LMFDB - Embedded newform 72.2.n.b.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,2,Mod(13,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("72.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	72.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.574922894553$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 $ x^16 - x^15 + x^14 + 2x^12 - 4x^11 - 8x^9 + 4x^8 - 16x^7 - 32x^5 + 32x^4 + 64x^2 - 128*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			13.1
Root			$1.05026 - 0.947078i$ of defining polynomial
Character	$\chi$	$=$	72.13
Dual form			72.2.n.b.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34532 + 0.436011i) q^{2} +(1.52768 + 0.816201i) q^{3} +(1.61979 - 1.17315i) q^{4} +(-0.602794 - 0.348023i) q^{5} +(-2.41110 - 0.431967i) q^{6} +(0.795065 + 1.37709i) q^{7} +(-1.66763 + 2.28452i) q^{8} +(1.66763 + 2.49379i) q^{9} +O(q^{10})$	\(q+(-1.34532 + 0.436011i) q^{2} +(1.52768 + 0.816201i) q^{3} +(1.61979 - 1.17315i) q^{4} +(-0.602794 - 0.348023i) q^{5} +(-2.41110 - 0.431967i) q^{6} +(0.795065 + 1.37709i) q^{7} +(-1.66763 + 2.28452i) q^{8} +(1.66763 + 2.49379i) q^{9} +(0.962695 + 0.205379i) q^{10} +(2.37222 - 1.36960i) q^{11} +(3.43205 - 0.470132i) q^{12} +(-4.76780 - 2.75269i) q^{13} +(-1.67005 - 1.50598i) q^{14} +(-0.636821 - 1.02367i) q^{15} +(1.24743 - 3.80052i) q^{16} -5.65175 q^{17} +(-3.33082 - 2.62785i) q^{18} -0.963328i q^{19} +(-1.38468 + 0.143445i) q^{20} +(0.0906219 + 2.75269i) q^{21} +(-2.59424 + 2.87688i) q^{22} +(3.28857 - 5.69597i) q^{23} +(-4.41223 + 2.12889i) q^{24} +(-2.25776 - 3.91055i) q^{25} +(7.61444 + 1.62444i) q^{26} +(0.512172 + 5.17085i) q^{27} +(2.90338 + 1.29787i) q^{28} +(2.85076 - 1.64589i) q^{29} +(1.30306 + 1.09951i) q^{30} +(-3.69844 + 6.40589i) q^{31} +(-0.0211236 + 5.65681i) q^{32} +(4.74188 - 0.156108i) q^{33} +(7.60343 - 2.46423i) q^{34} -1.10680i q^{35} +(5.62681 + 2.08303i) q^{36} +6.25538i q^{37} +(0.420022 + 1.29599i) q^{38} +(-5.03694 - 8.09673i) q^{39} +(1.80030 - 0.796718i) q^{40} +(-0.931886 + 1.61407i) q^{41} +(-1.32212 - 3.66375i) q^{42} +(-2.99838 + 1.73111i) q^{43} +(2.23574 - 5.00145i) q^{44} +(-0.137339 - 2.08362i) q^{45} +(-1.94068 + 9.09677i) q^{46} +(3.85668 + 6.67997i) q^{47} +(5.00766 - 4.78783i) q^{48} +(2.23574 - 3.87242i) q^{49} +(4.74246 + 4.27655i) q^{50} +(-8.63408 - 4.61296i) q^{51} +(-10.9522 + 1.13458i) q^{52} +2.54179i q^{53} +(-2.94359 - 6.73315i) q^{54} -1.90662 q^{55} +(-4.47186 - 0.480144i) q^{56} +(0.786270 - 1.47166i) q^{57} +(-3.11757 + 3.45722i) q^{58} +(-4.62019 - 2.66747i) q^{59} +(-2.23244 - 0.911041i) q^{60} +(7.93715 - 4.58252i) q^{61} +(2.18256 - 10.2305i) q^{62} +(-2.10831 + 4.27921i) q^{63} +(-2.43802 - 7.61945i) q^{64} +(1.91600 + 3.31861i) q^{65} +(-6.31129 + 2.27753i) q^{66} +(5.95780 + 3.43974i) q^{67} +(-9.15463 + 6.63036i) q^{68} +(9.67295 - 6.01750i) q^{69} +(0.482579 + 1.48901i) q^{70} +3.68351 q^{71} +(-8.47810 - 0.349000i) q^{72} +2.83201 q^{73} +(-2.72742 - 8.41550i) q^{74} +(-0.257341 - 7.81687i) q^{75} +(-1.13013 - 1.56039i) q^{76} +(3.77214 + 2.17785i) q^{77} +(10.3066 + 8.69655i) q^{78} +(2.87870 + 4.98605i) q^{79} +(-2.07461 + 1.85680i) q^{80} +(-3.43802 + 8.31745i) q^{81} +(0.549933 - 2.57776i) q^{82} +(-5.74968 + 3.31958i) q^{83} +(3.37612 + 4.35247i) q^{84} +(3.40684 + 1.96694i) q^{85} +(3.27900 - 3.63623i) q^{86} +(5.69844 - 0.187599i) q^{87} +(-0.827111 + 7.70337i) q^{88} -2.98701 q^{89} +(1.09325 + 2.74326i) q^{90} -8.75427i q^{91} +(-1.35545 - 13.0843i) q^{92} +(-10.8785 + 6.76749i) q^{93} +(-8.10103 - 7.30516i) q^{94} +(-0.335261 + 0.580689i) q^{95} +(-4.64937 + 8.62458i) q^{96} +(-1.24837 - 2.16224i) q^{97} +(-1.31938 + 6.18447i) q^{98} +(7.37150 + 3.63184i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} - q^{4} - 7 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q + q^2 - q^4 - 7 * q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9	$ 16 q + q^{2} - q^{4} - 7 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9} - 16 q^{10} - 16 q^{12} + 16 q^{14} - 10 q^{15} - 9 q^{16} - 28 q^{17} + 4 q^{18} - 8 q^{20} + q^{22} - 10 q^{23} + 7 q^{24} + 2 q^{25} + 28 q^{26} + 4 q^{28} + 22 q^{30} - 10 q^{31} + 11 q^{32} + q^{34} + 27 q^{36} + 23 q^{38} + 2 q^{39} + 6 q^{40} - 8 q^{41} + 8 q^{42} + 18 q^{44} - 20 q^{46} + 6 q^{47} + 39 q^{48} + 18 q^{49} - 23 q^{50} - 8 q^{52} - 29 q^{54} - 4 q^{55} + 10 q^{56} + 10 q^{57} - 14 q^{58} + 6 q^{60} - 52 q^{62} + 2 q^{63} + 26 q^{64} - 14 q^{65} - 72 q^{66} - 39 q^{68} + 72 q^{71} - 77 q^{72} - 44 q^{73} - 38 q^{74} + 5 q^{76} + 10 q^{78} - 30 q^{79} - 96 q^{80} + 10 q^{81} + 38 q^{82} - 28 q^{84} + 7 q^{86} + 42 q^{87} + 31 q^{88} + 64 q^{89} + 64 q^{90} - 30 q^{92} - 12 q^{94} + 44 q^{95} - 26 q^{96} + 66 q^{98}+O(q^{100}) $ 16 * q + q^2 - q^4 - 7 * q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9 - 16 * q^10 - 16 * q^12 + 16 * q^14 - 10 * q^15 - 9 * q^16 - 28 * q^17 + 4 * q^18 - 8 * q^20 + q^22 - 10 * q^23 + 7 * q^24 + 2 * q^25 + 28 * q^26 + 4 * q^28 + 22 * q^30 - 10 * q^31 + 11 * q^32 + q^34 + 27 * q^36 + 23 * q^38 + 2 * q^39 + 6 * q^40 - 8 * q^41 + 8 * q^42 + 18 * q^44 - 20 * q^46 + 6 * q^47 + 39 * q^48 + 18 * q^49 - 23 * q^50 - 8 * q^52 - 29 * q^54 - 4 * q^55 + 10 * q^56 + 10 * q^57 - 14 * q^58 + 6 * q^60 - 52 * q^62 + 2 * q^63 + 26 * q^64 - 14 * q^65 - 72 * q^66 - 39 * q^68 + 72 * q^71 - 77 * q^72 - 44 * q^73 - 38 * q^74 + 5 * q^76 + 10 * q^78 - 30 * q^79 - 96 * q^80 + 10 * q^81 + 38 * q^82 - 28 * q^84 + 7 * q^86 + 42 * q^87 + 31 * q^88 + 64 * q^89 + 64 * q^90 - 30 * q^92 - 12 * q^94 + 44 * q^95 - 26 * q^96 + 66 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.34532	+	0.436011i	−0.951287	+	0.308307i
$2$	−1.34532	+	0.436011i	−0.951287	+	0.308307i
$3$	1.52768	+	0.816201i	0.882008	+	0.471234i
$3$	1.52768	+	0.816201i	0.882008	+	0.471234i
$4$	1.61979	−	1.17315i	0.809894	−	0.586576i
$5$	−0.602794	−	0.348023i	−0.269578	−	0.155641i	0.359118	−	0.933292i	$-0.383078\pi$
$5$	−0.602794	−	0.348023i	−0.269578	−	0.155641i	−0.628696	+	0.777651i	$0.716411\pi$
$6$	−2.41110	−	0.431967i	−0.984328	−	0.176350i
$7$	0.795065	+	1.37709i	0.300506	+	0.520492i	0.976251	−	0.216644i	$-0.0695111\pi$
$7$	0.795065	+	1.37709i	0.300506	+	0.520492i	−0.675745	+	0.737136i	$0.736178\pi$
$8$	−1.66763	+	2.28452i	−0.589596	+	0.807698i
$9$	1.66763	+	2.49379i	0.555877	+	0.831265i
$10$	0.962695	+	0.205379i	0.304431	+	0.0649464i
$11$	2.37222	−	1.36960i	0.715252	−	0.412951i	−0.0977506	−	0.995211i	$-0.531165\pi$
$11$	2.37222	−	1.36960i	0.715252	−	0.412951i	0.813003	+	0.582260i	$0.197831\pi$
$12$	3.43205	−	0.470132i	0.990748	−	0.135715i
$13$	−4.76780	−	2.75269i	−1.32235	−	0.763460i	−0.338248	−	0.941057i	$-0.609834\pi$
$13$	−4.76780	−	2.75269i	−1.32235	−	0.763460i	−0.984103	+	0.177597i	$0.943168\pi$
$14$	−1.67005	−	1.50598i	−0.446339	−	0.402489i
$15$	−0.636821	−	1.02367i	−0.164427	−	0.264311i
$16$	1.24743	−	3.80052i	0.311857	−	0.950129i
$17$	−5.65175			−1.37075			−0.685375	−	0.728190i	$-0.740362\pi$
$17$	−5.65175			−1.37075			−0.685375	+	0.728190i	$0.740362\pi$
$18$	−3.33082	−	2.62785i	−0.785083	−	0.619391i
$19$		−	0.963328i		−	0.221003i	−0.993876	−	0.110501i	$-0.964754\pi$
$19$		−	0.963328i		−	0.221003i	0.993876	−	0.110501i	$-0.0352457\pi$
$20$	−1.38468	+	0.143445i	−0.309625	+	0.0320753i
$21$	0.0906219	+	2.75269i	0.0197753	+	0.600687i
$22$	−2.59424	+	2.87688i	−0.553095	+	0.613352i
$23$	3.28857	−	5.69597i	0.685714	−	1.18769i	−0.287498	−	0.957781i	$-0.592823\pi$
$23$	3.28857	−	5.69597i	0.685714	−	1.18769i	0.973212	−	0.229910i	$-0.0738432\pi$
$24$	−4.41223	+	2.12889i	−0.900644	+	0.434558i
$25$	−2.25776	−	3.91055i	−0.451552	−	0.782111i
$26$	7.61444	+	1.62444i	1.49332	+	0.318580i
$27$	0.512172	+	5.17085i	0.0985676	+	0.995130i
$28$	2.90338	+	1.29787i	0.548686	+	0.245274i
$29$	2.85076	−	1.64589i	0.529373	−	0.305634i	−0.211388	−	0.977402i	$-0.567798\pi$
$29$	2.85076	−	1.64589i	0.529373	−	0.305634i	0.740761	+	0.671768i	$0.234465\pi$
$30$	1.30306	+	1.09951i	0.237906	+	0.200742i
$31$	−3.69844	+	6.40589i	−0.664259	+	1.15053i	0.315226	+	0.949017i	$0.397920\pi$
$31$	−3.69844	+	6.40589i	−0.664259	+	1.15053i	−0.979486	+	0.201514i	$0.935414\pi$
$32$	−0.0211236	+	5.65681i	−0.00373416	+	0.999993i
$33$	4.74188	−	0.156108i	0.825455	−	0.0271749i
$34$	7.60343	−	2.46423i	1.30398	−	0.422611i
$35$		−	1.10680i		−	0.187084i
$36$	5.62681	+	2.08303i	0.937801	+	0.347172i
$37$			6.25538i			1.02838i	0.857677	+	0.514189i	$0.171907\pi$
$37$			6.25538i			1.02838i	−0.857677	+	0.514189i	$0.828093\pi$
$38$	0.420022	+	1.29599i	0.0681366	+	0.210237i
$39$	−5.03694	−	8.09673i	−0.806556	−	1.29651i
$40$	1.80030	−	0.796718i	0.284653	−	0.125972i
$41$	−0.931886	+	1.61407i	−0.145536	+	0.252076i	−0.929573	−	0.368639i	$-0.879824\pi$
$41$	−0.931886	+	1.61407i	−0.145536	+	0.252076i	0.784037	+	0.620714i	$0.213157\pi$
$42$	−1.32212	−	3.66375i	−0.204008	−	0.565329i
$43$	−2.99838	+	1.73111i	−0.457248	+	0.263992i	−0.710886	−	0.703307i	$-0.751706\pi$
$43$	−2.99838	+	1.73111i	−0.457248	+	0.263992i	0.253638	+	0.967299i	$0.418373\pi$
$44$	2.23574	−	5.00145i	0.337051	−	0.753996i
$45$	−0.137339	−	2.08362i	−0.0204733	−	0.310608i
$46$	−1.94068	+	9.09677i	−0.286138	+	1.34125i
$47$	3.85668	+	6.67997i	0.562555	+	0.974374i	0.997273	+	0.0738070i	$0.0235149\pi$
$47$	3.85668	+	6.67997i	0.562555	+	0.974374i	−0.434717	+	0.900567i	$0.643152\pi$
$48$	5.00766	−	4.78783i	0.722793	−	0.691064i
$49$	2.23574	−	3.87242i	0.319392	−	0.553203i
$50$	4.74246	+	4.27655i	0.670685	+	0.604795i
$51$	−8.63408	−	4.61296i	−1.20901	−	0.645944i
$52$	−10.9522	+	1.13458i	−1.51879	+	0.157338i
$53$			2.54179i			0.349141i	0.984645	+	0.174571i	$0.0558537\pi$
$53$			2.54179i			0.349141i	−0.984645	+	0.174571i	$0.944146\pi$
$54$	−2.94359	−	6.73315i	−0.400571	−	0.916266i
$55$	−1.90662			−0.257088
$56$	−4.47186	−	0.480144i	−0.597578	−	0.0641619i
$57$	0.786270	−	1.47166i	0.104144	−	0.194926i
$58$	−3.11757	+	3.45722i	−0.409357	+	0.453955i
$59$	−4.62019	−	2.66747i	−0.601498	−	0.347275i	0.168133	−	0.985764i	$-0.446226\pi$
$59$	−4.62019	−	2.66747i	−0.601498	−	0.347275i	−0.769631	+	0.638489i	$0.779560\pi$
$60$	−2.23244	−	0.911041i	−0.288206	−	0.117615i
$61$	7.93715	−	4.58252i	1.01625	−	0.586731i	0.103233	−	0.994657i	$-0.467081\pi$
$61$	7.93715	−	4.58252i	1.01625	−	0.586731i	0.913015	+	0.407926i	$0.133748\pi$
$62$	2.18256	−	10.2305i	0.277185	−	1.29928i
$63$	−2.10831	+	4.27921i	−0.265622	+	0.539130i
$64$	−2.43802	−	7.61945i	−0.304752	−	0.952432i
$65$	1.91600	+	3.31861i	0.237651	+	0.411623i
$66$	−6.31129	+	2.27753i	−0.776866	+	0.280344i
$67$	5.95780	+	3.43974i	0.727861	+	0.420231i	0.817639	−	0.575731i	$-0.195283\pi$
$67$	5.95780	+	3.43974i	0.727861	+	0.420231i	−0.0897783	+	0.995962i	$0.528616\pi$
$68$	−9.15463	+	6.63036i	−1.11016	+	0.804049i
$69$	9.67295	−	6.01750i	1.16449	−	0.724422i
$70$	0.482579	+	1.48901i	0.0576792	+	0.177971i
$71$	3.68351			0.437153			0.218576	−	0.975820i	$-0.429859\pi$
$71$	3.68351			0.437153			0.218576	+	0.975820i	$0.429859\pi$
$72$	−8.47810	−	0.349000i	−0.999154	−	0.0411301i
$73$	2.83201			0.331461			0.165731	−	0.986171i	$-0.447002\pi$
$73$	2.83201			0.331461			0.165731	+	0.986171i	$0.447002\pi$
$74$	−2.72742	−	8.41550i	−0.317056	−	0.978282i
$75$	−0.257341	−	7.81687i	−0.0297151	−	0.902615i
$76$	−1.13013	−	1.56039i	−0.129635	−	0.178989i
$77$	3.77214	+	2.17785i	0.429875	+	0.248189i
$78$	10.3066	+	8.69655i	1.16699	+	0.984691i
$79$	2.87870	+	4.98605i	0.323879	+	0.560975i	0.981285	−	0.192562i	$-0.0616797\pi$
$79$	2.87870	+	4.98605i	0.323879	+	0.560975i	−0.657406	+	0.753537i	$0.728346\pi$
$80$	−2.07461	+	1.85680i	−0.231948	+	0.207596i
$81$	−3.43802	+	8.31745i	−0.382002	+	0.924162i
$82$	0.549933	−	2.57776i	0.0607299	−	0.284666i
$83$	−5.74968	+	3.31958i	−0.631110	+	0.364371i	−0.781182	−	0.624304i	$-0.785383\pi$
$83$	−5.74968	+	3.31958i	−0.631110	+	0.364371i	0.150072	+	0.988675i	$0.452049\pi$
$84$	3.37612	+	4.35247i	0.368365	+	0.474893i
$85$	3.40684	+	1.96694i	0.369524	+	0.213345i
$86$	3.27900	−	3.63623i	0.353584	−	0.392105i
$87$	5.69844	−	0.187599i	0.610937	−	0.0201128i
$88$	−0.827111	+	7.70337i	−0.0881703	+	0.821182i
$89$	−2.98701			−0.316622			−0.158311	−	0.987389i	$-0.550605\pi$
$89$	−2.98701			−0.316622			−0.158311	+	0.987389i	$0.550605\pi$
$90$	1.09325	+	2.74326i	0.115238	+	0.289165i
$91$		−	8.75427i		−	0.917697i
$92$	−1.35545	−	13.0843i	−0.141316	−	1.36413i
$93$	−10.8785	+	6.76749i	−1.12805	+	0.701756i
$94$	−8.10103	−	7.30516i	−0.835557	−	0.753470i
$95$	−0.335261	+	0.580689i	−0.0343970	+	0.0595774i
$96$	−4.64937	+	8.62458i	−0.474524	+	0.880242i
$97$	−1.24837	−	2.16224i	−0.126753	−	0.219543i	0.795664	−	0.605738i	$-0.207122\pi$
$97$	−1.24837	−	2.16224i	−0.126753	−	0.219543i	−0.922417	+	0.386196i	$0.873789\pi$
$98$	−1.31938	+	6.18447i	−0.133277	+	0.624726i
$99$	7.37150	+	3.63184i	0.740864	+	0.365014i
$100$	−8.24477	−	3.68557i	−0.824477	−	0.368557i
$101$	−8.22136	+	4.74661i	−0.818056	+	0.472305i	−0.849746	−	0.527193i	$-0.823245\pi$
$101$	−8.22136	+	4.74661i	−0.818056	+	0.472305i	0.0316896	+	0.999498i	$0.489911\pi$
$102$	13.6269	+	2.44137i	1.34927	+	0.241732i
$103$	7.37220	−	12.7690i	0.726405	−	1.25817i	−0.231989	−	0.972719i	$-0.574523\pi$
$103$	7.37220	−	12.7690i	0.726405	−	1.25817i	0.958393	−	0.285451i	$-0.0921435\pi$
$104$	14.2395	−	6.30165i	1.39630	−	0.617927i
$105$	0.903375	−	1.69085i	0.0881604	−	0.165010i
$106$	−1.10825	−	3.41952i	−0.107643	−	0.332134i
$107$			7.83384i			0.757325i	0.925535	+	0.378663i	$0.123616\pi$
$107$			7.83384i			0.757325i	−0.925535	+	0.378663i	$0.876384\pi$
$108$	6.89580	+	7.77482i	0.663549	+	0.748133i
$109$		−	0.242400i		−	0.0232177i	−0.999933	−	0.0116089i	$-0.996305\pi$
$109$		−	0.242400i		−	0.0232177i	0.999933	−	0.0116089i	$-0.00369529\pi$
$110$	2.56501	−	0.831306i	0.244565	−	0.0792619i
$111$	−5.10565	+	9.55623i	−0.484607	+	0.907038i
$112$	6.22545	−	1.30383i	0.588249	−	0.123201i
$113$	4.34789	−	7.53076i	0.409015	−	0.708435i	−0.585765	−	0.810481i	$-0.699206\pi$
$113$	4.34789	−	7.53076i	0.409015	−	0.708435i	0.994780	+	0.102046i	$0.0325391\pi$
$114$	−0.416126	+	2.32268i	−0.0389738	+	0.217539i
$115$	−3.96466	+	2.28900i	−0.369706	+	0.213450i
$116$	2.68675	−	6.01037i	0.249459	−	0.558049i
$117$	−1.08629	−	16.4804i	−0.100427	−	1.52361i
$118$	7.37870	+	1.57415i	0.679264	+	0.144912i
$119$	−4.49350	−	7.78298i	−0.411919	−	0.713464i
$120$	3.40057	+	0.252277i	0.310428	+	0.0230296i
$121$	−1.74837	+	3.02827i	−0.158943	+	0.275297i
$122$	−8.68000	+	9.62565i	−0.785850	+	0.871466i
$123$	−2.74103	+	1.70519i	−0.247151	+	0.153751i
$124$	1.52439	+	14.7150i	0.136894	+	1.32145i
$125$			6.62325i			0.592401i
$126$	0.970575	−	6.67616i	0.0864657	−	0.594760i
$127$	−1.72754			−0.153295			−0.0766473	−	0.997058i	$-0.524422\pi$
$127$	−1.72754			−0.153295			−0.0766473	+	0.997058i	$0.524422\pi$
$128$	6.60209	+	9.18762i	0.583548	+	0.812079i
$129$	−5.99350	+	0.197313i	−0.527699	+	0.0173725i
$130$	−4.02460	−	3.62921i	−0.352980	−	0.318303i
$131$	5.74968	+	3.31958i	0.502352	+	0.290033i	0.729684	−	0.683784i	$-0.239667\pi$
$131$	5.74968	+	3.31958i	0.502352	+	0.290033i	−0.227332	+	0.973817i	$0.573000\pi$
$132$	7.49770	−	5.81581i	0.652591	−	0.506201i
$133$	1.32659	−	0.765908i	0.115030	−	0.0664127i
$134$	−9.51493	−	2.02989i	−0.821964	−	0.175356i
$135$	1.49084	−	3.29521i	0.128311	−	0.283606i
$136$	9.42503	−	12.9115i	0.808189	−	1.10715i
$137$	1.81325	+	3.14063i	0.154916	+	0.268322i	0.933028	−	0.359803i	$-0.117156\pi$
$137$	1.81325	+	3.14063i	0.154916	+	0.268322i	−0.778112	+	0.628125i	$0.783823\pi$
$138$	−10.3895	+	12.3130i	−0.884416	+	1.04815i
$139$	14.9919	+	8.65556i	1.27159	+	0.734155i	0.975288	−	0.220937i	$-0.0709117\pi$
$139$	14.9919	+	8.65556i	1.27159	+	0.734155i	0.296307	+	0.955093i	$0.404245\pi$
$140$	−1.29845	−	1.79279i	−0.109739	−	0.151518i
$141$	0.439587	+	13.3527i	0.0370199	+	1.12450i
$142$	−4.95552	+	1.60605i	−0.415858	+	0.134777i
$143$	−15.0804			−1.26109
$144$	11.5580	−	3.22703i	0.963163	−	0.268919i
$145$	−2.29123			−0.190276
$146$	−3.80996	+	1.23479i	−0.315315	+	0.102192i
$147$	6.57619	−	4.09102i	0.542395	−	0.337421i
$148$	7.33851	+	10.1324i	0.603222	+	0.832877i
$149$	−18.7251	−	10.8109i	−1.53402	−	0.885665i	−0.999171	−	0.0407158i	$-0.987036\pi$
$149$	−18.7251	−	10.8109i	−1.53402	−	0.885665i	−0.534846	−	0.844949i	$-0.679631\pi$
$150$	3.75445	+	10.4040i	0.306550	+	0.849484i
$151$	−6.35019	−	10.9988i	−0.516771	−	0.895073i	−0.999810	−	0.0194749i	$-0.993801\pi$
$151$	−6.35019	−	10.9988i	−0.516771	−	0.895073i	0.483039	−	0.875599i	$-0.339533\pi$
$152$	2.20074	+	1.60648i	0.178503	+	0.130302i
$153$	−9.42503	−	14.0943i	−0.761968	−	1.13946i
$154$	−6.02431	−	1.28521i	−0.485453	−	0.103565i
$155$	4.45880	−	2.57429i	0.358139	−	0.206772i
$156$	−17.6575	−	7.20589i	−1.41373	−	0.576933i
$157$	−15.1285	−	8.73443i	−1.20738	−	0.697083i	−0.245197	−	0.969473i	$-0.578853\pi$
$157$	−15.1285	−	8.73443i	−1.20738	−	0.697083i	−0.962187	+	0.272390i	$0.912186\pi$
$158$	−6.04675	−	5.45270i	−0.481054	−	0.433794i
$159$	−2.07461	+	3.88304i	−0.164527	+	0.307945i
$160$	1.98144	−	3.40254i	0.156646	−	0.268995i
$161$	10.4585			0.824245
$162$	0.998740	−	12.6887i	0.0784684	−	0.996917i
$163$		−	8.56748i		−	0.671057i	−0.942030	−	0.335528i	$-0.891085\pi$
$163$		−	8.56748i		−	0.671057i	0.942030	−	0.335528i	$-0.108915\pi$
$164$	0.384097	+	3.70770i	0.0299929	+	0.289523i
$165$	−2.91270	−	1.55618i	−0.226754	−	0.121149i
$166$	6.28781	−	6.97284i	0.488028	−	0.541197i
$167$	−5.97532	+	10.3496i	−0.462384	+	0.800873i	−0.999079	−	0.0429032i	$-0.986339\pi$
$167$	−5.97532	+	10.3496i	−0.462384	+	0.800873i	0.536695	+	0.843776i	$0.319673\pi$
$168$	−6.43969	−	4.38345i	−0.496833	−	0.338190i
$169$	8.65464	+	14.9903i	0.665741	+	1.15310i
$170$	−5.44091	−	1.16075i	−0.417299	−	0.0890254i
$171$	2.40234	−	1.60648i	0.183712	−	0.122850i
$172$	−2.82587	+	6.32159i	−0.215471	+	0.482017i
$173$	11.2973	−	6.52248i	0.858916	−	0.495895i	−0.00473326	−	0.999989i	$-0.501507\pi$
$173$	11.2973	−	6.52248i	0.858916	−	0.495895i	0.863649	+	0.504094i	$0.168173\pi$
$174$	−7.58445	+	2.73697i	−0.574975	+	0.207489i
$175$	3.59013	−	6.21829i	0.271388	−	0.470058i
$176$	−2.24603	−	10.7242i	−0.169301	−	0.808363i
$177$	−4.88100	−	7.84605i	−0.366878	−	0.589746i
$178$	4.01849	−	1.30237i	0.301199	−	0.0976167i
$179$		−	3.31875i		−	0.248055i	−0.992279	−	0.124028i	$-0.960419\pi$
$179$		−	3.31875i		−	0.248055i	0.992279	−	0.124028i	$-0.0395811\pi$
$180$	−2.66686	−	3.21390i	−0.198776	−	0.239550i
$181$			14.9128i			1.10846i	0.832363	+	0.554231i	$0.186987\pi$
$181$			14.9128i			1.10846i	−0.832363	+	0.554231i	$0.813013\pi$
$182$	3.81696	+	11.7773i	0.282932	+	0.872994i
$183$	15.8657	−	0.522318i	1.17283	−	0.0386108i
$184$	7.52841	+	17.0116i	0.555002	+	1.25411i
$185$	2.17702	−	3.77070i	0.160058	−	0.277228i
$186$	11.6844	−	13.8476i	0.856745	−	1.01536i
$187$	−13.4072	+	7.74065i	−0.980432	+	0.566053i
$188$	14.0836	+	6.29566i	1.02715	+	0.459158i
$189$	−6.71353	+	4.81647i	−0.488337	+	0.350346i
$190$	0.197847	−	0.927391i	0.0143533	−	0.0672800i
$191$	3.65884	+	6.33729i	0.264744	+	0.458550i	0.967497	−	0.252884i	$-0.0813792\pi$
$191$	3.65884	+	6.33729i	0.264744	+	0.458550i	−0.702752	+	0.711434i	$0.748046\pi$
$192$	2.49449	−	13.6300i	0.180024	−	0.983662i
$193$	−10.2354	+	17.7282i	−0.736759	+	1.27610i	0.217189	+	0.976130i	$0.430311\pi$
$193$	−10.2354	+	17.7282i	−0.736759	+	1.27610i	−0.953947	+	0.299974i	$0.903022\pi$
$194$	2.62223	+	2.36461i	0.188265	+	0.169769i
$195$	0.218387	+	6.63364i	0.0156390	+	0.475044i
$196$	−0.921510	−	8.89537i	−0.0658222	−	0.635384i
$197$		−	20.5437i		−	1.46368i	−0.681479	−	0.731838i	$-0.738663\pi$
$197$		−	20.5437i		−	1.46368i	0.681479	−	0.731838i	$-0.261337\pi$
$198$	−11.5006	−	1.67194i	−0.817310	−	0.118820i
$199$	1.95597			0.138655			0.0693275	−	0.997594i	$-0.477915\pi$
$199$	1.95597			0.138655			0.0693275	+	0.997594i	$0.477915\pi$
$200$	12.6988	+	1.36347i	0.897943	+	0.0964121i
$201$	6.29411	+	10.1176i	0.443952	+	0.713640i
$202$	8.99081	−	9.97033i	0.632591	−	0.701510i
$203$	4.53308	+	2.61718i	0.318160	+	0.183690i
$204$	−19.3971	+	2.65706i	−1.35807	+	0.186032i
$205$	1.12347	−	0.648636i	0.0784666	−	0.0453027i
$206$	−4.35055	+	20.3928i	−0.303117	+	1.42084i
$207$	19.6887	−	1.29776i	1.36846	−	0.0902003i
$208$	−16.4091	+	14.6863i	−1.13777	+	1.01831i
$209$	−1.31938	−	2.28523i	−0.0912633	−	0.158073i
$210$	−0.478103	+	2.66862i	−0.0329923	+	0.184152i
$211$	−9.10981	−	5.25955i	−0.627145	−	0.362082i	0.152501	−	0.988303i	$-0.451267\pi$
$211$	−9.10981	−	5.25955i	−0.627145	−	0.362082i	−0.779646	+	0.626221i	$0.784601\pi$
$212$	2.98190	+	4.11716i	0.204798	+	0.282767i
$213$	5.62724	+	3.00649i	0.385572	+	0.206001i
$214$	−3.41564	−	10.5390i	−0.233488	−	0.720434i
$215$	2.40987			0.164352
$216$	−12.6670	−	7.45300i	−0.861880	−	0.507112i
$217$	−11.7620			−0.798456
$218$	0.105689	+	0.326106i	0.00715817	+	0.0220867i
$219$	4.32641	+	2.31149i	0.292351	+	0.156196i
$220$	−3.08831	+	2.23675i	−0.208214	+	0.150802i
$221$	26.9464	+	15.5575i	1.81261	+	1.04651i
$222$	2.70212	−	15.0823i	0.181354	−	1.01226i
$223$	1.93129	+	3.34510i	0.129329	+	0.224004i	0.923417	−	0.383799i	$-0.125384\pi$
$223$	1.93129	+	3.34510i	0.129329	+	0.224004i	−0.794088	+	0.607803i	$0.792051\pi$
$224$	−7.80675	+	4.46844i	−0.521610	+	0.298560i
$225$	5.98701	−	12.1517i	0.399134	−	0.810116i
$226$	−2.56582	+	12.0270i	−0.170676	+	0.800027i
$227$	13.9183	−	8.03574i	0.923790	−	0.533351i	0.0389481	−	0.999241i	$-0.487599\pi$
$227$	13.9183	−	8.03574i	0.923790	−	0.533351i	0.884842	+	0.465891i	$0.154266\pi$
$228$	−0.452891	−	3.30619i	−0.0299934	−	0.218958i
$229$	7.46319	+	4.30888i	0.493182	+	0.284739i	0.725893	−	0.687807i	$-0.241427\pi$
$229$	7.46319	+	4.30888i	0.493182	+	0.284739i	−0.232712	+	0.972546i	$0.574760\pi$
$230$	4.33572	−	4.80808i	0.285889	−	0.317035i
$231$	3.98507	+	6.40589i	0.262199	+	0.421476i
$232$	−0.993962	+	9.25735i	−0.0652568	+	0.607775i
$233$	24.1535			1.58235			0.791176	−	0.611589i	$-0.209469\pi$
$233$	24.1535			1.58235			0.791176	+	0.611589i	$0.209469\pi$
$234$	8.64705	+	21.6978i	0.565275	+	1.41843i
$235$		−	5.36886i		−	0.350226i
$236$	−10.6131	+	1.09945i	−0.690853	+	0.0715684i
$237$	0.328116	+	9.96670i	0.0213134	+	0.647407i
$238$	9.43868	+	8.51140i	0.611819	+	0.551712i
$239$	−2.01493	+	3.48996i	−0.130335	+	0.225746i	−0.923806	−	0.382862i	$-0.874939\pi$
$239$	−2.01493	+	3.48996i	−0.130335	+	0.225746i	0.793471	+	0.608608i	$0.208272\pi$
$240$	−4.68487	+	1.14329i	−0.302407	+	0.0737994i
$241$	2.81649	+	4.87830i	0.181426	+	0.314239i	0.942366	−	0.334583i	$-0.108595\pi$
$241$	2.81649	+	4.87830i	0.181426	+	0.314239i	−0.760940	+	0.648822i	$0.775262\pi$
$242$	1.03177	−	4.83631i	0.0663244	−	0.310890i
$243$	−12.0409	+	9.90032i	−0.772425	+	0.635106i
$244$	7.48051	−	16.7342i	0.478891	−	1.07130i
$245$	−2.69539	+	1.55618i	−0.172202	+	0.0994209i
$246$	2.94410	−	3.48915i	0.187709	−	0.222460i
$247$	−2.65175	+	4.59296i	−0.168727	+	0.292243i
$248$	−8.46671	−	19.1318i	−0.537637	−	1.21487i
$249$	−11.4931	+	0.378368i	−0.728348	+	0.0239781i
$250$	−2.88781	−	8.91040i	−0.182641	−	0.563543i
$251$		−	13.8828i		−	0.876276i	−0.898908	−	0.438138i	$-0.855638\pi$
$251$		−	13.8828i		−	0.876276i	0.898908	−	0.438138i	$-0.144362\pi$
$252$	1.60515	+	9.40478i	0.101115	+	0.592445i
$253$		−	18.0161i		−	1.13267i
$254$	2.32410	−	0.753228i	0.145827	−	0.0472618i
$255$	3.59915	+	5.78553i	0.225388	+	0.362304i
$256$	−12.8879	−	9.48173i	−0.805491	−	0.592608i
$257$	−5.42539	+	9.39705i	−0.338427	+	0.586172i	−0.984137	−	0.177410i	$-0.943228\pi$
$257$	−5.42539	+	9.39705i	−0.338427	+	0.586172i	0.645710	+	0.763582i	$0.276561\pi$
$258$	7.97717	−	2.87869i	0.496637	−	0.179219i
$259$	−8.61423	+	4.97343i	−0.535262	+	0.309034i
$260$	6.99676	+	3.12769i	0.433921	+	0.193971i
$261$	8.85853	+	4.36448i	0.548329	+	0.270155i
$262$	−9.18256	−	1.95898i	−0.567300	−	0.121026i
$263$	−11.6051	−	20.1005i	−0.715598	−	1.23945i	−0.962728	−	0.270470i	$-0.912821\pi$
$263$	−11.6051	−	20.1005i	−0.715598	−	1.23945i	0.247130	−	0.968982i	$-0.420513\pi$
$264$	−7.55107	+	11.0932i	−0.464736	+	0.682740i
$265$	0.884601	−	1.53217i	0.0543406	−	0.0941207i
$266$	−1.45075	+	1.60880i	−0.0889512	+	0.0986421i
$267$	−4.56320	−	2.43800i	−0.279263	−	0.149203i
$268$	13.6857	−	1.41776i	0.835987	−	0.0866035i
$269$		−	4.01966i		−	0.245083i	−0.992463	−	0.122541i	$-0.960896\pi$
$269$		−	4.01966i		−	0.245083i	0.992463	−	0.122541i	$-0.0391044\pi$
$270$	−0.568917	+	5.08314i	−0.0346232	+	0.309350i
$271$	−6.75621			−0.410411			−0.205205	−	0.978719i	$-0.565786\pi$
$271$	−6.75621			−0.410411			−0.205205	+	0.978719i	$0.565786\pi$
$272$	−7.05014	+	21.4796i	−0.427478	+	1.30239i
$273$	7.14525	−	13.3738i	0.432450	−	0.809417i
$274$	−3.80875	−	3.43457i	−0.230095	−	0.207490i
$275$	−10.7118	−	6.18447i	−0.645947	−	0.372938i
$276$	8.60868	−	21.0949i	0.518182	−	1.26976i
$277$	1.83595	−	1.05999i	0.110312	−	0.0636885i	−0.443829	−	0.896111i	$-0.646380\pi$
$277$	1.83595	−	1.05999i	0.110312	−	0.0636885i	0.554141	+	0.832423i	$0.313047\pi$
$278$	−23.9428	−	5.10790i	−1.43600	−	0.306352i
$279$	−22.1426	+	1.45950i	−1.32564	+	0.0873781i
$280$	2.52851	+	1.84574i	0.151107	+	0.110304i
$281$	−13.0580	−	22.6171i	−0.778976	−	1.34923i	−0.932533	−	0.361086i	$-0.882406\pi$
$281$	−13.0580	−	22.6171i	−0.778976	−	1.34923i	0.153557	−	0.988140i	$-0.450927\pi$
$282$	−6.41332	−	17.7720i	−0.381908	−	1.05831i
$283$	−16.5376	−	9.54799i	−0.983058	−	0.567569i	−0.0798661	−	0.996806i	$-0.525449\pi$
$283$	−16.5376	−	9.54799i	−0.983058	−	0.567569i	−0.903192	+	0.429237i	$0.858783\pi$
$284$	5.96651	−	4.32132i	0.354047	−	0.256423i
$285$	−0.986131	+	0.613468i	−0.0584134	+	0.0363387i
$286$	20.2880	−	6.57522i	1.19965	−	0.388801i
$287$	−2.96364			−0.174938
$288$	−14.1422	+	9.38080i	−0.833335	+	0.552769i
$289$	14.9423			0.878956
$290$	3.08245	−	0.999003i	0.181007	−	0.0586635i
$291$	−0.142290	−	4.32215i	−0.00834120	−	0.253369i
$292$	4.58725	−	3.32237i	0.268448	−	0.194427i
$293$	−5.07116	−	2.92784i	−0.296261	−	0.171046i	0.344501	−	0.938786i	$-0.388048\pi$
$293$	−5.07116	−	2.92784i	−0.296261	−	0.171046i	−0.640762	+	0.767740i	$0.721381\pi$
$294$	−7.06337	+	8.37103i	−0.411944	+	0.488209i
$295$	1.85668	+	3.21587i	0.108100	+	0.187235i
$296$	−14.2905	−	10.4317i	−0.830619	−	0.606328i
$297$	8.29700	+	11.5649i	0.481441	+	0.671065i
$298$	29.9049	+	6.37984i	1.73235	+	0.369574i
$299$	−31.3585	+	18.1048i	−1.81351	+	1.04703i
$300$	−9.58722	−	12.3598i	−0.553518	−	0.713592i
$301$	−4.76780	−	2.75269i	−0.274812	−	0.158663i
$302$	13.3387	+	12.0282i	0.767555	+	0.692148i
$303$	−16.4338	+	0.541021i	−0.944098	+	0.0310808i
$304$	−3.66115	−	1.20168i	−0.209981	−	0.0689212i
$305$	−6.37929			−0.365277
$306$	18.8250	+	14.8520i	1.07615	+	0.849030i
$307$			13.7071i			0.782305i	0.920326	+	0.391152i	$0.127923\pi$
$307$			13.7071i			0.782305i	−0.920326	+	0.391152i	$0.872077\pi$
$308$	8.66501	−	0.897646i	0.493735	−	0.0511481i
$309$	21.6845	−	13.4898i	1.23359	−	0.767409i
$310$	−4.87610	+	5.40733i	−0.276944	+	0.307116i
$311$	−9.57980	+	16.5927i	−0.543221	+	0.940886i	0.455496	+	0.890238i	$0.349462\pi$
$311$	−9.57980	+	16.5927i	−0.543221	+	0.940886i	−0.998717	+	0.0506479i	$0.983871\pi$
$312$	26.8969	+	1.99539i	1.52273	+	0.112967i
$313$	−12.6102	−	21.8416i	−0.712773	−	1.23456i	−0.963812	−	0.266582i	$-0.914106\pi$
$313$	−12.6102	−	21.8416i	−0.712773	−	1.23456i	0.251039	−	0.967977i	$-0.419228\pi$
$314$	24.1610	+	5.15444i	1.36348	+	0.290882i
$315$	2.76014	−	1.84574i	0.155516	−	0.103996i
$316$	10.5123	+	4.69919i	0.591362	+	0.264350i
$317$	2.13931	−	1.23513i	0.120156	−	0.0693719i	−0.438718	−	0.898625i	$-0.644567\pi$
$317$	2.13931	−	1.23513i	0.120156	−	0.0693719i	0.558873	+	0.829253i	$0.311234\pi$
$318$	1.09797	−	6.12850i	0.0615710	−	0.343669i
$319$	4.50843	−	7.80883i	0.252424	−	0.437211i
$320$	−1.18212	+	5.44145i	−0.0660828	+	0.304186i
$321$	−6.39399	+	11.9676i	−0.356878	+	0.667967i
$322$	−14.0701	+	4.56002i	−0.784094	+	0.254120i
$323$			5.44449i			0.302939i
$324$	4.18878	+	17.5058i	0.232710	+	0.972546i
$325$			24.8597i			1.37897i
$326$	3.73552	+	11.5260i	0.206891	+	0.638368i
$327$	0.197847	−	0.370310i	0.0109410	−	0.0204782i
$328$	−2.13333	−	4.82058i	−0.117794	−	0.266172i
$329$	−6.13262	+	10.6220i	−0.338103	+	0.585611i
$330$	4.59704	+	0.823596i	0.253059	+	0.0453375i
$331$	24.4404	−	14.1107i	1.34336	−	0.775592i	0.356065	−	0.934461i	$-0.384118\pi$
$331$	24.4404	−	14.1107i	1.34336	−	0.775592i	0.987300	+	0.158869i	$0.0507848\pi$
$332$	−5.41889	+	12.1223i	−0.297400	+	0.665296i
$333$	−15.5996	+	10.4317i	−0.854854	+	0.571651i
$334$	3.52621	−	16.5288i	0.192946	−	0.904416i
$335$	−2.39422	−	4.14691i	−0.130810	−	0.226570i
$336$	10.5747	+	3.08937i	0.576897	+	0.168539i
$337$	5.60565	−	9.70927i	0.305359	−	0.528897i	−0.671982	−	0.740567i	$-0.734557\pi$
$337$	5.60565	−	9.70927i	0.305359	−	0.528897i	0.977341	+	0.211670i	$0.0678902\pi$
$338$	−18.1792	−	16.3932i	−0.988819	−	0.891675i
$339$	12.7888	−	7.95587i	0.694593	−	0.432103i
$340$	7.82588	−	0.810717i	0.424418	−	0.0439673i
$341$			20.2616i			1.09723i
$342$	−2.53149	+	3.20868i	−0.136887	+	0.173505i
$343$	18.2411			0.984929
$344$	1.04543	−	9.73669i	0.0563657	−	0.524967i
$345$	−7.92503	+	0.260901i	−0.426669	+	0.0140465i
$346$	−12.3546	+	13.7006i	−0.664188	+	0.736548i
$347$	17.8303	+	10.2943i	0.957180	+	0.552628i	0.895304	−	0.445455i	$-0.146958\pi$
$347$	17.8303	+	10.2943i	0.957180	+	0.552628i	0.0618763	+	0.998084i	$0.480292\pi$
$348$	9.01018	−	6.98901i	0.482996	−	0.374650i
$349$	2.93968	−	1.69723i	0.157358	−	0.0908505i	−0.419253	−	0.907869i	$-0.637708\pi$
$349$	2.93968	−	1.69723i	0.157358	−	0.0908505i	0.576611	+	0.817019i	$0.304375\pi$
$350$	−2.11864	+	9.93094i	−0.113246	+	0.530831i
$351$	11.7918	−	26.0634i	0.629401	−	1.39116i
$352$	7.69748	+	13.4482i	0.410277	+	0.716789i
$353$	−0.503241	−	0.871639i	−0.0267848	−	0.0463926i	0.852322	−	0.523017i	$-0.175194\pi$
$353$	−0.503241	−	0.871639i	−0.0267848	−	0.0463926i	−0.879107	+	0.476624i	$0.841860\pi$
$354$	9.98749	+	8.42731i	0.530829	+	0.447906i
$355$	−2.22040	−	1.28195i	−0.117847	−	0.0680388i
$356$	−4.83832	+	3.50422i	−0.256430	+	0.185723i
$357$	−0.512172	−	15.5575i	−0.0271070	−	0.823392i
$358$	1.44701	+	4.46479i	0.0764770	+	0.235972i
$359$	31.4772			1.66131			0.830653	−	0.556791i	$-0.187968\pi$
$359$	31.4772			1.66131			0.830653	+	0.556791i	$0.187968\pi$
$360$	4.98909	+	3.16095i	0.262948	+	0.166597i
$361$	18.0720			0.951158
$362$	−6.50216	−	20.0626i	−0.341746	−	1.05446i
$363$	−5.14264	+	3.19921i	−0.269918	+	0.167915i
$364$	−10.2701	−	14.1801i	−0.538299	−	0.743238i
$365$	−1.70712	−	0.985604i	−0.0893546	−	0.0515889i
$366$	−21.1168	+	7.62032i	−1.10379	+	0.398320i
$367$	−8.66667	−	15.0111i	−0.452397	−	0.783574i	0.546138	−	0.837695i	$-0.316098\pi$
$367$	−8.66667	−	15.0111i	−0.452397	−	0.783574i	−0.998534	+	0.0541214i	$0.982764\pi$
$368$	−17.5454	−	19.6036i	−0.914616	−	1.02191i
$369$	−5.57921	+	0.367747i	−0.290442	+	0.0191441i
$370$	−1.28472	+	6.02202i	−0.0667895	+	0.313070i
$371$	−3.50027	+	2.02088i	−0.181725	+	0.104919i
$372$	−9.68163	+	23.7241i	−0.501969	+	1.23004i
$373$	11.2742	+	6.50917i	0.583757	+	0.337032i	0.762625	−	0.646841i	$-0.223910\pi$
$373$	11.2742	+	6.50917i	0.583757	+	0.337032i	−0.178868	+	0.983873i	$0.557244\pi$
$374$	14.6620	−	16.2594i	0.758154	−	0.840752i
$375$	−5.40590	+	10.1182i	−0.279160	+	0.522503i
$376$	−21.6920	−	2.32907i	−1.11868	−	0.120113i
$377$	−18.1225			−0.933357
$378$	6.93183	−	9.40688i	0.356535	−	0.483838i
$379$			22.8643i			1.17446i	0.809421	+	0.587229i	$0.199781\pi$
$379$			22.8643i			1.17446i	−0.809421	+	0.587229i	$0.800219\pi$
$380$	0.138185	+	1.33390i	0.00708874	+	0.0684279i
$381$	−2.63914	−	1.41002i	−0.135207	−	0.0722377i
$382$	−7.68545	−	6.93041i	−0.393222	−	0.354590i
$383$	15.0117	−	26.0010i	0.767061	−	1.32859i	−0.172089	−	0.985081i	$-0.555052\pi$
$383$	15.0117	−	26.0010i	0.767061	−	1.32859i	0.939150	−	0.343508i	$-0.111615\pi$
$384$	2.58695	+	19.4244i	0.132015	+	0.991248i
$385$	−1.51588	−	2.62559i	−0.0772565	−	0.133812i
$386$	6.04020	−	28.3129i	0.307438	−	1.44109i
$387$	−9.31722	−	4.59047i	−0.473621	−	0.233347i
$388$	−4.55874	−	2.03785i	−0.231435	−	0.103456i
$389$	−32.9474	+	19.0222i	−1.67050	+	0.964463i	−0.703140	+	0.711051i	$0.748220\pi$
$389$	−32.9474	+	19.0222i	−1.67050	+	0.964463i	−0.967358	+	0.253412i	$0.918447\pi$
$390$	−3.18614	−	8.82916i	−0.161337	−	0.447082i
$391$	−18.5862	+	32.1922i	−0.939943	+	1.62803i
$392$	5.11821	+	11.5654i	0.258509	+	0.584139i
$393$	6.07425	+	9.76417i	0.306405	+	0.492537i
$394$	8.95728	+	27.6379i	0.451261	+	1.39238i
$395$		−	4.00742i		−	0.201635i
$396$	16.2010	−	2.76508i	0.814130	−	0.138950i
$397$		−	37.4510i		−	1.87961i	−0.341709	−	0.939806i	$-0.611006\pi$
$397$		−	37.4510i		−	1.87961i	0.341709	−	0.939806i	$-0.388994\pi$
$398$	−2.63141	+	0.852825i	−0.131901	+	0.0427483i
$399$	2.65175	−	0.0872987i	0.132753	−	0.00437040i
$400$	−17.6785	+	3.70252i	−0.883926	+	0.185126i
$401$	−2.35402	+	4.07728i	−0.117554	+	0.203610i	−0.918798	−	0.394728i	$-0.870839\pi$
$401$	−2.35402	+	4.07728i	−0.117554	+	0.203610i	0.801244	+	0.598338i	$0.204172\pi$
$402$	−12.8790	−	10.8671i	−0.642346	−	0.542003i
$403$	35.2669	−	20.3613i	1.75677	−	1.01427i
$404$	−7.74837	+	17.3334i	−0.385496	+	0.862369i
$405$	4.96708	−	3.81720i	0.246816	−	0.189678i
$406$	−7.23958	−	1.54447i	−0.359294	−	0.0766508i
$407$	8.56739	+	14.8391i	0.424670	+	0.735549i
$408$	24.9368	−	12.0320i	1.23456	−	0.595671i
$409$	5.36377	−	9.29032i	0.265221	−	0.459377i	−0.702400	−	0.711782i	$-0.747888\pi$
$409$	5.36377	−	9.29032i	0.265221	−	0.459377i	0.967622	+	0.252405i	$0.0812216\pi$
$410$	−1.22862	+	1.36247i	−0.0606771	+	0.0672876i
$411$	0.206675	+	6.27787i	0.0101945	+	0.309664i
$412$	−3.03861	−	29.3318i	−0.149702	−	1.44508i
$413$		−	8.48324i		−	0.417433i
$414$	−25.9218	+	10.3304i	−1.27399	+	0.507711i
$415$	4.62117			0.226844
$416$	15.6722	−	26.9124i	0.768392	−	1.31949i
$417$	15.8382	+	25.4594i	0.775598	+	1.24675i
$418$	2.77138	+	2.49911i	0.135552	+	0.122235i
$419$	−3.57600	−	2.06460i	−0.174699	−	0.100863i	0.410101	−	0.912040i	$-0.365494\pi$
$419$	−3.57600	−	2.06460i	−0.174699	−	0.100863i	−0.584800	+	0.811178i	$0.698827\pi$
$420$	−0.520343	−	3.79861i	−0.0253902	−	0.185353i
$421$	−13.7321	+	7.92824i	−0.669262	+	0.386399i	−0.795797	−	0.605563i	$-0.792948\pi$
$421$	−13.7321	+	7.92824i	−0.669262	+	0.386399i	0.126535	+	0.991962i	$0.459614\pi$
$422$	14.5489	+	3.10381i	0.708227	+	0.151091i
$423$	−10.2270	+	20.7575i	−0.497251	+	1.00926i
$424$	−5.80675	−	4.23876i	−0.282001	−	0.205852i
$425$	12.7603	+	22.1015i	0.618965	+	1.07208i
$426$	−8.88132	−	1.59116i	−0.430301	−	0.0770918i
$427$	12.6211	+	7.28679i	0.610778	+	0.352633i
$428$	9.19028	+	12.6892i	0.444229	+	0.613353i
$429$	−23.0381	−	12.3086i	−1.11229	−	0.594267i
$430$	−3.24205	+	1.05073i	−0.156346	+	0.0506708i
$431$	16.1853			0.779619			0.389810	−	0.920895i	$-0.372541\pi$
$431$	16.1853			0.779619			0.389810	+	0.920895i	$0.372541\pi$
$432$	20.2908	+	4.50374i	0.976241	+	0.216686i
$433$	−32.8306			−1.57774			−0.788868	−	0.614563i	$-0.789332\pi$
$433$	−32.8306			−1.57774			−0.788868	+	0.614563i	$0.789332\pi$
$434$	15.8237	−	5.12836i	0.759561	−	0.246169i
$435$	−3.50027	−	1.87011i	−0.167825	−	0.0896647i
$436$	−0.284372	−	0.392636i	−0.0136190	−	0.0188039i
$437$	−5.48709	−	3.16797i	−0.262483	−	0.151545i
$438$	−6.82825	−	1.22333i	−0.326266	−	0.0584532i
$439$	10.9273	+	18.9267i	0.521533	+	0.903321i	0.999686	+	0.0250450i	$0.00797290\pi$
$439$	10.9273	+	18.9267i	0.521533	+	0.903321i	−0.478154	+	0.878276i	$0.658694\pi$
$440$	3.17953	−	4.35569i	0.151578	−	0.207650i
$441$	13.3854	−	0.882284i	0.637401	−	0.0420135i
$442$	−43.0349	−	9.18095i	−2.04696	−	0.436693i
$443$	30.4500	−	17.5803i	1.44672	−	0.835265i	0.448436	−	0.893815i	$-0.351981\pi$
$443$	30.4500	−	17.5803i	1.44672	−	0.835265i	0.998284	+	0.0585501i	$0.0186477\pi$
$444$	2.94085	+	21.4688i	0.139567	+	1.01886i
$445$	1.80055	+	1.03955i	0.0853543	+	0.0492793i
$446$	−4.05671	−	3.65817i	−0.192091	−	0.173219i
$447$	−19.7821	−	31.7991i	−0.935660	−	1.50405i
$448$	8.55431	−	9.41533i	0.404153	−	0.444833i
$449$	3.21851			0.151891			0.0759453	−	0.997112i	$-0.475803\pi$
$449$	3.21851			0.151891			0.0759453	+	0.997112i	$0.475803\pi$
$450$	−2.75616	+	18.9584i	−0.129927	+	0.893709i
$451$			5.10526i			0.240397i
$452$	−1.79208	−	17.2990i	−0.0842921	−	0.813675i
$453$	−0.723798	−	21.9858i	−0.0340070	−	1.03298i
$454$	−15.2209	+	16.8792i	−0.714354	+	0.792180i
$455$	−3.04669	+	5.27703i	−0.142831	+	0.247391i
$456$	2.05082	+	4.25043i	0.0960386	+	0.199045i
$457$	4.05512	+	7.02368i	0.189691	+	0.328554i	0.945147	−	0.326645i	$-0.105918\pi$
$457$	4.05512	+	7.02368i	0.189691	+	0.328554i	−0.755456	+	0.655199i	$0.772585\pi$
$458$	−11.9191	−	2.54279i	−0.556944	−	0.118817i
$459$	−2.89467	−	29.2243i	−0.135112	−	1.36408i
$460$	−3.73657	+	8.35884i	−0.174218	+	0.389733i
$461$	18.1813	−	10.4970i	0.846789	−	0.488894i	−0.0127771	−	0.999918i	$-0.504067\pi$
$461$	18.1813	−	10.4970i	0.846789	−	0.488894i	0.859566	+	0.511024i	$0.170734\pi$
$462$	−8.15425	−	6.88045i	−0.379370	−	0.320107i
$463$	−4.45005	+	7.70772i	−0.206812	+	0.358208i	−0.950708	−	0.310086i	$-0.899642\pi$
$463$	−4.45005	+	7.70772i	−0.206812	+	0.358208i	0.743897	+	0.668294i	$0.232975\pi$
$464$	−2.69911	−	12.8875i	−0.125303	−	0.598287i
$465$	8.91276	−	0.293419i	0.413319	−	0.0136070i
$466$	−32.4943	+	10.5312i	−1.50527	+	0.487849i
$467$			26.0527i			1.20557i	0.797902	+	0.602787i	$0.205943\pi$
$467$			26.0527i			1.20557i	−0.797902	+	0.602787i	$0.794057\pi$
$468$	−21.0936	−	25.4204i	−0.975051	−	1.17506i
$469$			10.9392i			0.505128i
$470$	2.34089	+	7.22285i	0.107977	+	0.333165i
$471$	−15.9825	−	25.6913i	−0.736433	−	1.18379i
$472$	13.7986	−	6.10655i	0.635134	−	0.281077i
$473$	−4.74188	+	8.21317i	−0.218032	+	0.377642i
$474$	−4.78702	−	13.2654i	−0.219875	−	0.609299i
$475$	−3.76715	+	2.17496i	−0.172849	+	0.0997942i
$476$	−16.4091	−	7.33521i	−0.752112	−	0.336209i
$477$	−6.33869	+	4.23876i	−0.290229	+	0.194080i
$478$	1.18907	−	5.57365i	0.0543866	−	0.254933i
$479$	8.71143	+	15.0886i	0.398035	+	0.689418i	0.993483	−	0.113976i	$-0.0363588\pi$
$479$	8.71143	+	15.0886i	0.398035	+	0.689418i	−0.595448	+	0.803394i	$0.703025\pi$
$480$	5.80417	−	3.58076i	0.264923	−	0.163438i
$481$	17.2191	−	29.8244i	0.785125	−	1.35988i
$482$	−5.91608	−	5.33487i	−0.269470	−	0.242997i
$483$	15.9773	+	8.53624i	0.726991	+	0.388412i
$484$	0.720629	+	6.95626i	0.0327559	+	0.316194i
$485$			1.73785i			0.0789118i
$486$	11.8823	−	18.5691i	0.538991	−	0.842312i
$487$	−29.7367			−1.34750			−0.673750	−	0.738959i	$-0.735318\pi$
$487$	−29.7367			−1.34750			−0.673750	+	0.738959i	$0.735318\pi$
$488$	−2.76741	+	25.7745i	−0.125275	+	1.16676i
$489$	6.99279	−	13.0884i	0.316225	−	0.591878i
$490$	2.94765	−	3.26879i	0.133161	−	0.147669i
$491$	−20.6346	−	11.9134i	−0.931229	−	0.537645i	−0.0440286	−	0.999030i	$-0.514019\pi$
$491$	−20.6346	−	11.9134i	−0.931229	−	0.537645i	−0.887200	+	0.461385i	$0.847353\pi$
$492$	−2.43945	+	5.97769i	−0.109979	+	0.269495i
$493$	−16.1118	+	9.30215i	−0.725639	+	0.418948i
$494$	1.56487	−	7.33521i	0.0704070	−	0.330027i
$495$	−3.17953	−	4.75471i	−0.142909	−	0.213708i
$496$	19.7321	+	22.0469i	0.885999	+	0.989933i
$497$	2.92863	+	5.07254i	0.131367	+	0.227534i
$498$	15.2970	−	5.52017i	0.685476	−	0.247365i
$499$	16.8622	+	9.73540i	0.754856	+	0.435816i	0.827446	−	0.561546i	$-0.189793\pi$
$499$	16.8622	+	9.73540i	0.754856	+	0.435816i	−0.0725899	+	0.997362i	$0.523126\pi$
$500$	7.77008	+	10.7283i	0.347488	+	0.479782i
$501$	−17.5757	+	10.9338i	−0.785226	+	0.488485i
$502$	6.05307	+	18.6769i	0.270162	+	0.833590i
$503$	1.23494			0.0550631			0.0275316	−	0.999621i	$-0.491235\pi$
$503$	1.23494			0.0550631			0.0275316	+	0.999621i	$0.491235\pi$
$504$	−6.26003	−	11.9526i	−0.278844	−	0.532411i
$505$	6.60772			0.294040
$506$	7.85524	+	24.2375i	0.349208	+	1.07749i
$507$	0.986461	+	29.9643i	0.0438103	+	1.33076i
$508$	−2.79825	+	2.02667i	−0.124152	+	0.0899190i
$509$	−0.392870	−	0.226823i	−0.0174136	−	0.0100538i	0.491268	−	0.871009i	$-0.336534\pi$
$509$	−0.392870	−	0.226823i	−0.0174136	−	0.0100538i	−0.508682	+	0.860955i	$0.669867\pi$
$510$	−7.36458	−	6.21413i	−0.326109	−	0.275166i
$511$	2.25163	+	3.89993i	0.0996061	+	0.172523i
$512$	21.4725	+	7.13674i	0.948958	+	0.315403i
$513$	4.98123	−	0.493390i	0.219927	−	0.0217837i
$514$	3.20168	−	15.0076i	0.141220	−	0.661957i
$515$	−8.88784	+	5.13140i	−0.391645	+	0.226116i
$516$	−9.47673	+	7.35090i	−0.417190	+	0.323605i
$517$	18.2978	+	10.5643i	0.804737	+	0.464615i
$518$	9.42045	−	10.4468i	0.413911	−	0.459005i
$519$	22.5823	−	0.743436i	0.991254	−	0.0326332i
$520$	−10.7766	−	1.15708i	−0.472586	−	0.0507415i
$521$	−29.0873			−1.27434			−0.637170	−	0.770724i	$-0.719895\pi$
$521$	−29.0873			−1.27434			−0.637170	+	0.770724i	$0.719895\pi$
$522$	−13.8205	−	2.00922i	−0.604909	−	0.0879411i
$523$			2.95874i			0.129377i	0.997906	+	0.0646883i	$0.0206053\pi$
$523$			2.95874i			0.129377i	−0.997906	+	0.0646883i	$0.979395\pi$
$524$	13.2076	−	1.36824i	0.576979	−	0.0597717i
$525$	10.5600	−	6.56930i	0.460874	−	0.286708i
$526$	24.3766	+	21.9818i	1.06287	+	0.958452i
$527$	20.9026	−	36.2044i	0.910534	−	1.57709i
$528$	5.32185	−	18.2163i	0.231604	−	0.792763i
$529$	−10.1294	−	17.5446i	−0.440407	−	0.762808i
$530$	−0.522029	+	2.44697i	−0.0226755	+	0.106289i
$531$	−1.05265	−	15.9702i	−0.0456813	−	0.693046i
$532$	1.25027	−	2.79690i	0.0542061	−	0.121261i
$533$	8.88610	−	5.13039i	0.384900	−	0.222222i
$534$	7.20198	+	1.29029i	0.311660	+	0.0558363i
$535$	2.72636	−	4.72219i	0.117871	−	0.204158i
$536$	−17.7935	+	7.87447i	−0.768564	+	0.340125i
$537$	2.70877	−	5.07000i	0.116892	−	0.218787i
$538$	1.75262	+	5.40774i	0.0755607	+	0.233144i
$539$		−	12.2483i		−	0.527573i
$540$	−1.45093	−	7.08652i	−0.0624381	−	0.304955i
$541$		−	14.9753i		−	0.643838i	−0.946767	−	0.321919i	$-0.895672\pi$
$541$		−	14.9753i		−	0.643838i	0.946767	−	0.321919i	$-0.104328\pi$
$542$	9.08929	−	2.94578i	0.390418	−	0.126532i
$543$	−12.1719	+	22.7821i	−0.522345	+	0.977672i
$544$	0.119385	−	31.9709i	0.00511861	−	1.37074i
$545$	−0.0843608	+	0.146117i	−0.00361362	+	0.00625897i
$546$	−3.78156	+	21.1074i	−0.161836	+	0.903315i
$547$	−15.7731	+	9.10661i	−0.674409	+	0.389370i	−0.797745	−	0.602995i	$-0.793974\pi$
$547$	−15.7731	+	9.10661i	−0.674409	+	0.389370i	0.123336	+	0.992365i	$0.460641\pi$
$548$	6.62152	+	2.95995i	0.282857	+	0.126443i
$549$	24.6641	+	12.1517i	1.05264	+	0.518621i
$550$	17.1074	+	3.64964i	0.729460	+	0.155621i
$551$	−1.58553	−	2.74622i	−0.0675459	−	0.116993i
$552$	−2.38384	+	32.1330i	−0.101463	+	1.36767i
$553$	−4.57750	+	7.92846i	−0.194655	+	0.337153i
$554$	−2.00778	+	2.22652i	−0.0853025	+	0.0945958i
$555$	6.40345	−	3.98356i	0.271811	−	0.169093i
$556$	34.4380	−	3.56758i	1.46049	−	0.151299i
$557$			35.7359i			1.51418i	0.653310	+	0.757090i	$0.273380\pi$
$557$			35.7359i			1.51418i	−0.653310	+	0.757090i	$0.726620\pi$
$558$	29.1526	−	11.6179i	1.23413	−	0.491826i
$559$	19.0609			0.806190
$560$	−4.20643	−	1.38066i	−0.177754	−	0.0583434i
$561$	−26.7999	+	0.882284i	−1.13149	+	0.0372501i
$562$	27.4286	+	24.7339i	1.15700	+	1.04334i
$563$	8.04256	+	4.64337i	0.338953	+	0.195695i	0.659809	−	0.751433i	$-0.270637\pi$
$563$	8.04256	+	4.64337i	0.338953	+	0.195695i	−0.320856	+	0.947128i	$0.603970\pi$
$564$	16.3768	+	21.1129i	0.689588	+	0.889012i
$565$	−5.24176	+	3.02633i	−0.220523	+	0.127319i
$566$	26.4114	+	5.63454i	1.11016	+	0.236838i
$567$	−14.1873	+	1.87845i	−0.595813	+	0.0788873i
$568$	−6.14274	+	8.41504i	−0.257744	+	0.353087i
$569$	−5.66727	−	9.81599i	−0.237584	−	0.411508i	0.722436	−	0.691437i	$-0.243022\pi$
$569$	−5.66727	−	9.81599i	−0.237584	−	0.411508i	−0.960021	+	0.279930i	$0.909689\pi$
$570$	1.05919	−	1.25528i	0.0443644	−	0.0525778i
$571$	−37.7843	−	21.8148i	−1.58122	−	0.912920i	−0.994681	−	0.103002i	$-0.967155\pi$
$571$	−37.7843	−	21.8148i	−1.58122	−	0.912920i	−0.586543	−	0.809918i	$-0.699511\pi$
$572$	−24.4270	+	17.6916i	−1.02135	+	0.739723i
$573$	0.417036	+	12.6677i	0.0174219	+	0.529201i
$574$	3.98705	−	1.29218i	0.166416	−	0.0539345i
$575$	−29.6992			−1.23854
$576$	14.9356	−	18.7863i	0.622318	−	0.782764i
$577$	6.98123			0.290632			0.145316	−	0.989385i	$-0.453580\pi$
$577$	6.98123			0.290632			0.145316	+	0.989385i	$0.453580\pi$
$578$	−20.1022	+	6.51499i	−0.836139	+	0.270988i
$579$	−30.1062	+	18.7289i	−1.25117	+	0.778348i
$580$	−3.71131	+	2.68796i	−0.154104	+	0.111612i
$581$	−9.14274	−	5.27856i	−0.379305	−	0.218992i
$582$	2.07593	+	5.75264i	0.0860502	+	0.238455i
$583$	3.48124	+	6.02968i	0.144178	+	0.249724i
$584$	−4.72274	+	6.46976i	−0.195428	+	0.267721i
$585$	−5.08076	+	10.3123i	−0.210063	+	0.426363i
$586$	8.09892	+	1.72780i	0.334563	+	0.0713749i
$587$	−7.34574	+	4.24107i	−0.303191	+	0.175048i	−0.643876	−	0.765130i	$-0.722675\pi$
$587$	−7.34574	+	4.24107i	−0.303191	+	0.175048i	0.340684	+	0.940178i	$0.389341\pi$
$588$	5.85264	−	14.3415i	0.241359	−	0.591431i
$589$	6.17097	+	3.56281i	0.254270	+	0.146803i
$590$	−3.89999	−	3.51685i	−0.160560	−	0.144786i
$591$	16.7678	−	31.3842i	0.689734	−	1.29097i
$592$	23.7737	+	7.80313i	0.977092	+	0.320707i
$593$	−9.40869			−0.386368			−0.193184	−	0.981163i	$-0.561881\pi$
$593$	−9.40869			−0.386368			−0.193184	+	0.981163i	$0.561881\pi$
$594$	−16.2046	−	11.9410i	−0.664882	−	0.489945i
$595$			6.25538i			0.256445i
$596$	−43.0135	+	4.45595i	−1.76190	+	0.182523i
$597$	2.98810	+	1.59647i	0.122295	+	0.0653390i
$598$	34.2934	−	38.0295i	1.40236	−	1.55514i
$599$	−14.9623	+	25.9155i	−0.611344	+	1.05888i	0.379670	+	0.925122i	$0.376038\pi$
$599$	−14.9623	+	25.9155i	−0.611344	+	1.05888i	−0.991014	+	0.133757i	$0.957296\pi$
$600$	18.2869	+	12.4478i	0.746560	+	0.508178i
$601$	1.81973	+	3.15186i	0.0742282	+	0.128567i	0.900750	−	0.434337i	$-0.143017\pi$
$601$	1.81973	+	3.15186i	0.0742282	+	0.128567i	−0.826522	+	0.562904i	$0.809684\pi$
$602$	7.61444	+	1.62444i	0.310342	+	0.0662074i
$603$	1.35741	+	20.5937i	0.0552781	+	0.838641i
$604$	−23.1893	−	10.3661i	−0.943558	−	0.421789i
$605$	2.10782	−	1.21695i	0.0856950	−	0.0494760i
$606$	21.8729	−	7.89318i	0.888526	−	0.320639i
$607$	3.63358	−	6.29355i	0.147482	−	0.255447i	−0.782814	−	0.622256i	$-0.786216\pi$
$607$	3.63358	−	6.29355i	0.147482	−	0.255447i	0.930296	+	0.366809i	$0.119550\pi$
$608$	5.44937	+	0.0203490i	0.221001	+	0.000825260i
$609$	4.78897	+	7.69812i	0.194059	+	0.311944i
$610$	8.58221	−	2.78144i	0.347483	−	0.112617i
$611$		−	42.4651i		−	1.71795i
$612$	−31.8013	−	11.7728i	−1.28549	−	0.475886i
$613$		−	32.6469i		−	1.31859i	−0.751882	−	0.659297i	$-0.770854\pi$
$613$		−	32.6469i		−	1.31859i	0.751882	−	0.659297i	$-0.229146\pi$
$614$	−5.97645	−	18.4405i	−0.241190	−	0.744197i
$615$	2.24572	−	0.0739319i	0.0905563	−	0.00298122i
$616$	−11.2659	+	4.98567i	−0.453914	+	0.200878i
$617$	15.6751	−	27.1501i	0.631056	−	1.09302i	−0.356280	−	0.934379i	$-0.615955\pi$
$617$	15.6751	−	27.1501i	0.631056	−	1.09302i	0.987336	−	0.158642i	$-0.0507115\pi$
$618$	−23.2909	+	27.6029i	−0.936898	+	1.11035i
$619$	−1.72589	+	0.996445i	−0.0693695	+	0.0400505i	−0.534284	−	0.845305i	$-0.679419\pi$
$619$	−1.72589	+	0.996445i	−0.0693695	+	0.0400505i	0.464914	+	0.885356i	$0.346085\pi$
$620$	4.20227	−	9.40065i	0.168767	−	0.377539i
$621$	31.1373	+	14.0874i	1.24950	+	0.565307i
$622$	5.65332	−	26.4994i	0.226677	−	1.06253i
$623$	−2.37486	−	4.11339i	−0.0951469	−	0.164799i
$624$	−37.0550	+	9.04290i	−1.48339	+	0.362006i
$625$	−8.98375	+	15.5603i	−0.359350	+	0.622413i
$626$	26.4880	+	23.8858i	1.05867	+	0.954668i
$627$	−0.150383	−	4.56798i	−0.00600574	−	0.182428i
$628$	−34.7517	+	3.60008i	−1.38675	+	0.143659i
$629$		−	35.3538i		−	1.40965i
$630$	−2.90852	+	3.68657i	−0.115878	+	0.146876i
$631$	−15.4643			−0.615623			−0.307812	−	0.951447i	$-0.599597\pi$
$631$	−15.4643			−0.615623			−0.307812	+	0.951447i	$0.599597\pi$
$632$	−16.1913	−	1.73846i	−0.644056	−	0.0691523i
$633$	−9.62404	−	15.4704i	−0.382521	−	0.614892i
$634$	−2.33953	+	2.59441i	−0.0929147	+	0.103037i
$635$	1.04135	+	0.601225i	0.0413248	+	0.0238589i
$636$	1.19497	+	8.72354i	0.0473838	+	0.345911i
$637$	−21.3192	+	12.3086i	−0.844697	+	0.487686i
$638$	−2.66056	+	12.4711i	−0.105332	+	0.493737i
$639$	6.14274	+	9.18592i	0.243003	+	0.363390i
$640$	−0.782194	−	7.83593i	−0.0309189	−	0.309742i
$641$	−12.3638	−	21.4147i	−0.488340	−	0.845829i	0.511570	−	0.859241i	$-0.329064\pi$
$641$	−12.3638	−	21.4147i	−0.488340	−	0.845829i	−0.999910	+	0.0134123i	$0.995731\pi$
$642$	3.38396	−	18.8882i	0.133554	−	0.745456i
$643$	−40.0176	−	23.1042i	−1.57814	−	0.911141i	−0.995119	−	0.0986850i	$-0.968536\pi$
$643$	−40.0176	−	23.1042i	−1.57814	−	0.911141i	−0.583023	−	0.812456i	$-0.698130\pi$
$644$	16.9406	−	12.2694i	0.667551	−	0.483483i
$645$	3.68152	+	1.96694i	0.144960	+	0.0774482i
$646$	−2.37386	−	7.32460i	−0.0933983	−	0.288182i
$647$	−6.36971			−0.250419			−0.125210	−	0.992130i	$-0.539960\pi$
$647$	−6.36971			−0.250419			−0.125210	+	0.992130i	$0.539960\pi$
$648$	−13.2680	−	21.7246i	−0.521216	−	0.853425i
$649$	−14.6135			−0.573630
$650$	−10.8391	−	33.4443i	−0.425145	−	1.31179i
$651$	−17.9686	−	9.60016i	−0.704245	−	0.376260i
$652$	−10.0510	−	13.8775i	−0.393626	−	0.543485i
$653$	31.8848	+	18.4087i	1.24775	+	0.720389i	0.970660	−	0.240455i	$-0.0772968\pi$
$653$	31.8848	+	18.4087i	1.24775	+	0.720389i	0.277090	+	0.960844i	$0.410630\pi$
$654$	−0.104709	+	0.584450i	−0.00409444	+	0.0228538i
$655$	−2.31058	−	4.00205i	−0.0902820	−	0.156373i
$656$	4.97185	+	5.55509i	0.194118	+	0.216890i
$657$	4.72274	+	7.06244i	0.184252	+	0.275532i
$658$	3.61904	−	16.9639i	0.141085	−	0.661323i
$659$	6.46565	−	3.73294i	0.251866	−	0.145415i	−0.368752	−	0.929528i	$-0.620215\pi$
$659$	6.46565	−	3.73294i	0.251866	−	0.145415i	0.620618	+	0.784113i	$0.286882\pi$
$660$	−6.54360	+	0.896360i	−0.254709	+	0.0348908i
$661$	2.51984	+	1.45483i	0.0980102	+	0.0565862i	0.548204	−	0.836345i	$-0.315312\pi$
$661$	2.51984	+	1.45483i	0.0980102	+	0.0565862i	−0.450194	+	0.892931i	$0.648645\pi$
$662$	−26.7278	+	29.6397i	−1.03881	+	1.15198i
$663$	28.4675	+	45.7607i	1.10559	+	1.77720i
$664$	2.00471	−	18.6711i	0.0777980	−	0.724578i
$665$	−1.06622			−0.0413461
$666$	16.4382	−	20.8356i	0.636968	−	0.807362i
$667$		−	21.6505i		−	0.838310i
$668$	2.46286	+	23.7741i	0.0952908	+	0.919846i
$669$	0.220130	+	6.68657i	0.00851071	+	0.258518i
$670$	5.02909	+	4.53502i	0.194291	+	0.175203i
$671$	12.5525	−	21.7415i	0.484582	−	0.839321i
$672$	−15.5734	+	0.454485i	−0.600757	+	0.0175321i
$673$	21.0527	+	36.4643i	0.811522	+	1.40560i	0.911799	+	0.410637i	$0.134694\pi$
$673$	21.0527	+	36.4643i	0.811522	+	1.40560i	−0.100277	+	0.994960i	$0.531973\pi$
$674$	−3.30806	+	15.5062i	−0.127422	+	0.597278i
$675$	19.0645	−	13.6774i	0.733794	−	0.526444i
$676$	31.6046	+	14.1279i	1.21556	+	0.543379i
$677$	32.9941	−	19.0492i	1.26807	−	0.732119i	0.293445	−	0.955976i	$-0.405198\pi$
$677$	32.9941	−	19.0492i	1.26807	−	0.732119i	0.974622	+	0.223858i	$0.0718650\pi$
$678$	−13.7362	+	16.2793i	−0.527537	+	0.625202i
$679$	1.98507	−	3.43825i	0.0761801	−	0.131948i
$680$	−10.1749	+	4.50285i	−0.390188	+	0.172676i
$681$	27.8215	−	0.915918i	1.06612	−	0.0350981i
$682$	−8.83428	−	27.2584i	−0.338282	−	1.04378i
$683$			47.0728i			1.80119i	0.434659	+	0.900595i	$0.356869\pi$
$683$			47.0728i			1.80119i	−0.434659	+	0.900595i	$0.643131\pi$
$684$	2.00665	−	5.42046i	0.0767260	−	0.207257i
$685$		−	2.52421i		−	0.0964450i
$686$	−24.5402	+	7.95335i	−0.936951	+	0.303660i
$687$	7.88448	+	12.6741i	0.300812	+	0.483546i
$688$	2.83887	+	13.5548i	0.108231	+	0.516772i
$689$	6.99676	−	12.1187i	0.266555	−	0.461687i
$690$	10.5480	−	3.80640i	0.401554	−	0.144907i
$691$	3.38522	−	1.95446i	0.128780	−	0.0743512i	−0.434226	−	0.900804i	$-0.642978\pi$
$691$	3.38522	−	1.95446i	0.128780	−	0.0743512i	0.563006	+	0.826453i	$0.309645\pi$
$692$	10.6473	−	23.8185i	0.404750	−	0.905442i
$693$	0.859436	+	13.0388i	0.0326473	+	0.495302i
$694$	−28.4760	−	6.07498i	−1.08093	−	0.230603i
$695$	−6.02468	−	10.4350i	−0.228529	−	0.395824i
$696$	−9.07432	+	13.3310i	−0.343961	+	0.505311i
$697$	5.26678	−	9.12234i	0.199494	−	0.345533i
$698$	−3.21481	+	3.56505i	−0.121683	+	0.134939i
$699$	36.8990	+	19.7142i	1.39565	+	0.745658i
$700$	−1.47975	−	14.2841i	−0.0559292	−	0.539887i
$701$		−	16.4480i		−	0.621231i	−0.950536	−	0.310615i	$-0.899465\pi$
$701$		−	16.4480i		−	0.621231i	0.950536	−	0.310615i	$-0.100535\pi$
$702$	−4.49985	+	40.2051i	−0.169836	+	1.51744i
$703$	6.02598			0.227274
$704$	−16.2192	−	14.7359i	−0.611282	−	0.555381i
$705$	4.38207	−	8.20192i	0.165038	−	0.308902i
$706$	1.05707	+	0.953217i	0.0397832	+	0.0358748i
$707$	−13.0730	−	7.54772i	−0.491662	−	0.283861i
$708$	−17.1108	−	6.98279i	−0.643063	−	0.262429i
$709$	−6.84805	+	3.95372i	−0.257184	+	0.148485i	−0.623049	−	0.782183i	$-0.714106\pi$
$709$	−6.84805	+	3.95372i	−0.257184	+	0.148485i	0.365865	+	0.930668i	$0.380773\pi$
$710$	3.54610	+	0.756515i	0.133083	+	0.0283915i
$711$	−7.63358	+	15.4938i	−0.286282	+	0.581062i
$712$	4.98123	−	6.82387i	0.186679	−	0.255735i
$713$	24.3251	+	42.1324i	0.910984	+	1.57787i
$714$	7.47230	+	20.7066i	0.279644	+	0.774925i
$715$	9.09037	+	5.24833i	0.339961	+	0.196276i
$716$	−3.89340	−	5.37567i	−0.145503	−	0.200898i
$717$	−5.92668	+	3.68696i	−0.221336	+	0.137692i
$718$	−42.3471	+	13.7244i	−1.58038	+	0.512191i
$719$	−37.0556			−1.38194			−0.690970	−	0.722884i	$-0.742816\pi$
$719$	−37.0556			−1.38194			−0.690970	+	0.722884i	$0.742816\pi$
$720$	−8.09015	−	2.07720i	−0.301502	−	0.0774128i
$721$	23.4455			0.873156
$722$	−24.3127	+	7.87960i	−0.904824	+	0.293248i
$723$	0.321025	+	9.75131i	0.0119390	+	0.362655i
$724$	17.4950	+	24.1556i	0.650197	+	0.897736i
$725$	−12.8727	−	7.43204i	−0.478079	−	0.276019i
$726$	5.52362	−	6.54622i	0.205001	−	0.242953i
$727$	2.83467	+	4.90979i	0.105132	+	0.182094i	0.913792	−	0.406182i	$-0.133140\pi$
$727$	2.83467	+	4.90979i	0.105132	+	0.182094i	−0.808660	+	0.588276i	$0.799807\pi$
$728$	19.9993	+	14.5989i	0.741222	+	0.541071i
$729$	−26.4754	+	5.29673i	−0.980569	+	0.196175i
$730$	2.72636	+	0.581634i	0.100907	+	0.0215272i
$731$	16.9461	−	9.78381i	0.626773	−	0.361867i
$732$	25.0863	−	19.4589i	0.927217	−	0.719223i
$733$	10.8544	+	6.26677i	0.400915	+	0.231469i	0.686879	−	0.726772i	$-0.258980\pi$
$733$	10.8544	+	6.26677i	0.400915	+	0.231469i	−0.285964	+	0.958240i	$0.592314\pi$
$734$	18.2045	+	16.4160i	0.671940	+	0.605927i
$735$	−5.38786	+	0.177375i	−0.198734	+	0.00654256i
$736$	32.1516	+	18.7231i	1.18512	+	0.690144i
$737$	18.8443			0.694139
$738$	7.34549	−	2.92734i	0.270391	−	0.107757i
$739$		−	1.83358i		−	0.0674492i	−0.999431	−	0.0337246i	$-0.989263\pi$
$739$		−	1.83358i		−	0.0674492i	0.999431	−	0.0337246i	$-0.0107369\pi$
$740$	−0.897304	−	8.66172i	−0.0329856	−	0.318411i
$741$	−7.79981	+	4.85223i	−0.286533	+	0.178251i
$742$	3.82787	−	4.24490i	0.140526	−	0.155835i
$743$	−15.6588	+	27.1219i	−0.574467	+	0.995006i	0.421632	+	0.906767i	$0.361457\pi$
$743$	−15.6588	+	27.1219i	−0.574467	+	0.995006i	−0.996099	+	0.0882391i	$0.971876\pi$
$744$	2.68094	−	36.1379i	0.0982882	−	1.32488i
$745$	7.52491	+	13.0335i	0.275691	+	0.477511i
$746$	−18.0055	−	3.84125i	−0.659230	−	0.140638i
$747$	−17.8667	−	8.80269i	−0.653708	−	0.322074i
$748$	−12.6359	+	28.2669i	−0.462013	+	1.03354i
$749$	−10.7879	+	6.22841i	−0.394182	+	0.227581i
$750$	2.86103	−	15.9693i	0.104470	−	0.583117i
$751$	3.64466	−	6.31274i	0.132996	−	0.230355i	−0.791834	−	0.610736i	$-0.790874\pi$
$751$	3.64466	−	6.31274i	0.132996	−	0.230355i	0.924830	+	0.380381i	$0.124207\pi$
$752$	30.1983	−	6.32461i	1.10122	−	0.230635i
$753$	11.3312	−	21.2086i	0.412931	−	0.772883i
$754$	24.3806	−	7.90162i	0.887890	−	0.287760i
$755$			8.84005i			0.321722i
$756$	−5.22404	+	15.6776i	−0.189996	+	0.570190i
$757$		−	12.8156i		−	0.465792i	−0.972502	−	0.232896i	$-0.925180\pi$
$757$		−	12.8156i		−	0.465792i	0.972502	−	0.232896i	$-0.0748202\pi$
$758$	−9.96908	−	30.7598i	−0.362093	−	1.11725i
$759$	14.7048	−	27.5230i	0.533750	−	0.999020i
$760$	−0.767501	−	1.73428i	−0.0278402	−	0.0629090i
$761$	12.5800	−	21.7892i	0.456025	−	0.789859i	−0.542721	−	0.839913i	$-0.682606\pi$
$761$	12.5800	−	21.7892i	0.456025	−	0.789859i	0.998747	+	0.0500541i	$0.0159394\pi$
$762$	4.16528	+	0.746242i	0.150892	+	0.0270335i
$763$	0.333807	−	0.192724i	0.0120846	−	0.00697706i
$764$	13.3611	+	5.97269i	0.483389	+	0.216084i
$765$	0.776207	+	11.7761i	0.0280638	+	0.425765i
$766$	−8.85883	+	41.5250i	−0.320083	+	1.50036i
$767$	14.6854	+	25.4359i	0.530261	+	0.918439i
$768$	−11.9495	−	25.0042i	−0.431192	−	0.902260i
$769$	−10.7318	+	18.5880i	−0.386998	+	0.670300i	−0.992044	−	0.125890i	$-0.959821\pi$
$769$	−10.7318	+	18.5880i	−0.386998	+	0.670300i	0.605046	+	0.796190i	$0.293155\pi$
$770$	3.18414	+	2.87132i	0.114748	+	0.103475i
$771$	−15.9582	+	9.92750i	−0.574719	+	0.357530i
$772$	4.21873	+	40.7236i	0.151835	+	1.46567i
$773$			20.2122i			0.726981i	0.931598	+	0.363491i	$0.118415\pi$
$773$			20.2122i			0.726981i	−0.931598	+	0.363491i	$0.881585\pi$
$774$	14.5362	+	2.11326i	0.522492	+	0.0759594i
$775$	33.4007			1.19979
$776$	7.02150	+	0.753899i	0.252057	+	0.0270634i
$777$	−17.2191	+	0.566874i	−0.617733	+	0.0203365i
$778$	36.0310	−	39.9564i	1.29177	−	1.43251i
$779$	1.55488	+	0.897712i	0.0557095	+	0.0321639i
$780$	8.13601	+	10.4889i	0.291316	+	0.375562i
$781$	8.73811	−	5.04495i	0.312674	−	0.180523i
$782$	10.9682	−	51.4127i	0.392223	−	1.83851i
$783$	9.97073	+	13.8979i	0.356325	+	0.496670i
$784$	−11.9283	−	13.3276i	−0.426010	−	0.475984i
$785$	6.07957	+	10.5301i	0.216989	+	0.375836i
$786$	−12.4291	−	10.4875i	−0.443332	−	0.374077i
$787$	17.5726	+	10.1455i	0.626395	+	0.361649i	0.779355	−	0.626583i	$-0.215547\pi$
$787$	17.5726	+	10.1455i	0.626395	+	0.361649i	−0.152960	+	0.988232i	$0.548880\pi$
$788$	−24.1009	−	33.2764i	−0.858558	−	1.18542i
$789$	−1.32275	−	40.1793i	−0.0470912	−	1.43042i
$790$	1.74728	+	5.39127i	0.0621654	+	0.191813i
$791$	13.8274			0.491646
$792$	−20.5899	+	10.7837i	−0.731632	+	0.383183i
$793$	−50.4570			−1.79178
$794$	16.3291	+	50.3837i	0.579497	+	1.78805i
$795$	2.60195	−	1.61866i	0.0922818	−	0.0574081i
$796$	3.16826	−	2.29465i	0.112296	−	0.0813318i
$797$	−28.8758	−	16.6715i	−1.02283	−	0.590533i	−0.107910	−	0.994161i	$-0.534416\pi$
$797$	−28.8758	−	16.6715i	−1.02283	−	0.590533i	−0.914924	+	0.403627i	$0.867749\pi$
$798$	−3.52939	+	1.27364i	−0.124939	+	0.0450863i
$799$	−21.7970	−	37.7535i	−0.771122	−	1.33562i
$800$	22.1690	−	12.6891i	0.783792	−	0.448628i
$801$	−4.98123	−	7.44898i	−0.176003	−	0.263197i
$802$	1.38918	−	6.51164i	0.0490535	−	0.229934i
$803$	6.71815	−	3.87873i	0.237078	−	0.136877i
$804$	22.0646	+	9.00440i	0.778158	+	0.317561i
$805$	−6.30432	−	3.63980i	−0.222198	−	0.128286i
$806$	−38.5676	+	42.7693i	−1.35848	+	1.50649i
$807$	3.28085	−	6.14076i	0.115491	−	0.216165i
$808$	2.86650	−	26.6974i	0.100843	−	0.939212i
$809$	30.6920			1.07907			0.539536	−	0.841962i	$-0.318600\pi$
$809$	30.6920			1.07907			0.539536	+	0.841962i	$0.318600\pi$
$810$	−5.01799	+	7.30107i	−0.176314	+	0.256534i
$811$			49.5457i			1.73978i	0.493241	+	0.869892i	$0.335812\pi$
$811$			49.5457i			1.73978i	−0.493241	+	0.869892i	$0.664188\pi$
$812$	10.4130	−	1.07873i	0.365424	−	0.0378558i
$813$	−10.3213	−	5.51443i	−0.361985	−	0.193399i
$814$	−17.9959	−	16.2280i	−0.630757	−	0.568790i
$815$	−2.98168	+	5.16443i	−0.104444	+	0.180902i
$816$	−28.3020	+	27.0596i	−0.990769	+	0.947276i
$817$	1.66763	+	2.88842i	0.0583430	+	0.101053i
$818$	−3.16532	+	14.8372i	−0.110673	+	0.518769i
$819$	21.8314	−	14.5989i	0.762849	−	0.510127i
$820$	1.05884	−	2.36865i	0.0369761	−	0.0827170i
$821$	−32.9739	+	19.0375i	−1.15080	+	0.664414i	−0.949082	−	0.315030i	$-0.897985\pi$
$821$	−32.9739	+	19.0375i	−1.15080	+	0.664414i	−0.201716	+	0.979444i	$0.564652\pi$
$822$	−3.01527	−	8.35565i	−0.105169	−	0.291437i
$823$	11.2626	−	19.5074i	0.392589	−	0.679984i	−0.600201	−	0.799849i	$-0.704913\pi$
$823$	11.2626	−	19.5074i	0.392589	−	0.679984i	0.992790	+	0.119865i	$0.0382461\pi$
$824$	16.8769	+	38.1359i	0.587936	+	1.32853i
$825$	−11.3165	−	18.1909i	−0.393990	−	0.633326i
$826$	3.69879	+	11.4127i	0.128697	+	0.397099i
$827$		−	33.5317i		−	1.16601i	−0.812468	−	0.583006i	$-0.801876\pi$
$827$		−	33.5317i		−	1.16601i	0.812468	−	0.583006i	$-0.198124\pi$
$828$	30.3690	−	25.1999i	1.05540	−	0.875758i
$829$			37.7559i			1.31132i	0.755058	+	0.655658i	$0.227609\pi$
$829$			37.7559i			1.31132i	−0.755058	+	0.655658i	$0.772391\pi$
$830$	−6.21696	+	2.01488i	−0.215794	+	0.0699376i
$831$	3.66991	−	0.120818i	0.127308	−	0.00419113i
$832$	−9.35003	+	43.0392i	−0.324154	+	1.49212i
$833$	−12.6359	+	21.8860i	−0.437807	+	0.758304i
$834$	−32.4080	−	27.3454i	−1.12220	−	0.946895i
$835$	7.20378	−	4.15910i	0.249297	−	0.143932i
$836$	−4.81804	−	2.15376i	−0.166635	−	0.0744892i
$837$	−35.0181	−	15.8432i	−1.21040	−	0.547620i
$838$	5.71107	+	1.21838i	0.197286	+	0.0420884i
$839$	−9.90604	−	17.1578i	−0.341994	−	0.592352i	0.642809	−	0.766027i	$-0.277769\pi$
$839$	−9.90604	−	17.1578i	−0.341994	−	0.592352i	−0.984803	+	0.173675i	$0.944436\pi$
$840$	2.35627	+	4.88348i	0.0812989	+	0.168496i
$841$	−9.08210	+	15.7307i	−0.313176	+	0.542436i
$842$	15.0173	−	16.6534i	0.517531	−	0.573914i
$843$	−1.48836	−	45.2098i	−0.0512618	−	1.55711i
$844$	−20.9262	+	2.16784i	−0.720310	+	0.0746200i
$845$		−	12.0481i		−	0.414466i
$846$	4.70805	−	32.3846i	0.161866	−	1.11341i
$847$	−5.56028			−0.191053
$848$	9.66010	+	3.17069i	0.331729	+	0.108882i
$849$	−17.4711	−	28.0843i	−0.599607	−	0.963851i
$850$	−26.8032	−	24.1700i	−0.919342	−	0.829023i
$851$	35.6304	+	20.5712i	1.22140	+	0.705173i
$852$	12.6420	−	1.73174i	0.433108	−	0.0593283i
$853$	−5.95424	+	3.43768i	−0.203869	+	0.117704i	−0.598459	−	0.801153i	$-0.704220\pi$
$853$	−5.95424	+	3.43768i	−0.203869	+	0.117704i	0.394590	+	0.918857i	$0.370887\pi$
$854$	−20.1566	−	4.30015i	−0.689744	−	0.147148i
$855$	−2.00721	+	0.132303i	−0.0686451	+	0.00452466i
$856$	−17.8965	−	13.0639i	−0.611690	−	0.446516i
$857$	−3.87316	−	6.70851i	−0.132305	−	0.229158i	0.792260	−	0.610184i	$-0.208904\pi$
$857$	−3.87316	−	6.70851i	−0.132305	−	0.229158i	−0.924565	+	0.381025i	$0.875571\pi$
$858$	36.3603	+	6.51424i	1.24132	+	0.222392i
$859$	0.594592	+	0.343288i	0.0202872	+	0.0117128i	0.510109	−	0.860110i	$-0.329605\pi$
$859$	0.594592	+	0.343288i	0.0202872	+	0.0117128i	−0.489822	+	0.871822i	$0.662938\pi$
$860$	3.90348	−	2.82715i	0.133108	−	0.0964049i
$861$	−4.52750	−	2.41892i	−0.154297	−	0.0824367i
$862$	−21.7745	+	7.05698i	−0.741642	+	0.240362i
$863$	−42.9194			−1.46099			−0.730496	−	0.682917i	$-0.760711\pi$
$863$	−42.9194			−1.46099			−0.730496	+	0.682917i	$0.760711\pi$
$864$	−29.2614	+	2.78804i	−0.995491	+	0.0948509i
$865$	−9.07991			−0.308726
$866$	44.1677	−	14.3145i	1.50088	−	0.486426i
$867$	22.8270	+	12.1959i	0.775246	+	0.414194i
$868$	−19.0519	+	13.7986i	−0.646665	+	0.468355i
$869$	13.6578	+	7.88535i	0.463310	+	0.267492i
$870$	5.52439	+	0.989737i	0.187294	+	0.0335552i
$871$	−18.9371	−	32.8000i	−0.641658	−	1.11138i
$872$	0.553766	+	0.404233i	0.0187529	+	0.0136891i
$873$	3.31037	−	6.71901i	0.112039	−	0.227404i
$874$	8.76318	+	1.86951i	0.296419	+	0.0632372i
$875$	−9.12082	+	5.26591i	−0.308340	+	0.178020i
$876$	9.71959	−	1.33142i	0.328394	−	0.0449844i
$877$	14.7508	+	8.51640i	0.498100	+	0.287578i	0.727929	−	0.685653i	$-0.240483\pi$
$877$	14.7508	+	8.51640i	0.498100	+	0.287578i	−0.229828	+	0.973231i	$0.573817\pi$
$878$	−22.9530	−	20.6981i	−0.774627	−	0.698526i
$879$	−5.35742	−	8.61190i	−0.180701	−	0.290472i
$880$	−2.37836	+	7.24613i	−0.0801746	+	0.244267i
$881$	−7.90546			−0.266342			−0.133171	−	0.991093i	$-0.542516\pi$
$881$	−7.90546			−0.266342			−0.133171	+	0.991093i	$0.542516\pi$
$882$	−17.6230	+	7.02315i	−0.593398	+	0.236482i
$883$			7.53298i			0.253505i	0.991934	+	0.126752i	$0.0404554\pi$
$883$			7.53298i			0.253505i	−0.991934	+	0.126752i	$0.959545\pi$
$884$	61.8989	−	6.41237i	2.08188	−	0.215671i
$885$	0.211626	+	6.42826i	0.00711372	+	0.216083i
$886$	−33.2998	+	36.9277i	−1.11873	+	1.24061i
$887$	7.02719	−	12.1715i	0.235950	−	0.408677i	−0.723598	−	0.690221i	$-0.757513\pi$
$887$	7.02719	−	12.1715i	0.235950	−	0.408677i	0.959548	+	0.281544i	$0.0908465\pi$
$888$	−13.3170	−	27.6002i	−0.446890	−	0.926202i
$889$	−1.37351	−	2.37899i	−0.0460660	−	0.0797886i
$890$	−2.87558	−	0.613468i	−0.0963896	−	0.0205635i
$891$	3.23587	+	24.4396i	0.108406	+	0.818757i
$892$	7.05260	+	3.15265i	0.236138	+	0.105558i
$893$	6.43501	−	3.71525i	0.215339	−	0.124326i
$894$	40.4780	+	34.1548i	1.35379	+	1.14231i
$895$	−1.15500	+	2.00052i	−0.0386075	+	0.0668701i
$896$	−7.40312	+	16.3964i	−0.247321	+	0.547767i
$897$	−62.6831	+	2.06360i	−2.09293	+	0.0689016i
$898$	−4.32993	+	1.40331i	−0.144492	+	0.0468289i
$899$			24.3489i			0.812081i
$900$	−4.55817	−	26.7069i	−0.151939	−	0.890231i
$901$		−	14.3655i		−	0.478585i
$902$	−2.22595	−	6.86822i	−0.0741160	−	0.228687i
$903$	−5.03694	−	8.09673i	−0.167619	−	0.269442i
$904$	9.95347	+	22.4913i	0.331048	+	0.748051i
$905$	5.19001	−	8.98936i	0.172522	−	0.298816i
$906$	10.5598	+	29.2624i	0.350826	+	0.972178i
$907$	39.7958	−	22.9761i	1.32140	−	0.762910i	0.337447	−	0.941345i	$-0.390437\pi$
$907$	39.7958	−	22.9761i	1.32140	−	0.762910i	0.983952	+	0.178435i	$0.0571034\pi$
$908$	13.1176	−	29.3445i	0.435322	−	0.973831i
$909$	−25.5472	−	12.5868i	−0.847349	−	0.417478i
$910$	1.79794	−	8.42770i	0.0596012	−	0.279375i
$911$	25.7911	+	44.6715i	0.854497	+	1.48003i	0.877111	+	0.480288i	$0.159468\pi$
$911$	25.7911	+	44.6715i	0.854497	+	1.48003i	−0.0226136	+	0.999744i	$0.507199\pi$
$912$	−4.61226	−	4.82402i	−0.152727	−	0.159739i
$913$	−9.09302	+	15.7496i	−0.300935	+	0.521235i
$914$	−8.51785	−	7.68104i	−0.281746	−	0.254066i
$915$	−9.74553	−	5.20679i	−0.322177	−	0.172131i
$916$	17.1438	−	1.77600i	0.566446	−	0.0586805i
$917$			10.5571i			0.348627i
$918$	16.6364	+	38.0541i	0.549083	+	1.25597i
$919$	−21.2048			−0.699481			−0.349741	−	0.936847i	$-0.613730\pi$
$919$	−21.2048			−0.699481			−0.349741	+	0.936847i	$0.613730\pi$
$920$	1.38234	−	12.8745i	0.0455743	−	0.424461i
$921$	−11.1877	+	20.9401i	−0.368649	+	0.689999i
$922$	−19.8830	+	22.0491i	−0.654810	+	0.726149i
$923$	−17.5623	−	10.1396i	−0.578069	−	0.333748i
$924$	13.9701	+	5.70108i	0.459581	+	0.187552i
$925$	24.4620	−	14.1231i	0.804305	−	0.464366i
$926$	2.62611	−	12.3096i	0.0862992	−	0.404520i
$927$	44.1374	−	2.90927i	1.44966	−	0.0955528i
$928$	9.25027	+	16.1610i	0.303655	+	0.530511i
$929$	1.70516	+	2.95343i	0.0559446	+	0.0968989i	0.892641	−	0.450767i	$-0.148850\pi$
$929$	1.70516	+	2.95343i	0.0559446	+	0.0968989i	−0.836697	+	0.547666i	$0.815516\pi$
$930$	−11.8626	+	4.28081i	−0.388990	+	0.140373i
$931$	−3.73042	−	2.15376i	−0.122259	−	0.0705865i
$932$	39.1236	−	28.3358i	1.28154	−	0.928170i
$933$	−28.1779	+	17.5293i	−0.922502	+	0.573885i
$934$	−11.3593	−	35.0493i	−0.371687	−	1.14685i
$935$	10.7757			0.352403
$936$	39.4612	+	25.0016i	1.28983	+	0.817202i
$937$	29.4448			0.961919			0.480959	−	0.876743i	$-0.340288\pi$
$937$	29.4448			0.961919			0.480959	+	0.876743i	$0.340288\pi$
$938$	−4.76964	−	14.7168i	−0.155734	−	0.480521i
$939$	−1.43732	−	43.6595i	−0.0469053	−	1.42477i
$940$	−6.29849	−	8.69642i	−0.205434	−	0.283646i
$941$	−40.5880	−	23.4335i	−1.32313	−	0.763910i	−0.338904	−	0.940821i	$-0.610056\pi$
$941$	−40.5880	−	23.4335i	−1.32313	−	0.763910i	−0.984227	+	0.176911i	$0.943389\pi$
$942$	32.7033	+	27.5946i	1.06553	+	0.899080i
$943$	6.12914	+	10.6160i	0.199592	+	0.345704i
$944$	−15.9011	+	14.2316i	−0.517537	+	0.463201i
$945$	5.72312	−	0.566874i	0.186173	−	0.0184404i
$946$	2.79832	−	13.1169i	0.0909812	−	0.426467i
$947$	−31.5821	+	18.2340i	−1.02628	+	0.592524i	−0.915917	−	0.401367i	$-0.868535\pi$
$947$	−31.5821	+	18.2340i	−1.02628	+	0.592524i	−0.110365	+	0.993891i	$0.535202\pi$
$948$	12.2239	+	15.7590i	0.397015	+	0.511829i
$949$	−13.5024	−	7.79564i	−0.438308	−	0.253057i
$950$	4.11972	−	4.56855i	0.133661	−	0.148223i
$951$	4.27630	−	0.140781i	0.138669	−	0.00456514i
$952$	25.2738	+	2.71365i	0.819130	+	0.0879500i
$953$	38.0590			1.23285			0.616426	−	0.787413i	$-0.288580\pi$
$953$	38.0590			1.23285			0.616426	+	0.787413i	$0.288580\pi$
$954$	6.67944	−	8.46625i	0.216255	−	0.274105i
$955$		−	5.09344i		−	0.164820i
$956$	0.830495	+	8.01680i	0.0268601	+	0.259282i
$957$	13.2610	−	8.24963i	0.428668	−	0.266673i
$958$	−18.2985	−	16.5008i	−0.591198	−	0.533117i
$959$	−2.88330	+	4.99401i	−0.0931065	+	0.161265i
$960$	−6.24723	+	7.34796i	−0.201628	+	0.237154i
$961$	−11.8569	−	20.5368i	−0.382481	−	0.662477i
$962$	−10.1615	+	47.6312i	−0.327620	+	1.53569i
$963$	−19.5360	+	13.0639i	−0.629538	+	0.420980i
$964$	10.2851	+	4.59764i	0.331261	+	0.148080i
$965$	12.3397	−	7.12430i	0.397228	−	0.229339i
$966$	−25.2165	−	4.51773i	−0.811327	−	0.145356i
$967$	11.4864	−	19.8951i	0.369378	−	0.639782i	−0.620090	−	0.784531i	$-0.712904\pi$
$967$	11.4864	−	19.8951i	0.369378	−	0.639782i	0.989468	+	0.144749i	$0.0462374\pi$
$968$	−4.00249	−	9.04422i	−0.128645	−	0.290692i
$969$	−4.44380	+	8.31745i	−0.142755	+	0.267195i
$970$	−0.757723	−	2.33797i	−0.0243290	−	0.0750677i
$971$			53.8829i			1.72919i	0.502474	+	0.864593i	$0.332423\pi$
$971$			53.8829i			1.72919i	−0.502474	+	0.864593i	$0.667577\pi$
$972$	−7.88916	+	30.1622i	−0.253045	+	0.967455i
$973$			27.5269i			0.882473i
$974$	40.0055	−	12.9656i	1.28186	−	0.415443i
$975$	−20.2905	+	37.9777i	−0.649816	+	1.21626i
$976$	−7.51491	−	35.8816i	−0.240546	−	1.14854i
$977$	19.1024	−	33.0863i	0.611140	−	1.05853i	−0.379909	−	0.925024i	$-0.624045\pi$
$977$	19.1024	−	33.0863i	0.611140	−	1.05853i	0.991049	−	0.133501i	$-0.0426220\pi$
$978$	−3.70087	+	20.6571i	−0.118341	+	0.660540i
$979$	−7.08585	+	4.09102i	−0.226465	+	0.130749i
$980$	−2.54032	+	5.68279i	−0.0811475	+	0.181530i
$981$	0.604495	−	0.404233i	0.0193001	−	0.0129062i
$982$	32.9547	+	7.03045i	1.05163	+	0.224351i
$983$	−24.3307	−	42.1420i	−0.776028	−	1.34412i	−0.934215	−	0.356711i	$-0.883898\pi$
$983$	−24.3307	−	42.1420i	−0.776028	−	1.34412i	0.158186	−	0.987409i	$-0.449435\pi$
$984$	0.675510	−	9.10556i	0.0215345	−	0.290274i
$985$	−7.14968	+	12.3836i	−0.227808	+	0.394574i
$986$	17.6197	−	19.5393i	0.561126	−	0.622259i
$987$	−18.0384	+	11.2216i	−0.574169	+	0.357188i
$988$	1.09297	+	10.5505i	0.0347722	+	0.335657i
$989$			22.7715i			0.724093i
$990$	6.35060	+	5.01031i	0.201835	+	0.159238i
$991$	−12.7822			−0.406040			−0.203020	−	0.979175i	$-0.565076\pi$
$991$	−12.7822			−0.406040			−0.203020	+	0.979175i	$0.565076\pi$
$992$	−36.1588	−	21.0567i	−1.14804	−	0.668551i
$993$	48.8543	−	1.60834i	1.55034	−	0.0510392i
$994$	−6.15164	−	5.54728i	−0.195118	−	0.175949i
$995$	−1.17905	−	0.680723i	−0.0373783	−	0.0215804i
$996$	−18.1726	+	14.0961i	−0.575820	+	0.446651i
$997$	21.1161	−	12.1914i	0.668752	−	0.386104i	−0.126851	−	0.991922i	$-0.540487\pi$
$997$	21.1161	−	12.1914i	0.668752	−	0.386104i	0.795604	+	0.605817i	$0.207154\pi$
$998$	−26.9299	−	5.74514i	−0.852450	−	0.181859i
$999$	−32.3456	+	3.20383i	−1.02337	+	0.101365i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.2.n.b.13.1	✓	16
3.2	odd	2		216.2.n.b.37.8		16
4.3	odd	2		288.2.r.b.49.2		16
8.3	odd	2		288.2.r.b.49.7		16
8.5	even	2	inner	72.2.n.b.13.7	yes	16
9.2	odd	6		216.2.n.b.181.2		16
9.4	even	3		648.2.d.j.325.5		8
9.5	odd	6		648.2.d.k.325.4		8
9.7	even	3	inner	72.2.n.b.61.7	yes	16
12.11	even	2		864.2.r.b.145.5		16
24.5	odd	2		216.2.n.b.37.2		16
24.11	even	2		864.2.r.b.145.4		16
36.7	odd	6		288.2.r.b.241.7		16
36.11	even	6		864.2.r.b.721.4		16
36.23	even	6		2592.2.d.k.1297.4		8
36.31	odd	6		2592.2.d.j.1297.5		8
72.5	odd	6		648.2.d.k.325.3		8
72.11	even	6		864.2.r.b.721.5		16
72.13	even	6		648.2.d.j.325.6		8
72.29	odd	6		216.2.n.b.181.8		16
72.43	odd	6		288.2.r.b.241.2		16
72.59	even	6		2592.2.d.k.1297.5		8
72.61	even	6	inner	72.2.n.b.61.1	yes	16
72.67	odd	6		2592.2.d.j.1297.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.n.b.13.1	✓	16	1.1	even	1	trivial
72.2.n.b.13.7	yes	16	8.5	even	2	inner
72.2.n.b.61.1	yes	16	72.61	even	6	inner
72.2.n.b.61.7	yes	16	9.7	even	3	inner
216.2.n.b.37.2		16	24.5	odd	2
216.2.n.b.37.8		16	3.2	odd	2
216.2.n.b.181.2		16	9.2	odd	6
216.2.n.b.181.8		16	72.29	odd	6
288.2.r.b.49.2		16	4.3	odd	2
288.2.r.b.49.7		16	8.3	odd	2
288.2.r.b.241.2		16	72.43	odd	6
288.2.r.b.241.7		16	36.7	odd	6
648.2.d.j.325.5		8	9.4	even	3
648.2.d.j.325.6		8	72.13	even	6
648.2.d.k.325.3		8	72.5	odd	6
648.2.d.k.325.4		8	9.5	odd	6
864.2.r.b.145.4		16	24.11	even	2
864.2.r.b.145.5		16	12.11	even	2
864.2.r.b.721.4		16	36.11	even	6
864.2.r.b.721.5		16	72.11	even	6
2592.2.d.j.1297.4		8	72.67	odd	6
2592.2.d.j.1297.5		8	36.31	odd	6
2592.2.d.k.1297.4		8	36.23	even	6
2592.2.d.k.1297.5		8	72.59	even	6

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	72.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34532 + 0.436011i) q^{2} +(1.52768 + 0.816201i) q^{3} +(1.61979 - 1.17315i) q^{4} +(-0.602794 - 0.348023i) q^{5} +(-2.41110 - 0.431967i) q^{6} +(0.795065 + 1.37709i) q^{7} +(-1.66763 + 2.28452i) q^{8} +(1.66763 + 2.49379i) q^{9} +O(q^{10})\)	\(q+(-1.34532 + 0.436011i) q^{2} +(1.52768 + 0.816201i) q^{3} +(1.61979 - 1.17315i) q^{4} +(-0.602794 - 0.348023i) q^{5} +(-2.41110 - 0.431967i) q^{6} +(0.795065 + 1.37709i) q^{7} +(-1.66763 + 2.28452i) q^{8} +(1.66763 + 2.49379i) q^{9} +(0.962695 + 0.205379i) q^{10} +(2.37222 - 1.36960i) q^{11} +(3.43205 - 0.470132i) q^{12} +(-4.76780 - 2.75269i) q^{13} +(-1.67005 - 1.50598i) q^{14} +(-0.636821 - 1.02367i) q^{15} +(1.24743 - 3.80052i) q^{16} -5.65175 q^{17} +(-3.33082 - 2.62785i) q^{18} -0.963328i q^{19} +(-1.38468 + 0.143445i) q^{20} +(0.0906219 + 2.75269i) q^{21} +(-2.59424 + 2.87688i) q^{22} +(3.28857 - 5.69597i) q^{23} +(-4.41223 + 2.12889i) q^{24} +(-2.25776 - 3.91055i) q^{25} +(7.61444 + 1.62444i) q^{26} +(0.512172 + 5.17085i) q^{27} +(2.90338 + 1.29787i) q^{28} +(2.85076 - 1.64589i) q^{29} +(1.30306 + 1.09951i) q^{30} +(-3.69844 + 6.40589i) q^{31} +(-0.0211236 + 5.65681i) q^{32} +(4.74188 - 0.156108i) q^{33} +(7.60343 - 2.46423i) q^{34} -1.10680i q^{35} +(5.62681 + 2.08303i) q^{36} +6.25538i q^{37} +(0.420022 + 1.29599i) q^{38} +(-5.03694 - 8.09673i) q^{39} +(1.80030 - 0.796718i) q^{40} +(-0.931886 + 1.61407i) q^{41} +(-1.32212 - 3.66375i) q^{42} +(-2.99838 + 1.73111i) q^{43} +(2.23574 - 5.00145i) q^{44} +(-0.137339 - 2.08362i) q^{45} +(-1.94068 + 9.09677i) q^{46} +(3.85668 + 6.67997i) q^{47} +(5.00766 - 4.78783i) q^{48} +(2.23574 - 3.87242i) q^{49} +(4.74246 + 4.27655i) q^{50} +(-8.63408 - 4.61296i) q^{51} +(-10.9522 + 1.13458i) q^{52} +2.54179i q^{53} +(-2.94359 - 6.73315i) q^{54} -1.90662 q^{55} +(-4.47186 - 0.480144i) q^{56} +(0.786270 - 1.47166i) q^{57} +(-3.11757 + 3.45722i) q^{58} +(-4.62019 - 2.66747i) q^{59} +(-2.23244 - 0.911041i) q^{60} +(7.93715 - 4.58252i) q^{61} +(2.18256 - 10.2305i) q^{62} +(-2.10831 + 4.27921i) q^{63} +(-2.43802 - 7.61945i) q^{64} +(1.91600 + 3.31861i) q^{65} +(-6.31129 + 2.27753i) q^{66} +(5.95780 + 3.43974i) q^{67} +(-9.15463 + 6.63036i) q^{68} +(9.67295 - 6.01750i) q^{69} +(0.482579 + 1.48901i) q^{70} +3.68351 q^{71} +(-8.47810 - 0.349000i) q^{72} +2.83201 q^{73} +(-2.72742 - 8.41550i) q^{74} +(-0.257341 - 7.81687i) q^{75} +(-1.13013 - 1.56039i) q^{76} +(3.77214 + 2.17785i) q^{77} +(10.3066 + 8.69655i) q^{78} +(2.87870 + 4.98605i) q^{79} +(-2.07461 + 1.85680i) q^{80} +(-3.43802 + 8.31745i) q^{81} +(0.549933 - 2.57776i) q^{82} +(-5.74968 + 3.31958i) q^{83} +(3.37612 + 4.35247i) q^{84} +(3.40684 + 1.96694i) q^{85} +(3.27900 - 3.63623i) q^{86} +(5.69844 - 0.187599i) q^{87} +(-0.827111 + 7.70337i) q^{88} -2.98701 q^{89} +(1.09325 + 2.74326i) q^{90} -8.75427i q^{91} +(-1.35545 - 13.0843i) q^{92} +(-10.8785 + 6.76749i) q^{93} +(-8.10103 - 7.30516i) q^{94} +(-0.335261 + 0.580689i) q^{95} +(-4.64937 + 8.62458i) q^{96} +(-1.24837 - 2.16224i) q^{97} +(-1.31938 + 6.18447i) q^{98} +(7.37150 + 3.63184i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} - q^{4} - 7 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q + q^2 - q^4 - 7 * q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9	\( 16 q + q^{2} - q^{4} - 7 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9} - 16 q^{10} - 16 q^{12} + 16 q^{14} - 10 q^{15} - 9 q^{16} - 28 q^{17} + 4 q^{18} - 8 q^{20} + q^{22} - 10 q^{23} + 7 q^{24} + 2 q^{25} + 28 q^{26} + 4 q^{28} + 22 q^{30} - 10 q^{31} + 11 q^{32} + q^{34} + 27 q^{36} + 23 q^{38} + 2 q^{39} + 6 q^{40} - 8 q^{41} + 8 q^{42} + 18 q^{44} - 20 q^{46} + 6 q^{47} + 39 q^{48} + 18 q^{49} - 23 q^{50} - 8 q^{52} - 29 q^{54} - 4 q^{55} + 10 q^{56} + 10 q^{57} - 14 q^{58} + 6 q^{60} - 52 q^{62} + 2 q^{63} + 26 q^{64} - 14 q^{65} - 72 q^{66} - 39 q^{68} + 72 q^{71} - 77 q^{72} - 44 q^{73} - 38 q^{74} + 5 q^{76} + 10 q^{78} - 30 q^{79} - 96 q^{80} + 10 q^{81} + 38 q^{82} - 28 q^{84} + 7 q^{86} + 42 q^{87} + 31 q^{88} + 64 q^{89} + 64 q^{90} - 30 q^{92} - 12 q^{94} + 44 q^{95} - 26 q^{96} + 66 q^{98}+O(q^{100}) \) 16 * q + q^2 - q^4 - 7 * q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9 - 16 * q^10 - 16 * q^12 + 16 * q^14 - 10 * q^15 - 9 * q^16 - 28 * q^17 + 4 * q^18 - 8 * q^20 + q^22 - 10 * q^23 + 7 * q^24 + 2 * q^25 + 28 * q^26 + 4 * q^28 + 22 * q^30 - 10 * q^31 + 11 * q^32 + q^34 + 27 * q^36 + 23 * q^38 + 2 * q^39 + 6 * q^40 - 8 * q^41 + 8 * q^42 + 18 * q^44 - 20 * q^46 + 6 * q^47 + 39 * q^48 + 18 * q^49 - 23 * q^50 - 8 * q^52 - 29 * q^54 - 4 * q^55 + 10 * q^56 + 10 * q^57 - 14 * q^58 + 6 * q^60 - 52 * q^62 + 2 * q^63 + 26 * q^64 - 14 * q^65 - 72 * q^66 - 39 * q^68 + 72 * q^71 - 77 * q^72 - 44 * q^73 - 38 * q^74 + 5 * q^76 + 10 * q^78 - 30 * q^79 - 96 * q^80 + 10 * q^81 + 38 * q^82 - 28 * q^84 + 7 * q^86 + 42 * q^87 + 31 * q^88 + 64 * q^89 + 64 * q^90 - 30 * q^92 - 12 * q^94 + 44 * q^95 - 26 * q^96 + 66 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more