LMFDB - Embedded newform 420.2.l.h.239.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(239,420)]

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, 1, 0]))

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

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

chi := DirichletCharacter("420.239");

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.l (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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 9 x^{14} - 16 x^{13} + 18 x^{12} - 4 x^{11} - 36 x^{10} + 102 x^{9} - 170 x^{8} + \cdots + 256 $ x^16 - 4x^15 + 9x^14 - 16x^13 + 18x^12 - 4x^11 - 36x^10 + 102x^9 - 170x^8 + 204x^7 - 144x^6 - 32x^5 + 288x^4 - 512x^3 + 576x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			239.12
Root			$1.40708 - 0.141881i$ of defining polynomial
Character	$\chi$	$=$	420.239
Dual form			420.2.l.h.239.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.979286 + 1.02029i) q^{2} +(-1.71822 + 0.218455i) q^{3} +(-0.0819979 + 1.99832i) q^{4} +(2.22537 - 0.218455i) q^{5} +(-1.90552 - 1.53916i) q^{6} +1.00000 q^{7} +(-2.11917 + 1.87326i) q^{8} +(2.90455 - 0.750707i) q^{9} +O(q^{10})$	\(q+(0.979286 + 1.02029i) q^{2} +(-1.71822 + 0.218455i) q^{3} +(-0.0819979 + 1.99832i) q^{4} +(2.22537 - 0.218455i) q^{5} +(-1.90552 - 1.53916i) q^{6} +1.00000 q^{7} +(-2.11917 + 1.87326i) q^{8} +(2.90455 - 0.750707i) q^{9} +(2.40216 + 2.05660i) q^{10} +2.59032 q^{11} +(-0.295652 - 3.45146i) q^{12} +5.21794i q^{13} +(0.979286 + 1.02029i) q^{14} +(-3.77595 + 0.861497i) q^{15} +(-3.98655 - 0.327716i) q^{16} -3.91714 q^{17} +(3.61033 + 2.22834i) q^{18} -5.21794i q^{19} +(0.254067 + 4.46491i) q^{20} +(-1.71822 + 0.218455i) q^{21} +(2.53667 + 2.64289i) q^{22} +7.44926i q^{23} +(3.23198 - 3.68162i) q^{24} +(4.90455 - 0.972287i) q^{25} +(-5.32383 + 5.10985i) q^{26} +(-4.82667 + 1.92439i) q^{27} +(-0.0819979 + 1.99832i) q^{28} +8.44212i q^{29} +(-4.57672 - 3.00893i) q^{30} -1.42159i q^{31} +(-3.56961 - 4.38838i) q^{32} +(-4.45074 + 0.565869i) q^{33} +(-3.83600 - 3.99664i) q^{34} +(2.22537 - 0.218455i) q^{35} +(1.26198 + 5.86578i) q^{36} -7.99327i q^{37} +(5.32383 - 5.10985i) q^{38} +(-1.13988 - 8.96556i) q^{39} +(-4.30672 + 4.63165i) q^{40} -7.49305i q^{41} +(-1.90552 - 1.53916i) q^{42} +3.28066 q^{43} +(-0.212401 + 5.17629i) q^{44} +(6.29972 - 2.30512i) q^{45} +(-7.60043 + 7.29496i) q^{46} -4.36094i q^{47} +(6.92136 - 0.307795i) q^{48} +1.00000 q^{49} +(5.79498 + 4.05194i) q^{50} +(6.73051 - 0.855720i) q^{51} +(-10.4271 - 0.427860i) q^{52} +0.310553 q^{53} +(-6.69013 - 3.04008i) q^{54} +(5.76443 - 0.565869i) q^{55} +(-2.11917 + 1.87326i) q^{56} +(1.13988 + 8.96556i) q^{57} +(-8.61344 + 8.26725i) q^{58} -2.17097 q^{59} +(-1.41193 - 7.61620i) q^{60} +6.70066 q^{61} +(1.45044 - 1.39214i) q^{62} +(2.90455 - 0.750707i) q^{63} +(0.981770 - 7.93953i) q^{64} +(1.13988 + 11.6118i) q^{65} +(-4.93590 - 3.98692i) q^{66} +14.3540 q^{67} +(0.321198 - 7.82770i) q^{68} +(-1.62733 - 12.7995i) q^{69} +(2.40216 + 2.05660i) q^{70} -5.88636 q^{71} +(-4.74898 + 7.03187i) q^{72} -11.3594i q^{73} +(8.15549 - 7.82770i) q^{74} +(-8.21470 + 2.74203i) q^{75} +(10.4271 + 0.427860i) q^{76} +2.59032 q^{77} +(8.03123 - 9.94287i) q^{78} -7.09467i q^{79} +(-8.94315 + 0.141593i) q^{80} +(7.87288 - 4.36094i) q^{81} +(7.64511 - 7.33784i) q^{82} -0.802169i q^{83} +(-0.295652 - 3.45146i) q^{84} +(-8.71710 + 0.855720i) q^{85} +(3.21271 + 3.34724i) q^{86} +(-1.84422 - 14.5054i) q^{87} +(-5.48934 + 4.85236i) q^{88} +6.98449i q^{89} +(8.52112 + 4.17019i) q^{90} +5.21794i q^{91} +(-14.8860 - 0.610824i) q^{92} +(0.310553 + 2.44260i) q^{93} +(4.44944 - 4.27061i) q^{94} +(-1.13988 - 11.6118i) q^{95} +(7.09203 + 6.76040i) q^{96} -6.80482i q^{97} +(0.979286 + 1.02029i) q^{98} +(7.52373 - 1.94457i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{4} - 10 q^{6} + 16 q^{7}+O(q^{10}) $ 16 * q + 6 * q^4 - 10 * q^6 + 16 * q^7	$ 16 q + 6 q^{4} - 10 q^{6} + 16 q^{7} + 14 q^{10} + 16 q^{12} + 24 q^{15} - 10 q^{16} + 8 q^{18} - 12 q^{22} + 6 q^{24} + 32 q^{25} - 24 q^{27} + 6 q^{28} - 26 q^{30} - 76 q^{34} + 6 q^{36} + 2 q^{40} - 10 q^{42} - 16 q^{43} + 12 q^{45} - 52 q^{46} + 28 q^{48} + 16 q^{49} - 44 q^{52} - 6 q^{54} + 8 q^{55} + 4 q^{58} + 36 q^{60} + 40 q^{61} + 6 q^{64} - 8 q^{66} + 56 q^{67} - 64 q^{69} + 14 q^{70} - 16 q^{72} - 12 q^{75} + 44 q^{76} + 20 q^{78} + 16 q^{81} + 44 q^{82} + 16 q^{84} - 16 q^{85} - 16 q^{87} + 4 q^{88} - 10 q^{90} - 56 q^{94} + 34 q^{96}+O(q^{100}) $ 16 * q + 6 * q^4 - 10 * q^6 + 16 * q^7 + 14 * q^10 + 16 * q^12 + 24 * q^15 - 10 * q^16 + 8 * q^18 - 12 * q^22 + 6 * q^24 + 32 * q^25 - 24 * q^27 + 6 * q^28 - 26 * q^30 - 76 * q^34 + 6 * q^36 + 2 * q^40 - 10 * q^42 - 16 * q^43 + 12 * q^45 - 52 * q^46 + 28 * q^48 + 16 * q^49 - 44 * q^52 - 6 * q^54 + 8 * q^55 + 4 * q^58 + 36 * q^60 + 40 * q^61 + 6 * q^64 - 8 * q^66 + 56 * q^67 - 64 * q^69 + 14 * q^70 - 16 * q^72 - 12 * q^75 + 44 * q^76 + 20 * q^78 + 16 * q^81 + 44 * q^82 + 16 * q^84 - 16 * q^85 - 16 * q^87 + 4 * q^88 - 10 * q^90 - 56 * q^94 + 34 * q^96

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 $

$2$	0.979286	+	1.02029i	0.692460	+	0.721456i
$2$	0.979286	+	1.02029i	0.692460	+	0.721456i
$3$	−1.71822	+	0.218455i	−0.992014	+	0.126125i
$3$	−1.71822	+	0.218455i	−0.992014	+	0.126125i
$4$	−0.0819979	+	1.99832i	−0.0409990	+	0.999159i
$5$	2.22537	−	0.218455i	0.995216	−	0.0976961i
$5$	2.22537	−	0.218455i	0.995216	−	0.0976961i
$6$	−1.90552	−	1.53916i	−0.777924	−	0.628359i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.11917	+	1.87326i	−0.749240	+	0.662299i
$9$	2.90455	−	0.750707i	0.968185	−	0.250236i
$10$	2.40216	+	2.05660i	0.759631	+	0.650355i
$11$	2.59032			0.781012			0.390506	−	0.920600i	$-0.372300\pi$
$11$	2.59032			0.781012			0.390506	+	0.920600i	$0.372300\pi$
$12$	−0.295652	−	3.45146i	−0.0853475	−	0.996351i
$13$			5.21794i			1.44720i	0.690222	+	0.723598i	$0.257513\pi$
$13$			5.21794i			1.44720i	−0.690222	+	0.723598i	$0.742487\pi$
$14$	0.979286	+	1.02029i	0.261725	+	0.272685i
$15$	−3.77595	+	0.861497i	−0.974947	+	0.222438i
$16$	−3.98655	−	0.327716i	−0.996638	−	0.0819290i
$17$	−3.91714			−0.950047			−0.475023	−	0.879973i	$-0.657560\pi$
$17$	−3.91714			−0.950047			−0.475023	+	0.879973i	$0.657560\pi$
$18$	3.61033	+	2.22834i	0.850963	+	0.525225i
$19$		−	5.21794i		−	1.19708i	−0.801094	−	0.598538i	$-0.795748\pi$
$19$		−	5.21794i		−	1.19708i	0.801094	−	0.598538i	$-0.204252\pi$
$20$	0.254067	+	4.46491i	0.0568111	+	0.998385i
$21$	−1.71822	+	0.218455i	−0.374946	+	0.0476708i
$22$	2.53667	+	2.64289i	0.540819	+	0.563466i
$23$			7.44926i			1.55328i	0.629946	+	0.776639i	$0.283077\pi$
$23$			7.44926i			1.55328i	−0.629946	+	0.776639i	$0.716923\pi$
$24$	3.23198	−	3.68162i	0.659724	−	0.751508i
$25$	4.90455	−	0.972287i	0.980911	−	0.194457i
$26$	−5.32383	+	5.10985i	−1.04409	+	1.00212i
$27$	−4.82667	+	1.92439i	−0.928892	+	0.370350i
$28$	−0.0819979	+	1.99832i	−0.0154961	+	0.377647i
$29$			8.44212i			1.56766i	0.620975	+	0.783831i	$0.286737\pi$
$29$			8.44212i			1.56766i	−0.620975	+	0.783831i	$0.713263\pi$
$30$	−4.57672	−	3.00893i	−0.835591	−	0.549353i
$31$		−	1.42159i		−	0.255325i	−0.991818	−	0.127662i	$-0.959253\pi$
$31$		−	1.42159i		−	0.255325i	0.991818	−	0.127662i	$-0.0407474\pi$
$32$	−3.56961	−	4.38838i	−0.631024	−	0.775764i
$33$	−4.45074	+	0.565869i	−0.774775	+	0.0985052i
$34$	−3.83600	−	3.99664i	−0.657869	−	0.685418i
$35$	2.22537	−	0.218455i	0.376156	−	0.0369256i
$36$	1.26198	+	5.86578i	0.210331	+	0.977630i
$37$		−	7.99327i		−	1.31409i	−0.753853	−	0.657043i	$-0.771807\pi$
$37$		−	7.99327i		−	1.31409i	0.753853	−	0.657043i	$-0.228193\pi$
$38$	5.32383	−	5.10985i	0.863639	−	0.828928i
$39$	−1.13988	−	8.96556i	−0.182528	−	1.43564i
$40$	−4.30672	+	4.63165i	−0.680952	+	0.732328i
$41$		−	7.49305i		−	1.17022i	−0.810955	−	0.585109i	$-0.801052\pi$
$41$		−	7.49305i		−	1.17022i	0.810955	−	0.585109i	$-0.198948\pi$
$42$	−1.90552	−	1.53916i	−0.294028	−	0.237497i
$43$	3.28066			0.500296			0.250148	−	0.968208i	$-0.419521\pi$
$43$	3.28066			0.500296			0.250148	+	0.968208i	$0.419521\pi$
$44$	−0.212401	+	5.17629i	−0.0320207	+	0.780355i
$45$	6.29972	−	2.30512i	0.939106	−	0.343627i
$46$	−7.60043	+	7.29496i	−1.12062	+	1.07558i
$47$		−	4.36094i		−	0.636109i	−0.948072	−	0.318054i	$-0.896971\pi$
$47$		−	4.36094i		−	0.636109i	0.948072	−	0.318054i	$-0.103029\pi$
$48$	6.92136	−	0.307795i	0.999013	−	0.0444264i
$49$	1.00000			0.142857
$50$	5.79498	+	4.05194i	0.819534	+	0.573031i
$51$	6.73051	−	0.855720i	0.942460	−	0.119825i
$52$	−10.4271	−	0.427860i	−1.44598	−	0.0593335i
$53$	0.310553			0.0426578			0.0213289	−	0.999773i	$-0.493210\pi$
$53$	0.310553			0.0426578			0.0213289	+	0.999773i	$0.493210\pi$
$54$	−6.69013	−	3.04008i	−0.910412	−	0.413703i
$55$	5.76443	−	0.565869i	0.777276	−	0.0763018i
$56$	−2.11917	+	1.87326i	−0.283186	+	0.250325i
$57$	1.13988	+	8.96556i	0.150981	+	1.18752i
$58$	−8.61344	+	8.26725i	−1.13100	+	1.08554i
$59$	−2.17097			−0.282637			−0.141318	−	0.989964i	$-0.545134\pi$
$59$	−2.17097			−0.282637			−0.141318	+	0.989964i	$0.545134\pi$
$60$	−1.41193	−	7.61620i	−0.182279	−	0.983247i
$61$	6.70066			0.857932			0.428966	−	0.903321i	$-0.358878\pi$
$61$	6.70066			0.857932			0.428966	+	0.903321i	$0.358878\pi$
$62$	1.45044	−	1.39214i	0.184206	−	0.176802i
$63$	2.90455	−	0.750707i	0.365940	−	0.0945802i
$64$	0.981770	−	7.93953i	0.122721	−	0.992441i
$65$	1.13988	+	11.6118i	0.141385	+	1.44027i
$66$	−4.93590	−	3.98692i	−0.607568	−	0.490755i
$67$	14.3540			1.75362			0.876810	−	0.480837i	$-0.159667\pi$
$67$	14.3540			1.75362			0.876810	+	0.480837i	$0.159667\pi$
$68$	0.321198	−	7.82770i	0.0389509	−	0.949248i
$69$	−1.62733	−	12.7995i	−0.195907	−	1.54087i
$70$	2.40216	+	2.05660i	0.287113	+	0.245811i
$71$	−5.88636			−0.698582			−0.349291	−	0.937014i	$-0.613578\pi$
$71$	−5.88636			−0.698582			−0.349291	+	0.937014i	$0.613578\pi$
$72$	−4.74898	+	7.03187i	−0.559672	+	0.828714i
$73$		−	11.3594i		−	1.32952i	−0.747056	−	0.664761i	$-0.768533\pi$
$73$		−	11.3594i		−	1.32952i	0.747056	−	0.664761i	$-0.231467\pi$
$74$	8.15549	−	7.82770i	0.948056	−	0.909952i
$75$	−8.21470	+	2.74203i	−0.948552	+	0.316622i
$76$	10.4271	+	0.427860i	1.19607	+	0.0490789i
$77$	2.59032			0.295195
$78$	8.03123	−	9.94287i	0.909358	−	1.12581i
$79$		−	7.09467i		−	0.798213i	−0.916905	−	0.399106i	$-0.869320\pi$
$79$		−	7.09467i		−	0.798213i	0.916905	−	0.399106i	$-0.130680\pi$
$80$	−8.94315	+	0.141593i	−0.999875	+	0.0158306i
$81$	7.87288	−	4.36094i	0.874764	−	0.484549i
$82$	7.64511	−	7.33784i	0.844262	−	0.810329i
$83$		−	0.802169i		−	0.0880495i	−0.999030	−	0.0440247i	$-0.985982\pi$
$83$		−	0.802169i		−	0.0880495i	0.999030	−	0.0440247i	$-0.0140180\pi$
$84$	−0.295652	−	3.45146i	−0.0322583	−	0.376585i
$85$	−8.71710	+	0.855720i	−0.945502	+	0.0928159i
$86$	3.21271	+	3.34724i	0.346435	+	0.360942i
$87$	−1.84422	−	14.5054i	−0.197721	−	1.55514i
$88$	−5.48934	+	4.85236i	−0.585165	+	0.517263i
$89$			6.98449i			0.740355i	0.928961	+	0.370177i	$0.120703\pi$
$89$			6.98449i			0.740355i	−0.928961	+	0.370177i	$0.879297\pi$
$90$	8.52112	+	4.17019i	0.898205	+	0.439577i
$91$			5.21794i			0.546988i
$92$	−14.8860	−	0.610824i	−1.55197	−	0.0636828i
$93$	0.310553	+	2.44260i	0.0322029	+	0.253286i
$94$	4.44944	−	4.27061i	0.458925	−	0.440480i
$95$	−1.13988	−	11.6118i	−0.116950	−	1.19135i
$96$	7.09203	+	6.76040i	0.723828	+	0.689981i
$97$		−	6.80482i		−	0.690925i	−0.938433	−	0.345462i	$-0.887722\pi$
$97$		−	6.80482i		−	0.690925i	0.938433	−	0.345462i	$-0.112278\pi$
$98$	0.979286	+	1.02029i	0.0989228	+	0.103065i
$99$	7.52373	−	1.94457i	0.756164	−	0.195437i
$100$	1.54078	+	9.88059i	0.154078	+	0.988059i
$101$		−	0.802169i		−	0.0798188i	−0.999203	−	0.0399094i	$-0.987293\pi$
$101$		−	0.802169i		−	0.0798188i	0.999203	−	0.0399094i	$-0.0127069\pi$
$102$	7.46418	+	6.02910i	0.739064	+	0.596970i
$103$	−10.5284			−1.03740			−0.518699	−	0.854957i	$-0.673584\pi$
$103$	−10.5284			−1.03740			−0.518699	+	0.854957i	$0.673584\pi$
$104$	−9.77457	−	11.0577i	−0.958476	−	1.08430i
$105$	−3.77595	+	0.861497i	−0.368495	+	0.0840735i
$106$	0.304120	+	0.316856i	0.0295388	+	0.0307757i
$107$		−	12.3626i		−	1.19513i	−0.801819	−	0.597567i	$-0.796134\pi$
$107$		−	12.3626i		−	1.19513i	0.801819	−	0.597567i	$-0.203866\pi$
$108$	−3.44978	−	9.80301i	−0.331955	−	0.943295i
$109$	3.20087			0.306588			0.153294	−	0.988181i	$-0.451012\pi$
$109$	3.20087			0.306588			0.153294	+	0.988181i	$0.451012\pi$
$110$	6.22238	+	5.32726i	0.593280	+	0.507935i
$111$	1.74617	+	13.7342i	0.165739	+	1.30359i
$112$	−3.98655	−	0.327716i	−0.376694	−	0.0309662i
$113$	−13.7716			−1.29552			−0.647761	−	0.761844i	$-0.724294\pi$
$113$	−13.7716			−1.29552			−0.647761	+	0.761844i	$0.724294\pi$
$114$	−8.03123	+	9.94287i	−0.752194	+	0.931235i
$115$	1.62733	+	16.5774i	0.151749	+	1.54585i
$116$	−16.8700	−	0.692236i	−1.56634	−	0.0642725i
$117$	3.91714	+	15.1558i	0.362140	+	1.40115i
$118$	−2.12600	−	2.21503i	−0.195714	−	0.203910i
$119$	−3.91714			−0.359084
$120$	6.38808	−	8.89901i	0.583149	−	0.812365i
$121$	−4.29023			−0.390021
$122$	6.56187	+	6.83664i	0.594083	+	0.618961i
$123$	1.63690	+	12.8747i	0.147594	+	1.16087i
$124$	2.84079	+	0.116567i	0.255110	+	0.0104681i
$125$	10.7021	−	3.23512i	0.957221	−	0.289358i
$126$	3.61033	+	2.22834i	0.321634	+	0.198516i
$127$	−10.1371			−0.899522			−0.449761	−	0.893149i	$-0.648491\pi$
$127$	−10.1371			−0.899522			−0.449761	+	0.893149i	$0.648491\pi$
$128$	9.06208	−	6.77338i	0.800983	−	0.598688i
$129$	−5.63690	+	0.716677i	−0.496301	+	0.0630999i
$130$	−10.7312	+	12.5343i	−0.941190	+	1.09933i
$131$	9.38415			0.819897			0.409949	−	0.912109i	$-0.365547\pi$
$131$	9.38415			0.819897			0.409949	+	0.912109i	$0.365547\pi$
$132$	−0.765835	−	8.94040i	−0.0666574	−	0.778162i
$133$		−	5.21794i		−	0.452453i
$134$	14.0567	+	14.6453i	1.21431	+	1.26516i
$135$	−10.3207	+	5.33690i	−0.888267	+	0.459327i
$136$	8.30110	−	7.33784i	0.711813	−	0.629215i
$137$	1.13052			0.0965866			0.0482933	−	0.998833i	$-0.484622\pi$
$137$	1.13052			0.0965866			0.0482933	+	0.998833i	$0.484622\pi$
$138$	11.4656	−	14.1947i	0.976016	−	1.20833i
$139$		−	3.50650i		−	0.297417i	−0.988881	−	0.148709i	$-0.952488\pi$
$139$		−	3.50650i		−	0.297417i	0.988881	−	0.148709i	$-0.0475117\pi$
$140$	0.254067	+	4.46491i	0.0214726	+	0.377354i
$141$	0.952670	+	7.49305i	0.0802293	+	0.631029i
$142$	−5.76443	−	6.00582i	−0.483740	−	0.503997i
$143$			13.5161i			1.13028i
$144$	−11.8252	+	2.04087i	−0.985432	+	0.170072i
$145$	1.84422	+	18.7868i	0.153154	+	1.56016i
$146$	11.5900	−	11.1241i	0.959192	−	0.920640i
$147$	−1.71822	+	0.218455i	−0.141716	+	0.0180179i
$148$	15.9731	+	0.655432i	1.31298	+	0.0538762i
$149$			0.594053i			0.0486667i	0.999704	+	0.0243334i	$0.00774632\pi$
$149$			0.594053i			0.0486667i	−0.999704	+	0.0243334i	$0.992254\pi$
$150$	−10.8422	−	5.69618i	−0.885263	−	0.465091i
$151$			4.15404i			0.338051i	0.985612	+	0.169026i	$0.0540620\pi$
$151$			4.15404i			0.338051i	−0.985612	+	0.169026i	$0.945938\pi$
$152$	9.77457	+	11.0577i	0.792822	+	0.896898i
$153$	−11.3776	+	2.94063i	−0.919821	+	0.237736i
$154$	2.53667	+	2.64289i	0.204410	+	0.212970i
$155$	−0.310553	−	3.16356i	−0.0249442	−	0.254104i
$156$	18.0095	−	1.54270i	1.44192	−	0.123514i
$157$		−	5.21794i		−	0.416437i	−0.978082	−	0.208218i	$-0.933234\pi$
$157$		−	5.21794i		−	0.416437i	0.978082	−	0.208218i	$-0.0667665\pi$
$158$	7.23865	−	6.94771i	0.575876	−	0.552730i
$159$	−0.533599	+	0.0678419i	−0.0423171	+	0.00538022i
$160$	−8.90237	−	8.98598i	−0.703794	−	0.710404i
$161$			7.44926i			0.587084i
$162$	12.1592	+	3.76204i	0.955320	+	0.295574i
$163$	7.68157			0.601667			0.300834	−	0.953677i	$-0.402735\pi$
$163$	7.68157			0.601667			0.300834	+	0.953677i	$0.402735\pi$
$164$	14.9735	+	0.614415i	1.16923	+	0.0479777i
$165$	−9.78094	+	2.23156i	−0.761445	+	0.173726i
$166$	0.818448	−	0.785553i	0.0635239	−	0.0609707i
$167$			11.1409i			0.862109i	0.902326	+	0.431055i	$0.141858\pi$
$167$			11.1409i			0.862109i	−0.902326	+	0.431055i	$0.858142\pi$
$168$	3.23198	−	3.68162i	0.249352	−	0.284043i
$169$	−14.2269			−1.09437
$170$	−9.40962	−	8.05601i	−0.721685	−	0.617867i
$171$	−3.91714	−	15.1558i	−0.299551	−	1.15899i
$172$	−0.269007	+	6.55581i	−0.0205116	+	0.499875i
$173$	−10.6986			−0.813398			−0.406699	−	0.913562i	$-0.633320\pi$
$173$	−10.6986			−0.813398			−0.406699	+	0.913562i	$0.633320\pi$
$174$	12.9938	−	16.0866i	0.985054	−	1.21952i
$175$	4.90455	−	0.972287i	0.370749	−	0.0734980i
$176$	−10.3265	−	0.848890i	−0.778386	−	0.0639875i
$177$	3.73021	−	0.474260i	0.280380	−	0.0356476i
$178$	−7.12623	+	6.83981i	−0.534134	+	0.512666i
$179$	−1.75162			−0.130922			−0.0654612	−	0.997855i	$-0.520852\pi$
$179$	−1.75162			−0.130922			−0.0654612	+	0.997855i	$0.520852\pi$
$180$	4.08979	+	12.7779i	0.304835	+	0.952405i
$181$	−8.48377			−0.630594			−0.315297	−	0.948993i	$-0.602104\pi$
$181$	−8.48377			−0.630594			−0.315297	+	0.948993i	$0.602104\pi$
$182$	−5.32383	+	5.10985i	−0.394628	+	0.378768i
$183$	−11.5132	+	1.46379i	−0.851081	+	0.108207i
$184$	−13.9544	−	15.7863i	−1.02873	−	1.16378i
$185$	−1.74617	−	17.7880i	−0.128381	−	1.30780i
$186$	−2.18805	+	2.70886i	−0.160436	+	0.198623i
$187$	−10.1467			−0.741998
$188$	8.71455	+	0.357588i	0.635574	+	0.0260798i
$189$	−4.82667	+	1.92439i	−0.351088	+	0.139979i
$190$	10.7312	−	12.5343i	0.778525	−	0.909336i
$191$	−6.50747			−0.470864			−0.235432	−	0.971891i	$-0.575650\pi$
$191$	−6.50747			−0.470864			−0.235432	+	0.971891i	$0.575650\pi$
$192$	0.0475350	+	13.8563i	0.00343054	+	0.999994i
$193$		−	14.0919i		−	1.01436i	−0.861841	−	0.507178i	$-0.830689\pi$
$193$		−	14.0919i		−	1.01436i	0.861841	−	0.507178i	$-0.169311\pi$
$194$	6.94291	−	6.66386i	0.498472	−	0.478438i
$195$	−4.49524	−	19.7027i	−0.321911	−	1.41094i
$196$	−0.0819979	+	1.99832i	−0.00585699	+	0.142737i
$197$	17.8850			1.27426			0.637128	−	0.770758i	$-0.280122\pi$
$197$	17.8850			1.27426			0.637128	+	0.770758i	$0.280122\pi$
$198$	9.35192	+	5.77212i	0.664612	+	0.410207i
$199$			9.01429i			0.639006i	0.947585	+	0.319503i	$0.103516\pi$
$199$			9.01429i			0.639006i	−0.947585	+	0.319503i	$0.896484\pi$
$200$	−8.57224	+	11.2480i	−0.606149	+	0.795351i
$201$	−24.6633	+	3.13570i	−1.73962	+	0.221175i
$202$	0.818448	−	0.785553i	0.0575858	−	0.0552713i
$203$			8.44212i			0.592520i
$204$	1.15811	+	13.5199i	0.0810841	+	0.946580i
$205$	−1.63690	−	16.6748i	−0.114326	−	1.16462i
$206$	−10.3104	−	10.7421i	−0.718357	−	0.748438i
$207$	5.59222	+	21.6368i	0.388686	+	1.50386i
$208$	1.71000	−	20.8016i	0.118567	−	1.44233i
$209$		−	13.5161i		−	0.934931i
$210$	−4.57672	−	3.00893i	−0.315824	−	0.207636i
$211$			18.5648i			1.27806i	0.769184	+	0.639028i	$0.220663\pi$
$211$			18.5648i			1.27806i	−0.769184	+	0.639028i	$0.779337\pi$
$212$	−0.0254647	+	0.620584i	−0.00174892	+	0.0426219i
$213$	10.1141	−	1.28591i	0.693004	−	0.0881088i
$214$	12.6134	−	12.1065i	0.862237	−	0.827582i
$215$	7.30069	−	0.716677i	0.497903	−	0.0488770i
$216$	6.62363	−	13.1197i	0.450681	−	0.892685i
$217$		−	1.42159i		−	0.0965037i
$218$	3.13457	+	3.26583i	0.212300	+	0.221190i
$219$	2.48153	+	19.5180i	0.167686	+	1.31890i
$220$	0.658115	+	11.5656i	0.0443701	+	0.779750i
$221$		−	20.4394i		−	1.37490i
$222$	−12.3029	+	15.2313i	−0.825717	+	1.02226i
$223$	−4.74534			−0.317772			−0.158886	−	0.987297i	$-0.550790\pi$
$223$	−4.74534			−0.317772			−0.158886	+	0.987297i	$0.550790\pi$
$224$	−3.56961	−	4.38838i	−0.238505	−	0.293211i
$225$	13.5156	−	6.50595i	0.901043	−	0.433730i
$226$	−13.4863	−	14.0511i	−0.897096	−	0.934662i
$227$			23.7796i			1.57831i	0.614194	+	0.789155i	$0.289481\pi$
$227$			23.7796i			1.57831i	−0.614194	+	0.789155i	$0.710519\pi$
$228$	−18.0095	+	1.54270i	−1.19271	+	0.102168i
$229$	0.917556			0.0606338			0.0303169	−	0.999540i	$-0.490348\pi$
$229$	0.917556			0.0606338			0.0303169	+	0.999540i	$0.490348\pi$
$230$	−15.3202	+	17.8943i	−1.01018	+	1.17992i
$231$	−4.45074	+	0.565869i	−0.292837	+	0.0372315i
$232$	−15.8143	−	17.8903i	−1.03826	−	1.17455i
$233$	−18.4765			−1.21044			−0.605218	−	0.796060i	$-0.706914\pi$
$233$	−18.4765			−1.21044			−0.605218	+	0.796060i	$0.706914\pi$
$234$	−11.6273	+	18.8385i	−0.760103	+	1.23151i
$235$	−0.952670	−	9.70471i	−0.0621453	−	0.633066i
$236$	0.178015	−	4.33830i	0.0115878	−	0.282399i
$237$	1.54987	+	12.1902i	0.100675	+	0.791838i
$238$	−3.83600	−	3.99664i	−0.248651	−	0.259063i
$239$	21.4096			1.38487			0.692435	−	0.721481i	$-0.256538\pi$
$239$	21.4096			1.38487			0.692435	+	0.721481i	$0.256538\pi$
$240$	15.3354	−	2.19696i	0.989893	−	0.141813i
$241$	−3.47155			−0.223622			−0.111811	−	0.993729i	$-0.535665\pi$
$241$	−3.47155			−0.223622			−0.111811	+	0.993729i	$0.535665\pi$
$242$	−4.20136	−	4.37729i	−0.270074	−	0.281383i
$243$	−12.5747	+	9.21292i	−0.806665	+	0.591009i
$244$	−0.549440	+	13.3901i	−0.0351743	+	0.857211i
$245$	2.22537	−	0.218455i	0.142174	−	0.0139566i
$246$	−11.5330	+	14.2781i	−0.735317	+	0.910341i
$247$	27.2269			1.73240
$248$	2.66301	+	3.01259i	0.169101	+	0.191300i
$249$	0.175238	+	1.37830i	0.0111052	+	0.0873463i
$250$	13.7811	+	7.75112i	0.871596	+	0.490224i
$251$	−20.1915			−1.27448			−0.637239	−	0.770666i	$-0.719924\pi$
$251$	−20.1915			−1.27448			−0.637239	+	0.770666i	$0.719924\pi$
$252$	1.26198	+	5.86578i	0.0794976	+	0.369510i
$253$			19.2960i			1.21313i
$254$	−9.92712	−	10.3428i	−0.622883	−	0.648966i
$255$	14.7910	−	3.37461i	0.926245	−	0.211326i
$256$	15.7852	+	2.61291i	0.986575	+	0.163307i
$257$	3.29604			0.205601			0.102801	−	0.994702i	$-0.467220\pi$
$257$	3.29604			0.205601			0.102801	+	0.994702i	$0.467220\pi$
$258$	−6.25135	−	5.04946i	−0.389192	−	0.314365i
$259$		−	7.99327i		−	0.496678i
$260$	−23.2976	+	1.32571i	−1.44486	+	0.0822168i
$261$	6.33756	+	24.5206i	0.392285	+	1.51779i
$262$	9.18977	+	9.57459i	0.567746	+	0.591520i
$263$		−	13.6177i		−	0.839706i	−0.907592	−	0.419853i	$-0.862082\pi$
$263$		−	13.6177i		−	0.839706i	0.907592	−	0.419853i	$-0.137918\pi$
$264$	8.37186	−	9.53659i	0.515252	−	0.586936i
$265$	0.691096	−	0.0678419i	0.0424537	−	0.00416750i
$266$	5.32383	−	5.10985i	0.326425	−	0.313305i
$267$	−1.52580	−	12.0009i	−0.0933773	−	0.734442i
$268$	−1.17700	+	28.6839i	−0.0718966	+	1.75215i
$269$			9.10782i			0.555314i	0.960680	+	0.277657i	$0.0895578\pi$
$269$			9.10782i			0.555314i	−0.960680	+	0.277657i	$0.910442\pi$
$270$	−15.5522	−	5.30382i	−0.946474	−	0.322780i
$271$		−	3.46361i		−	0.210400i	−0.994451	−	0.105200i	$-0.966452\pi$
$271$		−	3.46361i		−	0.210400i	0.994451	−	0.105200i	$-0.0335482\pi$
$272$	15.6159	+	1.28371i	0.946853	+	0.0778364i
$273$	−1.13988	−	8.96556i	−0.0689890	−	0.542620i
$274$	1.10710	+	1.15346i	0.0668823	+	0.0696830i
$275$	12.7044	−	2.51854i	0.766103	−	0.151874i
$276$	25.7108	−	2.20239i	1.54761	−	0.132568i
$277$		−	25.1116i		−	1.50881i	−0.656411	−	0.754404i	$-0.727926\pi$
$277$		−	25.1116i		−	1.50881i	0.656411	−	0.754404i	$-0.272074\pi$
$278$	3.57766	−	3.43386i	0.214574	−	0.205949i
$279$	−1.06720	−	4.12908i	−0.0638914	−	0.247202i
$280$	−4.30672	+	4.63165i	−0.257376	+	0.276794i
$281$		−	3.00283i		−	0.179134i	−0.995981	−	0.0895669i	$-0.971452\pi$
$281$		−	3.00283i		−	0.179134i	0.995981	−	0.0895669i	$-0.0285483\pi$
$282$	−6.71218	+	8.30984i	−0.399704	+	0.494844i
$283$	25.5458			1.51854			0.759269	−	0.650777i	$-0.225557\pi$
$283$	25.5458			1.51854			0.759269	+	0.650777i	$0.225557\pi$
$284$	0.482669	−	11.7628i	0.0286411	−	0.697995i
$285$	4.49524	+	19.7027i	0.266275	+	1.16709i
$286$	−13.7904	+	13.2362i	−0.815445	+	0.782671i
$287$		−	7.49305i		−	0.442301i
$288$	−13.6625	−	10.0666i	−0.805071	−	0.593178i
$289$	−1.65598			−0.0974108
$290$	−17.3621	+	20.2793i	−1.01954	+	1.19084i
$291$	1.48655	+	11.6922i	0.0871429	+	0.685407i
$292$	22.6998	+	0.931450i	1.32840	+	0.0545090i
$293$	13.7448			0.802982			0.401491	−	0.915863i	$-0.368492\pi$
$293$	13.7448			0.802982			0.401491	+	0.915863i	$0.368492\pi$
$294$	−1.90552	−	1.53916i	−0.111132	−	0.0897655i
$295$	−4.83122	+	0.474260i	−0.281285	+	0.0276125i
$296$	14.9735	+	16.9391i	0.870317	+	0.984566i
$297$	−12.5026	+	4.98480i	−0.725476	+	0.289248i
$298$	−0.606109	+	0.581748i	−0.0351109	+	0.0336998i
$299$	−38.8698			−2.24790
$300$	−4.80586	−	16.6404i	−0.277466	−	0.960735i
$301$	3.28066			0.189094
$302$	−4.23834	+	4.06799i	−0.243889	+	0.234087i
$303$	0.175238	+	1.37830i	0.0100671	+	0.0791814i
$304$	−1.71000	+	20.8016i	−0.0980753	+	1.19305i
$305$	14.9115	−	1.46379i	0.853828	−	0.0838166i
$306$	−14.1422	−	8.72873i	−0.808455	−	0.498989i
$307$	−22.6537			−1.29292			−0.646459	−	0.762949i	$-0.723751\pi$
$307$	−22.6537			−1.29292			−0.646459	+	0.762949i	$0.723751\pi$
$308$	−0.212401	+	5.17629i	−0.0121027	+	0.294946i
$309$	18.0902	−	2.29999i	1.02911	−	0.130842i
$310$	2.92364	−	3.41489i	0.166052	−	0.193953i
$311$	−0.838700			−0.0475583			−0.0237791	−	0.999717i	$-0.507570\pi$
$311$	−0.838700			−0.0475583			−0.0237791	+	0.999717i	$0.507570\pi$
$312$	19.2105	+	16.8642i	1.08758	+	0.954750i
$313$			10.3135i			0.582952i	0.956578	+	0.291476i	$0.0941463\pi$
$313$			10.3135i			0.582952i	−0.956578	+	0.291476i	$0.905854\pi$
$314$	5.32383	−	5.10985i	0.300441	−	0.288366i
$315$	6.29972	−	2.30512i	0.354949	−	0.129879i
$316$	14.1774	+	0.581748i	0.797542	+	0.0327259i
$317$	22.4446			1.26061			0.630306	−	0.776347i	$-0.282929\pi$
$317$	22.4446			1.26061			0.630306	+	0.776347i	$0.282929\pi$
$318$	−0.591764	−	0.477991i	−0.0331845	−	0.0268044i
$319$			21.8678i			1.22436i
$320$	0.450371	−	17.8829i	0.0251765	−	0.999683i
$321$	2.70066	+	21.2416i	0.150736	+	1.18559i
$322$	−7.60043	+	7.29496i	−0.423556	+	0.406532i
$323$			20.4394i			1.13728i
$324$	8.06899	+	16.0901i	0.448277	+	0.893895i
$325$	5.07333	+	25.5917i	0.281418	+	1.41957i
$326$	7.52246	+	7.83746i	0.416630	+	0.434077i
$327$	−5.49979	+	0.699246i	−0.304139	+	0.0386684i
$328$	14.0365	+	15.8791i	0.775034	+	0.876774i
$329$		−	4.36094i		−	0.240426i
$330$	−11.8552	−	7.79410i	−0.652606	−	0.429051i
$331$		−	16.8534i		−	0.926346i	−0.886268	−	0.463173i	$-0.846711\pi$
$331$		−	16.8534i		−	0.926346i	0.886268	−	0.463173i	$-0.153289\pi$
$332$	1.60299	+	0.0657762i	0.0879754	+	0.00360994i
$333$	−6.00061	−	23.2169i	−0.328831	−	1.27228i
$334$	−11.3670	+	10.9101i	−0.621974	+	0.596976i
$335$	31.9430	−	3.13570i	1.74523	−	0.171322i
$336$	6.92136	−	0.307795i	0.377591	−	0.0167916i
$337$		−	9.20669i		−	0.501520i	−0.968049	−	0.250760i	$-0.919319\pi$
$337$		−	9.20669i		−	0.501520i	0.968049	−	0.250760i	$-0.0806805\pi$
$338$	−13.9322	−	14.5156i	−0.757810	−	0.789544i
$339$	23.6626	−	3.00847i	1.28518	−	0.163398i
$340$	−0.995217	−	17.4897i	−0.0539732	−	0.948513i
$341$		−	3.68237i		−	0.199412i
$342$	11.6273	−	18.8385i	0.628735	−	1.01867i
$343$	1.00000			0.0539949
$344$	−6.95228	+	6.14554i	−0.374842	+	0.331345i
$345$	−6.41752	−	28.1281i	−0.345508	−	1.51436i
$346$	−10.4770	−	10.9157i	−0.563246	−	0.586832i
$347$		−	19.6511i		−	1.05493i	−0.849578	−	0.527463i	$-0.823143\pi$
$347$		−	19.6511i		−	1.05493i	0.849578	−	0.527463i	$-0.176857\pi$
$348$	29.1376	−	2.49593i	1.56194	−	0.133796i
$349$	24.4464			1.30859			0.654293	−	0.756241i	$-0.272966\pi$
$349$	24.4464			1.30859			0.654293	+	0.756241i	$0.272966\pi$
$350$	5.79498	+	4.05194i	0.309755	+	0.216585i
$351$	−10.0414	−	25.1852i	−0.535969	−	1.34429i
$352$	−9.24644	−	11.3673i	−0.492837	−	0.605880i
$353$	−21.0990			−1.12299			−0.561493	−	0.827481i	$-0.689773\pi$
$353$	−21.0990			−1.12299			−0.561493	+	0.827481i	$0.689773\pi$
$354$	4.13682	+	3.34147i	0.219870	+	0.177597i
$355$	−13.0993	+	1.28591i	−0.695241	+	0.0682488i
$356$	−13.9572	−	0.572714i	−0.739732	−	0.0303538i
$357$	6.73051	−	0.855720i	0.356216	−	0.0452895i
$358$	−1.71534	−	1.78717i	−0.0906585	−	0.0944549i
$359$	−6.88134			−0.363183			−0.181592	−	0.983374i	$-0.558125\pi$
$359$	−6.88134			−0.363183			−0.181592	+	0.983374i	$0.558125\pi$
$360$	−9.03208	+	16.6860i	−0.476033	+	0.879428i
$361$	−8.22687			−0.432993
$362$	−8.30804	−	8.65593i	−0.436661	−	0.454946i
$363$	7.37155	−	0.937222i	0.386906	−	0.0491914i
$364$	−10.4271	−	0.427860i	−0.546529	−	0.0224260i
$365$	−2.48153	−	25.2790i	−0.129889	−	1.32316i
$366$	−12.7682	−	10.3134i	−0.667406	−	0.539089i
$367$	−3.52886			−0.184205			−0.0921025	−	0.995750i	$-0.529359\pi$
$367$	−3.52886			−0.184205			−0.0921025	+	0.995750i	$0.529359\pi$
$368$	2.44124	−	29.6969i	0.127258	−	1.54806i
$369$	−5.62509	−	21.7640i	−0.292830	−	1.13299i
$370$	16.4390	−	19.2011i	0.854622	−	0.998220i
$371$	0.310553			0.0161231
$372$	−4.90656	+	0.420296i	−0.254393	+	0.0217913i
$373$			28.7793i			1.49013i	0.666990	+	0.745067i	$0.267582\pi$
$373$			28.7793i			1.49013i	−0.666990	+	0.745067i	$0.732418\pi$
$374$	−9.93649	−	10.3526i	−0.513804	−	0.535319i
$375$	−17.6817	+	7.89657i	−0.913081	+	0.407777i
$376$	8.16919	+	9.24158i	0.421294	+	0.476598i
$377$	−44.0504			−2.26871
$378$	−6.69013	−	3.04008i	−0.344103	−	0.156365i
$379$			3.43866i			0.176632i	0.996093	+	0.0883159i	$0.0281485\pi$
$379$			3.43866i			0.176632i	−0.996093	+	0.0883159i	$0.971851\pi$
$380$	23.2976	−	1.32571i	1.19514	−	0.0680073i
$381$	17.4178	−	2.21450i	0.892339	−	0.113452i
$382$	−6.37267	−	6.63953i	−0.326054	−	0.339708i
$383$		−	7.87233i		−	0.402257i	−0.979565	−	0.201129i	$-0.935539\pi$
$383$		−	7.87233i		−	0.402257i	0.979565	−	0.201129i	$-0.0644609\pi$
$384$	−14.0910	+	13.6178i	−0.719077	+	0.694931i
$385$	5.76443	−	0.565869i	0.293783	−	0.0288394i
$386$	14.3779	−	13.8000i	0.731814	−	0.702401i
$387$	9.52886	−	2.46282i	0.484379	−	0.125192i
$388$	13.5982	+	0.557981i	0.690344	+	0.0283272i
$389$			28.0911i			1.42428i	0.702040	+	0.712138i	$0.252273\pi$
$389$			28.0911i			1.42428i	−0.702040	+	0.712138i	$0.747727\pi$
$390$	15.7004	−	23.8810i	0.795021	−	1.20926i
$391$		−	29.1798i		−	1.47569i
$392$	−2.11917	+	1.87326i	−0.107034	+	0.0946141i
$393$	−16.1240	+	2.05002i	−0.813350	+	0.103410i
$394$	17.5146	+	18.2480i	0.882371	+	0.919320i
$395$	−1.54987	−	15.7883i	−0.0779822	−	0.794394i
$396$	3.26895	+	15.1943i	0.164271	+	0.763541i
$397$			35.5295i			1.78317i	0.452849	+	0.891587i	$0.350408\pi$
$397$			35.5295i			1.78317i	−0.452849	+	0.891587i	$0.649592\pi$
$398$	−9.19722	+	8.82756i	−0.461015	+	0.442486i
$399$	1.13988	+	8.96556i	0.0570656	+	0.448839i
$400$	−19.8709	+	2.26877i	−0.993545	+	0.113439i
$401$		−	22.8146i		−	1.13931i	−0.821884	−	0.569655i	$-0.807077\pi$
$401$		−	22.8146i		−	1.13931i	0.821884	−	0.569655i	$-0.192923\pi$
$402$	−27.3518	−	22.0931i	−1.36418	−	1.10190i
$403$	7.41776			0.369505
$404$	1.60299	+	0.0657762i	0.0797517	+	0.00327249i
$405$	16.5674	−	11.4246i	0.823241	−	0.567692i
$406$	−8.61344	+	8.26725i	−0.427478	+	0.410296i
$407$		−	20.7052i		−	1.02632i
$408$	−12.6601	+	14.4214i	−0.626769	+	0.713968i
$409$	7.78311			0.384850			0.192425	−	0.981312i	$-0.438365\pi$
$409$	7.78311			0.384850			0.192425	+	0.981312i	$0.438365\pi$
$410$	15.4102	−	17.9995i	0.761057	−	0.888934i
$411$	−1.94248	+	0.246967i	−0.0958152	+	0.0121820i
$412$	0.863311	−	21.0392i	0.0425323	−	1.03653i
$413$	−2.17097			−0.106827
$414$	−16.5995	+	26.8943i	−0.815821	+	1.32178i
$415$	−0.175238	−	1.78512i	−0.00860209	−	0.0876283i
$416$	22.8983	−	18.6260i	1.12268	−	0.913215i
$417$	0.766012	+	6.02493i	0.0375118	+	0.295042i
$418$	13.7904	−	13.2362i	0.674512	−	0.647402i
$419$	−12.4304			−0.607265			−0.303633	−	0.952789i	$-0.598200\pi$
$419$	−12.4304			−0.607265			−0.303633	+	0.952789i	$0.598200\pi$
$420$	−1.41193	−	7.61620i	−0.0688949	−	0.371632i
$421$	−11.0706			−0.539550			−0.269775	−	0.962923i	$-0.586949\pi$
$421$	−11.0706			−0.539550			−0.269775	+	0.962923i	$0.586949\pi$
$422$	−18.9416	+	18.1803i	−0.922062	+	0.885002i
$423$	−3.27379	−	12.6666i	−0.159177	−	0.615871i
$424$	−0.658115	+	0.581748i	−0.0319609	+	0.0282522i
$425$	−19.2118	+	3.80859i	−0.931911	+	0.184744i
$426$	11.2166	+	9.06004i	0.543444	+	0.438960i
$427$	6.70066			0.324268
$428$	24.7043	+	1.01370i	1.19413	+	0.0489992i
$429$	−2.95267	−	23.2237i	−0.142556	−	1.12125i
$430$	7.88068	+	6.74701i	0.380040	+	0.325370i
$431$	35.0882			1.69014			0.845069	−	0.534657i	$-0.179559\pi$
$431$	35.0882			1.69014			0.845069	+	0.534657i	$0.179559\pi$
$432$	19.8724	−	6.08992i	0.956112	−	0.293002i
$433$			26.6805i			1.28218i	0.767464	+	0.641092i	$0.221518\pi$
$433$			26.6805i			1.28218i	−0.767464	+	0.641092i	$0.778482\pi$
$434$	1.45044	−	1.39214i	0.0696233	−	0.0668250i
$435$	−7.27286	−	31.8770i	−0.348707	−	1.52839i
$436$	−0.262465	+	6.39635i	−0.0125698	+	0.306330i
$437$	38.8698			1.85939
$438$	−17.4840	+	21.6456i	−0.835416	+	1.03427i
$439$			4.17900i			0.199453i	0.995015	+	0.0997264i	$0.0317967\pi$
$439$			4.17900i			0.199453i	−0.995015	+	0.0997264i	$0.968203\pi$
$440$	−11.1558	+	11.9975i	−0.531831	+	0.571957i
$441$	2.90455	−	0.750707i	0.138312	−	0.0357480i
$442$	20.8542	−	20.0160i	0.991933	−	0.952065i
$443$			11.2230i			0.533220i	0.963804	+	0.266610i	$0.0859036\pi$
$443$			11.2230i			0.533220i	−0.963804	+	0.266610i	$0.914096\pi$
$444$	−27.5885	+	2.36323i	−1.30929	+	0.112154i
$445$	1.52580	+	15.5431i	0.0723297	+	0.736813i
$446$	−4.64705	−	4.84164i	−0.220044	−	0.229258i
$447$	−0.129774	−	1.02071i	−0.00613810	−	0.0482781i
$448$	0.981770	−	7.93953i	0.0463843	−	0.375108i
$449$			22.5684i			1.06507i	0.846408	+	0.532535i	$0.178760\pi$
$449$			22.5684i			1.06507i	−0.846408	+	0.532535i	$0.821240\pi$
$450$	19.8737	+	7.41874i	0.936853	+	0.349723i
$451$		−	19.4094i		−	0.913954i
$452$	1.12924	−	27.5200i	0.0531150	−	1.29443i
$453$	−0.907471	−	7.13755i	−0.0426367	−	0.335352i
$454$	−24.2622	+	23.2871i	−1.13868	+	1.09292i
$455$	1.13988	+	11.6118i	0.0534386	+	0.544372i
$456$	−19.2105	−	16.8642i	−0.899612	−	0.789741i
$457$		−	17.9311i		−	0.838782i	−0.907806	−	0.419391i	$-0.862244\pi$
$457$		−	17.9311i		−	0.838782i	0.907806	−	0.419391i	$-0.137756\pi$
$458$	0.898550	+	0.936177i	0.0419865	+	0.0437447i
$459$	18.9067	−	7.53813i	0.882491	−	0.351850i
$460$	−33.2603	+	1.89261i	−1.55077	+	0.0882435i
$461$			38.7220i			1.80346i	0.432298	+	0.901731i	$0.357703\pi$
$461$			38.7220i			1.80346i	−0.432298	+	0.901731i	$0.642297\pi$
$462$	−4.93590	−	3.98692i	−0.229639	−	0.185488i
$463$	−35.6920			−1.65875			−0.829373	−	0.558695i	$-0.811302\pi$
$463$	−35.6920			−1.65875			−0.829373	+	0.558695i	$0.811302\pi$
$464$	2.76661	−	33.6549i	0.128437	−	1.56239i
$465$	1.22469	+	5.36785i	0.0567939	+	0.248928i
$466$	−18.0938	−	18.8514i	−0.838178	−	0.873276i
$467$		−	25.6778i		−	1.18823i	−0.804382	−	0.594113i	$-0.797503\pi$
$467$		−	25.6778i		−	1.18823i	0.804382	−	0.594113i	$-0.202497\pi$
$468$	−30.6073	+	6.58496i	−1.41482	+	0.304390i
$469$	14.3540			0.662806
$470$	8.96872	−	10.4757i	0.413696	−	0.483208i
$471$	1.13988	+	8.96556i	0.0525231	+	0.413111i
$472$	4.60066	−	4.06680i	0.211763	−	0.187190i
$473$	8.49797			0.390737
$474$	−10.9198	+	13.5190i	−0.501564	+	0.620949i
$475$	−5.07333	−	25.5917i	−0.232781	−	1.17423i
$476$	0.321198	−	7.82770i	0.0147221	−	0.358782i
$477$	0.902019	−	0.233135i	0.0413006	−	0.0106745i
$478$	20.9661	+	21.8440i	0.958966	+	0.999123i
$479$	2.75550			0.125902			0.0629510	−	0.998017i	$-0.479949\pi$
$479$	2.75550			0.125902			0.0629510	+	0.998017i	$0.479949\pi$
$480$	17.2593	+	13.4951i	0.787774	+	0.615965i
$481$	41.7084			1.90174
$482$	−3.39964	−	3.54200i	−0.154849	−	0.161334i
$483$	−1.62733	−	12.7995i	−0.0740460	−	0.582396i
$484$	0.351790	−	8.57324i	0.0159904	−	0.389693i
$485$	−1.48655	−	15.1432i	−0.0675006	−	0.687620i
$486$	−21.7141	−	3.80776i	−0.984970	−	0.172723i
$487$	−14.8260			−0.671828			−0.335914	−	0.941893i	$-0.609045\pi$
$487$	−14.8260			−0.671828			−0.335914	+	0.941893i	$0.609045\pi$
$488$	−14.1998	+	12.5521i	−0.642797	+	0.568207i
$489$	−13.1986	+	1.67808i	−0.596863	+	0.0758853i
$490$	2.40216	+	2.05660i	0.108519	+	0.0929078i
$491$	−26.6411			−1.20230			−0.601149	−	0.799137i	$-0.705290\pi$
$491$	−26.6411			−1.20230			−0.601149	+	0.799137i	$0.705290\pi$
$492$	−25.8620	+	2.21534i	−1.16595	+	0.0998752i
$493$		−	33.0690i		−	1.48935i
$494$	26.6629	+	27.7794i	1.19962	+	1.24985i
$495$	16.3183	−	5.97100i	0.733453	−	0.268376i
$496$	−0.465877	+	5.66724i	−0.0209185	+	0.254467i
$497$	−5.88636			−0.264039
$498$	−1.23466	+	1.52855i	−0.0553266	+	0.0684958i
$499$		−	6.94730i		−	0.311004i	−0.987836	−	0.155502i	$-0.950300\pi$
$499$		−	6.94730i		−	0.311004i	0.987836	−	0.155502i	$-0.0496995\pi$
$500$	5.58726	+	21.6514i	0.249870	+	0.968279i
$501$	−2.43379	−	19.1425i	−0.108734	−	0.855225i
$502$	−19.7733	−	20.6013i	−0.882525	−	0.919481i
$503$			7.16950i			0.319672i	0.987144	+	0.159836i	$0.0510965\pi$
$503$			7.16950i			0.319672i	−0.987144	+	0.159836i	$0.948903\pi$
$504$	−4.74898	+	7.03187i	−0.211536	+	0.313225i
$505$	−0.175238	−	1.78512i	−0.00779798	−	0.0794369i
$506$	−19.6876	+	18.8963i	−0.875220	+	0.840043i
$507$	24.4449	−	3.10793i	1.08564	−	0.138028i
$508$	0.831221	−	20.2572i	0.0368795	−	0.898766i
$509$		−	14.7435i		−	0.653493i	−0.945112	−	0.326746i	$-0.894048\pi$
$509$		−	14.7435i		−	0.653493i	0.945112	−	0.326746i	$-0.105952\pi$
$510$	17.9277	+	11.7864i	0.793850	+	0.521911i
$511$		−	11.3594i		−	0.502512i
$512$	12.7923	+	18.6643i	0.565345	+	0.824855i
$513$	10.0414	+	25.1852i	0.443337	+	1.11196i
$514$	3.22776	+	3.36293i	0.142371	+	0.148332i
$515$	−23.4297	+	2.29999i	−1.03244	+	0.101350i
$516$	−0.969935	−	11.3231i	−0.0426990	−	0.498471i
$517$		−	11.2962i		−	0.496808i
$518$	8.15549	−	7.82770i	0.358331	−	0.343929i
$519$	18.3825	−	2.33716i	0.806903	−	0.102590i
$520$	−24.1677	−	22.4722i	−1.05982	−	0.985471i
$521$			32.1306i			1.40767i	0.710365	+	0.703833i	$0.248530\pi$
$521$			32.1306i			1.40767i	−0.710365	+	0.703833i	$0.751470\pi$
$522$	−18.8119	+	30.4788i	−0.823375	+	1.33402i
$523$	−14.4315			−0.631048			−0.315524	−	0.948918i	$-0.602180\pi$
$523$	−14.4315			−0.631048			−0.315524	+	0.948918i	$0.602180\pi$
$524$	−0.769481	+	18.7525i	−0.0336149	+	0.819208i
$525$	−8.21470	+	2.74203i	−0.358519	+	0.119672i
$526$	13.8941	−	13.3357i	0.605811	−	0.581463i
$527$			5.56857i			0.242571i
$528$	17.9286	−	0.797288i	0.780241	−	0.0346975i
$529$	−32.4915			−1.41267
$530$	0.746000	+	0.638685i	0.0324042	+	0.0277427i
$531$	−6.30571	+	1.62977i	−0.273645	+	0.0707258i
$532$	10.4271	+	0.427860i	0.452072	+	0.0185501i
$533$	39.0983			1.69353
$534$	10.7502	−	13.3091i	0.465208	−	0.575939i
$535$	−2.70066	−	27.5113i	−0.116760	−	1.18942i
$536$	−30.4186	+	26.8888i	−1.31388	+	1.16142i
$537$	3.00967	−	0.382651i	0.129877	−	0.0165126i
$538$	−9.29265	+	8.91916i	−0.400635	+	0.384532i
$539$	2.59032			0.111573
$540$	−9.81855	−	21.0617i	−0.422523	−	0.906352i
$541$	−0.910229			−0.0391338			−0.0195669	−	0.999809i	$-0.506229\pi$
$541$	−0.910229			−0.0391338			−0.0195669	+	0.999809i	$0.506229\pi$
$542$	3.53390	−	3.39187i	0.151794	−	0.145693i
$543$	14.5770	−	1.85332i	0.625558	−	0.0795337i
$544$	13.9827	+	17.1899i	0.599502	+	0.737012i
$545$	7.12312	−	0.699246i	0.305121	−	0.0299524i
$546$	8.03123	−	9.94287i	0.343705	−	0.425515i
$547$	10.6984			0.457432			0.228716	−	0.973493i	$-0.426547\pi$
$547$	10.6984			0.457432			0.228716	+	0.973493i	$0.426547\pi$
$548$	−0.0927000	+	2.25913i	−0.00395995	+	0.0965053i
$549$	19.4624	−	5.03024i	0.830637	−	0.214685i
$550$	15.0109	+	10.4958i	0.640066	+	0.447544i
$551$	44.0504			1.87661
$552$	27.4254	+	24.0758i	1.16730	+	1.02474i
$553$		−	7.09467i		−	0.301696i
$554$	25.6212	−	24.5914i	1.08854	−	1.04479i
$555$	6.88618	+	30.1822i	0.292302	+	1.28116i
$556$	7.00710	+	0.287525i	0.297167	+	0.0121938i
$557$	−42.0516			−1.78178			−0.890891	−	0.454217i	$-0.849919\pi$
$557$	−42.0516			−1.78178			−0.890891	+	0.454217i	$0.849919\pi$
$558$	3.16779	−	5.13241i	0.134103	−	0.217272i
$559$			17.1183i			0.724026i
$560$	−8.94315	+	0.141593i	−0.377917	+	0.00598340i
$561$	17.4342	−	2.21659i	0.736072	−	0.0935845i
$562$	3.06377	−	2.94063i	0.129237	−	0.124043i
$563$		−	18.4258i		−	0.776557i	−0.921542	−	0.388278i	$-0.873070\pi$
$563$		−	18.4258i		−	0.776557i	0.921542	−	0.388278i	$-0.126930\pi$
$564$	−15.0516	+	1.28932i	−0.633788	+	0.0542903i
$565$	−30.6469	+	3.00847i	−1.28932	+	0.126567i
$566$	25.0166	+	26.0642i	1.05153	+	1.09556i
$567$	7.87288	−	4.36094i	0.330630	−	0.183142i
$568$	12.4742	−	11.0267i	0.523406	−	0.462670i
$569$			14.6523i			0.614256i	0.951668	+	0.307128i	$0.0993680\pi$
$569$			14.6523i			0.614256i	−0.951668	+	0.307128i	$0.900632\pi$
$570$	−15.7004	+	23.8810i	−0.657617	+	1.00027i
$571$			22.8980i			0.958251i	0.877746	+	0.479126i	$0.159046\pi$
$571$			22.8980i			0.958251i	−0.877746	+	0.479126i	$0.840954\pi$
$572$	−27.0096	−	1.10830i	−1.12933	−	0.0463402i
$573$	11.1813	−	1.42159i	0.467104	−	0.0593877i
$574$	7.64511	−	7.33784i	0.319101	−	0.306276i
$575$	7.24282	+	36.5353i	0.302047	+	1.52363i
$576$	−3.10866	−	23.7978i	−0.129527	−	0.991576i
$577$			10.6940i			0.445196i	0.974910	+	0.222598i	$0.0714537\pi$
$577$			10.6940i			0.445196i	−0.974910	+	0.222598i	$0.928546\pi$
$578$	−1.62168	−	1.68959i	−0.0674530	−	0.0702776i
$579$	3.07844	+	24.2130i	0.127936	+	1.00626i
$580$	−37.6933	+	2.14486i	−1.56513	+	0.0890606i
$581$		−	0.802169i		−	0.0332796i
$582$	−10.4737	+	12.9667i	−0.434149	+	0.537487i
$583$	0.804433			0.0333162
$584$	21.2792	+	24.0726i	0.880540	+	0.996131i
$585$	12.0280	+	32.8715i	0.497295	+	1.35907i
$586$	13.4601	+	14.0238i	0.556033	+	0.579317i
$587$			37.2958i			1.53936i	0.638429	+	0.769681i	$0.279585\pi$
$587$			37.2958i			1.53936i	−0.638429	+	0.769681i	$0.720415\pi$
$588$	−0.295652	−	3.45146i	−0.0121925	−	0.142336i
$589$	−7.41776			−0.305644
$590$	−5.21503	−	4.46483i	−0.214699	−	0.183814i
$591$	−30.7304	+	3.90707i	−1.26408	+	0.160716i
$592$	−2.61952	+	31.8656i	−0.107662	+	1.30967i
$593$	36.7676			1.50986			0.754932	−	0.655803i	$-0.227670\pi$
$593$	36.7676			1.50986			0.754932	+	0.655803i	$0.227670\pi$
$594$	−17.3296	−	7.87480i	−0.711042	−	0.323107i
$595$	−8.71710	+	0.855720i	−0.357366	+	0.0350811i
$596$	−1.18711	−	0.0487111i	−0.0486258	−	0.00199529i
$597$	−1.96922	−	15.4885i	−0.0805947	−	0.633903i
$598$	−38.0646	−	39.6586i	−1.55658	−	1.62176i
$599$	−41.0353			−1.67666			−0.838329	−	0.545165i	$-0.816467\pi$
$599$	−41.0353			−1.67666			−0.838329	+	0.545165i	$0.816467\pi$
$600$	12.2718	−	21.1991i	0.500995	−	0.865450i
$601$	44.1422			1.80060			0.900299	−	0.435273i	$-0.143348\pi$
$601$	44.1422			1.80060			0.900299	+	0.435273i	$0.143348\pi$
$602$	3.21271	+	3.34724i	0.130940	+	0.136423i
$603$	41.6920	−	10.7756i	1.69783	−	0.438818i
$604$	−8.30110	−	0.340623i	−0.337767	−	0.0138597i
$605$	−9.54735	+	0.937222i	−0.388155	+	0.0381035i
$606$	−1.23466	+	1.52855i	−0.0501548	+	0.0620929i
$607$	−3.68845			−0.149709			−0.0748547	−	0.997194i	$-0.523849\pi$
$607$	−3.68845			−0.149709			−0.0748547	+	0.997194i	$0.523849\pi$
$608$	−22.8983	+	18.6260i	−0.928649	+	0.755384i
$609$	−1.84422	−	14.5054i	−0.0747317	−	0.587789i
$610$	16.0961	+	13.7806i	0.651711	+	0.557960i
$611$	22.7551			0.920574
$612$	−4.94338	−	22.9771i	−0.199824	−	0.928795i
$613$		−	1.26095i		−	0.0509292i	−0.999676	−	0.0254646i	$-0.991893\pi$
$613$		−	1.26095i		−	0.0509292i	0.999676	−	0.0254646i	$-0.00810650\pi$
$614$	−22.1845	−	23.1135i	−0.895293	−	0.932784i
$615$	6.45524	+	28.2934i	0.260301	+	1.14090i
$616$	−5.48934	+	4.85236i	−0.221172	+	0.195507i
$617$	−33.9997			−1.36878			−0.684388	−	0.729118i	$-0.739931\pi$
$617$	−33.9997			−1.36878			−0.684388	+	0.729118i	$0.739931\pi$
$618$	20.0621	+	16.2049i	0.807017	+	0.651859i
$619$			31.7760i			1.27719i	0.769544	+	0.638594i	$0.220483\pi$
$619$			31.7760i			1.27719i	−0.769544	+	0.638594i	$0.779517\pi$
$620$	6.34727	−	0.361179i	0.254913	−	0.0145053i
$621$	−14.3353	−	35.9551i	−0.575257	−	1.44283i
$622$	−0.821327	−	0.855720i	−0.0329322	−	0.0343112i
$623$			6.98449i			0.279828i
$624$	1.60605	+	36.1152i	0.0642936	+	1.44577i
$625$	23.1093	−	9.53727i	0.924373	−	0.381491i
$626$	−10.5228	+	10.0998i	−0.420574	+	0.403671i
$627$	2.95267	+	23.2237i	0.117918	+	0.927465i
$628$	10.4271	+	0.427860i	0.416087	+	0.0170735i
$629$			31.3108i			1.24844i
$630$	8.52112	+	4.17019i	0.339490	+	0.166144i
$631$			19.1286i			0.761496i	0.924679	+	0.380748i	$0.124333\pi$
$631$			19.1286i			0.761496i	−0.924679	+	0.380748i	$0.875667\pi$
$632$	13.2902	+	15.0348i	0.528655	+	0.598053i
$633$	−4.05558	−	31.8985i	−0.161195	−	1.26785i
$634$	21.9796	+	22.9000i	0.872923	+	0.909477i
$635$	−22.5588	+	2.21450i	−0.895219	+	0.0878798i
$636$	−0.0918158	−	1.07186i	−0.00364073	−	0.0425021i
$637$			5.21794i			0.206742i
$638$	−22.3116	+	21.4148i	−0.883324	+	0.847821i
$639$	−17.0973	+	4.41893i	−0.676357	+	0.174810i
$640$	18.6868	−	17.0529i	0.738662	−	0.674076i
$641$		−	15.9909i		−	0.631602i	−0.948825	−	0.315801i	$-0.897727\pi$
$641$		−	15.9909i		−	0.631602i	0.948825	−	0.315801i	$-0.102273\pi$
$642$	−19.0279	+	23.5571i	−0.750972	+	0.929723i
$643$	9.69068			0.382163			0.191082	−	0.981574i	$-0.438800\pi$
$643$	9.69068			0.382163			0.191082	+	0.981574i	$0.438800\pi$
$644$	−14.8860	−	0.610824i	−0.586590	−	0.0240698i
$645$	−12.3876	+	2.82628i	−0.487762	+	0.111285i
$646$	−20.8542	+	20.0160i	−0.820498	+	0.787520i
$647$			23.7323i			0.933011i	0.884518	+	0.466506i	$0.154487\pi$
$647$			23.7323i			0.933011i	−0.884518	+	0.466506i	$0.845513\pi$
$648$	−8.51478	+	23.9896i	−0.334492	+	0.942399i
$649$	−5.62352			−0.220743
$650$	−21.1428	+	30.2378i	−0.829287	+	1.18603i
$651$	0.310553	+	2.44260i	0.0121715	+	0.0957331i
$652$	−0.629873	+	15.3502i	−0.0246677	+	0.601161i
$653$	−29.2117			−1.14314			−0.571570	−	0.820553i	$-0.693666\pi$
$653$	−29.2117			−1.14314			−0.571570	+	0.820553i	$0.693666\pi$
$654$	−6.09931	−	4.92664i	−0.238502	−	0.192647i
$655$	20.8832	−	2.05002i	0.815975	−	0.0801007i
$656$	−2.45559	+	29.8715i	−0.0958748	+	1.16628i
$657$	−8.52761	−	32.9941i	−0.332694	−	1.28722i
$658$	4.44944	−	4.27061i	0.173457	−	0.166486i
$659$	−23.0469			−0.897781			−0.448891	−	0.893587i	$-0.648181\pi$
$659$	−23.0469			−0.897781			−0.448891	+	0.893587i	$0.648181\pi$
$660$	−3.65734	−	19.7284i	−0.142362	−	0.767927i
$661$	−44.7206			−1.73943			−0.869715	−	0.493554i	$-0.835698\pi$
$661$	−44.7206			−1.73943			−0.869715	+	0.493554i	$0.835698\pi$
$662$	17.1954	−	16.5043i	0.668319	−	0.641457i
$663$	4.46509	+	35.1194i	0.173410	+	1.36392i
$664$	1.50267	+	1.69993i	0.0583150	+	0.0659702i
$665$	−1.13988	−	11.6118i	−0.0442028	−	0.450288i
$666$	17.8117	−	28.8584i	0.690191	−	1.11824i
$667$	−62.8875			−2.43501
$668$	−22.2631	−	0.913531i	−0.861384	−	0.0353456i
$669$	8.15354	−	1.03664i	0.315234	−	0.0400790i
$670$	34.4806	+	29.5205i	1.33210	+	1.14047i
$671$	17.3569			0.670055
$672$	7.09203	+	6.76040i	0.273581	+	0.260788i
$673$			13.7231i			0.528985i	0.964388	+	0.264493i	$0.0852045\pi$
$673$			13.7231i			0.528985i	−0.964388	+	0.264493i	$0.914795\pi$
$674$	9.39352	−	9.01598i	0.361825	−	0.347283i
$675$	−21.8016	+	14.1312i	−0.839143	+	0.543910i
$676$	1.16657	−	28.4298i	0.0448682	−	1.09345i
$677$	−6.48328			−0.249173			−0.124586	−	0.992209i	$-0.539760\pi$
$677$	−6.48328			−0.249173			−0.124586	+	0.992209i	$0.539760\pi$
$678$	26.2420	+	21.1966i	1.00782	+	0.814052i
$679$		−	6.80482i		−	0.261145i
$680$	16.8700	−	18.1428i	0.646936	−	0.695746i
$681$	−5.19478	−	40.8586i	−0.199064	−	1.56571i
$682$	3.75710	−	3.60610i	0.143867	−	0.138085i
$683$		−	6.26932i		−	0.239889i	−0.992781	−	0.119944i	$-0.961728\pi$
$683$		−	6.26932i		−	0.239889i	0.992781	−	0.119944i	$-0.0382716\pi$
$684$	30.6073	−	6.58496i	1.17030	−	0.251782i
$685$	2.51582	−	0.246967i	0.0961245	−	0.00943613i
$686$	0.979286	+	1.02029i	0.0373893	+	0.0389550i
$687$	−1.57656	+	0.200445i	−0.0601496	+	0.00764745i
$688$	−13.0785	−	1.07512i	−0.498614	−	0.0409887i
$689$			1.62045i			0.0617341i
$690$	22.4143	−	34.0932i	0.853298	−	1.29790i
$691$		−	24.4282i		−	0.929291i	−0.885497	−	0.464646i	$-0.846182\pi$
$691$		−	24.4282i		−	0.929291i	0.885497	−	0.464646i	$-0.153818\pi$
$692$	0.877262	−	21.3792i	0.0333485	−	0.812714i
$693$	7.52373	−	1.94457i	0.285803	−	0.0738683i
$694$	20.0499	−	19.2440i	0.761083	−	0.730493i
$695$	−0.766012	−	7.80326i	−0.0290565	−	0.295995i
$696$	31.0807	+	27.2847i	1.17811	+	1.03422i
$697$			29.3514i			1.11176i
$698$	23.9400	+	24.9425i	0.906144	+	0.944088i
$699$	31.7467	−	4.03628i	1.20077	−	0.152666i
$700$	1.54078	+	9.88059i	0.0582359	+	0.373451i
$701$			0.887840i			0.0335333i	0.999859	+	0.0167666i	$0.00533724\pi$
$701$			0.887840i			0.0335333i	−0.999859	+	0.0167666i	$0.994663\pi$
$702$	15.8630	−	34.9087i	0.598709	−	1.31754i
$703$	−41.7084			−1.57306
$704$	2.54310	−	20.5659i	0.0958467	−	0.775108i
$705$	3.75694	+	16.4667i	0.141495	+	0.620172i
$706$	−20.6620	−	21.5272i	−0.777623	−	0.810186i
$707$		−	0.802169i		−	0.0301687i
$708$	0.641853	+	7.49303i	0.0241223	+	0.281605i
$709$	25.1800			0.945653			0.472827	−	0.881156i	$-0.343234\pi$
$709$	25.1800			0.945653			0.472827	+	0.881156i	$0.343234\pi$
$710$	−14.1400	−	12.1059i	−0.530665	−	0.454326i
$711$	−5.32602	−	20.6069i	−0.199741	−	0.772818i
$712$	−13.0838	−	14.8013i	−0.490336	−	0.554703i
$713$	10.5898			0.396591
$714$	7.46418	+	6.02910i	0.279340	+	0.225634i
$715$	2.95267	+	30.0784i	0.110424	+	1.12487i
$716$	0.143629	−	3.50030i	0.00536768	−	0.130812i
$717$	−36.7863	+	4.67703i	−1.37381	+	0.174667i
$718$	−6.73880	−	7.02099i	−0.251490	−	0.262021i
$719$	39.7085			1.48088			0.740438	−	0.672124i	$-0.234618\pi$
$719$	39.7085			1.48088			0.740438	+	0.672124i	$0.234618\pi$
$720$	−25.8696	+	7.12495i	−0.964102	+	0.265531i
$721$	−10.5284			−0.392100
$722$	−8.05646	−	8.39382i	−0.299830	−	0.312386i
$723$	5.96489	−	0.758378i	0.221837	−	0.0282044i
$724$	0.695651	−	16.9533i	0.0258537	−	0.630063i
$725$	8.20816	+	41.4048i	0.304843	+	1.53774i
$726$	8.17510	+	6.60334i	0.303406	+	0.245073i
$727$	41.7978			1.55019			0.775097	−	0.631843i	$-0.217701\pi$
$727$	41.7978			1.55019			0.775097	+	0.631843i	$0.217701\pi$
$728$	−9.77457	−	11.0577i	−0.362270	−	0.409826i
$729$	19.5934	−	18.5768i	0.725682	−	0.688030i
$730$	23.3618	−	27.2872i	0.864661	−	1.00995i
$731$	−12.8508			−0.475305
$732$	−1.98107	−	23.1271i	−0.0732223	−	0.854802i
$733$		−	49.2249i		−	1.81816i	−0.416618	−	0.909082i	$-0.636785\pi$
$733$		−	49.2249i		−	1.81816i	0.416618	−	0.909082i	$-0.363215\pi$
$734$	−3.45576	−	3.60047i	−0.127555	−	0.132896i
$735$	−3.77595	+	0.861497i	−0.139278	+	0.0317768i
$736$	32.6902	−	26.5910i	1.20498	−	0.980156i
$737$	37.1815			1.36960
$738$	16.6971	−	27.0524i	0.614628	−	0.995813i
$739$			2.66405i			0.0979988i	0.998799	+	0.0489994i	$0.0156032\pi$
$739$			2.66405i			0.0979988i	−0.998799	+	0.0489994i	$0.984397\pi$
$740$	35.6893	−	2.03083i	1.31196	−	0.0746547i
$741$	−46.7817	+	5.94785i	−1.71857	+	0.218500i
$742$	0.304120	+	0.316856i	0.0111646	+	0.0116321i
$743$		−	12.1997i		−	0.447565i	−0.974639	−	0.223782i	$-0.928160\pi$
$743$		−	12.1997i		−	0.447565i	0.974639	−	0.223782i	$-0.0718405\pi$
$744$	−5.23375	−	4.59454i	−0.191879	−	0.168444i
$745$	0.129774	+	1.32199i	0.00475455	+	0.0484339i
$746$	−29.3633	+	28.1831i	−1.07507	+	1.03186i
$747$	−0.602194	−	2.32994i	−0.0220331	−	0.0852482i
$748$	0.832005	−	20.2763i	0.0304211	−	0.741374i
$749$		−	12.3626i		−	0.451718i
$750$	−25.3723	−	10.3076i	−0.926466	−	0.376379i
$751$			23.9798i			0.875036i	0.899210	+	0.437518i	$0.144142\pi$
$751$			23.9798i			0.875036i	−0.899210	+	0.437518i	$0.855858\pi$
$752$	−1.42915	+	17.3851i	−0.0521157	+	0.633970i
$753$	34.6935	−	4.41094i	1.26430	−	0.160744i
$754$	−43.1380	−	44.9444i	−1.57099	−	1.63678i
$755$	0.907471	+	9.24428i	0.0330263	+	0.336434i
$756$	−3.44978	−	9.80301i	−0.125467	−	0.356532i
$757$			21.6029i			0.785171i	0.919715	+	0.392586i	$0.128419\pi$
$757$			21.6029i			0.785171i	−0.919715	+	0.392586i	$0.871581\pi$
$758$	−3.50844	+	3.36743i	−0.127432	+	0.122310i
$759$	−4.21531	−	33.1547i	−0.153006	−	1.20344i
$760$	24.1677	+	22.4722i	0.876653	+	0.815152i
$761$		−	29.7868i		−	1.07977i	−0.841739	−	0.539885i	$-0.818468\pi$
$761$		−	29.7868i		−	1.07977i	0.841739	−	0.539885i	$-0.181532\pi$
$762$	19.3164	+	15.6026i	0.699760	+	0.565223i
$763$	3.20087			0.115879
$764$	0.533599	−	13.0040i	0.0193049	−	0.470468i
$765$	−24.6769	+	9.02948i	−0.892195	+	0.326461i
$766$	8.03209	−	7.70926i	0.290211	−	0.278547i
$767$		−	11.3280i		−	0.409030i
$768$	−27.6932	−	1.04120i	−0.999294	−	0.0375711i
$769$	−41.6702			−1.50267			−0.751333	−	0.659923i	$-0.770589\pi$
$769$	−41.6702			−1.50267			−0.751333	+	0.659923i	$0.770589\pi$
$770$	6.22238	+	5.32726i	0.224239	+	0.191981i
$771$	−5.66331	+	0.720036i	−0.203959	+	0.0259315i
$772$	28.1601	+	1.15551i	1.01350	+	0.0415875i
$773$	40.0458			1.44035			0.720173	−	0.693794i	$-0.244062\pi$
$773$	40.0458			1.44035			0.720173	+	0.693794i	$0.244062\pi$
$774$	11.8443	+	7.31043i	0.425734	+	0.262768i
$775$	−1.38219	−	6.97226i	−0.0496498	−	0.250451i
$776$	12.7472	+	14.4206i	0.457598	+	0.517668i
$777$	1.74617	+	13.7342i	0.0626435	+	0.492712i
$778$	−28.6612	+	27.5092i	−1.02755	+	0.986254i
$779$	−39.0983			−1.40084
$780$	39.7408	−	7.36734i	1.42295	−	0.263793i
$781$	−15.2476			−0.545601
$782$	29.7720	−	28.5754i	1.06464	−	1.02185i
$783$	−16.2460	−	40.7473i	−0.580583	−	1.45619i
$784$	−3.98655	−	0.327716i	−0.142377	−	0.0117041i
$785$	−1.13988	−	11.6118i	−0.0406842	−	0.414445i
$786$	−17.8817	−	14.4437i	−0.637818	−	0.515190i
$787$	−2.34667			−0.0836497			−0.0418248	−	0.999125i	$-0.513317\pi$
$787$	−2.34667			−0.0836497			−0.0418248	+	0.999125i	$0.513317\pi$
$788$	−1.46653	+	35.7400i	−0.0522431	+	1.27318i
$789$	2.97487	+	23.3983i	0.105908	+	0.833001i
$790$	14.5909	−	17.0426i	0.519121	−	0.606347i
$791$	−13.7716			−0.489661
$792$	−12.3014	+	18.2148i	−0.437110	+	0.647235i
$793$			34.9636i			1.24160i
$794$	−36.2505	+	34.7935i	−1.28648	+	1.23478i
$795$	−1.17263	+	0.267541i	−0.0415891	+	0.00948869i
$796$	−18.0134	−	0.739153i	−0.638469	−	0.0261986i
$797$	−1.79710			−0.0636566			−0.0318283	−	0.999493i	$-0.510133\pi$
$797$	−1.79710			−0.0636566			−0.0318283	+	0.999493i	$0.510133\pi$
$798$	−8.03123	+	9.94287i	−0.284302	+	0.351974i
$799$			17.0824i			0.604333i
$800$	−21.7741	−	18.0524i	−0.769831	−	0.638248i
$801$	5.24331	+	20.2868i	0.185263	+	0.716800i
$802$	23.2776	−	22.3421i	0.821962	−	0.788926i
$803$		−	29.4246i		−	1.03837i
$804$	−4.24379	−	49.5423i	−0.149667	−	1.74722i
$805$	1.62733	+	16.5774i	0.0573558	+	0.584276i
$806$	7.26411	+	7.56830i	0.255867	+	0.266582i
$807$	−1.98965	−	15.6492i	−0.0700390	−	0.550879i
$808$	1.50267	+	1.69993i	0.0528639	+	0.0598034i
$809$			15.1489i			0.532608i	0.963889	+	0.266304i	$0.0858025\pi$
$809$			15.1489i			0.532608i	−0.963889	+	0.266304i	$0.914197\pi$
$810$	27.8807	+	5.71568i	0.979626	+	0.200829i
$811$			9.38776i			0.329649i	0.986323	+	0.164824i	$0.0527057\pi$
$811$			9.38776i			0.329649i	−0.986323	+	0.164824i	$0.947294\pi$
$812$	−16.8700	−	0.692236i	−0.592022	−	0.0242927i
$813$	0.756644	+	5.95125i	0.0265367	+	0.208719i
$814$	21.1253	−	20.2763i	0.740443	−	0.710683i
$815$	17.0944	−	1.67808i	0.598789	−	0.0587805i
$816$	−27.1120	+	1.20568i	−0.949109	+	0.0422071i
$817$		−	17.1183i		−	0.598893i
$818$	7.62189	+	7.94105i	0.266493	+	0.277652i
$819$	3.91714	+	15.1558i	0.136876	+	0.529586i
$820$	33.4558	−	1.90374i	1.16833	−	0.0664814i
$821$		−	28.0354i		−	0.978442i	−0.872160	−	0.489221i	$-0.837281\pi$
$821$		−	28.0354i		−	0.978442i	0.872160	−	0.489221i	$-0.162719\pi$
$822$	−2.15422	−	1.74004i	−0.0751370	−	0.0606910i
$823$	−3.81868			−0.133111			−0.0665553	−	0.997783i	$-0.521201\pi$
$823$	−3.81868			−0.133111			−0.0665553	+	0.997783i	$0.521201\pi$
$824$	22.3116	−	19.7226i	0.777261	−	0.687068i
$825$	−21.2787	+	7.10274i	−0.740830	+	0.247286i
$826$	−2.12600	−	2.21503i	−0.0739731	−	0.0770707i
$827$			1.34786i			0.0468698i	0.999725	+	0.0234349i	$0.00746024\pi$
$827$			1.34786i			0.0468698i	−0.999725	+	0.0234349i	$0.992540\pi$
$828$	−43.6957	+	9.40086i	−1.51853	+	0.326702i
$829$	−27.1345			−0.942418			−0.471209	−	0.882021i	$-0.656182\pi$
$829$	−27.1345			−0.942418			−0.471209	+	0.882021i	$0.656182\pi$
$830$	1.64974	−	1.92694i	0.0572634	−	0.0668851i
$831$	5.48575	+	43.1472i	0.190298	+	1.49676i
$832$	41.4280	+	5.12281i	1.43626	+	0.177602i
$833$	−3.91714			−0.135721
$834$	−5.39705	+	6.68169i	−0.186885	+	0.231368i
$835$	2.43379	+	24.7927i	0.0842247	+	0.857985i
$836$	27.0096	+	1.10830i	0.934145	+	0.0383312i
$837$	2.73570	+	6.86154i	0.0945596	+	0.237169i
$838$	−12.1729	−	12.6827i	−0.420507	−	0.438115i
$839$	−21.9164			−0.756639			−0.378319	−	0.925675i	$-0.623498\pi$
$839$	−21.9164			−0.756639			−0.378319	+	0.925675i	$0.623498\pi$
$840$	6.38808	−	8.89901i	0.220410	−	0.307045i
$841$	−42.2693			−1.45756
$842$	−10.8413	−	11.2953i	−0.373617	−	0.389262i
$843$	0.655983	+	5.15952i	0.0225933	+	0.177703i
$844$	−37.0984	−	1.52228i	−1.27698	−	0.0523989i
$845$	−31.6601	+	3.10793i	−1.08914	+	0.106916i
$846$	9.71767	−	15.7444i	0.334100	−	0.541305i
$847$	−4.29023			−0.147414
$848$	−1.23804	−	0.101773i	−0.0425144	−	0.00349491i
$849$	−43.8932	+	5.58060i	−1.50641	+	0.191526i
$850$	−22.6998	−	15.8720i	−0.778596	−	0.544406i
$851$	59.5440			2.04114
$852$	1.74032	+	20.3165i	0.0596223	+	0.696033i
$853$			38.8167i			1.32906i	0.747262	+	0.664529i	$0.231368\pi$
$853$			38.8167i			1.32906i	−0.747262	+	0.664529i	$0.768632\pi$
$854$	6.56187	+	6.83664i	0.224542	+	0.233945i
$855$	−12.0280	−	32.8715i	−0.411347	−	1.12418i
$856$	23.1583	+	26.1984i	0.791535	+	0.895442i
$857$	−10.7861			−0.368446			−0.184223	−	0.982884i	$-0.558977\pi$
$857$	−10.7861			−0.368446			−0.184223	+	0.982884i	$0.558977\pi$
$858$	20.8035	−	25.7552i	0.710219	−	0.879269i
$859$		−	51.5660i		−	1.75941i	−0.475521	−	0.879704i	$-0.657741\pi$
$859$		−	51.5660i		−	1.75941i	0.475521	−	0.879704i	$-0.342259\pi$
$860$	0.833508	+	14.6479i	0.0284224	+	0.499488i
$861$	1.63690	+	12.8747i	0.0557852	+	0.438769i
$862$	34.3614	+	35.8002i	1.17035	+	1.21936i
$863$		−	54.5314i		−	1.85627i	−0.372242	−	0.928136i	$-0.621411\pi$
$863$		−	54.5314i		−	1.85627i	0.372242	−	0.928136i	$-0.378589\pi$
$864$	25.6743	+	14.3119i	0.873457	+	0.486901i
$865$	−23.8083	+	2.33716i	−0.809507	+	0.0794658i
$866$	−27.2220	+	26.1279i	−0.925040	+	0.887861i
$867$	2.84534	−	0.361758i	0.0966329	−	0.0122859i
$868$	2.84079	+	0.116567i	0.0964226	+	0.00395655i
$869$		−	18.3775i		−	0.623414i
$870$	25.4017	−	38.6372i	0.861199	−	1.30992i
$871$			74.8982i			2.53783i
$872$	−6.78319	+	5.99607i	−0.229708	+	0.203053i
$873$	−5.10843	−	19.7650i	−0.172894	−	0.668943i
$874$	38.0646	+	39.6586i	1.28756	+	1.34147i
$875$	10.7021	−	3.23512i	0.361795	−	0.109367i
$876$	−39.2067	+	3.35844i	−1.32467	+	0.113471i
$877$		−	11.9323i		−	0.402926i	−0.979496	−	0.201463i	$-0.935430\pi$
$877$		−	11.9323i		−	0.402926i	0.979496	−	0.201463i	$-0.0645697\pi$
$878$	−4.26381	+	4.09244i	−0.143896	+	0.138113i
$879$	−23.6166	+	3.00263i	−0.796570	+	0.101276i
$880$	−23.1656	+	0.366772i	−0.780914	+	0.0123639i
$881$			26.3677i			0.888352i	0.895940	+	0.444176i	$0.146503\pi$
$881$			26.3677i			0.888352i	−0.895940	+	0.444176i	$0.853497\pi$
$882$	3.61033	+	2.22834i	0.121566	+	0.0750322i
$883$	11.7927			0.396855			0.198428	−	0.980116i	$-0.436417\pi$
$883$	11.7927			0.396855			0.198428	+	0.980116i	$0.436417\pi$
$884$	40.8445	+	1.67599i	1.37375	+	0.0563696i
$885$	8.19749	−	1.87029i	0.275556	−	0.0628690i
$886$	−11.4507	+	10.9905i	−0.384695	+	0.369234i
$887$			42.6141i			1.43084i	0.698693	+	0.715421i	$0.253765\pi$
$887$			42.6141i			1.43084i	−0.698693	+	0.715421i	$0.746235\pi$
$888$	−29.4282	−	25.8341i	−0.987546	−	0.866935i
$889$	−10.1371			−0.339987
$890$	−14.3643	+	16.7779i	−0.481493	+	0.562396i
$891$	20.3933	−	11.2962i	0.683201	−	0.378438i
$892$	0.389108	−	9.48270i	0.0130283	−	0.317504i
$893$	−22.7551			−0.761471
$894$	0.914342	−	1.13198i	0.0305802	−	0.0378590i
$895$	−3.89801	+	0.382651i	−0.130296	+	0.0127906i
$896$	9.06208	−	6.77338i	0.302743	−	0.226283i
$897$	66.7868	−	8.49130i	2.22995	−	0.283516i
$898$	−23.0264	+	22.1009i	−0.768401	+	0.737518i
$899$	12.0012			0.400263
$900$	11.8927	+	27.5420i	0.396423	+	0.918068i
$901$	−1.21648			−0.0405269
$902$	19.8033	−	19.0074i	0.659378	−	0.632877i
$903$	−5.63690	+	0.716677i	−0.187584	+	0.0238495i
$904$	29.1843	−	25.7978i	0.970656	−	0.858022i
$905$	−18.8795	+	1.85332i	−0.627577	+	0.0616065i
$906$	6.39373	−	7.91559i	0.212417	−	0.262978i
$907$	−33.9202			−1.12630			−0.563151	−	0.826354i	$-0.690411\pi$
$907$	−33.9202			−1.12630			−0.563151	+	0.826354i	$0.690411\pi$
$908$	−47.5193	−	1.94988i	−1.57698	−	0.0647091i
$909$	−0.602194	−	2.32994i	−0.0199735	−	0.0772793i
$910$	−10.7312	+	12.5343i	−0.355737	+	0.415509i
$911$	34.4245			1.14053			0.570267	−	0.821459i	$-0.306840\pi$
$911$	34.4245			1.14053			0.570267	+	0.821459i	$0.306840\pi$
$912$	−1.60605	−	36.1152i	−0.0531818	−	1.19590i
$913$		−	2.07788i		−	0.0687677i
$914$	18.2950	−	17.5597i	0.605145	−	0.580823i
$915$	−25.3014	+	5.77260i	−0.836438	+	0.190836i
$916$	−0.0752377	+	1.83357i	−0.00248592	+	0.0605829i
$917$	9.38415			0.309892
$918$	26.2062	+	11.9084i	0.864934	+	0.393037i
$919$		−	31.6108i		−	1.04274i	−0.853330	−	0.521371i	$-0.825421\pi$
$919$		−	31.6108i		−	1.04274i	0.853330	−	0.521371i	$-0.174579\pi$
$920$	−34.5024	−	32.0819i	−1.13751	−	1.05771i
$921$	38.9241	−	4.94882i	1.28259	−	0.163069i
$922$	−39.5078	+	37.9199i	−1.30112	+	1.24882i
$923$		−	30.7147i		−	1.01099i
$924$	−0.765835	−	8.94040i	−0.0251941	−	0.294118i
$925$	−7.77176	−	39.2034i	−0.255534	−	1.28900i
$926$	−34.9526	−	36.4163i	−1.14862	−	1.19671i
$927$	−30.5805	+	7.90378i	−1.00439	+	0.259594i
$928$	37.0472	−	30.1350i	1.21613	−	0.989231i
$929$			16.4578i			0.539961i	0.962866	+	0.269981i	$0.0870173\pi$
$929$			16.4578i			0.539961i	−0.962866	+	0.269981i	$0.912983\pi$
$930$	−4.27746	+	6.50621i	−0.140263	+	0.213347i
$931$		−	5.21794i		−	0.171011i
$932$	1.51503	−	36.9219i	0.0496266	−	1.20942i
$933$	1.44107	−	0.183218i	0.0471785	−	0.00599829i
$934$	26.1989	−	25.1459i	0.857253	−	0.822798i
$935$	−22.5801	+	2.21659i	−0.738448	+	0.0724903i
$936$	−36.6919	−	24.7799i	−1.19931	−	0.809955i
$937$			2.36363i			0.0772166i	0.999254	+	0.0386083i	$0.0122925\pi$
$937$			2.36363i			0.0772166i	−0.999254	+	0.0386083i	$0.987708\pi$
$938$	14.0567	+	14.6453i	0.458966	+	0.478186i
$939$	−2.25303	−	17.7208i	−0.0735248	−	0.578296i
$940$	19.4712	−	1.10797i	0.635081	−	0.0361380i
$941$			14.1750i			0.462092i	0.972943	+	0.231046i	$0.0742148\pi$
$941$			14.1750i			0.462092i	−0.972943	+	0.231046i	$0.925785\pi$
$942$	−8.03123	+	9.94287i	−0.261672	+	0.323956i
$943$	55.8177			1.81767
$944$	8.65470	+	0.711462i	0.281686	+	0.0231561i
$945$	−10.3207	+	5.33690i	−0.335733	+	0.173609i
$946$	8.32194	+	8.67043i	0.270570	+	0.281900i
$947$		−	10.6426i		−	0.345838i	−0.984936	−	0.172919i	$-0.944680\pi$
$947$		−	10.6426i		−	0.345838i	0.984936	−	0.172919i	$-0.0553199\pi$
$948$	−24.4870	+	2.09756i	−0.795300	+	0.0681254i
$949$	59.2728			1.92408
$950$	21.1428	−	30.2378i	0.685962	−	0.981045i
$951$	−38.5647	+	4.90313i	−1.25055	+	0.158995i
$952$	8.30110	−	7.33784i	0.269040	−	0.237821i
$953$	−18.9335			−0.613316			−0.306658	−	0.951820i	$-0.599211\pi$
$953$	−18.9335			−0.613316			−0.306658	+	0.951820i	$0.599211\pi$
$954$	1.12120	+	0.692019i	0.0363002	+	0.0224049i
$955$	−14.4815	+	1.42159i	−0.468611	+	0.0460015i
$956$	−1.75554	+	42.7831i	−0.0567782	+	1.38370i
$957$	−4.77713	−	37.5737i	−0.154423	−	1.21458i
$958$	2.69842	+	2.81142i	0.0871821	+	0.0908329i
$959$	1.13052			0.0365063
$960$	3.13277	+	30.8251i	0.101110	+	0.994875i
$961$	28.9791			0.934809
$962$	40.8445	+	42.5548i	1.31688	+	1.37202i
$963$	−9.28066	−	35.9077i	−0.299065	−	1.15711i
$964$	0.284660	−	6.93727i	0.00916828	−	0.223434i
$965$	−3.07844	−	31.3597i	−0.0990986	−	1.00950i
$966$	11.4656	−	14.1947i	0.368899	−	0.456707i
$967$	40.7913			1.31176			0.655880	−	0.754865i	$-0.272298\pi$
$967$	40.7913			1.31176			0.655880	+	0.754865i	$0.272298\pi$
$968$	9.09172	−	8.03673i	0.292219	−	0.258310i
$969$	−4.46509	−	35.1194i	−0.143439	−	1.12820i
$970$	13.9948	−	16.3463i	0.449346	−	0.524848i
$971$	−42.1811			−1.35366			−0.676828	−	0.736141i	$-0.736646\pi$
$971$	−42.1811			−1.35366			−0.676828	+	0.736141i	$0.736646\pi$
$972$	−17.3793	−	25.8836i	−0.557440	−	0.830217i
$973$		−	3.50650i		−	0.112413i
$974$	−14.5189	−	15.1268i	−0.465214	−	0.484695i
$975$	−14.3077	−	42.8638i	−0.458214	−	1.37274i
$976$	−26.7125	−	2.19591i	−0.855048	−	0.0702895i
$977$	22.9935			0.735626			0.367813	−	0.929900i	$-0.380107\pi$
$977$	22.9935			0.735626			0.367813	+	0.929900i	$0.380107\pi$
$978$	−14.6374	−	11.8232i	−0.468051	−	0.378063i
$979$			18.0921i			0.578226i
$980$	0.254067	+	4.46491i	0.00811587	+	0.142626i
$981$	9.29710	−	2.40292i	0.296834	−	0.0767192i
$982$	−26.0893	−	27.1818i	−0.832543	−	0.867405i
$983$		−	20.6580i		−	0.658887i	−0.944175	−	0.329443i	$-0.893139\pi$
$983$		−	20.6580i		−	0.658887i	0.944175	−	0.329443i	$-0.106861\pi$
$984$	−27.5866	−	24.2174i	−0.879428	−	0.772022i
$985$	39.8008	−	3.90707i	1.26816	−	0.124490i
$986$	33.7401	−	32.3840i	1.07450	−	1.03132i
$987$	0.952670	+	7.49305i	0.0303238	+	0.238507i
$988$	−2.23255	+	54.4080i	−0.0710268	+	1.73095i
$989$			24.4385i			0.777099i
$990$	22.0725	+	10.8021i	0.701509	+	0.343315i
$991$		−	43.8395i		−	1.39261i	−0.717747	−	0.696304i	$-0.754826\pi$
$991$		−	43.8395i		−	1.39261i	0.717747	−	0.696304i	$-0.245174\pi$
$992$	−6.23847	+	5.07452i	−0.198072	+	0.161116i
$993$	3.68171	+	28.9578i	0.116835	+	0.918949i
$994$	−5.76443	−	6.00582i	−0.182837	−	0.190493i
$995$	1.96922	+	20.0601i	0.0624284	+	0.635949i
$996$	−2.76865	+	0.237163i	−0.0877282	+	0.00751480i
$997$			12.8964i			0.408433i	0.978926	+	0.204217i	$0.0654647\pi$
$997$			12.8964i			0.408433i	−0.978926	+	0.204217i	$0.934535\pi$
$998$	7.08829	−	6.80340i	0.224376	−	0.215358i
$999$	15.3822	+	38.5809i	0.486672	+	1.22064i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.l.h.239.12	yes	16
3.2	odd	2	inner	420.2.l.h.239.5	yes	16
4.3	odd	2		420.2.l.g.239.11	yes	16
5.4	even	2		420.2.l.g.239.5	✓	16
12.11	even	2		420.2.l.g.239.6	yes	16
15.14	odd	2		420.2.l.g.239.12	yes	16
20.19	odd	2	inner	420.2.l.h.239.6	yes	16
60.59	even	2	inner	420.2.l.h.239.11	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.l.g.239.5	✓	16	5.4	even	2
420.2.l.g.239.6	yes	16	12.11	even	2
420.2.l.g.239.11	yes	16	4.3	odd	2
420.2.l.g.239.12	yes	16	15.14	odd	2
420.2.l.h.239.5	yes	16	3.2	odd	2	inner
420.2.l.h.239.6	yes	16	20.19	odd	2	inner
420.2.l.h.239.11	yes	16	60.59	even	2	inner
420.2.l.h.239.12	yes	16	1.1	even	1	trivial

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.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.979286 + 1.02029i) q^{2} +(-1.71822 + 0.218455i) q^{3} +(-0.0819979 + 1.99832i) q^{4} +(2.22537 - 0.218455i) q^{5} +(-1.90552 - 1.53916i) q^{6} +1.00000 q^{7} +(-2.11917 + 1.87326i) q^{8} +(2.90455 - 0.750707i) q^{9} +O(q^{10})\)	\(q+(0.979286 + 1.02029i) q^{2} +(-1.71822 + 0.218455i) q^{3} +(-0.0819979 + 1.99832i) q^{4} +(2.22537 - 0.218455i) q^{5} +(-1.90552 - 1.53916i) q^{6} +1.00000 q^{7} +(-2.11917 + 1.87326i) q^{8} +(2.90455 - 0.750707i) q^{9} +(2.40216 + 2.05660i) q^{10} +2.59032 q^{11} +(-0.295652 - 3.45146i) q^{12} +5.21794i q^{13} +(0.979286 + 1.02029i) q^{14} +(-3.77595 + 0.861497i) q^{15} +(-3.98655 - 0.327716i) q^{16} -3.91714 q^{17} +(3.61033 + 2.22834i) q^{18} -5.21794i q^{19} +(0.254067 + 4.46491i) q^{20} +(-1.71822 + 0.218455i) q^{21} +(2.53667 + 2.64289i) q^{22} +7.44926i q^{23} +(3.23198 - 3.68162i) q^{24} +(4.90455 - 0.972287i) q^{25} +(-5.32383 + 5.10985i) q^{26} +(-4.82667 + 1.92439i) q^{27} +(-0.0819979 + 1.99832i) q^{28} +8.44212i q^{29} +(-4.57672 - 3.00893i) q^{30} -1.42159i q^{31} +(-3.56961 - 4.38838i) q^{32} +(-4.45074 + 0.565869i) q^{33} +(-3.83600 - 3.99664i) q^{34} +(2.22537 - 0.218455i) q^{35} +(1.26198 + 5.86578i) q^{36} -7.99327i q^{37} +(5.32383 - 5.10985i) q^{38} +(-1.13988 - 8.96556i) q^{39} +(-4.30672 + 4.63165i) q^{40} -7.49305i q^{41} +(-1.90552 - 1.53916i) q^{42} +3.28066 q^{43} +(-0.212401 + 5.17629i) q^{44} +(6.29972 - 2.30512i) q^{45} +(-7.60043 + 7.29496i) q^{46} -4.36094i q^{47} +(6.92136 - 0.307795i) q^{48} +1.00000 q^{49} +(5.79498 + 4.05194i) q^{50} +(6.73051 - 0.855720i) q^{51} +(-10.4271 - 0.427860i) q^{52} +0.310553 q^{53} +(-6.69013 - 3.04008i) q^{54} +(5.76443 - 0.565869i) q^{55} +(-2.11917 + 1.87326i) q^{56} +(1.13988 + 8.96556i) q^{57} +(-8.61344 + 8.26725i) q^{58} -2.17097 q^{59} +(-1.41193 - 7.61620i) q^{60} +6.70066 q^{61} +(1.45044 - 1.39214i) q^{62} +(2.90455 - 0.750707i) q^{63} +(0.981770 - 7.93953i) q^{64} +(1.13988 + 11.6118i) q^{65} +(-4.93590 - 3.98692i) q^{66} +14.3540 q^{67} +(0.321198 - 7.82770i) q^{68} +(-1.62733 - 12.7995i) q^{69} +(2.40216 + 2.05660i) q^{70} -5.88636 q^{71} +(-4.74898 + 7.03187i) q^{72} -11.3594i q^{73} +(8.15549 - 7.82770i) q^{74} +(-8.21470 + 2.74203i) q^{75} +(10.4271 + 0.427860i) q^{76} +2.59032 q^{77} +(8.03123 - 9.94287i) q^{78} -7.09467i q^{79} +(-8.94315 + 0.141593i) q^{80} +(7.87288 - 4.36094i) q^{81} +(7.64511 - 7.33784i) q^{82} -0.802169i q^{83} +(-0.295652 - 3.45146i) q^{84} +(-8.71710 + 0.855720i) q^{85} +(3.21271 + 3.34724i) q^{86} +(-1.84422 - 14.5054i) q^{87} +(-5.48934 + 4.85236i) q^{88} +6.98449i q^{89} +(8.52112 + 4.17019i) q^{90} +5.21794i q^{91} +(-14.8860 - 0.610824i) q^{92} +(0.310553 + 2.44260i) q^{93} +(4.44944 - 4.27061i) q^{94} +(-1.13988 - 11.6118i) q^{95} +(7.09203 + 6.76040i) q^{96} -6.80482i q^{97} +(0.979286 + 1.02029i) q^{98} +(7.52373 - 1.94457i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4} - 10 q^{6} + 16 q^{7}+O(q^{10}) \) 16 * q + 6 * q^4 - 10 * q^6 + 16 * q^7	\( 16 q + 6 q^{4} - 10 q^{6} + 16 q^{7} + 14 q^{10} + 16 q^{12} + 24 q^{15} - 10 q^{16} + 8 q^{18} - 12 q^{22} + 6 q^{24} + 32 q^{25} - 24 q^{27} + 6 q^{28} - 26 q^{30} - 76 q^{34} + 6 q^{36} + 2 q^{40} - 10 q^{42} - 16 q^{43} + 12 q^{45} - 52 q^{46} + 28 q^{48} + 16 q^{49} - 44 q^{52} - 6 q^{54} + 8 q^{55} + 4 q^{58} + 36 q^{60} + 40 q^{61} + 6 q^{64} - 8 q^{66} + 56 q^{67} - 64 q^{69} + 14 q^{70} - 16 q^{72} - 12 q^{75} + 44 q^{76} + 20 q^{78} + 16 q^{81} + 44 q^{82} + 16 q^{84} - 16 q^{85} - 16 q^{87} + 4 q^{88} - 10 q^{90} - 56 q^{94} + 34 q^{96}+O(q^{100}) \) 16 * q + 6 * q^4 - 10 * q^6 + 16 * q^7 + 14 * q^10 + 16 * q^12 + 24 * q^15 - 10 * q^16 + 8 * q^18 - 12 * q^22 + 6 * q^24 + 32 * q^25 - 24 * q^27 + 6 * q^28 - 26 * q^30 - 76 * q^34 + 6 * q^36 + 2 * q^40 - 10 * q^42 - 16 * q^43 + 12 * q^45 - 52 * q^46 + 28 * q^48 + 16 * q^49 - 44 * q^52 - 6 * q^54 + 8 * q^55 + 4 * q^58 + 36 * q^60 + 40 * q^61 + 6 * q^64 - 8 * q^66 + 56 * q^67 - 64 * q^69 + 14 * q^70 - 16 * q^72 - 12 * q^75 + 44 * q^76 + 20 * q^78 + 16 * q^81 + 44 * q^82 + 16 * q^84 - 16 * q^85 - 16 * q^87 + 4 * q^88 - 10 * q^90 - 56 * q^94 + 34 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more