LMFDB - Embedded newform 243.2.i.a.103.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(4,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(162))

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("243.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.i (of order $81$, degree $54$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			103.5
Character	$\chi$	$=$	243.103
Dual form			243.2.i.a.151.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.83535 - 0.510904i) q^{2} +(-1.59811 - 0.667855i) q^{3} +(1.39514 + 0.841972i) q^{4} +(2.94702 - 0.114358i) q^{5} +(2.59189 + 2.04223i) q^{6} +(-2.67089 - 0.417720i) q^{7} +(0.484358 + 0.513389i) q^{8} +(2.10794 + 2.13462i) q^{9} +(-5.46724 - 1.29576i) q^{10} +(0.589047 + 4.31259i) q^{11} +(-1.66728 - 2.27732i) q^{12} +(1.84548 - 2.69078i) q^{13} +(4.68860 + 2.13123i) q^{14} +(-4.78606 - 1.78543i) q^{15} +(-2.14553 - 4.07318i) q^{16} +(4.70279 - 2.36183i) q^{17} +(-2.77822 - 4.99472i) q^{18} +(0.0335399 + 0.575858i) q^{19} +(4.20780 + 2.32177i) q^{20} +(3.98941 + 2.45133i) q^{21} +(1.12221 - 8.21604i) q^{22} +(2.84305 - 7.36370i) q^{23} +(-0.431190 - 1.14393i) q^{24} +(3.68691 - 0.286569i) q^{25} +(-4.76183 + 3.99565i) q^{26} +(-1.94312 - 4.81916i) q^{27} +(-3.37456 - 2.83159i) q^{28} +(-0.495027 - 0.353824i) q^{29} +(7.87189 + 5.72209i) q^{30} +(5.02592 - 5.75907i) q^{31} +(1.55794 + 7.19223i) q^{32} +(1.93882 - 7.28541i) q^{33} +(-9.83791 + 1.93210i) q^{34} +(-7.91895 - 0.925592i) q^{35} +(1.14359 + 4.75292i) q^{36} +(1.86718 + 2.50805i) q^{37} +(0.232651 - 1.07404i) q^{38} +(-4.74634 + 3.06766i) q^{39} +(1.48612 + 1.45758i) q^{40} +(-2.17856 + 8.45769i) q^{41} +(-6.06956 - 6.53725i) q^{42} +(0.623280 + 0.565596i) q^{43} +(-2.80928 + 6.51263i) q^{44} +(6.45626 + 6.04971i) q^{45} +(-8.98013 + 12.0624i) q^{46} +(5.83765 + 6.68920i) q^{47} +(0.708504 + 7.94231i) q^{48} +(0.293432 + 0.0940850i) q^{49} +(-6.91316 - 1.35770i) q^{50} +(-9.09295 + 0.633694i) q^{51} +(4.84027 - 2.20017i) q^{52} +(2.35120 - 13.3343i) q^{53} +(1.10417 + 9.83757i) q^{54} +(2.22912 + 12.6419i) q^{55} +(-1.07921 - 1.57353i) q^{56} +(0.330989 - 0.942687i) q^{57} +(0.727777 + 0.902301i) q^{58} +(6.01839 - 2.45878i) q^{59} +(-5.17395 - 6.52065i) q^{60} +(4.92623 - 2.97299i) q^{61} +(-12.1666 + 8.00212i) q^{62} +(-4.73841 - 6.58185i) q^{63} +(0.279822 - 4.80436i) q^{64} +(5.13097 - 8.14083i) q^{65} +(-7.28054 + 12.3807i) q^{66} +(-7.89248 + 5.64120i) q^{67} +(8.54964 + 0.664531i) q^{68} +(-9.46141 + 9.86928i) q^{69} +(14.0611 + 5.74460i) q^{70} +(0.635585 + 2.12300i) q^{71} +(-0.0748917 + 2.11611i) q^{72} +(-5.07940 + 1.20384i) q^{73} +(-2.14554 - 5.55709i) q^{74} +(-6.08349 - 2.00435i) q^{75} +(-0.438064 + 0.831643i) q^{76} +(0.228172 - 11.7645i) q^{77} +(10.2785 - 3.20529i) q^{78} +(8.20313 - 8.04557i) q^{79} +(-6.78872 - 11.7584i) q^{80} +(-0.113174 + 8.99929i) q^{81} +(8.31948 - 14.4098i) q^{82} +(3.22782 + 12.5312i) q^{83} +(3.50184 + 6.77893i) q^{84} +(13.5891 - 7.49816i) q^{85} +(-0.854969 - 1.35650i) q^{86} +(0.554807 + 0.896058i) q^{87} +(-1.92873 + 2.39125i) q^{88} +(1.18058 - 3.94341i) q^{89} +(-8.75866 - 14.4018i) q^{90} +(-6.05307 + 6.41588i) q^{91} +(10.1665 - 7.87962i) q^{92} +(-11.8782 + 5.84706i) q^{93} +(-7.29657 - 15.2595i) q^{94} +(0.164697 + 1.69323i) q^{95} +(2.31360 - 12.5345i) q^{96} +(-4.78397 - 0.185640i) q^{97} +(-0.490480 - 0.322594i) q^{98} +(-7.96405 + 10.3481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) $ 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{81}\right)$

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 $

$2$	−1.83535	−	0.510904i	−1.29779	−	0.361263i	−0.450679	−	0.892686i	$-0.648818\pi$
$2$	−1.83535	−	0.510904i	−1.29779	−	0.361263i	−0.847107	+	0.531423i	$0.821658\pi$
$3$	−1.59811	−	0.667855i	−0.922672	−	0.385586i
$3$	−1.59811	−	0.667855i	−0.922672	−	0.385586i
$4$	1.39514	+	0.841972i	0.697571	+	0.420986i
$5$	2.94702	−	0.114358i	1.31795	−	0.0511424i	0.629826	−	0.776736i	$-0.283126\pi$
$5$	2.94702	−	0.114358i	1.31795	−	0.0511424i	0.688123	+	0.725594i	$0.258435\pi$
$6$	2.59189	+	2.04223i	1.05813	+	0.833736i
$7$	−2.67089	−	0.417720i	−1.00950	−	0.157883i	−0.371919	−	0.928265i	$-0.621300\pi$
$7$	−2.67089	−	0.417720i	−1.00950	−	0.157883i	−0.637583	+	0.770382i	$0.720066\pi$
$8$	0.484358	+	0.513389i	0.171246	+	0.181510i
$9$	2.10794	+	2.13462i	0.702647	+	0.711539i
$10$	−5.46724	−	1.29576i	−1.72889	−	0.409755i
$11$	0.589047	+	4.31259i	0.177604	+	1.30029i	0.836461	+	0.548026i	$0.184621\pi$
$11$	0.589047	+	4.31259i	0.177604	+	1.30029i	−0.658857	+	0.752268i	$0.728960\pi$
$12$	−1.66728	−	2.27732i	−0.481303	−	0.657405i
$13$	1.84548	−	2.69078i	0.511845	−	0.746288i	−0.479505	−	0.877539i	$-0.659184\pi$
$13$	1.84548	−	2.69078i	0.511845	−	0.746288i	0.991349	+	0.131252i	$0.0418996\pi$
$14$	4.68860	+	2.13123i	1.25308	+	0.569595i
$15$	−4.78606	−	1.78543i	−1.23575	−	0.460995i
$16$	−2.14553	−	4.07318i	−0.536382	−	1.01830i
$17$	4.70279	−	2.36183i	1.14059	−	0.572827i	0.224771	−	0.974412i	$-0.427837\pi$
$17$	4.70279	−	2.36183i	1.14059	−	0.572827i	0.915822	+	0.401584i	$0.131540\pi$
$18$	−2.77822	−	4.99472i	−0.654832	−	1.17727i
$19$	0.0335399	+	0.575858i	0.00769459	+	0.132111i	0.999968	+	0.00803807i	$0.00255862\pi$
$19$	0.0335399	+	0.575858i	0.00769459	+	0.132111i	−0.992273	+	0.124073i	$0.960404\pi$
$20$	4.20780	+	2.32177i	0.940893	+	0.519163i
$21$	3.98941	+	2.45133i	0.870561	+	0.534924i
$22$	1.12221	−	8.21604i	0.239256	−	1.75167i
$23$	2.84305	−	7.36370i	0.592818	−	1.53544i	−0.233573	−	0.972339i	$-0.575042\pi$
$23$	2.84305	−	7.36370i	0.592818	−	1.53544i	0.826390	−	0.563098i	$-0.190390\pi$
$24$	−0.431190	−	1.14393i	−0.0880162	−	0.233505i
$25$	3.68691	−	0.286569i	0.737382	−	0.0573138i
$26$	−4.76183	+	3.99565i	−0.933871	+	0.783611i
$27$	−1.94312	−	4.81916i	−0.373953	−	0.927448i
$28$	−3.37456	−	2.83159i	−0.637732	−	0.535121i
$29$	−0.495027	−	0.353824i	−0.0919242	−	0.0657035i	0.534601	−	0.845104i	$-0.320462\pi$
$29$	−0.495027	−	0.353824i	−0.0919242	−	0.0657035i	−0.626525	+	0.779401i	$0.715524\pi$
$30$	7.87189	+	5.72209i	1.43720	+	1.04471i
$31$	5.02592	−	5.75907i	0.902682	−	1.03436i	−0.0965560	−	0.995328i	$-0.530783\pi$
$31$	5.02592	−	5.75907i	0.902682	−	1.03436i	0.999238	−	0.0390313i	$-0.0124272\pi$
$32$	1.55794	+	7.19223i	0.275407	+	1.27142i
$33$	1.93882	−	7.28541i	0.337505	−	1.26823i
$34$	−9.83791	+	1.93210i	−1.68719	+	0.331353i
$35$	−7.91895	−	0.925592i	−1.33855	−	0.156454i
$36$	1.14359	+	4.75292i	0.190598	+	0.792153i
$37$	1.86718	+	2.50805i	0.306962	+	0.412321i	0.928658	−	0.370937i	$-0.120964\pi$
$37$	1.86718	+	2.50805i	0.306962	+	0.412321i	−0.621696	+	0.783259i	$0.713556\pi$
$38$	0.232651	−	1.07404i	0.0377409	−	0.174232i
$39$	−4.74634	+	3.06766i	−0.760023	+	0.491218i
$40$	1.48612	+	1.45758i	0.234977	+	0.230464i
$41$	−2.17856	+	8.45769i	−0.340234	+	1.32087i	0.538124	+	0.842866i	$0.319133\pi$
$41$	−2.17856	+	8.45769i	−0.340234	+	1.32087i	−0.878358	+	0.478003i	$0.841361\pi$
$42$	−6.06956	−	6.53725i	−0.936554	−	1.00872i
$43$	0.623280	+	0.565596i	0.0950492	+	0.0862526i	0.718147	−	0.695891i	$-0.244990\pi$
$43$	0.623280	+	0.565596i	0.0950492	+	0.0862526i	−0.623098	+	0.782144i	$0.714126\pi$
$44$	−2.80928	+	6.51263i	−0.423514	+	0.981816i
$45$	6.45626	+	6.04971i	0.962443	+	0.901837i
$46$	−8.98013	+	12.0624i	−1.32405	+	1.77851i
$47$	5.83765	+	6.68920i	0.851508	+	0.975720i	0.999913	−	0.0132066i	$-0.00420393\pi$
$47$	5.83765	+	6.68920i	0.851508	+	0.975720i	−0.148405	+	0.988927i	$0.547414\pi$
$48$	0.708504	+	7.94231i	0.102264	+	1.14637i
$49$	0.293432	+	0.0940850i	0.0419188	+	0.0134407i
$50$	−6.91316	−	1.35770i	−0.977669	−	0.192008i
$51$	−9.09295	+	0.633694i	−1.27327	+	0.0887350i
$52$	4.84027	−	2.20017i	0.671224	−	0.305109i
$53$	2.35120	−	13.3343i	0.322963	−	1.83161i	−0.200660	−	0.979661i	$-0.564309\pi$
$53$	2.35120	−	13.3343i	0.322963	−	1.83161i	0.523622	−	0.851950i	$-0.324580\pi$
$54$	1.10417	+	9.83757i	0.150258	+	1.33872i
$55$	2.22912	+	12.6419i	0.300574	+	1.70464i
$56$	−1.07921	−	1.57353i	−0.144216	−	0.210272i
$57$	0.330989	−	0.942687i	0.0438406	−	0.124862i
$58$	0.727777	+	0.902301i	0.0955617	+	0.118478i
$59$	6.01839	−	2.45878i	0.783528	−	0.320107i	0.0491009	−	0.998794i	$-0.484364\pi$
$59$	6.01839	−	2.45878i	0.783528	−	0.320107i	0.734427	+	0.678687i	$0.237451\pi$
$60$	−5.17395	−	6.52065i	−0.667954	−	0.841812i
$61$	4.92623	−	2.97299i	0.630739	−	0.380653i	−0.164999	−	0.986294i	$-0.552762\pi$
$61$	4.92623	−	2.97299i	0.630739	−	0.380653i	0.795738	+	0.605641i	$0.207083\pi$
$62$	−12.1666	+	8.00212i	−1.54516	+	1.01627i
$63$	−4.73841	−	6.58185i	−0.596983	−	0.829236i
$64$	0.279822	−	4.80436i	0.0349778	−	0.600545i
$65$	5.13097	−	8.14083i	0.636418	−	1.00975i
$66$	−7.28054	+	12.3807i	−0.896173	+	1.52396i
$67$	−7.89248	+	5.64120i	−0.964220	+	0.689183i	−0.950500	−	0.310723i	$-0.899429\pi$
$67$	−7.89248	+	5.64120i	−0.964220	+	0.689183i	−0.0137191	+	0.999906i	$0.504367\pi$
$68$	8.54964	+	0.664531i	1.03680	+	0.0805862i
$69$	−9.46141	+	9.86928i	−1.13902	+	1.18812i
$70$	14.0611	+	5.74460i	1.68063	+	0.686611i
$71$	0.635585	+	2.12300i	0.0754300	+	0.251954i	0.987385	−	0.158336i	$-0.0506128\pi$
$71$	0.635585	+	2.12300i	0.0754300	+	0.251954i	−0.911955	+	0.410290i	$0.865428\pi$
$72$	−0.0748917	+	2.11611i	−0.00882607	+	0.249386i
$73$	−5.07940	+	1.20384i	−0.594499	+	0.140899i	−0.516841	−	0.856081i	$-0.672892\pi$
$73$	−5.07940	+	1.20384i	−0.594499	+	0.140899i	−0.0776577	+	0.996980i	$0.524744\pi$
$74$	−2.14554	−	5.55709i	−0.249414	−	0.645999i
$75$	−6.08349	−	2.00435i	−0.702461	−	0.231442i
$76$	−0.438064	+	0.831643i	−0.0502493	+	0.0953960i
$77$	0.228172	−	11.7645i	0.0260027	−	1.34069i
$78$	10.2785	−	3.20529i	1.16381	−	0.362928i
$79$	8.20313	−	8.04557i	0.922924	−	0.905198i	−0.0728211	−	0.997345i	$-0.523200\pi$
$79$	8.20313	−	8.04557i	0.922924	−	0.905198i	0.995745	+	0.0921472i	$0.0293730\pi$
$80$	−6.78872	−	11.7584i	−0.759002	−	1.31463i
$81$	−0.113174	+	8.99929i	−0.0125748	+	0.999921i
$82$	8.31948	−	14.4098i	0.918732	−	1.59129i
$83$	3.22782	+	12.5312i	0.354300	+	1.37548i	0.858909	+	0.512128i	$0.171143\pi$
$83$	3.22782	+	12.5312i	0.354300	+	1.37548i	−0.504609	+	0.863348i	$0.668363\pi$
$84$	3.50184	+	6.77893i	0.382082	+	0.739642i
$85$	13.5891	−	7.49816i	1.47395	−	0.813290i
$86$	−0.854969	−	1.35650i	−0.0921937	−	0.146275i
$87$	0.554807	+	0.896058i	0.0594816	+	0.0960675i
$88$	−1.92873	+	2.39125i	−0.205603	+	0.254908i
$89$	1.18058	−	3.94341i	0.125141	−	0.418001i	−0.872343	−	0.488895i	$-0.837400\pi$
$89$	1.18058	−	3.94341i	0.125141	−	0.418001i	0.997484	+	0.0708941i	$0.0225852\pi$
$90$	−8.75866	−	14.4018i	−0.923244	−	1.51809i
$91$	−6.05307	+	6.41588i	−0.634534	+	0.672567i
$92$	10.1665	−	7.87962i	1.05993	−	0.821508i
$93$	−11.8782	+	5.84706i	−1.23171	+	0.606312i
$94$	−7.29657	−	15.2595i	−0.752583	−	1.57389i
$95$	0.164697	+	1.69323i	0.0168975	+	0.173722i
$96$	2.31360	−	12.5345i	0.236131	−	1.27930i
$97$	−4.78397	−	0.185640i	−0.485738	−	0.0188489i	−0.205257	−	0.978708i	$-0.565803\pi$
$97$	−4.78397	−	0.185640i	−0.485738	−	0.0188489i	−0.280482	+	0.959859i	$0.590494\pi$
$98$	−0.490480	−	0.322594i	−0.0495460	−	0.0325869i
$99$	−7.96405	+	10.3481i	−0.800417	+	1.04002i
$100$	5.38504	+	2.70447i	0.538504	+	0.270447i
$101$	0.178798	+	9.21880i	0.0177911	+	0.917305i	0.897300	+	0.441422i	$0.145526\pi$
$101$	0.178798	+	9.21880i	0.0177911	+	0.917305i	−0.879509	+	0.475883i	$0.842129\pi$
$102$	17.0125	+	3.48257i	1.68449	+	0.344826i
$103$	4.98182	+	3.86120i	0.490874	+	0.380456i	0.827754	−	0.561092i	$-0.189619\pi$
$103$	4.98182	+	3.86120i	0.490874	+	0.380456i	−0.336880	+	0.941548i	$0.609372\pi$
$104$	2.27529	−	0.355849i	0.223110	−	0.0348938i
$105$	12.0372	+	6.76791i	1.17471	+	0.660480i
$106$	−11.1278	+	23.2719i	−1.08083	+	2.26037i
$107$	−8.46716	−	3.08179i	−0.818551	−	0.297928i	−0.101400	−	0.994846i	$-0.532332\pi$
$107$	−8.46716	−	3.08179i	−0.818551	−	0.297928i	−0.717151	+	0.696918i	$0.754554\pi$
$108$	1.34667	−	8.35946i	0.129584	−	0.804389i
$109$	9.81756	−	3.57330i	0.940352	−	0.342260i	0.174047	−	0.984737i	$-0.444315\pi$
$109$	9.81756	−	3.57330i	0.940352	−	0.342260i	0.766305	+	0.642477i	$0.222093\pi$
$110$	2.36761	−	24.3412i	0.225743	−	2.32084i
$111$	−1.30895	−	5.25516i	−0.124240	−	0.498797i
$112$	4.02902	+	11.7753i	0.380706	+	1.11266i
$113$	−6.12995	+	5.56264i	−0.576658	+	0.523289i	−0.907309	−	0.420464i	$-0.861867\pi$
$113$	−6.12995	+	5.56264i	−0.576658	+	0.523289i	0.330652	+	0.943753i	$0.392731\pi$
$114$	−1.08910	+	1.56105i	−0.102004	+	0.146206i
$115$	7.53645	−	22.0261i	0.702778	−	2.05395i
$116$	−0.392723	−	0.910434i	−0.0364634	−	0.0845317i
$117$	9.63394	−	1.73260i	0.890658	−	0.160179i
$118$	−12.3020	+	1.43790i	−1.13249	+	0.132370i
$119$	−13.5472	+	4.34374i	−1.24187	+	0.398190i
$120$	−1.40154	−	3.32189i	−0.127943	−	0.303246i
$121$	−7.65436	+	2.13074i	−0.695851	+	0.193703i
$122$	−10.5603	+	2.93965i	−0.956080	+	0.266143i
$123$	9.13009	−	12.0614i	0.823233	−	1.08754i
$124$	11.8608	−	3.80303i	1.06514	−	0.341522i
$125$	−3.81386	+	0.445777i	−0.341122	+	0.0398715i
$126$	5.33393	+	14.5009i	0.475184	+	1.29184i
$127$	−3.31800	−	7.69199i	−0.294425	−	0.682553i	0.705226	−	0.708983i	$-0.250846\pi$
$127$	−3.31800	−	7.69199i	−0.294425	−	0.682553i	−0.999651	+	0.0264293i	$0.991586\pi$
$128$	1.79660	−	5.25076i	0.158799	−	0.464106i
$129$	−0.618336	−	1.32015i	−0.0544415	−	0.116232i
$130$	−13.5763	+	12.3198i	−1.19072	+	1.08052i
$131$	1.47113	+	4.29953i	0.128533	+	0.375652i	0.991584	−	0.129465i	$-0.0413260\pi$
$131$	1.47113	+	4.29953i	0.128533	+	0.375652i	−0.863051	+	0.505117i	$0.831449\pi$
$132$	8.83903	−	8.53174i	0.769339	−	0.742593i
$133$	0.150966	−	1.55206i	0.0130904	−	0.134581i
$134$	17.3675	−	6.32127i	1.50033	−	0.546075i
$135$	−6.27752	−	13.9800i	−0.540283	−	1.20320i
$136$	3.49037	+	1.27039i	0.299296	+	0.108935i
$137$	2.02186	−	4.22836i	0.172739	−	0.361253i	−0.797531	−	0.603278i	$-0.793861\pi$
$137$	2.02186	−	4.22836i	0.172739	−	0.361253i	0.970270	+	0.242025i	$0.0778116\pi$
$138$	22.4072	−	13.2797i	1.90743	−	1.13044i
$139$	2.85495	−	0.446507i	0.242154	−	0.0378722i	−0.0322771	−	0.999479i	$-0.510276\pi$
$139$	2.85495	−	0.446507i	0.242154	−	0.0378722i	0.274431	+	0.961607i	$0.411510\pi$
$140$	−10.2687	−	7.95887i	−0.867866	−	0.672647i
$141$	−4.86181	−	14.5888i	−0.409439	−	1.22860i
$142$	−0.0818694	−	4.22116i	−0.00687033	−	0.354232i
$143$	12.6913	+	6.37381i	1.06130	+	0.533005i
$144$	4.17204	−	13.1659i	0.347670	−	1.09716i
$145$	−1.49932	−	0.986118i	−0.124512	−	0.0818927i
$146$	9.93751	+	0.385621i	0.822434	+	0.0319142i
$147$	−0.406102	−	0.346328i	−0.0334947	−	0.0285647i
$148$	0.493264	+	5.07120i	0.0405461	+	0.416850i
$149$	7.64332	+	15.9846i	0.626165	+	1.30951i	0.933727	+	0.357985i	$0.116536\pi$
$149$	7.64332	+	15.9846i	0.626165	+	1.30951i	−0.307562	+	0.951528i	$0.599513\pi$
$150$	10.1413	+	6.78675i	0.828032	+	0.554136i
$151$	−0.737056	+	0.571262i	−0.0599808	+	0.0464886i	−0.642150	−	0.766579i	$-0.721957\pi$
$151$	−0.737056	+	0.571262i	−0.0599808	+	0.0464886i	0.582169	+	0.813068i	$0.302204\pi$
$152$	−0.279394	+	0.296140i	−0.0226618	+	0.0240202i
$153$	14.9548	+	5.06005i	1.20902	+	0.409081i
$154$	−6.42931	+	21.4754i	−0.518088	+	1.73054i
$155$	14.1529	−	17.5469i	1.13679	−	1.40940i
$156$	−9.20470	+	0.283531i	−0.736966	+	0.0227007i
$157$	−0.553431	−	0.878077i	−0.0441686	−	0.0700782i	0.823176	−	0.567786i	$-0.192200\pi$
$157$	−0.553431	−	0.878077i	−0.0441686	−	0.0700782i	−0.867345	+	0.497708i	$0.834175\pi$
$158$	−19.1661	+	10.5754i	−1.52477	+	0.841334i
$159$	−12.6629	+	19.7395i	−1.00423	+	1.56545i
$160$	5.41376	+	21.0175i	0.427995	+	1.66158i
$161$	−10.6694	+	18.4800i	−0.840870	+	1.45643i
$162$	4.80548	−	16.4590i	0.377554	−	1.29314i
$163$	−3.52004	−	6.09689i	−0.275711	−	0.477545i	0.694603	−	0.719393i	$-0.255580\pi$
$163$	−3.52004	−	6.09689i	−0.275711	−	0.477545i	−0.970314	+	0.241848i	$0.922247\pi$
$164$	−10.1605	+	9.96538i	−0.793404	+	0.778166i
$165$	4.88060	−	21.6920i	0.379954	−	1.68872i
$166$	0.478051	−	24.6482i	0.0371039	−	1.91307i
$167$	−7.51784	+	14.2723i	−0.581748	+	1.10442i	0.400405	+	0.916338i	$0.368869\pi$
$167$	−7.51784	+	14.2723i	−0.581748	+	1.10442i	−0.982153	+	0.188083i	$0.939773\pi$
$168$	0.673816	+	3.23544i	0.0519861	+	0.249620i
$169$	0.847826	+	2.19592i	0.0652174	+	0.168917i
$170$	−28.7716	+	6.81899i	−2.20668	+	0.522993i
$171$	−1.15854	+	1.28547i	−0.0885955	+	0.0983023i
$172$	0.393347	+	1.31387i	0.0299924	+	0.100182i
$173$	−16.1339	−	6.59141i	−1.22663	−	0.501135i	−0.330031	−	0.943970i	$-0.607059\pi$
$173$	−16.1339	−	6.59141i	−1.22663	−	0.501135i	−0.896603	+	0.442835i	$0.853973\pi$
$174$	−0.560464	−	1.92803i	−0.0424887	−	0.146164i
$175$	−9.96703	−	0.774699i	−0.753437	−	0.0585618i
$176$	16.3021	−	11.6521i	1.22882	−	0.878308i
$177$	−11.2602	−	0.0899926i	−0.846368	−	0.00676426i
$178$	−4.18148	+	6.63437i	−0.313415	+	0.497267i
$179$	1.21144	−	20.7996i	0.0905472	−	1.55464i	−0.581141	−	0.813803i	$-0.697394\pi$
$179$	1.21144	−	20.7996i	0.0905472	−	1.55464i	0.671689	−	0.740834i	$-0.265569\pi$
$180$	3.91371	+	13.8762i	0.291711	+	1.03427i
$181$	−12.3454	+	8.11973i	−0.917630	+	0.603534i	−0.918050	−	0.396465i	$-0.870237\pi$
$181$	−12.3454	+	8.11973i	−0.917630	+	0.603534i	0.000420068		1.00000i	$0.499866\pi$
$182$	14.3874	−	8.68283i	1.06646	−	0.643614i
$183$	−9.85821	+	1.46118i	−0.728739	+	0.108014i
$184$	5.15750	−	2.10707i	0.380216	−	0.155335i
$185$	5.78943	+	7.17777i	0.425647	+	0.527720i
$186$	24.7879	−	4.66276i	1.81754	−	0.341891i
$187$	12.9558	+	18.8899i	0.947418	+	1.38137i
$188$	2.51222	+	14.2475i	0.183223	+	1.03911i
$189$	3.17680	+	13.6831i	0.231078	+	0.995301i
$190$	0.562803	−	3.19181i	0.0408300	−	0.231558i
$191$	−19.2046	+	8.72954i	−1.38959	+	0.631647i	−0.962181	−	0.272410i	$-0.912179\pi$
$191$	−19.2046	+	8.72954i	−1.38959	+	0.631647i	−0.427411	+	0.904057i	$0.640574\pi$
$192$	−3.65580	+	7.49104i	−0.263835	+	0.540619i
$193$	−14.3546	−	2.81916i	−1.03327	−	0.202927i	−0.352796	−	0.935700i	$-0.614769\pi$
$193$	−14.3546	−	2.81916i	−1.03327	−	0.202927i	−0.680473	+	0.732773i	$0.738226\pi$
$194$	8.68539	+	2.78486i	0.623575	+	0.199941i
$195$	−13.6368	+	9.58324i	−0.976549	+	0.686270i
$196$	0.330161	+	0.378323i	0.0235830	+	0.0270231i
$197$	−12.6636	+	17.0101i	−0.902242	+	1.21192i	0.0744395	+	0.997226i	$0.476283\pi$
$197$	−12.6636	+	17.0101i	−0.902242	+	1.21192i	−0.976681	+	0.214695i	$0.931124\pi$
$198$	19.9037	−	14.9234i	1.41449	−	1.06056i
$199$	3.50981	−	8.13666i	0.248804	−	0.576793i	−0.747348	−	0.664433i	$-0.768673\pi$
$199$	3.50981	−	8.13666i	0.248804	−	0.576793i	0.996152	+	0.0876400i	$0.0279325\pi$
$200$	1.93290	+	1.75402i	0.136677	+	0.124028i
$201$	16.3806	−	3.74426i	1.15540	−	0.264100i
$202$	4.38176	−	17.0110i	0.308300	−	1.19689i
$203$	1.17436	+	1.15181i	0.0824242	+	0.0808411i
$204$	−13.2195	−	6.77191i	−0.925550	−	0.474129i
$205$	−5.45306	+	25.1741i	−0.380858	+	1.75824i
$206$	−7.17067	−	9.63188i	−0.499604	−	0.671085i
$207$	21.7117	−	9.45340i	1.50906	−	0.657057i
$208$	−14.9196	−	1.74385i	−1.03449	−	0.120914i
$209$	−2.46368	+	0.483852i	−0.170417	+	0.0334687i
$210$	−18.6347	−	18.5713i	−1.28592	−	1.28154i
$211$	0.809358	+	3.73641i	0.0557185	+	0.257225i	0.996694	−	0.0812502i	$-0.0258913\pi$
$211$	0.809358	+	3.73641i	0.0557185	+	0.257225i	−0.940975	+	0.338475i	$0.890089\pi$
$212$	14.5074	−	16.6236i	0.996372	−	1.14172i
$213$	0.402118	−	3.81728i	0.0275527	−	0.261555i
$214$	13.9657	+	9.98206i	0.954674	+	0.682360i
$215$	1.90150	+	1.59555i	0.129681	+	0.108815i
$216$	1.53294	−	3.33177i	0.104303	−	0.226698i
$217$	−15.8294	+	13.2824i	−1.07457	+	0.901669i
$218$	−19.8442	+	1.54242i	−1.34402	+	0.104466i
$219$	8.92146	+	1.46843i	0.602856	+	0.0992271i
$220$	−7.53423	+	19.5141i	−0.507958	+	1.31564i
$221$	2.32375	−	17.0129i	0.156312	−	1.14441i
$222$	−0.282508	+	10.3138i	−0.0189607	+	0.692216i
$223$	−21.8674	−	12.0659i	−1.46435	−	0.807992i	−0.467249	−	0.884126i	$-0.654755\pi$
$223$	−21.8674	−	12.0659i	−1.46435	−	0.807992i	−0.997098	+	0.0761338i	$0.975742\pi$
$224$	−1.15674	−	19.8604i	−0.0772879	−	1.32698i
$225$	8.38350	+	7.26606i	0.558900	+	0.484404i
$226$	14.0926	−	7.07755i	0.937423	−	0.470792i
$227$	0.567868	+	1.07807i	0.0376907	+	0.0715541i	0.902884	−	0.429885i	$-0.141446\pi$
$227$	0.567868	+	1.07807i	0.0376907	+	0.0715541i	−0.865193	+	0.501439i	$0.832804\pi$
$228$	1.25549	−	1.03650i	0.0831470	−	0.0686438i
$229$	−14.2095	−	6.45902i	−0.938991	−	0.426824i	−0.114961	−	0.993370i	$-0.536674\pi$
$229$	−14.2095	−	6.45902i	−0.938991	−	0.426824i	−0.824030	+	0.566546i	$0.808279\pi$
$230$	−25.0852	+	36.5752i	−1.65407	+	2.41169i
$231$	−8.22163	+	18.6486i	−0.540943	+	1.22699i
$232$	−0.0581207	−	0.425519i	−0.00381581	−	0.0279367i
$233$	11.3621	+	2.69288i	0.744359	+	0.176416i	0.585259	−	0.810846i	$-0.300993\pi$
$233$	11.3621	+	2.69288i	0.744359	+	0.176416i	0.159099	+	0.987263i	$0.449141\pi$
$234$	−18.5668	−	1.74209i	−1.21375	−	0.113884i
$235$	17.9686	+	19.0457i	1.17215	+	1.24240i
$236$	10.4667	+	1.63697i	0.681327	+	0.106558i
$237$	−18.4828	+	7.37925i	−1.20059	+	0.479334i
$238$	27.0831	−	1.05095i	1.75553	−	0.0681227i
$239$	−0.622167	−	0.375480i	−0.0402447	−	0.0242878i	0.496434	−	0.868074i	$-0.334642\pi$
$239$	−0.622167	−	0.375480i	−0.0402447	−	0.0242878i	−0.536679	+	0.843787i	$0.680321\pi$
$240$	2.99625	+	23.3252i	0.193407	+	1.50563i
$241$	−16.6418	−	4.63256i	−1.07199	−	0.298410i	−0.313164	−	0.949699i	$-0.601389\pi$
$241$	−16.6418	−	4.63256i	−1.07199	−	0.298410i	−0.758829	+	0.651289i	$0.774228\pi$
$242$	15.1370			0.973044
$243$	6.19108	−	14.3063i	0.397158	−	0.917750i
$244$	9.37596			0.600235
$245$	0.875509	+	0.243715i	0.0559342	+	0.0155704i
$246$	−22.9191	+	17.4722i	−1.46127	+	1.11399i
$247$	1.61140	+	0.972487i	0.102531	+	0.0618779i
$248$	5.39098	−	0.209195i	0.342328	−	0.0132839i
$249$	3.21058	−	22.1820i	0.203462	−	1.40573i
$250$	7.22751	+	1.13036i	0.457108	+	0.0714904i
$251$	21.0933	+	22.3575i	1.33139	+	1.41120i	0.842344	+	0.538940i	$0.181175\pi$
$251$	21.0933	+	22.3575i	1.33139	+	1.41120i	0.489050	+	0.872256i	$0.337343\pi$
$252$	−1.06901	−	13.1722i	−0.0673413	−	0.829772i
$253$	33.4313	+	7.92336i	2.10181	+	0.498137i
$254$	2.15981	+	15.8126i	0.135519	+	0.992173i
$255$	−26.7247	+	2.90736i	−1.67356	+	0.182066i
$256$	−11.4240	+	16.6566i	−0.713999	+	1.04104i
$257$	−8.91225	−	4.05111i	−0.555931	−	0.252702i	0.116084	−	0.993239i	$-0.462966\pi$
$257$	−8.91225	−	4.05111i	−0.555931	−	0.252702i	−0.672015	+	0.740538i	$0.734571\pi$
$258$	0.460393	+	2.73884i	0.0286628	+	0.170513i
$259$	−3.93936	−	7.47869i	−0.244780	−	0.464703i
$260$	14.0128	−	7.03748i	0.869036	−	0.436446i
$261$	−0.288209	−	1.80253i	−0.0178397	−	0.111574i
$262$	−0.503382	−	8.64273i	−0.0310990	−	0.533950i
$263$	−7.05204	−	3.89115i	−0.434847	−	0.239939i	0.250556	−	0.968102i	$-0.419386\pi$
$263$	−7.05204	−	3.89115i	−0.434847	−	0.239939i	−0.685403	+	0.728163i	$0.740374\pi$
$264$	4.67933	−	2.53338i	0.287993	−	0.155918i
$265$	5.40416	−	39.5655i	0.331975	−	2.43049i
$266$	−1.07003	+	2.77145i	−0.0656078	+	0.169928i
$267$	−4.52033	+	5.51357i	−0.276640	+	0.337425i
$268$	−15.7609	+	1.22503i	−0.962748	+	0.0748307i
$269$	21.6606	−	18.1754i	1.32067	−	1.10818i	0.334510	−	0.942392i	$-0.391429\pi$
$269$	21.6606	−	18.1754i	1.32067	−	1.10818i	0.986162	−	0.165784i	$-0.0530154\pi$
$270$	4.37901	+	28.8653i	0.266498	+	1.75669i
$271$	−20.5231	−	17.2209i	−1.24669	−	1.04610i	−0.996971	−	0.0777801i	$-0.975217\pi$
$271$	−20.5231	−	17.2209i	−1.24669	−	1.04610i	−0.249721	−	0.968318i	$-0.580339\pi$
$272$	−19.7101	−	14.0879i	−1.19510	−	0.854206i
$273$	13.9584	−	6.21074i	0.844799	−	0.375891i
$274$	−5.87109	+	6.72753i	−0.354686	+	0.406425i
$275$	3.40762	+	15.7313i	0.205487	+	0.948634i
$276$	−21.5097	+	5.80281i	−1.29473	+	0.349288i
$277$	2.98501	−	0.586237i	0.179352	−	0.0352236i	−0.102230	−	0.994761i	$-0.532598\pi$
$277$	2.98501	−	0.586237i	0.179352	−	0.0352236i	0.281582	+	0.959537i	$0.409141\pi$
$278$	−5.46795	−	0.639112i	−0.327946	−	0.0383314i
$279$	22.8877	−	1.41136i	1.37025	−	0.0844957i
$280$	−3.36041	−	4.51382i	−0.200823	−	0.269752i
$281$	0.347356	−	1.60358i	0.0207215	−	0.0956613i	−0.965802	−	0.259281i	$-0.916514\pi$
$281$	0.347356	−	1.60358i	0.0207215	−	0.0956613i	0.986524	+	0.163620i	$0.0523169\pi$
$282$	1.46964	+	29.2594i	0.0875158	+	1.74237i
$283$	16.1852	+	15.8743i	0.962108	+	0.943629i	0.998447	−	0.0557106i	$-0.0177424\pi$
$283$	16.1852	+	15.8743i	0.962108	+	0.943629i	−0.0363389	+	0.999340i	$0.511570\pi$
$284$	−0.900777	+	3.49703i	−0.0534513	+	0.207511i
$285$	0.867629	−	2.81597i	0.0513939	−	0.166804i
$286$	−20.0365	−	18.1822i	−1.18478	−	1.07513i
$287$	9.35164	−	21.6795i	0.552010	−	1.27970i
$288$	−12.0686	+	18.4864i	−0.711150	+	1.08932i
$289$	6.38626	−	8.57824i	0.375663	−	0.504602i
$290$	2.24796	+	2.57588i	0.132005	+	0.151261i
$291$	7.52135	+	3.49167i	0.440909	+	0.204685i
$292$	−8.10008	−	2.59719i	−0.474021	−	0.151989i
$293$	9.76298	+	1.91739i	0.570359	+	0.112015i	0.469574	−	0.882893i	$-0.344408\pi$
$293$	9.76298	+	1.91739i	0.570359	+	0.112015i	0.100785	+	0.994908i	$0.467864\pi$
$294$	0.568398	+	0.843111i	0.0331496	+	0.0491713i
$295$	17.4552	−	7.93435i	1.01628	−	0.461956i
$296$	−0.383226	+	2.17338i	−0.0222746	+	0.126325i
$297$	19.6385	−	11.2186i	1.13954	−	0.650968i
$298$	−5.86153	−	33.2424i	−0.339549	−	1.92568i
$299$	−14.5673	−	21.2396i	−0.842447	−	1.22832i
$300$	−6.79972	−	7.91848i	−0.392582	−	0.457173i
$301$	−1.42845	−	1.77100i	−0.0823345	−	0.102079i
$302$	1.64461	−	0.671899i	0.0946369	−	0.0386634i
$303$	5.87108	−	14.8521i	0.337285	−	0.853231i
$304$	2.27361	−	1.37213i	0.130401	−	0.0786972i
$305$	14.1777	−	9.32484i	0.811814	−	0.533939i
$306$	−24.8620	−	16.9274i	−1.42127	−	0.967675i
$307$	0.854376	−	14.6691i	0.0487618	−	0.837208i	−0.881925	−	0.471390i	$-0.843752\pi$
$307$	0.854376	−	14.6691i	0.0487618	−	0.837208i	0.930686	−	0.365818i	$-0.119211\pi$
$308$	10.2237	−	16.2210i	0.582551	−	0.924279i
$309$	−5.38280	−	9.49778i	−0.306217	−	0.540310i
$310$	−34.9403	+	24.9738i	−1.98447	+	1.41842i
$311$	−6.07999	−	0.472574i	−0.344764	−	0.0267972i	−0.0960569	−	0.995376i	$-0.530623\pi$
$311$	−6.07999	−	0.472574i	−0.344764	−	0.0267972i	−0.248708	+	0.968579i	$0.580006\pi$
$312$	−3.87383	−	0.950875i	−0.219312	−	0.0538327i
$313$	−12.2888	−	5.02051i	−0.694602	−	0.283776i	0.00327429	−	0.999995i	$-0.498958\pi$
$313$	−12.2888	−	5.02051i	−0.694602	−	0.283776i	−0.697876	+	0.716219i	$0.745871\pi$
$314$	0.567124	+	1.89433i	0.0320047	+	0.106903i
$315$	−14.7169	−	18.8550i	−0.829203	−	1.06236i
$316$	18.2187	−	4.31791i	1.02488	−	0.242901i
$317$	6.55288	+	16.9724i	0.368046	+	0.953264i	0.985955	+	0.167014i	$0.0534124\pi$
$317$	6.55288	+	16.9724i	0.368046	+	0.953264i	−0.617908	+	0.786250i	$0.712020\pi$
$318$	33.3258	−	29.7594i	1.86882	−	1.66882i
$319$	1.23430	−	2.34327i	0.0691077	−	0.131198i
$320$	0.275226	−	14.1906i	0.0153856	−	0.793277i
$321$	11.4733	+	10.5799i	0.640377	+	0.590512i
$322$	29.0237	−	28.4662i	1.61742	−	1.58636i
$323$	1.51781	+	2.62892i	0.0844531	+	0.146277i
$324$	−7.73504	+	12.4600i	−0.429725	+	0.692222i
$325$	6.03303	−	10.4495i	0.334652	−	0.579635i
$326$	3.34557	+	12.9883i	0.185294	+	0.719355i
$327$	−18.0760	−	0.846160i	−0.999607	−	0.0467928i
$328$	−5.39729	+	2.97810i	−0.298015	+	0.164438i
$329$	−12.7975	−	20.3046i	−0.705549	−	1.11943i
$330$	−20.0401	+	37.3188i	−1.10317	+	2.05433i
$331$	−2.43120	+	3.01422i	−0.133631	+	0.165676i	−0.840760	−	0.541408i	$-0.817891\pi$
$331$	−2.43120	+	3.01422i	−0.133631	+	0.165676i	0.707129	+	0.707085i	$0.249990\pi$
$332$	−6.04764	+	20.2005i	−0.331907	+	1.10865i
$333$	−1.41783	+	9.27253i	−0.0776968	+	0.508132i
$334$	21.0896	−	22.3537i	1.15397	−	1.22314i
$335$	−22.6142	+	17.5273i	−1.23555	+	0.957620i
$336$	1.42532	−	21.5090i	0.0777577	−	1.17341i
$337$	11.7344	+	24.5405i	0.639215	+	1.33680i	0.925532	+	0.378669i	$0.123618\pi$
$337$	11.7344	+	24.5405i	0.639215	+	1.33680i	−0.286318	+	0.958135i	$0.592431\pi$
$338$	−0.434149	−	4.46344i	−0.0236146	−	0.242779i
$339$	13.5114	−	4.79581i	0.733839	−	0.260473i
$340$	25.2720	+	0.980669i	1.37057	+	0.0531842i
$341$	27.7970	+	18.2824i	1.50529	+	0.990046i
$342$	2.78307	−	1.76738i	0.150491	−	0.0955691i
$343$	16.1662	+	8.11899i	0.872895	+	0.438384i
$344$	0.0115194	+	0.593936i	0.000621083	+	0.0320229i
$345$	−26.7544	+	30.1670i	−1.44041	+	1.62414i
$346$	26.2436	+	20.3404i	1.41087	+	1.09350i
$347$	−16.8812	+	2.64017i	−0.906231	+	0.141732i	−0.590426	−	0.807092i	$-0.701040\pi$
$347$	−16.8812	+	2.64017i	−0.906231	+	0.141732i	−0.315806	+	0.948824i	$0.602275\pi$
$348$	0.0195787	+	1.71726i	0.00104953	+	0.0920548i
$349$	−14.5995	+	30.5323i	−0.781493	+	1.63435i	−0.00848026	+	0.999964i	$0.502699\pi$
$349$	−14.5995	+	30.5323i	−0.781493	+	1.63435i	−0.773013	+	0.634390i	$0.781251\pi$
$350$	17.8972	+	6.51404i	0.956644	+	0.348190i
$351$	−16.5533	−	3.66517i	−0.883548	−	0.195632i
$352$	−30.0994	+	10.9553i	−1.60431	+	0.583919i
$353$	1.57672	−	16.2101i	0.0839205	−	0.862779i	−0.854996	−	0.518634i	$-0.826441\pi$
$353$	1.57672	−	16.2101i	0.0839205	−	0.862779i	0.938917	−	0.344144i	$-0.111831\pi$
$354$	20.6204	+	5.91804i	1.09596	+	0.314540i
$355$	2.11586	+	6.18385i	0.112298	+	0.328205i
$356$	4.96732	−	4.50760i	0.263268	−	0.238903i
$357$	24.5510	+	2.10577i	1.29938	+	0.111449i
$358$	−12.8500	+	37.5556i	−0.679144	+	1.98487i
$359$	−2.97661	−	6.90056i	−0.157099	−	0.364198i	0.821429	−	0.570311i	$-0.193177\pi$
$359$	−2.97661	−	6.90056i	−0.157099	−	0.364198i	−0.978528	+	0.206114i	$0.933918\pi$
$360$	0.0212866	+	6.24480i	0.00112190	+	0.329130i
$361$	18.5410	−	2.16714i	0.975844	−	0.114060i
$362$	26.8066	−	8.59518i	1.40892	−	0.451753i
$363$	13.6556	+	1.70684i	0.716732	+	0.0895858i
$364$	−13.8469	+	3.85454i	−0.725774	+	0.202033i
$365$	−14.8314	+	4.12862i	−0.776313	+	0.216102i
$366$	18.8397	+	2.35482i	0.984769	+	0.123088i
$367$	4.11329	−	1.31887i	0.214712	−	0.0688446i	−0.196023	−	0.980599i	$-0.562803\pi$
$367$	4.11329	−	1.31887i	0.214712	−	0.0688446i	0.410735	+	0.911755i	$0.365272\pi$
$368$	−36.0935	+	4.21873i	−1.88150	+	0.219916i
$369$	−22.6462	+	13.1779i	−1.17891	+	0.686015i
$370$	−6.95846	−	16.1315i	−0.361753	−	0.838638i
$371$	−11.8498	+	34.6324i	−0.615212	+	1.79802i
$372$	−21.4949	−	1.84365i	−1.11446	−	0.0955886i
$373$	−8.37068	+	7.59598i	−0.433417	+	0.393305i	−0.859299	−	0.511474i	$-0.829100\pi$
$373$	−8.37068	+	7.59598i	−0.433417	+	0.393305i	0.425882	+	0.904779i	$0.359964\pi$
$374$	−14.1274	−	41.2887i	−0.730508	−	2.13499i
$375$	6.39271	+	1.83470i	0.330118	+	0.0947437i
$376$	−0.606654	+	6.23695i	−0.0312858	+	0.321646i
$377$	−1.86563	+	0.679032i	−0.0960846	+	0.0349719i
$378$	1.16024	−	26.7363i	0.0596762	−	1.37517i
$379$	−4.04003	−	1.47045i	−0.207522	−	0.0755319i	0.236168	−	0.971712i	$-0.424109\pi$
$379$	−4.04003	−	1.47045i	−0.207522	−	0.0755319i	−0.443690	+	0.896180i	$0.646331\pi$
$380$	−1.19588	+	2.50097i	−0.0613473	+	0.128297i
$381$	0.165414	+	14.5086i	0.00847443	+	0.743299i
$382$	39.7070	−	6.21006i	2.03158	−	0.317734i
$383$	−12.1682	−	9.43104i	−0.621765	−	0.481904i	0.252342	−	0.967638i	$-0.418799\pi$
$383$	−12.1682	−	9.43104i	−0.621765	−	0.481904i	−0.874107	+	0.485734i	$0.838552\pi$
$384$	−6.37792	+	7.19145i	−0.325472	+	0.366987i
$385$	−0.672936	−	34.6964i	−0.0342960	−	1.76829i
$386$	24.9054	+	12.5080i	1.26765	+	0.636639i
$387$	0.106506	+	2.52271i	0.00541399	+	0.128236i
$388$	−6.51801	−	4.28696i	−0.330902	−	0.217637i
$389$	18.5472	+	0.719717i	0.940381	+	0.0364911i	0.504405	−	0.863467i	$-0.331712\pi$
$389$	18.5472	+	0.719717i	0.940381	+	0.0364911i	0.435976	+	0.899958i	$0.356403\pi$
$390$	29.9243	−	10.6215i	1.51528	−	0.537841i
$391$	−4.02151	−	41.3447i	−0.203376	−	2.09089i
$392$	0.0938236	+	0.196215i	0.00473881	+	0.00991037i
$393$	0.520432	−	7.85364i	0.0262523	−	0.396164i
$394$	31.9326	−	24.7496i	1.60874	−	1.24687i
$395$	23.2547	−	24.6486i	1.17007	−	1.24021i
$396$	−19.8238	+	7.73152i	−0.996181	+	0.388523i
$397$	−0.00656058	+	0.0219139i	−0.000329266	+	0.00109983i	−0.958154	−	0.286253i	$-0.907590\pi$
$397$	−0.00656058	+	0.0219139i	−0.000329266	+	0.00109983i	0.957825	+	0.287353i	$0.0927753\pi$
$398$	−10.5988	+	13.1404i	−0.531269	+	0.658670i
$399$	−1.27781	+	2.37955i	−0.0639707	+	0.119127i
$400$	−9.07761	−	14.4026i	−0.453880	−	0.720130i
$401$	1.61439	−	0.890782i	0.0806187	−	0.0444835i	−0.442291	−	0.896872i	$-0.645834\pi$
$401$	1.61439	−	0.890782i	0.0806187	−	0.0444835i	0.522910	+	0.852388i	$0.324846\pi$
$402$	−31.9770	−	1.49688i	−1.59487	−	0.0746577i
$403$	−6.22112	−	24.1519i	−0.309896	−	1.20309i
$404$	−7.51252	+	13.0121i	−0.373762	+	0.647375i
$405$	0.695615	+	26.5341i	0.0345654	+	1.31849i
$406$	−1.56690	−	2.71395i	−0.0777641	−	0.134691i
$407$	−9.71634	+	9.52972i	−0.481621	+	0.472371i
$408$	−4.72957	−	4.36128i	−0.234149	−	0.215916i
$409$	−0.235192	+	12.1265i	−0.0116295	+	0.599615i	0.947988	+	0.318306i	$0.103114\pi$
$409$	−0.235192	+	12.1265i	−0.0116295	+	0.599615i	−0.959617	+	0.281308i	$0.909232\pi$
$410$	22.8698	−	43.4173i	1.12946	−	2.14423i
$411$	−6.05509	+	5.40709i	−0.298675	+	0.266712i
$412$	3.69932	+	9.58148i	0.182252	+	0.472046i
$413$	−17.1016	+	4.05314i	−0.841513	+	0.199442i
$414$	−44.6782	+	6.25771i	−2.19581	+	0.307550i
$415$	10.9455	+	36.5606i	0.537294	+	1.79469i
$416$	22.2278	+	9.08107i	1.08981	+	0.445236i
$417$	−4.86075	−	1.19313i	−0.238032	−	0.0584276i
$418$	4.76891	+	0.370669i	0.233255	+	0.0181300i
$419$	19.7120	−	14.0893i	0.962996	−	0.688308i	0.0127860	−	0.999918i	$-0.495930\pi$
$419$	19.7120	−	14.0893i	0.962996	−	0.688308i	0.950210	+	0.311610i	$0.100868\pi$
$420$	11.0952	+	19.5772i	0.541392	+	0.955269i
$421$	−3.18020	+	5.04574i	−0.154994	+	0.245914i	−0.914500	−	0.404586i	$-0.867416\pi$
$421$	−3.18020	+	5.04574i	−0.154994	+	0.245914i	0.759506	+	0.650500i	$0.225440\pi$
$422$	0.423494	−	7.27111i	0.0206154	−	0.353952i
$423$	−1.97347	+	26.5616i	−0.0959532	+	1.29147i
$424$	7.98452	−	5.25150i	0.387763	−	0.255036i
$425$	16.6619	−	10.0555i	0.808221	−	0.487764i
$426$	−2.68829	+	6.80058i	−0.130248	+	0.329489i
$427$	−14.3993	+	5.88276i	−0.696831	+	0.284687i
$428$	−9.21810	−	11.4286i	−0.445574	−	0.552424i
$429$	−16.0254	−	18.6620i	−0.773712	−	0.901011i
$430$	−2.67474	−	3.89987i	−0.128987	−	0.188068i
$431$	5.12465	+	29.0633i	0.246846	+	1.39993i	0.816167	+	0.577817i	$0.196095\pi$
$431$	5.12465	+	29.0633i	0.246846	+	1.39993i	−0.569321	+	0.822116i	$0.692794\pi$
$432$	−15.4603	+	18.2543i	−0.743834	+	0.878261i
$433$	−1.65067	+	9.36143i	−0.0793262	+	0.449881i	0.919111	+	0.393999i	$0.128908\pi$
$433$	−1.65067	+	9.36143i	−0.0793262	+	0.449881i	−0.998437	+	0.0558830i	$0.982203\pi$
$434$	35.8384	−	16.2905i	1.72030	−	0.781971i
$435$	1.73750	+	2.57726i	0.0833068	+	0.123570i
$436$	16.7055	+	3.28085i	0.800049	+	0.157124i
$437$	4.33580	+	1.39022i	0.207410	+	0.0665032i
$438$	−15.6237	−	7.25308i	−0.746531	−	0.346565i
$439$	−0.0529657	−	0.0606920i	−0.00252791	−	0.00289667i	0.752171	−	0.658968i	$-0.229007\pi$
$439$	−0.0529657	−	0.0606920i	−0.00252791	−	0.00289667i	−0.754698	+	0.656072i	$0.772217\pi$
$440$	−5.41054	+	7.26762i	−0.257938	+	0.346470i
$441$	0.417701	+	0.824689i	0.0198905	+	0.0392709i
$442$	−12.9568	+	30.0373i	−0.616293	+	1.42873i
$443$	25.2756	+	22.9364i	1.20088	+	1.08974i	0.993773	+	0.111422i	$0.0355406\pi$
$443$	25.2756	+	22.9364i	1.20088	+	1.08974i	0.207107	+	0.978318i	$0.433595\pi$
$444$	2.59853	−	8.43378i	0.123321	−	0.400250i
$445$	3.02824	−	11.7563i	0.143552	−	0.557304i
$446$	33.9697	+	33.3172i	1.60851	+	1.57762i
$447$	−1.53948	−	30.6499i	−0.0728149	−	1.44969i
$448$	−2.75425	+	12.7150i	−0.130126	+	0.600729i
$449$	−20.9958	−	28.2023i	−0.990854	−	1.33095i	−0.943251	−	0.332081i	$-0.892249\pi$
$449$	−20.9958	−	28.2023i	−0.990854	−	1.33095i	−0.0476032	−	0.998866i	$-0.515158\pi$
$450$	−11.6744	−	17.6189i	−0.550335	−	0.830563i
$451$	−37.7578	−	4.41325i	−1.77795	−	0.207812i
$452$	−13.2357	+	2.59941i	−0.622557	+	0.122266i
$453$	1.55942	−	0.420695i	0.0732680	−	0.0197660i
$454$	−0.491445	−	2.26876i	−0.0230646	−	0.106478i
$455$	−17.1048	+	19.6000i	−0.801887	+	0.918861i
$456$	0.644282	−	0.286672i	0.0301713	−	0.0134246i
$457$	−8.24919	−	5.89617i	−0.385881	−	0.275811i	0.371962	−	0.928248i	$-0.378685\pi$
$457$	−8.24919	−	5.89617i	−0.385881	−	0.275811i	−0.757843	+	0.652437i	$0.773747\pi$
$458$	22.7795	+	19.1142i	1.06441	+	0.893149i
$459$	−20.5201	−	18.0742i	−0.957796	−	0.843630i
$460$	29.0598	−	24.3841i	1.35492	−	1.13691i
$461$	−17.2190	+	1.33836i	−0.801968	+	0.0623339i	−0.471932	−	0.881635i	$-0.656443\pi$
$461$	−17.2190	+	1.33836i	−0.801968	+	0.0623339i	−0.330035	+	0.943969i	$0.607061\pi$
$462$	24.6172	−	30.0263i	1.14530	−	1.39695i
$463$	8.94970	−	23.1803i	0.415928	−	1.07728i	−0.553705	−	0.832713i	$-0.686786\pi$
$463$	8.94970	−	23.1803i	0.415928	−	1.07728i	0.969632	−	0.244567i	$-0.0786457\pi$
$464$	−0.379096	+	2.77547i	−0.0175991	+	0.128848i
$465$	−34.3367	+	18.5898i	−1.59233	+	0.862082i
$466$	−19.4777	−	10.7473i	−0.902286	−	0.497860i
$467$	−0.391271	−	6.71786i	−0.0181059	−	0.310866i	−0.995187	−	0.0979970i	$-0.968756\pi$
$467$	−0.391271	−	6.71786i	−0.0181059	−	0.310866i	0.977081	−	0.212869i	$-0.0682806\pi$
$468$	14.8995	+	5.69428i	0.688731	+	0.263218i
$469$	23.4364	−	11.7702i	1.08219	−	0.543497i
$470$	−23.2482	−	44.1356i	−1.07236	−	2.03582i
$471$	0.298017	+	1.77288i	0.0137319	+	0.0816900i
$472$	4.17737	+	1.89885i	0.192279	+	0.0874015i
$473$	−2.07204	+	3.02111i	−0.0952726	+	0.138911i
$474$	37.6925	−	4.10054i	1.73127	−	0.188344i
$475$	0.288682	+	2.11353i	0.0132456	+	0.0969752i
$476$	−22.5576	−	5.34624i	−1.03392	−	0.245045i
$477$	33.4199	−	23.0891i	1.53019	−	1.05718i
$478$	0.950059	+	1.00700i	0.0434547	+	0.0460593i
$479$	−11.5631	−	1.80843i	−0.528330	−	0.0826293i	−0.115272	−	0.993334i	$-0.536774\pi$
$479$	−11.5631	−	1.80843i	−0.528330	−	0.0826293i	−0.413058	+	0.910705i	$0.635539\pi$
$480$	5.38483	−	37.2040i	0.245783	−	1.69812i
$481$	10.1945	−	0.395591i	0.464827	−	0.0180374i
$482$	28.1767	+	17.0047i	1.28341	+	0.774544i
$483$	29.3930	−	22.4076i	1.33743	−	1.01958i
$484$	−12.4729	−	3.47208i	−0.566952	−	0.157822i
$485$	−14.1197			−0.641142
$486$	−18.6719	+	23.0940i	−0.846976	+	1.04756i
$487$	12.2482			0.555018			0.277509	−	0.960723i	$-0.410491\pi$
$487$	12.2482			0.555018			0.277509	+	0.960723i	$0.410491\pi$
$488$	3.91236	+	1.08908i	0.177104	+	0.0493003i
$489$	1.55359	+	12.0944i	0.0702559	+	0.546927i
$490$	−1.48235	−	0.894602i	−0.0669657	−	0.0404140i
$491$	10.6518	−	0.413338i	0.480709	−	0.0186537i	0.202717	−	0.979237i	$-0.435023\pi$
$491$	10.6518	−	0.413338i	0.480709	−	0.0186537i	0.277991	+	0.960584i	$0.410331\pi$
$492$	22.8931	−	9.14006i	1.03210	−	0.412066i
$493$	−3.16368	−	0.494790i	−0.142485	−	0.0222842i
$494$	−2.46064	−	2.60812i	−0.110709	−	0.117345i
$495$	−22.2868	+	31.4068i	−1.00172	+	1.41163i
$496$	−34.2410	−	8.11526i	−1.53746	−	0.364386i
$497$	−0.810758	−	5.93580i	−0.0363675	−	0.266257i
$498$	−17.2254	+	39.0713i	−0.771888	+	1.75083i
$499$	−1.94472	+	2.83548i	−0.0870578	+	0.126933i	−0.865758	−	0.500463i	$-0.833163\pi$
$499$	−1.94472	+	2.83548i	−0.0870578	+	0.126933i	0.778700	+	0.627396i	$0.215879\pi$
$500$	−5.69621	−	2.58925i	−0.254742	−	0.115795i
$501$	21.5462	−	17.7879i	0.962612	−	0.794705i
$502$	−27.2909	−	51.8105i	−1.21805	−	2.31241i
$503$	−12.8559	+	6.45647i	−0.573216	+	0.287880i	−0.711698	−	0.702485i	$-0.752074\pi$
$503$	−12.8559	+	6.45647i	−0.573216	+	0.287880i	0.138483	+	0.990365i	$0.455777\pi$
$504$	1.08397	−	5.62062i	0.0482838	−	0.250362i
$505$	1.58117	+	27.1476i	0.0703610	+	1.20805i
$506$	−57.3099	−	31.6223i	−2.54774	−	1.40578i
$507$	0.111635	−	4.07556i	0.00495789	−	0.181002i
$508$	1.84736	−	13.5251i	0.0819634	−	0.600078i
$509$	−4.00720	+	10.3789i	−0.177616	+	0.460037i	−0.992890	−	0.119039i	$-0.962019\pi$
$509$	−4.00720	+	10.3789i	−0.177616	+	0.460037i	0.815274	+	0.579076i	$0.196587\pi$
$510$	50.5344	+	8.31771i	2.23770	+	0.368314i
$511$	14.0694	−	1.09356i	0.622393	−	0.0483762i
$512$	20.9744	−	17.5996i	0.926945	−	0.777799i
$513$	2.70998	−	1.28059i	0.119649	−	0.0565396i
$514$	14.2873	+	11.9885i	0.630187	+	0.528790i
$515$	15.1231	+	10.8094i	0.666404	+	0.476317i
$516$	0.248861	−	2.36241i	0.0109555	−	0.103999i
$517$	−25.4091	+	29.1156i	−1.11749	+	1.28050i
$518$	3.40920	+	15.7386i	0.149792	+	0.691515i
$519$	21.3816	+	21.3089i	0.938550	+	0.935356i
$520$	6.66464	−	1.30889i	0.292264	−	0.0573987i
$521$	−17.5572	−	2.05214i	−0.769193	−	0.0899058i	−0.277560	−	0.960708i	$-0.589526\pi$
$521$	−17.5572	−	2.05214i	−0.769193	−	0.0899058i	−0.491633	+	0.870802i	$0.663600\pi$
$522$	−0.391957	+	3.45552i	−0.0171555	+	0.151244i
$523$	5.66315	+	7.60693i	0.247632	+	0.332628i	0.908508	−	0.417867i	$-0.137222\pi$
$523$	5.66315	+	7.60693i	0.247632	+	0.332628i	−0.660876	+	0.750495i	$0.729815\pi$
$524$	−1.56765	+	7.23710i	−0.0684833	+	0.316154i
$525$	15.4111	+	7.89459i	0.672595	+	0.344548i
$526$	10.9549	+	10.7445i	0.477658	+	0.468483i
$527$	10.0339	−	38.9540i	0.437084	−	1.69686i
$528$	−33.8346	+	7.73388i	−1.47246	+	0.336574i
$529$	−29.1086	−	26.4146i	−1.26559	−	1.14846i
$530$	−30.1327	+	69.8554i	−1.30888	+	3.03432i
$531$	17.9350	+	7.66399i	0.778312	+	0.332589i
$532$	1.51741	−	2.03824i	0.0657882	−	0.0883689i
$533$	18.7373	+	21.4705i	0.811601	+	0.929992i
$534$	11.1133	−	7.80986i	0.480919	−	0.337966i
$535$	−25.3053	−	8.11383i	−1.09405	−	0.350792i
$536$	−6.71891	−	1.31955i	−0.290213	−	0.0569959i
$537$	−15.8271	+	32.4311i	−0.682991	+	1.39951i
$538$	−49.0407	+	22.2917i	−2.11429	+	0.961065i
$539$	−0.232905	+	1.32087i	−0.0100319	+	0.0568939i
$540$	3.01271	−	24.7895i	0.129646	−	1.06677i
$541$	2.32999	+	13.2140i	0.100174	+	0.568114i	0.993039	+	0.117789i	$0.0375808\pi$
$541$	2.32999	+	13.2140i	0.100174	+	0.568114i	−0.892865	+	0.450325i	$0.851308\pi$
$542$	28.8688	+	42.0918i	1.24002	+	1.80800i
$543$	25.1522	−	4.73129i	1.07939	−	0.203039i
$544$	24.3134	+	30.1439i	1.04243	+	1.29241i
$545$	28.5240	−	11.6533i	1.22183	−	0.499173i
$546$	−28.7915	+	4.26748i	−1.23216	+	0.182631i
$547$	3.42671	−	2.06803i	0.146515	−	0.0884225i	−0.441547	−	0.897238i	$-0.645570\pi$
$547$	3.42671	−	2.06803i	0.146515	−	0.0884225i	0.588062	+	0.808816i	$0.299891\pi$
$548$	6.38093	−	4.19681i	0.272580	−	0.179279i
$549$	16.7304	+	4.24871i	0.714036	+	0.181331i
$550$	1.78303	−	30.6134i	0.0760285	−	1.30536i
$551$	0.187149	−	0.296933i	0.00797283	−	0.0126498i
$552$	−9.64949	−	0.0771197i	−0.410709	−	0.00328243i
$553$	−25.2705	+	18.0622i	−1.07461	+	0.768085i
$554$	−5.77804	−	0.449105i	−0.245485	−	0.0190806i
$555$	−4.45847	−	15.3374i	−0.189251	−	0.651036i
$556$	4.35901	+	1.78085i	0.184863	+	0.0755250i
$557$	0.834823	+	2.78850i	0.0353726	+	0.118153i	0.973853	−	0.227181i	$-0.0729509\pi$
$557$	0.834823	+	2.78850i	0.0353726	+	0.118153i	−0.938480	+	0.345334i	$0.887766\pi$
$558$	−42.7280	−	9.10310i	−1.80882	−	0.385365i
$559$	2.67214	−	0.633310i	0.113020	−	0.0267862i
$560$	13.2202	+	34.2412i	0.558656	+	1.44695i
$561$	−8.08904	−	38.8409i	−0.341519	−	1.63986i
$562$	−1.45679	+	2.76565i	−0.0614511	+	0.116662i
$563$	−0.609188	+	31.4096i	−0.0256742	+	1.32375i	0.736524	+	0.676411i	$0.236466\pi$
$563$	−0.609188	+	31.4096i	−0.0256742	+	1.32375i	−0.762198	+	0.647344i	$0.775880\pi$
$564$	5.50045	−	24.4470i	0.231611	−	1.02940i
$565$	−17.4290	+	17.0942i	−0.733243	+	0.719160i
$566$	−21.5951	−	37.4039i	−0.907712	−	1.57220i
$567$	4.06145	−	23.9888i	0.170565	−	1.00744i
$568$	−0.782075	+	1.35459i	−0.0328151	+	0.0568375i
$569$	−0.922457	−	3.58120i	−0.0386714	−	0.150132i	0.946140	−	0.323756i	$-0.104946\pi$
$569$	−0.922457	−	3.58120i	−0.0386714	−	0.150132i	−0.984812	+	0.173625i	$0.944452\pi$
$570$	−3.03109	+	4.72501i	−0.126958	+	0.197909i
$571$	−28.9327	+	15.9644i	−1.21080	+	0.668089i	−0.954414	−	0.298487i	$-0.903518\pi$
$571$	−28.9327	+	15.9644i	−1.21080	+	0.668089i	−0.256382	+	0.966576i	$0.582531\pi$
$572$	12.3396	+	19.5781i	0.515944	+	0.818601i
$573$	36.5211	−	1.12496i	1.52569	−	0.0469957i
$574$	−28.2396	+	35.0117i	−1.17870	+	1.46136i
$575$	8.37187	−	27.9640i	0.349131	−	1.16618i
$576$	10.8453	−	9.52999i	0.451888	−	0.397083i
$577$	−24.2426	+	25.6956i	−1.00923	+	1.06972i	−0.0116702	+	0.999932i	$0.503715\pi$
$577$	−24.2426	+	25.6956i	−1.00923	+	1.06972i	−0.997562	+	0.0697914i	$0.977767\pi$
$578$	−16.1037	+	12.4813i	−0.669824	+	0.519153i
$579$	21.0576	+	14.0921i	0.875123	+	0.585650i
$580$	−1.26148	−	2.63816i	−0.0523801	−	0.109544i
$581$	−3.38664	−	34.8178i	−0.140502	−	1.44448i
$582$	−12.0204	−	10.2511i	−0.498261	−	0.424922i
$583$	58.8905	+	2.28522i	2.43899	+	0.0946441i
$584$	−3.07828	−	2.02462i	−0.127380	−	0.0837794i
$585$	28.1933	−	6.20775i	1.16565	−	0.256659i
$586$	−16.9388	−	8.50701i	−0.699737	−	0.351421i
$587$	0.719307	+	37.0873i	0.0296890	+	1.53076i	0.658134	+	0.752901i	$0.271346\pi$
$587$	0.719307	+	37.0873i	0.0296890	+	1.53076i	−0.628445	+	0.777854i	$0.716308\pi$
$588$	−0.274971	−	0.825103i	−0.0113396	−	0.0340267i
$589$	3.48497	+	2.70106i	0.143596	+	0.111295i
$590$	−36.0900	+	5.64437i	−1.48580	+	0.232375i
$591$	31.5981	−	18.7267i	1.29977	−	0.770313i
$592$	6.20968	−	12.9864i	0.255216	−	0.533739i
$593$	14.2684	+	5.19326i	0.585932	+	0.213262i	0.617939	−	0.786226i	$-0.287968\pi$
$593$	14.2684	+	5.19326i	0.585932	+	0.213262i	−0.0320074	+	0.999488i	$0.510190\pi$
$594$	−41.7750	+	10.5566i	−1.71405	+	0.433143i
$595$	−39.4272	+	14.3503i	−1.61636	+	0.588306i
$596$	−2.79512	+	28.7363i	−0.114492	+	1.17708i
$597$	−11.0432	+	10.6593i	−0.451968	+	0.436255i
$598$	15.8846	+	46.4245i	0.649570	+	1.89844i
$599$	−28.9497	+	26.2705i	−1.18285	+	1.07338i	−0.187005	+	0.982359i	$0.559878\pi$
$599$	−28.9497	+	26.2705i	−1.18285	+	1.07338i	−0.995849	+	0.0910237i	$0.970986\pi$
$600$	−1.91757	−	4.09402i	−0.0782846	−	0.167138i
$601$	6.72378	−	19.6510i	0.274269	−	0.801581i	−0.719932	−	0.694044i	$-0.755827\pi$
$601$	6.72378	−	19.6510i	0.274269	−	0.801581i	0.994201	−	0.107537i	$-0.0342963\pi$
$602$	1.71689	+	3.98020i	0.0699753	+	0.162221i
$603$	−28.6787	−	4.95609i	−1.16789	−	0.201828i
$604$	−1.50928	+	0.176410i	−0.0614119	+	0.00717802i
$605$	−22.3139	+	7.15467i	−0.907190	+	0.290879i
$606$	−18.3635	+	24.2592i	−0.745965	+	0.985463i
$607$	13.9219	−	3.87544i	0.565074	−	0.157299i	0.0261568	−	0.999658i	$-0.491673\pi$
$607$	13.9219	−	3.87544i	0.565074	−	0.157299i	0.538917	+	0.842359i	$0.318834\pi$
$608$	−4.08945	+	1.13838i	−0.165849	+	0.0461673i
$609$	−1.10753	−	2.62503i	−0.0448793	−	0.106371i
$610$	−30.7851	+	9.87086i	−1.24645	+	0.399659i
$611$	28.7724	−	3.36301i	1.16401	−	0.136053i
$612$	16.6036	+	19.6510i	0.671162	+	0.794345i
$613$	−2.13026	−	4.93849i	−0.0860403	−	0.199464i	0.869764	−	0.493468i	$-0.164271\pi$
$613$	−2.13026	−	4.93849i	−0.0860403	−	0.199464i	−0.955804	+	0.294005i	$0.905012\pi$
$614$	−9.06256	+	26.4863i	−0.365735	+	1.06890i
$615$	25.5273	−	36.5893i	1.02936	−	1.47542i
$616$	6.15029	−	5.58109i	0.247802	−	0.224868i
$617$	−7.87738	−	23.0225i	−0.317131	−	0.926851i	−0.983449	−	0.181183i	$-0.942007\pi$
$617$	−7.87738	−	23.0225i	−0.317131	−	0.926851i	0.666318	−	0.745668i	$-0.267869\pi$
$618$	5.02686	+	20.1818i	0.202210	+	0.811832i
$619$	3.30867	−	34.0161i	0.132987	−	1.36722i	−0.656903	−	0.753975i	$-0.728134\pi$
$619$	3.30867	−	34.0161i	0.132987	−	1.36722i	0.789890	−	0.613249i	$-0.210138\pi$
$620$	34.5193	−	12.5640i	1.38633	−	0.504582i
$621$	−41.0112	+	0.607392i	−1.64572	+	0.0243738i
$622$	10.9174	+	3.97362i	0.437750	+	0.159328i
$623$	−4.80044	+	10.0393i	−0.192326	+	0.402215i
$624$	22.6785	+	12.7510i	0.907868	+	0.510447i
$625$	−29.4566	+	4.60694i	−1.17827	+	0.184277i
$626$	19.9891	+	15.4927i	0.798927	+	0.619215i
$627$	4.26039	+	0.872132i	0.170144	+	0.0348296i
$628$	−0.0327972	−	1.69102i	−0.00130875	−	0.0674788i
$629$	14.7045	+	7.38489i	0.586307	+	0.294455i
$630$	17.3775	+	42.1244i	0.692336	+	1.67828i
$631$	5.94167	+	3.90790i	0.236534	+	0.155571i	0.662243	−	0.749289i	$-0.269605\pi$
$631$	5.94167	+	3.90790i	0.236534	+	0.155571i	−0.425709	+	0.904860i	$0.639975\pi$
$632$	8.10376	+	0.314463i	0.322350	+	0.0125087i
$633$	1.20193	−	6.51175i	0.0477725	−	0.258819i
$634$	−3.35555	−	34.4981i	−0.133266	−	1.37009i
$635$	−10.6579	−	22.2890i	−0.422944	−	0.884513i
$636$	−34.2867	+	16.8776i	−1.35955	+	0.669242i
$637$	0.794684	−	0.615927i	0.0314865	−	0.0244039i
$638$	−3.46256	+	3.67010i	−0.137084	+	0.145301i
$639$	−3.19202	+	5.83189i	−0.126274	+	0.230706i
$640$	4.69416	−	15.6796i	0.185553	−	0.619790i
$641$	18.5297	−	22.9732i	0.731878	−	0.907386i	−0.266528	−	0.963827i	$-0.585877\pi$
$641$	18.5297	−	22.9732i	0.731878	−	0.907386i	0.998406	+	0.0564412i	$0.0179753\pi$
$642$	−15.6522	−	25.2795i	−0.617742	−	0.997703i
$643$	−4.62450	−	7.33727i	−0.182373	−	0.289354i	0.742337	−	0.670026i	$-0.233717\pi$
$643$	−4.62450	−	7.33727i	−0.182373	−	0.289354i	−0.924710	+	0.380673i	$0.875693\pi$
$644$	−30.4451	+	16.7989i	−1.19970	+	0.661968i
$645$	−1.97322	−	3.81979i	−0.0776955	−	0.150404i
$646$	−1.44258	−	5.60044i	−0.0567575	−	0.220346i
$647$	−22.2567	+	38.5498i	−0.875002	+	1.51555i	−0.0182408	+	0.999834i	$0.505807\pi$
$647$	−22.2567	+	38.5498i	−0.875002	+	1.51555i	−0.856761	+	0.515714i	$0.827527\pi$
$648$	−4.67495	+	4.30077i	−0.183649	+	0.168950i
$649$	14.1488	+	24.5065i	0.555391	+	0.961965i
$650$	−16.4114	+	16.0962i	−0.643708	+	0.631344i
$651$	34.1678	−	10.6551i	1.33914	−	0.417606i
$652$	0.222456	−	11.4698i	0.00871206	−	0.449192i
$653$	16.6696	−	31.6464i	0.652330	−	1.23842i	−0.305803	−	0.952095i	$-0.598925\pi$
$653$	16.6696	−	31.6464i	0.652330	−	1.23842i	0.958133	−	0.286323i	$-0.0924332\pi$
$654$	32.7435	+	10.7881i	1.28037	+	0.421849i
$655$	4.82713	+	12.5026i	0.188612	+	0.488516i
$656$	39.1239	−	9.27252i	1.52753	−	0.362031i
$657$	−13.2768	−	8.30495i	−0.517978	−	0.324007i
$658$	13.1141	+	43.8043i	0.511243	+	1.70767i
$659$	−26.7663	−	10.9352i	−1.04267	−	0.425977i	−0.208810	−	0.977956i	$-0.566959\pi$
$659$	−26.7663	−	10.9352i	−1.04267	−	0.425977i	−0.833858	+	0.551979i	$0.813873\pi$
$660$	25.0732	−	26.1541i	0.975972	−	1.01805i
$661$	37.7591	+	2.93487i	1.46866	+	0.114153i	0.786744	−	0.617279i	$-0.211765\pi$
$661$	37.7591	+	2.93487i	1.46866	+	0.114153i	0.681914	+	0.731432i	$0.261148\pi$
$662$	6.00208	−	4.29003i	0.233277	−	0.166737i
$663$	−15.0757	+	25.6366i	−0.585493	+	0.995642i
$664$	−4.86995	+	7.72670i	−0.188991	+	0.299854i
$665$	0.267409	−	4.59124i	0.0103697	−	0.178041i
$666$	7.33959	−	16.2939i	0.284403	−	0.631377i
$667$	−4.01284	+	2.63929i	−0.155378	+	0.102194i
$668$	−22.5053	+	13.5820i	−0.870757	+	0.525504i
$669$	26.8883	+	33.8869i	1.03956	+	1.31014i
$670$	50.4597	−	20.6151i	1.94943	−	0.796429i
$671$	15.7231	+	19.4936i	0.606983	+	0.752541i
$672$	−11.4153	+	32.5118i	−0.440354	+	1.25417i
$673$	−17.8691	−	26.0538i	−0.688803	−	1.00430i	−0.998569	−	0.0534860i	$-0.982967\pi$
$673$	−17.8691	−	26.0538i	−0.688803	−	1.00430i	0.309766	−	0.950813i	$-0.399749\pi$
$674$	−8.99892	−	51.0354i	−0.346625	−	1.96581i
$675$	−8.54512	−	17.2110i	−0.328902	−	0.662450i
$676$	−0.666070	+	3.77747i	−0.0256181	+	0.145287i
$677$	13.4713	−	6.12347i	0.517745	−	0.235344i	−0.137855	−	0.990452i	$-0.544021\pi$
$677$	13.4713	−	6.12347i	0.517745	−	0.235344i	0.655600	+	0.755108i	$0.272416\pi$
$678$	−27.2483	+	1.89895i	−1.04646	+	0.0729289i
$679$	12.6999	+	2.49418i	0.487378	+	0.0957179i
$680$	10.4315	+	3.34472i	0.400029	+	0.128264i
$681$	−0.187524	−	2.10213i	−0.00718592	−	0.0805540i
$682$	−41.6766	−	47.7561i	−1.59588	−	1.82867i
$683$	6.33715	−	8.51226i	0.242484	−	0.325713i	−0.664175	−	0.747577i	$-0.731217\pi$
$683$	6.33715	−	8.51226i	0.242484	−	0.325713i	0.906659	+	0.421865i	$0.138624\pi$
$684$	−2.69865	+	0.817957i	−0.103186	+	0.0312754i
$685$	5.47492	−	12.6923i	0.209186	−	0.484947i
$686$	−25.5226	−	23.1606i	−0.974459	−	0.884274i
$687$	18.3947	+	19.8121i	0.701803	+	0.755880i
$688$	0.966513	−	3.75223i	0.0368479	−	0.143053i
$689$	−31.5406	−	30.9348i	−1.20160	−	1.17852i
$690$	64.5160	−	41.6980i	2.45608	−	1.58742i
$691$	−0.0718770	+	0.331821i	−0.00273433	+	0.0126231i	−0.978681	−	0.205388i	$-0.934154\pi$
$691$	−0.0718770	+	0.331821i	−0.00273433	+	0.0126231i	0.975946	+	0.218011i	$0.0699569\pi$
$692$	−16.9592	−	22.7802i	−0.644693	−	0.865973i
$693$	25.5937	−	24.3118i	0.972224	−	0.923530i
$694$	32.3318	+	3.77904i	1.22730	+	0.143450i
$695$	8.36256	−	1.64235i	0.317210	−	0.0622980i
$696$	−0.191301	+	0.718844i	−0.00725125	+	0.0272477i
$697$	9.73030	+	44.9201i	0.368561	+	1.70147i
$698$	42.3942	−	48.5783i	1.60464	−	1.83872i
$699$	−16.3596	−	11.8918i	−0.618775	−	0.449789i
$700$	−13.2531	−	9.47278i	−0.500922	−	0.358037i
$701$	−28.5457	−	23.9527i	−1.07816	−	0.904681i	−0.0823907	−	0.996600i	$-0.526256\pi$
$701$	−28.5457	−	23.9527i	−1.07816	−	0.904681i	−0.995767	+	0.0919188i	$0.970700\pi$
$702$	28.5085	+	15.1840i	1.07598	+	0.573083i
$703$	−1.38166	+	1.15935i	−0.0521102	+	0.0437257i
$704$	20.8841	−	1.62324i	0.787098	−	0.0611781i
$705$	−15.9962	−	42.4376i	−0.602453	−	1.59829i
$706$	−11.1757	+	28.9457i	−0.420601	+	1.08938i
$707$	3.37332	−	24.6971i	0.126867	−	0.928830i
$708$	−15.6338	−	9.60632i	−0.587554	−	0.361028i
$709$	23.5431	+	12.9905i	0.884181	+	0.487870i	0.859096	−	0.511815i	$-0.171027\pi$
$709$	23.5431	+	12.9905i	0.884181	+	0.487870i	0.0250850	+	0.999685i	$0.492014\pi$
$710$	−0.723995	−	12.4305i	−0.0271710	−	0.466509i
$711$	34.4659	+	0.550945i	1.29257	+	0.0206621i
$712$	2.59633	−	1.30393i	0.0973015	−	0.0488667i
$713$	−28.1190	−	53.3827i	−1.05307	−	1.99920i
$714$	−43.9837	−	16.4080i	−1.64605	−	0.614054i
$715$	38.1304	+	17.3324i	1.42600	+	0.648196i
$716$	19.2028	−	27.9984i	0.717643	−	1.04635i
$717$	0.743529	+	1.01558i	0.0277676	+	0.0379274i
$718$	1.93759	+	14.1857i	0.0723103	+	0.529405i
$719$	−37.6978	−	8.93455i	−1.40589	−	0.333203i	−0.543486	−	0.839418i	$-0.682896\pi$
$719$	−37.6978	−	8.93455i	−1.40589	−	0.333203i	−0.862407	+	0.506216i	$0.831044\pi$
$720$	10.7895	−	39.2773i	0.402100	−	1.46378i
$721$	−11.6930	−	12.3939i	−0.435470	−	0.461572i
$722$	−35.1364	−	5.49524i	−1.30764	−	0.204512i
$723$	23.5016	+	18.5177i	0.874035	+	0.688680i
$724$	−24.0602	+	0.933646i	−0.894191	+	0.0346987i
$725$	−1.92652	−	1.16266i	−0.0715490	−	0.0431800i
$726$	−24.1907	−	10.1093i	−0.897800	−	0.375192i
$727$	14.1793	+	3.94709i	0.525883	+	0.146390i	0.520932	−	0.853598i	$-0.325585\pi$
$727$	14.1793	+	3.94709i	0.525883	+	0.146390i	0.00495097	+	0.999988i	$0.498424\pi$
$728$	−6.22569			−0.230740
$729$	−19.4486	+	18.7284i	−0.720318	+	0.693644i
$730$	29.3302			1.08556
$731$	4.26699	+	1.18780i	0.157820	+	0.0439323i
$732$	−14.9839	−	6.26178i	−0.553820	−	0.231442i
$733$	−7.82473	−	4.72225i	−0.289013	−	0.174420i	0.364780	−	0.931094i	$-0.381144\pi$
$733$	−7.82473	−	4.72225i	−0.289013	−	0.174420i	−0.653793	+	0.756674i	$0.726823\pi$
$734$	−8.22313	+	0.319095i	−0.303521	+	0.0117780i
$735$	−1.23640	−	0.974197i	−0.0456052	−	0.0359338i
$736$	57.3907	+	8.97574i	2.11545	+	0.330850i
$737$	−28.9772	−	30.7141i	−1.06739	−	1.13137i
$738$	48.2963	−	12.6160i	1.77781	−	0.464402i
$739$	27.9445	+	6.62296i	1.02795	+	0.243630i	0.709795	−	0.704408i	$-0.248787\pi$
$739$	27.9445	+	6.62296i	1.02795	+	0.243630i	0.318159	+	0.948037i	$0.396936\pi$
$740$	2.03359	+	14.8885i	0.0747564	+	0.547313i
$741$	−1.92573	−	2.63033i	−0.0707434	−	0.0966276i
$742$	39.4423	−	57.5083i	1.44797	−	2.11120i
$743$	−28.0396	−	12.7456i	−1.02867	−	0.467590i	−0.172900	−	0.984939i	$-0.555314\pi$
$743$	−28.0396	−	12.7456i	−1.02867	−	0.467590i	−0.855774	+	0.517349i	$0.826919\pi$
$744$	−8.75512	−	3.26608i	−0.320978	−	0.119740i
$745$	24.3530	+	46.2331i	0.892226	+	1.69385i
$746$	19.2439	−	9.66466i	0.704570	−	0.353848i
$747$	−19.9452	+	33.3052i	−0.729757	+	1.21857i
$748$	2.17030	+	37.2625i	0.0793539	+	1.36245i
$749$	21.3275	+	11.7680i	0.779291	+	0.429994i
$750$	−10.7955	−	6.63338i	−0.394195	−	0.242217i
$751$	5.24462	−	38.3974i	0.191379	−	1.40114i	−0.604943	−	0.796269i	$-0.706804\pi$
$751$	5.24462	−	38.3974i	0.191379	−	1.40114i	0.796322	−	0.604873i	$-0.206776\pi$
$752$	14.7215	−	38.1296i	0.536838	−	1.39045i
$753$	−18.7779	−	49.8171i	−0.684303	−	1.81544i
$754$	3.77099	−	0.293105i	0.137331	−	0.0106742i
$755$	−2.10679	+	1.76781i	−0.0766741	+	0.0643372i
$756$	−7.08873	+	21.7647i	−0.257815	+	0.791573i
$757$	6.10708	+	5.12445i	0.221966	+	0.186251i	0.746989	−	0.664837i	$-0.231499\pi$
$757$	6.10708	+	5.12445i	0.221966	+	0.186251i	−0.525023	+	0.851088i	$0.675943\pi$
$758$	6.66359	+	4.76285i	0.242033	+	0.172995i
$759$	−48.1354	−	34.9897i	−1.74720	−	1.27004i
$760$	−0.789515	+	0.904684i	−0.0286387	+	0.0328163i
$761$	−3.81026	−	17.5901i	−0.138122	−	0.637641i	−0.992930	−	0.118698i	$-0.962128\pi$
$761$	−3.81026	−	17.5901i	−0.138122	−	0.637641i	0.854809	−	0.518943i	$-0.173674\pi$
$762$	7.10891	−	26.7128i	0.257529	−	0.967704i
$763$	−27.7143	+	5.44291i	−1.00332	+	0.197046i
$764$	−34.1431	−	3.99075i	−1.23525	−	0.144380i
$765$	44.6508	+	13.2019i	1.61435	+	0.477315i
$766$	17.5145	+	23.5260i	0.632823	+	0.850029i
$767$	4.49079	−	20.7318i	0.162153	−	0.748582i
$768$	29.3810	−	18.9896i	1.06020	−	0.685227i
$769$	34.9971	+	34.3249i	1.26203	+	1.23779i	0.958541	+	0.284953i	$0.0919781\pi$
$769$	34.9971	+	34.3249i	1.26203	+	1.23779i	0.303487	+	0.952836i	$0.401849\pi$
$770$	−16.4914	+	64.0237i	−0.594310	+	2.30725i
$771$	11.5372	+	12.4262i	0.415504	+	0.447520i
$772$	−17.6531	−	16.0193i	−0.635349	−	0.576548i
$773$	4.60233	−	10.6694i	0.165534	−	0.383752i	−0.815177	−	0.579211i	$-0.803361\pi$
$773$	4.60233	−	10.6694i	0.165534	−	0.383752i	0.980712	+	0.195460i	$0.0626199\pi$
$774$	1.09338	−	4.68445i	0.0393009	−	0.168379i
$775$	16.8797	−	22.6734i	0.606338	−	0.814453i
$776$	−2.22185	−	2.54595i	−0.0797596	−	0.0913944i
$777$	1.30087	+	14.5827i	0.0466685	+	0.523152i
$778$	−33.6729	−	10.7968i	−1.20723	−	0.387083i
$779$	−4.94350	−	0.970871i	−0.177119	−	0.0347851i
$780$	−27.0940	+	1.88820i	−0.970122	+	0.0676086i
$781$	−8.78124	+	3.99156i	−0.314217	+	0.142829i
$782$	−13.7423	+	77.9364i	−0.491424	+	2.78700i
$783$	−0.743239	+	3.07314i	−0.0265612	+	0.109825i
$784$	−0.246340	−	1.39706i	−0.00879785	−	0.0498951i
$785$	−1.73139	−	2.52443i	−0.0617959	−	0.0901006i
$786$	−4.96763	+	14.1483i	−0.177189	+	0.504652i
$787$	−1.25782	−	1.55945i	−0.0448363	−	0.0555883i	0.755450	−	0.655206i	$-0.227418\pi$
$787$	−1.25782	−	1.55945i	−0.0448363	−	0.0555883i	−0.800287	+	0.599618i	$0.795319\pi$
$788$	−31.9895	+	13.0692i	−1.13958	+	0.465569i
$789$	8.67124	+	10.9282i	0.308704	+	0.389056i
$790$	−55.2736	+	33.3578i	−1.96655	+	1.18682i
$791$	18.6961	−	12.2966i	0.664755	−	0.437216i
$792$	−9.17003	+	0.923513i	−0.325843	+	0.0328156i
$793$	1.09160	−	18.7420i	0.0387637	−	0.665548i
$794$	0.0232368	−	0.0368677i	0.000824643	−	0.00130839i
$795$	−35.0605	+	59.6210i	−1.24347	+	2.11454i
$796$	11.7475	−	8.39663i	0.416380	−	0.297611i
$797$	7.95764	+	0.618516i	0.281874	+	0.0219090i	0.217651	−	0.976027i	$-0.430160\pi$
$797$	7.95764	+	0.618516i	0.281874	+	0.0219090i	0.0642227	+	0.997936i	$0.479543\pi$
$798$	3.56096	−	3.71447i	0.126056	−	0.131491i
$799$	43.2519	+	17.6704i	1.53014	+	0.625132i
$800$	7.80504	+	26.0706i	0.275950	+	0.921736i
$801$	10.9063	−	5.79240i	0.385354	−	0.204664i
$802$	−3.41807	+	0.810096i	−0.120696	+	0.0286055i
$803$	−8.18367	−	21.1962i	−0.288796	−	0.747999i
$804$	26.0058	+	8.56822i	0.917154	+	0.302178i
$805$	−29.3298	+	55.6812i	−1.03374	+	1.96251i
$806$	−0.921368	+	47.5055i	−0.0324538	+	1.67331i
$807$	−46.7547	+	14.5803i	−1.64584	+	0.513250i
$808$	−4.64623	+	4.55699i	−0.163454	+	0.160314i
$809$	8.53106	+	14.7762i	0.299936	+	0.519505i	0.976121	−	0.217227i	$-0.0697013\pi$
$809$	8.53106	+	14.7762i	0.299936	+	0.519505i	−0.676185	+	0.736732i	$0.736368\pi$
$810$	12.2797	−	49.0546i	0.431463	−	1.72360i
$811$	11.6448	−	20.1693i	0.408903	−	0.708240i	−0.585865	−	0.810409i	$-0.699245\pi$
$811$	11.6448	−	20.1693i	0.408903	−	0.708240i	0.994767	+	0.102169i	$0.0325783\pi$
$812$	0.668614	+	2.59572i	0.0234637	+	0.0910918i
$813$	21.2972	+	41.2275i	0.746926	+	1.44591i
$814$	22.7016	−	12.5262i	0.795692	−	0.439044i
$815$	−11.0709	−	17.5651i	−0.387796	−	0.615279i
$816$	22.0903	+	35.6776i	0.773316	+	1.24897i
$817$	−0.304798	+	0.377891i	−0.0106635	+	0.0132207i
$818$	6.62711	−	22.1361i	0.231712	−	0.773970i
$819$	−26.4550	+	0.603310i	−0.924411	+	0.0210814i
$820$	−28.8037	+	30.5302i	−1.00587	+	1.06616i
$821$	38.8427	−	30.1054i	1.35562	−	1.05068i	0.362699	−	0.931906i	$-0.381855\pi$
$821$	38.8427	−	30.1054i	1.35562	−	1.05068i	0.992921	−	0.118778i	$-0.0378978\pi$
$822$	13.8757	−	6.83032i	0.483970	−	0.238235i
$823$	21.9200	+	45.8418i	0.764084	+	1.59795i	0.801027	+	0.598629i	$0.204288\pi$
$823$	21.9200	+	45.8418i	0.764084	+	1.59795i	−0.0369425	+	0.999317i	$0.511762\pi$
$824$	0.430684	+	4.42782i	0.0150036	+	0.154250i
$825$	5.06047	−	27.4162i	0.176183	−	0.954511i
$826$	33.4581	+	1.29832i	1.16415	+	0.0451745i
$827$	5.92467	+	3.89672i	0.206021	+	0.135502i	0.648327	−	0.761362i	$-0.275469\pi$
$827$	5.92467	+	3.89672i	0.206021	+	0.135502i	−0.442306	+	0.896864i	$0.645839\pi$
$828$	38.2503	+	5.09178i	1.32929	+	0.176951i
$829$	1.71053	+	0.859058i	0.0594090	+	0.0298363i	0.478256	−	0.878221i	$-0.341269\pi$
$829$	1.71053	+	0.859058i	0.0594090	+	0.0298363i	−0.418847	+	0.908057i	$0.637566\pi$
$830$	−1.40989	−	72.6934i	−0.0489379	−	2.52323i
$831$	−5.16191	−	1.05668i	−0.179065	−	0.0366558i
$832$	−12.4111	−	9.61930i	−0.430276	−	0.333489i
$833$	1.60216	−	0.250573i	0.0555115	−	0.00868184i
$834$	8.31158	+	4.67317i	0.287807	+	0.161819i
$835$	−20.5231	+	42.9205i	−0.710232	+	1.48532i
$836$	−3.84458	−	1.39931i	−0.132967	−	0.0483962i
$837$	−37.5198	−	13.0302i	−1.29687	−	0.450389i
$838$	−43.3767	+	15.7878i	−1.49842	+	0.545382i
$839$	−0.806394	+	8.29046i	−0.0278398	+	0.286218i	0.971041	+	0.238914i	$0.0767914\pi$
$839$	−0.806394	+	8.29046i	−0.0278398	+	0.286218i	−0.998881	+	0.0473042i	$0.984937\pi$
$840$	2.35575	+	9.45787i	0.0812812	+	0.326327i
$841$	−9.26842	−	27.0880i	−0.319601	−	0.934069i
$842$	8.41466	−	7.63590i	0.289988	−	0.263150i
$843$	−1.62607	+	2.33071i	−0.0560048	+	0.0802740i
$844$	−2.01679	+	5.89428i	−0.0694206	+	0.202889i
$845$	2.74969	+	6.37449i	0.0945920	+	0.219289i
$846$	17.1924	−	47.7414i	0.591087	−	1.64138i
$847$	21.3340	−	2.49359i	0.733046	−	0.0856807i
$848$	−59.3577	+	19.0323i	−2.03835	+	0.653571i
$849$	−15.2640	−	36.1783i	−0.523860	−	1.24164i
$850$	−35.7178	+	9.94272i	−1.22511	+	0.341033i
$851$	23.7770	−	6.61879i	0.815066	−	0.226889i
$852$	3.77505	−	4.98707i	0.129331	−	0.170854i
$853$	4.72296	−	1.51436i	0.161711	−	0.0518505i	−0.223368	−	0.974734i	$-0.571705\pi$
$853$	4.72296	−	1.51436i	0.161711	−	0.0518505i	0.385079	+	0.922884i	$0.374174\pi$
$854$	29.4332	−	3.44025i	1.00718	−	0.117723i
$855$	−3.26723	+	3.92080i	−0.111737	+	0.134088i
$856$	−2.51897	−	5.83964i	−0.0860967	−	0.199595i
$857$	−4.42633	+	12.9364i	−0.151200	+	0.441900i	−0.995588	−	0.0938329i	$-0.970088\pi$
$857$	−4.42633	+	12.9364i	−0.151200	+	0.441900i	0.844387	+	0.535733i	$0.179965\pi$
$858$	19.8776	+	42.4387i	0.678611	+	1.44883i
$859$	33.8660	−	30.7318i	1.15549	−	1.04856i	0.157357	−	0.987542i	$-0.449703\pi$
$859$	33.8660	−	30.7318i	1.15549	−	1.04856i	0.998137	−	0.0610133i	$-0.0194332\pi$
$860$	1.30945	+	3.82703i	0.0446520	+	0.130500i
$861$	−29.4238	+	28.4008i	−1.00276	+	0.967898i
$862$	5.44306	−	55.9595i	0.185391	−	1.90599i
$863$	12.7094	−	4.62586i	0.432634	−	0.157466i	−0.116518	−	0.993189i	$-0.537173\pi$
$863$	12.7094	−	4.62586i	0.432634	−	0.157466i	0.549152	+	0.835723i	$0.314951\pi$
$864$	31.6333	−	21.4833i	1.07619	−	0.730876i
$865$	−48.3006	−	17.5800i	−1.64227	−	0.597738i
$866$	7.81234	−	16.3381i	0.265474	−	0.555192i
$867$	−15.9350	+	9.44391i	−0.541181	+	0.320732i
$868$	−33.2676	+	5.20296i	−1.12918	+	0.176600i
$869$	39.5293	+	30.6375i	1.34094	+	1.03931i
$870$	−1.87219	−	5.61786i	−0.0634731	−	0.190463i
$871$	0.613805	+	31.6476i	0.0207980	+	1.07234i
$872$	6.58970	+	3.30947i	0.223156	+	0.112073i
$873$	−9.68805	−	10.6033i	−0.327891	−	0.358866i
$874$	−7.24743	−	4.76671i	−0.245148	−	0.161236i
$875$	10.3726	+	0.402505i	0.350659	+	0.0136072i
$876$	11.2103	+	9.56028i	0.378761	+	0.323012i
$877$	−4.34992	−	44.7210i	−0.146886	−	1.51012i	−0.721911	−	0.691986i	$-0.756736\pi$
$877$	−4.34992	−	44.7210i	−0.146886	−	1.51012i	0.575025	−	0.818136i	$-0.304992\pi$
$878$	0.0662027	+	0.138451i	0.00223423	+	0.00467250i
$879$	−14.3218	−	9.58445i	−0.483063	−	0.323276i
$880$	46.7103	−	36.2032i	1.57460	−	1.22041i
$881$	−20.7866	+	22.0325i	−0.700317	+	0.742293i	−0.975717	−	0.219037i	$-0.929708\pi$
$881$	−20.7866	+	22.0325i	−0.700317	+	0.742293i	0.275399	+	0.961330i	$0.411190\pi$
$882$	−0.345289	−	1.72700i	−0.0116265	−	0.0581510i
$883$	−2.83084	+	9.45568i	−0.0952655	+	0.318209i	−0.992318	−	0.123716i	$-0.960519\pi$
$883$	−2.83084	+	9.45568i	−0.0952655	+	0.318209i	0.897052	+	0.441925i	$0.145704\pi$
$884$	17.5663	−	21.7788i	0.590819	−	0.732501i
$885$	−33.1944	+	1.02248i	−1.11582	+	0.0343704i
$886$	−34.6712	−	55.0096i	−1.16480	−	1.84808i
$887$	−32.4589	+	17.9101i	−1.08986	+	0.601361i	−0.923071	−	0.384631i	$-0.874329\pi$
$887$	−32.4589	+	17.9101i	−1.08986	+	0.601361i	−0.166793	+	0.985992i	$0.553341\pi$
$888$	2.06394	−	3.21737i	0.0692614	−	0.107968i
$889$	5.64892	+	21.9304i	0.189459	+	0.735524i
$890$	−11.5642	+	20.0298i	−0.387634	+	0.671402i
$891$	−38.8769	+	4.81293i	−1.30242	+	0.161239i
$892$	−20.3489	−	35.2453i	−0.681332	−	1.18010i
$893$	−3.65624	+	3.58601i	−0.122351	+	0.120001i
$894$	−12.8337	+	57.0398i	−0.429222	+	1.90770i
$895$	1.19154	−	61.4355i	0.0398288	−	2.05356i
$896$	−6.99187	+	13.2737i	−0.233582	+	0.443444i
$897$	9.09520	+	43.6721i	0.303680	+	1.45817i
$898$	24.1260	+	62.4878i	0.805094	+	2.08524i
$899$	−4.52566	+	1.07260i	−0.150939	+	0.0357733i
$900$	5.57834	+	17.1959i	0.185945	+	0.573195i
$901$	−20.4362	−	68.2616i	−0.680828	−	2.27412i
$902$	67.0439	+	27.3904i	2.23232	+	0.912002i
$903$	1.10006	+	3.78426i	0.0366076	+	0.125932i
$904$	−5.82489	−	0.452746i	−0.193733	−	0.0150581i
$905$	−35.4538	+	25.3408i	−1.17852	+	0.842358i
$906$	−3.07701	−	0.0245918i	−0.102227	−	0.000817007i
$907$	3.35867	−	5.32890i	0.111523	−	0.176943i	−0.785586	−	0.618752i	$-0.787638\pi$
$907$	3.35867	−	5.32890i	0.111523	−	0.176943i	0.897109	+	0.441809i	$0.145663\pi$
$908$	−0.115449	+	1.98219i	−0.00383133	+	0.0657813i
$909$	−19.3017	+	19.8143i	−0.640197	+	0.657200i
$910$	41.4070	−	27.2338i	1.37263	−	0.902792i
$911$	33.5178	−	20.2281i	1.11049	−	0.670186i	0.161939	−	0.986801i	$-0.448225\pi$
$911$	33.5178	−	20.2281i	1.11049	−	0.670186i	0.948554	+	0.316615i	$0.102546\pi$
$912$	−4.54988	+	0.674383i	−0.150662	+	0.0223310i
$913$	−52.1405	+	21.3017i	−1.72560	+	0.704985i
$914$	12.1278	+	15.0361i	0.401151	+	0.497349i
$915$	−28.8853	+	5.43350i	−0.954918	+	0.179626i
$916$	−14.3860	−	20.9753i	−0.475326	−	0.693042i
$917$	−2.13322	−	12.0981i	−0.0704451	−	0.399514i
$918$	28.4273	+	43.6561i	0.938241	+	1.44087i
$919$	−2.62542	+	14.8895i	−0.0866046	+	0.491159i	0.910394	+	0.413742i	$0.135778\pi$
$919$	−2.62542	+	14.8895i	−0.0866046	+	0.491159i	−0.996999	+	0.0774172i	$0.975333\pi$
$920$	14.9583	−	6.79938i	0.493161	−	0.224169i
$921$	−11.1622	+	22.8723i	−0.367807	+	0.753667i
$922$	32.2866	+	6.34088i	1.06330	+	0.208826i
$923$	6.88548	+	2.20774i	0.226638	+	0.0726687i
$924$	−27.1720	+	19.0951i	−0.893892	+	0.628183i
$925$	7.60284	+	8.71189i	0.249980	+	0.286445i
$926$	−28.2687	+	37.9714i	−0.928967	+	1.24782i
$927$	2.25920	+	18.7735i	0.0742018	+	0.616602i
$928$	1.77356	−	4.11158i	0.0582201	−	0.134969i
$929$	−17.2620	−	15.6644i	−0.566347	−	0.513932i	0.337764	−	0.941231i	$-0.390330\pi$
$929$	−17.2620	−	15.6644i	−0.566347	−	0.513932i	−0.904111	+	0.427299i	$0.859465\pi$
$930$	72.5174	−	16.5760i	2.37794	−	0.543548i
$931$	−0.0443380	+	0.172131i	−0.00145312	+	0.00564135i
$932$	13.5845	+	13.3235i	0.444974	+	0.436427i
$933$	9.40091	+	4.81577i	0.307772	+	0.157661i
$934$	−2.71406	+	12.5295i	−0.0888068	+	0.409978i
$935$	40.3411	+	54.1875i	1.31930	+	1.77212i
$936$	5.55577	+	4.10676i	0.181596	+	0.134234i
$937$	−52.4311	−	6.12831i	−1.71285	−	0.200203i	−0.797626	−	0.603152i	$-0.793911\pi$
$937$	−52.4311	−	6.12831i	−1.71285	−	0.200203i	−0.915222	+	0.402949i	$0.867985\pi$
$938$	−49.0273	+	9.62865i	−1.60080	+	0.314387i
$939$	16.2859	+	16.2305i	0.531469	+	0.529661i
$940$	9.03289	+	41.7005i	0.294620	+	1.36012i
$941$	2.81203	−	3.22223i	0.0916695	−	0.105042i	−0.705768	−	0.708443i	$-0.749398\pi$
$941$	2.81203	−	3.22223i	0.0916695	−	0.105042i	0.797438	+	0.603401i	$0.206188\pi$
$942$	0.358805	−	3.40611i	0.0116905	−	0.110977i
$943$	56.0861	+	40.0879i	1.82641	+	1.30544i
$944$	−22.9277	−	19.2386i	−0.746233	−	0.626164i
$945$	10.9269	+	39.9612i	0.355451	+	1.29994i
$946$	5.34641	−	4.48617i	0.173827	−	0.145858i
$947$	56.6891	−	4.40623i	1.84215	−	0.143183i	0.891414	−	0.453189i	$-0.149714\pi$
$947$	56.6891	−	4.40623i	1.84215	−	0.143183i	0.950735	+	0.310006i	$0.100331\pi$
$948$	−31.9993	−	5.26692i	−1.03929	−	0.171062i
$949$	−6.13467	+	15.8892i	−0.199140	+	0.515785i
$950$	0.549977	−	4.02654i	0.0178436	−	0.130638i
$951$	0.862832	−	31.5002i	0.0279792	−	1.02146i
$952$	−8.79172	−	4.85107i	−0.284941	−	0.157224i
$953$	3.28034	+	56.3213i	0.106261	+	1.82443i	0.458698	+	0.888592i	$0.348316\pi$
$953$	3.28034	+	56.3213i	0.106261	+	1.82443i	−0.352438	+	0.935835i	$0.614647\pi$
$954$	−73.1334	+	25.3021i	−2.36778	+	0.819186i
$955$	−55.5980	+	27.9224i	−1.79911	+	0.903546i
$956$	−0.551868	−	1.04770i	−0.0178487	−	0.0338849i
$957$	−3.53752	+	2.92048i	−0.114352	+	0.0944056i
$958$	20.2983	+	9.22671i	0.655809	+	0.298102i
$959$	−7.16643	+	10.4489i	−0.231416	+	0.337413i
$960$	−9.91708	+	22.4943i	−0.320072	+	0.726002i
$961$	−3.71169	−	27.1744i	−0.119732	−	0.876594i
$962$	−18.9125	−	4.48234i	−0.609762	−	0.144516i
$963$	−11.2698	−	24.5704i	−0.363165	−	0.791769i
$964$	−19.3172	−	20.4750i	−0.622165	−	0.659456i
$965$	−42.6259	−	6.66656i	−1.37217	−	0.214604i
$966$	−65.3944	+	26.1087i	−2.10403	+	0.840033i
$967$	−32.0034	+	1.24188i	−1.02916	+	0.0399361i	−0.547819	−	0.836597i	$-0.684542\pi$
$967$	−32.0034	+	1.24188i	−1.02916	+	0.0399361i	−0.481342	+	0.876533i	$0.659850\pi$
$968$	−4.80135	−	2.89763i	−0.154321	−	0.0931333i
$969$	−0.669895	−	5.21499i	−0.0215201	−	0.167530i
$970$	25.9145	+	7.21380i	0.832066	+	0.231621i
$971$	2.48058			0.0796057			0.0398028	−	0.999208i	$-0.487327\pi$
$971$	2.48058			0.0796057			0.0398028	+	0.999208i	$0.487327\pi$
$972$	20.6829	−	14.7466i	0.663406	−	0.472998i
$973$	−7.81179			−0.250434
$974$	−22.4797	−	6.25764i	−0.720295	−	0.200508i
$975$	−16.6202	+	12.6703i	−0.532273	+	0.405775i
$976$	−22.6789	−	13.6868i	−0.725934	−	0.438103i
$977$	−12.1272	+	0.470589i	−0.387982	+	0.0150555i	−0.232029	−	0.972709i	$-0.574536\pi$
$977$	−12.1272	+	0.470589i	−0.387982	+	0.0150555i	−0.155953	+	0.987764i	$0.549845\pi$
$978$	3.32769	−	22.9911i	0.106408	−	0.735176i
$979$	17.7017	+	2.76850i	0.565750	+	0.0884817i
$980$	1.01626	+	1.07717i	0.0324632	+	0.0344090i
$981$	28.3225	+	13.4244i	0.904267	+	0.428609i
$982$	−19.7609	−	4.68342i	−0.630596	−	0.149454i
$983$	6.16010	+	45.0999i	0.196477	+	1.43846i	0.779701	+	0.626152i	$0.215371\pi$
$983$	6.16010	+	45.0999i	0.196477	+	1.43846i	−0.583224	+	0.812311i	$0.698209\pi$
$984$	10.6144	−	1.15474i	0.338375	−	0.0368117i
$985$	−35.3746	+	51.5774i	−1.12713	+	1.64339i
$986$	5.55366	+	2.52445i	0.176864	+	0.0803948i
$987$	6.89134	+	40.9960i	0.219354	+	1.30492i
$988$	1.42933	+	2.71351i	0.0454730	+	0.0863284i
$989$	5.93690	−	2.98162i	0.188782	−	0.0948100i
$990$	56.9499	−	46.2559i	1.80999	−	1.47011i
$991$	−2.14659	−	36.8556i	−0.0681888	−	1.17076i	−0.842767	−	0.538279i	$-0.819075\pi$
$991$	−2.14659	−	36.8556i	−0.0681888	−	1.17076i	0.774578	−	0.632478i	$-0.217962\pi$
$992$	49.2506	+	27.1753i	1.56371	+	0.862817i
$993$	5.89840	−	3.19338i	0.187180	−	0.101339i
$994$	−1.54460	+	11.3085i	−0.0489917	+	0.358683i
$995$	9.41301	−	24.3803i	0.298413	−	0.772908i
$996$	23.1558	−	28.2438i	0.733720	−	0.894939i
$997$	−8.09024	+	0.628823i	−0.256221	+	0.0199150i	−0.204960	−	0.978770i	$-0.565707\pi$
$997$	−8.09024	+	0.628823i	−0.256221	+	0.0199150i	−0.0512603	+	0.998685i	$0.516324\pi$
$998$	5.01790	−	4.21052i	0.158839	−	0.133282i
$999$	8.45856	−	13.8717i	0.267617	−	0.438880i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.i.a.103.5	✓	1404
3.2	odd	2		729.2.i.a.685.22		1404
243.92	odd	162		729.2.i.a.613.22		1404
243.151	even	81	inner	243.2.i.a.151.5	yes	1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.103.5	✓	1404	1.1	even	1	trivial
243.2.i.a.151.5	yes	1404	243.151	even	81	inner
729.2.i.a.613.22		1404	243.92	odd	162
729.2.i.a.685.22		1404	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.i (of order \(81\), degree \(54\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.83535 - 0.510904i) q^{2} +(-1.59811 - 0.667855i) q^{3} +(1.39514 + 0.841972i) q^{4} +(2.94702 - 0.114358i) q^{5} +(2.59189 + 2.04223i) q^{6} +(-2.67089 - 0.417720i) q^{7} +(0.484358 + 0.513389i) q^{8} +(2.10794 + 2.13462i) q^{9} +(-5.46724 - 1.29576i) q^{10} +(0.589047 + 4.31259i) q^{11} +(-1.66728 - 2.27732i) q^{12} +(1.84548 - 2.69078i) q^{13} +(4.68860 + 2.13123i) q^{14} +(-4.78606 - 1.78543i) q^{15} +(-2.14553 - 4.07318i) q^{16} +(4.70279 - 2.36183i) q^{17} +(-2.77822 - 4.99472i) q^{18} +(0.0335399 + 0.575858i) q^{19} +(4.20780 + 2.32177i) q^{20} +(3.98941 + 2.45133i) q^{21} +(1.12221 - 8.21604i) q^{22} +(2.84305 - 7.36370i) q^{23} +(-0.431190 - 1.14393i) q^{24} +(3.68691 - 0.286569i) q^{25} +(-4.76183 + 3.99565i) q^{26} +(-1.94312 - 4.81916i) q^{27} +(-3.37456 - 2.83159i) q^{28} +(-0.495027 - 0.353824i) q^{29} +(7.87189 + 5.72209i) q^{30} +(5.02592 - 5.75907i) q^{31} +(1.55794 + 7.19223i) q^{32} +(1.93882 - 7.28541i) q^{33} +(-9.83791 + 1.93210i) q^{34} +(-7.91895 - 0.925592i) q^{35} +(1.14359 + 4.75292i) q^{36} +(1.86718 + 2.50805i) q^{37} +(0.232651 - 1.07404i) q^{38} +(-4.74634 + 3.06766i) q^{39} +(1.48612 + 1.45758i) q^{40} +(-2.17856 + 8.45769i) q^{41} +(-6.06956 - 6.53725i) q^{42} +(0.623280 + 0.565596i) q^{43} +(-2.80928 + 6.51263i) q^{44} +(6.45626 + 6.04971i) q^{45} +(-8.98013 + 12.0624i) q^{46} +(5.83765 + 6.68920i) q^{47} +(0.708504 + 7.94231i) q^{48} +(0.293432 + 0.0940850i) q^{49} +(-6.91316 - 1.35770i) q^{50} +(-9.09295 + 0.633694i) q^{51} +(4.84027 - 2.20017i) q^{52} +(2.35120 - 13.3343i) q^{53} +(1.10417 + 9.83757i) q^{54} +(2.22912 + 12.6419i) q^{55} +(-1.07921 - 1.57353i) q^{56} +(0.330989 - 0.942687i) q^{57} +(0.727777 + 0.902301i) q^{58} +(6.01839 - 2.45878i) q^{59} +(-5.17395 - 6.52065i) q^{60} +(4.92623 - 2.97299i) q^{61} +(-12.1666 + 8.00212i) q^{62} +(-4.73841 - 6.58185i) q^{63} +(0.279822 - 4.80436i) q^{64} +(5.13097 - 8.14083i) q^{65} +(-7.28054 + 12.3807i) q^{66} +(-7.89248 + 5.64120i) q^{67} +(8.54964 + 0.664531i) q^{68} +(-9.46141 + 9.86928i) q^{69} +(14.0611 + 5.74460i) q^{70} +(0.635585 + 2.12300i) q^{71} +(-0.0748917 + 2.11611i) q^{72} +(-5.07940 + 1.20384i) q^{73} +(-2.14554 - 5.55709i) q^{74} +(-6.08349 - 2.00435i) q^{75} +(-0.438064 + 0.831643i) q^{76} +(0.228172 - 11.7645i) q^{77} +(10.2785 - 3.20529i) q^{78} +(8.20313 - 8.04557i) q^{79} +(-6.78872 - 11.7584i) q^{80} +(-0.113174 + 8.99929i) q^{81} +(8.31948 - 14.4098i) q^{82} +(3.22782 + 12.5312i) q^{83} +(3.50184 + 6.77893i) q^{84} +(13.5891 - 7.49816i) q^{85} +(-0.854969 - 1.35650i) q^{86} +(0.554807 + 0.896058i) q^{87} +(-1.92873 + 2.39125i) q^{88} +(1.18058 - 3.94341i) q^{89} +(-8.75866 - 14.4018i) q^{90} +(-6.05307 + 6.41588i) q^{91} +(10.1665 - 7.87962i) q^{92} +(-11.8782 + 5.84706i) q^{93} +(-7.29657 - 15.2595i) q^{94} +(0.164697 + 1.69323i) q^{95} +(2.31360 - 12.5345i) q^{96} +(-4.78397 - 0.185640i) q^{97} +(-0.490480 - 0.322594i) q^{98} +(-7.96405 + 10.3481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) \) 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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