LMFDB - Embedded newform 280.2.ba.b.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(19,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 5]))

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

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

chi := DirichletCharacter("280.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.4
Character	$\chi$	$=$	280.19
Dual form			280.2.ba.b.59.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36769 + 0.359747i) q^{2} +(-1.46528 - 2.53794i) q^{3} +(1.74116 - 0.984045i) q^{4} +(-1.36405 + 1.77183i) q^{5} +(2.91706 + 2.94399i) q^{6} +(1.45426 + 2.21023i) q^{7} +(-2.02737 + 1.97225i) q^{8} +(-2.79408 + 4.83948i) q^{9} +O(q^{10})$	\(q+(-1.36769 + 0.359747i) q^{2} +(-1.46528 - 2.53794i) q^{3} +(1.74116 - 0.984045i) q^{4} +(-1.36405 + 1.77183i) q^{5} +(2.91706 + 2.94399i) q^{6} +(1.45426 + 2.21023i) q^{7} +(-2.02737 + 1.97225i) q^{8} +(-2.79408 + 4.83948i) q^{9} +(1.22819 - 2.91403i) q^{10} +(-1.55174 - 2.68769i) q^{11} +(-5.04873 - 2.97706i) q^{12} +1.62644i q^{13} +(-2.78410 - 2.49975i) q^{14} +(6.49549 + 0.865643i) q^{15} +(2.06331 - 3.42677i) q^{16} +(2.52573 + 4.37469i) q^{17} +(2.08045 - 7.62408i) q^{18} +(6.55731 + 3.78587i) q^{19} +(-0.631472 + 4.42733i) q^{20} +(3.47853 - 6.92942i) q^{21} +(3.08919 + 3.11770i) q^{22} +(1.55633 - 2.69565i) q^{23} +(7.97610 + 2.25544i) q^{24} +(-1.27875 - 4.83371i) q^{25} +(-0.585108 - 2.22448i) q^{26} +7.58472 q^{27} +(4.70707 + 2.41732i) q^{28} +0.389298i q^{29} +(-9.19525 + 1.15280i) q^{30} +(3.31666 + 5.74462i) q^{31} +(-1.58920 + 5.42904i) q^{32} +(-4.54746 + 7.87643i) q^{33} +(-5.02820 - 5.07461i) q^{34} +(-5.89983 - 0.438163i) q^{35} +(-0.102678 + 11.1758i) q^{36} +(-0.553818 + 0.959241i) q^{37} +(-10.3303 - 2.81893i) q^{38} +(4.12781 - 2.38319i) q^{39} +(-0.729058 - 6.28239i) q^{40} -0.928523i q^{41} +(-2.26473 + 10.7287i) q^{42} -3.21202i q^{43} +(-5.34664 - 3.15273i) q^{44} +(-4.76348 - 11.5519i) q^{45} +(-1.15883 + 4.24670i) q^{46} +(2.82412 + 1.63050i) q^{47} +(-11.7202 - 0.215377i) q^{48} +(-2.77026 + 6.42850i) q^{49} +(3.48785 + 6.15101i) q^{50} +(7.40178 - 12.8203i) q^{51} +(1.60049 + 2.83191i) q^{52} +(5.44437 + 9.42993i) q^{53} +(-10.3736 + 2.72858i) q^{54} +(6.87877 + 0.916722i) q^{55} +(-7.30745 - 1.61280i) q^{56} -22.1894i q^{57} +(-0.140049 - 0.532440i) q^{58} +(-5.71232 + 3.29801i) q^{59} +(12.1616 - 4.88463i) q^{60} +(-3.21046 + 5.56068i) q^{61} +(-6.60277 - 6.66371i) q^{62} +(-14.7597 + 0.862304i) q^{63} +(0.220465 - 7.99696i) q^{64} +(-2.88178 - 2.21855i) q^{65} +(3.38600 - 12.4085i) q^{66} +(-2.80208 + 1.61778i) q^{67} +(8.70260 + 5.13162i) q^{68} -9.12183 q^{69} +(8.22678 - 1.52317i) q^{70} +7.22771i q^{71} +(-3.88004 - 15.3220i) q^{72} +(1.58632 + 2.74759i) q^{73} +(0.412369 - 1.51118i) q^{74} +(-10.3939 + 10.3281i) q^{75} +(15.1428 + 0.139124i) q^{76} +(3.68379 - 7.33831i) q^{77} +(-4.78823 + 4.74444i) q^{78} +(-6.81139 - 3.93256i) q^{79} +(3.25720 + 8.33011i) q^{80} +(-2.73150 - 4.73109i) q^{81} +(0.334033 + 1.26993i) q^{82} +10.3353 q^{83} +(-0.762164 - 15.4883i) q^{84} +(-11.1964 - 1.49213i) q^{85} +(1.15551 + 4.39306i) q^{86} +(0.988013 - 0.570429i) q^{87} +(8.44675 + 2.38853i) q^{88} +(-9.69972 - 5.60014i) q^{89} +(10.6707 + 14.0858i) q^{90} +(-3.59482 + 2.36527i) q^{91} +(0.0571926 - 6.22506i) q^{92} +(9.71964 - 16.8349i) q^{93} +(-4.44909 - 1.21406i) q^{94} +(-15.6524 + 6.45433i) q^{95} +(16.1072 - 3.92175i) q^{96} +10.5782 q^{97} +(1.47623 - 9.78881i) q^{98} +17.3427 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 6 q^{4} - 52 q^{9}+O(q^{10}) $ 80 * q + 6 * q^4 - 52 * q^9	$ 80 q + 6 q^{4} - 52 q^{9} - 12 q^{10} - 6 q^{14} + 10 q^{16} - 48 q^{19} + 12 q^{24} - 22 q^{25} + 54 q^{26} - 20 q^{30} - 22 q^{35} + 28 q^{36} + 12 q^{40} + 38 q^{44} + 14 q^{46} + 16 q^{49} - 40 q^{50} + 20 q^{51} + 60 q^{54} - 104 q^{56} - 60 q^{59} - 42 q^{60} - 60 q^{64} - 12 q^{65} + 84 q^{66} - 22 q^{70} + 34 q^{74} - 6 q^{75} - 96 q^{80} - 100 q^{84} - 8 q^{86} - 36 q^{89} + 72 q^{91} - 66 q^{94} + 96 q^{96} + 104 q^{99}+O(q^{100}) $ 80 * q + 6 * q^4 - 52 * q^9 - 12 * q^10 - 6 * q^14 + 10 * q^16 - 48 * q^19 + 12 * q^24 - 22 * q^25 + 54 * q^26 - 20 * q^30 - 22 * q^35 + 28 * q^36 + 12 * q^40 + 38 * q^44 + 14 * q^46 + 16 * q^49 - 40 * q^50 + 20 * q^51 + 60 * q^54 - 104 * q^56 - 60 * q^59 - 42 * q^60 - 60 * q^64 - 12 * q^65 + 84 * q^66 - 22 * q^70 + 34 * q^74 - 6 * q^75 - 96 * q^80 - 100 * q^84 - 8 * q^86 - 36 * q^89 + 72 * q^91 - 66 * q^94 + 96 * q^96 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.36769	+	0.359747i	−0.967105	+	0.254379i
$2$	−1.36769	+	0.359747i	−0.967105	+	0.254379i
$3$	−1.46528	−	2.53794i	−0.845978	−	1.46528i	−0.884769	−	0.466030i	$-0.845684\pi$
$3$	−1.46528	−	2.53794i	−0.845978	−	1.46528i	0.0387905	−	0.999247i	$-0.487650\pi$
$4$	1.74116	−	0.984045i	0.870582	−	0.492023i
$5$	−1.36405	+	1.77183i	−0.610020	+	0.792386i
$5$	−1.36405	+	1.77183i	−0.610020	+	0.792386i
$6$	2.91706	+	2.94399i	1.19089	+	1.20188i
$7$	1.45426	+	2.21023i	0.549658	+	0.835389i
$7$	1.45426	+	2.21023i	0.549658	+	0.835389i
$8$	−2.02737	+	1.97225i	−0.716784	+	0.697295i
$9$	−2.79408	+	4.83948i	−0.931359	+	1.61316i
$10$	1.22819	−	2.91403i	0.388387	−	0.921496i
$11$	−1.55174	−	2.68769i	−0.467867	−	0.810369i	0.531459	−	0.847084i	$-0.321644\pi$
$11$	−1.55174	−	2.68769i	−0.467867	−	0.810369i	−0.999326	+	0.0367148i	$0.988311\pi$
$12$	−5.04873	−	2.97706i	−1.45744	−	0.859404i
$13$			1.62644i			0.451094i	0.974232	+	0.225547i	$0.0724170\pi$
$13$			1.62644i			0.451094i	−0.974232	+	0.225547i	$0.927583\pi$
$14$	−2.78410	−	2.49975i	−0.744083	−	0.668087i
$15$	6.49549	+	0.865643i	1.67713	+	0.223508i
$16$	2.06331	−	3.42677i	0.515827	−	0.856693i
$17$	2.52573	+	4.37469i	0.612579	+	1.06102i	0.990804	+	0.135304i	$0.0432011\pi$
$17$	2.52573	+	4.37469i	0.612579	+	1.06102i	−0.378225	+	0.925714i	$0.623466\pi$
$18$	2.08045	−	7.62408i	0.490367	−	1.79701i
$19$	6.55731	+	3.78587i	1.50435	+	0.868537i	0.999987	+	0.00504564i	$0.00160608\pi$
$19$	6.55731	+	3.78587i	1.50435	+	0.868537i	0.504363	+	0.863492i	$0.331727\pi$
$20$	−0.631472	+	4.42733i	−0.141201	+	0.989981i
$21$	3.47853	−	6.92942i	0.759078	−	1.51212i
$22$	3.08919	+	3.11770i	0.658617	+	0.664696i
$23$	1.55633	−	2.69565i	0.324518	−	0.562081i	−0.656897	−	0.753980i	$-0.728131\pi$
$23$	1.55633	−	2.69565i	0.324518	−	0.562081i	0.981415	+	0.191899i	$0.0614647\pi$
$24$	7.97610	+	2.25544i	1.62811	+	0.460390i
$25$	−1.27875	−	4.83371i	−0.255750	−	0.966743i
$26$	−0.585108	−	2.22448i	−0.114749	−	0.436256i
$27$	7.58472			1.45968
$28$	4.70707	+	2.41732i	0.889554	+	0.456831i
$29$			0.389298i			0.0722908i	0.999347	+	0.0361454i	$0.0115079\pi$
$29$			0.389298i			0.0722908i	−0.999347	+	0.0361454i	$0.988492\pi$
$30$	−9.19525	+	1.15280i	−1.67881	+	0.210471i
$31$	3.31666	+	5.74462i	0.595689	+	1.03176i	0.993449	+	0.114274i	$0.0364542\pi$
$31$	3.31666	+	5.74462i	0.595689	+	1.03176i	−0.397760	+	0.917489i	$0.630212\pi$
$32$	−1.58920	+	5.42904i	−0.280934	+	0.959727i
$33$	−4.54746	+	7.87643i	−0.791611	+	1.37111i
$34$	−5.02820	−	5.07461i	−0.862329	−	0.870288i
$35$	−5.89983	−	0.438163i	−0.997254	−	0.0740631i
$36$	−0.102678	+	11.1758i	−0.0171130	+	1.86264i
$37$	−0.553818	+	0.959241i	−0.0910471	+	0.157698i	−0.907952	−	0.419074i	$-0.862355\pi$
$37$	−0.553818	+	0.959241i	−0.0910471	+	0.157698i	0.816905	+	0.576772i	$0.195688\pi$
$38$	−10.3303	−	2.81893i	−1.67580	−	0.457291i
$39$	4.12781	−	2.38319i	0.660979	−	0.381616i
$40$	−0.729058	−	6.28239i	−0.115274	−	0.993334i
$41$		−	0.928523i		−	0.145011i	−0.997368	−	0.0725055i	$-0.976901\pi$
$41$		−	0.928523i		−	0.145011i	0.997368	−	0.0725055i	$-0.0230995\pi$
$42$	−2.26473	+	10.7287i	−0.349455	+	1.65548i
$43$		−	3.21202i		−	0.489829i	−0.969545	−	0.244914i	$-0.921240\pi$
$43$		−	3.21202i		−	0.489829i	0.969545	−	0.244914i	$-0.0787598\pi$
$44$	−5.34664	−	3.15273i	−0.806037	−	0.475292i
$45$	−4.76348	−	11.5519i	−0.710098	−	1.72206i
$46$	−1.15883	+	4.24670i	−0.170861	+	0.626142i
$47$	2.82412	+	1.63050i	0.411940	+	0.237833i	0.691623	−	0.722259i	$-0.256896\pi$
$47$	2.82412	+	1.63050i	0.411940	+	0.237833i	−0.279683	+	0.960092i	$0.590229\pi$
$48$	−11.7202	−	0.215377i	−1.69167	−	0.0310870i
$49$	−2.77026	+	6.42850i	−0.395751	+	0.918358i
$50$	3.48785	+	6.15101i	0.493256	+	0.869884i
$51$	7.40178	−	12.8203i	1.03646	−	1.79520i
$52$	1.60049	+	2.83191i	0.221949	+	0.392715i
$53$	5.44437	+	9.42993i	0.747842	+	1.29530i	0.948855	+	0.315712i	$0.102243\pi$
$53$	5.44437	+	9.42993i	0.747842	+	1.29530i	−0.201013	+	0.979589i	$0.564423\pi$
$54$	−10.3736	+	2.72858i	−1.41166	+	0.371313i
$55$	6.87877	+	0.916722i	0.927533	+	0.123611i
$56$	−7.30745	−	1.61280i	−0.976500	−	0.215519i
$57$		−	22.1894i		−	2.93905i
$58$	−0.140049	−	0.532440i	−0.0183893	−	0.0699128i
$59$	−5.71232	+	3.29801i	−0.743681	+	0.429364i	−0.823406	−	0.567453i	$-0.807929\pi$
$59$	−5.71232	+	3.29801i	−0.743681	+	0.429364i	0.0797253	+	0.996817i	$0.474596\pi$
$60$	12.1616	−	4.88463i	1.57005	−	0.630603i
$61$	−3.21046	+	5.56068i	−0.411058	+	0.711973i	−0.995006	−	0.0998183i	$-0.968174\pi$
$61$	−3.21046	+	5.56068i	−0.411058	+	0.711973i	0.583948	+	0.811791i	$0.301507\pi$
$62$	−6.60277	−	6.66371i	−0.838553	−	0.846292i
$63$	−14.7597	+	0.862304i	−1.85955	+	0.108640i
$64$	0.220465	−	7.99696i	0.0275582	−	0.999620i
$65$	−2.88178	−	2.21855i	−0.357441	−	0.275177i
$66$	3.38600	−	12.4085i	0.416788	−	1.52738i
$67$	−2.80208	+	1.61778i	−0.342329	+	0.197644i	−0.661301	−	0.750120i	$-0.729996\pi$
$67$	−2.80208	+	1.61778i	−0.342329	+	0.197644i	0.318973	+	0.947764i	$0.396662\pi$
$68$	8.70260	+	5.13162i	1.05534	+	0.622301i
$69$	−9.12183			−1.09814
$70$	8.22678	−	1.52317i	0.983289	−	0.182054i
$71$			7.22771i			0.857771i	0.903359	+	0.428886i	$0.141094\pi$
$71$			7.22771i			0.857771i	−0.903359	+	0.428886i	$0.858906\pi$
$72$	−3.88004	−	15.3220i	−0.457267	−	1.80572i
$73$	1.58632	+	2.74759i	0.185665	+	0.321581i	0.943800	−	0.330516i	$-0.107223\pi$
$73$	1.58632	+	2.74759i	0.185665	+	0.321581i	−0.758136	+	0.652097i	$0.773890\pi$
$74$	0.412369	−	1.51118i	0.0479369	−	0.175671i
$75$	−10.3939	+	10.3281i	−1.20019	+	1.19259i
$76$	15.1428	+	0.139124i	1.73700	+	0.0159587i
$77$	3.68379	−	7.33831i	0.419807	−	0.836278i
$78$	−4.78823	+	4.74444i	−0.542160	+	0.537202i
$79$	−6.81139	−	3.93256i	−0.766342	−	0.442448i	0.0652264	−	0.997870i	$-0.479223\pi$
$79$	−6.81139	−	3.93256i	−0.766342	−	0.442448i	−0.831568	+	0.555423i	$0.812556\pi$
$80$	3.25720	+	8.33011i	0.364166	+	0.931334i
$81$	−2.73150	−	4.73109i	−0.303500	−	0.525677i
$82$	0.334033	+	1.26993i	0.0368878	+	0.140241i
$83$	10.3353			1.13444			0.567221	−	0.823566i	$-0.308019\pi$
$83$	10.3353			1.13444			0.567221	+	0.823566i	$0.308019\pi$
$84$	−0.762164	−	15.4883i	−0.0831589	−	1.68991i
$85$	−11.1964	−	1.49213i	−1.21442	−	0.161844i
$86$	1.15551	+	4.39306i	0.124602	+	0.473716i
$87$	0.988013	−	0.570429i	0.105926	−	0.0611565i
$88$	8.44675	+	2.38853i	0.900426	+	0.254618i
$89$	−9.69972	−	5.60014i	−1.02817	−	0.593613i	−0.111709	−	0.993741i	$-0.535632\pi$
$89$	−9.69972	−	5.60014i	−1.02817	−	0.593613i	−0.916459	+	0.400128i	$0.868966\pi$
$90$	10.6707	+	14.0858i	1.12479	+	1.48477i
$91$	−3.59482	+	2.36527i	−0.376840	+	0.247948i
$92$	0.0571926	−	6.22506i	0.00596275	−	0.649008i
$93$	9.71964	−	16.8349i	1.00788	−	1.74570i
$94$	−4.44909	−	1.21406i	−0.458888	−	0.125221i
$95$	−15.6524	+	6.45433i	−1.60590	+	0.662200i
$96$	16.1072	−	3.92175i	1.64393	−	0.400262i
$97$	10.5782			1.07405			0.537025	−	0.843566i	$-0.319548\pi$
$97$	10.5782			1.07405			0.537025	+	0.843566i	$0.319548\pi$
$98$	1.47623	−	9.78881i	0.149122	−	0.988819i
$99$	17.3427			1.74301
$100$	−6.98311	−	7.15794i	−0.698311	−	0.715794i
$101$	2.43704	+	4.22108i	0.242495	+	0.420013i	0.961424	−	0.275070i	$-0.0887009\pi$
$101$	2.43704	+	4.22108i	0.242495	+	0.420013i	−0.718929	+	0.695083i	$0.755368\pi$
$102$	−5.51132	+	20.1969i	−0.545702	+	1.99980i
$103$	−10.9818	−	6.34034i	−1.08207	−	0.624732i	−0.150614	−	0.988593i	$-0.548125\pi$
$103$	−10.9818	−	6.34034i	−1.08207	−	0.624732i	−0.931454	+	0.363860i	$0.881459\pi$
$104$	−3.20775	−	3.29741i	−0.314546	−	0.323337i
$105$	7.53286	+	15.6154i	0.735132	+	1.52391i
$106$	−10.8386	−	10.9386i	−1.05274	−	1.06246i
$107$	−7.60939	−	4.39329i	−0.735628	−	0.424715i	0.0848496	−	0.996394i	$-0.472959\pi$
$107$	−7.60939	−	4.39329i	−0.735628	−	0.424715i	−0.820477	+	0.571679i	$0.806292\pi$
$108$	13.2063	−	7.46371i	1.27077	−	0.718196i
$109$	−2.69246	+	1.55449i	−0.257891	+	0.148893i	−0.623372	−	0.781925i	$-0.714238\pi$
$109$	−2.69246	+	1.55449i	−0.257891	+	0.148893i	0.365481	+	0.930819i	$0.380904\pi$
$110$	−9.73783	+	1.22082i	−0.928466	+	0.116401i
$111$	3.24599			0.308095
$112$	10.5745	−	0.423018i	0.999201	−	0.0399715i
$113$			8.76776i			0.824801i	0.911003	+	0.412401i	$0.135310\pi$
$113$			8.76776i			0.824801i	−0.911003	+	0.412401i	$0.864690\pi$
$114$	7.98255	+	30.3482i	0.747635	+	2.84237i
$115$	2.65331	+	6.43454i	0.247423	+	0.600024i
$116$	0.383087	+	0.677832i	0.0355687	+	0.0629351i
$117$	−7.87115	−	4.54441i	−0.727688	−	0.420131i
$118$	6.62625	−	6.56565i	0.609996	−	0.604417i
$119$	−5.99602	+	11.9444i	−0.549654	+	1.09494i
$120$	−14.8760	+	11.0558i	−1.35799	+	1.00925i
$121$	0.684211	−	1.18509i	0.0622010	−	0.107735i
$122$	2.39049	−	8.76026i	0.216425	−	0.793117i
$123$	−2.35653	+	1.36054i	−0.212481	+	0.122676i
$124$	11.4278	+	6.73858i	1.02625	+	0.605143i
$125$	10.3088	+	4.32769i	0.922046	+	0.387080i
$126$	19.8765	−	6.48912i	1.77074	−	0.578096i
$127$	−5.82575			−0.516952			−0.258476	−	0.966018i	$-0.583220\pi$
$127$	−5.82575			−0.516952			−0.258476	+	0.966018i	$0.583220\pi$
$128$	2.57535	+	11.0167i	0.227631	+	0.973747i
$129$	−8.15190	+	4.70650i	−0.717735	+	0.414384i
$130$	4.73950	+	1.99758i	0.415682	+	0.175199i
$131$	14.8997	+	8.60235i	1.30179	+	0.751591i	0.980711	−	0.195461i	$-0.0626203\pi$
$131$	14.8997	+	8.60235i	1.30179	+	0.751591i	0.321082	+	0.947052i	$0.395954\pi$
$132$	−0.167112	+	18.1891i	−0.0145452	+	1.58315i
$133$	1.16839	+	19.9988i	0.101312	+	1.73412i
$134$	3.25040	−	3.22067i	0.280791	−	0.278223i
$135$	−10.3459	+	13.4388i	−0.890435	+	1.15663i
$136$	−13.7486	−	3.88775i	−1.17893	−	0.333372i
$137$	4.01092	−	2.31571i	0.342676	−	0.197844i	−0.318779	−	0.947829i	$-0.603273\pi$
$137$	4.01092	−	2.31571i	0.342676	−	0.197844i	0.661455	+	0.749985i	$0.269939\pi$
$138$	12.4759	−	3.28155i	1.06202	−	0.279344i
$139$		−	12.0576i		−	1.02271i	−0.859368	−	0.511357i	$-0.829143\pi$
$139$		−	12.0576i		−	1.02271i	0.859368	−	0.511357i	$-0.170857\pi$
$140$	−10.7038	+	5.04279i	−0.904632	+	0.426193i
$141$		−	9.55656i		−	0.804808i
$142$	−2.60014	−	9.88528i	−0.218199	−	0.829554i
$143$	4.37138	−	2.52382i	0.365553	−	0.211052i
$144$	10.8187	+	19.5600i	0.901562	+	1.63000i
$145$	−0.689769	−	0.531021i	−0.0572822	−	0.0440989i
$146$	−3.15803	−	3.18718i	−0.261361	−	0.263773i
$147$	20.3743	−	2.38881i	1.68045	−	0.197026i
$148$	−0.0203519	+	2.21518i	−0.00167292	+	0.182087i
$149$	15.0162	+	8.66962i	1.23018	+	0.710243i	0.967067	−	0.254523i	$-0.0819184\pi$
$149$	15.0162	+	8.66962i	1.23018	+	0.710243i	0.263110	+	0.964766i	$0.415252\pi$
$150$	10.5002	−	17.8649i	0.857337	−	1.45866i
$151$	16.8208	−	9.71149i	1.36886	−	0.790310i	0.378075	−	0.925775i	$-0.376586\pi$
$151$	16.8208	−	9.71149i	1.36886	−	0.790310i	0.990782	+	0.135465i	$0.0432529\pi$
$152$	−20.7608	+	5.25730i	−1.68392	+	0.426423i
$153$	−28.2283			−2.28212
$154$	−2.39836	+	11.3618i	−0.193266	+	0.915558i
$155$	−14.7025	−	1.95938i	−1.18094	−	0.157381i
$156$	4.84203	−	8.21148i	0.387673	−	0.657445i
$157$	−15.5317	+	8.96725i	−1.23957	+	0.715665i	−0.969006	−	0.247038i	$-0.920543\pi$
$157$	−15.5317	+	8.96725i	−1.23957	+	0.715665i	−0.270562	+	0.962703i	$0.587209\pi$
$158$	10.7306	+	2.92816i	0.853682	+	0.232952i
$159$	15.9550	−	27.6349i	1.26532	−	2.19159i
$160$	−7.45157	−	10.2213i	−0.589098	−	0.808061i
$161$	8.22132	−	0.480313i	0.647930	−	0.0378540i
$162$	5.43784	+	5.48803i	0.427237	+	0.431180i
$163$	−14.8747	−	8.58794i	−1.16508	−	0.672659i	−0.212564	−	0.977147i	$-0.568181\pi$
$163$	−14.8747	−	8.58794i	−1.16508	−	0.672659i	−0.952516	+	0.304488i	$0.901515\pi$
$164$	−0.913709	−	1.61671i	−0.0713487	−	0.126244i
$165$	−7.75273	−	18.8011i	−0.603549	−	1.46367i
$166$	−14.1355	+	3.71807i	−1.09712	+	0.288578i
$167$		−	23.1940i		−	1.79481i	−0.441210	−	0.897404i	$-0.645451\pi$
$167$		−	23.1940i		−	1.79481i	0.441210	−	0.897404i	$-0.354549\pi$
$168$	6.61427	+	20.9090i	0.510302	+	1.61317i
$169$	10.3547			0.796514
$170$	15.8500	−	1.98710i	1.21564	−	0.152404i
$171$	−36.6433	+	21.1560i	−2.80218	+	1.61784i
$172$	−3.16077	−	5.59266i	−0.241007	−	0.426436i
$173$	−13.5835	−	7.84243i	−1.03273	−	0.596249i	−0.114967	−	0.993369i	$-0.536676\pi$
$173$	−13.5835	−	7.84243i	−1.03273	−	0.596249i	−0.917766	+	0.397121i	$0.870009\pi$
$174$	−1.14609	+	1.13561i	−0.0868847	+	0.0860901i
$175$	8.82400	−	9.85581i	0.667032	−	0.745029i
$176$	−12.4118	−	0.228086i	−0.935576	−	0.0171926i
$177$	16.7403	+	9.66500i	1.25828	+	0.726466i
$178$	15.2809	+	4.16982i	1.14535	+	0.312541i
$179$	−1.80380	−	3.12428i	−0.134823	−	0.233520i	0.790707	−	0.612195i	$-0.209713\pi$
$179$	−1.80380	−	3.12428i	−0.134823	−	0.233520i	−0.925530	+	0.378675i	$0.876380\pi$
$180$	−19.6616	−	15.4263i	−1.46549	−	1.14981i
$181$	−3.98490			−0.296195			−0.148098	−	0.988973i	$-0.547315\pi$
$181$	−3.98490			−0.296195			−0.148098	+	0.988973i	$0.547315\pi$
$182$	4.06571	−	4.52819i	0.301370	−	0.335652i
$183$	18.8169			1.39098
$184$	2.16122	+	8.53455i	0.159328	+	0.629175i
$185$	−0.944176	−	2.28972i	−0.0694172	−	0.168344i
$186$	−7.23718	+	26.5216i	−0.530656	+	1.94466i
$187$	7.83854	−	13.5767i	0.573211	−	0.992830i
$188$	6.52174	+	0.0599183i	0.475647	+	0.00436999i
$189$	11.0302	+	16.7640i	0.802326	+	1.21940i
$190$	19.0857	−	14.4584i	1.38462	−	1.04892i
$191$	−8.00755	−	4.62316i	−0.579406	−	0.334520i	0.181491	−	0.983393i	$-0.441908\pi$
$191$	−8.00755	−	4.62316i	−0.579406	−	0.334520i	−0.760897	+	0.648872i	$0.775241\pi$
$192$	−20.6188	+	11.1582i	−1.48803	+	0.805277i
$193$	10.5917	−	6.11514i	0.762410	−	0.440177i	−0.0677506	−	0.997702i	$-0.521582\pi$
$193$	10.5917	−	6.11514i	0.762410	−	0.440177i	0.830160	+	0.557525i	$0.188249\pi$
$194$	−14.4677	+	3.80546i	−1.03872	+	0.273216i
$195$	−1.40792	+	10.5646i	−0.100823	+	0.756544i
$196$	1.50246	+	13.9191i	0.107319	+	0.994225i
$197$	7.38753			0.526340			0.263170	−	0.964750i	$-0.415232\pi$
$197$	7.38753			0.526340			0.263170	+	0.964750i	$0.415232\pi$
$198$	−23.7195	+	6.23898i	−1.68567	+	0.443385i
$199$	−2.81699	−	4.87917i	−0.199691	−	0.345875i	0.748737	−	0.662867i	$-0.230661\pi$
$199$	−2.81699	−	4.87917i	−0.199691	−	0.345875i	−0.948428	+	0.316992i	$0.897327\pi$
$200$	12.1258	+	7.27772i	0.857423	+	0.514612i
$201$	8.21166	+	4.74100i	0.579206	+	0.334405i
$202$	−4.85164	−	4.89642i	−0.341361	−	0.344511i
$203$	−0.860439	+	0.566140i	−0.0603910	+	0.0397353i
$204$	0.272003	−	29.6059i	0.0190440	−	2.07283i
$205$	1.64518	+	1.26655i	0.114905	+	0.0884597i
$206$	17.3006	+	4.72097i	1.20539	+	0.328926i
$207$	8.69702	+	15.0637i	0.604485	+	1.04700i
$208$	5.57345	+	3.35586i	0.386449	+	0.232687i
$209$		−	23.4987i		−	1.62544i
$210$	−15.9202	−	18.6472i	−1.09860	−	1.28678i
$211$	5.14042			0.353881			0.176940	−	0.984222i	$-0.443380\pi$
$211$	5.14042			0.353881			0.176940	+	0.984222i	$0.443380\pi$
$212$	18.7590	+	11.0616i	1.28838	+	0.759711i
$213$	18.3435	−	10.5906i	1.25687	−	0.725656i
$214$	11.9878	+	3.27121i	0.819468	+	0.223615i
$215$	5.69115	+	4.38135i	0.388133	+	0.298805i
$216$	−15.3770	+	14.9590i	−1.04628	+	1.01783i
$217$	−7.87366	+	15.6847i	−0.534499	+	1.06475i
$218$	3.12323	−	3.09467i	0.211532	−	0.209598i
$219$	4.64880	−	8.05195i	0.314137	−	0.544100i
$220$	12.8792	−	5.17286i	0.868314	−	0.348754i
$221$	−7.11519	+	4.10795i	−0.478619	+	0.276331i
$222$	−4.43951	+	1.16773i	−0.297961	+	0.0783731i
$223$			5.70766i			0.382213i	0.981569	+	0.191106i	$0.0612076\pi$
$223$			5.70766i			0.382213i	−0.981569	+	0.191106i	$0.938792\pi$
$224$	−14.3105	+	4.38272i	−0.956164	+	0.292833i
$225$	26.9656	+	7.31728i	1.79771	+	0.487818i
$226$	−3.15417	−	11.9916i	−0.209812	−	0.797669i
$227$	−9.24524	−	16.0132i	−0.613628	−	1.06283i	−0.990624	−	0.136620i	$-0.956376\pi$
$227$	−9.24524	−	16.0132i	−0.613628	−	1.06283i	0.376996	−	0.926215i	$-0.376957\pi$
$228$	−21.8354	−	38.6354i	−1.44608	−	2.55869i
$229$	−4.79008	+	8.29666i	−0.316537	+	0.548258i	−0.979763	−	0.200161i	$-0.935854\pi$
$229$	−4.79008	+	8.29666i	−0.316537	+	0.548258i	0.663226	+	0.748419i	$0.269187\pi$
$230$	−5.94372	−	7.84595i	−0.391917	−	0.517347i
$231$	−24.0219	+	1.40343i	−1.58053	+	0.0923389i
$232$	−0.767792	−	0.789251i	−0.0504080	−	0.0518169i
$233$	3.64278	+	2.10316i	0.238647	+	0.137783i	0.614555	−	0.788874i	$-0.289336\pi$
$233$	3.64278	+	2.10316i	0.238647	+	0.137783i	−0.375908	+	0.926657i	$0.622669\pi$
$234$	12.4001	+	3.38374i	0.810623	+	0.221202i
$235$	−6.74120	+	2.77976i	−0.439747	+	0.181332i
$236$	−6.70070	+	11.3636i	−0.436178	+	0.739705i
$237$			23.0492i			1.49720i
$238$	3.90376	−	18.4933i	0.253043	−	1.19874i
$239$		−	21.5399i		−	1.39330i	−0.717410	−	0.696651i	$-0.754673\pi$
$239$		−	21.5399i		−	1.39330i	0.717410	−	0.696651i	$-0.245327\pi$
$240$	16.3686	−	20.4725i	1.05659	−	1.32149i
$241$	7.51995	−	4.34165i	0.484403	−	0.279670i	−0.237847	−	0.971303i	$-0.576442\pi$
$241$	7.51995	−	4.34165i	0.484403	−	0.279670i	0.722249	+	0.691633i	$0.243108\pi$
$242$	−0.509459	+	1.86698i	−0.0327493	+	0.120014i
$243$	3.37228	−	5.84097i	0.216332	−	0.374698i
$244$	−0.117979	+	12.8413i	−0.00755285	+	0.822081i
$245$	−7.61144	−	13.6772i	−0.486277	−	0.873805i
$246$	2.73356	−	2.70856i	0.174285	−	0.172691i
$247$	−6.15750	+	10.6651i	−0.391792	+	0.678604i
$248$	−18.0539	−	5.10520i	−1.14642	−	0.324180i
$249$	−15.1440	−	26.2302i	−0.959713	−	1.66227i
$250$	−15.6561	−	2.21039i	−0.990180	−	0.139798i
$251$			11.2144i			0.707844i	0.935275	+	0.353922i	$0.115152\pi$
$251$			11.2144i			0.707844i	−0.935275	+	0.353922i	$0.884848\pi$
$252$	−24.8505	+	16.0256i	−1.56544	+	1.00952i
$253$	−9.66008			−0.607324
$254$	7.96784	−	2.09579i	0.499947	−	0.131502i
$255$	12.6189	+	30.6021i	0.790228	+	1.91638i
$256$	−7.48551	−	14.1410i	−0.467844	−	0.883811i
$257$	5.68553	−	9.84763i	0.354654	−	0.614278i	−0.632405	−	0.774638i	$-0.717932\pi$
$257$	5.68553	−	9.84763i	0.354654	−	0.614278i	0.987059	+	0.160360i	$0.0512654\pi$
$258$	9.45615	−	9.36967i	0.588714	−	0.583330i
$259$	−2.92554	+	0.170919i	−0.181784	+	0.0106204i
$260$	−7.20080	−	1.02705i	−0.446575	−	0.0636951i
$261$	−1.88400	−	1.08773i	−0.116617	−	0.0673287i
$262$	−23.4729	−	6.40525i	−1.45016	−	0.395718i
$263$	9.68088	+	16.7678i	0.596949	+	1.03395i	0.993269	+	0.115833i	$0.0369537\pi$
$263$	9.68088	+	16.7678i	0.596949	+	1.03395i	−0.396320	+	0.918112i	$0.629713\pi$
$264$	−6.31490	−	24.9372i	−0.388655	−	1.53478i
$265$	−24.1346	−	3.21638i	−1.48258	−	0.197580i
$266$	−8.79250	−	26.9319i	−0.539103	−	1.65130i
$267$			32.8230i			2.00874i
$268$	−3.28692	+	5.57420i	−0.200780	+	0.340499i
$269$	0.761782	+	1.31945i	0.0464467	+	0.0804480i	0.888314	−	0.459236i	$-0.151877\pi$
$269$	0.761782	+	1.31945i	0.0464467	+	0.0804480i	−0.841867	+	0.539684i	$0.818544\pi$
$270$	9.31546	−	22.1021i	0.566921	−	1.34509i
$271$	−9.32172	+	16.1457i	−0.566254	+	0.980781i	0.430677	+	0.902506i	$0.358275\pi$
$271$	−9.32172	+	16.1457i	−0.566254	+	0.980781i	−0.996932	+	0.0782754i	$0.975059\pi$
$272$	20.2024	+	0.371250i	1.22495	+	0.0225103i
$273$	11.2703	+	5.65764i	0.682111	+	0.342416i
$274$	−4.65264	+	4.61009i	−0.281076	+	0.278506i
$275$	−11.0072	+	10.9376i	−0.663762	+	0.659559i
$276$	−15.8826	+	8.97630i	−0.956021	+	0.540310i
$277$	−4.74717	−	8.22234i	−0.285230	−	0.494033i	0.687435	−	0.726246i	$-0.258737\pi$
$277$	−4.74717	−	8.22234i	−0.285230	−	0.494033i	−0.972665	+	0.232213i	$0.925403\pi$
$278$	4.33769	+	16.4911i	0.260157	+	0.989072i
$279$	−37.0680			−2.21920
$280$	12.8253	−	10.7476i	0.766459	−	0.642293i
$281$	−9.11431			−0.543714			−0.271857	−	0.962338i	$-0.587638\pi$
$281$	−9.11431			−0.543714			−0.271857	+	0.962338i	$0.587638\pi$
$282$	3.43794	+	13.0704i	0.204726	+	0.778333i
$283$	7.77457	+	13.4659i	0.462150	+	0.800467i	0.999068	−	0.0431671i	$-0.0137448\pi$
$283$	7.77457	+	13.4659i	0.462150	+	0.800467i	−0.536918	+	0.843635i	$0.680411\pi$
$284$	7.11239	+	12.5846i	0.422043	+	0.746760i
$285$	39.3158	+	30.2674i	2.32886	+	1.79288i
$286$	−5.07077	+	5.02439i	−0.299841	+	0.297099i
$287$	2.05225	−	1.35031i	0.121141	−	0.0797065i
$288$	−21.8334	−	22.8601i	−1.28654	−	1.34704i
$289$	−4.25859	+	7.37610i	−0.250506	+	0.433888i
$290$	1.13442	+	0.478131i	0.0666157	+	0.0280768i
$291$	−15.4999	−	26.8467i	−0.908623	−	1.57378i
$292$	5.46579	+	3.22299i	0.319861	+	0.188611i
$293$			8.72422i			0.509674i	0.966984	+	0.254837i	$0.0820219\pi$
$293$			8.72422i			0.509674i	−0.966984	+	0.254837i	$0.917978\pi$
$294$	−27.0064	+	10.5967i	−1.57505	+	0.618015i
$295$	1.94837	−	14.6199i	0.113438	−	0.851203i
$296$	−0.769068	−	3.03700i	−0.0447011	−	0.176522i
$297$	−11.7695	−	20.3854i	−0.682936	−	1.18288i
$298$	−23.6564	−	6.45534i	−1.37038	−	0.373948i
$299$	4.38432	+	2.53129i	0.253552	+	0.146388i
$300$	−7.93421	+	28.2111i	−0.458082	+	1.62877i
$301$	7.09932	−	4.67111i	0.409198	−	0.269238i
$302$	−19.5120	+	19.3336i	−1.12279	+	1.11252i
$303$	7.14189	−	12.3701i	0.410291	−	0.710644i
$304$	26.5031	−	14.6590i	1.52005	−	0.840751i
$305$	−5.47336	−	13.2734i	−0.313403	−	0.760034i
$306$	38.6076	−	10.1550i	2.20705	−	0.580525i
$307$	−7.13157			−0.407020			−0.203510	−	0.979073i	$-0.565235\pi$
$307$	−7.13157			−0.407020			−0.203510	+	0.979073i	$0.565235\pi$
$308$	−0.807137	−	16.4022i	−0.0459909	−	0.934603i
$309$			37.1614i			2.11404i
$310$	20.8134	−	2.60936i	1.18212	−	0.148202i
$311$	−15.8284	−	27.4155i	−0.897545	−	1.55459i	−0.830623	−	0.556835i	$-0.812016\pi$
$311$	−15.8284	−	27.4155i	−0.897545	−	1.55459i	−0.0669214	−	0.997758i	$-0.521318\pi$
$312$	−3.66835	+	12.9727i	−0.207680	+	0.734434i
$313$	11.5185	−	19.9506i	0.651063	−	1.12767i	−0.331802	−	0.943349i	$-0.607657\pi$
$313$	11.5185	−	19.9506i	0.651063	−	1.12767i	0.982865	−	0.184325i	$-0.0590101\pi$
$314$	18.0167	−	17.8519i	1.01674	−	1.00744i
$315$	18.6051	−	27.3279i	1.04828	−	1.53975i
$316$	−15.7296	−	0.144515i	−0.884858	−	0.00812961i
$317$	8.93503	−	15.4759i	0.501841	−	0.869214i	−0.498157	−	0.867087i	$-0.665990\pi$
$317$	8.93503	−	15.4759i	0.501841	−	0.869214i	0.999998	−	0.00212719i	$-0.000677106\pi$
$318$	−11.8800	+	43.5359i	−0.666198	+	2.44137i
$319$	1.04631	−	0.604089i	0.0585823	−	0.0338225i
$320$	13.8685	+	11.2989i	0.775274	+	0.631625i
$321$			25.7495i			1.43720i
$322$	−11.0714	+	3.61451i	−0.616987	+	0.201429i
$323$			38.2483i			2.12819i
$324$	−9.41159	−	5.54969i	−0.522866	−	0.308316i
$325$	7.86177	−	2.07982i	0.436092	−	0.115367i
$326$	23.4336	+	6.39452i	1.29786	+	0.354160i
$327$	7.89040	+	4.55553i	0.436340	+	0.251921i
$328$	1.83128	+	1.88246i	0.101115	+	0.103942i
$329$	0.503204	+	8.61313i	0.0277425	+	0.474857i
$330$	17.3670	+	22.9251i	0.956021	+	1.26199i
$331$	0.709904	−	1.22959i	0.0390199	−	0.0675844i	−0.845856	−	0.533411i	$-0.820910\pi$
$331$	0.709904	−	1.22959i	0.0390199	−	0.0675844i	0.884876	+	0.465827i	$0.154243\pi$
$332$	17.9954	−	10.1704i	0.987625	−	0.558171i
$333$	−3.09482	−	5.36038i	−0.169595	−	0.293747i
$334$	8.34397	+	31.7223i	0.456562	+	1.73577i
$335$	0.955739	−	7.17154i	0.0522176	−	0.391823i
$336$	−16.5682	−	26.2177i	−0.903872	−	1.43029i
$337$			9.43095i			0.513737i	0.966446	+	0.256868i	$0.0826907\pi$
$337$			9.43095i			0.513737i	−0.966446	+	0.256868i	$0.917309\pi$
$338$	−14.1620	+	3.72506i	−0.770312	+	0.202617i
$339$	22.2520	−	12.8472i	1.20856	−	0.697764i
$340$	−20.9631	+	8.41973i	−1.13688	+	0.456624i
$341$	10.2932	−	17.8283i	0.557406	−	0.965456i
$342$	42.5059	−	42.1172i	2.29846	−	2.27744i
$343$	−18.2372	+	3.22580i	−0.984714	+	0.174177i
$344$	6.33491	+	6.51196i	0.341555	+	0.351101i
$345$	12.4426	−	16.1623i	0.669888	−	0.870150i
$346$	21.3993	+	5.83942i	1.15043	+	0.313929i
$347$	6.57622	−	3.79678i	0.353030	−	0.203822i	−0.312989	−	0.949757i	$-0.601330\pi$
$347$	6.57622	−	3.79678i	0.353030	−	0.203822i	0.666019	+	0.745935i	$0.267997\pi$
$348$	1.15896	−	1.96546i	0.0621270	−	0.105360i
$349$	−7.65991			−0.410026			−0.205013	−	0.978759i	$-0.565724\pi$
$349$	−7.65991			−0.410026			−0.205013	+	0.978759i	$0.565724\pi$
$350$	−8.52292	+	16.6541i	−0.455569	+	0.890200i
$351$			12.3361i			0.658454i
$352$	17.0576	−	4.15316i	0.909173	−	0.221364i
$353$	−0.293236	−	0.507900i	−0.0156074	−	0.0270328i	0.858116	−	0.513455i	$-0.171635\pi$
$353$	−0.293236	−	0.507900i	−0.0156074	−	0.0270328i	−0.873724	+	0.486423i	$0.838302\pi$
$354$	−26.3725	−	7.19649i	−1.40168	−	0.382489i
$355$	−12.8063	−	9.85893i	−0.679686	−	0.523258i
$356$	−22.3996	−	0.205796i	−1.18718	−	0.0109072i
$357$	39.0999	−	2.28433i	2.06938	−	0.120899i
$358$	3.59100	+	3.62414i	0.189790	+	0.191542i
$359$	10.9912	+	6.34574i	0.580091	+	0.334916i	0.761169	−	0.648553i	$-0.224626\pi$
$359$	10.9912	+	6.34574i	0.580091	+	0.334916i	−0.181079	+	0.983469i	$0.557959\pi$
$360$	32.4406	+	14.0252i	1.70977	+	0.739194i
$361$	19.1656	+	33.1957i	1.00871	+	1.74714i
$362$	5.45011	−	1.43355i	0.286452	−	0.0753459i
$363$	−4.01024			−0.210483
$364$	−3.93164	+	7.65580i	−0.206074	+	0.401273i
$365$	−7.03206	−	0.937151i	−0.368075	−	0.0490527i
$366$	−25.7357	+	6.76931i	−1.34523	+	0.353837i
$367$	−22.8707	+	13.2044i	−1.19384	+	0.689264i	−0.959175	−	0.282812i	$-0.908733\pi$
$367$	−22.8707	+	13.2044i	−1.19384	+	0.689264i	−0.234665	+	0.972076i	$0.575399\pi$
$368$	−6.02616	−	10.8951i	−0.314136	−	0.567949i
$369$	4.49357	+	2.59436i	0.233926	+	0.135057i
$370$	2.11506	+	2.79197i	0.109957	+	0.145147i
$371$	−12.9248	+	25.7469i	−0.671023	+	1.33671i
$372$	0.357181	−	38.8769i	0.0185190	−	2.01567i
$373$	−5.88204	+	10.1880i	−0.304561	+	0.527515i	−0.977163	−	0.212489i	$-0.931843\pi$
$373$	−5.88204	+	10.1880i	−0.304561	+	0.527515i	0.672603	+	0.740004i	$0.265176\pi$
$374$	−5.83652	+	21.3887i	−0.301799	+	1.10598i
$375$	−4.12185	−	32.5043i	−0.212851	−	1.67851i
$376$	−8.94129	+	2.26422i	−0.461112	+	0.116768i
$377$	−0.633171			−0.0326100
$378$	−21.1167	−	18.9599i	−1.08612	−	0.975194i
$379$	3.03621			0.155960			0.0779799	−	0.996955i	$-0.475153\pi$
$379$	3.03621			0.155960			0.0779799	+	0.996955i	$0.475153\pi$
$380$	−20.9020	+	26.6407i	−1.07225	+	1.36664i
$381$	8.53634	+	14.7854i	0.437330	+	0.757478i
$382$	12.6150	+	3.44238i	0.645441	+	0.176127i
$383$	10.8418	+	6.25951i	0.553989	+	0.319846i	0.750729	−	0.660610i	$-0.229702\pi$
$383$	10.8418	+	6.25951i	0.553989	+	0.319846i	−0.196740	+	0.980456i	$0.563036\pi$
$384$	24.1861	−	22.6786i	1.23424	−	1.15731i
$385$	7.97735	+	16.5368i	0.406563	+	0.842795i
$386$	−12.2863	+	12.1740i	−0.625358	+	0.619639i
$387$	15.5445	+	8.97463i	0.790172	+	0.456206i
$388$	18.4183	−	10.4094i	0.935049	−	0.528457i
$389$	21.3594	−	12.3319i	1.08297	−	0.625251i	0.151271	−	0.988492i	$-0.451663\pi$
$389$	21.3594	−	12.3319i	1.08297	−	0.625251i	0.931695	+	0.363242i	$0.118330\pi$
$390$	−1.87496	−	14.9556i	−0.0949424	−	0.757304i
$391$	15.7235			0.795170
$392$	−7.06227	−	18.4966i	−0.356699	−	0.934220i
$393$		−	50.4193i		−	2.54332i
$394$	−10.1039	+	2.65764i	−0.509026	+	0.133890i
$395$	16.2589	−	6.70442i	0.818073	−	0.337336i
$396$	30.1965	−	17.0660i	1.51743	−	0.857599i
$397$	19.5980	+	11.3149i	0.983597	+	0.567880i	0.903354	−	0.428895i	$-0.141097\pi$
$397$	19.5980	+	11.3149i	0.983597	+	0.567880i	0.0802429	+	0.996775i	$0.474430\pi$
$398$	5.60804	+	5.65980i	0.281106	+	0.283700i
$399$	49.0437	−	32.2691i	2.45526	−	1.61548i
$400$	−19.2025	−	5.59146i	−0.960124	−	0.279573i
$401$	11.9623	−	20.7194i	0.597371	−	1.03468i	−0.395837	−	0.918321i	$-0.629546\pi$
$401$	11.9623	−	20.7194i	0.597371	−	1.03468i	0.993208	−	0.116355i	$-0.0371212\pi$
$402$	−12.9366	−	3.53012i	−0.645218	−	0.176066i
$403$	−9.34330	+	5.39436i	−0.465423	+	0.268712i
$404$	8.39703	+	4.95144i	0.417768	+	0.246343i
$405$	12.1086	+	1.61369i	0.601680	+	0.0801848i
$406$	0.973149	−	1.08385i	0.0482966	−	0.0537904i
$407$	3.43752			0.170392
$408$	10.2786	+	40.5896i	0.508866	+	2.00948i
$409$	−25.1282	+	14.5078i	−1.24251	+	0.717364i	−0.969605	−	0.244676i	$-0.921318\pi$
$409$	−25.1282	+	14.5078i	−1.24251	+	0.717364i	−0.272907	+	0.962040i	$0.587985\pi$
$410$	−2.70574	−	1.14040i	−0.133627	−	0.0563204i
$411$	−11.7542	−	6.78631i	−0.579794	−	0.334744i
$412$	−25.3603	−	0.232997i	−1.24941	−	0.0114789i
$413$	−15.5966	−	7.82940i	−0.767457	−	0.385259i
$414$	−17.3140	−	17.4738i	−0.850935	−	0.858788i
$415$	−14.0978	+	18.3123i	−0.692033	+	0.898916i
$416$	−8.83002	−	2.58475i	−0.432928	−	0.126728i
$417$	−30.6015	+	17.6678i	−1.49856	+	0.865194i
$418$	8.45358	+	32.1390i	0.413478	+	1.57197i
$419$			18.1727i			0.887794i	0.896078	+	0.443897i	$0.146404\pi$
$419$			18.1727i			0.887794i	−0.896078	+	0.443897i	$0.853596\pi$
$420$	28.4822	+	19.7763i	1.38979	+	0.964987i
$421$		−	30.9941i		−	1.51056i	−0.655403	−	0.755279i	$-0.727501\pi$
$421$		−	30.9941i		−	1.51056i	0.655403	−	0.755279i	$-0.272499\pi$
$422$	−7.03051	+	1.84925i	−0.342240	+	0.0900199i
$423$	−15.7816	+	9.11150i	−0.767327	+	0.443016i
$424$	−29.6359	−	8.38031i	−1.43925	−	0.406984i
$425$	17.9162	−	17.8028i	0.869064	−	0.863562i
$426$	−21.2783	+	21.0837i	−1.03094	+	1.02151i
$427$	−16.9593	+	0.990809i	−0.820716	+	0.0479486i
$428$	−17.5724	−	0.161446i	−0.849394	−	0.00780379i
$429$	−12.8106	−	7.39619i	−0.618500	−	0.357091i
$430$	−9.35992	−	3.94497i	−0.451375	−	0.190243i
$431$	−17.6956	+	10.2166i	−0.852369	+	0.492115i	−0.861449	−	0.507843i	$-0.830443\pi$
$431$	−17.6956	+	10.2166i	−0.852369	+	0.492115i	0.00908058	+	0.999959i	$0.497110\pi$
$432$	15.6496	−	25.9911i	0.752943	−	1.25050i
$433$	−2.57285			−0.123643			−0.0618216	−	0.998087i	$-0.519691\pi$
$433$	−2.57285			−0.123643			−0.0618216	+	0.998087i	$0.519691\pi$
$434$	5.12621	−	24.2844i	0.246066	−	1.16569i
$435$	−0.336993	+	2.52868i	−0.0161576	+	0.121241i
$436$	−3.15833	+	5.35613i	−0.151256	+	0.256512i
$437$	20.4107	−	11.7841i	0.976377	−	0.563711i
$438$	−3.46146	+	12.6850i	−0.165395	+	0.606112i
$439$	−7.66013	+	13.2677i	−0.365598	+	0.633234i	−0.988872	−	0.148769i	$-0.952469\pi$
$439$	−7.66013	+	13.2677i	−0.365598	+	0.633234i	0.623274	+	0.782003i	$0.285802\pi$
$440$	−15.7538	+	11.7081i	−0.751034	+	0.558163i
$441$	−23.3703	−	31.3683i	−1.11287	−	1.49373i
$442$	8.25356	−	8.17808i	0.392582	−	0.388992i
$443$	−5.24553	−	3.02851i	−0.249223	−	0.143889i	0.370185	−	0.928958i	$-0.379294\pi$
$443$	−5.24553	−	3.02851i	−0.249223	−	0.143889i	−0.619408	+	0.785069i	$0.712627\pi$
$444$	5.65180	−	3.19420i	0.268223	−	0.151590i
$445$	23.1534	−	9.54739i	1.09757	−	0.452590i
$446$	−2.05331	−	7.80632i	−0.0972270	−	0.369640i
$447$		−	50.8136i		−	2.40340i
$448$	17.9958	−	11.1424i	0.850220	−	0.526428i
$449$	−9.93819			−0.469012			−0.234506	−	0.972115i	$-0.575347\pi$
$449$	−9.93819			−0.469012			−0.234506	+	0.972115i	$0.575347\pi$
$450$	−39.5130	−	0.306998i	−1.86266	−	0.0144720i
$451$	−2.49558	+	1.44083i	−0.117512	+	0.0678458i
$452$	8.62787	+	15.2661i	0.405821	+	0.718058i
$453$	−49.2943	−	28.4601i	−2.31605	−	1.33717i
$454$	18.4053	+	18.5752i	0.863806	+	0.871778i
$455$	0.712648	−	9.59575i	0.0334095	−	0.449856i
$456$	43.7630	+	44.9861i	2.04939	+	2.10667i
$457$	−15.9573	−	9.21295i	−0.746451	−	0.430964i	0.0779590	−	0.996957i	$-0.475160\pi$
$457$	−15.9573	−	9.21295i	−0.746451	−	0.430964i	−0.824410	+	0.565993i	$0.808493\pi$
$458$	3.56666	−	13.0705i	0.166659	−	0.610744i
$459$	19.1569	+	33.1808i	0.894170	+	1.54875i
$460$	10.9517	+	8.59262i	0.510627	+	0.400633i
$461$	17.6061			0.819998			0.409999	−	0.912086i	$-0.365529\pi$
$461$	17.6061			0.819998			0.409999	+	0.912086i	$0.365529\pi$
$462$	32.3497	−	10.5613i	1.50505	−	0.491354i
$463$	28.5438			1.32654			0.663271	−	0.748379i	$-0.269168\pi$
$463$	28.5438			1.32654			0.663271	+	0.748379i	$0.269168\pi$
$464$	1.33403	+	0.803242i	0.0619310	+	0.0372896i
$465$	16.5705	+	40.1851i	0.768440	+	1.86354i
$466$	−5.73881	−	1.56600i	−0.265845	−	0.0725435i
$467$	−3.09243	+	5.35625i	−0.143101	+	0.247857i	−0.928663	−	0.370925i	$-0.879041\pi$
$467$	−3.09243	+	5.35625i	−0.143101	+	0.247857i	0.785562	+	0.618783i	$0.212374\pi$
$468$	−18.1769	−	0.167000i	−0.840226	−	0.00771956i
$469$	−7.65063	−	3.84058i	−0.353273	−	0.177341i
$470$	8.21988	−	6.22698i	0.379155	−	0.287229i
$471$	45.5166	+	26.2790i	2.09729	+	1.21087i
$472$	5.07649	−	17.9524i	0.233665	−	0.826327i
$473$	−8.63292	+	4.98422i	−0.396942	+	0.229175i
$474$	−8.29186	−	31.5242i	−0.380858	−	1.44795i
$475$	9.91463	−	36.5374i	0.454914	−	1.67645i
$476$	1.31376	+	26.6975i	0.0602159	+	1.22368i
$477$	−60.8480			−2.78604
$478$	7.74891	+	29.4600i	0.354427	+	1.34747i
$479$	−6.58753	−	11.4099i	−0.300992	−	0.521333i	0.675369	−	0.737480i	$-0.263984\pi$
$479$	−6.58753	−	11.4099i	−0.300992	−	0.521333i	−0.976361	+	0.216147i	$0.930651\pi$
$480$	−15.0223	+	33.8886i	−0.685670	+	1.54679i
$481$	−1.56015	−	0.900754i	−0.0711368	−	0.0410708i
$482$	−8.72309	+	8.64331i	−0.397326	+	0.393692i
$483$	−13.2655	−	20.1614i	−0.603602	−	0.917374i
$484$	0.0251436	−	2.73673i	0.00114289	−	0.124397i
$485$	−14.4291	+	18.7427i	−0.655192	+	0.851062i
$486$	−2.51098	+	9.20182i	−0.113900	+	0.417403i
$487$	−0.665258	−	1.15226i	−0.0301457	−	0.0522139i	0.850559	−	0.525880i	$-0.176264\pi$
$487$	−0.665258	−	1.15226i	−0.0301457	−	0.0522139i	−0.880705	+	0.473666i	$0.842930\pi$
$488$	−4.45826	−	17.6054i	−0.201816	−	0.796959i
$489$			50.3349i			2.27622i
$490$	15.3304	+	15.9680i	0.692559	+	0.721362i
$491$	43.7619			1.97495			0.987474	−	0.157779i	$-0.0504335\pi$
$491$	43.7619			1.97495			0.987474	+	0.157779i	$0.0504335\pi$
$492$	−2.76427	+	4.68787i	−0.124623	+	0.211345i
$493$	−1.70306	+	0.983260i	−0.0767018	+	0.0442838i
$494$	4.58483	−	16.8017i	0.206281	−	0.755945i
$495$	−23.6563	+	30.7283i	−1.06327	+	1.38113i
$496$	26.5288	+	0.487506i	1.19118	+	0.0218897i
$497$	−15.9749	+	10.5110i	−0.716573	+	0.471481i
$498$	30.1486	+	30.4269i	1.35099	+	1.36346i
$499$	−15.2053	+	26.3363i	−0.680681	+	1.17897i	0.294092	+	0.955777i	$0.404983\pi$
$499$	−15.2053	+	26.3363i	−0.680681	+	1.17897i	−0.974773	+	0.223197i	$0.928351\pi$
$500$	22.2079	−	2.60910i	0.993169	−	0.116682i
$501$	−58.8649	+	33.9857i	−2.62989	+	1.51837i
$502$	−4.03433	−	15.3378i	−0.180061	−	0.684559i
$503$			9.86442i			0.439833i	0.975519	+	0.219916i	$0.0705785\pi$
$503$			9.86442i			0.439833i	−0.975519	+	0.219916i	$0.929422\pi$
$504$	28.2227	−	30.8580i	1.25714	−	1.37452i
$505$	−10.8033	−	1.43973i	−0.480739	−	0.0640673i
$506$	13.2120	−	3.47518i	0.587346	−	0.154491i
$507$	−15.1725	−	26.2795i	−0.673833	−	1.16711i
$508$	−10.1436	+	5.73280i	−0.450049	+	0.254352i
$509$	7.69465	−	13.3275i	0.341059	−	0.590732i	−0.643570	−	0.765387i	$-0.722548\pi$
$509$	7.69465	−	13.3275i	0.341059	−	0.590732i	0.984630	+	0.174655i	$0.0558809\pi$
$510$	−28.2678	−	37.3147i	−1.25172	−	1.65232i
$511$	−3.76588	+	7.50184i	−0.166593	+	0.331862i
$512$	15.3250	+	16.6476i	0.677277	+	0.735728i
$513$	49.7354	+	28.7147i	2.19587	+	1.26779i
$514$	−4.23341	+	15.5139i	−0.186728	+	0.684288i
$515$	26.2137	−	10.8093i	1.15511	−	0.476316i
$516$	−9.56239	+	16.2166i	−0.420961	+	0.713898i
$517$		−	10.1205i		−	0.445098i
$518$	3.93975	−	1.28622i	0.173103	−	0.0565131i
$519$			45.9653i			2.01765i
$520$	10.2180	−	1.18577i	0.448087	−	0.0519995i
$521$	11.5108	−	6.64575i	0.504296	−	0.291156i	−0.226190	−	0.974083i	$-0.572627\pi$
$521$	11.5108	−	6.64575i	0.504296	−	0.291156i	0.730486	+	0.682928i	$0.239294\pi$
$522$	2.96804	+	0.809915i	0.129908	+	0.0354490i
$523$	−3.96445	+	6.86663i	−0.173353	+	0.300257i	−0.939590	−	0.342301i	$-0.888794\pi$
$523$	−3.96445	+	6.86663i	−0.173353	+	0.300257i	0.766237	+	0.642558i	$0.222127\pi$
$524$	34.4079	+	0.316122i	1.50312	+	0.0138099i
$525$	−37.9430	−	7.95323i	−1.65597	−	0.347108i
$526$	−19.2726	−	19.4505i	−0.840326	−	0.848082i
$527$	−16.7539	+	29.0187i	−0.729813	+	1.26407i
$528$	17.6079	+	31.8346i	0.766285	+	1.38542i
$529$	6.65566	+	11.5279i	0.289377	+	0.501215i
$530$	34.1658	−	4.28333i	1.48407	−	0.186056i
$531$		−	36.8596i		−	1.59957i
$532$	21.7141	+	33.6715i	0.941426	+	1.45984i
$533$	1.51019			0.0654136
$534$	−11.8080	−	44.8918i	−0.510981	−	1.94266i
$535$	18.1637	−	7.48989i	0.785286	−	0.323816i
$536$	2.49019	−	8.80625i	0.107560	−	0.380372i
$537$	−5.28615	+	9.15588i	−0.228114	+	0.395105i
$538$	−1.51655	−	1.53055i	−0.0653831	−	0.0659865i
$539$	21.5766	−	2.52976i	0.929368	−	0.108965i
$540$	−4.78954	+	33.5801i	−0.206109	+	1.44506i
$541$	−37.4487	−	21.6210i	−1.61005	−	0.929561i	−0.989358	−	0.145504i	$-0.953520\pi$
$541$	−37.4487	−	21.6210i	−1.61005	−	0.929561i	−0.620689	−	0.784057i	$-0.713147\pi$
$542$	6.94089	−	25.4358i	0.298137	−	1.09256i
$543$	5.83898	+	10.1134i	0.250575	+	0.434008i
$544$	−27.7642	+	6.75999i	−1.19038	+	0.289832i
$545$	0.918349	−	6.89098i	0.0393377	−	0.295177i
$546$	−17.4496	−	3.68345i	−0.746776	−	0.157637i
$547$		−	21.2017i		−	0.906519i	−0.891379	−	0.453260i	$-0.850261\pi$
$547$		−	21.2017i		−	0.906519i	0.891379	−	0.453260i	$-0.149739\pi$
$548$	4.70492	−	7.97896i	0.200984	−	0.340844i
$549$	−17.9406	−	31.0740i	−0.765684	−	1.32620i
$550$	11.1198	−	18.9190i	0.474149	−	0.806710i
$551$	−1.47383	+	2.55275i	−0.0627873	+	0.108751i
$552$	18.4933	−	17.9905i	0.787129	−	0.765728i
$553$	−1.21366	−	20.7737i	−0.0516101	−	0.883389i
$554$	9.45063	+	9.53786i	0.401519	+	0.405225i
$555$	−4.42768	+	5.75133i	−0.187945	+	0.244130i
$556$	−11.8653	−	20.9943i	−0.503199	−	0.890357i
$557$	1.74567	+	3.02359i	0.0739663	+	0.128113i	0.900636	−	0.434574i	$-0.143101\pi$
$557$	1.74567	+	3.02359i	0.0739663	+	0.128113i	−0.826670	+	0.562687i	$0.809768\pi$
$558$	50.6976	−	13.3351i	2.14620	−	0.564519i
$559$	5.22417			0.220959
$560$	−13.6747	+	19.3133i	−0.577860	+	0.816136i
$561$	−45.9425			−1.93970
$562$	12.4656	−	3.27884i	0.525828	−	0.138310i
$563$	7.10505	+	12.3063i	0.299442	+	0.518649i	0.976008	−	0.217733i	$-0.0698661\pi$
$563$	7.10505	+	12.3063i	0.299442	+	0.518649i	−0.676566	+	0.736382i	$0.736533\pi$
$564$	−9.40409	−	16.6395i	−0.395984	−	0.700651i
$565$	−15.5350	−	11.9596i	−0.653561	−	0.503146i
$566$	−15.4775	−	15.6204i	−0.650570	−	0.656574i
$567$	6.48451	−	12.9175i	0.272324	−	0.542483i
$568$	−14.2548	−	14.6532i	−0.598120	−	0.614836i
$569$	15.5447	−	26.9242i	0.651666	−	1.12872i	−0.331052	−	0.943613i	$-0.607404\pi$
$569$	15.5447	−	26.9242i	0.651666	−	1.12872i	0.982718	−	0.185107i	$-0.0592631\pi$
$570$	−64.6604	−	27.2527i	−2.70833	−	1.14149i
$571$	−4.74777	−	8.22337i	−0.198688	−	0.344137i	0.749415	−	0.662100i	$-0.230335\pi$
$571$	−4.74777	−	8.22337i	−0.198688	−	0.344137i	−0.948103	+	0.317963i	$0.897001\pi$
$572$	5.12774	−	8.69602i	0.214402	−	0.363599i
$573$			27.0969i			1.13199i
$574$	−2.32108	+	2.58510i	−0.0968800	+	0.107900i
$575$	−15.0201	−	4.07580i	−0.626383	−	0.169973i
$576$	38.0852	+	23.4111i	1.58688	+	0.975461i
$577$	16.2630	+	28.1683i	0.677037	+	1.17266i	0.975869	+	0.218356i	$0.0700695\pi$
$577$	16.2630	+	28.1683i	0.677037	+	1.17266i	−0.298832	+	0.954306i	$0.596597\pi$
$578$	3.17092	−	11.6203i	0.131893	−	0.483339i
$579$	−31.0397	−	17.9208i	−1.28996	−	0.744761i
$580$	−1.72355	−	0.245831i	−0.0715665	−	0.0102076i
$581$	15.0301	+	22.8433i	0.623556	+	0.947701i
$582$	30.8572	+	31.1420i	1.27907	+	1.29088i
$583$	16.8965	−	29.2656i	0.699781	−	1.21206i
$584$	−8.63498	−	2.44176i	−0.357318	−	0.101041i
$585$	18.7885	−	7.74753i	0.776810	−	0.320321i
$586$	−3.13851	−	11.9321i	−0.129651	−	0.492908i
$587$	18.4126			0.759968			0.379984	−	0.924993i	$-0.375929\pi$
$587$	18.4126			0.759968			0.379984	+	0.924993i	$0.375929\pi$
$588$	33.1244	−	24.2086i	1.36603	−	0.998344i
$589$			50.2256i			2.06951i
$590$	2.59469	+	20.6964i	0.106822	+	0.852059i
$591$	−10.8248	−	18.7491i	−0.445272	−	0.771234i
$592$	2.14440	+	3.87702i	0.0881343	+	0.159344i
$593$	−16.2273	+	28.1066i	−0.666377	+	1.15420i	0.312533	+	0.949907i	$0.398823\pi$
$593$	−16.2273	+	28.1066i	−0.666377	+	1.15420i	−0.978910	+	0.204292i	$0.934511\pi$
$594$	23.4307	+	23.6469i	0.961371	+	0.970244i
$595$	−12.9845	−	26.9166i	−0.532314	−	1.10347i
$596$	34.6770	+	0.318594i	1.42043	+	0.0130501i
$597$	−8.25534	+	14.2987i	−0.337869	+	0.585206i
$598$	−6.90702	−	1.88478i	−0.282449	−	0.0770743i
$599$	−16.2697	+	9.39332i	−0.664762	+	0.383801i	−0.794089	−	0.607801i	$-0.792052\pi$
$599$	−16.2697	+	9.39332i	−0.664762	+	0.383801i	0.129327	+	0.991602i	$0.458718\pi$
$600$	0.702721	−	41.4383i	0.0286885	−	1.69171i
$601$		−	37.1087i		−	1.51369i	−0.653592	−	0.756847i	$-0.726739\pi$
$601$		−	37.1087i		−	1.51369i	0.653592	−	0.756847i	$-0.273261\pi$
$602$	−8.02926	+	8.94260i	−0.327248	+	0.364473i
$603$		−	18.0808i		−	0.736309i
$604$	19.7312	−	33.4617i	0.802852	−	1.36154i
$605$	1.16648	+	2.82882i	0.0474240	+	0.115008i
$606$	−5.31780	+	19.4878i	−0.216021	+	0.791637i
$607$	−3.49971	−	2.02056i	−0.142049	−	0.0820119i	0.427291	−	0.904114i	$-0.359468\pi$
$607$	−3.49971	−	2.02056i	−0.142049	−	0.0820119i	−0.569340	+	0.822102i	$0.692801\pi$
$608$	−30.9745	+	29.5834i	−1.25618	+	1.19976i
$609$	2.69761	+	1.35419i	0.109313	+	0.0548744i
$610$	12.2609	+	16.1849i	0.496431	+	0.655309i
$611$	−2.65192	+	4.59327i	−0.107285	+	0.185824i
$612$	−49.1501	+	27.7779i	−1.98678	+	1.12286i
$613$	−15.5447	−	26.9242i	−0.627844	−	1.08746i	−0.987984	−	0.154559i	$-0.950604\pi$
$613$	−15.5447	−	26.9242i	−0.627844	−	1.08746i	0.360140	−	0.932898i	$-0.382729\pi$
$614$	9.75380	−	2.56556i	0.393631	−	0.103538i
$615$	0.803770	−	6.03122i	0.0324111	−	0.243202i
$616$	7.00456	+	22.1428i	0.282222	+	0.892160i
$617$			15.3302i			0.617170i	0.951197	+	0.308585i	$0.0998554\pi$
$617$			15.3302i			0.617170i	−0.951197	+	0.308585i	$0.900145\pi$
$618$	−13.3687	−	50.8254i	−0.537768	−	2.04450i
$619$	37.3373	−	21.5567i	1.50071	−	0.866438i	0.500715	−	0.865612i	$-0.333071\pi$
$619$	37.3373	−	21.5567i	1.50071	−	0.866438i	1.00000		0.000825626i	$-0.000262805\pi$
$620$	−27.5277	+	11.0564i	−1.10554	+	0.444034i
$621$	11.8043	−	20.4457i	0.473692	−	0.820459i
$622$	31.5110	+	31.8018i	1.26348	+	1.27514i
$623$	−1.72831	−	29.5827i	−0.0692431	−	1.18521i
$624$	0.350299	−	19.0623i	0.0140232	−	0.763104i
$625$	−21.7296	+	12.3622i	−0.869184	+	0.494489i
$626$	−8.57658	+	31.4300i	−0.342789	+	1.25620i
$627$	−59.6382	+	34.4321i	−2.38172	+	1.37509i
$628$	−18.2191	+	30.8974i	−0.727023	+	1.23294i
$629$	−5.59517			−0.223094
$630$	−15.6149	+	44.0692i	−0.622112	+	1.75576i
$631$		−	23.9995i		−	0.955404i	−0.878522	−	0.477702i	$-0.841470\pi$
$631$		−	23.9995i		−	0.955404i	0.878522	−	0.477702i	$-0.158530\pi$
$632$	21.5652	−	5.46101i	0.857818	−	0.217227i
$633$	−7.53214	−	13.0460i	−0.299376	−	0.518534i
$634$	−6.65296	+	24.3806i	−0.264223	+	0.968279i
$635$	7.94660	−	10.3222i	0.315351	−	0.409625i
$636$	0.586321	−	63.8174i	0.0232492	−	2.53053i
$637$	−10.4556	−	4.50567i	−0.414266	−	0.178521i
$638$	−1.21371	+	1.20261i	−0.0480514	+	0.0476120i
$639$	−34.9784	−	20.1948i	−1.38372	−	0.798893i
$640$	−23.0326	−	10.4642i	−0.910443	−	0.413634i
$641$	12.7941	+	22.1600i	0.505336	+	0.875267i	0.999981	+	0.00617237i	$0.00196474\pi$
$641$	12.7941	+	22.1600i	0.505336	+	0.875267i	−0.494645	+	0.869095i	$0.664702\pi$
$642$	−9.26331	−	35.2174i	−0.365593	−	1.38992i
$643$	48.1544			1.89902			0.949512	−	0.313731i	$-0.101579\pi$
$643$	48.1544			1.89902			0.949512	+	0.313731i	$0.101579\pi$
$644$	13.8420	−	8.92645i	0.545452	−	0.351751i
$645$	2.78046	−	20.8637i	0.109481	−	0.821506i
$646$	−13.7597	−	52.3118i	−0.541367	−	2.05818i
$647$	−11.2431	+	6.49122i	−0.442013	+	0.255196i	−0.704451	−	0.709752i	$-0.748807\pi$
$647$	−11.2431	+	6.49122i	−0.442013	+	0.255196i	0.262438	+	0.964949i	$0.415473\pi$
$648$	14.8686	+	4.20448i	0.584096	+	0.165168i
$649$	17.7281	+	10.2353i	0.695887	+	0.401771i
$650$	−10.0043	+	5.67279i	−0.392400	+	0.222505i
$651$	51.3440	−	2.99966i	2.01233	−	0.117566i
$652$	−34.3503	−	0.315593i	−1.34526	−	0.0123596i
$653$	10.4539	−	18.1068i	0.409094	−	0.708572i	−0.585694	−	0.810532i	$-0.699178\pi$
$653$	10.4539	−	18.1068i	0.409094	−	0.708572i	0.994789	+	0.101960i	$0.0325113\pi$
$654$	−12.4305	−	3.39201i	−0.486070	−	0.132638i
$655$	−35.5658	+	14.6657i	−1.38967	+	0.573037i
$656$	−3.18184	−	1.91583i	−0.124230	−	0.0748006i
$657$	−17.7292			−0.691682
$658$	−3.78677	−	11.5991i	−0.147624	−	0.452179i
$659$	−36.6633			−1.42820			−0.714099	−	0.700045i	$-0.753163\pi$
$659$	−36.6633			−1.42820			−0.714099	+	0.700045i	$0.753163\pi$
$660$	−31.9999	−	25.1068i	−1.24560	−	0.977282i
$661$	13.6519	+	23.6458i	0.530998	+	0.919715i	0.999346	+	0.0361712i	$0.0115162\pi$
$661$	13.6519	+	23.6458i	0.530998	+	0.919715i	−0.468348	+	0.883544i	$0.655151\pi$
$662$	−0.528590	+	1.93709i	−0.0205442	+	0.0752870i
$663$	20.8514	+	12.0386i	0.809803	+	0.467540i
$664$	−20.9534	+	20.3837i	−0.813150	+	0.791041i
$665$	−37.0282	−	25.2091i	−1.43589	−	0.977569i
$666$	6.16114	+	6.21801i	0.238739	+	0.240943i
$667$	1.04941	+	0.605877i	0.0406333	+	0.0234596i
$668$	−22.8240	−	40.3846i	−0.883086	−	1.56253i
$669$	14.4857	−	8.36330i	0.560048	−	0.323344i
$670$	1.27278	+	10.1523i	0.0491718	+	0.392217i
$671$	19.9272			0.769281
$672$	32.0920	+	29.8973i	1.23797	+	1.15332i
$673$		−	4.86055i		−	0.187360i	−0.995602	−	0.0936802i	$-0.970137\pi$
$673$		−	4.86055i		−	0.187360i	0.995602	−	0.0936802i	$-0.0298631\pi$
$674$	−3.39275	−	12.8986i	−0.130684	−	0.496837i
$675$	−9.69897	−	36.6624i	−0.373314	−	1.41114i
$676$	18.0292	−	10.1895i	0.693431	−	0.391903i
$677$	−3.37606	−	1.94917i	−0.129753	−	0.0749128i	0.433719	−	0.901048i	$-0.357201\pi$
$677$	−3.37606	−	1.94917i	−0.129753	−	0.0749128i	−0.563471	+	0.826136i	$0.690534\pi$
$678$	−25.8122	+	25.5761i	−0.991310	+	0.982244i
$679$	15.3834	+	23.3802i	0.590360	+	0.897250i
$680$	25.6421	−	19.0570i	0.983330	−	0.730803i
$681$	−27.0937	+	46.9276i	−1.03823	+	1.79827i
$682$	−7.66422	+	28.0865i	−0.293478	+	1.07549i
$683$	15.0819	−	8.70755i	0.577094	−	0.333185i	−0.182884	−	0.983135i	$-0.558543\pi$
$683$	15.0819	−	8.70755i	0.577094	−	0.333185i	0.759978	+	0.649949i	$0.225210\pi$
$684$	−42.9835	+	72.8947i	−1.64352	+	2.78720i
$685$	−1.36805	+	10.2654i	−0.0522706	+	0.392221i
$686$	23.7824	−	10.9727i	0.908015	−	0.418938i
$687$	28.0752			1.07113
$688$	−11.0069	−	6.62740i	−0.419633	−	0.252667i
$689$	−15.3373	+	8.85497i	−0.584303	+	0.337347i
$690$	−11.2033	+	26.5813i	−0.426503	+	1.01193i
$691$	12.1565	+	7.01858i	0.462456	+	0.266999i	0.713076	−	0.701086i	$-0.247301\pi$
$691$	12.1565	+	7.01858i	0.462456	+	0.266999i	−0.250620	+	0.968085i	$0.580635\pi$
$692$	−31.3684	−	0.288196i	−1.19245	−	0.0109556i
$693$	25.2208	+	38.3314i	0.958059	+	1.45609i
$694$	−7.62836	+	7.55860i	−0.289569	+	0.286920i
$695$	21.3640	+	16.4472i	0.810384	+	0.623877i
$696$	−0.878039	+	3.10508i	−0.0332820	+	0.117698i
$697$	4.06200	−	2.34520i	0.153859	−	0.0888306i
$698$	10.4764	−	2.75563i	0.396538	−	0.104302i
$699$		−	12.3269i		−	0.466245i
$700$	5.66547	−	25.8438i	0.214135	−	0.976804i
$701$		−	21.7579i		−	0.821786i	−0.911684	−	0.410893i	$-0.865217\pi$
$701$		−	21.7579i		−	0.821786i	0.911684	−	0.410893i	$-0.134783\pi$
$702$	−4.43788	−	16.8720i	−0.167497	−	0.636794i
$703$	−7.26311	+	4.19336i	−0.273933	+	0.158156i
$704$	−21.8355	+	11.8167i	−0.822955	+	0.445357i
$705$	16.9326	+	13.0356i	0.637718	+	0.490949i
$706$	0.583772	+	0.589160i	0.0219706	+	0.0221733i
$707$	−5.78548	+	11.5250i	−0.217585	+	0.433442i
$708$	38.6584	+	0.355173i	1.45287	+	0.0133482i
$709$	−26.5841	−	15.3484i	−0.998388	−	0.576420i	−0.0906173	−	0.995886i	$-0.528884\pi$
$709$	−26.5841	−	15.3484i	−0.998388	−	0.576420i	−0.907771	+	0.419466i	$0.862217\pi$
$710$	21.0617	+	8.87698i	0.790433	+	0.333147i
$711$	38.0631	−	21.9757i	1.42748	−	0.824155i
$712$	30.7098	−	7.77671i	1.15090	−	0.291445i
$713$	20.6473			0.773246
$714$	−52.6548	+	17.1903i	−1.97056	+	0.643331i
$715$	−1.49100	+	11.1879i	−0.0557601	+	0.418405i
$716$	−6.21516	−	3.66486i	−0.232271	−	0.136962i
$717$	−54.6669	+	31.5620i	−2.04157	+	1.17870i
$718$	−17.3154	−	4.72500i	−0.646204	−	0.176335i
$719$	11.7603	−	20.3694i	0.438585	−	0.759652i	−0.558995	−	0.829171i	$-0.688813\pi$
$719$	11.7603	−	20.3694i	0.438585	−	0.759652i	0.997581	+	0.0695187i	$0.0221463\pi$
$720$	−49.4143	−	7.51181i	−1.84156	−	0.279949i
$721$	−1.95675	−	33.4928i	−0.0728731	−	1.24734i
$722$	−38.1546	−	38.5068i	−1.41997	−	1.43307i
$723$	−22.0376	−	12.7234i	−0.819588	−	0.473189i
$724$	−6.93836	+	3.92132i	−0.257862	+	0.145735i
$725$	1.88175	−	0.497815i	0.0698866	−	0.0184884i
$726$	5.48477	−	1.44267i	0.203559	−	0.0535425i
$727$			29.2877i			1.08622i	0.839661	+	0.543110i	$0.182754\pi$
$727$			29.2877i			1.08622i	−0.839661	+	0.543110i	$0.817246\pi$
$728$	2.62313	−	11.8852i	0.0972196	−	0.440494i
$729$	−36.1543			−1.33905
$730$	9.95484	−	1.24803i	0.368445	−	0.0461916i
$731$	14.0516	−	8.11269i	0.519717	−	0.300059i
$732$	32.7633	−	18.5167i	1.21097	−	0.684395i
$733$	39.4427	+	22.7723i	1.45685	+	0.841113i	0.998855	−	0.0478408i	$-0.0152340\pi$
$733$	39.4427	+	22.7723i	1.45685	+	0.841113i	0.457996	+	0.888954i	$0.348567\pi$
$734$	26.5298	−	26.2872i	0.979234	−	0.970278i
$735$	−23.5590	+	39.3583i	−0.868986	+	1.45175i
$736$	12.1614	+	12.7333i	0.448276	+	0.469356i
$737$	8.69620	+	5.02076i	0.320329	+	0.184942i
$738$	−7.07914	−	1.93175i	−0.260587	−	0.0711086i
$739$	−6.91988	−	11.9856i	−0.254552	−	0.440897i	0.710222	−	0.703978i	$-0.248595\pi$
$739$	−6.91988	−	11.9856i	−0.254552	−	0.440897i	−0.964774	+	0.263081i	$0.915261\pi$
$740$	−3.89715	−	3.05767i	−0.143262	−	0.112402i
$741$	36.0898			1.32579
$742$	8.41481	−	39.8635i	0.308917	−	1.46343i
$743$	−36.5334			−1.34028			−0.670141	−	0.742234i	$-0.733766\pi$
$743$	−36.5334			−1.34028			−0.670141	+	0.742234i	$0.733766\pi$
$744$	13.4973	+	53.3002i	0.494836	+	1.95408i
$745$	−35.8439	+	14.7804i	−1.31322	+	0.541512i
$746$	4.37973	−	16.0501i	0.160353	−	0.587636i
$747$	−28.8775	+	50.0173i	−1.05657	+	1.83004i
$748$	0.288053	−	31.3528i	0.0105323	−	1.14637i
$749$	−1.35585	−	23.2075i	−0.0495417	−	0.847984i
$750$	17.3307	+	42.9731i	0.632829	+	1.56915i
$751$	29.3811	+	16.9632i	1.07213	+	0.618996i	0.928763	−	0.370673i	$-0.120873\pi$
$751$	29.3811	+	16.9632i	1.07213	+	0.618996i	0.143369	+	0.989669i	$0.454206\pi$
$752$	11.4144	−	6.31336i	0.416240	−	0.230225i
$753$	28.4613	−	16.4322i	1.03719	−	0.598821i
$754$	0.865984	−	0.227781i	0.0315373	−	0.00829530i
$755$	−5.73726	+	43.0505i	−0.208800	+	1.56677i
$756$	35.7019	+	18.3347i	1.29846	+	0.666827i
$757$	31.2178			1.13463			0.567315	−	0.823501i	$-0.307982\pi$
$757$	31.2178			1.13463			0.567315	+	0.823501i	$0.307982\pi$
$758$	−4.15261	+	1.09227i	−0.150829	+	0.0396729i
$759$	14.1547	+	24.5167i	0.513783	+	0.889899i
$760$	19.0036	−	43.9557i	0.689335	−	1.59444i
$761$	−17.6688	−	10.2011i	−0.640493	−	0.369789i	0.144312	−	0.989532i	$-0.453903\pi$
$761$	−17.6688	−	10.2011i	−0.640493	−	0.369789i	−0.784804	+	0.619744i	$0.787237\pi$
$762$	−16.9941	−	17.1509i	−0.615631	−	0.621313i
$763$	−7.35133	−	3.69033i	−0.266136	−	0.133599i
$764$	−18.4919	−	0.169894i	−0.669013	−	0.00614654i
$765$	38.5047	−	50.0157i	1.39214	−	1.80832i
$766$	−17.0801	−	4.66078i	−0.617128	−	0.168401i
$767$	−5.36403	−	9.29077i	−0.193684	−	0.335470i
$768$	−24.9205	+	39.7182i	−0.899242	+	1.43321i
$769$		−	5.57448i		−	0.201021i	−0.994936	−	0.100510i	$-0.967952\pi$
$769$		−	5.57448i		−	0.201021i	0.994936	−	0.100510i	$-0.0320476\pi$
$770$	−16.8596	−	19.7475i	−0.607579	−	0.711650i
$771$	−33.3235			−1.20012
$772$	12.4244	−	21.0702i	0.447163	−	0.758334i
$773$	32.8342	−	18.9569i	1.18097	−	0.681831i	0.224728	−	0.974422i	$-0.427851\pi$
$773$	32.8342	−	18.9569i	1.18097	−	0.681831i	0.956238	+	0.292591i	$0.0945174\pi$
$774$	−24.4887	−	6.68245i	−0.880229	−	0.240196i
$775$	23.5267	−	23.3777i	0.845102	−	0.839752i
$776$	−21.4459	+	20.8628i	−0.769861	+	0.748930i
$777$	4.72051	+	7.17439i	0.169347	+	0.257380i
$778$	−24.7768	+	24.5502i	−0.888290	+	0.880167i
$779$	3.51526	−	6.08862i	0.125947	−	0.218147i
$780$	7.94458	+	19.7801i	0.284462	+	0.708241i
$781$	19.4258	−	11.2155i	0.695111	−	0.401323i
$782$	−21.5049	+	5.65647i	−0.769013	+	0.202275i
$783$			2.95272i			0.105522i
$784$	16.3131	+	22.7570i	0.582611	+	0.812751i
$785$	5.29759	−	39.7513i	0.189079	−	1.41879i
$786$	18.1382	+	68.9581i	0.646967	+	2.45965i
$787$	18.8744	+	32.6914i	0.672800	+	1.16532i	0.977107	+	0.212749i	$0.0682418\pi$
$787$	18.8744	+	32.6914i	0.672800	+	1.16532i	−0.304307	+	0.952574i	$0.598425\pi$
$788$	12.8629	−	7.26966i	0.458222	−	0.258971i
$789$	28.3703	−	49.1389i	1.01001	−	1.74939i
$790$	−19.8253	+	15.0187i	−0.705351	+	0.534340i
$791$	−19.3788	+	12.7506i	−0.689030	+	0.453359i
$792$	−35.1601	+	34.2042i	−1.24936	+	1.21539i
$793$	−9.04414	−	5.22164i	−0.321167	−	0.185426i
$794$	−30.8746	−	8.42502i	−1.09570	−	0.298993i
$795$	27.2009	+	65.9649i	0.964718	+	2.33953i
$796$	−9.70616	−	5.72339i	−0.344026	−	0.202860i
$797$		−	28.3177i		−	1.00306i	−0.865139	−	0.501532i	$-0.832770\pi$
$797$		−	28.3177i		−	1.00306i	0.865139	−	0.501532i	$-0.167230\pi$
$798$	−55.4680	+	61.7775i	−1.96355	+	2.18690i
$799$			16.4728i			0.582767i
$800$	28.2746	+	0.739375i	0.999658	+	0.0261408i
$801$	54.2035	−	31.2944i	1.91519	−	1.10573i
$802$	−8.90707	+	32.6411i	−0.314520	+	1.15260i
$803$	4.92311	−	8.52707i	0.173733	−	0.300914i
$804$	18.9632	+	0.174224i	0.668781	+	0.00614441i
$805$	−10.3632	+	15.2219i	−0.365256	+	0.536502i
$806$	10.8382	−	10.7390i	0.381758	−	0.378266i
$807$	2.23244	−	3.86671i	0.0785857	−	0.136115i
$808$	−13.2658	−	3.75124i	−0.466690	−	0.131968i
$809$	0.715781	+	1.23977i	0.0251655	+	0.0435879i	0.878334	−	0.478048i	$-0.158655\pi$
$809$	0.715781	+	1.23977i	0.0251655	+	0.0435879i	−0.853168	+	0.521636i	$0.825322\pi$
$810$	−17.1413	+	2.14899i	−0.602285	+	0.0755078i
$811$			0.229410i			0.00805567i	0.999992	+	0.00402783i	$0.00128210\pi$
$811$			0.229410i			0.00805567i	−0.999992	+	0.00402783i	$0.998718\pi$
$812$	−0.941058	+	1.83245i	−0.0330247	+	0.0643065i
$813$	54.6357			1.91616
$814$	−4.70147	+	1.23664i	−0.164787	+	0.0433441i
$815$	35.5062	−	14.6411i	1.24373	−	0.512857i
$816$	−28.6599	−	51.8164i	−1.00330	−	1.81394i
$817$	12.1603	−	21.0622i	0.425434	−	0.736874i
$818$	29.1486	−	28.8820i	1.01916	−	1.00984i
$819$	−1.40249	−	24.0058i	−0.0490070	−	0.838831i
$820$	4.11088	+	0.586336i	0.143558	+	0.0204757i
$821$	2.36907	+	1.36778i	0.0826810	+	0.0477359i	0.540771	−	0.841170i	$-0.318133\pi$
$821$	2.36907	+	1.36778i	0.0826810	+	0.0477359i	−0.458089	+	0.888906i	$0.651466\pi$
$822$	18.5175	+	5.05304i	0.645873	+	0.176245i
$823$	1.56485	+	2.71040i	0.0545472	+	0.0944784i	0.892010	−	0.452016i	$-0.149295\pi$
$823$	1.56485	+	2.71040i	0.0545472	+	0.0944784i	−0.837462	+	0.546495i	$0.815962\pi$
$824$	34.7689	−	8.80461i	1.21123	−	0.306723i
$825$	43.8875	+	11.9091i	1.52797	+	0.414622i
$826$	24.1479	+	5.09739i	0.840213	+	0.177361i
$827$		−	32.3184i		−	1.12382i	−0.827198	−	0.561911i	$-0.810066\pi$
$827$		−	32.3184i		−	1.12382i	0.827198	−	0.561911i	$-0.189934\pi$
$828$	29.9663	+	17.6701i	1.04140	+	0.614078i
$829$	4.80290	+	8.31887i	0.166812	+	0.288926i	0.937297	−	0.348531i	$-0.113319\pi$
$829$	4.80290	+	8.31887i	0.166812	+	0.288926i	−0.770486	+	0.637457i	$0.779986\pi$
$830$	12.6936	−	30.1172i	0.440603	−	1.04538i
$831$	−13.9118	+	24.0960i	−0.482597	+	0.835882i
$832$	13.0066	+	0.358575i	0.450923	+	0.0124313i
$833$	−35.1196	+	4.11763i	−1.21682	+	0.142668i
$834$	35.4975	−	35.1728i	1.22918	−	1.21794i
$835$	41.0958	+	31.6377i	1.42218	+	1.09487i
$836$	−23.1238	−	40.9151i	−0.799753	−	1.41508i
$837$	25.1559	+	43.5713i	0.869516	+	1.50605i
$838$	−6.53756	−	24.8547i	−0.225836	−	0.858590i
$839$	−37.5135			−1.29511			−0.647555	−	0.762019i	$-0.724208\pi$
$839$	−37.5135			−1.29511			−0.647555	+	0.762019i	$0.724208\pi$
$840$	−46.0694	−	16.8016i	−1.58955	−	0.579709i
$841$	28.8484			0.994774
$842$	11.1500	+	42.3903i	0.384255	+	1.46087i
$843$	13.3550	+	23.1315i	0.459970	+	0.796692i
$844$	8.95031	−	5.05840i	0.308082	−	0.174117i
$845$	−14.1243	+	18.3467i	−0.485890	+	0.631146i
$846$	18.3065	−	18.1391i	0.629391	−	0.623635i
$847$	3.61434	−	0.211160i	0.124190	−	0.00725555i
$848$	43.5476	+	0.800253i	1.49543	+	0.0274808i
$849$	22.7838	−	39.4627i	0.781938	−	1.35436i
$850$	−18.0994	+	30.7940i	−0.620804	+	1.05623i
$851$	1.72385	+	2.98579i	0.0590928	+	0.102352i
$852$	21.5173	−	36.4908i	0.737172	−	1.25015i
$853$		−	38.6732i		−	1.32415i	−0.749439	−	0.662073i	$-0.769677\pi$
$853$		−	38.6732i		−	1.32415i	0.749439	−	0.662073i	$-0.230323\pi$
$854$	22.8386	−	7.45616i	0.781521	−	0.255144i
$855$	12.4983	−	93.7833i	0.427434	−	3.20732i
$856$	24.0917	−	6.10080i	0.823438	−	0.208521i
$857$	−6.47602	−	11.2168i	−0.221217	−	0.383158i	0.733961	−	0.679192i	$-0.237669\pi$
$857$	−6.47602	−	11.2168i	−0.221217	−	0.383158i	−0.955178	+	0.296033i	$0.904336\pi$
$858$	20.1817	+	5.50715i	0.688991	+	0.188011i
$859$	6.46557	+	3.73290i	0.220603	+	0.127365i	0.606229	−	0.795290i	$-0.292681\pi$
$859$	6.46557	+	3.73290i	0.220603	+	0.127365i	−0.385627	+	0.922655i	$0.626015\pi$
$860$	14.2207	+	2.02830i	0.484921	+	0.0691645i
$861$	−6.43413	−	3.22990i	−0.219275	−	0.110075i
$862$	20.5268	−	20.3391i	0.699146	−	0.692752i
$863$	−13.8213	+	23.9392i	−0.470482	+	0.814899i	−0.999430	−	0.0337553i	$-0.989253\pi$
$863$	−13.8213	+	23.9392i	−0.470482	+	0.814899i	0.528948	+	0.848654i	$0.322587\pi$
$864$	−12.0537	+	41.1777i	−0.410074	+	1.40090i
$865$	32.4239	−	13.3702i	1.10245	−	0.454599i
$866$	3.51887	−	0.925574i	0.119576	−	0.0314523i
$867$	24.9601			0.847689
$868$	1.72516	+	35.0578i	0.0585557	+	1.18994i
$869$			24.4092i			0.828026i
$870$	−0.448782	−	3.57969i	−0.0152151	−	0.121363i
$871$	−2.63123	−	4.55743i	−0.0891560	−	0.154423i
$872$	2.39277	−	8.46174i	0.0810294	−	0.286551i
$873$	−29.5562	+	51.1928i	−1.00033	+	1.73261i
$874$	−23.6763	+	23.4597i	−0.800862	+	0.793538i
$875$	5.42646	+	29.0784i	0.183448	+	0.983029i
$876$	0.170836	−	18.5944i	0.00577200	−	0.628247i
$877$	26.6238	−	46.1138i	0.899023	−	1.55715i	0.0702771	−	0.997528i	$-0.477612\pi$
$877$	26.6238	−	46.1138i	0.899023	−	1.55715i	0.828746	−	0.559625i	$-0.189055\pi$
$878$	5.70368	−	20.9019i	0.192490	−	0.705404i
$879$	22.1415	−	12.7834i	0.746814	−	0.431174i
$880$	17.3344	−	21.6805i	0.584344	−	0.730849i
$881$			48.2909i			1.62696i	0.581592	+	0.813480i	$0.302430\pi$
$881$			48.2909i			1.62696i	−0.581592	+	0.813480i	$0.697570\pi$
$882$	43.2481	+	34.4949i	1.45624	+	1.16150i
$883$		−	19.1196i		−	0.643426i	−0.946837	−	0.321713i	$-0.895741\pi$
$883$		−	19.1196i		−	0.643426i	0.946837	−	0.321713i	$-0.104259\pi$
$884$	−8.34630	+	14.1543i	−0.280716	+	0.476060i
$885$	−39.9592	+	16.4774i	−1.34321	+	0.553881i
$886$	8.26377	+	2.25501i	0.277627	+	0.0757585i
$887$	−29.2779	−	16.9036i	−0.983057	−	0.567568i	−0.0798654	−	0.996806i	$-0.525449\pi$
$887$	−29.2779	−	16.9036i	−0.983057	−	0.567568i	−0.903192	+	0.429237i	$0.858782\pi$
$888$	−6.58082	+	6.40190i	−0.220838	+	0.214834i
$889$	−8.47216	−	12.8763i	−0.284147	−	0.431856i
$890$	−28.2320	+	21.3872i	−0.946340	+	0.716902i
$891$	−8.47714	+	14.6828i	−0.283995	+	0.491894i
$892$	5.61659	+	9.93797i	0.188057	+	0.332748i
$893$	12.3457	+	21.3834i	0.413134	+	0.715570i
$894$	18.2800	+	69.4974i	0.611375	+	2.32434i
$895$	7.99616	+	1.06563i	0.267282	+	0.0356202i
$896$	−20.6042	+	21.7133i	−0.688339	+	0.725389i
$897$		−	14.8362i		−	0.495365i
$898$	13.5924	−	3.57523i	0.453584	−	0.119307i
$899$	−2.23637	+	1.29117i	−0.0745870	+	0.0430628i
$900$	54.1521	−	13.7948i	1.80507	−	0.459826i
$901$	−27.5020	+	47.6349i	−0.916224	+	1.58695i
$902$	2.89486	−	2.86838i	0.0963882	−	0.0955067i
$903$	−22.2574	−	11.1731i	−0.740682	−	0.371818i
$904$	−17.2922	−	17.7755i	−0.575130	−	0.591204i
$905$	5.43559	−	7.06055i	0.180685	−	0.234701i
$906$	77.6578	+	21.1912i	2.58001	+	0.704029i
$907$	−16.9052	+	9.76020i	−0.561327	+	0.324082i	−0.753678	−	0.657244i	$-0.771722\pi$
$907$	−16.9052	+	9.76020i	−0.561327	+	0.324082i	0.192351	+	0.981326i	$0.438389\pi$
$908$	−31.8552	−	18.7839i	−1.05715	−	0.623367i
$909$	−27.2371			−0.903399
$910$	2.47735	+	13.3804i	0.0821235	+	0.443556i
$911$			47.4878i			1.57334i	0.617373	+	0.786671i	$0.288197\pi$
$911$			47.4878i			1.57334i	−0.617373	+	0.786671i	$0.711803\pi$
$912$	−76.0379	−	45.7836i	−2.51787	−	1.51605i
$913$	−16.0376	−	27.7780i	−0.530768	−	0.919317i
$914$	25.1390	+	6.85990i	0.831525	+	0.226905i
$915$	−25.6671	+	33.3403i	−0.848528	+	1.10220i
$916$	−0.176027	+	19.1595i	−0.00581611	+	0.633048i
$917$	2.65484	+	45.4419i	0.0876707	+	1.50062i
$918$	−38.1375	−	38.4895i	−1.25872	−	1.27034i
$919$	2.97980	+	1.72039i	0.0982945	+	0.0567503i	0.548341	−	0.836255i	$-0.315259\pi$
$919$	2.97980	+	1.72039i	0.0982945	+	0.0567503i	−0.450047	+	0.893005i	$0.648593\pi$
$920$	−18.0698	−	7.81221i	−0.595743	−	0.257561i
$921$	10.4497	+	18.0995i	0.344330	+	0.596398i
$922$	−24.0797	+	6.33373i	−0.793024	+	0.208590i
$923$	−11.7555			−0.386936
$924$	−40.4451	+	26.0823i	−1.33055	+	0.858043i
$925$	5.34489	+	1.45037i	0.175739	+	0.0476878i
$926$	−39.0391	+	10.2685i	−1.28291	+	0.337445i
$927$	61.3679	−	35.4308i	2.01559	−	1.16370i
$928$	−2.11351	−	0.618674i	−0.0693794	−	0.0203090i
$929$	−14.8975	−	8.60107i	−0.488771	−	0.282192i	0.235293	−	0.971924i	$-0.424395\pi$
$929$	−14.8975	−	8.60107i	−0.488771	−	0.282192i	−0.724064	+	0.689732i	$0.757728\pi$
$930$	−37.1198	−	48.9997i	−1.21721	−	1.60676i
$931$	−42.5029	+	31.6659i	−1.39298	+	1.03781i
$932$	8.41229	+	0.0772877i	0.275554	+	0.00253164i
$933$	−46.3859	+	80.3428i	−1.51861	+	2.63030i
$934$	2.30260	−	8.43819i	0.0753434	−	0.276106i
$935$	13.3635	+	32.4079i	0.437034	+	1.05985i
$936$	24.9204	−	6.31066i	0.814550	−	0.206270i
$937$	−16.8939			−0.551901			−0.275950	−	0.961172i	$-0.588993\pi$
$937$	−16.8939			−0.551901			−0.275950	+	0.961172i	$0.588993\pi$
$938$	11.8453	+	2.50044i	0.386764	+	0.0816423i
$939$	−67.5111			−2.20314
$940$	−9.00212	+	11.4737i	−0.293617	+	0.374230i
$941$	28.6433	+	49.6117i	0.933746	+	1.61729i	0.776856	+	0.629679i	$0.216813\pi$
$941$	28.6433	+	49.6117i	0.933746	+	1.61729i	0.156890	+	0.987616i	$0.449853\pi$
$942$	−71.7065	−	19.5672i	−2.33632	−	0.637533i
$943$	−2.50297	−	1.44509i	−0.0815079	−	0.0470586i
$944$	−0.484765	+	26.3796i	−0.0157778	+	0.858584i
$945$	−44.7486	−	3.32335i	−1.45567	−	0.108109i
$946$	10.0141	−	9.92254i	0.325587	−	0.322610i
$947$	−28.0175	−	16.1759i	−0.910447	−	0.525647i	−0.0298722	−	0.999554i	$-0.509510\pi$
$947$	−28.0175	−	16.1759i	−0.910447	−	0.525647i	−0.880575	+	0.473907i	$0.842843\pi$
$948$	22.6814	+	40.1324i	0.736658	+	1.30344i
$949$	−4.46880	+	2.58006i	−0.145063	+	0.0837523i
$950$	−0.415970	+	53.5386i	−0.0134959	+	1.73702i
$951$	−52.3692			−1.69819
$952$	−11.4011	−	36.0413i	−0.369513	−	1.16811i
$953$			36.4296i			1.18007i	0.807377	+	0.590036i	$0.200886\pi$
$953$			36.4296i			1.18007i	−0.807377	+	0.590036i	$0.799114\pi$
$954$	83.2213	−	21.8899i	2.69439	−	0.708710i
$955$	19.1141	−	7.88180i	0.618519	−	0.255049i
$956$	−21.1963	−	37.5046i	−0.685536	−	1.21298i
$957$	−3.06628	−	1.77032i	−0.0991186	−	0.0572262i
$958$	13.1144	+	13.2354i	0.423707	+	0.427618i
$959$	10.9512	+	5.49744i	0.353632	+	0.177521i
$960$	8.35454	−	51.7534i	0.269642	−	1.67033i
$961$	−6.50040	+	11.2590i	−0.209690	+	0.363195i
$962$	2.45785	+	0.670695i	0.0792443	+	0.0216241i
$963$	42.5225	−	24.5504i	1.37027	−	0.791124i
$964$	8.82110	−	14.9595i	0.284108	−	0.481813i
$965$	−3.61265	+	27.1081i	−0.116295	+	0.872640i
$966$	25.3961	+	22.8023i	0.817107	+	0.733653i
$967$	15.8537			0.509822			0.254911	−	0.966964i	$-0.417954\pi$
$967$	15.8537			0.509822			0.254911	+	0.966964i	$0.417954\pi$
$968$	0.950140	+	3.75205i	0.0305387	+	0.120595i
$969$	97.0716	−	56.0443i	3.11839	−	1.80040i
$970$	12.9920	−	30.8251i	0.417147	−	0.989733i
$971$	−39.0664	−	22.5550i	−1.25370	−	0.723825i	−0.281859	−	0.959456i	$-0.590951\pi$
$971$	−39.0664	−	22.5550i	−1.25370	−	0.723825i	−0.971843	+	0.235631i	$0.924284\pi$
$972$	0.123926	−	13.4886i	0.00397493	−	0.432646i
$973$	26.6502	−	17.5349i	0.854365	−	0.562144i
$974$	1.32439	+	1.33661i	0.0424362	+	0.0428279i
$975$	−16.7981	−	16.9051i	−0.537970	−	0.541398i
$976$	12.4310	+	22.4749i	0.397907	+	0.719405i
$977$	17.5983	−	10.1604i	0.563019	−	0.325059i	−0.191338	−	0.981524i	$-0.561283\pi$
$977$	17.5983	−	10.1604i	0.563019	−	0.325059i	0.754356	+	0.656465i	$0.227949\pi$
$978$	−18.1078	−	68.8426i	−0.579023	−	2.20134i
$979$			34.7598i			1.11093i
$980$	−26.7118	−	16.3243i	−0.853276	−	0.521459i
$981$		−	17.3735i		−	0.554693i
$982$	−59.8529	+	15.7432i	−1.90998	+	0.502386i
$983$	−1.38824	+	0.801501i	−0.0442780	+	0.0255639i	−0.521976	−	0.852960i	$-0.674805\pi$
$983$	−1.38824	+	0.801501i	−0.0442780	+	0.0255639i	0.477698	+	0.878524i	$0.341471\pi$
$984$	2.09423	−	7.40600i	0.0667617	−	0.236095i
$985$	−10.0769	+	13.0894i	−0.321078	+	0.417064i
$986$	1.97553	−	1.95747i	0.0629138	−	0.0623384i
$987$	21.1222	−	13.8977i	0.672328	−	0.442369i
$988$	−0.226278	+	24.6290i	−0.00719886	+	0.783552i
$989$	−8.65847	−	4.99897i	−0.275323	−	0.158958i
$990$	21.3001	−	50.5371i	0.676962	−	1.60618i
$991$	23.9870	−	13.8489i	0.761971	−	0.439924i	−0.0680321	−	0.997683i	$-0.521672\pi$
$991$	23.9870	−	13.8489i	0.761971	−	0.439924i	0.830003	+	0.557759i	$0.188339\pi$
$992$	−36.4586	+	8.87687i	−1.15756	+	0.281841i
$993$	−4.16083			−0.132040
$994$	18.0675	−	20.1227i	0.573066	−	0.638253i
$995$	12.4876	+	1.66419i	0.395882	+	0.0527585i
$996$	−52.1800	−	30.7687i	−1.65339	−	0.974944i
$997$	36.4937	−	21.0697i	1.15577	−	0.667283i	0.205482	−	0.978661i	$-0.434124\pi$
$997$	36.4937	−	21.0697i	1.15577	−	0.667283i	0.950286	+	0.311378i	$0.100790\pi$
$998$	11.3217	−	41.4900i	0.358383	−	1.31334i
$999$	−4.20056	+	7.27558i	−0.132900	+	0.230189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.ba.b.19.4	✓	80
4.3	odd	2		1120.2.bq.b.719.37		80
5.4	even	2	inner	280.2.ba.b.19.37	yes	80
7.3	odd	6	inner	280.2.ba.b.59.24	yes	80
8.3	odd	2	inner	280.2.ba.b.19.17	yes	80
8.5	even	2		1120.2.bq.b.719.38		80
20.19	odd	2		1120.2.bq.b.719.3		80
28.3	even	6		1120.2.bq.b.1039.4		80
35.24	odd	6	inner	280.2.ba.b.59.17	yes	80
40.19	odd	2	inner	280.2.ba.b.19.24	yes	80
40.29	even	2		1120.2.bq.b.719.4		80
56.3	even	6	inner	280.2.ba.b.59.37	yes	80
56.45	odd	6		1120.2.bq.b.1039.3		80
140.59	even	6		1120.2.bq.b.1039.38		80
280.59	even	6	inner	280.2.ba.b.59.4	yes	80
280.269	odd	6		1120.2.bq.b.1039.37		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.ba.b.19.4	✓	80	1.1	even	1	trivial
280.2.ba.b.19.17	yes	80	8.3	odd	2	inner
280.2.ba.b.19.24	yes	80	40.19	odd	2	inner
280.2.ba.b.19.37	yes	80	5.4	even	2	inner
280.2.ba.b.59.4	yes	80	280.59	even	6	inner
280.2.ba.b.59.17	yes	80	35.24	odd	6	inner
280.2.ba.b.59.24	yes	80	7.3	odd	6	inner
280.2.ba.b.59.37	yes	80	56.3	even	6	inner
1120.2.bq.b.719.3		80	20.19	odd	2
1120.2.bq.b.719.4		80	40.29	even	2
1120.2.bq.b.719.37		80	4.3	odd	2
1120.2.bq.b.719.38		80	8.5	even	2
1120.2.bq.b.1039.3		80	56.45	odd	6
1120.2.bq.b.1039.4		80	28.3	even	6
1120.2.bq.b.1039.37		80	280.269	odd	6
1120.2.bq.b.1039.38		80	140.59	even	6

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36769 + 0.359747i) q^{2} +(-1.46528 - 2.53794i) q^{3} +(1.74116 - 0.984045i) q^{4} +(-1.36405 + 1.77183i) q^{5} +(2.91706 + 2.94399i) q^{6} +(1.45426 + 2.21023i) q^{7} +(-2.02737 + 1.97225i) q^{8} +(-2.79408 + 4.83948i) q^{9} +O(q^{10})\)	\(q+(-1.36769 + 0.359747i) q^{2} +(-1.46528 - 2.53794i) q^{3} +(1.74116 - 0.984045i) q^{4} +(-1.36405 + 1.77183i) q^{5} +(2.91706 + 2.94399i) q^{6} +(1.45426 + 2.21023i) q^{7} +(-2.02737 + 1.97225i) q^{8} +(-2.79408 + 4.83948i) q^{9} +(1.22819 - 2.91403i) q^{10} +(-1.55174 - 2.68769i) q^{11} +(-5.04873 - 2.97706i) q^{12} +1.62644i q^{13} +(-2.78410 - 2.49975i) q^{14} +(6.49549 + 0.865643i) q^{15} +(2.06331 - 3.42677i) q^{16} +(2.52573 + 4.37469i) q^{17} +(2.08045 - 7.62408i) q^{18} +(6.55731 + 3.78587i) q^{19} +(-0.631472 + 4.42733i) q^{20} +(3.47853 - 6.92942i) q^{21} +(3.08919 + 3.11770i) q^{22} +(1.55633 - 2.69565i) q^{23} +(7.97610 + 2.25544i) q^{24} +(-1.27875 - 4.83371i) q^{25} +(-0.585108 - 2.22448i) q^{26} +7.58472 q^{27} +(4.70707 + 2.41732i) q^{28} +0.389298i q^{29} +(-9.19525 + 1.15280i) q^{30} +(3.31666 + 5.74462i) q^{31} +(-1.58920 + 5.42904i) q^{32} +(-4.54746 + 7.87643i) q^{33} +(-5.02820 - 5.07461i) q^{34} +(-5.89983 - 0.438163i) q^{35} +(-0.102678 + 11.1758i) q^{36} +(-0.553818 + 0.959241i) q^{37} +(-10.3303 - 2.81893i) q^{38} +(4.12781 - 2.38319i) q^{39} +(-0.729058 - 6.28239i) q^{40} -0.928523i q^{41} +(-2.26473 + 10.7287i) q^{42} -3.21202i q^{43} +(-5.34664 - 3.15273i) q^{44} +(-4.76348 - 11.5519i) q^{45} +(-1.15883 + 4.24670i) q^{46} +(2.82412 + 1.63050i) q^{47} +(-11.7202 - 0.215377i) q^{48} +(-2.77026 + 6.42850i) q^{49} +(3.48785 + 6.15101i) q^{50} +(7.40178 - 12.8203i) q^{51} +(1.60049 + 2.83191i) q^{52} +(5.44437 + 9.42993i) q^{53} +(-10.3736 + 2.72858i) q^{54} +(6.87877 + 0.916722i) q^{55} +(-7.30745 - 1.61280i) q^{56} -22.1894i q^{57} +(-0.140049 - 0.532440i) q^{58} +(-5.71232 + 3.29801i) q^{59} +(12.1616 - 4.88463i) q^{60} +(-3.21046 + 5.56068i) q^{61} +(-6.60277 - 6.66371i) q^{62} +(-14.7597 + 0.862304i) q^{63} +(0.220465 - 7.99696i) q^{64} +(-2.88178 - 2.21855i) q^{65} +(3.38600 - 12.4085i) q^{66} +(-2.80208 + 1.61778i) q^{67} +(8.70260 + 5.13162i) q^{68} -9.12183 q^{69} +(8.22678 - 1.52317i) q^{70} +7.22771i q^{71} +(-3.88004 - 15.3220i) q^{72} +(1.58632 + 2.74759i) q^{73} +(0.412369 - 1.51118i) q^{74} +(-10.3939 + 10.3281i) q^{75} +(15.1428 + 0.139124i) q^{76} +(3.68379 - 7.33831i) q^{77} +(-4.78823 + 4.74444i) q^{78} +(-6.81139 - 3.93256i) q^{79} +(3.25720 + 8.33011i) q^{80} +(-2.73150 - 4.73109i) q^{81} +(0.334033 + 1.26993i) q^{82} +10.3353 q^{83} +(-0.762164 - 15.4883i) q^{84} +(-11.1964 - 1.49213i) q^{85} +(1.15551 + 4.39306i) q^{86} +(0.988013 - 0.570429i) q^{87} +(8.44675 + 2.38853i) q^{88} +(-9.69972 - 5.60014i) q^{89} +(10.6707 + 14.0858i) q^{90} +(-3.59482 + 2.36527i) q^{91} +(0.0571926 - 6.22506i) q^{92} +(9.71964 - 16.8349i) q^{93} +(-4.44909 - 1.21406i) q^{94} +(-15.6524 + 6.45433i) q^{95} +(16.1072 - 3.92175i) q^{96} +10.5782 q^{97} +(1.47623 - 9.78881i) q^{98} +17.3427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 6 q^{4} - 52 q^{9}+O(q^{10}) \) 80 * q + 6 * q^4 - 52 * q^9	\( 80 q + 6 q^{4} - 52 q^{9} - 12 q^{10} - 6 q^{14} + 10 q^{16} - 48 q^{19} + 12 q^{24} - 22 q^{25} + 54 q^{26} - 20 q^{30} - 22 q^{35} + 28 q^{36} + 12 q^{40} + 38 q^{44} + 14 q^{46} + 16 q^{49} - 40 q^{50} + 20 q^{51} + 60 q^{54} - 104 q^{56} - 60 q^{59} - 42 q^{60} - 60 q^{64} - 12 q^{65} + 84 q^{66} - 22 q^{70} + 34 q^{74} - 6 q^{75} - 96 q^{80} - 100 q^{84} - 8 q^{86} - 36 q^{89} + 72 q^{91} - 66 q^{94} + 96 q^{96} + 104 q^{99}+O(q^{100}) \) 80 * q + 6 * q^4 - 52 * q^9 - 12 * q^10 - 6 * q^14 + 10 * q^16 - 48 * q^19 + 12 * q^24 - 22 * q^25 + 54 * q^26 - 20 * q^30 - 22 * q^35 + 28 * q^36 + 12 * q^40 + 38 * q^44 + 14 * q^46 + 16 * q^49 - 40 * q^50 + 20 * q^51 + 60 * q^54 - 104 * q^56 - 60 * q^59 - 42 * q^60 - 60 * q^64 - 12 * q^65 + 84 * q^66 - 22 * q^70 + 34 * q^74 - 6 * q^75 - 96 * q^80 - 100 * q^84 - 8 * q^86 - 36 * q^89 + 72 * q^91 - 66 * q^94 + 96 * q^96 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more