LMFDB - Embedded newform 117.2.h.a.16.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(16,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("117.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.4
Character	$\chi$	$=$	117.16
Dual form			117.2.h.a.22.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.20426 q^{2} +(1.45393 - 0.941317i) q^{3} -0.549753 q^{4} +(1.89177 + 3.27665i) q^{5} +(-1.75092 + 1.13359i) q^{6} +(-0.150228 - 0.260203i) q^{7} +3.07057 q^{8} +(1.22785 - 2.73722i) q^{9} +O(q^{10})$	\(q-1.20426 q^{2} +(1.45393 - 0.941317i) q^{3} -0.549753 q^{4} +(1.89177 + 3.27665i) q^{5} +(-1.75092 + 1.13359i) q^{6} +(-0.150228 - 0.260203i) q^{7} +3.07057 q^{8} +(1.22785 - 2.73722i) q^{9} +(-2.27819 - 3.94594i) q^{10} +1.28462 q^{11} +(-0.799304 + 0.517492i) q^{12} +(0.423704 - 3.58057i) q^{13} +(0.180914 + 0.313352i) q^{14} +(5.83487 + 2.98327i) q^{15} -2.59827 q^{16} +(-2.63848 + 4.56998i) q^{17} +(-1.47865 + 3.29634i) q^{18} +(-0.829906 + 1.43744i) q^{19} +(-1.04001 - 1.80135i) q^{20} +(-0.463355 - 0.236905i) q^{21} -1.54702 q^{22} +(1.67399 - 2.89944i) q^{23} +(4.46441 - 2.89038i) q^{24} +(-4.65760 + 8.06721i) q^{25} +(-0.510251 + 4.31194i) q^{26} +(-0.791390 - 5.13553i) q^{27} +(0.0825883 + 0.143047i) q^{28} -9.63240 q^{29} +(-7.02672 - 3.59264i) q^{30} +(-3.29700 - 5.71056i) q^{31} -3.01215 q^{32} +(1.86775 - 1.20923i) q^{33} +(3.17742 - 5.50346i) q^{34} +(0.568394 - 0.984488i) q^{35} +(-0.675011 + 1.50480i) q^{36} +(1.97702 + 3.42430i) q^{37} +(0.999424 - 1.73105i) q^{38} +(-2.75441 - 5.60475i) q^{39} +(5.80882 + 10.0612i) q^{40} +(-1.43368 + 2.48321i) q^{41} +(0.558000 + 0.285296i) q^{42} +(0.0104220 + 0.0180514i) q^{43} -0.706223 q^{44} +(11.2917 - 1.15499i) q^{45} +(-2.01592 + 3.49168i) q^{46} +(0.954216 - 1.65275i) q^{47} +(-3.77771 + 2.44579i) q^{48} +(3.45486 - 5.98400i) q^{49} +(5.60898 - 9.71503i) q^{50} +(0.465627 + 9.12810i) q^{51} +(-0.232933 + 1.96843i) q^{52} -7.15248 q^{53} +(0.953041 + 6.18453i) q^{54} +(2.43021 + 4.20924i) q^{55} +(-0.461286 - 0.798970i) q^{56} +(0.146458 + 2.87114i) q^{57} +11.5999 q^{58} +8.73826 q^{59} +(-3.20774 - 1.64006i) q^{60} +(-2.56839 - 4.44858i) q^{61} +(3.97045 + 6.87702i) q^{62} +(-0.896689 + 0.0917194i) q^{63} +8.82395 q^{64} +(12.5338 - 5.38529i) q^{65} +(-2.24926 + 1.45623i) q^{66} +(-4.15570 + 7.19788i) q^{67} +(1.45051 - 2.51236i) q^{68} +(-0.295418 - 5.79134i) q^{69} +(-0.684496 + 1.18558i) q^{70} +(4.64070 - 8.03792i) q^{71} +(3.77018 - 8.40484i) q^{72} -4.69504 q^{73} +(-2.38085 - 4.12376i) q^{74} +(0.821952 + 16.1135i) q^{75} +(0.456243 - 0.790236i) q^{76} +(-0.192986 - 0.334261i) q^{77} +(3.31703 + 6.74959i) q^{78} +(6.65302 - 11.5234i) q^{79} +(-4.91533 - 8.51360i) q^{80} +(-5.98479 - 6.72177i) q^{81} +(1.72653 - 2.99044i) q^{82} +(-6.45522 + 11.1808i) q^{83} +(0.254730 + 0.130239i) q^{84} -19.9656 q^{85} +(-0.0125508 - 0.0217386i) q^{86} +(-14.0049 + 9.06714i) q^{87} +3.94451 q^{88} +(3.19907 + 5.54096i) q^{89} +(-13.5982 + 1.39091i) q^{90} +(-0.995325 + 0.427653i) q^{91} +(-0.920281 + 1.59397i) q^{92} +(-10.1691 - 5.19926i) q^{93} +(-1.14913 + 1.99035i) q^{94} -6.27997 q^{95} +(-4.37946 + 2.83539i) q^{96} +(1.88195 + 3.25964i) q^{97} +(-4.16056 + 7.20630i) q^{98} +(1.57731 - 3.51629i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} - q^{3} + 18 q^{4} - 2 q^{5} - 12 q^{6} + 3 q^{7} - 18 q^{8} - 3 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 - q^3 + 18 * q^4 - 2 * q^5 - 12 * q^6 + 3 * q^7 - 18 * q^8 - 3 * q^9	\( 24 q - 2 q^{2} - q^{3} + 18 q^{4} - 2 q^{5} - 12 q^{6} + 3 q^{7} - 18 q^{8} - 3 q^{9} + 6 q^{11} - 3 q^{12} + 2 q^{14} + 11 q^{15} + 6 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} - 11 q^{20} - 25 q^{21} - 18 q^{22} + 17 q^{23} - 12 q^{24} - 6 q^{25} - 12 q^{26} + 2 q^{27} - 24 q^{29} - 8 q^{30} - 6 q^{31} - 38 q^{32} + 11 q^{33} + 18 q^{35} - 28 q^{36} - 3 q^{37} + 8 q^{38} + 3 q^{39} - 12 q^{40} + 5 q^{41} + 15 q^{42} - 3 q^{43} + 44 q^{44} + 19 q^{45} - 6 q^{46} + 21 q^{47} + 23 q^{48} + 3 q^{49} - 20 q^{50} + 7 q^{51} - 24 q^{52} - 20 q^{53} + 39 q^{54} + 3 q^{55} + 40 q^{56} + 9 q^{57} + 18 q^{58} + 38 q^{59} + 51 q^{60} - 6 q^{61} + 19 q^{62} + 13 q^{63} - 42 q^{64} - 2 q^{65} - 18 q^{66} - 6 q^{67} - 31 q^{69} + 27 q^{70} + 14 q^{71} - 18 q^{72} + 6 q^{73} + 29 q^{74} + 74 q^{75} - 15 q^{76} + 4 q^{77} + 80 q^{78} + 3 q^{79} - 16 q^{80} - 27 q^{81} - 9 q^{82} - 33 q^{83} + 5 q^{84} + 72 q^{86} - 32 q^{87} - 78 q^{88} - q^{89} + 21 q^{90} - 6 q^{91} - 10 q^{92} - 84 q^{93} - 9 q^{94} - 100 q^{95} - 79 q^{96} + 24 q^{97} - 61 q^{98} + 18 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 - q^3 + 18 * q^4 - 2 * q^5 - 12 * q^6 + 3 * q^7 - 18 * q^8 - 3 * q^9 + 6 * q^11 - 3 * q^12 + 2 * q^14 + 11 * q^15 + 6 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 - 11 * q^20 - 25 * q^21 - 18 * q^22 + 17 * q^23 - 12 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 - 24 * q^29 - 8 * q^30 - 6 * q^31 - 38 * q^32 + 11 * q^33 + 18 * q^35 - 28 * q^36 - 3 * q^37 + 8 * q^38 + 3 * q^39 - 12 * q^40 + 5 * q^41 + 15 * q^42 - 3 * q^43 + 44 * q^44 + 19 * q^45 - 6 * q^46 + 21 * q^47 + 23 * q^48 + 3 * q^49 - 20 * q^50 + 7 * q^51 - 24 * q^52 - 20 * q^53 + 39 * q^54 + 3 * q^55 + 40 * q^56 + 9 * q^57 + 18 * q^58 + 38 * q^59 + 51 * q^60 - 6 * q^61 + 19 * q^62 + 13 * q^63 - 42 * q^64 - 2 * q^65 - 18 * q^66 - 6 * q^67 - 31 * q^69 + 27 * q^70 + 14 * q^71 - 18 * q^72 + 6 * q^73 + 29 * q^74 + 74 * q^75 - 15 * q^76 + 4 * q^77 + 80 * q^78 + 3 * q^79 - 16 * q^80 - 27 * q^81 - 9 * q^82 - 33 * q^83 + 5 * q^84 + 72 * q^86 - 32 * q^87 - 78 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 - 84 * q^93 - 9 * q^94 - 100 * q^95 - 79 * q^96 + 24 * q^97 - 61 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.20426			−0.851542			−0.425771	−	0.904831i	$-0.639997\pi$
$2$	−1.20426			−0.851542			−0.425771	+	0.904831i	$0.639997\pi$
$3$	1.45393	−	0.941317i	0.839429	−	0.543470i
$3$	1.45393	−	0.941317i	0.839429	−	0.543470i
$4$	−0.549753			−0.274876
$5$	1.89177	+	3.27665i	0.846026	+	1.46536i	0.884727	+	0.466110i	$0.154345\pi$
$5$	1.89177	+	3.27665i	0.846026	+	1.46536i	−0.0387007	+	0.999251i	$0.512322\pi$
$6$	−1.75092	+	1.13359i	−0.714809	+	0.462787i
$7$	−0.150228	−	0.260203i	−0.0567809	−	0.0983473i	0.836238	−	0.548367i	$-0.184750\pi$
$7$	−0.150228	−	0.260203i	−0.0567809	−	0.0983473i	−0.893019	+	0.450020i	$0.851417\pi$
$8$	3.07057			1.08561
$9$	1.22785	−	2.73722i	0.409282	−	0.912408i
$10$	−2.27819	−	3.94594i	−0.720427	−	1.24782i
$11$	1.28462			0.387327			0.193664	−	0.981068i	$-0.437963\pi$
$11$	1.28462			0.387327			0.193664	+	0.981068i	$0.437963\pi$
$12$	−0.799304	+	0.517492i	−0.230739	+	0.149387i
$13$	0.423704	−	3.58057i	0.117514	−	0.993071i
$13$	0.423704	−	3.58057i	0.117514	−	0.993071i
$14$	0.180914	+	0.313352i	0.0483513	+	0.0837469i
$15$	5.83487	+	2.98327i	1.50656	+	0.770276i
$16$	−2.59827			−0.649567
$17$	−2.63848	+	4.56998i	−0.639926	+	1.10838i	0.345523	+	0.938410i	$0.387702\pi$
$17$	−2.63848	+	4.56998i	−0.639926	+	1.10838i	−0.985449	+	0.169974i	$0.945632\pi$
$18$	−1.47865	+	3.29634i	−0.348520	+	0.776954i
$19$	−0.829906	+	1.43744i	−0.190393	+	0.329771i	−0.945381	−	0.325968i	$-0.894310\pi$
$19$	−0.829906	+	1.43744i	−0.190393	+	0.329771i	0.754987	+	0.655739i	$0.227643\pi$
$20$	−1.04001	−	1.80135i	−0.232553	−	0.402793i
$21$	−0.463355	−	0.236905i	−0.101112	−	0.0516969i
$22$	−1.54702			−0.329825
$23$	1.67399	−	2.89944i	0.349051	−	0.604574i	−0.637030	−	0.770839i	$-0.719837\pi$
$23$	1.67399	−	2.89944i	0.349051	−	0.604574i	0.986081	+	0.166265i	$0.0531706\pi$
$24$	4.46441	−	2.89038i	0.911293	−	0.589996i
$25$	−4.65760	+	8.06721i	−0.931521	+	1.61344i
$26$	−0.510251	+	4.31194i	−0.100068	+	0.845642i
$27$	−0.791390	−	5.13553i	−0.152303	−	0.988334i
$28$	0.0825883	+	0.143047i	0.0156077	+	0.0270334i
$29$	−9.63240			−1.78869			−0.894346	−	0.447376i	$-0.852359\pi$
$29$	−9.63240			−1.78869			−0.894346	+	0.447376i	$0.852359\pi$
$30$	−7.02672	−	3.59264i	−1.28290	−	0.655923i
$31$	−3.29700	−	5.71056i	−0.592158	−	1.02565i	−0.993941	−	0.109913i	$-0.964943\pi$
$31$	−3.29700	−	5.71056i	−0.592158	−	1.02565i	0.401783	−	0.915735i	$-0.368391\pi$
$32$	−3.01215			−0.532478
$33$	1.86775	−	1.20923i	0.325134	−	0.210500i
$34$	3.17742	−	5.50346i	0.544924	−	0.943836i
$35$	0.568394	−	0.984488i	0.0960762	−	0.166409i
$36$	−0.675011	+	1.50480i	−0.112502	+	0.250799i
$37$	1.97702	+	3.42430i	0.325020	+	0.562952i	0.981517	−	0.191378i	$-0.0612955\pi$
$37$	1.97702	+	3.42430i	0.325020	+	0.562952i	−0.656496	+	0.754329i	$0.727962\pi$
$38$	0.999424	−	1.73105i	0.162128	−	0.280814i
$39$	−2.75441	−	5.60475i	−0.441059	−	0.897478i
$40$	5.80882	+	10.0612i	0.918455	+	1.59081i
$41$	−1.43368	+	2.48321i	−0.223904	+	0.387813i	−0.955990	−	0.293399i	$-0.905213\pi$
$41$	−1.43368	+	2.48321i	−0.223904	+	0.387813i	0.732086	+	0.681212i	$0.238547\pi$
$42$	0.558000	+	0.285296i	0.0861013	+	0.0440221i
$43$	0.0104220	+	0.0180514i	0.00158933	+	0.00275281i	0.866819	−	0.498623i	$-0.166161\pi$
$43$	0.0104220	+	0.0180514i	0.00158933	+	0.00275281i	−0.865230	+	0.501376i	$0.832827\pi$
$44$	−0.706223			−0.106467
$45$	11.2917	−	1.15499i	1.68327	−	0.172176i
$46$	−2.01592	+	3.49168i	−0.297232	+	0.514821i
$47$	0.954216	−	1.65275i	0.139187	−	0.241079i	−0.788002	−	0.615672i	$-0.788884\pi$
$47$	0.954216	−	1.65275i	0.139187	−	0.241079i	0.927189	+	0.374594i	$0.122218\pi$
$48$	−3.77771	+	2.44579i	−0.545265	+	0.353020i
$49$	3.45486	−	5.98400i	0.493552	−	0.854857i
$50$	5.60898	−	9.71503i	0.793229	−	1.37391i
$51$	0.465627	+	9.12810i	0.0652008	+	1.27819i
$52$	−0.232933	+	1.96843i	−0.0323019	+	0.272972i
$53$	−7.15248			−0.982469			−0.491235	−	0.871027i	$-0.663454\pi$
$53$	−7.15248			−0.982469			−0.491235	+	0.871027i	$0.663454\pi$
$54$	0.953041	+	6.18453i	0.129693	+	0.841608i
$55$	2.43021	+	4.20924i	0.327689	+	0.567574i
$56$	−0.461286	−	0.798970i	−0.0616419	−	0.106767i
$57$	0.146458	+	2.87114i	0.0193988	+	0.380292i
$58$	11.5999			1.52315
$59$	8.73826			1.13762			0.568812	−	0.822468i	$-0.307403\pi$
$59$	8.73826			1.13762			0.568812	+	0.822468i	$0.307403\pi$
$60$	−3.20774	−	1.64006i	−0.414117	−	0.211731i
$61$	−2.56839	−	4.44858i	−0.328849	−	0.569583i	0.653435	−	0.756983i	$-0.273327\pi$
$61$	−2.56839	−	4.44858i	−0.328849	−	0.569583i	−0.982284	+	0.187400i	$0.939994\pi$
$62$	3.97045	+	6.87702i	0.504247	+	0.873382i
$63$	−0.896689	+	0.0917194i	−0.112972	+	0.0115556i
$64$	8.82395			1.10299
$65$	12.5338	−	5.38529i	1.55463	−	0.667963i
$66$	−2.24926	+	1.45623i	−0.276865	+	0.179250i
$67$	−4.15570	+	7.19788i	−0.507700	+	0.879361i	0.492261	+	0.870448i	$0.336171\pi$
$67$	−4.15570	+	7.19788i	−0.507700	+	0.879361i	−0.999960	+	0.00891361i	$0.997163\pi$
$68$	1.45051	−	2.51236i	0.175901	−	0.304669i
$69$	−0.295418	−	5.79134i	−0.0355641	−	0.697196i
$70$	−0.684496	+	1.18558i	−0.0818129	+	0.141704i
$71$	4.64070	−	8.03792i	0.550749	−	0.953926i	−0.447471	−	0.894298i	$-0.647675\pi$
$71$	4.64070	−	8.03792i	0.550749	−	0.953926i	0.998221	−	0.0596277i	$-0.0189913\pi$
$72$	3.77018	−	8.40484i	0.444321	−	0.990520i
$73$	−4.69504			−0.549512			−0.274756	−	0.961514i	$-0.588597\pi$
$73$	−4.69504			−0.549512			−0.274756	+	0.961514i	$0.588597\pi$
$74$	−2.38085	−	4.12376i	−0.276769	−	0.479377i
$75$	0.821952	+	16.1135i	0.0949108	+	1.86062i
$76$	0.456243	−	0.790236i	0.0523346	−	0.0906463i
$77$	−0.192986	−	0.334261i	−0.0219928	−	0.0380926i
$78$	3.31703	+	6.74959i	0.375580	+	0.764240i
$79$	6.65302	−	11.5234i	0.748523	−	1.29648i	−0.200007	−	0.979794i	$-0.564097\pi$
$79$	6.65302	−	11.5234i	0.748523	−	1.29648i	0.948530	−	0.316686i	$-0.102570\pi$
$80$	−4.91533	−	8.51360i	−0.549550	−	0.951849i
$81$	−5.98479	−	6.72177i	−0.664977	−	0.746864i
$82$	1.72653	−	2.99044i	0.190663	−	0.330239i
$83$	−6.45522	+	11.1808i	−0.708552	+	1.22725i	0.256842	+	0.966453i	$0.417318\pi$
$83$	−6.45522	+	11.1808i	−0.708552	+	1.22725i	−0.965394	+	0.260795i	$0.916015\pi$
$84$	0.254730	+	0.130239i	0.0277934	+	0.0142103i
$85$	−19.9656			−2.16558
$86$	−0.0125508	−	0.0217386i	−0.00135339	−	0.00234413i
$87$	−14.0049	+	9.06714i	−1.50148	+	0.972100i
$88$	3.94451			0.420486
$89$	3.19907	+	5.54096i	0.339101	+	0.587340i	0.984264	−	0.176705i	$-0.0565438\pi$
$89$	3.19907	+	5.54096i	0.339101	+	0.587340i	−0.645163	+	0.764045i	$0.723210\pi$
$90$	−13.5982	+	1.39091i	−1.43337	+	0.146615i
$91$	−0.995325	+	0.427653i	−0.104338	+	0.0448302i
$92$	−0.920281	+	1.59397i	−0.0959459	+	0.166183i
$93$	−10.1691	−	5.19926i	−1.05448	−	0.539138i
$94$	−1.14913	+	1.99035i	−0.118523	+	0.205289i
$95$	−6.27997			−0.644311
$96$	−4.37946	+	2.83539i	−0.446977	+	0.289385i
$97$	1.88195	+	3.25964i	0.191083	+	0.330966i	0.945610	−	0.325304i	$-0.105467\pi$
$97$	1.88195	+	3.25964i	0.191083	+	0.330966i	−0.754526	+	0.656270i	$0.772133\pi$
$98$	−4.16056	+	7.20630i	−0.420280	+	0.727946i
$99$	1.57731	−	3.51629i	0.158526	−	0.353400i
$100$	2.56053	−	4.43497i	0.256053	−	0.443497i
$101$	−4.99159			−0.496681			−0.248341	−	0.968673i	$-0.579885\pi$
$101$	−4.99159			−0.496681			−0.248341	+	0.968673i	$0.579885\pi$
$102$	−0.560737	−	10.9926i	−0.0555212	−	1.08843i
$103$	2.16757	+	3.75434i	0.213577	+	0.369926i	0.952831	−	0.303500i	$-0.0981553\pi$
$103$	2.16757	+	3.75434i	0.213577	+	0.369926i	−0.739254	+	0.673426i	$0.764822\pi$
$104$	1.30101	−	10.9944i	0.127575	−	1.07809i
$105$	−0.100308	−	1.96642i	−0.00978901	−	0.191903i
$106$	8.61347			0.836614
$107$	1.57507	+	2.72809i	0.152267	+	0.263735i	0.932061	−	0.362302i	$-0.118009\pi$
$107$	1.57507	+	2.72809i	0.152267	+	0.263735i	−0.779793	+	0.626037i	$0.784676\pi$
$108$	0.435069	+	2.82327i	0.0418645	+	0.271670i
$109$	14.2728			1.36708			0.683542	−	0.729911i	$-0.260439\pi$
$109$	14.2728			1.36708			0.683542	+	0.729911i	$0.260439\pi$
$110$	−2.92661	−	5.06903i	−0.279041	−	0.483313i
$111$	6.09781	+	3.11770i	0.578779	+	0.295919i
$112$	0.390332	+	0.676076i	0.0368829	+	0.0638831i
$113$	5.27775			0.496489			0.248244	−	0.968697i	$-0.420146\pi$
$113$	5.27775			0.496489			0.248244	+	0.968697i	$0.420146\pi$
$114$	−0.176374	−	3.45761i	−0.0165189	−	0.323835i
$115$	12.6672			1.18123
$116$	5.29544			0.491669
$117$	−9.28058	−	5.55616i	−0.857990	−	0.513667i
$118$	−10.5232			−0.968735
$119$	1.58550			0.145342
$120$	17.9164	+	9.16033i	1.63554	+	0.836220i
$121$	−9.34975			−0.849978
$122$	3.09301	+	5.35726i	0.280028	+	0.485023i
$123$	0.253010	+	4.95998i	0.0228131	+	0.447226i
$124$	1.81253	+	3.13940i	0.162770	+	0.281926i
$125$	−16.3268			−1.46031
$126$	1.07985	−	0.110454i	0.0962006	−	0.00984004i
$127$	−5.36180	−	9.28691i	−0.475783	−	0.824080i	0.523832	−	0.851821i	$-0.324502\pi$
$127$	−5.36180	−	9.28691i	−0.475783	−	0.824080i	−0.999615	+	0.0277416i	$0.991168\pi$
$128$	−4.60205			−0.406768
$129$	0.0321449	+	0.0164351i	0.00283020	+	0.00144703i
$130$	−15.0940	+	6.48530i	−1.32383	+	0.568799i
$131$	1.67220	+	2.89633i	0.146101	+	0.253054i	0.929783	−	0.368108i	$-0.119994\pi$
$131$	1.67220	+	2.89633i	0.146101	+	0.253054i	−0.783682	+	0.621162i	$0.786661\pi$
$132$	−1.02680	+	0.664779i	−0.0893715	+	0.0578616i
$133$	0.498700			0.0432428
$134$	5.00455	−	8.66814i	0.432327	−	0.748813i
$135$	15.3302	−	12.3084i	1.31941	−	1.05934i
$136$	−8.10165	+	14.0325i	−0.694710	+	1.20327i
$137$	7.87786	+	13.6448i	0.673051	+	1.16576i	0.977035	+	0.213081i	$0.0683497\pi$
$137$	7.87786	+	13.6448i	0.673051	+	1.16576i	−0.303984	+	0.952677i	$0.598317\pi$
$138$	0.355761	+	6.97430i	0.0302844	+	0.593692i
$139$	21.5508			1.82791			0.913956	−	0.405813i	$-0.133012\pi$
$139$	21.5508			1.82791			0.913956	+	0.405813i	$0.133012\pi$
$140$	−0.312476	+	0.541225i	−0.0264091	+	0.0457419i
$141$	−0.168396	−	3.30121i	−0.0141815	−	0.278012i
$142$	−5.58862	+	9.67977i	−0.468986	+	0.812308i
$143$	0.544298	−	4.59967i	0.0455165	−	0.384643i
$144$	−3.19027	+	7.11204i	−0.265856	+	0.592670i
$145$	−18.2223	−	31.5620i	−1.51328	−	2.62108i
$146$	5.65405			0.467933
$147$	−0.609698	−	11.9525i	−0.0502870	−	0.985822i
$148$	−1.08687	−	1.88252i	−0.0893405	−	0.154742i
$149$	−12.8737			−1.05466			−0.527328	−	0.849662i	$-0.676806\pi$
$149$	−12.8737			−1.05466			−0.527328	+	0.849662i	$0.676806\pi$
$150$	−0.989845	−	19.4048i	−0.0808205	−	1.58440i
$151$	−6.21526	+	10.7652i	−0.505791	+	0.876056i	0.494187	+	0.869356i	$0.335466\pi$
$151$	−6.21526	+	10.7652i	−0.505791	+	0.876056i	−0.999978	+	0.00669978i	$0.997867\pi$
$152$	−2.54828	+	4.41376i	−0.206693	+	0.358003i
$153$	9.26943	+	12.8334i	0.749389	+	1.03751i
$154$	0.232405	+	0.402538i	0.0187278	+	0.0324374i
$155$	12.4743	−	21.6062i	1.00196	−	1.73545i
$156$	1.51425	+	3.08123i	0.121237	+	0.246696i
$157$	5.64417	+	9.77599i	0.450454	+	0.780209i	0.998414	−	0.0562954i	$-0.0179288\pi$
$157$	5.64417	+	9.77599i	0.450454	+	0.780209i	−0.547960	+	0.836504i	$0.684596\pi$
$158$	−8.01198	+	13.8772i	−0.637399	+	1.10401i
$159$	−10.3992	+	6.73275i	−0.824713	+	0.533942i
$160$	−5.69830	−	9.86974i	−0.450490	−	0.780271i
$161$	−1.00592			−0.0792777
$162$	7.20726	+	8.09478i	0.566256	+	0.635986i
$163$	−3.30893	+	5.73124i	−0.259176	+	0.448905i	−0.966021	−	0.258462i	$-0.916784\pi$
$163$	−3.30893	+	5.73124i	−0.259176	+	0.448905i	0.706846	+	0.707368i	$0.250118\pi$
$164$	0.788171	−	1.36515i	0.0615458	−	0.106601i
$165$	7.49559	+	3.83236i	0.583531	+	0.298349i
$166$	7.77378	−	13.4646i	0.603362	−	1.04505i
$167$	−5.42722	+	9.40022i	−0.419971	+	0.727411i	−0.995936	−	0.0900632i	$-0.971293\pi$
$167$	−5.42722	+	9.40022i	−0.419971	+	0.727411i	0.575965	+	0.817474i	$0.304626\pi$
$168$	−1.42276	−	0.727434i	−0.109769	−	0.0561227i
$169$	−12.6409	−	3.03420i	−0.972381	−	0.233400i
$170$	24.0438			1.84408
$171$	2.91560	+	4.03659i	0.222961	+	0.308686i
$172$	−0.00572950	−	0.00992379i	−0.000436871	−	0.000756682i
$173$	−0.103551	−	0.179356i	−0.00787286	−	0.0136362i	0.862062	−	0.506803i	$-0.169173\pi$
$173$	−0.103551	−	0.179356i	−0.00787286	−	0.0136362i	−0.869935	+	0.493166i	$0.835839\pi$
$174$	16.8655	−	10.9192i	1.27857	−	0.827784i
$175$	2.79881			0.211570
$176$	−3.33778			−0.251595
$177$	12.7048	−	8.22547i	0.954955	−	0.618264i
$178$	−3.85252	−	6.67276i	−0.288759	−	0.500145i
$179$	−4.98833	−	8.64004i	−0.372845	−	0.645787i	0.617157	−	0.786840i	$-0.288285\pi$
$179$	−4.98833	−	8.64004i	−0.372845	−	0.645787i	−0.990002	+	0.141053i	$0.954951\pi$
$180$	−6.20765	+	0.634960i	−0.462691	+	0.0473271i
$181$	13.9599			1.03763			0.518814	−	0.854887i	$-0.326374\pi$
$181$	13.9599			1.03763			0.518814	+	0.854887i	$0.326374\pi$
$182$	1.19863	−	0.515006i	0.0888486	−	0.0381748i
$183$	−7.92179	−	4.05027i	−0.585596	−	0.299405i
$184$	5.14011	−	8.90293i	0.378934	−	0.656333i
$185$	−7.48015	+	12.9560i	−0.549952	+	0.952544i
$186$	12.2462	+	6.26127i	0.897936	+	0.459099i
$187$	−3.38944	+	5.87069i	−0.247861	+	0.429307i
$188$	−0.524583	+	0.908605i	−0.0382592	+	0.0662668i
$189$	−1.21739	+	0.977423i	−0.0885521	+	0.0710970i
$190$	7.56273			0.548658
$191$	6.93963	+	12.0198i	0.502134	+	0.869721i	0.999997	+	0.00246553i	$0.000784803\pi$
$191$	6.93963	+	12.0198i	0.502134	+	0.869721i	−0.497863	+	0.867256i	$0.665882\pi$
$192$	12.8294	−	8.30613i	0.925885	−	0.599443i
$193$	−4.02111	+	6.96477i	−0.289446	+	0.501335i	−0.973678	−	0.227930i	$-0.926804\pi$
$193$	−4.02111	+	6.96477i	−0.289446	+	0.501335i	0.684232	+	0.729265i	$0.260138\pi$
$194$	−2.26637	−	3.92546i	−0.162716	−	0.281832i
$195$	13.1541	−	19.6281i	0.941981	−	1.40560i
$196$	−1.89932	+	3.28972i	−0.135666	+	0.234980i
$197$	1.50401	+	2.60502i	0.107156	+	0.185600i	0.914617	−	0.404321i	$-0.132492\pi$
$197$	1.50401	+	2.60502i	0.107156	+	0.185600i	−0.807461	+	0.589921i	$0.799159\pi$
$198$	−1.89950	+	4.23453i	−0.134991	+	0.300935i
$199$	−10.4398	+	18.0823i	−0.740057	+	1.28182i	0.212411	+	0.977180i	$0.431868\pi$
$199$	−10.4398	+	18.0823i	−0.740057	+	1.28182i	−0.952469	+	0.304637i	$0.901465\pi$
$200$	−14.3015	+	24.7709i	−1.01127	+	1.75157i
$201$	0.733378	+	14.3771i	0.0517285	+	1.01408i
$202$	6.01118			0.422945
$203$	1.44706	+	2.50638i	0.101563	+	0.175913i
$204$	−0.255980	−	5.01820i	−0.0179222	−	0.351344i
$205$	−10.8488			−0.757714
$206$	−2.61032	−	4.52121i	−0.181870	−	0.315008i
$207$	−5.88101	−	8.14215i	−0.408758	−	0.565918i
$208$	−1.10090	+	9.30327i	−0.0763334	+	0.645066i
$209$	−1.06611	+	1.84656i	−0.0737445	+	0.127729i
$210$	0.120797	+	2.36808i	0.00833575	+	0.163413i
$211$	9.04250	−	15.6621i	0.622511	−	1.07822i	−0.366505	−	0.930416i	$-0.619446\pi$
$211$	9.04250	−	15.6621i	0.622511	−	1.07822i	0.989017	−	0.147805i	$-0.0472208\pi$
$212$	3.93210			0.270058
$213$	−0.818968	−	16.0550i	−0.0561148	−	1.10007i
$214$	−1.89679	−	3.28534i	−0.129662	−	0.224581i
$215$	−0.0394320	+	0.0682982i	−0.00268924	+	0.00465790i
$216$	−2.43002	−	15.7690i	−0.165342	−	1.07295i
$217$	−0.990602	+	1.71577i	−0.0672465	+	0.116474i
$218$	−17.1882			−1.16413
$219$	−6.82627	+	4.41952i	−0.461277	+	0.298643i
$220$	−1.33601	−	2.31404i	−0.0900739	−	0.156013i
$221$	15.2452	+	11.3836i	1.02550	+	0.765743i
$222$	−7.34337	−	3.75453i	−0.492854	−	0.251988i
$223$	22.7398			1.52277			0.761385	−	0.648300i	$-0.224520\pi$
$223$	22.7398			1.52277			0.761385	+	0.648300i	$0.224520\pi$
$224$	0.452509	+	0.783769i	0.0302345	+	0.0523677i
$225$	16.3629	+	22.6542i	1.09086	+	1.51028i
$226$	−6.35579			−0.422781
$227$	−2.45568	−	4.25336i	−0.162989	−	0.282305i	0.772950	−	0.634467i	$-0.218780\pi$
$227$	−2.45568	−	4.25336i	−0.162989	−	0.282305i	−0.935939	+	0.352161i	$0.885447\pi$
$228$	−0.0805156	−	1.57842i	−0.00533227	−	0.104533i
$229$	1.97040	+	3.41283i	0.130208	+	0.225526i	0.923757	−	0.382980i	$-0.125102\pi$
$229$	1.97040	+	3.41283i	0.130208	+	0.225526i	−0.793549	+	0.608506i	$0.791769\pi$
$230$	−15.2547			−1.00586
$231$	−0.595234	−	0.304333i	−0.0391635	−	0.0200236i
$232$	−29.5770			−1.94182
$233$	2.49782			0.163637			0.0818187	−	0.996647i	$-0.473927\pi$
$233$	2.49782			0.163637			0.0818187	+	0.996647i	$0.473927\pi$
$234$	11.1762	+	6.69107i	0.730614	+	0.437409i
$235$	7.22064			0.471023
$236$	−4.80388			−0.312706
$237$	−1.17409	−	23.0168i	−0.0762655	−	1.49510i
$238$	−1.90935			−0.123765
$239$	−4.25640	−	7.37230i	−0.275324	−	0.476874i	0.694893	−	0.719113i	$-0.255452\pi$
$239$	−4.25640	−	7.37230i	−0.275324	−	0.476874i	−0.970217	+	0.242239i	$0.922118\pi$
$240$	−15.1606	−	7.75132i	−0.978610	−	0.500346i
$241$	−8.11525	−	14.0560i	−0.522749	−	0.905428i	−0.999650	−	0.0264707i	$-0.991573\pi$
$241$	−8.11525	−	14.0560i	−0.522749	−	0.905428i	0.476900	−	0.878957i	$-0.341760\pi$
$242$	11.2596			0.723792
$243$	−15.0288	−	4.13943i	−0.964099	−	0.265544i
$244$	1.41198	+	2.44562i	0.0903927	+	0.156565i
$245$	26.1433			1.67023
$246$	−0.304690	−	5.97311i	−0.0194263	−	0.380832i
$247$	4.79521	+	3.58058i	0.305112	+	0.227827i
$248$	−10.1237	−	17.5347i	−0.642853	−	1.11345i
$249$	1.13919	+	22.3325i	0.0721930	+	1.41526i
$250$	19.6617			1.24352
$251$	11.7453	−	20.3434i	0.741356	−	1.28407i	−0.210522	−	0.977589i	$-0.567516\pi$
$251$	11.7453	−	20.3434i	0.741356	−	1.28407i	0.951878	−	0.306477i	$-0.0991503\pi$
$252$	0.492958	−	0.0504230i	0.0310534	−	0.00317635i
$253$	2.15044	−	3.72467i	0.135197	−	0.234168i
$254$	6.45701	+	11.1839i	0.405149	+	0.701738i
$255$	−29.0287	+	18.7940i	−1.81785	+	1.17692i
$256$	−12.1058			−0.756614
$257$	2.86567	−	4.96348i	0.178756	−	0.309614i	−0.762699	−	0.646754i	$-0.776126\pi$
$257$	2.86567	−	4.96348i	0.178756	−	0.309614i	0.941455	+	0.337140i	$0.109460\pi$
$258$	−0.0387109	−	0.0197922i	−0.00241004	−	0.00123221i
$259$	0.594008	−	1.02885i	0.0369099	−	0.0639298i
$260$	−6.89050	+	2.96058i	−0.427330	+	0.183607i
$261$	−11.8271	+	26.3660i	−0.732079	+	1.63202i
$262$	−2.01376	−	3.48794i	−0.124411	−	0.215486i
$263$	−0.533324			−0.0328862			−0.0164431	−	0.999865i	$-0.505234\pi$
$263$	−0.533324			−0.0328862			−0.0164431	+	0.999865i	$0.505234\pi$
$264$	5.73506	−	3.71304i	0.352968	−	0.228522i
$265$	−13.5309	−	23.4362i	−0.831195	−	1.43967i
$266$	−0.600566			−0.0368231
$267$	9.86704	+	5.04484i	0.603853	+	0.308739i
$268$	2.28461	−	3.95706i	0.139555	−	0.241716i
$269$	0.841875	−	1.45817i	0.0513300	−	0.0889062i	−0.839219	−	0.543794i	$-0.816987\pi$
$269$	0.841875	−	1.45817i	0.0513300	−	0.0889062i	0.890549	+	0.454888i	$0.150321\pi$
$270$	−18.4616	+	14.8225i	−1.12354	+	0.902068i
$271$	−2.99018	−	5.17914i	−0.181640	−	0.314610i	0.760799	−	0.648988i	$-0.224807\pi$
$271$	−2.99018	−	5.17914i	−0.181640	−	0.314610i	−0.942439	+	0.334377i	$0.891474\pi$
$272$	6.85548	−	11.8740i	0.415674	−	0.719969i
$273$	−1.04458	+	1.55870i	−0.0632209	+	0.0943365i
$274$	−9.48700	−	16.4320i	−0.573131	−	0.992692i
$275$	−5.98325	+	10.3633i	−0.360803	+	0.624930i
$276$	0.162407	+	3.18381i	0.00977574	+	0.191643i
$277$	0.241067	+	0.417541i	0.0144843	+	0.0250876i	0.873177	−	0.487404i	$-0.162056\pi$
$277$	0.241067	+	0.417541i	0.0144843	+	0.0250876i	−0.858692	+	0.512491i	$0.828723\pi$
$278$	−25.9528			−1.55654
$279$	−19.6793	+	2.01293i	−1.17817	+	0.120511i
$280$	1.74530	−	3.02294i	0.104301	−	0.180655i
$281$	6.37082	−	11.0346i	0.380051	−	0.658268i	−0.611018	−	0.791617i	$-0.709240\pi$
$281$	6.37082	−	11.0346i	0.380051	−	0.658268i	0.991069	+	0.133349i	$0.0425731\pi$
$282$	0.202792	+	3.97552i	0.0120761	+	0.236739i
$283$	−4.55670	+	7.89244i	−0.270868	+	0.469157i	−0.969084	−	0.246730i	$-0.920644\pi$
$283$	−4.55670	+	7.89244i	−0.270868	+	0.469157i	0.698217	+	0.715887i	$0.253977\pi$
$284$	−2.55124	+	4.41887i	−0.151388	+	0.262212i
$285$	−9.13066	+	5.91144i	−0.540853	+	0.350164i
$286$	−0.655478	+	5.53920i	−0.0387592	+	0.327540i
$287$	0.861518			0.0508538
$288$	−3.69845	+	8.24492i	−0.217933	+	0.485837i
$289$	−5.42317	−	9.39321i	−0.319010	−	0.552542i
$290$	21.9444	+	38.0089i	1.28862	+	2.23196i
$291$	5.80459	+	2.96778i	0.340271	+	0.173975i
$292$	2.58111			0.151048
$293$	4.10386			0.239750			0.119875	−	0.992789i	$-0.461751\pi$
$293$	4.10386			0.239750			0.119875	+	0.992789i	$0.461751\pi$
$294$	0.734236	+	14.3939i	0.0428215	+	0.839469i
$295$	16.5308	+	28.6322i	0.962460	+	1.66703i
$296$	6.07059	+	10.5146i	0.352846	+	0.611147i
$297$	−1.01663	−	6.59720i	−0.0589911	−	0.382808i
$298$	15.5033			0.898083
$299$	−9.67236	−	7.22234i	−0.559367	−	0.417679i
$300$	−0.451870	−	8.85842i	−0.0260887	−	0.511441i
$301$	0.00313134	−	0.00542364i	0.000180488	−	0.000312614i
$302$	7.48481	−	12.9641i	0.430702	−	0.745998i
$303$	−7.25743	+	4.69866i	−0.416929	+	0.269931i
$304$	2.15632	−	3.73485i	0.123673	−	0.214208i
$305$	9.71762	−	16.8314i	0.556429	−	0.963764i
$306$	−11.1628	−	15.4547i	−0.638136	−	0.883487i
$307$	21.0459			1.20115			0.600575	−	0.799568i	$-0.294938\pi$
$307$	21.0459			1.20115			0.600575	+	0.799568i	$0.294938\pi$
$308$	0.106094	+	0.183761i	0.00604529	+	0.0104708i
$309$	6.68552	+	3.41819i	0.380326	+	0.194454i
$310$	−15.0224	+	26.0195i	−0.853213	+	1.47781i
$311$	−13.8275	−	23.9500i	−0.784087	−	1.35808i	−0.929543	−	0.368714i	$-0.879798\pi$
$311$	−13.8275	−	23.9500i	−0.784087	−	1.35808i	0.145456	−	0.989365i	$-0.453535\pi$
$312$	−8.45762	−	17.2098i	−0.478818	−	0.974312i
$313$	−1.14415	+	1.98173i	−0.0646712	+	0.112014i	−0.896548	−	0.442946i	$-0.853933\pi$
$313$	−1.14415	+	1.98173i	−0.0646712	+	0.112014i	0.831877	+	0.554960i	$0.187267\pi$
$314$	−6.79706	−	11.7729i	−0.383580	−	0.664381i
$315$	−1.99686	−	2.76462i	−0.112511	−	0.155769i
$316$	−3.65752	+	6.33500i	−0.205751	+	0.356372i
$317$	10.1830	−	17.6374i	0.571932	−	0.990615i	−0.424436	−	0.905458i	$-0.639528\pi$
$317$	10.1830	−	17.6374i	0.571932	−	0.990615i	0.996368	−	0.0851568i	$-0.0271391\pi$
$318$	12.5234	−	8.10800i	0.702278	−	0.454674i
$319$	−12.3740			−0.692809
$320$	16.6929	+	28.9130i	0.933161	+	1.61628i
$321$	4.85804	+	2.48383i	0.271149	+	0.138634i
$322$	1.21139			0.0675083
$323$	−4.37938	−	7.58531i	−0.243675	−	0.422058i
$324$	3.29016	+	3.69531i	0.182786	+	0.205295i
$325$	26.9117	+	20.0950i	1.49280	+	1.11467i
$326$	3.98482	−	6.90192i	0.220699	−	0.382262i
$327$	20.7517	−	13.4352i	1.14757	−	0.742968i
$328$	−4.40223	+	7.62488i	−0.243072	+	0.421013i
$329$	−0.573400			−0.0316126
$330$	−9.02665	−	4.61517i	−0.496901	−	0.254057i
$331$	−8.72183	−	15.1067i	−0.479395	−	0.830337i	0.520325	−	0.853968i	$-0.325811\pi$
$331$	−8.72183	−	15.1067i	−0.479395	−	0.830337i	−0.999721	+	0.0236311i	$0.992477\pi$
$332$	3.54877	−	6.14666i	0.194764	−	0.337342i
$333$	11.8006	−	1.20704i	0.646667	−	0.0661454i
$334$	6.53580	−	11.3203i	0.357623	−	0.619421i
$335$	−31.4466			−1.71811
$336$	1.20392	+	0.615542i	0.0656791	+	0.0335806i
$337$	12.4840	+	21.6229i	0.680048	+	1.17788i	0.974966	+	0.222355i	$0.0713743\pi$
$337$	12.4840	+	21.6229i	0.680048	+	1.17788i	−0.294918	+	0.955523i	$0.595292\pi$
$338$	15.2230	+	3.65398i	0.828023	+	0.198750i
$339$	7.67350	−	4.96803i	0.416767	−	0.269827i
$340$	10.9762			0.595266
$341$	−4.23538	−	7.33590i	−0.229359	−	0.397261i
$342$	−3.51114	−	4.86111i	−0.189861	−	0.262859i
$343$	−4.17926			−0.225659
$344$	0.0320014	+	0.0554280i	0.00172540	+	0.00298848i
$345$	18.4173	−	11.9239i	0.991555	−	0.641960i
$346$	0.124703	+	0.215992i	0.00670407	+	0.0116118i
$347$	−10.1284			−0.543722			−0.271861	−	0.962336i	$-0.587639\pi$
$347$	−10.1284			−0.543722			−0.271861	+	0.962336i	$0.587639\pi$
$348$	7.69922	−	4.98469i	0.412721	−	0.267207i
$349$	22.5689			1.20809			0.604044	−	0.796951i	$-0.293555\pi$
$349$	22.5689			1.20809			0.604044	+	0.796951i	$0.293555\pi$
$350$	−3.37050			−0.180161
$351$	−18.7234	+	0.657681i	−0.999384	+	0.0351044i
$352$	−3.86946			−0.206243
$353$	24.9017			1.32539			0.662693	−	0.748891i	$-0.269413\pi$
$353$	24.9017			1.32539			0.662693	+	0.748891i	$0.269413\pi$
$354$	−15.3000	+	9.90562i	−0.813184	+	0.526478i
$355$	35.1166			1.86379
$356$	−1.75870	−	3.04616i	−0.0932109	−	0.161446i
$357$	2.30521	−	1.49245i	0.122004	−	0.0789890i
$358$	6.00726	+	10.4049i	0.317494	+	0.549915i
$359$	−35.7532			−1.88698			−0.943492	−	0.331395i	$-0.892481\pi$
$359$	−35.7532			−1.88698			−0.943492	+	0.331395i	$0.892481\pi$
$360$	34.6720	−	3.54648i	1.82738	−	0.186916i
$361$	8.12251	+	14.0686i	0.427501	+	0.740453i
$362$	−16.8113			−0.883584
$363$	−13.5939	+	8.80108i	−0.713496	+	0.461937i
$364$	0.547183	−	0.235103i	0.0286802	−	0.0123228i
$365$	−8.88194	−	15.3840i	−0.464902	−	0.805234i
$366$	9.53992	+	4.87759i	0.498659	+	0.254956i
$367$	−13.3838			−0.698627			−0.349313	−	0.937006i	$-0.613585\pi$
$367$	−13.3838			−0.698627			−0.349313	+	0.937006i	$0.613585\pi$
$368$	−4.34947	+	7.53351i	−0.226732	+	0.392711i
$369$	5.03677	+	6.97331i	0.262204	+	0.363016i
$370$	9.00806	−	15.6024i	0.468307	−	0.811131i
$371$	1.07450	+	1.86109i	0.0557854	+	0.0966232i
$372$	5.59047	+	2.85831i	0.289852	+	0.148196i
$373$	7.14941			0.370182			0.185091	−	0.982721i	$-0.440742\pi$
$373$	7.14941			0.370182			0.185091	+	0.982721i	$0.440742\pi$
$374$	4.08178	−	7.06985i	0.211064	−	0.365573i
$375$	−23.7381	+	15.3687i	−1.22583	+	0.793635i
$376$	2.92999	−	5.07489i	0.151103	−	0.261717i
$377$	−4.08129	+	34.4895i	−0.210197	+	1.77630i
$378$	1.46606	−	1.17707i	0.0754058	−	0.0605421i
$379$	13.7475	+	23.8114i	0.706162	+	1.22311i	0.966271	+	0.257529i	$0.0829082\pi$
$379$	13.7475	+	23.8114i	0.706162	+	1.22311i	−0.260109	+	0.965579i	$0.583758\pi$
$380$	3.45243			0.177106
$381$	−16.5376	−	8.45539i	−0.847248	−	0.433183i
$382$	−8.35713	−	14.4750i	−0.427588	−	0.740604i
$383$	−11.3250			−0.578680			−0.289340	−	0.957226i	$-0.593436\pi$
$383$	−11.3250			−0.578680			−0.289340	+	0.957226i	$0.593436\pi$
$384$	−6.69108	+	4.33199i	−0.341453	+	0.221066i
$385$	0.730170	−	1.26469i	0.0372129	−	0.0644547i
$386$	4.84247	−	8.38741i	0.246475	−	0.426908i
$387$	0.0622072	−	0.00636297i	0.00316217	−	0.000323448i
$388$	−1.03461	−	1.79200i	−0.0525243	−	0.0909748i
$389$	−7.75413	+	13.4306i	−0.393150	+	0.680956i	−0.992863	−	0.119259i	$-0.961948\pi$
$389$	−7.75413	+	13.4306i	−0.393150	+	0.680956i	0.599713	+	0.800215i	$0.295281\pi$
$390$	−15.8409	+	23.6374i	−0.802137	+	1.19693i
$391$	8.83359	+	15.3002i	0.446734	+	0.773766i
$392$	10.6084	−	18.3743i	0.535805	−	0.928042i
$393$	5.15763	+	2.63700i	0.260168	+	0.133019i
$394$	−1.81122	−	3.13713i	−0.0912481	−	0.158046i
$395$	50.3440			2.53308
$396$	−0.867132	+	1.93309i	−0.0435750	+	0.0971414i
$397$	−5.84662	+	10.1266i	−0.293434	+	0.508242i	−0.974619	−	0.223869i	$-0.928131\pi$
$397$	−5.84662	+	10.1266i	−0.293434	+	0.508242i	0.681186	+	0.732111i	$0.261465\pi$
$398$	12.5722	−	21.7758i	0.630190	−	1.09152i
$399$	0.725077	−	0.469435i	0.0362993	−	0.0235011i
$400$	12.1017	−	20.9608i	0.605085	−	1.04804i
$401$	−0.357848	+	0.619811i	−0.0178701	+	0.0309519i	−0.874822	−	0.484444i	$-0.839022\pi$
$401$	−0.357848	+	0.619811i	−0.0178701	+	0.0309519i	0.856952	+	0.515396i	$0.172355\pi$
$402$	−0.883179	−	17.3138i	−0.0440490	−	0.863532i
$403$	−21.8440	+	9.38553i	−1.08813	+	0.467527i
$404$	2.74414			0.136526
$405$	10.7030	−	32.3261i	0.531837	−	1.60630i
$406$	−1.74264	−	3.01833i	−0.0864855	−	0.149797i
$407$	2.53972	+	4.39892i	0.125889	+	0.218047i
$408$	1.42974	+	28.0285i	0.0707827	+	1.38762i
$409$	−3.49404			−0.172769			−0.0863846	−	0.996262i	$-0.527531\pi$
$409$	−3.49404			−0.172769			−0.0863846	+	0.996262i	$0.527531\pi$
$410$	13.0648			0.645225
$411$	24.2980	+	12.4231i	1.19853	+	0.612788i
$412$	−1.19163	−	2.06396i	−0.0587073	−	0.101684i
$413$	−1.31273	−	2.27372i	−0.0645953	−	0.111882i
$414$	7.08228	+	9.80528i	0.348075	+	0.481903i
$415$	−48.8472			−2.39782
$416$	−1.27626	+	10.7852i	−0.0625738	+	0.528788i
$417$	31.3334	−	20.2861i	1.53440	−	0.993415i
$418$	1.28388	−	2.22374i	0.0627965	−	0.108767i
$419$	9.13962	−	15.8303i	0.446500	−	0.773360i	−0.551656	−	0.834072i	$-0.686004\pi$
$419$	9.13962	−	15.8303i	0.446500	−	0.773360i	0.998155	+	0.0607117i	$0.0193370\pi$
$420$	0.0551443	+	1.08104i	0.00269077	+	0.0527496i
$421$	−1.70275	+	2.94926i	−0.0829871	+	0.143738i	−0.904532	−	0.426406i	$-0.859779\pi$
$421$	−1.70275	+	2.94926i	−0.0829871	+	0.143738i	0.821545	+	0.570144i	$0.193113\pi$
$422$	−10.8895	+	18.8612i	−0.530094	+	0.918150i
$423$	−3.35232	−	4.64123i	−0.162995	−	0.225664i
$424$	−21.9622			−1.06658
$425$	−24.5780	−	42.5704i	−1.19221	−	2.06497i
$426$	0.986252	+	19.3344i	0.0477841	+	0.936754i
$427$	−0.771688	+	1.33660i	−0.0373446	+	0.0646828i
$428$	−0.865896	−	1.49978i	−0.0418547	−	0.0724944i
$429$	−3.53837	−	7.19997i	−0.170834	−	0.347618i
$430$	0.0474864	−	0.0822489i	0.00229000	−	0.00396639i
$431$	−7.51196	−	13.0111i	−0.361839	−	0.626723i	0.626425	−	0.779482i	$-0.284518\pi$
$431$	−7.51196	−	13.0111i	−0.361839	−	0.626723i	−0.988263	+	0.152759i	$0.951184\pi$
$432$	2.05624	+	13.3435i	0.0989310	+	0.641989i
$433$	1.01128	−	1.75159i	0.0485991	−	0.0841762i	−0.840703	−	0.541497i	$-0.817858\pi$
$433$	1.01128	−	1.75159i	0.0485991	−	0.0841762i	0.889302	+	0.457321i	$0.151191\pi$
$434$	1.19294	−	2.06624i	0.0572632	−	0.0991827i
$435$	−56.2038	−	28.7360i	−2.69477	−	1.37779i
$436$	−7.84649			−0.375779
$437$	2.77851	+	4.81252i	0.132914	+	0.230214i
$438$	8.22062	−	5.32226i	0.392796	−	0.254307i
$439$	13.1733			0.628725			0.314363	−	0.949303i	$-0.398209\pi$
$439$	13.1733			0.628725			0.314363	+	0.949303i	$0.398209\pi$
$440$	7.46212	+	12.9248i	0.355743	+	0.616164i
$441$	−12.1375	−	16.8042i	−0.577977	−	0.800198i
$442$	−18.3592	−	13.7088i	−0.873259	−	0.652062i
$443$	−5.48308	+	9.49698i	−0.260509	+	0.451215i	−0.966377	−	0.257128i	$-0.917224\pi$
$443$	−5.48308	+	9.49698i	−0.260509	+	0.451215i	0.705868	+	0.708343i	$0.250557\pi$
$444$	−3.35229	−	1.71397i	−0.159093	−	0.0813413i
$445$	−12.1038	+	20.9645i	−0.573777	+	0.993811i
$446$	−27.3847			−1.29670
$447$	−18.7175	+	12.1182i	−0.885308	+	0.573173i
$448$	−1.32560	−	2.29601i	−0.0626289	−	0.108476i
$449$	−18.1471	+	31.4318i	−0.856416	+	1.48336i	0.0189089	+	0.999821i	$0.493981\pi$
$449$	−18.1471	+	31.4318i	−0.856416	+	1.48336i	−0.875325	+	0.483535i	$0.839353\pi$
$450$	−19.7053	−	27.2816i	−0.928915	−	1.28607i
$451$	−1.84174	+	3.18998i	−0.0867240	+	0.150210i
$452$	−2.90146			−0.136473
$453$	1.09684	+	21.5023i	0.0515340	+	1.01027i
$454$	2.95728	+	5.12216i	0.138792	+	0.240395i
$455$	−3.28420	−	2.45231i	−0.153965	−	0.114966i
$456$	0.449709	+	8.81605i	0.0210595	+	0.412849i
$457$	−33.9786			−1.58945			−0.794726	−	0.606968i	$-0.792386\pi$
$457$	−33.9786			−1.58945			−0.794726	+	0.606968i	$0.792386\pi$
$458$	−2.37288	−	4.10994i	−0.110877	−	0.192045i
$459$	25.5574	+	9.93337i	1.19292	+	0.463650i
$460$	−6.96385			−0.324691
$461$	5.76497	+	9.98523i	0.268502	+	0.465058i	0.968475	−	0.249110i	$-0.0801382\pi$
$461$	5.76497	+	9.98523i	0.268502	+	0.465058i	−0.699973	+	0.714169i	$0.746805\pi$
$462$	0.716818	+	0.366496i	0.0333494	+	0.0170509i
$463$	−15.1765	−	26.2864i	−0.705310	−	1.22163i	−0.966580	−	0.256366i	$-0.917475\pi$
$463$	−15.1765	−	26.2864i	−0.705310	−	1.22163i	0.261270	−	0.965266i	$-0.415859\pi$
$464$	25.0275			1.16187
$465$	−2.20141	−	43.1562i	−0.102088	−	2.00132i
$466$	−3.00803			−0.139344
$467$	−1.64762			−0.0762426			−0.0381213	−	0.999273i	$-0.512137\pi$
$467$	−1.64762			−0.0762426			−0.0381213	+	0.999273i	$0.512137\pi$
$468$	5.10202	+	3.05451i	0.235841	+	0.141195i
$469$	2.49721			0.115310
$470$	−8.69554			−0.401096
$471$	17.4086	+	8.90069i	0.802144	+	0.410122i
$472$	26.8314			1.23502
$473$	0.0133883	+	0.0231891i	0.000615592	+	0.00106624i
$474$	1.41392	+	27.7183i	0.0649433	+	1.27314i
$475$	−7.73074	−	13.3900i	−0.354711	−	0.614377i
$476$	−0.871631			−0.0399511
$477$	−8.78214	+	19.5780i	−0.402107	+	0.896413i
$478$	5.12582	+	8.87818i	0.234450	+	0.406079i
$479$	−10.5874			−0.483753			−0.241876	−	0.970307i	$-0.577763\pi$
$479$	−10.5874			−0.483753			−0.241876	+	0.970307i	$0.577763\pi$
$480$	−17.5755	−	8.98604i	−0.802208	−	0.410155i
$481$	13.0986	−	5.62797i	0.597246	−	0.256614i
$482$	9.77289	+	16.9271i	0.445143	+	0.771010i
$483$	−1.46254	+	0.946891i	−0.0665480	+	0.0430850i
$484$	5.14005			0.233639
$485$	−7.12045	+	12.3330i	−0.323323	+	0.560012i
$486$	18.0986	+	4.98495i	0.820970	+	0.226122i
$487$	13.3185	−	23.0683i	0.603517	−	1.04532i	−0.388767	−	0.921336i	$-0.627099\pi$
$487$	13.3185	−	23.0683i	0.603517	−	1.04532i	0.992284	−	0.123986i	$-0.0395679\pi$
$488$	−7.88642	−	13.6597i	−0.357002	−	0.618345i
$489$	0.583945	+	11.4476i	0.0264069	+	0.517678i
$490$	−31.4833			−1.42227
$491$	−11.6757	+	20.2228i	−0.526915	+	0.912644i	0.472593	+	0.881281i	$0.343318\pi$
$491$	−11.6757	+	20.2228i	−0.526915	+	0.912644i	−0.999508	+	0.0313629i	$0.990015\pi$
$492$	−0.139093	−	2.72676i	−0.00627078	−	0.122932i
$493$	25.4149	−	44.0199i	1.14463	−	1.98256i
$494$	−5.77469	−	4.31196i	−0.259816	−	0.194004i
$495$	14.5056	−	1.48372i	0.651976	−	0.0666884i
$496$	8.56647	+	14.8376i	0.384646	+	0.666226i
$497$	−2.78865			−0.125088
$498$	−1.37188	−	26.8942i	−0.0614754	−	1.20516i
$499$	−0.396185	−	0.686212i	−0.0177357	−	0.0307191i	0.857021	−	0.515281i	$-0.172312\pi$
$499$	−0.396185	−	0.686212i	−0.0177357	−	0.0307191i	−0.874757	+	0.484562i	$0.838979\pi$
$500$	8.97570			0.401405
$501$	0.957770	+	18.7760i	0.0427900	+	0.838851i
$502$	−14.1444	+	24.4988i	−0.631296	+	1.09344i
$503$	11.9019	−	20.6147i	0.530681	−	0.919166i	−0.468678	−	0.883369i	$-0.655270\pi$
$503$	11.9019	−	20.6147i	0.530681	−	0.919166i	0.999359	−	0.0357971i	$-0.0113970\pi$
$504$	−2.75335	+	0.281631i	−0.122644	+	0.0125448i
$505$	−9.44294	−	16.3557i	−0.420206	−	0.727817i
$506$	−2.58969	+	4.48548i	−0.115126	+	0.199404i
$507$	−21.2352	+	7.48761i	−0.943090	+	0.332536i
$508$	2.94766	+	5.10550i	0.130781	+	0.226520i
$509$	−12.1015	+	20.9604i	−0.536388	+	0.929052i	0.462706	+	0.886512i	$0.346878\pi$
$509$	−12.1015	+	20.9604i	−0.536388	+	0.929052i	−0.999095	+	0.0425404i	$0.986455\pi$
$510$	34.9582	−	22.6329i	1.54797	−	1.00220i
$511$	0.705326	+	1.22166i	0.0312018	+	0.0540431i
$512$	23.7827			1.05106
$513$	8.03879	+	3.12443i	0.354921	+	0.137947i
$514$	−3.45102	+	5.97734i	−0.152218	+	0.263649i
$515$	−8.20109	+	14.2047i	−0.361383	+	0.625934i
$516$	−0.0176718	−	0.00903526i	−0.000777956	−	0.000397755i
$517$	1.22580	−	2.12316i	0.0539108	−	0.0933763i
$518$	−0.715342	+	1.23901i	−0.0314303	+	0.0544389i
$519$	−0.319387	−	0.163297i	−0.0140196	−	0.00716795i
$520$	38.4859	−	16.5359i	1.68772	−	0.725148i
$521$	−10.2515			−0.449125			−0.224563	−	0.974460i	$-0.572095\pi$
$521$	−10.2515			−0.449125			−0.224563	+	0.974460i	$0.572095\pi$
$522$	14.2429	−	31.7516i	0.623396	−	1.38973i
$523$	−13.3127	−	23.0583i	−0.582124	−	1.00827i	−0.995227	−	0.0975847i	$-0.968888\pi$
$523$	−13.3127	−	23.0583i	−0.582124	−	1.00827i	0.413103	−	0.910684i	$-0.364445\pi$
$524$	−0.919295	−	1.59227i	−0.0401596	−	0.0695584i
$525$	4.06928	−	2.63457i	0.177598	−	0.114982i
$526$	0.642262			0.0280040
$527$	34.7963			1.51575
$528$	−4.85291	+	3.14191i	−0.211196	+	0.136734i
$529$	5.89551	+	10.2113i	0.256326	+	0.443970i
$530$	16.2947	+	28.2233i	0.707797	+	1.22594i
$531$	10.7292	−	23.9186i	0.465609	−	1.03798i
$532$	−0.274162			−0.0118864
$533$	8.28385	+	6.18555i	0.358814	+	0.267926i
$534$	−11.8825	−	6.07531i	−0.514206	−	0.262904i
$535$	−5.95933	+	10.3219i	−0.257644	+	0.446253i
$536$	−12.7604	+	22.1016i	−0.551164	+	0.954644i
$537$	−15.3857	−	7.86645i	−0.663943	−	0.339462i
$538$	−1.01384	+	1.75602i	−0.0437096	+	0.0757073i
$539$	4.43818	−	7.68716i	0.191166	−	0.331109i
$540$	−8.42782	+	6.76656i	−0.362675	+	0.291186i
$541$	−11.7447			−0.504943			−0.252471	−	0.967604i	$-0.581243\pi$
$541$	−11.7447			−0.504943			−0.252471	+	0.967604i	$0.581243\pi$
$542$	3.60096	+	6.23704i	0.154674	+	0.267904i
$543$	20.2967	−	13.1407i	0.871015	−	0.563920i
$544$	7.94750	−	13.7655i	0.340746	−	0.590190i
$545$	27.0008	+	46.7668i	1.15659	+	2.00327i
$546$	1.25795	−	1.87708i	0.0538352	−	0.0803315i
$547$	0.492671	−	0.853331i	0.0210651	−	0.0364858i	−0.855301	−	0.518132i	$-0.826628\pi$
$547$	0.492671	−	0.853331i	0.0210651	−	0.0364858i	0.876366	+	0.481646i	$0.159961\pi$
$548$	−4.33087	−	7.50129i	−0.185006	−	0.320439i
$549$	−15.3304	+	1.56809i	−0.654283	+	0.0669245i
$550$	7.20540	−	12.4801i	0.307239	−	0.532154i
$551$	7.99398	−	13.8460i	0.340555	−	0.589859i
$552$	−0.907102	−	17.7827i	−0.0386088	−	0.756883i
$553$	−3.99788			−0.170007
$554$	−0.290308	−	0.502828i	−0.0123340	−	0.0213631i
$555$	1.32006	+	25.8784i	0.0560335	+	1.09848i
$556$	−11.8476			−0.502450
$557$	12.1835	+	21.1025i	0.516233	+	0.894141i	0.999822	+	0.0188462i	$0.00599930\pi$
$557$	12.1835	+	21.1025i	0.516233	+	0.894141i	−0.483590	+	0.875295i	$0.660667\pi$
$558$	23.6990	−	2.42409i	1.00326	−	0.102620i
$559$	0.0690500	−	0.0296681i	0.00292050	−	0.00125483i
$560$	−1.47684	+	2.55796i	−0.0624079	+	0.108094i
$561$	0.598153	+	11.7261i	0.0252540	+	0.495078i
$562$	−7.67213	+	13.2885i	−0.323629	+	0.560543i
$563$	33.9591			1.43121			0.715603	−	0.698507i	$-0.246152\pi$
$563$	33.9591			1.43121			0.715603	+	0.698507i	$0.246152\pi$
$564$	0.0925759	+	1.81485i	0.00389815	+	0.0764190i
$565$	9.98430	+	17.2933i	0.420043	+	0.727535i
$566$	5.48746	−	9.50456i	0.230655	−	0.399507i
$567$	−0.849939	+	2.56706i	−0.0356941	+	0.107806i
$568$	14.2496	−	24.6810i	0.597899	−	1.03559i
$569$	−24.0616			−1.00871			−0.504356	−	0.863496i	$-0.668270\pi$
$569$	−24.0616			−1.00871			−0.504356	+	0.863496i	$0.668270\pi$
$570$	10.9957	−	7.11892i	0.460559	−	0.298179i
$571$	−2.33817	−	4.04984i	−0.0978495	−	0.169480i	0.812945	−	0.582341i	$-0.197863\pi$
$571$	−2.33817	−	4.04984i	−0.0978495	−	0.169480i	−0.910794	+	0.412860i	$0.864530\pi$
$572$	−0.299229	+	2.52868i	−0.0125114	+	0.105729i
$573$	21.4042	+	10.9436i	0.894172	+	0.457175i
$574$	−1.03749			−0.0433041
$575$	15.5936	+	27.0089i	0.650297	+	1.12635i
$576$	10.8344	−	24.1531i	0.451435	−	1.00638i
$577$	−24.2913			−1.01126			−0.505630	−	0.862750i	$-0.668740\pi$
$577$	−24.2913			−1.01126			−0.505630	+	0.862750i	$0.668740\pi$
$578$	6.53092	+	11.3119i	0.271651	+	0.470513i
$579$	0.709626	+	13.9115i	0.0294911	+	0.578140i
$580$	10.0178	+	17.3513i	0.415965	+	0.720473i
$581$	3.87902			0.160929
$582$	−6.99025	−	3.57399i	−0.289755	−	0.148147i
$583$	−9.18822			−0.380537
$584$	−14.4164			−0.596557
$585$	0.648819	−	40.9201i	0.0268254	−	1.69184i
$586$	−4.94212			−0.204157
$587$	−17.0334			−0.703045			−0.351522	−	0.936179i	$-0.614336\pi$
$587$	−17.0334			−0.703045			−0.351522	+	0.936179i	$0.614336\pi$
$588$	0.335183	+	6.57090i	0.0138227	+	0.270979i
$589$	10.9448			0.450972
$590$	−19.9074	−	34.4806i	−0.819575	−	1.41955i
$591$	4.63888	+	2.37178i	0.190818	+	0.0975619i
$592$	−5.13683	−	8.89725i	−0.211122	−	0.365675i
$593$	16.1029			0.661266			0.330633	−	0.943759i	$-0.392738\pi$
$593$	16.1029			0.661266			0.330633	+	0.943759i	$0.392738\pi$
$594$	1.22429	+	7.94476i	0.0502334	+	0.325977i
$595$	2.99940	+	5.19511i	0.122963	+	0.212979i
$596$	7.07736			0.289900
$597$	1.84236	+	36.1175i	0.0754030	+	1.47819i
$598$	11.6481	+	8.69760i	0.476324	+	0.355671i
$599$	−10.4601	−	18.1175i	−0.427390	−	0.740261i	0.569250	−	0.822164i	$-0.307234\pi$
$599$	−10.4601	−	18.1175i	−0.427390	−	0.740261i	−0.996640	+	0.0819032i	$0.973900\pi$
$600$	2.52386	+	49.4775i	0.103036	+	2.01991i
$601$	2.39968			0.0978850			0.0489425	−	0.998802i	$-0.484415\pi$
$601$	2.39968			0.0978850			0.0489425	+	0.998802i	$0.484415\pi$
$602$	−0.00377096	+	0.00653149i	−0.000153693	+	0.000266204i
$603$	14.5997	+	20.2130i	0.594544	+	0.823136i
$604$	3.41686	−	5.91817i	0.139030	−	0.240807i
$605$	−17.6876	−	30.6358i	−0.719103	−	1.24552i
$606$	8.73985	−	5.65842i	0.355032	−	0.229858i
$607$	−41.9024			−1.70076			−0.850382	−	0.526165i	$-0.823629\pi$
$607$	−41.9024			−1.70076			−0.850382	+	0.526165i	$0.823629\pi$
$608$	2.49980	−	4.32978i	0.101380	−	0.175596i
$609$	4.46322	+	2.28196i	0.180859	+	0.0924699i
$610$	−11.7026	+	20.2694i	−0.473823	+	0.820685i
$611$	−5.51349	−	4.11692i	−0.223052	−	0.166553i
$612$	−5.09589	−	7.05517i	−0.205989	−	0.285188i
$613$	−6.47866	−	11.2214i	−0.261671	−	0.453227i	0.705015	−	0.709192i	$-0.250940\pi$
$613$	−6.47866	−	11.2214i	−0.261671	−	0.453227i	−0.966686	+	0.255965i	$0.917607\pi$
$614$	−25.3447			−1.02283
$615$	−15.7734	+	10.2122i	−0.636047	+	0.411794i
$616$	−0.592576	−	1.02637i	−0.0238756	−	0.0413537i
$617$	−14.5666			−0.586431			−0.293216	−	0.956046i	$-0.594725\pi$
$617$	−14.5666			−0.586431			−0.293216	+	0.956046i	$0.594725\pi$
$618$	−8.05112	−	4.11640i	−0.323864	−	0.165586i
$619$	4.73531	−	8.20179i	0.190328	−	0.329658i	−0.755031	−	0.655689i	$-0.772378\pi$
$619$	4.73531	−	8.20179i	0.190328	−	0.329658i	0.945359	+	0.326031i	$0.105711\pi$
$620$	−6.85780	+	11.8781i	−0.275416	+	0.477034i
$621$	−16.2149	−	6.30225i	−0.650683	−	0.252901i
$622$	16.6520	+	28.8420i	0.667683	+	1.15646i
$623$	0.961181	−	1.66481i	0.0385089	−	0.0666994i
$624$	7.15670	+	14.5626i	0.286497	+	0.582972i
$625$	−7.59854	−	13.1611i	−0.303941	−	0.526442i
$626$	1.37786	−	2.38652i	0.0550703	−	0.0953845i
$627$	0.188142	+	3.68833i	0.00751368	+	0.147298i
$628$	−3.10290	−	5.37438i	−0.123819	−	0.214461i
$629$	−20.8654			−0.831956
$630$	2.40475	+	3.32933i	0.0958074	+	0.132644i
$631$	24.2342	−	41.9749i	0.964749	−	1.67099i	0.254461	−	0.967083i	$-0.418102\pi$
$631$	24.2342	−	41.9749i	0.964749	−	1.67099i	0.710288	−	0.703911i	$-0.248565\pi$
$632$	20.4286	−	35.3833i	0.812605	−	1.40747i
$633$	−1.59578	−	31.2834i	−0.0634264	−	1.24341i
$634$	−12.2629	+	21.2400i	−0.487024	+	0.843550i
$635$	20.2866	−	35.1374i	0.805049	−	1.39439i
$636$	5.71701	−	3.70135i	0.226694	−	0.146768i
$637$	−19.9623	−	14.9058i	−0.790934	−	0.590590i
$638$	14.9015			0.589956
$639$	−16.3035	−	22.5720i	−0.644958	−	0.892933i
$640$	−8.70603	−	15.0793i	−0.344136	−	0.596061i
$641$	0.384354	+	0.665720i	0.0151811	+	0.0262944i	0.873516	−	0.486795i	$-0.161834\pi$
$641$	0.384354	+	0.665720i	0.0151811	+	0.0262944i	−0.858335	+	0.513090i	$0.828501\pi$
$642$	−5.85035	−	2.99118i	−0.230895	−	0.118053i
$643$	−0.284528			−0.0112207			−0.00561034	−	0.999984i	$-0.501786\pi$
$643$	−0.284528			−0.0112207			−0.00561034	+	0.999984i	$0.501786\pi$
$644$	0.553008			0.0217916
$645$	0.00695877	+	0.136419i	0.000274001	+	0.00537149i
$646$	5.27392	+	9.13470i	0.207500	+	0.359400i
$647$	14.6716	+	25.4119i	0.576798	+	0.999044i	0.995844	+	0.0910787i	$0.0290315\pi$
$647$	14.6716	+	25.4119i	0.576798	+	0.999044i	−0.419045	+	0.907965i	$0.637635\pi$
$648$	−18.3767	−	20.6397i	−0.721906	−	0.810803i
$649$	11.2253			0.440633
$650$	−32.4088	−	24.1996i	−1.27118	−	0.949187i
$651$	0.174817	+	3.42709i	0.00685161	+	0.134318i
$652$	1.81910	−	3.15077i	0.0712413	−	0.123394i
$653$	24.8170	−	42.9843i	0.971164	−	1.68211i	0.279111	−	0.960259i	$-0.409960\pi$
$653$	24.8170	−	42.9843i	0.971164	−	1.68211i	0.692053	−	0.721846i	$-0.256706\pi$
$654$	−24.9904	+	16.1795i	−0.977203	+	0.632669i
$655$	−6.32683	+	10.9584i	−0.247210	+	0.428180i
$656$	3.72509	−	6.45205i	0.145440	−	0.251910i
$657$	−5.76478	+	12.8514i	−0.224905	+	0.501380i
$658$	0.690524			0.0269194
$659$	21.4051	+	37.0746i	0.833823	+	1.44422i	0.894985	+	0.446095i	$0.147186\pi$
$659$	21.4051	+	37.0746i	0.833823	+	1.44422i	−0.0611628	+	0.998128i	$0.519481\pi$
$660$	−4.12072	−	2.10685i	−0.160399	−	0.0820091i
$661$	17.6585	−	30.5855i	0.686837	−	1.18964i	−0.286019	−	0.958224i	$-0.592332\pi$
$661$	17.6585	−	30.5855i	0.686837	−	1.18964i	0.972856	−	0.231413i	$-0.0743348\pi$
$662$	10.5034	+	18.1924i	0.408225	+	0.707067i
$663$	32.8811	+	2.20041i	1.27700	+	0.0854567i
$664$	−19.8212	+	34.3313i	−0.769212	+	1.33231i
$665$	0.943427	+	1.63406i	0.0365845	+	0.0633663i
$666$	−14.2110	+	1.45359i	−0.550664	+	0.0563256i
$667$	−16.1246	+	27.9285i	−0.624345	+	1.08140i
$668$	2.98363	−	5.16780i	0.115440	−	0.199948i
$669$	33.0622	−	21.4054i	1.27826	−	0.827579i
$670$	37.8699			1.46304
$671$	−3.29940	−	5.71473i	−0.127372	−	0.220615i
$672$	1.39569	+	0.713593i	0.0538400	+	0.0275274i
$673$	34.7386			1.33907			0.669537	−	0.742779i	$-0.266493\pi$
$673$	34.7386			1.33907			0.669537	+	0.742779i	$0.266493\pi$
$674$	−15.0340	−	26.0397i	−0.579089	−	1.00301i
$675$	45.1154	+	17.5350i	1.73649	+	0.674921i
$676$	6.94940	+	1.66806i	0.267285	+	0.0641562i
$677$	9.05262	−	15.6796i	0.347920	−	0.602616i	−0.637959	−	0.770070i	$-0.720221\pi$
$677$	9.05262	−	15.6796i	0.347920	−	0.602616i	0.985880	+	0.167454i	$0.0535546\pi$
$678$	−9.24090	+	5.98282i	−0.354895	+	0.229769i
$679$	0.565444	−	0.979378i	0.0216998	−	0.0375851i
$680$	−61.3059			−2.35097
$681$	−7.57415	−	3.87253i	−0.290242	−	0.148396i
$682$	5.10051	+	8.83434i	0.195309	+	0.338284i
$683$	−11.6147	+	20.1173i	−0.444426	+	0.769768i	−0.998012	−	0.0630237i	$-0.979926\pi$
$683$	−11.6147	+	20.1173i	−0.444426	+	0.769768i	0.553586	+	0.832792i	$0.313259\pi$
$684$	−1.60286	−	2.21913i	−0.0612868	−	0.0848504i
$685$	−29.8062	+	51.6259i	−1.13884	+	1.97252i
$686$	5.03293			0.192158
$687$	6.07738	+	3.10726i	0.231867	+	0.118549i
$688$	−0.0270790	−	0.0469023i	−0.00103238	−	0.00178813i
$689$	−3.03054	+	25.6100i	−0.115454	+	0.975662i
$690$	−22.1793	+	14.3595i	−0.844351	+	0.546656i
$691$	−4.50951			−0.171550			−0.0857748	−	0.996315i	$-0.527337\pi$
$691$	−4.50951			−0.171550			−0.0857748	+	0.996315i	$0.527337\pi$
$692$	0.0569276	+	0.0986015i	0.00216406	+	0.00374827i
$693$	−1.15190	+	0.117824i	−0.0437572	+	0.00447578i
$694$	12.1973			0.463002
$695$	40.7691	+	70.6142i	1.54646	+	2.67855i
$696$	−43.0029	+	27.8413i	−1.63002	+	1.05532i
$697$	−7.56549	−	13.1038i	−0.286564	−	0.496343i
$698$	−27.1789			−1.02874
$699$	3.63166	−	2.35124i	0.137362	−	0.0889320i
$700$	−1.53865			−0.0581557
$701$	−12.6104			−0.476288			−0.238144	−	0.971230i	$-0.576539\pi$
$701$	−12.6104			−0.476288			−0.238144	+	0.971230i	$0.576539\pi$
$702$	22.5479	−	0.792021i	0.851017	−	0.0298929i
$703$	−6.56297			−0.247527
$704$	11.3354			0.427219
$705$	10.4983	−	6.79691i	0.395390	−	0.255986i
$706$	−29.9882			−1.12862
$707$	0.749876	+	1.29882i	0.0282020	+	0.0488473i
$708$	−6.98452	+	4.52197i	−0.262494	+	0.169946i
$709$	25.1270	+	43.5212i	0.943662	+	1.63447i	0.758407	+	0.651781i	$0.225978\pi$
$709$	25.1270	+	43.5212i	0.943662	+	1.63447i	0.185255	+	0.982690i	$0.440689\pi$
$710$	−42.2896			−1.58710
$711$	−23.3732	−	32.3597i	−0.876562	−	1.21358i
$712$	9.82298	+	17.0139i	0.368132	+	0.637623i
$713$	−22.0766			−0.826774
$714$	−2.77607	+	1.79731i	−0.103892	+	0.0672625i
$715$	16.1012	−	6.91805i	0.602149	−	0.258720i
$716$	2.74235	+	4.74989i	0.102486	+	0.177512i
$717$	−13.1282	−	6.71221i	−0.490281	−	0.250672i
$718$	43.0563			1.60685
$719$	21.5058	−	37.2492i	0.802031	−	1.38916i	−0.116246	−	0.993221i	$-0.537086\pi$
$719$	21.5058	−	37.2492i	0.802031	−	1.38916i	0.918277	−	0.395939i	$-0.129581\pi$
$720$	−29.3389	+	3.00098i	−1.09340	+	0.111840i
$721$	0.651259	−	1.12801i	0.0242542	−	0.0420094i
$722$	−9.78164	−	16.9423i	−0.364035	−	0.630527i
$723$	−25.0302	−	12.7975i	−0.930883	−	0.475944i
$724$	−7.67448			−0.285220
$725$	44.8639	−	77.7066i	1.66620	−	2.88595i
$726$	16.3706	−	10.5988i	0.607572	−	0.393359i
$727$	6.80760	−	11.7911i	0.252480	−	0.437308i	−0.711728	−	0.702455i	$-0.752087\pi$
$727$	6.80760	−	11.7911i	0.252480	−	0.437308i	0.964208	+	0.265147i	$0.0854205\pi$
$728$	−3.05622	+	1.31314i	−0.113271	+	0.0486681i
$729$	−25.7474	+	8.12842i	−0.953607	+	0.301053i
$730$	10.6962	+	18.5263i	0.395884	+	0.685690i
$731$	−0.109993			−0.00406823
$732$	4.35503	+	2.22665i	0.160966	+	0.0822993i
$733$	23.0761	+	39.9690i	0.852336	+	1.47629i	0.879095	+	0.476647i	$0.158148\pi$
$733$	23.0761	+	39.9690i	0.852336	+	1.47629i	−0.0267594	+	0.999642i	$0.508519\pi$
$734$	16.1176			0.594910
$735$	38.0106	−	24.6091i	1.40204	−	0.907720i
$736$	−5.04231	+	8.73353i	−0.185862	+	0.321922i
$737$	−5.33849	+	9.24654i	−0.196646	+	0.340601i
$738$	−6.06559	−	8.39770i	−0.223277	−	0.309123i
$739$	−0.339921	−	0.588761i	−0.0125042	−	0.0216579i	0.859706	−	0.510790i	$-0.170647\pi$
$739$	−0.339921	−	0.588761i	−0.0125042	−	0.0216579i	−0.872210	+	0.489132i	$0.837314\pi$
$740$	4.11223	−	7.12260i	0.151169	−	0.261832i
$741$	10.3424	+	0.692114i	0.379937	+	0.0254254i
$742$	−1.29398	−	2.24125i	−0.0475036	−	0.0822787i
$743$	−13.2649	+	22.9755i	−0.486642	+	0.842889i	−0.999882	−	0.0153563i	$-0.995112\pi$
$743$	−13.2649	+	22.9755i	−0.486642	+	0.842889i	0.513240	+	0.858245i	$0.328445\pi$
$744$	−31.2248	−	15.9647i	−1.14476	−	0.585294i
$745$	−24.3541	−	42.1826i	−0.892266	−	1.54545i
$746$	−8.60976			−0.315226
$747$	22.6783	+	31.3976i	0.829754	+	1.14878i
$748$	1.86336	−	3.22743i	0.0681310	−	0.118006i
$749$	0.473238	−	0.819672i	0.0172917	−	0.0299502i
$750$	28.5868	−	18.5079i	1.04384	−	0.675814i
$751$	−16.0066	+	27.7242i	−0.584088	+	1.01167i	0.410900	+	0.911680i	$0.365215\pi$
$751$	−16.0066	+	27.7242i	−0.584088	+	1.01167i	−0.994988	+	0.0999903i	$0.968119\pi$
$752$	−2.47931	+	4.29429i	−0.0904111	+	0.156597i
$753$	−2.07275	−	40.6340i	−0.0755353	−	1.48079i
$754$	4.91494	−	41.5344i	0.178992	−	1.51259i
$755$	−47.0315			−1.71165
$756$	0.669263	−	0.537341i	0.0243409	−	0.0195429i
$757$	10.5610	+	18.2922i	0.383846	+	0.664840i	0.991608	−	0.129278i	$-0.0412661\pi$
$757$	10.5610	+	18.2922i	0.383846	+	0.664840i	−0.607763	+	0.794119i	$0.707933\pi$
$758$	−16.5556	−	28.6751i	−0.601326	−	1.04153i
$759$	−0.379499	−	7.43967i	−0.0137750	−	0.270043i
$760$	−19.2831			−0.699471
$761$	−24.4460			−0.886166			−0.443083	−	0.896481i	$-0.646115\pi$
$761$	−24.4460			−0.886166			−0.443083	+	0.896481i	$0.646115\pi$
$762$	19.9156	+	10.1825i	0.721467	+	0.368873i
$763$	−2.14417	−	3.71381i	−0.0776242	−	0.134449i
$764$	−3.81508	−	6.60791i	−0.138025	−	0.239066i
$765$	−24.5147	+	54.6504i	−0.886331	+	1.97589i
$766$	13.6383			0.492770
$767$	3.70244	−	31.2879i	0.133687	−	1.12974i
$768$	−17.6011	+	11.3954i	−0.635123	+	0.411197i
$769$	4.36070	−	7.55296i	0.157251	−	0.272367i	−0.776625	−	0.629963i	$-0.783070\pi$
$769$	4.36070	−	7.55296i	0.157251	−	0.272367i	0.933876	+	0.357596i	$0.116404\pi$
$770$	−0.879316	+	1.52302i	−0.0316884	+	0.0548858i
$771$	−0.505720	−	9.91408i	−0.0182130	−	0.357047i
$772$	2.21062	−	3.82890i	0.0795619	−	0.137805i
$773$	−0.571592	+	0.990027i	−0.0205587	+	0.0356088i	−0.876122	−	0.482090i	$-0.839878\pi$
$773$	−0.571592	+	0.990027i	−0.0205587	+	0.0356088i	0.855563	+	0.517699i	$0.173211\pi$
$774$	−0.0749138	+	0.00766268i	−0.00269272	+	0.000275429i
$775$	61.4244			2.20643
$776$	5.77867	+	10.0090i	0.207442	+	0.359300i
$777$	−0.104828	−	2.05503i	−0.00376067	−	0.0737239i
$778$	9.33801	−	16.1739i	0.334784	−	0.579863i
$779$	−2.37964	−	4.12166i	−0.0852596	−	0.147674i
$780$	−7.23148	+	10.7906i	−0.258928	+	0.386366i
$781$	5.96153	−	10.3257i	0.213320	−	0.369481i
$782$	−10.6380	−	18.4255i	−0.380413	−	0.658894i
$783$	7.62299	+	49.4675i	0.272423	+	1.76782i
$784$	−8.97665	+	15.5480i	−0.320595	+	0.555286i
$785$	−21.3550	+	36.9879i	−0.762192	+	1.32015i
$786$	−6.21113	−	3.17564i	−0.221544	−	0.113271i
$787$	14.5911			0.520115			0.260058	−	0.965593i	$-0.416258\pi$
$787$	14.5911			0.520115			0.260058	+	0.965593i	$0.416258\pi$
$788$	−0.826834	−	1.43212i	−0.0294547	−	0.0510171i
$789$	−0.775418	+	0.502027i	−0.0276056	+	0.0178726i
$790$	−60.6274			−2.15702
$791$	−0.792866	−	1.37328i	−0.0281911	−	0.0488283i
$792$	4.84325	−	10.7970i	0.172097	−	0.383655i
$793$	−17.0167	+	7.31142i	−0.604281	+	0.259636i
$794$	7.04087	−	12.1951i	0.249871	−	0.432789i
$795$	−41.7338	−	21.3378i	−1.48015	−	0.756773i
$796$	5.73931	−	9.94077i	0.203424	−	0.352341i
$797$	−19.7945			−0.701158			−0.350579	−	0.936533i	$-0.614015\pi$
$797$	−19.7945			−0.701158			−0.350579	+	0.936533i	$0.614015\pi$
$798$	−0.873183	+	0.565323i	−0.0309103	+	0.0200122i
$799$	5.03537	+	8.72151i	0.178138	+	0.308545i
$800$	14.0294	−	24.2996i	0.496014	−	0.859121i
$801$	19.0948	−	1.95314i	0.674682	−	0.0690109i
$802$	0.430943	−	0.746415i	0.0152171	−	0.0263568i
$803$	−6.03133			−0.212841
$804$	−0.403177	−	7.90384i	−0.0142189	−	0.278747i
$805$	−1.90297	−	3.29605i	−0.0670710	−	0.116170i
$806$	26.3059	−	11.3026i	0.926587	−	0.398119i
$807$	−0.148570	−	2.91255i	−0.00522991	−	0.102527i
$808$	−15.3270			−0.539203
$809$	13.6595	+	23.6589i	0.480241	+	0.831802i	0.999743	−	0.0226673i	$-0.00721584\pi$
$809$	13.6595	+	23.6589i	0.480241	+	0.831802i	−0.519502	+	0.854469i	$0.673883\pi$
$810$	−12.8892	+	38.9291i	−0.452881	+	1.36783i
$811$	38.3231			1.34571			0.672854	−	0.739776i	$-0.265068\pi$
$811$	38.3231			1.34571			0.672854	+	0.739776i	$0.265068\pi$
$812$	−0.795523	−	1.37789i	−0.0279174	−	0.0483543i
$813$	−9.22273	−	4.71542i	−0.323455	−	0.165377i
$814$	−3.05849	−	5.29746i	−0.107200	−	0.185676i
$815$	−25.0390			−0.877078
$816$	−1.20982	−	23.7172i	−0.0423522	−	0.830269i
$817$	−0.0345970			−0.00121040
$818$	4.20774			0.147120
$819$	−0.0515236	+	3.24952i	−0.00180038	+	0.113547i
$820$	5.96416			0.208278
$821$	54.5956			1.90540			0.952700	−	0.303911i	$-0.0982925\pi$
$821$	54.5956			1.90540			0.952700	+	0.303911i	$0.0982925\pi$
$822$	−29.2612	−	14.9607i	−1.02060	−	0.521815i
$823$	−52.8320			−1.84161			−0.920804	−	0.390026i	$-0.872466\pi$
$823$	−52.8320			−1.84161			−0.920804	+	0.390026i	$0.872466\pi$
$824$	6.65567	+	11.5280i	0.231861	+	0.401596i
$825$	1.05589	+	20.6997i	0.0367615	+	0.720670i
$826$	1.58087	+	2.73815i	0.0550056	+	0.0952725i
$827$	20.8919			0.726482			0.363241	−	0.931695i	$-0.381670\pi$
$827$	20.8919			0.726482			0.363241	+	0.931695i	$0.381670\pi$
$828$	3.23310	+	4.47617i	0.112358	+	0.155558i
$829$	−7.33261	−	12.7005i	−0.254672	−	0.441105i	0.710134	−	0.704066i	$-0.248634\pi$
$829$	−7.33261	−	12.7005i	−0.254672	−	0.441105i	−0.964806	+	0.262961i	$0.915301\pi$
$830$	58.8249			2.04184
$831$	0.743534	+	0.380156i	0.0257929	+	0.0131875i
$832$	3.73874	−	31.5948i	0.129618	−	1.09535i
$833$	18.2312	+	31.5773i	0.631673	+	1.09409i
$834$	−37.7336	+	24.4298i	−1.30661	+	0.845934i
$835$	−41.0683			−1.42123
$836$	0.586098	−	1.01515i	0.0202706	−	0.0351098i
$837$	−26.7176	+	21.4511i	−0.923495	+	0.741459i
$838$	−11.0065	+	19.0638i	−0.380213	+	0.658549i
$839$	−2.25553	−	3.90669i	−0.0778696	−	0.134874i	0.824461	−	0.565919i	$-0.191478\pi$
$839$	−2.25553	−	3.90669i	−0.0778696	−	0.134874i	−0.902331	+	0.431045i	$0.858145\pi$
$840$	−0.308001	−	6.03803i	−0.0106271	−	0.208332i
$841$	63.7831			2.19942
$842$	2.05056	−	3.55168i	0.0706670	−	0.122399i
$843$	−1.12429	−	22.0405i	−0.0387226	−	0.759115i
$844$	−4.97114	+	8.61026i	−0.171114	+	0.296377i
$845$	−13.9718	−	47.1599i	−0.480644	−	1.62235i
$846$	4.03707	+	5.58925i	0.138797	+	0.192163i
$847$	1.40460	+	2.43283i	0.0482625	+	0.0835930i
$848$	18.5841			0.638179
$849$	0.804145	+	15.7644i	0.0275982	+	0.541032i
$850$	29.5984	+	51.2659i	1.01522	+	1.75841i
$851$	13.2381			0.453795
$852$	0.450230	+	8.82627i	0.0154246	+	0.302383i
$853$	11.4853	−	19.8932i	0.393250	−	0.681129i	−0.599626	−	0.800280i	$-0.704684\pi$
$853$	11.4853	−	19.8932i	0.393250	−	0.681129i	0.992876	+	0.119151i	$0.0380174\pi$
$854$	0.929315	−	1.60962i	0.0318005	−	0.0550801i
$855$	−7.71083	+	17.1897i	−0.263705	+	0.587875i
$856$	4.83635	+	8.37680i	0.165303	+	0.286313i
$857$	−20.3594	+	35.2635i	−0.695463	+	1.20458i	0.274561	+	0.961570i	$0.411467\pi$
$857$	−20.3594	+	35.2635i	−0.695463	+	1.20458i	−0.970024	+	0.243008i	$0.921866\pi$
$858$	4.26112	+	8.67065i	0.145472	+	0.296011i
$859$	−26.7637	−	46.3561i	−0.913167	−	1.58165i	−0.809563	−	0.587033i	$-0.800296\pi$
$859$	−26.7637	−	46.3561i	−0.913167	−	1.58165i	−0.103603	−	0.994619i	$-0.533037\pi$
$860$	0.0216778	−	0.0375471i	0.000739208	−	0.00128035i
$861$	1.25259	−	0.810961i	0.0426881	−	0.0276375i
$862$	9.04637	+	15.6688i	0.308121	+	0.533681i
$863$	26.8211			0.913000			0.456500	−	0.889724i	$-0.349103\pi$
$863$	26.8211			0.913000			0.456500	+	0.889724i	$0.349103\pi$
$864$	2.38378	+	15.4690i	0.0810980	+	0.526266i
$865$	0.391791	−	0.678601i	0.0133213	−	0.0230731i
$866$	−1.21785	+	2.10938i	−0.0413842	+	0.0716796i
$867$	−16.7269	−	8.55218i	−0.568076	−	0.290447i
$868$	0.544586	−	0.943251i	0.0184845	−	0.0320160i
$869$	8.54659	−	14.8031i	0.289923	−	0.502162i
$870$	67.6841	+	34.6057i	2.29471	+	1.17324i
$871$	24.0117	+	17.9295i	0.813606	+	0.607519i
$872$	43.8255			1.48412
$873$	11.2331	−	1.14900i	0.380183	−	0.0388877i
$874$	−3.34605	−	5.79553i	−0.113182	−	0.196037i
$875$	2.45274	+	4.24827i	0.0829178	+	0.143618i
$876$	3.75276	−	2.42964i	0.126794	−	0.0820900i
$877$	−24.6341			−0.831834			−0.415917	−	0.909403i	$-0.636539\pi$
$877$	−24.6341			−0.831834			−0.415917	+	0.909403i	$0.636539\pi$
$878$	−15.8641			−0.535386
$879$	5.96674	−	3.86303i	0.201253	−	0.130297i
$880$	−6.31432	−	10.9367i	−0.212856	−	0.368677i
$881$	−14.7520	−	25.5512i	−0.497008	−	0.860843i	0.502986	−	0.864294i	$-0.332235\pi$
$881$	−14.7520	−	25.5512i	−0.497008	−	0.860843i	−0.999994	+	0.00345150i	$0.998901\pi$
$882$	14.6167	+	20.2366i	0.492171	+	0.681402i
$883$	−29.2625			−0.984761			−0.492380	−	0.870380i	$-0.663873\pi$
$883$	−29.2625			−0.984761			−0.492380	+	0.870380i	$0.663873\pi$
$884$	−8.38110	−	6.25816i	−0.281887	−	0.210485i
$885$	50.9866	+	26.0686i	1.71390	+	0.876285i
$886$	6.60307	−	11.4369i	0.221834	−	0.384229i
$887$	−4.13251	+	7.15771i	−0.138756	+	0.240332i	−0.927026	−	0.374997i	$-0.877644\pi$
$887$	−4.13251	+	7.15771i	−0.138756	+	0.240332i	0.788270	+	0.615330i	$0.210977\pi$
$888$	18.7238	+	9.57313i	0.628328	+	0.321253i
$889$	−1.61098	+	2.79031i	−0.0540307	+	0.0935839i
$890$	14.5762	−	25.2467i	0.488595	−	0.846271i
$891$	−7.68818	−	8.63492i	−0.257564	−	0.289281i
$892$	−12.5013			−0.418574
$893$	1.58382	+	2.74326i	0.0530005	+	0.0917995i
$894$	22.5408	−	14.5935i	0.753877	−	0.488081i
$895$	18.8736	−	32.6900i	0.630874	−	1.09271i
$896$	0.691357	+	1.19747i	0.0230966	+	0.0400045i
$897$	−20.8615	−	1.39605i	−0.696545	−	0.0466128i
$898$	21.8539	−	37.8521i	0.729274	−	1.26314i
$899$	31.7580	+	55.0064i	1.05919	+	1.83457i
$900$	−8.99557	−	12.4542i	−0.299852	−	0.415140i
$901$	18.8717	−	32.6867i	0.628708	−	1.08895i
$902$	2.21793	−	3.84157i	0.0738491	−	0.127910i
$903$	−0.000552604	−	0.0108332i	−1.83895e−5	−	0.000360506i
$904$	16.2057			0.538994
$905$	26.4089	+	45.7415i	0.877861	+	1.52050i
$906$	−1.32088	−	25.8945i	−0.0438834	−	0.860286i
$907$	18.4346			0.612111			0.306056	−	0.952014i	$-0.400991\pi$
$907$	18.4346			0.612111			0.306056	+	0.952014i	$0.400991\pi$
$908$	1.35002	+	2.33830i	0.0448019	+	0.0775991i
$909$	−6.12889	+	13.6631i	−0.203283	+	0.453176i
$910$	3.95503	+	2.95322i	0.131108	+	0.0978983i
$911$	−23.0212	+	39.8739i	−0.762726	+	1.32108i	0.178715	+	0.983901i	$0.442806\pi$
$911$	−23.0212	+	39.8739i	−0.762726	+	1.32108i	−0.941441	+	0.337179i	$0.890527\pi$
$912$	−0.380536	−	7.46000i	−0.0126008	−	0.247025i
$913$	−8.29250	+	14.3630i	−0.274442	+	0.475347i
$914$	40.9192			1.35349
$915$	−1.71492	−	33.6191i	−0.0566935	−	1.11141i
$916$	−1.08323	−	1.87621i	−0.0357910	−	0.0619918i
$917$	0.502422	−	0.870220i	0.0165914	−	0.0287372i
$918$	−30.7778	−	11.9624i	−1.01582	−	0.394817i
$919$	16.5071	−	28.5912i	0.544520	−	0.943136i	−0.454117	−	0.890942i	$-0.650045\pi$
$919$	16.5071	−	28.5912i	0.544520	−	0.943136i	0.998637	−	0.0521939i	$-0.0166214\pi$
$920$	38.8957			1.28235
$921$	30.5993	−	19.8108i	1.00828	−	0.652789i
$922$	−6.94254	−	12.0248i	−0.228640	−	0.396017i
$923$	−26.8141	−	20.0220i	−0.882595	−	0.659033i
$924$	0.327232	+	0.167308i	0.0107651	+	0.00550402i
$925$	−36.8328			−1.21105
$926$	18.2764	+	31.6557i	0.600601	+	1.04027i
$927$	12.9379	−	1.32338i	0.424937	−	0.0434653i
$928$	29.0142			0.952438
$929$	−17.2035	−	29.7974i	−0.564429	−	0.977620i	−0.997103	−	0.0760691i	$-0.975763\pi$
$929$	−17.2035	−	29.7974i	−0.564429	−	0.977620i	0.432673	−	0.901551i	$-0.357570\pi$
$930$	2.65107	+	51.9714i	0.0869322	+	1.70421i
$931$	5.73442	+	9.93231i	0.187938	+	0.325518i
$932$	−1.37318			−0.0449801
$933$	−42.6488	−	21.8056i	−1.39626	−	0.713883i
$934$	1.98416			0.0649238
$935$	−25.6482			−0.838786
$936$	−28.4967	−	17.0606i	−0.931443	−	0.557642i
$937$	−3.49544			−0.114191			−0.0570956	−	0.998369i	$-0.518184\pi$
$937$	−3.49544			−0.114191			−0.0570956	+	0.998369i	$0.518184\pi$
$938$	−3.00730			−0.0981917
$939$	0.201914	+	3.95831i	0.00658922	+	0.129175i
$940$	−3.96957			−0.129473
$941$	−11.7060	−	20.2754i	−0.381605	−	0.660959i	0.609687	−	0.792642i	$-0.291295\pi$
$941$	−11.7060	−	20.2754i	−0.381605	−	0.660959i	−0.991292	+	0.131684i	$0.957962\pi$
$942$	−20.9645	−	10.7188i	−0.683059	−	0.349236i
$943$	4.79995	+	8.31375i	0.156308	+	0.270733i
$944$	−22.7043			−0.738963
$945$	−5.50569	−	2.13989i	−0.179100	−	0.0696108i
$946$	−0.0161230	−	0.0279258i	−0.000524203	−	0.000907946i
$947$	−40.6066			−1.31954			−0.659769	−	0.751468i	$-0.729346\pi$
$947$	−40.6066			−1.31954			−0.659769	+	0.751468i	$0.729346\pi$
$948$	0.645461	+	12.6536i	0.0209636	+	0.410968i
$949$	−1.98931	+	16.8109i	−0.0645756	+	0.545705i
$950$	9.30984	+	16.1251i	0.302051	+	0.523168i
$951$	−1.79704	−	35.2290i	−0.0582730	−	1.14238i
$952$	4.86838			0.157785
$953$	24.9334	−	43.1859i	0.807672	−	1.39893i	−0.106801	−	0.994280i	$-0.534061\pi$
$953$	24.9334	−	43.1859i	0.807672	−	1.39893i	0.914473	−	0.404648i	$-0.132606\pi$
$954$	10.5760	−	23.5770i	0.342411	−	0.763333i
$955$	−26.2564	+	45.4774i	−0.849637	+	1.47161i
$956$	2.33997	+	4.05294i	0.0756799	+	0.131082i
$957$	−17.9909	+	11.6478i	−0.581564	+	0.376521i
$958$	12.7501			0.411936
$959$	2.36695	−	4.09968i	0.0764328	−	0.132385i
$960$	51.4866	+	26.3242i	1.66172	+	0.849610i
$961$	−6.24036	+	10.8086i	−0.201302	+	0.348665i
$962$	−15.7742	+	6.77756i	−0.508580	+	0.218517i
$963$	9.40134	−	0.961631i	0.302954	−	0.0309881i
$964$	4.46138	+	7.72734i	0.143691	+	0.248881i
$965$	−30.4281			−0.979515
$966$	1.76128	−	1.14030i	0.0566684	−	0.0366887i
$967$	5.80396	+	10.0528i	0.186643	+	0.323275i	0.944129	−	0.329576i	$-0.106906\pi$
$967$	5.80396	+	10.0528i	0.186643	+	0.323275i	−0.757486	+	0.652851i	$0.773573\pi$
$968$	−28.7091			−0.922745
$969$	−13.5075	−	6.90615i	−0.433924	−	0.221858i
$970$	8.57489	−	14.8522i	0.275323	−	0.476874i
$971$	7.04458	−	12.2016i	0.226071	−	0.391567i	−0.730569	−	0.682839i	$-0.760745\pi$
$971$	7.04458	−	12.2016i	0.226071	−	0.391567i	0.956640	+	0.291272i	$0.0940785\pi$
$972$	8.26213	+	2.27566i	0.265008	+	0.0729919i
$973$	−3.23753	−	5.60756i	−0.103790	−	0.179770i
$974$	−16.0389	+	27.7802i	−0.513920	+	0.890136i
$975$	58.0436	+	3.88429i	1.85888	+	0.124397i
$976$	6.67336	+	11.5586i	0.213609	+	0.369982i
$977$	6.67495	−	11.5613i	0.213550	−	0.369880i	−0.739273	−	0.673406i	$-0.764831\pi$
$977$	6.67495	−	11.5613i	0.213550	−	0.369880i	0.952823	+	0.303526i	$0.0981639\pi$
$978$	−0.703223	−	13.7859i	−0.0224866	−	0.440825i
$979$	4.10959	+	7.11802i	0.131343	+	0.227493i
$980$	−14.3723			−0.459107
$981$	17.5247	−	39.0678i	0.559522	−	1.24734i
$982$	14.0606	−	24.3536i	0.448690	−	0.777154i
$983$	−8.77579	+	15.2001i	−0.279904	+	0.484808i	−0.971361	−	0.237610i	$-0.923636\pi$
$983$	−8.77579	+	15.2001i	−0.279904	+	0.484808i	0.691456	+	0.722418i	$0.256969\pi$
$984$	0.776884	+	15.2300i	0.0247661	+	0.485513i
$985$	−5.69049	+	9.85622i	−0.181314	+	0.314045i
$986$	−30.6062	+	53.0115i	−0.974701	+	1.68823i
$987$	−0.833686	+	0.539751i	−0.0265365	+	0.0171805i
$988$	−2.63618	−	1.96844i	−0.0838681	−	0.0626243i
$989$	0.0697851			0.00221904
$990$	−17.4685	+	1.78679i	−0.555185	+	0.0567880i
$991$	12.8289	+	22.2202i	0.407522	+	0.705849i	0.994611	−	0.103673i	$-0.0330596\pi$
$991$	12.8289	+	22.2202i	0.407522	+	0.705849i	−0.587089	+	0.809522i	$0.699726\pi$
$992$	9.93104	+	17.2011i	0.315311	+	0.546134i
$993$	−26.9011	−	13.7541i	−0.853681	−	0.436472i
$994$	3.35827			0.106518
$995$	−78.9988			−2.50443
$996$	−0.626271	−	12.2774i	−0.0198441	−	0.389023i
$997$	−9.11468	−	15.7871i	−0.288665	−	0.499982i	0.684826	−	0.728706i	$-0.259878\pi$
$997$	−9.11468	−	15.7871i	−0.288665	−	0.499982i	−0.973491	+	0.228724i	$0.926545\pi$
$998$	0.477110	+	0.826379i	0.0151027	+	0.0261586i
$999$	16.0210	−	12.8630i	0.506883	−	0.406968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.h.a.16.4	yes	24
3.2	odd	2		351.2.h.a.289.9		24
9.4	even	3		117.2.f.a.94.9	yes	24
9.5	odd	6		351.2.f.a.172.4		24
13.9	even	3		117.2.f.a.61.9	✓	24
39.35	odd	6		351.2.f.a.100.4		24
117.22	even	3	inner	117.2.h.a.22.4	yes	24
117.113	odd	6		351.2.h.a.334.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.f.a.61.9	✓	24	13.9	even	3
117.2.f.a.94.9	yes	24	9.4	even	3
117.2.h.a.16.4	yes	24	1.1	even	1	trivial
117.2.h.a.22.4	yes	24	117.22	even	3	inner
351.2.f.a.100.4		24	39.35	odd	6
351.2.f.a.172.4		24	9.5	odd	6
351.2.h.a.289.9		24	3.2	odd	2
351.2.h.a.334.9		24	117.113	odd	6

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.20426 q^{2} +(1.45393 - 0.941317i) q^{3} -0.549753 q^{4} +(1.89177 + 3.27665i) q^{5} +(-1.75092 + 1.13359i) q^{6} +(-0.150228 - 0.260203i) q^{7} +3.07057 q^{8} +(1.22785 - 2.73722i) q^{9} +O(q^{10})\)	\(q-1.20426 q^{2} +(1.45393 - 0.941317i) q^{3} -0.549753 q^{4} +(1.89177 + 3.27665i) q^{5} +(-1.75092 + 1.13359i) q^{6} +(-0.150228 - 0.260203i) q^{7} +3.07057 q^{8} +(1.22785 - 2.73722i) q^{9} +(-2.27819 - 3.94594i) q^{10} +1.28462 q^{11} +(-0.799304 + 0.517492i) q^{12} +(0.423704 - 3.58057i) q^{13} +(0.180914 + 0.313352i) q^{14} +(5.83487 + 2.98327i) q^{15} -2.59827 q^{16} +(-2.63848 + 4.56998i) q^{17} +(-1.47865 + 3.29634i) q^{18} +(-0.829906 + 1.43744i) q^{19} +(-1.04001 - 1.80135i) q^{20} +(-0.463355 - 0.236905i) q^{21} -1.54702 q^{22} +(1.67399 - 2.89944i) q^{23} +(4.46441 - 2.89038i) q^{24} +(-4.65760 + 8.06721i) q^{25} +(-0.510251 + 4.31194i) q^{26} +(-0.791390 - 5.13553i) q^{27} +(0.0825883 + 0.143047i) q^{28} -9.63240 q^{29} +(-7.02672 - 3.59264i) q^{30} +(-3.29700 - 5.71056i) q^{31} -3.01215 q^{32} +(1.86775 - 1.20923i) q^{33} +(3.17742 - 5.50346i) q^{34} +(0.568394 - 0.984488i) q^{35} +(-0.675011 + 1.50480i) q^{36} +(1.97702 + 3.42430i) q^{37} +(0.999424 - 1.73105i) q^{38} +(-2.75441 - 5.60475i) q^{39} +(5.80882 + 10.0612i) q^{40} +(-1.43368 + 2.48321i) q^{41} +(0.558000 + 0.285296i) q^{42} +(0.0104220 + 0.0180514i) q^{43} -0.706223 q^{44} +(11.2917 - 1.15499i) q^{45} +(-2.01592 + 3.49168i) q^{46} +(0.954216 - 1.65275i) q^{47} +(-3.77771 + 2.44579i) q^{48} +(3.45486 - 5.98400i) q^{49} +(5.60898 - 9.71503i) q^{50} +(0.465627 + 9.12810i) q^{51} +(-0.232933 + 1.96843i) q^{52} -7.15248 q^{53} +(0.953041 + 6.18453i) q^{54} +(2.43021 + 4.20924i) q^{55} +(-0.461286 - 0.798970i) q^{56} +(0.146458 + 2.87114i) q^{57} +11.5999 q^{58} +8.73826 q^{59} +(-3.20774 - 1.64006i) q^{60} +(-2.56839 - 4.44858i) q^{61} +(3.97045 + 6.87702i) q^{62} +(-0.896689 + 0.0917194i) q^{63} +8.82395 q^{64} +(12.5338 - 5.38529i) q^{65} +(-2.24926 + 1.45623i) q^{66} +(-4.15570 + 7.19788i) q^{67} +(1.45051 - 2.51236i) q^{68} +(-0.295418 - 5.79134i) q^{69} +(-0.684496 + 1.18558i) q^{70} +(4.64070 - 8.03792i) q^{71} +(3.77018 - 8.40484i) q^{72} -4.69504 q^{73} +(-2.38085 - 4.12376i) q^{74} +(0.821952 + 16.1135i) q^{75} +(0.456243 - 0.790236i) q^{76} +(-0.192986 - 0.334261i) q^{77} +(3.31703 + 6.74959i) q^{78} +(6.65302 - 11.5234i) q^{79} +(-4.91533 - 8.51360i) q^{80} +(-5.98479 - 6.72177i) q^{81} +(1.72653 - 2.99044i) q^{82} +(-6.45522 + 11.1808i) q^{83} +(0.254730 + 0.130239i) q^{84} -19.9656 q^{85} +(-0.0125508 - 0.0217386i) q^{86} +(-14.0049 + 9.06714i) q^{87} +3.94451 q^{88} +(3.19907 + 5.54096i) q^{89} +(-13.5982 + 1.39091i) q^{90} +(-0.995325 + 0.427653i) q^{91} +(-0.920281 + 1.59397i) q^{92} +(-10.1691 - 5.19926i) q^{93} +(-1.14913 + 1.99035i) q^{94} -6.27997 q^{95} +(-4.37946 + 2.83539i) q^{96} +(1.88195 + 3.25964i) q^{97} +(-4.16056 + 7.20630i) q^{98} +(1.57731 - 3.51629i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} - q^{3} + 18 q^{4} - 2 q^{5} - 12 q^{6} + 3 q^{7} - 18 q^{8} - 3 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 - q^3 + 18 * q^4 - 2 * q^5 - 12 * q^6 + 3 * q^7 - 18 * q^8 - 3 * q^9	\( 24 q - 2 q^{2} - q^{3} + 18 q^{4} - 2 q^{5} - 12 q^{6} + 3 q^{7} - 18 q^{8} - 3 q^{9} + 6 q^{11} - 3 q^{12} + 2 q^{14} + 11 q^{15} + 6 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} - 11 q^{20} - 25 q^{21} - 18 q^{22} + 17 q^{23} - 12 q^{24} - 6 q^{25} - 12 q^{26} + 2 q^{27} - 24 q^{29} - 8 q^{30} - 6 q^{31} - 38 q^{32} + 11 q^{33} + 18 q^{35} - 28 q^{36} - 3 q^{37} + 8 q^{38} + 3 q^{39} - 12 q^{40} + 5 q^{41} + 15 q^{42} - 3 q^{43} + 44 q^{44} + 19 q^{45} - 6 q^{46} + 21 q^{47} + 23 q^{48} + 3 q^{49} - 20 q^{50} + 7 q^{51} - 24 q^{52} - 20 q^{53} + 39 q^{54} + 3 q^{55} + 40 q^{56} + 9 q^{57} + 18 q^{58} + 38 q^{59} + 51 q^{60} - 6 q^{61} + 19 q^{62} + 13 q^{63} - 42 q^{64} - 2 q^{65} - 18 q^{66} - 6 q^{67} - 31 q^{69} + 27 q^{70} + 14 q^{71} - 18 q^{72} + 6 q^{73} + 29 q^{74} + 74 q^{75} - 15 q^{76} + 4 q^{77} + 80 q^{78} + 3 q^{79} - 16 q^{80} - 27 q^{81} - 9 q^{82} - 33 q^{83} + 5 q^{84} + 72 q^{86} - 32 q^{87} - 78 q^{88} - q^{89} + 21 q^{90} - 6 q^{91} - 10 q^{92} - 84 q^{93} - 9 q^{94} - 100 q^{95} - 79 q^{96} + 24 q^{97} - 61 q^{98} + 18 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 - q^3 + 18 * q^4 - 2 * q^5 - 12 * q^6 + 3 * q^7 - 18 * q^8 - 3 * q^9 + 6 * q^11 - 3 * q^12 + 2 * q^14 + 11 * q^15 + 6 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 - 11 * q^20 - 25 * q^21 - 18 * q^22 + 17 * q^23 - 12 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 - 24 * q^29 - 8 * q^30 - 6 * q^31 - 38 * q^32 + 11 * q^33 + 18 * q^35 - 28 * q^36 - 3 * q^37 + 8 * q^38 + 3 * q^39 - 12 * q^40 + 5 * q^41 + 15 * q^42 - 3 * q^43 + 44 * q^44 + 19 * q^45 - 6 * q^46 + 21 * q^47 + 23 * q^48 + 3 * q^49 - 20 * q^50 + 7 * q^51 - 24 * q^52 - 20 * q^53 + 39 * q^54 + 3 * q^55 + 40 * q^56 + 9 * q^57 + 18 * q^58 + 38 * q^59 + 51 * q^60 - 6 * q^61 + 19 * q^62 + 13 * q^63 - 42 * q^64 - 2 * q^65 - 18 * q^66 - 6 * q^67 - 31 * q^69 + 27 * q^70 + 14 * q^71 - 18 * q^72 + 6 * q^73 + 29 * q^74 + 74 * q^75 - 15 * q^76 + 4 * q^77 + 80 * q^78 + 3 * q^79 - 16 * q^80 - 27 * q^81 - 9 * q^82 - 33 * q^83 + 5 * q^84 + 72 * q^86 - 32 * q^87 - 78 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 - 84 * q^93 - 9 * q^94 - 100 * q^95 - 79 * q^96 + 24 * q^97 - 61 * q^98 + 18 * q^99

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