LMFDB - Embedded newform 966.2.be.b.19.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 45]))

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

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			19.10
Character	$\chi$	$=$	966.19
Dual form			966.2.be.b.661.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.995472 - 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-2.00286 + 1.03255i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(1.87452 - 1.86713i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})$	\(q+(-0.995472 - 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-2.00286 + 1.03255i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(1.87452 - 1.86713i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(2.09194 - 0.837488i) q^{10} +(0.288960 + 3.02612i) q^{11} +(0.814576 - 0.580057i) q^{12} +(1.85277 + 0.266388i) q^{13} +(-2.04351 + 1.68050i) q^{14} +(-0.634844 + 2.16208i) q^{15} +(0.928368 + 0.371662i) q^{16} +(-1.12818 + 3.25965i) q^{17} +(-0.0475819 + 0.998867i) q^{18} +(1.25162 + 3.61633i) q^{19} +(-2.16208 + 0.634844i) q^{20} +(-0.0577442 - 2.64512i) q^{21} -3.03989i q^{22} +(3.26330 - 3.51438i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.0450237 - 0.0632270i) q^{25} +(-1.81906 - 0.441299i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(2.19400 - 1.47864i) q^{28} +(-1.84603 - 2.13043i) q^{29} +(0.837488 - 2.09194i) q^{30} +(6.74420 - 1.63612i) q^{31} +(-0.888835 - 0.458227i) q^{32} +(2.38951 + 1.87914i) q^{33} +(1.43292 - 3.13765i) q^{34} +(-1.82650 + 5.67514i) q^{35} +(0.142315 - 0.989821i) q^{36} +(1.36468 - 0.0650077i) q^{37} +(-0.902202 - 3.71893i) q^{38} +(1.47135 - 1.15708i) q^{39} +(2.21264 - 0.426451i) q^{40} +(1.76243 - 2.74239i) q^{41} +(-0.193952 + 2.63863i) q^{42} +(-0.176483 - 0.601046i) q^{43} +(-0.288960 + 3.02612i) q^{44} +(1.12668 + 1.95146i) q^{45} +(-3.58259 + 3.18827i) q^{46} +(7.22015 + 4.16855i) q^{47} +(0.909632 - 0.415415i) q^{48} +(0.0276215 - 6.99995i) q^{49} +(-0.0508300 + 0.0586609i) q^{50} +(1.58059 + 3.06592i) q^{51} +(1.76887 + 0.612213i) q^{52} +(7.40086 + 9.41096i) q^{53} +(0.690079 + 0.723734i) q^{54} +(-3.70337 - 5.76255i) q^{55} +(-2.32462 + 1.26339i) q^{56} +(3.48098 + 1.58971i) q^{57} +(1.63516 + 2.29626i) q^{58} +(3.70857 + 9.26356i) q^{59} +(-1.03255 + 2.00286i) q^{60} +(4.09941 - 3.90878i) q^{61} +(-6.86918 + 0.987639i) q^{62} +(-1.95421 - 1.78355i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-3.98590 + 1.37953i) q^{65} +(-2.20007 - 2.09776i) q^{66} +(5.06470 + 3.60655i) q^{67} +(-1.72468 + 2.98724i) q^{68} +(-0.291536 - 4.78696i) q^{69} +(2.35768 - 5.47583i) q^{70} +(-3.94429 - 8.63680i) q^{71} +(-0.235759 + 0.971812i) q^{72} +(0.293133 - 1.52092i) q^{73} +(-1.36468 - 0.0650077i) q^{74} +(-0.0146896 - 0.0762168i) q^{75} +(0.544610 + 3.78785i) q^{76} +(6.19184 + 5.13299i) q^{77} +(-1.57468 + 1.01198i) q^{78} +(-6.88017 + 8.74885i) q^{79} +(-2.24315 + 0.214195i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(-2.01513 + 2.56244i) q^{82} +(9.62787 - 6.18746i) q^{83} +(0.443892 - 2.60825i) q^{84} +(-1.10616 - 7.69353i) q^{85} +(0.118551 + 0.615101i) q^{86} +(-2.81577 - 0.134132i) q^{87} +(0.575303 - 2.98495i) q^{88} +(3.61805 - 14.9138i) q^{89} +(-0.936078 - 2.04973i) q^{90} +(3.97043 - 2.96002i) q^{91} +(3.86943 - 2.83328i) q^{92} +(3.46991 - 6.01006i) q^{93} +(-6.79121 - 4.83600i) q^{94} +(-6.24087 - 5.95065i) q^{95} +(-0.945001 + 0.327068i) q^{96} +(1.47046 + 0.945007i) q^{97} +(-0.692884 + 6.96562i) q^{98} +(3.00895 - 0.432621i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9	$ 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) $ 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9 + 22 * q^14 + 16 * q^16 - 66 * q^17 - 16 * q^18 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−0.995472	−	0.0950560i	−0.703905	−	0.0672148i
$2$	−0.995472	−	0.0950560i	−0.703905	−	0.0672148i
$3$	0.690079	−	0.723734i	0.398417	−	0.417848i
$3$	0.690079	−	0.723734i	0.398417	−	0.417848i
$4$	0.981929	+	0.189251i	0.490964	+	0.0946256i
$5$	−2.00286	+	1.03255i	−0.895708	+	0.461770i	−0.843662	−	0.536875i	$-0.819605\pi$
$5$	−2.00286	+	1.03255i	−0.895708	+	0.461770i	−0.0520463	+	0.998645i	$0.516574\pi$
$6$	−0.755750	+	0.654861i	−0.308533	+	0.267346i
$7$	1.87452	−	1.86713i	0.708501	−	0.705710i
$7$	1.87452	−	1.86713i	0.708501	−	0.705710i
$8$	−0.959493	−	0.281733i	−0.339232	−	0.0996075i
$9$	−0.0475819	−	0.998867i	−0.0158606	−	0.332956i
$10$	2.09194	−	0.837488i	0.661531	−	0.264837i
$11$	0.288960	+	3.02612i	0.0871247	+	0.912411i	0.928345	+	0.371719i	$0.121231\pi$
$11$	0.288960	+	3.02612i	0.0871247	+	0.912411i	−0.841221	+	0.540692i	$0.818162\pi$
$12$	0.814576	−	0.580057i	0.235148	−	0.167448i
$13$	1.85277	+	0.266388i	0.513866	+	0.0738827i	0.394370	−	0.918952i	$-0.370963\pi$
$13$	1.85277	+	0.266388i	0.513866	+	0.0738827i	0.119496	+	0.992835i	$0.461872\pi$
$14$	−2.04351	+	1.68050i	−0.546151	+	0.449131i
$15$	−0.634844	+	2.16208i	−0.163916	+	0.558247i
$16$	0.928368	+	0.371662i	0.232092	+	0.0929156i
$17$	−1.12818	+	3.25965i	−0.273623	+	0.790581i	0.721543	+	0.692370i	$0.243433\pi$
$17$	−1.12818	+	3.25965i	−0.273623	+	0.790581i	−0.995166	+	0.0982114i	$0.968688\pi$
$18$	−0.0475819	+	0.998867i	−0.0112152	+	0.235435i
$19$	1.25162	+	3.61633i	0.287142	+	0.829643i	0.992659	+	0.120949i	$0.0385938\pi$
$19$	1.25162	+	3.61633i	0.287142	+	0.829643i	−0.705517	+	0.708693i	$0.749285\pi$
$20$	−2.16208	+	0.634844i	−0.483456	+	0.141955i
$21$	−0.0577442	−	2.64512i	−0.0126008	−	0.577213i
$22$		−	3.03989i		−	0.648107i
$23$	3.26330	−	3.51438i	0.680446	−	0.732798i
$23$	3.26330	−	3.51438i	0.680446	−	0.732798i
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	0.0450237	−	0.0632270i	0.00900474	−	0.0126454i
$26$	−1.81906	−	0.441299i	−0.356747	−	0.0865458i
$27$	−0.755750	−	0.654861i	−0.145444	−	0.126028i
$28$	2.19400	−	1.47864i	0.414627	−	0.279436i
$29$	−1.84603	−	2.13043i	−0.342799	−	0.395611i	0.558005	−	0.829838i	$-0.311567\pi$
$29$	−1.84603	−	2.13043i	−0.342799	−	0.395611i	−0.900803	+	0.434227i	$0.857022\pi$
$30$	0.837488	−	2.09194i	0.152904	−	0.381935i
$31$	6.74420	−	1.63612i	1.21129	−	0.293857i	0.421271	−	0.906935i	$-0.361584\pi$
$31$	6.74420	−	1.63612i	1.21129	−	0.293857i	0.790022	+	0.613078i	$0.210069\pi$
$32$	−0.888835	−	0.458227i	−0.157125	−	0.0810038i
$33$	2.38951	+	1.87914i	0.415961	+	0.327115i
$34$	1.43292	−	3.13765i	0.245743	−	0.538103i
$35$	−1.82650	+	5.67514i	−0.308734	+	0.959274i
$36$	0.142315	−	0.989821i	0.0237191	−	0.164970i
$37$	1.36468	−	0.0650077i	0.224352	−	0.0106872i	0.0648950	−	0.997892i	$-0.479329\pi$
$37$	1.36468	−	0.0650077i	0.224352	−	0.0106872i	0.159457	+	0.987205i	$0.449026\pi$
$38$	−0.902202	−	3.71893i	−0.146357	−	0.603290i
$39$	1.47135	−	1.15708i	0.235605	−	0.185282i
$40$	2.21264	−	0.426451i	0.349849	−	0.0674278i
$41$	1.76243	−	2.74239i	0.275245	−	0.428290i	−0.675919	−	0.736976i	$-0.736253\pi$
$41$	1.76243	−	2.74239i	0.275245	−	0.428290i	0.951164	+	0.308686i	$0.0998894\pi$
$42$	−0.193952	+	2.63863i	−0.0299275	+	0.407150i
$43$	−0.176483	−	0.601046i	−0.0269134	−	0.0916587i	0.944941	−	0.327240i	$-0.106119\pi$
$43$	−0.176483	−	0.601046i	−0.0269134	−	0.0916587i	−0.971855	+	0.235582i	$0.924300\pi$
$44$	−0.288960	+	3.02612i	−0.0435623	+	0.456205i
$45$	1.12668	+	1.95146i	0.167955	+	0.290907i
$46$	−3.58259	+	3.18827i	−0.528224	+	0.470084i
$47$	7.22015	+	4.16855i	1.05317	+	0.608046i	0.923534	−	0.383516i	$-0.125287\pi$
$47$	7.22015	+	4.16855i	1.05317	+	0.608046i	0.129632	+	0.991562i	$0.458620\pi$
$48$	0.909632	−	0.415415i	0.131294	−	0.0599600i
$49$	0.0276215	−	6.99995i	0.00394593	−	0.999992i
$50$	−0.0508300	+	0.0586609i	−0.00718844	+	0.00829590i
$51$	1.58059	+	3.06592i	0.221327	+	0.429314i
$52$	1.76887	+	0.612213i	0.245299	+	0.0848987i
$53$	7.40086	+	9.41096i	1.01659	+	1.29269i	0.955635	+	0.294553i	$0.0951709\pi$
$53$	7.40086	+	9.41096i	1.01659	+	1.29269i	0.0609510	+	0.998141i	$0.480587\pi$
$54$	0.690079	+	0.723734i	0.0939079	+	0.0984877i
$55$	−3.70337	−	5.76255i	−0.499362	−	0.777022i
$56$	−2.32462	+	1.26339i	−0.310640	+	0.168828i
$57$	3.48098	+	1.58971i	0.461067	+	0.210562i
$58$	1.63516	+	2.29626i	0.214707	+	0.301513i
$59$	3.70857	+	9.26356i	0.482815	+	1.20601i	0.947276	+	0.320419i	$0.103824\pi$
$59$	3.70857	+	9.26356i	0.482815	+	1.20601i	−0.464461	+	0.885593i	$0.653752\pi$
$60$	−1.03255	+	2.00286i	−0.133301	+	0.258569i
$61$	4.09941	−	3.90878i	0.524875	−	0.500468i	−0.380674	−	0.924709i	$-0.624308\pi$
$61$	4.09941	−	3.90878i	0.524875	−	0.500468i	0.905549	+	0.424242i	$0.139459\pi$
$62$	−6.86918	+	0.987639i	−0.872387	+	0.125430i
$63$	−1.95421	−	1.78355i	−0.246208	−	0.224706i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−3.98590	+	1.37953i	−0.494390	+	0.171110i
$66$	−2.20007	−	2.09776i	−0.270810	−	0.258217i
$67$	5.06470	+	3.60655i	0.618751	+	0.440611i	0.845968	−	0.533233i	$-0.179023\pi$
$67$	5.06470	+	3.60655i	0.618751	+	0.440611i	−0.227217	+	0.973844i	$0.572963\pi$
$68$	−1.72468	+	2.98724i	−0.209148	+	0.362256i
$69$	−0.291536	−	4.78696i	−0.0350968	−	0.576283i
$70$	2.35768	−	5.47583i	0.281797	−	0.654486i
$71$	−3.94429	−	8.63680i	−0.468102	−	1.02500i	−0.985565	−	0.169295i	$-0.945851\pi$
$71$	−3.94429	−	8.63680i	−0.468102	−	1.02500i	0.517464	−	0.855705i	$-0.326876\pi$
$72$	−0.235759	+	0.971812i	−0.0277845	+	0.114529i
$73$	0.293133	−	1.52092i	0.0343086	−	0.178010i	−0.960732	−	0.277477i	$-0.910502\pi$
$73$	0.293133	−	1.52092i	0.0343086	−	0.178010i	0.995041	+	0.0994671i	$0.0317138\pi$
$74$	−1.36468	−	0.0650077i	−0.158641	−	0.00755699i
$75$	−0.0146896	−	0.0762168i	−0.00169621	−	0.00880076i
$76$	0.544610	+	3.78785i	0.0624711	+	0.434496i
$77$	6.19184	+	5.13299i	0.705626	+	0.584959i
$78$	−1.57468	+	1.01198i	−0.178297	+	0.114585i
$79$	−6.88017	+	8.74885i	−0.774079	+	0.984322i	0.225869	+	0.974158i	$0.427478\pi$
$79$	−6.88017	+	8.74885i	−0.774079	+	0.984322i	−0.999948	+	0.0101643i	$0.996765\pi$
$80$	−2.24315	+	0.214195i	−0.250792	+	0.0239478i
$81$	−0.995472	+	0.0950560i	−0.110608	+	0.0105618i
$82$	−2.01513	+	2.56244i	−0.222534	+	0.282975i
$83$	9.62787	−	6.18746i	1.05680	−	0.679162i	0.107711	−	0.994182i	$-0.465648\pi$
$83$	9.62787	−	6.18746i	1.05680	−	0.679162i	0.949085	+	0.315020i	$0.102011\pi$
$84$	0.443892	−	2.60825i	0.0484326	−	0.284583i
$85$	−1.10616	−	7.69353i	−0.119980	−	0.834481i
$86$	0.118551	+	0.615101i	0.0127837	+	0.0663280i
$87$	−2.81577	−	0.134132i	−0.301882	−	0.0143804i
$88$	0.575303	−	2.98495i	0.0613275	−	0.318197i
$89$	3.61805	−	14.9138i	0.383512	−	1.58086i	−0.373610	−	0.927586i	$-0.621880\pi$
$89$	3.61805	−	14.9138i	0.383512	−	1.58086i	0.757122	−	0.653273i	$-0.226605\pi$
$90$	−0.936078	−	2.04973i	−0.0986713	−	0.216060i
$91$	3.97043	−	2.96002i	0.416214	−	0.310294i
$92$	3.86943	−	2.83328i	0.403416	−	0.295390i
$93$	3.46991	−	6.01006i	0.359813	−	0.623214i
$94$	−6.79121	−	4.83600i	−0.700460	−	0.498795i
$95$	−6.24087	−	5.95065i	−0.640299	−	0.610524i
$96$	−0.945001	+	0.327068i	−0.0964487	+	0.0333812i
$97$	1.47046	+	0.945007i	0.149303	+	0.0959509i	0.613159	−	0.789959i	$-0.289898\pi$
$97$	1.47046	+	0.945007i	0.149303	+	0.0959509i	−0.463857	+	0.885910i	$0.653535\pi$
$98$	−0.692884	+	6.96562i	−0.0699918	+	0.703634i
$99$	3.00895	−	0.432621i	0.302411	−	0.0434801i
$100$	0.0561759	−	0.0535636i	0.00561759	−	0.00535636i
$101$	−2.12614	+	4.12413i	−0.211558	+	0.410366i	−0.970608	−	0.240667i	$-0.922634\pi$
$101$	−2.12614	+	4.12413i	−0.211558	+	0.410366i	0.759049	+	0.651033i	$0.225664\pi$
$102$	−1.28200	−	3.20228i	−0.126937	−	0.317073i
$103$	3.87428	+	5.44067i	0.381744	+	0.536085i	0.960084	−	0.279711i	$-0.0902386\pi$
$103$	3.87428	+	5.44067i	0.381744	+	0.536085i	−0.578340	+	0.815796i	$0.696299\pi$
$104$	−1.70267	−	0.777583i	−0.166960	−	0.0762483i
$105$	2.84687	+	5.23819i	0.277826	+	0.511195i
$106$	−6.47278	−	10.0718i	−0.628692	−	0.978263i
$107$	5.08905	+	5.33724i	0.491977	+	0.515971i	0.922180	−	0.386762i	$-0.126406\pi$
$107$	5.08905	+	5.33724i	0.491977	+	0.515971i	−0.430203	+	0.902732i	$0.641558\pi$
$108$	−0.618159	−	0.786053i	−0.0594824	−	0.0756380i
$109$	2.27218	+	0.786409i	0.217635	+	0.0753243i	0.433710	−	0.901053i	$-0.357204\pi$
$109$	2.27218	+	0.786409i	0.217635	+	0.0753243i	−0.216075	+	0.976377i	$0.569325\pi$
$110$	3.13883	+	6.08849i	0.299276	+	0.580514i
$111$	0.894688	−	1.03253i	0.0849200	−	0.0980029i
$112$	2.43418	−	1.03670i	0.230009	−	0.0979589i
$113$	−10.2911	+	4.69979i	−0.968106	+	0.442119i	−0.835766	−	0.549085i	$-0.814976\pi$
$113$	−10.2911	+	4.69979i	−0.968106	+	0.442119i	−0.132339	+	0.991204i	$0.542249\pi$
$114$	−3.31411	−	1.91340i	−0.310394	−	0.179206i
$115$	−2.90719	+	10.4083i	−0.271097	+	0.970582i
$116$	−1.40948	−	2.44129i	−0.130867	−	0.226668i
$117$	0.177928	−	1.86335i	0.0164494	−	0.172266i
$118$	−2.81122	−	9.57414i	−0.258794	−	0.881371i
$119$	3.97142	+	8.21672i	0.364059	+	0.753226i
$120$	1.21826	−	1.89564i	0.111211	−	0.173048i
$121$	1.72728	−	0.332906i	0.157026	−	0.0302642i
$122$	−4.45240	+	3.50140i	−0.403101	+	0.317002i
$123$	−0.768547	−	3.16800i	−0.0692976	−	0.285649i
$124$	6.93196	−	0.330210i	0.622508	−	0.0296537i
$125$	1.57854	−	10.9790i	0.141189	−	0.981990i
$126$	1.77583	+	1.96123i	0.158203	+	0.174721i
$127$	4.46451	−	9.77592i	0.396162	−	0.867473i	−0.601484	−	0.798885i	$-0.705423\pi$
$127$	4.46451	−	9.77592i	0.396162	−	0.867473i	0.997645	−	0.0685876i	$-0.0218493\pi$
$128$	−0.786053	−	0.618159i	−0.0694779	−	0.0546381i
$129$	−0.556785	−	0.287043i	−0.0490222	−	0.0252727i
$130$	4.09899	−	0.994404i	0.359505	−	0.0872150i
$131$	−0.906583	+	2.26453i	−0.0792085	+	0.197853i	−0.962686	−	0.270620i	$-0.912771\pi$
$131$	−0.906583	+	2.26453i	−0.0792085	+	0.197853i	0.883478	+	0.468473i	$0.155196\pi$
$132$	1.99070	+	2.29740i	0.173269	+	0.199963i
$133$	9.09836	+	4.44192i	0.788928	+	0.385163i
$134$	−4.69894	−	4.07165i	−0.405926	−	0.351737i
$135$	2.18984	+	0.531249i	0.188471	+	0.0457226i
$136$	2.00083	−	2.80977i	0.171569	−	0.240936i
$137$	−7.12482	+	4.11352i	−0.608714	+	0.351441i	−0.772462	−	0.635061i	$-0.780975\pi$
$137$	−7.12482	+	4.11352i	−0.608714	+	0.351441i	0.163748	+	0.986502i	$0.447642\pi$
$138$	−0.164814	+	4.79300i	−0.0140299	+	0.408007i
$139$			5.91224i			0.501470i	0.968056	+	0.250735i	$0.0806722\pi$
$139$			5.91224i			0.501470i	−0.968056	+	0.250735i	$0.919328\pi$
$140$	−2.86752	+	5.22692i	−0.242349	+	0.441755i
$141$	7.99940	−	2.34883i	0.673671	−	0.197808i
$142$	3.10545	+	8.97262i	0.260604	+	0.752966i
$143$	−0.270747	+	5.68369i	−0.0226410	+	0.475294i
$144$	0.327068	−	0.945001i	0.0272557	−	0.0787501i
$145$	5.89711	+	2.36085i	0.489728	+	0.196058i
$146$	−0.436378	+	1.48617i	−0.0361149	+	0.122996i
$147$	−5.04704	−	4.85051i	−0.416273	−	0.400063i
$148$	1.35232	+	0.194434i	0.111160	+	0.0159824i
$149$	−7.47648	+	5.32397i	−0.612497	+	0.436157i	−0.843750	−	0.536737i	$-0.819657\pi$
$149$	−7.47648	+	5.32397i	−0.612497	+	0.436157i	0.231253	+	0.972894i	$0.425717\pi$
$150$	0.00737820	+	0.0772680i	0.000602428	+	0.00630891i
$151$	0.251654	−	0.100747i	0.0204793	−	0.00819868i	−0.361400	−	0.932411i	$-0.617701\pi$
$151$	0.251654	−	0.100747i	0.0204793	−	0.00819868i	0.381880	+	0.924212i	$0.375277\pi$
$152$	−0.182086	−	3.82247i	−0.0147692	−	0.310043i
$153$	3.30964	+	0.971798i	0.267568	+	0.0785652i
$154$	−5.67588	−	5.69832i	−0.457376	−	0.459184i
$155$	−11.8183	+	10.2406i	−0.949271	+	0.822548i
$156$	1.66374	−	0.857718i	0.133206	−	0.0686724i
$157$	15.3006	+	2.94896i	1.22112	+	0.235352i	0.758780	−	0.651348i	$-0.225796\pi$
$157$	15.3006	+	2.94896i	1.22112	+	0.235352i	0.462345	+	0.886700i	$0.347008\pi$
$158$	7.68064	−	8.05523i	0.611039	−	0.640840i
$159$	11.9182	+	1.13805i	0.945175	+	0.0902533i
$160$	2.25336			0.178144
$161$	−0.444695	−	12.6808i	−0.0350469	−	0.999386i
$162$	1.00000			0.0785674
$163$	−21.6586	−	2.06814i	−1.69643	−	0.161989i	−0.798460	−	0.602048i	$-0.794352\pi$
$163$	−21.6586	−	2.06814i	−1.69643	−	0.161989i	−0.897969	+	0.440059i	$0.854958\pi$
$164$	2.24958	−	2.35929i	0.175663	−	0.184230i
$165$	−6.72617	−	1.29636i	−0.523632	−	0.100922i
$166$	−10.1724	+	5.24425i	−0.789534	+	0.407033i
$167$	−1.81066	+	1.56895i	−0.140113	+	0.121409i	−0.722098	−	0.691791i	$-0.756822\pi$
$167$	−1.81066	+	1.56895i	−0.140113	+	0.121409i	0.581984	+	0.813200i	$0.302276\pi$
$168$	−0.689812	+	2.55424i	−0.0532201	+	0.197064i
$169$	−9.11162	−	2.67541i	−0.700894	−	0.205801i
$170$	0.369837	+	7.76384i	0.0283652	+	0.595460i
$171$	3.55268	−	1.42228i	0.271680	−	0.108764i
$172$	−0.0595451	−	0.623584i	−0.00454027	−	0.0475479i
$173$	10.3111	−	7.34252i	0.783940	−	0.558241i	−0.116515	−	0.993189i	$-0.537172\pi$
$173$	10.3111	−	7.34252i	0.783940	−	0.558241i	0.900456	+	0.434947i	$0.143233\pi$
$174$	2.79027	+	0.401180i	0.211530	+	0.0304134i
$175$	−0.0336555	−	0.202585i	−0.00254412	−	0.0153140i
$176$	−0.856436	+	2.91675i	−0.0645563	+	0.219859i
$177$	9.26356	+	3.70857i	0.696292	+	0.278753i
$178$	−5.01931	+	14.5024i	−0.376213	+	1.08700i
$179$	1.08351	−	22.7457i	0.0809855	−	1.70010i	−0.484059	−	0.875035i	$-0.660838\pi$
$179$	1.08351	−	22.7457i	0.0809855	−	1.70010i	0.565045	−	0.825060i	$-0.308859\pi$
$180$	0.737001	+	2.12942i	0.0549328	+	0.158718i
$181$	−16.0725	+	4.71932i	−1.19466	+	0.350784i	−0.817809	−	0.575489i	$-0.804812\pi$
$181$	−16.0725	+	4.71932i	−1.19466	+	0.350784i	−0.376852	+	0.926274i	$0.622993\pi$
$182$	−4.23382	+	2.56920i	−0.313831	+	0.190442i
$183$		−	5.66425i		−	0.418713i
$184$	−4.12123	+	2.45264i	−0.303821	+	0.180811i
$185$	−2.66614	+	1.53930i	−0.196019	+	0.113171i
$186$	−4.02549	+	5.65301i	−0.295163	+	0.414499i
$187$	−10.1901	−	2.47209i	−0.745174	−	0.180777i
$188$	6.30077	+	5.45964i	0.459531	+	0.398185i
$189$	−2.63938	+	0.183539i	−0.191986	+	0.0133505i
$190$	5.64696	+	6.51694i	0.409674	+	0.472789i
$191$	−7.25097	+	18.1120i	−0.524662	+	1.31054i	0.395307	+	0.918549i	$0.370638\pi$
$191$	−7.25097	+	18.1120i	−0.524662	+	1.31054i	−0.919968	+	0.391993i	$0.871786\pi$
$192$	0.971812	−	0.235759i	0.0701345	−	0.0170144i
$193$	−7.52115	−	3.87742i	−0.541384	−	0.279103i	0.165768	−	0.986165i	$-0.446990\pi$
$193$	−7.52115	−	3.87742i	−0.541384	−	0.279103i	−0.707152	+	0.707062i	$0.750020\pi$
$194$	−1.37397	−	1.08050i	−0.0986455	−	0.0775757i
$195$	−1.75217	+	3.83672i	−0.125476	+	0.274753i
$196$	1.35187	−	6.86822i	0.0965622	−	0.490587i
$197$	−2.06358	+	14.3525i	−0.147024	+	1.02258i	0.774032	+	0.633147i	$0.218237\pi$
$197$	−2.06358	+	14.3525i	−0.147024	+	1.02258i	−0.921056	+	0.389430i	$0.872672\pi$
$198$	−3.03645	+	0.144644i	−0.215791	+	0.0102794i
$199$	3.64748	+	15.0351i	0.258563	+	1.06581i	0.941949	+	0.335755i	$0.108991\pi$
$199$	3.64748	+	15.0351i	0.258563	+	1.06581i	−0.683386	+	0.730057i	$0.739493\pi$
$200$	−0.0610130	+	0.0479812i	−0.00431427	+	0.00339278i
$201$	6.10523	−	1.17669i	0.430629	−	0.0829970i
$202$	2.50853	−	3.90335i	0.176500	−	0.274639i
$203$	−7.43820	−	0.546743i	−0.522060	−	0.0383739i
$204$	0.971798	+	3.30964i	0.0680395	+	0.231721i
$205$	−0.698252	+	7.31243i	−0.0487681	+	0.510722i
$206$	−3.33957	−	5.78431i	−0.232679	−	0.403012i
$207$	−3.66567	−	3.09239i	−0.254782	−	0.214936i
$208$	1.62105	+	0.935911i	0.112399	+	0.0648937i
$209$	−10.5818	+	4.83254i	−0.731958	+	0.334274i
$210$	−2.33606	−	5.48509i	−0.161203	−	0.378507i
$211$	3.11678	−	3.59695i	0.214568	−	0.247624i	−0.638255	−	0.769825i	$-0.720343\pi$
$211$	3.11678	−	3.59695i	0.214568	−	0.247624i	0.852823	+	0.522201i	$0.174889\pi$
$212$	5.48608	+	10.6415i	0.376785	+	0.730862i
$213$	−8.97262	−	3.10545i	−0.614794	−	0.212782i
$214$	−4.55867	−	5.79682i	−0.311624	−	0.396263i
$215$	0.974081	+	1.02159i	0.0664318	+	0.0696716i
$216$	0.540641	+	0.841254i	0.0367859	+	0.0572401i
$217$	9.58724	−	15.6593i	0.650824	−	1.06302i
$218$	−2.18714	−	0.998832i	−0.148132	−	0.0676494i
$219$	−0.898456	−	1.26170i	−0.0607120	−	0.0852581i
$220$	−2.54587	−	6.35928i	−0.171643	−	0.428743i
$221$	−2.95858	+	5.73885i	−0.199016	+	0.386037i
$222$	−0.988785	+	0.942804i	−0.0663629	+	0.0632769i
$223$	−22.3029	+	3.20667i	−1.49351	+	0.214734i	−0.840167	−	0.542328i	$-0.817543\pi$
$223$	−22.3029	+	3.20667i	−1.49351	+	0.214734i	−0.653343	+	0.757062i	$0.726634\pi$
$224$	−2.52171	+	0.800622i	−0.168489	+	0.0534938i
$225$	−0.0652977	−	0.0419643i	−0.00435318	−	0.00279762i
$226$	10.6912	−	3.70028i	0.711171	−	0.246139i
$227$	−20.4770	−	19.5248i	−1.35911	−	1.29591i	−0.916969	−	0.398960i	$-0.869371\pi$
$227$	−20.4770	−	19.5248i	−1.35911	−	1.29591i	−0.442139	−	0.896947i	$-0.645780\pi$
$228$	3.11722	+	2.21976i	0.206443	+	0.147007i
$229$	0.737166	−	1.27681i	0.0487133	−	0.0843739i	−0.840641	−	0.541593i	$-0.817821\pi$
$229$	0.737166	−	1.27681i	0.0487133	−	0.0843739i	0.889354	+	0.457219i	$0.151155\pi$
$230$	3.88340	−	10.0849i	0.256064	−	0.664976i
$231$	7.98778	−	0.939075i	0.525557	−	0.0617866i
$232$	1.17104	+	2.56422i	0.0768825	+	0.168349i
$233$	−1.90140	+	7.83768i	−0.124565	+	0.513464i	0.875004	+	0.484115i	$0.160858\pi$
$233$	−1.90140	+	7.83768i	−0.124565	+	0.513464i	−0.999569	+	0.0293485i	$0.990657\pi$
$234$	−0.354245	+	1.83800i	−0.0231577	+	0.120154i
$235$	−18.7652	−	0.893897i	−1.22411	−	0.0583114i
$236$	1.88841	+	9.79801i	0.122925	+	0.637796i
$237$	1.58398	+	11.0168i	0.102890	+	0.715618i
$238$	−3.17239	−	8.55702i	−0.205635	−	0.554670i
$239$	−5.71274	+	3.67135i	−0.369526	+	0.237480i	−0.712203	−	0.701973i	$-0.752303\pi$
$239$	−5.71274	+	3.67135i	−0.369526	+	0.237480i	0.342677	+	0.939453i	$0.388666\pi$
$240$	−1.39293	+	1.77126i	−0.0899134	+	0.114334i
$241$	4.48302	−	0.428076i	0.288777	−	0.0275748i	0.0503374	−	0.998732i	$-0.483970\pi$
$241$	4.48302	−	0.428076i	0.288777	−	0.0275748i	0.238439	+	0.971157i	$0.423364\pi$
$242$	−1.75111	+	0.167210i	−0.112565	+	0.0107487i
$243$	−0.618159	+	0.786053i	−0.0396549	+	0.0504253i
$244$	4.76507	−	3.06232i	0.305052	−	0.196045i
$245$	7.17246	+	14.0485i	0.458232	+	0.897523i
$246$	0.463930	+	3.22671i	0.0295791	+	0.205727i
$247$	1.35562	+	7.03364i	0.0862562	+	0.447540i
$248$	−6.93196	−	0.330210i	−0.440180	−	0.0209683i
$249$	2.16592	−	11.2379i	0.137260	−	0.712170i
$250$	−2.61501	+	10.7792i	−0.165388	+	0.681738i
$251$	−10.4153	−	22.8064i	−0.657409	−	1.43953i	−0.884917	−	0.465749i	$-0.845785\pi$
$251$	−10.4153	−	22.8064i	−0.657409	−	1.43953i	0.227507	−	0.973776i	$-0.426942\pi$
$252$	−1.58136	−	2.12116i	−0.0996162	−	0.133620i
$253$	11.5779	+	8.85965i	0.727897	+	0.557002i
$254$	−5.37356	+	9.30728i	−0.337167	+	0.583991i
$255$	−6.33141	−	4.50858i	−0.396488	−	0.282338i
$256$	0.723734	+	0.690079i	0.0452334	+	0.0431299i
$257$	−0.840514	+	0.290905i	−0.0524298	+	0.0181461i	−0.353157	−	0.935564i	$-0.614892\pi$
$257$	−0.840514	+	0.290905i	−0.0524298	+	0.0181461i	0.300727	+	0.953710i	$0.402771\pi$
$258$	0.526979	+	0.338669i	0.0328083	+	0.0210846i
$259$	2.43673	−	2.66990i	0.151411	−	0.165899i
$260$	−4.17495	+	0.600267i	−0.258920	+	0.0372270i
$261$	−2.04018	+	1.94531i	−0.126284	+	0.120411i
$262$	1.11774	−	2.16810i	0.0690539	−	0.133946i
$263$	−8.76171	−	21.8857i	−0.540270	−	1.34953i	−0.907755	−	0.419500i	$-0.862205\pi$
$263$	−8.76171	−	21.8857i	−0.540270	−	1.34953i	0.367485	−	0.930030i	$-0.380219\pi$
$264$	−1.76331	−	2.47622i	−0.108524	−	0.152401i
$265$	−24.5402	−	11.2071i	−1.50749	−	0.688448i
$266$	−8.63493	−	5.28666i	−0.529442	−	0.324146i
$267$	−8.29688	−	12.9102i	−0.507761	−	0.790092i
$268$	4.29063	+	4.49988i	0.262092	+	0.274874i
$269$	−5.91569	−	7.52241i	−0.360686	−	0.458650i	0.571514	−	0.820592i	$-0.306356\pi$
$269$	−5.91569	−	7.52241i	−0.360686	−	0.458650i	−0.932200	+	0.361942i	$0.882114\pi$
$270$	−2.12942	−	0.737001i	−0.129593	−	0.0448525i
$271$	−9.41977	−	18.2718i	−0.572211	−	1.10993i	−0.980396	−	0.197035i	$-0.936869\pi$
$271$	−9.41977	−	18.2718i	−0.572211	−	1.10993i	0.408186	−	0.912899i	$-0.366161\pi$
$272$	−2.25885	+	2.60685i	−0.136963	+	0.158064i
$273$	0.597642	−	4.91618i	0.0361709	−	0.297541i
$274$	7.48357	−	3.41763i	0.452099	−	0.206467i
$275$	0.204343	+	0.117977i	0.0123223	+	0.00711430i
$276$	0.619671	−	4.75563i	0.0372998	−	0.286255i
$277$	6.29435	+	10.9021i	0.378191	+	0.655046i	0.990799	−	0.135341i	$-0.0432130\pi$
$277$	6.29435	+	10.9021i	0.378191	+	0.655046i	−0.612608	+	0.790387i	$0.709880\pi$
$278$	0.561994	−	5.88547i	0.0337062	−	0.352987i
$279$	−1.95517	−	6.65871i	−0.117053	−	0.398646i
$280$	3.35138	−	4.93068i	0.200283	−	0.294664i
$281$	1.60666	−	2.50001i	0.0958451	−	0.149138i	−0.790020	−	0.613082i	$-0.789930\pi$
$281$	1.60666	−	2.50001i	0.0958451	−	0.149138i	0.885865	+	0.463944i	$0.153566\pi$
$282$	−8.18645	+	1.57781i	−0.487496	+	0.0939571i
$283$	−16.8560	+	13.2557i	−1.00199	+	0.787970i	−0.977329	−	0.211726i	$-0.932092\pi$
$283$	−16.8560	+	13.2557i	−1.00199	+	0.787970i	−0.0246567	+	0.999696i	$0.507849\pi$
$284$	−2.23849	−	9.22719i	−0.132830	−	0.547533i
$285$	−8.61338	+	0.410306i	−0.510213	+	0.0243044i
$286$	0.809790	−	5.63221i	0.0478839	−	0.333040i
$287$	−1.81671	−	8.43135i	−0.107237	−	0.497687i
$288$	−0.415415	+	0.909632i	−0.0244786	+	0.0536006i
$289$	4.01036	+	3.15378i	0.235904	+	0.185517i
$290$	−5.64600	−	2.91071i	−0.331544	−	0.170923i
$291$	1.69867	−	0.412092i	0.0995776	−	0.0241573i
$292$	0.575672	−	1.43796i	0.0336886	−	0.0841502i
$293$	6.79518	+	7.84206i	0.396979	+	0.458138i	0.918687	−	0.394986i	$-0.129251\pi$
$293$	6.79518	+	7.84206i	0.396979	+	0.458138i	−0.521708	+	0.853124i	$0.674705\pi$
$294$	4.56311	+	5.30829i	0.266126	+	0.309586i
$295$	−16.9928	−	14.7244i	−0.989361	−	0.857286i
$296$	−1.32771	−	0.322100i	−0.0771719	−	0.0187217i
$297$	1.76331	−	2.47622i	0.102318	−	0.143685i
$298$	7.94870	−	4.58918i	0.460456	−	0.265844i
$299$	6.98234	−	5.64202i	0.403799	−	0.326287i
$300$		−	0.0776195i		−	0.00448136i
$301$	−1.45305	−	0.797154i	−0.0837527	−	0.0459472i
$302$	−0.260091	+	0.0763696i	−0.0149666	+	0.00439458i
$303$	1.51757	+	4.38473i	0.0871822	+	0.251896i
$304$	−0.182086	+	3.82247i	−0.0104434	+	0.219233i
$305$	−4.17455	+	12.0616i	−0.239034	+	0.690644i
$306$	−3.20228	−	1.28200i	−0.183062	−	0.0732870i
$307$	−3.31554	+	11.2917i	−0.189228	+	0.644451i	0.809154	+	0.587596i	$0.199926\pi$
$307$	−3.31554	+	11.2917i	−0.189228	+	0.644451i	−0.998382	+	0.0568553i	$0.981893\pi$
$308$	5.10852	+	6.21205i	0.291085	+	0.353964i
$309$	6.61116	+	0.950541i	0.376096	+	0.0540744i
$310$	12.7383	−	9.07087i	0.723484	−	0.515191i
$311$	0.163255	+	1.70969i	0.00925736	+	0.0969475i	0.998920	−	0.0464696i	$-0.0147970\pi$
$311$	0.163255	+	1.70969i	0.00925736	+	0.0969475i	−0.989662	+	0.143417i	$0.954191\pi$
$312$	−1.73774	+	0.695686i	−0.0983801	+	0.0393855i
$313$	−0.737893	−	15.4903i	−0.0417082	−	0.875563i	−0.918676	−	0.395013i	$-0.870740\pi$
$313$	−0.737893	−	15.4903i	−0.0417082	−	0.875563i	0.876967	−	0.480550i	$-0.159563\pi$
$314$	−14.9510	−	4.39002i	−0.843737	−	0.247743i
$315$	5.75562	+	1.55439i	0.324293	+	0.0875801i
$316$	−8.41156	+	7.28866i	−0.473187	+	0.410019i
$317$	−18.3562	+	9.46326i	−1.03099	+	0.531510i	−0.888783	−	0.458328i	$-0.848449\pi$
$317$	−18.3562	+	9.46326i	−1.03099	+	0.531510i	−0.142202	+	0.989838i	$0.545418\pi$
$318$	−11.7561	−	2.26579i	−0.659247	−	0.127059i
$319$	5.91352	−	6.20192i	0.331093	−	0.347241i
$320$	−2.24315	−	0.214195i	−0.125396	−	0.0119739i
$321$	7.37459			0.411610
$322$	−0.762704	+	12.6656i	−0.0425038	+	0.705828i
$323$	−13.2000			−0.734469
$324$	−0.995472	−	0.0950560i	−0.0553040	−	0.00528089i
$325$	0.100261	−	0.105151i	0.00556151	−	0.00583274i
$326$	21.3639	+	4.11755i	1.18324	+	0.228050i
$327$	2.13713	−	1.10177i	0.118184	−	0.0609280i
$328$	−2.46366	+	2.13477i	−0.136033	+	0.117873i
$329$	21.3175	−	5.66696i	1.17527	−	0.312430i
$330$	6.57249	+	1.92986i	0.361803	+	0.106235i
$331$	−0.344457	−	7.23103i	−0.0189330	−	0.397454i	−0.988366	−	0.152096i	$-0.951398\pi$
$331$	−0.344457	−	7.23103i	−0.0189330	−	0.397454i	0.969433	−	0.245357i	$-0.0789053\pi$
$332$	10.6249	−	4.25356i	0.583115	−	0.233444i
$333$	−0.129868	−	1.36004i	−0.00711673	−	0.0745297i
$334$	1.95160	−	1.38973i	0.106787	−	0.0760426i
$335$	−13.8678	−	1.99389i	−0.757681	−	0.108938i
$336$	0.929484	−	2.47711i	0.0507075	−	0.135137i
$337$	−8.34999	+	28.4374i	−0.454853	+	1.54909i	0.338886	+	0.940827i	$0.389950\pi$
$337$	−8.34999	+	28.4374i	−0.454853	+	1.54909i	−0.793739	+	0.608259i	$0.791868\pi$
$338$	8.81604	+	3.52941i	0.479530	+	0.191975i
$339$	−3.70028	+	10.6912i	−0.200971	+	0.580669i
$340$	0.369837	−	7.76384i	0.0200572	−	0.421053i
$341$	6.89992	+	19.9360i	0.373652	+	1.07960i
$342$	−3.67179	+	1.07813i	−0.198548	+	0.0582988i
$343$	−13.0181	−	13.1731i	−0.702909	−	0.711280i
$344$			0.626421i			0.0337743i
$345$	5.52668	+	9.28661i	0.297546	+	0.499974i
$346$	−10.9624	+	6.32914i	−0.589342	+	0.340257i
$347$	−4.46303	+	6.26746i	−0.239588	+	0.336455i	−0.916810	−	0.399325i	$-0.869245\pi$
$347$	−4.46303	+	6.26746i	−0.239588	+	0.336455i	0.677221	+	0.735779i	$0.263184\pi$
$348$	−2.73950	−	0.664595i	−0.146853	−	0.0356260i
$349$	6.05855	+	5.24976i	0.324307	+	0.281013i	0.801763	−	0.597642i	$-0.203896\pi$
$349$	6.05855	+	5.24976i	0.324307	+	0.281013i	−0.477456	+	0.878656i	$0.658441\pi$
$350$	0.0142462	+	0.204867i	0.000761490	+	0.0109506i
$351$	−1.22578	−	1.41463i	−0.0654274	−	0.0755073i
$352$	1.12981	−	2.82214i	0.0602192	−	0.150420i
$353$	9.72095	−	2.35828i	0.517394	−	0.125518i	0.0314449	−	0.999505i	$-0.489989\pi$
$353$	9.72095	−	2.35828i	0.517394	−	0.125518i	0.485949	+	0.873987i	$0.338474\pi$
$354$	−8.86909	−	4.57233i	−0.471387	−	0.243017i
$355$	16.8178	+	13.2257i	0.892596	+	0.701945i
$356$	6.37512	−	13.9596i	0.337881	−	0.739856i
$357$	8.68732	+	2.79594i	0.459782	+	0.147977i
$358$	−3.24073	+	22.5397i	−0.171278	+	1.19126i
$359$	−19.7261	+	0.939668i	−1.04110	+	0.0495938i	−0.561160	−	0.827707i	$-0.689645\pi$
$359$	−19.7261	+	0.939668i	−1.04110	+	0.0495938i	−0.479941	+	0.877301i	$0.659342\pi$
$360$	−0.531249	−	2.18984i	−0.0279993	−	0.115415i
$361$	3.42374	−	2.69246i	0.180197	−	0.141708i
$362$	16.4483	−	3.17016i	0.864506	−	0.166620i
$363$	0.951026	−	1.47983i	0.0499159	−	0.0776707i
$364$	4.45886	−	2.15512i	0.233708	−	0.112959i
$365$	0.983317	+	3.34887i	0.0514691	+	0.175288i
$366$	−0.538421	+	5.63860i	−0.0281437	+	0.294734i
$367$	3.55975	+	6.16567i	0.185818	+	0.321845i	0.943852	−	0.330369i	$-0.107173\pi$
$367$	3.55975	+	6.16567i	0.185818	+	0.321845i	−0.758034	+	0.652215i	$0.773840\pi$
$368$	4.33571	−	2.04979i	0.226014	−	0.106853i
$369$	−2.82314	−	1.62994i	−0.146967	−	0.0848515i
$370$	2.80039	−	1.27890i	0.145585	−	0.0664866i
$371$	31.4445	+	3.82260i	1.63252	+	0.198459i
$372$	4.54462	−	5.24477i	0.235627	−	0.271928i
$373$	8.50762	+	16.5025i	0.440508	+	0.854466i	0.999677	+	0.0254126i	$0.00808997\pi$
$373$	8.50762	+	16.5025i	0.440508	+	0.854466i	−0.559169	+	0.829054i	$0.688880\pi$
$374$	9.90898	+	3.42953i	0.512381	+	0.177337i
$375$	−6.85655	−	8.71881i	−0.354071	−	0.450237i
$376$	−5.75326	−	6.03385i	−0.296702	−	0.311172i
$377$	−2.85274	−	4.43895i	−0.146924	−	0.228618i
$378$	2.64487	+	0.0681812i	0.136038	+	0.00350686i
$379$	−24.2962	−	11.0957i	−1.24801	−	0.569947i	−0.321748	−	0.946825i	$-0.604270\pi$
$379$	−24.2962	−	11.0957i	−1.24801	−	0.569947i	−0.926263	+	0.376878i	$0.876998\pi$
$380$	−5.00192	−	7.02421i	−0.256593	−	0.360334i
$381$	−3.99430	−	9.97728i	−0.204634	−	0.511152i
$382$	8.93980	−	17.3408i	0.457400	−	0.887232i
$383$	7.75750	−	7.39676i	0.396390	−	0.377957i	−0.465504	−	0.885046i	$-0.654127\pi$
$383$	7.75750	−	7.39676i	0.396390	−	0.377957i	0.861894	+	0.507089i	$0.169278\pi$
$384$	−0.989821	+	0.142315i	−0.0505116	+	0.00726247i
$385$	−17.7015	−	3.88731i	−0.902151	−	0.198116i
$386$	7.11852	+	4.57479i	0.362323	+	0.232851i
$387$	−0.591968	+	0.204882i	−0.0300914	+	0.0104147i
$388$	1.26504	+	1.20622i	0.0642228	+	0.0612363i
$389$	5.38642	+	3.83565i	0.273102	+	0.194475i	0.708400	−	0.705811i	$-0.249417\pi$
$389$	5.38642	+	3.83565i	0.273102	+	0.194475i	−0.435297	+	0.900287i	$0.643357\pi$
$390$	2.10894	−	3.65279i	0.106790	−	0.184966i
$391$	7.77406	+	14.6021i	0.393151	+	0.738458i
$392$	−1.99862	+	6.70862i	−0.100945	+	0.338836i
$393$	1.01331	+	2.21883i	0.0511146	+	0.111925i
$394$	3.41854	−	14.0914i	0.172223	−	0.709914i
$395$	4.74644	−	24.6269i	0.238819	−	1.23911i
$396$	3.03645	+	0.144644i	0.152587	+	0.00726862i
$397$	5.70229	+	29.5863i	0.286190	+	1.48489i	0.785713	+	0.618592i	$0.212297\pi$
$397$	5.70229	+	29.5863i	0.286190	+	1.48489i	−0.499523	+	0.866301i	$0.666491\pi$
$398$	−2.20179	−	15.3138i	−0.110366	−	0.767610i
$399$	9.49335	−	3.51952i	0.475262	−	0.176196i
$400$	0.0652977	−	0.0419643i	0.00326488	−	0.00209821i
$401$	20.8026	−	26.4526i	1.03883	−	1.32098i	0.0932334	−	0.995644i	$-0.470280\pi$
$401$	20.8026	−	26.4526i	1.03883	−	1.32098i	0.945598	−	0.325337i	$-0.105478\pi$
$402$	−6.18943	+	0.591019i	−0.308701	+	0.0294774i
$403$	12.9313	−	1.23479i	0.644153	−	0.0615092i
$404$	−2.86821	+	3.64723i	−0.142699	+	0.181456i
$405$	1.89564	−	1.21826i	0.0941954	−	0.0605357i
$406$	7.35255	+	1.25131i	0.364901	+	0.0621017i
$407$	0.591059	+	4.11090i	0.0292977	+	0.203770i
$408$	−0.652796	−	3.38703i	−0.0323182	−	0.167683i
$409$	26.2833	+	1.25203i	1.29962	+	0.0619088i	0.685949	−	0.727649i	$-0.259387\pi$
$409$	26.2833	+	1.25203i	1.29962	+	0.0619088i	0.613676	+	0.789558i	$0.289690\pi$
$410$	1.39018	−	7.21294i	0.0686561	−	0.356222i
$411$	−1.93960	+	7.99513i	−0.0956732	+	0.394370i
$412$	2.77462	+	6.07556i	0.136695	+	0.299321i
$413$	24.2481	+	10.4403i	1.19317	+	0.513733i
$414$	3.35512	+	3.42683i	0.164895	+	0.168419i
$415$	−12.8945	+	22.3339i	−0.632965	+	1.09633i
$416$	−1.52474	−	1.08576i	−0.0747566	−	0.0532339i
$417$	4.27889	+	4.07991i	0.209538	+	0.199794i
$418$	10.9932	−	3.80480i	0.537697	−	0.186099i
$419$	16.5080	+	10.6090i	0.806468	+	0.518286i	0.877721	−	0.479173i	$-0.159063\pi$
$419$	16.5080	+	10.6090i	0.806468	+	0.518286i	−0.0712525	+	0.997458i	$0.522700\pi$
$420$	1.80409	+	5.68231i	0.0880304	+	0.277268i
$421$	37.2065	−	5.34949i	1.81334	−	0.260718i	0.849572	−	0.527473i	$-0.176860\pi$
$421$	37.2065	−	5.34949i	1.81334	−	0.260718i	0.963764	+	0.266755i	$0.0859514\pi$
$422$	−3.44457	+	3.28439i	−0.167679	+	0.159882i
$423$	3.82028	−	7.41032i	0.185749	−	0.360302i
$424$	−4.44970	−	11.1148i	−0.216096	−	0.539783i
$425$	0.155303	+	0.218093i	0.00753331	+	0.0105791i
$426$	8.63680	+	3.94429i	0.418454	+	0.191102i
$427$	0.386195	−	14.9812i	0.0186893	−	0.724991i
$428$	3.98701	+	6.20390i	0.192719	+	0.299877i
$429$	3.92664	+	4.11814i	0.189580	+	0.198826i
$430$	−0.872562	−	1.10955i	−0.0420787	−	0.0535074i
$431$	5.28011	+	1.82746i	0.254334	+	0.0880258i	0.451260	−	0.892393i	$-0.350975\pi$
$431$	5.28011	+	1.82746i	0.254334	+	0.0880258i	−0.196926	+	0.980418i	$0.563096\pi$
$432$	−0.458227	−	0.888835i	−0.0220464	−	0.0427641i
$433$	−1.19289	+	1.37667i	−0.0573269	+	0.0661587i	−0.783689	−	0.621154i	$-0.786664\pi$
$433$	−1.19289	+	1.37667i	−0.0573269	+	0.0661587i	0.726362	+	0.687312i	$0.241210\pi$
$434$	−11.0323	+	14.6770i	−0.529569	+	0.704520i
$435$	5.77810	−	2.63877i	0.277039	−	0.126519i
$436$	2.08229	+	1.20221i	0.0997235	+	0.0575754i
$437$	16.7936	+	7.40251i	0.803345	+	0.354110i
$438$	0.774455	+	1.34140i	0.0370049	+	0.0640944i
$439$	−1.68673	+	17.6642i	−0.0805032	+	0.843068i	0.861565	+	0.507647i	$0.169485\pi$
$439$	−1.68673	+	17.6642i	−0.0805032	+	0.843068i	−0.942068	+	0.335421i	$0.891121\pi$
$440$	1.92986	+	6.57249i	0.0920023	+	0.313331i
$441$	−6.99333	+	0.305481i	−0.333016	+	0.0145467i
$442$	3.49070	−	5.43163i	0.166036	−	0.258356i
$443$	21.6673	−	4.17603i	1.02944	−	0.198409i	0.353556	−	0.935413i	$-0.384972\pi$
$443$	21.6673	−	4.17603i	1.02944	−	0.198409i	0.675888	+	0.737004i	$0.263760\pi$
$444$	1.07393	−	0.844545i	0.0509663	−	0.0400803i
$445$	8.15276	+	33.6061i	0.386478	+	1.59308i
$446$	22.5067	−	1.07213i	1.06572	−	0.0507666i
$447$	−1.30622	+	9.08494i	−0.0617820	+	0.429703i
$448$	2.58639	−	0.557293i	0.122196	−	0.0263296i
$449$	1.11199	−	2.43492i	0.0524781	−	0.114911i	−0.881577	−	0.472041i	$-0.843517\pi$
$449$	1.11199	−	2.43492i	0.0524781	−	0.114911i	0.934055	+	0.357130i	$0.116245\pi$
$450$	0.0610130	+	0.0479812i	0.00287618	+	0.00226185i
$451$	8.80809	+	4.54089i	0.414757	+	0.213822i
$452$	−10.9946	+	2.66725i	−0.517141	+	0.125457i
$453$	0.100747	−	0.251654i	0.00473351	−	0.0118237i
$454$	18.5283	+	21.3829i	0.869578	+	1.00355i
$455$	−4.89586	+	10.0282i	−0.229522	+	0.470128i
$456$	−2.89210	−	2.50602i	−0.135435	−	0.117355i
$457$	−31.2949	−	7.59206i	−1.46391	−	0.355141i	−0.576873	−	0.816834i	$-0.695727\pi$
$457$	−31.2949	−	7.59206i	−1.46391	−	0.355141i	−0.887040	+	0.461692i	$0.847242\pi$
$458$	−0.855196	+	1.20095i	−0.0399607	+	0.0561169i
$459$	2.98724	−	1.72468i	0.139432	−	0.0805012i
$460$	−4.82445	+	9.67006i	−0.224941	+	0.450869i
$461$		−	16.8319i		−	0.783938i	−0.919978	−	0.391969i	$-0.871794\pi$
$461$		−	16.8319i		−	0.783938i	0.919978	−	0.391969i	$-0.128206\pi$
$462$	−8.04088	+	0.175536i	−0.374095	+	0.00816667i
$463$	10.4587	−	3.07096i	0.486059	−	0.142720i	−0.0295162	−	0.999564i	$-0.509397\pi$
$463$	10.4587	−	3.07096i	0.486059	−	0.142720i	0.515575	+	0.856845i	$0.327578\pi$
$464$	−0.921992	−	2.66392i	−0.0428024	−	0.123669i
$465$	−0.744081	+	15.6202i	−0.0345059	+	0.724369i
$466$	2.63781	−	7.62145i	0.122194	−	0.353057i
$467$	25.3772	+	10.1595i	1.17431	+	0.470125i	0.875044	−	0.484043i	$-0.160832\pi$
$467$	25.3772	+	10.1595i	1.17431	+	0.470125i	0.299271	+	0.954168i	$0.403257\pi$
$468$	0.527353	−	1.79600i	0.0243769	−	0.0830201i
$469$	16.2278	−	2.69592i	0.749329	−	0.124486i
$470$	18.5953	+	2.67360i	0.857736	+	0.123324i
$471$	12.6929	−	9.03859i	0.584859	−	0.416476i
$472$	−0.948500	−	9.93315i	−0.0436583	−	0.457210i
$473$	1.76784	−	0.707738i	0.0812856	−	0.0325418i
$474$	−0.529591	−	11.1175i	−0.0243249	−	0.510643i
$475$	0.285002	+	0.0836842i	0.0130768	+	0.00383970i
$476$	2.34463	+	8.81983i	0.107466	+	0.404256i
$477$	9.04815	−	7.84027i	0.414286	−	0.358981i
$478$	6.03585	−	3.11170i	0.276073	−	0.142326i
$479$	−2.84125	−	0.547606i	−0.129820	−	0.0250208i	0.123927	−	0.992291i	$-0.460451\pi$
$479$	−2.84125	−	0.547606i	−0.129820	−	0.0250208i	−0.253747	+	0.967271i	$0.581663\pi$
$480$	1.55499	−	1.63083i	0.0709755	−	0.0744369i
$481$	2.54575	+	0.243090i	0.116076	+	0.0110839i
$482$	−4.50341			−0.205125
$483$	−9.48439	−	8.42890i	−0.431555	−	0.383528i
$484$	1.75907			0.0799578
$485$	−3.92090	−	0.374400i	−0.178039	−	0.0170006i
$486$	0.690079	−	0.723734i	0.0313026	−	0.0328292i
$487$	−37.7963	−	7.28464i	−1.71271	−	0.330099i	−0.763757	−	0.645503i	$-0.776648\pi$
$487$	−37.7963	−	7.28464i	−1.71271	−	0.330099i	−0.948957	+	0.315405i	$0.897860\pi$
$488$	−5.03458	+	2.59551i	−0.227905	+	0.117493i
$489$	−16.4429	+	14.2479i	−0.743574	+	0.644310i
$490$	−5.80459	−	14.6666i	−0.262225	−	0.662571i
$491$	−9.18612	−	2.69729i	−0.414564	−	0.121727i	0.0677978	−	0.997699i	$-0.478403\pi$
$491$	−9.18612	−	2.69729i	−0.414564	−	0.121727i	−0.482362	+	0.875972i	$0.660221\pi$
$492$	−0.155112	−	3.25619i	−0.00699297	−	0.146801i
$493$	9.02710	−	3.61390i	0.406560	−	0.162762i
$494$	−0.680895	−	7.13065i	−0.0306349	−	0.320823i
$495$	−5.57981	+	3.97337i	−0.250794	+	0.178589i
$496$	6.86918	+	0.987639i	0.308435	+	0.0443463i
$497$	−23.5197	−	8.82530i	−1.05500	−	0.395869i
$498$	−3.22434	+	10.9811i	−0.144486	+	0.492074i
$499$	−32.7470	−	13.1099i	−1.46596	−	0.586881i	−0.504887	−	0.863185i	$-0.668466\pi$
$499$	−32.7470	−	13.1099i	−1.46596	−	0.586881i	−0.961070	+	0.276305i	$0.910890\pi$
$500$	3.62780	−	10.4818i	0.162240	−	0.468762i
$501$	−0.113999	+	2.39314i	−0.00509310	+	0.106917i
$502$	8.20028	+	23.6931i	0.365996	+	1.05748i
$503$	40.3665	−	11.8527i	1.79986	−	0.528485i	0.802208	−	0.597044i	$-0.203658\pi$
$503$	40.3665	−	11.8527i	1.79986	−	0.528485i	0.997647	+	0.0685590i	$0.0218401\pi$
$504$	1.37257	+	2.26187i	0.0611391	+	0.100752i
$505$		−	10.4554i		−	0.465260i
$506$	−10.6833	−	9.92009i	−0.474931	−	0.441002i
$507$	−8.22402	+	4.74814i	−0.365242	+	0.210872i
$508$	6.23394	−	8.75434i	0.276586	−	0.388411i
$509$	29.6666	+	7.19704i	1.31495	+	0.319003i	0.831088	−	0.556141i	$-0.187719\pi$
$509$	29.6666	+	7.19704i	1.31495	+	0.319003i	0.483862	+	0.875144i	$0.339234\pi$
$510$	5.87417	+	5.09000i	0.260113	+	0.225389i
$511$	−2.29028	−	3.39831i	−0.101316	−	0.150332i
$512$	−0.654861	−	0.755750i	−0.0289410	−	0.0333997i
$513$	1.42228	−	3.55268i	0.0627951	−	0.156855i
$514$	0.864360	−	0.209691i	0.0381253	−	0.00924909i
$515$	−13.3774	−	6.89653i	−0.589479	−	0.303898i
$516$	−0.492400	−	0.387228i	−0.0216767	−	0.0170467i
$517$	−10.5282	+	23.0536i	−0.463031	+	1.01390i
$518$	−2.67949	+	2.42618i	−0.117730	+	0.106600i
$519$	1.80146	−	12.5294i	0.0790753	−	0.549981i
$520$	4.21311	−	0.200695i	0.184757	−	0.00880106i
$521$	−4.82590	−	19.8926i	−0.211427	−	0.871513i	−0.974353	−	0.225027i	$-0.927753\pi$
$521$	−4.82590	−	19.8926i	−0.211427	−	0.871513i	0.762926	−	0.646486i	$-0.223762\pi$
$522$	2.21585	−	1.74257i	0.0969853	−	0.0762701i
$523$	13.7494	−	2.64999i	0.601221	−	0.115876i	0.120446	−	0.992720i	$-0.461568\pi$
$523$	13.7494	−	2.64999i	0.601221	−	0.115876i	0.480775	+	0.876844i	$0.340355\pi$
$524$	−1.31877	+	2.05204i	−0.0576106	+	0.0896438i
$525$	−0.169843	−	0.115442i	−0.00741255	−	0.00503831i
$526$	6.64167	+	22.6195i	0.289591	+	0.986255i
$527$	−2.27545	+	23.8296i	−0.0991200	+	1.03803i
$528$	1.51994	+	2.63262i	0.0661471	+	0.114570i
$529$	−1.70169	−	22.9370i	−0.0739864	−	0.997259i
$530$	23.3638	+	13.4891i	1.01486	+	0.585928i
$531$	9.07661	−	4.14515i	0.393891	−	0.179884i
$532$	8.09330	+	6.08352i	0.350889	+	0.263754i
$533$	3.99591	−	4.61153i	0.173082	−	0.199748i
$534$	7.03212	+	13.6404i	0.304310	+	0.590278i
$535$	−15.7036	−	5.43508i	−0.678928	−	0.234979i
$536$	−3.84346	−	4.88735i	−0.166012	−	0.211101i
$537$	−15.7141	−	16.4805i	−0.678116	−	0.711187i
$538$	5.17385	+	8.05067i	0.223061	+	0.347089i
$539$	21.1907	−	1.93912i	0.912748	−	0.0835237i
$540$	2.04973	+	0.936078i	0.0882062	+	0.0402824i
$541$	−24.9180	−	34.9924i	−1.07131	−	1.50444i	−0.848222	−	0.529641i	$-0.822327\pi$
$541$	−24.9180	−	34.9924i	−1.07131	−	1.50444i	−0.223085	−	0.974799i	$-0.571613\pi$
$542$	7.64027	+	19.0845i	0.328178	+	0.819749i
$543$	−7.67578	+	14.8889i	−0.329399	+	0.638945i
$544$	2.49642	−	2.38033i	0.107033	−	0.102056i
$545$	−5.36287	+	0.771064i	−0.229720	+	0.0330288i
$546$	−1.06225	+	4.83711i	−0.0454600	+	0.207009i
$547$	−21.0665	−	13.5386i	−0.900739	−	0.578870i	0.00627027	−	0.999980i	$-0.498004\pi$
$547$	−21.0665	−	13.5386i	−0.900739	−	0.578870i	−0.907009	+	0.421110i	$0.861640\pi$
$548$	−7.77455	+	2.69080i	−0.332112	+	0.114945i
$549$	−4.09941	−	3.90878i	−0.174958	−	0.166823i
$550$	−0.192203	−	0.136867i	−0.00819556	−	0.00583603i
$551$	5.39380	−	9.34234i	0.229784	−	0.397997i
$552$	−1.06892	+	4.67519i	−0.0454961	+	0.198989i
$553$	3.43828	+	29.2460i	0.146211	+	1.24367i
$554$	−5.22954	−	11.4511i	−0.222182	−	0.486510i
$555$	−0.725807	+	2.99182i	−0.0308088	+	0.126996i
$556$	−1.11890	+	5.80540i	−0.0474519	+	0.246204i
$557$	−30.8940	−	1.47166i	−1.30902	−	0.0623564i	−0.618567	−	0.785732i	$-0.712286\pi$
$557$	−30.8940	−	1.47166i	−1.30902	−	0.0623564i	−0.690454	+	0.723376i	$0.742589\pi$
$558$	1.31337	+	6.81441i	0.0555994	+	0.288477i
$559$	−0.166871	−	1.16061i	−0.00705789	−	0.0490887i
$560$	−3.80490	+	4.58978i	−0.160786	+	0.193954i
$561$	−8.82112	+	5.66899i	−0.372428	+	0.239345i
$562$	−1.83702	+	2.33596i	−0.0774901	+	0.0985366i
$563$	45.0900	−	4.30557i	1.90032	−	0.181458i	0.921806	−	0.387652i	$-0.126714\pi$
$563$	45.0900	−	4.30557i	1.90032	−	0.181458i	0.978511	+	0.206194i	$0.0661079\pi$
$564$	8.29936	−	0.792492i	0.349466	−	0.0333700i
$565$	15.7589	−	20.0391i	0.662983	−	0.843051i
$566$	18.0397	−	11.5934i	0.758266	−	0.487308i
$567$	−1.68855	+	2.03686i	−0.0709123	+	0.0855402i
$568$	1.35126	+	9.39819i	0.0566974	+	0.394339i
$569$	−4.22208	−	21.9062i	−0.176999	−	0.918356i	−0.956451	−	0.291894i	$-0.905715\pi$
$569$	−4.22208	−	21.9062i	−0.176999	−	0.918356i	0.779452	−	0.626462i	$-0.215498\pi$
$570$	8.61338	+	0.410306i	0.360775	+	0.0171858i
$571$	3.85853	−	20.0200i	0.161474	−	0.837809i	−0.807352	−	0.590070i	$-0.799100\pi$
$571$	3.85853	−	20.0200i	0.161474	−	0.837809i	0.968827	−	0.247739i	$-0.0796877\pi$
$572$	−1.34150	+	5.52974i	−0.0560909	+	0.231210i
$573$	8.10456	+	17.7465i	0.338573	+	0.741371i
$574$	1.00704	+	8.56586i	0.0420329	+	0.357532i
$575$	−0.0752773	−	0.364559i	−0.00313928	−	0.0152032i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−0.131402	−	0.0935707i	−0.00547032	−	0.00389540i	0.577318	−	0.816519i	$-0.304099\pi$
$577$	−0.131402	−	0.0935707i	−0.00547032	−	0.00389540i	−0.582789	+	0.812624i	$0.698039\pi$
$578$	−3.69242	−	3.52071i	−0.153584	−	0.146442i
$579$	−7.99641	+	2.76758i	−0.332319	+	0.115017i
$580$	5.34375	+	3.43422i	0.221887	+	0.142598i
$581$	6.49479	−	29.5750i	0.269449	−	1.22698i
$582$	−1.73015	+	0.248758i	−0.0717169	+	0.0103113i
$583$	−26.3402	+	25.1153i	−1.09090	+	1.04017i
$584$	−0.709752	+	1.37673i	−0.0293697	+	0.0569693i
$585$	1.56763	+	3.91575i	0.0648135	+	0.161896i
$586$	−6.01898	−	8.45247i	−0.248642	−	0.349168i
$587$	−40.8712	−	18.6652i	−1.68693	−	0.770397i	−0.999004	−	0.0446194i	$-0.985792\pi$
$587$	−40.8712	−	18.6652i	−1.68693	−	0.770397i	−0.687930	−	0.725777i	$-0.741480\pi$
$588$	−4.03787	−	5.71801i	−0.166519	−	0.235807i
$589$	14.3580	+	22.3414i	0.591609	+	0.920562i
$590$	15.5162	+	16.2730i	0.638794	+	0.669948i
$591$	8.96339	+	11.3979i	0.368705	+	0.468846i
$592$	1.29109	+	0.446849i	0.0530633	+	0.0183654i
$593$	−1.85350	−	3.59529i	−0.0761142	−	0.147641i	0.847708	−	0.530464i	$-0.177982\pi$
$593$	−1.85350	−	3.59529i	−0.0761142	−	0.147641i	−0.923822	+	0.382823i	$0.874952\pi$
$594$	−1.99070	+	2.29740i	−0.0816796	+	0.0942633i
$595$	−16.4384	−	12.3563i	−0.673908	−	0.506559i
$596$	−8.34894	+	3.81283i	−0.341986	+	0.156180i
$597$	13.3985	+	7.73562i	0.548363	+	0.316598i
$598$	−7.48703	+	4.95276i	−0.306167	+	0.202534i
$599$	6.18666	+	10.7156i	0.252780	+	0.437828i	0.964290	−	0.264848i	$-0.0853217\pi$
$599$	6.18666	+	10.7156i	0.252780	+	0.437828i	−0.711510	+	0.702676i	$0.751988\pi$
$600$	−0.00737820	+	0.0772680i	−0.000301214	+	0.00315445i
$601$	−7.42914	−	25.3013i	−0.303041	−	1.03206i	−0.960432	−	0.278514i	$-0.910158\pi$
$601$	−7.42914	−	25.3013i	−0.303041	−	1.03206i	0.657391	−	0.753550i	$-0.271660\pi$
$602$	1.37070	+	0.931666i	0.0558656	+	0.0379719i
$603$	3.36148	−	5.23057i	0.136890	−	0.213005i
$604$	0.266173	−	0.0513006i	0.0108304	−	0.00208739i
$605$	−3.11577	+	2.45027i	−0.126674	+	0.0996176i
$606$	−1.09390	−	4.50913i	−0.0444368	−	0.183171i
$607$	−24.1692	+	1.15132i	−0.980998	+	0.0467307i	−0.531949	−	0.846776i	$-0.678540\pi$
$607$	−24.1692	+	1.15132i	−0.980998	+	0.0467307i	−0.449049	+	0.893507i	$0.648237\pi$
$608$	0.544610	−	3.78785i	0.0220869	−	0.153618i
$609$	−5.52865	+	5.00599i	−0.224032	+	0.202853i
$610$	5.30218	−	11.6102i	0.214679	−	0.470081i
$611$	12.2668	+	9.64673i	0.496262	+	0.390265i
$612$	3.06592	+	1.58059i	0.123932	+	0.0638915i
$613$	−2.70722	+	0.656765i	−0.109344	+	0.0265265i	−0.290057	−	0.957009i	$-0.593674\pi$
$613$	−2.70722	+	0.656765i	−0.109344	+	0.0265265i	0.180714	+	0.983536i	$0.442159\pi$
$614$	4.37387	−	10.9254i	0.176515	−	0.440914i
$615$	4.81040	+	5.55150i	0.193974	+	0.223858i
$616$	−4.49490	−	6.66951i	−0.181105	−	0.268722i
$617$	−2.39894	−	2.07869i	−0.0965776	−	0.0836850i	0.605234	−	0.796048i	$-0.293080\pi$
$617$	−2.39894	−	2.07869i	−0.0965776	−	0.0836850i	−0.701811	+	0.712363i	$0.747625\pi$
$618$	−6.49087	−	1.57467i	−0.261101	−	0.0633424i
$619$	−20.0674	+	28.1807i	−0.806575	+	1.13268i	0.182199	+	0.983262i	$0.441678\pi$
$619$	−20.0674	+	28.1807i	−0.806575	+	1.13268i	−0.988775	+	0.149415i	$0.952261\pi$
$620$	−13.5428	+	7.81895i	−0.543892	+	0.314016i
$621$	−4.76767	+	0.518979i	−0.191320	+	0.0208259i
$622$		−	1.71746i		−	0.0688640i
$623$	−21.0640	−	34.7115i	−0.843910	−	1.39069i
$624$	1.79600	−	0.527353i	0.0718975	−	0.0211110i
$625$	8.30166	+	23.9861i	0.332067	+	0.959443i
$626$	−0.737893	+	15.4903i	−0.0294922	+	0.619116i
$627$	−3.80480	+	10.9932i	−0.151949	+	0.439028i
$628$	14.4661	+	5.79133i	0.577258	+	0.231099i
$629$	−1.32770	+	4.52172i	−0.0529387	+	0.180293i
$630$	−5.58181	−	2.09446i	−0.222385	−	0.0834453i
$631$	8.59208	+	1.23535i	0.342045	+	0.0491787i	0.311197	−	0.950345i	$-0.399270\pi$
$631$	8.59208	+	1.23535i	0.342045	+	0.0491787i	0.0308482	+	0.999524i	$0.490179\pi$
$632$	9.06631	−	6.45609i	0.360638	−	0.256809i
$633$	−0.452414	−	4.73790i	−0.0179819	−	0.188314i
$634$	19.1726	−	7.67555i	0.761441	−	0.304835i
$635$	1.15230	+	24.1897i	0.0457275	+	0.959938i
$636$	11.4875	+	3.37302i	0.455507	+	0.133749i
$637$	1.91588	−	12.9619i	0.0759098	−	0.513570i
$638$	−6.47627	+	5.61172i	−0.256398	+	0.222170i
$639$	−8.43934	+	4.35078i	−0.333855	+	0.172114i
$640$	2.21264	+	0.426451i	0.0874621	+	0.0168569i
$641$	1.11363	−	1.16794i	0.0439858	−	0.0461310i	−0.701374	−	0.712794i	$-0.747429\pi$
$641$	1.11363	−	1.16794i	0.0439858	−	0.0461310i	0.745359	+	0.666663i	$0.232278\pi$
$642$	−7.34120	−	0.701000i	−0.289734	−	0.0276662i
$643$	31.8694			1.25681			0.628404	−	0.777887i	$-0.283708\pi$
$643$	31.8694			1.25681			0.628404	+	0.777887i	$0.283708\pi$
$644$	1.96320	−	12.5358i	0.0773607	−	0.493979i
$645$	1.41155			0.0555797
$646$	13.1402	+	1.25474i	0.516996	+	0.0493671i
$647$	33.9166	−	35.5707i	1.33340	−	1.39843i	0.479910	−	0.877318i	$-0.340669\pi$
$647$	33.9166	−	35.5707i	1.33340	−	1.39843i	0.853489	−	0.521111i	$-0.174482\pi$
$648$	0.981929	+	0.189251i	0.0385738	+	0.00743449i
$649$	−26.9611	+	13.8994i	−1.05831	+	0.545599i
$650$	−0.109803	+	0.0951446i	−0.00430682	+	0.00373188i
$651$	−4.71719	−	17.7447i	−0.184881	−	0.695471i
$652$	−20.8758	−	6.12968i	−0.817558	−	0.240057i
$653$	−1.77695	−	37.3029i	−0.0695376	−	1.45977i	−0.716679	−	0.697403i	$-0.754339\pi$
$653$	−1.77695	−	37.3029i	−0.0695376	−	1.45977i	0.647141	−	0.762370i	$-0.275964\pi$
$654$	−2.23219	+	0.893632i	−0.0872854	+	0.0349438i
$655$	−0.522479	−	5.47165i	−0.0204149	−	0.213795i
$656$	2.65543	−	1.89092i	0.103677	−	0.0738280i
$657$	−1.53314	−	0.220433i	−0.0598137	−	0.00859991i
$658$	−21.7597	+	3.61494i	−0.848281	+	0.140925i
$659$	4.23778	−	14.4325i	0.165080	−	0.562212i	−0.834851	−	0.550476i	$-0.814446\pi$
$659$	4.23778	−	14.4325i	0.165080	−	0.562212i	0.999931	−	0.0117357i	$-0.00373567\pi$
$660$	−6.35928	−	2.54587i	−0.247535	−	0.0990979i
$661$	2.76704	−	7.99483i	0.107625	−	0.310963i	−0.878310	−	0.478092i	$-0.841328\pi$
$661$	2.76704	−	7.99483i	0.107625	−	0.310963i	0.985935	+	0.167129i	$0.0534497\pi$
$662$	−0.344457	+	7.23103i	−0.0133877	+	0.281042i
$663$	2.11174	+	6.10148i	0.0820134	+	0.236962i
$664$	−10.9811	+	3.22434i	−0.426149	+	0.125129i
$665$	−22.8093	+	0.497936i	−0.884506	+	0.0193091i
$666$			1.36623i			0.0529402i
$667$	−13.5113	−	0.464604i	−0.523159	−	0.0179895i
$668$	−2.07487	+	1.19792i	−0.0802790	+	0.0463491i
$669$	−13.0700	+	18.3542i	−0.505314	+	0.709614i
$670$	13.6155	+	3.30309i	0.526013	+	0.127609i
$671$	13.0130	+	11.2758i	0.502362	+	0.435299i
$672$	−1.16074	+	2.37754i	−0.0447765	+	0.0917155i
$673$	19.7989	+	22.8491i	0.763190	+	0.880768i	0.995777	−	0.0918078i	$-0.0292645\pi$
$673$	19.7989	+	22.8491i	0.763190	+	0.880768i	−0.232587	+	0.972576i	$0.574719\pi$
$674$	11.0153	−	27.5150i	0.424295	−	1.05984i
$675$	−0.0754315	+	0.0182995i	−0.00290336	+	0.000704348i
$676$	−8.44063	−	4.35145i	−0.324640	−	0.167363i
$677$	17.5704	+	13.8175i	0.675285	+	0.531050i	0.895869	−	0.444318i	$-0.146554\pi$
$677$	17.5704	+	13.8175i	0.675285	+	0.531050i	−0.220584	+	0.975368i	$0.570796\pi$
$678$	4.69979	−	10.2911i	0.180494	−	0.395227i
$679$	4.52086	−	0.974114i	0.173494	−	0.0373831i
$680$	−1.10616	+	7.69353i	−0.0424194	+	0.295033i
$681$	−28.2615	+	1.34626i	−1.08298	+	0.0515889i
$682$	−4.97364	−	20.5016i	−0.190450	−	0.785047i
$683$	−30.7867	+	24.2109i	−1.17802	+	0.926406i	−0.998356	−	0.0573219i	$-0.981744\pi$
$683$	−30.7867	+	24.2109i	−1.17802	+	0.926406i	−0.179665	+	0.983728i	$0.557501\pi$
$684$	3.75764	−	0.724227i	0.143677	−	0.0276915i
$685$	10.0226	−	15.5955i	0.382945	−	0.595875i
$686$	11.7069	+	14.3509i	0.446973	+	0.547919i
$687$	−0.415367	−	1.41461i	−0.0158472	−	0.0539708i
$688$	0.0595451	−	0.623584i	0.00227014	−	0.0237739i
$689$	11.2051	+	19.4078i	0.426881	+	0.739379i
$690$	−4.61890	−	9.76990i	−0.175839	−	0.371934i
$691$	−3.73038	−	2.15374i	−0.141910	−	0.0819320i	0.427364	−	0.904080i	$-0.359442\pi$
$691$	−3.73038	−	2.15374i	−0.141910	−	0.0819320i	−0.569274	+	0.822148i	$0.692776\pi$
$692$	11.5144	−	5.25844i	0.437711	−	0.199896i
$693$	4.83256	−	6.42906i	0.183574	−	0.244220i
$694$	5.03859	−	5.81484i	0.191262	−	0.220728i
$695$	−6.10467	−	11.8414i	−0.231563	−	0.449170i
$696$	2.66392	+	0.921992i	0.100976	+	0.0349480i
$697$	6.95091	+	8.83880i	0.263284	+	0.334793i
$698$	−5.53210	−	5.80190i	−0.209393	−	0.219605i
$699$	4.36028	+	6.78473i	0.164921	+	0.256622i
$700$	0.00529219	−	0.205294i	0.000200026	−	0.00775937i
$701$	−14.4131	−	6.58224i	−0.544375	−	0.248608i	0.124194	−	0.992258i	$-0.460366\pi$
$701$	−14.4131	−	6.58224i	−0.544375	−	0.248608i	−0.668569	+	0.743650i	$0.733093\pi$
$702$	1.08576	+	1.52474i	0.0409795	+	0.0575476i
$703$	1.94315	+	4.85376i	0.0732874	+	0.183063i
$704$	−1.39296	+	2.70196i	−0.0524991	+	0.101834i
$705$	−13.5964	+	12.9642i	−0.512071	+	0.488258i
$706$	−9.90110	+	1.42356i	−0.372633	+	0.0535765i
$707$	3.71483	+	11.7005i	0.139710	+	0.440044i
$708$	8.39430	+	5.39469i	0.315477	+	0.202745i
$709$	26.5350	−	9.18385i	0.996543	−	0.344907i	0.220363	−	0.975418i	$-0.429276\pi$
$709$	26.5350	−	9.18385i	0.996543	−	0.344907i	0.776180	+	0.630511i	$0.217155\pi$
$710$	−15.4845	−	14.7644i	−0.581122	−	0.554098i
$711$	9.06631	+	6.45609i	0.340013	+	0.242122i
$712$	−7.67319	+	13.2904i	−0.287565	+	0.498077i
$713$	16.2584	−	29.0408i	0.608882	−	1.08759i
$714$	−8.38221	−	3.60906i	−0.313696	−	0.135066i
$715$	−5.32641	−	11.6632i	−0.199196	−	0.436179i
$716$	5.36859	−	22.1296i	0.200634	−	0.827023i
$717$	−1.28516	+	6.66802i	−0.0479950	+	0.249022i
$718$	19.7261	+	0.939668i	0.736170	+	0.0350681i
$719$	2.71737	+	14.0991i	0.101341	+	0.525807i	0.996750	+	0.0805615i	$0.0256713\pi$
$719$	2.71737	+	14.0991i	0.101341	+	0.525807i	−0.895409	+	0.445245i	$0.853117\pi$
$720$	0.320686	+	2.23042i	0.0119513	+	0.0831229i
$721$	17.4209	+	2.96482i	0.648787	+	0.110416i
$722$	−3.66417	+	2.35482i	−0.136366	+	0.0876372i
$723$	2.78382	−	3.53992i	0.103531	−	0.131651i
$724$	−16.6752	+	1.59229i	−0.619729	+	0.0591770i
$725$	−0.217816	+	0.0207989i	−0.00808947	+	0.000772450i
$726$	−1.08739	+	1.38272i	−0.0403567	+	0.0513177i
$727$	−11.1267	+	7.15067i	−0.412665	+	0.265204i	−0.730460	−	0.682956i	$-0.760694\pi$
$727$	−11.1267	+	7.15067i	−0.412665	+	0.265204i	0.317795	+	0.948160i	$0.397058\pi$
$728$	−4.64353	+	1.72152i	−0.172101	+	0.0638038i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	−0.660534	−	3.42717i	−0.0244475	−	0.126845i
$731$	2.15831	+	0.102813i	0.0798278	+	0.00380267i
$732$	1.07197	−	5.56188i	0.0396210	−	0.205573i
$733$	5.87897	−	24.2334i	0.217145	−	0.895083i	−0.754054	−	0.656812i	$-0.771904\pi$
$733$	5.87897	−	24.2334i	0.217145	−	0.895083i	0.971199	−	0.238271i	$-0.0765805\pi$
$734$	−2.95755	−	6.47613i	−0.109165	−	0.239038i
$735$	15.1169	+	4.50359i	0.557596	+	0.166118i
$736$	−4.51092	+	1.62837i	−0.166275	+	0.0600225i
$737$	−9.45039	+	16.3686i	−0.348109	+	0.602943i
$738$	2.65543	+	1.89092i	0.0977476	+	0.0696057i
$739$	−22.5728	−	21.5232i	−0.830356	−	0.791743i	0.150061	−	0.988677i	$-0.452053\pi$
$739$	−22.5728	−	21.5232i	−0.830356	−	0.791743i	−0.980417	+	0.196934i	$0.936901\pi$
$740$	−2.90928	+	1.00691i	−0.106947	+	0.0370148i
$741$	6.02597	+	3.87266i	0.221370	+	0.142266i
$742$	−30.9388	−	6.79428i	−1.13580	−	0.249426i
$743$	−23.8211	+	3.42496i	−0.873911	+	0.125649i	−0.564653	−	0.825329i	$-0.690990\pi$
$743$	−23.8211	+	3.42496i	−0.873911	+	0.125649i	−0.309258	+	0.950978i	$0.600081\pi$
$744$	−5.02258	+	4.78902i	−0.184137	+	0.175574i
$745$	9.47710	−	18.3830i	0.347214	−	0.673502i
$746$	−6.90044	−	17.2365i	−0.252643	−	0.631072i
$747$	−6.63856	−	9.32256i	−0.242892	−	0.341095i
$748$	−9.53811	−	4.35591i	−0.348748	−	0.159268i
$749$	19.5049	+	0.502808i	0.712692	+	0.0183722i
$750$	5.99672	+	9.33109i	0.218969	+	0.340723i
$751$	32.3691	+	33.9478i	1.18117	+	1.23877i	0.964952	+	0.262425i	$0.0845223\pi$
$751$	32.3691	+	33.9478i	1.18117	+	1.23877i	0.216214	+	0.976346i	$0.430629\pi$
$752$	5.15366	+	6.55341i	0.187935	+	0.238978i
$753$	−23.6931	−	8.20028i	−0.863426	−	0.298835i
$754$	2.41788	+	4.69002i	0.0880538	+	0.170801i
$755$	−0.400002	+	0.461627i	−0.0145576	+	0.0168003i
$756$	−2.62642	−	0.319284i	−0.0955218	−	0.0116122i
$757$	10.9081	−	4.98157i	0.396462	−	0.181058i	−0.207200	−	0.978299i	$-0.566435\pi$
$757$	10.9081	−	4.98157i	0.396462	−	0.181058i	0.603662	+	0.797241i	$0.293708\pi$
$758$	23.1314	+	13.3549i	0.840172	+	0.485073i
$759$	14.4017	−	2.26546i	0.522749	−	0.0822311i
$760$	4.31157	+	7.46786i	0.156397	+	0.270888i
$761$	−0.155436	+	1.62780i	−0.00563455	+	0.0590077i	−0.997852	−	0.0655104i	$-0.979132\pi$
$761$	−0.155436	+	1.62780i	−0.00563455	+	0.0590077i	0.992217	+	0.124518i	$0.0397385\pi$
$762$	3.02781	+	10.3118i	0.109686	+	0.373557i
$763$	5.72757	−	2.76833i	0.207352	−	0.100220i
$764$	−10.5477	+	16.4125i	−0.381601	+	0.593783i
$765$	−7.63218	+	1.47098i	−0.275942	+	0.0531835i
$766$	−8.42548	+	6.62587i	−0.304425	+	0.239402i
$767$	4.40342	+	18.1512i	0.158998	+	0.655400i
$768$	0.998867	−	0.0475819i	0.0360435	−	0.00171696i
$769$	1.42693	−	9.92449i	0.0514563	−	0.357886i	−0.947784	−	0.318913i	$-0.896682\pi$
$769$	1.42693	−	9.92449i	0.0514563	−	0.357886i	0.999240	−	0.0389732i	$-0.0124087\pi$
$770$	17.2518	+	5.55234i	0.621712	+	0.200093i
$771$	−0.369483	+	0.809055i	−0.0133066	+	0.0291374i
$772$	−6.65142	−	5.23074i	−0.239390	−	0.188258i
$773$	0.212068	+	0.109329i	0.00762755	+	0.00393227i	0.462036	−	0.886861i	$-0.347119\pi$
$773$	0.212068	+	0.109329i	0.00762755	+	0.00393227i	−0.454409	+	0.890793i	$0.650149\pi$
$774$	0.608763	−	0.147684i	0.0218815	−	0.00530840i
$775$	0.200202	−	0.500080i	0.00719146	−	0.0179634i
$776$	−1.14466	−	1.32100i	−0.0410908	−	0.0474213i
$777$	−0.250755	−	3.60599i	−0.00899580	−	0.129364i
$778$	−4.99743	−	4.33030i	−0.179167	−	0.155249i
$779$	12.1233	+	2.94108i	0.434362	+	0.105375i
$780$	−2.44661	+	3.43579i	−0.0876028	+	0.123021i
$781$	24.9963	−	14.4316i	0.894438	−	0.516404i
$782$	−6.35084	−	15.2749i	−0.227106	−	0.546230i
$783$			2.81896i			0.100741i
$784$	2.62726	−	6.48826i	0.0938307	−	0.231724i
$785$	−33.6901	+	9.89229i	−1.20245	+	0.353071i
$786$	−0.797805	−	2.30511i	−0.0284568	−	0.0822204i
$787$	−2.31276	+	48.5508i	−0.0824410	+	1.73065i	0.457728	+	0.889092i	$0.348663\pi$
$787$	−2.31276	+	48.5508i	−0.0824410	+	1.73065i	−0.540169	+	0.841557i	$0.681640\pi$
$788$	−4.74253	+	13.7026i	−0.168946	+	0.488136i
$789$	−21.8857	−	8.76171i	−0.779152	−	0.311925i
$790$	−7.06588	+	24.0642i	−0.251393	+	0.856164i
$791$	−10.5157	+	28.0247i	−0.373895	+	0.996444i
$792$	−3.00895	−	0.432621i	−0.106918	−	0.0153725i
$793$	8.63651	−	6.15003i	0.306691	−	0.218394i
$794$	−2.86411	−	29.9943i	−0.101644	−	1.06446i
$795$	−25.0456	+	10.0268i	−0.888277	+	0.355613i
$796$	0.736151	+	15.4537i	0.0260922	+	0.547742i
$797$	−21.5048	−	6.31439i	−0.761740	−	0.223667i	−0.122285	−	0.992495i	$-0.539022\pi$
$797$	−21.5048	−	6.31439i	−0.761740	−	0.223667i	−0.639456	+	0.768828i	$0.720840\pi$
$798$	−9.78492	+	2.60118i	−0.346382	+	0.0920808i
$799$	−21.7336	+	18.8323i	−0.768880	+	0.666239i
$800$	−0.0689910	+	0.0355673i	−0.00243920	+	0.00125749i
$801$	−15.0691	−	2.90432i	−0.532439	−	0.102619i
$802$	−23.2229	+	24.3554i	−0.820028	+	0.860021i
$803$	4.68720	+	0.447573i	0.165408	+	0.0157945i
$804$	6.21759			0.219277
$805$	13.9842	+	24.9387i	0.492878	+	0.878974i
$806$	−12.9901			−0.457557
$807$	−9.52652	−	0.909672i	−0.335349	−	0.0320220i
$808$	3.20191	−	3.35807i	0.112643	−	0.118137i
$809$	2.69418	+	0.519261i	0.0947224	+	0.0182562i	0.236392	−	0.971658i	$-0.424035\pi$
$809$	2.69418	+	0.519261i	0.0947224	+	0.0182562i	−0.141670	+	0.989914i	$0.545247\pi$
$810$	−2.00286	+	1.03255i	−0.0703735	+	0.0362800i
$811$	19.6013	−	16.9846i	0.688294	−	0.596410i	−0.238876	−	0.971050i	$-0.576779\pi$
$811$	19.6013	−	16.9846i	0.688294	−	0.596410i	0.927170	+	0.374640i	$0.122234\pi$
$812$	−7.20031	−	1.94455i	−0.252681	−	0.0682404i
$813$	−19.7243	−	5.79158i	−0.691762	−	0.203120i
$814$	−0.197616	−	4.14847i	−0.00692644	−	0.145404i
$815$	45.5146	−	18.2213i	1.59431	−	0.638264i
$816$	0.327883	+	3.43374i	0.0114782	+	0.120205i
$817$	1.95269	−	1.39050i	0.0683160	−	0.0486476i
$818$	−26.0453	−	3.74474i	−0.910651	−	0.130932i
$819$	−3.14559	−	3.82509i	−0.109916	−	0.133659i
$820$	−2.06952	+	7.04814i	−0.0722708	+	0.246132i
$821$	1.84351	+	0.738031i	0.0643390	+	0.0257575i	0.403609	−	0.914932i	$-0.367756\pi$
$821$	1.84351	+	0.738031i	0.0643390	+	0.0257575i	−0.339270	+	0.940689i	$0.610180\pi$
$822$	2.69080	−	7.77455i	0.0938524	−	0.271169i
$823$	1.08011	−	22.6743i	0.0376502	−	0.790375i	−0.898542	−	0.438887i	$-0.855373\pi$
$823$	1.08011	−	22.6743i	0.0376502	−	0.790375i	0.936192	−	0.351488i	$-0.114324\pi$
$824$	−2.18453	−	6.31179i	−0.0761018	−	0.219882i
$825$	0.226397	−	0.0664761i	0.00788213	−	0.00231440i
$826$	−23.1459	−	12.6979i	−0.805348	−	0.441818i
$827$			41.4719i			1.44212i	0.692873	+	0.721060i	$0.256345\pi$
$827$			41.4719i			1.44212i	−0.692873	+	0.721060i	$0.743655\pi$
$828$	−3.01419	−	3.73024i	−0.104750	−	0.129635i
$829$	−17.8627	+	10.3130i	−0.620396	+	0.358186i	−0.777023	−	0.629472i	$-0.783271\pi$
$829$	−17.8627	+	10.3130i	−0.620396	+	0.358186i	0.156627	+	0.987658i	$0.449938\pi$
$830$	14.9591	−	21.0071i	0.519236	−	0.729165i
$831$	12.2338	+	2.96790i	0.424387	+	0.102955i
$832$	1.41463	+	1.22578i	0.0490434	+	0.0424964i
$833$	22.7862	+	7.98721i	0.789496	+	0.276740i
$834$	−3.87169	−	4.46817i	−0.134066	−	0.154720i
$835$	2.00650	−	5.01198i	0.0694376	−	0.173447i
$836$	−11.3051	+	2.74260i	−0.390996	+	0.0948546i
$837$	−6.16836	−	3.18001i	−0.213210	−	0.109917i
$838$	−15.4248	−	12.1302i	−0.532840	−	0.419030i
$839$	14.5703	−	31.9045i	0.503023	−	1.10147i	−0.472452	−	0.881357i	$-0.656631\pi$
$839$	14.5703	−	31.9045i	0.503023	−	1.10147i	0.975475	−	0.220111i	$-0.0706419\pi$
$840$	−1.25578	−	5.82807i	−0.0433285	−	0.201087i
$841$	2.99622	−	20.8392i	0.103318	−	0.718592i
$842$	−37.5466	+	1.78856i	−1.29394	+	0.0616380i
$843$	−0.700619	−	2.88799i	−0.0241306	−	0.0994678i
$844$	3.74118	−	2.94210i	0.128777	−	0.101271i
$845$	21.0118	−	4.04970i	0.722829	−	0.139314i
$846$	−4.50738	+	7.01362i	−0.154967	+	0.241133i
$847$	2.61624	−	3.84911i	0.0898950	−	0.132257i
$848$	3.37302	+	11.4875i	0.115830	+	0.394481i
$849$	−2.03837	+	21.3468i	−0.0699566	+	0.732619i
$850$	−0.133869	−	0.231868i	−0.00459166	−	0.00795300i
$851$	4.22490	−	5.00814i	0.144828	−	0.171677i
$852$	−8.22276	−	4.74741i	−0.281707	−	0.162644i
$853$	38.3351	−	17.5070i	1.31257	−	0.599429i	0.368637	−	0.929574i	$-0.379825\pi$
$853$	38.3351	−	17.5070i	1.31257	−	0.599429i	0.943931	+	0.330144i	$0.107097\pi$
$854$	−1.80850	+	14.8767i	−0.0618856	+	0.509069i
$855$	−5.64696	+	6.51694i	−0.193122	+	0.222875i
$856$	−3.37923	−	6.55480i	−0.115500	−	0.224038i
$857$	−22.4411	−	7.76695i	−0.766575	−	0.265314i	−0.0843298	−	0.996438i	$-0.526875\pi$
$857$	−22.4411	−	7.76695i	−0.766575	−	0.265314i	−0.682245	+	0.731124i	$0.738996\pi$
$858$	−3.51741	−	4.47275i	−0.120082	−	0.152697i
$859$	−23.7235	−	24.8805i	−0.809435	−	0.848911i	0.181481	−	0.983394i	$-0.441911\pi$
$859$	−23.7235	−	24.8805i	−0.809435	−	0.848911i	−0.990916	+	0.134484i	$0.957062\pi$
$860$	0.763142	+	1.18747i	0.0260229	+	0.0404924i
$861$	−7.35573	−	4.50348i	−0.250683	−	0.153478i
$862$	−5.08249	−	2.32109i	−0.173110	−	0.0790568i
$863$	−24.9860	−	35.0880i	−0.850535	−	1.19441i	−0.979236	−	0.202725i	$-0.935020\pi$
$863$	−24.9860	−	35.0880i	−0.850535	−	1.19441i	0.128701	−	0.991683i	$-0.458919\pi$
$864$	0.371662	+	0.928368i	0.0126442	+	0.0315837i
$865$	−13.0703	+	25.3528i	−0.444403	+	0.862021i
$866$	1.31835	−	1.25705i	0.0447995	−	0.0427162i
$867$	5.04997	−	0.726076i	0.171506	−	0.0246588i
$868$	12.3775	−	13.5619i	0.420121	−	0.460320i
$869$	−28.4632	−	18.2922i	−0.965548	−	0.620520i
$870$	−6.00277	+	2.07758i	−0.203513	+	0.0704365i
$871$	8.42297	+	8.03129i	0.285401	+	0.272130i
$872$	−1.95858	−	1.39470i	−0.0663260	−	0.0472305i
$873$	0.873969	−	1.51376i	0.0295794	−	0.0512330i
$874$	−16.0139	−	8.96532i	−0.541677	−	0.303256i
$875$	−17.5402	−	23.5276i	−0.592968	−	0.795379i
$876$	−0.643441	−	1.40894i	−0.0217398	−	0.0476036i
$877$	−4.58429	+	18.8967i	−0.154800	+	0.638096i	0.840546	+	0.541740i	$0.182234\pi$
$877$	−4.58429	+	18.8967i	−0.154800	+	0.638096i	−0.995347	+	0.0963566i	$0.969281\pi$
$878$	3.35819	−	17.4239i	0.113333	−	0.588029i
$879$	10.3648	+	0.493735i	0.349595	+	0.0166533i
$880$	−1.29636	−	6.72617i	−0.0437004	−	0.226739i
$881$	5.43509	+	37.8019i	0.183113	+	1.27358i	0.849347	+	0.527835i	$0.176996\pi$
$881$	5.43509	+	37.8019i	0.183113	+	1.27358i	−0.666234	+	0.745742i	$0.732095\pi$
$882$	6.99070	+	0.360661i	0.235389	+	0.0121441i
$883$	−4.33073	+	2.78319i	−0.145741	+	0.0936618i	−0.611479	−	0.791261i	$-0.709425\pi$
$883$	−4.33073	+	2.78319i	−0.145741	+	0.0936618i	0.465738	+	0.884922i	$0.345789\pi$
$884$	−3.99120	+	5.07522i	−0.134239	+	0.170698i
$885$	−22.3829	+	2.13731i	−0.752394	+	0.0718449i
$886$	−21.9661	+	2.09751i	−0.737967	+	0.0704673i
$887$	−24.9859	+	31.7722i	−0.838945	+	1.06681i	0.157901	+	0.987455i	$0.449527\pi$
$887$	−24.9859	+	31.7722i	−0.838945	+	1.06681i	−0.996847	+	0.0793511i	$0.974715\pi$
$888$	−1.14934	+	0.738638i	−0.0385694	+	0.0247871i
$889$	−9.88415	−	26.6610i	−0.331504	−	0.894180i
$890$	−4.92138	−	34.2289i	−0.164965	−	1.14736i
$891$	−0.575303	−	2.98495i	−0.0192734	−	0.0999997i
$892$	−22.5067	−	1.07213i	−0.753579	−	0.0358974i
$893$	−6.03796	+	31.3279i	−0.202052	+	1.04835i
$894$	2.16388	−	8.91964i	0.0723710	−	0.298317i
$895$	21.3159	+	46.6754i	0.712513	+	1.56019i
$896$	−2.62765	+	0.308917i	−0.0877838	+	0.0103202i
$897$	0.735040	−	8.94680i	0.0245423	−	0.298725i
$898$	−1.33841	+	2.31820i	−0.0446633	+	0.0773592i
$899$	−15.9356	−	11.3477i	−0.531483	−	0.378467i
$900$	−0.0561759	−	0.0535636i	−0.00187253	−	0.00178545i
$901$	−39.0259	+	13.5070i	−1.30014	+	0.449983i
$902$	−8.33657	−	5.35759i	−0.277577	−	0.178388i
$903$	−1.57965	+	0.501526i	−0.0525675	+	0.0166897i
$904$	11.1983	−	1.61008i	0.372451	−	0.0535503i
$905$	27.3182	−	26.0478i	0.908086	−	0.865858i
$906$	−0.124212	+	0.240938i	−0.00412667	+	0.00800462i
$907$	9.35606	+	23.3703i	0.310663	+	0.775998i	0.998732	+	0.0503525i	$0.0160345\pi$
$907$	9.35606	+	23.3703i	0.310663	+	0.775998i	−0.688069	+	0.725645i	$0.741541\pi$
$908$	−16.4119	−	23.0473i	−0.544647	−	0.764850i
$909$	4.22062	+	1.92749i	0.139989	+	0.0639310i
$910$	5.82693	−	9.51739i	0.193161	−	0.315498i
$911$	−14.3858	−	22.3847i	−0.476622	−	0.741638i	0.516806	−	0.856103i	$-0.327121\pi$
$911$	−14.3858	−	22.3847i	−0.476622	−	0.741638i	−0.993427	+	0.114465i	$0.963485\pi$
$912$	2.64079	+	2.76959i	0.0874454	+	0.0917101i
$913$	21.5061	+	27.3472i	0.711748	+	0.905061i
$914$	30.4315	+	10.5324i	1.00658	+	0.348382i
$915$	5.84861	+	11.3447i	0.193349	+	0.375045i
$916$	0.965482	−	1.11423i	0.0319004	−	0.0368150i
$917$	2.52879	+	5.93762i	0.0835079	+	0.196077i
$918$	−3.13765	+	1.43292i	−0.103558	+	0.0472933i
$919$	−0.248064	−	0.143220i	−0.00818287	−	0.00472438i	0.495903	−	0.868378i	$-0.334837\pi$
$919$	−0.248064	−	0.143220i	−0.00818287	−	0.00472438i	−0.504086	+	0.863654i	$0.668170\pi$
$920$	5.72180	−	9.16768i	0.188642	−	0.302249i
$921$	5.88420	+	10.1917i	0.193891	+	0.335829i
$922$	−1.59997	+	16.7556i	−0.0526922	+	0.551818i
$923$	−5.00713	−	17.0527i	−0.164812	−	0.561297i
$924$	8.02115	+	0.589593i	0.263877	+	0.0193962i
$925$	0.0573327	−	0.0892114i	0.00188509	−	0.00293325i
$926$	−10.7033	+	2.06289i	−0.351732	+	0.0677908i
$927$	5.25016	−	4.12877i	0.172438	−	0.135607i
$928$	0.664595	+	2.73950i	0.0218164	+	0.0899285i
$929$	−19.7962	+	0.943010i	−0.649493	+	0.0309391i	−0.369743	−	0.929134i	$-0.620554\pi$
$929$	−19.7962	+	0.943010i	−0.649493	+	0.0309391i	−0.279749	+	0.960073i	$0.590251\pi$
$930$	2.22550	−	15.4787i	0.0729772	−	0.507567i
$931$	25.3487	−	8.66141i	0.830769	−	0.283866i
$932$	−3.35033	+	7.33620i	−0.109744	+	0.240305i
$933$	1.35002	+	1.06167i	0.0441976	+	0.0347574i
$934$	−24.2965	−	12.5257i	−0.795007	−	0.409854i
$935$	22.9620	−	5.57051i	0.750936	−	0.182175i
$936$	−0.695686	+	1.73774i	−0.0227392	+	0.0567998i
$937$	−34.1124	−	39.3678i	−1.11440	−	1.28609i	−0.954254	−	0.298996i	$-0.903348\pi$
$937$	−34.1124	−	39.3678i	−1.11440	−	1.28609i	−0.160148	−	0.987093i	$-0.551197\pi$
$938$	−16.4106	+	1.14117i	−0.535824	+	0.0372604i
$939$	−11.7201	−	10.1555i	−0.382469	−	0.331412i
$940$	−18.2569	−	4.42908i	−0.595475	−	0.144461i
$941$	3.21047	−	4.50848i	0.104658	−	0.146972i	−0.758925	−	0.651178i	$-0.774275\pi$
$941$	3.21047	−	4.50848i	0.104658	−	0.146972i	0.863584	+	0.504206i	$0.168215\pi$
$942$	−13.4946	+	7.79112i	−0.439678	+	0.253848i
$943$	−3.88646	−	15.1431i	−0.126560	−	0.493127i
$944$			9.97833i			0.324767i
$945$	5.09680	−	3.09289i	0.165799	−	0.100612i
$946$	−1.82711	+	0.536489i	−0.0594046	+	0.0174428i
$947$	2.00056	+	5.78025i	0.0650096	+	0.187833i	0.972827	−	0.231532i	$-0.0743739\pi$
$947$	2.00056	+	5.78025i	0.0650096	+	0.187833i	−0.907818	+	0.419365i	$0.862253\pi$
$948$	−0.529591	+	11.1175i	−0.0172003	+	0.361079i
$949$	0.948263	−	2.73983i	0.0307819	−	0.0889385i
$950$	−0.275757	−	0.110396i	−0.00894674	−	0.00358173i
$951$	−5.81832	+	19.8154i	−0.188672	+	0.642558i
$952$	−1.49563	−	9.00277i	−0.0484737	−	0.291781i
$953$	−2.31020	−	0.332156i	−0.0748347	−	0.0107596i	0.104796	−	0.994494i	$-0.466581\pi$
$953$	−2.31020	−	0.332156i	−0.0748347	−	0.0107596i	−0.179630	+	0.983734i	$0.557490\pi$
$954$	−9.75244	+	6.94468i	−0.315747	+	0.224842i
$955$	−4.17885	−	43.7629i	−0.135225	−	1.41614i
$956$	−6.30431	+	2.52386i	−0.203896	+	0.0816276i
$957$	−0.407745	−	8.55963i	−0.0131805	−	0.276693i
$958$	2.77633	+	0.815204i	0.0896992	+	0.0263381i
$959$	−5.67510	+	21.0138i	−0.183259	+	0.678572i
$960$	−1.70297	+	1.47564i	−0.0549632	+	0.0476259i
$961$	15.2534	−	7.86367i	0.492045	−	0.253667i
$962$	−2.51112	−	0.483978i	−0.0809617	−	0.0156041i
$963$	5.08905	−	5.33724i	0.163992	−	0.171990i
$964$	4.48302	+	0.428076i	0.144388	+	0.0137874i
$965$	19.0675			0.613803
$966$	8.64022	+	9.29228i	0.277995	+	0.298974i
$967$	−17.8596			−0.574326			−0.287163	−	0.957882i	$-0.592712\pi$
$967$	−17.8596			−0.574326			−0.287163	+	0.957882i	$0.592712\pi$
$968$	−1.75111	−	0.167210i	−0.0562827	−	0.00537434i
$969$	−9.10906	+	9.55330i	−0.292625	+	0.306896i
$970$	3.86755	+	0.745410i	0.124180	+	0.0239337i
$971$	20.4870	−	10.5618i	0.657459	−	0.338944i	−0.0970058	−	0.995284i	$-0.530927\pi$
$971$	20.4870	−	10.5618i	0.657459	−	0.338944i	0.754465	+	0.656340i	$0.227896\pi$
$972$	−0.755750	+	0.654861i	−0.0242407	+	0.0210047i
$973$	11.0389	+	11.0826i	0.353892	+	0.355291i
$974$	36.9327	+	10.8444i	1.18340	+	0.347478i
$975$	−0.00691317	−	0.145125i	−0.000221399	−	0.00464773i
$976$	5.25850	−	2.10519i	0.168321	−	0.0673854i
$977$	4.19335	+	43.9148i	0.134157	+	1.40496i	0.772407	+	0.635128i	$0.219053\pi$
$977$	4.19335	+	43.9148i	0.134157	+	1.40496i	−0.638249	+	0.769830i	$0.720341\pi$
$978$	17.7228	−	12.6203i	0.566712	−	0.403554i
$979$	46.1765	+	6.63918i	1.47581	+	0.212189i
$980$	4.38415	+	15.1520i	0.140047	+	0.484012i
$981$	0.677403	−	2.30702i	0.0216278	−	0.0736576i
$982$	8.88813	+	3.55827i	0.283632	+	0.113549i
$983$	−12.9365	+	37.3776i	−0.412610	+	1.19216i	0.526986	+	0.849874i	$0.323322\pi$
$983$	−12.9365	+	37.3776i	−0.412610	+	1.19216i	−0.939596	+	0.342285i	$0.888799\pi$
$984$	−0.155112	+	3.25619i	−0.00494478	+	0.103804i
$985$	−10.6866	−	30.8769i	−0.340504	−	0.983821i
$986$	−9.32975	+	2.73946i	−0.297120	+	0.0872422i
$987$	10.6094	−	19.3389i	0.337701	−	0.615563i
$988$			7.16309i			0.227888i
$989$	−2.68822	−	1.34117i	−0.0854805	−	0.0426467i
$990$	5.93224	−	3.42498i	0.188539	−	0.108853i
$991$	13.7849	−	19.3581i	0.437890	−	0.614931i	−0.535375	−	0.844614i	$-0.679830\pi$
$991$	13.7849	−	19.3581i	0.437890	−	0.614931i	0.973265	+	0.229683i	$0.0737691\pi$
$992$	−6.74420	−	1.63612i	−0.214128	−	0.0519470i
$993$	−5.47105	−	4.74069i	−0.173618	−	0.150441i
$994$	22.5743	+	11.0210i	0.716014	+	0.349566i
$995$	−22.8299	−	26.3471i	−0.723757	−	0.835260i
$996$	4.25356	−	10.6249i	0.134779	−	0.336662i
$997$	9.26272	−	2.24711i	0.293353	−	0.0711667i	−0.0863815	−	0.996262i	$-0.527530\pi$
$997$	9.26272	−	2.24711i	0.293353	−	0.0711667i	0.379735	+	0.925095i	$0.376015\pi$
$998$	31.3525	+	16.1634i	0.992448	+	0.511642i
$999$	−1.07393	−	0.844545i	−0.0339775	−	0.0267202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.b.19.10	✓	320
7.3	odd	6	inner	966.2.be.b.157.10	yes	320
23.17	odd	22	inner	966.2.be.b.523.10	yes	320
161.17	even	66	inner	966.2.be.b.661.10	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.b.19.10	✓	320	1.1	even	1	trivial
966.2.be.b.157.10	yes	320	7.3	odd	6	inner
966.2.be.b.523.10	yes	320	23.17	odd	22	inner
966.2.be.b.661.10	yes	320	161.17	even	66	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.995472 - 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-2.00286 + 1.03255i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(1.87452 - 1.86713i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})\)	\(q+(-0.995472 - 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(-2.00286 + 1.03255i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(1.87452 - 1.86713i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(2.09194 - 0.837488i) q^{10} +(0.288960 + 3.02612i) q^{11} +(0.814576 - 0.580057i) q^{12} +(1.85277 + 0.266388i) q^{13} +(-2.04351 + 1.68050i) q^{14} +(-0.634844 + 2.16208i) q^{15} +(0.928368 + 0.371662i) q^{16} +(-1.12818 + 3.25965i) q^{17} +(-0.0475819 + 0.998867i) q^{18} +(1.25162 + 3.61633i) q^{19} +(-2.16208 + 0.634844i) q^{20} +(-0.0577442 - 2.64512i) q^{21} -3.03989i q^{22} +(3.26330 - 3.51438i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.0450237 - 0.0632270i) q^{25} +(-1.81906 - 0.441299i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(2.19400 - 1.47864i) q^{28} +(-1.84603 - 2.13043i) q^{29} +(0.837488 - 2.09194i) q^{30} +(6.74420 - 1.63612i) q^{31} +(-0.888835 - 0.458227i) q^{32} +(2.38951 + 1.87914i) q^{33} +(1.43292 - 3.13765i) q^{34} +(-1.82650 + 5.67514i) q^{35} +(0.142315 - 0.989821i) q^{36} +(1.36468 - 0.0650077i) q^{37} +(-0.902202 - 3.71893i) q^{38} +(1.47135 - 1.15708i) q^{39} +(2.21264 - 0.426451i) q^{40} +(1.76243 - 2.74239i) q^{41} +(-0.193952 + 2.63863i) q^{42} +(-0.176483 - 0.601046i) q^{43} +(-0.288960 + 3.02612i) q^{44} +(1.12668 + 1.95146i) q^{45} +(-3.58259 + 3.18827i) q^{46} +(7.22015 + 4.16855i) q^{47} +(0.909632 - 0.415415i) q^{48} +(0.0276215 - 6.99995i) q^{49} +(-0.0508300 + 0.0586609i) q^{50} +(1.58059 + 3.06592i) q^{51} +(1.76887 + 0.612213i) q^{52} +(7.40086 + 9.41096i) q^{53} +(0.690079 + 0.723734i) q^{54} +(-3.70337 - 5.76255i) q^{55} +(-2.32462 + 1.26339i) q^{56} +(3.48098 + 1.58971i) q^{57} +(1.63516 + 2.29626i) q^{58} +(3.70857 + 9.26356i) q^{59} +(-1.03255 + 2.00286i) q^{60} +(4.09941 - 3.90878i) q^{61} +(-6.86918 + 0.987639i) q^{62} +(-1.95421 - 1.78355i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-3.98590 + 1.37953i) q^{65} +(-2.20007 - 2.09776i) q^{66} +(5.06470 + 3.60655i) q^{67} +(-1.72468 + 2.98724i) q^{68} +(-0.291536 - 4.78696i) q^{69} +(2.35768 - 5.47583i) q^{70} +(-3.94429 - 8.63680i) q^{71} +(-0.235759 + 0.971812i) q^{72} +(0.293133 - 1.52092i) q^{73} +(-1.36468 - 0.0650077i) q^{74} +(-0.0146896 - 0.0762168i) q^{75} +(0.544610 + 3.78785i) q^{76} +(6.19184 + 5.13299i) q^{77} +(-1.57468 + 1.01198i) q^{78} +(-6.88017 + 8.74885i) q^{79} +(-2.24315 + 0.214195i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(-2.01513 + 2.56244i) q^{82} +(9.62787 - 6.18746i) q^{83} +(0.443892 - 2.60825i) q^{84} +(-1.10616 - 7.69353i) q^{85} +(0.118551 + 0.615101i) q^{86} +(-2.81577 - 0.134132i) q^{87} +(0.575303 - 2.98495i) q^{88} +(3.61805 - 14.9138i) q^{89} +(-0.936078 - 2.04973i) q^{90} +(3.97043 - 2.96002i) q^{91} +(3.86943 - 2.83328i) q^{92} +(3.46991 - 6.01006i) q^{93} +(-6.79121 - 4.83600i) q^{94} +(-6.24087 - 5.95065i) q^{95} +(-0.945001 + 0.327068i) q^{96} +(1.47046 + 0.945007i) q^{97} +(-0.692884 + 6.96562i) q^{98} +(3.00895 - 0.432621i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) \) 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9 + 22 * q^14 + 16 * q^16 - 66 * q^17 - 16 * q^18 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Introduction

L-functions

Modular forms

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