LMFDB - Embedded newform 240.2.bl.a.109.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(109,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("240.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bl (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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.5
Character	$\chi$	$=$	240.109
Dual form			240.2.bl.a.229.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20386 + 0.742113i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.898535 - 1.78679i) q^{4} +(-2.06370 - 0.860885i) q^{5} +(0.326501 - 1.37601i) q^{6} +0.707398 q^{7} +(0.244298 + 2.81786i) q^{8} -1.00000i q^{9} +(3.12328 - 0.495122i) q^{10} +(1.79993 - 1.79993i) q^{11} +(0.628094 + 1.89881i) q^{12} +(3.86348 - 3.86348i) q^{13} +(-0.851604 + 0.524969i) q^{14} +(2.06800 - 0.850522i) q^{15} +(-2.38527 - 3.21100i) q^{16} -0.244884i q^{17} +(0.742113 + 1.20386i) q^{18} +(1.53863 + 1.53863i) q^{19} +(-3.39254 + 2.91388i) q^{20} +(-0.500206 + 0.500206i) q^{21} +(-0.831102 + 3.50260i) q^{22} +6.92280 q^{23} +(-2.16527 - 1.81978i) q^{24} +(3.51775 + 3.55323i) q^{25} +(-1.78393 + 7.51820i) q^{26} +(0.707107 + 0.707107i) q^{27} +(0.635622 - 1.26397i) q^{28} +(-4.89882 - 4.89882i) q^{29} +(-1.85839 + 2.55859i) q^{30} +7.60734 q^{31} +(5.25444 + 2.09543i) q^{32} +2.54548i q^{33} +(0.181732 + 0.294805i) q^{34} +(-1.45986 - 0.608988i) q^{35} +(-1.78679 - 0.898535i) q^{36} +(-8.47863 - 8.47863i) q^{37} +(-2.99413 - 0.710450i) q^{38} +5.46378i q^{39} +(1.92169 - 6.02554i) q^{40} +2.12118i q^{41} +(0.230966 - 0.973384i) q^{42} +(-0.684507 - 0.684507i) q^{43} +(-1.59880 - 4.83340i) q^{44} +(-0.860885 + 2.06370i) q^{45} +(-8.33405 + 5.13750i) q^{46} -4.47342i q^{47} +(3.95716 + 0.583877i) q^{48} -6.49959 q^{49} +(-6.87176 - 1.66700i) q^{50} +(0.173159 + 0.173159i) q^{51} +(-3.43177 - 10.3747i) q^{52} +(1.47026 + 1.47026i) q^{53} +(-1.37601 - 0.326501i) q^{54} +(-5.26405 + 2.16499i) q^{55} +(0.172815 + 1.99335i) q^{56} -2.17595 q^{57} +(9.53295 + 2.26199i) q^{58} +(5.86121 - 5.86121i) q^{59} +(0.338461 - 4.45931i) q^{60} +(0.0537432 + 0.0537432i) q^{61} +(-9.15813 + 5.64551i) q^{62} -0.707398i q^{63} +(-7.88064 + 1.37679i) q^{64} +(-11.2991 + 4.64706i) q^{65} +(-1.88904 - 3.06439i) q^{66} +(-7.85550 + 7.85550i) q^{67} +(-0.437558 - 0.220037i) q^{68} +(-4.89516 + 4.89516i) q^{69} +(2.20940 - 0.350248i) q^{70} -2.08595i q^{71} +(2.81786 - 0.244298i) q^{72} +9.69951 q^{73} +(16.4992 + 3.91494i) q^{74} +(-4.99994 - 0.0250827i) q^{75} +(4.13173 - 1.36670i) q^{76} +(1.27326 - 1.27326i) q^{77} +(-4.05475 - 6.57760i) q^{78} -7.34690 q^{79} +(2.15819 + 8.67999i) q^{80} -1.00000 q^{81} +(-1.57415 - 2.55359i) q^{82} +(-6.80291 + 6.80291i) q^{83} +(0.444312 + 1.34322i) q^{84} +(-0.210817 + 0.505369i) q^{85} +(1.33203 + 0.316066i) q^{86} +6.92797 q^{87} +(5.51166 + 4.63222i) q^{88} -3.07483i q^{89} +(-0.495122 - 3.12328i) q^{90} +(2.73301 - 2.73301i) q^{91} +(6.22038 - 12.3696i) q^{92} +(-5.37920 + 5.37920i) q^{93} +(3.31978 + 5.38535i) q^{94} +(-1.85069 - 4.49986i) q^{95} +(-5.19715 + 2.23375i) q^{96} -1.39922i q^{97} +(7.82456 - 4.82343i) q^{98} +(-1.79993 - 1.79993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51}+ \cdots - 40 q^{96}+O(q^{100}) $ 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.20386	+	0.742113i	−0.851254	+	0.524753i
$2$	−1.20386	+	0.742113i	−0.851254	+	0.524753i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	0.898535	−	1.78679i	0.449268	−	0.893397i
$5$	−2.06370	−	0.860885i	−0.922917	−	0.385000i
$5$	−2.06370	−	0.860885i	−0.922917	−	0.385000i
$6$	0.326501	−	1.37601i	0.133293	−	0.561753i
$7$	0.707398			0.267371			0.133686	−	0.991024i	$-0.457319\pi$
$7$	0.707398			0.267371			0.133686	+	0.991024i	$0.457319\pi$
$8$	0.244298	+	2.81786i	0.0863722	+	0.996263i
$9$		−	1.00000i		−	0.333333i
$10$	3.12328	−	0.495122i	0.987667	−	0.156571i
$11$	1.79993	−	1.79993i	0.542699	−	0.542699i	−0.381621	−	0.924319i	$-0.624634\pi$
$11$	1.79993	−	1.79993i	0.542699	−	0.542699i	0.924319	+	0.381621i	$0.124634\pi$
$12$	0.628094	+	1.89881i	0.181315	+	0.548141i
$13$	3.86348	−	3.86348i	1.07154	−	1.07154i	0.0742996	−	0.997236i	$-0.476328\pi$
$13$	3.86348	−	3.86348i	1.07154	−	1.07154i	0.997236	−	0.0742996i	$-0.0236721\pi$
$14$	−0.851604	+	0.524969i	−0.227601	+	0.140304i
$15$	2.06800	−	0.850522i	0.533955	−	0.219604i
$16$	−2.38527	−	3.21100i	−0.596317	−	0.802749i
$17$		−	0.244884i		−	0.0593932i	−0.999559	−	0.0296966i	$-0.990546\pi$
$17$		−	0.244884i		−	0.0593932i	0.999559	−	0.0296966i	$-0.00945410\pi$
$18$	0.742113	+	1.20386i	0.174918	+	0.283751i
$19$	1.53863	+	1.53863i	0.352986	+	0.352986i	0.861219	−	0.508233i	$-0.169701\pi$
$19$	1.53863	+	1.53863i	0.352986	+	0.352986i	−0.508233	+	0.861219i	$0.669701\pi$
$20$	−3.39254	+	2.91388i	−0.758594	+	0.651563i
$21$	−0.500206	+	0.500206i	−0.109154	+	0.109154i
$22$	−0.831102	+	3.50260i	−0.177192	+	0.746757i
$23$	6.92280			1.44350			0.721752	−	0.692152i	$-0.243337\pi$
$23$	6.92280			1.44350			0.721752	+	0.692152i	$0.243337\pi$
$24$	−2.16527	−	1.81978i	−0.441984	−	0.371461i
$25$	3.51775	+	3.55323i	0.703551	+	0.710645i
$26$	−1.78393	+	7.51820i	−0.349857	+	1.47444i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	0.635622	−	1.26397i	0.120121	−	0.238869i
$29$	−4.89882	−	4.89882i	−0.909688	−	0.909688i	0.0865591	−	0.996247i	$-0.472413\pi$
$29$	−4.89882	−	4.89882i	−0.909688	−	0.909688i	−0.996247	+	0.0865591i	$0.972413\pi$
$30$	−1.85839	+	2.55859i	−0.339293	+	0.467133i
$31$	7.60734			1.36632			0.683159	−	0.730270i	$-0.260606\pi$
$31$	7.60734			1.36632			0.683159	+	0.730270i	$0.260606\pi$
$32$	5.25444	+	2.09543i	0.928863	+	0.370424i
$33$			2.54548i			0.443112i
$34$	0.181732	+	0.294805i	0.0311668	+	0.0505587i
$35$	−1.45986	−	0.608988i	−0.246761	−	0.102938i
$36$	−1.78679	−	0.898535i	−0.297799	−	0.149756i
$37$	−8.47863	−	8.47863i	−1.39388	−	1.39388i	−0.816420	−	0.577459i	$-0.804044\pi$
$37$	−8.47863	−	8.47863i	−1.39388	−	1.39388i	−0.577459	−	0.816420i	$-0.695956\pi$
$38$	−2.99413	−	0.710450i	−0.485712	−	0.115250i
$39$			5.46378i			0.874905i
$40$	1.92169	−	6.02554i	0.303846	−	0.952721i
$41$			2.12118i			0.331272i	0.986187	+	0.165636i	$0.0529677\pi$
$41$			2.12118i			0.331272i	−0.986187	+	0.165636i	$0.947032\pi$
$42$	0.230966	−	0.973384i	0.0356388	−	0.150196i
$43$	−0.684507	−	0.684507i	−0.104386	−	0.104386i	0.652985	−	0.757371i	$-0.273517\pi$
$43$	−0.684507	−	0.684507i	−0.104386	−	0.104386i	−0.757371	+	0.652985i	$0.773517\pi$
$44$	−1.59880	−	4.83340i	−0.241028	−	0.728662i
$45$	−0.860885	+	2.06370i	−0.128333	+	0.307639i
$46$	−8.33405	+	5.13750i	−1.22879	+	0.757484i
$47$		−	4.47342i		−	0.652515i	−0.945281	−	0.326258i	$-0.894212\pi$
$47$		−	4.47342i		−	0.652515i	0.945281	−	0.326258i	$-0.105788\pi$
$48$	3.95716	+	0.583877i	0.571166	+	0.0842754i
$49$	−6.49959			−0.928513
$50$	−6.87176	−	1.66700i	−0.971814	−	0.235749i
$51$	0.173159	+	0.173159i	0.0242472	+	0.0242472i
$52$	−3.43177	−	10.3747i	−0.475901	−	1.43871i
$53$	1.47026	+	1.47026i	0.201956	+	0.201956i	0.800838	−	0.598881i	$-0.204388\pi$
$53$	1.47026	+	1.47026i	0.201956	+	0.201956i	−0.598881	+	0.800838i	$0.704388\pi$
$54$	−1.37601	−	0.326501i	−0.187251	−	0.0444311i
$55$	−5.26405	+	2.16499i	−0.709804	+	0.291927i
$56$	0.172815	+	1.99335i	0.0230934	+	0.266372i
$57$	−2.17595			−0.288212
$58$	9.53295	+	2.26199i	1.25174	+	0.297014i
$59$	5.86121	−	5.86121i	0.763065	−	0.763065i	−0.213810	−	0.976875i	$-0.568587\pi$
$59$	5.86121	−	5.86121i	0.763065	−	0.763065i	0.976875	+	0.213810i	$0.0685874\pi$
$60$	0.338461	−	4.45931i	0.0436952	−	0.575694i
$61$	0.0537432	+	0.0537432i	0.00688112	+	0.00688112i	0.710539	−	0.703658i	$-0.248451\pi$
$61$	0.0537432	+	0.0537432i	0.00688112	+	0.00688112i	−0.703658	+	0.710539i	$0.748451\pi$
$62$	−9.15813	+	5.64551i	−1.16308	+	0.716980i
$63$		−	0.707398i		−	0.0891237i
$64$	−7.88064	+	1.37679i	−0.985080	+	0.172099i
$65$	−11.2991	+	4.64706i	−1.40148	+	0.576397i
$66$	−1.88904	−	3.06439i	−0.232524	−	0.377201i
$67$	−7.85550	+	7.85550i	−0.959702	+	0.959702i	−0.999219	−	0.0395170i	$-0.987418\pi$
$67$	−7.85550	+	7.85550i	−0.959702	+	0.959702i	0.0395170	+	0.999219i	$0.487418\pi$
$68$	−0.437558	−	0.220037i	−0.0530617	−	0.0266834i
$69$	−4.89516	+	4.89516i	−0.589308	+	0.589308i
$70$	2.20940	−	0.350248i	0.264074	−	0.0418626i
$71$		−	2.08595i		−	0.247557i	−0.992310	−	0.123778i	$-0.960499\pi$
$71$		−	2.08595i		−	0.247557i	0.992310	−	0.123778i	$-0.0395012\pi$
$72$	2.81786	−	0.244298i	0.332088	−	0.0287907i
$73$	9.69951			1.13524			0.567621	−	0.823290i	$-0.307864\pi$
$73$	9.69951			1.13524			0.567621	+	0.823290i	$0.307864\pi$
$74$	16.4992	+	3.91494i	1.91799	+	0.455103i
$75$	−4.99994	−	0.0250827i	−0.577343	−	0.00289630i
$76$	4.13173	−	1.36670i	0.473942	−	0.156772i
$77$	1.27326	−	1.27326i	0.145102	−	0.145102i
$78$	−4.05475	−	6.57760i	−0.459109	−	0.744767i
$79$	−7.34690			−0.826591			−0.413295	−	0.910597i	$-0.635622\pi$
$79$	−7.34690			−0.826591			−0.413295	+	0.910597i	$0.635622\pi$
$80$	2.15819	+	8.67999i	0.241293	+	0.970452i
$81$	−1.00000			−0.111111
$82$	−1.57415	−	2.55359i	−0.173836	−	0.281997i
$83$	−6.80291	+	6.80291i	−0.746716	+	0.746716i	−0.973861	−	0.227145i	$-0.927061\pi$
$83$	−6.80291	+	6.80291i	−0.746716	+	0.746716i	0.227145	+	0.973861i	$0.427061\pi$
$84$	0.444312	+	1.34322i	0.0484784	+	0.146557i
$85$	−0.210817	+	0.505369i	−0.0228663	+	0.0548149i
$86$	1.33203	+	0.316066i	0.143636	+	0.0340822i
$87$	6.92797			0.742757
$88$	5.51166	+	4.63222i	0.587545	+	0.493796i
$89$		−	3.07483i		−	0.325931i	−0.986632	−	0.162966i	$-0.947894\pi$
$89$		−	3.07483i		−	0.325931i	0.986632	−	0.162966i	$-0.0521060\pi$
$90$	−0.495122	−	3.12328i	−0.0521904	−	0.329222i
$91$	2.73301	−	2.73301i	0.286498	−	0.286498i
$92$	6.22038	−	12.3696i	0.648520	−	1.28962i
$93$	−5.37920	+	5.37920i	−0.557797	+	0.557797i
$94$	3.31978	+	5.38535i	0.342410	+	0.555456i
$95$	−1.85069	−	4.49986i	−0.189877	−	0.461676i
$96$	−5.19715	+	2.23375i	−0.530432	+	0.227982i
$97$		−	1.39922i		−	0.142070i	−0.997474	−	0.0710348i	$-0.977370\pi$
$97$		−	1.39922i		−	0.142070i	0.997474	−	0.0710348i	$-0.0226301\pi$
$98$	7.82456	−	4.82343i	0.790400	−	0.487240i
$99$	−1.79993	−	1.79993i	−0.180900	−	0.180900i
$100$	9.50971	−	3.09280i	0.950971	−	0.309280i
$101$	11.7916	−	11.7916i	1.17331	−	1.17331i	0.191895	−	0.981415i	$-0.438537\pi$
$101$	11.7916	−	11.7916i	1.17331	−	1.17331i	0.981415	−	0.191895i	$-0.0614633\pi$
$102$	−0.336963	−	0.0799549i	−0.0333643	−	0.00791672i
$103$	2.29240			0.225877			0.112938	−	0.993602i	$-0.463974\pi$
$103$	2.29240			0.225877			0.112938	+	0.993602i	$0.463974\pi$
$104$	11.8306	+	9.94289i	1.16008	+	0.974980i
$105$	1.46290	−	0.601657i	0.142764	−	0.0587157i
$106$	−2.86109	−	0.678882i	−0.277893	−	0.0659389i
$107$	9.49009	+	9.49009i	0.917442	+	0.917442i	0.996843	−	0.0794010i	$-0.0253008\pi$
$107$	9.49009	+	9.49009i	0.917442	+	0.917442i	−0.0794010	+	0.996843i	$0.525301\pi$
$108$	1.89881	−	0.628094i	0.182714	−	0.0604384i
$109$	11.9058	+	11.9058i	1.14037	+	1.14037i	0.988383	+	0.151984i	$0.0485662\pi$
$109$	11.9058	+	11.9058i	1.14037	+	1.14037i	0.151984	+	0.988383i	$0.451434\pi$
$110$	4.73049	−	6.51285i	0.451034	−	0.620976i
$111$	11.9906			1.13810
$112$	−1.68733	−	2.27145i	−0.159438	−	0.214632i
$113$			7.92806i			0.745809i	0.927870	+	0.372904i	$0.121638\pi$
$113$			7.92806i			0.745809i	−0.927870	+	0.372904i	$0.878362\pi$
$114$	2.61953	−	1.61480i	0.245342	−	0.151240i
$115$	−14.2866	−	5.95974i	−1.33223	−	0.555748i
$116$	−13.1549	+	4.35142i	−1.22141	+	0.404019i
$117$	−3.86348	−	3.86348i	−0.357179	−	0.357179i
$118$	−2.70637	+	11.4057i	−0.249141	+	1.04998i
$119$		−	0.173231i		−	0.0158800i
$120$	2.90186	+	5.61954i	0.264902	+	0.512992i
$121$			4.52052i			0.410956i
$122$	−0.104583	−	0.0248155i	−0.00946847	−	0.00224669i
$123$	−1.49990	−	1.49990i	−0.135241	−	0.135241i
$124$	6.83546	−	13.5927i	0.613843	−	1.22066i
$125$	−4.20068	−	10.3612i	−0.375721	−	0.926733i
$126$	0.524969	+	0.851604i	0.0467680	+	0.0758669i
$127$			19.4466i			1.72561i	0.505536	+	0.862806i	$0.331295\pi$
$127$			19.4466i			1.72561i	−0.505536	+	0.862806i	$0.668705\pi$
$128$	8.46541	−	7.50578i	0.748244	−	0.663424i
$129$	0.968040			0.0852311
$130$	10.1538	−	13.9796i	0.890548	−	1.22609i
$131$	−0.354049	−	0.354049i	−0.0309334	−	0.0309334i	0.691471	−	0.722404i	$-0.256963\pi$
$131$	−0.354049	−	0.354049i	−0.0309334	−	0.0309334i	−0.722404	+	0.691471i	$0.756963\pi$
$132$	4.54825	+	2.28721i	0.395875	+	0.199076i
$133$	1.08842	+	1.08842i	0.0943783	+	0.0943783i
$134$	3.62721	−	15.2866i	0.313343	−	1.32056i
$135$	−0.850522	−	2.06800i	−0.0732013	−	0.177985i
$136$	0.690049	−	0.0598246i	0.0591712	−	0.00512992i
$137$	−7.30033			−0.623709			−0.311854	−	0.950130i	$-0.600950\pi$
$137$	−7.30033			−0.623709			−0.311854	+	0.950130i	$0.600950\pi$
$138$	2.26030	−	9.52583i	0.192410	−	0.810892i
$139$	−8.85519	+	8.85519i	−0.751087	+	0.751087i	−0.974682	−	0.223595i	$-0.928221\pi$
$139$	−8.85519	+	8.85519i	−0.751087	+	0.751087i	0.223595	+	0.974682i	$0.428221\pi$
$140$	−2.39987	+	2.06127i	−0.202826	+	0.174209i
$141$	3.16319	+	3.16319i	0.266388	+	0.266388i
$142$	1.54801	+	2.51118i	0.129906	+	0.210734i
$143$		−	13.9080i		−	1.16304i
$144$	−3.21100	+	2.38527i	−0.267583	+	0.198772i
$145$	5.89239	+	14.3270i	0.489337	+	1.18980i
$146$	−11.6768	+	7.19814i	−0.966379	+	0.595722i
$147$	4.59590	−	4.59590i	0.379064	−	0.379064i
$148$	−22.7679	+	7.53122i	−1.87151	+	0.619063i
$149$	5.41385	−	5.41385i	0.443520	−	0.443520i	−0.449673	−	0.893193i	$-0.648460\pi$
$149$	5.41385	−	5.41385i	0.443520	−	0.443520i	0.893193	+	0.449673i	$0.148460\pi$
$150$	6.03782	−	3.68032i	0.492986	−	0.300497i
$151$		−	0.341548i		−	0.0277948i	−0.999903	−	0.0138974i	$-0.995576\pi$
$151$		−	0.341548i		−	0.0277948i	0.999903	−	0.0138974i	$-0.00442382\pi$
$152$	−3.95976	+	4.71153i	−0.321179	+	0.382155i
$153$	−0.244884			−0.0197977
$154$	−0.587920	+	2.47773i	−0.0473759	+	0.199661i
$155$	−15.6993	−	6.54904i	−1.26100	−	0.526032i
$156$	9.76265	+	4.90940i	0.781638	+	0.393067i
$157$	−2.86465	+	2.86465i	−0.228624	+	0.228624i	−0.812118	−	0.583494i	$-0.801685\pi$
$157$	−2.86465	+	2.86465i	−0.228624	+	0.228624i	0.583494	+	0.812118i	$0.301685\pi$
$158$	8.84460	−	5.45223i	0.703639	−	0.433756i
$159$	−2.07927			−0.164897
$160$	−9.03969	−	8.84783i	−0.714650	−	0.699482i
$161$	4.89717			0.385951
$162$	1.20386	−	0.742113i	0.0945838	−	0.0583059i
$163$	−5.94216	+	5.94216i	−0.465426	+	0.465426i	−0.900429	−	0.435003i	$-0.856747\pi$
$163$	−5.94216	+	5.94216i	−0.465426	+	0.465426i	0.435003	+	0.900429i	$0.356747\pi$
$164$	3.79011	+	1.90595i	0.295958	+	0.148830i
$165$	2.19137	−	5.25312i	0.170598	−	0.408955i
$166$	3.14119	−	13.2382i	0.243803	−	1.02749i
$167$	14.4595			1.11891			0.559454	−	0.828861i	$-0.311011\pi$
$167$	14.4595			1.11891			0.559454	+	0.828861i	$0.311011\pi$
$168$	−1.53171	−	1.28731i	−0.118174	−	0.0993180i
$169$		−	16.8529i		−	1.29638i
$170$	−0.121247	−	0.764841i	−0.00929926	−	0.0586606i
$171$	1.53863	−	1.53863i	0.117662	−	0.117662i
$172$	−1.83813	+	0.608020i	−0.140156	+	0.0463611i
$173$	−6.65096	+	6.65096i	−0.505663	+	0.505663i	−0.913192	−	0.407529i	$-0.866390\pi$
$173$	−6.65096	+	6.65096i	−0.505663	+	0.505663i	0.407529	+	0.913192i	$0.366390\pi$
$174$	−8.34028	+	5.14134i	−0.632275	+	0.389764i
$175$	2.48845	+	2.51354i	0.188109	+	0.190006i
$176$	−10.0729	−	1.48625i	−0.759271	−	0.112030i
$177$			8.28901i			0.623040i
$178$	2.28187	+	3.70165i	0.171033	+	0.277450i
$179$	17.2660	+	17.2660i	1.29052	+	1.29052i	0.934466	+	0.356052i	$0.115877\pi$
$179$	17.2660	+	17.2660i	1.29052	+	1.29052i	0.356052	+	0.934466i	$0.384123\pi$
$180$	2.91388	+	3.39254i	0.217188	+	0.252865i
$181$	5.12242	−	5.12242i	0.380746	−	0.380746i	−0.490625	−	0.871371i	$-0.663231\pi$
$181$	5.12242	−	5.12242i	0.380746	−	0.380746i	0.871371	+	0.490625i	$0.163231\pi$
$182$	−1.26195	+	5.31836i	−0.0935417	+	0.394223i
$183$	−0.0760044			−0.00561841
$184$	1.69122	+	19.5075i	0.124679	+	1.43811i
$185$	10.1983	+	24.7965i	0.749791	+	1.82308i
$186$	2.48380	−	10.4678i	0.182121	−	0.767533i
$187$	−0.440774	−	0.440774i	−0.0322326	−	0.0322326i
$188$	−7.99308	−	4.01953i	−0.582955	−	0.293154i
$189$	0.500206	+	0.500206i	0.0363846	+	0.0363846i
$190$	5.56738	+	4.04376i	0.403900	+	0.293365i
$191$	−17.8040			−1.28825			−0.644124	−	0.764921i	$-0.722778\pi$
$191$	−17.8040			−1.28825			−0.644124	+	0.764921i	$0.722778\pi$
$192$	4.59891	−	6.54599i	0.331898	−	0.472416i
$193$		−	17.2222i		−	1.23968i	−0.784727	−	0.619842i	$-0.787197\pi$
$193$		−	17.2222i		−	1.23968i	0.784727	−	0.619842i	$-0.212803\pi$
$194$	1.03838	+	1.68446i	0.0745515	+	0.120937i
$195$	4.70369	−	11.2756i	0.336838	−	0.807465i
$196$	−5.84011	+	11.6134i	−0.417151	+	0.829531i
$197$	−10.0764	−	10.0764i	−0.717915	−	0.717915i	0.250263	−	0.968178i	$-0.419483\pi$
$197$	−10.0764	−	10.0764i	−0.717915	−	0.717915i	−0.968178	+	0.250263i	$0.919483\pi$
$198$	3.50260	+	0.831102i	0.248919	+	0.0590638i
$199$		−	5.74179i		−	0.407025i	−0.979072	−	0.203513i	$-0.934764\pi$
$199$		−	5.74179i		−	0.407025i	0.979072	−	0.203513i	$-0.0652358\pi$
$200$	−9.15310	+	10.7806i	−0.647222	+	0.762301i
$201$		−	11.1094i		−	0.783593i
$202$	−5.44469	+	22.9461i	−0.383087	+	1.61448i
$203$	−3.46541	−	3.46541i	−0.243224	−	0.243224i
$204$	0.464990	−	0.153810i	0.0325558	−	0.0107689i
$205$	1.82609	−	4.37748i	0.127540	−	0.305737i
$206$	−2.75972	+	1.70122i	−0.192279	+	0.118530i
$207$		−	6.92280i		−	0.481168i
$208$	−21.6210	−	3.19018i	−1.49915	−	0.221199i
$209$	5.53885			0.383130
$210$	−1.31462	+	1.80994i	−0.0907172	+	0.124898i
$211$	−9.73318	−	9.73318i	−0.670060	−	0.670060i	0.287670	−	0.957730i	$-0.407119\pi$
$211$	−9.73318	−	9.73318i	−0.670060	−	0.670060i	−0.957730	+	0.287670i	$0.907119\pi$
$212$	3.94814	−	1.30598i	0.271160	−	0.0896947i
$213$	1.47499	+	1.47499i	0.101065	+	0.101065i
$214$	−18.4674	−	4.38197i	−1.26241	−	0.299545i
$215$	0.823339	+	2.00190i	0.0561512	+	0.136529i
$216$	−1.81978	+	2.16527i	−0.123820	+	0.147328i
$217$	5.38141			0.365314
$218$	−23.1683	−	5.49740i	−1.56915	−	0.372331i
$219$	−6.85859	+	6.85859i	−0.463460	+	0.463460i
$220$	−0.861547	+	11.3511i	−0.0580855	+	0.765291i
$221$	−0.946104	−	0.946104i	−0.0636419	−	0.0636419i
$222$	−14.4349	+	8.89838i	−0.968810	+	0.597220i
$223$		−	22.1037i		−	1.48017i	−0.672511	−	0.740087i	$-0.734784\pi$
$223$		−	22.1037i		−	1.48017i	0.672511	−	0.740087i	$-0.265216\pi$
$224$	3.71698	+	1.48231i	0.248351	+	0.0990407i
$225$	3.55323	−	3.51775i	0.236882	−	0.234517i
$226$	−5.88352	−	9.54423i	−0.391366	−	0.634873i
$227$	5.35387	−	5.35387i	0.355349	−	0.355349i	−0.506746	−	0.862095i	$-0.669152\pi$
$227$	5.35387	−	5.35387i	0.355349	−	0.355349i	0.862095	+	0.506746i	$0.169152\pi$
$228$	−1.95517	+	3.88798i	−0.129484	+	0.257488i
$229$	−18.3018	+	18.3018i	−1.20942	+	1.20942i	−0.238204	+	0.971215i	$0.576559\pi$
$229$	−18.3018	+	18.3018i	−1.20942	+	1.20942i	−0.971215	+	0.238204i	$0.923441\pi$
$230$	21.6218	−	3.42763i	1.42570	−	0.226011i
$231$			1.80067i			0.118475i
$232$	12.6074	−	15.0009i	0.827716	−	0.984860i
$233$	−12.0546			−0.789721			−0.394861	−	0.918741i	$-0.629207\pi$
$233$	−12.0546			−0.789721			−0.394861	+	0.918741i	$0.629207\pi$
$234$	7.51820	+	1.78393i	0.491480	+	0.116619i
$235$	−3.85110	+	9.23182i	−0.251218	+	0.602217i
$236$	−5.20628	−	15.7393i	−0.338900	−	1.02454i
$237$	5.19504	−	5.19504i	0.337454	−	0.337454i
$238$	0.128557	+	0.208544i	0.00833309	+	0.0135179i
$239$	−27.9193			−1.80595			−0.902974	−	0.429695i	$-0.858621\pi$
$239$	−27.9193			−1.80595			−0.902974	+	0.429695i	$0.858621\pi$
$240$	−7.66375	−	4.61161i	−0.494693	−	0.297678i
$241$	13.7118			0.883253			0.441626	−	0.897199i	$-0.354402\pi$
$241$	13.7118			0.883253			0.441626	+	0.897199i	$0.354402\pi$
$242$	−3.35474	−	5.44205i	−0.215651	−	0.349828i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	0.144318	−	0.0477379i	0.00923903	−	0.00305611i
$245$	13.4132	+	5.59540i	0.856940	+	0.357477i
$246$	2.91876	+	0.692566i	0.186093	+	0.0441564i
$247$	11.8889			0.756474
$248$	1.85845	+	21.4364i	0.118012	+	1.36121i
$249$		−	9.62077i		−	0.609691i
$250$	12.7462	+	9.35599i	0.806140	+	0.591725i
$251$	−9.07173	+	9.07173i	−0.572602	+	0.572602i	−0.932855	−	0.360252i	$-0.882691\pi$
$251$	−9.07173	+	9.07173i	−0.572602	+	0.572602i	0.360252	+	0.932855i	$0.382691\pi$
$252$	−1.26397	−	0.635622i	−0.0796229	−	0.0400404i
$253$	12.4605	−	12.4605i	0.783388	−	0.783388i
$254$	−14.4316	−	23.4110i	−0.905520	−	1.46893i
$255$	−0.208279	−	0.506420i	−0.0130430	−	0.0317132i
$256$	−4.62099	+	15.3182i	−0.288812	+	0.957386i
$257$		−	9.23416i		−	0.576011i	−0.957629	−	0.288006i	$-0.907008\pi$
$257$		−	9.23416i		−	0.576011i	0.957629	−	0.288006i	$-0.0929922\pi$
$258$	−1.16538	+	0.718395i	−0.0725534	+	0.0447253i
$259$	−5.99776	−	5.99776i	−0.372683	−	0.372683i
$260$	−1.84928	+	24.3647i	−0.114687	+	1.51103i
$261$	−4.89882	+	4.89882i	−0.303229	+	0.303229i
$262$	0.688969	+	0.163479i	0.0425646	+	0.0100998i
$263$	−18.5516			−1.14394			−0.571971	−	0.820274i	$-0.693821\pi$
$263$	−18.5516			−1.14394			−0.571971	+	0.820274i	$0.693821\pi$
$264$	−7.17280	+	0.621855i	−0.441456	+	0.0382725i
$265$	−1.76846	−	4.29992i	−0.108636	−	0.264142i
$266$	−2.11804	−	0.502571i	−0.129865	−	0.0308146i
$267$	2.17423	+	2.17423i	0.133061	+	0.133061i
$268$	6.97772	+	21.0946i	0.426232	+	1.28856i
$269$	14.3977	+	14.3977i	0.877844	+	0.877844i	0.993311	−	0.115467i	$-0.0368366\pi$
$269$	14.3977	+	14.3977i	0.877844	+	0.877844i	−0.115467	+	0.993311i	$0.536837\pi$
$270$	2.55859	+	1.85839i	0.155711	+	0.113098i
$271$	19.2974			1.17224			0.586118	−	0.810226i	$-0.300656\pi$
$271$	19.2974			1.17224			0.586118	+	0.810226i	$0.300656\pi$
$272$	−0.786322	+	0.584115i	−0.0476778	+	0.0354172i
$273$			3.86507i			0.233924i
$274$	8.78854	−	5.41767i	0.530935	−	0.327293i
$275$	12.7272	+	0.0638476i	0.767482	+	0.00385016i
$276$	4.34817	+	13.1451i	0.261729	+	0.791243i
$277$	3.52269	+	3.52269i	0.211658	+	0.211658i	0.804971	−	0.593314i	$-0.202181\pi$
$277$	3.52269	+	3.52269i	0.211658	+	0.211658i	−0.593314	+	0.804971i	$0.702181\pi$
$278$	4.08881	−	17.2319i	0.245231	−	1.03350i
$279$		−	7.60734i		−	0.455439i
$280$	1.35940	−	4.26245i	0.0812398	−	0.254730i
$281$			29.2076i			1.74238i	0.490945	+	0.871191i	$0.336652\pi$
$281$			29.2076i			1.74238i	−0.490945	+	0.871191i	$0.663348\pi$
$282$	−6.15546	−	1.46058i	−0.366552	−	0.0869760i
$283$	−9.84279	−	9.84279i	−0.585093	−	0.585093i	0.351205	−	0.936298i	$-0.385772\pi$
$283$	−9.84279	−	9.84279i	−0.585093	−	0.585093i	−0.936298	+	0.351205i	$0.885772\pi$
$284$	−3.72717	−	1.87430i	−0.221167	−	0.111219i
$285$	4.49052	+	1.87325i	0.265996	+	0.110961i
$286$	10.3213	+	16.7432i	0.610310	+	0.990044i
$287$			1.50052i			0.0885726i
$288$	2.09543	−	5.25444i	0.123475	−	0.309621i
$289$	16.9400			0.996472
$290$	−17.7259	−	12.8749i	−1.04090	−	0.756037i
$291$	0.989400	+	0.989400i	0.0579997	+	0.0579997i
$292$	8.71535	−	17.3310i	0.510027	−	1.01422i
$293$	11.8238	+	11.8238i	0.690755	+	0.690755i	0.962398	−	0.271643i	$-0.0875671\pi$
$293$	11.8238	+	11.8238i	0.690755	+	0.690755i	−0.271643	+	0.962398i	$0.587567\pi$
$294$	−2.12212	+	8.94348i	−0.123765	+	0.521595i
$295$	−17.1416	+	7.04998i	−0.998025	+	0.410466i
$296$	21.8203	−	25.9629i	1.26828	−	1.50906i
$297$	2.54548			0.147704
$298$	−2.49980	+	10.5352i	−0.144810	+	0.610287i
$299$	26.7461	−	26.7461i	1.54677	−	1.54677i
$300$	−4.53744	+	8.91132i	−0.261969	+	0.514495i
$301$	−0.484219	−	0.484219i	−0.0279099	−	0.0279099i
$302$	0.253468	+	0.411175i	0.0145854	+	0.0236604i
$303$			16.6759i			0.958004i
$304$	1.27049	−	8.61058i	0.0728676	−	0.493851i
$305$	−0.0646434	−	0.157177i	−0.00370147	−	0.00899992i
$306$	0.294805	−	0.181732i	0.0168529	−	0.0103889i
$307$	16.6232	−	16.6232i	0.948733	−	0.948733i	−0.0500151	−	0.998748i	$-0.515927\pi$
$307$	16.6232	−	16.6232i	0.948733	−	0.948733i	0.998748	+	0.0500151i	$0.0159269\pi$
$308$	−1.13099	−	3.41913i	−0.0644441	−	0.194823i
$309$	−1.62097	+	1.62097i	−0.0922139	+	0.0922139i
$310$	23.7598	−	3.76656i	1.34947	−	0.213926i
$311$			13.8069i			0.782920i	0.920195	+	0.391460i	$0.128030\pi$
$311$			13.8069i			0.782920i	−0.920195	+	0.391460i	$0.871970\pi$
$312$	−15.3962	+	1.33479i	−0.871636	+	0.0755675i
$313$	−7.40380			−0.418488			−0.209244	−	0.977864i	$-0.567100\pi$
$313$	−7.40380			−0.418488			−0.209244	+	0.977864i	$0.567100\pi$
$314$	1.32273	−	5.57452i	0.0746459	−	0.314588i
$315$	−0.608988	+	1.45986i	−0.0343126	+	0.0822538i
$316$	−6.60145	+	13.1274i	−0.371360	+	0.738474i
$317$	1.80712	−	1.80712i	0.101498	−	0.101498i	−0.654534	−	0.756032i	$-0.727135\pi$
$317$	1.80712	−	1.80712i	0.101498	−	0.101498i	0.756032	+	0.654534i	$0.227135\pi$
$318$	2.50314	−	1.54305i	0.140369	−	0.0865301i
$319$	−17.6350			−0.987372
$320$	17.4486	+	3.94303i	0.975405	+	0.220422i
$321$	−13.4210			−0.749088
$322$	−5.89549	+	3.63426i	−0.328543	+	0.202529i
$323$	0.376786	−	0.376786i	0.0209650	−	0.0209650i
$324$	−0.898535	+	1.78679i	−0.0499186	+	0.0992664i
$325$	27.3186	+	0.137046i	1.51536	+	0.00760197i
$326$	2.74375	−	11.5633i	0.151962	−	0.640430i
$327$	−16.8373			−0.931106
$328$	−5.97717	+	0.518198i	−0.330034	+	0.0286127i
$329$		−	3.16449i		−	0.174464i
$330$	1.26032	+	7.95024i	0.0693785	+	0.437647i
$331$	−5.82711	+	5.82711i	−0.320287	+	0.320287i	−0.848877	−	0.528590i	$-0.822721\pi$
$331$	−5.82711	+	5.82711i	−0.320287	+	0.320287i	0.528590	+	0.848877i	$0.322721\pi$
$332$	6.04275	+	18.2681i	0.331639	+	1.00259i
$333$	−8.47863	+	8.47863i	−0.464626	+	0.464626i
$334$	−17.4071	+	10.7306i	−0.952475	+	0.587151i
$335$	22.9741	−	9.44875i	1.25521	−	0.516240i
$336$	2.79928	+	0.413033i	0.152713	+	0.0225328i
$337$		−	25.5357i		−	1.39102i	−0.718516	−	0.695510i	$-0.755178\pi$
$337$		−	25.5357i		−	1.39102i	0.718516	−	0.695510i	$-0.244822\pi$
$338$	12.5068	+	20.2885i	0.680278	+	1.10355i
$339$	−5.60598	−	5.60598i	−0.304475	−	0.304475i
$340$	0.713563	+	0.830779i	0.0386984	+	0.0450553i
$341$	13.6927	−	13.6927i	0.741499	−	0.741499i
$342$	−0.710450	+	2.99413i	−0.0384168	+	0.161904i
$343$	−9.54958			−0.515629
$344$	1.76162	−	2.09607i	0.0949802	−	0.113012i
$345$	14.3163	−	5.88799i	0.770766	−	0.316999i
$346$	3.07102	−	12.9426i	0.165099	−	0.695796i
$347$	17.6028	+	17.6028i	0.944970	+	0.944970i	0.998563	−	0.0535933i	$-0.0170675\pi$
$347$	17.6028	+	17.6028i	0.944970	+	0.944970i	−0.0535933	+	0.998563i	$0.517067\pi$
$348$	6.22503	−	12.3789i	0.333697	−	0.663577i
$349$	−5.07562	−	5.07562i	−0.271692	−	0.271692i	0.558089	−	0.829781i	$-0.311535\pi$
$349$	−5.07562	−	5.07562i	−0.271692	−	0.271692i	−0.829781	+	0.558089i	$0.811535\pi$
$350$	−4.86107	−	1.17923i	−0.259835	−	0.0630325i
$351$	5.46378			0.291635
$352$	13.2292	−	5.68598i	0.705121	−	0.303064i
$353$		−	0.171535i		−	0.00912990i	−0.999990	−	0.00456495i	$-0.998547\pi$
$353$		−	0.171535i		−	0.00912990i	0.999990	−	0.00456495i	$-0.00145307\pi$
$354$	−6.15138	−	9.97876i	−0.326942	−	0.530365i
$355$	−1.79576	+	4.30479i	−0.0953093	+	0.228474i
$356$	−5.49409	−	2.76284i	−0.291186	−	0.146430i
$357$	0.122492	+	0.122492i	0.00648299	+	0.00648299i
$358$	−33.5990	−	7.97242i	−1.77576	−	0.421355i
$359$		−	17.1694i		−	0.906169i	−0.891468	−	0.453084i	$-0.850324\pi$
$359$		−	17.1694i		−	0.906169i	0.891468	−	0.453084i	$-0.149676\pi$
$360$	−6.02554	−	1.92169i	−0.317574	−	0.101282i
$361$		−	14.2652i		−	0.750802i
$362$	−2.36524	+	9.96807i	−0.124314	+	0.523910i
$363$	−3.19649	−	3.19649i	−0.167772	−	0.167772i
$364$	−2.42762	−	7.33904i	−0.127242	−	0.384670i
$365$	−20.0169	−	8.35016i	−1.04773	−	0.437068i
$366$	0.0914983	−	0.0564039i	0.00478269	−	0.00294828i
$367$			23.3124i			1.21690i	0.793593	+	0.608450i	$0.208208\pi$
$367$			23.3124i			1.21690i	−0.793593	+	0.608450i	$0.791792\pi$
$368$	−16.5127	−	22.2291i	−0.860786	−	1.15877i
$369$	2.12118			0.110424
$370$	−30.6791	−	22.2832i	−1.59493	−	1.15845i
$371$	1.04006	+	1.04006i	0.0539973	+	0.0539973i
$372$	4.77812	+	14.4449i	0.247734	+	0.748935i
$373$	1.11817	+	1.11817i	0.0578964	+	0.0578964i	0.735462	−	0.677566i	$-0.236965\pi$
$373$	1.11817	+	1.11817i	0.0578964	+	0.0578964i	−0.677566	+	0.735462i	$0.736965\pi$
$374$	0.857732	+	0.203524i	0.0443523	+	0.0105240i
$375$	10.2968	+	4.35614i	0.531724	+	0.224950i
$376$	12.6055	−	1.09285i	0.650077	−	0.0563592i
$377$	−37.8529			−1.94953
$378$	−0.973384	−	0.230966i	−0.0500655	−	0.0118796i
$379$	22.3707	−	22.3707i	1.14910	−	1.14910i	0.162375	−	0.986729i	$-0.448085\pi$
$379$	22.3707	−	22.3707i	1.14910	−	1.14910i	0.986729	−	0.162375i	$-0.0519153\pi$
$380$	−9.70325	−	0.736475i	−0.497766	−	0.0377804i
$381$	−13.7509	−	13.7509i	−0.704478	−	0.704478i
$382$	21.4334	−	13.2126i	1.09663	−	0.676013i
$383$			32.1168i			1.64109i	0.571579	+	0.820547i	$0.306331\pi$
$383$			32.1168i			1.64109i	−0.571579	+	0.820547i	$0.693669\pi$
$384$	−0.678560	+	11.2933i	−0.0346276	+	0.576311i
$385$	−3.72378	+	1.53151i	−0.189781	+	0.0780528i
$386$	12.7809	+	20.7331i	0.650529	+	1.05529i
$387$	−0.684507	+	0.684507i	−0.0347955	+	0.0347955i
$388$	−2.50012	−	1.25725i	−0.126925	−	0.0638273i
$389$	−22.7409	+	22.7409i	−1.15301	+	1.15301i	−0.167062	+	0.985946i	$0.553428\pi$
$389$	−22.7409	+	22.7409i	−1.15301	+	1.15301i	−0.985946	+	0.167062i	$0.946572\pi$
$390$	2.70524	+	17.0649i	0.136985	+	0.864115i
$391$		−	1.69529i		−	0.0857342i
$392$	−1.58783	−	18.3149i	−0.0801977	−	0.925043i
$393$	0.500701			0.0252570
$394$	19.6084	+	4.65270i	0.987857	+	0.234400i
$395$	15.1618	+	6.32484i	0.762874	+	0.318237i
$396$	−4.83340	+	1.59880i	−0.242887	+	0.0803428i
$397$	−21.6530	+	21.6530i	−1.08673	+	1.08673i	−0.0908707	+	0.995863i	$0.528965\pi$
$397$	−21.6530	+	21.6530i	−1.08673	+	1.08673i	−0.995863	+	0.0908707i	$0.971035\pi$
$398$	4.26106	+	6.91229i	0.213588	+	0.346482i
$399$	−1.53926			−0.0770596
$400$	3.01861	−	19.7709i	0.150930	−	0.988544i
$401$	17.1600			0.856931			0.428466	−	0.903558i	$-0.359054\pi$
$401$	17.1600			0.856931			0.428466	+	0.903558i	$0.359054\pi$
$402$	8.24440	+	13.3741i	0.411193	+	0.667037i
$403$	29.3908	−	29.3908i	1.46406	−	1.46406i
$404$	−10.4740	−	31.6644i	−0.521102	−	1.57536i
$405$	2.06370	+	0.860885i	0.102546	+	0.0427777i
$406$	6.74358	+	1.60013i	0.334678	+	0.0794129i
$407$	−30.5218			−1.51291
$408$	−0.445636	+	0.530241i	−0.0220623	+	0.0262508i
$409$		−	17.9588i		−	0.888006i	−0.896025	−	0.444003i	$-0.853558\pi$
$409$		−	17.9588i		−	0.888006i	0.896025	−	0.444003i	$-0.146442\pi$
$410$	1.05024	+	6.62502i	0.0518677	+	0.327187i
$411$	5.16211	−	5.16211i	0.254628	−	0.254628i
$412$	2.05980	−	4.09605i	0.101479	−	0.201798i
$413$	4.14621	−	4.14621i	0.204022	−	0.204022i
$414$	5.13750	+	8.33405i	0.252495	+	0.409596i
$415$	19.8957	−	8.18267i	0.976642	−	0.401671i
$416$	28.3961	−	12.2047i	1.39223	−	0.598387i
$417$		−	12.5231i		−	0.613260i
$418$	−6.66797	+	4.11045i	−0.326141	+	0.201049i
$419$	23.4031	+	23.4031i	1.14332	+	1.14332i	0.987840	+	0.155476i	$0.0496913\pi$
$419$	23.4031	+	23.4031i	1.14332	+	1.14332i	0.155476	+	0.987840i	$0.450309\pi$
$420$	0.239427	−	3.15450i	0.0116828	−	0.153924i
$421$	−27.0016	+	27.0016i	−1.31598	+	1.31598i	−0.399043	+	0.916932i	$0.630658\pi$
$421$	−27.0016	+	27.0016i	−1.31598	+	1.31598i	−0.916932	+	0.399043i	$0.869342\pi$
$422$	18.9405	+	4.49422i	0.922007	+	0.218775i
$423$	−4.47342			−0.217505
$424$	−3.78381	+	4.50218i	−0.183758	+	0.218645i
$425$	0.870129	−	0.861442i	0.0422075	−	0.0417861i
$426$	−2.87029	−	0.681065i	−0.139066	−	0.0329977i
$427$	0.0380178	+	0.0380178i	0.00183981	+	0.00183981i
$428$	25.4840	−	8.42966i	1.23182	−	0.407463i
$429$	9.83441	+	9.83441i	0.474810	+	0.474810i
$430$	−2.47682	−	1.79899i	−0.119443	−	0.0867551i
$431$	−28.4043			−1.36819			−0.684093	−	0.729395i	$-0.739802\pi$
$431$	−28.4043			−1.36819			−0.684093	+	0.729395i	$0.739802\pi$
$432$	0.583877	−	3.95716i	0.0280918	−	0.190389i
$433$			4.04564i			0.194421i	0.995264	+	0.0972106i	$0.0309920\pi$
$433$			4.04564i			0.194421i	−0.995264	+	0.0972106i	$0.969008\pi$
$434$	−6.47844	+	3.99362i	−0.310975	+	0.191700i
$435$	−14.2973	−	5.96419i	−0.685503	−	0.285961i
$436$	31.9709	−	10.5754i	1.53113	−	0.506471i
$437$	10.6516	+	10.6516i	0.509537	+	0.509537i
$438$	3.16690	−	13.3466i	0.151320	−	0.637725i
$439$			10.4690i			0.499660i	0.968290	+	0.249830i	$0.0803748\pi$
$439$			10.4690i			0.499660i	−0.968290	+	0.249830i	$0.919625\pi$
$440$	−7.38662	−	14.3044i	−0.352143	−	0.681937i
$441$			6.49959i			0.309504i
$442$	1.84109	+	0.436856i	0.0875717	+	0.0207791i
$443$	−1.81582	−	1.81582i	−0.0862722	−	0.0862722i	0.662654	−	0.748926i	$-0.269430\pi$
$443$	−1.81582	−	1.81582i	−0.0862722	−	0.0862722i	−0.748926	+	0.662654i	$0.769430\pi$
$444$	10.7740	−	21.4247i	0.511310	−	1.01677i
$445$	−2.64707	+	6.34554i	−0.125483	+	0.300807i
$446$	16.4035	+	26.6097i	0.776726	+	1.26000i
$447$			7.65634i			0.362132i
$448$	−5.57474	+	0.973939i	−0.263382	+	0.0460143i
$449$	−22.2064			−1.04799			−0.523993	−	0.851723i	$-0.675558\pi$
$449$	−22.2064			−1.04799			−0.523993	+	0.851723i	$0.675558\pi$
$450$	−1.66700	+	6.87176i	−0.0785830	+	0.323938i
$451$	3.81797	+	3.81797i	0.179781	+	0.179781i
$452$	14.1658	+	7.12364i	0.666303	+	0.335068i
$453$	0.241511	+	0.241511i	0.0113472	+	0.0113472i
$454$	−2.47211	+	10.4185i	−0.116022	+	0.488963i
$455$	−7.99294	+	3.28732i	−0.374715	+	0.154112i
$456$	−0.531580	−	6.13152i	−0.0248935	−	0.287135i
$457$	12.2280			0.572000			0.286000	−	0.958230i	$-0.407674\pi$
$457$	12.2280			0.572000			0.286000	+	0.958230i	$0.407674\pi$
$458$	8.45072	−	35.6148i	0.394876	−	1.66417i
$459$	0.173159	−	0.173159i	0.00808238	−	0.00808238i
$460$	−23.4859	+	20.1722i	−1.09503	+	0.940534i
$461$	0.723447	+	0.723447i	0.0336943	+	0.0336943i	0.723753	−	0.690059i	$-0.242415\pi$
$461$	0.723447	+	0.723447i	0.0336943	+	0.0336943i	−0.690059	+	0.723753i	$0.742415\pi$
$462$	−1.33630	−	2.16774i	−0.0621703	−	0.100853i
$463$			5.42343i			0.252048i	0.992027	+	0.126024i	$0.0402217\pi$
$463$			5.42343i			0.252048i	−0.992027	+	0.126024i	$0.959778\pi$
$464$	−4.04509	+	27.4151i	−0.187788	+	1.27271i
$465$	15.7320	−	6.47021i	0.729552	−	0.300049i
$466$	14.5120	−	8.94586i	0.672254	−	0.414409i
$467$	−13.3242	+	13.3242i	−0.616571	+	0.616571i	−0.944650	−	0.328079i	$-0.893599\pi$
$467$	−13.3242	+	13.3242i	−0.616571	+	0.616571i	0.328079	+	0.944650i	$0.393599\pi$
$468$	−10.3747	+	3.43177i	−0.479571	+	0.158634i
$469$	−5.55696	+	5.55696i	−0.256597	+	0.256597i
$470$	−2.21489	−	13.9717i	−0.102165	−	0.644468i
$471$		−	4.05122i		−	0.186671i
$472$	17.9479	+	15.0842i	0.826121	+	0.694306i
$473$	−2.46413			−0.113301
$474$	−2.39877	+	10.1094i	−0.110179	+	0.464340i
$475$	−0.0545788	+	10.8796i	−0.00250425	+	0.499191i
$476$	−0.309527	−	0.155654i	−0.0141872	−	0.00713438i
$477$	1.47026	−	1.47026i	0.0673188	−	0.0673188i
$478$	33.6108	−	20.7193i	1.53732	−	0.947678i
$479$	−1.25963			−0.0575541			−0.0287771	−	0.999586i	$-0.509161\pi$
$479$	−1.25963			−0.0575541			−0.0287771	+	0.999586i	$0.509161\pi$
$480$	12.6484	−	0.135663i	0.577317	−	0.00619215i
$481$	−65.5140			−2.98718
$482$	−16.5070	+	10.1757i	−0.751873	+	0.463490i
$483$	−3.46282	+	3.46282i	−0.157564	+	0.157564i
$484$	8.07724	+	4.06185i	0.367147	+	0.184629i
$485$	−1.20457	+	2.88758i	−0.0546967	+	0.131118i
$486$	−0.326501	+	1.37601i	−0.0148104	+	0.0624170i
$487$	15.8116			0.716491			0.358246	−	0.933627i	$-0.383375\pi$
$487$	15.8116			0.716491			0.358246	+	0.933627i	$0.383375\pi$
$488$	−0.138311	+	0.164570i	−0.00626106	+	0.00744974i
$489$		−	8.40349i		−	0.380019i
$490$	−20.3000	+	3.21809i	−0.917061	+	0.145378i
$491$	−15.6008	+	15.6008i	−0.704054	+	0.704054i	−0.965278	−	0.261224i	$-0.915874\pi$
$491$	−15.6008	+	15.6008i	−0.704054	+	0.704054i	0.261224	+	0.965278i	$0.415874\pi$
$492$	−4.02772	+	1.33230i	−0.181584	+	0.0600647i
$493$	−1.19964	+	1.19964i	−0.0540292	+	0.0540292i
$494$	−14.3125	+	8.82293i	−0.643952	+	0.396962i
$495$	2.16499	+	5.26405i	0.0973090	+	0.236601i
$496$	−18.1455	−	24.4271i	−0.814759	−	1.09681i
$497$		−	1.47560i		−	0.0661896i
$498$	7.13970	+	11.5820i	0.319938	+	0.519002i
$499$	25.6650	+	25.6650i	1.14892	+	1.14892i	0.986765	+	0.162159i	$0.0518459\pi$
$499$	25.6650	+	25.6650i	1.14892	+	1.14892i	0.162159	+	0.986765i	$0.448154\pi$
$500$	−22.2878	−	1.80414i	−0.996740	−	0.0806834i
$501$	−10.2244	+	10.2244i	−0.456792	+	0.456792i
$502$	4.18880	−	17.6533i	0.186955	−	0.787905i
$503$	4.72004			0.210456			0.105228	−	0.994448i	$-0.466443\pi$
$503$	4.72004			0.210456			0.105228	+	0.994448i	$0.466443\pi$
$504$	1.99335	−	0.172815i	0.0887907	−	0.00769781i
$505$	−34.4857	+	14.1832i	−1.53459	+	0.631144i
$506$	−5.75355	+	24.2478i	−0.255777	+	1.07795i
$507$	11.9168	+	11.9168i	0.529244	+	0.529244i
$508$	34.7472	+	17.4735i	1.54166	+	0.775261i
$509$	−11.8862	−	11.8862i	−0.526848	−	0.526848i	0.392783	−	0.919631i	$-0.371512\pi$
$509$	−11.8862	−	11.8862i	−0.526848	−	0.526848i	−0.919631	+	0.392783i	$0.871512\pi$
$510$	0.626559	+	0.455089i	0.0277445	+	0.0201517i
$511$	6.86141			0.303531
$512$	−5.80482	−	21.8702i	−0.256539	−	0.966534i
$513$			2.17595i			0.0960706i
$514$	6.85280	+	11.1166i	0.302264	+	0.490332i
$515$	−4.73084	−	1.97349i	−0.208466	−	0.0869625i
$516$	0.869818	−	1.72969i	0.0382916	−	0.0761453i
$517$	−8.05183	−	8.05183i	−0.354119	−	0.354119i
$518$	11.6715	+	2.76942i	0.512815	+	0.121681i
$519$		−	9.40587i		−	0.412872i
$520$	−15.8551	−	30.7039i	−0.695292	−	1.34646i
$521$		−	5.01467i		−	0.219696i	−0.993948	−	0.109848i	$-0.964964\pi$
$521$		−	5.01467i		−	0.219696i	0.993948	−	0.109848i	$-0.0350365\pi$
$522$	2.26199	−	9.53295i	0.0990046	−	0.417246i
$523$	18.9502	+	18.9502i	0.828635	+	0.828635i	0.987328	−	0.158693i	$-0.0507279\pi$
$523$	18.9502	+	18.9502i	0.828635	+	0.828635i	−0.158693	+	0.987328i	$0.550728\pi$
$524$	−0.950739	+	0.314487i	−0.0415332	+	0.0137384i
$525$	−3.53694	−	0.0177435i	−0.154365	−	0.000774388i
$526$	22.3335	−	13.7674i	0.973785	−	0.600287i
$527$		−	1.86292i		−	0.0811499i
$528$	8.17353	−	6.07166i	0.355707	−	0.264235i
$529$	24.9252			1.08370
$530$	5.32000	+	3.86408i	0.231086	+	0.167845i
$531$	−5.86121	−	5.86121i	−0.254355	−	0.254355i
$532$	2.92278	−	0.966802i	0.126718	−	0.0419162i
$533$	8.19512	+	8.19512i	0.354970	+	0.354970i
$534$	−4.23099	−	1.00393i	−0.183093	−	0.0434445i
$535$	−11.4149	−	27.7546i	−0.493508	−	1.19994i
$536$	−24.0548	−	20.2166i	−1.03901	−	0.873224i
$537$	−24.4178			−1.05370
$538$	−28.0175	−	6.64803i	−1.20792	−	0.286617i
$539$	−11.6988	+	11.6988i	−0.503903	+	0.503903i
$540$	−4.45931	−	0.338461i	−0.191898	−	0.0145651i
$541$	−22.8366	−	22.8366i	−0.981822	−	0.981822i	0.0180153	−	0.999838i	$-0.494265\pi$
$541$	−22.8366	−	22.8366i	−0.981822	−	0.981822i	−0.999838	+	0.0180153i	$0.994265\pi$
$542$	−23.2313	+	14.3209i	−0.997870	+	0.615134i
$543$			7.24419i			0.310878i
$544$	0.513139	−	1.28673i	0.0220007	−	0.0551681i
$545$	−14.3205	−	34.8195i	−0.613423	−	1.49150i
$546$	−2.86832	−	4.65298i	−0.122753	−	0.199129i
$547$	−0.00963023	+	0.00963023i	−0.000411759	+	0.000411759i	−0.707313	−	0.706901i	$-0.750093\pi$
$547$	−0.00963023	+	0.00963023i	−0.000411759	+	0.000411759i	0.706901	+	0.707313i	$0.250093\pi$
$548$	−6.55960	+	13.0442i	−0.280212	+	0.557220i
$549$	0.0537432	−	0.0537432i	0.00229371	−	0.00229371i
$550$	−15.3691	+	9.36820i	−0.655343	+	0.399461i
$551$		−	15.0749i		−	0.642214i
$552$	−14.9897	−	12.5980i	−0.638006	−	0.536206i
$553$	−5.19718			−0.221006
$554$	−6.85504	−	1.62657i	−0.291243	−	0.0691064i
$555$	−24.7450	−	10.3225i	−1.05037	−	0.438167i
$556$	7.86570	+	23.7791i	0.333580	+	1.00846i
$557$	25.6660	−	25.6660i	1.08750	−	1.08750i	0.0917192	−	0.995785i	$-0.470764\pi$
$557$	25.6660	−	25.6660i	1.08750	−	1.08750i	0.995785	−	0.0917192i	$-0.0292362\pi$
$558$	5.64551	+	9.15813i	0.238993	+	0.387695i
$559$	−5.28916			−0.223707
$560$	1.52670	+	6.14020i	0.0645148	+	0.259471i
$561$	0.623348			0.0263178
$562$	−21.6754	−	35.1618i	−0.914321	−	1.48321i
$563$	−6.16719	+	6.16719i	−0.259916	+	0.259916i	−0.825020	−	0.565104i	$-0.808836\pi$
$563$	−6.16719	+	6.16719i	−0.259916	+	0.259916i	0.565104	+	0.825020i	$0.308836\pi$
$564$	8.49420	−	2.80973i	0.357670	−	0.118311i
$565$	6.82515	−	16.3612i	0.287136	−	0.688319i
$566$	19.1538	+	4.54483i	0.805093	+	0.191033i
$567$	−0.707398			−0.0297079
$568$	5.87791	−	0.509593i	0.246632	−	0.0213820i
$569$		−	4.05892i		−	0.170159i	−0.996374	−	0.0850794i	$-0.972886\pi$
$569$		−	4.05892i		−	0.170159i	0.996374	−	0.0850794i	$-0.0271144\pi$
$570$	−6.79610	+	1.07736i	−0.284657	+	0.0451257i
$571$	−12.9113	+	12.9113i	−0.540323	+	0.540323i	−0.923624	−	0.383301i	$-0.874787\pi$
$571$	−12.9113	+	12.9113i	−0.540323	+	0.540323i	0.383301	+	0.923624i	$0.374787\pi$
$572$	−24.8507	−	12.4968i	−1.03906	−	0.522517i
$573$	12.5893	−	12.5893i	0.525925	−	0.525925i
$574$	−1.11355	−	1.80640i	−0.0464788	−	0.0753978i
$575$	24.3527	+	24.5983i	1.01558	+	1.02582i
$576$	1.37679	+	7.88064i	0.0573663	+	0.328360i
$577$			10.4193i			0.433761i	0.976198	+	0.216880i	$0.0695882\pi$
$577$			10.4193i			0.433761i	−0.976198	+	0.216880i	$0.930412\pi$
$578$	−20.3933	+	12.5714i	−0.848251	+	0.522902i
$579$	12.1780	+	12.1780i	0.506099	+	0.506099i
$580$	30.8940	+	2.34485i	1.28280	+	0.0973646i
$581$	−4.81236	+	4.81236i	−0.199650	+	0.199650i
$582$	−1.92534	−	0.456848i	−0.0798080	−	0.0189369i
$583$	5.29274			0.219203
$584$	2.36957	+	27.3318i	0.0980534	+	1.13100i
$585$	4.64706	+	11.2991i	0.192132	+	0.467160i
$586$	−23.0088	−	5.45955i	−0.950484	−	0.225532i
$587$	−27.7728	−	27.7728i	−1.14631	−	1.14631i	−0.987273	−	0.159033i	$-0.949162\pi$
$587$	−27.7728	−	27.7728i	−1.14631	−	1.14631i	−0.159033	−	0.987273i	$-0.550838\pi$
$588$	−4.08235	−	12.3415i	−0.168353	−	0.508956i
$589$	11.7049	+	11.7049i	0.482291	+	0.482291i
$590$	15.4042	−	21.2082i	0.634180	−	0.873128i
$591$	14.2502			0.586175
$592$	−7.00104	+	47.4487i	−0.287741	+	1.95013i
$593$		−	25.4466i		−	1.04496i	−0.852650	−	0.522482i	$-0.825006\pi$
$593$		−	25.4466i		−	1.04496i	0.852650	−	0.522482i	$-0.174994\pi$
$594$	−3.06439	+	1.88904i	−0.125734	+	0.0775081i
$595$	−0.149132	+	0.357497i	−0.00611380	+	0.0146559i
$596$	−4.80890	−	14.5380i	−0.196980	−	0.595498i
$597$	4.06006	+	4.06006i	0.166167	+	0.166167i
$598$	−12.3498	+	52.0470i	−0.505020	+	2.12836i
$599$			1.32051i			0.0539544i	0.999636	+	0.0269772i	$0.00858816\pi$
$599$			1.32051i			0.0539544i	−0.999636	+	0.0269772i	$0.991412\pi$
$600$	−1.15079	−	14.0952i	−0.0469809	−	0.575436i
$601$			23.8236i			0.971787i	0.874018	+	0.485893i	$0.161506\pi$
$601$			23.8236i			0.971787i	−0.874018	+	0.485893i	$0.838494\pi$
$602$	0.942275	+	0.223584i	0.0384043	+	0.00911261i
$603$	7.85550	+	7.85550i	0.319901	+	0.319901i
$604$	−0.610277	−	0.306893i	−0.0248318	−	0.0124873i
$605$	3.89165	−	9.32902i	0.158218	−	0.379279i
$606$	−12.3754	−	20.0753i	−0.502716	−	0.815505i
$607$			1.20300i			0.0488283i	0.999702	+	0.0244141i	$0.00777203\pi$
$607$			1.20300i			0.0488283i	−0.999702	+	0.0244141i	$0.992228\pi$
$608$	4.86054	+	11.3087i	0.197121	+	0.458630i
$609$	4.90083			0.198592
$610$	0.194464	+	0.141246i	0.00787363	+	0.00571886i
$611$	−17.2830	−	17.2830i	−0.699193	−	0.699193i
$612$	−0.220037	+	0.437558i	−0.00889447	+	0.0176872i
$613$	−4.84340	−	4.84340i	−0.195623	−	0.195623i	0.602498	−	0.798121i	$-0.294172\pi$
$613$	−4.84340	−	4.84340i	−0.195623	−	0.195623i	−0.798121	+	0.602498i	$0.794172\pi$
$614$	−7.67561	+	32.3481i	−0.309762	+	1.30546i
$615$	1.80411	+	4.38659i	0.0727486	+	0.176884i
$616$	3.89893	+	3.27682i	0.157092	+	0.132027i
$617$	26.9719			1.08585			0.542924	−	0.839782i	$-0.317317\pi$
$617$	26.9719			1.08585			0.542924	+	0.839782i	$0.317317\pi$
$618$	0.748471	−	3.15436i	0.0301079	−	0.126887i
$619$	19.9202	−	19.9202i	0.800660	−	0.800660i	−0.182539	−	0.983199i	$-0.558432\pi$
$619$	19.9202	−	19.9202i	0.800660	−	0.800660i	0.983199	+	0.182539i	$0.0584316\pi$
$620$	−25.8082	+	22.1669i	−1.03648	+	0.890243i
$621$	4.89516	+	4.89516i	0.196436	+	0.196436i
$622$	−10.2463	−	16.6216i	−0.410840	−	0.666464i
$623$		−	2.17513i		−	0.0871446i
$624$	17.5442	−	13.0326i	0.702329	−	0.521721i
$625$	−0.250824	+	24.9987i	−0.0100330	+	0.999950i
$626$	8.91310	−	5.49446i	0.356239	−	0.219603i
$627$	−3.91656	+	3.91656i	−0.156412	+	0.156412i
$628$	2.54455	+	7.69253i	0.101539	+	0.306965i
$629$	−2.07628	+	2.07628i	−0.0827868	+	0.0827868i
$630$	−0.350248	−	2.20940i	−0.0139542	−	0.0880245i
$631$		−	12.7975i		−	0.509462i	−0.967012	−	0.254731i	$-0.918013\pi$
$631$		−	12.7975i		−	0.509462i	0.967012	−	0.254731i	$-0.0819870\pi$
$632$	−1.79483	−	20.7025i	−0.0713945	−	0.823502i
$633$	13.7648			0.547101
$634$	−0.834425	+	3.51661i	−0.0331392	+	0.139662i
$635$	16.7413	−	40.1321i	0.664360	−	1.59260i
$636$	−1.86829	+	3.71522i	−0.0740827	+	0.147318i
$637$	−25.1110	+	25.1110i	−0.994934	+	0.994934i
$638$	21.2300	−	13.0872i	0.840505	−	0.518127i
$639$	−2.08595			−0.0825190
$640$	−23.9317	+	8.20197i	−0.945985	+	0.324211i
$641$	10.9406			0.432129			0.216064	−	0.976379i	$-0.430678\pi$
$641$	10.9406			0.432129			0.216064	+	0.976379i	$0.430678\pi$
$642$	16.1570	−	9.95992i	0.637664	−	0.393087i
$643$	18.2613	−	18.2613i	0.720157	−	0.720157i	−0.248480	−	0.968637i	$-0.579931\pi$
$643$	18.2613	−	18.2613i	0.720157	−	0.720157i	0.968637	+	0.248480i	$0.0799311\pi$
$644$	4.40028	−	8.75024i	0.173395	−	0.344808i
$645$	−1.99775	−	0.833371i	−0.0786612	−	0.0328140i
$646$	−0.173978	+	0.733215i	−0.00684508	+	0.0288479i
$647$	10.5055			0.413014			0.206507	−	0.978445i	$-0.433790\pi$
$647$	10.5055			0.413014			0.206507	+	0.978445i	$0.433790\pi$
$648$	−0.244298	−	2.81786i	−0.00959691	−	0.110696i
$649$		−	21.0995i		−	0.828228i
$650$	−32.9893	+	20.1085i	−1.29395	+	0.788720i
$651$	−3.80523	+	3.80523i	−0.149139	+	0.149139i
$652$	5.27818	+	15.9567i	0.206709	+	0.624911i
$653$	−11.1836	+	11.1836i	−0.437648	+	0.437648i	−0.891220	−	0.453572i	$-0.850150\pi$
$653$	−11.1836	+	11.1836i	−0.437648	+	0.437648i	0.453572	+	0.891220i	$0.350150\pi$
$654$	20.2697	−	12.4952i	0.792608	−	0.488601i
$655$	0.425857	+	1.03545i	0.0166396	+	0.0404583i
$656$	6.81109	−	5.05958i	0.265928	−	0.197543i
$657$		−	9.69951i		−	0.378414i
$658$	2.34841	+	3.80958i	0.0915505	+	0.148513i
$659$	2.60687	+	2.60687i	0.101549	+	0.101549i	0.756056	−	0.654507i	$-0.227124\pi$
$659$	2.60687	+	2.60687i	0.101549	+	0.101549i	−0.654507	+	0.756056i	$0.727124\pi$
$660$	−7.41723	−	8.63564i	−0.288715	−	0.336142i
$661$	15.9084	−	15.9084i	0.618766	−	0.618766i	−0.326449	−	0.945215i	$-0.605852\pi$
$661$	15.9084	−	15.9084i	0.618766	−	0.618766i	0.945215	+	0.326449i	$0.105852\pi$
$662$	2.69062	−	11.3394i	0.104574	−	0.440717i
$663$	1.33799			0.0519634
$664$	−20.8316	−	17.5077i	−0.808421	−	0.679430i
$665$	−1.30918	−	3.18319i	−0.0507677	−	0.123439i
$666$	3.91494	−	16.4992i	0.151701	−	0.639329i
$667$	−33.9135	−	33.9135i	−1.31314	−	1.31314i
$668$	12.9924	−	25.8361i	0.502689	−	0.999629i
$669$	15.6297	+	15.6297i	0.604278	+	0.604278i
$670$	−20.6455	+	28.4243i	−0.797604	+	1.09813i
$671$	0.193468			0.00746874
$672$	−3.67645	+	1.58015i	−0.141822	+	0.0609557i
$673$			27.1091i			1.04498i	0.852645	+	0.522490i	$0.174997\pi$
$673$			27.1091i			1.04498i	−0.852645	+	0.522490i	$0.825003\pi$
$674$	18.9504	+	30.7413i	0.729943	+	1.18411i
$675$	−0.0250827	+	4.99994i	−0.000965434	+	0.192448i
$676$	−30.1127	−	15.1429i	−1.15818	−	0.582420i
$677$	11.0637	+	11.0637i	0.425211	+	0.425211i	0.886993	−	0.461782i	$-0.152790\pi$
$677$	11.0637	+	11.0637i	0.425211	+	0.425211i	−0.461782	+	0.886993i	$0.652790\pi$
$678$	10.9091	+	2.58852i	0.418960	+	0.0994114i
$679$		−	0.989807i		−	0.0379853i
$680$	−1.47556	−	0.470592i	−0.0565851	−	0.0180464i
$681$			7.57152i			0.290141i
$682$	−6.32247	+	26.6455i	−0.242100	+	1.02031i
$683$	17.4289	+	17.4289i	0.666898	+	0.666898i	0.956997	−	0.290098i	$-0.0936881\pi$
$683$	17.4289	+	17.4289i	0.666898	+	0.666898i	−0.290098	+	0.956997i	$0.593688\pi$
$684$	−1.36670	−	4.13173i	−0.0522572	−	0.157981i
$685$	15.0657	+	6.28474i	0.575631	+	0.240128i
$686$	11.4963	−	7.08687i	0.438931	−	0.270578i
$687$		−	25.8827i		−	0.987487i
$688$	−0.565216	+	3.83068i	−0.0215487	+	0.146043i
$689$	11.3607			0.432807
$690$	−12.8652	+	17.7126i	−0.489771	+	0.674309i
$691$	26.0352	+	26.0352i	0.990426	+	0.990426i	0.999955	−	0.00952887i	$-0.00303318\pi$
$691$	26.0352	+	26.0352i	0.990426	+	0.990426i	−0.00952887	+	0.999955i	$0.503033\pi$
$692$	5.90777	+	17.8600i	0.224580	+	0.678936i
$693$	−1.27326	−	1.27326i	−0.0483673	−	0.0483673i
$694$	−34.2546	−	8.12797i	−1.30029	−	0.308533i
$695$	25.8978	−	10.6512i	0.982359	−	0.404023i
$696$	1.69249	+	19.5220i	0.0641536	+	0.739981i
$697$	0.519443			0.0196753
$698$	9.87700	+	2.34363i	0.373850	+	0.0887076i
$699$	8.52387	−	8.52387i	0.322402	−	0.322402i
$700$	6.72714	−	2.18784i	0.254262	−	0.0826926i
$701$	2.08057	+	2.08057i	0.0785822	+	0.0785822i	0.745305	−	0.666723i	$-0.232304\pi$
$701$	2.08057	+	2.08057i	0.0785822	+	0.0785822i	−0.666723	+	0.745305i	$0.732304\pi$
$702$	−6.57760	+	4.05475i	−0.248256	+	0.153036i
$703$		−	26.0910i		−	0.984039i
$704$	−11.7065	+	16.6627i	−0.441204	+	0.627999i
$705$	−3.80474	−	9.25102i	−0.143295	−	0.348414i
$706$	0.127299	+	0.206504i	0.00479095	+	0.00777187i
$707$	8.34137	−	8.34137i	0.313709	−	0.313709i
$708$	14.8107	+	7.44797i	0.556622	+	0.279912i
$709$	−3.27484	+	3.27484i	−0.122989	+	0.122989i	−0.765922	−	0.642933i	$-0.777717\pi$
$709$	−3.27484	+	3.27484i	−0.122989	+	0.122989i	0.642933	+	0.765922i	$0.277717\pi$
$710$	−1.03280	−	6.51500i	−0.0387603	−	0.244504i
$711$			7.34690i			0.275530i
$712$	8.66443	−	0.751173i	0.324713	−	0.0281514i
$713$	52.6641			1.97229
$714$	−0.238367	−	0.0565599i	−0.00892064	−	0.00211670i
$715$	−11.9732	+	28.7019i	−0.447771	+	1.07339i
$716$	46.3648	−	15.3366i	1.73273	−	0.573157i
$717$	19.7419	−	19.7419i	0.737275	−	0.737275i
$718$	12.7417	+	20.6695i	0.475515	+	0.771380i
$719$	−2.03220			−0.0757882			−0.0378941	−	0.999282i	$-0.512065\pi$
$719$	−2.03220			−0.0757882			−0.0378941	+	0.999282i	$0.512065\pi$
$720$	8.67999	−	2.15819i	0.323484	−	0.0804310i
$721$	1.62164			0.0603930
$722$	10.5864	+	17.1733i	0.393986	+	0.639123i
$723$	−9.69568	+	9.69568i	−0.360586	+	0.360586i
$724$	−4.55003	−	13.7554i	−0.169101	−	0.511215i
$725$	0.173772	−	34.6394i	0.00645375	−	1.28648i
$726$	6.22027	+	1.47595i	0.230856	+	0.0547778i
$727$	−6.37077			−0.236279			−0.118139	−	0.992997i	$-0.537693\pi$
$727$	−6.37077			−0.236279			−0.118139	+	0.992997i	$0.537693\pi$
$728$	8.36891	+	7.03357i	0.310172	+	0.260682i
$729$			1.00000i			0.0370370i
$730$	30.2942	−	4.80244i	1.12124	−	0.177746i
$731$	−0.167625	+	0.167625i	−0.00619984	+	0.00619984i
$732$	−0.0682926	+	0.135804i	−0.00252417	+	0.00501947i
$733$	6.95026	−	6.95026i	0.256714	−	0.256714i	−0.567002	−	0.823716i	$-0.691897\pi$
$733$	6.95026	−	6.95026i	0.256714	−	0.256714i	0.823716	+	0.567002i	$0.191897\pi$
$734$	−17.3005	−	28.0648i	−0.638572	−	1.03589i
$735$	−13.4411	+	5.52804i	−0.495784	+	0.203905i
$736$	36.3755	+	14.5063i	1.34082	+	0.534709i
$737$			28.2787i			1.04166i
$738$	−2.55359	+	1.57415i	−0.0939990	+	0.0579454i
$739$	0.0483355	+	0.0483355i	0.00177805	+	0.00177805i	0.707995	−	0.706217i	$-0.249600\pi$
$739$	0.0483355	+	0.0483355i	0.00177805	+	0.00177805i	−0.706217	+	0.707995i	$0.749600\pi$
$740$	53.4698	+	4.05835i	1.96559	+	0.149188i
$741$	−8.40674	+	8.40674i	−0.308829	+	0.308829i
$742$	−2.02393	−	0.480240i	−0.0743007	−	0.0176302i
$743$	0.148848			0.00546069			0.00273035	−	0.999996i	$-0.499131\pi$
$743$	0.148848			0.00546069			0.00273035	+	0.999996i	$0.499131\pi$
$744$	−16.4719	−	13.8437i	−0.603891	−	0.507534i
$745$	−15.8333	+	6.51188i	−0.580087	+	0.238577i
$746$	−2.17592	−	0.516304i	−0.0796659	−	0.0189032i
$747$	6.80291	+	6.80291i	0.248905	+	0.248905i
$748$	−1.18362	+	0.391521i	−0.0432776	+	0.0143154i
$749$	6.71327	+	6.71327i	0.245297	+	0.245297i
$750$	−15.6286	+	2.39724i	−0.570676	+	0.0875347i
$751$	1.69304			0.0617798			0.0308899	−	0.999523i	$-0.490166\pi$
$751$	1.69304			0.0617798			0.0308899	+	0.999523i	$0.490166\pi$
$752$	−14.3641	+	10.6703i	−0.523806	+	0.389106i
$753$		−	12.8294i		−	0.467528i
$754$	45.5695	−	28.0912i	1.65954	−	1.02302i
$755$	−0.294034	+	0.704855i	−0.0107010	+	0.0256523i
$756$	1.34322	−	0.444312i	0.0488523	−	0.0161595i
$757$	26.6876	+	26.6876i	0.969977	+	0.969977i	0.999562	−	0.0295851i	$-0.00941860\pi$
$757$	26.6876	+	26.6876i	0.969977	+	0.969977i	−0.0295851	+	0.999562i	$0.509419\pi$
$758$	−10.3295	+	43.5326i	−0.375183	+	1.58118i
$759$			17.6219i			0.639633i
$760$	12.2279	−	6.31430i	0.443551	−	0.229044i
$761$		−	17.1363i		−	0.621189i	−0.950542	−	0.310595i	$-0.899472\pi$
$761$		−	17.1363i		−	0.621189i	0.950542	−	0.310595i	$-0.100528\pi$
$762$	26.7587	+	6.34935i	0.969367	+	0.230013i
$763$	8.42212	+	8.42212i	0.304901	+	0.304901i
$764$	−15.9975	+	31.8120i	−0.578769	+	1.15092i
$765$	0.505369	+	0.210817i	0.0182716	+	0.00762211i
$766$	−23.8343	−	38.6640i	−0.861169	−	1.39699i
$767$		−	45.2893i		−	1.63530i
$768$	−7.56405	−	14.0991i	−0.272944	−	0.508758i
$769$	−25.6406			−0.924622			−0.462311	−	0.886718i	$-0.652980\pi$
$769$	−25.6406			−0.924622			−0.462311	+	0.886718i	$0.652980\pi$
$770$	3.34634	−	4.60718i	0.120594	−	0.166031i
$771$	6.52954	+	6.52954i	0.235156	+	0.235156i
$772$	−30.7726	−	15.4748i	−1.10753	−	0.556950i
$773$	−27.4452	−	27.4452i	−0.987137	−	0.987137i	0.0127818	−	0.999918i	$-0.495931\pi$
$773$	−27.4452	−	27.4452i	−0.987137	−	0.987137i	−0.999918	+	0.0127818i	$0.995931\pi$
$774$	0.316066	−	1.33203i	0.0113607	−	0.0478788i
$775$	26.7607	+	27.0306i	0.961274	+	0.970967i
$776$	3.94281	−	0.341827i	0.141539	−	0.0122709i
$777$	8.48212			0.304294
$778$	10.5004	−	44.2530i	0.376458	−	1.58655i
$779$	−3.26371	+	3.26371i	−0.116934	+	0.116934i
$780$	−15.9208	−	18.5361i	−0.570056	−	0.663698i
$781$	−3.75456	−	3.75456i	−0.134349	−	0.134349i
$782$	1.25809	+	2.04088i	0.0449893	+	0.0729816i
$783$		−	6.92797i		−	0.247586i
$784$	15.5033	+	20.8702i	0.553688	+	0.745363i
$785$	8.37792	−	3.44565i	0.299021	−	0.122981i
$786$	−0.602772	+	0.371577i	−0.0215002	+	0.0132537i
$787$	9.65912	−	9.65912i	0.344310	−	0.344310i	−0.513675	−	0.857985i	$-0.671716\pi$
$787$	9.65912	−	9.65912i	0.344310	−	0.344310i	0.857985	+	0.513675i	$0.171716\pi$
$788$	−27.0585	+	8.95047i	−0.963919	+	0.318847i
$789$	13.1180	−	13.1180i	0.467012	−	0.467012i
$790$	−22.9464	+	3.63761i	−0.816396	+	0.129420i
$791$			5.60829i			0.199408i
$792$	4.63222	−	5.51166i	0.164599	−	0.195848i
$793$	0.415271			0.0147467
$794$	9.99810	−	42.1361i	0.354819	−	1.49535i
$795$	4.29099	+	1.79001i	0.152186	+	0.0634851i
$796$	−10.2594	−	5.15921i	−0.363635	−	0.182863i
$797$	11.9978	−	11.9978i	0.424984	−	0.424984i	−0.461931	−	0.886916i	$-0.652843\pi$
$797$	11.9978	−	11.9978i	0.424984	−	0.424984i	0.886916	+	0.461931i	$0.152843\pi$
$798$	1.85305	−	1.14231i	0.0655973	−	0.0404373i
$799$	−1.09547			−0.0387549
$800$	11.0383	+	26.0414i	0.390262	+	0.920704i
$801$	−3.07483			−0.108644
$802$	−20.6582	+	12.7347i	−0.729466	+	0.449678i
$803$	17.4584	−	17.4584i	0.616094	−	0.616094i
$804$	−19.8501	−	9.98215i	−0.700060	−	0.352043i
$805$	−10.1063	−	4.21590i	−0.356201	−	0.148591i
$806$	−13.5710	+	57.1935i	−0.478016	+	2.01456i
$807$	−20.3614			−0.716756
$808$	36.1078	+	30.3464i	1.27027	+	1.06758i
$809$		−	36.2916i		−	1.27594i	−0.770060	−	0.637972i	$-0.779774\pi$
$809$		−	36.2916i		−	1.27594i	0.770060	−	0.637972i	$-0.220226\pi$
$810$	−3.12328	+	0.495122i	−0.109741	+	0.0173968i
$811$	17.0781	−	17.0781i	0.599693	−	0.599693i	−0.340538	−	0.940231i	$-0.610609\pi$
$811$	17.0781	−	17.0781i	0.599693	−	0.599693i	0.940231	+	0.340538i	$0.110609\pi$
$812$	−9.30577	+	3.07818i	−0.326569	+	0.108023i
$813$	−13.6453	+	13.6453i	−0.478563	+	0.478563i
$814$	36.7439	−	22.6507i	1.28787	−	0.793906i
$815$	17.3784	−	7.14735i	0.608738	−	0.250361i
$816$	0.142982	−	0.969045i	0.00500538	−	0.0339234i
$817$		−	2.10641i		−	0.0736939i
$818$	13.3275	+	21.6198i	0.465984	+	0.755919i
$819$	−2.73301	−	2.73301i	−0.0954992	−	0.0954992i
$820$	−6.18086	−	7.19617i	−0.215845	−	0.251301i
$821$	21.9249	−	21.9249i	0.765183	−	0.765183i	−0.212071	−	0.977254i	$-0.568021\pi$
$821$	21.9249	−	21.9249i	0.765183	−	0.765183i	0.977254	+	0.212071i	$0.0680209\pi$
$822$	−2.38356	+	10.0453i	−0.0831363	+	0.350370i
$823$	−4.38382			−0.152810			−0.0764052	−	0.997077i	$-0.524344\pi$
$823$	−4.38382			−0.152810			−0.0764052	+	0.997077i	$0.524344\pi$
$824$	0.560028	+	6.45966i	0.0195095	+	0.225033i
$825$	−9.04467	+	8.95438i	−0.314895	+	0.311751i
$826$	−1.91448	+	8.06839i	−0.0666132	+	0.280735i
$827$	21.5889	+	21.5889i	0.750718	+	0.750718i	0.974613	−	0.223895i	$-0.0718772\pi$
$827$	21.5889	+	21.5889i	0.750718	+	0.750718i	−0.223895	+	0.974613i	$0.571877\pi$
$828$	−12.3696	−	6.22038i	−0.429874	−	0.216173i
$829$	7.88066	+	7.88066i	0.273707	+	0.273707i	0.830590	−	0.556884i	$-0.188003\pi$
$829$	7.88066	+	7.88066i	0.273707	+	0.273707i	−0.556884	+	0.830590i	$0.688003\pi$
$830$	−17.8791	+	24.6156i	−0.620593	+	0.854421i
$831$	−4.98183			−0.172818
$832$	−25.1275	+	35.7659i	−0.871138	+	1.23996i
$833$			1.59165i			0.0551473i
$834$	9.29358	+	15.0760i	0.321810	+	0.522040i
$835$	−29.8401	−	12.4480i	−1.03266	−	0.430779i
$836$	4.97685	−	9.89678i	0.172128	−	0.342287i
$837$	5.37920	+	5.37920i	0.185932	+	0.185932i
$838$	−45.5417	−	10.8062i	−1.57321	−	0.373294i
$839$		−	6.03706i		−	0.208423i	−0.994555	−	0.104211i	$-0.966768\pi$
$839$		−	6.03706i		−	0.208423i	0.994555	−	0.104211i	$-0.0332318\pi$
$840$	2.05277	+	3.97525i	0.0708271	+	0.137159i
$841$			18.9968i			0.655063i
$842$	12.4678	−	52.5442i	0.429667	−	1.81079i
$843$	−20.6529	−	20.6529i	−0.711324	−	0.711324i
$844$	−26.1368	+	8.64558i	−0.899666	+	0.297593i
$845$	−14.5084	+	34.7794i	−0.499105	+	1.19645i
$846$	5.38535	−	3.31978i	0.185152	−	0.114137i
$847$			3.19781i			0.109878i
$848$	1.21404	−	8.22799i	0.0416902	−	0.282550i
$849$	13.9198			0.477727
$850$	−0.408221	+	1.68279i	−0.0140019	+	0.0577191i
$851$	−58.6959	−	58.6959i	−2.01207	−	2.01207i
$852$	3.96084	−	1.31017i	0.135696	−	0.0448858i
$853$	−12.6685	−	12.6685i	−0.433763	−	0.433763i	0.456144	−	0.889906i	$-0.349230\pi$
$853$	−12.6685	−	12.6685i	−0.433763	−	0.433763i	−0.889906	+	0.456144i	$0.849230\pi$
$854$	−0.0739815	−	0.0175544i	−0.00253160	−	0.000600700i
$855$	−4.49986	+	1.85069i	−0.153892	+	0.0632924i
$856$	−24.4233	+	29.0601i	−0.834772	+	0.993255i
$857$	4.79580			0.163821			0.0819106	−	0.996640i	$-0.473898\pi$
$857$	4.79580			0.163821			0.0819106	+	0.996640i	$0.473898\pi$
$858$	−19.1375	−	4.54096i	−0.653342	−	0.155026i
$859$	−34.0244	+	34.0244i	−1.16090	+	1.16090i	−0.176616	+	0.984280i	$0.556515\pi$
$859$	−34.0244	+	34.0244i	−1.16090	+	1.16090i	−0.984280	+	0.176616i	$0.943485\pi$
$860$	4.31679	+	0.327644i	0.147201	+	0.0111726i
$861$	−1.06102	−	1.06102i	−0.0361596	−	0.0361596i
$862$	34.1946	−	21.0792i	1.16467	−	0.717960i
$863$			8.20297i			0.279232i	0.990206	+	0.139616i	$0.0445869\pi$
$863$			8.20297i			0.279232i	−0.990206	+	0.139616i	$0.955413\pi$
$864$	2.23375	+	5.19715i	0.0759939	+	0.176811i
$865$	19.4513	−	7.99990i	0.661365	−	0.272005i
$866$	−3.00233	−	4.87037i	−0.102023	−	0.165502i
$867$	−11.9784	+	11.9784i	−0.406808	+	0.406808i
$868$	4.83539	−	9.61548i	0.164124	−	0.326371i
$869$	−13.2239	+	13.2239i	−0.448590	+	0.448590i
$870$	21.6380	−	3.43019i	0.733596	−	0.116294i
$871$			60.6991i			2.05671i
$872$	−30.6402	+	36.4573i	−1.03761	+	1.23460i
$873$	−1.39922			−0.0473565
$874$	−20.7277	−	4.91831i	−0.701127	−	0.166364i
$875$	−2.97155	−	7.32948i	−0.100457	−	0.247782i
$876$	6.09220	+	18.4176i	0.205836	+	0.622272i
$877$	−23.9525	+	23.9525i	−0.808817	+	0.808817i	−0.984455	−	0.175638i	$-0.943801\pi$
$877$	−23.9525	+	23.9525i	−0.808817	+	0.808817i	0.175638	+	0.984455i	$0.443801\pi$
$878$	−7.76922	−	12.6032i	−0.262198	−	0.425338i
$879$	−16.7214			−0.563999
$880$	19.5079	+	11.7388i	0.657612	+	0.395714i
$881$	27.4850			0.925993			0.462997	−	0.886360i	$-0.346774\pi$
$881$	27.4850			0.925993			0.462997	+	0.886360i	$0.346774\pi$
$882$	−4.82343	−	7.82456i	−0.162413	−	0.263467i
$883$	−22.9566	+	22.9566i	−0.772550	+	0.772550i	−0.978552	−	0.206001i	$-0.933955\pi$
$883$	−22.9566	+	22.9566i	−0.772550	+	0.772550i	0.206001	+	0.978552i	$0.433955\pi$
$884$	−2.54060	+	0.840386i	−0.0854497	+	0.0282652i
$885$	7.13588	−	17.1061i	0.239870	−	0.575014i
$886$	3.53353	+	0.838440i	0.118711	+	0.0281679i
$887$	8.52038			0.286086			0.143043	−	0.989716i	$-0.454311\pi$
$887$	8.52038			0.286086			0.143043	+	0.989716i	$0.454311\pi$
$888$	2.92927	+	33.7878i	0.0983000	+	1.13384i
$889$			13.7565i			0.461379i
$890$	−1.52241	−	9.60354i	−0.0510314	−	0.321911i
$891$	−1.79993	+	1.79993i	−0.0602998	+	0.0602998i
$892$	−39.4948	−	19.8610i	−1.32238	−	0.664994i
$893$	6.88294	−	6.88294i	0.230329	−	0.230329i
$894$	−5.68187	−	9.21712i	−0.190030	−	0.308267i
$895$	−20.7678	−	50.4958i	−0.694192	−	1.68789i
$896$	5.98841	−	5.30957i	0.200059	−	0.177380i
$897$			37.8247i			1.26293i
$898$	26.7333	−	16.4797i	0.892102	−	0.549934i
$899$	−37.2670	−	37.2670i	−1.24292	−	1.24292i
$900$	−3.09280	−	9.50971i	−0.103093	−	0.316990i
$901$	0.360044	−	0.360044i	0.0119948	−	0.0119948i
$902$	−7.42964	−	1.76291i	−0.247380	−	0.0586986i
$903$	0.684789			0.0227883
$904$	−22.3401	+	1.93680i	−0.743022	+	0.0644172i
$905$	−14.9810	+	6.16134i	−0.497984	+	0.204810i
$906$	−0.469973	−	0.111516i	−0.0156138	−	0.00370486i
$907$	−21.1812	−	21.1812i	−0.703312	−	0.703312i	0.261808	−	0.965120i	$-0.415681\pi$
$907$	−21.1812	−	21.1812i	−0.703312	−	0.703312i	−0.965120	+	0.261808i	$0.915681\pi$
$908$	−4.75563	−	14.3769i	−0.157821	−	0.477115i
$909$	−11.7916	−	11.7916i	−0.391104	−	0.391104i
$910$	7.18278	−	9.88913i	0.238107	−	0.327822i
$911$	−12.3002			−0.407525			−0.203763	−	0.979020i	$-0.565317\pi$
$911$	−12.3002			−0.407525			−0.203763	+	0.979020i	$0.565317\pi$
$912$	5.19023	+	6.98697i	0.171866	+	0.231362i
$913$			24.4895i			0.810484i
$914$	−14.7207	+	9.07454i	−0.486918	+	0.300159i
$915$	0.156851	+	0.0654311i	0.00518532	+	0.00216308i
$916$	16.2568	+	49.1465i	0.537139	+	1.62384i
$917$	−0.250454	−	0.250454i	−0.00827070	−	0.00827070i
$918$	−0.0799549	+	0.336963i	−0.00263891	+	0.0111214i
$919$		−	3.59430i		−	0.118565i	−0.998241	−	0.0592826i	$-0.981119\pi$
$919$		−	3.59430i		−	0.118565i	0.998241	−	0.0592826i	$-0.0188813\pi$
$920$	13.3035	−	41.7136i	0.438604	−	1.37526i
$921$			23.5087i			0.774638i
$922$	−1.40781	−	0.334046i	−0.0463636	−	0.0110012i
$923$	−8.05902	−	8.05902i	−0.265266	−	0.265266i
$924$	3.21742	+	1.61796i	0.105845	+	0.0532271i
$925$	0.300757	−	59.9522i	0.00988882	−	1.97122i
$926$	−4.02480	−	6.52903i	−0.132263	−	0.214557i
$927$		−	2.29240i		−	0.0752923i
$928$	−15.4754	−	36.0057i	−0.508005	−	1.18195i
$929$	−35.8527			−1.17629			−0.588145	−	0.808756i	$-0.700142\pi$
$929$	−35.8527			−1.17629			−0.588145	+	0.808756i	$0.700142\pi$
$930$	−14.1374	+	19.4641i	−0.463583	+	0.638253i
$931$	−10.0005	−	10.0005i	−0.327752	−	0.327752i
$932$	−10.8315	+	21.5390i	−0.354796	+	0.705535i
$933$	−9.76298	−	9.76298i	−0.319626	−	0.319626i
$934$	6.15234	−	25.9285i	0.201311	−	0.848406i
$935$	0.530171	+	1.28908i	0.0173385	+	0.0421575i
$936$	9.94289	−	11.8306i	0.324993	−	0.386694i
$937$	40.7563			1.33145			0.665725	−	0.746198i	$-0.268123\pi$
$937$	40.7563			1.33145			0.665725	+	0.746198i	$0.268123\pi$
$938$	2.56588	−	10.8137i	0.0837790	−	0.353079i
$939$	5.23528	−	5.23528i	0.170847	−	0.170847i
$940$	13.0350	+	15.1762i	0.425155	+	0.494994i
$941$	36.2143	+	36.2143i	1.18055	+	1.18055i	0.979602	+	0.200950i	$0.0644027\pi$
$941$	36.2143	+	36.2143i	1.18055	+	1.18055i	0.200950	+	0.979602i	$0.435597\pi$
$942$	3.00647	+	4.87709i	0.0979560	+	0.158904i
$943$			14.6845i			0.478193i
$944$	−32.8009	−	4.83976i	−1.06758	−	0.157521i
$945$	−0.601657	−	1.46290i	−0.0195719	−	0.0475880i
$946$	2.96645	−	1.82866i	0.0964477	−	0.0594549i
$947$	−36.5242	+	36.5242i	−1.18688	+	1.18688i	−0.208951	+	0.977926i	$0.567005\pi$
$947$	−36.5242	+	36.5242i	−1.18688	+	1.18688i	−0.977926	+	0.208951i	$0.932995\pi$
$948$	−4.61454	−	13.9504i	−0.149873	−	0.453088i
$949$	37.4738	−	37.4738i	1.21645	−	1.21645i
$950$	−8.00821	−	13.1380i	−0.259821	−	0.426253i
$951$			2.55566i			0.0828729i
$952$	0.488139	−	0.0423198i	0.0158207	−	0.00137159i
$953$	−16.0927			−0.521294			−0.260647	−	0.965434i	$-0.583936\pi$
$953$	−16.0927			−0.521294			−0.260647	+	0.965434i	$0.583936\pi$
$954$	−0.678882	+	2.86109i	−0.0219796	+	0.0926311i
$955$	36.7421	+	15.3272i	1.18895	+	0.495975i
$956$	−25.0865	+	49.8860i	−0.811354	+	1.61343i
$957$	12.4699	−	12.4699i	0.403093	−	0.403093i
$958$	1.51642	−	0.934791i	0.0489932	−	0.0302017i
$959$	−5.16423			−0.166762
$960$	−15.1261	+	9.54985i	−0.488194	+	0.308220i
$961$	26.8716			0.866826
$962$	78.8694	−	48.6188i	2.54285	−	1.56753i
$963$	9.49009	−	9.49009i	0.305814	−	0.305814i
$964$	12.3205	−	24.5001i	0.396817	−	0.789095i
$965$	−14.8264	+	35.5416i	−0.477278	+	1.14413i
$966$	1.59893	−	6.73855i	0.0514448	−	0.216809i
$967$	21.3561			0.686767			0.343384	−	0.939195i	$-0.388427\pi$
$967$	21.3561			0.686767			0.343384	+	0.939195i	$0.388427\pi$
$968$	−12.7382	+	1.10435i	−0.409421	+	0.0354952i
$969$			0.532856i			0.0171178i
$970$	−0.692786	−	4.37016i	−0.0222440	−	0.140317i
$971$	−20.0626	+	20.0626i	−0.643839	+	0.643839i	−0.951497	−	0.307658i	$-0.900455\pi$
$971$	−20.0626	+	20.0626i	−0.643839	+	0.643839i	0.307658	+	0.951497i	$0.400455\pi$
$972$	−0.628094	−	1.89881i	−0.0201461	−	0.0609045i
$973$	−6.26414	+	6.26414i	−0.200819	+	0.200819i
$974$	−19.0349	+	11.7340i	−0.609916	+	0.375981i
$975$	−19.4140	+	19.2202i	−0.621747	+	0.615540i
$976$	0.0443773	−	0.300761i	0.00142048	−	0.00962714i
$977$			27.7769i			0.888661i	0.895863	+	0.444331i	$0.146558\pi$
$977$			27.7769i			0.888661i	−0.895863	+	0.444331i	$0.853442\pi$
$978$	6.23634	+	10.1166i	0.199416	+	0.323493i
$979$	−5.53447	−	5.53447i	−0.176882	−	0.176882i
$980$	22.0501	−	18.9390i	0.704364	−	0.604985i
$981$	11.9058	−	11.9058i	0.380122	−	0.380122i
$982$	7.20354	−	30.3586i	0.229874	−	0.968783i
$983$	−0.428090			−0.0136540			−0.00682698	−	0.999977i	$-0.502173\pi$
$983$	−0.428090			−0.0136540			−0.00682698	+	0.999977i	$0.502173\pi$
$984$	3.86008	−	4.59292i	0.123055	−	0.146417i
$985$	12.1201	+	29.4694i	0.386179	+	0.938973i
$986$	0.553926	−	2.33447i	0.0176406	−	0.0743446i
$987$	2.23763	+	2.23763i	0.0712245	+	0.0712245i
$988$	10.6826	−	21.2431i	0.339859	−	0.675832i
$989$	−4.73871	−	4.73871i	−0.150682	−	0.150682i
$990$	−6.51285	−	4.73049i	−0.206992	−	0.150345i
$991$	−5.82267			−0.184963			−0.0924816	−	0.995714i	$-0.529480\pi$
$991$	−5.82267			−0.184963			−0.0924816	+	0.995714i	$0.529480\pi$
$992$	39.9723	+	15.9407i	1.26912	+	0.506117i
$993$		−	8.24078i		−	0.261513i
$994$	1.09506	+	1.77641i	0.0347332	+	0.0563442i
$995$	−4.94303	+	11.8494i	−0.156704	+	0.375650i
$996$	−17.1903	−	8.64460i	−0.544696	−	0.273915i
$997$	−20.1044	−	20.1044i	−0.636713	−	0.636713i	0.313030	−	0.949743i	$-0.398656\pi$
$997$	−20.1044	−	20.1044i	−0.636713	−	0.636713i	−0.949743	+	0.313030i	$0.898656\pi$
$998$	−49.9433	−	11.8506i	−1.58093	−	0.375125i
$999$		−	11.9906i		−	0.379366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bl.a.109.5	✓	48
3.2	odd	2		720.2.bm.h.109.20		48
4.3	odd	2		960.2.bl.a.529.15		48
5.4	even	2	inner	240.2.bl.a.109.20	yes	48
8.3	odd	2		1920.2.bl.b.289.7		48
8.5	even	2		1920.2.bl.a.289.18		48
15.14	odd	2		720.2.bm.h.109.5		48
16.3	odd	4		1920.2.bl.b.1249.18		48
16.5	even	4	inner	240.2.bl.a.229.20	yes	48
16.11	odd	4		960.2.bl.a.49.9		48
16.13	even	4		1920.2.bl.a.1249.7		48
20.19	odd	2		960.2.bl.a.529.9		48
40.19	odd	2		1920.2.bl.b.289.18		48
40.29	even	2		1920.2.bl.a.289.7		48
48.5	odd	4		720.2.bm.h.469.5		48
80.19	odd	4		1920.2.bl.b.1249.7		48
80.29	even	4		1920.2.bl.a.1249.18		48
80.59	odd	4		960.2.bl.a.49.15		48
80.69	even	4	inner	240.2.bl.a.229.5	yes	48
240.149	odd	4		720.2.bm.h.469.20		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.5	✓	48	1.1	even	1	trivial
240.2.bl.a.109.20	yes	48	5.4	even	2	inner
240.2.bl.a.229.5	yes	48	80.69	even	4	inner
240.2.bl.a.229.20	yes	48	16.5	even	4	inner
720.2.bm.h.109.5		48	15.14	odd	2
720.2.bm.h.109.20		48	3.2	odd	2
720.2.bm.h.469.5		48	48.5	odd	4
720.2.bm.h.469.20		48	240.149	odd	4
960.2.bl.a.49.9		48	16.11	odd	4
960.2.bl.a.49.15		48	80.59	odd	4
960.2.bl.a.529.9		48	20.19	odd	2
960.2.bl.a.529.15		48	4.3	odd	2
1920.2.bl.a.289.7		48	40.29	even	2
1920.2.bl.a.289.18		48	8.5	even	2
1920.2.bl.a.1249.7		48	16.13	even	4
1920.2.bl.a.1249.18		48	80.29	even	4
1920.2.bl.b.289.7		48	8.3	odd	2
1920.2.bl.b.289.18		48	40.19	odd	2
1920.2.bl.b.1249.7		48	80.19	odd	4
1920.2.bl.b.1249.18		48	16.3	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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20386 + 0.742113i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.898535 - 1.78679i) q^{4} +(-2.06370 - 0.860885i) q^{5} +(0.326501 - 1.37601i) q^{6} +0.707398 q^{7} +(0.244298 + 2.81786i) q^{8} -1.00000i q^{9} +(3.12328 - 0.495122i) q^{10} +(1.79993 - 1.79993i) q^{11} +(0.628094 + 1.89881i) q^{12} +(3.86348 - 3.86348i) q^{13} +(-0.851604 + 0.524969i) q^{14} +(2.06800 - 0.850522i) q^{15} +(-2.38527 - 3.21100i) q^{16} -0.244884i q^{17} +(0.742113 + 1.20386i) q^{18} +(1.53863 + 1.53863i) q^{19} +(-3.39254 + 2.91388i) q^{20} +(-0.500206 + 0.500206i) q^{21} +(-0.831102 + 3.50260i) q^{22} +6.92280 q^{23} +(-2.16527 - 1.81978i) q^{24} +(3.51775 + 3.55323i) q^{25} +(-1.78393 + 7.51820i) q^{26} +(0.707107 + 0.707107i) q^{27} +(0.635622 - 1.26397i) q^{28} +(-4.89882 - 4.89882i) q^{29} +(-1.85839 + 2.55859i) q^{30} +7.60734 q^{31} +(5.25444 + 2.09543i) q^{32} +2.54548i q^{33} +(0.181732 + 0.294805i) q^{34} +(-1.45986 - 0.608988i) q^{35} +(-1.78679 - 0.898535i) q^{36} +(-8.47863 - 8.47863i) q^{37} +(-2.99413 - 0.710450i) q^{38} +5.46378i q^{39} +(1.92169 - 6.02554i) q^{40} +2.12118i q^{41} +(0.230966 - 0.973384i) q^{42} +(-0.684507 - 0.684507i) q^{43} +(-1.59880 - 4.83340i) q^{44} +(-0.860885 + 2.06370i) q^{45} +(-8.33405 + 5.13750i) q^{46} -4.47342i q^{47} +(3.95716 + 0.583877i) q^{48} -6.49959 q^{49} +(-6.87176 - 1.66700i) q^{50} +(0.173159 + 0.173159i) q^{51} +(-3.43177 - 10.3747i) q^{52} +(1.47026 + 1.47026i) q^{53} +(-1.37601 - 0.326501i) q^{54} +(-5.26405 + 2.16499i) q^{55} +(0.172815 + 1.99335i) q^{56} -2.17595 q^{57} +(9.53295 + 2.26199i) q^{58} +(5.86121 - 5.86121i) q^{59} +(0.338461 - 4.45931i) q^{60} +(0.0537432 + 0.0537432i) q^{61} +(-9.15813 + 5.64551i) q^{62} -0.707398i q^{63} +(-7.88064 + 1.37679i) q^{64} +(-11.2991 + 4.64706i) q^{65} +(-1.88904 - 3.06439i) q^{66} +(-7.85550 + 7.85550i) q^{67} +(-0.437558 - 0.220037i) q^{68} +(-4.89516 + 4.89516i) q^{69} +(2.20940 - 0.350248i) q^{70} -2.08595i q^{71} +(2.81786 - 0.244298i) q^{72} +9.69951 q^{73} +(16.4992 + 3.91494i) q^{74} +(-4.99994 - 0.0250827i) q^{75} +(4.13173 - 1.36670i) q^{76} +(1.27326 - 1.27326i) q^{77} +(-4.05475 - 6.57760i) q^{78} -7.34690 q^{79} +(2.15819 + 8.67999i) q^{80} -1.00000 q^{81} +(-1.57415 - 2.55359i) q^{82} +(-6.80291 + 6.80291i) q^{83} +(0.444312 + 1.34322i) q^{84} +(-0.210817 + 0.505369i) q^{85} +(1.33203 + 0.316066i) q^{86} +6.92797 q^{87} +(5.51166 + 4.63222i) q^{88} -3.07483i q^{89} +(-0.495122 - 3.12328i) q^{90} +(2.73301 - 2.73301i) q^{91} +(6.22038 - 12.3696i) q^{92} +(-5.37920 + 5.37920i) q^{93} +(3.31978 + 5.38535i) q^{94} +(-1.85069 - 4.49986i) q^{95} +(-5.19715 + 2.23375i) q^{96} -1.39922i q^{97} +(7.82456 - 4.82343i) q^{98} +(-1.79993 - 1.79993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51}+ \cdots - 40 q^{96}+O(q^{100}) \) 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more