LMFDB - Embedded newform 280.2.ba.b.59.24

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			59.24
Character	$\chi$	$=$	280.59
Dual form			280.2.ba.b.19.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.372297 - 1.36433i) q^{2} +(1.46528 - 2.53794i) q^{3} +(-1.72279 - 1.01587i) q^{4} +(0.852425 + 2.06721i) q^{5} +(-2.91706 - 2.94399i) q^{6} +(1.45426 - 2.21023i) q^{7} +(-2.02737 + 1.97225i) q^{8} +(-2.79408 - 4.83948i) q^{9} +O(q^{10})$	\(q+(0.372297 - 1.36433i) q^{2} +(1.46528 - 2.53794i) q^{3} +(-1.72279 - 1.01587i) q^{4} +(0.852425 + 2.06721i) 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} +(3.13772 - 0.393372i) q^{10} +(-1.55174 + 2.68769i) q^{11} +(-5.10258 + 2.88380i) q^{12} -1.62644i q^{13} +(-2.47407 - 2.80695i) q^{14} +(6.49549 + 0.865643i) q^{15} +(1.93602 + 3.50026i) q^{16} +(-2.52573 + 4.37469i) q^{17} +(-7.64287 + 2.01032i) 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} +(2.03478 + 8.03523i) q^{24} +(-3.54674 + 3.52429i) q^{25} +(-2.21901 - 0.605520i) q^{26} -7.58472 q^{27} +(-4.75069 + 2.33043i) q^{28} +0.389298i q^{29} +(3.59927 - 8.53972i) q^{30} +(-3.31666 + 5.74462i) q^{31} +(5.49629 - 1.33823i) q^{32} +(4.54746 + 7.87643i) q^{33} +(5.02820 + 5.07461i) q^{34} +(5.80867 + 1.12221i) q^{35} +(-0.102678 + 11.1758i) q^{36} +(-0.553818 - 0.959241i) q^{37} +(-2.72390 - 10.3558i) q^{38} +(-4.12781 - 2.38319i) q^{39} +(-5.80524 - 2.50981i) q^{40} +0.928523i q^{41} +(-10.7491 + 2.16607i) q^{42} -3.21202i q^{43} +(5.40367 - 3.05396i) q^{44} +(7.62250 - 9.90125i) q^{45} +(4.25717 - 1.11977i) 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} +(-1.65226 + 2.80202i) q^{52} +(5.44437 - 9.42993i) q^{53} +(-2.82377 + 10.3481i) q^{54} +(-6.87877 - 0.916722i) q^{55} +(1.41081 + 7.34912i) q^{56} -22.1894i q^{57} +(0.531131 + 0.144934i) q^{58} +(-5.71232 - 3.29801i) q^{59} +(-10.3110 - 8.08990i) 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} +(3.36221 - 1.38642i) q^{65} +(12.4390 - 3.27186i) q^{66} +(2.80208 + 1.61778i) q^{67} +(8.79541 - 4.97086i) q^{68} +9.12183 q^{69} +(3.69361 - 7.50715i) q^{70} +7.22771i q^{71} +(15.2093 + 4.30081i) q^{72} +(-1.58632 + 2.74759i) q^{73} +(-1.51490 + 0.398468i) q^{74} +(3.74745 + 14.1655i) 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} +(-5.58549 + 6.98587i) q^{80} +(-2.73150 + 4.73109i) q^{81} +(1.26681 + 0.345686i) q^{82} -10.3353 q^{83} +(-1.04661 + 15.4717i) q^{84} +(-11.1964 - 1.49213i) q^{85} +(-4.38226 - 1.19582i) q^{86} +(0.988013 + 0.570429i) q^{87} +(-2.15485 - 8.50936i) 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} +(-1.17314 - 4.46005i) q^{94} +(13.4158 + 10.3282i) q^{95} +(4.65725 - 15.9101i) q^{96} -10.5782 q^{97} +(-9.80196 + 1.38624i) 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 $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.372297	−	1.36433i	0.263253	−	0.964727i
$2$	0.372297	−	1.36433i	0.263253	−	0.964727i
$3$	1.46528	−	2.53794i	0.845978	−	1.46528i	−0.0387905	−	0.999247i	$-0.512350\pi$
$3$	1.46528	−	2.53794i	0.845978	−	1.46528i	0.884769	−	0.466030i	$-0.154316\pi$
$4$	−1.72279	−	1.01587i	−0.861395	−	0.507935i
$5$	0.852425	+	2.06721i	0.381216	+	0.924486i
$5$	0.852425	+	2.06721i	0.381216	+	0.924486i
$6$	−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
$10$	3.13772	−	0.393372i	0.992233	−	0.124395i
$11$	−1.55174	+	2.68769i	−0.467867	+	0.810369i	−0.999326	−	0.0367148i	$-0.988311\pi$
$11$	−1.55174	+	2.68769i	−0.467867	+	0.810369i	0.531459	+	0.847084i	$0.321644\pi$
$12$	−5.10258	+	2.88380i	−1.47299	+	0.832481i
$13$		−	1.62644i		−	0.451094i	−0.974232	−	0.225547i	$-0.927583\pi$
$13$		−	1.62644i		−	0.451094i	0.974232	−	0.225547i	$-0.0724170\pi$
$14$	−2.47407	−	2.80695i	−0.661223	−	0.750189i
$15$	6.49549	+	0.865643i	1.67713	+	0.223508i
$16$	1.93602	+	3.50026i	0.484004	+	0.875066i
$17$	−2.52573	+	4.37469i	−0.612579	+	1.06102i	0.378225	+	0.925714i	$0.376534\pi$
$17$	−2.52573	+	4.37469i	−0.612579	+	1.06102i	−0.990804	+	0.135304i	$0.956799\pi$
$18$	−7.64287	+	2.01032i	−1.80144	+	0.473837i
$19$	6.55731	−	3.78587i	1.50435	−	0.868537i	0.504363	−	0.863492i	$-0.331727\pi$
$19$	6.55731	−	3.78587i	1.50435	−	0.868537i	0.999987	−	0.00504564i	$-0.00160608\pi$
$20$	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	0.981415	−	0.191899i	$-0.0614647\pi$
$23$	1.55633	+	2.69565i	0.324518	+	0.562081i	−0.656897	+	0.753980i	$0.728131\pi$
$24$	2.03478	+	8.03523i	0.415348	+	1.64018i
$25$	−3.54674	+	3.52429i	−0.709349	+	0.704858i
$26$	−2.21901	−	0.605520i	−0.435183	−	0.118752i
$27$	−7.58472			−1.45968
$28$	−4.75069	+	2.33043i	−0.897797	+	0.440410i
$29$			0.389298i			0.0722908i	0.999347	+	0.0361454i	$0.0115079\pi$
$29$			0.389298i			0.0722908i	−0.999347	+	0.0361454i	$0.988492\pi$
$30$	3.59927	−	8.53972i	0.657134	−	1.55913i
$31$	−3.31666	+	5.74462i	−0.595689	+	1.03176i	0.397760	+	0.917489i	$0.369788\pi$
$31$	−3.31666	+	5.74462i	−0.595689	+	1.03176i	−0.993449	+	0.114274i	$0.963546\pi$
$32$	5.49629	−	1.33823i	0.971615	−	0.236567i
$33$	4.54746	+	7.87643i	0.791611	+	1.37111i
$34$	5.02820	+	5.07461i	0.862329	+	0.870288i
$35$	5.80867	+	1.12221i	0.981844	+	0.189688i
$36$	−0.102678	+	11.1758i	−0.0171130	+	1.86264i
$37$	−0.553818	−	0.959241i	−0.0910471	−	0.157698i	0.816905	−	0.576772i	$-0.195688\pi$
$37$	−0.553818	−	0.959241i	−0.0910471	−	0.157698i	−0.907952	+	0.419074i	$0.862355\pi$
$38$	−2.72390	−	10.3558i	−0.441876	−	1.67993i
$39$	−4.12781	−	2.38319i	−0.660979	−	0.381616i
$40$	−5.80524	−	2.50981i	−0.917889	−	0.396837i
$41$			0.928523i			0.145011i	0.997368	+	0.0725055i	$0.0230995\pi$
$41$			0.928523i			0.145011i	−0.997368	+	0.0725055i	$0.976901\pi$
$42$	−10.7491	+	2.16607i	−1.65862	+	0.334231i
$43$		−	3.21202i		−	0.489829i	−0.969545	−	0.244914i	$-0.921240\pi$
$43$		−	3.21202i		−	0.489829i	0.969545	−	0.244914i	$-0.0787598\pi$
$44$	5.40367	−	3.05396i	0.814633	−	0.460402i
$45$	7.62250	−	9.90125i	1.13630	−	1.47599i
$46$	4.25717	−	1.11977i	0.627685	−	0.165101i
$47$	2.82412	−	1.63050i	0.411940	−	0.237833i	−0.279683	−	0.960092i	$-0.590229\pi$
$47$	2.82412	−	1.63050i	0.411940	−	0.237833i	0.691623	+	0.722259i	$0.256896\pi$
$48$	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
$52$	−1.65226	+	2.80202i	−0.229127	+	0.388571i
$53$	5.44437	−	9.42993i	0.747842	−	1.29530i	−0.201013	−	0.979589i	$-0.564423\pi$
$53$	5.44437	−	9.42993i	0.747842	−	1.29530i	0.948855	−	0.315712i	$-0.102243\pi$
$54$	−2.82377	+	10.3481i	−0.384266	+	1.40819i
$55$	−6.87877	−	0.916722i	−0.927533	−	0.123611i
$56$	1.41081	+	7.34912i	0.188527	+	0.982068i
$57$		−	22.1894i		−	2.93905i
$58$	0.531131	+	0.144934i	0.0697409	+	0.0190308i
$59$	−5.71232	−	3.29801i	−0.743681	−	0.429364i	0.0797253	−	0.996817i	$-0.474596\pi$
$59$	−5.71232	−	3.29801i	−0.743681	−	0.429364i	−0.823406	+	0.567453i	$0.807929\pi$
$60$	−10.3110	−	8.08990i	−1.33114	−	1.04440i
$61$	3.21046	+	5.56068i	0.411058	+	0.711973i	0.995006	−	0.0998183i	$-0.0318262\pi$
$61$	3.21046	+	5.56068i	0.411058	+	0.711973i	−0.583948	+	0.811791i	$0.698493\pi$
$62$	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
$65$	3.36221	−	1.38642i	0.417031	−	0.171964i
$66$	12.4390	−	3.27186i	1.53114	−	0.402739i
$67$	2.80208	+	1.61778i	0.342329	+	0.197644i	0.661301	−	0.750120i	$-0.270004\pi$
$67$	2.80208	+	1.61778i	0.342329	+	0.197644i	−0.318973	+	0.947764i	$0.603338\pi$
$68$	8.79541	−	4.97086i	1.06660	−	0.602805i
$69$	9.12183			1.09814
$70$	3.69361	−	7.50715i	0.441471	−	0.897276i
$71$			7.22771i			0.857771i	0.903359	+	0.428886i	$0.141094\pi$
$71$			7.22771i			0.857771i	−0.903359	+	0.428886i	$0.858906\pi$
$72$	15.2093	+	4.30081i	1.79243	+	0.506855i
$73$	−1.58632	+	2.74759i	−0.185665	+	0.321581i	−0.943800	−	0.330516i	$-0.892777\pi$
$73$	−1.58632	+	2.74759i	−0.185665	+	0.321581i	0.758136	+	0.652097i	$0.226110\pi$
$74$	−1.51490	+	0.398468i	−0.176104	+	0.0463210i
$75$	3.74745	+	14.1655i	0.432718	+	1.63569i
$76$	−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	$-0.520777\pi$
$79$	6.81139	−	3.93256i	0.766342	−	0.442448i	0.831568	+	0.555423i	$0.187444\pi$
$80$	−5.58549	+	6.98587i	−0.624476	+	0.781044i
$81$	−2.73150	+	4.73109i	−0.303500	+	0.525677i
$82$	1.26681	+	0.345686i	0.139896	+	0.0381746i
$83$	−10.3353			−1.13444			−0.567221	−	0.823566i	$-0.691981\pi$
$83$	−10.3353			−1.13444			−0.567221	+	0.823566i	$0.691981\pi$
$84$	−1.04661	+	15.4717i	−0.114194	+	1.68810i
$85$	−11.1964	−	1.49213i	−1.21442	−	0.161844i
$86$	−4.38226	−	1.19582i	−0.472551	−	0.128949i
$87$	0.988013	+	0.570429i	0.105926	+	0.0611565i
$88$	−2.15485	−	8.50936i	−0.229707	−	0.907101i
$89$	−9.69972	+	5.60014i	−1.02817	+	0.593613i	−0.916459	−	0.400128i	$-0.868966\pi$
$89$	−9.69972	+	5.60014i	−1.02817	+	0.593613i	−0.111709	+	0.993741i	$0.535632\pi$
$90$	−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
$94$	−1.17314	−	4.46005i	−0.121000	−	0.460020i
$95$	13.4158	+	10.3282i	1.37643	+	1.05965i
$96$	4.65725	−	15.9101i	0.475329	−	1.62382i
$97$	−10.5782			−1.07405			−0.537025	−	0.843566i	$-0.680452\pi$
$97$	−10.5782			−1.07405			−0.537025	+	0.843566i	$0.680452\pi$
$98$	−9.80196	+	1.38624i	−0.990147	+	0.140031i
$99$	17.3427			1.74301
$100$	9.69052	−	2.46858i	0.969052	−	0.246858i
$101$	−2.43704	+	4.22108i	−0.242495	+	0.420013i	−0.961424	−	0.275070i	$-0.911299\pi$
$101$	−2.43704	+	4.22108i	−0.242495	+	0.420013i	0.718929	+	0.695083i	$0.244632\pi$
$102$	20.2467	−	5.32553i	2.00472	−	0.527306i
$103$	−10.9818	+	6.34034i	−1.08207	+	0.624732i	−0.931454	−	0.363860i	$-0.881459\pi$
$103$	−10.9818	+	6.34034i	−1.08207	+	0.624732i	−0.150614	+	0.988593i	$0.548125\pi$
$104$	3.20775	+	3.29741i	0.314546	+	0.323337i
$105$	11.3594	−	13.0977i	1.10856	−	1.27820i
$106$	−10.8386	−	10.9386i	−1.05274	−	1.06246i
$107$	7.60939	−	4.39329i	0.735628	−	0.424715i	−0.0848496	−	0.996394i	$-0.527041\pi$
$107$	7.60939	−	4.39329i	0.735628	−	0.424715i	0.820477	+	0.571679i	$0.193708\pi$
$108$	13.0669	+	7.70510i	1.25736	+	0.741423i
$109$	2.69246	+	1.55449i	0.257891	+	0.148893i	0.623372	−	0.781925i	$-0.285762\pi$
$109$	2.69246	+	1.55449i	0.257891	+	0.148893i	−0.365481	+	0.930819i	$0.619096\pi$
$110$	−3.81165	+	9.04362i	−0.363427	+	0.862275i
$111$	−3.24599			−0.308095
$112$	10.5519	+	0.811248i	0.997058	+	0.0766557i
$113$			8.76776i			0.824801i	0.911003	+	0.412401i	$0.135310\pi$
$113$			8.76776i			0.824801i	−0.911003	+	0.412401i	$0.864690\pi$
$114$	−30.2736	−	8.26103i	−2.83538	−	0.773716i
$115$	−4.24582	+	5.51511i	−0.395925	+	0.514286i
$116$	0.395476	−	0.670679i	0.0367190	−	0.0622710i
$117$	−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
$122$	8.78185	−	2.30991i	0.795071	−	0.209129i
$123$	2.35653	+	1.36054i	0.212481	+	0.122676i
$124$	11.5497	−	6.52748i	1.03719	−	0.586185i
$125$	−10.3088	−	4.32769i	−0.922046	−	0.387080i
$126$	−6.67145	+	19.8161i	−0.594340	+	1.76535i
$127$	−5.82575			−0.516952			−0.258476	−	0.966018i	$-0.583220\pi$
$127$	−5.82575			−0.516952			−0.258476	+	0.966018i	$0.583220\pi$
$128$	−10.8284	−	3.27803i	−0.957106	−	0.289740i
$129$	−8.15190	−	4.70650i	−0.717735	−	0.414384i
$130$	−0.639798	−	5.10332i	−0.0561140	−	0.447591i
$131$	14.8997	−	8.60235i	1.30179	−	0.751591i	0.321082	−	0.947052i	$-0.395954\pi$
$131$	14.8997	−	8.60235i	1.30179	−	0.751591i	0.980711	+	0.195461i	$0.0626203\pi$
$132$	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
$135$	−6.46541	−	15.6792i	−0.556454	−	1.34945i
$136$	−3.50739	−	13.8505i	−0.300756	−	1.18767i
$137$	−4.01092	−	2.31571i	−0.342676	−	0.197844i	0.318779	−	0.947829i	$-0.396727\pi$
$137$	−4.01092	−	2.31571i	−0.342676	−	0.197844i	−0.661455	+	0.749985i	$0.730061\pi$
$138$	3.39603	−	12.4452i	0.289089	−	1.05940i
$139$			12.0576i			1.02271i	0.859368	+	0.511357i	$0.170857\pi$
$139$			12.0576i			1.02271i	−0.859368	+	0.511357i	$0.829143\pi$
$140$	−8.86710	−	7.83419i	−0.749407	−	0.662109i
$141$		−	9.55656i		−	0.804808i
$142$	9.86098	+	2.69085i	0.827515	+	0.225811i
$143$	4.37138	+	2.52382i	0.365553	+	0.211052i
$144$	11.5301	−	19.1493i	0.960841	−	1.59578i
$145$	−0.804762	+	0.331847i	−0.0668318	+	0.0275584i
$146$	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	$-0.918082\pi$
$149$	−15.0162	+	8.66962i	−1.23018	+	0.710243i	−0.263110	+	0.964766i	$0.584748\pi$
$150$	20.7215	+	0.160997i	1.69191	+	0.0131453i
$151$	−16.8208	−	9.71149i	−1.36886	−	0.790310i	−0.378075	−	0.925775i	$-0.623414\pi$
$151$	−16.8208	−	9.71149i	−1.36886	−	0.790310i	−0.990782	+	0.135465i	$0.956747\pi$
$152$	−5.82743	+	20.6080i	−0.472667	+	1.67153i
$153$	28.2283			2.28212
$154$	11.3833	−	2.29388i	0.917295	−	0.184846i
$155$	−14.7025	−	1.95938i	−1.18094	−	0.157381i
$156$	4.69034	+	8.29906i	0.375528	+	0.664457i
$157$	−15.5317	−	8.96725i	−1.23957	−	0.715665i	−0.270562	−	0.962703i	$-0.587209\pi$
$157$	−15.5317	−	8.96725i	−1.23957	−	0.715665i	−0.969006	+	0.247038i	$0.920543\pi$
$158$	−2.82945	−	10.7571i	−0.225099	−	0.855786i
$159$	−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	$-0.431819\pi$
$163$	14.8747	−	8.58794i	1.16508	−	0.672659i	0.952516	+	0.304488i	$0.0984853\pi$
$164$	0.943259	−	1.59965i	0.0736562	−	0.124912i
$165$	−12.4059	+	16.1146i	−0.965797	+	1.25452i
$166$	−3.84778	+	14.1007i	−0.298646	+	1.09443i
$167$			23.1940i			1.79481i	0.441210	+	0.897404i	$0.354549\pi$
$167$			23.1940i			1.79481i	−0.441210	+	0.897404i	$0.645451\pi$
$168$	20.7188	+	7.18797i	1.59849	+	0.554564i
$169$	10.3547			0.796514
$170$	−6.20413	+	14.7201i	−0.475835	+	1.12898i
$171$	−36.6433	−	21.1560i	−2.80218	−	1.61784i
$172$	−3.26300	+	5.53364i	−0.248801	+	0.421936i
$173$	−13.5835	+	7.84243i	−1.03273	+	0.596249i	−0.917766	−	0.397121i	$-0.870009\pi$
$173$	−13.5835	+	7.84243i	−1.03273	+	0.596249i	−0.114967	+	0.993369i	$0.536676\pi$
$174$	1.14609	−	1.13561i	0.0868847	−	0.0860901i
$175$	2.63161	+	12.9644i	0.198931	+	0.980013i
$176$	−12.4118	−	0.228086i	−0.935576	−	0.0171926i
$177$	−16.7403	+	9.66500i	−1.25828	+	0.726466i
$178$	4.02926	+	15.3185i	0.302006	+	1.14817i
$179$	−1.80380	+	3.12428i	−0.134823	+	0.233520i	−0.925530	−	0.378675i	$-0.876380\pi$
$179$	−1.80380	+	3.12428i	−0.134823	+	0.233520i	0.790707	+	0.612195i	$0.209713\pi$
$180$	−23.1904	+	9.31430i	−1.72851	+	0.694247i
$181$	3.98490			0.296195			0.148098	−	0.988973i	$-0.452685\pi$
$181$	3.98490			0.296195			0.148098	+	0.988973i	$0.452685\pi$
$182$	−4.56535	+	4.02394i	−0.338406	+	0.298274i
$183$	18.8169			1.39098
$184$	−8.47175	−	2.39560i	−0.624546	−	0.176606i
$185$	1.51087	−	1.96254i	0.111081	−	0.144289i
$186$	26.5870	−	6.99322i	1.94945	−	0.512767i
$187$	−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	$-0.558092\pi$
$191$	8.00755	−	4.62316i	0.579406	−	0.334520i	0.760897	+	0.648872i	$0.224759\pi$
$192$	−19.9727	−	12.2773i	−1.44141	−	0.886037i
$193$	−10.5917	−	6.11514i	−0.762410	−	0.440177i	0.0677506	−	0.997702i	$-0.478418\pi$
$193$	−10.5917	−	6.11514i	−0.762410	−	0.440177i	−0.830160	+	0.557525i	$0.811751\pi$
$194$	−3.93821	+	14.4321i	−0.282747	+	1.03616i
$195$	1.40792	−	10.5646i	0.100823	−	0.756544i
$196$	−1.75795	+	13.8892i	−0.125568	+	0.992085i
$197$	7.38753			0.526340			0.263170	−	0.964750i	$-0.415232\pi$
$197$	7.38753			0.526340			0.263170	+	0.964750i	$0.415232\pi$
$198$	6.45663	−	23.6612i	0.458853	−	1.68153i
$199$	2.81699	−	4.87917i	0.199691	−	0.345875i	−0.748737	−	0.662867i	$-0.769339\pi$
$199$	2.81699	−	4.87917i	0.199691	−	0.345875i	0.948428	+	0.316992i	$0.102673\pi$
$200$	0.239791	−	14.1401i	0.0169558	−	0.999856i
$201$	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
$205$	−1.91946	+	0.791496i	−0.134061	+	0.0552805i
$206$	4.56183	+	17.3433i	0.317838	+	1.20836i
$207$	8.69702	−	15.0637i	0.604485	−	1.04700i
$208$	5.69298	−	3.14882i	0.394737	−	0.218331i
$209$			23.4987i			1.62544i
$210$	−13.6405	−	20.3742i	−0.941283	−	1.40595i
$211$	5.14042			0.353881			0.176940	−	0.984222i	$-0.443380\pi$
$211$	5.14042			0.353881			0.176940	+	0.984222i	$0.443380\pi$
$212$	−18.9591	+	10.7150i	−1.30212	+	0.735911i
$213$	18.3435	+	10.5906i	1.25687	+	0.725656i
$214$	−3.16094	−	12.0173i	−0.216077	−	0.821487i
$215$	6.63993	−	2.73801i	0.452840	−	0.186730i
$216$	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
$220$	10.9194	+	8.56726i	0.736187	+	0.577605i
$221$	7.11519	+	4.10795i	0.478619	+	0.276331i
$222$	−1.20847	+	4.42860i	−0.0811072	+	0.297228i
$223$		−	5.70766i		−	0.382213i	−0.981569	−	0.191106i	$-0.938792\pi$
$223$		−	5.70766i		−	0.382213i	0.981569	−	0.191106i	$-0.0612076\pi$
$224$	5.03523	−	14.0942i	0.336431	−	0.941708i
$225$	26.9656	+	7.31728i	1.79771	+	0.487818i
$226$	11.9621	+	3.26421i	0.795708	+	0.217132i
$227$	9.24524	−	16.0132i	0.613628	−	1.06283i	−0.376996	−	0.926215i	$-0.623043\pi$
$227$	9.24524	−	16.0132i	0.613628	−	1.06283i	0.990624	−	0.136620i	$-0.0436239\pi$
$228$	−22.5415	+	38.2277i	−1.49285	+	2.53169i
$229$	4.79008	+	8.29666i	0.316537	+	0.548258i	0.979763	−	0.200161i	$-0.0641465\pi$
$229$	4.79008	+	8.29666i	0.316537	+	0.548258i	−0.663226	+	0.748419i	$0.730813\pi$
$230$	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	$-0.710664\pi$
$233$	−3.64278	+	2.10316i	−0.238647	+	0.137783i	0.375908	+	0.926657i	$0.377331\pi$
$234$	3.26967	+	12.4307i	0.213745	+	0.812621i
$235$	5.77794	+	4.44817i	0.376912	+	0.290166i
$236$	6.49078	+	11.4848i	0.422514	+	0.747594i
$237$		−	23.0492i		−	1.49720i
$238$	18.5284	−	3.73369i	1.20102	−	0.242019i
$239$		−	21.5399i		−	1.39330i	−0.717410	−	0.696651i	$-0.754673\pi$
$239$		−	21.5399i		−	1.39330i	0.717410	−	0.696651i	$-0.245327\pi$
$240$	9.54539	+	24.4118i	0.616152	+	1.57578i
$241$	7.51995	+	4.34165i	0.484403	+	0.279670i	0.722249	−	0.691633i	$-0.243108\pi$
$241$	7.51995	+	4.34165i	0.484403	+	0.279670i	−0.237847	+	0.971303i	$0.576442\pi$
$242$	1.87158	−	0.492285i	0.120310	−	0.0316453i
$243$	−3.37228	−	5.84097i	−0.216332	−	0.374698i
$244$	0.117979	−	12.8413i	0.00755285	−	0.822081i
$245$	10.9277	−	11.2065i	0.698142	−	0.715959i
$246$	2.73356	−	2.70856i	0.174285	−	0.172691i
$247$	−6.15750	−	10.6651i	−0.391792	−	0.678604i
$248$	−4.60572	−	18.1877i	−0.292464	−	1.15492i
$249$	−15.1440	+	26.2302i	−0.959713	+	1.66227i
$250$	−9.74232	+	12.4534i	−0.616158	+	0.787622i
$251$		−	11.2144i		−	0.707844i	−0.935275	−	0.353922i	$-0.884848\pi$
$251$		−	11.2144i		−	0.707844i	0.935275	−	0.353922i	$-0.115152\pi$
$252$	24.5519	+	16.4795i	1.54662	+	1.03811i
$253$	−9.66008			−0.607324
$254$	−2.16891	+	7.94825i	−0.136089	+	0.498717i
$255$	−20.1928	+	26.2294i	−1.26452	+	1.64255i
$256$	−8.50369	+	13.5531i	−0.531481	+	0.847070i
$257$	−5.68553	−	9.84763i	−0.354654	−	0.614278i	0.632405	−	0.774638i	$-0.282068\pi$
$257$	−5.68553	−	9.84763i	−0.354654	−	0.614278i	−0.987059	+	0.160360i	$0.948735\pi$
$258$	−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
$262$	−6.18933	−	23.5307i	−0.382378	−	1.45373i
$263$	9.68088	−	16.7678i	0.596949	−	1.03395i	−0.396320	−	0.918112i	$-0.629713\pi$
$263$	9.68088	−	16.7678i	0.596949	−	1.03395i	0.993269	−	0.115833i	$-0.0369537\pi$
$264$	−24.7537	−	6.99972i	−1.52348	−	0.430803i
$265$	24.1346	+	3.21638i	1.48258	+	0.197580i
$266$	−26.8500	−	9.03956i	−1.64628	−	0.554251i
$267$			32.8230i			2.00874i
$268$	−3.18394	−	5.63365i	−0.194490	−	0.344130i
$269$	−0.761782	+	1.31945i	−0.0464467	+	0.0804480i	−0.888314	−	0.459236i	$-0.848123\pi$
$269$	−0.761782	+	1.31945i	−0.0464467	+	0.0804480i	0.841867	+	0.539684i	$0.181456\pi$
$270$	−23.7987	+	2.98362i	−1.44834	+	0.181577i
$271$	9.32172	+	16.1457i	0.566254	+	0.980781i	0.996932	+	0.0782754i	$0.0249414\pi$
$271$	9.32172	+	16.1457i	0.566254	+	0.980781i	−0.430677	+	0.902506i	$0.641725\pi$
$272$	−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
$275$	−3.96858	−	15.0013i	−0.239314	−	0.904614i
$276$	−15.7150	−	9.26660i	−0.945932	−	0.557784i
$277$	−4.74717	+	8.22234i	−0.285230	+	0.494033i	−0.972665	−	0.232213i	$-0.925403\pi$
$277$	−4.74717	+	8.22234i	−0.285230	+	0.494033i	0.687435	+	0.726246i	$0.258737\pi$
$278$	16.4506	+	4.48901i	0.986640	+	0.269233i
$279$	37.0680			2.21920
$280$	−13.9896	+	9.18101i	−0.836039	+	0.548671i
$281$	−9.11431			−0.543714			−0.271857	−	0.962338i	$-0.587638\pi$
$281$	−9.11431			−0.543714			−0.271857	+	0.962338i	$0.587638\pi$
$282$	−13.0383	−	3.55787i	−0.776419	−	0.211868i
$283$	−7.77457	+	13.4659i	−0.462150	+	0.800467i	−0.999068	−	0.0431671i	$-0.986255\pi$
$283$	−7.77457	+	13.4659i	−0.462150	+	0.800467i	0.536918	+	0.843635i	$0.319589\pi$
$284$	7.34241	−	12.4518i	0.435692	−	0.738880i
$285$	45.8702	−	18.9148i	2.71712	−	1.12041i
$286$	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
$290$	0.153139	+	1.22151i	0.00899262	+	0.0717293i
$291$	−15.4999	+	26.8467i	−0.908623	+	1.57378i
$292$	5.52409	−	3.12202i	0.323273	−	0.182702i
$293$		−	8.72422i		−	0.509674i	−0.966984	−	0.254837i	$-0.917978\pi$
$293$		−	8.72422i		−	0.509674i	0.966984	−	0.254837i	$-0.0820219\pi$
$294$	−10.8444	+	26.9079i	−0.632459	+	1.56930i
$295$	1.94837	−	14.6199i	0.113438	−	0.851203i
$296$	3.01466	+	0.852470i	0.175223	+	0.0495488i
$297$	11.7695	−	20.3854i	0.682936	−	1.18288i
$298$	6.23773	+	23.7147i	0.361342	+	1.37376i
$299$	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
$304$	25.9466	+	15.6228i	1.48814	+	0.896031i
$305$	−8.75845	+	11.3768i	−0.501507	+	0.651432i
$306$	10.5093	−	38.5127i	0.600776	−	2.20162i
$307$	7.13157			0.407020			0.203510	−	0.979073i	$-0.434765\pi$
$307$	7.13157			0.407020			0.203510	+	0.979073i	$0.434765\pi$
$308$	1.10837	−	16.3846i	0.0631550	−	0.933600i
$309$			37.1614i			2.11404i
$310$	−8.14695	+	19.3296i	−0.462716	+	1.09785i
$311$	15.8284	−	27.4155i	0.897545	−	1.55459i	0.0669214	−	0.997758i	$-0.478682\pi$
$311$	15.8284	−	27.4155i	0.897545	−	1.55459i	0.830623	−	0.556835i	$-0.187984\pi$
$312$	13.0689	−	3.30946i	0.739878	−	0.187361i
$313$	−11.5185	−	19.9506i	−0.651063	−	1.12767i	−0.982865	−	0.184325i	$-0.940990\pi$
$313$	−11.5185	−	19.9506i	−0.651063	−	1.12767i	0.331802	−	0.943349i	$-0.392343\pi$
$314$	−18.0167	+	17.8519i	−1.01674	+	1.00744i
$315$	−10.7990	−	31.2465i	−0.608453	−	1.76054i
$316$	−15.7296	−	0.144515i	−0.884858	−	0.00812961i
$317$	8.93503	+	15.4759i	0.501841	+	0.869214i	0.999998	+	0.00212719i	$0.000677106\pi$
$317$	8.93503	+	15.4759i	0.501841	+	0.869214i	−0.498157	+	0.867087i	$0.665990\pi$
$318$	−43.6432	+	11.4795i	−2.44739	+	0.643741i
$319$	−1.04631	−	0.604089i	−0.0585823	−	0.0338225i
$320$	16.7194	−	6.36106i	0.934641	−	0.355594i
$321$		−	25.7495i		−	1.43720i
$322$	3.71607	−	11.0378i	0.207089	−	0.615111i
$323$			38.2483i			2.12819i
$324$	9.51197	−	5.37583i	0.528443	−	0.298657i
$325$	5.73206	+	5.76858i	0.317957	+	0.319983i
$326$	−6.17896	−	23.4913i	−0.342221	−	1.30106i
$327$	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	0.884876	−	0.465827i	$-0.154243\pi$
$331$	0.709904	+	1.22959i	0.0390199	+	0.0675844i	−0.845856	+	0.533411i	$0.820910\pi$
$332$	17.8055	+	10.4993i	0.977203	+	0.576223i
$333$	−3.09482	+	5.36038i	−0.169595	+	0.293747i
$334$	31.6443	+	8.63506i	1.73150	+	0.472489i
$335$	−0.955739	+	7.17154i	−0.0522176	+	0.391823i
$336$	17.5203	−	25.5912i	0.955811	−	1.39612i
$337$			9.43095i			0.513737i	0.966446	+	0.256868i	$0.0826907\pi$
$337$			9.43095i			0.513737i	−0.966446	+	0.256868i	$0.917309\pi$
$338$	3.85501	−	14.1272i	0.209685	−	0.768418i
$339$	22.2520	+	12.8472i	1.20856	+	0.697764i
$340$	17.7733	+	13.9447i	0.963890	+	0.756258i
$341$	−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
$345$	7.77568	+	18.8568i	0.418628	+	1.01521i
$346$	5.64257	+	21.4521i	0.303347	+	1.15327i
$347$	−6.57622	−	3.79678i	−0.353030	−	0.203822i	0.312989	−	0.949757i	$-0.398670\pi$
$347$	−6.57622	−	3.79678i	−0.353030	−	0.203822i	−0.666019	+	0.745935i	$0.732003\pi$
$348$	−1.12266	−	1.98642i	−0.0601807	−	0.106483i
$349$	7.65991			0.410026			0.205013	−	0.978759i	$-0.434276\pi$
$349$	7.65991			0.410026			0.205013	+	0.978759i	$0.434276\pi$
$350$	18.6674	+	1.23620i	0.997814	+	0.0660778i
$351$			12.3361i			0.658454i
$352$	−4.93206	+	16.8489i	−0.262880	+	0.898049i
$353$	0.293236	−	0.507900i	0.0156074	−	0.0270328i	−0.858116	−	0.513455i	$-0.828365\pi$
$353$	0.293236	−	0.507900i	0.0156074	−	0.0270328i	0.873724	+	0.486423i	$0.161698\pi$
$354$	6.95390	+	26.4375i	0.369596	+	1.40514i
$355$	−14.9412	+	6.16108i	−0.792997	+	0.326996i
$356$	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	$-0.775374\pi$
$359$	−10.9912	+	6.34574i	−0.580091	+	0.334916i	0.181079	+	0.983469i	$0.442041\pi$
$360$	4.07409	+	35.1070i	0.214723	+	1.85030i
$361$	19.1656	−	33.1957i	1.00871	−	1.74714i
$362$	1.48356	−	5.43671i	0.0779744	−	0.285747i
$363$	4.01024			0.210483
$364$	3.79031	+	7.72674i	0.198666	+	0.404991i
$365$	−7.03206	−	0.937151i	−0.368075	−	0.0490527i
$366$	7.00546	−	25.6724i	0.366181	−	1.34192i
$367$	−22.8707	−	13.2044i	−1.19384	−	0.689264i	−0.234665	−	0.972076i	$-0.575399\pi$
$367$	−22.8707	−	13.2044i	−1.19384	−	0.689264i	−0.959175	+	0.282812i	$0.908733\pi$
$368$	−6.42239	+	10.6664i	−0.334790	+	0.556024i
$369$	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	0.672603	−	0.740004i	$-0.265176\pi$
$373$	−5.88204	−	10.1880i	−0.304561	−	0.527515i	−0.977163	+	0.212489i	$0.931843\pi$
$374$	−21.4414	+	5.63978i	−1.10871	+	0.291626i
$375$	−26.0886	+	19.8218i	−1.34721	+	1.02359i
$376$	−2.50977	+	8.87549i	−0.129431	+	0.457719i
$377$	0.633171			0.0326100
$378$	18.7651	+	21.2900i	0.965175	+	1.09504i
$379$	3.03621			0.155960			0.0779799	−	0.996955i	$-0.475153\pi$
$379$	3.03621			0.155960			0.0779799	+	0.996955i	$0.475153\pi$
$380$	−12.6205	−	31.4220i	−0.647419	−	1.61192i
$381$	−8.53634	+	14.7854i	−0.437330	+	0.757478i
$382$	−3.32633	−	12.6461i	−0.170190	−	0.647032i
$383$	10.8418	−	6.25951i	0.553989	−	0.319846i	−0.196740	−	0.980456i	$-0.563036\pi$
$383$	10.8418	−	6.25951i	0.553989	−	0.319846i	0.750729	+	0.660610i	$0.229702\pi$
$384$	−24.1861	+	22.6786i	−1.23424	+	1.15731i
$385$	−12.0297	+	13.8705i	−0.613090	+	0.706908i
$386$	−12.2863	+	12.1740i	−0.625358	+	0.619639i
$387$	−15.5445	+	8.97463i	−0.790172	+	0.456206i
$388$	18.2240	+	10.7460i	0.925181	+	0.545548i
$389$	−21.3594	−	12.3319i	−1.08297	−	0.625251i	−0.151271	−	0.988492i	$-0.548337\pi$
$389$	−21.3594	−	12.3319i	−1.08297	−	0.625251i	−0.931695	+	0.363242i	$0.881670\pi$
$390$	−13.8894	−	5.85401i	−0.703316	−	0.296430i
$391$	−15.7235			−0.795170
$392$	18.2950	+	7.56932i	0.924035	+	0.382309i
$393$		−	50.4193i		−	2.54332i
$394$	2.75035	−	10.0790i	0.138561	−	0.507774i
$395$	13.9356	+	10.7284i	0.701178	+	0.539804i
$396$	−29.8779	−	17.6179i	−1.50142	−	0.885335i
$397$	19.5980	−	11.3149i	0.983597	−	0.567880i	0.0802429	−	0.996775i	$-0.474430\pi$
$397$	19.5980	−	11.3149i	0.983597	−	0.567880i	0.903354	+	0.428895i	$0.141097\pi$
$398$	−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	0.993208	+	0.116355i	$0.0371212\pi$
$401$	11.9623	+	20.7194i	0.597371	+	1.03468i	−0.395837	+	0.918321i	$0.629546\pi$
$402$	−3.41112	−	12.9685i	−0.170131	−	0.646808i
$403$	9.34330	+	5.39436i	0.465423	+	0.268712i
$404$	8.48659	−	4.79632i	0.422223	−	0.238626i
$405$	−12.1086	−	1.61369i	−0.601680	−	0.0801848i
$406$	1.09274	−	0.963150i	0.0542318	−	0.0478004i
$407$	3.43752			0.170392
$408$	−40.2909	−	11.3933i	−1.99470	−	0.564051i
$409$	−25.1282	−	14.5078i	−1.24251	−	0.717364i	−0.272907	−	0.962040i	$-0.587985\pi$
$409$	−25.1282	−	14.5078i	−1.24251	−	0.717364i	−0.969605	+	0.244676i	$0.921318\pi$
$410$	0.365255	+	2.91344i	0.0180387	+	0.143885i
$411$	−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
$415$	−8.81003	−	21.3652i	−0.432467	−	1.04878i
$416$	−2.17655	−	8.93940i	−0.106714	−	0.438290i
$417$	30.6015	+	17.6678i	1.49856	+	0.865194i
$418$	32.0600	+	8.74849i	1.56810	+	0.427902i
$419$		−	18.1727i		−	0.887794i	−0.896078	−	0.443897i	$-0.853596\pi$
$419$		−	18.1727i		−	0.887794i	0.896078	−	0.443897i	$-0.146404\pi$
$420$	−32.8754	+	11.0249i	−1.60416	+	0.537959i
$421$		−	30.9941i		−	1.51056i	−0.655403	−	0.755279i	$-0.727501\pi$
$421$		−	30.9941i		−	1.51056i	0.655403	−	0.755279i	$-0.272499\pi$
$422$	1.91376	−	7.01322i	0.0931603	−	0.341398i
$423$	−15.7816	−	9.11150i	−0.767327	−	0.443016i
$424$	7.56041	+	29.8556i	0.367166	+	1.44992i
$425$	−6.45955	−	24.4173i	−0.313334	−	1.18441i
$426$	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
$430$	−1.26352	−	10.0784i	−0.0609323	−	0.486024i
$431$	17.6956	+	10.2166i	0.852369	+	0.492115i	0.861449	−	0.507843i	$-0.169557\pi$
$431$	17.6956	+	10.2166i	0.852369	+	0.492115i	−0.00908058	+	0.999959i	$0.502890\pi$
$432$	−14.6841	−	26.5485i	−0.706491	−	1.27732i
$433$	2.57285			0.123643			0.0618216	−	0.998087i	$-0.480309\pi$
$433$	2.57285			0.123643			0.0618216	+	0.998087i	$0.480309\pi$
$434$	24.3305	−	4.90289i	1.16790	−	0.235346i
$435$	−0.336993	+	2.52868i	−0.0161576	+	0.121241i
$436$	−3.05938	−	5.41326i	−0.146518	−	0.259248i
$437$	20.4107	+	11.7841i	0.976377	+	0.563711i
$438$	12.7162	−	3.34478i	0.607606	−	0.159820i
$439$	7.66013	+	13.2677i	0.365598	+	0.633234i	0.988872	−	0.148769i	$-0.0475312\pi$
$439$	7.66013	+	13.2677i	0.365598	+	0.633234i	−0.623274	+	0.782003i	$0.714198\pi$
$440$	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	$-0.620706\pi$
$443$	5.24553	−	3.02851i	0.249223	−	0.143889i	0.619408	+	0.785069i	$0.287373\pi$
$444$	5.59216	+	3.29750i	0.265392	+	0.156493i
$445$	−19.8450	−	15.2777i	−0.940741	−	0.724232i
$446$	−7.78712	−	2.12494i	−0.368731	−	0.100619i
$447$			50.8136i			2.40340i
$448$	−17.3545	−	12.1169i	−0.819925	−	0.572472i
$449$	−9.93819			−0.469012			−0.234506	−	0.972115i	$-0.575347\pi$
$449$	−9.93819			−0.469012			−0.234506	+	0.972115i	$0.575347\pi$
$450$	20.0224	−	34.0658i	0.943864	−	1.60588i
$451$	−2.49558	−	1.44083i	−0.117512	−	0.0678458i
$452$	8.90691	−	15.1050i	0.418946	−	0.710480i
$453$	−49.2943	+	28.4601i	−2.31605	+	1.33717i
$454$	−18.4053	−	18.5752i	−0.863806	−	0.871778i
$455$	1.82521	−	9.44748i	0.0855671	−	0.442905i
$456$	43.7630	+	44.9861i	2.04939	+	2.10667i
$457$	15.9573	−	9.21295i	0.746451	−	0.430964i	−0.0779590	−	0.996957i	$-0.524840\pi$
$457$	15.9573	−	9.21295i	0.746451	−	0.430964i	0.824410	+	0.565993i	$0.191507\pi$
$458$	13.1027	−	3.44643i	0.612249	−	0.161041i
$459$	19.1569	−	33.1808i	0.894170	−	1.54875i
$460$	12.9173	−	5.18817i	0.602272	−	0.241900i
$461$	−17.6061			−0.819998			−0.409999	−	0.912086i	$-0.634471\pi$
$461$	−17.6061			−0.819998			−0.409999	+	0.912086i	$0.634471\pi$
$462$	10.8580	−	32.2513i	0.505161	−	1.50047i
$463$	28.5438			1.32654			0.663271	−	0.748379i	$-0.269168\pi$
$463$	28.5438			1.32654			0.663271	+	0.748379i	$0.269168\pi$
$464$	−1.36265	+	0.753687i	−0.0632592	+	0.0349890i
$465$	−26.5161	+	34.4431i	−1.22965	+	1.59726i
$466$	1.51321	+	5.75296i	0.0700981	+	0.266501i
$467$	3.09243	+	5.35625i	0.143101	+	0.247857i	0.928663	−	0.370925i	$-0.120959\pi$
$467$	3.09243	+	5.35625i	0.143101	+	0.247857i	−0.785562	+	0.618783i	$0.787626\pi$
$468$	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
$472$	18.0855	−	4.57983i	0.832452	−	0.210804i
$473$	8.63292	+	4.98422i	0.396942	+	0.229175i
$474$	−31.4467	−	8.58112i	−1.44439	−	0.394144i
$475$	−9.91463	+	36.5374i	−0.454914	+	1.67645i
$476$	1.80406	−	26.6688i	0.0826889	−	1.22236i
$477$	−60.8480			−2.78604
$478$	−29.3876	−	8.01924i	−1.34416	−	0.366791i
$479$	6.58753	−	11.4099i	0.300992	−	0.521333i	−0.675369	−	0.737480i	$-0.736016\pi$
$479$	6.58753	−	11.4099i	0.300992	−	0.521333i	0.976361	+	0.216147i	$0.0693490\pi$
$480$	36.8595	−	3.93462i	1.68240	−	0.179590i
$481$	−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
$485$	−9.01709	−	21.8673i	−0.409445	−	0.992944i
$486$	−9.22450	+	2.42634i	−0.418432	+	0.110061i
$487$	−0.665258	+	1.15226i	−0.0301457	+	0.0522139i	−0.880705	−	0.473666i	$-0.842930\pi$
$487$	−0.665258	+	1.15226i	−0.0301457	+	0.0522139i	0.850559	+	0.525880i	$0.176264\pi$
$488$	−17.4759	−	4.94174i	−0.791095	−	0.223702i
$489$		−	50.3349i		−	2.27622i
$490$	−11.2211	−	19.0811i	−0.506917	−	0.861995i
$491$	43.7619			1.97495			0.987474	−	0.157779i	$-0.0504335\pi$
$491$	43.7619			1.97495			0.987474	+	0.157779i	$0.0504335\pi$
$492$	−2.67767	−	4.73786i	−0.120719	−	0.213599i
$493$	−1.70306	−	0.983260i	−0.0767018	−	0.0442838i
$494$	−16.8431	+	4.43028i	−0.757808	+	0.199328i
$495$	14.7834	+	35.8511i	0.664462	+	1.61139i
$496$	−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	−0.974773	−	0.223197i	$-0.928351\pi$
$499$	−15.2053	−	26.3363i	−0.680681	−	1.17897i	0.294092	−	0.955777i	$-0.404983\pi$
$500$	13.3635	+	17.9281i	0.597635	+	0.801769i
$501$	58.8649	+	33.9857i	2.62989	+	1.51837i
$502$	−15.3001	−	4.17507i	−0.682876	−	0.186342i
$503$		−	9.86442i		−	0.439833i	−0.975519	−	0.219916i	$-0.929422\pi$
$503$		−	9.86442i		−	0.439833i	0.975519	−	0.219916i	$-0.0705785\pi$
$504$	31.6241	−	27.3616i	1.40865	−	1.21878i
$505$	−10.8033	−	1.43973i	−0.480739	−	0.0640673i
$506$	−3.59642	+	13.1795i	−0.159880	+	0.585902i
$507$	15.1725	−	26.2795i	0.673833	−	1.16711i
$508$	10.0366	+	5.91821i	0.445300	+	0.262578i
$509$	−7.69465	−	13.3275i	−0.341059	−	0.590732i	0.643570	−	0.765387i	$-0.277452\pi$
$509$	−7.69465	−	13.3275i	−0.341059	−	0.590732i	−0.984630	+	0.174655i	$0.944119\pi$
$510$	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
$514$	−15.5521	+	4.09070i	−0.685974	+	0.180433i
$515$	−22.4680	−	17.2970i	−0.990058	−	0.762199i
$516$	9.26282	+	16.3896i	0.407773	+	0.721512i
$517$			10.1205i			0.445098i
$518$	−1.32236	+	3.92777i	−0.0581011	+	0.172576i
$519$			45.9653i			2.01765i
$520$	−4.08207	+	9.44190i	−0.179011	+	0.414055i
$521$	11.5108	+	6.64575i	0.504296	+	0.291156i	0.730486	−	0.682928i	$-0.239294\pi$
$521$	11.5108	+	6.64575i	0.504296	+	0.291156i	−0.226190	+	0.974083i	$0.572627\pi$
$522$	−0.782613	−	2.97535i	−0.0342540	−	0.130228i
$523$	3.96445	+	6.86663i	0.173353	+	0.300257i	0.939590	−	0.342301i	$-0.111206\pi$
$523$	3.96445	+	6.86663i	0.173353	+	0.300257i	−0.766237	+	0.642558i	$0.777873\pi$
$524$	−34.4079	−	0.316122i	−1.50312	−	0.0138099i
$525$	36.7587	+	12.3175i	1.60428	+	0.537581i
$526$	−19.2726	−	19.4505i	−0.840326	−	0.848082i
$527$	−16.7539	−	29.0187i	−0.729813	−	1.26407i
$528$	−18.7656	+	31.1662i	−0.816669	+	1.35633i
$529$	6.65566	−	11.5279i	0.289377	−	0.501215i
$530$	13.3734	−	31.7301i	0.580904	−	1.37827i
$531$			36.8596i			1.59957i
$532$	−22.3291	+	33.2668i	−0.968089	+	1.44230i
$533$	1.51019			0.0654136
$534$	44.7814	+	12.2199i	1.93788	+	0.528807i
$535$	15.5683	+	11.9853i	0.673076	+	0.518170i
$536$	−8.87153	+	2.24656i	−0.383192	+	0.0970366i
$537$	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	0.620689	−	0.784057i	$-0.286853\pi$
$541$	37.4487	−	21.6210i	1.61005	−	0.929561i	0.989358	−	0.145504i	$-0.0464803\pi$
$542$	25.4985	−	6.70692i	1.09525	−	0.288087i
$543$	5.83898	−	10.1134i	0.250575	−	0.434008i
$544$	−8.02779	+	27.4245i	−0.344189	+	1.17582i
$545$	−0.918349	+	6.89098i	−0.0393377	+	0.295177i
$546$	3.52299	+	17.4827i	0.150770	+	0.748193i
$547$		−	21.2017i		−	0.906519i	−0.891379	−	0.453260i	$-0.850261\pi$
$547$		−	21.2017i		−	0.906519i	0.891379	−	0.453260i	$-0.149739\pi$
$548$	4.55752	+	8.06406i	0.194688	+	0.344480i
$549$	17.9406	−	31.0740i	0.765684	−	1.32620i
$550$	−21.9442	−	0.170497i	−0.935706	−	0.00727000i
$551$	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
$555$	−2.76696	−	6.71015i	−0.117451	−	0.284830i
$556$	12.2490	−	20.7728i	0.519473	−	0.880961i
$557$	1.74567	−	3.02359i	0.0739663	−	0.128113i	−0.826670	−	0.562687i	$-0.809768\pi$
$557$	1.74567	−	3.02359i	0.0739663	−	0.128113i	0.900636	+	0.434574i	$0.143101\pi$
$558$	13.8003	−	50.5729i	0.584212	−	2.14092i
$559$	−5.22417			−0.220959
$560$	7.31765	+	22.5045i	0.309227	+	0.950988i
$561$	−45.9425			−1.93970
$562$	−3.39322	+	12.4349i	−0.143135	+	0.524535i
$563$	−7.10505	+	12.3063i	−0.299442	+	0.518649i	−0.976008	−	0.217733i	$-0.930134\pi$
$563$	−7.10505	+	12.3063i	−0.299442	+	0.518649i	0.676566	+	0.736382i	$0.263467\pi$
$564$	−9.70823	+	16.4640i	−0.408790	+	0.693258i
$565$	−18.1248	+	7.47386i	−0.762517	+	0.314427i
$566$	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	0.982718	+	0.185107i	$0.0592631\pi$
$569$	15.5447	+	26.9242i	0.651666	+	1.12872i	−0.331052	+	0.943613i	$0.607404\pi$
$570$	−8.72868	−	69.6240i	−0.365604	−	2.91623i
$571$	−4.74777	+	8.22337i	−0.198688	+	0.344137i	−0.948103	−	0.317963i	$-0.897001\pi$
$571$	−4.74777	+	8.22337i	−0.198688	+	0.344137i	0.749415	+	0.662100i	$0.230335\pi$
$572$	−4.96710	−	8.78876i	−0.207685	−	0.367477i
$573$		−	27.0969i		−	1.13199i
$574$	2.60632	−	2.29723i	0.108786	−	0.0958846i
$575$	−15.0201	−	4.07580i	−0.626383	−	0.169973i
$576$	−39.3172	+	21.2772i	−1.63821	+	0.886549i
$577$	−16.2630	+	28.1683i	−0.677037	+	1.17266i	0.298832	+	0.954306i	$0.403403\pi$
$577$	−16.2630	+	28.1683i	−0.677037	+	1.17266i	−0.975869	+	0.218356i	$0.929931\pi$
$578$	−11.6489	+	3.06403i	−0.484530	+	0.127447i
$579$	−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
$584$	−2.20287	−	8.69899i	−0.0911553	−	0.359967i
$585$	−16.1038	−	12.3976i	−0.665811	−	0.512577i
$586$	−11.9027	−	3.24800i	−0.491697	−	0.134174i
$587$	−18.4126			−0.759968			−0.379984	−	0.924993i	$-0.624071\pi$
$587$	−18.4126			−0.759968			−0.379984	+	0.924993i	$0.624071\pi$
$588$	32.6740	+	24.8131i	1.34745	+	1.02327i
$589$			50.2256i			2.06951i
$590$	−19.2210	−	8.10115i	−0.791315	−	0.333519i
$591$	10.8248	−	18.7491i	0.445272	−	0.771234i
$592$	2.28540	−	3.79561i	0.0939292	−	0.155999i
$593$	16.2273	+	28.1066i	0.666377	+	1.15420i	0.978910	+	0.204292i	$0.0654893\pi$
$593$	16.2273	+	28.1066i	0.666377	+	1.15420i	−0.312533	+	0.949907i	$0.601177\pi$
$594$	−23.4307	−	23.6469i	−0.961371	−	0.970244i
$595$	−19.5804	+	22.5767i	−0.802719	+	0.925556i
$596$	34.6770	+	0.318594i	1.42043	+	0.0130501i
$597$	−8.25534	−	14.2987i	−0.337869	−	0.585206i
$598$	−1.82124	−	6.92404i	−0.0744762	−	0.283145i
$599$	16.2697	+	9.39332i	0.664762	+	0.383801i	0.794089	−	0.607801i	$-0.207948\pi$
$599$	16.2697	+	9.39332i	0.664762	+	0.383801i	−0.129327	+	0.991602i	$0.541282\pi$
$600$	−35.5353	−	21.3277i	−1.45072	−	0.870702i
$601$			37.1087i			1.51369i	0.653592	+	0.756847i	$0.273261\pi$
$601$			37.1087i			1.51369i	−0.653592	+	0.756847i	$0.726739\pi$
$602$	−9.01599	+	7.94677i	−0.367464	+	0.323886i
$603$		−	18.0808i		−	0.736309i
$604$	19.1131	+	33.8186i	0.777701	+	1.37606i
$605$	−1.86659	+	2.42461i	−0.0758878	+	0.0985744i
$606$	19.5358	−	5.13854i	0.793588	−	0.208739i
$607$	−3.49971	+	2.02056i	−0.142049	+	0.0820119i	−0.569340	−	0.822102i	$-0.692801\pi$
$607$	−3.49971	+	2.02056i	−0.142049	+	0.0820119i	0.427291	+	0.904114i	$0.359468\pi$
$608$	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
$612$	−48.6314	−	28.6763i	−1.96581	−	1.15917i
$613$	−15.5447	+	26.9242i	−0.627844	+	1.08746i	0.360140	+	0.932898i	$0.382729\pi$
$613$	−15.5447	+	26.9242i	−0.627844	+	1.08746i	−0.987984	+	0.154559i	$0.950604\pi$
$614$	2.65506	−	9.72981i	0.107149	−	0.392663i
$615$	−0.803770	+	6.03122i	−0.0324111	+	0.243202i
$616$	−21.9414	−	7.61211i	−0.884043	−	0.306701i
$617$			15.3302i			0.617170i	0.951197	+	0.308585i	$0.0998554\pi$
$617$			15.3302i			0.617170i	−0.951197	+	0.308585i	$0.900145\pi$
$618$	50.7004	+	13.8351i	2.03947	+	0.556528i
$619$	37.3373	+	21.5567i	1.50071	+	0.866438i	1.00000		0.000825626i	$0.000262805\pi$
$619$	37.3373	+	21.5567i	1.50071	+	0.866438i	0.500715	+	0.865612i	$0.333071\pi$
$620$	23.3389	+	18.3115i	0.937314	+	0.735407i
$621$	−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
$625$	0.158788	−	24.9995i	0.00635150	−	0.999980i
$626$	−31.5075	+	8.28747i	−1.25929	+	0.331234i
$627$	59.6382	+	34.4321i	2.38172	+	1.37509i
$628$	17.6484	+	31.2269i	0.704247	+	1.24609i
$629$	5.59517			0.223094
$630$	−46.6509	+	3.10038i	−1.85862	+	0.123522i
$631$		−	23.9995i		−	0.955404i	−0.878522	−	0.477702i	$-0.841470\pi$
$631$		−	23.9995i		−	0.955404i	0.878522	−	0.477702i	$-0.158530\pi$
$632$	−6.05323	+	21.4065i	−0.240785	+	0.851506i
$633$	7.53214	−	13.0460i	0.299376	−	0.518534i
$634$	24.4407	−	6.42869i	0.970666	−	0.255316i
$635$	−4.96602	−	12.0431i	−0.197070	−	0.477915i
$636$	−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
$640$	−2.45402	−	25.1789i	−0.0970038	−	0.995284i
$641$	12.7941	−	22.1600i	0.505336	−	0.875267i	−0.494645	−	0.869095i	$-0.664702\pi$
$641$	12.7941	−	22.1600i	0.505336	−	0.875267i	0.999981	−	0.00617237i	$-0.00196474\pi$
$642$	−35.1308	−	9.58646i	−1.38650	−	0.378347i
$643$	−48.1544			−1.89902			−0.949512	−	0.313731i	$-0.898421\pi$
$643$	−48.1544			−1.89902			−0.949512	+	0.313731i	$0.898421\pi$
$644$	−13.6757	−	9.17927i	−0.538897	−	0.361714i
$645$	2.78046	−	20.8637i	0.109481	−	0.821506i
$646$	52.1832	+	14.2397i	2.05312	+	0.560253i
$647$	−11.2431	−	6.49122i	−0.442013	−	0.255196i	0.262438	−	0.964949i	$-0.415473\pi$
$647$	−11.2431	−	6.49122i	−0.442013	−	0.255196i	−0.704451	+	0.709752i	$0.748807\pi$
$648$	−3.79313	−	14.9789i	−0.149008	−	0.588426i
$649$	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	0.994789	−	0.101960i	$-0.0325113\pi$
$653$	10.4539	+	18.1068i	0.409094	+	0.708572i	−0.585694	+	0.810532i	$0.699178\pi$
$654$	−3.27767	−	12.4611i	−0.128167	−	0.487268i
$655$	30.4838	+	23.4680i	1.19110	+	0.916971i
$656$	−3.25008	+	1.79763i	−0.126894	+	0.0701859i
$657$	17.7292			0.691682
$658$	−11.5638	−	3.89317i	−0.450804	−	0.151772i
$659$	−36.6633			−1.42820			−0.714099	−	0.700045i	$-0.753163\pi$
$659$	−36.6633			−1.42820			−0.714099	+	0.700045i	$0.753163\pi$
$660$	37.7431	−	15.1593i	1.46915	−	0.590077i
$661$	−13.6519	+	23.6458i	−0.530998	+	0.919715i	0.468348	+	0.883544i	$0.344849\pi$
$661$	−13.6519	+	23.6458i	−0.530998	+	0.919715i	−0.999346	+	0.0361712i	$0.988484\pi$
$662$	1.94186	−	0.510771i	0.0754726	−	0.0198517i
$663$	20.8514	−	12.0386i	0.809803	−	0.467540i
$664$	20.9534	−	20.3837i	0.813150	−	0.791041i
$665$	42.3378	−	14.6322i	1.64179	−	0.567412i
$666$	6.16114	+	6.21801i	0.238739	+	0.240943i
$667$	−1.04941	+	0.605877i	−0.0406333	+	0.0234596i
$668$	23.5621	−	39.9585i	0.911646	−	1.54604i
$669$	−14.4857	−	8.36330i	−0.560048	−	0.323344i
$670$	9.42853	+	3.97388i	0.364256	+	0.153524i
$671$	−19.9272			−0.769281
$672$	−28.3921	−	33.4310i	−1.09525	−	1.28963i
$673$		−	4.86055i		−	0.187360i	−0.995602	−	0.0936802i	$-0.970137\pi$
$673$		−	4.86055i		−	0.187360i	0.995602	−	0.0936802i	$-0.0298631\pi$
$674$	12.8669	+	3.51111i	0.495616	+	0.135243i
$675$	26.9011	−	26.7308i	1.03542	−	1.02887i
$676$	−17.8389	−	10.5190i	−0.686113	−	0.404577i
$677$	−3.37606	+	1.94917i	−0.129753	+	0.0749128i	−0.563471	−	0.826136i	$-0.690534\pi$
$677$	−3.37606	+	1.94917i	−0.129753	+	0.0749128i	0.433719	+	0.901048i	$0.357201\pi$
$678$	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
$682$	−28.1558	+	7.40586i	−1.07814	+	0.283585i
$683$	−15.0819	−	8.70755i	−0.577094	−	0.333185i	0.182884	−	0.983135i	$-0.441457\pi$
$683$	−15.0819	−	8.70755i	−0.577094	−	0.333185i	−0.759978	+	0.649949i	$0.774790\pi$
$684$	41.6369	+	73.6722i	1.59203	+	2.81693i
$685$	1.36805	−	10.2654i	0.0522706	−	0.392221i
$686$	−11.1907	+	23.6806i	−0.427262	+	0.904128i
$687$	28.0752			1.07113
$688$	11.2429	−	6.21852i	0.428632	−	0.237079i
$689$	−15.3373	−	8.85497i	−0.584303	−	0.337347i
$690$	28.6217	−	3.58827i	1.08961	−	0.136603i
$691$	12.1565	−	7.01858i	0.462456	−	0.266999i	−0.250620	−	0.968085i	$-0.580635\pi$
$691$	12.1565	−	7.01858i	0.462456	−	0.266999i	0.713076	+	0.701086i	$0.247301\pi$
$692$	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
$695$	−24.9257	+	10.2782i	−0.945485	+	0.389875i
$696$	−3.12810	+	0.792135i	−0.118570	+	0.0300258i
$697$	−4.06200	−	2.34520i	−0.153859	−	0.0888306i
$698$	2.85176	−	10.4506i	0.107941	−	0.395563i
$699$			12.3269i			0.466245i
$700$	8.63639	−	25.0083i	0.326425	−	0.945223i
$701$		−	21.7579i		−	0.821786i	−0.911684	−	0.410893i	$-0.865217\pi$
$701$		−	21.7579i		−	0.821786i	0.911684	−	0.410893i	$-0.134783\pi$
$702$	16.8306	+	4.59270i	0.635228	+	0.173340i
$703$	−7.26311	−	4.19336i	−0.273933	−	0.158156i
$704$	21.1513	+	13.0017i	0.797168	+	0.490022i
$705$	19.7555	−	8.14625i	0.744033	−	0.306805i
$706$	−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	$-0.471116\pi$
$709$	26.5841	−	15.3484i	0.998388	−	0.576420i	0.907771	+	0.419466i	$0.137783\pi$
$710$	2.84318	+	22.6785i	0.106703	+	0.851109i
$711$	−38.0631	−	21.9757i	−1.42748	−	0.824155i
$712$	8.62007	−	30.4838i	0.323051	−	1.14243i
$713$	−20.6473			−0.773246
$714$	17.6733	−	52.4947i	0.661408	−	1.96456i
$715$	−1.49100	+	11.1879i	−0.0557601	+	0.418405i
$716$	6.28144	−	3.55005i	0.234749	−	0.132672i
$717$	−54.6669	−	31.5620i	−2.04157	−	1.17870i
$718$	4.56572	+	17.3581i	0.170391	+	0.647797i
$719$	−11.7603	−	20.3694i	−0.438585	−	0.759652i	0.558995	−	0.829171i	$-0.311187\pi$
$719$	−11.7603	−	20.3694i	−0.438585	−	0.759652i	−0.997581	+	0.0695187i	$0.977854\pi$
$720$	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
$724$	−6.86514	−	4.04814i	−0.255141	−	0.150448i
$725$	−1.37200	−	1.38074i	−0.0509547	−	0.0512794i
$726$	1.49300	−	5.47128i	0.0554103	−	0.203058i
$727$		−	29.2877i		−	1.08622i	−0.839661	−	0.543110i	$-0.817246\pi$
$727$		−	29.2877i		−	1.08622i	0.839661	−	0.543110i	$-0.182754\pi$
$728$	11.9529	−	2.29460i	0.443005	−	0.0850435i
$729$	−36.1543			−1.33905
$730$	−3.89660	+	9.24516i	−0.144219	+	0.342179i
$731$	14.0516	+	8.11269i	0.519717	+	0.300059i
$732$	−32.4175	−	19.1155i	−1.19819	−	0.706529i
$733$	39.4427	−	22.7723i	1.45685	−	0.841113i	0.457996	−	0.888954i	$-0.348567\pi$
$733$	39.4427	−	22.7723i	1.45685	−	0.841113i	0.998855	+	0.0478408i	$0.0152340\pi$
$734$	−26.5298	+	26.2872i	−0.979234	+	0.970278i
$735$	−12.4294	−	44.1544i	−0.458465	−	1.62866i
$736$	12.1614	+	12.7333i	0.448276	+	0.469356i
$737$	−8.69620	+	5.02076i	−0.320329	+	0.184942i
$738$	−1.86663	−	7.09659i	−0.0687115	−	0.261229i
$739$	−6.91988	+	11.9856i	−0.254552	+	0.440897i	−0.964774	−	0.263081i	$-0.915261\pi$
$739$	−6.91988	+	11.9856i	−0.254552	+	0.440897i	0.710222	+	0.703978i	$0.248595\pi$
$740$	−4.59659	+	1.84620i	−0.168974	+	0.0678677i
$741$	−36.0898			−1.32579
$742$	−39.9391	+	8.04822i	−1.46621	+	0.295459i
$743$	−36.5334			−1.34028			−0.670141	−	0.742234i	$-0.733766\pi$
$743$	−36.5334			−1.34028			−0.670141	+	0.742234i	$0.733766\pi$
$744$	−52.9080	−	14.9611i	−1.93970	−	0.548499i
$745$	−30.7222	−	23.6515i	−1.12557	−	0.866525i
$746$	−16.0897	+	4.23209i	−0.589084	+	0.154948i
$747$	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	$-0.879127\pi$
$751$	−29.3811	+	16.9632i	−1.07213	+	0.618996i	−0.143369	+	0.989669i	$0.545794\pi$
$752$	11.1747	+	6.72847i	0.407500	+	0.245362i
$753$	−28.4613	−	16.4322i	−1.03719	−	0.598821i
$754$	0.235727	−	0.863854i	0.00858469	−	0.0314597i
$755$	5.73726	−	43.0505i	0.208800	−	1.56677i
$756$	36.0327	−	17.6757i	1.31050	−	0.642858i
$757$	31.2178			1.13463			0.567315	−	0.823501i	$-0.307982\pi$
$757$	31.2178			1.13463			0.567315	+	0.823501i	$0.307982\pi$
$758$	1.13037	−	4.14240i	0.0410569	−	0.150459i
$759$	−14.1547	+	24.5167i	−0.513783	+	0.889899i
$760$	−47.5686	+	5.52023i	−1.72549	+	0.200240i
$761$	−17.6688	+	10.2011i	−0.640493	+	0.369789i	−0.784804	−	0.619744i	$-0.787237\pi$
$761$	−17.6688	+	10.2011i	−0.640493	+	0.369789i	0.144312	+	0.989532i	$0.453903\pi$
$762$	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
$765$	24.0625	+	58.3539i	0.869981	+	2.10979i
$766$	−4.50367	−	17.1222i	−0.162724	−	0.618649i
$767$	−5.36403	+	9.29077i	−0.193684	+	0.335470i
$768$	21.9367	+	41.4409i	0.791572	+	1.49537i
$769$			5.57448i			0.201021i	0.994936	+	0.100510i	$0.0320476\pi$
$769$			5.57448i			0.201021i	−0.994936	+	0.100510i	$0.967952\pi$
$770$	14.4454	+	21.5764i	0.520575	+	0.777560i
$771$	−33.3235			−1.20012
$772$	12.0352	+	21.2949i	0.433155	+	0.766421i
$773$	32.8342	+	18.9569i	1.18097	+	0.681831i	0.956238	−	0.292591i	$-0.0945174\pi$
$773$	32.8342	+	18.9569i	1.18097	+	0.681831i	0.224728	+	0.974422i	$0.427851\pi$
$774$	6.45719	+	24.5491i	0.232099	+	0.882398i
$775$	−8.48235	−	32.0635i	−0.304695	−	1.15176i
$776$	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
$780$	−13.1578	+	16.7703i	−0.471124	+	0.600471i
$781$	−19.4258	−	11.2155i	−0.695111	−	0.401323i
$782$	−5.85380	+	21.4520i	−0.209331	+	0.767122i
$783$		−	2.95272i		−	0.105522i
$784$	17.1382	−	22.1423i	0.612079	−	0.790797i
$785$	5.29759	−	39.7513i	0.189079	−	1.41879i
$786$	−68.7885	−	18.7709i	−2.45361	−	0.669537i
$787$	−18.8744	+	32.6914i	−0.672800	+	1.16532i	0.304307	+	0.952574i	$0.401575\pi$
$787$	−18.8744	+	32.6914i	−0.672800	+	1.16532i	−0.977107	+	0.212749i	$0.931758\pi$
$788$	−12.7272	−	7.50477i	−0.453387	−	0.267346i
$789$	−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
$794$	−8.14101	−	30.9507i	−0.288914	−	1.09840i
$795$	43.5268	−	56.5392i	1.54374	−	2.00524i
$796$	−9.80968	+	5.54409i	−0.347695	+	0.196505i
$797$			28.3177i			1.00306i	0.865139	+	0.501532i	$0.167230\pi$
$797$			28.3177i			1.00306i	−0.865139	+	0.501532i	$0.832770\pi$
$798$	−62.2845	+	54.8981i	−2.20485	+	1.94337i
$799$			16.4728i			0.582767i
$800$	−14.7776	+	24.1168i	−0.522468	+	0.852659i
$801$	54.2035	+	31.2944i	1.91519	+	1.10573i
$802$	32.7216	−	8.60682i	1.15544	−	0.303917i
$803$	−4.92311	−	8.52707i	−0.173733	−	0.300914i
$804$	−18.9632	−	0.174224i	−0.668781	−	0.00614441i
$805$	6.01514	+	17.4046i	0.212006	+	0.613433i
$806$	10.8382	−	10.7390i	0.381758	−	0.378266i
$807$	2.23244	+	3.86671i	0.0785857	+	0.136115i
$808$	−3.38424	−	13.3642i	−0.119057	−	0.470149i
$809$	0.715781	−	1.23977i	0.0251655	−	0.0435879i	−0.853168	−	0.521636i	$-0.825322\pi$
$809$	0.715781	−	1.23977i	0.0251655	−	0.0435879i	0.878334	+	0.478048i	$0.158655\pi$
$810$	−6.70958	+	15.9193i	−0.235751	+	0.559348i
$811$		−	0.229410i		−	0.00805567i	−0.999992	−	0.00402783i	$-0.998718\pi$
$811$		−	0.229410i		−	0.00805567i	0.999992	−	0.00402783i	$-0.00128210\pi$
$812$	−0.907231	−	1.84944i	−0.0318376	−	0.0649025i
$813$	54.6357			1.91616
$814$	1.27978	−	4.68992i	0.0448562	−	0.164381i
$815$	30.4327	+	23.4287i	1.06601	+	0.820672i
$816$	−30.5443	+	50.7284i	−1.06927	+	1.77585i
$817$	−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	$-0.681867\pi$
$821$	−2.36907	+	1.36778i	−0.0826810	+	0.0477359i	0.458089	+	0.888906i	$0.348534\pi$
$822$	4.88270	+	18.5632i	0.170304	+	0.647465i
$823$	1.56485	−	2.71040i	0.0545472	−	0.0944784i	−0.837462	−	0.546495i	$-0.815962\pi$
$823$	1.56485	−	2.71040i	0.0545472	−	0.0944784i	0.892010	+	0.452016i	$0.149295\pi$
$824$	9.75943	−	34.5130i	0.339986	−	1.20232i
$825$	−43.8875	−	11.9091i	−1.52797	−	0.414622i
$826$	4.87533	+	24.1937i	0.169634	+	0.841807i
$827$		−	32.3184i		−	1.12382i	−0.827198	−	0.561911i	$-0.810066\pi$
$827$		−	32.3184i		−	1.12382i	0.827198	−	0.561911i	$-0.189934\pi$
$828$	−30.2859	+	17.1165i	−1.05251	+	0.594840i
$829$	−4.80290	+	8.31887i	−0.166812	+	0.288926i	−0.937297	−	0.348531i	$-0.886681\pi$
$829$	−4.80290	+	8.31887i	−0.166812	+	0.288926i	0.770486	+	0.637457i	$0.220014\pi$
$830$	−32.4291	+	4.06560i	−1.12563	+	0.141119i
$831$	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
$835$	−47.9470	+	19.7712i	−1.65927	+	0.684209i
$836$	23.8716	−	40.4833i	0.825618	−	1.40015i
$837$	25.1559	−	43.5713i	0.869516	−	1.50605i
$838$	−24.7935	−	6.76563i	−0.856479	−	0.233715i
$839$	37.5135			1.29511			0.647555	−	0.762019i	$-0.275792\pi$
$839$	37.5135			1.29511			0.647555	+	0.762019i	$0.275792\pi$
$840$	2.80217	+	48.9574i	0.0966839	+	1.68919i
$841$	28.8484			0.994774
$842$	−42.2861	−	11.5390i	−1.45728	−	0.397660i
$843$	−13.3550	+	23.1315i	−0.459970	+	0.796692i
$844$	−8.85586	−	5.22200i	−0.304831	−	0.179749i
$845$	8.82658	+	21.4053i	0.303644	+	0.736366i
$846$	−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
$850$	−35.7181	−	0.277513i	−1.22512	−	0.00951862i
$851$	1.72385	−	2.98579i	0.0590928	−	0.102352i
$852$	−20.8433	−	36.8800i	−0.714078	−	1.26349i
$853$			38.6732i			1.32415i	0.749439	+	0.662073i	$0.230323\pi$
$853$			38.6732i			1.32415i	−0.749439	+	0.662073i	$0.769677\pi$
$854$	7.66566	−	22.7691i	0.262314	−	0.779144i
$855$	12.4983	−	93.7833i	0.427434	−	3.20732i
$856$	−6.76241	+	23.9144i	−0.231134	+	0.817379i
$857$	6.47602	−	11.2168i	0.221217	−	0.383158i	−0.733961	−	0.679192i	$-0.762331\pi$
$857$	6.47602	−	11.2168i	0.221217	−	0.383158i	0.955178	+	0.296033i	$0.0956639\pi$
$858$	−5.32150	−	20.2314i	−0.181673	−	0.690689i
$859$	6.46557	−	3.73290i	0.220603	−	0.127365i	−0.385627	−	0.922655i	$-0.626015\pi$
$859$	6.46557	−	3.73290i	0.220603	−	0.127365i	0.606229	+	0.795290i	$0.292681\pi$
$860$	−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	0.528948	−	0.848654i	$-0.322587\pi$
$863$	−13.8213	−	23.9392i	−0.470482	−	0.814899i	−0.999430	+	0.0337553i	$0.989253\pi$
$864$	−41.6878	+	10.1501i	−1.41825	+	0.345313i
$865$	−27.7909	−	21.3949i	−0.944918	−	0.727448i
$866$	0.957863	−	3.51022i	0.0325495	−	0.119282i
$867$	−24.9601			−0.847689
$868$	2.36900	−	35.0201i	0.0804090	−	1.18866i
$869$			24.4092i			0.828026i
$870$	3.32449	+	1.40119i	0.112711	+	0.0475048i
$871$	2.63123	−	4.55743i	0.0891560	−	0.154423i
$872$	−8.52446	+	2.15867i	−0.288675	+	0.0731018i
$873$	29.5562	+	51.1928i	1.00033	+	1.73261i
$874$	23.6763	−	23.4597i	0.800862	−	0.793538i
$875$	−24.5569	+	16.4912i	−0.830173	+	0.557506i
$876$	0.170836	−	18.5944i	0.00577200	−	0.628247i
$877$	26.6238	+	46.1138i	0.899023	+	1.55715i	0.828746	+	0.559625i	$0.189055\pi$
$877$	26.6238	+	46.1138i	0.899023	+	1.55715i	0.0702771	+	0.997528i	$0.477612\pi$
$878$	20.9534	−	5.51141i	0.707143	−	0.186001i
$879$	−22.1415	−	12.7834i	−0.746814	−	0.431174i
$880$	−10.1086	−	25.8523i	−0.340762	−	0.871481i
$881$		−	48.2909i		−	1.62696i	−0.581592	−	0.813480i	$-0.697570\pi$
$881$		−	48.2909i		−	1.62696i	0.581592	−	0.813480i	$-0.302430\pi$
$882$	34.0961	+	43.5631i	1.14807	+	1.46685i
$883$		−	19.1196i		−	0.643426i	−0.946837	−	0.321713i	$-0.895741\pi$
$883$		−	19.1196i		−	0.643426i	0.946837	−	0.321713i	$-0.104259\pi$
$884$	−8.08483	−	14.3053i	−0.271922	−	0.481138i
$885$	−34.2494	−	26.3670i	−1.15128	−	0.886318i
$886$	−2.17899	−	8.28414i	−0.0732047	−	0.278311i
$887$	−29.2779	+	16.9036i	−0.983057	+	0.567568i	−0.903192	−	0.429237i	$-0.858782\pi$
$887$	−29.2779	+	16.9036i	−0.983057	+	0.567568i	−0.0798654	+	0.996806i	$0.525449\pi$
$888$	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
$892$	−5.79824	+	9.83310i	−0.194139	+	0.329236i
$893$	12.3457	−	21.3834i	0.413134	−	0.715570i
$894$	69.3265	+	18.9177i	2.31862	+	0.632703i
$895$	−7.99616	−	1.06563i	−0.267282	−	0.0356202i
$896$	−22.9925	+	19.1662i	−0.768126	+	0.640298i
$897$		−	14.8362i		−	0.495365i
$898$	−3.69995	+	13.5590i	−0.123469	+	0.452468i
$899$	−2.23637	−	1.29117i	−0.0745870	−	0.0430628i
$900$	−39.0227	−	39.9997i	−1.30076	−	1.33332i
$901$	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
$905$	3.39683	+	8.23763i	0.112914	+	0.273828i
$906$	20.4768	+	77.8492i	0.680297	+	2.58637i
$907$	16.9052	+	9.76020i	0.561327	+	0.324082i	0.753678	−	0.657244i	$-0.228278\pi$
$907$	16.9052	+	9.76020i	0.561327	+	0.324082i	−0.192351	+	0.981326i	$0.561611\pi$
$908$	−32.1950	+	18.1955i	−1.06843	+	0.603838i
$909$	27.2371			0.903399
$910$	−12.2100	−	6.00745i	−0.404756	−	0.199145i
$911$			47.4878i			1.57334i	0.617373	+	0.786671i	$0.288197\pi$
$911$			47.4878i			1.57334i	−0.617373	+	0.786671i	$0.711803\pi$
$912$	77.6687	−	42.9590i	2.57187	−	1.42251i
$913$	16.0376	−	27.7780i	0.530768	−	0.919317i
$914$	−6.62866	−	25.2010i	−0.219257	−	0.833574i
$915$	16.0400	+	38.8985i	0.530265	+	1.28594i
$916$	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	$-0.684741\pi$
$919$	−2.97980	+	1.72039i	−0.0982945	+	0.0567503i	0.450047	+	0.893005i	$0.351407\pi$
$920$	−2.26931	−	19.5550i	−0.0748170	−	0.644709i
$921$	10.4497	−	18.0995i	0.344330	−	0.596398i
$922$	−6.55469	+	24.0205i	−0.215867	+	0.791074i
$923$	11.7555			0.386936
$924$	−39.9590	−	26.8210i	−1.31456	−	0.882345i
$925$	5.34489	+	1.45037i	0.175739	+	0.0476878i
$926$	10.6268	−	38.9431i	0.349217	−	1.27975i
$927$	61.3679	+	35.4308i	2.01559	+	1.16370i
$928$	0.520969	+	2.13969i	0.0171016	+	0.0702388i
$929$	−14.8975	+	8.60107i	−0.488771	+	0.282192i	−0.724064	−	0.689732i	$-0.757728\pi$
$929$	−14.8975	+	8.60107i	−0.488771	+	0.282192i	0.235293	+	0.971924i	$0.424395\pi$
$930$	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
$934$	8.45899	−	2.22498i	0.276786	−	0.0728036i
$935$	21.3843	−	27.7771i	0.699341	−	0.908408i
$936$	6.99503	−	24.7371i	0.228640	−	0.808556i
$937$	16.8939			0.551901			0.275950	−	0.961172i	$-0.411007\pi$
$937$	16.8939			0.551901			0.275950	+	0.961172i	$0.411007\pi$
$938$	−2.39151	−	11.8678i	−0.0780856	−	0.387498i
$939$	−67.5111			−2.20314
$940$	−5.43543	−	13.5329i	−0.177284	−	0.441395i
$941$	−28.6433	+	49.6117i	−0.933746	+	1.61729i	−0.156890	+	0.987616i	$0.550147\pi$
$941$	−28.6433	+	49.6117i	−0.933746	+	1.61729i	−0.776856	+	0.629679i	$0.783187\pi$
$942$	18.9076	+	71.8833i	0.616042	+	2.34208i
$943$	−2.50297	+	1.44509i	−0.0815079	+	0.0470586i
$944$	0.484765	−	26.3796i	0.0157778	−	0.858584i
$945$	−44.0572	−	8.51164i	−1.43318	−	0.276884i
$946$	10.0141	−	9.92254i	0.325587	−	0.322610i
$947$	28.0175	−	16.1759i	0.910447	−	0.525647i	0.0298722	−	0.999554i	$-0.490490\pi$
$947$	28.0175	−	16.1759i	0.910447	−	0.525647i	0.880575	+	0.473907i	$0.157157\pi$
$948$	−23.4150	+	39.7089i	−0.760483	+	1.28968i
$949$	4.46880	+	2.58006i	0.145063	+	0.0837523i
$950$	46.1578	+	27.1295i	1.49756	+	0.880199i
$951$	52.3692			1.69819
$952$	−35.7134	−	12.3900i	−1.15748	−	0.401564i
$953$			36.4296i			1.18007i	0.807377	+	0.590036i	$0.200886\pi$
$953$			36.4296i			1.18007i	−0.807377	+	0.590036i	$0.799114\pi$
$954$	−22.6535	+	83.0167i	−0.733434	+	2.68776i
$955$	16.3829	+	12.6124i	0.530138	+	0.408129i
$956$	−21.8818	+	37.1088i	−0.707707	+	1.20018i
$957$	−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
$962$	0.648086	+	2.46391i	0.0208951	+	0.0794396i
$963$	−42.5225	−	24.5504i	−1.37027	−	0.791124i
$964$	−8.54475	−	15.1190i	−0.275208	−	0.486951i
$965$	3.61265	−	27.1081i	0.116295	−	0.872640i
$966$	−22.5681	−	25.6045i	−0.726115	−	0.823813i
$967$	15.8537			0.509822			0.254911	−	0.966964i	$-0.417954\pi$
$967$	15.8537			0.509822			0.254911	+	0.966964i	$0.417954\pi$
$968$	−3.72444	−	1.05318i	−0.119708	−	0.0338504i
$969$	97.0716	+	56.0443i	3.11839	+	1.80040i
$970$	−33.1913	+	4.16115i	−1.06571	+	0.133607i
$971$	−39.0664	+	22.5550i	−1.25370	+	0.723825i	−0.971843	−	0.235631i	$-0.924284\pi$
$971$	−39.0664	+	22.5550i	−1.25370	+	0.723825i	−0.281859	+	0.959456i	$0.590951\pi$
$972$	−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
$975$	23.0393	−	6.09502i	0.737849	−	0.195197i
$976$	−13.2484	+	22.0030i	−0.424070	+	0.704300i
$977$	−17.5983	−	10.1604i	−0.563019	−	0.325059i	0.191338	−	0.981524i	$-0.438717\pi$
$977$	−17.5983	−	10.1604i	−0.563019	−	0.325059i	−0.754356	+	0.656465i	$0.772051\pi$
$978$	−68.6733	−	18.7395i	−2.19593	−	0.599223i
$979$		−	34.7598i		−	1.11093i
$980$	−30.2104	+	8.20543i	−0.965037	+	0.262113i
$981$		−	17.3735i		−	0.554693i
$982$	16.2924	−	59.7057i	0.519912	−	1.90529i
$983$	−1.38824	−	0.801501i	−0.0442780	−	0.0255639i	0.477698	−	0.878524i	$-0.341471\pi$
$983$	−1.38824	−	0.801501i	−0.0442780	−	0.0255639i	−0.521976	+	0.852960i	$0.674805\pi$
$984$	−7.46090	+	1.88934i	−0.237845	+	0.0602300i
$985$	6.29731	+	15.2716i	0.200649	+	0.486594i
$986$	−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
$990$	54.4165	−	6.82214i	1.72947	−	0.216822i
$991$	−23.9870	−	13.8489i	−0.761971	−	0.439924i	0.0680321	−	0.997683i	$-0.478328\pi$
$991$	−23.9870	−	13.8489i	−0.761971	−	0.439924i	−0.830003	+	0.557759i	$0.811661\pi$
$992$	−10.5417	+	36.0125i	−0.334699	+	1.14340i
$993$	4.16083			0.132040
$994$	20.2878	−	17.8819i	0.643491	−	0.567178i
$995$	12.4876	+	1.66419i	0.395882	+	0.0527585i
$996$	52.7365	−	29.8048i	1.67102	−	0.944401i
$997$	36.4937	+	21.0697i	1.15577	+	0.667283i	0.950286	−	0.311378i	$-0.100790\pi$
$997$	36.4937	+	21.0697i	1.15577	+	0.667283i	0.205482	+	0.978661i	$0.434124\pi$
$998$	−41.5922	+	10.9401i	−1.31658	+	0.346302i
$999$	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.59.24	yes	80
4.3	odd	2		1120.2.bq.b.1039.4		80
5.4	even	2	inner	280.2.ba.b.59.17	yes	80
7.5	odd	6	inner	280.2.ba.b.19.4	✓	80
8.3	odd	2	inner	280.2.ba.b.59.37	yes	80
8.5	even	2		1120.2.bq.b.1039.3		80
20.19	odd	2		1120.2.bq.b.1039.38		80
28.19	even	6		1120.2.bq.b.719.37		80
35.19	odd	6	inner	280.2.ba.b.19.37	yes	80
40.19	odd	2	inner	280.2.ba.b.59.4	yes	80
40.29	even	2		1120.2.bq.b.1039.37		80
56.5	odd	6		1120.2.bq.b.719.38		80
56.19	even	6	inner	280.2.ba.b.19.17	yes	80
140.19	even	6		1120.2.bq.b.719.3		80
280.19	even	6	inner	280.2.ba.b.19.24	yes	80
280.229	odd	6		1120.2.bq.b.719.4		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.ba.b.19.4	✓	80	7.5	odd	6	inner
280.2.ba.b.19.17	yes	80	56.19	even	6	inner
280.2.ba.b.19.24	yes	80	280.19	even	6	inner
280.2.ba.b.19.37	yes	80	35.19	odd	6	inner
280.2.ba.b.59.4	yes	80	40.19	odd	2	inner
280.2.ba.b.59.17	yes	80	5.4	even	2	inner
280.2.ba.b.59.24	yes	80	1.1	even	1	trivial
280.2.ba.b.59.37	yes	80	8.3	odd	2	inner
1120.2.bq.b.719.3		80	140.19	even	6
1120.2.bq.b.719.4		80	280.229	odd	6
1120.2.bq.b.719.37		80	28.19	even	6
1120.2.bq.b.719.38		80	56.5	odd	6
1120.2.bq.b.1039.3		80	8.5	even	2
1120.2.bq.b.1039.4		80	4.3	odd	2
1120.2.bq.b.1039.37		80	40.29	even	2
1120.2.bq.b.1039.38		80	20.19	odd	2

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)

\(f(q)\)	\(=\)	\(q+(0.372297 - 1.36433i) q^{2} +(1.46528 - 2.53794i) q^{3} +(-1.72279 - 1.01587i) q^{4} +(0.852425 + 2.06721i) q^{5} +(-2.91706 - 2.94399i) q^{6} +(1.45426 - 2.21023i) q^{7} +(-2.02737 + 1.97225i) q^{8} +(-2.79408 - 4.83948i) q^{9} +O(q^{10})\)	\(q+(0.372297 - 1.36433i) q^{2} +(1.46528 - 2.53794i) q^{3} +(-1.72279 - 1.01587i) q^{4} +(0.852425 + 2.06721i) 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} +(3.13772 - 0.393372i) q^{10} +(-1.55174 + 2.68769i) q^{11} +(-5.10258 + 2.88380i) q^{12} -1.62644i q^{13} +(-2.47407 - 2.80695i) q^{14} +(6.49549 + 0.865643i) q^{15} +(1.93602 + 3.50026i) q^{16} +(-2.52573 + 4.37469i) q^{17} +(-7.64287 + 2.01032i) 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} +(2.03478 + 8.03523i) q^{24} +(-3.54674 + 3.52429i) q^{25} +(-2.21901 - 0.605520i) q^{26} -7.58472 q^{27} +(-4.75069 + 2.33043i) q^{28} +0.389298i q^{29} +(3.59927 - 8.53972i) q^{30} +(-3.31666 + 5.74462i) q^{31} +(5.49629 - 1.33823i) q^{32} +(4.54746 + 7.87643i) q^{33} +(5.02820 + 5.07461i) q^{34} +(5.80867 + 1.12221i) q^{35} +(-0.102678 + 11.1758i) q^{36} +(-0.553818 - 0.959241i) q^{37} +(-2.72390 - 10.3558i) q^{38} +(-4.12781 - 2.38319i) q^{39} +(-5.80524 - 2.50981i) q^{40} +0.928523i q^{41} +(-10.7491 + 2.16607i) q^{42} -3.21202i q^{43} +(5.40367 - 3.05396i) q^{44} +(7.62250 - 9.90125i) q^{45} +(4.25717 - 1.11977i) 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} +(-1.65226 + 2.80202i) q^{52} +(5.44437 - 9.42993i) q^{53} +(-2.82377 + 10.3481i) q^{54} +(-6.87877 - 0.916722i) q^{55} +(1.41081 + 7.34912i) q^{56} -22.1894i q^{57} +(0.531131 + 0.144934i) q^{58} +(-5.71232 - 3.29801i) q^{59} +(-10.3110 - 8.08990i) 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} +(3.36221 - 1.38642i) q^{65} +(12.4390 - 3.27186i) q^{66} +(2.80208 + 1.61778i) q^{67} +(8.79541 - 4.97086i) q^{68} +9.12183 q^{69} +(3.69361 - 7.50715i) q^{70} +7.22771i q^{71} +(15.2093 + 4.30081i) q^{72} +(-1.58632 + 2.74759i) q^{73} +(-1.51490 + 0.398468i) q^{74} +(3.74745 + 14.1655i) 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} +(-5.58549 + 6.98587i) q^{80} +(-2.73150 + 4.73109i) q^{81} +(1.26681 + 0.345686i) q^{82} -10.3353 q^{83} +(-1.04661 + 15.4717i) q^{84} +(-11.1964 - 1.49213i) q^{85} +(-4.38226 - 1.19582i) q^{86} +(0.988013 + 0.570429i) q^{87} +(-2.15485 - 8.50936i) 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} +(-1.17314 - 4.46005i) q^{94} +(13.4158 + 10.3282i) q^{95} +(4.65725 - 15.9101i) q^{96} -10.5782 q^{97} +(-9.80196 + 1.38624i) 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

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