LMFDB - Embedded newform 540.2.be.a.11.37

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [540,2,Mod(11,540)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("540.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.be (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$72$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.37
Character	$\chi$	$=$	540.11
Dual form			540.2.be.a.491.37

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0683360 + 1.41256i) q^{2} +(1.72248 + 0.181830i) q^{3} +(-1.99066 + 0.193058i) q^{4} +(0.342020 - 0.939693i) q^{5} +(-0.139139 + 2.44553i) q^{6} +(1.67026 + 0.294513i) q^{7} +(-0.408739 - 2.79874i) q^{8} +(2.93388 + 0.626399i) q^{9} +(1.35075 + 0.418910i) q^{10} +(3.70237 - 1.34755i) q^{11} +(-3.46398 - 0.0294250i) q^{12} +(-0.0310200 + 0.0260289i) q^{13} +(-0.301878 + 2.37948i) q^{14} +(0.759988 - 1.55641i) q^{15} +(3.92546 - 0.768624i) q^{16} +(0.268012 - 0.154737i) q^{17} +(-0.684338 + 4.18709i) q^{18} +(-3.04167 - 1.75611i) q^{19} +(-0.499431 + 1.93664i) q^{20} +(2.82344 + 0.810997i) q^{21} +(2.15650 + 5.13773i) q^{22} +(0.533249 + 3.02420i) q^{23} +(-0.195150 - 4.89509i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(-0.0388872 - 0.0420390i) q^{26} +(4.93964 + 1.61243i) q^{27} +(-3.38179 - 0.263818i) q^{28} +(-4.25454 + 5.07037i) q^{29} +(2.25046 + 0.967170i) q^{30} +(-6.28502 + 1.10822i) q^{31} +(1.35398 + 5.49243i) q^{32} +(6.62228 - 1.64793i) q^{33} +(0.236890 + 0.368009i) q^{34} +(0.848015 - 1.46881i) q^{35} +(-5.96128 - 0.680541i) q^{36} +(2.75045 + 4.76392i) q^{37} +(2.27275 - 4.41655i) q^{38} +(-0.0581642 + 0.0391939i) q^{39} +(-2.76975 - 0.573135i) q^{40} +(7.39196 + 8.80939i) q^{41} +(-0.952640 + 4.04371i) q^{42} +(-4.16599 - 11.4460i) q^{43} +(-7.11000 + 3.39729i) q^{44} +(1.59207 - 2.54270i) q^{45} +(-4.23543 + 0.959908i) q^{46} +(0.963510 - 5.46434i) q^{47} +(6.90128 - 0.610172i) q^{48} +(-3.87480 - 1.41031i) q^{49} +(0.855629 - 1.12601i) q^{50} +(0.489780 - 0.217798i) q^{51} +(0.0567253 - 0.0578033i) q^{52} +2.69669i q^{53} +(-1.94010 + 7.08774i) q^{54} -3.93997i q^{55} +(0.141561 - 4.79501i) q^{56} +(-4.91990 - 3.57793i) q^{57} +(-7.45294 - 5.66331i) q^{58} +(0.0398558 + 0.0145063i) q^{59} +(-1.21240 + 3.24501i) q^{60} +(0.476490 - 2.70231i) q^{61} +(-1.99492 - 8.80224i) q^{62} +(4.71586 + 1.91031i) q^{63} +(-7.66586 + 2.28791i) q^{64} +(0.0138497 + 0.0380517i) q^{65} +(2.78034 + 9.24176i) q^{66} +(-8.20404 - 9.77720i) q^{67} +(-0.503647 + 0.359770i) q^{68} +(0.368618 + 5.30609i) q^{69} +(2.13273 + 1.09750i) q^{70} +(-0.821448 - 1.42279i) q^{71} +(0.553936 - 8.46718i) q^{72} +(-2.41382 + 4.18086i) q^{73} +(-6.54138 + 4.21073i) q^{74} +(-1.20262 - 1.24648i) q^{75} +(6.39395 + 2.90860i) q^{76} +(6.58080 - 1.16037i) q^{77} +(-0.0593385 - 0.0794822i) q^{78} +(2.72669 - 3.24955i) q^{79} +(0.620315 - 3.95161i) q^{80} +(8.21525 + 3.67555i) q^{81} +(-11.9387 + 11.0436i) q^{82} +(-0.385408 - 0.323396i) q^{83} +(-5.77709 - 1.06933i) q^{84} +(-0.0537394 - 0.304772i) q^{85} +(15.8834 - 6.66689i) q^{86} +(-8.25031 + 7.96000i) q^{87} +(-5.28474 - 9.81115i) q^{88} +(-7.73690 - 4.46690i) q^{89} +(3.70052 + 2.07513i) q^{90} +(-0.0594775 + 0.0343393i) q^{91} +(-1.64536 - 5.91721i) q^{92} +(-11.0273 + 0.766076i) q^{93} +(7.78455 + 0.987606i) q^{94} +(-2.69051 + 2.25761i) q^{95} +(1.33351 + 9.70679i) q^{96} +(0.108860 - 0.0396219i) q^{97} +(1.72737 - 5.56978i) q^{98} +(11.7064 - 1.63439i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) $ 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	0.0683360	+	1.41256i	0.0483208	+	0.998832i
$2$	0.0683360	+	1.41256i	0.0483208	+	0.998832i
$3$	1.72248	+	0.181830i	0.994474	+	0.104980i
$3$	1.72248	+	0.181830i	0.994474	+	0.104980i
$4$	−1.99066	+	0.193058i	−0.995330	+	0.0965288i
$5$	0.342020	−	0.939693i	0.152956	−	0.420243i
$5$	0.342020	−	0.939693i	0.152956	−	0.420243i
$6$	−0.139139	+	2.44553i	−0.0568034	+	0.998385i
$7$	1.67026	+	0.294513i	0.631300	+	0.111315i	0.480137	−	0.877194i	$-0.340587\pi$
$7$	1.67026	+	0.294513i	0.631300	+	0.111315i	0.151163	+	0.988509i	$0.451698\pi$
$8$	−0.408739	−	2.79874i	−0.144511	−	0.989503i
$9$	2.93388	+	0.626399i	0.977958	+	0.208800i
$10$	1.35075	+	0.418910i	0.427143	+	0.132471i
$11$	3.70237	−	1.34755i	1.11631	−	0.406302i	0.283003	−	0.959119i	$-0.408669\pi$
$11$	3.70237	−	1.34755i	1.11631	−	0.406302i	0.833303	+	0.552817i	$0.186447\pi$
$12$	−3.46398	−	0.0294250i	−0.999964	−	0.00849427i
$13$	−0.0310200	+	0.0260289i	−0.00860341	+	0.00721912i	−0.647079	−	0.762423i	$-0.724010\pi$
$13$	−0.0310200	+	0.0260289i	−0.00860341	+	0.00721912i	0.638476	+	0.769642i	$0.279565\pi$
$14$	−0.301878	+	2.37948i	−0.0806803	+	0.635942i
$15$	0.759988	−	1.55641i	0.196228	−	0.401864i
$16$	3.92546	−	0.768624i	0.981364	−	0.192156i
$17$	0.268012	−	0.154737i	0.0650024	−	0.0375291i	−0.467147	−	0.884180i	$-0.654718\pi$
$17$	0.268012	−	0.154737i	0.0650024	−	0.0375291i	0.532149	+	0.846651i	$0.321385\pi$
$18$	−0.684338	+	4.18709i	−0.161300	+	0.986905i
$19$	−3.04167	−	1.75611i	−0.697806	−	0.402879i	0.108724	−	0.994072i	$-0.465324\pi$
$19$	−3.04167	−	1.75611i	−0.697806	−	0.402879i	−0.806530	+	0.591194i	$0.798657\pi$
$20$	−0.499431	+	1.93664i	−0.111676	+	0.433046i
$21$	2.82344	+	0.810997i	0.616126	+	0.176974i
$22$	2.15650	+	5.13773i	0.459768	+	1.09537i
$23$	0.533249	+	3.02420i	0.111190	+	0.630590i	0.988566	+	0.150787i	$0.0481808\pi$
$23$	0.533249	+	3.02420i	0.111190	+	0.630590i	−0.877376	+	0.479803i	$0.840708\pi$
$24$	−0.195150	−	4.89509i	−0.0398347	−	0.999206i
$25$	−0.766044	−	0.642788i	−0.153209	−	0.128558i
$26$	−0.0388872	−	0.0420390i	−0.00762641	−	0.00824452i
$27$	4.93964	+	1.61243i	0.950635	+	0.310312i
$28$	−3.38179	−	0.263818i	−0.639097	−	0.0498568i
$29$	−4.25454	+	5.07037i	−0.790049	+	0.941543i	−0.999341	−	0.0363099i	$-0.988440\pi$
$29$	−4.25454	+	5.07037i	−0.790049	+	0.941543i	0.209292	+	0.977853i	$0.432884\pi$
$30$	2.25046	+	0.967170i	0.410876	+	0.176580i
$31$	−6.28502	+	1.10822i	−1.12882	+	0.199042i	−0.706711	−	0.707502i	$-0.749822\pi$
$31$	−6.28502	+	1.10822i	−1.12882	+	0.199042i	−0.422111	+	0.906544i	$0.638711\pi$
$32$	1.35398	+	5.49243i	0.239352	+	0.970933i
$33$	6.62228	−	1.64793i	1.15279	−	0.286867i
$34$	0.236890	+	0.368009i	0.0406263	+	0.0631130i
$35$	0.848015	−	1.46881i	0.143341	−	0.248273i
$36$	−5.96128	−	0.680541i	−0.993547	−	0.113423i
$37$	2.75045	+	4.76392i	0.452172	+	0.783184i	0.998521	−	0.0543733i	$-0.0173161\pi$
$37$	2.75045	+	4.76392i	0.452172	+	0.783184i	−0.546349	+	0.837558i	$0.683983\pi$
$38$	2.27275	−	4.41655i	0.368689	−	0.716458i
$39$	−0.0581642	+	0.0391939i	−0.00931373	+	0.00627604i
$40$	−2.76975	−	0.573135i	−0.437936	−	0.0906206i
$41$	7.39196	+	8.80939i	1.15443	+	1.37580i	0.914291	+	0.405057i	$0.132748\pi$
$41$	7.39196	+	8.80939i	1.15443	+	1.37580i	0.240138	+	0.970739i	$0.422807\pi$
$42$	−0.952640	+	4.04371i	−0.146996	+	0.623958i
$43$	−4.16599	−	11.4460i	−0.635308	−	1.74549i	−0.665986	−	0.745965i	$-0.731989\pi$
$43$	−4.16599	−	11.4460i	−0.635308	−	1.74549i	0.0306778	−	0.999529i	$-0.490233\pi$
$44$	−7.11000	+	3.39729i	−1.07187	+	0.512160i
$45$	1.59207	−	2.54270i	0.237331	−	0.379043i
$46$	−4.23543	+	0.959908i	−0.624481	+	0.141531i
$47$	0.963510	−	5.46434i	0.140542	−	0.797055i	−0.830296	−	0.557322i	$-0.811829\pi$
$47$	0.963510	−	5.46434i	0.140542	−	0.797055i	0.970839	−	0.239733i	$-0.0770600\pi$
$48$	6.90128	−	0.610172i	0.996114	−	0.0880707i
$49$	−3.87480	−	1.41031i	−0.553544	−	0.201473i
$50$	0.855629	−	1.12601i	0.121004	−	0.159242i
$51$	0.489780	−	0.217798i	0.0685830	−	0.0304978i
$52$	0.0567253	−	0.0578033i	0.00786638	−	0.00801588i
$53$			2.69669i			0.370419i	0.982699	+	0.185209i	$0.0592963\pi$
$53$			2.69669i			0.370419i	−0.982699	+	0.185209i	$0.940704\pi$
$54$	−1.94010	+	7.08774i	−0.264014	+	0.964519i
$55$		−	3.93997i		−	0.531266i
$56$	0.141561	−	4.79501i	0.0189169	−	0.640760i
$57$	−4.91990	−	3.57793i	−0.651656	−	0.473908i
$58$	−7.45294	−	5.66331i	−0.978619	−	0.743630i
$59$	0.0398558	+	0.0145063i	0.00518879	+	0.00188856i	0.344613	−	0.938745i	$-0.388010\pi$
$59$	0.0398558	+	0.0145063i	0.00518879	+	0.00188856i	−0.339424	+	0.940633i	$0.610232\pi$
$60$	−1.21240	+	3.24501i	−0.156520	+	0.418929i
$61$	0.476490	−	2.70231i	0.0610083	−	0.345995i	−0.938990	−	0.343946i	$-0.888236\pi$
$61$	0.476490	−	2.70231i	0.0610083	−	0.345995i	0.999998	−	0.00204977i	$-0.000652461\pi$
$62$	−1.99492	−	8.80224i	−0.253355	−	1.11789i
$63$	4.71586	+	1.91031i	0.594143	+	0.240677i
$64$	−7.66586	+	2.28791i	−0.958233	+	0.285989i
$65$	0.0138497	+	0.0380517i	0.00171784	+	0.00471973i
$66$	2.78034	+	9.24176i	0.342236	+	1.13758i
$67$	−8.20404	−	9.77720i	−1.00228	−	1.19447i	−0.980862	−	0.194704i	$-0.937625\pi$
$67$	−8.20404	−	9.77720i	−1.00228	−	1.19447i	−0.0214212	−	0.999771i	$-0.506819\pi$
$68$	−0.503647	+	0.359770i	−0.0610762	+	0.0436285i
$69$	0.368618	+	5.30609i	0.0443764	+	0.638778i
$70$	2.13273	+	1.09750i	0.254910	+	0.131177i
$71$	−0.821448	−	1.42279i	−0.0974879	−	0.168854i	0.813156	−	0.582045i	$-0.197747\pi$
$71$	−0.821448	−	1.42279i	−0.0974879	−	0.168854i	−0.910644	+	0.413191i	$0.864414\pi$
$72$	0.553936	−	8.46718i	0.0652819	−	0.997867i
$73$	−2.41382	+	4.18086i	−0.282517	+	0.489333i	−0.972004	−	0.234965i	$-0.924503\pi$
$73$	−2.41382	+	4.18086i	−0.282517	+	0.489333i	0.689487	+	0.724298i	$0.257836\pi$
$74$	−6.54138	+	4.21073i	−0.760420	+	0.489488i
$75$	−1.20262	−	1.24648i	−0.138866	−	0.143931i
$76$	6.39395	+	2.90860i	0.733437	+	0.333639i
$77$	6.58080	−	1.16037i	0.749951	−	0.132237i
$78$	−0.0593385	−	0.0794822i	−0.00671876	−	0.00899959i
$79$	2.72669	−	3.24955i	0.306777	−	0.365603i	−0.590525	−	0.807019i	$-0.701079\pi$
$79$	2.72669	−	3.24955i	0.306777	−	0.365603i	0.897302	+	0.441416i	$0.145524\pi$
$80$	0.620315	−	3.95161i	0.0693534	−	0.441803i
$81$	8.21525	+	3.67555i	0.912805	+	0.408395i
$82$	−11.9387	+	11.0436i	−1.31841	+	1.21956i
$83$	−0.385408	−	0.323396i	−0.0423041	−	0.0354973i	0.621390	−	0.783501i	$-0.286568\pi$
$83$	−0.385408	−	0.323396i	−0.0423041	−	0.0354973i	−0.663695	+	0.748004i	$0.731013\pi$
$84$	−5.77709	−	1.06933i	−0.630332	−	0.116674i
$85$	−0.0537394	−	0.304772i	−0.00582886	−	0.0330571i
$86$	15.8834	−	6.66689i	1.71276	−	0.718909i
$87$	−8.25031	+	7.96000i	−0.884526	+	0.853401i
$88$	−5.28474	−	9.81115i	−0.563356	−	1.04587i
$89$	−7.73690	−	4.46690i	−0.820110	−	0.473491i	0.0303445	−	0.999539i	$-0.490340\pi$
$89$	−7.73690	−	4.46690i	−0.820110	−	0.473491i	−0.850454	+	0.526049i	$0.823673\pi$
$90$	3.70052	+	2.07513i	0.390069	+	0.218738i
$91$	−0.0594775	+	0.0343393i	−0.00623493	+	0.00359974i
$92$	−1.64536	−	5.91721i	−0.171541	−	0.616912i
$93$	−11.0273	+	0.766076i	−1.14348	+	0.0794384i
$94$	7.78455	+	0.987606i	0.802915	+	0.101864i
$95$	−2.69051	+	2.25761i	−0.276041	+	0.231626i
$96$	1.33351	+	9.70679i	0.136101	+	0.990695i
$97$	0.108860	−	0.0396219i	0.0110531	−	0.00402299i	−0.336488	−	0.941688i	$-0.609239\pi$
$97$	0.108860	−	0.0396219i	0.0110531	−	0.00402299i	0.347541	+	0.937665i	$0.387017\pi$
$98$	1.72737	−	5.56978i	0.174490	−	0.562632i
$99$	11.7064	−	1.63439i	1.17654	−	0.164262i
$100$	1.64903	+	1.13168i	0.164903	+	0.113168i
$101$	7.99682	+	1.41006i	0.795713	+	0.140306i	0.556703	−	0.830711i	$-0.312066\pi$
$101$	7.99682	+	1.41006i	0.795713	+	0.140306i	0.239010	+	0.971017i	$0.423177\pi$
$102$	0.341123	+	0.676962i	0.0337762	+	0.0670292i
$103$	−4.15914	+	11.4271i	−0.409812	+	1.12595i	0.547478	+	0.836820i	$0.315588\pi$
$103$	−4.15914	+	11.4271i	−0.409812	+	1.12595i	−0.957290	+	0.289130i	$0.906634\pi$
$104$	0.0855272	+	0.0761779i	0.00838663	+	0.00746986i
$105$	1.72776	−	2.37579i	0.168612	−	0.231854i
$106$	−3.80924	+	0.184281i	−0.369986	+	0.0178989i
$107$	−4.44522			−0.429736			−0.214868	−	0.976643i	$-0.568932\pi$
$107$	−4.44522			−0.429736			−0.214868	+	0.976643i	$0.568932\pi$
$108$	−10.1444	−	2.25616i	−0.976150	−	0.217099i
$109$	−14.9179			−1.42887			−0.714436	−	0.699700i	$-0.753317\pi$
$109$	−14.9179			−1.42887			−0.714436	+	0.699700i	$0.753317\pi$
$110$	5.56546	−	0.269242i	0.530646	−	0.0256712i
$111$	3.87137	+	8.70588i	0.367455	+	0.826326i
$112$	6.78292	−	0.127708i	0.640926	−	0.0120673i
$113$	1.68290	−	4.62372i	0.158314	−	0.434963i	−0.835023	−	0.550216i	$-0.814546\pi$
$113$	1.68290	−	4.62372i	0.158314	−	0.434963i	0.993336	+	0.115253i	$0.0367677\pi$
$114$	4.71784	−	7.19416i	0.441866	−	0.673794i
$115$	3.02420	+	0.533249i	0.282008	+	0.0497257i
$116$	7.49048	−	10.9147i	0.695473	−	1.01341i
$117$	−0.107313	+	0.0569346i	−0.00992112	+	0.00526361i
$118$	−0.0177675	+	0.0572901i	−0.00163563	+	0.00527398i
$119$	0.493222	−	0.179518i	0.0452136	−	0.0164564i
$120$	−4.66663	−	1.49084i	−0.426003	−	0.136094i
$121$	3.46513	−	2.90759i	0.315012	−	0.264326i
$122$	3.84974	+	0.488407i	0.348539	+	0.0442183i
$123$	11.1307	+	16.5181i	1.00362	+	1.48939i
$124$	12.2974	−	3.41946i	1.10434	−	0.307076i
$125$	−0.866025	+	0.500000i	−0.0774597	+	0.0447214i
$126$	−2.37617	+	6.79199i	−0.211686	+	0.605079i
$127$	−6.55553	−	3.78484i	−0.581709	−	0.335850i	0.180103	−	0.983648i	$-0.442357\pi$
$127$	−6.55553	−	3.78484i	−0.581709	−	0.335850i	−0.761812	+	0.647798i	$0.775690\pi$
$128$	−3.75567	−	10.6722i	−0.331957	−	0.943294i
$129$	−5.09461	−	20.4730i	−0.448556	−	1.80254i
$130$	−0.0528039	+	0.0221638i	−0.00463121	+	0.00194390i
$131$	−1.20458	−	6.83151i	−0.105245	−	0.596872i	−0.991122	−	0.132953i	$-0.957554\pi$
$131$	−1.20458	−	6.83151i	−0.105245	−	0.596872i	0.885878	−	0.463919i	$-0.153557\pi$
$132$	−12.8646	+	4.55894i	−1.11972	+	0.396805i
$133$	−4.56319	−	3.82897i	−0.395679	−	0.332014i
$134$	13.2503	−	12.2568i	1.14465	−	1.05883i
$135$	3.20464	−	4.09026i	0.275812	−	0.352034i
$136$	−0.542614	−	0.686847i	−0.0465288	−	0.0588967i
$137$	12.6884	−	15.1214i	1.08404	−	1.29191i	0.130234	−	0.991483i	$-0.458427\pi$
$137$	12.6884	−	15.1214i	1.08404	−	1.29191i	0.953805	−	0.300425i	$-0.0971286\pi$
$138$	−7.46999	+	0.883292i	−0.635888	+	0.0751908i
$139$	17.2744	−	3.04595i	1.46520	−	0.258354i	0.616551	−	0.787315i	$-0.288529\pi$
$139$	17.2744	−	3.04595i	1.46520	−	0.258354i	0.848646	+	0.528961i	$0.177418\pi$
$140$	−1.40455	+	3.08761i	−0.118706	+	0.260951i
$141$	2.65321	−	9.23701i	0.223441	−	0.777897i
$142$	1.95364	−	1.25757i	0.163946	−	0.105533i
$143$	−0.0797722	+	0.138170i	−0.00667089	+	0.0115543i
$144$	11.9983	+	0.203855i	0.999856	+	0.0169879i
$145$	3.30945	+	5.73213i	0.274835	+	0.476027i
$146$	−6.07068	−	3.12397i	−0.502413	−	0.258542i
$147$	−6.41784	−	3.13379i	−0.529334	−	0.258471i
$148$	−6.39493	−	8.95236i	−0.525660	−	0.735879i
$149$	3.78687	+	4.51302i	0.310233	+	0.369721i	0.898521	−	0.438930i	$-0.144643\pi$
$149$	3.78687	+	4.51302i	0.310233	+	0.369721i	−0.588289	+	0.808651i	$0.700198\pi$
$150$	1.67855	−	1.78395i	0.137053	−	0.145659i
$151$	5.86373	+	16.1105i	0.477184	+	1.31105i	0.911874	+	0.410471i	$0.134636\pi$
$151$	5.86373	+	16.1105i	0.477184	+	1.31105i	−0.434690	+	0.900580i	$0.643142\pi$
$152$	−3.67163	+	9.23061i	−0.297809	+	0.748702i
$153$	0.883239	−	0.286096i	0.0714057	−	0.0231295i
$154$	2.08880	+	9.21649i	0.168320	+	0.742686i
$155$	−1.10822	+	6.28502i	−0.0890142	+	0.504825i
$156$	0.108219	−	0.0892507i	0.00866442	−	0.00714578i
$157$	−21.7868	−	7.92976i	−1.73878	−	0.632864i	−0.739587	−	0.673062i	$-0.764979\pi$
$157$	−21.7868	−	7.92976i	−1.73878	−	0.632864i	−0.999192	+	0.0401980i	$0.987201\pi$
$158$	4.77652	+	3.62956i	0.379999	+	0.288753i
$159$	−0.490340	+	4.64499i	−0.0388865	+	0.368372i
$160$	5.62428	+	0.606197i	0.444638	+	0.0479241i
$161$			5.20827i			0.410469i
$162$	−4.63055	+	11.8557i	−0.363810	+	0.931473i
$163$		−	17.4150i		−	1.36405i	−0.731330	−	0.682024i	$-0.761100\pi$
$163$		−	17.4150i		−	1.36405i	0.731330	−	0.682024i	$-0.238900\pi$
$164$	−16.4156	−	16.1094i	−1.28184	−	1.25794i
$165$	0.716408	−	6.78653i	0.0557723	−	0.528331i
$166$	0.430480	−	0.566513i	0.0334117	−	0.0439699i
$167$	−14.1027	−	5.13295i	−1.09130	−	0.397200i	−0.267196	−	0.963642i	$-0.586097\pi$
$167$	−14.1027	−	5.13295i	−1.09130	−	0.397200i	−0.824101	+	0.566442i	$0.808319\pi$
$168$	1.11571	−	8.23357i	0.0860793	−	0.635234i
$169$	−2.25714	+	12.8009i	−0.173626	+	0.984684i
$170$	0.426836	−	0.0967371i	0.0327368	−	0.00741940i
$171$	−7.82385	−	7.05749i	−0.598304	−	0.539700i
$172$	10.5028	+	21.9808i	0.800831	+	1.67602i
$173$	8.12598	+	22.3260i	0.617807	+	1.69741i	0.712291	+	0.701884i	$0.247658\pi$
$173$	8.12598	+	22.3260i	0.617807	+	1.69741i	−0.0944841	+	0.995526i	$0.530120\pi$
$174$	−11.8078	−	11.1101i	−0.895146	−	0.842256i
$175$	−1.09019	−	1.29923i	−0.0824104	−	0.0982129i
$176$	13.4977	−	8.13548i	1.01743	−	0.613235i
$177$	0.0660132	+	0.0322339i	0.00496185	+	0.00242285i
$178$	5.78107	−	11.2341i	0.433309	−	0.842031i
$179$	10.2937	+	17.8292i	0.769386	+	1.33262i	0.937896	+	0.346915i	$0.112771\pi$
$179$	10.2937	+	17.8292i	0.769386	+	1.33262i	−0.168511	+	0.985700i	$0.553896\pi$
$180$	−2.67838	+	5.36901i	−0.199634	+	0.400183i
$181$	2.09055	−	3.62093i	0.155389	−	0.269142i	−0.777812	−	0.628498i	$-0.783670\pi$
$181$	2.09055	−	3.62093i	0.155389	−	0.269142i	0.933201	+	0.359356i	$0.117004\pi$
$182$	−0.0525709	−	0.0816690i	−0.00389681	−	0.00605371i
$183$	1.31211	−	4.56803i	0.0969938	−	0.337679i
$184$	8.24599	−	2.72853i	0.607903	−	0.201150i
$185$	5.41733	−	0.955222i	0.398290	−	0.0702293i
$186$	−1.83569	−	15.5244i	−0.134600	−	1.13831i
$187$	0.783762	−	0.934051i	0.0573143	−	0.0683045i
$188$	−0.863090	+	11.0636i	−0.0629473	+	0.806899i
$189$	7.77563	+	4.14797i	0.565594	+	0.301720i
$190$	−3.37287	−	3.64624i	−0.244694	−	0.264526i
$191$	−15.0300	−	12.6117i	−1.08754	−	0.912551i	−0.0910109	−	0.995850i	$-0.529010\pi$
$191$	−15.0300	−	12.6117i	−1.08754	−	0.912551i	−0.996525	+	0.0832992i	$0.973454\pi$
$192$	−13.6203	+	2.54699i	−0.982961	+	0.183813i
$193$	−2.41826	−	13.7146i	−0.174070	−	0.987200i	−0.939212	−	0.343338i	$-0.888442\pi$
$193$	−2.41826	−	13.7146i	−0.174070	−	0.987200i	0.765142	−	0.643862i	$-0.222669\pi$
$194$	0.0634074	+	0.151064i	0.00455239	+	0.0108458i
$195$	0.0169368	+	0.0680616i	0.00121287	+	0.00487399i
$196$	7.98569	+	2.05940i	0.570407	+	0.147100i
$197$	−20.0196	−	11.5583i	−1.42633	−	0.823494i	−0.429505	−	0.903065i	$-0.641312\pi$
$197$	−20.0196	−	11.5583i	−1.42633	−	0.823494i	−0.996829	+	0.0795703i	$0.974645\pi$
$198$	3.10864	+	16.4243i	0.220922	+	1.16722i
$199$	12.9400	−	7.47093i	0.917294	−	0.529600i	0.0345234	−	0.999404i	$-0.489009\pi$
$199$	12.9400	−	7.47093i	0.917294	−	0.529600i	0.882771	+	0.469804i	$0.155675\pi$
$200$	−1.48588	+	2.40669i	−0.105068	+	0.170179i
$201$	−12.3535	−	18.3328i	−0.871349	−	1.29309i
$202$	−1.44532	+	11.3924i	−0.101692	+	0.801564i
$203$	−8.59949	+	7.21583i	−0.603566	+	0.506452i
$204$	−0.932939	+	0.528118i	−0.0653188	+	0.0369756i
$205$	10.8063	−	3.93318i	0.754746	−	0.274705i
$206$	−16.4258	−	5.09416i	−1.14444	−	0.354927i
$207$	−0.329872	+	9.20666i	−0.0229277	+	0.639907i
$208$	−0.101761	+	0.126018i	−0.00705588	+	0.00873778i
$209$	−13.6278	−	2.40295i	−0.942655	−	0.166215i
$210$	3.47402	+	2.27822i	0.239730	+	0.157212i
$211$	−5.39622	+	14.8260i	−0.371491	+	1.02066i	0.603295	+	0.797518i	$0.293854\pi$
$211$	−5.39622	+	14.8260i	−0.371491	+	1.02066i	−0.974785	+	0.223144i	$0.928368\pi$
$212$	−0.520616	−	5.36819i	−0.0357561	−	0.368689i
$213$	−1.15622	−	2.60009i	−0.0792230	−	0.178155i
$214$	−0.303768	−	6.27915i	−0.0207652	−	0.429234i
$215$	−12.1805			−0.830706
$216$	2.49373	−	14.4838i	0.169677	−	0.985500i
$217$	−10.8240			−0.734783
$218$	−1.01943	−	21.0724i	−0.0690443	−	1.42720i
$219$	−4.91797	+	6.76255i	−0.332326	+	0.456971i
$220$	0.760642	+	7.84315i	0.0512825	+	0.528785i
$221$	−0.00428611	+	0.0117760i	−0.000288315	+	0.000792138i
$222$	−12.0330	+	6.06348i	−0.807605	+	0.406954i
$223$	0.791121	+	0.139496i	0.0529774	+	0.00934134i	0.200074	−	0.979781i	$-0.435882\pi$
$223$	0.791121	+	0.139496i	0.0529774	+	0.00934134i	−0.147097	+	0.989122i	$0.546993\pi$
$224$	0.643913	+	9.57256i	0.0430232	+	0.639594i
$225$	−1.84484	−	2.36571i	−0.122989	−	0.157714i
$226$	6.64629	+	2.06123i	0.442105	+	0.137111i
$227$	14.9564	−	5.44369i	0.992692	−	0.361310i	0.205930	−	0.978567i	$-0.433978\pi$
$227$	14.9564	−	5.44369i	0.992692	−	0.361310i	0.786762	+	0.617256i	$0.211756\pi$
$228$	10.4846	+	6.17261i	0.694359	+	0.408791i
$229$	−4.67362	+	3.92163i	−0.308841	+	0.259149i	−0.784013	−	0.620745i	$-0.786830\pi$
$229$	−4.67362	+	3.92163i	−0.308841	+	0.259149i	0.475172	+	0.879893i	$0.342386\pi$
$230$	−0.546585	+	4.30831i	−0.0360407	+	0.284082i
$231$	11.5463	−	0.802128i	0.759690	−	0.0527762i
$232$	15.9296	+	9.83489i	1.04583	+	0.645692i
$233$	−16.3175	+	9.42090i	−1.06899	+	0.617184i	−0.927906	−	0.372813i	$-0.878393\pi$
$233$	−16.3175	+	9.42090i	−1.06899	+	0.617184i	−0.141088	+	0.989997i	$0.545060\pi$
$234$	−0.0877570	−	0.147696i	−0.00573686	−	0.00965519i
$235$	−4.80526	−	2.77432i	−0.313460	−	0.180976i
$236$	−0.0821400	−	0.0211827i	−0.00534686	−	0.00137888i
$237$	5.28754	−	5.10149i	0.343463	−	0.331377i
$238$	0.287285	+	0.684439i	0.0186219	+	0.0443656i
$239$	1.78775	+	10.1388i	0.115640	+	0.655825i	0.986431	+	0.164173i	$0.0524957\pi$
$239$	1.78775	+	10.1388i	0.115640	+	0.655825i	−0.870792	+	0.491652i	$0.836393\pi$
$240$	1.78700	−	6.69377i	0.115351	−	0.432081i
$241$	18.1518	+	15.2312i	1.16926	+	0.981125i	0.999990	−	0.00444477i	$-0.00141482\pi$
$241$	18.1518	+	15.2312i	1.16926	+	0.981125i	0.169269	+	0.985570i	$0.445859\pi$
$242$	4.34394	+	4.69601i	0.279239	+	0.301871i
$243$	13.4823	+	7.82485i	0.864888	+	0.501964i
$244$	−0.426829	+	5.47137i	−0.0273249	+	0.350269i
$245$	−2.65052	+	3.15877i	−0.169336	+	0.201806i
$246$	−22.5722	+	16.8516i	−1.43915	+	1.07442i
$247$	0.140062	−	0.0246967i	0.00891194	−	0.00157141i
$248$	5.67055	+	17.1371i	0.360080	+	1.08821i
$249$	−0.605055	−	0.627122i	−0.0383438	−	0.0397423i
$250$	−0.765461	−	1.18915i	−0.0484120	−	0.0752082i
$251$	−1.94398	+	3.36707i	−0.122703	+	0.212528i	−0.920833	−	0.389958i	$-0.872490\pi$
$251$	−1.94398	+	3.36707i	−0.122703	+	0.212528i	0.798130	+	0.602486i	$0.205823\pi$
$252$	−9.75648	−	2.89235i	−0.614601	−	0.182201i
$253$	6.04955	+	10.4781i	0.380332	+	0.658754i
$254$	4.89833	−	9.51873i	0.307349	−	0.597258i
$255$	−0.0371484	−	0.534734i	−0.00232632	−	0.0334864i
$256$	14.8184	−	6.03440i	0.926152	−	0.377150i
$257$	9.43683	+	11.2464i	0.588654	+	0.701530i	0.975347	−	0.220678i	$-0.0708271\pi$
$257$	9.43683	+	11.2464i	0.588654	+	0.701530i	−0.386693	+	0.922208i	$0.626383\pi$
$258$	28.5712	−	8.59549i	1.77876	−	0.535132i
$259$	3.19095	+	8.76705i	0.198276	+	0.544758i
$260$	−0.0349162	−	0.0730742i	−0.00216541	−	0.00453187i
$261$	−15.6584	+	12.2108i	−0.969229	+	0.755828i
$262$	9.56761	−	2.16838i	0.591089	−	0.133963i
$263$	−5.12659	+	29.0743i	−0.316119	+	1.79280i	0.249754	+	0.968309i	$0.419650\pi$
$263$	−5.12659	+	29.0743i	−0.316119	+	1.79280i	−0.565874	+	0.824492i	$0.691461\pi$
$264$	−7.31890	−	17.8604i	−0.450447	−	1.09923i
$265$	2.53406	+	0.922322i	0.155666	+	0.0566578i
$266$	5.09683	−	6.70744i	0.312506	−	0.411260i
$267$	−12.5144	−	9.10095i	−0.765871	−	0.556969i
$268$	18.2190	+	17.8792i	1.11290	+	1.09215i
$269$			10.3586i			0.631573i	0.948830	+	0.315786i	$0.102268\pi$
$269$			10.3586i			0.631573i	−0.948830	+	0.315786i	$0.897732\pi$
$270$	5.99674	+	4.24724i	0.364950	+	0.258479i
$271$		−	5.35053i		−	0.325022i	−0.986707	−	0.162511i	$-0.948041\pi$
$271$		−	5.35053i		−	0.325022i	0.986707	−	0.162511i	$-0.0519592\pi$
$272$	0.933134	−	0.813412i	0.0565796	−	0.0493203i
$273$	−0.108693	+	0.0483340i	−0.00657838	+	0.00292531i
$274$	22.2270	+	16.8898i	1.34278	+	1.02035i
$275$	−3.70237	−	1.34755i	−0.223261	−	0.0812604i
$276$	−1.75817	−	10.4915i	−0.105830	−	0.631512i
$277$	0.697124	−	3.95359i	0.0418861	−	0.237548i	−0.956676	−	0.291155i	$-0.905961\pi$
$277$	0.697124	−	3.95359i	0.0418861	−	0.237548i	0.998562	+	0.0536066i	$0.0170717\pi$
$278$	5.48305	+	24.1930i	0.328851	+	1.45100i
$279$	−19.1336	−	0.685553i	−1.14550	−	0.0410430i
$280$	−4.45742	−	1.77301i	−0.266382	−	0.105958i
$281$	2.96056	+	8.13408i	0.176612	+	0.485238i	0.996138	−	0.0878045i	$-0.0279851\pi$
$281$	2.96056	+	8.13408i	0.176612	+	0.485238i	−0.819525	+	0.573043i	$0.805763\pi$
$282$	13.2292	+	3.11660i	0.787785	+	0.185591i
$283$	−7.15049	−	8.52163i	−0.425053	−	0.506558i	0.510435	−	0.859916i	$-0.329484\pi$
$283$	−7.15049	−	8.52163i	−0.425053	−	0.506558i	−0.935488	+	0.353358i	$0.885040\pi$
$284$	1.90990	+	2.67370i	0.113332	+	0.158655i
$285$	−5.04485	+	3.39947i	−0.298831	+	0.201367i
$286$	−0.200624	−	0.103241i	−0.0118632	−	0.00610478i
$287$	9.75204	+	16.8910i	0.575645	+	0.997046i
$288$	0.531955	+	16.9622i	0.0313458	+	0.999509i
$289$	−8.45211	+	14.6395i	−0.497183	+	0.861146i
$290$	−7.87083	+	5.06651i	−0.462191	+	0.297516i
$291$	0.194714	−	0.0484538i	0.0114143	−	0.00284041i
$292$	3.99795	−	8.78869i	0.233963	−	0.514319i
$293$	19.4607	−	3.43144i	1.13691	−	0.200467i	0.426654	−	0.904415i	$-0.359692\pi$
$293$	19.4607	−	3.43144i	1.13691	−	0.200467i	0.710252	+	0.703948i	$0.248581\pi$
$294$	3.98811	−	9.27974i	0.232591	−	0.541205i
$295$	0.0272630	−	0.0324908i	0.00158731	−	0.00189169i
$296$	12.2088	−	9.64500i	0.709619	−	0.560604i
$297$	20.4612	−	0.686625i	1.18728	−	0.0398420i
$298$	−6.11614	+	5.65759i	−0.354298	+	0.327735i
$299$	−0.0952581	−	0.0799310i	−0.00550892	−	0.00462253i
$300$	2.63465	+	2.24914i	0.152111	+	0.129854i
$301$	−3.58732	−	20.3447i	−0.206770	−	1.17265i
$302$	−22.3563	+	9.38380i	−1.28646	+	0.539977i
$303$	13.5180	+	3.88286i	0.776587	+	0.223064i
$304$	−13.2897	−	4.55563i	−0.762218	−	0.261283i
$305$	−2.37637	−	1.37200i	−0.136071	−	0.0785604i
$306$	0.464485	+	1.22808i	0.0265528	+	0.0702046i
$307$	−1.47047	+	0.848979i	−0.0839244	+	0.0484538i	−0.541375	−	0.840781i	$-0.682096\pi$
$307$	−1.47047	+	0.848979i	−0.0839244	+	0.0484538i	0.457451	+	0.889235i	$0.348763\pi$
$308$	−12.8761	+	3.58038i	−0.733685	+	0.204011i
$309$	−9.24184	+	18.9268i	−0.525750	+	1.07671i
$310$	−8.95371	−	1.13593i	−0.508536	−	0.0645167i
$311$	13.7746	−	11.5582i	0.781083	−	0.655407i	−0.162438	−	0.986719i	$-0.551936\pi$
$311$	13.7746	−	11.5582i	0.781083	−	0.655407i	0.943521	+	0.331312i	$0.107491\pi$
$312$	0.133467	+	0.146766i	0.00755610	+	0.00830901i
$313$	−31.0689	+	11.3081i	−1.75612	+	0.639174i	−0.999886	−	0.0151302i	$-0.995184\pi$
$313$	−31.0689	+	11.3081i	−1.75612	+	0.639174i	−0.756231	+	0.654304i	$0.772961\pi$
$314$	9.71245	−	31.3171i	0.548105	−	1.76733i
$315$	3.40803	−	3.77810i	0.192021	−	0.212872i
$316$	−4.80057	+	6.99516i	−0.270053	+	0.393508i
$317$	2.22767	+	0.392799i	0.125119	+	0.0220618i	0.235857	−	0.971788i	$-0.424210\pi$
$317$	2.22767	+	0.392799i	0.125119	+	0.0220618i	−0.110738	+	0.993850i	$0.535321\pi$
$318$	−6.59485	−	0.375216i	−0.369821	−	0.0210410i
$319$	−8.91929	+	24.5056i	−0.499385	+	1.37205i
$320$	−0.471949	+	7.98607i	−0.0263828	+	0.446435i
$321$	−7.65680	−	0.808277i	−0.427361	−	0.0451136i
$322$	−7.35700	+	0.355912i	−0.409989	+	0.0198342i
$323$	−1.08694			−0.0604787
$324$	−17.0634	−	5.73076i	−0.947965	−	0.318376i
$325$	0.0404938			0.00224619
$326$	24.5998	−	1.19007i	1.36245	−	0.0659119i
$327$	−25.6957	−	2.71252i	−1.42098	−	0.150003i
$328$	21.6338	−	24.2889i	1.19453	−	1.34113i
$329$	3.21863	−	8.84312i	0.177449	−	0.487537i
$330$	9.63535	+	0.548206i	0.530408	+	0.0301777i
$331$	34.3156	+	6.05077i	1.88616	+	0.332580i	0.993091	−	0.117345i	$-0.0374384\pi$
$331$	34.3156	+	6.05077i	1.88616	+	0.332580i	0.893066	+	0.449926i	$0.148550\pi$
$332$	0.829651	+	0.569366i	0.0455330	+	0.0312480i
$333$	5.08537	+	15.6996i	0.278677	+	0.860335i
$334$	6.28689	−	20.2717i	0.344004	−	1.10922i
$335$	−11.9935	+	4.36528i	−0.655275	+	0.238501i
$336$	11.7067	+	1.01337i	0.638651	+	0.0552837i
$337$	−0.733042	+	0.615095i	−0.0399313	+	0.0335064i	−0.662535	−	0.749031i	$-0.730519\pi$
$337$	−0.733042	+	0.615095i	−0.0399313	+	0.0335064i	0.622604	+	0.782537i	$0.286075\pi$
$338$	−18.2363	−	2.31359i	−0.991923	−	0.125843i
$339$	3.73949	−	7.65826i	0.203101	−	0.415940i
$340$	0.165815	+	0.596322i	0.00899260	+	0.0323401i
$341$	−21.7761	+	12.5724i	−1.17924	+	0.680834i
$342$	9.43449	−	11.5339i	0.510159	−	0.623684i
$343$	−16.3382	−	9.43288i	−0.882181	−	0.509328i
$344$	−30.3315	+	16.3379i	−1.63536	+	0.880883i
$345$	5.11217	+	1.46840i	0.275230	+	0.0790561i
$346$	−30.9815	+	13.0041i	−1.66557	+	0.699106i
$347$	−2.42709	−	13.7647i	−0.130293	−	0.738927i	−0.978023	−	0.208499i	$-0.933142\pi$
$347$	−2.42709	−	13.7647i	−0.130293	−	0.738927i	0.847730	−	0.530428i	$-0.177969\pi$
$348$	14.8868	−	17.4384i	0.798018	−	0.934798i
$349$	18.1674	+	15.2442i	0.972477	+	0.816006i	0.982938	−	0.183940i	$-0.0588851\pi$
$349$	18.1674	+	15.2442i	0.972477	+	0.816006i	−0.0104600	+	0.999945i	$0.503330\pi$
$350$	1.76075	−	1.62874i	0.0941160	−	0.0870599i
$351$	−0.195198	+	0.0785559i	−0.0104189	+	0.00419300i
$352$	12.4142	+	18.5104i	0.661682	+	0.986608i
$353$	12.3562	−	14.7255i	0.657652	−	0.783759i	−0.329395	−	0.944192i	$-0.606845\pi$
$353$	12.3562	−	14.7255i	0.657652	−	0.783759i	0.987047	+	0.160433i	$0.0512892\pi$
$354$	−0.0410213	+	0.0954504i	−0.00218026	+	0.00507313i
$355$	−1.61794	+	0.285286i	−0.0858712	+	0.0151414i
$356$	16.2639	+	7.39842i	0.861986	+	0.392115i
$357$	0.882207	−	0.219534i	0.0466913	−	0.0116189i
$358$	−24.4814	+	15.7588i	−1.29388	+	0.832880i
$359$	−13.1519	+	22.7797i	−0.694128	+	1.20227i	0.276345	+	0.961058i	$0.410877\pi$
$359$	−13.1519	+	22.7797i	−0.694128	+	1.20227i	−0.970474	+	0.241207i	$0.922457\pi$
$360$	−7.76709	−	3.41648i	−0.409362	−	0.180064i
$361$	−3.33218	−	5.77150i	−0.175378	−	0.303763i
$362$	5.25765	+	2.70558i	0.276336	+	0.142202i
$363$	6.49730	−	4.37820i	0.341020	−	0.229796i
$364$	0.111770	−	0.0798405i	0.00585834	−	0.00418478i
$365$	3.10315	+	3.69819i	0.162426	+	0.193572i
$366$	6.54229	+	1.54127i	0.341971	+	0.0805635i
$367$	−4.94597	−	13.5889i	−0.258177	−	0.709336i	−0.999280	−	0.0379446i	$-0.987919\pi$
$367$	−4.94597	−	13.5889i	−0.258177	−	0.709336i	0.741102	−	0.671392i	$-0.234303\pi$
$368$	4.41772	+	11.4615i	0.230290	+	0.597473i
$369$	16.1689	+	30.4760i	0.841719	+	1.58652i
$370$	1.71951	+	7.58704i	0.0893930	+	0.394432i
$371$	−0.794209	+	4.50418i	−0.0412333	+	0.233845i
$372$	21.8038	−	3.65391i	1.13047	−	0.189446i
$373$	−15.7277	−	5.72440i	−0.814348	−	0.296398i	−0.0989293	−	0.995094i	$-0.531542\pi$
$373$	−15.7277	−	5.72440i	−0.814348	−	0.296398i	−0.715419	+	0.698696i	$0.753764\pi$
$374$	1.37296	+	1.04328i	0.0709942	+	0.0539468i
$375$	−1.58263	+	0.703770i	−0.0817265	+	0.0363425i
$376$	−15.6871	−	0.463122i	−0.808999	−	0.0238837i
$377$		−	0.268024i		−	0.0138039i
$378$	−5.32790	+	11.2670i	−0.274038	+	0.579512i
$379$		−	2.76886i		−	0.142227i	−0.997468	−	0.0711133i	$-0.977345\pi$
$379$		−	2.76886i		−	0.142227i	0.997468	−	0.0711133i	$-0.0226552\pi$
$380$	4.92005	−	5.01355i	0.252393	−	0.257190i
$381$	−10.6036	−	7.71130i	−0.543237	−	0.395062i
$382$	16.7877	−	22.0927i	0.858934	−	1.13036i
$383$	−19.8173	−	7.21291i	−1.01262	−	0.368563i	−0.218180	−	0.975909i	$-0.570012\pi$
$383$	−19.8173	−	7.21291i	−1.01262	−	0.368563i	−0.794438	+	0.607346i	$0.792234\pi$
$384$	−4.52854	−	19.0655i	−0.231096	−	0.972931i
$385$	1.16037	−	6.58080i	0.0591380	−	0.335389i
$386$	19.2075	−	4.35314i	0.977635	−	0.221569i
$387$	−5.05276	−	36.1906i	−0.256846	−	1.83967i
$388$	−0.209054	+	0.0998900i	−0.0106131	+	0.00507115i
$389$	−2.67451	−	7.34815i	−0.135603	−	0.372566i	0.853242	−	0.521515i	$-0.174633\pi$
$389$	−2.67451	−	7.34815i	−0.135603	−	0.372566i	−0.988845	+	0.148949i	$0.952411\pi$
$390$	−0.0949838	+	0.0285754i	−0.00480969	+	0.00144697i
$391$	0.610872	+	0.728009i	0.0308931	+	0.0368170i
$392$	−2.36331	+	11.4210i	−0.119365	+	0.576848i
$393$	−0.832687	−	11.9862i	−0.0420035	−	0.604622i
$394$	14.9587	−	29.0687i	0.753611	−	1.46446i
$395$	−2.12099	−	3.67367i	−0.106719	−	0.184842i
$396$	−22.9879	+	5.51352i	−1.15519	+	0.277065i
$397$	11.5728	−	20.0447i	0.580821	−	1.00601i	−0.414561	−	0.910022i	$-0.636065\pi$
$397$	11.5728	−	20.0447i	0.580821	−	1.00601i	0.995382	−	0.0959906i	$-0.0306019\pi$
$398$	11.4374	+	17.7681i	0.573306	+	0.890632i
$399$	−7.16378	−	7.42505i	−0.358638	−	0.371718i
$400$	−3.50114	−	1.93444i	−0.175057	−	0.0967218i
$401$	−18.8769	+	3.32851i	−0.942669	+	0.166218i	−0.623803	−	0.781582i	$-0.714413\pi$
$401$	−18.8769	+	3.32851i	−0.942669	+	0.166218i	−0.318866	+	0.947800i	$0.603302\pi$
$402$	25.0520	−	18.7029i	1.24948	−	0.932815i
$403$	0.166116	−	0.197969i	0.00827481	−	0.00986154i
$404$	−16.1912	−	1.26309i	−0.805541	−	0.0628413i
$405$	6.26367	−	6.46270i	0.311244	−	0.321134i
$406$	−10.7805	−	11.6542i	−0.535025	−	0.578389i
$407$	16.6028	+	13.9314i	0.822971	+	0.690554i
$408$	−0.809752	−	1.28174i	−0.0400887	−	0.0634558i
$409$	−0.636759	−	3.61124i	−0.0314857	−	0.178564i	0.965009	−	0.262215i	$-0.0844530\pi$
$409$	−0.636759	−	3.61124i	−0.0314857	−	0.178564i	−0.996495	+	0.0836509i	$0.973342\pi$
$410$	6.29432	+	14.9958i	0.310854	+	0.740590i
$411$	24.6050	−	23.7392i	1.21367	−	1.17097i
$412$	6.07334	−	23.5505i	0.299212	−	1.16025i
$413$	0.0622974	+	0.0359674i	0.00306546	+	0.00176984i
$414$	−13.0275	+	0.163181i	−0.640268	+	0.00801992i
$415$	−0.435710	+	0.251558i	−0.0213882	+	0.0123485i
$416$	−0.184962	−	0.135133i	−0.00906852	−	0.00662542i
$417$	30.3087	−	2.10557i	1.48422	−	0.103110i
$418$	2.46304	−	19.4143i	0.120471	−	0.949585i
$419$	7.27852	−	6.10740i	0.355579	−	0.298366i	−0.447447	−	0.894311i	$-0.647667\pi$
$419$	7.27852	−	6.10740i	0.355579	−	0.298366i	0.803026	+	0.595944i	$0.203222\pi$
$420$	−2.98072	+	5.06295i	−0.145444	+	0.247047i
$421$	−2.15780	+	0.785374i	−0.105165	+	0.0382768i	−0.394067	−	0.919082i	$-0.628932\pi$
$421$	−2.15780	+	0.785374i	−0.105165	+	0.0382768i	0.288902	+	0.957359i	$0.406710\pi$
$422$	−21.3114	−	6.60934i	−1.03742	−	0.321738i
$423$	6.24967	−	15.4281i	0.303869	−	0.750142i
$424$	7.54732	−	1.10224i	0.366530	−	0.0535296i
$425$	−0.304772	−	0.0537394i	−0.0147836	−	0.00260675i
$426$	3.59378	−	1.81091i	0.174119	−	0.0877390i
$427$	1.59173	−	4.37324i	0.0770291	−	0.211636i
$428$	8.84892	−	0.858183i	0.427729	−	0.0414819i
$429$	−0.162529	+	0.223489i	−0.00784700	+	0.0107902i
$430$	−0.832369	−	17.2058i	−0.0401404	−	0.829736i
$431$	−24.4860			−1.17945			−0.589725	−	0.807604i	$-0.700764\pi$
$431$	−24.4860			−1.17945			−0.589725	+	0.807604i	$0.700764\pi$
$432$	20.6297	+	2.53279i	0.992547	+	0.121859i
$433$	35.4340			1.70285			0.851424	−	0.524478i	$-0.175740\pi$
$433$	35.4340			1.70285			0.851424	+	0.524478i	$0.175740\pi$
$434$	−0.739670	−	15.2896i	−0.0355053	−	0.733924i
$435$	4.65818	+	10.4752i	0.223343	+	0.502249i
$436$	29.6964	−	2.88001i	1.42220	−	0.137927i
$437$	3.68886	−	10.1351i	0.176462	−	0.484826i
$438$	−9.88859	−	6.48481i	−0.472495	−	0.309856i
$439$	−8.99509	−	1.58608i	−0.429312	−	0.0756993i	−0.0451831	−	0.998979i	$-0.514387\pi$
$439$	−8.99509	−	1.58608i	−0.429312	−	0.0756993i	−0.384129	+	0.923279i	$0.625498\pi$
$440$	−11.0270	+	1.61042i	−0.525690	+	0.0767739i
$441$	−10.4848	−	6.56486i	−0.499275	−	0.312612i
$442$	−0.0169272	−	0.00524967i	−0.000805144	−	0.000249701i
$443$	19.8571	−	7.22741i	0.943441	−	0.343384i	0.175917	−	0.984405i	$-0.443711\pi$
$443$	19.8571	−	7.22741i	0.943441	−	0.343384i	0.767524	+	0.641020i	$0.221489\pi$
$444$	−9.38733	−	16.5831i	−0.445503	−	0.786997i
$445$	−6.84369	+	5.74254i	−0.324422	+	0.272222i
$446$	−0.142985	+	1.12704i	−0.00677052	+	0.0533669i
$447$	5.70221	+	8.46215i	0.269705	+	0.400246i
$448$	−13.4778	+	1.56372i	−0.636768	+	0.0738787i
$449$	25.5989	−	14.7795i	1.20808	−	0.697488i	0.245744	−	0.969335i	$-0.420968\pi$
$449$	25.5989	−	14.7795i	1.20808	−	0.697488i	0.962341	+	0.271847i	$0.0876344\pi$
$450$	3.21564	−	2.76761i	0.151587	−	0.130466i
$451$	39.2388	+	22.6545i	1.84768	+	1.06676i
$452$	−2.45743	+	9.52915i	−0.115588	+	0.448214i
$453$	7.17078	+	28.8162i	0.336913	+	1.35390i
$454$	8.71161	+	20.7549i	0.408856	+	0.974074i
$455$	0.0119259	+	0.0676353i	0.000559096	+	0.00317079i
$456$	−8.00272	+	15.2319i	−0.374762	+	0.713301i
$457$	−3.55243	−	2.98085i	−0.166176	−	0.139438i	0.555907	−	0.831244i	$-0.312371\pi$
$457$	−3.55243	−	2.98085i	−0.166176	−	0.139438i	−0.722083	+	0.691806i	$0.756815\pi$
$458$	−5.85892	−	6.33378i	−0.273769	−	0.295958i
$459$	1.57338	−	0.332194i	0.0734392	−	0.0155055i
$460$	−6.12311	−	0.477672i	−0.285491	−	0.0222716i
$461$	4.21239	−	5.02014i	0.196191	−	0.233811i	−0.658976	−	0.752164i	$-0.729010\pi$
$461$	4.21239	−	5.02014i	0.196191	−	0.233811i	0.855167	+	0.518353i	$0.173455\pi$
$462$	1.92208	+	16.2550i	0.0894234	+	0.756252i
$463$	8.77182	−	1.54671i	0.407661	−	0.0718816i	0.0339424	−	0.999424i	$-0.489194\pi$
$463$	8.77182	−	1.54671i	0.407661	−	0.0718816i	0.373718	+	0.927542i	$0.378083\pi$
$464$	−12.8038	+	23.1736i	−0.594402	+	1.07581i
$465$	−3.05169	+	10.6243i	−0.141519	+	0.492691i
$466$	−14.4227	−	22.4057i	−0.668118	−	1.03792i
$467$	7.39794	−	12.8136i	0.342336	−	0.592943i	−0.642530	−	0.766260i	$-0.722115\pi$
$467$	7.39794	−	12.8136i	0.342336	−	0.592943i	0.984866	+	0.173317i	$0.0554486\pi$
$468$	0.202633	−	0.134055i	0.00936670	−	0.00619670i
$469$	−10.8234	−	18.7467i	−0.499778	−	0.865642i
$470$	3.59052	−	6.97730i	0.165618	−	0.321839i
$471$	−36.0855	−	17.6204i	−1.66273	−	0.811903i
$472$	0.0243088	−	0.117475i	0.00111890	−	0.00540724i
$473$	−30.8480	−	36.7633i	−1.41839	−	1.69038i
$474$	7.56749	+	7.12037i	0.347586	+	0.327049i
$475$	1.20125	+	3.30040i	0.0551170	+	0.151433i
$476$	−0.947180	+	0.452580i	−0.0434139	+	0.0207440i
$477$	−1.68920	+	7.91175i	−0.0773433	+	0.362254i
$478$	−14.1995	+	3.21815i	−0.649471	+	0.147195i
$479$	4.24654	−	24.0834i	0.194030	−	1.10040i	−0.719764	−	0.694218i	$-0.755750\pi$
$479$	4.24654	−	24.0834i	0.194030	−	1.10040i	0.913794	−	0.406178i	$-0.133139\pi$
$480$	9.57749	+	2.06683i	0.437150	+	0.0943373i
$481$	−0.209319	−	0.0761858i	−0.00954412	−	0.00347377i
$482$	−20.2745	+	26.6814i	−0.923479	+	1.21530i
$483$	−0.947022	+	8.97113i	−0.0430910	+	0.408201i
$484$	−6.33656	+	6.45699i	−0.288025	+	0.293499i
$485$		−	0.115847i		−	0.00526033i
$486$	−10.1318	+	19.5793i	−0.459586	+	0.888133i
$487$			18.9687i			0.859552i	0.902935	+	0.429776i	$0.141408\pi$
$487$			18.9687i			0.859552i	−0.902935	+	0.429776i	$0.858592\pi$
$488$	−7.75782	−	0.229031i	−0.351180	−	0.0103677i
$489$	3.16658	−	29.9970i	0.143198	−	1.35651i
$490$	−4.64308	−	3.52817i	−0.209753	−	0.159386i
$491$	−11.1738	−	4.06691i	−0.504264	−	0.183537i	0.0773466	−	0.997004i	$-0.475355\pi$
$491$	−11.1738	−	4.06691i	−0.504264	−	0.183537i	−0.581611	+	0.813467i	$0.697577\pi$
$492$	−25.3464	−	30.7330i	−1.14270	−	1.38555i
$493$	−0.355696	+	2.01725i	−0.0160197	+	0.0908524i
$494$	0.0444569	+	0.196159i	0.00200021	+	0.00882559i
$495$	2.46800	−	11.5594i	0.110928	−	0.519556i
$496$	−23.8198	+	9.18108i	−1.06954	+	0.412243i
$497$	−0.953005	−	2.61836i	−0.0427481	−	0.117450i
$498$	0.844502	−	0.897533i	0.0378430	−	0.0402194i
$499$	−6.91262	−	8.23814i	−0.309452	−	0.368790i	0.588795	−	0.808283i	$-0.299603\pi$
$499$	−6.91262	−	8.23814i	−0.309452	−	0.368790i	−0.898246	+	0.439493i	$0.855158\pi$
$500$	1.62743	−	1.16252i	0.0727810	−	0.0519896i
$501$	−23.3582	−	11.4057i	−1.04357	−	0.509569i
$502$	−4.88904	−	2.51590i	−0.218209	−	0.112290i
$503$	17.0360	+	29.5072i	0.759596	+	1.31566i	0.943057	+	0.332632i	$0.107937\pi$
$503$	17.0360	+	29.5072i	0.759596	+	1.31566i	−0.183461	+	0.983027i	$0.558730\pi$
$504$	3.41891	−	13.9793i	0.152290	−	0.622687i
$505$	4.06009	−	7.03229i	0.180672	−	0.312933i
$506$	−14.3876	+	9.26139i	−0.639607	+	0.411719i
$507$	−6.21547	+	21.6389i	−0.276039	+	0.961015i
$508$	13.7805	+	6.26873i	0.611412	+	0.278130i
$509$	32.1048	−	5.66094i	1.42302	−	0.250917i	0.591452	−	0.806340i	$-0.298555\pi$
$509$	32.1048	−	5.66094i	1.42302	−	0.250917i	0.831568	+	0.555423i	$0.187444\pi$
$510$	0.752807	−	0.0890160i	0.0333348	−	0.00394169i
$511$	−5.26304	+	6.27225i	−0.232823	+	0.277468i
$512$	9.53660	+	20.5196i	0.421462	+	0.906846i
$513$	−12.1932	−	13.5790i	−0.538341	−	0.599528i
$514$	−15.2413	+	14.0986i	−0.672266	+	0.621864i
$515$	9.31549	+	7.81663i	0.410490	+	0.344442i
$516$	14.0941	+	39.7712i	0.620458	+	1.75083i
$517$	−3.79620	−	21.5293i	−0.166957	−	0.946859i
$518$	−12.1659	+	5.10651i	−0.534541	+	0.224367i
$519$	9.93730	+	39.9336i	0.436199	+	1.75289i
$520$	0.100836	−	0.0543149i	0.00442194	−	0.00238186i
$521$	−23.3900	−	13.5042i	−1.02473	−	0.591630i	−0.109261	−	0.994013i	$-0.534849\pi$
$521$	−23.3900	−	13.5042i	−1.02473	−	0.591630i	−0.915471	+	0.402383i	$0.868182\pi$
$522$	−18.3185	−	21.2840i	−0.801779	−	0.931574i
$523$	9.85192	−	5.68801i	0.430794	−	0.248719i	−0.268891	−	0.963171i	$-0.586657\pi$
$523$	9.85192	−	5.68801i	0.430794	−	0.248719i	0.699685	+	0.714451i	$0.253324\pi$
$524$	3.71678	+	13.3667i	0.162368	+	0.583925i
$525$	−1.64159	−	2.43614i	−0.0716447	−	0.106322i
$526$	−41.4196	−	5.25480i	−1.80598	−	0.229120i
$527$	−1.51298	+	1.26954i	−0.0659063	+	0.0553019i
$528$	24.7288	−	11.5589i	1.07618	−	0.503037i
$529$	12.7515	−	4.64116i	0.554412	−	0.201790i
$530$	−1.12967	+	3.64254i	−0.0490697	+	0.158222i
$531$	0.107845	+	0.0675254i	0.00468009	+	0.00293035i
$532$	9.82297	+	6.74122i	0.425880	+	0.292269i
$533$	−0.458597	−	0.0808631i	−0.0198641	−	0.00350257i
$534$	12.0005	−	18.2993i	0.519311	−	0.791890i
$535$	−1.52035	+	4.17714i	−0.0657307	+	0.180594i
$536$	−24.0105	+	26.9573i	−1.03710	+	1.16438i
$537$	14.4888	+	32.5821i	0.625237	+	1.40602i
$538$	−14.6321	+	0.707863i	−0.630835	+	0.0305181i
$539$	−16.2464			−0.699783
$540$	−5.58970	+	8.76101i	−0.240542	+	0.377014i
$541$	40.7140			1.75043			0.875215	−	0.483735i	$-0.160720\pi$
$541$	40.7140			1.75043			0.875215	+	0.483735i	$0.160720\pi$
$542$	7.55795	−	0.365634i	0.324642	−	0.0157053i
$543$	4.25932	−	5.85686i	0.182785	−	0.251342i
$544$	1.21276	+	1.26252i	0.0519967	+	0.0541303i
$545$	−5.10221	+	14.0182i	−0.218555	+	0.600474i
$546$	−0.0757024	−	0.150232i	−0.00323976	−	0.00642934i
$547$	28.3382	+	4.99679i	1.21165	+	0.213647i	0.742729	−	0.669592i	$-0.233531\pi$
$547$	28.3382	+	4.99679i	1.21165	+	0.213647i	0.468924	+	0.883239i	$0.344642\pi$
$548$	−22.3389	+	32.5512i	−0.954271	+	1.39052i
$549$	3.09069	−	7.62977i	0.131907	−	0.325631i
$550$	1.65049	−	5.32191i	0.0703773	−	0.226927i
$551$	21.8450	−	7.95093i	0.930628	−	0.338721i
$552$	14.6997	−	3.20047i	0.625660	−	0.136221i
$553$	5.51133	−	4.62456i	0.234366	−	0.196656i
$554$	5.63232	+	0.714558i	0.239294	+	0.0303587i
$555$	9.50494	−	0.660315i	0.403462	−	0.0280288i
$556$	−33.7995	+	9.39840i	−1.43342	+	0.398581i
$557$	18.5904	−	10.7332i	0.787700	−	0.454779i	−0.0514520	−	0.998675i	$-0.516385\pi$
$557$	18.5904	−	10.7332i	0.787700	−	0.454779i	0.839152	+	0.543896i	$0.183052\pi$
$558$	−0.339130	−	27.0743i	−0.0143565	−	1.14615i
$559$	0.427155	+	0.246618i	0.0180667	+	0.0104308i
$560$	2.19989	−	6.41754i	0.0929623	−	0.271190i
$561$	1.51985	−	1.46637i	0.0641682	−	0.0619103i
$562$	−11.2876	+	4.73783i	−0.476138	+	0.199853i
$563$	−3.58495	−	20.3313i	−0.151088	−	0.856861i	−0.962276	−	0.272076i	$-0.912290\pi$
$563$	−3.58495	−	20.3313i	−0.151088	−	0.856861i	0.811188	−	0.584785i	$-0.198821\pi$
$564$	−3.49836	+	18.9000i	−0.147308	+	0.795833i
$565$	−3.76929	−	3.16281i	−0.158575	−	0.133060i
$566$	11.5487	−	10.6828i	0.485427	−	0.449033i
$567$	12.6391	+	8.55864i	0.530794	+	0.359429i
$568$	−3.64626	+	2.88057i	−0.152994	+	0.120866i
$569$	−22.6126	+	26.9486i	−0.947968	+	1.12974i	0.0434555	+	0.999055i	$0.486163\pi$
$569$	−22.6126	+	26.9486i	−0.947968	+	1.12974i	−0.991423	+	0.130689i	$0.958281\pi$
$570$	−5.14670	−	6.89386i	−0.215572	−	0.288752i
$571$	−15.8480	+	2.79443i	−0.663218	+	0.116943i	−0.495117	−	0.868826i	$-0.664875\pi$
$571$	−15.8480	+	2.79443i	−0.663218	+	0.116943i	−0.168102	+	0.985770i	$0.553764\pi$
$572$	0.132125	−	0.290449i	0.00552441	−	0.0121443i
$573$	−23.5958	−	24.4563i	−0.985727	−	1.02168i
$574$	−23.1932	+	14.9296i	−0.968066	+	0.623151i
$575$	1.53543	−	2.65944i	0.0640318	−	0.110906i
$576$	−23.9238	+	1.91055i	−0.996826	+	0.0796062i
$577$	21.9617	+	38.0388i	0.914277	+	1.58357i	0.807956	+	0.589243i	$0.200574\pi$
$577$	21.9617	+	38.0388i	0.914277	+	1.58357i	0.106321	+	0.994332i	$0.466093\pi$
$578$	−21.2568	−	10.9387i	−0.884165	−	0.454991i
$579$	−1.67166	−	24.0629i	−0.0694720	−	1.00002i
$580$	−7.69461	−	10.7718i	−0.319501	−	0.447275i
$581$	−0.548490	−	0.653664i	−0.0227552	−	0.0271186i
$582$	0.0817500	+	0.271734i	0.00338864	+	0.0112638i
$583$	3.63392	+	9.98413i	0.150502	+	0.413500i
$584$	12.6878	+	5.04677i	0.525024	+	0.208837i
$585$	0.0167977	+	0.120314i	0.000694500	+	0.00497439i
$586$	6.17699	+	27.2549i	0.255169	+	1.12589i
$587$	3.40361	−	19.3028i	0.140482	−	0.796712i	−0.830403	−	0.557164i	$-0.811890\pi$
$587$	3.40361	−	19.3028i	0.140482	−	0.796712i	0.970884	−	0.239548i	$-0.0769994\pi$
$588$	13.3807	+	4.99931i	0.551812	+	0.206168i
$589$	21.0631	+	7.66633i	0.867889	+	0.315886i
$590$	0.0477582	+	0.0362904i	0.00196618	+	0.00149405i
$591$	−32.3816	−	23.5491i	−1.33200	−	0.968680i
$592$	14.4585	+	16.5865i	0.594239	+	0.681702i
$593$			42.1820i			1.73221i	0.499864	+	0.866104i	$0.333383\pi$
$593$			42.1820i			1.73221i	−0.499864	+	0.866104i	$0.666617\pi$
$594$	2.36814	+	28.8558i	0.0971658	+	1.18397i
$595$		−	0.524876i		−	0.0215178i
$596$	−8.40965	−	8.25280i	−0.344473	−	0.338048i
$597$	23.6474	−	10.5156i	0.967823	−	0.430376i
$598$	0.106398	−	0.140020i	0.00435093	−	0.00572584i
$599$	19.0257	+	6.92480i	0.777370	+	0.282940i	0.700076	−	0.714069i	$-0.253150\pi$
$599$	19.0257	+	6.92480i	0.777370	+	0.282940i	0.0772946	+	0.997008i	$0.475372\pi$
$600$	−2.99701	+	3.87530i	−0.122352	+	0.158208i
$601$	−5.46729	+	31.0065i	−0.223015	+	1.26478i	0.643427	+	0.765507i	$0.277512\pi$
$601$	−5.46729	+	31.0065i	−0.223015	+	1.26478i	−0.866443	+	0.499276i	$0.833599\pi$
$602$	28.4930	−	6.45759i	1.16129	−	0.263192i
$603$	−17.9452	−	33.8241i	−0.730786	−	1.37742i
$604$	−14.7829	−	30.9384i	−0.601509	−	1.25887i
$605$	−1.54709	−	4.25061i	−0.0628983	−	0.172812i
$606$	−4.56101	+	19.3603i	−0.185278	+	0.786459i
$607$	−16.7261	−	19.9334i	−0.678891	−	0.809070i	0.311074	−	0.950386i	$-0.399311\pi$
$607$	−16.7261	−	19.9334i	−0.678891	−	0.809070i	−0.989965	+	0.141315i	$0.954867\pi$
$608$	5.52694	−	19.0839i	0.224147	−	0.773953i
$609$	−16.1245	+	10.8655i	−0.653398	+	0.440291i
$610$	1.77564	−	3.45053i	0.0718936	−	0.139708i
$611$	0.112343	+	0.194583i	0.00454489	+	0.00787198i
$612$	−1.70300	+	0.740035i	−0.0688396	+	0.0299142i
$613$	10.3561	−	17.9372i	0.418278	−	0.724478i	−0.577489	−	0.816399i	$-0.695967\pi$
$613$	10.3561	−	17.9372i	0.418278	−	0.724478i	0.995766	+	0.0919207i	$0.0293006\pi$
$614$	−1.29972	−	2.01912i	−0.0524525	−	0.0814850i
$615$	19.3288	−	4.80990i	0.779414	−	0.193954i
$616$	−5.93741	−	17.9436i	−0.239225	−	0.722970i
$617$	−17.6479	+	3.11180i	−0.710477	+	0.125276i	−0.517196	−	0.855867i	$-0.673024\pi$
$617$	−17.6479	+	3.11180i	−0.710477	+	0.125276i	−0.193281	+	0.981143i	$0.561913\pi$
$618$	−27.3668	−	11.7613i	−1.10085	−	0.473108i
$619$	7.15043	−	8.52155i	0.287400	−	0.342510i	−0.602956	−	0.797774i	$-0.706011\pi$
$619$	7.15043	−	8.52155i	0.287400	−	0.342510i	0.890356	+	0.455264i	$0.150455\pi$
$620$	0.992716	−	12.7253i	0.0398684	−	0.511060i
$621$	−2.24225	+	15.7983i	−0.0899784	+	0.633964i
$622$	17.2680	+	18.6676i	0.692384	+	0.748501i
$623$	−11.6071	−	9.73952i	−0.465029	−	0.390206i
$624$	−0.198196	+	0.198560i	−0.00793418	+	0.00794877i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	−18.0966	−	43.1139i	−0.723285	−	1.72318i
$627$	−23.0367	−	6.61698i	−0.919997	−	0.264257i
$628$	44.9011	+	11.5793i	1.79175	+	0.462066i
$629$	1.47431	+	0.851191i	0.0587845	+	0.0339392i
$630$	5.56968	+	4.55587i	0.221902	+	0.181510i
$631$	−17.2889	+	9.98178i	−0.688262	+	0.397368i	−0.802961	−	0.596032i	$-0.796743\pi$
$631$	−17.2889	+	9.98178i	−0.688262	+	0.397368i	0.114699	+	0.993400i	$0.463410\pi$
$632$	−10.2091	−	6.30309i	−0.406098	−	0.250723i
$633$	−11.9907	+	24.5563i	−0.476587	+	0.976024i
$634$	−0.402623	+	3.17357i	−0.0159902	+	0.126039i
$635$	−5.79870	+	4.86569i	−0.230115	+	0.193089i
$636$	0.0793501	−	9.34127i	0.00314644	−	0.370405i
$637$	0.156905	−	0.0571089i	0.00621682	−	0.00226274i
$638$	−35.2251	−	10.9244i	−1.39458	−	0.432503i
$639$	−1.51879	−	4.68884i	−0.0600825	−	0.185488i
$640$	−11.3131	−	0.120922i	−0.447188	−	0.00477986i
$641$	−3.69377	−	0.651310i	−0.145895	−	0.0257252i	0.100224	−	0.994965i	$-0.468044\pi$
$641$	−3.69377	−	0.651310i	−0.145895	−	0.0257252i	−0.246119	+	0.969240i	$0.579155\pi$
$642$	0.618505	−	10.8709i	0.0244105	−	0.429042i
$643$	3.99102	−	10.9652i	0.157390	−	0.432427i	−0.835785	−	0.549057i	$-0.814987\pi$
$643$	3.99102	−	10.9652i	0.157390	−	0.432427i	0.993175	+	0.116630i	$0.0372092\pi$
$644$	−1.00549	−	10.3679i	−0.0396221	−	0.408552i
$645$	−20.9807	−	2.21479i	−0.826116	−	0.0872075i
$646$	−0.0742768	−	1.53536i	−0.00292238	−	0.0604081i
$647$	22.7771			0.895462			0.447731	−	0.894168i	$-0.352232\pi$
$647$	22.7771			0.895462			0.447731	+	0.894168i	$0.352232\pi$
$648$	6.92901	−	24.4947i	0.272197	−	0.962241i
$649$	0.167109			0.00655960
$650$	0.00276718	+	0.0571999i	0.000108538	+	0.00224357i
$651$	−18.6442	−	1.96814i	−0.730722	−	0.0771374i
$652$	3.36210	+	34.6673i	0.131670	+	1.35768i
$653$	2.93372	−	8.06032i	0.114805	−	0.315425i	−0.868961	−	0.494881i	$-0.835212\pi$
$653$	2.93372	−	8.06032i	0.114805	−	0.315425i	0.983766	+	0.179456i	$0.0574338\pi$
$654$	2.07566	−	36.4822i	0.0811649	−	1.42657i
$655$	−6.83151	−	1.20458i	−0.266929	−	0.0470668i
$656$	35.7879	+	28.8993i	1.39728	+	1.12833i
$657$	−9.70074	+	10.7541i	−0.378462	+	0.419558i
$658$	12.7114	+	3.94221i	0.495542	+	0.153683i
$659$	45.8800	−	16.6990i	1.78723	−	0.650499i	0.787830	−	0.615892i	$-0.211204\pi$
$659$	45.8800	−	16.6990i	1.78723	−	0.650499i	0.999401	−	0.0346065i	$-0.0110178\pi$
$660$	−0.115934	+	13.6480i	−0.00451272	+	0.531247i
$661$	26.4609	−	22.2033i	1.02921	−	0.863610i	0.0384535	−	0.999260i	$-0.487757\pi$
$661$	26.4609	−	22.2033i	1.02921	−	0.863610i	0.990757	+	0.135650i	$0.0433124\pi$
$662$	−6.20209	+	48.8864i	−0.241051	+	1.90002i
$663$	−0.00952396	+	0.0195045i	−0.000369880	+	0.000757494i
$664$	−0.747569	+	1.21084i	−0.0290113	+	0.0469898i
$665$	−5.15876	+	2.97841i	−0.200048	+	0.115498i
$666$	−21.8292	+	8.25625i	−0.845864	+	0.319923i
$667$	−17.6025	−	10.1628i	−0.681573	−	0.393507i
$668$	29.0646	+	7.49534i	1.12454	+	0.290003i
$669$	1.33733	+	0.384129i	0.0517040	+	0.0148513i
$670$	−6.98581	−	16.6433i	−0.269886	−	0.642985i
$671$	−1.87736	−	10.6470i	−0.0724747	−	0.411024i
$672$	−0.631457	+	16.6056i	−0.0243590	+	0.640576i
$673$	14.4332	+	12.1109i	0.556357	+	0.466839i	0.877087	−	0.480332i	$-0.159484\pi$
$673$	14.4332	+	12.1109i	0.556357	+	0.466839i	−0.320730	+	0.947171i	$0.603928\pi$
$674$	−0.918953	−	0.993433i	−0.0353967	−	0.0382656i
$675$	−2.74754	−	4.41033i	−0.105753	−	0.169754i
$676$	2.02189	−	25.9180i	0.0777652	−	0.996845i
$677$	20.9004	−	24.9081i	0.803267	−	0.957297i	−0.196463	−	0.980511i	$-0.562946\pi$
$677$	20.9004	−	24.9081i	0.803267	−	0.957297i	0.999731	+	0.0232144i	$0.00739004\pi$
$678$	11.0733	+	4.75892i	0.425268	+	0.182765i
$679$	0.193494	−	0.0341183i	0.00742564	−	0.00130934i
$680$	−0.831010	+	0.274975i	−0.0318678	+	0.0105448i
$681$	26.7520	−	6.65711i	1.02514	−	0.255101i
$682$	−19.2474	−	29.9009i	−0.737021	−	1.14496i
$683$	6.43854	−	11.1519i	0.246364	−	0.426715i	−0.716150	−	0.697946i	$-0.754098\pi$
$683$	6.43854	−	11.1519i	0.246364	−	0.426715i	0.962514	+	0.271231i	$0.0874309\pi$
$684$	16.9371	+	12.5386i	0.647607	+	0.479426i
$685$	−9.86979	−	17.0950i	−0.377105	−	0.653166i
$686$	12.2080	−	23.7234i	0.466105	−	0.905762i
$687$	−8.76328	+	5.90512i	−0.334340	+	0.225295i
$688$	−25.1511	−	41.7286i	−0.958876	−	1.59089i
$689$	−0.0701918	−	0.0836513i	−0.00267410	−	0.00318686i
$690$	−1.72486	+	7.32160i	−0.0656645	+	0.278728i
$691$	5.88202	+	16.1607i	0.223763	+	0.614783i	0.999875	−	0.0158119i	$-0.00503328\pi$
$691$	5.88202	+	16.1607i	0.223763	+	0.614783i	−0.776112	+	0.630595i	$0.782811\pi$
$692$	−20.4863	−	42.8746i	−0.778771	−	1.62985i
$693$	20.0341	+	0.717816i	0.761032	+	0.0272676i
$694$	19.2776	−	4.36903i	0.731768	−	0.165846i
$695$	3.04595	−	17.2744i	0.115539	−	0.655256i
$696$	25.6502	+	19.8369i	0.972267	+	0.751915i
$697$	3.34427	+	1.21721i	0.126673	+	0.0461052i
$698$	−20.2919	+	26.7043i	−0.768061	+	1.01077i
$699$	−29.8195	+	13.2603i	−1.12788	+	0.501551i
$700$	2.42102	+	2.37587i	0.0915059	+	0.0897993i
$701$			27.1847i			1.02675i	0.858163	+	0.513377i	$0.171606\pi$
$701$			27.1847i			1.02675i	−0.858163	+	0.513377i	$0.828394\pi$
$702$	−0.124304	−	0.270360i	−0.00469156	−	0.0102041i
$703$		−	19.3204i		−	0.728681i
$704$	−25.2988	+	18.8008i	−0.953483	+	0.708582i
$705$	−7.77250	−	5.65245i	−0.292729	−	0.212883i
$706$	21.6450	+	16.4476i	0.814622	+	0.619012i
$707$	12.9415	+	4.71033i	0.486716	+	0.177150i
$708$	−0.137633	−	0.0514224i	−0.00517256	−	0.00193257i
$709$	0.0364386	−	0.206653i	0.00136848	−	0.00776103i	−0.984116	−	0.177527i	$-0.943190\pi$
$709$	0.0364386	−	0.206653i	0.00136848	−	0.00776103i	0.985484	+	0.169766i	$0.0543013\pi$
$710$	−0.513547	−	2.26594i	−0.0192731	−	0.0850392i
$711$	10.0353	−	7.82577i	0.376353	−	0.293489i
$712$	−9.33931	+	23.4794i	−0.350005	+	0.879926i
$713$	−6.70295	−	18.4162i	−0.251028	−	0.689693i
$714$	0.370391	+	1.23117i	0.0138615	+	0.0460754i
$715$	0.102553	+	0.122218i	0.00383527	+	0.00457070i
$716$	−23.9333	−	33.5046i	−0.894428	−	1.25212i
$717$	1.23581	+	17.7890i	0.0461523	+	0.664341i
$718$	−33.0764	−	17.0211i	−1.23440	−	0.635223i
$719$	−2.11376	−	3.66114i	−0.0788300	−	0.136538i	0.823915	−	0.566713i	$-0.191785\pi$
$719$	−2.11376	−	3.66114i	−0.0788300	−	0.136538i	−0.902745	+	0.430175i	$0.858452\pi$
$720$	4.29521	−	11.2050i	0.160073	−	0.417584i
$721$	−10.3123	+	17.8614i	−0.384050	+	0.665194i
$722$	7.92490	−	5.10131i	0.294934	−	0.189851i
$723$	28.4966	+	29.5359i	1.05980	+	1.09845i
$724$	−3.46252	+	7.61164i	−0.128683	+	0.282884i
$725$	6.51834	−	1.14936i	0.242085	−	0.0426861i
$726$	6.62847	+	8.87865i	0.246006	+	0.329518i
$727$	7.74042	−	9.22467i	0.287076	−	0.342124i	−0.603163	−	0.797618i	$-0.706093\pi$
$727$	7.74042	−	9.22467i	0.287076	−	0.342124i	0.890239	+	0.455494i	$0.150537\pi$
$728$	0.120418	+	0.152426i	0.00446297	+	0.00564928i
$729$	21.8002	+	15.9296i	0.807413	+	0.589986i
$730$	−5.01187	+	4.63611i	−0.185497	+	0.171590i
$731$	−2.88764	−	2.42302i	−0.106803	−	0.0896187i
$732$	−1.73007	+	9.34672i	−0.0639451	+	0.345465i
$733$	3.00789	+	17.0586i	0.111099	+	0.630074i	0.988608	+	0.150514i	$0.0480928\pi$
$733$	3.00789	+	17.0586i	0.111099	+	0.630074i	−0.877509	+	0.479561i	$0.840796\pi$
$734$	18.8572	−	7.91510i	0.696033	−	0.292152i
$735$	−5.13983	+	4.95897i	−0.189586	+	0.182914i
$736$	−15.8882	+	7.02354i	−0.585647	+	0.258891i
$737$	−43.5496	−	25.1434i	−1.60417	−	0.926169i
$738$	−41.9443	+	24.9222i	−1.54399	+	0.917397i
$739$	−10.6143	+	6.12817i	−0.390453	+	0.225428i	−0.682356	−	0.731020i	$-0.739045\pi$
$739$	−10.6143	+	6.12817i	−0.390453	+	0.225428i	0.291903	+	0.956448i	$0.405711\pi$
$740$	−10.5997	+	2.94738i	−0.389651	+	0.108348i
$741$	0.245745	−	0.0170721i	0.00902766	−	0.000627158i
$742$	−6.41671	−	0.814071i	−0.235565	−	0.0298855i
$743$	−2.48339	+	2.08381i	−0.0911067	+	0.0764476i	−0.687203	−	0.726465i	$-0.741162\pi$
$743$	−2.48339	+	2.08381i	−0.0911067	+	0.0764476i	0.596097	+	0.802913i	$0.296717\pi$
$744$	6.65135	+	30.5495i	0.243850	+	1.12000i
$745$	5.53604	−	2.01495i	0.202825	−	0.0738221i
$746$	7.01131	−	22.6075i	0.256702	−	0.827719i
$747$	−0.928165	−	1.19022i	−0.0339598	−	0.0435480i
$748$	−1.37988	+	2.01069i	−0.0504533	+	0.0735181i
$749$	−7.42469	−	1.30917i	−0.271292	−	0.0478362i
$750$	−1.10227	−	2.18746i	−0.0402492	−	0.0798749i
$751$	−12.8556	+	35.3205i	−0.469109	+	1.28887i	0.449353	+	0.893354i	$0.351655\pi$
$751$	−12.8556	+	35.3205i	−0.469109	+	1.28887i	−0.918461	+	0.395511i	$0.870568\pi$
$752$	−0.417802	−	22.1906i	−0.0152357	−	0.809208i
$753$	−3.96070	+	5.44624i	−0.144336	+	0.198472i
$754$	0.378600	−	0.0183157i	0.0137878	−	0.000667017i
$755$	17.1444			0.623949
$756$	−16.2794	−	6.75605i	−0.592077	−	0.245715i
$757$	15.1165			0.549419			0.274710	−	0.961527i	$-0.411418\pi$
$757$	15.1165			0.549419			0.274710	+	0.961527i	$0.411418\pi$
$758$	3.91118	−	0.189213i	0.142061	−	0.00687251i
$759$	8.51498	+	19.1484i	0.309074	+	0.695041i
$760$	7.41817	+	6.60726i	0.269085	+	0.239671i
$761$	−1.54013	+	4.23147i	−0.0558297	+	0.153391i	−0.964472	−	0.264184i	$-0.914897\pi$
$761$	−1.54013	+	4.23147i	−0.0558297	+	0.153391i	0.908643	+	0.417574i	$0.137120\pi$
$762$	10.1681	−	15.5052i	0.368351	−	0.561692i
$763$	−24.9168	−	4.39350i	−0.902048	−	0.159055i
$764$	32.3545	+	22.2040i	1.17054	+	0.803311i
$765$	0.0332437	−	0.927824i	0.00120193	−	0.0335456i
$766$	8.83445	−	28.4861i	0.319202	−	1.02924i
$767$	−0.00161391		0.000587416i	−5.82750e−5		2.12104e-5i
$768$	26.6217	−	7.69969i	0.960628	−	0.277839i
$769$	−18.8601	+	15.8255i	−0.680114	+	0.570683i	−0.916040	−	0.401088i	$-0.868632\pi$
$769$	−18.8601	+	15.8255i	−0.680114	+	0.570683i	0.235926	+	0.971771i	$0.424188\pi$
$770$	9.37508	+	1.18939i	0.337854	+	0.0428627i
$771$	14.2098	+	21.0876i	0.511754	+	0.759450i
$772$	7.46164	+	26.8343i	0.268550	+	0.965787i
$773$	46.2256	−	26.6884i	1.66262	−	0.959913i	0.691161	−	0.722701i	$-0.257100\pi$
$773$	46.2256	−	26.6884i	1.66262	−	0.959913i	0.971458	−	0.237213i	$-0.0762338\pi$
$774$	50.7762	−	9.61046i	1.82511	−	0.345441i
$775$	5.52695	+	3.19099i	0.198534	+	0.114624i
$776$	−0.155387	−	0.288476i	−0.00557806	−	0.0103557i
$777$	3.90222	+	15.6813i	0.139992	+	0.562563i
$778$	10.1970	−	4.28005i	0.365578	−	0.153447i
$779$	−7.01363	−	39.7763i	−0.251290	−	1.42513i
$780$	−0.0468553	−	0.132218i	−0.00167769	−	0.00473415i
$781$	−4.95858	−	4.16074i	−0.177432	−	0.148883i
$782$	−0.986612	+	0.912643i	−0.0352812	+	0.0326360i
$783$	−29.1915	+	18.1857i	−1.04322	+	0.649902i
$784$	−16.2944	−	2.55786i	−0.581942	−	0.0913521i
$785$	−14.9031	+	17.7608i	−0.531913	+	0.633910i
$786$	16.8743	−	1.99531i	0.601886	−	0.0711703i
$787$	10.9671	−	1.93379i	0.390934	−	0.0689322i	0.0252735	−	0.999681i	$-0.491954\pi$
$787$	10.9671	−	1.93379i	0.390934	−	0.0689322i	0.365660	+	0.930748i	$0.380843\pi$
$788$	42.0835	+	19.1437i	1.49916	+	0.681966i
$789$	−14.1171	+	49.1478i	−0.502581	+	1.74971i
$790$	5.04434	−	3.24708i	0.179470	−	0.115526i
$791$	4.17262	−	7.22720i	0.148361	−	0.256970i
$792$	−9.35908	−	32.0951i	−0.332561	−	1.14045i
$793$	0.0555574	+	0.0962282i	0.00197290	+	0.00341717i
$794$	29.1051	+	14.9775i	1.03290	+	0.531532i
$795$	4.19716	+	2.04945i	0.148858	+	0.0726865i
$796$	−24.3169	+	17.3703i	−0.861889	+	0.615672i
$797$	−1.71176	−	2.04000i	−0.0606337	−	0.0722605i	0.734875	−	0.678202i	$-0.237241\pi$
$797$	−1.71176	−	2.04000i	−0.0606337	−	0.0722605i	−0.795509	+	0.605942i	$0.792796\pi$
$798$	9.99880	−	10.6267i	0.353954	−	0.376180i
$799$	−0.587301	−	1.61360i	−0.0207772	−	0.0570849i
$800$	2.49326	−	5.07776i	0.0881499	−	0.179526i
$801$	−19.9010	−	17.9517i	−0.703169	−	0.634293i
$802$	−5.99170	−	26.4374i	−0.211574	−	0.933536i
$803$	−3.30293	+	18.7318i	−0.116558	+	0.661032i
$804$	28.1309	+	34.1094i	0.992101	+	1.20295i
$805$	4.89417	+	1.78133i	0.172497	+	0.0627837i
$806$	0.290995	+	0.221120i	0.0102499	+	0.00778863i
$807$	−1.88350	+	17.8424i	−0.0663025	+	0.628083i
$808$	0.677759	−	22.9574i	0.0238435	−	0.807637i
$809$		−	51.9236i		−	1.82554i	−0.408478	−	0.912768i	$-0.633940\pi$
$809$		−	51.9236i		−	1.82554i	0.408478	−	0.912768i	$-0.366060\pi$
$810$	9.55699	+	8.40618i	0.335798	+	0.295363i
$811$			34.7292i			1.21951i	0.792591	+	0.609754i	$0.208732\pi$
$811$			34.7292i			1.21951i	−0.792591	+	0.609754i	$0.791268\pi$
$812$	15.7256	−	16.0245i	0.551860	−	0.562349i
$813$	0.972889	−	9.21618i	0.0341207	−	0.323226i
$814$	−18.5444	+	24.4045i	−0.649981	+	0.855378i
$815$	−16.3647	−	5.95628i	−0.573232	−	0.208639i
$816$	1.75521	−	1.23141i	0.0614446	−	0.0431081i
$817$	−7.42879	+	42.1307i	−0.259900	+	1.47397i
$818$	5.05758	−	1.14624i	0.176834	−	0.0400773i
$819$	−0.196010	+	0.0634907i	−0.00684913	+	0.00221854i
$820$	−20.7524	+	9.91586i	−0.724705	+	0.346277i
$821$	17.8511	+	49.0456i	0.623009	+	1.71170i	0.699499	+	0.714633i	$0.253406\pi$
$821$	17.8511	+	49.0456i	0.623009	+	1.71170i	−0.0764902	+	0.997070i	$0.524371\pi$
$822$	35.2145	+	33.1338i	1.22825	+	1.15567i
$823$	15.2713	+	18.1996i	0.532322	+	0.634397i	0.963448	−	0.267895i	$-0.0863279\pi$
$823$	15.2713	+	18.1996i	0.532322	+	0.634397i	−0.431126	+	0.902292i	$0.641883\pi$
$824$	33.6816	+	6.96962i	1.17335	+	0.242798i
$825$	−6.13222	−	2.99433i	−0.213497	−	0.104249i
$826$	−0.0465491	+	0.0904568i	−0.00161965	+	0.00314740i
$827$	−3.08466	−	5.34278i	−0.107264	−	0.185787i	0.807397	−	0.590009i	$-0.200876\pi$
$827$	−3.08466	−	5.34278i	−0.107264	−	0.185787i	−0.914661	+	0.404222i	$0.867542\pi$
$828$	−1.12075	−	18.3910i	−0.0389488	−	0.639132i
$829$	20.6661	−	35.7947i	0.717763	−	1.24320i	−0.244122	−	0.969745i	$-0.578500\pi$
$829$	20.6661	−	35.7947i	0.717763	−	1.24320i	0.961884	−	0.273457i	$-0.0881670\pi$
$830$	−0.385115	−	0.598277i	−0.0133675	−	0.0207665i
$831$	1.91966	−	6.68322i	0.0665924	−	0.231838i
$832$	0.178244	−	0.270505i	0.00617949	−	0.00937807i
$833$	−1.25672	+	0.221594i	−0.0435428	+	0.00767776i
$834$	5.04541	+	42.6690i	0.174708	+	1.47751i
$835$	−9.64680	+	11.4966i	−0.333841	+	0.397856i
$836$	27.5922	+	2.15251i	0.954297	+	0.0744460i
$837$	−32.8327	−	4.65993i	−1.13486	−	0.161071i
$838$	9.12447	+	9.86400i	0.315200	+	0.340746i
$839$	−2.25648	−	1.89341i	−0.0779024	−	0.0653679i	0.603005	−	0.797737i	$-0.293970\pi$
$839$	−2.25648	−	1.89341i	−0.0779024	−	0.0653679i	−0.680907	+	0.732370i	$0.738414\pi$
$840$	−7.35543	−	3.86447i	−0.253786	−	0.133337i
$841$	−2.57168	−	14.5847i	−0.0886788	−	0.502922i
$842$	−1.25684	−	2.99435i	−0.0433137	−	0.103192i
$843$	3.62049	+	14.5491i	0.124696	+	0.501098i
$844$	7.87977	−	30.5553i	0.271233	−	1.05176i
$845$	11.2569	+	6.49918i	0.387249	+	0.223579i
$846$	22.2203	+	7.77375i	0.763949	+	0.267267i
$847$	6.64400	−	3.83591i	0.228290	−	0.131804i
$848$	2.07274	+	10.5857i	0.0711782	+	0.363516i
$849$	−10.7671	−	15.9785i	−0.369526	−	0.548381i
$850$	0.0550834	−	0.434181i	0.00188935	−	0.0148923i
$851$	−12.9404	+	10.8583i	−0.443591	+	0.372217i
$852$	2.80361	+	4.95268i	0.0960501	+	0.169676i
$853$	−36.0690	+	13.1280i	−1.23498	+	0.449495i	−0.875299	−	0.483581i	$-0.839336\pi$
$853$	−36.0690	+	13.1280i	−1.23498	+	0.449495i	−0.359678	+	0.933076i	$0.617113\pi$
$854$	6.28624	+	1.94957i	0.215111	+	0.0667127i
$855$	−9.30779	+	4.93821i	−0.318320	+	0.168883i
$856$	1.81694	+	12.4410i	0.0621016	+	0.425225i
$857$	42.2543	+	7.45057i	1.44338	+	0.254507i	0.839843	−	0.542829i	$-0.182647\pi$
$857$	42.2543	+	7.45057i	1.44338	+	0.254507i	0.603536	+	0.797336i	$0.293758\pi$
$858$	−0.326799	−	0.214311i	−0.0111567	−	0.00731644i
$859$	−3.15534	+	8.66924i	−0.107659	+	0.295791i	−0.981811	−	0.189862i	$-0.939196\pi$
$859$	−3.15534	+	8.66924i	−0.107659	+	0.295791i	0.874152	+	0.485653i	$0.161418\pi$
$860$	24.2473	−	2.35155i	0.826827	−	0.0801871i
$861$	13.7264	+	30.8677i	0.467794	+	1.05197i
$862$	−1.67328	−	34.5880i	−0.0569920	−	1.17807i
$863$	−16.1039			−0.548183			−0.274091	−	0.961704i	$-0.588377\pi$
$863$	−16.1039			−0.548183			−0.274091	+	0.961704i	$0.588377\pi$
$864$	−2.16797	+	29.3138i	−0.0737557	+	0.997276i
$865$	23.7588			0.807823
$866$	2.42141	+	50.0527i	0.0822830	+	1.70086i
$867$	−17.2205	+	23.6794i	−0.584839	+	0.804194i
$868$	21.5470	−	2.08966i	0.731351	−	0.0709276i
$869$	5.71629	−	15.7054i	0.193912	−	0.532768i
$870$	−14.4786	+	7.29580i	−0.490870	+	0.247351i
$871$	0.508979	+	0.0897468i	0.0172461	+	0.00304095i
$872$	6.09752	+	41.7512i	0.206488	+	1.41387i
$873$	0.344201	−	0.0480558i	0.0116495	−	0.00162644i
$874$	14.5685	+	4.51815i	0.492786	+	0.152829i
$875$	−1.59375	+	0.580077i	−0.0538785	+	0.0196102i
$876$	8.48445	−	14.4114i	0.286663	−	0.486916i
$877$	−22.2045	+	18.6317i	−0.749791	+	0.629149i	−0.935448	−	0.353465i	$-0.885003\pi$
$877$	−22.2045	+	18.6317i	−0.749791	+	0.629149i	0.185657	+	0.982615i	$0.440559\pi$
$878$	1.62574	−	12.8145i	0.0548662	−	0.432469i
$879$	34.1446	−	2.37205i	1.15167	−	0.0800072i
$880$	−3.02836	−	15.4662i	−0.102086	−	0.521366i
$881$	1.85975	−	1.07373i	0.0626567	−	0.0361748i	−0.468344	−	0.883546i	$-0.655149\pi$
$881$	1.85975	−	1.07373i	0.0626567	−	0.0361748i	0.531001	+	0.847371i	$0.321816\pi$
$882$	8.55678	−	15.2590i	0.288122	−	0.513797i
$883$	−6.35198	−	3.66732i	−0.213761	−	0.123415i	0.389297	−	0.921112i	$-0.372718\pi$
$883$	−6.35198	−	3.66732i	−0.213761	−	0.123415i	−0.603058	+	0.797697i	$0.706051\pi$
$884$	0.00625874	−	0.0242694i	0.000210504	−	0.000816270i
$885$	0.0528678	−	0.0510075i	0.00177713	−	0.00171460i
$886$	11.5661	+	27.5555i	0.388571	+	0.925746i
$887$	3.93749	+	22.3306i	0.132208	+	0.749788i	0.976763	+	0.214320i	$0.0687537\pi$
$887$	3.93749	+	22.3306i	0.132208	+	0.749788i	−0.844555	+	0.535468i	$0.820135\pi$
$888$	22.7831	−	14.3934i	0.764551	−	0.483011i
$889$	−9.83478	−	8.25236i	−0.329848	−	0.276775i
$890$	−8.57936	−	9.27471i	−0.287581	−	0.310889i
$891$	35.3688	+	2.53777i	1.18490	+	0.0850185i
$892$	−1.60178	−	0.124957i	−0.0536317	−	0.00418388i
$893$	−12.5266	+	14.9287i	−0.419188	+	0.499568i
$894$	−11.5636	+	8.63299i	−0.386746	+	0.288730i
$895$	20.2746	−	3.57496i	0.677705	−	0.119498i
$896$	−3.12987	−	18.9314i	−0.104562	−	0.632454i
$897$	−0.149546	−	0.155000i	−0.00499320	−	0.00517531i
$898$	22.6263	+	35.1500i	0.755049	+	1.17297i
$899$	21.1208	−	36.5823i	0.704418	−	1.22009i
$900$	4.12916	+	4.35316i	0.137639	+	0.145105i
$901$	0.417276	+	0.722744i	0.0139015	+	0.0240781i
$902$	−29.3195	+	56.9754i	−0.976233	+	1.89707i
$903$	−2.47980	−	35.6957i	−0.0825227	−	1.18788i
$904$	−13.6284	−	2.82009i	−0.453275	−	0.0937948i
$905$	−2.68755	−	3.20290i	−0.0893373	−	0.106468i
$906$	−40.2146	+	12.0984i	−1.33604	+	0.401941i
$907$	−3.60507	−	9.90484i	−0.119704	−	0.328885i	0.865340	−	0.501185i	$-0.167102\pi$
$907$	−3.60507	−	9.90484i	−0.119704	−	0.328885i	−0.985045	+	0.172300i	$0.944880\pi$
$908$	−28.7222	+	13.7240i	−0.953180	+	0.455446i
$909$	22.5784	+	9.14613i	0.748879	+	0.303358i
$910$	−0.0947240	+	0.0214680i	−0.00314007	+	0.000711658i
$911$	5.36163	−	30.4073i	0.177639	−	1.00744i	−0.757415	−	0.652933i	$-0.773538\pi$
$911$	5.36163	−	30.4073i	0.177639	−	1.00744i	0.935054	−	0.354505i	$-0.115351\pi$
$912$	−22.0629	−	10.2634i	−0.730576	−	0.339857i
$913$	−1.86272	−	0.677973i	−0.0616469	−	0.0224376i
$914$	3.96787	−	5.22173i	0.131245	−	0.172720i
$915$	−3.84378	−	2.79534i	−0.127071	−	0.0924110i
$916$	8.54648	−	8.70891i	0.282384	−	0.287751i
$917$		−	11.7652i		−	0.388521i
$918$	0.576763	+	2.19980i	0.0190360	+	0.0726042i
$919$		−	27.4485i		−	0.905442i	−0.891652	−	0.452721i	$-0.850453\pi$
$919$		−	27.4485i		−	0.905442i	0.891652	−	0.452721i	$-0.149547\pi$
$920$	0.256312	−	8.68191i	0.00845036	−	0.286234i
$921$	−2.68723	+	1.19497i	−0.0885473	+	0.0393757i
$922$	7.37911	+	5.60721i	0.243018	+	0.184664i
$923$	0.0625150	+	0.0227536i	0.00205771	+	0.000748944i
$924$	−22.8299	+	3.82586i	−0.751048	+	0.125862i
$925$	0.955222	−	5.41733i	0.0314075	−	0.178121i
$926$	2.78425	+	12.2850i	0.0914961	+	0.403711i
$927$	−19.3603	+	30.9205i	−0.635877	+	1.01556i
$928$	−33.6092	−	16.5026i	−1.10327	−	0.541724i
$929$	−3.58913	−	9.86106i	−0.117756	−	0.323531i	0.866786	−	0.498680i	$-0.166182\pi$
$929$	−3.58913	−	9.86106i	−0.117756	−	0.323531i	−0.984542	+	0.175149i	$0.943959\pi$
$930$	−15.2160	−	3.58468i	−0.498953	−	0.117546i
$931$	9.30920	+	11.0943i	0.305097	+	0.363600i
$932$	30.6638	−	21.9040i	1.00443	−	0.717490i
$933$	25.8280	−	17.4042i	0.845572	−	0.569787i
$934$	18.6056	+	9.57442i	0.608793	+	0.313285i
$935$	−0.609658	−	1.05596i	−0.0199380	−	0.0345336i
$936$	0.203208	+	0.277071i	0.00664207	+	0.00905633i
$937$	−18.2771	+	31.6568i	−0.597086	+	1.03418i	0.396163	+	0.918180i	$0.370342\pi$
$937$	−18.2771	+	31.6568i	−0.597086	+	1.03418i	−0.993249	+	0.116003i	$0.962992\pi$
$938$	25.7412	−	16.5698i	0.840481	−	0.541023i
$939$	−55.5717	+	13.8288i	−1.81351	+	0.451285i
$940$	10.1012	+	4.59503i	0.329466	+	0.149873i
$941$	−38.3786	+	6.76719i	−1.25111	+	0.220604i	−0.759670	−	0.650308i	$-0.774640\pi$
$941$	−38.3786	+	6.76719i	−1.25111	+	0.220604i	−0.491438	+	0.870913i	$0.663529\pi$
$942$	22.4239	−	52.1771i	0.730610	−	1.70002i
$943$	−22.6996	+	27.0524i	−0.739202	+	0.880947i
$944$	0.167602	+	0.0263099i	0.00545499	+	0.000856313i
$945$	6.55723	−	5.88801i	0.213307	−	0.191537i
$946$	49.8224	−	46.0870i	1.61986	−	1.49842i
$947$	27.7168	+	23.2571i	0.900674	+	0.755755i	0.970322	−	0.241816i	$-0.0777431\pi$
$947$	27.7168	+	23.2571i	0.900674	+	0.755755i	−0.0696479	+	0.997572i	$0.522188\pi$
$948$	−9.54083	+	11.1761i	−0.309872	+	0.362984i
$949$	−0.0339464	−	0.192520i	−0.00110195	−	0.00624945i
$950$	−4.57993	+	1.92237i	−0.148593	+	0.0623700i
$951$	3.76570	+	1.08165i	0.122111	+	0.0350748i
$952$	−0.704023	−	1.30702i	−0.0228175	−	0.0423608i
$953$	−9.14347	−	5.27899i	−0.296186	−	0.171003i	0.344542	−	0.938771i	$-0.388034\pi$
$953$	−9.14347	−	5.27899i	−0.296186	−	0.171003i	−0.640728	+	0.767768i	$0.721368\pi$
$954$	−11.2913	−	1.84545i	−0.365568	−	0.0597485i
$955$	−16.9917	+	9.81016i	−0.549838	+	0.317449i
$956$	−5.51617	−	19.8378i	−0.178406	−	0.641600i
$957$	−19.8192	+	40.5885i	−0.640663	+	1.31204i
$958$	34.3094	+	4.35275i	1.10849	+	0.140631i
$959$	25.6464	−	21.5198i	0.828164	−	0.694912i
$960$	−2.26503	+	13.6700i	−0.0731037	+	0.441198i
$961$	9.14283	−	3.32772i	0.294930	−	0.107346i
$962$	0.0933131	−	0.300882i	0.00300854	−	0.00970082i
$963$	−13.0417	−	2.78448i	−0.420264	−	0.0897286i
$964$	−39.0745	−	26.8157i	−1.25851	−	0.863676i
$965$	−13.7146	−	2.41826i	−0.441489	−	0.0778464i
$966$	−12.7370	−	0.724675i	−0.409806	−	0.0233160i
$967$	−16.7788	+	46.0993i	−0.539569	+	1.48245i	0.307800	+	0.951451i	$0.400407\pi$
$967$	−16.7788	+	46.0993i	−0.539569	+	1.48245i	−0.847370	+	0.531004i	$0.821815\pi$
$968$	−9.55391	−	8.50954i	−0.307074	−	0.273507i
$969$	−1.87223	−	0.197638i	−0.0601445	−	0.00634905i
$970$	0.163641	−	0.00791649i	0.00525418	−	0.000254183i
$971$	−27.2151			−0.873373			−0.436687	−	0.899614i	$-0.643848\pi$
$971$	−27.2151			−0.873373			−0.436687	+	0.899614i	$0.643848\pi$
$972$	−28.3493	−	12.9738i	−0.909304	−	0.416134i
$973$	29.7499			0.953738
$974$	−26.7944	+	1.29624i	−0.858548	+	0.0415343i
$975$	0.0697497	+	0.00736300i	0.00223378	+	0.000235805i
$976$	−0.206618	−	10.9740i	−0.00661369	−	0.351271i
$977$	8.69543	−	23.8905i	0.278191	−	0.764324i	−0.719376	−	0.694620i	$-0.755572\pi$
$977$	8.69543	−	23.8905i	0.278191	−	0.764324i	0.997568	−	0.0697039i	$-0.0222055\pi$
$978$	42.5890	+	2.42311i	1.36185	+	0.0774826i
$979$	−34.6642	−	6.11224i	−1.10787	−	0.195348i
$980$	4.66647	−	6.79974i	0.149065	−	0.217210i
$981$	−43.7672	−	9.34454i	−1.39738	−	0.298348i
$982$	4.98120	−	16.0615i	0.158956	−	0.512544i
$983$	26.1675	−	9.52421i	0.834615	−	0.303775i	0.110863	−	0.993836i	$-0.464638\pi$
$983$	26.1675	−	9.52421i	0.834615	−	0.303775i	0.723752	+	0.690061i	$0.242416\pi$
$984$	41.6802	−	37.9035i	1.32872	−	1.20832i
$985$	−17.7083	+	14.8591i	−0.564234	+	0.473449i
$986$	−2.87380	−	0.364591i	−0.0915203	−	0.0116110i
$987$	7.15198	−	14.6468i	0.227650	−	0.466214i
$988$	−0.274048	+	0.0762028i	−0.00871863	+	0.00242433i
$989$	32.3934	−	18.7024i	1.03005	−	0.594700i
$990$	16.4970	+	2.69627i	0.524309	+	0.0856932i
$991$	−6.96294	−	4.02006i	−0.221185	−	0.127701i	0.385314	−	0.922786i	$-0.374093\pi$
$991$	−6.96294	−	4.02006i	−0.221185	−	0.127701i	−0.606499	+	0.795084i	$0.707427\pi$
$992$	−14.5966	−	33.0195i	−0.463442	−	1.04837i
$993$	58.0078	+	16.6620i	1.84082	+	0.528751i
$994$	3.63347	−	1.52511i	0.115247	−	0.0483735i
$995$	−2.59463	−	14.7149i	−0.0822552	−	0.466492i
$996$	1.32553	+	1.13158i	0.0420010	+	0.0358554i
$997$	−25.1060	−	21.0664i	−0.795115	−	0.667180i	0.151891	−	0.988397i	$-0.451464\pi$
$997$	−25.1060	−	21.0664i	−0.795115	−	0.667180i	−0.947006	+	0.321217i	$0.895908\pi$
$998$	11.1645	−	10.3275i	0.353406	−	0.326910i
$999$	5.90477	+	27.9670i	0.186819	+	0.884836i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.be.a.11.37	yes	432
4.3	odd	2	inner	540.2.be.a.11.4	✓	432
27.5	odd	18	inner	540.2.be.a.491.4	yes	432
108.59	even	18	inner	540.2.be.a.491.37	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.be.a.11.4	✓	432	4.3	odd	2	inner
540.2.be.a.11.37	yes	432	1.1	even	1	trivial
540.2.be.a.491.4	yes	432	27.5	odd	18	inner
540.2.be.a.491.37	yes	432	108.59	even	18	inner

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:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0683360 + 1.41256i) q^{2} +(1.72248 + 0.181830i) q^{3} +(-1.99066 + 0.193058i) q^{4} +(0.342020 - 0.939693i) q^{5} +(-0.139139 + 2.44553i) q^{6} +(1.67026 + 0.294513i) q^{7} +(-0.408739 - 2.79874i) q^{8} +(2.93388 + 0.626399i) q^{9} +(1.35075 + 0.418910i) q^{10} +(3.70237 - 1.34755i) q^{11} +(-3.46398 - 0.0294250i) q^{12} +(-0.0310200 + 0.0260289i) q^{13} +(-0.301878 + 2.37948i) q^{14} +(0.759988 - 1.55641i) q^{15} +(3.92546 - 0.768624i) q^{16} +(0.268012 - 0.154737i) q^{17} +(-0.684338 + 4.18709i) q^{18} +(-3.04167 - 1.75611i) q^{19} +(-0.499431 + 1.93664i) q^{20} +(2.82344 + 0.810997i) q^{21} +(2.15650 + 5.13773i) q^{22} +(0.533249 + 3.02420i) q^{23} +(-0.195150 - 4.89509i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(-0.0388872 - 0.0420390i) q^{26} +(4.93964 + 1.61243i) q^{27} +(-3.38179 - 0.263818i) q^{28} +(-4.25454 + 5.07037i) q^{29} +(2.25046 + 0.967170i) q^{30} +(-6.28502 + 1.10822i) q^{31} +(1.35398 + 5.49243i) q^{32} +(6.62228 - 1.64793i) q^{33} +(0.236890 + 0.368009i) q^{34} +(0.848015 - 1.46881i) q^{35} +(-5.96128 - 0.680541i) q^{36} +(2.75045 + 4.76392i) q^{37} +(2.27275 - 4.41655i) q^{38} +(-0.0581642 + 0.0391939i) q^{39} +(-2.76975 - 0.573135i) q^{40} +(7.39196 + 8.80939i) q^{41} +(-0.952640 + 4.04371i) q^{42} +(-4.16599 - 11.4460i) q^{43} +(-7.11000 + 3.39729i) q^{44} +(1.59207 - 2.54270i) q^{45} +(-4.23543 + 0.959908i) q^{46} +(0.963510 - 5.46434i) q^{47} +(6.90128 - 0.610172i) q^{48} +(-3.87480 - 1.41031i) q^{49} +(0.855629 - 1.12601i) q^{50} +(0.489780 - 0.217798i) q^{51} +(0.0567253 - 0.0578033i) q^{52} +2.69669i q^{53} +(-1.94010 + 7.08774i) q^{54} -3.93997i q^{55} +(0.141561 - 4.79501i) q^{56} +(-4.91990 - 3.57793i) q^{57} +(-7.45294 - 5.66331i) q^{58} +(0.0398558 + 0.0145063i) q^{59} +(-1.21240 + 3.24501i) q^{60} +(0.476490 - 2.70231i) q^{61} +(-1.99492 - 8.80224i) q^{62} +(4.71586 + 1.91031i) q^{63} +(-7.66586 + 2.28791i) q^{64} +(0.0138497 + 0.0380517i) q^{65} +(2.78034 + 9.24176i) q^{66} +(-8.20404 - 9.77720i) q^{67} +(-0.503647 + 0.359770i) q^{68} +(0.368618 + 5.30609i) q^{69} +(2.13273 + 1.09750i) q^{70} +(-0.821448 - 1.42279i) q^{71} +(0.553936 - 8.46718i) q^{72} +(-2.41382 + 4.18086i) q^{73} +(-6.54138 + 4.21073i) q^{74} +(-1.20262 - 1.24648i) q^{75} +(6.39395 + 2.90860i) q^{76} +(6.58080 - 1.16037i) q^{77} +(-0.0593385 - 0.0794822i) q^{78} +(2.72669 - 3.24955i) q^{79} +(0.620315 - 3.95161i) q^{80} +(8.21525 + 3.67555i) q^{81} +(-11.9387 + 11.0436i) q^{82} +(-0.385408 - 0.323396i) q^{83} +(-5.77709 - 1.06933i) q^{84} +(-0.0537394 - 0.304772i) q^{85} +(15.8834 - 6.66689i) q^{86} +(-8.25031 + 7.96000i) q^{87} +(-5.28474 - 9.81115i) q^{88} +(-7.73690 - 4.46690i) q^{89} +(3.70052 + 2.07513i) q^{90} +(-0.0594775 + 0.0343393i) q^{91} +(-1.64536 - 5.91721i) q^{92} +(-11.0273 + 0.766076i) q^{93} +(7.78455 + 0.987606i) q^{94} +(-2.69051 + 2.25761i) q^{95} +(1.33351 + 9.70679i) q^{96} +(0.108860 - 0.0396219i) q^{97} +(1.72737 - 5.56978i) q^{98} +(11.7064 - 1.63439i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) \) 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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