LMFDB - Embedded newform 420.2.n.b.71.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(71,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0, 0]))

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

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

chi := DirichletCharacter("420.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.n (of order $2$, degree $1$, 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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.19
Character	$\chi$	$=$	420.71
Dual form			420.2.n.b.71.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19442 - 0.757207i) q^{2} +(-0.667879 + 1.59810i) q^{3} +(0.853276 - 1.80884i) q^{4} -1.00000i q^{5} +(0.412368 + 2.41453i) q^{6} -1.00000i q^{7} +(-0.350500 - 2.80663i) q^{8} +(-2.10788 - 2.13468i) q^{9} +O(q^{10})$	\(q+(1.19442 - 0.757207i) q^{2} +(-0.667879 + 1.59810i) q^{3} +(0.853276 - 1.80884i) q^{4} -1.00000i q^{5} +(0.412368 + 2.41453i) q^{6} -1.00000i q^{7} +(-0.350500 - 2.80663i) q^{8} +(-2.10788 - 2.13468i) q^{9} +(-0.757207 - 1.19442i) q^{10} +6.52007 q^{11} +(2.32084 + 2.57171i) q^{12} +0.852819 q^{13} +(-0.757207 - 1.19442i) q^{14} +(1.59810 + 0.667879i) q^{15} +(-2.54384 - 3.08689i) q^{16} -4.75118i q^{17} +(-4.13408 - 0.953605i) q^{18} +5.33314i q^{19} +(-1.80884 - 0.853276i) q^{20} +(1.59810 + 0.667879i) q^{21} +(7.78770 - 4.93704i) q^{22} +0.680081 q^{23} +(4.71937 + 1.31435i) q^{24} -1.00000 q^{25} +(1.01862 - 0.645760i) q^{26} +(4.81925 - 1.94290i) q^{27} +(-1.80884 - 0.853276i) q^{28} -0.963476i q^{29} +(2.41453 - 0.412368i) q^{30} +7.17468i q^{31} +(-5.37582 - 1.76083i) q^{32} +(-4.35462 + 10.4198i) q^{33} +(-3.59763 - 5.67490i) q^{34} -1.00000 q^{35} +(-5.65990 + 1.99135i) q^{36} -1.92133 q^{37} +(4.03829 + 6.37001i) q^{38} +(-0.569580 + 1.36289i) q^{39} +(-2.80663 + 0.350500i) q^{40} +6.55405i q^{41} +(2.41453 - 0.412368i) q^{42} -8.66947i q^{43} +(5.56342 - 11.7938i) q^{44} +(-2.13468 + 2.10788i) q^{45} +(0.812302 - 0.514962i) q^{46} -8.50098 q^{47} +(6.63215 - 2.00366i) q^{48} -1.00000 q^{49} +(-1.19442 + 0.757207i) q^{50} +(7.59288 + 3.17321i) q^{51} +(0.727690 - 1.54262i) q^{52} +1.34848i q^{53} +(4.28503 - 5.96980i) q^{54} -6.52007i q^{55} +(-2.80663 + 0.350500i) q^{56} +(-8.52292 - 3.56189i) q^{57} +(-0.729551 - 1.15079i) q^{58} +0.990010 q^{59} +(2.57171 - 2.32084i) q^{60} -9.34821 q^{61} +(5.43271 + 8.56957i) q^{62} +(-2.13468 + 2.10788i) q^{63} +(-7.75430 + 1.96745i) q^{64} -0.852819i q^{65} +(2.68867 + 15.7429i) q^{66} +12.1617i q^{67} +(-8.59415 - 4.05407i) q^{68} +(-0.454211 + 1.08684i) q^{69} +(-1.19442 + 0.757207i) q^{70} -6.95364 q^{71} +(-5.25244 + 6.66423i) q^{72} +9.97510 q^{73} +(-2.29487 + 1.45484i) q^{74} +(0.667879 - 1.59810i) q^{75} +(9.64683 + 4.55064i) q^{76} -6.52007i q^{77} +(0.351675 + 2.05916i) q^{78} +12.5813i q^{79} +(-3.08689 + 2.54384i) q^{80} +(-0.113716 + 8.99928i) q^{81} +(4.96277 + 7.82828i) q^{82} -9.19190 q^{83} +(2.57171 - 2.32084i) q^{84} -4.75118 q^{85} +(-6.56458 - 10.3550i) q^{86} +(1.53974 + 0.643485i) q^{87} +(-2.28528 - 18.2994i) q^{88} -1.22380i q^{89} +(-0.953605 + 4.13408i) q^{90} -0.852819i q^{91} +(0.580297 - 1.23016i) q^{92} +(-11.4659 - 4.79181i) q^{93} +(-10.1537 + 6.43700i) q^{94} +5.33314 q^{95} +(6.40438 - 7.41511i) q^{96} +11.1919 q^{97} +(-1.19442 + 0.757207i) q^{98} +(-13.7435 - 13.9183i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9	$ 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9} + 2 q^{10} + 16 q^{12} + 2 q^{14} + 6 q^{16} - 24 q^{18} - 8 q^{20} + 8 q^{22} + 14 q^{24} - 24 q^{25} + 20 q^{26} - 8 q^{28} - 8 q^{30} - 20 q^{32} + 16 q^{33} - 16 q^{34} - 24 q^{35} + 30 q^{36} + 60 q^{38} + 12 q^{39} - 14 q^{40} - 8 q^{42} - 24 q^{44} - 12 q^{46} - 8 q^{47} + 36 q^{48} - 24 q^{49} - 36 q^{51} + 20 q^{52} - 38 q^{54} - 14 q^{56} - 24 q^{57} + 44 q^{58} + 8 q^{59} + 14 q^{60} + 16 q^{61} + 28 q^{62} - 22 q^{64} - 12 q^{66} - 32 q^{68} - 72 q^{71} + 56 q^{72} - 24 q^{73} + 64 q^{74} + 48 q^{76} - 92 q^{78} - 20 q^{81} - 16 q^{82} + 40 q^{83} + 14 q^{84} - 16 q^{85} + 40 q^{86} + 80 q^{87} - 12 q^{88} - 10 q^{90} - 108 q^{92} - 48 q^{93} - 36 q^{94} + 34 q^{96} + 24 q^{97} - 84 q^{99}+O(q^{100}) $ 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9 + 2 * q^10 + 16 * q^12 + 2 * q^14 + 6 * q^16 - 24 * q^18 - 8 * q^20 + 8 * q^22 + 14 * q^24 - 24 * q^25 + 20 * q^26 - 8 * q^28 - 8 * q^30 - 20 * q^32 + 16 * q^33 - 16 * q^34 - 24 * q^35 + 30 * q^36 + 60 * q^38 + 12 * q^39 - 14 * q^40 - 8 * q^42 - 24 * q^44 - 12 * q^46 - 8 * q^47 + 36 * q^48 - 24 * q^49 - 36 * q^51 + 20 * q^52 - 38 * q^54 - 14 * q^56 - 24 * q^57 + 44 * q^58 + 8 * q^59 + 14 * q^60 + 16 * q^61 + 28 * q^62 - 22 * q^64 - 12 * q^66 - 32 * q^68 - 72 * q^71 + 56 * q^72 - 24 * q^73 + 64 * q^74 + 48 * q^76 - 92 * q^78 - 20 * q^81 - 16 * q^82 + 40 * q^83 + 14 * q^84 - 16 * q^85 + 40 * q^86 + 80 * q^87 - 12 * q^88 - 10 * q^90 - 108 * q^92 - 48 * q^93 - 36 * q^94 + 34 * q^96 + 24 * q^97 - 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	1.19442	−	0.757207i	0.844582	−	0.535426i
$2$	1.19442	−	0.757207i	0.844582	−	0.535426i
$3$	−0.667879	+	1.59810i	−0.385600	+	0.922666i
$3$	−0.667879	+	1.59810i	−0.385600	+	0.922666i
$4$	0.853276	−	1.80884i	0.426638	−	0.904422i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.412368	+	2.41453i	0.168349	+	0.985728i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−0.350500	−	2.80663i	−0.123920	−	0.992292i
$9$	−2.10788	−	2.13468i	−0.702625	−	0.711560i
$10$	−0.757207	−	1.19442i	−0.239450	−	0.377709i
$11$	6.52007			1.96587			0.982937	−	0.183940i	$-0.0588853\pi$
$11$	6.52007			1.96587			0.982937	+	0.183940i	$0.0588853\pi$
$12$	2.32084	+	2.57171i	0.669968	+	0.742390i
$13$	0.852819			0.236529			0.118265	−	0.992982i	$-0.462267\pi$
$13$	0.852819			0.236529			0.118265	+	0.992982i	$0.462267\pi$
$14$	−0.757207	−	1.19442i	−0.202372	−	0.319222i
$15$	1.59810	+	0.667879i	0.412629	+	0.172446i
$16$	−2.54384	−	3.08689i	−0.635960	−	0.771722i
$17$		−	4.75118i		−	1.15233i	−0.817333	−	0.576165i	$-0.804548\pi$
$17$		−	4.75118i		−	1.15233i	0.817333	−	0.576165i	$-0.195452\pi$
$18$	−4.13408	−	0.953605i	−0.974413	−	0.224767i
$19$			5.33314i			1.22351i	0.791048	+	0.611754i	$0.209536\pi$
$19$			5.33314i			1.22351i	−0.791048	+	0.611754i	$0.790464\pi$
$20$	−1.80884	−	0.853276i	−0.404470	−	0.190798i
$21$	1.59810	+	0.667879i	0.348735	+	0.145743i
$22$	7.78770	−	4.93704i	1.66034	−	1.05258i
$23$	0.680081			0.141807			0.0709033	−	0.997483i	$-0.477412\pi$
$23$	0.680081			0.141807			0.0709033	+	0.997483i	$0.477412\pi$
$24$	4.71937	+	1.31435i	0.963338	+	0.268291i
$25$	−1.00000			−0.200000
$26$	1.01862	−	0.645760i	0.199769	−	0.126644i
$27$	4.81925	−	1.94290i	0.927465	−	0.373911i
$28$	−1.80884	−	0.853276i	−0.341840	−	0.161254i
$29$		−	0.963476i		−	0.178913i	−0.995991	−	0.0894565i	$-0.971487\pi$
$29$		−	0.963476i		−	0.178913i	0.995991	−	0.0894565i	$-0.0285130\pi$
$30$	2.41453	−	0.412368i	0.440831	−	0.0752878i
$31$			7.17468i			1.28861i	0.764769	+	0.644305i	$0.222853\pi$
$31$			7.17468i			1.28861i	−0.764769	+	0.644305i	$0.777147\pi$
$32$	−5.37582	−	1.76083i	−0.950321	−	0.311273i
$33$	−4.35462	+	10.4198i	−0.758041	+	1.81385i
$34$	−3.59763	−	5.67490i	−0.616988	−	0.973238i
$35$	−1.00000			−0.169031
$36$	−5.65990	+	1.99135i	−0.943317	+	0.331892i
$37$	−1.92133			−0.315865			−0.157932	−	0.987450i	$-0.550483\pi$
$37$	−1.92133			−0.315865			−0.157932	+	0.987450i	$0.550483\pi$
$38$	4.03829	+	6.37001i	0.655097	+	1.03335i
$39$	−0.569580	+	1.36289i	−0.0912057	+	0.218238i
$40$	−2.80663	+	0.350500i	−0.443767	+	0.0554189i
$41$			6.55405i			1.02357i	0.859114	+	0.511785i	$0.171016\pi$
$41$			6.55405i			1.02357i	−0.859114	+	0.511785i	$0.828984\pi$
$42$	2.41453	−	0.412368i	0.372570	−	0.0636298i
$43$		−	8.66947i		−	1.32208i	−0.750350	−	0.661041i	$-0.770115\pi$
$43$		−	8.66947i		−	1.32208i	0.750350	−	0.661041i	$-0.229885\pi$
$44$	5.56342	−	11.7938i	0.838717	−	1.77798i
$45$	−2.13468	+	2.10788i	−0.318219	+	0.314224i
$46$	0.812302	−	0.514962i	0.119767	−	0.0759270i
$47$	−8.50098			−1.24000			−0.619998	−	0.784604i	$-0.712867\pi$
$47$	−8.50098			−1.24000			−0.619998	+	0.784604i	$0.712867\pi$
$48$	6.63215	−	2.00366i	0.957268	−	0.289203i
$49$	−1.00000			−0.142857
$50$	−1.19442	+	0.757207i	−0.168916	+	0.107085i
$51$	7.59288	+	3.17321i	1.06322	+	0.444339i
$52$	0.727690	−	1.54262i	0.100912	−	0.213923i
$53$			1.34848i			0.185227i	0.995702	+	0.0926137i	$0.0295222\pi$
$53$			1.34848i			0.185227i	−0.995702	+	0.0926137i	$0.970478\pi$
$54$	4.28503	−	5.96980i	0.583118	−	0.812387i
$55$		−	6.52007i		−	0.879166i
$56$	−2.80663	+	0.350500i	−0.375051	+	0.0468375i
$57$	−8.52292	−	3.56189i	−1.12889	−	0.471784i
$58$	−0.729551	−	1.15079i	−0.0957947	−	0.151107i
$59$	0.990010			0.128888			0.0644442	−	0.997921i	$-0.479473\pi$
$59$	0.990010			0.128888			0.0644442	+	0.997921i	$0.479473\pi$
$60$	2.57171	−	2.32084i	0.332007	−	0.299619i
$61$	−9.34821			−1.19692			−0.598458	−	0.801154i	$-0.704220\pi$
$61$	−9.34821			−1.19692			−0.598458	+	0.801154i	$0.704220\pi$
$62$	5.43271	+	8.56957i	0.689955	+	1.08834i
$63$	−2.13468	+	2.10788i	−0.268944	+	0.265567i
$64$	−7.75430	+	1.96745i	−0.969287	+	0.245931i
$65$		−	0.852819i		−	0.105779i
$66$	2.68867	+	15.7429i	0.330952	+	1.93782i
$67$			12.1617i			1.48579i	0.669409	+	0.742894i	$0.266548\pi$
$67$			12.1617i			1.48579i	−0.669409	+	0.742894i	$0.733452\pi$
$68$	−8.59415	−	4.05407i	−1.04219	−	0.491628i
$69$	−0.454211	+	1.08684i	−0.0546806	+	0.130840i
$70$	−1.19442	+	0.757207i	−0.142760	+	0.0905035i
$71$	−6.95364			−0.825245			−0.412623	−	0.910902i	$-0.635387\pi$
$71$	−6.95364			−0.825245			−0.412623	+	0.910902i	$0.635387\pi$
$72$	−5.25244	+	6.66423i	−0.619006	+	0.785387i
$73$	9.97510			1.16750			0.583749	−	0.811934i	$-0.301585\pi$
$73$	9.97510			1.16750			0.583749	+	0.811934i	$0.301585\pi$
$74$	−2.29487	+	1.45484i	−0.266774	+	0.169122i
$75$	0.667879	−	1.59810i	0.0771200	−	0.184533i
$76$	9.64683	+	4.55064i	1.10657	+	0.521995i
$77$		−	6.52007i		−	0.743031i
$78$	0.351675	+	2.05916i	0.0398194	+	0.233154i
$79$			12.5813i			1.41551i	0.706458	+	0.707755i	$0.250292\pi$
$79$			12.5813i			1.41551i	−0.706458	+	0.707755i	$0.749708\pi$
$80$	−3.08689	+	2.54384i	−0.345125	+	0.284410i
$81$	−0.113716	+	8.99928i	−0.0126351	+	0.999920i
$82$	4.96277	+	7.82828i	0.548046	+	0.864489i
$83$	−9.19190			−1.00894			−0.504471	−	0.863429i	$-0.668312\pi$
$83$	−9.19190			−1.00894			−0.504471	+	0.863429i	$0.668312\pi$
$84$	2.57171	−	2.32084i	0.280597	−	0.253224i
$85$	−4.75118			−0.515338
$86$	−6.56458	−	10.3550i	−0.707877	−	1.11661i
$87$	1.53974	+	0.643485i	0.165077	+	0.0689889i
$88$	−2.28528	−	18.2994i	−0.243612	−	1.95072i
$89$		−	1.22380i		−	0.129723i	−0.997894	−	0.0648614i	$-0.979339\pi$
$89$		−	1.22380i		−	0.129723i	0.997894	−	0.0648614i	$-0.0206605\pi$
$90$	−0.953605	+	4.13408i	−0.100519	+	0.435771i
$91$		−	0.852819i		−	0.0893997i
$92$	0.580297	−	1.23016i	0.0605001	−	0.128253i
$93$	−11.4659	−	4.79181i	−1.18896	−	0.496888i
$94$	−10.1537	+	6.43700i	−1.04728	+	0.663926i
$95$	5.33314			0.547169
$96$	6.40438	−	7.41511i	0.653645	−	0.756802i
$97$	11.1919			1.13636			0.568180	−	0.822904i	$-0.307648\pi$
$97$	11.1919			1.13636			0.568180	+	0.822904i	$0.307648\pi$
$98$	−1.19442	+	0.757207i	−0.120655	+	0.0764894i
$99$	−13.7435	−	13.9183i	−1.38127	−	1.39884i
$100$	−0.853276	+	1.80884i	−0.0853276	+	0.180884i
$101$			5.62486i			0.559694i	0.960045	+	0.279847i	$0.0902838\pi$
$101$			5.62486i			0.559694i	−0.960045	+	0.279847i	$0.909716\pi$
$102$	11.4719	−	1.95924i	1.13588	−	0.193993i
$103$		−	0.793497i		−	0.0781856i	−0.999236	−	0.0390928i	$-0.987553\pi$
$103$		−	0.793497i		−	0.0781856i	0.999236	−	0.0390928i	$-0.0124468\pi$
$104$	−0.298913	−	2.39354i	−0.0293108	−	0.234706i
$105$	0.667879	−	1.59810i	0.0651783	−	0.155959i
$106$	1.02108	+	1.61065i	0.0991756	+	0.156440i
$107$	−5.46738			−0.528551			−0.264276	−	0.964447i	$-0.585133\pi$
$107$	−5.46738			−0.528551			−0.264276	+	0.964447i	$0.585133\pi$
$108$	0.597744	−	10.3751i	0.0575179	−	0.998344i
$109$	11.8020			1.13043			0.565214	−	0.824945i	$-0.308794\pi$
$109$	11.8020			1.13043			0.565214	+	0.824945i	$0.308794\pi$
$110$	−4.93704	−	7.78770i	−0.470728	−	0.742528i
$111$	1.28322	−	3.07049i	0.121797	−	0.291438i
$112$	−3.08689	+	2.54384i	−0.291683	+	0.240370i
$113$		−	1.60607i		−	0.151087i	−0.997143	−	0.0755433i	$-0.975931\pi$
$113$		−	1.60607i		−	0.151087i	0.997143	−	0.0755433i	$-0.0240691\pi$
$114$	−12.8770	+	2.19922i	−1.20604	+	0.205976i
$115$		−	0.680081i		−	0.0634179i
$116$	−1.74278	−	0.822111i	−0.161813	−	0.0763311i
$117$	−1.79764	−	1.82050i	−0.166192	−	0.168305i
$118$	1.18249	−	0.749642i	0.108857	−	0.0690102i
$119$	−4.75118			−0.435540
$120$	1.31435	−	4.71937i	0.119983	−	0.430818i
$121$	31.5113			2.86466
$122$	−11.1657	+	7.07853i	−1.01089	+	0.640860i
$123$	−10.4741	−	4.37731i	−0.944413	−	0.394689i
$124$	12.9779	+	6.12198i	1.16545	+	0.549770i
$125$			1.00000i			0.0894427i
$126$	−0.953605	+	4.13408i	−0.0849539	+	0.368293i
$127$			21.1741i			1.87890i	0.342688	+	0.939449i	$0.388663\pi$
$127$			21.1741i			1.87890i	−0.342688	+	0.939449i	$0.611337\pi$
$128$	−7.77212	+	8.22156i	−0.686965	+	0.726690i
$129$	13.8547	+	5.79016i	1.21984	+	0.509795i
$130$	−0.645760	−	1.01862i	−0.0566369	−	0.0893392i
$131$	18.2263			1.59244			0.796220	−	0.605007i	$-0.206830\pi$
$131$	18.2263			1.59244			0.796220	+	0.605007i	$0.206830\pi$
$132$	15.1320	+	16.7677i	1.31707	+	1.45945i
$133$	5.33314			0.462442
$134$	9.20893	+	14.5262i	0.795530	+	1.25487i
$135$	−1.94290	−	4.81925i	−0.167218	−	0.414775i
$136$	−13.3348	+	1.66529i	−1.14345	+	0.142797i
$137$		−	0.169312i		−	0.0144653i	−0.999974	−	0.00723264i	$-0.997698\pi$
$137$		−	0.169312i		−	0.0144653i	0.999974	−	0.00723264i	$-0.00230224\pi$
$138$	0.280444	+	1.64207i	0.0238729	+	0.139783i
$139$		−	7.94749i		−	0.674097i	−0.941487	−	0.337049i	$-0.890571\pi$
$139$		−	7.94749i		−	0.674097i	0.941487	−	0.337049i	$-0.109429\pi$
$140$	−0.853276	+	1.80884i	−0.0721150	+	0.152875i
$141$	5.67762	−	13.5855i	0.478142	−	1.14410i
$142$	−8.30556	+	5.26534i	−0.696987	+	0.441858i
$143$	5.56044			0.464987
$144$	−1.22742	+	11.9371i	−0.102285	+	0.994755i
$145$	−0.963476			−0.0800123
$146$	11.9145	−	7.55321i	0.986047	−	0.625108i
$147$	0.667879	−	1.59810i	0.0550857	−	0.131809i
$148$	−1.63942	+	3.47539i	−0.134760	+	0.285675i
$149$		−	14.1997i		−	1.16329i	−0.813444	−	0.581643i	$-0.802410\pi$
$149$		−	14.1997i		−	1.16329i	0.813444	−	0.581643i	$-0.197590\pi$
$150$	−0.412368	−	2.41453i	−0.0336697	−	0.197146i
$151$		−	3.09825i		−	0.252132i	−0.992022	−	0.126066i	$-0.959765\pi$
$151$		−	3.09825i		−	0.252132i	0.992022	−	0.126066i	$-0.0402351\pi$
$152$	14.9681	−	1.86927i	1.21408	−	0.151618i
$153$	−10.1423	+	10.0149i	−0.819952	+	0.809657i
$154$	−4.93704	−	7.78770i	−0.397838	−	0.627551i
$155$	7.17468			0.576284
$156$	1.97926	+	2.19321i	0.158467	+	0.175597i
$157$	−15.6967			−1.25273			−0.626366	−	0.779529i	$-0.715458\pi$
$157$	−15.6967			−1.25273			−0.626366	+	0.779529i	$0.715458\pi$
$158$	9.52667	+	15.0274i	0.757901	+	1.19551i
$159$	−2.15501	−	0.900619i	−0.170903	−	0.0714237i
$160$	−1.76083	+	5.37582i	−0.139206	+	0.424996i
$161$		−	0.680081i		−	0.0535979i
$162$	6.67849	+	10.8350i	0.524712	+	0.851280i
$163$		−	1.82320i		−	0.142804i	−0.997448	−	0.0714020i	$-0.977253\pi$
$163$		−	1.82320i		−	0.142804i	0.997448	−	0.0714020i	$-0.0227473\pi$
$164$	11.8553	+	5.59241i	0.925740	+	0.436694i
$165$	10.4198	+	4.35462i	0.811177	+	0.339006i
$166$	−10.9790	+	6.96017i	−0.852135	+	0.540214i
$167$	−8.35285			−0.646363			−0.323182	−	0.946337i	$-0.604752\pi$
$167$	−8.35285			−0.646363			−0.323182	+	0.946337i	$0.604752\pi$
$168$	1.31435	−	4.71937i	0.101404	−	0.364108i
$169$	−12.2727			−0.944054
$170$	−5.67490	+	3.59763i	−0.435245	+	0.275925i
$171$	11.3846	−	11.2416i	0.870599	−	0.859667i
$172$	−15.6817	−	7.39745i	−1.19572	−	0.564051i
$173$		−	15.4907i		−	1.17774i	−0.808228	−	0.588869i	$-0.799573\pi$
$173$		−	15.4907i		−	1.17774i	0.808228	−	0.588869i	$-0.200427\pi$
$174$	2.32634	−	0.397307i	0.176360	−	0.0301198i
$175$			1.00000i			0.0755929i
$176$	−16.5860	−	20.1267i	−1.25022	−	1.51711i
$177$	−0.661207	+	1.58214i	−0.0496993	+	0.118921i
$178$	−0.926672	−	1.46173i	−0.0694570	−	0.109562i
$179$	17.0691			1.27580			0.637901	−	0.770119i	$-0.279803\pi$
$179$	17.0691			1.27580			0.637901	+	0.770119i	$0.279803\pi$
$180$	1.99135	+	5.65990i	0.148426	+	0.421864i
$181$	12.1188			0.900780			0.450390	−	0.892832i	$-0.351285\pi$
$181$	12.1188			0.900780			0.450390	+	0.892832i	$0.351285\pi$
$182$	−0.645760	−	1.01862i	−0.0478669	−	0.0755054i
$183$	6.24347	−	14.9394i	0.461531	−	1.10435i
$184$	−0.238368	−	1.90873i	−0.0175727	−	0.140714i
$185$			1.92133i			0.141259i
$186$	−17.3235	+	2.95861i	−1.27022	+	0.216936i
$187$		−	30.9780i		−	2.26534i
$188$	−7.25368	+	15.3770i	−0.529029	+	1.12148i
$189$	−1.94290	−	4.81925i	−0.141325	−	0.350549i
$190$	6.37001	−	4.03829i	0.462129	−	0.292969i
$191$	−0.241765			−0.0174935			−0.00874674	−	0.999962i	$-0.502784\pi$
$191$	−0.241765			−0.0174935			−0.00874674	+	0.999962i	$0.502784\pi$
$192$	2.03475	−	13.7062i	0.146845	−	0.989159i
$193$	−5.65545			−0.407088			−0.203544	−	0.979066i	$-0.565246\pi$
$193$	−5.65545			−0.407088			−0.203544	+	0.979066i	$0.565246\pi$
$194$	13.3678	−	8.47455i	0.959750	−	0.608437i
$195$	1.36289	+	0.569580i	0.0975989	+	0.0407884i
$196$	−0.853276	+	1.80884i	−0.0609483	+	0.129203i
$197$		−	0.381520i		−	0.0271822i	−0.999908	−	0.0135911i	$-0.995674\pi$
$197$		−	0.381520i		−	0.0271822i	0.999908	−	0.0135911i	$-0.00432631\pi$
$198$	−26.9545	−	6.21757i	−1.91557	−	0.441864i
$199$		−	0.221262i		−	0.0156848i	−0.999969	−	0.00784242i	$-0.997504\pi$
$199$		−	0.221262i		−	0.0156848i	0.999969	−	0.00784242i	$-0.00249634\pi$
$200$	0.350500	+	2.80663i	0.0247841	+	0.198458i
$201$	−19.4357	−	8.12254i	−1.37089	−	0.572920i
$202$	4.25918	+	6.71844i	0.299675	+	0.472708i
$203$	−0.963476			−0.0676228
$204$	12.2187	−	11.0267i	0.855478	−	0.772025i
$205$	6.55405			0.457754
$206$	−0.600841	−	0.947768i	−0.0418626	−	0.0660341i
$207$	−1.43353	−	1.45175i	−0.0996369	−	0.100904i
$208$	−2.16944	−	2.63256i	−0.150423	−	0.182535i
$209$			34.7725i			2.40526i
$210$	−0.412368	−	2.41453i	−0.0284561	−	0.166618i
$211$		−	3.23202i		−	0.222501i	−0.993792	−	0.111251i	$-0.964514\pi$
$211$		−	3.23202i		−	0.222501i	0.993792	−	0.111251i	$-0.0354857\pi$
$212$	2.43918	+	1.15062i	0.167524	+	0.0790251i
$213$	4.64419	−	11.1126i	0.318214	−	0.761426i
$214$	−6.53034	+	4.13994i	−0.446405	+	0.283000i
$215$	−8.66947			−0.591253
$216$	−7.14214	−	12.8448i	−0.485961	−	0.873981i
$217$	7.17468			0.487049
$218$	14.0965	−	8.93656i	0.954738	−	0.605260i
$219$	−6.66216	+	15.9413i	−0.450187	+	1.07721i
$220$	−11.7938	−	5.56342i	−0.795137	−	0.375086i
$221$		−	4.05190i		−	0.272560i
$222$	−0.792295	−	4.63911i	−0.0531754	−	0.311356i
$223$			0.450241i			0.0301504i	0.999886	+	0.0150752i	$0.00479876\pi$
$223$			0.450241i			0.0301504i	−0.999886	+	0.0150752i	$0.995201\pi$
$224$	−1.76083	+	5.37582i	−0.117650	+	0.359187i
$225$	2.10788	+	2.13468i	0.140525	+	0.142312i
$226$	−1.21613	−	1.91832i	−0.0808957	−	0.127605i
$227$	−27.3822			−1.81742			−0.908710	−	0.417427i	$-0.862932\pi$
$227$	−27.3822			−1.81742			−0.908710	+	0.417427i	$0.862932\pi$
$228$	−13.7153	+	12.3774i	−0.908319	+	0.819711i
$229$	−26.5550			−1.75480			−0.877402	−	0.479756i	$-0.840725\pi$
$229$	−26.5550			−1.75480			−0.877402	+	0.479756i	$0.840725\pi$
$230$	−0.514962	−	0.812302i	−0.0339556	−	0.0535616i
$231$	10.4198	+	4.35462i	0.685569	+	0.286513i
$232$	−2.70412	+	0.337698i	−0.177534	+	0.0221710i
$233$		−	7.25476i		−	0.475275i	−0.971354	−	0.237638i	$-0.923627\pi$
$233$		−	7.25476i		−	0.475275i	0.971354	−	0.237638i	$-0.0763731\pi$
$234$	−3.52562	−	0.813253i	−0.230477	−	0.0531640i
$235$			8.50098i			0.554543i
$236$	0.844752	−	1.79078i	0.0549887	−	0.116570i
$237$	−20.1063	−	8.40280i	−1.30604	−	0.545821i
$238$	−5.67490	+	3.59763i	−0.367849	+	0.233199i
$239$	−21.3974			−1.38408			−0.692042	−	0.721857i	$-0.743289\pi$
$239$	−21.3974			−1.38408			−0.692042	+	0.721857i	$0.743289\pi$
$240$	−2.00366	−	6.63215i	−0.129335	−	0.428103i
$241$	8.56021			0.551412			0.275706	−	0.961242i	$-0.411088\pi$
$241$	8.56021			0.551412			0.275706	+	0.961242i	$0.411088\pi$
$242$	37.6377	−	23.8606i	2.41944	−	1.53382i
$243$	−14.3058	−	6.19216i	−0.917720	−	0.397227i
$244$	−7.97661	+	16.9095i	−0.510650	+	1.08252i
$245$			1.00000i			0.0638877i
$246$	−15.8249	+	2.70268i	−1.00896	+	0.172317i
$247$			4.54821i			0.289395i
$248$	20.1366	−	2.51472i	1.27868	−	0.159685i
$249$	6.13907	−	14.6896i	0.389048	−	0.930917i
$250$	0.757207	+	1.19442i	0.0478900	+	0.0755417i
$251$	17.8136			1.12438			0.562191	−	0.827008i	$-0.309959\pi$
$251$	17.8136			1.12438			0.562191	+	0.827008i	$0.309959\pi$
$252$	1.99135	+	5.65990i	0.125443	+	0.356541i
$253$	4.43417			0.278774
$254$	16.0332	+	25.2908i	1.00601	+	1.58688i
$255$	3.17321	−	7.59288i	0.198714	−	0.475485i
$256$	−3.05775	+	15.7051i	−0.191110	+	0.981569i
$257$			10.2455i			0.639095i	0.947570	+	0.319548i	$0.103531\pi$
$257$			10.2455i			0.639095i	−0.947570	+	0.319548i	$0.896469\pi$
$258$	20.9327	−	3.57502i	1.30321	−	0.222571i
$259$			1.92133i			0.119386i
$260$	−1.54262	−	0.727690i	−0.0956691	−	0.0451294i
$261$	−2.05671	+	2.03089i	−0.127307	+	0.125709i
$262$	21.7699	−	13.8011i	1.34495	−	0.852634i
$263$	24.1590			1.48971			0.744853	−	0.667229i	$-0.232520\pi$
$263$	24.1590			1.48971			0.744853	+	0.667229i	$0.232520\pi$
$264$	30.7706	+	8.56965i	1.89380	+	0.527426i
$265$	1.34848			0.0828362
$266$	6.37001	−	4.03829i	0.390570	−	0.247604i
$267$	1.95576	+	0.817352i	0.119691	+	0.0500211i
$268$	21.9986	+	10.3773i	1.34378	+	0.633894i
$269$		−	11.6024i		−	0.707412i	−0.935357	−	0.353706i	$-0.884921\pi$
$269$		−	11.6024i		−	0.707412i	0.935357	−	0.353706i	$-0.115079\pi$
$270$	−5.96980	−	4.28503i	−0.363311	−	0.260778i
$271$		−	26.0883i		−	1.58475i	−0.610035	−	0.792374i	$-0.708845\pi$
$271$		−	26.0883i		−	1.58475i	0.610035	−	0.792374i	$-0.291155\pi$
$272$	−14.6664	+	12.0862i	−0.889279	+	0.732836i
$273$	1.36289	+	0.569580i	0.0824861	+	0.0344725i
$274$	−0.128204	−	0.202229i	−0.00774509	−	0.0122171i
$275$	−6.52007			−0.393175
$276$	1.57836	+	1.74897i	0.0950060	+	0.105276i
$277$	24.9885			1.50142			0.750708	−	0.660634i	$-0.229713\pi$
$277$	24.9885			1.50142			0.750708	+	0.660634i	$0.229713\pi$
$278$	−6.01789	−	9.49263i	−0.360929	−	0.569330i
$279$	15.3156	−	15.1233i	0.916923	−	0.905410i
$280$	0.350500	+	2.80663i	0.0209464	+	0.167728i
$281$			28.1047i			1.67659i	0.545220	+	0.838293i	$0.316446\pi$
$281$			28.1047i			1.67659i	−0.545220	+	0.838293i	$0.683554\pi$
$282$	−3.50553	−	20.5259i	−0.208752	−	1.22230i
$283$			3.66995i			0.218156i	0.994033	+	0.109078i	$0.0347899\pi$
$283$			3.66995i			0.218156i	−0.994033	+	0.109078i	$0.965210\pi$
$284$	−5.93337	+	12.5781i	−0.352081	+	0.746370i
$285$	−3.56189	+	8.52292i	−0.210988	+	0.504854i
$286$	6.64150	−	4.21040i	0.392720	−	0.248966i
$287$	6.55405			0.386873
$288$	7.57277	+	15.1873i	0.446230	+	0.894918i
$289$	−5.57372			−0.327866
$290$	−1.15079	+	0.729551i	−0.0675770	+	0.0428407i
$291$	−7.47480	+	17.8858i	−0.438181	+	1.04848i
$292$	8.51151	−	18.0434i	0.498099	−	1.05591i
$293$		−	20.8141i		−	1.21597i	−0.793948	−	0.607986i	$-0.791978\pi$
$293$		−	20.8141i		−	1.21597i	0.793948	−	0.607986i	$-0.208022\pi$
$294$	−0.412368	−	2.41453i	−0.0240498	−	0.140818i
$295$		−	0.990010i		−	0.0576406i
$296$	0.673426	+	5.39245i	0.0391421	+	0.313430i
$297$	31.4218	−	12.6678i	1.82328	−	0.735063i
$298$	−10.7521	−	16.9604i	−0.622854	−	0.982491i
$299$	0.579986			0.0335414
$300$	−2.32084	−	2.57171i	−0.133994	−	0.148478i
$301$	−8.66947			−0.499700
$302$	−2.34601	−	3.70061i	−0.134998	−	0.212946i
$303$	−8.98911	−	3.75672i	−0.516411	−	0.215818i
$304$	16.4628	−	13.5667i	0.944207	−	0.778102i
$305$			9.34821i			0.535277i
$306$	−4.53075	+	19.6418i	−0.259006	+	1.12285i
$307$			6.44104i			0.367610i	0.982963	+	0.183805i	$0.0588414\pi$
$307$			6.44104i			0.367610i	−0.982963	+	0.183805i	$0.941159\pi$
$308$	−11.7938	−	5.56342i	−0.672014	−	0.317005i
$309$	1.26809	+	0.529960i	0.0721392	+	0.0301483i
$310$	8.56957	−	5.43271i	0.486719	−	0.308557i
$311$	−9.64409			−0.546866			−0.273433	−	0.961891i	$-0.588159\pi$
$311$	−9.64409			−0.546866			−0.273433	+	0.961891i	$0.588159\pi$
$312$	4.02477	+	1.12090i	0.227858	+	0.0634586i
$313$	−15.9891			−0.903756			−0.451878	−	0.892080i	$-0.649246\pi$
$313$	−15.9891			−0.903756			−0.451878	+	0.892080i	$0.649246\pi$
$314$	−18.7484	+	11.8856i	−1.05803	+	0.670745i
$315$	2.10788	+	2.13468i	0.118765	+	0.120276i
$316$	22.7577	+	10.7353i	1.28022	+	0.603911i
$317$			4.30892i			0.242013i	0.992652	+	0.121007i	$0.0386122\pi$
$317$			4.30892i			0.242013i	−0.992652	+	0.121007i	$0.961388\pi$
$318$	−3.25594	+	0.556069i	−0.182584	+	0.0311828i
$319$		−	6.28193i		−	0.351721i
$320$	1.96745	+	7.75430i	0.109984	+	0.433479i
$321$	3.65155	−	8.73744i	0.203809	−	0.487676i
$322$	−0.514962	−	0.812302i	−0.0286977	−	0.0452678i
$323$	25.3387			1.40988
$324$	16.1813	+	7.88457i	0.898960	+	0.438031i
$325$	−0.852819			−0.0473059
$326$	−1.38054	−	2.17766i	−0.0764609	−	0.120610i
$327$	−7.88231	+	18.8608i	−0.435893	+	1.04301i
$328$	18.3948	−	2.29719i	1.01568	−	0.126841i
$329$			8.50098i			0.468674i
$330$	15.7429	−	2.68867i	0.866618	−	0.148006i
$331$		−	20.8330i		−	1.14509i	−0.819875	−	0.572543i	$-0.805957\pi$
$331$		−	20.8330i		−	1.14509i	0.819875	−	0.572543i	$-0.194043\pi$
$332$	−7.84323	+	16.6267i	−0.430453	+	0.912510i
$333$	4.04993	+	4.10142i	0.221935	+	0.224757i
$334$	−9.97681	+	6.32484i	−0.545907	+	0.346080i
$335$	12.1617			0.664465
$336$	−2.00366	−	6.63215i	−0.109308	−	0.361813i
$337$	−7.35217			−0.400498			−0.200249	−	0.979745i	$-0.564175\pi$
$337$	−7.35217			−0.400498			−0.200249	+	0.979745i	$0.564175\pi$
$338$	−14.6588	+	9.29297i	−0.797331	+	0.505471i
$339$	2.56667	+	1.07266i	0.139402	+	0.0582590i
$340$	−4.05407	+	8.59415i	−0.219863	+	0.466083i
$341$			46.7794i			2.53325i
$342$	5.08571	−	22.0477i	0.275004	−	1.19220i
$343$			1.00000i			0.0539949i
$344$	−24.3320	+	3.03865i	−1.31189	+	0.163833i
$345$	1.08684	+	0.454211i	0.0585135	+	0.0244539i
$346$	−11.7297	−	18.5024i	−0.630592	−	0.994697i
$347$	−15.1078			−0.811031			−0.405515	−	0.914088i	$-0.632908\pi$
$347$	−15.1078			−0.811031			−0.405515	+	0.914088i	$0.632908\pi$
$348$	2.47778	−	2.23607i	0.132823	−	0.119866i
$349$	−2.83517			−0.151763			−0.0758815	−	0.997117i	$-0.524177\pi$
$349$	−2.83517			−0.151763			−0.0758815	+	0.997117i	$0.524177\pi$
$350$	0.757207	+	1.19442i	0.0404744	+	0.0638444i
$351$	4.10995	−	1.65694i	0.219373	−	0.0884410i
$352$	−35.0507	−	11.4807i	−1.86821	−	0.611924i
$353$			18.8766i			1.00470i	0.864664	+	0.502350i	$0.167531\pi$
$353$			18.8766i			1.00470i	−0.864664	+	0.502350i	$0.832469\pi$
$354$	0.408249	+	2.39041i	0.0216982	+	0.127049i
$355$			6.95364i			0.369061i
$356$	−2.21367	−	1.04424i	−0.117324	−	0.0553447i
$357$	3.17321	−	7.59288i	0.167944	−	0.401858i
$358$	20.3876	−	12.9248i	1.07752	−	0.683097i
$359$	9.85347			0.520047			0.260023	−	0.965602i	$-0.416270\pi$
$359$	9.85347			0.520047			0.260023	+	0.965602i	$0.416270\pi$
$360$	6.66423	+	5.25244i	0.351236	+	0.276828i
$361$	−9.44242			−0.496970
$362$	14.4749	−	9.17641i	0.760783	−	0.482301i
$363$	−21.0457	+	50.3584i	−1.10461	+	2.64313i
$364$	−1.54262	−	0.727690i	−0.0808551	−	0.0381413i
$365$		−	9.97510i		−	0.522121i
$366$	−3.85491	−	22.5715i	−0.201499	−	1.17983i
$367$		−	17.0522i		−	0.890116i	−0.895502	−	0.445058i	$-0.853183\pi$
$367$		−	17.0522i		−	0.890116i	0.895502	−	0.445058i	$-0.146817\pi$
$368$	−1.73002	−	2.09933i	−0.0901833	−	0.109435i
$369$	13.9908	−	13.8151i	0.728331	−	0.719186i
$370$	1.45484	+	2.29487i	0.0756337	+	0.119305i
$371$	1.34848			0.0700094
$372$	−18.4512	+	16.6513i	−0.956651	+	0.863328i
$373$	29.9912			1.55288			0.776442	−	0.630189i	$-0.217023\pi$
$373$	29.9912			1.55288			0.776442	+	0.630189i	$0.217023\pi$
$374$	−23.4568	−	37.0008i	−1.21292	−	1.91326i
$375$	−1.59810	−	0.667879i	−0.0825258	−	0.0344891i
$376$	2.97959	+	23.8591i	0.153661	+	1.23044i
$377$		−	0.821671i		−	0.0423182i
$378$	−5.96980	−	4.28503i	−0.307054	−	0.220398i
$379$			32.1658i			1.65225i	0.563489	+	0.826124i	$0.309459\pi$
$379$			32.1658i			1.65225i	−0.563489	+	0.826124i	$0.690541\pi$
$380$	4.55064	−	9.64683i	0.233443	−	0.494872i
$381$	−33.8384	−	14.1417i	−1.73360	−	0.724503i
$382$	−0.288768	+	0.183066i	−0.0147747	+	0.00936646i
$383$	−13.5590			−0.692834			−0.346417	−	0.938081i	$-0.612602\pi$
$383$	−13.5590			−0.692834			−0.346417	+	0.938081i	$0.612602\pi$
$384$	−7.94808	−	17.9117i	−0.405599	−	0.914051i
$385$	−6.52007			−0.332293
$386$	−6.75498	+	4.28235i	−0.343820	+	0.217966i
$387$	−18.5066	+	18.2742i	−0.940741	+	0.928929i
$388$	9.54974	−	20.2443i	0.484815	−	1.02775i
$389$		−	24.5393i		−	1.24419i	−0.782941	−	0.622096i	$-0.786281\pi$
$389$		−	24.5393i		−	1.24419i	0.782941	−	0.622096i	$-0.213719\pi$
$390$	2.05916	−	0.351675i	0.104269	−	0.0178078i
$391$		−	3.23119i		−	0.163408i
$392$	0.350500	+	2.80663i	0.0177029	+	0.141756i
$393$	−12.1730	+	29.1275i	−0.614045	+	1.46929i
$394$	−0.288889	−	0.455695i	−0.0145540	−	0.0229576i
$395$	12.5813			0.633036
$396$	−36.9030	+	12.9837i	−1.85444	+	0.652458i
$397$	10.0568			0.504739			0.252369	−	0.967631i	$-0.418790\pi$
$397$	10.0568			0.504739			0.252369	+	0.967631i	$0.418790\pi$
$398$	−0.167541	−	0.264279i	−0.00839807	−	0.0132471i
$399$	−3.56189	+	8.52292i	−0.178318	+	0.426680i
$400$	2.54384	+	3.08689i	0.127192	+	0.154344i
$401$		−	12.9225i		−	0.645320i	−0.946515	−	0.322660i	$-0.895423\pi$
$401$		−	12.9225i		−	0.645320i	0.946515	−	0.322660i	$-0.104577\pi$
$402$	−29.3648	+	5.01510i	−1.46458	+	0.250130i
$403$			6.11870i			0.304794i
$404$	10.1745	+	4.79956i	0.506200	+	0.238787i
$405$	8.99928	+	0.113716i	0.447178	+	0.00565059i
$406$	−1.15079	+	0.729551i	−0.0571130	+	0.0362070i
$407$	−12.5272			−0.620950
$408$	6.24471	−	22.4226i	0.309159	−	1.11008i
$409$	−5.26264			−0.260221			−0.130111	−	0.991499i	$-0.541533\pi$
$409$	−5.26264			−0.260221			−0.130111	+	0.991499i	$0.541533\pi$
$410$	7.82828	−	4.96277i	0.386611	−	0.245094i
$411$	0.270578	+	0.113080i	0.0133466	+	0.00557781i
$412$	−1.43531	−	0.677072i	−0.0707128	−	0.0333569i
$413$		−	0.990010i		−	0.0487152i
$414$	−2.81151	−	0.648529i	−0.138178	−	0.0318734i
$415$			9.19190i			0.451213i
$416$	−4.58461	−	1.50167i	−0.224779	−	0.0736252i
$417$	12.7009	+	5.30796i	0.621966	+	0.259932i
$418$	26.3299	+	41.5329i	1.28784	+	2.03144i
$419$	−8.98426			−0.438910			−0.219455	−	0.975623i	$-0.570428\pi$
$419$	−8.98426			−0.438910			−0.219455	+	0.975623i	$0.570428\pi$
$420$	−2.32084	−	2.57171i	−0.113245	−	0.125487i
$421$	−37.3111			−1.81843			−0.909216	−	0.416325i	$-0.863318\pi$
$421$	−37.3111			−1.81843			−0.909216	+	0.416325i	$0.863318\pi$
$422$	−2.44731	−	3.86039i	−0.119133	−	0.187921i
$423$	17.9190	+	18.1469i	0.871252	+	0.882331i
$424$	3.78467	−	0.472641i	0.183800	−	0.0229535i
$425$			4.75118i			0.230466i
$426$	−2.86746	−	16.7898i	−0.138929	−	0.813467i
$427$			9.34821i			0.452392i
$428$	−4.66518	+	9.88964i	−0.225500	+	0.478034i
$429$	−3.71370	+	8.88616i	−0.179299	+	0.429028i
$430$	−10.3550	+	6.56458i	−0.499362	+	0.316572i
$431$	−14.1085			−0.679582			−0.339791	−	0.940501i	$-0.610356\pi$
$431$	−14.1085			−0.679582			−0.339791	+	0.940501i	$0.610356\pi$
$432$	−18.2569	−	9.93405i	−0.878386	−	0.477952i
$433$	−9.65505			−0.463992			−0.231996	−	0.972717i	$-0.574526\pi$
$433$	−9.65505			−0.463992			−0.231996	+	0.972717i	$0.574526\pi$
$434$	8.56957	−	5.43271i	0.411353	−	0.260779i
$435$	0.643485	−	1.53974i	0.0308528	−	0.0738247i
$436$	10.0704	−	21.3480i	0.482283	−	1.02238i
$437$			3.62697i			0.173501i
$438$	4.11341	+	24.0852i	0.196547	+	1.15083i
$439$		−	16.1802i		−	0.772239i	−0.922449	−	0.386120i	$-0.873815\pi$
$439$		−	16.1802i		−	0.772239i	0.922449	−	0.386120i	$-0.126185\pi$
$440$	−18.2994	+	2.28528i	−0.872389	+	0.108947i
$441$	2.10788	+	2.13468i	0.100375	+	0.101651i
$442$	−3.06812	−	4.83967i	−0.145936	−	0.230199i
$443$	36.0737			1.71391			0.856956	−	0.515389i	$-0.172353\pi$
$443$	36.0737			1.71391			0.856956	+	0.515389i	$0.172353\pi$
$444$	−4.45910	−	4.94111i	−0.211619	−	0.234495i
$445$	−1.22380			−0.0580138
$446$	0.340926	+	0.537777i	0.0161433	+	0.0254645i
$447$	22.6926	+	9.48369i	1.07332	+	0.448563i
$448$	1.96745	+	7.75430i	0.0929530	+	0.366356i
$449$			10.2247i			0.482533i	0.970459	+	0.241266i	$0.0775627\pi$
$449$			10.2247i			0.482533i	−0.970459	+	0.241266i	$0.922437\pi$
$450$	4.13408	+	0.953605i	0.194883	+	0.0449534i
$451$			42.7328i			2.01221i
$452$	−2.90514	−	1.37042i	−0.136646	−	0.0644593i
$453$	4.95132	+	2.06925i	0.232633	+	0.0972220i
$454$	−32.7058	+	20.7340i	−1.53496	+	0.973094i
$455$	−0.852819			−0.0399808
$456$	−7.00962	+	25.1691i	−0.328255	+	1.17865i
$457$	−28.7990			−1.34716			−0.673579	−	0.739115i	$-0.735244\pi$
$457$	−28.7990			−1.34716			−0.673579	+	0.739115i	$0.735244\pi$
$458$	−31.7178	+	20.1076i	−1.48208	+	0.939568i
$459$	−9.23107	−	22.8971i	−0.430869	−	1.06875i
$460$	−1.23016	−	0.580297i	−0.0573565	−	0.0270565i
$461$		−	6.59738i		−	0.307271i	−0.988128	−	0.153635i	$-0.950902\pi$
$461$		−	6.59738i		−	0.307271i	0.988128	−	0.153635i	$-0.0490981\pi$
$462$	15.7429	−	2.68867i	0.732426	−	0.125088i
$463$			25.6690i			1.19294i	0.802636	+	0.596469i	$0.203430\pi$
$463$			25.6690i			1.19294i	−0.802636	+	0.596469i	$0.796570\pi$
$464$	−2.97414	+	2.45093i	−0.138071	+	0.113782i
$465$	−4.79181	+	11.4659i	−0.222215	+	0.531718i
$466$	−5.49335	−	8.66523i	−0.254475	−	0.401409i
$467$	−0.353477			−0.0163569			−0.00817847	−	0.999967i	$-0.502603\pi$
$467$	−0.353477			−0.0163569			−0.00817847	+	0.999967i	$0.502603\pi$
$468$	−4.82687	+	1.69826i	−0.223122	+	0.0785022i
$469$	12.1617			0.561575
$470$	6.43700	+	10.1537i	0.296917	+	0.468357i
$471$	10.4835	−	25.0849i	0.483053	−	1.15585i
$472$	−0.346999	−	2.77859i	−0.0159719	−	0.127895i
$473$		−	56.5256i		−	2.59905i
$474$	−30.3780	+	5.18814i	−1.39531	+	0.238299i
$475$		−	5.33314i		−	0.244701i
$476$	−4.05407	+	8.59415i	−0.185818	+	0.393912i
$477$	2.87857	−	2.84242i	0.131800	−	0.130146i
$478$	−25.5575	+	16.2023i	−1.16897	+	0.741074i
$479$	−5.71472			−0.261112			−0.130556	−	0.991441i	$-0.541676\pi$
$479$	−5.71472			−0.261112			−0.130556	+	0.991441i	$0.541676\pi$
$480$	−7.41511	−	6.40438i	−0.338452	−	0.292319i
$481$	−1.63855			−0.0747113
$482$	10.2245	−	6.48185i	0.465713	−	0.295240i
$483$	1.08684	+	0.454211i	0.0494529	+	0.0206673i
$484$	26.8878	−	56.9991i	1.22217	−	2.59087i
$485$		−	11.1919i		−	0.508196i
$486$	−21.7759	+	3.43645i	−0.987776	+	0.155880i
$487$			18.4300i			0.835143i	0.908644	+	0.417571i	$0.137119\pi$
$487$			18.4300i			0.835143i	−0.908644	+	0.417571i	$0.862881\pi$
$488$	3.27655	+	26.2369i	0.148322	+	1.18769i
$489$	2.91366	+	1.21768i	0.131760	+	0.0550652i
$490$	0.757207	+	1.19442i	0.0342071	+	0.0539584i
$491$	−17.7245			−0.799896			−0.399948	−	0.916538i	$-0.630972\pi$
$491$	−17.7245			−0.799896			−0.399948	+	0.916538i	$0.630972\pi$
$492$	−16.8551	+	15.2109i	−0.759888	+	0.685760i
$493$	−4.57765			−0.206167
$494$	3.44393	+	5.43247i	0.154950	+	0.244418i
$495$	−13.9183	+	13.7435i	−0.625579	+	0.617724i
$496$	22.1474	−	18.2512i	0.994448	−	0.819504i
$497$			6.95364i			0.311913i
$498$	−3.79045	−	22.1941i	−0.169854	−	0.994542i
$499$		−	17.4418i		−	0.780804i	−0.920645	−	0.390402i	$-0.872336\pi$
$499$		−	17.4418i		−	0.780804i	0.920645	−	0.390402i	$-0.127664\pi$
$500$	1.80884	+	0.853276i	0.0808940	+	0.0381597i
$501$	5.57869	−	13.3487i	0.249238	−	0.596377i
$502$	21.2769	−	13.4885i	0.949633	−	0.602023i
$503$	−30.7787			−1.37235			−0.686177	−	0.727434i	$-0.740713\pi$
$503$	−30.7787			−1.37235			−0.686177	+	0.727434i	$0.740713\pi$
$504$	6.66423	+	5.25244i	0.296848	+	0.233962i
$505$	5.62486			0.250303
$506$	5.29626	−	3.35759i	0.235448	−	0.149263i
$507$	8.19667	−	19.6131i	0.364027	−	0.871046i
$508$	38.3007	+	18.0674i	1.69932	+	0.801609i
$509$		−	29.0579i		−	1.28797i	−0.765039	−	0.643984i	$-0.777280\pi$
$509$		−	29.0579i		−	1.28797i	0.765039	−	0.643984i	$-0.222720\pi$
$510$	−1.95924	−	11.4719i	−0.0867564	−	0.507983i
$511$		−	9.97510i		−	0.441273i
$512$	8.23976	+	21.0738i	0.364150	+	0.931340i
$513$	10.3618	+	25.7017i	0.457483	+	1.13476i
$514$	7.75794	+	12.2374i	0.342188	+	0.539768i
$515$	−0.793497			−0.0349656
$516$	22.2954	−	20.1205i	0.981500	−	0.885753i
$517$	−55.4270			−2.43768
$518$	1.45484	+	2.29487i	0.0639222	+	0.100831i
$519$	24.7558	+	10.3459i	1.08666	+	0.454136i
$520$	−2.39354	+	0.298913i	−0.104964	+	0.0131082i
$521$			26.1786i			1.14690i	0.819239	+	0.573452i	$0.194396\pi$
$521$			26.1786i			1.14690i	−0.819239	+	0.573452i	$0.805604\pi$
$522$	−0.918776	+	3.98309i	−0.0402137	+	0.174335i
$523$		−	10.8080i		−	0.472600i	−0.971680	−	0.236300i	$-0.924065\pi$
$523$		−	10.8080i		−	0.472600i	0.971680	−	0.236300i	$-0.0759348\pi$
$524$	15.5521	−	32.9686i	0.679395	−	1.44024i
$525$	−1.59810	−	0.667879i	−0.0697470	−	0.0291486i
$526$	28.8559	−	18.2933i	1.25818	−	0.797627i
$527$	34.0882			1.48490
$528$	43.2421	−	13.0640i	1.88187	−	0.568537i
$529$	−22.5375			−0.979891
$530$	1.61065	−	1.02108i	0.0699620	−	0.0443527i
$531$	−2.08682	−	2.11335i	−0.0905602	−	0.0917118i
$532$	4.55064	−	9.64683i	0.197295	−	0.418243i
$533$			5.58942i			0.242104i
$534$	2.95491	−	0.504657i	0.127871	−	0.0218387i
$535$			5.46738i			0.236375i
$536$	34.1334	−	4.26268i	1.47434	−	0.184120i
$537$	−11.4001	+	27.2781i	−0.491949	+	1.17714i
$538$	−8.78543	−	13.8582i	−0.378767	−	0.597467i
$539$	−6.52007			−0.280839
$540$	−10.3751	−	0.597744i	−0.446473	−	0.0257228i
$541$	28.3304			1.21802			0.609009	−	0.793163i	$-0.291567\pi$
$541$	28.3304			1.21802			0.609009	+	0.793163i	$0.291567\pi$
$542$	−19.7542	−	31.1603i	−0.848516	−	1.33845i
$543$	−8.09386	+	19.3670i	−0.347341	+	0.831119i
$544$	−8.36600	+	25.5415i	−0.358689	+	1.09508i
$545$		−	11.8020i		−	0.505542i
$546$	2.05916	−	0.351675i	0.0881238	−	0.0150503i
$547$		−	33.1748i		−	1.41845i	−0.704982	−	0.709225i	$-0.749045\pi$
$547$		−	33.1748i		−	1.41845i	0.704982	−	0.709225i	$-0.250955\pi$
$548$	−0.306259	−	0.144470i	−0.0130827	−	0.00617144i
$549$	19.7049	+	19.9554i	0.840984	+	0.851677i
$550$	−7.78770	+	4.93704i	−0.332069	+	0.210516i
$551$	5.13836			0.218901
$552$	3.20955	+	0.893864i	0.136608	+	0.0380454i
$553$	12.5813			0.535013
$554$	29.8468	−	18.9215i	1.26807	−	0.803897i
$555$	−3.07049	−	1.28322i	−0.130335	−	0.0544694i
$556$	−14.3758	−	6.78140i	−0.609669	−	0.287595i
$557$			41.7615i			1.76949i	0.466073	+	0.884746i	$0.345668\pi$
$557$			41.7615i			1.76949i	−0.466073	+	0.884746i	$0.654332\pi$
$558$	6.84181	−	29.6607i	0.289637	−	1.25564i
$559$		−	7.39349i		−	0.312711i
$560$	2.54384	+	3.08689i	0.107497	+	0.130445i
$561$	49.5061	+	20.6896i	2.09015	+	0.873514i
$562$	21.2811	+	33.5688i	0.897687	+	1.41601i
$563$	−2.01929			−0.0851029			−0.0425515	−	0.999094i	$-0.513549\pi$
$563$	−2.01929			−0.0851029			−0.0425515	+	0.999094i	$0.513549\pi$
$564$	−19.7294	−	21.8621i	−0.830758	−	0.920560i
$565$	−1.60607			−0.0675680
$566$	2.77891	+	4.38347i	0.116806	+	0.184251i
$567$	8.99928	+	0.113716i	0.377934	+	0.00477562i
$568$	2.43725	+	19.5163i	0.102265	+	0.818884i
$569$		−	0.449864i		−	0.0188593i	−0.999956	−	0.00942964i	$-0.996998\pi$
$569$		−	0.449864i		−	0.0188593i	0.999956	−	0.00942964i	$-0.00300159\pi$
$570$	2.19922	+	12.8770i	0.0921151	+	0.539360i
$571$			9.49838i			0.397495i	0.980051	+	0.198747i	$0.0636873\pi$
$571$			9.49838i			0.397495i	−0.980051	+	0.198747i	$0.936313\pi$
$572$	4.74459	−	10.0580i	0.198381	−	0.420545i
$573$	0.161469	−	0.386365i	0.00674548	−	0.0161406i
$574$	7.82828	−	4.96277i	0.326746	−	0.207142i
$575$	−0.680081			−0.0283613
$576$	20.5450	+	12.4058i	0.856040	+	0.516909i
$577$	−3.02142			−0.125783			−0.0628917	−	0.998020i	$-0.520032\pi$
$577$	−3.02142			−0.125783			−0.0628917	+	0.998020i	$0.520032\pi$
$578$	−6.65736	+	4.22046i	−0.276910	+	0.175548i
$579$	3.77716	−	9.03800i	0.156973	−	0.375607i
$580$	−0.822111	+	1.74278i	−0.0341363	+	0.0723650i
$581$			9.19190i			0.381344i
$582$	4.61517	+	27.0231i	0.191305	+	1.12014i
$583$			8.79216i			0.364134i
$584$	−3.49627	−	27.9964i	−0.144677	−	1.15850i
$585$	−1.82050	+	1.79764i	−0.0752682	+	0.0743231i
$586$	−15.7606	−	24.8607i	−0.651063	−	1.02699i
$587$	27.7870			1.14689			0.573447	−	0.819243i	$-0.305606\pi$
$587$	27.7870			1.14689			0.573447	+	0.819243i	$0.305606\pi$
$588$	−2.32084	−	2.57171i	−0.0957098	−	0.106056i
$589$	−38.2636			−1.57662
$590$	−0.749642	−	1.18249i	−0.0308623	−	0.0486822i
$591$	0.609709	+	0.254809i	0.0250801	+	0.0104814i
$592$	4.88756	+	5.93093i	0.200877	+	0.243760i
$593$			5.64735i			0.231909i	0.993255	+	0.115955i	$0.0369927\pi$
$593$			5.64735i			0.231909i	−0.993255	+	0.115955i	$0.963007\pi$
$594$	27.9387	−	38.9235i	1.14634	−	1.59705i
$595$			4.75118i			0.194779i
$596$	−25.6851	−	12.1163i	−1.05210	−	0.496302i
$597$	0.353600	+	0.147776i	0.0144719	+	0.00604807i
$598$	0.692746	−	0.439169i	0.0283285	−	0.0179590i
$599$	20.4722			0.836471			0.418235	−	0.908339i	$-0.362649\pi$
$599$	20.4722			0.836471			0.418235	+	0.908339i	$0.362649\pi$
$600$	−4.71937	−	1.31435i	−0.192668	−	0.0536581i
$601$	−2.61274			−0.106576			−0.0532879	−	0.998579i	$-0.516970\pi$
$601$	−2.61274			−0.106576			−0.0532879	+	0.998579i	$0.516970\pi$
$602$	−10.3550	+	6.56458i	−0.422038	+	0.267552i
$603$	25.9614	−	25.6354i	1.05723	−	1.04395i
$604$	−5.60425	−	2.64366i	−0.228034	−	0.107569i
$605$		−	31.5113i		−	1.28112i
$606$	−13.5814	+	2.31951i	−0.551706	+	0.0942237i
$607$		−	8.55849i		−	0.347378i	−0.984801	−	0.173689i	$-0.944431\pi$
$607$		−	8.55849i		−	0.347378i	0.984801	−	0.173689i	$-0.0555688\pi$
$608$	9.39074	−	28.6700i	0.380845	−	1.16272i
$609$	0.643485	−	1.53974i	0.0260753	−	0.0623932i
$610$	7.07853	+	11.1657i	0.286601	+	0.452085i
$611$	−7.24980			−0.293295
$612$	9.46127	+	26.8912i	0.382449	+	1.08701i
$613$	11.2613			0.454838			0.227419	−	0.973797i	$-0.426971\pi$
$613$	11.2613			0.454838			0.227419	+	0.973797i	$0.426971\pi$
$614$	4.87720	+	7.69330i	0.196828	+	0.310477i
$615$	−4.37731	+	10.4741i	−0.176510	+	0.422354i
$616$	−18.2994	+	2.28528i	−0.737304	+	0.0920767i
$617$		−	31.1902i		−	1.25567i	−0.778346	−	0.627836i	$-0.783941\pi$
$617$		−	31.1902i		−	1.25567i	0.778346	−	0.627836i	$-0.216059\pi$
$618$	1.91592	−	0.327213i	0.0770697	−	0.0131624i
$619$			20.5917i			0.827652i	0.910356	+	0.413826i	$0.135808\pi$
$619$			20.5917i			0.827652i	−0.910356	+	0.413826i	$0.864192\pi$
$620$	6.12198	−	12.9779i	0.245865	−	0.521204i
$621$	3.27748	−	1.32133i	0.131521	−	0.0530231i
$622$	−11.5191	+	7.30257i	−0.461873	+	0.292806i
$623$	−1.22380			−0.0490306
$624$	5.65602	−	1.70876i	0.226422	−	0.0684050i
$625$	1.00000			0.0400000
$626$	−19.0977	+	12.1070i	−0.763296	+	0.483894i
$627$	−55.5700	−	23.2238i	−2.21925	−	0.927469i
$628$	−13.3936	+	28.3929i	−0.534463	+	1.13300i
$629$			9.12859i			0.363981i
$630$	4.13408	+	0.953605i	0.164706	+	0.0379925i
$631$		−	7.68351i		−	0.305876i	−0.988236	−	0.152938i	$-0.951127\pi$
$631$		−	7.68351i		−	0.305876i	0.988236	−	0.152938i	$-0.0488734\pi$
$632$	35.3111	−	4.40976i	1.40460	−	0.175411i
$633$	5.16510	+	2.15860i	0.205294	+	0.0857965i
$634$	3.26274	+	5.14666i	0.129580	+	0.204400i
$635$	21.1741			0.840269
$636$	−3.46789	+	3.12960i	−0.137511	+	0.124097i
$637$	−0.852819			−0.0337899
$638$	−4.75672	−	7.50326i	−0.188320	−	0.297057i
$639$	14.6574	+	14.8438i	0.579838	+	0.587211i
$640$	8.22156	+	7.77212i	0.324986	+	0.307220i
$641$		−	23.4434i		−	0.925957i	−0.886370	−	0.462978i	$-0.846781\pi$
$641$		−	23.4434i		−	0.925957i	0.886370	−	0.462978i	$-0.153219\pi$
$642$	−2.25457	−	13.2011i	−0.0889809	−	0.521008i
$643$		−	26.4969i		−	1.04494i	−0.852659	−	0.522468i	$-0.825011\pi$
$643$		−	26.4969i		−	1.04494i	0.852659	−	0.522468i	$-0.174989\pi$
$644$	−1.23016	−	0.580297i	−0.0484751	−	0.0228669i
$645$	5.79016	−	13.8547i	0.227987	−	0.545529i
$646$	30.2651	−	19.1867i	1.19076	−	0.754889i
$647$	35.3244			1.38874			0.694372	−	0.719616i	$-0.255682\pi$
$647$	35.3244			1.38874			0.694372	+	0.719616i	$0.255682\pi$
$648$	25.2975	−	2.83509i	0.993779	−	0.111373i
$649$	6.45494			0.253378
$650$	−1.01862	+	0.645760i	−0.0399537	+	0.0253288i
$651$	−4.79181	+	11.4659i	−0.187806	+	0.449383i
$652$	−3.29788	−	1.55569i	−0.129155	−	0.0609256i
$653$			13.4699i			0.527119i	0.964643	+	0.263559i	$0.0848965\pi$
$653$			13.4699i			0.527119i	−0.964643	+	0.263559i	$0.915103\pi$
$654$	4.86677	+	28.4963i	0.190306	+	1.11429i
$655$		−	18.2263i		−	0.712161i
$656$	20.2316	−	16.6724i	0.789911	−	0.650950i
$657$	−21.0263	−	21.2936i	−0.820313	−	0.830744i
$658$	6.43700	+	10.1537i	0.250940	+	0.395834i
$659$	−11.1837			−0.435654			−0.217827	−	0.975987i	$-0.569897\pi$
$659$	−11.1837			−0.435654			−0.217827	+	0.975987i	$0.569897\pi$
$660$	16.7677	−	15.1320i	0.652684	−	0.589013i
$661$	−18.5009			−0.719600			−0.359800	−	0.933029i	$-0.617155\pi$
$661$	−18.5009			−0.719600			−0.359800	+	0.933029i	$0.617155\pi$
$662$	−15.7749	−	24.8834i	−0.613109	−	0.967119i
$663$	6.47536	+	2.70618i	0.251482	+	0.105099i
$664$	3.22176	+	25.7982i	0.125029	+	1.00117i
$665$		−	5.33314i		−	0.206810i
$666$	7.94294	+	1.83219i	0.307782	+	0.0709959i
$667$		−	0.655242i		−	0.0253711i
$668$	−7.12729	+	15.1090i	−0.275763	+	0.584585i
$669$	−0.719533	−	0.300706i	−0.0278187	−	0.0116260i
$670$	14.5262	−	9.20893i	0.561195	−	0.355772i
$671$	−60.9510			−2.35299
$672$	−7.41511	−	6.40438i	−0.286044	−	0.247054i
$673$	−1.69647			−0.0653942			−0.0326971	−	0.999465i	$-0.510410\pi$
$673$	−1.69647			−0.0653942			−0.0326971	+	0.999465i	$0.510410\pi$
$674$	−8.78158	+	5.56711i	−0.338254	+	0.214437i
$675$	−4.81925	+	1.94290i	−0.185493	+	0.0747822i
$676$	−10.4720	+	22.1994i	−0.402769	+	0.853824i
$677$		−	13.0156i		−	0.500229i	−0.968216	−	0.250114i	$-0.919532\pi$
$677$		−	13.0156i		−	0.500229i	0.968216	−	0.250114i	$-0.0804682\pi$
$678$	3.87791	−	0.662293i	0.148930	−	0.0254352i
$679$		−	11.1919i		−	0.429504i
$680$	1.66529	+	13.3348i	0.0638609	+	0.511366i
$681$	18.2880	−	43.7596i	0.700797	−	1.67687i
$682$	35.4217	+	55.8742i	1.35637	+	2.13953i
$683$	−9.38507			−0.359110			−0.179555	−	0.983748i	$-0.557466\pi$
$683$	−9.38507			−0.359110			−0.179555	+	0.983748i	$0.557466\pi$
$684$	−10.6202	−	30.1851i	−0.406072	−	1.15416i
$685$	−0.169312			−0.00646907
$686$	0.757207	+	1.19442i	0.0289103	+	0.0456031i
$687$	17.7355	−	42.4377i	0.676652	−	1.61910i
$688$	−26.7617	+	22.0538i	−1.02028	+	0.840792i
$689$			1.15001i			0.0438117i
$690$	1.64207	−	0.280444i	0.0625127	−	0.0106763i
$691$			14.7532i			0.561237i	0.959819	+	0.280619i	$0.0905396\pi$
$691$			14.7532i			0.561237i	−0.959819	+	0.280619i	$0.909460\pi$
$692$	−28.0203	−	13.2179i	−1.06517	−	0.502468i
$693$	−13.9183	+	13.7435i	−0.528711	+	0.522072i
$694$	−18.0451	+	11.4398i	−0.684982	+	0.434247i
$695$	−7.94749			−0.301465
$696$	1.26634	−	4.54700i	0.0480007	−	0.172354i
$697$	31.1395			1.17949
$698$	−3.38638	+	2.14681i	−0.128176	+	0.0812579i
$699$	11.5939	+	4.84530i	0.438520	+	0.183266i
$700$	1.80884	+	0.853276i	0.0683679	+	0.0322508i
$701$		−	40.7278i		−	1.53827i	−0.639087	−	0.769135i	$-0.720687\pi$
$701$		−	40.7278i		−	1.53827i	0.639087	−	0.769135i	$-0.279313\pi$
$702$	3.65435	−	5.09116i	0.137925	−	0.192154i
$703$		−	10.2467i		−	0.386463i
$704$	−50.5586	+	12.8279i	−1.90550	+	0.483469i
$705$	−13.5855	−	5.67762i	−0.511658	−	0.213832i
$706$	14.2935	+	22.5466i	0.537943	+	0.848553i
$707$	5.62486			0.211545
$708$	2.29765	+	2.54602i	0.0863511	+	0.0956854i
$709$	−21.4176			−0.804353			−0.402177	−	0.915562i	$-0.631746\pi$
$709$	−21.4176			−0.804353			−0.402177	+	0.915562i	$0.631746\pi$
$710$	5.26534	+	8.30556i	0.197605	+	0.311702i
$711$	26.8571	−	26.5199i	1.00722	−	0.994574i
$712$	−3.43476	+	0.428943i	−0.128723	+	0.0160753i
$713$			4.87936i			0.182733i
$714$	−1.95924	−	11.4719i	−0.0733226	−	0.429324i
$715$		−	5.56044i		−	0.207949i
$716$	14.5646	−	30.8753i	0.544305	−	1.15386i
$717$	14.2909	−	34.1953i	0.533702	−	1.27705i
$718$	11.7692	−	7.46112i	0.439222	−	0.278446i
$719$	−16.5255			−0.616298			−0.308149	−	0.951338i	$-0.599710\pi$
$719$	−16.5255			−0.616298			−0.308149	+	0.951338i	$0.599710\pi$
$720$	11.9371	+	1.22742i	0.444868	+	0.0457431i
$721$	−0.793497			−0.0295514
$722$	−11.2782	+	7.14986i	−0.419732	+	0.266090i
$723$	−5.71718	+	13.6801i	−0.212624	+	0.508769i
$724$	10.3406	−	21.9210i	0.384307	−	0.814686i
$725$			0.963476i			0.0357826i
$726$	12.9943	+	76.0850i	0.482262	+	2.82378i
$727$		−	3.29970i		−	0.122379i	−0.998126	−	0.0611895i	$-0.980511\pi$
$727$		−	3.29970i		−	0.122379i	0.998126	−	0.0611895i	$-0.0194894\pi$
$728$	−2.39354	+	0.298913i	−0.0887106	+	0.0110785i
$729$	19.4503	−	18.7266i	0.720381	−	0.693579i
$730$	−7.55321	−	11.9145i	−0.279557	−	0.440974i
$731$	−41.1902			−1.52348
$732$	−21.6957	−	24.0409i	−0.801896	−	0.888578i
$733$	42.6140			1.57399			0.786993	−	0.616962i	$-0.211637\pi$
$733$	42.6140			1.57399			0.786993	+	0.616962i	$0.211637\pi$
$734$	−12.9120	−	20.3674i	−0.476591	−	0.751776i
$735$	−1.59810	−	0.667879i	−0.0589470	−	0.0246351i
$736$	−3.65599	−	1.19750i	−0.134762	−	0.0441406i
$737$			79.2952i			2.92088i
$738$	6.24997	−	27.0950i	0.230065	−	0.997379i
$739$		−	12.2285i		−	0.449831i	−0.974378	−	0.224916i	$-0.927789\pi$
$739$		−	12.2285i		−	0.449831i	0.974378	−	0.224916i	$-0.0722107\pi$
$740$	3.47539	+	1.63942i	0.127758	+	0.0602664i
$741$	−7.26851	−	3.03765i	−0.267015	−	0.111591i
$742$	1.61065	−	1.02108i	0.0591287	−	0.0374849i
$743$	14.9326			0.547823			0.273912	−	0.961755i	$-0.411682\pi$
$743$	14.9326			0.547823			0.273912	+	0.961755i	$0.411682\pi$
$744$	−9.43003	+	33.8600i	−0.345722	+	1.24137i
$745$	−14.1997			−0.520238
$746$	35.8220	−	22.7095i	1.31154	−	0.831454i
$747$	19.3754	+	19.6218i	0.708908	+	0.717923i
$748$	−56.0345	−	26.4328i	−2.04882	−	0.966479i
$749$			5.46738i			0.199774i
$750$	−2.41453	+	0.412368i	−0.0881661	+	0.0150576i
$751$		−	43.9565i		−	1.60400i	−0.597326	−	0.801999i	$-0.703770\pi$
$751$		−	43.9565i		−	1.60400i	0.597326	−	0.801999i	$-0.296230\pi$
$752$	21.6251	+	26.2416i	0.788588	+	0.956932i
$753$	−11.8973	+	28.4679i	−0.433561	+	1.03743i
$754$	−0.622175	−	0.981420i	−0.0226583	−	0.0357412i
$755$	−3.09825			−0.112757
$756$	−10.3751	−	0.597744i	−0.377339	−	0.0217397i
$757$	−4.40849			−0.160229			−0.0801147	−	0.996786i	$-0.525529\pi$
$757$	−4.40849			−0.160229			−0.0801147	+	0.996786i	$0.525529\pi$
$758$	24.3562	+	38.4195i	0.884656	+	1.39546i
$759$	−2.96149	+	7.08627i	−0.107495	+	0.257215i
$760$	−1.86927	−	14.9681i	−0.0678054	−	0.542951i
$761$		−	18.4899i		−	0.670258i	−0.942172	−	0.335129i	$-0.891220\pi$
$761$		−	18.4899i		−	0.670258i	0.942172	−	0.335129i	$-0.108780\pi$
$762$	−51.1255	+	8.73153i	−1.85208	+	0.316310i
$763$		−	11.8020i		−	0.427261i
$764$	−0.206292	+	0.437315i	−0.00746338	+	0.0158215i
$765$	10.0149	+	10.1423i	0.362090	+	0.366694i
$766$	−16.1952	+	10.2670i	−0.585155	+	0.370961i
$767$	0.844300			0.0304859
$768$	−23.0562	−	15.3757i	−0.831968	−	0.554823i
$769$	51.5767			1.85990			0.929951	−	0.367684i	$-0.119849\pi$
$769$	51.5767			1.85990			0.929951	+	0.367684i	$0.119849\pi$
$770$	−7.78770	+	4.93704i	−0.280649	+	0.177919i
$771$	−16.3733	−	6.84273i	−0.589671	−	0.246435i
$772$	−4.82566	+	10.2298i	−0.173679	+	0.368180i
$773$		−	16.3629i		−	0.588532i	−0.955724	−	0.294266i	$-0.904925\pi$
$773$		−	16.3629i		−	0.588532i	0.955724	−	0.294266i	$-0.0950752\pi$
$774$	−8.26726	+	35.8403i	−0.297160	+	1.28825i
$775$		−	7.17468i		−	0.257722i
$776$	−3.92275	−	31.4114i	−0.140818	−	1.12760i
$777$	−3.07049	−	1.28322i	−0.110153	−	0.0460351i
$778$	−18.5813	−	29.3102i	−0.666173	−	1.05082i
$779$	−34.9537			−1.25235
$780$	2.19321	−	1.97926i	0.0785294	−	0.0708687i
$781$	−45.3382			−1.62233
$782$	−2.44668	−	3.85939i	−0.0874930	−	0.138012i
$783$	−1.87194	−	4.64323i	−0.0668976	−	0.165935i
$784$	2.54384	+	3.08689i	0.0908514	+	0.110246i
$785$			15.6967i			0.560239i
$786$	7.51595	+	44.0079i	0.268085	+	1.56971i
$787$			7.62090i			0.271656i	0.990732	+	0.135828i	$0.0433694\pi$
$787$			7.62090i			0.271656i	−0.990732	+	0.135828i	$0.956631\pi$
$788$	−0.690110	−	0.325542i	−0.0245842	−	0.0115969i
$789$	−16.1353	+	38.6085i	−0.574430	+	1.37450i
$790$	15.0274	−	9.52667i	0.534651	−	0.338944i
$791$	−1.60607			−0.0571054
$792$	−34.2463	+	43.4512i	−1.21689	+	1.54397i
$793$	−7.97233			−0.283106
$794$	12.0121	−	7.61511i	0.426293	−	0.270250i
$795$	−0.900619	+	2.15501i	−0.0319416	+	0.0764302i
$796$	−0.400228	−	0.188797i	−0.0141857	−	0.00669175i
$797$		−	44.1616i		−	1.56428i	−0.623101	−	0.782141i	$-0.714128\pi$
$797$		−	44.1616i		−	1.56428i	0.623101	−	0.782141i	$-0.285872\pi$
$798$	2.19922	+	12.8770i	0.0778515	+	0.455842i
$799$			40.3897i			1.42889i
$800$	5.37582	+	1.76083i	0.190064	+	0.0622546i
$801$	−2.61243	+	2.57962i	−0.0923056	+	0.0911465i
$802$	−9.78502	−	15.4349i	−0.345521	−	0.545026i
$803$	65.0384			2.29515
$804$	−31.2764	+	28.2254i	−1.10303	+	0.995432i
$805$	−0.680081			−0.0239697
$806$	4.63312	+	7.30829i	0.163195	+	0.257424i
$807$	18.5419	+	7.74901i	0.652705	+	0.272778i
$808$	15.7869	−	1.97151i	0.555380	−	0.0693576i
$809$			2.20787i			0.0776244i	0.999247	+	0.0388122i	$0.0123574\pi$
$809$			2.20787i			0.0776244i	−0.999247	+	0.0388122i	$0.987643\pi$
$810$	10.8350	−	6.67849i	0.380704	−	0.234658i
$811$		−	5.17520i		−	0.181726i	−0.995863	−	0.0908629i	$-0.971037\pi$
$811$		−	5.17520i		−	0.181726i	0.995863	−	0.0908629i	$-0.0289625\pi$
$812$	−0.822111	+	1.74278i	−0.0288504	+	0.0611596i
$813$	41.6918	+	17.4238i	1.46219	+	0.611079i
$814$	−14.9627	+	9.48568i	−0.524444	+	0.332473i
$815$	−1.82320			−0.0638639
$816$	−9.51973	−	31.5105i	−0.333257	−	1.10309i
$817$	46.2356			1.61758
$818$	−6.28581	+	3.98491i	−0.219778	+	0.139329i
$819$	−1.82050	+	1.79764i	−0.0636133	+	0.0628145i
$820$	5.59241	−	11.8553i	0.195295	−	0.414003i
$821$			24.2612i			0.846720i	0.905961	+	0.423360i	$0.139149\pi$
$821$			24.2612i			0.846720i	−0.905961	+	0.423360i	$0.860851\pi$
$822$	0.408808	−	0.0698188i	0.0142588	−	0.00243521i
$823$		−	23.6722i		−	0.825161i	−0.910921	−	0.412580i	$-0.864628\pi$
$823$		−	23.6722i		−	0.825161i	0.910921	−	0.412580i	$-0.135372\pi$
$824$	−2.22705	+	0.278121i	−0.0775829	+	0.00968879i
$825$	4.35462	−	10.4198i	0.151608	−	0.362769i
$826$	−0.749642	−	1.18249i	−0.0260834	−	0.0411440i
$827$	15.3614			0.534168			0.267084	−	0.963673i	$-0.413940\pi$
$827$	15.3614			0.534168			0.267084	+	0.963673i	$0.413940\pi$
$828$	−3.84919	+	1.35428i	−0.133769	+	0.0470644i
$829$	36.0430			1.25182			0.625912	−	0.779893i	$-0.284727\pi$
$829$	36.0430			1.25182			0.625912	+	0.779893i	$0.284727\pi$
$830$	6.96017	+	10.9790i	0.241591	+	0.381086i
$831$	−16.6893	+	39.9343i	−0.578946	+	1.38531i
$832$	−6.61301	+	1.67787i	−0.229265	+	0.0581698i
$833$			4.75118i			0.164619i
$834$	19.1894	−	3.27729i	0.664476	−	0.113483i
$835$			8.35285i			0.289062i
$836$	62.8980	+	29.6705i	2.17537	+	1.02618i
$837$	13.9397	+	34.5765i	0.481826	+	1.19514i
$838$	−10.7310	+	6.80294i	−0.370695	+	0.235004i
$839$	−5.71874			−0.197433			−0.0987165	−	0.995116i	$-0.531474\pi$
$839$	−5.71874			−0.197433			−0.0987165	+	0.995116i	$0.531474\pi$
$840$	−4.71937	−	1.31435i	−0.162834	−	0.0453494i
$841$	28.0717			0.967990
$842$	−44.5651	+	28.2522i	−1.53581	+	0.973635i
$843$	−44.9142	−	18.7705i	−1.54693	−	0.646491i
$844$	−5.84622	−	2.75780i	−0.201235	−	0.0949275i
$845$			12.2727i			0.422194i
$846$	35.1438	+	8.10658i	1.20827	+	0.278710i
$847$		−	31.5113i		−	1.08274i
$848$	4.16260	−	3.43031i	0.142944	−	0.117797i
$849$	−5.86497	−	2.45108i	−0.201285	−	0.0841210i
$850$	3.59763	+	5.67490i	0.123398	+	0.194648i
$851$	−1.30666			−0.0447917
$852$	−16.1383	−	17.8828i	−0.552888	−	0.612653i
$853$	−1.17719			−0.0403061			−0.0201530	−	0.999797i	$-0.506415\pi$
$853$	−1.17719			−0.0403061			−0.0201530	+	0.999797i	$0.506415\pi$
$854$	7.07853	+	11.1657i	0.242222	+	0.382082i
$855$	−11.2416	−	11.3846i	−0.384455	−	0.389344i
$856$	1.91632	+	15.3449i	0.0654983	+	0.524477i
$857$		−	43.4141i		−	1.48300i	−0.670955	−	0.741499i	$-0.734115\pi$
$857$		−	43.4141i		−	1.48300i	0.670955	−	0.741499i	$-0.265885\pi$
$858$	2.29295	+	13.4258i	0.0782800	+	0.458351i
$859$		−	17.3822i		−	0.593072i	−0.955022	−	0.296536i	$-0.904169\pi$
$859$		−	17.3822i		−	0.593072i	0.955022	−	0.296536i	$-0.0958315\pi$
$860$	−7.39745	+	15.6817i	−0.252251	+	0.534743i
$861$	−4.37731	+	10.4741i	−0.149178	+	0.356955i
$862$	−16.8515	+	10.6830i	−0.573963	+	0.363866i
$863$	−46.8521			−1.59486			−0.797432	−	0.603409i	$-0.793809\pi$
$863$	−46.8521			−1.59486			−0.797432	+	0.603409i	$0.793809\pi$
$864$	−29.3285	+	1.95883i	−0.997777	+	0.0666407i
$865$	−15.4907			−0.526701
$866$	−11.5322	+	7.31087i	−0.391879	+	0.248433i
$867$	3.72257	−	8.90739i	0.126425	−	0.302511i
$868$	6.12198	−	12.9779i	0.207793	−	0.440498i
$869$			82.0312i			2.78272i
$870$	−0.397307	−	2.32634i	−0.0134700	−	0.0788704i
$871$			10.3717i			0.351433i
$872$	−4.13660	−	33.1238i	−0.140083	−	1.12171i
$873$	−23.5910	−	23.8910i	−0.798436	−	0.808589i
$874$	2.74636	+	4.33212i	0.0928972	+	0.146536i
$875$	1.00000			0.0338062
$876$	23.1506	+	25.6531i	0.782186	+	0.866738i
$877$	−36.7510			−1.24099			−0.620497	−	0.784209i	$-0.713069\pi$
$877$	−36.7510			−1.24099			−0.620497	+	0.784209i	$0.713069\pi$
$878$	−12.2518	−	19.3260i	−0.413477	−	0.652220i
$879$	33.2631	+	13.9013i	1.12194	+	0.468878i
$880$	−20.1267	+	16.5860i	−0.678472	+	0.559114i
$881$		−	23.9369i		−	0.806456i	−0.915099	−	0.403228i	$-0.867888\pi$
$881$		−	23.9369i		−	0.806456i	0.915099	−	0.403228i	$-0.132112\pi$
$882$	4.13408	+	0.953605i	0.139202	+	0.0321096i
$883$			17.3412i			0.583578i	0.956483	+	0.291789i	$0.0942505\pi$
$883$			17.3412i			0.583578i	−0.956483	+	0.291789i	$0.905750\pi$
$884$	−7.32925	−	3.45739i	−0.246510	−	0.116285i
$885$	1.58214	+	0.661207i	0.0531831	+	0.0222262i
$886$	43.0871	−	27.3152i	1.44754	−	0.917673i
$887$	−23.2531			−0.780763			−0.390381	−	0.920653i	$-0.627657\pi$
$887$	−23.2531			−0.780763			−0.390381	+	0.920653i	$0.627657\pi$
$888$	−9.06747	−	2.52530i	−0.304284	−	0.0847435i
$889$	21.1741			0.710157
$890$	−1.46173	+	0.926672i	−0.0489974	+	0.0310621i
$891$	−0.741436	+	58.6759i	−0.0248390	+	1.96572i
$892$	0.814417	+	0.384180i	0.0272687	+	0.0128633i
$893$		−	45.3370i		−	1.51714i
$894$	34.2856	−	5.85551i	1.14668	−	0.195838i
$895$		−	17.0691i		−	0.570556i
$896$	8.22156	+	7.77212i	0.274663	+	0.259648i
$897$	−0.387360	+	0.926878i	−0.0129336	+	0.0309476i
$898$	7.74220	+	12.2126i	0.258360	+	0.407538i
$899$	6.91263			0.230549
$900$	5.65990	−	1.99135i	0.188663	−	0.0663783i
$901$	6.40685			0.213443
$902$	32.3576	+	51.0409i	1.07739	+	1.69948i
$903$	5.79016	−	13.8547i	0.192684	−	0.461056i
$904$	−4.50764	+	0.562928i	−0.149922	+	0.0187227i
$905$		−	12.1188i		−	0.402841i
$906$	7.48081	−	1.27762i	0.248533	−	0.0424460i
$907$		−	4.04253i		−	0.134230i	−0.997745	−	0.0671151i	$-0.978621\pi$
$907$		−	4.04253i		−	0.134230i	0.997745	−	0.0671151i	$-0.0213795\pi$
$908$	−23.3646	+	49.5302i	−0.775381	+	1.64372i
$909$	12.0073	−	11.8565i	0.398256	−	0.393255i
$910$	−1.01862	+	0.645760i	−0.0337670	+	0.0214067i
$911$	−16.0767			−0.532646			−0.266323	−	0.963884i	$-0.585809\pi$
$911$	−16.0767			−0.532646			−0.266323	+	0.963884i	$0.585809\pi$
$912$	10.6858	+	35.3702i	0.353842	+	1.17122i
$913$	−59.9318			−1.98345
$914$	−34.3980	+	21.8068i	−1.13779	+	0.721304i
$915$	−14.9394	−	6.24347i	−0.493882	−	0.206403i
$916$	−22.6587	+	48.0339i	−0.748666	+	1.58708i
$917$		−	18.2263i		−	0.601886i
$918$	−28.3636	−	20.3589i	−0.936139	−	0.671945i
$919$		−	6.51710i		−	0.214979i	−0.994206	−	0.107490i	$-0.965719\pi$
$919$		−	6.51710i		−	0.214979i	0.994206	−	0.107490i	$-0.0342812\pi$
$920$	−1.90873	+	0.238368i	−0.0629290	+	0.00785877i
$921$	−10.2935	−	4.30183i	−0.339181	−	0.141750i
$922$	−4.99558	−	7.88004i	−0.164521	−	0.259515i
$923$	−5.93020			−0.195195
$924$	16.7677	−	15.1320i	0.551618	−	0.497807i
$925$	1.92133			0.0631729
$926$	19.4367	+	30.6595i	0.638730	+	1.00753i
$927$	−1.69386	+	1.67259i	−0.0556337	+	0.0549352i
$928$	−1.69651	+	5.17948i	−0.0556908	+	0.170025i
$929$		−	31.4045i		−	1.03035i	−0.857086	−	0.515174i	$-0.827727\pi$
$929$		−	31.4045i		−	1.03035i	0.857086	−	0.515174i	$-0.172273\pi$
$930$	2.95861	+	17.3235i	0.0970166	+	0.568059i
$931$		−	5.33314i		−	0.174787i
$932$	−13.1227	−	6.19031i	−0.429850	−	0.202770i
$933$	6.44108	−	15.4123i	0.210872	−	0.504575i
$934$	−0.422199	+	0.267655i	−0.0138148	+	0.00875793i
$935$	−30.9780			−1.01309
$936$	−4.47938	+	5.68338i	−0.146413	+	0.185767i
$937$	43.8711			1.43321			0.716603	−	0.697482i	$-0.245696\pi$
$937$	43.8711			1.43321			0.716603	+	0.697482i	$0.245696\pi$
$938$	14.5262	−	9.20893i	0.474297	−	0.300682i
$939$	10.6788	−	25.5522i	0.348488	−	0.833865i
$940$	15.3770	+	7.25368i	0.501541	+	0.236589i
$941$			2.57985i			0.0841007i	0.999115	+	0.0420503i	$0.0133890\pi$
$941$			2.57985i			0.0841007i	−0.999115	+	0.0420503i	$0.986611\pi$
$942$	−6.47281	−	37.9001i	−0.210896	−	1.23485i
$943$			4.45728i			0.145149i
$944$	−2.51843	−	3.05605i	−0.0819678	−	0.0994660i
$945$	−4.81925	+	1.94290i	−0.156770	+	0.0632025i
$946$	−42.8015	−	67.5153i	−1.39160	−	2.19511i
$947$	13.7301			0.446169			0.223084	−	0.974799i	$-0.428387\pi$
$947$	13.7301			0.446169			0.223084	+	0.974799i	$0.428387\pi$
$948$	−32.3556	+	29.1992i	−1.05086	+	0.948347i
$949$	8.50696			0.276147
$950$	−4.03829	−	6.37001i	−0.131019	−	0.206670i
$951$	−6.88611	−	2.87784i	−0.223297	−	0.0933202i
$952$	1.66529	+	13.3348i	0.0539723	+	0.432183i
$953$		−	27.9513i		−	0.905431i	−0.891655	−	0.452716i	$-0.850455\pi$
$953$		−	27.9513i		−	0.905431i	0.891655	−	0.452716i	$-0.149545\pi$
$954$	1.28591	−	5.57471i	0.0416330	−	0.180488i
$955$			0.241765i			0.00782332i
$956$	−18.2579	+	38.7046i	−0.590503	+	1.25180i
$957$	10.0392	+	4.19557i	0.324521	+	0.135623i
$958$	−6.82578	+	4.32723i	−0.220531	+	0.139806i
$959$	−0.169312			−0.00546737
$960$	−13.7062	−	2.03475i	−0.442366	−	0.0656712i
$961$	−20.4760			−0.660515
$962$	−1.95711	+	1.24072i	−0.0630998	+	0.0400024i
$963$	11.5246	+	11.6711i	0.371374	+	0.376096i
$964$	7.30423	−	15.4841i	0.235253	−	0.498709i
$965$			5.65545i			0.182055i
$966$	1.64207	−	0.280444i	0.0528329	−	0.00902313i
$967$		−	0.268786i		−	0.00864359i	−0.999991	−	0.00432179i	$-0.998624\pi$
$967$		−	0.268786i		−	0.00864359i	0.999991	−	0.00432179i	$-0.00137567\pi$
$968$	−11.0447	−	88.4404i	−0.354991	−	2.84258i
$969$	−16.9232	+	40.4939i	−0.543651	+	1.30085i
$970$	−8.47455	−	13.3678i	−0.272101	−	0.429213i
$971$	13.6197			0.437078			0.218539	−	0.975828i	$-0.429871\pi$
$971$	13.6197			0.437078			0.218539	+	0.975828i	$0.429871\pi$
$972$	−23.4075	+	20.5934i	−0.750796	+	0.660535i
$973$	−7.94749			−0.254785
$974$	13.9553	+	22.0131i	0.447157	+	0.705346i
$975$	0.569580	−	1.36289i	0.0182411	−	0.0436475i
$976$	23.7804	+	28.8569i	0.761191	+	0.923686i
$977$			19.0302i			0.608830i	0.952540	+	0.304415i	$0.0984609\pi$
$977$			19.0302i			0.608830i	−0.952540	+	0.304415i	$0.901539\pi$
$978$	4.40217	−	0.751829i	0.140766	−	0.0240408i
$979$		−	7.97928i		−	0.255019i
$980$	1.80884	+	0.853276i	0.0577814	+	0.0272569i
$981$	−24.8772	−	25.1935i	−0.794267	−	0.804367i
$982$	−21.1705	+	13.4211i	−0.675578	+	0.428285i
$983$	−26.2176			−0.836212			−0.418106	−	0.908398i	$-0.637306\pi$
$983$	−26.2176			−0.836212			−0.418106	+	0.908398i	$0.637306\pi$
$984$	−8.61431	+	30.9310i	−0.274614	+	0.986044i
$985$	−0.381520			−0.0121562
$986$	−5.46763	+	3.46623i	−0.174125	+	0.110387i
$987$	−13.5855	−	5.67762i	−0.432430	−	0.180721i
$988$	8.22700	+	3.88088i	0.261736	+	0.123467i
$989$		−	5.89594i		−	0.187480i
$990$	−6.21757	+	26.9545i	−0.197607	+	0.856670i
$991$			53.3167i			1.69366i	0.531863	+	0.846831i	$0.321492\pi$
$991$			53.3167i			1.69366i	−0.531863	+	0.846831i	$0.678508\pi$
$992$	12.6334	−	38.5698i	0.401110	−	1.22459i
$993$	33.2933	+	13.9139i	1.05653	+	0.441545i
$994$	5.26534	+	8.30556i	0.167007	+	0.263436i
$995$	−0.221262			−0.00701447
$996$	−21.3329	−	23.6389i	−0.675959	−	0.749028i
$997$	37.9115			1.20067			0.600335	−	0.799748i	$-0.295034\pi$
$997$	37.9115			1.20067			0.600335	+	0.799748i	$0.295034\pi$
$998$	−13.2071	−	20.8329i	−0.418063	−	0.659453i
$999$	−9.25936	+	3.73295i	−0.292953	+	0.118105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.n.b.71.19	yes	24
3.2	odd	2		420.2.n.a.71.6	yes	24
4.3	odd	2		420.2.n.a.71.5	✓	24
12.11	even	2	inner	420.2.n.b.71.20	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.n.a.71.5	✓	24	4.3	odd	2
420.2.n.a.71.6	yes	24	3.2	odd	2
420.2.n.b.71.19	yes	24	1.1	even	1	trivial
420.2.n.b.71.20	yes	24	12.11	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19442 - 0.757207i) q^{2} +(-0.667879 + 1.59810i) q^{3} +(0.853276 - 1.80884i) q^{4} -1.00000i q^{5} +(0.412368 + 2.41453i) q^{6} -1.00000i q^{7} +(-0.350500 - 2.80663i) q^{8} +(-2.10788 - 2.13468i) q^{9} +O(q^{10})\)	\(q+(1.19442 - 0.757207i) q^{2} +(-0.667879 + 1.59810i) q^{3} +(0.853276 - 1.80884i) q^{4} -1.00000i q^{5} +(0.412368 + 2.41453i) q^{6} -1.00000i q^{7} +(-0.350500 - 2.80663i) q^{8} +(-2.10788 - 2.13468i) q^{9} +(-0.757207 - 1.19442i) q^{10} +6.52007 q^{11} +(2.32084 + 2.57171i) q^{12} +0.852819 q^{13} +(-0.757207 - 1.19442i) q^{14} +(1.59810 + 0.667879i) q^{15} +(-2.54384 - 3.08689i) q^{16} -4.75118i q^{17} +(-4.13408 - 0.953605i) q^{18} +5.33314i q^{19} +(-1.80884 - 0.853276i) q^{20} +(1.59810 + 0.667879i) q^{21} +(7.78770 - 4.93704i) q^{22} +0.680081 q^{23} +(4.71937 + 1.31435i) q^{24} -1.00000 q^{25} +(1.01862 - 0.645760i) q^{26} +(4.81925 - 1.94290i) q^{27} +(-1.80884 - 0.853276i) q^{28} -0.963476i q^{29} +(2.41453 - 0.412368i) q^{30} +7.17468i q^{31} +(-5.37582 - 1.76083i) q^{32} +(-4.35462 + 10.4198i) q^{33} +(-3.59763 - 5.67490i) q^{34} -1.00000 q^{35} +(-5.65990 + 1.99135i) q^{36} -1.92133 q^{37} +(4.03829 + 6.37001i) q^{38} +(-0.569580 + 1.36289i) q^{39} +(-2.80663 + 0.350500i) q^{40} +6.55405i q^{41} +(2.41453 - 0.412368i) q^{42} -8.66947i q^{43} +(5.56342 - 11.7938i) q^{44} +(-2.13468 + 2.10788i) q^{45} +(0.812302 - 0.514962i) q^{46} -8.50098 q^{47} +(6.63215 - 2.00366i) q^{48} -1.00000 q^{49} +(-1.19442 + 0.757207i) q^{50} +(7.59288 + 3.17321i) q^{51} +(0.727690 - 1.54262i) q^{52} +1.34848i q^{53} +(4.28503 - 5.96980i) q^{54} -6.52007i q^{55} +(-2.80663 + 0.350500i) q^{56} +(-8.52292 - 3.56189i) q^{57} +(-0.729551 - 1.15079i) q^{58} +0.990010 q^{59} +(2.57171 - 2.32084i) q^{60} -9.34821 q^{61} +(5.43271 + 8.56957i) q^{62} +(-2.13468 + 2.10788i) q^{63} +(-7.75430 + 1.96745i) q^{64} -0.852819i q^{65} +(2.68867 + 15.7429i) q^{66} +12.1617i q^{67} +(-8.59415 - 4.05407i) q^{68} +(-0.454211 + 1.08684i) q^{69} +(-1.19442 + 0.757207i) q^{70} -6.95364 q^{71} +(-5.25244 + 6.66423i) q^{72} +9.97510 q^{73} +(-2.29487 + 1.45484i) q^{74} +(0.667879 - 1.59810i) q^{75} +(9.64683 + 4.55064i) q^{76} -6.52007i q^{77} +(0.351675 + 2.05916i) q^{78} +12.5813i q^{79} +(-3.08689 + 2.54384i) q^{80} +(-0.113716 + 8.99928i) q^{81} +(4.96277 + 7.82828i) q^{82} -9.19190 q^{83} +(2.57171 - 2.32084i) q^{84} -4.75118 q^{85} +(-6.56458 - 10.3550i) q^{86} +(1.53974 + 0.643485i) q^{87} +(-2.28528 - 18.2994i) q^{88} -1.22380i q^{89} +(-0.953605 + 4.13408i) q^{90} -0.852819i q^{91} +(0.580297 - 1.23016i) q^{92} +(-11.4659 - 4.79181i) q^{93} +(-10.1537 + 6.43700i) q^{94} +5.33314 q^{95} +(6.40438 - 7.41511i) q^{96} +11.1919 q^{97} +(-1.19442 + 0.757207i) q^{98} +(-13.7435 - 13.9183i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9	\( 24 q + 2 q^{4} + 6 q^{6} + 4 q^{9} + 2 q^{10} + 16 q^{12} + 2 q^{14} + 6 q^{16} - 24 q^{18} - 8 q^{20} + 8 q^{22} + 14 q^{24} - 24 q^{25} + 20 q^{26} - 8 q^{28} - 8 q^{30} - 20 q^{32} + 16 q^{33} - 16 q^{34} - 24 q^{35} + 30 q^{36} + 60 q^{38} + 12 q^{39} - 14 q^{40} - 8 q^{42} - 24 q^{44} - 12 q^{46} - 8 q^{47} + 36 q^{48} - 24 q^{49} - 36 q^{51} + 20 q^{52} - 38 q^{54} - 14 q^{56} - 24 q^{57} + 44 q^{58} + 8 q^{59} + 14 q^{60} + 16 q^{61} + 28 q^{62} - 22 q^{64} - 12 q^{66} - 32 q^{68} - 72 q^{71} + 56 q^{72} - 24 q^{73} + 64 q^{74} + 48 q^{76} - 92 q^{78} - 20 q^{81} - 16 q^{82} + 40 q^{83} + 14 q^{84} - 16 q^{85} + 40 q^{86} + 80 q^{87} - 12 q^{88} - 10 q^{90} - 108 q^{92} - 48 q^{93} - 36 q^{94} + 34 q^{96} + 24 q^{97} - 84 q^{99}+O(q^{100}) \) 24 * q + 2 * q^4 + 6 * q^6 + 4 * q^9 + 2 * q^10 + 16 * q^12 + 2 * q^14 + 6 * q^16 - 24 * q^18 - 8 * q^20 + 8 * q^22 + 14 * q^24 - 24 * q^25 + 20 * q^26 - 8 * q^28 - 8 * q^30 - 20 * q^32 + 16 * q^33 - 16 * q^34 - 24 * q^35 + 30 * q^36 + 60 * q^38 + 12 * q^39 - 14 * q^40 - 8 * q^42 - 24 * q^44 - 12 * q^46 - 8 * q^47 + 36 * q^48 - 24 * q^49 - 36 * q^51 + 20 * q^52 - 38 * q^54 - 14 * q^56 - 24 * q^57 + 44 * q^58 + 8 * q^59 + 14 * q^60 + 16 * q^61 + 28 * q^62 - 22 * q^64 - 12 * q^66 - 32 * q^68 - 72 * q^71 + 56 * q^72 - 24 * q^73 + 64 * q^74 + 48 * q^76 - 92 * q^78 - 20 * q^81 - 16 * q^82 + 40 * q^83 + 14 * q^84 - 16 * q^85 + 40 * q^86 + 80 * q^87 - 12 * q^88 - 10 * q^90 - 108 * q^92 - 48 * q^93 - 36 * q^94 + 34 * q^96 + 24 * q^97 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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