339149i
$431$	−2.95248	+	0.699750i	−0.142216	+	0.0337057i	−0.301107	−	0.953590i	$-0.597356\pi$
$431$	−2.95248	+	0.699750i	−0.142216	+	0.0337057i	0.158891	+	0.987296i	$0.449208\pi$
$432$	9.35787	+	5.67533i	0.450231	+	0.273054i
$433$	−22.5283	−	5.33930i	−1.08264	−	0.256590i	−0.349685	−	0.936867i	$-0.613711\pi$
$433$	−22.5283	−	5.33930i	−1.08264	−	0.256590i	−0.732955	+	0.680277i	$0.761859\pi$
$434$	−0.717056	−	0.0932235i	−0.0344198	−	0.00447487i
$435$	9.99435	−	22.5868i	0.479192	−	1.08295i
$436$	2.18634	−	25.9559i	0.104706	−	1.24306i
$437$	5.51053	−	1.61101i	0.263604	−	0.0770648i
$438$	10.0483	−	24.3944i	0.480126	−	1.16561i
$439$	16.4599	−	4.35345i	0.785589	−	0.207779i	0.159155	−	0.987254i	$-0.449123\pi$
$439$	16.4599	−	4.35345i	0.785589	−	0.207779i	0.626434	+	0.779475i	$0.284514\pi$
$440$	24.1544	+	27.6779i	1.15152	+	1.31949i
$441$	11.1289	−	17.4337i	0.529946	−	0.830177i
$442$	−1.79722	+	92.6642i	−0.0854851	+	4.40759i
$443$	−0.117305	+	1.06316i	−0.00557331	+	0.0505123i	−0.996434	−	0.0843785i	$-0.973110\pi$
$443$	−0.117305	+	1.06316i	−0.00557331	+	0.0505123i	0.990860	+	0.134891i	$0.0430684\pi$
$444$	−52.8659	+	41.2783i	−2.50890	+	1.95898i
$445$	−0.263745	−	0.215559i	−0.0125027	−	0.0102185i
$446$	−19.9617	+	17.1945i	−0.945212	+	0.814181i
$447$	−0.119945	+	0.253172i	−0.00567322	+	0.0119746i
$448$	1.60638	−	3.25079i	0.0758942	−	0.153585i
$449$	8.84281	−	10.1327i	0.417318	−	0.478194i	−0.505833	−	0.862632i	$-0.668815\pi$
$449$	8.84281	−	10.1327i	0.417318	−	0.478194i	0.923151	+	0.384438i	$0.125605\pi$
$450$	−13.7409	+	31.3570i	−0.647751	+	1.47818i
$451$	1.53076	+	0.239407i	0.0720809	+	0.0112732i
$452$	19.5541	−	13.5979i	0.919746	−	0.639593i
$453$	28.3074	−	0.467464i	1.33000	−	0.0219634i
$454$	3.18528	+	6.44598i	0.149493	+	0.302525i
$455$	−5.66749	−	1.49898i	−0.265696	−	0.0702734i
$456$	−6.62144	−	0.836725i	−0.310078	−	0.0391832i
$457$	7.55295	+	3.91632i	0.353312	+	0.183198i	0.627765	−	0.778403i	$-0.283970\pi$
$457$	7.55295	+	3.91632i	0.353312	+	0.183198i	−0.274453	+	0.961601i	$0.588497\pi$
$458$	12.6423	+	16.9816i	0.590738	+	0.793499i
$459$	−21.2683	−	27.9361i	−0.992719	−	1.30395i
$460$	−40.4715	+	54.3627i	−1.88700	+	2.53467i
$461$	−16.5988	+	8.06922i	−0.773083	+	0.375821i	−0.781309	−	0.624145i	$-0.785447\pi$
$461$	−16.5988	+	8.06922i	−0.773083	+	0.375821i	0.00822587	+	0.999966i	$0.497382\pi$
$462$	0.114001	−	3.96597i	0.00530382	−	0.184514i
$463$	31.9272	−	6.70011i	1.48378	−	0.311380i	0.607944	−	0.793980i	$-0.291995\pi$
$463$	31.9272	−	6.70011i	1.48378	−	0.311380i	0.875841	+	0.482600i	$0.160307\pi$
$464$	−8.34225	+	4.74477i	−0.387279	+	0.220270i
$465$	3.80700	+	3.34173i	0.176546	+	0.154969i
$466$	−9.57922	−	47.1614i	−0.443749	−	2.18471i
$467$	−23.2357	+	1.80602i	−1.07522	+	0.0835728i	−0.602871	−	0.797838i	$-0.705977\pi$
$467$	−23.2357	+	1.80602i	−1.07522	+	0.0835728i	−0.472350	+	0.881411i	$0.656594\pi$
$468$	52.6948	−	35.2016i	2.43582	−	1.62719i
$469$	−0.380010	−	3.90685i	−0.0175472	−	0.180401i
$470$	−32.2048	+	49.6612i	−1.48550	+	2.29070i
$471$	−13.1299	−	13.8173i	−0.604993	−	0.636668i
$472$	36.8161	−	4.78641i	1.69460	−	0.220312i
$473$	26.9267	+	2.79492i	1.23809	+	0.128510i
$474$	4.79864	+	5.90594i	0.220409	+	0.271269i
$475$	−0.0301183	−	4.65919i	−0.00138192	−	0.213778i
$476$	5.96283	−	5.41098i	0.273306	−	0.248012i
$477$	30.1240	+	18.9568i	1.37928	+	0.867972i
$478$	11.4472	+	21.7320i	0.523582	+	0.993997i
$479$	8.43309	+	10.7365i	0.385318	+	0.490564i	0.939845	−	0.341601i	$-0.110969\pi$
$479$	8.43309	+	10.7365i	0.385318	+	0.490564i	−0.554527	+	0.832165i	$0.687101\pi$
$480$	−13.7138	+	7.86507i	−0.625945	+	0.358990i
$481$	13.6551	+	59.3218i	0.622621	+	2.70484i
$482$	−11.4387	+	18.6799i	−0.521020	+	0.850845i
$483$	3.26971	−	0.610475i	0.148777	−	0.0277776i
$484$	−4.00557	−	7.14974i	−0.182071	−	0.324988i
$485$	20.0884	−	34.7942i	0.912168	−	1.57992i
$486$	−11.3811	+	35.3164i	−0.516259	+	1.60198i
$487$	6.53064	+	11.3114i	0.295931	+	0.512568i	0.975201	−	0.221321i	$-0.0710367\pi$
$487$	6.53064	+	11.3114i	0.295931	+	0.512568i	−0.679270	+	0.733889i	$0.737703\pi$
$488$	23.5173	−	39.5435i	1.06458	−	1.79005i
$489$	−0.390257	−	38.8373i	−0.0176480	−	1.75629i
$490$	−24.5205	−	45.1264i	−1.10772	−	2.03860i
$491$	13.5444	−	12.6140i	0.611252	−	0.569264i	−0.313617	−	0.949550i	$-0.601541\pi$
$491$	13.5444	−	12.6140i	0.611252	−	0.569264i	0.924869	+	0.380286i	$0.124174\pi$
$492$	1.14549	−	3.11924i	0.0516429	−	0.140626i
$493$	30.4781	−	4.36380i	1.37266	−	0.196536i
$494$	−7.10757	+	11.2769i	−0.319785	+	0.507373i
$495$	−16.1467	+	22.6241i	−0.725741	+	1.01688i
$496$	−0.416698	−	1.92369i	−0.0187103	−	0.0863764i
$497$	−0.658266	+	0.385745i	−0.0295273	+	0.0173030i
$498$	5.55507	+	3.32540i	0.248929	+	0.149015i
$499$	−0.173615	+	0.239612i	−0.00777209	+	0.0107265i	−0.813645	−	0.581363i	$-0.802520\pi$
$499$	−0.173615	+	0.239612i	−0.00777209	+	0.0107265i	0.805872	+	0.592089i	$0.201697\pi$
$500$	−1.43341	−	1.87432i	−0.0641040	−	0.0838221i
$501$	0.381832	+	0.876535i	0.0170590	+	0.0391607i
$502$	−27.1805	−	53.2597i	−1.21313	−	2.37710i
$503$	22.3018	−	15.9404i	0.994388	−	0.710746i	0.0369299	−	0.999318i	$-0.488242\pi$
$503$	22.3018	−	15.9404i	0.994388	−	0.710746i	0.957458	+	0.288572i	$0.0931805\pi$
$504$	−3.76877	−	0.864731i	−0.167874	−	0.0385182i
$505$	3.68916	−	7.71523i	0.164166	−	0.343323i
$506$	−31.1874	+	27.5743i	−1.38645	+	1.22583i
$507$	−5.30813	−	34.5924i	−0.235742	−	1.53630i
$508$	0.0512111	−	7.92217i	0.00227212	−	0.351490i
$509$	7.58894	+	8.47232i	0.336374	+	0.375529i	0.889006	−	0.457896i	$-0.151397\pi$
$509$	7.58894	+	8.47232i	0.336374	+	0.375529i	−0.552632	+	0.833426i	$0.686376\pi$
$510$	−86.2587	+	12.6660i	−3.81960	+	0.560862i
$511$	−0.147792	+	2.07498i	−0.00653795	+	0.0917916i
$512$	22.6907	+	2.65217i	1.00280	+	0.117210i
$513$	−0.542887	−	5.02054i	−0.0239690	−	0.221662i
$514$	5.76228	−	0.673514i	0.254163	−	0.0297074i
$515$	−0.261067	−	5.76558i	−0.0115040	−	0.254062i
$516$	17.1707	−	55.4624i	0.755897	−	2.44160i
$517$	−16.5792	+	16.6868i	−0.729154	+	0.733883i
$518$	4.53567	−	6.79999i	0.199286	−	0.298775i
$519$	−4.52864	+	3.92921i	−0.198785	+	0.172473i
$520$	−6.00176	−	71.2522i	−0.263195	−	3.12461i
$521$	−1.93864	−	5.02120i	−0.0849332	−	0.219983i	0.883910	−	0.467657i	$-0.154902\pi$
$521$	−1.93864	−	5.02120i	−0.0849332	−	0.219983i	−0.968843	+	0.247674i	$0.920334\pi$
$522$	−22.1919	−	23.7952i	−0.971315	−	1.04149i
$523$	9.00461	+	26.3170i	0.393744	+	1.15076i	0.947960	+	0.318388i	$0.103142\pi$
$523$	9.00461	+	26.3170i	0.393744	+	1.15076i	−0.554216	+	0.832373i	$0.686982\pi$
$524$	−27.3457	+	1.77014i	−1.19460	+	0.0773289i
$525$	0.251701	−	2.68764i	0.0109851	−	0.117298i
$526$	−1.35783	−	7.15823i	−0.0592044	−	0.312114i
$527$	−1.01602	+	6.23228i	−0.0442587	+	0.271482i
$528$	10.2725	−	3.33440i	0.447054	−	0.145111i
$529$	−9.59059	−	7.04403i	−0.416982	−	0.306262i
$530$	77.3813	−	42.6972i	3.36123	−	1.85465i
$531$	9.96643	+	26.2629i	0.432506	+	1.13971i
$532$	1.13636	−	0.223175i	0.0492676	−	0.00967584i
$533$	−2.12559	−	2.13937i	−0.0920694	−	0.0926665i
$534$	−0.397617	+	0.207982i	−0.0172066	+	0.00900025i
$535$	−5.41147	+	22.1925i	−0.233958	+	0.959465i
$536$	43.3261	−	20.3740i	1.87140	−	0.880024i
$537$	−24.0938	−	5.94865i	−1.03972	−	0.256703i
$538$	−30.4282	+	39.7878i	−1.31185	+	1.71537i
$539$	−5.85377	−	19.5530i	−0.252140	−	0.842206i
$540$	40.8136	+	43.4490i	1.75634	+	1.86975i
$541$	9.09384	−	30.3755i	0.390975	−	1.30595i	−0.505491	−	0.862832i	$-0.668689\pi$
$541$	9.09384	−	30.3755i	0.390975	−	1.30595i	0.896465	−	0.443114i	$-0.146126\pi$
$542$	−19.2704	−	26.5957i	−0.827736	−	1.14238i
$543$	−5.87758	+	4.11861i	−0.252231	+	0.176746i
$544$	−17.3761	−	9.29676i	−0.744995	−	0.398595i
$545$	7.74075	−	20.8472i	0.331577	−	0.892998i
$546$	−4.74856	+	6.09040i	−0.203220	+	0.260645i
$547$	−10.7338	+	0.277604i	−0.458946	+	0.0118695i	−0.254636	−	0.967037i	$-0.581956\pi$
$547$	−10.7338	+	0.277604i	−0.458946	+	0.0118695i	−0.204309	+	0.978906i	$0.565495\pi$
$548$	80.7075	+	22.4665i	3.44765	+	0.959720i
$549$	33.2240	+	10.3908i	1.41797	+	0.443470i
$550$	14.5741	+	30.4792i	0.621442	+	1.29964i
$551$	4.07730	+	1.72760i	0.173699	+	0.0735983i
$552$	20.4110	+	35.0621i	0.868751	+	1.49234i
$553$	−0.505519	−	0.323201i	−0.0214969	−	0.0137439i
$554$	−25.2137	+	17.0543i	−1.07123	+	0.724569i
$555$	−52.9309	+	21.8464i	−2.24679	+	0.927326i
$556$	−31.0535	−	5.26882i	−1.31696	−	0.223448i
$557$	−16.6335	+	6.79553i	−0.704784	+	0.287936i	−0.702118	−	0.712061i	$-0.747762\pi$
$557$	−16.6335	+	6.79553i	−0.704784	+	0.287936i	−0.00266585	+	0.999996i	$0.500849\pi$
$558$	6.01832	−	2.88296i	0.254776	−	0.122046i
$559$	−39.0218	−	35.4104i	−1.65045	−	1.49770i
$560$	−1.42967	+	1.59609i	−0.0604146	+	0.0674471i
$561$	−34.5835	−	2.11422i	−1.46012	−	0.0892626i
$562$	−6.14810	+	12.0471i	−0.259342	+	0.508175i
$563$	6.59323	+	44.0190i	0.277871	+	1.85518i	0.481915	+	0.876218i	$0.339941\pi$
$563$	6.59323	+	44.0190i	0.277871	+	1.85518i	−0.204044	+	0.978962i	$0.565408\pi$
$564$	28.1443	+	41.8688i	1.18509	+	1.76299i
$565$	19.1958	−	6.70694i	0.807572	−	0.282163i
$566$	39.0115	−	32.7345i	1.63978	−	1.37593i
$567$	−0.0230296	−	2.92556i	−0.000967154	−	0.122862i
$568$	−7.12882	−	5.98179i	−0.299119	−	0.250991i
$569$	21.6239	+	8.18858i	0.906523	+	0.343283i	0.763026	−	0.646368i	$-0.223713\pi$
$569$	21.6239	+	8.18858i	0.906523	+	0.343283i	0.143497	+	0.989651i	$0.454165\pi$
$570$	−11.5630	−	4.85058i	−0.484321	−	0.203168i
$571$	1.69640	−	8.35190i	0.0709922	−	0.349516i	−0.928785	−	0.370619i	$-0.879146\pi$
$571$	1.69640	−	8.35190i	0.0709922	−	0.349516i	0.999777	+	0.0211027i	$0.00671770\pi$
$572$	7.66133	−	62.0649i	0.320336	−	2.59506i
$573$	5.25512	+	22.4612i	0.219536	+	0.938329i
$574$	−0.0130862	+	0.404741i	−0.000546206	+	0.0168936i
$575$	−22.3862	+	17.3506i	−0.933567	+	0.723569i
$576$	3.90828	+	33.2346i	0.162845	+	1.38477i
$577$	−24.1110	−	38.2548i	−1.00376	−	1.59257i	−0.787580	−	0.616212i	$-0.788666\pi$
$577$	−24.1110	−	38.2548i	−1.00376	−	1.59257i	−0.216175	−	0.976355i	$-0.569358\pi$
$578$	−44.1841	−	51.9706i	−1.83782	−	2.16169i
$579$	6.98145	−	27.5115i	0.290139	−	1.14334i
$580$	−50.7049	+	12.7118i	−2.10540	+	0.527828i
$581$	−0.498208	−	0.111295i	−0.0206692	−	0.00461730i
$582$	−31.7578	−	42.3405i	−1.31640	−	1.75507i
$583$	33.5819	−	10.2908i	1.39082	−	0.426200i
$584$	−24.4436	+	6.80435i	−1.01148	+	0.281566i
$585$	51.3990	−	16.8877i	2.12509	−	0.698219i
$586$	5.44307	−	55.9596i	0.224851	−	2.31167i
$587$	34.3420	+	27.3350i	1.41745	+	1.12824i	0.972561	+	0.232647i	$0.0747387\pi$
$587$	34.3420	+	27.3350i	1.41745	+	1.12824i	0.444884	+	0.895588i	$0.353245\pi$
$588$	−43.5804	+	4.11229i	−1.79722	+	0.169588i
$589$	−0.588258	+	0.691926i	−0.0242388	+	0.0285103i
$590$	69.0473	+	9.88609i	2.84263	+	0.407004i
$591$	9.10678	−	16.9038i	0.374603	−	0.695330i
$592$	21.5820	+	5.41065i	0.887015	+	0.222376i
$593$	3.05303	+	1.53329i	0.125373	+	0.0629646i	0.510380	−	0.859949i	$-0.329505\pi$
$593$	3.05303	+	1.53329i	0.125373	+	0.0629646i	−0.385007	+	0.922914i	$0.625801\pi$
$594$	19.0537	+	31.2680i	0.781783	+	1.28294i
$595$	6.14305	−	3.08516i	0.251841	−	0.126479i
$596$	0.578649	−	0.129265i	0.0237024	−	0.00529489i
$597$	−6.33628	+	34.0701i	−0.259327	+	1.39439i
$598$	80.6982	−	7.32307i	3.29999	−	0.299463i
$599$	3.12354	+	28.3095i	0.127625	+	1.15669i	0.872198	+	0.489154i	$0.162694\pi$
$599$	3.12354	+	28.3095i	0.127625	+	1.15669i	−0.744573	+	0.667541i	$0.767347\pi$
$600$	31.9079	−	8.12101i	1.30263	−	0.331539i
$601$	−26.1337	−	2.37154i	−1.06601	−	0.0967370i	−0.456665	−	0.889639i	$-0.650956\pi$
$601$	−26.1337	−	2.37154i	−1.06601	−	0.0967370i	−0.609349	+	0.792902i	$0.708569\pi$
$602$	0.137204	+	7.07419i	0.00559201	+	0.288322i
$603$	22.5799	+	28.3271i	0.919526	+	1.15357i
$604$	−37.6176	−	46.6385i	−1.53064	−	1.89770i
$605$	−1.65751	−	6.79748i	−0.0673875	−	0.276357i
$606$	−7.43791	−	8.46149i	−0.302144	−	0.343725i
$607$	−16.9051	+	30.1747i	−0.686155	+	1.22475i	0.278297	+	0.960495i	$0.410230\pi$
$607$	−16.9051	+	30.1747i	−0.686155	+	1.22475i	−0.964452	+	0.264259i	$0.914873\pi$
$608$	−1.44878	−	2.43608i	−0.0587558	−	0.0987960i
$609$	2.25069	+	1.23138i	0.0912026	+	0.0498979i
$610$	62.4889	−	59.7234i	2.53010	−	2.41813i
$611$	45.2363	−	7.07482i	1.83006	−	0.286217i
$612$	−18.9500	+	71.8524i	−0.766009	+	2.90446i
$613$	−37.4543	+	22.6038i	−1.51276	+	0.912957i	−0.514296	+	0.857613i	$0.671947\pi$
$613$	−37.4543	+	22.6038i	−1.51276	+	0.912957i	−0.998467	+	0.0553445i	$0.982374\pi$
$614$	−29.9364	+	42.4608i	−1.20813	+	1.71358i
$615$	1.65627	−	2.30320i	0.0667874	−	0.0928741i
$616$	−3.07536	+	2.25877i	−0.123910	+	0.0910085i
$617$	−8.86237	+	19.1669i	−0.356786	+	0.771631i	0.643197	+	0.765701i	$0.277608\pi$
$617$	−8.86237	+	19.1669i	−0.356786	+	0.771631i	−0.999982	+	0.00592984i	$0.998112\pi$
$618$	−7.11996	−	2.66706i	−0.286407	−	0.107285i
$619$	16.4817	+	17.9284i	0.662456	+	0.720603i	0.973218	−	0.229885i	$-0.0738350\pi$
$619$	16.4817	+	17.9284i	0.662456	+	0.720603i	−0.310761	+	0.950488i	$0.600584\pi$
$620$	0.623370	−	10.7028i	0.0250351	−	0.429837i
$621$	−22.2374	+	21.1609i	−0.892357	+	0.849157i
$622$	−2.72449	−	46.7777i	−0.109242	−	1.87562i
$623$	0.0246107	−	0.0254193i	0.000986007	−	0.00101840i
$624$	−19.9574	−	6.60536i	−0.798935	−	0.264426i
$625$	−9.67223	−	24.1190i	−0.386889	−	0.964759i
$626$	−19.6710	−	55.1525i	−0.786213	−	2.20434i
$627$	−4.10143	−	2.83039i	−0.163795	−	0.113035i
$628$	−5.97562	+	39.8956i	−0.238453	+	1.59201i
$629$	−58.0715	−	41.5070i	−2.31546	−	1.65499i
$630$	−6.38565	−	3.46398i	−0.254410	−	0.138008i
$631$	27.4096	+	26.8832i	1.09116	+	1.07020i	0.997212	+	0.0746244i	$0.0237758\pi$
$631$	27.4096	+	26.8832i	1.09116	+	1.07020i	0.0939476	+	0.995577i	$0.470051\pi$
$632$	1.64167	−	7.13190i	0.0653022	−	0.283692i
$633$	−0.595667	−	1.96402i	−0.0236756	−	0.0780628i
$634$	−11.1359	−	35.5186i	−0.442263	−	1.41062i
$635$	1.85589	−	6.50398i	0.0736488	−	0.258103i
$636$	−7.56127	−	74.9480i	−0.299824	−	2.97188i
$637$	−13.3462	+	37.4193i	−0.528797	+	1.48261i
$638$	−32.0847	+	1.24503i	−1.27024	+	0.0492912i
$639$	3.15565	−	6.29445i	0.124835	−	0.249005i
$640$	60.0229	+	24.5220i	2.37261	+	0.969318i
$641$	38.2769	+	23.7807i	1.51185	+	0.939280i	0.996613	+	0.0822309i	$0.0262045\pi$
$641$	38.2769	+	23.7807i	1.51185	+	0.939280i	0.515234	+	0.857049i	$0.327705\pi$
$642$	24.0856	+	18.0391i	0.950583	+	0.711947i
$643$	30.3486	−	12.8591i	1.19683	−	0.507112i	0.301910	−	0.953336i	$-0.402376\pi$
$643$	30.3486	−	12.8591i	1.19683	−	0.507112i	0.894921	+	0.446224i	$0.147232\pi$
$644$	−5.27391	−	4.66292i	−0.207821	−	0.183745i
$645$	26.8203	−	41.6847i	1.05605	−	1.64133i
$646$	−2.51502	−	15.4271i	−0.0989522	−	0.606971i
$647$	11.5152	−	4.19118i	0.452709	−	0.164772i	−0.105595	−	0.994409i	$-0.533675\pi$
$647$	11.5152	−	4.19118i	0.452709	−	0.164772i	0.558304	+	0.829637i	$0.311452\pi$
$648$	33.5155	−	12.2521i	1.31661	−	0.481307i
$649$	26.0485	+	9.48088i	1.02249	+	0.372157i
$650$	12.2554	−	64.6080i	0.480696	−	2.53413i
$651$	−0.379073	+	0.364906i	−0.0148570	+	0.0143018i
$652$	−64.3142	+	51.1918i	−2.51874	+	2.00482i
$653$	−11.8095	−	18.2108i	−0.462141	−	0.712643i	0.528530	−	0.848914i	$-0.322743\pi$
$653$	−11.8095	−	18.2108i	−0.462141	−	0.712643i	−0.990672	+	0.136271i	$0.956488\pi$
$654$	−21.2506	−	20.1649i	−0.830964	−	0.788510i
$655$	−22.8961	−	4.80488i	−0.894626	−	0.187742i
$656$	−1.04967	+	0.336565i	−0.0409829	+	0.0131406i
$657$	−9.28658	−	16.8023i	−0.362304	−	0.655522i
$658$	−4.85936	−	3.76629i	−0.189438	−	0.146825i
$659$	−1.91435	+	2.31162i	−0.0745727	+	0.0900480i	−0.806153	−	0.591708i	$-0.798454\pi$
$659$	−1.91435	+	2.31162i	−0.0745727	+	0.0900480i	0.731580	+	0.681756i	$0.238783\pi$
$660$	58.7734	−	2.49167i	2.28775	−	0.0969880i
$661$	−30.2888	−	14.7244i	−1.17810	−	0.572712i	−0.258667	−	0.965967i	$-0.583283\pi$
$661$	−30.2888	−	14.7244i	−1.17810	−	0.572712i	−0.919430	+	0.393255i	$0.871349\pi$
$662$	−68.8371	+	35.6930i	−2.67543	+	1.38725i
$663$	51.8180	+	43.1650i	2.01245	+	1.67639i
$664$	−0.762818	−	6.17962i	−0.0296031	−	0.239816i
$665$	0.985715	+	0.0766158i	0.0382244	+	0.00297103i
$666$	−0.922132	+	75.4288i	−0.0357319	+	2.92281i
$667$	−6.71449	−	26.0672i	−0.259986	−	1.00933i
$668$	0.966103	−	1.77797i	0.0373796	−	0.0687917i
$669$	0.688190	+	19.1588i	0.0266070	+	0.740722i
$670$	88.6839	−	15.0469i	3.42616	−	0.581314i
$671$	29.1793	−	18.1285i	1.12646	−	0.699844i
$672$	−0.694503	−	1.48800i	−0.0267911	−	0.0574008i
$673$	11.7175	−	26.2266i	0.451677	−	1.01096i	−0.534485	−	0.845178i	$-0.679495\pi$
$673$	11.7175	−	26.2266i	0.451677	−	1.01096i	0.986162	−	0.165785i	$-0.0530157\pi$
$674$	18.3201	+	19.4182i	0.705665	+	0.747962i
$675$	11.5621	+	22.0664i	0.445025	+	0.849337i
$676$	−50.8293	+	53.8759i	−1.95497	+	2.07215i
$677$	−10.4020	−	24.9983i	−0.399781	−	0.960763i	−0.988334	−	0.152304i	$-0.951331\pi$
$677$	−10.4020	−	24.9983i	−0.399781	−	0.960763i	0.588552	−	0.808459i	$-0.299698\pi$
$678$	1.80732	−	26.7257i	0.0694096	−	1.02639i
$679$	3.42620	+	2.38258i	0.131485	+	0.0914351i
$680$	60.6146	+	57.9321i	2.32446	+	2.22159i
$681$	5.11014	+	1.12235i	0.195821	+	0.0430084i
$682$	1.72494	−	6.35533i	0.0660514	−	0.243358i
$683$	5.61167	−	16.4007i	0.214725	−	0.627557i	−0.785240	−	0.619191i	$-0.787461\pi$
$683$	5.61167	−	16.4007i	0.214725	−	0.627557i	0.999965	−	0.00836558i	$-0.00266288\pi$
$684$	−7.67312	+	7.43951i	−0.293389	+	0.284457i
$685$	61.2354	+	36.9558i	2.33969	+	1.41201i
$686$	9.84394	−	4.32195i	0.375843	−	0.165013i
$687$	15.3957	+	0.542171i	0.587384	+	0.0206851i
$688$	−18.0119	+	6.82077i	−0.686697	+	0.260039i
$689$	−64.5401	−	22.5501i	−2.45878	−	0.859091i
$690$	19.2776	+	73.7450i	0.733885	+	2.80742i
$691$	17.6272	+	26.4272i	0.670572	+	1.00534i	0.998167	+	0.0605213i	$0.0192763\pi$
$691$	17.6272	+	26.4272i	0.670572	+	1.00534i	−0.327595	+	0.944818i	$0.606238\pi$
$692$	12.4514	+	2.44537i	0.473330	+	0.0929591i
$693$	−2.20091	−	1.86850i	−0.0836058	−	0.0709783i
$694$	−26.0109	+	32.2484i	−0.987359	+	1.22413i
$695$	−24.3341	−	11.4431i	−0.923045	−	0.434061i
$696$	−4.92425	+	30.9023i	−0.186653	+	1.17135i
$697$	3.52896	+	0.228437i	0.133669	+	0.00865265i
$698$	−13.7534	−	50.6726i	−0.520573	−	1.91799i
$699$	−31.1454	−	16.0080i	−1.17803	−	0.605478i
$700$	−4.81339	+	3.07742i	−0.181929	+	0.116315i
$701$	−9.02423	+	20.9205i	−0.340840	+	0.790157i	0.658455	+	0.752620i	$0.271210\pi$
$701$	−9.02423	+	20.9205i	−0.340840	+	0.790157i	−0.999295	+	0.0375367i	$0.988049\pi$
$702$	6.13678	−	71.0070i	0.231618	−	2.67999i
$703$	−4.06625	−	9.42664i	−0.153362	−	0.355532i
$704$	27.3531	+	18.5014i	1.03091	+	0.697297i
$705$	13.5619	+	40.8792i	0.510769	+	1.53960i
$706$	1.24191	−	3.78885i	0.0467399	−	0.142595i
$707$	0.766393	+	0.449108i	0.0288232	+	0.0168904i
$708$	30.8649	−	50.8115i	1.15997	−	1.90961i
$709$	33.9862	+	11.3838i	1.27638	+	0.427529i	0.873097	−	0.487547i	$-0.162108\pi$
$709$	33.9862	+	11.3838i	1.27638	+	0.427529i	0.403282	+	0.915076i	$0.367869\pi$
$710$	−9.88906	−	14.4186i	−0.371130	−	0.541120i
$711$	5.53716	−	0.0396907i	0.207660	−	0.00148852i
$712$	0.392868	+	0.178580i	0.0147234	+	0.00669259i
$713$	5.51331	+	0.285367i	0.206475	+	0.0106871i
$714$	−0.558946	−	9.03855i	−0.0209180	−	0.338259i
$715$	20.5109	−	49.2921i	0.767062	−	1.84342i
$716$	21.4254	+	47.9552i	0.800704	+	1.79217i
$717$	17.5505	+	3.38152i	0.655435	+	0.126285i
$718$	0.693817	+	0.394618i	0.0258930	+	0.0147270i
$719$	−30.4991	−	9.77913i	−1.13742	−	0.364700i	−0.323819	−	0.946119i	$-0.604967\pi$
$719$	−30.4991	−	9.77913i	−1.13742	−	0.364700i	−0.813604	+	0.581419i	$0.802498\pi$
$720$	3.04186	−	19.5397i	0.113364	−	0.728201i
$721$	0.599037	+	0.0232453i	0.0223093	+	0.000865702i
$722$	−15.9965	+	39.8894i	−0.595328	+	1.48453i
$723$	5.40821	+	14.9932i	0.201133	+	0.557601i
$724$	14.5229	+	4.45037i	0.539740	+	0.165397i
$725$	−21.8382	−	0.564791i	−0.811051	−	0.0209758i
$726$	−9.09266	−	1.50924i	−0.337460	−	0.0560131i
$727$	19.6683	+	0.254294i	0.729458	+	0.00943123i	0.376766	−	0.926308i	$-0.377036\pi$
$727$	19.6683	+	0.254294i	0.729458	+	0.00943123i	0.352692	+	0.935739i	$0.385266\pi$
$728$	7.42721			0.275271
$729$	14.8843	+	22.5268i	0.551272	+	0.834326i
$730$	−47.6704			−1.76436
$731$	61.7834	+	0.798803i	2.28514	+	0.0295448i
$732$	−25.8926	−	68.9750i	−0.957020	−	2.54939i
$733$	28.8866	+	0.747079i	1.06695	+	0.0275940i	0.555340	−	0.831624i	$-0.312588\pi$
$733$	28.8866	+	0.747079i	1.06695	+	0.0275940i	0.511610	+	0.859218i	$0.329049\pi$
$734$	73.8331	+	22.6253i	2.72523	+	0.835113i
$735$	−36.7848	−	6.59546i	−1.35683	−	0.243277i
$736$	−6.41289	+	15.9914i	−0.236382	+	0.589450i
$737$	35.7211	+	1.38614i	1.31580	+	0.0510592i
$738$	−1.93326	−	3.19831i	−0.0711643	−	0.117731i
$739$	−22.9564	−	7.36067i	−0.844464	−	0.270767i	−0.148562	−	0.988903i	$-0.547464\pi$
$739$	−22.9564	−	7.36067i	−0.844464	−	0.270767i	−0.695902	+	0.718137i	$0.744995\pi$
$740$	105.344	+	59.9157i	3.87252	+	2.20255i
$741$	3.17300	+	9.16606i	0.116563	+	0.336724i
$742$	3.74469	+	8.38153i	0.137472	+	0.307696i
$743$	2.79240	−	6.71076i	0.102443	−	0.246194i	−0.863795	−	0.503843i	$-0.831919\pi$
$743$	2.79240	−	6.71076i	0.102443	−	0.246194i	0.966239	+	0.257649i	$0.0829479\pi$
$744$	−5.74542	−	2.85972i	−0.210637	−	0.104842i
$745$	0.505513	+	0.0261652i	0.0185206	+	0.000958618i
$746$	−27.7091	−	12.5954i	−1.01450	−	0.461149i
$747$	4.41537	−	1.64300i	0.161550	−	0.0601143i
$748$	41.4760	+	60.4734i	1.51651	+	2.21113i
$749$	−2.24983	−	0.753592i	−0.0822071	−	0.0275357i
$750$	−2.65312	−	0.0591021i	−0.0968784	−	0.00215811i
$751$	−1.01156	−	0.592773i	−0.0369122	−	0.0216306i	0.487016	−	0.873393i	$-0.338085\pi$
$751$	−1.01156	−	0.592773i	−0.0369122	−	0.0216306i	−0.523928	+	0.851763i	$0.675534\pi$
$752$	5.21267	−	15.9029i	0.190086	−	0.579919i
$753$	−42.6145	−	8.78356i	−1.55296	−	0.320091i
$754$	51.7685	+	35.0157i	1.88530	+	1.27520i
$755$	−20.2613	−	46.9711i	−0.737386	−	1.70945i
$756$	−4.85298	+	3.84557i	−0.176501	+	0.139862i
$757$	0.590154	−	1.36813i	0.0214495	−	0.0497255i	−0.907155	−	0.420797i	$-0.861750\pi$
$757$	0.590154	−	1.36813i	0.0214495	−	0.0497255i	0.928604	+	0.371072i	$0.121010\pi$
$758$	3.26028	−	2.08445i	0.118419	−	0.0757105i
$759$	1.47868	+	30.2560i	0.0536726	+	1.09822i
$760$	3.15879	+	11.6382i	0.114581	+	0.422161i
$761$	46.3175	+	2.99823i	1.67901	+	0.108686i	0.874428	−	0.485156i	$-0.161237\pi$
$761$	46.3175	+	2.99823i	1.67901	+	0.108686i	0.804582	+	0.593841i	$0.202389\pi$
$762$	−6.91912	−	5.61378i	−0.250653	−	0.203366i
$763$	2.09029	+	0.982954i	0.0756734	+	0.0355853i
$764$	30.6505	−	38.0007i	1.10890	−	1.37482i
$765$	−32.0362	+	54.7575i	−1.15827	+	1.97976i
$766$	−44.9574	−	8.82935i	−1.62438	−	0.319017i
$767$	−29.9403	−	44.8874i	−1.08108	−	1.62079i
$768$	33.2766	−	32.8723i	1.20077	−	1.18618i
$769$	−26.4012	−	9.22450i	−0.952052	−	0.332644i	−0.191186	−	0.981554i	$-0.561233\pi$
$769$	−26.4012	−	9.22450i	−0.952052	−	0.332644i	−0.760865	+	0.648910i	$0.775225\pi$
$770$	−6.70435	+	2.53881i	−0.241608	+	0.0914924i
$771$	2.23814	−	3.57943i	0.0806046	−	0.128910i
$772$	−55.0036	+	24.1491i	−1.97962	+	0.869146i
$773$	15.7970	+	9.53355i	0.568179	+	0.342898i	0.771515	−	0.636211i	$-0.219499\pi$
$773$	15.7970	+	9.53355i	0.568179	+	0.342898i	−0.203336	+	0.979109i	$0.565178\pi$
$774$	−36.6222	−	54.0615i	−1.31636	−	1.94320i
$775$	1.45044	−	4.23907i	0.0521013	−	0.152272i
$776$	−13.3331	+	49.1240i	−0.478629	+	1.76345i
$777$	−1.79971	−	5.66903i	−0.0645643	−	0.203375i
$778$	28.5686	+	27.3043i	1.02423	+	0.978907i
$779$	0.417573	+	0.290381i	0.0149611	+	0.0104040i
$780$	−95.0739	−	63.8117i	−3.40419	−	2.28483i
$781$	−2.66940	−	6.41517i	−0.0955188	−	0.229553i
$782$	−65.2040	+	69.1122i	−2.33169	+	2.47145i
$783$	−23.6092	+	1.78337i	−0.843725	+	0.0637324i
$784$	9.96501	+	10.5623i	0.355893	+	0.377225i
$785$	−14.0488	+	31.4446i	−0.501423	+	1.12231i
$786$	−17.6683	+	25.2519i	−0.630209	+	0.900706i
$787$	−34.1704	+	21.2294i	−1.21804	+	0.756745i	−0.976890	−	0.213743i	$-0.931435\pi$
$787$	−34.1704	+	21.2294i	−1.21804	+	0.756745i	−0.241152	+	0.970487i	$0.577525\pi$
$788$	−40.0645	+	6.79772i	−1.42724	+	0.242159i
$789$	−4.68359	−	2.48431i	−0.166740	−	0.0884439i
$790$	6.56469	−	12.0813i	0.233561	−	0.429835i
$791$	0.526838	+	2.04531i	0.0187322	+	0.0727229i
$792$	12.4477	−	32.9411i	0.442308	−	1.17051i
$793$	−66.6644	−	5.18156i	−2.36732	−	0.184003i
$794$	−3.12878	−	25.3464i	−0.111036	−	0.899509i
$795$	10.9404	−	63.3732i	0.388015	−	2.24762i
$796$	65.1108	−	33.7609i	2.30779	−	1.19662i
$797$	7.49202	+	3.64212i	0.265381	+	0.129011i	0.565115	−	0.825012i	$-0.308832\pi$
$797$	7.49202	+	3.64212i	0.265381	+	0.129011i	−0.299734	+	0.954023i	$0.596898\pi$
$798$	0.602865	−	1.15453i	0.0213412	−	0.0408698i
$799$	−34.2441	+	41.3505i	−1.21147	+	1.46288i
$800$	11.0517	+	8.56570i	0.390736	+	0.302843i
$801$	−0.0626995	+	0.320447i	−0.00221538	+	0.0113224i
$802$	46.3383	−	14.8578i	1.63626	−	0.524646i
$803$	−18.5410	−	3.89094i	−0.654299	−	0.137308i
$804$	17.8957	−	74.5504i	0.631133	−	2.62919i
$805$	−3.27003	−	5.04255i	−0.115254	−	0.177726i
$806$	−10.0289	+	7.98262i	−0.353252	+	0.281176i
$807$	8.76148	+	35.3796i	0.308419	+	1.24542i
$808$	−2.01920	+	10.6448i	−0.0710352	+	0.374483i
$809$	−10.4554	−	3.80547i	−0.367594	−	0.133793i	0.151617	−	0.988439i	$-0.451552\pi$
$809$	−10.4554	−	3.80547i	−0.367594	−	0.133793i	−0.519211	+	0.854646i	$0.673774\pi$
$810$	66.8348	−	5.28946i	2.34834	−	0.185853i
$811$	−8.90543	+	3.24131i	−0.312712	+	0.113818i	−0.493608	−	0.869684i	$-0.664322\pi$
$811$	−8.90543	+	3.24131i	−0.312712	+	0.113818i	0.180896	+	0.983502i	$0.442100\pi$
$812$	−0.873655	−	5.35898i	−0.0306593	−	0.188063i
$813$	−23.8712	−	1.14980i	−0.837201	−	0.0403252i
$814$	55.7684	+	49.3076i	1.95468	+	1.72823i
$815$	−64.6165	+	27.3788i	−2.26342	+	0.959037i
$816$	22.6626	−	9.69838i	0.793351	−	0.339511i
$817$	7.54853	+	4.68975i	0.264090	+	0.164074i
$818$	−49.3301	−	20.1536i	−1.72479	−	0.704653i
$819$	1.29982	+	5.46723i	0.0454195	+	0.191041i
$820$	−5.99956	+	0.232810i	−0.209514	+	0.00813009i
$821$	−11.4163	+	32.0084i	−0.398433	+	1.11710i	0.559181	+	0.829046i	$0.311116\pi$
$821$	−11.4163	+	32.0084i	−0.398433	+	1.11710i	−0.957614	+	0.288055i	$0.906991\pi$
$822$	76.4567	−	55.0630i	2.66673	−	1.92054i
$823$	−2.54559	+	8.92103i	−0.0887336	+	0.310967i	−0.993331	−	0.115300i	$-0.963217\pi$
$823$	−2.54559	+	8.92103i	−0.0887336	+	0.310967i	0.904597	+	0.426268i	$0.140172\pi$
$824$	2.18751	+	6.97719i	0.0762055	+	0.243062i
$825$	23.9412	+	5.58363i	0.833527	+	0.194397i
$826$	−1.62523	+	7.06048i	−0.0565491	+	0.245665i
$827$	−24.1902	−	23.7255i	−0.841174	−	0.825018i	0.145223	−	0.989399i	$-0.453610\pi$
$827$	−24.1902	−	23.7255i	−0.841174	−	0.825018i	−0.986397	+	0.164381i	$0.947437\pi$
$828$	64.2572	+	9.57831i	2.23309	+	0.332869i
$829$	−20.5466	−	14.6859i	−0.713614	−	0.510061i	0.165775	−	0.986164i	$-0.446987\pi$
$829$	−20.5466	−	14.6859i	−0.713614	−	0.510061i	−0.879390	+	0.476103i	$0.842049\pi$
$830$	1.73286	−	11.5692i	0.0601483	−	0.401574i
$831$	−1.78005	+	22.0783i	−0.0617494	+	0.765889i
$832$	−21.5932	−	60.5418i	−0.748611	−	2.09891i
$833$	−17.3395	−	43.2383i	−0.600778	−	1.49812i
$834$	−26.4544	+	23.5591i	−0.916042	+	0.815786i
$835$	1.20165	−	1.24113i	0.0415848	−	0.0429510i
$836$	0.613235	+	10.5288i	0.0212092	+	0.364147i
$837$	1.09957	−	4.72973i	0.0380066	−	0.163483i
$838$	−1.49465	+	25.6621i	−0.0516318	+	0.886484i
$839$	25.9283	+	28.2041i	0.895144	+	0.973715i	0.999784	−	0.0207955i	$-0.00661990\pi$
$839$	25.9283	+	28.2041i	0.895144	+	0.973715i	−0.104639	+	0.994510i	$0.533369\pi$
$840$	1.14887	+	6.89151i	0.0396397	+	0.237780i
$841$	−3.45735	+	7.47732i	−0.119219	+	0.257838i
$842$	−68.9491	+	50.6413i	−2.37614	+	1.74521i
$843$	4.04683	+	8.97132i	0.139380	+	0.308989i
$844$	−2.50291	+	3.55006i	−0.0861539	+	0.122198i
$845$	−54.1402	+	32.6738i	−1.86248	+	1.12401i
$846$	56.5416	+	4.72259i	1.94394	+	0.162366i
$847$	0.718017	−	0.112296i	0.0246714	−	0.00385853i
$848$	−18.0649	+	17.2654i	−0.620351	+	0.592897i
$849$	−0.851366	−	37.0472i	−0.0292188	−	1.27146i
$850$	39.4155	+	66.2758i	1.35194	+	2.27324i
$851$	−30.5019	+	54.4444i	−1.04559	+	1.86633i
$852$	−14.6124	+	2.92421i	−0.500613	+	0.100182i
$853$	11.4002	+	46.7526i	0.390337	+	1.60078i	0.745855	+	0.666108i	$0.232041\pi$
$853$	11.4002	+	46.7526i	0.390337	+	1.60078i	−0.355518	+	0.934669i	$0.615696\pi$
$854$	5.63681	+	6.98855i	0.192888	+	0.239143i
$855$	−8.01414	+	4.36199i	−0.274078	+	0.149177i
$856$	−0.561188	−	28.9347i	−0.0191810	−	0.988968i
$857$	−39.3629	−	3.57204i	−1.34461	−	0.122019i	−0.605630	−	0.795746i	$-0.707079\pi$
$857$	−39.3629	−	3.57204i	−1.34461	−	0.122019i	−0.738980	+	0.673728i	$0.764692\pi$
$858$	−49.1032	−	50.3541i	−1.67635	−	1.71906i
$859$	−0.786254	−	7.12602i	−0.0268266	−	0.243137i	−0.999919	−	0.0127216i	$-0.995950\pi$
$859$	−0.786254	−	7.12602i	−0.0268266	−	0.243137i	0.973092	−	0.230415i	$-0.0740084\pi$
$860$	−104.477	+	9.48089i	−3.56263	+	0.323296i
$861$	0.223951	+	0.191511i	0.00763222	+	0.00652669i
$862$	7.04868	−	1.57461i	0.240079	−	0.0536314i
$863$	31.8275	−	15.9844i	1.08342	−	0.544115i	0.184772	−	0.982781i	$-0.440845\pi$
$863$	31.8275	−	15.9844i	1.08342	−	0.544115i	0.898650	+	0.438666i	$0.144549\pi$
$864$	12.8550	+	8.02538i	0.437336	+	0.273029i
$865$	9.68096	+	4.86196i	0.329162	+	0.165312i
$866$	53.4549	+	13.4012i	1.81647	+	0.455393i
$867$	−49.6156	+	1.46114i	−1.68504	+	0.0496230i
$868$	1.10235	+	0.157833i	0.0374163	+	0.00535721i
$869$	3.53939	−	4.16312i	0.120065	−	0.141224i
$870$	−24.4825	+	53.4510i	−0.830033	+	1.81216i
$871$	−54.4416	−	43.3335i	−1.84468	−	1.46830i
$872$	−2.72754	+	28.0416i	−0.0923663	+	0.949608i
$873$	−38.4940	−	1.21748i	−1.30282	−	0.0412053i
$874$	−13.1651	+	3.66476i	−0.445316	+	0.123962i
$875$	0.200062	−	0.0613067i	0.00676335	−	0.00207254i
$876$	−15.9593	+	37.3654i	−0.539214	+	1.26246i
$877$	16.3347	+	3.64903i	0.551584	+	0.123219i	0.484923	−	0.874557i	$-0.338848\pi$
$877$	16.3347	+	3.64903i	0.551584	+	0.123219i	0.0666613	+	0.997776i	$0.478765\pi$
$878$	−39.3100	+	9.85507i	−1.32665	+	0.332593i
$879$	−29.3108	−	28.5425i	−0.988630	−	0.962714i
$880$	−12.6400	−	14.8675i	−0.426094	−	0.501184i
$881$	6.43769	+	10.2141i	0.216891	+	0.344122i	0.936750	−	0.349999i	$-0.113818\pi$
$881$	6.43769	+	10.2141i	0.216891	+	0.344122i	−0.719859	+	0.694121i	$0.755793\pi$
$882$	−27.0241	+	41.1513i	−0.909950	+	1.38563i
$883$	−10.5735	+	8.19508i	−0.355827	+	0.275786i	−0.774793	−	0.632216i	$-0.782146\pi$
$883$	−10.5735	+	8.19508i	−0.355827	+	0.275786i	0.418966	+	0.908002i	$0.362393\pi$
$884$	4.61250	−	142.660i	0.155135	−	4.79817i
$885$	37.0185	−	34.7242i	1.24436	−	1.16724i
$886$	0.311911	−	2.52681i	0.0104788	−	0.0848897i
$887$	7.04391	−	34.6793i	0.236511	−	1.16442i	−0.670041	−	0.742324i	$-0.733724\pi$
$887$	7.04391	−	34.6793i	0.236511	−	1.16442i	0.906553	−	0.422093i	$-0.138704\pi$
$888$	57.7534	−	43.9046i	1.93808	−	1.47334i
$889$	0.657008	+	0.248797i	0.0220353	+	0.00834437i
$890$	0.621101	+	0.521166i	0.0208194	+	0.0174695i
$891$	26.4266	+	3.39788i	0.885326	+	0.113833i
$892$	31.0817	−	26.0807i	1.04069	−	0.873245i
$893$	−7.28969	+	2.54699i	−0.243940	+	0.0852319i
$894$	0.293271	−	0.598879i	0.00980844	−	0.0200295i
$895$	6.64233	+	44.3468i	0.222029	+	1.48235i
$896$	−3.06143	+	5.99881i	−0.102275	+	0.200406i
$897$	32.5422	−	49.1690i	1.08655	−	1.64170i
$898$	−21.3585	+	23.8447i	−0.712741	+	0.795707i
$899$	3.15334	+	2.86150i	0.105170	+	0.0954364i
$900$	21.7841	−	48.0137i	0.726138	−	1.60046i
$901$	74.2122	−	30.3190i	2.47237	−	1.01007i
$902$	−3.63598	−	0.616915i	−0.121065	−	0.0205410i
$903$	4.08070	+	3.13944i	0.135797	+	0.104474i
$904$	−21.3385	+	14.4332i	−0.709709	+	0.480041i
$905$	10.9257	+	6.98528i	0.363182	+	0.232198i
$906$	−67.3884	+	0.241519i	−2.23883	+	0.00802394i
$907$	−36.1197	−	15.3043i	−1.19933	−	0.508172i	−0.303615	−	0.952795i	$-0.598194\pi$
$907$	−36.1197	−	15.3043i	−1.19933	−	0.508172i	−0.895718	+	0.444623i	$0.853338\pi$
$908$	−4.77674	−	9.98970i	−0.158522	−	0.331520i
$909$	−8.18912	+	0.376580i	−0.271616	+	0.0124904i
$910$	13.4430	+	3.74211i	0.445630	+	0.124050i
$911$	6.01045	−	0.155445i	0.199135	−	0.00515013i	0.0738422	−	0.997270i	$-0.476474\pi$
$911$	6.01045	−	0.155445i	0.199135	−	0.00515013i	0.125293	+	0.992120i	$0.460013\pi$
$912$	3.51136	+	0.489915i	0.116273	+	0.0162227i
$913$	1.61828	−	4.35833i	0.0535573	−	0.144240i
$914$	−17.8562	−	9.55359i	−0.590629	−	0.316005i
$915$	−5.50405	−	62.6576i	−0.181958	−	2.07140i
$916$	−19.1301	−	26.4020i	−0.632076	−	0.872348i
$917$	0.696942	−	2.32795i	0.0230151	−	0.0768757i
$918$	49.7607	+	67.1448i	1.64235	+	2.21611i
$919$	−9.58245	−	32.0076i	−0.316096	−	1.05583i	−0.957453	−	0.288591i	$-0.906813\pi$
$919$	−9.58245	−	32.0076i	−0.316096	−	1.05583i	0.641357	−	0.767243i	$-0.278372\pi$
$920$	44.5315	−	58.2292i	1.46816	−	1.91976i
$921$	10.5035	+	36.3159i	0.346103	+	1.19665i
$922$	39.7548	−	18.6947i	1.30926	−	0.615676i
$923$	−3.20404	+	13.1398i	−0.105462	+	0.432502i
$924$	−0.254514	+	6.10501i	−0.00837291	+	0.200840i
$925$	35.6963	+	35.9278i	1.17369	+	1.18130i
$926$	−76.1957	+	14.9644i	−2.50395	+	0.491759i
$927$	−4.75314	+	2.83131i	−0.156113	+	0.0929924i
$928$	−11.6353	+	6.42010i	−0.381948	+	0.210750i
$929$	−10.5252	−	7.73049i	−0.345321	−	0.253629i	0.405557	−	0.914070i	$-0.367077\pi$
$929$	−10.5252	−	7.73049i	−0.345321	−	0.253629i	−0.750879	+	0.660440i	$0.770370\pi$
$930$	−8.95816	−	8.07075i	−0.293750	−	0.264650i
$931$	1.07807	−	6.61285i	0.0353322	−	0.216727i
$932$	13.8123	+	72.8155i	0.452436	+	2.38515i
$933$	−27.8099	−	19.7271i	−0.910456	−	0.645838i
$934$	55.3586	−	3.58347i	1.81139	−	0.117255i
$935$	20.2672	+	59.2332i	0.662809	+	1.93713i
$936$	−57.4834	+	37.3349i	−1.87890	+	1.22033i
$937$	−11.7395	−	30.4060i	−0.383512	−	0.993322i	−0.981440	−	0.191772i	$-0.938577\pi$
$937$	−11.7395	−	30.4060i	−0.383512	−	0.993322i	0.597927	−	0.801550i	$-0.295991\pi$
$938$	0.784234	+	9.31032i	0.0256061	+	0.303993i
$939$	−40.2743	−	13.9100i	−1.31430	−	0.453935i
$940$	50.5815	−	75.8332i	1.64979	−	2.47340i
$941$	26.5170	−	26.6889i	0.864429	−	0.870035i	−0.128135	−	0.991757i	$-0.540899\pi$
$941$	26.5170	−	26.6889i	0.864429	−	0.870035i	0.992564	+	0.121722i	$0.0388416\pi$
$942$	30.8251	+	33.2904i	1.00433	+	1.08466i
$943$	−0.139852	−	3.08859i	−0.00455421	−	0.100578i
$944$	−19.5884	+	2.28956i	−0.637549	+	0.0745187i
$945$	−4.87184	+	2.05176i	−0.158481	+	0.0667438i
$946$	−64.0018	−	7.48074i	−2.08088	−	0.243220i
$947$	0.492208	−	6.91050i	0.0159946	−	0.224561i	−0.983136	−	0.182875i	$-0.941460\pi$
$947$	0.492208	−	6.91050i	0.0159946	−	0.224561i	0.999131	−	0.0416860i	$-0.0132729\pi$
$948$	−7.27194	−	9.19022i	−0.236182	−	0.298484i
$949$	24.6036	+	27.4676i	0.798668	+	0.891636i
$950$	−0.0716901	+	11.0902i	−0.00232593	+	0.359814i
$951$	−25.2400	−	9.82856i	−0.818464	−	0.318713i
$952$	−6.52466	+	5.76878i	−0.211466	+	0.186967i
$953$	−2.92311	+	6.11316i	−0.0946887	+	0.198025i	−0.944062	−	0.329768i	$-0.893030\pi$
$953$	−2.92311	+	6.11316i	−0.0946887	+	0.198025i	0.849373	+	0.527792i	$0.176980\pi$
$954$	−71.1143	−	46.0458i	−2.30241	−	1.49079i
$955$	33.9092	−	24.2368i	1.09727	−	0.784285i
$956$	−17.1951	−	33.6934i	−0.556129	−	1.08972i
$957$	−13.8850	+	18.7911i	−0.448839	+	0.607429i
$958$	−19.7411	−	25.8133i	−0.637805	−	0.833991i
$959$	−4.35895	+	6.01592i	−0.140758	+	0.194264i
$960$	52.8350	−	29.4006i	1.70524	−	0.948901i
$961$	25.9926	−	15.2317i	0.838470	−	0.491345i
$962$	−30.6749	−	141.611i	−0.988999	−	4.56573i
$963$	21.2009	−	5.47690i	0.683189	−	0.176491i
$964$	17.9867	−	28.5378i	0.579311	−	0.919140i
$965$	−50.7674	+	7.26881i	−1.63426	+	0.233991i
$966$	−7.80097	+	1.35237i	−0.250992	+	0.0435117i
$967$	−31.6117	+	29.4402i	−1.01656	+	0.946733i	−0.998589	−	0.0531054i	$-0.983088\pi$
$967$	−31.6117	+	29.4402i	−1.01656	+	0.946733i	−0.0179746	+	0.999838i	$0.505722\pi$
$968$	4.23218	+	7.78870i	0.136027	+	0.250338i
$969$	−9.90678	−	5.58772i	−0.318252	−	0.179503i
$970$	−48.8829	+	82.1949i	−1.56953	+	2.63912i
$971$	−12.5305	−	21.7034i	−0.402121	−	0.696495i	0.591860	−	0.806040i	$-0.298394\pi$
$971$	−12.5305	−	21.7034i	−0.402121	−	0.696495i	−0.993982	+	0.109546i	$0.965060\pi$
$972$	18.2292	−	54.1578i	0.584701	−	1.73711i
$973$	1.39656	−	2.41891i	0.0447716	−	0.0775467i
$974$	−15.1954	−	27.1230i	−0.486892	−	0.869078i
$975$	−31.1250	−	36.3453i	−0.996798	−	1.16398i
$976$	−12.7632	+	20.8428i	−0.408540	+	0.667161i
$977$	11.8514	+	51.4858i	0.379159	+	1.64718i	0.710524	+	0.703673i	$0.248458\pi$
$977$	11.8514	+	51.4858i	0.379159	+	1.64718i	−0.331365	+	0.943503i	$0.607509\pi$
$978$	−0.266271	+	92.4482i	−0.00851440	+	2.95617i
$979$	0.199034	+	0.253399i	0.00636116	+	0.00809867i
$980$	36.8612	+	69.9792i	1.17749	+	2.23540i
$981$	−21.1190	+	2.89974i	−0.674278	+	0.0925816i
$982$	−32.6251	+	29.6057i	−1.04111	+	0.944756i
$983$	0.00329698	+	0.510032i	0.000105157	+	0.0162675i	0.999999	+	0.00166982i	$0.000531519\pi$
$983$	0.00329698	+	0.510032i	0.000105157	+	0.0162675i	−0.999893	+	0.0145977i	$0.995353\pi$
$984$	−1.28251	+	3.35754i	−0.0408849	+	0.107035i
$985$	−34.5080	−	3.58184i	−1.09952	−	0.114127i
$986$	−72.6747	+	9.44835i	−2.31443	+	0.300897i
$987$	−4.34940	+	1.04730i	−0.138443	+	0.0333361i
$988$	11.1696	−	17.2241i	0.355353	−	0.547971i
$989$	−5.22978	−	53.7668i	−0.166297	−	1.70969i
$990$	39.1268	−	53.3505i	1.24353	−	1.69559i
$991$	−24.6350	+	1.91478i	−0.782556	+	0.0608250i	−0.462553	−	0.886592i	$-0.653066\pi$
$991$	−24.6350	+	1.91478i	−0.782556	+	0.0608250i	−0.320003	+	0.947417i	$0.603684\pi$
$992$	−0.542509	−	2.67094i	−0.0172247	−	0.0848024i
$993$	−11.0329	+	55.3344i	−0.350120	+	1.75598i
$994$	1.57860	−	0.897850i	0.0500701	−	0.0284781i
$995$	61.2808	−	12.8601i	1.94273	−	0.407693i
$996$	−8.48816	−	5.23145i	−0.268958	−	0.165765i
$997$	−22.6392	+	11.0057i	−0.716990	+	0.348553i	−0.759468	−	0.650545i	$-0.774541\pi$
$997$	−22.6392	+	11.0057i	−0.716990	+	0.348553i	0.0424781	+	0.999097i	$0.486475\pi$
$998$	0.420593	−	0.564954i	0.0133136	−	0.0178833i
$999$	42.4259	+	34.8291i	1.34230	+	1.10194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.k.a.4.9	✓	12960
729.547	even	243	inner	729.2.k.a.547.9	yes	12960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.k.a.4.9	✓	12960	1.1	even	1	trivial
729.2.k.a.547.9	yes	12960	729.547	even	243	inner

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.k (of order \(243\), degree \(162\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.38009 - 0.0307723i) q^{2} +(-1.09995 + 1.33795i) q^{3} +(3.66453 + 0.0947738i) q^{4} +(2.99225 + 0.916937i) q^{5} +(2.65915 - 3.15058i) q^{6} +(-0.120994 + 0.301715i) q^{7} +(-3.96199 - 0.153743i) q^{8} +(-0.580208 - 2.94336i) q^{9} +O(q^{10})\)	\(q+(-2.38009 - 0.0307723i) q^{2} +(-1.09995 + 1.33795i) q^{3} +(3.66453 + 0.0947738i) q^{4} +(2.99225 + 0.916937i) q^{5} +(2.65915 - 3.15058i) q^{6} +(-0.120994 + 0.301715i) q^{7} +(-3.96199 - 0.153743i) q^{8} +(-0.580208 - 2.94336i) q^{9} +(-7.09359 - 2.27447i) q^{10} +(-2.57335 - 1.46363i) q^{11} +(-4.15761 + 4.79870i) q^{12} +(2.35060 + 5.26122i) q^{13} +(0.297261 - 0.714385i) q^{14} +(-4.51815 + 2.99488i) q^{15} +(2.10343 + 0.108873i) q^{16} +(-6.15139 - 2.79615i) q^{17} +(1.29037 + 7.02330i) q^{18} +(-0.549676 - 0.801448i) q^{19} +(10.8783 + 3.64373i) q^{20} +(-0.270591 - 0.493757i) q^{21} +(6.07976 + 3.56275i) q^{22} +(-1.84006 + 5.61370i) q^{23} +(4.56370 - 5.13182i) q^{24} +(3.97120 + 2.68609i) q^{25} +(-5.43273 - 12.5945i) q^{26} +(4.57626 + 2.46127i) q^{27} +(-0.471982 + 1.09418i) q^{28} +(-3.83899 + 2.45443i) q^{29} +(10.8457 - 6.98905i) q^{30} +(-0.244785 - 0.901881i) q^{31} +(2.91038 + 0.188395i) q^{32} +(4.78883 - 1.83309i) q^{33} +(14.5548 + 6.84437i) q^{34} +(-0.638699 + 0.791863i) q^{35} +(-1.84724 - 10.8410i) q^{36} +(10.3658 + 2.03577i) q^{37} +(1.28361 + 1.92443i) q^{38} +(-9.62478 - 2.64211i) q^{39} +(-11.7143 - 4.09293i) q^{40} +(-0.489437 + 0.185341i) q^{41} +(0.628836 + 1.18351i) q^{42} +(-8.37284 + 3.67607i) q^{43} +(-9.29141 - 5.60740i) q^{44} +(0.962748 - 9.33927i) q^{45} +(4.55226 - 13.3045i) q^{46} +(2.08127 - 7.66820i) q^{47} +(-2.45934 + 2.69452i) q^{48} +(4.98406 + 4.76349i) q^{49} +(-9.36915 - 6.51532i) q^{50} +(10.5073 - 5.15460i) q^{51} +(8.11521 + 19.5026i) q^{52} +(-8.14164 + 8.62964i) q^{53} +(-10.8162 - 5.99885i) q^{54} +(-6.35805 - 6.73914i) q^{55} +(0.525765 - 1.17679i) q^{56} +(1.67691 + 0.146116i) q^{57} +(9.21264 - 5.72363i) q^{58} +(-9.23154 + 1.56631i) q^{59} +(-16.8407 + 10.5466i) q^{60} +(-5.54009 + 10.1957i) q^{61} +(0.554857 + 2.15409i) q^{62} +(0.958258 + 0.181072i) q^{63} +(-11.1210 - 0.864392i) q^{64} +(2.20937 + 17.8982i) q^{65} +(-11.4542 + 4.21555i) q^{66} +(-10.7198 + 5.55835i) q^{67} +(-22.2769 - 10.8296i) q^{68} +(-5.48686 - 8.63672i) q^{69} +(1.54453 - 1.86505i) q^{70} +(1.85510 + 1.43781i) q^{71} +(1.84626 + 11.7507i) q^{72} +(6.09372 - 1.95387i) q^{73} +(-24.6088 - 5.16429i) q^{74} +(-7.96198 + 2.35869i) q^{75} +(-1.93835 - 2.98902i) q^{76} +(0.752960 - 0.599329i) q^{77} +(22.8265 + 6.58462i) q^{78} +(-0.343987 + 1.81343i) q^{79} +(6.19415 + 2.25449i) q^{80} +(-8.32672 + 3.41552i) q^{81} +(1.17061 - 0.426066i) q^{82} +(0.252678 + 1.54992i) q^{83} +(-0.944794 - 1.83503i) q^{84} +(-15.8426 - 14.0072i) q^{85} +(20.0412 - 8.49170i) q^{86} +(0.938797 - 7.83613i) q^{87} +(9.97057 + 6.19451i) q^{88} +(-0.100757 - 0.0411636i) q^{89} +(-2.57881 + 22.1986i) q^{90} +(-1.87180 + 0.0726343i) q^{91} +(-7.27500 + 20.3972i) q^{92} +(1.47592 + 0.664517i) q^{93} +(-5.18958 + 18.1869i) q^{94} +(-0.909891 - 2.90215i) q^{95} +(-3.45335 + 3.68672i) q^{96} +(2.87978 - 12.5106i) q^{97} +(-11.7159 - 11.4909i) q^{98} +(-2.81490 + 8.42351i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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