LMFDB - Embedded newform 280.2.n.b.139.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(139,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))

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

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

chi := DirichletCharacter("280.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.n (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			139.1
Character	$\chi$	$=$	280.139
Dual form			280.2.n.b.139.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27891 - 0.603655i) q^{2} -1.64952 q^{3} +(1.27120 + 1.54404i) q^{4} +(-1.78913 - 1.34127i) q^{5} +(2.10957 + 0.995738i) q^{6} +(-0.157160 + 2.64108i) q^{7} +(-0.693682 - 2.74204i) q^{8} -0.279099 q^{9} +O(q^{10})$	\(q+(-1.27891 - 0.603655i) q^{2} -1.64952 q^{3} +(1.27120 + 1.54404i) q^{4} +(-1.78913 - 1.34127i) q^{5} +(2.10957 + 0.995738i) q^{6} +(-0.157160 + 2.64108i) q^{7} +(-0.693682 - 2.74204i) q^{8} -0.279099 q^{9} +(1.47847 + 2.79538i) q^{10} +4.28531 q^{11} +(-2.09687 - 2.54691i) q^{12} -0.653942i q^{13} +(1.79529 - 3.28282i) q^{14} +(2.95120 + 2.21245i) q^{15} +(-0.768095 + 3.92556i) q^{16} +2.74692 q^{17} +(0.356942 + 0.168480i) q^{18} -3.03045i q^{19} +(-0.203376 - 4.46751i) q^{20} +(0.259238 - 4.35650i) q^{21} +(-5.48051 - 2.58685i) q^{22} +7.21687 q^{23} +(1.14424 + 4.52304i) q^{24} +(1.40199 + 4.79942i) q^{25} +(-0.394756 + 0.836331i) q^{26} +5.40892 q^{27} +(-4.27770 + 3.11468i) q^{28} -7.72977i q^{29} +(-2.43875 - 4.61102i) q^{30} +5.52714 q^{31} +(3.35201 - 4.55676i) q^{32} -7.06869 q^{33} +(-3.51305 - 1.65819i) q^{34} +(3.82358 - 4.51445i) q^{35} +(-0.354792 - 0.430940i) q^{36} +1.78693 q^{37} +(-1.82934 + 3.87566i) q^{38} +1.07869i q^{39} +(-2.43673 + 5.83629i) q^{40} +3.66414i q^{41} +(-2.96136 + 5.41506i) q^{42} +6.86633i q^{43} +(5.44749 + 6.61668i) q^{44} +(0.499346 + 0.374348i) q^{45} +(-9.22970 - 4.35650i) q^{46} -4.60316i q^{47} +(1.26698 - 6.47527i) q^{48} +(-6.95060 - 0.830144i) q^{49} +(1.10419 - 6.98432i) q^{50} -4.53109 q^{51} +(1.00971 - 0.831292i) q^{52} -7.10358 q^{53} +(-6.91751 - 3.26512i) q^{54} +(-7.66699 - 5.74776i) q^{55} +(7.35098 - 1.40113i) q^{56} +4.99877i q^{57} +(-4.66612 + 9.88565i) q^{58} +12.8771i q^{59} +(0.335472 + 7.36922i) q^{60} +10.3872 q^{61} +(-7.06869 - 3.33648i) q^{62} +(0.0438633 - 0.737124i) q^{63} +(-7.03761 + 3.80421i) q^{64} +(-0.877114 + 1.16999i) q^{65} +(9.04019 + 4.26705i) q^{66} -0.822281i q^{67} +(3.49189 + 4.24134i) q^{68} -11.9043 q^{69} +(-7.61517 + 3.46543i) q^{70} +11.4141i q^{71} +(0.193606 + 0.765303i) q^{72} +5.19041 q^{73} +(-2.28531 - 1.07869i) q^{74} +(-2.31260 - 7.91672i) q^{75} +(4.67912 - 3.85231i) q^{76} +(-0.673480 + 11.3179i) q^{77} +(0.651155 - 1.37954i) q^{78} -1.45817i q^{79} +(6.63946 - 5.99312i) q^{80} -8.08481 q^{81} +(2.21188 - 4.68609i) q^{82} -4.62805 q^{83} +(7.05614 - 5.13772i) q^{84} +(-4.91460 - 3.68436i) q^{85} +(4.14490 - 8.78139i) q^{86} +12.7504i q^{87} +(-2.97264 - 11.7505i) q^{88} -14.0351i q^{89} +(-0.412639 - 0.780188i) q^{90} +(1.72711 + 0.102774i) q^{91} +(9.17410 + 11.1431i) q^{92} -9.11710 q^{93} +(-2.77872 + 5.88701i) q^{94} +(-4.06465 + 5.42187i) q^{95} +(-5.52918 + 7.51644i) q^{96} +13.5648 q^{97} +(8.38805 + 5.25744i) q^{98} -1.19603 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{4} + 40 q^{9}+O(q^{10}) $ 40 * q - 12 * q^4 + 40 * q^9	$ 40 q - 12 q^{4} + 40 q^{9} - 12 q^{14} - 28 q^{16} + 16 q^{25} - 28 q^{30} + 16 q^{35} - 28 q^{36} - 8 q^{44} - 32 q^{46} + 8 q^{49} + 4 q^{50} - 32 q^{51} - 4 q^{56} + 12 q^{60} - 84 q^{64} - 24 q^{65} + 40 q^{70} + 80 q^{74} - 72 q^{81} - 8 q^{84} + 80 q^{86} - 128 q^{99}+O(q^{100}) $ 40 * q - 12 * q^4 + 40 * q^9 - 12 * q^14 - 28 * q^16 + 16 * q^25 - 28 * q^30 + 16 * q^35 - 28 * q^36 - 8 * q^44 - 32 * q^46 + 8 * q^49 + 4 * q^50 - 32 * q^51 - 4 * q^56 + 12 * q^60 - 84 * q^64 - 24 * q^65 + 40 * q^70 + 80 * q^74 - 72 * q^81 - 8 * q^84 + 80 * q^86 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.27891	−	0.603655i	−0.904323	−	0.426849i
$2$	−1.27891	−	0.603655i	−0.904323	−	0.426849i
$3$	−1.64952			−0.952348			−0.476174	−	0.879351i	$-0.657977\pi$
$3$	−1.64952			−0.952348			−0.476174	+	0.879351i	$0.657977\pi$
$4$	1.27120	+	1.54404i	0.635601	+	0.772018i
$5$	−1.78913	−	1.34127i	−0.800124	−	0.599834i
$5$	−1.78913	−	1.34127i	−0.800124	−	0.599834i
$6$	2.10957	+	0.995738i	0.861230	+	0.406508i
$7$	−0.157160	+	2.64108i	−0.0594009	+	0.998234i
$7$	−0.157160	+	2.64108i	−0.0594009	+	0.998234i
$8$	−0.693682	−	2.74204i	−0.245254	−	0.969459i
$9$	−0.279099			−0.0930332
$10$	1.47847	+	2.79538i	0.467532	+	0.883976i
$11$	4.28531			1.29207			0.646035	−	0.763308i	$-0.276426\pi$
$11$	4.28531			1.29207			0.646035	+	0.763308i	$0.276426\pi$
$12$	−2.09687	−	2.54691i	−0.605313	−	0.735230i
$13$		−	0.653942i		−	0.181371i	−0.995880	−	0.0906855i	$-0.971094\pi$
$13$		−	0.653942i		−	0.181371i	0.995880	−	0.0906855i	$-0.0289058\pi$
$14$	1.79529	−	3.28282i	0.479812	−	0.877371i
$15$	2.95120	+	2.21245i	0.761997	+	0.571251i
$16$	−0.768095	+	3.92556i	−0.192024	+	0.981390i
$17$	2.74692			0.666226			0.333113	−	0.942887i	$-0.391901\pi$
$17$	2.74692			0.666226			0.333113	+	0.942887i	$0.391901\pi$
$18$	0.356942	+	0.168480i	0.0841320	+	0.0397111i
$19$		−	3.03045i		−	0.695232i	−0.937637	−	0.347616i	$-0.886991\pi$
$19$		−	3.03045i		−	0.695232i	0.937637	−	0.347616i	$-0.113009\pi$
$20$	−0.203376	−	4.46751i	−0.0454763	−	0.998965i
$21$	0.259238	−	4.35650i	0.0565703	−	0.950666i
$22$	−5.48051	−	2.58685i	−1.16845	−	0.551518i
$23$	7.21687			1.50482			0.752411	−	0.658694i	$-0.228891\pi$
$23$	7.21687			1.50482			0.752411	+	0.658694i	$0.228891\pi$
$24$	1.14424	+	4.52304i	0.233567	+	0.923262i
$25$	1.40199	+	4.79942i	0.280397	+	0.959884i
$26$	−0.394756	+	0.836331i	−0.0774179	+	0.164018i
$27$	5.40892			1.04095
$28$	−4.27770	+	3.11468i	−0.808410	+	0.588620i
$29$		−	7.72977i		−	1.43538i	−0.696361	−	0.717691i	$-0.745199\pi$
$29$		−	7.72977i		−	1.43538i	0.696361	−	0.717691i	$-0.254801\pi$
$30$	−2.43875	−	4.61102i	−0.445253	−	0.841853i
$31$	5.52714			0.992703			0.496352	−	0.868122i	$-0.334673\pi$
$31$	5.52714			0.992703			0.496352	+	0.868122i	$0.334673\pi$
$32$	3.35201	−	4.55676i	0.592556	−	0.805529i
$33$	−7.06869			−1.23050
$34$	−3.51305	−	1.65819i	−0.602483	−	0.284378i
$35$	3.82358	−	4.51445i	0.646303	−	0.763081i
$36$	−0.354792	−	0.430940i	−0.0591319	−	0.0718233i
$37$	1.78693			0.293769			0.146885	−	0.989154i	$-0.453075\pi$
$37$	1.78693			0.293769			0.146885	+	0.989154i	$0.453075\pi$
$38$	−1.82934	+	3.87566i	−0.296759	+	0.628714i
$39$			1.07869i			0.172728i
$40$	−2.43673	+	5.83629i	−0.385282	+	0.922799i
$41$			3.66414i			0.572242i	0.958193	+	0.286121i	$0.0923660\pi$
$41$			3.66414i			0.572242i	−0.958193	+	0.286121i	$0.907634\pi$
$42$	−2.96136	+	5.41506i	−0.456948	+	0.835563i
$43$			6.86633i			1.04711i	0.851993	+	0.523553i	$0.175394\pi$
$43$			6.86633i			1.04711i	−0.851993	+	0.523553i	$0.824606\pi$
$44$	5.44749	+	6.61668i	0.821241	+	0.997502i
$45$	0.499346	+	0.374348i	0.0744381	+	0.0558045i
$46$	−9.22970	−	4.35650i	−1.36085	−	0.642331i
$47$		−	4.60316i		−	0.671440i	−0.941962	−	0.335720i	$-0.891020\pi$
$47$		−	4.60316i		−	0.671440i	0.941962	−	0.335720i	$-0.108980\pi$
$48$	1.26698	−	6.47527i	0.182873	−	0.934625i
$49$	−6.95060	−	0.830144i	−0.992943	−	0.118592i
$50$	1.10419	−	6.98432i	0.156155	−	0.987732i
$51$	−4.53109			−0.634479
$52$	1.00971	−	0.831292i	0.140022	−	0.115280i
$53$	−7.10358			−0.975751			−0.487876	−	0.872913i	$-0.662228\pi$
$53$	−7.10358			−0.975751			−0.487876	+	0.872913i	$0.662228\pi$
$54$	−6.91751	−	3.26512i	−0.941353	−	0.444327i
$55$	−7.66699	−	5.74776i	−1.03382	−	0.775028i
$56$	7.35098	−	1.40113i	0.982315	−	0.187234i
$57$			4.99877i			0.662103i
$58$	−4.66612	+	9.88565i	−0.612691	+	1.29805i
$59$			12.8771i			1.67645i	0.545322	+	0.838226i	$0.316407\pi$
$59$			12.8771i			1.67645i	−0.545322	+	0.838226i	$0.683593\pi$
$60$	0.335472	+	7.36922i	0.0433093	+	0.951363i
$61$	10.3872			1.32994			0.664971	−	0.746870i	$-0.268444\pi$
$61$	10.3872			1.32994			0.664971	+	0.746870i	$0.268444\pi$
$62$	−7.06869	−	3.33648i	−0.897724	−	0.423734i
$63$	0.0438633	−	0.737124i	0.00552625	−	0.0928689i
$64$	−7.03761	+	3.80421i	−0.879701	+	0.475527i
$65$	−0.877114	+	1.16999i	−0.108793	+	0.145119i
$66$	9.04019	+	4.26705i	1.11277	+	0.525237i
$67$		−	0.822281i		−	0.100458i	−0.998738	−	0.0502288i	$-0.984005\pi$
$67$		−	0.822281i		−	0.100458i	0.998738	−	0.0502288i	$-0.0159951\pi$
$68$	3.49189	+	4.24134i	0.423454	+	0.514338i
$69$	−11.9043			−1.43311
$70$	−7.61517	+	3.46543i	−0.910187	+	0.414198i
$71$			11.4141i			1.35461i	0.735703	+	0.677304i	$0.236852\pi$
$71$			11.4141i			1.35461i	−0.735703	+	0.677304i	$0.763148\pi$
$72$	0.193606	+	0.765303i	0.0228167	+	0.0901918i
$73$	5.19041			0.607492			0.303746	−	0.952753i	$-0.401763\pi$
$73$	5.19041			0.607492			0.303746	+	0.952753i	$0.401763\pi$
$74$	−2.28531	−	1.07869i	−0.265662	−	0.125395i
$75$	−2.31260	−	7.91672i	−0.267036	−	0.914144i
$76$	4.67912	−	3.85231i	0.536732	−	0.441890i
$77$	−0.673480	+	11.3179i	−0.0767501	+	1.28979i
$78$	0.651155	−	1.37954i	0.0737288	−	0.156202i
$79$		−	1.45817i		−	0.164057i	−0.996630	−	0.0820284i	$-0.973860\pi$
$79$		−	1.45817i		−	0.164057i	0.996630	−	0.0820284i	$-0.0261398\pi$
$80$	6.63946	−	5.99312i	0.742315	−	0.670052i
$81$	−8.08481			−0.898312
$82$	2.21188	−	4.68609i	0.244261	−	0.517492i
$83$	−4.62805			−0.507995			−0.253997	−	0.967205i	$-0.581745\pi$
$83$	−4.62805			−0.507995			−0.253997	+	0.967205i	$0.581745\pi$
$84$	7.05614	−	5.13772i	0.769888	−	0.560571i
$85$	−4.91460	−	3.68436i	−0.533063	−	0.399625i
$86$	4.14490	−	8.78139i	0.446956	−	0.946922i
$87$			12.7504i			1.36698i
$88$	−2.97264	−	11.7505i	−0.316885	−	1.25261i
$89$		−	14.0351i		−	1.48772i	−0.668335	−	0.743860i	$-0.732993\pi$
$89$		−	14.0351i		−	1.48772i	0.668335	−	0.743860i	$-0.267007\pi$
$90$	−0.412639	−	0.780188i	−0.0434960	−	0.0822391i
$91$	1.72711	+	0.102774i	0.181051	+	0.0107736i
$92$	9.17410	+	11.1431i	0.956466	+	1.16175i
$93$	−9.11710			−0.945399
$94$	−2.77872	+	5.88701i	−0.286603	+	0.607199i
$95$	−4.06465	+	5.42187i	−0.417024	+	0.556272i
$96$	−5.52918	+	7.51644i	−0.564320	+	0.767144i
$97$	13.5648			1.37729			0.688647	−	0.725097i	$-0.258205\pi$
$97$	13.5648			1.37729			0.688647	+	0.725097i	$0.258205\pi$
$98$	8.38805	+	5.25744i	0.847321	+	0.531082i
$99$	−1.19603			−0.120205
$100$	−5.62827	+	8.26575i	−0.562827	+	0.826575i
$101$	4.42833			0.440635			0.220318	−	0.975428i	$-0.429291\pi$
$101$	4.42833			0.440635			0.220318	+	0.975428i	$0.429291\pi$
$102$	5.79483	+	2.73521i	0.573774	+	0.270826i
$103$		−	6.53701i		−	0.644111i	−0.946721	−	0.322055i	$-0.895626\pi$
$103$		−	6.53701i		−	0.644111i	0.946721	−	0.322055i	$-0.104374\pi$
$104$	−1.79314	+	0.453628i	−0.175832	+	0.0444819i
$105$	−6.30706	+	7.44665i	−0.615506	+	0.726718i
$106$	9.08481	+	4.28811i	0.882394	+	0.416498i
$107$		−	11.1165i		−	1.07468i	−0.843367	−	0.537338i	$-0.819430\pi$
$107$		−	11.1165i		−	1.07468i	0.843367	−	0.537338i	$-0.180570\pi$
$108$	6.87583	+	8.35157i	0.661627	+	0.803631i
$109$			1.93311i			0.185158i	0.995705	+	0.0925792i	$0.0295111\pi$
$109$			1.93311i			0.185158i	−0.995705	+	0.0925792i	$0.970489\pi$
$110$	6.33569	+	11.9791i	0.604085	+	1.14216i
$111$	−2.94756			−0.279770
$112$	−10.2470	−	2.64554i	−0.968251	−	0.249980i
$113$		−	18.7314i		−	1.76210i	−0.473019	−	0.881052i	$-0.656836\pi$
$113$		−	18.7314i		−	1.76210i	0.473019	−	0.881052i	$-0.343164\pi$
$114$	3.01753	−	6.39295i	0.282618	−	0.598755i
$115$	−12.9119	−	9.67978i	−1.20404	−	0.902644i
$116$	11.9350	−	9.82610i	1.10814	−	0.912330i
$117$			0.182515i			0.0168735i
$118$	7.77331	−	16.4686i	0.715591	−	1.51605i
$119$	−0.431706	+	7.25483i	−0.0395744	+	0.665049i
$120$	4.01943	−	9.62706i	0.366922	−	0.878826i
$121$	7.36390			0.669446
$122$	−13.2842	−	6.27027i	−1.20270	−	0.567683i
$123$		−	6.04405i		−	0.544974i
$124$	7.02610	+	8.53410i	0.630963	+	0.766385i
$125$	3.92898	−	10.4672i	0.351419	−	0.936218i
$126$	−0.501066	+	0.916234i	−0.0446385	+	0.0816246i
$127$	4.24112			0.376339			0.188169	−	0.982137i	$-0.439745\pi$
$127$	4.24112			0.376339			0.188169	+	0.982137i	$0.439745\pi$
$128$	11.2969	−	0.616941i	0.998512	−	0.0545304i
$129$		−	11.3261i		−	0.997209i
$130$	1.82802	−	0.966832i	0.160328	−	0.0847968i
$131$		−	10.8980i		−	0.952160i	−0.879402	−	0.476080i	$-0.842057\pi$
$131$		−	10.8980i		−	0.952160i	0.879402	−	0.476080i	$-0.157943\pi$
$132$	−8.98573	−	10.9143i	−0.782107	−	0.949969i
$133$	8.00365	+	0.476265i	0.694004	+	0.0412974i
$134$	−0.496374	+	1.05162i	−0.0428802	+	0.0908461i
$135$	−9.67728	−	7.25483i	−0.832888	−	0.624397i
$136$	−1.90549	−	7.53217i	−0.163394	−	0.645879i
$137$			4.30335i			0.367660i	0.982958	+	0.183830i	$0.0588496\pi$
$137$			4.30335i			0.367660i	−0.982958	+	0.183830i	$0.941150\pi$
$138$	15.2245	+	7.18611i	1.29600	+	0.611723i
$139$			20.2054i			1.71380i	0.515486	+	0.856898i	$0.327611\pi$
$139$			20.2054i			1.71380i	−0.515486	+	0.856898i	$0.672389\pi$
$140$	11.8310	+	0.164981i	0.999903	+	0.0139434i
$141$			7.59299i			0.639445i
$142$	6.89020	−	14.5976i	0.578213	−	1.22500i
$143$		−	2.80235i		−	0.234344i
$144$	0.214375	−	1.09562i	0.0178646	−	0.0913018i
$145$	−10.3677	+	13.8296i	−0.860992	+	1.14848i
$146$	−6.63805	−	3.13322i	−0.549369	−	0.259307i
$147$	11.4651	+	1.36934i	0.945627	+	0.112941i
$148$	2.27154	+	2.75908i	0.186720	+	0.226795i
$149$			6.55563i			0.537058i	0.963272	+	0.268529i	$0.0865375\pi$
$149$			6.55563i			0.537058i	−0.963272	+	0.268529i	$0.913463\pi$
$150$	−1.82137	+	11.5207i	−0.148714	+	0.940665i
$151$		−	12.4928i		−	1.01665i	−0.861165	−	0.508326i	$-0.830265\pi$
$151$		−	12.4928i		−	1.01665i	0.861165	−	0.508326i	$-0.169735\pi$
$152$	−8.30962	+	2.10217i	−0.673999	+	0.170508i
$153$	−0.766664			−0.0619811
$154$	7.69339	−	14.0679i	0.619951	−	1.13363i
$155$	−9.88878	−	7.41339i	−0.794286	−	0.595458i
$156$	−1.66553	+	1.37123i	−0.133349	+	0.109786i
$157$			2.10669i			0.168132i	0.996460	+	0.0840659i	$0.0267906\pi$
$157$			2.10669i			0.168132i	−0.996460	+	0.0840659i	$0.973209\pi$
$158$	−0.880231	+	1.86486i	−0.0700274	+	0.148360i
$159$	11.7175			0.929255
$160$	−12.1090	+	3.65670i	−0.957303	+	0.289087i
$161$	−1.13420	+	19.0603i	−0.0893878	+	1.50216i
$162$	10.3397	+	4.88043i	0.812364	+	0.383443i
$163$			11.1165i			0.870714i	0.900258	+	0.435357i	$0.143378\pi$
$163$			11.1165i			0.870714i	−0.900258	+	0.435357i	$0.856622\pi$
$164$	−5.65756	+	4.65786i	−0.441781	+	0.363718i
$165$	12.6468	+	9.48102i	0.984553	+	0.738097i
$166$	5.91885	+	2.79375i	0.459392	+	0.216837i
$167$			6.53701i			0.505849i	0.967486	+	0.252924i	$0.0813924\pi$
$167$			6.53701i			0.505849i	−0.967486	+	0.252924i	$0.918608\pi$
$168$	−12.1255	+	2.31118i	−0.935506	+	0.178312i
$169$	12.5724			0.967105
$170$	4.06123	+	7.67868i	0.311482	+	0.588928i
$171$			0.845796i			0.0646796i
$172$	−10.6019	+	8.72849i	−0.808385	+	0.665541i
$173$		−	3.15397i		−	0.239792i	−0.992786	−	0.119896i	$-0.961744\pi$
$173$		−	3.15397i		−	0.239792i	0.992786	−	0.119896i	$-0.0382561\pi$
$174$	7.69683	−	16.3065i	0.583495	−	1.23620i
$175$	−12.8960	+	2.94848i	−0.974845	+	0.222884i
$176$	−3.29153	+	16.8223i	−0.248108	+	1.26803i
$177$		−	21.2409i		−	1.59657i
$178$	−8.47238	+	17.9496i	−0.635032	+	1.34538i
$179$	12.9736			0.969691			0.484846	−	0.874600i	$-0.338876\pi$
$179$	12.9736			0.969691			0.484846	+	0.874600i	$0.338876\pi$
$180$	0.0567622	+	1.24688i	0.00423081	+	0.0929369i
$181$	−13.8168			−1.02700			−0.513498	−	0.858091i	$-0.671651\pi$
$181$	−13.8168			−1.02700			−0.513498	+	0.858091i	$0.671651\pi$
$182$	−2.14678	−	1.17402i	−0.159130	−	0.0870240i
$183$	−17.1338			−1.26657
$184$	−5.00621	−	19.7890i	−0.369063	−	1.45886i
$185$	−3.19705	−	2.39675i	−0.235052	−	0.176213i
$186$	11.6599	+	5.50358i	0.854946	+	0.403542i
$187$	11.7714			0.860811
$188$	7.10745	−	5.85155i	0.518364	−	0.426768i
$189$	−0.850067	+	14.2854i	−0.0618332	+	1.03911i
$190$	8.47124	−	4.48041i	0.614568	−	0.325043i
$191$			1.45817i			0.105509i	0.998608	+	0.0527547i	$0.0168001\pi$
$191$			1.45817i			0.105509i	−0.998608	+	0.0527547i	$0.983200\pi$
$192$	11.6086	−	6.27511i	0.837782	−	0.452867i
$193$		−	0.169527i		−	0.0122028i	−0.999981	−	0.00610140i	$-0.998058\pi$
$193$		−	0.169527i		−	0.0122028i	0.999981	−	0.00610140i	$-0.00194215\pi$
$194$	−17.3481	−	8.18844i	−1.24552	−	0.587896i
$195$	1.44681	−	1.92991i	0.103608	−	0.138204i
$196$	−7.55384	−	11.7873i	−0.539560	−	0.841947i
$197$	−14.2204			−1.01316			−0.506580	−	0.862193i	$-0.669090\pi$
$197$	−14.2204			−1.01316			−0.506580	+	0.862193i	$0.669090\pi$
$198$	1.52961	+	0.721989i	0.108705	+	0.0513095i
$199$	14.6548			1.03885			0.519425	−	0.854516i	$-0.326146\pi$
$199$	14.6548			1.03885			0.519425	+	0.854516i	$0.326146\pi$
$200$	12.1877	−	7.17358i	0.861800	−	0.507249i
$201$			1.35637i			0.0956706i
$202$	−5.66342	−	2.67318i	−0.398477	−	0.188085i
$203$	20.4149	+	1.21481i	1.43285	+	0.0852630i
$204$	−5.75992	−	6.99616i	−0.403275	−	0.489829i
$205$	4.91460	−	6.55563i	0.343251	−	0.457865i
$206$	−3.94610	+	8.36022i	−0.274938	+	0.582484i
$207$	−2.01423			−0.139998
$208$	2.56709	+	0.502290i	0.177996	+	0.0348275i
$209$		−	12.9864i		−	0.898289i
$210$	12.5613	−	5.71627i	0.866815	−	0.394460i
$211$	−6.29774			−0.433554			−0.216777	−	0.976221i	$-0.569554\pi$
$211$	−6.29774			−0.433554			−0.216777	+	0.976221i	$0.569554\pi$
$212$	−9.03007	−	10.9682i	−0.620188	−	0.753297i
$213$		−	18.8278i		−	1.29006i
$214$	−6.71055	+	14.2170i	−0.458724	+	0.971855i
$215$	9.20961	−	12.2848i	0.628090	−	0.837815i
$216$	−3.75207	−	14.8315i	−0.255296	−	1.00916i
$217$	−0.868645	+	14.5976i	−0.0589675	+	0.990950i
$218$	1.16693	−	2.47227i	0.0790346	−	0.167443i
$219$	−8.56167			−0.578544
$220$	−0.871531	−	19.1447i	−0.0587586	−	1.29073i
$221$		−	1.79633i		−	0.120834i
$222$	3.76966	+	1.77931i	0.253003	+	0.119420i
$223$			13.4829i			0.902883i	0.892301	+	0.451442i	$0.149090\pi$
$223$			13.4829i			0.902883i	−0.892301	+	0.451442i	$0.850910\pi$
$224$	11.5080	+	9.56905i	0.768908	+	0.639359i
$225$	−0.391293	−	1.33952i	−0.0260862	−	0.0893010i
$226$	−11.3073	+	23.9557i	−0.752152	+	1.59351i
$227$	−16.6555			−1.10547			−0.552733	−	0.833358i	$-0.686415\pi$
$227$	−16.6555			−1.10547			−0.552733	+	0.833358i	$0.686415\pi$
$228$	−7.71828	+	6.35444i	−0.511155	+	0.420833i
$229$	6.62594			0.437855			0.218927	−	0.975741i	$-0.429744\pi$
$229$	6.62594			0.437855			0.218927	+	0.975741i	$0.429744\pi$
$230$	10.6699	+	20.1739i	0.703553	+	1.33023i
$231$	1.11092	−	18.6690i	0.0730928	−	1.22833i
$232$	−21.1954	+	5.36200i	−1.39154	+	0.352033i
$233$			18.9010i			1.23824i	0.785295	+	0.619121i	$0.212511\pi$
$233$			18.9010i			1.23824i	−0.785295	+	0.619121i	$0.787489\pi$
$234$	0.110176	−	0.233419i	0.00720244	−	0.0152591i
$235$	−6.17409	+	8.23567i	−0.402753	+	0.537236i
$236$	−19.8827	+	16.3694i	−1.29425	+	1.06555i
$237$			2.40527i			0.156239i
$238$	4.93153	−	9.01765i	0.319663	−	0.584527i
$239$		−	12.3019i		−	0.795744i	−0.917441	−	0.397872i	$-0.869749\pi$
$239$		−	12.3019i		−	0.795744i	0.917441	−	0.397872i	$-0.130251\pi$
$240$	−10.9519	+	9.88575i	−0.706942	+	0.638122i
$241$		−	23.4479i		−	1.51041i	−0.655487	−	0.755206i	$-0.727537\pi$
$241$		−	23.4479i		−	1.51041i	0.655487	−	0.755206i	$-0.272463\pi$
$242$	−9.41774	−	4.44526i	−0.605395	−	0.285752i
$243$	−2.89076			−0.185443
$244$	13.2042	+	16.0382i	0.845311	+	1.02674i
$245$	11.3221	+	10.8079i	0.723342	+	0.690490i
$246$	−3.64852	+	7.72977i	−0.232621	+	0.492832i
$247$	−1.98174			−0.126095
$248$	−3.83407	−	15.1557i	−0.243464	−	0.962385i
$249$	7.63405			0.483788
$250$	−11.3434	+	11.0149i	−0.717420	+	0.696641i
$251$		−	6.27693i		−	0.396196i	−0.980182	−	0.198098i	$-0.936523\pi$
$251$		−	6.27693i		−	0.396196i	0.980182	−	0.198098i	$-0.0634765\pi$
$252$	1.19390	−	0.869306i	0.0752089	−	0.0547612i
$253$	30.9266			1.94434
$254$	−5.42400	−	2.56017i	−0.340332	−	0.160640i
$255$	8.10671	+	6.07741i	0.507662	+	0.380582i
$256$	−14.8201	−	6.03041i	−0.926254	−	0.376900i
$257$	−14.2394			−0.888227			−0.444113	−	0.895971i	$-0.646481\pi$
$257$	−14.2394			−0.888227			−0.444113	+	0.895971i	$0.646481\pi$
$258$	−6.83707	+	14.4850i	−0.425657	+	0.901799i
$259$	−0.280834	+	4.71942i	−0.0174501	+	0.293250i
$260$	−2.92149	+	0.132996i	−0.181183	+	0.00824809i
$261$			2.15738i			0.133538i
$262$	−6.57862	+	13.9375i	−0.406428	+	0.861061i
$263$	9.91693			0.611504			0.305752	−	0.952111i	$-0.401092\pi$
$263$	9.91693			0.611504			0.305752	+	0.952111i	$0.401092\pi$
$264$	4.90342	+	19.3827i	0.301785	+	1.19292i
$265$	12.7092	+	9.52782i	0.780722	+	0.585289i
$266$	−9.94841	−	5.44054i	−0.609976	−	0.333581i
$267$			23.1512i			1.41683i
$268$	1.26963	−	1.04528i	0.0775551	−	0.0638509i
$269$	−22.8100			−1.39075			−0.695375	−	0.718647i	$-0.744762\pi$
$269$	−22.8100			−1.39075			−0.695375	+	0.718647i	$0.744762\pi$
$270$	7.99692	+	15.1200i	0.486677	+	0.920173i
$271$	−24.9833			−1.51763			−0.758814	−	0.651307i	$-0.774221\pi$
$271$	−24.9833			−1.51763			−0.758814	+	0.651307i	$0.774221\pi$
$272$	−2.10989	+	10.7832i	−0.127931	+	0.653828i
$273$	−2.84890	−	0.169527i	−0.172423	−	0.0102602i
$274$	2.59774	−	5.50358i	0.156935	−	0.332483i
$275$	6.00795	+	20.5670i	0.362293	+	1.24024i
$276$	−15.1328	−	18.3807i	−0.910888	−	1.10639i
$277$	18.2797			1.09832			0.549161	−	0.835716i	$-0.314947\pi$
$277$	18.2797			1.09832			0.549161	+	0.835716i	$0.314947\pi$
$278$	12.1971	−	25.8407i	0.731531	−	1.54983i
$279$	−1.54262			−0.0923543
$280$	−15.0312	−	7.35284i	−0.898283	−	0.439416i
$281$	9.68206			0.577583			0.288792	−	0.957392i	$-0.406747\pi$
$281$	9.68206			0.577583			0.288792	+	0.957392i	$0.406747\pi$
$282$	4.58355	−	9.71072i	0.272946	−	0.578265i
$283$	−22.4055			−1.33187			−0.665933	−	0.746012i	$-0.731966\pi$
$283$	−22.4055			−1.33187			−0.665933	+	0.746012i	$0.731966\pi$
$284$	−17.6238	+	14.5097i	−1.04578	+	0.860990i
$285$	6.70470	−	8.94345i	0.397152	−	0.529764i
$286$	−1.69165	+	3.58394i	−0.100029	+	0.211923i
$287$	−9.67728	−	0.575856i	−0.571232	−	0.0339917i
$288$	−0.935543	+	1.27179i	−0.0551274	+	0.0749409i
$289$	−9.45443			−0.556143
$290$	21.6076	−	11.4282i	1.26884	−	0.671088i
$291$	−22.3753			−1.31166
$292$	6.59806	+	8.01419i	0.386122	+	0.468995i
$293$			24.8371i			1.45100i	0.688221	+	0.725501i	$0.258392\pi$
$293$			24.8371i			1.45100i	−0.688221	+	0.725501i	$0.741608\pi$
$294$	−13.8362	−	8.67223i	−0.806944	−	0.505775i
$295$	17.2716	−	23.0388i	1.00559	−	1.34137i
$296$	−1.23956	−	4.89983i	−0.0720479	−	0.284797i
$297$	23.1789			1.34498
$298$	3.95734	−	8.38403i	0.229242	−	0.485674i
$299$		−	4.71942i		−	0.272931i
$300$	9.28392	−	13.6345i	0.536007	−	0.787187i
$301$	−18.1345	−	1.07911i	−1.04526	−	0.0621990i
$302$	−7.54136	+	15.9771i	−0.433956	+	0.919382i
$303$	−7.30460			−0.419638
$304$	11.8962	+	2.32767i	0.682294	+	0.133501i
$305$	−18.5840	−	13.9320i	−1.06412	−	0.797745i
$306$	0.980491	+	0.462800i	0.0560509	+	0.0264565i
$307$	3.84432			0.219407			0.109704	−	0.993964i	$-0.465010\pi$
$307$	3.84432			0.219407			0.109704	+	0.993964i	$0.465010\pi$
$308$	−18.3313	+	13.3474i	−1.04452	+	0.760538i
$309$			10.7829i			0.613418i
$310$	8.17169	+	15.4504i	0.464121	+	0.877526i
$311$	−21.5403			−1.22144			−0.610720	−	0.791847i	$-0.709120\pi$
$311$	−21.5403			−1.22144			−0.610720	+	0.791847i	$0.709120\pi$
$312$	2.95781	−	0.748266i	0.167453	−	0.0423622i
$313$	−21.0315			−1.18877			−0.594385	−	0.804181i	$-0.702604\pi$
$313$	−21.0315			−1.18877			−0.594385	+	0.804181i	$0.702604\pi$
$314$	1.27171	−	2.69425i	0.0717668	−	0.152045i
$315$	−1.06716	+	1.25998i	−0.0601276	+	0.0709918i
$316$	2.25147	−	1.85363i	0.126655	−	0.104275i
$317$	13.5083			0.758700			0.379350	−	0.925253i	$-0.376148\pi$
$317$	13.5083			0.758700			0.379350	+	0.925253i	$0.376148\pi$
$318$	−14.9855	−	7.07330i	−0.840346	−	0.396651i
$319$		−	33.1245i		−	1.85462i
$320$	17.6937	+	2.63310i	0.989107	+	0.147195i
$321$			18.3369i			1.02347i
$322$	12.9564	−	23.6917i	0.722032	−	1.32029i
$323$		−	8.32439i		−	0.463181i
$324$	−10.2774	−	12.4832i	−0.570967	−	0.693513i
$325$	3.13854	−	0.916818i	0.174095	−	0.0508559i
$326$	6.71055	−	14.2170i	0.371663	−	0.787407i
$327$		−	3.18870i		−	0.176335i
$328$	10.0472	−	2.54175i	0.554765	−	0.140344i
$329$	12.1573	+	0.723433i	0.670255	+	0.0398842i
$330$	−10.4508	−	19.7597i	−0.575299	−	1.08773i
$331$	23.4776			1.29044			0.645222	−	0.763996i	$-0.276765\pi$
$331$	23.4776			1.29044			0.645222	+	0.763996i	$0.276765\pi$
$332$	−5.88319	−	7.14588i	−0.322882	−	0.392181i
$333$	−0.498731			−0.0273303
$334$	3.94610	−	8.36022i	0.215921	−	0.457451i
$335$	−1.10290	+	1.47117i	−0.0602579	+	0.0803786i
$336$	16.9026	+	4.36386i	0.922112	+	0.238068i
$337$			7.16922i			0.390532i	0.980750	+	0.195266i	$0.0625570\pi$
$337$			7.16922i			0.390532i	−0.980750	+	0.195266i	$0.937443\pi$
$338$	−16.0789	−	7.58937i	−0.874575	−	0.412807i
$339$			30.8978i			1.67814i
$340$	−0.558658	−	12.2719i	−0.0302975	−	0.665537i
$341$	23.6855			1.28264
$342$	0.510569	−	1.08169i	0.0276084	−	0.0584913i
$343$	3.28483	−	18.2266i	0.177364	−	0.984145i
$344$	18.8278	−	4.76305i	1.01513	−	0.256806i
$345$	21.2984	+	15.9669i	1.14667	+	0.859631i
$346$	−1.90391	+	4.03363i	−0.102355	+	0.216849i
$347$		−	12.0346i		−	0.646053i	−0.946390	−	0.323026i	$-0.895300\pi$
$347$		−	12.0346i		−	0.646053i	0.946390	−	0.323026i	$-0.104700\pi$
$348$	−19.6870	+	16.2083i	−1.05534	+	0.868856i
$349$	18.0622			0.966846			0.483423	−	0.875387i	$-0.339393\pi$
$349$	18.0622			0.966846			0.483423	+	0.875387i	$0.339393\pi$
$350$	18.2726	+	4.01390i	0.976713	+	0.214552i
$351$		−	3.53712i		−	0.188798i
$352$	14.3644	−	19.5271i	0.765625	−	1.04080i
$353$	30.7451			1.63640			0.818198	−	0.574936i	$-0.194973\pi$
$353$	30.7451			1.63640			0.818198	+	0.574936i	$0.194973\pi$
$354$	−12.8222	+	27.1652i	−0.681492	+	1.44381i
$355$	15.3094	−	20.4214i	0.812541	−	1.08386i
$356$	21.6707	−	17.8415i	1.14855	−	0.945596i
$357$	0.712105	−	11.9670i	0.0376886	−	0.633358i
$358$	−16.5920	−	7.83157i	−0.876914	−	0.413911i
$359$			29.3988i			1.55161i	0.630973	+	0.775805i	$0.282656\pi$
$359$			29.3988i			1.55161i	−0.630973	+	0.775805i	$0.717344\pi$
$360$	0.680091	−	1.62891i	0.0358440	−	0.0858509i
$361$	9.81640			0.516653
$362$	17.6704	+	8.34059i	0.928736	+	0.438372i
$363$	−12.1469			−0.637545
$364$	2.03682	+	2.79737i	0.106759	+	0.146622i
$365$	−9.28634	−	6.96175i	−0.486069	−	0.364395i
$366$	21.9125	+	10.3429i	1.14539	+	0.540632i
$367$		−	8.00107i		−	0.417652i	−0.977953	−	0.208826i	$-0.933036\pi$
$367$		−	8.00107i		−	0.417652i	0.977953	−	0.208826i	$-0.0669643\pi$
$368$	−5.54324	+	28.3303i	−0.288961	+	1.47682i
$369$		−	1.02266i		−	0.0532375i
$370$	2.64191	+	4.99514i	0.137347	+	0.259685i
$371$	1.11640	−	18.7611i	0.0579605	−	0.974028i
$372$	−11.5897	−	14.0771i	−0.600896	−	0.729865i
$373$	11.2999			0.585084			0.292542	−	0.956253i	$-0.405499\pi$
$373$	11.2999			0.585084			0.292542	+	0.956253i	$0.405499\pi$
$374$	−15.0545	−	7.10587i	−0.778451	−	0.367436i
$375$	−6.48092	+	17.2659i	−0.334673	+	0.891606i
$376$	−12.6221	+	3.19313i	−0.650934	+	0.164673i
$377$	−5.05483			−0.260337
$378$	9.71061	−	17.7565i	0.499460	−	0.913298i
$379$	1.19603			0.0614359			0.0307179	−	0.999528i	$-0.490221\pi$
$379$	1.19603			0.0614359			0.0307179	+	0.999528i	$0.490221\pi$
$380$	−13.5385	+	0.616321i	−0.694513	+	0.0316166i
$381$	−6.99579			−0.358405
$382$	0.880231	−	1.86486i	0.0450366	−	0.0954146i
$383$			0.133029i			0.00679746i	0.999994	+	0.00339873i	$0.00108185\pi$
$383$			0.133029i			0.00679746i	−0.999994	+	0.00339873i	$0.998918\pi$
$384$	−18.6344	+	1.01765i	−0.950931	+	0.0519319i
$385$	16.3852	−	19.3458i	0.835069	−	0.985954i
$386$	−0.102336	+	0.216809i	−0.00520874	+	0.0110353i
$387$		−	1.91639i		−	0.0974156i
$388$	17.2436	+	20.9445i	0.875409	+	1.06330i
$389$		−	34.7285i		−	1.76081i	−0.474227	−	0.880403i	$-0.657272\pi$
$389$		−	34.7285i		−	1.76081i	0.474227	−	0.880403i	$-0.342728\pi$
$390$	−3.01534	+	1.59480i	−0.152688	+	0.0807560i
$391$	19.8242			1.00255
$392$	2.54521	+	19.6347i	0.128553	+	0.991703i
$393$			17.9764i			0.906788i
$394$	18.1865	+	8.58420i	0.916223	+	0.432466i
$395$	−1.95580	+	2.60886i	−0.0984070	+	0.131266i
$396$	−1.52039	−	1.84671i	−0.0764026	−	0.0928007i
$397$			16.9934i			0.852872i	0.904518	+	0.426436i	$0.140231\pi$
$397$			16.9934i			0.852872i	−0.904518	+	0.426436i	$0.859769\pi$
$398$	−18.7421	−	8.84643i	−0.939455	−	0.443431i
$399$	−13.2021	−	0.785606i	−0.660934	−	0.0393295i
$400$	−19.9173	+	1.81717i	−0.995864	+	0.0908586i
$401$	−16.1306			−0.805522			−0.402761	−	0.915305i	$-0.631949\pi$
$401$	−16.1306			−0.805522			−0.402761	+	0.915305i	$0.631949\pi$
$402$	0.818777	−	1.73466i	0.0408369	−	0.0865171i
$403$		−	3.61443i		−	0.180048i
$404$	5.62930	+	6.83750i	0.280068	+	0.340178i
$405$	14.4648	+	10.8439i	0.718761	+	0.538838i
$406$	−25.3755	−	13.8772i	−1.25936	−	0.688715i
$407$	7.65754			0.379570
$408$	3.14313	+	12.4244i	0.155608	+	0.615101i
$409$		−	30.1548i		−	1.49106i	−0.666474	−	0.745528i	$-0.732197\pi$
$409$		−	30.1548i		−	1.49106i	0.666474	−	0.745528i	$-0.267803\pi$
$410$	−10.2426	+	5.41731i	−0.505848	+	0.267542i
$411$		−	7.09844i		−	0.350140i
$412$	10.0934	−	8.30985i	0.497265	−	0.409397i
$413$	−34.0094	−	2.02376i	−1.67349	−	0.0995828i
$414$	2.57600	+	1.21590i	0.126604	+	0.0597581i
$415$	8.28020	+	6.20747i	0.406459	+	0.304713i
$416$	−2.97986	−	2.19202i	−0.146100	−	0.107473i
$417$		−	33.3290i		−	1.63213i
$418$	−7.83931	+	16.6084i	−0.383433	+	0.812343i
$419$			21.3822i			1.04459i	0.852765	+	0.522295i	$0.174924\pi$
$419$			21.3822i			1.04459i	−0.852765	+	0.522295i	$0.825076\pi$
$420$	−19.5154	−	0.272138i	−0.952255	−	0.0132790i
$421$			23.1352i			1.12754i	0.825932	+	0.563770i	$0.190650\pi$
$421$			23.1352i			1.12754i	−0.825932	+	0.563770i	$0.809350\pi$
$422$	8.05422	+	3.80166i	0.392073	+	0.185062i
$423$			1.28474i			0.0624662i
$424$	4.92762	+	19.4783i	0.239306	+	0.945951i
$425$	3.85114	+	13.1836i	0.186808	+	0.639500i
$426$	−11.3655	+	24.0790i	−0.550660	+	1.16663i
$427$	−1.63245	+	27.4333i	−0.0789997	+	1.32759i
$428$	17.1643	−	14.1314i	0.829669	−	0.683065i
$429$			4.62251i			0.223177i
$430$	−19.1940	+	10.1516i	−0.925616	+	0.489556i
$431$			33.6949i			1.62303i	0.584334	+	0.811513i	$0.301356\pi$
$431$			33.6949i			1.62303i	−0.584334	+	0.811513i	$0.698644\pi$
$432$	−4.15457	+	21.2331i	−0.199887	+	1.02158i
$433$	−17.1125			−0.822374			−0.411187	−	0.911551i	$-0.634886\pi$
$433$	−17.1125			−0.822374			−0.411187	+	0.911551i	$0.634886\pi$
$434$	9.92283	−	18.1446i	0.476311	−	0.870969i
$435$	17.1017	−	22.8121i	0.819964	−	1.09376i
$436$	−2.98479	+	2.45737i	−0.142946	+	0.117687i
$437$		−	21.8703i		−	1.04620i
$438$	10.9496	+	5.16829i	0.523191	+	0.246951i
$439$	19.6297			0.936875			0.468438	−	0.883497i	$-0.344817\pi$
$439$	19.6297			0.936875			0.468438	+	0.883497i	$0.344817\pi$
$440$	−10.4422	+	25.0103i	−0.497811	+	1.19232i
$441$	1.93991	+	0.231693i	0.0923766	+	0.0110330i
$442$	−1.08436	+	2.29733i	−0.0515778	+	0.109273i
$443$		−	21.2348i		−	1.00889i	−0.863442	−	0.504447i	$-0.831696\pi$
$443$		−	21.2348i		−	1.00889i	0.863442	−	0.504447i	$-0.168304\pi$
$444$	−3.74695	−	4.55115i	−0.177822	−	0.215988i
$445$	−18.8249	+	25.1107i	−0.892386	+	1.19036i
$446$	8.13903	−	17.2434i	0.385394	−	0.816498i
$447$		−	10.8136i		−	0.511466i
$448$	−8.94120	−	19.1848i	−0.422432	−	0.906395i
$449$	−35.3939			−1.67034			−0.835171	−	0.549990i	$-0.814632\pi$
$449$	−35.3939			−1.67034			−0.835171	+	0.549990i	$0.814632\pi$
$450$	−0.308178	+	1.94932i	−0.0145276	+	0.0918919i
$451$			15.7020i			0.739377i
$452$	28.9220	−	23.8114i	1.36038	−	1.11999i
$453$			20.6071i			0.968206i
$454$	21.3009	+	10.0542i	0.999699	+	0.471867i
$455$	−2.95219	−	2.50040i	−0.138401	−	0.117221i
$456$	13.7068	−	3.46755i	0.641882	−	0.162383i
$457$		−	8.03416i		−	0.375822i	−0.982186	−	0.187911i	$-0.939828\pi$
$457$		−	8.03416i		−	0.375822i	0.982186	−	0.187911i	$-0.0601717\pi$
$458$	−8.47396	−	3.99978i	−0.395962	−	0.186898i
$459$	14.8579			0.693506
$460$	−1.46774	−	32.2414i	−0.0684338	−	1.50326i
$461$	−11.0797			−0.516034			−0.258017	−	0.966140i	$-0.583069\pi$
$461$	−11.0797			−0.516034			−0.258017	+	0.966140i	$0.583069\pi$
$462$	−12.6904	+	23.2052i	−0.590410	+	1.07961i
$463$	−17.8011			−0.827286			−0.413643	−	0.910439i	$-0.635744\pi$
$463$	−17.8011			−0.827286			−0.413643	+	0.910439i	$0.635744\pi$
$464$	30.3437	+	5.93720i	1.40867	+	0.275627i
$465$	16.3117	+	12.2285i	0.756436	+	0.567083i
$466$	11.4097	−	24.1725i	0.528542	−	1.11977i
$467$	0.174021			0.00805275			0.00402638	−	0.999992i	$-0.498718\pi$
$467$	0.174021			0.00805275			0.00402638	+	0.999992i	$0.498718\pi$
$468$	−0.281810	+	0.232013i	−0.0130267	+	0.0107248i
$469$	2.17171	+	0.129230i	0.100280	+	0.00596727i
$470$	12.8676	−	6.80563i	0.593537	−	0.313920i
$471$		−	3.47501i		−	0.160120i
$472$	35.3095	−	8.93260i	1.62525	−	0.411156i
$473$			29.4244i			1.35293i
$474$	1.45196	−	3.07612i	0.0666905	−	0.141291i
$475$	14.5444	−	4.24864i	0.667342	−	0.194941i
$476$	−11.7505	+	8.55578i	−0.538584	+	0.392154i
$477$	1.98260			0.0907772
$478$	−7.42611	+	15.7330i	−0.339662	+	0.719610i
$479$	18.8032			0.859142			0.429571	−	0.903033i	$-0.358665\pi$
$479$	18.8032			0.859142			0.429571	+	0.903033i	$0.358665\pi$
$480$	19.9740	−	6.03178i	0.911685	−	0.275312i
$481$		−	1.16855i		−	0.0532812i
$482$	−14.1544	+	29.9877i	−0.644717	+	1.36590i
$483$	1.87089	−	31.4403i	0.0851283	−	1.43058i
$484$	9.36100	+	11.3701i	0.425500	+	0.516824i
$485$	−24.2692	−	18.1940i	−1.10201	−	0.826148i
$486$	3.69702	+	1.74502i	0.167700	+	0.0791559i
$487$	−7.58838			−0.343862			−0.171931	−	0.985109i	$-0.555001\pi$
$487$	−7.58838			−0.343862			−0.171931	+	0.985109i	$0.555001\pi$
$488$	−7.20539	−	28.4821i	−0.326173	−	1.28932i
$489$		−	18.3369i		−	0.829223i
$490$	−7.95567	−	20.6569i	−0.359400	−	0.933183i
$491$	11.4052			0.514709			0.257354	−	0.966317i	$-0.417149\pi$
$491$	11.4052			0.514709			0.257354	+	0.966317i	$0.417149\pi$
$492$	9.33223	−	7.68321i	0.420730	−	0.346386i
$493$		−	21.2331i		−	0.956289i
$494$	2.53446	+	1.19629i	0.114031	+	0.0538234i
$495$	2.13985	+	1.60420i	0.0961792	+	0.0721033i
$496$	−4.24536	+	21.6971i	−0.190622	+	0.974229i
$497$	−30.1456	−	1.79385i	−1.35222	−	0.0804650i
$498$	−9.76323	−	4.60833i	−0.437501	−	0.206504i
$499$	−14.0504			−0.628984			−0.314492	−	0.949260i	$-0.601834\pi$
$499$	−14.0504			−0.628984			−0.314492	+	0.949260i	$0.601834\pi$
$500$	21.1563	−	7.23947i	0.946140	−	0.323759i
$501$		−	10.7829i		−	0.481744i
$502$	−3.78910	+	8.02761i	−0.169116	+	0.358290i
$503$			34.0777i			1.51945i	0.650245	+	0.759724i	$0.274666\pi$
$503$			34.0777i			1.51945i	−0.650245	+	0.759724i	$0.725334\pi$
$504$	−2.05165	+	0.391054i	−0.0913879	+	0.0174189i
$505$	−7.92287	−	5.93959i	−0.352563	−	0.264308i
$506$	−39.5522	−	18.6690i	−1.75831	−	0.829937i
$507$	−20.7383			−0.921020
$508$	5.39132	+	6.54844i	0.239201	+	0.290540i
$509$	−34.0250			−1.50813			−0.754066	−	0.656799i	$-0.771910\pi$
$509$	−34.0250			−1.50813			−0.754066	+	0.656799i	$0.771910\pi$
$510$	−6.69906	−	12.6661i	−0.296639	−	0.560864i
$511$	−0.815725	+	13.7083i	−0.0360856	+	0.606419i
$512$	15.3132	+	16.6585i	0.676753	+	0.736210i
$513$		−	16.3915i		−	0.723700i
$514$	18.2108	+	8.59566i	0.803244	+	0.379138i
$515$	−8.76790	+	11.6956i	−0.386360	+	0.515368i
$516$	17.4879	−	14.3978i	0.769864	−	0.633827i
$517$		−	19.7260i		−	0.867548i
$518$	3.20806	−	5.86617i	0.140954	−	0.257745i
$519$			5.20252i			0.228365i
$520$	3.81660	+	1.59348i	0.167369	+	0.0698789i
$521$			16.8086i			0.736397i	0.929747	+	0.368199i	$0.120025\pi$
$521$			16.8086i			0.736397i	−0.929747	+	0.368199i	$0.879975\pi$
$522$	1.30231	−	2.75908i	0.0570006	−	0.120762i
$523$	22.3205			0.976009			0.488004	−	0.872841i	$-0.337725\pi$
$523$	22.3205			0.976009			0.488004	+	0.872841i	$0.337725\pi$
$524$	16.8269	−	13.8535i	0.735085	−	0.605194i
$525$	21.2721	−	4.86356i	0.928392	−	0.212263i
$526$	−12.6828	−	5.98640i	−0.552997	−	0.261020i
$527$	15.1826			0.661364
$528$	5.42942	−	27.7486i	0.236285	−	1.20760i
$529$	29.0832			1.26449
$530$	−10.5024	−	19.8572i	−0.456195	−	0.862541i
$531$		−	3.59399i		−	0.155966i
$532$	9.43888	+	12.9634i	0.409227	+	0.562033i
$533$	2.39613			0.103788
$534$	13.9753	−	29.6082i	0.604771	−	1.28127i
$535$	−14.9103	+	19.8890i	−0.644628	+	0.859874i
$536$	−2.25473	+	0.570401i	−0.0973895	+	0.0246376i
$537$	−21.4001			−0.923483
$538$	29.1718	+	13.7694i	1.25769	+	0.593639i
$539$	−29.7855	−	3.55743i	−1.28295	−	0.153229i
$540$	−1.10005	−	24.1644i	−0.0473385	−	1.03987i
$541$		−	17.7871i		−	0.764725i	−0.924012	−	0.382363i	$-0.875111\pi$
$541$		−	17.7871i		−	0.764725i	0.924012	−	0.382363i	$-0.124889\pi$
$542$	31.9513	+	15.0813i	1.37243	+	0.647797i
$543$	22.7910			0.978057
$544$	9.20769	−	12.5171i	0.394776	−	0.536664i
$545$	2.59283	−	3.45859i	0.111064	−	0.148150i
$546$	3.54114	+	1.93656i	0.151547	+	0.0828772i
$547$		−	18.9544i		−	0.810433i	−0.914221	−	0.405217i	$-0.867196\pi$
$547$		−	18.9544i		−	0.810433i	0.914221	−	0.405217i	$-0.132804\pi$
$548$	−6.64453	+	5.47042i	−0.283840	+	0.233685i
$549$	−2.89905			−0.123729
$550$	4.73178	−	29.9300i	0.201764	−	1.27622i
$551$	−23.4247			−0.997924
$552$	8.25782	+	32.6422i	0.351476	+	1.38935i
$553$	3.85114	+	0.229166i	0.163767	+	0.00974513i
$554$	−23.3781	−	11.0347i	−0.993239	−	0.468818i
$555$	5.27358	+	3.95348i	0.223851	+	0.167816i
$556$	−31.1978	+	25.6851i	−1.32308	+	1.08929i
$557$	−31.6828			−1.34244			−0.671222	−	0.741257i	$-0.734230\pi$
$557$	−31.6828			−1.34244			−0.671222	+	0.741257i	$0.734230\pi$
$558$	1.97287	+	0.931211i	0.0835181	+	0.0394213i
$559$	4.49019			0.189915
$560$	14.7849	+	18.4772i	0.624774	+	0.780805i
$561$	−19.4171			−0.819791
$562$	−12.3824	−	5.84462i	−0.522322	−	0.246540i
$563$	28.7146			1.21018			0.605089	−	0.796158i	$-0.293138\pi$
$563$	28.7146			1.21018			0.605089	+	0.796158i	$0.293138\pi$
$564$	−11.7238	+	9.65222i	−0.493663	+	0.406432i
$565$	−25.1239	+	33.5130i	−1.05697	+	1.40990i
$566$	28.6545	+	13.5252i	1.20444	+	0.568505i
$567$	1.27061	−	21.3526i	0.0533605	−	0.896725i
$568$	31.2981	−	7.91778i	1.31324	−	0.332223i
$569$	−33.3673			−1.39883			−0.699415	−	0.714716i	$-0.746556\pi$
$569$	−33.3673			−1.39883			−0.699415	+	0.714716i	$0.746556\pi$
$570$	−13.9734	+	7.39051i	−0.585283	+	0.309554i
$571$	−5.13284			−0.214803			−0.107401	−	0.994216i	$-0.534253\pi$
$571$	−5.13284			−0.214803			−0.107401	+	0.994216i	$0.534253\pi$
$572$	4.32693	−	3.56235i	0.180918	−	0.148949i
$573$		−	2.40527i		−	0.100482i
$574$	12.0287	+	6.57820i	0.502069	+	0.274569i
$575$	10.1180	+	34.6368i	0.421948	+	1.44445i
$576$	1.96419	−	1.06175i	0.0818414	−	0.0442397i
$577$	−12.6961			−0.528547			−0.264273	−	0.964448i	$-0.585132\pi$
$577$	−12.6961			−0.528547			−0.264273	+	0.964448i	$0.585132\pi$
$578$	12.0913	+	5.70722i	0.502933	+	0.237389i
$579$			0.279637i			0.0116213i
$580$	−34.5328	+	1.57205i	−1.43390	+	0.0652760i
$581$	0.727345	−	12.2231i	0.0301754	−	0.507098i
$582$	28.6159	+	13.5070i	1.18617	+	0.559881i
$583$	−30.4410			−1.26074
$584$	−3.60050	−	14.2323i	−0.148990	−	0.588939i
$585$	0.244802	−	0.326543i	0.0101213	−	0.0135009i
$586$	14.9931	−	31.7644i	0.619358	−	1.31217i
$587$	−37.6568			−1.55426			−0.777132	−	0.629338i	$-0.783326\pi$
$587$	−37.6568			−1.55426			−0.777132	+	0.629338i	$0.783326\pi$
$588$	12.4602	+	19.4433i	0.513849	+	0.801827i
$589$		−	16.7497i		−	0.690159i
$590$	−35.9963	+	19.0383i	−1.48194	+	0.783796i
$591$	23.4567			0.964880
$592$	−1.37253	+	7.01469i	−0.0564106	+	0.288302i
$593$	17.2487			0.708319			0.354160	−	0.935185i	$-0.384767\pi$
$593$	17.2487			0.708319			0.354160	+	0.935185i	$0.384767\pi$
$594$	−29.6437	−	13.9921i	−1.21629	−	0.574102i
$595$	10.5031	−	12.4008i	0.430584	−	0.508384i
$596$	−10.1221	+	8.33352i	−0.414618	+	0.341354i
$597$	−24.1733			−0.989346
$598$	−2.84890	+	6.03569i	−0.116500	+	0.246818i
$599$			9.63914i			0.393845i	0.980419	+	0.196922i	$0.0630947\pi$
$599$			9.63914i			0.393845i	−0.980419	+	0.196922i	$0.936905\pi$
$600$	−20.1038	+	11.8329i	−0.820733	+	0.483077i
$601$		−	9.73336i		−	0.397032i	−0.980098	−	0.198516i	$-0.936388\pi$
$601$		−	9.73336i		−	0.397032i	0.980098	−	0.198516i	$-0.0636122\pi$
$602$	22.5409	+	12.3271i	0.918700	+	0.502414i
$603$			0.229498i			0.00934589i
$604$	19.2894	−	15.8809i	0.784873	−	0.646184i
$605$	−13.1750	−	9.87699i	−0.535640	−	0.401557i
$606$	9.34189	+	4.40946i	0.379489	+	0.179122i
$607$			7.64571i			0.310330i	0.987889	+	0.155165i	$0.0495909\pi$
$607$			7.64571i			0.310330i	−0.987889	+	0.155165i	$0.950409\pi$
$608$	−13.8090	−	10.1581i	−0.560029	−	0.411964i
$609$	−33.6748	−	2.00385i	−1.36457	−	0.0812001i
$610$	15.3571	+	29.0361i	0.621790	+	1.17564i
$611$	−3.01020			−0.121780
$612$	−0.974584	−	1.18376i	−0.0393952	−	0.0478505i
$613$	−28.4460			−1.14892			−0.574462	−	0.818531i	$-0.694789\pi$
$613$	−28.4460			−1.14892			−0.574462	+	0.818531i	$0.694789\pi$
$614$	−4.91653	−	2.32065i	−0.198415	−	0.0936536i
$615$	−8.10671	+	10.8136i	−0.326894	+	0.436047i
$616$	31.5012	−	6.00428i	1.26922	−	0.241919i
$617$			45.2679i			1.82242i	0.411947	+	0.911208i	$0.364849\pi$
$617$			45.2679i			1.82242i	−0.411947	+	0.911208i	$0.635151\pi$
$618$	6.50915	−	13.7903i	0.261836	−	0.554728i
$619$		−	23.2332i		−	0.933820i	−0.884305	−	0.466910i	$-0.845367\pi$
$619$		−	23.2332i		−	0.933820i	0.884305	−	0.466910i	$-0.154633\pi$
$620$	−1.12409	−	24.6925i	−0.0451445	−	0.991676i
$621$	39.0355			1.56644
$622$	27.5481	+	13.0029i	1.10458	+	0.521370i
$623$	37.0679	+	2.20576i	1.48509	+	0.0883720i
$624$	−4.23446	−	0.828534i	−0.169514	−	0.0331679i
$625$	−21.0689	+	13.4574i	−0.842755	+	0.538298i
$626$	26.8973	+	12.6958i	1.07503	+	0.507424i
$627$			21.4213i			0.855483i
$628$	−3.25280	+	2.67802i	−0.129801	+	0.106865i
$629$	4.90855			0.195717
$630$	2.12539	−	0.967199i	0.0846776	−	0.0385341i
$631$			6.63265i			0.264042i	0.991247	+	0.132021i	$0.0421466\pi$
$631$			6.63265i			0.264042i	−0.991247	+	0.132021i	$0.957853\pi$
$632$	−3.99837	+	1.01151i	−0.159046	+	0.0402355i
$633$	10.3882			0.412895
$634$	−17.2758	−	8.15433i	−0.686110	−	0.323850i
$635$	−7.58792	−	5.68849i	−0.301118	−	0.225741i
$636$	14.8952	+	18.0922i	0.590635	+	0.717401i
$637$	−0.542866	+	4.54529i	−0.0215091	+	0.180091i
$638$	−19.9958	+	42.3631i	−0.791640	+	1.67717i
$639$		−	3.18568i		−	0.126024i
$640$	−21.0391	−	14.0484i	−0.831643	−	0.555311i
$641$	−13.2544			−0.523518			−0.261759	−	0.965133i	$-0.584303\pi$
$641$	−13.2544			−0.523518			−0.261759	+	0.965133i	$0.584303\pi$
$642$	11.0692	−	23.4512i	0.436865	−	0.925544i
$643$	−6.27471			−0.247450			−0.123725	−	0.992317i	$-0.539484\pi$
$643$	−6.27471			−0.247450			−0.123725	+	0.992317i	$0.539484\pi$
$644$	−30.8716	+	22.4783i	−1.21651	+	0.885768i
$645$	−15.1914	+	20.2639i	−0.598161	+	0.797891i
$646$	−5.02506	+	10.6461i	−0.197708	+	0.418866i
$647$		−	2.23961i		−	0.0880482i	−0.999030	−	0.0440241i	$-0.985982\pi$
$647$		−	2.23961i		−	0.0880482i	0.999030	−	0.0440241i	$-0.0140178\pi$
$648$	5.60828	+	22.1689i	0.220314	+	0.870876i
$649$			55.1823i			2.16609i
$650$	−4.56734	−	0.722074i	−0.179146	−	0.0283221i
$651$	1.43284	−	24.0790i	0.0561575	−	0.943729i
$652$	−17.1643	+	14.1314i	−0.672207	+	0.553427i
$653$	10.5854			0.414240			0.207120	−	0.978316i	$-0.433591\pi$
$653$	10.5854			0.414240			0.207120	+	0.978316i	$0.433591\pi$
$654$	−1.92487	+	4.07804i	−0.0752685	+	0.159464i
$655$	−14.6171	+	19.4979i	−0.571139	+	0.761847i
$656$	−14.3838	−	2.81440i	−0.561593	−	0.109884i
$657$	−1.44864			−0.0565169
$658$	−15.1114	−	8.26403i	−0.589102	−	0.322165i
$659$	18.0753			0.704113			0.352057	−	0.935979i	$-0.385482\pi$
$659$	18.0753			0.704113			0.352057	+	0.935979i	$0.385482\pi$
$660$	1.43760	+	31.5794i	0.0559587	+	1.22923i
$661$	−2.03564			−0.0791773			−0.0395887	−	0.999216i	$-0.512605\pi$
$661$	−2.03564			−0.0791773			−0.0395887	+	0.999216i	$0.512605\pi$
$662$	−30.0256	−	14.1723i	−1.16698	−	0.550824i
$663$			2.96307i			0.115076i
$664$	3.21040	+	12.6903i	0.124588	+	0.492480i
$665$	−13.6808	−	11.5872i	−0.530518	−	0.449331i
$666$	0.637830	+	0.301061i	0.0247154	+	0.0116659i
$667$		−	55.7848i		−	2.16000i
$668$	−10.0934	+	8.30985i	−0.390525	+	0.321518i
$669$		−	22.2403i		−	0.859859i
$670$	2.29859	−	1.21572i	0.0888021	−	0.0469672i
$671$	44.5123			1.71838
$672$	−18.9826	−	15.7843i	−0.732268	−	0.608893i
$673$		−	21.8265i		−	0.841348i	−0.907212	−	0.420674i	$-0.861794\pi$
$673$		−	21.8265i		−	0.841348i	0.907212	−	0.420674i	$-0.138206\pi$
$674$	4.32773	−	9.16876i	0.166698	−	0.353167i
$675$	7.58324	+	25.9597i	0.291879	+	0.999189i
$676$	15.9820	+	19.4122i	0.614692	+	0.746622i
$677$		−	46.7075i		−	1.79511i	−0.440898	−	0.897557i	$-0.645340\pi$
$677$		−	46.7075i		−	1.79511i	0.440898	−	0.897557i	$-0.354660\pi$
$678$	18.6516	−	39.5154i	0.716310	−	1.51758i
$679$	−2.13184	+	35.8256i	−0.0818125	+	1.37486i
$680$	−6.69351	+	16.0318i	−0.256685	+	0.614793i
$681$	27.4736			1.05279
$682$	−30.2915	−	14.2979i	−1.15992	−	0.547494i
$683$			14.4642i			0.553459i	0.960948	+	0.276730i	$0.0892506\pi$
$683$			14.4642i			0.553459i	−0.960948	+	0.276730i	$0.910749\pi$
$684$	−1.30594	+	1.07518i	−0.0499338	+	0.0411104i
$685$	5.77196	−	7.69926i	0.220535	−	0.294174i
$686$	−15.2036	+	21.3272i	−0.580476	+	0.814278i
$687$	−10.9296			−0.416990
$688$	−26.9542	−	5.27399i	−1.02762	−	0.201069i
$689$			4.64533i			0.176973i
$690$	−17.6002	−	33.2771i	−0.670027	−	1.26684i
$691$			44.2102i			1.68184i	0.541162	+	0.840918i	$0.317985\pi$
$691$			44.2102i			1.68184i	−0.541162	+	0.840918i	$0.682015\pi$
$692$	4.86984	−	4.00933i	0.185124	−	0.152412i
$693$	0.187968	−	3.15881i	0.00714031	−	0.119993i
$694$	−7.26476	+	15.3912i	−0.275767	+	0.584240i
$695$	27.1008	−	36.1500i	1.02799	−	1.37125i
$696$	34.9621	−	8.84471i	1.32524	−	0.335258i
$697$			10.0651i			0.381243i
$698$	−23.0998	−	10.9033i	−0.874341	−	0.412697i
$699$		−	31.1774i		−	1.17924i
$700$	−20.9460	−	16.1638i	−0.791683	−	0.610933i
$701$		−	40.5612i		−	1.53197i	−0.642855	−	0.765987i	$-0.722250\pi$
$701$		−	40.5612i		−	1.53197i	0.642855	−	0.765987i	$-0.277750\pi$
$702$	−2.13520	+	4.52365i	−0.0805880	+	0.170734i
$703$		−	5.41519i		−	0.204238i
$704$	−30.1584	+	16.3022i	−1.13664	+	0.614414i
$705$	10.1843	−	13.5849i	0.383561	−	0.511635i
$706$	−39.3201	−	18.5594i	−1.47983	−	0.698494i
$707$	−0.695956	+	11.6956i	−0.0261741	+	0.439857i
$708$	32.7968	−	27.0015i	1.23258	−	1.01478i
$709$			26.0155i			0.977033i	0.872555	+	0.488516i	$0.162462\pi$
$709$			26.0155i			0.977033i	−0.872555	+	0.488516i	$0.837538\pi$
$710$	−31.9068	+	16.8754i	−1.19744	+	0.633323i
$711$			0.406974i			0.0152627i
$712$	−38.4849	+	9.73592i	−1.44228	+	0.364869i
$713$	39.8886			1.49384
$714$	−8.13463	+	14.8747i	−0.304431	+	0.556673i
$715$	−3.75871	+	5.01377i	−0.140568	+	0.187504i
$716$	16.4920	+	20.0317i	0.616336	+	0.748619i
$717$			20.2922i			0.757825i
$718$	17.7467	−	37.5983i	0.662302	−	1.40316i
$719$	−33.6315			−1.25425			−0.627123	−	0.778921i	$-0.715767\pi$
$719$	−33.6315			−1.25425			−0.627123	+	0.778921i	$0.715767\pi$
$720$	−1.85307	+	1.67268i	−0.0690599	+	0.0623370i
$721$	17.2648	+	1.02736i	0.642973	+	0.0382608i
$722$	−12.5543	−	5.92572i	−0.467221	−	0.220532i
$723$			38.6777i			1.43844i
$724$	−17.5639	−	21.3337i	−0.652759	−	0.792859i
$725$	37.0984	−	10.8370i	1.37780	−	0.402477i
$726$	15.5347	+	7.33252i	0.576547	+	0.272135i
$727$		−	19.0381i		−	0.706084i	−0.935607	−	0.353042i	$-0.885147\pi$
$727$		−	19.0381i		−	0.706084i	0.935607	−	0.353042i	$-0.114853\pi$
$728$	−0.916258	−	4.80711i	−0.0339588	−	0.178163i
$729$	29.0228			1.07492
$730$	7.67385	+	14.5092i	0.284022	+	0.537008i
$731$			18.8613i			0.697609i
$732$	−21.7805	−	26.4552i	−0.805031	−	0.977813i
$733$			9.09491i			0.335928i	0.985793	+	0.167964i	$0.0537192\pi$
$733$			9.09491i			0.335928i	−0.985793	+	0.167964i	$0.946281\pi$
$734$	−4.82988	+	10.2326i	−0.178274	+	0.377693i
$735$	−18.6760	−	17.8278i	−0.688873	−	0.657587i
$736$	24.1910	−	32.8856i	0.891692	−	1.21218i
$737$		−	3.52373i		−	0.129798i
$738$	−0.617333	+	1.30788i	−0.0227243	+	0.0481439i
$739$	17.9634			0.660794			0.330397	−	0.943842i	$-0.392817\pi$
$739$	17.9634			0.660794			0.330397	+	0.943842i	$0.392817\pi$
$740$	−0.363419	−	7.98312i	−0.0133595	−	0.293465i
$741$	3.26891			0.120086
$742$	−12.7530	+	23.3198i	−0.468177	+	0.856096i
$743$	−7.72670			−0.283465			−0.141733	−	0.989905i	$-0.545267\pi$
$743$	−7.72670			−0.283465			−0.141733	+	0.989905i	$0.545267\pi$
$744$	6.32436	+	24.9995i	0.231862	+	0.916525i
$745$	8.79287	−	11.7289i	0.322146	−	0.429713i
$746$	−14.4515	−	6.82121i	−0.529105	−	0.249742i
$747$	1.29169			0.0472604
$748$	14.9638	+	18.1755i	0.547132	+	0.664561i
$749$	29.3597	+	1.74708i	1.07278	+	0.0638367i
$750$	18.7111	−	18.1692i	0.683233	−	0.663445i
$751$		−	19.1852i		−	0.700079i	−0.936735	−	0.350040i	$-0.886168\pi$
$751$		−	19.1852i		−	0.700079i	0.936735	−	0.350040i	$-0.113832\pi$
$752$	18.0700	+	3.53567i	0.658945	+	0.128932i
$753$			10.3539i			0.377317i
$754$	6.46465	+	3.05137i	0.235429	+	0.111124i
$755$	−16.7563	+	22.3513i	−0.609823	+	0.813447i
$756$	−23.1378	+	16.8471i	−0.841513	+	0.612723i
$757$	−28.1700			−1.02386			−0.511928	−	0.859028i	$-0.671069\pi$
$757$	−28.1700			−1.02386			−0.511928	+	0.859028i	$0.671069\pi$
$758$	−1.52961	−	0.721989i	−0.0555579	−	0.0262238i
$759$	−51.0138			−1.85168
$760$	17.6866	+	7.38439i	0.641559	+	0.267860i
$761$		−	10.7556i		−	0.389889i	−0.980814	−	0.194944i	$-0.937547\pi$
$761$		−	10.7556i		−	0.389889i	0.980814	−	0.194944i	$-0.0624527\pi$
$762$	8.94696	+	4.22305i	0.324114	+	0.152985i
$763$	−5.10550	−	0.303808i	−0.184832	−	0.0109986i
$764$	−2.25147	+	1.85363i	−0.0814552	+	0.0670619i
$765$	1.37166	+	1.02830i	0.0495926	+	0.0371784i
$766$	0.0803035	−	0.170131i	0.00290148	−	0.00614710i
$767$	8.42087			0.304060
$768$	24.4459	+	9.94725i	0.882116	+	0.358940i
$769$			10.9826i			0.396041i	0.980198	+	0.198021i	$0.0634513\pi$
$769$			10.9826i			0.396041i	−0.980198	+	0.198021i	$0.936549\pi$
$770$	−32.6334	+	14.8504i	−1.17603	+	0.535173i
$771$	23.4880			0.845901
$772$	0.261755	−	0.215502i	0.00942077	−	0.00775610i
$773$			41.2363i			1.48317i	0.670860	+	0.741584i	$0.265925\pi$
$773$			41.2363i			1.48317i	−0.670860	+	0.741584i	$0.734075\pi$
$774$	−1.15684	+	2.45088i	−0.0415817	+	0.0880951i
$775$	7.74897	+	26.5271i	0.278351	+	0.952880i
$776$	−9.40963	−	37.1952i	−0.337786	−	1.33523i
$777$	0.463239	−	7.78475i	0.0166186	−	0.279276i
$778$	−20.9640	+	44.4145i	−0.751597	+	1.59234i
$779$	11.1040			0.397841
$780$	4.81905	−	0.219380i	0.172550	−	0.00785505i
$781$			48.9131i			1.75025i
$782$	−25.3532	−	11.9670i	−0.906630	−	0.427937i
$783$		−	41.8098i		−	1.49416i
$784$	8.59750	−	26.6474i	0.307054	−	0.951692i
$785$	2.82564	−	3.76914i	0.100851	−	0.134526i
$786$	10.8515	−	22.9901i	0.387061	−	0.820030i
$787$	−19.2874			−0.687520			−0.343760	−	0.939057i	$-0.611701\pi$
$787$	−19.2874			−0.687520			−0.343760	+	0.939057i	$0.611701\pi$
$788$	−18.0770	−	21.9568i	−0.643965	−	0.782177i
$789$	−16.3581			−0.582365
$790$	4.07613	−	2.15586i	0.145022	−	0.0767019i
$791$	49.4712	+	2.94383i	1.75899	+	0.104671i
$792$	0.829663	+	3.27956i	0.0294808	+	0.116534i
$793$		−	6.79261i		−	0.241213i
$794$	10.2581	−	21.7329i	0.364047	−	0.771272i
$795$	−20.9641	−	15.7163i	−0.743519	−	0.557399i
$796$	18.6292	+	22.6275i	0.660293	+	0.802010i
$797$			12.5999i			0.446312i	0.974783	+	0.223156i	$0.0716359\pi$
$797$			12.5999i			0.446312i	−0.974783	+	0.223156i	$0.928364\pi$
$798$	16.4101	+	8.97425i	0.580910	+	0.317685i
$799$		−	12.6445i		−	0.447331i
$800$	26.5693	+	9.69917i	0.939366	+	0.342918i
$801$			3.91720i			0.138407i
$802$	20.6295	+	9.73729i	0.728452	+	0.343836i
$803$	22.2425			0.784922
$804$	−2.09428	+	1.72421i	−0.0738594	+	0.0608083i
$805$	27.5943	−	32.5802i	0.972571	−	1.14830i
$806$	−2.18187	+	4.62251i	−0.0768530	+	0.162821i
$807$	37.6254			1.32448
$808$	−3.07185	−	12.1427i	−0.108067	−	0.427178i
$809$	32.5568			1.14464			0.572319	−	0.820031i	$-0.306044\pi$
$809$	32.5568			1.14464			0.572319	+	0.820031i	$0.306044\pi$
$810$	−11.9531	−	22.6001i	−0.419990	−	0.794086i
$811$		−	8.59304i		−	0.301742i	−0.988553	−	0.150871i	$-0.951792\pi$
$811$		−	8.59304i		−	0.301742i	0.988553	−	0.150871i	$-0.0482079\pi$
$812$	24.0758	+	33.0657i	0.844895	+	1.16038i
$813$	41.2103			1.44531
$814$	−9.79328	−	4.62251i	−0.343254	−	0.162019i
$815$	14.9103	−	19.8890i	0.522285	−	0.696680i
$816$	3.48030	−	17.7871i	0.121835	−	0.622671i
$817$	20.8080			0.727981
$818$	−18.2031	+	38.5651i	−0.636455	+	1.34840i
$819$	−0.482037	−	0.0286841i	−0.0168437	−	0.00100230i
$820$	16.3696	−	0.745199i	0.571650	−	0.0260235i
$821$		−	4.48573i		−	0.156553i	−0.996932	−	0.0782765i	$-0.975058\pi$
$821$		−	4.48573i		−	0.156553i	0.996932	−	0.0782765i	$-0.0249417\pi$
$822$	−4.28501	+	9.07824i	−0.149457	+	0.316640i
$823$	26.6081			0.927500			0.463750	−	0.885966i	$-0.346504\pi$
$823$	26.6081			0.927500			0.463750	+	0.885966i	$0.346504\pi$
$824$	−17.9248	+	4.53461i	−0.624439	+	0.157970i
$825$	−9.91020	−	33.9256i	−0.345029	−	1.18114i
$826$	42.2732	+	23.1181i	1.47087	+	0.804383i
$827$		−	3.71024i		−	0.129018i	−0.997917	−	0.0645088i	$-0.979452\pi$
$827$		−	3.71024i		−	0.129018i	0.997917	−	0.0645088i	$-0.0205480\pi$
$828$	−2.56049	−	3.11004i	−0.0889830	−	0.108081i
$829$	26.1759			0.909127			0.454564	−	0.890714i	$-0.349795\pi$
$829$	26.1759			0.909127			0.454564	+	0.890714i	$0.349795\pi$
$830$	−6.84242	−	12.9372i	−0.237504	−	0.449055i
$831$	−30.1527			−1.04599
$832$	2.48774	+	4.60219i	0.0862467	+	0.159552i
$833$	−19.0927	−	2.28034i	−0.661524	−	0.0790091i
$834$	−20.1192	+	42.6247i	−0.696672	+	1.47597i
$835$	8.76790	−	11.6956i	0.303426	−	0.404742i
$836$	20.0515	−	16.5083i	0.693495	−	0.570953i
$837$	29.8959			1.03335
$838$	12.9075	−	27.3459i	0.445882	−	0.944647i
$839$	−5.16939			−0.178467			−0.0892337	−	0.996011i	$-0.528442\pi$
$839$	−5.16939			−0.178467			−0.0892337	+	0.996011i	$0.528442\pi$
$840$	24.7941	+	12.1286i	0.855479	+	0.418477i
$841$	−30.7494			−1.06032
$842$	13.9657	−	29.5877i	0.481289	−	1.01966i
$843$	−15.9707			−0.550060
$844$	−8.00569	−	9.72394i	−0.275567	−	0.334712i
$845$	−22.4936	−	16.8629i	−0.773804	−	0.580103i
$846$	0.775540	−	1.64306i	0.0266636	−	0.0564897i
$847$	−1.15731	+	19.4487i	−0.0397657	+	0.668264i
$848$	5.45622	−	27.8855i	0.187367	−	0.957593i
$849$	36.9581			1.26840
$850$	3.03311	−	19.1854i	0.104035	−	0.658053i
$851$	12.8960			0.442070
$852$	29.0708	−	23.9339i	0.995949	−	0.819962i
$853$		−	30.2469i		−	1.03563i	−0.855492	−	0.517817i	$-0.826745\pi$
$853$		−	30.2469i		−	1.03563i	0.855492	−	0.517817i	$-0.173255\pi$
$854$	18.6480	−	34.0992i	0.638122	−	1.16685i
$855$	1.13444	−	1.51324i	0.0387971	−	0.0517517i
$856$	−30.4820	+	7.71134i	−1.04185	+	0.263568i
$857$	−6.05906			−0.206974			−0.103487	−	0.994631i	$-0.533000\pi$
$857$	−6.05906			−0.206974			−0.103487	+	0.994631i	$0.533000\pi$
$858$	2.79040	−	5.91176i	0.0952628	−	0.201824i
$859$			14.8595i			0.506999i	0.967336	+	0.253499i	$0.0815816\pi$
$859$			14.8595i			0.506999i	−0.967336	+	0.253499i	$0.918418\pi$
$860$	30.6754	−	1.39645i	1.04602	−	0.0476185i
$861$	15.9628	+	0.949883i	0.544011	+	0.0323719i
$862$	20.3401	−	43.0926i	0.692786	−	1.46774i
$863$	−20.3195			−0.691685			−0.345842	−	0.938293i	$-0.612407\pi$
$863$	−20.3195			−0.691685			−0.345842	+	0.938293i	$0.612407\pi$
$864$	18.1307	−	24.6472i	0.616820	−	0.838514i
$865$	−4.23033	+	5.64287i	−0.143835	+	0.191863i
$866$	21.8853	+	10.3300i	0.743691	+	0.351029i
$867$	15.5952			0.529642
$868$	−23.6435	+	17.2153i	−0.802511	+	0.584325i
$869$		−	6.24871i		−	0.211973i
$870$	−35.6421	+	18.8510i	−1.20838	+	0.639109i
$871$	−0.537724			−0.0182201
$872$	5.30068	−	1.34096i	0.179504	−	0.0454108i
$873$	−3.78592			−0.128134
$874$	−13.2021	+	27.9701i	−0.446569	+	0.946103i
$875$	27.0273	+	12.0218i	0.913690	+	0.406411i
$876$	−10.8836	−	13.2195i	−0.367723	−	0.446646i
$877$	11.6772			0.394311			0.197156	−	0.980372i	$-0.436830\pi$
$877$	11.6772			0.394311			0.197156	+	0.980372i	$0.436830\pi$
$878$	−25.1046	−	11.8496i	−0.847238	−	0.399904i
$879$		−	40.9692i		−	1.38186i
$880$	28.4522	−	25.6824i	0.959123	−	0.865754i
$881$		−	29.5171i		−	0.994457i	−0.867620	−	0.497229i	$-0.834351\pi$
$881$		−	29.5171i		−	0.994457i	0.867620	−	0.497229i	$-0.165649\pi$
$882$	−2.34110	−	1.46735i	−0.0788289	−	0.0494082i
$883$			14.0952i			0.474341i	0.971468	+	0.237170i	$0.0762200\pi$
$883$			14.0952i			0.474341i	−0.971468	+	0.237170i	$0.923780\pi$
$884$	2.77359	−	2.28349i	0.0932860	−	0.0768022i
$885$	−28.4898	+	38.0028i	−0.957676	+	1.27745i
$886$	−12.8185	+	27.1573i	−0.430645	+	0.912367i
$887$		−	43.7425i		−	1.46873i	−0.678755	−	0.734365i	$-0.737480\pi$
$887$		−	43.7425i		−	1.46873i	0.678755	−	0.734365i	$-0.262520\pi$
$888$	2.04467	+	8.08235i	0.0686147	+	0.271226i
$889$	−0.666535	+	11.2011i	−0.0223549	+	0.375674i
$890$	39.2335	−	20.7505i	1.31511	−	0.695558i
$891$	−34.6459			−1.16068
$892$	−20.8181	+	17.1395i	−0.697042	+	0.573873i
$893$	−13.9496			−0.466807
$894$	−6.52769	+	13.8296i	−0.218319	+	0.462530i
$895$	−23.2114	−	17.4011i	−0.775873	−	0.581654i
$896$	−0.146026	+	29.9329i	−0.00487839	+	0.999988i
$897$			7.78475i			0.259925i
$898$	45.2655	+	21.3657i	1.51053	+	0.712983i
$899$		−	42.7235i		−	1.42491i
$900$	1.57085	−	2.30697i	0.0523616	−	0.0768988i
$901$	−19.5129			−0.650071
$902$	9.47858	−	20.0814i	0.315602	−	0.668636i
$903$	29.9132	+	1.78001i	0.995448	+	0.0592351i
$904$	−51.3624	+	12.9937i	−1.70829	+	0.432163i
$905$	24.7201	+	18.5321i	0.821724	+	0.616027i
$906$	12.4396	−	26.3545i	0.413277	−	0.875571i
$907$			16.5671i			0.550103i	0.961430	+	0.275051i	$0.0886949\pi$
$907$			16.5671i			0.550103i	−0.961430	+	0.275051i	$0.911305\pi$
$908$	−21.1725	−	25.7167i	−0.702635	−	0.853440i
$909$	−1.23594			−0.0409937
$910$	2.26619	+	4.97988i	0.0751234	+	0.165081i
$911$		−	21.4989i		−	0.712291i	−0.934431	−	0.356145i	$-0.884091\pi$
$911$		−	21.4989i		−	0.712291i	0.934431	−	0.356145i	$-0.115909\pi$
$912$	−19.6230	−	3.83953i	−0.649781	−	0.127139i
$913$	−19.8327			−0.656365
$914$	−4.84986	+	10.2749i	−0.160419	+	0.339865i
$915$	30.6546	+	22.9811i	1.01341	+	0.759731i
$916$	8.42291	+	10.2307i	0.278301	+	0.338032i
$917$	28.7824	+	1.71273i	0.950479	+	0.0565592i
$918$	−19.0018	−	8.96903i	−0.627154	−	0.296022i
$919$			13.6195i			0.449267i	0.974443	+	0.224634i	$0.0721185\pi$
$919$			13.6195i			0.449267i	−0.974443	+	0.224634i	$0.927881\pi$
$920$	−17.5856	+	42.1198i	−0.579780	+	1.38865i
$921$	−6.34127			−0.208952
$922$	14.1699	+	6.68833i	0.466662	+	0.220269i
$923$	7.46419			0.245687
$924$	30.2378	−	22.0167i	0.994749	−	0.724297i
$925$	2.50525	+	8.57622i	0.0823720	+	0.281984i
$926$	22.7659	+	10.7457i	0.748134	+	0.353126i
$927$			1.82448i			0.0599237i
$928$	−35.2227	−	25.9102i	−1.15624	−	0.850545i
$929$			21.0198i			0.689639i	0.938669	+	0.344819i	$0.112060\pi$
$929$			21.0198i			0.689639i	−0.938669	+	0.344819i	$0.887940\pi$
$930$	−13.4793	−	25.4857i	−0.442004	−	0.835710i
$931$	−2.51571	+	21.0634i	−0.0824490	+	0.690326i
$932$	−29.1838	+	24.0269i	−0.955946	+	0.787028i
$933$	35.5311			1.16324
$934$	−0.222557	−	0.105049i	−0.00728229	−	0.00343731i
$935$	−21.0606	−	15.7886i	−0.688755	−	0.516344i
$936$	0.500464	−	0.126607i	0.0163582	−	0.00413829i
$937$	−44.6810			−1.45967			−0.729833	−	0.683626i	$-0.760402\pi$
$937$	−44.6810			−1.45967			−0.729833	+	0.683626i	$0.760402\pi$
$938$	−2.69940	−	1.47624i	−0.0881386	−	0.0482008i
$939$	34.6917			1.13212
$940$	−20.5647	+	0.936175i	−0.670746	+	0.0305347i
$941$	25.5764			0.833768			0.416884	−	0.908960i	$-0.363122\pi$
$941$	25.5764			0.833768			0.416884	+	0.908960i	$0.363122\pi$
$942$	−2.09771	+	4.44421i	−0.0683470	+	0.144800i
$943$			26.4436i			0.861123i
$944$	−50.5498	−	9.89081i	−1.64525	−	0.321919i
$945$	20.6815	−	24.4183i	0.672768	−	0.794327i
$946$	17.7622	−	37.6310i	0.577498	−	1.22349i
$947$			5.85755i			0.190345i	0.995461	+	0.0951724i	$0.0303402\pi$
$947$			5.85755i			0.190345i	−0.995461	+	0.0951724i	$0.969660\pi$
$948$	−3.71383	+	3.05759i	−0.120620	+	0.0993058i
$949$		−	3.39423i		−	0.110181i
$950$	−21.1656	−	3.34618i	−0.686703	−	0.108564i
$951$	−22.2821			−0.722546
$952$	20.1925	−	3.84879i	0.654444	−	0.124740i
$953$		−	44.7593i		−	1.44990i	−0.688804	−	0.724948i	$-0.741864\pi$
$953$		−	44.7593i		−	1.44990i	0.688804	−	0.724948i	$-0.258136\pi$
$954$	−2.53556	−	1.19681i	−0.0820919	−	0.0387481i
$955$	1.95580	−	2.60886i	0.0632882	−	0.0844207i
$956$	18.9946	−	15.6382i	0.614329	−	0.505775i
$957$			54.6394i			1.76624i
$958$	−24.0476	−	11.3507i	−0.776942	−	0.366724i
$959$	−11.3655	−	0.676315i	−0.367011	−	0.0218393i
$960$	−29.1860	−	4.34334i	−0.941975	−	0.140181i
$961$	−0.450759			−0.0145406
$962$	−0.705400	+	1.49446i	−0.0227430	+	0.0481834i
$963$			3.10262i			0.0999805i
$964$	36.2044	−	29.8070i	1.16607	−	0.960019i
$965$	−0.227381	+	0.303305i	−0.00731965	+	0.00976375i
$966$	−21.3718	+	39.0798i	−0.687626	+	1.25737i
$967$	−3.93728			−0.126614			−0.0633071	−	0.997994i	$-0.520165\pi$
$967$	−3.93728			−0.126614			−0.0633071	+	0.997994i	$0.520165\pi$
$968$	−5.10821	−	20.1922i	−0.164184	−	0.649000i
$969$			13.7312i			0.441110i
$970$	20.0551	+	37.9186i	0.643929	+	1.21749i
$971$			15.3709i			0.493275i	0.969108	+	0.246638i	$0.0793258\pi$
$971$			15.3709i			0.493275i	−0.969108	+	0.246638i	$0.920674\pi$
$972$	−3.67474	−	4.46344i	−0.117867	−	0.143165i
$973$	−53.3639	−	3.17547i	−1.71077	−	0.101801i
$974$	9.70483	+	4.58077i	0.310963	+	0.146777i
$975$	−5.17708	+	1.51231i	−0.165799	+	0.0484325i
$976$	−7.97833	+	40.7755i	−0.255380	+	1.30519i
$977$			11.8589i			0.379401i	0.981842	+	0.189700i	$0.0607517\pi$
$977$			11.8589i			0.379401i	−0.981842	+	0.189700i	$0.939248\pi$
$978$	−11.0692	+	23.4512i	−0.353953	+	0.749886i
$979$		−	60.1449i		−	1.92224i
$980$	−2.29509	+	31.2207i	−0.0733139	+	0.997309i
$981$		−	0.539530i		−	0.0172259i
$982$	−14.5862	−	6.88479i	−0.465463	−	0.219703i
$983$			57.6194i			1.83777i	0.394522	+	0.918887i	$0.370910\pi$
$983$			57.6194i			1.83777i	−0.394522	+	0.918887i	$0.629090\pi$
$984$	−16.5731	+	4.19265i	−0.528330	+	0.133657i
$985$	25.4421	+	19.0734i	0.810653	+	0.607728i
$986$	−12.8174	+	27.1551i	−0.408191	+	0.864794i
$987$	−20.0537	−	1.19331i	−0.638316	−	0.0379836i
$988$	−2.51919	−	3.05987i	−0.0801460	−	0.0973475i
$989$			49.5534i			1.57571i
$990$	−1.76829	−	3.34335i	−0.0561999	−	0.106259i
$991$			0.855504i			0.0271760i	0.999908	+	0.0135880i	$0.00432532\pi$
$991$			0.855504i			0.0271760i	−0.999908	+	0.0135880i	$0.995675\pi$
$992$	18.5270	−	25.1858i	0.588233	−	0.799651i
$993$	−38.7266			−1.22895
$994$	37.4706	+	20.4917i	1.18849	+	0.649958i
$995$	−26.2193	−	19.6560i	−0.831208	−	0.623138i
$996$	9.70441	+	11.7872i	0.307496	+	0.373493i
$997$		−	39.7529i		−	1.25899i	−0.777005	−	0.629494i	$-0.783262\pi$
$997$		−	39.7529i		−	1.25899i	0.777005	−	0.629494i	$-0.216738\pi$
$998$	17.9692	+	8.48162i	0.568805	+	0.268481i
$999$	9.66536			0.305798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.n.b.139.1	✓	40
4.3	odd	2		1120.2.n.b.559.32		40
5.4	even	2	inner	280.2.n.b.139.40	yes	40
7.6	odd	2	inner	280.2.n.b.139.2	yes	40
8.3	odd	2	inner	280.2.n.b.139.37	yes	40
8.5	even	2		1120.2.n.b.559.31		40
20.19	odd	2		1120.2.n.b.559.12		40
28.27	even	2		1120.2.n.b.559.11		40
35.34	odd	2	inner	280.2.n.b.139.39	yes	40
40.19	odd	2	inner	280.2.n.b.139.4	yes	40
40.29	even	2		1120.2.n.b.559.10		40
56.13	odd	2		1120.2.n.b.559.9		40
56.27	even	2	inner	280.2.n.b.139.38	yes	40
140.139	even	2		1120.2.n.b.559.30		40
280.69	odd	2		1120.2.n.b.559.29		40
280.139	even	2	inner	280.2.n.b.139.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.n.b.139.1	✓	40	1.1	even	1	trivial
280.2.n.b.139.2	yes	40	7.6	odd	2	inner
280.2.n.b.139.3	yes	40	280.139	even	2	inner
280.2.n.b.139.4	yes	40	40.19	odd	2	inner
280.2.n.b.139.37	yes	40	8.3	odd	2	inner
280.2.n.b.139.38	yes	40	56.27	even	2	inner
280.2.n.b.139.39	yes	40	35.34	odd	2	inner
280.2.n.b.139.40	yes	40	5.4	even	2	inner
1120.2.n.b.559.9		40	56.13	odd	2
1120.2.n.b.559.10		40	40.29	even	2
1120.2.n.b.559.11		40	28.27	even	2
1120.2.n.b.559.12		40	20.19	odd	2
1120.2.n.b.559.29		40	280.69	odd	2
1120.2.n.b.559.30		40	140.139	even	2
1120.2.n.b.559.31		40	8.5	even	2
1120.2.n.b.559.32		40	4.3	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.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27891 - 0.603655i) q^{2} -1.64952 q^{3} +(1.27120 + 1.54404i) q^{4} +(-1.78913 - 1.34127i) q^{5} +(2.10957 + 0.995738i) q^{6} +(-0.157160 + 2.64108i) q^{7} +(-0.693682 - 2.74204i) q^{8} -0.279099 q^{9} +O(q^{10})\)	\(q+(-1.27891 - 0.603655i) q^{2} -1.64952 q^{3} +(1.27120 + 1.54404i) q^{4} +(-1.78913 - 1.34127i) q^{5} +(2.10957 + 0.995738i) q^{6} +(-0.157160 + 2.64108i) q^{7} +(-0.693682 - 2.74204i) q^{8} -0.279099 q^{9} +(1.47847 + 2.79538i) q^{10} +4.28531 q^{11} +(-2.09687 - 2.54691i) q^{12} -0.653942i q^{13} +(1.79529 - 3.28282i) q^{14} +(2.95120 + 2.21245i) q^{15} +(-0.768095 + 3.92556i) q^{16} +2.74692 q^{17} +(0.356942 + 0.168480i) q^{18} -3.03045i q^{19} +(-0.203376 - 4.46751i) q^{20} +(0.259238 - 4.35650i) q^{21} +(-5.48051 - 2.58685i) q^{22} +7.21687 q^{23} +(1.14424 + 4.52304i) q^{24} +(1.40199 + 4.79942i) q^{25} +(-0.394756 + 0.836331i) q^{26} +5.40892 q^{27} +(-4.27770 + 3.11468i) q^{28} -7.72977i q^{29} +(-2.43875 - 4.61102i) q^{30} +5.52714 q^{31} +(3.35201 - 4.55676i) q^{32} -7.06869 q^{33} +(-3.51305 - 1.65819i) q^{34} +(3.82358 - 4.51445i) q^{35} +(-0.354792 - 0.430940i) q^{36} +1.78693 q^{37} +(-1.82934 + 3.87566i) q^{38} +1.07869i q^{39} +(-2.43673 + 5.83629i) q^{40} +3.66414i q^{41} +(-2.96136 + 5.41506i) q^{42} +6.86633i q^{43} +(5.44749 + 6.61668i) q^{44} +(0.499346 + 0.374348i) q^{45} +(-9.22970 - 4.35650i) q^{46} -4.60316i q^{47} +(1.26698 - 6.47527i) q^{48} +(-6.95060 - 0.830144i) q^{49} +(1.10419 - 6.98432i) q^{50} -4.53109 q^{51} +(1.00971 - 0.831292i) q^{52} -7.10358 q^{53} +(-6.91751 - 3.26512i) q^{54} +(-7.66699 - 5.74776i) q^{55} +(7.35098 - 1.40113i) q^{56} +4.99877i q^{57} +(-4.66612 + 9.88565i) q^{58} +12.8771i q^{59} +(0.335472 + 7.36922i) q^{60} +10.3872 q^{61} +(-7.06869 - 3.33648i) q^{62} +(0.0438633 - 0.737124i) q^{63} +(-7.03761 + 3.80421i) q^{64} +(-0.877114 + 1.16999i) q^{65} +(9.04019 + 4.26705i) q^{66} -0.822281i q^{67} +(3.49189 + 4.24134i) q^{68} -11.9043 q^{69} +(-7.61517 + 3.46543i) q^{70} +11.4141i q^{71} +(0.193606 + 0.765303i) q^{72} +5.19041 q^{73} +(-2.28531 - 1.07869i) q^{74} +(-2.31260 - 7.91672i) q^{75} +(4.67912 - 3.85231i) q^{76} +(-0.673480 + 11.3179i) q^{77} +(0.651155 - 1.37954i) q^{78} -1.45817i q^{79} +(6.63946 - 5.99312i) q^{80} -8.08481 q^{81} +(2.21188 - 4.68609i) q^{82} -4.62805 q^{83} +(7.05614 - 5.13772i) q^{84} +(-4.91460 - 3.68436i) q^{85} +(4.14490 - 8.78139i) q^{86} +12.7504i q^{87} +(-2.97264 - 11.7505i) q^{88} -14.0351i q^{89} +(-0.412639 - 0.780188i) q^{90} +(1.72711 + 0.102774i) q^{91} +(9.17410 + 11.1431i) q^{92} -9.11710 q^{93} +(-2.77872 + 5.88701i) q^{94} +(-4.06465 + 5.42187i) q^{95} +(-5.52918 + 7.51644i) q^{96} +13.5648 q^{97} +(8.38805 + 5.25744i) q^{98} -1.19603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{4} + 40 q^{9}+O(q^{10}) \) 40 * q - 12 * q^4 + 40 * q^9	\( 40 q - 12 q^{4} + 40 q^{9} - 12 q^{14} - 28 q^{16} + 16 q^{25} - 28 q^{30} + 16 q^{35} - 28 q^{36} - 8 q^{44} - 32 q^{46} + 8 q^{49} + 4 q^{50} - 32 q^{51} - 4 q^{56} + 12 q^{60} - 84 q^{64} - 24 q^{65} + 40 q^{70} + 80 q^{74} - 72 q^{81} - 8 q^{84} + 80 q^{86} - 128 q^{99}+O(q^{100}) \) 40 * q - 12 * q^4 + 40 * q^9 - 12 * q^14 - 28 * q^16 + 16 * q^25 - 28 * q^30 + 16 * q^35 - 28 * q^36 - 8 * q^44 - 32 * q^46 + 8 * q^49 + 4 * q^50 - 32 * q^51 - 4 * q^56 + 12 * q^60 - 84 * q^64 - 24 * q^65 + 40 * q^70 + 80 * q^74 - 72 * q^81 - 8 * q^84 + 80 * q^86 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more