LMFDB - Embedded newform 114.2.l.a.59.2

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			59.2
Root			$1.47158 + 0.913487i$ of defining polynomial
Character	$\chi$	$=$	114.59
Dual form			114.2.l.a.29.2

$q$-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 $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

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

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	0.964779	+	0.263063i	$0.0847327\pi$
$5$	0.882820	+	2.42553i	0.394809	+	1.08473i	−0.569970	+	0.821666i	$0.693045\pi$
$6$	−1.69526	−	0.355087i	−0.692088	−	0.144964i
$7$	−1.58376	−	2.74316i	−0.598607	−	1.03682i	−0.993027	−	0.117887i	$-0.962388\pi$
$7$	−1.58376	−	2.74316i	−0.598607	−	1.03682i	0.394420	−	0.918930i	$-0.370945\pi$
$8$	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	0.789622	−	0.613594i	$-0.210277\pi$
$11$	2.16590	+	1.25049i	0.653045	+	0.377036i	−0.136577	+	0.990629i	$0.543610\pi$
$12$	0.644072	−	1.60785i	0.185928	−	0.464145i
$13$	2.71907	+	3.24046i	0.754135	+	0.898743i	0.997462	−	0.0712015i	$-0.0226833\pi$
$13$	2.71907	+	3.24046i	0.754135	+	0.898743i	−0.243327	+	0.969944i	$0.578239\pi$
$14$	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	0.0109180	−	0.999940i	$-0.496525\pi$
$17$	−1.32278	−	0.233243i	−0.320822	−	0.0565696i	−0.331740	+	0.943371i	$0.607636\pi$
$18$	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	−0.726080	−	0.687611i	$-0.758660\pi$
$23$	1.30503	−	3.58554i	0.272117	−	0.747636i	0.998197	−	0.0600255i	$-0.0191182\pi$
$24$	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	0.819172	+	0.573547i	$0.194433\pi$
$29$	1.32242	+	7.49981i	0.245567	+	1.39268i	−0.573606	+	0.819132i	$0.694456\pi$
$30$	−0.635337	−	4.42538i	−0.115996	−	0.807961i
$31$	6.89193	−	3.97906i	1.23783	−	0.714660i	0.269177	−	0.963091i	$-0.413248\pi$
$31$	6.89193	−	3.97906i	1.23783	−	0.714660i	0.968650	+	0.248431i	$0.0799149\pi$
$32$	−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	$-0.890451\pi$
$37$		−	4.10469i		−	0.674806i	0.941360	−	0.337403i	$-0.109549\pi$
$38$	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	0.167509	−	0.985871i	$-0.446428\pi$
$41$	−4.95792	−	4.16019i	−0.774297	−	0.649712i	−0.941805	+	0.336158i	$0.890872\pi$
$42$	1.71083	+	5.21275i	0.263987	+	0.804345i
$43$	−11.7465	+	4.27537i	−1.79132	+	0.651987i	−0.792191	+	0.610273i	$0.791060\pi$
$43$	−11.7465	+	4.27537i	−1.79132	+	0.651987i	−0.999130	+	0.0417144i	$0.986718\pi$
$44$	−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	−0.604414	−	0.796671i	$-0.706593\pi$
$47$	−6.16940	+	1.08783i	−0.899899	+	0.158676i	−0.295486	+	0.955347i	$0.595481\pi$
$48$	−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	0.568853	−	0.822440i	$-0.307388\pi$
$53$	3.46508	+	1.26118i	0.475965	+	0.173237i	−0.0928877	+	0.995677i	$0.529610\pi$
$54$	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	−0.702796	−	0.711392i	$-0.748065\pi$
$59$	1.54335	−	8.75275i	0.200927	−	1.13951i	0.903722	−	0.428119i	$-0.140824\pi$
$60$	4.46848	+	0.142775i	0.576878	+	0.0184322i
$61$	−0.133301	−	0.0485177i	−0.0170675	−	0.00621206i	0.333472	−	0.942760i	$-0.391780\pi$
$61$	−0.133301	−	0.0485177i	−0.0170675	−	0.00621206i	−0.350540	+	0.936548i	$0.614002\pi$
$62$	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	−0.440930	−	0.897542i	$-0.645351\pi$
$67$	−4.48795	+	0.791347i	−0.548291	+	0.0966784i	−0.107361	+	0.994220i	$0.534240\pi$
$68$	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	−0.797178	−	0.603745i	$-0.793675\pi$
$71$	−8.59275	+	3.12750i	−1.01977	+	0.371166i	−0.222594	+	0.974911i	$0.571452\pi$
$72$	−1.66280	+	2.49702i	−0.195962	+	0.294277i
$73$	−1.67672	−	1.40694i	−0.196245	−	0.164670i	0.539370	−	0.842069i	$-0.318662\pi$
$73$	−1.67672	−	1.40694i	−0.196245	−	0.164670i	−0.735615	+	0.677399i	$0.763107\pi$
$74$	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	−0.273040	−	0.962003i	$-0.588029\pi$
$79$	6.41515	−	7.64528i	0.721760	−	0.860161i	0.994801	+	0.101842i	$0.0324736\pi$
$80$	−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	−0.988735	−	0.149673i	$-0.952178\pi$
$83$	−12.3308	+	7.11920i	−1.35348	+	0.781433i	−0.364747	+	0.931107i	$0.618844\pi$
$84$	−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	0.372879	−	0.927880i	$-0.378371\pi$
$89$	12.7492	−	10.6978i	1.35141	−	1.13397i	0.978533	−	0.206089i	$-0.0660737\pi$
$90$	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	0.200923	−	0.979607i	$-0.435606\pi$
$97$	0.538573	+	0.0949649i	0.0546838	+	0.00964223i	−0.146239	+	0.989249i	$0.546717\pi$
$98$	−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	0.244771	−	0.969581i	$-0.421287\pi$
$101$	−7.56338	−	9.01368i	−0.752584	−	0.896895i	−0.997355	+	0.0726860i	$0.976843\pi$
$102$	2.15964	+	0.865111i	0.213837	+	0.0856588i
$103$	6.77528	+	3.91171i	0.667588	+	0.385432i	0.795162	−	0.606397i	$-0.207386\pi$
$103$	6.77528	+	3.91171i	0.667588	+	0.385432i	−0.127574	+	0.991829i	$0.540719\pi$
$104$	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	0.696227	−	0.717822i	$-0.254861\pi$
$107$	−2.82951	−	4.90085i	−0.273539	−	0.473783i	−0.969765	+	0.244039i	$0.921528\pi$
$108$	−2.23620	+	4.69035i	−0.215178	+	0.451329i
$109$	5.64501	+	15.5095i	0.540694	+	1.48554i	0.845944	+	0.533271i	$0.179038\pi$
$109$	5.64501	+	15.5095i	0.540694	+	1.48554i	−0.305251	+	0.952272i	$0.598740\pi$
$110$	−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	0.941747	−	0.336322i	$-0.109183\pi$
$127$	5.03745	+	6.00340i	0.447001	+	0.532715i	−0.494746	+	0.869038i	$0.664739\pi$
$128$	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	0.363908	−	0.931435i	$-0.381442\pi$
$131$	4.43285	+	0.781631i	0.387300	+	0.0682914i	0.0233919	+	0.999726i	$0.492553\pi$
$132$	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	−0.770104	−	0.637919i	$-0.779796\pi$
$137$	2.69063	−	7.39245i	0.229876	−	0.631580i	0.999980	+	0.00633905i	$0.00201780\pi$
$138$	−3.48554	+	5.61503i	−0.296709	+	0.477983i
$139$	−5.76780	+	4.83976i	−0.489219	+	0.410503i	−0.853746	−	0.520689i	$-0.825675\pi$
$139$	−5.76780	+	4.83976i	−0.489219	+	0.410503i	0.364528	+	0.931193i	$0.381230\pi$
$140$	−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	−0.994691	−	0.102905i	$-0.967186\pi$
$149$	−8.79633	+	10.4831i	−0.720624	+	0.858806i	0.274068	+	0.961710i	$0.411631\pi$
$150$	2.53854	−	1.35944i	0.207271	−	0.110998i
$151$			8.63653i			0.702831i	0.936220	+	0.351415i	$0.114300\pi$
$151$			8.63653i			0.702831i	−0.936220	+	0.351415i	$0.885700\pi$
$152$	−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	−0.467597	−	0.883942i	$-0.654880\pi$
$157$	−3.22785	+	1.17484i	−0.257610	+	0.0937625i	0.209987	+	0.977704i	$0.432658\pi$
$158$	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	−0.675958	−	0.736940i	$-0.736270\pi$
$163$	3.83308	−	6.63909i	0.300230	−	0.520014i	0.976188	+	0.216926i	$0.0696032\pi$
$164$	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	0.425895	−	0.904773i	$-0.359959\pi$
$167$	2.20429	+	0.802294i	0.170573	+	0.0620834i	−0.255322	+	0.966856i	$0.582182\pi$
$168$	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	0.712649	+	0.701521i	$0.247495\pi$
$173$	−2.59056	+	14.6918i	−0.196956	+	1.11700i	−0.909605	+	0.415474i	$0.863616\pi$
$174$	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	−0.862360	−	0.506296i	$-0.831014\pi$
$179$	0.0974666	−	0.168817i	0.00728500	−	0.0126180i	0.869645	+	0.493678i	$0.164348\pi$
$180$	−0.494335	+	7.72778i	−0.0368455	+	0.575995i
$181$	−7.00507	+	1.23518i	−0.520683	+	0.0918105i	−0.427812	−	0.903868i	$-0.640715\pi$
$181$	−7.00507	+	1.23518i	−0.520683	+	0.0918105i	−0.0928709	+	0.995678i	$0.529604\pi$
$182$	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	$0.133404\pi$
$191$			11.2480i			0.813878i	−0.913455	+	0.406939i	$0.866596\pi$
$192$	1.52689	−	0.817681i	0.110194	−	0.0590110i
$193$	−10.3664	+	12.3541i	−0.746187	+	0.889271i	−0.996891	−	0.0787930i	$-0.974893\pi$
$193$	−10.3664	+	12.3541i	−0.746187	+	0.889271i	0.250704	+	0.968064i	$0.419338\pi$
$194$	−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	0.415157	−	0.909750i	$-0.363727\pi$
$197$	19.7987	−	11.4308i	1.41060	−	0.814411i	0.995445	+	0.0953383i	$0.0303933\pi$
$198$	5.17986	−	5.42797i	0.368116	−	0.385749i
$199$	0.0579780	+	0.328809i	0.00410995	+	0.0233087i	0.986794	−	0.161982i	$-0.0517885\pi$
$199$	0.0579780	+	0.328809i	0.00410995	+	0.0233087i	−0.982684	+	0.185290i	$0.940677\pi$
$200$	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	0.259919	−	0.965630i	$-0.416304\pi$
$211$	2.52603	+	0.445407i	0.173899	+	0.0306631i	−0.0860206	+	0.996293i	$0.527415\pi$
$212$	−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	0.992362	−	0.123356i	$-0.0393658\pi$
$223$	2.28294	+	6.27232i	0.152877	+	0.420026i	−0.839486	+	0.543382i	$0.817144\pi$
$224$	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	0.989582	−	0.143970i	$-0.0459870\pi$
$233$	2.12137	+	5.82843i	0.138976	+	0.381833i	−0.850606	+	0.525803i	$0.823765\pi$
$234$	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	0.516041	−	0.856564i	$-0.327405\pi$
$239$	0.498666	+	0.287905i	0.0322560	+	0.0186230i	−0.483785	+	0.875187i	$0.660738\pi$
$240$	−4.15016	−	1.66247i	−0.267892	−	0.107312i
$241$	−1.09166	−	1.30099i	−0.0703198	−	0.0838039i	0.729738	−	0.683727i	$-0.239642\pi$
$241$	−1.09166	−	1.30099i	−0.0703198	−	0.0838039i	−0.800058	+	0.599923i	$0.795198\pi$
$242$	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	−0.987449	−	0.157941i	$-0.949514\pi$
$251$	−2.05161	+	5.63675i	−0.129496	+	0.355789i	0.857952	+	0.513730i	$0.171737\pi$
$252$	−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	−0.902744	−	0.430178i	$-0.858451\pi$
$257$	−3.23144	−	18.3264i	−0.201572	−	1.14317i	0.701172	−	0.712992i	$-0.252660\pi$
$258$	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	−0.721835	−	0.692065i	$-0.756701\pi$
$263$	1.37946	−	1.64398i	0.0850614	−	0.101372i	0.806896	+	0.590693i	$0.201146\pi$
$264$	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	−0.999079	−	0.0429154i	$-0.986335\pi$
$269$	−19.9247	−	16.7188i	−1.21483	−	1.01936i	−0.215752	−	0.976448i	$-0.569220\pi$
$270$	1.05460	+	13.3707i	0.0641809	+	0.813718i
$271$	4.62857	−	1.68466i	0.281166	−	0.102336i	−0.197588	−	0.980285i	$-0.563311\pi$
$271$	4.62857	−	1.68466i	0.281166	−	0.102336i	0.478754	+	0.877949i	$0.341089\pi$
$272$	−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	−0.890319	−	0.455338i	$-0.849518\pi$
$277$	−0.845901	+	1.46514i	−0.0508252	+	0.0880319i	0.839493	+	0.543370i	$0.182852\pi$
$278$	−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	0.992213	−	0.124555i	$-0.0397502\pi$
$281$	28.0317	+	10.2027i	1.67223	+	0.608642i	0.680017	+	0.733196i	$0.261972\pi$
$282$	10.8450	+	0.346516i	0.645811	+	0.0206347i
$283$	4.10223	−	23.2649i	0.243852	−	1.38296i	−0.579290	−	0.815121i	$-0.696670\pi$
$283$	4.10223	−	23.2649i	0.243852	−	1.38296i	0.823143	−	0.567834i	$-0.192219\pi$
$284$	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	−0.969062	−	0.246817i	$-0.920615\pi$
$293$	−4.63502	+	8.02810i	−0.270781	+	0.469006i	0.698281	+	0.715824i	$0.253949\pi$
$294$	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	−0.713349	−	0.700809i	$-0.752823\pi$
$307$	1.76414	−	2.10242i	0.100685	−	0.119991i	0.814034	+	0.580818i	$0.197267\pi$
$308$	−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	−0.942520	−	0.334148i	$-0.891551\pi$
$311$	−19.8290	+	11.4483i	−1.12440	+	0.649172i	−0.181879	+	0.983321i	$0.558218\pi$
$312$	1.04121	+	7.25243i	0.0589467	+	0.410588i
$313$	−2.33240	−	13.2277i	−0.131835	−	0.747673i	−0.977012	−	0.213186i	$-0.931616\pi$
$313$	−2.33240	−	13.2277i	−0.131835	−	0.747673i	0.845177	−	0.534487i	$-0.179495\pi$
$314$	−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	−0.968947	−	0.247270i	$-0.920466\pi$
$317$	−15.9117	+	13.3515i	−0.893689	+	0.749894i	0.0752579	+	0.997164i	$0.476022\pi$
$318$	−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	0.698651	−	0.715463i	$-0.253784\pi$
$331$	7.79345	+	4.49955i	0.428367	+	0.247318i	−0.270284	+	0.962781i	$0.587118\pi$
$332$	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	0.999967	+	0.00808963i	$0.00257504\pi$
$337$	4.39017	+	12.0619i	0.239148	+	0.657053i	−0.760819	+	0.648964i	$0.775203\pi$
$338$	−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	−0.999498	−	0.0316932i	$-0.989910\pi$
$347$	−4.73541	−	13.0104i	−0.254210	−	0.698436i	0.745288	−	0.666743i	$-0.232312\pi$
$348$	12.9103	+	2.70417i	0.692063	+	0.144959i
$349$	−10.3158	−	17.8674i	−0.552190	−	0.956421i	−0.998116	−	0.0613514i	$-0.980459\pi$
$349$	−10.3158	−	17.8674i	−0.552190	−	0.956421i	0.445926	−	0.895070i	$-0.352874\pi$
$350$	−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	−0.128053	−	0.991767i	$-0.540873\pi$
$353$	−19.7460	−	11.4004i	−1.05098	−	0.606781i	−0.922922	+	0.384987i	$0.874206\pi$
$354$	−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	−0.0226346	−	0.999744i	$-0.507205\pi$
$359$	−7.31056	−	1.28905i	−0.385837	−	0.0680334i	−0.363202	+	0.931710i	$0.618317\pi$
$360$	−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	−0.946676	−	0.322188i	$-0.895582\pi$
$367$	−15.2065	+	12.7597i	−0.793771	+	0.666053i	0.152904	+	0.988241i	$0.451137\pi$
$368$	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	−0.00727484	−	0.999974i	$-0.502316\pi$
$373$	16.5145	−	9.53467i	0.855090	−	0.493687i	0.862365	+	0.506287i	$0.168982\pi$
$374$	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	$0.281142\pi$
$379$			30.0894i			1.54559i	−0.634656	+	0.772795i	$0.718858\pi$
$380$	−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	0.752750	−	0.658307i	$-0.228727\pi$
$383$	4.60213	+	3.86165i	0.235158	+	0.197321i	−0.517592	+	0.855628i	$0.673171\pi$
$384$	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	0.371353	−	0.928492i	$-0.378894\pi$
$389$	20.4701	−	3.60942i	1.03787	−	0.183005i	0.666520	+	0.745487i	$0.267783\pi$
$390$	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	−0.903928	−	0.427686i	$-0.859329\pi$
$397$	1.82838	−	10.3692i	0.0917636	−	0.520417i	0.995691	−	0.0927316i	$-0.0295599\pi$
$398$	−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	0.918561	+	0.395280i	$0.129352\pi$
$401$	−1.59795	+	9.06241i	−0.0797977	+	0.452555i	−0.998358	+	0.0572753i	$0.981759\pi$
$402$	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	0.432651	−	0.901561i	$-0.357578\pi$
$409$	23.2080	−	4.09220i	1.14756	−	0.202346i	0.714911	+	0.699215i	$0.246467\pi$
$410$	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	$-0.833744\pi$
$419$		−	20.4238i		−	0.997766i	0.866669	−	0.498883i	$-0.166256\pi$
$420$	−6.68536	−	12.4839i	−0.326212	−	0.609150i
$421$	−0.259039	+	0.308710i	−0.0126248	+	0.0150456i	−0.772320	−	0.635234i	$-0.780904\pi$
$421$	−0.259039	+	0.308710i	−0.0126248	+	0.0150456i	0.759695	+	0.650279i	$0.225348\pi$
$422$	−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	−0.454087	−	0.890957i	$-0.650035\pi$
$431$	7.15165	−	6.00095i	0.344483	−	0.289055i	0.798570	+	0.601902i	$0.205590\pi$
$432$	3.70554	−	3.64266i	0.178283	−	0.175258i
$433$	−7.03421	+	19.3263i	−0.338043	+	0.928765i	0.647907	+	0.761720i	$0.275645\pi$
$433$	−7.03421	+	19.3263i	−0.338043	+	0.928765i	−0.985949	+	0.167045i	$0.946577\pi$
$434$	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	−0.465040	−	0.885290i	$-0.653960\pi$
$439$	−25.2438	−	4.45116i	−1.20482	−	0.212442i	−0.739781	+	0.672847i	$0.765071\pi$
$440$	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	0.188649	−	0.982045i	$-0.439589\pi$
$443$	−17.0745	−	20.3486i	−0.811235	−	0.966792i	−0.999884	+	0.0152527i	$0.995145\pi$
$444$	−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	0.968228	−	0.250068i	$-0.0804531\pi$
$449$	5.66925	+	9.81944i	0.267549	+	0.463408i	−0.700680	+	0.713476i	$0.747120\pi$
$450$	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	−0.940669	−	0.339326i	$-0.889801\pi$
$461$	−9.40832	−	25.8492i	−0.438189	−	1.20392i	0.502480	−	0.864589i	$-0.332421\pi$
$462$	−2.81297	+	13.4297i	−0.130871	+	0.624806i
$463$	−4.52654	−	7.84019i	−0.210366	−	0.364365i	0.741463	−	0.670994i	$-0.234132\pi$
$463$	−4.52654	−	7.84019i	−0.210366	−	0.364365i	−0.951829	+	0.306629i	$0.900799\pi$
$464$	−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	0.850239	−	0.526397i	$-0.176457\pi$
$467$	17.7092	+	10.2244i	0.819486	+	0.473130i	−0.0307535	+	0.999527i	$0.509791\pi$
$468$	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	−0.838822	−	0.544405i	$-0.816755\pi$
$479$	3.36367	−	9.24160i	0.153690	−	0.422259i	0.992512	+	0.122146i	$0.0389776\pi$
$480$	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	−0.645192	−	0.764020i	$-0.723223\pi$
$487$	−6.75564	+	3.90037i	−0.306127	+	0.176743i	0.339065	+	0.940763i	$0.389889\pi$
$488$	−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	−0.999942	−	0.0107379i	$-0.996582\pi$
$491$	−18.0754	+	21.5414i	−0.815729	+	0.972148i	0.184213	+	0.982886i	$0.441026\pi$
$492$	−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	−0.613182	−	0.789942i	$-0.710111\pi$
$499$	−12.8477	+	4.67618i	−0.575142	+	0.209334i	0.0380402	+	0.999276i	$0.487888\pi$
$500$	−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	0.436144	−	0.899877i	$-0.356344\pi$
$503$	25.8762	−	4.56267i	1.15376	−	0.203439i	0.717618	+	0.696437i	$0.245233\pi$
$504$	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	0.830368	−	0.557215i	$-0.188130\pi$
$509$	25.0043	+	9.10082i	1.10830	+	0.403387i	0.277928	+	0.960602i	$0.410352\pi$
$510$	−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	−0.547307	−	0.836932i	$-0.684347\pi$
$521$	10.2977	−	17.8362i	0.451151	−	0.781417i	0.998458	+	0.0555154i	$0.0176802\pi$
$522$	22.7999	+	1.45848i	0.997925	+	0.0638358i
$523$	7.47024	−	1.31720i	0.326651	−	0.0575973i	−0.00791816	−	0.999969i	$-0.502520\pi$
$523$	7.47024	−	1.31720i	0.326651	−	0.0575973i	0.334569	+	0.942371i	$0.391409\pi$
$524$	−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	0.555966	+	0.831205i	$0.312349\pi$
$541$	7.39225	+	41.9235i	0.317818	+	1.80243i	−0.238148	+	0.971229i	$0.576540\pi$
$542$	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	−0.948321	−	0.317311i	$-0.897220\pi$
$547$	−0.418676	+	1.15030i	−0.0179013	+	0.0491833i	0.930420	+	0.366495i	$0.119442\pi$
$548$	−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	0.975249	−	0.221110i	$-0.0709681\pi$
$557$	13.8808	+	16.5425i	0.588147	+	0.700927i	−0.387101	+	0.922037i	$0.626524\pi$
$558$	−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	0.998377	+	0.0569541i	$0.0181389\pi$
$563$	13.0149	+	22.5424i	0.548512	+	0.950051i	−0.449865	+	0.893097i	$0.648528\pi$
$564$	−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	0.694293	+	0.719692i	$0.255717\pi$
$577$	23.3103	+	40.3745i	0.970418	+	1.68081i	0.276125	+	0.961122i	$0.410950\pi$
$578$	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	0.473041	−	0.881040i	$-0.343156\pi$
$587$	14.9298	+	2.63253i	0.616220	+	0.108656i	0.143180	+	0.989697i	$0.454267\pi$
$588$	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	−0.947613	−	0.319421i	$-0.896511\pi$
$593$	−0.398860	+	1.09586i	−0.0163792	+	0.0450015i	0.931234	+	0.364423i	$0.118734\pi$
$594$	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	−0.929868	−	0.367892i	$-0.880079\pi$
$599$	−4.45202	−	25.2486i	−0.181905	−	1.03163i	0.747964	−	0.663739i	$-0.231032\pi$
$600$	−2.85040	+	0.409223i	−0.116367	+	0.0167064i
$601$	−26.4639	+	15.2789i	−1.07948	+	0.623240i	−0.930757	−	0.365639i	$-0.880851\pi$
$601$	−26.4639	+	15.2789i	−1.07948	+	0.623240i	−0.148726	+	0.988878i	$0.547517\pi$
$602$	−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	$-0.949225\pi$
$607$		−	7.82667i		−	0.317675i	0.987305	−	0.158837i	$-0.0507745\pi$
$608$	−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	0.354519	−	0.935049i	$-0.384645\pi$
$613$	30.3824	−	11.0583i	1.22713	−	0.446640i	0.872615	+	0.488408i	$0.162422\pi$
$614$	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	−0.643545	−	0.765408i	$-0.722537\pi$
$617$	−24.5040	+	4.32072i	−0.986495	+	0.173946i	−0.342950	+	0.939354i	$0.611426\pi$
$618$	−10.0969	−	9.03718i	−0.406156	−	0.363529i
$619$	−3.60285	+	6.24032i	−0.144811	+	0.250820i	−0.929302	−	0.369320i	$-0.879591\pi$
$619$	−3.60285	+	6.24032i	−0.144811	+	0.250820i	0.784492	+	0.620140i	$0.212924\pi$
$620$	−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	0.767695	−	0.640815i	$-0.221404\pi$
$631$	23.7099	+	8.62969i	0.943876	+	0.343543i	0.176180	+	0.984358i	$0.443626\pi$
$632$	−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	−0.171524	−	0.985180i	$-0.554869\pi$
$641$	8.36361	−	3.04411i	0.330343	−	0.120235i	0.501867	+	0.864945i	$0.332647\pi$
$642$	3.05653	+	9.31295i	0.120631	+	0.367553i
$643$	5.41716	+	4.54553i	0.213632	+	0.179258i	0.743324	−	0.668932i	$-0.233248\pi$
$643$	5.41716	+	4.54553i	0.213632	+	0.179258i	−0.529692	+	0.848190i	$0.677693\pi$
$644$	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	$-0.950546\pi$
$647$		−	7.87198i		−	0.309479i	0.987955	−	0.154740i	$-0.0494539\pi$
$648$	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	−0.472277	−	0.881450i	$-0.656568\pi$
$653$	1.40402	−	0.810613i	0.0549437	−	0.0317217i	0.527220	+	0.849729i	$0.323234\pi$
$654$	−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	−0.443493	−	0.896278i	$-0.646261\pi$
$659$	9.29693	−	7.80105i	0.362157	−	0.303886i	0.805650	+	0.592392i	$0.201816\pi$
$660$	9.49976	+	5.89700i	0.369778	+	0.229541i
$661$	−10.0965	+	27.7400i	−0.392710	+	1.07896i	0.573050	+	0.819521i	$0.305760\pi$
$661$	−10.0965	+	27.7400i	−0.392710	+	1.07896i	−0.965759	+	0.259440i	$0.916462\pi$
$662$	−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	0.424077	−	0.905626i	$-0.360599\pi$
$673$	−3.84411	−	2.21940i	−0.148180	−	0.0855516i	−0.572257	+	0.820075i	$0.693932\pi$
$674$	−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	0.854057	−	0.520179i	$-0.174135\pi$
$677$	−0.610403	−	1.05725i	−0.0234597	−	0.0406334i	−0.877517	+	0.479546i	$0.840801\pi$
$678$	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	0.961366	+	0.275274i	$0.0887686\pi$
$691$	18.9023	+	32.7397i	0.719077	+	1.24548i	−0.242289	+	0.970204i	$0.577898\pi$
$692$	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	−0.280929	−	0.959729i	$-0.590642\pi$
$701$	−23.1182	−	4.07636i	−0.873162	−	0.153962i	−0.592233	+	0.805767i	$0.701754\pi$
$702$	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	−0.145735	−	0.989324i	$-0.546555\pi$
$709$	21.3882	−	17.9469i	0.803252	−	0.674009i	0.948987	+	0.315315i	$0.102110\pi$
$710$	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	0.00394505	−	0.999992i	$-0.498744\pi$
$719$	26.4940	−	31.5743i	0.988060	−	1.17752i	0.984115	−	0.177532i	$-0.0568113\pi$
$720$	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	−0.264148	−	0.964482i	$-0.585091\pi$
$727$	4.13772	−	1.50601i	0.153460	−	0.0558548i	0.417608	+	0.908627i	$0.362869\pi$
$728$	−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	−0.575007	−	0.818149i	$-0.695001\pi$
$733$	11.3991	−	19.7438i	0.421034	−	0.729253i	0.996041	+	0.0888960i	$0.0283339\pi$
$734$	−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	0.160151	+	0.987093i	$0.448802\pi$
$739$	−8.91510	+	50.5600i	−0.327947	+	1.85988i	−0.488098	+	0.872789i	$0.662309\pi$
$740$	−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	−0.981835	−	0.189737i	$-0.939237\pi$
$743$	0.154876	−	0.878343i	0.00568183	−	0.0322233i	0.987517	+	0.157513i	$0.0503477\pi$
$744$	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	−0.353110	−	0.935582i	$-0.614876\pi$
$751$	−10.0009	+	1.76342i	−0.364936	+	0.0643481i	−0.0118266	+	0.999930i	$0.503765\pi$
$752$	−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	0.885664	−	0.464326i	$-0.153703\pi$
$757$	16.0181	+	13.4408i	0.582187	+	0.488513i	−0.303478	+	0.952839i	$0.598148\pi$
$758$	−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	$0.142791\pi$
$761$			23.9282i			0.867396i	−0.901058	+	0.433698i	$0.857209\pi$
$762$	−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	−0.986208	−	0.165511i	$-0.947073\pi$
$769$	−3.21910	−	18.2564i	−0.116084	−	0.658344i	0.870124	−	0.492833i	$-0.164039\pi$
$770$	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	−0.00900488	−	0.999959i	$-0.502866\pi$
$773$	27.0855	−	22.7275i	0.974199	−	0.817450i	0.983204	+	0.182509i	$0.0584219\pi$
$774$	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	0.606388	−	0.795169i	$-0.292618\pi$
$787$	6.19829	+	3.57858i	0.220945	+	0.127563i	−0.385443	+	0.922732i	$0.625951\pi$
$788$	−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	0.619004	−	0.785388i	$-0.287536\pi$
$809$	7.06352	+	4.07812i	0.248340	+	0.143379i	−0.370664	+	0.928767i	$0.620870\pi$
$810$	−23.2053	+	1.08610i	−0.815352	+	0.0381618i
$811$	−1.94231	−	2.31476i	−0.0682038	−	0.0812821i	0.730864	−	0.682523i	$-0.239117\pi$
$811$	−1.94231	−	2.31476i	−0.0682038	−	0.0812821i	−0.799068	+	0.601241i	$0.794673\pi$
$812$	−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	−0.960680	−	0.277657i	$-0.910442\pi$
$821$	−1.32613	+	3.64350i	−0.0462821	+	0.127159i	0.914398	+	0.404816i	$0.132664\pi$
$822$	−7.18629	+	11.5767i	−0.250651	+	0.403785i
$823$	9.67720	−	8.12014i	0.337326	−	0.283050i	−0.458351	−	0.888771i	$-0.651560\pi$
$823$	9.67720	−	8.12014i	0.337326	−	0.283050i	0.795677	+	0.605721i	$0.207115\pi$
$824$	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	0.927908	+	0.372810i	$0.121606\pi$
$827$	5.27611	+	29.9223i	0.183468	+	1.04050i	−0.744439	+	0.667690i	$0.767283\pi$
$828$	7.90274	−	8.28127i	0.274639	−	0.287794i
$829$	20.5261	−	11.8507i	0.712901	−	0.411593i	−0.0992334	−	0.995064i	$-0.531639\pi$
$829$	20.5261	−	11.8507i	0.712901	−	0.411593i	0.812134	+	0.583471i	$0.198306\pi$
$830$	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	0.813759	−	0.581203i	$-0.197418\pi$
$839$	11.0849	+	9.30133i	0.382693	+	0.321118i	−0.431066	+	0.902321i	$0.641862\pi$
$840$	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	−0.320127	−	0.947375i	$-0.603725\pi$
$853$	8.89956	−	50.4719i	0.304715	−	1.72813i	0.624842	−	0.780751i	$-0.285163\pi$
$854$	−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	−0.876644	−	0.481139i	$-0.840223\pi$
$857$	3.26971	−	18.5435i	0.111691	−	0.633433i	0.988335	−	0.152293i	$-0.0486658\pi$
$858$	0.585186	−	18.3147i	0.0199779	−	0.625255i
$859$	22.7939	+	8.29631i	0.777719	+	0.283066i	0.700221	−	0.713926i	$-0.253085\pi$
$859$	22.7939	+	8.29631i	0.777719	+	0.283066i	0.0774977	+	0.996993i	$0.475307\pi$
$860$	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	−0.983560	−	0.180581i	$-0.942202\pi$
$863$	−9.85277	+	17.0655i	−0.335392	+	0.580916i	0.648168	+	0.761497i	$0.275535\pi$
$864$	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	−0.968120	−	0.250488i	$-0.919409\pi$
$877$	−16.3863	+	19.5284i	−0.553324	+	0.659426i	0.414795	+	0.909915i	$0.363853\pi$
$878$	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	−0.876784	−	0.480884i	$-0.840316\pi$
$881$	−26.6755	+	15.4011i	−0.898719	+	0.518876i	−0.0219346	+	0.999759i	$0.506983\pi$
$882$	6.58317	+	6.28226i	0.221667	+	0.211535i
$883$	−1.74964	−	9.92270i	−0.0588801	−	0.333926i	0.941111	−	0.338097i	$-0.109783\pi$
$883$	−1.74964	−	9.92270i	−0.0588801	−	0.333926i	−0.999991	+	0.00417162i	$0.998672\pi$
$884$	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	−0.854324	−	0.519741i	$-0.826028\pi$
$887$	−14.6182	+	12.2661i	−0.490831	+	0.411856i	0.363493	+	0.931597i	$0.381584\pi$
$888$	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	0.961137	−	0.276070i	$-0.0890323\pi$
$907$	1.42779	+	3.92281i	0.0474089	+	0.130255i	−0.913729	+	0.406325i	$0.866810\pi$
$908$	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	0.610969	−	0.791654i	$-0.290780\pi$
$919$	−11.5230	−	19.9584i	−0.380108	−	0.658367i	−0.991077	+	0.133287i	$0.957447\pi$
$920$	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	0.592962	−	0.805230i	$-0.297958\pi$
$929$	26.6622	+	4.70127i	0.874760	+	0.154244i	0.281798	+	0.959474i	$0.409069\pi$
$930$	−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	−0.0129567	−	0.999916i	$-0.504124\pi$
$937$	29.6774	−	24.9023i	0.969518	−	0.813523i	0.982475	+	0.186393i	$0.0596799\pi$
$938$	−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	0.989849	+	0.142125i	$0.0453935\pi$
$941$	3.32233	+	18.8419i	0.108305	+	0.614227i	−0.881544	+	0.472102i	$0.843495\pi$
$942$	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	−0.146950	−	0.989144i	$-0.546946\pi$
$947$	26.2400	−	31.2716i	0.852684	−	1.01619i	0.999634	−	0.0270453i	$-0.00860982\pi$
$948$	−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	0.974773	−	0.223197i	$-0.0716492\pi$
$953$	28.5318	+	23.9410i	0.924235	+	0.775525i	−0.0505382	+	0.998722i	$0.516094\pi$
$954$	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	−0.237611	−	0.971361i	$-0.576364\pi$
$967$	9.88547	−	56.0633i	0.317895	−	1.80287i	0.555506	−	0.831513i	$-0.312525\pi$
$968$	−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	−0.598776	−	0.800916i	$-0.704346\pi$
$971$	7.41064	−	42.0279i	0.237819	−	1.34874i	0.836595	−	0.547822i	$-0.184543\pi$
$972$	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	−0.415899	−	0.909411i	$-0.636533\pi$
$977$	18.1173	−	31.3801i	0.579623	−	1.00394i	0.995522	−	0.0945264i	$-0.0301337\pi$
$978$	−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	0.648809	−	0.760951i	$-0.275267\pi$
$983$	51.2605	−	18.6573i	1.63496	−	0.595075i	0.986147	+	0.165876i	$0.0530451\pi$
$984$	−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	−0.614190	−	0.789158i	$-0.710517\pi$
$991$	8.48805	−	10.1157i	0.269632	−	0.321335i	0.883822	+	0.467823i	$0.154962\pi$
$992$	−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	−0.997212	−	0.0746156i	$-0.976227\pi$
$997$	−2.70472	−	15.3392i	−0.0856593	−	0.485798i	0.911553	−	0.411182i	$-0.134884\pi$
$998$	−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.59.2	yes	18
3.2	odd	2		114.2.l.b.59.1	yes	18
4.3	odd	2		912.2.cc.d.401.2		18
12.11	even	2		912.2.cc.c.401.3		18
19.10	odd	18		114.2.l.b.29.1	yes	18
57.29	even	18	inner	114.2.l.a.29.2	✓	18
76.67	even	18		912.2.cc.c.257.3		18
228.143	odd	18		912.2.cc.d.257.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.29.2	✓	18	57.29	even	18	inner
114.2.l.a.59.2	yes	18	1.1	even	1	trivial
114.2.l.b.29.1	yes	18	19.10	odd	18
114.2.l.b.59.1	yes	18	3.2	odd	2
912.2.cc.c.257.3		18	76.67	even	18
912.2.cc.c.401.3		18	12.11	even	2
912.2.cc.d.257.2		18	228.143	odd	18
912.2.cc.d.401.2		18	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
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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