LMFDB - Embedded newform 114.2.l.b.59.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [114,2,Mod(29,114)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [18,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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			59.1
Root			$1.47158 - 0.913487i$ of defining polynomial
Character	$\chi$	$=$	114.59
Dual form			114.2.l.b.29.1

$q$-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} +(-1.69526 + 0.355087i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.882820 - 2.42553i) q^{5} +(0.0553136 + 1.73117i) q^{6} +(-1.58376 - 2.74316i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.74783 - 1.20393i) q^{9} +(-2.54198 + 0.448219i) q^{10} +(-2.16590 - 1.25049i) q^{11} +(1.71447 + 0.246141i) q^{12} +(2.71907 + 3.24046i) q^{13} +(-2.97650 + 1.08336i) q^{14} +(2.35788 + 3.79843i) 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} +(3.65896 + 4.08800i) q^{21} +(-1.60759 + 1.91586i) q^{22} +(-1.30503 + 3.58554i) q^{23} +(0.540116 - 1.64568i) q^{24} +(-1.27359 + 1.06867i) q^{25} +(3.66340 - 2.11506i) q^{26} +(-4.23078 + 3.01670i) q^{27} +(0.550036 + 3.11941i) q^{28} +(-1.32242 - 7.49981i) q^{29} +(4.15016 - 1.66247i) q^{30} +(6.89193 - 3.97906i) q^{31} +(0.766044 - 0.642788i) q^{32} +(4.11581 + 1.35082i) q^{33} +(0.459398 - 1.26219i) q^{34} +(-5.25543 + 6.26318i) q^{35} +(-2.99388 + 0.191514i) 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} +(4.66127 - 2.89350i) q^{42} +(-11.7465 + 4.27537i) q^{43} +(1.60759 + 1.91586i) q^{44} +(-5.34601 - 5.60207i) q^{45} +(3.30445 + 1.90782i) q^{46} +(6.16940 - 1.08783i) q^{47} +(-1.52689 - 0.817681i) q^{48} +(-1.51662 + 2.62686i) q^{49} +(0.831277 + 1.43981i) q^{50} +(-2.32529 + 0.0742967i) q^{51} +(-1.44679 - 3.97502i) q^{52} +(-3.46508 - 1.26118i) q^{53} +(2.23620 + 4.69035i) q^{54} +(-1.12098 + 6.35742i) q^{55} +3.16753 q^{56} +(-4.26694 + 6.22842i) q^{57} -7.61550 q^{58} +(-1.54335 + 8.75275i) q^{59} +(-0.916549 - 4.37580i) q^{60} +(-0.133301 - 0.0485177i) q^{61} +(-2.72184 - 7.47818i) q^{62} +(-7.65449 - 5.63098i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(5.45938 - 9.45593i) q^{65} +(2.04500 - 3.81871i) q^{66} +(-4.48795 + 0.791347i) q^{67} +(-1.16324 - 0.671595i) q^{68} +(0.939187 - 6.54182i) q^{69} +(5.25543 + 6.26318i) q^{70} +(8.59275 - 3.12750i) q^{71} +(-0.331277 + 2.98165i) 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} +(-5.45938 + 4.88641i) q^{78} +(6.41515 - 7.64528i) q^{79} +(0.882820 - 2.42553i) q^{80} +(6.10110 - 6.61639i) q^{81} +(4.95792 - 4.16019i) q^{82} +(12.3308 - 7.11920i) q^{83} +(-2.04012 - 5.09290i) q^{84} +(-0.602044 - 3.41436i) q^{85} +(2.17066 + 12.3104i) q^{86} +(4.90493 + 12.2446i) q^{87} +(2.16590 - 1.25049i) q^{88} +(-12.7492 + 10.6978i) q^{89} +(-6.44529 + 4.29200i) q^{90} +(4.58274 - 12.5910i) q^{91} +(2.45265 - 2.92296i) q^{92} +(-10.2707 + 9.19278i) 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} +(-7.45703 - 0.828515i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9} - 12 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{17} - 6 q^{19} - 24 q^{22} + 3 q^{24} - 18 q^{25} + 18 q^{26} - 6 q^{27} + 6 q^{28} - 6 q^{29} - 24 q^{33} - 6 q^{34} - 24 q^{35}+ \cdots - 102 q^{99}+O(q^{100}) $ 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 - 12 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^17 - 6 * q^19 - 24 * q^22 + 3 * q^24 - 18 * q^25 + 18 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 - 24 * q^33 - 6 * q^34 - 24 * q^35 + 3 * q^38 + 6 * q^39 + 3 * q^41 - 6 * q^43 + 24 * q^44 - 54 * q^45 + 18 * q^46 + 30 * q^47 + 21 * q^49 + 3 * q^50 + 42 * q^51 - 6 * q^52 - 60 * q^53 + 54 * q^54 + 30 * q^55 + 12 * q^57 + 12 * q^58 + 3 * q^59 + 24 * q^60 + 54 * q^61 + 6 * q^62 - 18 * q^63 - 9 * q^64 + 24 * q^65 - 27 * q^66 - 15 * q^67 - 27 * q^68 + 30 * q^69 + 24 * q^70 + 36 * q^71 + 6 * q^72 - 42 * q^73 + 6 * q^74 - 24 * q^78 - 6 * q^79 - 3 * q^81 + 3 * q^82 + 36 * q^83 - 30 * q^84 - 6 * q^86 - 60 * q^89 - 18 * q^91 - 66 * q^93 + 6 * q^95 + 9 * q^97 + 12 * q^98 - 102 * q^99

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
$3$	−1.69526	+	0.355087i	−0.978760	+	0.205010i
$3$	−1.69526	+	0.355087i	−0.978760	+	0.205010i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−0.882820	−	2.42553i	−0.394809	−	1.08473i	−0.964779	−	0.263063i	$-0.915267\pi$
$5$	−0.882820	−	2.42553i	−0.394809	−	1.08473i	0.569970	−	0.821666i	$-0.306955\pi$
$6$	0.0553136	+	1.73117i	0.0225817	+	0.706746i
$7$	−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
$9$	2.74783	−	1.20393i	0.915942	−	0.401311i
$10$	−2.54198	+	0.448219i	−0.803844	+	0.141739i
$11$	−2.16590	−	1.25049i	−0.653045	−	0.377036i	0.136577	−	0.990629i	$-0.456390\pi$
$11$	−2.16590	−	1.25049i	−0.653045	−	0.377036i	−0.789622	+	0.613594i	$0.789723\pi$
$12$	1.71447	+	0.246141i	0.494925	+	0.0710547i
$13$	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
$15$	2.35788	+	3.79843i	0.608803	+	0.980749i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	1.32278	+	0.233243i	0.320822	+	0.0565696i	0.331740	−	0.943371i	$-0.392364\pi$
$17$	1.32278	+	0.233243i	0.320822	+	0.0565696i	−0.0109180	+	0.999940i	$0.503475\pi$
$18$	−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
$21$	3.65896	+	4.08800i	0.798450	+	0.892075i
$22$	−1.60759	+	1.91586i	−0.342740	+	0.408462i
$23$	−1.30503	+	3.58554i	−0.272117	+	0.747636i	0.726080	+	0.687611i	$0.241340\pi$
$23$	−1.30503	+	3.58554i	−0.272117	+	0.747636i	−0.998197	+	0.0600255i	$0.980882\pi$
$24$	0.540116	−	1.64568i	0.110251	−	0.335924i
$25$	−1.27359	+	1.06867i	−0.254718	+	0.213734i
$26$	3.66340	−	2.11506i	0.718451	−	0.414798i
$27$	−4.23078	+	3.01670i	−0.814215	+	0.580564i
$28$	0.550036	+	3.11941i	0.103947	+	0.589513i
$29$	−1.32242	−	7.49981i	−0.245567	−	1.39268i	−0.819172	−	0.573547i	$-0.805567\pi$
$29$	−1.32242	−	7.49981i	−0.245567	−	1.39268i	0.573606	−	0.819132i	$-0.305544\pi$
$30$	4.15016	−	1.66247i	0.757712	−	0.303525i
$31$	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
$33$	4.11581	+	1.35082i	0.716470	+	0.235147i
$34$	0.459398	−	1.26219i	0.0787861	−	0.216463i
$35$	−5.25543	+	6.26318i	−0.888330	+	1.05867i
$36$	−2.99388	+	0.191514i	−0.498980	+	0.0319190i
$37$		−	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	0.941805	−	0.336158i	$-0.109128\pi$
$41$	4.95792	+	4.16019i	0.774297	+	0.649712i	−0.167509	+	0.985871i	$0.553572\pi$
$42$	4.66127	−	2.89350i	0.719249	−	0.446476i
$43$	−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
$45$	−5.34601	−	5.60207i	−0.796935	−	0.835108i
$46$	3.30445	+	1.90782i	0.487214	+	0.281293i
$47$	6.16940	−	1.08783i	0.899899	−	0.158676i	0.295486	−	0.955347i	$-0.404519\pi$
$47$	6.16940	−	1.08783i	0.899899	−	0.158676i	0.604414	+	0.796671i	$0.293407\pi$
$48$	−1.52689	−	0.817681i	−0.220388	−	0.118022i
$49$	−1.51662	+	2.62686i	−0.216660	+	0.375266i
$50$	0.831277	+	1.43981i	0.117560	+	0.203621i
$51$	−2.32529	+	0.0742967i	−0.325605	+	0.0104036i
$52$	−1.44679	−	3.97502i	−0.200633	−	0.551236i
$53$	−3.46508	−	1.26118i	−0.475965	−	0.173237i	0.0928877	−	0.995677i	$-0.470390\pi$
$53$	−3.46508	−	1.26118i	−0.475965	−	0.173237i	−0.568853	+	0.822440i	$0.692612\pi$
$54$	2.23620	+	4.69035i	0.304308	+	0.638276i
$55$	−1.12098	+	6.35742i	−0.151153	+	0.857234i
$56$	3.16753			0.423279
$57$	−4.26694	+	6.22842i	−0.565170	+	0.824974i
$58$	−7.61550			−0.999964
$59$	−1.54335	+	8.75275i	−0.200927	+	1.13951i	0.702796	+	0.711392i	$0.251935\pi$
$59$	−1.54335	+	8.75275i	−0.200927	+	1.13951i	−0.903722	+	0.428119i	$0.859176\pi$
$60$	−0.916549	−	4.37580i	−0.118326	−	0.564913i
$61$	−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
$63$	−7.65449	−	5.63098i	−0.964375	−	0.709437i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	5.45938	−	9.45593i	0.677153	−	1.17286i
$66$	2.04500	−	3.81871i	0.251722	−	0.470051i
$67$	−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
$69$	0.939187	−	6.54182i	0.113065	−	0.787543i
$70$	5.25543	+	6.26318i	0.628144	+	0.748593i
$71$	8.59275	−	3.12750i	1.01977	−	0.371166i	0.222594	−	0.974911i	$-0.428548\pi$
$71$	8.59275	−	3.12750i	1.01977	−	0.371166i	0.797178	+	0.603745i	$0.206325\pi$
$72$	−0.331277	+	2.98165i	−0.0390414	+	0.351391i
$73$	−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
$78$	−5.45938	+	4.88641i	−0.618153	+	0.553277i
$79$	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
$81$	6.10110	−	6.61639i	0.677900	−	0.735155i
$82$	4.95792	−	4.16019i	0.547511	−	0.459416i
$83$	12.3308	−	7.11920i	1.35348	−	0.781433i	0.364747	−	0.931107i	$-0.381156\pi$
$83$	12.3308	−	7.11920i	1.35348	−	0.781433i	0.988735	+	0.149673i	$0.0478222\pi$
$84$	−2.04012	−	5.09290i	−0.222595	−	0.555681i
$85$	−0.602044	−	3.41436i	−0.0653008	−	0.370339i
$86$	2.17066	+	12.3104i	0.234068	+	1.32747i
$87$	4.90493	+	12.2446i	0.525864	+	1.31275i
$88$	2.16590	−	1.25049i	0.230886	−	0.133302i
$89$	−12.7492	+	10.6978i	−1.35141	+	1.13397i	−0.372879	+	0.927880i	$0.621629\pi$
$89$	−12.7492	+	10.6978i	−1.35141	+	1.13397i	−0.978533	+	0.206089i	$0.933926\pi$
$90$	−6.44529	+	4.29200i	−0.679393	+	0.452416i
$91$	4.58274	−	12.5910i	0.480402	−	1.31989i
$92$	2.45265	−	2.92296i	0.255707	−	0.304739i
$93$	−10.2707	+	9.19278i	−1.06502	+	0.953247i
$94$		−	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
$99$	−7.45703	−	0.828515i	−0.749460	−	0.0832689i
$100$	1.56229	−	0.568627i	0.156229	−	0.0568627i
$101$	7.56338	+	9.01368i	0.752584	+	0.896895i	0.997355	−	0.0726860i	$-0.0231571\pi$
$101$	7.56338	+	9.01368i	0.752584	+	0.896895i	−0.244771	+	0.969581i	$0.578713\pi$
$102$	−0.330614	+	2.30286i	−0.0327357	+	0.228017i
$103$	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
$105$	6.68536	−	12.4839i	0.652424	−	1.21830i
$106$	−1.84373	+	3.19343i	−0.179079	+	0.310174i
$107$	2.82951	+	4.90085i	0.273539	+	0.473783i	0.969765	−	0.244039i	$-0.0784725\pi$
$107$	2.82951	+	4.90085i	0.273539	+	0.473783i	−0.696227	+	0.717822i	$0.745139\pi$
$108$	5.00741	−	1.38776i	0.481838	−	0.133537i
$109$	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
$111$	1.45752	+	6.95852i	0.138342	+	0.660473i
$112$	0.550036	−	3.11941i	0.0519735	−	0.294756i
$113$	5.15697			0.485127			0.242564	−	0.970136i	$-0.422012\pi$
$113$	5.15697			0.485127			0.242564	+	0.970136i	$0.422012\pi$
$114$	5.39285	+	5.28367i	0.505087	+	0.494861i
$115$	9.84893			0.918417
$116$	−1.32242	+	7.49981i	−0.122783	+	0.696339i
$117$	11.3728	+	5.63065i	1.05142	+	0.520554i
$118$	8.35178	+	3.03980i	0.768843	+	0.279836i
$119$	−1.45516	−	3.99801i	−0.133394	−	0.366497i
$120$	−4.46848	+	0.142775i	−0.407914	+	0.0130335i
$121$	−2.37257	−	4.10941i	−0.215688	−	0.373583i
$122$	−0.0709282	+	0.122851i	−0.00642154	+	0.0111224i
$123$	−9.88220	−	5.29211i	−0.891048	−	0.477174i
$124$	−7.83721	+	1.38191i	−0.703802	+	0.124099i
$125$	−7.46045	−	4.30729i	−0.667283	−	0.385256i
$126$	−6.87462	+	6.56039i	−0.612440	+	0.584446i
$127$	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
$129$	18.3952	−	11.4189i	1.61961	−	1.00538i
$130$	−8.36426	−	7.01845i	−0.733594	−	0.615559i
$131$	−4.43285	−	0.781631i	−0.387300	−	0.0682914i	−0.0233919	−	0.999726i	$-0.507447\pi$
$131$	−4.43285	−	0.781631i	−0.387300	−	0.0682914i	−0.363908	+	0.931435i	$0.618558\pi$
$132$	−3.40559	−	2.67704i	−0.296418	−	0.233006i
$133$	−13.2557	−	3.86224i	−1.14942	−	0.334898i
$134$			4.55719i			0.393681i
$135$	11.0521	+	7.59868i	0.951214	+	0.653990i
$136$	−0.863386	+	1.02894i	−0.0740347	+	0.0882312i
$137$	−2.69063	+	7.39245i	−0.229876	+	0.631580i	−0.999980	−	0.00633905i	$-0.997982\pi$
$137$	−2.69063	+	7.39245i	−0.229876	+	0.631580i	0.770104	+	0.637919i	$0.220204\pi$
$138$	−6.27935	−	2.06089i	−0.534534	−	0.175435i
$139$	−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
$141$	−10.0725	+	4.03483i	−0.848255	+	0.339794i
$142$	−1.58788	−	9.00529i	−0.133252	−	0.755707i
$143$	−1.83710	−	10.4187i	−0.153626	−	0.871255i
$144$	2.87883	+	0.844003i	0.239902	+	0.0703336i
$145$	−17.0235	+	9.82854i	−1.41373	+	0.816216i
$146$	−1.67672	+	1.40694i	−0.138767	+	0.116439i
$147$	1.63830	−	4.99175i	0.135125	−	0.411713i
$148$	−1.40389	+	3.85714i	−0.115399	+	0.317055i
$149$	8.79633	−	10.4831i	0.720624	−	0.858806i	−0.274068	−	0.961710i	$-0.588369\pi$
$149$	8.79633	−	10.4831i	0.720624	−	0.858806i	0.994691	+	0.102905i	$0.0328137\pi$
$150$	−1.92049	−	2.14569i	−0.156808	−	0.175195i
$151$			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
$156$	3.86416	+	6.22496i	0.309381	+	0.498396i
$157$	−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
$159$	6.32204	+	0.907634i	0.501371	+	0.0719800i
$160$	−2.23538	−	1.29060i	−0.176722	−	0.102031i
$161$	11.9026	−	2.09874i	0.938053	−	0.165404i
$162$	−5.45643	−	7.15733i	−0.428698	−	0.562333i
$163$	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
$165$	−0.357076	−	11.1755i	−0.0277983	−	0.870014i
$166$	−4.86982	−	13.3797i	−0.377971	−	1.03847i
$167$	−2.20429	−	0.802294i	−0.170573	−	0.0620834i	0.255322	−	0.966856i	$-0.417818\pi$
$167$	−2.20429	−	0.802294i	−0.170573	−	0.0620834i	−0.425895	+	0.904773i	$0.640041\pi$
$168$	−5.36979	+	1.12475i	−0.414288	+	0.0867763i
$169$	−0.849826	+	4.81960i	−0.0653712	+	0.370739i
$170$	−3.46703			−0.265909
$171$	5.02195	−	12.0739i	0.384038	−	0.923317i
$172$	12.5003			0.953142
$173$	2.59056	−	14.6918i	0.196956	−	1.11700i	−0.712649	−	0.701521i	$-0.752505\pi$
$173$	2.59056	−	14.6918i	0.196956	−	1.11700i	0.909605	−	0.415474i	$-0.136384\pi$
$174$	12.9103	−	2.70417i	0.978725	−	0.205002i
$175$	4.94860	+	1.80114i	0.374079	+	0.136154i
$176$	−0.855383	−	2.35014i	−0.0644769	−	0.177149i
$177$	−0.491615	−	15.3862i	−0.0369520	−	1.15650i
$178$	8.32145	+	14.4132i	0.623719	+	1.08031i
$179$	−0.0974666	+	0.168817i	−0.00728500	+	0.0126180i	−0.869645	−	0.493678i	$-0.835652\pi$
$179$	−0.0974666	+	0.168817i	−0.00728500	+	0.0126180i	0.862360	+	0.506296i	$0.168986\pi$
$180$	3.10758	+	7.09267i	0.231625	+	0.528656i
$181$	−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
$183$	0.243209	+	0.0349166i	0.0179785	+	0.00258111i
$184$	−2.45265	−	2.92296i	−0.180812	−	0.215483i
$185$	−9.95603	+	3.62370i	−0.731982	+	0.266420i
$186$	7.26963	+	11.7110i	0.533035	+	0.858691i
$187$	−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	$-0.133404\pi$
$192$	1.15515	+	1.29060i	0.0833655	+	0.0931408i
$193$	−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
$195$	−5.89740	+	17.9688i	−0.422322	+	1.28677i
$196$	2.32360	−	1.94973i	0.165971	−	0.139266i
$197$	−19.7987	+	11.4308i	−1.41060	+	0.814411i	−0.995445	−	0.0953383i	$-0.969607\pi$
$197$	−19.7987	+	11.4308i	−1.41060	+	0.814411i	−0.415157	+	0.909750i	$0.636273\pi$
$198$	−2.11083	+	7.19987i	−0.150010	+	0.511673i
$199$	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
$201$	7.32726	−	2.93516i	0.516825	−	0.207030i
$202$	10.1901	−	5.88326i	0.716974	−	0.413945i
$203$	−18.4788	+	15.5055i	−1.29696	+	1.08827i
$204$	2.21047	+	0.725479i	0.154764	+	0.0507937i
$205$	5.71370	−	15.6983i	0.399062	−	1.09641i
$206$	5.02879	−	5.99308i	0.350373	−	0.417558i
$207$	0.730751	+	11.4236i	0.0507907	+	0.793995i
$208$			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
$213$	−13.4564	+	8.35311i	−0.922019	+	0.572346i
$214$	5.31773	−	1.93550i	0.363513	−	0.132308i
$215$	20.7400	+	24.7170i	1.41446	+	1.68569i
$216$	−0.497145	−	5.17232i	−0.0338265	−	0.351931i
$217$	−21.8304	−	12.6038i	−1.48194	−	0.855600i
$218$	16.2542	−	2.86605i	1.10087	−	0.194113i
$219$	3.34207	+	1.78974i	0.225836	+	0.120940i
$220$	3.22774	−	5.59062i	0.217614	−	0.376919i
$221$	2.84093	+	4.92064i	0.191102	+	0.330998i
$222$	7.10590	−	0.227045i	0.476917	−	0.0152383i
$223$	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
$225$	−2.21300	+	4.46983i	−0.147533	+	0.297989i
$226$	0.895499	−	5.07863i	0.0595677	−	0.337825i
$227$	20.0547			1.33108			0.665539	−	0.746363i	$-0.268202\pi$
$227$	20.0547			1.33108			0.665539	+	0.746363i	$0.268202\pi$
$228$	6.13986	−	4.39342i	0.406622	−	0.290961i
$229$	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
$231$	−2.81297	−	13.4297i	−0.185080	−	0.883609i
$232$	7.15623	+	2.60466i	0.469830	+	0.171004i
$233$	−2.12137	−	5.82843i	−0.138976	−	0.381833i	0.850606	−	0.525803i	$-0.176235\pi$
$233$	−2.12137	−	5.82843i	−0.138976	−	0.381833i	−0.989582	+	0.143970i	$0.954013\pi$
$234$	7.51998	−	10.2223i	0.491597	−	0.668253i
$235$	−8.08503	−	14.0037i	−0.527409	−	0.913500i
$236$	4.44389	−	7.69704i	0.289272	−	0.501035i
$237$	−8.16062	+	15.2387i	−0.530089	+	0.989859i
$238$	−4.18996	+	0.738802i	−0.271595	+	0.0478895i
$239$	−0.498666	−	0.287905i	−0.0322560	−	0.0186230i	0.483785	−	0.875187i	$-0.339262\pi$
$239$	−0.498666	−	0.287905i	−0.0322560	−	0.0186230i	−0.516041	+	0.856564i	$0.672595\pi$
$240$	−0.635337	+	4.42538i	−0.0410108	+	0.285657i
$241$	−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
$243$	−7.99356	+	13.3829i	−0.512787	+	0.858516i
$244$	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
$249$	−18.3760	+	16.4474i	−1.16453	+	1.04231i
$250$	−5.53735	+	6.59916i	−0.350213	+	0.417367i
$251$	2.05161	−	5.63675i	0.129496	−	0.355789i	−0.857952	−	0.513730i	$-0.828263\pi$
$251$	2.05161	−	5.63675i	0.129496	−	0.355789i	0.987449	+	0.157941i	$0.0504856\pi$
$252$	5.26696	+	7.90938i	0.331787	+	0.498244i
$253$	7.31023	−	6.13401i	0.459590	−	0.385642i
$254$	6.78694	−	3.91844i	0.425850	−	0.245865i
$255$	2.23302	+	5.57446i	0.139837	+	0.349086i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	3.23144	+	18.3264i	0.201572	+	1.14317i	0.902744	+	0.430178i	$0.141549\pi$
$257$	3.23144	+	18.3264i	0.201572	+	1.14317i	−0.701172	+	0.712992i	$0.747340\pi$
$258$	−8.05112	−	20.0986i	−0.501241	−	1.25129i
$259$	−11.2598	+	6.50086i	−0.699651	+	0.403944i
$260$	−8.36426	+	7.01845i	−0.518729	+	0.435266i
$261$	−12.6630	−	19.0161i	−0.783822	−	1.17706i
$262$	−1.53951	+	4.22977i	−0.0951113	+	0.261316i
$263$	−1.37946	+	1.64398i	−0.0850614	+	0.101372i	−0.806896	−	0.590693i	$-0.798854\pi$
$263$	−1.37946	+	1.64398i	−0.0850614	+	0.101372i	0.721835	+	0.692065i	$0.243299\pi$
$264$	−3.22774	+	2.88899i	−0.198654	+	0.177805i
$265$			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	$0.0136646\pi$
$269$	19.9247	+	16.7188i	1.21483	+	1.01936i	0.215752	+	0.976448i	$0.430780\pi$
$270$	9.40242	−	9.56470i	0.572213	−	0.582089i
$271$	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
$273$	−3.29805	+	22.9723i	−0.199607	+	1.39035i
$274$	6.81292	+	3.93344i	0.411583	+	0.237628i
$275$	4.09483	−	0.722029i	0.246928	−	0.0435400i
$276$	−3.11998	+	5.82608i	−0.187801	+	0.350689i
$277$	−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
$279$	14.1473	−	19.2312i	0.846977	−	1.15134i
$280$	−2.79636	−	7.68293i	−0.167114	−	0.459143i
$281$	−28.0317	−	10.2027i	−1.67223	−	0.608642i	−0.680017	−	0.733196i	$-0.738028\pi$
$281$	−28.0317	−	10.2027i	−1.67223	−	0.608642i	−0.992213	+	0.124555i	$0.960250\pi$
$282$	2.22447	+	10.6201i	0.132465	+	0.632417i
$283$	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
$285$	18.8741	+	4.85101i	1.11801	+	0.287349i
$286$	−10.5794			−0.625574
$287$	3.55989	−	20.1891i	0.210134	−	1.19173i
$288$	1.33108	−	2.68853i	0.0784349	−	0.158423i
$289$	−14.2794	−	5.19728i	−0.839966	−	0.305723i
$290$	6.72312	+	18.4716i	0.394795	+	1.08469i
$291$	−0.946743	+	0.0302500i	−0.0554991	+	0.00177328i
$292$	1.09440	+	1.89556i	0.0640451	+	0.110929i
$293$	4.63502	−	8.02810i	0.270781	−	0.469006i	−0.698281	−	0.715824i	$-0.746051\pi$
$293$	4.63502	−	8.02810i	0.270781	−	0.469006i	0.969062	+	0.246817i	$0.0793847\pi$
$294$	−4.63143	−	2.48022i	−0.270110	−	0.144649i
$295$	22.5925	−	3.98367i	1.31539	−	0.231938i
$296$	3.55476	+	2.05234i	0.206616	+	0.119290i
$297$	12.9358	−	1.24335i	0.750612	−	0.0721463i
$298$	−8.79633	−	10.4831i	−0.509558	−	0.607267i
$299$	−15.1673	+	5.52043i	−0.877146	+	0.319255i
$300$	−2.44658	+	1.51872i	−0.141253	+	0.0876834i
$301$	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
$306$	−0.257240	−	4.02135i	−0.0147054	−	0.229885i
$307$	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
$309$	−12.8749	−	4.22555i	−0.732425	−	0.240383i
$310$	−15.7356	+	13.2038i	−0.893724	+	0.749924i
$311$	19.8290	−	11.4483i	1.12440	−	0.649172i	0.181879	−	0.983321i	$-0.441782\pi$
$311$	19.8290	−	11.4483i	1.12440	−	0.649172i	0.942520	+	0.334148i	$0.108449\pi$
$312$	6.80139	−	2.72450i	0.385053	−	0.154245i
$313$	−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
$315$	−6.90057	+	23.5373i	−0.388803	+	1.32618i
$316$	−8.64310	+	4.99010i	−0.486213	+	0.280715i
$317$	15.9117	−	13.3515i	0.893689	−	0.749894i	−0.0752579	−	0.997164i	$-0.523978\pi$
$317$	15.9117	−	13.3515i	0.893689	−	0.749894i	0.968947	+	0.247270i	$0.0795336\pi$
$318$	1.99166	−	6.06839i	0.111687	−	0.340298i
$319$	−6.51417	+	17.8975i	−0.364723	+	1.00207i
$320$	−1.65916	+	1.97731i	−0.0927498	+	0.110535i
$321$	−6.53699	−	7.30350i	−0.364859	−	0.407642i
$322$		−	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
$327$	−15.0770	−	24.2882i	−0.833760	−	1.34314i
$328$	−6.08179	+	2.21359i	−0.335811	+	0.122225i
$329$	−12.7550	−	15.2008i	−0.703204	−	0.838046i
$330$	−11.0678	−	1.58896i	−0.609260	−	0.0874693i
$331$	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
$333$	−4.94176	−	11.2790i	−0.270807	−	0.618083i
$334$	−1.17288	+	2.03148i	−0.0641769	+	0.111158i
$335$	5.88149	+	10.1870i	0.321340	+	0.556577i
$336$	0.175207	+	5.48352i	0.00955835	+	0.299151i
$337$	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
$339$	−8.74242	+	1.83117i	−0.474823	+	0.0994558i
$340$	−0.602044	+	3.41436i	−0.0326504	+	0.185170i
$341$	−19.9030			−1.07781
$342$	−11.0185	−	7.04227i	−0.595810	−	0.380803i
$343$	−12.5648			−0.678437
$344$	2.17066	−	12.3104i	0.117034	−	0.663734i
$345$	−16.6965	+	3.49723i	−0.898910	+	0.188284i
$346$	−14.0187	−	5.10240i	−0.753652	−	0.274307i
$347$	4.73541	+	13.0104i	0.254210	+	0.698436i	0.999498	+	0.0316932i	$0.0100899\pi$
$347$	4.73541	+	13.0104i	0.254210	+	0.698436i	−0.745288	+	0.666743i	$0.767688\pi$
$348$	−0.421241	−	13.1837i	−0.0225809	−	0.706721i
$349$	−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
$351$	−21.2793	−	5.50708i	−1.13581	−	0.293946i
$352$	−2.46298	+	0.434289i	−0.131277	+	0.0231477i
$353$	19.7460	+	11.4004i	1.05098	+	0.606781i	0.922922	−	0.384987i	$-0.125794\pi$
$353$	19.7460	+	11.4004i	1.05098	+	0.606781i	0.128053	+	0.991767i	$0.459127\pi$
$354$	−15.2378	−	2.18764i	−0.809882	−	0.116272i
$355$	−15.1717	−	18.0809i	−0.805230	−	0.959636i
$356$	15.6392	−	5.69220i	0.828876	−	0.301686i
$357$	3.88651	+	6.26097i	0.205696	+	0.331366i
$358$	0.149328	+	0.125301i	0.00789221	+	0.00662235i
$359$	7.31056	+	1.28905i	0.385837	+	0.0680334i	0.363202	−	0.931710i	$-0.381683\pi$
$359$	7.31056	+	1.28905i	0.385837	+	0.0680334i	0.0226346	+	0.999744i	$0.492795\pi$
$360$	7.52454	−	1.82874i	0.396578	−	0.0963831i
$361$	0.824917	−	18.9821i	0.0434167	−	0.999057i
$362$			7.11314i			0.373858i
$363$	5.48133	+	6.12406i	0.287695	+	0.321430i
$364$	−8.61274	+	10.2643i	−0.451430	+	0.537993i
$365$	−1.93232	+	5.30901i	−0.101142	+	0.277886i
$366$	0.0766189	−	0.233451i	0.00400494	−	0.0122027i
$367$	−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
$369$	18.6321	+	5.46248i	0.969947	+	0.284365i
$370$	1.83980	+	10.4340i	0.0956467	+	0.542439i
$371$	2.02823	+	11.5027i	0.105301	+	0.597189i
$372$	12.7954	−	5.12560i	0.663412	−	0.265750i
$373$	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
$375$	14.1769	+	4.65288i	0.732091	+	0.240274i
$376$	−2.14261	+	5.88677i	−0.110497	+	0.303587i
$377$	20.7071	−	24.6778i	1.06647	−	1.27097i
$378$	9.32478	−	13.5627i	0.479615	−	0.697588i
$379$			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	0.517592	−	0.855628i	$-0.326829\pi$
$383$	−4.60213	−	3.86165i	−0.235158	−	0.197321i	−0.752750	+	0.658307i	$0.771273\pi$
$384$	1.47158	−	0.913487i	0.0750962	−	0.0466162i
$385$	19.2148	−	6.99361i	0.979276	−	0.356427i
$386$	10.3664	+	12.3541i	0.527634	+	0.628809i
$387$	−27.1300	+	25.8899i	−1.37910	+	1.31606i
$388$	−0.473613	−	0.273441i	−0.0240441	−	0.0138818i
$389$	−20.4701	+	3.60942i	−1.03787	+	0.183005i	−0.666520	−	0.745487i	$-0.732217\pi$
$389$	−20.4701	+	3.60942i	−1.03787	+	0.183005i	−0.371353	+	0.928492i	$0.621106\pi$
$390$	16.6718	+	8.92806i	0.844208	+	0.452090i
$391$	−2.56257	+	4.43850i	−0.129595	+	0.224465i
$392$	−1.51662	−	2.62686i	−0.0766009	−	0.132677i
$393$	7.79238	−	0.248979i	0.393074	−	0.0125593i
$394$	7.81913	+	21.4829i	0.393922	+	1.08229i
$395$	−24.2072	−	8.81072i	−1.21800	−	0.443315i
$396$	6.72395	+	3.32900i	0.337891	+	0.167289i
$397$	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
$399$	23.8434	+	1.84056i	1.19366	+	0.0921432i
$400$	−1.66255			−0.0831277
$401$	1.59795	−	9.06241i	0.0797977	−	0.452555i	−0.918561	−	0.395280i	$-0.870648\pi$
$401$	1.59795	−	9.06241i	0.0797977	−	0.452555i	0.998358	−	0.0572753i	$-0.0182413\pi$
$402$	−1.61820	−	7.72562i	−0.0807084	−	0.385319i
$403$	31.6336	+	11.5137i	1.57578	+	0.573538i
$404$	−4.02439	−	11.0569i	−0.200221	−	0.550102i
$405$	−21.4344	−	8.95729i	−1.06508	−	0.445092i
$406$	12.0612	+	20.8905i	0.598585	+	1.03678i
$407$	−5.13285	+	8.89036i	−0.254426	+	0.440679i
$408$	1.09830	−	2.05091i	0.0543740	−	0.101535i
$409$	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
$411$	1.93636	−	13.4875i	0.0955136	−	0.665292i
$412$	−5.02879	−	5.99308i	−0.247751	−	0.295258i
$413$	26.4545	−	9.62865i	1.30174	−	0.473795i
$414$	11.3769	+	1.26404i	0.559146	+	0.0621241i
$415$	−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	$0.833744\pi$
$420$	−10.5519	+	9.44447i	−0.514881	+	0.460843i
$421$	−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
$423$	15.6428	−	10.4167i	0.760577	−	0.506478i
$424$	2.82476	−	2.37025i	0.137182	−	0.115110i
$425$	−1.93394	+	1.11656i	−0.0938101	+	0.0541613i
$426$	5.88953	+	14.7025i	0.285349	+	0.712338i
$427$	0.0780261	+	0.442508i	0.00377595	+	0.0214144i
$428$	−0.982678	−	5.57304i	−0.0474995	−	0.269383i
$429$	6.81391	+	17.0101i	0.328979	+	0.821255i
$430$	27.9430	−	16.1329i	1.34753	−	0.777997i
$431$	−7.15165	+	6.00095i	−0.344483	+	0.289055i	−0.798570	−	0.601902i	$-0.794410\pi$
$431$	−7.15165	+	6.00095i	−0.344483	+	0.289055i	0.454087	+	0.890957i	$0.349965\pi$
$432$	−5.18006	−	0.408571i	−0.249226	−	0.0196574i
$433$	−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
$435$	25.3694	−	22.7068i	1.21637	−	1.08871i
$436$		−	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
$441$	−1.00484	+	9.04407i	−0.0478497	+	0.430670i
$442$	5.33920	−	1.94331i	0.253960	−	0.0924339i
$443$	17.0745	+	20.3486i	0.811235	+	0.966792i	0.999884	−	0.0152527i	$-0.00485526\pi$
$443$	17.0745	+	20.3486i	0.811235	+	0.966792i	−0.188649	+	0.982045i	$0.560411\pi$
$444$	1.01033	−	7.03737i	0.0479482	−	0.333979i
$445$	37.2032	+	21.4793i	1.76360	+	1.01821i
$446$	6.57346	−	1.15908i	0.311262	−	0.0548839i
$447$	−11.1897	+	20.8950i	−0.529254	+	0.988300i
$448$	−1.58376	+	2.74316i	−0.0748258	+	0.129602i
$449$	−5.66925	−	9.81944i	−0.267549	−	0.463408i	0.700680	−	0.713476i	$-0.252880\pi$
$449$	−5.66925	−	9.81944i	−0.267549	−	0.463408i	−0.968228	+	0.250068i	$0.919547\pi$
$450$	4.01764	+	2.95556i	0.189394	+	0.139326i
$451$	−5.53612	−	15.2104i	−0.260686	−	0.716229i
$452$	−4.84597	−	1.76379i	−0.227935	−	0.0829616i
$453$	−3.06672	−	14.6412i	−0.144087	−	0.687903i
$454$	3.48246	−	19.7500i	0.163440	−	0.926915i
$455$	−34.5855			−1.62139
$456$	−3.26050	−	6.80949i	−0.152687	−	0.318884i
$457$	−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
$459$	−6.30004	+	3.00364i	−0.294061	+	0.140198i
$460$	−9.25496	−	3.36853i	−0.431515	−	0.157059i
$461$	9.40832	+	25.8492i	0.438189	+	1.20392i	0.940669	+	0.339326i	$0.110199\pi$
$461$	9.40832	+	25.8492i	0.438189	+	1.20392i	−0.502480	+	0.864589i	$0.667579\pi$
$462$	−13.7141	+	0.438189i	−0.638039	+	0.0203864i
$463$	−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
$465$	31.3645	+	16.7963i	1.45450	+	0.778911i
$466$	−6.10825	+	1.07705i	−0.282959	+	0.0498934i
$467$	−17.7092	−	10.2244i	−0.819486	−	0.473130i	0.0307535	−	0.999527i	$-0.490209\pi$
$467$	−17.7092	−	10.2244i	−0.819486	−	0.473130i	−0.850239	+	0.526397i	$0.823543\pi$
$468$	−8.76117	−	9.18082i	−0.404985	−	0.424384i
$469$	9.27865	+	11.0579i	0.428448	+	0.510605i
$470$	−15.1949	+	5.53049i	−0.700888	+	0.255102i
$471$	5.05488	−	3.13783i	0.232916	−	0.144584i
$472$	−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
$477$	−11.0398	+	0.706200i	−0.505478	+	0.0323347i
$478$	−0.370124	+	0.441096i	−0.0169291	+	0.0201753i
$479$	−3.36367	+	9.24160i	−0.153690	+	0.422259i	−0.992512	−	0.122146i	$-0.961022\pi$
$479$	−3.36367	+	9.24160i	−0.153690	+	0.422259i	0.838822	+	0.544405i	$0.183245\pi$
$480$	4.24783	+	1.39414i	0.193886	+	0.0636337i
$481$	13.3011	−	11.1609i	0.606477	−	0.508895i
$482$	−1.47079	+	0.849159i	−0.0669925	+	0.0386781i
$483$	−19.4327	+	7.78437i	−0.884220	+	0.354201i
$484$	0.823985	+	4.67305i	0.0374539	+	0.212411i
$485$	−0.245123	−	1.39016i	−0.0111305	−	0.0631239i
$486$	11.7916	+	10.1960i	0.534876	+	0.462502i
$487$	−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
$489$	−4.14062	+	12.6161i	−0.187245	+	0.570519i
$490$	2.67780	−	7.35721i	0.120971	−	0.332365i
$491$	18.0754	−	21.5414i	0.815729	−	0.972148i	−0.184213	−	0.982886i	$-0.558974\pi$
$491$	18.0754	−	21.5414i	0.815729	−	0.972148i	0.999942	+	0.0107379i	$0.00341805\pi$
$492$	7.47622	+	8.35287i	0.337054	+	0.376577i
$493$		−	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
$498$	13.0066	+	20.9529i	0.582839	+	0.938922i
$499$	−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
$501$	4.02173	+	0.577385i	0.179677	+	0.0257957i
$502$	−5.19486	−	2.99925i	−0.231858	−	0.133863i
$503$	−25.8762	+	4.56267i	−1.15376	+	0.203439i	−0.717618	−	0.696437i	$-0.754767\pi$
$503$	−25.8762	+	4.56267i	−1.15376	+	0.203439i	−0.436144	+	0.899877i	$0.643656\pi$
$504$	8.70382	−	3.81349i	0.387699	−	0.169866i
$505$	15.1858	−	26.3026i	0.675761	−	1.17045i
$506$	−4.77142	−	8.26433i	−0.212115	−	0.367394i
$507$	−0.270702	−	8.47225i	−0.0120223	−	0.376266i
$508$	−2.68037	−	7.36426i	−0.118922	−	0.326736i
$509$	−25.0043	−	9.10082i	−1.10830	−	0.403387i	−0.277928	−	0.960602i	$-0.589648\pi$
$509$	−25.0043	−	9.10082i	−1.10830	−	0.403387i	−0.830368	+	0.557215i	$0.811870\pi$
$510$	5.87753	−	1.23110i	0.260261	−	0.0545140i
$511$	−1.20392	+	6.82777i	−0.0532583	+	0.302043i
$512$	1.00000			0.0441942
$513$	−4.22622	+	22.2517i	−0.186592	+	0.982437i
$514$	18.6091			0.820813
$515$	3.50661	−	19.8869i	0.154520	−	0.876324i
$516$	−21.1913	+	4.43871i	−0.932897	+	0.195403i
$517$	−14.7226	−	5.35860i	−0.647501	−	0.235671i
$518$	4.44685	+	12.2176i	0.195383	+	0.536811i
$519$	0.825191	+	25.8263i	0.0362219	+	1.13365i
$520$	5.45938	+	9.45593i	0.239410	+	0.414670i
$521$	−10.2977	+	17.8362i	−0.451151	+	0.781417i	−0.998458	−	0.0555154i	$-0.982320\pi$
$521$	−10.2977	+	17.8362i	−0.451151	+	0.781417i	0.547307	+	0.836932i	$0.315653\pi$
$522$	−20.9261	+	9.16855i	−0.915909	+	0.401296i
$523$	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
$525$	−9.02874	−	1.29622i	−0.394046	−	0.0565719i
$526$	1.37946	+	1.64398i	0.0601475	+	0.0716810i
$527$	10.0446	−	3.65594i	0.437550	−	0.159255i
$528$	2.28460	+	3.68037i	0.0994246	+	0.160168i
$529$	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
$534$	−19.2250	−	21.4793i	−0.831946	−	0.929498i
$535$	9.38920	−	11.1896i	0.405931	−	0.483769i
$536$	1.55865	−	4.28235i	0.0673234	−	0.184970i
$537$	0.105287	−	0.320799i	0.00454345	−	0.0138435i
$538$	19.9247	−	16.7188i	0.859015	−	0.720799i
$539$	6.56971	−	3.79302i	0.282977	−	0.163377i
$540$	−7.78668	−	10.9205i	−0.335085	−	0.469942i
$541$	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
$543$	11.4368	−	4.58137i	0.490802	−	0.196605i
$544$	1.16324	−	0.671595i	0.0498734	−	0.0287944i
$545$	32.6353	−	27.3842i	1.39794	−	1.17301i
$546$	22.0506	+	7.23704i	0.943678	+	0.309717i
$547$	−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
$549$	−0.424701	+	0.0271675i	−0.0181258	+	0.00115948i
$550$		−	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
$555$	15.5914	−	9.67838i	0.661816	−	0.410824i
$556$	7.07526	−	2.57518i	0.300058	−	0.109212i
$557$	−13.8808	−	16.5425i	−0.588147	−	0.700927i	0.387101	−	0.922037i	$-0.373476\pi$
$557$	−13.8808	−	16.5425i	−0.588147	−	0.700927i	−0.975249	+	0.221110i	$0.929032\pi$
$558$	−16.4824	−	17.2718i	−0.697754	−	0.731175i
$559$	−45.7937	−	26.4390i	−1.93687	−	1.11825i
$560$	−8.05179	+	1.41975i	−0.340250	+	0.0599953i
$561$	5.12926	+	2.74682i	0.216557	+	0.115971i
$562$	−14.9153	+	25.8341i	−0.629166	+	1.08975i
$563$	−13.0149	−	22.5424i	−0.548512	−	0.950051i	−0.998377	−	0.0569541i	$-0.981861\pi$
$563$	−13.0149	−	22.5424i	−0.548512	−	0.950051i	0.449865	−	0.893097i	$-0.351472\pi$
$564$	10.8450	−	0.346516i	0.456658	−	0.0145909i
$565$	−4.55268	−	12.5084i	−0.191533	−	0.526231i
$566$	−22.1991	−	8.07982i	−0.933099	−	0.339620i
$567$	−27.8125	−	6.25748i	−1.16802	−	0.262789i
$568$	−1.58788	+	9.00529i	−0.0666258	+	0.377854i
$569$	−4.80544			−0.201455			−0.100727	−	0.994914i	$-0.532117\pi$
$569$	−4.80544			−0.201455			−0.100727	+	0.994914i	$0.532117\pi$
$570$	8.05478	−	17.7450i	0.337377	−	0.743258i
$571$	−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
$573$	3.99403	+	19.0683i	0.166853	+	0.796591i
$574$	−19.2642	−	7.01161i	−0.804074	−	0.292659i
$575$	−2.16968	−	5.96115i	−0.0904820	−	0.248597i
$576$	−2.41655	−	1.77772i	−0.100690	−	0.0740717i
$577$	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
$579$	13.1869	−	24.6245i	0.548028	−	1.02336i
$580$	19.3584	−	3.41342i	0.803816	−	0.141734i
$581$	−39.0582	−	22.5503i	−1.62041	−	0.935543i
$582$	−0.134610	+	0.937613i	−0.00557976	+	0.0388653i
$583$	5.92793	+	7.06463i	0.245510	+	0.292587i
$584$	2.05680	−	0.748615i	0.0851112	−	0.0309779i
$585$	3.61714	−	32.5560i	0.149550	−	1.34602i
$586$	−7.10127	−	5.95867i	−0.293351	−	0.246150i
$587$	−14.9298	−	2.63253i	−0.616220	−	0.108656i	−0.143180	−	0.989697i	$-0.545733\pi$
$587$	−14.9298	−	2.63253i	−0.616220	−	0.108656i	−0.473041	+	0.881040i	$0.656844\pi$
$588$	−3.24678	+	4.13038i	−0.133895	+	0.170334i
$589$	9.70350	−	33.3038i	0.399826	−	1.37226i
$590$		−	22.9411i		−	0.944469i
$591$	29.5051	−	26.4085i	1.21368	−	1.08630i
$592$	2.63844	−	3.14437i	0.108439	−	0.129233i
$593$	0.398860	−	1.09586i	0.0163792	−	0.0450015i	−0.931234	−	0.364423i	$-0.881266\pi$
$593$	0.398860	−	1.09586i	0.0163792	−	0.0450015i	0.947613	+	0.319421i	$0.103489\pi$
$594$	1.02182	−	12.9552i	0.0419259	−	0.531558i
$595$	−8.41264	+	7.05905i	−0.344885	+	0.289393i
$596$	−11.8513	+	6.84233i	−0.485447	+	0.280273i
$597$	−0.215044	−	0.536831i	−0.00880116	−	0.0219710i
$598$	2.80280	+	15.8955i	0.114615	+	0.650014i
$599$	4.45202	+	25.2486i	0.181905	+	1.03163i	0.929868	+	0.367892i	$0.119921\pi$
$599$	4.45202	+	25.2486i	0.181905	+	1.03163i	−0.747964	+	0.663739i	$0.768968\pi$
$600$	1.07080	+	2.67313i	0.0437154	+	0.109130i
$601$	−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
$603$	−11.3794	+	7.57767i	−0.463404	+	0.308587i
$604$	2.95387	−	8.11568i	0.120191	−	0.330222i
$605$	−7.87294	+	9.38261i	−0.320081	+	0.381457i
$606$	−15.1858	+	13.5921i	−0.616882	+	0.552139i
$607$		−	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
$612$	−4.00493	−	0.444968i	−0.161890	−	0.0179868i
$613$	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
$615$	−4.11197	+	28.6415i	−0.165810	+	1.15494i
$616$	−6.86057	−	3.96095i	−0.276420	−	0.159591i
$617$	24.5040	−	4.32072i	0.986495	−	0.173946i	0.342950	−	0.939354i	$-0.388574\pi$
$617$	24.5040	−	4.32072i	0.986495	−	0.173946i	0.643545	+	0.765408i	$0.277463\pi$
$618$	−6.39705	+	11.9455i	−0.257327	+	0.480519i
$619$	−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
$621$	−5.29519	−	19.1065i	−0.212489	−	0.766718i
$622$	−7.83109	−	21.5157i	−0.313998	−	0.862702i
$623$	49.5376	+	18.0302i	1.98468	+	0.722366i
$624$	−1.50206	−	7.17117i	−0.0601307	−	0.287077i
$625$	−5.30472	+	30.0846i	−0.212189	+	1.20338i
$626$	−13.4317			−0.536841
$627$	17.0303	−	8.15441i	0.680126	−	0.325656i
$628$	3.43500			0.137072
$629$	0.957388	−	5.42961i	0.0381735	−	0.216493i
$630$	21.9815	+	10.8829i	0.875762	+	0.433587i
$631$	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
$633$	−4.44044	+	0.141879i	−0.176492	+	0.00563919i
$634$	−10.3856	−	17.9884i	−0.412465	−	0.714411i
$635$	10.1142	−	17.5184i	0.401372	−	0.695196i
$636$	−5.63035	−	3.01516i	−0.223258	−	0.119559i
$637$	−12.6361	+	2.22808i	−0.500659	+	0.0882796i
$638$	16.4945	+	9.52308i	0.653022	+	0.377022i
$639$	19.8461	−	18.9389i	0.785099	−	0.749212i
$640$	1.65916	+	1.97731i	0.0655840	+	0.0781600i
$641$	−8.36361	+	3.04411i	−0.330343	+	0.120235i	−0.501867	−	0.864945i	$-0.667353\pi$
$641$	−8.36361	+	3.04411i	−0.330343	+	0.120235i	0.171524	+	0.985180i	$0.445131\pi$
$642$	−8.32768	+	5.16943i	−0.328667	+	0.204021i
$643$	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	$0.0494539\pi$
$647$			7.87198i			0.309479i	−0.987955	+	0.154740i	$0.950546\pi$
$648$	2.67942	+	8.59190i	0.105257	+	0.337522i
$649$	14.2879	−	17.0277i	0.560850	−	0.668395i
$650$	−2.40536	+	6.60868i	−0.0943461	+	0.259214i
$651$	41.4837	+	13.6150i	1.62587	+	0.533614i
$652$	−5.87262	+	4.92772i	−0.229990	+	0.192984i
$653$	−1.40402	+	0.810613i	−0.0549437	+	0.0317217i	−0.527220	−	0.849729i	$-0.676766\pi$
$653$	−1.40402	+	0.810613i	−0.0549437	+	0.0317217i	0.472277	+	0.881450i	$0.343432\pi$
$654$	−26.5373	+	10.6303i	−1.03769	+	0.415679i
$655$	2.01754	+	11.4420i	0.0788318	+	0.447077i
$656$	1.12387	+	6.37378i	0.0438797	+	0.248854i
$657$	−6.30120	−	1.84736i	−0.245833	−	0.0720723i
$658$	−17.1847	+	9.92160i	−0.669930	+	0.386784i
$659$	−9.29693	+	7.80105i	−0.362157	+	0.303886i	−0.805650	−	0.592392i	$-0.798184\pi$
$659$	−9.29693	+	7.80105i	−0.362157	+	0.303886i	0.443493	+	0.896278i	$0.353739\pi$
$660$	−3.48672	+	10.6237i	−0.135720	+	0.413527i
$661$	−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
$663$	−6.56338	−	7.33299i	−0.254900	−	0.284790i
$664$			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
$669$	−6.09740	−	9.82258i	−0.235739	−	0.379763i
$670$	11.0536	−	4.02317i	0.427037	−	0.155429i
$671$	0.228047	+	0.271776i	0.00880367	+	0.0104918i
$672$	5.43064	+	0.779658i	0.209491	+	0.0300760i
$673$	−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
$675$	2.16443	−	8.36335i	0.0833091	−	0.321905i
$676$	2.44698	−	4.23829i	0.0941145	−	0.163011i
$677$	0.610403	+	1.05725i	0.0234597	+	0.0406334i	0.877517	−	0.479546i	$-0.159199\pi$
$677$	0.610403	+	1.05725i	0.0234597	+	0.0406334i	−0.854057	+	0.520179i	$0.825865\pi$
$678$	0.285251	+	8.92758i	0.0109550	+	0.342862i
$679$	−0.592469	−	1.62779i	−0.0227369	−	0.0624690i
$680$	3.25794	+	1.18579i	0.124936	+	0.0454732i
$681$	−33.9980	+	7.12117i	−1.30281	+	0.272884i
$682$	−3.45612	+	19.6006i	−0.132342	+	0.750547i
$683$	40.7336			1.55863			0.779313	−	0.626635i	$-0.215568\pi$
$683$	40.7336			1.55863			0.779313	+	0.626635i	$0.215568\pi$
$684$	−8.84862	+	9.62818i	−0.338335	+	0.368143i
$685$	20.3059			0.775850
$686$	−2.18186	+	12.3739i	−0.0833038	+	0.472439i
$687$	−27.9834	+	5.86136i	−1.06763	+	0.223625i
$688$	−11.7465	−	4.27537i	−0.447830	−	0.162997i
$689$	−5.33497	−	14.6577i	−0.203246	−	0.558414i
$690$	0.544779	+	17.0501i	0.0207394	+	0.649088i
$691$	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
$693$	9.53743	+	21.7680i	0.362297	+	0.826898i
$694$	13.6351	−	2.40423i	0.517580	−	0.0912633i
$695$	16.8309	+	9.71733i	0.638433	+	0.368599i
$696$	−13.0566	−	1.87449i	−0.494908	−	0.0710522i
$697$	5.58792	+	6.65943i	0.211658	+	0.252244i
$698$	−19.3873	+	7.05640i	−0.733820	+	0.267088i
$699$	5.66589	+	9.12744i	0.214304	+	0.345231i
$700$	−4.03414	−	3.38504i	−0.152476	−	0.127943i
$701$	23.1182	+	4.07636i	0.873162	+	0.153962i	0.592233	−	0.805767i	$-0.298246\pi$
$701$	23.1182	+	4.07636i	0.873162	+	0.153962i	0.280929	+	0.959729i	$0.409358\pi$
$702$	−9.11853	+	19.9997i	−0.344157	+	0.754841i
$703$	−12.3738	−	12.9232i	−0.466687	−	0.487408i
$704$			2.50097i			0.0942589i
$705$	18.6788	+	20.8690i	0.703483	+	0.785973i
$706$	14.6560	−	17.4664i	0.551587	−	0.657356i
$707$	12.7474	−	35.0231i	0.479414	−	1.31718i
$708$	−4.80043	+	14.6265i	−0.180411	+	0.549696i
$709$	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
$711$	8.42332	−	28.7313i	0.315899	−	1.07751i
$712$	−2.89001	−	16.3901i	−0.108308	−	0.614243i
$713$	5.27289	+	29.9041i	0.197471	+	1.11992i
$714$	6.84074	−	2.74026i	0.256008	−	0.102552i
$715$	−23.6490	+	13.6538i	−0.884423	+	0.510622i
$716$	0.149328	−	0.125301i	0.00558063	−	0.00468271i
$717$	0.947601	+	0.311004i	0.0353888	+	0.0116147i
$718$	2.53893	−	6.97566i	0.0947521	−	0.260329i
$719$	−26.4940	+	31.5743i	−0.988060	+	1.17752i	−0.00394505	+	0.999992i	$0.501256\pi$
$719$	−26.4940	+	31.5743i	−0.988060	+	1.17752i	−0.984115	+	0.177532i	$0.943189\pi$
$720$	−0.494335	−	7.72778i	−0.0184228	−	0.287997i
$721$		−	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
$726$	6.98285	−	4.33462i	0.259158	−	0.160873i
$727$	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
$729$	8.79906	−	25.5260i	0.325891	−	0.945407i
$730$	4.89281	+	2.82486i	0.181091	+	0.104553i
$731$	−16.5352	+	2.91561i	−0.611578	+	0.107838i
$732$	−0.216599	−	0.115993i	−0.00800574	−	0.00428723i
$733$	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
$735$	−13.5540	+	0.433071i	−0.499945	+	0.0159741i
$736$	1.30503	+	3.58554i	0.0481040	+	0.132165i
$737$	10.7100	+	3.89814i	0.394510	+	0.143590i
$738$	8.61491	−	17.4005i	0.317119	−	0.640520i
$739$	−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
$741$	−31.7851	+	3.10865i	−1.16765	+	0.114199i
$742$	11.6801			0.428791
$743$	−0.154876	+	0.878343i	−0.00568183	+	0.0322233i	−0.987517	−	0.157513i	$-0.949652\pi$
$743$	−0.154876	+	0.878343i	−0.00568183	+	0.0322233i	0.981835	+	0.189737i	$0.0607634\pi$
$744$	−2.82583	−	13.4911i	−0.103600	−	0.494607i
$745$	−33.1925	−	12.0811i	−1.21608	−	0.442617i
$746$	−6.52210	−	17.9193i	−0.238791	−	0.656073i
$747$	25.3119	−	34.4078i	0.926114	−	1.25891i
$748$	1.67964	+	2.90922i	0.0614137	+	0.106372i
$749$	8.96255	−	15.5236i	0.327484	−	0.567220i
$750$	7.04398	−	13.1535i	0.257210	−	0.480300i
$751$	−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
$753$	−1.47648	+	10.2843i	−0.0538058	+	0.374780i
$754$	−20.7071	−	24.6778i	−0.754108	−	0.898711i
$755$	20.9481	−	7.62450i	0.762381	−	0.277484i
$756$	−11.7374	−	11.5382i	−0.426885	−	0.419642i
$757$	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	$-0.857209\pi$
$761$		−	23.9282i		−	0.867396i	0.901058	−	0.433698i	$-0.142791\pi$
$762$	−10.1142	+	9.05274i	−0.366401	+	0.327946i
$763$	33.6048	−	40.0486i	1.21657	−	1.44986i
$764$	−3.84705	+	10.5697i	−0.139181	+	0.382397i
$765$	−5.76497	−	8.65725i	−0.208433	−	0.313003i
$766$	−4.60213	+	3.86165i	−0.166282	+	0.139527i
$767$	−32.5594	+	18.7982i	−1.17565	+	0.678764i
$768$	−0.644072	−	1.60785i	−0.0232409	−	0.0580182i
$769$	−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
$771$	−11.9856	−	29.9206i	−0.431651	−	1.07756i
$772$	13.9666	−	8.06359i	0.502667	−	0.290215i
$773$	−27.0855	+	22.7275i	−0.974199	+	0.817450i	−0.983204	−	0.182509i	$-0.941578\pi$
$773$	−27.0855	+	22.7275i	−0.974199	+	0.817450i	0.00900488	+	0.999959i	$0.497134\pi$
$774$	20.7855	+	31.2136i	0.747120	+	1.12195i
$775$	−4.52520	+	12.4329i	−0.162550	+	0.446602i
$776$	−0.351528	+	0.418935i	−0.0126191	+	0.0150389i
$777$	16.7800	−	15.0189i	0.601978	−	0.538799i
$778$			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
$783$	28.2195	+	27.7407i	1.00848	+	0.991372i
$784$	−2.85031	+	1.03743i	−0.101797	+	0.0370510i
$785$	5.69922	+	6.79206i	0.203414	+	0.242419i
$786$	1.10794	−	7.71723i	0.0395188	−	0.275265i
$787$	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
$789$	1.75480	−	3.27681i	0.0624724	−	0.116658i
$790$	−12.8804	+	22.3095i	−0.458264	+	0.793737i
$791$	−8.16743	−	14.1464i	−0.290400	−	0.502988i
$792$	4.44603	−	6.04372i	0.157983	−	0.214754i
$793$	−0.205236	−	0.563881i	−0.00728815	−	0.0200240i
$794$	−9.89421	−	3.60120i	−0.351133	−	0.127802i
$795$	−3.37973	−	16.1356i	−0.119867	−	0.572270i
$796$	0.0579780	−	0.328809i	0.00205497	−	0.0116543i
$797$	−13.5711			−0.480714			−0.240357	−	0.970685i	$-0.577265\pi$
$797$	−13.5711			−0.480714			−0.240357	+	0.970685i	$0.577265\pi$
$798$	5.95296	−	23.1615i	0.210732	−	0.819910i
$799$	8.41451			0.297684
$800$	−0.288700	+	1.63730i	−0.0102071	+	0.0578872i
$801$	−22.1531	+	44.7450i	−0.782741	+	1.58099i
$802$	−8.64725	−	3.14734i	−0.305345	−	0.111136i
$803$	1.87227	+	5.14401i	0.0660708	+	0.181528i
$804$	−7.88925	+	0.252074i	−0.278232	+	0.00888997i
$805$	−15.5984	−	27.0172i	−0.549771	−	0.952231i
$806$	16.8319	−	29.1537i	0.592879	−	1.02690i
$807$	−39.7142	−	21.2678i	−1.39801	−	0.748660i
$808$	−11.5878	+	2.04324i	−0.407656	+	0.0718808i
$809$	−7.06352	−	4.07812i	−0.248340	−	0.143379i	0.370664	−	0.928767i	$-0.379130\pi$
$809$	−7.06352	−	4.07812i	−0.248340	−	0.143379i	−0.619004	+	0.785388i	$0.712464\pi$
$810$	−12.5433	+	19.5534i	−0.440725	+	0.687035i
$811$	−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
$813$	−7.24844	+	4.49949i	−0.254214	+	0.157804i
$814$	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
$819$	−2.56611	−	40.1151i	−0.0896670	−	1.40174i
$820$	−10.7382	+	12.7973i	−0.374996	+	0.446903i
$821$	1.32613	−	3.64350i	0.0462821	−	0.127159i	−0.914398	−	0.404816i	$-0.867336\pi$
$821$	1.32613	−	3.64350i	0.0462821	−	0.127159i	0.960680	+	0.277657i	$0.0895578\pi$
$822$	−12.9464	−	4.24903i	−0.451557	−	0.148202i
$823$	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
$825$	−6.68543	+	2.67805i	−0.232757	+	0.0932378i
$826$	−4.88859	−	27.7246i	−0.170096	−	0.964662i
$827$	−5.27611	−	29.9223i	−0.183468	−	1.04050i	−0.927908	−	0.372810i	$-0.878394\pi$
$827$	−5.27611	−	29.9223i	−0.183468	−	1.04050i	0.744439	−	0.667690i	$-0.232717\pi$
$828$	3.22042	−	10.9846i	0.111917	−	0.381741i
$829$	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
$831$	0.913769	−	2.78417i	0.0316983	−	0.0965818i
$832$	1.44679	−	3.97502i	0.0501583	−	0.137809i
$833$	−2.61886	+	3.12103i	−0.0907380	+	0.108137i
$834$	−8.69747	−	9.71733i	−0.301169	−	0.336483i
$835$			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	$-0.358138\pi$
$839$	−11.0849	−	9.30133i	−0.382693	−	0.321118i	−0.813759	+	0.581203i	$0.802582\pi$
$840$	7.46867	+	12.0316i	0.257694	+	0.415131i
$841$	−27.2472	+	9.91717i	−0.939559	+	0.341971i
$842$	0.259039	+	0.308710i	0.00892707	+	0.0106389i
$843$	51.1439	+	7.34255i	1.76149	+	0.252891i
$844$	−2.22135	−	1.28250i	−0.0764621	−	0.0441454i
$845$	12.4403	−	2.19356i	0.427960	−	0.0754609i
$846$	−7.54212	−	17.2139i	−0.259303	−	0.591828i
$847$	−7.51519	+	13.0167i	−0.258225	+	0.447259i
$848$	−1.84373	−	3.19343i	−0.0633139	−	0.109663i
$849$	1.30672	+	40.8968i	0.0448464	+	1.40357i
$850$	0.763774	+	2.09845i	0.0261972	+	0.0719763i
$851$	14.7175	+	5.35673i	0.504510	+	0.183627i
$852$	15.5018	−	3.24699i	0.531084	−	0.111240i
$853$	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
$855$	−33.7191	−	1.52177i	−1.15317	−	0.0520434i
$856$	−5.65902			−0.193421
$857$	−3.26971	+	18.5435i	−0.111691	+	0.633433i	0.876644	+	0.481139i	$0.159777\pi$
$857$	−3.26971	+	18.5435i	−0.111691	+	0.633433i	−0.988335	+	0.152293i	$0.951334\pi$
$858$	17.9349	−	3.75662i	0.612287	−	0.128249i
$859$	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
$861$	1.13396	+	35.4899i	0.0386453	+	1.20949i
$862$	4.66791	+	8.08505i	0.158990	+	0.275378i
$863$	9.85277	−	17.0655i	0.335392	−	0.580916i	−0.648168	−	0.761497i	$-0.724465\pi$
$863$	9.85277	−	17.0655i	0.335392	−	0.580916i	0.983560	+	0.180581i	$0.0577979\pi$
$864$	−1.30187	+	5.03042i	−0.0442906	+	0.171138i
$865$	−37.9223	+	6.68673i	−1.28940	+	0.227356i
$866$	17.8113	+	10.2833i	0.605251	+	0.349442i
$867$	26.0528	+	3.74032i	0.884801	+	0.127028i
$868$	16.2031	+	19.3101i	0.549969	+	0.655428i
$869$	−23.4549	+	8.53689i	−0.795653	+	0.289594i
$870$	−17.9565	−	28.9269i	−0.608782	−	0.980715i
$871$	−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
$876$	−2.52839	−	2.82486i	−0.0854263	−	0.0954433i
$877$	−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
$879$	−5.00690	+	15.2556i	−0.168879	+	0.514557i
$880$	−4.94519	+	4.14951i	−0.166702	+	0.139880i
$881$	26.6755	−	15.4011i	0.898719	−	0.518876i	0.0219346	−	0.999759i	$-0.493017\pi$
$881$	26.6755	−	15.4011i	0.898719	−	0.518876i	0.876784	+	0.480884i	$0.159684\pi$
$882$	8.73218	+	2.56006i	0.294028	+	0.0862018i
$883$	−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
$885$	−36.8857	+	14.7757i	−1.23990	+	0.496679i
$886$	23.0044	−	13.2816i	0.772849	−	0.446205i
$887$	14.6182	−	12.2661i	0.490831	−	0.411856i	−0.363493	−	0.931597i	$-0.618416\pi$
$887$	14.6182	−	12.2661i	0.490831	−	0.411856i	0.854324	+	0.519741i	$0.173972\pi$
$888$	−6.75502	−	2.21701i	−0.226683	−	0.0743979i
$889$	8.49015	−	23.3265i	0.284751	−	0.782346i
$890$	27.6132	−	32.9081i	0.925597	−	1.10308i
$891$	−21.4881	+	6.70114i	−0.719878	+	0.224497i
$892$		−	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
$897$	23.7523	−	14.7443i	0.793065	−	0.492297i
$898$	−10.6547	+	3.87800i	−0.355552	+	0.129410i
$899$	−38.9562	−	46.4261i	−1.29926	−	1.54840i
$900$	3.60831	−	3.44338i	0.120277	−	0.114779i
$901$	−4.28939	−	2.47648i	−0.142900	−	0.0825035i
$902$	−15.9406	+	2.81076i	−0.530765	+	0.0935882i
$903$	−60.4576	−	32.3762i	−2.01190	−	1.07741i
$904$	−2.57849	+	4.46607i	−0.0857592	+	0.148539i
$905$	9.18019	+	15.9006i	0.305160	+	0.528552i
$906$	−14.9513	+	0.477717i	−0.496723	+	0.0158711i
$907$	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
$909$	31.6347	+	15.6622i	1.04926	+	0.519484i
$910$	−6.00571	+	34.0601i	−0.199087	+	1.12908i
$911$	32.6294			1.08106			0.540530	−	0.841325i	$-0.318224\pi$
$911$	32.6294			1.08106			0.540530	+	0.841325i	$0.318224\pi$
$912$	−7.27222	+	2.02851i	−0.240807	+	0.0671706i
$913$	−35.6098			−1.17851
$914$	−3.71066	+	21.0442i	−0.122738	+	0.696079i
$915$	−0.130018	−	0.620735i	−0.00429827	−	0.0205209i
$916$	−15.5113	−	5.64566i	−0.512509	−	0.186538i
$917$	4.87645	+	13.3979i	0.161034	+	0.442439i
$918$	1.86402	+	6.72590i	0.0615218	+	0.221988i
$919$	−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
$921$	−2.24413	+	4.19057i	−0.0739467	+	0.138084i
$922$	27.0902	−	4.77673i	0.892168	−	0.157313i
$923$	33.4989	+	19.3406i	1.10263	+	0.636603i
$924$	−1.94990	+	13.5819i	−0.0641471	+	0.446811i
$925$	4.38655	+	5.22769i	0.144229	+	0.171885i
$926$	−8.50711	+	3.09633i	−0.279561	+	0.101752i
$927$	23.3267	+	2.59172i	0.766150	+	0.0851232i
$928$	−5.83381	−	4.89515i	−0.191504	−	0.160691i
$929$	−26.6622	−	4.70127i	−0.874760	−	0.154244i	−0.281798	−	0.959474i	$-0.590931\pi$
$929$	−26.6622	−	4.70127i	−0.874760	−	0.154244i	−0.592962	+	0.805230i	$0.702042\pi$
$930$	21.9875	−	27.9714i	0.721000	−	0.917218i
$931$	3.14389	+	12.8424i	0.103037	+	0.420891i
$932$			6.20248i			0.203169i
$933$	−29.5502	+	26.4489i	−0.967431	+	0.865897i
$934$	−13.1443	+	15.6647i	−0.430094	+	0.512566i
$935$	−2.96564	+	8.14803i	−0.0969868	+	0.266469i
$936$	−10.5627	+	7.03384i	−0.345253	+	0.229908i
$937$	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
$939$	8.65101	+	21.5962i	0.282315	+	0.704765i
$940$	2.80790	+	15.9244i	0.0915837	+	0.519397i
$941$	−3.32233	−	18.8419i	−0.108305	−	0.614227i	−0.989849	−	0.142125i	$-0.954607\pi$
$941$	−3.32233	−	18.8419i	−0.108305	−	0.614227i	0.881544	−	0.472102i	$-0.156505\pi$
$942$	−2.21239	−	5.52296i	−0.0720835	−	0.179948i
$943$	−21.3867	+	12.3476i	−0.696448	+	0.402094i
$944$	−6.80843	+	5.71295i	−0.221596	+	0.185941i
$945$	3.34047	−	42.3522i	0.108666	−	1.37772i
$946$	10.6926	−	29.3776i	0.347646	−	0.955148i
$947$	−26.2400	+	31.2716i	−0.852684	+	1.01619i	0.146950	+	0.989144i	$0.453054\pi$
$947$	−26.2400	+	31.2716i	−0.852684	+	1.01619i	−0.999634	+	0.0270453i	$0.991390\pi$
$948$	12.8804	−	11.5286i	0.418336	−	0.374431i
$949$		−	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	$-0.483906\pi$
$953$	−28.5318	−	23.9410i	−0.924235	−	0.775525i	−0.974773	+	0.223197i	$0.928351\pi$
$954$	−1.22157	+	10.9947i	−0.0395498	+	0.355967i
$955$	−27.2824	+	9.92997i	−0.882837	+	0.321326i
$956$	0.370124	+	0.441096i	0.0119707	+	0.0142661i
$957$	4.68804	−	32.6541i	0.151543	−	1.05556i
$958$	8.51710	+	4.91735i	0.275175	+	0.158872i
$959$	24.5400	−	4.32707i	0.792438	−	0.139728i
$960$	2.11059	−	3.94120i	0.0681190	−	0.127202i
$961$	16.1658	−	28.0000i	0.521477	−	0.903225i
$962$	−8.68167	−	15.0371i	−0.279908	−	0.484815i
$963$	13.6753	+	10.0602i	0.440680	+	0.324184i
$964$	0.580859	+	1.59590i	0.0187082	+	0.0514004i
$965$	39.1169	+	14.2374i	1.25922	+	0.458318i
$966$	4.29165	+	20.4892i	0.138082	+	0.659230i
$967$	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
$969$	−7.09698	+	7.24362i	−0.227988	+	0.232699i
$970$	−1.41161			−0.0453239
$971$	−7.41064	+	42.0279i	−0.237819	+	1.34874i	0.598776	+	0.800916i	$0.295654\pi$
$971$	−7.41064	+	42.0279i	−0.237819	+	1.34874i	−0.836595	+	0.547822i	$0.815457\pi$
$972$	12.0887	−	9.84189i	0.387746	−	0.315679i
$973$	22.4111	+	8.15697i	0.718466	+	0.261500i
$974$	2.66801	+	7.33030i	0.0854886	+	0.234878i
$975$	12.1750	−	0.389010i	0.389911	−	0.0124583i
$976$	−0.0709282	−	0.122851i	−0.00227036	−	0.00393237i
$977$	−18.1173	+	31.3801i	−0.579623	+	1.00394i	0.415899	+	0.909411i	$0.363467\pi$
$977$	−18.1173	+	31.3801i	−0.579623	+	1.00394i	−0.995522	+	0.0945264i	$0.969866\pi$
$978$	11.7054	+	6.26847i	0.374297	+	0.200444i
$979$	40.9910	−	7.22783i	1.31008	−	0.231002i
$980$	−6.78044	−	3.91469i	−0.216593	−	0.125050i
$981$	34.1839	+	35.8213i	1.09141	+	1.14369i
$982$	−18.0754	−	21.5414i	−0.576808	−	0.687413i
$983$	−51.2605	+	18.6573i	−1.63496	+	0.595075i	−0.986147	−	0.165876i	$-0.946955\pi$
$983$	−51.2605	+	18.6573i	−1.63496	+	0.595075i	−0.648809	+	0.760951i	$0.724733\pi$
$984$	9.52421	−	5.91218i	0.303621	−	0.188473i
$985$	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
$990$	19.3270	−	1.23632i	0.614251	−	0.0392927i
$991$	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
$993$	−14.8097	−	4.86056i	−0.469971	−	0.154245i
$994$	−22.1881	+	18.6181i	−0.703765	+	0.590529i
$995$	0.746352	−	0.430907i	0.0236610	−	0.0136607i
$996$	22.8932	−	9.17055i	0.725397	−	0.290580i
$997$	−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
$999$	12.3826	+	17.3660i	0.391768	+	0.549437i

Twists

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

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

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} +(-1.69526 + 0.355087i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.882820 - 2.42553i) q^{5} +(0.0553136 + 1.73117i) q^{6} +(-1.58376 - 2.74316i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.74783 - 1.20393i) q^{9} +(-2.54198 + 0.448219i) q^{10} +(-2.16590 - 1.25049i) q^{11} +(1.71447 + 0.246141i) q^{12} +(2.71907 + 3.24046i) q^{13} +(-2.97650 + 1.08336i) q^{14} +(2.35788 + 3.79843i) 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} +(3.65896 + 4.08800i) q^{21} +(-1.60759 + 1.91586i) q^{22} +(-1.30503 + 3.58554i) q^{23} +(0.540116 - 1.64568i) q^{24} +(-1.27359 + 1.06867i) q^{25} +(3.66340 - 2.11506i) q^{26} +(-4.23078 + 3.01670i) q^{27} +(0.550036 + 3.11941i) q^{28} +(-1.32242 - 7.49981i) q^{29} +(4.15016 - 1.66247i) q^{30} +(6.89193 - 3.97906i) q^{31} +(0.766044 - 0.642788i) q^{32} +(4.11581 + 1.35082i) q^{33} +(0.459398 - 1.26219i) q^{34} +(-5.25543 + 6.26318i) q^{35} +(-2.99388 + 0.191514i) 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} +(4.66127 - 2.89350i) q^{42} +(-11.7465 + 4.27537i) q^{43} +(1.60759 + 1.91586i) q^{44} +(-5.34601 - 5.60207i) q^{45} +(3.30445 + 1.90782i) q^{46} +(6.16940 - 1.08783i) q^{47} +(-1.52689 - 0.817681i) q^{48} +(-1.51662 + 2.62686i) q^{49} +(0.831277 + 1.43981i) q^{50} +(-2.32529 + 0.0742967i) q^{51} +(-1.44679 - 3.97502i) q^{52} +(-3.46508 - 1.26118i) q^{53} +(2.23620 + 4.69035i) q^{54} +(-1.12098 + 6.35742i) q^{55} +3.16753 q^{56} +(-4.26694 + 6.22842i) q^{57} -7.61550 q^{58} +(-1.54335 + 8.75275i) q^{59} +(-0.916549 - 4.37580i) q^{60} +(-0.133301 - 0.0485177i) q^{61} +(-2.72184 - 7.47818i) q^{62} +(-7.65449 - 5.63098i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(5.45938 - 9.45593i) q^{65} +(2.04500 - 3.81871i) q^{66} +(-4.48795 + 0.791347i) q^{67} +(-1.16324 - 0.671595i) q^{68} +(0.939187 - 6.54182i) q^{69} +(5.25543 + 6.26318i) q^{70} +(8.59275 - 3.12750i) q^{71} +(-0.331277 + 2.98165i) 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} +(-5.45938 + 4.88641i) q^{78} +(6.41515 - 7.64528i) q^{79} +(0.882820 - 2.42553i) q^{80} +(6.10110 - 6.61639i) q^{81} +(4.95792 - 4.16019i) q^{82} +(12.3308 - 7.11920i) q^{83} +(-2.04012 - 5.09290i) q^{84} +(-0.602044 - 3.41436i) q^{85} +(2.17066 + 12.3104i) q^{86} +(4.90493 + 12.2446i) q^{87} +(2.16590 - 1.25049i) q^{88} +(-12.7492 + 10.6978i) q^{89} +(-6.44529 + 4.29200i) q^{90} +(4.58274 - 12.5910i) q^{91} +(2.45265 - 2.92296i) q^{92} +(-10.2707 + 9.19278i) 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} +(-7.45703 - 0.828515i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9} - 12 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{17} - 6 q^{19} - 24 q^{22} + 3 q^{24} - 18 q^{25} + 18 q^{26} - 6 q^{27} + 6 q^{28} - 6 q^{29} - 24 q^{33} - 6 q^{34} - 24 q^{35}+ \cdots - 102 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 - 12 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^17 - 6 * q^19 - 24 * q^22 + 3 * q^24 - 18 * q^25 + 18 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 - 24 * q^33 - 6 * q^34 - 24 * q^35 + 3 * q^38 + 6 * q^39 + 3 * q^41 - 6 * q^43 + 24 * q^44 - 54 * q^45 + 18 * q^46 + 30 * q^47 + 21 * q^49 + 3 * q^50 + 42 * q^51 - 6 * q^52 - 60 * q^53 + 54 * q^54 + 30 * q^55 + 12 * q^57 + 12 * q^58 + 3 * q^59 + 24 * q^60 + 54 * q^61 + 6 * q^62 - 18 * q^63 - 9 * q^64 + 24 * q^65 - 27 * q^66 - 15 * q^67 - 27 * q^68 + 30 * q^69 + 24 * q^70 + 36 * q^71 + 6 * q^72 - 42 * q^73 + 6 * q^74 - 24 * q^78 - 6 * q^79 - 3 * q^81 + 3 * q^82 + 36 * q^83 - 30 * q^84 - 6 * q^86 - 60 * q^89 - 18 * q^91 - 66 * q^93 + 6 * q^95 + 9 * q^97 + 12 * q^98 - 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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