LMFDB - Embedded newform 243.2.i.a.103.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("243.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			103.23
Character	$\chi$	$=$	243.103
Dual form			243.2.i.a.151.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.02543 + 0.563818i) q^{2} +(-0.0981720 - 1.72927i) q^{3} +(2.07216 + 1.25056i) q^{4} +(-1.27054 + 0.0493029i) q^{5} +(0.776151 - 3.55787i) q^{6} +(4.39851 + 0.687914i) q^{7} +(0.606370 + 0.642715i) q^{8} +(-2.98072 + 0.339531i) q^{9} +(-2.60120 - 0.616496i) q^{10} +(0.0413646 + 0.302842i) q^{11} +(1.95912 - 3.70609i) q^{12} +(1.95043 - 2.84380i) q^{13} +(8.52104 + 3.87329i) q^{14} +(0.209990 + 2.19227i) q^{15} +(-1.39012 - 2.63908i) q^{16} +(-6.95270 + 3.49177i) q^{17} +(-6.22870 - 0.992889i) q^{18} +(0.466686 + 8.01269i) q^{19} +(-2.69443 - 1.48672i) q^{20} +(0.757777 - 7.67373i) q^{21} +(-0.0869667 + 0.636709i) q^{22} +(1.39733 - 3.61918i) q^{23} +(1.05190 - 1.11167i) q^{24} +(-3.37311 + 0.262179i) q^{25} +(5.55385 - 4.66024i) q^{26} +(0.879763 + 5.12113i) q^{27} +(8.25415 + 6.92605i) q^{28} +(2.53701 + 1.81334i) q^{29} +(-0.810721 + 4.55869i) q^{30} +(-2.85491 + 3.27137i) q^{31} +(-1.70176 - 7.85622i) q^{32} +(0.519634 - 0.101261i) q^{33} +(-16.0510 + 3.15231i) q^{34} +(-5.62241 - 0.657166i) q^{35} +(-6.60114 - 3.02400i) q^{36} +(1.50445 + 2.02083i) q^{37} +(-3.57246 + 16.4923i) q^{38} +(-5.10916 - 3.09363i) q^{39} +(-0.802107 - 0.786701i) q^{40} +(-0.728308 + 2.82746i) q^{41} +(5.86142 - 15.1154i) q^{42} +(-6.63437 - 6.02037i) q^{43} +(-0.293007 + 0.679266i) q^{44} +(3.77040 - 0.578347i) q^{45} +(4.87077 - 6.54258i) q^{46} +(-0.229710 - 0.263218i) q^{47} +(-4.42720 + 2.66297i) q^{48} +(12.2079 + 3.91431i) q^{49} +(-6.97985 - 1.37080i) q^{50} +(6.72077 + 11.6803i) q^{51} +(7.59793 - 3.45368i) q^{52} +(0.771083 - 4.37303i) q^{53} +(-1.10549 + 10.8686i) q^{54} +(-0.0674864 - 0.382735i) q^{55} +(2.22499 + 3.24412i) q^{56} +(13.8103 - 1.59365i) q^{57} +(4.11614 + 5.10322i) q^{58} +(2.57549 - 1.05221i) q^{59} +(-2.30642 + 4.80534i) q^{60} +(10.2081 - 6.16060i) q^{61} +(-7.62689 + 5.01629i) q^{62} +(-13.3443 - 0.557053i) q^{63} +(0.635797 - 10.9162i) q^{64} +(-2.33790 + 3.70933i) q^{65} +(1.10958 + 0.0878816i) q^{66} +(5.48432 - 3.91995i) q^{67} +(-18.7738 - 1.45921i) q^{68} +(-6.39571 - 2.06106i) q^{69} +(-11.0173 - 4.50107i) q^{70} +(-0.934287 - 3.12074i) q^{71} +(-2.02564 - 1.70987i) q^{72} +(-4.31382 + 1.02239i) q^{73} +(1.90779 + 4.94130i) q^{74} +(0.784523 + 5.80728i) q^{75} +(-9.05327 + 17.1872i) q^{76} +(-0.0263870 + 1.36051i) q^{77} +(-8.60402 - 9.14659i) q^{78} +(9.02377 - 8.85045i) q^{79} +(1.89632 + 3.28453i) q^{80} +(8.76944 - 2.02410i) q^{81} +(-3.06932 + 5.31621i) q^{82} +(-0.101470 - 0.393932i) q^{83} +(11.1667 - 14.9536i) q^{84} +(8.66155 - 4.77924i) q^{85} +(-10.0431 - 15.9345i) q^{86} +(2.88669 - 4.56518i) q^{87} +(-0.169559 + 0.210220i) q^{88} +(2.03708 - 6.80431i) q^{89} +(7.96278 + 0.954416i) q^{90} +(10.5353 - 11.1667i) q^{91} +(7.42149 - 5.75209i) q^{92} +(5.93734 + 4.61575i) q^{93} +(-0.316855 - 0.662646i) q^{94} +(-0.987994 - 10.1575i) q^{95} +(-13.4184 + 3.71407i) q^{96} +(-11.4753 - 0.445293i) q^{97} +(22.5194 + 14.8112i) q^{98} +(-0.226121 - 0.888644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) $ 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.02543	+	0.563818i	1.43220	+	0.398680i	0.895488	−	0.445086i	$-0.146827\pi$
$2$	2.02543	+	0.563818i	1.43220	+	0.398680i	0.536711	+	0.843766i	$0.319667\pi$
$3$	−0.0981720	−	1.72927i	−0.0566796	−	0.998392i
$3$	−0.0981720	−	1.72927i	−0.0566796	−	0.998392i
$4$	2.07216	+	1.25056i	1.03608	+	0.625278i
$5$	−1.27054	+	0.0493029i	−0.568204	+	0.0220489i	−0.321277	−	0.946985i	$-0.604112\pi$
$5$	−1.27054	+	0.0493029i	−0.568204	+	0.0220489i	−0.246927	+	0.969034i	$0.579421\pi$
$6$	0.776151	−	3.55787i	0.316862	−	1.45249i
$7$	4.39851	+	0.687914i	1.66248	+	0.260007i	0.914757	−	0.404004i	$-0.132382\pi$
$7$	4.39851	+	0.687914i	1.66248	+	0.260007i	0.747723	+	0.664011i	$0.231147\pi$
$8$	0.606370	+	0.642715i	0.214384	+	0.227234i
$9$	−2.98072	+	0.339531i	−0.993575	+	0.113177i
$10$	−2.60120	−	0.616496i	−0.822572	−	0.194953i
$11$	0.0413646	+	0.302842i	0.0124719	+	0.0913103i	0.995984	−	0.0895324i	$-0.0285373\pi$
$11$	0.0413646	+	0.302842i	0.0124719	+	0.0913103i	−0.983512	+	0.180843i	$0.942118\pi$
$12$	1.95912	−	3.70609i	0.565548	−	1.06986i
$13$	1.95043	−	2.84380i	0.540952	−	0.788727i	−0.453793	−	0.891107i	$-0.649930\pi$
$13$	1.95043	−	2.84380i	0.540952	−	0.788727i	0.994745	+	0.102380i	$0.0326456\pi$
$14$	8.52104	+	3.87329i	2.27734	+	1.03518i
$15$	0.209990	+	2.19227i	0.0542191	+	0.566041i
$16$	−1.39012	−	2.63908i	−0.347530	−	0.659770i
$17$	−6.95270	+	3.49177i	−1.68628	+	0.846880i	−0.694412	+	0.719577i	$0.744336\pi$
$17$	−6.95270	+	3.49177i	−1.68628	+	0.846880i	−0.991864	+	0.127303i	$0.959368\pi$
$18$	−6.22870	−	0.992889i	−1.46812	−	0.234026i
$19$	0.466686	+	8.01269i	0.107065	+	1.83824i	0.443199	+	0.896423i	$0.353843\pi$
$19$	0.466686	+	8.01269i	0.107065	+	1.83824i	−0.336134	+	0.941814i	$0.609120\pi$
$20$	−2.69443	−	1.48672i	−0.602492	−	0.332441i
$21$	0.757777	−	7.67373i	0.165360	−	1.67454i
$22$	−0.0869667	+	0.636709i	−0.0185414	+	0.135747i
$23$	1.39733	−	3.61918i	0.291364	−	0.754652i	−0.707487	−	0.706727i	$-0.750171\pi$
$23$	1.39733	−	3.61918i	0.291364	−	0.754652i	0.998851	−	0.0479255i	$-0.0152610\pi$
$24$	1.05190	−	1.11167i	0.214717	−	0.226919i
$25$	−3.37311	+	0.262179i	−0.674623	+	0.0524358i
$26$	5.55385	−	4.66024i	1.08920	−	0.913948i
$27$	0.879763	+	5.12113i	0.169310	+	0.985563i
$28$	8.25415	+	6.92605i	1.55989	+	1.30890i
$29$	2.53701	+	1.81334i	0.471110	+	0.336729i	0.792140	−	0.610340i	$-0.208967\pi$
$29$	2.53701	+	1.81334i	0.471110	+	0.336729i	−0.321030	+	0.947069i	$0.604029\pi$
$30$	−0.810721	+	4.55869i	−0.148017	+	0.832299i
$31$	−2.85491	+	3.27137i	−0.512757	+	0.587555i	−0.950180	−	0.311701i	$-0.899101\pi$
$31$	−2.85491	+	3.27137i	−0.512757	+	0.587555i	0.437423	+	0.899256i	$0.355891\pi$
$32$	−1.70176	−	7.85622i	−0.300832	−	1.38880i
$33$	0.519634	−	0.101261i	0.0904566	−	0.0176273i
$34$	−16.0510	+	3.15231i	−2.75272	+	0.540616i
$35$	−5.62241	−	0.657166i	−0.950361	−	0.111081i
$36$	−6.60114	−	3.02400i	−1.10019	−	0.504000i
$37$	1.50445	+	2.02083i	0.247331	+	0.332223i	0.908400	−	0.418102i	$-0.137305\pi$
$37$	1.50445	+	2.02083i	0.247331	+	0.332223i	−0.661069	+	0.750325i	$0.729897\pi$
$38$	−3.57246	+	16.4923i	−0.579529	+	2.67541i
$39$	−5.10916	−	3.09363i	−0.818120	−	0.495378i
$40$	−0.802107	−	0.786701i	−0.126824	−	0.124388i
$41$	−0.728308	+	2.82746i	−0.113743	+	0.441576i	−0.999756	−	0.0220836i	$-0.992970\pi$
$41$	−0.728308	+	2.82746i	−0.113743	+	0.441576i	0.886014	+	0.463659i	$0.153464\pi$
$42$	5.86142	−	15.1154i	0.904436	−	2.33236i
$43$	−6.63437	−	6.02037i	−1.01173	−	0.918098i	−0.0150828	−	0.999886i	$-0.504801\pi$
$43$	−6.63437	−	6.02037i	−1.01173	−	0.918098i	−0.996650	+	0.0817879i	$0.973937\pi$
$44$	−0.293007	+	0.679266i	−0.0441724	+	0.102403i
$45$	3.77040	−	0.578347i	0.562058	−	0.0862149i
$46$	4.87077	−	6.54258i	0.718156	−	0.964651i
$47$	−0.229710	−	0.263218i	−0.0335066	−	0.0383943i	0.736438	−	0.676505i	$-0.236506\pi$
$47$	−0.229710	−	0.263218i	−0.0335066	−	0.0383943i	−0.769945	+	0.638111i	$0.779716\pi$
$48$	−4.42720	+	2.66297i	−0.639011	+	0.384367i
$49$	12.2079	+	3.91431i	1.74399	+	0.559188i
$50$	−6.97985	−	1.37080i	−0.987099	−	0.193860i
$51$	6.72077	+	11.6803i	0.941096	+	1.63556i
$52$	7.59793	−	3.45368i	1.05364	−	0.478940i
$53$	0.771083	−	4.37303i	0.105916	−	0.600682i	−0.884934	−	0.465716i	$-0.845797\pi$
$53$	0.771083	−	4.37303i	0.105916	−	0.600682i	0.990850	−	0.134965i	$-0.0430922\pi$
$54$	−1.10549	+	10.8686i	−0.150438	+	1.47902i
$55$	−0.0674864	−	0.382735i	−0.00909987	−	0.0516079i
$56$	2.22499	+	3.24412i	0.297327	+	0.433513i
$57$	13.8103	−	1.59365i	1.82921	−	0.211084i
$58$	4.11614	+	5.10322i	0.540476	+	0.670085i
$59$	2.57549	−	1.05221i	0.335301	−	0.136985i	−0.204296	−	0.978909i	$-0.565490\pi$
$59$	2.57549	−	1.05221i	0.335301	−	0.136985i	0.539596	+	0.841924i	$0.318577\pi$
$60$	−2.30642	+	4.80534i	−0.297758	+	0.620366i
$61$	10.2081	−	6.16060i	1.30701	−	0.788784i	0.319688	−	0.947523i	$-0.396422\pi$
$61$	10.2081	−	6.16060i	1.30701	−	0.788784i	0.987321	+	0.158739i	$0.0507429\pi$
$62$	−7.62689	+	5.01629i	−0.968617	+	0.637069i
$63$	−13.3443	−	0.557053i	−1.68123	−	0.0701821i
$64$	0.635797	−	10.9162i	0.0794747	−	1.36453i
$65$	−2.33790	+	3.70933i	−0.289981	+	0.460086i
$66$	1.10958	+	0.0878816i	0.136580	+	0.0108175i
$67$	5.48432	−	3.91995i	0.670016	−	0.478899i	−0.194895	−	0.980824i	$-0.562437\pi$
$67$	5.48432	−	3.91995i	0.670016	−	0.478899i	0.864911	+	0.501926i	$0.167375\pi$
$68$	−18.7738	−	1.45921i	−2.27665	−	0.176955i
$69$	−6.39571	−	2.06106i	−0.769953	−	0.248122i
$70$	−11.0173	−	4.50107i	−1.31682	−	0.537980i
$71$	−0.934287	−	3.12074i	−0.110879	−	0.370363i	0.884481	−	0.466576i	$-0.154512\pi$
$71$	−0.934287	−	3.12074i	−0.110879	−	0.370363i	−0.995361	+	0.0962123i	$0.969327\pi$
$72$	−2.02564	−	1.70987i	−0.238724	−	0.201511i
$73$	−4.31382	+	1.02239i	−0.504895	+	0.119662i	−0.475167	−	0.879896i	$-0.657612\pi$
$73$	−4.31382	+	1.02239i	−0.504895	+	0.119662i	−0.0297280	+	0.999558i	$0.509464\pi$
$74$	1.90779	+	4.94130i	0.221776	+	0.574415i
$75$	0.784523	+	5.80728i	0.0905889	+	0.670566i
$76$	−9.05327	+	17.1872i	−1.03848	+	1.97151i
$77$	−0.0263870	+	1.36051i	−0.00300708	+	0.155044i
$78$	−8.60402	−	9.14659i	−0.974214	−	1.03565i
$79$	9.02377	−	8.85045i	1.01525	−	0.995754i	0.0152622	−	0.999884i	$-0.495142\pi$
$79$	9.02377	−	8.85045i	1.01525	−	0.995754i	0.999991	+	0.00412970i	$0.00131453\pi$
$80$	1.89632	+	3.28453i	0.212015	+	0.367221i
$81$	8.76944	−	2.02410i	0.974382	−	0.224900i
$82$	−3.06932	+	5.31621i	−0.338949	+	0.587077i
$83$	−0.101470	−	0.393932i	−0.0111378	−	0.0432397i	0.962580	−	0.270999i	$-0.0873539\pi$
$83$	−0.101470	−	0.393932i	−0.0111378	−	0.0432397i	−0.973718	+	0.227759i	$0.926860\pi$
$84$	11.1667	−	14.9536i	1.21838	−	1.63157i
$85$	8.66155	−	4.77924i	0.939477	−	0.518381i
$86$	−10.0431	−	15.9345i	−1.08297	−	1.71826i
$87$	2.88669	−	4.56518i	0.309486	−	0.489438i
$88$	−0.169559	+	0.210220i	−0.0180750	+	0.0224095i
$89$	2.03708	−	6.80431i	0.215930	−	0.721256i	−0.779555	−	0.626334i	$-0.784555\pi$
$89$	2.03708	−	6.80431i	0.215930	−	0.721256i	0.995485	−	0.0949220i	$-0.0302602\pi$
$90$	7.96278	+	0.954416i	0.839351	+	0.100604i
$91$	10.5353	−	11.1667i	1.10440	−	1.17059i
$92$	7.42149	−	5.75209i	0.773744	−	0.599697i
$93$	5.93734	+	4.61575i	0.615673	+	0.478631i
$94$	−0.316855	−	0.662646i	−0.0326811	−	0.0683467i
$95$	−0.987994	−	10.1575i	−0.101366	−	1.04213i
$96$	−13.4184	+	3.71407i	−1.36951	+	0.379065i
$97$	−11.4753	−	0.445293i	−1.16514	−	0.0452127i	−0.551066	−	0.834462i	$-0.685779\pi$
$97$	−11.4753	−	0.445293i	−1.16514	−	0.0452127i	−0.614073	+	0.789249i	$0.710470\pi$
$98$	22.5194	+	14.8112i	2.27480	+	1.49616i
$99$	−0.226121	−	0.888644i	−0.0227260	−	0.0893121i
$100$	−7.31751	−	3.67499i	−0.731751	−	0.367499i
$101$	0.205424	+	10.5916i	0.0204405	+	1.05391i	0.859894	+	0.510473i	$0.170530\pi$
$101$	0.205424	+	10.5916i	0.0204405	+	1.05391i	−0.839453	+	0.543432i	$0.817125\pi$
$102$	7.02693	+	27.4469i	0.695770	+	2.71765i
$103$	−2.96955	−	2.30158i	−0.292598	−	0.226781i	0.455716	−	0.890125i	$-0.349383\pi$
$103$	−2.96955	−	2.30158i	−0.292598	−	0.226781i	−0.748314	+	0.663344i	$0.769136\pi$
$104$	3.01043	−	0.470823i	0.295197	−	0.0461680i
$105$	−0.584452	+	9.78717i	−0.0570366	+	0.955130i
$106$	4.02737	−	8.42253i	0.391173	−	0.818069i
$107$	−12.7984	−	4.65825i	−1.23727	−	0.450330i	−0.361190	−	0.932492i	$-0.617629\pi$
$107$	−12.7984	−	4.65825i	−1.23727	−	0.450330i	−0.876082	+	0.482162i	$0.839852\pi$
$108$	−4.58125	+	11.7120i	−0.440831	+	1.12699i
$109$	0.649699	−	0.236471i	0.0622299	−	0.0226498i	−0.310718	−	0.950502i	$-0.600569\pi$
$109$	0.649699	−	0.236471i	0.0622299	−	0.0226498i	0.372948	+	0.927852i	$0.378347\pi$
$110$	0.0791034	−	0.813254i	0.00754221	−	0.0775407i
$111$	3.34686	−	2.79999i	0.317670	−	0.265763i
$112$	−4.29900	−	12.5643i	−0.406217	−	1.18721i
$113$	−3.77910	+	3.42935i	−0.355508	+	0.322606i	−0.830116	−	0.557591i	$-0.811726\pi$
$113$	−3.77910	+	3.42935i	−0.355508	+	0.322606i	0.474608	+	0.880197i	$0.342590\pi$
$114$	28.8703	+	4.55865i	2.70395	+	0.426957i
$115$	−1.59694	+	4.66722i	−0.148915	+	0.435221i
$116$	2.98940	+	6.93020i	0.277559	+	0.643453i
$117$	−4.84814	+	9.13881i	−0.448211	+	0.844883i
$118$	5.80975	−	0.679062i	0.534831	−	0.0625127i
$119$	−32.9835	+	10.5757i	−3.02360	+	0.969477i
$120$	−1.28167	+	1.46429i	−0.117000	+	0.133671i
$121$	10.5071	−	2.92484i	0.955189	−	0.265895i
$122$	24.1492	−	6.72240i	2.18637	−	0.608617i
$123$	4.96094	+	0.981860i	0.447313	+	0.0885314i
$124$	−10.0069	+	3.20857i	−0.898643	+	0.288138i
$125$	10.5873	−	1.23747i	0.946955	−	0.110683i
$126$	−26.7140	−	8.65204i	−2.37987	−	0.770785i
$127$	1.90220	+	4.40979i	0.168793	+	0.391306i	0.981526	−	0.191331i	$-0.0612804\pi$
$127$	1.90220	+	4.40979i	0.168793	+	0.391306i	−0.812733	+	0.582637i	$0.802021\pi$
$128$	2.23791	−	6.54054i	0.197805	−	0.578107i
$129$	−9.75952	+	12.0636i	−0.859278	+	1.06214i
$130$	−6.82665	+	6.19485i	−0.598737	+	0.543325i
$131$	4.74803	+	13.8766i	0.414837	+	1.21241i	0.933857	+	0.357646i	$0.116420\pi$
$131$	4.74803	+	13.8766i	0.414837	+	1.21241i	−0.519020	+	0.854762i	$0.673703\pi$
$132$	1.20340	+	0.440002i	0.104742	+	0.0382973i
$133$	−3.45932	+	35.5649i	−0.299961	+	3.08387i
$134$	13.3183	−	4.84745i	1.15052	−	0.418756i
$135$	−1.37026	−	6.46325i	−0.117934	−	0.556268i
$136$	−6.46012	−	2.35129i	−0.553951	−	0.201622i
$137$	7.61387	−	15.9231i	0.650497	−	1.36040i	−0.267402	−	0.963585i	$-0.586165\pi$
$137$	7.61387	−	15.9231i	0.650497	−	1.36040i	0.917899	−	0.396814i	$-0.129884\pi$
$138$	−11.7920	−	7.78056i	−1.00380	−	0.662325i
$139$	−0.742794	+	0.116171i	−0.0630030	+	0.00985349i	−0.185942	−	0.982561i	$-0.559534\pi$
$139$	−0.742794	+	0.116171i	−0.0630030	+	0.00985349i	0.122939	+	0.992414i	$0.460768\pi$
$140$	−10.8287	−	8.39290i	−0.915194	−	0.709329i
$141$	−0.432623	+	0.423070i	−0.0364335	+	0.0356289i
$142$	−0.132809	−	6.84762i	−0.0111451	−	0.574639i
$143$	0.941900	+	0.473040i	0.0787656	+	0.0395576i
$144$	5.03962	+	7.39438i	0.419968	+	0.616198i
$145$	−3.31278	−	2.17885i	−0.275111	−	0.180944i
$146$	−9.31381	−	0.361418i	−0.770816	−	0.0299112i
$147$	5.57042	−	21.4950i	0.459440	−	1.77288i
$148$	0.590307	+	6.06889i	0.0485230	+	0.498860i
$149$	5.05212	+	10.5656i	0.413886	+	0.865569i	0.998526	+	0.0542762i	$0.0172852\pi$
$149$	5.05212	+	10.5656i	0.413886	+	0.865569i	−0.584640	+	0.811293i	$0.698764\pi$
$150$	−1.68525	+	12.2046i	−0.137600	+	0.996500i
$151$	−13.9478	+	10.8104i	−1.13506	+	0.879736i	−0.993904	−	0.110252i	$-0.964834\pi$
$151$	−13.9478	+	10.8104i	−1.13506	+	0.879736i	−0.141154	+	0.989988i	$0.545081\pi$
$152$	−4.86689	+	5.15860i	−0.394757	+	0.418418i
$153$	19.5385	−	12.7687i	1.57959	−	1.03229i
$154$	−0.820525	+	2.74075i	−0.0661198	+	0.220856i
$155$	3.46600	−	4.29717i	0.278396	−	0.345157i
$156$	−6.71824	−	12.7998i	−0.537890	−	1.02480i
$157$	−0.227240	−	0.360541i	−0.0181358	−	0.0287743i	0.836796	−	0.547514i	$-0.184426\pi$
$157$	−0.227240	−	0.360541i	−0.0181358	−	0.0287743i	−0.854932	+	0.518740i	$0.826401\pi$
$158$	23.2671	−	12.8382i	1.85103	−	1.02136i
$159$	−7.63783	−	0.904099i	−0.605719	−	0.0716997i
$160$	2.54950	+	9.89777i	0.201556	+	0.782487i
$161$	8.63587	−	14.9578i	0.680602	−	1.17884i
$162$	18.9031	+	0.844694i	1.48517	+	0.0663654i
$163$	0.971273	+	1.68229i	0.0760760	+	0.131767i	0.901554	−	0.432667i	$-0.142428\pi$
$163$	0.971273	+	1.68229i	0.0760760	+	0.131767i	−0.825478	+	0.564435i	$0.809094\pi$
$164$	−5.04507	+	4.94817i	−0.393954	+	0.386387i
$165$	−0.655225	+	0.154276i	−0.0510092	+	0.0120104i
$166$	0.0165846	−	0.855095i	0.00128721	−	0.0663683i
$167$	6.65976	−	12.6433i	0.515348	−	0.978364i	−0.479553	−	0.877513i	$-0.659201\pi$
$167$	6.65976	−	12.6433i	0.515348	−	0.978364i	0.994901	−	0.100851i	$-0.0321567\pi$
$168$	5.39151	−	4.16608i	0.415964	−	0.321420i
$169$	0.399308	+	1.03423i	0.0307160	+	0.0795565i
$170$	20.2380	−	4.79650i	1.55219	−	0.367875i
$171$	−4.11162	−	23.7252i	−0.314423	−	1.81431i
$172$	−6.21868	−	20.7718i	−0.474170	−	1.58384i
$173$	6.34793	+	2.59341i	0.482624	+	0.197174i	0.606436	−	0.795132i	$-0.292598\pi$
$173$	6.34793	+	2.59341i	0.482624	+	0.197174i	−0.123812	+	0.992306i	$0.539512\pi$
$174$	8.42073	−	7.61890i	0.638374	−	0.577587i
$175$	−15.0170	−	1.16722i	−1.13518	−	0.0882333i
$176$	0.741722	−	0.530151i	0.0559094	−	0.0399617i
$177$	−2.07238	−	4.35042i	−0.155770	−	0.326998i
$178$	7.96237	−	12.6332i	0.596805	−	0.946895i
$179$	−0.396395	+	6.80583i	−0.0296279	+	0.508692i	0.950550	+	0.310572i	$0.100521\pi$
$179$	−0.396395	+	6.80583i	−0.0296279	+	0.508692i	−0.980178	+	0.198120i	$0.936516\pi$
$180$	8.53613	+	3.51667i	0.636246	+	0.262117i
$181$	−4.77429	+	3.14010i	−0.354870	+	0.233402i	−0.714409	−	0.699728i	$-0.753304\pi$
$181$	−4.77429	+	3.14010i	−0.354870	+	0.233402i	0.359539	+	0.933130i	$0.382934\pi$
$182$	27.6345	−	16.6775i	2.04841	−	1.23622i
$183$	−11.6555	−	17.0477i	−0.861596	−	1.26020i
$184$	3.17340	−	1.29648i	0.233946	−	0.0955776i
$185$	−2.01111	−	2.49338i	−0.147859	−	0.183317i
$186$	9.42324	+	12.6965i	0.690946	+	0.930951i
$187$	−1.34505	−	1.96113i	−0.0983599	−	0.143412i
$188$	−0.146827	−	0.832695i	−0.0107084	−	0.0607306i
$189$	0.346744	+	23.1306i	0.0252219	+	1.68250i
$190$	3.72585	−	21.1303i	0.270301	−	1.53295i
$191$	−5.62928	+	2.55882i	−0.407320	+	0.185150i	−0.606983	−	0.794715i	$-0.707620\pi$
$191$	−5.62928	+	2.55882i	−0.407320	+	0.185150i	0.199663	+	0.979865i	$0.436015\pi$
$192$	−18.9395	−	0.0277964i	−1.36684	−	0.00200603i
$193$	4.91108	+	0.964505i	0.353507	+	0.0694266i	0.366314	−	0.930491i	$-0.380620\pi$
$193$	4.91108	+	0.964505i	0.353507	+	0.0694266i	−0.0128064	+	0.999918i	$0.504077\pi$
$194$	−22.9914	−	7.37189i	−1.65068	−	0.529271i
$195$	6.64393	+	3.67870i	0.475782	+	0.263437i
$196$	20.4017	+	23.3778i	1.45727	+	1.66984i
$197$	−5.70503	+	7.66319i	−0.406467	+	0.545980i	−0.957474	−	0.288521i	$-0.906836\pi$
$197$	−5.70503	+	7.66319i	−0.406467	+	0.545980i	0.551007	+	0.834501i	$0.314244\pi$
$198$	0.0430414	−	1.92738i	0.00305882	−	0.136973i
$199$	2.17258	−	5.03661i	0.154010	−	0.357036i	−0.823690	−	0.567040i	$-0.808088\pi$
$199$	2.17258	−	5.03661i	0.154010	−	0.357036i	0.977701	+	0.210004i	$0.0673477\pi$
$200$	−2.21386	−	2.00897i	−0.156544	−	0.142056i
$201$	−7.31705	−	9.09902i	−0.516105	−	0.641795i
$202$	−5.55567	+	21.5684i	−0.390896	+	1.51755i
$203$	9.91162	+	9.72125i	0.695659	+	0.682298i
$204$	−0.680310	+	32.6081i	−0.0476312	+	2.28302i
$205$	0.785944	−	3.62832i	0.0548927	−	0.253413i
$206$	−4.71696	−	6.33598i	−0.328646	−	0.441448i
$207$	−2.93624	+	11.2622i	−0.204083	+	0.782779i
$208$	−10.2163	−	1.19412i	−0.708375	−	0.0827972i
$209$	−2.40728	+	0.472774i	−0.166515	+	0.0327024i
$210$	−6.70195	+	19.4937i	−0.462479	+	1.34520i
$211$	2.63348	+	12.1575i	0.181296	+	0.836957i	0.973857	+	0.227163i	$0.0729452\pi$
$211$	2.63348	+	12.1575i	0.181296	+	0.836957i	−0.792560	+	0.609794i	$0.791252\pi$
$212$	7.06652	−	8.09734i	0.485331	−	0.556127i
$213$	−5.30486	+	1.92200i	−0.363483	+	0.131693i
$214$	−23.2960	−	16.6510i	−1.59248	−	1.13824i
$215$	8.72608	+	7.32205i	0.595114	+	0.499360i
$216$	−2.75797	+	3.67074i	−0.187656	+	0.249762i
$217$	−14.8078	+	12.4252i	−1.00522	+	0.843478i
$218$	1.44925	−	0.112645i	0.0981556	−	0.00762925i
$219$	2.19149	+	7.35938i	0.148087	+	0.497301i
$220$	0.338788	−	0.877483i	0.0228411	−	0.0591599i
$221$	−3.63085	+	26.5825i	−0.244237	+	1.78813i
$222$	8.35753	−	3.78417i	0.560921	−	0.253977i
$223$	−17.6050	−	9.71405i	−1.17892	−	0.650501i	−0.232235	−	0.972660i	$-0.574604\pi$
$223$	−17.6050	−	9.71405i	−1.17892	−	0.650501i	−0.946686	+	0.322158i	$0.895592\pi$
$224$	−2.08082	−	35.7263i	−0.139031	−	2.38707i
$225$	9.96531	−	1.92676i	0.664354	−	0.128451i
$226$	−9.58785	+	4.81520i	−0.637774	+	0.320302i
$227$	−11.2474	−	21.3527i	−0.746519	−	1.41723i	−0.903040	−	0.429556i	$-0.858670\pi$
$227$	−11.2474	−	21.3527i	−0.746519	−	1.41723i	0.156521	−	0.987675i	$-0.449972\pi$
$228$	30.6100	+	13.9682i	2.02720	+	0.925067i
$229$	−8.99223	−	4.08747i	−0.594223	−	0.270108i	0.0940401	−	0.995568i	$-0.470022\pi$
$229$	−8.99223	−	4.08747i	−0.594223	−	0.270108i	−0.688264	+	0.725461i	$0.741627\pi$
$230$	−5.86596	+	8.55277i	−0.386790	+	0.563953i
$231$	2.35527	−	0.0879336i	0.154966	−	0.00578561i
$232$	0.372902	+	2.73013i	0.0244822	+	0.179242i
$233$	3.77592	+	0.894910i	0.247369	+	0.0586275i	0.352430	−	0.935838i	$-0.385356\pi$
$233$	3.77592	+	0.894910i	0.247369	+	0.0586275i	−0.105061	+	0.994466i	$0.533504\pi$
$234$	−14.9722	+	15.7766i	−0.978764	+	1.03135i
$235$	0.304834	+	0.323105i	0.0198852	+	0.0210770i
$236$	6.65268	+	1.04046i	0.433053	+	0.0677282i
$237$	−16.1907	−	14.7356i	−1.05170	−	0.957183i
$238$	−72.7688	+	2.82376i	−4.71690	+	0.183037i
$239$	−16.1160	−	9.72608i	−1.04246	−	0.629128i	−0.111318	−	0.993785i	$-0.535507\pi$
$239$	−16.1160	−	9.72608i	−1.04246	−	0.629128i	−0.931142	+	0.364657i	$0.881186\pi$
$240$	5.49366	−	3.60170i	0.354614	−	0.232488i
$241$	−7.39774	−	2.05930i	−0.476531	−	0.132651i	0.0215759	−	0.999767i	$-0.493132\pi$
$241$	−7.39774	−	2.05930i	−0.476531	−	0.132651i	−0.498107	+	0.867116i	$0.665971\pi$
$242$	22.9305			1.47403
$243$	−4.36111	−	14.9660i	−0.279766	−	0.960068i
$244$	28.8569			1.84738
$245$	−15.7037	−	4.37142i	−1.00327	−	0.279280i
$246$	9.49447	+	4.78576i	0.605345	+	0.305129i
$247$	23.6967	+	14.3010i	1.50778	+	0.909953i
$248$	−3.83369	+	0.148765i	−0.243439	+	0.00944656i
$249$	−0.671252	+	0.214142i	−0.0425389	+	0.0135707i
$250$	22.1415	+	3.46287i	1.40035	+	0.219011i
$251$	14.2128	+	15.0647i	0.897105	+	0.950876i	0.999035	−	0.0439158i	$-0.0139833\pi$
$251$	14.2128	+	15.0647i	0.897105	+	0.950876i	−0.101930	+	0.994792i	$0.532502\pi$
$252$	−26.9549	−	17.8421i	−1.69800	−	1.12395i
$253$	1.15384	+	0.273465i	0.0725414	+	0.0171926i
$254$	1.36646	+	10.0042i	0.0857392	+	0.627722i
$255$	−9.11490	−	14.5089i	−0.570797	−	0.908585i
$256$	−4.14909	+	6.04952i	−0.259318	+	0.378095i
$257$	−5.95450	−	2.70665i	−0.371431	−	0.168836i	0.219393	−	0.975637i	$-0.429592\pi$
$257$	−5.95450	−	2.70665i	−0.371431	−	0.168836i	−0.590824	+	0.806800i	$0.701197\pi$
$258$	−26.5690	+	18.9315i	−1.65411	+	1.17862i
$259$	5.22719	+	9.92358i	0.324802	+	0.616621i
$260$	−9.48323	+	4.76265i	−0.588125	+	0.295367i
$261$	−8.17780	−	4.54368i	−0.506193	−	0.281247i
$262$	1.79292	+	30.7833i	0.110767	+	1.90180i
$263$	−4.77665	−	2.63564i	−0.294541	−	0.162521i	0.328959	−	0.944344i	$-0.393302\pi$
$263$	−4.77665	−	2.63564i	−0.294541	−	0.162521i	−0.623500	+	0.781823i	$0.714290\pi$
$264$	0.380172	+	0.272575i	0.0233980	+	0.0167758i
$265$	−0.764091	+	5.59414i	−0.0469378	+	0.343645i
$266$	−27.0588	+	70.0840i	−1.65908	+	4.29713i
$267$	−11.9665	−	2.85466i	−0.732335	−	0.174702i
$268$	16.2665	−	1.26433i	0.993635	−	0.0772314i
$269$	−14.2376	+	11.9467i	−0.868079	+	0.728405i	−0.963693	−	0.267014i	$-0.913963\pi$
$269$	−14.2376	+	11.9467i	−0.868079	+	0.728405i	0.0956136	+	0.995419i	$0.469519\pi$
$270$	0.868718	−	13.8635i	0.0528685	−	0.843704i
$271$	2.60029	+	2.18190i	0.157956	+	0.132541i	0.718340	−	0.695692i	$-0.244902\pi$
$271$	2.60029	+	2.18190i	0.157956	+	0.132541i	−0.560384	+	0.828233i	$0.689347\pi$
$272$	18.8802	+	13.4947i	1.14478	+	0.818238i
$273$	−20.3445	−	17.1220i	−1.23131	−	1.03627i
$274$	24.3991	−	27.9583i	1.47400	−	1.68902i
$275$	−0.218926	−	1.01068i	−0.0132018	−	0.0609461i
$276$	−10.6755	−	12.2690i	−0.642588	−	0.738510i
$277$	11.8391	−	2.32513i	0.711345	−	0.139704i	0.176065	−	0.984378i	$-0.443663\pi$
$277$	11.8391	−	2.32513i	0.711345	−	0.139704i	0.535280	+	0.844675i	$0.320206\pi$
$278$	−1.56998	−	0.183504i	−0.0941612	−	0.0110059i
$279$	7.39898	−	10.7204i	0.442965	−	0.641812i
$280$	−2.98689	−	4.01209i	−0.178501	−	0.239768i
$281$	4.81522	−	22.2295i	0.287252	−	1.32610i	−0.574389	−	0.818583i	$-0.694760\pi$
$281$	4.81522	−	22.2295i	0.287252	−	1.32610i	0.861640	−	0.507519i	$-0.169437\pi$
$282$	−1.11479	+	0.612980i	−0.0663845	+	0.0365024i
$283$	1.16736	+	1.14494i	0.0693924	+	0.0680596i	0.734086	−	0.679056i	$-0.237611\pi$
$283$	1.16736	+	1.14494i	0.0693924	+	0.0680596i	−0.664694	+	0.747116i	$0.731438\pi$
$284$	1.96666	−	7.63505i	0.116700	−	0.453057i
$285$	−17.4680	+	2.70568i	−1.03471	+	0.160271i
$286$	1.64105	+	1.48917i	0.0970372	+	0.0880566i
$287$	−5.14852	+	11.9356i	−0.303908	+	0.704537i
$288$	7.73992	+	22.8394i	0.456079	+	1.34583i
$289$	25.9958	−	34.9184i	1.52916	−	2.05402i
$290$	−5.48134	−	6.28092i	−0.321875	−	0.368828i
$291$	0.356520	+	19.8875i	0.0208996	+	1.16583i
$292$	−10.2175	−	3.27611i	−0.597934	−	0.191720i
$293$	30.2253	+	5.93605i	1.76578	+	0.346788i	0.966988	−	0.254821i	$-0.0820165\pi$
$293$	30.2253	+	5.93605i	1.76578	+	0.346788i	0.798791	+	0.601608i	$0.205473\pi$
$294$	23.4018	−	40.3961i	1.36482	−	2.35595i
$295$	−3.22040	+	1.46385i	−0.187499	+	0.0852287i
$296$	−0.386563	+	2.19231i	−0.0224685	+	0.127425i
$297$	−1.51450	+	0.478263i	−0.0878804	+	0.0277516i
$298$	4.27566	+	24.2484i	0.247682	+	1.40467i
$299$	−7.56682	−	11.0327i	−0.437601	−	0.638037i
$300$	−5.63666	+	13.0147i	−0.325433	+	0.751404i
$301$	−25.0399	−	31.0446i	−1.44327	−	1.78938i
$302$	−34.3455	+	14.0317i	−1.97636	+	0.807432i
$303$	18.2956	−	1.39503i	1.05105	−	0.0801425i
$304$	20.4974	−	12.3702i	1.17560	−	0.709481i
$305$	−12.6661	+	8.33059i	−0.725256	+	0.477008i
$306$	46.7732	−	14.8460i	2.67384	−	0.848687i
$307$	−0.327766	+	5.62752i	−0.0187066	+	0.321179i	0.975954	+	0.217977i	$0.0699459\pi$
$307$	−0.327766	+	5.62752i	−0.0187066	+	0.321179i	−0.994660	+	0.103202i	$0.967091\pi$
$308$	−1.75607	+	2.78620i	−0.100061	+	0.158758i
$309$	−3.68851	+	5.36109i	−0.209832	+	0.304982i
$310$	9.44298	−	6.74944i	0.536325	−	0.383342i
$311$	−10.2693	−	0.798194i	−0.582319	−	0.0452614i	−0.217045	−	0.976162i	$-0.569642\pi$
$311$	−10.2693	−	0.798194i	−0.582319	−	0.0452614i	−0.365274	+	0.930900i	$0.619025\pi$
$312$	−1.10972	−	5.15962i	−0.0628254	−	0.292106i
$313$	−6.21727	−	2.54003i	−0.351421	−	0.143571i	0.195614	−	0.980681i	$-0.437330\pi$
$313$	−6.21727	−	2.54003i	−0.351421	−	0.143571i	−0.547035	+	0.837110i	$0.684244\pi$
$314$	−0.256981	−	0.858375i	−0.0145023	−	0.0484409i
$315$	16.9820	+	0.0498472i	0.956827	+	0.00280857i
$316$	29.7667	−	7.05484i	1.67451	−	0.396866i
$317$	7.94335	+	20.5738i	0.446143	+	1.15554i	0.955502	+	0.294985i	$0.0953148\pi$
$317$	7.94335	+	20.5738i	0.446143	+	1.15554i	−0.509359	+	0.860554i	$0.670117\pi$
$318$	−14.9602	−	6.13754i	−0.838925	−	0.344176i
$319$	−0.444214	+	0.843320i	−0.0248712	+	0.0472169i
$320$	−0.269607	+	13.9009i	−0.0150715	+	0.777082i
$321$	−6.79891	+	22.5892i	−0.379478	+	1.26081i
$322$	25.9249	−	25.4269i	1.44474	−	1.41699i
$323$	−31.2232	−	54.0802i	−1.73731	−	3.00910i
$324$	20.7029	+	6.77242i	1.15016	+	0.376245i
$325$	−5.83344	+	10.1038i	−0.323581	+	0.560459i
$326$	1.01874	+	3.95500i	0.0564229	+	0.219047i
$327$	−0.472704	−	1.10029i	−0.0261406	−	0.0608460i
$328$	−2.25888	+	1.24640i	−0.124726	+	0.0688207i
$329$	−0.829309	−	1.31579i	−0.0457213	−	0.0725418i
$330$	−1.41410	−	0.0569521i	−0.0778436	−	0.00313511i
$331$	−2.89324	+	3.58705i	−0.159027	+	0.197162i	−0.851610	−	0.524175i	$-0.824374\pi$
$331$	−2.89324	+	3.58705i	−0.159027	+	0.197162i	0.692584	+	0.721338i	$0.256472\pi$
$332$	0.282371	−	0.943186i	0.0154971	−	0.0517640i
$333$	−5.17050	−	5.51273i	−0.283341	−	0.302096i
$334$	20.6174	−	21.8532i	1.12813	−	1.19575i
$335$	−6.77480	+	5.25086i	−0.370147	+	0.286885i
$336$	−21.3050	+	8.66758i	−1.16228	+	0.472855i
$337$	−5.52792	−	11.5607i	−0.301125	−	0.629750i	0.694872	−	0.719133i	$-0.255461\pi$
$337$	−5.52792	−	11.5607i	−0.301125	−	0.629750i	−0.995997	+	0.0893836i	$0.971510\pi$
$338$	0.225653	+	2.31991i	0.0122739	+	0.126187i
$339$	6.30126	+	6.19840i	0.342237	+	0.336651i
$340$	23.9248	+	0.928392i	1.29751	+	0.0503491i
$341$	−1.10880	−	0.729269i	−0.0600449	−	0.0394921i
$342$	5.04887	−	50.3720i	0.273012	−	2.72381i
$343$	23.1549	+	11.6288i	1.25025	+	0.627899i
$344$	−0.153503	−	7.91458i	−0.00827633	−	0.426726i
$345$	8.22765	+	2.30334i	0.442962	+	0.124008i
$346$	11.3951	+	8.83187i	0.612605	+	0.474804i
$347$	29.6350	−	4.63483i	1.59089	−	0.248811i	0.703798	−	0.710400i	$-0.251486\pi$
$347$	29.6350	−	4.63483i	1.59089	−	0.248811i	0.887094	+	0.461589i	$0.152721\pi$
$348$	11.6907	−	5.84982i	0.626687	−	0.313583i
$349$	3.49423	−	7.30757i	0.187042	−	0.391165i	−0.787191	−	0.616709i	$-0.788465\pi$
$349$	3.49423	−	7.30757i	0.187042	−	0.391165i	0.974233	+	0.225544i	$0.0724160\pi$
$350$	−29.7579	−	10.8310i	−1.59063	−	0.578941i
$351$	16.2794	+	7.48655i	0.868929	+	0.399602i
$352$	2.30880	−	0.840335i	0.123060	−	0.0447900i
$353$	−1.94929	+	20.0405i	−0.103750	+	1.06665i	0.788478	+	0.615063i	$0.210869\pi$
$353$	−1.94929	+	20.0405i	−0.103750	+	1.06665i	−0.892229	+	0.451584i	$0.850859\pi$
$354$	−1.74463	−	9.97994i	−0.0927262	−	0.530428i
$355$	1.34091	+	3.91897i	0.0711683	+	0.207997i
$356$	12.7303	−	11.5522i	0.674706	−	0.612263i
$357$	21.5263	+	55.9991i	1.13929	+	2.96379i
$358$	−4.64012	+	13.5613i	−0.245238	+	0.716736i
$359$	3.83515	+	8.89089i	0.202412	+	0.469243i	0.988941	−	0.148310i	$-0.0473833\pi$
$359$	3.83515	+	8.89089i	0.202412	+	0.469243i	−0.786529	+	0.617553i	$0.788124\pi$
$360$	2.65797	+	2.07260i	0.140087	+	0.109236i
$361$	−45.1139	+	5.27306i	−2.37441	+	0.277529i
$362$	−11.4405	+	3.66823i	−0.601297	+	0.192798i
$363$	−6.08934	−	17.8824i	−0.319607	−	0.938582i
$364$	35.7954	−	9.96434i	1.87619	−	0.522273i
$365$	5.43049	−	1.51168i	0.284245	−	0.0791250i
$366$	−13.9956	−	41.1005i	−0.731561	−	2.14836i
$367$	−2.14957	+	0.689233i	−0.112207	+	0.0359777i	−0.360899	−	0.932605i	$-0.617530\pi$
$367$	−2.14957	+	0.689233i	−0.112207	+	0.0359777i	0.248692	+	0.968583i	$0.419999\pi$
$368$	−11.4938	+	1.34343i	−0.599154	+	0.0700311i
$369$	1.21087	−	8.67517i	0.0630355	−	0.451612i
$370$	−2.66755	−	6.18408i	−0.138679	−	0.321495i
$371$	6.39988	−	18.7044i	0.332265	−	0.971082i
$372$	6.53087	+	16.9895i	0.338610	+	0.880867i
$373$	2.71982	−	2.46810i	0.140827	−	0.127793i	−0.598550	−	0.801086i	$-0.704256\pi$
$373$	2.71982	−	2.46810i	0.140827	−	0.127793i	0.739377	+	0.673292i	$0.235120\pi$
$374$	−1.61859	−	4.73051i	−0.0836954	−	0.244609i
$375$	−3.17930	−	18.1867i	−0.164178	−	0.939159i
$376$	0.0298851	−	0.307245i	0.00154121	−	0.0158450i
$377$	10.1050	−	3.67793i	0.520435	−	0.189423i
$378$	−12.3391	+	47.0449i	−0.634656	+	2.41973i
$379$	−25.0947	−	9.13373i	−1.28903	−	0.469168i	−0.395620	−	0.918414i	$-0.629470\pi$
$379$	−25.0947	−	9.13373i	−1.28903	−	0.469168i	−0.893408	+	0.449246i	$0.851693\pi$
$380$	10.6552	−	22.2834i	0.546600	−	1.14312i
$381$	7.43896	−	3.72232i	0.381109	−	0.190700i
$382$	−12.8444	+	2.00884i	−0.657179	+	0.102781i
$383$	14.8230	+	11.4887i	0.757420	+	0.587045i	0.916413	−	0.400235i	$-0.131072\pi$
$383$	14.8230	+	11.4887i	0.757420	+	0.587045i	−0.158993	+	0.987280i	$0.550825\pi$
$384$	−11.5300	−	3.22784i	−0.588389	−	0.164720i
$385$	−0.0335511	−	1.72989i	−0.00170992	−	0.0881632i
$386$	9.40327	+	4.72250i	0.478614	+	0.240369i
$387$	21.8193	+	15.6925i	1.10914	+	0.797695i
$388$	−23.2218	−	15.2732i	−1.17891	−	0.775379i
$389$	28.8247	+	1.11853i	1.46147	+	0.0567116i	0.757182	−	0.653204i	$-0.226576\pi$
$389$	28.8247	+	1.11853i	1.46147	+	0.0567116i	0.704286	+	0.709916i	$0.251267\pi$
$390$	11.3827	+	11.1969i	0.576387	+	0.566979i
$391$	2.92214	+	30.0423i	0.147779	+	1.51930i
$392$	4.88673	+	10.2197i	0.246817	+	0.516175i
$393$	23.5303	−	9.57290i	1.18695	−	0.482889i
$394$	−15.8758	+	12.3047i	−0.799812	+	0.619901i
$395$	−11.0287	+	11.6898i	−0.554916	+	0.588177i
$396$	0.642741	−	2.12419i	0.0322989	−	0.106745i
$397$	10.7257	−	35.8263i	0.538307	−	1.79807i	−0.0617229	−	0.998093i	$-0.519660\pi$
$397$	10.7257	−	35.8263i	0.538307	−	1.79807i	0.600030	−	0.799978i	$-0.295155\pi$
$398$	7.24016	−	8.97639i	0.362916	−	0.449946i
$399$	61.8409	+	2.49061i	3.09592	+	0.124686i
$400$	5.38095	+	8.53746i	0.269047	+	0.426873i
$401$	−3.41840	+	1.88620i	−0.170707	+	0.0941921i	−0.566165	−	0.824292i	$-0.691574\pi$
$401$	−3.41840	+	1.88620i	−0.170707	+	0.0941921i	0.395458	+	0.918484i	$0.370586\pi$
$402$	−9.69002	−	22.5549i	−0.483294	−	1.12494i
$403$	3.73479	+	14.4994i	0.186043	+	0.722265i
$404$	−12.8197	+	22.2044i	−0.637806	+	1.10471i
$405$	−11.0422	+	3.00406i	−0.548689	+	0.149273i
$406$	14.5943	+	25.2781i	0.724304	+	1.25453i
$407$	−0.549762	+	0.539203i	−0.0272507	+	0.0267273i
$408$	−3.43181	+	11.4021i	−0.169900	+	0.564488i
$409$	0.497713	−	25.6619i	0.0246103	−	1.26890i	−0.760415	−	0.649438i	$-0.775004\pi$
$409$	0.497713	−	25.6619i	0.0246103	−	1.26890i	0.785025	−	0.619464i	$-0.212650\pi$
$410$	3.63759	−	6.90580i	0.179648	−	0.341053i
$411$	−28.2827	−	11.6032i	−1.39508	−	0.572344i
$412$	−3.27514	−	8.48282i	−0.161355	−	0.417919i
$413$	12.0522	−	2.85642i	0.593048	−	0.140555i
$414$	−12.2970	+	21.1554i	−0.604365	+	1.03973i
$415$	0.148345	+	0.495505i	0.00728195	+	0.0243234i
$416$	−25.6607	−	10.4835i	−1.25812	−	0.513998i
$417$	0.273812	+	1.27308i	0.0134086	+	0.0623432i
$418$	−5.14234	−	0.399694i	−0.251520	−	0.0195497i
$419$	−14.1957	+	10.1465i	−0.693507	+	0.495689i	−0.872782	−	0.488110i	$-0.837686\pi$
$419$	−14.1957	+	10.1465i	−0.693507	+	0.495689i	0.179275	+	0.983799i	$0.442625\pi$
$420$	−13.4505	+	19.5497i	−0.656316	+	0.953928i
$421$	−5.35349	+	8.49389i	−0.260913	+	0.413967i	−0.950731	−	0.310016i	$-0.899666\pi$
$421$	−5.35349	+	8.49389i	−0.260913	+	0.413967i	0.689818	+	0.723982i	$0.257690\pi$
$422$	−1.52068	+	26.1090i	−0.0740255	+	1.27097i
$423$	0.774072	+	0.706587i	0.0376367	+	0.0343555i
$424$	3.27817	−	2.15609i	0.159202	−	0.104709i
$425$	22.5368	−	13.6010i	1.09319	−	0.659746i
$426$	−11.8283	+	0.901907i	−0.573084	+	0.0436975i
$427$	49.1382	−	20.0752i	2.37797	−	0.971506i
$428$	−20.6950	−	25.6578i	−1.00033	−	1.24022i
$429$	0.725544	−	1.67524i	0.0350296	−	0.0808811i
$430$	13.5458	+	19.7503i	0.653237	+	0.952442i
$431$	−2.16526	−	12.2798i	−0.104297	−	0.591498i	−0.991499	−	0.130116i	$-0.958465\pi$
$431$	−2.16526	−	12.2798i	−0.104297	−	0.591498i	0.887202	−	0.461382i	$-0.152646\pi$
$432$	12.2921	−	9.44076i	0.591404	−	0.454219i
$433$	−6.71847	+	38.1024i	−0.322869	+	1.83108i	0.201375	+	0.979514i	$0.435459\pi$
$433$	−6.71847	+	38.1024i	−0.322869	+	1.83108i	−0.524244	+	0.851568i	$0.675652\pi$
$434$	−36.9977	+	16.8175i	−1.77595	+	0.807268i
$435$	−3.44259	+	5.94258i	−0.165059	+	0.284925i
$436$	1.64200	+	0.322479i	0.0786376	+	0.0154439i
$437$	29.6515	+	9.50738i	1.41842	+	0.454800i
$438$	0.289367	+	16.1415i	0.0138265	+	0.771273i
$439$	7.64117	+	8.75581i	0.364693	+	0.417892i	0.906230	−	0.422785i	$-0.138947\pi$
$439$	7.64117	+	8.75581i	0.364693	+	0.417892i	−0.541537	+	0.840677i	$0.682157\pi$
$440$	0.205067	−	0.275453i	0.00977620	−	0.0131317i
$441$	−37.7175	−	7.52252i	−1.79607	−	0.358215i
$442$	−22.3418	+	51.7940i	−1.06269	+	2.46359i
$443$	−0.240326	−	0.218084i	−0.0114182	−	0.0103615i	0.666279	−	0.745703i	$-0.267886\pi$
$443$	−0.240326	−	0.218084i	−0.0114182	−	0.0103615i	−0.677697	+	0.735341i	$0.737022\pi$
$444$	10.4368	−	1.61659i	0.495308	−	0.0767201i
$445$	−2.25272	+	8.74561i	−0.106789	+	0.414582i
$446$	−30.1809	−	29.6012i	−1.42911	−	1.40166i
$447$	17.7748	−	9.77371i	0.840719	−	0.462281i
$448$	10.3060	−	47.5777i	0.486912	−	2.24784i
$449$	9.28761	+	12.4754i	0.438310	+	0.588752i	0.965308	−	0.261114i	$-0.0840900\pi$
$449$	9.28761	+	12.4754i	0.438310	+	0.588752i	−0.526998	+	0.849866i	$0.676683\pi$
$450$	21.2704	+	1.71609i	1.00270	+	0.0808975i
$451$	−0.886401	−	0.103605i	−0.0417390	−	0.00487859i
$452$	−12.1195	+	2.38019i	−0.570053	+	0.111955i
$453$	20.0633	+	23.0582i	0.942656	+	1.08337i
$454$	−10.7419	−	49.5901i	−0.504142	−	2.32738i
$455$	−12.8350	+	14.7072i	−0.601713	+	0.689486i
$456$	9.39839	+	7.90972i	0.440120	+	0.370406i
$457$	24.5294	+	17.5325i	1.14743	+	0.820137i	0.986000	−	0.166746i	$-0.0533261\pi$
$457$	24.5294	+	17.5325i	1.14743	+	0.820137i	0.161435	+	0.986883i	$0.448388\pi$
$458$	−15.9086	−	13.3489i	−0.743360	−	0.623753i
$459$	−23.9986	−	32.5338i	−1.12016	−	1.51855i
$460$	−9.14573	+	7.67418i	−0.426422	+	0.357811i
$461$	33.6136	−	2.61265i	1.56554	−	0.121683i	0.734777	−	0.678309i	$-0.237287\pi$
$461$	33.6136	−	2.61265i	1.56554	−	0.121683i	0.830764	+	0.556625i	$0.187904\pi$
$462$	4.82003	+	1.14984i	0.224248	+	0.0534955i
$463$	−7.72979	+	20.0207i	−0.359234	+	0.930439i	0.628989	+	0.777414i	$0.283469\pi$
$463$	−7.72979	+	20.0207i	−0.359234	+	0.930439i	−0.988222	+	0.153024i	$0.951099\pi$
$464$	1.25881	−	9.21612i	0.0584388	−	0.427848i
$465$	−7.77121	−	5.57178i	−0.360381	−	0.258385i
$466$	7.14332	+	3.94151i	0.330908	+	0.182587i
$467$	2.07111	+	35.5596i	0.0958397	+	1.64550i	0.613339	+	0.789820i	$0.289826\pi$
$467$	2.07111	+	35.5596i	0.0958397	+	1.64550i	−0.517499	+	0.855684i	$0.673137\pi$
$468$	−21.4747	+	12.8742i	−0.992669	+	0.595111i
$469$	26.8194	−	13.4692i	1.23841	−	0.621951i
$470$	0.435248	+	0.826299i	0.0200765	+	0.0381143i
$471$	−0.601163	+	0.428354i	−0.0277001	+	0.0197375i
$472$	2.23797	+	1.01728i	0.103011	+	0.0468242i
$473$	1.54879	−	2.25820i	0.0712136	−	0.103832i
$474$	−24.4849	−	38.9747i	−1.12463	−	1.79017i
$475$	−3.67495	−	26.9054i	−0.168618	−	1.23450i
$476$	−81.5728	−	19.3331i	−3.73888	−	0.886131i
$477$	−0.813607	+	13.2966i	−0.0372525	+	0.608809i
$478$	−27.1582	−	28.7860i	−1.24219	−	1.31664i
$479$	−38.9663	−	6.09422i	−1.78042	−	0.278452i	−0.823184	−	0.567775i	$-0.807804\pi$
$479$	−38.9663	−	6.09422i	−1.78042	−	0.278452i	−0.957231	+	0.289323i	$0.906570\pi$
$480$	16.8656	−	5.38045i	0.769805	−	0.245583i
$481$	8.68116	−	0.336869i	0.395827	−	0.0153599i
$482$	−13.8226	−	8.34197i	−0.629601	−	0.379966i
$483$	−26.7138	−	13.4653i	−1.21552	−	0.612692i
$484$	25.4300	+	7.07894i	1.15591	+	0.321770i
$485$	14.6018			0.663034
$486$	−0.395058	−	32.7715i	−0.0179202	−	1.48655i
$487$	−43.1512			−1.95537			−0.977684	−	0.210079i	$-0.932628\pi$
$487$	−43.1512			−1.95537			−0.977684	+	0.210079i	$0.932628\pi$
$488$	10.1494	+	2.82527i	0.459440	+	0.127894i
$489$	2.81378	−	1.84474i	0.127244	−	0.0834222i
$490$	−29.3421	−	17.7081i	−1.32554	−	0.799968i
$491$	39.3080	−	1.52533i	1.77394	−	0.0688371i	0.869115	−	0.494611i	$-0.164689\pi$
$491$	39.3080	−	1.52533i	1.77394	−	0.0688371i	0.904830	+	0.425773i	$0.139998\pi$
$492$	9.05199	+	8.23850i	0.408095	+	0.371420i
$493$	−23.9708	−	3.74897i	−1.07959	−	0.168845i
$494$	39.9329	+	42.3264i	1.79667	+	1.90436i
$495$	0.331109	+	1.11791i	0.0148822	+	0.0502464i
$496$	12.6021	+	2.98674i	0.565849	+	0.134109i
$497$	−1.96267	−	14.3693i	−0.0880379	−	0.644551i
$498$	−1.48032	+	0.0552673i	−0.0663345	+	0.00247659i
$499$	−8.60295	+	12.5434i	−0.385121	+	0.561520i	−0.967972	−	0.251059i	$-0.919221\pi$
$499$	−8.60295	+	12.5434i	−0.385121	+	0.561520i	0.582851	+	0.812579i	$0.301937\pi$
$500$	23.4861	+	10.6757i	1.05033	+	0.477433i
$501$	−22.5174	−	10.2753i	−1.00600	−	0.459066i
$502$	20.2934	+	38.5260i	0.905738	+	1.71950i
$503$	25.5520	−	12.8327i	1.13931	−	0.572181i	0.223861	−	0.974621i	$-0.428134\pi$
$503$	25.5520	−	12.8327i	1.13931	−	0.572181i	0.915446	+	0.402440i	$0.131838\pi$
$504$	−7.73356	−	8.91437i	−0.344480	−	0.397077i
$505$	−0.783197	−	13.4470i	−0.0348518	−	0.598383i
$506$	2.18285	+	1.20444i	0.0970393	+	0.0535440i
$507$	1.74927	−	0.792044i	0.0776877	−	0.0351759i
$508$	−1.57303	+	11.5166i	−0.0697918	+	0.510967i
$509$	−0.820458	+	2.12504i	−0.0363662	+	0.0941907i	−0.949877	−	0.312623i	$-0.898792\pi$
$509$	−0.820458	+	2.12504i	−0.0363662	+	0.0941907i	0.913511	+	0.406814i	$0.133360\pi$
$510$	−10.2812	−	34.5260i	−0.455261	−	1.52884i
$511$	−19.6777	+	1.52947i	−0.870491	+	0.0676599i
$512$	−22.4056	+	18.8005i	−0.990196	+	0.830873i
$513$	−40.6235	+	9.43923i	−1.79357	+	0.416752i
$514$	−10.5344	−	8.83940i	−0.464652	−	0.389889i
$515$	3.88642	+	2.77784i	0.171256	+	0.122406i
$516$	−35.3095	+	12.7930i	−1.55442	+	0.563179i
$517$	0.0702117	−	0.0804537i	0.00308791	−	0.00353835i
$518$	4.99224	+	23.0468i	0.219347	+	1.01262i
$519$	3.86152	−	11.2319i	0.169502	−	0.493024i
$520$	−3.80167	+	0.746624i	−0.166714	+	0.0327416i
$521$	−18.3527	−	2.14512i	−0.804046	−	0.0939795i	−0.295865	−	0.955230i	$-0.595608\pi$
$521$	−18.3527	−	2.14512i	−0.804046	−	0.0939795i	−0.508181	+	0.861250i	$0.669682\pi$
$522$	−14.0018	−	13.8137i	−0.612842	−	0.604610i
$523$	9.24118	+	12.4131i	0.404089	+	0.542785i	0.956861	−	0.290547i	$-0.0938374\pi$
$523$	9.24118	+	12.4131i	0.404089	+	0.542785i	−0.552772	+	0.833333i	$0.686430\pi$
$524$	−7.51483	+	34.6923i	−0.328287	+	1.51554i
$525$	−0.544176	+	26.0830i	−0.0237498	+	1.13836i
$526$	−8.18877	−	8.03148i	−0.357047	−	0.350189i
$527$	8.42646	−	32.7135i	0.367062	−	1.42502i
$528$	−0.989589	−	1.23059i	−0.0430663	−	0.0535545i
$529$	5.88656	+	5.34177i	0.255937	+	0.232251i
$530$	−4.70169	+	10.8998i	−0.204229	+	0.473455i
$531$	−7.31958	+	4.01079i	−0.317643	+	0.174054i
$532$	−51.6442	+	69.3702i	−2.23906	+	3.00758i
$533$	6.62022	+	7.58593i	0.286754	+	0.328583i
$534$	−22.6278	−	12.5288i	−0.979199	−	0.542176i
$535$	16.4906	+	5.28751i	0.712952	+	0.228599i
$536$	5.84494	+	1.14791i	0.252463	+	0.0495821i
$537$	11.8080	+	0.0173300i	0.509553	+	0.000747843i
$538$	−35.5730	+	16.1699i	−1.53366	+	0.697135i
$539$	−0.680444	+	3.85899i	−0.0293088	+	0.166218i
$540$	5.24324	−	15.1065i	0.225633	−	0.650080i
$541$	−1.99478	−	11.3130i	−0.0857624	−	0.486383i	−0.997189	−	0.0749210i	$-0.976130\pi$
$541$	−1.99478	−	11.3130i	−0.0857624	−	0.486383i	0.911427	−	0.411462i	$-0.134982\pi$
$542$	4.03652	+	5.88538i	0.173383	+	0.252799i
$543$	5.89877	+	7.94775i	0.253140	+	0.341070i
$544$	39.2640	+	48.6797i	1.68343	+	2.08713i
$545$	−0.813812	+	0.332479i	−0.0348599	+	0.0142418i
$546$	−31.5528	−	46.1502i	−1.35034	−	1.97505i
$547$	−27.5720	+	16.6398i	−1.17889	+	0.711465i	−0.964190	−	0.265214i	$-0.914557\pi$
$547$	−27.5720	+	16.6398i	−1.17889	+	0.711465i	−0.214703	+	0.976679i	$0.568878\pi$
$548$	35.6898	−	23.4736i	1.52459	−	1.00274i
$549$	−28.3357	+	21.8290i	−1.20934	+	0.931639i
$550$	0.126417	−	2.17049i	0.00539043	−	0.0925502i
$551$	−13.3458	+	21.1745i	−0.568549	+	0.902064i
$552$	−2.55349	−	5.36038i	−0.108684	−	0.228153i
$553$	45.7795	−	32.7212i	1.94674	−	1.39145i
$554$	25.2904	+	1.96572i	1.07448	+	0.0835155i
$555$	−4.11428	+	3.72252i	−0.174642	+	0.158012i
$556$	−1.68447	−	0.688181i	−0.0714373	−	0.0291854i
$557$	−4.91838	−	16.4285i	−0.208399	−	0.696100i	−0.996727	−	0.0808446i	$-0.974238\pi$
$557$	−4.91838	−	16.4285i	−0.208399	−	0.696100i	0.788328	−	0.615255i	$-0.210947\pi$
$558$	21.0305	−	17.5417i	0.890291	−	0.742601i
$559$	−30.0606	+	7.12449i	−1.27143	+	0.301334i
$560$	6.08152	+	15.7515i	0.256991	+	0.665624i
$561$	−3.25928	+	2.51848i	−0.137607	+	0.106330i
$562$	22.2863	−	42.3095i	0.940092	−	1.78472i
$563$	−0.112124	+	5.78111i	−0.00472548	+	0.243645i	0.990000	+	0.141069i	$0.0450540\pi$
$563$	−0.112124	+	5.78111i	−0.00472548	+	0.243645i	−0.994725	+	0.102576i	$0.967292\pi$
$564$	−1.42554	+	0.335650i	−0.0600260	+	0.0141334i
$565$	4.63243	−	4.54346i	0.194888	−	0.191145i
$566$	1.71888	+	2.97718i	0.0722497	+	0.125140i
$567$	39.9649	−	2.87039i	1.67837	−	0.120545i
$568$	1.43922	−	2.49280i	0.0603883	−	0.104596i
$569$	5.48878	+	21.3088i	0.230102	+	0.893310i	0.974282	+	0.225331i	$0.0723464\pi$
$569$	5.48878	+	21.3088i	0.230102	+	0.893310i	−0.744181	+	0.667979i	$0.767160\pi$
$570$	−36.9057	−	4.36858i	−1.54581	−	0.182979i
$571$	21.2092	−	11.7027i	0.887577	−	0.489744i	0.0273326	−	0.999626i	$-0.491299\pi$
$571$	21.2092	−	11.7027i	0.887577	−	0.489744i	0.860244	+	0.509882i	$0.170311\pi$
$572$	1.36021	+	2.15811i	0.0568731	+	0.0902353i
$573$	4.97752	+	9.48332i	0.207939	+	0.396171i
$574$	−17.1575	+	21.2720i	−0.716141	+	0.887875i
$575$	−3.76449	+	12.5743i	−0.156990	+	0.524384i
$576$	1.81126	+	32.7541i	0.0754690	+	1.36475i
$577$	−18.8099	+	19.9374i	−0.783068	+	0.830003i	−0.988900	−	0.148584i	$-0.952528\pi$
$577$	−18.8099	+	19.9374i	−0.783068	+	0.830003i	0.205832	+	0.978587i	$0.434010\pi$
$578$	72.3404	−	56.0680i	3.00896	−	2.33212i
$579$	1.18576	−	8.58725i	0.0492783	−	0.356874i
$580$	−4.13984	−	8.65774i	−0.171897	−	0.359493i
$581$	−0.175327	−	1.80252i	−0.00727379	−	0.0747811i
$582$	−10.4908	+	40.4819i	−0.434860	+	1.67803i
$583$	1.35623	+	0.0526280i	0.0561694	+	0.00217963i
$584$	−3.27288	−	2.15261i	−0.135433	−	0.0890755i
$585$	5.70920	−	11.8503i	0.236046	−	0.489949i
$586$	57.8725	+	29.0646i	2.39069	+	1.20065i
$587$	−0.0957648	−	4.93761i	−0.00395264	−	0.203797i	−0.996582	−	0.0826081i	$-0.973675\pi$
$587$	−0.0957648	−	4.93761i	−0.00395264	−	0.203797i	0.992629	−	0.121189i	$-0.0386707\pi$
$588$	38.4235	−	37.5751i	1.58456	−	1.54957i
$589$	−27.5448	−	21.3488i	−1.13496	−	0.879663i
$590$	−7.34806	+	1.14922i	−0.302515	+	0.0473124i
$591$	13.8118	+	9.11321i	0.568140	+	0.374867i
$592$	3.24176	−	6.77957i	0.133236	−	0.278639i
$593$	6.11543	+	2.22584i	0.251131	+	0.0914041i	0.464518	−	0.885564i	$-0.346227\pi$
$593$	6.11543	+	2.22584i	0.251131	+	0.0914041i	−0.213388	+	0.976968i	$0.568450\pi$
$594$	−3.33718	+	0.114785i	−0.136926	+	0.00470968i
$595$	41.3856	−	15.0631i	1.69664	−	0.617528i
$596$	−2.74408	+	28.2116i	−0.112402	+	1.15559i
$597$	−8.92293	−	3.26252i	−0.365191	−	0.133526i
$598$	−9.10567	−	26.6123i	−0.372359	−	1.08826i
$599$	−15.9256	+	14.4517i	−0.650703	+	0.590481i	−0.929030	−	0.370005i	$-0.879356\pi$
$599$	−15.9256	+	14.4517i	−0.650703	+	0.590481i	0.278327	+	0.960486i	$0.410220\pi$
$600$	−3.25671	+	4.02558i	−0.132955	+	0.164344i
$601$	−12.2625	+	35.8386i	−0.500199	+	1.46189i	0.350666	+	0.936501i	$0.385955\pi$
$601$	−12.2625	+	35.8386i	−0.500199	+	1.46189i	−0.850865	+	0.525385i	$0.823921\pi$
$602$	−33.2131	−	76.9966i	−1.35367	−	3.13815i
$603$	−15.0163	+	13.5464i	−0.611511	+	0.551652i
$604$	−42.4211	+	4.95832i	−1.72609	+	0.201751i
$605$	−13.2055	+	4.23417i	−0.536880	+	0.172144i
$606$	37.8430	+	7.48982i	1.53727	+	0.304253i
$607$	9.64724	−	2.68549i	0.391569	−	0.109001i	−0.0667916	−	0.997767i	$-0.521276\pi$
$607$	9.64724	−	2.68549i	0.391569	−	0.109001i	0.458361	+	0.888766i	$0.348437\pi$
$608$	62.1553	−	17.3021i	2.52073	−	0.701693i
$609$	15.8376	−	18.0942i	0.641771	−	0.733213i
$610$	−30.3512	+	9.73172i	−1.22888	+	0.394026i
$611$	−1.19657	+	0.139859i	−0.0484081	+	0.00565810i
$612$	56.4549	−	2.02476i	2.28205	−	0.0818462i
$613$	6.03527	+	13.9913i	0.243762	+	0.565105i	0.995543	−	0.0943087i	$-0.0300641\pi$
$613$	6.03527	+	13.9913i	0.243762	+	0.565105i	−0.751781	+	0.659413i	$0.770805\pi$
$614$	−3.83676	+	11.2134i	−0.154839	+	0.452535i
$615$	−6.35150	−	1.00291i	−0.256117	−	0.0404411i
$616$	−0.890419	+	0.808012i	−0.0358760	+	0.0325557i
$617$	−7.19187	−	21.0190i	−0.289534	−	0.846195i	−0.991044	−	0.133535i	$-0.957367\pi$
$617$	−7.19187	−	21.0190i	−0.289534	−	0.846195i	0.701510	−	0.712660i	$-0.252510\pi$
$618$	−10.4935	+	8.77890i	−0.422111	+	0.353139i
$619$	0.0117882	−	0.121193i	0.000473808	−	0.00487117i	−0.995063	−	0.0992462i	$-0.968357\pi$
$619$	0.0117882	−	0.121193i	0.000473808	−	0.00487117i	0.995537	+	0.0943750i	$0.0300853\pi$
$620$	12.5560	−	4.57000i	0.504260	−	0.183535i
$621$	19.7637	+	3.97191i	0.793088	+	0.159387i
$622$	−20.3498	−	7.40672i	−0.815952	−	0.296982i
$623$	13.6409	−	28.5275i	0.546511	−	1.14293i
$624$	−1.06199	+	17.7840i	−0.0425137	+	0.711930i
$625$	3.32270	−	0.519660i	0.132908	−	0.0207864i
$626$	−11.1605	−	8.65008i	−0.446065	−	0.345727i
$627$	1.05388	+	4.11641i	0.0420878	+	0.164393i
$628$	−0.0200016	−	1.03128i	−0.000798150	−	0.0411524i
$629$	−17.5163	−	8.79701i	−0.698420	−	0.350760i
$630$	34.3678	+	9.67572i	1.36925	+	0.385490i
$631$	8.64926	+	5.68870i	0.344321	+	0.226464i	0.709877	−	0.704326i	$-0.248751\pi$
$631$	8.64926	+	5.68870i	0.344321	+	0.226464i	−0.365555	+	0.930790i	$0.619121\pi$
$632$	11.1601	+	0.433061i	0.443923	+	0.0172262i
$633$	20.7650	−	5.74752i	0.825336	−	0.228443i
$634$	4.48886	+	46.1495i	0.178275	+	1.83283i
$635$	−2.63424	−	5.50905i	−0.104537	−	0.218620i
$636$	−14.6962	−	11.4250i	−0.582742	−	0.453030i
$637$	34.9422	−	27.0823i	1.38446	−	1.07304i
$638$	−1.37521	+	1.45763i	−0.0544449	+	0.0577083i
$639$	3.84444	+	8.98484i	0.152084	+	0.355435i
$640$	−2.52089	+	8.42037i	−0.0996471	+	0.332844i
$641$	2.63182	−	3.26294i	0.103951	−	0.128878i	−0.723718	−	0.690096i	$-0.757568\pi$
$641$	2.63182	−	3.26294i	0.103951	−	0.128878i	0.827668	+	0.561218i	$0.189667\pi$
$642$	−26.5070	+	41.9196i	−1.04615	+	1.65444i
$643$	−1.99798	−	3.17001i	−0.0787925	−	0.125013i	0.804278	−	0.594253i	$-0.202552\pi$
$643$	−1.99798	−	3.17001i	−0.0787925	−	0.125013i	−0.883070	+	0.469241i	$0.844528\pi$
$644$	36.6005	−	20.1953i	1.44226	−	0.795805i
$645$	11.8051	−	15.8085i	0.464826	−	0.622461i
$646$	−32.7492	−	127.140i	−1.28850	−	5.00226i
$647$	−23.3221	+	40.3951i	−0.916887	+	1.58809i	−0.112772	+	0.993621i	$0.535973\pi$
$647$	−23.3221	+	40.3951i	−0.916887	+	1.58809i	−0.804115	+	0.594474i	$0.797360\pi$
$648$	6.61844	+	4.40889i	0.259997	+	0.173198i
$649$	0.425186	+	0.736444i	0.0166900	+	0.0289080i
$650$	−17.5120	+	17.1756i	−0.686876	+	0.673683i
$651$	22.9402	+	24.3868i	0.899097	+	0.955794i
$652$	−0.0911684	+	4.70062i	−0.00357043	+	0.184090i
$653$	17.7554	−	33.7078i	0.694822	−	1.31909i	−0.242340	−	0.970191i	$-0.577915\pi$
$653$	17.7554	−	33.7078i	0.694822	−	1.31909i	0.937162	−	0.348895i	$-0.113443\pi$
$654$	−0.337068	−	2.49508i	−0.0131804	−	0.0975653i
$655$	−6.71673	−	17.3968i	−0.262445	−	0.679748i
$656$	8.47434	−	2.00845i	0.330867	−	0.0784170i
$657$	12.5112	−	4.51215i	0.488108	−	0.176036i
$658$	−0.937846	−	3.13262i	−0.0365610	−	0.122122i
$659$	−12.1664	−	4.97052i	−0.473935	−	0.193624i	0.128631	−	0.991692i	$-0.458942\pi$
$659$	−12.1664	−	4.97052i	−0.473935	−	0.193624i	−0.602567	+	0.798069i	$0.705855\pi$
$660$	−1.55066	−	0.499711i	−0.0603594	−	0.0194512i
$661$	−16.9129	−	1.31458i	−0.657837	−	0.0511312i	−0.255765	−	0.966739i	$-0.582327\pi$
$661$	−16.9129	−	1.31458i	−0.657837	−	0.0511312i	−0.402073	+	0.915608i	$0.631710\pi$
$662$	−7.88251	+	5.63408i	−0.306363	+	0.218975i
$663$	46.3247	+	3.66905i	1.79910	+	0.142494i
$664$	0.191657	−	0.304085i	0.00743775	−	0.0118008i
$665$	2.64176	−	45.3574i	0.102443	−	1.75888i
$666$	−7.36432	−	14.0809i	−0.285362	−	0.545624i
$667$	10.1079	−	6.64805i	0.391378	−	0.257413i
$668$	29.6112	−	17.8704i	1.14569	−	0.691428i
$669$	−15.0699	+	31.3975i	−0.582635	+	1.21390i
$670$	−16.6824	+	6.81553i	−0.644499	+	0.263307i
$671$	2.28794	+	2.83660i	0.0883249	+	0.109506i
$672$	−61.5761	+	7.10562i	−2.37535	+	0.274105i
$673$	−11.0433	−	16.1015i	−0.425688	−	0.620669i	0.551212	−	0.834365i	$-0.314166\pi$
$673$	−11.0433	−	16.1015i	−0.425688	−	0.620669i	−0.976900	+	0.213697i	$0.931450\pi$
$674$	−4.67833	−	26.5321i	−0.180202	−	1.02198i
$675$	−4.31020	−	17.0435i	−0.165900	−	0.656005i
$676$	−0.465937	+	2.64246i	−0.0179206	+	0.101633i
$677$	41.2654	−	18.7574i	1.58596	−	0.720906i	0.589723	−	0.807606i	$-0.299237\pi$
$677$	41.2654	−	18.7574i	1.58596	−	0.720906i	0.996234	+	0.0866996i	$0.0276320\pi$
$678$	9.26802	+	16.1072i	0.355936	+	0.618594i
$679$	−50.1678	−	9.85264i	−1.92526	−	0.378110i
$680$	8.32379	+	2.66892i	0.319203	+	0.102348i
$681$	−35.8204	+	21.5461i	−1.37264	+	0.825647i
$682$	−1.83463	−	2.10225i	−0.0702515	−	0.0804992i
$683$	3.50729	−	4.71111i	0.134203	−	0.180266i	−0.729942	−	0.683509i	$-0.760453\pi$
$683$	3.50729	−	4.71111i	0.134203	−	0.180266i	0.864145	+	0.503244i	$0.167860\pi$
$684$	21.1497	−	54.3042i	0.808679	−	2.07637i
$685$	−8.88870	+	20.6063i	−0.339620	+	0.787327i
$686$	40.3423	+	36.6087i	1.54027	+	1.39772i
$687$	−6.18554	+	15.9512i	−0.235993	+	0.608578i
$688$	−6.66566	+	25.8777i	−0.254126	+	0.986577i
$689$	−10.9321	−	10.7221i	−0.416478	−	0.408479i
$690$	15.3659	+	9.30416i	0.584970	+	0.354203i
$691$	−0.420680	+	1.94208i	−0.0160034	+	0.0738800i	−0.984637	−	0.174613i	$-0.944133\pi$
$691$	−0.420680	+	1.94208i	−0.0160034	+	0.0738800i	0.968634	+	0.248493i	$0.0799352\pi$
$692$	9.91073	+	13.3124i	0.376749	+	0.506062i
$693$	−0.383282	−	4.06426i	−0.0145597	−	0.154389i
$694$	62.6370	+	7.32122i	2.37767	+	0.277910i
$695$	0.938025	−	0.184222i	0.0355813	−	0.00698794i
$696$	4.68451	−	0.912869i	0.177566	−	0.0346022i
$697$	−4.80917	−	22.2016i	−0.182160	−	0.840945i
$698$	11.1975	−	12.8309i	0.423831	−	0.485656i
$699$	1.17685	−	6.61743i	0.0445125	−	0.250294i
$700$	−29.6581	−	21.1983i	−1.12097	−	0.801220i
$701$	−6.38533	−	5.35793i	−0.241171	−	0.202366i	0.514189	−	0.857677i	$-0.328093\pi$
$701$	−6.38533	−	5.35793i	−0.241171	−	0.202366i	−0.755359	+	0.655311i	$0.772538\pi$
$702$	28.7518	+	24.3421i	1.08517	+	0.918734i
$703$	−15.4902	+	12.9978i	−0.584224	+	0.490222i
$704$	3.33219	−	0.258998i	0.125587	−	0.00976136i
$705$	0.528808	−	0.558858i	0.0199161	−	0.0210478i
$706$	−15.2474	+	39.4916i	−0.573842	+	1.48629i
$707$	−6.38256	+	46.7286i	−0.240041	+	1.75741i
$708$	1.14613	−	11.6064i	0.0430741	−	0.436195i
$709$	20.2204	+	11.1571i	0.759392	+	0.419015i	0.815017	−	0.579437i	$-0.196728\pi$
$709$	20.2204	+	11.1571i	0.759392	+	0.419015i	−0.0556253	+	0.998452i	$0.517715\pi$
$710$	0.506347	+	8.69365i	0.0190029	+	0.326267i
$711$	−23.8924	+	29.4446i	−0.896034	+	1.10426i
$712$	5.60846	−	2.81667i	0.210186	−	0.105559i
$713$	7.85041	+	14.9036i	0.294000	+	0.558146i
$714$	12.0269	+	125.559i	0.450095	+	4.69894i
$715$	−1.22005	−	0.554579i	−0.0456272	−	0.0207401i
$716$	−9.33247	+	13.6071i	−0.348771	+	0.508520i
$717$	−15.2368	+	28.8237i	−0.569030	+	1.07644i
$718$	2.75501	+	20.1702i	0.102816	+	0.752747i
$719$	−50.4503	−	11.9569i	−1.88148	−	0.445919i	−0.881809	−	0.471607i	$-0.843674\pi$
$719$	−50.4503	−	11.9569i	−1.88148	−	0.445919i	−0.999670	+	0.0256879i	$0.991822\pi$
$720$	−6.76761	−	9.14641i	−0.252214	−	0.340867i
$721$	−11.4783	−	12.1663i	−0.427475	−	0.453097i
$722$	−94.3483	−	14.7558i	−3.51128	−	0.549154i
$723$	−2.83483	+	12.9948i	−0.105429	+	0.483283i
$724$	−13.8200	+	0.536277i	−0.513615	+	0.0199306i
$725$	−9.03303	−	5.45146i	−0.335478	−	0.202462i
$726$	−2.25113	−	39.6529i	−0.0835473	−	1.47166i
$727$	45.4706	+	12.6576i	1.68641	+	0.469445i	0.972905	−	0.231203i	$-0.0742662\pi$
$727$	45.4706	+	12.6576i	1.68641	+	0.469445i	0.713507	+	0.700648i	$0.247106\pi$
$728$	13.5653			0.502763
$729$	−25.4520	+	9.01077i	−0.942668	+	0.333732i
$730$	11.8514			0.438641
$731$	67.1486	+	18.6921i	2.48358	+	0.691352i
$732$	−2.83294	−	49.9013i	−0.104708	−	1.84441i
$733$	−31.4336	−	18.9703i	−1.16103	−	0.700683i	−0.200724	−	0.979648i	$-0.564330\pi$
$733$	−31.4336	−	18.9703i	−1.16103	−	0.700683i	−0.960301	+	0.278965i	$0.910009\pi$
$734$	−4.74242	+	0.184028i	−0.175046	+	0.00679258i
$735$	−6.01769	+	27.5850i	−0.221966	+	1.01749i
$736$	−30.8110	−	4.81876i	−1.13571	−	0.177622i
$737$	1.41398	+	1.49873i	0.0520847	+	0.0552066i
$738$	7.34377	−	16.8883i	0.270328	−	0.621666i
$739$	−31.3668	−	7.43407i	−1.15385	−	0.273467i	−0.391215	−	0.920299i	$-0.627945\pi$
$739$	−31.3668	−	7.43407i	−1.15385	−	0.273467i	−0.762632	+	0.646833i	$0.776093\pi$
$740$	−1.04922	−	7.68169i	−0.0385703	−	0.282384i
$741$	22.4039	−	42.3819i	0.823029	−	1.55694i
$742$	23.5084	−	34.2761i	0.863021	−	1.25832i
$743$	22.8905	+	10.4050i	0.839771	+	0.381723i	0.787052	−	0.616887i	$-0.211606\pi$
$743$	22.8905	+	10.4050i	0.839771	+	0.381723i	0.0527187	+	0.998609i	$0.483211\pi$
$744$	0.633614	+	6.61486i	0.0232294	+	0.242513i
$745$	−6.93986	−	13.1750i	−0.254257	−	0.482694i
$746$	6.90037	−	3.46550i	0.252640	−	0.126881i
$747$	0.436208	+	1.13975i	0.0159600	+	0.0417013i
$748$	−0.334657	−	5.74585i	−0.0122363	−	0.210089i
$749$	−53.0896	−	29.2936i	−1.93985	−	1.07036i
$750$	3.81455	−	38.6286i	0.139288	−	1.41052i
$751$	−3.73259	+	27.3274i	−0.136204	+	0.997191i	0.788104	+	0.615543i	$0.211063\pi$
$751$	−3.73259	+	27.3274i	−0.136204	+	0.997191i	−0.924308	+	0.381648i	$0.875357\pi$
$752$	−0.375329	+	0.972127i	−0.0136869	+	0.0354498i
$753$	24.6556	−	26.0567i	0.898500	−	0.949558i
$754$	22.5408	−	1.75201i	0.820886	−	0.0638043i
$755$	17.1883	−	14.4227i	0.625547	−	0.524896i
$756$	−28.2075	+	48.3639i	−1.02590	+	1.75898i
$757$	−6.23353	−	5.23055i	−0.226561	−	0.190108i	0.522440	−	0.852676i	$-0.325022\pi$
$757$	−6.23353	−	5.23055i	−0.226561	−	0.190108i	−0.749001	+	0.662569i	$0.769466\pi$
$758$	−45.6779	−	32.6486i	−1.65910	−	1.18585i
$759$	0.359620	−	2.02215i	0.0130534	−	0.0733992i
$760$	5.92926	−	6.79418i	0.215077	−	0.246451i
$761$	−2.91446	−	13.4546i	−0.105649	−	0.487730i	−0.999245	−	0.0388574i	$-0.987628\pi$
$761$	−2.91446	−	13.4546i	−0.105649	−	0.487730i	0.893596	−	0.448873i	$-0.148174\pi$
$762$	17.1658	−	3.34510i	0.621853	−	0.121180i
$763$	3.02038	−	0.593183i	0.109345	−	0.0214747i
$764$	−14.8647	−	1.73744i	−0.537787	−	0.0628583i
$765$	−24.1950	+	17.1865i	−0.874772	+	0.621378i
$766$	23.5455	+	31.6271i	0.850733	+	1.14273i
$767$	2.03106	−	9.37644i	0.0733375	−	0.338563i
$768$	10.8686	+	6.58099i	0.392185	+	0.237471i
$769$	0.938893	+	0.920860i	0.0338574	+	0.0332071i	0.716949	−	0.697125i	$-0.245538\pi$
$769$	0.938893	+	0.920860i	0.0338574	+	0.0332071i	−0.683092	+	0.730333i	$0.739365\pi$
$770$	0.907386	−	3.52269i	0.0326999	−	0.126949i
$771$	−4.09596	+	10.5626i	−0.147512	+	0.380404i
$772$	8.97038	+	8.14019i	0.322851	+	0.292972i
$773$	9.31617	−	21.5973i	0.335079	−	0.776801i	−0.664485	−	0.747301i	$-0.731349\pi$
$773$	9.31617	−	21.5973i	0.335079	−	0.776801i	0.999565	−	0.0295001i	$-0.00939153\pi$
$774$	35.3459	+	44.0863i	1.27048	+	1.58465i
$775$	8.77226	−	11.7832i	0.315109	−	0.423265i
$776$	−6.67207	−	7.64534i	−0.239513	−	0.274452i
$777$	16.6474	−	10.0134i	0.597220	−	0.359230i
$778$	57.7518	+	18.5174i	2.07050	+	0.663880i
$779$	−22.9955	−	4.51617i	−0.823899	−	0.161808i
$780$	9.16689	+	15.9315i	0.328227	+	0.570438i
$781$	0.906444	−	0.412029i	0.0324351	−	0.0147436i
$782$	−11.0198	+	62.4962i	−0.394066	+	2.23486i
$783$	−7.05441	+	14.5877i	−0.252104	+	0.521320i
$784$	−6.64031	−	37.6591i	−0.237154	−	1.34497i
$785$	0.306494	+	0.446880i	0.0109393	+	0.0159498i
$786$	53.0564	−	6.12249i	1.89246	−	0.218382i
$787$	10.1607	+	12.5973i	0.362191	+	0.449046i	0.926375	−	0.376603i	$-0.122908\pi$
$787$	10.1607	+	12.5973i	0.362191	+	0.449046i	−0.564184	+	0.825649i	$0.690809\pi$
$788$	−21.4050	+	8.74490i	−0.762521	+	0.311524i
$789$	−4.08880	+	8.51884i	−0.145565	+	0.303279i
$790$	−28.9289	+	17.4587i	−1.02924	+	0.621152i
$791$	−18.9815	+	12.4843i	−0.674904	+	0.443892i
$792$	0.434032	−	0.684178i	0.0154227	−	0.0243112i
$793$	2.39063	−	41.0455i	0.0848936	−	1.45757i
$794$	41.9237	−	66.5165i	1.48782	−	2.36058i
$795$	9.74877	+	0.772130i	0.345753	+	0.0273846i
$796$	10.8005	−	7.71974i	0.382814	−	0.273619i
$797$	−39.3305	−	3.05701i	−1.39316	−	0.108285i	−0.641138	−	0.767425i	$-0.721537\pi$
$797$	−39.3305	−	3.05701i	−1.39316	−	0.108285i	−0.752020	+	0.659141i	$0.770920\pi$
$798$	123.850	+	39.9116i	4.38426	+	1.41285i
$799$	2.51620	+	1.02798i	0.0890168	+	0.0363674i
$800$	7.79999	+	26.0538i	0.275771	+	0.921140i
$801$	−3.76169	+	20.9734i	−0.132913	+	0.741060i
$802$	−7.98723	+	1.89301i	−0.282039	+	0.0668444i
$803$	−0.488063	−	1.26412i	−0.0172234	−	0.0446097i
$804$	−3.78328	−	28.0050i	−0.133426	−	0.987660i
$805$	−10.2348	+	19.4303i	−0.360729	+	0.684827i
$806$	−0.610423	+	31.4733i	−0.0215012	+	1.10860i
$807$	22.0568	+	23.4477i	0.776436	+	0.825398i
$808$	−6.68282	+	6.55447i	−0.235101	+	0.230585i
$809$	22.3619	+	38.7319i	0.786202	+	1.36174i	0.928279	+	0.371886i	$0.121289\pi$
$809$	22.3619	+	38.7319i	0.786202	+	1.36174i	−0.142077	+	0.989856i	$0.545378\pi$
$810$	−24.0589	−	0.141241i	−0.845344	−	0.00496271i
$811$	13.4063	−	23.2204i	0.470759	−	0.815378i	−0.528682	−	0.848820i	$-0.677314\pi$
$811$	13.4063	−	23.2204i	0.470759	−	0.815378i	0.999441	+	0.0334420i	$0.0106469\pi$
$812$	8.38151	+	32.5390i	0.294133	+	1.14190i
$813$	3.51781	−	4.71079i	0.123375	−	0.165215i
$814$	−1.41752	+	0.782154i	−0.0496840	+	0.0274145i
$815$	−1.31699	−	2.08954i	−0.0461320	−	0.0731935i
$816$	21.4825	−	33.9736i	0.752037	−	1.18931i
$817$	45.1432	−	55.9688i	1.57936	−	1.95810i
$818$	15.4768	−	51.6960i	0.541132	−	1.80751i
$819$	−27.6113	+	36.8620i	−0.964817	+	1.28806i
$820$	6.16602	−	6.53560i	0.215327	−	0.228233i
$821$	−12.8394	+	9.95130i	−0.448099	+	0.347303i	−0.811522	−	0.584321i	$-0.801361\pi$
$821$	−12.8394	+	9.95130i	−0.448099	+	0.347303i	0.363424	+	0.931624i	$0.381608\pi$
$822$	−50.7426	−	39.4479i	−1.76985	−	1.37590i
$823$	−20.8116	−	43.5237i	−0.725446	−	1.51714i	−0.851063	−	0.525064i	$-0.824042\pi$
$823$	−20.8116	−	43.5237i	−0.725446	−	1.51714i	0.125617	−	0.992079i	$-0.459909\pi$
$824$	−0.321390	−	3.30418i	−0.0111962	−	0.115107i
$825$	−1.72624	+	0.477802i	−0.0600998	+	0.0166349i
$826$	26.0214	+	1.00975i	0.905399	+	0.0351336i
$827$	−36.8029	−	24.2057i	−1.27976	−	0.841713i	−0.286555	−	0.958064i	$-0.592510\pi$
$827$	−36.8029	−	24.2057i	−1.27976	−	0.841713i	−0.993208	+	0.116351i	$0.962880\pi$
$828$	−20.1684	+	19.6652i	−0.700901	+	0.683414i
$829$	−7.68253	−	3.85831i	−0.266825	−	0.134005i	0.310357	−	0.950620i	$-0.399551\pi$
$829$	−7.68253	−	3.85831i	−0.266825	−	0.134005i	−0.577182	+	0.816615i	$0.695848\pi$
$830$	0.0210873	+	1.08725i	0.000731949	+	0.0377391i
$831$	−5.18304	−	20.2448i	−0.179798	−	0.702283i
$832$	−29.8034	−	23.0994i	−1.03325	−	0.800827i
$833$	−98.5459	+	15.4123i	−3.41441	+	0.534004i
$834$	−0.163200	+	2.73293i	−0.00565115	+	0.0946336i
$835$	−7.83817	+	16.3921i	−0.271251	+	0.567274i
$836$	−5.57949	−	2.03077i	−0.192971	−	0.0702356i
$837$	−19.2648	−	11.7424i	−0.665887	−	0.405875i
$838$	−34.4733	+	12.5473i	−1.19086	+	0.433438i
$839$	1.31599	−	13.5296i	0.0454330	−	0.467092i	−0.944798	−	0.327654i	$-0.893742\pi$
$839$	1.31599	−	13.5296i	0.0454330	−	0.467092i	0.990231	−	0.139438i	$-0.0445297\pi$
$840$	−6.64475	+	5.55901i	−0.229266	+	0.191804i
$841$	−6.24010	−	18.2374i	−0.215176	−	0.628875i
$842$	−15.6322	+	14.1854i	−0.538720	+	0.488862i
$843$	−38.9135	−	6.14448i	−1.34025	−	0.211627i
$844$	−9.74664	+	28.4856i	−0.335493	+	0.980516i
$845$	−0.558329	−	1.29435i	−0.0192071	−	0.0445271i
$846$	1.16945	+	1.86758i	0.0402064	+	0.0642088i
$847$	48.2275	−	5.63699i	1.65712	−	0.193689i
$848$	−12.6127	+	4.04409i	−0.433121	+	0.138875i
$849$	1.86530	−	2.13108i	0.0640171	−	0.0731385i
$850$	53.3153	−	14.8413i	1.82870	−	0.509053i
$851$	9.41598	−	2.62112i	0.322776	−	0.0898508i
$852$	−13.3961	−	2.65133i	−0.458943	−	0.0908332i
$853$	1.82662	−	0.585681i	0.0625421	−	0.0200533i	−0.273890	−	0.961761i	$-0.588311\pi$
$853$	1.82662	−	0.585681i	0.0625421	−	0.0200533i	0.336432	+	0.941708i	$0.390780\pi$
$854$	110.845	−	12.9559i	3.79304	−	0.443343i
$855$	6.39371	+	29.9411i	0.218660	+	1.02397i
$856$	−4.76666	−	11.0504i	−0.162921	−	0.377694i
$857$	−2.74607	+	8.02568i	−0.0938038	+	0.274152i	−0.983068	−	0.183242i	$-0.941341\pi$
$857$	−2.74607	+	8.02568i	−0.0938038	+	0.274152i	0.889264	+	0.457394i	$0.151217\pi$
$858$	2.41407	−	2.98400i	0.0824150	−	0.101872i
$859$	−11.7803	+	10.6900i	−0.401938	+	0.364739i	−0.847758	−	0.530383i	$-0.822048\pi$
$859$	−11.7803	+	10.6900i	−0.401938	+	0.364739i	0.445820	+	0.895123i	$0.352912\pi$
$860$	8.92521	+	26.0849i	0.304347	+	0.889488i
$861$	21.1453	+	7.73142i	0.720630	+	0.263486i
$862$	2.53799	−	26.0928i	0.0864442	−	0.888724i
$863$	26.8817	−	9.78413i	0.915063	−	0.333056i	0.158790	−	0.987312i	$-0.449241\pi$
$863$	26.8817	−	9.78413i	0.915063	−	0.333056i	0.756272	+	0.654257i	$0.227018\pi$
$864$	38.7356	−	15.6266i	1.31781	−	0.531627i
$865$	−8.19318	−	2.98207i	−0.278577	−	0.101394i
$866$	−35.0906	+	73.3858i	−1.19243	+	2.49375i
$867$	−62.9353	−	41.5256i	−2.13739	−	1.41028i
$868$	−46.2225	+	7.22907i	−1.56889	+	0.245371i
$869$	3.05355	+	2.36668i	0.103585	+	0.0802842i
$870$	−10.3233	+	10.0953i	−0.349992	+	0.342263i
$871$	−0.450776	−	23.2419i	−0.0152740	−	0.787521i
$872$	0.545941	+	0.274182i	0.0184879	+	0.00928497i
$873$	34.3558	−	2.56892i	1.16277	−	0.0869447i
$874$	54.6968	+	35.9746i	1.85015	+	1.21686i
$875$	47.4195	+	1.84009i	1.60307	+	0.0622065i
$876$	−4.66219	+	17.9904i	−0.157521	+	0.607839i
$877$	3.40405	+	34.9967i	0.114947	+	1.18175i	0.858405	+	0.512973i	$0.171456\pi$
$877$	3.40405	+	34.9967i	0.114947	+	1.18175i	−0.743458	+	0.668782i	$0.766816\pi$
$878$	10.5400	+	22.0425i	0.355708	+	0.743900i
$879$	7.29774	−	52.8503i	0.246147	−	1.78260i
$880$	−0.916253	+	0.710149i	−0.0308869	+	0.0239391i
$881$	22.4854	−	23.8332i	0.757554	−	0.802960i	−0.227759	−	0.973717i	$-0.573140\pi$
$881$	22.4854	−	23.8332i	0.757554	−	0.802960i	0.985313	+	0.170757i	$0.0546214\pi$
$882$	−72.1530	−	36.5022i	−2.42952	−	1.22909i
$883$	9.66049	−	32.2683i	0.325102	−	1.08591i	−0.626715	−	0.779248i	$-0.715601\pi$
$883$	9.66049	−	32.2683i	0.325102	−	1.08591i	0.951817	−	0.306667i	$-0.0992136\pi$
$884$	−40.7666	+	50.5427i	−1.37113	+	1.69993i
$885$	2.84754	+	5.42522i	0.0957191	+	0.182367i
$886$	−0.363804	−	0.577215i	−0.0122222	−	0.0193919i
$887$	−14.3318	+	7.90796i	−0.481215	+	0.265523i	−0.705120	−	0.709088i	$-0.749107\pi$
$887$	−14.3318	+	7.90796i	−0.481215	+	0.265523i	0.223905	+	0.974611i	$0.428119\pi$
$888$	3.82903	+	0.453247i	0.128494	+	0.0152100i
$889$	5.33328	+	20.7051i	0.178872	+	0.694425i
$890$	−9.49368	+	16.4435i	−0.318229	+	0.551189i
$891$	0.975725	+	2.57203i	0.0326880	+	0.0861662i
$892$	−24.3325	−	42.1452i	−0.814713	−	1.41112i
$893$	2.00188	−	1.96343i	0.0669905	−	0.0657038i
$894$	41.5123	−	9.77426i	1.38838	−	0.326900i
$895$	0.168089	−	8.66665i	0.00561861	−	0.289694i
$896$	14.3428	−	27.2291i	0.479159	−	0.909661i
$897$	−18.3356	+	14.1682i	−0.612209	+	0.473061i
$898$	11.7776	+	30.5047i	0.393023	+	1.01796i
$899$	−13.1750	+	3.12254i	−0.439412	+	0.104143i
$900$	23.0592	+	8.46961i	0.768642	+	0.282320i
$901$	9.90853	+	33.0968i	0.330101	+	1.10261i
$902$	−1.73693	−	0.709615i	−0.0578336	−	0.0236276i
$903$	−51.2261	+	46.3483i	−1.70470	+	1.54237i
$904$	−4.49562	−	0.349428i	−0.149522	−	0.0116218i
$905$	5.91112	−	4.22502i	0.196492	−	0.140444i
$906$	27.6363	+	58.0150i	0.918154	+	1.92742i
$907$	18.2033	−	28.8815i	0.604430	−	0.958993i	−0.394762	−	0.918784i	$-0.629173\pi$
$907$	18.2033	−	28.8815i	0.604430	−	0.958993i	0.999191	−	0.0402094i	$-0.0128025\pi$
$908$	3.39628	−	58.3119i	0.112709	−	1.93515i
$909$	−4.20849	−	31.5009i	−0.139587	−	1.04482i
$910$	−34.2886	+	22.5520i	−1.13666	+	0.747591i
$911$	31.5283	−	19.0274i	1.04458	−	0.630407i	0.112869	−	0.993610i	$-0.463996\pi$
$911$	31.5283	−	19.0274i	1.04458	−	0.630407i	0.931710	+	0.363203i	$0.118317\pi$
$912$	−23.4037	−	34.2310i	−0.774973	−	1.13350i
$913$	0.115102	−	0.0470243i	0.00380932	−	0.00155628i
$914$	39.7974	+	49.3411i	1.31638	+	1.63206i
$915$	15.6493	+	21.0851i	0.517349	+	0.697053i
$916$	−13.5217	−	19.7152i	−0.446771	−	0.651408i
$917$	11.3383	+	64.3028i	0.374424	+	2.12346i
$918$	−30.2644	−	79.4258i	−0.998875	−	2.62144i
$919$	2.21386	−	12.5555i	0.0730287	−	0.414166i	−0.926275	−	0.376849i	$-0.877008\pi$
$919$	2.21386	−	12.5555i	0.0730287	−	0.414166i	0.999303	−	0.0373174i	$-0.0118812\pi$
$920$	−3.96803	+	1.80369i	−0.130822	+	0.0594659i
$921$	9.76365	+	0.0143296i	0.321723	+	0.000472175i
$922$	69.5552	+	13.6602i	2.29068	+	0.449874i
$923$	−10.6970	−	3.42986i	−0.352096	−	0.112895i
$924$	4.99047	+	2.76319i	0.164174	+	0.0909022i
$925$	−5.60451	−	6.42206i	−0.184275	−	0.211156i
$926$	−26.9442	+	36.1923i	−0.885441	+	1.18935i
$927$	9.63287	+	5.85211i	0.316385	+	0.192208i
$928$	9.92863	−	23.0172i	0.325923	−	0.755575i
$929$	−30.7346	−	27.8901i	−1.00837	−	0.915046i	−0.0119778	−	0.999928i	$-0.503813\pi$
$929$	−30.7346	−	27.8901i	−1.00837	−	0.915046i	−0.996391	+	0.0848824i	$0.972949\pi$
$930$	−12.5986	−	15.6668i	−0.413125	−	0.513735i
$931$	−25.6669	+	99.6451i	−0.841199	+	3.26574i
$932$	6.70518	+	6.57640i	0.219636	+	0.215417i
$933$	−0.372132	+	17.8367i	−0.0121830	+	0.583949i
$934$	−15.8543	+	73.1914i	−0.518767	+	2.39490i
$935$	1.80564	+	2.42539i	0.0590506	+	0.0793187i
$936$	−8.81341	+	2.42553i	−0.288075	+	0.0792809i
$937$	−20.7457	−	2.42483i	−0.677733	−	0.0792156i	−0.229739	−	0.973252i	$-0.573787\pi$
$937$	−20.7457	−	2.42483i	−0.677733	−	0.0792156i	−0.447994	+	0.894037i	$0.647861\pi$
$938$	61.9152	−	12.1597i	2.02160	−	0.397030i
$939$	−3.78203	+	11.0007i	−0.123422	+	0.358993i
$940$	0.227604	+	1.05074i	0.00742362	+	0.0342713i
$941$	16.2050	−	18.5689i	0.528267	−	0.605327i	−0.425838	−	0.904800i	$-0.640021\pi$
$941$	16.2050	−	18.5689i	0.528267	−	0.605327i	0.954105	+	0.299472i	$0.0968106\pi$
$942$	−1.45913	+	0.528656i	−0.0475411	+	0.0172246i
$943$	9.21543	+	6.58679i	0.300096	+	0.214495i
$944$	−6.35710	−	5.33424i	−0.206906	−	0.173615i
$945$	−1.58096	−	29.3713i	−0.0514285	−	0.955448i
$946$	4.41020	−	3.70059i	0.143388	−	0.120317i
$947$	−12.0534	+	0.936861i	−0.391681	+	0.0304439i	−0.271823	−	0.962347i	$-0.587627\pi$
$947$	−12.0534	+	0.936861i	−0.391681	+	0.0304439i	−0.119858	+	0.992791i	$0.538244\pi$
$948$	−15.1219	−	50.7820i	−0.491138	−	1.64932i
$949$	−5.50633	+	14.2617i	−0.178743	+	0.462956i
$950$	7.72638	−	56.5671i	0.250677	−	1.83528i
$951$	34.7978	−	15.7559i	1.12839	−	0.510921i
$952$	−26.7974	−	14.7862i	−0.868509	−	0.479223i
$953$	1.61763	+	27.7737i	0.0524002	+	0.899677i	0.917415	+	0.397931i	$0.130272\pi$
$953$	1.61763	+	27.7737i	0.0524002	+	0.899677i	−0.865015	+	0.501746i	$0.832691\pi$
$954$	−9.14477	+	26.4727i	−0.296073	+	0.857084i
$955$	7.02609	−	3.52863i	0.227359	−	0.114184i
$956$	−21.2320	−	40.3080i	−0.686693	−	1.30365i
$957$	1.50193	+	0.685375i	0.0485506	+	0.0221550i
$958$	−75.4876	−	34.3133i	−2.43890	−	1.10861i
$959$	44.4434	−	64.8001i	1.43515	−	2.09250i
$960$	24.0648	−	0.898453i	0.776688	−	0.0289975i
$961$	1.64396	+	12.0359i	0.0530308	+	0.388254i
$962$	17.7731	+	4.21229i	0.573027	+	0.135810i
$963$	39.7302	+	9.53949i	1.28029	+	0.307406i
$964$	−12.7540	−	13.5185i	−0.410780	−	0.435402i
$965$	−6.28729	−	0.983315i	−0.202395	−	0.0316540i
$966$	−46.5150	−	42.3348i	−1.49660	−	1.36210i
$967$	13.2525	−	0.514259i	0.426173	−	0.0165375i	0.175203	−	0.984532i	$-0.443942\pi$
$967$	13.2525	−	0.514259i	0.426173	−	0.0165375i	0.250970	+	0.967995i	$0.419250\pi$
$968$	8.25102	+	4.97951i	0.265198	+	0.160048i
$969$	−90.4539	+	59.3025i	−2.90580	+	1.90507i
$970$	29.5750	+	8.23276i	0.949596	+	0.264338i
$971$	−34.4989			−1.10712			−0.553561	−	0.832808i	$-0.686732\pi$
$971$	−34.4989			−1.10712			−0.553561	+	0.832808i	$0.686732\pi$
$972$	9.67886	−	36.4657i	0.310450	−	1.16964i
$973$	−3.34710			−0.107303
$974$	−87.4000	−	24.3295i	−2.80048	−	0.779566i
$975$	18.0449	+	9.09566i	0.577898	+	0.291294i
$976$	−30.4487	−	18.3759i	−0.974640	−	0.588198i
$977$	35.8742	−	1.39208i	1.14772	−	0.0445367i	0.542116	−	0.840304i	$-0.317623\pi$
$977$	35.8742	−	1.39208i	1.14772	−	0.0445367i	0.605603	+	0.795767i	$0.292932\pi$
$978$	6.73924	−	2.14995i	0.215497	−	0.0687477i
$979$	2.14490	+	0.335456i	0.0685512	+	0.0107212i
$980$	−27.0739	−	28.6966i	−0.864843	−	0.916680i
$981$	−1.85628	+	0.925448i	−0.0592666	+	0.0295473i
$982$	80.4758	+	19.0731i	2.56808	+	0.608647i
$983$	−0.626154	−	4.58426i	−0.0199712	−	0.146215i	0.978114	−	0.208070i	$-0.0667182\pi$
$983$	−0.626154	−	4.58426i	−0.0199712	−	0.146215i	−0.998085	+	0.0618548i	$0.980298\pi$
$984$	2.37711	+	3.78384i	0.0757794	+	0.120624i
$985$	6.87067	−	10.0177i	0.218918	−	0.319190i
$986$	−46.4376	−	21.1085i	−1.47887	−	0.672231i
$987$	−2.19393	+	1.56327i	−0.0698337	+	0.0497594i
$988$	31.2191	+	59.2681i	0.993213	+	1.88557i
$989$	−31.0593	+	15.5986i	−0.987627	+	0.496005i
$990$	0.0403395	+	2.45094i	0.00128207	+	0.0778961i
$991$	−0.113620	−	1.95078i	−0.00360926	−	0.0619685i	0.996023	−	0.0891011i	$-0.0283994\pi$
$991$	−0.113620	−	1.95078i	−0.00360926	−	0.0619685i	−0.999632	+	0.0271326i	$0.991362\pi$
$992$	30.5590	+	16.8617i	0.970248	+	0.535360i
$993$	6.48700	+	4.65103i	0.205859	+	0.147596i
$994$	4.12641	−	30.2107i	0.130882	−	0.958224i
$995$	−2.51204	+	6.50635i	−0.0796370	+	0.206265i
$996$	−1.65874	−	0.395701i	−0.0525592	−	0.0125383i
$997$	−37.4385	+	2.90995i	−1.18569	+	0.0921591i	−0.655149	−	0.755500i	$-0.727394\pi$
$997$	−37.4385	+	2.90995i	−1.18569	+	0.0921591i	−0.530541	+	0.847659i	$0.678011\pi$
$998$	−24.4969	+	20.5553i	−0.775436	+	0.650668i
$999$	−9.02539	+	9.48236i	−0.285551	+	0.300009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.i.a.103.23	✓	1404
3.2	odd	2		729.2.i.a.685.4		1404
243.92	odd	162		729.2.i.a.613.4		1404
243.151	even	81	inner	243.2.i.a.151.23	yes	1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.103.23	✓	1404	1.1	even	1	trivial
243.2.i.a.151.23	yes	1404	243.151	even	81	inner
729.2.i.a.613.4		1404	243.92	odd	162
729.2.i.a.685.4		1404	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.02543 + 0.563818i) q^{2} +(-0.0981720 - 1.72927i) q^{3} +(2.07216 + 1.25056i) q^{4} +(-1.27054 + 0.0493029i) q^{5} +(0.776151 - 3.55787i) q^{6} +(4.39851 + 0.687914i) q^{7} +(0.606370 + 0.642715i) q^{8} +(-2.98072 + 0.339531i) q^{9} +(-2.60120 - 0.616496i) q^{10} +(0.0413646 + 0.302842i) q^{11} +(1.95912 - 3.70609i) q^{12} +(1.95043 - 2.84380i) q^{13} +(8.52104 + 3.87329i) q^{14} +(0.209990 + 2.19227i) q^{15} +(-1.39012 - 2.63908i) q^{16} +(-6.95270 + 3.49177i) q^{17} +(-6.22870 - 0.992889i) q^{18} +(0.466686 + 8.01269i) q^{19} +(-2.69443 - 1.48672i) q^{20} +(0.757777 - 7.67373i) q^{21} +(-0.0869667 + 0.636709i) q^{22} +(1.39733 - 3.61918i) q^{23} +(1.05190 - 1.11167i) q^{24} +(-3.37311 + 0.262179i) q^{25} +(5.55385 - 4.66024i) q^{26} +(0.879763 + 5.12113i) q^{27} +(8.25415 + 6.92605i) q^{28} +(2.53701 + 1.81334i) q^{29} +(-0.810721 + 4.55869i) q^{30} +(-2.85491 + 3.27137i) q^{31} +(-1.70176 - 7.85622i) q^{32} +(0.519634 - 0.101261i) q^{33} +(-16.0510 + 3.15231i) q^{34} +(-5.62241 - 0.657166i) q^{35} +(-6.60114 - 3.02400i) q^{36} +(1.50445 + 2.02083i) q^{37} +(-3.57246 + 16.4923i) q^{38} +(-5.10916 - 3.09363i) q^{39} +(-0.802107 - 0.786701i) q^{40} +(-0.728308 + 2.82746i) q^{41} +(5.86142 - 15.1154i) q^{42} +(-6.63437 - 6.02037i) q^{43} +(-0.293007 + 0.679266i) q^{44} +(3.77040 - 0.578347i) q^{45} +(4.87077 - 6.54258i) q^{46} +(-0.229710 - 0.263218i) q^{47} +(-4.42720 + 2.66297i) q^{48} +(12.2079 + 3.91431i) q^{49} +(-6.97985 - 1.37080i) q^{50} +(6.72077 + 11.6803i) q^{51} +(7.59793 - 3.45368i) q^{52} +(0.771083 - 4.37303i) q^{53} +(-1.10549 + 10.8686i) q^{54} +(-0.0674864 - 0.382735i) q^{55} +(2.22499 + 3.24412i) q^{56} +(13.8103 - 1.59365i) q^{57} +(4.11614 + 5.10322i) q^{58} +(2.57549 - 1.05221i) q^{59} +(-2.30642 + 4.80534i) q^{60} +(10.2081 - 6.16060i) q^{61} +(-7.62689 + 5.01629i) q^{62} +(-13.3443 - 0.557053i) q^{63} +(0.635797 - 10.9162i) q^{64} +(-2.33790 + 3.70933i) q^{65} +(1.10958 + 0.0878816i) q^{66} +(5.48432 - 3.91995i) q^{67} +(-18.7738 - 1.45921i) q^{68} +(-6.39571 - 2.06106i) q^{69} +(-11.0173 - 4.50107i) q^{70} +(-0.934287 - 3.12074i) q^{71} +(-2.02564 - 1.70987i) q^{72} +(-4.31382 + 1.02239i) q^{73} +(1.90779 + 4.94130i) q^{74} +(0.784523 + 5.80728i) q^{75} +(-9.05327 + 17.1872i) q^{76} +(-0.0263870 + 1.36051i) q^{77} +(-8.60402 - 9.14659i) q^{78} +(9.02377 - 8.85045i) q^{79} +(1.89632 + 3.28453i) q^{80} +(8.76944 - 2.02410i) q^{81} +(-3.06932 + 5.31621i) q^{82} +(-0.101470 - 0.393932i) q^{83} +(11.1667 - 14.9536i) q^{84} +(8.66155 - 4.77924i) q^{85} +(-10.0431 - 15.9345i) q^{86} +(2.88669 - 4.56518i) q^{87} +(-0.169559 + 0.210220i) q^{88} +(2.03708 - 6.80431i) q^{89} +(7.96278 + 0.954416i) q^{90} +(10.5353 - 11.1667i) q^{91} +(7.42149 - 5.75209i) q^{92} +(5.93734 + 4.61575i) q^{93} +(-0.316855 - 0.662646i) q^{94} +(-0.987994 - 10.1575i) q^{95} +(-13.4184 + 3.71407i) q^{96} +(-11.4753 - 0.445293i) q^{97} +(22.5194 + 14.8112i) q^{98} +(-0.226121 - 0.888644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) \) 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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