LMFDB - Embedded newform 216.2.v.b.11.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(11,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 13]))

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

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

chi := DirichletCharacter("216.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.v (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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.18
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.143175 + 1.40695i) q^{2} +(0.584277 + 1.63053i) q^{3} +(-1.95900 + 0.402879i) q^{4} +(2.25103 + 0.819307i) q^{5} +(-2.21041 + 1.05550i) q^{6} +(4.05746 + 0.715440i) q^{7} +(-0.847309 - 2.69853i) q^{8} +(-2.31724 + 1.90536i) q^{9} +(-0.830431 + 3.28438i) q^{10} +(-1.59930 - 4.39403i) q^{11} +(-1.80150 - 2.95881i) q^{12} +(-2.03556 - 2.42589i) q^{13} +(-0.425661 + 5.81107i) q^{14} +(-0.0206784 + 4.14906i) q^{15} +(3.67538 - 1.57848i) q^{16} +(-5.30643 + 3.06367i) q^{17} +(-3.01251 - 2.98744i) q^{18} +(1.49474 - 2.58897i) q^{19} +(-4.73985 - 0.698133i) q^{20} +(1.20414 + 7.03382i) q^{21} +(5.95319 - 2.87924i) q^{22} +(-0.264216 - 1.49844i) q^{23} +(3.90497 - 2.95825i) q^{24} +(0.565634 + 0.474623i) q^{25} +(3.12166 - 3.21125i) q^{26} +(-4.46065 - 2.66507i) q^{27} +(-8.23682 + 0.233116i) q^{28} +(-1.88755 - 1.58384i) q^{29} +(-5.84047 + 0.564947i) q^{30} +(8.06739 - 1.42250i) q^{31} +(2.74706 + 4.94506i) q^{32} +(6.23016 - 5.17503i) q^{33} +(-5.07017 - 7.02723i) q^{34} +(8.54729 + 4.93478i) q^{35} +(3.77185 - 4.66617i) q^{36} +(-0.515395 + 0.297563i) q^{37} +(3.85655 + 1.73235i) q^{38} +(2.76615 - 4.73643i) q^{39} +(0.303610 - 6.76867i) q^{40} +(4.89056 + 5.82834i) q^{41} +(-9.72382 + 2.70123i) q^{42} +(-4.63264 + 1.68614i) q^{43} +(4.90329 + 7.96360i) q^{44} +(-6.77724 + 2.39049i) q^{45} +(2.07040 - 0.586277i) q^{46} +(-0.750048 + 4.25374i) q^{47} +(4.72119 + 5.07053i) q^{48} +(9.37332 + 3.41161i) q^{49} +(-0.586786 + 0.863772i) q^{50} +(-8.09583 - 6.86225i) q^{51} +(4.96501 + 3.93224i) q^{52} -6.46197 q^{53} +(3.11095 - 6.65747i) q^{54} -11.2014i q^{55} +(-1.50729 - 11.5554i) q^{56} +(5.09473 + 0.924543i) q^{57} +(1.95813 - 2.88244i) q^{58} +(-0.703302 + 1.93231i) q^{59} +(-1.63106 - 8.13635i) q^{60} +(7.44916 + 1.31349i) q^{61} +(3.15643 + 11.1467i) q^{62} +(-10.7653 + 6.07308i) q^{63} +(-6.56414 + 4.57298i) q^{64} +(-2.59456 - 7.12849i) q^{65} +(8.17300 + 8.02457i) q^{66} +(5.64581 - 4.73740i) q^{67} +(9.16103 - 8.13959i) q^{68} +(2.28888 - 1.30632i) q^{69} +(-5.71922 + 12.7321i) q^{70} +(-1.78204 - 3.08659i) q^{71} +(7.10509 + 4.63872i) q^{72} +(-5.85735 + 10.1452i) q^{73} +(-0.492447 - 0.682530i) q^{74} +(-0.443399 + 1.19959i) q^{75} +(-1.88516 + 5.67400i) q^{76} +(-3.34542 - 18.9728i) q^{77} +(7.05995 + 3.21368i) q^{78} +(6.66637 - 7.94467i) q^{79} +(9.56663 - 0.541939i) q^{80} +(1.73920 - 8.83036i) q^{81} +(-7.49997 + 7.71524i) q^{82} +(-5.79227 + 6.90296i) q^{83} +(-5.19269 - 13.2942i) q^{84} +(-14.4550 + 2.54881i) q^{85} +(-3.03559 - 6.27647i) q^{86} +(1.47964 - 4.00310i) q^{87} +(-10.5023 + 8.03885i) q^{88} +(-7.85955 - 4.53771i) q^{89} +(-4.33362 - 9.19297i) q^{90} +(-6.52364 - 11.2993i) q^{91} +(1.12129 + 2.82901i) q^{92} +(7.03302 + 12.3230i) q^{93} +(-6.09217 - 0.446251i) q^{94} +(5.48587 - 4.60319i) q^{95} +(-6.45802 + 7.36844i) q^{96} +(-4.05740 + 1.47677i) q^{97} +(-3.45793 + 13.6762i) q^{98} +(12.0782 + 7.13479i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25}+ \cdots - 12 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	0.143175	+	1.40695i	0.101240	+	0.994862i
$2$	0.143175	+	1.40695i	0.101240	+	0.994862i
$3$	0.584277	+	1.63053i	0.337333	+	0.941386i
$3$	0.584277	+	1.63053i	0.337333	+	0.941386i
$4$	−1.95900	+	0.402879i	−0.979501	+	0.201439i
$5$	2.25103	+	0.819307i	1.00669	+	0.366405i	0.792161	−	0.610313i	$-0.208956\pi$
$5$	2.25103	+	0.819307i	1.00669	+	0.366405i	0.214529	+	0.976718i	$0.431178\pi$
$6$	−2.21041	+	1.05550i	−0.902397	+	0.430905i
$7$	4.05746	+	0.715440i	1.53358	+	0.270411i	0.875753	−	0.482760i	$-0.160366\pi$
$7$	4.05746	+	0.715440i	1.53358	+	0.270411i	0.657825	+	0.753171i	$0.271477\pi$
$8$	−0.847309	−	2.69853i	−0.299569	−	0.954075i
$9$	−2.31724	+	1.90536i	−0.772413	+	0.635120i
$10$	−0.830431	+	3.28438i	−0.262605	+	1.03861i
$11$	−1.59930	−	4.39403i	−0.482206	−	1.32485i	−0.907598	−	0.419841i	$-0.862086\pi$
$11$	−1.59930	−	4.39403i	−0.482206	−	1.32485i	0.425391	−	0.905010i	$-0.360136\pi$
$12$	−1.80150	−	2.95881i	−0.520050	−	0.854136i
$13$	−2.03556	−	2.42589i	−0.564563	−	0.672820i	0.405942	−	0.913899i	$-0.366943\pi$
$13$	−2.03556	−	2.42589i	−0.564563	−	0.672820i	−0.970506	+	0.241078i	$0.922499\pi$
$14$	−0.425661	+	5.81107i	−0.113763	+	1.55307i
$15$	−0.0206784	+	4.14906i	−0.00533915	+	1.07128i
$16$	3.67538	−	1.57848i	0.918844	−	0.394620i
$17$	−5.30643	+	3.06367i	−1.28700	+	0.743049i	−0.978118	−	0.208051i	$-0.933288\pi$
$17$	−5.30643	+	3.06367i	−1.28700	+	0.743049i	−0.308881	+	0.951101i	$0.599955\pi$
$18$	−3.01251	−	2.98744i	−0.710056	−	0.704145i
$19$	1.49474	−	2.58897i	0.342917	−	0.593950i	−0.642056	−	0.766658i	$-0.721918\pi$
$19$	1.49474	−	2.58897i	0.342917	−	0.593950i	0.984973	+	0.172708i	$0.0552515\pi$
$20$	−4.73985	−	0.698133i	−1.05986	−	0.156107i
$21$	1.20414	+	7.03382i	0.262765	+	1.53491i
$22$	5.95319	−	2.87924i	1.26923	−	0.613856i
$23$	−0.264216	−	1.49844i	−0.0550929	−	0.312447i	0.944791	−	0.327673i	$-0.106264\pi$
$23$	−0.264216	−	1.49844i	−0.0550929	−	0.312447i	−0.999884	+	0.0152258i	$0.995153\pi$
$24$	3.90497	−	2.95825i	0.797098	−	0.603850i
$25$	0.565634	+	0.474623i	0.113127	+	0.0949247i
$26$	3.12166	−	3.21125i	0.612207	−	0.629779i
$27$	−4.46065	−	2.66507i	−0.858453	−	0.512892i
$28$	−8.23682	+	0.233116i	−1.55661	+	0.0440548i
$29$	−1.88755	−	1.58384i	−0.350508	−	0.294111i	0.450486	−	0.892784i	$-0.351251\pi$
$29$	−1.88755	−	1.58384i	−0.350508	−	0.294111i	−0.800994	+	0.598672i	$0.795695\pi$
$30$	−5.84047	+	0.564947i	−1.06632	+	0.103145i
$31$	8.06739	−	1.42250i	1.44895	−	0.255488i	0.606850	−	0.794816i	$-0.292433\pi$
$31$	8.06739	−	1.42250i	1.44895	−	0.255488i	0.842096	+	0.539328i	$0.181322\pi$
$32$	2.74706	+	4.94506i	0.485616	+	0.874172i
$33$	6.23016	−	5.17503i	1.08453	−	0.900857i
$34$	−5.07017	−	7.02723i	−0.869527	−	1.20516i
$35$	8.54729	+	4.93478i	1.44476	+	0.834131i
$36$	3.77185	−	4.66617i	0.628642	−	0.777695i
$37$	−0.515395	+	0.297563i	−0.0847304	+	0.0489191i	−0.541767	−	0.840529i	$-0.682244\pi$
$37$	−0.515395	+	0.297563i	−0.0847304	+	0.0489191i	0.457036	+	0.889448i	$0.348911\pi$
$38$	3.85655	+	1.73235i	0.625616	+	0.281024i
$39$	2.76615	−	4.73643i	0.442938	−	0.758436i
$40$	0.303610	−	6.76867i	0.0480050	−	1.07022i
$41$	4.89056	+	5.82834i	0.763777	+	0.910235i	0.998081	−	0.0619291i	$-0.0197253\pi$
$41$	4.89056	+	5.82834i	0.763777	+	0.910235i	−0.234303	+	0.972164i	$0.575281\pi$
$42$	−9.72382	+	2.70123i	−1.50042	+	0.416808i
$43$	−4.63264	+	1.68614i	−0.706471	+	0.257134i	−0.670171	−	0.742207i	$-0.733779\pi$
$43$	−4.63264	+	1.68614i	−0.706471	+	0.257134i	−0.0362998	+	0.999341i	$0.511557\pi$
$44$	4.90329	+	7.96360i	0.739199	+	1.20056i
$45$	−6.77724	+	2.39049i	−1.01029	+	0.356353i
$46$	2.07040	−	0.586277i	0.305264	−	0.0864419i
$47$	−0.750048	+	4.25374i	−0.109406	+	0.620471i	0.879963	+	0.475042i	$0.157567\pi$
$47$	−0.750048	+	4.25374i	−0.109406	+	0.620471i	−0.989369	+	0.145429i	$0.953544\pi$
$48$	4.72119	+	5.07053i	0.681446	+	0.731869i
$49$	9.37332	+	3.41161i	1.33905	+	0.487373i
$50$	−0.586786	+	0.863772i	−0.0829840	+	0.122156i
$51$	−8.09583	−	6.86225i	−1.13364	−	0.960908i
$52$	4.96501	+	3.93224i	0.688523	+	0.545303i
$53$	−6.46197			−0.887619			−0.443810	−	0.896121i	$-0.646373\pi$
$53$	−6.46197			−0.887619			−0.443810	+	0.896121i	$0.646373\pi$
$54$	3.11095	−	6.65747i	0.423347	−	0.905968i
$55$		−	11.2014i		−	1.51040i
$56$	−1.50729	−	11.5554i	−0.201420	−	1.54415i
$57$	5.09473	+	0.924543i	0.674814	+	0.122459i
$58$	1.95813	−	2.88244i	0.257115	−	0.378483i
$59$	−0.703302	+	1.93231i	−0.0915621	+	0.251565i	−0.977017	−	0.213160i	$-0.931624\pi$
$59$	−0.703302	+	1.93231i	−0.0915621	+	0.251565i	0.885455	+	0.464725i	$0.153847\pi$
$60$	−1.63106	−	8.13635i	−0.210569	−	1.05040i
$61$	7.44916	+	1.31349i	0.953767	+	0.168175i	0.628814	−	0.777555i	$-0.283541\pi$
$61$	7.44916	+	1.31349i	0.953767	+	0.168175i	0.324953	+	0.945730i	$0.394652\pi$
$62$	3.15643	+	11.1467i	0.400867	+	1.41564i
$63$	−10.7653	+	6.07308i	−1.35630	+	0.765137i
$64$	−6.56414	+	4.57298i	−0.820517	+	0.571622i
$65$	−2.59456	−	7.12849i	−0.321815	−	0.884180i
$66$	8.17300	+	8.02457i	1.00603	+	0.987757i
$67$	5.64581	−	4.73740i	0.689746	−	0.578766i	−0.229090	−	0.973405i	$-0.573575\pi$
$67$	5.64581	−	4.73740i	0.689746	−	0.578766i	0.918836	+	0.394640i	$0.129131\pi$
$68$	9.16103	−	8.13959i	1.11094	−	0.987070i
$69$	2.28888	−	1.30632i	0.275549	−	0.157262i
$70$	−5.71922	+	12.7321i	−0.683578	+	1.52178i
$71$	−1.78204	−	3.08659i	−0.211489	−	0.366310i	0.740691	−	0.671845i	$-0.234498\pi$
$71$	−1.78204	−	3.08659i	−0.211489	−	0.366310i	−0.952181	+	0.305535i	$0.901165\pi$
$72$	7.10509	+	4.63872i	0.837343	+	0.546678i
$73$	−5.85735	+	10.1452i	−0.685551	+	1.18741i	0.287712	+	0.957717i	$0.407105\pi$
$73$	−5.85735	+	10.1452i	−0.685551	+	1.18741i	−0.973263	+	0.229693i	$0.926228\pi$
$74$	−0.492447	−	0.682530i	−0.0572458	−	0.0793425i
$75$	−0.443399	+	1.19959i	−0.0511994	+	0.138517i
$76$	−1.88516	+	5.67400i	−0.216243	+	0.650852i
$77$	−3.34542	−	18.9728i	−0.381246	−	2.16216i
$78$	7.05995	+	3.21368i	0.799382	+	0.363878i
$79$	6.66637	−	7.94467i	0.750025	−	0.893845i	−0.247149	−	0.968978i	$-0.579494\pi$
$79$	6.66637	−	7.94467i	0.750025	−	0.893845i	0.997174	+	0.0751326i	$0.0239380\pi$
$80$	9.56663	−	0.541939i	1.06958	−	0.0605906i
$81$	1.73920	−	8.83036i	0.193245	−	0.981151i
$82$	−7.49997	+	7.71524i	−0.828233	+	0.852005i
$83$	−5.79227	+	6.90296i	−0.635784	+	0.757698i	−0.983698	−	0.179829i	$-0.942446\pi$
$83$	−5.79227	+	6.90296i	−0.635784	+	0.757698i	0.347914	+	0.937526i	$0.386890\pi$
$84$	−5.19269	−	13.2942i	−0.566569	−	1.45051i
$85$	−14.4550	+	2.54881i	−1.56787	+	0.276457i
$86$	−3.03559	−	6.27647i	−0.327336	−	0.676809i
$87$	1.47964	−	4.00310i	0.158634	−	0.429177i
$88$	−10.5023	+	8.03885i	−1.11955	+	0.856945i
$89$	−7.85955	−	4.53771i	−0.833110	−	0.480996i	0.0218062	−	0.999762i	$-0.493058\pi$
$89$	−7.85955	−	4.53771i	−0.833110	−	0.480996i	−0.854916	+	0.518766i	$0.826392\pi$
$90$	−4.33362	−	9.19297i	−0.456803	−	0.969024i
$91$	−6.52364	−	11.2993i	−0.683864	−	1.18449i
$92$	1.12129	+	2.82901i	0.116903	+	0.294944i
$93$	7.03302	+	12.3230i	0.729290	+	1.27783i
$94$	−6.09217	−	0.446251i	−0.628359	−	0.0460273i
$95$	5.48587	−	4.60319i	0.562838	−	0.472277i
$96$	−6.45802	+	7.36844i	−0.659119	+	0.752039i
$97$	−4.05740	+	1.47677i	−0.411966	+	0.149943i	−0.539685	−	0.841867i	$-0.681457\pi$
$97$	−4.05740	+	1.47677i	−0.411966	+	0.149943i	0.127719	+	0.991810i	$0.459234\pi$
$98$	−3.45793	+	13.6762i	−0.349304	+	1.38151i
$99$	12.0782	+	7.13479i	1.21390	+	0.717074i
$100$	−1.29929	−	0.701906i	−0.129929	−	0.0701906i
$101$	−0.990975	+	5.62010i	−0.0986057	+	0.559221i	0.894977	+	0.446112i	$0.147192\pi$
$101$	−0.990975	+	5.62010i	−0.0986057	+	0.559221i	−0.993583	+	0.113108i	$0.963919\pi$
$102$	8.49571	−	12.3729i	0.841201	−	1.22510i
$103$	−4.27439	+	11.7438i	−0.421168	+	1.15715i	0.529871	+	0.848079i	$0.322241\pi$
$103$	−4.27439	+	11.7438i	−0.421168	+	1.15715i	−0.951039	+	0.309072i	$0.899982\pi$
$104$	−4.82159	+	7.54850i	−0.472795	+	0.740192i
$105$	−3.05231	+	16.8199i	−0.297875	+	1.64145i
$106$	−0.925190	−	9.09165i	−0.0898624	−	0.883059i
$107$		−	8.13371i		−	0.786315i	−0.919471	−	0.393158i	$-0.871383\pi$
$107$		−	8.13371i		−	0.786315i	0.919471	−	0.393158i	$-0.128617\pi$
$108$	9.81213	+	3.42377i	0.944172	+	0.329452i
$109$			8.76344i			0.839385i	0.907666	+	0.419692i	$0.137862\pi$
$109$			8.76344i			0.839385i	−0.907666	+	0.419692i	$0.862138\pi$
$110$	15.7598	−	1.60376i	1.50264	−	0.152912i
$111$	−0.786319	−	0.666506i	−0.0746341	−	0.0632619i
$112$	16.0420	−	3.77511i	1.51583	−	0.356715i
$113$	1.18927	−	3.26748i	0.111877	−	0.307379i	−0.871101	−	0.491104i	$-0.836593\pi$
$113$	1.18927	−	3.26748i	0.111877	−	0.307379i	0.982978	+	0.183725i	$0.0588156\pi$
$114$	−0.571346	+	7.30039i	−0.0535115	+	0.683744i
$115$	0.632928	−	3.58951i	0.0590208	−	0.334724i
$116$	4.33580	+	2.34229i	0.402569	+	0.217476i
$117$	9.33908	+	1.74289i	0.863398	+	0.161130i
$118$	−2.81935	−	0.712851i	−0.259542	−	0.0656233i
$119$	−23.7225	+	8.63430i	−2.17464	+	0.791505i
$120$	11.2139	−	3.45973i	1.02368	−	0.315829i
$121$	−8.32328	+	6.98407i	−0.756662	+	0.634915i
$122$	−0.781477	+	10.6686i	−0.0707516	+	0.965893i
$123$	−6.64583	+	11.3796i	−0.599235	+	1.02606i
$124$	−15.2309	+	6.03686i	−1.36778	+	0.542126i
$125$	−5.10434	−	8.84097i	−0.456546	−	0.790760i
$126$	−10.0858	−	14.2767i	−0.898517	−	1.27187i
$127$	−4.96577	−	2.86699i	−0.440641	−	0.254404i	0.263228	−	0.964734i	$-0.415213\pi$
$127$	−4.96577	−	2.86699i	−0.440641	−	0.254404i	−0.703870	+	0.710329i	$0.748546\pi$
$128$	−7.37376	−	8.58066i	−0.651754	−	0.758430i
$129$	−5.45605	−	6.56847i	−0.480378	−	0.578322i
$130$	9.65793	−	4.67103i	0.847057	−	0.409676i
$131$	7.04845	−	1.24283i	0.615826	−	0.108587i	0.142971	−	0.989727i	$-0.454334\pi$
$131$	7.04845	−	1.24283i	0.615826	−	0.108587i	0.472855	+	0.881140i	$0.343223\pi$
$132$	−10.1200	+	12.6479i	−0.880832	+	1.10086i
$133$	7.91712	−	9.43526i	0.686501	−	0.818140i
$134$	7.47361	+	7.26509i	0.645622	+	0.627608i
$135$	−7.85754	−	9.65377i	−0.676270	−	0.830865i
$136$	12.7636	+	11.7237i	1.09447	+	1.00530i
$137$	4.63512	−	5.52392i	0.396005	−	0.471940i	−0.530792	−	0.847502i	$-0.678106\pi$
$137$	4.63512	−	5.52392i	0.396005	−	0.471940i	0.926798	+	0.375561i	$0.122550\pi$
$138$	2.16563	+	3.03330i	0.184351	+	0.258212i
$139$	−0.394266	−	2.23600i	−0.0334412	−	0.189655i	0.963511	−	0.267669i	$-0.0862532\pi$
$139$	−0.394266	−	2.23600i	−0.0334412	−	0.189655i	−0.996952	+	0.0780140i	$0.975142\pi$
$140$	−18.7323	−	6.22373i	−1.58317	−	0.526001i
$141$	−7.37407	+	1.26239i	−0.621009	+	0.106312i
$142$	4.08752	−	2.94916i	0.343017	−	0.247488i
$143$	−7.40396	+	12.8240i	−0.619151	+	1.07240i
$144$	−5.50916	+	10.6606i	−0.459097	+	0.888386i
$145$	−2.95126	−	5.11174i	−0.245089	−	0.424507i
$146$	−15.1124	−	6.78845i	−1.25071	−	0.561816i
$147$	−0.0861054	+	17.2768i	−0.00710186	+	1.42496i
$148$	0.889777	−	0.790569i	0.0731393	−	0.0649843i
$149$	−3.55018	+	2.97895i	−0.290842	+	0.244045i	−0.776520	−	0.630092i	$-0.783017\pi$
$149$	−3.55018	+	2.97895i	−0.290842	+	0.244045i	0.485678	+	0.874138i	$0.338573\pi$
$150$	−1.75125	−	0.452088i	−0.142989	−	0.0369128i
$151$	7.61676	+	20.9269i	0.619843	+	1.70300i	0.707371	+	0.706842i	$0.249881\pi$
$151$	7.61676	+	20.9269i	0.619843	+	1.70300i	−0.0875282	+	0.996162i	$0.527897\pi$
$152$	−8.25292	−	1.83995i	−0.669400	−	0.149240i
$153$	6.45888	−	17.2099i	0.522170	−	1.39134i
$154$	26.2148	−	7.42326i	2.11245	−	0.598184i
$155$	19.3254	+	3.40758i	1.55225	+	0.273704i
$156$	−3.51068	+	10.3931i	−0.281079	+	0.832114i
$157$	1.71761	−	4.71909i	0.137080	−	0.376624i	−0.852091	−	0.523394i	$-0.824665\pi$
$157$	1.71761	−	4.71909i	0.137080	−	0.376624i	0.989171	+	0.146770i	$0.0468877\pi$
$158$	12.1322	+	8.24175i	0.965185	+	0.655679i
$159$	−3.77558	−	10.5364i	−0.299423	−	0.835592i
$160$	2.13218	+	13.3822i	0.168564	+	1.05795i
$161$		−	6.26891i		−	0.494060i
$162$	12.6729	+	1.18268i	0.995674	+	0.0929205i
$163$	−12.6738			−0.992689			−0.496344	−	0.868126i	$-0.665325\pi$
$163$	−12.6738			−0.992689			−0.496344	+	0.868126i	$0.665325\pi$
$164$	−11.9287	−	9.44744i	−0.931478	−	0.737721i
$165$	18.2642	−	6.54472i	1.42187	−	0.509506i
$166$	−10.5414	−	7.16109i	−0.818171	−	0.555808i
$167$	19.6853	+	7.16486i	1.52329	+	0.554434i	0.961968	−	0.273161i	$-0.0880691\pi$
$167$	19.6853	+	7.16486i	1.52329	+	0.554434i	0.561326	+	0.827595i	$0.310291\pi$
$168$	17.9607	−	9.20922i	1.38570	−	0.710507i
$169$	0.516005	−	2.92641i	0.0396927	−	0.225108i
$170$	−5.65563	−	19.9725i	−0.433767	−	1.53182i
$171$	1.46924	+	8.84729i	0.112356	+	0.676569i
$172$	8.39604	−	5.16955i	0.640192	−	0.394174i
$173$	15.8132	−	5.75554i	1.20226	−	0.437586i	0.338245	−	0.941058i	$-0.390167\pi$
$173$	15.8132	−	5.75554i	1.20226	−	0.437586i	0.864011	+	0.503472i	$0.167944\pi$
$174$	5.84399	+	1.50864i	0.443032	+	0.114369i
$175$	1.95548	+	2.33045i	0.147820	+	0.176165i
$176$	−12.8139	−	13.6253i	−0.965885	−	1.02704i
$177$	−3.56160	−	0.0177506i	−0.267706	−	0.00133422i
$178$	5.25903	−	11.7077i	0.394181	−	0.877526i
$179$	0.422508	−	0.243935i	0.0315797	−	0.0182326i	−0.484127	−	0.874998i	$-0.660863\pi$
$179$	0.422508	−	0.243935i	0.0315797	−	0.0182326i	0.515707	+	0.856765i	$0.327529\pi$
$180$	12.3136	−	7.41337i	0.917798	−	0.552560i
$181$	−16.2854	−	9.40235i	−1.21048	−	0.698872i	−0.247617	−	0.968858i	$-0.579647\pi$
$181$	−16.2854	−	9.40235i	−1.21048	−	0.698872i	−0.962864	+	0.269987i	$0.912981\pi$
$182$	14.9635	−	10.7962i	1.10917	−	0.800267i
$183$	2.21070	+	12.9135i	0.163419	+	0.954593i
$184$	−3.81972	+	1.98264i	−0.281594	+	0.146162i
$185$	−1.40396	+	0.247556i	−0.103221	+	0.0182007i
$186$	−16.3308	+	11.6594i	−1.19743	+	0.854910i
$187$	21.9484	+	18.4169i	1.60503	+	1.34678i
$188$	−0.244393	−	8.63525i	−0.0178242	−	0.629791i
$189$	−16.1922	−	14.0047i	−1.17781	−	1.01869i
$190$	7.26188	+	7.05926i	0.526832	+	0.512133i
$191$	5.12972	+	4.30435i	0.371174	+	0.311452i	0.809226	−	0.587498i	$-0.199887\pi$
$191$	5.12972	+	4.30435i	0.371174	+	0.311452i	−0.438052	+	0.898950i	$0.644331\pi$
$192$	−11.2916	−	8.03112i	−0.814904	−	0.579596i
$193$	−0.619300	−	3.51222i	−0.0445782	−	0.252815i	0.954372	−	0.298619i	$-0.0965261\pi$
$193$	−0.619300	−	3.51222i	−0.0445782	−	0.252815i	−0.998950	+	0.0458041i	$0.985415\pi$
$194$	−2.65866	−	5.49711i	−0.190880	−	0.394669i
$195$	10.1073	−	8.39551i	0.723796	−	0.601215i
$196$	−19.7368	−	2.90704i	−1.40977	−	0.207646i
$197$	7.68889	−	13.3175i	0.547811	−	0.948836i	−0.450614	−	0.892719i	$-0.648795\pi$
$197$	7.68889	−	13.3175i	0.547811	−	0.948836i	0.998424	−	0.0561167i	$-0.0178719\pi$
$198$	−8.30899	+	18.0149i	−0.590494	+	1.28026i
$199$	5.28658	−	3.05221i	0.374756	−	0.216365i	−0.300778	−	0.953694i	$-0.597246\pi$
$199$	5.28658	−	3.05221i	0.374756	−	0.216365i	0.675534	+	0.737329i	$0.263913\pi$
$200$	0.801519	−	1.92853i	0.0566760	−	0.136368i
$201$	11.0232	+	6.43770i	0.777515	+	0.454080i
$202$	−8.04906	−	0.589594i	−0.566330	−	0.0414837i
$203$	−6.52551	−	7.77680i	−0.458001	−	0.545824i
$204$	18.6244	+	10.1815i	1.30397	+	0.712850i
$205$	6.23358	+	17.1266i	0.435372	+	1.19618i
$206$	−17.1349	−	4.33243i	−1.19384	−	0.301855i
$207$	3.46733	+	2.96883i	0.240996	+	0.206348i
$208$	−11.3107	−	5.70296i	−0.784254	−	0.395429i
$209$	−13.7666	−	2.42742i	−0.952253	−	0.167908i
$210$	−24.1017	−	1.88626i	−1.66318	−	0.130164i
$211$	−15.9756	−	5.81464i	−1.09981	−	0.400296i	−0.272561	−	0.962139i	$-0.587871\pi$
$211$	−15.9756	−	5.81464i	−1.09981	−	0.400296i	−0.827244	+	0.561842i	$0.810093\pi$
$212$	12.6590	−	2.60339i	0.869424	−	0.178801i
$213$	3.99156	−	4.70909i	0.273497	−	0.322661i
$214$	11.4437	−	1.16454i	0.782275	−	0.0796064i
$215$	−11.8097			−0.805412
$216$	−3.41221	+	14.2953i	−0.232172	+	0.972675i
$217$	33.7509			2.29116
$218$	−12.3297	+	1.25470i	−0.835072	+	0.0849792i
$219$	−19.9644	−	3.62295i	−1.34907	−	0.244816i
$220$	4.51280	+	21.9436i	0.304253	+	1.47943i
$221$	18.2337	+	6.63652i	1.22653	+	0.446421i
$222$	0.825158	−	1.20174i	0.0553810	−	0.0806552i
$223$	−11.2135	−	1.97724i	−0.750910	−	0.132406i	−0.214922	−	0.976631i	$-0.568950\pi$
$223$	−11.2135	−	1.97724i	−0.750910	−	0.132406i	−0.535988	+	0.844226i	$0.680061\pi$
$224$	7.60820	+	22.0298i	0.508344	+	1.47193i
$225$	−2.21504	−	0.0220795i	−0.147669	−	0.00147197i
$226$	4.76745	+	1.20542i	0.317126	+	0.0801830i
$227$	3.72368	+	10.2307i	0.247149	+	0.679038i	0.999788	+	0.0206033i	$0.00655870\pi$
$227$	3.72368	+	10.2307i	0.247149	+	0.679038i	−0.752638	+	0.658434i	$0.771219\pi$
$228$	−10.3531	+	0.241377i	−0.685649	+	0.0159856i
$229$	5.38064	+	6.41240i	0.355563	+	0.423743i	0.913943	−	0.405842i	$-0.133022\pi$
$229$	5.38064	+	6.41240i	0.355563	+	0.423743i	−0.558381	+	0.829585i	$0.688577\pi$
$230$	5.14087	+	0.376569i	0.338979	+	0.0248302i
$231$	28.9811	−	16.5402i	1.90681	−	1.08827i
$232$	−2.67470	+	6.43560i	−0.175603	+	0.422518i
$233$	−15.9080	+	9.18450i	−1.04217	+	0.601697i	−0.920447	−	0.390867i	$-0.872175\pi$
$233$	−15.9080	+	9.18450i	−1.04217	+	0.601697i	−0.121722	+	0.992564i	$0.538842\pi$
$234$	−1.11503	+	13.3891i	−0.0728918	+	0.875275i
$235$	−5.17349	+	8.96075i	−0.337481	+	0.584535i
$236$	0.599285	−	4.06874i	0.0390101	−	0.264852i
$237$	16.8490	+	6.22781i	1.09446	+	0.404540i
$238$	−15.5445	−	32.1402i	−1.00760	−	2.08334i
$239$	−3.49917	−	19.8448i	−0.226343	−	1.28365i	−0.860102	−	0.510123i	$-0.829600\pi$
$239$	−3.49917	−	19.8448i	−0.226343	−	1.28365i	0.633759	−	0.773531i	$-0.281511\pi$
$240$	6.47321	+	15.2820i	0.417844	+	0.986450i
$241$	0.238032	+	0.199733i	0.0153330	+	0.0128659i	0.650422	−	0.759573i	$-0.274592\pi$
$241$	0.238032	+	0.199733i	0.0153330	+	0.0128659i	−0.635089	+	0.772439i	$0.719037\pi$
$242$	−11.0179	−	10.7105i	−0.708257	−	0.688496i
$243$	15.4143	−	2.32356i	0.988829	−	0.149056i
$244$	−15.1221	+	0.427982i	−0.968093	+	0.0273987i
$245$	18.3044	+	15.3592i	1.16943	+	0.981266i
$246$	−16.9620	−	7.72107i	−1.08146	−	0.492278i
$247$	−9.32319	+	1.64393i	−0.593221	+	0.104601i
$248$	−10.6742	−	20.5648i	−0.677814	−	1.30587i
$249$	−14.6397	−	5.41121i	−0.927756	−	0.342922i
$250$	11.7080	−	8.44733i	0.740477	−	0.534256i
$251$	−0.0158716	−	0.00916350i	−0.00100181	−	0.000578395i	0.499499	−	0.866314i	$-0.333517\pi$
$251$	−0.0158716	−	0.00916350i	−0.00100181	−	0.000578395i	−0.500501	+	0.865736i	$0.666851\pi$
$252$	18.6425	−	16.2343i	1.17437	−	1.02266i
$253$	−6.16165	+	3.55743i	−0.387380	+	0.223654i
$254$	3.32273	−	7.39706i	0.208487	−	0.464133i
$255$	−12.6016	−	22.0801i	−0.789145	−	1.38271i
$256$	11.0168	−	11.6030i	0.688550	−	0.725189i
$257$	−5.91651	−	7.05103i	−0.369062	−	0.439831i	0.549268	−	0.835646i	$-0.314907\pi$
$257$	−5.91651	−	7.05103i	−0.369062	−	0.439831i	−0.918330	+	0.395815i	$0.870462\pi$
$258$	8.46033	−	8.61681i	0.526717	−	0.536459i
$259$	−2.30408	+	0.838618i	−0.143169	+	0.0521092i
$260$	7.95466	+	12.9194i	0.493327	+	0.801229i
$261$	7.39168	+	0.0736804i	0.457533	+	0.00456070i
$262$	2.75776	+	9.73886i	0.170375	+	0.601669i
$263$	−0.155563	+	0.882240i	−0.00959241	+	0.0544013i	−0.989228	−	0.146381i	$-0.953237\pi$
$263$	−0.155563	+	0.882240i	−0.00959241	+	0.0544013i	0.979636	+	0.200783i	$0.0643485\pi$
$264$	−19.2438	−	12.4274i	−1.18438	−	0.764855i
$265$	−14.5461	−	5.29433i	−0.893557	−	0.325228i
$266$	14.4084	+	9.78808i	0.883438	+	0.600146i
$267$	2.80671	−	15.4665i	0.171768	−	0.946534i
$268$	−9.15156	+	11.5552i	−0.559021	+	0.705843i
$269$	4.12054			0.251234			0.125617	−	0.992079i	$-0.459909\pi$
$269$	4.12054			0.251234			0.125617	+	0.992079i	$0.459909\pi$
$270$	12.4574	−	12.4373i	0.758130	−	0.756912i
$271$		−	15.6915i		−	0.953190i	−0.879123	−	0.476595i	$-0.841871\pi$
$271$		−	15.6915i		−	0.953190i	0.879123	−	0.476595i	$-0.158129\pi$
$272$	−14.6672	+	19.6362i	−0.889330	+	1.19062i
$273$	14.6122	−	17.2389i	0.884369	−	1.04335i
$274$	8.43550	+	5.73048i	0.509607	+	0.346191i
$275$	1.18089	−	3.24448i	0.0712106	−	0.195649i
$276$	−3.95763	+	3.48122i	−0.238221	+	0.209545i
$277$	−8.12008	−	1.43179i	−0.487888	−	0.0860279i	−0.0757077	−	0.997130i	$-0.524122\pi$
$277$	−8.12008	−	1.43179i	−0.487888	−	0.0860279i	−0.412181	+	0.911102i	$0.635233\pi$
$278$	3.08948	−	0.874850i	0.185295	−	0.0524700i
$279$	−15.9837	+	18.6676i	−0.956920	+	1.11760i
$280$	6.07447	−	27.2464i	0.363019	−	1.62829i
$281$	6.18239	+	16.9860i	0.368810	+	1.01330i	0.975815	+	0.218600i	$0.0701488\pi$
$281$	6.18239	+	16.9860i	0.368810	+	1.01330i	−0.607004	+	0.794699i	$0.707629\pi$
$282$	−2.83189	−	10.1942i	−0.168637	−	0.607055i
$283$	22.4795	−	18.8626i	1.33627	−	1.12126i	0.353701	−	0.935359i	$-0.384923\pi$
$283$	22.4795	−	18.8626i	1.33627	−	1.12126i	0.982568	−	0.185904i	$-0.0595213\pi$
$284$	4.73454	+	5.32868i	0.280943	+	0.316199i
$285$	10.7109	+	6.25532i	0.634458	+	0.370533i
$286$	−19.1028	−	8.58091i	−1.12957	−	0.507400i
$287$	15.6734	+	27.1472i	0.925174	+	1.60245i
$288$	−15.7877	−	6.22476i	−0.930301	−	0.366798i
$289$	10.2722	−	17.7919i	0.604244	−	1.04658i
$290$	6.76940	−	4.88415i	0.397513	−	0.286807i
$291$	−4.77856	−	5.75285i	−0.280124	−	0.337238i
$292$	7.38727	−	22.2343i	0.432307	−	1.30117i
$293$	4.30771	+	24.4302i	0.251659	+	1.42723i	0.804505	+	0.593946i	$0.202431\pi$
$293$	4.30771	+	24.4302i	0.251659	+	1.42723i	−0.552845	+	0.833284i	$0.686458\pi$
$294$	−24.3198	+	2.35245i	−1.41836	+	0.137198i
$295$	−3.16630	+	3.77345i	−0.184349	+	0.219699i
$296$	1.23968	+	1.13868i	0.0720551	+	0.0661845i
$297$	−4.57647	+	23.8625i	−0.265554	+	1.38464i
$298$	−4.69952	−	4.56840i	−0.272236	−	0.264640i
$299$	−3.09723	+	3.69113i	−0.179117	+	0.213464i
$300$	0.385330	−	2.52864i	0.0222470	−	0.145991i
$301$	−20.0031	+	3.52709i	−1.15296	+	0.203298i
$302$	−28.3525	+	13.7126i	−1.63150	+	0.789070i
$303$	−9.74273	+	1.66788i	−0.559705	+	0.0958174i
$304$	1.40711	−	11.8749i	0.0807031	−	0.681070i
$305$	15.6921	+	9.05984i	0.898527	+	0.518765i
$306$	25.1382	+	6.62328i	1.43706	+	0.378628i
$307$	10.7520	+	18.6230i	0.613649	+	1.06287i	0.990620	+	0.136646i	$0.0436323\pi$
$307$	10.7520	+	18.6230i	0.613649	+	1.06287i	−0.376971	+	0.926225i	$0.623034\pi$
$308$	14.1974	+	35.8200i	0.808974	+	2.04104i
$309$	−21.6460	−	0.107881i	−1.23140	−	0.00613715i
$310$	−2.02739	+	27.6777i	−0.115148	+	1.57199i
$311$	5.62268	−	4.71799i	0.318833	−	0.267533i	−0.469298	−	0.883040i	$-0.655493\pi$
$311$	5.62268	−	4.71799i	0.318833	−	0.267533i	0.788131	+	0.615507i	$0.211049\pi$
$312$	−15.1252	−	3.45131i	−0.856295	−	0.195392i
$313$	−16.4259	+	5.97854i	−0.928447	+	0.337927i	−0.761594	−	0.648055i	$-0.775583\pi$
$313$	−16.4259	+	5.97854i	−0.928447	+	0.337927i	−0.166853	+	0.985982i	$0.553361\pi$
$314$	6.88543	+	1.74093i	0.388567	+	0.0982464i
$315$	−29.2087	+	4.85060i	−1.64572	+	0.273300i
$316$	−9.85869	+	18.2494i	−0.554595	+	1.02661i
$317$	−5.03136	+	28.5343i	−0.282590	+	1.60264i	0.431181	+	0.902265i	$0.358097\pi$
$317$	−5.03136	+	28.5343i	−0.282590	+	1.60264i	−0.713771	+	0.700380i	$0.753014\pi$
$318$	14.2836	−	6.82059i	0.800985	−	0.382480i
$319$	−3.94069	+	10.8270i	−0.220636	+	0.606194i
$320$	−18.5227	+	4.91585i	−1.03545	+	0.274804i
$321$	13.2622	−	4.75234i	0.740226	−	0.265250i
$322$	8.82003	−	0.897550i	0.491521	−	0.0500185i
$323$			18.3176i			1.01922i
$324$	0.150457	+	17.9994i	0.00835872	+	0.999965i
$325$		−	2.33829i		−	0.129705i
$326$	−1.81457	−	17.8314i	−0.100500	−	0.987588i
$327$	−14.2890	+	5.12028i	−0.790185	+	0.283152i
$328$	11.5842	−	18.1357i	0.639628	−	1.00138i
$329$	−6.08659	+	16.7228i	−0.335565	+	0.921956i
$330$	11.8231	+	24.7597i	0.650838	+	1.36298i
$331$	−2.07515	+	11.7688i	−0.114061	+	0.646870i	0.873150	+	0.487451i	$0.162073\pi$
$331$	−2.07515	+	11.7688i	−0.114061	+	0.646870i	−0.987211	+	0.159419i	$0.949038\pi$
$332$	8.56601	−	15.8565i	0.470121	−	0.870238i
$333$	0.627328	−	1.67154i	0.0343774	−	0.0915997i
$334$	−7.26215	+	28.7220i	−0.397367	+	1.57160i
$335$	16.5903	−	6.03836i	0.906423	−	0.329911i
$336$	15.5284	+	23.9512i	0.847144	+	1.30665i
$337$	−22.1743	+	18.6064i	−1.20791	+	1.01356i	−0.208542	+	0.978013i	$0.566872\pi$
$337$	−22.1743	+	18.6064i	−1.20791	+	1.01356i	−0.999368	+	0.0355438i	$0.988684\pi$
$338$	4.19118	+	0.307004i	0.227970	+	0.0166988i
$339$	6.02259	+	0.0300159i	0.327102	+	0.00163024i
$340$	27.2905	−	10.8167i	1.48004	−	0.586620i
$341$	−19.1527	−	33.1734i	−1.03717	−	1.79644i
$342$	−12.2373	+	3.33386i	−0.661718	+	0.180274i
$343$	10.6146	+	6.12833i	0.573133	+	0.330899i
$344$	8.47538	+	11.0726i	0.456962	+	0.596997i
$345$	6.22260	−	1.06526i	0.335014	−	0.0573519i
$346$	10.3618	+	21.4243i	0.557054	+	1.15178i
$347$	−15.5409	+	2.74028i	−0.834279	+	0.147106i	−0.574441	−	0.818546i	$-0.694780\pi$
$347$	−15.5409	+	2.74028i	−0.834279	+	0.147106i	−0.259838	+	0.965652i	$0.583669\pi$
$348$	−1.28586	+	8.43819i	−0.0689294	+	0.452334i
$349$	15.4275	−	18.3858i	0.825817	−	0.984171i	−0.174183	−	0.984713i	$-0.555728\pi$
$349$	15.4275	−	18.3858i	0.825817	−	0.984171i	1.00000		0.000542788i	$0.000172775\pi$
$350$	−2.99884	+	3.08491i	−0.160295	+	0.164896i
$351$	2.61479	+	16.2460i	0.139567	+	0.867145i
$352$	17.3354	−	19.9793i	0.923981	−	1.06490i
$353$	21.7345	−	25.9022i	1.15681	−	1.37864i	0.244244	−	0.969714i	$-0.421460\pi$
$353$	21.7345	−	25.9022i	1.15681	−	1.37864i	0.912569	−	0.408923i	$-0.134095\pi$
$354$	−0.484957	−	5.01353i	−0.0257752	−	0.266466i
$355$	−1.48256	−	8.40802i	−0.0786862	−	0.446252i
$356$	17.2250	+	5.72294i	0.912924	+	0.303315i
$357$	−27.9390	−	33.6354i	−1.47869	−	1.78018i
$358$	0.403696	+	0.559521i	0.0213360	+	0.0295716i
$359$	3.04964	−	5.28214i	0.160954	−	0.278781i	−0.774257	−	0.632871i	$-0.781876\pi$
$359$	3.04964	−	5.28214i	0.160954	−	0.278781i	0.935211	+	0.354091i	$0.115210\pi$
$360$	12.1932	+	16.2631i	0.642639	+	0.857142i
$361$	5.03149	+	8.71480i	0.264815	+	0.458673i
$362$	10.8970	−	24.2588i	0.572732	−	1.27502i
$363$	−16.2508	−	9.49071i	−0.852947	−	0.498133i
$364$	17.3321	+	19.5071i	0.908447	+	1.02245i
$365$	−21.4971	+	18.0382i	−1.12521	+	0.944163i
$366$	−17.8521	+	4.95922i	−0.933144	+	0.259223i
$367$	−9.94356	−	27.3197i	−0.519050	−	1.42608i	−0.871569	−	0.490273i	$-0.836897\pi$
$367$	−9.94356	−	27.3197i	−0.519050	−	1.42608i	0.352519	−	0.935804i	$-0.385325\pi$
$368$	−3.33636	−	5.09029i	−0.173920	−	0.265350i
$369$	−22.4377	−	4.18739i	−1.16806	−	0.217987i
$370$	−0.549311	−	1.93986i	−0.0285573	−	0.100848i
$371$	−26.2192	−	4.62315i	−1.36123	−	0.240022i
$372$	−18.7424	−	21.3073i	−0.971746	−	1.10473i
$373$	−7.26237	+	19.9532i	−0.376031	+	1.03314i	0.596955	+	0.802275i	$0.296377\pi$
$373$	−7.26237	+	19.9532i	−0.376031	+	1.03314i	−0.972986	+	0.230863i	$0.925845\pi$
$374$	−22.7692	+	33.5171i	−1.17737	+	1.73313i
$375$	11.4331	−	13.4883i	0.590402	−	0.696535i
$376$	12.1144	−	1.58020i	0.624750	−	0.0814925i
$377$			7.80298i			0.401874i
$378$	17.3856	−	24.7868i	0.894219	−	1.27489i
$379$	−16.4361			−0.844264			−0.422132	−	0.906534i	$-0.638718\pi$
$379$	−16.4361			−0.844264			−0.422132	+	0.906534i	$0.638718\pi$
$380$	−8.89230	+	11.2278i	−0.456165	+	0.575974i
$381$	1.77332	−	9.77195i	0.0908499	−	0.500632i
$382$	−5.32154	+	7.83352i	−0.272274	+	0.400798i
$383$	16.5808	+	6.03491i	0.847239	+	0.308370i	0.728914	−	0.684605i	$-0.240025\pi$
$383$	16.5808	+	6.03491i	0.847239	+	0.308370i	0.118325	+	0.992975i	$0.462248\pi$
$384$	9.68269	−	17.0366i	0.494117	−	0.869395i
$385$	8.01393	−	45.4493i	0.408428	−	2.31631i
$386$	4.85284	−	1.37418i	0.247003	−	0.0699441i
$387$	7.52223	−	12.7340i	0.382376	−	0.647308i
$388$	7.35349	−	4.52764i	0.373317	−	0.229856i
$389$	8.73655	−	3.17984i	0.442961	−	0.161225i	−0.110904	−	0.993831i	$-0.535375\pi$
$389$	8.73655	−	3.17984i	0.442961	−	0.161225i	0.553865	+	0.832607i	$0.313152\pi$
$390$	13.2591	+	13.0184i	0.671403	+	0.659210i
$391$	5.99278	+	7.14192i	0.303068	+	0.361182i
$392$	1.26424	−	28.1849i	0.0638537	−	1.42355i
$393$	6.14472	+	10.7665i	0.309960	+	0.543100i
$394$	19.8379	+	8.91113i	0.999421	+	0.448936i
$395$	21.5153	−	12.4219i	1.08255	−	0.625012i
$396$	−26.5356	−	9.11104i	−1.33346	−	0.457847i
$397$	−7.08243	−	4.08904i	−0.355457	−	0.205223i	0.311629	−	0.950204i	$-0.399125\pi$
$397$	−7.08243	−	4.08904i	−0.355457	−	0.205223i	−0.667086	+	0.744981i	$0.732459\pi$
$398$	5.05120	+	7.00094i	0.253194	+	0.350926i
$399$	20.0102	+	7.39628i	1.00176	+	0.370277i
$400$	2.82810	+	0.851578i	0.141405	+	0.0425789i
$401$	13.6368	−	2.40454i	0.680992	−	0.120077i	0.177557	−	0.984111i	$-0.443181\pi$
$401$	13.6368	−	2.40454i	0.680992	−	0.120077i	0.503435	+	0.864033i	$0.332069\pi$
$402$	−7.47926	+	16.4308i	−0.373032	+	0.819491i
$403$	−19.8725	−	16.6750i	−0.989920	−	0.830641i
$404$	−0.322895	−	11.4090i	−0.0160646	−	0.567620i
$405$	11.1498	−	18.4524i	0.554036	−	0.916908i
$406$	10.0073	−	10.2945i	0.496652	−	0.510907i
$407$	2.13177	+	1.78877i	0.105668	+	0.0886660i
$408$	−11.6583	+	27.6613i	−0.577174	+	1.36944i
$409$	5.90748	+	33.5030i	0.292106	+	1.65662i	0.678737	+	0.734381i	$0.262527\pi$
$409$	5.90748	+	33.5030i	0.292106	+	1.65662i	−0.386631	+	0.922234i	$0.626361\pi$
$410$	−23.2038	+	11.2224i	−1.14595	+	0.554236i
$411$	11.7151	+	4.33019i	0.577863	+	0.213593i
$412$	3.64222	−	24.7282i	0.179439	−	1.21827i
$413$	−4.23607	+	7.33709i	−0.208443	+	0.361035i
$414$	−3.68055	+	5.30341i	−0.180889	+	0.260648i
$415$	−18.6942	+	10.7931i	−0.917661	+	0.529812i
$416$	6.40436	−	16.7300i	0.314000	−	0.820258i
$417$	3.41549	−	1.94930i	0.167257	−	0.0954578i
$418$	1.44422	−	19.7164i	0.0706393	−	0.964359i
$419$	−5.23370	−	6.23728i	−0.255683	−	0.304711i	0.622900	−	0.782302i	$-0.285955\pi$
$419$	−5.23370	−	6.23728i	−0.255683	−	0.304711i	−0.878582	+	0.477591i	$0.841510\pi$
$420$	−0.796890	−	34.1799i	−0.0388842	−	1.66781i
$421$	0.105414	+	0.289623i	0.00513758	+	0.0141154i	0.942235	−	0.334953i	$-0.108720\pi$
$421$	0.105414	+	0.289623i	0.00513758	+	0.0141154i	−0.937097	+	0.349068i	$0.886498\pi$
$422$	5.89359	−	23.3093i	0.286896	−	1.13468i
$423$	−6.36686	−	11.2860i	−0.309567	−	0.548746i
$424$	5.47528	+	17.4378i	0.265903	+	0.846855i
$425$	−4.45559	−	0.785641i	−0.216128	−	0.0381092i
$426$	7.19693	+	4.94169i	0.348692	+	0.239426i
$427$	29.2850	+	10.6589i	1.41720	+	0.515818i
$428$	3.27690	+	15.9339i	0.158395	+	0.770196i
$429$	−25.2359	−	4.57957i	−1.21840	−	0.221104i
$430$	−1.69085	−	16.6156i	−0.0815398	−	0.801274i
$431$	7.32094			0.352637			0.176319	−	0.984333i	$-0.443581\pi$
$431$	7.32094			0.352637			0.176319	+	0.984333i	$0.443581\pi$
$432$	−20.6013	−	2.75407i	−0.991182	−	0.132505i
$433$	−7.42545			−0.356845			−0.178422	−	0.983954i	$-0.557099\pi$
$433$	−7.42545			−0.356845			−0.178422	+	0.983954i	$0.557099\pi$
$434$	4.83227	+	47.4857i	0.231956	+	2.27939i
$435$	6.61048	−	7.79879i	0.316948	−	0.373923i
$436$	−3.53060	−	17.1676i	−0.169085	−	0.822178i
$437$	−4.27436	−	1.55574i	−0.204470	−	0.0744212i
$438$	2.23890	−	28.6076i	0.106979	−	1.36692i
$439$	−32.1605	−	5.67077i	−1.53494	−	0.270651i	−0.658654	−	0.752446i	$-0.728874\pi$
$439$	−32.1605	−	5.67077i	−1.53494	−	0.270651i	−0.876284	+	0.481795i	$0.839985\pi$
$440$	−30.2273	+	9.49104i	−1.44103	+	0.452468i
$441$	−28.2206	+	9.95403i	−1.34384	+	0.474001i
$442$	−6.72663	+	26.6040i	−0.319953	+	1.26542i
$443$	4.72732	+	12.9882i	0.224602	+	0.617088i	0.999895	−	0.0145136i	$-0.00461998\pi$
$443$	4.72732	+	12.9882i	0.224602	+	0.617088i	−0.775293	+	0.631602i	$0.782398\pi$
$444$	1.80892	+	0.988895i	0.0858476	+	0.0469309i
$445$	−13.9743	−	16.6539i	−0.662444	−	0.789470i
$446$	1.17638	−	16.0599i	0.0557034	−	0.760456i
$447$	−6.93155	−	4.04813i	−0.327851	−	0.191470i
$448$	−29.9054	+	13.8584i	−1.41290	+	0.654750i
$449$	13.8069	−	7.97139i	0.651586	−	0.376193i	−0.137478	−	0.990505i	$-0.543900\pi$
$449$	13.8069	−	7.97139i	0.651586	−	0.376193i	0.789063	+	0.614312i	$0.210566\pi$
$450$	−0.286073	−	3.11960i	−0.0134856	−	0.147060i
$451$	17.7885	−	30.8105i	0.837627	−	1.45081i
$452$	−1.01338	+	6.88014i	−0.0476653	+	0.323615i
$453$	−29.6715	+	24.6464i	−1.39409	+	1.15799i
$454$	−13.8610	+	6.70381i	−0.650527	+	0.314625i
$455$	−5.42732	−	30.7798i	−0.254437	−	1.44298i
$456$	−1.82190	−	14.5317i	−0.0853184	−	0.680507i
$457$	3.17040	+	2.66028i	0.148305	+	0.124443i	0.713922	−	0.700226i	$-0.246917\pi$
$457$	3.17040	+	2.66028i	0.148305	+	0.124443i	−0.565616	+	0.824668i	$0.691362\pi$
$458$	−8.25153	+	8.48837i	−0.385569	+	0.396636i
$459$	31.8350	+	0.476018i	1.48593	+	0.0222186i
$460$	0.206231	+	7.28685i	0.00961555	+	0.339751i
$461$	−9.38412	−	7.87421i	−0.437062	−	0.366739i	0.397546	−	0.917582i	$-0.369862\pi$
$461$	−9.38412	−	7.87421i	−0.437062	−	0.366739i	−0.834609	+	0.550843i	$0.814306\pi$
$462$	27.4205	+	38.4067i	1.27572	+	1.78684i
$463$	19.1902	−	3.38375i	0.891843	−	0.157256i	0.291095	−	0.956694i	$-0.405981\pi$
$463$	19.1902	−	3.38375i	0.891843	−	0.157256i	0.600748	+	0.799438i	$0.294869\pi$
$464$	−9.43750	−	2.84175i	−0.438125	−	0.131925i
$465$	5.73521	+	33.5015i	0.265964	+	1.55360i
$466$	−15.1997	−	21.0668i	−0.704114	−	0.975899i
$467$	−8.34898	−	4.82029i	−0.386345	−	0.223056i	0.294230	−	0.955735i	$-0.404937\pi$
$467$	−8.34898	−	4.82029i	−0.386345	−	0.223056i	−0.680575	+	0.732678i	$0.738270\pi$
$468$	−18.9974	+	0.348196i	−0.878157	+	0.0160954i
$469$	26.2970	−	15.1826i	1.21428	−	0.701067i
$470$	−13.3480	−	5.99588i	−0.615698	−	0.276569i
$471$	8.69817	+	0.0433507i	0.400790	+	0.00199749i
$472$	5.81030	+	0.260622i	0.267441	+	0.0119961i
$473$	14.8179	+	17.6593i	0.681329	+	0.811977i
$474$	−6.34985	+	24.5973i	−0.291658	+	1.12979i
$475$	2.07426	−	0.754970i	0.0951737	−	0.0346404i
$476$	42.9939	−	26.4719i	1.97062	−	1.21334i
$477$	14.9739	−	12.3124i	0.685609	−	0.563745i
$478$	27.4196	−	7.76443i	1.25414	−	0.355137i
$479$	4.24791	−	24.0911i	0.194092	−	1.10075i	−0.719614	−	0.694374i	$-0.755681\pi$
$479$	4.24791	−	24.0911i	0.194092	−	1.10075i	0.913706	−	0.406376i	$-0.133208\pi$
$480$	−20.5742	+	11.2955i	−0.939079	+	0.515565i
$481$	1.77097	+	0.644582i	0.0807494	+	0.0293904i
$482$	−0.246933	+	0.363496i	−0.0112475	+	0.0165568i
$483$	10.2216	−	3.66278i	0.465101	−	0.166662i
$484$	13.4916	−	17.0351i	0.613255	−	0.774321i
$485$	−10.3432			−0.469662
$486$	5.47606	+	21.3545i	0.248399	+	0.968658i
$487$		−	37.9129i		−	1.71800i	−0.511977	−	0.858999i	$-0.671087\pi$
$487$		−	37.9129i		−	1.71800i	0.511977	−	0.858999i	$-0.328913\pi$
$488$	−2.76725	−	21.2147i	−0.125267	−	0.960345i
$489$	−7.40501	−	20.6650i	−0.334866	−	0.934503i
$490$	−18.9889	+	27.9524i	−0.857832	+	1.26276i
$491$	11.1005	−	30.4983i	0.500957	−	1.37637i	−0.389384	−	0.921076i	$-0.627312\pi$
$491$	11.1005	−	30.4983i	0.500957	−	1.37637i	0.890341	−	0.455294i	$-0.150466\pi$
$492$	8.43462	−	24.9701i	0.380262	−	1.12574i
$493$	14.8685	+	2.62172i	0.669643	+	0.118076i
$494$	−3.64777	−	12.8819i	−0.164121	−	0.579583i
$495$	21.3427	+	25.9563i	0.959283	+	1.16665i
$496$	27.4053	−	17.9624i	1.23054	−	0.806537i
$497$	−5.02230	−	13.7987i	−0.225281	−	0.618954i
$498$	5.51725	−	21.3721i	0.247234	−	0.957707i
$499$	−21.5797	+	18.1075i	−0.966039	+	0.810603i	−0.981925	−	0.189270i	$-0.939388\pi$
$499$	−21.5797	+	18.1075i	−0.966039	+	0.810603i	0.0158855	+	0.999874i	$0.494943\pi$
$500$	13.5612	+	15.2630i	0.606477	+	0.682584i
$501$	−0.180834	+	36.2837i	−0.00807906	+	1.62104i
$502$	0.0106201	−	0.0236426i	0.000474000	−	0.00105522i
$503$	−11.6283	−	20.1409i	−0.518482	−	0.898038i	−0.999769	−	0.0214747i	$-0.993164\pi$
$503$	−11.6283	−	20.1409i	−0.518482	−	0.898038i	0.481287	−	0.876563i	$-0.340169\pi$
$504$	25.5099	+	23.9047i	1.13630	+	1.06480i
$505$	−6.83529	+	11.8391i	−0.304167	+	0.526832i
$506$	−5.88731	−	8.15979i	−0.261723	−	0.362747i
$507$	5.07308	−	0.868474i	0.225303	−	0.0385703i
$508$	10.8830	+	3.61584i	0.482855	+	0.160427i
$509$	−3.70129	−	20.9911i	−0.164057	−	0.930412i	−0.950032	−	0.312154i	$-0.898950\pi$
$509$	−3.70129	−	20.9911i	−0.164057	−	0.930412i	0.785975	−	0.618258i	$-0.212161\pi$
$510$	29.2613	−	20.8911i	1.29571	−	0.925075i
$511$	−31.0243	+	36.9733i	−1.37243	+	1.63560i
$512$	17.9022	+	13.8388i	0.791171	+	0.611594i
$513$	−13.5673	+	7.56491i	−0.599011	+	0.333999i
$514$	9.07333	−	9.33375i	0.400207	−	0.411694i
$515$	−19.2435	+	22.9335i	−0.847971	+	1.01057i
$516$	13.3347	+	10.6695i	0.587028	+	0.469700i
$517$	19.8906	−	3.50725i	0.874788	−	0.154249i
$518$	−1.50978	−	3.12166i	−0.0663359	−	0.137158i
$519$	18.6239	+	22.4211i	0.817497	+	0.984175i
$520$	−17.0381	+	13.0415i	−0.747168	+	0.571909i
$521$	−15.4557	−	8.92337i	−0.677128	−	0.390940i	0.121644	−	0.992574i	$-0.461183\pi$
$521$	−15.4557	−	8.92337i	−0.677128	−	0.390940i	−0.798772	+	0.601634i	$0.794517\pi$
$522$	0.954637	+	10.4103i	0.0417833	+	0.455644i
$523$	18.6467	+	32.2970i	0.815363	+	1.41225i	0.909067	+	0.416650i	$0.136796\pi$
$523$	18.6467	+	32.2970i	0.815363	+	1.41225i	−0.0937040	+	0.995600i	$0.529871\pi$
$524$	−13.3072	+	5.27438i	−0.581329	+	0.230412i
$525$	−2.65732	+	4.55008i	−0.115975	+	0.198582i
$526$	−1.26354	−	0.0925541i	−0.0550929	−	0.00403555i
$527$	−38.4510	+	32.2642i	−1.67495	+	1.40545i
$528$	14.7295	−	28.8544i	0.641019	−	1.25573i
$529$	19.4374	−	7.07464i	0.845105	−	0.307593i
$530$	5.36622	−	21.2236i	0.233094	−	0.921892i
$531$	−2.05202	−	5.81766i	−0.0890501	−	0.252465i
$532$	−11.7084	+	21.6733i	−0.507623	+	0.939658i
$533$	4.18387	−	23.7279i	0.181224	−	1.02777i
$534$	22.1624	+	1.73448i	0.959060	+	0.0750584i
$535$	6.66400	−	18.3092i	0.288110	−	0.791575i
$536$	−17.5678	−	11.2214i	−0.758812	−	0.484689i
$537$	0.644605	+	0.546385i	0.0278168	+	0.0235783i
$538$	0.589957	+	5.79738i	0.0254349	+	0.249943i
$539$		−	46.6428i		−	2.00905i
$540$	19.2822	+	15.7461i	0.829776	+	0.677605i
$541$			43.7115i			1.87930i	0.342134	+	0.939651i	$0.388850\pi$
$541$			43.7115i			1.87930i	−0.342134	+	0.939651i	$0.611150\pi$
$542$	22.0771	−	2.24663i	0.948293	−	0.0965008i
$543$	5.81563	−	32.0473i	0.249573	−	1.37528i
$544$	−29.7271	−	17.8246i	−1.27454	−	0.764222i
$545$	−7.17994	+	19.7267i	−0.307555	+	0.845000i
$546$	26.3463	+	18.0904i	1.12752	+	0.774197i
$547$	3.72897	−	21.1481i	0.159439	−	0.904225i	−0.795175	−	0.606380i	$-0.792621\pi$
$547$	3.72897	−	21.1481i	0.159439	−	0.904225i	0.954614	−	0.297845i	$-0.0962679\pi$
$548$	−6.85474	+	12.6888i	−0.292820	+	0.542037i
$549$	−19.7642	+	11.1497i	−0.843514	+	0.475856i
$550$	4.73389	+	1.19693i	0.201854	+	0.0510372i
$551$	−6.92190	+	2.51937i	−0.294883	+	0.107329i
$552$	−5.46453	−	5.06975i	−0.232586	−	0.215783i
$553$	32.7325	−	27.4658i	1.39193	−	1.16797i
$554$	0.851862	−	11.6295i	0.0361921	−	0.494091i
$555$	−1.22395	−	2.14456i	−0.0519538	−	0.0910314i
$556$	1.67320	+	4.22148i	0.0709596	+	0.179031i
$557$	21.0581	+	36.4737i	0.892260	+	1.54544i	0.837160	+	0.546958i	$0.184214\pi$
$557$	21.0581	+	36.4737i	0.892260	+	1.54544i	0.0550997	+	0.998481i	$0.482452\pi$
$558$	−28.5527	−	19.8155i	−1.20873	−	0.838858i
$559$	13.5204	+	7.80602i	0.571853	+	0.330159i
$560$	39.2040	+	4.64546i	1.65667	+	0.196306i
$561$	−17.2053	+	46.5481i	−0.726410	+	1.96526i
$562$	−23.0132	+	11.1303i	−0.970753	+	0.469501i
$563$	−37.4245	+	6.59896i	−1.57726	+	0.278113i	−0.892633	−	0.450784i	$-0.851144\pi$
$563$	−37.4245	+	6.59896i	−1.57726	+	0.278113i	−0.684624	+	0.728897i	$0.740033\pi$
$564$	13.9372	−	5.44387i	0.586863	−	0.229228i
$565$	5.35414	−	6.38082i	0.225251	−	0.268443i
$566$	29.7571	+	28.9269i	1.25079	+	1.21589i
$567$	13.3744	−	34.5846i	0.561670	−	1.45241i
$568$	−6.81931	+	7.42418i	−0.286132	+	0.311512i
$569$	−14.1090	+	16.8145i	−0.591481	+	0.704900i	−0.975890	−	0.218263i	$-0.929961\pi$
$569$	−14.1090	+	16.8145i	−0.591481	+	0.704900i	0.384409	+	0.923163i	$0.374405\pi$
$570$	−7.26737	+	15.9653i	−0.304397	+	0.668711i
$571$	3.32137	+	18.8364i	0.138995	+	0.788280i	0.971994	+	0.235005i	$0.0755108\pi$
$571$	3.32137	+	18.8364i	0.138995	+	0.788280i	−0.832999	+	0.553274i	$0.813378\pi$
$572$	9.33785	−	28.1052i	0.390435	−	1.17514i
$573$	−4.02118	+	10.8791i	−0.167987	+	0.454480i
$574$	−35.9507	+	25.9385i	−1.50055	+	1.08265i
$575$	0.561747	−	0.972974i	0.0234265	−	0.0405758i
$576$	6.49751	−	23.1037i	0.270730	−	0.962655i
$577$	−6.15628	−	10.6630i	−0.256289	−	0.443906i	0.708956	−	0.705253i	$-0.249167\pi$
$577$	−6.15628	−	10.6630i	−0.256289	−	0.443906i	−0.965245	+	0.261347i	$0.915833\pi$
$578$	26.5030	+	11.9050i	1.10238	+	0.495184i
$579$	5.36493	−	3.06190i	0.222959	−	0.127248i
$580$	7.84094	+	8.82491i	0.325578	+	0.366434i
$581$	−28.4406	+	23.8645i	−1.17991	+	0.990065i
$582$	7.40979	−	7.54685i	0.307146	−	0.312827i
$583$	10.3346	+	28.3941i	0.428016	+	1.17596i
$584$	32.3402	+	7.21010i	1.33825	+	0.298356i
$585$	19.5946	+	11.5749i	0.810135	+	0.478561i
$586$	−33.7553	+	9.55852i	−1.39442	+	0.394859i
$587$	−22.8381	−	4.02697i	−0.942628	−	0.166211i	−0.318844	−	0.947807i	$-0.603295\pi$
$587$	−22.8381	−	4.02697i	−0.942628	−	0.166211i	−0.623784	+	0.781596i	$0.714406\pi$
$588$	−6.79176	−	33.8799i	−0.280088	−	1.39718i
$589$	8.37587	−	23.0125i	0.345122	−	0.948214i
$590$	−5.76238	−	3.91456i	−0.237234	−	0.161160i
$591$	26.2071	+	4.75581i	1.07801	+	0.195628i
$592$	−1.42457	+	1.90720i	−0.0585496	+	0.0783853i
$593$			8.83919i			0.362982i	0.983393	+	0.181491i	$0.0580923\pi$
$593$			8.83919i			0.362982i	−0.983393	+	0.181491i	$0.941908\pi$
$594$	−34.2285	−	3.02235i	−1.40441	−	0.124009i
$595$	−60.4742			−2.47920
$596$	5.75465	−	7.26606i	0.235719	−	0.297629i
$597$	8.06554	+	6.83658i	0.330101	+	0.279803i
$598$	−5.63668	−	3.82916i	−0.230501	−	0.156586i
$599$	26.0480	+	9.48068i	1.06429	+	0.387370i	0.814039	−	0.580810i	$-0.197264\pi$
$599$	26.0480	+	9.48068i	1.06429	+	0.387370i	0.250252	+	0.968181i	$0.419486\pi$
$600$	3.61284	+	0.180101i	0.147493	+	0.00735259i
$601$	−1.57170	+	8.91355i	−0.0641109	+	0.363591i	0.935827	+	0.352459i	$0.114655\pi$
$601$	−1.57170	+	8.91355i	−0.0641109	+	0.363591i	−0.999938	+	0.0111318i	$0.996457\pi$
$602$	−7.82637	−	27.6383i	−0.318979	−	1.12645i
$603$	−4.05625	+	21.7350i	−0.165183	+	0.885118i
$604$	−23.3522	−	37.9271i	−0.950189	−	1.54323i
$605$	−24.4580	+	8.90199i	−0.994360	+	0.361917i
$606$	−3.74154	−	13.4687i	−0.151990	−	0.547129i
$607$	25.4111	+	30.2837i	1.03140	+	1.22918i	0.972981	+	0.230887i	$0.0741628\pi$
$607$	25.4111	+	30.2837i	1.03140	+	1.22918i	0.0584230	+	0.998292i	$0.481393\pi$
$608$	16.9088	+	0.279544i	0.685741	+	0.0113370i
$609$	8.86757	−	15.1838i	0.359332	−	0.615280i
$610$	−10.5000	+	23.3751i	−0.425133	+	0.946430i
$611$	11.8459	−	6.83921i	0.479232	−	0.276685i
$612$	−5.71945	+	36.3164i	−0.231195	+	1.46800i
$613$	35.9899	+	20.7788i	1.45362	+	0.839247i	0.998684	−	0.0512782i	$-0.0163295\pi$
$613$	35.9899	+	20.7788i	1.45362	+	0.839247i	0.454934	+	0.890525i	$0.349663\pi$
$614$	−24.6622	+	17.7938i	−0.995284	+	0.718101i
$615$	−24.2833	+	20.1707i	−0.979197	+	0.813362i
$616$	−48.3642	+	25.1036i	−1.94865	+	1.01145i
$617$	31.5076	−	5.55563i	1.26845	−	0.223661i	0.501379	−	0.865228i	$-0.332826\pi$
$617$	31.5076	−	5.55563i	1.26845	−	0.223661i	0.767068	+	0.641566i	$0.221715\pi$
$618$	−2.94738	−	30.4702i	−0.118561	−	1.22569i
$619$	16.5318	+	13.8718i	0.664469	+	0.557556i	0.911423	−	0.411472i	$-0.134985\pi$
$619$	16.5318	+	13.8718i	0.664469	+	0.557556i	−0.246954	+	0.969027i	$0.579430\pi$
$620$	−39.2313	+	1.11031i	−1.57557	+	0.0445913i
$621$	−2.81487	+	7.38819i	−0.112957	+	0.296478i
$622$	7.44299	+	7.23532i	0.298437	+	0.290110i
$623$	−28.6434	−	24.0346i	−1.14757	−	0.962927i
$624$	2.69027	−	21.7745i	0.107697	−	0.871677i
$625$	−4.88762	−	27.7191i	−0.195505	−	1.10876i
$626$	−10.7633	−	22.2544i	−0.430186	−	0.889465i
$627$	−4.08552	−	23.8650i	−0.163160	−	0.953078i
$628$	−1.46358	+	9.93670i	−0.0584031	+	0.396517i
$629$	1.82327	−	3.15800i	0.0726986	−	0.125918i
$630$	−11.0065	−	40.4006i	−0.438509	−	1.60960i
$631$	4.57723	−	2.64266i	0.182216	−	0.105203i	−0.406117	−	0.913821i	$-0.633118\pi$
$631$	4.57723	−	2.64266i	0.182216	−	0.105203i	0.588334	+	0.808618i	$0.299784\pi$
$632$	−27.0874	−	11.2578i	−1.07748	−	0.447812i
$633$	0.146755	−	29.4460i	0.00583301	−	1.17037i
$634$	−40.8666	−	2.99348i	−1.62302	−	0.118886i
$635$	−8.82914	−	10.5222i	−0.350374	−	0.417559i
$636$	11.6413	+	19.1198i	0.461606	+	0.758148i
$637$	−10.8038	−	29.6832i	−0.428062	−	1.17609i
$638$	−15.7972	−	3.99420i	−0.625416	−	0.158132i
$639$	10.0105	+	3.75693i	0.396008	+	0.148622i
$640$	−9.56833	−	25.3567i	−0.378221	−	1.00231i
$641$	32.6852	+	5.76327i	1.29099	+	0.227636i	0.776639	−	0.629946i	$-0.216923\pi$
$641$	32.6852	+	5.76327i	1.29099	+	0.227636i	0.514347	+	0.857582i	$0.328034\pi$
$642$	8.58511	+	17.9788i	0.338827	+	0.709568i
$643$	7.58213	+	2.75967i	0.299010	+	0.108831i	0.487169	−	0.873308i	$-0.338030\pi$
$643$	7.58213	+	2.75967i	0.299010	+	0.108831i	−0.188159	+	0.982139i	$0.560252\pi$
$644$	2.52561	+	12.2808i	0.0995230	+	0.483932i
$645$	−6.90012	−	19.2560i	−0.271692	−	0.758204i
$646$	−25.7719	+	2.62262i	−1.01398	+	0.103185i
$647$	24.3144			0.955899			0.477949	−	0.878387i	$-0.341380\pi$
$647$	24.3144			0.955899			0.477949	+	0.878387i	$0.341380\pi$
$648$	−25.3026	+	2.78874i	−0.993981	+	0.109552i
$649$	9.61540			0.377438
$650$	3.28985	−	0.334784i	0.129039	−	0.0131313i
$651$	19.7199	+	55.0317i	0.772882	+	2.15686i
$652$	24.8280	−	5.10600i	0.972339	−	0.199966i
$653$	16.3970	+	5.96802i	0.641664	+	0.233546i	0.642300	−	0.766453i	$-0.277980\pi$
$653$	16.3970	+	5.96802i	0.641664	+	0.233546i	−0.000636328		1.00000i	$0.500203\pi$
$654$	−9.24979	−	19.3708i	−0.361695	−	0.757459i
$655$	16.8845	+	2.97720i	0.659733	+	0.116329i
$656$	27.1746	+	13.7017i	1.06099	+	0.534962i
$657$	−5.75743	−	34.6693i	−0.224619	−	1.35258i
$658$	−24.3995	−	6.16923i	−0.951191	−	0.240502i
$659$	2.56608	+	7.05026i	0.0999605	+	0.274639i	0.979585	−	0.201029i	$-0.0644286\pi$
$659$	2.56608	+	7.05026i	0.0999605	+	0.274639i	−0.879625	+	0.475668i	$0.842206\pi$
$660$	−33.1429	+	20.1794i	−1.29008	+	0.785481i
$661$	2.14185	+	2.55256i	0.0833084	+	0.0992831i	0.806089	−	0.591795i	$-0.201580\pi$
$661$	2.14185	+	2.55256i	0.0833084	+	0.0992831i	−0.722780	+	0.691078i	$0.757136\pi$
$662$	−16.8551	−	1.23464i	−0.655093	−	0.0479856i
$663$	−0.167499	+	33.6081i	−0.00650512	+	1.30523i
$664$	23.5357	+	9.78168i	0.913361	+	0.379603i
$665$	25.5520	−	14.7525i	0.990864	−	0.572076i
$666$	2.44158	+	0.643296i	0.0946095	+	0.0249272i
$667$	−1.87457	+	3.24686i	−0.0725838	+	0.125719i
$668$	−41.4501	−	6.10520i	−1.60375	−	0.236217i
$669$	−3.32784	−	19.4391i	−0.128662	−	0.751560i
$670$	10.8710	+	22.4771i	0.419982	+	0.868365i
$671$	−6.14191	−	34.8325i	−0.237106	−	1.34469i
$672$	−31.4749	+	25.2769i	−1.21417	+	0.975077i
$673$	−23.1052	−	19.3875i	−0.890639	−	0.747335i	0.0776994	−	0.996977i	$-0.475243\pi$
$673$	−23.1052	−	19.3875i	−0.890639	−	0.747335i	−0.968338	+	0.249642i	$0.919687\pi$
$674$	−29.3531	−	28.5341i	−1.13064	−	1.09909i
$675$	−1.25820	−	3.62458i	−0.0484280	−	0.139510i
$676$	0.168133	+	5.94073i	0.00646665	+	0.228490i
$677$	2.61657	+	2.19556i	0.100563	+	0.0843823i	0.691683	−	0.722201i	$-0.256870\pi$
$677$	2.61657	+	2.19556i	0.100563	+	0.0843823i	−0.591120	+	0.806584i	$0.701314\pi$
$678$	0.820051	+	8.47776i	0.0314939	+	0.325586i
$679$	−17.5193	+	3.08912i	−0.672329	+	0.118550i
$680$	19.1259	+	36.8477i	0.733444	+	1.41304i
$681$	−14.5058	+	12.0491i	−0.555865	+	0.461724i
$682$	43.9310	−	31.6964i	1.68221	−	1.21372i
$683$	17.2082	+	9.93518i	0.658455	+	0.380159i	0.791688	−	0.610926i	$-0.209203\pi$
$683$	17.2082	+	9.93518i	0.658455	+	0.380159i	−0.133233	+	0.991085i	$0.542536\pi$
$684$	−6.44263	−	16.7399i	−0.246340	−	0.640067i
$685$	14.9596	−	8.63691i	0.571576	−	0.329999i
$686$	−7.10250	+	15.8116i	−0.271175	+	0.603689i
$687$	−7.31180	+	12.5199i	−0.278963	+	0.477664i
$688$	−14.3652	+	13.5097i	−0.547667	+	0.515054i
$689$	13.1537	+	15.6760i	0.501117	+	0.597208i
$690$	2.38969	+	8.60235i	0.0909739	+	0.327486i
$691$	−7.73987	+	2.81708i	−0.294439	+	0.107167i	−0.485016	−	0.874505i	$-0.661186\pi$
$691$	−7.73987	+	2.81708i	−0.294439	+	0.107167i	0.190577	+	0.981672i	$0.438964\pi$
$692$	−28.6593	+	17.6459i	−1.08946	+	0.670797i
$693$	43.9022	+	37.5904i	1.66771	+	1.42794i
$694$	−6.08049	−	21.4729i	−0.230812	−	0.815099i
$695$	0.944462	−	5.35631i	0.0358255	−	0.203176i
$696$	−12.0562	−	0.601004i	−0.456989	−	0.0227810i
$697$	−43.8076	−	15.9447i	−1.65933	−	0.603947i
$698$	28.0767	+	19.0733i	1.06272	+	0.721937i
$699$	−24.2703	−	20.5722i	−0.917987	−	0.778111i
$700$	−4.76967	−	3.77753i	−0.180277	−	0.142777i
$701$	−11.7959			−0.445526			−0.222763	−	0.974873i	$-0.571508\pi$
$701$	−11.7959			−0.445526			−0.222763	+	0.974873i	$0.571508\pi$
$702$	−22.4828	+	6.00488i	−0.848560	+	0.226639i
$703$			1.77912i			0.0671009i
$704$	30.5918	+	21.5295i	1.15297	+	0.811423i
$705$	−17.6335	−	3.19996i	−0.664116	−	0.120517i
$706$	39.5549	+	26.8708i	1.48867	+	1.01130i
$707$	−8.04169	+	22.0944i	−0.302439	+	0.830944i
$708$	6.98434	−	1.40012i	0.262487	−	0.0526197i
$709$	2.70606	+	0.477152i	0.101628	+	0.0179198i	0.224231	−	0.974536i	$-0.428013\pi$
$709$	2.70606	+	0.477152i	0.101628	+	0.0179198i	−0.122603	+	0.992456i	$0.539124\pi$
$710$	11.6174	−	3.28970i	0.435993	−	0.123460i
$711$	−0.310120	+	31.1115i	−0.0116304	+	1.16677i
$712$	−5.58569	+	25.0541i	−0.209333	+	0.938941i
$713$	−4.26307	−	11.7127i	−0.159653	−	0.438643i
$714$	43.3231	−	44.1244i	1.62133	−	1.65132i
$715$	−27.1733	+	22.8011i	−1.01623	+	0.852714i
$716$	−0.729418	+	0.648089i	−0.0272596	+	0.0242202i
$717$	30.3130	−	17.3004i	1.13206	−	0.646094i
$718$	7.86832	+	3.53442i	0.293643	+	0.131903i
$719$	−14.1260	−	24.4670i	−0.526811	−	0.912464i	−0.999512	−	0.0312409i	$-0.990054\pi$
$719$	−14.1260	−	24.4670i	−0.526811	−	0.912464i	0.472701	−	0.881223i	$-0.343279\pi$
$720$	−21.1356	+	19.4837i	−0.787677	+	0.726114i
$721$	−25.7452	+	44.5919i	−0.958800	+	1.66069i
$722$	−11.5409	+	8.32678i	−0.429507	+	0.309891i
$723$	−0.186593	+	0.504818i	−0.00693947	+	0.0187744i
$724$	35.6911	+	11.8582i	1.32645	+	0.440707i
$725$	−0.315933	−	1.79175i	−0.0117335	−	0.0665438i
$726$	11.0262	−	24.2229i	0.409222	−	0.898995i
$727$	14.8952	−	17.7514i	0.552433	−	0.658364i	−0.415494	−	0.909596i	$-0.636391\pi$
$727$	14.8952	−	17.7514i	0.552433	−	0.658364i	0.967927	+	0.251232i	$0.0808358\pi$
$728$	−24.9639	+	27.1782i	−0.925224	+	1.00729i
$729$	12.7949	+	23.7759i	0.473884	+	0.880588i
$730$	−28.4567	−	27.6627i	−1.05323	−	1.02384i
$731$	19.4170	−	23.1403i	0.718164	−	0.855875i
$732$	−9.53333	−	24.4069i	−0.352362	−	0.902106i
$733$	47.0785	−	8.30121i	1.73888	−	0.306612i	0.787889	−	0.615817i	$-0.211174\pi$
$733$	47.0785	−	8.30121i	1.73888	−	0.306612i	0.950996	+	0.309205i	$0.100063\pi$
$734$	37.0137	−	17.9016i	1.36620	−	0.660759i
$735$	−14.3488	+	38.8199i	−0.529264	+	1.43189i
$736$	6.68408	−	5.42288i	0.246379	−	0.199890i
$737$	−29.8456	−	17.2314i	−1.09938	−	0.634726i
$738$	2.67893	−	32.1682i	0.0986127	−	1.18413i
$739$	−1.99397	−	3.45366i	−0.0733494	−	0.127045i	0.827018	−	0.562176i	$-0.190035\pi$
$739$	−1.99397	−	3.45366i	−0.0733494	−	0.127045i	−0.900367	+	0.435131i	$0.856702\pi$
$740$	2.65063	−	1.05059i	0.0974391	−	0.0386205i
$741$	−8.12780	−	14.2412i	−0.298582	−	0.523164i
$742$	2.75061	−	37.5510i	0.100978	−	1.37854i
$743$	−16.4338	+	13.7896i	−0.602899	+	0.505893i	−0.892376	−	0.451292i	$-0.850963\pi$
$743$	−16.4338	+	13.7896i	−0.602899	+	0.505893i	0.289477	+	0.957185i	$0.406519\pi$
$744$	27.2948	−	29.4202i	1.00068	−	1.07860i
$745$	−10.4322	+	3.79702i	−0.382207	+	0.139112i
$746$	−29.1129	−	7.36098i	−1.06590	−	0.269505i
$747$	0.269457	−	27.0322i	0.00985892	−	0.989055i
$748$	−50.4168	−	27.2362i	−1.84342	−	0.995855i
$749$	5.81918	−	33.0022i	0.212628	−	1.20588i
$750$	20.6143	+	14.1546i	0.752728	+	0.516852i
$751$	9.59163	−	26.3528i	0.350003	−	0.961626i	−0.632365	−	0.774671i	$-0.717916\pi$
$751$	9.59163	−	26.3528i	0.350003	−	0.961626i	0.982368	−	0.186956i	$-0.0598621\pi$
$752$	3.95773	+	16.8180i	0.144323	+	0.613290i
$753$	0.00566790	−	0.0312332i	0.000206550	−	0.00113820i
$754$	−10.9784	+	1.11719i	−0.399809	+	0.0406856i
$755$			53.3474i			1.94151i
$756$	37.3629	+	20.9118i	1.35887	+	0.760555i
$757$			51.0475i			1.85535i	0.373386	+	0.927676i	$0.378197\pi$
$757$			51.0475i			1.85535i	−0.373386	+	0.927676i	$0.621803\pi$
$758$	−2.35323	−	23.1247i	−0.0854732	−	0.839927i
$759$	−9.40060	−	7.96822i	−0.341220	−	0.289228i
$760$	−17.0701	−	10.9035i	−0.619196	−	0.395510i
$761$	14.1919	−	38.9919i	0.514455	−	1.41345i	−0.362094	−	0.932142i	$-0.617938\pi$
$761$	14.1919	−	38.9919i	0.514455	−	1.41345i	0.876549	−	0.481312i	$-0.159840\pi$
$762$	14.0025	+	1.09587i	0.507257	+	0.0396992i
$763$	−6.26972	+	35.5573i	−0.226979	+	1.28726i
$764$	−11.7833	−	6.36557i	−0.426303	−	0.230298i
$765$	28.6393	−	33.4482i	1.03546	−	1.20932i
$766$	−6.11686	+	24.1923i	−0.221011	+	0.874105i
$767$	6.11917	−	2.22720i	0.220951	−	0.0804194i
$768$	25.3559	+	11.1838i	0.914953	+	0.403561i
$769$	−8.38249	+	7.03375i	−0.302280	+	0.253643i	−0.781293	−	0.624165i	$-0.785439\pi$
$769$	−8.38249	+	7.03375i	−0.302280	+	0.253643i	0.479012	+	0.877808i	$0.340995\pi$
$770$	65.0921	+	4.76800i	2.34576	+	0.171827i
$771$	8.04001	−	13.7668i	0.289554	−	0.495799i
$772$	2.62821	+	6.63095i	0.0945913	+	0.238653i
$773$	9.53635	+	16.5174i	0.342999	+	0.594091i	0.984988	−	0.172622i	$-0.0552240\pi$
$773$	9.53635	+	16.5174i	0.342999	+	0.594091i	−0.641989	+	0.766714i	$0.721891\pi$
$774$	18.9931	+	8.76019i	0.682694	+	0.314878i
$775$	5.23834	+	3.02436i	0.188167	+	0.108638i
$776$	7.42298	+	9.69773i	0.266470	+	0.348128i
$777$	−2.71361	−	3.26689i	−0.0973504	−	0.117199i
$778$	5.72473	+	11.8366i	0.205241	+	0.424362i
$779$	22.3995	−	3.94964i	0.802547	−	0.141511i
$780$	−16.4178	+	20.5188i	−0.587850	+	0.734692i
$781$	−10.7125	+	12.7667i	−0.383325	+	0.456829i
$782$	−9.19029	+	9.45407i	−0.328644	+	0.338077i
$783$	4.19865	+	12.0954i	0.150048	+	0.432254i
$784$	39.8356	−	2.25664i	1.42270	−	0.0805944i
$785$	7.73276	−	9.21555i	0.275994	−	0.328917i
$786$	−14.2682	+	10.1868i	−0.508929	+	0.363351i
$787$	−7.49429	−	42.5022i	−0.267143	−	1.51504i	−0.762863	−	0.646560i	$-0.776207\pi$
$787$	−7.49429	−	42.5022i	−0.267143	−	1.51504i	0.495721	−	0.868482i	$-0.334904\pi$
$788$	−9.69719	+	29.1868i	−0.345448	+	1.03974i
$789$	−1.52941	+	0.261823i	−0.0544484	+	0.00932116i
$790$	20.5573	+	28.4924i	0.731398	+	1.01371i
$791$	7.16310	−	12.4069i	0.254691	−	0.441137i
$792$	9.01952	−	38.6387i	0.320495	−	1.37297i
$793$	−11.9769	−	20.7445i	−0.425310	−	0.736659i
$794$	4.73904	−	10.5501i	0.168182	−	0.374407i
$795$	0.133623	−	26.8111i	0.00473914	−	0.950892i
$796$	−9.12675	+	8.10913i	−0.323489	+	0.287421i
$797$	−29.5764	+	24.8175i	−1.04765	+	0.879082i	−0.992844	−	0.119415i	$-0.961898\pi$
$797$	−29.5764	+	24.8175i	−1.04765	+	0.879082i	−0.0548050	+	0.998497i	$0.517454\pi$
$798$	−7.54121	+	29.2123i	−0.266956	+	1.03410i
$799$	−9.05196	−	24.8701i	−0.320235	−	0.879840i
$800$	−0.793213	+	4.10092i	−0.0280443	+	0.144989i
$801$	26.8584	−	4.46030i	0.948996	−	0.157597i
$802$	5.33552	+	18.8421i	0.188404	+	0.665336i
$803$	53.9461	+	9.51216i	1.90372	+	0.335677i
$804$	−24.1880	−	8.17046i	−0.853047	−	0.288150i
$805$	5.13616	−	14.1115i	0.181026	−	0.497365i
$806$	20.6156	−	30.3470i	0.726154	−	1.06893i
$807$	2.40754	+	6.71865i	0.0847493	+	0.236508i
$808$	16.0057	−	2.08778i	0.563077	−	0.0734479i
$809$			22.9539i			0.807018i	0.914976	+	0.403509i	$0.132210\pi$
$809$			22.9539i			0.807018i	−0.914976	+	0.403509i	$0.867790\pi$
$810$	27.5579	+	13.0452i	0.968288	+	0.458362i
$811$	52.2072			1.83324			0.916622	−	0.399755i	$-0.130905\pi$
$811$	52.2072			1.83324			0.916622	+	0.399755i	$0.130905\pi$
$812$	15.9166	+	12.6058i	0.558563	+	0.442376i
$813$	25.5854	−	9.16818i	0.897320	−	0.321542i
$814$	−2.21149	+	3.25540i	−0.0775126	+	0.114102i
$815$	−28.5291	−	10.3837i	−0.999329	−	0.363726i
$816$	−40.5872	−	12.4423i	−1.42083	−	0.435566i
$817$	−2.55923	+	14.5141i	−0.0895361	+	0.507785i
$818$	−46.2911	+	13.1083i	−1.61853	+	0.458321i
$819$	36.6460	+	13.7533i	1.28052	+	0.480578i
$820$	−19.1116	−	31.0397i	−0.667404	−	1.08395i
$821$	31.4028	−	11.4297i	1.09597	−	0.398899i	0.270138	−	0.962821i	$-0.412931\pi$
$821$	31.4028	−	11.4297i	1.09597	−	0.398899i	0.825828	+	0.563922i	$0.190708\pi$
$822$	−4.41504	+	17.1025i	−0.153992	+	0.596518i
$823$	−17.5246	−	20.8850i	−0.610869	−	0.728006i	0.368602	−	0.929587i	$-0.379836\pi$
$823$	−17.5246	−	20.8850i	−0.610869	−	0.728006i	−0.979472	+	0.201581i	$0.935392\pi$
$824$	35.3127	+	1.58396i	1.23018	+	0.0551798i
$825$	5.98018	+	0.0298045i	0.208203	+	0.00103766i
$826$	−10.9294	−	4.90944i	−0.380283	−	0.170821i
$827$	−16.9312	+	9.77521i	−0.588754	+	0.339917i	−0.764605	−	0.644500i	$-0.777066\pi$
$827$	−16.9312	+	9.77521i	−0.588754	+	0.339917i	0.175851	+	0.984417i	$0.443732\pi$
$828$	−7.98858	−	4.41903i	−0.277622	−	0.153572i
$829$	−33.6076	−	19.4034i	−1.16724	−	0.673907i	−0.214212	−	0.976787i	$-0.568718\pi$
$829$	−33.6076	−	19.4034i	−1.16724	−	0.673907i	−0.953028	+	0.302881i	$0.902052\pi$
$830$	−17.8618	−	24.7564i	−0.619994	−	0.859308i
$831$	−2.40981	−	14.0766i	−0.0835952	−	0.488311i
$832$	24.4552	+	6.61529i	0.847833	+	0.229344i
$833$	−60.1909	+	10.6133i	−2.08549	+	0.367728i
$834$	3.23158	+	4.52633i	0.111900	+	0.156734i
$835$	38.4419	+	32.2566i	1.33034	+	1.11629i
$836$	27.9467	−	0.790939i	0.966556	−	0.0273552i
$837$	−39.7769	−	15.1548i	−1.37489	−	0.523828i
$838$	8.02619	−	8.25656i	0.277260	−	0.285218i
$839$	−15.7664	−	13.2295i	−0.544315	−	0.456735i	0.328695	−	0.944436i	$-0.393391\pi$
$839$	−15.7664	−	13.2295i	−0.544315	−	0.456735i	−0.873011	+	0.487701i	$0.837836\pi$
$840$	47.9752	−	6.01488i	1.65530	−	0.207533i
$841$	−3.98151	−	22.5803i	−0.137294	−	0.778631i
$842$	−0.392392	+	0.189779i	−0.0135227	+	0.00654022i
$843$	−24.0839	+	20.0051i	−0.829492	+	0.689011i
$844$	33.6388	+	4.95467i	1.15790	+	0.170547i
$845$	3.55917	−	6.16466i	0.122439	−	0.212071i
$846$	14.9673	−	10.5737i	0.514586	−	0.363532i
$847$	−38.7681	+	22.3828i	−1.33209	+	0.769082i
$848$	−23.7502	+	10.2001i	−0.815584	+	0.350272i
$849$	43.8902	+	25.6325i	1.50631	+	0.879706i
$850$	0.467427	−	6.38127i	0.0160326	−	0.218876i
$851$	0.582057	+	0.693669i	0.0199527	+	0.0237787i
$852$	−5.92228	+	10.8332i	−0.202894	+	0.371140i
$853$	−2.46287	−	6.76669i	−0.0843271	−	0.231687i	0.890361	−	0.455255i	$-0.150452\pi$
$853$	−2.46287	−	6.76669i	−0.0843271	−	0.231687i	−0.974688	+	0.223568i	$0.928230\pi$
$854$	−10.8036	+	42.7285i	−0.369691	+	1.46214i
$855$	−3.94134	+	21.1192i	−0.134791	+	0.722263i
$856$	−21.9491	+	6.89176i	−0.750203	+	0.235555i
$857$	29.3590	+	5.17678i	1.00288	+	0.176835i	0.650894	−	0.759169i	$-0.274394\pi$
$857$	29.3590	+	5.17678i	1.00288	+	0.176835i	0.351989	+	0.936004i	$0.385505\pi$
$858$	2.83007	−	36.1613i	0.0966170	−	1.23453i
$859$	3.08290	+	1.12209i	0.105187	+	0.0382851i	0.394078	−	0.919077i	$-0.371064\pi$
$859$	3.08290	+	1.12209i	0.105187	+	0.0382851i	−0.288890	+	0.957362i	$0.593286\pi$
$860$	23.1352	−	4.75786i	0.788902	−	0.162242i
$861$	−35.1066	+	41.4175i	−1.19643	+	1.41150i
$862$	1.04817	+	10.3002i	0.0357009	+	0.350825i
$863$	−4.17144			−0.141998			−0.0709988	−	0.997476i	$-0.522619\pi$
$863$	−4.17144			−0.141998			−0.0709988	+	0.997476i	$0.522619\pi$
$864$	0.925240	−	29.3793i	0.0314773	−	0.999504i
$865$	40.3115			1.37063
$866$	−1.06314	−	10.4472i	−0.0361269	−	0.355011i
$867$	35.0120	+	6.35363i	1.18907	+	0.215781i
$868$	−66.1180	+	13.5975i	−2.24419	+	0.461529i
$869$	−45.5706	−	16.5864i	−1.54588	−	0.562654i
$870$	11.9189	+	8.18400i	0.404090	+	0.277464i
$871$	−22.9848	−	4.05284i	−0.778810	−	0.137325i
$872$	23.6484	−	7.42533i	0.800836	−	0.251454i
$873$	6.58818	−	11.1528i	0.222976	−	0.377466i
$874$	1.57686	−	6.23654i	0.0533382	−	0.210954i
$875$	−14.3855	−	39.5238i	−0.486318	−	1.33615i
$876$	40.5699	−	0.945870i	1.37073	−	0.0319580i
$877$	−33.1422	−	39.4974i	−1.11913	−	1.33373i	−0.936547	−	0.350542i	$-0.885997\pi$
$877$	−33.1422	−	39.4974i	−1.11913	−	1.33373i	−0.182587	−	0.983190i	$-0.558447\pi$
$878$	3.37390	−	46.0601i	0.113864	−	1.55445i
$879$	−37.3173	+	21.2979i	−1.25868	+	0.718360i
$880$	−17.6812	−	41.1694i	−0.596033	−	1.38782i
$881$	−22.9746	+	13.2644i	−0.774035	+	0.446889i	−0.834312	−	0.551292i	$-0.814135\pi$
$881$	−22.9746	+	13.2644i	−0.774035	+	0.446889i	0.0602771	+	0.998182i	$0.480802\pi$
$882$	−18.0453	−	38.2797i	−0.607616	−	1.28894i
$883$	13.5287	−	23.4324i	0.455278	−	0.788565i	−0.543426	−	0.839457i	$-0.682873\pi$
$883$	13.5287	−	23.4324i	0.455278	−	0.788565i	0.998704	+	0.0508924i	$0.0162065\pi$
$884$	−38.3936	−	5.65500i	−1.29132	−	0.190198i
$885$	−8.00272	−	2.95800i	−0.269008	−	0.0994321i
$886$	−17.5969	+	8.51067i	−0.591179	+	0.285922i
$887$	7.50574	+	42.5672i	0.252018	+	1.42927i	0.803612	+	0.595153i	$0.202909\pi$
$887$	7.50574	+	42.5672i	0.252018	+	1.42927i	−0.551594	+	0.834113i	$0.685980\pi$
$888$	−1.13233	+	2.68664i	−0.0379986	+	0.0901578i
$889$	−18.0973	−	15.1854i	−0.606964	−	0.509303i
$890$	21.4304	−	22.0455i	0.718348	−	0.738966i
$891$	−41.5824	+	6.48024i	−1.39306	+	0.217096i
$892$	22.7638	−	0.644255i	0.762188	−	0.0215713i
$893$	9.89166	+	8.30009i	0.331012	+	0.277752i
$894$	4.70308	−	10.3319i	0.157294	−	0.345551i
$895$	1.15093	−	0.202941i	0.0384715	−	0.00678356i
$896$	−23.7798	−	40.0912i	−0.794427	−	1.33935i
$897$	−7.82814	−	2.89347i	−0.261374	−	0.0966102i
$898$	13.1921	+	18.2842i	0.440227	+	0.610152i
$899$	−17.4806	−	10.0924i	−0.583010	−	0.336601i
$900$	4.34816	−	0.849138i	0.144939	−	0.0283046i
$901$	34.2900	−	19.7973i	1.14237	−	0.659545i
$902$	45.8957	+	20.6162i	1.52816	+	0.686443i
$903$	−17.4384	−	30.5548i	−0.580313	−	1.01680i
$904$	−9.82508	−	0.440706i	−0.326777	−	0.0146577i
$905$	−28.9554	−	34.5076i	−0.962509	−	1.14707i
$906$	−38.9244	−	38.2175i	−1.29318	−	1.26969i
$907$	21.6817	−	7.89150i	0.719930	−	0.262033i	0.0440338	−	0.999030i	$-0.485979\pi$
$907$	21.6817	−	7.89150i	0.719930	−	0.262033i	0.675896	+	0.736997i	$0.263757\pi$
$908$	−11.4164	−	18.5418i	−0.378868	−	0.615332i
$909$	−8.41198	−	14.9113i	−0.279008	−	0.494576i
$910$	42.5286	−	12.0428i	1.40981	−	0.399216i
$911$	−3.41789	+	19.3838i	−0.113240	+	0.642214i	0.874367	+	0.485265i	$0.161277\pi$
$911$	−3.41789	+	19.3838i	−0.113240	+	0.642214i	−0.987607	+	0.156949i	$0.949834\pi$
$912$	20.1844	−	4.64389i	0.668373	−	0.153774i
$913$	39.5954	+	14.4115i	1.31042	+	0.476952i
$914$	−3.28896	+	4.84147i	−0.108789	+	0.160142i
$915$	−5.60378	+	30.8799i	−0.185255	+	1.02086i
$916$	−13.1241	−	10.3942i	−0.433633	−	0.343433i
$917$	29.4880			0.973780
$918$	3.88824	+	44.8584i	0.128331	+	1.48055i
$919$			18.0402i			0.595092i	0.954708	+	0.297546i	$0.0961681\pi$
$919$			18.0402i			0.595092i	−0.954708	+	0.297546i	$0.903832\pi$
$920$	−10.2227	+	1.33345i	−0.337032	+	0.0439625i
$921$	−24.0832	+	28.4124i	−0.793568	+	0.936221i
$922$	9.73504	−	14.3304i	0.320606	−	0.471945i
$923$	−3.86026	+	10.6060i	−0.127062	+	0.349100i
$924$	−50.1103	+	44.0781i	−1.64851	+	1.45006i
$925$	−0.432755	−	0.0763065i	−0.0142289	−	0.00250894i
$926$	7.50830	+	26.5151i	0.246738	+	0.871340i
$927$	−12.4714	−	35.3574i	−0.409613	−	1.16129i
$928$	2.64699	−	13.6849i	0.0868915	−	0.449230i
$929$	−5.86387	−	16.1108i	−0.192387	−	0.528580i	0.805567	−	0.592504i	$-0.201861\pi$
$929$	−5.86387	−	16.1108i	−0.192387	−	0.528580i	−0.997955	+	0.0639244i	$0.979638\pi$
$930$	−46.3137	+	12.8657i	−1.51869	+	0.421883i
$931$	22.8432	−	19.1678i	0.748657	−	0.628198i
$932$	27.4636	−	24.4015i	0.899601	−	0.799297i
$933$	10.9780	+	6.41132i	0.359404	+	0.209897i
$934$	5.58653	−	12.4367i	0.182797	−	0.406942i
$935$	34.3174	+	59.4395i	1.12230	+	1.94388i
$936$	−3.20985	−	26.6786i	−0.104917	−	0.872016i
$937$	19.1412	−	33.1536i	0.625317	−	1.08308i	−0.363162	−	0.931726i	$-0.618303\pi$
$937$	19.1412	−	33.1536i	0.625317	−	1.08308i	0.988479	−	0.151355i	$-0.0483638\pi$
$938$	25.1262	+	34.8248i	0.820399	+	1.13707i
$939$	−19.3454	−	23.2898i	−0.631315	−	0.760032i
$940$	6.52479	−	19.6384i	0.212815	−	0.640535i
$941$	−6.94675	−	39.3970i	−0.226457	−	1.28430i	−0.859879	−	0.510497i	$-0.829461\pi$
$941$	−6.94675	−	39.3970i	−0.226457	−	1.28430i	0.633422	−	0.773807i	$-0.281650\pi$
$942$	1.18437	+	12.2441i	0.0385887	+	0.398933i
$943$	7.44128	−	8.86818i	0.242322	−	0.288788i
$944$	0.465206	+	8.21210i	0.0151412	+	0.267281i
$945$	−24.9750	−	44.7915i	−0.812437	−	1.45707i
$946$	−22.7242	+	23.3764i	−0.738827	+	0.760033i
$947$	−4.30723	+	5.13316i	−0.139966	+	0.166805i	−0.831474	−	0.555564i	$-0.812502\pi$
$947$	−4.30723	+	5.13316i	−0.139966	+	0.166805i	0.691508	+	0.722369i	$0.256947\pi$
$948$	−35.5163	−	5.41218i	−1.15352	−	0.175780i
$949$	36.5342	−	6.44197i	1.18595	−	0.209115i
$950$	1.35919	+	2.81029i	0.0440978	+	0.0911778i
$951$	−49.4656	+	8.46815i	−1.60403	+	0.274599i
$952$	43.4002	+	56.7001i	1.40661	+	1.83766i
$953$	−12.7276	−	7.34828i	−0.412287	−	0.238034i	0.279485	−	0.960150i	$-0.409836\pi$
$953$	−12.7276	−	7.34828i	−0.412287	−	0.238034i	−0.691772	+	0.722116i	$0.743170\pi$
$954$	19.4668	+	19.3047i	0.630259	+	0.625013i
$955$	8.02056	+	13.8920i	0.259539	+	0.449535i
$956$	14.8499	+	37.4663i	0.480281	+	1.21175i
$957$	−19.9561	−	0.0994590i	−0.645090	−	0.00321505i
$958$	34.5031	+	2.52735i	1.11474	+	0.0816550i
$959$	22.7589	−	19.0970i	0.734922	−	0.616673i
$960$	−18.8378	−	27.3296i	−0.607988	−	0.882058i
$961$	33.9288	−	12.3491i	1.09448	−	0.398357i
$962$	−0.653334	+	2.58395i	−0.0210643	+	0.0833100i
$963$	15.4976	+	18.8477i	0.499404	+	0.607360i
$964$	−0.546774	−	0.295379i	−0.0176104	−	0.00951352i
$965$	1.48353	−	8.41350i	0.0477564	−	0.270840i
$966$	6.61682	+	13.8569i	0.212893	+	0.445838i
$967$	−0.607342	+	1.66866i	−0.0195308	+	0.0536605i	−0.949075	−	0.315050i	$-0.897979\pi$
$967$	−0.607342	+	1.66866i	−0.0195308	+	0.0536605i	0.929544	+	0.368711i	$0.120201\pi$
$968$	25.8991	+	16.5430i	0.832429	+	0.531712i
$969$	−29.8673	+	10.7026i	−0.959477	+	0.343816i
$970$	−1.48089	−	14.5524i	−0.0475485	−	0.467249i
$971$			19.2618i			0.618139i	0.951039	+	0.309070i	$0.100018\pi$
$971$			19.2618i			0.618139i	−0.951039	+	0.309070i	$0.899982\pi$
$972$	−29.2606	+	10.7619i	−0.938533	+	0.345190i
$973$		−	9.35455i		−	0.299893i
$974$	53.3415	−	5.42817i	1.70917	−	0.173930i
$975$	3.81265	−	1.36621i	0.122102	−	0.0437537i
$976$	29.4518	−	6.93078i	0.942729	−	0.221849i
$977$	−2.40805	+	6.61607i	−0.0770404	+	0.211667i	−0.972234	−	0.234011i	$-0.924815\pi$
$977$	−2.40805	+	6.61607i	−0.0770404	+	0.211667i	0.895194	+	0.445677i	$0.147037\pi$
$978$	28.0143	−	13.3772i	0.895799	−	0.427755i
$979$	−7.36910	+	41.7922i	−0.235517	+	1.33569i
$980$	−42.0463	−	22.7143i	−1.34312	−	0.725582i
$981$	−16.6975	−	20.3070i	−0.533110	−	0.648352i
$982$	44.4988	+	11.2512i	1.42001	+	0.359040i
$983$	−12.4609	+	4.53541i	−0.397442	+	0.144657i	−0.533006	−	0.846112i	$-0.678938\pi$
$983$	−12.4609	+	4.53541i	−0.397442	+	0.144657i	0.135564	+	0.990769i	$0.456715\pi$
$984$	36.3392	+	8.29198i	1.15845	+	0.264339i
$985$	28.2190	−	23.6786i	0.899133	−	0.754463i
$986$	−1.55982	+	21.2946i	−0.0496749	+	0.678157i
$987$	−30.8232	−	0.153619i	−0.981113	−	0.00488975i
$988$	17.6018	−	6.97658i	0.559989	−	0.221955i
$989$	3.75061	+	6.49625i	0.119262	+	0.206569i
$990$	−33.4635	+	33.7443i	−1.06354	+	1.07247i
$991$	41.4853	+	23.9516i	1.31783	+	0.760847i	0.983378	−	0.181568i	$-0.0581172\pi$
$991$	41.4853	+	23.9516i	1.31783	+	0.760847i	0.334447	+	0.942415i	$0.391451\pi$
$992$	29.1959	+	35.9861i	0.926972	+	1.14256i
$993$	−20.4018	+	3.49263i	−0.647430	+	0.110835i
$994$	18.6949	−	9.04173i	0.592967	−	0.286786i
$995$	14.4009	−	2.53927i	0.456540	−	0.0805003i
$996$	30.8594	+	4.70253i	0.977816	+	0.149005i
$997$	−39.4281	+	46.9886i	−1.24870	+	1.48814i	−0.442192	+	0.896920i	$0.645799\pi$
$997$	−39.4281	+	46.9886i	−1.24870	+	1.48814i	−0.806508	+	0.591223i	$0.798645\pi$
$998$	−28.5660	−	27.7689i	−0.904240	−	0.879011i
$999$	3.09202	+	0.0462339i	0.0978273	+	0.00146278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.11.18	yes	192
3.2	odd	2		648.2.v.b.35.15		192
4.3	odd	2		864.2.bh.b.335.12		192
8.3	odd	2	inner	216.2.v.b.11.1	✓	192
8.5	even	2		864.2.bh.b.335.11		192
24.11	even	2		648.2.v.b.35.32		192
27.5	odd	18	inner	216.2.v.b.59.1	yes	192
27.22	even	9		648.2.v.b.611.32		192
108.59	even	18		864.2.bh.b.815.11		192
216.5	odd	18		864.2.bh.b.815.12		192
216.59	even	18	inner	216.2.v.b.59.18	yes	192
216.211	odd	18		648.2.v.b.611.15		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.1	✓	192	8.3	odd	2	inner
216.2.v.b.11.18	yes	192	1.1	even	1	trivial
216.2.v.b.59.1	yes	192	27.5	odd	18	inner
216.2.v.b.59.18	yes	192	216.59	even	18	inner
648.2.v.b.35.15		192	3.2	odd	2
648.2.v.b.35.32		192	24.11	even	2
648.2.v.b.611.15		192	216.211	odd	18
648.2.v.b.611.32		192	27.22	even	9
864.2.bh.b.335.11		192	8.5	even	2
864.2.bh.b.335.12		192	4.3	odd	2
864.2.bh.b.815.11		192	108.59	even	18
864.2.bh.b.815.12		192	216.5	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.143175 + 1.40695i) q^{2} +(0.584277 + 1.63053i) q^{3} +(-1.95900 + 0.402879i) q^{4} +(2.25103 + 0.819307i) q^{5} +(-2.21041 + 1.05550i) q^{6} +(4.05746 + 0.715440i) q^{7} +(-0.847309 - 2.69853i) q^{8} +(-2.31724 + 1.90536i) q^{9} +(-0.830431 + 3.28438i) q^{10} +(-1.59930 - 4.39403i) q^{11} +(-1.80150 - 2.95881i) q^{12} +(-2.03556 - 2.42589i) q^{13} +(-0.425661 + 5.81107i) q^{14} +(-0.0206784 + 4.14906i) q^{15} +(3.67538 - 1.57848i) q^{16} +(-5.30643 + 3.06367i) q^{17} +(-3.01251 - 2.98744i) q^{18} +(1.49474 - 2.58897i) q^{19} +(-4.73985 - 0.698133i) q^{20} +(1.20414 + 7.03382i) q^{21} +(5.95319 - 2.87924i) q^{22} +(-0.264216 - 1.49844i) q^{23} +(3.90497 - 2.95825i) q^{24} +(0.565634 + 0.474623i) q^{25} +(3.12166 - 3.21125i) q^{26} +(-4.46065 - 2.66507i) q^{27} +(-8.23682 + 0.233116i) q^{28} +(-1.88755 - 1.58384i) q^{29} +(-5.84047 + 0.564947i) q^{30} +(8.06739 - 1.42250i) q^{31} +(2.74706 + 4.94506i) q^{32} +(6.23016 - 5.17503i) q^{33} +(-5.07017 - 7.02723i) q^{34} +(8.54729 + 4.93478i) q^{35} +(3.77185 - 4.66617i) q^{36} +(-0.515395 + 0.297563i) q^{37} +(3.85655 + 1.73235i) q^{38} +(2.76615 - 4.73643i) q^{39} +(0.303610 - 6.76867i) q^{40} +(4.89056 + 5.82834i) q^{41} +(-9.72382 + 2.70123i) q^{42} +(-4.63264 + 1.68614i) q^{43} +(4.90329 + 7.96360i) q^{44} +(-6.77724 + 2.39049i) q^{45} +(2.07040 - 0.586277i) q^{46} +(-0.750048 + 4.25374i) q^{47} +(4.72119 + 5.07053i) q^{48} +(9.37332 + 3.41161i) q^{49} +(-0.586786 + 0.863772i) q^{50} +(-8.09583 - 6.86225i) q^{51} +(4.96501 + 3.93224i) q^{52} -6.46197 q^{53} +(3.11095 - 6.65747i) q^{54} -11.2014i q^{55} +(-1.50729 - 11.5554i) q^{56} +(5.09473 + 0.924543i) q^{57} +(1.95813 - 2.88244i) q^{58} +(-0.703302 + 1.93231i) q^{59} +(-1.63106 - 8.13635i) q^{60} +(7.44916 + 1.31349i) q^{61} +(3.15643 + 11.1467i) q^{62} +(-10.7653 + 6.07308i) q^{63} +(-6.56414 + 4.57298i) q^{64} +(-2.59456 - 7.12849i) q^{65} +(8.17300 + 8.02457i) q^{66} +(5.64581 - 4.73740i) q^{67} +(9.16103 - 8.13959i) q^{68} +(2.28888 - 1.30632i) q^{69} +(-5.71922 + 12.7321i) q^{70} +(-1.78204 - 3.08659i) q^{71} +(7.10509 + 4.63872i) q^{72} +(-5.85735 + 10.1452i) q^{73} +(-0.492447 - 0.682530i) q^{74} +(-0.443399 + 1.19959i) q^{75} +(-1.88516 + 5.67400i) q^{76} +(-3.34542 - 18.9728i) q^{77} +(7.05995 + 3.21368i) q^{78} +(6.66637 - 7.94467i) q^{79} +(9.56663 - 0.541939i) q^{80} +(1.73920 - 8.83036i) q^{81} +(-7.49997 + 7.71524i) q^{82} +(-5.79227 + 6.90296i) q^{83} +(-5.19269 - 13.2942i) q^{84} +(-14.4550 + 2.54881i) q^{85} +(-3.03559 - 6.27647i) q^{86} +(1.47964 - 4.00310i) q^{87} +(-10.5023 + 8.03885i) q^{88} +(-7.85955 - 4.53771i) q^{89} +(-4.33362 - 9.19297i) q^{90} +(-6.52364 - 11.2993i) q^{91} +(1.12129 + 2.82901i) q^{92} +(7.03302 + 12.3230i) q^{93} +(-6.09217 - 0.446251i) q^{94} +(5.48587 - 4.60319i) q^{95} +(-6.45802 + 7.36844i) q^{96} +(-4.05740 + 1.47677i) q^{97} +(-3.45793 + 13.6762i) q^{98} +(12.0782 + 7.13479i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25}+ \cdots - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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