LMFDB - Embedded newform 192.2.s.a.155.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(11,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8]))

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

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

chi := DirichletCharacter("192.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.s (of order $16$, degree $8$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			155.23
Character	$\chi$	$=$	192.155
Dual form			192.2.s.a.83.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.933236 + 1.06258i) q^{2} +(-1.40331 - 1.01525i) q^{3} +(-0.258140 + 1.98327i) q^{4} +(2.52227 + 0.501712i) q^{5} +(-0.230838 - 2.43859i) q^{6} +(0.531558 + 0.220179i) q^{7} +(-2.34828 + 1.57657i) q^{8} +(0.938541 + 2.84941i) q^{9} +O(q^{10})$	\(q+(0.933236 + 1.06258i) q^{2} +(-1.40331 - 1.01525i) q^{3} +(-0.258140 + 1.98327i) q^{4} +(2.52227 + 0.501712i) q^{5} +(-0.230838 - 2.43859i) q^{6} +(0.531558 + 0.220179i) q^{7} +(-2.34828 + 1.57657i) q^{8} +(0.938541 + 2.84941i) q^{9} +(1.82077 + 3.14833i) q^{10} +(2.56088 - 1.71113i) q^{11} +(2.37576 - 2.52106i) q^{12} +(1.02147 + 5.13528i) q^{13} +(0.262113 + 0.770300i) q^{14} +(-3.03016 - 3.26479i) q^{15} +(-3.86673 - 1.02392i) q^{16} +(-2.91436 - 2.91436i) q^{17} +(-2.15184 + 3.65645i) q^{18} +(-0.478548 - 2.40582i) q^{19} +(-1.64613 + 4.87284i) q^{20} +(-0.522403 - 0.848642i) q^{21} +(4.20811 + 1.12425i) q^{22} +(0.232730 - 0.0963998i) q^{23} +(4.89597 + 0.171682i) q^{24} +(1.49076 + 0.617492i) q^{25} +(-4.50336 + 5.87782i) q^{26} +(1.57580 - 4.95145i) q^{27} +(-0.573890 + 0.997387i) q^{28} +(5.60827 - 8.39338i) q^{29} +(0.641232 - 6.26660i) q^{30} -8.55147 q^{31} +(-2.52058 - 5.06426i) q^{32} +(-5.33092 - 0.198695i) q^{33} +(0.376944 - 5.81651i) q^{34} +(1.23027 + 0.822040i) q^{35} +(-5.89343 + 1.12584i) q^{36} +(0.160643 + 0.0319538i) q^{37} +(2.10977 - 2.75369i) q^{38} +(3.78015 - 8.24342i) q^{39} +(-6.71400 + 2.79838i) q^{40} +(-1.65650 - 3.99914i) q^{41} +(0.414221 - 1.34708i) q^{42} +(-3.71926 + 2.48513i) q^{43} +(2.73256 + 5.52063i) q^{44} +(0.937677 + 7.65787i) q^{45} +(0.319624 + 0.157329i) q^{46} +(0.621755 - 0.621755i) q^{47} +(4.38667 + 5.36257i) q^{48} +(-4.71567 - 4.71567i) q^{49} +(0.735097 + 2.16031i) q^{50} +(1.13094 + 7.04853i) q^{51} +(-10.4483 + 0.700234i) q^{52} +(2.49304 + 3.73109i) q^{53} +(6.73189 - 2.94647i) q^{54} +(7.31774 - 3.03111i) q^{55} +(-1.59538 + 0.320996i) q^{56} +(-1.77096 + 3.86195i) q^{57} +(14.1525 - 1.87378i) q^{58} +(-1.43711 + 7.22485i) q^{59} +(7.25717 - 5.16687i) q^{60} +(1.99480 - 2.98544i) q^{61} +(-7.98054 - 9.08659i) q^{62} +(-0.128490 + 1.72127i) q^{63} +(3.02887 - 7.40445i) q^{64} +13.4651i q^{65} +(-4.76388 - 5.84995i) q^{66} +(10.2761 + 6.86625i) q^{67} +(6.53227 - 5.02765i) q^{68} +(-0.424461 - 0.101000i) q^{69} +(0.274652 + 2.07441i) q^{70} +(5.15693 - 12.4499i) q^{71} +(-6.69625 - 5.21155i) q^{72} +(3.83983 + 9.27018i) q^{73} +(0.115964 + 0.200515i) q^{74} +(-1.46508 - 2.38002i) q^{75} +(4.89493 - 0.328052i) q^{76} +(1.73801 - 0.345712i) q^{77} +(12.2870 - 3.67636i) q^{78} +(-6.48617 + 6.48617i) q^{79} +(-9.23924 - 4.52259i) q^{80} +(-7.23828 + 5.34858i) q^{81} +(2.70349 - 5.49230i) q^{82} +(-11.1417 + 2.21623i) q^{83} +(1.81794 - 0.816999i) q^{84} +(-5.88864 - 8.81298i) q^{85} +(-6.11158 - 1.63278i) q^{86} +(-16.3915 + 6.08469i) q^{87} +(-3.31597 + 8.05562i) q^{88} +(-6.98167 + 16.8552i) q^{89} +(-7.26201 + 8.14296i) q^{90} +(-0.587708 + 2.95461i) q^{91} +(0.131110 + 0.486451i) q^{92} +(12.0003 + 8.68187i) q^{93} +(1.24091 + 0.0804181i) q^{94} -6.30824i q^{95} +(-1.60434 + 9.66572i) q^{96} -14.1018i q^{97} +(0.609928 - 9.41160i) q^{98} +(7.27920 + 5.69104i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{9}{16}\right)$

Coefficient data

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

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

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

$2$	0.933236	+	1.06258i	0.659898	+	0.751355i
$2$	0.933236	+	1.06258i	0.659898	+	0.751355i
$3$	−1.40331	−	1.01525i	−0.810200	−	0.586154i
$3$	−1.40331	−	1.01525i	−0.810200	−	0.586154i
$4$	−0.258140	+	1.98327i	−0.129070	+	0.991636i
$5$	2.52227	+	0.501712i	1.12800	+	0.224372i	0.723605	−	0.690214i	$-0.242484\pi$
$5$	2.52227	+	0.501712i	1.12800	+	0.224372i	0.404390	+	0.914586i	$0.367484\pi$
$6$	−0.230838	−	2.43859i	−0.0942391	−	0.995550i
$7$	0.531558	+	0.220179i	0.200910	+	0.0832197i	0.480870	−	0.876792i	$-0.340321\pi$
$7$	0.531558	+	0.220179i	0.200910	+	0.0832197i	−0.279960	+	0.960012i	$0.590321\pi$
$8$	−2.34828	+	1.57657i	−0.830244	+	0.557401i
$9$	0.938541	+	2.84941i	0.312847	+	0.949803i
$10$	1.82077	+	3.14833i	0.575779	+	0.995588i
$11$	2.56088	−	1.71113i	0.772135	−	0.515924i	−0.105983	−	0.994368i	$-0.533799\pi$
$11$	2.56088	−	1.71113i	0.772135	−	0.515924i	0.878118	+	0.478444i	$0.158799\pi$
$12$	2.37576	−	2.52106i	0.685823	−	0.727768i
$13$	1.02147	+	5.13528i	0.283305	+	1.42427i	0.816043	+	0.577991i	$0.196163\pi$
$13$	1.02147	+	5.13528i	0.283305	+	1.42427i	−0.532738	+	0.846280i	$0.678837\pi$
$14$	0.262113	+	0.770300i	0.0700526	+	0.205871i
$15$	−3.03016	−	3.26479i	−0.782385	−	0.842965i
$16$	−3.86673	−	1.02392i	−0.966682	−	0.255980i
$17$	−2.91436	−	2.91436i	−0.706835	−	0.706835i	0.259033	−	0.965868i	$-0.416596\pi$
$17$	−2.91436	−	2.91436i	−0.706835	−	0.706835i	−0.965868	+	0.259033i	$0.916596\pi$
$18$	−2.15184	+	3.65645i	−0.507193	+	0.861833i
$19$	−0.478548	−	2.40582i	−0.109786	−	0.551933i	−0.996053	−	0.0887583i	$-0.971710\pi$
$19$	−0.478548	−	2.40582i	−0.109786	−	0.551933i	0.886267	−	0.463175i	$-0.153290\pi$
$20$	−1.64613	+	4.87284i	−0.368086	+	1.08960i
$21$	−0.522403	−	0.848642i	−0.113998	−	0.185189i
$22$	4.20811	+	1.12425i	0.897173	+	0.239691i
$23$	0.232730	−	0.0963998i	0.0485275	−	0.0201007i	−0.358288	−	0.933611i	$-0.616639\pi$
$23$	0.232730	−	0.0963998i	0.0485275	−	0.0201007i	0.406815	+	0.913510i	$0.366639\pi$
$24$	4.89597	+	0.171682i	0.999386	+	0.0350445i
$25$	1.49076	+	0.617492i	0.298152	+	0.123498i
$26$	−4.50336	+	5.87782i	−0.883181	+	1.15274i
$27$	1.57580	−	4.95145i	0.303262	−	0.952907i
$28$	−0.573890	+	0.997387i	−0.108455	+	0.188488i
$29$	5.60827	−	8.39338i	1.04143	−	1.55861i	0.230845	−	0.972991i	$-0.425851\pi$
$29$	5.60827	−	8.39338i	1.04143	−	1.55861i	0.810586	−	0.585620i	$-0.199149\pi$
$30$	0.641232	−	6.26660i	0.117072	−	1.14412i
$31$	−8.55147			−1.53589			−0.767945	−	0.640516i	$-0.778720\pi$
$31$	−8.55147			−1.53589			−0.767945	+	0.640516i	$0.778720\pi$
$32$	−2.52058	−	5.06426i	−0.445579	−	0.895243i
$33$	−5.33092	−	0.198695i	−0.927995	−	0.0345884i
$34$	0.376944	−	5.81651i	0.0646454	−	0.997524i
$35$	1.23027	+	0.822040i	0.207954	+	0.138950i
$36$	−5.89343	+	1.12584i	−0.982238	+	0.187639i
$37$	0.160643	+	0.0319538i	0.0264095	+	0.00525317i	0.208277	−	0.978070i	$-0.433214\pi$
$37$	0.160643	+	0.0319538i	0.0264095	+	0.00525317i	−0.181868	+	0.983323i	$0.558214\pi$
$38$	2.10977	−	2.75369i	0.342250	−	0.446708i
$39$	3.78015	−	8.24342i	0.605308	−	1.32000i
$40$	−6.71400	+	2.79838i	−1.06158	+	0.442462i
$41$	−1.65650	−	3.99914i	−0.258701	−	0.624560i	0.740152	−	0.672440i	$-0.234754\pi$
$41$	−1.65650	−	3.99914i	−0.258701	−	0.624560i	−0.998853	+	0.0478795i	$0.984754\pi$
$42$	0.414221	−	1.34708i	0.0639157	−	0.207858i
$43$	−3.71926	+	2.48513i	−0.567181	+	0.378978i	−0.805847	−	0.592123i	$-0.798290\pi$
$43$	−3.71926	+	2.48513i	−0.567181	+	0.378978i	0.238666	+	0.971102i	$0.423290\pi$
$44$	2.73256	+	5.52063i	0.411950	+	0.832267i
$45$	0.937677	+	7.65787i	0.139781	+	1.14157i
$46$	0.319624	+	0.157329i	0.0471260	+	0.0231970i
$47$	0.621755	−	0.621755i	0.0906923	−	0.0906923i	−0.660305	−	0.750997i	$-0.729573\pi$
$47$	0.621755	−	0.621755i	0.0906923	−	0.0906923i	0.750997	+	0.660305i	$0.229573\pi$
$48$	4.38667	+	5.36257i	0.633162	+	0.774020i
$49$	−4.71567	−	4.71567i	−0.673667	−	0.673667i
$50$	0.735097	+	2.16031i	0.103958	+	0.305514i
$51$	1.13094	+	7.04853i	0.158363	+	0.986992i
$52$	−10.4483	+	0.700234i	−1.44892	+	0.0971050i
$53$	2.49304	+	3.73109i	0.342445	+	0.512505i	0.962220	−	0.272275i	$-0.0877759\pi$
$53$	2.49304	+	3.73109i	0.342445	+	0.512505i	−0.619774	+	0.784780i	$0.712776\pi$
$54$	6.73189	−	2.94647i	0.916094	−	0.400963i
$55$	7.31774	−	3.03111i	0.986724	−	0.408715i
$56$	−1.59538	+	0.320996i	−0.213191	+	0.0428948i
$57$	−1.77096	+	3.86195i	−0.234569	+	0.511528i
$58$	14.1525	−	1.87378i	1.85831	−	0.246039i
$59$	−1.43711	+	7.22485i	−0.187096	+	0.940595i	0.767126	+	0.641496i	$0.221686\pi$
$59$	−1.43711	+	7.22485i	−0.187096	+	0.940595i	−0.954222	+	0.299099i	$0.903314\pi$
$60$	7.25717	−	5.16687i	0.936897	−	0.667039i
$61$	1.99480	−	2.98544i	0.255408	−	0.382246i	−0.681501	−	0.731817i	$-0.738673\pi$
$61$	1.99480	−	2.98544i	0.255408	−	0.382246i	0.936910	+	0.349571i	$0.113673\pi$
$62$	−7.98054	−	9.08659i	−1.01353	−	1.15400i
$63$	−0.128490	+	1.72127i	−0.0161882	+	0.216860i
$64$	3.02887	−	7.40445i	0.378609	−	0.925557i
$65$			13.4651i			1.67014i
$66$	−4.76388	−	5.84995i	−0.586394	−	0.720079i
$67$	10.2761	+	6.86625i	1.25542	+	0.838846i	0.992049	−	0.125848i	$-0.0401653\pi$
$67$	10.2761	+	6.86625i	1.25542	+	0.838846i	0.263372	+	0.964694i	$0.415165\pi$
$68$	6.53227	−	5.02765i	0.792154	−	0.609692i
$69$	−0.424461	−	0.101000i	−0.0510991	−	0.0121590i
$70$	0.274652	+	2.07441i	0.0328272	+	0.247940i
$71$	5.15693	−	12.4499i	0.612015	−	1.47753i	−0.248769	−	0.968563i	$-0.580026\pi$
$71$	5.15693	−	12.4499i	0.612015	−	1.47753i	0.860784	−	0.508971i	$-0.169974\pi$
$72$	−6.69625	−	5.21155i	−0.789161	−	0.614187i
$73$	3.83983	+	9.27018i	0.449419	+	1.08499i	0.972540	+	0.232734i	$0.0747673\pi$
$73$	3.83983	+	9.27018i	0.449419	+	1.08499i	−0.523122	+	0.852258i	$0.675233\pi$
$74$	0.115964	+	0.200515i	0.0134806	+	0.0233094i
$75$	−1.46508	−	2.38002i	−0.169173	−	0.274821i
$76$	4.89493	−	0.328052i	0.561487	−	0.0376301i
$77$	1.73801	−	0.345712i	0.198065	−	0.0393975i
$78$	12.2870	−	3.67636i	1.39123	−	0.416266i
$79$	−6.48617	+	6.48617i	−0.729751	+	0.729751i	−0.970570	−	0.240819i	$-0.922584\pi$
$79$	−6.48617	+	6.48617i	−0.729751	+	0.729751i	0.240819	+	0.970570i	$0.422584\pi$
$80$	−9.23924	−	4.52259i	−1.03298	−	0.505641i
$81$	−7.23828	+	5.34858i	−0.804253	+	0.594287i
$82$	2.70349	−	5.49230i	0.298550	−	0.606523i
$83$	−11.1417	+	2.21623i	−1.22296	+	0.243263i	−0.764014	−	0.645200i	$-0.776774\pi$
$83$	−11.1417	+	2.21623i	−1.22296	+	0.243263i	−0.458950	+	0.888462i	$0.651774\pi$
$84$	1.81794	−	0.816999i	0.198353	−	0.0891419i
$85$	−5.88864	−	8.81298i	−0.638713	−	0.955901i
$86$	−6.11158	−	1.63278i	−0.659029	−	0.176068i
$87$	−16.3915	+	6.08469i	−1.75735	+	0.652347i
$88$	−3.31597	+	8.05562i	−0.353484	+	0.858732i
$89$	−6.98167	+	16.8552i	−0.740055	+	1.78665i	−0.134396	+	0.990928i	$0.542909\pi$
$89$	−6.98167	+	16.8552i	−0.740055	+	1.78665i	−0.605660	+	0.795724i	$0.707091\pi$
$90$	−7.26201	+	8.14296i	−0.765483	+	0.858343i
$91$	−0.587708	+	2.95461i	−0.0616085	+	0.309727i
$92$	0.131110	+	0.486451i	0.0136692	+	0.0507160i
$93$	12.0003	+	8.68187i	1.24438	+	0.900267i
$94$	1.24091	+	0.0804181i	0.127990	+	0.00829450i
$95$		−	6.30824i		−	0.647211i
$96$	−1.60434	+	9.66572i	−0.163742	+	0.986503i
$97$		−	14.1018i		−	1.43182i	−0.698191	−	0.715912i	$-0.746011\pi$
$97$		−	14.1018i		−	1.43182i	0.698191	−	0.715912i	$-0.253989\pi$
$98$	0.609928	−	9.41160i	0.0616120	−	0.950715i
$99$	7.27920	+	5.69104i	0.731587	+	0.571971i
$100$	−1.60948	+	2.79718i	−0.160948	+	0.279718i
$101$	2.19261	−	11.0230i	0.218172	−	1.09683i	−0.704045	−	0.710155i	$-0.748625\pi$
$101$	2.19261	−	11.0230i	0.218172	−	1.09683i	0.922217	−	0.386672i	$-0.126375\pi$
$102$	−6.43417	+	7.77966i	−0.637078	+	0.770301i
$103$	0.269146	−	0.649775i	0.0265197	−	0.0640243i	−0.910065	−	0.414466i	$-0.863968\pi$
$103$	0.269146	−	0.649775i	0.0265197	−	0.0640243i	0.936585	+	0.350442i	$0.113968\pi$
$104$	−10.4948	−	10.4487i	−1.02910	−	1.02458i
$105$	−0.891871	−	2.40260i	−0.0870377	−	0.234470i
$106$	−1.63798	+	6.13104i	−0.159095	+	0.595499i
$107$	5.38813	+	8.06390i	0.520890	+	0.779567i	0.994891	−	0.100957i	$-0.0321906\pi$
$107$	5.38813	+	8.06390i	0.520890	+	0.779567i	−0.474001	+	0.880524i	$0.657191\pi$
$108$	9.41329	+	4.40340i	0.905795	+	0.423717i
$109$	8.43267	−	1.67736i	0.807703	−	0.160662i	0.226068	−	0.974112i	$-0.427413\pi$
$109$	8.43267	−	1.67736i	0.807703	−	0.160662i	0.581636	+	0.813449i	$0.302413\pi$
$110$	10.0500	+	4.94692i	0.958227	+	0.471671i
$111$	−0.192990	−	0.207933i	−0.0183178	−	0.0197361i
$112$	−1.82995	−	1.39564i	−0.172914	−	0.131876i
$113$	5.31014	−	5.31014i	0.499536	−	0.499536i	−0.411758	−	0.911293i	$-0.635085\pi$
$113$	5.31014	−	5.31014i	0.499536	−	0.499536i	0.911293	+	0.411758i	$0.135085\pi$
$114$	−5.75634	+	1.72234i	−0.539131	+	0.161311i
$115$	0.635373	−	0.126384i	0.0592488	−	0.0117853i
$116$	15.1986	+	13.2894i	1.41116	+	1.23389i
$117$	−13.6738	+	7.73026i	−1.26415	+	0.714663i
$118$	−9.01812	+	5.21545i	−0.830185	+	0.480121i
$119$	−0.907471	−	2.19083i	−0.0831877	−	0.200833i
$120$	12.2628	+	2.88940i	1.11944	+	0.263765i
$121$	−0.579352	+	1.39868i	−0.0526684	+	0.127153i
$122$	5.03388	−	0.666484i	0.455746	−	0.0603406i
$123$	−1.73554	+	7.29377i	−0.156489	+	0.657657i
$124$	2.20747	−	16.9599i	0.198237	−	1.52304i
$125$	−7.24111	−	4.83835i	−0.647664	−	0.432755i
$126$	−1.94890	+	1.46983i	−0.173622	+	0.130942i
$127$			5.30196i			0.470473i	0.971938	+	0.235236i	$0.0755864\pi$
$127$			5.30196i			0.470473i	−0.971938	+	0.235236i	$0.924414\pi$
$128$	10.6945	−	3.69170i	0.945265	−	0.326303i
$129$	7.74228	+	0.288572i	0.681670	+	0.0254073i
$130$	−14.3077	+	12.5661i	−1.25487	+	1.10212i
$131$	6.00708	−	8.99024i	0.524841	−	0.785481i	−0.470448	−	0.882428i	$-0.655908\pi$
$131$	6.00708	−	8.99024i	0.524841	−	0.785481i	0.995290	+	0.0969470i	$0.0309077\pi$
$132$	1.77019	−	10.5214i	0.154075	−	0.915768i
$133$	0.275334	−	1.38420i	0.0238745	−	0.120025i
$134$	2.29408	+	17.3269i	0.198179	+	1.49682i
$135$	6.45880	−	11.6983i	0.555885	−	1.00683i
$136$	11.4384	+	2.24906i	0.980836	+	0.192855i
$137$	−4.91575	+	2.03617i	−0.419981	+	0.173962i	−0.582658	−	0.812718i	$-0.697987\pi$
$137$	−4.91575	+	2.03617i	−0.419981	+	0.173962i	0.162677	+	0.986679i	$0.447987\pi$
$138$	−0.288802	−	0.545279i	−0.0245845	−	0.0464172i
$139$	−6.32677	−	9.46869i	−0.536630	−	0.803123i	0.459758	−	0.888044i	$-0.347936\pi$
$139$	−6.32677	−	9.46869i	−0.536630	−	0.803123i	−0.996388	+	0.0849209i	$0.972936\pi$
$140$	−1.94791	+	2.22776i	−0.164628	+	0.188280i
$141$	−1.50375	+	0.241277i	−0.126638	+	0.0203192i
$142$	18.0416	−	6.13909i	1.51402	−	0.515181i
$143$	11.4030	+	11.4030i	0.953566	+	0.953566i
$144$	−0.711512	−	11.9789i	−0.0592927	−	0.998241i
$145$	18.3567	−	18.3567i	1.52444	−	1.52444i
$146$	−6.26681	+	12.7314i	−0.518645	+	1.05366i
$147$	1.82996	+	11.4051i	0.150932	+	0.940678i
$148$	−0.104841	+	0.310349i	−0.00861789	+	0.0255105i
$149$	4.81210	−	3.21534i	0.394223	−	0.263411i	−0.342622	−	0.939473i	$-0.611315\pi$
$149$	4.81210	−	3.21534i	0.394223	−	0.263411i	0.736845	+	0.676062i	$0.236315\pi$
$150$	1.16169	−	3.77789i	0.0948513	−	0.308463i
$151$	3.53454	+	8.53314i	0.287637	+	0.694417i	0.999972	−	0.00742185i	$-0.00236247\pi$
$151$	3.53454	+	8.53314i	0.287637	+	0.694417i	−0.712335	+	0.701839i	$0.752362\pi$
$152$	4.91671	+	4.89509i	0.398797	+	0.397044i
$153$	5.56895	−	11.0394i	0.450223	−	0.892486i
$154$	1.98932	+	1.52414i	0.160304	+	0.122819i
$155$	−21.5692	−	4.29037i	−1.73248	−	0.344611i
$156$	15.3731	+	9.62501i	1.23084	+	0.770618i
$157$	−10.0504	−	6.71544i	−0.802106	−	0.535950i	0.0856167	−	0.996328i	$-0.472714\pi$
$157$	−10.0504	−	6.71544i	−0.802106	−	0.535950i	−0.887723	+	0.460378i	$0.847714\pi$
$158$	−12.9452	−	0.838924i	−1.02986	−	0.0667412i
$159$	0.289490	−	7.76692i	0.0229581	−	0.615957i
$160$	−3.81679	−	14.0381i	−0.301744	−	1.10981i
$161$	0.144935			0.0114224
$162$	−12.4383	−	2.69974i	−0.977245	−	0.212112i
$163$	−2.01144	+	3.01033i	−0.157548	+	0.235788i	−0.901843	−	0.432063i	$-0.857786\pi$
$163$	−2.01144	+	3.01033i	−0.157548	+	0.235788i	0.744295	+	0.667851i	$0.232786\pi$
$164$	8.35898	−	2.25295i	0.652727	−	0.175926i
$165$	−13.3464	−	3.17575i	−1.03901	−	0.247232i
$166$	−12.7528	−	9.77068i	−0.989808	−	0.758352i
$167$	14.7326	+	6.10245i	1.14004	+	0.472222i	0.871184	−	0.490957i	$-0.163353\pi$
$167$	14.7326	+	6.10245i	1.14004	+	0.472222i	0.268861	+	0.963179i	$0.413353\pi$
$168$	2.56469	+	1.16925i	0.197870	+	0.0902094i
$169$	−13.3173	+	5.51620i	−1.02441	+	0.424323i
$170$	3.86897	−	14.4817i	0.296736	−	1.11070i
$171$	6.40604	−	3.62154i	0.489882	−	0.276946i
$172$	−3.96859	−	8.01780i	−0.302602	−	0.611352i
$173$	3.09006	+	15.5348i	0.234933	+	1.18109i	0.900536	+	0.434781i	$0.143174\pi$
$173$	3.09006	+	15.5348i	0.234933	+	1.18109i	−0.665604	+	0.746305i	$0.731826\pi$
$174$	−21.7626	−	11.7388i	−1.64982	−	0.889913i
$175$	0.656466	+	0.656466i	0.0496242	+	0.0496242i
$176$	−11.6543	+	3.99432i	−0.878476	+	0.301083i
$177$	9.35172	−	8.67965i	0.702918	−	0.652403i
$178$	−24.4255	+	8.31136i	−1.83077	+	0.622963i
$179$	2.11197	+	10.6176i	0.157856	+	0.793597i	0.975862	+	0.218387i	$0.0700796\pi$
$179$	2.11197	+	10.6176i	0.157856	+	0.793597i	−0.818006	+	0.575210i	$0.804920\pi$
$180$	−15.4297	−	0.117132i	−1.15006	−	0.00873053i
$181$	7.77413	−	5.19451i	0.577846	−	0.386105i	−0.232027	−	0.972709i	$-0.574536\pi$
$181$	7.77413	−	5.19451i	0.577846	−	0.386105i	0.809873	+	0.586605i	$0.199536\pi$
$182$	−3.68797	+	2.13286i	−0.273370	+	0.158098i
$183$	−5.83028	+	2.16426i	−0.430987	+	0.159987i
$184$	−0.394534	+	0.593288i	−0.0290855	+	0.0437378i
$185$	0.389153	+	0.161192i	0.0286111	+	0.0118511i
$186$	1.97400	+	20.8535i	0.144741	+	1.52905i
$187$	−12.4502	−	2.47649i	−0.910446	−	0.181099i
$188$	1.07261	+	1.39361i	0.0782281	+	0.101639i
$189$	1.92783	−	2.28503i	0.140229	−	0.166211i
$190$	6.70299	−	5.88708i	0.486286	−	0.427093i
$191$	−6.25764			−0.452787			−0.226393	−	0.974036i	$-0.572693\pi$
$191$	−6.25764			−0.452787			−0.226393	+	0.974036i	$0.572693\pi$
$192$	−11.7678	+	7.31567i	−0.849267	+	0.527963i
$193$	−9.67963			−0.696755			−0.348378	−	0.937354i	$-0.613267\pi$
$193$	−9.67963			−0.696755			−0.348378	+	0.937354i	$0.613267\pi$
$194$	14.9843	−	13.1603i	1.07581	−	0.944857i
$195$	13.6704	−	18.8956i	0.978957	−	1.35314i
$196$	10.5698	−	8.13515i	0.754983	−	0.581082i
$197$	−0.859999	−	0.171064i	−0.0612724	−	0.0121878i	0.164359	−	0.986401i	$-0.447444\pi$
$197$	−0.859999	−	0.171064i	−0.0612724	−	0.0121878i	−0.225631	+	0.974213i	$0.572444\pi$
$198$	0.746043	+	13.0458i	0.0530189	+	0.927124i
$199$	9.72228	+	4.02710i	0.689194	+	0.285474i	0.699664	−	0.714472i	$-0.253333\pi$
$199$	9.72228	+	4.02710i	0.689194	+	0.285474i	−0.0104702	+	0.999945i	$0.503333\pi$
$200$	−4.47424	+	0.900235i	−0.316377	+	0.0636562i
$201$	−7.44953	−	20.0682i	−0.525449	−	1.41550i
$202$	13.7590	−	7.95723i	0.968078	−	0.559869i
$203$	4.82916	−	3.22674i	0.338941	−	0.226473i
$204$	−14.2711	+	0.423458i	−0.999176	+	0.0296480i
$205$	−2.17173	−	10.9180i	−0.151680	−	0.762547i
$206$	0.941613	−	0.320406i	0.0656053	−	0.0223237i
$207$	0.493109	+	0.572667i	0.0342734	+	0.0398031i
$208$	1.30837	−	20.9026i	0.0907194	−	1.44934i
$209$	−5.34217	−	5.34217i	−0.369526	−	0.369526i
$210$	1.72062	−	3.18988i	0.118734	−	0.220123i
$211$	4.49836	+	22.6148i	0.309680	+	1.55687i	0.751482	+	0.659754i	$0.229340\pi$
$211$	4.49836	+	22.6148i	0.309680	+	1.55687i	−0.441802	+	0.897113i	$0.645660\pi$
$212$	−8.04332	+	3.98123i	−0.552418	+	0.273432i
$213$	−19.8765	+	12.2355i	−1.36192	+	0.838363i
$214$	−3.54012	+	13.2508i	−0.241998	+	0.905808i
$215$	−10.6278	+	4.40218i	−0.724810	+	0.300226i
$216$	4.10588	+	14.1118i	0.279370	+	0.960184i
$217$	−4.54560	−	1.88285i	−0.308576	−	0.127816i
$218$	9.65200	+	7.39498i	0.653716	+	0.500852i
$219$	4.02307	−	16.9073i	0.271854	−	1.14249i
$220$	4.12251	+	15.2955i	0.277940	+	1.03122i
$221$	11.9891	−	17.9430i	0.806475	−	1.20697i
$222$	0.0408398	−	0.399117i	0.00274099	−	0.0267870i
$223$	3.44606			0.230765			0.115383	−	0.993321i	$-0.463191\pi$
$223$	3.44606			0.230765			0.115383	+	0.993321i	$0.463191\pi$
$224$	−0.224792	−	3.24692i	−0.0150195	−	0.216944i
$225$	−0.360351	+	4.82733i	−0.0240234	+	0.321822i
$226$	10.5980	+	0.686816i	0.704972	+	0.0456863i
$227$	−19.8617	−	13.2712i	−1.31827	−	0.880838i	−0.320475	−	0.947257i	$-0.603843\pi$
$227$	−19.8617	−	13.2712i	−1.31827	−	0.880838i	−0.997792	+	0.0664192i	$0.978843\pi$
$228$	−7.20214	−	4.50921i	−0.476973	−	0.298630i
$229$	−11.7273	−	2.33271i	−0.774963	−	0.154150i	−0.208262	−	0.978073i	$-0.566781\pi$
$229$	−11.7273	−	2.33271i	−0.774963	−	0.154150i	−0.566701	+	0.823923i	$0.691781\pi$
$230$	0.727246	+	0.557187i	0.0479532	+	0.0367398i
$231$	−2.78995	−	1.27937i	−0.183565	−	0.0841766i
$232$	0.0629070	+	28.5518i	0.00413005	+	1.87452i
$233$	−2.21224	−	5.34083i	−0.144929	−	0.349889i	0.834700	−	0.550705i	$-0.185641\pi$
$233$	−2.21224	−	5.34083i	−0.144929	−	0.349889i	−0.979629	+	0.200815i	$0.935641\pi$
$234$	−20.9749	−	7.31533i	−1.37117	−	0.478218i
$235$	1.88018	−	1.25630i	0.122649	−	0.0819517i
$236$	−13.9579	−	4.71520i	−0.908579	−	0.306933i
$237$	15.6872	−	2.51701i	1.01899	−	0.163498i
$238$	1.48104	−	3.00882i	0.0960015	−	0.195033i
$239$	−2.42905	+	2.42905i	−0.157122	+	0.157122i	−0.781290	−	0.624168i	$-0.785438\pi$
$239$	−2.42905	+	2.42905i	−0.157122	+	0.157122i	0.624168	+	0.781290i	$0.285438\pi$
$240$	8.37393	+	15.7267i	0.540535	+	1.01515i
$241$	1.48886	+	1.48886i	0.0959059	+	0.0959059i	0.753432	−	0.657526i	$-0.228397\pi$
$241$	1.48886	+	1.48886i	0.0959059	+	0.0959059i	−0.657526	+	0.753432i	$0.728397\pi$
$242$	−2.02688	+	0.689693i	−0.130293	+	0.0443352i
$243$	15.5877	−	0.157048i	0.999949	−	0.0100746i
$244$	5.40599	+	4.72690i	0.346083	+	0.302608i
$245$	−9.52831	−	14.2601i	−0.608742	−	0.911046i
$246$	−9.36987	+	4.96267i	−0.597401	+	0.316408i
$247$	11.8657	−	4.91495i	0.754999	−	0.312731i
$248$	20.0813	−	13.4820i	1.27516	−	0.856106i
$249$	17.8853	+	8.20158i	1.13343	+	0.519754i
$250$	−1.61654	−	12.2096i	−0.102239	−	0.772200i
$251$	4.93152	−	24.7924i	0.311275	−	1.56488i	−0.435737	−	0.900074i	$-0.643512\pi$
$251$	4.93152	−	24.7924i	0.311275	−	1.56488i	0.747012	−	0.664811i	$-0.231488\pi$
$252$	−3.38058	−	0.699159i	−0.212957	−	0.0440429i
$253$	0.431041	−	0.645099i	0.0270993	−	0.0405570i
$254$	−5.63374	+	4.94798i	−0.353492	+	0.310464i
$255$	−0.683786	+	18.3457i	−0.0428204	+	1.14886i
$256$	13.9032	+	7.91845i	0.868948	+	0.494903i
$257$			19.9753i			1.24603i	0.782211	+	0.623014i	$0.214092\pi$
$257$			19.9753i			1.24603i	−0.782211	+	0.623014i	$0.785908\pi$
$258$	6.91875	+	8.49607i	0.430742	+	0.528942i
$259$	0.0783553	+	0.0523553i	0.00486876	+	0.00325320i
$260$	−26.7049	−	3.47587i	−1.65617	−	0.215564i
$261$	29.1798	+	8.10274i	1.80618	+	0.501547i
$262$	15.1588	−	2.00703i	0.936517	−	0.123995i
$263$	−6.85130	+	16.5405i	−0.422469	+	1.01993i	0.559148	+	0.829068i	$0.311129\pi$
$263$	−6.85130	+	16.5405i	−0.422469	+	1.01993i	−0.981617	+	0.190863i	$0.938871\pi$
$264$	12.8318	−	7.93797i	0.789741	−	0.488548i
$265$	4.41619	+	10.6616i	0.271285	+	0.654939i
$266$	1.72777	−	0.999222i	0.105936	−	0.0612662i
$267$	26.9097	−	16.5649i	1.64685	−	1.01376i
$268$	−16.2703	+	18.6078i	−0.993866	+	1.13665i
$269$	−8.84888	+	1.76015i	−0.539526	+	0.107318i	−0.457329	−	0.889298i	$-0.651194\pi$
$269$	−8.84888	+	1.76015i	−0.539526	+	0.107318i	−0.0821970	+	0.996616i	$0.526194\pi$
$270$	18.4580	−	4.05434i	1.12332	−	0.246739i
$271$	−2.73434	+	2.73434i	−0.166099	+	0.166099i	−0.785262	−	0.619163i	$-0.787472\pi$
$271$	−2.73434	+	2.73434i	−0.166099	+	0.166099i	0.619163	+	0.785262i	$0.287472\pi$
$272$	8.28495	+	14.2531i	0.502349	+	0.864221i
$273$	3.82439	−	3.54955i	0.231463	−	0.214829i
$274$	−6.75114	−	3.32313i	−0.407851	−	0.200758i
$275$	4.87427	−	0.969552i	0.293929	−	0.0584662i
$276$	0.309880	−	0.815749i	0.0186526	−	0.0491023i
$277$	11.9323	+	17.8580i	0.716945	+	1.07298i	0.993703	+	0.112044i	$0.0357398\pi$
$277$	11.9323	+	17.8580i	0.716945	+	1.07298i	−0.276758	+	0.960940i	$0.589260\pi$
$278$	4.15683	−	15.5592i	0.249310	−	0.933179i
$279$	−8.02591	−	24.3666i	−0.480499	−	1.45879i
$280$	−4.18502	+	0.00922067i	−0.250103	+	0.000551041i
$281$	2.99365	−	7.22732i	0.178586	−	0.431146i	−0.809084	−	0.587693i	$-0.800036\pi$
$281$	2.99365	−	7.22732i	0.178586	−	0.431146i	0.987670	+	0.156547i	$0.0500363\pi$
$282$	−1.65973	−	1.37268i	−0.0988354	−	0.0817419i
$283$	−3.52302	+	17.7114i	−0.209422	+	1.05283i	0.722830	+	0.691025i	$0.242841\pi$
$283$	−3.52302	+	17.7114i	−0.209422	+	1.05283i	−0.932252	+	0.361809i	$0.882159\pi$
$284$	23.3604	+	13.4414i	1.38618	+	0.797600i
$285$	−6.40443	+	8.85239i	−0.379365	+	0.524370i
$286$	−1.47487	+	22.7582i	−0.0872108	+	1.34572i
$287$		−	2.49050i		−	0.147010i
$288$	12.0645	−	11.9352i	0.710906	−	0.703287i
$289$		−	0.0130484i		−	0.000767550i
$290$	36.6365	+	2.37426i	2.15137	+	0.139421i
$291$	−14.3169	+	19.7892i	−0.839269	+	1.16006i
$292$	−19.3765	+	5.22243i	−1.13392	+	0.305620i
$293$	−3.28501	+	16.5149i	−0.191913	+	0.964810i	0.757991	+	0.652265i	$0.226181\pi$
$293$	−3.28501	+	16.5149i	−0.191913	+	0.964810i	−0.949903	+	0.312544i	$0.898819\pi$
$294$	−10.4110	+	12.5881i	−0.607184	+	0.734155i
$295$	−7.24958	+	17.5020i	−0.422087	+	1.01901i
$296$	−0.427611	+	0.178227i	−0.0248544	+	0.0103592i
$297$	−4.43713	−	15.3765i	−0.257468	−	0.892234i
$298$	7.90738	+	2.11255i	0.458062	+	0.122377i
$299$	0.732767	+	1.09666i	0.0423770	+	0.0634216i
$300$	5.09842	−	2.29128i	0.294358	−	0.132287i
$301$	−2.52417	+	0.502089i	−0.145491	+	0.0289399i
$302$	−5.76856	+	11.7192i	−0.331943	+	0.674362i
$303$	−14.2680	+	13.2426i	−0.819673	+	0.760766i
$304$	−0.612959	+	9.79265i	−0.0351556	+	0.561647i
$305$	6.52927	−	6.52927i	0.373865	−	0.373865i
$306$	16.9274	−	4.38497i	0.967676	−	0.250672i
$307$	8.11462	−	1.61410i	0.463126	−	0.0921215i	0.0419881	−	0.999118i	$-0.486631\pi$
$307$	8.11462	−	1.61410i	0.463126	−	0.0921215i	0.421138	+	0.906997i	$0.361631\pi$
$308$	0.236991	+	3.53619i	0.0135038	+	0.201493i
$309$	−1.03738	+	0.638585i	−0.0590143	+	0.0363278i
$310$	−15.5703	−	26.9228i	−0.884332	−	1.52911i
$311$	6.92955	+	16.7294i	0.392939	+	0.948639i	0.989296	+	0.145920i	$0.0466141\pi$
$311$	6.92955	+	16.7294i	0.392939	+	0.948639i	−0.596358	+	0.802719i	$0.703386\pi$
$312$	4.11945	+	25.3176i	0.233218	+	1.43332i
$313$	−10.1171	+	24.4247i	−0.571850	+	1.38057i	0.328129	+	0.944633i	$0.393582\pi$
$313$	−10.1171	+	24.4247i	−0.571850	+	1.38057i	−0.899979	+	0.435934i	$0.856418\pi$
$314$	−2.24370	−	16.9464i	−0.126619	−	0.956339i
$315$	−1.18767	+	4.27706i	−0.0669176	+	0.240985i
$316$	−11.1895	−	14.5382i	−0.629458	−	0.817836i
$317$	−21.9045	−	14.6361i	−1.23028	−	0.822045i	−0.241349	−	0.970438i	$-0.577590\pi$
$317$	−21.9045	−	14.6361i	−1.23028	−	0.822045i	−0.988928	+	0.148394i	$0.952590\pi$
$318$	8.52312	−	6.94077i	0.477953	−	0.389219i
$319$		−	31.0909i		−	1.74076i
$320$	11.3545	−	17.1565i	0.634738	−	0.959075i
$321$	0.625667	−	16.7864i	0.0349213	−	0.936927i
$322$	0.135258	+	0.154004i	0.00753764	+	0.00858231i
$323$	−5.61676	+	8.40608i	−0.312525	+	0.467727i
$324$	−8.73920	−	15.7362i	−0.485511	−	0.874231i
$325$	−1.64823	+	8.28622i	−0.0914274	+	0.459637i
$326$	−5.07586	+	0.672043i	−0.281126	+	0.0372210i
$327$	−13.5366	−	6.20740i	−0.748574	−	0.343270i
$328$	10.1948	+	6.77953i	0.562916	+	0.374337i
$329$	0.467396	−	0.193602i	0.0257684	−	0.0106736i
$330$	−9.08084	−	17.1453i	−0.499884	−	0.943816i
$331$	−3.00475	−	4.49693i	−0.165156	−	0.247174i	0.739656	−	0.672986i	$-0.234988\pi$
$331$	−3.00475	−	4.49693i	−0.165156	−	0.247174i	−0.904812	+	0.425812i	$0.859988\pi$
$332$	−1.51926	−	22.6692i	−0.0833802	−	1.24413i
$333$	0.0597202	+	0.487726i	0.00327265	+	0.0267272i
$334$	7.26469	+	21.3496i	0.397506	+	1.16820i
$335$	22.4742	+	22.4742i	1.22790	+	1.22790i
$336$	1.15105	+	3.81637i	0.0627949	+	0.208200i
$337$	−6.89599	+	6.89599i	−0.375648	+	0.375648i	−0.869529	−	0.493881i	$-0.835578\pi$
$337$	−6.89599	+	6.89599i	−0.375648	+	0.375648i	0.493881	+	0.869529i	$0.335578\pi$
$338$	−18.2896	−	9.00272i	−0.994820	−	0.489683i
$339$	−12.8429	+	2.06065i	−0.697529	+	0.111919i
$340$	18.9986	−	9.40380i	1.03034	−	0.509992i
$341$	−21.8993	+	14.6327i	−1.18591	+	0.792403i
$342$	9.82651	+	3.42715i	0.531357	+	0.185319i
$343$	−3.00961	−	7.26585i	−0.162504	−	0.392319i
$344$	4.81590	−	11.6994i	0.259656	−	0.630792i
$345$	−1.01993	−	0.467707i	−0.0549114	−	0.0251805i
$346$	−13.6231	+	17.7810i	−0.732384	+	0.955914i
$347$	−20.4589	−	4.06952i	−1.09829	−	0.218463i	−0.387501	−	0.921869i	$-0.626661\pi$
$347$	−20.4589	−	4.06952i	−1.09829	−	0.218463i	−0.710788	+	0.703406i	$0.751661\pi$
$348$	−7.83630	−	34.0795i	−0.420070	−	1.82685i
$349$	15.5293	+	10.3763i	0.831262	+	0.555432i	0.896809	−	0.442418i	$-0.145879\pi$
$349$	15.5293	+	10.3763i	0.831262	+	0.555432i	−0.0655466	+	0.997850i	$0.520879\pi$
$350$	−0.0849077	+	1.31018i	−0.00453851	+	0.0700323i
$351$	27.0367	+	3.03440i	1.44311	+	0.161964i
$352$	−15.1205	−	8.65594i	−0.805925	−	0.461363i
$353$	−22.6859			−1.20745			−0.603724	−	0.797193i	$-0.706317\pi$
$353$	−22.6859			−1.20745			−0.603724	+	0.797193i	$0.706317\pi$
$354$	17.9502	+	1.83676i	0.954041	+	0.0976225i
$355$	19.2535	−	28.8148i	1.02187	−	1.52933i
$356$	−31.6263	−	18.1975i	−1.67619	−	0.964468i
$357$	−0.950775	+	3.99571i	−0.0503203	+	0.211476i
$358$	−9.31105	+	12.1529i	−0.492104	+	0.642299i
$359$	14.6073	+	6.05052i	0.770941	+	0.319334i	0.733254	−	0.679955i	$-0.238001\pi$
$359$	14.6073	+	6.05052i	0.770941	+	0.319334i	0.0376877	+	0.999290i	$0.488001\pi$
$360$	−14.2751	−	16.5045i	−0.752363	−	0.869866i
$361$	11.9947	−	4.96838i	0.631302	−	0.261494i
$362$	12.7747	+	3.41291i	0.671421	+	0.179378i
$363$	2.23302	−	1.37459i	0.117203	−	0.0721474i
$364$	−5.70807	−	1.92828i	−0.299184	−	0.101070i
$365$	5.03416	+	25.3084i	0.263500	+	1.32470i
$366$	−7.74072	−	4.17535i	−0.404614	−	0.218249i
$367$	−10.0709	−	10.0709i	−0.525697	−	0.525697i	0.393589	−	0.919286i	$-0.371233\pi$
$367$	−10.0709	−	10.0709i	−0.525697	−	0.525697i	−0.919286	+	0.393589i	$0.871233\pi$
$368$	−0.998608	+	0.134455i	−0.0520560	+	0.00700894i
$369$	9.84049	−	8.47340i	0.512276	−	0.441107i
$370$	0.191892	+	0.563936i	0.00997601	+	0.0293176i
$371$	0.503687	+	2.53221i	0.0261501	+	0.131466i
$372$	−20.3163	+	21.5588i	−1.05335	+	1.11777i
$373$	0.615090	−	0.410990i	0.0318482	−	0.0212803i	−0.539544	−	0.841957i	$-0.681403\pi$
$373$	0.615090	−	0.410990i	0.0318482	−	0.0212803i	0.571392	+	0.820677i	$0.306403\pi$
$374$	−8.98748	−	15.5404i	−0.464732	−	0.803575i
$375$	5.24937	+	14.1412i	0.271076	+	0.730249i
$376$	−0.479818	+	2.44030i	−0.0247447	+	0.125849i
$377$	48.8310	+	20.2265i	2.51493	+	1.04172i
$378$	4.22714	−	0.0840012i	0.217421	−	0.00432056i
$379$	−12.1892	−	2.42459i	−0.626119	−	0.124543i	−0.128174	−	0.991752i	$-0.540912\pi$
$379$	−12.1892	−	2.42459i	−0.626119	−	0.124543i	−0.497945	+	0.867209i	$0.665912\pi$
$380$	12.5109	+	1.62841i	0.641798	+	0.0835354i
$381$	5.38281	−	7.44028i	0.275770	−	0.381177i
$382$	−5.83986	−	6.64922i	−0.298793	−	0.340204i
$383$	−20.3912			−1.04194			−0.520971	−	0.853574i	$-0.674430\pi$
$383$	−20.3912			−1.04194			−0.520971	+	0.853574i	$0.674430\pi$
$384$	−18.7556	−	5.67694i	−0.957117	−	0.289700i
$385$	4.55719			0.232256
$386$	−9.03339	−	10.2854i	−0.459787	−	0.523511i
$387$	−10.5718	−	8.26529i	−0.537396	−	0.420148i
$388$	27.9677	+	3.64024i	1.41985	+	0.184805i
$389$	4.94748	+	0.984114i	0.250847	+	0.0498966i	0.318912	−	0.947784i	$-0.396683\pi$
$389$	4.94748	+	0.984114i	0.250847	+	0.0498966i	−0.0680650	+	0.997681i	$0.521683\pi$
$390$	32.8358	−	3.10825i	1.66270	−	0.157392i
$391$	−0.959201	−	0.397314i	−0.0485089	−	0.0200930i
$392$	18.5083	+	3.63916i	0.934811	+	0.183805i
$393$	−17.5571	+	6.51738i	−0.885639	+	0.328758i
$394$	−0.620813	−	1.07346i	−0.0312761	−	0.0540801i
$395$	−19.6141	+	13.1057i	−0.986892	+	0.659420i
$396$	−13.1659	+	12.9675i	−0.661613	+	0.651643i
$397$	1.17277	+	5.89594i	0.0588599	+	0.295909i	0.998991	−	0.0449034i	$-0.0142980\pi$
$397$	1.17277	+	5.89594i	0.0588599	+	0.295909i	−0.940131	+	0.340812i	$0.889298\pi$
$398$	4.79408	+	14.0889i	0.240306	+	0.706213i
$399$	−1.79169	+	1.66292i	−0.0896965	+	0.0832504i
$400$	−5.13209	−	3.91410i	−0.256605	−	0.195705i
$401$	8.06745	+	8.06745i	0.402869	+	0.402869i	0.879243	−	0.476374i	$-0.158049\pi$
$401$	8.06745	+	8.06745i	0.402869	+	0.402869i	−0.476374	+	0.879243i	$0.658049\pi$
$402$	14.3719	−	26.6441i	0.716803	−	1.32889i
$403$	−8.73508	−	43.9142i	−0.435125	−	2.18752i
$404$	21.2955	+	7.19400i	1.05949	+	0.357915i
$405$	−20.9404	+	9.85906i	−1.04054	+	0.489901i
$406$	7.93542	+	2.12004i	0.393828	+	0.105216i
$407$	0.466064	−	0.193050i	0.0231019	−	0.00956913i
$408$	−13.7683	−	14.7689i	−0.681630	−	0.731172i
$409$	19.5437	+	8.09527i	0.966374	+	0.400285i	0.809361	−	0.587311i	$-0.199814\pi$
$409$	19.5437	+	8.09527i	0.966374	+	0.400285i	0.157013	+	0.987597i	$0.449814\pi$
$410$	9.57449	−	12.4967i	0.472850	−	0.617169i
$411$	8.96552	+	2.13333i	0.442237	+	0.105230i
$412$	1.21920	+	0.701522i	0.0600658	+	0.0345615i
$413$	−2.35466	+	3.52400i	−0.115865	+	0.173405i
$414$	−0.148316	+	1.05840i	−0.00728932	+	0.0520175i
$415$	−29.2144			−1.43408
$416$	23.4317	−	18.1169i	1.14883	−	0.888252i
$417$	−0.734662	+	19.7107i	−0.0359765	+	0.965238i
$418$	0.690959	−	10.6620i	0.0337959	−	0.521494i
$419$	−17.3568	−	11.5974i	−0.847935	−	0.566572i	0.0539522	−	0.998544i	$-0.482818\pi$
$419$	−17.3568	−	11.5974i	−0.847935	−	0.566572i	−0.901887	+	0.431971i	$0.857818\pi$
$420$	4.99524	−	1.14862i	0.243743	−	0.0560467i
$421$	21.1574	+	4.20847i	1.03115	+	0.205108i	0.681535	−	0.731786i	$-0.261313\pi$
$421$	21.1574	+	4.20847i	1.03115	+	0.205108i	0.349614	+	0.936894i	$0.386313\pi$
$422$	−19.8319	+	25.8848i	−0.965403	+	1.26005i
$423$	2.35518	+	1.18809i	0.114513	+	0.0577670i
$424$	−11.7367	−	4.83122i	−0.569984	−	0.234625i
$425$	−2.54501	−	6.14420i	−0.123451	−	0.298037i
$426$	−31.5506	−	9.70171i	−1.52863	−	0.470049i
$427$	1.71768	−	1.14772i	0.0831245	−	0.0555420i
$428$	−17.3838	+	8.60451i	−0.840278	+	0.415915i
$429$	−4.42503	−	27.5788i	−0.213642	−	1.33152i
$430$	−14.5959	−	7.18458i	−0.703877	−	0.346471i
$431$	14.4331	−	14.4331i	0.695217	−	0.695217i	−0.268158	−	0.963375i	$-0.586415\pi$
$431$	14.4331	−	14.4331i	0.695217	−	0.695217i	0.963375	+	0.268158i	$0.0864150\pi$
$432$	−11.1631	+	17.5324i	−0.537084	+	0.843529i
$433$	2.71152	+	2.71152i	0.130307	+	0.130307i	0.769252	−	0.638945i	$-0.220629\pi$
$433$	2.71152	+	2.71152i	0.130307	+	0.130307i	−0.638945	+	0.769252i	$0.720629\pi$
$434$	−2.24145	−	6.58720i	−0.107593	−	0.316196i
$435$	−44.3966	+	7.12346i	−2.12865	+	0.341544i
$436$	1.14986	+	17.1573i	0.0550682	+	0.821684i
$437$	−0.343293	−	0.513774i	−0.0164219	−	0.0245771i
$438$	21.7198	−	11.5037i	1.03781	−	0.549667i
$439$	−3.90052	+	1.61565i	−0.186162	+	0.0771107i	−0.473817	−	0.880623i	$-0.657124\pi$
$439$	−3.90052	+	1.61565i	−0.186162	+	0.0771107i	0.287655	+	0.957734i	$0.407124\pi$
$440$	−12.4054	+	18.6548i	−0.591404	+	0.889334i
$441$	9.01103	−	17.8627i	0.429097	−	0.850607i
$442$	30.2545	−	4.00568i	1.43906	−	0.190531i
$443$	4.98879	−	25.0803i	0.237025	−	1.19160i	−0.660564	−	0.750769i	$-0.729683\pi$
$443$	4.98879	−	25.0803i	0.237025	−	1.19160i	0.897589	−	0.440833i	$-0.145317\pi$
$444$	0.462206	−	0.329075i	0.0219353	−	0.0156172i
$445$	−26.0662	+	39.0108i	−1.23565	+	1.84929i
$446$	3.21599	+	3.66170i	0.152281	+	0.173387i
$447$	−10.0172	−	0.373364i	−0.473799	−	0.0176595i
$448$	3.24032	−	3.26901i	0.153091	−	0.154446i
$449$			4.79833i			0.226447i	0.993570	+	0.113224i	$0.0361177\pi$
$449$			4.79833i			0.226447i	−0.993570	+	0.113224i	$0.963882\pi$
$450$	−5.46570	+	4.12214i	−0.257655	+	0.194319i
$451$	−11.0851	−	7.40685i	−0.521978	−	0.348775i
$452$	9.16069	+	11.9022i	0.430882	+	0.559832i
$453$	3.70321	−	15.5631i	0.173992	−	0.731216i
$454$	−4.43403	−	33.4897i	−0.208099	−	1.57175i
$455$	−2.96472	+	7.15747i	−0.138988	+	0.335547i
$456$	−1.92992	−	11.8610i	−0.0903767	−	0.555442i
$457$	−0.757243	−	1.82815i	−0.0354224	−	0.0855171i	0.905178	−	0.425032i	$-0.139737\pi$
$457$	−0.757243	−	1.82815i	−0.0354224	−	0.0855171i	−0.940601	+	0.339515i	$0.889737\pi$
$458$	−8.46567	−	14.6381i	−0.395575	−	0.683995i
$459$	−19.0227	+	9.83786i	−0.887905	+	0.459192i
$460$	0.0866379	+	1.29274i	0.00403951	+	0.0602744i
$461$	2.48380	−	0.494058i	0.115682	−	0.0230106i	−0.136910	−	0.990584i	$-0.543717\pi$
$461$	2.48380	−	0.494058i	0.115682	−	0.0230106i	0.252592	+	0.967573i	$0.418717\pi$
$462$	−1.24425	−	4.15849i	−0.0578877	−	0.193471i
$463$	13.2879	−	13.2879i	0.617543	−	0.617543i	−0.327358	−	0.944901i	$-0.606158\pi$
$463$	13.2879	−	13.2879i	0.617543	−	0.617543i	0.944901	+	0.327358i	$0.106158\pi$
$464$	−30.2798	+	26.7125i	−1.40571	+	1.24010i
$465$	25.9124	+	27.9188i	1.20166	+	1.29470i
$466$	3.61050	−	7.33494i	0.167253	−	0.339784i
$467$	38.6434	−	7.68664i	1.78820	−	0.355695i	0.813911	−	0.580990i	$-0.197334\pi$
$467$	38.6434	−	7.68664i	1.78820	−	0.355695i	0.974291	+	0.225295i	$0.0723345\pi$
$468$	−11.8015	−	29.1144i	−0.545522	−	1.34581i
$469$	3.95053	+	5.91238i	0.182418	+	0.273008i
$470$	3.08956	+	0.825414i	0.142511	+	0.0380735i
$471$	7.28591	+	19.6274i	0.335717	+	0.904385i
$472$	−8.01571	−	19.2317i	−0.368953	−	0.885210i
$473$	−5.27221	+	12.7282i	−0.242416	+	0.585245i
$474$	17.3143	+	14.3198i	0.795274	+	0.657732i
$475$	0.772178	−	3.88200i	0.0354299	−	0.178118i
$476$	4.57926	−	1.23422i	0.209890	−	0.0565704i
$477$	−8.29160	+	10.6055i	−0.379646	+	0.485591i
$478$	−4.84793	−	0.314174i	−0.221739	−	0.0143700i
$479$		−	32.0168i		−	1.46288i	−0.681904	−	0.731442i	$-0.738848\pi$
$479$		−	32.0168i		−	1.46288i	0.681904	−	0.731442i	$-0.261152\pi$
$480$	−8.89598	+	23.5747i	−0.406044	+	1.07603i
$481$			0.857584i			0.0391025i
$482$	−0.192570	+	2.97149i	−0.00877132	+	0.135348i
$483$	−0.203388	−	0.147145i	−0.00925446	−	0.00669531i
$484$	−2.62441	−	1.51007i	−0.119291	−	0.0686394i
$485$	7.07505	−	35.5687i	0.321262	−	1.61509i
$486$	14.7139	+	16.4165i	0.667434	+	0.744669i
$487$	10.6267	−	25.6552i	0.481543	−	1.16255i	−0.477332	−	0.878723i	$-0.658396\pi$
$487$	10.6267	−	25.6552i	0.481543	−	1.16255i	0.958876	−	0.283826i	$-0.0916037\pi$
$488$	0.0223754	+	10.1556i	0.00101288	+	0.459722i
$489$	5.87891	−	2.18231i	0.265853	−	0.0986875i
$490$	6.26032	−	23.4326i	0.282812	−	1.05858i
$491$	15.8815	+	23.7683i	0.716722	+	1.07265i	0.993733	+	0.111783i	$0.0356563\pi$
$491$	15.8815	+	23.7683i	0.716722	+	1.07265i	−0.277011	+	0.960867i	$0.589344\pi$
$492$	−14.0175	−	5.32487i	−0.631959	−	0.240063i
$493$	−40.8058	+	8.11678i	−1.83780	+	0.365561i
$494$	16.2961	+	8.02146i	0.733195	+	0.360902i
$495$	15.5049	+	18.0064i	0.696892	+	0.809329i
$496$	33.0662	+	8.75603i	1.48472	+	0.393157i
$497$	5.48241	−	5.48241i	0.245920	−	0.245920i
$498$	7.97640	+	26.6585i	0.357431	+	1.19460i
$499$	14.1043	−	2.80552i	0.631394	−	0.125592i	0.130990	−	0.991384i	$-0.458185\pi$
$499$	14.1043	−	2.80552i	0.631394	−	0.125592i	0.500405	+	0.865792i	$0.333185\pi$
$500$	11.4650	−	13.1121i	0.512730	−	0.586391i
$501$	−14.4789	−	23.5209i	−0.646869	−	1.05084i
$502$	30.9461	−	17.8971i	1.38119	−	0.798786i
$503$	−10.5626	−	25.5004i	−0.470963	−	1.13701i	−0.963738	−	0.266849i	$-0.914017\pi$
$503$	−10.5626	−	25.5004i	−0.470963	−	1.13701i	0.492775	−	0.870157i	$-0.335983\pi$
$504$	−2.41197	−	4.24461i	−0.107438	−	0.189070i
$505$	11.0607	−	26.7029i	0.492195	−	1.18826i
$506$	1.08773	−	0.144015i	0.0483555	−	0.00640226i
$507$	24.2885	+	5.77943i	1.07869	+	0.256673i
$508$	−10.5152	−	1.36865i	−0.466538	−	0.0607238i
$509$	−2.90361	−	1.94013i	−0.128700	−	0.0859947i	0.489554	−	0.871973i	$-0.337160\pi$
$509$	−2.90361	−	1.94013i	−0.128700	−	0.0859947i	−0.618254	+	0.785978i	$0.712160\pi$
$510$	−20.1319	+	16.3943i	−0.891456	+	0.725954i
$511$			5.77309i			0.255386i
$512$	4.56098	+	22.1630i	0.201569	+	0.979474i
$513$	−12.6664	−	1.42158i	−0.559235	−	0.0627644i
$514$	−21.2253	+	18.6417i	−0.936210	+	0.822251i
$515$	1.00486	−	1.50388i	0.0442794	−	0.0662688i
$516$	−2.57090	+	15.2805i	−0.113178	+	0.672689i
$517$	0.528340	−	2.65614i	0.0232364	−	0.116817i
$518$	0.0174924	+	0.132118i	0.000768574	+	0.00580495i
$519$	11.4353	−	24.9372i	0.501956	−	1.09462i
$520$	−21.2286	−	31.6198i	−0.930936	−	1.38662i
$521$	17.2062	−	7.12705i	0.753818	−	0.312242i	0.0275196	−	0.999621i	$-0.491239\pi$
$521$	17.2062	−	7.12705i	0.753818	−	0.312242i	0.726298	+	0.687380i	$0.241239\pi$
$522$	18.6218	+	38.5675i	0.815056	+	1.68805i
$523$	18.4620	+	27.6303i	0.807286	+	1.20819i	0.974967	+	0.222348i	$0.0713720\pi$
$523$	18.4620	+	27.6303i	0.807286	+	1.20819i	−0.167681	+	0.985841i	$0.553628\pi$
$524$	16.2794	+	14.2344i	0.711169	+	0.621833i
$525$	−0.254747	−	1.58770i	−0.0111181	−	0.0692929i
$526$	−23.9694	+	8.15616i	−1.04512	+	0.355626i
$527$	24.9220	+	24.9220i	1.08562	+	1.08562i
$528$	20.4098	+	6.22675i	0.888222	+	0.270984i
$529$	−16.2186	+	16.2186i	−0.705156	+	0.705156i
$530$	−7.20745	+	14.6424i	−0.313072	+	0.636024i
$531$	−21.9353	+	2.68590i	−0.951913	+	0.116558i
$532$	2.67417	+	0.903380i	0.115940	+	0.0391665i
$533$	18.8446	−	12.5916i	0.816252	−	0.545402i
$534$	42.7146	+	13.1346i	1.84844	+	0.568389i
$535$	9.54459	+	23.0427i	0.412648	+	0.996222i
$536$	−34.9562	+	0.0770175i	−1.50988	+	0.00332665i
$537$	7.81576	−	17.0439i	0.337275	−	0.735500i
$538$	−10.1284	−	7.75998i	−0.436666	−	0.334556i
$539$	−20.1454	−	4.00717i	−0.867724	−	0.172601i
$540$	21.5337	+	15.8293i	0.926662	+	0.681186i
$541$	−30.7516	−	20.5475i	−1.32211	−	0.883407i	−0.324075	−	0.946031i	$-0.605053\pi$
$541$	−30.7516	−	20.5475i	−1.32211	−	0.883407i	−0.998037	+	0.0626238i	$0.980053\pi$
$542$	−5.45723	−	0.353661i	−0.234408	−	0.0151910i
$543$	−16.1832	−	0.603183i	−0.694488	−	0.0258851i
$544$	−7.41319	+	22.1049i	−0.317838	+	0.947740i
$545$	22.1111			0.947134
$546$	7.34073	+	0.751143i	0.314154	+	0.0321459i
$547$	0.821575	−	1.22957i	0.0351280	−	0.0525728i	−0.813490	−	0.581579i	$-0.802435\pi$
$547$	0.821575	−	1.22957i	0.0351280	−	0.0525728i	0.848618	+	0.529006i	$0.177435\pi$
$548$	−2.76933	−	10.2749i	−0.118300	−	0.438921i
$549$	10.3789	+	2.88206i	0.442962	+	0.123003i
$550$	5.57907	+	4.27446i	0.237892	+	0.182264i
$551$	−22.8768	−	9.47588i	−0.974584	−	0.403686i
$552$	1.15599	−	0.432015i	0.0492021	−	0.0183878i
$553$	−4.87589	+	2.01966i	−0.207344	+	0.0858847i
$554$	−7.83981	+	29.3448i	−0.333082	+	1.24674i
$555$	−0.382451	−	0.621289i	−0.0162341	−	0.0263723i
$556$	20.4122	−	10.1035i	0.865668	−	0.428482i
$557$	0.115798	+	0.582157i	0.00490653	+	0.0246668i	0.983161	−	0.182741i	$-0.0584971\pi$
$557$	0.115798	+	0.582157i	0.00490653	+	0.0246668i	−0.978254	+	0.207408i	$0.933497\pi$
$558$	18.4014	−	31.2680i	0.778992	−	1.32368i
$559$	−16.5609	−	16.5609i	−0.700453	−	0.700453i
$560$	−3.91541	−	4.43830i	−0.165456	−	0.187553i
$561$	14.9571	+	16.1153i	0.631491	+	0.680388i
$562$	10.4734	−	3.56381i	0.441792	−	0.150330i
$563$	0.199069	+	1.00079i	0.00838974	+	0.0421781i	0.984753	−	0.173956i	$-0.0556551\pi$
$563$	0.199069	+	1.00079i	0.00838974	+	0.0421781i	−0.976364	+	0.216134i	$0.930655\pi$
$564$	−0.0903414	−	3.04462i	−0.00380406	−	0.128202i
$565$	16.0578	−	10.7295i	0.675556	−	0.451392i
$566$	−22.1076	+	12.7855i	−0.929250	+	0.537413i
$567$	−5.02521	+	1.24937i	−0.211039	+	0.0524685i
$568$	7.51822	+	37.3662i	0.315457	+	1.56785i
$569$	−30.2339	−	12.5233i	−1.26747	−	0.525003i	−0.355276	−	0.934762i	$-0.615613\pi$
$569$	−30.2339	−	12.5233i	−1.26747	−	0.525003i	−0.912194	+	0.409758i	$0.865613\pi$
$570$	−15.3832	+	1.45618i	−0.644331	+	0.0609926i
$571$	33.6563	+	6.69466i	1.40847	+	0.280163i	0.840021	−	0.542553i	$-0.182542\pi$
$571$	33.6563	+	6.69466i	1.40847	+	0.280163i	0.568452	+	0.822716i	$0.307542\pi$
$572$	−25.5588	+	19.6717i	−1.06867	+	0.822513i
$573$	8.78139	+	6.35306i	0.366848	+	0.265403i
$574$	2.64635	−	2.32422i	0.110456	−	0.0970113i
$575$	0.406470			0.0169510
$576$	23.9411	+	1.68110i	0.997544	+	0.0700460i
$577$	−0.528419			−0.0219984			−0.0109992	−	0.999940i	$-0.503501\pi$
$577$	−0.528419			−0.0219984			−0.0109992	+	0.999940i	$0.503501\pi$
$578$	0.0138649	−	0.0121772i	0.000576703	−	0.000506505i
$579$	13.5835	+	9.82723i	0.564511	+	0.408406i
$580$	31.6677	+	41.1448i	1.31493	+	1.70845i
$581$	−6.41044	−	1.27512i	−0.265950	−	0.0529007i
$582$	−34.3886	+	3.25523i	−1.42545	+	0.134934i
$583$	12.7688	+	5.28899i	0.528828	+	0.219048i
$584$	−23.6321	−	15.7152i	−0.977903	−	0.650302i
$585$	−38.3675	+	12.6375i	−1.58630	+	0.522498i
$586$	−20.6140	+	11.9217i	−0.851558	+	0.492481i
$587$	26.8802	−	17.9608i	1.10946	−	0.741320i	0.140885	−	0.990026i	$-0.455005\pi$
$587$	26.8802	−	17.9608i	1.10946	−	0.741320i	0.968579	+	0.248706i	$0.0800052\pi$
$588$	−23.0918	+	0.685191i	−0.952290	+	0.0282568i
$589$	4.09229	+	20.5733i	0.168620	+	0.847708i
$590$	−25.3628	+	8.63030i	−1.04417	+	0.355304i
$591$	1.03317	+	1.11317i	0.0424989	+	0.0457896i
$592$	−0.588443	−	0.288042i	−0.0241848	−	0.0118384i
$593$	−17.0616	−	17.0616i	−0.700634	−	0.700634i	0.263912	−	0.964547i	$-0.414987\pi$
$593$	−17.0616	−	17.0616i	−0.700634	−	0.700634i	−0.964547	+	0.263912i	$0.914987\pi$
$594$	12.1978	−	19.0647i	0.500482	−	0.782233i
$595$	−1.18973	−	5.98116i	−0.0487741	−	0.245204i
$596$	5.13471	+	10.3737i	0.210326	+	0.424924i
$597$	−9.55484	−	15.5218i	−0.391053	−	0.635264i
$598$	−0.481444	+	1.80207i	−0.0196877	+	0.0736920i
$599$	26.0295	−	10.7818i	1.06354	−	0.440531i	0.218830	−	0.975763i	$-0.429776\pi$
$599$	26.0295	−	10.7818i	1.06354	−	0.440531i	0.844705	+	0.535232i	$0.179776\pi$
$600$	7.19270	+	3.27916i	0.293641	+	0.133871i
$601$	−22.1716	−	9.18376i	−0.904396	−	0.374613i	−0.118487	−	0.992956i	$-0.537805\pi$
$601$	−22.1716	−	9.18376i	−0.904396	−	0.374613i	−0.785909	+	0.618342i	$0.787805\pi$
$602$	−2.88916	−	2.21356i	−0.117753	−	0.0902180i
$603$	−9.92025	+	35.7250i	−0.403984	+	1.45483i
$604$	−17.8359	+	4.80722i	−0.725734	+	0.195603i
$605$	−2.16302	+	3.23719i	−0.0879393	+	0.131610i
$606$	−27.3866	−	2.80234i	−1.11251	−	0.113837i
$607$	28.3755			1.15173			0.575863	−	0.817546i	$-0.304666\pi$
$607$	28.3755			1.15173			0.575863	+	0.817546i	$0.304666\pi$
$608$	−10.9775	+	8.48754i	−0.445196	+	0.344215i
$609$	−10.0527	−	0.374688i	−0.407358	−	0.0151831i
$610$	13.0312	+	0.844499i	0.527618	+	0.0341928i
$611$	3.82799	+	2.55778i	0.154864	+	0.103477i
$612$	20.4566	+	13.8945i	0.826911	+	0.561650i
$613$	44.2783	+	8.80751i	1.78839	+	0.355732i	0.974342	−	0.225073i	$-0.0722619\pi$
$613$	44.2783	+	8.80751i	1.78839	+	0.355732i	0.814043	+	0.580804i	$0.197262\pi$
$614$	9.28796	+	7.11607i	0.374832	+	0.287181i
$615$	−8.03689	+	17.5262i	−0.324079	+	0.706723i
$616$	−3.53631	+	3.55192i	−0.142482	+	0.143111i
$617$	−8.58868	−	20.7349i	−0.345767	−	0.834756i	−0.997110	−	0.0759722i	$-0.975794\pi$
$617$	−8.58868	−	20.7349i	−0.345767	−	0.834756i	0.651343	−	0.758784i	$-0.274206\pi$
$618$	−1.64666	−	0.506343i	−0.0662385	−	0.0203681i
$619$	−17.6693	+	11.8063i	−0.710191	+	0.474534i	−0.857452	−	0.514563i	$-0.827954\pi$
$619$	−17.6693	+	11.8063i	−0.710191	+	0.474534i	0.147262	+	0.989098i	$0.452954\pi$
$620$	14.0768	−	41.6700i	0.565339	−	1.67351i
$621$	−0.110584	−	1.30426i	−0.00443758	−	0.0523380i
$622$	−11.3094	+	22.9757i	−0.453465	+	0.921241i
$623$	−7.42232	+	7.42232i	−0.297369	+	0.297369i
$624$	−23.0574	+	28.0045i	−0.923036	+	1.12108i
$625$	−21.5415	−	21.5415i	−0.861660	−	0.861660i
$626$	−35.3948	+	12.0439i	−1.41466	+	0.481371i
$627$	2.07308	+	12.9203i	0.0827907	+	0.515989i
$628$	15.9129	−	18.1991i	0.634995	−	0.726222i
$629$	−0.375045	−	0.561294i	−0.0149540	−	0.0223803i
$630$	−5.65308	+	2.72952i	−0.225224	+	0.108747i
$631$	−35.8753	+	14.8600i	−1.42817	+	0.591568i	−0.956899	−	0.290420i	$-0.906205\pi$
$631$	−35.8753	+	14.8600i	−1.42817	+	0.591568i	−0.471272	+	0.881988i	$0.656205\pi$
$632$	5.00548	−	25.4572i	0.199107	−	1.01263i
$633$	16.6471	−	36.3025i	0.661661	−	1.44289i
$634$	−4.89007	−	36.9341i	−0.194209	−	1.46684i
$635$	−2.66006	+	13.3730i	−0.105561	+	0.530691i
$636$	15.3292	+	2.57909i	0.607842	+	0.102267i
$637$	19.3994	−	29.0332i	0.768631	−	1.15034i
$638$	33.0365	−	29.0152i	1.30793	−	1.14872i
$639$	40.3149	+	3.00943i	1.59483	+	0.119051i
$640$	28.8265	−	3.94595i	1.13947	−	0.155977i
$641$		−	20.0547i		−	0.792112i	−0.918226	−	0.396056i	$-0.870379\pi$
$641$		−	20.0547i		−	0.792112i	0.918226	−	0.396056i	$-0.129621\pi$
$642$	18.4208	−	15.0009i	0.727009	−	0.592038i
$643$	−25.5229	−	17.0538i	−1.00652	−	0.672538i	−0.0610164	−	0.998137i	$-0.519434\pi$
$643$	−25.5229	−	17.0538i	−1.00652	−	0.672538i	−0.945508	+	0.325599i	$0.894434\pi$
$644$	−0.0374133	+	0.287444i	−0.00147429	+	0.0113269i
$645$	19.3834	+	4.61225i	0.763220	+	0.181607i
$646$	−14.1739	+	1.87662i	−0.557664	+	0.0738345i
$647$	−2.24611	+	5.42260i	−0.0883039	+	0.213184i	−0.961862	−	0.273536i	$-0.911807\pi$
$647$	−2.24611	+	5.42260i	−0.0883039	+	0.213184i	0.873558	+	0.486720i	$0.161807\pi$
$648$	8.56513	−	23.9716i	0.336470	−	0.941694i
$649$	8.68236	+	20.9611i	0.340812	+	0.822794i
$650$	−10.3429	+	5.98163i	−0.405683	+	0.234619i
$651$	4.46732	+	7.25713i	0.175088	+	0.284429i
$652$	−5.45108	−	4.76632i	−0.213481	−	0.186663i
$653$	26.4232	−	5.25590i	1.03402	−	0.205679i	0.351226	−	0.936291i	$-0.385765\pi$
$653$	26.4232	−	5.25590i	1.03402	−	0.205679i	0.682793	+	0.730612i	$0.260765\pi$
$654$	−6.03697	−	20.1766i	−0.236064	−	0.788968i
$655$	19.6620	−	19.6620i	0.768259	−	0.768259i
$656$	2.31042	+	17.1597i	0.0902068	+	0.669974i
$657$	−22.8107	+	19.6417i	−0.889930	+	0.766296i
$658$	0.641908	+	0.315968i	0.0250242	+	0.0123177i
$659$	2.96569	−	0.589912i	0.115527	−	0.0229797i	−0.136988	−	0.990573i	$-0.543742\pi$
$659$	2.96569	−	0.589912i	0.115527	−	0.0229797i	0.252515	+	0.967593i	$0.418742\pi$
$660$	9.74360	−	25.6497i	0.379269	−	0.998413i
$661$	−4.60037	−	6.88495i	−0.178934	−	0.267793i	0.731151	−	0.682216i	$-0.238984\pi$
$661$	−4.60037	−	6.88495i	−0.178934	−	0.267793i	−0.910085	+	0.414423i	$0.863984\pi$
$662$	1.97419	−	7.38948i	0.0767290	−	0.287200i
$663$	−35.0410	+	13.0076i	−1.36088	+	0.505172i
$664$	22.6699	−	22.7700i	0.879763	−	0.883648i
$665$	1.38894	−	3.35319i	0.0538607	−	0.130031i
$666$	−0.462514	+	0.518621i	−0.0179220	+	0.0200962i
$667$	0.496092	−	2.49402i	0.0192088	−	0.0965690i
$668$	−15.9059	+	27.6435i	−0.615417	+	1.06956i
$669$	−4.83588	−	3.49861i	−0.186966	−	0.135264i
$670$	−2.90682	+	44.8543i	−0.112300	+	1.73287i
$671$		−	11.0587i		−	0.426917i
$672$	−2.98098	+	4.78465i	−0.114994	+	0.184572i
$673$		−	9.96105i		−	0.383970i	−0.981398	−	0.191985i	$-0.938507\pi$
$673$		−	9.96105i		−	0.383970i	0.981398	−	0.191985i	$-0.0614925\pi$
$674$	−13.7631	−	0.891931i	−0.530135	−	0.0343559i
$675$	5.40662	−	6.40837i	0.208101	−	0.246658i
$676$	−7.50240	−	27.8357i	−0.288554	−	1.07060i
$677$	−3.33626	+	16.7725i	−0.128223	+	0.644620i	0.862202	+	0.506565i	$0.169085\pi$
$677$	−3.33626	+	16.7725i	−0.128223	+	0.644620i	−0.990425	+	0.138055i	$0.955915\pi$
$678$	−14.1750	−	11.7235i	−0.544389	−	0.450237i
$679$	3.10492	−	7.49594i	0.119156	−	0.287668i
$680$	27.7225	+	11.4115i	1.06311	+	0.437612i
$681$	14.3985	+	38.7881i	0.551753	+	1.48636i
$682$	−35.9856	−	9.61398i	−1.37796	−	0.368138i
$683$	17.2932	+	25.8811i	0.661705	+	0.990311i	0.998806	+	0.0488430i	$0.0155534\pi$
$683$	17.2932	+	25.8811i	0.661705	+	0.990311i	−0.337102	+	0.941468i	$0.609447\pi$
$684$	5.52885	+	13.6398i	0.211401	+	0.521530i
$685$	−13.4204	+	2.66949i	−0.512769	+	0.101996i
$686$	4.91184	−	9.97870i	0.187535	−	0.380989i
$687$	14.0887	+	15.1796i	0.537519	+	0.579139i
$688$	16.9259	−	5.80109i	0.645295	−	0.221164i
$689$	−16.6137	+	16.6137i	−0.632930	+	0.632930i
$690$	−0.454866	−	1.52024i	−0.0173164	−	0.0578745i
$691$	−9.31918	+	1.85370i	−0.354518	+	0.0705180i	−0.369137	−	0.929375i	$-0.620347\pi$
$691$	−9.31918	+	1.85370i	−0.354518	+	0.0705180i	0.0146186	+	0.999893i	$0.495347\pi$
$692$	−31.6073	+	2.11828i	−1.20153	+	0.0805250i
$693$	2.61627	+	4.62784i	0.0993839	+	0.175797i
$694$	−14.7688	−	25.5369i	−0.560615	−	0.969368i
$695$	−11.2073	−	27.0568i	−0.425118	−	1.02632i
$696$	28.8989	−	40.1309i	1.09541	−	1.52116i
$697$	−6.82729	+	16.4825i	−0.258602	+	0.624321i
$698$	3.46683	+	26.1846i	0.131222	+	0.991102i
$699$	−2.31781	+	9.74080i	−0.0876677	+	0.368431i
$700$	−1.47141	+	1.13249i	−0.0556141	+	0.0428041i
$701$	23.9246	+	15.9859i	0.903622	+	0.603781i	0.918202	−	0.396113i	$-0.129641\pi$
$701$	23.9246	+	15.9859i	0.903622	+	0.603781i	−0.0145802	+	0.999894i	$0.504641\pi$
$702$	22.0074	+	31.5604i	0.830615	+	1.19117i
$703$		−	0.401769i		−	0.0151530i
$704$	−4.91339	−	24.1447i	−0.185180	−	0.909989i
$705$	−3.91392	−	0.145880i	−0.147407	−	0.00549417i
$706$	−21.1713	−	24.1055i	−0.796792	−	0.907223i
$707$	3.59252	−	5.37659i	0.135111	−	0.202207i
$708$	14.8001	+	20.7876i	0.556220	+	0.781244i
$709$	2.58842	−	13.0129i	0.0972103	−	0.488709i	−0.901253	−	0.433293i	$-0.857351\pi$
$709$	2.58842	−	13.0129i	0.0972103	−	0.488709i	0.998463	−	0.0554160i	$-0.0176485\pi$
$710$	48.5860	−	6.43277i	1.82340	−	0.241418i
$711$	−24.5693	−	12.3942i	−0.921420	−	0.464819i
$712$	−10.1785	−	50.5879i	−0.381455	−	1.89586i
$713$	−1.99018	+	0.824360i	−0.0745328	+	0.0308725i
$714$	−5.13305	+	2.71867i	−0.192100	+	0.101744i
$715$	23.0405	+	34.4825i	0.861664	+	1.28957i
$716$	−21.6028	+	1.44779i	−0.807333	+	0.0541065i
$717$	5.87479	−	0.942613i	0.219398	−	0.0352025i
$718$	7.20288	+	21.1679i	0.268809	+	0.789979i
$719$	−21.0099	−	21.0099i	−0.783536	−	0.783536i	0.196890	−	0.980426i	$-0.436916\pi$
$719$	−21.0099	−	21.0099i	−0.783536	−	0.783536i	−0.980426	+	0.196890i	$0.936916\pi$
$720$	4.21532	−	30.5710i	0.157096	−	1.13931i
$721$	0.286133	−	0.286133i	0.0106562	−	0.0106562i
$722$	16.4732	+	8.10866i	0.613070	+	0.301773i
$723$	−0.577765	−	3.60089i	−0.0214873	−	0.133919i
$724$	8.29530	+	16.7591i	0.308292	+	0.622847i
$725$	13.5434	−	9.04943i	0.502990	−	0.336087i
$726$	3.54454	+	1.08993i	0.131550	+	0.0404512i
$727$	−3.03708	−	7.33217i	−0.112639	−	0.271935i	0.857500	−	0.514484i	$-0.172017\pi$
$727$	−3.03708	−	7.33217i	−0.112639	−	0.271935i	−0.970139	+	0.242549i	$0.922017\pi$
$728$	−3.27803	−	7.86481i	−0.121492	−	0.291489i
$729$	−22.0337	−	15.6050i	−0.816064	−	0.577962i
$730$	−22.1941	+	28.9679i	−0.821440	+	1.07215i
$731$	18.0818	+	3.59669i	0.668779	+	0.133028i
$732$	−2.78729	−	12.1217i	−0.103021	−	0.448031i
$733$	−8.33279	−	5.56779i	−0.307779	−	0.205651i	0.392082	−	0.919930i	$-0.371755\pi$
$733$	−8.33279	−	5.56779i	−0.307779	−	0.205651i	−0.699861	+	0.714279i	$0.746755\pi$
$734$	1.30258	−	20.0997i	0.0480790	−	0.741892i
$735$	−1.10642	+	29.6849i	−0.0408110	+	1.09495i
$736$	−1.07481	−	0.935620i	−0.0396179	−	0.0344874i
$737$	38.0648			1.40214
$738$	18.1871	+	2.54860i	0.669478	+	0.0938152i
$739$	−6.56698	+	9.82817i	−0.241570	+	0.361535i	−0.932367	−	0.361514i	$-0.882260\pi$
$739$	−6.56698	+	9.82817i	−0.241570	+	0.361535i	0.690797	+	0.723049i	$0.257260\pi$
$740$	−0.420144	+	0.730186i	−0.0154448	+	0.0268422i
$741$	−21.6412	−	5.14949i	−0.795009	−	0.189171i
$742$	−2.22061	+	2.89835i	−0.0815210	+	0.106402i
$743$	−0.275509	−	0.114120i	−0.0101074	−	0.00418664i	0.377624	−	0.925959i	$-0.376741\pi$
$743$	−0.275509	−	0.114120i	−0.0101074	−	0.00418664i	−0.387731	+	0.921772i	$0.626741\pi$
$744$	−41.8677	−	1.46814i	−1.53495	−	0.0538245i
$745$	13.7506	−	5.69569i	0.503784	−	0.208674i
$746$	1.01073	+	0.270030i	0.0370056	+	0.00988649i
$747$	−16.7719	−	29.6673i	−0.613652	−	1.08547i
$748$	8.12543	−	24.0528i	0.297095	−	0.879456i
$749$	1.08860	+	5.47278i	0.0397767	+	0.199971i
$750$	−10.1272	+	18.7750i	−0.369794	+	0.685564i
$751$	18.1872	+	18.1872i	0.663659	+	0.663659i	0.956241	−	0.292582i	$-0.0945143\pi$
$751$	18.1872	+	18.1872i	0.663659	+	0.663659i	−0.292582	+	0.956241i	$0.594514\pi$
$752$	−3.04079	+	1.76753i	−0.110886	+	0.0644551i
$753$	−32.0909	+	29.7847i	−1.16946	+	1.08541i
$754$	24.0787	+	70.7628i	0.876895	+	2.57703i
$755$	4.63391	+	23.2963i	0.168645	+	0.847838i
$756$	4.03418	+	4.41327i	0.146722	+	0.160509i
$757$	7.39600	−	4.94185i	0.268812	−	0.179615i	−0.413857	−	0.910342i	$-0.635819\pi$
$757$	7.39600	−	4.94185i	0.268812	−	0.179615i	0.682670	+	0.730727i	$0.260819\pi$
$758$	−8.79912	−	15.2147i	−0.319599	−	0.552623i
$759$	−1.25982	+	0.467658i	−0.0457285	+	0.0169749i
$760$	9.94536	+	14.8135i	0.360756	+	0.537343i
$761$	−38.4211	−	15.9145i	−1.39276	−	0.576902i	−0.444901	−	0.895580i	$-0.646761\pi$
$761$	−38.4211	−	15.9145i	−1.39276	−	0.576902i	−0.947863	+	0.318678i	$0.896761\pi$
$762$	12.9293	−	1.22389i	0.468379	−	0.0443369i
$763$	4.85177	+	0.965078i	0.175646	+	0.0349382i
$764$	1.61534	−	12.4106i	0.0584411	−	0.448999i
$765$	19.5851	−	25.0505i	0.708099	−	0.905703i
$766$	−19.0298	−	21.6672i	−0.687575	−	0.782869i
$767$	−38.5696			−1.39267
$768$	−11.4712	−	25.2272i	−0.413932	−	0.910308i
$769$	12.5895			0.453989			0.226995	−	0.973896i	$-0.427110\pi$
$769$	12.5895			0.453989			0.226995	+	0.973896i	$0.427110\pi$
$770$	4.25294	+	4.84237i	0.153265	+	0.174507i
$771$	20.2799	−	28.0315i	0.730364	−	1.00953i
$772$	2.49870	−	19.1973i	0.0899301	−	0.690927i
$773$	−2.63888	−	0.524907i	−0.0949141	−	0.0188796i	0.147405	−	0.989076i	$-0.452908\pi$
$773$	−2.63888	−	0.524907i	−0.0949141	−	0.0188796i	−0.242319	+	0.970197i	$0.577908\pi$
$774$	−1.08350	−	18.9468i	−0.0389457	−	0.681030i
$775$	−12.7482	−	5.28047i	−0.457928	−	0.189680i
$776$	22.2325	+	33.1151i	0.798100	+	1.18876i
$777$	−0.0568029	−	0.153021i	−0.00203779	−	0.00548959i
$778$	3.57147	+	6.17549i	0.128043	+	0.221402i
$779$	−8.82850	+	5.89901i	−0.316314	+	0.211354i
$780$	33.9463	+	31.9898i	1.21547	+	1.14542i
$781$	−8.09712	−	40.7069i	−0.289738	−	1.45661i
$782$	−0.472984	−	1.39001i	−0.0169139	−	0.0497067i
$783$	−32.7219	−	40.9954i	−1.16938	−	1.46505i
$784$	13.4057	+	23.0627i	0.478777	+	0.823668i
$785$	−21.9806	−	21.9806i	−0.784520	−	0.784520i
$786$	−23.3101	−	12.5735i	−0.831446	−	0.448483i
$787$	−6.40280	−	32.1890i	−0.228235	−	1.14742i	−0.909604	−	0.415475i	$-0.863615\pi$
$787$	−6.40280	−	32.1890i	−0.228235	−	1.14742i	0.681369	−	0.731940i	$-0.261385\pi$
$788$	0.561267	−	1.66145i	0.0199943	−	0.0591868i
$789$	26.4072	−	16.2556i	0.940121	−	0.578716i
$790$	−32.2304	−	8.61075i	−1.14671	−	0.306357i
$791$	3.99183	−	1.65347i	0.141933	−	0.0587906i
$792$	−26.0659	−	1.88803i	−0.926213	−	0.0670883i
$793$	17.3687	+	7.19434i	0.616780	+	0.255479i
$794$	−5.17041	+	6.74847i	−0.183491	+	0.239494i
$795$	4.62693	−	19.4451i	0.164100	−	0.689646i
$796$	−10.4965	+	18.2424i	−0.372040	+	0.646583i
$797$	17.6440	−	26.4061i	0.624981	−	0.935351i	−0.374984	−	0.927031i	$-0.622352\pi$
$797$	17.6440	−	26.4061i	0.624981	−	0.935351i	0.999965	−	0.00831949i	$-0.00264821\pi$
$798$	−3.43905	−	0.351902i	−0.121741	−	0.0124572i
$799$	−3.62403			−0.128209
$800$	−0.630430	−	9.10602i	−0.0222891	−	0.321946i
$801$	−54.5801	−	4.07430i	−1.92849	−	0.143958i
$802$	−1.04345	+	16.1011i	−0.0368454	+	0.568550i
$803$	25.6958	+	17.1694i	0.906786	+	0.605895i
$804$	41.7237	−	9.59404i	1.47148	−	0.338356i
$805$	0.365565	+	0.0727153i	0.0128845	+	0.00256288i
$806$	38.5103	−	50.2640i	1.35647	−	1.77047i
$807$	14.2047	+	6.51378i	0.500029	+	0.229296i
$808$	12.2296	+	29.3419i	0.430236	+	1.03224i
$809$	2.32673	+	5.61722i	0.0818035	+	0.197491i	0.959489	−	0.281746i	$-0.0909135\pi$
$809$	2.32673	+	5.61722i	0.0818035	+	0.197491i	−0.877686	+	0.479237i	$0.840913\pi$
$810$	−30.0183	−	13.0499i	−1.05474	−	0.458528i
$811$	−30.9598	+	20.6867i	−1.08715	+	0.726407i	−0.963979	−	0.265979i	$-0.914305\pi$
$811$	−30.9598	+	20.6867i	−1.08715	+	0.726407i	−0.123167	+	0.992386i	$0.539305\pi$
$812$	5.15291	+	10.4105i	0.180832	+	0.365337i
$813$	6.61315	−	1.06108i	0.231933	−	0.0372139i
$814$	0.640078	+	0.315067i	0.0224347	+	0.0110431i
$815$	−6.58373	+	6.58373i	−0.230618	+	0.230618i
$816$	2.84410	−	28.4128i	0.0995635	−	0.994645i
$817$	7.75861	+	7.75861i	0.271440	+	0.271440i
$818$	9.63706	+	28.3215i	0.336952	+	0.990238i
$819$	−8.97047	+	1.09840i	−0.313454	+	0.0383812i
$820$	22.2140	−	1.48875i	0.775746	−	0.0519895i
$821$	26.2946	+	39.3527i	0.917689	+	1.37342i	0.927643	+	0.373468i	$0.121831\pi$
$821$	26.2946	+	39.3527i	0.917689	+	1.37342i	−0.00995435	+	0.999950i	$0.503169\pi$
$822$	6.10012	+	11.5175i	0.212766	+	0.401718i
$823$	4.34586	−	1.80011i	0.151487	−	0.0627481i	−0.305652	−	0.952143i	$-0.598874\pi$
$823$	4.34586	−	1.80011i	0.151487	−	0.0627481i	0.457139	+	0.889395i	$0.348874\pi$
$824$	0.392384	+	1.95018i	0.0136694	+	0.0679378i
$825$	−7.82443	−	3.58801i	−0.272412	−	0.124919i
$826$	−5.94198	+	0.786717i	−0.206748	+	0.0273734i
$827$	−1.04781	+	5.26772i	−0.0364361	+	0.183176i	−0.994718	−	0.102650i	$-0.967268\pi$
$827$	−1.04781	+	5.26772i	−0.0364361	+	0.183176i	0.958282	+	0.285826i	$0.0922680\pi$
$828$	−1.26305	+	0.830141i	−0.0438938	+	0.0288494i
$829$	−13.1649	+	19.7026i	−0.457235	+	0.684301i	−0.986427	−	0.164202i	$-0.947495\pi$
$829$	−13.1649	+	19.7026i	−0.457235	+	0.684301i	0.529192	+	0.848502i	$0.322495\pi$
$830$	−27.2640	−	31.0426i	−0.946346	−	1.07750i
$831$	1.38558	−	37.1746i	0.0480651	−	1.28957i
$832$	41.1179	+	7.99066i	1.42551	+	0.277026i
$833$			27.4863i			0.952344i
$834$	−21.6298	+	17.6141i	−0.748978	+	0.609927i
$835$	34.0980	+	22.7836i	1.18001	+	0.788458i
$836$	11.9740	−	9.21595i	0.414129	−	0.318740i
$837$	−13.4754	+	42.3422i	−0.465777	+	1.46356i
$838$	−3.87482	−	29.2661i	−0.133854	−	1.01098i
$839$	−12.2964	+	29.6861i	−0.424519	+	1.02488i	0.556479	+	0.830862i	$0.312152\pi$
$839$	−12.2964	+	29.6861i	−0.424519	+	1.02488i	−0.980998	+	0.194018i	$0.937848\pi$
$840$	5.88223	+	4.23590i	0.202956	+	0.146152i
$841$	−27.8982	−	67.3522i	−0.962007	−	2.32249i
$842$	15.2730	+	26.4089i	0.526344	+	0.910110i
$843$	−11.5385	+	7.10285i	−0.397408	+	0.244635i
$844$	−46.0125	+	3.08370i	−1.58381	+	0.106145i
$845$	−36.3574	+	7.23193i	−1.25073	+	0.248786i
$846$	0.935498	+	3.61133i	0.0321631	+	0.124160i
$847$	−0.615919	+	0.615919i	−0.0211632	+	0.0211632i
$848$	−5.81955	−	16.9798i	−0.199844	−	0.583089i
$849$	22.9254	−	21.2778i	0.786797	−	0.730253i
$850$	4.15359	−	8.43826i	0.142467	−	0.289430i
$851$	0.0404666	−	0.00804931i	0.00138718	−	0.000275927i
$852$	−19.1354	−	42.5790i	−0.655568	−	1.45873i
$853$	17.0462	+	25.5115i	0.583652	+	0.873497i	0.999352	−	0.0360053i	$-0.0114633\pi$
$853$	17.0462	+	25.5115i	0.583652	+	0.873497i	−0.415700	+	0.909502i	$0.636463\pi$
$854$	2.82254	+	0.754077i	0.0965855	+	0.0258040i
$855$	17.9748	−	5.92054i	0.614724	−	0.202478i
$856$	−25.3661	−	10.4416i	−0.866997	−	0.356886i
$857$	−14.9863	+	36.1801i	−0.511922	+	1.23589i	0.430842	+	0.902427i	$0.358217\pi$
$857$	−14.9863	+	36.1801i	−0.511922	+	1.23589i	−0.942764	+	0.333461i	$0.891783\pi$
$858$	25.1750	−	30.4394i	0.859459	−	1.03919i
$859$	1.34438	−	6.75868i	0.0458698	−	0.230603i	−0.951049	−	0.309039i	$-0.899993\pi$
$859$	1.34438	−	6.75868i	0.0458698	−	0.230603i	0.996919	+	0.0784360i	$0.0249926\pi$
$860$	−5.98726	−	22.2142i	−0.204164	−	0.757498i
$861$	−2.52848	+	3.49494i	−0.0861702	+	0.119107i
$862$	28.8057	+	1.86678i	0.981127	+	0.0635828i
$863$		−	10.5863i		−	0.360361i	−0.983634	−	0.180180i	$-0.942332\pi$
$863$		−	10.5863i		−	0.360361i	0.983634	−	0.180180i	$-0.0576681\pi$
$864$	−29.0473	+	4.50026i	−0.988210	+	0.153102i
$865$			40.7333i			1.38497i
$866$	−0.350709	+	5.41169i	−0.0119176	+	0.183897i
$867$	−0.0132473	+	0.0183109i	−0.000449903	+	0.000621869i
$868$	4.90760	−	8.52912i	0.166575	−	0.289497i
$869$	−5.51166	+	27.7090i	−0.186970	+	0.939963i
$870$	−49.0018	−	40.5269i	−1.66132	−	1.37399i
$871$	−24.7634	+	59.7842i	−0.839076	+	2.02571i
$872$	−17.1578	+	17.2336i	−0.581037	+	0.583603i
$873$	40.1819	−	13.2352i	1.35995	−	0.447942i
$874$	0.225551	−	0.844248i	0.00762938	−	0.0285571i
$875$	−2.78377	−	4.16620i	−0.0941085	−	0.140843i
$876$	32.4932	+	12.3433i	1.09784	+	0.417041i
$877$	−27.6024	+	5.49047i	−0.932068	+	0.185400i	−0.637693	−	0.770290i	$-0.720111\pi$
$877$	−27.6024	+	5.49047i	−0.932068	+	0.185400i	−0.294375	+	0.955690i	$0.595111\pi$
$878$	−5.35686	−	2.63682i	−0.180785	−	0.0889884i
$879$	21.3766	−	19.8403i	0.721015	−	0.669198i
$880$	−31.3993	+	4.22768i	−1.05847	+	0.142515i
$881$	4.36865	−	4.36865i	0.147184	−	0.147184i	−0.629675	−	0.776859i	$-0.716812\pi$
$881$	4.36865	−	4.36865i	0.147184	−	0.147184i	0.776859	+	0.629675i	$0.216812\pi$
$882$	27.3900	−	7.09524i	0.922268	−	0.238909i
$883$	11.1110	−	2.21013i	0.373917	−	0.0743766i	−0.00455479	−	0.999990i	$-0.501450\pi$
$883$	11.1110	−	2.21013i	0.373917	−	0.0743766i	0.378471	+	0.925613i	$0.376450\pi$
$884$	32.4909	+	28.4094i	1.09279	+	0.955513i
$885$	27.9423	−	17.2006i	0.939270	−	0.578192i
$886$	31.3055	−	18.1049i	1.05173	−	0.608246i
$887$	5.92428	+	14.3025i	0.198918	+	0.480230i	0.991590	−	0.129418i	$-0.0413109\pi$
$887$	5.92428	+	14.3025i	0.198918	+	0.480230i	−0.792672	+	0.609648i	$0.791311\pi$
$888$	0.781015	+	0.184024i	0.0262091	+	0.00617545i
$889$	−1.16738	+	2.81830i	−0.0391526	+	0.0945227i
$890$	−65.7778	+	8.70896i	−2.20488	+	0.291925i
$891$	−9.38429	+	26.0827i	−0.314385	+	0.873804i
$892$	−0.889564	+	6.83447i	−0.0297848	+	0.228835i
$893$	−1.79337	−	1.19829i	−0.0600129	−	0.0400993i
$894$	−8.95172	−	10.9925i	−0.299390	−	0.367645i
$895$			27.8401i			0.930592i
$896$	6.49756	+	0.392336i	0.217068	+	0.0131070i
$897$	0.0850885	−	2.28289i	0.00284102	−	0.0762236i
$898$	−5.09860	+	4.47798i	−0.170142	+	0.149432i
$899$	−47.9590	+	71.7757i	−1.59952	+	2.39385i
$900$	−9.48087	−	1.96080i	−0.316029	−	0.0653599i
$901$	3.60814	−	18.1393i	0.120205	−	0.604309i
$902$	−2.47470	−	18.6911i	−0.0823986	−	0.622347i
$903$	4.05193	+	1.85808i	0.134840	+	0.0618329i
$904$	−4.09792	+	20.8415i	−0.136295	+	0.693178i
$905$	22.2146	−	9.20160i	0.738439	−	0.305872i
$906$	19.9929	−	10.5891i	0.664220	−	0.351798i
$907$	−24.3449	−	36.4347i	−0.808359	−	1.20980i	−0.974654	−	0.223719i	$-0.928180\pi$
$907$	−24.3449	−	36.4347i	−0.808359	−	1.20980i	0.166294	−	0.986076i	$-0.446820\pi$
$908$	31.4474	−	35.9653i	1.04362	−	1.19355i
$909$	33.4668	−	4.09788i	1.11002	−	0.135918i
$910$	−10.3721	+	3.52937i	−0.343833	+	0.116997i
$911$	−13.8338	−	13.8338i	−0.458333	−	0.458333i	0.439775	−	0.898108i	$-0.355058\pi$
$911$	−13.8338	−	13.8338i	−0.458333	−	0.458333i	−0.898108	+	0.439775i	$0.855058\pi$
$912$	10.8021	−	13.1198i	0.357695	−	0.434440i
$913$	−24.7404	+	24.7404i	−0.818788	+	0.818788i
$914$	1.23586	−	2.51072i	0.0408786	−	0.0830473i
$915$	−15.7914	+	2.53374i	−0.522048	+	0.0837629i
$916$	7.65368	−	22.6563i	0.252885	−	0.748584i
$917$	5.17257	−	3.45620i	0.170813	−	0.114134i
$918$	−28.2062	−	11.0321i	−0.930943	−	0.364112i
$919$	12.4165	+	29.9760i	0.409582	+	0.988818i	0.985248	+	0.171133i	$0.0547427\pi$
$919$	12.4165	+	29.9760i	0.409582	+	0.988818i	−0.575666	+	0.817685i	$0.695257\pi$
$920$	−1.29278	+	1.29849i	−0.0426218	+	0.0428100i
$921$	−13.0260	−	5.97328i	−0.429222	−	0.196826i
$922$	2.84294	+	2.17815i	0.0936273	+	0.0717336i
$923$	69.2015	+	13.7650i	2.27779	+	0.453082i
$924$	3.25754	−	5.20297i	0.107165	−	0.171165i
$925$	0.219748	+	0.146831i	0.00722527	+	0.00482777i
$926$	26.5203	+	1.71867i	0.871510	+	0.0564790i
$927$	2.10408	+	0.157066i	0.0691071	+	0.00515871i
$928$	−56.6423	−	7.24560i	−1.85937	−	0.237848i
$929$	−10.1017			−0.331426			−0.165713	−	0.986174i	$-0.552993\pi$
$929$	−10.1017			−0.331426			−0.165713	+	0.986174i	$0.552993\pi$
$930$	−5.48348	+	53.5887i	−0.179810	+	1.75724i
$931$	−9.08839	+	13.6017i	−0.297860	+	0.445779i
$932$	11.1634	−	3.00880i	0.365669	−	0.0985565i
$933$	7.26023	−	30.5117i	0.237689	−	0.998909i
$934$	44.2310	+	33.8881i	1.44728	+	1.10885i
$935$	−30.1602	−	12.4928i	−0.986346	−	0.408558i
$936$	19.9227	−	39.7106i	0.651195	−	1.29798i
$937$	−14.3874	+	5.95944i	−0.470014	+	0.194686i	−0.605103	−	0.796147i	$-0.706868\pi$
$937$	−14.3874	+	5.95944i	−0.470014	+	0.194686i	0.135089	+	0.990834i	$0.456868\pi$
$938$	−2.59558	+	9.71539i	−0.0847488	+	0.317219i
$939$	38.9945	−	24.0041i	1.27254	−	0.783343i
$940$	2.00623	+	4.05320i	0.0654359	+	0.132201i
$941$	1.66631	+	8.37712i	0.0543203	+	0.273086i	0.998394	−	0.0566473i	$-0.0180410\pi$
$941$	1.66631	+	8.37712i	0.0543203	+	0.273086i	−0.944074	+	0.329734i	$0.893041\pi$
$942$	−14.0562	+	26.0589i	−0.457975	+	0.849044i
$943$	−0.771032	−	0.771032i	−0.0251083	−	0.0251083i
$944$	12.9546	−	26.4650i	0.421636	−	0.861363i
$945$	6.00895	−	4.79625i	0.195471	−	0.156022i
$946$	−18.4450	+	6.27633i	−0.599697	+	0.204061i
$947$	−9.67004	−	48.6146i	−0.314234	−	1.57976i	−0.738519	−	0.674233i	$-0.764474\pi$
$947$	−9.67004	−	48.6146i	−0.314234	−	1.57976i	0.424285	−	0.905529i	$-0.360526\pi$
$948$	0.942445	+	31.7616i	0.0306092	+	1.03157i
$949$	−43.6827	+	29.1878i	−1.41800	+	0.947478i
$950$	4.84555	−	2.80232i	0.157210	−	0.0909194i
$951$	15.8794	+	42.7774i	0.514925	+	1.38715i
$952$	5.58499	+	3.71400i	0.181011	+	0.120371i
$953$	−20.1579	−	8.34969i	−0.652980	−	0.270473i	0.0315014	−	0.999504i	$-0.489971\pi$
$953$	−20.1579	−	8.34969i	−0.652980	−	0.270473i	−0.684481	+	0.729031i	$0.739971\pi$
$954$	−19.0072	+	1.08695i	−0.615379	+	0.0351914i
$955$	−15.7835	−	3.13953i	−0.510742	−	0.101593i
$956$	−4.19043	−	5.44449i	−0.135528	−	0.176087i
$957$	−31.5650	+	43.6301i	−1.02035	+	1.41036i
$958$	34.0203	−	29.8792i	1.09915	−	0.965354i
$959$	−3.06133			−0.0988554
$960$	−33.3520	+	12.5481i	−1.07643	+	0.404988i
$961$	42.1276			1.35896
$962$	−0.911249	+	0.800329i	−0.0293799	+	0.0258036i
$963$	−17.9204	+	22.9213i	−0.577477	+	0.738629i
$964$	−3.33715	+	2.56848i	−0.107482	+	0.0827251i
$965$	−24.4147	−	4.85639i	−0.785937	−	0.156333i
$966$	−0.0334564	−	0.353436i	−0.00107644	−	0.0113716i
$967$	8.72716	+	3.61491i	0.280647	+	0.116248i	0.518567	−	0.855037i	$-0.326466\pi$
$967$	8.72716	+	3.61491i	0.280647	+	0.116248i	−0.237920	+	0.971285i	$0.576466\pi$
$968$	−0.844631	−	4.19789i	−0.0271475	−	0.134925i
$969$	16.4163	−	6.09390i	0.527368	−	0.195764i
$970$	44.3972	−	25.6762i	1.42551	−	0.824413i
$971$	9.92277	−	6.63018i	0.318437	−	0.212773i	−0.386071	−	0.922469i	$-0.626168\pi$
$971$	9.92277	−	6.63018i	0.318437	−	0.212773i	0.704508	+	0.709697i	$0.251168\pi$
$972$	−3.71232	+	30.9551i	−0.119073	+	0.992886i
$973$	−1.27825	−	6.42618i	−0.0409787	−	0.206014i
$974$	37.1779	−	12.6507i	1.19126	−	0.405353i
$975$	10.7255	−	9.95474i	0.343492	−	0.318807i
$976$	−10.7702	+	9.50134i	−0.344746	+	0.304131i
$977$	−18.8141	−	18.8141i	−0.601918	−	0.601918i	0.338903	−	0.940821i	$-0.389944\pi$
$977$	−18.8141	−	18.8141i	−0.601918	−	0.601918i	−0.940821	+	0.338903i	$0.889944\pi$
$978$	7.80528	+	4.21018i	0.249585	+	0.134627i
$979$	10.9622	+	55.1108i	0.350354	+	1.76135i
$980$	30.7413	−	15.2161i	0.981996	−	0.486061i
$981$	12.6939	+	22.4539i	0.405285	+	0.716897i
$982$	−10.4345	+	39.0568i	−0.332978	+	1.24635i
$983$	20.3923	−	8.44678i	0.650415	−	0.269411i	−0.0329841	−	0.999456i	$-0.510501\pi$
$983$	20.3923	−	8.44678i	0.650415	−	0.269411i	0.683399	+	0.730045i	$0.260501\pi$
$984$	−7.42358	−	19.8641i	−0.236655	−	0.633243i
$985$	−2.08333	−	0.862943i	−0.0663804	−	0.0274956i
$986$	−46.7062	−	35.7844i	−1.48743	−	1.13961i
$987$	−0.852454	−	0.202840i	−0.0271339	−	0.00645648i
$988$	6.68467	+	24.8017i	0.212668	+	0.789048i
$989$	−0.626015	+	0.936898i	−0.0199061	+	0.0297916i
$990$	−4.66350	+	33.2794i	−0.148216	+	1.05769i
$991$	50.8770			1.61616			0.808081	−	0.589071i	$-0.200506\pi$
$991$	50.8770			1.61616			0.808081	+	0.589071i	$0.200506\pi$
$992$	21.5546	+	43.3068i	0.684360	+	1.37499i
$993$	−0.348910	+	9.36114i	−0.0110723	+	0.297067i
$994$	10.9419	+	0.709098i	0.347055	+	0.0224912i
$995$	22.5018	+	15.0352i	0.713356	+	0.476649i
$996$	−20.8828	+	33.3542i	−0.661698	+	1.05687i
$997$	2.90999	+	0.578833i	0.0921603	+	0.0183318i	0.240955	−	0.970536i	$-0.422539\pi$
$997$	2.90999	+	0.578833i	0.0921603	+	0.0183318i	−0.148795	+	0.988868i	$0.547539\pi$
$998$	16.1437	+	12.3687i	0.511020	+	0.391524i
$999$	0.411358	−	0.745061i	0.0130148	−	0.0235727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.s.a.155.23	yes	240
3.2	odd	2	inner	192.2.s.a.155.8	yes	240
4.3	odd	2		768.2.s.a.527.24		240
12.11	even	2		768.2.s.a.527.25		240
64.19	odd	16	inner	192.2.s.a.83.8	✓	240
64.45	even	16		768.2.s.a.239.25		240
192.83	even	16	inner	192.2.s.a.83.23	yes	240
192.173	odd	16		768.2.s.a.239.24		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.83.8	✓	240	64.19	odd	16	inner
192.2.s.a.83.23	yes	240	192.83	even	16	inner
192.2.s.a.155.8	yes	240	3.2	odd	2	inner
192.2.s.a.155.23	yes	240	1.1	even	1	trivial
768.2.s.a.239.24		240	192.173	odd	16
768.2.s.a.239.25		240	64.45	even	16
768.2.s.a.527.24		240	4.3	odd	2
768.2.s.a.527.25		240	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.933236 + 1.06258i) q^{2} +(-1.40331 - 1.01525i) q^{3} +(-0.258140 + 1.98327i) q^{4} +(2.52227 + 0.501712i) q^{5} +(-0.230838 - 2.43859i) q^{6} +(0.531558 + 0.220179i) q^{7} +(-2.34828 + 1.57657i) q^{8} +(0.938541 + 2.84941i) q^{9} +O(q^{10})\)	\(q+(0.933236 + 1.06258i) q^{2} +(-1.40331 - 1.01525i) q^{3} +(-0.258140 + 1.98327i) q^{4} +(2.52227 + 0.501712i) q^{5} +(-0.230838 - 2.43859i) q^{6} +(0.531558 + 0.220179i) q^{7} +(-2.34828 + 1.57657i) q^{8} +(0.938541 + 2.84941i) q^{9} +(1.82077 + 3.14833i) q^{10} +(2.56088 - 1.71113i) q^{11} +(2.37576 - 2.52106i) q^{12} +(1.02147 + 5.13528i) q^{13} +(0.262113 + 0.770300i) q^{14} +(-3.03016 - 3.26479i) q^{15} +(-3.86673 - 1.02392i) q^{16} +(-2.91436 - 2.91436i) q^{17} +(-2.15184 + 3.65645i) q^{18} +(-0.478548 - 2.40582i) q^{19} +(-1.64613 + 4.87284i) q^{20} +(-0.522403 - 0.848642i) q^{21} +(4.20811 + 1.12425i) q^{22} +(0.232730 - 0.0963998i) q^{23} +(4.89597 + 0.171682i) q^{24} +(1.49076 + 0.617492i) q^{25} +(-4.50336 + 5.87782i) q^{26} +(1.57580 - 4.95145i) q^{27} +(-0.573890 + 0.997387i) q^{28} +(5.60827 - 8.39338i) q^{29} +(0.641232 - 6.26660i) q^{30} -8.55147 q^{31} +(-2.52058 - 5.06426i) q^{32} +(-5.33092 - 0.198695i) q^{33} +(0.376944 - 5.81651i) q^{34} +(1.23027 + 0.822040i) q^{35} +(-5.89343 + 1.12584i) q^{36} +(0.160643 + 0.0319538i) q^{37} +(2.10977 - 2.75369i) q^{38} +(3.78015 - 8.24342i) q^{39} +(-6.71400 + 2.79838i) q^{40} +(-1.65650 - 3.99914i) q^{41} +(0.414221 - 1.34708i) q^{42} +(-3.71926 + 2.48513i) q^{43} +(2.73256 + 5.52063i) q^{44} +(0.937677 + 7.65787i) q^{45} +(0.319624 + 0.157329i) q^{46} +(0.621755 - 0.621755i) q^{47} +(4.38667 + 5.36257i) q^{48} +(-4.71567 - 4.71567i) q^{49} +(0.735097 + 2.16031i) q^{50} +(1.13094 + 7.04853i) q^{51} +(-10.4483 + 0.700234i) q^{52} +(2.49304 + 3.73109i) q^{53} +(6.73189 - 2.94647i) q^{54} +(7.31774 - 3.03111i) q^{55} +(-1.59538 + 0.320996i) q^{56} +(-1.77096 + 3.86195i) q^{57} +(14.1525 - 1.87378i) q^{58} +(-1.43711 + 7.22485i) q^{59} +(7.25717 - 5.16687i) q^{60} +(1.99480 - 2.98544i) q^{61} +(-7.98054 - 9.08659i) q^{62} +(-0.128490 + 1.72127i) q^{63} +(3.02887 - 7.40445i) q^{64} +13.4651i q^{65} +(-4.76388 - 5.84995i) q^{66} +(10.2761 + 6.86625i) q^{67} +(6.53227 - 5.02765i) q^{68} +(-0.424461 - 0.101000i) q^{69} +(0.274652 + 2.07441i) q^{70} +(5.15693 - 12.4499i) q^{71} +(-6.69625 - 5.21155i) q^{72} +(3.83983 + 9.27018i) q^{73} +(0.115964 + 0.200515i) q^{74} +(-1.46508 - 2.38002i) q^{75} +(4.89493 - 0.328052i) q^{76} +(1.73801 - 0.345712i) q^{77} +(12.2870 - 3.67636i) q^{78} +(-6.48617 + 6.48617i) q^{79} +(-9.23924 - 4.52259i) q^{80} +(-7.23828 + 5.34858i) q^{81} +(2.70349 - 5.49230i) q^{82} +(-11.1417 + 2.21623i) q^{83} +(1.81794 - 0.816999i) q^{84} +(-5.88864 - 8.81298i) q^{85} +(-6.11158 - 1.63278i) q^{86} +(-16.3915 + 6.08469i) q^{87} +(-3.31597 + 8.05562i) q^{88} +(-6.98167 + 16.8552i) q^{89} +(-7.26201 + 8.14296i) q^{90} +(-0.587708 + 2.95461i) q^{91} +(0.131110 + 0.486451i) q^{92} +(12.0003 + 8.68187i) q^{93} +(1.24091 + 0.0804181i) q^{94} -6.30824i q^{95} +(-1.60434 + 9.66572i) q^{96} -14.1018i q^{97} +(0.609928 - 9.41160i) q^{98} +(7.27920 + 5.69104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

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