LMFDB - Embedded newform 120.2.w.c.53.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,2,Mod(53,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("120.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	120.w (of order $4$, degree $2$, 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:	$0.958204824255$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.14
Character	$\chi$	$=$	120.53
Dual form			120.2.w.c.77.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30986 - 0.533177i) q^{2} +(-0.667305 + 1.59834i) q^{3} +(1.43144 - 1.39677i) q^{4} +(0.143028 + 2.23149i) q^{5} +(-0.0218716 + 2.44939i) q^{6} +(0.582772 - 0.582772i) q^{7} +(1.13026 - 2.59278i) q^{8} +(-2.10941 - 2.13317i) q^{9} +O(q^{10})$	\(q+(1.30986 - 0.533177i) q^{2} +(-0.667305 + 1.59834i) q^{3} +(1.43144 - 1.39677i) q^{4} +(0.143028 + 2.23149i) q^{5} +(-0.0218716 + 2.44939i) q^{6} +(0.582772 - 0.582772i) q^{7} +(1.13026 - 2.59278i) q^{8} +(-2.10941 - 2.13317i) q^{9} +(1.37713 + 2.84667i) q^{10} -3.68607 q^{11} +(1.27731 + 3.22001i) q^{12} +(3.88771 - 3.88771i) q^{13} +(0.452626 - 1.07407i) q^{14} +(-3.66213 - 1.26047i) q^{15} +(0.0980619 - 3.99880i) q^{16} +(0.880105 + 0.880105i) q^{17} +(-3.90038 - 1.66945i) q^{18} -6.32919 q^{19} +(3.32162 + 2.99447i) q^{20} +(0.542584 + 1.32036i) q^{21} +(-4.82821 + 1.96533i) q^{22} +(-2.06626 + 2.06626i) q^{23} +(3.38993 + 3.53672i) q^{24} +(-4.95909 + 0.638332i) q^{25} +(3.01950 - 7.16518i) q^{26} +(4.81715 - 1.94809i) q^{27} +(0.0202063 - 1.64820i) q^{28} +1.37122i q^{29} +(-5.46892 + 0.301526i) q^{30} +3.32075 q^{31} +(-2.00362 - 5.29013i) q^{32} +(2.45973 - 5.89160i) q^{33} +(1.62206 + 0.683558i) q^{34} +(1.38380 + 1.21710i) q^{35} +(-5.99904 - 0.107144i) q^{36} +(2.44147 + 2.44147i) q^{37} +(-8.29032 + 3.37458i) q^{38} +(3.61961 + 8.80819i) q^{39} +(5.94742 + 2.15132i) q^{40} -0.648104i q^{41} +(1.41469 + 1.44018i) q^{42} +(0.819412 - 0.819412i) q^{43} +(-5.27640 + 5.14859i) q^{44} +(4.45843 - 5.01223i) q^{45} +(-1.60482 + 3.80818i) q^{46} +(6.28508 + 6.28508i) q^{47} +(6.32602 + 2.82515i) q^{48} +6.32075i q^{49} +(-6.15534 + 3.48020i) q^{50} +(-1.99401 + 0.819412i) q^{51} +(0.134798 - 10.9953i) q^{52} +(-5.60782 - 5.60782i) q^{53} +(5.27109 - 5.12011i) q^{54} +(-0.527212 - 8.22542i) q^{55} +(-0.852318 - 2.16968i) q^{56} +(4.22349 - 10.1162i) q^{57} +(0.731106 + 1.79611i) q^{58} -6.12026i q^{59} +(-7.00273 + 3.31086i) q^{60} +5.13471i q^{61} +(4.34971 - 1.77055i) q^{62} +(-2.47245 - 0.0138443i) q^{63} +(-5.44503 - 5.86102i) q^{64} +(9.23144 + 8.11933i) q^{65} +(0.0806201 - 9.02862i) q^{66} +(4.90636 + 4.90636i) q^{67} +(2.48912 + 0.0305156i) q^{68} +(-1.92377 - 4.68141i) q^{69} +(2.46151 + 0.856408i) q^{70} -4.13251i q^{71} +(-7.91501 + 3.05821i) q^{72} +(4.69820 + 4.69820i) q^{73} +(4.49972 + 1.89624i) q^{74} +(2.28895 - 8.35229i) q^{75} +(-9.05987 + 8.84042i) q^{76} +(-2.14814 + 2.14814i) q^{77} +(9.43750 + 9.60756i) q^{78} -1.10079i q^{79} +(8.93730 - 0.353117i) q^{80} +(-0.100786 + 8.99944i) q^{81} +(-0.345554 - 0.848922i) q^{82} +(6.27439 + 6.27439i) q^{83} +(2.62091 + 1.13215i) q^{84} +(-1.83806 + 2.08982i) q^{85} +(0.636420 - 1.51020i) q^{86} +(-2.19169 - 0.915024i) q^{87} +(-4.16621 + 9.55717i) q^{88} -15.3562 q^{89} +(3.16749 - 8.94243i) q^{90} -4.53130i q^{91} +(-0.0716428 + 5.84382i) q^{92} +(-2.21595 + 5.30771i) q^{93} +(11.5836 + 4.88148i) q^{94} +(-0.905253 - 14.1235i) q^{95} +(9.79248 + 0.327652i) q^{96} +(-5.42154 + 5.42154i) q^{97} +(3.37008 + 8.27927i) q^{98} +(7.77542 + 7.86299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{6}+O(q^{10}) $ 32 * q - 4 * q^6	$ 32 q - 4 q^{6} + 4 q^{10} - 8 q^{12} - 28 q^{15} + 28 q^{16} - 20 q^{18} - 52 q^{22} - 8 q^{25} + 12 q^{28} - 32 q^{30} - 32 q^{31} + 8 q^{33} - 20 q^{36} + 24 q^{40} + 16 q^{42} + 24 q^{46} + 44 q^{48} + 8 q^{52} + 8 q^{55} - 16 q^{57} + 28 q^{58} + 56 q^{60} + 48 q^{63} + 16 q^{66} + 20 q^{70} + 32 q^{72} - 64 q^{73} - 88 q^{76} + 64 q^{78} + 48 q^{81} + 64 q^{82} - 8 q^{87} - 52 q^{88} + 84 q^{90} - 52 q^{96} + 16 q^{97}+O(q^{100}) $ 32 * q - 4 * q^6 + 4 * q^10 - 8 * q^12 - 28 * q^15 + 28 * q^16 - 20 * q^18 - 52 * q^22 - 8 * q^25 + 12 * q^28 - 32 * q^30 - 32 * q^31 + 8 * q^33 - 20 * q^36 + 24 * q^40 + 16 * q^42 + 24 * q^46 + 44 * q^48 + 8 * q^52 + 8 * q^55 - 16 * q^57 + 28 * q^58 + 56 * q^60 + 48 * q^63 + 16 * q^66 + 20 * q^70 + 32 * q^72 - 64 * q^73 - 88 * q^76 + 64 * q^78 + 48 * q^81 + 64 * q^82 - 8 * q^87 - 52 * q^88 + 84 * q^90 - 52 * q^96 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.30986	−	0.533177i	0.926208	−	0.377013i
$2$	1.30986	−	0.533177i	0.926208	−	0.377013i
$3$	−0.667305	+	1.59834i	−0.385268	+	0.922805i
$3$	−0.667305	+	1.59834i	−0.385268	+	0.922805i
$4$	1.43144	−	1.39677i	0.715722	−	0.698385i
$5$	0.143028	+	2.23149i	0.0639642	+	0.997952i
$5$	0.143028	+	2.23149i	0.0639642	+	0.997952i
$6$	−0.0218716	+	2.44939i	−0.00892904	+	0.999960i
$7$	0.582772	−	0.582772i	0.220267	−	0.220267i	−0.588344	−	0.808611i	$-0.700220\pi$
$7$	0.582772	−	0.582772i	0.220267	−	0.220267i	0.808611	+	0.588344i	$0.200220\pi$
$8$	1.13026	−	2.59278i	0.399606	−	0.916687i
$9$	−2.10941	−	2.13317i	−0.703136	−	0.711055i
$10$	1.37713	+	2.84667i	0.435485	+	0.900196i
$11$	−3.68607			−1.11139			−0.555695	−	0.831386i	$-0.687548\pi$
$11$	−3.68607			−1.11139			−0.555695	+	0.831386i	$0.687548\pi$
$12$	1.27731	+	3.22001i	0.368728	+	0.929537i
$13$	3.88771	−	3.88771i	1.07826	−	1.07826i	0.0815911	−	0.996666i	$-0.474000\pi$
$13$	3.88771	−	3.88771i	1.07826	−	1.07826i	0.996666	−	0.0815911i	$-0.0260002\pi$
$14$	0.452626	−	1.07407i	0.120969	−	0.287057i
$15$	−3.66213	−	1.26047i	−0.945558	−	0.325453i
$16$	0.0980619	−	3.99880i	0.0245155	−	0.999699i
$17$	0.880105	+	0.880105i	0.213457	+	0.213457i	0.805734	−	0.592277i	$-0.201771\pi$
$17$	0.880105	+	0.880105i	0.213457	+	0.213457i	−0.592277	+	0.805734i	$0.701771\pi$
$18$	−3.90038	−	1.66945i	−0.919328	−	0.393493i
$19$	−6.32919			−1.45201			−0.726007	−	0.687687i	$-0.758626\pi$
$19$	−6.32919			−1.45201			−0.726007	+	0.687687i	$0.758626\pi$
$20$	3.32162	+	2.99447i	0.742736	+	0.669585i
$21$	0.542584	+	1.32036i	0.118402	+	0.288125i
$22$	−4.82821	+	1.96533i	−1.02938	+	0.419009i
$23$	−2.06626	+	2.06626i	−0.430844	+	0.430844i	−0.888916	−	0.458071i	$-0.848540\pi$
$23$	−2.06626	+	2.06626i	−0.430844	+	0.430844i	0.458071	+	0.888916i	$0.348540\pi$
$24$	3.38993	+	3.53672i	0.691967	+	0.721929i
$25$	−4.95909	+	0.638332i	−0.991817	+	0.127666i
$26$	3.01950	−	7.16518i	0.592173	−	1.40521i
$27$	4.81715	−	1.94809i	0.927061	−	0.374910i
$28$	0.0202063	−	1.64820i	0.00381863	−	0.311481i
$29$			1.37122i			0.254630i	0.991862	+	0.127315i	$0.0406359\pi$
$29$			1.37122i			0.254630i	−0.991862	+	0.127315i	$0.959364\pi$
$30$	−5.46892	+	0.301526i	−0.998484	+	0.0550509i
$31$	3.32075			0.596425			0.298212	−	0.954500i	$-0.403610\pi$
$31$	3.32075			0.596425			0.298212	+	0.954500i	$0.403610\pi$
$32$	−2.00362	−	5.29013i	−0.354194	−	0.935172i
$33$	2.45973	−	5.89160i	0.428184	−	1.02560i
$34$	1.62206	+	0.683558i	0.278181	+	0.117229i
$35$	1.38380	+	1.21710i	0.233905	+	0.205727i
$36$	−5.99904	−	0.107144i	−0.999841	−	0.0178574i
$37$	2.44147	+	2.44147i	0.401376	+	0.401376i	0.878718	−	0.477342i	$-0.158400\pi$
$37$	2.44147	+	2.44147i	0.401376	+	0.401376i	−0.477342	+	0.878718i	$0.658400\pi$
$38$	−8.29032	+	3.37458i	−1.34487	+	0.547429i
$39$	3.61961	+	8.80819i	0.579602	+	1.41044i
$40$	5.94742	+	2.15132i	0.940370	+	0.340153i
$41$		−	0.648104i		−	0.101217i	−0.998719	−	0.0506084i	$-0.983884\pi$
$41$		−	0.648104i		−	0.101217i	0.998719	−	0.0506084i	$-0.0161160\pi$
$42$	1.41469	+	1.44018i	0.218292	+	0.222225i
$43$	0.819412	−	0.819412i	0.124959	−	0.124959i	−0.641861	−	0.766821i	$-0.721838\pi$
$43$	0.819412	−	0.819412i	0.124959	−	0.124959i	0.766821	+	0.641861i	$0.221838\pi$
$44$	−5.27640	+	5.14859i	−0.795447	+	0.776179i
$45$	4.45843	−	5.01223i	0.664623	−	0.747179i
$46$	−1.60482	+	3.80818i	−0.236617	+	0.561485i
$47$	6.28508	+	6.28508i	0.916772	+	0.916772i	0.996793	−	0.0800208i	$-0.0254987\pi$
$47$	6.28508	+	6.28508i	0.916772	+	0.916772i	−0.0800208	+	0.996793i	$0.525499\pi$
$48$	6.32602	+	2.82515i	0.913082	+	0.407776i
$49$			6.32075i			0.902965i
$50$	−6.15534	+	3.48020i	−0.870497	+	0.492174i
$51$	−1.99401	+	0.819412i	−0.279217	+	0.114741i
$52$	0.134798	−	10.9953i	0.0186931	−	1.52477i
$53$	−5.60782	−	5.60782i	−0.770293	−	0.770293i	0.207864	−	0.978158i	$-0.433349\pi$
$53$	−5.60782	−	5.60782i	−0.770293	−	0.770293i	−0.978158	+	0.207864i	$0.933349\pi$
$54$	5.27109	−	5.12011i	0.717305	−	0.696759i
$55$	−0.527212	−	8.22542i	−0.0710892	−	1.10911i
$56$	−0.852318	−	2.16968i	−0.113896	−	0.289936i
$57$	4.22349	−	10.1162i	0.559415	−	1.33993i
$58$	0.731106	+	1.79611i	0.0959989	+	0.235840i
$59$		−	6.12026i		−	0.796790i	−0.917214	−	0.398395i	$-0.869567\pi$
$59$		−	6.12026i		−	0.796790i	0.917214	−	0.398395i	$-0.130433\pi$
$60$	−7.00273	+	3.31086i	−0.904048	+	0.427430i
$61$			5.13471i			0.657432i	0.944429	+	0.328716i	$0.106616\pi$
$61$			5.13471i			0.657432i	−0.944429	+	0.328716i	$0.893384\pi$
$62$	4.34971	−	1.77055i	0.552413	−	0.224860i
$63$	−2.47245	−	0.0138443i	−0.311500	−	0.00174421i
$64$	−5.44503	−	5.86102i	−0.680629	−	0.732628i
$65$	9.23144	+	8.11933i	1.14502	+	1.00708i
$66$	0.0806201	−	9.02862i	0.00992365	−	1.11135i
$67$	4.90636	+	4.90636i	0.599408	+	0.599408i	0.940155	−	0.340747i	$-0.110680\pi$
$67$	4.90636	+	4.90636i	0.599408	+	0.599408i	−0.340747	+	0.940155i	$0.610680\pi$
$68$	2.48912	+	0.0305156i	0.301851	+	0.00370056i
$69$	−1.92377	−	4.68141i	−0.231594	−	0.563576i
$70$	2.46151	+	0.856408i	0.294207	+	0.102360i
$71$		−	4.13251i		−	0.490439i	−0.969468	−	0.245220i	$-0.921140\pi$
$71$		−	4.13251i		−	0.490439i	0.969468	−	0.245220i	$-0.0788601\pi$
$72$	−7.91501	+	3.05821i	−0.932793	+	0.360414i
$73$	4.69820	+	4.69820i	0.549883	+	0.549883i	0.926407	−	0.376524i	$-0.122881\pi$
$73$	4.69820	+	4.69820i	0.549883	+	0.549883i	−0.376524	+	0.926407i	$0.622881\pi$
$74$	4.49972	+	1.89624i	0.523082	+	0.220433i
$75$	2.28895	−	8.35229i	0.264305	−	0.964439i
$76$	−9.05987	+	8.84042i	−1.03924	+	1.01407i
$77$	−2.14814	+	2.14814i	−0.244803	+	0.244803i
$78$	9.43750	+	9.60756i	1.06859	+	1.08784i
$79$		−	1.10079i		−	0.123848i	−0.998081	−	0.0619241i	$-0.980276\pi$
$79$		−	1.10079i		−	0.123848i	0.998081	−	0.0619241i	$-0.0197237\pi$
$80$	8.93730	−	0.353117i	0.999220	−	0.0394797i
$81$	−0.100786	+	8.99944i	−0.0111985	+	0.999937i
$82$	−0.345554	−	0.848922i	−0.0381601	−	0.0937478i
$83$	6.27439	+	6.27439i	0.688703	+	0.688703i	0.961945	−	0.273242i	$-0.0880960\pi$
$83$	6.27439	+	6.27439i	0.688703	+	0.688703i	−0.273242	+	0.961945i	$0.588096\pi$
$84$	2.62091	+	1.13215i	0.285965	+	0.123528i
$85$	−1.83806	+	2.08982i	−0.199366	+	0.226673i
$86$	0.636420	−	1.51020i	0.0686269	−	0.162849i
$87$	−2.19169	−	0.915024i	−0.234974	−	0.0981009i
$88$	−4.16621	+	9.55717i	−0.444119	+	1.01880i
$89$	−15.3562			−1.62775			−0.813875	−	0.581040i	$-0.802646\pi$
$89$	−15.3562			−1.62775			−0.813875	+	0.581040i	$0.802646\pi$
$90$	3.16749	−	8.94243i	0.333883	−	0.942615i
$91$		−	4.53130i		−	0.475009i
$92$	−0.0716428	+	5.84382i	−0.00746928	+	0.609260i
$93$	−2.21595	+	5.30771i	−0.229784	+	0.550384i
$94$	11.5836	+	4.88148i	1.19476	+	0.503486i
$95$	−0.905253	−	14.1235i	−0.0928770	−	1.44904i
$96$	9.79248	+	0.327652i	0.999441	+	0.0334409i
$97$	−5.42154	+	5.42154i	−0.550474	+	0.550474i	−0.926578	−	0.376104i	$-0.877264\pi$
$97$	−5.42154	+	5.42154i	−0.550474	+	0.550474i	0.376104	+	0.926578i	$0.377264\pi$
$98$	3.37008	+	8.27927i	0.340430	+	0.836333i
$99$	7.77542	+	7.86299i	0.781459	+	0.790260i
$100$	−6.20705	+	7.84044i	−0.620705	+	0.784044i
$101$	9.84442			0.979556			0.489778	−	0.871847i	$-0.337078\pi$
$101$	9.84442			0.979556			0.489778	+	0.871847i	$0.337078\pi$
$102$	−2.17497	+	2.13647i	−0.215354	+	0.211542i
$103$	−8.28098	−	8.28098i	−0.815949	−	0.815949i	0.169569	−	0.985518i	$-0.445762\pi$
$103$	−8.28098	−	8.28098i	−0.815949	−	0.815949i	−0.985518	+	0.169569i	$0.945762\pi$
$104$	−5.68587	−	14.4741i	−0.557545	−	1.41930i
$105$	−2.86876	+	1.39962i	−0.279962	+	0.136589i
$106$	−10.3354	−	4.35547i	−1.00386	−	0.423041i
$107$	−5.84678	+	5.84678i	−0.565230	+	0.565230i	−0.930788	−	0.365559i	$-0.880878\pi$
$107$	−5.84678	+	5.84678i	−0.565230	+	0.565230i	0.365559	+	0.930788i	$0.380878\pi$
$108$	4.17444	−	9.51704i	0.401686	−	0.915777i
$109$	−11.7033			−1.12097			−0.560487	−	0.828163i	$-0.689386\pi$
$109$	−11.7033			−1.12097			−0.560487	+	0.828163i	$0.689386\pi$
$110$	−5.07618	−	10.4930i	−0.483995	−	1.00047i
$111$	−5.53152	+	2.27311i	−0.525029	+	0.215754i
$112$	−2.27324	−	2.38754i	−0.214801	−	0.225601i
$113$	8.58333	−	8.58333i	0.807452	−	0.807452i	−0.176796	−	0.984248i	$-0.556573\pi$
$113$	8.58333	−	8.58333i	0.807452	−	0.807452i	0.984248	+	0.176796i	$0.0565731\pi$
$114$	0.138429	−	15.5027i	0.0129651	−	1.45196i
$115$	−4.90636	−	4.31530i	−0.457521	−	0.402403i
$116$	1.91529	+	1.96283i	0.177830	+	0.182244i
$117$	−16.4939	−	0.0923560i	−1.52486	−	0.00853832i
$118$	−3.26318	−	8.01666i	−0.300400	−	0.737993i
$119$	1.02580			0.0940350
$120$	−7.40729	+	8.07045i	−0.676190	+	0.736728i
$121$	2.58708			0.235189
$122$	2.73771	+	6.72573i	0.247861	+	0.608919i
$123$	1.03589	+	0.432483i	0.0934033	+	0.0389956i
$124$	4.75347	−	4.63833i	0.426874	−	0.416535i
$125$	−2.13372	−	10.9748i	−0.190846	−	0.981620i
$126$	−3.24594	+	1.30012i	−0.289171	+	0.115824i
$127$	−0.0146460	+	0.0146460i	−0.00129962	+	0.00129962i	−0.707756	−	0.706457i	$-0.750293\pi$
$127$	−0.0146460	+	0.0146460i	−0.00129962	+	0.00129962i	0.706457	+	0.707756i	$0.250293\pi$
$128$	−10.2572	−	4.77393i	−0.906615	−	0.421959i
$129$	0.762905	+	1.85650i	0.0671701	+	0.163456i
$130$	16.4209	+	5.71316i	1.44021	+	0.501077i
$131$	5.23989			0.457811			0.228906	−	0.973449i	$-0.426485\pi$
$131$	5.23989			0.457811			0.228906	+	0.973449i	$0.426485\pi$
$132$	−4.70826	−	11.8692i	−0.409801	−	1.03308i
$133$	−3.68847	+	3.68847i	−0.319831	+	0.319831i
$134$	9.04259	+	3.81066i	0.781161	+	0.329191i
$135$	5.03613	+	10.4708i	0.433441	+	0.901182i
$136$	3.27666	−	1.28717i	0.280972	−	0.110374i
$137$	−14.0984	−	14.0984i	−1.20450	−	1.20450i	−0.972782	−	0.231722i	$-0.925564\pi$
$137$	−14.0984	−	14.0984i	−1.20450	−	1.20450i	−0.231722	−	0.972782i	$-0.574436\pi$
$138$	−5.01588	−	5.10627i	−0.426980	−	0.434674i
$139$	9.22166			0.782171			0.391085	−	0.920354i	$-0.372100\pi$
$139$	9.22166			0.782171			0.391085	+	0.920354i	$0.372100\pi$
$140$	3.68084	−	0.190650i	0.311088	−	0.0161128i
$141$	−14.2398	+	5.85165i	−1.19921	+	0.492798i
$142$	−2.20336	−	5.41300i	−0.184902	−	0.454249i
$143$	−14.3304	+	14.3304i	−1.19836	+	1.19836i
$144$	−8.73695	+	8.22592i	−0.728079	+	0.685493i
$145$	−3.05987	+	0.196124i	−0.254109	+	0.0162872i
$146$	8.65895	+	3.64899i	0.716619	+	0.301993i
$147$	−10.1027	−	4.21787i	−0.833260	−	0.347884i
$148$	6.90501	+	0.0846526i	0.567589	+	0.00695840i
$149$			14.0054i			1.14737i	0.819076	+	0.573685i	$0.194487\pi$
$149$			14.0054i			1.14737i	−0.819076	+	0.573685i	$0.805513\pi$
$150$	−1.45506	−	12.1607i	−0.118805	−	0.992918i
$151$	13.1301			1.06851			0.534255	−	0.845323i	$-0.320592\pi$
$151$	13.1301			1.06851			0.534255	+	0.845323i	$0.320592\pi$
$152$	−7.15361	+	16.4102i	−0.580234	+	1.33104i
$153$	0.0209077	−	3.73391i	0.00169028	−	0.301869i
$154$	−1.66841	+	3.95909i	−0.134444	+	0.319032i
$155$	0.474962	+	7.41023i	0.0381498	+	0.595204i
$156$	17.4843	+	7.55265i	1.39986	+	0.604696i
$157$	6.36936	+	6.36936i	0.508330	+	0.508330i	0.914014	−	0.405683i	$-0.132966\pi$
$157$	6.36936	+	6.36936i	0.508330	+	0.508330i	−0.405683	+	0.914014i	$0.632966\pi$
$158$	−0.586914	−	1.44187i	−0.0466924	−	0.114709i
$159$	12.7054	−	5.22110i	1.00760	−	0.414060i
$160$	11.5183	−	5.22770i	0.910601	−	0.413286i
$161$			2.40831i			0.189802i
$162$	4.66628	+	11.8417i	0.366618	+	0.930372i
$163$	3.46013	−	3.46013i	0.271018	−	0.271018i	−0.558492	−	0.829510i	$-0.688620\pi$
$163$	3.46013	−	3.46013i	0.271018	−	0.271018i	0.829510	+	0.558492i	$0.188620\pi$
$164$	−0.905253	−	0.927724i	−0.0706884	−	0.0724431i
$165$	13.4989	+	4.64619i	1.05088	+	0.361706i
$166$	11.5639	+	4.87318i	0.897533	+	0.378232i
$167$	0.954151	+	0.954151i	0.0738345	+	0.0738345i	0.743060	−	0.669225i	$-0.233374\pi$
$167$	0.954151	+	0.954151i	0.0738345	+	0.0738345i	−0.669225	+	0.743060i	$0.733374\pi$
$168$	4.03666	+	0.0855420i	0.311435	+	0.00659971i
$169$		−	17.2286i		−	1.32528i
$170$	−1.29335	+	3.71738i	−0.0991955	+	0.285110i
$171$	13.3508	+	13.5012i	1.02096	+	1.03246i
$172$	0.0284113	−	2.31747i	0.00216634	−	0.176706i
$173$	1.80240	+	1.80240i	0.137034	+	0.137034i	0.772296	−	0.635262i	$-0.219108\pi$
$173$	1.80240	+	1.80240i	0.137034	+	0.137034i	−0.635262	+	0.772296i	$0.719108\pi$
$174$	−3.35867	−	0.0299909i	−0.254620	−	0.00227360i
$175$	−2.51801	+	3.26202i	−0.190344	+	0.246585i
$176$	−0.361463	+	14.7398i	−0.0272463	+	1.11106i
$177$	9.78228	+	4.08408i	0.735281	+	0.306978i
$178$	−20.1144	+	8.18756i	−1.50763	+	0.613683i
$179$		−	24.0166i		−	1.79508i	−0.440930	−	0.897541i	$-0.645351\pi$
$179$		−	24.0166i		−	1.79508i	0.440930	−	0.897541i	$-0.354649\pi$
$180$	−0.618942	−	13.4021i	−0.0461332	−	0.998935i
$181$		−	21.7210i		−	1.61451i	−0.590205	−	0.807253i	$-0.700953\pi$
$181$		−	21.7210i		−	1.61451i	0.590205	−	0.807253i	$-0.299047\pi$
$182$	−2.41599	−	5.93535i	−0.179085	−	0.439957i
$183$	−8.20703	−	3.42641i	−0.606681	−	0.253288i
$184$	3.02195	+	7.69276i	0.222781	+	0.567117i
$185$	−5.09892	+	5.79732i	−0.374880	+	0.426228i
$186$	−0.0726302	+	8.13383i	−0.00532550	+	0.596401i
$187$	−3.24412	−	3.24412i	−0.237234	−	0.237234i
$188$	17.7755	+	0.217921i	1.29641	+	0.0158935i
$189$	1.67201	−	3.94259i	0.121621	−	0.286781i
$190$	−8.71609	−	18.0171i	−0.632331	−	1.30710i
$191$		−	12.9839i		−	0.939479i	−0.882805	−	0.469739i	$-0.844348\pi$
$191$		−	12.9839i		−	0.939479i	0.882805	−	0.469739i	$-0.155652\pi$
$192$	13.0014	−	4.79195i	0.938297	−	0.345829i
$193$	9.48630	+	9.48630i	0.682839	+	0.682839i	0.960639	−	0.277800i	$-0.0896053\pi$
$193$	9.48630	+	9.48630i	0.682839	+	0.682839i	−0.277800	+	0.960639i	$0.589605\pi$
$194$	−4.21079	+	9.99208i	−0.302317	+	0.717389i
$195$	−19.1377	+	9.33695i	−1.37048	+	0.668633i
$196$	8.82864	+	9.04780i	0.630617	+	0.646272i
$197$	12.8606	−	12.8606i	0.916280	−	0.916280i	−0.0804765	−	0.996757i	$-0.525644\pi$
$197$	12.8606	−	12.8606i	0.916280	−	0.916280i	0.996757	+	0.0804765i	$0.0256442\pi$
$198$	14.3770	+	6.15370i	1.02173	+	0.437324i
$199$			0.0463625i			0.00328655i	0.999999	+	0.00164328i	$0.000523071\pi$
$199$			0.0463625i			0.00328655i	−0.999999	+	0.00164328i	$0.999477\pi$
$200$	−3.94999	+	13.5793i	−0.279306	+	0.960202i
$201$	−11.1161	+	4.56802i	−0.784069	+	0.322203i
$202$	12.8948	−	5.24882i	0.907273	−	0.369306i
$203$	0.799111	+	0.799111i	0.0560866	+	0.0560866i
$204$	−1.70978	+	3.95812i	−0.119708	+	0.277123i
$205$	1.44624	−	0.0926972i	0.101010	−	0.00647425i
$206$	−15.2621	−	6.43165i	−1.06336	−	0.448115i
$207$	8.76625	+	0.0490858i	0.609296	+	0.00341170i
$208$	−15.1649	−	15.9274i	−1.05150	−	1.10437i
$209$	23.3298			1.61376
$210$	−3.01141	+	3.36285i	−0.207807	+	0.232059i
$211$		−	0.591066i		−	0.0406907i	−0.999793	−	0.0203453i	$-0.993523\pi$
$211$		−	0.591066i		−	0.0406907i	0.999793	−	0.0203453i	$-0.00647657\pi$
$212$	−15.8601	−	0.194439i	−1.08928	−	0.0133541i
$213$	6.60518	+	2.75765i	0.452579	+	0.188951i
$214$	−4.54107	+	10.7758i	−0.310421	+	0.736619i
$215$	1.94571	+	1.71131i	0.132696	+	0.116710i
$216$	0.393647	−	14.6917i	0.0267843	−	0.999641i
$217$	1.93524	−	1.93524i	0.131373	−	0.131373i
$218$	−15.3296	+	6.23994i	−1.03825	+	0.422622i
$219$	−10.6445	+	4.37421i	−0.719287	+	0.295582i
$220$	−12.2437	−	11.0378i	−0.825470	−	0.744170i
$221$	6.84318			0.460322
$222$	−6.03353	+	5.92673i	−0.404944	+	0.397776i
$223$	16.8577	+	16.8577i	1.12888	+	1.12888i	0.990360	+	0.138517i	$0.0442335\pi$
$223$	16.8577	+	16.8577i	1.12888	+	1.12888i	0.138517	+	0.990360i	$0.455767\pi$
$224$	−4.25060	−	1.91529i	−0.284005	−	0.127970i
$225$	11.8224	+	9.23204i	0.788161	+	0.615470i
$226$	6.66649	−	15.8194i	0.443448	−	1.05229i
$227$	7.23390	−	7.23390i	0.480131	−	0.480131i	−0.425043	−	0.905173i	$-0.639741\pi$
$227$	7.23390	−	7.23390i	0.480131	−	0.480131i	0.905173	+	0.425043i	$0.139741\pi$
$228$	−8.08434	−	20.3800i	−0.535399	−	1.34970i
$229$	23.0081			1.52042			0.760210	−	0.649677i	$-0.225096\pi$
$229$	23.0081			1.52042			0.760210	+	0.649677i	$0.225096\pi$
$230$	−8.72744	−	3.03645i	−0.575471	−	0.200218i
$231$	−2.00000	−	4.86692i	−0.131590	−	0.320220i
$232$	3.55529	+	1.54984i	0.233416	+	0.101752i
$233$	−4.45082	+	4.45082i	−0.291583	+	0.291583i	−0.837705	−	0.546122i	$-0.816103\pi$
$233$	−4.45082	+	4.45082i	−0.291583	+	0.291583i	0.546122	+	0.837705i	$0.316103\pi$
$234$	−21.6539	+	8.67320i	−1.41556	+	0.566985i
$235$	−13.1261	+	14.9240i	−0.856254	+	0.973536i
$236$	−8.54860	−	8.76081i	−0.556466	−	0.570280i
$237$	1.75944	+	0.734560i	0.114288	+	0.0477148i
$238$	1.34365	−	0.546934i	0.0870959	−	0.0354524i
$239$	4.03472			0.260984			0.130492	−	0.991449i	$-0.458344\pi$
$239$	4.03472			0.260984			0.130492	+	0.991449i	$0.458344\pi$
$240$	−5.39950	+	14.5205i	−0.348536	+	0.937295i
$241$	−11.4612			−0.738279			−0.369139	−	0.929374i	$-0.620347\pi$
$241$	−11.4612			−0.738279			−0.369139	+	0.929374i	$0.620347\pi$
$242$	3.38871	−	1.37937i	0.217834	−	0.0886696i
$243$	−14.3169	−	6.16646i	−0.918432	−	0.395578i
$244$	7.17201	+	7.35005i	0.459141	+	0.470538i
$245$	−14.1047	+	0.904047i	−0.901116	+	0.0577574i
$246$	1.58746	+	0.0141751i	0.101213	+	0.000903769i
$247$	−24.6060	+	24.6060i	−1.56564	+	1.56564i
$248$	3.75331	−	8.60999i	0.238335	−	0.546735i
$249$	−14.2156	+	5.84170i	−0.900874	+	0.370203i
$250$	−8.64641	−	13.2378i	−0.546847	−	0.837233i
$251$	−17.4804			−1.10335			−0.551677	−	0.834058i	$-0.686012\pi$
$251$	−17.4804			−1.10335			−0.551677	+	0.834058i	$0.686012\pi$
$252$	−3.55851	+	3.43363i	−0.224165	+	0.216299i
$253$	7.61636	−	7.61636i	0.478836	−	0.478836i
$254$	−0.0113752	+	0.0269930i	−0.000713745	+	0.00169369i
$255$	−2.11371	−	4.33241i	−0.132366	−	0.271306i
$256$	−15.9808	−	0.784260i	−0.998798	−	0.0490162i
$257$	6.77283	+	6.77283i	0.422477	+	0.422477i	0.886056	−	0.463578i	$-0.153435\pi$
$257$	6.77283	+	6.77283i	0.422477	+	0.422477i	−0.463578	+	0.886056i	$0.653435\pi$
$258$	1.98914	+	2.02498i	0.123838	+	0.126070i
$259$	2.84565			0.176820
$260$	24.5551	−	1.27184i	1.52284	−	0.0788760i
$261$	2.92505	−	2.89247i	0.181056	−	0.179040i
$262$	6.86350	−	2.79379i	0.424028	−	0.172601i
$263$	15.3708	−	15.3708i	0.947805	−	0.947805i	−0.0508987	−	0.998704i	$-0.516209\pi$
$263$	15.3708	−	15.3708i	0.947805	−	0.947805i	0.998704	+	0.0508987i	$0.0162086\pi$
$264$	−12.4955	−	13.0366i	−0.769046	−	0.802345i
$265$	11.7117	−	13.3159i	0.719445	−	0.817987i
$266$	−2.86476	+	6.79798i	−0.175649	+	0.416811i
$267$	10.2472	−	24.5444i	0.627121	−	1.50209i
$268$	13.8762	+	0.170117i	0.847627	+	0.0103916i
$269$			9.58859i			0.584627i	0.956323	+	0.292313i	$0.0944250\pi$
$269$			9.58859i			0.584627i	−0.956323	+	0.292313i	$0.905575\pi$
$270$	12.1794	+	11.0301i	0.741214	+	0.671268i
$271$	−20.9078			−1.27006			−0.635030	−	0.772487i	$-0.719012\pi$
$271$	−20.9078			−1.27006			−0.635030	+	0.772487i	$0.719012\pi$
$272$	3.60567	−	3.43306i	0.218626	−	0.208160i
$273$	7.24257	+	3.02376i	0.438341	+	0.183006i
$274$	−25.9837	−	10.9499i	−1.56974	−	0.661507i
$275$	18.2795	−	2.35293i	1.10230	−	0.141887i
$276$	−9.29263	−	4.01412i	−0.559350	−	0.241621i
$277$	−8.86336	−	8.86336i	−0.532547	−	0.532547i	0.388782	−	0.921330i	$-0.372896\pi$
$277$	−8.86336	−	8.86336i	−0.532547	−	0.532547i	−0.921330	+	0.388782i	$0.872896\pi$
$278$	12.0790	−	4.91678i	0.724453	−	0.294889i
$279$	−7.00483	−	7.08372i	−0.419368	−	0.424091i
$280$	4.71972	−	2.21226i	0.282057	−	0.132208i
$281$		−	12.1925i		−	0.727341i	−0.931528	−	0.363670i	$-0.881523\pi$
$281$		−	12.1925i		−	0.727341i	0.931528	−	0.363670i	$-0.118477\pi$
$282$	−15.5321	+	15.2571i	−0.924922	+	0.908550i
$283$	−11.6799	+	11.6799i	−0.694298	+	0.694298i	−0.963175	−	0.268877i	$-0.913348\pi$
$283$	−11.6799	+	11.6799i	−0.694298	+	0.694298i	0.268877	+	0.963175i	$0.413348\pi$
$284$	−5.77217	−	5.91546i	−0.342516	−	0.351018i
$285$	23.1783	+	7.97778i	1.37296	+	0.472563i
$286$	−11.1301	+	26.4113i	−0.658135	+	1.56173i
$287$	−0.377697	−	0.377697i	−0.0222947	−	0.0222947i
$288$	−7.05827	+	15.4331i	−0.415912	+	0.909405i
$289$		−	15.4508i		−	0.908872i
$290$	−3.90342	+	1.88835i	−0.229217	+	0.110888i
$291$	−5.04767	−	12.2833i	−0.295900	−	0.720060i
$292$	13.2875	+	0.162900i	0.777594	+	0.00953298i
$293$	−5.16432	−	5.16432i	−0.301703	−	0.301703i	0.539977	−	0.841680i	$-0.318433\pi$
$293$	−5.16432	−	5.16432i	−0.301703	−	0.301703i	−0.841680	+	0.539977i	$0.818433\pi$
$294$	−15.4820	−	0.138245i	−0.902929	−	0.00806261i
$295$	13.6573	−	0.875370i	0.795158	−	0.0509660i
$296$	9.08971	−	3.57071i	0.528328	−	0.207544i
$297$	−17.7563	+	7.18079i	−1.03033	+	0.416672i
$298$	7.46739	+	18.3451i	0.432574	+	1.06270i
$299$			16.0660i			0.929122i
$300$	−8.38974	−	15.1530i	−0.484382	−	0.874857i
$301$		−	0.955061i		−	0.0550488i
$302$	17.1985	−	7.00066i	0.989663	−	0.402843i
$303$	−6.56923	+	15.7348i	−0.377392	+	0.903939i
$304$	−0.620652	+	25.3091i	−0.0355968	+	1.45158i
$305$	−11.4580	+	0.734409i	−0.656086	+	0.0420521i
$306$	−1.96345	−	4.90203i	−0.112243	−	0.280230i
$307$	9.19824	+	9.19824i	0.524972	+	0.524972i	0.919069	−	0.394097i	$-0.128943\pi$
$307$	9.19824	+	9.19824i	0.524972	+	0.524972i	−0.394097	+	0.919069i	$0.628943\pi$
$308$	−0.0744818	+	6.07539i	−0.00424399	+	0.346177i
$309$	18.7618	−	7.70992i	1.06732	−	0.438602i
$310$	4.57310	+	9.45309i	0.259734	+	0.536899i
$311$			30.5690i			1.73341i	0.498821	+	0.866705i	$0.333767\pi$
$311$			30.5690i			1.73341i	−0.498821	+	0.866705i	$0.666233\pi$
$312$	26.9288	+	0.570656i	1.52454	+	0.0323071i
$313$	−16.4612	−	16.4612i	−0.930440	−	0.930440i	0.0672931	−	0.997733i	$-0.478564\pi$
$313$	−16.4612	−	16.4612i	−0.930440	−	0.930440i	−0.997733	+	0.0672931i	$0.978564\pi$
$314$	11.7389	+	4.94694i	0.662467	+	0.279172i
$315$	−0.322737	−	5.51923i	−0.0181842	−	0.310974i
$316$	−1.53755	−	1.57571i	−0.0864937	−	0.0886408i
$317$	−0.000616701	0	0.000616701i	−3.46374e−5	0	3.46374e-5i	−0.707124	−	0.707089i	$-0.750008\pi$
$317$	−0.000616701	0	0.000616701i	−3.46374e−5	0	3.46374e-5i	0.707089	+	0.707124i	$0.250008\pi$
$318$	13.8584	−	13.6131i	0.777141	−	0.763385i
$319$		−	5.05442i		−	0.282993i
$320$	12.3000	−	12.9888i	0.687592	−	0.726097i
$321$	−5.44358	−	13.2468i	−0.303831	−	0.739362i
$322$	1.28406	+	3.15454i	0.0715578	+	0.175796i
$323$	−5.57034	−	5.57034i	−0.309942	−	0.309942i
$324$	12.4259	+	13.0230i	0.690327	+	0.723498i
$325$	−16.7978	+	21.7611i	−0.931777	+	1.20709i
$326$	2.68740	−	6.37713i	0.148842	−	0.353196i
$327$	7.80967	−	18.7059i	0.431876	−	1.03444i
$328$	−1.68039	−	0.732524i	−0.0927841	−	0.0404469i
$329$	7.32553			0.403870
$330$	20.1588	−	1.11145i	1.10971	−	0.0611831i
$331$		−	8.28613i		−	0.455447i	−0.973726	−	0.227724i	$-0.926872\pi$
$331$		−	8.28613i		−	0.455447i	0.973726	−	0.227724i	$-0.0731283\pi$
$332$	17.7453	+	0.217550i	0.973901	+	0.0119396i
$333$	0.0579994	−	10.3581i	0.00317835	−	0.567622i
$334$	1.75853	+	0.741069i	0.0962226	+	0.0405495i
$335$	−10.2467	+	11.6502i	−0.559839	+	0.636521i
$336$	5.33305	−	2.04021i	0.290942	−	0.111302i
$337$	2.27666	−	2.27666i	0.124018	−	0.124018i	−0.642374	−	0.766392i	$-0.722050\pi$
$337$	2.27666	−	2.27666i	0.124018	−	0.124018i	0.766392	+	0.642374i	$0.222050\pi$
$338$	−9.18590	−	22.5670i	−0.499647	−	1.22748i
$339$	7.99142	+	19.4468i	0.434035	+	1.05621i
$340$	0.287920	+	5.55882i	0.0156147	+	0.301469i
$341$	−12.2405			−0.662861
$342$	24.6862	+	10.5663i	1.33488	+	0.571357i
$343$	7.76296	+	7.76296i	0.419161	+	0.419161i
$344$	−1.19841	−	3.05070i	−0.0646139	−	0.164483i
$345$	10.1714	−	4.96244i	0.547608	−	0.267169i
$346$	3.32189	+	1.39989i	0.178586	+	0.0752584i
$347$	−18.6384	+	18.6384i	−1.00056	+	1.00056i	−0.000564305		1.00000i	$0.500180\pi$
$347$	−18.6384	+	18.6384i	−1.00056	+	1.00056i	−1.00000		0.000564305i	$0.999820\pi$
$348$	−4.41536	+	1.75148i	−0.236688	+	0.0938892i
$349$	−17.7267			−0.948889			−0.474445	−	0.880285i	$-0.657351\pi$
$349$	−17.7267			−0.948889			−0.474445	+	0.880285i	$0.657351\pi$
$350$	−1.55900	+	5.61532i	−0.0833321	+	0.300152i
$351$	11.1541	−	26.3013i	0.595360	−	1.40386i
$352$	7.38548	+	19.4998i	0.393648	+	1.03934i
$353$	−10.5779	+	10.5779i	−0.563007	+	0.563007i	−0.930160	−	0.367153i	$-0.880332\pi$
$353$	−10.5779	+	10.5779i	−0.563007	+	0.563007i	0.367153	+	0.930160i	$0.380332\pi$
$354$	14.9909	+	0.133860i	0.796758	+	0.00711457i
$355$	9.22166	−	0.591066i	0.489435	−	0.0313705i
$356$	−21.9815	+	21.4490i	−1.16502	+	1.13680i
$357$	−0.684521	+	1.63958i	−0.0362287	+	0.0867759i
$358$	−12.8051	−	31.4582i	−0.676770	−	1.66262i
$359$	−24.7266			−1.30502			−0.652510	−	0.757780i	$-0.726284\pi$
$359$	−24.7266			−1.30502			−0.652510	+	0.757780i	$0.726284\pi$
$360$	−7.95643	−	17.2248i	−0.419341	−	0.907829i
$361$	21.0586			1.10835
$362$	−11.5811	−	28.4513i	−0.608691	−	1.49537i
$363$	−1.72637	+	4.13505i	−0.0906111	+	0.217034i
$364$	−6.32919	−	6.48630i	−0.331739	−	0.339974i
$365$	−9.81201	+	11.1560i	−0.513584	+	0.583930i
$366$	−12.5769	−	0.112304i	−0.657406	−	0.00587024i
$367$	9.33767	−	9.33767i	0.487423	−	0.487423i	−0.420069	−	0.907492i	$-0.637994\pi$
$367$	9.33767	−	9.33767i	0.487423	−	0.487423i	0.907492	+	0.420069i	$0.137994\pi$
$368$	8.05992	+	8.46516i	0.420152	+	0.441277i
$369$	−1.38251	+	1.36712i	−0.0719707	+	0.0711692i
$370$	−3.58785	+	10.3123i	−0.186524	+	0.536110i
$371$	−6.53616			−0.339341
$372$	4.24164	+	10.6929i	0.219919	+	0.554399i
$373$	−11.9025	+	11.9025i	−0.616291	+	0.616291i	−0.944578	−	0.328287i	$-0.893529\pi$
$373$	−11.9025	+	11.9025i	−0.616291	+	0.616291i	0.328287	+	0.944578i	$0.393529\pi$
$374$	−5.97903	−	2.51964i	−0.309168	−	0.130288i
$375$	18.9654	+	3.91314i	0.979370	+	0.202074i
$376$	23.3996	−	9.19207i	1.20674	−	0.474045i
$377$	5.33092	+	5.33092i	0.274557	+	0.274557i
$378$	0.0879865	−	6.05570i	0.00452554	−	0.311472i
$379$	−2.73341			−0.140406			−0.0702029	−	0.997533i	$-0.522365\pi$
$379$	−2.73341			−0.140406			−0.0702029	+	0.997533i	$0.522365\pi$
$380$	−21.0231	−	18.9526i	−1.07846	−	0.972247i
$381$	−0.0136360	−	0.0331827i	−0.000698593	−	0.00170000i
$382$	−6.92270	−	17.0070i	−0.354196	−	0.870153i
$383$	17.6065	−	17.6065i	0.899651	−	0.899651i	−0.0957539	−	0.995405i	$-0.530526\pi$
$383$	17.6065	−	17.6065i	0.899651	−	0.899651i	0.995405	+	0.0957539i	$0.0305262\pi$
$384$	14.4750	−	13.2088i	0.738676	−	0.674060i
$385$	−5.10079	−	4.48630i	−0.259960	−	0.228643i
$386$	17.4836	+	7.36780i	0.889890	+	0.375011i
$387$	−3.47642	−	0.0194659i	−0.176716	−	0.000989506i
$388$	−0.187980	+	15.3333i	−0.00954322	+	0.778429i
$389$			25.1335i			1.27432i	0.770731	+	0.637160i	$0.219891\pi$
$389$			25.1335i			1.27432i	−0.770731	+	0.637160i	$0.780109\pi$
$390$	−20.0893	+	22.4338i	−1.01726	+	1.13598i
$391$	−3.63704			−0.183933
$392$	16.3883	+	7.14408i	0.827736	+	0.360831i
$393$	−3.49660	+	8.37515i	−0.176380	+	0.422470i
$394$	9.98855	−	23.7025i	0.503216	−	1.19412i
$395$	2.45639	−	0.157444i	0.123594	−	0.00792185i
$396$	22.1129	+	0.394941i	1.11121	+	0.0198465i
$397$	5.42664	+	5.42664i	0.272355	+	0.272355i	0.830048	−	0.557692i	$-0.188313\pi$
$397$	5.42664	+	5.42664i	0.272355	+	0.272355i	−0.557692	+	0.830048i	$0.688313\pi$
$398$	0.0247195	+	0.0607282i	0.00123907	+	0.00304403i
$399$	−3.43411	−	8.35678i	−0.171921	−	0.418362i
$400$	2.06626	+	19.8930i	0.103313	+	0.994649i
$401$			5.15831i			0.257594i	0.991671	+	0.128797i	$0.0411115\pi$
$401$			5.15831i			0.257594i	−0.991671	+	0.128797i	$0.958888\pi$
$402$	−12.1249	+	11.9103i	−0.604736	+	0.594032i
$403$	12.9101	−	12.9101i	0.643099	−	0.643099i
$404$	14.0917	−	13.7504i	0.701090	−	0.684108i
$405$	−20.0966	+	1.06227i	−0.998606	+	0.0527847i
$406$	1.47279	+	0.620652i	0.0730933	+	0.0308025i
$407$	−8.99944	−	8.99944i	−0.446085	−	0.446085i
$408$	−0.129186	+	6.09617i	−0.00639565	+	0.301806i
$409$			14.1638i			0.700356i	0.936683	+	0.350178i	$0.113879\pi$
$409$			14.1638i			0.700356i	−0.936683	+	0.350178i	$0.886121\pi$
$410$	1.84494	−	0.892521i	0.0911149	−	0.0440785i
$411$	31.9419	−	13.1261i	1.57558	−	0.647464i
$412$	−23.4204	−	0.287124i	−1.15384	−	0.0141456i
$413$	−3.56672	−	3.56672i	−0.175507	−	0.175507i
$414$	11.5087	−	4.60967i	0.565621	−	0.226553i
$415$	−13.1038	+	14.8986i	−0.643241	+	0.731345i
$416$	−28.3560	−	12.7770i	−1.39027	−	0.626444i
$417$	−6.15365	+	14.7394i	−0.301346	+	0.721791i
$418$	30.5587	−	12.4389i	1.49467	−	0.608407i
$419$			4.80514i			0.234746i	0.993088	+	0.117373i	$0.0374474\pi$
$419$			4.80514i			0.234746i	−0.993088	+	0.117373i	$0.962553\pi$
$420$	−2.15152	+	6.01047i	−0.104983	+	0.293281i
$421$			15.2187i			0.741716i	0.928690	+	0.370858i	$0.120936\pi$
$421$			15.2187i			0.741716i	−0.928690	+	0.370858i	$0.879064\pi$
$422$	−0.315143	−	0.774212i	−0.0153409	−	0.0376880i
$423$	0.149308	−	26.6649i	0.00725958	−	1.29649i
$424$	−20.8781	+	8.20157i	−1.01393	+	0.398304i
$425$	−4.92631	−	3.80272i	−0.238961	−	0.184459i
$426$	10.1221	+	0.0903846i	0.490420	+	0.00437915i
$427$	2.99236	+	2.99236i	0.144811	+	0.144811i
$428$	−0.202724	+	16.5359i	−0.00979903	+	0.799295i
$429$	−13.3421	−	32.4676i	−0.644164	−	1.56755i
$430$	3.46103	+	1.20416i	0.166906	+	0.0580698i
$431$			27.8760i			1.34274i	0.741122	+	0.671370i	$0.234294\pi$
$431$			27.8760i			1.34274i	−0.741122	+	0.671370i	$0.765706\pi$
$432$	−7.31764	−	19.4538i	−0.352070	−	0.935974i
$433$	−2.78003	−	2.78003i	−0.133600	−	0.133600i	0.637145	−	0.770744i	$-0.280115\pi$
$433$	−2.78003	−	2.78003i	−0.133600	−	0.133600i	−0.770744	+	0.637145i	$0.780115\pi$
$434$	1.50306	−	3.56672i	0.0721492	−	0.171208i
$435$	1.72839	−	5.02160i	0.0828701	−	0.240767i
$436$	−16.7526	+	16.3468i	−0.802305	+	0.782872i
$437$	13.0777	−	13.0777i	0.625592	−	0.625592i
$438$	−11.6105	+	11.4050i	−0.554771	+	0.544951i
$439$			10.8174i			0.516286i	0.966107	+	0.258143i	$0.0831105\pi$
$439$			10.8174i			0.516286i	−0.966107	+	0.258143i	$0.916889\pi$
$440$	−21.9226	−	7.92990i	−1.04512	−	0.378043i
$441$	13.4832	−	13.3331i	0.642058	−	0.634907i
$442$	8.96358	−	3.64863i	0.426354	−	0.173548i
$443$	5.74963	+	5.74963i	0.273173	+	0.273173i	0.830376	−	0.557203i	$-0.188126\pi$
$443$	5.74963	+	5.74963i	0.273173	+	0.273173i	−0.557203	+	0.830376i	$0.688126\pi$
$444$	−4.74305	+	10.9801i	−0.225095	+	0.521092i
$445$	−2.19637	−	34.2671i	−0.104118	−	1.62442i
$446$	31.0693	+	13.0930i	1.47118	+	0.619973i
$447$	−22.3855	−	9.34590i	−1.05880	−	0.442046i
$448$	−6.58885	−	0.242427i	−0.311294	−	0.0114536i
$449$	6.91183			0.326189			0.163095	−	0.986610i	$-0.447852\pi$
$449$	6.91183			0.326189			0.163095	+	0.986610i	$0.447852\pi$
$450$	20.4080	+	5.78920i	0.962041	+	0.272906i
$451$			2.38895i			0.112491i
$452$	0.297608	−	24.2755i	0.0139983	−	1.14182i
$453$	−8.76176	+	20.9864i	−0.411663	+	0.986026i
$454$	5.61841	−	13.3323i	0.263685	−	0.625716i
$455$	10.1115	−	0.648104i	0.474036	−	0.0303836i
$456$	−21.4555	−	22.3845i	−1.00475	−	1.04825i
$457$	−5.15748	+	5.15748i	−0.241257	+	0.241257i	−0.817370	−	0.576113i	$-0.804569\pi$
$457$	−5.15748	+	5.15748i	−0.241257	+	0.241257i	0.576113	+	0.817370i	$0.304569\pi$
$458$	30.1373	−	12.2674i	1.40823	−	0.573219i
$459$	5.95412	+	2.52507i	0.277915	+	0.117860i
$460$	−13.0507	+	0.675961i	−0.608490	+	0.0315169i
$461$	18.4555			0.859558			0.429779	−	0.902934i	$-0.358592\pi$
$461$	18.4555			0.859558			0.429779	+	0.902934i	$0.358592\pi$
$462$	−5.21464	−	5.30861i	−0.242607	−	0.246979i
$463$	−19.6899	−	19.6899i	−0.915068	−	0.915068i	0.0815977	−	0.996665i	$-0.473998\pi$
$463$	−19.6899	−	19.6899i	−0.915068	−	0.915068i	−0.996665	+	0.0815977i	$0.973998\pi$
$464$	5.48325	+	0.134465i	0.254553	+	0.00624238i
$465$	−12.1610	−	4.18572i	−0.563955	−	0.194108i
$466$	−3.45685	+	8.20301i	−0.160136	+	0.379997i
$467$	2.07946	−	2.07946i	0.0962257	−	0.0962257i	−0.657355	−	0.753581i	$-0.728325\pi$
$467$	2.07946	−	2.07946i	0.0962257	−	0.0962257i	0.753581	+	0.657355i	$0.228325\pi$
$468$	−23.7391	+	22.9060i	−1.09734	+	1.05883i
$469$	5.71858			0.264060
$470$	−9.23619	+	26.5469i	−0.426034	+	1.22452i
$471$	−14.4307	+	5.93013i	−0.664933	+	0.273246i
$472$	−15.8685	−	6.91747i	−0.730407	−	0.318402i
$473$	−3.02041	+	3.02041i	−0.138879	+	0.138879i
$474$	2.69626	+	0.0240759i	0.123843	+	0.00110584i
$475$	31.3870	−	4.04012i	1.44013	−	0.185374i
$476$	1.46838	−	1.43281i	0.0673029	−	0.0656727i
$477$	−0.133219	+	23.7916i	−0.00609967	+	1.08934i
$478$	5.28490	−	2.15122i	0.241725	−	0.0983945i
$479$	19.7088			0.900517			0.450259	−	0.892898i	$-0.351332\pi$
$479$	19.7088			0.900517			0.450259	+	0.892898i	$0.351332\pi$
$480$	0.669449	+	21.8987i	0.0305560	+	0.999533i
$481$	18.9835			0.865573
$482$	−15.0125	+	6.11083i	−0.683799	+	0.278341i
$483$	−3.84931	−	1.60708i	−0.175150	−	0.0731246i
$484$	3.70326	−	3.61356i	0.168330	−	0.164253i
$485$	−12.8735	−	11.3227i	−0.584557	−	0.514136i
$486$	−22.0409	−	0.443697i	−0.999797	−	0.0201265i
$487$	4.21395	−	4.21395i	0.190952	−	0.190952i	−0.605155	−	0.796107i	$-0.706889\pi$
$487$	4.21395	−	4.21395i	0.190952	−	0.190952i	0.796107	+	0.605155i	$0.206889\pi$
$488$	13.3132	+	5.80354i	0.602659	+	0.262714i
$489$	3.22151	+	7.83943i	0.145682	+	0.354511i
$490$	−17.9931	+	8.70447i	−0.812845	+	0.393228i
$491$	−27.7215			−1.25105			−0.625527	−	0.780203i	$-0.715116\pi$
$491$	−27.7215			−1.25105			−0.625527	+	0.780203i	$0.715116\pi$
$492$	2.08690	−	0.827831i	0.0940848	−	0.0373215i
$493$	−1.20682	+	1.20682i	−0.0543525	+	0.0543525i
$494$	−19.1110	+	45.3497i	−0.859843	+	2.04038i
$495$	−16.4341	+	18.4754i	−0.738656	+	0.830407i
$496$	0.325640	−	13.2790i	0.0146216	−	0.596246i
$497$	−2.40831	−	2.40831i	−0.108028	−	0.108028i
$498$	−15.5057	+	15.2312i	−0.694825	+	0.682527i
$499$	−5.14705			−0.230414			−0.115207	−	0.993342i	$-0.536753\pi$
$499$	−5.14705			−0.230414			−0.115207	+	0.993342i	$0.536753\pi$
$500$	−18.3836	−	12.7296i	−0.822142	−	0.569283i
$501$	−2.16177	+	0.888353i	−0.0965809	+	0.0396887i
$502$	−22.8968	+	9.32016i	−1.02193	+	0.415979i
$503$	12.2281	−	12.2281i	0.545224	−	0.545224i	−0.379832	−	0.925056i	$-0.624018\pi$
$503$	12.2281	−	12.2281i	0.545224	−	0.545224i	0.925056	+	0.379832i	$0.124018\pi$
$504$	−2.83040	+	6.39488i	−0.126076	+	0.284851i
$505$	1.40803	+	21.9677i	0.0626565	+	0.977550i
$506$	5.91546	−	14.0372i	0.262974	−	0.624030i
$507$	27.5372	+	11.4967i	1.22297	+	0.510587i
$508$	−0.000507817		0.0414220i	−2.25307e−5		0.00183780i
$509$		−	35.8361i		−	1.58841i	−0.607651	−	0.794204i	$-0.707888\pi$
$509$		−	35.8361i		−	1.58841i	0.607651	−	0.794204i	$-0.292112\pi$
$510$	−5.07860	−	4.54785i	−0.224884	−	0.201382i
$511$	5.47596			0.242242
$512$	−21.3506	+	7.49332i	−0.943574	+	0.331161i
$513$	−30.4886	+	12.3298i	−1.34611	+	0.544375i
$514$	12.4825	+	5.26031i	0.550581	+	0.232022i
$515$	17.2945	−	19.6633i	0.762086	−	0.866469i
$516$	3.68516	+	1.59187i	0.162230	+	0.0700783i
$517$	−23.1672	−	23.1672i	−1.01889	−	1.01889i
$518$	3.72738	−	1.51723i	0.163772	−	0.0666634i
$519$	−4.08361	+	1.67811i	−0.179251	+	0.0736608i
$520$	31.4856	−	14.7582i	1.38073	−	0.647188i
$521$			18.1715i			0.796107i	0.917362	+	0.398054i	$0.130314\pi$
$521$			18.1715i			0.796107i	−0.917362	+	0.398054i	$0.869686\pi$
$522$	2.28919	−	5.34829i	0.100195	−	0.234088i
$523$	21.7444	−	21.7444i	0.950815	−	0.950815i	−0.0480305	−	0.998846i	$-0.515294\pi$
$523$	21.7444	−	21.7444i	0.950815	−	0.950815i	0.998846	+	0.0480305i	$0.0152945\pi$
$524$	7.50061	−	7.31893i	0.327666	−	0.319729i
$525$	−3.53355	−	6.20141i	−0.154217	−	0.270652i
$526$	11.9382	−	28.3289i	0.520529	−	1.23520i
$527$	2.92261	+	2.92261i	0.127311	+	0.127311i
$528$	−23.3181	−	10.4137i	−1.01479	−	0.453198i
$529$			14.4612i			0.628746i
$530$	8.24093	−	23.6863i	0.357963	−	1.02887i
$531$	−13.0555	+	12.9101i	−0.566561	+	0.560252i
$532$	−0.127889	+	10.4318i	−0.00554471	+	0.452275i
$533$	−2.51964	−	2.51964i	−0.109138	−	0.109138i
$534$	0.335864	−	37.6133i	0.0145342	−	1.62768i
$535$	−13.8833	−	12.2108i	−0.600227	−	0.527918i
$536$	18.2666	−	7.17567i	0.788996	−	0.309942i
$537$	38.3867	+	16.0264i	1.65651	+	0.691589i
$538$	5.11242	+	12.5597i	0.220412	+	0.541486i
$539$		−	23.2987i		−	1.00355i
$540$	21.8342	+	7.95402i	0.939596	+	0.342286i
$541$			26.6843i			1.14725i	0.819119	+	0.573623i	$0.194463\pi$
$541$			26.6843i			1.14725i	−0.819119	+	0.573623i	$0.805537\pi$
$542$	−27.3862	+	11.1476i	−1.17634	+	0.478830i
$543$	34.7176	+	14.4945i	1.48987	+	0.622019i
$544$	2.89247	−	6.41927i	0.124014	−	0.275224i
$545$	−1.67390	−	26.1158i	−0.0717022	−	1.11868i
$546$	11.0989	+	0.0991067i	0.474990	+	0.00424138i
$547$	−22.2551	−	22.2551i	−0.951559	−	0.951559i	0.0473207	−	0.998880i	$-0.484932\pi$
$547$	−22.2551	−	22.2551i	−0.951559	−	0.951559i	−0.998880	+	0.0473207i	$0.984932\pi$
$548$	−39.8732	−	0.488829i	−1.70330	−	0.0208817i
$549$	10.9532	−	10.8312i	0.467470	−	0.462264i
$550$	22.6890	−	12.8282i	0.967462	−	0.546998i
$551$		−	8.67873i		−	0.369726i
$552$	−14.3122	−	0.303295i	−0.609169	−	0.0129091i
$553$	−0.641507	−	0.641507i	−0.0272797	−	0.0272797i
$554$	−16.3355	−	6.88398i	−0.694027	−	0.292472i
$555$	−5.86358	−	12.0184i	−0.248895	−	0.510153i
$556$	13.2003	−	12.8805i	0.559817	−	0.546257i
$557$	−7.30615	+	7.30615i	−0.309572	+	0.309572i	−0.844743	−	0.535172i	$-0.820247\pi$
$557$	−7.30615	+	7.30615i	−0.309572	+	0.309572i	0.535172	+	0.844743i	$0.320247\pi$
$558$	−12.9522	−	5.54383i	−0.548310	−	0.234689i
$559$		−	6.37128i		−	0.269476i
$560$	5.00262	−	5.41419i	0.211399	−	0.228791i
$561$	7.35005	−	3.02041i	0.310319	−	0.127522i
$562$	−6.50074	−	15.9704i	−0.274217	−	0.673669i
$563$	21.3458	+	21.3458i	0.899616	+	0.899616i	0.995402	−	0.0957856i	$-0.0305363\pi$
$563$	21.3458	+	21.3458i	0.899616	+	0.899616i	−0.0957856	+	0.995402i	$0.530536\pi$
$564$	−12.2100	+	28.2660i	−0.514134	+	1.19021i
$565$	20.3813	+	17.9260i	0.857447	+	0.754150i
$566$	−9.07152	+	21.5264i	−0.381304	+	0.904823i
$567$	5.18588	+	5.30335i	0.217787	+	0.222720i
$568$	−10.7147	−	4.67081i	−0.449579	−	0.195983i
$569$	35.6410			1.49415			0.747075	−	0.664740i	$-0.231458\pi$
$569$	35.6410			1.49415			0.747075	+	0.664740i	$0.231458\pi$
$570$	34.6138	−	1.90842i	1.44981	−	0.0799347i
$571$			9.49296i			0.397268i	0.980074	+	0.198634i	$0.0636505\pi$
$571$			9.49296i			0.397268i	−0.980074	+	0.198634i	$0.936350\pi$
$572$	−0.496873	+	40.5293i	−0.0207753	+	1.69462i
$573$	20.7527	+	8.66419i	0.866955	+	0.361952i
$574$	−0.696108	−	0.293349i	−0.0290550	−	0.0122441i
$575$	8.92779	−	11.5657i	0.372314	−	0.482323i
$576$	−1.01673	+	23.9785i	−0.0423636	+	0.999102i
$577$	10.6312	−	10.6312i	0.442582	−	0.442582i	−0.450297	−	0.892879i	$-0.648682\pi$
$577$	10.6312	−	10.6312i	0.442582	−	0.442582i	0.892879	+	0.450297i	$0.148682\pi$
$578$	−8.23803	−	20.2384i	−0.342657	−	0.841805i
$579$	−21.4926	+	8.83212i	−0.893203	+	0.367050i
$580$	−4.10609	+	4.55468i	−0.170496	+	0.189123i
$581$	7.31307			0.303397
$582$	−13.1609	−	13.3981i	−0.545537	−	0.555367i
$583$	20.6708	+	20.6708i	0.856097	+	0.856097i
$584$	17.4916	−	6.87124i	0.723808	−	0.284334i
$585$	−2.15300	−	36.8192i	−0.0890157	−	1.52229i
$586$	−9.51801	−	4.01102i	−0.393186	−	0.165694i
$587$	−17.1910	+	17.1910i	−0.709550	+	0.709550i	−0.966441	−	0.256891i	$-0.917302\pi$
$587$	−17.1910	+	17.1910i	−0.709550	+	0.709550i	0.256891	+	0.966441i	$0.417302\pi$
$588$	−20.3529	+	8.07357i	−0.839339	+	0.332949i
$589$	−21.0177			−0.866018
$590$	17.4224	−	8.42837i	0.717267	−	0.346990i
$591$	11.9737	+	29.1376i	0.492534	+	1.19856i
$592$	10.0024	−	9.52355i	0.411095	−	0.391415i
$593$	−9.69544	+	9.69544i	−0.398144	+	0.398144i	−0.877578	−	0.479434i	$-0.840842\pi$
$593$	−9.69544	+	9.69544i	−0.398144	+	0.398144i	0.479434	+	0.877578i	$0.340842\pi$
$594$	−19.4296	+	18.8731i	−0.797206	+	0.774372i
$595$	0.146719	+	2.28906i	0.00601487	+	0.0938424i
$596$	19.5624	+	20.0480i	0.801307	+	0.821198i
$597$	−0.0741033	−	0.0309379i	−0.00303285	−	0.00126621i
$598$	8.56604	+	21.0442i	0.350291	+	0.860560i
$599$	−26.8502			−1.09707			−0.548535	−	0.836128i	$-0.684814\pi$
$599$	−26.8502			−1.09707			−0.548535	+	0.836128i	$0.684814\pi$
$600$	−19.0686	−	15.3750i	−0.778471	−	0.627681i
$601$	−42.9566			−1.75224			−0.876119	−	0.482095i	$-0.839876\pi$
$601$	−42.9566			−1.75224			−0.876119	+	0.482095i	$0.839876\pi$
$602$	−0.509217	−	1.25099i	−0.0207541	−	0.0509866i
$603$	0.116555	−	20.8156i	0.00474649	−	0.847677i
$604$	18.7950	−	18.3397i	0.764756	−	0.746232i
$605$	0.370026	+	5.77305i	0.0150437	+	0.234708i
$606$	−0.215313	+	24.1128i	−0.00874650	+	0.979517i
$607$	32.0417	−	32.0417i	1.30053	−	1.30053i	0.372498	−	0.928033i	$-0.378501\pi$
$607$	32.0417	−	32.0417i	1.30053	−	1.30053i	0.928033	−	0.372498i	$-0.121499\pi$
$608$	12.6813	+	33.4822i	0.514294	+	1.35788i
$609$	−1.81051	+	0.744004i	−0.0733654	+	0.0301486i
$610$	−14.6168	+	7.07114i	−0.591818	+	0.286302i
$611$	48.8691			1.97703
$612$	−5.18549	−	5.37408i	−0.209611	−	0.217234i
$613$	20.1419	−	20.1419i	0.813522	−	0.813522i	−0.171638	−	0.985160i	$-0.554906\pi$
$613$	20.1419	−	20.1419i	0.813522	−	0.813522i	0.985160	+	0.171638i	$0.0549060\pi$
$614$	16.9527	+	7.14408i	0.684154	+	0.288311i
$615$	−0.816918	+	2.37344i	−0.0329413	+	0.0957064i
$616$	3.14170	+	7.99760i	0.126583	+	0.322232i
$617$	7.33463	+	7.33463i	0.295281	+	0.295281i	0.839162	−	0.543881i	$-0.183046\pi$
$617$	7.33463	+	7.33463i	0.295281	+	0.295281i	−0.543881	+	0.839162i	$0.683046\pi$
$618$	20.4645	−	20.1022i	0.823202	−	0.808631i
$619$	−11.9287			−0.479456			−0.239728	−	0.970840i	$-0.577058\pi$
$619$	−11.9287			−0.479456			−0.239728	+	0.970840i	$0.577058\pi$
$620$	11.0303	+	9.94391i	0.442986	+	0.399357i
$621$	−5.92821	+	13.9787i	−0.237891	+	0.560947i
$622$	16.2987	+	40.0410i	0.653519	+	1.60550i
$623$	−8.94914	+	8.94914i	−0.358540	+	0.358540i
$624$	35.5771	−	13.6104i	1.42422	−	0.544850i
$625$	24.1851	−	6.33109i	0.967403	−	0.253244i
$626$	−30.3385	−	12.7850i	−1.21257	−	0.510993i
$627$	−15.5681	+	37.2890i	−0.621729	+	1.48918i
$628$	18.0139	+	0.220843i	0.718834	+	0.00881260i
$629$			4.29751i			0.171353i
$630$	−3.36547	−	7.05732i	−0.134084	−	0.281170i
$631$	7.13985			0.284233			0.142116	−	0.989850i	$-0.454609\pi$
$631$	7.13985			0.284233			0.142116	+	0.989850i	$0.454609\pi$
$632$	−2.85410	−	1.24417i	−0.113530	−	0.0494905i
$633$	0.944728	+	0.394421i	0.0375496	+	0.0156768i
$634$	−0.000478978		0.00113660i	−1.90227e−5		4.51402e-5i
$635$	−0.0347772	−	0.0305876i	−0.00138009	−	0.00121383i
$636$	10.8943	−	25.2202i	0.431988	−	1.00005i
$637$	24.5733	+	24.5733i	0.973628	+	0.973628i
$638$	−2.69490	−	6.62057i	−0.106692	−	0.262111i
$639$	−8.81533	+	8.71716i	−0.348729	+	0.344846i
$640$	9.18590	−	23.5716i	0.363104	−	0.931748i
$641$		−	30.0187i		−	1.18567i	−0.805325	−	0.592834i	$-0.798009\pi$
$641$		−	30.0187i		−	1.18567i	0.805325	−	0.592834i	$-0.201991\pi$
$642$	−14.1932	−	14.4489i	−0.560160	−	0.570254i
$643$	−32.7048	+	32.7048i	−1.28975	+	1.28975i	−0.354812	+	0.934938i	$0.615455\pi$
$643$	−32.7048	+	32.7048i	−1.28975	+	1.28975i	−0.934938	+	0.354812i	$0.884545\pi$
$644$	3.36386	+	3.44736i	0.132555	+	0.135845i
$645$	−4.03364	+	1.96795i	−0.158825	+	0.0774878i
$646$	−10.2663	−	4.32637i	−0.403923	−	0.170219i
$647$	−2.53026	−	2.53026i	−0.0994747	−	0.0994747i	0.655618	−	0.755093i	$-0.272408\pi$
$647$	−2.53026	−	2.53026i	−0.0994747	−	0.0994747i	−0.755093	+	0.655618i	$0.772408\pi$
$648$	23.2197	+	10.4330i	0.912154	+	0.409847i
$649$			22.5597i			0.885545i
$650$	−10.4002	+	37.4602i	−0.407929	+	1.46931i
$651$	1.80179	+	4.38458i	0.0706176	+	0.171845i
$652$	0.119972	−	9.78598i	0.00469847	−	0.383248i
$653$	23.8061	+	23.8061i	0.931604	+	0.931604i	0.997806	−	0.0662023i	$-0.0210883\pi$
$653$	23.8061	+	23.8061i	0.931604	+	0.931604i	−0.0662023	+	0.997806i	$0.521088\pi$
$654$	0.255970	−	28.6660i	0.0100092	−	1.12093i
$655$	0.749453	+	11.6928i	0.0292835	+	0.456874i
$656$	−2.59164	−	0.0635543i	−0.101186	−	0.00248138i
$657$	0.111610	−	19.9325i	0.00435432	−	0.777640i
$658$	9.59539	−	3.90581i	0.374067	−	0.152264i
$659$		−	15.7130i		−	0.612093i	−0.952017	−	0.306047i	$-0.900994\pi$
$659$		−	15.7130i		−	0.612093i	0.952017	−	0.306047i	$-0.0990063\pi$
$660$	25.8125	−	12.2040i	1.00475	−	0.475042i
$661$		−	25.2637i		−	0.982643i	−0.870978	−	0.491322i	$-0.836514\pi$
$661$		−	25.2637i		−	0.982643i	0.870978	−	0.491322i	$-0.163486\pi$
$662$	−4.41798	−	10.8536i	−0.171710	−	0.421839i
$663$	−4.56649	+	10.9378i	−0.177348	+	0.424788i
$664$	23.3598	−	9.17644i	0.906536	−	0.356115i
$665$	−8.75834	−	7.70323i	−0.339634	−	0.298718i
$666$	−5.44675	−	13.5986i	−0.211057	−	0.526935i
$667$	−2.83330	−	2.83330i	−0.109706	−	0.109706i
$668$	2.69854	+	0.0330830i	0.104410	+	0.00128002i
$669$	−38.1937	+	15.6952i	−1.47665	+	0.606812i
$670$	−7.21011	+	20.7235i	−0.278551	+	0.800617i
$671$		−	18.9269i		−	0.730664i
$672$	5.89773	−	5.51584i	0.227510	−	0.212778i
$673$	−15.4486	−	15.4486i	−0.595498	−	0.595498i	0.343613	−	0.939111i	$-0.388349\pi$
$673$	−15.4486	−	15.4486i	−0.595498	−	0.595498i	−0.939111	+	0.343613i	$0.888349\pi$
$674$	1.76824	−	4.19597i	0.0681099	−	0.161623i
$675$	−22.6451	+	12.7357i	−0.871612	+	0.490197i
$676$	−24.0644	−	24.6618i	−0.925554	−	0.948529i
$677$	3.86002	−	3.86002i	0.148353	−	0.148353i	−0.629029	−	0.777382i	$-0.716547\pi$
$677$	3.86002	−	3.86002i	0.148353	−	0.148353i	0.777382	+	0.629029i	$0.216547\pi$
$678$	20.8362	+	21.2117i	0.800210	+	0.814630i
$679$			6.31904i			0.242503i
$680$	3.34097	+	7.12774i	0.128120	+	0.273336i
$681$	6.73505	+	16.3895i	0.258088	+	0.628046i
$682$	−16.0333	+	6.52637i	−0.613947	+	0.249908i
$683$	−20.9584	−	20.9584i	−0.801949	−	0.801949i	0.181451	−	0.983400i	$-0.441921\pi$
$683$	−20.9584	−	20.9584i	−0.801949	−	0.801949i	−0.983400	+	0.181451i	$0.941921\pi$
$684$	37.9691	+	0.678136i	1.45178	+	0.0259292i
$685$	29.4439	−	33.4768i	1.12499	−	1.27908i
$686$	14.3074	+	6.02932i	0.546259	+	0.230201i
$687$	−15.3534	+	36.7749i	−0.585770	+	1.40305i
$688$	−3.19631	−	3.35702i	−0.121858	−	0.127985i
$689$	−43.6032			−1.66115
$690$	10.6772	−	11.9232i	0.406473	−	0.453909i
$691$			26.8902i			1.02295i	0.859298	+	0.511475i	$0.170901\pi$
$691$			26.8902i			1.02295i	−0.859298	+	0.511475i	$0.829099\pi$
$692$	5.09759	+	0.0624943i	0.193781	+	0.00237568i
$693$	9.11363	+	0.0510309i	0.346198	+	0.00193850i
$694$	−14.4761	+	34.3513i	−0.549504	+	1.30396i
$695$	1.31896	+	20.5780i	0.0500309	+	0.780569i
$696$	−4.84963	+	4.64836i	−0.183825	+	0.176196i
$697$	0.570399	−	0.570399i	0.0216054	−	0.0216054i
$698$	−23.2194	+	9.45148i	−0.878869	+	0.357744i
$699$	−4.14389	−	10.0840i	−0.156736	−	0.381412i
$700$	0.951897	+	8.18648i	0.0359783	+	0.309420i
$701$	−35.7956			−1.35198			−0.675990	−	0.736911i	$-0.736284\pi$
$701$	−35.7956			−1.35198			−0.675990	+	0.736911i	$0.736284\pi$
$702$	0.586964	−	40.3980i	0.0221535	−	1.52472i
$703$	−15.4525	−	15.4525i	−0.582804	−	0.582804i
$704$	20.0708	+	21.6041i	0.756445	+	0.814236i
$705$	−15.0946	−	30.9389i	−0.568495	−	1.16523i
$706$	−8.21566	+	19.4955i	−0.309200	+	0.733723i
$707$	5.73705	−	5.73705i	0.215764	−	0.215764i
$708$	19.7073	−	7.81748i	0.740646	−	0.293799i
$709$	31.6856			1.18998			0.594988	−	0.803735i	$-0.297157\pi$
$709$	31.6856			1.18998			0.594988	+	0.803735i	$0.297157\pi$
$710$	11.7639	−	5.69099i	0.441491	−	0.213579i
$711$	−2.34816	+	2.32201i	−0.0880628	+	0.0870821i
$712$	−17.3564	+	39.8152i	−0.650459	+	1.49214i
$713$	−6.86153	+	6.86153i	−0.256966	+	0.256966i
$714$	−0.0224359	+	2.51259i	−0.000839642	+	0.0940312i
$715$	−34.0277	−	29.9284i	−1.27256	−	1.11926i
$716$	−33.5456	−	34.3784i	−1.25366	−	1.28478i
$717$	−2.69238	+	6.44887i	−0.100549	+	0.240837i
$718$	−32.3883	+	13.1837i	−1.20872	+	0.492010i
$719$	−47.9558			−1.78845			−0.894225	−	0.447618i	$-0.852272\pi$
$719$	−47.9558			−1.78845			−0.894225	+	0.447618i	$0.852272\pi$
$720$	−19.6057	−	18.3199i	−0.730660	−	0.682741i
$721$	−9.65184			−0.359453
$722$	27.5837	−	11.2280i	1.02656	−	0.417861i
$723$	7.64809	−	18.3189i	0.284435	−	0.681287i
$724$	−30.3392	−	31.0923i	−1.12755	−	1.15554i
$725$	−0.875297	−	6.80002i	−0.0325077	−	0.252546i
$726$	−0.0565836	+	6.33678i	−0.00210002	+	0.235180i
$727$	20.8052	−	20.8052i	0.771622	−	0.771622i	−0.206768	−	0.978390i	$-0.566295\pi$
$727$	20.8052	−	20.8052i	0.771622	−	0.771622i	0.978390	+	0.206768i	$0.0662946\pi$
$728$	−11.7487	−	5.12153i	−0.435435	−	0.189817i
$729$	19.4099	−	18.7685i	0.718884	−	0.695130i
$730$	−6.90421	+	19.8443i	−0.255536	+	0.734469i
$731$	1.44234			0.0533468
$732$	−16.5338	+	6.55862i	−0.611108	+	0.242414i
$733$	−11.3990	+	11.3990i	−0.421033	+	0.421033i	−0.885559	−	0.464526i	$-0.846225\pi$
$733$	−11.3990	+	11.3990i	−0.421033	+	0.421033i	0.464526	+	0.885559i	$0.346225\pi$
$734$	7.25237	−	17.2096i	0.267690	−	0.635219i
$735$	7.96715	−	23.1474i	0.293873	−	0.853806i
$736$	15.0708	+	6.79077i	0.555516	+	0.250311i
$737$	−18.0852	−	18.0852i	−0.666176	−	0.666176i
$738$	−1.08198	+	2.52785i	−0.0398281	+	0.0930514i
$739$	−9.60683			−0.353393			−0.176697	−	0.984265i	$-0.556541\pi$
$739$	−9.60683			−0.353393			−0.176697	+	0.984265i	$0.556541\pi$
$740$	0.798711	+	15.4206i	0.0293612	+	0.566871i
$741$	−22.9092	−	55.7487i	−0.841591	−	2.04798i
$742$	−8.56143	+	3.48493i	−0.314300	+	0.127936i
$743$	2.71436	−	2.71436i	0.0995802	−	0.0995802i	−0.655562	−	0.755142i	$-0.727568\pi$
$743$	2.71436	−	2.71436i	0.0995802	−	0.0995802i	0.755142	+	0.655562i	$0.227568\pi$
$744$	11.2571	+	11.7446i	0.412706	+	0.430577i
$745$	−31.2530	+	2.00318i	−1.14502	+	0.0733907i
$746$	−9.24445	+	21.9368i	−0.338463	+	0.803163i
$747$	0.149054	−	26.6196i	0.00545359	−	0.973958i
$748$	−9.17508	−	0.112483i	−0.335474	−	0.00411277i
$749$			6.81468i			0.249003i
$750$	26.9284	−	4.98628i	0.983285	−	0.182073i
$751$	−18.9690			−0.692189			−0.346094	−	0.938200i	$-0.612492\pi$
$751$	−18.9690			−0.692189			−0.346094	+	0.938200i	$0.612492\pi$
$752$	25.7491	−	24.5164i	0.938972	−	0.894022i
$753$	11.6648	−	27.9397i	0.425087	−	1.01818i
$754$	9.82507	+	4.14041i	0.357808	+	0.150785i
$755$	1.87797	+	29.2996i	0.0683464	+	1.06632i
$756$	−3.11352	−	7.97901i	−0.113237	−	0.290194i
$757$	−0.279592	−	0.279592i	−0.0101620	−	0.0101620i	0.702008	−	0.712170i	$-0.252287\pi$
$757$	−0.279592	−	0.279592i	−0.0101620	−	0.0101620i	−0.712170	+	0.702008i	$0.752287\pi$
$758$	−3.58037	+	1.45739i	−0.130045	+	0.0529349i
$759$	7.09113	+	17.2560i	0.257392	+	0.626353i
$760$	−37.6423	−	13.6161i	−1.36543	−	0.493907i
$761$		−	20.3237i		−	0.736733i	−0.929681	−	0.368366i	$-0.879917\pi$
$761$		−	20.3237i		−	0.736733i	0.929681	−	0.368366i	$-0.120083\pi$
$762$	−0.0355534	−	0.0361941i	−0.00128797	−	0.00131117i
$763$	−6.82036	+	6.82036i	−0.246914	+	0.246914i
$764$	−18.1355	−	18.5857i	−0.656118	−	0.672406i
$765$	8.33517	−	0.487399i	0.301359	−	0.0176220i
$766$	13.6746	−	32.4494i	0.494083	−	1.17244i
$767$	−23.7938	−	23.7938i	−0.859144	−	0.859144i
$768$	11.9176	−	25.0194i	0.430038	−	0.902811i
$769$			25.1716i			0.907711i	0.891075	+	0.453855i	$0.149952\pi$
$769$			25.1716i			0.907711i	−0.891075	+	0.453855i	$0.850048\pi$
$770$	−9.07329	−	3.15678i	−0.326979	−	0.113762i
$771$	−15.3448	+	6.30577i	−0.552631	+	0.227097i
$772$	26.8293	+	0.328916i	0.965607	+	0.0118379i
$773$	24.0474	+	24.0474i	0.864925	+	0.864925i	0.991905	−	0.126980i	$-0.0405284\pi$
$773$	24.0474	+	24.0474i	0.864925	+	0.864925i	−0.126980	+	0.991905i	$0.540528\pi$
$774$	−4.56398	+	1.82805i	−0.164049	+	0.0657079i
$775$	−16.4679	+	2.11974i	−0.591545	+	0.0761434i
$776$	7.92913	+	20.1846i	0.284639	+	0.724585i
$777$	−1.89891	+	4.54832i	−0.0681231	+	0.163170i
$778$	13.4006	+	32.9213i	0.480436	+	1.18029i
$779$			4.10197i			0.146968i
$780$	−14.3529	+	40.0963i	−0.513917	+	1.43568i
$781$			15.2327i			0.545070i
$782$	−4.76400	+	1.93919i	−0.170360	+	0.0693453i
$783$	2.67127	+	6.60539i	0.0954634	+	0.236058i
$784$	25.2754	+	0.619825i	0.902693	+	0.0221366i
$785$	−13.3022	+	15.1242i	−0.474774	+	0.539804i
$786$	−0.114605	+	12.8345i	−0.00408782	+	0.457793i
$787$	−6.79695	−	6.79695i	−0.242285	−	0.242285i	0.575510	−	0.817795i	$-0.304804\pi$
$787$	−6.79695	−	6.79695i	−0.242285	−	0.242285i	−0.817795	+	0.575510i	$0.804804\pi$
$788$	0.445912	−	36.3725i	0.0158850	−	1.29572i
$789$	14.3108	+	34.8249i	0.509479	+	1.23980i
$790$	3.13357	−	1.51592i	0.111488	−	0.0539341i
$791$		−	10.0043i		−	0.355710i
$792$	29.1752	−	11.2728i	1.03670	−	0.400560i
$793$	19.9623	+	19.9623i	0.708881	+	0.708881i
$794$	10.0015	+	4.21476i	0.354939	+	0.149576i
$795$	13.4681	+	27.6051i	0.477663	+	0.979052i
$796$	0.0647578	+	0.0663654i	0.00229528	+	0.00235226i
$797$	6.72322	−	6.72322i	0.238149	−	0.238149i	−0.577935	−	0.816083i	$-0.696141\pi$
$797$	6.72322	−	6.72322i	0.238149	−	0.238149i	0.816083	+	0.577935i	$0.196141\pi$
$798$	−8.95384	−	9.11519i	−0.316963	−	0.322674i
$799$			11.0630i			0.391382i
$800$	13.3130	+	24.9552i	0.470685	+	0.882301i
$801$	32.3924	+	32.7572i	1.14453	+	1.15742i
$802$	2.75030	+	6.75665i	0.0971164	+	0.238585i
$803$	−17.3179	−	17.3179i	−0.611135	−	0.611135i
$804$	−9.53159	+	22.0655i	−0.336153	+	0.778190i
$805$	−5.37412	+	0.344457i	−0.189413	+	0.0121405i
$806$	10.0270	−	23.7938i	0.353187	−	0.838101i
$807$	−15.3259	−	6.39851i	−0.539496	−	0.225238i
$808$	11.1267	−	25.5244i	0.391437	−	0.897946i
$809$	35.3381			1.24242			0.621212	−	0.783643i	$-0.286641\pi$
$809$	35.3381			1.24242			0.621212	+	0.783643i	$0.286641\pi$
$810$	−25.7572	+	12.1065i	−0.905016	+	0.425377i
$811$			37.1596i			1.30485i	0.757854	+	0.652425i	$0.226248\pi$
$811$			37.1596i			1.30485i	−0.757854	+	0.652425i	$0.773752\pi$
$812$	2.26006	+	0.0277074i	0.0793125	+	0.000972338i
$813$	13.9519	−	33.4179i	0.489314	−	1.17202i
$814$	−16.5863	−	6.98967i	−0.581348	−	0.244988i
$815$	8.21613	+	7.22634i	0.287798	+	0.253128i
$816$	3.08113	+	8.05399i	0.107861	+	0.281946i
$817$	−5.18621	+	5.18621i	−0.181443	+	0.181443i
$818$	7.55184	+	18.5526i	0.264044	+	0.648676i
$819$	−9.66601	+	9.55836i	−0.337758	+	0.333996i
$820$	1.94073	−	2.15275i	0.0677732	−	0.0751774i
$821$	28.5674			0.997010			0.498505	−	0.866887i	$-0.333882\pi$
$821$	28.5674			0.997010			0.498505	+	0.866887i	$0.333882\pi$
$822$	34.8408	−	34.2241i	1.21521	−	1.19370i
$823$	−28.5682	−	28.5682i	−0.995823	−	0.995823i	0.00416817	−	0.999991i	$-0.498673\pi$
$823$	−28.5682	−	28.5682i	−0.995823	−	0.995823i	−0.999991	+	0.00416817i	$0.998673\pi$
$824$	−30.8304	+	12.1111i	−1.07403	+	0.421911i
$825$	−8.43721	+	30.7871i	−0.293746	+	1.07187i
$826$	−6.57357	−	2.77019i	−0.228724	−	0.0963872i
$827$	−5.31276	+	5.31276i	−0.184743	+	0.184743i	−0.793419	−	0.608676i	$-0.791701\pi$
$827$	−5.31276	+	5.31276i	−0.184743	+	0.184743i	0.608676	+	0.793419i	$0.291701\pi$
$828$	12.6170	−	12.1742i	0.438469	−	0.423082i
$829$	−4.51176			−0.156700			−0.0783500	−	0.996926i	$-0.524965\pi$
$829$	−4.51176			−0.156700			−0.0783500	+	0.996926i	$0.524965\pi$
$830$	−9.22048	+	26.5017i	−0.320048	+	0.919888i
$831$	20.0813	−	8.25214i	0.696611	−	0.286263i
$832$	−43.9547	−	1.61725i	−1.52385	−	0.0560679i
$833$	−5.56292	+	5.56292i	−0.192744	+	0.192744i
$834$	−0.201692	+	22.5875i	−0.00698403	+	0.782140i
$835$	−1.99271	+	2.26565i	−0.0689605	+	0.0784060i
$836$	33.3953	−	32.5864i	1.15500	−	1.12702i
$837$	15.9966	−	6.46913i	0.552922	−	0.223606i
$838$	2.56199	+	6.29404i	0.0885025	+	0.217424i
$839$	42.7255			1.47505			0.737523	−	0.675322i	$-0.235995\pi$
$839$	42.7255			1.47505			0.737523	+	0.675322i	$0.235995\pi$
$840$	0.386470	+	9.01999i	0.0133345	+	0.311219i
$841$	27.1197			0.935164
$842$	8.11428	+	19.9343i	0.279637	+	0.686983i
$843$	19.4877	+	8.13608i	0.671193	+	0.280221i
$844$	−0.825584	−	0.846078i	−0.0284178	−	0.0291232i
$845$	38.4454	−	2.46418i	1.32256	−	0.0847702i
$846$	−14.0215	−	35.0068i	−0.482071	−	1.20356i
$847$	1.50768	−	1.50768i	0.0518045	−	0.0518045i
$848$	−22.9745	+	21.8746i	−0.788946	+	0.751178i
$849$	−10.8744	−	26.4625i	−0.373210	−	0.908192i
$850$	−8.48028	−	2.35441i	−0.290871	−	0.0807556i
$851$	−10.0894			−0.345861
$852$	13.3067	−	5.27851i	0.455881	−	0.180839i
$853$	−28.1027	+	28.1027i	−0.962217	+	0.962217i	−0.999312	−	0.0370946i	$-0.988190\pi$
$853$	−28.1027	+	28.1027i	−0.962217	+	0.962217i	0.0370946	+	0.999312i	$0.488190\pi$
$854$	5.51503	+	2.32410i	0.188720	+	0.0795292i
$855$	−28.2182	+	31.7233i	−0.965043	+	1.08491i
$856$	8.55106	+	21.7678i	0.292269	+	0.744008i
$857$	35.8406	+	35.8406i	1.22429	+	1.22429i	0.966092	+	0.258198i	$0.0831287\pi$
$857$	35.8406	+	35.8406i	1.22429	+	1.22429i	0.258198	+	0.966092i	$0.416871\pi$
$858$	−34.7872	−	35.4141i	−1.18762	−	1.20902i
$859$	−1.55128			−0.0529289			−0.0264645	−	0.999650i	$-0.508425\pi$
$859$	−1.55128			−0.0529289			−0.0264645	+	0.999650i	$0.508425\pi$
$860$	5.17548	−	0.268065i	0.176482	−	0.00914094i
$861$	0.855728	−	0.351651i	0.0291631	−	0.0119842i
$862$	14.8629	+	36.5136i	0.506231	+	1.24366i
$863$	22.7893	−	22.7893i	0.775758	−	0.775758i	−0.203348	−	0.979107i	$-0.565182\pi$
$863$	22.7893	−	22.7893i	0.775758	−	0.775758i	0.979107	+	0.203348i	$0.0651823\pi$
$864$	−19.9574	−	21.5801i	−0.678965	−	0.734171i
$865$	−3.76425	+	4.27984i	−0.127988	+	0.145519i
$866$	−5.12369	−	2.15919i	−0.174110	−	0.0733723i
$867$	24.6957	+	10.3104i	0.838712	+	0.350160i
$868$	0.0671001	−	5.47328i	0.00227753	−	0.185775i
$869$			4.05757i			0.137644i
$870$	−0.413460	−	7.49912i	−0.0140176	−	0.254244i
$871$	38.1490			1.29263
$872$	−13.2278	+	30.3441i	−0.447948	+	1.02758i
$873$	23.0013	+	0.128793i	0.778476	+	0.00435900i
$874$	10.1572	−	24.1027i	0.343572	−	0.815285i
$875$	−7.63931	−	5.15236i	−0.258256	−	0.174182i
$876$	−9.12720	+	21.1293i	−0.308379	+	0.713894i
$877$	22.8089	+	22.8089i	0.770202	+	0.770202i	0.978142	−	0.207940i	$-0.0666758\pi$
$877$	22.8089	+	22.8089i	0.770202	+	0.770202i	−0.207940	+	0.978142i	$0.566676\pi$
$878$	5.76759	+	14.1692i	0.194647	+	0.478188i
$879$	11.7005	−	4.80819i	0.394649	−	0.162176i
$880$	−32.9435	+	1.30161i	−1.11052	+	0.0438774i
$881$		−	1.47551i		−	0.0497114i	−0.999691	−	0.0248557i	$-0.992087\pi$
$881$		−	1.47551i		−	0.0497114i	0.999691	−	0.0248557i	$-0.00791262\pi$
$882$	10.5522	−	24.6533i	0.355310	−	0.830121i
$883$	−3.02812	+	3.02812i	−0.101904	+	0.101904i	−0.756221	−	0.654316i	$-0.772956\pi$
$883$	−3.02812	+	3.02812i	−0.101904	+	0.101904i	0.654316	+	0.756221i	$0.272956\pi$
$884$	9.79563	−	9.55836i	0.329463	−	0.321482i
$885$	−7.71443	+	22.4132i	−0.259318	+	0.753411i
$886$	10.5968	+	4.46561i	0.356005	+	0.150025i
$887$	19.9170	+	19.9170i	0.668749	+	0.668749i	0.957426	−	0.288678i	$-0.0932156\pi$
$887$	19.9170	+	19.9170i	0.668749	+	0.668749i	−0.288678	+	0.957426i	$0.593216\pi$
$888$	−0.358371	+	16.9112i	−0.0120261	+	0.567504i
$889$			0.0170705i			0.000572528i
$890$	−21.1474	−	43.7139i	−0.708861	−	1.46529i
$891$	0.371504	−	33.1725i	0.0124459	−	1.11132i
$892$	47.6773	+	0.584504i	1.59635	+	0.0195706i
$893$	−39.7794	−	39.7794i	−1.33117	−	1.33117i
$894$	−34.3048	−	0.306321i	−1.14733	−	0.0102449i
$895$	53.5927	−	3.43505i	1.79141	−	0.114821i
$896$	−8.75970	+	3.19548i	−0.292641	+	0.106754i
$897$	−25.6790	−	10.7209i	−0.857398	−	0.357961i
$898$	9.05349	−	3.68523i	0.302119	−	0.122978i
$899$			4.55350i			0.151868i
$900$	29.8182	−	3.29804i	0.993939	−	0.109935i
$901$		−	9.87094i		−	0.328849i
$902$	1.27374	+	3.12918i	0.0424108	+	0.104190i
$903$	1.52652	+	0.637317i	0.0507993	+	0.0212086i
$904$	−12.5533	−	31.9561i	−0.417518	−	1.06284i
$905$	48.4701	−	3.10671i	1.61120	−	0.103271i
$906$	−0.287176	+	32.1607i	−0.00954077	+	1.06847i
$907$	6.11318	+	6.11318i	0.202985	+	0.202985i	0.801278	−	0.598293i	$-0.204154\pi$
$907$	6.11318	+	6.11318i	0.202985	+	0.202985i	−0.598293	+	0.801278i	$0.704154\pi$
$908$	0.250819	−	20.4590i	0.00832372	−	0.678956i
$909$	−20.7659	−	20.9998i	−0.688762	−	0.696518i
$910$	12.8991	−	6.24017i	0.427601	−	0.206860i
$911$			28.1492i			0.932625i	0.884620	+	0.466313i	$0.154418\pi$
$911$			28.1492i			0.932625i	−0.884620	+	0.466313i	$0.845582\pi$
$912$	−40.0385	−	17.8809i	−1.32581	−	0.592096i
$913$	−23.1278	−	23.1278i	−0.765419	−	0.765419i
$914$	−4.00570	+	9.50541i	−0.132497	+	0.314411i
$915$	6.47217	−	18.8040i	0.213963	−	0.621640i
$916$	32.9349	−	32.1371i	1.08820	−	1.06184i
$917$	3.05366	−	3.05366i	0.100841	−	0.100841i
$918$	9.14535	+	0.132878i	0.301842	+	0.00438561i
$919$		−	49.4285i		−	1.63049i	−0.579113	−	0.815247i	$-0.696601\pi$
$919$		−	49.4285i		−	1.63049i	0.579113	−	0.815247i	$-0.303399\pi$
$920$	−16.7341	+	7.84373i	−0.551706	+	0.258600i
$921$	−20.8400	+	8.56393i	−0.686701	+	0.282191i
$922$	24.1740	−	9.84005i	0.796129	−	0.324065i
$923$	−16.0660	−	16.0660i	−0.528819	−	0.528819i
$924$	−9.66086	−	4.17318i	−0.317819	−	0.137288i
$925$	−13.6660	−	10.5490i	−0.449334	−	0.346849i
$926$	−36.2892	−	15.2927i	−1.19254	−	0.502550i
$927$	−0.196722	+	35.1327i	−0.00646120	+	1.15391i
$928$	7.25396	−	2.74741i	0.238123	−	0.0901883i
$929$	−38.9204			−1.27694			−0.638468	−	0.769649i	$-0.720431\pi$
$929$	−38.9204			−1.27694			−0.638468	+	0.769649i	$0.720431\pi$
$930$	−18.1609	+	1.00129i	−0.595521	+	0.0328337i
$931$		−	40.0052i		−	1.31112i
$932$	−0.154322	+	12.5879i	−0.00505499	+	0.412329i
$933$	−48.8598	−	20.3988i	−1.59960	−	0.667828i
$934$	1.61507	−	3.83251i	0.0528466	−	0.125403i
$935$	6.77522	−	7.70323i	0.221574	−	0.251922i
$936$	−18.8818	+	42.6607i	−0.617172	+	1.39441i
$937$	−4.49303	+	4.49303i	−0.146781	+	0.146781i	−0.776678	−	0.629897i	$-0.783097\pi$
$937$	−4.49303	+	4.49303i	−0.146781	+	0.146781i	0.629897	+	0.776678i	$0.283097\pi$
$938$	7.49052	−	3.04902i	0.244574	−	0.0995540i
$939$	37.2952	−	15.3260i	1.21708	−	0.500145i
$940$	2.05612	+	39.6971i	0.0670632	+	1.29478i
$941$	−23.2736			−0.758696			−0.379348	−	0.925254i	$-0.623852\pi$
$941$	−23.2736			−0.758696			−0.379348	+	0.925254i	$0.623852\pi$
$942$	−15.7404	+	15.4618i	−0.512849	+	0.503771i
$943$	1.33915	+	1.33915i	0.0436087	+	0.0436087i
$944$	−24.4737	−	0.600164i	−0.796550	−	0.0195337i
$945$	9.03700	+	3.16716i	0.293974	+	0.103028i
$946$	−2.34589	+	5.56671i	−0.0762713	+	0.180989i
$947$	28.1797	−	28.1797i	0.915717	−	0.915717i	−0.0809978	−	0.996714i	$-0.525811\pi$
$947$	28.1797	−	28.1797i	0.915717	−	0.915717i	0.996714	+	0.0809978i	$0.0258107\pi$
$948$	3.54454	−	1.40605i	0.115121	−	0.0456663i
$949$	36.5305			1.18583
$950$	38.9583	−	22.0268i	1.26397	−	0.714644i
$951$	−0.000574173	−	0.00139723i	−1.86188e−5	−	4.53082e-5i
$952$	1.15942	−	2.65968i	0.0375770	−	0.0862006i
$953$	28.5653	−	28.5653i	0.925321	−	0.925321i	−0.0720776	−	0.997399i	$-0.522963\pi$
$953$	28.5653	−	28.5653i	0.925321	−	0.925321i	0.997399	+	0.0720776i	$0.0229629\pi$
$954$	12.5106	+	31.2346i	0.405047	+	1.01126i
$955$	28.9733	−	1.85706i	0.937555	−	0.0600930i
$956$	5.77547	−	5.63557i	0.186792	−	0.182267i
$957$	8.07871	+	3.37284i	0.261148	+	0.109028i
$958$	25.8157	−	10.5083i	0.834066	−	0.339507i
$959$	−16.4323			−0.530625
$960$	12.5528	+	28.3272i	0.405139	+	0.914255i
$961$	−19.9726			−0.644277
$962$	24.8656	−	10.1216i	0.801700	−	0.326332i
$963$	24.8054	+	0.138895i	0.799343	+	0.00447584i
$964$	−16.4060	+	16.0086i	−0.528402	+	0.515603i
$965$	−19.8118	+	22.5254i	−0.637763	+	0.725118i
$966$	−5.89890	−	0.0526736i	−0.189794	−	0.00169475i
$967$	−37.0606	+	37.0606i	−1.19179	+	1.19179i	−0.215225	+	0.976565i	$0.569048\pi$
$967$	−37.0606	+	37.0606i	−1.19179	+	1.19179i	−0.976565	+	0.215225i	$0.930952\pi$
$968$	2.92407	−	6.70774i	0.0939832	−	0.215595i
$969$	12.6204	−	5.18621i	0.405427	−	0.166605i
$970$	−22.8995	−	7.96719i	−0.735258	−	0.255811i
$971$	11.8114			0.379044			0.189522	−	0.981876i	$-0.439306\pi$
$971$	11.8114			0.379044			0.189522	+	0.981876i	$0.439306\pi$
$972$	−29.1070	+	11.1706i	−0.933608	+	0.358296i
$973$	5.37412	−	5.37412i	0.172287	−	0.172287i
$974$	3.27288	−	7.76644i	0.104870	−	0.248853i
$975$	−23.5725	−	41.3700i	−0.754925	−	1.32490i
$976$	20.5327	+	0.503519i	0.657234	+	0.0161173i
$977$	−5.34002	−	5.34002i	−0.170842	−	0.170842i	0.616507	−	0.787349i	$-0.288547\pi$
$977$	−5.34002	−	5.34002i	−0.170842	−	0.170842i	−0.787349	+	0.616507i	$0.788547\pi$
$978$	8.39953	+	8.55088i	0.268587	+	0.273427i
$979$	56.6038			1.80907
$980$	−18.9273	+	20.9951i	−0.604611	+	0.670664i
$981$	24.6871	+	24.9651i	0.788197	+	0.797074i
$982$	−36.3111	+	14.7805i	−1.15874	+	0.471664i
$983$	−42.6490	+	42.6490i	−1.36029	+	1.36029i	−0.486753	+	0.873540i	$0.661819\pi$
$983$	−42.6490	+	42.6490i	−1.36029	+	1.36029i	−0.873540	+	0.486753i	$0.838181\pi$
$984$	2.29216	−	2.19703i	0.0730714	−	0.0700387i
$985$	30.5377	+	26.8589i	0.973013	+	0.855795i
$986$	−0.937311	+	2.22421i	−0.0298501	+	0.0708333i
$987$	−4.88836	+	11.7087i	−0.155598	+	0.372693i
$988$	−0.853159	+	69.5912i	−0.0271426	+	2.21399i
$989$			3.38623i			0.107676i
$990$	−11.6756	+	32.9624i	−0.371075	+	1.04761i
$991$	−31.5197			−1.00126			−0.500629	−	0.865662i	$-0.666898\pi$
$991$	−31.5197			−1.00126			−0.500629	+	0.865662i	$0.666898\pi$
$992$	−6.65353	−	17.5672i	−0.211250	−	0.557760i
$993$	13.2441	+	5.52938i	0.420289	+	0.175469i
$994$	−4.43860	−	1.87048i	−0.140784	−	0.0593282i
$995$	−0.103457	+	0.00663115i	−0.00327982	+	0.000210222i
$996$	−12.1892	+	28.2179i	−0.386231	+	0.894120i
$997$	−38.3474	−	38.3474i	−1.21447	−	1.21447i	−0.969540	−	0.244935i	$-0.921233\pi$
$997$	−38.3474	−	38.3474i	−1.21447	−	1.21447i	−0.244935	−	0.969540i	$-0.578767\pi$
$998$	−6.74190	+	2.74429i	−0.213411	+	0.0868690i
$999$	16.5172	+	7.00473i	0.522580	+	0.221620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.2.w.c.53.14	yes	32
3.2	odd	2	inner	120.2.w.c.53.3	✓	32
4.3	odd	2		480.2.bi.c.113.11		32
5.2	odd	4	inner	120.2.w.c.77.11	yes	32
5.3	odd	4		600.2.w.j.557.6		32
5.4	even	2		600.2.w.j.293.3		32
8.3	odd	2		480.2.bi.c.113.6		32
8.5	even	2	inner	120.2.w.c.53.6	yes	32
12.11	even	2		480.2.bi.c.113.14		32
15.2	even	4	inner	120.2.w.c.77.6	yes	32
15.8	even	4		600.2.w.j.557.11		32
15.14	odd	2		600.2.w.j.293.14		32
20.7	even	4		480.2.bi.c.17.3		32
24.5	odd	2	inner	120.2.w.c.53.11	yes	32
24.11	even	2		480.2.bi.c.113.3		32
40.13	odd	4		600.2.w.j.557.14		32
40.27	even	4		480.2.bi.c.17.14		32
40.29	even	2		600.2.w.j.293.11		32
40.37	odd	4	inner	120.2.w.c.77.3	yes	32
60.47	odd	4		480.2.bi.c.17.6		32
120.29	odd	2		600.2.w.j.293.6		32
120.53	even	4		600.2.w.j.557.3		32
120.77	even	4	inner	120.2.w.c.77.14	yes	32
120.107	odd	4		480.2.bi.c.17.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.w.c.53.3	✓	32	3.2	odd	2	inner
120.2.w.c.53.6	yes	32	8.5	even	2	inner
120.2.w.c.53.11	yes	32	24.5	odd	2	inner
120.2.w.c.53.14	yes	32	1.1	even	1	trivial
120.2.w.c.77.3	yes	32	40.37	odd	4	inner
120.2.w.c.77.6	yes	32	15.2	even	4	inner
120.2.w.c.77.11	yes	32	5.2	odd	4	inner
120.2.w.c.77.14	yes	32	120.77	even	4	inner
480.2.bi.c.17.3		32	20.7	even	4
480.2.bi.c.17.6		32	60.47	odd	4
480.2.bi.c.17.11		32	120.107	odd	4
480.2.bi.c.17.14		32	40.27	even	4
480.2.bi.c.113.3		32	24.11	even	2
480.2.bi.c.113.6		32	8.3	odd	2
480.2.bi.c.113.11		32	4.3	odd	2
480.2.bi.c.113.14		32	12.11	even	2
600.2.w.j.293.3		32	5.4	even	2
600.2.w.j.293.6		32	120.29	odd	2
600.2.w.j.293.11		32	40.29	even	2
600.2.w.j.293.14		32	15.14	odd	2
600.2.w.j.557.3		32	120.53	even	4
600.2.w.j.557.6		32	5.3	odd	4
600.2.w.j.557.11		32	15.8	even	4
600.2.w.j.557.14		32	40.13	odd	4

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	120.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30986 - 0.533177i) q^{2} +(-0.667305 + 1.59834i) q^{3} +(1.43144 - 1.39677i) q^{4} +(0.143028 + 2.23149i) q^{5} +(-0.0218716 + 2.44939i) q^{6} +(0.582772 - 0.582772i) q^{7} +(1.13026 - 2.59278i) q^{8} +(-2.10941 - 2.13317i) q^{9} +O(q^{10})\)	\(q+(1.30986 - 0.533177i) q^{2} +(-0.667305 + 1.59834i) q^{3} +(1.43144 - 1.39677i) q^{4} +(0.143028 + 2.23149i) q^{5} +(-0.0218716 + 2.44939i) q^{6} +(0.582772 - 0.582772i) q^{7} +(1.13026 - 2.59278i) q^{8} +(-2.10941 - 2.13317i) q^{9} +(1.37713 + 2.84667i) q^{10} -3.68607 q^{11} +(1.27731 + 3.22001i) q^{12} +(3.88771 - 3.88771i) q^{13} +(0.452626 - 1.07407i) q^{14} +(-3.66213 - 1.26047i) q^{15} +(0.0980619 - 3.99880i) q^{16} +(0.880105 + 0.880105i) q^{17} +(-3.90038 - 1.66945i) q^{18} -6.32919 q^{19} +(3.32162 + 2.99447i) q^{20} +(0.542584 + 1.32036i) q^{21} +(-4.82821 + 1.96533i) q^{22} +(-2.06626 + 2.06626i) q^{23} +(3.38993 + 3.53672i) q^{24} +(-4.95909 + 0.638332i) q^{25} +(3.01950 - 7.16518i) q^{26} +(4.81715 - 1.94809i) q^{27} +(0.0202063 - 1.64820i) q^{28} +1.37122i q^{29} +(-5.46892 + 0.301526i) q^{30} +3.32075 q^{31} +(-2.00362 - 5.29013i) q^{32} +(2.45973 - 5.89160i) q^{33} +(1.62206 + 0.683558i) q^{34} +(1.38380 + 1.21710i) q^{35} +(-5.99904 - 0.107144i) q^{36} +(2.44147 + 2.44147i) q^{37} +(-8.29032 + 3.37458i) q^{38} +(3.61961 + 8.80819i) q^{39} +(5.94742 + 2.15132i) q^{40} -0.648104i q^{41} +(1.41469 + 1.44018i) q^{42} +(0.819412 - 0.819412i) q^{43} +(-5.27640 + 5.14859i) q^{44} +(4.45843 - 5.01223i) q^{45} +(-1.60482 + 3.80818i) q^{46} +(6.28508 + 6.28508i) q^{47} +(6.32602 + 2.82515i) q^{48} +6.32075i q^{49} +(-6.15534 + 3.48020i) q^{50} +(-1.99401 + 0.819412i) q^{51} +(0.134798 - 10.9953i) q^{52} +(-5.60782 - 5.60782i) q^{53} +(5.27109 - 5.12011i) q^{54} +(-0.527212 - 8.22542i) q^{55} +(-0.852318 - 2.16968i) q^{56} +(4.22349 - 10.1162i) q^{57} +(0.731106 + 1.79611i) q^{58} -6.12026i q^{59} +(-7.00273 + 3.31086i) q^{60} +5.13471i q^{61} +(4.34971 - 1.77055i) q^{62} +(-2.47245 - 0.0138443i) q^{63} +(-5.44503 - 5.86102i) q^{64} +(9.23144 + 8.11933i) q^{65} +(0.0806201 - 9.02862i) q^{66} +(4.90636 + 4.90636i) q^{67} +(2.48912 + 0.0305156i) q^{68} +(-1.92377 - 4.68141i) q^{69} +(2.46151 + 0.856408i) q^{70} -4.13251i q^{71} +(-7.91501 + 3.05821i) q^{72} +(4.69820 + 4.69820i) q^{73} +(4.49972 + 1.89624i) q^{74} +(2.28895 - 8.35229i) q^{75} +(-9.05987 + 8.84042i) q^{76} +(-2.14814 + 2.14814i) q^{77} +(9.43750 + 9.60756i) q^{78} -1.10079i q^{79} +(8.93730 - 0.353117i) q^{80} +(-0.100786 + 8.99944i) q^{81} +(-0.345554 - 0.848922i) q^{82} +(6.27439 + 6.27439i) q^{83} +(2.62091 + 1.13215i) q^{84} +(-1.83806 + 2.08982i) q^{85} +(0.636420 - 1.51020i) q^{86} +(-2.19169 - 0.915024i) q^{87} +(-4.16621 + 9.55717i) q^{88} -15.3562 q^{89} +(3.16749 - 8.94243i) q^{90} -4.53130i q^{91} +(-0.0716428 + 5.84382i) q^{92} +(-2.21595 + 5.30771i) q^{93} +(11.5836 + 4.88148i) q^{94} +(-0.905253 - 14.1235i) q^{95} +(9.79248 + 0.327652i) q^{96} +(-5.42154 + 5.42154i) q^{97} +(3.37008 + 8.27927i) q^{98} +(7.77542 + 7.86299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{6}+O(q^{10}) \) 32 * q - 4 * q^6	\( 32 q - 4 q^{6} + 4 q^{10} - 8 q^{12} - 28 q^{15} + 28 q^{16} - 20 q^{18} - 52 q^{22} - 8 q^{25} + 12 q^{28} - 32 q^{30} - 32 q^{31} + 8 q^{33} - 20 q^{36} + 24 q^{40} + 16 q^{42} + 24 q^{46} + 44 q^{48} + 8 q^{52} + 8 q^{55} - 16 q^{57} + 28 q^{58} + 56 q^{60} + 48 q^{63} + 16 q^{66} + 20 q^{70} + 32 q^{72} - 64 q^{73} - 88 q^{76} + 64 q^{78} + 48 q^{81} + 64 q^{82} - 8 q^{87} - 52 q^{88} + 84 q^{90} - 52 q^{96} + 16 q^{97}+O(q^{100}) \) 32 * q - 4 * q^6 + 4 * q^10 - 8 * q^12 - 28 * q^15 + 28 * q^16 - 20 * q^18 - 52 * q^22 - 8 * q^25 + 12 * q^28 - 32 * q^30 - 32 * q^31 + 8 * q^33 - 20 * q^36 + 24 * q^40 + 16 * q^42 + 24 * q^46 + 44 * q^48 + 8 * q^52 + 8 * q^55 - 16 * q^57 + 28 * q^58 + 56 * q^60 + 48 * q^63 + 16 * q^66 + 20 * q^70 + 32 * q^72 - 64 * q^73 - 88 * q^76 + 64 * q^78 + 48 * q^81 + 64 * q^82 - 8 * q^87 - 52 * q^88 + 84 * q^90 - 52 * q^96 + 16 * q^97

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