LMFDB - Embedded newform 114.2.l.a.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(29,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 17]))

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

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

chi := DirichletCharacter("114.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.l (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 $ x^18 - x^15 - 18x^14 + 36x^13 + 10x^12 + 18x^11 + 90x^10 - 567x^9 + 270x^8 + 162x^7 + 270x^6 + 2916x^5 - 4374x^4 - 729x^3 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.2
Root			$1.47158 - 0.913487i$ of defining polynomial
Character	$\chi$	$=$	114.29
Dual form			114.2.l.a.59.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(-0.0553136 - 1.73117i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.882820 - 2.42553i) q^{5} +(-1.69526 + 0.355087i) q^{6} +(-1.58376 + 2.74316i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.99388 + 0.191514i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.0553136 - 1.73117i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.882820 - 2.42553i) q^{5} +(-1.69526 + 0.355087i) q^{6} +(-1.58376 + 2.74316i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.99388 + 0.191514i) q^{9} +(-2.54198 - 0.448219i) q^{10} +(2.16590 - 1.25049i) q^{11} +(0.644072 + 1.60785i) q^{12} +(2.71907 - 3.24046i) q^{13} +(2.97650 + 1.08336i) q^{14} +(-4.24783 - 1.39414i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.32278 + 0.233243i) q^{17} +(0.708487 + 2.91514i) q^{18} +(3.14841 + 3.01455i) q^{19} +2.58119i q^{20} +(4.83647 + 2.59003i) q^{21} +(-1.60759 - 1.91586i) q^{22} +(1.30503 + 3.58554i) q^{23} +(1.47158 - 0.913487i) q^{24} +(-1.27359 - 1.06867i) q^{25} +(-3.66340 - 2.11506i) q^{26} +(0.497145 + 5.17232i) q^{27} +(0.550036 - 3.11941i) q^{28} +(1.32242 - 7.49981i) q^{29} +(-0.635337 + 4.42538i) q^{30} +(6.89193 + 3.97906i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-2.28460 - 3.68037i) q^{33} +(0.459398 + 1.26219i) q^{34} +(5.25543 + 6.26318i) q^{35} +(2.74783 - 1.20393i) q^{36} +4.10469i q^{37} +(2.42204 - 3.62405i) q^{38} +(-5.76019 - 4.52793i) q^{39} +(2.54198 - 0.448219i) q^{40} +(-4.95792 + 4.16019i) q^{41} +(1.71083 - 5.21275i) q^{42} +(-11.7465 - 4.27537i) q^{43} +(-1.60759 + 1.91586i) q^{44} +(-2.17853 + 7.43081i) q^{45} +(3.30445 - 1.90782i) q^{46} +(-6.16940 - 1.08783i) q^{47} +(-1.15515 - 1.29060i) q^{48} +(-1.51662 - 2.62686i) q^{49} +(-0.831277 + 1.43981i) q^{50} +(0.476950 + 2.27706i) q^{51} +(-1.44679 + 3.97502i) q^{52} +(3.46508 - 1.26118i) q^{53} +(5.00741 - 1.38776i) q^{54} +(-1.12098 - 6.35742i) q^{55} -3.16753 q^{56} +(5.04455 - 5.61716i) q^{57} -7.61550 q^{58} +(1.54335 + 8.75275i) q^{59} +(4.46848 - 0.142775i) q^{60} +(-0.133301 + 0.0485177i) q^{61} +(2.72184 - 7.47818i) q^{62} +(4.21625 - 8.51601i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-5.45938 - 9.45593i) q^{65} +(-3.22774 + 2.88899i) q^{66} +(-4.48795 - 0.791347i) q^{67} +(1.16324 - 0.671595i) q^{68} +(6.13498 - 2.45755i) q^{69} +(5.25543 - 6.26318i) q^{70} +(-8.59275 - 3.12750i) q^{71} +(-1.66280 - 2.49702i) q^{72} +(-1.67672 + 1.40694i) q^{73} +(4.04233 - 0.712771i) q^{74} +(-1.77960 + 2.26391i) q^{75} +(-3.98957 - 1.75594i) q^{76} +7.92190i q^{77} +(-3.45889 + 6.45894i) q^{78} +(6.41515 + 7.64528i) q^{79} +(-0.882820 - 2.42553i) q^{80} +(8.92664 - 1.14674i) q^{81} +(4.95792 + 4.16019i) q^{82} +(-12.3308 - 7.11920i) q^{83} +(-5.43064 - 0.779658i) q^{84} +(-0.602044 + 3.41436i) q^{85} +(-2.17066 + 12.3104i) q^{86} +(-13.0566 - 1.87449i) q^{87} +(2.16590 + 1.25049i) q^{88} +(12.7492 + 10.6978i) q^{89} +(7.69622 + 0.855091i) q^{90} +(4.58274 + 12.5910i) q^{91} +(-2.45265 - 2.92296i) q^{92} +(6.50720 - 12.1512i) q^{93} +6.26457i q^{94} +(10.0914 - 4.97524i) q^{95} +(-1.07040 + 1.36171i) q^{96} +(0.538573 - 0.0949649i) q^{97} +(-2.32360 + 1.94973i) q^{98} +(-6.24498 + 4.15861i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{6} + 9 q^{8}+O(q^{10}) $ 18 * q + 3 * q^6 + 9 * q^8	$ 18 q + 3 q^{6} + 9 q^{8} - 12 q^{13} + 12 q^{14} - 24 q^{15} - 6 q^{17} - 6 q^{19} - 24 q^{22} - 18 q^{25} - 18 q^{26} - 3 q^{27} + 6 q^{28} + 6 q^{29} - 27 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} - 3 q^{38} + 6 q^{39} - 3 q^{41} - 6 q^{43} - 24 q^{44} + 54 q^{45} + 18 q^{46} - 30 q^{47} + 6 q^{48} + 21 q^{49} - 3 q^{50} - 33 q^{51} - 6 q^{52} + 60 q^{53} + 30 q^{55} + 12 q^{57} + 12 q^{58} - 3 q^{59} + 18 q^{60} + 54 q^{61} - 6 q^{62} + 84 q^{63} - 9 q^{64} - 24 q^{65} + 30 q^{66} - 15 q^{67} + 27 q^{68} + 24 q^{69} + 24 q^{70} - 36 q^{71} - 42 q^{73} - 6 q^{74} - 18 q^{78} - 6 q^{79} + 3 q^{82} - 36 q^{83} - 24 q^{84} + 6 q^{86} - 54 q^{87} + 60 q^{89} - 12 q^{90} - 18 q^{91} - 84 q^{93} - 6 q^{95} + 9 q^{97} - 12 q^{98} - 30 q^{99}+O(q^{100}) $ 18 * q + 3 * q^6 + 9 * q^8 - 12 * q^13 + 12 * q^14 - 24 * q^15 - 6 * q^17 - 6 * q^19 - 24 * q^22 - 18 * q^25 - 18 * q^26 - 3 * q^27 + 6 * q^28 + 6 * q^29 - 27 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 - 3 * q^38 + 6 * q^39 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 54 * q^45 + 18 * q^46 - 30 * q^47 + 6 * q^48 + 21 * q^49 - 3 * q^50 - 33 * q^51 - 6 * q^52 + 60 * q^53 + 30 * q^55 + 12 * q^57 + 12 * q^58 - 3 * q^59 + 18 * q^60 + 54 * q^61 - 6 * q^62 + 84 * q^63 - 9 * q^64 - 24 * q^65 + 30 * q^66 - 15 * q^67 + 27 * q^68 + 24 * q^69 + 24 * q^70 - 36 * q^71 - 42 * q^73 - 6 * q^74 - 18 * q^78 - 6 * q^79 + 3 * q^82 - 36 * q^83 - 24 * q^84 + 6 * q^86 - 54 * q^87 + 60 * q^89 - 12 * q^90 - 18 * q^91 - 84 * q^93 - 6 * q^95 + 9 * q^97 - 12 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$	−0.0553136	−	1.73117i	−0.0319353	−	0.999490i
$3$	−0.0553136	−	1.73117i	−0.0319353	−	0.999490i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	0.882820	−	2.42553i	0.394809	−	1.08473i	−0.569970	−	0.821666i	$-0.693045\pi$
$5$	0.882820	−	2.42553i	0.394809	−	1.08473i	0.964779	−	0.263063i	$-0.0847327\pi$
$6$	−1.69526	+	0.355087i	−0.692088	+	0.144964i
$7$	−1.58376	+	2.74316i	−0.598607	+	1.03682i	0.394420	+	0.918930i	$0.370945\pi$
$7$	−1.58376	+	2.74316i	−0.598607	+	1.03682i	−0.993027	+	0.117887i	$0.962388\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−2.99388	+	0.191514i	−0.997960	+	0.0638380i
$10$	−2.54198	−	0.448219i	−0.803844	−	0.141739i
$11$	2.16590	−	1.25049i	0.653045	−	0.377036i	−0.136577	−	0.990629i	$-0.543610\pi$
$11$	2.16590	−	1.25049i	0.653045	−	0.377036i	0.789622	+	0.613594i	$0.210277\pi$
$12$	0.644072	+	1.60785i	0.185928	+	0.464145i
$13$	2.71907	−	3.24046i	0.754135	−	0.898743i	−0.243327	−	0.969944i	$-0.578239\pi$
$13$	2.71907	−	3.24046i	0.754135	−	0.898743i	0.997462	+	0.0712015i	$0.0226833\pi$
$14$	2.97650	+	1.08336i	0.795504	+	0.289540i
$15$	−4.24783	−	1.39414i	−1.09678	−	0.359966i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−1.32278	+	0.233243i	−0.320822	+	0.0565696i	−0.331740	−	0.943371i	$-0.607636\pi$
$17$	−1.32278	+	0.233243i	−0.320822	+	0.0565696i	0.0109180	+	0.999940i	$0.496525\pi$
$18$	0.708487	+	2.91514i	0.166992	+	0.687105i
$19$	3.14841	+	3.01455i	0.722294	+	0.691586i
$19$	3.14841	+	3.01455i	0.722294	+	0.691586i
$20$			2.58119i			0.577172i
$21$	4.83647	+	2.59003i	1.05541	+	0.565190i
$22$	−1.60759	−	1.91586i	−0.342740	−	0.408462i
$23$	1.30503	+	3.58554i	0.272117	+	0.747636i	0.998197	+	0.0600255i	$0.0191182\pi$
$23$	1.30503	+	3.58554i	0.272117	+	0.747636i	−0.726080	+	0.687611i	$0.758660\pi$
$24$	1.47158	−	0.913487i	0.300385	−	0.186465i
$25$	−1.27359	−	1.06867i	−0.254718	−	0.213734i
$26$	−3.66340	−	2.11506i	−0.718451	−	0.414798i
$27$	0.497145	+	5.17232i	0.0956757	+	0.995413i
$28$	0.550036	−	3.11941i	0.103947	−	0.589513i
$29$	1.32242	−	7.49981i	0.245567	−	1.39268i	−0.573606	−	0.819132i	$-0.694456\pi$
$29$	1.32242	−	7.49981i	0.245567	−	1.39268i	0.819172	−	0.573547i	$-0.194433\pi$
$30$	−0.635337	+	4.42538i	−0.115996	+	0.807961i
$31$	6.89193	+	3.97906i	1.23783	+	0.714660i	0.968650	−	0.248431i	$-0.0799149\pi$
$31$	6.89193	+	3.97906i	1.23783	+	0.714660i	0.269177	+	0.963091i	$0.413248\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	−2.28460	−	3.68037i	−0.397699	−	0.640671i
$34$	0.459398	+	1.26219i	0.0787861	+	0.216463i
$35$	5.25543	+	6.26318i	0.888330	+	1.05867i
$36$	2.74783	−	1.20393i	0.457971	−	0.200655i
$37$			4.10469i			0.674806i	0.941360	+	0.337403i	$0.109549\pi$
$37$			4.10469i			0.674806i	−0.941360	+	0.337403i	$0.890451\pi$
$38$	2.42204	−	3.62405i	0.392907	−	0.587898i
$39$	−5.76019	−	4.52793i	−0.922368	−	0.725048i
$40$	2.54198	−	0.448219i	0.401922	−	0.0708697i
$41$	−4.95792	+	4.16019i	−0.774297	+	0.649712i	−0.941805	−	0.336158i	$-0.890872\pi$
$41$	−4.95792	+	4.16019i	−0.774297	+	0.649712i	0.167509	+	0.985871i	$0.446428\pi$
$42$	1.71083	−	5.21275i	0.263987	−	0.804345i
$43$	−11.7465	−	4.27537i	−1.79132	−	0.651987i	−0.999130	−	0.0417144i	$-0.986718\pi$
$43$	−11.7465	−	4.27537i	−1.79132	−	0.651987i	−0.792191	−	0.610273i	$-0.791060\pi$
$44$	−1.60759	+	1.91586i	−0.242354	+	0.288826i
$45$	−2.17853	+	7.43081i	−0.324757	+	1.10772i
$46$	3.30445	−	1.90782i	0.487214	−	0.281293i
$47$	−6.16940	−	1.08783i	−0.899899	−	0.158676i	−0.295486	−	0.955347i	$-0.595481\pi$
$47$	−6.16940	−	1.08783i	−0.899899	−	0.158676i	−0.604414	+	0.796671i	$0.706593\pi$
$48$	−1.15515	−	1.29060i	−0.166731	−	0.186282i
$49$	−1.51662	−	2.62686i	−0.216660	−	0.375266i
$50$	−0.831277	+	1.43981i	−0.117560	+	0.203621i
$51$	0.476950	+	2.27706i	0.0667863	+	0.318852i
$52$	−1.44679	+	3.97502i	−0.200633	+	0.551236i
$53$	3.46508	−	1.26118i	0.475965	−	0.173237i	−0.0928877	−	0.995677i	$-0.529610\pi$
$53$	3.46508	−	1.26118i	0.475965	−	0.173237i	0.568853	+	0.822440i	$0.307388\pi$
$54$	5.00741	−	1.38776i	0.681422	−	0.188850i
$55$	−1.12098	−	6.35742i	−0.151153	−	0.857234i
$56$	−3.16753			−0.423279
$57$	5.04455	−	5.61716i	0.668167	−	0.744011i
$58$	−7.61550			−0.999964
$59$	1.54335	+	8.75275i	0.200927	+	1.13951i	0.903722	+	0.428119i	$0.140824\pi$
$59$	1.54335	+	8.75275i	0.200927	+	1.13951i	−0.702796	+	0.711392i	$0.748065\pi$
$60$	4.46848	−	0.142775i	0.576878	−	0.0184322i
$61$	−0.133301	+	0.0485177i	−0.0170675	+	0.00621206i	−0.350540	−	0.936548i	$-0.614002\pi$
$61$	−0.133301	+	0.0485177i	−0.0170675	+	0.00621206i	0.333472	+	0.942760i	$0.391780\pi$
$62$	2.72184	−	7.47818i	0.345673	−	0.949730i
$63$	4.21625	−	8.51601i	0.531197	−	1.07292i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−5.45938	−	9.45593i	−0.677153	−	1.17286i
$66$	−3.22774	+	2.88899i	−0.397308	+	0.355610i
$67$	−4.48795	−	0.791347i	−0.548291	−	0.0966784i	−0.107361	−	0.994220i	$-0.534240\pi$
$67$	−4.48795	−	0.791347i	−0.548291	−	0.0966784i	−0.440930	+	0.897542i	$0.645351\pi$
$68$	1.16324	−	0.671595i	0.141063	−	0.0814429i
$69$	6.13498	−	2.45755i	0.738565	−	0.295855i
$70$	5.25543	−	6.26318i	0.628144	−	0.748593i
$71$	−8.59275	−	3.12750i	−1.01977	−	0.371166i	−0.222594	−	0.974911i	$-0.571452\pi$
$71$	−8.59275	−	3.12750i	−1.01977	−	0.371166i	−0.797178	+	0.603745i	$0.793675\pi$
$72$	−1.66280	−	2.49702i	−0.195962	−	0.294277i
$73$	−1.67672	+	1.40694i	−0.196245	+	0.164670i	−0.735615	−	0.677399i	$-0.763107\pi$
$73$	−1.67672	+	1.40694i	−0.196245	+	0.164670i	0.539370	+	0.842069i	$0.318662\pi$
$74$	4.04233	−	0.712771i	0.469911	−	0.0828580i
$75$	−1.77960	+	2.26391i	−0.205490	+	0.261414i
$76$	−3.98957	−	1.75594i	−0.457635	−	0.201420i
$77$			7.92190i			0.902784i
$78$	−3.45889	+	6.45894i	−0.391642	+	0.731331i
$79$	6.41515	+	7.64528i	0.721760	+	0.860161i	0.994801	−	0.101842i	$-0.0324736\pi$
$79$	6.41515	+	7.64528i	0.721760	+	0.860161i	−0.273040	+	0.962003i	$0.588029\pi$
$80$	−0.882820	−	2.42553i	−0.0987023	−	0.271182i
$81$	8.92664	−	1.14674i	0.991849	−	0.127416i
$82$	4.95792	+	4.16019i	0.547511	+	0.459416i
$83$	−12.3308	−	7.11920i	−1.35348	−	0.781433i	−0.364747	−	0.931107i	$-0.618844\pi$
$83$	−12.3308	−	7.11920i	−1.35348	−	0.781433i	−0.988735	+	0.149673i	$0.952178\pi$
$84$	−5.43064	−	0.779658i	−0.592531	−	0.0850677i
$85$	−0.602044	+	3.41436i	−0.0653008	+	0.370339i
$86$	−2.17066	+	12.3104i	−0.234068	+	1.32747i
$87$	−13.0566	−	1.87449i	−1.39981	−	0.200966i
$88$	2.16590	+	1.25049i	0.230886	+	0.133302i
$89$	12.7492	+	10.6978i	1.35141	+	1.13397i	0.978533	+	0.206089i	$0.0660737\pi$
$89$	12.7492	+	10.6978i	1.35141	+	1.13397i	0.372879	+	0.927880i	$0.378371\pi$
$90$	7.69622	+	0.855091i	0.811253	+	0.0901345i
$91$	4.58274	+	12.5910i	0.480402	+	1.31989i
$92$	−2.45265	−	2.92296i	−0.255707	−	0.304739i
$93$	6.50720	−	12.1512i	0.674765	−	1.26002i
$94$			6.26457i			0.646141i
$95$	10.0914	−	4.97524i	1.03535	−	0.510448i
$96$	−1.07040	+	1.36171i	−0.109247	+	0.138979i
$97$	0.538573	−	0.0949649i	0.0546838	−	0.00964223i	−0.146239	−	0.989249i	$-0.546717\pi$
$97$	0.538573	−	0.0949649i	0.0546838	−	0.00964223i	0.200923	+	0.979607i	$0.435606\pi$
$98$	−2.32360	+	1.94973i	−0.234719	+	0.196952i
$99$	−6.24498	+	4.15861i	−0.627644	+	0.417956i
$100$	1.56229	+	0.568627i	0.156229	+	0.0568627i
$101$	−7.56338	+	9.01368i	−0.752584	+	0.896895i	−0.997355	−	0.0726860i	$-0.976843\pi$
$101$	−7.56338	+	9.01368i	−0.752584	+	0.896895i	0.244771	+	0.969581i	$0.421287\pi$
$102$	2.15964	−	0.865111i	0.213837	−	0.0856588i
$103$	6.77528	−	3.91171i	0.667588	−	0.385432i	−0.127574	−	0.991829i	$-0.540719\pi$
$103$	6.77528	−	3.91171i	0.667588	−	0.385432i	0.795162	+	0.606397i	$0.207386\pi$
$104$	4.16586	+	0.734553i	0.408496	+	0.0720289i
$105$	10.5519	−	9.44447i	1.02976	−	0.921686i
$106$	−1.84373	−	3.19343i	−0.179079	−	0.310174i
$107$	−2.82951	+	4.90085i	−0.273539	+	0.473783i	−0.969765	−	0.244039i	$-0.921528\pi$
$107$	−2.82951	+	4.90085i	−0.273539	+	0.473783i	0.696227	+	0.717822i	$0.254861\pi$
$108$	−2.23620	−	4.69035i	−0.215178	−	0.451329i
$109$	5.64501	−	15.5095i	0.540694	−	1.48554i	−0.305251	−	0.952272i	$-0.598740\pi$
$109$	5.64501	−	15.5095i	0.540694	−	1.48554i	0.845944	−	0.533271i	$-0.179038\pi$
$110$	−6.06618	+	2.20791i	−0.578387	+	0.210516i
$111$	7.10590	−	0.227045i	0.674462	−	0.0215502i
$112$	0.550036	+	3.11941i	0.0519735	+	0.294756i
$113$	−5.15697			−0.485127			−0.242564	−	0.970136i	$-0.577988\pi$
$113$	−5.15697			−0.485127			−0.242564	+	0.970136i	$0.577988\pi$
$114$	−6.40780	−	3.99250i	−0.600146	−	0.373932i
$115$	9.84893			0.918417
$116$	1.32242	+	7.49981i	0.122783	+	0.696339i
$117$	−7.51998	+	10.2223i	−0.695223	+	0.945052i
$118$	8.35178	−	3.03980i	0.768843	−	0.279836i
$119$	1.45516	−	3.99801i	0.133394	−	0.366497i
$120$	−0.916549	−	4.37580i	−0.0836691	−	0.399454i
$121$	−2.37257	+	4.10941i	−0.215688	+	0.373583i
$122$	0.0709282	+	0.122851i	0.00642154	+	0.0111224i
$123$	7.47622	+	8.35287i	0.674108	+	0.753153i
$124$	−7.83721	−	1.38191i	−0.703802	−	0.124099i
$125$	7.46045	−	4.30729i	0.667283	−	0.385256i
$126$	−9.11878	−	2.67340i	−0.812365	−	0.238166i
$127$	5.03745	−	6.00340i	0.447001	−	0.532715i	−0.494746	−	0.869038i	$-0.664739\pi$
$127$	5.03745	−	6.00340i	0.447001	−	0.532715i	0.941747	+	0.336322i	$0.109183\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	−6.75164	+	20.5716i	−0.594448	+	1.81123i
$130$	−8.36426	+	7.01845i	−0.733594	+	0.615559i
$131$	4.43285	−	0.781631i	0.387300	−	0.0682914i	0.0233919	−	0.999726i	$-0.492553\pi$
$131$	4.43285	−	0.781631i	0.387300	−	0.0682914i	0.363908	+	0.931435i	$0.381442\pi$
$132$	3.40559	+	2.67704i	0.296418	+	0.233006i
$133$	−13.2557	+	3.86224i	−1.14942	+	0.334898i
$134$			4.55719i			0.393681i
$135$	12.9845	+	3.36038i	1.11753	+	0.289216i
$136$	−0.863386	−	1.02894i	−0.0740347	−	0.0882312i
$137$	2.69063	+	7.39245i	0.229876	+	0.631580i	0.999980	−	0.00633905i	$-0.00201780\pi$
$137$	2.69063	+	7.39245i	0.229876	+	0.631580i	−0.770104	+	0.637919i	$0.779796\pi$
$138$	−3.48554	−	5.61503i	−0.296709	−	0.477983i
$139$	−5.76780	−	4.83976i	−0.489219	−	0.410503i	0.364528	−	0.931193i	$-0.381230\pi$
$139$	−5.76780	−	4.83976i	−0.489219	−	0.410503i	−0.853746	+	0.520689i	$0.825675\pi$
$140$	−7.08063	−	4.08800i	−0.598422	−	0.345499i
$141$	−1.54197	+	10.7404i	−0.129857	+	0.904507i
$142$	−1.58788	+	9.00529i	−0.133252	+	0.755707i
$143$	1.83710	−	10.4187i	0.153626	−	0.871255i
$144$	−2.17034	+	2.07114i	−0.180862	+	0.172595i
$145$	−17.0235	−	9.82854i	−1.41373	−	0.816216i
$146$	1.67672	+	1.40694i	0.138767	+	0.116439i
$147$	−4.46365	+	2.77082i	−0.368156	+	0.228534i
$148$	−1.40389	−	3.85714i	−0.115399	−	0.317055i
$149$	−8.79633	−	10.4831i	−0.720624	−	0.858806i	0.274068	−	0.961710i	$-0.411631\pi$
$149$	−8.79633	−	10.4831i	−0.720624	−	0.858806i	−0.994691	+	0.102905i	$0.967186\pi$
$150$	2.53854	+	1.35944i	0.207271	+	0.110998i
$151$		−	8.63653i		−	0.702831i	−0.936220	−	0.351415i	$-0.885700\pi$
$151$		−	8.63653i		−	0.702831i	0.936220	−	0.351415i	$-0.114300\pi$
$152$	−1.03648	+	4.23388i	−0.0840695	+	0.343413i
$153$	3.91559	−	0.951632i	0.316557	−	0.0769349i
$154$	7.80155	−	1.37562i	0.628667	−	0.110851i
$155$	15.7356	−	13.2038i	1.26392	−	1.06055i
$156$	6.96145	+	2.28476i	0.557362	+	0.182927i
$157$	−3.22785	−	1.17484i	−0.257610	−	0.0937625i	0.209987	−	0.977704i	$-0.432658\pi$
$157$	−3.22785	−	1.17484i	−0.257610	−	0.0937625i	−0.467597	+	0.883942i	$0.654880\pi$
$158$	6.41515	−	7.64528i	0.510362	−	0.608225i
$159$	−2.37499	−	5.92887i	−0.188349	−	0.470190i
$160$	−2.23538	+	1.29060i	−0.176722	+	0.102031i
$161$	−11.9026	−	2.09874i	−0.938053	−	0.165404i
$162$	−2.67942	−	8.59190i	−0.210515	−	0.675043i
$163$	3.83308	+	6.63909i	0.300230	+	0.520014i	0.976188	−	0.216926i	$-0.0696032\pi$
$163$	3.83308	+	6.63909i	0.300230	+	0.520014i	−0.675958	+	0.736940i	$0.736270\pi$
$164$	3.23605	−	5.60501i	0.252693	−	0.437677i
$165$	−10.9437	+	2.29226i	−0.851969	+	0.178452i
$166$	−4.86982	+	13.3797i	−0.377971	+	1.03847i
$167$	2.20429	−	0.802294i	0.170573	−	0.0620834i	−0.255322	−	0.966856i	$-0.582182\pi$
$167$	2.20429	−	0.802294i	0.170573	−	0.0620834i	0.425895	+	0.904773i	$0.359959\pi$
$168$	0.175207	+	5.48352i	0.0135175	+	0.423063i
$169$	−0.849826	−	4.81960i	−0.0653712	−	0.370739i
$170$	3.46703			0.265909
$171$	−10.0033	−	8.42225i	−0.764970	−	0.644066i
$172$	12.5003			0.953142
$173$	−2.59056	−	14.6918i	−0.196956	−	1.11700i	−0.909605	−	0.415474i	$-0.863616\pi$
$173$	−2.59056	−	14.6918i	−0.196956	−	1.11700i	0.712649	−	0.701521i	$-0.247495\pi$
$174$	0.421241	+	13.1837i	0.0319342	+	0.999454i
$175$	4.94860	−	1.80114i	0.374079	−	0.136154i
$176$	0.855383	−	2.35014i	0.0644769	−	0.177149i
$177$	15.0671	−	3.15594i	1.13251	−	0.237215i
$178$	8.32145	−	14.4132i	0.623719	−	1.08031i
$179$	0.0974666	+	0.168817i	0.00728500	+	0.0126180i	0.869645	−	0.493678i	$-0.164348\pi$
$179$	0.0974666	+	0.168817i	0.00728500	+	0.0126180i	−0.862360	+	0.506296i	$0.831014\pi$
$180$	−0.494335	−	7.72778i	−0.0368455	−	0.575995i
$181$	−7.00507	−	1.23518i	−0.520683	−	0.0918105i	−0.0928709	−	0.995678i	$-0.529604\pi$
$181$	−7.00507	−	1.23518i	−0.520683	−	0.0918105i	−0.427812	+	0.903868i	$0.640715\pi$
$182$	11.6039	−	6.69952i	0.860139	−	0.496602i
$183$	0.0913657	+	0.228083i	0.00675395	+	0.0168604i
$184$	−2.45265	+	2.92296i	−0.180812	+	0.215483i
$185$	9.95603	+	3.62370i	0.731982	+	0.266420i
$186$	−13.0965	−	4.29831i	−0.960285	−	0.315167i
$187$	−2.57336	+	2.15930i	−0.188183	+	0.157904i
$188$	6.16940	−	1.08783i	0.449950	−	0.0793382i
$189$	−14.9759	−	6.82798i	−1.08933	−	0.496662i
$190$	−6.65200	−	9.07411i	−0.482587	−	0.658305i
$191$		−	11.2480i		−	0.813878i	−0.913455	−	0.406939i	$-0.866596\pi$
$191$		−	11.2480i		−	0.813878i	0.913455	−	0.406939i	$-0.133404\pi$
$192$	1.52689	+	0.817681i	0.110194	+	0.0590110i
$193$	−10.3664	−	12.3541i	−0.746187	−	0.889271i	0.250704	−	0.968064i	$-0.419338\pi$
$193$	−10.3664	−	12.3541i	−0.746187	−	0.889271i	−0.996891	+	0.0787930i	$0.974893\pi$
$194$	−0.187044	−	0.513900i	−0.0134290	−	0.0368959i
$195$	−16.0678	+	9.97415i	−1.15064	+	0.714263i
$196$	2.32360	+	1.94973i	0.165971	+	0.139266i
$197$	19.7987	+	11.4308i	1.41060	+	0.814411i	0.995445	−	0.0953383i	$-0.0303933\pi$
$197$	19.7987	+	11.4308i	1.41060	+	0.814411i	0.415157	+	0.909750i	$0.363727\pi$
$198$	5.17986	+	5.42797i	0.368116	+	0.385749i
$199$	0.0579780	−	0.328809i	0.00410995	−	0.0233087i	−0.982684	−	0.185290i	$-0.940677\pi$
$199$	0.0579780	−	0.328809i	0.00410995	−	0.0233087i	0.986794	+	0.161982i	$0.0517885\pi$
$200$	0.288700	−	1.63730i	0.0204141	−	0.115774i
$201$	−1.12171	+	7.81317i	−0.0791193	+	0.551098i
$202$	10.1901	+	5.88326i	0.716974	+	0.413945i
$203$	18.4788	+	15.5055i	1.29696	+	1.08827i
$204$	−1.22699	−	1.97661i	−0.0859062	−	0.138390i
$205$	5.71370	+	15.6983i	0.399062	+	1.09641i
$206$	−5.02879	−	5.99308i	−0.350373	−	0.417558i
$207$	−4.59378	−	10.4847i	−0.319290	−	0.728740i
$208$		−	4.23012i		−	0.293306i
$209$	10.5888	+	2.59220i	0.732443	+	0.179306i
$210$	−11.1333	−	8.75159i	−0.768271	−	0.603917i
$211$	2.52603	−	0.445407i	0.173899	−	0.0306631i	−0.0860206	−	0.996293i	$-0.527415\pi$
$211$	2.52603	−	0.445407i	0.173899	−	0.0306631i	0.259919	+	0.965630i	$0.416304\pi$
$212$	−2.82476	+	2.37025i	−0.194005	+	0.162790i
$213$	−4.93894	+	15.0485i	−0.338410	+	1.03110i
$214$	5.31773	+	1.93550i	0.363513	+	0.132308i
$215$	−20.7400	+	24.7170i	−1.41446	+	1.68569i
$216$	−4.23078	+	3.01670i	−0.287868	+	0.205260i
$217$	−21.8304	+	12.6038i	−1.48194	+	0.855600i
$218$	−16.2542	−	2.86605i	−1.10087	−	0.194113i
$219$	2.52839	+	2.82486i	0.170853	+	0.190887i
$220$	3.22774	+	5.59062i	0.217614	+	0.376919i
$221$	−2.84093	+	4.92064i	−0.191102	+	0.330998i
$222$	−1.45752	−	6.95852i	−0.0978225	−	0.467025i
$223$	2.28294	−	6.27232i	0.152877	−	0.420026i	−0.839486	−	0.543382i	$-0.817144\pi$
$223$	2.28294	−	6.27232i	0.152877	−	0.420026i	0.992362	+	0.123356i	$0.0393658\pi$
$224$	2.97650	−	1.08336i	0.198876	−	0.0723849i
$225$	4.01764	+	2.95556i	0.267843	+	0.197037i
$226$	0.895499	+	5.07863i	0.0595677	+	0.337825i
$227$	−20.0547			−1.33108			−0.665539	−	0.746363i	$-0.731798\pi$
$227$	−20.0547			−1.33108			−0.665539	+	0.746363i	$0.731798\pi$
$228$	−2.81914	+	7.00374i	−0.186702	+	0.463834i
$229$	16.5068			1.09080			0.545400	−	0.838176i	$-0.316378\pi$
$229$	16.5068			1.09080			0.545400	+	0.838176i	$0.316378\pi$
$230$	−1.71025	−	9.69930i	−0.112770	−	0.639553i
$231$	13.7141	−	0.438189i	0.902324	−	0.0288307i
$232$	7.15623	−	2.60466i	0.469830	−	0.171004i
$233$	2.12137	−	5.82843i	0.138976	−	0.381833i	−0.850606	−	0.525803i	$-0.823765\pi$
$233$	2.12137	−	5.82843i	0.138976	−	0.381833i	0.989582	+	0.143970i	$0.0459870\pi$
$234$	11.3728	+	5.63065i	0.743465	+	0.368087i
$235$	−8.08503	+	14.0037i	−0.527409	+	0.913500i
$236$	−4.44389	−	7.69704i	−0.289272	−	0.501035i
$237$	12.8804	−	11.5286i	0.836672	−	0.748862i
$238$	−4.18996	−	0.738802i	−0.271595	−	0.0478895i
$239$	0.498666	−	0.287905i	0.0322560	−	0.0186230i	−0.483785	−	0.875187i	$-0.660738\pi$
$239$	0.498666	−	0.287905i	0.0322560	−	0.0186230i	0.516041	+	0.856564i	$0.327405\pi$
$240$	−4.15016	+	1.66247i	−0.267892	+	0.107312i
$241$	−1.09166	+	1.30099i	−0.0703198	+	0.0838039i	−0.800058	−	0.599923i	$-0.795198\pi$
$241$	−1.09166	+	1.30099i	−0.0703198	+	0.0838039i	0.729738	+	0.683727i	$0.239642\pi$
$242$	4.45897	+	1.62293i	0.286634	+	0.104326i
$243$	−2.47897	−	15.3901i	−0.159026	−	0.987274i
$244$	0.108668	−	0.0911835i	0.00695677	−	0.00583743i
$245$	−7.71043	+	1.35956i	−0.492601	+	0.0868589i
$246$	6.92774	−	8.81310i	0.441697	−	0.561903i
$247$	18.3293	−	2.00550i	1.16627	−	0.127607i
$248$			7.95811i			0.505341i
$249$	−11.6425	+	21.7405i	−0.737811	+	1.37775i
$250$	−5.53735	−	6.59916i	−0.350213	−	0.417367i
$251$	−2.05161	−	5.63675i	−0.129496	−	0.355789i	0.857952	−	0.513730i	$-0.171737\pi$
$251$	−2.05161	−	5.63675i	−0.129496	−	0.355789i	−0.987449	+	0.157941i	$0.949514\pi$
$252$	−1.04933	+	9.44447i	−0.0661016	+	0.594946i
$253$	7.31023	+	6.13401i	0.459590	+	0.385642i
$254$	−6.78694	−	3.91844i	−0.425850	−	0.245865i
$255$	5.94413	+	0.853378i	0.372236	+	0.0534406i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−3.23144	+	18.3264i	−0.201572	+	1.14317i	0.701172	+	0.712992i	$0.252660\pi$
$257$	−3.23144	+	18.3264i	−0.201572	+	1.14317i	−0.902744	+	0.430178i	$0.858451\pi$
$258$	21.4315	+	3.07684i	1.33427	+	0.191556i
$259$	−11.2598	−	6.50086i	−0.699651	−	0.403944i
$260$	8.36426	+	7.01845i	0.518729	+	0.435266i
$261$	−2.52284	+	22.7068i	−0.156160	+	1.40551i
$262$	−1.53951	−	4.22977i	−0.0951113	−	0.261316i
$263$	1.37946	+	1.64398i	0.0850614	+	0.101372i	0.806896	−	0.590693i	$-0.201146\pi$
$263$	1.37946	+	1.64398i	0.0850614	+	0.101372i	−0.721835	+	0.692065i	$0.756701\pi$
$264$	2.04500	−	3.81871i	0.125861	−	0.235026i
$265$		−	9.51804i		−	0.584688i
$266$	6.10540	+	12.3837i	0.374346	+	0.759293i
$267$	17.8146	−	22.6627i	1.09023	−	1.38694i
$268$	4.48795	−	0.791347i	0.274145	−	0.0483392i
$269$	−19.9247	+	16.7188i	−1.21483	+	1.01936i	−0.215752	+	0.976448i	$0.569220\pi$
$269$	−19.9247	+	16.7188i	−1.21483	+	1.01936i	−0.999079	+	0.0429154i	$0.986335\pi$
$270$	1.05460	−	13.3707i	0.0641809	−	0.813718i
$271$	4.62857	+	1.68466i	0.281166	+	0.102336i	0.478754	−	0.877949i	$-0.341089\pi$
$271$	4.62857	+	1.68466i	0.281166	+	0.102336i	−0.197588	+	0.980285i	$0.563311\pi$
$272$	−0.863386	+	1.02894i	−0.0523505	+	0.0623889i
$273$	21.5436	−	8.62995i	1.30388	−	0.522308i
$274$	6.81292	−	3.93344i	0.411583	−	0.237628i
$275$	−4.09483	−	0.722029i	−0.246928	−	0.0435400i
$276$	−4.92446	+	4.40763i	−0.296418	+	0.265308i
$277$	−0.845901	−	1.46514i	−0.0508252	−	0.0880319i	0.839493	−	0.543370i	$-0.182852\pi$
$277$	−0.845901	−	1.46514i	−0.0508252	−	0.0880319i	−0.890319	+	0.455338i	$0.849518\pi$
$278$	−3.76467	+	6.52059i	−0.225790	+	0.391079i
$279$	−21.3957	−	10.5929i	−1.28092	−	0.634182i
$280$	−2.79636	+	7.68293i	−0.167114	+	0.459143i
$281$	28.0317	−	10.2027i	1.67223	−	0.608642i	0.680017	−	0.733196i	$-0.261972\pi$
$281$	28.0317	−	10.2027i	1.67223	−	0.608642i	0.992213	+	0.124555i	$0.0397502\pi$
$282$	10.8450	−	0.346516i	0.645811	−	0.0206347i
$283$	4.10223	+	23.2649i	0.243852	+	1.38296i	0.823143	+	0.567834i	$0.192219\pi$
$283$	4.10223	+	23.2649i	0.243852	+	1.38296i	−0.579290	+	0.815121i	$0.696670\pi$
$284$	9.14421			0.542609
$285$	−9.17116	−	17.1946i	−0.543252	−	1.01852i
$286$	−10.5794			−0.625574
$287$	−3.55989	−	20.1891i	−0.210134	−	1.19173i
$288$	2.41655	+	1.77772i	0.142396	+	0.104753i
$289$	−14.2794	+	5.19728i	−0.839966	+	0.305723i
$290$	−6.72312	+	18.4716i	−0.394795	+	1.08469i
$291$	−0.194191	−	0.927107i	−0.0113837	−	0.0543480i
$292$	1.09440	−	1.89556i	0.0640451	−	0.110929i
$293$	−4.63502	−	8.02810i	−0.270781	−	0.469006i	0.698281	−	0.715824i	$-0.253949\pi$
$293$	−4.63502	−	8.02810i	−0.270781	−	0.469006i	−0.969062	+	0.246817i	$0.920615\pi$
$294$	3.50383	+	3.91469i	0.204348	+	0.228309i
$295$	22.5925	+	3.98367i	1.31539	+	0.231938i
$296$	−3.55476	+	2.05234i	−0.206616	+	0.119290i
$297$	7.54468	+	10.5811i	0.437787	+	0.613976i
$298$	−8.79633	+	10.4831i	−0.509558	+	0.607267i
$299$	15.1673	+	5.52043i	0.877146	+	0.319255i
$300$	0.897973	−	2.73604i	0.0518445	−	0.157965i
$301$	30.3317	−	25.4513i	1.74829	−	1.46699i
$302$	−8.50532	+	1.49972i	−0.489426	+	0.0862991i
$303$	16.0226	+	12.5949i	0.920472	+	0.723558i
$304$	4.34954	+	0.285527i	0.249463	+	0.0163761i
$305$			0.366159i			0.0209662i
$306$	−1.61711	−	3.69085i	−0.0924440	−	0.210992i
$307$	1.76414	+	2.10242i	0.100685	+	0.119991i	0.814034	−	0.580818i	$-0.197267\pi$
$307$	1.76414	+	2.10242i	0.100685	+	0.119991i	−0.713349	+	0.700809i	$0.752823\pi$
$308$	−2.70945	−	7.44415i	−0.154385	−	0.424170i
$309$	−7.14658	−	11.5128i	−0.406555	−	0.654938i
$310$	−15.7356	−	13.2038i	−0.893724	−	0.749924i
$311$	−19.8290	−	11.4483i	−1.12440	−	0.649172i	−0.181879	−	0.983321i	$-0.558218\pi$
$311$	−19.8290	−	11.4483i	−1.12440	−	0.649172i	−0.942520	+	0.334148i	$0.891551\pi$
$312$	1.04121	−	7.25243i	0.0589467	−	0.410588i
$313$	−2.33240	+	13.2277i	−0.131835	+	0.747673i	0.845177	+	0.534487i	$0.179495\pi$
$313$	−2.33240	+	13.2277i	−0.131835	+	0.747673i	−0.977012	+	0.213186i	$0.931616\pi$
$314$	−0.596482	+	3.38282i	−0.0336614	+	0.190903i
$315$	−16.9336	−	17.7447i	−0.954102	−	0.999802i
$316$	−8.64310	−	4.99010i	−0.486213	−	0.280715i
$317$	−15.9117	−	13.3515i	−0.893689	−	0.749894i	0.0752579	−	0.997164i	$-0.476022\pi$
$317$	−15.9117	−	13.3515i	−0.893689	−	0.749894i	−0.968947	+	0.247270i	$0.920466\pi$
$318$	−5.42638	+	3.36844i	−0.304296	+	0.188893i
$319$	−6.51417	−	17.8975i	−0.364723	−	1.00207i
$320$	1.65916	+	1.97731i	0.0927498	+	0.110535i
$321$	8.64070	+	4.62727i	0.482277	+	0.258269i
$322$			12.0862i			0.673536i
$323$	−4.86778	−	3.25326i	−0.270851	−	0.181016i
$324$	−7.99609	+	4.13068i	−0.444227	+	0.229482i
$325$	−6.92597	+	1.22124i	−0.384184	+	0.0677419i
$326$	5.87262	−	4.92772i	0.325254	−	0.272921i
$327$	−27.1618	−	8.91456i	−1.50205	−	0.492977i
$328$	−6.08179	−	2.21359i	−0.335811	−	0.122225i
$329$	12.7550	−	15.2008i	0.703204	−	0.838046i
$330$	4.15780	+	10.3794i	0.228879	+	0.571369i
$331$	7.79345	−	4.49955i	0.428367	−	0.247318i	−0.270284	−	0.962781i	$-0.587118\pi$
$331$	7.79345	−	4.49955i	0.428367	−	0.247318i	0.698651	+	0.715463i	$0.253784\pi$
$332$	14.0221	+	2.47247i	0.769562	+	0.135694i
$333$	−0.786106	−	12.2889i	−0.0430783	−	0.673430i
$334$	−1.17288	−	2.03148i	−0.0641769	−	0.111158i
$335$	−5.88149	+	10.1870i	−0.321340	+	0.556577i
$336$	5.36979	−	1.12475i	0.292946	−	0.0613601i
$337$	4.39017	−	12.0619i	0.239148	−	0.657053i	−0.760819	−	0.648964i	$-0.775203\pi$
$337$	4.39017	−	12.0619i	0.239148	−	0.657053i	0.999967	−	0.00808963i	$-0.00257504\pi$
$338$	−4.59881	+	1.67383i	−0.250142	+	0.0910444i
$339$	0.285251	+	8.92758i	0.0154927	+	0.484880i
$340$	−0.602044	−	3.41436i	−0.0326504	−	0.185170i
$341$	19.9030			1.07781
$342$	−6.55725	+	11.3138i	−0.354575	+	0.611781i
$343$	−12.5648			−0.678437
$344$	−2.17066	−	12.3104i	−0.117034	−	0.663734i
$345$	−0.544779	−	17.0501i	−0.0293299	−	0.917949i
$346$	−14.0187	+	5.10240i	−0.753652	+	0.274307i
$347$	−4.73541	+	13.0104i	−0.254210	+	0.698436i	0.745288	+	0.666743i	$0.232312\pi$
$347$	−4.73541	+	13.0104i	−0.254210	+	0.698436i	−0.999498	+	0.0316932i	$0.989910\pi$
$348$	12.9103	−	2.70417i	0.692063	−	0.144959i
$349$	−10.3158	+	17.8674i	−0.552190	+	0.956421i	0.445926	+	0.895070i	$0.352874\pi$
$349$	−10.3158	+	17.8674i	−0.552190	+	0.956421i	−0.998116	+	0.0613514i	$0.980459\pi$
$350$	−2.63310	−	4.56065i	−0.140745	−	0.243777i
$351$	18.1125	+	12.4529i	0.966772	+	0.664687i
$352$	−2.46298	−	0.434289i	−0.131277	−	0.0231477i
$353$	−19.7460	+	11.4004i	−1.05098	+	0.606781i	−0.922922	−	0.384987i	$-0.874206\pi$
$353$	−19.7460	+	11.4004i	−1.05098	+	0.606781i	−0.128053	+	0.991767i	$0.540873\pi$
$354$	−5.72437	−	14.2902i	−0.304247	−	0.759515i
$355$	−15.1717	+	18.0809i	−0.805230	+	0.959636i
$356$	−15.6392	−	5.69220i	−0.828876	−	0.301686i
$357$	−7.00172	−	2.29798i	−0.370570	−	0.121622i
$358$	0.149328	−	0.125301i	0.00789221	−	0.00662235i
$359$	−7.31056	+	1.28905i	−0.385837	+	0.0680334i	−0.363202	−	0.931710i	$-0.618317\pi$
$359$	−7.31056	+	1.28905i	−0.385837	+	0.0680334i	−0.0226346	+	0.999744i	$0.507205\pi$
$360$	−7.52454	+	1.82874i	−0.396578	+	0.0963831i
$361$	0.824917	+	18.9821i	0.0434167	+	0.999057i
$362$			7.11314i			0.373858i
$363$	7.24532	+	3.88001i	0.380281	+	0.203648i
$364$	−8.61274	−	10.2643i	−0.451430	−	0.537993i
$365$	1.93232	+	5.30901i	0.101142	+	0.277886i
$366$	0.208753	−	0.129584i	0.0109117	−	0.00677346i
$367$	−15.2065	−	12.7597i	−0.793771	−	0.666053i	0.152904	−	0.988241i	$-0.451137\pi$
$367$	−15.2065	−	12.7597i	−0.793771	−	0.666053i	−0.946676	+	0.322188i	$0.895582\pi$
$368$	3.30445	+	1.90782i	0.172256	+	0.0994522i
$369$	14.0467	−	13.4046i	0.731241	−	0.697817i
$370$	1.83980	−	10.4340i	0.0956467	−	0.542439i
$371$	−2.02823	+	11.5027i	−0.105301	+	0.597189i
$372$	−1.95882	+	13.6440i	−0.101560	+	0.707407i
$373$	16.5145	+	9.53467i	0.855090	+	0.493687i	0.862365	−	0.506287i	$-0.168982\pi$
$373$	16.5145	+	9.53467i	0.855090	+	0.493687i	−0.00727484	+	0.999974i	$0.502316\pi$
$374$	2.57336	+	2.15930i	0.133065	+	0.111655i
$375$	−7.86931	−	12.6770i	−0.406370	−	0.654640i
$376$	−2.14261	−	5.88677i	−0.110497	−	0.303587i
$377$	−20.7071	−	24.6778i	−1.06647	−	1.27097i
$378$	−4.12372	+	15.9340i	−0.212101	+	0.819557i
$379$		−	30.0894i		−	1.54559i	−0.634656	−	0.772795i	$-0.718858\pi$
$379$		−	30.0894i		−	1.54559i	0.634656	−	0.772795i	$-0.281142\pi$
$380$	−7.78115	+	8.12664i	−0.399164	+	0.416888i
$381$	−10.6715	−	8.38860i	−0.546719	−	0.429761i
$382$	−11.0771	+	1.95320i	−0.566755	+	0.0999342i
$383$	4.60213	−	3.86165i	0.235158	−	0.197321i	−0.517592	−	0.855628i	$-0.673171\pi$
$383$	4.60213	−	3.86165i	0.235158	−	0.197321i	0.752750	+	0.658307i	$0.228727\pi$
$384$	0.540116	−	1.64568i	0.0275627	−	0.0839809i
$385$	19.2148	+	6.99361i	0.979276	+	0.356427i
$386$	−10.3664	+	12.3541i	−0.527634	+	0.628809i
$387$	35.9863	+	10.5503i	1.82929	+	0.536303i
$388$	−0.473613	+	0.273441i	−0.0240441	+	0.0138818i
$389$	20.4701	+	3.60942i	1.03787	+	0.183005i	0.666520	−	0.745487i	$-0.267783\pi$
$389$	20.4701	+	3.60942i	1.03787	+	0.183005i	0.371353	+	0.928492i	$0.378894\pi$
$390$	12.6128	+	14.0917i	0.638672	+	0.713562i
$391$	−2.56257	−	4.43850i	−0.129595	−	0.224465i
$392$	1.51662	−	2.62686i	0.0766009	−	0.132677i
$393$	−1.59833	−	7.63076i	−0.0806251	−	0.384921i
$394$	7.81913	−	21.4829i	0.393922	−	1.08229i
$395$	24.2072	−	8.81072i	1.21800	−	0.443315i
$396$	4.44603	−	6.04372i	0.223421	−	0.303708i
$397$	1.82838	+	10.3692i	0.0917636	+	0.520417i	0.995691	+	0.0927316i	$0.0295599\pi$
$397$	1.82838	+	10.3692i	0.0917636	+	0.520417i	−0.903928	+	0.427686i	$0.859329\pi$
$398$	−0.333882			−0.0167360
$399$	7.41940	+	22.7343i	0.371435	+	1.13814i
$400$	−1.66255			−0.0831277
$401$	−1.59795	−	9.06241i	−0.0797977	−	0.452555i	−0.998358	−	0.0572753i	$-0.981759\pi$
$401$	−1.59795	−	9.06241i	−0.0797977	−	0.452555i	0.918561	−	0.395280i	$-0.129352\pi$
$402$	7.88925	−	0.252074i	0.393480	−	0.0125723i
$403$	31.6336	−	11.5137i	1.57578	−	0.573538i
$404$	4.02439	−	11.0569i	0.200221	−	0.550102i
$405$	5.09917	−	22.6642i	0.253380	−	1.12619i
$406$	12.0612	−	20.8905i	0.598585	−	1.03678i
$407$	5.13285	+	8.89036i	0.254426	+	0.440679i
$408$	−1.73352	+	1.55158i	−0.0858218	+	0.0768147i
$409$	23.2080	+	4.09220i	1.14756	+	0.202346i	0.714911	−	0.699215i	$-0.246467\pi$
$409$	23.2080	+	4.09220i	1.14756	+	0.202346i	0.432651	+	0.901561i	$0.357578\pi$
$410$	14.4676	−	8.35287i	0.714504	−	0.412519i
$411$	12.6487	−	5.06684i	0.623916	−	0.249929i
$412$	−5.02879	+	5.99308i	−0.247751	+	0.295258i
$413$	−26.4545	−	9.62865i	−1.30174	−	0.473795i
$414$	−9.52775	+	6.34465i	−0.468263	+	0.311822i
$415$	−28.1537	+	23.6238i	−1.38201	+	1.15964i
$416$	−4.16586	+	0.734553i	−0.204248	+	0.0360144i
$417$	−8.05940	+	10.2527i	−0.394670	+	0.502079i
$418$	0.714095	−	10.8781i	0.0349275	−	0.532064i
$419$			20.4238i			0.997766i	0.866669	+	0.498883i	$0.166256\pi$
$419$			20.4238i			0.997766i	−0.866669	+	0.498883i	$0.833744\pi$
$420$	−6.68536	+	12.4839i	−0.326212	+	0.609150i
$421$	−0.259039	−	0.308710i	−0.0126248	−	0.0150456i	0.759695	−	0.650279i	$-0.225348\pi$
$421$	−0.259039	−	0.308710i	−0.0126248	−	0.0150456i	−0.772320	+	0.635234i	$0.780904\pi$
$422$	−0.877280	−	2.41031i	−0.0427053	−	0.117332i
$423$	18.6788	+	2.07531i	0.908193	+	0.100905i
$424$	2.82476	+	2.37025i	0.137182	+	0.115110i
$425$	1.93394	+	1.11656i	0.0938101	+	0.0541613i
$426$	15.6775	+	2.25076i	0.759577	+	0.109050i
$427$	0.0780261	−	0.442508i	0.00377595	−	0.0214144i
$428$	0.982678	−	5.57304i	0.0474995	−	0.269383i
$429$	−18.1381	−	2.60403i	−0.875717	−	0.125724i
$430$	27.9430	+	16.1329i	1.34753	+	0.777997i
$431$	7.15165	+	6.00095i	0.344483	+	0.289055i	0.798570	−	0.601902i	$-0.205590\pi$
$431$	7.15165	+	6.00095i	0.344483	+	0.289055i	−0.454087	+	0.890957i	$0.650035\pi$
$432$	3.70554	+	3.64266i	0.178283	+	0.175258i
$433$	−7.03421	−	19.3263i	−0.338043	−	0.928765i	−0.985949	−	0.167045i	$-0.946577\pi$
$433$	−7.03421	−	19.3263i	−0.338043	−	0.928765i	0.647907	−	0.761720i	$-0.275645\pi$
$434$	16.2031	+	19.3101i	0.777774	+	0.926915i
$435$	−16.0732	+	30.0142i	−0.770652	+	1.43907i
$436$			16.5049i			0.790441i
$437$	−6.70004	+	15.2228i	−0.320506	+	0.728206i
$438$	2.34290	−	2.98051i	0.111948	−	0.142414i
$439$	−25.2438	+	4.45116i	−1.20482	+	0.212442i	−0.739781	−	0.672847i	$-0.765071\pi$
$439$	−25.2438	+	4.45116i	−1.20482	+	0.212442i	−0.465040	+	0.885290i	$0.653960\pi$
$440$	4.94519	−	4.14951i	0.235753	−	0.197820i
$441$	5.04366	+	7.57406i	0.240174	+	0.360670i
$442$	5.33920	+	1.94331i	0.253960	+	0.0924339i
$443$	−17.0745	+	20.3486i	−0.811235	+	0.966792i	−0.999884	−	0.0152527i	$-0.995145\pi$
$443$	−17.0745	+	20.3486i	−0.811235	+	0.966792i	0.188649	+	0.982045i	$0.439589\pi$
$444$	−6.59971	+	2.64371i	−0.313208	+	0.125465i
$445$	37.2032	−	21.4793i	1.76360	−	1.01821i
$446$	−6.57346	−	1.15908i	−0.311262	−	0.0548839i
$447$	−17.6614	+	15.8078i	−0.835354	+	0.747682i
$448$	−1.58376	−	2.74316i	−0.0748258	−	0.129602i
$449$	5.66925	−	9.81944i	0.267549	−	0.463408i	−0.700680	−	0.713476i	$-0.747120\pi$
$449$	5.66925	−	9.81944i	0.267549	−	0.463408i	0.968228	+	0.250068i	$0.0804531\pi$
$450$	2.21300	−	4.46983i	0.104322	−	0.210710i
$451$	−5.53612	+	15.2104i	−0.260686	+	0.716229i
$452$	4.84597	−	1.76379i	0.227935	−	0.0829616i
$453$	−14.9513	+	0.477717i	−0.702472	+	0.0224451i
$454$	3.48246	+	19.7500i	0.163440	+	0.926915i
$455$	34.5855			1.62139
$456$	7.38688	+	1.56013i	0.345922	+	0.0730596i
$457$	−21.3688			−0.999591			−0.499796	−	0.866143i	$-0.666592\pi$
$457$	−21.3688			−0.999591			−0.499796	+	0.866143i	$0.666592\pi$
$458$	−2.86638	−	16.2560i	−0.133937	−	0.759594i
$459$	−1.86402	−	6.72590i	−0.0870050	−	0.313938i
$460$	−9.25496	+	3.36853i	−0.431515	+	0.157059i
$461$	−9.40832	+	25.8492i	−0.438189	+	1.20392i	0.502480	+	0.864589i	$0.332421\pi$
$461$	−9.40832	+	25.8492i	−0.438189	+	1.20392i	−0.940669	+	0.339326i	$0.889801\pi$
$462$	−2.81297	−	13.4297i	−0.130871	−	0.624806i
$463$	−4.52654	+	7.84019i	−0.210366	+	0.364365i	−0.951829	−	0.306629i	$-0.900799\pi$
$463$	−4.52654	+	7.84019i	−0.210366	+	0.364365i	0.741463	+	0.670994i	$0.234132\pi$
$464$	−3.80775	−	6.59522i	−0.176770	−	0.306175i
$465$	−23.7283	−	26.5107i	−1.10038	−	1.22940i
$466$	−6.10825	−	1.07705i	−0.282959	−	0.0498934i
$467$	17.7092	−	10.2244i	0.819486	−	0.473130i	−0.0307535	−	0.999527i	$-0.509791\pi$
$467$	17.7092	−	10.2244i	0.819486	−	0.473130i	0.850239	+	0.526397i	$0.176457\pi$
$468$	3.57024	−	12.1778i	0.165034	−	0.562919i
$469$	9.27865	−	11.0579i	0.428448	−	0.510605i
$470$	15.1949	+	5.53049i	0.700888	+	0.255102i
$471$	−1.85530	+	5.65293i	−0.0854878	+	0.260473i
$472$	−6.80843	+	5.71295i	−0.313383	+	0.262960i
$473$	−30.7880	+	5.42876i	−1.41564	+	0.249615i
$474$	−13.5901	−	10.6828i	−0.624214	−	0.490678i
$475$	−0.788217	−	7.20391i	−0.0361659	−	0.330538i
$476$			4.25459i			0.195009i
$477$	−10.1325	+	4.43945i	−0.463935	+	0.203268i
$478$	−0.370124	−	0.441096i	−0.0169291	−	0.0201753i
$479$	3.36367	+	9.24160i	0.153690	+	0.422259i	0.992512	−	0.122146i	$-0.0389776\pi$
$479$	3.36367	+	9.24160i	0.153690	+	0.422259i	−0.838822	+	0.544405i	$0.816755\pi$
$480$	2.35788	+	3.79843i	0.107622	+	0.173374i
$481$	13.3011	+	11.1609i	0.606477	+	0.508895i
$482$	1.47079	+	0.849159i	0.0669925	+	0.0386781i
$483$	−2.97490	+	20.7214i	−0.135363	+	0.942857i
$484$	0.823985	−	4.67305i	0.0374539	−	0.212411i
$485$	0.245123	−	1.39016i	0.0111305	−	0.0631239i
$486$	−14.7258	+	5.11376i	−0.667976	+	0.231965i
$487$	−6.75564	−	3.90037i	−0.306127	−	0.176743i	0.339065	−	0.940763i	$-0.389889\pi$
$487$	−6.75564	−	3.90037i	−0.306127	−	0.176743i	−0.645192	+	0.764020i	$0.723223\pi$
$488$	−0.108668	−	0.0911835i	−0.00491918	−	0.00412768i
$489$	11.2814	−	7.00294i	0.510161	−	0.316684i
$490$	2.67780	+	7.35721i	0.120971	+	0.332365i
$491$	−18.0754	−	21.5414i	−0.815729	−	0.972148i	0.184213	−	0.982886i	$-0.441026\pi$
$491$	−18.0754	−	21.5414i	−0.815729	−	0.972148i	−0.999942	+	0.0107379i	$0.996582\pi$
$492$	−9.88220	−	5.29211i	−0.445524	−	0.238587i
$493$			10.2291i			0.460694i
$494$	−5.15788	−	17.7026i	−0.232064	−	0.796477i
$495$	4.57363	+	18.8187i	0.205569	+	0.845836i
$496$	7.83721	−	1.38191i	0.351901	−	0.0620497i
$497$	22.1881	−	18.6181i	0.995274	−	0.835134i
$498$	23.4319	+	7.69039i	1.05001	+	0.344615i
$499$	−12.8477	−	4.67618i	−0.575142	−	0.209334i	0.0380402	−	0.999276i	$-0.487888\pi$
$499$	−12.8477	−	4.67618i	−0.575142	−	0.209334i	−0.613182	+	0.789942i	$0.710111\pi$
$500$	−5.53735	+	6.59916i	−0.247638	+	0.295123i
$501$	−1.51083	−	3.77161i	−0.0674990	−	0.168503i
$502$	−5.19486	+	2.99925i	−0.231858	+	0.133863i
$503$	25.8762	+	4.56267i	1.15376	+	0.203439i	0.717618	−	0.696437i	$-0.245233\pi$
$503$	25.8762	+	4.56267i	1.15376	+	0.203439i	0.436144	+	0.899877i	$0.356344\pi$
$504$	9.48320	−	0.606627i	0.422415	−	0.0270213i
$505$	15.1858	+	26.3026i	0.675761	+	1.17045i
$506$	4.77142	−	8.26433i	0.212115	−	0.367394i
$507$	−8.29653	+	1.73778i	−0.368462	+	0.0771775i
$508$	−2.68037	+	7.36426i	−0.118922	+	0.326736i
$509$	25.0043	−	9.10082i	1.10830	−	0.403387i	0.277928	−	0.960602i	$-0.410352\pi$
$509$	25.0043	−	9.10082i	1.10830	−	0.403387i	0.830368	+	0.557215i	$0.188130\pi$
$510$	−0.191774	−	6.00201i	−0.00849190	−	0.265774i
$511$	−1.20392	−	6.82777i	−0.0532583	−	0.302043i
$512$	−1.00000			−0.0441942
$513$	−14.0270	+	17.7832i	−0.619308	+	0.785148i
$514$	18.6091			0.820813
$515$	−3.50661	−	19.8869i	−0.154520	−	0.876324i
$516$	−0.691439	−	21.6402i	−0.0304389	−	0.952656i
$517$	−14.7226	+	5.35860i	−0.647501	+	0.235671i
$518$	−4.44685	+	12.2176i	−0.195383	+	0.536811i
$519$	−25.2906	+	5.29734i	−1.11014	+	0.232528i
$520$	5.45938	−	9.45593i	0.239410	−	0.414670i
$521$	10.2977	+	17.8362i	0.451151	+	0.781417i	0.998458	−	0.0555154i	$-0.0176802\pi$
$521$	10.2977	+	17.8362i	0.451151	+	0.781417i	−0.547307	+	0.836932i	$0.684347\pi$
$522$	22.7999	−	1.45848i	0.997925	−	0.0638358i
$523$	7.47024	+	1.31720i	0.326651	+	0.0575973i	0.334569	−	0.942371i	$-0.391409\pi$
$523$	7.47024	+	1.31720i	0.326651	+	0.0575973i	−0.00791816	+	0.999969i	$0.502520\pi$
$524$	−3.89818	+	2.25062i	−0.170293	+	0.0983186i
$525$	−3.39180	−	8.46723i	−0.148031	−	0.369540i
$526$	1.37946	−	1.64398i	0.0601475	−	0.0716810i
$527$	−10.0446	−	3.65594i	−0.437550	−	0.159255i
$528$	−4.11581	−	1.35082i	−0.179118	−	0.0587867i
$529$	6.46604	−	5.42566i	0.281132	−	0.235898i
$530$	−9.37344	+	1.65279i	−0.407156	+	0.0717926i
$531$	−6.29687	−	25.9091i	−0.273261	−	1.12436i
$532$	11.1354	−	8.16305i	0.482779	−	0.353913i
$533$			27.3778i			1.18586i
$534$	−25.4119	−	13.6086i	−1.09968	−	0.588901i
$535$	9.38920	+	11.1896i	0.405931	+	0.483769i
$536$	−1.55865	−	4.28235i	−0.0673234	−	0.184970i
$537$	0.286860	−	0.178069i	0.0123789	−	0.00768424i
$538$	19.9247	+	16.7188i	0.859015	+	0.720799i
$539$	−6.56971	−	3.79302i	−0.282977	−	0.163377i
$540$	−13.3507	+	1.28323i	−0.574524	+	0.0552213i
$541$	7.39225	−	41.9235i	0.317818	−	1.80243i	−0.238148	−	0.971229i	$-0.576540\pi$
$541$	7.39225	−	41.9235i	0.317818	−	1.80243i	0.555966	−	0.831205i	$-0.312349\pi$
$542$	0.855325	−	4.85079i	0.0367394	−	0.208359i
$543$	−1.75083	+	12.1953i	−0.0751354	+	0.523349i
$544$	1.16324	+	0.671595i	0.0498734	+	0.0287944i
$545$	−32.6353	−	27.3842i	−1.39794	−	1.17301i
$546$	−12.2398	−	19.7177i	−0.523817	−	0.843841i
$547$	−0.418676	−	1.15030i	−0.0179013	−	0.0491833i	0.930420	−	0.366495i	$-0.119442\pi$
$547$	−0.418676	−	1.15030i	−0.0179013	−	0.0491833i	−0.948321	+	0.317311i	$0.897220\pi$
$548$	−5.05673	−	6.02638i	−0.216013	−	0.257434i
$549$	0.389797	−	0.170785i	0.0166361	−	0.00728894i
$550$			4.15800i			0.177298i
$551$	26.7721	−	19.6259i	1.14053	−	0.836093i
$552$	5.19579	+	4.08427i	0.221148	+	0.173838i
$553$	−31.1323	+	5.48946i	−1.32388	+	0.233436i
$554$	−1.29599	+	1.08747i	−0.0550615	+	0.0462021i
$555$	5.72253	−	17.4360i	0.242908	−	0.740117i
$556$	7.07526	+	2.57518i	0.300058	+	0.109212i
$557$	13.8808	−	16.5425i	0.588147	−	0.700927i	−0.387101	−	0.922037i	$-0.626524\pi$
$557$	13.8808	−	16.5425i	0.588147	−	0.700927i	0.975249	+	0.221110i	$0.0709681\pi$
$558$	−6.71667	+	22.9101i	−0.284339	+	0.969860i
$559$	−45.7937	+	26.4390i	−1.93687	+	1.11825i
$560$	8.05179	+	1.41975i	0.340250	+	0.0599953i
$561$	3.88046	+	4.33547i	0.163833	+	0.183044i
$562$	−14.9153	−	25.8341i	−0.629166	−	1.08975i
$563$	13.0149	−	22.5424i	0.548512	−	0.950051i	−0.449865	−	0.893097i	$-0.648528\pi$
$563$	13.0149	−	22.5424i	0.548512	−	0.950051i	0.998377	−	0.0569541i	$-0.0181389\pi$
$564$	−2.22447	−	10.6201i	−0.0936671	−	0.447186i
$565$	−4.55268	+	12.5084i	−0.191533	+	0.526231i
$566$	22.1991	−	8.07982i	0.933099	−	0.339620i
$567$	−10.9920	+	26.3034i	−0.461621	+	1.10464i
$568$	−1.58788	−	9.00529i	−0.0666258	−	0.377854i
$569$	4.80544			0.201455			0.100727	−	0.994914i	$-0.467883\pi$
$569$	4.80544			0.201455			0.100727	+	0.994914i	$0.467883\pi$
$570$	−15.3409	+	12.0176i	−0.642558	+	0.503364i
$571$	−46.6475			−1.95214			−0.976068	−	0.217466i	$-0.930221\pi$
$571$	−46.6475			−1.95214			−0.976068	+	0.217466i	$0.930221\pi$
$572$	1.83710	+	10.4187i	0.0768129	+	0.435628i
$573$	−19.4722	+	0.622168i	−0.813462	+	0.0259914i
$574$	−19.2642	+	7.01161i	−0.804074	+	0.292659i
$575$	2.16968	−	5.96115i	0.0904820	−	0.248597i
$576$	1.33108	−	2.68853i	0.0554618	−	0.112022i
$577$	23.3103	−	40.3745i	0.970418	−	1.68081i	0.276125	−	0.961122i	$-0.410950\pi$
$577$	23.3103	−	40.3745i	0.970418	−	1.68081i	0.694293	−	0.719692i	$-0.255717\pi$
$578$	7.59792	+	13.1600i	0.316032	+	0.547383i
$579$	−20.8137	+	18.6293i	−0.864987	+	0.774205i
$580$	19.3584	+	3.41342i	0.803816	+	0.141734i
$581$	39.0582	−	22.5503i	1.62041	−	0.935543i
$582$	−0.879301	+	0.352231i	−0.0364482	+	0.0146004i
$583$	5.92793	−	7.06463i	0.245510	−	0.292587i
$584$	−2.05680	−	0.748615i	−0.0851112	−	0.0309779i
$585$	18.1557	+	27.2644i	0.750645	+	1.12724i
$586$	−7.10127	+	5.95867i	−0.293351	+	0.246150i
$587$	14.9298	−	2.63253i	0.616220	−	0.108656i	0.143180	−	0.989697i	$-0.454267\pi$
$587$	14.9298	−	2.63253i	0.616220	−	0.108656i	0.473041	+	0.881040i	$0.343156\pi$
$588$	3.24678	−	4.13038i	0.133895	−	0.170334i
$589$	9.70350	+	33.3038i	0.399826	+	1.37226i
$590$		−	22.9411i		−	0.944469i
$591$	18.6935	−	34.9072i	0.768948	−	1.43589i
$592$	2.63844	+	3.14437i	0.108439	+	0.129233i
$593$	−0.398860	−	1.09586i	−0.0163792	−	0.0450015i	0.931234	−	0.364423i	$-0.118734\pi$
$593$	−0.398860	−	1.09586i	−0.0163792	−	0.0450015i	−0.947613	+	0.319421i	$0.896511\pi$
$594$	9.11020	−	9.26744i	0.373796	−	0.380248i
$595$	−8.41264	−	7.05905i	−0.344885	−	0.289393i
$596$	11.8513	+	6.84233i	0.485447	+	0.280273i
$597$	−0.572431	−	0.0821819i	−0.0234280	−	0.00336348i
$598$	2.80280	−	15.8955i	0.114615	−	0.650014i
$599$	−4.45202	+	25.2486i	−0.181905	+	1.03163i	0.747964	+	0.663739i	$0.231032\pi$
$599$	−4.45202	+	25.2486i	−0.181905	+	1.03163i	−0.929868	+	0.367892i	$0.880079\pi$
$600$	−2.85040	−	0.409223i	−0.116367	−	0.0167064i
$601$	−26.4639	−	15.2789i	−1.07948	−	0.623240i	−0.148726	−	0.988878i	$-0.547517\pi$
$601$	−26.4639	−	15.2789i	−1.07948	−	0.623240i	−0.930757	+	0.365639i	$0.880851\pi$
$602$	−30.3317	−	25.4513i	−1.23623	−	1.03732i
$603$	13.5879	+	1.50969i	0.553344	+	0.0614794i
$604$	2.95387	+	8.11568i	0.120191	+	0.330222i
$605$	7.87294	+	9.38261i	0.320081	+	0.381457i
$606$	9.62126	−	17.9662i	0.390837	−	0.729828i
$607$			7.82667i			0.317675i	0.987305	+	0.158837i	$0.0507745\pi$
$607$			7.82667i			0.317675i	−0.987305	+	0.158837i	$0.949225\pi$
$608$	−0.474100	−	4.33304i	−0.0192273	−	0.175728i
$609$	25.8205	−	32.8475i	1.04630	−	1.33105i
$610$	0.360596	−	0.0635828i	0.0146001	−	0.00257439i
$611$	−20.3001	+	17.0338i	−0.821254	+	0.689114i
$612$	−3.35397	+	2.23345i	−0.135576	+	0.0902819i
$613$	30.3824	+	11.0583i	1.22713	+	0.446640i	0.872615	−	0.488408i	$-0.162422\pi$
$613$	30.3824	+	11.0583i	1.22713	+	0.446640i	0.354519	+	0.935049i	$0.384645\pi$
$614$	1.76414	−	2.10242i	0.0711948	−	0.0848466i
$615$	26.8603	−	10.7597i	1.08311	−	0.433873i
$616$	−6.86057	+	3.96095i	−0.276420	+	0.159591i
$617$	−24.5040	−	4.32072i	−0.986495	−	0.173946i	−0.342950	−	0.939354i	$-0.611426\pi$
$617$	−24.5040	−	4.32072i	−0.986495	−	0.173946i	−0.643545	+	0.765408i	$0.722537\pi$
$618$	−10.0969	+	9.03718i	−0.406156	+	0.363529i
$619$	−3.60285	−	6.24032i	−0.144811	−	0.250820i	0.784492	−	0.620140i	$-0.212924\pi$
$619$	−3.60285	−	6.24032i	−0.144811	−	0.250820i	−0.929302	+	0.369320i	$0.879591\pi$
$620$	−10.2707	+	17.7894i	−0.412482	+	0.714439i
$621$	−17.8967	+	8.53255i	−0.718171	+	0.342400i
$622$	−7.83109	+	21.5157i	−0.313998	+	0.862702i
$623$	−49.5376	+	18.0302i	−1.98468	+	0.722366i
$624$	−7.32305	+	0.233983i	−0.293157	+	0.00936683i
$625$	−5.30472	−	30.0846i	−0.212189	−	1.20338i
$626$	13.4317			0.536841
$627$	3.90183	−	18.4744i	0.155824	−	0.737796i
$628$	3.43500			0.137072
$629$	−0.957388	−	5.42961i	−0.0381735	−	0.216493i
$630$	−14.5347	+	19.7577i	−0.579074	+	0.787166i
$631$	23.7099	−	8.62969i	0.943876	−	0.343543i	0.176180	−	0.984358i	$-0.443626\pi$
$631$	23.7099	−	8.62969i	0.943876	−	0.343543i	0.767695	+	0.640815i	$0.221404\pi$
$632$	−3.41343	+	9.37832i	−0.135779	+	0.373049i
$633$	−0.910797	−	4.34834i	−0.0362009	−	0.172831i
$634$	−10.3856	+	17.9884i	−0.412465	+	0.714411i
$635$	−10.1142	−	17.5184i	−0.401372	−	0.695196i
$636$	4.25955	+	4.75902i	0.168902	+	0.188707i
$637$	−12.6361	−	2.22808i	−0.500659	−	0.0882796i
$638$	−16.4945	+	9.52308i	−0.653022	+	0.377022i
$639$	26.3246	+	7.71774i	1.04139	+	0.305309i
$640$	1.65916	−	1.97731i	0.0655840	−	0.0781600i
$641$	8.36361	+	3.04411i	0.330343	+	0.120235i	0.501867	−	0.864945i	$-0.332647\pi$
$641$	8.36361	+	3.04411i	0.330343	+	0.120235i	−0.171524	+	0.985180i	$0.554869\pi$
$642$	3.05653	−	9.31295i	0.120631	−	0.367553i
$643$	5.41716	−	4.54553i	0.213632	−	0.179258i	−0.529692	−	0.848190i	$-0.677693\pi$
$643$	5.41716	−	4.54553i	0.213632	−	0.179258i	0.743324	+	0.668932i	$0.233248\pi$
$644$	11.9026	−	2.09874i	0.469027	−	0.0827021i
$645$	43.9365	+	34.5373i	1.73000	+	1.35990i
$646$	−2.35856	+	5.35875i	−0.0927962	+	0.210837i
$647$			7.87198i			0.309479i	0.987955	+	0.154740i	$0.0494539\pi$
$647$			7.87198i			0.309479i	−0.987955	+	0.154740i	$0.950546\pi$
$648$	5.45643	+	7.15733i	0.214349	+	0.281166i
$649$	14.2879	+	17.0277i	0.560850	+	0.668395i
$650$	2.40536	+	6.60868i	0.0943461	+	0.259214i
$651$	23.0268	+	37.0949i	0.902490	+	1.45386i
$652$	−5.87262	−	4.92772i	−0.229990	−	0.192984i
$653$	1.40402	+	0.810613i	0.0549437	+	0.0317217i	0.527220	−	0.849729i	$-0.323234\pi$
$653$	1.40402	+	0.810613i	0.0549437	+	0.0317217i	−0.472277	+	0.881450i	$0.656568\pi$
$654$	−4.06253	+	28.2972i	−0.158857	+	1.10651i
$655$	2.01754	−	11.4420i	0.0788318	−	0.447077i
$656$	−1.12387	+	6.37378i	−0.0438797	+	0.248854i
$657$	4.75046	−	4.53332i	0.185333	−	0.176862i
$658$	−17.1847	−	9.92160i	−0.669930	−	0.386784i
$659$	9.29693	+	7.80105i	0.362157	+	0.303886i	0.805650	−	0.592392i	$-0.201816\pi$
$659$	9.29693	+	7.80105i	0.362157	+	0.303886i	−0.443493	+	0.896278i	$0.646261\pi$
$660$	9.49976	−	5.89700i	0.369778	−	0.229541i
$661$	−10.0965	−	27.7400i	−0.392710	−	1.07896i	−0.965759	−	0.259440i	$-0.916462\pi$
$661$	−10.0965	−	27.7400i	−0.392710	−	1.07896i	0.573050	−	0.819521i	$-0.305760\pi$
$662$	−5.78451	−	6.89371i	−0.224821	−	0.267932i
$663$	8.67559	+	4.64595i	0.336932	+	0.180434i
$664$		−	14.2384i		−	0.552557i
$665$	−2.33447	+	35.5618i	−0.0905268	+	1.37903i
$666$	−11.9657	+	2.90812i	−0.463663	+	0.112687i
$667$	28.6166	−	5.04588i	1.10804	−	0.195377i
$668$	−1.79695	+	1.50782i	−0.0695261	+	0.0583393i
$669$	−10.9847	−	3.60520i	−0.424694	−	0.139385i
$670$	11.0536	+	4.02317i	0.427037	+	0.155429i
$671$	−0.228047	+	0.271776i	−0.00880367	+	0.0104918i
$672$	−2.04012	−	5.09290i	−0.0786992	−	0.196463i
$673$	−3.84411	+	2.21940i	−0.148180	+	0.0855516i	−0.572257	−	0.820075i	$-0.693932\pi$
$673$	−3.84411	+	2.21940i	−0.148180	+	0.0855516i	0.424077	+	0.905626i	$0.360599\pi$
$674$	−12.6410	−	2.22895i	−0.486913	−	0.0858559i
$675$	4.89434	−	7.11870i	0.188383	−	0.273999i
$676$	2.44698	+	4.23829i	0.0941145	+	0.163011i
$677$	−0.610403	+	1.05725i	−0.0234597	+	0.0406334i	−0.877517	−	0.479546i	$-0.840801\pi$
$677$	−0.610403	+	1.05725i	−0.0234597	+	0.0406334i	0.854057	+	0.520179i	$0.174135\pi$
$678$	8.74242	−	1.83117i	0.335750	−	0.0703259i
$679$	−0.592469	+	1.62779i	−0.0227369	+	0.0624690i
$680$	−3.25794	+	1.18579i	−0.124936	+	0.0454732i
$681$	1.10930	+	34.7181i	0.0425084	+	1.33040i
$682$	−3.45612	−	19.6006i	−0.132342	−	0.750547i
$683$	−40.7336			−1.55863			−0.779313	−	0.626635i	$-0.784432\pi$
$683$	−40.7336			−1.55863			−0.779313	+	0.626635i	$0.784432\pi$
$684$	12.2806	+	4.49301i	0.469560	+	0.171794i
$685$	20.3059			0.775850
$686$	2.18186	+	12.3739i	0.0833038	+	0.472439i
$687$	−0.913051	−	28.5760i	−0.0348351	−	1.09024i
$688$	−11.7465	+	4.27537i	−0.447830	+	0.162997i
$689$	5.33497	−	14.6577i	0.203246	−	0.558414i
$690$	−16.6965	+	3.49723i	−0.635625	+	0.133137i
$691$	18.9023	−	32.7397i	0.719077	−	1.24548i	−0.242289	−	0.970204i	$-0.577898\pi$
$691$	18.9023	−	32.7397i	0.719077	−	1.24548i	0.961366	−	0.275274i	$-0.0887686\pi$
$692$	7.45921	+	12.9197i	0.283557	+	0.491135i
$693$	−1.51716	−	23.7172i	−0.0576320	−	0.900943i
$694$	13.6351	+	2.40423i	0.517580	+	0.0912633i
$695$	−16.8309	+	9.71733i	−0.638433	+	0.368599i
$696$	−4.90493	−	12.2446i	−0.185921	−	0.464129i
$697$	5.58792	−	6.65943i	0.211658	−	0.252244i
$698$	19.3873	+	7.05640i	0.733820	+	0.267088i
$699$	−10.2073	−	3.35006i	−0.386077	−	0.126711i
$700$	−4.03414	+	3.38504i	−0.152476	+	0.127943i
$701$	−23.1182	+	4.07636i	−0.873162	+	0.153962i	−0.592233	−	0.805767i	$-0.701754\pi$
$701$	−23.1182	+	4.07636i	−0.873162	+	0.153962i	−0.280929	+	0.959729i	$0.590642\pi$
$702$	9.11853	−	19.9997i	0.344157	−	0.754841i
$703$	−12.3738	+	12.9232i	−0.466687	+	0.487408i
$704$			2.50097i			0.0942589i
$705$	24.6899	+	13.2219i	0.929877	+	0.497967i
$706$	14.6560	+	17.4664i	0.551587	+	0.657356i
$707$	−12.7474	−	35.0231i	−0.479414	−	1.31718i
$708$	−13.0791	+	8.11886i	−0.491541	+	0.305126i
$709$	21.3882	+	17.9469i	0.803252	+	0.674009i	0.948987	−	0.315315i	$-0.102110\pi$
$709$	21.3882	+	17.9469i	0.803252	+	0.674009i	−0.145735	+	0.989324i	$0.546555\pi$
$710$	20.4408	+	11.8015i	0.767128	+	0.442902i
$711$	−20.6704	−	21.6605i	−0.775199	−	0.812330i
$712$	−2.89001	+	16.3901i	−0.108308	+	0.614243i
$713$	−5.27289	+	29.9041i	−0.197471	+	1.11992i
$714$	−1.04723	+	7.29438i	−0.0391916	+	0.272985i
$715$	−23.6490	−	13.6538i	−0.884423	−	0.510622i
$716$	−0.149328	−	0.125301i	−0.00558063	−	0.00468271i
$717$	−0.525995	−	0.847349i	−0.0196436	−	0.0316448i
$718$	2.53893	+	6.97566i	0.0947521	+	0.260329i
$719$	26.4940	+	31.5743i	0.988060	+	1.17752i	0.984115	+	0.177532i	$0.0568113\pi$
$719$	26.4940	+	31.5743i	0.988060	+	1.17752i	0.00394505	+	0.999992i	$0.498744\pi$
$720$	3.10758	+	7.09267i	0.115813	+	0.264328i
$721$			24.7809i			0.922889i
$722$	18.5505	−	4.10859i	0.690377	−	0.152906i
$723$	2.31261	+	1.81788i	0.0860069	+	0.0676077i
$724$	7.00507	−	1.23518i	0.260341	−	0.0459052i
$725$	−9.69903	+	8.13846i	−0.360213	+	0.302255i
$726$	2.56293	−	7.80900i	0.0951192	−	0.289819i
$727$	4.13772	+	1.50601i	0.153460	+	0.0558548i	0.417608	−	0.908627i	$-0.362869\pi$
$727$	4.13772	+	1.50601i	0.153460	+	0.0558548i	−0.264148	+	0.964482i	$0.585091\pi$
$728$	−8.61274	+	10.2643i	−0.319209	+	0.380419i
$729$	−26.5057	+	5.14278i	−0.981692	+	0.190474i
$730$	4.89281	−	2.82486i	0.181091	−	0.104553i
$731$	16.5352	+	2.91561i	0.611578	+	0.107838i
$732$	−0.163865	−	0.183079i	−0.00605662	−	0.00676680i
$733$	11.3991	+	19.7438i	0.421034	+	0.729253i	0.996041	−	0.0888960i	$-0.0283339\pi$
$733$	11.3991	+	19.7438i	0.421034	+	0.729253i	−0.575007	+	0.818149i	$0.695001\pi$
$734$	−9.92532	+	17.1912i	−0.366350	+	0.634537i
$735$	2.78011	+	13.2728i	0.102546	+	0.489576i
$736$	1.30503	−	3.58554i	0.0481040	−	0.132165i
$737$	−10.7100	+	3.89814i	−0.394510	+	0.143590i
$738$	−15.6402	−	11.5056i	−0.575722	−	0.423527i
$739$	−8.91510	−	50.5600i	−0.327947	−	1.85988i	−0.488098	−	0.872789i	$-0.662309\pi$
$739$	−8.91510	−	50.5600i	−0.327947	−	1.85988i	0.160151	−	0.987093i	$-0.448802\pi$
$740$	−10.5950			−0.389479
$741$	−4.48572	−	31.6201i	−0.164787	−	1.16160i
$742$	11.6801			0.428791
$743$	0.154876	+	0.878343i	0.00568183	+	0.0322233i	0.987517	−	0.157513i	$-0.0503477\pi$
$743$	0.154876	+	0.878343i	0.00568183	+	0.0322233i	−0.981835	+	0.189737i	$0.939237\pi$
$744$	13.7768	−	0.440192i	0.505083	−	0.0161382i
$745$	−33.1925	+	12.0811i	−1.21608	+	0.442617i
$746$	6.52210	−	17.9193i	0.238791	−	0.656073i
$747$	38.2804	+	18.9525i	1.40061	+	0.693436i
$748$	1.67964	−	2.90922i	0.0614137	−	0.106372i
$749$	−8.96255	−	15.5236i	−0.327484	−	0.567220i
$750$	−11.1180	+	9.95110i	−0.405970	+	0.363363i
$751$	−10.0009	−	1.76342i	−0.364936	−	0.0643481i	−0.0118266	−	0.999930i	$-0.503765\pi$
$751$	−10.0009	−	1.76342i	−0.364936	−	0.0643481i	−0.353110	+	0.935582i	$0.614876\pi$
$752$	−5.42528	+	3.13228i	−0.197839	+	0.114223i
$753$	−9.64468	+	3.86347i	−0.351472	+	0.140793i
$754$	−20.7071	+	24.6778i	−0.754108	+	0.898711i
$755$	−20.9481	−	7.62450i	−0.762381	−	0.277484i
$756$	16.4080	+	1.29416i	0.596753	+	0.0470681i
$757$	16.0181	−	13.4408i	0.582187	−	0.488513i	−0.303478	−	0.952839i	$-0.598148\pi$
$757$	16.0181	−	13.4408i	0.582187	−	0.488513i	0.885664	+	0.464326i	$0.153703\pi$
$758$	−29.6323	+	5.22497i	−1.07629	+	0.189780i
$759$	10.2146	−	12.9945i	0.370768	−	0.471672i
$760$	9.35436	+	6.25176i	0.339318	+	0.226775i
$761$		−	23.9282i		−	0.867396i	−0.901058	−	0.433698i	$-0.857209\pi$
$761$		−	23.9282i		−	0.867396i	0.901058	−	0.433698i	$-0.142791\pi$
$762$	−6.40807	+	11.9661i	−0.232140	+	0.433485i
$763$	33.6048	+	40.0486i	1.21657	+	1.44986i
$764$	3.84705	+	10.5697i	0.139181	+	0.382397i
$765$	1.14855	−	10.3375i	0.0415259	−	0.373753i
$766$	−4.60213	−	3.86165i	−0.166282	−	0.139527i
$767$	32.5594	+	18.7982i	1.17565	+	0.678764i
$768$	−1.71447	−	0.246141i	−0.0618657	−	0.00888184i
$769$	−3.21910	+	18.2564i	−0.116084	+	0.658344i	0.870124	+	0.492833i	$0.164039\pi$
$769$	−3.21910	+	18.2564i	−0.116084	+	0.658344i	−0.986208	+	0.165511i	$0.947073\pi$
$770$	3.55075	−	20.1373i	0.127960	−	0.725698i
$771$	31.9048	+	4.58047i	1.14902	+	0.164961i
$772$	13.9666	+	8.06359i	0.502667	+	0.290215i
$773$	27.0855	+	22.7275i	0.974199	+	0.817450i	0.983204	−	0.182509i	$-0.0584219\pi$
$773$	27.0855	+	22.7275i	0.974199	+	0.817450i	−0.00900488	+	0.999959i	$0.502866\pi$
$774$	4.14108	−	37.2717i	0.148848	−	1.33970i
$775$	−4.52520	−	12.4329i	−0.162550	−	0.446602i
$776$	0.351528	+	0.418935i	0.0126191	+	0.0150389i
$777$	−10.6313	+	19.8522i	−0.381394	+	0.712194i
$778$		−	20.7858i		−	0.745209i
$779$	−28.1507	−	1.84796i	−1.00860	−	0.0662100i
$780$	11.6874	−	14.8681i	0.418478	−	0.532365i
$781$	−22.5220	+	3.97123i	−0.805900	+	0.142102i
$782$	−3.92609	+	3.29438i	−0.140397	+	0.117807i
$783$	39.4488	+	3.11147i	1.40978	+	0.111195i
$784$	−2.85031	−	1.03743i	−0.101797	−	0.0370510i
$785$	−5.69922	+	6.79206i	−0.203414	+	0.242419i
$786$	−7.23729	+	2.89912i	−0.258146	+	0.103408i
$787$	6.19829	−	3.57858i	0.220945	−	0.127563i	−0.385443	−	0.922732i	$-0.625951\pi$
$787$	6.19829	−	3.57858i	0.220945	−	0.127563i	0.606388	+	0.795169i	$0.292618\pi$
$788$	−22.5143	−	3.96988i	−0.802039	−	0.141421i
$789$	2.76970	−	2.47902i	0.0986041	−	0.0882554i
$790$	−12.8804	−	22.3095i	−0.458264	−	0.793737i
$791$	8.16743	−	14.1464i	0.290400	−	0.502988i
$792$	−6.72395	−	3.32900i	−0.238925	−	0.118291i
$793$	−0.205236	+	0.563881i	−0.00728815	+	0.0200240i
$794$	9.89421	−	3.60120i	0.351133	−	0.127802i
$795$	−16.4773	+	0.526477i	−0.584390	+	0.0186722i
$796$	0.0579780	+	0.328809i	0.00205497	+	0.0116543i
$797$	13.5711			0.480714			0.240357	−	0.970685i	$-0.422735\pi$
$797$	13.5711			0.480714			0.240357	+	0.970685i	$0.422735\pi$
$798$	21.1005	−	11.2544i	0.746950	−	0.398403i
$799$	8.41451			0.297684
$800$	0.288700	+	1.63730i	0.0102071	+	0.0578872i
$801$	−40.2184	−	29.5864i	−1.42105	−	1.04538i
$802$	−8.64725	+	3.14734i	−0.305345	+	0.111136i
$803$	−1.87227	+	5.14401i	−0.0660708	+	0.181528i
$804$	−1.61820	−	7.72562i	−0.0570695	−	0.272462i
$805$	−15.5984	+	27.0172i	−0.549771	+	0.952231i
$806$	−16.8319	−	29.1537i	−0.592879	−	1.02690i
$807$	30.0452	+	33.5682i	1.05764	+	1.18166i
$808$	−11.5878	−	2.04324i	−0.407656	−	0.0718808i
$809$	7.06352	−	4.07812i	0.248340	−	0.143379i	−0.370664	−	0.928767i	$-0.620870\pi$
$809$	7.06352	−	4.07812i	0.248340	−	0.143379i	0.619004	+	0.785388i	$0.287536\pi$
$810$	−23.2053	−	1.08610i	−0.815352	−	0.0381618i
$811$	−1.94231	+	2.31476i	−0.0682038	+	0.0812821i	−0.799068	−	0.601241i	$-0.794673\pi$
$811$	−1.94231	+	2.31476i	−0.0682038	+	0.0812821i	0.730864	+	0.682523i	$0.239117\pi$
$812$	−22.6676	−	8.25032i	−0.795476	−	0.289530i
$813$	2.66041	−	8.10601i	0.0933046	−	0.284290i
$814$	7.86399	−	6.59867i	0.275633	−	0.231283i
$815$	19.4872	−	3.43612i	0.682608	−	0.120362i
$816$	1.82903	+	1.43775i	0.0640289	+	0.0503314i
$817$	−24.0943	−	48.8710i	−0.842954	−	1.70978i
$818$		−	23.5660i		−	0.823967i
$819$	−16.1315	−	36.8182i	−0.563681	−	1.28653i
$820$	−10.7382	−	12.7973i	−0.374996	−	0.446903i
$821$	−1.32613	−	3.64350i	−0.0462821	−	0.127159i	0.914398	−	0.404816i	$-0.132664\pi$
$821$	−1.32613	−	3.64350i	−0.0462821	−	0.127159i	−0.960680	+	0.277657i	$0.910442\pi$
$822$	−7.18629	−	11.5767i	−0.250651	−	0.403785i
$823$	9.67720	+	8.12014i	0.337326	+	0.283050i	0.795677	−	0.605721i	$-0.207115\pi$
$823$	9.67720	+	8.12014i	0.337326	+	0.283050i	−0.458351	+	0.888771i	$0.651560\pi$
$824$	6.77528	+	3.91171i	0.236028	+	0.136271i
$825$	−1.02345	+	7.12878i	−0.0356321	+	0.248192i
$826$	−4.88859	+	27.7246i	−0.170096	+	0.964662i
$827$	5.27611	−	29.9223i	0.183468	−	1.04050i	−0.744439	−	0.667690i	$-0.767283\pi$
$827$	5.27611	−	29.9223i	0.183468	−	1.04050i	0.927908	−	0.372810i	$-0.121606\pi$
$828$	7.90274	+	8.28127i	0.274639	+	0.287794i
$829$	20.5261	+	11.8507i	0.712901	+	0.411593i	0.812134	−	0.583471i	$-0.198306\pi$
$829$	20.5261	+	11.8507i	0.712901	+	0.411593i	−0.0992334	+	0.995064i	$0.531639\pi$
$830$	28.1537	+	23.6238i	0.977229	+	0.819992i
$831$	−2.48962	+	1.54544i	−0.0863639	+	0.0536106i
$832$	1.44679	+	3.97502i	0.0501583	+	0.137809i
$833$	2.61886	+	3.12103i	0.0907380	+	0.108137i
$834$	11.4965	+	6.15659i	0.398090	+	0.213185i
$835$		−	6.05484i		−	0.209536i
$836$	−10.8368	+	1.18571i	−0.374799	+	0.0410087i
$837$	−17.1546	+	37.6254i	−0.592951	+	1.30052i
$838$	20.1135	−	3.54655i	0.694809	−	0.122514i
$839$	11.0849	−	9.30133i	0.382693	−	0.321118i	−0.431066	−	0.902321i	$-0.641862\pi$
$839$	11.0849	−	9.30133i	0.382693	−	0.321118i	0.813759	+	0.581203i	$0.197418\pi$
$840$	13.4551	+	4.41599i	0.464245	+	0.152366i
$841$	−27.2472	−	9.91717i	−0.939559	−	0.341971i
$842$	−0.259039	+	0.308710i	−0.00892707	+	0.0106389i
$843$	−19.2131	−	47.9632i	−0.661735	−	1.65194i
$844$	−2.22135	+	1.28250i	−0.0764621	+	0.0441454i
$845$	−12.4403	−	2.19356i	−0.427960	−	0.0754609i
$846$	−1.19975	−	18.7554i	−0.0412484	−	0.644823i
$847$	−7.51519	−	13.0167i	−0.258225	−	0.447259i
$848$	1.84373	−	3.19343i	0.0633139	−	0.109663i
$849$	40.0486	−	8.38852i	1.37446	−	0.287893i
$850$	0.763774	−	2.09845i	0.0261972	−	0.0719763i
$851$	−14.7175	+	5.35673i	−0.504510	+	0.183627i
$852$	−0.505799	−	15.8302i	−0.0173284	−	0.542332i
$853$	8.89956	+	50.4719i	0.304715	+	1.72813i	0.624842	+	0.780751i	$0.285163\pi$
$853$	8.89956	+	50.4719i	0.304715	+	1.72813i	−0.320127	+	0.947375i	$0.603725\pi$
$854$	−0.449334			−0.0153759
$855$	−29.2595	+	16.8279i	−1.00065	+	0.575502i
$856$	−5.65902			−0.193421
$857$	3.26971	+	18.5435i	0.111691	+	0.633433i	0.988335	+	0.152293i	$0.0486658\pi$
$857$	3.26971	+	18.5435i	0.111691	+	0.633433i	−0.876644	+	0.481139i	$0.840223\pi$
$858$	0.585186	+	18.3147i	0.0199779	+	0.625255i
$859$	22.7939	−	8.29631i	0.777719	−	0.283066i	0.0774977	−	0.996993i	$-0.475307\pi$
$859$	22.7939	−	8.29631i	0.777719	−	0.283066i	0.700221	+	0.713926i	$0.253085\pi$
$860$	11.0355	−	30.3199i	0.376309	−	1.03390i
$861$	−34.7538	+	7.27949i	−1.18441	+	0.248084i
$862$	4.66791	−	8.08505i	0.158990	−	0.275378i
$863$	−9.85277	−	17.0655i	−0.335392	−	0.580916i	0.648168	−	0.761497i	$-0.275535\pi$
$863$	−9.85277	−	17.0655i	−0.335392	−	0.580916i	−0.983560	+	0.180581i	$0.942202\pi$
$864$	2.94386	−	4.28178i	0.100152	−	0.145669i
$865$	−37.9223	−	6.68673i	−1.28940	−	0.227356i
$866$	−17.8113	+	10.2833i	−0.605251	+	0.349442i
$867$	9.78721	+	24.4326i	0.332391	+	0.829774i
$868$	16.2031	−	19.3101i	0.549969	−	0.655428i
$869$	23.4549	+	8.53689i	0.795653	+	0.289594i
$870$	32.3493	+	10.6171i	1.09674	+	0.359954i
$871$	−14.7674	+	12.3913i	−0.500374	+	0.419864i
$872$	16.2542	−	2.86605i	0.550435	−	0.0970565i
$873$	−1.59424	+	0.387458i	−0.0539567	+	0.0131135i
$874$	16.1550	+	3.95484i	0.546451	+	0.133774i
$875$			27.2870i			0.922468i
$876$	−3.34207	−	1.78974i	−0.112918	−	0.0604698i
$877$	−16.3863	−	19.5284i	−0.553324	−	0.659426i	0.414795	−	0.909915i	$-0.363853\pi$
$877$	−16.3863	−	19.5284i	−0.553324	−	0.659426i	−0.968120	+	0.250488i	$0.919409\pi$
$878$	8.76708	+	24.0874i	0.295875	+	0.812909i
$879$	−13.6416	+	8.46806i	−0.460120	+	0.285621i
$880$	−4.94519	−	4.14951i	−0.166702	−	0.139880i
$881$	−26.6755	−	15.4011i	−0.898719	−	0.518876i	−0.0219346	−	0.999759i	$-0.506983\pi$
$881$	−26.6755	−	15.4011i	−0.898719	−	0.518876i	−0.876784	+	0.480884i	$0.840316\pi$
$882$	6.58317	−	6.28226i	0.221667	−	0.211535i
$883$	−1.74964	+	9.92270i	−0.0588801	+	0.333926i	−0.999991	−	0.00417162i	$-0.998672\pi$
$883$	−1.74964	+	9.92270i	−0.0588801	+	0.333926i	0.941111	+	0.338097i	$0.109783\pi$
$884$	0.986645	−	5.59554i	0.0331845	−	0.188198i
$885$	5.64673	−	39.3318i	0.189813	−	1.32212i
$886$	23.0044	+	13.2816i	0.772849	+	0.446205i
$887$	−14.6182	−	12.2661i	−0.490831	−	0.411856i	0.363493	−	0.931597i	$-0.381584\pi$
$887$	−14.6182	−	12.2661i	−0.490831	−	0.411856i	−0.854324	+	0.519741i	$0.826028\pi$
$888$	3.74958	+	6.04037i	0.125828	+	0.202701i
$889$	8.49015	+	23.3265i	0.284751	+	0.782346i
$890$	−27.6132	−	32.9081i	−0.925597	−	1.10308i
$891$	17.9003	−	13.6464i	0.599682	−	0.457171i
$892$			6.67486i			0.223491i
$893$	−16.1444	−	22.0229i	−0.540253	−	0.736969i
$894$	18.6345	+	14.6481i	0.623231	+	0.489905i
$895$	0.495516	−	0.0873729i	0.0165633	−	0.00292055i
$896$	−2.42647	+	2.03605i	−0.0810626	+	0.0680196i
$897$	8.71784	−	26.5624i	0.291080	−	0.886894i
$898$	−10.6547	−	3.87800i	−0.355552	−	0.129410i
$899$	38.9562	−	46.4261i	1.29926	−	1.54840i
$900$	−4.78621	−	1.40320i	−0.159540	−	0.0467734i
$901$	−4.28939	+	2.47648i	−0.142900	+	0.0825035i
$902$	15.9406	+	2.81076i	0.530765	+	0.0935882i
$903$	−45.7382	−	51.1014i	−1.52207	−	1.70055i
$904$	−2.57849	−	4.46607i	−0.0857592	−	0.148539i
$905$	−9.18019	+	15.9006i	−0.305160	+	0.528552i
$906$	3.06672	+	14.6412i	0.101885	+	0.486421i
$907$	1.42779	−	3.92281i	0.0474089	−	0.130255i	−0.913729	−	0.406325i	$-0.866810\pi$
$907$	1.42779	−	3.92281i	0.0474089	−	0.130255i	0.961137	+	0.276070i	$0.0890323\pi$
$908$	18.8453	−	6.85911i	0.625402	−	0.227628i
$909$	20.9176	−	28.4344i	0.693793	−	0.943109i
$910$	−6.00571	−	34.0601i	−0.199087	−	1.12908i
$911$	−32.6294			−1.08106			−0.540530	−	0.841325i	$-0.681776\pi$
$911$	−32.6294			−1.08106			−0.540530	+	0.841325i	$0.681776\pi$
$912$	0.253706	−	7.54557i	0.00840106	−	0.249859i
$913$	−35.6098			−1.17851
$914$	3.71066	+	21.0442i	0.122738	+	0.696079i
$915$	0.633882	−	0.0202535i	0.0209555	−	0.000669561i
$916$	−15.5113	+	5.64566i	−0.512509	+	0.186538i
$917$	−4.87645	+	13.3979i	−0.161034	+	0.442439i
$918$	−6.30004	+	3.00364i	−0.207932	+	0.0991349i
$919$	−11.5230	+	19.9584i	−0.380108	+	0.658367i	−0.991077	−	0.133287i	$-0.957447\pi$
$919$	−11.5230	+	19.9584i	−0.380108	+	0.658367i	0.610969	+	0.791654i	$0.290780\pi$
$920$	4.92446	+	8.52942i	0.162355	+	0.281207i
$921$	3.54205	−	3.17031i	0.116715	−	0.104465i
$922$	27.0902	+	4.77673i	0.892168	+	0.157313i
$923$	−33.4989	+	19.3406i	−1.10263	+	0.636603i
$924$	−12.7372	+	5.10227i	−0.419023	+	0.167852i
$925$	4.38655	−	5.22769i	0.144229	−	0.171885i
$926$	8.50711	+	3.09633i	0.279561	+	0.101752i
$927$	−19.5352	+	13.0087i	−0.641621	+	0.427263i
$928$	−5.83381	+	4.89515i	−0.191504	+	0.160691i
$929$	26.6622	−	4.70127i	0.874760	−	0.154244i	0.281798	−	0.959474i	$-0.409069\pi$
$929$	26.6622	−	4.70127i	0.874760	−	0.154244i	0.592962	+	0.805230i	$0.297958\pi$
$930$	−21.9875	+	27.9714i	−0.721000	+	0.917218i
$931$	3.14389	−	12.8424i	0.103037	−	0.420891i
$932$			6.20248i			0.203169i
$933$	−18.7221	+	34.9606i	−0.612933	+	1.14456i
$934$	−13.1443	−	15.6647i	−0.430094	−	0.512566i
$935$	2.96564	+	8.14803i	0.0969868	+	0.266469i
$936$	−12.6128	−	1.40134i	−0.412261	−	0.0458044i
$937$	29.6774	+	24.9023i	0.969518	+	0.813523i	0.982475	−	0.186393i	$-0.0596799\pi$
$937$	29.6774	+	24.9023i	0.969518	+	0.813523i	−0.0129567	+	0.999916i	$0.504124\pi$
$938$	−12.5011	−	7.21751i	−0.408175	−	0.235660i
$939$	23.0284	+	3.30610i	0.751502	+	0.107891i
$940$	2.80790	−	15.9244i	0.0915837	−	0.519397i
$941$	3.32233	−	18.8419i	0.108305	−	0.614227i	−0.881544	−	0.472102i	$-0.843495\pi$
$941$	3.32233	−	18.8419i	0.108305	−	0.614227i	0.989849	−	0.142125i	$-0.0453935\pi$
$942$	5.88922	+	0.845495i	0.191881	+	0.0275477i
$943$	−21.3867	−	12.3476i	−0.696448	−	0.402094i
$944$	6.80843	+	5.71295i	0.221596	+	0.185941i
$945$	−29.7824	+	30.2965i	−0.968823	+	0.985544i
$946$	10.6926	+	29.3776i	0.347646	+	0.955148i
$947$	26.2400	+	31.2716i	0.852684	+	1.01619i	0.999634	+	0.0270453i	$0.00860982\pi$
$947$	26.2400	+	31.2716i	0.852684	+	1.01619i	−0.146950	+	0.989144i	$0.546946\pi$
$948$	−8.16062	+	15.2387i	−0.265044	+	0.494929i
$949$			9.25892i			0.300557i
$950$	−6.95760	+	2.02719i	−0.225734	+	0.0657707i
$951$	−22.2335	+	28.2843i	−0.720971	+	0.917181i
$952$	4.18996	−	0.738802i	0.135797	−	0.0239447i
$953$	28.5318	−	23.9410i	0.924235	−	0.775525i	−0.0505382	−	0.998722i	$-0.516094\pi$
$953$	28.5318	−	23.9410i	0.924235	−	0.775525i	0.974773	+	0.223197i	$0.0716492\pi$
$954$	6.13149	+	9.20765i	0.198514	+	0.298109i
$955$	−27.2824	−	9.92997i	−0.882837	−	0.321326i
$956$	−0.370124	+	0.441096i	−0.0119707	+	0.0142661i
$957$	−30.6233	+	12.2671i	−0.989911	+	0.396539i
$958$	8.51710	−	4.91735i	0.275175	−	0.158872i
$959$	−24.5400	−	4.32707i	−0.792438	−	0.139728i
$960$	3.33128	−	2.98165i	0.107517	−	0.0962324i
$961$	16.1658	+	28.0000i	0.521477	+	0.903225i
$962$	8.68167	−	15.0371i	0.279908	−	0.484815i
$963$	7.53263	−	15.2145i	0.242735	−	0.490279i
$964$	0.580859	−	1.59590i	0.0187082	−	0.0514004i
$965$	−39.1169	+	14.2374i	−1.25922	+	0.458318i
$966$	20.9232	−	0.668530i	0.673193	−	0.0215096i
$967$	9.88547	+	56.0633i	0.317895	+	1.80287i	0.555506	+	0.831513i	$0.312525\pi$
$967$	9.88547	+	56.0633i	0.317895	+	1.80287i	−0.237611	+	0.971361i	$0.576364\pi$
$968$	−4.74514			−0.152515
$969$	−5.36269	+	8.60690i	−0.172274	+	0.276493i
$970$	−1.41161			−0.0453239
$971$	7.41064	+	42.0279i	0.237819	+	1.34874i	0.836595	+	0.547822i	$0.184543\pi$
$971$	7.41064	+	42.0279i	0.237819	+	1.34874i	−0.598776	+	0.800916i	$0.704346\pi$
$972$	7.59318	+	13.6141i	0.243552	+	0.436672i
$973$	22.4111	−	8.15697i	0.718466	−	0.261500i
$974$	−2.66801	+	7.33030i	−0.0854886	+	0.234878i
$975$	2.49726	+	11.9225i	0.0799764	+	0.381824i
$976$	−0.0709282	+	0.122851i	−0.00227036	+	0.00393237i
$977$	18.1173	+	31.3801i	0.579623	+	1.00394i	0.995522	+	0.0945264i	$0.0301337\pi$
$977$	18.1173	+	31.3801i	0.579623	+	1.00394i	−0.415899	+	0.909411i	$0.636533\pi$
$978$	−8.85554	−	9.89392i	−0.283169	−	0.316373i
$979$	40.9910	+	7.22783i	1.31008	+	0.231002i
$980$	6.78044	−	3.91469i	0.216593	−	0.125050i
$981$	−13.9302	+	47.5148i	−0.444757	+	1.51703i
$982$	−18.0754	+	21.5414i	−0.576808	+	0.687413i
$983$	51.2605	+	18.6573i	1.63496	+	0.595075i	0.986147	−	0.165876i	$-0.0530451\pi$
$983$	51.2605	+	18.6573i	1.63496	+	0.595075i	0.648809	+	0.760951i	$0.275267\pi$
$984$	−3.49569	+	10.6510i	−0.111438	+	0.339543i
$985$	45.2045	−	37.9311i	1.44033	−	1.20858i
$986$	10.0737	−	1.77626i	0.320811	−	0.0565676i
$987$	−27.0206	−	21.2402i	−0.860076	−	0.676082i
$988$	−16.5380	+	8.15354i	−0.526143	+	0.259399i
$989$		−	47.6969i		−	1.51667i
$990$	17.7386	−	7.77197i	0.563768	−	0.247009i
$991$	8.48805	+	10.1157i	0.269632	+	0.321335i	0.883822	−	0.467823i	$-0.154962\pi$
$991$	8.48805	+	10.1157i	0.269632	+	0.321335i	−0.614190	+	0.789158i	$0.710517\pi$
$992$	−2.72184	−	7.47818i	−0.0864184	−	0.237432i
$993$	−8.22056	−	13.2429i	−0.260872	−	0.420250i
$994$	−22.1881	−	18.6181i	−0.703765	−	0.590529i
$995$	−0.746352	−	0.430907i	−0.0236610	−	0.0136607i
$996$	3.50465	−	24.4113i	0.111049	−	0.773503i
$997$	−2.70472	+	15.3392i	−0.0856593	+	0.485798i	0.911553	+	0.411182i	$0.134884\pi$
$997$	−2.70472	+	15.3392i	−0.0856593	+	0.485798i	−0.997212	+	0.0746156i	$0.976227\pi$
$998$	−2.37416	+	13.4645i	−0.0751526	+	0.426212i
$999$	−21.2307	+	2.04063i	−0.671711	+	0.0645625i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.l.a.29.2	✓	18
3.2	odd	2		114.2.l.b.29.1	yes	18
4.3	odd	2		912.2.cc.d.257.2		18
12.11	even	2		912.2.cc.c.257.3		18
19.2	odd	18		114.2.l.b.59.1	yes	18
57.2	even	18	inner	114.2.l.a.59.2	yes	18
76.59	even	18		912.2.cc.c.401.3		18
228.59	odd	18		912.2.cc.d.401.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.29.2	✓	18	1.1	even	1	trivial
114.2.l.a.59.2	yes	18	57.2	even	18	inner
114.2.l.b.29.1	yes	18	3.2	odd	2
114.2.l.b.59.1	yes	18	19.2	odd	18
912.2.cc.c.257.3		18	12.11	even	2
912.2.cc.c.401.3		18	76.59	even	18
912.2.cc.d.257.2		18	4.3	odd	2
912.2.cc.d.401.2		18	228.59	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.0553136 - 1.73117i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.882820 - 2.42553i) q^{5} +(-1.69526 + 0.355087i) q^{6} +(-1.58376 + 2.74316i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.99388 + 0.191514i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.0553136 - 1.73117i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.882820 - 2.42553i) q^{5} +(-1.69526 + 0.355087i) q^{6} +(-1.58376 + 2.74316i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.99388 + 0.191514i) q^{9} +(-2.54198 - 0.448219i) q^{10} +(2.16590 - 1.25049i) q^{11} +(0.644072 + 1.60785i) q^{12} +(2.71907 - 3.24046i) q^{13} +(2.97650 + 1.08336i) q^{14} +(-4.24783 - 1.39414i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.32278 + 0.233243i) q^{17} +(0.708487 + 2.91514i) q^{18} +(3.14841 + 3.01455i) q^{19} +2.58119i q^{20} +(4.83647 + 2.59003i) q^{21} +(-1.60759 - 1.91586i) q^{22} +(1.30503 + 3.58554i) q^{23} +(1.47158 - 0.913487i) q^{24} +(-1.27359 - 1.06867i) q^{25} +(-3.66340 - 2.11506i) q^{26} +(0.497145 + 5.17232i) q^{27} +(0.550036 - 3.11941i) q^{28} +(1.32242 - 7.49981i) q^{29} +(-0.635337 + 4.42538i) q^{30} +(6.89193 + 3.97906i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-2.28460 - 3.68037i) q^{33} +(0.459398 + 1.26219i) q^{34} +(5.25543 + 6.26318i) q^{35} +(2.74783 - 1.20393i) q^{36} +4.10469i q^{37} +(2.42204 - 3.62405i) q^{38} +(-5.76019 - 4.52793i) q^{39} +(2.54198 - 0.448219i) q^{40} +(-4.95792 + 4.16019i) q^{41} +(1.71083 - 5.21275i) q^{42} +(-11.7465 - 4.27537i) q^{43} +(-1.60759 + 1.91586i) q^{44} +(-2.17853 + 7.43081i) q^{45} +(3.30445 - 1.90782i) q^{46} +(-6.16940 - 1.08783i) q^{47} +(-1.15515 - 1.29060i) q^{48} +(-1.51662 - 2.62686i) q^{49} +(-0.831277 + 1.43981i) q^{50} +(0.476950 + 2.27706i) q^{51} +(-1.44679 + 3.97502i) q^{52} +(3.46508 - 1.26118i) q^{53} +(5.00741 - 1.38776i) q^{54} +(-1.12098 - 6.35742i) q^{55} -3.16753 q^{56} +(5.04455 - 5.61716i) q^{57} -7.61550 q^{58} +(1.54335 + 8.75275i) q^{59} +(4.46848 - 0.142775i) q^{60} +(-0.133301 + 0.0485177i) q^{61} +(2.72184 - 7.47818i) q^{62} +(4.21625 - 8.51601i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-5.45938 - 9.45593i) q^{65} +(-3.22774 + 2.88899i) q^{66} +(-4.48795 - 0.791347i) q^{67} +(1.16324 - 0.671595i) q^{68} +(6.13498 - 2.45755i) q^{69} +(5.25543 - 6.26318i) q^{70} +(-8.59275 - 3.12750i) q^{71} +(-1.66280 - 2.49702i) q^{72} +(-1.67672 + 1.40694i) q^{73} +(4.04233 - 0.712771i) q^{74} +(-1.77960 + 2.26391i) q^{75} +(-3.98957 - 1.75594i) q^{76} +7.92190i q^{77} +(-3.45889 + 6.45894i) q^{78} +(6.41515 + 7.64528i) q^{79} +(-0.882820 - 2.42553i) q^{80} +(8.92664 - 1.14674i) q^{81} +(4.95792 + 4.16019i) q^{82} +(-12.3308 - 7.11920i) q^{83} +(-5.43064 - 0.779658i) q^{84} +(-0.602044 + 3.41436i) q^{85} +(-2.17066 + 12.3104i) q^{86} +(-13.0566 - 1.87449i) q^{87} +(2.16590 + 1.25049i) q^{88} +(12.7492 + 10.6978i) q^{89} +(7.69622 + 0.855091i) q^{90} +(4.58274 + 12.5910i) q^{91} +(-2.45265 - 2.92296i) q^{92} +(6.50720 - 12.1512i) q^{93} +6.26457i q^{94} +(10.0914 - 4.97524i) q^{95} +(-1.07040 + 1.36171i) q^{96} +(0.538573 - 0.0949649i) q^{97} +(-2.32360 + 1.94973i) q^{98} +(-6.24498 + 4.15861i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{6} + 9 q^{8}+O(q^{10}) \) 18 * q + 3 * q^6 + 9 * q^8	\( 18 q + 3 q^{6} + 9 q^{8} - 12 q^{13} + 12 q^{14} - 24 q^{15} - 6 q^{17} - 6 q^{19} - 24 q^{22} - 18 q^{25} - 18 q^{26} - 3 q^{27} + 6 q^{28} + 6 q^{29} - 27 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} - 3 q^{38} + 6 q^{39} - 3 q^{41} - 6 q^{43} - 24 q^{44} + 54 q^{45} + 18 q^{46} - 30 q^{47} + 6 q^{48} + 21 q^{49} - 3 q^{50} - 33 q^{51} - 6 q^{52} + 60 q^{53} + 30 q^{55} + 12 q^{57} + 12 q^{58} - 3 q^{59} + 18 q^{60} + 54 q^{61} - 6 q^{62} + 84 q^{63} - 9 q^{64} - 24 q^{65} + 30 q^{66} - 15 q^{67} + 27 q^{68} + 24 q^{69} + 24 q^{70} - 36 q^{71} - 42 q^{73} - 6 q^{74} - 18 q^{78} - 6 q^{79} + 3 q^{82} - 36 q^{83} - 24 q^{84} + 6 q^{86} - 54 q^{87} + 60 q^{89} - 12 q^{90} - 18 q^{91} - 84 q^{93} - 6 q^{95} + 9 q^{97} - 12 q^{98} - 30 q^{99}+O(q^{100}) \) 18 * q + 3 * q^6 + 9 * q^8 - 12 * q^13 + 12 * q^14 - 24 * q^15 - 6 * q^17 - 6 * q^19 - 24 * q^22 - 18 * q^25 - 18 * q^26 - 3 * q^27 + 6 * q^28 + 6 * q^29 - 27 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 - 3 * q^38 + 6 * q^39 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 54 * q^45 + 18 * q^46 - 30 * q^47 + 6 * q^48 + 21 * q^49 - 3 * q^50 - 33 * q^51 - 6 * q^52 + 60 * q^53 + 30 * q^55 + 12 * q^57 + 12 * q^58 - 3 * q^59 + 18 * q^60 + 54 * q^61 - 6 * q^62 + 84 * q^63 - 9 * q^64 - 24 * q^65 + 30 * q^66 - 15 * q^67 + 27 * q^68 + 24 * q^69 + 24 * q^70 - 36 * q^71 - 42 * q^73 - 6 * q^74 - 18 * q^78 - 6 * q^79 + 3 * q^82 - 36 * q^83 - 24 * q^84 + 6 * q^86 - 54 * q^87 + 60 * q^89 - 12 * q^90 - 18 * q^91 - 84 * q^93 - 6 * q^95 + 9 * q^97 - 12 * q^98 - 30 * q^99

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