LMFDB - Embedded newform 420.2.l.h.239.6

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			239.6
Root			$0.545199 - 1.30490i$ of defining polynomial
Character	$\chi$	$=$	420.239
Dual form			420.2.l.h.239.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.979286 + 1.02029i) q^{2} +(-1.71822 + 0.218455i) q^{3} +(-0.0819979 - 1.99832i) q^{4} +(-2.22537 - 0.218455i) q^{5} +(1.45974 - 1.96702i) q^{6} +1.00000 q^{7} +(2.11917 + 1.87326i) q^{8} +(2.90455 - 0.750707i) q^{9} +O(q^{10})$	\(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} +(1.45974 - 1.96702i) 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} +(0.577433 + 3.41564i) q^{12} -5.21794i q^{13} +(-0.979286 + 1.02029i) q^{14} +(3.87140 - 0.110790i) q^{15} +(-3.98655 + 0.327716i) q^{16} +3.91714 q^{17} +(-2.07845 + 3.69866i) 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} +(-4.05042 - 2.75573i) 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} +(-3.67817 + 4.05846i) 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} +(-1.73832 - 5.74267i) 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} +(1.45974 - 1.96702i) q^{42} +3.28066 q^{43} +(0.212401 + 5.17629i) q^{44} +(-6.62771 + 1.03609i) q^{45} +(-7.60043 - 7.29496i) q^{46} -4.36094i q^{47} +(6.77818 - 1.43397i) 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} +(2.76324 - 6.80915i) 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} +(-0.538840 - 7.72720i) 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} +(-3.78120 + 5.09521i) 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} +(7.56152 + 3.85012i) q^{72} +11.3594i q^{73} +(-8.15549 - 7.82770i) q^{74} +(-8.63950 - 0.599178i) q^{75} +(10.4271 - 0.427860i) q^{76} -2.59032 q^{77} +(-10.2638 - 7.61683i) 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} +(0.577433 + 3.41564i) 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} +(5.43331 - 7.77683i) 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} +(-5.17471 + 8.32000i) 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
$6$	1.45974	−	1.96702i	0.595936	−	0.803032i
$7$	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	$-0.627700\pi$
$11$	−2.59032			−0.781012			−0.390506	+	0.920600i	$0.627700\pi$
$12$	0.577433	+	3.41564i	0.166691	+	0.986009i
$13$		−	5.21794i		−	1.44720i	−0.690222	−	0.723598i	$-0.742487\pi$
$13$		−	5.21794i		−	1.44720i	0.690222	−	0.723598i	$-0.257513\pi$
$14$	−0.979286	+	1.02029i	−0.261725	+	0.272685i
$15$	3.87140	−	0.110790i	0.999591	−	0.0286058i
$16$	−3.98655	+	0.327716i	−0.996638	+	0.0819290i
$17$	3.91714			0.950047			0.475023	−	0.879973i	$-0.342440\pi$
$17$	3.91714			0.950047			0.475023	+	0.879973i	$0.342440\pi$
$18$	−2.07845	+	3.69866i	−0.489895	+	0.871782i
$19$			5.21794i			1.19708i	0.801094	+	0.598538i	$0.204252\pi$
$19$			5.21794i			1.19708i	−0.801094	+	0.598538i	$0.795748\pi$
$20$	−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	$0.716923\pi$
$24$	−4.05042	−	2.75573i	−0.826789	−	0.562512i
$25$	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	$0.713263\pi$
$30$	−3.67817	+	4.05846i	−0.671539	+	0.740970i
$31$			1.42159i			0.255325i	0.991818	+	0.127662i	$0.0407474\pi$
$31$			1.42159i			0.255325i	−0.991818	+	0.127662i	$0.959253\pi$
$32$	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
$36$	−1.73832	−	5.74267i	−0.289720	−	0.957111i
$37$			7.99327i			1.31409i	0.753853	+	0.657043i	$0.228193\pi$
$37$			7.99327i			1.31409i	−0.753853	+	0.657043i	$0.771807\pi$
$38$	−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	$-0.198948\pi$
$42$	1.45974	−	1.96702i	0.225243	−	0.303517i
$43$	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
$45$	−6.62771	+	1.03609i	−0.988000	+	0.154451i
$46$	−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	$-0.103029\pi$
$48$	6.77818	−	1.43397i	0.978346	−	0.206976i
$49$	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	$-0.506790\pi$
$53$	−0.310553			−0.0426578			−0.0213289	+	0.999773i	$0.506790\pi$
$54$	2.76324	−	6.80915i	0.376029	−	0.926608i
$55$	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	$-0.454866\pi$
$59$	2.17097			0.282637			0.141318	+	0.989964i	$0.454866\pi$
$60$	−0.538840	−	7.72720i	−0.0695640	−	0.997577i
$61$	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
$66$	−3.78120	+	5.09521i	−0.465433	+	0.627177i
$67$	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	$-0.386422\pi$
$71$	5.88636			0.698582			0.349291	+	0.937014i	$0.386422\pi$
$72$	7.56152	+	3.85012i	0.891134	+	0.453741i
$73$			11.3594i			1.32952i	0.747056	+	0.664761i	$0.231467\pi$
$73$			11.3594i			1.32952i	−0.747056	+	0.664761i	$0.768533\pi$
$74$	−8.15549	−	7.82770i	−0.948056	−	0.909952i
$75$	−8.63950	−	0.599178i	−0.997604	−	0.0691871i
$76$	10.4271	−	0.427860i	1.19607	−	0.0490789i
$77$	−2.59032			−0.295195
$78$	−10.2638	−	7.61683i	−1.16214	−	0.862436i
$79$			7.09467i			0.798213i	0.916905	+	0.399106i	$0.130680\pi$
$79$			7.09467i			0.798213i	−0.916905	+	0.399106i	$0.869320\pi$
$80$	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	$-0.0140180\pi$
$84$	0.577433	+	3.41564i	0.0630031	+	0.372676i
$85$	−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	$0.879297\pi$
$90$	5.43331	−	7.77683i	0.572721	−	0.819750i
$91$		−	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
$96$	−5.17471	+	8.32000i	−0.528141	+	0.849157i
$97$			6.80482i			0.690925i	0.938433	+	0.345462i	$0.112278\pi$
$97$			6.80482i			0.690925i	−0.938433	+	0.345462i	$0.887722\pi$
$98$	−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	$-0.0127069\pi$
$102$	5.71801	−	7.70509i	0.566167	−	0.762918i
$103$	−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
$105$	3.87140	−	0.110790i	0.377810	−	0.0108120i
$106$	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	$-0.203866\pi$
$108$	4.24133	+	9.48742i	0.408122	+	0.912927i
$109$	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	$-0.275706\pi$
$113$	13.7716			1.29552			0.647761	+	0.761844i	$0.275706\pi$
$114$	10.2638	+	7.61683i	0.961291	+	0.713382i
$115$	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
$120$	8.41169	+	7.01737i	0.767879	+	0.640595i
$121$	−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
$126$	−2.07845	+	3.69866i	−0.185163	+	0.329502i
$127$	−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	$-0.634453\pi$
$131$	−9.38415			−0.819897			−0.409949	+	0.912109i	$0.634453\pi$
$132$	−1.49574	−	8.84760i	−0.130187	−	0.770085i
$133$			5.21794i			0.452453i
$134$	−14.0567	+	14.6453i	−1.21431	+	1.26516i
$135$	11.1615	−	3.22808i	0.960631	−	0.277829i
$136$	8.30110	+	7.33784i	0.711813	+	0.629215i
$137$	−1.13052			−0.0965866			−0.0482933	−	0.998833i	$-0.515378\pi$
$137$	−1.13052			−0.0965866			−0.0482933	+	0.998833i	$0.515378\pi$
$138$	14.6528	+	10.8740i	1.24733	+	0.925655i
$139$			3.50650i			0.297417i	0.988881	+	0.148709i	$0.0475117\pi$
$139$			3.50650i			0.297417i	−0.988881	+	0.148709i	$0.952488\pi$
$140$	−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
$144$	−11.3331	+	3.94460i	−0.944429	+	0.328717i
$145$	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	$0.992254\pi$
$150$	9.07188	−	8.22806i	0.740716	−	0.671818i
$151$		−	4.15404i		−	0.338051i	−0.985612	−	0.169026i	$-0.945938\pi$
$151$		−	4.15404i		−	0.338051i	0.985612	−	0.169026i	$-0.0540620\pi$
$152$	−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
$156$	17.8226	−	3.01301i	1.42695	−	0.241234i
$157$			5.21794i			0.416437i	0.978082	+	0.208218i	$0.0667665\pi$
$157$			5.21794i			0.416437i	−0.978082	+	0.208218i	$0.933234\pi$
$158$	−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
$162$	−3.26036	+	12.3033i	−0.256158	+	0.966635i
$163$	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
$165$	−10.0282	+	0.286982i	−0.780692	+	0.0223415i
$166$	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	$0.858142\pi$
$168$	−4.05042	−	2.75573i	−0.312497	−	0.212609i
$169$	−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	$-0.366680\pi$
$173$	10.6986			0.813398			0.406699	+	0.913562i	$0.366680\pi$
$174$	16.6058	+	12.3233i	1.25888	+	0.934226i
$175$	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	$-0.479148\pi$
$179$	1.75162			0.130922			0.0654612	+	0.997855i	$0.479148\pi$
$180$	2.61389	+	13.1593i	0.194828	+	0.980837i
$181$	−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
$186$	2.79629	+	2.07515i	0.205034	+	0.152157i
$187$	−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	$-0.424350\pi$
$191$	6.50747			0.470864			0.235432	+	0.971891i	$0.424350\pi$
$192$	−3.42133	−	13.4274i	−0.246913	−	0.969038i
$193$			14.0919i			1.01436i	0.861841	+	0.507178i	$0.169311\pi$
$193$			14.0919i			1.01436i	−0.861841	+	0.507178i	$0.830689\pi$
$194$	−6.94291	−	6.66386i	−0.498472	−	0.478438i
$195$	−0.578095	−	20.2007i	−0.0413982	−	1.44660i
$196$	−0.0819979	−	1.99832i	−0.00585699	−	0.142737i
$197$	−17.8850			−1.27426			−0.637128	−	0.770758i	$-0.719878\pi$
$197$	−17.8850			−1.27426			−0.637128	+	0.770758i	$0.719878\pi$
$198$	5.38385	−	9.58071i	0.382614	−	0.680872i
$199$		−	9.01429i		−	0.639006i	−0.947585	−	0.319503i	$-0.896484\pi$
$199$		−	9.01429i		−	0.639006i	0.947585	−	0.319503i	$-0.103516\pi$
$200$	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
$204$	2.26189	+	13.3795i	0.158364	+	0.936755i
$205$	−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
$210$	−3.67817	+	4.05846i	−0.253818	+	0.280060i
$211$		−	18.5648i		−	1.27806i	−0.769184	−	0.639028i	$-0.779337\pi$
$211$		−	18.5648i		−	1.27806i	0.769184	−	0.639028i	$-0.220663\pi$
$212$	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
$216$	−13.8334	−	4.96350i	−0.941246	−	0.337723i
$217$			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
$222$	15.7229	+	11.6681i	1.05525	+	0.783112i
$223$	−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
$225$	14.9755	−	0.857824i	0.998363	−	0.0571883i
$226$	−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	$0.710519\pi$
$228$	−17.8226	+	3.01301i	−1.18033	+	0.199541i
$229$	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	$-0.293086\pi$
$233$	18.4765			1.21044			0.605218	+	0.796060i	$0.293086\pi$
$234$	19.2994	+	10.8452i	1.26164	+	0.708974i
$235$	−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	$-0.743462\pi$
$239$	−21.4096			−1.38487			−0.692435	+	0.721481i	$0.743462\pi$
$240$	−15.3972	+	1.71039i	−0.993887	+	0.110405i
$241$	−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
$246$	−14.7390	−	10.9379i	−0.939722	−	0.697376i
$247$	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	$-0.280076\pi$
$251$	20.1915			1.27448			0.637239	+	0.770666i	$0.280076\pi$
$252$	−1.73832	−	5.74267i	−0.109504	−	0.361754i
$253$		−	19.2960i		−	1.21313i
$254$	9.92712	−	10.3428i	0.622883	−	0.648966i
$255$	15.1648	−	0.433980i	0.949658	−	0.0271769i
$256$	15.7852	−	2.61291i	0.986575	−	0.163307i
$257$	−3.29604			−0.205601			−0.102801	−	0.994702i	$-0.532780\pi$
$257$	−3.29604			−0.205601			−0.102801	+	0.994702i	$0.532780\pi$
$258$	4.78891	−	6.45312i	0.298145	−	0.401754i
$259$			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	$-0.137918\pi$
$264$	10.4919	+	7.13824i	0.645732	+	0.439328i
$265$	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	$0.910442\pi$
$270$	−7.63673	+	14.5492i	−0.464756	+	0.885439i
$271$			3.46361i			0.210400i	0.994451	+	0.105200i	$0.0335482\pi$
$271$			3.46361i			0.210400i	−0.994451	+	0.105200i	$0.966452\pi$
$272$	−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
$276$	−25.4440	+	4.30145i	−1.53155	+	0.258917i
$277$			25.1116i			1.50881i	0.656411	+	0.754404i	$0.272074\pi$
$277$			25.1116i			1.50881i	−0.656411	+	0.754404i	$0.727926\pi$
$278$	−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	$-0.0285483\pi$
$282$	−8.57805	−	6.36584i	−0.510815	−	0.379080i
$283$	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
$285$	0.578095	+	20.2007i	0.0342434	+	1.19659i
$286$	−13.7904	−	13.2362i	−0.815445	−	0.782671i
$287$		−	7.49305i		−	0.442301i
$288$	7.07373	−	15.4260i	0.416824	−	0.908987i
$289$	−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	$-0.631508\pi$
$293$	−13.7448			−0.802982			−0.401491	+	0.915863i	$0.631508\pi$
$294$	1.45974	−	1.96702i	0.0851338	−	0.114719i
$295$	−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
$300$	−0.488927	+	17.3136i	−0.0282282	+	0.999602i
$301$	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
$306$	−8.14158	+	14.4882i	−0.465423	+	0.828233i
$307$	−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	$-0.492430\pi$
$311$	0.838700			0.0475583			0.0237791	+	0.999717i	$0.492430\pi$
$312$	−14.3792	+	21.1349i	−0.814064	+	1.19653i
$313$		−	10.3135i		−	0.582952i	−0.956578	−	0.291476i	$-0.905854\pi$
$313$		−	10.3135i		−	0.582952i	0.956578	−	0.291476i	$-0.0941463\pi$
$314$	−5.32383	−	5.10985i	−0.300441	−	0.288366i
$315$	−6.62771	+	1.03609i	−0.373429	+	0.0583769i
$316$	14.1774	−	0.581748i	0.797542	−	0.0327259i
$317$	−22.4446			−1.26061			−0.630306	−	0.776347i	$-0.717071\pi$
$317$	−22.4446			−1.26061			−0.630306	+	0.776347i	$0.717071\pi$
$318$	−0.453327	+	0.610864i	−0.0254213	+	0.0342555i
$319$		−	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
$324$	−9.36011	−	15.3749i	−0.520006	−	0.854163i
$325$	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
$330$	9.52764	−	10.5127i	0.524479	−	0.578706i
$331$			16.8534i			0.926346i	0.886268	+	0.463173i	$0.153289\pi$
$331$			16.8534i			0.926346i	−0.886268	+	0.463173i	$0.846711\pi$
$332$	−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
$336$	6.77818	−	1.43397i	0.369780	−	0.0782295i
$337$			9.20669i			0.501520i	0.968049	+	0.250760i	$0.0806805\pi$
$337$			9.20669i			0.501520i	−0.968049	+	0.250760i	$0.919319\pi$
$338$	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
$342$	−19.2994	−	10.8452i	−1.04359	−	0.586442i
$343$	1.00000			0.0539949
$344$	6.95228	+	6.14554i	0.374842	+	0.331345i
$345$	0.825303	+	28.8391i	0.0444328	+	1.55264i
$346$	−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	$-0.176857\pi$
$348$	−28.8352	+	4.87476i	−1.54573	+	0.261314i
$349$	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	$-0.310227\pi$
$353$	21.0990			1.12299			0.561493	+	0.827481i	$0.310227\pi$
$354$	3.16906	−	4.27034i	0.168433	−	0.226966i
$355$	−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	$-0.441875\pi$
$359$	6.88134			0.363183			0.181592	+	0.983374i	$0.441875\pi$
$360$	−15.9861	−	10.2198i	−0.842542	−	0.538631i
$361$	−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
$366$	9.78122	−	13.1803i	0.511273	−	0.688947i
$367$	−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
$372$	−4.85563	+	0.820873i	−0.251753	+	0.0425603i
$373$		−	28.7793i		−	1.49013i	−0.666990	−	0.745067i	$-0.732418\pi$
$373$		−	28.7793i		−	1.49013i	0.666990	−	0.745067i	$-0.267582\pi$
$374$	9.93649	−	10.3526i	0.513804	−	0.535319i
$375$	19.0952	+	3.22074i	0.986072	+	0.166318i
$376$	8.16919	−	9.24158i	0.421294	−	0.476598i
$377$	44.0504			2.26871
$378$	2.76324	−	6.80915i	0.142126	−	0.350225i
$379$		−	3.43866i		−	0.176632i	−0.996093	−	0.0883159i	$-0.971851\pi$
$379$		−	3.43866i		−	0.176632i	0.996093	−	0.0883159i	$-0.0281485\pi$
$380$	−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	$-0.0644609\pi$
$384$	17.0503	+	9.65849i	0.870096	+	0.492883i
$385$	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	$0.747727\pi$
$390$	21.1768	+	19.1925i	1.07233	+	0.971848i
$391$			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
$396$	4.50281	+	14.8754i	0.226275	+	0.747515i
$397$		−	35.5295i		−	1.78317i	−0.452849	−	0.891587i	$-0.649592\pi$
$397$		−	35.5295i		−	1.78317i	0.452849	−	0.891587i	$-0.350408\pi$
$398$	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	$-0.192923\pi$
$402$	20.9531	−	28.2346i	1.04505	−	1.40821i
$403$	7.41776			0.369505
$404$	−1.60299	+	0.0657762i	−0.0797517	+	0.00327249i
$405$	−18.4727	+	7.98484i	−0.917918	+	0.396770i
$406$	−8.61344	−	8.26725i	−0.427478	−	0.410296i
$407$		−	20.7052i		−	1.02632i
$408$	−15.8661	−	10.7946i	−0.785489	−	0.534413i
$409$	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
$414$	−27.5523	−	15.4829i	−1.35412	−	0.760943i
$415$	−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	$-0.401800\pi$
$419$	12.4304			0.607265			0.303633	+	0.952789i	$0.401800\pi$
$420$	−0.538840	−	7.72720i	−0.0262927	−	0.377049i
$421$	−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
$426$	8.59255	−	11.5786i	0.416311	−	0.560984i
$427$	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	$-0.820441\pi$
$431$	−35.0882			−1.69014			−0.845069	+	0.534657i	$0.820441\pi$
$432$	18.6111	−	9.25347i	0.895427	−	0.445208i
$433$		−	26.6805i		−	1.28218i	−0.767464	−	0.641092i	$-0.778482\pi$
$433$		−	26.6805i		−	1.28218i	0.767464	−	0.641092i	$-0.221518\pi$
$434$	−1.45044	−	1.39214i	−0.0696233	−	0.0668250i
$435$	0.935301	+	32.6828i	0.0448443	+	1.56702i
$436$	−0.262465	−	6.39635i	−0.0125698	−	0.306330i
$437$	−38.8698			−1.85939
$438$	22.3442	+	16.5818i	1.06765	+	0.792310i
$439$		−	4.17900i		−	0.199453i	−0.995015	−	0.0997264i	$-0.968203\pi$
$439$		−	4.17900i		−	0.199453i	0.995015	−	0.0997264i	$-0.0317967\pi$
$440$	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	$0.914096\pi$
$444$	−27.3021	+	4.61558i	−1.29570	+	0.219046i
$445$	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	$0.821240\pi$
$450$	−13.7900	+	16.1194i	−0.650068	+	0.759876i
$451$			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
$456$	14.3792	−	21.1349i	0.673370	−	0.989730i
$457$			17.9311i			0.838782i	0.907806	+	0.419391i	$0.137756\pi$
$457$			17.9311i			0.838782i	−0.907806	+	0.419391i	$0.862244\pi$
$458$	−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	$0.642297\pi$
$462$	−3.78120	+	5.09521i	−0.175917	+	0.237051i
$463$	−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
$465$	0.157498	+	5.50354i	0.00730378	+	0.255220i
$466$	−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	$-0.202497\pi$
$468$	−29.9649	+	9.07044i	−1.38513	+	0.419281i
$469$	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
$474$	13.9553	+	10.3564i	0.640990	+	0.475684i
$475$	−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	$-0.520051\pi$
$479$	−2.75550			−0.125902			−0.0629510	+	0.998017i	$0.520051\pi$
$480$	13.3332	−	17.3847i	0.608574	−	0.793497i
$481$	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
$486$	2.91430	−	21.8519i	0.132195	−	0.991224i
$487$	−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	$-0.294710\pi$
$491$	26.6411			1.20230			0.601149	+	0.799137i	$0.294710\pi$
$492$	25.5935	−	4.32674i	1.15385	−	0.195064i
$493$			33.0690i			1.48935i
$494$	−26.6629	+	27.7794i	−1.19962	+	1.24985i
$495$	17.1679	−	2.68380i	0.771640	−	0.120628i
$496$	−0.465877	−	5.66724i	−0.0209185	−	0.254467i
$497$	5.88636			0.264039
$498$	−1.57788	−	1.17096i	−0.0707065	−	0.0524719i
$499$			6.94730i			0.311004i	0.987836	+	0.155502i	$0.0496995\pi$
$499$			6.94730i			0.311004i	−0.987836	+	0.155502i	$0.950300\pi$
$500$	−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	$0.948903\pi$
$504$	7.56152	+	3.85012i	0.336817	+	0.171498i
$505$	−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	$-0.105952\pi$
$510$	−14.4079	+	15.8976i	−0.637993	+	0.703956i
$511$			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
$516$	1.89436	+	11.2055i	0.0833947	+	0.493297i
$517$			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	$0.751470\pi$
$522$	−31.2245	−	17.5465i	−1.36666	−	0.767989i
$523$	−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
$525$	−8.63950	−	0.599178i	−0.377059	−	0.0261503i
$526$	13.8941	+	13.3357i	0.605811	+	0.581463i
$527$			5.56857i			0.242571i
$528$	−17.5577	+	3.71445i	−0.764100	+	0.161651i
$529$	−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
$534$	13.7386	+	10.1955i	0.594528	+	0.441204i
$535$	−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
$540$	−7.36596	−	22.0396i	−0.316980	−	0.948432i
$541$	−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
$546$	−10.2638	−	7.61683i	−0.439249	−	0.325970i
$547$	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
$552$	20.5282	−	30.1727i	0.873737	−	1.28423i
$553$			7.09467i			0.301696i
$554$	−25.6212	−	24.5914i	−1.08854	−	1.04479i
$555$	0.885574	+	30.9451i	0.0375905	+	1.31355i
$556$	7.00710	−	0.287525i	0.297167	−	0.0121938i
$557$	42.0516			1.78178			0.890891	−	0.454217i	$-0.150081\pi$
$557$	42.0516			1.78178			0.890891	+	0.454217i	$0.150081\pi$
$558$	−5.25797	−	2.95470i	−0.222588	−	0.125082i
$559$		−	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	$-0.126930\pi$
$564$	14.8954	−	2.51815i	0.627209	−	0.106033i
$565$	−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	$0.900632\pi$
$570$	−21.1768	−	19.1925i	−0.886998	−	0.803883i
$571$		−	22.8980i		−	0.958251i	−0.877746	−	0.479126i	$-0.840954\pi$
$571$		−	22.8980i		−	0.958251i	0.877746	−	0.479126i	$-0.159046\pi$
$572$	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
$576$	8.81187	+	22.3238i	0.367161	+	0.930157i
$577$		−	10.6940i		−	0.445196i	−0.974910	−	0.222598i	$-0.928546\pi$
$577$		−	10.6940i		−	0.445196i	0.974910	−	0.222598i	$-0.0714537\pi$
$578$	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
$582$	13.3852	+	9.93327i	0.554834	+	0.411747i
$583$	0.804433			0.0333162
$584$	−21.2792	+	24.0726i	−0.880540	+	0.996131i
$585$	5.40624	+	34.5830i	0.223521	+	1.42983i
$586$	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	$0.720415\pi$
$588$	0.577433	+	3.41564i	0.0238129	+	0.140858i
$589$	−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	$-0.772330\pi$
$593$	−36.7676			−1.50986			−0.754932	+	0.655803i	$0.772330\pi$
$594$	−7.15768	+	17.6379i	−0.293683	+	0.723692i
$595$	−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	$-0.183533\pi$
$599$	41.0353			1.67666			0.838329	+	0.545165i	$0.183533\pi$
$600$	−17.1862	−	17.4538i	−0.701622	−	0.712549i
$601$	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
$606$	−1.57788	−	1.17096i	−0.0640970	−	0.0475669i
$607$	−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
$612$	−6.80925	−	22.4949i	−0.275248	−	0.909301i
$613$			1.26095i			0.0509292i	0.999676	+	0.0254646i	$0.00810650\pi$
$613$			1.26095i			0.0509292i	−0.999676	+	0.0254646i	$0.991893\pi$
$614$	22.1845	−	23.1135i	0.895293	−	0.932784i
$615$	−0.830155	−	29.0086i	−0.0334751	−	1.16974i
$616$	−5.48934	−	4.85236i	−0.221172	−	0.195507i
$617$	33.9997			1.36878			0.684388	−	0.729118i	$-0.260069\pi$
$617$	33.9997			1.36878			0.684388	+	0.729118i	$0.260069\pi$
$618$	−15.3688	+	20.7096i	−0.618224	+	0.833064i
$619$		−	31.7760i		−	1.27719i	−0.769544	−	0.638594i	$-0.779517\pi$
$619$		−	31.7760i		−	1.27719i	0.769544	−	0.638594i	$-0.220483\pi$
$620$	−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
$624$	−7.48237	−	35.3681i	−0.299534	−	1.41586i
$625$	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
$630$	5.43331	−	7.77683i	0.216468	−	0.309837i
$631$		−	19.1286i		−	0.761496i	−0.924679	−	0.380748i	$-0.875667\pi$
$631$		−	19.1286i		−	0.761496i	0.924679	−	0.380748i	$-0.124333\pi$
$632$	−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
$636$	−0.179324	−	1.06074i	−0.00711065	−	0.0420610i
$637$		−	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	$-0.102273\pi$
$642$	−24.3174	−	18.0461i	−0.959730	−	0.712223i
$643$	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
$645$	12.7007	−	0.363464i	0.500091	−	0.0143114i
$646$	−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	$0.845513\pi$
$648$	24.8532	+	5.50639i	0.976324	+	0.216312i
$649$	−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	$-0.306334\pi$
$653$	29.2117			1.14314			0.571570	+	0.820553i	$0.306334\pi$
$654$	4.67244	−	6.29617i	0.182707	−	0.246200i
$655$	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	$-0.351819\pi$
$659$	23.0469			0.897781			0.448891	+	0.893587i	$0.351819\pi$
$660$	1.39577	+	20.0159i	0.0543303	+	0.779120i
$661$	−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
$666$	−29.5644	−	16.6136i	−1.14560	−	0.643764i
$667$	−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
$672$	−5.17471	+	8.32000i	−0.199619	+	0.320951i
$673$		−	13.7231i		−	0.528985i	−0.964388	−	0.264493i	$-0.914795\pi$
$673$		−	13.7231i		−	0.528985i	0.964388	−	0.264493i	$-0.0852045\pi$
$674$	−9.39352	−	9.01598i	−0.361825	−	0.347283i
$675$	−25.5437	+	4.74539i	−0.983178	+	0.182650i
$676$	1.16657	+	28.4298i	0.0448682	+	1.09345i
$677$	6.48328			0.249173			0.124586	−	0.992209i	$-0.460240\pi$
$677$	6.48328			0.249173			0.124586	+	0.992209i	$0.460240\pi$
$678$	20.1029	−	27.0889i	0.772048	−	1.04034i
$679$			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	$-0.0382716\pi$
$684$	29.9649	−	9.07044i	1.14574	−	0.346817i
$685$	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
$690$	−30.2325	−	27.3996i	−1.15093	−	1.04309i
$691$			24.4282i			0.929291i	0.885497	+	0.464646i	$0.153818\pi$
$691$			24.4282i			0.929291i	−0.885497	+	0.464646i	$0.846182\pi$
$692$	−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
$696$	23.2642	−	34.1941i	0.881828	−	1.29613i
$697$		−	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	$0.994663\pi$
$702$	−35.5297	−	14.4184i	−1.34098	−	0.544188i
$703$	−41.7084			−1.57306
$704$	−2.54310	−	20.5659i	−0.0958467	−	0.775108i
$705$	−0.483148	−	16.8829i	−0.0181964	−	0.635848i
$706$	−20.6620	+	21.5272i	−0.777623	+	0.810186i
$707$		−	0.802169i		−	0.0301687i
$708$	1.25359	+	7.41525i	0.0471129	+	0.278682i
$709$	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
$714$	5.71801	−	7.70509i	0.213991	−	0.288356i
$715$	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	$-0.765382\pi$
$719$	−39.7085			−1.48088			−0.740438	+	0.672124i	$0.765382\pi$
$720$	26.0822	−	6.30242i	0.972025	−	0.234877i
$721$	−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
$726$	−6.26262	+	8.43895i	−0.232427	+	0.313199i
$727$	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
$732$	3.86918	+	22.8870i	0.143009	+	0.845929i
$733$			49.2249i			1.81816i	0.416618	+	0.909082i	$0.363215\pi$
$733$			49.2249i			1.81816i	−0.416618	+	0.909082i	$0.636785\pi$
$734$	3.45576	−	3.60047i	0.127555	−	0.132896i
$735$	3.87140	−	0.110790i	0.142799	−	0.00408655i
$736$	32.6902	+	26.5910i	1.20498	+	0.980156i
$737$	−37.1815			−1.36960
$738$	27.7142	+	15.5739i	1.02017	+	0.573284i
$739$		−	2.66405i		−	0.0979988i	−0.998799	−	0.0489994i	$-0.984397\pi$
$739$		−	2.66405i		−	0.0979988i	0.998799	−	0.0489994i	$-0.0156032\pi$
$740$	−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	$-0.0718405\pi$
$744$	3.91752	−	5.75804i	0.143623	−	0.211100i
$745$	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
$750$	−21.9858	+	16.3287i	−0.802807	+	0.596240i
$751$		−	23.9798i		−	0.875036i	−0.899210	−	0.437518i	$-0.855858\pi$
$751$		−	23.9798i		−	0.875036i	0.899210	−	0.437518i	$-0.144142\pi$
$752$	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
$756$	4.24133	+	9.48742i	0.154256	+	0.345054i
$757$		−	21.6029i		−	0.785171i	−0.919715	−	0.392586i	$-0.871581\pi$
$757$		−	21.6029i		−	0.785171i	0.919715	−	0.392586i	$-0.128419\pi$
$758$	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	$-0.181532\pi$
$762$	−14.7975	+	19.9399i	−0.536058	+	0.722345i
$763$	3.20087			0.115879
$764$	−0.533599	−	13.0040i	−0.0193049	−	0.470468i
$765$	−25.9617	+	4.05851i	−0.938647	+	0.146736i
$766$	8.03209	+	7.70926i	0.290211	+	0.278547i
$767$		−	11.3280i		−	0.409030i
$768$	−26.5516	+	7.93791i	−0.958100	+	0.286435i
$769$	−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	$-0.755938\pi$
$773$	−40.0458			−1.44035			−0.720173	+	0.693794i	$0.755938\pi$
$774$	−6.81868	+	12.1340i	−0.245093	+	0.436149i
$775$	−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
$780$	−40.3201	+	2.81163i	−1.44369	+	0.100673i
$781$	−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
$786$	−13.6984	+	18.4588i	−0.488607	+	0.658404i
$787$	−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
$792$	−19.5868	−	9.97305i	−0.695986	−	0.354377i
$793$		−	34.9636i		−	1.24160i
$794$	36.2505	+	34.7935i	1.28648	+	1.23478i
$795$	−1.20228	+	0.0344062i	−0.0426403	+	0.00122026i
$796$	−18.0134	+	0.739153i	−0.638469	+	0.0261986i
$797$	1.79710			0.0636566			0.0318283	−	0.999493i	$-0.489867\pi$
$797$	1.79710			0.0636566			0.0318283	+	0.999493i	$0.489867\pi$
$798$	10.2638	+	7.61683i	0.363334	+	0.269633i
$799$		−	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
$804$	8.28847	+	49.0280i	0.292312	+	1.72909i
$805$	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	$0.914197\pi$
$810$	9.94322	−	26.6671i	0.349369	−	0.936985i
$811$		−	9.38776i		−	0.329649i	−0.986323	−	0.164824i	$-0.947294\pi$
$811$		−	9.38776i		−	0.329649i	0.986323	−	0.164824i	$-0.0527057\pi$
$812$	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
$816$	26.5511	−	5.61707i	0.929475	−	0.196637i
$817$			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	$-0.162719\pi$
$822$	−1.65026	+	2.22375i	−0.0575594	+	0.0775621i
$823$	−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
$825$	22.3791	+	1.55206i	0.779140	+	0.0540359i
$826$	−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	$0.992540\pi$
$828$	42.7786	−	12.9492i	1.48666	−	0.450016i
$829$	−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
$834$	6.89734	+	5.11857i	0.238835	+	0.177242i
$835$	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	$-0.376502\pi$
$839$	21.9164			0.756639			0.378319	+	0.925675i	$0.376502\pi$
$840$	8.41169	+	7.01737i	0.290231	+	0.242122i
$841$	−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
$846$	16.1296	+	9.06399i	0.554548	+	0.311626i
$847$	−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
$852$	3.39898	+	20.1057i	0.116447	+	0.688809i
$853$		−	38.8167i		−	1.32906i	−0.747262	−	0.664529i	$-0.768632\pi$
$853$		−	38.8167i		−	1.32906i	0.747262	−	0.664529i	$-0.231368\pi$
$854$	−6.56187	+	6.83664i	−0.224542	+	0.233945i
$855$	−5.40624	−	34.5830i	−0.184890	−	1.18271i
$856$	23.1583	−	26.1984i	0.791535	−	0.895442i
$857$	10.7861			0.368446			0.184223	−	0.982884i	$-0.441023\pi$
$857$	10.7861			0.368446			0.184223	+	0.982884i	$0.441023\pi$
$858$	26.5865	+	19.7301i	0.907648	+	0.673573i
$859$			51.5660i			1.75941i	0.475521	+	0.879704i	$0.342259\pi$
$859$			51.5660i			1.75941i	−0.475521	+	0.879704i	$0.657741\pi$
$860$	−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	$-0.378589\pi$
$864$	−8.78433	+	28.0506i	−0.298849	+	0.954300i
$865$	−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
$870$	−34.2620	−	31.0515i	−1.16159	−	1.05275i
$871$		−	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
$876$	−38.7997	+	6.55931i	−1.31092	+	0.221619i
$877$			11.9323i			0.402926i	0.979496	+	0.201463i	$0.0645697\pi$
$877$			11.9323i			0.402926i	−0.979496	+	0.201463i	$0.935430\pi$
$878$	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	$0.853497\pi$
$882$	−2.07845	+	3.69866i	−0.0699850	+	0.124540i
$883$	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
$885$	8.40470	−	0.240522i	0.282521	−	0.00808506i
$886$	−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	$0.746235\pi$
$888$	22.0273	−	32.3761i	0.739189	−	1.08647i
$889$	−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
$894$	1.16851	+	0.867163i	0.0390809	+	0.0290023i
$895$	−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
$900$	−2.94216	−	29.8554i	−0.0980720	−	0.995179i
$901$	−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
$906$	−8.17107	−	6.06382i	−0.271466	−	0.201457i
$907$	−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	$-0.693160\pi$
$911$	−34.4245			−1.14053			−0.570267	+	0.821459i	$0.693160\pi$
$912$	7.48237	+	35.3681i	0.247766	+	1.17116i
$913$			2.07788i			0.0687677i
$914$	−18.2950	−	17.5597i	−0.605145	−	0.580823i
$915$	25.9409	−	0.742366i	0.857581	−	0.0245419i
$916$	−0.0752377	−	1.83357i	−0.00248592	−	0.0605829i
$917$	−9.38415			−0.309892
$918$	10.8240	−	26.6724i	0.357245	−	0.880321i
$919$			31.6108i			1.04274i	0.853330	+	0.521371i	$0.174579\pi$
$919$			31.6108i			1.04274i	−0.853330	+	0.521371i	$0.825421\pi$
$920$	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
$924$	−1.49574	−	8.84760i	−0.0492062	−	0.291065i
$925$	−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	$0.912983\pi$
$930$	−5.76946	−	5.22884i	−0.189188	−	0.171461i
$931$			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
$936$	20.0897	−	39.4555i	0.656652	−	1.28964i
$937$		−	2.36363i		−	0.0772166i	−0.999254	−	0.0386083i	$-0.987708\pi$
$937$		−	2.36363i		−	0.0772166i	0.999254	−	0.0386083i	$-0.0122925\pi$
$938$	−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	$0.925785\pi$
$942$	10.2638	+	7.61683i	0.334412	+	0.248170i
$943$	55.8177			1.81767
$944$	−8.65470	+	0.711462i	−0.281686	+	0.0231561i
$945$	11.1615	−	3.22808i	0.363084	−	0.105010i
$946$	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	$-0.0553199\pi$
$948$	−24.2328	+	4.09670i	−0.787045	+	0.133055i
$949$	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	$-0.400789\pi$
$953$	18.9335			0.613316			0.306658	+	0.951820i	$0.400789\pi$
$954$	0.645469	−	1.14863i	0.0208978	−	0.0371883i
$955$	−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
$960$	4.68044	+	30.6283i	0.151061	+	0.988525i
$961$	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
$966$	14.6528	+	10.8740i	0.471447	+	0.349865i
$967$	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	$-0.263354\pi$
$971$	42.1811			1.35366			0.676828	+	0.736141i	$0.263354\pi$
$972$	19.4414	+	24.3727i	0.623585	+	0.781756i
$973$			3.50650i			0.112413i
$974$	14.5189	−	15.1268i	0.465214	−	0.484695i
$975$	−3.12647	+	45.0804i	−0.100127	+	1.44373i
$976$	−26.7125	+	2.19591i	−0.855048	+	0.0702895i
$977$	−22.9935			−0.735626			−0.367813	−	0.929900i	$-0.619893\pi$
$977$	−22.9935			−0.735626			−0.367813	+	0.929900i	$0.619893\pi$
$978$	11.2131	−	15.1098i	0.358555	−	0.483158i
$979$		−	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	$-0.106861\pi$
$984$	−20.6489	+	30.3500i	−0.658262	+	0.967524i
$985$	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
$990$	−14.0740	+	20.1445i	−0.447302	+	0.640235i
$991$			43.8395i			1.39261i	0.717747	+	0.696304i	$0.245174\pi$
$991$			43.8395i			1.39261i	−0.717747	+	0.696304i	$0.754826\pi$
$992$	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
$996$	2.73992	−	0.463199i	0.0868176	−	0.0146770i
$997$		−	12.8964i		−	0.408433i	−0.978926	−	0.204217i	$-0.934535\pi$
$997$		−	12.8964i		−	0.408433i	0.978926	−	0.204217i	$-0.0654647\pi$
$998$	−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.239.6	yes	16
3.2	odd	2	inner	420.2.l.h.239.11	yes	16
4.3	odd	2		420.2.l.g.239.5	✓	16
5.4	even	2		420.2.l.g.239.11	yes	16
12.11	even	2		420.2.l.g.239.12	yes	16
15.14	odd	2		420.2.l.g.239.6	yes	16
20.19	odd	2	inner	420.2.l.h.239.12	yes	16
60.59	even	2	inner	420.2.l.h.239.5	yes	16

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

\(f(q)\)	\(=\)	\(q+(-0.979286 + 1.02029i) q^{2} +(-1.71822 + 0.218455i) q^{3} +(-0.0819979 - 1.99832i) q^{4} +(-2.22537 - 0.218455i) q^{5} +(1.45974 - 1.96702i) q^{6} +1.00000 q^{7} +(2.11917 + 1.87326i) q^{8} +(2.90455 - 0.750707i) q^{9} +O(q^{10})\)	\(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} +(1.45974 - 1.96702i) 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} +(0.577433 + 3.41564i) q^{12} -5.21794i q^{13} +(-0.979286 + 1.02029i) q^{14} +(3.87140 - 0.110790i) q^{15} +(-3.98655 + 0.327716i) q^{16} +3.91714 q^{17} +(-2.07845 + 3.69866i) 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} +(-4.05042 - 2.75573i) 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} +(-3.67817 + 4.05846i) 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} +(-1.73832 - 5.74267i) 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} +(1.45974 - 1.96702i) q^{42} +3.28066 q^{43} +(0.212401 + 5.17629i) q^{44} +(-6.62771 + 1.03609i) q^{45} +(-7.60043 - 7.29496i) q^{46} -4.36094i q^{47} +(6.77818 - 1.43397i) 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} +(2.76324 - 6.80915i) 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} +(-0.538840 - 7.72720i) 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} +(-3.78120 + 5.09521i) 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} +(7.56152 + 3.85012i) q^{72} +11.3594i q^{73} +(-8.15549 - 7.82770i) q^{74} +(-8.63950 - 0.599178i) q^{75} +(10.4271 - 0.427860i) q^{76} -2.59032 q^{77} +(-10.2638 - 7.61683i) 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} +(0.577433 + 3.41564i) 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} +(5.43331 - 7.77683i) 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} +(-5.17471 + 8.32000i) 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

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