LMFDB - Embedded newform 588.2.o.f.31.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(19,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,-4,12,4,0,-8,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.7
Character	$\chi$	$=$	588.31
Dual form			588.2.o.f.19.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.306932 - 1.38050i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.81159 + 0.847441i) q^{4} +(-0.110790 + 0.0639645i) q^{5} +(-1.34902 - 0.424442i) q^{6} +(1.72593 + 2.24080i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.122308 + 0.133313i) q^{10} +(-3.45938 - 1.99727i) q^{11} +(-0.171888 + 1.99260i) q^{12} -0.891655i q^{13} +0.127929i q^{15} +(2.56369 - 3.07042i) q^{16} +(-5.04756 - 2.91421i) q^{17} +(-1.04209 + 0.956063i) q^{18} +(-3.15745 - 5.46886i) q^{19} +(0.146499 - 0.209765i) q^{20} +(-1.69545 + 5.38872i) q^{22} +(-5.72040 + 3.30268i) q^{23} +(2.80355 - 0.374300i) q^{24} +(-2.49182 + 4.31595i) q^{25} +(-1.23093 + 0.273677i) q^{26} -1.00000 q^{27} +2.82968 q^{29} +(0.176607 - 0.0392655i) q^{30} +(4.22668 - 7.32083i) q^{31} +(-5.02561 - 2.59677i) q^{32} +(-3.45938 + 1.99727i) q^{33} +(-2.47383 + 7.86264i) q^{34} +(1.63970 + 1.14516i) q^{36} +(4.33956 + 7.51634i) q^{37} +(-6.58067 + 6.03744i) q^{38} +(-0.772196 - 0.445827i) q^{39} +(-0.334547 - 0.137859i) q^{40} +3.24650i q^{41} -0.881836i q^{43} +(7.95954 + 0.686614i) q^{44} +(0.110790 + 0.0639645i) q^{45} +(6.31513 + 6.88335i) q^{46} +(-5.00678 - 8.67200i) q^{47} +(-1.37722 - 3.75543i) q^{48} +(6.72301 + 2.11526i) q^{50} +(-5.04756 + 2.91421i) q^{51} +(0.755625 + 1.61531i) q^{52} +(3.76727 - 6.52510i) q^{53} +(0.306932 + 1.38050i) q^{54} +0.511019 q^{55} -6.31490 q^{57} +(-0.868519 - 3.90639i) q^{58} +(-0.294409 + 0.509932i) q^{59} +(-0.108412 - 0.231754i) q^{60} +(-1.46181 + 0.843974i) q^{61} +(-11.4037 - 3.58796i) q^{62} +(-2.04234 + 7.73491i) q^{64} +(0.0570343 + 0.0987862i) q^{65} +(3.81904 + 4.16266i) q^{66} +(5.50132 + 3.17619i) q^{67} +(11.6137 + 1.00183i) q^{68} +6.60535i q^{69} -11.3856i q^{71} +(1.07762 - 2.61510i) q^{72} +(13.4354 + 7.75696i) q^{73} +(9.04439 - 8.29778i) q^{74} +(2.49182 + 4.31595i) q^{75} +(10.3545 + 7.23156i) q^{76} +(-0.378456 + 1.20286i) q^{78} +(-8.50718 + 4.91162i) q^{79} +(-0.0876323 + 0.504157i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.48180 - 0.996452i) q^{82} +1.48021 q^{83} +0.745624 q^{85} +(-1.21738 + 0.270663i) q^{86} +(1.41484 - 2.45058i) q^{87} +(-1.49516 - 11.1989i) q^{88} +(0.389696 - 0.224991i) q^{89} +(0.0542984 - 0.172579i) q^{90} +(7.56418 - 10.8308i) q^{92} +(-4.22668 - 7.32083i) q^{93} +(-10.4350 + 9.57360i) q^{94} +(0.699626 + 0.403929i) q^{95} +(-4.76168 + 3.05392i) q^{96} -16.2042i q^{97} +3.99455i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 12 q^{3} + 4 q^{4} - 8 q^{6} + 8 q^{8} - 12 q^{9} - 4 q^{12} + 4 q^{16} - 4 q^{18} + 48 q^{20} + 4 q^{24} + 12 q^{25} + 24 q^{26} - 24 q^{27} + 64 q^{29} + 16 q^{31} - 4 q^{32} - 64 q^{34}+ \cdots + 4 q^{96}+O(q^{100}) $ 24 * q - 4 * q^2 + 12 * q^3 + 4 * q^4 - 8 * q^6 + 8 * q^8 - 12 * q^9 - 4 * q^12 + 4 * q^16 - 4 * q^18 + 48 * q^20 + 4 * q^24 + 12 * q^25 + 24 * q^26 - 24 * q^27 + 64 * q^29 + 16 * q^31 - 4 * q^32 - 64 * q^34 - 8 * q^36 - 32 * q^37 - 24 * q^38 - 32 * q^40 + 24 * q^44 - 24 * q^46 + 8 * q^48 - 56 * q^50 + 32 * q^52 + 32 * q^53 + 4 * q^54 - 32 * q^55 - 16 * q^58 - 16 * q^59 + 24 * q^60 - 16 * q^62 - 8 * q^64 - 8 * q^68 - 4 * q^72 + 32 * q^74 - 12 * q^75 + 64 * q^76 + 48 * q^78 - 16 * q^80 - 12 * q^81 + 32 * q^82 + 32 * q^83 + 32 * q^85 + 24 * q^86 + 32 * q^87 - 24 * q^88 - 16 * q^93 + 4 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.306932	−	1.38050i	−0.217033	−	0.976164i
$2$	−0.306932	−	1.38050i	−0.217033	−	0.976164i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.81159	+	0.847441i	−0.905793	+	0.423720i
$5$	−0.110790	+	0.0639645i	−0.0495467	+	0.0286058i	−0.524569	−	0.851368i	$-0.675773\pi$
$5$	−0.110790	+	0.0639645i	−0.0495467	+	0.0286058i	0.475022	+	0.879974i	$0.342440\pi$
$6$	−1.34902	−	0.424442i	−0.550734	−	0.173278i
$7$		0			0
$7$		0			0
$8$	1.72593	+	2.24080i	0.610208	+	0.792241i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.122308	+	0.133313i	0.0386772	+	0.0421573i
$11$	−3.45938	−	1.99727i	−1.04304	−	0.602201i	−0.122349	−	0.992487i	$-0.539043\pi$
$11$	−3.45938	−	1.99727i	−1.04304	−	0.602201i	−0.920693	+	0.390286i	$0.872376\pi$
$12$	−0.171888	+	1.99260i	−0.0496197	+	0.575214i
$13$		−	0.891655i		−	0.247301i	−0.992326	−	0.123650i	$-0.960540\pi$
$13$		−	0.891655i		−	0.247301i	0.992326	−	0.123650i	$-0.0394601\pi$
$14$		0			0
$15$			0.127929i			0.0330311i
$16$	2.56369	−	3.07042i	0.640922	−	0.767606i
$17$	−5.04756	−	2.91421i	−1.22421	−	0.706800i	−0.258400	−	0.966038i	$-0.583195\pi$
$17$	−5.04756	−	2.91421i	−1.22421	−	0.706800i	−0.965813	+	0.259238i	$0.916529\pi$
$18$	−1.04209	+	0.956063i	−0.245622	+	0.225346i
$19$	−3.15745	−	5.46886i	−0.724368	−	1.25464i	−0.959234	−	0.282615i	$-0.908798\pi$
$19$	−3.15745	−	5.46886i	−0.724368	−	1.25464i	0.234865	−	0.972028i	$-0.424535\pi$
$20$	0.146499	−	0.209765i	0.0327582	−	0.0469049i
$21$		0			0
$22$	−1.69545	+	5.38872i	−0.361472	+	1.14888i
$23$	−5.72040	+	3.30268i	−1.19279	+	0.688656i	−0.958938	−	0.283617i	$-0.908465\pi$
$23$	−5.72040	+	3.30268i	−1.19279	+	0.688656i	−0.233849	+	0.972273i	$0.575132\pi$
$24$	2.80355	−	0.374300i	0.572273	−	0.0764036i
$25$	−2.49182	+	4.31595i	−0.498363	+	0.863191i
$26$	−1.23093	+	0.273677i	−0.241406	+	0.0536725i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	2.82968			0.525459			0.262729	−	0.964870i	$-0.415377\pi$
$29$	2.82968			0.525459			0.262729	+	0.964870i	$0.415377\pi$
$30$	0.176607	−	0.0392655i	0.0322438	−	0.00716886i
$31$	4.22668	−	7.32083i	0.759135	−	1.31486i	−0.184158	−	0.982897i	$-0.558956\pi$
$31$	4.22668	−	7.32083i	0.759135	−	1.31486i	0.943292	−	0.331963i	$-0.107711\pi$
$32$	−5.02561	−	2.59677i	−0.888411	−	0.459049i
$33$	−3.45938	+	1.99727i	−0.602201	+	0.347681i
$34$	−2.47383	+	7.86264i	−0.424258	+	1.34843i
$35$		0			0
$36$	1.63970	+	1.14516i	0.273283	+	0.190860i
$37$	4.33956	+	7.51634i	0.713419	+	1.23568i	0.963566	+	0.267471i	$0.0861878\pi$
$37$	4.33956	+	7.51634i	0.713419	+	1.23568i	−0.250147	+	0.968208i	$0.580479\pi$
$38$	−6.58067	+	6.03744i	−1.06753	+	0.979402i
$39$	−0.772196	−	0.445827i	−0.123650	−	0.0713895i
$40$	−0.334547	−	0.137859i	−0.0528965	−	0.0217975i
$41$			3.24650i			0.507018i	0.967333	+	0.253509i	$0.0815847\pi$
$41$			3.24650i			0.507018i	−0.967333	+	0.253509i	$0.918415\pi$
$42$		0			0
$43$		−	0.881836i		−	0.134479i	−0.997737	−	0.0672394i	$-0.978581\pi$
$43$		−	0.881836i		−	0.134479i	0.997737	−	0.0672394i	$-0.0214191\pi$
$44$	7.95954	+	0.686614i	1.19995	+	0.103511i
$45$	0.110790	+	0.0639645i	0.0165156	+	0.00953527i
$46$	6.31513	+	6.88335i	0.931115	+	1.01489i
$47$	−5.00678	−	8.67200i	−0.730314	−	1.26494i	−0.956749	−	0.290915i	$-0.906040\pi$
$47$	−5.00678	−	8.67200i	−0.730314	−	1.26494i	0.226435	−	0.974026i	$-0.427293\pi$
$48$	−1.37722	−	3.75543i	−0.198785	−	0.542050i
$49$		0			0
$50$	6.72301	+	2.11526i	0.950777	+	0.299143i
$51$	−5.04756	+	2.91421i	−0.706800	+	0.408071i
$52$	0.755625	+	1.61531i	0.104786	+	0.224003i
$53$	3.76727	−	6.52510i	0.517474	−	0.896292i	−0.482320	−	0.875995i	$-0.660206\pi$
$53$	3.76727	−	6.52510i	0.517474	−	0.896292i	0.999794	−	0.0202966i	$-0.00646106\pi$
$54$	0.306932	+	1.38050i	0.0417681	+	0.187863i
$55$	0.511019			0.0689057
$56$		0			0
$57$	−6.31490			−0.836428
$58$	−0.868519	−	3.90639i	−0.114042	−	0.512934i
$59$	−0.294409	+	0.509932i	−0.0383288	+	0.0663875i	−0.884553	−	0.466439i	$-0.845537\pi$
$59$	−0.294409	+	0.509932i	−0.0383288	+	0.0663875i	0.846225	+	0.532826i	$0.178870\pi$
$60$	−0.108412	−	0.231754i	−0.0139960	−	0.0299194i
$61$	−1.46181	+	0.843974i	−0.187165	+	0.108060i	−0.590655	−	0.806924i	$-0.701130\pi$
$61$	−1.46181	+	0.843974i	−0.187165	+	0.108060i	0.403490	+	0.914984i	$0.367797\pi$
$62$	−11.4037	−	3.58796i	−1.44828	−	0.455672i
$63$		0			0
$64$	−2.04234	+	7.73491i	−0.255292	+	0.966864i
$65$	0.0570343	+	0.0987862i	0.00707423	+	0.0122529i
$66$	3.81904	+	4.16266i	0.470091	+	0.512388i
$67$	5.50132	+	3.17619i	0.672094	+	0.388033i	0.796869	−	0.604151i	$-0.206488\pi$
$67$	5.50132	+	3.17619i	0.672094	+	0.388033i	−0.124776	+	0.992185i	$0.539821\pi$
$68$	11.6137	+	1.00183i	1.40837	+	0.121490i
$69$			6.60535i			0.795191i
$70$		0			0
$71$		−	11.3856i		−	1.35122i	−0.737259	−	0.675610i	$-0.763880\pi$
$71$		−	11.3856i		−	1.35122i	0.737259	−	0.675610i	$-0.236120\pi$
$72$	1.07762	−	2.61510i	0.126999	−	0.308192i
$73$	13.4354	+	7.75696i	1.57250	+	0.907883i	0.995861	+	0.0908839i	$0.0289692\pi$
$73$	13.4354	+	7.75696i	1.57250	+	0.907883i	0.576639	+	0.816999i	$0.304364\pi$
$74$	9.04439	−	8.29778i	1.05139	−	0.964598i
$75$	2.49182	+	4.31595i	0.287730	+	0.498363i
$76$	10.3545	+	7.23156i	1.18775	+	0.829517i
$77$		0			0
$78$	−0.378456	+	1.20286i	−0.0428517	+	0.136197i
$79$	−8.50718	+	4.91162i	−0.957132	+	0.552601i	−0.895289	−	0.445485i	$-0.853031\pi$
$79$	−8.50718	+	4.91162i	−0.957132	+	0.552601i	−0.0618431	+	0.998086i	$0.519698\pi$
$80$	−0.0876323	+	0.504157i	−0.00979759	+	0.0563664i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.48180	−	0.996452i	0.494932	−	0.110040i
$83$	1.48021			0.162474			0.0812371	−	0.996695i	$-0.474113\pi$
$83$	1.48021			0.162474			0.0812371	+	0.996695i	$0.474113\pi$
$84$		0			0
$85$	0.745624			0.0808743
$86$	−1.21738	+	0.270663i	−0.131273	+	0.0291864i
$87$	1.41484	−	2.45058i	0.151687	−	0.262729i
$88$	−1.49516	−	11.1989i	−0.159384	−	1.19381i
$89$	0.389696	−	0.224991i	0.0413077	−	0.0238490i	−0.479204	−	0.877704i	$-0.659075\pi$
$89$	0.389696	−	0.224991i	0.0413077	−	0.0238490i	0.520512	+	0.853855i	$0.325741\pi$
$90$	0.0542984	−	0.172579i	0.00572356	−	0.0181914i
$91$		0			0
$92$	7.56418	−	10.8308i	0.788620	−	1.12919i
$93$	−4.22668	−	7.32083i	−0.438287	−	0.759135i
$94$	−10.4350	+	9.57360i	−1.07629	+	0.987441i
$95$	0.699626	+	0.403929i	0.0717801	+	0.0414423i
$96$	−4.76168	+	3.05392i	−0.485987	+	0.311689i
$97$		−	16.2042i		−	1.64529i	−0.568555	−	0.822645i	$-0.692497\pi$
$97$		−	16.2042i		−	1.64529i	0.568555	−	0.822645i	$-0.307503\pi$
$98$		0			0
$99$			3.99455i			0.401467i
$100$	0.856626	−	9.93039i	0.0856626	−	0.993039i
$101$	−10.4495	−	6.03304i	−1.03977	−	0.600310i	−0.120000	−	0.992774i	$-0.538289\pi$
$101$	−10.4495	−	6.03304i	−1.03977	−	0.600310i	−0.919767	+	0.392464i	$0.871623\pi$
$102$	5.57234	+	6.07372i	0.551744	+	0.601388i
$103$	1.64215	+	2.84429i	0.161806	+	0.280256i	0.935516	−	0.353283i	$-0.114935\pi$
$103$	1.64215	+	2.84429i	0.161806	+	0.280256i	−0.773710	+	0.633539i	$0.781601\pi$
$104$	1.99802	−	1.53893i	0.195922	−	0.150905i
$105$		0			0
$106$	−10.1642	−	3.19797i	−0.987237	−	0.310615i
$107$	2.88857	−	1.66772i	0.279249	−	0.161224i	−0.353835	−	0.935308i	$-0.615122\pi$
$107$	2.88857	−	1.66772i	0.279249	−	0.161224i	0.633083	+	0.774084i	$0.281789\pi$
$108$	1.81159	−	0.847441i	0.174320	−	0.0815450i
$109$	−2.23048	+	3.86331i	−0.213641	+	0.370038i	−0.952851	−	0.303437i	$-0.901866\pi$
$109$	−2.23048	+	3.86331i	−0.213641	+	0.370038i	0.739210	+	0.673475i	$0.235199\pi$
$110$	−0.156848	−	0.705464i	−0.0149548	−	0.0672633i
$111$	8.67912			0.823786
$112$		0			0
$113$	−9.16272			−0.861956			−0.430978	−	0.902362i	$-0.641831\pi$
$113$	−9.16272			−0.861956			−0.430978	+	0.902362i	$0.641831\pi$
$114$	1.93824	+	8.71774i	0.181533	+	0.816492i
$115$	0.422508	−	0.731806i	0.0393991	−	0.0682412i
$116$	−5.12621	+	2.39799i	−0.475957	+	0.222648i
$117$	−0.772196	+	0.445827i	−0.0713895	+	0.0412168i
$118$	0.794327	+	0.249919i	0.0731237	+	0.0230069i
$119$		0			0
$120$	−0.286663	+	0.220796i	−0.0261686	+	0.0201559i
$121$	2.47821	+	4.29238i	0.225291	+	0.390216i
$122$	1.61379	+	1.75899i	0.146105	+	0.159251i
$123$	2.81155	+	1.62325i	0.253509	+	0.146363i
$124$	−1.45303	+	16.8442i	−0.130486	+	1.51265i
$125$		−	1.27720i		−	0.114236i
$126$		0			0
$127$		−	14.0775i		−	1.24917i	−0.780955	−	0.624587i	$-0.785267\pi$
$127$		−	14.0775i		−	1.24917i	0.780955	−	0.624587i	$-0.214733\pi$
$128$	11.3049	+	0.445371i	0.999225	+	0.0393656i
$129$	−0.763693	−	0.440918i	−0.0672394	−	0.0388207i
$130$	0.118869	−	0.109057i	0.0104255	−	0.00956490i
$131$	4.88483	+	8.46078i	0.426790	+	0.739222i	0.996586	−	0.0825645i	$-0.0263111\pi$
$131$	4.88483	+	8.46078i	0.426790	+	0.739222i	−0.569796	+	0.821786i	$0.692978\pi$
$132$	4.57439	−	6.54985i	0.398150	−	0.570092i
$133$		0			0
$134$	2.69622	−	8.56948i	0.232918	−	0.740290i
$135$	0.110790	−	0.0639645i	0.00953527	−	0.00550519i
$136$	−2.18158	−	16.3403i	−0.187069	−	1.40117i
$137$	1.98426	−	3.43684i	0.169527	−	0.293629i	−0.768727	−	0.639577i	$-0.779109\pi$
$137$	1.98426	−	3.43684i	0.169527	−	0.293629i	0.938254	+	0.345948i	$0.112443\pi$
$138$	9.11872	−	2.02739i	0.776237	−	0.172583i
$139$	−0.262023			−0.0222245			−0.0111122	−	0.999938i	$-0.503537\pi$
$139$	−0.262023			−0.0222245			−0.0111122	+	0.999938i	$0.503537\pi$
$140$		0			0
$141$	−10.0136			−0.843294
$142$	−15.7179	+	3.49459i	−1.31901	+	0.293260i
$143$	−1.78088	+	3.08457i	−0.148925	+	0.257945i
$144$	−3.94091	−	0.685007i	−0.328409	−	0.0570839i
$145$	−0.313500	+	0.180999i	−0.0260348	+	0.0150312i
$146$	6.58476	−	20.9286i	0.544958	−	1.73206i
$147$		0			0
$148$	−14.2311	−	9.93897i	−1.16979	−	0.816979i
$149$	−1.34774	−	2.33436i	−0.110411	−	0.191238i	0.805525	−	0.592562i	$-0.201884\pi$
$149$	−1.34774	−	2.33436i	−0.110411	−	0.191238i	−0.915936	+	0.401324i	$0.868550\pi$
$150$	5.19338	−	4.76467i	0.424037	−	0.389033i
$151$	−3.73832	−	2.15832i	−0.304220	−	0.175642i	0.340117	−	0.940383i	$-0.389533\pi$
$151$	−3.73832	−	2.15832i	−0.304220	−	0.175642i	−0.644337	+	0.764741i	$0.722867\pi$
$152$	6.80507	−	16.5141i	0.551964	−	1.33947i
$153$			5.82842i			0.471200i
$154$		0			0
$155$			1.08143i			0.0868626i
$156$	1.77671	+	0.153265i	0.142251	+	0.0122710i
$157$	2.77661	+	1.60308i	0.221598	+	0.127940i	0.606690	−	0.794939i	$-0.292497\pi$
$157$	2.77661	+	1.60308i	0.221598	+	0.127940i	−0.385092	+	0.922878i	$0.625830\pi$
$158$	9.39164	+	10.2367i	0.747159	+	0.814386i
$159$	−3.76727	−	6.52510i	−0.298764	−	0.517474i
$160$	0.722888	−	0.0337648i	0.0571493	−	0.00266934i
$161$		0			0
$162$	1.34902	+	0.424442i	0.105989	+	0.0333473i
$163$	20.1454	−	11.6309i	1.57791	−	0.911006i	0.582757	−	0.812646i	$-0.301974\pi$
$163$	20.1454	−	11.6309i	1.57791	−	0.911006i	0.995151	−	0.0983597i	$-0.0313596\pi$
$164$	−2.75121	−	5.88131i	−0.214834	−	0.459253i
$165$	0.255509	−	0.442555i	0.0198914	−	0.0344529i
$166$	−0.454323	−	2.04344i	−0.0352623	−	0.158602i
$167$	9.66864			0.748182			0.374091	−	0.927392i	$-0.377955\pi$
$167$	9.66864			0.748182			0.374091	+	0.927392i	$0.377955\pi$
$168$		0			0
$169$	12.2050			0.938842
$170$	−0.228856	−	1.02934i	−0.0175524	−	0.0789466i
$171$	−3.15745	+	5.46886i	−0.241456	+	0.418214i
$172$	0.747304	+	1.59752i	0.0569814	+	0.121810i
$173$	17.9324	−	10.3533i	1.36337	−	0.787145i	0.373303	−	0.927709i	$-0.378225\pi$
$173$	17.9324	−	10.3533i	1.36337	−	0.787145i	0.990071	+	0.140565i	$0.0448919\pi$
$174$	−3.81729	−	1.20104i	−0.289388	−	0.0910503i
$175$		0			0
$176$	−15.0012	+	5.50137i	−1.13076	+	0.414682i
$177$	0.294409	+	0.509932i	0.0221292	+	0.0383288i
$178$	−0.430212	−	0.468921i	−0.0322457	−	0.0351471i
$179$	−1.27126	−	0.733963i	−0.0950185	−	0.0548589i	0.451738	−	0.892151i	$-0.350804\pi$
$179$	−1.27126	−	0.733963i	−0.0950185	−	0.0548589i	−0.546756	+	0.837292i	$0.684138\pi$
$180$	−0.254911	−	0.0219894i	−0.0190000	−	0.00163900i
$181$		−	23.5472i		−	1.75025i	−0.483898	−	0.875124i	$-0.660779\pi$
$181$		−	23.5472i		−	1.75025i	0.483898	−	0.875124i	$-0.339221\pi$
$182$		0			0
$183$			1.68795i			0.124777i
$184$	−17.2736	−	7.11808i	−1.27343	−	0.524752i
$185$	−0.961558	−	0.555156i	−0.0706951	−	0.0408159i
$186$	−8.80914	+	8.08195i	−0.645917	+	0.592597i
$187$	11.6410	+	20.1627i	0.851271	+	1.47444i
$188$	16.4192	+	11.4671i	1.19749	+	0.836326i
$189$		0			0
$190$	0.342889	−	1.08982i	0.0248758	−	0.0790635i
$191$	3.19674	−	1.84564i	0.231308	−	0.133546i	−0.379867	−	0.925041i	$-0.624030\pi$
$191$	3.19674	−	1.84564i	0.231308	−	0.133546i	0.611175	+	0.791495i	$0.290697\pi$
$192$	5.67746	+	5.63617i	0.409735	+	0.406756i
$193$	1.35837	−	2.35277i	0.0977777	−	0.169356i	−0.812987	−	0.582282i	$-0.802160\pi$
$193$	1.35837	−	2.35277i	0.0977777	−	0.169356i	0.910764	+	0.412926i	$0.135493\pi$
$194$	−22.3700	+	4.97359i	−1.60607	+	0.357083i
$195$	0.114069			0.00816862
$196$		0			0
$197$	4.09843			0.292001			0.146001	−	0.989284i	$-0.453360\pi$
$197$	4.09843			0.292001			0.146001	+	0.989284i	$0.453360\pi$
$198$	5.51449	−	1.22605i	0.391898	−	0.0871318i
$199$	0.104115	−	0.180332i	0.00738048	−	0.0127834i	−0.862312	−	0.506378i	$-0.830984\pi$
$199$	0.104115	−	0.180332i	0.00738048	−	0.0127834i	0.869692	+	0.493595i	$0.164317\pi$
$200$	−13.9719	+	1.86537i	−0.987961	+	0.131902i
$201$	5.50132	−	3.17619i	0.388033	−	0.224031i
$202$	−5.12135	+	16.2774i	−0.360337	+	1.14527i
$203$		0			0
$204$	6.67447	−	9.55685i	0.467306	−	0.669114i
$205$	−0.207661	−	0.359679i	−0.0145036	−	0.0251210i
$206$	3.42253	−	3.14000i	0.238459	−	0.218774i
$207$	5.72040	+	3.30268i	0.397596	+	0.229552i
$208$	−2.73776	−	2.28592i	−0.189829	−	0.158500i
$209$			25.2252i			1.74486i
$210$		0			0
$211$			16.5850i			1.14176i	0.821034	+	0.570880i	$0.193398\pi$
$211$			16.5850i			1.14176i	−0.821034	+	0.570880i	$0.806602\pi$
$212$	−1.29510	+	15.0133i	−0.0889475	+	1.03112i
$213$	−9.86020	−	5.69279i	−0.675610	−	0.390064i
$214$	−3.18889	−	3.47581i	−0.217988	−	0.237602i
$215$	0.0564062	+	0.0976985i	0.00384687	+	0.00666298i
$216$	−1.72593	−	2.24080i	−0.117435	−	0.152467i
$217$		0			0
$218$	6.01792	+	1.89342i	0.407585	+	0.128238i
$219$	13.4354	−	7.75696i	0.907883	−	0.524167i
$220$	−0.925754	+	0.433058i	−0.0624143	+	0.0291968i
$221$	−2.59847	+	4.50068i	−0.174792	+	0.302749i
$222$	−2.66390	−	11.9816i	−0.178789	−	0.804150i
$223$	−21.3432			−1.42925			−0.714624	−	0.699509i	$-0.753402\pi$
$223$	−21.3432			−1.42925			−0.714624	+	0.699509i	$0.753402\pi$
$224$		0			0
$225$	4.98363			0.332242
$226$	2.81233	+	12.6492i	0.187073	+	0.841411i
$227$	−13.4986	+	23.3803i	−0.895935	+	1.55180i	−0.0632918	+	0.997995i	$0.520160\pi$
$227$	−13.4986	+	23.3803i	−0.895935	+	1.55180i	−0.832643	+	0.553810i	$0.813173\pi$
$228$	11.4400	−	5.35150i	0.757631	−	0.354412i
$229$	2.52614	−	1.45847i	0.166932	−	0.0963783i	−0.414206	−	0.910183i	$-0.635941\pi$
$229$	2.52614	−	1.45847i	0.166932	−	0.0963783i	0.581138	+	0.813805i	$0.302607\pi$
$230$	−1.13994	−	0.358660i	−0.0751656	−	0.0236494i
$231$		0			0
$232$	4.88383	+	6.34074i	0.320639	+	0.416290i
$233$	−10.1995	−	17.6660i	−0.668189	−	1.15734i	−0.978410	−	0.206673i	$-0.933736\pi$
$233$	−10.1995	−	17.6660i	−0.668189	−	1.15734i	0.310221	−	0.950665i	$-0.399597\pi$
$234$	0.852478	+	0.929181i	0.0557282	+	0.0607425i
$235$	1.10940	+	0.640513i	0.0723693	+	0.0417824i
$236$	0.101211	−	1.17328i	0.00658826	−	0.0763741i
$237$			9.82324i			0.638088i
$238$		0			0
$239$			25.2554i			1.63364i	0.576895	+	0.816818i	$0.304264\pi$
$239$			25.2554i			1.63364i	−0.576895	+	0.816818i	$0.695736\pi$
$240$	0.392796	+	0.327970i	0.0253549	+	0.0211704i
$241$	7.10954	+	4.10469i	0.457965	+	0.264406i	0.711188	−	0.703001i	$-0.248157\pi$
$241$	7.10954	+	4.10469i	0.457965	+	0.264406i	−0.253223	+	0.967408i	$0.581491\pi$
$242$	5.16501	−	4.73864i	0.332019	−	0.304611i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	1.93297	−	2.76773i	0.123746	−	0.177186i
$245$		0			0
$246$	1.37795	−	4.37958i	0.0878548	−	0.279232i
$247$	−4.87634	+	2.81535i	−0.310274	+	0.179137i
$248$	23.6994	−	3.16409i	1.50492	−	0.200920i
$249$	0.740105	−	1.28190i	0.0469023	−	0.0812371i
$250$	−1.76318	+	0.392012i	−0.111513	+	0.0247930i
$251$	−6.55180			−0.413546			−0.206773	−	0.978389i	$-0.566296\pi$
$251$	−6.55180			−0.413546			−0.206773	+	0.978389i	$0.566296\pi$
$252$		0			0
$253$	26.3854			1.65884
$254$	−19.4340	+	4.32082i	−1.21940	+	0.271113i
$255$	0.372812	−	0.645730i	0.0233464	−	0.0404372i
$256$	−2.85501	−	15.7432i	−0.178438	−	0.983951i
$257$	−16.2399	+	9.37612i	−1.01302	+	0.584866i	−0.912074	−	0.410026i	$-0.865520\pi$
$257$	−16.2399	+	9.37612i	−1.01302	+	0.584866i	−0.100944	+	0.994892i	$0.532186\pi$
$258$	−0.374288	+	1.18961i	−0.0233022	+	0.0740621i
$259$		0			0
$260$	−0.187038	−	0.130627i	−0.0115996	−	0.00810112i
$261$	−1.41484	−	2.45058i	−0.0875765	−	0.151687i
$262$	10.1808	−	9.34042i	0.628974	−	0.577053i
$263$	1.82321	+	1.05263i	0.112424	+	0.0649079i	0.555158	−	0.831745i	$-0.312658\pi$
$263$	1.82321	+	1.05263i	0.112424	+	0.0649079i	−0.442734	+	0.896653i	$0.645991\pi$
$264$	−10.4461	−	4.30461i	−0.642915	−	0.264931i
$265$			0.963886i			0.0592111i
$266$		0			0
$267$		−	0.449983i		−	0.0275385i
$268$	−12.6578	−	1.09190i	−0.773195	−	0.0666982i
$269$	10.2209	+	5.90104i	0.623180	+	0.359793i	0.778106	−	0.628133i	$-0.216181\pi$
$269$	10.2209	+	5.90104i	0.623180	+	0.359793i	−0.154926	+	0.987926i	$0.549514\pi$
$270$	−0.122308	−	0.133313i	−0.00744344	−	0.00811318i
$271$	−5.66213	−	9.80709i	−0.343950	−	0.595738i	0.641213	−	0.767363i	$-0.278432\pi$
$271$	−5.66213	−	9.80709i	−0.343950	−	0.595738i	−0.985162	+	0.171625i	$0.945098\pi$
$272$	−21.8882	+	8.02702i	−1.32717	+	0.486710i
$273$		0			0
$274$	−5.35361	−	1.68441i	−0.323423	−	0.101759i
$275$	17.2403	−	9.95368i	1.03963	−	0.600230i
$276$	−5.59765	−	11.9662i	−0.336939	−	0.720278i
$277$	5.88192	−	10.1878i	0.353410	−	0.612125i	−0.633434	−	0.773797i	$-0.718355\pi$
$277$	5.88192	−	10.1878i	0.353410	−	0.612125i	0.986845	+	0.161672i	$0.0516886\pi$
$278$	0.0804231	+	0.361724i	0.00482345	+	0.0216947i
$279$	−8.45337			−0.506090
$280$		0			0
$281$	−9.80481			−0.584906			−0.292453	−	0.956280i	$-0.594471\pi$
$281$	−9.80481			−0.584906			−0.292453	+	0.956280i	$0.594471\pi$
$282$	3.07348	+	13.8238i	0.183023	+	0.823194i
$283$	−12.3233	+	21.3445i	−0.732542	+	1.26880i	0.223252	+	0.974761i	$0.428333\pi$
$283$	−12.3233	+	21.3445i	−0.732542	+	1.26880i	−0.955794	+	0.294039i	$0.905001\pi$
$284$	9.64861	+	20.6260i	0.572540	+	1.22393i
$285$	0.699626	−	0.403929i	0.0414423	−	0.0239267i
$286$	4.80487	+	1.51176i	0.284118	+	0.0893922i
$287$		0			0
$288$	0.263934	+	5.65069i	0.0155524	+	0.332970i
$289$	8.48525	+	14.6969i	0.499132	+	0.864522i
$290$	0.346093	+	0.377234i	0.0203233	+	0.0221519i
$291$	−14.0333	−	8.10212i	−0.822645	−	0.474954i
$292$	−30.9130	−	2.66665i	−1.80905	−	0.156054i
$293$		−	2.41042i		−	0.140818i	−0.997518	−	0.0704091i	$-0.977570\pi$
$293$		−	2.41042i		−	0.140818i	0.997518	−	0.0704091i	$-0.0224305\pi$
$294$		0			0
$295$		−	0.0753270i		−	0.00438571i
$296$	−9.35281	+	22.6967i	−0.543621	+	1.31922i
$297$	3.45938	+	1.99727i	0.200734	+	0.115894i
$298$	−2.80893	+	2.57705i	−0.162717	+	0.149285i
$299$	2.94485	+	5.10062i	0.170305	+	0.294977i
$300$	−8.17166	−	5.70705i	−0.471791	−	0.329497i
$301$		0			0
$302$	−1.83216	+	5.82323i	−0.105429	+	0.335089i
$303$	−10.4495	+	6.03304i	−0.600310	+	0.346589i
$304$	−24.8864	−	4.32575i	−1.42733	−	0.248099i
$305$	0.107969	−	0.187007i	0.00618228	−	0.0107080i
$306$	8.04616	−	1.78893i	0.459968	−	0.102266i
$307$	−24.4054			−1.39289			−0.696446	−	0.717609i	$-0.745236\pi$
$307$	−24.4054			−1.39289			−0.696446	+	0.717609i	$0.745236\pi$
$308$		0			0
$309$	3.28431			0.186838
$310$	1.49292	−	0.331925i	0.0847922	−	0.0188521i
$311$	15.5933	−	27.0084i	0.884215	−	1.53151i	0.0376050	−	0.999293i	$-0.488027\pi$
$311$	15.5933	−	27.0084i	0.884215	−	1.53151i	0.846610	−	0.532213i	$-0.178640\pi$
$312$	−0.333746	−	2.49980i	−0.0188947	−	0.141523i
$313$	−2.19804	+	1.26904i	−0.124240	+	0.0717302i	−0.560832	−	0.827929i	$-0.689519\pi$
$313$	−2.19804	+	1.26904i	−0.124240	+	0.0717302i	0.436592	+	0.899660i	$0.356185\pi$
$314$	1.36083	−	4.32516i	0.0767959	−	0.244083i
$315$		0			0
$316$	11.2492	−	16.1072i	0.632816	−	0.906098i
$317$	9.12602	+	15.8067i	0.512568	+	0.887795i	0.999894	+	0.0145742i	$0.00463927\pi$
$317$	9.12602	+	15.8067i	0.512568	+	0.887795i	−0.487325	+	0.873221i	$0.662027\pi$
$318$	−7.85164	+	7.20349i	−0.440298	+	0.403952i
$319$	−9.78895	−	5.65165i	−0.548076	−	0.316432i
$320$	−0.268489	−	0.987586i	−0.0150090	−	0.0552078i
$321$		−	3.33543i		−	0.186166i
$322$		0			0
$323$			36.8059i			2.04793i
$324$	0.171888	−	1.99260i	0.00954932	−	0.110700i
$325$	3.84834	+	2.22184i	0.213468	+	0.123246i
$326$	−22.2398	−	24.2409i	−1.23175	−	1.34258i
$327$	2.23048	+	3.86331i	0.123346	+	0.213641i
$328$	−7.27474	+	5.60322i	−0.401680	+	0.309386i
$329$		0			0
$330$	−0.689373	−	0.216898i	−0.0379487	−	0.0119398i
$331$	17.9504	−	10.3637i	0.986644	−	0.569639i	0.0823747	−	0.996601i	$-0.473750\pi$
$331$	17.9504	−	10.3637i	0.986644	−	0.569639i	0.904270	+	0.426962i	$0.140416\pi$
$332$	−2.68153	+	1.25439i	−0.147168	+	0.0688436i
$333$	4.33956	−	7.51634i	0.237806	−	0.411893i
$334$	−2.96761	−	13.3476i	−0.162380	−	0.730348i
$335$	−0.812654			−0.0444000
$336$		0			0
$337$	−0.330532			−0.0180052			−0.00900261	−	0.999959i	$-0.502866\pi$
$337$	−0.330532			−0.0180052			−0.00900261	+	0.999959i	$0.502866\pi$
$338$	−3.74608	−	16.8490i	−0.203760	−	0.916464i
$339$	−4.58136	+	7.93515i	−0.248825	+	0.430978i
$340$	−1.35076	+	0.631872i	−0.0732554	+	0.0342681i
$341$	−29.2434	+	16.8837i	−1.58362	+	0.914303i
$342$	8.51891	+	2.68031i	0.460650	+	0.144934i
$343$		0			0
$344$	1.97602	−	1.52199i	0.106540	−	0.0820600i
$345$	−0.422508	−	0.731806i	−0.0227471	−	0.0393991i
$346$	−19.7968	−	21.5780i	−1.06428	−	1.16004i
$347$	19.0483	+	10.9975i	1.02257	+	0.590378i	0.914846	−	0.403803i	$-0.132312\pi$
$347$	19.0483	+	10.9975i	1.02257	+	0.590378i	0.107719	+	0.994181i	$0.465645\pi$
$348$	−0.486388	+	5.63843i	−0.0260731	+	0.302251i
$349$			26.6709i			1.42766i	0.700318	+	0.713831i	$0.253041\pi$
$349$			26.6709i			1.42766i	−0.700318	+	0.713831i	$0.746959\pi$
$350$		0			0
$351$			0.891655i			0.0475930i
$352$	12.1990	+	19.0207i	0.650210	+	1.01381i
$353$	6.73045	+	3.88583i	0.358226	+	0.206822i	0.668302	−	0.743890i	$-0.267021\pi$
$353$	6.73045	+	3.88583i	0.358226	+	0.206822i	−0.310076	+	0.950712i	$0.600355\pi$
$354$	0.613600	−	0.562948i	0.0326125	−	0.0299203i
$355$	0.728273	+	1.26141i	0.0386527	+	0.0669485i
$356$	−0.515302	+	0.737836i	−0.0273109	+	0.0391052i
$357$		0			0
$358$	−0.623049	+	1.98026i	−0.0329292	+	0.104660i
$359$	−14.5380	+	8.39350i	−0.767285	+	0.442992i	−0.831905	−	0.554918i	$-0.812750\pi$
$359$	−14.5380	+	8.39350i	−0.767285	+	0.442992i	0.0646204	+	0.997910i	$0.479416\pi$
$360$	0.0478838	+	0.358656i	0.00252370	+	0.0189028i
$361$	−10.4390	+	18.0808i	−0.549419	+	0.951621i
$362$	−32.5070	+	7.22737i	−1.70853	+	0.379862i
$363$	4.95641			0.260144
$364$		0			0
$365$	−1.98468			−0.103883
$366$	2.33022	−	0.518085i	0.121803	−	0.0270807i
$367$	2.01820	−	3.49562i	0.105349	−	0.182470i	−0.808532	−	0.588453i	$-0.799737\pi$
$367$	2.01820	−	3.49562i	0.105349	−	0.182470i	0.913881	+	0.405983i	$0.133071\pi$
$368$	−4.52471	+	26.0311i	−0.235867	+	1.35696i
$369$	2.81155	−	1.62325i	0.146363	−	0.0845029i
$370$	−0.471263	+	1.49783i	−0.0244998	+	0.0778685i
$371$		0			0
$372$	13.8610	+	9.68045i	0.718658	+	0.501908i
$373$	−10.3895	−	17.9951i	−0.537948	−	0.931753i	−0.999014	−	0.0443876i	$-0.985866\pi$
$373$	−10.3895	−	17.9951i	−0.537948	−	0.931753i	0.461066	−	0.887366i	$-0.347467\pi$
$374$	24.2618	−	22.2590i	1.25455	−	1.15098i
$375$	−1.10608	−	0.638598i	−0.0571180	−	0.0329771i
$376$	10.7908	−	26.1864i	0.556495	−	1.35046i
$377$		−	2.52310i		−	0.129946i
$378$		0			0
$379$			10.7800i			0.553732i	0.960909	+	0.276866i	$0.0892958\pi$
$379$			10.7800i			0.553732i	−0.960909	+	0.276866i	$0.910704\pi$
$380$	−1.60974	−	0.138861i	−0.0825779	−	0.00712342i
$381$	−12.1915	−	7.03874i	−0.624587	−	0.360606i
$382$	−3.52910	−	3.84663i	−0.180564	−	0.196811i
$383$	3.26491	+	5.65498i	0.166829	+	0.288956i	0.937303	−	0.348515i	$-0.113314\pi$
$383$	3.26491	+	5.65498i	0.166829	+	0.288956i	−0.770474	+	0.637471i	$0.779981\pi$
$384$	6.03817	−	9.56768i	0.308134	−	0.488249i
$385$		0			0
$386$	−3.66493	−	1.15310i	−0.186540	−	0.0586912i
$387$	−0.763693	+	0.440918i	−0.0388207	+	0.0224131i
$388$	13.7321	+	29.3554i	0.697143	+	1.49029i
$389$	−15.9348	+	27.5999i	−0.807928	+	1.39937i	0.106368	+	0.994327i	$0.466078\pi$
$389$	−15.9348	+	27.5999i	−0.807928	+	1.39937i	−0.914296	+	0.405046i	$0.867255\pi$
$390$	−0.0350112	−	0.157472i	−0.00177286	−	0.00797391i
$391$	38.4988			1.94697
$392$		0			0
$393$	9.76967			0.492814
$394$	−1.25794	−	5.65791i	−0.0633740	−	0.285041i
$395$	0.628339	−	1.08832i	0.0316152	−	0.0547591i
$396$	−3.38514	−	7.23647i	−0.170110	−	0.363646i
$397$	13.3557	−	7.71089i	0.670301	−	0.386999i	−0.125889	−	0.992044i	$-0.540178\pi$
$397$	13.3557	−	7.71089i	0.670301	−	0.386999i	0.796191	+	0.605046i	$0.206845\pi$
$398$	−0.280905	−	0.0883811i	−0.0140805	−	0.00443015i
$399$		0			0
$400$	6.86357	+	18.7157i	0.343178	+	0.935785i
$401$	−13.8479	−	23.9853i	−0.691533	−	1.19777i	−0.971336	−	0.237712i	$-0.923602\pi$
$401$	−13.8479	−	23.9853i	−0.691533	−	1.19777i	0.279803	−	0.960057i	$-0.409731\pi$
$402$	−6.07328	−	6.61973i	−0.302907	−	0.330162i
$403$	−6.52765	−	3.76874i	−0.325166	−	0.187734i
$404$	24.0429	+	2.07401i	1.19618	+	0.103186i
$405$		−	0.127929i		−	0.00635684i
$406$		0			0
$407$		−	34.6692i		−	1.71849i
$408$	−15.2419	−	6.28084i	−0.754586	−	0.310948i
$409$	−21.5187	−	12.4238i	−1.06403	−	0.614319i	−0.137486	−	0.990504i	$-0.543902\pi$
$409$	−21.5187	−	12.4238i	−1.06403	−	0.614319i	−0.926545	+	0.376185i	$0.877236\pi$
$410$	−0.432801	+	0.397073i	−0.0213745	+	0.0196100i
$411$	−1.98426	−	3.43684i	−0.0978764	−	0.169527i
$412$	−5.38527	−	3.76105i	−0.265313	−	0.185294i
$413$		0			0
$414$	2.80359	−	8.91074i	0.137789	−	0.437939i
$415$	−0.163992	+	0.0946810i	−0.00805006	+	0.00464771i
$416$	−2.31543	+	4.48111i	−0.113523	+	0.219704i
$417$	−0.131011	+	0.226918i	−0.00641566	+	0.0111122i
$418$	34.8234	−	7.74240i	1.70327	−	0.378693i
$419$	−21.9087			−1.07031			−0.535155	−	0.844754i	$-0.679747\pi$
$419$	−21.9087			−1.07031			−0.535155	+	0.844754i	$0.679747\pi$
$420$		0			0
$421$	−18.8226			−0.917357			−0.458679	−	0.888602i	$-0.651677\pi$
$421$	−18.8226			−0.917357			−0.458679	+	0.888602i	$0.651677\pi$
$422$	22.8957	−	5.09047i	1.11455	−	0.247800i
$423$	−5.00678	+	8.67200i	−0.243438	+	0.421647i
$424$	21.1235	−	2.82018i	1.02585	−	0.136960i
$425$	25.1552	−	14.5234i	1.22021	−	0.704486i
$426$	−4.83252	+	15.3594i	−0.234136	+	0.744163i
$427$		0			0
$428$	−3.81960	+	5.46911i	−0.184628	+	0.264359i
$429$	1.78088	+	3.08457i	0.0859816	+	0.148925i
$430$	0.117560	−	0.107856i	0.00566926	−	0.00520127i
$431$	−18.9190	−	10.9229i	−0.911295	−	0.526137i	−0.0304476	−	0.999536i	$-0.509693\pi$
$431$	−18.9190	−	10.9229i	−0.911295	−	0.526137i	−0.880848	+	0.473400i	$0.843027\pi$
$432$	−2.56369	+	3.07042i	−0.123346	+	0.147726i
$433$		−	23.7440i		−	1.14107i	−0.821275	−	0.570533i	$-0.806737\pi$
$433$		−	23.7440i		−	1.14107i	0.821275	−	0.570533i	$-0.193263\pi$
$434$		0			0
$435$			0.361999i			0.0173565i
$436$	0.766785	−	8.88891i	0.0367223	−	0.425702i
$437$	36.1238	+	20.8561i	1.72803	+	0.997681i
$438$	−14.8323	−	16.1668i	−0.708714	−	0.772482i
$439$	−15.9429	−	27.6140i	−0.760914	−	1.31794i	−0.942380	−	0.334545i	$-0.891417\pi$
$439$	−15.9429	−	27.6140i	−0.760914	−	1.31794i	0.181466	−	0.983397i	$-0.441916\pi$
$440$	0.881982	+	1.14509i	0.0420468	+	0.0545900i
$441$		0			0
$442$	7.01076	+	2.20580i	0.333468	+	0.104919i
$443$	13.5814	−	7.84122i	0.645272	−	0.372548i	−0.141371	−	0.989957i	$-0.545151\pi$
$443$	13.5814	−	7.84122i	0.645272	−	0.372548i	0.786642	+	0.617409i	$0.211818\pi$
$444$	−15.7230	+	7.35504i	−0.746179	+	0.349055i
$445$	−0.0287829	+	0.0498535i	−0.00136444	+	0.00236328i
$446$	6.55090	+	29.4644i	0.310194	+	1.39518i
$447$	−2.69549			−0.127492
$448$		0			0
$449$	−9.72484			−0.458943			−0.229472	−	0.973315i	$-0.573700\pi$
$449$	−9.72484			−0.458943			−0.229472	+	0.973315i	$0.573700\pi$
$450$	−1.52963	−	6.87993i	−0.0721077	−	0.324323i
$451$	6.48414	−	11.2309i	0.305326	−	0.528841i
$452$	16.5991	−	7.76486i	0.780754	−	0.365228i
$453$	−3.73832	+	2.15832i	−0.175642	+	0.101407i
$454$	36.4198	+	11.4588i	1.70926	+	0.537786i
$455$		0			0
$456$	−10.8991	−	14.1504i	−0.510395	−	0.662653i
$457$	5.70383	+	9.87933i	0.266814	+	0.462135i	0.968037	−	0.250806i	$-0.0806957\pi$
$457$	5.70383	+	9.87933i	0.266814	+	0.462135i	−0.701223	+	0.712942i	$0.747362\pi$
$458$	−2.78877	−	3.03970i	−0.130311	−	0.142036i
$459$	5.04756	+	2.91421i	0.235600	+	0.136024i
$460$	−0.145248	+	1.68378i	−0.00677222	+	0.0785066i
$461$		−	19.6446i		−	0.914940i	−0.889225	−	0.457470i	$-0.848756\pi$
$461$		−	19.6446i		−	0.914940i	0.889225	−	0.457470i	$-0.151244\pi$
$462$		0			0
$463$		−	6.73057i		−	0.312796i	−0.987694	−	0.156398i	$-0.950012\pi$
$463$		−	6.73057i		−	0.312796i	0.987694	−	0.156398i	$-0.0499883\pi$
$464$	7.25443	−	8.68833i	0.336778	−	0.403345i
$465$	0.936547	+	0.540715i	0.0434313	+	0.0250751i
$466$	−21.2575	+	19.5027i	−0.984733	+	0.903444i
$467$	11.0608	+	19.1579i	0.511833	+	0.886522i	0.999906	+	0.0137185i	$0.00436686\pi$
$467$	11.0608	+	19.1579i	0.511833	+	0.886522i	−0.488072	+	0.872803i	$0.662300\pi$
$468$	1.02109	−	1.46204i	0.0471997	−	0.0675830i
$469$		0			0
$470$	0.543721	−	1.72813i	0.0250800	−	0.0797125i
$471$	2.77661	−	1.60308i	0.127940	−	0.0738660i
$472$	−1.65078	+	0.220395i	−0.0759835	+	0.0101445i
$473$	−1.76127	+	3.05061i	−0.0809832	+	0.140267i
$474$	13.5610	−	3.01506i	0.622879	−	0.138486i
$475$	31.4711			1.44399
$476$		0			0
$477$	−7.53454			−0.344983
$478$	34.8652	−	7.75168i	1.59470	−	0.354554i
$479$	10.6325	−	18.4159i	0.485809	−	0.841446i	−0.514058	−	0.857755i	$-0.671858\pi$
$479$	10.6325	−	18.4159i	0.485809	−	0.841446i	0.999867	+	0.0163095i	$0.00519170\pi$
$480$	0.332203	−	0.642922i	0.0151629	−	0.0293452i
$481$	6.70198	−	3.86939i	0.305584	−	0.176429i
$482$	3.48441	−	11.0746i	0.158710	−	0.504434i
$483$		0			0
$484$	−8.12702	−	5.67588i	−0.369410	−	0.257995i
$485$	1.03650	+	1.79526i	0.0470648	+	0.0815187i
$486$	1.04209	−	0.956063i	0.0472700	−	0.0433679i
$487$	30.6868	+	17.7171i	1.39055	+	0.802836i	0.993376	−	0.114906i	$-0.0366566\pi$
$487$	30.6868	+	17.7171i	1.39055	+	0.802836i	0.397177	+	0.917742i	$0.369990\pi$
$488$	−4.41415	−	1.81897i	−0.199819	−	0.0823410i
$489$		−	23.2619i		−	1.05194i
$490$		0			0
$491$		−	15.1925i		−	0.685628i	−0.939403	−	0.342814i	$-0.888620\pi$
$491$		−	15.1925i		−	0.685628i	0.939403	−	0.342814i	$-0.111380\pi$
$492$	−6.46897	−	0.558033i	−0.291644	−	0.0251581i
$493$	−14.2830	−	8.24629i	−0.643274	−	0.371394i
$494$	5.38331	+	5.86768i	0.242207	+	0.264000i
$495$	−0.255509	−	0.442555i	−0.0114843	−	0.0198914i
$496$	−11.6422	−	31.7460i	−0.522748	−	1.42544i
$497$		0			0
$498$	−1.99683	−	0.628263i	−0.0894801	−	0.0281532i
$499$	−9.60373	+	5.54472i	−0.429922	+	0.248216i	−0.699313	−	0.714815i	$-0.746511\pi$
$499$	−9.60373	+	5.54472i	−0.429922	+	0.248216i	0.269391	+	0.963031i	$0.413178\pi$
$500$	1.08235	+	2.31375i	0.0484041	+	0.103474i
$501$	4.83432	−	8.37329i	0.215982	−	0.374091i
$502$	2.01095	+	9.04479i	0.0897533	+	0.403689i
$503$	5.67396			0.252989			0.126495	−	0.991967i	$-0.459627\pi$
$503$	5.67396			0.252989			0.126495	+	0.991967i	$0.459627\pi$
$504$		0			0
$505$	1.54360			0.0686894
$506$	−8.09851	−	36.4252i	−0.360023	−	1.61930i
$507$	6.10248	−	10.5698i	0.271020	−	0.469421i
$508$	11.9298	+	25.5026i	0.529301	+	1.13149i
$509$	−11.0839	+	6.39931i	−0.491286	+	0.283644i	−0.725108	−	0.688635i	$-0.758210\pi$
$509$	−11.0839	+	6.39931i	−0.491286	+	0.283644i	0.233822	+	0.972279i	$0.424877\pi$
$510$	−1.00586	−	0.316474i	−0.0445402	−	0.0140137i
$511$		0			0
$512$	−20.8573	+	8.77344i	−0.921771	+	0.387735i
$513$	3.15745	+	5.46886i	0.139405	+	0.241456i
$514$	17.9283	+	19.5415i	0.790784	+	0.861937i
$515$	−0.363867	−	0.210079i	−0.0160339	−	0.00925719i
$516$	1.75715	+	0.151577i	0.0773541	+	0.00667280i
$517$			39.9997i			1.75918i
$518$		0			0
$519$		−	20.7065i		−	0.908916i
$520$	−0.122923	+	0.298300i	−0.00539052	+	0.0130813i
$521$	−24.4767	−	14.1316i	−1.07234	−	0.619117i	−0.143521	−	0.989647i	$-0.545843\pi$
$521$	−24.4767	−	14.1316i	−1.07234	−	0.619117i	−0.928820	+	0.370531i	$0.879176\pi$
$522$	−2.94877	+	2.70535i	−0.129064	+	0.118410i
$523$	5.38111	+	9.32036i	0.235300	+	0.407551i	0.959360	−	0.282186i	$-0.0910595\pi$
$523$	5.38111	+	9.32036i	0.235300	+	0.407551i	−0.724060	+	0.689737i	$0.757726\pi$
$524$	−16.0193	−	11.1878i	−0.699807	−	0.488742i
$525$		0			0
$526$	0.893560	−	2.84003i	0.0389611	−	0.123831i
$527$	−42.6689	+	24.6349i	−1.85869	+	1.07311i
$528$	−2.73629	+	15.7421i	−0.119082	+	0.685089i
$529$	10.3153	−	17.8667i	0.448493	−	0.776813i
$530$	1.33065	−	0.295847i	0.0577997	−	0.0128508i
$531$	0.588819			0.0255526
$532$		0			0
$533$	2.89475			0.125386
$534$	−0.621203	+	0.138114i	−0.0268821	+	0.00597677i
$535$	−0.213349	+	0.369532i	−0.00922390	+	0.0159763i
$536$	2.37770	+	17.8092i	0.102701	+	0.769241i
$537$	−1.27126	+	0.733963i	−0.0548589	+	0.0316728i
$538$	5.00930	−	15.9212i	0.215966	−	0.686413i
$539$		0			0
$540$	−0.146499	+	0.209765i	−0.00630432	+	0.00902685i
$541$	2.66295	+	4.61237i	0.114489	+	0.198301i	0.917575	−	0.397562i	$-0.130144\pi$
$541$	2.66295	+	4.61237i	0.114489	+	0.198301i	−0.803086	+	0.595863i	$0.796810\pi$
$542$	−11.8009	+	10.8267i	−0.506890	+	0.465047i
$543$	−20.3925	−	11.7736i	−0.875124	−	0.505253i
$544$	17.7995	+	27.7531i	0.763149	+	1.18990i
$545$		−	0.570686i		−	0.0244455i
$546$		0			0
$547$		−	18.5001i		−	0.791007i	−0.918465	−	0.395503i	$-0.870570\pi$
$547$		−	18.5001i		−	0.791007i	0.918465	−	0.395503i	$-0.129430\pi$
$548$	−0.682141	+	7.90768i	−0.0291396	+	0.337799i
$549$	1.46181	+	0.843974i	0.0623884	+	0.0360199i
$550$	−19.0327	−	20.7452i	−0.811557	−	0.884578i
$551$	−8.93458	−	15.4751i	−0.380626	−	0.659263i
$552$	−14.8013	+	11.4004i	−0.629983	+	0.485232i
$553$		0			0
$554$	−15.8696	−	4.99307i	−0.674236	−	0.212135i
$555$	−0.961558	+	0.555156i	−0.0408159	+	0.0235650i
$556$	0.474677	−	0.222049i	0.0201308	−	0.00941697i
$557$	14.9681	−	25.9255i	0.634219	−	1.09850i	−0.352461	−	0.935827i	$-0.614655\pi$
$557$	14.9681	−	25.9255i	0.634219	−	1.09850i	0.986680	−	0.162673i	$-0.0520116\pi$
$558$	2.59460	+	11.6699i	0.109838	+	0.494027i
$559$	−0.786294			−0.0332567
$560$		0			0
$561$	23.2819			0.982963
$562$	3.00940	+	13.5356i	0.126944	+	0.570964i
$563$	6.18858	−	10.7189i	0.260818	−	0.451749i	−0.705642	−	0.708569i	$-0.749341\pi$
$563$	6.18858	−	10.7189i	0.260818	−	0.451749i	0.966459	+	0.256819i	$0.0826746\pi$
$564$	18.1404	−	8.48590i	0.763850	−	0.357321i
$565$	1.01514	−	0.586089i	0.0427071	−	0.0246570i
$566$	33.2486	+	10.4610i	1.39754	+	0.439709i
$567$		0			0
$568$	25.5128	−	19.6507i	1.07049	−	0.824525i
$569$	18.3617	+	31.8033i	0.769761	+	1.33327i	0.937692	+	0.347467i	$0.112958\pi$
$569$	18.3617	+	31.8033i	0.769761	+	1.33327i	−0.167931	+	0.985799i	$0.553709\pi$
$570$	−0.772364	−	0.841858i	−0.0323507	−	0.0352616i
$571$	−5.47430	−	3.16059i	−0.229092	−	0.132267i	0.381061	−	0.924550i	$-0.375559\pi$
$571$	−5.47430	−	3.16059i	−0.229092	−	0.132267i	−0.610153	+	0.792283i	$0.708892\pi$
$572$	0.612223	−	7.09716i	0.0255983	−	0.296747i
$573$		−	3.69128i		−	0.154206i
$574$		0			0
$575$		−	32.9187i		−	1.37280i
$576$	7.71980	−	2.09874i	0.321658	−	0.0874474i
$577$	−4.40430	−	2.54283i	−0.183354	−	0.105859i	0.405514	−	0.914089i	$-0.367093\pi$
$577$	−4.40430	−	2.54283i	−0.183354	−	0.105859i	−0.588867	+	0.808230i	$0.700426\pi$
$578$	17.6847	−	16.2249i	0.735587	−	0.674865i
$579$	−1.35837	−	2.35277i	−0.0564520	−	0.0977777i
$580$	0.414546	−	0.593569i	0.0172131	−	0.0246466i
$581$		0			0
$582$	−6.87775	+	21.8598i	−0.285092	+	0.906118i
$583$	−26.0648	+	15.0485i	−1.07950	+	0.623247i
$584$	5.80686	+	43.4941i	0.240289	+	1.79980i
$585$	0.0570343	−	0.0987862i	0.00235808	−	0.00408431i
$586$	−3.32759	+	0.739833i	−0.137462	+	0.0305622i
$587$	30.0719			1.24120			0.620601	−	0.784127i	$-0.286889\pi$
$587$	30.0719			1.24120			0.620601	+	0.784127i	$0.286889\pi$
$588$		0			0
$589$	−53.3821			−2.19957
$590$	−0.103989	+	0.0231202i	−0.00428117	+	0.000951845i
$591$	2.04922	−	3.54935i	0.0842935	−	0.146001i
$592$	34.2036	+	5.94526i	1.40576	+	0.244349i
$593$	−18.6666	+	10.7772i	−0.766545	+	0.442565i	−0.831641	−	0.555314i	$-0.812598\pi$
$593$	−18.6666	+	10.7772i	−0.766545	+	0.442565i	0.0650955	+	0.997879i	$0.479265\pi$
$594$	1.69545	−	5.38872i	0.0695653	−	0.221102i
$595$		0			0
$596$	4.41978	+	3.08676i	0.181041	+	0.126439i
$597$	−0.104115	−	0.180332i	−0.00426112	−	0.00738048i
$598$	6.13757	−	5.63092i	0.250984	−	0.230265i
$599$	15.8953	+	9.17715i	0.649464	+	0.374968i	0.788251	−	0.615354i	$-0.210987\pi$
$599$	15.8953	+	9.17715i	0.649464	+	0.374968i	−0.138787	+	0.990322i	$0.544320\pi$
$600$	−5.37048	+	13.0327i	−0.219249	+	0.532057i
$601$			12.2204i			0.498482i	0.968441	+	0.249241i	$0.0801812\pi$
$601$			12.2204i			0.498482i	−0.968441	+	0.249241i	$0.919819\pi$
$602$		0			0
$603$		−	6.35238i		−	0.258689i
$604$	8.60135	+	0.741979i	0.349984	+	0.0301907i
$605$	−0.549120	−	0.317034i	−0.0223249	−	0.0128893i
$606$	11.5359	+	12.5739i	0.468615	+	0.510780i
$607$	−13.2875	−	23.0146i	−0.539322	−	0.934133i	−0.998941	−	0.0460167i	$-0.985347\pi$
$607$	−13.2875	−	23.0146i	−0.539322	−	0.934133i	0.459619	−	0.888116i	$-0.347986\pi$
$608$	1.66671	+	35.6835i	0.0675942	+	1.44716i
$609$		0			0
$610$	−0.291304	−	0.0916530i	−0.0117945	−	0.00371092i
$611$	−7.73243	+	4.46432i	−0.312821	+	0.180607i
$612$	−4.93924	−	10.5587i	−0.199657	−	0.426810i
$613$	9.57949	−	16.5922i	0.386912	−	0.670151i	−0.605120	−	0.796134i	$-0.706875\pi$
$613$	9.57949	−	16.5922i	0.386912	−	0.670151i	0.992032	+	0.125983i	$0.0402084\pi$
$614$	7.49080	+	33.6918i	0.302304	+	1.35969i
$615$	−0.415321			−0.0167474
$616$		0			0
$617$	−14.7860			−0.595263			−0.297632	−	0.954681i	$-0.596197\pi$
$617$	−14.7860			−0.595263			−0.297632	+	0.954681i	$0.596197\pi$
$618$	−1.00806	−	4.53400i	−0.0405500	−	0.182384i
$619$	−12.6747	+	21.9532i	−0.509439	+	0.882374i	0.490501	+	0.871440i	$0.336814\pi$
$619$	−12.6747	+	21.9532i	−0.509439	+	0.882374i	−0.999940	+	0.0109337i	$0.996520\pi$
$620$	−0.916449	−	1.95911i	−0.0368055	−	0.0786796i
$621$	5.72040	−	3.30268i	0.229552	−	0.132532i
$622$	−42.0713	−	13.2369i	−1.68691	−	0.530751i
$623$		0			0
$624$	−3.34855	+	1.22801i	−0.134049	+	0.0491596i
$625$	−12.3774	−	21.4383i	−0.495096	−	0.857531i
$626$	2.42656	+	2.64489i	0.0969847	+	0.105711i
$627$	21.8456	+	12.6126i	0.872430	+	0.503698i
$628$	−6.38859	−	0.551099i	−0.254932	−	0.0219913i
$629$		−	50.5856i		−	2.01698i
$630$		0			0
$631$		−	36.7075i		−	1.46130i	−0.682752	−	0.730650i	$-0.739217\pi$
$631$		−	36.7075i		−	1.46130i	0.682752	−	0.730650i	$-0.260783\pi$
$632$	−25.6887	−	10.5857i	−1.02184	−	0.421078i
$633$	14.3630	+	8.29251i	0.570880	+	0.329598i
$634$	19.0202	−	17.4501i	0.755389	−	0.693032i
$635$	0.900459	+	1.55964i	0.0357336	+	0.0618925i
$636$	12.3544	+	8.62825i	0.489883	+	0.342132i
$637$		0			0
$638$	−4.79760	+	15.2484i	−0.189939	+	0.603688i
$639$	−9.86020	+	5.69279i	−0.390064	+	0.225203i
$640$	−1.28096	+	0.673772i	−0.0506344	+	0.0266332i
$641$	3.64685	−	6.31654i	0.144042	−	0.249488i	−0.784973	−	0.619530i	$-0.787323\pi$
$641$	3.64685	−	6.31654i	0.144042	−	0.249488i	0.929015	+	0.370042i	$0.120657\pi$
$642$	−4.60458	+	1.02375i	−0.181728	+	0.0404042i
$643$	−20.6956			−0.816155			−0.408077	−	0.912947i	$-0.633801\pi$
$643$	−20.6956			−0.816155			−0.408077	+	0.912947i	$0.633801\pi$
$644$		0			0
$645$	0.112812			0.00444199
$646$	50.8107	−	11.2969i	1.99912	−	0.444470i
$647$	−7.92738	+	13.7306i	−0.311658	+	0.539807i	−0.978721	−	0.205194i	$-0.934218\pi$
$647$	−7.92738	+	13.7306i	−0.311658	+	0.539807i	0.667064	+	0.745001i	$0.267551\pi$
$648$	−2.80355	+	0.374300i	−0.110134	+	0.0147039i
$649$	2.03695	−	1.17603i	0.0799572	−	0.0461633i
$650$	1.88608	−	5.99461i	0.0739783	−	0.235128i
$651$		0			0
$652$	−26.6386	+	38.1425i	−1.04325	+	1.49377i
$653$	14.4081	+	24.9555i	0.563831	+	0.976584i	0.997157	+	0.0753469i	$0.0240064\pi$
$653$	14.4081	+	24.9555i	0.563831	+	0.976584i	−0.433326	+	0.901237i	$0.642660\pi$
$654$	4.64871	−	4.26496i	0.181779	−	0.166773i
$655$	−1.08238	−	0.624912i	−0.0422921	−	0.0244173i
$656$	9.96812	+	8.32301i	0.389190	+	0.324959i
$657$		−	15.5139i		−	0.605256i
$658$		0			0
$659$			20.6316i			0.803693i	0.915707	+	0.401846i	$0.131631\pi$
$659$			20.6316i			0.803693i	−0.915707	+	0.401846i	$0.868369\pi$
$660$	−0.0878379	+	1.01826i	−0.00341908	+	0.0396355i
$661$	−20.7427	−	11.9758i	−0.806799	−	0.465806i	0.0390440	−	0.999237i	$-0.487569\pi$
$661$	−20.7427	−	11.9758i	−0.806799	−	0.465806i	−0.845843	+	0.533432i	$0.820902\pi$
$662$	−19.8167	−	21.5997i	−0.770196	−	0.839496i
$663$	2.59847	+	4.50068i	0.100916	+	0.174792i
$664$	2.55474	+	3.31685i	0.0991431	+	0.128719i
$665$		0			0
$666$	−11.7083	−	3.68378i	−0.453687	−	0.142744i
$667$	−16.1869	+	9.34553i	−0.626760	+	0.361860i
$668$	−17.5156	+	8.19360i	−0.677698	+	0.317020i
$669$	−10.6716	+	18.4838i	−0.412588	+	0.714624i
$670$	0.249429	+	1.12187i	0.00963629	+	0.0433417i
$671$	6.74259			0.260295
$672$		0			0
$673$	3.43936			0.132577			0.0662887	−	0.997800i	$-0.478884\pi$
$673$	3.43936			0.132577			0.0662887	+	0.997800i	$0.478884\pi$
$674$	0.101451	+	0.456301i	0.00390773	+	0.0175761i
$675$	2.49182	−	4.31595i	0.0959101	−	0.166121i
$676$	−22.1103	+	10.3430i	−0.850397	+	0.397807i
$677$	28.7477	−	16.5975i	1.10486	−	0.637893i	0.167369	−	0.985894i	$-0.446473\pi$
$677$	28.7477	−	16.5975i	1.10486	−	0.637893i	0.937494	+	0.348002i	$0.113140\pi$
$678$	12.3607	+	3.88904i	0.474709	+	0.149358i
$679$		0			0
$680$	1.28689	+	1.67079i	0.0493501	+	0.0640720i
$681$	13.4986	+	23.3803i	0.517268	+	0.895935i
$682$	32.2837	+	35.1885i	1.23621	+	1.34744i
$683$	7.39676	+	4.27052i	0.283029	+	0.163407i	0.634794	−	0.772682i	$-0.281085\pi$
$683$	7.39676	+	4.27052i	0.283029	+	0.163407i	−0.351765	+	0.936088i	$0.614418\pi$
$684$	1.08545	−	12.5831i	0.0415034	−	0.481125i
$685$			0.507689i			0.0193978i
$686$		0			0
$687$		−	2.91694i		−	0.111288i
$688$	−2.70761	−	2.26075i	−0.103227	−	0.0861904i
$689$	−5.81814	−	3.35910i	−0.221653	−	0.127972i
$690$	−0.880580	+	0.807889i	−0.0335231	+	0.0307558i
$691$	1.22924	+	2.12910i	0.0467625	+	0.0809950i	0.888459	−	0.458956i	$-0.151776\pi$
$691$	1.22924	+	2.12910i	0.0467625	+	0.0809950i	−0.841697	+	0.539950i	$0.818443\pi$
$692$	−23.7123	+	33.9525i	−0.901406	+	1.29068i
$693$		0			0
$694$	9.33563	−	29.6717i	0.354375	−	1.12632i
$695$	0.0290295	−	0.0167602i	0.00110115	−	0.000635749i
$696$	7.93316	−	1.05915i	0.300706	−	0.0401470i
$697$	9.46098	−	16.3869i	0.358360	−	0.620698i
$698$	36.8193	−	8.18615i	1.39363	−	0.309850i
$699$	−20.3989			−0.771559
$700$		0			0
$701$	43.1693			1.63048			0.815241	−	0.579123i	$-0.196605\pi$
$701$	43.1693			1.63048			0.815241	+	0.579123i	$0.196605\pi$
$702$	1.23093	−	0.273677i	0.0464586	−	0.0103293i
$703$	27.4039	−	47.4649i	1.03356	−	1.79017i
$704$	22.5140	−	22.6789i	0.848527	−	0.854743i
$705$	1.10940	−	0.640513i	0.0417824	−	0.0241231i
$706$	3.29861	−	10.4841i	0.124145	−	0.394574i
$707$		0			0
$708$	−0.965485	−	0.674291i	−0.0362852	−	0.0253414i
$709$	−13.0399	−	22.5857i	−0.489723	−	0.848226i	0.510207	−	0.860052i	$-0.329569\pi$
$709$	−13.0399	−	22.5857i	−0.489723	−	0.848226i	−0.999930	+	0.0118261i	$0.996236\pi$
$710$	1.51785	−	1.39255i	0.0569638	−	0.0522615i
$711$	8.50718	+	4.91162i	0.319044	+	0.184200i
$712$	1.17675	+	0.484911i	0.0441005	+	0.0181728i
$713$			55.8375i			2.09113i
$714$		0			0
$715$		−	0.455652i		−	0.0170404i
$716$	2.92499	+	0.252318i	0.109312	+	0.00942958i
$717$	21.8718	+	12.6277i	0.816818	+	0.471590i
$718$	16.0494	+	17.4935i	0.598959	+	0.652852i
$719$	−19.0610	−	33.0146i	−0.710854	−	1.23124i	−0.964537	−	0.263948i	$-0.914975\pi$
$719$	−19.0610	−	33.0146i	−0.710854	−	1.23124i	0.253683	−	0.967287i	$-0.418358\pi$
$720$	0.480429	−	0.176187i	0.0179045	−	0.00656608i
$721$		0			0
$722$	28.1647	+	8.86146i	1.04818	+	0.329789i
$723$	7.10954	−	4.10469i	0.264406	−	0.152655i
$724$	19.9548	+	42.6578i	0.741616	+	1.58536i
$725$	−7.05105	+	12.2128i	−0.261870	+	0.453571i
$726$	−1.52128	−	6.84235i	−0.0564599	−	0.253943i
$727$	30.8059			1.14253			0.571264	−	0.820766i	$-0.306453\pi$
$727$	30.8059			1.14253			0.571264	+	0.820766i	$0.306453\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	0.609161	+	2.73986i	0.0225461	+	0.101407i
$731$	−2.56986	+	4.45112i	−0.0950496	+	0.164631i
$732$	−1.43044	−	3.05786i	−0.0528705	−	0.113022i
$733$	−35.6019	+	20.5548i	−1.31499	+	0.759207i	−0.982917	−	0.184048i	$-0.941080\pi$
$733$	−35.6019	+	20.5548i	−1.31499	+	0.759207i	−0.332068	+	0.943255i	$0.607746\pi$
$734$	−5.44517	−	1.71322i	−0.200985	−	0.0632360i
$735$		0			0
$736$	37.3248	−	1.74337i	1.37581	−	0.0642617i
$737$	−12.6874	−	21.9753i	−0.467348	−	0.809471i
$738$	−3.10385	−	3.38313i	−0.114254	−	0.124535i
$739$	−24.9833	−	14.4241i	−0.919027	−	0.530600i	−0.0357022	−	0.999362i	$-0.511367\pi$
$739$	−24.9833	−	14.4241i	−0.919027	−	0.530600i	−0.883324	+	0.468762i	$0.844700\pi$
$740$	2.21241	+	0.190849i	0.0813297	+	0.00701575i
$741$			5.63071i			0.206849i
$742$		0			0
$743$			0.365822i			0.0134207i	0.999977	+	0.00671036i	$0.00213599\pi$
$743$			0.365822i			0.0134207i	−0.999977	+	0.00671036i	$0.997864\pi$
$744$	9.10954	−	22.1064i	0.333972	−	0.810459i
$745$	0.298632	+	0.172415i	0.0109410	+	0.00631681i
$746$	−21.6535	+	19.8660i	−0.792792	+	0.727347i
$747$	−0.740105	−	1.28190i	−0.0270790	−	0.0469023i
$748$	−38.1753	−	26.6615i	−1.39583	−	0.974841i
$749$		0			0
$750$	−0.542096	+	1.72296i	−0.0197945	+	0.0629136i
$751$	−17.2878	+	9.98114i	−0.630842	+	0.364217i	−0.781078	−	0.624433i	$-0.785330\pi$
$751$	−17.2878	+	9.98114i	−0.630842	+	0.364217i	0.150236	+	0.988650i	$0.451997\pi$
$752$	−39.4625	−	6.85936i	−1.43905	−	0.250135i
$753$	−3.27590	+	5.67402i	−0.119380	+	0.206773i
$754$	−3.48315	+	0.774419i	−0.126849	+	0.0282027i
$755$	0.552224			0.0200975
$756$		0			0
$757$	−3.04476			−0.110664			−0.0553319	−	0.998468i	$-0.517622\pi$
$757$	−3.04476			−0.110664			−0.0553319	+	0.998468i	$0.517622\pi$
$758$	14.8818	−	3.30872i	0.540533	−	0.120178i
$759$	13.1927	−	22.8504i	0.478865	−	0.829418i
$760$	0.302381	+	2.26487i	0.0109685	+	0.0821556i
$761$	6.51310	−	3.76034i	0.236100	−	0.136312i	−0.377283	−	0.926098i	$-0.623142\pi$
$761$	6.51310	−	3.76034i	0.236100	−	0.136312i	0.613383	+	0.789786i	$0.289808\pi$
$762$	−5.97507	+	18.9908i	−0.216454	+	0.687963i
$763$		0			0
$764$	−4.22711	+	6.05259i	−0.152931	+	0.218975i
$765$	−0.372812	−	0.645730i	−0.0134791	−	0.0233464i
$766$	6.80463	−	6.24291i	0.245861	−	0.225566i
$767$	0.454683	+	0.262512i	0.0164177	+	0.00947874i
$768$	−15.0615	−	5.39910i	−0.543486	−	0.194823i
$769$			42.4363i			1.53029i	0.643857	+	0.765146i	$0.277333\pi$
$769$			42.4363i			1.53029i	−0.643857	+	0.765146i	$0.722667\pi$
$770$		0			0
$771$			18.7522i			0.675346i
$772$	−0.466975	+	5.41338i	−0.0168068	+	0.194832i
$773$	20.5807	+	11.8823i	0.740237	+	0.427376i	0.822155	−	0.569263i	$-0.192771\pi$
$773$	20.5807	+	11.8823i	0.740237	+	0.427376i	−0.0819185	+	0.996639i	$0.526105\pi$
$774$	0.843091	+	0.918950i	0.0303043	+	0.0330310i
$775$	21.0642	+	36.4843i	0.756650	+	1.31056i
$776$	36.3104	−	27.9673i	1.30347	−	1.00397i
$777$		0			0
$778$	42.9928	+	13.5268i	1.54137	+	0.484960i
$779$	17.7546	−	10.2506i	0.636126	−	0.367267i
$780$	−0.206645	+	0.0966663i	−0.00739908	+	0.00346121i
$781$	−22.7401	+	39.3871i	−0.813706	+	1.40938i
$782$	−11.8165	−	53.1477i	−0.422557	−	1.90056i
$783$	−2.82968			−0.101125
$784$		0			0
$785$	−0.410160			−0.0146393
$786$	−2.99862	−	13.4871i	−0.106957	−	0.481068i
$787$	−9.97597	+	17.2789i	−0.355605	+	0.615926i	−0.987221	−	0.159355i	$-0.949058\pi$
$787$	−9.97597	+	17.2789i	−0.355605	+	0.615926i	0.631616	+	0.775281i	$0.282392\pi$
$788$	−7.42466	+	3.47318i	−0.264493	+	0.123727i
$789$	1.82321	−	1.05263i	0.0649079	−	0.0374746i
$790$	−1.69528	−	0.533387i	−0.0603154	−	0.0189770i
$791$		0			0
$792$	−8.95097	+	6.89430i	−0.318059	+	0.244978i
$793$	0.752534	+	1.30343i	0.0267233	+	0.0462860i
$794$	−14.7442	−	16.0708i	−0.523252	−	0.570333i
$795$	0.834750	+	0.481943i	0.0296055	+	0.0170928i
$796$	−0.0357920	+	0.414917i	−0.00126862	+	0.0147064i
$797$		−	27.9236i		−	0.989106i	−0.869147	−	0.494553i	$-0.835332\pi$
$797$		−	27.9236i		−	0.989106i	0.869147	−	0.494553i	$-0.164668\pi$
$798$		0			0
$799$			58.3633i			2.06474i
$800$	23.7305	−	15.2196i	0.838998	−	0.538095i
$801$	−0.389696	−	0.224991i	−0.0137692	−	0.00794968i
$802$	−28.8615	+	26.4790i	−1.01913	+	0.935006i
$803$	−30.9855	−	53.6685i	−1.09346	−	1.89392i
$804$	−7.27449	+	10.4160i	−0.256551	+	0.367344i
$805$		0			0
$806$	−3.19922	+	10.1682i	−0.112688	+	0.358160i
$807$	10.2209	−	5.90104i	0.359793	−	0.207727i
$808$	−4.51633	−	33.8279i	−0.158884	−	1.19006i
$809$	10.8699	−	18.8273i	0.382166	−	0.661932i	−0.609205	−	0.793013i	$-0.708511\pi$
$809$	10.8699	−	18.8273i	0.382166	−	0.661932i	0.991372	+	0.131081i	$0.0418448\pi$
$810$	−0.176607	+	0.0392655i	−0.00620532	+	0.00137965i
$811$	−21.4122			−0.751885			−0.375942	−	0.926643i	$-0.622681\pi$
$811$	−21.4122			−0.751885			−0.375942	+	0.926643i	$0.622681\pi$
$812$		0			0
$813$	−11.3243			−0.397159
$814$	−47.8609	+	10.6411i	−1.67752	+	0.372969i
$815$	−1.48794	+	2.57718i	−0.0521201	+	0.0902747i
$816$	−3.99251	+	22.9693i	−0.139766	+	0.804086i
$817$	−4.82264	+	2.78435i	−0.168723	+	0.0974122i
$818$	−10.5464	+	33.5199i	−0.368746	+	1.17200i
$819$		0			0
$820$	0.681001	+	0.475609i	0.0237816	+	0.0166090i
$821$	13.3550	+	23.1315i	0.466092	+	0.807294i	0.999250	−	0.0387210i	$-0.0123284\pi$
$821$	13.3550	+	23.1315i	0.466092	+	0.807294i	−0.533158	+	0.846015i	$0.678995\pi$
$822$	−4.13554	+	3.79416i	−0.144244	+	0.132336i
$823$	−20.9990	−	12.1238i	−0.731979	−	0.422608i	0.0871667	−	0.996194i	$-0.472219\pi$
$823$	−20.9990	−	12.1238i	−0.731979	−	0.422608i	−0.819146	+	0.573585i	$0.805552\pi$
$824$	−3.53924	+	8.58877i	−0.123295	+	0.299204i
$825$		−	19.9074i		−	0.693085i
$826$		0			0
$827$		−	34.2930i		−	1.19248i	−0.802805	−	0.596242i	$-0.796660\pi$
$827$		−	34.2930i		−	1.19248i	0.802805	−	0.596242i	$-0.203340\pi$
$828$	−13.1618	−	1.13538i	−0.457405	−	0.0394572i
$829$	0.699010	+	0.403574i	0.0242776	+	0.0140167i	0.512090	−	0.858932i	$-0.328872\pi$
$829$	0.699010	+	0.403574i	0.0242776	+	0.0140167i	−0.487812	+	0.872949i	$0.662205\pi$
$830$	0.181042	+	0.197331i	0.00628406	+	0.00684947i
$831$	−5.88192	−	10.1878i	−0.204042	−	0.353410i
$832$	6.89687	+	1.82106i	0.239106	+	0.0631340i
$833$		0			0
$834$	0.353473	+	0.111213i	0.0122398	+	0.00385101i
$835$	−1.07119	+	0.618450i	−0.0370699	+	0.0214023i
$836$	−21.3768	−	45.6975i	−0.739333	−	1.58048i
$837$	−4.22668	+	7.32083i	−0.146096	+	0.253045i
$838$	6.72447	+	30.2450i	0.232293	+	1.04480i
$839$	−27.7282			−0.957284			−0.478642	−	0.878010i	$-0.658871\pi$
$839$	−27.7282			−0.957284			−0.478642	+	0.878010i	$0.658871\pi$
$840$		0			0
$841$	−20.9929			−0.723893
$842$	5.77725	+	25.9847i	0.199097	+	0.895491i
$843$	−4.90240	+	8.49121i	−0.168848	+	0.292453i
$844$	−14.0548	−	30.0452i	−0.483787	−	1.03420i
$845$	−1.35218	+	0.780684i	−0.0465165	+	0.0268563i
$846$	13.5085	+	4.25018i	0.464431	+	0.146124i
$847$		0			0
$848$	−10.3767	−	28.2954i	−0.356338	−	0.971670i
$849$	12.3233	+	21.3445i	0.422933	+	0.732542i
$850$	−27.7705	−	30.2692i	−0.952520	−	1.03822i
$851$	−49.6481	−	28.6643i	−1.70191	−	0.982600i
$852$	22.6869	+	1.95704i	0.777241	+	0.0670472i
$853$			16.3380i			0.559402i	0.960087	+	0.279701i	$0.0902354\pi$
$853$			16.3380i			0.559402i	−0.960087	+	0.279701i	$0.909765\pi$
$854$		0			0
$855$		−	0.807859i		−	0.0276282i
$856$	8.72248	+	3.59434i	0.298128	+	0.122852i
$857$	−25.5734	−	14.7648i	−0.873569	−	0.504355i	−0.00503640	−	0.999987i	$-0.501603\pi$
$857$	−25.5734	−	14.7648i	−0.873569	−	0.504355i	−0.868533	+	0.495632i	$0.834936\pi$
$858$	3.71166	−	3.40526i	0.126714	−	0.116254i
$859$	7.56296	+	13.0994i	0.258045	+	0.446947i	0.965718	−	0.259593i	$-0.0835884\pi$
$859$	7.56296	+	13.0994i	0.258045	+	0.446947i	−0.707673	+	0.706540i	$0.750255\pi$
$860$	−0.184978	−	0.129188i	−0.00630771	−	0.00440528i
$861$		0			0
$862$	−9.27225	+	29.4703i	−0.315814	+	1.00376i
$863$	14.0116	−	8.08962i	0.476962	−	0.275374i	−0.242188	−	0.970229i	$-0.577865\pi$
$863$	14.0116	−	8.08962i	0.476962	−	0.275374i	0.719149	+	0.694856i	$0.244532\pi$
$864$	5.02561	+	2.59677i	0.170975	+	0.0883440i
$865$	−1.32448	+	2.29407i	−0.0450338	+	0.0780008i
$866$	−32.7788	+	7.28779i	−1.11387	+	0.247649i
$867$	16.9705			0.576348
$868$		0			0
$869$	39.2394			1.33111
$870$	0.499741	−	0.111109i	0.0169428	−	0.00376694i
$871$	2.83207	−	4.90528i	0.0959609	−	0.166209i
$872$	−12.5065	+	1.66974i	−0.423525	+	0.0565444i
$873$	−14.0333	+	8.10212i	−0.474954	+	0.274215i
$874$	17.7044	−	56.2704i	0.598859	−	1.90337i
$875$		0			0
$876$	−17.7659	+	25.4381i	−0.600254	+	0.859475i
$877$	−19.8411	−	34.3658i	−0.669987	−	1.16045i	−0.977907	−	0.209039i	$-0.932967\pi$
$877$	−19.8411	−	34.3658i	−0.669987	−	1.16045i	0.307921	−	0.951412i	$-0.400367\pi$
$878$	−33.2278	+	30.4849i	−1.12138	+	1.02881i
$879$	−2.08748	−	1.20521i	−0.0704091	−	0.0406507i
$880$	1.31009	−	1.56904i	0.0441632	−	0.0528925i
$881$		−	27.4290i		−	0.924106i	−0.886852	−	0.462053i	$-0.847113\pi$
$881$		−	27.4290i		−	0.924106i	0.886852	−	0.462053i	$-0.152887\pi$
$882$		0			0
$883$			37.1425i			1.24994i	0.780647	+	0.624972i	$0.214890\pi$
$883$			37.1425i			1.24994i	−0.780647	+	0.624972i	$0.785110\pi$
$884$	0.893290	−	10.3554i	0.0300446	−	0.348291i
$885$	−0.0652351	−	0.0376635i	−0.00219285	−	0.00126605i
$886$	−14.9934	−	16.3425i	−0.503713	−	0.549036i
$887$	13.8563	+	23.9998i	0.465248	+	0.805834i	0.999213	−	0.0396732i	$-0.0126317\pi$
$887$	13.8563	+	23.9998i	0.465248	+	0.805834i	−0.533964	+	0.845507i	$0.679298\pi$
$888$	14.9795	+	19.4481i	0.502681	+	0.652637i
$889$		0			0
$890$	0.0776574	+	0.0244334i	0.00260308	+	0.000819008i
$891$	3.45938	−	1.99727i	0.115894	−	0.0669112i
$892$	38.6651	−	18.0871i	1.29460	−	0.605601i
$893$	−31.6173	+	54.7628i	−1.05803	+	1.83257i
$894$	0.827330	+	3.72113i	0.0276700	+	0.124453i
$895$	0.187790			0.00627714
$896$		0			0
$897$	5.88969			0.196651
$898$	2.98486	+	13.4252i	0.0996060	+	0.448004i
$899$	11.9602	−	20.7156i	0.398894	−	0.690905i
$900$	−9.02828	+	4.22333i	−0.300943	+	0.140778i
$901$	−38.0311	+	21.9572i	−1.26700	+	0.731502i
$902$	−17.4944	−	5.50428i	−0.582501	−	0.183273i
$903$		0			0
$904$	−15.8142	−	20.5318i	−0.525973	−	0.682877i
$905$	1.50618	+	2.60879i	0.0500673	+	0.0867190i
$906$	4.12698	+	4.49832i	0.137110	+	0.149447i
$907$	34.6185	+	19.9870i	1.14949	+	0.663658i	0.948763	−	0.315989i	$-0.102336\pi$
$907$	34.6185	+	19.9870i	1.14949	+	0.663658i	0.200727	+	0.979647i	$0.435670\pi$
$908$	4.64050	−	53.7947i	0.154000	−	1.78524i
$909$			12.0661i			0.400207i
$910$		0			0
$911$			35.0711i			1.16196i	0.813918	+	0.580979i	$0.197330\pi$
$911$			35.0711i			1.16196i	−0.813918	+	0.580979i	$0.802670\pi$
$912$	−16.1894	+	19.3894i	−0.536085	+	0.642047i
$913$	−5.12061	−	2.95639i	−0.169467	−	0.0978421i
$914$	11.8878	−	10.9064i	0.393213	−	0.360753i
$915$	−0.107969	−	0.187007i	−0.00356934	−	0.00618228i
$916$	−3.34036	+	4.78290i	−0.110369	+	0.158031i
$917$		0			0
$918$	2.47383	−	7.86264i	0.0816484	−	0.259506i
$919$	−0.286521	+	0.165423i	−0.00945146	+	0.00545681i	−0.504718	−	0.863284i	$-0.668404\pi$
$919$	−0.286521	+	0.165423i	−0.00945146	+	0.00545681i	0.495267	+	0.868741i	$0.335070\pi$
$920$	2.36905	−	0.316289i	0.0781052	−	0.0104278i
$921$	−12.2027	+	21.1357i	−0.402093	+	0.696446i
$922$	−27.1195	+	6.02955i	−0.893132	+	0.198573i
$923$	−10.1520			−0.334157
$924$		0			0
$925$	−43.2536			−1.42217
$926$	−9.29159	+	2.06583i	−0.305341	+	0.0678872i
$927$	1.64215	−	2.84429i	0.0539354	−	0.0934188i
$928$	−14.2209	−	7.34805i	−0.466823	−	0.241211i
$929$	24.6448	−	14.2287i	0.808571	−	0.466829i	−0.0378883	−	0.999282i	$-0.512063\pi$
$929$	24.6448	−	14.2287i	0.808571	−	0.466829i	0.846459	+	0.532453i	$0.178730\pi$
$930$	0.459004	−	1.45887i	0.0150513	−	0.0478382i
$931$		0			0
$932$	33.4481	+	23.3600i	1.09563	+	0.765183i
$933$	−15.5933	−	27.0084i	−0.510502	−	0.884215i
$934$	23.0526	−	21.1497i	0.754306	−	0.692038i
$935$	−2.57940	−	1.48922i	−0.0843553	−	0.0487026i
$936$	−2.33176	−	0.960867i	−0.0762161	−	0.0314069i
$937$		−	11.8966i		−	0.388645i	−0.980938	−	0.194323i	$-0.937749\pi$
$937$		−	11.8966i		−	0.388645i	0.980938	−	0.194323i	$-0.0622509\pi$
$938$		0			0
$939$			2.53807i			0.0828269i
$940$	−2.55257	−	0.220193i	−0.0832557	−	0.00718189i
$941$	−14.5463	−	8.39834i	−0.474197	−	0.273778i	0.243798	−	0.969826i	$-0.421607\pi$
$941$	−14.5463	−	8.39834i	−0.474197	−	0.273778i	−0.717995	+	0.696048i	$0.754940\pi$
$942$	−3.06529	−	3.34109i	−0.0998725	−	0.108859i
$943$	−10.7221	−	18.5713i	−0.349161	−	0.604764i
$944$	0.810934	+	2.21127i	0.0263936	+	0.0719707i
$945$		0			0
$946$	4.75197	+	1.49511i	0.154500	+	0.0486103i
$947$	17.8680	−	10.3161i	0.580631	−	0.335227i	−0.180753	−	0.983528i	$-0.557854\pi$
$947$	17.8680	−	10.3161i	0.580631	−	0.335227i	0.761384	+	0.648301i	$0.224520\pi$
$948$	−8.32462	−	17.7957i	−0.270371	−	0.577976i
$949$	6.91653	−	11.9798i	0.224520	−	0.388880i
$950$	−9.65948	−	43.4460i	−0.313395	−	1.40958i
$951$	18.2520			0.591863
$952$		0			0
$953$	21.9025			0.709492			0.354746	−	0.934963i	$-0.384567\pi$
$953$	21.9025			0.709492			0.354746	+	0.934963i	$0.384567\pi$
$954$	2.31259	+	10.4015i	0.0748728	+	0.336760i
$955$	−0.236111	+	0.408956i	−0.00764037	+	0.0132335i
$956$	−21.4025	−	45.7523i	−0.692205	−	1.47974i
$957$	−9.78895	+	5.65165i	−0.316432	+	0.182692i
$958$	−28.6867	−	9.02571i	−0.926826	−	0.291608i
$959$		0			0
$960$	−0.989520	−	0.261274i	−0.0319366	−	0.00843260i
$961$	−20.2297	−	35.0389i	−0.652571	−	1.13029i
$962$	−7.39876	−	8.06448i	−0.238546	−	0.260009i
$963$	−2.88857	−	1.66772i	−0.0930829	−	0.0537414i
$964$	−16.3580	−	1.41109i	−0.526856	−	0.0454482i
$965$			0.347550i			0.0111880i
$966$		0			0
$967$		−	0.651178i		−	0.0209405i	−0.999945	−	0.0104702i	$-0.996667\pi$
$967$		−	0.651178i		−	0.0209405i	0.999945	−	0.0104702i	$-0.00333284\pi$
$968$	−5.34114	+	12.9615i	−0.171671	+	0.416598i
$969$	31.8748	+	18.4029i	1.02397	+	0.591188i
$970$	2.16024	−	1.98191i	0.0693610	−	0.0636353i
$971$	29.7321	+	51.4974i	0.954147	+	1.65263i	0.736308	+	0.676646i	$0.236567\pi$
$971$	29.7321	+	51.4974i	0.954147	+	1.65263i	0.217839	+	0.975985i	$0.430099\pi$
$972$	−1.63970	−	1.14516i	−0.0525933	−	0.0367310i
$973$		0			0
$974$	15.0397	−	47.8012i	0.481904	−	1.53165i
$975$	3.84834	−	2.22184i	0.123246	−	0.0711558i
$976$	−1.15626	+	6.65205i	−0.0370109	+	0.212927i
$977$	11.1218	−	19.2636i	0.355819	−	0.616297i	−0.631438	−	0.775426i	$-0.717535\pi$
$977$	11.1218	−	19.2636i	0.355819	−	0.616297i	0.987258	+	0.159129i	$0.0508685\pi$
$978$	−32.1131	+	7.13981i	−1.02687	+	0.228306i
$979$	−1.79748			−0.0574476
$980$		0			0
$981$	4.46096			0.142428
$982$	−20.9733	+	4.66306i	−0.669286	+	0.148804i
$983$	−9.54779	+	16.5373i	−0.304527	+	0.527457i	−0.977156	−	0.212523i	$-0.931832\pi$
$983$	−9.54779	+	16.5373i	−0.304527	+	0.527457i	0.672629	+	0.739980i	$0.265165\pi$
$984$	1.21516	+	9.10172i	0.0387380	+	0.290152i
$985$	−0.454065	+	0.262154i	−0.0144677	+	0.00835293i
$986$	−7.00014	+	22.2488i	−0.222930	+	0.708546i
$987$		0			0
$988$	6.44806	−	9.23266i	0.205140	−	0.293730i
$989$	2.91242	+	5.04446i	0.0926096	+	0.160404i
$990$	−0.532525	+	0.488566i	−0.0169248	+	0.0155276i
$991$	−23.6878	−	13.6762i	−0.752468	−	0.434438i	0.0741168	−	0.997250i	$-0.476386\pi$
$991$	−23.6878	−	13.6762i	−0.752468	−	0.434438i	−0.826585	+	0.562812i	$0.809720\pi$
$992$	−40.2522	+	25.8159i	−1.27801	+	0.819656i
$993$		−	20.7274i		−	0.657763i
$994$		0			0
$995$			0.0266385i			0.000844499i
$996$	−0.254430	+	2.94947i	−0.00806193	+	0.0934575i
$997$	−28.3135	−	16.3468i	−0.896697	−	0.517708i	−0.0205701	−	0.999788i	$-0.506548\pi$
$997$	−28.3135	−	16.3468i	−0.896697	−	0.517708i	−0.876127	+	0.482080i	$0.839881\pi$
$998$	10.6022	+	11.5561i	0.335607	+	0.365804i
$999$	−4.33956	−	7.51634i	−0.137298	−	0.237806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.o.f.31.7		24
4.3	odd	2		588.2.o.e.31.4		24
7.2	even	3	inner	588.2.o.f.19.4		24
7.3	odd	6		588.2.b.d.391.12	yes	12
7.4	even	3		588.2.b.c.391.12	yes	12
7.5	odd	6		588.2.o.e.19.4		24
7.6	odd	2		588.2.o.e.31.7		24
21.11	odd	6		1764.2.b.l.1567.1		12
21.17	even	6		1764.2.b.m.1567.1		12
28.3	even	6		588.2.b.c.391.11	✓	12
28.11	odd	6		588.2.b.d.391.11	yes	12
28.19	even	6	inner	588.2.o.f.19.7		24
28.23	odd	6		588.2.o.e.19.7		24
28.27	even	2	inner	588.2.o.f.31.4		24
84.11	even	6		1764.2.b.m.1567.2		12
84.59	odd	6		1764.2.b.l.1567.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.b.c.391.11	✓	12	28.3	even	6
588.2.b.c.391.12	yes	12	7.4	even	3
588.2.b.d.391.11	yes	12	28.11	odd	6
588.2.b.d.391.12	yes	12	7.3	odd	6
588.2.o.e.19.4		24	7.5	odd	6
588.2.o.e.19.7		24	28.23	odd	6
588.2.o.e.31.4		24	4.3	odd	2
588.2.o.e.31.7		24	7.6	odd	2
588.2.o.f.19.4		24	7.2	even	3	inner
588.2.o.f.19.7		24	28.19	even	6	inner
588.2.o.f.31.4		24	28.27	even	2	inner
588.2.o.f.31.7		24	1.1	even	1	trivial
1764.2.b.l.1567.1		12	21.11	odd	6
1764.2.b.l.1567.2		12	84.59	odd	6
1764.2.b.m.1567.1		12	21.17	even	6
1764.2.b.m.1567.2		12	84.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.306932 - 1.38050i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.81159 + 0.847441i) q^{4} +(-0.110790 + 0.0639645i) q^{5} +(-1.34902 - 0.424442i) q^{6} +(1.72593 + 2.24080i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.122308 + 0.133313i) q^{10} +(-3.45938 - 1.99727i) q^{11} +(-0.171888 + 1.99260i) q^{12} -0.891655i q^{13} +0.127929i q^{15} +(2.56369 - 3.07042i) q^{16} +(-5.04756 - 2.91421i) q^{17} +(-1.04209 + 0.956063i) q^{18} +(-3.15745 - 5.46886i) q^{19} +(0.146499 - 0.209765i) q^{20} +(-1.69545 + 5.38872i) q^{22} +(-5.72040 + 3.30268i) q^{23} +(2.80355 - 0.374300i) q^{24} +(-2.49182 + 4.31595i) q^{25} +(-1.23093 + 0.273677i) q^{26} -1.00000 q^{27} +2.82968 q^{29} +(0.176607 - 0.0392655i) q^{30} +(4.22668 - 7.32083i) q^{31} +(-5.02561 - 2.59677i) q^{32} +(-3.45938 + 1.99727i) q^{33} +(-2.47383 + 7.86264i) q^{34} +(1.63970 + 1.14516i) q^{36} +(4.33956 + 7.51634i) q^{37} +(-6.58067 + 6.03744i) q^{38} +(-0.772196 - 0.445827i) q^{39} +(-0.334547 - 0.137859i) q^{40} +3.24650i q^{41} -0.881836i q^{43} +(7.95954 + 0.686614i) q^{44} +(0.110790 + 0.0639645i) q^{45} +(6.31513 + 6.88335i) q^{46} +(-5.00678 - 8.67200i) q^{47} +(-1.37722 - 3.75543i) q^{48} +(6.72301 + 2.11526i) q^{50} +(-5.04756 + 2.91421i) q^{51} +(0.755625 + 1.61531i) q^{52} +(3.76727 - 6.52510i) q^{53} +(0.306932 + 1.38050i) q^{54} +0.511019 q^{55} -6.31490 q^{57} +(-0.868519 - 3.90639i) q^{58} +(-0.294409 + 0.509932i) q^{59} +(-0.108412 - 0.231754i) q^{60} +(-1.46181 + 0.843974i) q^{61} +(-11.4037 - 3.58796i) q^{62} +(-2.04234 + 7.73491i) q^{64} +(0.0570343 + 0.0987862i) q^{65} +(3.81904 + 4.16266i) q^{66} +(5.50132 + 3.17619i) q^{67} +(11.6137 + 1.00183i) q^{68} +6.60535i q^{69} -11.3856i q^{71} +(1.07762 - 2.61510i) q^{72} +(13.4354 + 7.75696i) q^{73} +(9.04439 - 8.29778i) q^{74} +(2.49182 + 4.31595i) q^{75} +(10.3545 + 7.23156i) q^{76} +(-0.378456 + 1.20286i) q^{78} +(-8.50718 + 4.91162i) q^{79} +(-0.0876323 + 0.504157i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.48180 - 0.996452i) q^{82} +1.48021 q^{83} +0.745624 q^{85} +(-1.21738 + 0.270663i) q^{86} +(1.41484 - 2.45058i) q^{87} +(-1.49516 - 11.1989i) q^{88} +(0.389696 - 0.224991i) q^{89} +(0.0542984 - 0.172579i) q^{90} +(7.56418 - 10.8308i) q^{92} +(-4.22668 - 7.32083i) q^{93} +(-10.4350 + 9.57360i) q^{94} +(0.699626 + 0.403929i) q^{95} +(-4.76168 + 3.05392i) q^{96} -16.2042i q^{97} +3.99455i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 12 q^{3} + 4 q^{4} - 8 q^{6} + 8 q^{8} - 12 q^{9} - 4 q^{12} + 4 q^{16} - 4 q^{18} + 48 q^{20} + 4 q^{24} + 12 q^{25} + 24 q^{26} - 24 q^{27} + 64 q^{29} + 16 q^{31} - 4 q^{32} - 64 q^{34}+ \cdots + 4 q^{96}+O(q^{100}) \) 24 * q - 4 * q^2 + 12 * q^3 + 4 * q^4 - 8 * q^6 + 8 * q^8 - 12 * q^9 - 4 * q^12 + 4 * q^16 - 4 * q^18 + 48 * q^20 + 4 * q^24 + 12 * q^25 + 24 * q^26 - 24 * q^27 + 64 * q^29 + 16 * q^31 - 4 * q^32 - 64 * q^34 - 8 * q^36 - 32 * q^37 - 24 * q^38 - 32 * q^40 + 24 * q^44 - 24 * q^46 + 8 * q^48 - 56 * q^50 + 32 * q^52 + 32 * q^53 + 4 * q^54 - 32 * q^55 - 16 * q^58 - 16 * q^59 + 24 * q^60 - 16 * q^62 - 8 * q^64 - 8 * q^68 - 4 * q^72 + 32 * q^74 - 12 * q^75 + 64 * q^76 + 48 * q^78 - 16 * q^80 - 12 * q^81 + 32 * q^82 + 32 * q^83 + 32 * q^85 + 24 * q^86 + 32 * q^87 - 24 * q^88 - 16 * q^93 + 4 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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