LMFDB - Embedded newform 588.2.o.f.19.4

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			19.4
Character	$\chi$	$=$	588.19
Dual form			588.2.o.f.31.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.04209 + 0.956063i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.171888 - 1.99260i) 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} +(-0.176607 + 0.0392655i) q^{10} +(3.45938 - 1.99727i) q^{11} +(1.81159 - 0.847441i) q^{12} -0.891655i q^{13} +0.127929i q^{15} +(-3.94091 - 0.685007i) q^{16} +(5.04756 - 2.91421i) q^{17} +(-0.306932 - 1.38050i) 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} +(-1.07762 + 2.61510i) q^{24} +(-2.49182 - 4.31595i) q^{25} +(0.852478 + 0.929181i) q^{26} -1.00000 q^{27} +2.82968 q^{29} +(-0.122308 - 0.133313i) q^{30} +(4.22668 + 7.32083i) q^{31} +(4.76168 - 3.05392i) 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} +(-1.93824 - 8.71774i) q^{38} +(0.772196 - 0.445827i) q^{39} +(0.0478838 + 0.358656i) q^{40} +3.24650i q^{41} -0.881836i q^{43} +(-3.38514 - 7.23647i) q^{44} +(-0.110790 + 0.0639645i) q^{45} +(-9.11872 + 2.02739i) 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} +(-1.77671 - 0.153265i) q^{52} +(3.76727 + 6.52510i) q^{53} +(1.04209 - 0.956063i) q^{54} +0.511019 q^{55} -6.31490 q^{57} +(-2.94877 + 2.70535i) q^{58} +(-0.294409 - 0.509932i) q^{59} +(0.254911 + 0.0219894i) 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} +(-5.51449 + 1.22605i) q^{66} +(-5.50132 + 3.17619i) q^{67} +(-4.93924 - 10.5587i) q^{68} +6.60535i q^{69} -11.3856i q^{71} +(-2.80355 + 0.374300i) q^{72} +(-13.4354 + 7.75696i) q^{73} +(2.66390 + 11.9816i) 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} +(-0.392796 - 0.327970i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.10385 - 3.38313i) q^{82} +1.48021 q^{83} +0.745624 q^{85} +(0.843091 + 0.918950i) q^{86} +(1.41484 + 2.45058i) q^{87} +(10.4461 + 4.30461i) 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} +(-3.07348 - 13.8238i) q^{94} +(-0.699626 + 0.403929i) q^{95} +(5.02561 + 2.59677i) 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 $

$2$	−1.04209	+	0.956063i	−0.736866	+	0.676038i
$2$	−1.04209	+	0.956063i	−0.736866	+	0.676038i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.171888	−	1.99260i	0.0859439	−	0.996300i
$5$	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
$10$	−0.176607	+	0.0392655i	−0.0558479	+	0.0124168i
$11$	3.45938	−	1.99727i	1.04304	−	0.602201i	0.122349	−	0.992487i	$-0.460957\pi$
$11$	3.45938	−	1.99727i	1.04304	−	0.602201i	0.920693	+	0.390286i	$0.127624\pi$
$12$	1.81159	−	0.847441i	0.522960	−	0.244635i
$13$		−	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
$16$	−3.94091	−	0.685007i	−0.985227	−	0.171252i
$17$	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	$0.0834714\pi$
$18$	−0.306932	−	1.38050i	−0.0723445	−	0.325388i
$19$	−3.15745	+	5.46886i	−0.724368	+	1.25464i	0.234865	+	0.972028i	$0.424535\pi$
$19$	−3.15745	+	5.46886i	−0.724368	+	1.25464i	−0.959234	+	0.282615i	$0.908798\pi$
$20$	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	$-0.0915345\pi$
$23$	5.72040	+	3.30268i	1.19279	+	0.688656i	0.233849	+	0.972273i	$0.424868\pi$
$24$	−1.07762	+	2.61510i	−0.219969	+	0.533804i
$25$	−2.49182	−	4.31595i	−0.498363	−	0.863191i
$26$	0.852478	+	0.929181i	0.167185	+	0.182227i
$27$	−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	$0.415377\pi$
$30$	−0.122308	−	0.133313i	−0.0223303	−	0.0243395i
$31$	4.22668	+	7.32083i	0.759135	+	1.31486i	0.943292	+	0.331963i	$0.107711\pi$
$31$	4.22668	+	7.32083i	0.759135	+	1.31486i	−0.184158	+	0.982897i	$0.558956\pi$
$32$	4.76168	−	3.05392i	0.841754	−	0.539862i
$33$	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	$-0.0861878\pi$
$38$	−1.93824	−	8.71774i	−0.314424	−	1.41420i
$39$	0.772196	−	0.445827i	0.123650	−	0.0713895i
$40$	0.0478838	+	0.358656i	0.00757110	+	0.0567084i
$41$			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	$-0.0214191\pi$
$44$	−3.38514	−	7.23647i	−0.510329	−	1.09094i
$45$	−0.110790	+	0.0639645i	−0.0165156	+	0.00953527i
$46$	−9.11872	+	2.02739i	−1.34448	+	0.298922i
$47$	−5.00678	+	8.67200i	−0.730314	+	1.26494i	0.226435	+	0.974026i	$0.427293\pi$
$47$	−5.00678	+	8.67200i	−0.730314	+	1.26494i	−0.956749	+	0.290915i	$0.906040\pi$
$48$	−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
$52$	−1.77671	−	0.153265i	−0.246386	−	0.0212540i
$53$	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	$0.660206\pi$
$54$	1.04209	−	0.956063i	0.141810	−	0.130104i
$55$	0.511019			0.0689057
$56$		0			0
$57$	−6.31490			−0.836428
$58$	−2.94877	+	2.70535i	−0.387193	+	0.355230i
$59$	−0.294409	−	0.509932i	−0.0383288	−	0.0663875i	0.846225	−	0.532826i	$-0.178870\pi$
$59$	−0.294409	−	0.509932i	−0.0383288	−	0.0663875i	−0.884553	+	0.466439i	$0.845537\pi$
$60$	0.254911	+	0.0219894i	0.0329089	+	0.00283882i
$61$	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
$66$	−5.51449	+	1.22605i	−0.678787	+	0.150917i
$67$	−5.50132	+	3.17619i	−0.672094	+	0.388033i	−0.796869	−	0.604151i	$-0.793512\pi$
$67$	−5.50132	+	3.17619i	−0.672094	+	0.388033i	0.124776	+	0.992185i	$0.460179\pi$
$68$	−4.93924	−	10.5587i	−0.598971	−	1.28043i
$69$			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	$-0.236120\pi$
$72$	−2.80355	+	0.374300i	−0.330402	+	0.0441117i
$73$	−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	$0.971031\pi$
$74$	2.66390	+	11.9816i	0.309672	+	1.39283i
$75$	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	$-0.146969\pi$
$79$	8.50718	+	4.91162i	0.957132	+	0.552601i	0.0618431	+	0.998086i	$0.480302\pi$
$80$	−0.392796	−	0.327970i	−0.0439160	−	0.0366682i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.10385	−	3.38313i	−0.342763	−	0.373604i
$83$	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
$86$	0.843091	+	0.918950i	0.0909128	+	0.0990929i
$87$	1.41484	+	2.45058i	0.151687	+	0.262729i
$88$	10.4461	+	4.30461i	1.11356	+	0.458873i
$89$	−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
$94$	−3.07348	−	13.8238i	−0.317005	−	1.42581i
$95$	−0.699626	+	0.403929i	−0.0717801	+	0.0414423i
$96$	5.02561	+	2.59677i	0.512924	+	0.265032i
$97$		−	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
$100$	−9.02828	+	4.22333i	−0.902828	+	0.422333i
$101$	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	$0.128377\pi$
$102$	−8.04616	+	1.78893i	−0.796689	+	0.177130i
$103$	1.64215	−	2.84429i	0.161806	−	0.280256i	−0.773710	−	0.633539i	$-0.781601\pi$
$103$	1.64215	−	2.84429i	0.161806	−	0.280256i	0.935516	+	0.353283i	$0.114935\pi$
$104$	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	$-0.384878\pi$
$107$	−2.88857	−	1.66772i	−0.279249	−	0.161224i	−0.633083	+	0.774084i	$0.718211\pi$
$108$	−0.171888	+	1.99260i	−0.0165399	+	0.191738i
$109$	−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	$0.901866\pi$
$110$	−0.532525	+	0.488566i	−0.0507743	+	0.0465829i
$111$	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	$0.641831\pi$
$114$	6.58067	−	6.03744i	0.616336	−	0.565458i
$115$	0.422508	+	0.731806i	0.0393991	+	0.0682412i
$116$	0.486388	−	5.63843i	0.0451600	−	0.523515i
$117$	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
$122$	−2.33022	+	0.518085i	−0.210968	+	0.0469052i
$123$	−2.81155	+	1.62325i	−0.253509	+	0.146363i
$124$	15.3140	−	7.16373i	1.37524	−	0.643322i
$125$		−	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	$-0.214733\pi$
$128$	−5.26677	−	10.0130i	−0.465521	−	0.885037i
$129$	0.763693	−	0.440918i	0.0672394	−	0.0388207i
$130$	0.0350112	+	0.157472i	0.00307069	+	0.0138112i
$131$	4.88483	−	8.46078i	0.426790	−	0.739222i	−0.569796	−	0.821786i	$-0.692978\pi$
$131$	4.88483	−	8.46078i	0.426790	−	0.739222i	0.996586	+	0.0825645i	$0.0263111\pi$
$132$	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
$136$	15.2419	+	6.28084i	1.30698	+	0.538577i
$137$	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	$0.779109\pi$
$138$	−6.31513	−	6.88335i	−0.537580	−	0.585949i
$139$	−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
$142$	10.8853	+	11.8648i	0.913477	+	0.995669i
$143$	−1.78088	−	3.08457i	−0.148925	−	0.257945i
$144$	2.56369	−	3.07042i	0.213641	−	0.255869i
$145$	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	$0.201884\pi$
$150$	1.52963	+	6.87993i	0.124894	+	0.561744i
$151$	3.73832	−	2.15832i	0.304220	−	0.175642i	−0.340117	−	0.940383i	$-0.610467\pi$
$151$	3.73832	−	2.15832i	0.304220	−	0.175642i	0.644337	+	0.764741i	$0.277133\pi$
$152$	−17.7041	+	2.36366i	−1.43600	+	0.191719i
$153$			5.82842i			0.471200i
$154$		0			0
$155$			1.08143i			0.0868626i
$156$	−0.755625	−	1.61531i	−0.0604984	−	0.129328i
$157$	−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	$0.374170\pi$
$158$	−13.5610	+	3.01506i	−1.07886	+	0.239866i
$159$	−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	$-0.968640\pi$
$163$	−20.1454	−	11.6309i	−1.57791	−	0.911006i	−0.582757	−	0.812646i	$-0.698026\pi$
$164$	6.46897	+	0.558033i	0.505142	+	0.0435751i
$165$	0.255509	+	0.442555i	0.0198914	+	0.0344529i
$166$	−1.54251	+	1.41517i	−0.119722	+	0.109839i
$167$	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
$170$	−0.777005	+	0.712864i	−0.0595936	+	0.0546741i
$171$	−3.15745	−	5.46886i	−0.241456	−	0.418214i
$172$	−1.75715	−	0.151577i	−0.133981	−	0.0115576i
$173$	−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
$178$	0.621203	−	0.138114i	0.0465611	−	0.0103521i
$179$	1.27126	−	0.733963i	0.0950185	−	0.0548589i	−0.451738	−	0.892151i	$-0.649196\pi$
$179$	1.27126	−	0.733963i	0.0950185	−	0.0548589i	0.546756	+	0.837292i	$0.315862\pi$
$180$	0.108412	+	0.231754i	0.00808057	+	0.0172740i
$181$		−	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
$184$	2.47238	+	18.5184i	0.182266	+	1.36520i
$185$	0.961558	−	0.555156i	0.0706951	−	0.0408159i
$186$	−2.59460	−	11.6699i	−0.190246	−	0.855679i
$187$	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	$-0.375970\pi$
$191$	−3.19674	−	1.84564i	−0.231308	−	0.133546i	−0.611175	+	0.791495i	$0.709303\pi$
$192$	−7.71980	+	2.09874i	−0.557129	+	0.151463i
$193$	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	$0.802160\pi$
$194$	15.4923	+	16.8862i	1.11228	+	1.21236i
$195$	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	$0.453360\pi$
$198$	−3.81904	−	4.16266i	−0.271407	−	0.295828i
$199$	0.104115	+	0.180332i	0.00738048	+	0.0127834i	0.869692	−	0.493595i	$-0.164317\pi$
$199$	0.104115	+	0.180332i	0.00738048	+	0.0127834i	−0.862312	+	0.506378i	$0.830984\pi$
$200$	5.37048	−	13.0327i	0.379750	−	0.921550i
$201$	−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
$206$	1.00806	+	4.53400i	0.0702346	+	0.315899i
$207$	−5.72040	+	3.30268i	−0.397596	+	0.229552i
$208$	−0.610790	+	3.51393i	−0.0423507	+	0.243647i
$209$			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	$0.806602\pi$
$212$	13.6495	−	6.38508i	0.937449	−	0.438529i
$213$	9.86020	−	5.69279i	0.675610	−	0.390064i
$214$	4.60458	−	1.02375i	0.314763	−	0.0699821i
$215$	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
$220$	0.0878379	−	1.01826i	0.00592203	−	0.0686508i
$221$	−2.59847	−	4.50068i	−0.174792	−	0.302749i
$222$	−9.04439	+	8.29778i	−0.607020	+	0.556911i
$223$	−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
$226$	9.54835	−	8.76014i	0.635147	−	0.582716i
$227$	−13.4986	−	23.3803i	−0.895935	−	1.55180i	−0.832643	−	0.553810i	$-0.813173\pi$
$227$	−13.4986	−	23.3803i	−0.895935	−	1.55180i	−0.0632918	−	0.997995i	$-0.520160\pi$
$228$	−1.08545	+	12.5831i	−0.0718859	+	0.833334i
$229$	−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	$0.933736\pi$
$234$	−1.23093	+	0.273677i	−0.0804686	+	0.0178908i
$235$	−1.10940	+	0.640513i	−0.0723693	+	0.0417824i
$236$	−1.06670	+	0.498989i	−0.0694360	+	0.0324814i
$237$			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	$0.695736\pi$
$240$	0.0876323	−	0.504157i	0.00565664	−	0.0325432i
$241$	−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	$0.418509\pi$
$242$	1.52128	+	6.84235i	0.0977915	+	0.439843i
$243$	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
$248$	−9.10954	+	22.1064i	−0.578456	+	1.40376i
$249$	0.740105	+	1.28190i	0.0469023	+	0.0812371i
$250$	1.22108	+	1.33095i	0.0772279	+	0.0841766i
$251$	−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
$254$	13.4590	+	14.6700i	0.844490	+	0.920475i
$255$	0.372812	+	0.645730i	0.0233464	+	0.0404372i
$256$	15.0615	+	5.39910i	0.941346	+	0.337444i
$257$	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
$262$	2.99862	+	13.4871i	0.185255	+	0.833234i
$263$	−1.82321	+	1.05263i	−0.112424	+	0.0649079i	−0.555158	−	0.831745i	$-0.687342\pi$
$263$	−1.82321	+	1.05263i	−0.112424	+	0.0649079i	0.442734	+	0.896653i	$0.354009\pi$
$264$	1.49516	+	11.1989i	0.0920207	+	0.689246i
$265$			0.963886i			0.0592111i
$266$		0			0
$267$		−	0.449983i		−	0.0275385i
$268$	5.38327	+	11.5079i	0.328835	+	0.702956i
$269$	−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	$0.450486\pi$
$270$	0.176607	−	0.0392655i	0.0107479	−	0.00238962i
$271$	−5.66213	+	9.80709i	−0.343950	+	0.595738i	−0.985162	−	0.171625i	$-0.945098\pi$
$271$	−5.66213	+	9.80709i	−0.343950	+	0.595738i	0.641213	+	0.767363i	$0.278432\pi$
$272$	−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
$276$	13.1618	+	1.13538i	0.792249	+	0.0683418i
$277$	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	$0.718355\pi$
$278$	0.273050	−	0.250510i	0.0163765	−	0.0150246i
$279$	−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	$0.594471\pi$
$282$	10.4350	−	9.57360i	0.621395	−	0.570099i
$283$	−12.3233	−	21.3445i	−0.732542	−	1.26880i	−0.955794	−	0.294039i	$-0.905001\pi$
$283$	−12.3233	−	21.3445i	−0.732542	−	1.26880i	0.223252	−	0.974761i	$-0.428333\pi$
$284$	−22.6869	−	1.95704i	−1.34622	−	0.116129i
$285$	−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
$290$	−0.499741	+	0.111109i	−0.0293458	+	0.00652453i
$291$	14.0333	−	8.10212i	0.822645	−	0.474954i
$292$	13.1471	+	28.1048i	0.769377	+	1.64471i
$293$		−	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
$296$	24.3324	−	3.24859i	1.41429	−	0.188821i
$297$	−3.45938	+	1.99727i	−0.200734	+	0.115894i
$298$	−0.827330	−	3.72113i	−0.0479259	−	0.215559i
$299$	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
$304$	16.1894	−	19.3894i	0.928527	−	1.11206i
$305$	0.107969	+	0.187007i	0.00618228	+	0.0107080i
$306$	−5.57234	−	6.07372i	−0.318549	−	0.347211i
$307$	−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
$310$	−1.03392	−	1.12694i	−0.0587225	−	0.0640061i
$311$	15.5933	+	27.0084i	0.884215	+	1.53151i	0.846610	+	0.532213i	$0.178640\pi$
$311$	15.5933	+	27.0084i	0.884215	+	1.53151i	0.0376050	+	0.999293i	$0.488027\pi$
$312$	2.33176	+	0.960867i	0.132010	+	0.0543984i
$313$	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	$-0.00463927\pi$
$318$	−2.31259	−	10.4015i	−0.129684	−	0.583285i
$319$	9.78895	−	5.65165i	0.548076	−	0.316432i
$320$	−0.721030	+	0.726312i	−0.0403068	+	0.0406021i
$321$		−	3.33543i		−	0.186166i
$322$		0			0
$323$			36.8059i			2.04793i
$324$	−1.81159	+	0.847441i	−0.100644	+	0.0470800i
$325$	−3.84834	+	2.22184i	−0.213468	+	0.123246i
$326$	32.1131	−	7.13981i	1.77858	−	0.395437i
$327$	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	$-0.526250\pi$
$331$	−17.9504	−	10.3637i	−0.986644	−	0.569639i	−0.904270	+	0.426962i	$0.859584\pi$
$332$	0.254430	−	2.94947i	0.0139637	−	0.161873i
$333$	4.33956	+	7.51634i	0.237806	+	0.411893i
$334$	−10.0756	+	9.24383i	−0.551310	+	0.505800i
$335$	−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	$0.502866\pi$
$338$	−12.7186	+	11.6687i	−0.691801	+	0.634694i
$339$	−4.58136	−	7.93515i	−0.248825	−	0.430978i
$340$	0.128164	−	1.48573i	0.00695065	−	0.0805751i
$341$	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
$346$	28.5855	−	6.35549i	1.53676	−	0.341673i
$347$	−19.0483	+	10.9975i	−1.02257	+	0.590378i	−0.914846	−	0.403803i	$-0.867688\pi$
$347$	−19.0483	+	10.9975i	−1.02257	+	0.590378i	−0.107719	+	0.994181i	$0.534355\pi$
$348$	5.12621	−	2.39799i	0.274794	−	0.128546i
$349$			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
$352$	10.3729	−	20.0750i	0.552879	−	1.07000i
$353$	−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	$0.399645\pi$
$354$	0.180727	+	0.812867i	0.00960554	+	0.0432034i
$355$	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	$-0.187250\pi$
$359$	14.5380	+	8.39350i	0.767285	+	0.442992i	−0.0646204	+	0.997910i	$0.520584\pi$
$360$	−0.334547	−	0.137859i	−0.0176322	−	0.00726582i
$361$	−10.4390	−	18.0808i	−0.549419	−	0.951621i
$362$	22.5126	+	24.5382i	1.18324	+	1.28970i
$363$	4.95641			0.260144
$364$		0			0
$365$	−1.98468			−0.103883
$366$	−1.61379	−	1.75899i	−0.0843539	−	0.0919438i
$367$	2.01820	+	3.49562i	0.105349	+	0.182470i	0.913881	−	0.405983i	$-0.133071\pi$
$367$	2.01820	+	3.49562i	0.105349	+	0.182470i	−0.808532	+	0.588453i	$0.799737\pi$
$368$	−20.2812	−	16.9341i	−1.05723	−	0.882749i
$369$	−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	$0.985866\pi$
$374$	7.14595	+	32.1408i	0.369508	+	1.66196i
$375$	1.10608	−	0.638598i	0.0571180	−	0.0329771i
$376$	−28.0735	+	3.74808i	−1.44778	+	0.193292i
$377$		−	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	$0.910704\pi$
$380$	0.684612	+	1.46351i	0.0351199	+	0.0750762i
$381$	12.1915	−	7.03874i	0.624587	−	0.360606i
$382$	5.09583	−	1.13297i	0.260725	−	0.0579678i
$383$	3.26491	−	5.65498i	0.166829	−	0.288956i	−0.770474	−	0.637471i	$-0.779981\pi$
$383$	3.26491	−	5.65498i	0.166829	−	0.288956i	0.937303	+	0.348515i	$0.113314\pi$
$384$	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
$388$	−32.2886	−	2.78531i	−1.63920	−	0.141403i
$389$	−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	$-0.466078\pi$
$390$	−0.118869	+	0.109057i	−0.00601918	+	0.00552230i
$391$	38.4988			1.94697
$392$		0			0
$393$	9.76967			0.492814
$394$	−4.27092	+	3.91836i	−0.215166	+	0.197404i
$395$	0.628339	+	1.08832i	0.0316152	+	0.0547591i
$396$	7.95954	+	0.686614i	0.399982	+	0.0345036i
$397$	−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	$0.923602\pi$
$402$	8.76949	−	1.94975i	0.437383	−	0.0972445i
$403$	6.52765	−	3.76874i	0.325166	−	0.187734i
$404$	−10.2253	−	21.8587i	−0.508727	−	1.08751i
$405$		−	0.127929i		−	0.00635684i
$406$		0			0
$407$		−	34.6692i		−	1.71849i
$408$	2.18158	+	16.3403i	0.108004	+	0.808964i
$409$	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	$0.122764\pi$
$410$	−0.127475	−	0.573353i	−0.00629555	−	0.0283159i
$411$	−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
$416$	−2.72304	−	4.24577i	−0.133508	−	0.208166i
$417$	−0.131011	−	0.226918i	−0.00641566	−	0.0111122i
$418$	−24.1168	−	26.2868i	−1.17959	−	1.28573i
$419$	−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	$0.651677\pi$
$422$	−15.8563	−	17.2830i	−0.771874	−	0.841324i
$423$	−5.00678	−	8.67200i	−0.243438	−	0.421647i
$424$	−8.11939	+	19.7036i	−0.394312	+	0.956889i
$425$	−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
$430$	0.0346257	+	0.155738i	0.00166980	+	0.00751036i
$431$	18.9190	−	10.9229i	0.911295	−	0.526137i	0.0304476	−	0.999536i	$-0.490307\pi$
$431$	18.9190	−	10.9229i	0.911295	−	0.526137i	0.880848	+	0.473400i	$0.156973\pi$
$432$	3.94091	+	0.685007i	0.189607	+	0.0329574i
$433$		−	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
$436$	−8.08141	+	3.78040i	−0.387030	+	0.181048i
$437$	−36.1238	+	20.8561i	−1.72803	+	0.997681i
$438$	21.4170	−	4.76171i	1.02335	−	0.227523i
$439$	−15.9429	+	27.6140i	−0.760914	+	1.31794i	0.181466	+	0.983397i	$0.441916\pi$
$439$	−15.9429	+	27.6140i	−0.760914	+	1.31794i	−0.942380	+	0.334545i	$0.891417\pi$
$440$	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	$-0.454849\pi$
$443$	−13.5814	−	7.84122i	−0.645272	−	0.372548i	−0.786642	+	0.617409i	$0.788182\pi$
$444$	1.49183	−	17.2940i	0.0707993	−	0.820738i
$445$	−0.0287829	−	0.0498535i	−0.00136444	−	0.00236328i
$446$	22.2415	−	20.4055i	1.05316	−	0.966226i
$447$	−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	$0.573700\pi$
$450$	−5.19338	+	4.76467i	−0.244818	+	0.224609i
$451$	6.48414	+	11.2309i	0.305326	+	0.528841i
$452$	−1.57496	+	18.2576i	−0.0740799	+	0.858767i
$453$	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	$0.0806957\pi$
$458$	4.02684	−	0.895300i	0.188162	−	0.0418346i
$459$	−5.04756	+	2.91421i	−0.235600	+	0.136024i
$460$	1.53082	−	0.716101i	0.0713748	−	0.0333884i
$461$		−	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	$-0.0499883\pi$
$464$	−11.1515	−	1.93835i	−0.517697	−	0.0899858i
$465$	−0.936547	+	0.540715i	−0.0434313	+	0.0250751i
$466$	−6.26108	−	28.1608i	−0.290039	−	1.30453i
$467$	11.0608	−	19.1579i	0.511833	−	0.886522i	−0.488072	−	0.872803i	$-0.662300\pi$
$467$	11.0608	−	19.1579i	0.511833	−	0.886522i	0.999906	−	0.0137185i	$-0.00436686\pi$
$468$	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
$472$	0.634524	−	1.53982i	0.0292064	−	0.0708759i
$473$	−1.76127	−	3.05061i	−0.0809832	−	0.140267i
$474$	−9.39164	−	10.2367i	−0.431372	−	0.470186i
$475$	31.4711			1.44399
$476$		0			0
$477$	−7.53454			−0.344983
$478$	−24.1458	−	26.3183i	−1.10440	−	1.20377i
$479$	10.6325	+	18.4159i	0.485809	+	0.841446i	0.999867	−	0.0163095i	$-0.00519170\pi$
$479$	10.6325	+	18.4159i	0.485809	+	0.841446i	−0.514058	+	0.857755i	$0.671858\pi$
$480$	0.390685	+	0.609157i	0.0178322	+	0.0278041i
$481$	−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
$486$	0.306932	+	1.38050i	0.0139227	+	0.0626210i
$487$	−30.6868	+	17.7171i	−1.39055	+	0.802836i	−0.993376	−	0.114906i	$-0.963343\pi$
$487$	−30.6868	+	17.7171i	−1.39055	+	0.802836i	−0.397177	+	0.917742i	$0.630010\pi$
$488$	0.631799	+	4.73225i	0.0286002	+	0.214219i
$489$		−	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	$-0.111380\pi$
$492$	2.75121	+	5.88131i	0.124034	+	0.265150i
$493$	14.2830	−	8.24629i	0.643274	−	0.371394i
$494$	−7.77322	+	1.72824i	−0.349734	+	0.0777573i
$495$	−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	$-0.253489\pi$
$499$	9.60373	+	5.54472i	0.429922	+	0.248216i	−0.269391	+	0.963031i	$0.586822\pi$
$500$	−2.54494	−	0.219534i	−0.113813	−	0.00981788i
$501$	4.83432	+	8.37329i	0.215982	+	0.374091i
$502$	6.82754	−	6.26393i	0.304728	−	0.279573i
$503$	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
$506$	−27.4959	+	25.2261i	−1.22234	+	1.12144i
$507$	6.10248	+	10.5698i	0.271020	+	0.469421i
$508$	−28.0508	−	2.41975i	−1.24455	−	0.107359i
$509$	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
$514$	−25.8876	+	5.75566i	−1.14185	+	0.253871i
$515$	0.363867	−	0.210079i	0.0160339	−	0.00925719i
$516$	−0.747304	−	1.59752i	−0.0328982	−	0.0703270i
$517$			39.9997i			1.75918i
$518$		0			0
$519$		−	20.7065i		−	0.908916i
$520$	0.319797	−	0.0426958i	0.0140240	−	0.00187234i
$521$	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	$0.120824\pi$
$522$	−0.868519	−	3.90639i	−0.0380140	−	0.170978i
$523$	5.38111	−	9.32036i	0.235300	−	0.407551i	−0.724060	−	0.689737i	$-0.757726\pi$
$523$	5.38111	−	9.32036i	0.235300	−	0.407551i	0.959360	+	0.282186i	$0.0910595\pi$
$524$	−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
$528$	−12.2650	−	10.2408i	−0.533764	−	0.445673i
$529$	10.3153	+	17.8667i	0.448493	+	0.776813i
$530$	−0.921536	−	1.00445i	−0.0400290	−	0.0436306i
$531$	0.588819			0.0255526
$532$		0			0
$533$	2.89475			0.125386
$534$	0.430212	+	0.468921i	0.0186171	+	0.0202922i
$535$	−0.213349	−	0.369532i	−0.00922390	−	0.0159763i
$536$	−16.6121	−	6.84547i	−0.717533	−	0.295679i
$537$	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	$0.130144\pi$
$542$	−3.47577	−	15.6332i	−0.149297	−	0.671503i
$543$	20.3925	−	11.7736i	0.875124	−	0.505253i
$544$	15.1351	−	29.2914i	0.648912	−	1.25586i
$545$		−	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	$-0.129430\pi$
$548$	7.18932	−	3.36309i	0.307113	−	0.143664i
$549$	−1.46181	+	0.843974i	−0.0623884	+	0.0360199i
$550$	27.4822	−	6.11020i	1.17185	−	0.260540i
$551$	−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
$556$	−0.0450385	+	0.522107i	−0.00191006	+	0.0221423i
$557$	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	$0.614655\pi$
$558$	8.80914	−	8.08195i	0.372920	−	0.342136i
$559$	−0.786294			−0.0332567
$560$		0			0
$561$	23.2819			0.982963
$562$	10.2175	−	9.37401i	0.430997	−	0.395419i
$563$	6.18858	+	10.7189i	0.260818	+	0.451749i	0.966459	−	0.256819i	$-0.0826746\pi$
$563$	6.18858	+	10.7189i	0.260818	+	0.451749i	−0.705642	+	0.708569i	$0.749341\pi$
$564$	−1.72121	+	19.9530i	−0.0724760	+	0.840174i
$565$	−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	$-0.112958\pi$
$570$	1.11525	−	0.247957i	0.0467128	−	0.0103858i
$571$	5.47430	−	3.16059i	0.229092	−	0.132267i	−0.381061	−	0.924550i	$-0.624441\pi$
$571$	5.47430	−	3.16059i	0.229092	−	0.132267i	0.610153	+	0.792283i	$0.291108\pi$
$572$	−6.45243	+	3.01838i	−0.269790	+	0.126205i
$573$		−	3.69128i		−	0.154206i
$574$		0			0
$575$		−	32.9187i		−	1.37280i
$576$	−5.67746	−	5.63617i	−0.236561	−	0.234841i
$577$	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	$0.299574\pi$
$578$	5.20878	+	23.4278i	0.216657	+	0.974470i
$579$	−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
$584$	−40.5704	−	16.7181i	−1.67881	−	0.691802i
$585$	0.0570343	+	0.0987862i	0.00235808	+	0.00408431i
$586$	2.30451	+	2.51186i	0.0951985	+	0.103764i
$587$	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
$590$	0.0720174	+	0.0784973i	0.00296491	+	0.00323168i
$591$	2.04922	+	3.54935i	0.0842935	+	0.146001i
$592$	−22.2506	+	26.6486i	−0.914492	+	1.09525i
$593$	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
$598$	1.80773	+	8.13075i	0.0739237	+	0.332491i
$599$	−15.8953	+	9.17715i	−0.649464	+	0.374968i	−0.788251	−	0.615354i	$-0.789013\pi$
$599$	−15.8953	+	9.17715i	−0.649464	+	0.374968i	0.138787	+	0.990322i	$0.455680\pi$
$600$	13.9719	−	1.86537i	0.570399	−	0.0761536i
$601$			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
$604$	−3.65810	−	7.81997i	−0.148846	−	0.318190i
$605$	0.549120	−	0.317034i	0.0223249	−	0.0128893i
$606$	−16.6573	+	3.70346i	−0.676656	+	0.150443i
$607$	−13.2875	+	23.0146i	−0.539322	+	0.934133i	0.459619	+	0.888116i	$0.347986\pi$
$607$	−13.2875	+	23.0146i	−0.539322	+	0.934133i	−0.998941	+	0.0460167i	$0.985347\pi$
$608$	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
$612$	11.6137	+	1.00183i	0.469456	+	0.0404968i
$613$	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	$0.706875\pi$
$614$	25.4326	−	23.3331i	1.02638	−	0.941649i
$615$	−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	$0.596197\pi$
$618$	−3.42253	+	3.14000i	−0.137674	+	0.126309i
$619$	−12.6747	−	21.9532i	−0.509439	−	0.882374i	−0.999940	−	0.0109337i	$-0.996520\pi$
$619$	−12.6747	−	21.9532i	−0.509439	−	0.882374i	0.490501	−	0.871440i	$-0.336814\pi$
$620$	2.15486	+	0.185885i	0.0865412	+	0.00746531i
$621$	−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
$626$	−3.50382	+	0.779015i	−0.140041	+	0.0311357i
$627$	−21.8456	+	12.6126i	−0.872430	+	0.503698i
$628$	2.71703	+	5.80823i	0.108421	+	0.231774i
$629$		−	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	$-0.260783\pi$
$632$	3.67684	+	27.5400i	0.146257	+	1.09548i
$633$	−14.3630	+	8.29251i	−0.570880	+	0.329598i
$634$	5.60213	+	25.1970i	0.222489	+	1.00070i
$635$	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
$640$	0.0569759	−	1.44623i	0.00225217	−	0.0571673i
$641$	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	$0.787323\pi$
$642$	3.18889	+	3.47581i	0.125855	+	0.137179i
$643$	−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
$646$	−35.1887	−	38.3549i	−1.38448	−	1.50905i
$647$	−7.92738	−	13.7306i	−0.311658	−	0.539807i	0.667064	−	0.745001i	$-0.267551\pi$
$647$	−7.92738	−	13.7306i	−0.311658	−	0.539807i	−0.978721	+	0.205194i	$0.934218\pi$
$648$	1.07762	−	2.61510i	0.0423330	−	0.102731i
$649$	−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	$-0.0240064\pi$
$654$	1.36921	+	6.15838i	0.0535403	+	0.240812i
$655$	1.08238	−	0.624912i	0.0422921	−	0.0244173i
$656$	2.22387	−	12.7941i	0.0868277	−	0.499528i
$657$		−	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	$0.868369\pi$
$660$	0.925754	−	0.433058i	0.0360349	−	0.0168568i
$661$	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	$0.179098\pi$
$662$	28.6142	−	6.36188i	1.11212	−	0.247261i
$663$	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
$668$	1.66192	−	19.2657i	0.0643017	−	0.745414i
$669$	−10.6716	−	18.4838i	−0.412588	−	0.714624i
$670$	0.846856	−	0.776948i	0.0327169	−	0.0300161i
$671$	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	$0.478884\pi$
$674$	0.344443	−	0.316009i	0.0132674	−	0.0121722i
$675$	2.49182	+	4.31595i	0.0959101	+	0.166121i
$676$	2.09788	−	24.3196i	0.0806878	−	0.935369i
$677$	−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
$682$	−46.6160	+	10.3643i	−1.78502	+	0.396868i
$683$	−7.39676	+	4.27052i	−0.283029	+	0.163407i	−0.634794	−	0.772682i	$-0.718915\pi$
$683$	−7.39676	+	4.27052i	−0.283029	+	0.163407i	0.351765	+	0.936088i	$0.385582\pi$
$684$	−11.4400	+	5.35150i	−0.437419	+	0.204620i
$685$			0.507689i			0.0193978i
$686$		0			0
$687$		−	2.91694i		−	0.111288i
$688$	−0.604064	+	3.47524i	−0.0230297	+	0.132492i
$689$	5.81814	−	3.35910i	0.221653	−	0.127972i
$690$	−0.259362	−	1.16655i	−0.00987375	−	0.0444098i
$691$	1.22924	−	2.12910i	0.0467625	−	0.0809950i	−0.841697	−	0.539950i	$-0.818443\pi$
$691$	1.22924	−	2.12910i	0.0467625	−	0.0809950i	0.888459	+	0.458956i	$0.151776\pi$
$692$	−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
$696$	−3.04933	+	7.39989i	−0.115585	+	0.280492i
$697$	9.46098	+	16.3869i	0.358360	+	0.620698i
$698$	−25.4991	−	27.7934i	−0.965154	−	1.05200i
$699$	−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	$0.196605\pi$
$702$	−0.852478	−	0.929181i	−0.0321747	−	0.0350697i
$703$	27.4039	+	47.4649i	1.03356	+	1.79017i
$704$	8.38351	+	30.8371i	0.315965	+	1.16222i
$705$	−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	$0.329569\pi$
$710$	0.447060	+	2.01077i	0.0167779	+	0.0754628i
$711$	−8.50718	+	4.91162i	−0.319044	+	0.184200i
$712$	−0.168428	−	1.26155i	−0.00631212	−	0.0472786i
$713$			55.8375i			2.09113i
$714$		0			0
$715$		−	0.455652i		−	0.0170404i
$716$	−1.24398	−	2.65927i	−0.0464897	−	0.0993817i
$717$	−21.8718	+	12.6277i	−0.816818	+	0.471590i
$718$	−23.1745	+	5.15246i	−0.864866	+	0.192288i
$719$	−19.0610	+	33.0146i	−0.710854	+	1.23124i	0.253683	+	0.967287i	$0.418358\pi$
$719$	−19.0610	+	33.0146i	−0.710854	+	1.23124i	−0.964537	+	0.263948i	$0.914975\pi$
$720$	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
$724$	−46.9201	−	4.04747i	−1.74377	−	0.150423i
$725$	−7.05105	−	12.2128i	−0.261870	−	0.453571i
$726$	−5.16501	+	4.73864i	−0.191691	+	0.175867i
$727$	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
$730$	2.06821	−	1.89748i	0.0765478	−	0.0702288i
$731$	−2.56986	−	4.45112i	−0.0950496	−	0.164631i
$732$	3.36341	+	0.290138i	0.124315	+	0.0107238i
$733$	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
$738$	4.48180	−	0.996452i	0.164977	−	0.0366799i
$739$	24.9833	−	14.4241i	0.919027	−	0.530600i	0.0357022	−	0.999362i	$-0.488633\pi$
$739$	24.9833	−	14.4241i	0.919027	−	0.530600i	0.883324	+	0.468762i	$0.155300\pi$
$740$	−0.940923	−	2.01142i	−0.0345890	−	0.0739414i
$741$			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	$0.997864\pi$
$744$	−23.6994	+	3.16409i	−0.868864	+	0.116001i
$745$	−0.298632	+	0.172415i	−0.0109410	+	0.00631681i
$746$	−6.37773	−	28.6855i	−0.233505	−	1.05025i
$747$	−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	$-0.214670\pi$
$751$	17.2878	+	9.98114i	0.630842	+	0.364217i	−0.150236	+	0.988650i	$0.548003\pi$
$752$	25.6717	−	30.7459i	0.936149	−	1.12119i
$753$	−3.27590	−	5.67402i	−0.119380	−	0.206773i
$754$	2.41224	+	2.62929i	0.0878487	+	0.0957530i
$755$	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	$0.517622\pi$
$758$	−10.3064	−	11.2337i	−0.374344	−	0.408026i
$759$	13.1927	+	22.8504i	0.478865	+	0.829418i
$760$	−2.11263	−	0.870566i	−0.0766331	−	0.0315788i
$761$	−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
$766$	2.00421	+	9.01444i	0.0724149	+	0.325705i
$767$	−0.454683	+	0.262512i	−0.0164177	+	0.00947874i
$768$	2.85501	+	15.7432i	0.103021	+	0.568084i
$769$			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
$772$	4.92161	−	2.30228i	0.177133	−	0.0828608i
$773$	−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	$0.473895\pi$
$774$	−1.21738	+	0.270663i	−0.0437578	+	0.00972879i
$775$	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
$780$	0.0196070	−	0.227293i	0.000702043	−	0.00813839i
$781$	−22.7401	−	39.3871i	−0.813706	−	1.40938i
$782$	−40.1190	+	36.8073i	−1.43465	+	1.31622i
$783$	−2.82968			−0.101125
$784$		0			0
$785$	−0.410160			−0.0146393
$786$	−10.1808	+	9.34042i	−0.363138	+	0.333162i
$787$	−9.97597	−	17.2789i	−0.355605	−	0.615926i	0.631616	−	0.775281i	$-0.282392\pi$
$787$	−9.97597	−	17.2789i	−0.355605	−	0.615926i	−0.987221	+	0.159355i	$0.949058\pi$
$788$	0.704471	−	8.16654i	0.0250957	−	0.290921i
$789$	−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
$794$	21.2898	−	4.73343i	0.755548	−	0.167983i
$795$	−0.834750	+	0.481943i	−0.0296055	+	0.0170928i
$796$	0.377225	−	0.176462i	0.0133704	−	0.00625452i
$797$		−	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
$800$	−25.0458	−	12.9414i	−0.885503	−	0.457547i
$801$	0.389696	−	0.224991i	0.0137692	−	0.00794968i
$802$	−8.50073	−	38.2343i	−0.300171	−	1.35010i
$803$	−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
$808$	31.5540	+	13.0027i	1.11006	+	0.457433i
$809$	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	$0.708511\pi$
$810$	0.122308	+	0.133313i	0.00429747	+	0.00468414i
$811$	−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
$814$	33.1459	+	36.1283i	1.16176	+	1.26629i
$815$	−1.48794	−	2.57718i	−0.0521201	−	0.0902747i
$816$	−17.8957	−	14.9423i	−0.626476	−	0.523084i
$817$	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	$0.0123284\pi$
$822$	−1.21807	−	5.47857i	−0.0424849	−	0.191087i
$823$	20.9990	−	12.1238i	0.731979	−	0.422608i	−0.0871667	−	0.996194i	$-0.527781\pi$
$823$	20.9990	−	12.1238i	0.731979	−	0.422608i	0.819146	+	0.573585i	$0.194448\pi$
$824$	9.20772	−	1.22931i	0.320766	−	0.0428252i
$825$		−	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	$-0.203340\pi$
$828$	5.59765	+	11.9662i	0.194532	+	0.415853i
$829$	−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	$0.337795\pi$
$830$	−0.261415	+	0.0581211i	−0.00907385	+	0.00201741i
$831$	−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
$836$	50.2636	+	4.33590i	1.73840	+	0.149960i
$837$	−4.22668	−	7.32083i	−0.146096	−	0.253045i
$838$	22.8307	−	20.9461i	0.788675	−	0.723570i
$839$	−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
$842$	19.6148	−	17.9956i	0.675969	−	0.620169i
$843$	−4.90240	−	8.49121i	−0.168848	−	0.292453i
$844$	33.0473	+	2.85076i	1.13754	+	0.0981273i
$845$	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
$850$	40.0991	−	8.91535i	1.37539	−	0.305794i
$851$	49.6481	−	28.6643i	1.70191	−	0.982600i
$852$	−9.64861	−	20.6260i	−0.330556	−	0.706634i
$853$			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
$856$	−1.24845	−	9.35106i	−0.0426712	−	0.319613i
$857$	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	$0.165064\pi$
$858$	1.09322	+	4.91702i	0.0373218	+	0.167864i
$859$	7.56296	−	13.0994i	0.258045	−	0.446947i	−0.707673	−	0.706540i	$-0.750255\pi$
$859$	7.56296	−	13.0994i	0.258045	−	0.446947i	0.965718	+	0.259593i	$0.0835884\pi$
$860$	−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	$-0.422135\pi$
$863$	−14.0116	−	8.08962i	−0.476962	−	0.275374i	−0.719149	+	0.694856i	$0.755468\pi$
$864$	−4.76168	+	3.05392i	−0.161996	+	0.103896i
$865$	−1.32448	−	2.29407i	−0.0450338	−	0.0780008i
$866$	22.7008	+	24.7433i	0.771404	+	0.840813i
$867$	16.9705			0.576348
$868$		0			0
$869$	39.2394			1.33111
$870$	−0.346093	−	0.377234i	−0.0117337	−	0.0127894i
$871$	2.83207	+	4.90528i	0.0959609	+	0.166209i
$872$	4.80723	−	11.6658i	0.162793	−	0.395055i
$873$	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	$0.932967\pi$
$878$	−9.78677	−	44.0186i	−0.330288	−	1.48555i
$879$	2.08748	−	1.20521i	0.0704091	−	0.0406507i
$880$	−2.01388	−	0.350051i	−0.0678878	−	0.0118002i
$881$		−	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	$0.785110\pi$
$884$	−9.41470	+	4.40410i	−0.316651	+	0.148126i
$885$	0.0652351	−	0.0376635i	0.00219285	−	0.00126605i
$886$	21.6497	−	4.81344i	0.727335	−	0.161711i
$887$	13.8563	−	23.9998i	0.465248	−	0.805834i	−0.533964	−	0.845507i	$-0.679298\pi$
$887$	13.8563	−	23.9998i	0.465248	−	0.805834i	0.999213	+	0.0396732i	$0.0126317\pi$
$888$	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
$892$	−3.66864	+	42.5285i	−0.122835	+	1.42396i
$893$	−31.6173	−	54.7628i	−1.05803	−	1.83257i
$894$	2.80893	−	2.57705i	0.0939446	−	0.0861896i
$895$	0.187790			0.00627714
$896$		0			0
$897$	5.88969			0.196651
$898$	10.1341	−	9.29756i	0.338180	−	0.310263i
$899$	11.9602	+	20.7156i	0.398894	+	0.690905i
$900$	0.856626	−	9.93039i	0.0285542	−	0.331013i
$901$	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
$906$	−5.95915	+	1.32491i	−0.197979	+	0.0440173i
$907$	−34.6185	+	19.9870i	−1.14949	+	0.663658i	−0.948763	−	0.315989i	$-0.897664\pi$
$907$	−34.6185	+	19.9870i	−1.14949	+	0.663658i	−0.200727	+	0.979647i	$0.564330\pi$
$908$	−48.9078	+	22.8786i	−1.62306	+	0.759252i
$909$			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	$0.802670\pi$
$912$	24.8864	+	4.32575i	0.824072	+	0.143240i
$913$	5.12061	−	2.95639i	0.169467	−	0.0978421i
$914$	3.50137	+	15.7483i	0.115815	+	0.520909i
$915$	−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	$-0.331596\pi$
$919$	0.286521	+	0.165423i	0.00945146	+	0.00545681i	−0.495267	+	0.868741i	$0.664930\pi$
$920$	−0.910609	+	2.20980i	−0.0300219	+	0.0728549i
$921$	−12.2027	−	21.1357i	−0.402093	−	0.696446i
$922$	18.7815	+	20.4714i	0.618535	+	0.674189i
$923$	−10.1520			−0.334157
$924$		0			0
$925$	−43.2536			−1.42217
$926$	6.43485	+	7.01384i	0.211462	+	0.230489i
$927$	1.64215	+	2.84429i	0.0539354	+	0.0934188i
$928$	13.4740	−	8.64163i	0.442307	−	0.283675i
$929$	−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
$934$	6.78983	+	30.5390i	0.222170	+	0.999267i
$935$	2.57940	−	1.48922i	0.0843553	−	0.0487026i
$936$	0.333746	+	2.49980i	0.0109088	+	0.0817085i
$937$		−	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
$940$	1.08559	+	2.32069i	0.0354081	+	0.0756925i
$941$	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	$0.245060\pi$
$942$	4.42611	−	0.984071i	0.144211	−	0.0320628i
$943$	−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	$-0.442146\pi$
$947$	−17.8680	−	10.3161i	−0.580631	−	0.335227i	−0.761384	+	0.648301i	$0.775480\pi$
$948$	19.5738	+	1.68850i	0.635727	+	0.0548398i
$949$	6.91653	+	11.9798i	0.224520	+	0.388880i
$950$	−32.7956	+	30.0884i	−1.06403	+	0.976196i
$951$	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	$0.384567\pi$
$954$	7.85164	−	7.20349i	0.254206	−	0.233222i
$955$	−0.236111	−	0.408956i	−0.00764037	−	0.0132335i
$956$	50.3239	+	4.34110i	1.62759	+	0.140401i
$957$	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
$962$	10.6834	−	2.37528i	0.344447	−	0.0765819i
$963$	2.88857	−	1.66772i	0.0930829	−	0.0537414i
$964$	6.95697	+	14.8720i	0.224069	+	0.478995i
$965$			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	$-0.00333284\pi$
$968$	13.8956	−	1.85518i	0.446620	−	0.0596279i
$969$	−31.8748	+	18.4029i	−1.02397	+	0.591188i
$970$	0.636266	+	2.86177i	0.0204293	+	0.0918860i
$971$	29.7321	−	51.4974i	0.954147	−	1.65263i	0.217839	−	0.975985i	$-0.430099\pi$
$971$	29.7321	−	51.4974i	0.954147	−	1.65263i	0.736308	−	0.676646i	$-0.236567\pi$
$972$	−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
$976$	−5.18272	−	4.32737i	−0.165895	−	0.138516i
$977$	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	$0.717535\pi$
$978$	22.2398	+	24.2409i	0.711151	+	0.775138i
$979$	−1.79748			−0.0574476
$980$		0			0
$981$	4.46096			0.142428
$982$	14.5250	+	15.8319i	0.463511	+	0.505216i
$983$	−9.54779	−	16.5373i	−0.304527	−	0.527457i	0.672629	−	0.739980i	$-0.265165\pi$
$983$	−9.54779	−	16.5373i	−0.304527	−	0.527457i	−0.977156	+	0.212523i	$0.931832\pi$
$984$	−8.48990	−	3.49850i	−0.270648	−	0.111528i
$985$	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
$990$	−0.156848	−	0.705464i	−0.00498495	−	0.0224211i
$991$	23.6878	−	13.6762i	0.752468	−	0.434438i	−0.0741168	−	0.997250i	$-0.523614\pi$
$991$	23.6878	−	13.6762i	0.752468	−	0.434438i	0.826585	+	0.562812i	$0.190280\pi$
$992$	42.4833	+	21.9515i	1.34885	+	0.696960i
$993$		−	20.7274i		−	0.657763i
$994$		0			0
$995$			0.0266385i			0.000844499i
$996$	2.68153	−	1.25439i	0.0849675	−	0.0397469i
$997$	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	$0.160119\pi$
$998$	−15.3090	+	3.40370i	−0.484599	+	0.107742i
$999$	−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.19.4		24
4.3	odd	2		588.2.o.e.19.7		24
7.2	even	3		588.2.b.c.391.12	yes	12
7.3	odd	6		588.2.o.e.31.7		24
7.4	even	3	inner	588.2.o.f.31.7		24
7.5	odd	6		588.2.b.d.391.12	yes	12
7.6	odd	2		588.2.o.e.19.4		24
21.2	odd	6		1764.2.b.l.1567.1		12
21.5	even	6		1764.2.b.m.1567.1		12
28.3	even	6	inner	588.2.o.f.31.4		24
28.11	odd	6		588.2.o.e.31.4		24
28.19	even	6		588.2.b.c.391.11	✓	12
28.23	odd	6		588.2.b.d.391.11	yes	12
28.27	even	2	inner	588.2.o.f.19.7		24
84.23	even	6		1764.2.b.m.1567.2		12
84.47	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	28.19	even	6
588.2.b.c.391.12	yes	12	7.2	even	3
588.2.b.d.391.11	yes	12	28.23	odd	6
588.2.b.d.391.12	yes	12	7.5	odd	6
588.2.o.e.19.4		24	7.6	odd	2
588.2.o.e.19.7		24	4.3	odd	2
588.2.o.e.31.4		24	28.11	odd	6
588.2.o.e.31.7		24	7.3	odd	6
588.2.o.f.19.4		24	1.1	even	1	trivial
588.2.o.f.19.7		24	28.27	even	2	inner
588.2.o.f.31.4		24	28.3	even	6	inner
588.2.o.f.31.7		24	7.4	even	3	inner
1764.2.b.l.1567.1		12	21.2	odd	6
1764.2.b.l.1567.2		12	84.47	odd	6
1764.2.b.m.1567.1		12	21.5	even	6
1764.2.b.m.1567.2		12	84.23	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+(-1.04209 + 0.956063i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.171888 - 1.99260i) 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} +(-0.176607 + 0.0392655i) q^{10} +(3.45938 - 1.99727i) q^{11} +(1.81159 - 0.847441i) q^{12} -0.891655i q^{13} +0.127929i q^{15} +(-3.94091 - 0.685007i) q^{16} +(5.04756 - 2.91421i) q^{17} +(-0.306932 - 1.38050i) 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} +(-1.07762 + 2.61510i) q^{24} +(-2.49182 - 4.31595i) q^{25} +(0.852478 + 0.929181i) q^{26} -1.00000 q^{27} +2.82968 q^{29} +(-0.122308 - 0.133313i) q^{30} +(4.22668 + 7.32083i) q^{31} +(4.76168 - 3.05392i) 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} +(-1.93824 - 8.71774i) q^{38} +(0.772196 - 0.445827i) q^{39} +(0.0478838 + 0.358656i) q^{40} +3.24650i q^{41} -0.881836i q^{43} +(-3.38514 - 7.23647i) q^{44} +(-0.110790 + 0.0639645i) q^{45} +(-9.11872 + 2.02739i) 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} +(-1.77671 - 0.153265i) q^{52} +(3.76727 + 6.52510i) q^{53} +(1.04209 - 0.956063i) q^{54} +0.511019 q^{55} -6.31490 q^{57} +(-2.94877 + 2.70535i) q^{58} +(-0.294409 - 0.509932i) q^{59} +(0.254911 + 0.0219894i) 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} +(-5.51449 + 1.22605i) q^{66} +(-5.50132 + 3.17619i) q^{67} +(-4.93924 - 10.5587i) q^{68} +6.60535i q^{69} -11.3856i q^{71} +(-2.80355 + 0.374300i) q^{72} +(-13.4354 + 7.75696i) q^{73} +(2.66390 + 11.9816i) 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} +(-0.392796 - 0.327970i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.10385 - 3.38313i) q^{82} +1.48021 q^{83} +0.745624 q^{85} +(0.843091 + 0.918950i) q^{86} +(1.41484 + 2.45058i) q^{87} +(10.4461 + 4.30461i) 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} +(-3.07348 - 13.8238i) q^{94} +(-0.699626 + 0.403929i) q^{95} +(5.02561 + 2.59677i) 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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Representations

Groups

Database

Properties

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