LMFDB - Embedded newform 228.2.v.a.23.6

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			23.6
Character	$\chi$	$=$	228.23
Dual form			228.2.v.a.119.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18680 + 0.769092i) q^{2} +(1.18231 - 1.26576i) q^{3} +(0.816994 - 1.82552i) q^{4} +(2.15444 + 2.56756i) q^{5} +(-0.429685 + 2.41151i) q^{6} +(0.213070 + 0.123016i) q^{7} +(0.434383 + 2.79487i) q^{8} +(-0.204279 - 2.99304i) q^{9} +O(q^{10})$	\(q+(-1.18680 + 0.769092i) q^{2} +(1.18231 - 1.26576i) q^{3} +(0.816994 - 1.82552i) q^{4} +(2.15444 + 2.56756i) q^{5} +(-0.429685 + 2.41151i) q^{6} +(0.213070 + 0.123016i) q^{7} +(0.434383 + 2.79487i) q^{8} +(-0.204279 - 2.99304i) q^{9} +(-4.53159 - 1.39022i) q^{10} +(-0.216520 - 0.375023i) q^{11} +(-1.34472 - 3.19245i) q^{12} +(-0.637288 + 3.61424i) q^{13} +(-0.347482 + 0.0178749i) q^{14} +(5.79713 + 0.308661i) q^{15} +(-2.66504 - 2.98288i) 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} +(0.407623 - 0.124251i) q^{21} +(0.545393 + 0.278554i) q^{22} +(-2.66908 - 2.23962i) q^{23} +(4.05120 + 2.75459i) q^{24} +(-1.08252 + 6.13929i) q^{25} +(-2.02335 - 4.77952i) q^{26} +(-4.02998 - 3.28013i) q^{27} +(0.398644 - 0.288459i) q^{28} +(2.58348 + 7.09806i) q^{29} +(-7.11743 + 4.09221i) q^{30} +(-0.864431 - 0.499079i) q^{31} +(5.45698 + 1.49042i) q^{32} +(-0.730682 - 0.169333i) q^{33} +(1.70811 + 7.43132i) q^{34} +(0.143195 + 0.812100i) q^{35} +(-5.63074 - 2.07238i) q^{36} -2.40057 q^{37} +(-6.02235 + 1.31581i) q^{38} +(3.82128 + 5.07981i) q^{39} +(-6.24016 + 7.13669i) q^{40} +(3.84502 - 0.677980i) q^{41} +(-0.388206 + 0.460961i) q^{42} +(-7.53380 - 8.97843i) q^{43} +(-0.861507 + 0.0888691i) q^{44} +(7.24470 - 6.97282i) q^{45} +(4.89014 + 0.605219i) q^{46} +(-6.81452 + 2.48028i) q^{47} +(-6.92650 - 0.153398i) q^{48} +(-3.46973 - 6.00976i) q^{49} +(-3.43694 - 8.11867i) q^{50} +(-4.23279 - 8.32446i) q^{51} +(6.07721 + 4.11620i) q^{52} +(0.847549 - 1.01007i) q^{53} +(7.30551 + 0.793442i) q^{54} +(0.496417 - 1.36389i) q^{55} +(-0.251260 + 0.648938i) q^{56} +(6.76644 - 3.34892i) q^{57} +(-8.52514 - 6.43705i) q^{58} +(-6.93061 - 2.52253i) q^{59} +(5.29969 - 10.3306i) q^{60} +(-7.70314 - 6.46370i) q^{61} +(1.40975 - 0.0725190i) q^{62} +(0.324665 - 0.662855i) q^{63} +(-7.62262 + 2.42809i) q^{64} +(-10.6528 + 6.15039i) q^{65} +(0.997407 - 0.360997i) q^{66} +(3.65875 + 10.0523i) q^{67} +(-7.74256 - 7.50580i) q^{68} +(-5.99049 + 0.730471i) q^{69} +(-0.794524 - 0.853671i) q^{70} +(5.42107 - 4.54882i) q^{71} +(8.27642 - 1.87106i) q^{72} +(1.84726 + 10.4763i) q^{73} +(2.84900 - 1.84626i) q^{74} +(6.49096 + 8.62876i) q^{75} +(6.13535 - 6.19334i) q^{76} -0.106541i q^{77} +(-8.44194 - 3.08981i) q^{78} +(0.945539 - 0.166724i) q^{79} +(1.91705 - 13.2691i) q^{80} +(-8.91654 + 1.22283i) q^{81} +(-4.04184 + 3.76180i) q^{82} +(-7.47672 + 12.9501i) q^{83} +(0.106202 - 0.845636i) q^{84} +(16.9818 - 6.18087i) q^{85} +(15.8464 + 4.86143i) q^{86} +(12.0389 + 5.12206i) q^{87} +(0.954090 - 0.768049i) q^{88} +(-8.14323 - 1.43587i) q^{89} +(-3.23528 + 13.8472i) q^{90} +(-0.580396 + 0.691689i) q^{91} +(-6.26909 + 3.04269i) q^{92} +(-1.65374 + 0.504092i) 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} +(8.73994 + 4.46384i) q^{98} +(-1.07823 + 0.724661i) 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 $

$2$	−1.18680	+	0.769092i	−0.839195	+	0.543830i
$2$	−1.18680	+	0.769092i	−0.839195	+	0.543830i
$3$	1.18231	−	1.26576i	0.682608	−	0.730785i
$3$	1.18231	−	1.26576i	0.682608	−	0.730785i
$4$	0.816994	−	1.82552i	0.408497	−	0.912760i
$5$	2.15444	+	2.56756i	0.963495	+	1.14825i	0.988902	+	0.148572i	$0.0474676\pi$
$5$	2.15444	+	2.56756i	0.963495	+	1.14825i	−0.0254063	+	0.999677i	$0.508088\pi$
$6$	−0.429685	+	2.41151i	−0.175418	+	0.984494i
$7$	0.213070	+	0.123016i	0.0805328	+	0.0464956i	0.539726	−	0.841841i	$-0.318528\pi$
$7$	0.213070	+	0.123016i	0.0805328	+	0.0464956i	−0.459193	+	0.888337i	$0.651861\pi$
$8$	0.434383	+	2.79487i	0.153577	+	0.988137i
$9$	−0.204279	−	2.99304i	−0.0680931	−	0.997679i
$10$	−4.53159	−	1.39022i	−1.43301	−	0.439627i
$11$	−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	$0.854128\pi$
$12$	−1.34472	−	3.19245i	−0.388188	−	0.921580i
$13$	−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	$0.885594\pi$
$14$	−0.347482	+	0.0178749i	−0.0928684	+	0.00477726i
$15$	5.79713	+	0.308661i	1.49681	+	0.0796959i
$16$	−2.66504	−	2.98288i	−0.666260	−	0.745719i
$17$	1.84409	−	5.06660i	0.447258	−	1.22883i	−0.487368	−	0.873197i	$-0.662043\pi$
$17$	1.84409	−	5.06660i	0.447258	−	1.22883i	0.934626	−	0.355633i	$-0.115735\pi$
$18$	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
$21$	0.407623	−	0.124251i	0.0889506	−	0.0271139i
$22$	0.545393	+	0.278554i	0.116278	+	0.0593880i
$23$	−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	$0.840557\pi$
$24$	4.05120	+	2.75459i	0.826949	+	0.562278i
$25$	−1.08252	+	6.13929i	−0.216504	+	1.22786i
$26$	−2.02335	−	4.77952i	−0.396812	−	0.937341i
$27$	−4.02998	−	3.28013i	−0.775570	−	0.631262i
$28$	0.398644	−	0.288459i	0.0753367	−	0.0545137i
$29$	2.58348	+	7.09806i	0.479741	+	1.31808i	0.909714	+	0.415235i	$0.136301\pi$
$29$	2.58348	+	7.09806i	0.479741	+	1.31808i	−0.429974	+	0.902842i	$0.641477\pi$
$30$	−7.11743	+	4.09221i	−1.29946	+	0.747132i
$31$	−0.864431	−	0.499079i	−0.155256	−	0.0896373i	0.420359	−	0.907358i	$-0.361904\pi$
$31$	−0.864431	−	0.499079i	−0.155256	−	0.0896373i	−0.575615	+	0.817721i	$0.695237\pi$
$32$	5.45698	+	1.49042i	0.964667	+	0.263472i
$33$	−0.730682	−	0.169333i	−0.127195	−	0.0294771i
$34$	1.70811	+	7.43132i	0.292939	+	1.27446i
$35$	0.143195	+	0.812100i	0.0242044	+	0.137270i
$36$	−5.63074	−	2.07238i	−0.938457	−	0.345396i
$37$	−2.40057			−0.394651			−0.197326	−	0.980338i	$-0.563226\pi$
$37$	−2.40057			−0.394651			−0.197326	+	0.980338i	$0.563226\pi$
$38$	−6.02235	+	1.31581i	−0.976953	+	0.213452i
$39$	3.82128	+	5.07981i	0.611894	+	0.813421i
$40$	−6.24016	+	7.13669i	−0.986656	+	1.12841i
$41$	3.84502	−	0.677980i	0.600491	−	0.105883i	0.134864	−	0.990864i	$-0.456940\pi$
$41$	3.84502	−	0.677980i	0.600491	−	0.105883i	0.465626	+	0.884981i	$0.345829\pi$
$42$	−0.388206	+	0.460961i	−0.0599016	+	0.0711278i
$43$	−7.53380	−	8.97843i	−1.14889	−	1.36920i	−0.918174	−	0.396177i	$-0.870337\pi$
$43$	−7.53380	−	8.97843i	−1.14889	−	1.36920i	−0.230719	−	0.973020i	$-0.574108\pi$
$44$	−0.861507	+	0.0888691i	−0.129877	+	0.0133975i
$45$	7.24470	−	6.97282i	1.07998	−	1.03945i
$46$	4.89014	+	0.605219i	0.721011	+	0.0892347i
$47$	−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	$0.566283\pi$
$48$	−6.92650	−	0.153398i	−0.999755	−	0.0221411i
$49$	−3.46973	−	6.00976i	−0.495676	−	0.858537i
$50$	−3.43694	−	8.11867i	−0.486057	−	1.14815i
$51$	−4.23279	−	8.32446i	−0.592709	−	1.16566i
$52$	6.07721	+	4.11620i	0.842757	+	0.570814i
$53$	0.847549	−	1.01007i	0.116420	−	0.138744i	−0.704687	−	0.709518i	$-0.748913\pi$
$53$	0.847549	−	1.01007i	0.116420	−	0.138744i	0.821107	+	0.570775i	$0.193357\pi$
$54$	7.30551	+	0.793442i	0.994154	+	0.107974i
$55$	0.496417	−	1.36389i	0.0669368	−	0.183907i
$56$	−0.251260	+	0.648938i	−0.0335760	+	0.0867180i
$57$	6.76644	−	3.34892i	0.896237	−	0.443575i
$58$	−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	$0.770510\pi$
$60$	5.29969	−	10.3306i	0.684187	−	1.33367i
$61$	−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	$0.944846\pi$
$62$	1.40975	−	0.0725190i	0.179038	−	0.00920992i
$63$	0.324665	−	0.662855i	0.0409040	−	0.0835119i
$64$	−7.62262	+	2.42809i	−0.952828	+	0.303511i
$65$	−10.6528	+	6.15039i	−1.32132	+	0.762862i
$66$	0.997407	−	0.360997i	0.122772	−	0.0444357i
$67$	3.65875	+	10.0523i	0.446987	+	1.22809i	0.934811	+	0.355145i	$0.115569\pi$
$67$	3.65875	+	10.0523i	0.446987	+	1.22809i	−0.487824	+	0.872942i	$0.662209\pi$
$68$	−7.74256	−	7.50580i	−0.938923	−	0.910212i
$69$	−5.99049	+	0.730471i	−0.721171	+	0.0879384i
$70$	−0.794524	−	0.853671i	−0.0949638	−	0.102033i
$71$	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	$0.139834\pi$
$72$	8.27642	−	1.87106i	0.975386	−	0.220506i
$73$	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	$0.730546\pi$
$74$	2.84900	−	1.84626i	0.331190	−	0.214623i
$75$	6.49096	+	8.62876i	0.749512	+	0.996363i
$76$	6.13535	−	6.19334i	0.703773	−	0.710425i
$77$		−	0.106541i		−	0.0121415i
$78$	−8.44194	−	3.08981i	−0.955861	−	0.349852i
$79$	0.945539	−	0.166724i	0.106382	−	0.0187579i	−0.120204	−	0.992749i	$-0.538355\pi$
$79$	0.945539	−	0.166724i	0.106382	−	0.0187579i	0.226585	+	0.973991i	$0.427244\pi$
$80$	1.91705	−	13.2691i	0.214333	−	1.48353i
$81$	−8.91654	+	1.22283i	−0.990727	+	0.135870i
$82$	−4.04184	+	3.76180i	−0.446347	+	0.415421i
$83$	−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	$0.860264\pi$
$84$	0.106202	−	0.845636i	0.0115876	−	0.0922664i
$85$	16.9818	−	6.18087i	1.84193	−	0.670409i
$86$	15.8464	+	4.86143i	1.70876	+	0.524221i
$87$	12.0389	+	5.12206i	1.29071	+	0.549142i
$88$	0.954090	−	0.768049i	0.101706	−	0.0818743i
$89$	−8.14323	−	1.43587i	−0.863181	−	0.152202i	−0.275506	−	0.961299i	$-0.588845\pi$
$89$	−8.14323	−	1.43587i	−0.863181	−	0.152202i	−0.587675	+	0.809097i	$0.699957\pi$
$90$	−3.23528	+	13.8472i	−0.341028	+	1.45962i
$91$	−0.580396	+	0.691689i	−0.0608420	+	0.0725087i
$92$	−6.26909	+	3.04269i	−0.653598	+	0.317223i
$93$	−1.65374	+	0.504092i	−0.171485	+	0.0522719i
$94$	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	$0.821512\pi$
$98$	8.73994	+	4.46384i	0.882867	+	0.450916i
$99$	−1.07823	+	0.724661i	−0.108366	+	0.0728312i
$100$	10.3230	+	6.99193i	1.03230	+	0.699193i
$101$	−6.03717	−	1.06452i	−0.600720	−	0.105923i	−0.134986	−	0.990848i	$-0.543099\pi$
$101$	−6.03717	−	1.06452i	−0.600720	−	0.105923i	−0.465735	+	0.884924i	$0.654210\pi$
$102$	11.4258	+	6.62408i	1.13132	+	0.655882i
$103$	−11.7517	+	6.78485i	−1.15793	+	0.668531i	−0.950807	−	0.309784i	$-0.899743\pi$
$103$	−11.7517	+	6.78485i	−1.15793	+	0.668531i	−0.207123	+	0.978315i	$0.566410\pi$
$104$	−10.3782	−	0.211175i	−1.01766	−	0.0207075i
$105$	1.19722	+	0.778905i	0.116837	+	0.0760133i
$106$	−0.229036	+	1.85060i	−0.0222459	+	0.179746i
$107$	−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	$0.168775\pi$
$108$	−9.28042	+	4.67695i	−0.893008	+	0.450040i
$109$	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	$0.0944959\pi$
$110$	0.459812	+	2.00046i	0.0438413	+	0.190736i
$111$	−2.83822	+	3.03854i	−0.269392	+	0.288405i
$112$	−0.200898	−	0.963403i	−0.0189831	−	0.0910330i
$113$			10.6439i			1.00129i	0.865652	+	0.500645i	$0.166904\pi$
$113$			10.6439i			1.00129i	−0.865652	+	0.500645i	$0.833096\pi$
$114$	−5.45479	+	9.17852i	−0.510888	+	0.859647i
$115$		−	11.6781i		−	1.08899i
$116$	15.0683	+	1.08288i	1.39906	+	0.100543i
$117$	10.9477	+	1.16911i	1.01212	+	0.108084i
$118$	10.1653	−	2.33653i	0.935793	−	0.215095i
$119$	1.01619	−	0.852686i	0.0931541	−	0.0781656i
$120$	1.65550	+	16.3363i	0.151126	+	1.49129i
$121$	5.40624	−	9.36388i	0.491476	−	0.851262i
$122$	14.1133	+	1.74671i	1.27776	+	0.158139i
$123$	3.68785	−	5.66844i	0.332522	−	0.511106i
$124$	−1.61731	+	1.17029i	−0.145239	+	0.105095i
$125$	−3.58188	+	2.06800i	−0.320373	+	0.184967i
$126$	0.124484	+	1.03637i	0.0110899	+	0.0923276i
$127$	0.549323	+	0.0968605i	0.0487446	+	0.00859498i	0.197967	−	0.980209i	$-0.436566\pi$
$127$	0.549323	+	0.0968605i	0.0487446	+	0.00859498i	−0.149223	+	0.988804i	$0.547677\pi$
$128$	7.17911	−	8.74416i	0.634550	−	0.772882i
$129$	−20.2718	−	1.07935i	−1.78483	−	0.0950312i
$130$	7.91253	−	15.4923i	0.693975	−	1.35876i
$131$	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
$135$	−0.260401	−	17.4141i	−0.0224117	−	1.49877i
$136$	14.9615	+	2.95316i	1.28294	+	0.253231i
$137$	7.52026	−	8.96229i	0.642499	−	0.765700i	−0.342264	−	0.939604i	$-0.611194\pi$
$137$	7.52026	−	8.96229i	0.642499	−	0.765700i	0.984763	+	0.173904i	$0.0556381\pi$
$138$	6.54772	−	5.47417i	0.557379	−	0.465992i
$139$	18.2370	+	3.21567i	1.54684	+	0.272750i	0.880917	−	0.473270i	$-0.156926\pi$
$139$	18.2370	+	3.21567i	1.54684	+	0.272750i	0.665924	+	0.746020i	$0.268038\pi$
$140$	1.59949	+	0.402076i	0.135182	+	0.0339816i
$141$	−4.91745	+	11.5580i	−0.414124	+	0.973359i
$142$	−2.93527	+	9.56785i	−0.246323	+	0.802916i
$143$	1.49341	−	0.543557i	0.124885	−	0.0454545i
$144$	−8.38345	+	8.58591i	−0.698621	+	0.715492i
$145$	−12.6588	+	21.9256i	−1.05125	+	1.82082i
$146$	−10.2496	−	11.0126i	−0.848261	−	0.911408i
$147$	−11.7092	−	2.71356i	−0.965758	−	0.223811i
$148$	−1.96125	+	4.38229i	−0.161214	+	0.360222i
$149$	14.7391	−	2.59889i	1.20747	−	0.212910i	0.466545	−	0.884497i	$-0.345498\pi$
$149$	14.7391	−	2.59889i	1.20747	−	0.212910i	0.740925	+	0.671588i	$0.234387\pi$
$150$	−14.3398	−	5.24847i	−1.17084	−	0.428536i
$151$		−	0.0481124i		−	0.00391533i	−0.999998	−	0.00195767i	$-0.999377\pi$
$151$		−	0.0481124i		−	0.00391533i	0.999998	−	0.00195767i	$-0.000623145\pi$
$152$	−2.51819	+	12.0689i	−0.204252	+	0.978918i
$153$	−15.5412	−	4.48443i	−1.25643	−	0.362545i
$154$	0.0819402	+	0.126443i	0.00660293	+	0.0101891i
$155$	−0.580947	−	3.29472i	−0.0466628	−	0.264638i
$156$	12.3953	−	2.82564i	0.992415	−	0.226232i
$157$	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	$-0.104115\pi$
$158$	−0.993941	+	0.925075i	−0.0790737	+	0.0735951i
$159$	−0.276435	−	2.26701i	−0.0219227	−	0.179785i
$160$	7.92999	+	17.2222i	0.626921	+	1.36153i
$161$	−0.293190	−	0.805534i	−0.0231066	−	0.0634849i
$162$	9.64169	−	8.30890i	0.757523	−	0.652809i
$163$	−5.91526	+	3.41518i	−0.463319	+	0.267497i	−0.713439	−	0.700717i	$-0.752863\pi$
$163$	−5.91526	+	3.41518i	−0.463319	+	0.267497i	0.250120	+	0.968215i	$0.419530\pi$
$164$	1.90369	−	7.57306i	0.148653	−	0.591356i
$165$	−1.13944	−	2.24089i	−0.0887051	−	0.174453i
$166$	−1.08641	−	21.1194i	−0.0843216	−	1.63919i
$167$	−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	$0.983569\pi$
$168$	0.524331	+	1.08528i	0.0404530	+	0.0837312i
$169$	−0.440604	−	0.160367i	−0.0338926	−	0.0123359i
$170$	−15.4004	+	20.3960i	−1.18115	+	1.56430i
$171$	3.76113	−	12.5241i	0.287620	−	0.957744i
$172$	−22.5454	+	6.41776i	−1.71907	+	0.489350i
$173$	−2.05125	+	5.63577i	−0.155954	+	0.428480i	−0.992921	−	0.118773i	$-0.962104\pi$
$173$	−2.05125	+	5.63577i	−0.155954	+	0.428480i	0.836968	+	0.547252i	$0.184326\pi$
$174$	−18.2271	+	3.18016i	−1.38179	+	0.241087i
$175$	−0.985882	+	1.17493i	−0.0745257	+	0.0888162i
$176$	−0.541614	+	1.64530i	−0.0408257	+	0.124019i
$177$	−11.3871	+	5.79004i	−0.855903	+	0.435206i
$178$	10.7687	−	4.55880i	0.807149	−	0.341697i
$179$	−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	$0.848585\pi$
$180$	−6.81014	−	18.9221i	−0.507598	−	1.41037i
$181$	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	$0.385209\pi$
$182$	0.156842	−	1.26727i	0.0116259	−	0.0939367i
$183$	−17.2890	+	2.10819i	−1.27804	+	0.155842i
$184$	5.10005	−	8.43258i	0.375981	−	0.621658i
$185$	−5.17189	−	6.16362i	−0.380245	−	0.453158i
$186$	1.57497	−	1.87013i	0.115482	−	0.137125i
$187$	−2.29937	+	0.405442i	−0.168147	+	0.0296488i
$188$	−1.03962	+	14.4664i	−0.0758222	+	1.05507i
$189$	−0.455158	−	1.19465i	−0.0331078	−	0.0868979i
$190$	−16.3532	−	12.6279i	−1.18639	−	0.916126i
$191$	2.19792			0.159036			0.0795178	−	0.996833i	$-0.474662\pi$
$191$	2.19792			0.159036			0.0795178	+	0.996833i	$0.474662\pi$
$192$	−5.93895	+	12.5191i	−0.428606	+	0.903491i
$193$	−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	$0.990550\pi$
$194$	16.6667	−	3.83089i	1.19660	−	0.275042i
$195$	−4.81002	+	20.7555i	−0.344453	+	1.48633i
$196$	−13.8057	+	1.42413i	−0.986120	+	0.101724i
$197$	2.75783	+	1.59223i	0.196487	+	0.113442i	0.595016	−	0.803714i	$-0.297146\pi$
$197$	2.75783	+	1.59223i	0.196487	+	0.113442i	−0.398529	+	0.917156i	$0.630479\pi$
$198$	0.722311	−	1.68929i	0.0513324	−	0.120052i
$199$	4.75473	+	13.0635i	0.337054	+	0.926047i	0.986226	+	0.165406i	$0.0528933\pi$
$199$	4.75473	+	13.0635i	0.337054	+	0.926047i	−0.649172	+	0.760642i	$0.724884\pi$
$200$	−17.6288	−	0.358711i	−1.24654	−	0.0253647i
$201$	17.0496	+	7.25390i	1.20258	+	0.511650i
$202$	7.98363	−	3.37977i	0.561726	−	0.237800i
$203$	−0.322712	+	1.83019i	−0.0226499	+	0.128454i
$204$	−18.6546	+	0.925997i	−1.30609	+	0.0648328i
$205$	10.0246	+	8.41165i	0.700150	+	0.587495i
$206$	8.72876	−	17.0904i	0.608162	−	1.19075i
$207$	−6.15803	+	8.44615i	−0.428013	+	0.587048i
$208$	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	$-0.669204\pi$
$211$	6.32604	−	17.3807i	0.435503	−	1.19653i	0.942389	−	0.334520i	$-0.108574\pi$
$212$	−1.15146	−	2.37244i	−0.0790825	−	0.162940i
$213$	0.651697	−	12.2399i	0.0446535	−	0.838662i
$214$	−0.00995620	−	0.193545i	−0.000680592	−	0.0132305i
$215$	6.82156	−	38.6870i	0.465227	−	2.63843i
$216$	7.41700	−	12.6881i	0.504663	−	0.863316i
$217$	−0.122789	−	0.212677i	−0.00833548	−	0.0144375i
$218$	−4.71586	+	15.3719i	−0.319399	+	1.04112i
$219$	15.4445	+	10.0481i	1.04364	+	0.678987i
$220$	−2.08424	−	2.02051i	−0.140520	−	0.136223i
$221$	17.1367	+	9.89387i	1.15274	+	0.665534i
$222$	1.03149	−	5.78900i	0.0692291	−	0.388532i
$223$	15.1632	+	18.0708i	1.01541	+	1.21011i	0.977522	+	0.210831i	$0.0676171\pi$
$223$	15.1632	+	18.0708i	1.01541	+	1.21011i	0.0378834	+	0.999282i	$0.487938\pi$
$224$	0.979372	+	0.988858i	0.0654370	+	0.0660709i
$225$	18.5962	+	1.98590i	1.23975	+	0.132393i
$226$	−8.18612	−	12.6322i	−0.544532	−	0.840278i
$227$	5.25383			0.348709			0.174355	−	0.984683i	$-0.444216\pi$
$227$	5.25383			0.348709			0.174355	+	0.984683i	$0.444216\pi$
$228$	−0.585371	−	15.0883i	−0.0387671	−	0.999248i
$229$	−13.7689			−0.909876			−0.454938	−	0.890523i	$-0.650339\pi$
$229$	−13.7689			−0.909876			−0.454938	+	0.890523i	$0.650339\pi$
$230$	8.98157	+	13.8596i	0.592227	+	0.913878i
$231$	−0.134855	−	0.125965i	−0.00887284	−	0.00828790i
$232$	−18.7160	+	10.3038i	−1.22876	+	0.676476i
$233$	7.15539	+	8.52746i	0.468765	+	0.558652i	0.947685	−	0.319206i	$-0.103416\pi$
$233$	7.15539	+	8.52746i	0.468765	+	0.558652i	−0.478920	+	0.877858i	$0.658972\pi$
$234$	−13.8920	+	7.03232i	−0.908145	+	0.459717i
$235$	−21.0498	−	12.1531i	−1.37314	−	0.792780i
$236$	−10.2672	+	10.5911i	−0.668338	+	0.689419i
$237$	0.906890	−	1.39394i	0.0589088	−	0.0905463i
$238$	−0.550223	+	1.79351i	−0.0356657	+	0.116256i
$239$	−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	$0.898728\pi$
$240$	−14.5289	−	18.1147i	−0.937836	−	1.16930i
$241$	−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	$0.949120\pi$
$242$	0.785556	+	15.2710i	0.0504975	+	0.981654i
$243$	−8.99432	+	12.7319i	−0.576986	+	0.816754i
$244$	−18.0930	+	8.78143i	−1.15829	+	0.562173i
$245$	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
$249$	7.55181	+	24.7747i	0.478576	+	1.57003i
$250$	2.66050	−	5.20910i	0.168265	−	0.329452i
$251$	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	$0.555934\pi$
$252$	−0.944805	−	1.13423i	−0.0595171	−	0.0714498i
$253$	−0.262002	+	1.48589i	−0.0164719	+	0.0934169i
$254$	−0.726432	+	0.307526i	−0.0455804	+	0.0192959i
$255$	12.2543	−	28.8025i	0.767393	−	1.80368i
$256$	−1.79512	+	15.8990i	−0.112195	+	0.993686i
$257$	−7.75574	−	21.3087i	−0.483790	−	1.32920i	−0.906220	−	0.422806i	$-0.861045\pi$
$257$	−7.75574	−	21.3087i	−0.483790	−	1.32920i	0.422430	−	0.906396i	$-0.361177\pi$
$258$	24.8887	−	14.3099i	1.54950	−	0.890896i
$259$	−0.511489	−	0.295308i	−0.0317824	−	0.0183496i
$260$	2.52439	+	24.4717i	0.156556	+	1.51767i
$261$	20.7170	−	9.18245i	1.28235	−	0.568379i
$262$	−16.4001	+	3.76960i	−1.01320	+	0.232887i
$263$	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	$0.787736\pi$
$264$	0.155868	−	2.11572i	0.00959303	−	0.130213i
$265$	4.41941			0.271482
$266$	−1.44504	−	0.460485i	−0.0886014	−	0.0282341i
$267$	−11.4453	+	8.60970i	−0.700441	+	0.526905i
$268$	21.3399	+	1.53358i	1.30354	+	0.0936783i
$269$	0.996932	−	0.175786i	0.0607840	−	0.0107179i	−0.143173	−	0.989698i	$-0.545731\pi$
$269$	0.996932	−	0.175786i	0.0607840	−	0.0107179i	0.203957	+	0.978980i	$0.434620\pi$
$270$	13.7021	+	20.4668i	0.833882	+	1.24557i
$271$	−7.37124	−	8.78470i	−0.447771	−	0.533632i	0.494191	−	0.869354i	$-0.335464\pi$
$271$	−7.37124	−	8.78470i	−0.447771	−	0.533632i	−0.941961	+	0.335721i	$0.891020\pi$
$272$	−20.0276	+	8.00199i	−1.21435	+	0.485192i
$273$	0.189301	+	1.55243i	0.0114570	+	0.0939574i
$274$	−2.03222	+	16.4202i	−0.122771	+	0.991982i
$275$	2.53676	−	0.923306i	0.152973	−	0.0556774i
$276$	−3.56071	+	11.5326i	−0.214330	+	0.694178i
$277$	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	$0.756505\pi$
$278$	−24.1168	+	10.2096i	−1.44643	+	0.612329i
$279$	−1.31718	+	2.68922i	−0.0788573	+	0.161000i
$280$	−2.20751	+	0.752974i	−0.131924	+	0.0449988i
$281$	−4.01636	+	4.78651i	−0.239596	+	0.285540i	−0.872421	−	0.488756i	$-0.837451\pi$
$281$	−4.01636	+	4.78651i	−0.239596	+	0.285540i	0.632825	+	0.774295i	$0.281895\pi$
$282$	−3.05312	−	17.4990i	−0.181811	−	1.04205i
$283$	2.45199	−	6.73678i	0.145756	−	0.400460i	−0.845234	−	0.534396i	$-0.820539\pi$
$283$	2.45199	−	6.73678i	0.145756	−	0.400460i	0.990990	+	0.133935i	$0.0427615\pi$
$284$	−3.87497	−	13.6126i	−0.229937	−	0.807761i
$285$	23.1765	+	10.1582i	1.37286	+	0.601721i
$286$	−1.35434	+	1.79366i	−0.0800835	+	0.106062i
$287$	0.902659	+	0.328541i	0.0532822	+	0.0193932i
$288$	3.34614	−	16.6374i	0.197173	−	0.980369i
$289$	−9.24697	−	7.75913i	−0.543940	−	0.456419i
$290$	−1.83939	−	35.7571i	−0.108013	−	2.09973i
$291$	−18.6698	+	9.49314i	−1.09444	+	0.556498i
$292$	20.6339	+	5.18688i	1.20751	+	0.303539i
$293$	−3.60599	+	2.08192i	−0.210664	+	0.121627i	−0.601620	−	0.798782i	$-0.705478\pi$
$293$	−3.60599	+	2.08192i	−0.210664	+	0.121627i	0.390956	+	0.920409i	$0.372144\pi$
$294$	15.9835	−	5.78499i	0.932175	−	0.337387i
$295$	−8.45482	−	23.2294i	−0.492259	−	1.35247i
$296$	−1.04277	−	6.70929i	−0.0606096	−	0.389970i
$297$	−0.357556	+	2.22155i	−0.0207475	+	0.128907i
$298$	−15.4935	+	14.4201i	−0.897517	+	0.835332i
$299$	9.79550	−	8.21940i	0.566488	−	0.475340i
$300$	21.0550	−	4.79973i	1.21561	−	0.277113i
$301$	−0.500735	−	2.83981i	−0.0288619	−	0.163684i
$302$	0.0370029	+	0.0570999i	0.00212928	+	0.00328573i
$303$	−8.48523	+	6.38299i	−0.487464	+	0.366693i
$304$	−6.29352	−	16.2601i	−0.360958	−	0.932582i
$305$		−	33.7040i		−	1.92988i
$306$	21.8933	−	6.63051i	1.25156	−	0.379041i
$307$	26.2478	−	4.62819i	1.49804	−	0.264145i	0.636279	−	0.771459i	$-0.280473\pi$
$307$	26.2478	−	4.62819i	1.49804	−	0.264145i	0.861761	+	0.507314i	$0.169361\pi$
$308$	−0.194493	−	0.0870437i	−0.0110823	−	0.00495978i
$309$	−5.30621	+	22.8966i	−0.301859	+	1.30254i
$310$	3.22341	+	3.46337i	0.183077	+	0.196706i
$311$	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	$-0.0289494\pi$
$312$	−12.5375	+	12.8866i	−0.709798	+	0.729558i
$313$	−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	$0.426450\pi$
$314$	−9.68700	+	31.5759i	−0.546669	+	1.78193i
$315$	2.40139	−	0.594484i	0.135303	−	0.0334954i
$316$	0.468142	−	1.86231i	0.0263351	−	0.104763i
$317$	−16.1156	−	2.84161i	−0.905142	−	0.159601i	−0.298345	−	0.954458i	$-0.596435\pi$
$317$	−16.1156	−	2.84161i	−0.905142	−	0.159601i	−0.606797	+	0.794857i	$0.707546\pi$
$318$	2.07161	+	2.47788i	0.116170	+	0.138953i
$319$	2.10256	−	2.50574i	0.117721	−	0.140294i
$320$	−22.6568	−	14.3404i	−1.26655	−	0.801652i
$321$	0.0692072	+	0.227043i	0.00386277	+	0.0126723i
$322$	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
$326$	4.39365	−	8.60252i	0.243342	−	0.476450i
$327$	1.04703	−	19.6648i	0.0579008	−	1.08747i
$328$	3.56508	+	10.4518i	0.196848	+	0.577106i
$329$	−1.75708	−	0.309821i	−0.0968711	−	0.0170810i
$330$	3.07574	+	1.78316i	0.169314	+	0.0981596i
$331$	9.02730	−	5.21191i	0.496185	−	0.286473i	−0.230952	−	0.972965i	$-0.574184\pi$
$331$	9.02730	−	5.21191i	0.496185	−	0.286473i	0.727137	+	0.686493i	$0.240851\pi$
$332$	17.5321	+	24.2290i	0.962201	+	1.32974i
$333$	0.490387	+	7.18500i	0.0268731	+	0.393736i
$334$	26.5478	+	3.28564i	1.45263	+	0.179782i
$335$	−17.9274	+	31.0512i	−0.979480	+	1.69651i
$336$	−1.45696	−	0.884754i	−0.0794836	−	0.0482673i
$337$	−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	$0.339401\pi$
$338$	0.646246	−	0.148542i	0.0351511	−	0.00807959i
$339$	13.4725	+	12.5844i	0.731728	+	0.683489i
$340$	2.59074	−	36.0503i	0.140502	−	1.95510i
$341$			0.432242i			0.0234072i
$342$	5.16851	+	17.7563i	0.279481	+	0.960151i
$343$		−	3.42955i		−	0.185178i
$344$	21.8210	−	24.9561i	1.17651	−	1.34554i
$345$	−14.7817	−	13.8072i	−0.795820	−	0.743355i
$346$	−1.90000	−	8.26614i	−0.102144	−	0.444390i
$347$	−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	$0.515952\pi$
$348$	19.1861	−	17.7925i	1.02848	−	0.953781i
$349$	−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	$0.910959\pi$
$350$	0.266418	−	2.15264i	0.0142406	−	0.115063i
$351$	14.4235	−	12.4749i	0.769867	−	0.665862i
$352$	−0.622602	−	2.36920i	−0.0331848	−	0.126279i
$353$	−3.14132	+	1.81364i	−0.167195	+	0.0965303i	−0.581263	−	0.813716i	$-0.697441\pi$
$353$	−3.14132	+	1.81364i	−0.167195	+	0.0965303i	0.414067	+	0.910246i	$0.364108\pi$
$354$	9.06109	−	15.6293i	0.481592	−	0.830689i
$355$	23.3588	+	4.11878i	1.23975	+	0.218602i
$356$	−9.27419	+	13.6925i	−0.491531	+	0.725703i
$357$	0.122162	−	2.29439i	0.00646550	−	0.121432i
$358$	1.61409	+	0.824378i	0.0853071	+	0.0435698i
$359$	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
$363$	−5.46053	−	17.9140i	−0.286604	−	0.940241i
$364$	0.788511	+	1.62463i	0.0413292	+	0.0851537i
$365$	−22.9188	+	27.3135i	−1.19962	+	1.42966i
$366$	18.8972	−	15.7988i	0.987772	−	0.825818i
$367$	1.38430	+	0.244089i	0.0722599	+	0.0127414i	0.209661	−	0.977774i	$-0.432764\pi$
$367$	1.38430	+	0.244089i	0.0722599	+	0.0127414i	−0.137401	+	0.990515i	$0.543875\pi$
$368$	0.432681	+	13.9302i	0.0225551	+	0.726162i
$369$	−2.81468	−	11.3698i	−0.146526	−	0.591887i
$370$	10.8784	+	3.33733i	0.565541	+	0.173499i
$371$	0.304842	−	0.110953i	0.0158266	−	0.00576040i
$372$	−0.430866	+	3.43077i	−0.0223394	+	0.177877i
$373$	−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	$0.245414\pi$
$374$	2.41708	−	2.24961i	0.124984	−	0.116324i
$375$	−1.61731	+	6.97881i	−0.0835177	+	0.360384i
$376$	−9.89219	−	17.9683i	−0.510151	−	0.926646i
$377$	−27.3005	+	4.81382i	−1.40605	+	0.247924i
$378$	1.45898	+	1.06775i	0.0750416	+	0.0549192i
$379$			5.34855i			0.274737i	0.990520	+	0.137368i	$0.0438644\pi$
$379$			5.34855i			0.274737i	−0.990520	+	0.137368i	$0.956136\pi$
$380$	29.1200	+	2.40970i	1.49383	+	0.123615i
$381$	0.772073	−	0.580790i	0.0395545	−	0.0297548i
$382$	−2.60849	+	1.69040i	−0.133462	+	0.0864884i
$383$	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	$0.868438\pi$
$384$	−2.58003	−	19.4253i	−0.131661	−	0.991295i
$385$	0.273552	−	0.229537i	0.0139415	−	0.0116983i
$386$	3.86406	+	4.15171i	0.196675	+	0.211317i
$387$	−25.3338	+	24.3830i	−1.28779	+	1.23946i
$388$	−16.8337	+	17.3647i	−0.854604	+	0.881560i
$389$	−0.112367	−	0.308725i	−0.00569722	−	0.0156530i	0.936811	−	0.349835i	$-0.113762\pi$
$389$	−0.112367	−	0.308725i	−0.00569722	−	0.0156530i	−0.942509	+	0.334182i	$0.891540\pi$
$390$	−10.2544	−	28.3320i	−0.519250	−	1.43465i
$391$	−16.2693	+	9.39307i	−0.822772	+	0.475028i
$392$	15.2893	−	12.3080i	0.772227	−	0.621648i
$393$	18.3711	−	9.34127i	0.926701	−	0.471205i
$394$	−4.49757	+	0.231360i	−0.226584	+	0.0116558i
$395$	2.46518	+	2.06853i	0.124037	+	0.104079i
$396$	0.441977	+	2.56037i	0.0222102	+	0.128663i
$397$	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
$399$	1.85369	+	0.118826i	0.0928007	+	0.00594876i
$400$	21.1977	−	13.1324i	1.05989	−	0.656621i
$401$	2.21821	−	6.09449i	0.110772	−	0.304344i	−0.871903	−	0.489678i	$-0.837114\pi$
$401$	2.21821	−	6.09449i	0.110772	−	0.304344i	0.982676	+	0.185334i	$0.0593366\pi$
$402$	−25.8134	+	4.50376i	−1.28745	+	0.224627i
$403$	2.35468	−	2.80620i	0.117295	−	0.139787i
$404$	−6.87562	+	10.1513i	−0.342075	+	0.505044i
$405$	−22.3499	−	20.2593i	−1.11057	−	1.00669i
$406$	−1.02459	−	2.42027i	−0.0508496	−	0.120116i
$407$	0.519771	+	0.900270i	0.0257641	+	0.0446247i
$408$	21.4272	−	15.4461i	1.06080	−	0.764696i
$409$	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	$0.301959\pi$
$410$	−18.3666	−	2.27310i	−0.907060	−	0.112261i
$411$	−2.45280	−	20.1150i	−0.120988	−	0.992202i
$412$	2.78480	+	26.9961i	0.137197	+	1.33000i
$413$	−1.16639	−	1.39005i	−0.0573943	−	0.0683999i
$414$	0.812488	−	14.7600i	0.0399316	−	0.725414i
$415$	−49.3582	+	8.70319i	−2.42290	+	0.427223i
$416$	−8.86441	+	18.7730i	−0.434614	+	0.920423i
$417$	25.6321	−	19.2817i	1.25521	−	0.944227i
$418$	1.79742	+	1.97362i	0.0879145	+	0.0965329i
$419$	25.0964			1.22604			0.613020	−	0.790067i	$-0.289954\pi$
$419$	25.0964			1.22604			0.613020	+	0.790067i	$0.289954\pi$
$420$	2.40003	−	1.54919i	0.117109	−	0.0755928i
$421$	−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	$-0.249173\pi$
$422$	5.85957	+	25.4927i	0.285239	+	1.24096i
$423$	8.81565	+	19.8895i	0.428631	+	0.967058i
$424$	3.19118	+	1.93003i	0.154977	+	0.0937308i
$425$	29.1090	+	16.8061i	1.41199	+	0.815216i
$426$	8.64016	+	15.0275i	0.418617	+	0.728085i
$427$	−0.846168	−	2.32483i	−0.0409489	−	0.112506i
$428$	0.160670	+	0.222043i	0.00776629	+	0.0107328i
$429$	1.07767	−	2.53295i	0.0520302	−	0.122292i
$430$	21.6580	+	51.1602i	1.04444	+	2.46716i
$431$	−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	$0.835376\pi$
$432$	0.955817	+	20.7626i	0.0459868	+	0.998942i
$433$	−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	$0.753980\pi$
$434$	0.309295	+	0.157969i	0.0148466	+	0.00758277i
$435$	12.7859	+	41.9458i	0.613036	+	2.01115i
$436$	−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	$0.534928\pi$
$439$	−13.9237	+	38.2551i	−0.664542	+	1.82581i	−0.555032	+	0.831829i	$0.687294\pi$
$440$	4.02754	+	0.794969i	0.192006	+	0.0378987i
$441$	−17.2786	+	11.6127i	−0.822792	+	0.552986i
$442$	−27.9471	+	1.43763i	−1.32931	+	0.0683813i
$443$	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	$-0.128583\pi$
$444$	3.22810	+	7.66370i	0.153199	+	0.363703i
$445$	−13.8574	−	24.0018i	−0.656905	−	1.13779i
$446$	−31.8939	−	9.78457i	−1.51022	−	0.463313i
$447$	14.1366	−	21.7288i	0.668638	−	1.02774i
$448$	−1.92284	−	0.420351i	−0.0908458	−	0.0198597i
$449$	−6.18347	−	3.57003i	−0.291816	−	0.168480i	0.346944	−	0.937886i	$-0.387219\pi$
$449$	−6.18347	−	3.57003i	−0.291816	−	0.168480i	−0.638761	+	0.769406i	$0.720553\pi$
$450$	−23.5974	+	11.9454i	−1.11239	+	0.563110i
$451$	−1.08678	−	1.29517i	−0.0511745	−	0.0609874i
$452$	19.4306	+	8.69598i	0.913938	+	0.409024i
$453$	−0.0608986	−	0.0568839i	−0.00286127	−	0.00267264i
$454$	−6.23526	+	4.04068i	−0.292635	+	0.189639i
$455$	−3.02638			−0.141879
$456$	12.2990	+	17.4566i	0.575955	+	0.817482i
$457$	9.63717			0.450808			0.225404	−	0.974265i	$-0.427630\pi$
$457$	9.63717			0.450808			0.225404	+	0.974265i	$0.427630\pi$
$458$	16.3410	−	10.5896i	0.763563	−	0.494818i
$459$	−24.0508	+	14.3694i	−1.12259	+	0.670707i
$460$	−21.3187	−	9.54098i	−0.993989	−	0.444851i
$461$	19.7319	+	23.5156i	0.919008	+	1.09523i	0.995173	+	0.0981358i	$0.0312880\pi$
$461$	19.7319	+	23.5156i	0.919008	+	1.09523i	−0.0761651	+	0.997095i	$0.524268\pi$
$462$	0.256925	+	0.0457793i	0.0119533	+	0.00212984i
$463$	13.2536	+	7.65197i	0.615947	+	0.355617i	0.775289	−	0.631606i	$-0.217604\pi$
$463$	13.2536	+	7.65197i	0.615947	+	0.355617i	−0.159342	+	0.987223i	$0.550937\pi$
$464$	14.2876	−	26.6228i	0.663283	−	1.23593i
$465$	−4.85717	−	3.16004i	−0.225246	−	0.146543i
$466$	−15.0504	−	4.61725i	−0.697198	−	0.213890i
$467$	−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	$-0.353281\pi$
$468$	11.0785	−	19.0302i	0.512103	−	0.879669i
$469$	−0.457027	+	2.59193i	−0.0211036	+	0.119684i
$470$	34.3287	−	1.76591i	1.58347	−	0.0814554i
$471$	2.15073	−	40.3941i	0.0991006	−	1.86126i
$472$	4.03963	−	20.4659i	0.185939	−	0.942020i
$473$	−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
$477$	−3.19631	−	2.33041i	−0.146349	−	0.106702i
$478$	7.94413	+	4.05739i	0.363356	+	0.185581i
$479$	−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	$0.755488\pi$
$480$	31.1748	+	10.3245i	1.42293	+	0.471248i
$481$	1.52986	−	8.67625i	0.0697554	−	0.395603i
$482$	−5.61768	−	13.2700i	−0.255878	−	0.604431i
$483$	−1.36625	−	0.581284i	−0.0621666	−	0.0264493i
$484$	−12.6771	−	17.5194i	−0.576231	−	0.796338i
$485$	−13.8622	−	38.0861i	−0.629451	−	1.72940i
$486$	0.882436	−	22.0277i	0.0400281	−	0.999199i
$487$	−0.626702	−	0.361827i	−0.0283986	−	0.0163959i	0.485733	−	0.874107i	$-0.338553\pi$
$487$	−0.626702	−	0.361827i	−0.0283986	−	0.0163959i	−0.514132	+	0.857711i	$0.671886\pi$
$488$	14.7191	−	24.3370i	0.666303	−	1.10169i
$489$	−2.67090	+	11.5251i	−0.120782	+	0.521183i
$490$	7.36850	+	32.0574i	0.332875	+	1.44821i
$491$	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	$0.842789\pi$
$492$	−7.33489	−	11.3633i	−0.330682	−	0.512298i
$493$	40.7272			1.83426
$494$	−0.917680	−	22.6048i	−0.0412884	−	1.01704i
$495$	−4.18359	−	1.20718i	−0.188038	−	0.0542586i
$496$	0.815050	+	3.90856i	0.0365968	+	0.175499i
$497$	1.71464	−	0.302338i	0.0769122	−	0.0135617i
$498$	−28.0165	−	23.5946i	−1.25545	−	1.05730i
$499$	−22.7913	−	27.1616i	−1.02028	−	1.21592i	−0.976195	−	0.216893i	$-0.930408\pi$
$499$	−22.7913	−	27.1616i	−1.02028	−	1.21592i	−0.0440828	−	0.999028i	$-0.514037\pi$
$500$	0.848797	+	8.22833i	0.0379593	+	0.367982i
$501$	−32.5215	+	3.96562i	−1.45295	+	0.177171i
$502$	−22.1899	−	2.74629i	−0.990383	−	0.122573i
$503$	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	$-0.0454344\pi$
$504$	1.99362	+	0.619465i	0.0888031	+	0.0275932i
$505$	−10.2735	−	17.7942i	−0.457165	−	0.791833i
$506$	−0.831840	−	1.96496i	−0.0369798	−	0.0873530i
$507$	−0.723916	+	0.368094i	−0.0321502	+	0.0163476i
$508$	0.625615	−	0.923666i	0.0277572	−	0.0409810i
$509$	8.41817	−	10.0324i	0.373129	−	0.444678i	−0.546504	−	0.837456i	$-0.684042\pi$
$509$	8.41817	−	10.0324i	0.373129	−	0.444678i	0.919633	+	0.392779i	$0.128486\pi$
$510$	7.60838	+	43.6075i	0.336905	+	1.93097i
$511$	−0.895158	+	2.45943i	−0.0395994	+	0.108799i
$512$	−10.0973	−	20.2495i	−0.446243	−	0.894912i
$513$	−11.4057	−	19.5681i	−0.503573	−	0.863953i
$514$	25.5929	+	19.3243i	1.12885	+	0.852360i
$515$	−42.7389	−	15.5557i	−1.88330	−	0.685465i
$516$	−18.5323	+	36.1247i	−0.815840	+	1.59030i
$517$	2.40564	+	2.01857i	0.105800	+	0.0887768i
$518$	0.834155	−	0.0429099i	0.0366507	−	0.00188535i
$519$	4.70829	+	9.25962i	0.206671	+	0.406452i
$520$	−21.8170	−	27.1016i	−0.956737	−	1.18848i
$521$	−6.79220	+	3.92148i	−0.297572	+	0.171803i	−0.641351	−	0.767247i	$-0.721626\pi$
$521$	−6.79220	+	3.92148i	−0.297572	+	0.171803i	0.343780	+	0.939050i	$0.388293\pi$
$522$	−17.5248	+	26.8310i	−0.767040	+	1.17436i
$523$	3.90938	+	10.7409i	0.170945	+	0.469668i	0.995349	−	0.0963341i	$-0.0307117\pi$
$523$	3.90938	+	10.7409i	0.170945	+	0.469668i	−0.824404	+	0.566002i	$0.808489\pi$
$524$	16.5644	−	17.0869i	0.723621	−	0.746446i
$525$	0.321554	+	2.63702i	0.0140338	+	0.115089i
$526$	−14.7710	−	15.8706i	−0.644048	−	0.691993i
$527$	−4.12272	+	3.45937i	−0.179589	+	0.150693i
$528$	1.44220	+	2.63081i	0.0627636	+	0.114491i
$529$	−1.88584	−	10.6951i	−0.0819932	−	0.465006i
$530$	−5.24496	+	3.39894i	−0.227827	+	0.147640i
$531$	−6.13426	+	21.2589i	−0.266204	+	0.922556i
$532$	2.06914	−	0.564868i	0.0897084	−	0.0244901i
$533$			14.3289i			0.620653i
$534$	6.96164	−	19.0205i	0.301260	−	0.823097i
$535$	−0.452335	+	0.0797588i	−0.0195561	+	0.00344827i
$536$	−26.5057	+	14.5923i	−1.14487	+	0.630291i
$537$	−2.16244	−	0.501139i	−0.0933164	−	0.0216257i
$538$	−1.04796	+	0.975356i	−0.0451810	+	0.0420506i
$539$	−1.50253	+	2.60246i	−0.0647186	+	0.112096i
$540$	−32.0025	−	13.7518i	−1.37717	−	0.591785i
$541$	−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	$0.568448\pi$
$542$	15.5044	+	4.75653i	0.665972	+	0.204310i
$543$	0.210951	−	0.495821i	0.00905279	−	0.0212777i
$544$	17.6145	−	24.8999i	0.755217	−	1.06757i
$545$	37.5286	+	6.61731i	1.60755	+	0.283454i
$546$	−1.41863	−	1.69684i	−0.0607116	−	0.0726179i
$547$	5.16251	−	6.15244i	0.220733	−	0.263059i	−0.644302	−	0.764771i	$-0.722852\pi$
$547$	5.16251	−	6.15244i	0.220733	−	0.263059i	0.865035	+	0.501712i	$0.167296\pi$
$548$	−10.2168	−	21.0505i	−0.436441	−	0.899233i
$549$	−17.7725	+	24.3762i	−0.758512	+	1.04035i
$550$	−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
$554$	−10.0207	−	5.11796i	−0.425738	−	0.217441i
$555$	−13.9164	−	0.740963i	−0.590719	−	0.0314521i
$556$	20.7698	−	30.6648i	0.880835	−	1.30048i
$557$	−22.7675	−	4.01453i	−0.964691	−	0.170101i	−0.330952	−	0.943648i	$-0.607370\pi$
$557$	−22.7675	−	4.01453i	−0.964691	−	0.170101i	−0.633739	+	0.773547i	$0.718481\pi$
$558$	−0.505034	−	4.20461i	−0.0213798	−	0.177995i
$559$	37.2514	−	21.5071i	1.57557	−	0.909654i
$560$	2.04077	−	2.59141i	0.0862384	−	0.109507i
$561$	−2.20538	+	3.38980i	−0.0931114	+	0.143118i
$562$	1.08535	−	8.76960i	0.0457829	−	0.369923i
$563$	−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	$0.306401\pi$
$564$	17.0818	+	18.4197i	0.719274	+	0.775610i
$565$	−27.3288	+	22.9316i	−1.14973	+	0.964739i
$566$	2.27118	+	9.88103i	0.0954650	+	0.415331i
$567$	−2.05027	−	0.836327i	−0.0861033	−	0.0351224i
$568$	15.0682	+	13.1753i	0.632247	+	0.552822i
$569$			29.7662i			1.24786i	0.781479	+	0.623931i	$0.214466\pi$
$569$			29.7662i			1.24786i	−0.781479	+	0.623931i	$0.785534\pi$
$570$	−35.3185	+	5.76905i	−1.47933	+	0.241639i
$571$		−	26.5655i		−	1.11173i	−0.831272	−	0.555866i	$-0.812387\pi$
$571$		−	26.5655i		−	1.11173i	0.831272	−	0.555866i	$-0.187613\pi$
$572$	0.227834	−	3.17033i	0.00952623	−	0.132558i
$573$	2.59862	−	2.78203i	0.108559	−	0.116221i
$574$	−1.32395	+	0.304315i	−0.0552608	+	0.0127019i
$575$	16.6390	−	13.9618i	0.693894	−	0.582247i
$576$	8.82450	+	22.3188i	0.367688	+	0.929949i
$577$	−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	$0.232202\pi$
$578$	16.9418	+	2.09677i	0.704686	+	0.0872142i
$579$	−5.82253	−	3.78810i	−0.241976	−	0.157428i
$580$	29.6835	+	41.0219i	1.23254	+	1.70334i
$581$	−3.18612	+	1.83951i	−0.132183	+	0.0763157i
$582$	14.8562	−	25.6253i	0.615811	−	1.06220i
$583$	−0.562311	−	0.0991505i	−0.0232885	−	0.00410640i
$584$	−28.4775	+	9.71357i	−1.17841	+	0.401950i
$585$	20.5845	+	30.6278i	0.851064	+	1.26630i
$586$	2.67840	−	5.24416i	0.110644	−	0.216634i
$587$	−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
$591$	5.27600	−	1.60823i	0.217025	−	0.0661536i
$592$	6.39762	+	7.16061i	0.262941	+	0.294299i
$593$	−0.796696	+	0.949466i	−0.0327164	+	0.0389899i	−0.782155	−	0.623084i	$-0.785879\pi$
$593$	−0.796696	+	0.949466i	−0.0327164	+	0.0389899i	0.749438	+	0.662074i	$0.230324\pi$
$594$	−1.28423	−	2.91153i	−0.0526925	−	0.119462i
$595$	4.37865	+	0.772074i	0.179507	+	0.0316519i
$596$	7.29740	−	29.0297i	0.298913	−	1.18910i
$597$	22.1568	+	9.42680i	0.906817	+	0.385813i
$598$	−5.30383	+	17.2884i	−0.216890	+	0.706977i
$599$	−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	$0.654445\pi$
$600$	−21.2967	+	21.8896i	−0.869435	+	0.893639i
$601$	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	$-0.0391825\pi$
$602$	2.77835	+	2.98518i	0.113237	+	0.121667i
$603$	29.3396	−	13.0043i	1.19480	−	0.529574i
$604$	−0.0878302	−	0.0393076i	−0.00357376	−	0.00159940i
$605$	35.6898	−	6.29307i	1.45100	−	0.255850i
$606$	5.16117	−	14.1013i	0.209658	−	0.572825i
$607$		−	33.5519i		−	1.36183i	−0.732362	−	0.680915i	$-0.761582\pi$
$607$		−	33.5519i		−	1.36183i	0.732362	−	0.680915i	$-0.238418\pi$
$608$	19.9747	+	14.4572i	0.810081	+	0.586318i
$609$	1.93503	+	2.57233i	0.0784113	+	0.104236i
$610$	25.9215	+	39.9999i	1.04953	+	1.61955i
$611$	−4.62153	−	26.2100i	−0.186967	−	1.06034i
$612$	−20.8835	+	24.7070i	−0.844165	+	0.998723i
$613$	−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	$0.477451\pi$
$614$	−27.5914	+	25.6797i	−1.11350	+	1.03635i
$615$	22.4993	−	2.74353i	0.907260	−	0.110630i
$616$	0.297770	−	0.0462797i	0.0119975	−	0.00186466i
$617$	4.78269	+	13.1403i	0.192544	+	0.529010i	0.997970	−	0.0636860i	$-0.0202856\pi$
$617$	4.78269	+	13.1403i	0.192544	+	0.529010i	−0.805426	+	0.592696i	$0.798063\pi$
$618$	−11.3122	−	31.2547i	−0.455043	−	1.25725i
$619$	3.36565	−	1.94316i	0.135277	−	0.0781021i	−0.430834	−	0.902431i	$-0.641781\pi$
$619$	3.36565	−	1.94316i	0.135277	−	0.0781021i	0.566111	+	0.824329i	$0.308447\pi$
$620$	−6.48920	−	1.63123i	−0.260613	−	0.0655119i
$621$	3.41006	+	17.7805i	0.136841	+	0.713509i
$622$	1.47750	+	28.7221i	0.0592424	+	1.15165i
$623$	−1.55844	−	1.30769i	−0.0624376	−	0.0523914i
$624$	4.96860	−	24.9363i	0.198903	−	0.998251i
$625$	16.2635	+	5.91944i	0.650541	+	0.236778i
$626$	3.54992	−	4.70146i	0.141883	−	0.187908i
$627$	−2.72099	−	1.81247i	−0.108666	−	0.0723829i
$628$	−12.7882	−	44.9245i	−0.510305	−	1.79268i
$629$	−4.42687	+	12.1627i	−0.176511	+	0.484960i
$630$	−2.39276	+	2.55243i	−0.0953300	+	0.101691i
$631$	3.21131	−	3.82709i	0.127840	−	0.152354i	−0.698327	−	0.715779i	$-0.746072\pi$
$631$	3.21131	−	3.82709i	0.127840	−	0.152354i	0.826167	+	0.563425i	$0.190516\pi$
$632$	0.876699	+	2.57024i	0.0348732	+	0.102239i
$633$	−14.5203	−	28.5566i	−0.577131	−	1.13502i
$634$	21.3115	−	9.02195i	0.846387	−	0.358307i
$635$	0.934789	+	1.61910i	0.0370960	+	0.0642521i
$636$	−4.36431	−	1.34749i	−0.173056	−	0.0534316i
$637$	23.9319	−	8.71051i	0.948218	−	0.345123i
$638$	−0.568181	+	4.59087i	−0.0224945	+	0.181754i
$639$	−14.7222	−	15.2962i	−0.582401	−	0.605110i
$640$	37.9182	−	0.405946i	1.49885	−	0.0160464i
$641$	−9.89934	−	11.7976i	−0.391000	−	0.465976i	0.534254	−	0.845324i	$-0.320593\pi$
$641$	−9.89934	−	11.7976i	−0.391000	−	0.465976i	−0.925254	+	0.379348i	$0.876148\pi$
$642$	−0.256753	−	0.216229i	−0.0101332	−	0.00853386i
$643$	24.3580	−	4.29496i	0.960584	−	0.169377i	0.328695	−	0.944436i	$-0.393391\pi$
$643$	24.3580	−	4.29496i	0.960584	−	0.169377i	0.631889	+	0.775059i	$0.282280\pi$
$644$	−1.71005	−	0.122892i	−0.0673855	−	0.00484262i
$645$	−40.9031	−	54.3745i	−1.61056	−	2.14099i
$646$	−4.43908	+	32.9393i	−0.174653	+	1.29598i
$647$	−7.61455			−0.299359			−0.149680	−	0.988735i	$-0.547824\pi$
$647$	−7.61455			−0.299359			−0.149680	+	0.988735i	$0.547824\pi$
$648$	−7.29085	−	24.3894i	−0.286412	−	0.958107i
$649$	0.554604	+	3.14532i	0.0217701	+	0.123465i
$650$	31.5332	−	7.24799i	1.23683	−	0.284290i
$651$	−0.414373	−	0.0960294i	−0.0162406	−	0.00376369i
$652$	1.40174	+	13.5886i	0.0548963	+	0.532171i
$653$	7.96800	+	4.60033i	0.311812	+	0.180025i	0.647737	−	0.761864i	$-0.275716\pi$
$653$	7.96800	+	4.60033i	0.311812	+	0.180025i	−0.335925	+	0.941889i	$0.609049\pi$
$654$	13.8814	+	24.1435i	0.542807	+	0.944085i
$655$	13.6405	+	37.4768i	0.532976	+	1.46434i
$656$	−12.2695	−	9.66237i	−0.479042	−	0.377252i
$657$	30.9786	−	7.66900i	1.20859	−	0.299196i
$658$	2.32359	−	0.983662i	0.0905829	−	0.0383472i
$659$	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	$-0.153644\pi$
$660$	−5.02170	+	0.249272i	−0.195469	+	0.00970290i
$661$	−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	$0.874080\pi$
$662$	−6.70517	+	13.1283i	−0.260604	+	0.510247i
$663$	32.7841	−	9.99324i	1.27323	−	0.388105i
$664$	−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
$668$	−34.0340	+	16.5183i	−1.31681	+	0.639113i
$669$	40.8010	+	2.17240i	1.57746	+	0.0839897i
$670$	−2.60495	−	50.6395i	−0.100638	−	1.95637i
$671$	−0.756157	+	4.28838i	−0.0291911	+	0.165551i
$672$	2.40958	−	0.0705075i	0.0929514	−	0.00271989i
$673$	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	$0.712317\pi$
$674$	2.92980	−	9.54999i	0.112852	−	0.367852i
$675$	24.5002	−	21.1904i	0.943014	−	0.815618i
$676$	−0.652723	+	0.673312i	−0.0251047	+	0.0258966i
$677$	34.1118	+	19.6945i	1.31102	+	0.756920i	0.982266	−	0.187494i	$-0.0600366\pi$
$677$	34.1118	+	19.6945i	1.31102	+	0.756920i	0.328758	+	0.944414i	$0.393370\pi$
$678$	−25.6678	−	4.57351i	−0.985765	−	0.175645i
$679$	−1.91237	−	2.27908i	−0.0733901	−	0.0874629i
$680$	24.6513	+	44.7771i	0.945335	+	1.71712i
$681$	6.21167	−	6.65008i	0.238032	−	0.254831i
$682$	−0.332434	−	0.512985i	−0.0127296	−	0.0196432i
$683$	32.3086			1.23625			0.618127	−	0.786078i	$-0.287892\pi$
$683$	32.3086			1.23625			0.618127	+	0.786078i	$0.287892\pi$
$684$	−19.7902	−	17.0982i	−0.756698	−	0.653764i
$685$	39.2132			1.49826
$686$	2.63764	+	4.07019i	0.100706	+	0.155401i
$687$	−16.2792	+	17.4281i	−0.621088	+	0.664924i
$688$	−6.70368	+	46.4003i	−0.255575	+	1.76899i
$689$	3.11050	+	3.70695i	0.118501	+	0.141224i
$690$	28.1620	+	5.01793i	1.07211	+	0.191029i
$691$	22.5874	+	13.0408i	0.859265	+	0.496097i	0.863766	−	0.503893i	$-0.168099\pi$
$691$	22.5874	+	13.0408i	0.859265	+	0.496097i	−0.00450107	+	0.999990i	$0.501433\pi$
$692$	8.61234	+	8.34899i	0.327392	+	0.317381i
$693$	−0.318882	+	0.0217642i	−0.0121133	+	0.000826754i
$694$	10.5135	−	34.2700i	0.399088	−	1.30087i
$695$	31.0341	+	53.7526i	1.17719	+	2.03895i
$696$	−9.08601	+	35.8721i	−0.344404	+	1.35973i
$697$	3.65551	−	20.7314i	0.138462	−	0.785258i
$698$	−1.95357	−	37.9768i	−0.0739438	−	1.43744i
$699$	19.2536	+	1.02513i	0.728238	+	0.0387741i
$700$	1.33939	+	2.75966i	0.0506243	+	0.104305i
$701$	17.2787	−	47.4727i	0.652606	−	1.79302i	0.0447137	−	0.999000i	$-0.485762\pi$
$701$	17.2787	−	47.4727i	0.652606	−	1.79302i	0.607892	−	0.794020i	$-0.292015\pi$
$702$	−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
$705$	−40.2702	+	12.2751i	−1.51667	+	0.462309i
$706$	2.33326	−	4.56839i	0.0878135	−	0.171934i
$707$	−1.15538	−	0.969483i	−0.0434527	−	0.0364611i
$708$	1.26667	+	25.5177i	0.0476045	+	0.959014i
$709$	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	$0.0239365\pi$
$710$	−30.8899	+	13.0769i	−1.15928	+	0.490766i
$711$	−0.692166	−	2.79598i	−0.0259582	−	0.104857i
$712$	0.475799	−	23.3830i	0.0178313	−	0.876316i
$713$	1.18948	+	3.26808i	0.0445465	+	0.122390i
$714$	1.61962	+	2.81694i	0.0606126	+	0.105421i
$715$	4.61308	+	2.66336i	0.172519	+	0.0996041i
$716$	−2.54962	+	0.263007i	−0.0952838	+	0.00982904i
$717$	−10.6430	−	2.46648i	−0.397471	−	0.0921124i
$718$	−17.0190	+	3.91188i	−0.635145	+	0.145990i
$719$	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	$0.886434\pi$
$720$	−40.1065	−	3.02721i	−1.49468	−	0.112817i
$721$	−3.33857			−0.124335
$722$	−26.5889	−	3.87667i	−0.989538	−	0.144275i
$723$	10.6095	+	14.1037i	0.394571	+	0.524523i
$724$	0.0445982	−	0.620588i	0.00165748	−	0.0230640i
$725$	−46.3737	+	8.17693i	−1.72228	+	0.303684i
$726$	20.2581	+	17.0607i	0.751848	+	0.633182i
$727$	−2.20017	−	2.62206i	−0.0815997	−	0.0972467i	0.723700	−	0.690115i	$-0.242440\pi$
$727$	−2.20017	−	2.62206i	−0.0815997	−	0.0972467i	−0.805300	+	0.592868i	$0.797996\pi$
$728$	−2.18530	−	1.32167i	−0.0809924	−	0.0489845i
$729$	5.48145	+	26.4377i	0.203017	+	0.979175i
$730$	6.19341	−	50.0424i	0.229228	−	1.85215i
$731$	−59.3831	+	21.6137i	−2.19636	+	0.799411i
$732$	−10.2765	+	33.2838i	−0.379829	+	1.23020i
$733$	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	$0.644974\pi$
$734$	−1.83062	+	0.774968i	−0.0675693	+	0.0286046i
$735$	−18.2595	−	35.9103i	−0.673513	−	1.32457i
$736$	−11.2271	−	16.1996i	−0.413837	−	0.597126i
$737$	2.97766	−	3.54864i	0.109684	−	0.130716i
$738$	12.0849	+	11.3289i	0.444850	+	0.417023i
$739$	−3.59602	+	9.87998i	−0.132282	+	0.363441i	−0.988095	−	0.153843i	$-0.950835\pi$
$739$	−3.59602	+	9.87998i	−0.132282	+	0.363441i	0.855814	+	0.517284i	$0.173057\pi$
$740$	−15.4772	+	4.40574i	−0.568953	+	0.161958i
$741$	7.79163	+	26.5898i	0.286233	+	0.976800i
$742$	−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	$0.807685\pi$
$744$	−2.12723	−	4.40302i	−0.0779879	−	0.161423i
$745$	38.4272	+	32.2443i	1.40787	+	1.18134i
$746$	−0.687198	−	13.3589i	−0.0251601	−	0.489104i
$747$	40.2873	+	19.7327i	1.47404	+	0.721980i
$748$	−1.13843	+	4.52879i	−0.0416253	+	0.165589i
$749$	−0.0291987	+	0.0168579i	−0.00106690	+	0.000615973i
$750$	−3.44792	−	9.52632i	−0.125900	−	0.347852i
$751$	15.6700	+	43.0529i	0.571805	+	1.57102i	0.801650	+	0.597794i	$0.203956\pi$
$751$	15.6700	+	43.0529i	0.571805	+	1.57102i	−0.229844	+	0.973227i	$0.573822\pi$
$752$	25.5594	+	13.7168i	0.932054	+	0.500201i
$753$	27.1830	−	3.31465i	0.990602	−	0.120792i
$754$	28.6980	−	26.7097i	1.04512	−	0.972709i
$755$	0.123532	−	0.103655i	0.00449578	−	0.00377241i
$756$	−2.55271	−	0.145122i	−0.0928413	−	0.00527802i
$757$	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	$0.838564\pi$
$758$	−4.11353	−	6.34767i	−0.149410	−	0.230558i
$759$	1.57100	+	2.08841i	0.0570238	+	0.0758046i
$760$	−36.4130	+	19.5362i	−1.32084	+	0.708651i
$761$			48.0784i			1.74284i	0.490537	+	0.871420i	$0.336801\pi$
$761$			48.0784i			1.74284i	−0.490537	+	0.871420i	$0.663199\pi$
$762$	−0.469616	+	1.28308i	−0.0170124	+	0.0464810i
$763$	2.75478	−	0.485741i	0.0997296	−	0.0175850i
$764$	1.79569	−	4.01234i	0.0649656	−	0.145161i
$765$	−21.9686	−	49.5645i	−0.794276	−	1.79201i
$766$	−8.91961	−	9.58361i	−0.322279	−	0.346270i
$767$	13.5338	−	23.4413i	0.488679	−	0.846417i
$768$	18.0018	+	21.0697i	0.649586	+	0.760288i
$769$	−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	$0.464477\pi$
$770$	−0.148116	+	0.482802i	−0.00533774	+	0.0173990i
$771$	−36.1414	−	15.3767i	−1.30160	−	0.553777i
$772$	−7.77892	−	1.95544i	−0.279969	−	0.0703778i
$773$	−50.8301	−	8.96272i	−1.82823	−	0.322366i	−0.849512	−	0.527570i	$-0.823103\pi$
$773$	−50.8301	−	8.96272i	−1.82823	−	0.322366i	−0.978719	+	0.205203i	$0.934214\pi$
$774$	11.3133	−	48.4218i	0.406650	−	1.74049i
$775$	3.99976	−	4.76672i	0.143675	−	0.171226i
$776$	6.62323	−	33.5552i	0.237760	−	1.20456i
$777$	−0.978527	+	0.298274i	−0.0351045	+	0.0107005i
$778$	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
$782$	12.0843	−	23.6603i	0.432132	−	0.846090i
$783$	12.8712	−	37.0792i	0.459979	−	1.32510i
$784$	−8.67938	+	26.3660i	−0.309978	+	0.941644i
$785$	77.0887	+	13.5928i	2.75141	+	0.485148i
$786$	−14.6186	+	25.2153i	−0.521427	+	0.899401i
$787$	−33.7237	+	19.4704i	−1.20212	+	0.694044i	−0.961026	−	0.276459i	$-0.910839\pi$
$787$	−33.7237	+	19.4704i	−1.20212	+	0.694044i	−0.241093	+	0.970502i	$0.577506\pi$
$788$	5.15979	−	3.73363i	0.183810	−	0.133005i
$789$	22.2576	+	14.4807i	0.792392	+	0.515525i
$790$	−4.51658	−	0.558986i	−0.160693	−	0.0198878i
$791$	−1.30936	+	2.26788i	−0.0465556	+	0.0806367i
$792$	−2.49370	−	2.69873i	−0.0886097	−	0.0958951i
$793$	28.2705	−	23.7218i	1.00392	−	0.842385i
$794$	−23.9712	+	5.50985i	−0.850706	+	0.195537i
$795$	5.22512	−	5.59390i	0.185316	−	0.198395i
$796$	27.7323	+	1.99296i	0.982944	+	0.0706387i
$797$		−	38.6893i		−	1.37045i	−0.728333	−	0.685223i	$-0.759705\pi$
$797$		−	38.6893i		−	1.37045i	0.728333	−	0.685223i	$-0.240295\pi$
$798$	−2.29135	+	1.28464i	−0.0811131	+	0.0454757i
$799$			39.1003i			1.38327i
$800$	−15.0574	+	31.8886i	−0.532360	+	1.12743i
$801$	−2.63412	+	24.6663i	−0.0930721	+	0.871541i
$802$	2.05465	+	8.93896i	0.0725521	+	0.315646i
$803$	3.52889	−	2.96109i	0.124532	−	0.104495i
$804$	27.1715	−	25.1979i	0.958266	−	0.888663i
$805$	1.43660	−	2.48826i	0.0506334	−	0.0876996i
$806$	−0.636313	+	5.14138i	−0.0224132	+	0.181097i
$807$	0.956182	−	1.46971i	0.0336592	−	0.0517362i
$808$	0.352744	−	17.3355i	0.0124095	−	0.609861i
$809$	11.6149	−	6.70589i	0.408359	−	0.235766i	−0.281725	−	0.959495i	$-0.590907\pi$
$809$	11.6149	−	6.70589i	0.408359	−	0.235766i	0.690085	+	0.723729i	$0.257573\pi$
$810$	42.1061	+	6.85461i	1.47946	+	0.240846i
$811$	4.73261	+	0.834487i	0.166184	+	0.0293028i	0.256121	−	0.966645i	$-0.417555\pi$
$811$	4.73261	+	0.834487i	0.166184	+	0.0293028i	−0.0899367	+	0.995947i	$0.528666\pi$
$812$	3.07739	+	2.08437i	0.107995	+	0.0731471i
$813$	−19.8344	−	1.05606i	−0.695622	−	0.0370375i
$814$	−1.30926	−	0.668690i	−0.0458894	−	0.0234376i
$815$	−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
$819$	2.18881	+	1.59585i	0.0764833	+	0.0557634i
$820$	23.5457	−	11.4279i	0.822251	−	0.399078i
$821$	3.30537	−	3.93919i	0.115358	−	0.137479i	−0.705275	−	0.708934i	$-0.749176\pi$
$821$	3.30537	−	3.93919i	0.115358	−	0.137479i	0.820633	+	0.571455i	$0.193621\pi$
$822$	18.3813	+	21.9861i	0.641121	+	0.766854i
$823$	−1.86962	−	0.329664i	−0.0651709	−	0.0114914i	0.140968	−	0.990014i	$-0.454979\pi$
$823$	−1.86962	−	0.329664i	−0.0651709	−	0.0114914i	−0.206139	+	0.978523i	$0.566090\pi$
$824$	−24.0675	−	29.8973i	−0.838432	−	1.04152i
$825$	1.83056	−	4.30256i	0.0637320	−	0.149796i
$826$	2.45335	+	0.752651i	0.0853630	+	0.0261881i
$827$	−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	$0.552689\pi$
$828$	10.3875	+	18.1421i	0.360992	+	0.630480i
$829$	−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	$0.204671\pi$
$830$	51.8848	−	48.2900i	1.80095	−	1.67617i
$831$	13.4250	+	3.11121i	0.465710	+	0.107927i
$832$	−3.91789	−	29.0974i	−0.135828	−	1.00877i
$833$	−36.8475	+	6.49721i	−1.27669	+	0.225115i
$834$	−15.5908	+	42.5969i	−0.539865	+	1.47501i
$835$		−	63.3989i		−	2.19401i
$836$	−3.65107	−	0.959917i	−0.126275	−	0.0331994i
$837$	1.84659	+	4.84673i	0.0638275	+	0.167527i
$838$	−29.7845	+	19.3015i	−1.02889	+	0.666758i
$839$	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	$0.825361\pi$
$840$	−1.65689	+	3.68443i	−0.0571680	+	0.127125i
$841$	−21.4928	+	18.0346i	−0.741130	+	0.621882i
$842$	22.5941	+	24.2761i	0.778643	+	0.836608i
$843$	1.30997	+	10.7429i	0.0451178	+	0.370005i
$844$	−26.5604	−	25.7482i	−0.914246	−	0.886290i
$845$	−0.537503	−	1.47678i	−0.0184907	−	0.0508027i
$846$	−25.7592	−	16.8248i	−0.885621	−	0.578448i
$847$	2.30381	−	1.33011i	0.0791599	−	0.0457030i
$848$	−5.27167	+	0.163741i	−0.181030	+	0.00562290i
$849$	−5.62811	−	11.0686i	−0.193156	−	0.379873i
$850$	−47.4721	+	2.44202i	−1.62828	+	0.0837606i
$851$	6.40731	+	5.37637i	0.219640	+	0.184300i
$852$	−21.8117	−	11.1896i	−0.747256	−	0.383349i
$853$	−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
$855$	40.2596	−	17.3256i	1.37685	−	0.592522i
$856$	−0.361455	−	0.139950i	−0.0123543	−	0.00478340i
$857$	1.87109	−	5.14079i	0.0639154	−	0.175606i	−0.903624	−	0.428327i	$-0.859103\pi$
$857$	1.87109	−	5.14079i	0.0639154	−	0.175606i	0.967539	+	0.252721i	$0.0813254\pi$
$858$	0.669095	+	3.83493i	0.0228425	+	0.130922i
$859$	−26.8813	+	32.0359i	−0.917178	+	1.09305i	0.0781920	+	0.996938i	$0.475085\pi$
$859$	−26.8813	+	32.0359i	−0.917178	+	1.09305i	−0.995370	+	0.0961124i	$0.969359\pi$
$860$	−65.0507	−	44.0599i	−2.21821	−	1.50243i
$861$	1.48308	−	0.754108i	0.0505431	−	0.0256999i
$862$	−14.6015	−	34.4914i	−0.497329	−	1.17478i
$863$	−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	$-0.452129\pi$
$864$	−17.1027	−	23.9060i	−0.581847	−	0.813298i
$865$	−18.8895	+	6.87521i	−0.642262	+	0.233764i
$866$	5.81786	+	0.720036i	0.197699	+	0.0244678i
$867$	−20.7540	+	2.53071i	−0.704842	+	0.0859473i
$868$	−0.488565	+	0.0503981i	−0.0165830	+	0.00171062i
$869$	−0.267253	−	0.318500i	−0.00906595	−	0.0108044i
$870$	−47.4345	−	39.9478i	−1.60818	−	1.35436i
$871$	−38.6632	+	6.81737i	−1.31005	+	0.230998i
$872$	24.2088	+	21.1676i	0.819814	+	0.716827i
$873$	−10.0575	+	34.8553i	−0.340395	+	1.17967i
$874$	19.0210	+	9.97578i	0.643395	+	0.337436i
$875$	−1.01759			−0.0344007
$876$	30.9610	−	19.9850i	1.04608	−	0.675230i
$877$	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	$0.676000\pi$
$878$	−12.8970	−	56.1098i	−0.435253	−	1.89361i
$879$	−1.62820	+	7.02578i	−0.0549178	+	0.236974i
$880$	−5.39130	+	2.15408i	−0.181741	+	0.0726141i
$881$	−7.35957	−	4.24905i	−0.247950	−	0.143154i	0.370875	−	0.928683i	$-0.379058\pi$
$881$	−7.35957	−	4.24905i	−0.247950	−	0.143154i	−0.618825	+	0.785529i	$0.712391\pi$
$882$	11.5750	−	27.0708i	0.389752	−	0.911523i
$883$	7.80047	+	21.4316i	0.262507	+	0.721231i	0.998997	+	0.0447830i	$0.0142596\pi$
$883$	7.80047	+	21.4316i	0.262507	+	0.721231i	−0.736490	+	0.676448i	$0.763518\pi$
$884$	32.0620	−	23.2001i	1.07836	−	0.780304i
$885$	−39.3990	−	16.7627i	−1.32438	−	0.563471i
$886$	12.6892	+	29.9741i	0.426300	+	1.00700i
$887$	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	$-0.0165590\pi$
$888$	−9.72520	−	6.61258i	−0.326356	−	0.221904i
$889$	0.105129	+	0.0882135i	0.00352590	+	0.00295859i
$890$	34.9056	+	17.8277i	1.17004	+	0.597585i
$891$	2.38920	+	3.07914i	0.0800411	+	0.103155i
$892$	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
$896$	2.60532	−	0.979970i	0.0870377	−	0.0327385i
$897$	1.17757	−	22.1166i	0.0393180	−	0.738452i
$898$	10.0842	−	0.518745i	0.336515	−	0.0173108i
$899$	1.30925	−	7.42514i	0.0436660	−	0.247642i
$900$	18.8183	−	32.3253i	0.627277	−	1.07751i
$901$	−3.55466	−	6.15685i	−0.118423	−	0.205114i
$902$	2.28590	+	0.701280i	0.0761122	+	0.0233501i
$903$	−4.18653	−	2.72373i	−0.139319	−	0.0906400i
$904$	−29.7482	+	4.62351i	−0.989412	+	0.153776i
$905$	0.903004	+	0.521350i	0.0300169	+	0.0173302i
$906$	0.116024	+	0.0206732i	0.00385462	+	0.000686821i
$907$	−18.8889	−	22.5109i	−0.627196	−	0.747463i	0.355094	−	0.934831i	$-0.384449\pi$
$907$	−18.8889	−	22.5109i	−0.627196	−	0.747463i	−0.982290	+	0.187368i	$0.940004\pi$
$908$	4.29235	−	9.59098i	0.142447	−	0.318288i
$909$	−1.95286	+	18.2869i	−0.0647724	+	0.606539i
$910$	3.59171	−	2.32757i	0.119064	−	0.0771581i
$911$	−14.7379			−0.488289			−0.244144	−	0.969739i	$-0.578507\pi$
$911$	−14.7379			−0.488289			−0.244144	+	0.969739i	$0.578507\pi$
$912$	−28.0223	−	11.2585i	−0.927910	−	0.372805i
$913$	6.47543			0.214305
$914$	−11.4374	+	7.41187i	−0.378316	+	0.245163i
$915$	−42.6610	−	39.8486i	−1.41033	−	1.31735i
$916$	−11.2491	+	25.1354i	−0.371682	+	0.830498i
$917$	1.88178	+	2.24262i	0.0621418	+	0.0740577i
$918$	17.4921	−	35.5509i	0.577324	−	1.17335i
$919$	−31.9449	−	18.4434i	−1.05376	−	0.608391i	−0.130064	−	0.991506i	$-0.541518\pi$
$919$	−31.9449	−	18.4434i	−1.05376	−	0.608391i	−0.923701	+	0.383114i	$0.874851\pi$
$920$	32.6389	−	5.07279i	1.07607	−	0.167245i
$921$	25.1749	−	38.6953i	0.829541	−	1.27505i
$922$	−41.5036	−	12.7327i	−1.36685	−	0.419328i
$923$	12.9857	+	22.4920i	0.427431	+	0.740332i
$924$	−0.340128	+	0.143268i	−0.0111894	+	0.00471319i
$925$	2.59867	−	14.7378i	0.0854438	−	0.484576i
$926$	−21.6145	+	1.11187i	−0.710295	+	0.0365384i
$927$	22.7079	+	33.7873i	0.745826	+	1.10972i
$928$	3.51892	+	42.5845i	0.115514	+	1.39790i
$929$	−4.19322	+	11.5208i	−0.137575	+	0.377984i	−0.989279	−	0.146039i	$-0.953347\pi$
$929$	−4.19322	+	11.5208i	−0.137575	+	0.377984i	0.851704	+	0.524024i	$0.175570\pi$
$930$	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
$933$	−10.2704	−	33.6933i	−0.336236	−	1.10307i
$934$	30.1159	+	15.3814i	0.985423	+	0.503295i
$935$	−5.99486	−	5.03028i	−0.196053	−	0.164508i
$936$	1.48799	+	31.1054i	0.0486365	+	1.01671i
$937$	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	$-0.292049\pi$
$938$	−1.45103	−	3.42760i	−0.0473779	−	0.111915i
$939$	−2.82472	+	6.63924i	−0.0921814	+	0.216663i
$940$	−39.3833	+	28.4978i	−1.28454	+	0.929494i
$941$	2.38139	+	6.54280i	0.0776310	+	0.213289i	0.972437	−	0.233166i	$-0.0749085\pi$
$941$	2.38139	+	6.54280i	0.0776310	+	0.213289i	−0.894806	+	0.446455i	$0.852686\pi$
$942$	28.5143	+	49.5939i	0.929046	+	1.61586i
$943$	−11.7811	−	6.80180i	−0.383644	−	0.221497i
$944$	10.9459	+	27.3958i	0.356260	+	0.891658i
$945$	2.08672	−	3.74244i	0.0678811	−	0.121742i
$946$	−1.60790	−	6.99535i	−0.0522774	−	0.227438i
$947$	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	$0.921152\pi$
$948$	−1.80375	−	2.79439i	−0.0585829	−	0.0907575i
$949$	−39.0412			−1.26733
$950$	−1.55881	−	38.3973i	−0.0505743	−	1.24577i
$951$	−22.6504	+	17.0387i	−0.734491	+	0.552519i
$952$	2.82456	+	2.46973i	0.0915446	+	0.0800445i
$953$	−4.58605	+	0.808644i	−0.148557	+	0.0261945i	−0.247432	−	0.968905i	$-0.579587\pi$
$953$	−4.58605	+	0.808644i	−0.148557	+	0.0261945i	0.0988752	+	0.995100i	$0.468476\pi$
$954$	5.58569	+	0.307473i	0.180843	+	0.00995482i
$955$	4.73528	+	5.64329i	0.153230	+	0.182613i
$956$	−12.5486	+	1.29446i	−0.405851	+	0.0418657i
$957$	−0.685769	−	5.62389i	−0.0221677	−	0.181795i
$958$	6.40876	+	0.793169i	0.207058	+	0.0256261i
$959$	2.70484	−	0.984482i	0.0873439	−	0.0317906i
$960$	−44.9388	+	11.7231i	−1.45039	+	0.378363i
$961$	−15.0018	−	25.9839i	−0.483930	−	0.838192i
$962$	4.85720	+	11.4736i	0.156602	+	0.369923i
$963$	0.369206	+	0.180836i	0.0118975	+	0.00582737i
$964$	16.8729	+	11.4283i	0.543440	+	0.368081i
$965$	8.64031	−	10.2971i	0.278141	−	0.331476i
$966$	2.06853	−	0.360905i	0.0665539	−	0.0116119i
$967$	5.09363	−	13.9946i	0.163800	−	0.450037i	−0.830453	−	0.557088i	$-0.811919\pi$
$967$	5.09363	−	13.9946i	0.163800	−	0.450037i	0.994254	+	0.107051i	$0.0341408\pi$
$968$	28.5192	+	11.0422i	0.916643	+	0.354911i
$969$	−4.48969	−	40.4585i	−0.144230	−	1.29972i
$970$	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	$0.252233\pi$
$972$	15.8941	+	26.8212i	0.509803	+	0.860291i
$973$	3.49017	+	2.92860i	0.111890	+	0.0938866i
$974$	1.02205	−	0.0525754i	0.0327486	−	0.00168462i
$975$	−35.3230	+	17.9609i	−1.13124	+	0.575209i
$976$	1.24875	+	40.2036i	0.0399715	+	1.28688i
$977$	5.75949	−	3.32524i	0.184262	−	0.106384i	−0.405031	−	0.914303i	$-0.632739\pi$
$977$	5.75949	−	3.32524i	0.184262	−	0.106384i	0.589294	+	0.807919i	$0.299406\pi$
$978$	−5.69403	−	15.7322i	−0.182075	−	0.503059i
$979$	1.22469	+	3.36480i	0.0391411	+	0.107539i
$980$	−33.4001	−	32.3787i	−1.06693	−	1.03430i
$981$	−23.6530	−	24.5752i	−0.755181	−	0.784626i
$982$	−13.4059	−	14.4038i	−0.427798	−	0.459645i
$983$	−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	$0.292390\pi$
$984$	17.4445	+	7.84480i	0.556110	+	0.250083i
$985$	1.85342	+	10.5113i	0.0590549	+	0.334917i
$986$	−48.3351	+	31.3230i	−1.53930	+	0.997526i
$987$	−2.46958	+	1.85773i	−0.0786075	+	0.0591323i
$988$	18.4743	+	26.1216i	0.587744	+	0.831038i
$989$			40.8370i			1.29854i
$990$	5.89352	−	1.78489i	0.187308	−	0.0567274i
$991$	36.8660	−	6.50046i	1.17109	−	0.206494i	0.445923	−	0.895071i	$-0.352876\pi$
$991$	36.8660	−	6.50046i	1.17109	−	0.206494i	0.725163	+	0.688577i	$0.241764\pi$
$992$	−3.97334	−	4.01183i	−0.126154	−	0.127376i
$993$	4.07607	−	17.5885i	0.129350	−	0.558153i
$994$	−1.80241	+	1.67753i	−0.0571691	+	0.0532081i
$995$	−23.2976	+	40.3526i	−0.738583	+	1.27926i
$996$	51.3965	+	6.45482i	1.62856	+	0.204529i
$997$	−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	$0.556572\pi$
$998$	47.9385	+	14.7068i	1.51747	+	0.465536i
$999$	9.67425	+	7.87419i	0.306080	+	0.249129i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.18680 + 0.769092i) q^{2} +(1.18231 - 1.26576i) q^{3} +(0.816994 - 1.82552i) q^{4} +(2.15444 + 2.56756i) q^{5} +(-0.429685 + 2.41151i) q^{6} +(0.213070 + 0.123016i) q^{7} +(0.434383 + 2.79487i) q^{8} +(-0.204279 - 2.99304i) q^{9} +O(q^{10})\)	\(q+(-1.18680 + 0.769092i) q^{2} +(1.18231 - 1.26576i) q^{3} +(0.816994 - 1.82552i) q^{4} +(2.15444 + 2.56756i) q^{5} +(-0.429685 + 2.41151i) q^{6} +(0.213070 + 0.123016i) q^{7} +(0.434383 + 2.79487i) q^{8} +(-0.204279 - 2.99304i) q^{9} +(-4.53159 - 1.39022i) q^{10} +(-0.216520 - 0.375023i) q^{11} +(-1.34472 - 3.19245i) q^{12} +(-0.637288 + 3.61424i) q^{13} +(-0.347482 + 0.0178749i) q^{14} +(5.79713 + 0.308661i) q^{15} +(-2.66504 - 2.98288i) 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} +(0.407623 - 0.124251i) q^{21} +(0.545393 + 0.278554i) q^{22} +(-2.66908 - 2.23962i) q^{23} +(4.05120 + 2.75459i) q^{24} +(-1.08252 + 6.13929i) q^{25} +(-2.02335 - 4.77952i) q^{26} +(-4.02998 - 3.28013i) q^{27} +(0.398644 - 0.288459i) q^{28} +(2.58348 + 7.09806i) q^{29} +(-7.11743 + 4.09221i) q^{30} +(-0.864431 - 0.499079i) q^{31} +(5.45698 + 1.49042i) q^{32} +(-0.730682 - 0.169333i) q^{33} +(1.70811 + 7.43132i) q^{34} +(0.143195 + 0.812100i) q^{35} +(-5.63074 - 2.07238i) q^{36} -2.40057 q^{37} +(-6.02235 + 1.31581i) q^{38} +(3.82128 + 5.07981i) q^{39} +(-6.24016 + 7.13669i) q^{40} +(3.84502 - 0.677980i) q^{41} +(-0.388206 + 0.460961i) q^{42} +(-7.53380 - 8.97843i) q^{43} +(-0.861507 + 0.0888691i) q^{44} +(7.24470 - 6.97282i) q^{45} +(4.89014 + 0.605219i) q^{46} +(-6.81452 + 2.48028i) q^{47} +(-6.92650 - 0.153398i) q^{48} +(-3.46973 - 6.00976i) q^{49} +(-3.43694 - 8.11867i) q^{50} +(-4.23279 - 8.32446i) q^{51} +(6.07721 + 4.11620i) q^{52} +(0.847549 - 1.01007i) q^{53} +(7.30551 + 0.793442i) q^{54} +(0.496417 - 1.36389i) q^{55} +(-0.251260 + 0.648938i) q^{56} +(6.76644 - 3.34892i) q^{57} +(-8.52514 - 6.43705i) q^{58} +(-6.93061 - 2.52253i) q^{59} +(5.29969 - 10.3306i) q^{60} +(-7.70314 - 6.46370i) q^{61} +(1.40975 - 0.0725190i) q^{62} +(0.324665 - 0.662855i) q^{63} +(-7.62262 + 2.42809i) q^{64} +(-10.6528 + 6.15039i) q^{65} +(0.997407 - 0.360997i) q^{66} +(3.65875 + 10.0523i) q^{67} +(-7.74256 - 7.50580i) q^{68} +(-5.99049 + 0.730471i) q^{69} +(-0.794524 - 0.853671i) q^{70} +(5.42107 - 4.54882i) q^{71} +(8.27642 - 1.87106i) q^{72} +(1.84726 + 10.4763i) q^{73} +(2.84900 - 1.84626i) q^{74} +(6.49096 + 8.62876i) q^{75} +(6.13535 - 6.19334i) q^{76} -0.106541i q^{77} +(-8.44194 - 3.08981i) q^{78} +(0.945539 - 0.166724i) q^{79} +(1.91705 - 13.2691i) q^{80} +(-8.91654 + 1.22283i) q^{81} +(-4.04184 + 3.76180i) q^{82} +(-7.47672 + 12.9501i) q^{83} +(0.106202 - 0.845636i) q^{84} +(16.9818 - 6.18087i) q^{85} +(15.8464 + 4.86143i) q^{86} +(12.0389 + 5.12206i) q^{87} +(0.954090 - 0.768049i) q^{88} +(-8.14323 - 1.43587i) q^{89} +(-3.23528 + 13.8472i) q^{90} +(-0.580396 + 0.691689i) q^{91} +(-6.26909 + 3.04269i) q^{92} +(-1.65374 + 0.504092i) 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} +(8.73994 + 4.46384i) q^{98} +(-1.07823 + 0.724661i) 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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