LMFDB - Embedded newform 729.2.k.a.4.18

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			4.18
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.82547 - 0.0236016i) q^{2} +(1.47646 + 0.905578i) q^{3} +(1.33244 + 0.0344602i) q^{4} +(2.72027 + 0.833593i) q^{5} +(-2.67385 - 1.68795i) q^{6} +(1.26149 - 3.14568i) q^{7} +(1.21698 + 0.0472244i) q^{8} +(1.35986 + 2.67410i) q^{9} +O(q^{10})$	\(q+(-1.82547 - 0.0236016i) q^{2} +(1.47646 + 0.905578i) q^{3} +(1.33244 + 0.0344602i) q^{4} +(2.72027 + 0.833593i) q^{5} +(-2.67385 - 1.68795i) q^{6} +(1.26149 - 3.14568i) q^{7} +(1.21698 + 0.0472244i) q^{8} +(1.35986 + 2.67410i) q^{9} +(-4.94609 - 1.58590i) q^{10} +(3.49339 + 1.98691i) q^{11} +(1.93609 + 1.25751i) q^{12} +(1.89759 + 4.24727i) q^{13} +(-2.37704 + 5.71256i) q^{14} +(3.26148 + 3.69418i) q^{15} +(-4.88265 - 0.252724i) q^{16} +(-4.20414 - 1.91102i) q^{17} +(-2.41926 - 4.91357i) q^{18} +(-0.127033 - 0.185219i) q^{19} +(3.59587 + 1.20445i) q^{20} +(4.71119 - 3.50209i) q^{21} +(-6.33018 - 3.70950i) q^{22} +(2.01071 - 6.13431i) q^{23} +(1.75406 + 1.17180i) q^{24} +(2.56342 + 1.73388i) q^{25} +(-3.36374 - 7.79803i) q^{26} +(-0.413832 + 5.17965i) q^{27} +(1.78925 - 4.14796i) q^{28} +(4.61356 - 2.94965i) q^{29} +(-5.86654 - 6.82058i) q^{30} +(-0.792742 - 2.92076i) q^{31} +(6.47645 + 0.419233i) q^{32} +(3.35854 + 6.09714i) q^{33} +(7.62941 + 3.58772i) q^{34} +(6.05380 - 7.50553i) q^{35} +(1.71978 + 3.60993i) q^{36} +(-11.5174 - 2.26194i) q^{37} +(0.227524 + 0.341110i) q^{38} +(-1.04452 + 7.98933i) q^{39} +(3.27115 + 1.14293i) q^{40} +(-0.528605 + 0.200173i) q^{41} +(-8.68277 + 6.28176i) q^{42} +(-5.16076 + 2.26581i) q^{43} +(4.58627 + 2.76783i) q^{44} +(1.47007 + 8.40783i) q^{45} +(-3.81526 + 11.1505i) q^{46} +(-0.358792 + 1.32192i) q^{47} +(-6.98017 - 4.79476i) q^{48} +(-3.24350 - 3.09995i) q^{49} +(-4.63852 - 3.22563i) q^{50} +(-4.47666 - 6.62871i) q^{51} +(2.38206 + 5.72462i) q^{52} +(1.85497 - 1.96615i) q^{53} +(0.877684 - 9.44551i) q^{54} +(7.84670 + 8.31701i) q^{55} +(1.68376 - 3.76866i) q^{56} +(-0.0198290 - 0.388507i) q^{57} +(-8.49152 + 5.27561i) q^{58} +(5.24916 - 0.890622i) q^{59} +(4.21843 + 5.03467i) q^{60} +(-6.99384 + 12.8711i) q^{61} +(1.37819 + 5.35046i) q^{62} +(10.1273 - 0.904340i) q^{63} +(-2.06367 - 0.160401i) q^{64} +(1.62146 + 13.1355i) q^{65} +(-5.98701 - 11.2094i) q^{66} +(-6.25549 + 3.24356i) q^{67} +(-5.53591 - 2.69119i) q^{68} +(8.52382 - 7.23619i) q^{69} +(-11.2282 + 13.5582i) q^{70} +(-5.07756 - 3.93541i) q^{71} +(1.52864 + 3.31854i) q^{72} +(12.6226 - 4.04726i) q^{73} +(20.9712 + 4.40092i) q^{74} +(2.21463 + 4.88137i) q^{75} +(-0.162882 - 0.251171i) q^{76} +(10.6571 - 8.48263i) q^{77} +(2.09530 - 14.5596i) q^{78} +(1.91235 - 10.0815i) q^{79} +(-13.0715 - 4.75762i) q^{80} +(-5.30158 + 7.27277i) q^{81} +(0.969675 - 0.352933i) q^{82} +(2.55818 + 15.6918i) q^{83} +(6.39806 - 4.50398i) q^{84} +(-9.84338 - 8.70302i) q^{85} +(9.47427 - 4.01436i) q^{86} +(9.48287 - 0.177102i) q^{87} +(4.15756 + 2.58301i) q^{88} +(-1.35362 - 0.553016i) q^{89} +(-2.48512 - 15.3829i) q^{90} +(15.7543 - 0.611340i) q^{91} +(2.89054 - 8.10431i) q^{92} +(1.47453 - 5.03027i) q^{93} +(0.686162 - 2.40466i) q^{94} +(-0.191168 - 0.609740i) q^{95} +(9.18255 + 6.48391i) q^{96} +(-3.05069 + 13.2531i) q^{97} +(5.84773 + 5.73542i) q^{98} +(-0.562685 + 12.0436i) 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 $

$2$	−1.82547	−	0.0236016i	−1.29080	−	0.0166889i	−0.635526	−	0.772080i	$-0.719217\pi$
$2$	−1.82547	−	0.0236016i	−1.29080	−	0.0166889i	−0.655274	+	0.755391i	$0.727447\pi$
$3$	1.47646	+	0.905578i	0.852433	+	0.522836i
$3$	1.47646	+	0.905578i	0.852433	+	0.522836i
$4$	1.33244	+	0.0344602i	0.666220	+	0.0172301i
$5$	2.72027	+	0.833593i	1.21654	+	0.372794i	0.834322	−	0.551277i	$-0.185859\pi$
$5$	2.72027	+	0.833593i	1.21654	+	0.372794i	0.382220	+	0.924071i	$0.375160\pi$
$6$	−2.67385	−	1.68795i	−1.09160	−	0.689102i
$7$	1.26149	−	3.14568i	0.476797	−	1.18896i	−0.474383	−	0.880318i	$-0.657329\pi$
$7$	1.26149	−	3.14568i	0.476797	−	1.18896i	0.951180	−	0.308637i	$-0.0998727\pi$
$8$	1.21698	+	0.0472244i	0.430268	+	0.0166964i
$9$	1.35986	+	2.67410i	0.453286	+	0.891365i
$10$	−4.94609	−	1.58590i	−1.56409	−	0.501505i
$11$	3.49339	+	1.98691i	1.05330	+	0.599077i	0.919968	−	0.391994i	$-0.128215\pi$
$11$	3.49339	+	1.98691i	1.05330	+	0.599077i	0.133330	+	0.991072i	$0.457433\pi$
$12$	1.93609	+	1.25751i	0.558900	+	0.363011i
$13$	1.89759	+	4.24727i	0.526297	+	1.17798i	0.960783	+	0.277302i	$0.0894402\pi$
$13$	1.89759	+	4.24727i	0.526297	+	1.17798i	−0.434486	+	0.900678i	$0.643070\pi$
$14$	−2.37704	+	5.71256i	−0.635291	+	1.52675i
$15$	3.26148	+	3.69418i	0.842111	+	0.953834i
$16$	−4.88265	−	0.252724i	−1.22066	−	0.0631810i
$17$	−4.20414	−	1.91102i	−1.01965	−	0.463489i	−0.166995	−	0.985958i	$-0.553406\pi$
$17$	−4.20414	−	1.91102i	−1.01965	−	0.463489i	−0.852659	+	0.522469i	$0.825011\pi$
$18$	−2.41926	−	4.91357i	−0.570225	−	1.15814i
$19$	−0.127033	−	0.185219i	−0.0291435	−	0.0424922i	0.809830	−	0.586665i	$-0.199560\pi$
$19$	−0.127033	−	0.185219i	−0.0291435	−	0.0424922i	−0.838973	+	0.544173i	$0.816843\pi$
$20$	3.59587	+	1.20445i	0.804061	+	0.269324i
$21$	4.71119	−	3.50209i	1.02807	−	0.764219i
$22$	−6.33018	−	3.70950i	−1.34960	−	0.790867i
$23$	2.01071	−	6.13431i	0.419262	−	1.27909i	−0.493195	−	0.869919i	$-0.664171\pi$
$23$	2.01071	−	6.13431i	0.419262	−	1.27909i	0.912457	−	0.409173i	$-0.134183\pi$
$24$	1.75406	+	1.17180i	0.358045	+	0.239192i
$25$	2.56342	+	1.73388i	0.512684	+	0.346775i
$26$	−3.36374	−	7.79803i	−0.659684	−	1.52932i
$27$	−0.413832	+	5.17965i	−0.0796419	+	0.996824i
$28$	1.78925	−	4.14796i	0.338137	−	0.783890i
$29$	4.61356	−	2.94965i	0.856717	−	0.547737i	−0.0354872	−	0.999370i	$-0.511298\pi$
$29$	4.61356	−	2.94965i	0.856717	−	0.547737i	0.892204	+	0.451633i	$0.149158\pi$
$30$	−5.86654	−	6.82058i	−1.07108	−	1.24526i
$31$	−0.792742	−	2.92076i	−0.142381	−	0.524584i	−0.999948	−	0.0102119i	$-0.996749\pi$
$31$	−0.792742	−	2.92076i	−0.142381	−	0.524584i	0.857567	−	0.514372i	$-0.171975\pi$
$32$	6.47645	+	0.419233i	1.14488	+	0.0741107i
$33$	3.35854	+	6.09714i	0.584647	+	1.06138i
$34$	7.62941	+	3.58772i	1.30843	+	0.615289i
$35$	6.05380	−	7.50553i	1.02328	−	1.26867i
$36$	1.71978	+	3.60993i	0.286630	+	0.601656i
$37$	−11.5174	−	2.26194i	−1.89345	−	0.371861i	−0.896048	−	0.443958i	$-0.853574\pi$
$37$	−11.5174	−	2.26194i	−1.89345	−	0.371861i	−0.997398	+	0.0720972i	$0.977031\pi$
$38$	0.227524	+	0.341110i	0.0369092	+	0.0553353i
$39$	−1.04452	+	7.98933i	−0.167258	+	1.27932i
$40$	3.27115	+	1.14293i	0.517214	+	0.180713i
$41$	−0.528605	+	0.200173i	−0.0825542	+	0.0312617i	−0.395072	−	0.918650i	$-0.629280\pi$
$41$	−0.528605	+	0.200173i	−0.0825542	+	0.0312617i	0.312518	+	0.949912i	$0.398828\pi$
$42$	−8.68277	+	6.28176i	−1.33978	+	0.969296i
$43$	−5.16076	+	2.26581i	−0.787008	+	0.345533i	−0.756494	−	0.654001i	$-0.773089\pi$
$43$	−5.16076	+	2.26581i	−0.787008	+	0.345533i	−0.0305148	+	0.999534i	$0.509715\pi$
$44$	4.58627	+	2.76783i	0.691406	+	0.417266i
$45$	1.47007	+	8.40783i	0.219145	+	1.25337i
$46$	−3.81526	+	11.1505i	−0.562529	+	1.64405i
$47$	−0.358792	+	1.32192i	−0.0523351	+	0.192822i	−0.986424	−	0.164218i	$-0.947490\pi$
$47$	−0.358792	+	1.32192i	−0.0523351	+	0.192822i	0.934089	+	0.357040i	$0.116214\pi$
$48$	−6.98017	−	4.79476i	−1.00750	−	0.692064i
$49$	−3.24350	−	3.09995i	−0.463357	−	0.442851i
$50$	−4.63852	−	3.22563i	−0.655986	−	0.456174i
$51$	−4.47666	−	6.62871i	−0.626858	−	0.928205i
$52$	2.38206	+	5.72462i	0.330333	+	0.793862i
$53$	1.85497	−	1.96615i	0.254799	−	0.270071i	−0.587330	−	0.809348i	$-0.699821\pi$
$53$	1.85497	−	1.96615i	0.254799	−	0.270071i	0.842129	+	0.539277i	$0.181302\pi$
$54$	0.877684	−	9.44551i	0.119438	−	1.28537i
$55$	7.84670	+	8.31701i	1.05805	+	1.12147i
$56$	1.68376	−	3.76866i	0.225001	−	0.503608i
$57$	−0.0198290	−	0.388507i	−0.00262642	−	0.0514590i
$58$	−8.49152	+	5.27561i	−1.11499	+	0.692721i
$59$	5.24916	−	0.890622i	0.683383	−	0.115949i	0.184780	−	0.982780i	$-0.440843\pi$
$59$	5.24916	−	0.890622i	0.683383	−	0.115949i	0.498602	+	0.866831i	$0.333847\pi$
$60$	4.21843	+	5.03467i	0.544596	+	0.649973i
$61$	−6.99384	+	12.8711i	−0.895469	+	1.64798i	−0.142628	+	0.989776i	$0.545555\pi$
$61$	−6.99384	+	12.8711i	−0.895469	+	1.64798i	−0.752841	+	0.658202i	$0.771317\pi$
$62$	1.37819	+	5.35046i	0.175030	+	0.679509i
$63$	10.1273	−	0.904340i	1.27592	−	0.113936i
$64$	−2.06367	−	0.160401i	−0.257959	−	0.0200501i
$65$	1.62146	+	13.1355i	0.201117	+	1.62926i
$66$	−5.98701	−	11.2094i	−0.736950	−	1.37978i
$67$	−6.25549	+	3.24356i	−0.764230	+	0.396265i	−0.797606	−	0.603178i	$-0.793901\pi$
$67$	−6.25549	+	3.24356i	−0.764230	+	0.396265i	0.0333764	+	0.999443i	$0.489374\pi$
$68$	−5.53591	−	2.69119i	−0.671327	−	0.326355i
$69$	8.52382	−	7.23619i	1.02615	−	0.871135i
$70$	−11.2282	+	13.5582i	−1.34202	+	1.62052i
$71$	−5.07756	−	3.93541i	−0.602596	−	0.467047i	0.265047	−	0.964236i	$-0.414613\pi$
$71$	−5.07756	−	3.93541i	−0.602596	−	0.467047i	−0.867643	+	0.497189i	$0.834366\pi$
$72$	1.52864	+	3.31854i	0.180152	+	0.391094i
$73$	12.6226	−	4.04726i	1.47736	−	0.473696i	0.545996	−	0.837788i	$-0.316151\pi$
$73$	12.6226	−	4.04726i	1.47736	−	0.473696i	0.931363	+	0.364092i	$0.118621\pi$
$74$	20.9712	+	4.40092i	2.43785	+	0.511597i
$75$	2.21463	+	4.88137i	0.255723	+	0.563653i
$76$	−0.162882	−	0.251171i	−0.0186838	−	0.0288113i
$77$	10.6571	−	8.48263i	1.21448	−	0.966686i
$78$	2.09530	−	14.5596i	0.237246	−	1.64855i
$79$	1.91235	−	10.0815i	0.215156	−	1.13426i	−0.694688	−	0.719311i	$-0.744458\pi$
$79$	1.91235	−	10.0815i	0.215156	−	1.13426i	0.909844	−	0.414950i	$-0.136201\pi$
$80$	−13.0715	−	4.75762i	−1.46143	−	0.531918i
$81$	−5.30158	+	7.27277i	−0.589064	+	0.808086i
$82$	0.969675	−	0.352933i	0.107083	−	0.0389749i
$83$	2.55818	+	15.6918i	0.280797	+	1.72240i	0.622522	+	0.782603i	$0.286108\pi$
$83$	2.55818	+	15.6918i	0.280797	+	1.72240i	−0.341725	+	0.939800i	$0.611011\pi$
$84$	6.39806	−	4.50398i	0.698085	−	0.491424i
$85$	−9.84338	−	8.70302i	−1.06766	−	0.943975i
$86$	9.47427	−	4.01436i	1.02164	−	0.432880i
$87$	9.48287	−	0.177102i	1.01667	−	0.0189873i
$88$	4.15756	+	2.58301i	0.443198	+	0.275350i
$89$	−1.35362	−	0.553016i	−0.143484	−	0.0586195i	0.305321	−	0.952250i	$-0.401236\pi$
$89$	−1.35362	−	0.553016i	−0.143484	−	0.0586195i	−0.448804	+	0.893630i	$0.648150\pi$
$90$	−2.48512	−	15.3829i	−0.261955	−	1.62150i
$91$	15.7543	−	0.611340i	1.65150	−	0.0640858i
$92$	2.89054	−	8.10431i	0.301359	−	0.844932i
$93$	1.47453	−	5.03027i	0.152901	−	0.521614i
$94$	0.686162	−	2.40466i	0.0707722	−	0.248022i
$95$	−0.191168	−	0.609740i	−0.0196134	−	0.0625580i
$96$	9.18255	+	6.48391i	0.937190	+	0.661761i
$97$	−3.05069	+	13.2531i	−0.309751	+	1.34565i	0.550100	+	0.835099i	$0.314590\pi$
$97$	−3.05069	+	13.2531i	−0.309751	+	1.34565i	−0.859850	+	0.510546i	$0.829443\pi$
$98$	5.84773	+	5.73542i	0.590710	+	0.579364i
$99$	−0.562685	+	12.0436i	−0.0565519	+	1.21043i
$100$	3.35586	+	2.39862i	0.335586	+	0.239862i
$101$	−0.924841	+	6.17460i	−0.0920251	+	0.614396i	0.894034	+	0.447999i	$0.147863\pi$
$101$	−0.924841	+	6.17460i	−0.0920251	+	0.614396i	−0.986059	+	0.166396i	$0.946787\pi$
$102$	8.01554	+	12.2061i	0.793657	+	1.20859i
$103$	−2.71581	−	7.61441i	−0.267597	−	0.750270i	−0.997754	−	0.0669910i	$-0.978660\pi$
$103$	−2.71581	−	7.61441i	−0.267597	−	0.750270i	0.730157	−	0.683279i	$-0.239447\pi$
$104$	2.10876	+	5.25846i	0.206781	+	0.515634i
$105$	15.7350	−	5.59942i	1.53558	−	0.546447i
$106$	−3.43258	+	3.54536i	−0.333402	+	0.344356i
$107$	0.240826	+	4.13482i	0.0232815	+	0.399729i	0.989738	+	0.142897i	$0.0456416\pi$
$107$	0.240826	+	4.13482i	0.0232815	+	0.399729i	−0.966456	+	0.256832i	$0.917321\pi$
$108$	−0.729898	+	6.88731i	−0.0702344	+	0.662731i
$109$	−0.0782423	+	1.34337i	−0.00749426	+	0.128671i	0.992486	+	0.122360i	$0.0390461\pi$
$109$	−0.0782423	+	1.34337i	−0.00749426	+	0.128671i	−0.999980	+	0.00631174i	$0.997991\pi$
$110$	−14.1276	−	15.3676i	−1.34701	−	1.46525i
$111$	−14.9566	−	13.7695i	−1.41961	−	1.30695i
$112$	−6.95438	+	15.0404i	−0.657127	+	1.42119i
$113$	−0.225336	+	0.165503i	−0.0211978	+	0.0155692i	−0.602509	−	0.798112i	$-0.705832\pi$
$113$	−0.225336	+	0.165503i	−0.0211978	+	0.0155692i	0.581311	+	0.813681i	$0.302540\pi$
$114$	0.0270278	+	0.709675i	0.00253138	+	0.0664671i
$115$	10.5832	−	15.0109i	0.986887	−	1.39977i
$116$	6.24894	−	3.77125i	0.580199	−	0.350152i
$117$	−8.77716	+	10.8500i	−0.811448	+	1.00308i
$118$	−9.60319	+	1.50191i	−0.884045	+	0.138262i
$119$	−11.3149	+	10.8142i	−1.03724	+	0.991332i
$120$	3.79471	+	4.64977i	0.346408	+	0.424464i
$121$	2.63328	+	4.42777i	0.239389	+	0.402524i
$122$	13.0708	−	23.3307i	1.18337	−	2.11227i
$123$	−0.961735	−	0.183146i	−0.0867167	−	0.0165137i
$124$	−0.955631	−	3.91905i	−0.0858182	−	0.351941i
$125$	−3.40317	−	4.21927i	−0.304389	−	0.377383i
$126$	−18.5084	+	1.41182i	−1.64886	+	0.125775i
$127$	−0.275607	−	14.2102i	−0.0244562	−	1.26096i	−0.788193	−	0.615428i	$-0.788983\pi$
$127$	−0.275607	−	14.2102i	−0.0244562	−	1.26096i	0.763737	−	0.645527i	$-0.223362\pi$
$128$	−9.16351	−	0.831556i	−0.809947	−	0.0734998i
$129$	−9.67152	−	1.32809i	−0.851529	−	0.116932i
$130$	−2.64990	−	24.0168i	−0.232412	−	2.10641i
$131$	17.0064	−	1.54327i	1.48585	−	0.134836i	0.682739	−	0.730662i	$-0.260788\pi$
$131$	17.0064	−	1.54327i	1.48585	−	0.134836i	0.803113	+	0.595826i	$0.203175\pi$
$132$	4.26495	+	8.23980i	0.371216	+	0.717183i
$133$	−0.742891	+	0.165955i	−0.0644168	+	0.0143901i
$134$	11.4957	−	5.77338i	0.993081	−	0.498744i
$135$	−5.44345	+	13.7451i	−0.468498	+	1.18299i
$136$	−5.02611	−	2.52421i	−0.430985	−	0.216449i
$137$	−20.6073	−	5.16628i	−1.76060	−	0.441385i	−0.778175	−	0.628048i	$-0.783854\pi$
$137$	−20.6073	−	5.16628i	−1.76060	−	0.441385i	−0.982424	+	0.186662i	$0.940233\pi$
$138$	−15.7307	+	13.0083i	−1.33909	+	1.10734i
$139$	4.34212	+	0.621699i	0.368294	+	0.0527318i	0.323406	−	0.946260i	$-0.395172\pi$
$139$	4.34212	+	0.621699i	0.368294	+	0.0527318i	0.0448877	+	0.998992i	$0.485707\pi$
$140$	8.32497	−	9.79206i	0.703588	−	0.827580i
$141$	−1.72685	+	1.62685i	−0.145427	+	0.137006i
$142$	9.17604	+	7.30380i	0.770036	+	0.612921i
$143$	−1.80993	+	18.6077i	−0.151354	+	1.55606i
$144$	−5.96390	−	13.4003i	−0.496991	−	1.11670i
$145$	15.0089	−	4.17802i	1.24642	−	0.346966i
$146$	−23.1376	+	7.09023i	−1.91488	+	0.586791i
$147$	−1.98164	−	7.51419i	−0.163443	−	0.619760i
$148$	−15.2683	−	3.41079i	−1.25504	−	0.280365i
$149$	3.28537	−	0.823648i	0.269148	−	0.0674759i	−0.106250	−	0.994339i	$-0.533884\pi$
$149$	3.28537	−	0.823648i	0.269148	−	0.0674759i	0.375398	+	0.926864i	$0.377506\pi$
$150$	−3.92752	−	8.96306i	−0.320680	−	0.731830i
$151$	−2.49570	−	2.93551i	−0.203097	−	0.238888i	0.650904	−	0.759160i	$-0.274390\pi$
$151$	−2.49570	−	2.93551i	−0.203097	−	0.238888i	−0.854001	+	0.520272i	$0.825831\pi$
$152$	−0.145850	−	0.231407i	−0.0118300	−	0.0187696i
$153$	−0.606787	−	13.8410i	−0.0490558	−	1.11898i
$154$	−19.6543	+	15.2332i	−1.58379	+	1.22753i
$155$	0.278253	−	8.60608i	0.0223498	−	0.691257i
$156$	−1.66708	+	10.6093i	−0.133473	+	0.849424i
$157$	1.61047	−	13.0465i	0.128530	−	1.04123i	−0.780693	−	0.624915i	$-0.785134\pi$
$157$	1.61047	−	13.0465i	0.128530	−	1.04123i	0.909223	−	0.416310i	$-0.136677\pi$
$158$	−3.72887	+	18.3584i	−0.296653	+	1.46051i
$159$	4.51928	−	1.22312i	0.358402	−	0.0969997i
$160$	17.2682	+	6.53915i	1.36517	+	0.516965i
$161$	−16.7601	−	14.0634i	−1.32088	−	1.10835i
$162$	9.84951	−	13.1511i	0.773850	−	1.03325i
$163$	8.81374	−	7.39560i	0.690345	−	0.579268i	−0.228664	−	0.973506i	$-0.573436\pi$
$163$	8.81374	−	7.39560i	0.690345	−	0.579268i	0.919009	+	0.394237i	$0.128991\pi$
$164$	−0.711232	+	0.248502i	−0.0555379	+	0.0194048i
$165$	4.05361	+	19.3855i	0.315573	+	1.50916i
$166$	−4.29952	−	28.7053i	−0.333708	−	2.22796i
$167$	4.83051	−	9.46527i	0.373796	−	0.732445i	−0.625045	−	0.780589i	$-0.714919\pi$
$167$	4.83051	−	9.46527i	0.373796	−	0.732445i	0.998840	+	0.0481444i	$0.0153308\pi$
$168$	5.89881	−	4.03949i	0.455103	−	0.311654i
$169$	−5.76476	+	6.43580i	−0.443443	+	0.495062i
$170$	17.7634	+	16.1194i	1.36239	+	1.23630i
$171$	0.322547	−	0.591571i	0.0246658	−	0.0452386i
$172$	−6.95448	+	2.84122i	−0.530274	+	0.216641i
$173$	18.9761	+	3.21966i	1.44272	+	0.244786i	0.835388	−	0.549660i	$-0.185243\pi$
$173$	18.9761	+	3.21966i	1.44272	+	0.244786i	0.607335	+	0.794446i	$0.292239\pi$
$174$	−17.3148	+	0.0994828i	−1.31263	+	0.00754177i
$175$	8.68794	−	5.87645i	0.656747	−	0.444218i
$176$	−16.5549	−	10.5843i	−1.24787	−	0.797820i
$177$	8.55669	+	3.43856i	0.643161	+	0.258458i
$178$	2.45794	+	1.04146i	0.184230	+	0.0780607i
$179$	8.29266	+	17.3426i	0.619823	+	1.29625i	0.937479	+	0.348043i	$0.113154\pi$
$179$	8.29266	+	17.3426i	0.619823	+	1.29625i	−0.317656	+	0.948206i	$0.602896\pi$
$180$	1.66904	+	11.2536i	0.124403	+	0.838793i
$181$	−0.147890	−	0.0411681i	−0.0109926	−	0.00306000i	0.262672	−	0.964885i	$-0.415396\pi$
$181$	−0.147890	−	0.0411681i	−0.0109926	−	0.00306000i	−0.273665	+	0.961825i	$0.588236\pi$
$182$	−28.7734	+	0.744153i	−2.13283	+	0.0551603i
$183$	−21.9819	+	12.6702i	−1.62495	+	0.936609i
$184$	2.73668	−	7.37038i	0.201751	−	0.543352i
$185$	−29.4448	−	15.7539i	−2.16483	−	1.15825i
$186$	−2.81042	+	9.14778i	−0.206070	+	0.670748i
$187$	−10.8897	−	15.0292i	−0.796333	−	1.09904i
$188$	−0.523622	+	1.74902i	−0.0381891	+	0.127560i
$189$	15.7715	+	7.83583i	1.14721	+	0.569973i
$190$	0.334579	+	1.11757i	0.0242729	+	0.0810772i
$191$	−5.88757	+	7.69855i	−0.426009	+	0.557048i	−0.956909	−	0.290387i	$-0.906216\pi$
$191$	−5.88757	+	7.69855i	−0.426009	+	0.557048i	0.530900	+	0.847434i	$0.321854\pi$
$192$	−2.90167	−	2.10564i	−0.209410	−	0.151961i
$193$	−23.8740	+	11.2267i	−1.71849	+	0.808115i	−0.725727	+	0.687982i	$0.758497\pi$
$193$	−23.8740	+	11.2267i	−1.71849	+	0.808115i	−0.992758	+	0.120133i	$0.961668\pi$
$194$	5.88173	−	24.1210i	0.422283	−	1.73179i
$195$	−9.50124	+	20.8624i	−0.680398	+	1.49399i
$196$	−4.21494	−	4.24227i	−0.301067	−	0.303020i
$197$	−6.62011	+	1.30015i	−0.471663	+	0.0926316i	−0.422895	−	0.906179i	$-0.638986\pi$
$197$	−6.62011	+	1.30015i	−0.471663	+	0.0926316i	−0.0487678	+	0.998810i	$0.515529\pi$
$198$	1.31141	−	21.9719i	0.0931979	−	1.56147i
$199$	−19.1798	+	10.5830i	−1.35962	+	0.750206i	−0.984269	−	0.176677i	$-0.943465\pi$
$199$	−19.1798	+	10.5830i	−1.35962	+	0.750206i	−0.375350	+	0.926883i	$0.622477\pi$
$200$	3.03776	+	2.23115i	0.214802	+	0.157766i
$201$	−12.1733	−	0.875849i	−0.858636	−	0.0617776i
$202$	1.83400	−	11.2497i	0.129040	−	0.791526i
$203$	−3.45873	−	18.2337i	−0.242755	−	1.27976i
$204$	−5.73645	−	8.98662i	−0.401632	−	0.629189i
$205$	−1.60481	+	0.103883i	−0.112085	+	0.00725547i
$206$	4.77790	+	13.9640i	0.332892	+	0.972915i
$207$	19.1380	−	2.96495i	1.33018	−	0.206078i
$208$	−8.19188	−	21.2175i	−0.568005	−	1.47117i
$209$	−0.0757630	−	0.899448i	−0.00524063	−	0.0622161i
$210$	−28.8559	+	9.85018i	−1.99125	+	0.679727i
$211$	−10.1432	+	15.2070i	−0.698286	+	1.04689i	0.297458	+	0.954735i	$0.403861\pi$
$211$	−10.1432	+	15.2070i	−0.698286	+	1.04689i	−0.995745	+	0.0921549i	$0.970624\pi$
$212$	2.53938	−	2.55585i	0.174406	−	0.175537i
$213$	−3.93299	−	10.4086i	−0.269484	−	0.713185i
$214$	−0.342031	−	7.55367i	−0.0233808	−	0.516358i
$215$	−15.9274	+	1.86165i	−1.08624	+	0.126963i
$216$	−0.748231	+	6.28399i	−0.0509107	+	0.427571i
$217$	−10.1878	−	1.19078i	−0.691593	−	0.0808356i
$218$	0.174534	−	2.45043i	0.0118210	−	0.165964i
$219$	22.3018	+	5.45510i	1.50702	+	0.368622i
$220$	10.1686	+	11.3523i	0.685570	+	0.765373i
$221$	0.138868	−	21.4824i	0.00934129	−	1.44506i
$222$	26.9777	+	25.4888i	1.81063	+	1.71070i
$223$	−3.59737	+	3.18061i	−0.240898	+	0.212989i	−0.774210	−	0.632929i	$-0.781852\pi$
$223$	−3.59737	+	3.18061i	−0.240898	+	0.212989i	0.533312	+	0.845919i	$0.320947\pi$
$224$	9.48872	−	19.8440i	0.633991	−	1.32588i
$225$	−1.15066	+	9.21266i	−0.0767110	+	0.614177i
$226$	0.415249	−	0.296802i	0.0276220	−	0.0197430i
$227$	−1.65889	−	3.25056i	−0.110104	−	0.215747i	0.829104	−	0.559094i	$-0.188851\pi$
$227$	−1.65889	−	3.25056i	−0.110104	−	0.215747i	−0.939209	+	0.343347i	$0.888439\pi$
$228$	−0.0130329	−	0.518346i	−0.000863126	−	0.0343283i
$229$	−17.4922	−	22.8728i	−1.15592	−	1.51148i	−0.822562	−	0.568675i	$-0.807456\pi$
$229$	−17.4922	−	22.8728i	−1.15592	−	1.51148i	−0.333358	−	0.942800i	$-0.608182\pi$
$230$	−19.6735	+	27.1520i	−1.29723	+	1.79035i
$231$	23.4164	−	2.87345i	1.54069	−	0.189059i
$232$	5.75391	−	3.37180i	0.377763	−	0.221370i
$233$	−2.27810	−	10.5169i	−0.149243	−	0.688983i	−0.989229	−	0.146375i	$-0.953239\pi$
$233$	−2.27810	−	10.5169i	−0.149243	−	0.688983i	0.839986	−	0.542608i	$-0.182563\pi$
$234$	16.2785	−	19.5992i	1.06416	−	1.28124i
$235$	−2.07796	+	3.29690i	−0.135551	+	0.215066i
$236$	7.02488	−	1.00581i	0.457281	−	0.0654728i
$237$	11.9531	−	13.1532i	0.776439	−	0.854391i
$238$	20.9102	−	19.4738i	1.35541	−	1.26230i
$239$	8.73127	+	16.0686i	0.564779	+	1.03939i	0.990884	+	0.134719i	$0.0430131\pi$
$239$	8.73127	+	16.0686i	0.564779	+	1.03939i	−0.426105	+	0.904674i	$0.640115\pi$
$240$	−14.9911	−	18.8617i	−0.967669	−	1.21751i
$241$	1.40956	−	2.37012i	0.0907975	−	0.152673i	−0.810694	−	0.585471i	$-0.800910\pi$
$241$	1.40956	−	2.37012i	0.0907975	−	0.152673i	0.901491	+	0.432798i	$0.142474\pi$
$242$	−4.70246	−	8.14489i	−0.302285	−	0.523574i
$243$	−14.4136	+	5.93695i	−0.924635	+	0.380856i
$244$	−9.76241	+	16.9090i	−0.624974	+	1.08249i
$245$	−6.23909	−	11.1365i	−0.398601	−	0.711483i
$246$	1.75129	+	0.357026i	0.111658	+	0.0227631i
$247$	0.545619	−	0.891015i	0.0347169	−	0.0566939i
$248$	−0.826821	−	3.59195i	−0.0525032	−	0.228089i
$249$	−10.4331	+	25.4850i	−0.661173	+	1.61504i
$250$	6.11280	+	7.78246i	0.386607	+	0.492206i
$251$	−4.56359	−	8.66376i	−0.288051	−	0.546851i	0.697427	−	0.716656i	$-0.254328\pi$
$251$	−4.56359	−	8.66376i	−0.288051	−	0.546851i	−0.985478	+	0.169805i	$0.945686\pi$
$252$	13.5252	−	0.855990i	0.852006	−	0.0539223i
$253$	19.2125	−	17.4344i	1.20788	−	1.09609i
$254$	0.167727	+	25.9468i	0.0105242	+	1.62805i
$255$	−6.65208	−	21.7636i	−0.416569	−	1.36289i
$256$	20.8257	+	2.16165i	1.30161	+	0.135103i
$257$	−12.4432	+	1.61773i	−0.776188	+	0.100911i	−0.506734	−	0.862102i	$-0.669148\pi$
$257$	−12.4432	+	1.61773i	−0.776188	+	0.100911i	−0.269453	+	0.963013i	$0.586843\pi$
$258$	17.6237	+	2.65265i	1.09720	+	0.165147i
$259$	−21.6443	+	33.3766i	−1.34491	+	2.07392i
$260$	1.70785	+	17.5582i	0.105916	+	1.08891i
$261$	14.1614	+	8.32600i	0.876571	+	0.515366i
$262$	−31.0810	+	2.41580i	−1.92019	+	0.149249i
$263$	−2.75858	−	13.5813i	−0.170101	−	0.837461i	−0.971078	−	0.238764i	$-0.923258\pi$
$263$	−2.75858	−	13.5813i	−0.170101	−	0.837461i	0.800976	−	0.598696i	$-0.204314\pi$
$264$	3.79935	+	7.57871i	0.233834	+	0.466437i
$265$	6.68498	−	3.80217i	0.410655	−	0.233565i
$266$	1.36004	−	0.285412i	0.0833894	−	0.0174997i
$267$	−1.49777	−	2.04232i	−0.0916619	−	0.124988i
$268$	−8.44684	+	4.10629i	−0.515973	+	0.250832i
$269$	−1.07753	+	1.44737i	−0.0656982	+	0.0882480i	−0.833758	−	0.552130i	$-0.813815\pi$
$269$	−1.07753	+	1.44737i	−0.0656982	+	0.0882480i	0.768060	+	0.640378i	$0.221222\pi$
$270$	10.2612	−	24.9627i	0.624480	−	1.51918i
$271$	10.9767	+	14.7442i	0.666784	+	0.895646i	0.998866	−	0.0476040i	$-0.0151586\pi$
$271$	10.9767	+	14.7442i	0.666784	+	0.895646i	−0.332082	+	0.943250i	$0.607751\pi$
$272$	20.0444	+	10.3933i	1.21537	+	0.630187i
$273$	23.8142	+	13.3642i	1.44130	+	0.808836i
$274$	37.4960	+	9.91724i	2.26521	+	0.599122i
$275$	5.50998	+	11.1504i	0.332264	+	0.672395i
$276$	11.6068	−	9.34806i	0.698649	−	0.562687i
$277$	19.3550	−	13.4595i	1.16293	−	0.808704i	0.178408	−	0.983957i	$-0.442905\pi$
$277$	19.3550	−	13.4595i	1.16293	−	0.808704i	0.984524	+	0.175252i	$0.0560741\pi$
$278$	−7.91172	−	1.23737i	−0.474514	−	0.0742126i
$279$	6.73237	−	6.09168i	0.403057	−	0.364699i
$280$	7.72180	−	8.84821i	0.461466	−	0.528781i
$281$	6.97077	−	14.1066i	0.415841	−	0.841527i	−0.583722	−	0.811954i	$-0.698404\pi$
$281$	6.97077	−	14.1066i	0.415841	−	0.841527i	0.999563	−	0.0295735i	$-0.00941491\pi$
$282$	3.19070	−	2.92900i	0.190003	−	0.174420i
$283$	7.14449	−	6.15408i	0.424696	−	0.365822i	−0.414133	−	0.910216i	$-0.635915\pi$
$283$	7.14449	−	6.15408i	0.424696	−	0.365822i	0.838829	+	0.544394i	$0.183240\pi$
$284$	−6.62993	−	5.41867i	−0.393414	−	0.321539i
$285$	0.269917	−	1.07337i	0.0159885	−	0.0635811i
$286$	3.74314	−	33.9251i	0.221337	−	2.00603i
$287$	−0.0371479	+	1.91534i	−0.00219277	+	0.113059i
$288$	7.68597	+	17.8887i	0.452900	+	1.05410i
$289$	2.84493	+	3.25993i	0.167349	+	0.191761i
$290$	−27.4969	+	7.27261i	−1.61468	+	0.427062i
$291$	−16.5059	+	16.8050i	−0.967593	+	0.985124i
$292$	16.9583	−	4.95776i	0.992408	−	0.290131i
$293$	−0.314312	+	3.73147i	−0.0183623	+	0.217995i	0.981311	+	0.192429i	$0.0616366\pi$
$293$	−0.314312	+	3.73147i	−0.0183623	+	0.217995i	−0.999673	+	0.0255655i	$0.991861\pi$
$294$	3.44006	+	13.7637i	0.200629	+	0.802714i
$295$	15.0216	+	1.95293i	0.874589	+	0.113704i
$296$	−13.9096	−	3.29664i	−0.808480	−	0.191613i
$297$	−11.7372	+	17.2723i	−0.681061	+	1.00224i
$298$	−6.01677	+	1.42600i	−0.348542	+	0.0826061i
$299$	29.8695	−	3.10038i	1.72740	−	0.179299i
$300$	2.78264	+	6.58046i	0.160656	+	0.379923i
$301$	0.617298	+	19.0924i	0.0355805	+	1.10047i
$302$	4.48653	+	5.41758i	0.258171	+	0.311747i
$303$	−6.95707	+	8.27902i	−0.399673	+	0.475617i
$304$	0.573450	+	0.936465i	0.0328896	+	0.0537100i
$305$	−29.7544	+	29.1829i	−1.70373	+	1.67101i
$306$	0.780999	+	25.2806i	0.0446468	+	1.44519i
$307$	4.28915	−	6.25373i	0.244795	−	0.356919i	−0.682737	−	0.730664i	$-0.739210\pi$
$307$	4.28915	−	6.25373i	0.244795	−	0.356919i	0.927532	+	0.373745i	$0.121926\pi$
$308$	14.4922	−	10.9354i	0.825770	−	0.623100i
$309$	2.88567	−	13.7017i	0.164160	−	0.779465i
$310$	−0.711059	+	15.7035i	−0.0403854	+	0.891901i
$311$	−0.318444	−	4.47089i	−0.0180573	−	0.253521i	−0.998414	−	0.0562903i	$-0.982073\pi$
$311$	−0.318444	−	4.47089i	−0.0180573	−	0.253521i	0.980357	−	0.197230i	$-0.0631947\pi$
$312$	−1.64846	+	9.67354i	−0.0933254	+	0.547656i
$313$	−1.02911	−	2.77158i	−0.0581687	−	0.156659i	0.905100	−	0.425200i	$-0.139796\pi$
$313$	−1.02911	−	2.77158i	−0.0581687	−	0.156659i	−0.963268	+	0.268541i	$0.913459\pi$
$314$	−3.24778	+	23.7780i	−0.183283	+	1.34187i
$315$	28.3028	+	5.98199i	1.59468	+	0.337047i
$316$	2.89550	−	13.3671i	0.162885	−	0.751960i
$317$	−6.00109	−	18.3082i	−0.337055	−	1.02829i	−0.967675	−	0.252202i	$-0.918845\pi$
$317$	−6.00109	−	18.3082i	−0.337055	−	1.02829i	0.630620	−	0.776092i	$-0.282801\pi$
$318$	−8.27866	+	2.12610i	−0.464244	+	0.119226i
$319$	21.9777	−	1.13756i	1.23051	−	0.0636909i
$320$	−5.48003	−	2.15660i	−0.306343	−	0.120557i
$321$	−3.38884	+	6.32298i	−0.189146	+	0.352914i
$322$	30.2631	+	26.0678i	1.68649	+	1.45270i
$323$	0.180109	+	1.02145i	0.0100215	+	0.0568350i
$324$	−7.31466	+	9.50784i	−0.406370	+	0.528213i
$325$	−2.49992	+	14.1777i	−0.138670	+	0.786439i
$326$	−16.2637	+	13.2924i	−0.900765	+	0.736198i
$327$	−1.33205	+	1.91257i	−0.0736624	+	0.105766i
$328$	−0.652755	+	0.218643i	−0.0360424	+	0.0120726i
$329$	3.70574	+	2.79623i	0.204304	+	0.154161i
$330$	−6.94221	−	35.4833i	−0.382156	−	1.95329i
$331$	−1.99410	+	1.06690i	−0.109606	+	0.0586423i	−0.525644	−	0.850705i	$-0.676175\pi$
$331$	−1.99410	+	1.06690i	−0.109606	+	0.0586423i	0.416038	+	0.909347i	$0.363418\pi$
$332$	2.86788	+	20.9966i	0.157395	+	1.15234i
$333$	−9.61334	−	33.8745i	−0.526808	−	1.85631i
$334$	−9.04132	+	17.1645i	−0.494719	+	0.939201i
$335$	−19.7204	+	3.60884i	−1.07744	+	0.197172i
$336$	−23.8882	+	15.9089i	−1.30321	+	0.867899i
$337$	−16.3743	−	16.9123i	−0.891967	−	0.921272i	0.105353	−	0.994435i	$-0.466403\pi$
$337$	−16.3743	−	16.9123i	−0.891967	−	0.921272i	−0.997320	+	0.0731628i	$0.976691\pi$
$338$	10.6753	−	11.6123i	0.580658	−	0.631625i
$339$	−0.482575	+	0.0402993i	−0.0262099	+	0.00218876i
$340$	−12.8158	−	11.9355i	−0.695035	−	0.647291i
$341$	3.03394	−	11.7785i	0.164297	−	0.637840i
$342$	−0.602760	+	1.07228i	−0.0325935	+	0.0579823i
$343$	7.75470	−	3.52494i	0.418714	−	0.190329i
$344$	−6.38755	+	2.51374i	−0.344394	+	0.135532i
$345$	29.2191	−	12.5790i	1.57311	−	0.677231i
$346$	−34.5642	−	6.32524i	−1.85818	−	0.340047i
$347$	−16.1685	+	20.5849i	−0.867973	+	1.10505i	0.125625	+	0.992078i	$0.459906\pi$
$347$	−16.1685	+	20.5849i	−0.867973	+	1.10505i	−0.993598	+	0.112976i	$0.963962\pi$
$348$	12.6415	+	0.0908040i	0.677653	+	0.00486760i
$349$	6.38158	+	22.3643i	0.341598	+	1.19713i	0.923412	+	0.383811i	$0.125389\pi$
$349$	6.38158	+	22.3643i	0.341598	+	1.19713i	−0.581813	+	0.813322i	$0.697657\pi$
$350$	−15.9982	+	10.5222i	−0.855142	+	0.562436i
$351$	−22.7846	+	8.07119i	−1.21615	+	0.430808i
$352$	21.7918	+	14.3327i	1.16151	+	0.763935i
$353$	−0.530284	+	1.69137i	−0.0282242	+	0.0900226i	−0.967252	−	0.253820i	$-0.918313\pi$
$353$	−0.530284	+	1.69137i	−0.0282242	+	0.0900226i	0.939027	+	0.343842i	$0.111729\pi$
$354$	−15.5388	−	6.47893i	−0.825878	−	0.344351i
$355$	−10.5318	−	14.9380i	−0.558971	−	0.792827i
$356$	−1.78456	−	0.783506i	−0.0945817	−	0.0415258i
$357$	−26.4990	+	5.72012i	−1.40248	+	0.302741i
$358$	−14.7287	−	31.8541i	−0.778434	−	1.68354i
$359$	18.3170	+	10.1069i	0.966736	+	0.533422i	0.886187	−	0.463329i	$-0.153345\pi$
$359$	18.3170	+	10.1069i	0.966736	+	0.533422i	0.0805490	+	0.996751i	$0.474333\pi$
$360$	1.39199	+	10.3016i	0.0733644	+	0.542942i
$361$	6.82521	−	17.6777i	0.359221	−	0.930407i
$362$	0.268997	+	0.0786415i	0.0141382	+	0.00413330i
$363$	−0.121768	+	8.92205i	−0.00639114	+	0.468286i
$364$	21.0128	−	0.271676i	1.10137	−	0.0142397i
$365$	37.7105	−	0.487563i	1.97386	−	0.0255202i
$366$	40.4263	−	22.6102i	2.11312	−	1.18186i
$367$	−2.49969	−	0.730786i	−0.130483	−	0.0381467i	0.214714	−	0.976677i	$-0.431118\pi$
$367$	−2.49969	−	0.730786i	−0.130483	−	0.0381467i	−0.345197	+	0.938530i	$0.612188\pi$
$368$	−11.3679	+	29.4435i	−0.592591	+	1.53485i
$369$	−1.25411	−	1.14133i	−0.0652862	−	0.0594154i
$370$	53.3788	+	29.4532i	2.77503	+	1.53120i
$371$	−3.84486	−	8.31540i	−0.199615	−	0.431714i
$372$	2.13806	−	6.65172i	0.110853	−	0.344875i
$373$	24.6910	+	10.8405i	1.27845	+	0.561300i	0.927055	−	0.374925i	$-0.122332\pi$
$373$	24.6910	+	10.8405i	1.27845	+	0.561300i	0.351399	+	0.936226i	$0.385706\pi$
$374$	19.5240	+	27.6923i	1.00956	+	1.43193i
$375$	−1.20376	−	9.31141i	−0.0621619	−	0.480839i
$376$	−0.499070	+	1.59181i	−0.0257376	+	0.0820914i
$377$	21.2826	+	13.9978i	1.09611	+	0.720923i
$378$	−28.6053	−	14.6763i	−1.47130	−	0.754866i
$379$	−7.10925	+	4.67583i	−0.365178	+	0.240181i	−0.718815	−	0.695202i	$-0.755315\pi$
$379$	−7.10925	+	4.67583i	−0.365178	+	0.240181i	0.353637	+	0.935383i	$0.384945\pi$
$380$	−0.233708	−	0.819030i	−0.0119889	−	0.0420154i
$381$	12.4616	−	21.2304i	0.638425	−	1.08767i
$382$	10.9293	−	13.9145i	0.559189	−	0.711928i
$383$	−16.1853	−	2.96191i	−0.827031	−	0.151346i	−0.250183	−	0.968198i	$-0.580491\pi$
$383$	−16.1853	−	2.96191i	−0.827031	−	0.151346i	−0.576847	+	0.816852i	$0.695717\pi$
$384$	−12.7765	−	9.52603i	−0.651998	−	0.486123i
$385$	36.0612	−	14.1914i	1.83785	−	0.723261i
$386$	43.8461	−	19.9305i	2.23171	−	1.01444i
$387$	−13.0769	−	10.7192i	−0.664736	−	0.544887i
$388$	−4.52156	+	17.5538i	−0.229548	+	0.891159i
$389$	9.11329	+	8.48727i	0.462062	+	0.430322i	0.877702	−	0.479208i	$-0.159076\pi$
$389$	9.11329	+	8.48727i	0.462062	+	0.430322i	−0.415640	+	0.909529i	$0.636442\pi$
$390$	17.8366	−	37.8594i	0.903190	−	1.91709i
$391$	−20.1760	+	21.9470i	−1.02035	+	1.10991i
$392$	−3.80088	−	3.92576i	−0.191974	−	0.198281i
$393$	26.5067	+	13.1220i	1.33709	+	0.661918i
$394$	12.1155	−	2.21713i	0.610369	−	0.111697i
$395$	13.6060	−	25.8304i	0.684593	−	1.29967i
$396$	−1.16477	+	16.0280i	−0.0585318	+	0.805436i
$397$	−4.09359	−	29.9704i	−0.205451	−	1.50417i	−0.747748	−	0.663982i	$-0.768865\pi$
$397$	−4.09359	−	29.9704i	−0.205451	−	1.50417i	0.542297	−	0.840187i	$-0.317555\pi$
$398$	35.2618	−	18.8662i	1.76752	−	0.945675i
$399$	−1.24713	−	0.427720i	−0.0624347	−	0.0214128i
$400$	−12.0781	−	9.11375i	−0.603905	−	0.455688i
$401$	17.0612	−	5.71474i	0.851997	−	0.285380i	0.142245	−	0.989832i	$-0.454568\pi$
$401$	17.0612	−	5.71474i	0.851997	−	0.285380i	0.709753	+	0.704451i	$0.248807\pi$
$402$	22.2012	+	1.88614i	1.10730	+	0.0940722i
$403$	10.9010	−	8.90939i	0.543015	−	0.443808i
$404$	−1.44507	+	8.19541i	−0.0718950	+	0.407737i
$405$	−20.4843	+	15.3646i	−1.01787	+	0.763471i
$406$	5.88345	+	33.3667i	0.291991	+	1.65596i
$407$	−35.7405	−	30.7859i	−1.77159	−	1.52600i
$408$	−5.13497	−	8.27842i	−0.254219	−	0.409843i
$409$	−34.4364	−	13.5520i	−1.70277	−	0.670104i	−0.703592	−	0.710604i	$-0.748422\pi$
$409$	−34.4364	−	13.5520i	−1.70277	−	0.670104i	−0.999180	+	0.0405001i	$0.987105\pi$
$410$	2.93198	−	0.151758i	0.144800	−	0.00749480i
$411$	−25.7473	−	26.2893i	−1.27002	−	1.29676i
$412$	−3.35626	−	10.2393i	−0.165351	−	0.504456i
$413$	3.82013	−	17.6357i	0.187976	−	0.867795i
$414$	−35.0058	+	4.96073i	−1.72044	+	0.243807i
$415$	−6.12166	+	44.8185i	−0.300501	+	2.20005i
$416$	10.5090	+	28.3027i	0.515248	+	1.38766i
$417$	5.84796	+	4.85004i	0.286376	+	0.237508i
$418$	0.117074	+	1.64370i	0.00572629	+	0.0803960i
$419$	−1.25343	+	27.6816i	−0.0612340	+	1.35234i	0.704741	+	0.709465i	$0.251063\pi$
$419$	−1.25343	+	27.6816i	−0.0612340	+	1.35234i	−0.765975	+	0.642870i	$0.777743\pi$
$420$	21.1589	−	6.91865i	1.03245	−	0.337596i
$421$	−4.98462	+	3.76124i	−0.242936	+	0.183312i	−0.716785	−	0.697295i	$-0.754387\pi$
$421$	−4.98462	+	3.76124i	−0.242936	+	0.183312i	0.473849	+	0.880606i	$0.342864\pi$
$422$	18.8750	−	27.5204i	0.918819	−	1.33967i
$423$	−4.02286	+	0.838183i	−0.195598	+	0.0407539i
$424$	2.35031	−	2.30517i	0.114141	−	0.111949i
$425$	−7.46352	−	12.1882i	−0.362034	−	0.591214i
$426$	6.93388	+	19.0934i	0.335948	+	0.925077i
$427$	31.6658	+	38.2371i	1.53242	+	1.85042i
$428$	0.178399	+	5.51770i	0.00862326	+	0.266708i
$429$	−19.5230	+	25.8345i	−0.942581	+	1.24730i
$430$	29.1189	−	3.02247i	1.40424	−	0.145756i
$431$	3.20216	−	0.758927i	0.154243	−	0.0365562i	−0.152769	−	0.988262i	$-0.548819\pi$
$431$	3.20216	−	0.758927i	0.154243	−	0.0365562i	0.307012	+	0.951706i	$0.400671\pi$
$432$	3.32962	−	25.1858i	0.160196	−	1.21175i
$433$	9.24847	+	2.19193i	0.444453	+	0.105337i	0.446748	−	0.894660i	$-0.352582\pi$
$433$	9.24847	+	2.19193i	0.444453	+	0.105337i	−0.00229451	+	0.999997i	$0.500730\pi$
$434$	18.5694	+	2.41418i	0.891359	+	0.115885i
$435$	25.9436	+	7.42309i	1.24390	+	0.355910i
$436$	−0.150546	+	1.78726i	−0.00720985	+	0.0855943i
$437$	−1.39162	+	0.406840i	−0.0665701	+	0.0194618i
$438$	−40.5824	−	10.4845i	−1.93910	−	0.500967i
$439$	−35.4028	+	9.36362i	−1.68968	+	0.446901i	−0.969141	−	0.246508i	$-0.920717\pi$
$439$	−35.4028	+	9.36362i	−1.68968	+	0.446901i	−0.720544	+	0.693409i	$0.756108\pi$
$440$	9.15652	+	10.4922i	0.436520	+	0.500196i
$441$	3.87889	−	12.8889i	0.184709	−	0.613758i
$442$	−0.760519	+	39.2122i	−0.0361742	+	1.86513i
$443$	1.43435	−	12.9999i	0.0681480	−	0.617643i	−0.910702	−	0.413064i	$-0.864459\pi$
$443$	1.43435	−	12.9999i	0.0681480	−	0.617643i	0.978850	−	0.204579i	$-0.0655825\pi$
$444$	−19.4542	−	18.8625i	−0.923256	−	0.895174i
$445$	−3.22123	−	2.63272i	−0.152701	−	0.124803i
$446$	6.64195	−	5.72120i	0.314505	−	0.270907i
$447$	5.59659	+	1.75908i	0.264710	+	0.0832015i
$448$	−3.10786	+	6.28930i	−0.146833	+	0.297141i
$449$	7.36858	−	8.44346i	0.347745	−	0.398472i	−0.552743	−	0.833351i	$-0.686419\pi$
$449$	7.36858	−	8.44346i	0.347745	−	0.398472i	0.900488	+	0.434880i	$0.143209\pi$
$450$	2.31793	−	16.7902i	0.109268	−	0.791500i
$451$	−2.24435	−	0.351010i	−0.105682	−	0.0165284i
$452$	−0.305950	+	0.212758i	−0.0143907	+	0.0100073i
$453$	−1.02646	−	6.59421i	−0.0482273	−	0.309823i
$454$	2.95153	+	5.97294i	0.138522	+	0.280324i
$455$	43.3656	+	11.4697i	2.03301	+	0.537707i
$456$	−0.00578451	−	0.473742i	−0.000270884	−	0.0221850i
$457$	12.5146	+	6.48899i	0.585407	+	0.303542i	0.727278	−	0.686343i	$-0.240785\pi$
$457$	12.5146	+	6.48899i	0.585407	+	0.303542i	−0.141871	+	0.989885i	$0.545312\pi$
$458$	31.3917	+	42.1663i	1.46684	+	1.97030i
$459$	11.6382	−	20.9851i	0.543224	−	0.979501i
$460$	14.6187	−	19.6364i	0.681602	−	0.915550i
$461$	4.40894	−	2.14333i	0.205345	−	0.0998248i	−0.331678	−	0.943393i	$-0.607615\pi$
$461$	4.40894	−	2.14333i	0.205345	−	0.0998248i	0.537023	+	0.843568i	$0.319549\pi$
$462$	−42.8137	+	4.69273i	−1.99187	+	0.218325i
$463$	−30.6972	+	6.44197i	−1.42662	+	0.299384i	−0.853930	−	0.520389i	$-0.825787\pi$
$463$	−30.6972	+	6.44197i	−1.42662	+	0.299384i	−0.572689	+	0.819773i	$0.694100\pi$
$464$	−23.2719	+	13.2362i	−1.08037	+	0.614474i
$465$	8.20430	−	12.4545i	0.380465	−	0.577565i
$466$	3.91038	+	19.2520i	0.181145	+	0.891830i
$467$	10.2362	−	0.795621i	0.473675	−	0.0368169i	0.161563	−	0.986862i	$-0.448346\pi$
$467$	10.2362	−	0.795621i	0.473675	−	0.0368169i	0.312112	+	0.950045i	$0.398964\pi$
$468$	−12.0689	+	14.1545i	−0.557886	+	0.654293i
$469$	2.31200	+	23.7695i	0.106758	+	1.09757i
$470$	3.87105	−	5.96934i	0.178558	−	0.275345i
$471$	14.1924	−	17.8042i	0.653953	−	0.820375i
$472$	6.43019	−	0.835981i	0.295973	−	0.0384792i
$473$	−22.5305	−	2.33861i	−1.03596	−	0.107529i
$474$	−22.1305	+	23.7286i	−1.01649	+	1.08989i
$475$	−0.00449303	−	0.695055i	−0.000206154	−	0.0318913i
$476$	−15.4491	+	14.0193i	−0.708108	+	0.642573i
$477$	7.78016	+	2.28668i	0.356229	+	0.104700i
$478$	−15.5594	−	29.5388i	−0.711671	−	1.35107i
$479$	11.6637	+	14.8496i	0.532930	+	0.678496i	0.975945	−	0.218018i	$-0.0699593\pi$
$479$	11.6637	+	14.8496i	0.532930	+	0.678496i	−0.443015	+	0.896514i	$0.646091\pi$
$480$	19.5741	+	25.2925i	0.893430	+	1.15444i
$481$	−12.2482	−	53.2096i	−0.558469	−	2.42615i
$482$	−2.62904	+	4.29331i	−0.119749	+	0.195555i
$483$	−12.0101	−	35.9416i	−0.546477	−	1.63540i
$484$	3.35610	+	5.99048i	0.152550	+	0.272295i
$485$	−19.3464	+	33.5089i	−0.878473	+	1.52156i
$486$	26.4517	−	10.4975i	1.19987	−	0.476177i
$487$	−1.57621	−	2.73007i	−0.0714248	−	0.123711i	0.828101	−	0.560579i	$-0.189421\pi$
$487$	−1.57621	−	2.73007i	−0.0714248	−	0.123711i	−0.899526	+	0.436867i	$0.856088\pi$
$488$	−9.11920	+	15.3336i	−0.412807	+	0.694121i
$489$	19.7104	−	2.93777i	0.891336	−	0.132851i
$490$	11.1264	+	20.4765i	0.502640	+	0.925034i
$491$	−10.9278	+	10.1771i	−0.493165	+	0.459288i	−0.888253	−	0.459355i	$-0.848080\pi$
$491$	−10.9278	+	10.1771i	−0.493165	+	0.459288i	0.395088	+	0.918643i	$0.370714\pi$
$492$	−1.27514	−	0.277173i	−0.0574879	−	0.0124959i
$493$	−25.0329	+	3.58417i	−1.12742	+	0.161423i
$494$	−1.01704	+	1.61364i	−0.0457587	+	0.0726011i
$495$	−11.5701	+	32.2928i	−0.520038	+	1.45145i
$496$	3.13254	+	14.4614i	0.140655	+	0.649336i
$497$	−18.7848	+	11.0079i	−0.842614	+	0.493773i
$498$	19.6468	−	46.2757i	0.880395	−	2.07366i
$499$	7.21387	−	9.95608i	0.322937	−	0.445695i	−0.617041	−	0.786931i	$-0.711669\pi$
$499$	7.21387	−	9.95608i	0.322937	−	0.445695i	0.939978	+	0.341236i	$0.110846\pi$
$500$	−4.38913	−	5.73920i	−0.196288	−	0.256665i
$501$	15.7036	−	9.60067i	0.701584	−	0.428926i
$502$	8.12620	+	15.9231i	0.362690	+	0.710683i
$503$	33.9997	−	24.3015i	1.51597	−	1.08355i	0.546769	−	0.837283i	$-0.315858\pi$
$503$	33.9997	−	24.3015i	1.51597	−	1.08355i	0.969202	−	0.246268i	$-0.0792042\pi$
$504$	12.3674	−	0.622309i	0.550889	−	0.0277199i
$505$	−7.66292	+	16.0256i	−0.340996	+	0.713132i
$506$	−35.4833	+	31.3726i	−1.57743	+	1.39468i
$507$	−14.3395	+	4.28175i	−0.636842	+	0.190159i
$508$	0.122458	−	18.9438i	0.00543319	−	0.840495i
$509$	−21.3848	−	23.8741i	−0.947864	−	1.05820i	−0.998230	−	0.0594690i	$-0.981059\pi$
$509$	−21.3848	−	23.8741i	−0.947864	−	1.05820i	0.0503657	−	0.998731i	$-0.483961\pi$
$510$	11.6295	+	39.8857i	0.514962	+	1.76617i
$511$	3.19179	−	44.8121i	0.141196	−	1.98237i
$512$	−19.6877	−	2.30117i	−0.870084	−	0.101698i
$513$	1.01194	−	0.581338i	0.0446783	−	0.0256667i
$514$	22.7529	−	2.65943i	1.00359	−	0.117303i
$515$	−1.04041	−	22.9771i	−0.0458459	−	1.01249i
$516$	−12.8409	−	2.10289i	−0.565291	−	0.0925744i
$517$	−3.87995	+	3.90511i	−0.170640	+	0.171747i
$518$	40.2988	−	60.4170i	1.77063	−	2.65457i
$519$	25.1017	+	21.9380i	1.10184	+	0.962971i
$520$	1.35297	+	16.0623i	0.0593316	+	0.704377i
$521$	3.22139	+	8.34360i	0.141132	+	0.365540i	0.985370	−	0.170428i	$-0.0545149\pi$
$521$	3.22139	+	8.34360i	0.141132	+	0.365540i	−0.844239	+	0.535967i	$0.819947\pi$
$522$	−25.6547	−	15.5331i	−1.12288	−	0.679864i
$523$	−13.2068	−	38.5984i	−0.577495	−	1.68779i	−0.716574	−	0.697511i	$-0.754291\pi$
$523$	−13.2068	−	38.5984i	−0.577495	−	1.68779i	0.139080	−	0.990281i	$-0.455586\pi$
$524$	22.7131	−	1.47027i	0.992228	−	0.0642289i
$525$	18.1490	−	0.808718i	0.792086	−	0.0352953i
$526$	4.71516	+	24.8574i	0.205591	+	1.08383i
$527$	−2.24882	+	13.7942i	−0.0979601	+	0.600885i
$528$	−14.8577	−	30.6190i	−0.646599	−	1.33252i
$529$	−15.0495	−	11.0535i	−0.654328	−	0.480586i
$530$	−12.2929	+	6.78296i	−0.533971	+	0.294633i
$531$	9.51972	+	12.8256i	0.413120	+	0.556586i
$532$	−0.995576	+	0.195525i	−0.0431637	+	0.00847708i
$533$	−1.85326	−	1.86528i	−0.0802737	−	0.0807943i
$534$	2.68592	+	3.76353i	0.116231	+	0.162864i
$535$	−2.79165	+	11.4486i	−0.120694	+	0.494966i
$536$	−7.76599	+	3.65195i	−0.335440	+	0.157740i
$537$	−3.46134	+	33.1153i	−0.149368	+	1.42903i
$538$	2.00116	−	2.61670i	0.0862760	−	0.112814i
$539$	−5.17147	−	17.2739i	−0.222751	−	0.744040i
$540$	−7.72673	+	18.1269i	−0.332506	+	0.780058i
$541$	−7.21612	+	24.1035i	−0.310245	+	1.03629i	0.650649	+	0.759378i	$0.274497\pi$
$541$	−7.21612	+	24.1035i	−0.310245	+	1.03629i	−0.960895	+	0.276914i	$0.910688\pi$
$542$	−19.6895	−	27.1741i	−0.845737	−	1.16723i
$543$	−0.181073	−	0.194709i	−0.00777059	−	0.00835578i
$544$	−26.4267	−	14.1391i	−1.13304	−	0.606209i
$545$	−1.33266	+	3.58910i	−0.0570850	+	0.153740i
$546$	−43.1567	−	24.9579i	−1.84693	−	1.06810i
$547$	−15.4156	+	0.398686i	−0.659124	+	0.0170466i	−0.353970	−	0.935257i	$-0.615169\pi$
$547$	−15.4156	+	0.398686i	−0.659124	+	0.0170466i	−0.305153	+	0.952303i	$0.598708\pi$
$548$	−27.2799	−	7.59389i	−1.16534	−	0.324395i
$549$	−43.9292	−	1.19931i	−1.87485	−	0.0511853i
$550$	−9.79512	−	20.4848i	−0.417665	−	0.873473i
$551$	−1.13241	−	0.479815i	−0.0482422	−	0.0204408i
$552$	10.7151	−	8.40378i	0.456063	−	0.357689i
$553$	−29.3009	−	18.7334i	−1.24600	−	0.796623i
$554$	−35.6496	+	24.1131i	−1.51461	+	1.02447i
$555$	−29.2077	−	49.9246i	−1.23980	−	2.11918i
$556$	5.76419	+	0.978006i	0.244456	+	0.0414767i
$557$	−21.2427	+	8.67861i	−0.900084	+	0.367725i	−0.780541	−	0.625104i	$-0.785056\pi$
$557$	−21.2427	+	8.67861i	−0.900084	+	0.367725i	−0.119543	+	0.992829i	$0.538143\pi$
$558$	−12.4335	+	10.9613i	−0.526352	+	0.464027i
$559$	−19.4165	−	17.6196i	−0.821231	−	0.745228i
$560$	−31.4554	+	35.1170i	−1.32923	+	1.48396i
$561$	−2.46806	−	32.0514i	−0.104202	−	1.35321i
$562$	−13.0578	+	25.5866i	−0.550812	+	1.07930i
$563$	1.11039	+	7.41341i	0.0467974	+	0.312438i	0.999951	+	0.00994958i	$0.00316710\pi$
$563$	1.11039	+	7.41341i	0.0467974	+	0.312438i	−0.953153	+	0.302488i	$0.902183\pi$
$564$	−2.35698	+	2.10817i	−0.0992467	+	0.0887701i
$565$	−0.750936	+	0.262375i	−0.0315921	+	0.0110382i
$566$	−13.1873	+	11.0654i	−0.554303	+	0.465115i
$567$	16.1900	+	25.8516i	0.679914	+	1.08566i
$568$	−5.99345	−	5.02910i	−0.251480	−	0.211016i
$569$	−19.5542	−	7.40479i	−0.819753	−	0.310425i	−0.0915618	−	0.995799i	$-0.529186\pi$
$569$	−19.5542	−	7.40479i	−0.819753	−	0.310425i	−0.728191	+	0.685374i	$0.759639\pi$
$570$	−0.518057	+	1.95304i	−0.0216990	+	0.0818037i
$571$	−1.21127	+	5.96347i	−0.0506902	+	0.249563i	−0.997358	−	0.0726494i	$-0.976855\pi$
$571$	−1.21127	+	5.96347i	−0.0506902	+	0.249563i	0.946667	+	0.322213i	$0.104427\pi$
$572$	−3.05285	+	24.7313i	−0.127646	+	1.03407i
$573$	−15.6644	+	6.03494i	−0.654389	+	0.252113i
$574$	0.113017	−	3.49551i	0.00471725	−	0.145900i
$575$	15.7904	−	12.2385i	0.658506	−	0.510381i
$576$	−2.37737	−	5.73657i	−0.0990570	−	0.239024i
$577$	−6.49732	−	10.3087i	−0.270487	−	0.429157i	0.683078	−	0.730346i	$-0.260641\pi$
$577$	−6.49732	−	10.3087i	−0.270487	−	0.429157i	−0.953564	+	0.301189i	$0.902616\pi$
$578$	−5.11639	−	6.01804i	−0.212814	−	0.250317i
$579$	−45.4155	−	5.04399i	−1.88741	−	0.209621i
$580$	20.1425	−	5.04975i	0.836371	−	0.209680i
$581$	52.5886	+	11.7478i	2.18174	+	0.487381i
$582$	30.5276	−	30.2873i	1.26541	−	1.25545i
$583$	10.3867	−	3.18287i	0.430173	−	0.131821i
$584$	15.5525	−	4.32935i	0.643569	−	0.179150i
$585$	−32.9207	+	22.1984i	−1.36110	+	0.917790i
$586$	0.661834	−	6.80425i	0.0273401	−	0.281081i
$587$	35.5283	+	28.2792i	1.46641	+	1.16721i	0.950565	+	0.310525i	$0.100505\pi$
$587$	35.5283	+	28.2792i	1.46641	+	1.16721i	0.515844	+	0.856683i	$0.327479\pi$
$588$	−2.38147	−	10.0805i	−0.0982102	−	0.415713i
$589$	−0.440276	+	0.517865i	−0.0181413	+	0.0213382i
$590$	−27.3753	−	3.91955i	−1.12702	−	0.161365i
$591$	−10.9517	−	4.07541i	−0.450493	−	0.167640i
$592$	55.6637	+	13.9550i	2.28776	+	0.573546i
$593$	−22.6670	−	11.3838i	−0.930821	−	0.467476i	−0.0822824	−	0.996609i	$-0.526221\pi$
$593$	−22.6670	−	11.3838i	−0.930821	−	0.467476i	−0.848539	+	0.529133i	$0.822517\pi$
$594$	21.8335	−	31.2530i	0.895840	−	1.28233i
$595$	−39.7942	+	19.9854i	−1.63140	+	0.819321i
$596$	4.40594	−	0.984247i	0.180474	−	0.0403163i
$597$	−37.9018	−	1.74350i	−1.55122	−	0.0713567i
$598$	−54.5990	+	4.95467i	−2.23272	+	0.202611i
$599$	−1.30511	−	11.8285i	−0.0533254	−	0.483301i	−0.990809	−	0.135271i	$-0.956809\pi$
$599$	−1.30511	−	11.8285i	−0.0533254	−	0.483301i	0.937483	−	0.348030i	$-0.113149\pi$
$600$	2.46464	+	6.04513i	0.100618	+	0.246791i
$601$	−6.52681	−	0.592285i	−0.266234	−	0.0241598i	−0.0435530	−	0.999051i	$-0.513868\pi$
$601$	−6.52681	−	0.592285i	−0.266234	−	0.0241598i	−0.222681	+	0.974891i	$0.571481\pi$
$602$	−0.676246	−	34.8671i	−0.0275617	−	1.42108i
$603$	−17.1802	−	12.3170i	−0.699631	−	0.501587i
$604$	−3.22421	−	3.99739i	−0.131191	−	0.162652i
$605$	3.47227	+	14.2398i	0.141168	+	0.578931i
$606$	12.8953	−	14.9489i	0.523836	−	0.607257i
$607$	−12.7211	+	22.7066i	−0.516334	+	0.921631i	0.482617	+	0.875832i	$0.339686\pi$
$607$	−12.7211	+	22.7066i	−0.516334	+	0.921631i	−0.998951	+	0.0457993i	$0.985417\pi$
$608$	−0.745075	−	1.25282i	−0.0302168	−	0.0508085i
$609$	11.4054	−	30.0535i	0.462170	−	1.21783i
$610$	55.0044	−	52.5702i	2.22706	−	2.12850i
$611$	−6.29540	+	0.984583i	−0.254685	+	0.0398320i
$612$	−0.331544	−	18.4632i	−0.0134019	−	0.746330i
$613$	−14.8578	+	8.96670i	−0.600099	+	0.362162i	−0.783979	−	0.620787i	$-0.786813\pi$
$613$	−14.8578	+	8.96670i	−0.600099	+	0.362162i	0.183880	+	0.982949i	$0.441134\pi$
$614$	−7.97730	+	11.3148i	−0.321938	+	0.456626i
$615$	−2.46351	−	1.29990i	−0.0993383	−	0.0524171i
$616$	13.3700	−	9.81993i	0.538694	−	0.395656i
$617$	−0.144413	+	0.312327i	−0.00581386	+	0.0125738i	−0.910554	−	0.413390i	$-0.864345\pi$
$617$	−0.144413	+	0.312327i	−0.00581386	+	0.0125738i	0.904740	+	0.425964i	$0.140065\pi$
$618$	−5.59107	+	24.9440i	−0.224906	+	1.00339i
$619$	21.9297	+	23.8546i	0.881430	+	0.958796i	0.999414	−	0.0342191i	$-0.0108944\pi$
$619$	21.9297	+	23.8546i	0.881430	+	0.958796i	−0.117985	+	0.993015i	$0.537643\pi$
$620$	0.667323	−	11.4575i	0.0268003	−	0.460144i
$621$	30.9414	+	12.9533i	1.24164	+	0.519799i
$622$	0.475788	+	8.16897i	0.0190774	+	0.327546i
$623$	−3.44719	+	3.56044i	−0.138109	+	0.142646i
$624$	7.11914	−	38.7451i	0.284994	−	1.55105i
$625$	−11.4998	−	28.6764i	−0.459994	−	1.14705i
$626$	1.81319	+	5.08371i	0.0724697	+	0.203186i
$627$	0.702660	−	1.39661i	0.0280615	−	0.0557751i
$628$	2.59544	−	17.3282i	0.103569	−	0.691470i
$629$	44.0980	+	31.5194i	1.75830	+	1.25676i
$630$	−51.5247	−	11.5879i	−2.05279	−	0.461674i
$631$	29.5060	+	28.9393i	1.17462	+	1.15206i	0.985424	+	0.170116i	$0.0544141\pi$
$631$	29.5060	+	28.9393i	1.17462	+	1.15206i	0.189192	+	0.981940i	$0.439413\pi$
$632$	2.80339	−	12.1787i	0.111513	−	0.484444i
$633$	−28.7471	+	13.2670i	−1.14259	+	0.527315i
$634$	10.5227	+	33.5627i	0.417909	+	1.33295i
$635$	11.0958	−	38.8854i	0.440325	−	1.54312i
$636$	6.06382	−	1.47400i	0.240446	−	0.0584478i
$637$	7.01152	−	19.6584i	0.277806	−	0.778896i
$638$	−40.1464	+	1.55786i	−1.58941	+	0.0616764i
$639$	3.61890	−	18.9295i	0.143162	−	0.748839i
$640$	−24.2340	−	9.90069i	−0.957935	−	0.391359i
$641$	14.4563	+	8.98142i	0.570990	+	0.354745i	0.782519	−	0.622627i	$-0.213935\pi$
$641$	14.4563	+	8.98142i	0.570990	+	0.354745i	−0.211528	+	0.977372i	$0.567844\pi$
$642$	6.33544	−	11.4624i	0.250040	−	0.452385i
$643$	4.21622	−	1.78646i	0.166272	−	0.0704513i	−0.305407	−	0.952222i	$-0.598792\pi$
$643$	4.21622	−	1.78646i	0.166272	−	0.0704513i	0.471678	+	0.881771i	$0.343648\pi$
$644$	−21.8472	−	19.3162i	−0.860899	−	0.761164i
$645$	−25.2020	−	11.6749i	−0.992330	−	0.459698i
$646$	−0.304675	−	1.86887i	−0.0119873	−	0.0735298i
$647$	−7.55667	+	2.75040i	−0.297083	+	0.108129i	−0.486262	−	0.873813i	$-0.661640\pi$
$647$	−7.55667	+	2.75040i	−0.297083	+	0.108129i	0.189178	+	0.981943i	$0.439418\pi$
$648$	−6.79538	+	8.60047i	−0.266948	+	0.337858i
$649$	20.1070	+	7.31834i	0.789268	+	0.287270i
$650$	4.89813	−	25.8220i	0.192121	−	1.01282i
$651$	−13.9635	−	10.9840i	−0.547273	−	0.430497i
$652$	11.9986	−	9.55047i	0.469903	−	0.374025i
$653$	−12.8443	−	19.8065i	−0.502636	−	0.775088i	0.492838	−	0.870121i	$-0.335960\pi$
$653$	−12.8443	−	19.8065i	−0.502636	−	0.775088i	−0.995474	+	0.0950329i	$0.969704\pi$
$654$	2.47675	−	3.45990i	0.0968485	−	0.135293i
$655$	47.5484	+	9.97829i	1.85787	+	0.389884i
$656$	2.63158	−	0.843782i	0.102746	−	0.0329442i
$657$	27.9876	+	28.2502i	1.09190	+	1.10215i
$658$	−6.69870	−	5.19189i	−0.261143	−	0.202401i
$659$	−29.9310	+	36.1423i	−1.16595	+	1.40790i	−0.270509	+	0.962717i	$0.587192\pi$
$659$	−29.9310	+	36.1423i	−1.16595	+	1.40790i	−0.895438	+	0.445187i	$0.853137\pi$
$660$	4.73317	+	25.9697i	0.184238	+	1.01087i
$661$	35.7510	+	17.3797i	1.39055	+	0.675994i	0.972602	−	0.232476i	$-0.0746828\pi$
$661$	35.7510	+	17.3797i	1.39055	+	0.675994i	0.417950	+	0.908470i	$0.362749\pi$
$662$	3.66534	−	1.90053i	0.142457	−	0.0738663i
$663$	19.6590	−	31.5921i	0.763494	−	1.22694i
$664$	2.37222	+	19.2175i	0.0920600	+	0.745783i
$665$	−2.15920	−	0.167827i	−0.0837303	−	0.00650803i
$666$	16.7493	+	62.0636i	0.649024	+	2.40492i
$667$	−8.81756	−	34.2319i	−0.341417	−	1.32546i
$668$	6.76253	−	12.4454i	0.261650	−	0.481529i
$669$	−8.19166	+	1.43834i	−0.316708	+	0.0556095i
$670$	36.0842	−	6.12238i	1.39405	−	0.236528i
$671$	−50.0060	+	31.0677i	−1.93046	+	1.19936i
$672$	31.9800	−	20.7060i	1.23365	−	0.798752i
$673$	−14.9048	+	33.3605i	−0.574536	+	1.28595i	0.360949	+	0.932586i	$0.382453\pi$
$673$	−14.9048	+	33.3605i	−0.574536	+	1.28595i	−0.935485	+	0.353367i	$0.885037\pi$
$674$	29.4916	+	31.2593i	1.13598	+	1.20406i
$675$	−10.0417	+	12.5601i	−0.386505	+	0.483438i
$676$	−7.90298	+	8.37666i	−0.303961	+	0.322179i
$677$	−3.93637	−	9.45996i	−0.151287	−	0.363576i	0.829543	−	0.558443i	$-0.188601\pi$
$677$	−3.93637	−	9.45996i	−0.151287	−	0.363576i	−0.980830	+	0.194867i	$0.937572\pi$
$678$	0.881875	−	0.0621755i	0.0338682	−	0.00238784i
$679$	37.8415	+	26.3150i	1.45222	+	1.00988i
$680$	−11.5682	−	11.0563i	−0.443621	−	0.423988i
$681$	0.494353	−	6.30157i	0.0189437	−	0.241477i
$682$	−5.81634	+	21.4296i	−0.222719	+	0.820582i
$683$	7.40273	−	21.6353i	0.283258	−	0.827851i	−0.709172	−	0.705036i	$-0.750931\pi$
$683$	7.40273	−	21.6353i	0.283258	−	0.827851i	0.992429	−	0.122816i	$-0.0391924\pi$
$684$	0.450160	−	0.777118i	0.0172123	−	0.0297138i
$685$	−51.7508	−	31.2318i	−1.97730	−	1.19330i
$686$	−14.2391	+	6.25164i	−0.543653	+	0.238689i
$687$	−5.11348	−	49.6113i	−0.195091	−	1.89279i
$688$	25.7708	−	9.75893i	0.982503	−	0.372056i
$689$	11.8707	+	4.14760i	0.452239	+	0.158011i
$690$	−53.6354	+	22.2729i	−2.04187	+	0.847916i
$691$	20.3451	+	30.5020i	0.773966	+	1.16035i	0.983208	+	0.182486i	$0.0584145\pi$
$691$	20.3451	+	30.5020i	0.773966	+	1.16035i	−0.209243	+	0.977864i	$0.567100\pi$
$692$	25.1735	+	4.94392i	0.956953	+	0.187940i
$693$	37.1755	+	16.9628i	1.41218	+	0.644365i
$694$	30.0010	−	37.1954i	1.13882	−	1.41192i
$695$	11.2935	+	5.31075i	0.428387	+	0.201448i
$696$	11.5488	+	0.232293i	0.437758	+	0.00880505i
$697$	2.60486	+	0.168618i	0.0986661	+	0.00638686i
$698$	−11.1215	−	40.9759i	−0.420956	−	1.55096i
$699$	6.16033	−	17.5907i	0.233005	−	0.665342i
$700$	11.7787	−	7.53062i	0.445192	−	0.284631i
$701$	1.96298	−	4.55070i	0.0741408	−	0.171878i	−0.877115	−	0.480280i	$-0.840535\pi$
$701$	1.96298	−	4.55070i	0.0741408	−	0.171878i	0.951256	+	0.308402i	$0.0997943\pi$
$702$	41.7831	−	14.1959i	1.57700	−	0.535791i
$703$	1.04414	+	2.42058i	0.0393804	+	0.0912940i
$704$	−6.89051	−	4.66068i	−0.259696	−	0.175656i
$705$	−6.05362	+	2.98599i	−0.227992	+	0.112459i
$706$	1.00793	−	3.07503i	0.0379341	−	0.115730i
$707$	18.2566	+	10.6984i	0.686612	+	0.402356i
$708$	11.2828	+	4.87654i	0.424033	+	0.183272i
$709$	−4.83579	−	1.61977i	−0.181612	−	0.0608318i	0.225345	−	0.974279i	$-0.427649\pi$
$709$	−4.83579	−	1.61977i	−0.181612	−	0.0608318i	−0.406957	+	0.913447i	$0.633410\pi$
$710$	18.8729	+	27.5174i	0.708288	+	1.03271i
$711$	29.5595	−	8.59563i	1.10857	−	0.322361i
$712$	−1.62122	−	0.736934i	−0.0607577	−	0.0276178i
$713$	−19.5108	−	1.00987i	−0.730685	−	0.0378200i
$714$	48.5081	−	9.81646i	1.81537	−	0.367372i
$715$	−20.4348	+	49.1093i	−0.764218	+	1.83658i
$716$	10.4518	+	23.3938i	0.390604	+	0.874267i
$717$	−1.66003	+	31.6315i	−0.0619949	+	1.18130i
$718$	−33.1986	−	18.8821i	−1.23896	−	0.704675i
$719$	45.5310	+	14.5989i	1.69802	+	0.544448i	0.987278	−	0.159006i	$-0.0508290\pi$
$719$	45.5310	+	14.5989i	1.69802	+	0.544448i	0.710741	+	0.703454i	$0.248360\pi$
$720$	−5.05297	−	41.4240i	−0.188313	−	1.54378i
$721$	−27.3785	−	1.06241i	−1.01963	−	0.0395662i
$722$	−12.8764	+	32.1090i	−0.479210	+	1.19497i
$723$	4.22748	−	2.22292i	0.157222	−	0.0826714i
$724$	−0.195636	−	0.0599504i	−0.00727077	−	0.00222804i
$725$	16.9408	+	0.438132i	0.629167	+	0.0162718i
$726$	0.432858	−	16.2840i	0.0160649	−	0.604357i
$727$	24.8286	+	0.321011i	0.920841	+	0.0119056i	0.471897	−	0.881654i	$-0.343570\pi$
$727$	24.8286	+	0.321011i	0.920841	+	0.0119056i	0.448945	+	0.893560i	$0.351800\pi$
$728$	19.2016			0.711658
$729$	−26.6575	−	4.28700i	−0.987314	−	0.158778i
$730$	−68.8508			−2.54828
$731$	26.0265	+	0.336499i	0.962627	+	0.0124459i
$732$	−29.7262	+	16.1248i	−1.09871	+	0.595989i
$733$	40.8012	+	1.05522i	1.50702	+	0.0389754i	0.770502	−	0.637437i	$-0.220006\pi$
$733$	40.8012	+	1.05522i	1.50702	+	0.0389754i	0.736523	+	0.676413i	$0.236466\pi$
$734$	4.54586	+	1.39302i	0.167791	+	0.0514174i
$735$	0.873193	−	22.0925i	0.0322082	−	0.814895i
$736$	15.5939	−	38.8855i	0.574800	−	1.43334i
$737$	−28.2976	−	1.09808i	−1.04235	−	0.0404481i
$738$	2.26239	+	2.11307i	0.0832799	+	0.0777830i
$739$	29.5572	+	9.47712i	1.08728	+	0.348622i	0.794317	−	0.607503i	$-0.207829\pi$
$739$	29.5572	+	9.47712i	1.08728	+	0.348622i	0.292960	+	0.956125i	$0.405360\pi$
$740$	−38.6906	−	22.0058i	−1.42229	−	0.808949i
$741$	1.61247	−	0.821446i	0.0592354	−	0.0301766i
$742$	6.82241	+	15.2702i	0.250459	+	0.560588i
$743$	−9.52193	+	22.8833i	−0.349326	+	0.839507i	0.647660	+	0.761929i	$0.275748\pi$
$743$	−9.52193	+	22.8833i	−0.349326	+	0.839507i	−0.996986	+	0.0775782i	$0.975281\pi$
$744$	2.03202	−	6.05211i	0.0744975	−	0.221881i
$745$	9.62368	+	0.498118i	0.352584	+	0.0182496i
$746$	−44.8168	−	20.3717i	−1.64086	−	0.745862i
$747$	−38.4827	+	28.1795i	−1.40801	+	1.03103i
$748$	−13.9919	−	20.4008i	−0.511596	−	0.745925i
$749$	13.3106	+	4.45846i	0.486360	+	0.162909i
$750$	1.97766	+	17.0261i	0.0722140	+	0.621705i
$751$	−20.6984	−	12.1293i	−0.755296	−	0.442605i	0.0769331	−	0.997036i	$-0.475487\pi$
$751$	−20.6984	−	12.1293i	−0.755296	−	0.442605i	−0.832229	+	0.554431i	$0.812936\pi$
$752$	2.08594	−	6.36382i	0.0760663	−	0.232064i
$753$	1.10776	−	16.9244i	0.0403691	−	0.616758i
$754$	−38.5203	−	26.0548i	−1.40283	−	0.948860i
$755$	−4.34195	−	10.0658i	−0.158020	−	0.366331i
$756$	20.7445	+	10.9843i	0.754470	+	0.399494i
$757$	−1.36550	+	3.16558i	−0.0496299	+	0.115055i	−0.941227	−	0.337774i	$-0.890326\pi$
$757$	−1.36550	+	3.16558i	−0.0496299	+	0.115055i	0.891597	+	0.452829i	$0.149585\pi$
$758$	13.0881	−	8.36778i	0.475380	−	0.303931i
$759$	44.1548	−	8.34278i	1.60272	−	0.302824i
$760$	−0.203853	−	0.751070i	−0.00739452	−	0.0272442i
$761$	27.7673	+	1.79744i	1.00657	+	0.0651570i	0.559063	−	0.829125i	$-0.311161\pi$
$761$	27.7673	+	1.79744i	1.00657	+	0.0651570i	0.447503	+	0.894282i	$0.352313\pi$
$762$	−23.2492	+	38.4613i	−0.842231	+	1.39331i
$763$	4.12711	+	1.94077i	0.149411	+	0.0702604i
$764$	−8.11012	+	10.0550i	−0.293414	+	0.363776i
$765$	9.88712	−	38.1570i	0.357470	−	1.37957i
$766$	29.4758	+	5.78887i	1.06501	+	0.209160i
$767$	13.7435	+	20.6046i	0.496248	+	0.743988i
$768$	28.7908	+	22.0509i	1.03890	+	0.795694i
$769$	−33.4954	−	11.7032i	−1.20787	−	0.422028i	−0.350422	−	0.936592i	$-0.613962\pi$
$769$	−33.4954	−	11.7032i	−1.20787	−	0.422028i	−0.857452	+	0.514564i	$0.827954\pi$
$770$	−66.1634	+	25.0548i	−2.38436	+	0.902914i
$771$	−19.8369	−	8.87981i	−0.714408	−	0.319799i
$772$	−32.1975	+	14.1362i	−1.15881	+	0.508773i
$773$	−33.6460	−	20.3054i	−1.21016	−	0.730336i	−0.239525	−	0.970890i	$-0.576992\pi$
$773$	−33.6460	−	20.3054i	−1.21016	−	0.730336i	−0.970636	+	0.240554i	$0.922671\pi$
$774$	23.6184	+	19.8762i	0.848947	+	0.714434i
$775$	3.03210	−	8.86165i	0.108916	−	0.318320i
$776$	−4.33850	+	15.9847i	−0.155743	+	0.573816i
$777$	−62.1821	+	29.6785i	−2.23077	+	1.06471i
$778$	−16.4357	−	15.7083i	−0.589248	−	0.563170i
$779$	0.104226	+	0.0724791i	0.00373429	+	0.00259683i
$780$	−13.3787	+	27.4705i	−0.479036	+	0.983602i
$781$	−9.91861	−	23.8366i	−0.354916	−	0.852941i
$782$	37.3487	−	39.5873i	1.33559	−	1.41564i
$783$	13.3689	+	25.1173i	0.477767	+	0.897618i
$784$	15.0534	+	15.9557i	0.537623	+	0.569847i
$785$	15.2564	−	34.1476i	0.544524	−	1.21878i
$786$	−48.0774	−	24.5794i	−1.71487	−	0.876719i
$787$	39.2312	−	24.3735i	1.39844	−	0.868823i	0.399587	−	0.916695i	$-0.369153\pi$
$787$	39.2312	−	24.3735i	1.39844	−	0.868823i	0.998853	+	0.0478722i	$0.0152440\pi$
$788$	−8.86570	+	1.50424i	−0.315827	+	0.0535862i
$789$	8.22602	−	22.5504i	0.292854	−	0.802814i
$790$	−25.4470	+	46.8314i	−0.905362	+	1.66619i
$791$	0.236362	+	0.917614i	0.00840407	+	0.0326266i
$792$	−1.25353	+	14.6302i	−0.0445422	+	0.519863i
$793$	−67.9386	−	5.28060i	−2.41257	−	0.187520i
$794$	6.76536	+	54.8065i	0.240094	+	1.94501i
$795$	13.3132	+	0.440025i	0.472172	+	0.0156061i
$796$	−25.9206	+	13.4402i	−0.918731	+	0.476376i
$797$	41.3723	+	20.1124i	1.46548	+	0.712419i	0.986249	−	0.165269i	$-0.0528491\pi$
$797$	41.3723	+	20.1124i	1.46548	+	0.712419i	0.479233	+	0.877688i	$0.340915\pi$
$798$	2.26650	+	0.810223i	0.0802334	+	0.0286816i
$799$	4.03462	−	4.87189i	0.142735	−	0.172355i
$800$	15.8750	+	12.3040i	0.561265	+	0.435013i
$801$	−0.361916	−	4.37174i	−0.0127877	−	0.154468i
$802$	−31.2796	+	10.0294i	−1.10452	+	0.354150i
$803$	52.1371	+	10.9413i	1.83988	+	0.386109i
$804$	−16.1900	−	1.58651i	−0.570976	−	0.0559519i
$805$	−33.8688	−	52.2273i	−1.19372	−	1.84077i
$806$	−20.1096	+	16.0065i	−0.708330	+	0.563805i
$807$	−2.90164	+	1.16120i	−0.102143	+	0.0408762i
$808$	−1.41711	+	7.47070i	−0.0498536	+	0.262818i
$809$	−46.6780	−	16.9894i	−1.64111	−	0.597315i	−0.653877	−	0.756601i	$-0.726859\pi$
$809$	−46.6780	−	16.9894i	−1.64111	−	0.597315i	−0.987233	+	0.159286i	$0.949081\pi$
$810$	37.7560	−	27.5640i	1.32661	−	0.968501i
$811$	47.6562	−	17.3454i	1.67344	−	0.609081i	0.681048	−	0.732239i	$-0.261524\pi$
$811$	47.6562	−	17.3454i	1.67344	−	0.609081i	0.992387	+	0.123158i	$0.0393022\pi$
$812$	−3.98021	−	24.4145i	−0.139678	−	0.856782i
$813$	2.85454	+	31.7094i	0.100113	+	1.11210i
$814$	64.5164	+	57.0421i	2.26130	+	1.99933i
$815$	30.1407	−	12.7710i	1.05578	−	0.447348i
$816$	20.1827	+	33.4970i	0.706537	+	1.17263i
$817$	1.07526	+	0.668038i	0.0376186	+	0.0233717i
$818$	62.5427	+	25.5515i	2.18675	+	0.893387i
$819$	23.0584	+	41.2973i	0.805726	+	1.44304i
$820$	−2.14189	+	0.0831152i	−0.0747981	+	0.00290251i
$821$	12.7618	−	35.7808i	0.445390	−	1.24876i	−0.482497	−	0.875898i	$-0.660270\pi$
$821$	12.7618	−	35.7808i	0.445390	−	1.24876i	0.927888	−	0.372860i	$-0.121623\pi$
$822$	46.3804	+	48.5979i	1.61770	+	1.69505i
$823$	−4.43944	+	15.5581i	−0.154749	+	0.542320i	0.845220	+	0.534419i	$0.179470\pi$
$823$	−4.43944	+	15.5581i	−0.154749	+	0.542320i	−0.999969	+	0.00790066i	$0.997485\pi$
$824$	−2.94550	−	9.39485i	−0.102611	−	0.327285i
$825$	−1.96231	+	21.4528i	−0.0683190	+	0.746892i
$826$	−7.38975	+	32.1032i	−0.257122	+	1.11701i
$827$	−3.58029	−	3.51153i	−0.124499	−	0.122108i	0.635301	−	0.772265i	$-0.280876\pi$
$827$	−3.58029	−	3.51153i	−0.124499	−	0.122108i	−0.759800	+	0.650157i	$0.774703\pi$
$828$	25.6024	−	3.29112i	0.889745	−	0.114374i
$829$	−2.87182	−	2.05265i	−0.0997423	−	0.0712915i	0.530527	−	0.847668i	$-0.321994\pi$
$829$	−2.87182	−	2.05265i	−0.0997423	−	0.0712915i	−0.630270	+	0.776376i	$0.717056\pi$
$830$	12.2327	−	81.6702i	0.424603	−	2.83481i
$831$	40.7655	−	2.34493i	1.41414	−	0.0813446i
$832$	−3.23473	−	9.06934i	−0.112144	−	0.314423i
$833$	7.71205	+	19.2310i	0.267207	+	0.666315i
$834$	−10.5608	−	8.99161i	−0.365690	−	0.311354i
$835$	21.0305	−	21.7214i	0.727789	−	0.751701i
$836$	−0.0699544	−	1.20107i	−0.00241942	−	0.0415399i
$837$	15.4566	−	2.89742i	0.534257	−	0.100149i
$838$	2.94142	−	50.5023i	0.101610	−	1.74457i
$839$	−32.2375	−	35.0672i	−1.11296	−	1.21065i	−0.975466	−	0.220150i	$-0.929345\pi$
$839$	−32.2375	−	35.0672i	−1.11296	−	1.21065i	−0.137497	−	0.990502i	$-0.543906\pi$
$840$	19.4137	−	6.07131i	0.669835	−	0.209480i
$841$	0.413557	−	0.894412i	0.0142606	−	0.0308418i
$842$	9.18804	−	6.74837i	0.316641	−	0.232564i
$843$	23.0666	−	14.5152i	0.794457	−	0.499930i
$844$	−14.0392	+	19.9128i	−0.483250	+	0.685427i
$845$	−21.0465	+	12.7017i	−0.724023	+	0.436950i
$846$	7.36337	−	1.43513i	0.253158	−	0.0493408i
$847$	17.2502	−	2.69788i	0.592723	−	0.0927002i
$848$	−9.55404	+	9.13123i	−0.328087	+	0.313568i
$849$	16.1215	−	2.61634i	0.553290	−	0.0897926i
$850$	13.3367	+	22.4253i	0.457446	+	0.769181i
$851$	−37.0335	+	66.1030i	−1.26949	+	2.26598i
$852$	−4.88179	−	14.0044i	−0.167247	−	0.479781i
$853$	6.12990	+	25.1388i	0.209884	+	0.860736i	0.975954	+	0.217978i	$0.0699463\pi$
$853$	6.12990	+	25.1388i	0.209884	+	0.860736i	−0.766070	+	0.642757i	$0.777790\pi$
$854$	−56.9024	−	70.5479i	−1.94716	−	2.41410i
$855$	1.37054	−	1.34036i	0.0468716	−	0.0458394i
$856$	0.0978162	+	5.04338i	0.00334329	+	0.172379i
$857$	19.3967	+	1.76018i	0.662578	+	0.0601266i	0.416517	−	0.909128i	$-0.363251\pi$
$857$	19.3967	+	1.76018i	0.662578	+	0.0601266i	0.246061	+	0.969254i	$0.420864\pi$
$858$	36.2484	−	46.6992i	1.23750	−	1.59429i
$859$	1.22405	+	11.0939i	0.0417640	+	0.378518i	0.996666	+	0.0815954i	$0.0260015\pi$
$859$	1.22405	+	11.0939i	0.0417640	+	0.378518i	−0.954902	+	0.296923i	$0.904040\pi$
$860$	−21.2865	+	1.93167i	−0.725863	+	0.0658695i
$861$	−1.78933	+	2.79427i	−0.0609803	+	0.0952286i
$862$	−5.86336	+	1.30982i	−0.199707	+	0.0446126i
$863$	51.8028	−	26.0163i	1.76339	−	0.885607i	0.808579	−	0.588388i	$-0.200237\pi$
$863$	51.8028	−	26.0163i	1.76339	−	0.885607i	0.954809	−	0.297219i	$-0.0960590\pi$
$864$	−4.85164	+	33.3722i	−0.165056	+	1.13535i
$865$	48.9361	+	24.5767i	1.66388	+	0.835631i
$866$	−16.8310	−	4.21957i	−0.571942	−	0.143387i
$867$	1.24830	+	7.38946i	0.0423945	+	0.250959i
$868$	−13.5336	−	1.93772i	−0.459360	−	0.0657705i
$869$	26.7117	−	31.4191i	0.906134	−	1.06582i
$870$	−47.1840	−	14.1629i	−1.59969	−	0.480168i
$871$	−25.6466	−	20.4138i	−0.869003	−	0.691695i
$872$	−0.158659	+	1.63116i	−0.00537288	+	0.0552380i
$873$	−39.5885	+	9.86444i	−1.33987	+	0.333861i
$874$	2.54995	−	0.709828i	0.0862535	−	0.0240103i
$875$	−17.5655	+	5.38274i	−0.593823	+	0.181970i
$876$	29.5278	+	8.03712i	0.997652	+	0.271549i
$877$	−16.9100	−	3.77753i	−0.571009	−	0.127558i	−0.0770249	−	0.997029i	$-0.524542\pi$
$877$	−16.9100	−	3.77753i	−0.571009	−	0.127558i	−0.493984	+	0.869471i	$0.664460\pi$
$878$	64.8477	−	16.2574i	2.18850	−	0.548661i
$879$	−3.84320	+	5.22472i	−0.129628	+	0.176225i
$880$	−36.2108	−	42.5921i	−1.22067	−	1.43578i
$881$	13.7488	+	21.8139i	0.463208	+	0.734929i	0.993616	−	0.112813i	$-0.0359862\pi$
$881$	13.7488	+	21.8139i	0.463208	+	0.734929i	−0.530409	+	0.847742i	$0.677961\pi$
$882$	−7.38497	+	23.4367i	−0.248665	+	0.789156i
$883$	−9.70112	+	7.51894i	−0.326469	+	0.253032i	−0.762628	−	0.646837i	$-0.776091\pi$
$883$	−9.70112	+	7.51894i	−0.326469	+	0.253032i	0.436160	+	0.899869i	$0.356338\pi$
$884$	0.925323	−	28.6193i	0.0311220	−	0.962570i
$885$	20.4102	+	16.4866i	0.686080	+	0.554192i
$886$	−2.92517	+	23.6970i	−0.0982732	+	0.796116i
$887$	5.31813	−	26.1828i	0.178565	−	0.879131i	−0.786594	−	0.617470i	$-0.788158\pi$
$887$	5.31813	−	26.1828i	0.178565	−	0.879131i	0.965160	−	0.261661i	$-0.0842703\pi$
$888$	−17.5516	−	17.4636i	−0.588993	−	0.586040i
$889$	−45.0485	−	17.0590i	−1.51088	−	0.572142i
$890$	5.81811	+	4.88197i	0.195023	+	0.163644i
$891$	−32.9709	+	14.8729i	−1.10457	+	0.498260i
$892$	−4.90288	+	4.11401i	−0.164161	+	0.137747i
$893$	0.290424	−	0.101473i	0.00971867	−	0.00339567i
$894$	−10.1749	−	3.34323i	−0.340299	−	0.111814i
$895$	8.10158	+	54.0893i	0.270806	+	1.80801i
$896$	−14.1754	+	27.7765i	−0.473568	+	0.927947i
$897$	46.9088	+	22.4716i	1.56624	+	0.750306i
$898$	−13.6504	+	15.2393i	−0.455519	+	0.508543i
$899$	−12.2726	−	11.1368i	−0.409314	−	0.371432i
$900$	−1.85066	+	12.2357i	−0.0616887	+	0.407856i
$901$	−11.5559	+	4.72109i	−0.384982	+	0.157282i
$902$	4.08870	+	0.693727i	0.136139	+	0.0230986i
$903$	−16.3782	+	28.7481i	−0.545033	+	0.956678i
$904$	−0.282045	+	0.190773i	−0.00938068	+	0.00634501i
$905$	−0.367984	−	0.235269i	−0.0122322	−	0.00782060i
$906$	1.71814	+	12.0617i	0.0570812	+	0.400724i
$907$	−13.5730	−	5.75105i	−0.450685	−	0.190961i	0.152930	−	0.988237i	$-0.451129\pi$
$907$	−13.5730	−	5.75105i	−0.450685	−	0.190961i	−0.603614	+	0.797276i	$0.706273\pi$
$908$	−2.09836	−	4.38834i	−0.0696364	−	0.145632i
$909$	−17.7691	+	5.92346i	−0.589365	+	0.196469i
$910$	−78.8918	−	21.9610i	−2.61524	−	0.728001i
$911$	9.09316	−	0.235172i	0.301270	−	0.00779159i	0.125076	−	0.992147i	$-0.460082\pi$
$911$	9.09316	−	0.235172i	0.301270	−	0.00779159i	0.176193	+	0.984356i	$0.443622\pi$
$912$	−0.00136698	+	1.90196i	−4.52653e−5	+	0.0629800i
$913$	−22.2416	+	59.9006i	−0.736089	+	1.98242i
$914$	−22.6918	−	12.1408i	−0.750577	−	0.401582i
$915$	−70.3585	+	16.1424i	−2.32598	+	0.533652i
$916$	−22.5192	−	31.0794i	−0.744054	−	1.02689i
$917$	16.5987	−	55.4434i	0.548136	−	1.83090i
$918$	−21.7404	+	38.0329i	−0.717540	+	1.25527i
$919$	−7.51341	−	25.0965i	−0.247844	−	0.827858i	−0.987870	−	0.155280i	$-0.950372\pi$
$919$	−7.51341	−	25.0965i	−0.247844	−	0.827858i	0.740026	−	0.672578i	$-0.234813\pi$
$920$	13.5884	−	17.7681i	0.447997	−	0.585798i
$921$	11.9960	−	5.34921i	0.395281	−	0.176263i
$922$	−8.09895	+	3.80852i	−0.266725	+	0.125427i
$923$	7.07961	−	29.0336i	0.233028	−	0.955651i
$924$	31.3000	−	3.02177i	1.02969	−	0.0994089i
$925$	−25.6020	−	25.7680i	−0.841788	−	0.847247i
$926$	56.1887	−	11.0351i	1.84648	−	0.362636i
$927$	16.6686	−	17.6168i	0.547467	−	0.578613i
$928$	31.1161	−	17.1691i	1.02143	−	0.563604i
$929$	−4.35544	−	3.19896i	−0.142897	−	0.104954i	0.518182	−	0.855271i	$-0.326609\pi$
$929$	−4.35544	−	3.19896i	−0.142897	−	0.104954i	−0.661079	+	0.750316i	$0.729901\pi$
$930$	−15.2706	+	22.5417i	−0.500744	+	0.739171i
$931$	−0.162139	+	0.994556i	−0.00531388	+	0.0325952i
$932$	−2.67302	−	14.0916i	−0.0875575	−	0.461586i
$933$	3.57857	−	6.88945i	0.117157	−	0.225551i
$934$	−18.7046	+	1.21079i	−0.612034	+	0.0396182i
$935$	−17.0947	−	49.9610i	−0.559055	−	1.63390i
$936$	−11.1940	+	12.7898i	−0.365888	+	0.418047i
$937$	4.80704	+	12.4505i	0.157039	+	0.406741i	0.988966	−	0.148144i	$-0.0473300\pi$
$937$	4.80704	+	12.4505i	0.157039	+	0.406741i	−0.831927	+	0.554885i	$0.812762\pi$
$938$	−3.65949	−	43.4450i	−0.119487	−	1.41853i
$939$	0.990444	−	5.02406i	0.0323219	−	0.163954i
$940$	−2.88236	+	4.32132i	−0.0940124	+	0.140946i
$941$	1.39753	−	1.40659i	0.0455581	−	0.0458536i	−0.686239	−	0.727376i	$-0.740740\pi$
$941$	1.39753	−	1.40659i	0.0455581	−	0.0458536i	0.731797	+	0.681523i	$0.238682\pi$
$942$	−26.3280	+	32.1661i	−0.857813	+	1.04803i
$943$	0.165051	+	3.64511i	0.00537481	+	0.118701i
$944$	−25.8549	+	3.02201i	−0.841506	+	0.0983579i
$945$	36.3708	+	34.4626i	1.18314	+	1.12107i
$946$	41.0736	+	4.80081i	1.33542	+	0.156088i
$947$	3.83448	−	53.8353i	0.124604	−	1.74941i	−0.417117	−	0.908853i	$-0.636960\pi$
$947$	3.83448	−	53.8353i	0.124604	−	1.74941i	0.541721	−	0.840558i	$-0.317773\pi$
$948$	16.3801	−	17.1139i	0.532000	−	0.555834i
$949$	41.1422	+	45.9314i	1.33553	+	1.49100i
$950$	−0.00820255	+	1.26891i	−0.000266126	+	0.0411688i
$951$	7.71919	−	32.4658i	0.250312	−	1.05278i
$952$	−14.2807	+	12.6263i	−0.462841	+	0.409220i
$953$	2.53893	−	5.30972i	0.0822440	−	0.171999i	−0.856937	−	0.515421i	$-0.827636\pi$
$953$	2.53893	−	5.30972i	0.0822440	−	0.171999i	0.939181	+	0.343422i	$0.111586\pi$
$954$	−14.1485	−	4.35788i	−0.458073	−	0.141091i
$955$	−22.4332	+	16.0343i	−0.725922	+	0.518858i
$956$	11.0802	+	21.7113i	0.358358	+	0.702195i
$957$	33.4793	+	18.2230i	1.08223	+	0.589065i
$958$	−20.9413	−	27.3827i	−0.676583	−	0.884696i
$959$	−42.2473	+	58.3067i	−1.36423	+	1.88282i
$960$	−6.13807	−	8.14672i	−0.198105	−	0.262934i
$961$	18.8436	−	11.0424i	0.607859	−	0.356207i
$962$	21.1028	+	97.4215i	0.680382	+	3.14099i
$963$	−10.7294	+	6.26676i	−0.345751	+	0.201944i
$964$	1.95982	−	3.10947i	0.0631216	−	0.100149i
$965$	−74.3021	+	10.6385i	−2.39187	+	0.342464i
$966$	21.0757	+	65.8936i	0.678100	+	2.12009i
$967$	34.7538	−	32.3665i	1.11761	−	1.04084i	0.118756	−	0.992923i	$-0.462109\pi$
$967$	34.7538	−	32.3665i	1.11761	−	1.04084i	0.998852	−	0.0479130i	$-0.0152570\pi$
$968$	2.99555	+	5.51287i	0.0962806	+	0.177190i
$969$	−0.659079	+	1.67123i	−0.0211727	+	0.0536877i
$970$	36.1070	−	60.7128i	1.15933	−	1.94937i
$971$	10.6094	+	18.3760i	0.340471	+	0.589714i	0.984520	−	0.175271i	$-0.0560801\pi$
$971$	10.6094	+	18.3760i	0.340471	+	0.589714i	−0.644049	+	0.764984i	$0.722747\pi$
$972$	−19.4099	+	7.41394i	−0.622572	+	0.237802i
$973$	7.43319	−	12.8747i	0.238297	−	0.412743i
$974$	2.81288	+	5.02086i	0.0901305	+	0.160879i
$975$	−16.5301	+	18.6690i	−0.529386	+	0.597885i
$976$	37.4013	−	61.0777i	1.19719	−	1.95505i
$977$	7.02938	+	30.5377i	0.224890	+	0.976986i	0.955685	+	0.294390i	$0.0951164\pi$
$977$	7.02938	+	30.5377i	0.224890	+	0.976986i	−0.730795	+	0.682596i	$0.760851\pi$
$978$	−36.0500	+	4.89761i	−1.15275	+	0.156608i
$979$	−3.62994	−	4.62143i	−0.116013	−	0.147702i
$980$	−7.92944	−	15.0537i	−0.253297	−	0.480872i
$981$	−3.69870	+	1.61756i	−0.118090	+	0.0516448i
$982$	20.1885	−	18.3201i	0.644242	−	0.584618i
$983$	−0.0119583	−	1.84991i	−0.000381410	−	0.0590028i	−0.999735	−	0.0230401i	$-0.992665\pi$
$983$	−0.0119583	−	1.84991i	−0.000381410	−	0.0590028i	0.999353	−	0.0359627i	$-0.0114498\pi$
$984$	−1.16176	−	0.268303i	−0.0370357	−	0.00855318i
$985$	−19.0923	−	1.98173i	−0.608330	−	0.0631431i
$986$	45.7813	−	5.95197i	1.45797	−	0.189549i
$987$	2.93916	+	7.48435i	0.0935545	+	0.238230i
$988$	0.757709	−	1.16842i	0.0241059	−	0.0371724i
$989$	3.52241	+	36.2136i	0.112006	+	1.15152i
$990$	21.8830	−	58.6763i	0.695488	−	1.86486i
$991$	20.6215	−	1.60283i	0.655063	−	0.0509155i	0.254340	−	0.967115i	$-0.418142\pi$
$991$	20.6215	−	1.60283i	0.655063	−	0.0509155i	0.400723	+	0.916199i	$0.368759\pi$
$992$	−3.90967	−	19.2485i	−0.124132	−	0.611140i
$993$	−3.91037	−	0.230573i	−0.124092	−	0.00731701i
$994$	34.5508	−	19.6513i	1.09589	−	0.623300i
$995$	−60.9961	+	12.8004i	−1.93371	+	0.405799i
$996$	−14.7797	+	33.5977i	−0.468314	+	1.06458i
$997$	−35.1878	+	17.1060i	−1.11441	+	0.541752i	−0.900393	−	0.435078i	$-0.856721\pi$
$997$	−35.1878	+	17.1060i	−1.11441	+	0.541752i	−0.214017	+	0.976830i	$0.568655\pi$
$998$	−13.4037	+	18.0042i	−0.424285	+	0.569914i
$999$	16.4823	−	58.7199i	0.521477	−	1.85782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.k.a.4.18	✓	12960
729.547	even	243	inner	729.2.k.a.547.18	yes	12960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.k.a.4.18	✓	12960	1.1	even	1	trivial
729.2.k.a.547.18	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)

\(f(q)\)	\(=\)	\(q+(-1.82547 - 0.0236016i) q^{2} +(1.47646 + 0.905578i) q^{3} +(1.33244 + 0.0344602i) q^{4} +(2.72027 + 0.833593i) q^{5} +(-2.67385 - 1.68795i) q^{6} +(1.26149 - 3.14568i) q^{7} +(1.21698 + 0.0472244i) q^{8} +(1.35986 + 2.67410i) q^{9} +O(q^{10})\)	\(q+(-1.82547 - 0.0236016i) q^{2} +(1.47646 + 0.905578i) q^{3} +(1.33244 + 0.0344602i) q^{4} +(2.72027 + 0.833593i) q^{5} +(-2.67385 - 1.68795i) q^{6} +(1.26149 - 3.14568i) q^{7} +(1.21698 + 0.0472244i) q^{8} +(1.35986 + 2.67410i) q^{9} +(-4.94609 - 1.58590i) q^{10} +(3.49339 + 1.98691i) q^{11} +(1.93609 + 1.25751i) q^{12} +(1.89759 + 4.24727i) q^{13} +(-2.37704 + 5.71256i) q^{14} +(3.26148 + 3.69418i) q^{15} +(-4.88265 - 0.252724i) q^{16} +(-4.20414 - 1.91102i) q^{17} +(-2.41926 - 4.91357i) q^{18} +(-0.127033 - 0.185219i) q^{19} +(3.59587 + 1.20445i) q^{20} +(4.71119 - 3.50209i) q^{21} +(-6.33018 - 3.70950i) q^{22} +(2.01071 - 6.13431i) q^{23} +(1.75406 + 1.17180i) q^{24} +(2.56342 + 1.73388i) q^{25} +(-3.36374 - 7.79803i) q^{26} +(-0.413832 + 5.17965i) q^{27} +(1.78925 - 4.14796i) q^{28} +(4.61356 - 2.94965i) q^{29} +(-5.86654 - 6.82058i) q^{30} +(-0.792742 - 2.92076i) q^{31} +(6.47645 + 0.419233i) q^{32} +(3.35854 + 6.09714i) q^{33} +(7.62941 + 3.58772i) q^{34} +(6.05380 - 7.50553i) q^{35} +(1.71978 + 3.60993i) q^{36} +(-11.5174 - 2.26194i) q^{37} +(0.227524 + 0.341110i) q^{38} +(-1.04452 + 7.98933i) q^{39} +(3.27115 + 1.14293i) q^{40} +(-0.528605 + 0.200173i) q^{41} +(-8.68277 + 6.28176i) q^{42} +(-5.16076 + 2.26581i) q^{43} +(4.58627 + 2.76783i) q^{44} +(1.47007 + 8.40783i) q^{45} +(-3.81526 + 11.1505i) q^{46} +(-0.358792 + 1.32192i) q^{47} +(-6.98017 - 4.79476i) q^{48} +(-3.24350 - 3.09995i) q^{49} +(-4.63852 - 3.22563i) q^{50} +(-4.47666 - 6.62871i) q^{51} +(2.38206 + 5.72462i) q^{52} +(1.85497 - 1.96615i) q^{53} +(0.877684 - 9.44551i) q^{54} +(7.84670 + 8.31701i) q^{55} +(1.68376 - 3.76866i) q^{56} +(-0.0198290 - 0.388507i) q^{57} +(-8.49152 + 5.27561i) q^{58} +(5.24916 - 0.890622i) q^{59} +(4.21843 + 5.03467i) q^{60} +(-6.99384 + 12.8711i) q^{61} +(1.37819 + 5.35046i) q^{62} +(10.1273 - 0.904340i) q^{63} +(-2.06367 - 0.160401i) q^{64} +(1.62146 + 13.1355i) q^{65} +(-5.98701 - 11.2094i) q^{66} +(-6.25549 + 3.24356i) q^{67} +(-5.53591 - 2.69119i) q^{68} +(8.52382 - 7.23619i) q^{69} +(-11.2282 + 13.5582i) q^{70} +(-5.07756 - 3.93541i) q^{71} +(1.52864 + 3.31854i) q^{72} +(12.6226 - 4.04726i) q^{73} +(20.9712 + 4.40092i) q^{74} +(2.21463 + 4.88137i) q^{75} +(-0.162882 - 0.251171i) q^{76} +(10.6571 - 8.48263i) q^{77} +(2.09530 - 14.5596i) q^{78} +(1.91235 - 10.0815i) q^{79} +(-13.0715 - 4.75762i) q^{80} +(-5.30158 + 7.27277i) q^{81} +(0.969675 - 0.352933i) q^{82} +(2.55818 + 15.6918i) q^{83} +(6.39806 - 4.50398i) q^{84} +(-9.84338 - 8.70302i) q^{85} +(9.47427 - 4.01436i) q^{86} +(9.48287 - 0.177102i) q^{87} +(4.15756 + 2.58301i) q^{88} +(-1.35362 - 0.553016i) q^{89} +(-2.48512 - 15.3829i) q^{90} +(15.7543 - 0.611340i) q^{91} +(2.89054 - 8.10431i) q^{92} +(1.47453 - 5.03027i) q^{93} +(0.686162 - 2.40466i) q^{94} +(-0.191168 - 0.609740i) q^{95} +(9.18255 + 6.48391i) q^{96} +(-3.05069 + 13.2531i) q^{97} +(5.84773 + 5.73542i) q^{98} +(-0.562685 + 12.0436i) 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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