LMFDB - Embedded newform 81.2.g.a.79.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(4,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(54))

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("81.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.g (of order $27$, degree $18$, 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:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			79.6
Character	$\chi$	$=$	81.79
Dual form			81.2.g.a.40.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0620019 - 1.06453i) q^{2} +(-0.676807 - 1.59434i) q^{3} +(0.857095 + 0.100180i) q^{4} +(-0.830696 + 0.196879i) q^{5} +(-1.73919 + 0.621630i) q^{6} +(-0.171051 - 0.229762i) q^{7} +(0.530120 - 3.00646i) q^{8} +(-2.08386 + 2.15813i) q^{9} +O(q^{10})$	\(q+(0.0620019 - 1.06453i) q^{2} +(-0.676807 - 1.59434i) q^{3} +(0.857095 + 0.100180i) q^{4} +(-0.830696 + 0.196879i) q^{5} +(-1.73919 + 0.621630i) q^{6} +(-0.171051 - 0.229762i) q^{7} +(0.530120 - 3.00646i) q^{8} +(-2.08386 + 2.15813i) q^{9} +(0.158079 + 0.896509i) q^{10} +(-1.24185 + 1.31629i) q^{11} +(-0.420366 - 1.43431i) q^{12} +(4.99610 + 2.50914i) q^{13} +(-0.255194 + 0.167844i) q^{14} +(0.876113 + 1.19117i) q^{15} +(-1.48827 - 0.352725i) q^{16} +(4.42908 + 1.61205i) q^{17} +(2.16819 + 2.35215i) q^{18} +(-1.75427 + 0.638503i) q^{19} +(-0.731709 + 0.0855245i) q^{20} +(-0.250551 + 0.428219i) q^{21} +(1.32423 + 1.40360i) q^{22} +(-0.809320 + 1.08711i) q^{23} +(-5.15212 + 1.18960i) q^{24} +(-3.81687 + 1.91690i) q^{25} +(2.98082 - 5.16294i) q^{26} +(4.85117 + 1.86176i) q^{27} +(-0.123590 - 0.214064i) q^{28} +(-5.00267 - 3.29031i) q^{29} +(1.32235 - 0.858795i) q^{30} +(-1.68608 - 3.90878i) q^{31} +(1.28337 - 4.28675i) q^{32} +(2.93911 + 1.08907i) q^{33} +(1.99069 - 4.61494i) q^{34} +(0.187327 + 0.157186i) q^{35} +(-2.00227 + 1.64096i) q^{36} +(-5.46107 + 4.58238i) q^{37} +(0.570938 + 1.90707i) q^{38} +(0.619030 - 9.66371i) q^{39} +(0.151539 + 2.60183i) q^{40} +(0.667300 + 11.4571i) q^{41} +(0.440318 + 0.293269i) q^{42} +(-3.64800 - 12.1852i) q^{43} +(-1.19625 + 1.00377i) q^{44} +(1.30617 - 2.20302i) q^{45} +(1.10708 + 0.928949i) q^{46} +(-0.811830 + 1.88203i) q^{47} +(0.444903 + 2.61153i) q^{48} +(1.98409 - 6.62732i) q^{49} +(1.80395 + 4.18203i) q^{50} +(-0.427465 - 8.15252i) q^{51} +(4.03077 + 2.65108i) q^{52} +(-1.54131 - 2.66962i) q^{53} +(2.28268 - 5.04879i) q^{54} +(0.772454 - 1.33793i) q^{55} +(-0.781449 + 0.392458i) q^{56} +(2.20530 + 2.36477i) q^{57} +(-3.81281 + 5.12149i) q^{58} +(0.865599 + 0.917481i) q^{59} +(0.631581 + 1.10871i) q^{60} +(-2.75203 + 0.321666i) q^{61} +(-4.26556 + 1.55254i) q^{62} +(0.852303 + 0.109642i) q^{63} +(-7.35831 - 2.67821i) q^{64} +(-4.64424 - 1.10071i) q^{65} +(1.34158 - 3.06125i) q^{66} +(5.24754 - 3.45136i) q^{67} +(3.63465 + 1.82539i) q^{68} +(2.28097 + 0.554574i) q^{69} +(0.178944 - 0.189670i) q^{70} +(2.24048 + 12.7064i) q^{71} +(5.38363 + 7.40913i) q^{72} +(-1.11508 + 6.32396i) q^{73} +(4.53949 + 6.09759i) q^{74} +(5.63949 + 4.78803i) q^{75} +(-1.56754 + 0.371515i) q^{76} +(0.514853 + 0.0601777i) q^{77} +(-10.2489 - 1.25814i) q^{78} +(-0.414301 + 7.11327i) q^{79} +1.30574 q^{80} +(-0.315018 - 8.99449i) q^{81} +12.2378 q^{82} +(0.788222 - 13.5333i) q^{83} +(-0.257645 + 0.341924i) q^{84} +(-3.99660 - 0.467135i) q^{85} +(-13.1977 + 3.12791i) q^{86} +(-1.86004 + 10.2029i) q^{87} +(3.29903 + 4.43137i) q^{88} +(-0.0750415 + 0.425581i) q^{89} +(-2.26419 - 1.52705i) q^{90} +(-0.278086 - 1.57711i) q^{91} +(-0.802570 + 0.850675i) q^{92} +(-5.09079 + 5.33369i) q^{93} +(1.95315 + 0.980908i) q^{94} +(1.33156 - 0.875782i) q^{95} +(-7.70314 + 0.855171i) q^{96} +(9.81910 + 2.32717i) q^{97} +(-6.93197 - 2.52303i) q^{98} +(-0.252861 - 5.42304i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) $ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{14}{27}\right)$

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 $

$2$	0.0620019	−	1.06453i	0.0438419	−	0.752737i	−0.902723	−	0.430223i	$-0.858435\pi$
$2$	0.0620019	−	1.06453i	0.0438419	−	0.752737i	0.946565	−	0.322514i	$-0.104528\pi$
$3$	−0.676807	−	1.59434i	−0.390755	−	0.920495i
$3$	−0.676807	−	1.59434i	−0.390755	−	0.920495i
$4$	0.857095	+	0.100180i	0.428547	+	0.0500900i
$5$	−0.830696	+	0.196879i	−0.371499	+	0.0880468i	−0.412124	−	0.911128i	$-0.635213\pi$
$5$	−0.830696	+	0.196879i	−0.371499	+	0.0880468i	0.0406256	+	0.999174i	$0.487065\pi$
$6$	−1.73919	+	0.621630i	−0.710022	+	0.253779i
$7$	−0.171051	−	0.229762i	−0.0646514	−	0.0868419i	0.768621	−	0.639704i	$-0.220943\pi$
$7$	−0.171051	−	0.229762i	−0.0646514	−	0.0868419i	−0.833273	+	0.552862i	$0.813536\pi$
$8$	0.530120	−	3.00646i	0.187426	−	1.06295i
$9$	−2.08386	+	2.15813i	−0.694621	+	0.719375i
$10$	0.158079	+	0.896509i	0.0499889	+	0.283501i
$11$	−1.24185	+	1.31629i	−0.374433	+	0.396875i	−0.886998	−	0.461773i	$-0.847214\pi$
$11$	−1.24185	+	1.31629i	−0.374433	+	0.396875i	0.512566	+	0.858648i	$0.328695\pi$
$12$	−0.420366	−	1.43431i	−0.121349	−	0.414049i
$13$	4.99610	+	2.50914i	1.38567	+	0.695910i	0.976292	−	0.216455i	$-0.0694496\pi$
$13$	4.99610	+	2.50914i	1.38567	+	0.695910i	0.409378	+	0.912365i	$0.365746\pi$
$14$	−0.255194	+	0.167844i	−0.0682035	+	0.0448582i
$15$	0.876113	+	1.19117i	0.226212	+	0.307558i
$16$	−1.48827	−	0.352725i	−0.372066	−	0.0881813i
$17$	4.42908	+	1.61205i	1.07421	+	0.390980i	0.817749	−	0.575574i	$-0.195222\pi$
$17$	4.42908	+	1.61205i	1.07421	+	0.390980i	0.256460	+	0.966555i	$0.417444\pi$
$18$	2.16819	+	2.35215i	0.511047	+	0.554406i
$19$	−1.75427	+	0.638503i	−0.402458	+	0.146483i	−0.535315	−	0.844652i	$-0.679807\pi$
$19$	−1.75427	+	0.638503i	−0.402458	+	0.146483i	0.132857	+	0.991135i	$0.457585\pi$
$20$	−0.731709	+	0.0855245i	−0.163615	+	0.0191239i
$21$	−0.250551	+	0.428219i	−0.0546747	+	0.0934451i
$22$	1.32423	+	1.40360i	0.282327	+	0.299249i
$23$	−0.809320	+	1.08711i	−0.168755	+	0.226677i	−0.878453	−	0.477829i	$-0.841424\pi$
$23$	−0.809320	+	1.08711i	−0.168755	+	0.226677i	0.709698	+	0.704506i	$0.248831\pi$
$24$	−5.15212	+	1.18960i	−1.05167	+	0.242826i
$25$	−3.81687	+	1.91690i	−0.763374	+	0.383381i
$26$	2.98082	−	5.16294i	0.584587	−	1.01254i
$27$	4.85117	+	1.86176i	0.933608	+	0.358296i
$28$	−0.123590	−	0.214064i	−0.0233563	−	0.0404542i
$29$	−5.00267	−	3.29031i	−0.928973	−	0.610995i	−0.00772467	−	0.999970i	$-0.502459\pi$
$29$	−5.00267	−	3.29031i	−0.928973	−	0.610995i	−0.921248	+	0.388975i	$0.872829\pi$
$30$	1.32235	−	0.858795i	0.241428	−	0.156794i
$31$	−1.68608	−	3.90878i	−0.302830	−	0.702038i	0.697058	−	0.717014i	$-0.254492\pi$
$31$	−1.68608	−	3.90878i	−0.302830	−	0.702038i	−0.999888	+	0.0149767i	$0.995233\pi$
$32$	1.28337	−	4.28675i	0.226870	−	0.757797i
$33$	2.93911	+	1.08907i	0.511633	+	0.189582i
$34$	1.99069	−	4.61494i	0.341401	−	0.791456i
$35$	0.187327	+	0.157186i	0.0316641	+	0.0265693i
$36$	−2.00227	+	1.64096i	−0.333712	+	0.273493i
$37$	−5.46107	+	4.58238i	−0.897794	+	0.753339i	−0.969758	−	0.244068i	$-0.921518\pi$
$37$	−5.46107	+	4.58238i	−0.897794	+	0.753339i	0.0719637	+	0.997407i	$0.477073\pi$
$38$	0.570938	+	1.90707i	0.0926184	+	0.309367i
$39$	0.619030	−	9.66371i	0.0991241	−	1.54743i
$40$	0.151539	+	2.60183i	0.0239604	+	0.411385i
$41$	0.667300	+	11.4571i	0.104215	+	1.78930i	0.495077	+	0.868849i	$0.335140\pi$
$41$	0.667300	+	11.4571i	0.104215	+	1.78930i	−0.390862	+	0.920449i	$0.627823\pi$
$42$	0.440318	+	0.293269i	0.0679426	+	0.0452525i
$43$	−3.64800	−	12.1852i	−0.556315	−	1.85822i	−0.511605	−	0.859221i	$-0.670949\pi$
$43$	−3.64800	−	12.1852i	−0.556315	−	1.85822i	−0.0447098	−	0.999000i	$-0.514236\pi$
$44$	−1.19625	+	1.00377i	−0.180342	+	0.151325i
$45$	1.30617	−	2.20302i	0.194712	−	0.328406i
$46$	1.10708	+	0.928949i	0.163230	+	0.136966i
$47$	−0.811830	+	1.88203i	−0.118418	+	0.274523i	−0.967108	−	0.254368i	$-0.918133\pi$
$47$	−0.811830	+	1.88203i	−0.118418	+	0.274523i	0.848690	+	0.528891i	$0.177392\pi$
$48$	0.444903	+	2.61153i	0.0642162	+	0.376942i
$49$	1.98409	−	6.62732i	0.283442	−	0.946761i
$50$	1.80395	+	4.18203i	0.255117	+	0.591428i
$51$	−0.427465	−	8.15252i	−0.0598571	−	1.14158i
$52$	4.03077	+	2.65108i	0.558967	+	0.367639i
$53$	−1.54131	−	2.66962i	−0.211715	−	0.366701i	0.740537	−	0.672016i	$-0.234571\pi$
$53$	−1.54131	−	2.66962i	−0.211715	−	0.366701i	−0.952251	+	0.305315i	$0.901238\pi$
$54$	2.28268	−	5.04879i	0.310634	−	0.687053i
$55$	0.772454	−	1.33793i	0.104158	−	0.180406i
$56$	−0.781449	+	0.392458i	−0.104425	+	0.0524444i
$57$	2.20530	+	2.36477i	0.292099	+	0.313222i
$58$	−3.81281	+	5.12149i	−0.500647	+	0.672485i
$59$	0.865599	+	0.917481i	0.112691	+	0.119446i	0.781263	−	0.624202i	$-0.214576\pi$
$59$	0.865599	+	0.917481i	0.112691	+	0.119446i	−0.668572	+	0.743647i	$0.733094\pi$
$60$	0.631581	+	1.10871i	0.0815368	+	0.143134i
$61$	−2.75203	+	0.321666i	−0.352362	+	0.0411852i	−0.290433	−	0.956895i	$-0.593799\pi$
$61$	−2.75203	+	0.321666i	−0.352362	+	0.0411852i	−0.0619288	+	0.998081i	$0.519725\pi$
$62$	−4.26556	+	1.55254i	−0.541726	+	0.197172i
$63$	0.852303	+	0.109642i	0.107380	+	0.0138136i
$64$	−7.35831	−	2.67821i	−0.919789	−	0.334776i
$65$	−4.64424	−	1.10071i	−0.576047	−	0.136526i
$66$	1.34158	−	3.06125i	0.165137	−	0.376813i
$67$	5.24754	−	3.45136i	0.641089	−	0.421651i	−0.186913	−	0.982377i	$-0.559848\pi$
$67$	5.24754	−	3.45136i	0.641089	−	0.421651i	0.828002	+	0.560726i	$0.189478\pi$
$68$	3.63465	+	1.82539i	0.440766	+	0.221361i
$69$	2.28097	+	0.554574i	0.274597	+	0.0667628i
$70$	0.178944	−	0.189670i	0.0213879	−	0.0226699i
$71$	2.24048	+	12.7064i	0.265896	+	1.50797i	0.766472	+	0.642278i	$0.222011\pi$
$71$	2.24048	+	12.7064i	0.265896	+	1.50797i	−0.500576	+	0.865693i	$0.666878\pi$
$72$	5.38363	+	7.40913i	0.634466	+	0.873174i
$73$	−1.11508	+	6.32396i	−0.130511	+	0.740164i	0.847370	+	0.531002i	$0.178184\pi$
$73$	−1.11508	+	6.32396i	−0.130511	+	0.740164i	−0.977881	+	0.209161i	$0.932927\pi$
$74$	4.53949	+	6.09759i	0.527705	+	0.708831i
$75$	5.63949	+	4.78803i	0.651192	+	0.552874i
$76$	−1.56754	+	0.371515i	−0.179810	+	0.0426157i
$77$	0.514853	+	0.0601777i	0.0586730	+	0.00685789i
$78$	−10.2489	−	1.25814i	−1.16046	−	0.142457i
$79$	−0.414301	+	7.11327i	−0.0466125	+	0.800305i	0.891296	+	0.453422i	$0.149797\pi$
$79$	−0.414301	+	7.11327i	−0.0466125	+	0.800305i	−0.937908	+	0.346883i	$0.887240\pi$
$80$	1.30574			0.145986
$81$	−0.315018	−	8.99449i	−0.0350020	−	0.999387i
$82$	12.2378			1.35144
$83$	0.788222	−	13.5333i	0.0865186	−	1.48547i	−0.623798	−	0.781585i	$-0.714411\pi$
$83$	0.788222	−	13.5333i	0.0865186	−	1.48547i	0.710317	−	0.703882i	$-0.248552\pi$
$84$	−0.257645	+	0.341924i	−0.0281114	+	0.0373070i
$85$	−3.99660	−	0.467135i	−0.433492	−	0.0506680i
$86$	−13.1977	+	3.12791i	−1.42314	+	0.337291i
$87$	−1.86004	+	10.2029i	−0.199417	+	1.09386i
$88$	3.29903	+	4.43137i	0.351678	+	0.472386i
$89$	−0.0750415	+	0.425581i	−0.00795438	+	0.0451115i	−0.988527	−	0.151047i	$-0.951736\pi$
$89$	−0.0750415	+	0.425581i	−0.00795438	+	0.0451115i	0.980572	+	0.196158i	$0.0628467\pi$
$90$	−2.26419	−	1.52705i	−0.238667	−	0.160965i
$91$	−0.278086	−	1.57711i	−0.0291514	−	0.165326i
$92$	−0.802570	+	0.850675i	−0.0836737	+	0.0886890i
$93$	−5.09079	+	5.33369i	−0.527890	+	0.553078i
$94$	1.95315	+	0.980908i	0.201452	+	0.101173i
$95$	1.33156	−	0.875782i	0.136615	−	0.0898533i
$96$	−7.70314	+	0.855171i	−0.786198	+	0.0872805i
$97$	9.81910	+	2.32717i	0.996979	+	0.236288i	0.696544	−	0.717514i	$-0.254720\pi$
$97$	9.81910	+	2.32717i	0.996979	+	0.236288i	0.300435	+	0.953802i	$0.402868\pi$
$98$	−6.93197	−	2.52303i	−0.700235	−	0.254865i
$99$	−0.252861	−	5.42304i	−0.0254135	−	0.545036i
$100$	−3.46345	+	1.26059i	−0.346345	+	0.126059i
$101$	9.21574	−	1.07717i	0.917000	−	0.107182i	0.355517	−	0.934670i	$-0.384305\pi$
$101$	9.21574	−	1.07717i	0.917000	−	0.107182i	0.561484	+	0.827488i	$0.310231\pi$
$102$	−8.70512	−	0.0504216i	−0.861935	−	0.00499249i
$103$	−10.0582	−	10.6610i	−0.991062	−	1.05046i	−0.998724	−	0.0504934i	$-0.983921\pi$
$103$	−10.0582	−	10.6610i	−0.991062	−	1.05046i	0.00766268	−	0.999971i	$-0.497561\pi$
$104$	10.1922	−	13.6905i	0.999424	−	1.34246i
$105$	0.123824	−	0.405048i	0.0120840	−	0.0395287i
$106$	−2.93746	+	1.47525i	−0.285311	+	0.143289i
$107$	0.0376376	−	0.0651902i	0.00363856	−	0.00630218i	−0.864200	−	0.503148i	$-0.832175\pi$
$107$	0.0376376	−	0.0651902i	0.00363856	−	0.00630218i	0.867839	+	0.496846i	$0.165508\pi$
$108$	3.97140	+	2.08170i	0.382148	+	0.200311i
$109$	−2.64599	−	4.58298i	−0.253440	−	0.438970i	0.711031	−	0.703161i	$-0.248229\pi$
$109$	−2.64599	−	4.58298i	−0.253440	−	0.438970i	−0.964470	+	0.264191i	$0.914895\pi$
$110$	−1.37637	−	0.905255i	−0.131232	−	0.0863127i
$111$	11.0020	+	5.60543i	1.04426	+	0.532044i
$112$	0.173527	+	0.402281i	0.0163968	+	0.0380120i
$113$	5.31080	−	17.7393i	0.499598	−	1.66877i	−0.220884	−	0.975300i	$-0.570894\pi$
$113$	5.31080	−	17.7393i	0.499598	−	1.66877i	0.720482	−	0.693473i	$-0.243921\pi$
$114$	2.65411	−	2.20099i	0.248580	−	0.206141i
$115$	0.458271	−	1.06239i	0.0427340	−	0.0990686i
$116$	−3.95814	−	3.32128i	−0.367504	−	0.308373i
$117$	−15.8262	+	5.55352i	−1.46314	+	0.513423i
$118$	1.03036	−	0.864571i	0.0948520	−	0.0795903i
$119$	−0.387212	−	1.29338i	−0.0354957	−	0.118564i
$120$	4.04564	−	2.00254i	0.369315	−	0.182806i
$121$	0.449180	+	7.71212i	0.0408345	+	0.701102i
$122$	0.171793	+	2.94957i	0.0155534	+	0.267041i
$123$	17.8149	−	8.81815i	1.60632	−	0.795106i
$124$	−1.05355	−	3.51911i	−0.0946117	−	0.316025i
$125$	6.06315	−	5.08759i	0.542305	−	0.455048i
$126$	0.169562	−	0.900505i	0.0151058	−	0.0802234i
$127$	8.52895	+	7.15664i	0.756822	+	0.635049i	0.937297	−	0.348531i	$-0.113319\pi$
$127$	8.52895	+	7.15664i	0.756822	+	0.635049i	−0.180476	+	0.983579i	$0.557764\pi$
$128$	0.237440	−	0.550448i	0.0209869	−	0.0486532i
$129$	−16.9584	+	14.0632i	−1.49310	+	1.23819i
$130$	−1.45969	+	4.87569i	−0.128023	+	0.427627i
$131$	0.109301	+	0.253387i	0.00954964	+	0.0221386i	0.922924	−	0.384982i	$-0.125792\pi$
$131$	0.109301	+	0.253387i	0.00954964	+	0.0221386i	−0.913375	+	0.407120i	$0.866533\pi$
$132$	2.40999	+	1.22787i	0.209763	+	0.106873i
$133$	0.446775	+	0.293848i	0.0387403	+	0.0254799i
$134$	−3.34872	−	5.80016i	−0.289285	−	0.501057i
$135$	−4.39639	−	0.591467i	−0.378381	−	0.0509053i
$136$	7.19452	−	12.4613i	0.616925	−	1.06855i
$137$	9.41666	−	4.72923i	0.804520	−	0.404045i	0.00150106	−	0.999999i	$-0.499522\pi$
$137$	9.41666	−	4.72923i	0.804520	−	0.404045i	0.803019	+	0.595954i	$0.203226\pi$
$138$	0.731785	−	2.39378i	0.0622937	−	0.203772i
$139$	0.323608	−	0.434682i	0.0274481	−	0.0368692i	−0.788187	−	0.615435i	$-0.788980\pi$
$139$	0.323608	−	0.434682i	0.0274481	−	0.0368692i	0.815635	+	0.578566i	$0.196388\pi$
$140$	0.144810	+	0.153490i	0.0122387	+	0.0129723i
$141$	3.55006	+	0.0205626i	0.298969	+	0.00173168i
$142$	13.6653	−	1.59724i	1.14676	−	0.134037i
$143$	−9.50717	+	3.46033i	−0.795029	+	0.289367i
$144$	3.86257	−	2.47683i	0.321881	−	0.206403i
$145$	4.80349	+	1.74833i	0.398908	+	0.145191i
$146$	6.66291	+	1.57914i	0.551427	+	0.130691i
$147$	−11.9091	+	1.32210i	−0.982244	+	0.109045i
$148$	−5.13972	+	3.38045i	−0.422482	+	0.277871i
$149$	−17.5539	−	8.81592i	−1.43807	−	0.722228i	−0.452547	−	0.891741i	$-0.649484\pi$
$149$	−17.5539	−	8.81592i	−1.43807	−	0.722228i	−0.985528	+	0.169512i	$0.945781\pi$
$150$	5.44666	−	5.70654i	0.444718	−	0.465937i
$151$	−10.1784	+	10.7885i	−0.828306	+	0.877953i	−0.994129	−	0.108202i	$-0.965491\pi$
$151$	−10.1784	+	10.7885i	−0.828306	+	0.877953i	0.165823	+	0.986156i	$0.446972\pi$
$152$	0.989660	+	5.61264i	0.0802720	+	0.455245i
$153$	−12.7086	+	6.19921i	−1.02743	+	0.501177i
$154$	0.0959829	−	0.544346i	0.00773452	−	0.0438647i
$155$	2.17018	+	2.91506i	0.174313	+	0.234143i
$156$	1.49868	−	8.22070i	0.119990	−	0.658183i
$157$	5.68309	−	1.34692i	0.453560	−	0.107496i	0.00251501	−	0.999997i	$-0.499199\pi$
$157$	5.68309	−	1.34692i	0.453560	−	0.107496i	0.451045	+	0.892501i	$0.351051\pi$
$158$	7.54660	+	0.882071i	0.600376	+	0.0701738i
$159$	−3.21313	+	4.26419i	−0.254818	+	0.338172i
$160$	−0.222120	+	3.81365i	−0.0175601	+	0.301496i
$161$	0.388211			0.0305953
$162$	−9.59444	−	0.222328i	−0.753810	−	0.0174678i
$163$	−6.88988			−0.539657			−0.269828	−	0.962908i	$-0.586967\pi$
$163$	−6.88988			−0.539657			−0.269828	+	0.962908i	$0.586967\pi$
$164$	−0.575833	+	9.88667i	−0.0449650	+	0.772019i
$165$	−2.65592	−	0.326037i	−0.206763	−	0.0253819i
$166$	−14.3577	−	1.67817i	−1.11437	−	0.130252i
$167$	−17.2656	+	4.09202i	−1.33605	+	0.316650i	−0.835706	−	0.549177i	$-0.814941\pi$
$167$	−17.2656	+	4.09202i	−1.33605	+	0.316650i	−0.500344	+	0.865827i	$0.666793\pi$
$168$	1.15460	+	0.980279i	0.0890796	+	0.0756302i
$169$	10.9022	+	14.6442i	0.838633	+	1.12648i
$170$	−0.745077	+	4.22554i	−0.0571448	+	0.324084i
$171$	2.27770	−	5.11650i	0.174180	−	0.391268i
$172$	−1.90597	−	10.8093i	−0.145329	−	0.824202i
$173$	−9.59858	+	10.1739i	−0.729767	+	0.773507i	−0.980914	−	0.194441i	$-0.937711\pi$
$173$	−9.59858	+	10.1739i	−0.729767	+	0.773507i	0.251147	+	0.967949i	$0.419192\pi$
$174$	10.7460	+	2.61267i	0.814649	+	0.198066i
$175$	1.09331	+	0.549082i	0.0826466	+	0.0415067i
$176$	2.31249	−	1.52095i	0.174311	−	0.114646i
$177$	0.876937	−	2.00102i	0.0659146	−	0.150406i
$178$	0.448392	+	0.106271i	0.0336084	+	0.00796533i
$179$	9.85261	+	3.58606i	0.736418	+	0.268034i	0.682879	−	0.730531i	$-0.260728\pi$
$179$	9.85261	+	3.58606i	0.736418	+	0.268034i	0.0535392	+	0.998566i	$0.482950\pi$
$180$	1.34021	−	1.75734i	0.0998933	−	0.130985i
$181$	11.6610	−	4.24426i	0.866755	−	0.315473i	0.129903	−	0.991527i	$-0.458533\pi$
$181$	11.6610	−	4.24426i	0.866755	−	0.315473i	0.736852	+	0.676054i	$0.236311\pi$
$182$	−1.69612	+	0.198248i	−0.125725	+	0.0146951i
$183$	2.37544	+	4.16998i	0.175598	+	0.308254i
$184$	2.83930	+	3.00949i	0.209316	+	0.221862i
$185$	3.63432	−	4.88174i	0.267200	−	0.358912i
$186$	5.36224	+	5.75000i	0.393178	+	0.421610i
$187$	−7.62219	+	3.82801i	−0.557390	+	0.279932i
$188$	−0.884358	+	1.53175i	−0.0644984	+	0.111715i
$189$	−0.402038	−	1.43307i	−0.0292439	−	0.104241i
$190$	−0.849737	−	1.47179i	−0.0616464	−	0.106775i
$191$	11.8067	+	7.76541i	0.854305	+	0.561885i	0.899414	−	0.437097i	$-0.143993\pi$
$191$	11.8067	+	7.76541i	0.854305	+	0.561885i	−0.0451095	+	0.998982i	$0.514364\pi$
$192$	0.710175	+	13.5443i	0.0512525	+	0.977476i
$193$	8.73369	+	20.2470i	0.628665	+	1.45741i	0.873001	+	0.487718i	$0.162171\pi$
$193$	8.73369	+	20.2470i	0.628665	+	1.45741i	−0.244337	+	0.969690i	$0.578570\pi$
$194$	3.08615	−	10.3084i	0.221572	−	0.740103i
$195$	1.38835	+	8.14948i	0.0994220	+	0.583597i
$196$	2.36448	−	5.48148i	0.168891	−	0.391534i
$197$	−1.28639	−	1.07941i	−0.0916516	−	0.0769049i	0.595811	−	0.803125i	$-0.296831\pi$
$197$	−1.28639	−	1.07941i	−0.0916516	−	0.0769049i	−0.687462	+	0.726220i	$0.741275\pi$
$198$	−5.78867	−	0.0670603i	−0.411383	−	0.00476577i
$199$	8.18059	−	6.86433i	0.579906	−	0.486599i	−0.305010	−	0.952349i	$-0.598660\pi$
$199$	8.18059	−	6.86433i	0.579906	−	0.486599i	0.884916	+	0.465750i	$0.154215\pi$
$200$	3.73970	+	12.4915i	0.264437	+	0.883280i
$201$	−9.05422	−	6.03047i	−0.638636	−	0.425357i
$202$	−0.575283	−	9.87723i	−0.0404768	−	0.694959i
$203$	0.0997264	+	1.71224i	0.00699942	+	0.120175i
$204$	0.450342	−	7.03031i	0.0315302	−	0.492220i
$205$	−2.80998	−	9.38600i	−0.196258	−	0.655546i
$206$	−11.9726	+	10.0462i	−0.834173	+	0.699954i
$207$	−0.659598	−	4.01199i	−0.0458452	−	0.278853i
$208$	−6.55049	−	5.49652i	−0.454195	−	0.381115i
$209$	1.33810	−	3.10205i	0.0925580	−	0.214574i
$210$	−0.423509	−	0.156929i	−0.0292249	−	0.0108291i
$211$	2.99616	−	10.0079i	0.206264	−	0.688970i	−0.790777	−	0.612104i	$-0.790323\pi$
$211$	2.99616	−	10.0079i	0.206264	−	0.688970i	0.997041	−	0.0768663i	$-0.0244914\pi$
$212$	−1.05360	−	2.44253i	−0.0723618	−	0.167753i
$213$	18.7420	−	12.1719i	1.28418	−	0.834003i
$214$	−0.0670634	−	0.0441083i	−0.00458436	−	0.00301518i
$215$	5.42938	+	9.40396i	0.370281	+	0.641345i
$216$	8.16902	−	13.5979i	0.555831	−	0.925220i
$217$	−0.609682	+	1.05600i	−0.0413879	+	0.0716860i
$218$	−5.04278	+	2.53258i	−0.341540	+	0.171528i
$219$	10.8373	−	2.50227i	0.732315	−	0.169088i
$220$	0.796100	−	1.06935i	0.0536730	−	0.0720954i
$221$	18.0833	+	19.1672i	1.21641	+	1.28932i
$222$	6.64930	−	11.3644i	0.446272	−	0.762729i
$223$	−13.5406	+	1.58267i	−0.906745	+	0.105983i	−0.556666	−	0.830737i	$-0.687920\pi$
$223$	−13.5406	+	1.58267i	−0.906745	+	0.105983i	−0.350080	+	0.936720i	$0.613845\pi$
$224$	−1.20445	+	0.438385i	−0.0804759	+	0.0292908i
$225$	3.81692	−	12.2318i	0.254461	−	0.815457i
$226$	−18.5548	−	6.75338i	−1.23424	−	0.449228i
$227$	−12.7468	−	3.02105i	−0.846035	−	0.200514i	−0.215335	−	0.976540i	$-0.569084\pi$
$227$	−12.7468	−	3.02105i	−0.846035	−	0.200514i	−0.630701	+	0.776026i	$0.717232\pi$
$228$	1.65325	+	2.24776i	0.109489	+	0.148862i
$229$	−1.44112	+	0.947842i	−0.0952321	+	0.0626351i	−0.596232	−	0.802812i	$-0.703336\pi$
$229$	−1.44112	+	0.947842i	−0.0952321	+	0.0626351i	0.501000	+	0.865447i	$0.332966\pi$
$230$	−1.10254	−	0.553714i	−0.0726991	−	0.0365108i
$231$	−0.252512	−	0.861582i	−0.0166141	−	0.0566879i
$232$	−12.5442	+	13.2961i	−0.823568	+	0.872931i
$233$	−4.21198	−	23.8873i	−0.275936	−	1.56491i	−0.735972	−	0.677011i	$-0.763275\pi$
$233$	−4.21198	−	23.8873i	−0.275936	−	1.56491i	0.460036	−	0.887900i	$-0.347836\pi$
$234$	4.93064	+	17.1919i	0.322326	+	1.12387i
$235$	0.303852	−	1.72323i	0.0198211	−	0.112411i
$236$	0.649987	+	0.873084i	0.0423106	+	0.0568330i
$237$	11.6214	−	4.15377i	0.754891	−	0.269816i
$238$	−1.40085	+	0.332007i	−0.0908035	+	0.0215208i
$239$	−21.9948	−	2.57082i	−1.42272	−	0.166293i	−0.630342	−	0.776317i	$-0.717085\pi$
$239$	−21.9948	−	2.57082i	−1.42272	−	0.166293i	−0.792383	+	0.610025i	$0.791160\pi$
$240$	−0.883735	−	2.08180i	−0.0570448	−	0.134380i
$241$	1.05087	−	18.0427i	0.0676924	−	1.16223i	−0.777894	−	0.628395i	$-0.783712\pi$
$241$	1.05087	−	18.0427i	0.0676924	−	1.16223i	0.845587	−	0.533838i	$-0.179251\pi$
$242$	8.23764			0.529536
$243$	−14.1271	+	6.58978i	−0.906254	+	0.422734i
$244$	−2.39098			−0.153067
$245$	−0.343398	+	5.89592i	−0.0219389	+	0.376676i
$246$	−8.28264	−	19.5113i	−0.528082	−	1.24399i
$247$	−10.3666	−	1.21169i	−0.659613	−	0.0770977i
$248$	−12.6454	+	2.99702i	−0.802986	+	0.190311i
$249$	−22.1101	+	7.90270i	−1.40117	+	0.500813i
$250$	−5.03997	−	6.76985i	−0.318756	−	0.428163i
$251$	−1.74420	+	9.89185i	−0.110093	+	0.624368i	0.878970	+	0.476876i	$0.158231\pi$
$251$	−1.74420	+	9.89185i	−0.110093	+	0.624368i	−0.989063	+	0.147492i	$0.952880\pi$
$252$	0.719521	+	0.179358i	0.0453256	+	0.0112985i
$253$	−0.425886	−	2.41532i	−0.0267752	−	0.151850i
$254$	8.14727	−	8.63560i	0.511205	−	0.541846i
$255$	1.96015	+	6.68811i	0.122749	+	0.418826i
$256$	−14.5665	−	7.31558i	−0.910407	−	0.457224i
$257$	7.66502	−	5.04136i	0.478131	−	0.314472i	−0.287468	−	0.957790i	$-0.592813\pi$
$257$	7.66502	−	5.04136i	0.478131	−	0.314472i	0.765598	+	0.643319i	$0.222443\pi$
$258$	13.9192	+	18.9246i	0.866574	+	1.17820i
$259$	1.98698	+	0.470923i	0.123465	+	0.0292617i
$260$	−3.87029	−	1.40867i	−0.240025	−	0.0873620i
$261$	17.5258	−	3.93984i	1.08482	−	0.243870i
$262$	0.276516	−	0.100643i	0.0170832	−	0.00621777i
$263$	23.6049	−	2.75902i	1.45554	−	0.170128i	0.648765	−	0.760988i	$-0.275286\pi$
$263$	23.6049	−	2.75902i	1.45554	−	0.170128i	0.806774	+	0.590860i	$0.201212\pi$
$264$	4.83232	−	8.25898i	0.297409	−	0.508305i
$265$	1.80595	+	1.91419i	0.110939	+	0.117588i
$266$	0.340512	−	0.457387i	0.0208781	−	0.0280442i
$267$	0.729312	−	0.168395i	0.0446331	−	0.0103056i
$268$	4.84339	−	2.43244i	0.295857	−	0.148585i
$269$	3.35091	−	5.80395i	0.204309	−	0.353873i	−0.745604	−	0.666390i	$-0.767839\pi$
$269$	3.35091	−	5.80395i	0.204309	−	0.353873i	0.949912	+	0.312517i	$0.101172\pi$
$270$	−0.902219	+	4.64342i	−0.0549073	+	0.282590i
$271$	4.74494	+	8.21848i	0.288235	+	0.499237i	0.973388	−	0.229161i	$-0.0735984\pi$
$271$	4.74494	+	8.21848i	0.288235	+	0.499237i	−0.685154	+	0.728398i	$0.740265\pi$
$272$	−6.02303	−	3.96141i	−0.365200	−	0.240196i
$273$	−2.32624	+	1.51076i	−0.140790	+	0.0914355i
$274$	−4.45056	−	10.3175i	−0.268868	−	0.623306i
$275$	2.21679	−	7.40460i	0.133678	−	0.446514i
$276$	1.89945	+	0.703830i	0.114334	+	0.0423656i
$277$	−0.549103	+	1.27296i	−0.0329924	+	0.0764850i	−0.933916	−	0.357494i	$-0.883631\pi$
$277$	−0.549103	+	1.27296i	−0.0329924	+	0.0764850i	0.900923	+	0.433979i	$0.142891\pi$
$278$	−0.442668	−	0.371442i	−0.0265494	−	0.0222776i
$279$	11.9492	+	4.50659i	0.715381	+	0.269802i
$280$	0.571880	−	0.479864i	0.0341764	−	0.0286774i
$281$	−4.59261	−	15.3404i	−0.273972	−	0.915130i	−0.978638	−	0.205591i	$-0.934088\pi$
$281$	−4.59261	−	15.3404i	−0.273972	−	0.915130i	0.704666	−	0.709539i	$-0.251097\pi$
$282$	0.242000	−	3.77788i	0.0144109	−	0.224969i
$283$	0.0182649	+	0.313595i	0.00108573	+	0.0186413i	0.998808	−	0.0488216i	$-0.0155466\pi$
$283$	0.0182649	+	0.313595i	0.00108573	+	0.0186413i	−0.997722	+	0.0674630i	$0.978510\pi$
$284$	0.647377	+	11.1150i	0.0384147	+	0.659556i
$285$	−2.29751	−	1.53023i	−0.136093	−	0.0906431i
$286$	3.09416	+	10.3352i	0.182962	+	0.611134i
$287$	2.51826	−	2.11307i	0.148648	−	0.124731i
$288$	6.57698	+	11.7027i	0.387552	+	0.689586i
$289$	3.99528	+	3.35244i	0.235016	+	0.197202i
$290$	2.15898	−	5.00507i	0.126779	−	0.293908i
$291$	−2.93533	−	17.2301i	−0.172072	−	1.01004i
$292$	−1.58927	+	5.30853i	−0.0930049	+	0.310658i
$293$	7.39195	+	17.1365i	0.431842	+	1.00112i	0.985700	+	0.168511i	$0.0538959\pi$
$293$	7.39195	+	17.1365i	0.431842	+	1.00112i	−0.553858	+	0.832611i	$0.686845\pi$
$294$	0.669028	+	12.7596i	0.0390185	+	0.744152i
$295$	−0.899683	−	0.591731i	−0.0523815	−	0.0344519i
$296$	10.8817	+	18.8477i	0.632488	+	1.09550i
$297$	−8.47505	+	4.07350i	−0.491772	+	0.236368i
$298$	−10.4732	+	18.1401i	−0.606696	+	1.05083i
$299$	−6.77114	+	3.40060i	−0.391585	+	0.196662i
$300$	4.35391	+	4.66876i	0.251373	+	0.269551i
$301$	−2.17569	+	2.92246i	−0.125405	+	0.168448i
$302$	10.8536	+	11.5041i	0.624554	+	0.661988i
$303$	−7.95465	−	13.9640i	−0.456983	−	0.802212i
$304$	2.83604	−	0.331486i	0.162658	−	0.0190120i
$305$	2.22277	−	0.809023i	0.127276	−	0.0463245i
$306$	5.81130	+	13.9131i	0.332210	+	0.795358i
$307$	25.4414	+	9.25992i	1.45202	+	0.528491i	0.943154	−	0.332356i	$-0.107843\pi$
$307$	25.4414	+	9.25992i	1.45202	+	0.528491i	0.508864	+	0.860847i	$0.330066\pi$
$308$	0.435249	+	0.103156i	0.0248006	+	0.00587786i
$309$	−10.1899	+	23.2517i	−0.579685	+	1.32274i
$310$	3.23772	−	2.12948i	0.183890	−	0.120947i
$311$	−11.0648	−	5.55697i	−0.627429	−	0.315107i	0.106521	−	0.994310i	$-0.466029\pi$
$311$	−11.0648	−	5.55697i	−0.627429	−	0.315107i	−0.733950	+	0.679204i	$0.762325\pi$
$312$	−28.7254	−	6.98402i	−1.62626	−	0.395392i
$313$	14.7287	−	15.6115i	0.832513	−	0.882413i	−0.162025	−	0.986787i	$-0.551802\pi$
$313$	14.7287	−	15.6115i	0.832513	−	0.882413i	0.994538	+	0.104374i	$0.0332839\pi$
$314$	−1.08147	−	6.13334i	−0.0610311	−	0.346124i
$315$	−0.729592	+	0.0767210i	−0.0411078	+	0.00432274i
$316$	−1.06770	+	6.05524i	−0.0600629	+	0.340634i
$317$	−14.0963	−	18.9346i	−0.791727	−	1.06347i	−0.996411	−	0.0846456i	$-0.973024\pi$
$317$	−14.0963	−	18.9346i	−0.791727	−	1.06347i	0.204684	−	0.978828i	$-0.434383\pi$
$318$	4.34014	+	3.68486i	0.243383	+	0.206637i
$319$	10.5436	−	2.49887i	0.590327	−	0.139910i
$320$	6.63980	+	0.776082i	0.371176	+	0.0433843i
$321$	−0.129409	−	0.0158861i	−0.00722291	−	0.000886674i
$322$	0.0240698	−	0.413262i	0.00134136	−	0.0230302i
$323$	−8.79912			−0.489596
$324$	0.631067	−	7.74069i	0.0350593	−	0.430038i
$325$	−23.8792			−1.32458
$326$	−0.427185	+	7.33449i	−0.0236596	+	0.406220i
$327$	−5.51603	+	7.32041i	−0.305037	+	0.404819i
$328$	34.7991	+	4.06743i	1.92146	+	0.224586i
$329$	0.571285	−	0.135397i	0.0314959	−	0.00746468i
$330$	−0.511748	+	2.80709i	−0.0281708	+	0.154525i
$331$	−0.506276	−	0.680047i	−0.0278275	−	0.0373788i	0.787992	−	0.615686i	$-0.211121\pi$
$331$	−0.506276	−	0.680047i	−0.0278275	−	0.0373788i	−0.815819	+	0.578307i	$0.803714\pi$
$332$	2.03134	−	11.5203i	0.111484	−	0.632259i
$333$	1.49077	−	21.3347i	0.0816937	−	1.16914i
$334$	3.28558	+	18.6334i	0.179779	+	1.01958i
$335$	−3.67961	+	3.90016i	−0.201039	+	0.213089i
$336$	0.523930	−	0.548928i	0.0285827	−	0.0299465i
$337$	1.82639	+	0.917245i	0.0994895	+	0.0499655i	0.497848	−	0.867264i	$-0.334124\pi$
$337$	1.82639	+	0.917245i	0.0994895	+	0.0499655i	−0.398359	+	0.917230i	$0.630420\pi$
$338$	16.2652	−	10.6978i	0.884710	−	0.581883i
$339$	−31.8769	+	3.53885i	−1.73132	+	0.192204i
$340$	−3.37867	−	0.800759i	−0.183234	−	0.0434272i
$341$	7.23894	+	2.63476i	0.392011	+	0.142680i
$342$	−5.30545	−	2.74191i	−0.286886	−	0.148266i
$343$	−3.74626	+	1.36353i	−0.202279	+	0.0736236i
$344$	−38.5681	+	4.50797i	−2.07945	+	0.243053i
$345$	−2.00398	−	0.0116074i	−0.107891	−	0.000624922i
$346$	10.2353	+	10.8488i	0.550253	+	0.583234i
$347$	−3.88352	+	5.21647i	−0.208478	+	0.280035i	−0.894047	−	0.447973i	$-0.852146\pi$
$347$	−3.88352	+	5.21647i	−0.208478	+	0.280035i	0.685569	+	0.728008i	$0.259554\pi$
$348$	−2.61636	+	8.55850i	−0.140251	+	0.458784i
$349$	5.91656	−	2.97141i	0.316706	−	0.159056i	−0.283344	−	0.959018i	$-0.591444\pi$
$349$	5.91656	−	2.97141i	0.316706	−	0.159056i	0.600050	+	0.799963i	$0.295147\pi$
$350$	0.652302	−	1.12982i	0.0348670	−	0.0603914i
$351$	19.5655	+	21.4738i	1.04433	+	1.14619i
$352$	4.04883	+	7.01279i	0.215804	+	0.373783i
$353$	0.252536	+	0.166095i	0.0134411	+	0.00884037i	0.556212	−	0.831041i	$-0.312254\pi$
$353$	0.252536	+	0.166095i	0.0134411	+	0.00884037i	−0.542771	+	0.839881i	$0.682625\pi$
$354$	−2.07578	−	1.05759i	−0.110326	−	0.0562105i
$355$	−4.36277	−	10.1140i	−0.231552	−	0.536798i
$356$	−0.106952	+	0.357246i	−0.00566847	+	0.0189340i
$357$	−1.80002	+	1.49272i	−0.0952672	+	0.0790029i
$358$	4.42835	−	10.2661i	0.234045	−	0.542578i
$359$	3.14494	+	2.63892i	0.165984	+	0.139277i	0.721996	−	0.691897i	$-0.243225\pi$
$359$	3.14494	+	2.63892i	0.165984	+	0.139277i	−0.556012	+	0.831174i	$0.687669\pi$
$360$	−5.93086	−	5.09481i	−0.312584	−	0.268520i
$361$	−11.8851	+	9.97274i	−0.625529	+	0.524881i
$362$	−3.79514	−	12.6766i	−0.199468	−	0.666270i
$363$	11.9918	−	5.93577i	0.629405	−	0.311547i
$364$	−0.0803519	−	1.37959i	−0.00421158	−	0.0723101i
$365$	−0.318756	−	5.47283i	−0.0166844	−	0.286461i
$366$	4.58635	−	2.27018i	0.239732	−	0.118664i
$367$	2.57975	+	8.61696i	0.134662	+	0.449802i	0.998547	−	0.0538869i	$-0.0171610\pi$
$367$	2.57975	+	8.61696i	0.134662	+	0.449802i	−0.863885	+	0.503689i	$0.831976\pi$
$368$	1.58793	−	1.33243i	0.0827767	−	0.0694579i
$369$	−26.1164	−	22.4349i	−1.35957	−	1.16792i
$370$	−4.97142	−	4.17152i	−0.258452	−	0.216867i
$371$	−0.349735	+	0.810776i	−0.0181573	+	0.0420934i
$372$	−4.89762	+	4.06148i	−0.253930	+	0.210578i
$373$	−1.50869	+	5.03939i	−0.0781172	+	0.260929i	−0.988123	−	0.153666i	$-0.950892\pi$
$373$	−1.50869	+	5.03939i	−0.0781172	+	0.260929i	0.910006	+	0.414596i	$0.136077\pi$
$374$	3.60244	+	8.35140i	0.186278	+	0.431840i
$375$	−12.2150	−	6.22343i	−0.630777	−	0.321377i
$376$	5.22790	+	3.43844i	0.269608	+	0.177324i
$377$	−16.7380	−	28.9911i	−0.862053	−	1.49312i
$378$	−1.55048	+	0.339128i	−0.0797479	+	0.0174429i
$379$	−3.76722	+	6.52502i	−0.193509	+	0.335168i	−0.946411	−	0.322965i	$-0.895320\pi$
$379$	−3.76722	+	6.52502i	−0.193509	+	0.335168i	0.752902	+	0.658133i	$0.228654\pi$
$380$	1.22901	−	0.617232i	0.0630469	−	0.0316633i
$381$	5.63769	−	18.4417i	0.288827	−	0.944799i
$382$	8.99856	−	12.0872i	0.460406	−	0.618433i
$383$	24.4454	+	25.9106i	1.24910	+	1.32397i	0.925962	+	0.377617i	$0.123256\pi$
$383$	24.4454	+	25.9106i	1.24910	+	1.32397i	0.323138	+	0.946352i	$0.395262\pi$
$384$	−1.03831	−	0.00601405i	−0.0529858	−	0.000306903i
$385$	−0.439534	+	0.0513742i	−0.0224007	+	0.00261827i
$386$	22.0950	−	8.04193i	1.12461	−	0.409324i
$387$	33.8991	+	17.5194i	1.72319	+	0.890561i
$388$	8.18276	+	2.97828i	0.415417	+	0.151199i
$389$	12.3217	+	2.92030i	0.624736	+	0.148065i	0.530778	−	0.847511i	$-0.321900\pi$
$389$	12.3217	+	2.92030i	0.624736	+	0.148065i	0.0939581	+	0.995576i	$0.470048\pi$
$390$	8.76146	−	0.972661i	0.443654	−	0.0492526i
$391$	−5.33701	+	3.51021i	−0.269904	+	0.177519i
$392$	−18.8730	−	9.47837i	−0.953230	−	0.478730i
$393$	0.330011	−	0.345757i	0.0166469	−	0.0174411i
$394$	−1.22883	+	1.30248i	−0.0619073	+	0.0656179i
$395$	−1.05629	−	5.99053i	−0.0531478	−	0.301416i
$396$	0.326554	−	4.67339i	0.0164100	−	0.234847i
$397$	1.88601	−	10.6961i	0.0946564	−	0.536823i	−0.900196	−	0.435486i	$-0.856577\pi$
$397$	1.88601	−	10.6961i	0.0946564	−	0.536823i	0.994852	−	0.101337i	$-0.0323122\pi$
$398$	−6.80008	−	9.13409i	−0.340857	−	0.457850i
$399$	0.166115	−	0.911191i	0.00831616	−	0.0456166i
$400$	6.35665	−	1.50655i	0.317833	−	0.0753277i
$401$	−5.70021	−	0.666259i	−0.284655	−	0.0332714i	−0.0274326	−	0.999624i	$-0.508733\pi$
$401$	−5.70021	−	0.666259i	−0.284655	−	0.0332714i	−0.257222	+	0.966352i	$0.582807\pi$
$402$	−6.98100	+	9.26460i	−0.348181	+	0.462076i
$403$	1.38382	−	23.7593i	0.0689330	−	1.18353i
$404$	8.00667			0.398347
$405$	2.03251	+	7.40967i	0.100996	+	0.368189i
$406$	1.82891			0.0907674
$407$	0.750115	−	12.8790i	0.0371818	−	0.638387i
$408$	−24.7369	−	3.03666i	−1.22466	−	0.150337i
$409$	29.3611	+	3.43182i	1.45181	+	0.169693i	0.805145	−	0.593078i	$-0.202088\pi$
$409$	29.3611	+	3.43182i	1.45181	+	0.169693i	0.646669	+	0.762771i	$0.276162\pi$
$410$	−10.1659	+	2.40936i	−0.502058	+	0.118990i
$411$	−13.9133	−	11.8126i	−0.686291	−	0.582674i
$412$	−7.55279	−	10.1452i	−0.372099	−	0.499816i
$413$	0.0627404	−	0.355818i	0.00308725	−	0.0175087i
$414$	−4.31179	+	0.453411i	−0.211913	+	0.0222839i
$415$	2.00964	+	11.3972i	0.0986491	+	0.559467i
$416$	17.1679	−	18.1969i	0.841724	−	0.892176i
$417$	−0.912053	−	0.221748i	−0.0446634	−	0.0108590i
$418$	−3.21927	−	1.61678i	−0.157460	−	0.0790792i
$419$	7.46487	−	4.90972i	0.364683	−	0.239856i	−0.353921	−	0.935275i	$-0.615152\pi$
$419$	7.46487	−	4.90972i	0.364683	−	0.239856i	0.718604	+	0.695420i	$0.244782\pi$
$420$	0.146707	−	0.334760i	0.00715857	−	0.0163346i
$421$	2.46378	+	0.583927i	0.120077	+	0.0284589i	0.290215	−	0.956961i	$-0.406273\pi$
$421$	2.46378	+	0.583927i	0.120077	+	0.0284589i	−0.170138	+	0.985420i	$0.554421\pi$
$422$	−10.4679	−	3.81001i	−0.509570	−	0.185468i
$423$	−2.36992	−	5.67394i	−0.115230	−	0.275876i
$424$	−8.84319	+	3.21866i	−0.429463	+	0.156312i
$425$	−19.9954	+	2.33712i	−0.969918	+	0.113367i
$426$	−11.7953	−	20.7061i	−0.571484	−	1.00321i
$427$	0.544646	+	0.577291i	0.0263572	+	0.0279371i
$428$	0.0387898	−	0.0521037i	0.00187497	−	0.00251853i
$429$	11.9515	+	12.8157i	0.577022	+	0.618749i
$430$	10.3474	−	5.19668i	0.498998	−	0.250606i
$431$	−14.8594	+	25.7372i	−0.715750	+	1.23972i	0.246919	+	0.969036i	$0.420582\pi$
$431$	−14.8594	+	25.7372i	−0.715750	+	1.23972i	−0.962669	+	0.270680i	$0.912751\pi$
$432$	−6.56314	−	4.48193i	−0.315769	−	0.215637i
$433$	0.612994	+	1.06174i	0.0294586	+	0.0510238i	0.880379	−	0.474271i	$-0.157288\pi$
$433$	0.612994	+	1.06174i	0.0294586	+	0.0510238i	−0.850920	+	0.525295i	$0.823955\pi$
$434$	1.08634	+	0.714499i	0.0521462	+	0.0342971i
$435$	−0.463601	−	8.84170i	−0.0222280	−	0.423927i
$436$	−1.80874	−	4.19313i	−0.0866228	−	0.200814i
$437$	0.725648	−	2.42383i	0.0347125	−	0.115948i
$438$	−1.99182	−	11.6917i	−0.0951726	−	0.558653i
$439$	−6.87558	+	15.9394i	−0.328153	+	0.760745i	0.671649	+	0.740869i	$0.265586\pi$
$439$	−6.87558	+	15.9394i	−0.328153	+	0.760745i	−0.999802	+	0.0198755i	$0.993673\pi$
$440$	−3.61294	−	3.03162i	−0.172240	−	0.144527i
$441$	10.1680	+	18.0924i	0.484192	+	0.861541i
$442$	21.5252	−	18.0618i	1.02385	−	0.859113i
$443$	3.43732	+	11.4815i	0.163312	+	0.545500i	0.999998	−	0.00218326i	$-0.000694954\pi$
$443$	3.43732	+	11.4815i	0.163312	+	0.545500i	−0.836686	+	0.547684i	$0.815510\pi$
$444$	8.86819	+	5.90657i	0.420866	+	0.280313i
$445$	−0.0214512	−	0.368303i	−0.00101688	−	0.0174592i
$446$	0.845257	+	14.5125i	0.0400241	+	0.687187i
$447$	−2.17498	+	33.9537i	−0.102873	+	1.60595i
$448$	0.643300	+	2.14877i	0.0303931	+	0.101520i
$449$	15.0015	−	12.5878i	0.707965	−	0.594053i	−0.216063	−	0.976380i	$-0.569322\pi$
$449$	15.0015	−	12.5878i	0.707965	−	0.594053i	0.924027	+	0.382327i	$0.124877\pi$
$450$	−12.7845	−	4.82162i	−0.602668	−	0.227293i
$451$	−15.9095	−	13.3497i	−0.749150	−	0.628611i
$452$	6.32898	−	14.6722i	0.297690	−	0.690124i
$453$	24.0893	+	8.92615i	1.13182	+	0.419387i
$454$	−4.00633	+	13.3821i	−0.188026	+	0.628051i
$455$	0.541504	+	1.25535i	0.0253861	+	0.0588516i
$456$	8.27867	−	5.37653i	0.387684	−	0.251779i
$457$	−20.0661	−	13.1977i	−0.938650	−	0.617360i	−0.0147081	−	0.999892i	$-0.504682\pi$
$457$	−20.0661	−	13.1977i	−0.938650	−	0.617360i	−0.923942	+	0.382532i	$0.875052\pi$
$458$	0.919654	+	1.59289i	0.0429726	+	0.0744308i
$459$	18.4850	+	16.0662i	0.862804	+	0.749908i
$460$	0.499212	−	0.864661i	0.0232759	−	0.0403150i
$461$	−12.6601	+	6.35812i	−0.589638	+	0.296127i	−0.718491	−	0.695537i	$-0.755167\pi$
$461$	−12.6601	+	6.35812i	−0.589638	+	0.296127i	0.128853	+	0.991664i	$0.458870\pi$
$462$	−0.932837	+	0.215388i	−0.0433995	+	0.0100207i
$463$	−6.57379	+	8.83013i	−0.305510	+	0.410371i	−0.928191	−	0.372105i	$-0.878636\pi$
$463$	−6.57379	+	8.83013i	−0.305510	+	0.410371i	0.622681	+	0.782476i	$0.286044\pi$
$464$	6.28473	+	6.66142i	0.291761	+	0.309249i
$465$	3.17881	−	5.43294i	0.147414	−	0.251947i
$466$	−25.6900	+	3.00273i	−1.19006	+	0.139099i
$467$	36.6170	−	13.3275i	1.69443	−	0.616723i	0.699261	−	0.714867i	$-0.253513\pi$
$467$	36.6170	−	13.3275i	1.69443	−	0.616723i	0.995172	+	0.0981436i	$0.0312904\pi$
$468$	−14.1209	+	3.17442i	−0.652741	+	0.146738i
$469$	−1.69059	−	0.615324i	−0.0780642	−	0.0284130i
$470$	−1.81559	−	0.430304i	−0.0837471	−	0.0198484i
$471$	−5.99381	−	8.14920i	−0.276180	−	0.375495i
$472$	3.21725	−	2.11602i	0.148086	−	0.0973975i
$473$	20.5695	+	10.3304i	0.945784	+	0.474991i
$474$	−3.70127	−	12.6289i	−0.170005	−	0.580063i
$475$	5.47188	−	5.79986i	0.251067	−	0.266116i
$476$	−0.202307	−	1.14734i	−0.00927272	−	0.0525882i
$477$	8.97325	+	2.23679i	0.410857	+	0.102416i
$478$	−4.10044	+	23.2547i	−0.187550	+	1.06365i
$479$	8.43225	+	11.3265i	0.385280	+	0.517520i	0.951879	−	0.306473i	$-0.0991489\pi$
$479$	8.43225	+	11.3265i	0.385280	+	0.517520i	−0.566600	+	0.823993i	$0.691741\pi$
$480$	6.23061	−	2.22697i	0.284387	−	0.101647i
$481$	−38.7819	+	9.19148i	−1.76830	+	0.419095i
$482$	−19.1419	−	2.23736i	−0.871888	−	0.101909i
$483$	−0.262744	−	0.618941i	−0.0119553	−	0.0281628i
$484$	−0.387611	+	6.65502i	−0.0176187	+	0.302501i
$485$	−8.61486			−0.391181
$486$	6.13912	+	15.4473i	0.278476	+	0.700704i
$487$	−11.6224			−0.526663			−0.263332	−	0.964705i	$-0.584821\pi$
$487$	−11.6224			−0.526663			−0.263332	+	0.964705i	$0.584821\pi$
$488$	−0.491830	+	8.44440i	−0.0222641	+	0.382260i
$489$	4.66312	+	10.9848i	0.210873	+	0.496751i
$490$	6.25510	+	0.731116i	0.282576	+	0.0330285i
$491$	−5.11177	+	1.21151i	−0.230691	+	0.0546747i	−0.344335	−	0.938847i	$-0.611896\pi$
$491$	−5.11177	+	1.21151i	−0.230691	+	0.0546747i	0.113644	+	0.993521i	$0.463748\pi$
$492$	16.1525	−	5.77329i	0.728210	−	0.260280i
$493$	−16.8531	−	22.6376i	−0.759025	−	1.01955i
$494$	−1.93263	+	10.9605i	−0.0869530	+	0.493135i
$495$	1.27773	+	4.45511i	0.0574297	+	0.200242i
$496$	1.13061	+	6.41203i	0.0507660	+	0.287909i
$497$	2.53621	−	2.68822i	0.113764	−	0.120583i
$498$	7.04180	+	24.0269i	0.315551	+	1.07667i
$499$	4.92977	+	2.47583i	0.220687	+	0.110833i	0.555708	−	0.831377i	$-0.312447\pi$
$499$	4.92977	+	2.47583i	0.220687	+	0.110833i	−0.335021	+	0.942211i	$0.608743\pi$
$500$	5.70637	−	3.75314i	0.255197	−	0.167846i
$501$	18.2095	+	24.7578i	0.813542	+	1.10609i
$502$	10.4220	+	2.47007i	0.465158	+	0.110245i
$503$	−31.2754	−	11.3833i	−1.39450	−	0.507557i	−0.467959	−	0.883750i	$-0.655011\pi$
$503$	−31.2754	−	11.3833i	−1.39450	−	0.507557i	−0.926541	+	0.376193i	$0.877233\pi$
$504$	0.781459	−	2.50429i	0.0348089	−	0.111550i
$505$	−7.44341	+	2.70918i	−0.331227	+	0.120557i
$506$	−2.59759	+	0.303615i	−0.115477	+	0.0134973i
$507$	15.9692	−	27.2932i	0.709218	−	1.21213i
$508$	6.59316	+	6.98835i	0.292524	+	0.310058i
$509$	−13.1753	+	17.6975i	−0.583986	+	0.784429i	−0.991685	−	0.128687i	$-0.958924\pi$
$509$	−13.1753	+	17.6975i	−0.583986	+	0.784429i	0.407700	+	0.913116i	$0.366331\pi$
$510$	7.24124	−	1.67197i	0.320647	−	0.0740359i
$511$	1.64374	−	0.825519i	0.0727149	−	0.0365188i
$512$	−8.09134	+	14.0146i	−0.357590	+	0.619364i
$513$	−9.69902	−	0.168551i	−0.428222	−	0.00744169i
$514$	−4.89144	−	8.47222i	−0.215752	−	0.373694i
$515$	10.4542	+	6.87585i	0.460668	+	0.302986i
$516$	−15.9438	+	10.3546i	−0.701885	+	0.455835i
$517$	−1.46912	−	3.40581i	−0.0646120	−	0.149787i
$518$	0.624509	−	2.08600i	0.0274393	−	0.0916538i
$519$	22.7171	+	8.41767i	0.997169	+	0.369495i
$520$	−5.77124	+	13.3792i	−0.253085	+	0.586718i
$521$	21.4866	+	18.0294i	0.941345	+	0.789882i	0.977819	−	0.209453i	$-0.0671682\pi$
$521$	21.4866	+	18.0294i	0.941345	+	0.789882i	−0.0364742	+	0.999335i	$0.511613\pi$
$522$	−3.10745	−	18.9010i	−0.136009	−	0.827276i
$523$	−6.29841	+	5.28500i	−0.275410	+	0.231097i	−0.770022	−	0.638017i	$-0.779755\pi$
$523$	−6.29841	+	5.28500i	−0.275410	+	0.231097i	0.494612	+	0.869114i	$0.335310\pi$
$524$	0.0682967	+	0.228127i	0.00298355	+	0.00996577i
$525$	0.135464	−	2.11474i	0.00591214	−	0.0922947i
$526$	−1.47351	−	25.2992i	−0.0642481	−	1.10310i
$527$	−1.16664	−	20.0304i	−0.0508194	−	0.872536i
$528$	−3.99003	−	2.65752i	−0.173644	−	0.115654i
$529$	6.06968	+	20.2741i	0.263899	+	0.881484i
$530$	2.14969	−	1.80381i	0.0933766	−	0.0783523i
$531$	−3.78383	−	0.0438348i	−0.164204	−	0.00190227i
$532$	0.353491	+	0.296614i	0.0153258	+	0.0128598i
$533$	−25.4135	+	58.9152i	−1.10078	+	2.55190i
$534$	−0.134043	−	0.786816i	−0.00580059	−	0.0340488i
$535$	−0.0184309	+	0.0615633i	−0.000796835	+	0.00266162i
$536$	−7.59456	−	17.6062i	−0.328035	−	0.760470i
$537$	−0.950908	−	18.1355i	−0.0410347	−	0.782605i
$538$	−5.97072	−	3.92701i	−0.257416	−	0.169305i
$539$	6.25951	+	10.8418i	0.269616	+	0.466989i
$540$	−3.70887	−	0.947373i	−0.159604	−	0.0407685i
$541$	0.833782	−	1.44415i	0.0358471	−	0.0620889i	−0.847545	−	0.530723i	$-0.821920\pi$
$541$	0.833782	−	1.44415i	0.0358471	−	0.0620889i	0.883392	+	0.468634i	$0.155254\pi$
$542$	9.04302	−	4.54157i	0.388431	−	0.195077i
$543$	−14.6590	−	15.7191i	−0.629080	−	0.674571i
$544$	12.5946	−	16.9175i	0.539989	−	0.725331i
$545$	3.10030	+	3.28613i	0.132802	+	0.140762i
$546$	1.46402	+	2.57002i	0.0626543	+	0.109987i
$547$	−17.7238	+	2.07162i	−0.757817	+	0.0885761i	−0.486222	−	0.873835i	$-0.661625\pi$
$547$	−17.7238	+	2.07162i	−0.757817	+	0.0885761i	−0.271595	+	0.962412i	$0.587551\pi$
$548$	8.54475	−	3.11003i	0.365013	−	0.132854i
$549$	5.04066	−	6.60954i	0.215130	−	0.282088i
$550$	−7.74498	−	2.81894i	−0.330247	−	0.120200i
$551$	10.8769	+	2.57788i	0.463373	+	0.109821i
$552$	2.87650	−	6.56367i	0.122432	−	0.279368i
$553$	1.70522	−	1.12154i	0.0725135	−	0.0476929i
$554$	1.32106	+	0.663463i	0.0561266	+	0.0281879i
$555$	−10.2429	−	2.49036i	−0.434787	−	0.105710i
$556$	0.320910	−	0.340144i	0.0136096	−	0.0144253i
$557$	3.03540	+	17.2146i	0.128614	+	0.729407i	0.979095	+	0.203402i	$0.0651997\pi$
$557$	3.03540	+	17.2146i	0.128614	+	0.729407i	−0.850481	+	0.526005i	$0.823689\pi$
$558$	5.53828	−	12.4409i	0.234454	−	0.526665i
$559$	12.3485	−	70.0317i	0.522285	−	2.96203i
$560$	−0.223349	−	0.300010i	−0.00943821	−	0.0126777i
$561$	11.2619	+	9.56156i	0.475478	+	0.403690i
$562$	−16.6151	+	3.93784i	−0.700864	+	0.166108i
$563$	−34.3322	−	4.01286i	−1.44693	−	0.169122i	−0.643923	−	0.765090i	$-0.722694\pi$
$563$	−34.3322	−	4.01286i	−1.44693	−	0.169122i	−0.803008	+	0.595968i	$0.796768\pi$
$564$	3.04068	+	0.373269i	0.128036	+	0.0157175i
$565$	−0.919171	+	15.7816i	−0.0386698	+	0.663935i
$566$	0.334965			0.0140796
$567$	−2.01271	+	1.61090i	−0.0845257	+	0.0676514i
$568$	39.3890			1.65273
$569$	−1.48326	+	25.4665i	−0.0621814	+	1.06761i	0.812515	+	0.582941i	$0.198098\pi$
$569$	−1.48326	+	25.4665i	−0.0621814	+	1.06761i	−0.874696	+	0.484672i	$0.838939\pi$
$570$	−1.77143	+	2.35089i	−0.0741970	+	0.0984680i
$571$	−22.0467	−	2.57689i	−0.922625	−	0.107839i	−0.358501	−	0.933529i	$-0.616712\pi$
$571$	−22.0467	−	2.57689i	−0.922625	−	0.107839i	−0.564124	+	0.825690i	$0.690786\pi$
$572$	−8.49520	+	2.01340i	−0.355202	+	0.0841845i
$573$	4.38985	−	24.0797i	0.183389	−	1.00594i
$574$	−2.09330	−	2.81178i	−0.0873725	−	0.117362i
$575$	1.00519	−	5.70073i	0.0419194	−	0.237737i
$576$	21.1136	−	10.2991i	0.879734	−	0.429131i
$577$	−3.76924	−	21.3764i	−0.156915	−	0.889911i	−0.957014	−	0.290042i	$-0.906331\pi$
$577$	−3.76924	−	21.3764i	−0.156915	−	0.889911i	0.800098	−	0.599869i	$-0.204781\pi$
$578$	3.81649	−	4.04524i	0.158745	−	0.168260i
$579$	26.3696	−	27.6278i	1.09588	−	1.14817i
$580$	3.94190	+	1.97970i	0.163679	+	0.0822025i
$581$	−3.24425	+	2.13378i	−0.134594	+	0.0885241i
$582$	−18.5239	+	2.05645i	−0.767842	+	0.0852426i
$583$	5.42806	+	1.28647i	0.224807	+	0.0532803i
$584$	18.4216	+	6.70492i	0.762292	+	0.277452i
$585$	12.0534	−	7.72914i	0.498348	−	0.319561i
$586$	18.7006	−	6.80646i	0.772515	−	0.281172i
$587$	20.2064	−	2.36179i	0.834007	−	0.0974814i	0.311638	−	0.950201i	$-0.399122\pi$
$587$	20.2064	−	2.36179i	0.834007	−	0.0974814i	0.522369	+	0.852720i	$0.325048\pi$
$588$	−10.3397	−	0.0598892i	−0.426400	−	0.00246979i
$589$	5.45362	+	5.78050i	0.224713	+	0.238181i
$590$	−0.685697	+	0.921052i	−0.0282297	+	0.0379191i
$591$	−0.850313	+	2.78150i	−0.0349772	+	0.114416i
$592$	9.74384	−	4.89354i	0.400469	−	0.201123i
$593$	0.579087	−	1.00301i	0.0237803	−	0.0411886i	−0.853890	−	0.520453i	$-0.825763\pi$
$593$	0.579087	−	1.00301i	0.0237803	−	0.0411886i	0.877671	+	0.479264i	$0.159096\pi$
$594$	3.81089	+	9.27451i	0.156363	+	0.380538i
$595$	0.576294	+	0.998171i	0.0236258	+	0.0409210i
$596$	−14.1622	−	9.31463i	−0.580107	−	0.381542i
$597$	−16.4808	−	8.39684i	−0.674513	−	0.343660i
$598$	3.20022	+	7.41894i	0.130867	+	0.303383i
$599$	13.0121	−	43.4636i	0.531662	−	1.77587i	−0.0937678	−	0.995594i	$-0.529891\pi$
$599$	13.0121	−	43.4636i	0.531662	−	1.77587i	0.625430	−	0.780280i	$-0.284924\pi$
$600$	17.3846	−	14.4167i	0.709724	−	0.588558i
$601$	−12.9464	+	30.0132i	−0.528095	+	1.22426i	0.420362	+	0.907357i	$0.361903\pi$
$601$	−12.9464	+	30.0132i	−0.528095	+	1.22426i	−0.948457	+	0.316906i	$0.897356\pi$
$602$	2.97615	+	2.49729i	0.121299	+	0.101782i
$603$	−3.48669	+	18.5170i	−0.141989	+	0.754071i
$604$	−9.80464	+	8.22707i	−0.398945	+	0.334755i
$605$	−1.89148	−	6.31800i	−0.0768998	−	0.256863i
$606$	−15.3583	+	7.60218i	−0.623890	+	0.308817i
$607$	−0.0357006	−	0.612956i	−0.00144904	−	0.0248791i	0.997506	−	0.0705799i	$-0.0224850\pi$
$607$	−0.0357006	−	0.612956i	−0.00144904	−	0.0248791i	−0.998955	+	0.0457008i	$0.985448\pi$
$608$	0.485724	+	8.33956i	0.0196987	+	0.338214i
$609$	2.66240	−	1.31785i	0.107886	−	0.0534020i
$610$	−0.723414	−	2.41637i	−0.0292902	−	0.0978360i
$611$	−8.77827	+	7.36585i	−0.355131	+	0.297990i
$612$	−11.5135	+	4.04016i	−0.465407	+	0.163314i
$613$	−15.6352	−	13.1195i	−0.631499	−	0.529891i	0.269895	−	0.962890i	$-0.413011\pi$
$613$	−15.6352	−	13.1195i	−0.631499	−	0.529891i	−0.901394	+	0.432999i	$0.857455\pi$
$614$	11.4349	−	26.5090i	0.461474	−	1.06982i
$615$	−13.0627	+	10.8326i	−0.526738	+	0.436812i
$616$	0.453856	−	1.51599i	0.0182864	−	0.0610808i
$617$	3.82942	+	8.87760i	0.154167	+	0.357399i	0.977743	−	0.209807i	$-0.0672836\pi$
$617$	3.82942	+	8.87760i	0.154167	+	0.357399i	−0.823576	+	0.567206i	$0.808024\pi$
$618$	24.1203	+	12.2891i	0.970262	+	0.494342i
$619$	22.4428	+	14.7608i	0.902051	+	0.593288i	0.913586	−	0.406645i	$-0.133302\pi$
$619$	22.4428	+	14.7608i	0.902051	+	0.593288i	−0.0115353	+	0.999933i	$0.503672\pi$
$620$	1.56802	+	2.71589i	0.0629732	+	0.109073i
$621$	−5.95008	+	3.76697i	−0.238768	+	0.151163i
$622$	−6.60160	+	11.4343i	−0.264700	+	0.458474i
$623$	0.110618	−	0.0555546i	0.00443183	−	0.00222575i
$624$	−4.32992	+	14.1638i	−0.173335	+	0.567006i
$625$	8.71786	−	11.7101i	0.348715	−	0.468405i
$626$	−15.7057	−	16.6471i	−0.627726	−	0.665350i
$627$	−5.85137	−	0.0338922i	−0.233681	−	0.00135353i
$628$	5.00588	−	0.585104i	0.199757	−	0.0233482i
$629$	−31.5746	+	11.4922i	−1.25896	+	0.458224i
$630$	0.0364358	+	0.781430i	0.00145164	+	0.0311329i
$631$	29.6208	+	10.7811i	1.17918	+	0.429188i	0.855914	−	0.517119i	$-0.172996\pi$
$631$	29.6208	+	10.7811i	1.17918	+	0.429188i	0.323270	+	0.946307i	$0.395218\pi$
$632$	21.1661	+	5.01647i	0.841944	+	0.199544i
$633$	−17.9838	+	1.99649i	−0.714792	+	0.0793533i
$634$	−21.0305	+	13.8320i	−0.835227	+	0.549337i
$635$	−8.49395	−	4.26582i	−0.337072	−	0.169284i
$636$	−3.18114	+	3.33292i	−0.126140	+	0.132159i
$637$	26.5416	−	28.1324i	1.05162	−	1.11465i
$638$	−2.00641	−	11.3789i	−0.0794344	−	0.450495i
$639$	−32.0908	−	21.6432i	−1.26949	−	0.856190i
$640$	−0.0888692	+	0.504002i	−0.00351286	+	0.0199224i
$641$	−6.77315	−	9.09792i	−0.267523	−	0.359346i	0.647979	−	0.761658i	$-0.275614\pi$
$641$	−6.77315	−	9.09792i	−0.267523	−	0.359346i	−0.915503	+	0.402312i	$0.868207\pi$
$642$	−0.0249348	+	0.136775i	−0.000984099	+	0.00539808i
$643$	12.8636	−	3.04874i	0.507292	−	0.120230i	0.0310031	−	0.999519i	$-0.490130\pi$
$643$	12.8636	−	3.04874i	0.507292	−	0.120230i	0.476289	+	0.879289i	$0.341982\pi$
$644$	0.332733	+	0.0388910i	0.0131115	+	0.00153252i
$645$	11.3185	−	15.0210i	0.445666	−	0.591450i
$646$	−0.545562	+	9.36694i	−0.0214648	+	0.368537i
$647$	−36.5943			−1.43867			−0.719336	−	0.694663i	$-0.755554\pi$
$647$	−36.5943			−1.43867			−0.719336	+	0.694663i	$0.755554\pi$
$648$	−27.2086	−	3.82107i	−1.06885	−	0.150106i
$649$	−2.28261			−0.0896005
$650$	−1.48056	+	25.4202i	−0.0580723	+	0.997062i
$651$	2.09626	+	0.257334i	0.0821591	+	0.0100857i
$652$	−5.90528	−	0.690228i	−0.231269	−	0.0270314i
$653$	26.5618	−	6.29526i	1.03944	−	0.246352i	0.324756	−	0.945798i	$-0.394718\pi$
$653$	26.5618	−	6.29526i	1.03944	−	0.246352i	0.714686	+	0.699445i	$0.246570\pi$
$654$	7.45080	+	6.32586i	0.291349	+	0.247361i
$655$	−0.140682	−	0.188969i	−0.00549691	−	0.00738363i
$656$	3.04809	−	17.2866i	0.119008	−	0.674928i
$657$	−11.3242	−	15.5848i	−0.441800	−	0.608020i
$658$	−0.108714	−	0.616545i	−0.00423809	−	0.0240354i
$659$	10.1285	−	10.7356i	0.394549	−	0.418198i	−0.499396	−	0.866374i	$-0.666445\pi$
$659$	10.1285	−	10.7356i	0.394549	−	0.418198i	0.893945	+	0.448176i	$0.147926\pi$
$660$	−2.24371	−	0.545515i	−0.0873364	−	0.0212341i
$661$	−24.8613	−	12.4858i	−0.966993	−	0.485642i	−0.106060	−	0.994360i	$-0.533823\pi$
$661$	−24.8613	−	12.4858i	−0.966993	−	0.485642i	−0.860934	+	0.508717i	$0.830120\pi$
$662$	−0.755321	+	0.496783i	−0.0293564	+	0.0193080i
$663$	18.3201	−	41.8034i	0.711496	−	1.62351i
$664$	−40.2694	−	9.54401i	−1.56275	−	0.370380i
$665$	−0.428987	−	0.156138i	−0.0166354	−	0.00605479i
$666$	−22.6191	−	2.90977i	−0.876471	−	0.112751i
$667$	7.62568	−	2.77552i	0.295267	−	0.107469i
$668$	−15.2082	+	1.77758i	−0.588422	+	0.0687766i
$669$	11.6877	+	20.5172i	0.451872	+	0.793241i
$670$	3.92370	+	4.15888i	0.151586	+	0.160671i
$671$	2.99421	−	4.02192i	0.115590	−	0.155265i
$672$	1.51412	+	1.62361i	0.0584084	+	0.0626321i
$673$	29.3895	−	14.7600i	1.13288	−	0.568955i	0.219320	−	0.975653i	$-0.429616\pi$
$673$	29.3895	−	14.7600i	1.13288	−	0.568955i	0.913563	+	0.406698i	$0.133320\pi$
$674$	1.08967	−	1.88737i	0.0419727	−	0.0726989i
$675$	−22.0851	+	2.19312i	−0.850055	+	0.0844134i
$676$	7.87718	+	13.6437i	0.302968	+	0.524757i
$677$	20.1441	+	13.2490i	0.774201	+	0.509200i	0.874070	−	0.485801i	$-0.161472\pi$
$677$	20.1441	+	13.2490i	0.774201	+	0.509200i	−0.0998686	+	0.995001i	$0.531842\pi$
$678$	1.79078	+	34.1534i	0.0687746	+	1.31165i
$679$	−1.14488	−	2.65412i	−0.0439363	−	0.101856i
$680$	−3.52310	+	11.7680i	−0.135105	+	0.451282i
$681$	3.81054	+	22.3675i	0.146020	+	0.857123i
$682$	3.25361	−	7.54272i	0.124587	−	0.288826i
$683$	−10.1873	−	8.54816i	−0.389806	−	0.327086i	0.426731	−	0.904378i	$-0.359665\pi$
$683$	−10.1873	−	8.54816i	−0.389806	−	0.327086i	−0.816538	+	0.577292i	$0.804109\pi$
$684$	2.46477	−	4.15715i	0.0942430	−	0.158952i
$685$	−6.89130	+	5.78249i	−0.263303	+	0.220938i
$686$	1.21924	+	4.07255i	0.0465509	+	0.155491i
$687$	2.48655	+	1.65614i	0.0948677	+	0.0631857i
$688$	1.13117	+	19.4215i	0.0431256	+	0.740438i
$689$	−1.00208	−	17.2051i	−0.0381762	−	0.655460i
$690$	−0.136607	+	2.13258i	−0.00520054	+	0.0811859i
$691$	12.5726	+	41.9955i	0.478285	+	1.59758i	0.767986	+	0.640467i	$0.221259\pi$
$691$	12.5726	+	41.9955i	0.478285	+	1.59758i	−0.289700	+	0.957117i	$0.593556\pi$
$692$	−9.24612	+	7.75841i	−0.351485	+	0.294931i
$693$	−1.20276	+	0.985716i	−0.0456889	+	0.0374443i
$694$	5.31231	+	4.45756i	0.201653	+	0.169207i
$695$	−0.183241	+	0.424800i	−0.00695072	+	0.0161136i
$696$	29.6885	+	11.0009i	1.12534	+	0.416988i
$697$	−15.5139	+	51.8201i	−0.587632	+	1.96283i
$698$	−2.79632	−	6.48259i	−0.105842	−	0.245370i
$699$	−35.2339	+	22.8825i	−1.33267	+	0.865494i
$700$	0.882065	+	0.580143i	0.0333389	+	0.0219274i
$701$	−3.65194	−	6.32534i	−0.137932	−	0.238905i	0.788782	−	0.614673i	$-0.210712\pi$
$701$	−3.65194	−	6.32534i	−0.137932	−	0.238905i	−0.926714	+	0.375768i	$0.877379\pi$
$702$	24.0726	−	19.4967i	0.908563	−	0.735855i
$703$	6.65434	−	11.5257i	0.250973	−	0.434699i
$704$	12.6632	−	6.35971i	0.477263	−	0.239691i
$705$	−2.95307	+	0.681850i	−0.111219	+	0.0256800i
$706$	0.192471	−	0.258534i	0.00724376	−	0.00973005i
$707$	−1.82386	−	1.93318i	−0.0685932	−	0.0727046i
$708$	0.952081	−	1.62721i	0.0357814	−	0.0611544i
$709$	43.4298	−	5.07622i	1.63104	−	0.190641i	0.749251	−	0.662286i	$-0.230413\pi$
$709$	43.4298	−	5.07622i	1.63104	−	0.190641i	0.881789	+	0.471644i	$0.156339\pi$
$710$	−11.0372	+	4.01722i	−0.414219	+	0.150764i
$711$	−14.4880	−	15.7172i	−0.543342	−	0.589441i
$712$	1.23971	+	0.451219i	0.0464602	+	0.0169101i
$713$	5.61384	+	1.33050i	0.210240	+	0.0498278i
$714$	1.47744	+	2.00873i	0.0552917	+	0.0751748i
$715$	7.21631	−	4.74624i	0.269875	−	0.177499i
$716$	8.08537	+	4.06062i	0.302164	+	0.151753i
$717$	10.7875	+	36.8072i	0.402865	+	1.37459i
$718$	3.00420	−	3.18427i	0.112116	−	0.118836i
$719$	−1.93615	−	10.9804i	−0.0722061	−	0.409501i	−0.999391	−	0.0348968i	$-0.988890\pi$
$719$	−1.93615	−	10.9804i	−0.0722061	−	0.409501i	0.927185	−	0.374604i	$-0.122221\pi$
$720$	−2.72099	+	2.81795i	−0.101405	+	0.105019i
$721$	−0.729037	+	4.13457i	−0.0271508	+	0.153980i
$722$	9.87940	+	13.2703i	0.367673	+	0.493871i
$723$	−29.4775	+	10.5360i	−1.09628	+	0.391838i
$724$	10.4198	−	2.46953i	0.387248	−	0.0917794i
$725$	25.4017	+	2.96904i	0.943397	+	0.110267i
$726$	−5.57529	−	13.1336i	−0.206919	−	0.487435i
$727$	−1.69160	+	29.0436i	−0.0627378	+	1.07717i	0.809195	+	0.587540i	$0.199904\pi$
$727$	−1.69160	+	29.0436i	−0.0627378	+	1.07717i	−0.871933	+	0.489626i	$0.837133\pi$
$728$	−4.88893			−0.181196
$729$	20.0677	+	18.0634i	0.743248	+	0.669016i
$730$	−5.84576			−0.216361
$731$	3.48586	−	59.8499i	0.128929	−	2.21363i
$732$	1.61823	+	3.81204i	0.0598115	+	0.140897i
$733$	−17.2429	−	2.01540i	−0.636880	−	0.0744406i	−0.208475	−	0.978028i	$-0.566850\pi$
$733$	−17.2429	−	2.01540i	−0.636880	−	0.0744406i	−0.428404	+	0.903587i	$0.640924\pi$
$734$	9.33297	−	2.21196i	0.344486	−	0.0816448i
$735$	9.63254	−	3.44291i	0.355301	−	0.126993i
$736$	3.62149	+	4.86451i	0.133490	+	0.179308i
$737$	−1.97369	+	11.1933i	−0.0727017	+	0.412312i
$738$	−25.5019	+	26.4107i	−0.938739	+	0.972193i
$739$	3.59215	+	20.3721i	0.132139	+	0.749400i	0.976809	+	0.214112i	$0.0686857\pi$
$739$	3.59215	+	20.3721i	0.132139	+	0.749400i	−0.844670	+	0.535288i	$0.820203\pi$
$740$	3.60401	−	3.82002i	0.132486	−	0.140427i
$741$	5.08436	+	17.3480i	0.186779	+	0.637296i
$742$	0.841412	+	0.422573i	0.0308892	+	0.0155131i
$743$	31.8353	−	20.9384i	1.16792	−	0.768154i	0.190966	−	0.981597i	$-0.438838\pi$
$743$	31.8353	−	20.9384i	1.16792	−	0.768154i	0.976956	+	0.213442i	$0.0684675\pi$
$744$	13.3368	+	18.1328i	0.488951	+	0.664779i
$745$	16.3177	+	3.86736i	0.597833	+	0.141689i
$746$	5.27104	+	1.91850i	0.192986	+	0.0702413i
$747$	27.5639	+	29.9025i	1.00851	+	1.09408i
$748$	−6.91643	+	2.51737i	−0.252890	+	0.0920443i
$749$	−0.0214162	+	0.00250320i	−0.000782531	+	9.14648e-5i
$750$	−7.38239	+	12.6173i	−0.269567	+	0.460720i
$751$	−23.5042	−	24.9130i	−0.857680	−	0.909087i	0.139018	−	0.990290i	$-0.455605\pi$
$751$	−23.5042	−	24.9130i	−0.857680	−	0.909087i	−0.996698	+	0.0812024i	$0.974124\pi$
$752$	1.87206	−	2.51461i	0.0682670	−	0.0916985i
$753$	16.9515	−	3.91402i	0.617747	−	0.142635i
$754$	−31.8997	+	16.0207i	−1.16172	+	0.583438i
$755$	6.33114	−	10.9659i	0.230414	−	0.399088i
$756$	−0.201019	−	1.26855i	−0.00731100	−	0.0461369i
$757$	−14.5877	−	25.2666i	−0.530198	−	0.918330i	−0.999379	−	0.0352284i	$-0.988784\pi$
$757$	−14.5877	−	25.2666i	−0.530198	−	0.918330i	0.469181	−	0.883102i	$-0.344549\pi$
$758$	6.71251	+	4.41489i	0.243810	+	0.160356i
$759$	−3.56261	+	2.31372i	−0.129315	+	0.0839826i
$760$	−1.92712	−	4.46756i	−0.0699039	−	0.162055i
$761$	−3.53905	+	11.8213i	−0.128291	+	0.428520i	−0.997867	−	0.0652779i	$-0.979207\pi$
$761$	−3.53905	+	11.8213i	−0.128291	+	0.428520i	0.869577	+	0.493798i	$0.164392\pi$
$762$	−19.2822	−	7.14491i	−0.698522	−	0.258833i
$763$	−0.600395	+	1.39187i	−0.0217358	+	0.0503892i
$764$	9.34155	+	7.83849i	0.337965	+	0.283587i
$765$	9.33651	−	7.65172i	0.337562	−	0.276648i
$766$	29.0983	−	24.4163i	1.05136	−	0.882198i
$767$	2.02254	+	6.75574i	0.0730295	+	0.243936i
$768$	−1.80483	+	28.1753i	−0.0651261	+	1.01669i
$769$	−0.161303	−	2.76946i	−0.00581673	−	0.0998693i	0.994150	−	0.108007i	$-0.0344468\pi$
$769$	−0.161303	−	2.76946i	−0.00581673	−	0.0998693i	−0.999967	+	0.00813737i	$0.997410\pi$
$770$	0.0274375	+	0.471083i	0.000988778	+	0.0169767i
$771$	−13.2254	−	8.80865i	−0.476301	−	0.317236i
$772$	5.45726	+	18.2285i	0.196411	+	0.656058i
$773$	−21.3606	+	17.9237i	−0.768287	+	0.644669i	−0.940270	−	0.340431i	$-0.889427\pi$
$773$	−21.3606	+	17.9237i	−0.768287	+	0.644669i	0.171983	+	0.985100i	$0.444983\pi$
$774$	20.7517	−	35.0004i	0.745906	−	1.25806i
$775$	13.9283	+	11.6872i	0.500320	+	0.419818i
$776$	12.2019	−	28.2871i	0.438021	−	1.01545i
$777$	−0.593989	−	3.48665i	−0.0213092	−	0.125083i
$778$	3.87272	−	12.9358i	0.138844	−	0.463770i
$779$	−8.48603	−	19.6728i	−0.304043	−	0.704852i
$780$	0.373534	+	7.12397i	0.0133747	+	0.255079i
$781$	−19.5076	−	12.8303i	−0.698036	−	0.459106i
$782$	3.40582	+	5.89906i	0.121792	+	0.210950i
$783$	−18.1430	−	25.2756i	−0.648379	−	0.903277i
$784$	−5.29048	+	9.16338i	−0.188946	+	0.327263i
$785$	−4.45575	+	2.23776i	−0.159032	+	0.0798691i
$786$	−0.347608	−	0.372745i	−0.0123988	−	0.0132954i
$787$	−0.836491	+	1.12360i	−0.0298177	+	0.0400521i	−0.816782	−	0.576946i	$-0.804244\pi$
$787$	−0.836491	+	1.12360i	−0.0298177	+	0.0400521i	0.786964	+	0.616999i	$0.211652\pi$
$788$	−0.994425	−	1.05403i	−0.0354249	−	0.0375482i
$789$	−20.3748	−	35.7670i	−0.725361	−	1.27334i
$790$	−6.44260	+	0.753032i	−0.229217	+	0.0267917i
$791$	−4.98424	+	1.81411i	−0.177219	+	0.0645025i
$792$	−16.4382	−	2.11465i	−0.584106	−	0.0751407i
$793$	−14.5565	−	5.29815i	−0.516918	−	0.188143i
$794$	−11.2694	−	2.67090i	−0.399937	−	0.0947867i
$795$	1.82960	−	4.17484i	0.0648894	−	0.148066i
$796$	7.69921	−	5.06385i	0.272891	−	0.179483i
$797$	−10.0188	−	5.03163i	−0.354884	−	0.178230i	0.262421	−	0.964954i	$-0.415479\pi$
$797$	−10.0188	−	5.03163i	−0.354884	−	0.178230i	−0.617305	+	0.786724i	$0.711775\pi$
$798$	−0.959692	−	0.233330i	−0.0339727	−	0.00825980i
$799$	−6.62960	+	7.02697i	−0.234538	+	0.248596i
$800$	3.31883	+	18.8220i	0.117338	+	0.665460i
$801$	−0.762082	−	1.04880i	−0.0269268	−	0.0370576i
$802$	−1.06268	+	6.02674i	−0.0375244	+	0.212812i
$803$	−6.93937	−	9.32120i	−0.244885	−	0.328938i
$804$	−7.15620	−	6.07574i	−0.252380	−	0.214275i
$805$	−0.322485	+	0.0764304i	−0.0113661	+	0.00269382i
$806$	−25.2067	−	2.94624i	−0.887868	−	0.103777i
$807$	−11.5214	−	1.41435i	−0.405573	−	0.0497876i
$808$	1.64699	−	28.2778i	0.0579411	−	0.994810i
$809$	2.44943			0.0861173			0.0430587	−	0.999073i	$-0.486290\pi$
$809$	2.44943			0.0861173			0.0430587	+	0.999073i	$0.486290\pi$
$810$	8.01384	−	1.70425i	0.281578	−	0.0598813i
$811$	11.9053			0.418050			0.209025	−	0.977910i	$-0.432971\pi$
$811$	11.9053			0.418050			0.209025	+	0.977910i	$0.432971\pi$
$812$	−0.0860569	+	1.47754i	−0.00302000	+	0.0518515i
$813$	9.89167	−	13.1274i	0.346916	−	0.460398i
$814$	−13.6636	−	1.59704i	−0.478907	−	0.0559762i
$815$	5.72340	−	1.35647i	0.200482	−	0.0475151i
$816$	−2.23942	+	12.2839i	−0.0783954	+	0.430022i
$817$	14.1799	+	19.0469i	0.496091	+	0.666365i
$818$	5.47372	−	31.0430i	0.191384	−	1.08539i
$819$	3.98309	+	2.68633i	0.139180	+	0.0938680i
$820$	−1.46813	−	8.32619i	−0.0512694	−	0.290763i
$821$	−16.6721	+	17.6714i	−0.581861	+	0.616737i	−0.949703	−	0.313151i	$-0.898615\pi$
$821$	−16.6721	+	17.6714i	−0.581861	+	0.616737i	0.367842	+	0.929888i	$0.380097\pi$
$822$	−13.4376	+	14.0787i	−0.468688	+	0.491051i
$823$	27.7306	+	13.9268i	0.966629	+	0.485459i	0.860810	−	0.508926i	$-0.169957\pi$
$823$	27.7306	+	13.9268i	0.966629	+	0.485459i	0.105818	+	0.994385i	$0.466254\pi$
$824$	−37.3841	+	24.5879i	−1.30234	+	0.856560i
$825$	−13.3058	+	1.47716i	−0.463249	+	0.0514280i
$826$	−0.374890	−	0.0888505i	−0.0130441	−	0.00309150i
$827$	9.52144	+	3.46552i	0.331093	+	0.120508i	0.502217	−	0.864741i	$-0.332518\pi$
$827$	9.52144	+	3.46552i	0.331093	+	0.120508i	−0.171124	+	0.985249i	$0.554740\pi$
$828$	−0.163416	−	3.50474i	−0.00567910	−	0.121798i
$829$	−16.7991	+	6.11438i	−0.583458	+	0.212361i	−0.616850	−	0.787081i	$-0.711591\pi$
$829$	−16.7991	+	6.11438i	−0.583458	+	0.212361i	0.0333918	+	0.999442i	$0.489369\pi$
$830$	12.2573	−	1.43267i	0.425456	−	0.0497287i
$831$	2.40118	+	0.0139081i	0.0832960	+	0.000482466i
$832$	−30.0429	−	31.8436i	−1.04155	−	1.10398i
$833$	19.4713	−	26.1545i	0.674640	−	0.906199i
$834$	−0.292606	+	0.957159i	−0.0101321	+	0.0331437i
$835$	13.5368	−	6.79845i	0.468461	−	0.235270i
$836$	1.45764	−	2.52470i	0.0504135	−	0.0873187i
$837$	−0.902260	−	22.1012i	−0.0311867	−	0.763931i
$838$	−4.76371	−	8.25099i	−0.164560	−	0.285026i
$839$	−20.6000	−	13.5488i	−0.711191	−	0.467757i	0.141658	−	0.989916i	$-0.454757\pi$
$839$	−20.6000	−	13.5488i	−0.711191	−	0.467757i	−0.852849	+	0.522158i	$0.825127\pi$
$840$	−1.15212	−	0.586998i	−0.0397519	−	0.0202533i
$841$	2.71428	+	6.29241i	0.0935960	+	0.216980i
$842$	0.774368	−	2.58657i	0.0266865	−	0.0891390i
$843$	−21.3495	+	17.7047i	−0.735317	+	0.609781i
$844$	3.57058	−	8.27754i	0.122905	−	0.284925i
$845$	−11.9396	−	10.0185i	−0.410734	−	0.344647i
$846$	−6.18702	+	2.17106i	−0.212714	+	0.0746426i
$847$	1.69512	−	1.42237i	0.0582450	−	0.0488734i
$848$	1.35223	+	4.51676i	0.0464358	+	0.155106i
$849$	0.487617	−	0.241364i	0.0167350	−	0.00828359i
$850$	1.24819	+	21.4306i	0.0428125	+	0.735063i
$851$	−0.561779	−	9.64537i	−0.0192575	−	0.330639i
$852$	17.2830	−	8.55487i	0.592107	−	0.293085i
$853$	−0.596781	−	1.99339i	−0.0204334	−	0.0682522i	0.947165	−	0.320747i	$-0.103934\pi$
$853$	−0.596781	−	1.99339i	−0.0204334	−	0.0682522i	−0.967598	+	0.252495i	$0.918749\pi$
$854$	0.648313	−	0.543999i	0.0221848	−	0.0186153i
$855$	−0.884746	+	4.69869i	−0.0302577	+	0.160692i
$856$	−0.176040	−	0.147715i	−0.00601691	−	0.00504879i
$857$	−4.89536	+	11.3487i	−0.167222	+	0.387665i	−0.981135	−	0.193322i	$-0.938074\pi$
$857$	−4.89536	+	11.3487i	−0.167222	+	0.387665i	0.813913	+	0.580987i	$0.197333\pi$
$858$	14.3837	−	11.9281i	0.491053	−	0.407219i
$859$	11.2346	−	37.5261i	0.383319	−	1.28037i	−0.521015	−	0.853548i	$-0.674446\pi$
$859$	11.2346	−	37.5261i	0.383319	−	1.28037i	0.904334	−	0.426826i	$-0.140368\pi$
$860$	3.71140	+	8.60400i	0.126558	+	0.293394i
$861$	−5.07334	−	2.58483i	−0.172899	−	0.0880909i
$862$	26.4767	+	17.4140i	0.901800	+	0.593123i
$863$	12.2220	+	21.1691i	0.416040	+	0.720603i	0.995537	−	0.0943715i	$-0.0300842\pi$
$863$	12.2220	+	21.1691i	0.416040	+	0.720603i	−0.579497	+	0.814975i	$0.696751\pi$
$864$	14.2067	−	18.4064i	0.483323	−	0.626199i
$865$	5.97048	−	10.3412i	0.203003	−	0.351611i
$866$	1.16826	−	0.586721i	0.0396990	−	0.0199376i
$867$	2.64090	−	8.63880i	0.0896898	−	0.293389i
$868$	−0.628346	+	0.844015i	−0.0213274	+	0.0286477i
$869$	−8.84860	−	9.37896i	−0.300168	−	0.318160i
$870$	−9.44101	−	0.0546841i	−0.320080	−	0.00185396i
$871$	34.8772	−	4.07656i	1.18177	−	0.138129i
$872$	−15.1813	+	5.52553i	−0.514102	+	0.187118i
$873$	−25.4840	+	16.3414i	−0.862503	+	0.553071i
$874$	−2.53525	−	0.922757i	−0.0857563	−	0.0312127i
$875$	−2.20605	−	0.522842i	−0.0745780	−	0.0176753i
$876$	9.53924	−	1.05901i	0.322301	−	0.0357805i
$877$	11.3307	−	7.45229i	0.382609	−	0.251646i	−0.343606	−	0.939114i	$-0.611648\pi$
$877$	11.3307	−	7.45229i	0.382609	−	0.251646i	0.726214	+	0.687468i	$0.241278\pi$
$878$	16.5417	+	8.30753i	0.558254	+	0.280366i
$879$	22.3185	−	23.3834i	0.752784	−	0.788702i
$880$	−1.62154	+	1.71873i	−0.0546620	+	0.0579383i
$881$	−2.84380	−	16.1280i	−0.0958101	−	0.543366i	−0.994496	−	0.104774i	$-0.966588\pi$
$881$	−2.84380	−	16.1280i	−0.0958101	−	0.543366i	0.898686	−	0.438593i	$-0.144523\pi$
$882$	19.8903	−	9.70242i	0.669742	−	0.326697i
$883$	−7.98860	+	45.3056i	−0.268838	+	1.52465i	0.489042	+	0.872260i	$0.337347\pi$
$883$	−7.98860	+	45.3056i	−0.268838	+	1.52465i	−0.757880	+	0.652394i	$0.773765\pi$
$884$	13.5789	+	18.2397i	0.456709	+	0.613466i
$885$	−0.334510	+	1.83489i	−0.0112444	+	0.0616792i
$886$	12.4355	−	2.94726i	0.417778	−	0.0990153i
$887$	49.0922	+	5.73806i	1.64836	+	0.192665i	0.888967	−	0.457971i	$-0.151424\pi$
$887$	49.0922	+	5.73806i	1.64836	+	0.192665i	0.759389	+	0.650637i	$0.225498\pi$
$888$	22.6849	−	30.1055i	0.761256	−	1.01027i
$889$	0.185434	−	3.18378i	0.00621926	−	0.106781i
$890$	−0.393400			−0.0131868
$891$	12.2305	+	10.7552i	0.409738	+	0.360312i
$892$	−11.7641			−0.393892
$893$	0.222487	−	3.81996i	0.00744525	−	0.127830i
$894$	36.0099	+	4.42052i	1.20435	+	0.147844i
$895$	−8.89054	−	1.03916i	−0.297178	−	0.0347351i
$896$	−0.167087	+	0.0396002i	−0.00558197	+	0.00132295i
$897$	10.0045	+	8.49398i	0.334040	+	0.283606i
$898$	−12.4699	−	16.7500i	−0.416127	−	0.558956i
$899$	−4.42618	+	25.1021i	−0.147621	+	0.837201i
$900$	4.49685	−	10.1015i	0.149895	−	0.336716i
$901$	−2.52300	−	14.3086i	−0.0840532	−	0.476690i
$902$	−15.1976	+	16.1085i	−0.506023	+	0.536353i
$903$	6.13193	+	1.49086i	0.204058	+	0.0496127i
$904$	−50.5172	−	25.3707i	−1.68018	−	0.843817i
$905$	−8.85115	+	5.82149i	−0.294222	+	0.193513i
$906$	10.9958	−	25.0904i	0.365309	−	0.833573i
$907$	−46.5158	−	11.0244i	−1.54453	−	0.366061i	−0.631967	−	0.774995i	$-0.717752\pi$
$907$	−46.5158	−	11.0244i	−1.54453	−	0.366061i	−0.912564	+	0.408935i	$0.865900\pi$
$908$	−10.6226	−	3.86630i	−0.352523	−	0.128308i
$909$	−16.8797	+	22.1334i	−0.559864	+	0.734119i
$910$	1.36993	−	0.498614i	0.0454127	−	0.0165289i
$911$	32.9908	−	3.85607i	1.09303	−	0.127757i	0.449579	−	0.893241i	$-0.351574\pi$
$911$	32.9908	−	3.85607i	1.09303	−	0.127757i	0.643456	+	0.765483i	$0.277500\pi$
$912$	−2.44795	−	4.29727i	−0.0810599	−	0.142297i
$913$	16.8348	+	17.8438i	0.557150	+	0.590544i
$914$	−15.2934	+	20.5427i	−0.505862	+	0.679491i
$915$	−2.79425	−	2.99631i	−0.0923751	−	0.0990550i
$916$	−1.33013	+	0.668018i	−0.0439489	+	0.0220720i
$917$	0.0395228	−	0.0684554i	0.00130516	−	0.00226060i
$918$	18.2491	−	18.6817i	0.602310	−	0.616587i
$919$	13.4983	+	23.3798i	0.445268	+	0.771228i	0.998071	−	0.0620848i	$-0.0197749\pi$
$919$	13.4983	+	23.3798i	0.445268	+	0.771228i	−0.552802	+	0.833312i	$0.686442\pi$
$920$	−2.95110	−	1.94097i	−0.0972950	−	0.0639919i
$921$	−2.45544	−	46.8295i	−0.0809094	−	1.54309i
$922$	5.98347	+	13.8712i	0.197055	+	0.456825i
$923$	−20.6884	+	69.1041i	−0.680967	+	2.27459i
$924$	−0.130114	−	0.763754i	−0.00428043	−	0.0251257i
$925$	12.0602	−	27.9587i	0.396537	−	0.919276i
$926$	8.99236	+	7.54549i	0.295507	+	0.247960i
$927$	43.9678	+	0.509356i	1.44409	+	0.0167294i
$928$	−20.5250	+	17.2225i	−0.673766	+	0.565357i
$929$	−0.250564	−	0.836943i	−0.00822075	−	0.0274592i	0.953781	−	0.300503i	$-0.0971547\pi$
$929$	−0.250564	−	0.836943i	−0.00822075	−	0.0274592i	−0.962001	+	0.273044i	$0.911969\pi$
$930$	−5.58644	−	3.72079i	−0.183187	−	0.122010i
$931$	0.750931	+	12.8930i	0.0246108	+	0.422551i
$932$	−1.21703	−	20.8957i	−0.0398653	−	0.684460i
$933$	−1.37096	+	21.4021i	−0.0448832	+	0.700674i
$934$	−11.9172	−	39.8063i	−0.389943	−	1.30250i
$935$	5.57807	−	4.68056i	0.182422	−	0.153071i
$936$	8.30664	+	50.5250i	0.271511	+	1.65146i
$937$	12.6271	+	10.5954i	0.412511	+	0.346138i	0.825306	−	0.564686i	$-0.191003\pi$
$937$	12.6271	+	10.5954i	0.412511	+	0.346138i	−0.412795	+	0.910824i	$0.635447\pi$
$938$	−0.759852	+	1.76153i	−0.0248100	+	0.0575161i
$939$	−34.8585	−	12.9166i	−1.13756	−	0.421517i
$940$	0.433063	−	1.44653i	0.0141250	−	0.0471807i
$941$	12.0402	+	27.9123i	0.392499	+	0.909916i	0.993830	+	0.110915i	$0.0353782\pi$
$941$	12.0402	+	27.9123i	0.392499	+	0.909916i	−0.601331	+	0.799000i	$0.705363\pi$
$942$	−9.04670	+	5.87533i	−0.294758	+	0.191429i
$943$	−12.9951	−	8.54703i	−0.423180	−	0.278330i
$944$	−0.964622	−	1.67077i	−0.0313958	−	0.0543791i
$945$	0.616112	+	1.11129i	0.0200421	+	0.0361504i
$946$	12.2723	−	21.2563i	0.399008	−	0.691102i
$947$	−11.4315	+	5.74112i	−0.371474	+	0.186561i	−0.624735	−	0.780837i	$-0.714793\pi$
$947$	−11.4315	+	5.74112i	−0.371474	+	0.186561i	0.253261	+	0.967398i	$0.418497\pi$
$948$	10.3768	−	2.39594i	0.337022	−	0.0778167i
$949$	−21.4388	+	28.7973i	−0.695932	+	0.934799i
$950$	−5.83486	−	6.18459i	−0.189308	−	0.200655i
$951$	−20.6478	+	35.2894i	−0.669551	+	1.14434i
$952$	−4.09376	+	0.478492i	−0.132680	+	0.0155080i
$953$	−28.8328	+	10.4943i	−0.933986	+	0.339943i	−0.763788	−	0.645467i	$-0.776663\pi$
$953$	−28.8328	+	10.4943i	−0.933986	+	0.339943i	−0.170198	+	0.985410i	$0.554441\pi$
$954$	2.93750	−	9.41362i	0.0951049	−	0.304777i
$955$	−11.3367	−	4.12620i	−0.366845	−	0.133521i
$956$	−18.5941	−	4.40688i	−0.601376	−	0.142529i
$957$	−11.1200	−	15.1188i	−0.359459	−	0.488722i
$958$	12.5802	−	8.27413i	0.406448	−	0.267325i
$959$	−2.69733	−	1.35465i	−0.0871013	−	0.0437439i
$960$	−3.25652	−	11.1114i	−0.105104	−	0.358618i
$961$	8.83780	−	9.36752i	0.285090	−	0.302178i
$962$	7.38006	+	41.8544i	0.237943	+	1.34944i
$963$	0.0622571	+	0.217074i	0.00200621	+	0.00699512i
$964$	2.70821	−	15.3590i	0.0872257	−	0.494681i
$965$	−11.2412	−	15.0996i	−0.361868	−	0.486073i
$966$	−0.675173	+	0.241323i	−0.0217233	+	0.00776445i
$967$	16.4488	−	3.89843i	0.528956	−	0.125365i	0.0425444	−	0.999095i	$-0.486454\pi$
$967$	16.4488	−	3.89843i	0.528956	−	0.125365i	0.486412	+	0.873730i	$0.338305\pi$
$968$	23.4243	+	2.73791i	0.752886	+	0.0879998i
$969$	5.95531	+	14.0288i	0.191312	+	0.450671i
$970$	−0.534137	+	9.17079i	−0.0171501	+	0.294456i
$971$	53.7751			1.72572			0.862862	−	0.505439i	$-0.168670\pi$
$971$	53.7751			1.72572			0.862862	+	0.505439i	$0.168670\pi$
$972$	−12.7684	+	4.23281i	−0.409547	+	0.135768i
$973$	−0.155227			−0.00497635
$974$	−0.720613	+	12.3724i	−0.0230899	+	0.396439i
$975$	16.1616	+	38.0717i	0.517587	+	1.21927i
$976$	4.20921	+	0.491986i	0.134734	+	0.0157481i
$977$	−14.4610	+	3.42733i	−0.462650	+	0.109650i	−0.455329	−	0.890323i	$-0.650478\pi$
$977$	−14.4610	+	3.42733i	−0.462650	+	0.109650i	−0.00732063	+	0.999973i	$0.502330\pi$
$978$	11.9828	−	4.28295i	0.383168	−	0.136954i
$979$	−0.466997	−	0.627285i	−0.0149253	−	0.0200481i
$980$	−0.884978	+	5.01896i	−0.0282696	+	0.160325i
$981$	15.4045	+	3.83994i	0.491829	+	0.122600i
$982$	0.972752	+	5.51675i	0.0310418	+	0.176047i
$983$	−12.2104	+	12.9422i	−0.389450	+	0.412793i	−0.892201	−	0.451638i	$-0.850840\pi$
$983$	−12.2104	+	12.9422i	−0.389450	+	0.412793i	0.502751	+	0.864431i	$0.332321\pi$
$984$	−17.0674	−	58.2346i	−0.544089	−	1.85645i
$985$	1.28111	+	0.643400i	0.0408197	+	0.0205004i
$986$	−25.1434	+	16.5371i	−0.800728	+	0.526647i
$987$	−0.602519	−	0.819187i	−0.0191784	−	0.0260750i
$988$	−8.76380	−	2.07706i	−0.278814	−	0.0660800i
$989$	16.1990	+	5.89594i	0.515097	+	0.187480i
$990$	4.82183	−	1.08396i	0.153248	−	0.0344505i
$991$	12.0174	−	4.37398i	0.381746	−	0.138944i	−0.144017	−	0.989575i	$-0.546002\pi$
$991$	12.0174	−	4.37398i	0.381746	−	0.138944i	0.525763	+	0.850631i	$0.323780\pi$
$992$	−18.9198	+	2.21141i	−0.600705	+	0.0702123i
$993$	−0.741578	+	1.26744i	−0.0235333	+	0.0402210i
$994$	−2.70445	−	2.86655i	−0.0857798	−	0.0909213i
$995$	−5.44414	+	7.31275i	−0.172591	+	0.231830i
$996$	−19.7422	+	4.55837i	−0.625555	+	0.144438i
$997$	−54.9375	+	27.5906i	−1.73989	+	0.873804i	−0.767293	+	0.641297i	$0.778397\pi$
$997$	−54.9375	+	27.5906i	−1.73989	+	0.873804i	−0.972595	+	0.232508i	$0.925307\pi$
$998$	2.94125	−	5.09439i	0.0931036	−	0.161260i
$999$	−35.0239	+	12.0627i	−1.10811	+	0.381647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.79.6	yes	144
3.2	odd	2		243.2.g.a.235.3		144
9.2	odd	6		729.2.g.b.460.6		144
9.4	even	3		729.2.g.d.703.6		144
9.5	odd	6		729.2.g.a.703.3		144
9.7	even	3		729.2.g.c.460.3		144
81.11	odd	54		6561.2.a.d.1.46		72
81.13	even	27		729.2.g.d.28.6		144
81.14	odd	54		729.2.g.b.271.6		144
81.40	even	27	inner	81.2.g.a.40.6	✓	144
81.41	odd	54		243.2.g.a.91.3		144
81.67	even	27		729.2.g.c.271.3		144
81.68	odd	54		729.2.g.a.28.3		144
81.70	even	27		6561.2.a.c.1.27		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.40.6	✓	144	81.40	even	27	inner
81.2.g.a.79.6	yes	144	1.1	even	1	trivial
243.2.g.a.91.3		144	81.41	odd	54
243.2.g.a.235.3		144	3.2	odd	2
729.2.g.a.28.3		144	81.68	odd	54
729.2.g.a.703.3		144	9.5	odd	6
729.2.g.b.271.6		144	81.14	odd	54
729.2.g.b.460.6		144	9.2	odd	6
729.2.g.c.271.3		144	81.67	even	27
729.2.g.c.460.3		144	9.7	even	3
729.2.g.d.28.6		144	81.13	even	27
729.2.g.d.703.6		144	9.4	even	3
6561.2.a.c.1.27		72	81.70	even	27
6561.2.a.d.1.46		72	81.11	odd	54

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0620019 - 1.06453i) q^{2} +(-0.676807 - 1.59434i) q^{3} +(0.857095 + 0.100180i) q^{4} +(-0.830696 + 0.196879i) q^{5} +(-1.73919 + 0.621630i) q^{6} +(-0.171051 - 0.229762i) q^{7} +(0.530120 - 3.00646i) q^{8} +(-2.08386 + 2.15813i) q^{9} +O(q^{10})\)	\(q+(0.0620019 - 1.06453i) q^{2} +(-0.676807 - 1.59434i) q^{3} +(0.857095 + 0.100180i) q^{4} +(-0.830696 + 0.196879i) q^{5} +(-1.73919 + 0.621630i) q^{6} +(-0.171051 - 0.229762i) q^{7} +(0.530120 - 3.00646i) q^{8} +(-2.08386 + 2.15813i) q^{9} +(0.158079 + 0.896509i) q^{10} +(-1.24185 + 1.31629i) q^{11} +(-0.420366 - 1.43431i) q^{12} +(4.99610 + 2.50914i) q^{13} +(-0.255194 + 0.167844i) q^{14} +(0.876113 + 1.19117i) q^{15} +(-1.48827 - 0.352725i) q^{16} +(4.42908 + 1.61205i) q^{17} +(2.16819 + 2.35215i) q^{18} +(-1.75427 + 0.638503i) q^{19} +(-0.731709 + 0.0855245i) q^{20} +(-0.250551 + 0.428219i) q^{21} +(1.32423 + 1.40360i) q^{22} +(-0.809320 + 1.08711i) q^{23} +(-5.15212 + 1.18960i) q^{24} +(-3.81687 + 1.91690i) q^{25} +(2.98082 - 5.16294i) q^{26} +(4.85117 + 1.86176i) q^{27} +(-0.123590 - 0.214064i) q^{28} +(-5.00267 - 3.29031i) q^{29} +(1.32235 - 0.858795i) q^{30} +(-1.68608 - 3.90878i) q^{31} +(1.28337 - 4.28675i) q^{32} +(2.93911 + 1.08907i) q^{33} +(1.99069 - 4.61494i) q^{34} +(0.187327 + 0.157186i) q^{35} +(-2.00227 + 1.64096i) q^{36} +(-5.46107 + 4.58238i) q^{37} +(0.570938 + 1.90707i) q^{38} +(0.619030 - 9.66371i) q^{39} +(0.151539 + 2.60183i) q^{40} +(0.667300 + 11.4571i) q^{41} +(0.440318 + 0.293269i) q^{42} +(-3.64800 - 12.1852i) q^{43} +(-1.19625 + 1.00377i) q^{44} +(1.30617 - 2.20302i) q^{45} +(1.10708 + 0.928949i) q^{46} +(-0.811830 + 1.88203i) q^{47} +(0.444903 + 2.61153i) q^{48} +(1.98409 - 6.62732i) q^{49} +(1.80395 + 4.18203i) q^{50} +(-0.427465 - 8.15252i) q^{51} +(4.03077 + 2.65108i) q^{52} +(-1.54131 - 2.66962i) q^{53} +(2.28268 - 5.04879i) q^{54} +(0.772454 - 1.33793i) q^{55} +(-0.781449 + 0.392458i) q^{56} +(2.20530 + 2.36477i) q^{57} +(-3.81281 + 5.12149i) q^{58} +(0.865599 + 0.917481i) q^{59} +(0.631581 + 1.10871i) q^{60} +(-2.75203 + 0.321666i) q^{61} +(-4.26556 + 1.55254i) q^{62} +(0.852303 + 0.109642i) q^{63} +(-7.35831 - 2.67821i) q^{64} +(-4.64424 - 1.10071i) q^{65} +(1.34158 - 3.06125i) q^{66} +(5.24754 - 3.45136i) q^{67} +(3.63465 + 1.82539i) q^{68} +(2.28097 + 0.554574i) q^{69} +(0.178944 - 0.189670i) q^{70} +(2.24048 + 12.7064i) q^{71} +(5.38363 + 7.40913i) q^{72} +(-1.11508 + 6.32396i) q^{73} +(4.53949 + 6.09759i) q^{74} +(5.63949 + 4.78803i) q^{75} +(-1.56754 + 0.371515i) q^{76} +(0.514853 + 0.0601777i) q^{77} +(-10.2489 - 1.25814i) q^{78} +(-0.414301 + 7.11327i) q^{79} +1.30574 q^{80} +(-0.315018 - 8.99449i) q^{81} +12.2378 q^{82} +(0.788222 - 13.5333i) q^{83} +(-0.257645 + 0.341924i) q^{84} +(-3.99660 - 0.467135i) q^{85} +(-13.1977 + 3.12791i) q^{86} +(-1.86004 + 10.2029i) q^{87} +(3.29903 + 4.43137i) q^{88} +(-0.0750415 + 0.425581i) q^{89} +(-2.26419 - 1.52705i) q^{90} +(-0.278086 - 1.57711i) q^{91} +(-0.802570 + 0.850675i) q^{92} +(-5.09079 + 5.33369i) q^{93} +(1.95315 + 0.980908i) q^{94} +(1.33156 - 0.875782i) q^{95} +(-7.70314 + 0.855171i) q^{96} +(9.81910 + 2.32717i) q^{97} +(-6.93197 - 2.52303i) q^{98} +(-0.252861 - 5.42304i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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