LMFDB - Embedded newform 588.2.o.e.19.7

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			19.7
Character	$\chi$	$=$	588.19
Dual form			588.2.o.e.31.7

$q$-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 $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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	$-0.324227\pi$
$5$	0.110790	+	0.0639645i	0.0495467	+	0.0286058i	−0.475022	+	0.879974i	$0.657560\pi$
$6$	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	−0.920693	−	0.390286i	$-0.872376\pi$
$11$	−3.45938	+	1.99727i	−1.04304	+	0.602201i	−0.122349	+	0.992487i	$0.539043\pi$
$12$	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	$-0.416805\pi$
$17$	5.04756	−	2.91421i	1.22421	−	0.706800i	0.965813	+	0.259238i	$0.0834714\pi$
$18$	−1.04209	−	0.956063i	−0.245622	−	0.225346i
$19$	3.15745	−	5.46886i	0.724368	−	1.25464i	−0.234865	−	0.972028i	$-0.575465\pi$
$19$	3.15745	−	5.46886i	0.724368	−	1.25464i	0.959234	−	0.282615i	$-0.0912018\pi$
$20$	−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	−0.233849	−	0.972273i	$-0.575132\pi$
$23$	−5.72040	−	3.30268i	−1.19279	−	0.688656i	−0.958938	+	0.283617i	$0.908465\pi$
$24$	−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	−0.943292	−	0.331963i	$-0.892289\pi$
$31$	−4.22668	−	7.32083i	−0.759135	−	1.31486i	0.184158	−	0.982897i	$-0.441044\pi$
$32$	−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	−0.250147	−	0.968208i	$-0.580479\pi$
$37$	4.33956	−	7.51634i	0.713419	−	1.23568i	0.963566	−	0.267471i	$-0.0861878\pi$
$38$	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	$0.0214191\pi$
$43$			0.881836i			0.134479i	−0.997737	+	0.0672394i	$0.978581\pi$
$44$	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	−0.226435	−	0.974026i	$-0.572707\pi$
$47$	5.00678	−	8.67200i	0.730314	−	1.26494i	0.956749	−	0.290915i	$-0.0939597\pi$
$48$	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	0.999794	+	0.0202966i	$0.00646106\pi$
$53$	3.76727	+	6.52510i	0.517474	+	0.896292i	−0.482320	+	0.875995i	$0.660206\pi$
$54$	−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	$-0.154463\pi$
$59$	0.294409	+	0.509932i	0.0383288	+	0.0663875i	−0.846225	+	0.532826i	$0.821130\pi$
$60$	−0.108412	+	0.231754i	−0.0139960	+	0.0299194i
$61$	1.46181	+	0.843974i	0.187165	+	0.108060i	0.590655	−	0.806924i	$-0.298870\pi$
$61$	1.46181	+	0.843974i	0.187165	+	0.108060i	−0.403490	+	0.914984i	$0.632203\pi$
$62$	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	−0.124776	−	0.992185i	$-0.539821\pi$
$67$	5.50132	−	3.17619i	0.672094	−	0.388033i	0.796869	+	0.604151i	$0.206488\pi$
$68$	−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	$0.236120\pi$
$71$			11.3856i			1.35122i	−0.737259	+	0.675610i	$0.763880\pi$
$72$	1.07762	+	2.61510i	0.126999	+	0.308192i
$73$	−13.4354	+	7.75696i	−1.57250	+	0.907883i	−0.576639	+	0.816999i	$0.695636\pi$
$73$	−13.4354	+	7.75696i	−1.57250	+	0.907883i	−0.995861	+	0.0908839i	$0.971031\pi$
$74$	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	−0.0618431	−	0.998086i	$-0.519698\pi$
$79$	−8.50718	−	4.91162i	−0.957132	−	0.552601i	−0.895289	+	0.445485i	$0.853031\pi$
$80$	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	$-0.525887\pi$
$83$	−1.48021			−0.162474			−0.0812371	+	0.996695i	$0.525887\pi$
$84$		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	$-0.340925\pi$
$89$	−0.389696	−	0.224991i	−0.0413077	−	0.0238490i	−0.520512	+	0.853855i	$0.674259\pi$
$90$	−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	$-0.461711\pi$
$101$	10.4495	−	6.03304i	1.03977	−	0.600310i	0.919767	+	0.392464i	$0.128377\pi$
$102$	5.57234	−	6.07372i	0.551744	−	0.601388i
$103$	−1.64215	+	2.84429i	−0.161806	+	0.280256i	−0.935516	−	0.353283i	$-0.885065\pi$
$103$	−1.64215	+	2.84429i	−0.161806	+	0.280256i	0.773710	+	0.633539i	$0.218399\pi$
$104$	−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	0.633083	−	0.774084i	$-0.281789\pi$
$107$	2.88857	+	1.66772i	0.279249	+	0.161224i	−0.353835	+	0.935308i	$0.615122\pi$
$108$	−1.81159	−	0.847441i	−0.174320	−	0.0815450i
$109$	−2.23048	−	3.86331i	−0.213641	−	0.370038i	0.739210	−	0.673475i	$-0.235199\pi$
$109$	−2.23048	−	3.86331i	−0.213641	−	0.370038i	−0.952851	+	0.303437i	$0.901866\pi$
$110$	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	$0.214733\pi$
$127$			14.0775i			1.24917i	−0.780955	+	0.624587i	$0.785267\pi$
$128$	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	$-0.973689\pi$
$131$	−4.88483	+	8.46078i	−0.426790	+	0.739222i	0.569796	+	0.821786i	$0.307022\pi$
$132$	−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	0.938254	−	0.345948i	$-0.112443\pi$
$137$	1.98426	+	3.43684i	0.169527	+	0.293629i	−0.768727	+	0.639577i	$0.779109\pi$
$138$	−9.11872	−	2.02739i	−0.776237	−	0.172583i
$139$	0.262023			0.0222245			0.0111122	−	0.999938i	$-0.496463\pi$
$139$	0.262023			0.0222245			0.0111122	+	0.999938i	$0.496463\pi$
$140$		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	−0.915936	−	0.401324i	$-0.868550\pi$
$149$	−1.34774	+	2.33436i	−0.110411	+	0.191238i	0.805525	+	0.592562i	$0.201884\pi$
$150$	−5.19338	−	4.76467i	−0.424037	−	0.389033i
$151$	−3.73832	+	2.15832i	−0.304220	+	0.175642i	−0.644337	−	0.764741i	$-0.722867\pi$
$151$	−3.73832	+	2.15832i	−0.304220	+	0.175642i	0.340117	+	0.940383i	$0.389533\pi$
$152$	−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	$-0.707503\pi$
$157$	−2.77661	+	1.60308i	−0.221598	+	0.127940i	0.385092	+	0.922878i	$0.374170\pi$
$158$	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	0.995151	+	0.0983597i	$0.0313596\pi$
$163$	20.1454	+	11.6309i	1.57791	+	0.911006i	0.582757	+	0.812646i	$0.301974\pi$
$164$	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	$-0.622045\pi$
$167$	−9.66864			−0.748182			−0.374091	+	0.927392i	$0.622045\pi$
$168$		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	$-0.621775\pi$
$173$	−17.9324	−	10.3533i	−1.36337	−	0.787145i	−0.990071	+	0.140565i	$0.955108\pi$
$174$	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	−0.546756	−	0.837292i	$-0.684138\pi$
$179$	−1.27126	+	0.733963i	−0.0950185	+	0.0548589i	0.451738	+	0.892151i	$0.350804\pi$
$180$	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	0.611175	−	0.791495i	$-0.290697\pi$
$191$	3.19674	+	1.84564i	0.231308	+	0.133546i	−0.379867	+	0.925041i	$0.624030\pi$
$192$	−5.67746	+	5.63617i	−0.409735	+	0.406756i
$193$	1.35837	+	2.35277i	0.0977777	+	0.169356i	0.910764	−	0.412926i	$-0.135493\pi$
$193$	1.35837	+	2.35277i	0.0977777	+	0.169356i	−0.812987	+	0.582282i	$0.802160\pi$
$194$	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	$-0.169016\pi$
$199$	−0.104115	−	0.180332i	−0.00738048	−	0.0127834i	−0.869692	+	0.493595i	$0.835683\pi$
$200$	−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	$-0.806602\pi$
$211$		−	16.5850i		−	1.14176i	0.821034	−	0.570880i	$-0.193398\pi$
$212$	−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	$-0.246598\pi$
$223$	21.3432			1.42925			0.714624	+	0.699509i	$0.246598\pi$
$224$		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	0.832643	+	0.553810i	$0.186827\pi$
$227$	13.4986	+	23.3803i	0.895935	+	1.55180i	0.0632918	+	0.997995i	$0.479840\pi$
$228$	11.4400	+	5.35150i	0.757631	+	0.354412i
$229$	−2.52614	−	1.45847i	−0.166932	−	0.0963783i	0.414206	−	0.910183i	$-0.364059\pi$
$229$	−2.52614	−	1.45847i	−0.166932	−	0.0963783i	−0.581138	+	0.813805i	$0.697393\pi$
$230$	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	0.310221	+	0.950665i	$0.399597\pi$
$233$	−10.1995	+	17.6660i	−0.668189	+	1.15734i	−0.978410	+	0.206673i	$0.933736\pi$
$234$	−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	$-0.695736\pi$
$239$		−	25.2554i		−	1.63364i	0.576895	−	0.816818i	$-0.304264\pi$
$240$	0.392796	−	0.327970i	0.0253549	−	0.0211704i
$241$	−7.10954	+	4.10469i	−0.457965	+	0.264406i	−0.711188	−	0.703001i	$-0.751843\pi$
$241$	−7.10954	+	4.10469i	−0.457965	+	0.264406i	0.253223	+	0.967408i	$0.418509\pi$
$242$	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	$-0.433704\pi$
$251$	6.55180			0.413546			0.206773	+	0.978389i	$0.433704\pi$
$252$		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	$-0.134480\pi$
$257$	16.2399	+	9.37612i	1.01302	+	0.584866i	0.100944	+	0.994892i	$0.467814\pi$
$258$	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	−0.442734	−	0.896653i	$-0.645991\pi$
$263$	1.82321	−	1.05263i	0.112424	−	0.0649079i	0.555158	+	0.831745i	$0.312658\pi$
$264$	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	$-0.783819\pi$
$269$	−10.2209	+	5.90104i	−0.623180	+	0.359793i	0.154926	+	0.987926i	$0.450486\pi$
$270$	−0.122308	+	0.133313i	−0.00744344	+	0.00811318i
$271$	5.66213	−	9.80709i	0.343950	−	0.595738i	−0.641213	−	0.767363i	$-0.721568\pi$
$271$	5.66213	−	9.80709i	0.343950	−	0.595738i	0.985162	+	0.171625i	$0.0549017\pi$
$272$	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	0.986845	−	0.161672i	$-0.0516886\pi$
$277$	5.88192	+	10.1878i	0.353410	+	0.612125i	−0.633434	+	0.773797i	$0.718355\pi$
$278$	−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	0.955794	+	0.294039i	$0.0949994\pi$
$283$	12.3233	+	21.3445i	0.732542	+	1.26880i	−0.223252	+	0.974761i	$0.571667\pi$
$284$	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	$-0.254764\pi$
$307$	24.4054			1.39289			0.696446	+	0.717609i	$0.254764\pi$
$308$		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	−0.846610	−	0.532213i	$-0.821360\pi$
$311$	−15.5933	−	27.0084i	−0.884215	−	1.53151i	−0.0376050	−	0.999293i	$-0.511973\pi$
$312$	−0.333746	+	2.49980i	−0.0188947	+	0.141523i
$313$	2.19804	+	1.26904i	0.124240	+	0.0717302i	0.560832	−	0.827929i	$-0.310481\pi$
$313$	2.19804	+	1.26904i	0.124240	+	0.0717302i	−0.436592	+	0.899660i	$0.643815\pi$
$314$	−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	−0.487325	−	0.873221i	$-0.662027\pi$
$317$	9.12602	−	15.8067i	0.512568	−	0.887795i	0.999894	−	0.0145742i	$-0.00463927\pi$
$318$	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	0.904270	−	0.426962i	$-0.140416\pi$
$331$	17.9504	+	10.3637i	0.986644	+	0.569639i	0.0823747	+	0.996601i	$0.473750\pi$
$332$	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	0.107719	−	0.994181i	$-0.465645\pi$
$347$	19.0483	−	10.9975i	1.02257	−	0.590378i	0.914846	+	0.403803i	$0.132312\pi$
$348$	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	$-0.732979\pi$
$353$	−6.73045	+	3.88583i	−0.358226	+	0.206822i	0.310076	+	0.950712i	$0.399645\pi$
$354$	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	0.0646204	−	0.997910i	$-0.479416\pi$
$359$	−14.5380	−	8.39350i	−0.767285	−	0.442992i	−0.831905	+	0.554918i	$0.812750\pi$
$360$	−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	$-0.200263\pi$
$367$	−2.01820	−	3.49562i	−0.105349	−	0.182470i	−0.913881	+	0.405983i	$0.866929\pi$
$368$	−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	0.461066	+	0.887366i	$0.347467\pi$
$373$	−10.3895	+	17.9951i	−0.537948	+	0.931753i	−0.999014	+	0.0443876i	$0.985866\pi$
$374$	−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	$-0.910704\pi$
$379$		−	10.7800i		−	0.553732i	0.960909	−	0.276866i	$-0.0892958\pi$
$380$	−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	$-0.886686\pi$
$383$	−3.26491	+	5.65498i	−0.166829	+	0.288956i	0.770474	+	0.637471i	$0.220019\pi$
$384$	−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	−0.914296	−	0.405046i	$-0.867255\pi$
$389$	−15.9348	−	27.5999i	−0.807928	−	1.39937i	0.106368	−	0.994327i	$-0.466078\pi$
$390$	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	$-0.459822\pi$
$397$	−13.3557	−	7.71089i	−0.670301	−	0.386999i	−0.796191	+	0.605046i	$0.793155\pi$
$398$	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	0.279803	+	0.960057i	$0.409731\pi$
$401$	−13.8479	+	23.9853i	−0.691533	+	1.19777i	−0.971336	+	0.237712i	$0.923602\pi$
$402$	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	$-0.456098\pi$
$409$	21.5187	−	12.4238i	1.06403	−	0.614319i	0.926545	+	0.376185i	$0.122764\pi$
$410$	−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	$-0.320253\pi$
$419$	21.9087			1.07031			0.535155	+	0.844754i	$0.320253\pi$
$420$		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	−0.880848	−	0.473400i	$-0.843027\pi$
$431$	−18.9190	+	10.9229i	−0.911295	+	0.526137i	−0.0304476	+	0.999536i	$0.509693\pi$
$432$	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	−0.181466	−	0.983397i	$-0.558084\pi$
$439$	15.9429	−	27.6140i	0.760914	−	1.31794i	0.942380	−	0.334545i	$-0.108583\pi$
$440$	−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	0.786642	−	0.617409i	$-0.211818\pi$
$443$	13.5814	+	7.84122i	0.645272	+	0.372548i	−0.141371	+	0.989957i	$0.545151\pi$
$444$	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	−0.701223	−	0.712942i	$-0.747362\pi$
$457$	5.70383	−	9.87933i	0.266814	−	0.462135i	0.968037	+	0.250806i	$0.0806957\pi$
$458$	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	$0.0499883\pi$
$463$			6.73057i			0.312796i	−0.987694	+	0.156398i	$0.950012\pi$
$464$	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	0.488072	+	0.872803i	$0.337700\pi$
$467$	−11.0608	+	19.1579i	−0.511833	+	0.886522i	−0.999906	+	0.0137185i	$0.995633\pi$
$468$	−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	$-0.328142\pi$
$479$	−10.6325	−	18.4159i	−0.485809	−	0.841446i	−0.999867	+	0.0163095i	$0.994808\pi$
$480$	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	0.397177	−	0.917742i	$-0.369990\pi$
$487$	30.6868	−	17.7171i	1.39055	−	0.802836i	0.993376	+	0.114906i	$0.0366566\pi$
$488$	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	$0.111380\pi$
$491$			15.1925i			0.685628i	−0.939403	+	0.342814i	$0.888620\pi$
$492$	−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	0.269391	−	0.963031i	$-0.413178\pi$
$499$	−9.60373	−	5.54472i	−0.429922	−	0.248216i	−0.699313	+	0.714815i	$0.746511\pi$
$500$	−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	$-0.540373\pi$
$503$	−5.67396			−0.252989			−0.126495	+	0.991967i	$0.540373\pi$
$504$		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	$-0.241790\pi$
$509$	11.0839	+	6.39931i	0.491286	+	0.283644i	−0.233822	+	0.972279i	$0.575123\pi$
$510$	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	$-0.454157\pi$
$521$	24.4767	−	14.1316i	1.07234	−	0.619117i	0.928820	+	0.370531i	$0.120824\pi$
$522$	−2.94877	−	2.70535i	−0.129064	−	0.118410i
$523$	−5.38111	+	9.32036i	−0.235300	+	0.407551i	−0.959360	−	0.282186i	$-0.908941\pi$
$523$	−5.38111	+	9.32036i	−0.235300	+	0.407551i	0.724060	+	0.689737i	$0.242274\pi$
$524$	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	−0.803086	−	0.595863i	$-0.796810\pi$
$541$	2.66295	−	4.61237i	0.114489	−	0.198301i	0.917575	+	0.397562i	$0.130144\pi$
$542$	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	$0.129430\pi$
$547$			18.5001i			0.791007i	−0.918465	+	0.395503i	$0.870570\pi$
$548$	−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	0.986680	+	0.162673i	$0.0520116\pi$
$557$	14.9681	+	25.9255i	0.634219	+	1.09850i	−0.352461	+	0.935827i	$0.614655\pi$
$558$	−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	$-0.250659\pi$
$563$	−6.18858	−	10.7189i	−0.260818	−	0.451749i	−0.966459	+	0.256819i	$0.917325\pi$
$564$	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	−0.167931	−	0.985799i	$-0.553709\pi$
$569$	18.3617	−	31.8033i	0.769761	−	1.33327i	0.937692	−	0.347467i	$-0.112958\pi$
$570$	0.772364	−	0.841858i	0.0323507	−	0.0352616i
$571$	−5.47430	+	3.16059i	−0.229092	+	0.132267i	−0.610153	−	0.792283i	$-0.708892\pi$
$571$	−5.47430	+	3.16059i	−0.229092	+	0.132267i	0.381061	+	0.924550i	$0.375559\pi$
$572$	−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	$-0.632907\pi$
$577$	4.40430	−	2.54283i	0.183354	−	0.105859i	0.588867	+	0.808230i	$0.299574\pi$
$578$	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	$-0.713111\pi$
$587$	−30.0719			−1.24120			−0.620601	+	0.784127i	$0.713111\pi$
$588$		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	$-0.187402\pi$
$593$	18.6666	+	10.7772i	0.766545	+	0.442565i	−0.0650955	+	0.997879i	$0.520735\pi$
$594$	−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	−0.138787	−	0.990322i	$-0.544320\pi$
$599$	15.8953	−	9.17715i	0.649464	−	0.374968i	0.788251	+	0.615354i	$0.210987\pi$
$600$	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	−0.459619	−	0.888116i	$-0.652014\pi$
$607$	13.2875	−	23.0146i	0.539322	−	0.934133i	0.998941	−	0.0460167i	$-0.0146527\pi$
$608$	−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	0.992032	−	0.125983i	$-0.0402084\pi$
$613$	9.57949	+	16.5922i	0.386912	+	0.670151i	−0.605120	+	0.796134i	$0.706875\pi$
$614$	−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	0.999940	+	0.0109337i	$0.00348038\pi$
$619$	12.6747	+	21.9532i	0.509439	+	0.882374i	−0.490501	+	0.871440i	$0.663186\pi$
$620$	−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	$0.260783\pi$
$631$			36.7075i			1.46130i	−0.682752	+	0.730650i	$0.739217\pi$
$632$	−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	0.929015	−	0.370042i	$-0.120657\pi$
$641$	3.64685	+	6.31654i	0.144042	+	0.249488i	−0.784973	+	0.619530i	$0.787323\pi$
$642$	4.60458	+	1.02375i	0.181728	+	0.0404042i
$643$	20.6956			0.816155			0.408077	−	0.912947i	$-0.366199\pi$
$643$	20.6956			0.816155			0.408077	+	0.912947i	$0.366199\pi$
$644$		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	$-0.0657825\pi$
$647$	7.92738	+	13.7306i	0.311658	+	0.539807i	−0.667064	+	0.745001i	$0.732449\pi$
$648$	−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	−0.433326	−	0.901237i	$-0.642660\pi$
$653$	14.4081	−	24.9555i	0.563831	−	0.976584i	0.997157	−	0.0753469i	$-0.0240064\pi$
$654$	−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	$-0.868369\pi$
$659$		−	20.6316i		−	0.803693i	0.915707	−	0.401846i	$-0.131631\pi$
$660$	−0.0878379	−	1.01826i	−0.00341908	−	0.0396355i
$661$	20.7427	−	11.9758i	0.806799	−	0.465806i	−0.0390440	−	0.999237i	$-0.512431\pi$
$661$	20.7427	−	11.9758i	0.806799	−	0.465806i	0.845843	+	0.533432i	$0.179098\pi$
$662$	−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	$-0.553527\pi$
$677$	−28.7477	−	16.5975i	−1.10486	−	0.637893i	−0.937494	+	0.348002i	$0.886860\pi$
$678$	−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	−0.351765	−	0.936088i	$-0.614418\pi$
$683$	7.39676	−	4.27052i	0.283029	−	0.163407i	0.634794	+	0.772682i	$0.281085\pi$
$684$	−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	$-0.848224\pi$
$691$	−1.22924	+	2.12910i	−0.0467625	+	0.0809950i	0.841697	+	0.539950i	$0.181557\pi$
$692$	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	−0.999930	−	0.0118261i	$-0.996236\pi$
$709$	−13.0399	+	22.5857i	−0.489723	+	0.848226i	0.510207	+	0.860052i	$0.329569\pi$
$710$	−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	−0.253683	−	0.967287i	$-0.581642\pi$
$719$	19.0610	−	33.0146i	0.710854	−	1.23124i	0.964537	−	0.263948i	$-0.0850246\pi$
$720$	−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	$-0.693547\pi$
$727$	−30.8059			−1.14253			−0.571264	+	0.820766i	$0.693547\pi$
$728$		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	$-0.0589203\pi$
$733$	35.6019	+	20.5548i	1.31499	+	0.759207i	0.332068	+	0.943255i	$0.392254\pi$
$734$	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	−0.883324	−	0.468762i	$-0.844700\pi$
$739$	−24.9833	+	14.4241i	−0.919027	+	0.530600i	−0.0357022	+	0.999362i	$0.511367\pi$
$740$	−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	$-0.997864\pi$
$743$		−	0.365822i		−	0.0134207i	0.999977	−	0.00671036i	$-0.00213599\pi$
$744$	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	0.150236	−	0.988650i	$-0.451997\pi$
$751$	−17.2878	−	9.98114i	−0.630842	−	0.364217i	−0.781078	+	0.624433i	$0.785330\pi$
$752$	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	$-0.376858\pi$
$761$	−6.51310	−	3.76034i	−0.236100	−	0.136312i	−0.613383	+	0.789786i	$0.710192\pi$
$762$	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	$-0.807229\pi$
$773$	−20.5807	+	11.8823i	−0.740237	+	0.427376i	0.0819185	+	0.996639i	$0.473895\pi$
$774$	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	$-0.0509416\pi$
$787$	9.97597	+	17.2789i	0.355605	+	0.615926i	−0.631616	+	0.775281i	$0.717608\pi$
$788$	−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	0.991372	−	0.131081i	$-0.0418448\pi$
$809$	10.8699	+	18.8273i	0.382166	+	0.661932i	−0.609205	+	0.793013i	$0.708511\pi$
$810$	0.176607	+	0.0392655i	0.00620532	+	0.00137965i
$811$	21.4122			0.751885			0.375942	−	0.926643i	$-0.377319\pi$
$811$	21.4122			0.751885			0.375942	+	0.926643i	$0.377319\pi$
$812$		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	−0.533158	−	0.846015i	$-0.678995\pi$
$821$	13.3550	−	23.1315i	0.466092	−	0.807294i	0.999250	+	0.0387210i	$0.0123284\pi$
$822$	4.13554	+	3.79416i	0.144244	+	0.132336i
$823$	−20.9990	+	12.1238i	−0.731979	+	0.422608i	−0.819146	−	0.573585i	$-0.805552\pi$
$823$	−20.9990	+	12.1238i	−0.731979	+	0.422608i	0.0871667	+	0.996194i	$0.472219\pi$
$824$	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	$0.203340\pi$
$827$			34.2930i			1.19248i	−0.802805	+	0.596242i	$0.796660\pi$
$828$	−13.1618	+	1.13538i	−0.457405	+	0.0394572i
$829$	−0.699010	+	0.403574i	−0.0242776	+	0.0140167i	−0.512090	−	0.858932i	$-0.671128\pi$
$829$	−0.699010	+	0.403574i	−0.0242776	+	0.0140167i	0.487812	+	0.872949i	$0.337795\pi$
$830$	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	$-0.341129\pi$
$839$	27.7282			0.957284			0.478642	+	0.878010i	$0.341129\pi$
$840$		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	$-0.498397\pi$
$857$	25.5734	−	14.7648i	0.873569	−	0.504355i	0.868533	+	0.495632i	$0.165064\pi$
$858$	3.71166	+	3.40526i	0.126714	+	0.116254i
$859$	−7.56296	+	13.0994i	−0.258045	+	0.446947i	−0.965718	−	0.259593i	$-0.916412\pi$
$859$	−7.56296	+	13.0994i	−0.258045	+	0.446947i	0.707673	+	0.706540i	$0.249745\pi$
$860$	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	0.719149	−	0.694856i	$-0.244532\pi$
$863$	14.0116	+	8.08962i	0.476962	+	0.275374i	−0.242188	+	0.970229i	$0.577865\pi$
$864$	−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	0.307921	+	0.951412i	$0.400367\pi$
$877$	−19.8411	+	34.3658i	−0.669987	+	1.16045i	−0.977907	+	0.209039i	$0.932967\pi$
$878$	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	$-0.785110\pi$
$883$		−	37.1425i		−	1.24994i	0.780647	−	0.624972i	$-0.214890\pi$
$884$	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	$-0.987368\pi$
$887$	−13.8563	+	23.9998i	−0.465248	+	0.805834i	0.533964	+	0.845507i	$0.320702\pi$
$888$	−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	0.200727	−	0.979647i	$-0.435670\pi$
$907$	34.6185	−	19.9870i	1.14949	−	0.663658i	0.948763	+	0.315989i	$0.102336\pi$
$908$	−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	$-0.802670\pi$
$911$		−	35.0711i		−	1.16196i	0.813918	−	0.580979i	$-0.197330\pi$
$912$	−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	0.495267	−	0.868741i	$-0.335070\pi$
$919$	−0.286521	−	0.165423i	−0.00945146	−	0.00545681i	−0.504718	+	0.863284i	$0.668404\pi$
$920$	−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	$-0.487937\pi$
$929$	−24.6448	−	14.2287i	−0.808571	−	0.466829i	−0.846459	+	0.532453i	$0.821270\pi$
$930$	−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	$-0.578393\pi$
$941$	14.5463	−	8.39834i	0.474197	−	0.273778i	0.717995	+	0.696048i	$0.245060\pi$
$942$	−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	0.761384	−	0.648301i	$-0.224520\pi$
$947$	17.8680	+	10.3161i	0.580631	+	0.335227i	−0.180753	+	0.983528i	$0.557854\pi$
$948$	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	$0.00333284\pi$
$967$			0.651178i			0.0209405i	−0.999945	+	0.0104702i	$0.996667\pi$
$968$	−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	−0.217839	+	0.975985i	$0.569901\pi$
$971$	−29.7321	+	51.4974i	−0.954147	+	1.65263i	−0.736308	+	0.676646i	$0.763433\pi$
$972$	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	0.987258	−	0.159129i	$-0.0508685\pi$
$977$	11.1218	+	19.2636i	0.355819	+	0.616297i	−0.631438	+	0.775426i	$0.717535\pi$
$978$	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	$-0.0681682\pi$
$983$	9.54779	+	16.5373i	0.304527	+	0.527457i	−0.672629	+	0.739980i	$0.734835\pi$
$984$	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	−0.826585	−	0.562812i	$-0.809720\pi$
$991$	−23.6878	+	13.6762i	−0.752468	+	0.434438i	0.0741168	+	0.997250i	$0.476386\pi$
$992$	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	$-0.493452\pi$
$997$	28.3135	−	16.3468i	0.896697	−	0.517708i	0.876127	+	0.482080i	$0.160119\pi$
$998$	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.e.19.7		24
4.3	odd	2		588.2.o.f.19.4		24
7.2	even	3		588.2.b.d.391.11	yes	12
7.3	odd	6		588.2.o.f.31.4		24
7.4	even	3	inner	588.2.o.e.31.4		24
7.5	odd	6		588.2.b.c.391.11	✓	12
7.6	odd	2		588.2.o.f.19.7		24
21.2	odd	6		1764.2.b.m.1567.2		12
21.5	even	6		1764.2.b.l.1567.2		12
28.3	even	6	inner	588.2.o.e.31.7		24
28.11	odd	6		588.2.o.f.31.7		24
28.19	even	6		588.2.b.d.391.12	yes	12
28.23	odd	6		588.2.b.c.391.12	yes	12
28.27	even	2	inner	588.2.o.e.19.4		24
84.23	even	6		1764.2.b.l.1567.1		12
84.47	odd	6		1764.2.b.m.1567.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.b.c.391.11	✓	12	7.5	odd	6
588.2.b.c.391.12	yes	12	28.23	odd	6
588.2.b.d.391.11	yes	12	7.2	even	3
588.2.b.d.391.12	yes	12	28.19	even	6
588.2.o.e.19.4		24	28.27	even	2	inner
588.2.o.e.19.7		24	1.1	even	1	trivial
588.2.o.e.31.4		24	7.4	even	3	inner
588.2.o.e.31.7		24	28.3	even	6	inner
588.2.o.f.19.4		24	4.3	odd	2
588.2.o.f.19.7		24	7.6	odd	2
588.2.o.f.31.4		24	7.3	odd	6
588.2.o.f.31.7		24	28.11	odd	6
1764.2.b.l.1567.1		12	84.23	even	6
1764.2.b.l.1567.2		12	21.5	even	6
1764.2.b.m.1567.1		12	84.47	odd	6
1764.2.b.m.1567.2		12	21.2	odd	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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