LMFDB - Embedded newform 228.2.v.a.23.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,2,Mod(23,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 2]))

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

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

chi := DirichletCharacter("228.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.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:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			23.14
Character	$\chi$	$=$	228.23
Dual form			228.2.v.a.119.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.414780 - 1.35202i) q^{2} +(-1.54392 - 0.785048i) q^{3} +(-1.65592 + 1.12158i) q^{4} +(-2.15444 - 2.56756i) q^{5} +(-0.421012 + 2.41304i) q^{6} +(-0.213070 - 0.123016i) q^{7} +(2.20324 + 1.77362i) q^{8} +(1.76740 + 2.42411i) q^{9} +O(q^{10})$	\(q+(-0.414780 - 1.35202i) q^{2} +(-1.54392 - 0.785048i) q^{3} +(-1.65592 + 1.12158i) q^{4} +(-2.15444 - 2.56756i) q^{5} +(-0.421012 + 2.41304i) q^{6} +(-0.213070 - 0.123016i) q^{7} +(2.20324 + 1.77362i) q^{8} +(1.76740 + 2.42411i) q^{9} +(-2.57778 + 3.97782i) q^{10} +(-0.216520 - 0.375023i) q^{11} +(3.43710 - 0.431661i) q^{12} +(-0.637288 + 3.61424i) q^{13} +(-0.0779429 + 0.339099i) q^{14} +(1.31063 + 5.65546i) q^{15} +(1.48411 - 3.71449i) q^{16} +(-1.84409 + 5.06660i) q^{17} +(2.54436 - 3.39503i) q^{18} +(-4.07965 - 1.53507i) q^{19} +(6.44730 + 1.83529i) q^{20} +(0.232390 + 0.357197i) q^{21} +(-0.417231 + 0.448291i) q^{22} +(-2.66908 - 2.23962i) q^{23} +(-2.00925 - 4.46799i) q^{24} +(-1.08252 + 6.13929i) q^{25} +(5.15086 - 0.637487i) q^{26} +(-0.825690 - 5.13013i) q^{27} +(0.490798 - 0.0352709i) q^{28} +(-2.58348 - 7.09806i) q^{29} +(7.10267 - 4.11777i) q^{30} +(0.864431 + 0.499079i) q^{31} +(-5.63764 - 0.465860i) q^{32} +(0.0398788 + 0.748985i) q^{33} +(7.61503 + 0.391726i) q^{34} +(0.143195 + 0.812100i) q^{35} +(-5.64550 - 2.03184i) q^{36} -2.40057 q^{37} +(-0.383286 + 6.15249i) q^{38} +(3.82128 - 5.07981i) q^{39} +(-0.192861 - 9.47812i) q^{40} +(-3.84502 + 0.677980i) q^{41} +(0.386547 - 0.462354i) q^{42} +(7.53380 + 8.97843i) q^{43} +(0.779157 + 0.378163i) q^{44} +(2.41629 - 9.76051i) q^{45} +(-1.92093 + 4.53759i) q^{46} +(-6.81452 + 2.48028i) q^{47} +(-5.20741 + 4.56978i) q^{48} +(-3.46973 - 6.00976i) q^{49} +(8.74945 - 1.08286i) q^{50} +(6.82465 - 6.37474i) q^{51} +(-2.99837 - 6.69965i) q^{52} +(-0.847549 + 1.01007i) q^{53} +(-6.59356 + 3.24422i) q^{54} +(-0.496417 + 1.36389i) q^{55} +(-0.251260 - 0.648938i) q^{56} +(5.09357 + 5.57275i) q^{57} +(-8.52514 + 6.43705i) q^{58} +(-6.93061 - 2.52253i) q^{59} +(-8.51335 - 7.89499i) q^{60} +(-7.70314 - 6.46370i) q^{61} +(0.316217 - 1.37574i) q^{62} +(-0.0783757 - 0.733922i) q^{63} +(1.70853 + 7.81543i) q^{64} +(10.6528 - 6.15039i) q^{65} +(0.996102 - 0.364581i) q^{66} +(-3.65875 - 10.0523i) q^{67} +(-2.62894 - 10.4582i) q^{68} +(2.36264 + 5.55315i) q^{69} +(1.03858 - 0.530445i) q^{70} +(5.42107 - 4.54882i) q^{71} +(-0.405447 + 8.47559i) q^{72} +(1.84726 + 10.4763i) q^{73} +(0.995708 + 3.24562i) q^{74} +(6.49096 - 8.62876i) q^{75} +(8.47726 - 2.03372i) q^{76} +0.106541i q^{77} +(-8.45299 - 3.05944i) q^{78} +(-0.945539 + 0.166724i) q^{79} +(-12.7346 + 4.19208i) q^{80} +(-2.75260 + 8.56874i) q^{81} +(2.51148 + 4.91733i) q^{82} +(-7.47672 + 12.9501i) q^{83} +(-0.785443 - 0.330844i) q^{84} +(16.9818 - 6.18087i) q^{85} +(9.01415 - 13.9099i) q^{86} +(-1.58362 + 12.9870i) q^{87} +(0.188105 - 1.21029i) q^{88} +(8.14323 + 1.43587i) q^{89} +(-14.1986 + 0.781587i) q^{90} +(0.580396 - 0.691689i) q^{91} +(6.93168 + 0.715040i) q^{92} +(-0.942814 - 1.44916i) q^{93} +(6.17992 + 8.18460i) q^{94} +(4.84799 + 13.7820i) q^{95} +(8.33836 + 5.14507i) q^{96} +(-11.3632 - 4.13586i) q^{97} +(-6.68614 + 7.18387i) q^{98} +(0.526420 - 1.18768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9}+O(q^{10}) $ 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9	$ 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 36 q^{13} - 6 q^{16} - 12 q^{18} - 30 q^{21} - 18 q^{24} - 24 q^{25} - 36 q^{28} + 12 q^{33} + 30 q^{34} - 66 q^{36} - 48 q^{37} - 42 q^{40} - 117 q^{42} - 6 q^{45} - 6 q^{46} - 81 q^{48} + 24 q^{49} + 12 q^{52} + 33 q^{54} - 12 q^{57} + 48 q^{58} - 18 q^{60} - 48 q^{61} + 36 q^{64} - 18 q^{66} - 6 q^{69} - 18 q^{70} + 12 q^{72} - 132 q^{73} + 60 q^{76} - 39 q^{78} + 18 q^{81} + 132 q^{82} - 45 q^{84} - 144 q^{85} + 114 q^{88} + 72 q^{90} - 30 q^{93} + 138 q^{96} - 60 q^{97}+O(q^{100}) $ 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9 - 18 * q^10 - 3 * q^12 - 36 * q^13 - 6 * q^16 - 12 * q^18 - 30 * q^21 - 18 * q^24 - 24 * q^25 - 36 * q^28 + 12 * q^33 + 30 * q^34 - 66 * q^36 - 48 * q^37 - 42 * q^40 - 117 * q^42 - 6 * q^45 - 6 * q^46 - 81 * q^48 + 24 * q^49 + 12 * q^52 + 33 * q^54 - 12 * q^57 + 48 * q^58 - 18 * q^60 - 48 * q^61 + 36 * q^64 - 18 * q^66 - 6 * q^69 - 18 * q^70 + 12 * q^72 - 132 * q^73 + 60 * q^76 - 39 * q^78 + 18 * q^81 + 132 * q^82 - 45 * q^84 - 144 * q^85 + 114 * q^88 + 72 * q^90 - 30 * q^93 + 138 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$	$-1$

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 $

$2$	−0.414780	−	1.35202i	−0.293293	−	0.956022i
$2$	−0.414780	−	1.35202i	−0.293293	−	0.956022i
$3$	−1.54392	−	0.785048i	−0.891385	−	0.453248i
$3$	−1.54392	−	0.785048i	−0.891385	−	0.453248i
$4$	−1.65592	+	1.12158i	−0.827958	+	0.560790i
$5$	−2.15444	−	2.56756i	−0.963495	−	1.14825i	−0.988902	−	0.148572i	$-0.952532\pi$
$5$	−2.15444	−	2.56756i	−0.963495	−	1.14825i	0.0254063	−	0.999677i	$-0.491912\pi$
$6$	−0.421012	+	2.41304i	−0.171878	+	0.985118i
$7$	−0.213070	−	0.123016i	−0.0805328	−	0.0464956i	0.459193	−	0.888337i	$-0.348139\pi$
$7$	−0.213070	−	0.123016i	−0.0805328	−	0.0464956i	−0.539726	+	0.841841i	$0.681472\pi$
$8$	2.20324	+	1.77362i	0.778963	+	0.627070i
$9$	1.76740	+	2.42411i	0.589133	+	0.808036i
$10$	−2.57778	+	3.97782i	−0.815165	+	1.25790i
$11$	−0.216520	−	0.375023i	−0.0652832	−	0.113074i	0.831536	−	0.555470i	$-0.187462\pi$
$11$	−0.216520	−	0.375023i	−0.0652832	−	0.113074i	−0.896820	+	0.442397i	$0.854128\pi$
$12$	3.43710	−	0.431661i	0.992206	−	0.124610i
$13$	−0.637288	+	3.61424i	−0.176752	+	1.00241i	0.759350	+	0.650682i	$0.225517\pi$
$13$	−0.637288	+	3.61424i	−0.176752	+	1.00241i	−0.936102	+	0.351728i	$0.885594\pi$
$14$	−0.0779429	+	0.339099i	−0.0208311	+	0.0906280i
$15$	1.31063	+	5.65546i	0.338404	+	1.46023i
$16$	1.48411	−	3.71449i	0.371029	−	0.928621i
$17$	−1.84409	+	5.06660i	−0.447258	+	1.22883i	0.487368	+	0.873197i	$0.337957\pi$
$17$	−1.84409	+	5.06660i	−0.447258	+	1.22883i	−0.934626	+	0.355633i	$0.884265\pi$
$18$	2.54436	−	3.39503i	0.599712	−	0.800216i
$19$	−4.07965	−	1.53507i	−0.935937	−	0.352169i
$19$	−4.07965	−	1.53507i	−0.935937	−	0.352169i
$20$	6.44730	+	1.83529i	1.44166	+	0.410383i
$21$	0.232390	+	0.357197i	0.0507116	+	0.0779467i
$22$	−0.417231	+	0.448291i	−0.0889539	+	0.0955760i
$23$	−2.66908	−	2.23962i	−0.556541	−	0.466993i	0.320608	−	0.947212i	$-0.396113\pi$
$23$	−2.66908	−	2.23962i	−0.556541	−	0.466993i	−0.877149	+	0.480219i	$0.840557\pi$
$24$	−2.00925	−	4.46799i	−0.410137	−	0.912024i
$25$	−1.08252	+	6.13929i	−0.216504	+	1.22786i
$26$	5.15086	−	0.637487i	1.01017	−	0.125021i
$27$	−0.825690	−	5.13013i	−0.158904	−	0.987294i
$28$	0.490798	−	0.0352709i	0.0927520	−	0.00666557i
$29$	−2.58348	−	7.09806i	−0.479741	−	1.31808i	−0.909714	−	0.415235i	$-0.863699\pi$
$29$	−2.58348	−	7.09806i	−0.479741	−	1.31808i	0.429974	−	0.902842i	$-0.358523\pi$
$30$	7.10267	−	4.11777i	1.29676	−	0.751799i
$31$	0.864431	+	0.499079i	0.155256	+	0.0896373i	0.575615	−	0.817721i	$-0.304763\pi$
$31$	0.864431	+	0.499079i	0.155256	+	0.0896373i	−0.420359	+	0.907358i	$0.638096\pi$
$32$	−5.63764	−	0.465860i	−0.996603	−	0.0823532i
$33$	0.0398788	+	0.748985i	0.00694201	+	0.130382i
$34$	7.61503	+	0.391726i	1.30597	+	0.0671805i
$35$	0.143195	+	0.812100i	0.0242044	+	0.137270i
$36$	−5.64550	−	2.03184i	−0.940916	−	0.338640i
$37$	−2.40057			−0.394651			−0.197326	−	0.980338i	$-0.563226\pi$
$37$	−2.40057			−0.394651			−0.197326	+	0.980338i	$0.563226\pi$
$38$	−0.383286	+	6.15249i	−0.0621772	+	0.998065i
$39$	3.82128	−	5.07981i	0.611894	−	0.813421i
$40$	−0.192861	−	9.47812i	−0.0304940	−	1.49862i
$41$	−3.84502	+	0.677980i	−0.600491	+	0.105883i	−0.465626	−	0.884981i	$-0.654171\pi$
$41$	−3.84502	+	0.677980i	−0.600491	+	0.105883i	−0.134864	+	0.990864i	$0.543060\pi$
$42$	0.386547	−	0.462354i	0.0596454	−	0.0713427i
$43$	7.53380	+	8.97843i	1.14889	+	1.36920i	0.918174	+	0.396177i	$0.129663\pi$
$43$	7.53380	+	8.97843i	1.14889	+	1.36920i	0.230719	+	0.973020i	$0.425892\pi$
$44$	0.779157	+	0.378163i	0.117462	+	0.0570102i
$45$	2.41629	−	9.76051i	0.360199	−	1.45501i
$46$	−1.92093	+	4.53759i	−0.283226	+	0.669031i
$47$	−6.81452	+	2.48028i	−0.994000	+	0.361787i	−0.787268	−	0.616611i	$-0.788505\pi$
$47$	−6.81452	+	2.48028i	−0.994000	+	0.361787i	−0.206732	+	0.978398i	$0.566283\pi$
$48$	−5.20741	+	4.56978i	−0.751625	+	0.659591i
$49$	−3.46973	−	6.00976i	−0.495676	−	0.858537i
$50$	8.74945	−	1.08286i	1.23736	−	0.153139i
$51$	6.82465	−	6.37474i	0.955643	−	0.892642i
$52$	−2.99837	−	6.69965i	−0.415799	−	0.929074i
$53$	−0.847549	+	1.01007i	−0.116420	+	0.138744i	−0.821107	−	0.570775i	$-0.806643\pi$
$53$	−0.847549	+	1.01007i	−0.116420	+	0.138744i	0.704687	+	0.709518i	$0.251087\pi$
$54$	−6.59356	+	3.24422i	−0.897270	+	0.441483i
$55$	−0.496417	+	1.36389i	−0.0669368	+	0.183907i
$56$	−0.251260	−	0.648938i	−0.0335760	−	0.0867180i
$57$	5.09357	+	5.57275i	0.674660	+	0.738129i
$58$	−8.52514	+	6.43705i	−1.11941	+	0.845226i
$59$	−6.93061	−	2.52253i	−0.902288	−	0.328406i	−0.151119	−	0.988516i	$-0.548288\pi$
$59$	−6.93061	−	2.52253i	−0.902288	−	0.328406i	−0.751169	+	0.660110i	$0.770510\pi$
$60$	−8.51335	−	7.89499i	−1.09907	−	1.01924i
$61$	−7.70314	−	6.46370i	−0.986286	−	0.827593i	−0.00126051	−	0.999999i	$-0.500401\pi$
$61$	−7.70314	−	6.46370i	−0.986286	−	0.827593i	−0.985026	+	0.172407i	$0.944846\pi$
$62$	0.316217	−	1.37574i	0.0401596	−	0.174719i
$63$	−0.0783757	−	0.733922i	−0.00987441	−	0.0924655i
$64$	1.70853	+	7.81543i	0.213566	+	0.976929i
$65$	10.6528	−	6.15039i	1.32132	−	0.762862i
$66$	0.996102	−	0.364581i	0.122612	−	0.0448768i
$67$	−3.65875	−	10.0523i	−0.446987	−	1.22809i	−0.934811	−	0.355145i	$-0.884431\pi$
$67$	−3.65875	−	10.0523i	−0.446987	−	1.22809i	0.487824	−	0.872942i	$-0.337791\pi$
$68$	−2.62894	−	10.4582i	−0.318805	−	1.26824i
$69$	2.36264	+	5.55315i	0.284428	+	0.668521i
$70$	1.03858	−	0.530445i	0.124134	−	0.0634003i
$71$	5.42107	−	4.54882i	0.643363	−	0.539845i	−0.261686	−	0.965153i	$-0.584279\pi$
$71$	5.42107	−	4.54882i	0.643363	−	0.539845i	0.905049	+	0.425308i	$0.139834\pi$
$72$	−0.405447	+	8.47559i	−0.0477824	+	0.998858i
$73$	1.84726	+	10.4763i	0.216205	+	1.22616i	0.878803	+	0.477184i	$0.158343\pi$
$73$	1.84726	+	10.4763i	0.216205	+	1.22616i	−0.662598	+	0.748975i	$0.730546\pi$
$74$	0.995708	+	3.24562i	0.115749	+	0.377296i
$75$	6.49096	−	8.62876i	0.749512	−	0.996363i
$76$	8.47726	−	2.03372i	0.972409	−	0.233283i
$77$			0.106541i			0.0121415i
$78$	−8.45299	−	3.05944i	−0.957113	−	0.346413i
$79$	−0.945539	+	0.166724i	−0.106382	+	0.0187579i	−0.226585	−	0.973991i	$-0.572756\pi$
$79$	−0.945539	+	0.166724i	−0.106382	+	0.0187579i	0.120204	+	0.992749i	$0.461645\pi$
$80$	−12.7346	+	4.19208i	−1.42377	+	0.468689i
$81$	−2.75260	+	8.56874i	−0.305844	+	0.952082i
$82$	2.51148	+	4.91733i	0.277346	+	0.543028i
$83$	−7.47672	+	12.9501i	−0.820676	+	1.42145i	0.0845032	+	0.996423i	$0.473070\pi$
$83$	−7.47672	+	12.9501i	−0.820676	+	1.42145i	−0.905179	+	0.425030i	$0.860264\pi$
$84$	−0.785443	−	0.330844i	−0.0856989	−	0.0360980i
$85$	16.9818	−	6.18087i	1.84193	−	0.670409i
$86$	9.01415	−	13.9099i	0.972021	−	1.49994i
$87$	−1.58362	+	12.9870i	−0.169782	+	1.39235i
$88$	0.188105	−	1.21029i	0.0200520	−	0.129017i
$89$	8.14323	+	1.43587i	0.863181	+	0.152202i	0.587675	−	0.809097i	$-0.300043\pi$
$89$	8.14323	+	1.43587i	0.863181	+	0.152202i	0.275506	+	0.961299i	$0.411155\pi$
$90$	−14.1986	+	0.781587i	−1.49667	+	0.0823865i
$91$	0.580396	−	0.691689i	0.0608420	−	0.0725087i
$92$	6.93168	+	0.715040i	0.722678	+	0.0745481i
$93$	−0.942814	−	1.44916i	−0.0977652	−	0.150271i
$94$	6.17992	+	8.18460i	0.637410	+	0.844177i
$95$	4.84799	+	13.7820i	0.497393	+	1.41400i
$96$	8.33836	+	5.14507i	0.851030	+	0.525116i
$97$	−11.3632	−	4.13586i	−1.15376	−	0.419933i	−0.306893	−	0.951744i	$-0.599289\pi$
$97$	−11.3632	−	4.13586i	−1.15376	−	0.419933i	−0.846863	+	0.531811i	$0.821512\pi$
$98$	−6.68614	+	7.18387i	−0.675402	+	0.725681i
$99$	0.526420	−	1.18768i	0.0529072	−	0.119367i
$100$	−5.09314	−	11.3803i	−0.509314	−	1.13803i
$101$	6.03717	+	1.06452i	0.600720	+	0.105923i	0.465735	−	0.884924i	$-0.345790\pi$
$101$	6.03717	+	1.06452i	0.600720	+	0.105923i	0.134986	+	0.990848i	$0.456901\pi$
$102$	−11.4495	−	6.58296i	−1.13367	−	0.651810i
$103$	11.7517	−	6.78485i	1.15793	−	0.668531i	0.207123	−	0.978315i	$-0.433590\pi$
$103$	11.7517	−	6.78485i	1.15793	−	0.668531i	0.950807	+	0.309784i	$0.100257\pi$
$104$	−7.81440	+	6.83273i	−0.766265	+	0.670004i
$105$	0.416455	−	1.36624i	0.0406418	−	0.133331i
$106$	1.71718	+	0.726947i	0.166787	+	0.0706073i
$107$	−0.0685191	+	0.118678i	−0.00662399	+	0.0114731i	−0.869318	−	0.494252i	$-0.835442\pi$
$107$	−0.0685191	+	0.118678i	−0.00662399	+	0.0114731i	0.862694	+	0.505726i	$0.168775\pi$
$108$	7.12113	+	7.56899i	0.685231	+	0.728326i
$109$	8.70959	−	7.30822i	0.834228	−	0.700000i	−0.122030	−	0.992526i	$-0.538940\pi$
$109$	8.70959	−	7.30822i	0.834228	−	0.700000i	0.956257	+	0.292526i	$0.0944959\pi$
$110$	2.04991	+	0.105450i	0.195452	+	0.0100543i
$111$	3.70630	+	1.88456i	0.351786	+	0.178875i
$112$	−0.773160	+	0.608875i	−0.0730568	+	0.0575332i
$113$		−	10.6439i		−	1.00129i	−0.865652	−	0.500645i	$-0.833096\pi$
$113$		−	10.6439i		−	1.00129i	0.865652	−	0.500645i	$-0.166904\pi$
$114$	5.42176	−	9.19807i	0.507794	−	0.861478i
$115$			11.6781i			1.08899i
$116$	12.2391	+	8.85621i	1.13637	+	0.822278i
$117$	−9.88765	+	4.84296i	−0.914114	+	0.447731i
$118$	−0.535843	+	10.4166i	−0.0493284	+	0.958927i
$119$	1.01619	−	0.852686i	0.0931541	−	0.0781656i
$120$	−7.14301	+	14.7849i	−0.652065	+	1.34967i
$121$	5.40624	−	9.36388i	0.491476	−	0.851262i
$122$	−5.54395	+	13.0958i	−0.501926	+	1.18564i
$123$	6.46866	+	1.97177i	0.583259	+	0.177789i
$124$	−1.99118	+	0.143095i	−0.178813	+	0.0128503i
$125$	3.58188	−	2.06800i	0.320373	−	0.184967i
$126$	−0.959768	+	0.410381i	−0.0855030	+	0.0365597i
$127$	−0.549323	−	0.0968605i	−0.0487446	−	0.00859498i	0.149223	−	0.988804i	$-0.452323\pi$
$127$	−0.549323	−	0.0968605i	−0.0487446	−	0.00859498i	−0.197967	+	0.980209i	$0.563434\pi$
$128$	9.85796	−	5.55164i	0.871328	−	0.490700i
$129$	−4.58311	−	19.7764i	−0.403520	−	1.74121i
$130$	−12.7340	−	11.8517i	−1.11685	−	1.03947i
$131$	11.1814	+	4.06969i	0.976922	+	0.355571i	0.780643	−	0.624977i	$-0.214892\pi$
$131$	11.1814	+	4.06969i	0.976922	+	0.355571i	0.196280	+	0.980548i	$0.437114\pi$
$132$	−0.906083	−	1.19553i	−0.0788644	−	0.104058i
$133$	0.680413	+	0.828938i	0.0589992	+	0.0718781i
$134$	−12.0734	+	9.11620i	−1.04298	+	0.787520i
$135$	−11.3930	+	13.1726i	−0.980556	+	1.13371i
$136$	−13.0492	+	7.89220i	−1.11896	+	0.676751i
$137$	−7.52026	+	8.96229i	−0.642499	+	0.765700i	−0.984763	−	0.173904i	$-0.944362\pi$
$137$	−7.52026	+	8.96229i	−0.642499	+	0.765700i	0.342264	+	0.939604i	$0.388806\pi$
$138$	6.52800	−	5.49767i	0.555700	−	0.467993i
$139$	−18.2370	−	3.21567i	−1.54684	−	0.272750i	−0.665924	−	0.746020i	$-0.731962\pi$
$139$	−18.2370	−	3.21567i	−1.54684	−	0.272750i	−0.880917	+	0.473270i	$0.843074\pi$
$140$	−1.14795	−	1.18416i	−0.0970199	−	0.100080i
$141$	12.4682	+	1.52036i	1.05002	+	0.128037i
$142$	−8.39864	−	5.44264i	−0.704798	−	0.456736i
$143$	1.49341	−	0.543557i	0.124885	−	0.0454545i
$144$	11.6273	−	2.96733i	0.968945	−	0.247277i
$145$	−12.6588	+	21.9256i	−1.05125	+	1.82082i
$146$	13.3980	−	6.84289i	1.10882	−	0.566321i
$147$	0.639059	+	12.0025i	0.0527087	+	0.989950i
$148$	3.97514	−	2.69243i	0.326755	−	0.221317i
$149$	−14.7391	+	2.59889i	−1.20747	+	0.212910i	−0.740925	−	0.671588i	$-0.765613\pi$
$149$	−14.7391	+	2.59889i	−1.20747	+	0.212910i	−0.466545	+	0.884497i	$0.654502\pi$
$150$	−14.3586	−	5.19688i	−1.17237	−	0.424324i
$151$			0.0481124i			0.00391533i	0.999998	+	0.00195767i	$0.000623145\pi$
$151$			0.0481124i			0.00391533i	−0.999998	+	0.00195767i	$0.999377\pi$
$152$	−6.26582	−	10.6179i	−0.508225	−	0.861224i
$153$	−15.5412	+	4.48443i	−1.25643	+	0.362545i
$154$	0.144046	−	0.0441912i	0.0116076	−	0.00356103i
$155$	−0.580947	−	3.29472i	−0.0466628	−	0.264638i
$156$	−0.630296	+	12.6976i	−0.0504641	+	1.01662i
$157$	17.8906	−	15.0120i	1.42783	−	1.19809i	0.480847	−	0.876804i	$-0.340329\pi$
$157$	17.8906	−	15.0120i	1.42783	−	1.19809i	0.946982	−	0.321287i	$-0.104115\pi$
$158$	0.617605	+	1.20923i	0.0491340	+	0.0962015i
$159$	2.10150	−	0.894104i	0.166660	−	0.0709070i
$160$	10.9498	+	15.4787i	0.865661	+	1.22370i
$161$	0.293190	+	0.805534i	0.0231066	+	0.0634849i
$162$	12.7268	+	0.167427i	0.999913	+	0.0131543i
$163$	5.91526	−	3.41518i	0.463319	−	0.267497i	−0.250120	−	0.968215i	$-0.580470\pi$
$163$	5.91526	−	3.41518i	0.463319	−	0.267497i	0.713439	+	0.700717i	$0.247137\pi$
$164$	5.60661	−	5.43517i	0.437803	−	0.424416i
$165$	1.83715	−	1.71604i	0.143022	−	0.133593i
$166$	20.6099	+	4.73725i	1.59964	+	0.367682i
$167$	−14.4900	−	12.1586i	−1.12127	−	0.940858i	−0.122603	−	0.992456i	$-0.539124\pi$
$167$	−14.4900	−	12.1586i	−1.12127	−	0.940858i	−0.998668	+	0.0515975i	$0.983569\pi$
$168$	−0.121522	+	1.19916i	−0.00937561	+	0.0925174i
$169$	−0.440604	−	0.160367i	−0.0338926	−	0.0123359i
$170$	−15.4004	−	20.3960i	−1.18115	−	1.56430i
$171$	−3.48921	−	12.6026i	−0.266826	−	0.963745i
$172$	−22.5454	−	6.41776i	−1.71907	−	0.489350i
$173$	2.05125	−	5.63577i	0.155954	−	0.428480i	−0.836968	−	0.547252i	$-0.815674\pi$
$173$	2.05125	−	5.63577i	0.155954	−	0.428480i	0.992921	+	0.118773i	$0.0378960\pi$
$174$	18.2156	−	3.24567i	1.38092	−	0.246053i
$175$	0.985882	−	1.17493i	0.0745257	−	0.0888162i
$176$	−1.71436	+	0.247682i	−0.129225	+	0.0186697i
$177$	8.72002	+	9.33546i	0.655437	+	0.701696i
$178$	−1.43632	−	11.6054i	−0.107657	−	0.869860i
$179$	−0.640788	−	1.10988i	−0.0478947	−	0.0829561i	0.841084	−	0.540904i	$-0.181918\pi$
$179$	−0.640788	−	1.10988i	−0.0478947	−	0.0829561i	−0.888979	+	0.457948i	$0.848585\pi$
$180$	6.94602	+	18.8726i	0.517726	+	1.40668i
$181$	0.292333	−	0.106401i	0.0217289	−	0.00790869i	−0.331133	−	0.943584i	$-0.607431\pi$
$181$	0.292333	−	0.106401i	0.0217289	−	0.00790869i	0.352862	+	0.935675i	$0.385209\pi$
$182$	−1.17591	−	0.497808i	−0.0871645	−	0.0369000i
$183$	6.81875	+	16.0268i	0.504056	+	1.18474i
$184$	−1.90837	−	9.66835i	−0.140687	−	0.712760i
$185$	5.17189	+	6.16362i	0.380245	+	0.453158i
$186$	−1.56823	+	1.87578i	−0.114988	+	0.137539i
$187$	2.29937	−	0.405442i	0.168147	−	0.0296488i
$188$	8.50244	−	11.7502i	0.620104	−	0.856970i
$189$	−0.455158	+	1.19465i	−0.0331078	+	0.0868979i
$190$	16.6227	−	12.2711i	1.20593	−	0.890236i
$191$	2.19792			0.159036			0.0795178	−	0.996833i	$-0.474662\pi$
$191$	2.19792			0.159036			0.0795178	+	0.996833i	$0.474662\pi$
$192$	3.49765	−	13.4077i	0.252421	−	0.967617i
$193$	−0.696410	−	3.94954i	−0.0501287	−	0.284294i	0.949431	−	0.313977i	$-0.101661\pi$
$193$	−0.696410	−	3.94954i	−0.0501287	−	0.284294i	−0.999559	+	0.0296828i	$0.990550\pi$
$194$	−0.878549	+	17.0787i	−0.0630762	+	1.22618i
$195$	−21.2755	+	1.13278i	−1.52357	+	0.0811204i
$196$	12.4860	+	6.06006i	0.891858	+	0.432862i
$197$	−2.75783	−	1.59223i	−0.196487	−	0.113442i	0.398529	−	0.917156i	$-0.369521\pi$
$197$	−2.75783	−	1.59223i	−0.196487	−	0.113442i	−0.595016	+	0.803714i	$0.702854\pi$
$198$	−1.82412	−	0.219103i	−0.129635	−	0.0155710i
$199$	−4.75473	−	13.0635i	−0.337054	−	0.926047i	−0.986226	−	0.165406i	$-0.947107\pi$
$199$	−4.75473	−	13.0635i	−0.337054	−	0.926047i	0.649172	−	0.760642i	$-0.275116\pi$
$200$	−13.2738	+	11.6063i	−0.938602	+	0.820691i
$201$	−2.24273	+	18.3923i	−0.158190	+	1.29729i
$202$	−1.06485	−	8.60391i	−0.0749224	−	0.605369i
$203$	−0.322712	+	1.83019i	−0.0226499	+	0.128454i
$204$	−4.15127	+	18.2104i	−0.290647	+	1.27499i
$205$	10.0246	+	8.41165i	0.700150	+	0.587495i
$206$	−14.0476	−	13.0743i	−0.978744	−	0.910931i
$207$	0.711757	−	10.4284i	0.0494705	−	0.724826i
$208$	12.4792	+	7.73115i	0.865280	+	0.536059i
$209$	0.307639	+	1.86234i	0.0212799	+	0.128821i
$210$	−2.01991	+	0.00363106i	−0.139387	+	0.000250567i
$211$	−6.32604	+	17.3807i	−0.435503	+	1.19653i	0.506886	+	0.862013i	$0.330796\pi$
$211$	−6.32604	+	17.3807i	−0.435503	+	1.19653i	−0.942389	+	0.334520i	$0.891426\pi$
$212$	0.270596	−	2.62318i	0.0185846	−	0.180161i
$213$	−11.9408	+	2.76723i	−0.818167	+	0.189607i
$214$	0.188876	+	0.0434137i	0.0129113	+	0.00296770i
$215$	6.82156	−	38.6870i	0.465227	−	2.63843i
$216$	7.27972	−	12.7674i	0.495322	−	0.868709i
$217$	−0.122789	−	0.212677i	−0.00833548	−	0.0144375i
$218$	−13.4934	−	8.74425i	−0.913889	−	0.592235i
$219$	5.37238	−	17.6248i	0.363032	−	1.19097i
$220$	−0.707692	−	2.81526i	−0.0477126	−	0.189805i
$221$	−17.1367	−	9.89387i	−1.15274	−	0.665534i
$222$	1.01067	−	5.79267i	0.0678317	−	0.388778i
$223$	−15.1632	−	18.0708i	−1.01541	−	1.21011i	−0.977522	−	0.210831i	$-0.932383\pi$
$223$	−15.1632	−	18.0708i	−1.01541	−	1.21011i	−0.0378834	−	0.999282i	$-0.512062\pi$
$224$	1.14390	+	0.792779i	0.0764301	+	0.0529698i
$225$	−16.7955	+	8.22642i	−1.11970	+	0.548428i
$226$	−14.3907	+	4.41486i	−0.957256	+	0.293672i
$227$	5.25383			0.348709			0.174355	−	0.984683i	$-0.444216\pi$
$227$	5.25383			0.348709			0.174355	+	0.984683i	$0.444216\pi$
$228$	−14.6848	−	3.51516i	−0.972525	−	0.232797i
$229$	−13.7689			−0.909876			−0.454938	−	0.890523i	$-0.650339\pi$
$229$	−13.7689			−0.909876			−0.454938	+	0.890523i	$0.650339\pi$
$230$	15.7891	−	4.84386i	1.04110	−	0.319395i
$231$	0.0836401	−	0.164492i	0.00550311	−	0.0108228i
$232$	6.89725	−	20.2208i	0.452827	−	1.32756i
$233$	−7.15539	−	8.52746i	−0.468765	−	0.558652i	0.478920	−	0.877858i	$-0.341028\pi$
$233$	−7.15539	−	8.52746i	−0.468765	−	0.558652i	−0.947685	+	0.319206i	$0.896584\pi$
$234$	10.6490	+	11.3595i	0.696145	+	0.742597i
$235$	21.0498	+	12.1531i	1.37314	+	0.792780i
$236$	14.3057	−	3.59613i	0.931224	−	0.234088i
$237$	1.59073	+	0.484884i	0.103329	+	0.0314966i
$238$	−1.57434	−	1.02023i	−0.102050	−	0.0661320i
$239$	−3.15380	−	5.46254i	−0.204002	−	0.353342i	0.745812	−	0.666156i	$-0.232062\pi$
$239$	−3.15380	−	5.46254i	−0.204002	−	0.353342i	−0.949814	+	0.312814i	$0.898728\pi$
$240$	22.9523	+	3.52502i	1.48156	+	0.227539i
$241$	−1.76938	+	10.0347i	−0.113976	+	0.646390i	0.873276	+	0.487226i	$0.161991\pi$
$241$	−1.76938	+	10.0347i	−0.113976	+	0.646390i	−0.987252	+	0.159164i	$0.949120\pi$
$242$	−14.9025	−	3.42540i	−0.957972	−	0.220193i
$243$	10.9767	−	11.0686i	0.704153	−	0.710048i
$244$	20.0053	+	2.06366i	1.28071	+	0.132112i
$245$	−7.95509	+	21.8564i	−0.508232	+	1.39636i
$246$	−0.0171918	−	9.56361i	−0.00109611	−	0.609753i
$247$	8.14802	−	13.7666i	0.518446	−	0.875946i
$248$	1.01937	+	2.63276i	0.0647300	+	0.167181i
$249$	21.7099	−	14.1243i	1.37581	−	0.895092i
$250$	−4.28167	−	3.98501i	−0.270796	−	0.252034i
$251$	12.1114	+	10.1627i	0.764466	+	0.641463i	0.939285	−	0.343137i	$-0.111490\pi$
$251$	12.1114	+	10.1627i	0.764466	+	0.641463i	−0.174819	+	0.984601i	$0.555934\pi$
$252$	0.952936	+	1.12741i	0.0600293	+	0.0710200i
$253$	−0.262002	+	1.48589i	−0.0164719	+	0.0934169i
$254$	0.0968907	+	0.782872i	0.00607946	+	0.0491217i
$255$	−31.0709	−	3.78873i	−1.94573	−	0.237260i
$256$	−11.5948	−	11.0254i	−0.724675	−	0.689090i
$257$	7.75574	+	21.3087i	0.483790	+	1.32920i	0.906220	+	0.422806i	$0.138955\pi$
$257$	7.75574	+	21.3087i	0.483790	+	1.32920i	−0.422430	+	0.906396i	$0.638823\pi$
$258$	−24.8371	+	14.3993i	−1.54629	+	0.896461i
$259$	0.511489	+	0.295308i	0.0317824	+	0.0183496i
$260$	−10.7420	+	22.1325i	−0.666189	+	1.37260i
$261$	12.6404	−	18.8077i	0.782422	−	1.16417i
$262$	0.864494	−	16.8055i	0.0534086	−	1.03825i
$263$	2.66215	+	15.0978i	0.164155	+	0.930970i	0.949931	+	0.312459i	$0.101153\pi$
$263$	2.66215	+	15.0978i	0.164155	+	0.930970i	−0.785776	+	0.618511i	$0.787736\pi$
$264$	−1.24056	+	1.72092i	−0.0763509	+	0.105916i
$265$	4.41941			0.271482
$266$	0.838520	−	1.26376i	0.0514129	−	0.0774860i
$267$	−11.4453	−	8.60970i	−0.700441	−	0.526905i
$268$	17.3331	+	12.5422i	1.05879	+	0.766139i
$269$	−0.996932	+	0.175786i	−0.0607840	+	0.0107179i	−0.203957	−	0.978980i	$-0.565380\pi$
$269$	−0.996932	+	0.175786i	−0.0607840	+	0.0107179i	0.143173	+	0.989698i	$0.454269\pi$
$270$	22.5352	+	9.93989i	1.37145	+	0.604922i
$271$	7.37124	+	8.78470i	0.447771	+	0.533632i	0.941961	−	0.335721i	$-0.108980\pi$
$271$	7.37124	+	8.78470i	0.447771	+	0.533632i	−0.494191	+	0.869354i	$0.664536\pi$
$272$	16.0830	+	14.3693i	0.975173	+	0.871264i
$273$	−1.43910	+	0.612276i	−0.0870980	+	0.0370566i
$274$	15.2364	+	6.45016i	0.920467	+	0.389669i
$275$	2.53676	−	0.923306i	0.152973	−	0.0556774i
$276$	−10.1406	−	6.54567i	−0.610395	−	0.394003i
$277$	3.97818	+	6.89042i	0.239026	+	0.414005i	0.960435	−	0.278504i	$-0.0898386\pi$
$277$	3.97818	+	6.89042i	0.239026	+	0.414005i	−0.721409	+	0.692509i	$0.756505\pi$
$278$	3.21668	+	25.9906i	0.192923	+	1.55881i
$279$	0.317973	+	2.97755i	0.0190365	+	0.178261i
$280$	−1.12487	+	2.04322i	−0.0672236	+	0.122106i
$281$	4.01636	−	4.78651i	0.239596	−	0.285540i	−0.632825	−	0.774295i	$-0.718105\pi$
$281$	4.01636	−	4.78651i	0.239596	−	0.285540i	0.872421	+	0.488756i	$0.162549\pi$
$282$	−3.11602	−	17.4879i	−0.185556	−	1.04139i
$283$	−2.45199	+	6.73678i	−0.145756	+	0.400460i	−0.990990	−	0.133935i	$-0.957239\pi$
$283$	−2.45199	+	6.73678i	−0.145756	+	0.400460i	0.845234	+	0.534396i	$0.179461\pi$
$284$	−3.87497	+	13.6126i	−0.229937	+	0.807761i
$285$	3.33459	−	25.0842i	0.197524	−	1.48586i
$286$	−1.35434	−	1.79366i	−0.0800835	−	0.106062i
$287$	0.902659	+	0.328541i	0.0532822	+	0.0193932i
$288$	−8.83467	−	14.4896i	−0.520588	−	0.853808i
$289$	−9.24697	−	7.75913i	−0.543940	−	0.456419i
$290$	34.8944	+	8.02059i	2.04907	+	0.470986i
$291$	14.2970	+	15.3061i	0.838107	+	0.897258i
$292$	−14.8089	−	15.2760i	−0.866627	−	0.893963i
$293$	3.60599	−	2.08192i	0.210664	−	0.121627i	−0.390956	−	0.920409i	$-0.627856\pi$
$293$	3.60599	−	2.08192i	0.210664	−	0.121627i	0.601620	+	0.798782i	$0.294522\pi$
$294$	15.9626	−	5.84242i	0.930956	−	0.340737i
$295$	8.45482	+	23.2294i	0.492259	+	1.35247i
$296$	−5.28903	−	4.25771i	−0.307419	−	0.247474i
$297$	−1.74514	+	1.42043i	−0.101263	+	0.0824216i
$298$	9.62721	+	18.8495i	0.557690	+	1.09192i
$299$	9.79550	−	8.21940i	0.566488	−	0.475340i
$300$	−1.07064	+	21.5686i	−0.0618137	+	1.24527i
$301$	−0.500735	−	2.83981i	−0.0288619	−	0.163684i
$302$	0.0650490	−	0.0199561i	0.00374315	−	0.00114834i
$303$	−8.48523	−	6.38299i	−0.487464	−	0.366693i
$304$	−11.7567	+	12.8756i	−0.674291	+	0.738466i
$305$			33.7040i			1.92988i
$306$	12.5092	+	19.1520i	0.715104	+	1.09485i
$307$	−26.2478	+	4.62819i	−1.49804	+	0.264145i	−0.861761	−	0.507314i	$-0.830639\pi$
$307$	−26.2478	+	4.62819i	−1.49804	+	0.264145i	−0.636279	+	0.771459i	$0.719527\pi$
$308$	−0.119495	−	0.176424i	−0.00680885	−	0.0100527i
$309$	−23.4702	+	1.24964i	−1.33517	+	0.0710895i
$310$	−4.21356	+	2.15203i	−0.239314	+	0.122227i
$311$	10.1682	−	17.6119i	0.576588	−	0.998679i	−0.419280	−	0.907857i	$-0.637717\pi$
$311$	10.1682	−	17.6119i	0.576588	−	0.998679i	0.995867	−	0.0908218i	$-0.0289494\pi$
$312$	17.4289	−	4.41454i	0.986715	−	0.249924i
$313$	−3.91445	+	1.42474i	−0.221258	+	0.0805313i	−0.450271	−	0.892892i	$-0.648673\pi$
$313$	−3.91445	+	1.42474i	−0.221258	+	0.0805313i	0.229013	+	0.973423i	$0.426450\pi$
$314$	−27.7173	−	17.9618i	−1.56417	−	1.01364i
$315$	−1.71553	+	1.78243i	−0.0966594	+	0.100428i
$316$	1.37874	−	1.33658i	0.0775601	−	0.0751885i
$317$	16.1156	+	2.84161i	0.905142	+	0.159601i	0.606797	−	0.794857i	$-0.292454\pi$
$317$	16.1156	+	2.84161i	0.905142	+	0.159601i	0.298345	+	0.954458i	$0.403565\pi$
$318$	−2.08051	−	2.47042i	−0.116669	−	0.138534i
$319$	−2.10256	+	2.50574i	−0.117721	+	0.140294i
$320$	16.3857	−	21.2246i	0.915988	−	1.18649i
$321$	0.198956	−	0.129440i	0.0111047	−	0.00722462i
$322$	0.967488	−	0.730518i	0.0539160	−	0.0407102i
$323$	15.3008	−	17.8391i	0.851360	−	0.992597i
$324$	−5.05246	−	17.2764i	−0.280692	−	0.959798i
$325$	−21.4990	−	7.82499i	−1.19255	−	0.434052i
$326$	−7.07092	−	6.58101i	−0.391622	−	0.364488i
$327$	−19.1842	+	4.44588i	−1.06089	+	0.245858i
$328$	−9.67397	−	5.32586i	−0.534156	−	0.294071i
$329$	1.75708	+	0.309821i	0.0968711	+	0.0170810i
$330$	−3.08213	−	1.77209i	−0.169666	−	0.0975502i
$331$	−9.02730	+	5.21191i	−0.496185	+	0.286473i	−0.727137	−	0.686493i	$-0.759149\pi$
$331$	−9.02730	+	5.21191i	−0.496185	+	0.286473i	0.230952	+	0.972965i	$0.425816\pi$
$332$	−2.14371	−	29.8299i	−0.117651	−	1.63713i
$333$	−4.24277	−	5.81924i	−0.232502	−	0.318893i
$334$	−10.4285	+	24.6339i	−0.570620	+	1.34791i
$335$	−17.9274	+	31.0512i	−0.979480	+	1.69651i
$336$	1.67170	−	0.333088i	0.0911985	−	0.0181714i
$337$	−5.41096	+	4.54033i	−0.294754	+	0.247328i	−0.778157	−	0.628070i	$-0.783845\pi$
$337$	−5.41096	+	4.54033i	−0.294754	+	0.247328i	0.483403	+	0.875398i	$0.339401\pi$
$338$	−0.0340655	+	0.662222i	−0.00185292	+	0.0360201i
$339$	−8.35594	+	16.4333i	−0.453833	+	0.892535i
$340$	−21.1881	+	29.2814i	−1.14908	+	1.58801i
$341$		−	0.432242i		−	0.0234072i
$342$	−15.5917	+	9.94478i	−0.843103	+	0.537752i
$343$			3.42955i			0.185178i
$344$	0.674410	+	33.1437i	0.0363618	+	1.78699i
$345$	9.16791	−	18.0302i	0.493583	−	0.970712i
$346$	−8.47049	−	0.435732i	−0.455376	−	0.0234251i
$347$	−19.4171	+	16.2929i	−1.04237	+	0.874648i	−0.992270	−	0.124096i	$-0.960397\pi$
$347$	−19.4171	+	16.2929i	−1.04237	+	0.874648i	−0.0500949	+	0.998744i	$0.515952\pi$
$348$	−11.9436	−	23.2816i	−0.640247	−	1.24802i
$349$	−13.4446	+	23.2867i	−0.719672	+	1.24651i	0.241457	+	0.970411i	$0.422375\pi$
$349$	−13.4446	+	23.2867i	−0.719672	+	1.24651i	−0.961130	+	0.276098i	$0.910959\pi$
$350$	−1.99745	−	0.845596i	−0.106768	−	0.0451990i
$351$	19.0677	+	0.285129i	1.01776	+	0.0152190i
$352$	1.04595	+	2.21511i	0.0557494	+	0.118066i
$353$	3.14132	−	1.81364i	0.167195	−	0.0965303i	−0.414067	−	0.910246i	$-0.635892\pi$
$353$	3.14132	−	1.81364i	0.167195	−	0.0965303i	0.581263	+	0.813716i	$0.302559\pi$
$354$	9.00484	−	15.6618i	0.478602	−	0.832415i
$355$	−23.3588	−	4.11878i	−1.23975	−	0.218602i
$356$	−15.0950	+	6.75561i	−0.800031	+	0.358047i
$357$	−2.23832	+	0.518723i	−0.118464	+	0.0274537i
$358$	−1.23479	+	1.32671i	−0.0652607	+	0.0701189i
$359$	11.6034	+	4.22330i	0.612405	+	0.222897i	0.629555	−	0.776956i	$-0.283237\pi$
$359$	11.6034	+	4.22330i	0.612405	+	0.222897i	−0.0171504	+	0.999853i	$0.505459\pi$
$360$	22.6351	−	17.2191i	1.19298	−	0.907529i
$361$	14.2871	+	12.5251i	0.751954	+	0.659215i
$362$	−0.265109	−	0.351107i	−0.0139338	−	0.0184538i
$363$	−15.6979	+	10.2130i	−0.823927	+	0.536041i
$364$	−0.185302	+	1.79634i	−0.00971246	+	0.0941537i
$365$	22.9188	−	27.3135i	1.19962	−	1.42966i
$366$	18.8403	−	15.8667i	0.984797	−	0.829364i
$367$	−1.38430	−	0.244089i	−0.0722599	−	0.0127414i	0.137401	−	0.990515i	$-0.456125\pi$
$367$	−1.38430	−	0.244089i	−0.0722599	−	0.0127414i	−0.209661	+	0.977774i	$0.567236\pi$
$368$	−12.2803	+	6.59039i	−0.640152	+	0.343548i
$369$	−8.43918	−	8.12247i	−0.439326	−	0.422839i
$370$	6.18814	−	9.54904i	0.321706	−	0.496431i
$371$	0.304842	−	0.110953i	0.0158266	−	0.00576040i
$372$	3.18657	+	1.34224i	0.165216	+	0.0695922i
$373$	−4.72933	+	8.19144i	−0.244876	+	0.424137i	−0.962097	−	0.272709i	$-0.912080\pi$
$373$	−4.72933	+	8.19144i	−0.244876	+	0.424137i	0.717221	+	0.696846i	$0.245414\pi$
$374$	−1.50190	−	2.94063i	−0.0776613	−	0.152056i
$375$	−7.15363	+	0.380886i	−0.369412	+	0.0196689i
$376$	−19.4131	−	6.62174i	−1.00115	−	0.341490i
$377$	27.3005	−	4.81382i	1.40605	−	0.247924i
$378$	1.80398	+	0.119867i	0.0927866	+	0.00616528i
$379$		−	5.34855i		−	0.274737i	−0.990520	−	0.137368i	$-0.956136\pi$
$379$		−	5.34855i		−	0.274737i	0.990520	−	0.137368i	$-0.0438644\pi$
$380$	−23.4855	−	17.3844i	−1.20478	−	0.891800i
$381$	0.772073	+	0.580790i	0.0395545	+	0.0297548i
$382$	−0.911651	−	2.97163i	−0.0466441	−	0.152042i
$383$	1.60756	+	9.11692i	0.0821424	+	0.465853i	0.997937	+	0.0642053i	$0.0204512\pi$
$383$	1.60756	+	9.11692i	0.0821424	+	0.465853i	−0.915794	+	0.401648i	$0.868438\pi$
$384$	−19.5782	+	0.832343i	−0.999098	+	0.0424753i
$385$	0.273552	−	0.229537i	0.0139415	−	0.0116983i
$386$	−5.05100	+	2.57975i	−0.257089	+	0.131306i
$387$	−8.44945	+	34.1312i	−0.429510	+	1.73499i
$388$	23.4552	−	5.89608i	1.19076	−	0.299328i
$389$	0.112367	+	0.308725i	0.00569722	+	0.0156530i	0.942509	−	0.334182i	$-0.108460\pi$
$389$	0.112367	+	0.308725i	0.00569722	+	0.0156530i	−0.936811	+	0.349835i	$0.886238\pi$
$390$	10.3562	+	28.2950i	0.524405	+	1.43277i
$391$	16.2693	−	9.39307i	0.822772	−	0.475028i
$392$	3.01439	−	19.3949i	0.152249	−	0.979592i
$393$	−14.0683	−	15.0612i	−0.709652	−	0.759738i
$394$	−1.00884	+	4.38907i	−0.0508247	+	0.221118i
$395$	2.46518	+	2.06853i	0.124037	+	0.104079i
$396$	0.460376	+	2.55713i	0.0231347	+	0.128500i
$397$	16.3433	+	5.94848i	0.820247	+	0.298546i	0.717850	−	0.696198i	$-0.245126\pi$
$397$	16.3433	+	5.94848i	0.820247	+	0.298546i	0.102397	+	0.994744i	$0.467349\pi$
$398$	−15.6900	+	11.8470i	−0.786466	+	0.593834i
$399$	−0.399749	−	1.81397i	−0.0200125	−	0.0908123i
$400$	21.1977	+	13.1324i	1.05989	+	0.656621i
$401$	−2.21821	+	6.09449i	−0.110772	+	0.304344i	−0.982676	−	0.185334i	$-0.940663\pi$
$401$	−2.21821	+	6.09449i	−0.110772	+	0.304344i	0.871903	+	0.489678i	$0.162886\pi$
$402$	25.7970	−	4.59654i	1.28664	−	0.229255i
$403$	−2.35468	+	2.80620i	−0.117295	+	0.139787i
$404$	−11.1910	+	5.00842i	−0.556772	+	0.249178i
$405$	27.9311	−	11.3934i	1.38791	−	0.566141i
$406$	2.60831	−	0.322813i	0.129448	−	0.0160209i
$407$	0.519771	+	0.900270i	0.0257641	+	0.0446247i
$408$	26.3427	−	1.94071i	1.30416	−	0.0960795i
$409$	10.2514	−	3.73122i	0.506901	−	0.184497i	−0.0758941	−	0.997116i	$-0.524181\pi$
$409$	10.2514	−	3.73122i	0.506901	−	0.184497i	0.582795	+	0.812619i	$0.301959\pi$
$410$	7.21472	−	17.0425i	0.356309	−	0.841667i
$411$	18.6465	−	7.93333i	0.919766	−	0.391323i
$412$	−11.8501	+	24.4156i	−0.583811	+	1.20287i
$413$	1.16639	+	1.39005i	0.0573943	+	0.0683999i
$414$	−14.3947	+	3.36319i	−0.707459	+	0.165292i
$415$	49.3582	−	8.70319i	2.42290	−	0.427223i
$416$	5.27653	−	20.0789i	0.258703	−	0.984449i
$417$	25.6321	+	19.2817i	1.25521	+	0.944227i
$418$	2.39031	−	1.18839i	0.116914	−	0.0581262i
$419$	25.0964			1.22604			0.613020	−	0.790067i	$-0.289954\pi$
$419$	25.0964			1.22604			0.613020	+	0.790067i	$0.289954\pi$
$420$	0.842728	+	2.72946i	0.0411209	+	0.133184i
$421$	−4.07208	−	23.0939i	−0.198461	−	1.12553i	−0.907403	−	0.420261i	$-0.861939\pi$
$421$	−4.07208	−	23.0939i	−0.198461	−	1.12553i	0.708942	−	0.705266i	$-0.249173\pi$
$422$	26.1229	+	1.34379i	1.27164	+	0.0654148i
$423$	−18.0565	−	12.1355i	−0.877935	−	0.590048i
$424$	−3.65884	+	0.722193i	−0.177689	+	0.0350728i
$425$	−29.1090	−	16.8061i	−1.41199	−	0.815216i
$426$	8.69413	+	14.9964i	0.421232	+	0.726576i
$427$	0.846168	+	2.32483i	0.0409489	+	0.112506i
$428$	−0.0196457	−	0.273371i	−0.000949610	−	0.0132139i
$429$	−2.73243	−	0.333188i	−0.131923	−	0.0160865i
$430$	−55.1350	+	6.82369i	−2.65885	+	0.329067i
$431$	−4.59899	+	26.0822i	−0.221526	+	1.25633i	0.647691	+	0.761903i	$0.275735\pi$
$431$	−4.59899	+	26.0822i	−0.221526	+	1.25633i	−0.869217	+	0.494431i	$0.835376\pi$
$432$	−20.2812	−	4.54669i	−0.975780	−	0.218753i
$433$	−3.17543	−	2.66450i	−0.152602	−	0.128048i	0.563290	−	0.826259i	$-0.309535\pi$
$433$	−3.17543	−	2.66450i	−0.152602	−	0.128048i	−0.715892	+	0.698211i	$0.753980\pi$
$434$	−0.236613	+	0.254228i	−0.0113578	+	0.0122033i
$435$	36.7568	−	23.9137i	1.76235	−	1.14658i
$436$	−6.22560	+	21.8703i	−0.298152	+	1.04740i
$437$	7.45093	+	13.2341i	0.356426	+	0.633072i
$438$	−26.0574	+	0.0468417i	−1.24507	+	0.00223818i
$439$	13.9237	−	38.2551i	0.664542	−	1.82581i	0.109510	−	0.993986i	$-0.465072\pi$
$439$	13.9237	−	38.2551i	0.664542	−	1.82581i	0.555032	−	0.831829i	$-0.312706\pi$
$440$	−3.51276	+	2.12453i	−0.167464	+	0.101283i
$441$	8.43589	−	19.0327i	0.401709	−	0.906317i
$442$	−6.26876	+	27.2729i	−0.298175	+	1.29724i
$443$	3.99666	−	22.6662i	0.189887	−	1.07690i	−0.729627	−	0.683846i	$-0.760306\pi$
$443$	3.99666	−	22.6662i	0.189887	−	1.07690i	0.919514	−	0.393058i	$-0.128583\pi$
$444$	−8.25101	+	1.03623i	−0.391576	+	0.0491775i
$445$	−13.8574	−	24.0018i	−0.656905	−	1.13779i
$446$	−18.1427	+	27.9964i	−0.859084	+	1.32567i
$447$	24.7962	+	7.55837i	1.17282	+	0.357499i
$448$	0.597387	−	1.87541i	0.0282239	−	0.0886046i
$449$	6.18347	+	3.57003i	0.291816	+	0.168480i	0.638761	−	0.769406i	$-0.279447\pi$
$449$	6.18347	+	3.57003i	0.291816	+	0.168480i	−0.346944	+	0.937886i	$0.612781\pi$
$450$	18.0887	+	19.2958i	0.852711	+	0.909610i
$451$	1.08678	+	1.29517i	0.0511745	+	0.0609874i
$452$	11.9380	+	17.6253i	0.561514	+	0.829027i
$453$	0.0377706	−	0.0742819i	0.00177462	−	0.00349007i
$454$	−2.17918	−	7.10329i	−0.102274	−	0.333374i
$455$	−3.02638			−0.141879
$456$	1.33840	+	21.3122i	0.0626762	+	0.998034i
$457$	9.63717			0.450808			0.225404	−	0.974265i	$-0.427630\pi$
$457$	9.63717			0.450808			0.225404	+	0.974265i	$0.427630\pi$
$458$	5.71107	+	18.6159i	0.266861	+	0.869862i
$459$	27.5149	+	5.27698i	1.28429	+	0.246309i
$460$	−13.0980	−	19.3380i	−0.610697	−	0.901640i
$461$	−19.7319	−	23.5156i	−0.919008	−	1.09523i	−0.995173	−	0.0981358i	$-0.968712\pi$
$461$	−19.7319	−	23.5156i	−0.919008	−	1.09523i	0.0761651	−	0.997095i	$-0.475732\pi$
$462$	−0.257088	−	0.0448553i	−0.0119608	−	0.00208686i
$463$	−13.2536	−	7.65197i	−0.615947	−	0.355617i	0.159342	−	0.987223i	$-0.449063\pi$
$463$	−13.2536	−	7.65197i	−0.615947	−	0.355617i	−0.775289	+	0.631606i	$0.782396\pi$
$464$	−30.1998	−	0.938026i	−1.40199	−	0.0435468i
$465$	−1.68957	+	5.54286i	−0.0783520	+	0.257044i
$466$	−8.56139	+	13.2112i	−0.396599	+	0.611999i
$467$	−11.9559	−	20.7083i	−0.553255	−	0.958266i	−0.998037	−	0.0626270i	$-0.980052\pi$
$467$	−11.9559	−	20.7083i	−0.553255	−	0.958266i	0.444782	−	0.895639i	$-0.353281\pi$
$468$	10.9414	−	19.1093i	0.505765	−	0.883329i
$469$	−0.457027	+	2.59193i	−0.0211036	+	0.119684i
$470$	7.70021	−	33.5006i	0.355184	−	1.54527i
$471$	−39.4070	+	9.13242i	−1.81578	+	0.420800i
$472$	−10.7958	−	17.8500i	−0.496915	−	0.821614i
$473$	1.73590	−	4.76936i	0.0798169	−	0.219295i
$474$	−0.00422769	−	2.35181i	−0.000194184	−	0.108022i
$475$	13.8405	−	23.3844i	0.635047	−	1.07295i
$476$	−0.726371	+	2.55172i	−0.0332932	+	0.116958i
$477$	−3.94648	−	0.269353i	−0.180697	−	0.0123328i
$478$	−6.07733	+	6.52975i	−0.277971	+	0.298664i
$479$	−3.49795	−	2.93513i	−0.159826	−	0.134110i	0.559368	−	0.828920i	$-0.311044\pi$
$479$	−3.49795	−	2.93513i	−0.159826	−	0.134110i	−0.719193	+	0.694810i	$0.755488\pi$
$480$	−4.75422	−	32.4940i	−0.217000	−	1.48314i
$481$	1.52986	−	8.67625i	0.0697554	−	0.395603i
$482$	14.3010	−	1.76993i	0.651392	−	0.0806183i
$483$	0.179719	−	1.47385i	0.00817750	−	0.0670625i
$484$	1.55007	+	21.5693i	0.0704576	+	0.980424i
$485$	13.8622	+	38.0861i	0.629451	+	1.72940i
$486$	−19.5178	−	10.2497i	−0.885345	−	0.464934i
$487$	0.626702	+	0.361827i	0.0283986	+	0.0163959i	0.514132	−	0.857711i	$-0.328114\pi$
$487$	0.626702	+	0.361827i	0.0283986	+	0.0163959i	−0.485733	+	0.874107i	$0.661447\pi$
$488$	−5.50769	−	27.9036i	−0.249322	−	1.26313i
$489$	−11.8138	+	0.629011i	−0.534238	+	0.0284448i
$490$	32.8499	+	1.68984i	1.48401	+	0.0763392i
$491$	2.41611	+	13.7024i	0.109037	+	0.618381i	0.989531	+	0.144323i	$0.0461004\pi$
$491$	2.41611	+	13.7024i	0.109037	+	0.618381i	−0.880493	+	0.474059i	$0.842789\pi$
$492$	−12.9231	+	3.99003i	−0.582616	+	0.179885i
$493$	40.7272			1.83426
$494$	−21.9923	−	5.30620i	−0.989481	−	0.238737i
$495$	−4.18359	+	1.20718i	−0.188038	+	0.0542586i
$496$	3.13674	−	2.47022i	0.140844	−	0.110916i
$497$	−1.71464	+	0.302338i	−0.0769122	+	0.0135617i
$498$	−28.1012	−	23.4937i	−1.25924	−	1.05278i
$499$	22.7913	+	27.1616i	1.02028	+	1.21592i	0.976195	+	0.216893i	$0.0695921\pi$
$499$	22.7913	+	27.1616i	1.02028	+	1.21592i	0.0440828	+	0.999028i	$0.485963\pi$
$500$	−3.61186	+	7.44180i	−0.161527	+	0.332807i
$501$	12.8264	+	30.1473i	0.573042	+	1.34688i
$502$	8.71659	−	20.5902i	0.389040	−	0.918983i
$503$	41.2562	−	15.0160i	1.83952	−	0.669531i	0.849692	−	0.527279i	$-0.176788\pi$
$503$	41.2562	−	15.0160i	1.83952	−	0.669531i	0.989830	−	0.142252i	$-0.0454344\pi$
$504$	1.12902	−	1.75601i	0.0502905	−	0.0782191i
$505$	−10.2735	−	17.7942i	−0.457165	−	0.791833i
$506$	2.11762	−	0.262084i	0.0941398	−	0.0116510i
$507$	0.554363	+	0.593489i	0.0246201	+	0.0263578i
$508$	1.01827	−	0.455717i	0.0451784	−	0.0202192i
$509$	−8.41817	+	10.0324i	−0.373129	+	0.444678i	−0.919633	−	0.392779i	$-0.871514\pi$
$509$	−8.41817	+	10.0324i	−0.373129	+	0.444678i	0.546504	+	0.837456i	$0.315958\pi$
$510$	7.76512	+	43.5799i	0.343845	+	1.92975i
$511$	0.895158	−	2.45943i	0.0395994	−	0.108799i
$512$	−10.0973	+	20.2495i	−0.446243	+	0.894912i
$513$	−4.50657	+	22.1966i	−0.198970	+	0.980006i
$514$	25.5929	−	19.3243i	1.12885	−	0.852360i
$515$	−42.7389	−	15.5557i	−1.88330	−	0.685465i
$516$	29.7701	+	27.6077i	1.31055	+	1.21536i
$517$	2.40564	+	2.01857i	0.105800	+	0.0887768i
$518$	0.187108	−	0.814031i	0.00822103	−	0.0357665i
$519$	−7.59132	+	7.09086i	−0.333222	+	0.311254i
$520$	34.3791	+	5.34325i	1.50762	+	0.234317i
$521$	6.79220	−	3.92148i	0.297572	−	0.171803i	−0.343780	−	0.939050i	$-0.611707\pi$
$521$	6.79220	−	3.92148i	0.297572	−	0.171803i	0.641351	+	0.767247i	$0.278374\pi$
$522$	−30.6714	−	9.28902i	−1.34245	−	0.406569i
$523$	−3.90938	−	10.7409i	−0.170945	−	0.469668i	0.824404	−	0.566002i	$-0.191511\pi$
$523$	−3.90938	−	10.7409i	−0.170945	−	0.469668i	−0.995349	+	0.0963341i	$0.969288\pi$
$524$	−23.0799	+	5.80176i	−1.00825	+	0.253451i
$525$	−2.44450	+	1.04003i	−0.106687	+	0.0453908i
$526$	19.3083	−	9.86153i	0.841883	−	0.429983i
$527$	−4.12272	+	3.45937i	−0.179589	+	0.150693i
$528$	2.84128	+	0.963451i	0.123651	+	0.0419288i
$529$	−1.88584	−	10.6951i	−0.0819932	−	0.465006i
$530$	−1.83308	−	5.97513i	−0.0796240	−	0.259543i
$531$	−6.13426	−	21.2589i	−0.266204	−	0.922556i
$532$	−2.05643	−	0.609515i	−0.0891574	−	0.0264258i
$533$		−	14.3289i		−	0.620653i
$534$	−6.89321	+	19.0454i	−0.298299	+	0.824175i
$535$	0.452335	−	0.0797588i	0.0195561	−	0.00344827i
$536$	9.76794	−	28.6369i	0.421911	−	1.23693i
$537$	0.118021	+	2.21661i	0.00509298	+	0.0956540i
$538$	0.651173	+	1.27496i	0.0280741	+	0.0549674i
$539$	−1.50253	+	2.60246i	−0.0647186	+	0.112096i
$540$	4.09180	−	34.5909i	0.176083	−	1.48855i
$541$	−23.3716	+	8.50657i	−1.00482	+	0.365726i	−0.791443	−	0.611243i	$-0.790670\pi$
$541$	−23.3716	+	8.50657i	−1.00482	+	0.365726i	−0.213381	+	0.976969i	$0.568448\pi$
$542$	8.81965	−	13.6098i	0.378836	−	0.584590i
$543$	−0.534869	−	0.0652211i	−0.0229534	−	0.00279891i
$544$	12.7566	−	27.7046i	0.546936	−	1.18782i
$545$	−37.5286	−	6.61731i	−1.60755	−	0.283454i
$546$	1.42472	+	1.69173i	0.0609722	+	0.0723992i
$547$	−5.16251	+	6.15244i	−0.220733	+	0.263059i	−0.865035	−	0.501712i	$-0.832704\pi$
$547$	−5.16251	+	6.15244i	−0.220733	+	0.263059i	0.644302	+	0.764771i	$0.277148\pi$
$548$	2.40098	−	23.2754i	0.102565	−	0.994275i
$549$	2.05418	−	30.0972i	0.0876703	−	1.28452i
$550$	−2.30052	−	3.04678i	−0.0980947	−	0.129915i
$551$	−0.356293	+	32.9234i	−0.0151786	+	1.40259i
$552$	−4.64374	+	16.4254i	−0.197651	+	0.699110i
$553$	0.221975	+	0.0807925i	0.00943936	+	0.00343564i
$554$	7.66591	−	8.23659i	0.325693	−	0.349939i
$555$	−3.14627	−	13.5763i	−0.133552	−	0.576283i
$556$	33.8056	−	15.1294i	1.43367	−	0.641628i
$557$	22.7675	+	4.01453i	0.964691	+	0.170101i	0.633739	−	0.773547i	$-0.281519\pi$
$557$	22.7675	+	4.01453i	0.964691	+	0.170101i	0.330952	+	0.943648i	$0.392630\pi$
$558$	3.89381	−	1.66493i	0.164838	−	0.0704821i
$559$	−37.2514	+	21.5071i	−1.57557	+	0.909654i
$560$	3.22905	+	0.673353i	0.136452	+	0.0284544i
$561$	−3.86835	−	1.17915i	−0.163322	−	0.0497836i
$562$	−8.13737	−	3.44485i	−0.343254	−	0.145312i
$563$	−10.0848	+	17.4674i	−0.425024	+	0.736163i	−0.996423	−	0.0845098i	$-0.973068\pi$
$563$	−10.0848	+	17.4674i	−0.425024	+	0.736163i	0.571399	+	0.820672i	$0.306401\pi$
$564$	−22.3516	+	11.4666i	−0.941171	+	0.482829i
$565$	−27.3288	+	22.9316i	−1.14973	+	0.964739i
$566$	10.1253	+	0.520858i	0.425598	+	0.0218933i
$567$	1.64058	−	1.48712i	0.0688981	−	0.0624534i
$568$	20.0118	−	0.407201i	0.839677	−	0.0170858i
$569$		−	29.7662i		−	1.24786i	−0.781479	−	0.623931i	$-0.785534\pi$
$569$		−	29.7662i		−	1.24786i	0.781479	−	0.623931i	$-0.214466\pi$
$570$	−35.2975	+	5.89599i	−1.47845	+	0.246956i
$571$			26.5655i			1.11173i	0.831272	+	0.555866i	$0.187613\pi$
$571$			26.5655i			1.11173i	−0.831272	+	0.555866i	$0.812387\pi$
$572$	−1.86332	+	2.57506i	−0.0779093	+	0.107669i
$573$	−3.39341	−	1.72547i	−0.141762	−	0.0720825i
$574$	0.0697895	−	1.35668i	0.00291296	−	0.0566269i
$575$	16.6390	−	13.9618i	0.693894	−	0.582247i
$576$	−15.9258	+	17.9546i	−0.663575	+	0.748110i
$577$	−4.91066	+	8.50551i	−0.204433	+	0.354089i	−0.949952	−	0.312396i	$-0.898869\pi$
$577$	−4.91066	+	8.50551i	−0.204433	+	0.354089i	0.745519	+	0.666485i	$0.232202\pi$
$578$	−6.65505	+	15.7204i	−0.276813	+	0.653883i
$579$	−2.02537	+	6.64450i	−0.0841716	+	0.276136i
$580$	−3.62950	−	50.5048i	−0.150707	−	2.09710i
$581$	3.18612	−	1.83951i	0.132183	−	0.0763157i
$582$	14.7640	−	25.6785i	0.611988	−	1.06441i
$583$	0.562311	+	0.0991505i	0.0232885	+	0.00410640i
$584$	−14.5111	+	26.3582i	−0.600472	+	1.09071i
$585$	33.7370	+	14.9533i	1.39485	+	0.618243i
$586$	−4.31049	−	4.01183i	−0.178065	−	0.165727i
$587$	−34.1410	−	12.4263i	−1.40915	−	0.512889i	−0.478271	−	0.878212i	$-0.658736\pi$
$587$	−34.1410	−	12.4263i	−1.40915	−	0.512889i	−0.930881	+	0.365323i	$0.880958\pi$
$588$	−14.5200	−	19.1584i	−0.598795	−	0.790079i
$589$	−2.76046	−	3.36303i	−0.113743	−	0.138571i
$590$	27.8998	−	21.0662i	1.14861	−	0.867281i
$591$	3.00790	+	4.62332i	0.123728	+	0.190178i
$592$	−3.56272	+	8.91689i	−0.146427	+	0.366482i
$593$	0.796696	−	0.949466i	0.0327164	−	0.0389899i	−0.749438	−	0.662074i	$-0.769676\pi$
$593$	0.796696	−	0.949466i	0.0327164	−	0.0389899i	0.782155	+	0.623084i	$0.214121\pi$
$594$	2.64429	+	1.77030i	0.108497	+	0.0726363i
$595$	−4.37865	−	0.772074i	−0.179507	−	0.0316519i
$596$	21.4918	−	20.8346i	0.880337	−	0.853418i
$597$	−2.91454	+	23.9017i	−0.119284	+	0.978233i
$598$	−15.1758	−	9.83447i	−0.620583	−	0.402162i
$599$	−34.0748	+	12.4022i	−1.39226	+	0.506741i	−0.925871	−	0.377840i	$-0.876667\pi$
$599$	−34.0748	+	12.4022i	−1.39226	+	0.506741i	−0.466387	+	0.884581i	$0.654445\pi$
$600$	29.6053	−	7.49869i	1.20863	−	0.306133i
$601$	14.7717	−	25.5854i	0.602551	−	1.04365i	−0.389882	−	0.920865i	$-0.627484\pi$
$601$	14.7717	−	25.5854i	0.602551	−	1.04365i	0.992433	−	0.122785i	$-0.0391825\pi$
$602$	−3.63178	+	1.85490i	−0.148020	+	0.0756000i
$603$	17.9015	−	26.6357i	0.729003	−	1.08469i
$604$	−0.0539620	−	0.0796702i	−0.00219568	−	0.00324173i
$605$	−35.6898	+	6.29307i	−1.45100	+	0.255850i
$606$	−5.11044	+	14.1197i	−0.207597	+	0.573575i
$607$			33.5519i			1.36183i	0.732362	+	0.680915i	$0.238418\pi$
$607$			33.5519i			1.36183i	−0.732362	+	0.680915i	$0.761582\pi$
$608$	22.2845	+	10.5547i	0.903755	+	0.428050i
$609$	1.93503	−	2.57233i	0.0784113	−	0.104236i
$610$	45.5684	−	13.9797i	1.84501	−	0.566022i
$611$	−4.62153	−	26.2100i	−0.186967	−	1.06034i
$612$	20.7053	−	24.8566i	0.836962	−	1.00477i
$613$	−22.2648	+	18.6824i	−0.899266	+	0.754574i	−0.970047	−	0.242918i	$-0.921895\pi$
$613$	−22.2648	+	18.6824i	−0.899266	+	0.754574i	0.0707808	+	0.997492i	$0.477451\pi$
$614$	17.1445	+	33.5679i	0.691894	+	1.35469i
$615$	−8.87369	−	20.8568i	−0.357822	−	0.841025i
$616$	−0.188964	+	0.234736i	−0.00761359	+	0.00945779i
$617$	−4.78269	−	13.1403i	−0.192544	−	0.529010i	0.805426	−	0.592696i	$-0.201937\pi$
$617$	−4.78269	−	13.1403i	−0.192544	−	0.529010i	−0.997970	+	0.0636860i	$0.979714\pi$
$618$	11.4245	+	31.2138i	0.459560	+	1.25560i
$619$	−3.36565	+	1.94316i	−0.135277	+	0.0781021i	−0.566111	−	0.824329i	$-0.691553\pi$
$619$	−3.36565	+	1.94316i	−0.135277	+	0.0781021i	0.430834	+	0.902431i	$0.358219\pi$
$620$	4.65729	+	4.80419i	0.187041	+	0.192941i
$621$	−9.28572	+	15.5419i	−0.372623	+	0.623676i
$622$	−28.0292	−	6.44260i	−1.12387	−	0.258325i
$623$	−1.55844	−	1.30769i	−0.0624376	−	0.0523914i
$624$	−13.1977	−	21.7331i	−0.528330	−	0.870020i
$625$	16.2635	+	5.91944i	0.650541	+	0.236778i
$626$	3.54992	+	4.70146i	0.141883	+	0.187908i
$627$	0.987052	−	3.11682i	0.0394191	−	0.124474i
$628$	−12.7882	+	44.9245i	−0.510305	+	1.79268i
$629$	4.42687	−	12.1627i	0.176511	−	0.484960i
$630$	3.12144	+	1.58012i	0.124361	+	0.0629536i
$631$	−3.21131	+	3.82709i	−0.127840	+	0.152354i	−0.826167	−	0.563425i	$-0.809484\pi$
$631$	−3.21131	+	3.82709i	−0.127840	+	0.152354i	0.698327	+	0.715779i	$0.253928\pi$
$632$	−2.37896	−	1.30970i	−0.0946298	−	0.0520970i
$633$	23.4116	−	21.8682i	0.930526	−	0.869181i
$634$	−2.84250	−	22.9672i	−0.112890	−	0.912146i
$635$	0.934789	+	1.61910i	0.0370960	+	0.0642521i
$636$	−2.47710	+	3.83757i	−0.0982236	+	0.152169i
$637$	23.9319	−	8.71051i	0.948218	−	0.345123i
$638$	4.25990	+	1.80338i	0.168651	+	0.0713964i
$639$	20.6080	+	5.10168i	0.815241	+	0.201819i
$640$	−35.4926	−	13.3502i	−1.40297	−	0.527714i
$641$	9.89934	+	11.7976i	0.391000	+	0.465976i	0.925254	−	0.379348i	$-0.123852\pi$
$641$	9.89934	+	11.7976i	0.391000	+	0.465976i	−0.534254	+	0.845324i	$0.679407\pi$
$642$	−0.257528	−	0.215304i	−0.0101638	−	0.00849738i
$643$	−24.3580	+	4.29496i	−0.960584	+	0.169377i	−0.631889	−	0.775059i	$-0.717720\pi$
$643$	−24.3580	+	4.29496i	−0.960584	+	0.169377i	−0.328695	+	0.944436i	$0.606609\pi$
$644$	−1.38897	−	1.00506i	−0.0547331	−	0.0396049i
$645$	−40.9031	+	54.3745i	−1.61056	+	2.14099i
$646$	−30.4654	−	13.2877i	−1.19864	−	0.522797i
$647$	−7.61455			−0.299359			−0.149680	−	0.988735i	$-0.547824\pi$
$647$	−7.61455			−0.299359			−0.149680	+	0.988735i	$0.547824\pi$
$648$	−21.2623	+	13.9969i	−0.835263	+	0.549850i
$649$	0.554604	+	3.14532i	0.0217701	+	0.123465i
$650$	−1.66220	+	32.3127i	−0.0651970	+	1.26741i
$651$	0.0226154	+	0.424753i	0.000886369	+	0.0166474i
$652$	−5.96478	+	12.2897i	−0.233599	+	0.481302i
$653$	−7.96800	−	4.60033i	−0.311812	−	0.180025i	0.335925	−	0.941889i	$-0.390951\pi$
$653$	−7.96800	−	4.60033i	−0.311812	−	0.180025i	−0.647737	+	0.761864i	$0.724284\pi$
$654$	13.9682	+	24.0934i	0.546198	+	0.942127i
$655$	−13.6405	−	37.4768i	−0.532976	−	1.46434i
$656$	−3.18810	+	15.2885i	−0.124474	+	0.596914i
$657$	−22.1309	+	22.9938i	−0.863407	+	0.897073i
$658$	−0.309918	−	2.50412i	−0.0120818	−	0.0976207i
$659$	5.44661	−	30.8893i	0.212170	−	1.20328i	−0.673581	−	0.739114i	$-0.735245\pi$
$659$	5.44661	−	30.8893i	0.212170	−	1.20328i	0.885751	−	0.464162i	$-0.153644\pi$
$660$	−1.11749	+	4.90212i	−0.0434984	+	0.190815i
$661$	−18.0872	−	15.1770i	−0.703511	−	0.590316i	0.219259	−	0.975667i	$-0.429636\pi$
$661$	−18.0872	−	15.1770i	−0.703511	−	0.590316i	−0.922770	+	0.385351i	$0.874080\pi$
$662$	10.7910	+	10.0433i	0.419402	+	0.390344i
$663$	18.6906	+	28.7285i	0.725882	+	1.11572i
$664$	−39.4415	+	15.2712i	−1.53063	+	0.592637i
$665$	0.662442	−	3.53290i	0.0256884	−	0.137000i
$666$	−6.10792	+	8.15001i	−0.236677	+	0.315807i
$667$	−9.00145	+	24.7313i	−0.348537	+	0.957599i
$668$	37.6311	+	3.88185i	1.45599	+	0.150193i
$669$	9.22441	+	39.8039i	0.356636	+	1.53891i
$670$	49.4178	+	11.3588i	1.90918	+	0.438830i
$671$	−0.756157	+	4.28838i	−0.0291911	+	0.165551i
$672$	−1.14373	−	2.12201i	−0.0441202	−	0.0818582i
$673$	9.62696	+	16.6744i	0.371092	+	0.642750i	0.989734	−	0.142923i	$-0.0456501\pi$
$673$	9.62696	+	16.6744i	0.371092	+	0.642750i	−0.618642	+	0.785673i	$0.712317\pi$
$674$	8.38297	+	5.43248i	0.322900	+	0.209251i
$675$	32.3892	+	0.484330i	1.24666	+	0.0186419i
$676$	0.909467	−	0.228619i	0.0349795	−	0.00879303i
$677$	−34.1118	−	19.6945i	−1.31102	−	0.756920i	−0.328758	−	0.944414i	$-0.606630\pi$
$677$	−34.1118	−	19.6945i	−1.31102	−	0.756920i	−0.982266	+	0.187494i	$0.939963\pi$
$678$	25.6840	+	4.48120i	0.986390	+	0.172099i
$679$	1.91237	+	2.27908i	0.0733901	+	0.0874629i
$680$	48.3775	+	16.5014i	1.85519	+	0.632798i
$681$	−8.11152	−	4.12451i	−0.310834	−	0.158052i
$682$	−0.584400	+	0.179285i	−0.0223778	+	0.00686518i
$683$	32.3086			1.23625			0.618127	−	0.786078i	$-0.287892\pi$
$683$	32.3086			1.23625			0.618127	+	0.786078i	$0.287892\pi$
$684$	19.9127	+	16.9554i	0.761380	+	0.648306i
$685$	39.2132			1.49826
$686$	4.63682	−	1.42251i	0.177035	−	0.0543116i
$687$	21.2582	+	10.8093i	0.811049	+	0.412399i
$688$	44.5313	−	14.6592i	1.69774	−	0.558875i
$689$	−3.11050	−	3.70695i	−0.118501	−	0.141224i
$690$	−28.1798	−	4.91665i	−1.07279	−	0.187173i
$691$	−22.5874	−	13.0408i	−0.859265	−	0.496097i	0.00450107	−	0.999990i	$-0.498567\pi$
$691$	−22.5874	−	13.0408i	−0.859265	−	0.496097i	−0.863766	+	0.503893i	$0.831901\pi$
$692$	2.92427	+	11.6330i	0.111164	+	0.442220i
$693$	−0.258268	+	0.188301i	−0.00981078	+	0.00715297i
$694$	30.0821	+	19.4944i	1.14190	+	0.739996i
$695$	31.0341	+	53.7526i	1.17719	+	2.03895i
$696$	−26.5232	+	25.8048i	−1.00536	+	0.978127i
$697$	3.65551	−	20.7314i	0.138462	−	0.785258i
$698$	37.0606	+	8.51850i	1.40277	+	0.322430i
$699$	4.35291	+	18.7831i	0.164642	+	0.710441i
$700$	−0.314761	+	3.05133i	−0.0118968	+	0.115329i
$701$	−17.2787	+	47.4727i	−0.652606	+	1.79302i	−0.0447137	+	0.999000i	$0.514238\pi$
$701$	−17.2787	+	47.4727i	−0.652606	+	1.79302i	−0.607892	+	0.794020i	$0.707985\pi$
$702$	−7.52341	−	25.8982i	−0.283953	−	0.977465i
$703$	9.79350	+	3.68504i	0.369369	+	0.138984i
$704$	2.56104	−	2.33293i	0.0965227	−	0.0879257i
$705$	−22.9585	−	35.2885i	−0.864667	−	1.32904i
$706$	−3.75503	−	3.49486i	−0.141322	−	0.131531i
$707$	−1.15538	−	0.969483i	−0.0434527	−	0.0364611i
$708$	−24.9101	−	5.67853i	−0.936178	−	0.213412i
$709$	0.917080	−	5.20102i	0.0344417	−	0.195328i	−0.962732	−	0.270456i	$-0.912825\pi$
$709$	0.917080	−	5.20102i	0.0344417	−	0.195328i	0.997174	+	0.0751280i	$0.0239365\pi$
$710$	4.12006	+	33.2899i	0.154623	+	1.24935i
$711$	−2.07530	−	1.99742i	−0.0778300	−	0.0749091i
$712$	15.3948	+	17.6066i	0.576944	+	0.659835i
$713$	−1.18948	−	3.26808i	−0.0445465	−	0.122390i
$714$	1.62973	+	2.81110i	0.0609912	+	0.105203i
$715$	−4.61308	−	2.66336i	−0.172519	−	0.0996041i
$716$	2.30591	+	1.11917i	0.0861758	+	0.0418253i
$717$	0.580869	+	10.9096i	0.0216930	+	0.407427i
$718$	0.897123	−	17.4398i	0.0334803	−	0.650847i
$719$	1.68778	+	9.57186i	0.0629434	+	0.356970i	0.999970	+	0.00771257i	$0.00245501\pi$
$719$	1.68778	+	9.57186i	0.0629434	+	0.356970i	−0.937027	+	0.349257i	$0.886434\pi$
$720$	−32.6692	−	23.4610i	−1.21751	−	0.874339i
$721$	−3.33857			−0.124335
$722$	11.0082	−	24.5116i	0.409681	−	0.912229i
$723$	10.6095	−	14.1037i	0.394571	−	0.524523i
$724$	−0.364742	+	0.504065i	−0.0135555	+	0.0187334i
$725$	46.3737	−	8.17693i	1.72228	−	0.303684i
$726$	20.3193	+	16.9878i	0.754120	+	0.630475i
$727$	2.20017	+	2.62206i	0.0815997	+	0.0972467i	0.805300	−	0.592868i	$-0.202004\pi$
$727$	2.20017	+	2.62206i	0.0815997	+	0.0972467i	−0.723700	+	0.690115i	$0.757560\pi$
$728$	2.50555	−	0.494553i	0.0928617	−	0.0183293i
$729$	−25.6365	+	8.47180i	−0.949499	+	0.313770i
$730$	−46.4347	−	19.6575i	−1.71862	−	0.727559i
$731$	−59.3831	+	21.6137i	−2.19636	+	0.799411i
$732$	−29.2666	−	18.8913i	−1.08173	−	0.698241i
$733$	15.1022	+	26.1578i	0.557813	+	0.966160i	0.997679	+	0.0680967i	$0.0216926\pi$
$733$	15.1022	+	26.1578i	0.557813	+	0.966160i	−0.439866	+	0.898063i	$0.644974\pi$
$734$	0.244165	+	1.97284i	0.00901231	+	0.0728190i
$735$	29.4404	−	27.4995i	1.08593	−	1.01434i
$736$	14.0039	+	13.8696i	0.516192	+	0.511240i
$737$	−2.97766	+	3.54864i	−0.109684	+	0.130716i
$738$	−7.48134	+	14.7790i	−0.275392	+	0.544021i
$739$	3.59602	−	9.87998i	0.132282	−	0.363441i	−0.855814	−	0.517284i	$-0.826943\pi$
$739$	3.59602	−	9.87998i	0.132282	−	0.363441i	0.988095	+	0.153843i	$0.0491651\pi$
$740$	−15.4772	−	4.40574i	−0.568953	−	0.161958i
$741$	−23.3873	+	14.8579i	−0.859155	+	0.545820i
$742$	−0.276453	−	0.366131i	−0.0101489	−	0.0134411i
$743$	−29.6634	−	10.7966i	−1.08824	−	0.396089i	−0.265274	−	0.964173i	$-0.585462\pi$
$743$	−29.6634	−	10.7966i	−1.08824	−	0.396089i	−0.822970	+	0.568084i	$0.807685\pi$
$744$	0.493018	−	4.86504i	0.0180749	−	0.178361i
$745$	38.4272	+	32.2443i	1.40787	+	1.18134i
$746$	13.0366	+	2.99651i	0.477305	+	0.109710i
$747$	−44.6067	+	4.76356i	−1.63207	+	0.174289i
$748$	−3.35283	+	3.25031i	−0.122592	+	0.118843i
$749$	0.0291987	−	0.0168579i	0.00106690	−	0.000615973i
$750$	3.48214	+	9.51386i	0.127150	+	0.347397i
$751$	−15.6700	−	43.0529i	−0.571805	−	1.57102i	−0.801650	−	0.597794i	$-0.796044\pi$
$751$	−15.6700	−	43.0529i	−0.571805	−	1.57102i	0.229844	−	0.973227i	$-0.426178\pi$
$752$	−0.900556	+	28.9935i	−0.0328399	+	1.05728i
$753$	−10.7209	−	25.1985i	−0.390692	−	0.918283i
$754$	−17.8321	−	34.9142i	−0.649406	−	1.27150i
$755$	0.123532	−	0.103655i	0.00449578	−	0.00377241i
$756$	−0.586191	−	2.48873i	−0.0213196	−	0.0905143i
$757$	3.12014	+	17.6952i	0.113403	+	0.643143i	0.987528	+	0.157442i	$0.0503246\pi$
$757$	3.12014	+	17.6952i	0.113403	+	0.643143i	−0.874125	+	0.485701i	$0.838564\pi$
$758$	−7.23135	+	2.21847i	−0.262655	+	0.0805785i
$759$	1.57100	−	2.08841i	0.0570238	−	0.0758046i
$760$	−13.7628	+	38.9635i	−0.499227	+	1.41335i
$761$		−	48.0784i		−	1.74284i	−0.490537	−	0.871420i	$-0.663199\pi$
$761$		−	48.0784i		−	1.74284i	0.490537	−	0.871420i	$-0.336801\pi$
$762$	0.465000	−	1.28476i	0.0168452	−	0.0465419i
$763$	−2.75478	+	0.485741i	−0.0997296	+	0.0175850i
$764$	−3.63956	+	2.46514i	−0.131675	+	0.0891856i
$765$	44.9967	+	30.2416i	1.62686	+	1.09339i
$766$	11.6595	−	5.95497i	0.421274	−	0.215162i
$767$	13.5338	−	23.4413i	0.488679	−	0.846417i
$768$	9.24599	+	26.1249i	0.333636	+	0.942702i
$769$	−12.2601	+	4.46231i	−0.442110	+	0.160915i	−0.553477	−	0.832864i	$-0.686699\pi$
$769$	−12.2601	+	4.46231i	−0.442110	+	0.160915i	0.111367	+	0.993779i	$0.464477\pi$
$770$	−0.423803	−	0.274640i	−0.0152728	−	0.00989734i
$771$	4.75410	−	38.9877i	0.171215	−	1.40411i
$772$	5.58292	+	5.75902i	0.200934	+	0.207272i
$773$	50.8301	+	8.96272i	1.82823	+	0.322366i	0.978719	−	0.205203i	$-0.0657856\pi$
$773$	50.8301	+	8.96272i	1.82823	+	0.322366i	0.849512	+	0.527570i	$0.176897\pi$
$774$	49.6507	−	2.73311i	1.78466	−	0.0982395i
$775$	−3.99976	+	4.76672i	−0.143675	+	0.171226i
$776$	−17.7003	−	29.2663i	−0.635405	−	1.05060i
$777$	−0.557869	−	0.857477i	−0.0200134	−	0.0307618i
$778$	0.370795	−	0.279975i	0.0132936	−	0.0100376i
$779$	16.7271	+	3.13644i	0.599310	+	0.112375i
$780$	33.9598	−	25.7379i	1.21596	−	0.921566i
$781$	−2.87968	−	1.04812i	−0.103043	−	0.0375046i
$782$	−19.4478	−	18.1003i	−0.695451	−	0.647266i
$783$	−34.2808	+	19.1144i	−1.22510	+	0.683093i
$784$	−27.4726	+	3.96911i	−0.981166	+	0.141754i
$785$	−77.0887	−	13.5928i	−2.75141	−	0.485148i
$786$	−14.5278	+	25.2677i	−0.518190	+	0.901270i
$787$	33.7237	−	19.4704i	1.20212	−	0.694044i	0.241093	−	0.970502i	$-0.422494\pi$
$787$	33.7237	−	19.4704i	1.20212	−	0.694044i	0.961026	+	0.276459i	$0.0891608\pi$
$788$	6.35255	−	0.456523i	0.226300	−	0.0162630i
$789$	7.74234	−	25.3998i	0.275634	−	0.904255i
$790$	1.77419	−	4.19096i	0.0631229	−	0.149108i
$791$	−1.30936	+	2.26788i	−0.0465556	+	0.0806367i
$792$	3.26633	−	1.68308i	0.116064	−	0.0598057i
$793$	28.2705	−	23.7218i	1.00392	−	0.842385i
$794$	1.26359	−	24.5638i	0.0448432	−	0.871736i
$795$	−6.82323	−	3.46945i	−0.241995	−	0.123049i
$796$	22.5252	+	16.2993i	0.798384	+	0.577712i
$797$			38.6893i			1.37045i	0.728333	+	0.685223i	$0.240295\pi$
$797$			38.6893i			1.37045i	−0.728333	+	0.685223i	$0.759705\pi$
$798$	−2.28672	+	1.29287i	−0.0809490	+	0.0457670i
$799$		−	39.1003i		−	1.38327i
$800$	8.96291	−	34.1068i	0.316887	−	1.20586i
$801$	10.9116	+	22.2778i	0.385544	+	0.787149i
$802$	9.15995	+	0.471199i	0.323449	+	0.0166386i
$803$	3.52889	−	2.96109i	0.124532	−	0.104495i
$804$	−16.9147	−	32.9715i	−0.596535	−	1.16282i
$805$	1.43660	−	2.48826i	0.0506334	−	0.0876996i
$806$	4.77072	+	2.01962i	0.168041	+	0.0711382i
$807$	1.67719	+	0.511239i	0.0590398	+	0.0179965i
$808$	11.4133	+	13.0530i	0.401517	+	0.459204i
$809$	−11.6149	+	6.70589i	−0.408359	+	0.235766i	−0.690085	−	0.723729i	$-0.742427\pi$
$809$	−11.6149	+	6.70589i	−0.408359	+	0.235766i	0.281725	+	0.959495i	$0.409093\pi$
$810$	−26.9893	−	33.0376i	−0.948307	−	1.16082i
$811$	−4.73261	−	0.834487i	−0.166184	−	0.0293028i	0.0899367	−	0.995947i	$-0.471334\pi$
$811$	−4.73261	−	0.834487i	−0.166184	−	0.0293028i	−0.256121	+	0.966645i	$0.582445\pi$
$812$	−1.51832	−	3.39259i	−0.0532826	−	0.119057i
$813$	−4.48422	−	19.3497i	−0.157268	−	0.678623i
$814$	1.00159	−	1.07615i	0.0351058	−	0.0377192i
$815$	−21.5128	−	7.83001i	−0.753560	−	0.274273i
$816$	−13.5503	−	34.8109i	−0.474356	−	1.21863i
$817$	−16.9528	−	48.1938i	−0.593103	−	1.68609i
$818$	−9.29677	−	12.3125i	−0.325054	−	0.430497i
$819$	2.70252	+	0.184451i	0.0944337	+	0.00644524i
$820$	−26.0343	−	2.68557i	−0.909156	−	0.0937843i
$821$	−3.30537	+	3.93919i	−0.115358	+	0.137479i	−0.820633	−	0.571455i	$-0.806379\pi$
$821$	−3.30537	+	3.93919i	−0.115358	+	0.137479i	0.705275	+	0.708934i	$0.250824\pi$
$822$	−18.4602	−	21.9199i	−0.643874	−	0.764544i
$823$	1.86962	+	0.329664i	0.0651709	+	0.0114914i	0.206139	−	0.978523i	$-0.433910\pi$
$823$	1.86962	+	0.329664i	0.0651709	+	0.0114914i	−0.140968	+	0.990014i	$0.545021\pi$
$824$	37.9256	+	5.89444i	1.32120	+	0.205343i
$825$	−4.64141	−	0.565966i	−0.161593	−	0.0197044i
$826$	1.39558	−	2.15355i	0.0485585	−	0.0749315i
$827$	−26.6007	+	9.68188i	−0.924998	+	0.336672i	−0.760225	−	0.649660i	$-0.774911\pi$
$827$	−26.6007	+	9.68188i	−0.924998	+	0.336672i	−0.164773	+	0.986331i	$0.552689\pi$
$828$	10.5177	+	18.0669i	0.365516	+	0.627868i
$829$	−3.42947	+	5.94002i	−0.119110	+	0.206305i	−0.919415	−	0.393288i	$-0.871338\pi$
$829$	−3.42947	+	5.94002i	−0.119110	+	0.206305i	0.800305	+	0.599593i	$0.204671\pi$
$830$	−32.2397	−	63.1234i	−1.11905	−	2.19104i
$831$	−0.732705	−	13.7613i	−0.0254173	−	0.477376i
$832$	−29.3357	+	1.19434i	−1.01703	+	0.0414063i
$833$	36.8475	−	6.49721i	1.27669	−	0.225115i
$834$	15.4375	−	42.6527i	0.534558	−	1.47694i
$835$			63.3989i			2.19401i
$836$	−2.59819	−	2.73883i	−0.0898601	−	0.0947245i
$837$	1.84659	−	4.84673i	0.0638275	−	0.167527i
$838$	−10.4095	−	33.9309i	−0.359590	−	1.17212i
$839$	3.67625	+	20.8490i	0.126918	+	0.719789i	0.980150	+	0.198257i	$0.0635281\pi$
$839$	3.67625	+	20.8490i	0.126918	+	0.719789i	−0.853232	+	0.521532i	$0.825361\pi$
$840$	3.34074	−	2.27151i	0.115266	−	0.0783745i
$841$	−21.4928	+	18.0346i	−0.741130	+	0.621882i
$842$	−29.5344	+	15.0844i	−1.01782	+	0.519843i
$843$	−9.95860	+	4.23698i	−0.342992	+	0.145929i
$844$	−9.01841	−	35.8761i	−0.310426	−	1.23490i
$845$	0.537503	+	1.47678i	0.0184907	+	0.0508027i
$846$	−8.91797	+	29.4463i	−0.306606	+	1.01238i
$847$	−2.30381	+	1.33011i	−0.0791599	+	0.0457030i
$848$	2.49403	+	4.64727i	0.0856453	+	0.159588i
$849$	9.07438	−	8.47615i	0.311432	−	0.290901i
$850$	−10.6484	+	46.3268i	−0.365236	+	1.58900i
$851$	6.40731	+	5.37637i	0.219640	+	0.184300i
$852$	16.6692	−	17.9748i	0.571078	−	0.615807i
$853$	−30.3591	−	11.0498i	−1.03948	−	0.378339i	−0.234795	−	0.972045i	$-0.575442\pi$
$853$	−30.3591	−	11.0498i	−1.03948	−	0.378339i	−0.804682	+	0.593706i	$0.797664\pi$
$854$	2.79224	−	2.10833i	0.0955485	−	0.0721455i
$855$	−24.8407	+	36.1103i	−0.849533	+	1.23495i
$856$	−0.361455	+	0.139950i	−0.0123543	+	0.00478340i
$857$	−1.87109	+	5.14079i	−0.0639154	+	0.175606i	−0.967539	−	0.252721i	$-0.918675\pi$
$857$	−1.87109	+	5.14079i	−0.0639154	+	0.175606i	0.903624	+	0.428327i	$0.140897\pi$
$858$	0.682879	+	3.83250i	0.0233131	+	0.130839i
$859$	26.8813	−	32.0359i	0.917178	−	1.09305i	−0.0781920	−	0.996938i	$-0.524915\pi$
$859$	26.8813	−	32.0359i	0.917178	−	1.09305i	0.995370	−	0.0961124i	$-0.0306408\pi$
$860$	32.0946	+	71.7133i	1.09442	+	2.44540i
$861$	−1.13572	−	1.21587i	−0.0387051	−	0.0414368i
$862$	37.1712	−	4.60042i	1.26606	−	0.156691i
$863$	−22.9533	−	39.7562i	−0.781338	−	1.35332i	−0.931162	−	0.364605i	$-0.881204\pi$
$863$	−22.9533	−	39.7562i	−0.781338	−	1.35332i	0.149824	−	0.988713i	$-0.452129\pi$
$864$	2.26502	+	29.3065i	0.0770576	+	0.997027i
$865$	−18.8895	+	6.87521i	−0.642262	+	0.233764i
$866$	−2.28536	+	5.39843i	−0.0776596	+	0.183446i
$867$	8.18533	+	19.2388i	0.277988	+	0.653385i
$868$	0.441863	+	0.214458i	0.0149978	+	0.00727917i
$869$	0.267253	+	0.318500i	0.00906595	+	0.0108044i
$870$	−47.5778	−	39.7770i	−1.61304	−	1.34857i
$871$	38.6632	−	6.81737i	1.31005	−	0.230998i
$872$	32.1513	−	0.654217i	1.08878	−	0.0221546i
$873$	−10.0575	−	34.8553i	−0.340395	−	1.17967i
$874$	14.8023	−	15.5630i	0.500694	−	0.526428i
$875$	−1.01759			−0.0344007
$876$	10.8714	+	35.2108i	0.367311	+	1.18966i
$877$	7.68148	+	43.5638i	0.259385	+	1.47105i	0.784560	+	0.620052i	$0.212889\pi$
$877$	7.68148	+	43.5638i	0.259385	+	1.47105i	−0.525175	+	0.850994i	$0.676000\pi$
$878$	−57.4969	−	2.95771i	−1.94043	−	0.0998178i
$879$	−7.20178	+	0.383450i	−0.242910	+	0.0129334i
$880$	4.32942	+	3.86811i	0.145945	+	0.130394i
$881$	7.35957	+	4.24905i	0.247950	+	0.143154i	0.618825	−	0.785529i	$-0.287609\pi$
$881$	7.35957	+	4.24905i	0.247950	+	0.143154i	−0.370875	+	0.928683i	$0.620942\pi$
$882$	−29.2316	−	3.51113i	−0.984278	−	0.118226i
$883$	−7.80047	−	21.4316i	−0.262507	−	0.721231i	−0.998997	−	0.0447830i	$-0.985740\pi$
$883$	−7.80047	−	21.4316i	−0.262507	−	0.721231i	0.736490	−	0.676448i	$-0.236482\pi$
$884$	39.4737	−	2.83676i	1.32764	−	0.0954104i
$885$	5.18261	−	42.5019i	0.174212	−	1.42869i
$886$	−32.3029	+	3.99791i	−1.08524	+	0.134312i
$887$	2.32334	−	13.1763i	0.0780102	−	0.442418i	−0.920637	−	0.390420i	$-0.872330\pi$
$887$	2.32334	−	13.1763i	0.0780102	−	0.442418i	0.998647	−	0.0519983i	$-0.0165590\pi$
$888$	4.82336	+	10.7257i	0.161861	+	0.359932i
$889$	0.105129	+	0.0882135i	0.00352590	+	0.00295859i
$890$	−26.7031	+	28.6910i	−0.895089	+	0.961723i
$891$	3.80947	−	0.823013i	0.127622	−	0.0275720i
$892$	45.3770	+	12.9170i	1.51933	+	0.432493i
$893$	31.6083	+	0.342060i	1.05773	+	0.0114466i
$894$	−0.0659012	−	36.6601i	−0.00220407	−	1.22610i
$895$	−1.46914	+	4.03643i	−0.0491079	+	0.134923i
$896$	−2.78337	−	0.0297983i	−0.0929859	−	0.000995492i
$897$	−21.5761	+	5.00019i	−0.720406	+	0.166952i
$898$	2.26197	−	9.84096i	0.0754830	−	0.328397i
$899$	1.30925	−	7.42514i	0.0436660	−	0.247642i
$900$	18.5854	−	32.4598i	0.619513	−	1.08199i
$901$	−3.55466	−	6.15685i	−0.118423	−	0.205114i
$902$	1.30033	−	2.00656i	0.0432962	−	0.0668112i
$903$	−1.45629	+	4.77755i	−0.0484622	+	0.158987i
$904$	18.8782	−	23.4510i	0.627880	−	0.779968i
$905$	−0.903004	−	0.521350i	−0.0300169	−	0.0173302i
$906$	−0.116097	−	0.0202559i	−0.00385707	−	0.000672958i
$907$	18.8889	+	22.5109i	0.627196	+	0.747463i	0.982290	−	0.187368i	$-0.0599956\pi$
$907$	18.8889	+	22.5109i	0.627196	+	0.747463i	−0.355094	+	0.934831i	$0.615551\pi$
$908$	−8.69991	+	5.89260i	−0.288717	+	0.195553i
$909$	8.08959	+	16.5162i	0.268315	+	0.547807i
$910$	1.25528	+	4.09173i	0.0416122	+	0.135640i
$911$	−14.7379			−0.488289			−0.244144	−	0.969739i	$-0.578507\pi$
$911$	−14.7379			−0.488289			−0.244144	+	0.969739i	$0.578507\pi$
$912$	28.2593	−	10.6494i	0.935760	−	0.352637i
$913$	6.47543			0.214305
$914$	−3.99730	−	13.0296i	−0.132219	−	0.430982i
$915$	26.4592	−	52.0364i	0.874715	−	1.72027i
$916$	22.8002	−	15.4430i	0.753339	−	0.510250i
$917$	−1.88178	−	2.24262i	−0.0621418	−	0.0740577i
$918$	−4.27805	−	39.3895i	−0.141197	−	1.30005i
$919$	31.9449	+	18.4434i	1.05376	+	0.608391i	0.923701	−	0.383114i	$-0.125149\pi$
$919$	31.9449	+	18.4434i	1.05376	+	0.608391i	0.130064	+	0.991506i	$0.458482\pi$
$920$	−20.7126	+	25.7298i	−0.682875	+	0.848285i
$921$	44.1579	+	13.4602i	1.45505	+	0.443529i
$922$	−23.6092	+	36.4318i	−0.777526	+	1.19982i
$923$	12.9857	+	22.4920i	0.427431	+	0.740332i
$924$	0.0459898	+	0.366194i	0.00151295	+	0.0120469i
$925$	2.59867	−	14.7378i	0.0854438	−	0.484576i
$926$	−4.84829	+	21.0930i	−0.159325	+	0.693159i
$927$	37.2172	+	16.4959i	1.22237	+	0.541795i
$928$	11.2580	+	41.2198i	0.369563	+	1.35311i
$929$	4.19322	−	11.5208i	0.137575	−	0.377984i	−0.851704	−	0.524024i	$-0.824430\pi$
$929$	4.19322	−	11.5208i	0.137575	−	0.377984i	0.989279	+	0.146039i	$0.0466526\pi$
$930$	8.19486	−	0.0147313i	0.268720	−	0.000483059i
$931$	4.92993	+	29.8440i	0.161572	+	0.978097i
$932$	21.4130	+	6.09541i	0.701405	+	0.199662i
$933$	−29.5252	+	19.2089i	−0.966610	+	0.628870i
$934$	−23.0390	+	24.7541i	−0.753858	+	0.809977i
$935$	−5.99486	−	5.03028i	−0.196053	−	0.164508i
$936$	−30.3744	−	6.86678i	−0.992820	−	0.224448i
$937$	9.43561	−	53.5120i	0.308248	−	1.74816i	−0.299561	−	0.954077i	$-0.596840\pi$
$937$	9.43561	−	53.5120i	0.308248	−	1.74816i	0.607809	−	0.794084i	$-0.292049\pi$
$938$	3.69391	−	0.457170i	0.120610	−	0.0149271i
$939$	7.16211	+	0.873336i	0.233727	+	0.0285003i
$940$	−48.4873	+	3.48452i	−1.58148	+	0.113652i
$941$	−2.38139	−	6.54280i	−0.0776310	−	0.213289i	0.894806	−	0.446455i	$-0.147314\pi$
$941$	−2.38139	−	6.54280i	−0.0776310	−	0.213289i	−0.972437	+	0.233166i	$0.925092\pi$
$942$	28.6924	+	49.4911i	0.934850	+	1.61251i
$943$	11.7811	+	6.80180i	0.383644	+	0.221497i
$944$	−19.6557	+	21.9999i	−0.639740	+	0.716036i
$945$	4.04794	−	1.40515i	0.131680	−	0.0457096i
$946$	−7.16828	−	0.368745i	−0.233061	−	0.0119889i
$947$	0.781352	+	4.43127i	0.0253905	+	0.143997i	0.994868	−	0.101185i	$-0.0322634\pi$
$947$	0.781352	+	4.43127i	0.0253905	+	0.143997i	−0.969477	+	0.245182i	$0.921152\pi$
$948$	−3.17795	+	0.981201i	−0.103215	+	0.0318679i
$949$	−39.0412			−1.26733
$950$	−37.3570	−	9.01330i	−1.21202	−	0.292430i
$951$	−22.6504	−	17.0387i	−0.734491	−	0.552519i
$952$	3.75125	−	0.0763307i	0.121579	−	0.00247389i
$953$	4.58605	−	0.808644i	0.148557	−	0.0261945i	−0.0988752	−	0.995100i	$-0.531524\pi$
$953$	4.58605	−	0.808644i	0.148557	−	0.0261945i	0.247432	+	0.968905i	$0.420413\pi$
$954$	1.27275	+	5.44744i	0.0412067	+	0.176367i
$955$	−4.73528	−	5.64329i	−0.153230	−	0.182613i
$956$	11.3491	+	5.50827i	0.367056	+	0.178150i
$957$	5.21332	−	2.21805i	0.168523	−	0.0716995i
$958$	−2.51748	+	5.94673i	−0.0813360	+	0.192130i
$959$	2.70484	−	0.984482i	0.0873439	−	0.0317906i
$960$	−41.9606	+	19.9057i	−1.35427	+	0.642452i
$961$	−15.0018	−	25.9839i	−0.483930	−	0.838192i
$962$	−12.3650	+	1.53033i	−0.398664	+	0.0493399i
$963$	−0.408790	+	0.0436548i	−0.0131731	+	0.00140676i
$964$	−8.32474	−	18.6011i	−0.268122	−	0.599100i
$965$	−8.64031	+	10.2971i	−0.278141	+	0.331476i
$966$	−2.06722	+	0.368339i	−0.0665117	+	0.0118511i
$967$	−5.09363	+	13.9946i	−0.163800	+	0.450037i	−0.994254	−	0.107051i	$-0.965859\pi$
$967$	−5.09363	+	13.9946i	−0.163800	+	0.450037i	0.830453	+	0.557088i	$0.188081\pi$
$968$	28.5192	−	11.0422i	0.916643	−	0.354911i
$969$	−37.6279	+	15.5304i	−1.20878	+	0.498909i
$970$	45.7434	−	34.5393i	1.46873	−	1.10899i
$971$	52.9014	+	19.2546i	1.69769	+	0.617908i	0.995559	−	0.0941414i	$-0.0300106\pi$
$971$	52.9014	+	19.2546i	1.69769	+	0.617908i	0.702129	+	0.712049i	$0.252233\pi$
$972$	−5.76216	+	30.6398i	−0.184821	+	0.982772i
$973$	3.49017	+	2.92860i	0.111890	+	0.0938866i
$974$	0.229254	−	0.997392i	0.00734576	−	0.0319585i
$975$	27.0498	+	28.9589i	0.866287	+	0.927428i
$976$	−35.4417	+	19.0203i	−1.13446	+	0.608826i
$977$	−5.75949	+	3.32524i	−0.184262	+	0.106384i	−0.589294	−	0.807919i	$-0.700594\pi$
$977$	−5.75949	+	3.32524i	−0.184262	+	0.106384i	0.405031	+	0.914303i	$0.367261\pi$
$978$	5.75056	+	15.7116i	0.183882	+	0.502401i
$979$	−1.22469	−	3.36480i	−0.0391411	−	0.107539i
$980$	−11.3408	−	45.1147i	−0.362268	−	1.44114i
$981$	33.1092	+	8.19645i	1.05710	+	0.261693i
$982$	17.5238	−	8.95010i	0.559207	−	0.285609i
$983$	−2.20426	+	1.84960i	−0.0703051	+	0.0589930i	−0.677263	−	0.735741i	$-0.736834\pi$
$983$	−2.20426	+	1.84960i	−0.0703051	+	0.0589930i	0.606958	+	0.794734i	$0.292390\pi$
$984$	10.7548	+	15.8172i	0.342851	+	0.504235i
$985$	1.85342	+	10.5113i	0.0590549	+	0.334917i
$986$	−16.8928	−	55.0640i	−0.537976	−	1.75359i
$987$	−2.46958	−	1.85773i	−0.0786075	−	0.0591323i
$988$	1.94788	+	31.9349i	0.0619702	+	1.01599i
$989$		−	40.8370i		−	1.29854i
$990$	3.36740	+	5.15559i	0.107023	+	0.163855i
$991$	−36.8660	+	6.50046i	−1.17109	+	0.206494i	−0.725163	−	0.688577i	$-0.758236\pi$
$991$	−36.8660	+	6.50046i	−1.17109	+	0.206494i	−0.445923	+	0.895071i	$0.647124\pi$
$992$	−4.64085	−	3.21633i	−0.147347	−	0.102119i
$993$	18.0291	−	0.959935i	0.572135	−	0.0304626i
$994$	1.11996	+	2.19283i	0.0355231	+	0.0695522i
$995$	−23.2976	+	40.3526i	−0.738583	+	1.27926i
$996$	−20.1082	+	47.7381i	−0.637153	+	1.51264i
$997$	−29.8351	+	10.8591i	−0.944887	+	0.343911i	−0.768094	−	0.640337i	$-0.778795\pi$
$997$	−29.8351	+	10.8591i	−0.944887	+	0.343911i	−0.176793	+	0.984248i	$0.556572\pi$
$998$	27.2697	−	42.0804i	0.863206	−	1.33203i
$999$	1.98213	+	12.3152i	0.0627118	+	0.389637i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.v.a.23.14	yes	216
3.2	odd	2	inner	228.2.v.a.23.23	yes	216
4.3	odd	2	inner	228.2.v.a.23.31	yes	216
12.11	even	2	inner	228.2.v.a.23.6	✓	216
19.5	even	9	inner	228.2.v.a.119.6	yes	216
57.5	odd	18	inner	228.2.v.a.119.31	yes	216
76.43	odd	18	inner	228.2.v.a.119.23	yes	216
228.119	even	18	inner	228.2.v.a.119.14	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.v.a.23.6	✓	216	12.11	even	2	inner
228.2.v.a.23.14	yes	216	1.1	even	1	trivial
228.2.v.a.23.23	yes	216	3.2	odd	2	inner
228.2.v.a.23.31	yes	216	4.3	odd	2	inner
228.2.v.a.119.6	yes	216	19.5	even	9	inner
228.2.v.a.119.14	yes	216	228.119	even	18	inner
228.2.v.a.119.23	yes	216	76.43	odd	18	inner
228.2.v.a.119.31	yes	216	57.5	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.414780 - 1.35202i) q^{2} +(-1.54392 - 0.785048i) q^{3} +(-1.65592 + 1.12158i) q^{4} +(-2.15444 - 2.56756i) q^{5} +(-0.421012 + 2.41304i) q^{6} +(-0.213070 - 0.123016i) q^{7} +(2.20324 + 1.77362i) q^{8} +(1.76740 + 2.42411i) q^{9} +O(q^{10})\)	\(q+(-0.414780 - 1.35202i) q^{2} +(-1.54392 - 0.785048i) q^{3} +(-1.65592 + 1.12158i) q^{4} +(-2.15444 - 2.56756i) q^{5} +(-0.421012 + 2.41304i) q^{6} +(-0.213070 - 0.123016i) q^{7} +(2.20324 + 1.77362i) q^{8} +(1.76740 + 2.42411i) q^{9} +(-2.57778 + 3.97782i) q^{10} +(-0.216520 - 0.375023i) q^{11} +(3.43710 - 0.431661i) q^{12} +(-0.637288 + 3.61424i) q^{13} +(-0.0779429 + 0.339099i) q^{14} +(1.31063 + 5.65546i) q^{15} +(1.48411 - 3.71449i) q^{16} +(-1.84409 + 5.06660i) q^{17} +(2.54436 - 3.39503i) q^{18} +(-4.07965 - 1.53507i) q^{19} +(6.44730 + 1.83529i) q^{20} +(0.232390 + 0.357197i) q^{21} +(-0.417231 + 0.448291i) q^{22} +(-2.66908 - 2.23962i) q^{23} +(-2.00925 - 4.46799i) q^{24} +(-1.08252 + 6.13929i) q^{25} +(5.15086 - 0.637487i) q^{26} +(-0.825690 - 5.13013i) q^{27} +(0.490798 - 0.0352709i) q^{28} +(-2.58348 - 7.09806i) q^{29} +(7.10267 - 4.11777i) q^{30} +(0.864431 + 0.499079i) q^{31} +(-5.63764 - 0.465860i) q^{32} +(0.0398788 + 0.748985i) q^{33} +(7.61503 + 0.391726i) q^{34} +(0.143195 + 0.812100i) q^{35} +(-5.64550 - 2.03184i) q^{36} -2.40057 q^{37} +(-0.383286 + 6.15249i) q^{38} +(3.82128 - 5.07981i) q^{39} +(-0.192861 - 9.47812i) q^{40} +(-3.84502 + 0.677980i) q^{41} +(0.386547 - 0.462354i) q^{42} +(7.53380 + 8.97843i) q^{43} +(0.779157 + 0.378163i) q^{44} +(2.41629 - 9.76051i) q^{45} +(-1.92093 + 4.53759i) q^{46} +(-6.81452 + 2.48028i) q^{47} +(-5.20741 + 4.56978i) q^{48} +(-3.46973 - 6.00976i) q^{49} +(8.74945 - 1.08286i) q^{50} +(6.82465 - 6.37474i) q^{51} +(-2.99837 - 6.69965i) q^{52} +(-0.847549 + 1.01007i) q^{53} +(-6.59356 + 3.24422i) q^{54} +(-0.496417 + 1.36389i) q^{55} +(-0.251260 - 0.648938i) q^{56} +(5.09357 + 5.57275i) q^{57} +(-8.52514 + 6.43705i) q^{58} +(-6.93061 - 2.52253i) q^{59} +(-8.51335 - 7.89499i) q^{60} +(-7.70314 - 6.46370i) q^{61} +(0.316217 - 1.37574i) q^{62} +(-0.0783757 - 0.733922i) q^{63} +(1.70853 + 7.81543i) q^{64} +(10.6528 - 6.15039i) q^{65} +(0.996102 - 0.364581i) q^{66} +(-3.65875 - 10.0523i) q^{67} +(-2.62894 - 10.4582i) q^{68} +(2.36264 + 5.55315i) q^{69} +(1.03858 - 0.530445i) q^{70} +(5.42107 - 4.54882i) q^{71} +(-0.405447 + 8.47559i) q^{72} +(1.84726 + 10.4763i) q^{73} +(0.995708 + 3.24562i) q^{74} +(6.49096 - 8.62876i) q^{75} +(8.47726 - 2.03372i) q^{76} +0.106541i q^{77} +(-8.45299 - 3.05944i) q^{78} +(-0.945539 + 0.166724i) q^{79} +(-12.7346 + 4.19208i) q^{80} +(-2.75260 + 8.56874i) q^{81} +(2.51148 + 4.91733i) q^{82} +(-7.47672 + 12.9501i) q^{83} +(-0.785443 - 0.330844i) q^{84} +(16.9818 - 6.18087i) q^{85} +(9.01415 - 13.9099i) q^{86} +(-1.58362 + 12.9870i) q^{87} +(0.188105 - 1.21029i) q^{88} +(8.14323 + 1.43587i) q^{89} +(-14.1986 + 0.781587i) q^{90} +(0.580396 - 0.691689i) q^{91} +(6.93168 + 0.715040i) q^{92} +(-0.942814 - 1.44916i) q^{93} +(6.17992 + 8.18460i) q^{94} +(4.84799 + 13.7820i) q^{95} +(8.33836 + 5.14507i) q^{96} +(-11.3632 - 4.13586i) q^{97} +(-6.68614 + 7.18387i) q^{98} +(0.526420 - 1.18768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9}+O(q^{10}) \) 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9	\( 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 36 q^{13} - 6 q^{16} - 12 q^{18} - 30 q^{21} - 18 q^{24} - 24 q^{25} - 36 q^{28} + 12 q^{33} + 30 q^{34} - 66 q^{36} - 48 q^{37} - 42 q^{40} - 117 q^{42} - 6 q^{45} - 6 q^{46} - 81 q^{48} + 24 q^{49} + 12 q^{52} + 33 q^{54} - 12 q^{57} + 48 q^{58} - 18 q^{60} - 48 q^{61} + 36 q^{64} - 18 q^{66} - 6 q^{69} - 18 q^{70} + 12 q^{72} - 132 q^{73} + 60 q^{76} - 39 q^{78} + 18 q^{81} + 132 q^{82} - 45 q^{84} - 144 q^{85} + 114 q^{88} + 72 q^{90} - 30 q^{93} + 138 q^{96} - 60 q^{97}+O(q^{100}) \) 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9 - 18 * q^10 - 3 * q^12 - 36 * q^13 - 6 * q^16 - 12 * q^18 - 30 * q^21 - 18 * q^24 - 24 * q^25 - 36 * q^28 + 12 * q^33 + 30 * q^34 - 66 * q^36 - 48 * q^37 - 42 * q^40 - 117 * q^42 - 6 * q^45 - 6 * q^46 - 81 * q^48 + 24 * q^49 + 12 * q^52 + 33 * q^54 - 12 * q^57 + 48 * q^58 - 18 * q^60 - 48 * q^61 + 36 * q^64 - 18 * q^66 - 6 * q^69 - 18 * q^70 + 12 * q^72 - 132 * q^73 + 60 * q^76 - 39 * q^78 + 18 * q^81 + 132 * q^82 - 45 * q^84 - 144 * q^85 + 114 * q^88 + 72 * q^90 - 30 * q^93 + 138 * q^96 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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