LMFDB - Embedded newform 216.2.t.a.133.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(13,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("216.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			133.25
Character	$\chi$	$=$	216.133
Dual form			216.2.t.a.13.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.974655 - 1.02472i) q^{2} +(1.67042 + 0.457945i) q^{3} +(-0.100097 - 1.99749i) q^{4} +(-1.52309 - 1.81515i) q^{5} +(2.09734 - 1.26537i) q^{6} +(0.767101 - 0.279202i) q^{7} +(-2.14443 - 1.84430i) q^{8} +(2.58057 + 1.52992i) q^{9} +O(q^{10})$	\(q+(0.974655 - 1.02472i) q^{2} +(1.67042 + 0.457945i) q^{3} +(-0.100097 - 1.99749i) q^{4} +(-1.52309 - 1.81515i) q^{5} +(2.09734 - 1.26537i) q^{6} +(0.767101 - 0.279202i) q^{7} +(-2.14443 - 1.84430i) q^{8} +(2.58057 + 1.52992i) q^{9} +(-3.34451 - 0.208404i) q^{10} +(-3.58256 + 4.26953i) q^{11} +(0.747538 - 3.38248i) q^{12} +(2.36616 - 0.417219i) q^{13} +(0.461555 - 1.05819i) q^{14} +(-1.71296 - 3.72954i) q^{15} +(-3.97996 + 0.399886i) q^{16} +(1.52854 + 2.64751i) q^{17} +(4.08290 - 1.15322i) q^{18} +(0.631691 + 0.364707i) q^{19} +(-3.47329 + 3.22406i) q^{20} +(1.40924 - 0.115093i) q^{21} +(0.883308 + 7.83244i) q^{22} +(6.38462 + 2.32381i) q^{23} +(-2.73750 - 4.06277i) q^{24} +(-0.106720 + 0.605238i) q^{25} +(1.87866 - 2.83130i) q^{26} +(3.61001 + 3.73735i) q^{27} +(-0.634489 - 1.50433i) q^{28} +(-9.24326 - 1.62984i) q^{29} +(-5.49128 - 1.87972i) q^{30} +(1.92800 + 0.701734i) q^{31} +(-3.46932 + 4.46809i) q^{32} +(-7.93957 + 5.49127i) q^{33} +(4.20276 + 1.01408i) q^{34} +(-1.67516 - 0.967153i) q^{35} +(2.79769 - 5.30782i) q^{36} +(-4.61364 + 2.66369i) q^{37} +(0.989402 - 0.291842i) q^{38} +(4.14354 + 0.386644i) q^{39} +(-0.0815103 + 6.70149i) q^{40} +(-1.29167 - 7.32541i) q^{41} +(1.25558 - 1.55625i) q^{42} +(4.42023 - 5.26782i) q^{43} +(8.88696 + 6.72878i) q^{44} +(-1.15342 - 7.01433i) q^{45} +(8.60405 - 4.27752i) q^{46} +(-10.2350 + 3.72522i) q^{47} +(-6.83131 - 1.15463i) q^{48} +(-4.85182 + 4.07116i) q^{49} +(0.516184 + 0.699256i) q^{50} +(1.34089 + 5.12243i) q^{51} +(-1.07024 - 4.68464i) q^{52} -2.99582i q^{53} +(7.34825 - 0.0566171i) q^{54} +13.2064 q^{55} +(-2.15993 - 0.816032i) q^{56} +(0.888170 + 0.898491i) q^{57} +(-10.6791 + 7.88321i) q^{58} +(-0.837520 - 0.998118i) q^{59} +(-7.27828 + 3.79494i) q^{60} +(0.528763 + 1.45277i) q^{61} +(2.59821 - 1.29171i) q^{62} +(2.40672 + 0.453099i) q^{63} +(1.19715 + 7.90992i) q^{64} +(-4.36120 - 3.65948i) q^{65} +(-2.11133 + 13.4879i) q^{66} +(4.70399 - 0.829441i) q^{67} +(5.13539 - 3.31826i) q^{68} +(9.60078 + 6.80553i) q^{69} +(-2.62376 + 0.773926i) q^{70} +(-4.37210 - 7.57270i) q^{71} +(-2.71224 - 8.04013i) q^{72} +(-2.62609 + 4.54853i) q^{73} +(-1.76718 + 7.32386i) q^{74} +(-0.455432 + 0.962127i) q^{75} +(0.665269 - 1.29830i) q^{76} +(-1.55613 + 4.27542i) q^{77} +(4.43472 - 3.86912i) q^{78} +(-0.739506 + 4.19395i) q^{79} +(6.78770 + 6.61516i) q^{80} +(4.31872 + 7.89612i) q^{81} +(-8.76541 - 5.81615i) q^{82} +(14.1745 + 2.49935i) q^{83} +(-0.370958 - 2.80342i) q^{84} +(2.47752 - 6.80694i) q^{85} +(-1.08984 - 9.66379i) q^{86} +(-14.6937 - 6.95541i) q^{87} +(15.5568 - 2.54840i) q^{88} +(4.96560 - 8.60067i) q^{89} +(-8.31190 - 5.65461i) q^{90} +(1.69860 - 0.980687i) q^{91} +(4.00272 - 12.9858i) q^{92} +(2.89920 + 2.05510i) q^{93} +(-6.15825 + 14.1188i) q^{94} +(-0.300125 - 1.70209i) q^{95} +(-7.84134 + 5.87481i) q^{96} +(-11.8735 - 9.96305i) q^{97} +(-0.557054 + 8.93973i) q^{98} +(-15.7771 + 5.53682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.974655	−	1.02472i	0.689185	−	0.724586i
$2$	0.974655	−	1.02472i	0.689185	−	0.724586i
$3$	1.67042	+	0.457945i	0.964415	+	0.264395i
$3$	1.67042	+	0.457945i	0.964415	+	0.264395i
$4$	−0.100097	−	1.99749i	−0.0500484	−	0.998747i
$5$	−1.52309	−	1.81515i	−0.681147	−	0.811760i	0.309108	−	0.951027i	$-0.399970\pi$
$5$	−1.52309	−	1.81515i	−0.681147	−	0.811760i	−0.990255	+	0.139268i	$0.955525\pi$
$6$	2.09734	−	1.26537i	0.856236	−	0.516584i
$7$	0.767101	−	0.279202i	0.289937	−	0.105528i	−0.192957	−	0.981207i	$-0.561808\pi$
$7$	0.767101	−	0.279202i	0.289937	−	0.105528i	0.482894	+	0.875679i	$0.339586\pi$
$8$	−2.14443	−	1.84430i	−0.758170	−	0.652057i
$9$	2.58057	+	1.52992i	0.860191	+	0.509972i
$10$	−3.34451	−	0.208404i	−1.05763	−	0.0659030i
$11$	−3.58256	+	4.26953i	−1.08018	+	1.28731i	−0.124723	+	0.992192i	$0.539804\pi$
$11$	−3.58256	+	4.26953i	−1.08018	+	1.28731i	−0.955460	+	0.295120i	$0.904640\pi$
$12$	0.747538	−	3.38248i	0.215796	−	0.976439i
$13$	2.36616	−	0.417219i	0.656256	−	0.115716i	0.164402	−	0.986393i	$-0.447431\pi$
$13$	2.36616	−	0.417219i	0.656256	−	0.115716i	0.491854	+	0.870678i	$0.336319\pi$
$14$	0.461555	−	1.05819i	0.123356	−	0.282813i
$15$	−1.71296	−	3.72954i	−0.442283	−	0.962964i
$16$	−3.97996	+	0.399886i	−0.994990	+	0.0999715i
$17$	1.52854	+	2.64751i	0.370726	+	0.642116i	0.989677	−	0.143313i	$-0.0457755\pi$
$17$	1.52854	+	2.64751i	0.370726	+	0.642116i	−0.618951	+	0.785429i	$0.712442\pi$
$18$	4.08290	−	1.15322i	0.962349	−	0.271817i
$19$	0.631691	+	0.364707i	0.144920	+	0.0836695i	0.570707	−	0.821154i	$-0.306669\pi$
$19$	0.631691	+	0.364707i	0.144920	+	0.0836695i	−0.425787	+	0.904823i	$0.640003\pi$
$20$	−3.47329	+	3.22406i	−0.776652	+	0.720921i
$21$	1.40924	−	0.115093i	0.307521	−	0.0251154i
$22$	0.883308	+	7.83244i	0.188322	+	1.66988i
$23$	6.38462	+	2.32381i	1.33128	+	0.484548i	0.907057	−	0.421008i	$-0.138323\pi$
$23$	6.38462	+	2.32381i	1.33128	+	0.484548i	0.424228	+	0.905556i	$0.360546\pi$
$24$	−2.73750	−	4.06277i	−0.558790	−	0.829309i
$25$	−0.106720	+	0.605238i	−0.0213440	+	0.121048i
$26$	1.87866	−	2.83130i	0.368436	−	0.555263i
$27$	3.61001	+	3.73735i	0.694747	+	0.719254i
$28$	−0.634489	−	1.50433i	−0.119907	−	0.284292i
$29$	−9.24326	−	1.62984i	−1.71643	−	0.302653i	−0.773045	−	0.634351i	$-0.781267\pi$
$29$	−9.24326	−	1.62984i	−1.71643	−	0.302653i	−0.943385	+	0.331698i	$0.892378\pi$
$30$	−5.49128	−	1.87972i	−1.00257	−	0.343188i
$31$	1.92800	+	0.701734i	0.346279	+	0.126035i	0.509304	−	0.860587i	$-0.329903\pi$
$31$	1.92800	+	0.701734i	0.346279	+	0.126035i	−0.163025	+	0.986622i	$0.552125\pi$
$32$	−3.46932	+	4.46809i	−0.613294	+	0.789854i
$33$	−7.93957	+	5.49127i	−1.38210	+	0.955908i
$34$	4.20276	+	1.01408i	0.720767	+	0.173914i
$35$	−1.67516	−	0.967153i	−0.283154	−	0.163479i
$36$	2.79769	−	5.30782i	0.466282	−	0.884636i
$37$	−4.61364	+	2.66369i	−0.758478	+	0.437907i	−0.828749	−	0.559621i	$-0.810947\pi$
$37$	−4.61364	+	2.66369i	−0.758478	+	0.437907i	0.0702711	+	0.997528i	$0.477614\pi$
$38$	0.989402	−	0.291842i	0.160502	−	0.0473430i
$39$	4.14354	+	0.386644i	0.663497	+	0.0619126i
$40$	−0.0815103	+	6.70149i	−0.0128879	+	1.05960i
$41$	−1.29167	−	7.32541i	−0.201725	−	1.14404i	−0.902511	−	0.430666i	$-0.858279\pi$
$41$	−1.29167	−	7.32541i	−0.201725	−	1.14404i	0.700787	−	0.713371i	$-0.252832\pi$
$42$	1.25558	−	1.55625i	0.193740	−	0.240134i
$43$	4.42023	−	5.26782i	0.674078	−	0.803335i	−0.315255	−	0.949007i	$-0.602090\pi$
$43$	4.42023	−	5.26782i	0.674078	−	0.803335i	0.989333	+	0.145672i	$0.0465344\pi$
$44$	8.88696	+	6.72878i	1.33976	+	1.01440i
$45$	−1.15342	−	7.01433i	−0.171942	−	1.04563i
$46$	8.60405	−	4.27752i	1.26860	−	0.630686i
$47$	−10.2350	+	3.72522i	−1.49292	+	0.543380i	−0.954217	−	0.299114i	$-0.903309\pi$
$47$	−10.2350	+	3.72522i	−1.49292	+	0.543380i	−0.538706	+	0.842494i	$0.681087\pi$
$48$	−6.83131	−	1.15463i	−0.986015	−	0.166656i
$49$	−4.85182	+	4.07116i	−0.693117	+	0.581594i
$50$	0.516184	+	0.699256i	0.0729994	+	0.0988897i
$51$	1.34089	+	5.12243i	0.187762	+	0.717284i
$52$	−1.07024	−	4.68464i	−0.148415	−	0.649642i
$53$		−	2.99582i		−	0.411507i	−0.978604	−	0.205754i	$-0.934035\pi$
$53$		−	2.99582i		−	0.411507i	0.978604	−	0.205754i	$-0.0659645\pi$
$54$	7.34825	−	0.0566171i	0.999970	−	0.00770462i
$55$	13.2064			1.78075
$56$	−2.15993	−	0.816032i	−0.288632	−	0.109047i
$57$	0.888170	+	0.898491i	0.117641	+	0.119008i
$58$	−10.6791	+	7.88321i	−1.40224	+	1.03512i
$59$	−0.837520	−	0.998118i	−0.109036	−	0.129944i	0.708766	−	0.705443i	$-0.249252\pi$
$59$	−0.837520	−	0.998118i	−0.109036	−	0.129944i	−0.817802	+	0.575500i	$0.804808\pi$
$60$	−7.27828	+	3.79494i	−0.939622	+	0.489924i
$61$	0.528763	+	1.45277i	0.0677012	+	0.186008i	0.968929	−	0.247337i	$-0.0795555\pi$
$61$	0.528763	+	1.45277i	0.0677012	+	0.186008i	−0.901228	+	0.433345i	$0.857333\pi$
$62$	2.59821	−	1.29171i	0.329973	−	0.164047i
$63$	2.40672	+	0.453099i	0.303218	+	0.0570851i
$64$	1.19715	+	7.90992i	0.149644	+	0.988740i
$65$	−4.36120	−	3.65948i	−0.540940	−	0.453903i
$66$	−2.11133	+	13.4879i	−0.259887	+	1.66025i
$67$	4.70399	−	0.829441i	0.574684	−	0.101332i	0.121250	−	0.992622i	$-0.461310\pi$
$67$	4.70399	−	0.829441i	0.574684	−	0.101332i	0.453434	+	0.891290i	$0.350199\pi$
$68$	5.13539	−	3.31826i	0.622757	−	0.402398i
$69$	9.60078	+	6.80553i	1.15580	+	0.819289i
$70$	−2.62376	+	0.773926i	−0.313599	+	0.0925019i
$71$	−4.37210	−	7.57270i	−0.518873	−	0.898714i	−0.999759	−	0.0219314i	$-0.993018\pi$
$71$	−4.37210	−	7.57270i	−0.518873	−	0.898714i	0.480887	−	0.876783i	$-0.340315\pi$
$72$	−2.71224	−	8.04013i	−0.319641	−	0.947539i
$73$	−2.62609	+	4.54853i	−0.307361	+	0.532365i	−0.977784	−	0.209614i	$-0.932779\pi$
$73$	−2.62609	+	4.54853i	−0.307361	+	0.532365i	0.670423	+	0.741979i	$0.266113\pi$
$74$	−1.76718	+	7.32386i	−0.205430	+	0.851381i
$75$	−0.455432	+	0.962127i	−0.0525887	+	0.111097i
$76$	0.665269	−	1.29830i	0.0763116	−	0.148926i
$77$	−1.55613	+	4.27542i	−0.177337	+	0.487230i
$78$	4.43472	−	3.86912i	0.502133	−	0.438091i
$79$	−0.739506	+	4.19395i	−0.0832010	+	0.471856i	0.914529	+	0.404520i	$0.132561\pi$
$79$	−0.739506	+	4.19395i	−0.0832010	+	0.471856i	−0.997730	+	0.0673365i	$0.978550\pi$
$80$	6.78770	+	6.61516i	0.758888	+	0.739598i
$81$	4.31872	+	7.89612i	0.479857	+	0.877347i
$82$	−8.76541	−	5.81615i	−0.967978	−	0.642286i
$83$	14.1745	+	2.49935i	1.55585	+	0.274339i	0.884408	−	0.466716i	$-0.154563\pi$
$83$	14.1745	+	2.49935i	1.55585	+	0.274339i	0.671445	+	0.741054i	$0.265674\pi$
$84$	−0.370958	−	2.80342i	−0.0404749	−	0.305878i
$85$	2.47752	−	6.80694i	0.268725	−	0.738316i
$86$	−1.08984	−	9.66379i	−0.117521	−	1.04207i
$87$	−14.6937	−	6.95541i	−1.57533	−	0.745698i
$88$	15.5568	−	2.54840i	1.65836	−	0.271661i
$89$	4.96560	−	8.60067i	0.526352	−	0.911669i	−0.473176	−	0.880968i	$-0.656893\pi$
$89$	4.96560	−	8.60067i	0.526352	−	0.911669i	0.999529	−	0.0307010i	$-0.00977397\pi$
$90$	−8.31190	−	5.65461i	−0.876151	−	0.596048i
$91$	1.69860	−	0.980687i	0.178062	−	0.102804i
$92$	4.00272	−	12.9858i	0.417312	−	1.35387i
$93$	2.89920	+	2.05510i	0.300633	+	0.213104i
$94$	−6.15825	+	14.1188i	−0.635175	+	1.45624i
$95$	−0.300125	−	1.70209i	−0.0307922	−	0.174631i
$96$	−7.84134	+	5.87481i	−0.800303	+	0.599595i
$97$	−11.8735	−	9.96305i	−1.20557	−	1.01159i	−0.999453	−	0.0330678i	$-0.989472\pi$
$97$	−11.8735	−	9.96305i	−1.20557	−	1.01159i	−0.206119	−	0.978527i	$-0.566083\pi$
$98$	−0.557054	+	8.93973i	−0.0562710	+	0.903049i
$99$	−15.7771	+	5.53682i	−1.58566	+	0.556471i
$100$	1.21964	+	0.152590i	0.121964	+	0.0152590i
$101$	−3.29440	−	9.05130i	−0.327805	−	0.900638i	−0.988666	−	0.150129i	$-0.952031\pi$
$101$	−3.29440	−	9.05130i	−0.327805	−	0.900638i	0.660861	−	0.750508i	$-0.270191\pi$
$102$	6.55596	+	3.61857i	0.649136	+	0.358292i
$103$	−0.566175	+	0.475077i	−0.0557869	+	0.0468108i	−0.670255	−	0.742131i	$-0.733815\pi$
$103$	−0.566175	+	0.475077i	−0.0557869	+	0.0468108i	0.614468	+	0.788942i	$0.289371\pi$
$104$	−5.84355	−	3.46921i	−0.573007	−	0.340184i
$105$	−2.35531	−	2.38268i	−0.229854	−	0.232526i
$106$	−3.06987	−	2.91989i	−0.298172	−	0.283604i
$107$		−	2.41557i		−	0.233522i	−0.993160	−	0.116761i	$-0.962749\pi$
$107$		−	2.41557i		−	0.233522i	0.993160	−	0.116761i	$-0.0372512\pi$
$108$	7.10399	−	7.58507i	0.683582	−	0.729874i
$109$		−	5.27617i		−	0.505365i	−0.967549	−	0.252683i	$-0.918687\pi$
$109$		−	5.27617i		−	0.505365i	0.967549	−	0.252683i	$-0.0813129\pi$
$110$	12.8717	−	13.5329i	1.22727	−	1.29031i
$111$	−8.92652	+	2.33667i	−0.847267	+	0.221787i
$112$	−2.94138	+	1.41797i	−0.277935	+	0.133985i
$113$	10.7854	−	9.05004i	1.01461	−	0.851356i	0.0256661	−	0.999671i	$-0.491829\pi$
$113$	10.7854	−	9.05004i	1.01461	−	0.851356i	0.988940	+	0.148315i	$0.0473849\pi$
$114$	1.78636	−	0.0344060i	0.167308	−	0.00322242i
$115$	−5.50629	−	15.1284i	−0.513464	−	1.41073i
$116$	−2.33037	+	18.6265i	−0.216369	+	1.72943i
$117$	6.74437	+	2.54337i	0.623517	+	0.235135i
$118$	−1.83908	−	0.114597i	−0.169301	−	0.0105495i
$119$	1.91174	+	1.60414i	0.175249	+	0.147051i
$120$	−3.20507	+	11.1569i	−0.292581	+	1.01848i
$121$	−3.48402	−	19.7588i	−0.316729	−	1.79626i
$122$	2.00404	+	0.874111i	0.181437	+	0.0791383i
$123$	1.19701	−	12.8280i	0.107931	−	1.15666i
$124$	1.20872	−	3.92141i	0.108546	−	0.352153i
$125$	−8.99914	+	5.19565i	−0.804907	+	0.464713i
$126$	2.81002	−	2.02459i	0.250336	−	0.180365i
$127$	6.59181	−	11.4173i	0.584928	−	1.01313i	−0.409956	−	0.912105i	$-0.634456\pi$
$127$	6.59181	−	11.4173i	0.584928	−	1.01313i	0.994884	−	0.101020i	$-0.0322108\pi$
$128$	9.27225	+	6.48270i	0.819559	+	0.572995i
$129$	9.79598	−	6.77523i	0.862488	−	0.596526i
$130$	−8.00060	+	0.902273i	−0.701699	+	0.0791346i
$131$	−4.87820	+	13.4028i	−0.426211	+	1.17100i	0.521884	+	0.853016i	$0.325229\pi$
$131$	−4.87820	+	13.4028i	−0.426211	+	1.17100i	−0.948095	+	0.317988i	$0.896993\pi$
$132$	11.7635	+	15.3096i	1.02388	+	1.33253i
$133$	0.586398	+	0.103398i	0.0508471	+	0.00896572i
$134$	3.73483	−	5.62869i	0.322640	−	0.486245i
$135$	1.28548	−	12.2450i	0.110636	−	1.05389i
$136$	1.60495	−	8.49649i	0.137623	−	0.728568i
$137$	−2.35896	+	13.3783i	−0.201539	+	1.14299i	0.701254	+	0.712912i	$0.252624\pi$
$137$	−2.35896	+	13.3783i	−0.201539	+	1.14299i	−0.902793	+	0.430075i	$0.858487\pi$
$138$	16.3312	−	3.20506i	1.39020	−	0.272833i
$139$	−3.70358	+	10.1755i	−0.314133	+	0.863074i	0.677678	+	0.735359i	$0.262986\pi$
$139$	−3.70358	+	10.1755i	−0.314133	+	0.863074i	−0.991811	+	0.127715i	$0.959236\pi$
$140$	−1.76420	+	3.44293i	−0.149102	+	0.290981i
$141$	−18.8026	+	1.53562i	−1.58346	+	0.129323i
$142$	−12.0212	−	2.90059i	−1.00879	−	0.243412i
$143$	−6.69560	+	11.5971i	−0.559915	+	0.969800i
$144$	−10.8824	−	5.05707i	−0.906864	−	0.421423i
$145$	11.1199	+	19.2603i	0.923460	+	1.59948i
$146$	2.10143	+	7.12425i	0.173915	+	0.589607i
$147$	−9.96892	+	4.57866i	−0.822223	+	0.377642i
$148$	5.78251	+	8.94909i	0.475319	+	0.735611i
$149$	10.8534	−	1.91374i	0.889141	−	0.156780i	0.289623	−	0.957141i	$-0.406470\pi$
$149$	10.8534	−	1.91374i	0.889141	−	0.156780i	0.599518	+	0.800361i	$0.295359\pi$
$150$	0.542021	+	1.40443i	0.0442558	+	0.114671i
$151$	−0.654630	−	0.549300i	−0.0532730	−	0.0447014i	0.615762	−	0.787932i	$-0.288848\pi$
$151$	−0.654630	−	0.549300i	−0.0532730	−	0.0447014i	−0.669035	+	0.743231i	$0.733293\pi$
$152$	−0.681989	−	1.94711i	−0.0553166	−	0.157932i
$153$	−0.105956	+	9.17064i	−0.00856605	+	0.741403i
$154$	2.86442	+	5.76165i	0.230821	+	0.464287i
$155$	−1.66277	−	4.56841i	−0.133557	−	0.366944i
$156$	0.357564	−	8.31540i	0.0286280	−	0.665765i
$157$	2.44013	+	2.90803i	0.194743	+	0.232086i	0.854576	−	0.519327i	$-0.173817\pi$
$157$	2.44013	+	2.90803i	0.194743	+	0.232086i	−0.659832	+	0.751413i	$0.729373\pi$
$158$	3.57685	+	4.84544i	0.284559	+	0.385482i
$159$	1.37192	−	5.00426i	0.108800	−	0.396863i
$160$	13.3943	−	0.507982i	1.05892	−	0.0401595i
$161$	5.54646			0.437122
$162$	12.3006	+	3.27052i	0.966423	+	0.256956i
$163$		−	15.6828i		−	1.22837i	−0.789162	−	0.614186i	$-0.789485\pi$
$163$		−	15.6828i		−	1.22837i	0.789162	−	0.614186i	$-0.210515\pi$
$164$	−14.5032	+	3.31335i	−1.13251	+	0.258729i
$165$	22.0602	+	6.04780i	1.71738	+	0.470821i
$166$	16.3764	−	12.0889i	1.27105	−	0.938278i
$167$	0.331925	−	0.278519i	0.0256852	−	0.0215524i	−0.629855	−	0.776713i	$-0.716886\pi$
$167$	0.331925	−	0.278519i	0.0256852	−	0.0215524i	0.655540	+	0.755161i	$0.272441\pi$
$168$	−3.23427	−	2.35224i	−0.249530	−	0.181479i
$169$	−6.79134	+	2.47185i	−0.522411	+	0.190142i
$170$	−4.56047	−	9.17318i	−0.349772	−	0.703551i
$171$	1.07215	+	1.90759i	0.0819896	+	0.145877i
$172$	−10.9649	−	8.30208i	−0.836065	−	0.633028i
$173$	−4.07848	+	4.86054i	−0.310081	+	0.369540i	−0.898468	−	0.439039i	$-0.855319\pi$
$173$	−4.07848	+	4.86054i	−0.310081	+	0.369540i	0.588387	+	0.808580i	$0.299763\pi$
$174$	−21.4486	+	8.27780i	−1.62602	+	0.627538i
$175$	0.0871188	+	0.494075i	0.00658556	+	0.0373486i
$176$	12.5511	−	18.4252i	0.946077	−	1.38885i
$177$	−0.941924	−	2.05081i	−0.0707993	−	0.154148i
$178$	−3.97352	−	13.4710i	−0.297828	−	1.00970i
$179$	22.8480	−	13.1913i	1.70774	−	0.985966i	0.770398	−	0.637564i	$-0.220058\pi$
$179$	22.8480	−	13.1913i	1.70774	−	0.985966i	0.937345	−	0.348402i	$-0.113276\pi$
$180$	−13.8956	+	3.00607i	−1.03572	+	0.224059i
$181$	10.1392	+	5.85386i	0.753639	+	0.435114i	0.827007	−	0.562191i	$-0.190041\pi$
$181$	10.1392	+	5.85386i	0.753639	+	0.435114i	−0.0733680	+	0.997305i	$0.523375\pi$
$182$	0.650620	−	2.69642i	0.0482271	−	0.199872i
$183$	0.217968	+	2.66887i	0.0161127	+	0.197288i
$184$	−9.40556	−	16.7584i	−0.693387	−	1.23544i
$185$	11.8620	+	4.31741i	0.872110	+	0.317422i
$186$	4.93162	−	0.967850i	0.361604	−	0.0709662i
$187$	−16.7797	−	2.95872i	−1.22706	−	0.216363i
$188$	8.46560	+	20.0714i	0.617417	+	1.46386i
$189$	3.81272	+	1.85901i	0.277335	+	0.135223i
$190$	−2.03669	−	1.35141i	−0.147757	−	0.0980416i
$191$	−3.61178	+	20.4834i	−0.261339	+	1.48213i	0.517921	+	0.855428i	$0.326706\pi$
$191$	−3.61178	+	20.4834i	−0.261339	+	1.48213i	−0.779261	+	0.626700i	$0.784405\pi$
$192$	−1.62257	+	13.7611i	−0.117099	+	0.993120i
$193$	−3.79638	−	1.38177i	−0.273270	−	0.0994620i	0.201750	−	0.979437i	$-0.435337\pi$
$193$	−3.79638	−	1.38177i	−0.273270	−	0.0994620i	−0.475020	+	0.879975i	$0.657559\pi$
$194$	−21.7819	+	2.45647i	−1.56385	+	0.176364i
$195$	−5.60917	−	8.11004i	−0.401681	−	0.580772i
$196$	8.61777	+	9.28397i	0.615555	+	0.663141i
$197$	15.7235	+	9.07798i	1.12025	+	0.646779i	0.941466	−	0.337108i	$-0.109449\pi$
$197$	15.7235	+	9.07798i	1.12025	+	0.646779i	0.178788	+	0.983888i	$0.442782\pi$
$198$	−9.70353	+	21.5636i	−0.689600	+	1.53246i
$199$	8.84948	+	15.3277i	0.627323	+	1.08656i	0.988087	+	0.153898i	$0.0491827\pi$
$199$	8.84948	+	15.3277i	0.627323	+	1.08656i	−0.360764	+	0.932657i	$0.617484\pi$
$200$	1.34509	−	1.10107i	0.0951122	−	0.0778572i
$201$	8.23746	+	0.768658i	0.581026	+	0.0542170i
$202$	−12.4859	−	5.44605i	−0.878507	−	0.383183i
$203$	−7.54557	+	1.33049i	−0.529595	+	0.0933819i
$204$	10.0978	−	3.19115i	0.706988	−	0.223425i
$205$	−11.3294	+	13.5018i	−0.791279	+	0.943009i
$206$	−0.0650046	+	1.04321i	−0.00452908	+	0.0726837i
$207$	12.9207	+	15.7647i	0.898053	+	1.09572i
$208$	−9.25040	+	2.60671i	−0.641400	+	0.180743i
$209$	−3.82020	+	1.39044i	−0.264249	+	0.0961786i
$210$	−4.73719	+	0.0912401i	−0.326897	+	0.00629616i
$211$	−2.99419	−	3.56833i	−0.206128	−	0.245654i	0.653069	−	0.757298i	$-0.273481\pi$
$211$	−2.99419	−	3.56833i	−0.206128	−	0.245654i	−0.859197	+	0.511644i	$0.829037\pi$
$212$	−5.98413	+	0.299872i	−0.410991	+	0.0205953i
$213$	−3.83534	−	14.6517i	−0.262793	−	1.00392i
$214$	−2.47528	−	2.35435i	−0.169207	−	0.160940i
$215$	−16.2943			−1.11126
$216$	−0.848629	−	14.6724i	−0.0577419	−	0.998332i
$217$	1.67490			0.113699
$218$	−5.40659	−	5.14244i	−0.366180	−	0.348290i
$219$	−6.46964	+	6.39532i	−0.437178	+	0.432156i
$220$	−1.32192	−	26.3797i	−0.0891238	−	1.77852i
$221$	4.72138	+	5.62672i	0.317594	+	0.378494i
$222$	−6.30584	+	11.4246i	−0.423220	+	0.766770i
$223$	−23.9911	+	8.73206i	−1.60656	+	0.584742i	−0.980756	−	0.195235i	$-0.937453\pi$
$223$	−23.9911	+	8.73206i	−1.60656	+	0.584742i	−0.625808	+	0.779977i	$0.715231\pi$
$224$	−1.41382	+	4.39612i	−0.0944646	+	0.293728i
$225$	−1.20136	+	1.39859i	−0.0800907	+	0.0932392i
$226$	1.23831	−	19.8727i	0.0823712	−	1.32191i
$227$	−5.61519	+	6.69192i	−0.372693	+	0.444158i	−0.919494	−	0.393104i	$-0.871401\pi$
$227$	−5.61519	+	6.69192i	−0.372693	+	0.444158i	0.546801	+	0.837263i	$0.315846\pi$
$228$	1.70583	−	1.86405i	0.112971	−	0.123450i
$229$	7.54563	−	1.33050i	0.498629	−	0.0879218i	0.0813232	−	0.996688i	$-0.474085\pi$
$229$	7.54563	−	1.33050i	0.498629	−	0.0879218i	0.417306	+	0.908766i	$0.362974\pi$
$230$	−20.8691	−	9.10257i	−1.37607	−	0.600206i
$231$	−4.55728	+	6.42911i	−0.299847	+	0.423004i
$232$	16.8156	+	20.5424i	1.10400	+	1.34867i
$233$	−4.64693	−	8.04871i	−0.304430	−	0.527289i	0.672704	−	0.739912i	$-0.265133\pi$
$233$	−4.64693	−	8.04871i	−0.304430	−	0.527289i	−0.977134	+	0.212623i	$0.931799\pi$
$234$	9.17967	−	4.43218i	0.600094	−	0.289740i
$235$	22.3506	+	12.9041i	1.45799	+	0.841773i
$236$	−1.90990	+	1.77285i	−0.124324	+	0.115403i
$237$	−3.15588	+	6.66698i	−0.204996	+	0.433067i
$238$	3.50708	−	0.395513i	0.227330	−	0.0256373i
$239$	7.97388	+	2.90226i	0.515788	+	0.187731i	0.586781	−	0.809745i	$-0.300395\pi$
$239$	7.97388	+	2.90226i	0.515788	+	0.187731i	−0.0709937	+	0.997477i	$0.522617\pi$
$240$	8.30889	+	14.1585i	0.536337	+	0.913924i
$241$	0.538985	−	3.05674i	0.0347191	−	0.196902i	−0.962515	−	0.271229i	$-0.912570\pi$
$241$	0.538985	−	3.05674i	0.0347191	−	0.196902i	0.997234	+	0.0743274i	$0.0236810\pi$
$242$	−23.6430	−	15.6879i	−1.51983	−	1.00846i
$243$	3.59806	+	15.1675i	0.230816	+	0.972997i
$244$	2.84896	−	1.20162i	0.182386	−	0.0769258i
$245$	14.7795	+	2.60603i	0.944230	+	0.166493i
$246$	−11.9784	−	13.7295i	−0.763715	−	0.875358i
$247$	1.64685	+	0.599403i	0.104786	+	0.0381391i
$248$	−2.84025	−	5.06062i	−0.180356	−	0.321349i
$249$	22.5327	+	10.6661i	1.42795	+	0.675935i
$250$	−3.44697	+	14.2855i	−0.218005	+	0.903497i
$251$	−7.67295	−	4.42998i	−0.484312	−	0.279618i	0.237899	−	0.971290i	$-0.423541\pi$
$251$	−7.67295	−	4.42998i	−0.484312	−	0.279618i	−0.722212	+	0.691672i	$0.756874\pi$
$252$	0.664157	−	4.85275i	0.0418380	−	0.305695i
$253$	−32.7949	+	18.9341i	−2.06180	+	1.19038i
$254$	−5.27483	−	17.8827i	−0.330972	−	1.12206i
$255$	7.25569	−	10.2358i	0.454369	−	0.640993i
$256$	15.6802	−	3.18306i	0.980011	−	0.198941i
$257$	−2.93606	−	16.6512i	−0.183146	−	1.03868i	−0.928314	−	0.371798i	$-0.878742\pi$
$257$	−2.93606	−	16.6512i	−0.183146	−	1.03868i	0.745167	−	0.666878i	$-0.232370\pi$
$258$	2.60500	−	16.6416i	0.162180	−	1.03606i
$259$	−2.79542	+	3.33146i	−0.173699	+	0.207007i
$260$	−6.87325	+	9.07777i	−0.426261	+	0.562979i
$261$	−21.3594	−	18.3473i	−1.32211	−	1.13567i
$262$	8.97949	+	18.0618i	0.554755	+	1.11586i
$263$	25.9536	−	9.44634i	1.60037	−	0.582487i	0.620866	−	0.783917i	$-0.286781\pi$
$263$	25.9536	−	9.44634i	1.60037	−	0.582487i	0.979503	+	0.201430i	$0.0645590\pi$
$264$	27.1534	+	2.86727i	1.67118	+	0.176468i
$265$	−5.43786	+	4.56290i	−0.334045	+	0.280297i
$266$	0.677489	−	0.500116i	0.0415395	−	0.0306641i
$267$	12.2332	−	12.0927i	0.748662	−	0.740062i
$268$	−2.12766	−	9.31317i	−0.129967	−	0.568893i
$269$		−	0.151914i		−	0.00926235i	−0.999989	−	0.00463118i	$-0.998526\pi$
$269$		−	0.151914i		−	0.00926235i	0.999989	−	0.00463118i	$-0.00147415\pi$
$270$	−11.2948	−	13.2519i	−0.687381	−	0.806487i
$271$	−15.3499			−0.932442			−0.466221	−	0.884668i	$-0.654385\pi$
$271$	−15.3499			−0.932442			−0.466221	+	0.884668i	$0.654385\pi$
$272$	−7.14224	−	9.92576i	−0.433062	−	0.601838i
$273$	3.28647	−	0.860290i	0.198906	−	0.0520671i
$274$	11.4098	+	15.4565i	0.689294	+	0.933762i
$275$	−2.20175	−	2.62395i	−0.132771	−	0.158230i
$276$	12.6330	−	19.8587i	0.760417	−	1.19535i
$277$	7.89627	+	21.6948i	0.474441	+	1.30351i	0.914150	+	0.405375i	$0.132859\pi$
$277$	7.89627	+	21.6948i	0.474441	+	1.30351i	−0.439710	+	0.898140i	$0.644919\pi$
$278$	6.81731	+	13.7127i	0.408875	+	0.822434i
$279$	3.90175	+	4.76055i	0.233591	+	0.285007i
$280$	1.80854	+	5.16348i	0.108081	+	0.308577i
$281$	4.24157	+	3.55910i	0.253031	+	0.212318i	0.760476	−	0.649366i	$-0.224966\pi$
$281$	4.24157	+	3.55910i	0.253031	+	0.212318i	−0.507445	+	0.861684i	$0.669410\pi$
$282$	−16.7525	+	20.7641i	−0.997594	+	1.23648i
$283$	−5.09313	+	0.898056i	−0.302755	+	0.0533839i	−0.322962	−	0.946412i	$-0.604679\pi$
$283$	−5.09313	+	0.898056i	−0.302755	+	0.0533839i	0.0202070	+	0.999796i	$0.493567\pi$
$284$	−14.6888	+	9.49125i	−0.871619	+	0.563202i
$285$	0.278132	−	2.98065i	0.0164751	−	0.176558i
$286$	5.35789	+	18.1643i	0.316819	+	1.07408i
$287$	−3.03611	−	5.25870i	−0.179216	−	0.310411i
$288$	−15.7886	+	6.22247i	−0.930354	+	0.366663i
$289$	3.82711	−	6.62876i	0.225124	−	0.389927i
$290$	30.5745	+	7.37732i	1.79539	+	0.433211i
$291$	−15.2712	−	22.0798i	−0.895211	−	1.29434i
$292$	9.34852	+	4.79031i	0.547080	+	0.280332i
$293$	5.24603	−	14.4133i	0.306476	−	0.842036i	−0.686861	−	0.726789i	$-0.741012\pi$
$293$	5.24603	−	14.4133i	0.306476	−	0.842036i	0.993337	−	0.115247i	$-0.0367660\pi$
$294$	−5.02441	+	14.6780i	−0.293030	+	0.856036i
$295$	−0.536113	+	3.04045i	−0.0312137	+	0.177022i
$296$	14.8062	+	2.79683i	0.860596	+	0.162562i
$297$	−28.8898	+	2.02375i	−1.67636	+	0.117430i
$298$	8.61723	−	12.9869i	0.499182	−	0.752309i
$299$	16.0766	+	2.83474i	0.929733	+	0.163937i
$300$	1.96743	+	0.813416i	0.113590	+	0.0469626i
$301$	1.91998	−	5.27509i	0.110666	−	0.304051i
$302$	−1.20092	+	0.135434i	−0.0691049	+	0.00779335i
$303$	−1.35803	−	16.6281i	−0.0780165	−	0.955258i
$304$	−2.65995	−	1.19891i	−0.152558	−	0.0687625i
$305$	1.83163	−	3.17248i	0.104879	−	0.181656i
$306$	9.29406	+	9.04679i	0.531306	+	0.517170i
$307$	−13.3505	+	7.70794i	−0.761956	+	0.439916i	−0.829998	−	0.557767i	$-0.811658\pi$
$307$	−13.3505	+	7.70794i	−0.761956	+	0.439916i	0.0680415	+	0.997682i	$0.478325\pi$
$308$	8.69589	+	2.68040i	0.495494	+	0.152730i
$309$	−1.16331	+	0.534300i	−0.0661782	+	0.0303952i
$310$	−6.30196	−	2.74876i	−0.357927	−	0.156119i
$311$	3.82602	+	21.6984i	0.216954	+	1.23040i	0.877484	+	0.479605i	$0.159220\pi$
$311$	3.82602	+	21.6984i	0.216954	+	1.23040i	−0.660531	+	0.750799i	$0.729669\pi$
$312$	−8.17244	−	8.47104i	−0.462673	−	0.479578i
$313$	21.5889	+	18.1152i	1.22027	+	1.02393i	0.998810	+	0.0487638i	$0.0155281\pi$
$313$	21.5889	+	18.1152i	1.22027	+	1.02393i	0.221465	+	0.975168i	$0.428916\pi$
$314$	5.35820	+	0.333881i	0.302381	+	0.0188420i
$315$	−2.84321	−	5.05866i	−0.160197	−	0.285023i
$316$	8.45141	+	1.05736i	0.475429	+	0.0594810i
$317$	−12.0843	−	33.2014i	−0.678722	−	1.86477i	−0.456307	−	0.889823i	$-0.650828\pi$
$317$	−12.0843	−	33.2014i	−0.678722	−	1.86477i	−0.222416	−	0.974952i	$-0.571394\pi$
$318$	−3.79081	−	6.28325i	−0.212578	−	0.352347i
$319$	40.0732	−	33.6254i	2.24367	−	1.88266i
$320$	12.5343	−	14.2205i	0.700690	−	0.794952i
$321$	1.10620	−	4.03501i	0.0617420	−	0.225212i
$322$	5.40588	−	5.68356i	0.301258	−	0.316733i
$323$			2.22988i			0.124074i
$324$	15.3402	−	9.41698i	0.852231	−	0.523166i
$325$			1.47662i			0.0819080i
$326$	−16.0705	−	15.2853i	−0.890060	−	0.846575i
$327$	2.41619	−	8.81339i	0.133616	−	0.487382i
$328$	−10.7403	+	18.0910i	−0.593035	+	0.998910i
$329$	−6.81117	+	5.71525i	−0.375512	+	0.315092i
$330$	27.6984	−	16.7110i	1.52474	−	0.919908i
$331$	2.25679	+	6.20048i	0.124044	+	0.340809i	0.986135	−	0.165945i	$-0.0530674\pi$
$331$	2.25679	+	6.20048i	0.124044	+	0.340809i	−0.862091	+	0.506754i	$0.830845\pi$
$332$	3.57360	−	28.5636i	0.196127	−	1.56763i
$333$	−15.9811	−	0.184643i	−0.875756	−	0.0101183i
$334$	0.0381095	−	0.611590i	0.00208526	−	0.0334647i
$335$	−8.67017	−	7.27514i	−0.473702	−	0.397483i
$336$	−5.56268	+	1.02160i	−0.303469	+	0.0557329i
$337$	−3.49402	−	19.8156i	−0.190331	−	1.07942i	−0.918912	−	0.394462i	$-0.870931\pi$
$337$	−3.49402	−	19.8156i	−0.190331	−	1.07942i	0.728581	−	0.684960i	$-0.240180\pi$
$338$	−4.08626	+	9.36841i	−0.222263	+	0.509574i
$339$	22.1605	−	10.1782i	1.20359	−	0.552804i
$340$	−13.8448	−	4.26748i	−0.750840	−	0.231437i
$341$	−9.90325	+	5.71764i	−0.536291	+	0.309628i
$342$	2.99972	+	0.760582i	0.162206	+	0.0411276i
$343$	−5.44232	+	9.42638i	−0.293858	+	0.508977i
$344$	−19.1943	+	3.14427i	−1.03489	+	0.169527i
$345$	−2.26982	−	27.7923i	−0.122203	−	1.49629i
$346$	1.00558	+	8.91664i	0.0540603	+	0.479362i
$347$	−1.25968	+	3.46095i	−0.0676232	+	0.185793i	−0.968901	−	0.247448i	$-0.920408\pi$
$347$	−1.25968	+	3.46095i	−0.0676232	+	0.185793i	0.901278	+	0.433241i	$0.142630\pi$
$348$	−12.4226	+	30.0468i	−0.665920	+	1.61068i
$349$	25.7001	+	4.53163i	1.37570	+	0.242572i	0.812120	−	0.583491i	$-0.198314\pi$
$349$	25.7001	+	4.53163i	1.37570	+	0.242572i	0.563577	+	0.826063i	$0.309425\pi$
$350$	0.591199	+	0.392280i	0.0316009	+	0.0209683i
$351$	10.1012	+	7.33703i	0.539161	+	0.391622i
$352$	−6.64761	−	30.8196i	−0.354319	−	1.64269i
$353$	−5.13961	+	29.1482i	−0.273554	+	1.55140i	0.469965	+	0.882685i	$0.344267\pi$
$353$	−5.13961	+	29.1482i	−0.273554	+	1.55140i	−0.743519	+	0.668715i	$0.766845\pi$
$354$	−3.01955	−	1.03362i	−0.160487	−	0.0549365i
$355$	−7.08647	+	19.4699i	−0.376111	+	1.03336i
$356$	−17.6768	−	9.05785i	−0.936869	−	0.480065i
$357$	2.45879	+	3.55505i	0.130133	+	0.188153i
$358$	8.75155	−	36.2698i	0.462534	−	1.91692i
$359$	6.44307	−	11.1597i	0.340052	−	0.588988i	−0.644390	−	0.764697i	$-0.722889\pi$
$359$	6.44307	−	11.1597i	0.340052	−	0.588988i	0.984442	+	0.175709i	$0.0562219\pi$
$360$	−10.4631	+	17.1690i	−0.551451	+	0.904885i
$361$	−9.23398	−	15.9937i	−0.485999	−	0.841775i
$362$	15.8808	−	4.68432i	0.834674	−	0.246202i
$363$	3.22870	−	34.6009i	0.169463	−	1.81608i
$364$	−2.12894	−	3.29478i	−0.111587	−	0.172693i
$365$	12.2560	−	2.16107i	0.641510	−	0.113116i
$366$	2.94728	+	2.37787i	0.154057	+	0.124293i
$367$	−7.76761	−	6.51780i	−0.405466	−	0.340226i	0.417136	−	0.908844i	$-0.363034\pi$
$367$	−7.76761	−	6.51780i	−0.405466	−	0.340226i	−0.822602	+	0.568618i	$0.807478\pi$
$368$	−26.3398	−	6.69556i	−1.37306	−	0.349030i
$369$	7.87402	−	20.8799i	0.409905	−	1.08696i
$370$	15.9855	−	7.94721i	0.831045	−	0.413156i
$371$	−0.836438	−	2.29810i	−0.0434257	−	0.119311i
$372$	3.81486	−	5.99685i	0.197791	−	0.310922i
$373$	6.70393	+	7.98944i	0.347117	+	0.413677i	0.911150	−	0.412074i	$-0.135196\pi$
$373$	6.70393	+	7.98944i	0.347117	+	0.413677i	−0.564034	+	0.825752i	$0.690751\pi$
$374$	−19.3863	+	14.3108i	−1.00244	+	0.739993i
$375$	−17.4116	+	4.55779i	−0.899132	+	0.235363i
$376$	28.8186	+	10.8878i	1.48620	+	0.561497i
$377$	−22.5511			−1.16144
$378$	5.62105	−	2.09508i	0.289115	−	0.107759i
$379$			14.1280i			0.725707i	0.931846	+	0.362853i	$0.118197\pi$
$379$			14.1280i			0.725707i	−0.931846	+	0.362853i	$0.881803\pi$
$380$	−3.36988	+	0.769873i	−0.172871	+	0.0394936i
$381$	16.2396	−	16.0530i	0.831978	−	0.822421i
$382$	17.4695	+	23.6653i	0.893818	+	1.21082i
$383$	−8.29387	+	6.95938i	−0.423797	+	0.355608i	−0.829605	−	0.558350i	$-0.811434\pi$
$383$	−8.29387	+	6.95938i	−0.423797	+	0.355608i	0.405808	+	0.913958i	$0.366990\pi$
$384$	12.5198	+	15.0750i	0.638898	+	0.769291i
$385$	10.1307	−	3.68726i	0.516306	−	0.187920i
$386$	−5.11609	+	2.54348i	−0.260402	+	0.129460i
$387$	19.4660	−	6.83142i	0.989514	−	0.347261i
$388$	−18.7126	+	24.7145i	−0.949990	+	1.25469i
$389$	−11.3791	+	13.5611i	−0.576945	+	0.687577i	−0.973041	−	0.230633i	$-0.925920\pi$
$389$	−11.3791	+	13.5611i	−0.576945	+	0.687577i	0.396096	+	0.918209i	$0.370365\pi$
$390$	−13.7775	−	2.15666i	−0.697652	−	0.109207i
$391$	3.60684	+	20.4554i	0.182406	+	1.03447i
$392$	17.9128	+	0.217874i	0.904733	+	0.0110043i
$393$	−14.2863	+	20.1542i	−0.720651	+	1.01665i
$394$	24.6274	−	7.26429i	1.24071	−	0.365970i
$395$	8.73898	−	5.04545i	0.439706	−	0.253864i
$396$	12.6390	+	30.9604i	0.635134	+	1.55582i
$397$	−29.7791	−	17.1929i	−1.49457	−	0.862889i	−0.494587	−	0.869128i	$-0.664681\pi$
$397$	−29.7791	−	17.1929i	−1.49457	−	0.862889i	−0.999981	+	0.00623882i	$0.998014\pi$
$398$	24.3318	+	5.87103i	1.21964	+	0.294288i
$399$	0.932177	+	0.441255i	0.0466672	+	0.0220904i
$400$	0.182714	−	2.45150i	0.00913572	−	0.122575i
$401$	−7.23952	−	2.63497i	−0.361525	−	0.131584i	0.154870	−	0.987935i	$-0.450504\pi$
$401$	−7.23952	−	2.63497i	−0.361525	−	0.131584i	−0.516395	+	0.856351i	$0.672726\pi$
$402$	8.81634	−	7.69190i	0.439719	−	0.383637i
$403$	4.85474	+	0.856021i	0.241832	+	0.0426415i
$404$	−17.7501	+	7.48655i	−0.883103	+	0.372470i
$405$	7.75484	−	19.8656i	0.385341	−	0.987131i
$406$	−5.99095	+	9.02885i	−0.297326	+	0.448094i
$407$	5.15596	−	29.2409i	0.255571	−	1.44942i
$408$	6.57185	−	13.4577i	0.325355	−	0.666255i
$409$	0.988723	+	0.359866i	0.0488892	+	0.0177942i	0.366349	−	0.930478i	$-0.380608\pi$
$409$	0.988723	+	0.359866i	0.0488892	+	0.0177942i	−0.317460	+	0.948272i	$0.602830\pi$
$410$	2.79335	+	24.7691i	0.137954	+	1.22326i
$411$	−10.0670	+	21.2671i	−0.496567	+	1.04903i
$412$	1.00564	+	1.08338i	0.0495442	+	0.0533742i
$413$	−0.921140	−	0.531820i	−0.0453263	−	0.0261692i
$414$	28.7476	+	2.12500i	1.41287	+	0.104438i
$415$	−17.0524	−	29.5356i	−0.837067	−	1.44984i
$416$	−6.34480	+	12.0197i	−0.311080	+	0.589314i
$417$	−10.8463	+	15.3013i	−0.531147	+	0.749306i
$418$	−2.29857	+	5.26983i	−0.112427	+	0.257756i
$419$	−5.20073	+	0.917030i	−0.254073	+	0.0447998i	−0.299234	−	0.954180i	$-0.596731\pi$
$419$	−5.20073	+	0.917030i	−0.254073	+	0.0447998i	0.0451611	+	0.998980i	$0.485620\pi$
$420$	−4.52362	+	4.94321i	−0.220730	+	0.241204i
$421$	20.0672	−	23.9151i	0.978013	−	1.16555i	−0.00818210	−	0.999967i	$-0.502604\pi$
$421$	20.0672	−	23.9151i	0.978013	−	1.16555i	0.986196	−	0.165585i	$-0.0529511\pi$
$422$	−6.57484	−	0.409693i	−0.320058	−	0.0199435i
$423$	−32.1114	−	6.04543i	−1.56131	−	0.293939i
$424$	−5.52517	+	6.42432i	−0.268326	+	0.311992i
$425$	−1.76550	+	0.642590i	−0.0856394	+	0.0311702i
$426$	−18.7520	−	10.3502i	−0.908539	−	0.501470i
$427$	0.811230	+	0.966786i	0.0392582	+	0.0467861i
$428$	−4.82509	+	0.241791i	−0.233230	+	0.0116874i
$429$	−16.4953	+	16.3058i	−0.796400	+	0.787251i
$430$	−15.8813	+	16.6971i	−0.765864	+	0.805204i
$431$	3.25058			0.156575			0.0782874	−	0.996931i	$-0.475055\pi$
$431$	3.25058			0.156575			0.0782874	+	0.996931i	$0.475055\pi$
$432$	−15.8622	−	13.4309i	−0.763171	−	0.646196i
$433$	−5.78000			−0.277769			−0.138885	−	0.990309i	$-0.544352\pi$
$433$	−5.78000			−0.277769			−0.138885	+	0.990309i	$0.544352\pi$
$434$	1.63244	−	1.71630i	0.0783599	−	0.0823849i
$435$	9.75475	+	37.2650i	0.467705	+	1.78672i
$436$	−10.5391	+	0.528128i	−0.504732	+	0.0252928i
$437$	3.18559	+	3.79644i	0.152388	+	0.181608i
$438$	0.247742	+	12.8628i	0.0118376	+	0.614608i
$439$	−9.84846	+	3.58454i	−0.470041	+	0.171081i	−0.566171	−	0.824288i	$-0.691576\pi$
$439$	−9.84846	+	3.58454i	−0.470041	+	0.171081i	0.0961299	+	0.995369i	$0.469354\pi$
$440$	−28.3202	−	24.3565i	−1.35011	−	1.16115i
$441$	−18.7490	+	3.08305i	−0.892810	+	0.146812i
$442$	10.3675	+	0.646023i	0.493132	+	0.0307282i
$443$	−6.84059	+	8.15230i	−0.325006	+	0.387327i	−0.903663	−	0.428244i	$-0.859133\pi$
$443$	−6.84059	+	8.15230i	−0.325006	+	0.387327i	0.578657	+	0.815571i	$0.303577\pi$
$444$	5.56100	+	17.5968i	0.263913	+	0.835105i
$445$	−23.1745	+	4.08630i	−1.09858	+	0.193709i
$446$	−14.4352	+	33.0949i	−0.683525	+	1.56709i
$447$	19.0060	+	1.77350i	0.898952	+	0.0838835i
$448$	3.12680	+	5.73346i	0.147728	+	0.270881i
$449$	10.3809	+	17.9803i	0.489906	+	0.848542i	0.999933	−	0.0116165i	$-0.00369773\pi$
$449$	10.3809	+	17.9803i	0.489906	+	0.848542i	−0.510026	+	0.860159i	$0.670364\pi$
$450$	0.262248	+	2.59420i	0.0123625	+	0.122292i
$451$	35.9035	+	20.7289i	1.69063	+	0.976087i
$452$	−19.1570	−	20.6379i	−0.901068	−	0.970726i
$453$	−0.841955	−	1.21734i	−0.0395585	−	0.0571958i
$454$	1.38447	+	12.2763i	0.0649763	+	0.576155i
$455$	−4.36722	−	1.58954i	−0.204738	−	0.0745186i
$456$	−0.247535	−	3.56480i	−0.0115919	−	0.166937i
$457$	−2.42319	+	13.7426i	−0.113352	+	0.642851i	0.874201	+	0.485564i	$0.161386\pi$
$457$	−2.42319	+	13.7426i	−0.113352	+	0.642851i	−0.987553	+	0.157287i	$0.949725\pi$
$458$	5.99100	−	9.02893i	0.279941	−	0.421894i
$459$	−4.37664	+	15.2703i	−0.204284	+	0.712755i
$460$	−29.6677	+	12.5131i	−1.38327	+	0.583426i
$461$	0.0322801	+	0.00569184i	0.00150343	+	0.000265096i	0.174400	−	0.984675i	$-0.444201\pi$
$461$	0.0322801	+	0.00569184i	0.00150343	+	0.000265096i	−0.172896	+	0.984940i	$0.555313\pi$
$462$	2.14625	+	10.9361i	0.0998526	+	0.508793i
$463$	−24.6873	−	8.98546i	−1.14732	−	0.417590i	−0.302767	−	0.953065i	$-0.597910\pi$
$463$	−24.6873	−	8.98546i	−1.14732	−	0.417590i	−0.844551	+	0.535475i	$0.820133\pi$
$464$	37.4396	+	2.79044i	1.73809	+	0.129543i
$465$	−0.685429	−	8.39260i	−0.0317860	−	0.389197i
$466$	−12.7768	−	3.08292i	−0.591875	−	0.142814i
$467$	−6.99161	−	4.03661i	−0.323533	−	0.186792i	0.329433	−	0.944179i	$-0.393142\pi$
$467$	−6.99161	−	4.03661i	−0.323533	−	0.186792i	−0.652966	+	0.757387i	$0.726476\pi$
$468$	4.40527	−	13.7264i	0.203634	−	0.634504i
$469$	3.37686	−	1.94963i	0.155929	−	0.0900255i
$470$	35.0073	−	10.3260i	1.61476	−	0.476304i
$471$	2.74431	+	5.97507i	0.126451	+	0.275316i
$472$	−0.0448210	+	3.68503i	−0.00206306	+	0.169617i
$473$	6.65539	+	37.7446i	0.306015	+	1.73550i
$474$	3.75589	+	9.73189i	0.172514	+	0.447001i
$475$	−0.288148	+	0.343402i	−0.0132211	+	0.0157564i
$476$	3.01290	−	3.97925i	0.138096	−	0.182389i
$477$	4.58335	−	7.73093i	0.209857	−	0.353975i
$478$	10.7458	−	5.34229i	0.491501	−	0.244351i
$479$	23.7888	−	8.65842i	1.08694	−	0.395613i	0.264453	−	0.964399i	$-0.414809\pi$
$479$	23.7888	−	8.65842i	1.08694	−	0.395613i	0.822486	+	0.568785i	$0.192587\pi$
$480$	22.6067	+	5.28533i	1.03185	+	0.241241i
$481$	−9.80529	+	8.22762i	−0.447083	+	0.375147i
$482$	−2.60697	−	3.53157i	−0.118744	−	0.160859i
$483$	9.26489	+	2.53997i	0.421567	+	0.115573i
$484$	−39.1194	+	8.93710i	−1.77815	+	0.406232i
$485$			36.7268i			1.66768i
$486$	19.0493	+	11.0961i	0.864095	+	0.503329i
$487$	−11.9724			−0.542520			−0.271260	−	0.962506i	$-0.587440\pi$
$487$	−11.9724			−0.542520			−0.271260	+	0.962506i	$0.587440\pi$
$488$	1.54543	−	4.09055i	0.0699584	−	0.185170i
$489$	7.18185	−	26.1968i	0.324775	−	1.18466i
$490$	17.0754	−	12.6049i	0.771387	−	0.569431i
$491$	2.49167	+	2.96946i	0.112448	+	0.134010i	0.819332	−	0.573319i	$-0.194344\pi$
$491$	2.49167	+	2.96946i	0.112448	+	0.134010i	−0.706885	+	0.707329i	$0.749900\pi$
$492$	−25.7436	−	1.10698i	−1.16061	−	0.0499066i
$493$	−9.81370	−	26.9629i	−0.441987	−	1.21435i
$494$	2.21933	−	1.10334i	0.0998522	−	0.0496418i
$495$	34.0801	+	20.2047i	1.53179	+	0.908133i
$496$	−7.95397	−	2.02190i	−0.357144	−	0.0907858i
$497$	−5.46816	−	4.58833i	−0.245280	−	0.205815i
$498$	32.8914	−	12.6940i	1.47390	−	0.568830i
$499$	−7.13635	+	1.25833i	−0.319467	+	0.0563307i	−0.331082	−	0.943602i	$-0.607414\pi$
$499$	−7.13635	+	1.25833i	−0.319467	+	0.0563307i	0.0116153	+	0.999933i	$0.496303\pi$
$500$	11.2791	+	17.4556i	0.504415	+	0.780640i
$501$	0.681999	−	0.313238i	0.0304695	−	0.0139944i
$502$	−12.0180	+	3.54492i	−0.536388	+	0.158217i
$503$	−14.1108	−	24.4406i	−0.629168	−	1.08975i	−0.987719	−	0.156241i	$-0.950062\pi$
$503$	−14.1108	−	24.4406i	−0.629168	−	1.08975i	0.358551	−	0.933510i	$-0.383271\pi$
$504$	−4.32538	−	5.41033i	−0.192668	−	0.240995i
$505$	−11.4118	+	19.7658i	−0.507818	+	0.879566i
$506$	−12.5615	+	52.0597i	−0.558427	+	2.31434i
$507$	−12.4763	+	1.01895i	−0.554093	+	0.0452531i
$508$	−23.4659	−	12.0243i	−1.04113	−	0.533490i
$509$	4.18088	−	11.4869i	0.185314	−	0.509147i	−0.811895	−	0.583803i	$-0.801564\pi$
$509$	4.18088	−	11.4869i	0.185314	−	0.509147i	0.997209	+	0.0746568i	$0.0237861\pi$
$510$	−3.41707	−	17.4115i	−0.151310	−	0.770992i
$511$	−0.744521	+	4.22239i	−0.0329357	+	0.186788i
$512$	12.0210	−	19.1702i	0.531259	−	0.847209i
$513$	0.917372	+	3.67745i	0.0405030	+	0.162363i
$514$	−19.9245	−	13.2206i	−0.878831	−	0.583134i
$515$	1.72467	+	0.304106i	0.0759982	+	0.0134005i
$516$	−14.5140	−	18.8892i	−0.638944	−	0.831552i
$517$	20.7624	−	57.0444i	0.913131	−	2.50881i
$518$	0.689233	+	6.11154i	0.0302832	+	0.268526i
$519$	−9.03861	+	6.25140i	−0.396751	+	0.274406i
$520$	2.60312	+	15.8908i	0.114154	+	0.696859i
$521$	3.67878	−	6.37183i	0.161170	−	0.279155i	−0.774118	−	0.633041i	$-0.781807\pi$
$521$	3.67878	−	6.37183i	0.161170	−	0.279155i	0.935289	+	0.353886i	$0.115140\pi$
$522$	−39.6189	+	4.00508i	−1.73407	+	0.175297i
$523$	15.4796	−	8.93716i	0.676877	−	0.390795i	−0.121801	−	0.992555i	$-0.538867\pi$
$523$	15.4796	−	8.93716i	0.676877	−	0.390795i	0.798677	+	0.601760i	$0.205533\pi$
$524$	27.2602	+	8.40261i	1.19087	+	0.367070i
$525$	−0.0807346	+	0.865206i	−0.00352355	+	0.0377607i
$526$	15.6160	−	35.8021i	0.680889	−	1.56104i
$527$	1.08918	+	6.17703i	0.0474453	+	0.269076i
$528$	29.4033	−	25.0300i	1.27962	−	1.08929i
$529$	17.7442	+	14.8892i	0.771487	+	0.647355i
$530$	−0.624339	+	10.0195i	−0.0271196	+	0.435220i
$531$	−0.634246	−	3.85705i	−0.0275239	−	0.167382i
$532$	0.147840	−	1.18168i	0.00640966	−	0.0512321i
$533$	−6.11260	−	16.7942i	−0.264766	−	0.727438i
$534$	−0.468448	−	24.3218i	−0.0202717	−	1.05251i
$535$	−4.38462	+	3.67914i	−0.189564	+	0.159063i
$536$	−11.6171	−	6.89688i	−0.501783	−	0.297900i
$537$	44.2066	−	11.5718i	1.90766	−	0.499362i
$538$	−0.155669	−	0.148064i	−0.00671137	−	0.00638347i
$539$		−	35.3002i		−	1.52049i
$540$	−24.5881	−	1.34205i	−1.05810	−	0.0577525i
$541$		−	16.9095i		−	0.726997i	−0.931595	−	0.363499i	$-0.881582\pi$
$541$		−	16.9095i		−	0.726997i	0.931595	−	0.363499i	$-0.118418\pi$
$542$	−14.9609	+	15.7294i	−0.642625	+	0.675634i
$543$	14.2559	+	14.4216i	0.611779	+	0.618888i
$544$	−17.1323	−	2.35540i	−0.734543	−	0.100987i
$545$	−9.57704	+	8.03609i	−0.410235	+	0.344228i
$546$	2.32162	−	4.20619i	0.0993560	−	0.180008i
$547$	−7.35226	−	20.2002i	−0.314360	−	0.863696i	−0.991763	−	0.128085i	$-0.959117\pi$
$547$	−7.35226	−	20.2002i	−0.314360	−	0.863696i	0.677403	−	0.735612i	$-0.263105\pi$
$548$	26.9592	+	3.37288i	1.15164	+	0.144082i
$549$	−0.858096	+	4.55793i	−0.0366226	+	0.194528i
$550$	−4.83475	−	0.301264i	−0.206155	−	0.0128460i
$551$	−5.24447	−	4.40063i	−0.223422	−	0.187473i
$552$	−8.03679	−	32.3007i	−0.342069	−	1.37481i
$553$	0.603683	+	3.42365i	0.0256712	+	0.145589i
$554$	29.9272	+	13.0535i	1.27149	+	0.554590i
$555$	17.8373	+	12.6440i	0.757151	+	0.536708i
$556$	20.6962	+	6.37933i	0.877714	+	0.270544i
$557$	4.92698	−	2.84459i	0.208763	−	0.120529i	−0.391974	−	0.919976i	$-0.628208\pi$
$557$	4.92698	−	2.84459i	0.208763	−	0.120529i	0.600736	+	0.799447i	$0.294874\pi$
$558$	8.68108	+	0.641699i	0.367499	+	0.0271653i
$559$	8.26115	−	14.3087i	0.349409	−	0.605195i
$560$	7.05382	+	3.17936i	0.298078	+	0.134353i
$561$	−26.6742	−	12.6265i	−1.12619	−	0.533091i
$562$	7.78115	−	0.877524i	0.328228	−	0.0370161i
$563$	2.37413	−	6.52288i	0.100058	−	0.274907i	−0.879556	−	0.475795i	$-0.842161\pi$
$563$	2.37413	−	6.52288i	0.100058	−	0.274907i	0.979614	+	0.200888i	$0.0643828\pi$
$564$	4.94947	+	37.4043i	0.208410	+	1.57501i
$565$	−32.8543	−	5.79311i	−1.38219	−	0.243718i
$566$	−4.04379	+	6.09432i	−0.169973	+	0.256163i
$567$	5.51751	+	4.85133i	0.231713	+	0.203737i
$568$	−4.59063	+	24.3026i	−0.192619	+	1.01971i
$569$	4.94312	−	28.0338i	0.207226	−	1.17524i	−0.686671	−	0.726968i	$-0.740929\pi$
$569$	4.94312	−	28.0338i	0.207226	−	1.17524i	0.893898	−	0.448271i	$-0.147960\pi$
$570$	−2.78324	−	3.19011i	−0.116577	−	0.133619i
$571$	−4.68351	+	12.8678i	−0.195999	+	0.538503i	−0.998292	−	0.0584282i	$-0.981391\pi$
$571$	−4.68351	+	12.8678i	−0.195999	+	0.538503i	0.802293	+	0.596931i	$0.203613\pi$
$572$	23.8354	+	12.2136i	0.996608	+	0.510676i
$573$	−15.4134	+	32.5618i	−0.643906	+	1.36029i
$574$	−8.34784	−	2.01425i	−0.348432	−	0.0840733i
$575$	−2.08782	+	3.61622i	−0.0870682	+	0.150807i
$576$	−9.01217	+	22.2437i	−0.375507	+	0.926819i
$577$	5.00377	+	8.66678i	0.208309	+	0.360803i	0.951182	−	0.308630i	$-0.0998705\pi$
$577$	5.00377	+	8.66678i	0.208309	+	0.360803i	−0.742873	+	0.669433i	$0.766537\pi$
$578$	−3.06250	−	10.3825i	−0.127383	−	0.431854i
$579$	−5.70876	−	4.04667i	−0.237248	−	0.168174i
$580$	37.3592	−	24.1399i	1.55126	−	1.00235i
$581$	11.5711	−	2.04030i	0.480050	−	0.0846457i
$582$	−37.5097	−	5.87158i	−1.55483	−	0.243385i
$583$	12.7907	+	10.7327i	0.529738	+	0.444503i
$584$	14.0203	−	4.91070i	0.580164	−	0.203206i
$585$	−5.65570	−	16.1158i	−0.233834	−	0.666307i
$586$	−9.65655	−	19.4237i	−0.398909	−	0.802387i
$587$	3.75574	+	10.3188i	0.155016	+	0.425903i	0.992753	−	0.120171i	$-0.0383442\pi$
$587$	3.75574	+	10.3188i	0.155016	+	0.425903i	−0.837737	+	0.546073i	$0.816122\pi$
$588$	10.1437	+	19.4545i	0.418319	+	0.802292i
$589$	0.961972	+	1.14643i	0.0396373	+	0.0472380i
$590$	2.59308	+	3.51275i	0.106755	+	0.144618i
$591$	22.1076	+	22.3645i	0.909385	+	0.919952i
$592$	17.2969	−	12.4463i	0.710900	−	0.511540i
$593$	20.1534			0.827600			0.413800	−	0.910368i	$-0.364201\pi$
$593$	20.1534			0.827600			0.413800	+	0.910368i	$0.364201\pi$
$594$	−26.0838	+	31.5764i	−1.07023	+	1.29560i
$595$		−	5.91334i		−	0.242423i
$596$	−4.90907	−	21.4879i	−0.201083	−	0.880180i
$597$	7.76304	+	29.6563i	0.317720	+	1.21375i
$598$	18.5739	−	13.7111i	0.759545	−	0.560688i
$599$	19.4387	−	16.3110i	0.794245	−	0.666451i	−0.152547	−	0.988296i	$-0.548748\pi$
$599$	19.4387	−	16.3110i	0.794245	−	0.666451i	0.946792	+	0.321845i	$0.104303\pi$
$600$	2.75109	−	1.22326i	0.112313	−	0.0499394i
$601$	33.1175	−	12.0538i	1.35089	−	0.491685i	0.437666	−	0.899137i	$-0.355805\pi$
$601$	33.1175	−	12.0538i	1.35089	−	0.491685i	0.913226	+	0.407453i	$0.133583\pi$
$602$	−3.53417	−	7.10882i	−0.144042	−	0.289734i
$603$	13.4080	+	5.05628i	0.546015	+	0.205908i
$604$	−1.03170	+	1.36260i	−0.0419791	+	0.0554435i
$605$	−30.5588	+	36.4185i	−1.24239	+	1.48062i
$606$	−18.3627	−	14.8150i	−0.745934	−	0.601820i
$607$	6.30962	+	35.7836i	0.256099	+	1.45241i	0.793235	+	0.608916i	$0.208395\pi$
$607$	6.30962	+	35.7836i	0.256099	+	1.45241i	−0.537135	+	0.843496i	$0.680494\pi$
$608$	−3.82108	+	1.55717i	−0.154965	+	0.0631515i
$609$	−13.2135	−	1.23299i	−0.535439	−	0.0499632i
$610$	−1.46569	−	4.96898i	−0.0593441	−	0.201188i
$611$	−22.6634	+	13.0847i	−0.916863	+	0.529351i
$612$	18.3289	−	0.706306i	0.740902	−	0.0285507i
$613$	4.83669	+	2.79246i	0.195352	+	0.112786i	0.594486	−	0.804106i	$-0.297356\pi$
$613$	4.83669	+	2.79246i	0.195352	+	0.112786i	−0.399134	+	0.916893i	$0.630689\pi$
$614$	−5.11370	+	21.1931i	−0.206372	+	0.855285i
$615$	−25.1079	+	17.3654i	−1.01245	+	0.700242i
$616$	11.2221	−	6.29838i	0.452153	−	0.253769i
$617$	−33.3230	−	12.1286i	−1.34154	−	0.488279i	−0.431239	−	0.902238i	$-0.641924\pi$
$617$	−33.3230	−	12.1286i	−1.34154	−	0.488279i	−0.910296	+	0.413959i	$0.864146\pi$
$618$	−0.586316	+	1.71282i	−0.0235851	+	0.0688997i
$619$	3.57695	+	0.630714i	0.143770	+	0.0253505i	0.245070	−	0.969505i	$-0.421189\pi$
$619$	3.57695	+	0.630714i	0.143770	+	0.0253505i	−0.101300	+	0.994856i	$0.532300\pi$
$620$	−8.95893	+	3.77865i	−0.359799	+	0.151754i
$621$	14.3636	+	32.2506i	0.576393	+	1.29417i
$622$	25.9638	+	17.2279i	1.04105	+	0.690775i
$623$	1.40779	−	7.98399i	0.0564020	−	0.319872i
$624$	−16.6457	+	0.118114i	−0.666363	+	0.00472833i
$625$	26.0249	+	9.47231i	1.04100	+	0.378892i
$626$	39.6047	−	4.46644i	1.58292	−	0.178515i
$627$	−7.01806	+	0.573170i	−0.280274	+	0.0228902i
$628$	5.56453	−	5.16523i	0.222049	−	0.206115i
$629$	−14.1043	−	8.14312i	−0.562375	−	0.324687i
$630$	−7.95485	−	2.01696i	−0.316929	−	0.0803576i
$631$	−7.14123	−	12.3690i	−0.284288	−	0.492401i	0.688148	−	0.725570i	$-0.258424\pi$
$631$	−7.14123	−	12.3690i	−0.284288	−	0.492401i	−0.972436	+	0.233169i	$0.925090\pi$
$632$	9.32070	−	7.62976i	0.370757	−	0.303495i
$633$	−3.36744	−	7.33177i	−0.133844	−	0.291412i
$634$	−45.8001	−	19.9768i	−1.81895	−	0.793382i
$635$	−30.7641	+	5.42454i	−1.22084	+	0.215266i
$636$	−10.1333	−	2.23949i	−0.401811	−	0.0888015i
$637$	−9.78164	+	11.6573i	−0.387563	+	0.461879i
$638$	4.60094	−	73.8369i	0.182153	−	2.92323i
$639$	0.303067	−	26.2309i	0.0119891	−	1.03768i
$640$	−2.35542	−	26.7043i	−0.0931062	−	1.05558i
$641$	−23.2736	+	8.47090i	−0.919252	+	0.334580i	−0.757941	−	0.652323i	$-0.773794\pi$
$641$	−23.2736	+	8.47090i	−0.919252	+	0.334580i	−0.161311	+	0.986904i	$0.551572\pi$
$642$	−3.05659	−	5.06628i	−0.120634	−	0.199950i
$643$	−0.0600848	−	0.0716063i	−0.00236951	−	0.00282388i	0.764858	−	0.644198i	$-0.222809\pi$
$643$	−0.0600848	−	0.0716063i	−0.00236951	−	0.00282388i	−0.767228	+	0.641375i	$0.778364\pi$
$644$	−0.555183	−	11.0790i	−0.0218773	−	0.436575i
$645$	−27.2182	−	7.46188i	−1.07172	−	0.293811i
$646$	2.28500	+	2.17336i	0.0899021	+	0.0855098i
$647$	28.7206			1.12912			0.564562	−	0.825391i	$-0.309045\pi$
$647$	28.7206			1.12912			0.564562	+	0.825391i	$0.309045\pi$
$648$	5.30159	−	24.8977i	0.208266	−	0.978072i
$649$	7.26196			0.285057
$650$	1.51312	+	1.43919i	0.0593494	+	0.0564498i
$651$	2.79777	+	0.767010i	0.109653	+	0.0300615i
$652$	−31.3263	+	1.56980i	−1.22683	+	0.0614781i
$653$	15.4192	+	18.3759i	0.603402	+	0.719106i	0.978122	−	0.208032i	$-0.0667057\pi$
$653$	15.4192	+	18.3759i	0.603402	+	0.719106i	−0.374720	+	0.927138i	$0.622261\pi$
$654$	−6.67629	−	11.0659i	−0.261064	−	0.432712i
$655$	31.7580	−	11.5590i	1.24089	−	0.451646i
$656$	8.07011	+	28.6383i	0.315085	+	1.11814i
$657$	−13.7357	+	7.72010i	−0.535880	+	0.301190i
$658$	−0.782014	+	12.5499i	−0.0304861	+	0.489247i
$659$	−0.657648	+	0.783755i	−0.0256183	+	0.0305307i	−0.778701	−	0.627395i	$-0.784121\pi$
$659$	−0.657648	+	0.783755i	−0.0256183	+	0.0305307i	0.753083	+	0.657925i	$0.228566\pi$
$660$	9.87229	−	44.6704i	0.384279	−	1.73879i
$661$	9.39844	−	1.65720i	0.365557	−	0.0644575i	0.0121473	−	0.999926i	$-0.496133\pi$
$661$	9.39844	−	1.65720i	0.365557	−	0.0644575i	0.353410	+	0.935469i	$0.385022\pi$
$662$	8.55334	+	3.73075i	0.332435	+	0.145000i
$663$	5.30993	+	11.5611i	0.206221	+	0.448995i
$664$	−25.7867	−	31.5016i	−1.00072	−	1.22250i
$665$	−0.705455	−	1.22188i	−0.0273564	−	0.0473826i
$666$	−15.7652	+	16.1961i	−0.610890	+	0.627587i
$667$	−55.2272	−	31.8855i	−2.13841	−	1.23461i
$668$	−0.589564	−	0.635140i	−0.0228109	−	0.0245743i
$669$	−44.0739	+	3.59955i	−1.70400	+	0.139167i
$670$	−15.9054	+	1.79374i	−0.614479	+	0.0692982i
$671$	−8.09695	−	2.94705i	−0.312579	−	0.113770i
$672$	−4.37484	+	6.69589i	−0.168763	+	0.258300i
$673$	5.67344	−	32.1757i	0.218695	−	1.24028i	−0.655683	−	0.755037i	$-0.727619\pi$
$673$	5.67344	−	32.1757i	0.218695	−	1.24028i	0.874378	−	0.485246i	$-0.161270\pi$
$674$	−23.7108	−	15.7329i	−0.913307	−	0.606010i
$675$	−2.64725	+	1.78607i	−0.101893	+	0.0687457i
$676$	5.61729	+	13.3182i	0.216050	+	0.512240i
$677$	42.8943	+	7.56342i	1.64856	+	0.290686i	0.919302	−	0.393553i	$-0.128754\pi$
$677$	42.8943	+	7.56342i	1.64856	+	0.290686i	0.729258	+	0.684238i	$0.239865\pi$
$678$	11.1691	−	32.6285i	0.428946	−	1.25309i
$679$	−11.8899	−	4.32756i	−0.456292	−	0.166077i
$680$	−17.8669	+	10.0277i	−0.685163	+	0.384545i
$681$	−12.4442	+	8.60684i	−0.476864	+	0.329815i
$682$	−3.79327	+	15.7208i	−0.145252	+	0.601979i
$683$	3.57110	+	2.06177i	0.136644	+	0.0788916i	0.566764	−	0.823880i	$-0.308195\pi$
$683$	3.57110	+	2.06177i	0.136644	+	0.0788916i	−0.430119	+	0.902772i	$0.641529\pi$
$684$	3.70307	−	2.33256i	0.141590	−	0.0891878i
$685$	27.8766	−	16.0945i	1.06511	−	0.614941i
$686$	4.35500	+	14.7643i	0.166275	+	0.563704i
$687$	13.2136	+	1.23300i	0.504131	+	0.0470418i
$688$	−15.4858	+	22.7333i	−0.590391	+	0.866699i
$689$	−1.24991	−	7.08860i	−0.0476178	−	0.270054i
$690$	−30.6916	−	24.7620i	−1.16841	−	0.942672i
$691$	10.8896	−	12.9777i	0.414260	−	0.493696i	−0.518053	−	0.855349i	$-0.673343\pi$
$691$	10.8896	−	12.9777i	0.414260	−	0.493696i	0.932313	+	0.361653i	$0.117787\pi$
$692$	10.1171	+	7.66021i	0.384596	+	0.291198i
$693$	−10.5567	+	8.65230i	−0.401017	+	0.328674i
$694$	2.31874	+	4.66405i	0.0880182	+	0.177045i
$695$	24.1109	−	8.77566i	0.914579	−	0.332880i
$696$	18.6818	+	42.0149i	0.708131	+	1.59257i
$697$	17.4198	−	14.6169i	0.659820	−	0.553655i
$698$	29.6924	−	21.9186i	1.12387	−	0.829633i
$699$	−4.07643	−	15.5727i	−0.154185	−	0.589015i
$700$	0.978192	−	0.223475i	0.0369722	−	0.00844655i
$701$		−	8.56815i		−	0.323615i	−0.986822	−	0.161807i	$-0.948268\pi$
$701$		−	8.56815i		−	0.323615i	0.986822	−	0.161807i	$-0.0517323\pi$
$702$	17.3636	−	3.19979i	0.655345	−	0.120768i
$703$	−3.88586			−0.146558
$704$	−38.0605	−	23.2265i	−1.43446	−	0.875382i
$705$	31.4254	+	31.7906i	1.18355	+	1.19730i
$706$	24.8593	+	33.6760i	0.935593	+	1.26741i
$707$	−5.05428	−	6.02346i	−0.190086	−	0.226535i
$708$	−4.00219	+	2.08677i	−0.150412	+	0.0784255i
$709$	14.2988	+	39.2856i	0.537002	+	1.47540i	0.850584	+	0.525839i	$0.176249\pi$
$709$	14.2988	+	39.2856i	0.537002	+	1.47540i	−0.313582	+	0.949561i	$0.601529\pi$
$710$	13.0443	+	26.2381i	0.489545	+	0.984698i
$711$	−8.32474	+	9.69141i	−0.312202	+	0.363456i
$712$	−26.5105	+	9.28549i	−0.993524	+	0.347988i
$713$	10.6788	+	8.96061i	0.399925	+	0.335577i
$714$	6.03940	+	0.945377i	0.226019	+	0.0353798i
$715$	31.2485	−	5.50996i	1.16863	−	0.206061i
$716$	−28.6366	−	44.3184i	−1.07020	−	1.65626i
$717$	11.9906	+	8.49957i	0.447798	+	0.317422i
$718$	−5.15581	−	17.4792i	−0.192413	−	0.652319i
$719$	15.6713	+	27.1435i	0.584441	+	1.01228i	0.994945	+	0.100423i	$0.0320195\pi$
$719$	15.6713	+	27.1435i	0.584441	+	1.01228i	−0.410504	+	0.911859i	$0.634647\pi$
$720$	7.39551	+	27.4555i	0.275614	+	1.02321i
$721$	−0.301671	+	0.522510i	−0.0112348	+	0.0194593i
$722$	−25.3890	−	6.12612i	−0.944881	−	0.227991i
$723$	2.30015	−	4.85920i	0.0855434	−	0.180715i
$724$	10.6781	−	20.8389i	0.396850	−	0.774472i
$725$	1.97288	−	5.42043i	0.0732708	−	0.201310i
$726$	−32.3094	−	37.0325i	−1.19911	−	1.37440i
$727$	−4.66774	+	26.4721i	−0.173117	+	0.981794i	0.767178	+	0.641434i	$0.221660\pi$
$727$	−4.66774	+	26.4721i	−0.173117	+	0.981794i	−0.940295	+	0.340360i	$0.889451\pi$
$728$	−5.45120	−	1.02971i	−0.202035	−	0.0381634i
$729$	−0.935632	+	26.9838i	−0.0346530	+	0.999399i
$730$	9.73091	−	14.6653i	0.360157	−	0.542786i
$731$	20.7031	+	3.65052i	0.765733	+	0.135019i
$732$	5.30922	−	0.702535i	0.196235	−	0.0259664i
$733$	0.226255	−	0.621630i	0.00835691	−	0.0229604i	−0.935444	−	0.353475i	$-0.885000\pi$
$733$	0.226255	−	0.621630i	0.00835691	−	0.0229604i	0.943801	+	0.330514i	$0.107222\pi$
$734$	−14.2496	+	1.60701i	−0.525964	+	0.0593159i
$735$	23.4945	+	11.1214i	0.866609	+	0.410218i
$736$	−32.5333	+	20.4650i	−1.19919	+	0.754350i
$737$	−13.3110	+	23.0554i	−0.490318	+	0.849255i
$738$	−13.7216	−	28.4193i	−0.505098	−	1.04613i
$739$	2.80715	−	1.62071i	0.103263	−	0.0596186i	−0.447479	−	0.894294i	$-0.647678\pi$
$739$	2.80715	−	1.62071i	0.103263	−	0.0596186i	0.550742	+	0.834676i	$0.314345\pi$
$740$	7.43665	−	24.1264i	0.273377	−	0.886904i
$741$	2.47642	+	1.75542i	0.0909737	+	0.0644869i
$742$	−3.17014	−	1.38274i	−0.116379	−	0.0507618i
$743$	−4.35112	−	24.6764i	−0.159627	−	0.905290i	−0.954433	−	0.298426i	$-0.903538\pi$
$743$	−4.35112	−	24.6764i	−0.159627	−	0.905290i	0.794806	−	0.606864i	$-0.207573\pi$
$744$	−2.42692	−	9.75401i	−0.0889750	−	0.357599i
$745$	−20.0044	−	16.7857i	−0.732903	−	0.614979i
$746$	14.7209	+	0.917295i	0.538972	+	0.0335846i
$747$	32.7545	+	28.1355i	1.19843	+	1.02942i
$748$	−4.23043	+	33.8136i	−0.154680	+	1.23635i
$749$	−0.674433	−	1.85299i	−0.0246432	−	0.0677067i
$750$	−12.2999	+	22.2843i	−0.449127	+	0.813707i
$751$	−13.0260	+	10.9301i	−0.475325	+	0.398845i	−0.848732	−	0.528823i	$-0.822634\pi$
$751$	−13.0260	+	10.9301i	−0.475325	+	0.398845i	0.373408	+	0.927667i	$0.378189\pi$
$752$	39.2451	−	18.9191i	1.43112	−	0.689907i
$753$	−10.7883	−	10.9137i	−0.393149	−	0.397717i
$754$	−21.9795	+	23.1085i	−0.800446	+	0.841562i
$755$			2.02488i			0.0736931i
$756$	3.33171	−	7.80197i	0.121173	−	0.283755i
$757$		−	11.7321i		−	0.426412i	−0.977007	−	0.213206i	$-0.931609\pi$
$757$		−	11.7321i		−	0.426412i	0.977007	−	0.213206i	$-0.0683906\pi$
$758$	14.4772	+	13.7699i	0.525837	+	0.500146i
$759$	−63.4518	+	16.6096i	−2.30316	+	0.602891i
$760$	−2.49557	+	4.20354i	−0.0905238	+	0.152478i
$761$	0.0993911	−	0.0833990i	0.00360292	−	0.00302321i	−0.640984	−	0.767554i	$-0.721474\pi$
$761$	0.0993911	−	0.0833990i	0.00360292	−	0.00302321i	0.644587	+	0.764531i	$0.277029\pi$
$762$	−0.621863	−	32.2871i	−0.0225277	−	1.16964i
$763$	−1.47312	−	4.04736i	−0.0533304	−	0.146524i
$764$	41.2770	+	5.16418i	1.49335	+	0.186833i
$765$	16.8075	−	13.7754i	0.607675	−	0.498051i
$766$	−0.952248	+	15.2819i	−0.0344061	+	0.552156i
$767$	−2.39814	−	2.01228i	−0.0865920	−	0.0726593i
$768$	27.6501	+	1.86363i	0.997736	+	0.0672478i
$769$	1.99390	+	11.3080i	0.0719020	+	0.407776i	0.999422	+	0.0340023i	$0.0108254\pi$
$769$	1.99390	+	11.3080i	0.0719020	+	0.407776i	−0.927520	+	0.373774i	$0.878064\pi$
$770$	6.09549	−	13.9749i	0.219666	−	0.503619i
$771$	2.72090	−	29.1590i	0.0979909	−	1.05014i
$772$	−2.38007	+	7.72156i	−0.0856607	+	0.277905i
$773$	−13.9804	+	8.07158i	−0.502839	+	0.290314i	−0.729885	−	0.683570i	$-0.760427\pi$
$773$	−13.9804	+	8.07158i	−0.502839	+	0.290314i	0.227046	+	0.973884i	$0.427093\pi$
$774$	11.9724	−	26.6055i	0.430338	−	0.956315i
$775$	−0.630472	+	1.09201i	−0.0226472	+	0.0392261i
$776$	7.08708	+	43.2633i	0.254411	+	1.55306i
$777$	−6.19514	+	4.28476i	−0.222249	+	0.153715i
$778$	2.80561	+	24.8778i	0.100586	+	0.891914i
$779$	1.85569	−	5.09847i	0.0664871	−	0.182672i
$780$	−15.6383	+	12.0161i	−0.559941	+	0.430245i
$781$	47.9952	+	8.46285i	1.71740	+	0.302825i
$782$	24.4765	+	16.2410i	0.875276	+	0.580775i
$783$	−27.2770	−	40.4291i	−0.974800	−	1.44482i
$784$	17.6821	−	18.1432i	0.631502	−	0.647973i
$785$	1.56197	−	8.85840i	0.0557493	−	0.316170i
$786$	6.72815	+	34.2829i	0.239985	+	1.22283i
$787$	−10.3024	+	28.3055i	−0.367240	+	1.00898i	0.609167	+	0.793042i	$0.291504\pi$
$787$	−10.3024	+	28.3055i	−0.367240	+	1.00898i	−0.976406	+	0.215941i	$0.930718\pi$
$788$	16.5593	−	32.3163i	0.589902	−	1.15122i
$789$	47.6792	−	3.89399i	1.69743	−	0.138630i
$790$	3.34732	−	13.8726i	0.119092	−	0.493564i
$791$	5.74672	−	9.95360i	0.204330	−	0.353909i
$792$	44.0444	+	17.2243i	1.56505	+	0.612038i
$793$	1.85726	+	3.21687i	0.0659533	+	0.114234i
$794$	−46.6422	+	13.7580i	−1.65527	+	0.488252i
$795$	−11.1730	+	5.13170i	−0.396267	+	0.182003i
$796$	29.7313	−	19.2110i	1.05380	−	0.680917i
$797$	−22.3243	+	3.93637i	−0.790767	+	0.139434i	−0.554422	−	0.832236i	$-0.687061\pi$
$797$	−22.3243	+	3.93637i	−0.790767	+	0.139434i	−0.236345	+	0.971669i	$0.575949\pi$
$798$	1.36071	−	0.525148i	0.0481687	−	0.0185900i
$799$	−25.5072	−	21.4031i	−0.902379	−	0.757186i
$800$	−2.33401	−	2.57660i	−0.0825198	−	0.0910964i
$801$	25.9724	−	14.5977i	0.917689	−	0.515784i
$802$	−9.75614	+	4.85029i	−0.344501	+	0.171270i
$803$	−10.0119	−	27.5076i	−0.353313	−	0.970721i
$804$	0.710846	−	16.5312i	0.0250696	−	0.583011i
$805$	−8.44777	−	10.0677i	−0.297745	−	0.354838i
$806$	5.60887	−	4.14042i	0.197564	−	0.145840i
$807$	0.0695682	−	0.253759i	0.00244892	−	0.00893275i
$808$	−9.62865	+	25.4857i	−0.338735	+	0.896584i
$809$	41.9562			1.47510			0.737551	−	0.675292i	$-0.235982\pi$
$809$	41.9562			1.47510			0.737551	+	0.675292i	$0.235982\pi$
$810$	−12.7984	−	27.3086i	−0.449690	−	0.959528i
$811$		−	14.6317i		−	0.513787i	−0.966440	−	0.256893i	$-0.917301\pi$
$811$		−	14.6317i		−	0.513787i	0.966440	−	0.256893i	$-0.0826989\pi$
$812$	3.41293	+	14.9391i	0.119770	+	0.524258i
$813$	−25.6408	−	7.02942i	−0.899261	−	0.246533i
$814$	−24.9384	−	33.7832i	−0.874091	−	1.18410i
$815$	−28.4666	+	23.8863i	−0.997142	+	0.836701i
$816$	−7.38506	−	19.8509i	−0.258529	−	0.694920i
$817$	4.71343	−	1.71555i	0.164902	−	0.0600194i
$818$	1.33243	−	0.662418i	0.0465871	−	0.0231609i
$819$	5.88373	+	0.0679797i	0.205594	+	0.00237540i
$820$	28.1039	+	21.2789i	0.981430	+	0.743091i
$821$	26.1627	−	31.1794i	0.913083	−	1.08817i	−0.0827134	−	0.996573i	$-0.526359\pi$
$821$	26.1627	−	31.1794i	0.913083	−	1.08817i	0.995796	−	0.0915963i	$-0.0291969\pi$
$822$	11.9809	+	31.0439i	0.417883	+	1.08278i
$823$	9.20245	+	52.1897i	0.320777	+	1.81922i	0.537825	+	0.843057i	$0.319246\pi$
$823$	9.20245	+	52.1897i	0.320777	+	1.81922i	−0.217048	+	0.976161i	$0.569643\pi$
$824$	2.09031	+	0.0254244i	0.0728193	+	0.000885702i
$825$	−2.47622	−	5.39136i	−0.0862108	−	0.187703i
$826$	−1.44276	+	0.425568i	−0.0502000	+	0.0148074i
$827$	−33.8387	+	19.5368i	−1.17669	+	0.679360i	−0.955246	−	0.295813i	$-0.904409\pi$
$827$	−33.8387	+	19.5368i	−1.17669	+	0.679360i	−0.221441	+	0.975174i	$0.571076\pi$
$828$	30.1965	−	27.3871i	1.04940	−	0.951767i
$829$	12.8078	+	7.39457i	0.444832	+	0.256824i	0.705645	−	0.708565i	$-0.250657\pi$
$829$	12.8078	+	7.39457i	0.444832	+	0.256824i	−0.260813	+	0.965389i	$0.583991\pi$
$830$	−46.8858	−	11.3131i	−1.62743	−	0.392683i
$831$	3.25502	+	39.8554i	0.112915	+	1.38257i
$832$	6.13282	+	18.2167i	0.212617	+	0.631550i
$833$	−18.1947	−	6.62232i	−0.630408	−	0.229450i
$834$	5.10807	+	26.0279i	0.176878	+	0.901271i
$835$	−1.01111	−	0.178285i	−0.0349907	−	0.00616981i
$836$	3.15978	+	7.49164i	0.109283	+	0.259104i
$837$	4.33747	+	9.73888i	0.149925	+	0.336625i
$838$	−4.12922	+	6.22308i	−0.142642	+	0.214973i
$839$	−1.90754	+	10.8182i	−0.0658556	+	0.373486i	0.934012	+	0.357240i	$0.116282\pi$
$839$	−1.90754	+	10.8182i	−0.0658556	+	0.373486i	−0.999868	+	0.0162452i	$0.994829\pi$
$840$	0.656429	+	9.45337i	0.0226490	+	0.326172i
$841$	55.5304	+	20.2114i	1.91484	+	0.696945i
$842$	−4.94771	−	43.8722i	−0.170509	−	1.51193i
$843$	5.45532	+	7.88759i	0.187891	+	0.271663i
$844$	−6.82801	+	6.33805i	−0.235030	+	0.218165i
$845$	14.8306	+	8.56245i	0.510188	+	0.294557i
$846$	−37.4923	+	27.0129i	−1.28901	+	0.928723i
$847$	−8.18930	−	14.1843i	−0.281388	−	0.487378i
$848$	1.19798	+	11.9232i	0.0411390	+	0.409446i
$849$	−8.91890	−	0.832245i	−0.306096	−	0.0285626i
$850$	−1.06228	+	2.43545i	−0.0364359	+	0.0835351i
$851$	−35.6462	+	6.28539i	−1.22194	+	0.215460i
$852$	−28.8828	+	9.12767i	−0.989510	+	0.312709i
$853$	−18.0653	+	21.5293i	−0.618543	+	0.737151i	−0.980819	−	0.194920i	$-0.937555\pi$
$853$	−18.0653	+	21.5293i	−0.618543	+	0.737151i	0.362276	+	0.932071i	$0.382000\pi$
$854$	1.78135	+	0.111000i	0.0609567	+	0.00379835i
$855$	1.82957	−	4.85155i	0.0625699	−	0.165919i
$856$	−4.45503	+	5.18002i	−0.152270	+	0.177050i
$857$	44.7520	−	16.2884i	1.52870	−	0.556401i	0.565397	−	0.824819i	$-0.308723\pi$
$857$	44.7520	−	16.2884i	1.52870	−	0.556401i	0.963303	+	0.268417i	$0.0865006\pi$
$858$	0.631655	+	32.7955i	0.0215644	+	1.11962i
$859$	−30.7024	−	36.5896i	−1.04755	−	1.24842i	−0.967830	−	0.251605i	$-0.919042\pi$
$859$	−30.7024	−	36.5896i	−1.04755	−	1.24842i	−0.0797208	−	0.996817i	$-0.525403\pi$
$860$	1.63101	+	32.5477i	0.0556169	+	1.10987i
$861$	−2.66337	−	10.1746i	−0.0907674	−	0.346749i
$862$	3.16819	−	3.33093i	0.107909	−	0.113452i
$863$	−51.9526			−1.76849			−0.884244	−	0.467026i	$-0.845325\pi$
$863$	−51.9526			−1.76849			−0.884244	+	0.467026i	$0.845325\pi$
$864$	−29.2231	+	3.16380i	−0.994191	+	0.107635i
$865$	15.0345			0.511189
$866$	−5.63350	+	5.92287i	−0.191434	+	0.201267i
$867$	9.42847	−	9.32017i	0.320208	−	0.316529i
$868$	−0.167652	−	3.34559i	−0.00569048	−	0.113557i
$869$	−15.2569	−	18.1824i	−0.517554	−	0.616796i
$870$	47.6936	+	26.3246i	1.61697	+	0.892488i
$871$	10.7844	−	3.92519i	0.365414	−	0.133000i
$872$	−9.73081	+	11.3144i	−0.329527	+	0.383153i
$873$	−15.3978	−	43.8759i	−0.521137	−	1.48497i
$874$	6.99514	+	0.435883i	0.236614	+	0.0147440i
$875$	−5.45261	+	6.49817i	−0.184332	+	0.219678i
$876$	13.4222	+	12.2829i	0.453494	+	0.415001i
$877$	−18.6056	+	3.28068i	−0.628268	+	0.110781i	−0.478711	−	0.877973i	$-0.658896\pi$
$877$	−18.6056	+	3.28068i	−0.628268	+	0.110781i	−0.149557	+	0.988753i	$0.547785\pi$
$878$	−5.92569	+	13.5856i	−0.199982	+	0.458491i
$879$	15.3636	−	21.6739i	0.518200	−	0.731041i
$880$	−52.5610	+	5.28105i	−1.77183	+	0.178024i
$881$	7.13948	+	12.3659i	0.240535	+	0.416619i	0.960867	−	0.277011i	$-0.0893437\pi$
$881$	7.13948	+	12.3659i	0.240535	+	0.416619i	−0.720332	+	0.693630i	$0.756010\pi$
$882$	−15.1145	+	22.2174i	−0.508933	+	0.748098i
$883$	8.00129	+	4.61954i	0.269265	+	0.155460i	0.628553	−	0.777766i	$-0.283647\pi$
$883$	8.00129	+	4.61954i	0.269265	+	0.155460i	−0.359289	+	0.933226i	$0.616981\pi$
$884$	10.7667	−	9.99414i	0.362125	−	0.336139i
$885$	−2.28789	+	4.83330i	−0.0769066	+	0.162470i
$886$	1.68660	+	14.9554i	0.0566624	+	0.502435i
$887$	−14.3955	−	5.23952i	−0.483352	−	0.175926i	0.0888391	−	0.996046i	$-0.471684\pi$
$887$	−14.3955	−	5.23952i	−0.483352	−	0.175926i	−0.572191	+	0.820120i	$0.693907\pi$
$888$	23.4518	+	11.4523i	0.786990	+	0.384314i
$889$	1.86884	−	10.5987i	0.0626788	−	0.355469i
$890$	−18.3999	+	27.7301i	−0.616765	+	0.929516i
$891$	−49.1848	−	9.84944i	−1.64775	−	0.329969i
$892$	19.8437	+	47.0481i	0.664415	+	1.57529i
$893$	−7.82395	−	1.37957i	−0.261818	−	0.0461657i
$894$	20.3416	−	17.7472i	0.680325	−	0.593557i
$895$	−58.7439	−	21.3810i	−1.96359	−	0.714689i
$896$	8.92274	+	2.38405i	0.298088	+	0.0796456i
$897$	25.5564	+	12.0974i	0.853304	+	0.403920i
$898$	28.5426	+	6.88704i	0.952477	+	0.229824i
$899$	−16.6773	−	9.62863i	−0.556218	−	0.321133i
$900$	2.91392	+	2.25972i	0.0971308	+	0.0753239i
$901$	7.93147	−	4.57923i	0.264235	−	0.152556i
$902$	56.2349	−	16.5875i	1.87242	−	0.552303i
$903$	5.62285	−	7.93234i	0.187117	−	0.263972i
$904$	−39.8195	−	0.484325i	−1.32438	−	0.0161084i
$905$	−4.81727	−	27.3201i	−0.160131	−	0.908151i
$906$	−2.06805	−	0.323722i	−0.0687063	−	0.0107549i
$907$	−5.65685	+	6.74157i	−0.187833	+	0.223850i	−0.851740	−	0.523965i	$-0.824452\pi$
$907$	−5.65685	+	6.74157i	−0.187833	+	0.223850i	0.663907	+	0.747815i	$0.268897\pi$
$908$	13.9291	+	10.5465i	0.462255	+	0.349997i
$909$	5.34627	−	28.3977i	0.177325	−	0.941892i
$910$	−5.88536	+	2.92592i	−0.195098	+	0.0969933i
$911$	−30.8181	+	11.2169i	−1.02105	+	0.371632i	−0.797667	−	0.603098i	$-0.793933\pi$
$911$	−30.8181	+	11.2169i	−1.02105	+	0.371632i	−0.223384	+	0.974731i	$0.571710\pi$
$912$	−3.89418	−	3.22079i	−0.128949	−	0.106651i
$913$	−61.4520	+	51.5644i	−2.03377	+	1.70653i
$914$	11.7205	+	15.8774i	0.387680	+	0.525176i
$915$	4.51240	−	4.46057i	0.149176	−	0.147462i
$916$	−3.41296	−	14.9392i	−0.112767	−	0.493604i
$917$			11.6433i			0.384495i
$918$	11.3820	+	19.3681i	0.375662	+	0.639241i
$919$	0.483799			0.0159591			0.00797953	−	0.999968i	$-0.497460\pi$
$919$	0.483799			0.0159591			0.00797953	+	0.999968i	$0.497460\pi$
$920$	−16.0934	+	42.5970i	−0.530584	+	1.40438i
$921$	−25.8308	+	6.76165i	−0.851153	+	0.222804i
$922$	0.0372944	−	0.0275304i	0.00122823	−	0.000906665i
$923$	−13.5046	−	16.0941i	−0.444509	−	0.529745i
$924$	13.2983	+	8.45961i	0.437481	+	0.278301i
$925$	−1.11980	−	3.07662i	−0.0368187	−	0.101159i
$926$	−33.2692	+	16.5399i	−1.09329	+	0.543534i
$927$	−2.18789	+	0.359772i	−0.0718596	+	0.0118165i
$928$	39.3501	−	35.6453i	1.29173	−	1.17011i
$929$	−36.5895	−	30.7023i	−1.20046	−	1.00731i	−0.999617	−	0.0276865i	$-0.991186\pi$
$929$	−36.5895	−	30.7023i	−1.20046	−	1.00731i	−0.200847	−	0.979623i	$-0.564370\pi$
$930$	−9.26811	−	7.47751i	−0.303913	−	0.245197i
$931$	−4.54963	+	0.802223i	−0.149108	+	0.0262918i
$932$	−15.6121	+	10.0879i	−0.511392	+	0.330439i
$933$	−3.54564	+	37.9975i	−0.116079	+	1.24398i
$934$	−10.9508	+	3.23014i	−0.358321	+	0.105693i
$935$	20.1866	+	34.9641i	0.660171	+	1.14345i
$936$	−9.77210	−	17.8927i	−0.319411	−	0.584841i
$937$	4.51081	−	7.81296i	0.147362	−	0.255238i	−0.782890	−	0.622160i	$-0.786255\pi$
$937$	4.51081	−	7.81296i	0.147362	−	0.255238i	0.930252	+	0.366922i	$0.119588\pi$
$938$	1.29345	−	5.36055i	0.0422326	−	0.175028i
$939$	27.7666	+	40.1464i	0.906129	+	1.31013i
$940$	23.5387	−	45.9369i	0.767748	−	1.49830i
$941$	−11.2893	+	31.0172i	−0.368022	+	1.01113i	0.608091	+	0.793867i	$0.291935\pi$
$941$	−11.2893	+	31.0172i	−0.368022	+	1.01113i	−0.976113	+	0.217264i	$0.930287\pi$
$942$	8.79752	+	3.01148i	0.286639	+	0.0981193i
$943$	8.77606	−	49.7715i	0.285788	−	1.62078i
$944$	3.73243	+	3.63756i	0.121480	+	0.118392i
$945$	−2.43275	−	9.75210i	−0.0791373	−	0.317236i
$946$	45.1643	+	29.9680i	1.46842	+	0.974345i
$947$	5.66103	+	0.998192i	0.183959	+	0.0324369i	0.264868	−	0.964285i	$-0.414671\pi$
$947$	5.66103	+	0.998192i	0.183959	+	0.0324369i	−0.0809098	+	0.996721i	$0.525783\pi$
$948$	13.6331	+	5.63650i	0.442784	+	0.183065i
$949$	−4.31604	+	11.8582i	−0.140105	+	0.384934i
$950$	0.0710451	+	0.629969i	0.00230501	+	0.0204389i
$951$	−4.98142	−	60.9940i	−0.161534	−	1.97787i
$952$	−1.14108	−	6.96577i	−0.0369827	−	0.225762i
$953$	−24.5955	+	42.6006i	−0.796726	+	1.37997i	0.125012	+	0.992155i	$0.460103\pi$
$953$	−24.5955	+	42.6006i	−0.796726	+	1.37997i	−0.921738	+	0.387814i	$0.873230\pi$
$954$	−3.45484	−	12.2316i	−0.111855	−	0.396013i
$955$	42.6815	−	24.6422i	1.38114	−	0.797403i
$956$	4.99908	−	16.2183i	0.161682	−	0.524537i
$957$	82.3374	−	37.8171i	2.66159	−	1.22245i
$958$	14.3134	−	32.8158i	0.462446	−	1.06023i
$959$	1.92569	+	10.9211i	0.0621839	+	0.352662i
$960$	27.4497	−	18.0142i	0.885936	−	0.581405i
$961$	−20.5226	−	17.2205i	−0.662020	−	0.555501i
$962$	−1.12578	+	18.0668i	−0.0362966	+	0.582496i
$963$	3.69562	−	6.23356i	0.119090	−	0.200874i
$964$	−6.15976	−	0.770650i	−0.198393	−	0.0248210i
$965$	3.27412	+	8.99557i	0.105398	+	0.289578i
$966$	11.6328	−	7.01831i	0.374280	−	0.225810i
$967$	18.4054	−	15.4439i	0.591876	−	0.496643i	−0.296947	−	0.954894i	$-0.595968\pi$
$967$	18.4054	−	15.4439i	0.591876	−	0.496643i	0.888823	+	0.458251i	$0.151524\pi$
$968$	−28.9699	+	48.7970i	−0.931128	+	1.56839i
$969$	−1.02116	+	3.72482i	−0.0328044	+	0.119659i
$970$	37.6347	+	35.7960i	1.20838	+	1.14934i
$971$			17.8707i			0.573497i	0.958006	+	0.286749i	$0.0925745\pi$
$971$			17.8707i			0.573497i	−0.958006	+	0.286749i	$0.907426\pi$
$972$	29.9369	−	8.70533i	0.960226	−	0.279224i
$973$			8.83968i			0.283387i
$974$	−11.6689	+	12.2683i	−0.373897	+	0.393102i
$975$	−0.676209	+	2.46656i	−0.0216560	+	0.0789933i
$976$	−2.68540	−	5.57050i	−0.0859575	−	0.178308i
$977$	13.5441	−	11.3648i	0.433313	−	0.363593i	−0.399887	−	0.916564i	$-0.630951\pi$
$977$	13.5441	−	11.3648i	0.433313	−	0.363593i	0.833200	+	0.552972i	$0.186506\pi$
$978$	−19.8445	−	32.8922i	−0.634557	−	1.05178i
$979$	18.9313	+	52.0132i	0.605045	+	1.66235i
$980$	3.72614	−	29.7829i	0.119027	−	0.951379i
$981$	8.07209	−	13.6155i	0.257722	−	0.434711i
$982$	5.47138	+	0.340934i	0.174599	+	0.0108796i
$983$	−21.1295	−	17.7297i	−0.673926	−	0.565491i	0.240299	−	0.970699i	$-0.422755\pi$
$983$	−21.1295	−	17.7297i	−0.673926	−	0.565491i	−0.914224	+	0.405208i	$0.867199\pi$
$984$	−26.2255	+	25.3011i	−0.836039	+	0.806569i
$985$	−7.47047	−	42.3671i	−0.238029	−	1.34993i
$986$	−37.1944	−	16.2233i	−1.18451	−	0.516654i
$987$	−13.9947	+	6.42770i	−0.445458	+	0.204596i
$988$	1.03246	−	3.34956i	0.0328469	−	0.106564i
$989$	40.4629	−	23.3612i	1.28664	−	0.742844i
$990$	53.9204	−	15.2299i	1.71370	−	0.484039i
$991$	−10.5626	+	18.2950i	−0.335532	+	0.581159i	−0.983587	−	0.180435i	$-0.942250\pi$
$991$	−10.5626	+	18.2950i	−0.335532	+	0.581159i	0.648054	+	0.761594i	$0.275583\pi$
$992$	−9.82425	+	6.17994i	−0.311920	+	0.196213i
$993$	0.930299	+	11.3909i	0.0295221	+	0.361478i
$994$	−10.0313	+	1.13129i	−0.318174	+	0.0358823i
$995$	14.3436	−	39.4087i	0.454722	−	1.24934i
$996$	19.0500	−	46.0766i	0.603621	−	1.45999i
$997$	−56.4719	−	9.95752i	−1.78848	−	0.315358i	−0.821502	−	0.570206i	$-0.806864\pi$
$997$	−56.4719	−	9.95752i	−1.78848	−	0.315358i	−0.966981	+	0.254848i	$0.917975\pi$
$998$	−5.66604	+	8.53919i	−0.179355	+	0.270303i
$999$	−26.6104	−	7.62687i	−0.841917	−	0.241303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.133.25	yes	204
3.2	odd	2		648.2.t.a.397.10		204
4.3	odd	2		864.2.bf.a.241.3		204
8.3	odd	2		864.2.bf.a.241.32		204
8.5	even	2	inner	216.2.t.a.133.14	yes	204
24.5	odd	2		648.2.t.a.397.21		204
27.13	even	9	inner	216.2.t.a.13.14	✓	204
27.14	odd	18		648.2.t.a.253.21		204
108.67	odd	18		864.2.bf.a.337.32		204
216.13	even	18	inner	216.2.t.a.13.25	yes	204
216.67	odd	18		864.2.bf.a.337.3		204
216.149	odd	18		648.2.t.a.253.10		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.14	✓	204	27.13	even	9	inner
216.2.t.a.13.25	yes	204	216.13	even	18	inner
216.2.t.a.133.14	yes	204	8.5	even	2	inner
216.2.t.a.133.25	yes	204	1.1	even	1	trivial
648.2.t.a.253.10		204	216.149	odd	18
648.2.t.a.253.21		204	27.14	odd	18
648.2.t.a.397.10		204	3.2	odd	2
648.2.t.a.397.21		204	24.5	odd	2
864.2.bf.a.241.3		204	4.3	odd	2
864.2.bf.a.241.32		204	8.3	odd	2
864.2.bf.a.337.3		204	216.67	odd	18
864.2.bf.a.337.32		204	108.67	odd	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.974655 - 1.02472i) q^{2} +(1.67042 + 0.457945i) q^{3} +(-0.100097 - 1.99749i) q^{4} +(-1.52309 - 1.81515i) q^{5} +(2.09734 - 1.26537i) q^{6} +(0.767101 - 0.279202i) q^{7} +(-2.14443 - 1.84430i) q^{8} +(2.58057 + 1.52992i) q^{9} +O(q^{10})\)	\(q+(0.974655 - 1.02472i) q^{2} +(1.67042 + 0.457945i) q^{3} +(-0.100097 - 1.99749i) q^{4} +(-1.52309 - 1.81515i) q^{5} +(2.09734 - 1.26537i) q^{6} +(0.767101 - 0.279202i) q^{7} +(-2.14443 - 1.84430i) q^{8} +(2.58057 + 1.52992i) q^{9} +(-3.34451 - 0.208404i) q^{10} +(-3.58256 + 4.26953i) q^{11} +(0.747538 - 3.38248i) q^{12} +(2.36616 - 0.417219i) q^{13} +(0.461555 - 1.05819i) q^{14} +(-1.71296 - 3.72954i) q^{15} +(-3.97996 + 0.399886i) q^{16} +(1.52854 + 2.64751i) q^{17} +(4.08290 - 1.15322i) q^{18} +(0.631691 + 0.364707i) q^{19} +(-3.47329 + 3.22406i) q^{20} +(1.40924 - 0.115093i) q^{21} +(0.883308 + 7.83244i) q^{22} +(6.38462 + 2.32381i) q^{23} +(-2.73750 - 4.06277i) q^{24} +(-0.106720 + 0.605238i) q^{25} +(1.87866 - 2.83130i) q^{26} +(3.61001 + 3.73735i) q^{27} +(-0.634489 - 1.50433i) q^{28} +(-9.24326 - 1.62984i) q^{29} +(-5.49128 - 1.87972i) q^{30} +(1.92800 + 0.701734i) q^{31} +(-3.46932 + 4.46809i) q^{32} +(-7.93957 + 5.49127i) q^{33} +(4.20276 + 1.01408i) q^{34} +(-1.67516 - 0.967153i) q^{35} +(2.79769 - 5.30782i) q^{36} +(-4.61364 + 2.66369i) q^{37} +(0.989402 - 0.291842i) q^{38} +(4.14354 + 0.386644i) q^{39} +(-0.0815103 + 6.70149i) q^{40} +(-1.29167 - 7.32541i) q^{41} +(1.25558 - 1.55625i) q^{42} +(4.42023 - 5.26782i) q^{43} +(8.88696 + 6.72878i) q^{44} +(-1.15342 - 7.01433i) q^{45} +(8.60405 - 4.27752i) q^{46} +(-10.2350 + 3.72522i) q^{47} +(-6.83131 - 1.15463i) q^{48} +(-4.85182 + 4.07116i) q^{49} +(0.516184 + 0.699256i) q^{50} +(1.34089 + 5.12243i) q^{51} +(-1.07024 - 4.68464i) q^{52} -2.99582i q^{53} +(7.34825 - 0.0566171i) q^{54} +13.2064 q^{55} +(-2.15993 - 0.816032i) q^{56} +(0.888170 + 0.898491i) q^{57} +(-10.6791 + 7.88321i) q^{58} +(-0.837520 - 0.998118i) q^{59} +(-7.27828 + 3.79494i) q^{60} +(0.528763 + 1.45277i) q^{61} +(2.59821 - 1.29171i) q^{62} +(2.40672 + 0.453099i) q^{63} +(1.19715 + 7.90992i) q^{64} +(-4.36120 - 3.65948i) q^{65} +(-2.11133 + 13.4879i) q^{66} +(4.70399 - 0.829441i) q^{67} +(5.13539 - 3.31826i) q^{68} +(9.60078 + 6.80553i) q^{69} +(-2.62376 + 0.773926i) q^{70} +(-4.37210 - 7.57270i) q^{71} +(-2.71224 - 8.04013i) q^{72} +(-2.62609 + 4.54853i) q^{73} +(-1.76718 + 7.32386i) q^{74} +(-0.455432 + 0.962127i) q^{75} +(0.665269 - 1.29830i) q^{76} +(-1.55613 + 4.27542i) q^{77} +(4.43472 - 3.86912i) q^{78} +(-0.739506 + 4.19395i) q^{79} +(6.78770 + 6.61516i) q^{80} +(4.31872 + 7.89612i) q^{81} +(-8.76541 - 5.81615i) q^{82} +(14.1745 + 2.49935i) q^{83} +(-0.370958 - 2.80342i) q^{84} +(2.47752 - 6.80694i) q^{85} +(-1.08984 - 9.66379i) q^{86} +(-14.6937 - 6.95541i) q^{87} +(15.5568 - 2.54840i) q^{88} +(4.96560 - 8.60067i) q^{89} +(-8.31190 - 5.65461i) q^{90} +(1.69860 - 0.980687i) q^{91} +(4.00272 - 12.9858i) q^{92} +(2.89920 + 2.05510i) q^{93} +(-6.15825 + 14.1188i) q^{94} +(-0.300125 - 1.70209i) q^{95} +(-7.84134 + 5.87481i) q^{96} +(-11.8735 - 9.96305i) q^{97} +(-0.557054 + 8.93973i) q^{98} +(-15.7771 + 5.53682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

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