LMFDB - Embedded newform 420.2.l.h.239.16

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			239.16
Root			$0.978323 - 1.02122i$ of defining polynomial
Character	$\chi$	$=$	420.239
Dual form			420.2.l.h.239.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38390 + 0.291259i) q^{2} +(0.751690 - 1.56044i) q^{3} +(1.83034 + 0.806145i) q^{4} +(1.60157 + 1.56044i) q^{5} +(1.49475 - 1.94055i) q^{6} +1.00000 q^{7} +(2.29820 + 1.64872i) q^{8} +(-1.86993 - 2.34593i) q^{9} +O(q^{10})$	\(q+(1.38390 + 0.291259i) q^{2} +(0.751690 - 1.56044i) q^{3} +(1.83034 + 0.806145i) q^{4} +(1.60157 + 1.56044i) q^{5} +(1.49475 - 1.94055i) q^{6} +1.00000 q^{7} +(2.29820 + 1.64872i) q^{8} +(-1.86993 - 2.34593i) q^{9} +(1.76192 + 2.62595i) q^{10} -4.26126 q^{11} +(2.63378 - 2.25015i) q^{12} +2.35966i q^{13} +(1.38390 + 0.291259i) q^{14} +(3.63885 - 1.32619i) q^{15} +(2.70026 + 2.95103i) q^{16} -5.53558 q^{17} +(-1.90451 - 3.79115i) q^{18} -2.35966i q^{19} +(1.67348 + 4.14722i) q^{20} +(0.751690 - 1.56044i) q^{21} +(-5.89714 - 1.24113i) q^{22} -3.99662i q^{23} +(4.30026 - 2.34686i) q^{24} +(0.130075 + 4.99831i) q^{25} +(-0.687271 + 3.26552i) q^{26} +(-5.06628 + 1.15449i) q^{27} +(1.83034 + 0.806145i) q^{28} -7.60838i q^{29} +(5.42205 - 0.775461i) q^{30} +1.98850i q^{31} +(2.87737 + 4.87040i) q^{32} +(-3.20315 + 6.64943i) q^{33} +(-7.66067 - 1.61229i) q^{34} +(1.60157 + 1.56044i) q^{35} +(-1.53143 - 5.80127i) q^{36} -3.22458i q^{37} +(0.687271 - 3.26552i) q^{38} +(3.68209 + 1.77373i) q^{39} +(1.10801 + 6.22674i) q^{40} -6.59489i q^{41} +(1.49475 - 1.94055i) q^{42} +8.36902 q^{43} +(-7.79954 - 3.43519i) q^{44} +(0.665850 - 6.67508i) q^{45} +(1.16405 - 5.53091i) q^{46} +8.77342i q^{47} +(6.63466 - 1.99533i) q^{48} +1.00000 q^{49} +(-1.27579 + 6.95502i) q^{50} +(-4.16104 + 8.63793i) q^{51} +(-1.90222 + 4.31896i) q^{52} +3.10293 q^{53} +(-7.34745 + 0.122095i) q^{54} +(-6.82472 - 6.64943i) q^{55} +(2.29820 + 1.64872i) q^{56} +(-3.68209 - 1.77373i) q^{57} +(2.21601 - 10.5292i) q^{58} -10.5673 q^{59} +(7.72942 + 0.506065i) q^{60} -5.55782 q^{61} +(-0.579168 + 2.75187i) q^{62} +(-1.86993 - 2.34593i) q^{63} +(2.56343 + 7.57818i) q^{64} +(-3.68209 + 3.77916i) q^{65} +(-6.36953 + 8.26917i) q^{66} +2.57474 q^{67} +(-10.1320 - 4.46248i) q^{68} +(-6.23647 - 3.00422i) q^{69} +(1.76192 + 2.62595i) q^{70} +4.93153 q^{71} +(-0.429674 - 8.47440i) q^{72} +8.76054i q^{73} +(0.939188 - 4.46248i) q^{74} +(7.89732 + 3.55420i) q^{75} +(1.90222 - 4.31896i) q^{76} -4.26126 q^{77} +(4.57902 + 3.52710i) q^{78} +2.79504i q^{79} +(-0.280231 + 8.93988i) q^{80} +(-2.00676 + 8.77342i) q^{81} +(1.92082 - 9.12664i) q^{82} +17.6662i q^{83} +(2.63378 - 2.25015i) q^{84} +(-8.86564 - 8.63793i) q^{85} +(11.5819 + 2.43755i) q^{86} +(-11.8724 - 5.71914i) q^{87} +(-9.79322 - 7.02564i) q^{88} -1.70873i q^{89} +(2.86564 - 9.04368i) q^{90} +2.35966i q^{91} +(3.22185 - 7.31516i) q^{92} +(3.10293 + 1.49473i) q^{93} +(-2.55534 + 12.1415i) q^{94} +(3.68209 - 3.77916i) q^{95} +(9.76283 - 0.828921i) q^{96} -12.4923i q^{97} +(1.38390 + 0.291259i) q^{98} +(7.96824 + 9.99662i) 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 $

$2$	1.38390	+	0.291259i	0.978562	+	0.205951i
$2$	1.38390	+	0.291259i	0.978562	+	0.205951i
$3$	0.751690	−	1.56044i	0.433988	−	0.900919i
$3$	0.751690	−	1.56044i	0.433988	−	0.900919i
$4$	1.83034	+	0.806145i	0.915168	+	0.403072i
$5$	1.60157	+	1.56044i	0.716245	+	0.697849i
$5$	1.60157	+	1.56044i	0.716245	+	0.697849i
$6$	1.49475	−	1.94055i	0.610230	−	0.792224i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	2.29820	+	1.64872i	0.812536	+	0.582911i
$9$	−1.86993	−	2.34593i	−0.623308	−	0.781976i
$10$	1.76192	+	2.62595i	0.557168	+	0.830400i
$11$	−4.26126			−1.28482			−0.642409	−	0.766362i	$-0.722065\pi$
$11$	−4.26126			−1.28482			−0.642409	+	0.766362i	$0.722065\pi$
$12$	2.63378	−	2.25015i	0.760308	−	0.649563i
$13$			2.35966i			0.654451i	0.944946	+	0.327225i	$0.106114\pi$
$13$			2.35966i			0.654451i	−0.944946	+	0.327225i	$0.893886\pi$
$14$	1.38390	+	0.291259i	0.369862	+	0.0778423i
$15$	3.63885	−	1.32619i	0.939547	−	0.342421i
$16$	2.70026	+	2.95103i	0.675065	+	0.737758i
$17$	−5.53558			−1.34258			−0.671288	−	0.741196i	$-0.734259\pi$
$17$	−5.53558			−1.34258			−0.671288	+	0.741196i	$0.734259\pi$
$18$	−1.90451	−	3.79115i	−0.448897	−	0.893583i
$19$		−	2.35966i		−	0.541342i	−0.962672	−	0.270671i	$-0.912754\pi$
$19$		−	2.35966i		−	0.541342i	0.962672	−	0.270671i	$-0.0872456\pi$
$20$	1.67348	+	4.14722i	0.374202	+	0.927347i
$21$	0.751690	−	1.56044i	0.164032	−	0.340515i
$22$	−5.89714	−	1.24113i	−1.25728	−	0.264610i
$23$		−	3.99662i		−	0.833353i	−0.909055	−	0.416676i	$-0.863195\pi$
$23$		−	3.99662i		−	0.833353i	0.909055	−	0.416676i	$-0.136805\pi$
$24$	4.30026	−	2.34686i	0.877787	−	0.479052i
$25$	0.130075	+	4.99831i	0.0260149	+	0.999662i
$26$	−0.687271	+	3.26552i	−0.134785	+	0.640421i
$27$	−5.06628	+	1.15449i	−0.975005	+	0.222182i
$28$	1.83034	+	0.806145i	0.345901	+	0.152347i
$29$		−	7.60838i		−	1.41284i	−0.707792	−	0.706421i	$-0.750309\pi$
$29$		−	7.60838i		−	1.41284i	0.707792	−	0.706421i	$-0.249691\pi$
$30$	5.42205	−	0.775461i	0.989927	−	0.141579i
$31$			1.98850i			0.357145i	0.983927	+	0.178572i	$0.0571479\pi$
$31$			1.98850i			0.357145i	−0.983927	+	0.178572i	$0.942852\pi$
$32$	2.87737	+	4.87040i	0.508651	+	0.860973i
$33$	−3.20315	+	6.64943i	−0.557596	+	1.15752i
$34$	−7.66067	−	1.61229i	−1.31379	−	0.276505i
$35$	1.60157	+	1.56044i	0.270715	+	0.263762i
$36$	−1.53143	−	5.80127i	−0.255239	−	0.966878i
$37$		−	3.22458i		−	0.530117i	−0.964232	−	0.265059i	$-0.914609\pi$
$37$		−	3.22458i		−	0.530117i	0.964232	−	0.265059i	$-0.0853913\pi$
$38$	0.687271	−	3.26552i	0.111490	−	0.529737i
$39$	3.68209	+	1.77373i	0.589607	+	0.284024i
$40$	1.10801	+	6.22674i	0.175191	+	0.984534i
$41$		−	6.59489i		−	1.02995i	−0.857206	−	0.514974i	$-0.827801\pi$
$41$		−	6.59489i		−	1.02995i	0.857206	−	0.514974i	$-0.172199\pi$
$42$	1.49475	−	1.94055i	0.230645	−	0.299433i
$43$	8.36902			1.27626			0.638132	−	0.769927i	$-0.279707\pi$
$43$	8.36902			1.27626			0.638132	+	0.769927i	$0.279707\pi$
$44$	−7.79954	−	3.43519i	−1.17583	−	0.517875i
$45$	0.665850	−	6.67508i	0.0992590	−	0.995062i
$46$	1.16405	−	5.53091i	0.171630	−	0.815488i
$47$			8.77342i			1.27974i	0.768485	+	0.639868i	$0.221011\pi$
$47$			8.77342i			1.27974i	−0.768485	+	0.639868i	$0.778989\pi$
$48$	6.63466	−	1.99533i	0.957630	−	0.288001i
$49$	1.00000			0.142857
$50$	−1.27579	+	6.95502i	−0.180424	+	0.983589i
$51$	−4.16104	+	8.63793i	−0.582662	+	1.20955i
$52$	−1.90222	+	4.31896i	−0.263791	+	0.598933i
$53$	3.10293			0.426220			0.213110	−	0.977028i	$-0.431641\pi$
$53$	3.10293			0.426220			0.213110	+	0.977028i	$0.431641\pi$
$54$	−7.34745	+	0.122095i	−0.999862	+	0.0166150i
$55$	−6.82472	−	6.64943i	−0.920246	−	0.896609i
$56$	2.29820	+	1.64872i	0.307110	+	0.220320i
$57$	−3.68209	−	1.77373i	−0.487705	−	0.234936i
$58$	2.21601	−	10.5292i	0.290977	−	1.38255i
$59$	−10.5673			−1.37575			−0.687875	−	0.725829i	$-0.741456\pi$
$59$	−10.5673			−1.37575			−0.687875	+	0.725829i	$0.741456\pi$
$60$	7.72942	+	0.506065i	0.997864	+	0.0653328i
$61$	−5.55782			−0.711605			−0.355803	−	0.934561i	$-0.615792\pi$
$61$	−5.55782			−0.711605			−0.355803	+	0.934561i	$0.615792\pi$
$62$	−0.579168	+	2.75187i	−0.0735544	+	0.349488i
$63$	−1.86993	−	2.34593i	−0.235588	−	0.295559i
$64$	2.56343	+	7.57818i	0.320429	+	0.947273i
$65$	−3.68209	+	3.77916i	−0.456708	+	0.468747i
$66$	−6.36953	+	8.26917i	−0.784035	+	1.01786i
$67$	2.57474			0.314554			0.157277	−	0.987555i	$-0.449728\pi$
$67$	2.57474			0.314554			0.157277	+	0.987555i	$0.449728\pi$
$68$	−10.1320	−	4.46248i	−1.22868	−	0.541155i
$69$	−6.23647	−	3.00422i	−0.750783	−	0.361665i
$70$	1.76192	+	2.62595i	0.210590	+	0.313862i
$71$	4.93153			0.585265			0.292632	−	0.956225i	$-0.405469\pi$
$71$	4.93153			0.585265			0.292632	+	0.956225i	$0.405469\pi$
$72$	−0.429674	−	8.47440i	−0.0506376	−	0.998717i
$73$			8.76054i			1.02534i	0.858585	+	0.512672i	$0.171344\pi$
$73$			8.76054i			1.02534i	−0.858585	+	0.512672i	$0.828656\pi$
$74$	0.939188	−	4.46248i	0.109178	−	0.518753i
$75$	7.89732	+	3.55420i	0.911904	+	0.410404i
$76$	1.90222	−	4.31896i	0.218200	−	0.495419i
$77$	−4.26126			−0.485616
$78$	4.57902	+	3.52710i	0.518472	+	0.399365i
$79$			2.79504i			0.314467i	0.987561	+	0.157233i	$0.0502575\pi$
$79$			2.79504i			0.314467i	−0.987561	+	0.157233i	$0.949743\pi$
$80$	−0.280231	+	8.93988i	−0.0313308	+	0.999509i
$81$	−2.00676	+	8.77342i	−0.222973	+	0.974825i
$82$	1.92082	−	9.12664i	0.212119	−	1.00787i
$83$			17.6662i			1.93912i	0.244850	+	0.969561i	$0.421261\pi$
$83$			17.6662i			1.93912i	−0.244850	+	0.969561i	$0.578739\pi$
$84$	2.63378	−	2.25015i	0.287369	−	0.245512i
$85$	−8.86564	−	8.63793i	−0.961614	−	0.936915i
$86$	11.5819	+	2.43755i	1.24890	+	0.262848i
$87$	−11.8724	−	5.71914i	−1.27286	−	0.613157i
$88$	−9.79322	−	7.02564i	−1.04396	−	0.748936i
$89$		−	1.70873i		−	0.181125i	−0.995891	−	0.0905626i	$-0.971133\pi$
$89$		−	1.70873i		−	0.181125i	0.995891	−	0.0905626i	$-0.0288665\pi$
$90$	2.86564	−	9.04368i	0.302065	−	0.953287i
$91$			2.35966i			0.247359i
$92$	3.22185	−	7.31516i	0.335901	−	0.762658i
$93$	3.10293	+	1.49473i	0.321758	+	0.154997i
$94$	−2.55534	+	12.1415i	−0.263563	+	1.25230i
$95$	3.68209	−	3.77916i	0.377775	−	0.387734i
$96$	9.76283	−	0.828921i	0.996415	−	0.0846014i
$97$		−	12.4923i		−	1.26840i	−0.773168	−	0.634201i	$-0.781329\pi$
$97$		−	12.4923i		−	1.26840i	0.773168	−	0.634201i	$-0.218671\pi$
$98$	1.38390	+	0.291259i	0.139795	+	0.0294216i
$99$	7.96824	+	9.99662i	0.800838	+	1.00470i
$100$	−3.79128	+	9.25344i	−0.379128	+	0.925344i
$101$			17.6662i			1.75786i	0.476954	+	0.878928i	$0.341741\pi$
$101$			17.6662i			1.75786i	−0.476954	+	0.878928i	$0.658259\pi$
$102$	−8.27432	+	10.7421i	−0.819280	+	1.06362i
$103$	4.10887			0.404859			0.202430	−	0.979297i	$-0.435116\pi$
$103$	4.10887			0.404859			0.202430	+	0.979297i	$0.435116\pi$
$104$	−3.89042	+	5.42296i	−0.381487	+	0.531765i
$105$	3.63885	−	1.32619i	0.355115	−	0.129423i
$106$	4.29413	+	0.903755i	0.417082	+	0.0877805i
$107$		−	6.12509i		−	0.592135i	−0.955167	−	0.296067i	$-0.904325\pi$
$107$		−	6.12509i		−	0.592135i	0.955167	−	0.296067i	$-0.0956753\pi$
$108$	−10.2037	−	1.97105i	−0.981849	−	0.189664i
$109$	−14.3281			−1.37238			−0.686192	−	0.727421i	$-0.740719\pi$
$109$	−14.3281			−1.37238			−0.686192	+	0.727421i	$0.740719\pi$
$110$	−7.50800	−	11.1899i	−0.715860	−	1.06691i
$111$	−5.03175	−	2.42388i	−0.477593	−	0.230065i
$112$	2.70026	+	2.95103i	0.255151	+	0.278846i
$113$	5.21916			0.490977			0.245488	−	0.969400i	$-0.421052\pi$
$113$	5.21916			0.490977			0.245488	+	0.969400i	$0.421052\pi$
$114$	−4.57902	−	3.52710i	−0.428865	−	0.330343i
$115$	6.23647	−	6.40088i	0.581554	−	0.596885i
$116$	6.13346	−	13.9259i	0.569477	−	1.29299i
$117$	5.53558	−	4.41238i	0.511765	−	0.407925i
$118$	−14.6241	−	3.07783i	−1.34626	−	0.283337i
$119$	−5.53558			−0.507446
$120$	10.5493	+	2.95161i	0.963016	+	0.269443i
$121$	7.15836			0.650760
$122$	−7.69144	−	1.61876i	−0.696350	−	0.146556i
$123$	−10.2909	−	4.95731i	−0.927900	−	0.446986i
$124$	−1.60302	+	3.63962i	−0.143955	+	0.326848i
$125$	−7.59122	+	8.20813i	−0.678979	+	0.734157i
$126$	−1.90451	−	3.79115i	−0.169667	−	0.337743i
$127$	7.06120			0.626580			0.313290	−	0.949658i	$-0.398569\pi$
$127$	7.06120			0.626580			0.313290	+	0.949658i	$0.398569\pi$
$128$	1.34030	+	11.2340i	0.118467	+	0.992958i
$129$	6.29091	−	13.0593i	0.553884	−	1.14981i
$130$	−6.19635	+	4.15752i	−0.543456	+	0.364639i
$131$	15.4327			1.34836			0.674179	−	0.738568i	$-0.264498\pi$
$131$	15.4327			1.34836			0.674179	+	0.738568i	$0.264498\pi$
$132$	−11.2232	+	9.58849i	−0.976857	+	0.834571i
$133$		−	2.35966i		−	0.204608i
$134$	3.56317	+	0.749915i	0.307811	+	0.0647828i
$135$	−9.91552	−	6.05660i	−0.853392	−	0.521269i
$136$	−12.7219	−	9.12664i	−1.09089	−	0.782603i
$137$	19.1901			1.63952			0.819760	−	0.572708i	$-0.194107\pi$
$137$	19.1901			1.63952			0.819760	+	0.572708i	$0.194107\pi$
$138$	−7.75562	−	5.97395i	−0.660202	−	0.508537i
$139$		−	19.6355i		−	1.66546i	−0.553677	−	0.832731i	$-0.686776\pi$
$139$		−	19.6355i		−	1.66546i	0.553677	−	0.832731i	$-0.313224\pi$
$140$	1.67348	+	4.14722i	0.141435	+	0.350504i
$141$	13.6904	+	6.59489i	1.15294	+	0.555390i
$142$	6.82472	+	1.43635i	0.572718	+	0.120536i
$143$		−	10.0551i		−	0.840851i
$144$	1.87362	−	11.8528i	0.156135	−	0.987736i
$145$	11.8724	−	12.1854i	0.985949	−	1.01194i
$146$	−2.55159	+	12.1237i	−0.211171	+	1.00336i
$147$	0.751690	−	1.56044i	0.0619983	−	0.128703i
$148$	2.59948	−	5.90206i	0.213676	−	0.485147i
$149$			3.69671i			0.302846i	0.988469	+	0.151423i	$0.0483856\pi$
$149$			3.69671i			0.302846i	−0.988469	+	0.151423i	$0.951614\pi$
$150$	9.89387	+	7.21881i	0.807831	+	0.589414i
$151$		−	15.7811i		−	1.28425i	−0.766600	−	0.642125i	$-0.778053\pi$
$151$		−	15.7811i		−	1.28425i	0.766600	−	0.642125i	$-0.221947\pi$
$152$	3.89042	−	5.42296i	0.315555	−	0.439860i
$153$	10.3511	+	12.9861i	0.836839	+	1.04986i
$154$	−5.89714	−	1.24113i	−0.475205	−	0.100013i
$155$	−3.10293	+	3.18473i	−0.249233	+	0.255803i
$156$	5.30959	+	6.21482i	0.425107	+	0.497584i
$157$		−	2.35966i		−	0.188321i	−0.995557	−	0.0941605i	$-0.969983\pi$
$157$		−	2.35966i		−	0.188321i	0.995557	−	0.0941605i	$-0.0300167\pi$
$158$	−0.814081	+	3.86804i	−0.0647648	+	0.307725i
$159$	2.33244	−	4.84192i	0.184974	−	0.383989i
$160$	−2.99163	+	12.2902i	−0.236509	+	0.971629i
$161$		−	3.99662i		−	0.314978i
$162$	−5.33248	+	11.5570i	−0.418960	+	0.908005i
$163$	−1.20603			−0.0944639			−0.0472320	−	0.998884i	$-0.515040\pi$
$163$	−1.20603			−0.0944639			−0.0472320	+	0.998884i	$0.515040\pi$
$164$	5.31644	−	12.0709i	0.415144	−	0.942576i
$165$	−15.5061	+	5.65124i	−1.20715	+	0.439949i
$166$	−5.14545	+	24.4482i	−0.399365	+	1.89755i
$167$		−	8.50522i		−	0.658154i	−0.944303	−	0.329077i	$-0.893262\pi$
$167$		−	8.50522i		−	0.658154i	0.944303	−	0.329077i	$-0.106738\pi$
$168$	4.30026	−	2.34686i	0.331772	−	0.181065i
$169$	7.43202			0.571694
$170$	−9.75325	−	14.5362i	−0.748040	−	1.11488i
$171$	−5.53558	+	4.41238i	−0.423317	+	0.337423i
$172$	15.3181	+	6.74664i	1.16800	+	0.514427i
$173$	9.98425			0.759089			0.379544	−	0.925174i	$-0.376081\pi$
$173$	9.98425			0.759089			0.379544	+	0.925174i	$0.376081\pi$
$174$	−14.7644	−	11.3726i	−1.11929	−	0.862158i
$175$	0.130075	+	4.99831i	0.00983272	+	0.377837i
$176$	−11.5065	−	12.5751i	−0.867337	−	0.947885i
$177$	−7.94336	+	16.4897i	−0.597059	+	1.23944i
$178$	0.497684	−	2.36471i	0.0373030	−	0.177242i
$179$	−25.3959			−1.89818			−0.949091	−	0.315003i	$-0.897994\pi$
$179$	−25.3959			−1.89818			−0.949091	+	0.315003i	$0.897994\pi$
$180$	6.59981	−	11.6809i	0.491921	−	0.870640i
$181$	9.19375			0.683366			0.341683	−	0.939815i	$-0.389003\pi$
$181$	9.19375			0.683366			0.341683	+	0.939815i	$0.389003\pi$
$182$	−0.687271	+	3.26552i	−0.0509439	+	0.242056i
$183$	−4.17775	+	8.67262i	−0.308828	+	0.641099i
$184$	6.58932	−	9.18502i	0.485771	−	0.677129i
$185$	5.03175	−	5.16440i	0.369942	−	0.379694i
$186$	3.85877	+	2.97231i	0.282939	+	0.217940i
$187$	23.5886			1.72497
$188$	−7.07265	+	16.0583i	−0.515826	+	1.17117i
$189$	−5.06628	+	1.15449i	−0.368517	+	0.0839768i
$190$	6.19635	−	4.15752i	0.449531	−	0.301619i
$191$	−1.27432			−0.0922067			−0.0461033	−	0.998937i	$-0.514680\pi$
$191$	−1.27432			−0.0922067			−0.0461033	+	0.998937i	$0.514680\pi$
$192$	13.7522	+	1.69637i	0.992478	+	0.122425i
$193$			22.5532i			1.62341i	0.584066	+	0.811706i	$0.301461\pi$
$193$			22.5532i			1.62341i	−0.584066	+	0.811706i	$0.698539\pi$
$194$	3.63850	−	17.2881i	0.261229	−	1.24121i
$195$	3.12935	+	8.58643i	0.224098	+	0.614887i
$196$	1.83034	+	0.806145i	0.130738	+	0.0575818i
$197$	−9.07681			−0.646696			−0.323348	−	0.946280i	$-0.604808\pi$
$197$	−9.07681			−0.646696			−0.323348	+	0.946280i	$0.604808\pi$
$198$	8.11561	+	16.1551i	0.576752	+	1.14809i
$199$			6.70781i			0.475504i	0.971326	+	0.237752i	$0.0764106\pi$
$199$			6.70781i			0.475504i	−0.971326	+	0.237752i	$0.923589\pi$
$200$	−7.94189	+	11.7016i	−0.561576	+	0.827425i
$201$	1.93540	−	4.01771i	0.136513	−	0.283388i
$202$	−5.14545	+	24.4482i	−0.362033	+	1.72017i
$203$		−	7.60838i		−	0.534004i
$204$	−14.5795	+	12.4559i	−1.02077	+	0.872088i
$205$	10.2909	−	10.5622i	0.718748	−	0.737696i
$206$	5.68625	+	1.19675i	0.396180	+	0.0833813i
$207$	−9.37578	+	7.47338i	−0.651662	+	0.519436i
$208$	−6.96342	+	6.37169i	−0.482826	+	0.441797i
$209$			10.0551i			0.695527i
$210$	5.42205	−	0.775461i	0.374157	−	0.0535119i
$211$		−	1.73995i		−	0.119783i	−0.998205	−	0.0598915i	$-0.980925\pi$
$211$		−	1.73995i		−	0.119783i	0.998205	−	0.0598915i	$-0.0190755\pi$
$212$	5.67940	+	2.50141i	0.390063	+	0.171797i
$213$	3.70698	−	7.69534i	0.253998	−	0.527276i
$214$	1.78399	−	8.47649i	0.121951	−	0.579441i
$215$	13.4036	+	13.0593i	0.914118	+	0.890639i
$216$	−13.5467	−	5.69964i	−0.921739	−	0.387811i
$217$			1.98850i			0.134988i
$218$	−19.8286	−	4.17319i	−1.34296	−	0.282644i
$219$	13.6703	+	6.58520i	0.923751	+	0.444987i
$220$	−7.13114	−	17.6724i	−0.480781	−	1.19147i
$221$		−	13.0621i		−	0.878650i
$222$	−6.25744	−	4.81994i	−0.419972	−	0.323493i
$223$	4.47294			0.299530			0.149765	−	0.988722i	$-0.452148\pi$
$223$	4.47294			0.299530			0.149765	+	0.988722i	$0.452148\pi$
$224$	2.87737	+	4.87040i	0.192252	+	0.325417i
$225$	11.4824	−	9.65161i	0.765496	−	0.643441i
$226$	7.22277	+	1.52013i	0.480452	+	0.101117i
$227$			7.06743i			0.469082i	0.972106	+	0.234541i	$0.0753587\pi$
$227$			7.06743i			0.469082i	−0.972106	+	0.234541i	$0.924641\pi$
$228$	−5.30959	−	6.21482i	−0.351636	−	0.411587i
$229$	−5.92188			−0.391329			−0.195665	−	0.980671i	$-0.562686\pi$
$229$	−5.92188			−0.391329			−0.195665	+	0.980671i	$0.562686\pi$
$230$	10.4949	−	7.04172i	0.692016	−	0.464317i
$231$	−3.20315	+	6.64943i	−0.210752	+	0.437500i
$232$	12.5441	−	17.4856i	0.823562	−	1.14798i
$233$	17.9820			1.17804			0.589019	−	0.808119i	$-0.299514\pi$
$233$	17.9820			1.17804			0.589019	+	0.808119i	$0.299514\pi$
$234$	8.94582	−	4.49399i	0.584806	−	0.293781i
$235$	−13.6904	+	14.0513i	−0.893061	+	0.916604i
$236$	−19.3418	−	8.51880i	−1.25904	−	0.554527i
$237$	4.36148	+	2.10100i	0.283309	+	0.136475i
$238$	−7.66067	−	1.61229i	−0.496568	−	0.104509i
$239$	15.2452			0.986133			0.493066	−	0.869992i	$-0.335876\pi$
$239$	15.2452			0.986133			0.493066	+	0.869992i	$0.335876\pi$
$240$	13.7395	+	7.15730i	0.886879	+	0.462002i
$241$	−18.1089			−1.16650			−0.583248	−	0.812294i	$-0.698218\pi$
$241$	−18.1089			−1.16650			−0.583248	+	0.812294i	$0.698218\pi$
$242$	9.90642	+	2.08494i	0.636809	+	0.134025i
$243$	12.1819	+	9.72631i	0.781470	+	0.623943i
$244$	−10.1727	−	4.48040i	−0.651239	−	0.286828i
$245$	1.60157	+	1.56044i	0.102321	+	0.0996926i
$246$	−12.7977	−	9.85772i	−0.815951	−	0.628505i
$247$	5.56798			0.354282
$248$	−3.27848	+	4.56996i	−0.208184	+	0.290193i
$249$	27.5671	+	13.2795i	1.74699	+	0.841556i
$250$	−12.8961	+	9.14819i	−0.815624	+	0.578582i
$251$	12.4831			0.787928			0.393964	−	0.919126i	$-0.371103\pi$
$251$	12.4831			0.787928			0.393964	+	0.919126i	$0.371103\pi$
$252$	−1.53143	−	5.80127i	−0.0964713	−	0.365446i
$253$			17.0306i			1.07071i
$254$	9.77196	+	2.05664i	0.613147	+	0.129045i
$255$	−20.1432	+	7.34123i	−1.26141	+	0.459726i
$256$	−1.41717	+	15.9371i	−0.0885734	+	0.996070i
$257$	−0.670267			−0.0418101			−0.0209051	−	0.999781i	$-0.506655\pi$
$257$	−0.670267			−0.0418101			−0.0209051	+	0.999781i	$0.506655\pi$
$258$	12.5096	−	16.2405i	0.778814	−	1.01109i
$259$		−	3.22458i		−	0.200366i
$260$	−9.78602	+	3.94884i	−0.606903	+	0.244897i
$261$	−17.8487	+	14.2271i	−1.10481	+	0.880636i
$262$	21.3572	+	4.49490i	1.31945	+	0.277696i
$263$		−	27.9923i		−	1.72608i	−0.505136	−	0.863039i	$-0.668558\pi$
$263$		−	27.9923i		−	1.72608i	0.505136	−	0.863039i	$-0.331442\pi$
$264$	−18.3245	+	10.0006i	−1.12780	+	0.615495i
$265$	4.96956	+	4.84192i	0.305278	+	0.297437i
$266$	0.687271	−	3.26552i	0.0421393	−	0.200222i
$267$	−2.66637	−	1.28444i	−0.163179	−	0.0786062i
$268$	4.71263	+	2.07561i	0.287870	+	0.126788i
$269$			7.51282i			0.458065i	0.973419	+	0.229032i	$0.0735562\pi$
$269$			7.51282i			0.458065i	−0.973419	+	0.229032i	$0.926444\pi$
$270$	−11.9580	−	11.2697i	−0.727741	−	0.685852i
$271$		−	4.97797i		−	0.302390i	−0.988504	−	0.151195i	$-0.951688\pi$
$271$		−	4.97797i		−	0.302390i	0.988504	−	0.151195i	$-0.0483121\pi$
$272$	−14.9475	−	16.3357i	−0.906327	−	0.990496i
$273$	3.68209	+	1.77373i	0.222850	+	0.107351i
$274$	26.5571	+	5.58929i	1.60437	+	0.337661i
$275$	−0.554282	−	21.2991i	−0.0334245	−	1.28438i
$276$	−8.99301	−	10.5262i	−0.541315	−	0.633604i
$277$		−	22.9726i		−	1.38029i	−0.723671	−	0.690145i	$-0.757547\pi$
$277$		−	22.9726i		−	1.38029i	0.723671	−	0.690145i	$-0.242453\pi$
$278$	5.71902	−	27.1735i	0.343004	−	1.62976i
$279$	4.66487	−	3.71834i	0.279279	−	0.222611i
$280$	1.10801	+	6.22674i	0.0662160	+	0.372119i
$281$		−	9.38371i		−	0.559785i	−0.960031	−	0.279893i	$-0.909701\pi$
$281$		−	9.38371i		−	0.559785i	0.960031	−	0.279893i	$-0.0902989\pi$
$282$	17.0252	+	13.1141i	1.01384	+	0.780932i
$283$	−27.4695			−1.63289			−0.816447	−	0.577420i	$-0.804060\pi$
$283$	−27.4695			−1.63289			−0.816447	+	0.577420i	$0.804060\pi$
$284$	9.02636	+	3.97553i	0.535616	+	0.235904i
$285$	−3.12935	−	8.58643i	−0.185367	−	0.508616i
$286$	2.92864	−	13.9152i	0.173174	−	0.822825i
$287$		−	6.59489i		−	0.389284i
$288$	6.04514	−	15.8574i	0.356213	−	0.934405i
$289$	13.6427			0.802511
$290$	19.9793	−	13.4054i	1.17322	−	0.787190i
$291$	−19.4935	−	9.39035i	−1.14273	−	0.550472i
$292$	−7.06226	+	16.0347i	−0.413287	+	0.938361i
$293$	−9.17703			−0.536128			−0.268064	−	0.963401i	$-0.586384\pi$
$293$	−9.17703			−0.536128			−0.268064	+	0.963401i	$0.586384\pi$
$294$	1.49475	−	1.94055i	0.0871757	−	0.113175i
$295$	−16.9244	−	16.4897i	−0.985374	−	0.960065i
$296$	5.31644	−	7.41072i	0.309012	−	0.430739i
$297$	21.5887	−	4.91958i	1.25271	−	0.285463i
$298$	−1.07670	+	5.11586i	−0.0623716	+	0.296354i
$299$	9.43065			0.545388
$300$	11.5895	+	12.8718i	0.669123	+	0.743152i
$301$	8.36902			0.482382
$302$	4.59640	−	21.8394i	0.264493	−	1.25672i
$303$	27.5671	+	13.2795i	1.58369	+	0.762889i
$304$	6.96342	−	6.37169i	0.399380	−	0.365441i
$305$	−8.90125	−	8.67262i	−0.509684	−	0.496593i
$306$	10.5426	+	20.9862i	0.602679	+	1.19970i
$307$	−12.5920			−0.718662			−0.359331	−	0.933210i	$-0.616995\pi$
$307$	−12.5920			−0.718662			−0.359331	+	0.933210i	$0.616995\pi$
$308$	−7.79954	−	3.43519i	−0.444420	−	0.195738i
$309$	3.08860	−	6.41164i	0.175704	−	0.364745i
$310$	−5.22171	+	3.50357i	−0.296573	+	0.198990i
$311$	29.6572			1.68171			0.840853	−	0.541264i	$-0.182054\pi$
$311$	29.6572			1.68171			0.840853	+	0.541264i	$0.182054\pi$
$312$	5.53779	+	10.1471i	0.313516	+	0.574468i
$313$			7.25570i			0.410116i	0.978750	+	0.205058i	$0.0657384\pi$
$313$			7.25570i			0.410116i	−0.978750	+	0.205058i	$0.934262\pi$
$314$	0.687271	−	3.26552i	0.0387850	−	0.184284i
$315$	0.665850	−	6.67508i	0.0375164	−	0.376098i
$316$	−2.25321	+	5.11586i	−0.126753	+	0.287790i
$317$	−23.8052			−1.33703			−0.668516	−	0.743698i	$-0.733070\pi$
$317$	−23.8052			−1.33703			−0.668516	+	0.743698i	$0.733070\pi$
$318$	4.63810	−	6.02137i	0.260092	−	0.337662i
$319$			32.4213i			1.81525i
$320$	−7.71975	+	16.1371i	−0.431547	+	0.902090i
$321$	−9.55782	−	4.60417i	−0.533465	−	0.256980i
$322$	1.16405	−	5.53091i	0.0648701	−	0.308225i
$323$			13.0621i			0.726793i
$324$	−10.7457	+	14.4406i	−0.596983	+	0.802254i
$325$	−11.7943	+	0.306932i	−0.654229	+	0.0170255i
$326$	−1.66903	−	0.351269i	−0.0924388	−	0.0194550i
$327$	−10.7703	+	22.3581i	−0.595598	+	1.23641i
$328$	10.8731	−	15.1564i	0.600369	−	0.836870i
$329$			8.77342i			0.483694i
$330$	−23.1048	+	3.30444i	−1.27188	+	0.181904i
$331$		−	15.5359i		−	0.853931i	−0.904268	−	0.426965i	$-0.859583\pi$
$331$		−	15.5359i		−	0.853931i	0.904268	−	0.426965i	$-0.140417\pi$
$332$	−14.2415	+	32.3352i	−0.781606	+	1.77462i
$333$	−7.56463	+	6.02972i	−0.414539	+	0.330427i
$334$	2.47722	−	11.7703i	0.135548	−	0.644045i
$335$	4.12363	+	4.01771i	0.225298	+	0.219511i
$336$	6.63466	−	1.99533i	0.361950	−	0.108854i
$337$			25.5426i			1.39140i	0.718335	+	0.695698i	$0.244905\pi$
$337$			25.5426i			1.39140i	−0.718335	+	0.695698i	$0.755095\pi$
$338$	10.2851	+	2.16464i	0.559438	+	0.117741i
$339$	3.92319	−	8.14416i	0.213078	−	0.442330i
$340$	−9.26369	−	22.9573i	−0.502394	−	1.24503i
$341$		−	8.47351i		−	0.458866i
$342$	−8.94582	+	4.49399i	−0.483734	+	0.243007i
$343$	1.00000			0.0539949
$344$	19.2337	+	13.7982i	1.03701	+	0.743949i
$345$	−5.30028	−	14.5431i	−0.285357	−	0.782974i
$346$	13.8172	+	2.90800i	0.742815	+	0.156335i
$347$		−	14.6969i		−	0.788971i	−0.918902	−	0.394486i	$-0.870923\pi$
$347$		−	14.6969i		−	0.788971i	0.918902	−	0.394486i	$-0.129077\pi$
$348$	−17.1200	−	20.0388i	−0.917730	−	1.07419i
$349$	−7.57133			−0.405284			−0.202642	−	0.979253i	$-0.564953\pi$
$349$	−7.57133			−0.405284			−0.202642	+	0.979253i	$0.564953\pi$
$350$	−1.27579	+	6.95502i	−0.0681940	+	0.371762i
$351$	−2.72420	−	11.9547i	−0.145407	−	0.638093i
$352$	−12.2612	−	20.7540i	−0.653525	−	1.10619i
$353$	−12.1423			−0.646270			−0.323135	−	0.946353i	$-0.604737\pi$
$353$	−12.1423			−0.646270			−0.323135	+	0.946353i	$0.604737\pi$
$354$	−15.7955	+	20.5064i	−0.839524	+	1.08990i
$355$	7.89821	+	7.69534i	0.419193	+	0.408426i
$356$	1.37749	−	3.12755i	0.0730066	−	0.165760i
$357$	−4.16104	+	8.63793i	−0.220226	+	0.457168i
$358$	−35.1453	−	7.39680i	−1.85749	−	0.390933i
$359$	−28.2322			−1.49004			−0.745019	−	0.667043i	$-0.767560\pi$
$359$	−28.2322			−1.49004			−0.745019	+	0.667043i	$0.767560\pi$
$360$	12.5356	−	14.2428i	0.660684	−	0.750664i
$361$	13.4320			0.706949
$362$	12.7232	+	2.67776i	0.668716	+	0.140740i
$363$	5.38086	−	11.1702i	0.282422	−	0.586281i
$364$	−1.90222	+	4.31896i	−0.0997036	+	0.226375i
$365$	−13.6703	+	14.0306i	−0.715534	+	0.734397i
$366$	−8.30756	+	10.7852i	−0.434243	+	0.563751i
$367$	21.6494			1.13009			0.565046	−	0.825059i	$-0.308858\pi$
$367$	21.6494			1.13009			0.565046	+	0.825059i	$0.308858\pi$
$368$	11.7941	−	10.7919i	0.614813	−	0.562568i
$369$	−15.4711	+	12.3320i	−0.805395	+	0.641976i
$370$	8.46760	−	5.68145i	0.440209	−	0.295364i
$371$	3.10293			0.161096
$372$	4.47443	+	5.23727i	0.231988	+	0.271540i
$373$		−	16.6519i		−	0.862202i	−0.902304	−	0.431101i	$-0.858125\pi$
$373$		−	16.6519i		−	0.862202i	0.902304	−	0.431101i	$-0.141875\pi$
$374$	32.6441	+	6.87039i	1.68799	+	0.355259i
$375$	7.10203	+	18.0156i	0.366747	+	0.930321i
$376$	−14.4649	+	20.1631i	−0.745972	+	1.03983i
$377$	17.9532			0.924635
$378$	−7.34745	+	0.122095i	−0.377912	+	0.00627989i
$379$			24.4774i			1.25732i	0.777680	+	0.628661i	$0.216397\pi$
$379$			24.4774i			1.25732i	−0.777680	+	0.628661i	$0.783603\pi$
$380$	9.78602	−	3.94884i	0.502012	−	0.202571i
$381$	5.30783	−	11.0185i	0.271928	−	0.564497i
$382$	−1.76353	−	0.371158i	−0.0902300	−	0.0189901i
$383$		−	8.91391i		−	0.455480i	−0.973722	−	0.227740i	$-0.926866\pi$
$383$		−	8.91391i		−	0.455480i	0.973722	−	0.227740i	$-0.0731336\pi$
$384$	18.5375	+	6.35305i	0.945988	+	0.324203i
$385$	−6.82472	−	6.64943i	−0.347820	−	0.338886i
$386$	−6.56881	+	31.2112i	−0.334344	+	1.58861i
$387$	−15.6494	−	19.6331i	−0.795506	−	0.998008i
$388$	10.0706	−	22.8651i	0.511258	−	1.16080i
$389$		−	18.7014i		−	0.948199i	−0.880471	−	0.474099i	$-0.842774\pi$
$389$		−	18.7014i		−	0.948199i	0.880471	−	0.474099i	$-0.157226\pi$
$390$	1.82982	+	12.7942i	0.0926566	+	0.647859i
$391$			22.1236i			1.11884i
$392$	2.29820	+	1.64872i	0.116077	+	0.0832731i
$393$	11.6006	−	24.0817i	0.585171	−	1.21476i
$394$	−12.5614	−	2.64370i	−0.632832	−	0.133188i
$395$	−4.36148	+	4.47646i	−0.219450	+	0.225235i
$396$	6.52584	+	24.7207i	0.327936	+	1.24226i
$397$		−	6.46511i		−	0.324474i	−0.986752	−	0.162237i	$-0.948129\pi$
$397$		−	6.46511i		−	0.324474i	0.986752	−	0.162237i	$-0.0518710\pi$
$398$	−1.95371	+	9.28291i	−0.0979307	+	0.465310i
$399$	−3.68209	−	1.77373i	−0.184335	−	0.0887975i
$400$	−14.3989	+	13.8806i	−0.719946	+	0.694030i
$401$		−	11.5122i		−	0.574891i	−0.957797	−	0.287446i	$-0.907194\pi$
$401$		−	11.5122i		−	0.574891i	0.957797	−	0.287446i	$-0.0928060\pi$
$402$	3.84859	−	4.99639i	0.191950	−	0.249197i
$403$	−4.69217			−0.233734
$404$	−14.2415	+	32.3352i	−0.708543	+	1.60873i
$405$	−16.9043	+	10.9199i	−0.839983	+	0.542612i
$406$	2.21601	−	10.5292i	0.109979	−	0.522556i
$407$			13.7408i			0.681105i
$408$	−23.8044	+	12.9913i	−1.17850	+	0.643164i
$409$	2.36407			0.116896			0.0584478	−	0.998290i	$-0.481385\pi$
$409$	2.36407			0.116896			0.0584478	+	0.998290i	$0.481385\pi$
$410$	17.3179	−	11.6197i	0.855269	−	0.573854i
$411$	14.4250	−	29.9449i	0.711532	−	1.47707i
$412$	7.52062	+	3.31235i	0.370514	+	0.163188i
$413$	−10.5673			−0.519985
$414$	−15.1518	+	7.61160i	−0.744670	+	0.374090i
$415$	−27.5671	+	28.2938i	−1.35321	+	1.38889i
$416$	−11.4925	+	6.78960i	−0.563464	+	0.332887i
$417$	−30.6400	−	14.7598i	−1.50045	−	0.722791i
$418$	−2.92864	+	13.9152i	−0.143245	+	0.680616i
$419$	−16.2399			−0.793370			−0.396685	−	0.917955i	$-0.629839\pi$
$419$	−16.2399			−0.793370			−0.396685	+	0.917955i	$0.629839\pi$
$420$	7.72942	+	0.506065i	0.377157	+	0.0246935i
$421$	−39.6839			−1.93408			−0.967038	−	0.254631i	$-0.918046\pi$
$421$	−39.6839			−1.93408			−0.967038	+	0.254631i	$0.918046\pi$
$422$	0.506776	−	2.40791i	0.0246694	−	0.117215i
$423$	20.5818	−	16.4056i	1.00072	−	0.797670i
$424$	7.13114	+	5.11586i	0.346319	+	0.248448i
$425$	−0.720039	−	27.6686i	−0.0349270	−	1.34212i
$426$	7.37141	−	9.56986i	0.357146	−	0.463661i
$427$	−5.55782			−0.268962
$428$	4.93771	−	11.2110i	0.238673	−	0.541903i
$429$	−15.6904	−	7.55832i	−0.757538	−	0.364919i
$430$	14.7455	+	21.9767i	0.711093	+	1.05981i
$431$	−28.9399			−1.39399			−0.696993	−	0.717078i	$-0.745479\pi$
$431$	−28.9399			−1.39399			−0.696993	+	0.717078i	$0.745479\pi$
$432$	−17.0872	−	11.8333i	−0.822109	−	0.569331i
$433$		−	1.05176i		−	0.0505442i	−0.999681	−	0.0252721i	$-0.991955\pi$
$433$		−	1.05176i		−	0.0505442i	0.999681	−	0.0252721i	$-0.00804521\pi$
$434$	−0.579168	+	2.75187i	−0.0278010	+	0.132094i
$435$	−10.0902	−	27.6858i	−0.483786	−	1.32743i
$436$	−26.2252	−	11.5505i	−1.25596	−	0.553170i
$437$	−9.43065			−0.451129
$438$	17.0002	+	13.0948i	0.812302	+	0.625695i
$439$		−	35.2806i		−	1.68385i	−0.539594	−	0.841925i	$-0.681422\pi$
$439$		−	35.2806i		−	1.68385i	0.539594	−	0.841925i	$-0.318578\pi$
$440$	−4.72150	−	26.5338i	−0.225089	−	1.26495i
$441$	−1.86993	−	2.34593i	−0.0890441	−	0.111711i
$442$	3.80445	−	18.0766i	0.180959	−	0.859814i
$443$			39.1697i			1.86101i	0.366282	+	0.930504i	$0.380631\pi$
$443$			39.1697i			1.86101i	−0.366282	+	0.930504i	$0.619369\pi$
$444$	−7.25580	−	8.49284i	−0.344345	−	0.403052i
$445$	2.66637	−	2.73666i	0.126398	−	0.129730i
$446$	6.19009	+	1.30279i	0.293109	+	0.0616887i
$447$	5.76848	+	2.77878i	0.272840	+	0.131432i
$448$	2.56343	+	7.57818i	0.121111	+	0.358035i
$449$			28.6875i			1.35385i	0.736053	+	0.676924i	$0.236688\pi$
$449$			28.6875i			1.35385i	−0.736053	+	0.676924i	$0.763312\pi$
$450$	18.7016	−	10.0125i	0.881603	−	0.471992i
$451$			28.1026i			1.32330i
$452$	9.55281	+	4.20740i	0.449326	+	0.197899i
$453$	−24.6254	−	11.8625i	−1.15700	−	0.557349i
$454$	−2.05845	+	9.78059i	−0.0966080	+	0.459026i
$455$	−3.68209	+	3.77916i	−0.172619	+	0.177170i
$456$	−5.53779	−	10.1471i	−0.259331	−	0.475183i
$457$			3.54746i			0.165943i	0.996552	+	0.0829715i	$0.0264411\pi$
$457$			3.54746i			0.165943i	−0.996552	+	0.0829715i	$0.973559\pi$
$458$	−8.19527	−	1.72480i	−0.382940	−	0.0805948i
$459$	28.0448	−	6.39078i	1.30902	−	0.298296i
$460$	16.5749	−	6.68826i	0.772807	−	0.311842i
$461$			9.66570i			0.450177i	0.974338	+	0.225088i	$0.0722671\pi$
$461$			9.66570i			0.450177i	−0.974338	+	0.225088i	$0.927733\pi$
$462$	−6.36953	+	8.26917i	−0.296337	+	0.384717i
$463$	10.8146			0.502595			0.251298	−	0.967910i	$-0.419143\pi$
$463$	10.8146			0.502595			0.251298	+	0.967910i	$0.419143\pi$
$464$	22.4526	−	20.5446i	1.04234	−	0.953760i
$465$	2.63713	+	7.23584i	0.122294	+	0.335554i
$466$	24.8852	+	5.23741i	1.15278	+	0.242618i
$467$			21.3391i			0.987457i	0.869616	+	0.493728i	$0.164366\pi$
$467$			21.3391i			0.987457i	−0.869616	+	0.493728i	$0.835634\pi$
$468$	13.6890	−	3.61366i	0.632774	−	0.167041i
$469$	2.57474			0.118890
$470$	−23.0386	+	15.4581i	−1.06269	+	0.713027i
$471$	−3.68209	−	1.77373i	−0.169662	−	0.0817291i
$472$	−24.2858	−	17.4226i	−1.11785	−	0.801940i
$473$	−35.6626			−1.63977
$474$	5.42390	+	4.17789i	0.249128	+	0.191897i
$475$	11.7943	−	0.306932i	0.541159	−	0.0140830i
$476$	−10.1320	−	4.46248i	−0.464399	−	0.204538i
$477$	−5.80224	−	7.27924i	−0.265666	−	0.333294i
$478$	21.0978	+	4.44032i	0.964992	+	0.203095i
$479$	−3.12390			−0.142735			−0.0713673	−	0.997450i	$-0.522736\pi$
$479$	−3.12390			−0.142735			−0.0713673	+	0.997450i	$0.522736\pi$
$480$	16.9294	+	13.9067i	0.772717	+	0.634751i
$481$	7.60890			0.346936
$482$	−25.0608	−	5.27437i	−1.14149	−	0.240241i
$483$	−6.23647	−	3.00422i	−0.283769	−	0.136697i
$484$	13.1022	+	5.77067i	0.595554	+	0.262303i
$485$	19.4935	−	20.0074i	0.885153	−	0.908488i
$486$	14.0256	+	17.0083i	0.636215	+	0.771512i
$487$	−7.14304			−0.323682			−0.161841	−	0.986817i	$-0.551743\pi$
$487$	−7.14304			−0.323682			−0.161841	+	0.986817i	$0.551743\pi$
$488$	−12.7730	−	9.16330i	−0.578205	−	0.414803i
$489$	−0.906564	+	1.88194i	−0.0409962	+	0.0851043i
$490$	1.76192	+	2.62595i	0.0795954	+	0.118629i
$491$	4.63607			0.209223			0.104612	−	0.994513i	$-0.466640\pi$
$491$	4.63607			0.209223			0.104612	+	0.994513i	$0.466640\pi$
$492$	−14.8395	−	17.3695i	−0.669017	−	0.783078i
$493$			42.1169i			1.89685i
$494$	7.70550	+	1.62172i	0.346687	+	0.0729648i
$495$	−2.83736	+	28.4443i	−0.127530	+	1.27847i
$496$	−5.86812	+	5.36947i	−0.263486	+	0.241096i
$497$	4.93153			0.221209
$498$	34.2821	+	26.4066i	1.53622	+	1.18331i
$499$		−	19.2408i		−	0.861337i	−0.902510	−	0.430669i	$-0.858278\pi$
$499$		−	19.2408i		−	0.861337i	0.902510	−	0.430669i	$-0.141722\pi$
$500$	−20.5114	+	8.90402i	−0.917299	+	0.398200i
$501$	−13.2719	−	6.39329i	−0.592943	−	0.285631i
$502$	17.2753	+	3.63582i	0.771036	+	0.162275i
$503$			5.94184i			0.264933i	0.991187	+	0.132467i	$0.0422898\pi$
$503$			5.94184i			0.264933i	−0.991187	+	0.132467i	$0.957710\pi$
$504$	−0.429674	−	8.47440i	−0.0191392	−	0.377480i
$505$	−27.5671	+	28.2938i	−1.22672	+	1.25906i
$506$	−4.96033	+	23.5686i	−0.220514	+	1.04775i
$507$	5.58657	−	11.5972i	0.248108	−	0.515050i
$508$	12.9244	+	5.69235i	0.573426	+	0.252557i
$509$		−	10.9791i		−	0.486640i	−0.969946	−	0.243320i	$-0.921763\pi$
$509$		−	10.9791i		−	0.486640i	0.969946	−	0.243320i	$-0.0782366\pi$
$510$	−30.0142	+	4.29263i	−1.32905	+	0.190081i
$511$			8.76054i			0.387543i
$512$	−6.60305	+	21.6425i	−0.291816	+	0.956474i
$513$	2.72420	+	11.9547i	0.120276	+	0.527812i
$514$	−0.927581	−	0.195222i	−0.0409138	−	0.00861085i
$515$	6.58066	+	6.41164i	0.289979	+	0.282531i
$516$	22.0422	−	18.8316i	0.970353	−	0.829014i
$517$		−	37.3858i		−	1.64423i
$518$	0.939188	−	4.46248i	0.0412655	−	0.196070i
$519$	7.50506	−	15.5798i	0.329436	−	0.683877i
$520$	−14.6930	+	2.61451i	−0.644329	+	0.114654i
$521$		−	2.33795i		−	0.102427i	−0.998688	−	0.0512137i	$-0.983691\pi$
$521$		−	2.33795i		−	0.102427i	0.998688	−	0.0512137i	$-0.0163089\pi$
$522$	−28.8446	+	14.4902i	−1.26249	+	0.634221i
$523$	−30.5065			−1.33396			−0.666979	−	0.745077i	$-0.732413\pi$
$523$	−30.5065			−1.33396			−0.666979	+	0.745077i	$0.732413\pi$
$524$	28.2469	+	12.4409i	1.23397	+	0.543485i
$525$	7.89732	+	3.55420i	0.344667	+	0.155118i
$526$	8.15301	−	38.7384i	0.355488	−	1.68908i
$527$		−	11.0075i		−	0.479494i
$528$	−28.2720	+	8.50261i	−1.23038	+	0.370029i
$529$	7.02703			0.305523
$530$	5.46711	+	8.14814i	0.237476	+	0.353933i
$531$	19.7601	+	24.7902i	0.857516	+	1.07580i
$532$	1.90222	−	4.31896i	0.0824719	−	0.187251i
$533$	15.5617			0.674051
$534$	−3.31587	−	2.55413i	−0.143492	−	0.110528i
$535$	9.55782	−	9.80978i	0.413220	−	0.424114i
$536$	5.91725	+	4.24502i	0.255586	+	0.183357i
$537$	−19.0899	+	39.6287i	−0.823788	+	1.71011i
$538$	−2.18818	+	10.3970i	−0.0943390	+	0.448245i
$539$	−4.26126			−0.183546
$540$	−13.2662	−	19.0790i	−0.570888	−	0.821028i
$541$	−5.37083			−0.230910			−0.115455	−	0.993313i	$-0.536833\pi$
$541$	−5.37083			−0.230910			−0.115455	+	0.993313i	$0.536833\pi$
$542$	1.44988	−	6.88899i	0.0622776	−	0.295907i
$543$	6.91085	−	14.3463i	0.296573	−	0.615657i
$544$	−15.9279	−	26.9605i	−0.682903	−	1.15592i
$545$	−22.9475	−	22.3581i	−0.982963	−	0.957716i
$546$	4.57902	+	3.52710i	0.195964	+	0.150946i
$547$	3.67685			0.157211			0.0786054	−	0.996906i	$-0.474953\pi$
$547$	3.67685			0.157211			0.0786054	+	0.996906i	$0.474953\pi$
$548$	35.1243	+	15.4700i	1.50044	+	0.660845i
$549$	10.3927	+	13.0382i	0.443550	+	0.556458i
$550$	5.43649	−	29.6372i	0.231813	−	1.26373i
$551$	−17.9532			−0.764831
$552$	−9.37953	−	17.1865i	−0.399219	−	0.731506i
$553$			2.79504i			0.118857i
$554$	6.69098	−	31.7917i	0.284272	−	1.35070i
$555$	−4.27640	−	11.7338i	−0.181523	−	0.498070i
$556$	15.8291	−	35.9396i	0.671302	−	1.52418i
$557$	22.5971			0.957469			0.478734	−	0.877960i	$-0.341096\pi$
$557$	22.5971			0.957469			0.478734	+	0.877960i	$0.341096\pi$
$558$	7.53870	−	3.78711i	0.319139	−	0.160321i
$559$			19.7480i			0.835252i
$560$	−0.280231	+	8.93988i	−0.0118419	+	0.377779i
$561$	17.7313	−	36.8085i	0.748616	−	1.55406i
$562$	2.73309	−	12.9861i	0.115289	−	0.547785i
$563$		−	19.4526i		−	0.819830i	−0.912124	−	0.409915i	$-0.865558\pi$
$563$		−	19.4526i		−	0.819830i	0.912124	−	0.409915i	$-0.134442\pi$
$564$	19.7415	+	23.1073i	0.831269	+	0.972992i
$565$	8.35886	+	8.14416i	0.351660	+	0.342628i
$566$	−38.0150	−	8.00075i	−1.59789	−	0.336297i
$567$	−2.00676	+	8.77342i	−0.0842759	+	0.368449i
$568$	11.3336	+	8.13072i	0.475549	+	0.341158i
$569$			9.18211i			0.384934i	0.981303	+	0.192467i	$0.0616489\pi$
$569$			9.18211i			0.384934i	−0.981303	+	0.192467i	$0.938351\pi$
$570$	−1.82982	−	12.7942i	−0.0766428	−	0.535889i
$571$		−	42.6241i		−	1.78376i	−0.452271	−	0.891881i	$-0.649386\pi$
$571$		−	42.6241i		−	1.78376i	0.452271	−	0.891881i	$-0.350614\pi$
$572$	8.10588	−	18.4042i	0.338924	−	0.769520i
$573$	−0.957894	+	1.98850i	−0.0400166	+	0.0830707i
$574$	1.92082	−	9.12664i	0.0801736	−	0.380939i
$575$	19.9763	−	0.519859i	0.833071	−	0.0216796i
$576$	12.9845	−	20.1843i	0.541019	−	0.841011i
$577$		−	7.50091i		−	0.312267i	−0.987736	−	0.156134i	$-0.950097\pi$
$577$		−	7.50091i		−	0.312267i	0.987736	−	0.156134i	$-0.0499030\pi$
$578$	18.8801	+	3.97356i	0.785307	+	0.165278i
$579$	35.1928	+	16.9530i	1.46256	+	0.704542i
$580$	31.5537	−	12.7325i	1.31019	−	0.528687i
$581$			17.6662i			0.732919i
$582$	−24.2419	−	18.6729i	−1.00486	−	0.774017i
$583$	−13.2224			−0.547615
$584$	−14.4437	+	20.1334i	−0.597684	+	0.833128i
$585$	15.7509	+	1.57118i	0.651219	+	0.0649602i
$586$	−12.7001	−	2.67289i	−0.524634	−	0.110416i
$587$		−	2.98768i		−	0.123315i	−0.998097	−	0.0616574i	$-0.980361\pi$
$587$		−	2.98768i		−	0.123315i	0.998097	−	0.0616574i	$-0.0196386\pi$
$588$	2.63378	−	2.25015i	0.108615	−	0.0927948i
$589$	4.69217			0.193338
$590$	−18.6188	−	27.7493i	−0.766524	−	1.14242i
$591$	−6.82294	+	14.1638i	−0.280658	+	0.582620i
$592$	9.51583	−	8.70721i	0.391098	−	0.357864i
$593$	34.2847			1.40790			0.703951	−	0.710249i	$-0.251417\pi$
$593$	34.2847			1.40790			0.703951	+	0.710249i	$0.251417\pi$
$594$	31.3094	−	0.520279i	1.28464	−	0.0213473i
$595$	−8.86564	−	8.63793i	−0.363456	−	0.354121i
$596$	−2.98008	+	6.76622i	−0.122069	+	0.277155i
$597$	10.4671	+	5.04219i	0.428390	+	0.206363i
$598$	13.0510	+	2.74676i	0.533697	+	0.112323i
$599$	29.2910			1.19680			0.598399	−	0.801198i	$-0.295804\pi$
$599$	29.2910			1.19680			0.598399	+	0.801198i	$0.295804\pi$
$600$	12.2897	+	21.1887i	0.501725	+	0.865027i
$601$	20.8808			0.851744			0.425872	−	0.904783i	$-0.359967\pi$
$601$	20.8808			0.851744			0.425872	+	0.904783i	$0.359967\pi$
$602$	11.5819	+	2.43755i	0.472041	+	0.0993473i
$603$	−4.81456	−	6.04015i	−0.196064	−	0.245974i
$604$	12.7219	−	28.8848i	0.517645	−	1.17530i
$605$	11.4646	+	11.1702i	0.466104	+	0.454132i
$606$	34.2821	+	26.4066i	1.39262	+	1.07270i
$607$	−23.7448			−0.963772			−0.481886	−	0.876234i	$-0.660048\pi$
$607$	−23.7448			−0.963772			−0.481886	+	0.876234i	$0.660048\pi$
$608$	11.4925	−	6.78960i	0.466081	−	0.275354i
$609$	−11.8724	−	5.71914i	−0.481094	−	0.231751i
$610$	−9.79243	−	14.5946i	−0.396484	−	0.590917i
$611$	−20.7023			−0.837524
$612$	8.47738	+	32.1134i	0.342678	+	1.29811i
$613$		−	27.1948i		−	1.09839i	−0.835695	−	0.549194i	$-0.814935\pi$
$613$		−	27.1948i		−	1.09839i	0.835695	−	0.549194i	$-0.185065\pi$
$614$	−17.4260	−	3.66753i	−0.703256	−	0.148009i
$615$	−8.74608	−	23.9978i	−0.352676	−	0.967685i
$616$	−9.79322	−	7.02564i	−0.394580	−	0.283071i
$617$	−2.19480			−0.0883594			−0.0441797	−	0.999024i	$-0.514067\pi$
$617$	−2.19480			−0.0883594			−0.0441797	+	0.999024i	$0.514067\pi$
$618$	6.14175	−	7.97346i	0.247057	−	0.320739i
$619$			3.84429i			0.154515i	0.997011	+	0.0772575i	$0.0246163\pi$
$619$			3.84429i			0.154515i	−0.997011	+	0.0772575i	$0.975384\pi$
$620$	−8.24675	+	3.32771i	−0.331197	+	0.133644i
$621$	4.61406	+	20.2480i	0.185156	+	0.812523i
$622$	41.0425	+	8.63793i	1.64565	+	0.346349i
$623$		−	1.70873i		−	0.0684589i
$624$	4.70829	+	15.6555i	0.188482	+	0.626722i
$625$	−24.9662	+	1.30031i	−0.998646	+	0.0520123i
$626$	−2.11329	+	10.0411i	−0.0844640	+	0.401324i
$627$	15.6904	+	7.55832i	0.626613	+	0.301850i
$628$	1.90222	−	4.31896i	0.0759070	−	0.172345i
$629$			17.8499i			0.711723i
$630$	2.86564	−	9.04368i	0.114170	−	0.360309i
$631$			29.7816i			1.18559i	0.805354	+	0.592794i	$0.201975\pi$
$631$			29.7816i			1.18559i	−0.805354	+	0.592794i	$0.798025\pi$
$632$	−4.60825	+	6.42356i	−0.183306	+	0.255515i
$633$	−2.71508	−	1.30790i	−0.107915	−	0.0519844i
$634$	−32.9439	−	6.93348i	−1.30837	−	0.275364i
$635$	11.3090	+	11.0185i	0.448785	+	0.437258i
$636$	8.17243	−	6.98206i	0.324058	−	0.276857i
$637$			2.35966i			0.0934930i
$638$	−9.44301	+	44.8677i	−0.373852	+	1.77633i
$639$	−9.22159	−	11.5690i	−0.364801	−	0.457663i
$640$	−15.3834	+	20.0836i	−0.608083	+	0.793874i
$641$		−	0.652477i		−	0.0257713i	−0.999917	−	0.0128857i	$-0.995898\pi$
$641$		−	0.652477i		−	0.0257713i	0.999917	−	0.0128857i	$-0.00410174\pi$
$642$	−11.8860	−	9.15549i	−0.469104	−	0.361338i
$643$	24.5101			0.966585			0.483293	−	0.875459i	$-0.339441\pi$
$643$	24.5101			0.966585			0.483293	+	0.875459i	$0.339441\pi$
$644$	3.22185	−	7.31516i	0.126959	−	0.288258i
$645$	30.4536	−	11.0989i	1.19911	−	0.437019i
$646$	−3.80445	+	18.0766i	−0.149684	+	0.711212i
$647$			15.8619i			0.623597i	0.950148	+	0.311799i	$0.100931\pi$
$647$			15.8619i			0.623597i	−0.950148	+	0.311799i	$0.899069\pi$
$648$	−19.0769	+	16.8545i	−0.749410	+	0.662106i
$649$	45.0302			1.76759
$650$	−16.4115	−	3.01043i	−0.643711	−	0.118079i
$651$	3.10293	+	1.49473i	0.121613	+	0.0585832i
$652$	−2.20745	−	0.972238i	−0.0864504	−	0.0380758i
$653$	8.06914			0.315770			0.157885	−	0.987458i	$-0.449532\pi$
$653$	8.06914			0.315770			0.157885	+	0.987458i	$0.449532\pi$
$654$	−21.4170	+	27.8043i	−0.837469	+	1.08724i
$655$	24.7165	+	24.0817i	0.965754	+	0.940949i
$656$	19.4617	−	17.8079i	0.759853	−	0.695283i
$657$	20.5516	−	16.3815i	0.801794	−	0.639105i
$658$	−2.55534	+	12.1415i	−0.0996175	+	0.473325i
$659$	−28.1450			−1.09637			−0.548187	−	0.836356i	$-0.684682\pi$
$659$	−28.1450			−1.09637			−0.548187	+	0.836356i	$0.684682\pi$
$660$	−32.9371	−	2.15648i	−1.28207	−	0.0839408i
$661$	21.6937			0.843788			0.421894	−	0.906645i	$-0.361365\pi$
$661$	21.6937			0.843788			0.421894	+	0.906645i	$0.361365\pi$
$662$	4.52498	−	21.5001i	0.175868	−	0.835624i
$663$	−20.3825	−	9.81863i	−0.791592	−	0.381324i
$664$	−29.1267	+	40.6005i	−1.13034	+	1.57561i
$665$	3.68209	−	3.77916i	0.142785	−	0.146550i
$666$	−12.2249	+	6.14124i	−0.473704	+	0.237968i
$667$	−30.4078			−1.17740
$668$	6.85644	−	15.5674i	0.265284	−	0.602322i
$669$	3.36226	−	6.97974i	0.129993	−	0.269852i
$670$	4.53648	+	6.76114i	0.175259	+	0.261206i
$671$	23.6833			0.914284
$672$	9.76283	−	0.828921i	0.376609	−	0.0319763i
$673$		−	20.1486i		−	0.776670i	−0.921518	−	0.388335i	$-0.873050\pi$
$673$		−	20.1486i		−	0.776670i	0.921518	−	0.388335i	$-0.126950\pi$
$674$	−7.43952	+	35.3483i	−0.286560	+	1.36157i
$675$	−6.42949	−	25.1726i	−0.247471	−	0.968895i
$676$	13.6031	+	5.99129i	0.523196	+	0.230434i
$677$	−16.5910			−0.637643			−0.318822	−	0.947815i	$-0.603287\pi$
$677$	−16.5910			−0.637643			−0.318822	+	0.947815i	$0.603287\pi$
$678$	7.80134	−	10.1280i	0.299609	−	0.388964i
$679$		−	12.4923i		−	0.479411i
$680$	−6.13346	−	34.4687i	−0.235207	−	1.32181i
$681$	11.0283	+	5.31252i	0.422605	+	0.203576i
$682$	2.46799	−	11.7265i	0.0945041	−	0.449029i
$683$			33.8254i			1.29429i	0.762366	+	0.647146i	$0.224037\pi$
$683$			33.8254i			1.29429i	−0.762366	+	0.647146i	$0.775963\pi$
$684$	−13.6890	+	3.61366i	−0.523412	+	0.138172i
$685$	30.7343	+	29.9449i	1.17430	+	1.14414i
$686$	1.38390	+	0.291259i	0.0528374	+	0.0111203i
$687$	−4.45142	+	9.24073i	−0.169832	+	0.352556i
$688$	22.5986	+	24.6973i	0.861562	+	0.941574i
$689$			7.32184i			0.278940i
$690$	−3.09922	−	21.6699i	−0.117985	−	0.824958i
$691$			9.92480i			0.377557i	0.982020	+	0.188779i	$0.0604528\pi$
$691$			9.92480i			0.377557i	−0.982020	+	0.188779i	$0.939547\pi$
$692$	18.2745	+	8.04875i	0.694694	+	0.305968i
$693$	7.96824	+	9.99662i	0.302688	+	0.379740i
$694$	4.28061	−	20.3390i	0.162490	−	0.772058i
$695$	30.6400	−	31.4477i	1.16224	−	1.19288i
$696$	−17.8559	−	32.7180i	−0.676824	−	1.24017i
$697$			36.5066i			1.38278i
$698$	−10.4779	−	2.20522i	−0.396596	−	0.0834688i
$699$	13.5169	−	28.0597i	0.511255	−	1.06132i
$700$	−3.79128	+	9.25344i	−0.143297	+	0.349747i
$701$			10.6226i			0.401212i	0.979672	+	0.200606i	$0.0642911\pi$
$701$			10.6226i			0.401212i	−0.979672	+	0.200606i	$0.935709\pi$
$702$	−0.288102	−	17.3375i	−0.0108737	−	0.654361i
$703$	−7.60890			−0.286975
$704$	−10.9234	−	32.2926i	−0.411693	−	1.21707i
$705$	11.6352	+	31.9252i	0.438208	+	1.20237i
$706$	−16.8037	−	3.53656i	−0.632416	−	0.133100i
$707$			17.6662i			0.664407i
$708$	−27.8321	+	23.7781i	−1.04599	+	0.893637i
$709$	5.71777			0.214735			0.107368	−	0.994219i	$-0.465758\pi$
$709$	5.71777			0.214735			0.107368	+	0.994219i	$0.465758\pi$
$710$	8.68896	+	12.9500i	0.326091	+	0.486004i
$711$	6.55696	−	5.22652i	0.245905	−	0.196010i
$712$	2.81722	−	3.92700i	0.105580	−	0.147171i
$713$	7.94727			0.297628
$714$	−8.27432	+	10.7421i	−0.309659	+	0.402011i
$715$	15.6904	−	16.1040i	0.586787	−	0.602256i
$716$	−46.4831	−	20.4728i	−1.73715	−	0.765104i
$717$	11.4597	−	23.7892i	0.427970	−	0.888425i
$718$	−39.0704	−	8.22289i	−1.45810	−	0.306875i
$719$	−39.0878			−1.45773			−0.728865	−	0.684657i	$-0.759952\pi$
$719$	−39.0878			−1.45773			−0.728865	+	0.684657i	$0.759952\pi$
$720$	21.4963	−	16.0595i	0.801121	−	0.598503i
$721$	4.10887			0.153022
$722$	18.5885	+	3.91220i	0.691793	+	0.145597i
$723$	−13.6123	+	28.2578i	−0.506245	+	1.05092i
$724$	16.8276	+	7.41149i	0.625395	+	0.275446i
$725$	38.0290	−	0.989658i	1.41236	−	0.0367550i
$726$	10.7000	−	13.8911i	0.397113	−	0.515548i
$727$	13.7786			0.511022			0.255511	−	0.966806i	$-0.417756\pi$
$727$	13.7786			0.511022			0.255511	+	0.966806i	$0.417756\pi$
$728$	−3.89042	+	5.42296i	−0.144188	+	0.200988i
$729$	24.3343	−	11.6979i	0.901271	−	0.433257i
$730$	−23.0048	+	15.4354i	−0.851445	+	0.571288i
$731$	−46.3274			−1.71348
$732$	−14.6381	+	12.5059i	−0.541039	+	0.462233i
$733$		−	47.8346i		−	1.76681i	−0.468608	−	0.883406i	$-0.655244\pi$
$733$		−	47.8346i		−	1.76681i	0.468608	−	0.883406i	$-0.344756\pi$
$734$	29.9606	+	6.30560i	1.10587	+	0.232744i
$735$	3.63885	−	1.32619i	0.134221	−	0.0489172i
$736$	19.4651	−	11.4997i	0.717494	−	0.423886i
$737$	−10.9716			−0.404145
$738$	−25.0022	+	12.5600i	−0.920345	+	0.462341i
$739$			21.1260i			0.777132i	0.921421	+	0.388566i	$0.127029\pi$
$739$			21.1260i			0.777132i	−0.921421	+	0.388566i	$0.872971\pi$
$740$	13.3730	−	5.39627i	0.491603	−	0.198371i
$741$	4.18539	−	8.68848i	0.153754	−	0.319179i
$742$	4.29413	+	0.903755i	0.157642	+	0.0331779i
$743$			7.09640i			0.260342i	0.991492	+	0.130171i	$0.0415526\pi$
$743$			7.09640i			0.260342i	−0.991492	+	0.130171i	$0.958447\pi$
$744$	4.66674	+	8.55106i	0.171091	+	0.313497i
$745$	−5.76848	+	5.92055i	−0.211341	+	0.216912i
$746$	4.85002	−	23.0445i	0.177572	−	0.843719i
$747$	41.4437	−	33.0346i	1.51635	−	1.20867i
$748$	43.1750	+	19.0158i	1.57864	+	0.695287i
$749$		−	6.12509i		−	0.223806i
$750$	4.58126	+	27.0002i	0.167284	+	0.985909i
$751$			9.67374i			0.353000i	0.984301	+	0.176500i	$0.0564775\pi$
$751$			9.67374i			0.353000i	−0.984301	+	0.176500i	$0.943522\pi$
$752$	−25.8906	+	23.6905i	−0.944135	+	0.863905i
$753$	9.38343	−	19.4791i	0.341951	−	0.709859i
$754$	24.8453	+	5.22903i	0.904813	+	0.190430i
$755$	24.6254	−	25.2746i	0.896212	−	0.919838i
$756$	−10.2037	−	1.97105i	−0.371104	−	0.0716863i
$757$			28.2092i			1.02528i	0.858603	+	0.512641i	$0.171333\pi$
$757$			28.2092i			1.02528i	−0.858603	+	0.512641i	$0.828667\pi$
$758$	−7.12928	+	33.8742i	−0.258947	+	1.23037i
$759$	26.5752	+	12.8018i	0.964620	+	0.464674i
$760$	14.6930	−	2.61451i	0.532970	−	0.0948383i
$761$			19.3411i			0.701114i	0.936541	+	0.350557i	$0.114008\pi$
$761$			19.3411i			0.701114i	−0.936541	+	0.350557i	$0.885992\pi$
$762$	10.5547	−	13.7026i	0.382358	−	0.496392i
$763$	−14.3281			−0.518712
$764$	−2.33244	−	1.02729i	−0.0843846	−	0.0371660i
$765$	−3.68587	+	36.9504i	−0.133263	+	1.33595i
$766$	2.59626	−	12.3359i	0.0938066	−	0.445715i
$767$		−	24.9353i		−	0.900361i
$768$	23.8036	+	14.1912i	0.858938	+	0.512080i
$769$	−14.3125			−0.516121			−0.258060	−	0.966129i	$-0.583083\pi$
$769$	−14.3125			−0.516121			−0.258060	+	0.966129i	$0.583083\pi$
$770$	−7.50800	−	11.1899i	−0.270570	−	0.403255i
$771$	−0.503833	+	1.04591i	−0.0181451	+	0.0376675i
$772$	−18.1811	+	41.2799i	−0.654352	+	1.48569i
$773$	−32.0270			−1.15193			−0.575966	−	0.817473i	$-0.695374\pi$
$773$	−32.0270			−1.15193			−0.575966	+	0.817473i	$0.695374\pi$
$774$	−15.9389	−	31.7283i	−0.572911	−	1.14045i
$775$	−9.93913	+	0.258653i	−0.357024	+	0.00929110i
$776$	20.5964	−	28.7098i	0.739366	−	1.03062i
$777$	−5.03175	−	2.42388i	−0.180513	−	0.0869563i
$778$	5.44695	−	25.8808i	0.195283	−	0.927872i
$779$	−15.5617			−0.557555
$780$	−1.19414	+	18.2388i	−0.0427571	+	0.653053i
$781$	−21.0145			−0.751959
$782$	−6.44371	+	30.6168i	−0.230426	+	1.09485i
$783$	8.78380	+	38.5462i	0.313908	+	1.37753i
$784$	2.70026	+	2.95103i	0.0964379	+	0.105394i
$785$	3.68209	−	3.77916i	0.131420	−	0.134884i
$786$	23.0680	−	29.9478i	0.822808	−	1.06820i
$787$	−1.86745			−0.0665673			−0.0332837	−	0.999446i	$-0.510596\pi$
$787$	−1.86745			−0.0665673			−0.0332837	+	0.999446i	$0.510596\pi$
$788$	−16.6136	−	7.31722i	−0.591835	−	0.260665i
$789$	−43.6802	−	21.0415i	−1.55506	−	0.749098i
$790$	−7.33965	+	4.92464i	−0.261133	+	0.175211i
$791$	5.21916			0.185572
$792$	1.83095	+	36.1116i	0.0650601	+	1.28317i
$793$		−	13.1145i		−	0.465711i
$794$	1.88302	−	8.94703i	0.0668259	−	0.317518i
$795$	11.2911	−	4.11507i	0.400453	−	0.145946i
$796$	−5.40747	+	12.2775i	−0.191663	+	0.435166i
$797$	16.3905			0.580583			0.290291	−	0.956938i	$-0.406248\pi$
$797$	16.3905			0.580583			0.290291	+	0.956938i	$0.406248\pi$
$798$	−4.57902	−	3.52710i	−0.162096	−	0.124858i
$799$		−	48.5660i		−	1.71814i
$800$	−23.9695	+	15.0155i	−0.847449	+	0.530877i
$801$	−4.00856	+	3.19520i	−0.141636	+	0.112897i
$802$	3.35303	−	15.9317i	0.118400	−	0.562567i
$803$		−	37.3309i		−	1.31738i
$804$	6.78129	−	5.79355i	0.239158	−	0.204323i
$805$	6.23647	−	6.40088i	0.219807	−	0.225601i
$806$	−6.49348	−	1.36664i	−0.228723	−	0.0481378i
$807$	11.7233	+	5.64731i	0.412679	+	0.198795i
$808$	−29.1267	+	40.6005i	−1.02467	+	1.42832i
$809$			26.4113i			0.928571i	0.885686	+	0.464285i	$0.153689\pi$
$809$			26.4113i			0.928571i	−0.885686	+	0.464285i	$0.846311\pi$
$810$	−26.5744	+	10.1884i	−0.933728	+	0.357984i
$811$			45.6077i			1.60150i	0.598997	+	0.800751i	$0.295566\pi$
$811$			45.6077i			1.60150i	−0.598997	+	0.800751i	$0.704434\pi$
$812$	6.13346	−	13.9259i	0.215242	−	0.488703i
$813$	−7.76780	−	3.74189i	−0.272429	−	0.131234i
$814$	−4.00213	+	19.0158i	−0.140274	+	0.666504i
$815$	−1.93155	−	1.88194i	−0.0676593	−	0.0659215i
$816$	−36.7267	+	11.0453i	−1.28569	+	0.386663i
$817$		−	19.7480i		−	0.690896i
$818$	3.27163	+	0.688557i	0.114390	+	0.0240748i
$819$	5.53558	−	4.41238i	0.193429	−	0.154181i
$820$	27.3505	−	11.0364i	0.955120	−	0.385408i
$821$			20.3674i			0.710826i	0.934709	+	0.355413i	$0.115660\pi$
$821$			20.3674i			0.710826i	−0.934709	+	0.355413i	$0.884340\pi$
$822$	28.6844	−	37.2392i	1.00048	−	1.29887i
$823$	22.2672			0.776187			0.388093	−	0.921620i	$-0.373134\pi$
$823$	22.2672			0.776187			0.388093	+	0.921620i	$0.373134\pi$
$824$	9.44301	+	6.77439i	0.328963	+	0.235997i
$825$	−33.6525	−	15.1454i	−1.17163	−	0.527295i
$826$	−14.6241	−	3.07783i	−0.508837	−	0.107091i
$827$		−	21.5118i		−	0.748037i	−0.927421	−	0.374018i	$-0.877980\pi$
$827$		−	21.5118i		−	0.748037i	0.927421	−	0.374018i	$-0.122020\pi$
$828$	−23.1855	+	6.12056i	−0.805750	+	0.212704i
$829$	−25.7140			−0.893086			−0.446543	−	0.894762i	$-0.647345\pi$
$829$	−25.7140			−0.893086			−0.446543	+	0.894762i	$0.647345\pi$
$830$	−46.3908	+	31.1265i	−1.61025	+	1.08042i
$831$	−35.8473	−	17.2683i	−1.24353	−	0.599029i
$832$	−17.8819	+	6.04881i	−0.619943	+	0.209705i
$833$	−5.53558			−0.191797
$834$	−38.1036	−	29.3502i	−1.31942	−	1.01631i
$835$	13.2719	−	13.6217i	0.459292	−	0.471400i
$836$	−8.10588	+	18.4042i	−0.280348	+	0.636524i
$837$	−2.29570	−	10.0743i	−0.0793511	−	0.348218i
$838$	−22.4743	−	4.73001i	−0.776362	−	0.163396i
$839$	−8.95494			−0.309159			−0.154579	−	0.987980i	$-0.549402\pi$
$839$	−8.95494			−0.309159			−0.154579	+	0.987980i	$0.549402\pi$
$840$	10.5493	+	2.95161i	0.363986	+	0.101840i
$841$	−28.8875			−0.996121
$842$	−54.9184	−	11.5583i	−1.89261	−	0.398326i
$843$	−14.6427	−	7.05364i	−0.504321	−	0.242940i
$844$	1.40265	−	3.18469i	0.0482812	−	0.109622i
$845$	11.9029	+	11.5972i	0.409473	+	0.398956i
$846$	33.2614	−	16.7091i	1.14355	−	0.574469i
$847$	7.15836			0.245964
$848$	8.37871	+	9.15683i	0.287726	+	0.314447i
$849$	−20.6486	+	42.8645i	−0.708657	+	1.47111i
$850$	7.06226	−	38.5001i	0.242233	−	1.32054i
$851$	−12.8874			−0.441775
$852$	12.9886	−	11.0967i	0.444981	−	0.380167i
$853$		−	31.3330i		−	1.07282i	−0.843957	−	0.536410i	$-0.819780\pi$
$853$		−	31.3330i		−	1.07282i	0.843957	−	0.536410i	$-0.180220\pi$
$854$	−7.69144	−	1.61876i	−0.263196	−	0.0553930i
$855$	−15.7509	−	1.57118i	−0.538669	−	0.0537331i
$856$	10.0986	−	14.0767i	0.345162	−	0.481131i
$857$	1.44596			0.0493932			0.0246966	−	0.999695i	$-0.492138\pi$
$857$	1.44596			0.0493932			0.0246966	+	0.999695i	$0.492138\pi$
$858$	−19.5124	−	15.0299i	−0.666143	−	0.513112i
$859$			39.0149i			1.33117i	0.746322	+	0.665585i	$0.231818\pi$
$859$			39.0149i			1.33117i	−0.746322	+	0.665585i	$0.768182\pi$
$860$	14.0054	+	34.7082i	0.477580	+	1.18354i
$861$	−10.2909	−	4.95731i	−0.350713	−	0.168945i
$862$	−40.0498	−	8.42900i	−1.36410	−	0.287093i
$863$			16.7184i			0.569101i	0.958661	+	0.284551i	$0.0918444\pi$
$863$			16.7184i			0.569101i	−0.958661	+	0.284551i	$0.908156\pi$
$864$	−20.2004	−	21.3529i	−0.687230	−	0.726440i
$865$	15.9905	+	15.5798i	0.543694	+	0.529729i
$866$	0.306333	−	1.45552i	0.0104096	−	0.0494606i
$867$	10.2551	−	21.2886i	0.348280	−	0.722997i
$868$	−1.60302	+	3.63962i	−0.0544100	+	0.123537i
$869$		−	11.9104i		−	0.404033i
$870$	−5.90000	−	41.2531i	−0.200029	−	1.39861i
$871$			6.07549i			0.205860i
$872$	−32.9288	−	23.6231i	−1.11511	−	0.799978i
$873$	−29.3061	+	23.3597i	−0.991861	+	0.790606i
$874$	−13.0510	−	2.74676i	−0.441458	−	0.0929106i
$875$	−7.59122	+	8.20813i	−0.256630	+	0.277485i
$876$	19.7125	+	23.0733i	0.666025	+	0.779576i
$877$			55.7676i			1.88314i	0.336821	+	0.941569i	$0.390648\pi$
$877$			55.7676i			1.88314i	−0.336821	+	0.941569i	$0.609352\pi$
$878$	10.2758	−	48.8247i	0.346791	−	1.64775i
$879$	−6.89828	+	14.3202i	−0.232673	+	0.483007i
$880$	1.19414	−	38.0952i	0.0402544	−	1.28419i
$881$			14.0011i			0.471709i	0.971788	+	0.235855i	$0.0757889\pi$
$881$			14.0011i			0.471709i	−0.971788	+	0.235855i	$0.924211\pi$
$882$	−1.90451	−	3.79115i	−0.0641282	−	0.127655i
$883$	−10.1633			−0.342023			−0.171011	−	0.985269i	$-0.554703\pi$
$883$	−10.1633			−0.342023			−0.171011	+	0.985269i	$0.554703\pi$
$884$	10.5299	−	23.9080i	0.354160	−	0.804113i
$885$	−38.4529	+	14.0143i	−1.29258	+	0.471085i
$886$	−11.4085	+	54.2068i	−0.383277	+	1.82111i
$887$		−	15.5039i		−	0.520570i	−0.965532	−	0.260285i	$-0.916184\pi$
$887$		−	15.5039i		−	0.520570i	0.965532	−	0.260285i	$-0.0838165\pi$
$888$	−7.56765	−	13.8665i	−0.253954	−	0.465330i
$889$	7.06120			0.236825
$890$	4.48705	−	3.01065i	0.150406	−	0.100917i
$891$	8.55132	−	37.3858i	0.286480	−	1.25247i
$892$	8.18699	+	3.60584i	0.274121	+	0.120732i
$893$	20.7023			0.692775
$894$	7.17364	+	5.52567i	0.239922	+	0.184806i
$895$	−40.6734	−	39.6287i	−1.35956	−	1.32464i
$896$	1.34030	+	11.2340i	0.0447764	+	0.375303i
$897$	7.08892	−	14.7159i	0.236692	−	0.491351i
$898$	−8.35551	+	39.7006i	−0.278827	+	1.32482i
$899$	15.1293			0.504589
$900$	28.7973	−	8.40918i	0.959911	−	0.280306i
$901$	−17.1765			−0.572232
$902$	−8.18513	+	38.8910i	−0.272535	+	1.29493i
$903$	6.29091	−	13.0593i	0.209348	−	0.434587i
$904$	11.9947	+	8.60494i	0.398936	+	0.286196i
$905$	14.7245	+	14.3463i	0.489458	+	0.476886i
$906$	−30.6240	−	23.5889i	−1.01741	−	0.783687i
$907$	−11.3029			−0.375306			−0.187653	−	0.982235i	$-0.560088\pi$
$907$	−11.3029			−0.375306			−0.187653	+	0.982235i	$0.560088\pi$
$908$	−5.69737	+	12.9358i	−0.189074	+	0.429289i
$909$	41.4437	−	33.0346i	1.37460	−	1.09569i
$910$	−6.19635	+	4.15752i	−0.205407	+	0.137821i
$911$	17.7939			0.589538			0.294769	−	0.955569i	$-0.404757\pi$
$911$	17.7939			0.589538			0.294769	+	0.955569i	$0.404757\pi$
$912$	−4.70829	−	15.6555i	−0.155907	−	0.518406i
$913$		−	75.2805i		−	2.49142i
$914$	−1.03323	+	4.90931i	−0.0341762	+	0.162386i
$915$	−20.2241	+	7.37072i	−0.668587	+	0.243668i
$916$	−10.8390	−	4.77390i	−0.358132	−	0.157734i
$917$	15.4327			0.509631
$918$	40.6725	−	0.675868i	1.34239	−	0.0223070i
$919$			8.27687i			0.273029i	0.990638	+	0.136514i	$0.0435900\pi$
$919$			8.27687i			0.273029i	−0.990638	+	0.136514i	$0.956410\pi$
$920$	24.8859	−	4.42828i	0.820464	−	0.145996i
$921$	−9.46526	+	19.6490i	−0.311891	+	0.647456i
$922$	−2.81522	+	13.3763i	−0.0927145	+	0.440526i
$923$			11.6367i			0.383027i
$924$	−11.2232	+	9.58849i	−0.369217	+	0.315438i
$925$	16.1174	−	0.419436i	0.529938	−	0.0137910i
$926$	14.9662	+	3.14984i	0.491821	+	0.103510i
$927$	−7.68329	−	9.63912i	−0.252352	−	0.316590i
$928$	37.0559	−	21.8921i	1.21642	−	0.718644i
$929$			24.1545i			0.792484i	0.918146	+	0.396242i	$0.129686\pi$
$929$			24.1545i			0.792484i	−0.918146	+	0.396242i	$0.870314\pi$
$930$	1.54200	+	10.7817i	0.0505643	+	0.353547i
$931$		−	2.35966i		−	0.0773346i
$932$	32.9131	+	14.4961i	1.07810	+	0.474835i
$933$	22.2930	−	46.2782i	0.729840	−	1.51508i
$934$	−6.21521	+	29.5311i	−0.203368	+	0.966288i
$935$	37.7788	+	36.8085i	1.23550	+	1.20377i
$936$	19.9967	−	1.01388i	0.653611	−	0.0331398i
$937$		−	11.3880i		−	0.372031i	−0.982547	−	0.186015i	$-0.940443\pi$
$937$		−	11.3880i		−	0.372031i	0.982547	−	0.186015i	$-0.0595574\pi$
$938$	3.56317	+	0.749915i	0.116342	+	0.0244856i
$939$	11.3221	+	5.45403i	0.369481	+	0.177986i
$940$	−36.3853	+	14.6821i	−1.18676	+	0.478879i
$941$		−	50.5703i		−	1.64855i	−0.566192	−	0.824273i	$-0.691584\pi$
$941$		−	50.5703i		−	1.64855i	0.566192	−	0.824273i	$-0.308416\pi$
$942$	−4.57902	−	3.52710i	−0.149193	−	0.114919i
$943$	−26.3573			−0.858311
$944$	−28.5346	−	31.1845i	−0.928721	−	1.01497i
$945$	−9.91552	−	6.05660i	−0.322552	−	0.197021i
$946$	−49.3533	−	10.3871i	−1.60462	−	0.337712i
$947$			13.4542i			0.437204i	0.975814	+	0.218602i	$0.0701496\pi$
$947$			13.4542i			0.437204i	−0.975814	+	0.218602i	$0.929850\pi$
$948$	6.28927	+	7.36153i	0.204266	+	0.239091i
$949$	−20.6719			−0.671037
$950$	16.4115	+	3.01043i	0.532458	+	0.0976713i
$951$	−17.8941	+	37.1465i	−0.580256	+	1.20456i
$952$	−12.7219	−	9.12664i	−0.412318	−	0.295796i
$953$	−32.0027			−1.03667			−0.518334	−	0.855178i	$-0.673448\pi$
$953$	−32.0027			−1.03667			−0.518334	+	0.855178i	$0.673448\pi$
$954$	−5.90955	−	11.7637i	−0.191329	−	0.380863i
$955$	−2.04092	−	1.98850i	−0.0660426	−	0.0643463i
$956$	27.9039	+	12.2899i	0.902477	+	0.397483i
$957$	50.5914	+	24.3708i	1.63539	+	0.787795i
$958$	−4.32315	−	0.909864i	−0.139675	−	0.0293964i
$959$	19.1901			0.619680
$960$	19.3780	+	24.1763i	0.625423	+	0.780286i
$961$	27.0459			0.872448
$962$	10.5299	+	2.21616i	0.339498	+	0.0714519i
$963$	−14.3690	+	11.4535i	−0.463035	+	0.369083i
$964$	−33.1453	−	14.5984i	−1.06754	−	0.470182i
$965$	−35.1928	+	36.1205i	−1.13290	+	1.16276i
$966$	−7.75562	−	5.97395i	−0.249533	−	0.192209i
$967$	−26.7128			−0.859025			−0.429512	−	0.903061i	$-0.641315\pi$
$967$	−26.7128			−0.859025			−0.429512	+	0.903061i	$0.641315\pi$
$968$	16.4513	+	11.8021i	0.528765	+	0.379335i
$969$	20.3825	+	9.81863i	0.654782	+	0.315420i
$970$	32.8043	−	22.0105i	1.05328	−	0.706713i
$971$	−36.2660			−1.16383			−0.581915	−	0.813249i	$-0.697697\pi$
$971$	−36.2660			−1.16383			−0.581915	+	0.813249i	$0.697697\pi$
$972$	14.4562	+	27.6228i	0.463682	+	0.886002i
$973$		−	19.6355i		−	0.629486i
$974$	−9.88522	−	2.08047i	−0.316743	−	0.0666627i
$975$	−8.38670	+	18.6350i	−0.268589	+	0.596796i
$976$	−15.0076	−	16.4013i	−0.480380	−	0.524993i
$977$	20.2293			0.647192			0.323596	−	0.946195i	$-0.395108\pi$
$977$	20.2293			0.647192			0.323596	+	0.946195i	$0.395108\pi$
$978$	−1.80272	+	2.34037i	−0.0576447	+	0.0748366i
$979$			7.28136i			0.232713i
$980$	1.67348	+	4.14722i	0.0534574	+	0.132478i
$981$	26.7925	+	33.6127i	0.855418	+	1.07317i
$982$	6.41584	+	1.35030i	0.204738	+	0.0430898i
$983$		−	27.9495i		−	0.891452i	−0.895169	−	0.445726i	$-0.852946\pi$
$983$		−	27.9495i		−	0.891452i	0.895169	−	0.445726i	$-0.147054\pi$
$984$	−15.4773	−	28.3597i	−0.493399	−	0.904075i
$985$	−14.5372	−	14.1638i	−0.463193	−	0.451296i
$986$	−12.2669	+	58.2853i	−0.390658	+	1.85618i
$987$	13.6904	+	6.59489i	0.435769	+	0.209918i
$988$	10.1913	+	4.48860i	0.324228	+	0.142801i
$989$		−	33.4478i		−	1.06358i
$990$	−12.2113	+	38.5375i	−0.388099	+	1.22480i
$991$		−	58.2259i		−	1.84961i	−0.380444	−	0.924804i	$-0.624229\pi$
$991$		−	58.2259i		−	1.84961i	0.380444	−	0.924804i	$-0.375771\pi$
$992$	−9.68478	+	5.72164i	−0.307492	+	0.181662i
$993$	−24.2428	−	11.6782i	−0.769322	−	0.370596i
$994$	6.82472	+	1.43635i	0.216467	+	0.0455584i
$995$	−10.4671	+	10.7431i	−0.331830	+	0.340578i
$996$	39.7518	+	46.5290i	1.25958	+	1.47433i
$997$			40.3711i			1.27856i	0.768972	+	0.639282i	$0.220768\pi$
$997$			40.3711i			1.27856i	−0.768972	+	0.639282i	$0.779232\pi$
$998$	5.60406	−	26.6273i	0.177393	−	0.842872i
$999$	3.72274	+	16.3366i	0.117782	+	0.516867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.l.h.239.16	yes	16
3.2	odd	2	inner	420.2.l.h.239.1	yes	16
4.3	odd	2		420.2.l.g.239.15	yes	16
5.4	even	2		420.2.l.g.239.1	✓	16
12.11	even	2		420.2.l.g.239.2	yes	16
15.14	odd	2		420.2.l.g.239.16	yes	16
20.19	odd	2	inner	420.2.l.h.239.2	yes	16
60.59	even	2	inner	420.2.l.h.239.15	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.l.g.239.1	✓	16	5.4	even	2
420.2.l.g.239.2	yes	16	12.11	even	2
420.2.l.g.239.15	yes	16	4.3	odd	2
420.2.l.g.239.16	yes	16	15.14	odd	2
420.2.l.h.239.1	yes	16	3.2	odd	2	inner
420.2.l.h.239.2	yes	16	20.19	odd	2	inner
420.2.l.h.239.15	yes	16	60.59	even	2	inner
420.2.l.h.239.16	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)

\(f(q)\)	\(=\)	\(q+(1.38390 + 0.291259i) q^{2} +(0.751690 - 1.56044i) q^{3} +(1.83034 + 0.806145i) q^{4} +(1.60157 + 1.56044i) q^{5} +(1.49475 - 1.94055i) q^{6} +1.00000 q^{7} +(2.29820 + 1.64872i) q^{8} +(-1.86993 - 2.34593i) q^{9} +O(q^{10})\)	\(q+(1.38390 + 0.291259i) q^{2} +(0.751690 - 1.56044i) q^{3} +(1.83034 + 0.806145i) q^{4} +(1.60157 + 1.56044i) q^{5} +(1.49475 - 1.94055i) q^{6} +1.00000 q^{7} +(2.29820 + 1.64872i) q^{8} +(-1.86993 - 2.34593i) q^{9} +(1.76192 + 2.62595i) q^{10} -4.26126 q^{11} +(2.63378 - 2.25015i) q^{12} +2.35966i q^{13} +(1.38390 + 0.291259i) q^{14} +(3.63885 - 1.32619i) q^{15} +(2.70026 + 2.95103i) q^{16} -5.53558 q^{17} +(-1.90451 - 3.79115i) q^{18} -2.35966i q^{19} +(1.67348 + 4.14722i) q^{20} +(0.751690 - 1.56044i) q^{21} +(-5.89714 - 1.24113i) q^{22} -3.99662i q^{23} +(4.30026 - 2.34686i) q^{24} +(0.130075 + 4.99831i) q^{25} +(-0.687271 + 3.26552i) q^{26} +(-5.06628 + 1.15449i) q^{27} +(1.83034 + 0.806145i) q^{28} -7.60838i q^{29} +(5.42205 - 0.775461i) q^{30} +1.98850i q^{31} +(2.87737 + 4.87040i) q^{32} +(-3.20315 + 6.64943i) q^{33} +(-7.66067 - 1.61229i) q^{34} +(1.60157 + 1.56044i) q^{35} +(-1.53143 - 5.80127i) q^{36} -3.22458i q^{37} +(0.687271 - 3.26552i) q^{38} +(3.68209 + 1.77373i) q^{39} +(1.10801 + 6.22674i) q^{40} -6.59489i q^{41} +(1.49475 - 1.94055i) q^{42} +8.36902 q^{43} +(-7.79954 - 3.43519i) q^{44} +(0.665850 - 6.67508i) q^{45} +(1.16405 - 5.53091i) q^{46} +8.77342i q^{47} +(6.63466 - 1.99533i) q^{48} +1.00000 q^{49} +(-1.27579 + 6.95502i) q^{50} +(-4.16104 + 8.63793i) q^{51} +(-1.90222 + 4.31896i) q^{52} +3.10293 q^{53} +(-7.34745 + 0.122095i) q^{54} +(-6.82472 - 6.64943i) q^{55} +(2.29820 + 1.64872i) q^{56} +(-3.68209 - 1.77373i) q^{57} +(2.21601 - 10.5292i) q^{58} -10.5673 q^{59} +(7.72942 + 0.506065i) q^{60} -5.55782 q^{61} +(-0.579168 + 2.75187i) q^{62} +(-1.86993 - 2.34593i) q^{63} +(2.56343 + 7.57818i) q^{64} +(-3.68209 + 3.77916i) q^{65} +(-6.36953 + 8.26917i) q^{66} +2.57474 q^{67} +(-10.1320 - 4.46248i) q^{68} +(-6.23647 - 3.00422i) q^{69} +(1.76192 + 2.62595i) q^{70} +4.93153 q^{71} +(-0.429674 - 8.47440i) q^{72} +8.76054i q^{73} +(0.939188 - 4.46248i) q^{74} +(7.89732 + 3.55420i) q^{75} +(1.90222 - 4.31896i) q^{76} -4.26126 q^{77} +(4.57902 + 3.52710i) q^{78} +2.79504i q^{79} +(-0.280231 + 8.93988i) q^{80} +(-2.00676 + 8.77342i) q^{81} +(1.92082 - 9.12664i) q^{82} +17.6662i q^{83} +(2.63378 - 2.25015i) q^{84} +(-8.86564 - 8.63793i) q^{85} +(11.5819 + 2.43755i) q^{86} +(-11.8724 - 5.71914i) q^{87} +(-9.79322 - 7.02564i) q^{88} -1.70873i q^{89} +(2.86564 - 9.04368i) q^{90} +2.35966i q^{91} +(3.22185 - 7.31516i) q^{92} +(3.10293 + 1.49473i) q^{93} +(-2.55534 + 12.1415i) q^{94} +(3.68209 - 3.77916i) q^{95} +(9.76283 - 0.828921i) q^{96} -12.4923i q^{97} +(1.38390 + 0.291259i) q^{98} +(7.96824 + 9.99662i) 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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