LMFDB - Embedded newform 720.2.cf.a.11.60

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(11,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2, 0]))

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

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

chi := DirichletCharacter("720.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cf (of order $12$, degree $4$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.60
Character	$\chi$	$=$	720.11
Dual form			720.2.cf.a.131.60

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.497003 - 1.32400i) q^{2} +(-1.08862 - 1.34718i) q^{3} +(-1.50598 - 1.31607i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(-2.32472 + 0.771787i) q^{6} +(-1.95990 + 3.39465i) q^{7} +(-2.49096 + 1.33983i) q^{8} +(-0.629804 + 2.93315i) q^{9} +O(q^{10})$	\(q+(0.497003 - 1.32400i) q^{2} +(-1.08862 - 1.34718i) q^{3} +(-1.50598 - 1.31607i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(-2.32472 + 0.771787i) q^{6} +(-1.95990 + 3.39465i) q^{7} +(-2.49096 + 1.33983i) q^{8} +(-0.629804 + 2.93315i) q^{9} +(-0.822746 + 1.15026i) q^{10} +(4.49613 - 1.20473i) q^{11} +(-0.133546 + 3.46153i) q^{12} +(-0.501569 - 0.134395i) q^{13} +(3.52046 + 4.28207i) q^{14} +(0.702852 + 1.58303i) q^{15} +(0.535927 + 3.96394i) q^{16} +5.09834i q^{17} +(3.57048 + 2.29165i) q^{18} +(-2.04286 - 2.04286i) q^{19} +(1.11404 + 1.66100i) q^{20} +(6.70681 - 1.05515i) q^{21} +(0.639516 - 6.55165i) q^{22} +(1.14260 - 0.659681i) q^{23} +(4.51670 + 1.89721i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-0.427221 + 0.597284i) q^{26} +(4.63710 - 2.34463i) q^{27} +(7.41916 - 2.53290i) q^{28} +(-5.24529 + 1.40547i) q^{29} +(2.44526 - 0.143805i) q^{30} +(-0.445110 + 0.256985i) q^{31} +(5.51463 + 1.26052i) q^{32} +(-6.51758 - 4.74561i) q^{33} +(6.75022 + 2.53389i) q^{34} +(2.77172 - 2.77172i) q^{35} +(4.80869 - 3.58838i) q^{36} +(-1.69603 - 1.69603i) q^{37} +(-3.72007 + 1.68945i) q^{38} +(0.364964 + 0.822010i) q^{39} +(2.75285 - 0.649469i) q^{40} +(4.41864 + 7.65330i) q^{41} +(1.93629 - 9.40426i) q^{42} +(1.83472 + 6.84727i) q^{43} +(-8.35658 - 4.10291i) q^{44} +(1.36750 - 2.67020i) q^{45} +(-0.305544 - 1.84067i) q^{46} +(-3.84243 + 6.65529i) q^{47} +(4.75672 - 5.03722i) q^{48} +(-4.18245 - 7.24421i) q^{49} +(1.09242 - 0.898120i) q^{50} +(6.86839 - 5.55016i) q^{51} +(0.578477 + 0.862494i) q^{52} +(-7.55075 + 7.55075i) q^{53} +(-0.799642 - 7.30483i) q^{54} -4.65474 q^{55} +(0.333778 - 11.0819i) q^{56} +(-0.528204 + 4.97601i) q^{57} +(-0.746075 + 7.64331i) q^{58} +(1.89990 - 7.09053i) q^{59} +(1.02490 - 3.30901i) q^{60} +(1.55182 + 5.79146i) q^{61} +(0.119028 + 0.717050i) q^{62} +(-8.72266 - 7.88665i) q^{63} +(4.40972 - 6.67491i) q^{64} +(0.449694 + 0.259631i) q^{65} +(-9.52247 + 6.27073i) q^{66} +(2.71727 - 10.1410i) q^{67} +(6.70976 - 7.67797i) q^{68} +(-2.13257 - 0.821149i) q^{69} +(-2.29222 - 5.04733i) q^{70} -8.02244i q^{71} +(-2.36110 - 8.15017i) q^{72} +12.2268i q^{73} +(-3.08848 + 1.40262i) q^{74} +(-0.269183 - 1.71101i) q^{75} +(0.387955 + 5.76505i) q^{76} +(-4.72233 + 17.6240i) q^{77} +(1.26973 - 0.0746727i) q^{78} +(0.100100 + 0.0577927i) q^{79} +(0.508276 - 3.96758i) q^{80} +(-8.20669 - 3.69461i) q^{81} +(12.3291 - 2.04658i) q^{82} +(3.95500 + 14.7603i) q^{83} +(-11.4889 - 7.23760i) q^{84} +(1.31955 - 4.92462i) q^{85} +(9.97768 + 0.973936i) q^{86} +(7.60357 + 5.53634i) q^{87} +(-9.58552 + 9.02499i) q^{88} +4.49770 q^{89} +(-2.85570 - 3.13767i) q^{90} +(1.43925 - 1.43925i) q^{91} +(-2.58891 - 0.510277i) q^{92} +(0.830762 + 0.319886i) q^{93} +(6.90194 + 8.39510i) q^{94} +(1.44452 + 2.50198i) q^{95} +(-4.30520 - 8.80144i) q^{96} +(-2.35136 + 4.07268i) q^{97} +(-11.6701 + 1.93718i) q^{98} +(0.701981 + 13.9466i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 12 q^{6}+O(q^{10}) $ 384 * q - 12 * q^6	$ 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) $ 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.497003	−	1.32400i	0.351434	−	0.936213i
$2$	0.497003	−	1.32400i	0.351434	−	0.936213i
$3$	−1.08862	−	1.34718i	−0.628516	−	0.777796i
$3$	−1.08862	−	1.34718i	−0.628516	−	0.777796i
$4$	−1.50598	−	1.31607i	−0.752988	−	0.658034i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$6$	−2.32472	+	0.771787i	−0.949065	+	0.315081i
$7$	−1.95990	+	3.39465i	−0.740774	+	1.28306i	0.211369	+	0.977406i	$0.432208\pi$
$7$	−1.95990	+	3.39465i	−0.740774	+	1.28306i	−0.952143	+	0.305652i	$0.901126\pi$
$8$	−2.49096	+	1.33983i	−0.880686	+	0.473701i
$9$	−0.629804	+	2.93315i	−0.209935	+	0.977715i
$10$	−0.822746	+	1.15026i	−0.260175	+	0.363743i
$11$	4.49613	−	1.20473i	1.35563	−	0.363241i	0.493423	−	0.869790i	$-0.335746\pi$
$11$	4.49613	−	1.20473i	1.35563	−	0.363241i	0.862211	+	0.506549i	$0.169079\pi$
$12$	−0.133546	+	3.46153i	−0.0385515	+	0.999257i
$13$	−0.501569	−	0.134395i	−0.139110	−	0.0372744i	0.188592	−	0.982056i	$-0.439608\pi$
$13$	−0.501569	−	0.134395i	−0.139110	−	0.0372744i	−0.327702	+	0.944781i	$0.606274\pi$
$14$	3.52046	+	4.28207i	0.940882	+	1.14443i
$15$	0.702852	+	1.58303i	0.181475	+	0.408738i
$16$	0.535927	+	3.96394i	0.133982	+	0.990984i
$17$			5.09834i			1.23653i	0.785970	+	0.618264i	$0.212164\pi$
$17$			5.09834i			1.23653i	−0.785970	+	0.618264i	$0.787836\pi$
$18$	3.57048	+	2.29165i	0.841571	+	0.540146i
$19$	−2.04286	−	2.04286i	−0.468665	−	0.468665i	0.432817	−	0.901482i	$-0.357520\pi$
$19$	−2.04286	−	2.04286i	−0.468665	−	0.468665i	−0.901482	+	0.432817i	$0.857520\pi$
$20$	1.11404	+	1.66100i	0.249106	+	0.371411i
$21$	6.70681	−	1.05515i	1.46355	−	0.230252i
$22$	0.639516	−	6.55165i	0.136345	−	1.39682i
$23$	1.14260	−	0.659681i	0.238249	−	0.137553i	−0.376123	−	0.926570i	$-0.622743\pi$
$23$	1.14260	−	0.659681i	0.238249	−	0.137553i	0.614372	+	0.789017i	$0.289410\pi$
$24$	4.51670	+	1.89721i	0.921968	+	0.387265i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	−0.427221	+	0.597284i	−0.0837849	+	0.117137i
$27$	4.63710	−	2.34463i	0.892411	−	0.451224i
$28$	7.41916	−	2.53290i	1.40209	−	0.478673i
$29$	−5.24529	+	1.40547i	−0.974026	+	0.260990i	−0.710527	−	0.703670i	$-0.751543\pi$
$29$	−5.24529	+	1.40547i	−0.974026	+	0.260990i	−0.263499	+	0.964660i	$0.584877\pi$
$30$	2.44526	−	0.143805i	0.446442	−	0.0262552i
$31$	−0.445110	+	0.256985i	−0.0799442	+	0.0461558i	−0.539439	−	0.842025i	$-0.681364\pi$
$31$	−0.445110	+	0.256985i	−0.0799442	+	0.0461558i	0.459495	+	0.888180i	$0.348030\pi$
$32$	5.51463	+	1.26052i	0.974857	+	0.222830i
$33$	−6.51758	−	4.74561i	−1.13457	−	0.826105i
$34$	6.75022	+	2.53389i	1.15765	+	0.434558i
$35$	2.77172	−	2.77172i	0.468507	−	0.468507i
$36$	4.80869	−	3.58838i	0.801449	−	0.598064i
$37$	−1.69603	−	1.69603i	−0.278825	−	0.278825i	0.553815	−	0.832640i	$-0.313172\pi$
$37$	−1.69603	−	1.69603i	−0.278825	−	0.278825i	−0.832640	+	0.553815i	$0.813172\pi$
$38$	−3.72007	+	1.68945i	−0.603474	+	0.274065i
$39$	0.364964	+	0.822010i	0.0584410	+	0.131627i
$40$	2.75285	−	0.649469i	0.435264	−	0.102690i
$41$	4.41864	+	7.65330i	0.690075	+	1.19524i	0.971813	+	0.235753i	$0.0757558\pi$
$41$	4.41864	+	7.65330i	0.690075	+	1.19524i	−0.281738	+	0.959491i	$0.590911\pi$
$42$	1.93629	−	9.40426i	0.298776	−	1.45111i
$43$	1.83472	+	6.84727i	0.279792	+	1.04420i	0.952561	+	0.304346i	$0.0984380\pi$
$43$	1.83472	+	6.84727i	0.279792	+	1.04420i	−0.672769	+	0.739852i	$0.734895\pi$
$44$	−8.35658	−	4.10291i	−1.25980	−	0.618538i
$45$	1.36750	−	2.67020i	0.203855	−	0.398049i
$46$	−0.305544	−	1.84067i	−0.0450501	−	0.271392i
$47$	−3.84243	+	6.65529i	−0.560477	+	0.970774i	0.436978	+	0.899472i	$0.356049\pi$
$47$	−3.84243	+	6.65529i	−0.560477	+	0.970774i	−0.997455	+	0.0713020i	$0.977285\pi$
$48$	4.75672	−	5.03722i	0.686574	−	0.727060i
$49$	−4.18245	−	7.24421i	−0.597492	−	1.03489i
$50$	1.09242	−	0.898120i	0.154491	−	0.127013i
$51$	6.86839	−	5.55016i	0.961768	−	0.777178i
$52$	0.578477	+	0.862494i	0.0802204	+	0.119606i
$53$	−7.55075	+	7.55075i	−1.03717	+	1.03717i	−0.0378932	+	0.999282i	$0.512065\pi$
$53$	−7.55075	+	7.55075i	−1.03717	+	1.03717i	−0.999282	+	0.0378932i	$0.987935\pi$
$54$	−0.799642	−	7.30483i	−0.108817	−	0.994062i
$55$	−4.65474			−0.627645
$56$	0.333778	−	11.0819i	0.0446030	−	1.48088i
$57$	−0.528204	+	4.97601i	−0.0699623	+	0.659089i
$58$	−0.746075	+	7.64331i	−0.0979645	+	1.00362i
$59$	1.89990	−	7.09053i	0.247346	−	0.923109i	−0.724843	−	0.688914i	$-0.758088\pi$
$59$	1.89990	−	7.09053i	0.247346	−	0.923109i	0.972190	−	0.234195i	$-0.0752454\pi$
$60$	1.02490	−	3.30901i	0.132315	−	0.427192i
$61$	1.55182	+	5.79146i	0.198690	+	0.741521i	0.991281	+	0.131767i	$0.0420650\pi$
$61$	1.55182	+	5.79146i	0.198690	+	0.741521i	−0.792591	+	0.609754i	$0.791268\pi$
$62$	0.119028	+	0.717050i	0.0151165	+	0.0910655i
$63$	−8.72266	−	7.88665i	−1.09895	−	0.993625i
$64$	4.40972	−	6.67491i	0.551215	−	0.834364i
$65$	0.449694	+	0.259631i	0.0557777	+	0.0322033i
$66$	−9.52247	+	6.27073i	−1.17213	+	0.771873i
$67$	2.71727	−	10.1410i	0.331968	−	1.23892i	−0.575152	−	0.818047i	$-0.695057\pi$
$67$	2.71727	−	10.1410i	0.331968	−	1.23892i	0.907119	−	0.420873i	$-0.138276\pi$
$68$	6.70976	−	7.67797i	0.813678	−	0.931091i
$69$	−2.13257	−	0.821149i	−0.256731	−	0.0988547i
$70$	−2.29222	−	5.04733i	−0.273973	−	0.603271i
$71$		−	8.02244i		−	0.952089i	−0.879421	−	0.476044i	$-0.842070\pi$
$71$		−	8.02244i		−	0.952089i	0.879421	−	0.476044i	$-0.157930\pi$
$72$	−2.36110	−	8.15017i	−0.278258	−	0.960506i
$73$			12.2268i			1.43104i	0.698593	+	0.715520i	$0.253810\pi$
$73$			12.2268i			1.43104i	−0.698593	+	0.715520i	$0.746190\pi$
$74$	−3.08848	+	1.40262i	−0.359029	+	0.163051i
$75$	−0.269183	−	1.71101i	−0.0310826	−	0.197570i
$76$	0.387955	+	5.76505i	0.0445015	+	0.661296i
$77$	−4.72233	+	17.6240i	−0.538159	+	2.00844i
$78$	1.26973	−	0.0746727i	0.143769	−	0.00845502i
$79$	0.100100	+	0.0577927i	0.0112621	+	0.00650218i	0.505620	−	0.862756i	$-0.331264\pi$
$79$	0.100100	+	0.0577927i	0.0112621	+	0.00650218i	−0.494358	+	0.869258i	$0.664597\pi$
$80$	0.508276	−	3.96758i	0.0568270	−	0.443588i
$81$	−8.20669	−	3.69461i	−0.911855	−	0.410513i
$82$	12.3291	−	2.04658i	1.36152	−	0.226007i
$83$	3.95500	+	14.7603i	0.434118	+	1.62015i	0.743168	+	0.669105i	$0.233322\pi$
$83$	3.95500	+	14.7603i	0.434118	+	1.62015i	−0.309050	+	0.951046i	$0.600011\pi$
$84$	−11.4889	−	7.23760i	−1.25355	−	0.789687i
$85$	1.31955	−	4.92462i	0.143125	−	0.534150i
$86$	9.97768	+	0.973936i	1.07592	+	0.105022i
$87$	7.60357	+	5.53634i	0.815188	+	0.593558i
$88$	−9.58552	+	9.02499i	−1.02182	+	0.962067i
$89$	4.49770			0.476755			0.238378	−	0.971173i	$-0.423384\pi$
$89$	4.49770			0.476755			0.238378	+	0.971173i	$0.423384\pi$
$90$	−2.85570	−	3.13767i	−0.301017	−	0.330739i
$91$	1.43925	−	1.43925i	0.150874	−	0.150874i
$92$	−2.58891	−	0.510277i	−0.269913	−	0.0532001i
$93$	0.830762	+	0.319886i	0.0861460	+	0.0331706i
$94$	6.90194	+	8.39510i	0.711880	+	0.865889i
$95$	1.44452	+	2.50198i	0.148205	+	0.256698i
$96$	−4.30520	−	8.80144i	−0.439397	−	0.898293i
$97$	−2.35136	+	4.07268i	−0.238745	+	0.413518i	−0.960354	−	0.278782i	$-0.910069\pi$
$97$	−2.35136	+	4.07268i	−0.238745	+	0.413518i	0.721610	+	0.692300i	$0.243403\pi$
$98$	−11.6701	+	1.93718i	−1.17885	+	0.195685i
$99$	0.701981	+	13.9466i	0.0705518	+	1.40168i
$100$	−0.646179	−	1.89274i	−0.0646179	−	0.189274i
$101$	5.06165	+	18.8903i	0.503653	+	1.87966i	0.474837	+	0.880074i	$0.342507\pi$
$101$	5.06165	+	18.8903i	0.503653	+	1.87966i	0.0288157	+	0.999585i	$0.490826\pi$
$102$	−3.93483	−	11.8522i	−0.389606	−	1.17355i
$103$	−3.96350	−	6.86498i	−0.390535	−	0.676427i	0.601985	−	0.798507i	$-0.294377\pi$
$103$	−3.96350	−	6.86498i	−0.390535	−	0.676427i	−0.992520	+	0.122080i	$0.961043\pi$
$104$	1.42945	−	0.337245i	0.140169	−	0.0330695i
$105$	−6.75138	−	0.716659i	−0.658867	−	0.0699388i
$106$	6.24448	+	13.7500i	0.606517	+	1.33551i
$107$	12.3560	+	12.3560i	1.19450	+	1.19450i	0.975789	+	0.218713i	$0.0701859\pi$
$107$	12.3560	+	12.3560i	1.19450	+	1.19450i	0.218713	+	0.975789i	$0.429814\pi$
$108$	−10.0691	−	2.57179i	−0.968895	−	0.247471i
$109$	4.72344	−	4.72344i	0.452424	−	0.452424i	−0.443735	−	0.896158i	$-0.646347\pi$
$109$	4.72344	−	4.72344i	0.452424	−	0.452424i	0.896158	+	0.443735i	$0.146347\pi$
$110$	−2.31342	+	6.16289i	−0.220576	+	0.587609i
$111$	−0.438527	+	4.13120i	−0.0416231	+	0.392116i
$112$	−14.5066	−	5.94964i	−1.37074	−	0.562189i
$113$	−14.8482	+	8.57261i	−1.39680	+	0.806443i	−0.994056	−	0.108870i	$-0.965277\pi$
$113$	−14.8482	+	8.57261i	−1.39680	+	0.806443i	−0.402744	+	0.915313i	$0.631944\pi$
$114$	6.32574	+	3.17244i	0.592460	+	0.297126i
$115$	−1.27441	+	0.341476i	−0.118839	+	0.0318428i
$116$	9.74898	+	4.78656i	0.905170	+	0.444421i
$117$	0.710090	−	1.38653i	0.0656478	−	0.128185i
$118$	−8.44364	−	6.03950i	−0.777300	−	0.555981i
$119$	−17.3071	−	9.99225i	−1.58654	−	0.915988i
$120$	−3.87177	−	3.00157i	−0.353442	−	0.274004i
$121$	9.23752	−	5.33329i	0.839775	−	0.484844i
$122$	8.43918	+	0.823760i	0.764047	+	0.0745798i
$123$	5.50017	−	14.2843i	0.495934	−	1.28797i
$124$	1.00853	+	0.198783i	0.0905691	+	0.0178513i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−14.7771	+	7.62915i	−1.31645	+	0.679659i
$127$		−	9.16052i		−	0.812865i	−0.913681	−	0.406432i	$-0.866773\pi$
$127$		−	9.16052i		−	0.812865i	0.913681	−	0.406432i	$-0.133227\pi$
$128$	−6.64597	−	9.15593i	−0.587426	−	0.809278i
$129$	7.22721	−	9.92579i	0.636320	−	0.873917i
$130$	0.567252	−	0.466360i	0.0497513	−	0.0409024i
$131$	−17.9701	−	4.81507i	−1.57006	−	0.420695i	−0.634226	−	0.773148i	$-0.718681\pi$
$131$	−17.9701	−	4.81507i	−1.57006	−	0.420695i	−0.935830	+	0.352453i	$0.885348\pi$
$132$	3.56978	+	15.7244i	0.310709	+	1.36863i
$133$	10.9386	−	2.93099i	0.948498	−	0.254149i
$134$	−12.0762	−	8.63779i	−1.04323	−	0.746191i
$135$	−5.08593	+	1.06456i	−0.437727	+	0.0916231i
$136$	−6.83090	−	12.6997i	−0.585745	−	1.08899i
$137$	2.75645	−	4.77431i	0.235500	−	0.407897i	−0.723918	−	0.689886i	$-0.757661\pi$
$137$	2.75645	−	4.77431i	0.235500	−	0.407897i	0.959418	+	0.281989i	$0.0909940\pi$
$138$	−2.14710	+	2.41542i	−0.182773	+	0.205614i
$139$	9.54965	+	2.55882i	0.809991	+	0.217036i	0.639966	−	0.768403i	$-0.278948\pi$
$139$	9.54965	+	2.55882i	0.809991	+	0.217036i	0.170025	+	0.985440i	$0.445615\pi$
$140$	−7.82192	+	0.526371i	−0.661073	+	0.0444865i
$141$	13.1489	−	2.06864i	1.10733	−	0.174211i
$142$	−10.6217	−	3.98718i	−0.891357	−	0.334597i
$143$	−2.41703			−0.202122
$144$	−11.9643	−	0.924549i	−0.997028	−	0.0770457i
$145$	5.43033			0.450964
$146$	16.1883	+	6.07676i	1.33976	+	0.502916i
$147$	−5.20617	+	13.5207i	−0.429398	+	1.11517i
$148$	0.322089	+	4.78627i	0.0264755	+	0.393429i
$149$	−12.8647	−	3.44708i	−1.05392	−	0.282396i	−0.310046	−	0.950721i	$-0.600345\pi$
$149$	−12.8647	−	3.44708i	−1.05392	−	0.282396i	−0.743869	+	0.668326i	$0.767011\pi$
$150$	−2.39916	−	0.493976i	−0.195891	−	0.0403329i
$151$	0.851058	−	1.47408i	0.0692581	−	0.119959i	−0.829317	−	0.558779i	$-0.811270\pi$
$151$	0.851058	−	1.47408i	0.0692581	−	0.119959i	0.898575	+	0.438820i	$0.144603\pi$
$152$	7.82576	+	2.35159i	0.634753	+	0.190739i
$153$	−14.9542	−	3.21095i	−1.20897	−	0.259590i
$154$	20.9872	+	15.0115i	1.69120	+	1.20966i
$155$	0.496456	−	0.133025i	0.0398763	−	0.0106848i
$156$	0.532194	−	1.71825i	0.0426096	−	0.137570i
$157$	−19.3932	−	5.19640i	−1.54775	−	0.414718i	−0.618989	−	0.785400i	$-0.712457\pi$
$157$	−19.3932	−	5.19640i	−1.54775	−	0.414718i	−0.928760	+	0.370682i	$0.879124\pi$
$158$	0.126268	−	0.103809i	0.0100453	−	0.00825864i
$159$	18.3921	+	1.95233i	1.45859	+	0.154830i
$160$	−5.00047	−	2.64486i	−0.395322	−	0.209094i
$161$			5.17164i			0.407583i
$162$	−8.97044	+	9.02946i	−0.704784	+	0.709422i
$163$	−3.35875	−	3.35875i	−0.263078	−	0.263078i	0.563225	−	0.826303i	$-0.309560\pi$
$163$	−3.35875	−	3.35875i	−0.263078	−	0.263078i	−0.826303	+	0.563225i	$0.809560\pi$
$164$	3.41791	−	17.3409i	0.266894	−	1.35410i
$165$	5.06725	+	6.27078i	0.394485	+	0.488180i
$166$	21.5083	+	2.09946i	1.66937	+	0.162950i
$167$	−19.8844	+	11.4802i	−1.53870	+	0.888368i	−0.539784	+	0.841804i	$0.681494\pi$
$167$	−19.8844	+	11.4802i	−1.53870	+	0.888368i	−0.998915	+	0.0465644i	$0.985173\pi$
$168$	−15.2927	+	11.6143i	−1.17985	+	0.896063i
$169$	−11.0248	−	6.36518i	−0.848063	−	0.489629i
$170$	−5.86440	−	4.19464i	−0.449779	−	0.321714i
$171$	7.27861	−	4.70541i	0.556609	−	0.359832i
$172$	6.24843	−	12.7264i	0.476438	−	0.970382i
$173$	4.66752	−	1.25066i	0.354865	−	0.0950858i	−0.0769824	−	0.997032i	$-0.524529\pi$
$173$	4.66752	−	1.25066i	0.354865	−	0.0950858i	0.431848	+	0.901947i	$0.357862\pi$
$174$	11.1091	−	7.31558i	0.842182	−	0.554593i
$175$	−3.39465	+	1.95990i	−0.256612	+	0.148155i
$176$	7.18509	+	17.1767i	0.541596	+	1.29474i
$177$	−11.6205	+	5.15939i	−0.873452	+	0.387804i
$178$	2.23537	−	5.95498i	0.167548	−	0.446344i
$179$	−4.78519	+	4.78519i	−0.357662	+	0.357662i	−0.862951	−	0.505288i	$-0.831386\pi$
$179$	−4.78519	+	4.78519i	−0.357662	+	0.357662i	0.505288	+	0.862951i	$0.331386\pi$
$180$	−5.57358	+	2.22153i	−0.415430	+	0.165583i
$181$	−1.33669	−	1.33669i	−0.0993556	−	0.0993556i	0.655682	−	0.755037i	$-0.272381\pi$
$181$	−1.33669	−	1.33669i	−0.0993556	−	0.0993556i	−0.755037	+	0.655682i	$0.772381\pi$
$182$	−1.19026	−	2.62089i	−0.0882281	−	0.194273i
$183$	6.11281	−	8.39529i	0.451872	−	0.620598i
$184$	−1.96231	+	3.17412i	−0.144663	+	0.234000i
$185$	1.19927	+	2.07720i	0.0881724	+	0.152719i
$186$	0.836422	−	0.940949i	0.0613294	−	0.0689937i
$187$	6.14214	+	22.9228i	0.449158	+	1.67628i
$188$	14.5454	−	4.96580i	1.06083	−	0.362168i
$189$	−1.12908	+	20.3366i	−0.0821287	+	1.47927i
$190$	4.03057	−	0.669059i	0.292408	−	0.0485386i
$191$	2.69188	−	4.66248i	0.194778	−	0.337365i	−0.752050	−	0.659106i	$-0.770935\pi$
$191$	2.69188	−	4.66248i	0.194778	−	0.337365i	0.946828	+	0.321741i	$0.104268\pi$
$192$	−13.7928	+	1.32576i	−0.995412	+	0.0956783i
$193$	−8.85778	−	15.3421i	−0.637597	−	1.10435i	−0.985959	−	0.166990i	$-0.946595\pi$
$193$	−8.85778	−	15.3421i	−0.637597	−	1.10435i	0.348362	−	0.937360i	$-0.386738\pi$
$194$	4.22361	+	5.13735i	0.303237	+	0.368840i
$195$	−0.139776	−	0.888460i	−0.0100096	−	0.0636240i
$196$	−3.23521	+	16.4140i	−0.231087	+	1.17243i
$197$	5.05847	−	5.05847i	0.360401	−	0.360401i	−0.503559	−	0.863961i	$-0.667976\pi$
$197$	5.05847	−	5.05847i	0.360401	−	0.360401i	0.863961	+	0.503559i	$0.167976\pi$
$198$	18.8142	+	6.00205i	1.33707	+	0.426547i
$199$	4.23486			0.300201			0.150101	−	0.988671i	$-0.452040\pi$
$199$	4.23486			0.300201			0.150101	+	0.988671i	$0.452040\pi$
$200$	−2.82715	−	0.0851517i	−0.199909	−	0.00602113i
$201$	−16.6199	+	7.37905i	−1.17227	+	0.520478i
$202$	27.5265	+	2.68691i	1.93676	+	0.189050i
$203$	5.50918	−	20.5605i	0.386669	−	1.44307i
$204$	−17.6480	−	0.680865i	−1.23561	−	0.0476701i
$205$	−2.28725	−	8.53615i	−0.159749	−	0.596190i
$206$	−11.0591	+	1.83577i	−0.770527	+	0.127904i
$207$	1.21533	+	3.76688i	0.0844710	+	0.261817i
$208$	0.263928	−	2.06021i	0.0183001	−	0.142850i
$209$	−11.6461	−	6.72387i	−0.805576	−	0.465099i
$210$	−4.30431	+	8.58267i	−0.297026	+	0.592261i
$211$	1.06353	−	3.96914i	0.0732163	−	0.273247i	−0.919607	−	0.392840i	$-0.871492\pi$
$211$	1.06353	−	3.96914i	0.0732163	−	0.273247i	0.992823	+	0.119594i	$0.0381592\pi$
$212$	21.3085	−	1.43394i	1.46348	−	0.0984836i
$213$	−10.8077	+	8.73341i	−0.740531	+	0.598403i
$214$	22.5004	−	10.2185i	1.53810	−	0.698519i
$215$		−	7.08882i		−	0.483453i
$216$	−8.40942	+	12.0533i	−0.572188	+	0.820122i
$217$		−	2.01466i		−	0.136764i
$218$	−3.90629	−	8.60142i	−0.264568	−	0.582562i
$219$	16.4717	−	13.3104i	1.11306	−	0.899431i
$220$	7.00992	+	6.12595i	0.472609	+	0.413012i
$221$	0.685191	−	2.55717i	0.0460909	−	0.172014i
$222$	5.25177	+	2.63383i	0.352476	+	0.176771i
$223$	−15.1406	−	8.74144i	−1.01389	−	0.585370i	−0.101563	−	0.994829i	$-0.532384\pi$
$223$	−15.1406	−	8.74144i	−1.01389	−	0.585370i	−0.912329	+	0.409459i	$0.865718\pi$
$224$	−15.0872	+	16.2497i	−1.00805	+	1.08573i
$225$	−2.01200	+	2.22528i	−0.134133	+	0.148352i
$226$	3.97057	+	23.9197i	0.264119	+	1.59111i
$227$	−3.22300	−	12.0284i	−0.213918	−	0.798354i	−0.986545	−	0.163493i	$-0.947724\pi$
$227$	−3.22300	−	12.0284i	−0.213918	−	0.798354i	0.772626	−	0.634861i	$-0.218943\pi$
$228$	7.34424	−	6.79860i	0.486384	−	0.450248i
$229$	−4.05022	+	15.1156i	−0.267646	+	0.998868i	0.692965	+	0.720971i	$0.256304\pi$
$229$	−4.05022	+	15.1156i	−0.267646	+	0.998868i	−0.960611	+	0.277897i	$0.910363\pi$
$230$	−0.181268	+	1.85703i	−0.0119524	+	0.122449i
$231$	28.8835	−	12.8240i	1.90040	−	0.843757i
$232$	11.1827	−	10.5288i	0.734180	−	0.691247i
$233$	−12.1413			−0.795404			−0.397702	−	0.917515i	$-0.630192\pi$
$233$	−12.1413			−0.795404			−0.397702	+	0.917515i	$0.630192\pi$
$234$	−1.48286	−	1.62927i	−0.0969374	−	0.106509i
$235$	5.43402	−	5.43402i	0.354477	−	0.354477i
$236$	−12.1928	+	8.17777i	−0.793686	+	0.532327i
$237$	−0.0311136	−	0.197767i	−0.00202104	−	0.0128464i
$238$	−21.8315	+	17.9485i	−1.41512	+	1.16343i
$239$	9.33033	+	16.1606i	0.603529	+	1.04534i	0.992282	+	0.124001i	$0.0395725\pi$
$239$	9.33033	+	16.1606i	0.603529	+	1.04534i	−0.388753	+	0.921342i	$0.627094\pi$
$240$	−5.89837	+	3.63445i	−0.380738	+	0.234603i
$241$	−0.0167827	+	0.0290685i	−0.00108107	+	0.00187246i	−0.866565	−	0.499063i	$-0.833677\pi$
$241$	−0.0167827	+	0.0290685i	−0.00108107	+	0.00187246i	0.865484	+	0.500936i	$0.167011\pi$
$242$	−2.47022	−	14.8812i	−0.158792	−	0.956598i
$243$	3.95667	+	15.0780i	0.253820	+	0.967251i
$244$	5.28496	−	10.7641i	0.338335	−	0.689101i
$245$	2.16499	+	8.07987i	0.138316	+	0.516204i
$246$	−16.1788	−	14.3816i	−1.03152	−	0.916936i
$247$	0.750085	+	1.29919i	0.0477268	+	0.0826652i
$248$	0.764435	−	1.23651i	0.0485417	−	0.0785184i
$249$	15.5793	−	21.3965i	0.987297	−	1.35595i
$250$	−1.28765	+	0.584778i	−0.0814379	+	0.0369846i
$251$	−3.10957	−	3.10957i	−0.196274	−	0.196274i	0.602126	−	0.798401i	$-0.294320\pi$
$251$	−3.10957	−	3.10957i	−0.196274	−	0.196274i	−0.798401	+	0.602126i	$0.794320\pi$
$252$	2.75674	+	23.3567i	0.173658	+	1.47134i
$253$	4.34254	−	4.34254i	0.273013	−	0.273013i
$254$	−12.1286	−	4.55281i	−0.761014	−	0.285668i
$255$	−8.07085	+	3.58337i	−0.505416	+	0.224400i
$256$	−15.4256	+	4.24876i	−0.964098	+	0.265548i
$257$	26.3728	−	15.2264i	1.64509	−	0.949795i	0.666109	−	0.745854i	$-0.267958\pi$
$257$	26.3728	−	15.2264i	1.64509	−	0.949795i	0.978983	−	0.203941i	$-0.0653749\pi$
$258$	−9.54985	−	14.5020i	−0.594548	−	0.902855i
$259$	9.08148	−	2.43338i	0.564296	−	0.151203i
$260$	−0.335536	−	0.982826i	−0.0208091	−	0.0609523i
$261$	−0.818948	−	16.2704i	−0.0506916	−	1.00711i
$262$	−15.3064	+	21.3994i	−0.945631	+	1.32206i
$263$	18.6197	+	10.7501i	1.14814	+	0.662881i	0.948434	−	0.316975i	$-0.102667\pi$
$263$	18.6197	+	10.7501i	1.14814	+	0.662881i	0.199709	+	0.979855i	$0.436000\pi$
$264$	22.5933	+	3.08865i	1.39052	+	0.190093i
$265$	9.24774	−	5.33918i	0.568084	−	0.327984i
$266$	1.55588	−	15.9395i	0.0953969	−	0.977313i
$267$	−4.89630	−	6.05923i	−0.299648	−	0.370819i
$268$	−17.4384	+	11.6960i	−1.06522	+	0.714446i
$269$	7.49727	+	7.49727i	0.457117	+	0.457117i	0.897708	−	0.440591i	$-0.145231\pi$
$269$	7.49727	+	7.49727i	0.457117	+	0.457117i	−0.440591	+	0.897708i	$0.645231\pi$
$270$	−1.11824	+	7.26289i	−0.0680536	+	0.442005i
$271$			28.6452i			1.74007i	0.492990	+	0.870035i	$0.335904\pi$
$271$			28.6452i			1.74007i	−0.492990	+	0.870035i	$0.664096\pi$
$272$	−20.2095	+	2.73234i	−1.22538	+	0.165672i
$273$	−3.50573	−	0.372134i	−0.212177	−	0.0225226i
$274$	−4.95125	−	6.02240i	−0.299116	−	0.363827i
$275$	4.49613	+	1.20473i	0.271127	+	0.0726482i
$276$	2.13091	+	4.04324i	0.128266	+	0.243374i
$277$	8.70742	−	2.33315i	0.523178	−	0.140185i	0.0124420	−	0.999923i	$-0.496039\pi$
$277$	8.70742	−	2.33315i	0.523178	−	0.140185i	0.510736	+	0.859737i	$0.329373\pi$
$278$	8.13410	−	11.3720i	0.487851	−	0.682050i
$279$	−0.473441	−	1.46742i	−0.0283442	−	0.0878524i
$280$	−3.19060	+	10.6179i	−0.190675	+	0.634539i
$281$	9.22694	−	15.9815i	0.550433	−	0.953378i	−0.447810	−	0.894129i	$-0.647796\pi$
$281$	9.22694	−	15.9815i	0.550433	−	0.953378i	0.998243	−	0.0592496i	$-0.0188708\pi$
$282$	3.79614	−	18.4373i	0.226057	−	1.09792i
$283$	1.55046	+	0.415445i	0.0921653	+	0.0246956i	0.304607	−	0.952478i	$-0.401475\pi$
$283$	1.55046	+	0.415445i	0.0921653	+	0.0246956i	−0.212442	+	0.977174i	$0.568142\pi$
$284$	−10.5581	+	12.0816i	−0.626507	+	0.716911i
$285$	1.79809	−	4.66975i	0.106510	−	0.276612i
$286$	−1.20127	+	3.20016i	−0.0710326	+	0.189229i
$287$	−34.6404			−2.04476
$288$	−7.17042	+	15.3813i	−0.422521	+	0.906353i
$289$	−8.99305			−0.529003
$290$	2.69889	−	7.18978i	0.158484	−	0.422198i
$291$	8.04639	−	1.26589i	0.471687	−	0.0742079i
$292$	16.0913	−	18.4133i	0.941673	−	1.07756i
$293$	−12.7580	−	3.41850i	−0.745330	−	0.199711i	−0.133884	−	0.990997i	$-0.542745\pi$
$293$	−12.7580	−	3.41850i	−0.745330	−	0.199711i	−0.611446	+	0.791286i	$0.709412\pi$
$294$	15.3140	+	13.6128i	0.893132	+	0.793917i
$295$	−3.67033	+	6.35720i	−0.213695	+	0.370130i
$296$	6.49712	+	1.95234i	0.377638	+	0.113478i
$297$	18.0244	−	16.1282i	1.04588	−	0.935854i
$298$	−10.9577	+	15.3197i	−0.634764	+	0.887445i
$299$	−0.661750	+	0.177315i	−0.0382700	+	0.0102544i
$300$	−1.84642	+	2.93100i	−0.106603	+	0.169221i
$301$	−26.8400	−	7.19175i	−1.54703	−	0.414526i
$302$	−1.52870	−	1.85942i	−0.0879671	−	0.106998i
$303$	19.9385	−	27.3834i	1.14544	−	1.57314i
$304$	7.00294	−	9.19260i	0.401646	−	0.527231i
$305$		−	5.99576i		−	0.343316i
$306$	−11.6836	+	18.2035i	−0.667906	+	1.04063i
$307$	−20.8596	−	20.8596i	−1.19052	−	1.19052i	−0.976921	−	0.213601i	$-0.931481\pi$
$307$	−20.8596	−	20.8596i	−1.19052	−	1.19052i	−0.213601	−	0.976921i	$-0.568519\pi$
$308$	30.3061	−	20.3264i	1.72685	−	1.15820i
$309$	−4.93364	+	12.8129i	−0.280665	+	0.728902i
$310$	0.0706145	−	0.723424i	0.00401063	−	0.0410877i
$311$	22.3804	−	12.9214i	1.26908	−	0.732703i	0.294265	−	0.955724i	$-0.404925\pi$
$311$	22.3804	−	12.9214i	1.26908	−	0.732703i	0.974814	+	0.223021i	$0.0715918\pi$
$312$	−2.01046	−	1.55860i	−0.113820	−	0.0882384i
$313$	21.0445	+	12.1501i	1.18951	+	0.686762i	0.958194	−	0.286118i	$-0.0923649\pi$
$313$	21.0445	+	12.1501i	1.18951	+	0.686762i	0.231312	+	0.972880i	$0.425698\pi$
$314$	−16.5186	+	23.0941i	−0.932196	+	1.30328i
$315$	6.38423	+	9.87551i	0.359710	+	0.556422i
$316$	−0.0746888	−	0.218773i	−0.00420157	−	0.0123069i
$317$	12.6036	−	3.37713i	0.707889	−	0.189678i	0.113127	−	0.993580i	$-0.463913\pi$
$317$	12.6036	−	3.37713i	0.707889	−	0.189678i	0.594762	+	0.803902i	$0.297246\pi$
$318$	11.7258	−	23.3810i	0.657553	−	1.31114i
$319$	−21.8903	+	12.6384i	−1.22562	+	0.707613i
$320$	−5.98705	+	5.30615i	−0.334686	+	0.296623i
$321$	3.19479	−	30.0969i	0.178316	−	1.67984i
$322$	6.84728	+	2.57032i	0.381584	+	0.143238i
$323$	10.4152	−	10.4152i	0.579517	−	0.579517i
$324$	7.49672	+	16.3646i	0.416484	+	0.909143i
$325$	−0.367174	−	0.367174i	−0.0203671	−	0.0203671i
$326$	−6.11631	+	2.77769i	−0.338751	+	0.153842i
$327$	−11.5054	−	1.22130i	−0.636249	−	0.0675379i
$328$	−21.2607	−	13.1438i	−1.17393	−	0.725746i
$329$	−15.0616	−	26.0875i	−0.830373	−	1.43825i
$330$	10.8210	−	3.59246i	0.595675	−	0.197759i
$331$	−1.30555	−	4.87237i	−0.0717593	−	0.267809i	0.920720	−	0.390225i	$-0.127603\pi$
$331$	−1.30555	−	4.87237i	−0.0717593	−	0.267809i	−0.992479	+	0.122415i	$0.960936\pi$
$332$	13.4694	−	27.4337i	0.739229	−	1.50562i
$333$	6.04287	−	3.90654i	0.331147	−	0.214077i
$334$	5.31731	+	32.0327i	0.290950	+	1.75275i
$335$	−5.24937	+	9.09217i	−0.286804	+	0.496758i
$336$	7.77689	+	26.0199i	0.424264	+	1.41950i
$337$	10.8463	+	18.7863i	0.590835	+	1.02336i	0.994120	+	0.108282i	$0.0345349\pi$
$337$	10.8463	+	18.7863i	0.590835	+	1.02336i	−0.403285	+	0.915074i	$0.632132\pi$
$338$	−13.9069	+	11.4334i	−0.756436	+	0.621895i
$339$	27.7129	+	10.6709i	1.50516	+	0.579564i
$340$	−8.46834	+	5.67974i	−0.459260	+	0.308027i
$341$	−1.69168	+	1.69168i	−0.0916094	+	0.0916094i
$342$	−2.61249	−	11.9755i	−0.141267	−	0.647562i
$343$	5.35011			0.288879
$344$	−13.7444	−	14.5980i	−0.741047	−	0.787073i
$345$	1.84738	+	1.34512i	0.0994594	+	0.0724188i
$346$	0.663895	−	6.80140i	0.0356912	−	0.365646i
$347$	−1.79611	+	6.70316i	−0.0964201	+	0.359845i	−0.997231	−	0.0743671i	$-0.976306\pi$
$347$	−1.79611	+	6.70316i	−0.0964201	+	0.359845i	0.900811	+	0.434212i	$0.142973\pi$
$348$	−4.16459	−	18.3444i	−0.223245	−	0.983364i
$349$	−3.50494	−	13.0806i	−0.187615	−	0.700188i	−0.994056	−	0.108873i	$-0.965276\pi$
$349$	−3.50494	−	13.0806i	−0.187615	−	0.700188i	0.806441	−	0.591315i	$-0.201391\pi$
$350$	0.907769	+	5.46861i	0.0485223	+	0.292310i
$351$	−2.64093	+	0.552788i	−0.140962	+	0.0295056i
$352$	26.3131	−	0.976209i	1.40249	−	0.0520321i
$353$	27.4785	+	15.8647i	1.46253	+	0.844395i	0.999128	−	0.0417508i	$-0.0132935\pi$
$353$	27.4785	+	15.8647i	1.46253	+	0.844395i	0.463407	+	0.886146i	$0.346627\pi$
$354$	1.05563	+	17.9499i	0.0561059	+	0.954024i
$355$	−2.07636	+	7.74908i	−0.110202	+	0.411279i
$356$	−6.77343	−	5.91928i	−0.358991	−	0.313721i
$357$	5.37949	+	34.1936i	0.284713	+	1.80972i
$358$	3.95736	+	8.71388i	0.209153	+	0.460543i
$359$			11.8000i			0.622783i	0.950282	+	0.311391i	$0.100795\pi$
$359$			11.8000i			0.622783i	−0.950282	+	0.311391i	$0.899205\pi$
$360$	0.171230	+	8.48355i	0.00902461	+	0.447123i
$361$		−	10.6534i		−	0.560707i
$362$	−2.43413	+	1.10545i	−0.127935	+	0.0581010i
$363$	−17.2411	−	6.63870i	−0.904922	−	0.348441i
$364$	−4.06163	+	0.273324i	−0.212887	+	0.0143261i
$365$	3.16453	−	11.8102i	0.165639	−	0.618173i
$366$	−8.07732	−	12.2659i	−0.422208	−	0.641148i
$367$	7.87757	+	4.54812i	0.411206	+	0.237410i	0.691308	−	0.722560i	$-0.257035\pi$
$367$	7.87757	+	4.54812i	0.411206	+	0.237410i	−0.280102	+	0.959970i	$0.590368\pi$
$368$	3.22728	+	4.17565i	0.168234	+	0.217671i
$369$	−25.2311	+	8.14042i	−1.31348	+	0.423774i
$370$	3.34627	−	0.555468i	0.173964	−	0.0288774i
$371$	−10.8334	−	40.4309i	−0.562444	−	2.09907i
$372$	−0.830116	−	1.57508i	−0.0430395	−	0.0816641i
$373$	5.42317	−	20.2395i	0.280801	−	1.04796i	−0.671052	−	0.741410i	$-0.734157\pi$
$373$	5.42317	−	20.2395i	0.280801	−	1.04796i	0.951853	−	0.306554i	$-0.0991759\pi$
$374$	33.4025	+	3.26047i	1.72720	+	0.168595i
$375$	−0.182830	+	1.72237i	−0.00944131	+	0.0889430i
$376$	0.654380	−	21.7262i	0.0337470	−	1.12045i
$377$	2.81976			0.145225
$378$	26.3646	+	11.6023i	1.35605	+	0.596756i
$379$	4.86659	−	4.86659i	0.249980	−	0.249980i	−0.570982	−	0.820962i	$-0.693438\pi$
$379$	4.86659	−	4.86659i	0.249980	−	0.249980i	0.820962	+	0.570982i	$0.193438\pi$
$380$	1.11737	−	5.66902i	0.0573198	−	0.290814i
$381$	−12.3409	+	9.97234i	−0.632243	+	0.510899i
$382$	−4.83527	−	5.88133i	−0.247394	−	0.300915i
$383$	8.00493	+	13.8649i	0.409033	+	0.708466i	0.994782	−	0.102027i	$-0.0325328\pi$
$383$	8.00493	+	13.8649i	0.409033	+	0.708466i	−0.585749	+	0.810493i	$0.699199\pi$
$384$	−5.09977	+	18.9207i	−0.260247	+	0.965542i
$385$	9.12284	−	15.8012i	0.464943	−	0.805304i
$386$	−24.7154	+	4.10266i	−1.25798	+	0.208820i
$387$	−21.2396	+	1.06907i	−1.07967	+	0.0543436i
$388$	8.90102	−	3.03880i	0.451881	−	0.154272i
$389$	6.74015	+	25.1546i	0.341739	+	1.27539i	0.896376	+	0.443295i	$0.146191\pi$
$389$	6.74015	+	25.1546i	0.341739	+	1.27539i	−0.554636	+	0.832093i	$0.687143\pi$
$390$	−1.24579	−	0.256503i	−0.0630833	−	0.0129885i
$391$	3.36328	+	5.82536i	0.170088	+	0.294601i
$392$	20.1243	+	12.4412i	1.01643	+	0.628377i
$393$	13.0759	+	29.4508i	0.659590	+	1.48560i
$394$	−4.18337	−	9.21152i	−0.210755	−	0.464070i
$395$	−0.0817312	−	0.0817312i	−0.00411234	−	0.00411234i
$396$	17.2975	−	21.9270i	0.869230	−	1.10187i
$397$	26.8643	−	26.8643i	1.34828	−	1.34828i	0.460747	−	0.887531i	$-0.347581\pi$
$397$	26.8643	−	26.8643i	1.34828	−	1.34828i	0.887531	−	0.460747i	$-0.152419\pi$
$398$	2.10474	−	5.60697i	0.105501	−	0.281052i
$399$	−15.8566	−	11.5456i	−0.793823	−	0.578002i
$400$	−1.51784	+	3.70083i	−0.0758920	+	0.185042i
$401$	−0.438704	+	0.253286i	−0.0219078	+	0.0126485i	−0.510914	−	0.859632i	$-0.670693\pi$
$401$	−0.438704	+	0.253286i	−0.0219078	+	0.0126485i	0.489006	+	0.872280i	$0.337360\pi$
$402$	1.50978	+	25.6722i	0.0753008	+	1.28041i
$403$	0.257791	−	0.0690749i	0.0128415	−	0.00344086i
$404$	17.2382	−	35.1099i	0.857635	−	1.74678i
$405$	6.97082	+	5.69277i	0.346383	+	0.282876i
$406$	−24.4842	−	17.5128i	−1.21513	−	0.869147i
$407$	−9.66883	−	5.58230i	−0.479266	−	0.276704i
$408$	−9.67259	+	23.0277i	−0.478865	+	1.14004i
$409$	0.733919	−	0.423728i	0.0362900	−	0.0209520i	−0.481745	−	0.876311i	$-0.659997\pi$
$409$	0.733919	−	0.423728i	0.0362900	−	0.0209520i	0.518035	+	0.855359i	$0.326664\pi$
$410$	−12.4387	−	1.21416i	−0.614302	−	0.0599629i
$411$	−9.43261	+	1.48398i	−0.465276	+	0.0731993i
$412$	−3.06585	+	15.5547i	−0.151044	+	0.766327i
$413$	20.3463	+	20.3463i	1.00117	+	1.00117i
$414$	5.59139	+	0.263056i	0.274802	+	0.0129285i
$415$		−	15.2810i		−	0.750113i
$416$	−2.59656	−	1.37337i	−0.127307	−	0.0673352i
$417$	−6.94876	−	15.6507i	−0.340282	−	0.766419i
$418$	−14.6906	+	12.0777i	−0.718539	+	0.590738i
$419$	−12.9827	−	3.47871i	−0.634247	−	0.169946i	−0.0726509	−	0.997357i	$-0.523146\pi$
$419$	−12.9827	−	3.47871i	−0.634247	−	0.169946i	−0.561596	+	0.827411i	$0.689813\pi$
$420$	9.22424	+	9.96454i	0.450097	+	0.486220i
$421$	19.7743	−	5.29852i	0.963742	−	0.258234i	0.257558	−	0.966263i	$-0.417082\pi$
$421$	19.7743	−	5.29852i	0.963742	−	0.258234i	0.706183	+	0.708029i	$0.250415\pi$
$422$	−4.72658	−	3.38079i	−0.230086	−	0.164574i
$423$	−17.1010	−	15.4620i	−0.831477	−	0.751786i
$424$	8.69186	−	28.9253i	0.422114	−	1.40474i
$425$	−2.54917	+	4.41529i	−0.123653	+	0.214173i
$426$	6.19161	+	18.6500i	0.299985	+	0.903594i
$427$	−22.7014	−	6.08283i	−1.09860	−	0.294369i
$428$	−2.34650	−	34.8693i	−0.113422	−	1.68547i
$429$	2.63123	+	3.25618i	0.127037	+	0.157210i
$430$	−9.38562	−	3.52316i	−0.452615	−	0.169902i
$431$	33.6914			1.62286			0.811430	−	0.584450i	$-0.198690\pi$
$431$	33.6914			1.62286			0.811430	+	0.584450i	$0.198690\pi$
$432$	11.7791	+	17.1246i	0.566722	+	0.823909i
$433$	−36.2636			−1.74272			−0.871359	−	0.490646i	$-0.836761\pi$
$433$	−36.2636			−1.74272			−0.871359	+	0.490646i	$0.836761\pi$
$434$	−2.66742	−	1.00129i	−0.128040	−	0.0480636i
$435$	−5.91157	−	7.31564i	−0.283438	−	0.350758i
$436$	−13.3298	+	0.897017i	−0.638380	+	0.0429593i
$437$	−3.68181	−	0.986538i	−0.176125	−	0.0471925i
$438$	−9.43648	−	28.4240i	−0.450893	−	1.35815i
$439$	−4.50267	+	7.79886i	−0.214901	+	0.372219i	−0.953242	−	0.302208i	$-0.902276\pi$
$439$	−4.50267	+	7.79886i	−0.214901	+	0.372219i	0.738341	+	0.674428i	$0.235609\pi$
$440$	11.5947	−	6.23655i	0.552758	−	0.297316i
$441$	23.8824	−	7.70529i	1.13726	−	0.366919i
$442$	−3.04516	−	2.17811i	−0.144843	−	0.103602i
$443$	−13.9200	+	3.72985i	−0.661359	+	0.177210i	−0.573859	−	0.818954i	$-0.694554\pi$
$443$	−13.9200	+	3.72985i	−0.661359	+	0.177210i	−0.0874995	+	0.996165i	$0.527888\pi$
$444$	6.09735	−	5.64435i	0.289367	−	0.267869i
$445$	−4.34444	−	1.16409i	−0.205946	−	0.0551832i
$446$	−19.0986	+	15.7017i	−0.904347	+	0.743499i
$447$	9.36092	+	21.0836i	0.442756	+	0.997222i
$448$	14.0164	+	28.0516i	0.662212	+	1.32532i
$449$			18.1820i			0.858064i	0.903289	+	0.429032i	$0.141145\pi$
$449$			18.1820i			0.858064i	−0.903289	+	0.429032i	$0.858855\pi$
$450$	1.94631	+	3.76987i	0.0917498	+	0.177713i
$451$	29.0870	+	29.0870i	1.36965	+	1.36965i
$452$	33.6432	+	6.63110i	1.58244	+	0.311900i
$453$	−2.91233	+	0.458181i	−0.136833	+	0.0215272i
$454$	−17.5275	−	1.71089i	−0.822607	−	0.0802959i
$455$	−1.76271	+	1.01770i	−0.0826373	+	0.0477107i
$456$	−5.35127	−	13.1027i	−0.250596	−	0.613591i
$457$	1.59938	+	0.923401i	0.0748157	+	0.0431949i	0.536941	−	0.843620i	$-0.319580\pi$
$457$	1.59938	+	0.923401i	0.0748157	+	0.0431949i	−0.462125	+	0.886815i	$0.652913\pi$
$458$	18.0002	+	12.8750i	0.841093	+	0.601610i
$459$	11.9537	+	23.6415i	0.557951	+	1.10349i
$460$	2.36863	+	1.16295i	0.110438	+	0.0542228i
$461$	0.177988	−	0.0476917i	0.00828972	−	0.00222122i	−0.254672	−	0.967028i	$-0.581967\pi$
$461$	0.177988	−	0.0476917i	0.00828972	−	0.00222122i	0.262962	+	0.964806i	$0.415301\pi$
$462$	−2.62383	−	44.6155i	−0.122071	−	2.07570i
$463$	−0.722226	+	0.416977i	−0.0335647	+	0.0193786i	−0.516688	−	0.856173i	$-0.672835\pi$
$463$	−0.722226	+	0.416977i	−0.0335647	+	0.0193786i	0.483124	+	0.875552i	$0.339502\pi$
$464$	−8.38230	−	20.0388i	−0.389138	−	0.930276i
$465$	−0.719662	−	0.524003i	−0.0333735	−	0.0243001i
$466$	−6.03427	+	16.0752i	−0.279532	+	0.744668i
$467$	27.1455	−	27.1455i	1.25615	−	1.25615i	0.303227	−	0.952918i	$-0.401936\pi$
$467$	27.1455	−	27.1455i	1.25615	−	1.25615i	0.952918	−	0.303227i	$-0.0980640\pi$
$468$	−2.89415	+	1.15356i	−0.133782	+	0.0533232i
$469$	29.0996	+	29.0996i	1.34369	+	1.34369i
$470$	−4.49395	−	9.89540i	−0.207290	−	0.456441i
$471$	14.1114	+	31.7831i	0.650219	+	1.46449i
$472$	4.76753	+	20.2077i	0.219443	+	0.930137i
$473$	16.4983	+	28.5759i	0.758592	+	1.31392i
$474$	−0.277308	−	0.0570963i	−0.0127372	−	0.00262252i
$475$	−0.747739	−	2.79060i	−0.0343086	−	0.128042i
$476$	12.9136	+	37.8254i	0.591893	+	1.73372i
$477$	−17.3920	−	26.9029i	−0.796323	−	1.23180i
$478$	26.0339	−	4.32153i	1.19076	−	0.197662i
$479$	−0.246294	+	0.426594i	−0.0112535	+	0.0194916i	−0.871597	−	0.490223i	$-0.836915\pi$
$479$	−0.246294	+	0.426594i	−0.0112535	+	0.0194916i	0.860344	+	0.509714i	$0.170249\pi$
$480$	1.88052	+	9.61580i	0.0858336	+	0.438899i
$481$	0.622737	+	1.07861i	0.0283944	+	0.0491805i
$482$	0.0301457	+	0.0366675i	0.00137310	+	0.00167016i
$483$	6.96715	−	5.62997i	0.317016	−	0.256172i
$484$	−20.9305	−	4.12541i	−0.951384	−	0.187519i
$485$	3.32533	−	3.32533i	0.150995	−	0.150995i
$486$	21.9298	+	2.25515i	0.994754	+	0.102296i
$487$	−26.0059			−1.17844			−0.589220	−	0.807973i	$-0.700565\pi$
$487$	−26.0059			−1.17844			−0.589220	+	0.807973i	$0.700565\pi$
$488$	−11.6251	−	12.3471i	−0.526242	−	0.558927i
$489$	−0.868442	+	8.18127i	−0.0392723	+	0.369970i
$490$	11.7738	+	1.14926i	0.531885	+	0.0519181i
$491$	3.61079	−	13.4756i	0.162953	−	0.608147i	−0.835340	−	0.549734i	$-0.814729\pi$
$491$	3.61079	−	13.4756i	0.162953	−	0.608147i	0.998292	−	0.0584136i	$-0.0186042\pi$
$492$	−27.0822	+	14.2732i	−1.22096	+	0.643483i
$493$	−7.16557	−	26.7423i	−0.322721	−	1.20441i
$494$	2.09292	−	0.347417i	0.0941650	−	0.0156310i
$495$	2.93157	−	13.6530i	0.131764	−	0.613658i
$496$	−1.25722	−	1.62666i	−0.0564507	−	0.0730394i
$497$	27.2334	+	15.7232i	1.22159	+	0.705283i
$498$	−20.5861	−	31.2612i	−0.922484	−	1.40085i
$499$	6.41001	−	23.9225i	0.286951	−	1.07092i	−0.660450	−	0.750870i	$-0.729635\pi$
$499$	6.41001	−	23.9225i	0.286951	−	1.07092i	0.947402	−	0.320047i	$-0.103699\pi$
$500$	0.134285	+	1.99549i	0.00600540	+	0.0892409i
$501$	37.1126	+	14.2902i	1.65807	+	0.638441i
$502$	−5.66255	+	2.57162i	−0.252732	+	0.114777i
$503$		−	6.82289i		−	0.304217i	−0.988364	−	0.152109i	$-0.951394\pi$
$503$		−	6.82289i		−	0.304217i	0.988364	−	0.152109i	$-0.0486064\pi$
$504$	32.2945	+	7.95842i	1.43851	+	0.354496i
$505$		−	19.5567i		−	0.870262i
$506$	−3.59129	−	7.90780i	−0.159652	−	0.351545i
$507$	3.42680	+	21.7817i	0.152189	+	0.967361i
$508$	−12.0559	+	13.7955i	−0.534893	+	0.612077i
$509$	−4.62429	+	17.2581i	−0.204968	+	0.764951i	0.784491	+	0.620140i	$0.212924\pi$
$509$	−4.62429	+	17.2581i	−0.204968	+	0.764951i	−0.989459	+	0.144811i	$0.953743\pi$
$510$	0.733169	+	12.4668i	0.0324653	+	0.552039i
$511$	−41.5058	−	23.9634i	−1.83611	−	1.06008i
$512$	−2.04117	+	22.5352i	−0.0902078	+	0.995923i
$513$	−14.2627	−	4.68321i	−0.629714	−	0.206769i
$514$	−7.05240	−	42.4853i	−0.311068	−	1.87395i
$515$	2.05166	+	7.65690i	0.0904069	+	0.337403i
$516$	−23.9470	+	5.43650i	−1.05421	+	0.239329i
$517$	−9.25823	+	34.5522i	−0.407176	+	1.51960i
$518$	1.29172	−	13.2333i	0.0567551	−	0.581439i
$519$	−6.76603	−	4.92651i	−0.296996	−	0.216250i
$520$	−1.46803	−	0.0442160i	−0.0643773	−	0.00193900i
$521$	0.273092			0.0119644			0.00598218	−	0.999982i	$-0.498096\pi$
$521$	0.273092			0.0119644			0.00598218	+	0.999982i	$0.498096\pi$
$522$	−21.9491	−	7.00214i	−0.960685	−	0.306475i
$523$	−13.8336	+	13.8336i	−0.604902	+	0.604902i	−0.941609	−	0.336708i	$-0.890687\pi$
$523$	−13.8336	+	13.8336i	−0.604902	+	0.604902i	0.336708	+	0.941609i	$0.390687\pi$
$524$	20.7256	+	30.9013i	0.905401	+	1.34993i
$525$	6.33584	+	2.43962i	0.276519	+	0.106474i
$526$	23.4873	−	19.3098i	1.02409	−	0.841947i
$527$	−1.31019	−	2.26932i	−0.0570730	−	0.0988533i
$528$	15.3183	−	28.3786i	0.666645	−	1.23502i
$529$	−10.6296	+	18.4111i	−0.462158	+	0.800482i
$530$	−2.47295	−	14.8976i	−0.107418	−	0.647112i
$531$	19.6010	+	10.0383i	0.850611	+	0.435627i
$532$	−20.3307	−	9.98196i	−0.881447	−	0.432773i
$533$	−1.18768	−	4.43250i	−0.0514443	−	0.191993i
$534$	−10.4559	+	3.47126i	−0.452472	+	0.150216i
$535$	−8.73703	−	15.1330i	−0.377735	−	0.654256i
$536$	6.81860	+	28.9015i	0.294519	+	1.24835i
$537$	11.6558	+	1.23726i	0.502985	+	0.0533919i
$538$	13.6526	−	6.20025i	0.588605	−	0.267312i
$539$	−27.5322	−	27.5322i	−1.18589	−	1.18589i
$540$	9.06033	+	5.09023i	0.389895	+	0.219048i
$541$	−16.4533	+	16.4533i	−0.707383	+	0.707383i	−0.965984	−	0.258601i	$-0.916738\pi$
$541$	−16.4533	+	16.4533i	−0.707383	+	0.707383i	0.258601	+	0.965984i	$0.416738\pi$
$542$	37.9263	+	14.2367i	1.62908	+	0.611520i
$543$	−0.345617	+	3.25592i	−0.0148318	+	0.139725i
$544$	−6.42654	+	28.1154i	−0.275536	+	1.20544i
$545$	−5.78501	+	3.33998i	−0.247803	+	0.143069i
$546$	−2.23507	+	4.45666i	−0.0956520	+	0.190727i
$547$	−24.7241	+	6.62479i	−1.05712	+	0.283256i	−0.745193	−	0.666849i	$-0.767643\pi$
$547$	−24.7241	+	6.62479i	−1.05712	+	0.283256i	−0.311932	+	0.950105i	$0.600976\pi$
$548$	−10.4345	+	3.56232i	−0.445739	+	0.152175i
$549$	−17.9645	+	0.904221i	−0.766708	+	0.0385912i
$550$	3.82966	−	5.35414i	0.163297	−	0.228301i
$551$	13.5866	+	7.84422i	0.578808	+	0.334175i
$552$	6.41234	−	0.811835i	0.272927	−	0.0345540i
$553$	−0.392372	+	0.226536i	−0.0166854	+	0.00963329i
$554$	1.23852	−	12.6882i	0.0526196	−	0.539072i
$555$	1.49282	−	3.87693i	0.0633665	−	0.164567i
$556$	−11.0140	−	16.4215i	−0.467096	−	0.696428i
$557$	18.8272	+	18.8272i	0.797734	+	0.797734i	0.982738	−	0.185004i	$-0.0592298\pi$
$557$	18.8272	+	18.8272i	0.797734	+	0.797734i	−0.185004	+	0.982738i	$0.559230\pi$
$558$	−2.17818	−	0.102476i	−0.0922096	−	0.00433815i
$559$		−	3.68095i		−	0.155688i
$560$	12.4724	+	9.50149i	0.527054	+	0.401511i
$561$	24.1947	−	33.2288i	1.02150	−	1.40292i
$562$	−16.5738	−	20.1594i	−0.699124	−	0.850372i
$563$	−22.1769	−	5.94229i	−0.934645	−	0.250438i	−0.240811	−	0.970572i	$-0.577413\pi$
$563$	−22.1769	−	5.94229i	−0.934645	−	0.250438i	−0.693834	+	0.720135i	$0.744080\pi$
$564$	−22.5243	−	14.1895i	−0.948445	−	0.597485i
$565$	16.5610	−	4.43751i	0.696727	−	0.186687i
$566$	1.32063	−	1.84634i	0.0555104	−	0.0776074i
$567$	28.6263	−	20.6178i	1.20219	−	0.865866i
$568$	10.7487	+	19.9835i	0.451005	+	0.838491i
$569$	5.09524	−	8.82522i	0.213604	−	0.369972i	−0.739236	−	0.673446i	$-0.764813\pi$
$569$	5.09524	−	8.82522i	0.213604	−	0.369972i	0.952840	+	0.303474i	$0.0981466\pi$
$570$	−5.28911	−	4.70156i	−0.221537	−	0.196927i
$571$	24.1301	+	6.46563i	1.00981	+	0.270578i	0.725551	−	0.688169i	$-0.241585\pi$
$571$	24.1301	+	6.46563i	1.00981	+	0.270578i	0.284261	+	0.958747i	$0.408252\pi$
$572$	3.63999	+	3.18097i	0.152195	+	0.133003i
$573$	−9.21166	+	1.44922i	−0.384823	+	0.0605420i
$574$	−17.2164	+	45.8640i	−0.718598	+	1.91433i
$575$	1.31936			0.0550212
$576$	16.8012	+	17.1382i	0.700051	+	0.714093i
$577$	28.6171			1.19135			0.595673	−	0.803227i	$-0.296886\pi$
$577$	28.6171			1.19135			0.595673	+	0.803227i	$0.296886\pi$
$578$	−4.46957	+	11.9068i	−0.185910	+	0.495259i
$579$	−11.0259	+	28.6348i	−0.458220	+	1.19002i
$580$	−8.17794	−	7.14668i	−0.339571	−	0.296750i
$581$	−57.8575	−	15.5029i	−2.40033	−	0.643167i
$582$	2.32303	−	11.2826i	0.0962927	−	0.467679i
$583$	−24.8525	+	43.0458i	−1.02929	+	1.78277i
$584$	−16.3818	−	30.4564i	−0.677885	−	1.26030i
$585$	−1.04475	+	1.15550i	−0.0431953	+	0.0477741i
$586$	−10.8669	+	15.1926i	−0.448906	+	0.627602i
$587$	12.7224	−	3.40896i	0.525110	−	0.140703i	0.0134808	−	0.999909i	$-0.495709\pi$
$587$	12.7224	−	3.40896i	0.525110	−	0.140703i	0.511629	+	0.859206i	$0.329042\pi$
$588$	25.6346	−	13.5102i	1.05715	−	0.557152i
$589$	1.43428	+	0.384315i	0.0590986	+	0.0158354i
$590$	6.59279	+	8.01908i	0.271421	+	0.330140i
$591$	−12.3215	−	1.30792i	−0.506837	−	0.0538008i
$592$	5.81400	−	7.63190i	0.238954	−	0.313669i
$593$		−	7.58813i		−	0.311607i	−0.987788	−	0.155804i	$-0.950203\pi$
$593$		−	7.58813i		−	0.311607i	0.987788	−	0.155804i	$-0.0497967\pi$
$594$	−12.3957	−	31.8801i	−0.508601	−	1.30806i
$595$	14.1312	+	14.1312i	0.579322	+	0.579322i
$596$	14.8373	+	22.1220i	0.607759	+	0.906153i
$597$	−4.61016	−	5.70513i	−0.188681	−	0.233496i
$598$	−0.0941254	+	0.964287i	−0.00384908	+	0.0394326i
$599$	5.85860	−	3.38247i	0.239376	−	0.138204i	−0.375514	−	0.926817i	$-0.622534\pi$
$599$	5.85860	−	3.38247i	0.239376	−	0.138204i	0.614890	+	0.788613i	$0.289200\pi$
$600$	2.96298	+	3.90138i	0.120963	+	0.159273i
$601$	−26.2481	−	15.1544i	−1.07068	−	0.618159i	−0.142315	−	0.989821i	$-0.545455\pi$
$601$	−26.2481	−	15.1544i	−1.07068	−	0.618159i	−0.928368	+	0.371662i	$0.878788\pi$
$602$	−22.8615	+	31.9619i	−0.931764	+	1.30267i
$603$	28.0337	+	14.3570i	1.14162	+	0.584662i
$604$	−3.22166	+	1.09987i	−0.131087	+	0.0447532i
$605$	−10.3031	+	2.76071i	−0.418881	+	0.112239i
$606$	−26.3462	−	40.0083i	−1.07024	−	1.62523i
$607$	−7.31843	+	4.22530i	−0.297046	+	0.171500i	−0.641115	−	0.767445i	$-0.721528\pi$
$607$	−7.31843	+	4.22530i	−0.297046	+	0.171500i	0.344069	+	0.938944i	$0.388195\pi$
$608$	−8.69055	−	13.8407i	−0.352448	−	0.561314i
$609$	−33.6962	+	14.9608i	−1.36544	+	0.606241i
$610$	−7.93842	−	2.97991i	−0.321417	−	0.120653i
$611$	2.82168	−	2.82168i	0.114153	−	0.114153i
$612$	18.2948	+	24.5163i	0.739523	+	0.991014i
$613$	−8.48077	−	8.48077i	−0.342535	−	0.342535i	0.514784	−	0.857320i	$-0.327872\pi$
$613$	−8.48077	−	8.48077i	−0.342535	−	0.342535i	−0.857320	+	0.514784i	$0.827872\pi$
$614$	−37.9855	+	17.2509i	−1.53297	+	0.696192i
$615$	−9.00980	+	12.3740i	−0.363310	+	0.498967i
$616$	−11.8500	−	50.2276i	−0.477450	−	2.02373i
$617$	−21.3129	−	36.9150i	−0.858024	−	1.48614i	−0.873811	−	0.486265i	$-0.838359\pi$
$617$	−21.3129	−	36.9150i	−0.858024	−	1.48614i	0.0157878	−	0.999875i	$-0.494974\pi$
$618$	14.5124	+	12.9002i	0.583772	+	0.518923i
$619$	3.68731	+	13.7612i	0.148205	+	0.553110i	0.999592	+	0.0285710i	$0.00909566\pi$
$619$	3.68731	+	13.7612i	0.148205	+	0.553110i	−0.851386	+	0.524539i	$0.824238\pi$
$620$	−0.922721	−	0.453038i	−0.0370574	−	0.0181944i
$621$	3.75165	−	5.73798i	0.150549	−	0.230257i
$622$	−5.98479	−	36.0538i	−0.239968	−	1.44562i
$623$	−8.81506	+	15.2681i	−0.353168	+	0.611705i
$624$	−3.06280	+	1.88723i	−0.122610	+	0.0755497i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	26.5459	−	21.8244i	1.06099	−	0.872279i
$627$	3.61990	+	23.0091i	0.144565	+	0.918897i
$628$	22.3669	+	33.3485i	0.892537	+	1.33075i
$629$	8.64693	−	8.64693i	0.344776	−	0.344776i
$630$	16.2482	−	3.54459i	0.647344	−	0.141220i
$631$	−22.8364			−0.909102			−0.454551	−	0.890721i	$-0.650200\pi$
$631$	−22.8364			−0.909102			−0.454551	+	0.890721i	$0.650200\pi$
$632$	−0.326776	−	0.00984228i	−0.0129985	−	0.000391505i
$633$	−6.50494	+	2.88813i	−0.258548	+	0.114793i
$634$	1.79270	−	18.3657i	0.0711972	−	0.729394i
$635$	−2.37092	+	8.84838i	−0.0940870	+	0.351137i
$636$	−25.1287	−	27.1455i	−0.996419	−	1.07639i
$637$	1.12420	+	4.19557i	0.0445424	+	0.166234i
$638$	5.85371	+	35.2642i	0.231751	+	1.39612i
$639$	23.5310	+	5.05257i	0.930872	+	0.199876i
$640$	4.04978	+	10.5641i	0.160082	+	0.417581i
$641$	18.9548	+	10.9436i	0.748670	+	0.432245i	0.825213	−	0.564821i	$-0.191055\pi$
$641$	18.9548	+	10.9436i	0.748670	+	0.432245i	−0.0765429	+	0.997066i	$0.524388\pi$
$642$	−38.2606	−	19.1881i	−1.51002	−	0.757296i
$643$	11.7587	−	43.8839i	0.463716	−	1.73061i	−0.197394	−	0.980324i	$-0.563248\pi$
$643$	11.7587	−	43.8839i	0.463716	−	1.73061i	0.661111	−	0.750288i	$-0.270085\pi$
$644$	6.80624	−	7.78837i	0.268203	−	0.306905i
$645$	−9.54993	+	7.71704i	−0.376028	+	0.303858i
$646$	−8.61338	−	18.9662i	−0.338889	−	0.746213i
$647$			12.7139i			0.499833i	0.968267	+	0.249917i	$0.0804032\pi$
$647$			12.7139i			0.499833i	−0.968267	+	0.249917i	$0.919597\pi$
$648$	25.3927	−	1.79245i	0.997518	−	0.0704139i
$649$		−	34.1688i		−	1.34124i
$650$	−0.668626	+	0.303653i	−0.0262257	+	0.0119103i
$651$	−2.71412	+	2.19320i	−0.106375	+	0.0859584i
$652$	0.637852	+	9.47855i	0.0249802	+	0.371209i
$653$	0.640491	−	2.39034i	0.0250643	−	0.0935414i	−0.952261	−	0.305286i	$-0.901248\pi$
$653$	0.640491	−	2.39034i	0.0250643	−	0.0935414i	0.977325	+	0.211745i	$0.0679146\pi$
$654$	−7.33521	+	14.6262i	−0.286830	+	0.571929i
$655$	16.1116	+	9.30201i	0.629530	+	0.363460i
$656$	−27.9691	+	21.6168i	−1.09201	+	0.843994i
$657$	−35.8630	−	7.70049i	−1.39915	−	0.300425i
$658$	−42.0256	+	6.97608i	−1.63833	+	0.271956i
$659$	−0.181763	−	0.678350i	−0.00708050	−	0.0264248i	0.962295	−	0.272007i	$-0.0876875\pi$
$659$	−0.181763	−	0.678350i	−0.00708050	−	0.0264248i	−0.969376	+	0.245582i	$0.921021\pi$
$660$	0.621623	−	16.1125i	0.0241967	−	0.627178i
$661$	−7.02942	+	26.2341i	−0.273413	+	1.02039i	0.683485	+	0.729965i	$0.260463\pi$
$661$	−7.02942	+	26.2341i	−0.273413	+	1.02039i	−0.956898	+	0.290425i	$0.906203\pi$
$662$	−7.09989	−	0.693031i	−0.275945	−	0.0269354i
$663$	−4.19088	+	1.86071i	−0.162760	+	0.0722640i
$664$	−29.6280	−	31.4682i	−1.14979	−	1.22120i
$665$	−11.3245			−0.439145
$666$	−2.16895	−	9.94234i	−0.0840450	−	0.385258i
$667$	−5.06611	+	5.06611i	−0.196161	+	0.196161i
$668$	45.0542	+	8.88022i	1.74320	+	0.343586i
$669$	4.70609	+	29.9133i	0.181948	+	1.15652i
$670$	9.42912	+	11.4690i	0.364279	+	0.443087i
$671$	13.9543	+	24.1696i	0.538701	+	0.933058i
$672$	38.3156	+	2.63533i	1.47806	+	0.101660i
$673$	0.154811	−	0.268140i	0.00596751	−	0.0103360i	−0.863026	−	0.505159i	$-0.831434\pi$
$673$	0.154811	−	0.268140i	0.00596751	−	0.0103360i	0.868994	+	0.494823i	$0.164767\pi$
$674$	30.2638	−	5.02368i	1.16572	−	0.193505i
$675$	5.18816	+	0.288046i	0.199692	+	0.0110869i
$676$	8.22610	+	24.0952i	0.316388	+	0.926740i
$677$	2.76996	+	10.3376i	0.106458	+	0.397307i	0.998507	−	0.0546328i	$-0.0173988\pi$
$677$	2.76996	+	10.3376i	0.106458	+	0.397307i	−0.892048	+	0.451940i	$0.850732\pi$
$678$	27.9017	−	31.3886i	1.07156	−	1.20547i
$679$	−9.21688	−	15.9641i	−0.353712	−	0.612646i
$680$	3.31121	+	14.0350i	0.126979	+	0.538216i
$681$	−12.6958	+	17.4364i	−0.486506	+	0.668163i
$682$	1.39902	+	3.08056i	0.0535712	+	0.117961i
$683$	10.8579	+	10.8579i	0.415465	+	0.415465i	0.883637	−	0.468172i	$-0.155087\pi$
$683$	10.8579	+	10.8579i	0.415465	+	0.415465i	−0.468172	+	0.883637i	$0.655087\pi$
$684$	−17.1541	−	2.49292i	−0.655902	−	0.0953192i
$685$	−3.89821	+	3.89821i	−0.148943	+	0.148943i
$686$	2.65902	−	7.08358i	0.101522	−	0.270452i
$687$	24.7727	−	10.9988i	0.945136	−	0.419631i
$688$	−26.1589	+	10.9424i	−0.997297	+	0.417173i
$689$	4.80200	−	2.77244i	0.182942	−	0.105621i
$690$	2.69910	−	1.77741i	0.102753	−	0.0676647i
$691$	−23.4115	+	6.27310i	−0.890616	+	0.238640i	−0.674982	−	0.737834i	$-0.735849\pi$
$691$	−23.4115	+	6.27310i	−0.890616	+	0.238640i	−0.215634	+	0.976474i	$0.569182\pi$
$692$	−8.67513	−	4.25932i	−0.329779	−	0.161915i
$693$	−48.7195	−	24.9509i	−1.85070	−	0.947807i
$694$	7.98235	+	5.70954i	0.303006	+	0.216731i
$695$	−8.56198	−	4.94326i	−0.324775	−	0.187509i
$696$	−26.3579	−	3.60330i	−0.999094	−	0.136583i
$697$	−39.0191	+	22.5277i	−1.47795	+	0.853297i
$698$	−19.0607	−	1.86055i	−0.721460	−	0.0704227i
$699$	13.2173	+	16.3566i	0.499925	+	0.618663i
$700$	7.69163	+	1.51603i	0.290716	+	0.0573005i
$701$	7.18412	+	7.18412i	0.271341	+	0.271341i	0.829640	−	0.558299i	$-0.188546\pi$
$701$	7.18412	+	7.18412i	0.271341	+	0.271341i	−0.558299	+	0.829640i	$0.688546\pi$
$702$	−0.580657	+	3.77134i	−0.0219155	+	0.142340i
$703$			6.92950i			0.261351i
$704$	11.7852	−	35.3238i	0.444170	−	1.33132i
$705$	−13.2362	−	1.40503i	−0.498505	−	0.0529163i
$706$	34.6619	−	28.4969i	1.30452	−	1.07249i
$707$	−74.0465	−	19.8407i	−2.78480	−	0.746186i
$708$	24.2903	+	7.52348i	0.912887	+	0.282750i
$709$	41.6585	−	11.1624i	1.56452	−	0.419211i	0.630428	−	0.776248i	$-0.282879\pi$
$709$	41.6585	−	11.1624i	1.56452	−	0.419211i	0.934091	+	0.357036i	$0.116213\pi$
$710$	9.22786	+	6.60043i	0.346316	+	0.247710i
$711$	−0.232558	+	0.257209i	−0.00872159	+	0.00964610i
$712$	−11.2036	+	6.02615i	−0.419872	+	0.225839i
$713$	−0.339056	+	0.587262i	−0.0126977	+	0.0219931i
$714$	47.9461	+	9.87186i	1.79434	+	0.369445i
$715$	2.33467	+	0.625573i	0.0873117	+	0.0233951i
$716$	13.5040	−	0.908744i	0.504669	−	0.0339614i
$717$	11.6141	−	30.1625i	0.433736	−	1.12644i
$718$	15.6233	+	5.86466i	0.583057	+	0.218867i
$719$	−19.9591			−0.744349			−0.372175	−	0.928163i	$-0.621388\pi$
$719$	−19.9591			−0.744349			−0.372175	+	0.928163i	$0.621388\pi$
$720$	11.3174	+	3.98964i	0.421773	+	0.148685i
$721$	31.0723			1.15719
$722$	−14.1052	−	5.29479i	−0.524941	−	0.197052i
$723$	0.0574306	−	0.00903522i	0.00213587	−	0.000336024i
$724$	0.253848	+	3.77221i	0.00943419	+	0.140193i
$725$	−5.24529	−	1.40547i	−0.194805	−	0.0521979i
$726$	−17.3585	+	19.5278i	−0.644236	+	0.724745i
$727$	−22.5449	+	39.0490i	−0.836146	+	1.44825i	0.0569484	+	0.998377i	$0.481863\pi$
$727$	−22.5449	+	39.0490i	−0.836146	+	1.44825i	−0.893094	+	0.449870i	$0.851470\pi$
$728$	−1.65676	+	5.51346i	−0.0614036	+	0.204342i
$729$	16.0055	−	21.7445i	0.592795	−	0.805354i
$730$	−14.0640	−	10.0596i	−0.520531	−	0.372321i
$731$	−34.9097	+	9.35402i	−1.29118	+	0.345971i
$732$	−20.2545	+	4.59823i	−0.748629	+	0.169955i
$733$	42.8873	+	11.4916i	1.58408	+	0.424453i	0.940186	−	0.340662i	$-0.110651\pi$
$733$	42.8873	+	11.4916i	1.58408	+	0.424453i	0.643893	+	0.765115i	$0.277318\pi$
$734$	9.93691	−	8.16951i	0.366778	−	0.301542i
$735$	8.52820	−	11.7126i	0.314567	−	0.432024i
$736$	7.13255	−	2.19762i	0.262909	−	0.0810055i
$737$		−	48.8688i		−	1.80011i
$738$	−1.76199	+	37.4519i	−0.0648597	+	1.37862i
$739$	20.2147	+	20.2147i	0.743611	+	0.743611i	0.973271	−	0.229660i	$-0.0737614\pi$
$739$	20.2147	+	20.2147i	0.743611	+	0.743611i	−0.229660	+	0.973271i	$0.573761\pi$
$740$	0.927664	−	4.70654i	0.0341016	−	0.173016i
$741$	0.933681	−	2.42482i	0.0342996	−	0.0890781i
$742$	−58.9150	−	5.75077i	−2.16284	−	0.211118i
$743$	33.0816	−	19.0997i	1.21365	−	0.700698i	0.250094	−	0.968222i	$-0.419539\pi$
$743$	33.0816	−	19.0997i	1.21365	−	0.700698i	0.963551	+	0.267523i	$0.0862052\pi$
$744$	−2.49798	+	0.316258i	−0.0915806	+	0.0115946i
$745$	11.5341	+	6.65924i	0.422579	+	0.243976i
$746$	−24.1019	−	17.2394i	−0.882434	−	0.631180i
$747$	−45.7849	+	2.30452i	−1.67518	+	0.0843181i
$748$	20.9180	−	42.6047i	0.764839	−	1.55778i
$749$	−66.1611	+	17.7278i	−2.41747	+	0.647760i
$750$	2.18956	+	1.09809i	0.0799516	+	0.0400967i
$751$	−3.13014	+	1.80719i	−0.114220	+	0.0659452i	−0.556022	−	0.831168i	$-0.687673\pi$
$751$	−3.13014	+	1.80719i	−0.114220	+	0.0659452i	0.441801	+	0.897113i	$0.354340\pi$
$752$	−28.4404	−	11.6644i	−1.03712	−	0.425357i
$753$	−0.804013	+	7.57430i	−0.0292999	+	0.276023i
$754$	1.40143	−	3.73338i	0.0510371	−	0.135962i
$755$	−1.20358	+	1.20358i	−0.0438027	+	0.0438027i
$756$	28.4647	−	29.1405i	1.03525	−	1.05983i
$757$	−11.7439	−	11.7439i	−0.426841	−	0.426841i	0.460710	−	0.887551i	$-0.347595\pi$
$757$	−11.7439	−	11.7439i	−0.426841	−	0.426841i	−0.887551	+	0.460710i	$0.847595\pi$
$758$	−4.02467	−	8.86209i	−0.146183	−	0.321886i
$759$	−10.5776	−	1.12281i	−0.383942	−	0.0407555i
$760$	−6.95047	−	4.29692i	−0.252120	−	0.155866i
$761$	−0.247746	−	0.429108i	−0.00898077	−	0.0155552i	0.861500	−	0.507757i	$-0.169525\pi$
$761$	−0.247746	−	0.429108i	−0.00898077	−	0.0155552i	−0.870481	+	0.492202i	$0.836192\pi$
$762$	7.06997	+	21.2957i	0.256118	+	0.771461i
$763$	6.77695	+	25.2919i	0.245342	+	0.915630i
$764$	−10.1901	+	3.47888i	−0.368663	+	0.125861i
$765$	13.6136	+	6.97197i	0.492199	+	0.252072i
$766$	22.3357	−	3.70764i	0.807023	−	0.133963i
$767$	−1.90586	+	3.30105i	−0.0688167	+	0.119194i
$768$	22.5165	+	16.1558i	0.812493	+	0.582971i
$769$	20.7043	+	35.8610i	0.746617	+	1.29318i	0.949435	+	0.313963i	$0.101657\pi$
$769$	20.7043	+	35.8610i	0.746617	+	1.29318i	−0.202818	+	0.979216i	$0.565010\pi$
$770$	−16.3868	−	19.9319i	−0.590539	−	0.718297i
$771$	−49.2228	−	18.9533i	−1.77271	−	0.682586i
$772$	−6.85168	+	34.7623i	−0.246597	+	1.25112i
$773$	−0.291585	+	0.291585i	−0.0104876	+	0.0104876i	−0.712331	−	0.701844i	$-0.752361\pi$
$773$	−0.291585	+	0.291585i	−0.0104876	+	0.0104876i	0.701844	+	0.712331i	$0.252361\pi$
$774$	−9.14068	+	28.6526i	−0.328555	+	1.02990i
$775$	−0.513969			−0.0184623
$776$	0.400445	−	13.2953i	0.0143751	−	0.477273i
$777$	−13.1645	−	9.58539i	−0.472274	−	0.343874i
$778$	36.6547	+	3.57792i	1.31413	+	0.128274i
$779$	6.60797	−	24.6613i	0.236755	−	0.883583i
$780$	−0.958775	+	1.52196i	−0.0343296	+	0.0544947i
$781$	−9.66491	−	36.0699i	−0.345838	−	1.29068i
$782$	9.38437	−	1.55777i	0.335584	−	0.0557057i
$783$	−21.0277	+	18.8156i	−0.751467	+	0.672414i
$784$	26.4741	−	20.4613i	0.945503	−	0.730761i
$785$	17.3875	+	10.0387i	0.620586	+	0.358296i
$786$	45.4918	−	2.67536i	1.62264	−	0.0954269i
$787$	1.95277	−	7.28783i	0.0696087	−	0.259783i	−0.922348	−	0.386360i	$-0.873732\pi$
$787$	1.95277	−	7.28783i	0.0696087	−	0.259783i	0.991957	+	0.126577i	$0.0403990\pi$
$788$	−14.2752	+	0.960642i	−0.508534	+	0.0342215i
$789$	−5.78749	−	36.7870i	−0.206040	−	1.30965i
$790$	−0.148833	+	0.0675918i	−0.00529524	+	0.00240481i
$791$		−	67.2059i		−	2.38957i
$792$	−20.4346	−	33.7997i	−0.726112	−	1.20102i
$793$		−	3.11337i		−	0.110559i
$794$	−22.2168	−	48.9200i	−0.788444	−	1.73611i
$795$	−17.2602	−	6.64604i	−0.612155	−	0.235711i
$796$	−6.37760	−	5.57337i	−0.226048	−	0.197543i
$797$	−1.85472	+	6.92192i	−0.0656976	+	0.245187i	−0.990963	−	0.134133i	$-0.957175\pi$
$797$	−1.85472	+	6.92192i	−0.0656976	+	0.245187i	0.925266	+	0.379319i	$0.123842\pi$
$798$	−23.1672	+	15.2560i	−0.820109	+	0.540058i
$799$	−33.9309	−	19.5900i	−1.20039	−	0.693045i
$800$	4.14555	+	3.84895i	0.146567	+	0.136081i
$801$	−2.83267	+	13.1924i	−0.100087	+	0.466131i
$802$	0.117314	+	0.706729i	0.00414251	+	0.0249555i
$803$	14.7301	+	54.9733i	0.519812	+	1.93997i
$804$	34.7405	+	10.7602i	1.22520	+	0.379483i
$805$	1.33852	−	4.99542i	0.0471766	−	0.176066i
$806$	0.0366674	−	0.375647i	0.00129155	−	0.0132316i
$807$	1.93850	−	18.2619i	0.0682385	−	0.642849i
$808$	−37.9182	−	40.2732i	−1.33396	−	1.41681i
$809$	17.3929			0.611501			0.305751	−	0.952112i	$-0.401093\pi$
$809$	17.3929			0.611501			0.305751	+	0.952112i	$0.401093\pi$
$810$	11.0018	−	6.40007i	0.386563	−	0.224876i
$811$	−30.3341	+	30.3341i	−1.06518	+	1.06518i	−0.0674527	+	0.997722i	$0.521487\pi$
$811$	−30.3341	+	30.3341i	−1.06518	+	1.06518i	−0.997722	+	0.0674527i	$0.978513\pi$
$812$	−35.3558	+	23.7132i	−1.24074	+	0.832171i
$813$	38.5903	−	31.1838i	1.35342	−	1.09366i
$814$	−12.1964	+	10.0272i	−0.427485	+	0.351452i
$815$	2.37500	+	4.11362i	0.0831925	+	0.144094i
$816$	25.6814	+	24.2514i	0.899030	+	0.848968i
$817$	10.2399	−	17.7361i	0.358250	−	0.620508i
$818$	−0.196258	−	1.18231i	−0.00686201	−	0.0413384i
$819$	3.31509	+	5.12798i	0.115838	+	0.179186i
$820$	−7.78961	+	15.8654i	−0.272025	+	0.554044i
$821$	−14.1826	−	52.9300i	−0.494975	−	1.84727i	−0.530172	−	0.847890i	$-0.677872\pi$
$821$	−14.1826	−	52.9300i	−0.494975	−	1.84727i	0.0351968	−	0.999380i	$-0.488794\pi$
$822$	−2.72324	+	13.2264i	−0.0949839	+	0.461322i
$823$	−15.0963	−	26.1476i	−0.526226	−	0.911449i	−0.999533	−	0.0305522i	$-0.990273\pi$
$823$	−15.0963	−	26.1476i	−0.526226	−	0.911449i	0.473308	−	0.880897i	$-0.343060\pi$
$824$	19.0708	+	11.7900i	0.664363	+	0.410723i
$825$	−3.27159	−	7.36861i	−0.113902	−	0.256542i
$826$	37.0507	−	16.8264i	1.28916	−	0.585465i
$827$	−22.2545	−	22.2545i	−0.773864	−	0.773864i	0.204916	−	0.978780i	$-0.434308\pi$
$827$	−22.2545	−	22.2545i	−0.773864	−	0.773864i	−0.978780	+	0.204916i	$0.934308\pi$
$828$	3.12723	−	7.27229i	0.108679	−	0.252730i
$829$	14.3065	−	14.3065i	0.496884	−	0.496884i	−0.413582	−	0.910467i	$-0.635723\pi$
$829$	14.3065	−	14.3065i	0.496884	−	0.496884i	0.910467	+	0.413582i	$0.135723\pi$
$830$	−20.2321	−	7.59469i	−0.702265	−	0.263615i
$831$	−12.6223	−	9.19058i	−0.437862	−	0.318818i
$832$	−3.10885	+	2.75528i	−0.107780	+	0.0955222i
$833$	36.9334	−	21.3235i	1.27967	−	0.738816i
$834$	−24.1752	+	1.42174i	−0.837118	+	0.0492307i
$835$	22.1781	−	5.94261i	0.767506	−	0.205653i
$836$	8.68964	+	25.4530i	0.300538	+	0.880311i
$837$	−1.46149	+	2.23528i	−0.0505165	+	0.0772626i
$838$	−11.0583	+	15.4602i	−0.382002	+	0.534065i
$839$	−16.1964	−	9.35101i	−0.559163	−	0.322833i	0.193647	−	0.981071i	$-0.437968\pi$
$839$	−16.1964	−	9.35101i	−0.559163	−	0.322833i	−0.752809	+	0.658239i	$0.771302\pi$
$840$	17.7776	−	7.26052i	0.613385	−	0.250512i
$841$	0.423004	−	0.244222i	0.0145864	−	0.00842144i
$842$	2.81264	−	28.8147i	0.0969301	−	0.993019i
$843$	−31.5747	+	4.96747i	−1.08749	+	0.171089i
$844$	−6.82531	+	4.57775i	−0.234937	+	0.157573i
$845$	9.00173	+	9.00173i	0.309669	+	0.309669i
$846$	−28.9709	+	14.9571i	−0.996041	+	0.514236i
$847$			41.8109i			1.43664i
$848$	−33.9773	−	25.8840i	−1.16679	−	0.888861i
$849$	−1.12819	−	2.54102i	−0.0387192	−	0.0872074i
$850$	4.57892	+	5.56952i	0.157056	+	0.191033i
$851$	−3.05672	−	0.819046i	−0.104783	−	0.0280765i
$852$	27.7699	+	1.07137i	0.951381	+	0.0367045i
$853$	0.104738	−	0.0280645i	0.00358616	−	0.000960909i	−0.257026	−	0.966405i	$-0.582742\pi$
$853$	0.104738	−	0.0280645i	0.00358616	−	0.000960909i	0.260612	+	0.965444i	$0.416076\pi$
$854$	−19.3364	+	27.0336i	−0.661677	+	0.925070i
$855$	−8.24845	+	2.66123i	−0.282091	+	0.0910122i
$856$	−47.3333	−	14.2233i	−1.61782	−	0.486144i
$857$	−16.5009	+	28.5803i	−0.563659	+	0.976285i	0.433514	+	0.901147i	$0.357273\pi$
$857$	−16.5009	+	28.5803i	−0.563659	+	0.976285i	−0.997173	+	0.0751387i	$0.976060\pi$
$858$	5.61893	−	1.86543i	0.191827	−	0.0636847i
$859$	23.2337	+	6.22545i	0.792723	+	0.212410i	0.632387	−	0.774653i	$-0.282075\pi$
$859$	23.2337	+	6.22545i	0.792723	+	0.212410i	0.160337	+	0.987062i	$0.448742\pi$
$860$	−9.32937	+	10.6756i	−0.318129	+	0.364034i
$861$	37.7103	+	46.6670i	1.28516	+	1.59041i
$862$	16.7448	−	44.6076i	0.570329	−	1.51934i
$863$	46.3450			1.57760			0.788801	−	0.614649i	$-0.210702\pi$
$863$	46.3450			1.57760			0.788801	+	0.614649i	$0.210702\pi$
$864$	28.5273	−	7.08459i	0.970520	−	0.241023i
$865$	−4.83217			−0.164299
$866$	−18.0231	+	48.0132i	−0.612451	+	1.63156i
$867$	9.79003	+	12.1153i	0.332487	+	0.411457i
$868$	−2.65143	+	3.03403i	−0.0899954	+	0.102982i
$869$	0.519687	+	0.139250i	0.0176292	+	0.00472372i
$870$	−12.6240	+	4.19105i	−0.427994	+	0.142090i
$871$	−2.72580	+	4.72122i	−0.0923601	+	0.159972i
$872$	−5.43728	+	18.0945i	−0.184129	+	0.612757i
$873$	−10.4649	−	9.46188i	−0.354182	−	0.320236i
$874$	−3.13605	+	4.38442i	−0.106079	+	0.148305i
$875$	3.78624	−	1.01452i	0.127998	−	0.0342971i
$876$	−42.3234	−	1.63285i	−1.42998	−	0.0551688i
$877$	8.25301	+	2.21139i	0.278684	+	0.0746732i	0.395454	−	0.918486i	$-0.370587\pi$
$877$	8.25301	+	2.21139i	0.278684	+	0.0746732i	−0.116770	+	0.993159i	$0.537254\pi$
$878$	8.08788	+	9.83761i	0.272953	+	0.332003i
$879$	9.28330	+	20.9088i	0.313118	+	0.705237i
$880$	−2.49460	−	18.4511i	−0.0840930	−	0.621986i
$881$			18.8450i			0.634903i	0.948275	+	0.317451i	$0.102827\pi$
$881$			18.8450i			0.634903i	−0.948275	+	0.317451i	$0.897173\pi$
$882$	1.66780	−	35.4500i	0.0561579	−	1.19366i
$883$	14.2957	+	14.2957i	0.481087	+	0.481087i	0.905479	−	0.424392i	$-0.139512\pi$
$883$	14.2957	+	14.2957i	0.481087	+	0.481087i	−0.424392	+	0.905479i	$0.639512\pi$
$884$	−4.39729	+	2.94927i	−0.147897	+	0.0991948i
$885$	12.5599	−	1.97598i	0.422197	−	0.0664218i
$886$	−1.97994	+	20.2839i	−0.0665173	+	0.681450i
$887$	−12.9929	+	7.50144i	−0.436258	+	0.251874i	−0.702009	−	0.712168i	$-0.747713\pi$
$887$	−12.9929	+	7.50144i	−0.436258	+	0.251874i	0.265751	+	0.964042i	$0.414380\pi$
$888$	−4.44275	−	10.8782i	−0.149089	−	0.365048i
$889$	31.0968	+	17.9537i	1.04295	+	0.602149i
$890$	−3.70046	+	5.17351i	−0.124040	+	0.173416i
$891$	−41.3494	−	6.72458i	−1.38526	−	0.225282i
$892$	11.2971	+	33.0905i	0.378254	+	1.10795i
$893$	21.4454	−	5.74628i	0.717643	−	0.192292i
$894$	32.5672	−	1.91527i	1.08921	−	0.0640563i
$895$	5.86064	−	3.38364i	0.195900	−	0.113103i
$896$	44.1067	−	4.61600i	1.47350	−	0.154210i
$897$	0.959273	+	0.698469i	0.0320292	+	0.0233212i
$898$	24.0731	+	9.03653i	0.803330	+	0.301553i
$899$	1.97355	−	1.97355i	0.0658216	−	0.0658216i
$900$	5.95864	−	0.703285i	0.198621	−	0.0234428i
$901$	−38.4963	−	38.4963i	−1.28250	−	1.28250i
$902$	52.9676	−	24.0550i	1.76363	−	0.800942i
$903$	19.5300	+	43.9875i	0.649917	+	1.46381i
$904$	25.5003	−	41.2480i	0.848129	−	1.37189i
$905$	0.945184	+	1.63711i	0.0314190	+	0.0544193i
$906$	−0.840804	+	4.08366i	−0.0279338	+	0.135670i
$907$	−5.18393	−	19.3467i	−0.172130	−	0.642397i	−0.997023	−	0.0771079i	$-0.975431\pi$
$907$	−5.18393	−	19.3467i	−0.172130	−	0.642397i	0.824893	−	0.565289i	$-0.191235\pi$
$908$	−10.9764	+	22.3562i	−0.364266	+	0.741916i
$909$	−58.5960	+	2.94935i	−1.94351	+	0.0978238i
$910$	0.471370	+	2.83964i	0.0156258	+	0.0941333i
$911$	−17.8354	+	30.8918i	−0.590913	+	1.02349i	0.403197	+	0.915113i	$0.367899\pi$
$911$	−17.8354	+	30.8918i	−0.590913	+	1.02349i	−0.994110	+	0.108378i	$0.965434\pi$
$912$	−20.0077	+	0.573014i	−0.662520	+	0.0189744i
$913$	35.5644	+	61.5994i	1.17701	+	2.03864i
$914$	2.01748	−	1.65865i	0.0667324	−	0.0548633i
$915$	−8.07739	+	6.52712i	−0.267030	+	0.215780i
$916$	25.9927	−	17.4334i	0.858824	−	0.576016i
$917$	51.5652	−	51.5652i	1.70283	−	1.70283i
$918$	37.2425	−	4.07684i	1.22919	−	0.134556i
$919$	38.0356			1.25468			0.627339	−	0.778746i	$-0.284144\pi$
$919$	38.0356			1.25468			0.627339	+	0.778746i	$0.284144\pi$
$920$	2.71697	−	2.55809i	0.0895758	−	0.0843376i
$921$	−5.39349	+	50.8100i	−0.177721	+	1.67425i
$922$	0.0253165	−	0.259360i	0.000833753	−	0.00854155i
$923$	−1.07818	+	4.02381i	−0.0354886	+	0.132445i
$924$	−60.3752	−	18.7001i	−1.98620	−	0.615187i
$925$	−0.620790	−	2.31682i	−0.0204114	−	0.0761765i
$926$	0.193131	+	1.16347i	0.00634669	+	0.0382340i
$927$	22.6322	−	7.30193i	0.743340	−	0.239827i
$928$	−30.6974	+	1.13887i	−1.00769	+	0.0373852i
$929$	−9.73250	−	5.61906i	−0.319313	−	0.184355i	0.331773	−	0.943359i	$-0.392353\pi$
$929$	−9.73250	−	5.61906i	−0.319313	−	0.184355i	−0.651086	+	0.759004i	$0.725686\pi$
$930$	−1.05146	+	0.692405i	−0.0344786	+	0.0227048i
$931$	−6.25476	+	23.3431i	−0.204991	+	0.765038i
$932$	18.2845	+	15.9788i	0.598930	+	0.523403i
$933$	−41.7713	−	16.0841i	−1.36753	−	0.526569i
$934$	−22.4494	−	49.4322i	−0.734567	−	1.61747i
$935$		−	23.7314i		−	0.776100i
$936$	0.0889133	+	4.40519i	0.00290622	+	0.143988i
$937$			31.0009i			1.01276i	0.862312	+	0.506378i	$0.169016\pi$
$937$			31.0009i			1.01276i	−0.862312	+	0.506378i	$0.830984\pi$
$938$	52.9906	−	24.0654i	1.73020	−	0.785763i
$939$	−6.54117	−	41.5776i	−0.213463	−	1.35683i
$940$	−15.3351	+	1.03196i	−0.500174	+	0.0336589i
$941$	11.8209	−	44.1161i	0.385349	−	1.43814i	−0.452267	−	0.891883i	$-0.649384\pi$
$941$	11.8209	−	44.1161i	0.385349	−	1.43814i	0.837616	−	0.546260i	$-0.183949\pi$
$942$	49.0944	−	2.88723i	1.59958	−	0.0940711i
$943$	10.0975	+	5.82978i	0.328819	+	0.189844i
$944$	29.1246	+	3.73108i	0.947926	+	0.121436i
$945$	6.35411	−	19.3514i	0.206699	−	0.629502i
$946$	46.0343	−	7.64151i	1.49670	−	0.248447i
$947$	11.5474	+	43.0954i	0.375239	+	1.40041i	0.852995	+	0.521920i	$0.174784\pi$
$947$	11.5474	+	43.0954i	0.375239	+	1.40041i	−0.477755	+	0.878493i	$0.658549\pi$
$948$	−0.213419	+	0.338780i	−0.00693152	+	0.0110031i
$949$	1.64322	−	6.13258i	0.0533412	−	0.199072i
$950$	−4.06640	−	0.396927i	−0.131931	−	0.0128780i
$951$	−18.2702	−	13.3029i	−0.592451	−	0.431378i
$952$	56.4991	+	1.70171i	1.83115	+	0.0551529i
$953$	3.36275			0.108930			0.0544650	−	0.998516i	$-0.482655\pi$
$953$	3.36275			0.108930			0.0544650	+	0.998516i	$0.482655\pi$
$954$	−44.2635	+	9.65619i	−1.43308	+	0.312631i
$955$	−3.80690	+	3.80690i	−0.123188	+	0.123188i
$956$	7.21721	−	36.6168i	0.233421	−	1.18427i
$957$	40.8565	+	15.7318i	1.32070	+	0.508538i
$958$	0.442403	+	0.538113i	0.0142934	+	0.0173856i
$959$	10.8048	+	18.7144i	0.348904	+	0.604319i
$960$	13.6660	+	2.28927i	0.441068	+	0.0738857i
$961$	−15.3679	+	26.6180i	−0.495739	+	0.858646i
$962$	1.73759	−	0.288433i	0.0560222	−	0.00929946i
$963$	−44.0239	+	28.4602i	−1.41865	+	0.917116i
$964$	0.0635304	−	0.0216893i	0.00204618	−	0.000698564i
$965$	4.58512	+	17.1119i	0.147600	+	0.550852i
$966$	−3.99140	−	12.0226i	−0.128421	−	0.386822i
$967$	1.61183	+	2.79178i	0.0518331	+	0.0897775i	0.890778	−	0.454439i	$-0.150160\pi$
$967$	1.61183	+	2.79178i	0.0518331	+	0.0897775i	−0.838945	+	0.544217i	$0.816827\pi$
$968$	−15.8646	+	25.6617i	−0.509906	+	0.824798i
$969$	−25.3694	−	2.69296i	−0.814982	−	0.0865104i
$970$	−2.75005	−	6.05545i	−0.0882988	−	0.194429i
$971$	1.17144	+	1.17144i	0.0375932	+	0.0375932i	0.725653	−	0.688060i	$-0.241538\pi$
$971$	1.17144	+	1.17144i	0.0375932	+	0.0375932i	−0.688060	+	0.725653i	$0.741538\pi$
$972$	13.8850	−	27.9143i	0.445361	−	0.895351i
$973$	−27.4027	+	27.4027i	−0.878491	+	0.878491i
$974$	−12.9250	+	34.4319i	−0.414144	+	1.10327i
$975$	−0.0949368	+	0.894364i	−0.00304041	+	0.0286426i
$976$	−22.1253	+	9.25511i	−0.708214	+	0.296249i
$977$	0.0949382	−	0.0548126i	0.00303734	−	0.00175361i	−0.498481	−	0.866901i	$-0.666108\pi$
$977$	0.0949382	−	0.0548126i	0.00303734	−	0.00175361i	0.501518	+	0.865147i	$0.332775\pi$
$978$	10.4004	+	5.21594i	0.332569	+	0.166787i
$979$	20.2222	−	5.41853i	0.646306	−	0.173177i
$980$	7.37323	−	15.0174i	0.235529	−	0.479712i
$981$	10.8797	+	16.8294i	0.347362	+	0.537321i
$982$	−16.0472	−	11.4781i	−0.512088	−	0.366282i
$983$	−0.0725698	−	0.0418982i	−0.00231462	−	0.00133634i	0.498842	−	0.866693i	$-0.333759\pi$
$983$	−0.0725698	−	0.0418982i	−0.00231462	−	0.00133634i	−0.501157	+	0.865356i	$0.667092\pi$
$984$	5.43778	+	42.9508i	0.173350	+	1.36922i
$985$	−6.19534	+	3.57688i	−0.197400	+	0.113969i
$986$	−38.9682	−	3.80374i	−1.24100	−	0.121136i
$987$	−18.7482	+	48.6901i	−0.596762	+	1.54982i
$988$	0.580207	−	2.94371i	0.0184588	−	0.0936517i
$989$	6.61337	+	6.61337i	0.210293	+	0.210293i
$990$	−16.6197	−	10.6670i	−0.528208	−	0.339020i
$991$		−	30.9246i		−	0.982352i	−0.871060	−	0.491176i	$-0.836567\pi$
$991$		−	30.9246i		−	0.982352i	0.871060	−	0.491176i	$-0.163433\pi$
$992$	−2.77855	+	0.856105i	−0.0882191	+	0.0271813i
$993$	−5.14272	+	7.06297i	−0.163199	+	0.224137i
$994$	34.3527	−	28.2427i	1.08960	−	0.895803i
$995$	−4.09056	−	1.09606i	−0.129680	−	0.0347475i
$996$	−51.6213	+	11.7192i	−1.63568	+	0.371336i
$997$	1.98322	−	0.531401i	0.0628091	−	0.0168296i	−0.227278	−	0.973830i	$-0.572983\pi$
$997$	1.98322	−	0.531401i	0.0628091	−	0.0168296i	0.290087	+	0.957000i	$0.406316\pi$
$998$	−28.4877	−	20.3764i	−0.901762	−	0.645004i
$999$	−11.8412	−	3.88811i	−0.374640	−	0.123014i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cf.a.11.60	✓	384
9.5	odd	6	inner	720.2.cf.a.491.28	yes	384
16.3	odd	4	inner	720.2.cf.a.371.28	yes	384
144.131	even	12	inner	720.2.cf.a.131.60	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.cf.a.11.60	✓	384	1.1	even	1	trivial
720.2.cf.a.131.60	yes	384	144.131	even	12	inner
720.2.cf.a.371.28	yes	384	16.3	odd	4	inner
720.2.cf.a.491.28	yes	384	9.5	odd	6	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.497003 - 1.32400i) q^{2} +(-1.08862 - 1.34718i) q^{3} +(-1.50598 - 1.31607i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(-2.32472 + 0.771787i) q^{6} +(-1.95990 + 3.39465i) q^{7} +(-2.49096 + 1.33983i) q^{8} +(-0.629804 + 2.93315i) q^{9} +O(q^{10})\)	\(q+(0.497003 - 1.32400i) q^{2} +(-1.08862 - 1.34718i) q^{3} +(-1.50598 - 1.31607i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(-2.32472 + 0.771787i) q^{6} +(-1.95990 + 3.39465i) q^{7} +(-2.49096 + 1.33983i) q^{8} +(-0.629804 + 2.93315i) q^{9} +(-0.822746 + 1.15026i) q^{10} +(4.49613 - 1.20473i) q^{11} +(-0.133546 + 3.46153i) q^{12} +(-0.501569 - 0.134395i) q^{13} +(3.52046 + 4.28207i) q^{14} +(0.702852 + 1.58303i) q^{15} +(0.535927 + 3.96394i) q^{16} +5.09834i q^{17} +(3.57048 + 2.29165i) q^{18} +(-2.04286 - 2.04286i) q^{19} +(1.11404 + 1.66100i) q^{20} +(6.70681 - 1.05515i) q^{21} +(0.639516 - 6.55165i) q^{22} +(1.14260 - 0.659681i) q^{23} +(4.51670 + 1.89721i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-0.427221 + 0.597284i) q^{26} +(4.63710 - 2.34463i) q^{27} +(7.41916 - 2.53290i) q^{28} +(-5.24529 + 1.40547i) q^{29} +(2.44526 - 0.143805i) q^{30} +(-0.445110 + 0.256985i) q^{31} +(5.51463 + 1.26052i) q^{32} +(-6.51758 - 4.74561i) q^{33} +(6.75022 + 2.53389i) q^{34} +(2.77172 - 2.77172i) q^{35} +(4.80869 - 3.58838i) q^{36} +(-1.69603 - 1.69603i) q^{37} +(-3.72007 + 1.68945i) q^{38} +(0.364964 + 0.822010i) q^{39} +(2.75285 - 0.649469i) q^{40} +(4.41864 + 7.65330i) q^{41} +(1.93629 - 9.40426i) q^{42} +(1.83472 + 6.84727i) q^{43} +(-8.35658 - 4.10291i) q^{44} +(1.36750 - 2.67020i) q^{45} +(-0.305544 - 1.84067i) q^{46} +(-3.84243 + 6.65529i) q^{47} +(4.75672 - 5.03722i) q^{48} +(-4.18245 - 7.24421i) q^{49} +(1.09242 - 0.898120i) q^{50} +(6.86839 - 5.55016i) q^{51} +(0.578477 + 0.862494i) q^{52} +(-7.55075 + 7.55075i) q^{53} +(-0.799642 - 7.30483i) q^{54} -4.65474 q^{55} +(0.333778 - 11.0819i) q^{56} +(-0.528204 + 4.97601i) q^{57} +(-0.746075 + 7.64331i) q^{58} +(1.89990 - 7.09053i) q^{59} +(1.02490 - 3.30901i) q^{60} +(1.55182 + 5.79146i) q^{61} +(0.119028 + 0.717050i) q^{62} +(-8.72266 - 7.88665i) q^{63} +(4.40972 - 6.67491i) q^{64} +(0.449694 + 0.259631i) q^{65} +(-9.52247 + 6.27073i) q^{66} +(2.71727 - 10.1410i) q^{67} +(6.70976 - 7.67797i) q^{68} +(-2.13257 - 0.821149i) q^{69} +(-2.29222 - 5.04733i) q^{70} -8.02244i q^{71} +(-2.36110 - 8.15017i) q^{72} +12.2268i q^{73} +(-3.08848 + 1.40262i) q^{74} +(-0.269183 - 1.71101i) q^{75} +(0.387955 + 5.76505i) q^{76} +(-4.72233 + 17.6240i) q^{77} +(1.26973 - 0.0746727i) q^{78} +(0.100100 + 0.0577927i) q^{79} +(0.508276 - 3.96758i) q^{80} +(-8.20669 - 3.69461i) q^{81} +(12.3291 - 2.04658i) q^{82} +(3.95500 + 14.7603i) q^{83} +(-11.4889 - 7.23760i) q^{84} +(1.31955 - 4.92462i) q^{85} +(9.97768 + 0.973936i) q^{86} +(7.60357 + 5.53634i) q^{87} +(-9.58552 + 9.02499i) q^{88} +4.49770 q^{89} +(-2.85570 - 3.13767i) q^{90} +(1.43925 - 1.43925i) q^{91} +(-2.58891 - 0.510277i) q^{92} +(0.830762 + 0.319886i) q^{93} +(6.90194 + 8.39510i) q^{94} +(1.44452 + 2.50198i) q^{95} +(-4.30520 - 8.80144i) q^{96} +(-2.35136 + 4.07268i) q^{97} +(-11.6701 + 1.93718i) q^{98} +(0.701981 + 13.9466i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 12 q^{6}+O(q^{10}) \) 384 * q - 12 * q^6	\( 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) \) 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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