LMFDB - Embedded newform 280.2.w.a.43.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(43,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3, 0]))

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

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

chi := DirichletCharacter("280.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.w (of order $4$, 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:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.13
Character	$\chi$	$=$	280.43
Dual form			280.2.w.a.267.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.690254 + 1.23432i) q^{2} +(2.03800 + 2.03800i) q^{3} +(-1.04710 - 1.70399i) q^{4} +(-1.22676 + 1.86951i) q^{5} +(-3.92228 + 1.10881i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(2.82604 - 0.116271i) q^{8} +5.30689i q^{9} +O(q^{10})$	\(q+(-0.690254 + 1.23432i) q^{2} +(2.03800 + 2.03800i) q^{3} +(-1.04710 - 1.70399i) q^{4} +(-1.22676 + 1.86951i) q^{5} +(-3.92228 + 1.10881i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(2.82604 - 0.116271i) q^{8} +5.30689i q^{9} +(-1.46080 - 2.80465i) q^{10} -1.33341 q^{11} +(1.33874 - 5.60672i) q^{12} +(-2.58476 + 2.58476i) q^{13} +(1.36088 - 0.384714i) q^{14} +(-6.31019 + 1.30993i) q^{15} +(-1.80717 + 3.56849i) q^{16} +(3.37680 - 3.37680i) q^{17} +(-6.55040 - 3.66310i) q^{18} +6.20644i q^{19} +(4.47016 + 0.132823i) q^{20} -2.88217i q^{21} +(0.920389 - 1.64585i) q^{22} +(4.26143 - 4.26143i) q^{23} +(5.99642 + 5.52250i) q^{24} +(-1.99013 - 4.58687i) q^{25} +(-1.40629 - 4.97457i) q^{26} +(-4.70143 + 4.70143i) q^{27} +(-0.464492 + 1.94531i) q^{28} +8.84843 q^{29} +(2.73877 - 8.69299i) q^{30} +2.87458i q^{31} +(-3.15726 - 4.69379i) q^{32} +(-2.71748 - 2.71748i) q^{33} +(1.83720 + 6.49890i) q^{34} +(2.18939 - 0.454494i) q^{35} +(9.04288 - 5.55684i) q^{36} +(-3.25361 - 3.25361i) q^{37} +(-7.66074 - 4.28402i) q^{38} -10.5355 q^{39} +(-3.24949 + 5.42594i) q^{40} -4.30135 q^{41} +(3.55752 + 1.98943i) q^{42} +(0.490171 + 0.490171i) q^{43} +(1.39621 + 2.27211i) q^{44} +(-9.92127 - 6.51027i) q^{45} +(2.31850 + 8.20144i) q^{46} +(8.38536 + 8.38536i) q^{47} +(-10.9556 + 3.58958i) q^{48} +1.00000i q^{49} +(7.03537 + 0.709648i) q^{50} +13.7638 q^{51} +(7.11091 + 1.69791i) q^{52} +(1.22630 - 1.22630i) q^{53} +(-2.55790 - 9.04826i) q^{54} +(1.63577 - 2.49282i) q^{55} +(-2.08053 - 1.91609i) q^{56} +(-12.6487 + 12.6487i) q^{57} +(-6.10766 + 10.9218i) q^{58} -3.35433i q^{59} +(8.83950 + 9.38089i) q^{60} -0.498207i q^{61} +(-3.54815 - 1.98419i) q^{62} +(3.75254 - 3.75254i) q^{63} +(7.97296 - 0.657170i) q^{64} +(-1.66136 - 8.00312i) q^{65} +(5.23000 - 1.47849i) q^{66} +(7.16083 - 7.16083i) q^{67} +(-9.28987 - 2.21819i) q^{68} +17.3696 q^{69} +(-0.950245 + 3.01613i) q^{70} +8.65751i q^{71} +(0.617035 + 14.9975i) q^{72} +(-2.32039 - 2.32039i) q^{73} +(6.26182 - 1.77018i) q^{74} +(5.29216 - 13.4039i) q^{75} +(10.5757 - 6.49876i) q^{76} +(0.942861 + 0.942861i) q^{77} +(7.27216 - 13.0042i) q^{78} +0.155109 q^{79} +(-4.45437 - 7.75619i) q^{80} -3.24238 q^{81} +(2.96902 - 5.30925i) q^{82} +(11.3004 + 11.3004i) q^{83} +(-4.91119 + 3.01791i) q^{84} +(2.17044 + 10.4555i) q^{85} +(-0.943372 + 0.266686i) q^{86} +(18.0331 + 18.0331i) q^{87} +(-3.76826 + 0.155036i) q^{88} -4.54563i q^{89} +(14.8840 - 7.75230i) q^{90} +3.65541 q^{91} +(-11.7236 - 2.79930i) q^{92} +(-5.85839 + 5.85839i) q^{93} +(-16.1383 + 4.56220i) q^{94} +(-11.6030 - 7.61380i) q^{95} +(3.13145 - 16.0005i) q^{96} +(4.05986 - 4.05986i) q^{97} +(-1.23432 - 0.690254i) q^{98} -7.07624i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 8 q^{6}+O(q^{10}) $ 72 * q + 8 * q^6	$ 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) $ 72 * q + 8 * q^6 + 16 * q^10 - 16 * q^12 - 8 * q^16 + 8 * q^17 - 28 * q^18 - 20 * q^20 - 36 * q^22 - 8 * q^25 - 32 * q^26 - 4 * q^30 + 40 * q^32 + 64 * q^36 - 4 * q^40 + 20 * q^42 - 64 * q^43 + 48 * q^46 - 80 * q^48 - 32 * q^51 + 16 * q^52 - 24 * q^56 + 4 * q^58 - 80 * q^60 - 40 * q^62 - 8 * q^65 + 32 * q^66 - 24 * q^68 + 40 * q^72 - 40 * q^73 + 112 * q^75 - 8 * q^76 + 28 * q^78 - 20 * q^80 - 72 * q^81 + 24 * q^82 + 80 * q^83 + 8 * q^86 - 88 * q^88 + 136 * q^90 - 96 * q^92 - 56 * q^96 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.690254	+	1.23432i	−0.488083	+	0.872797i
$2$	−0.690254	+	1.23432i	−0.488083	+	0.872797i
$3$	2.03800	+	2.03800i	1.17664	+	1.17664i	0.980595	+	0.196045i	$0.0628098\pi$
$3$	2.03800	+	2.03800i	1.17664	+	1.17664i	0.196045	+	0.980595i	$0.437190\pi$
$4$	−1.04710	−	1.70399i	−0.523549	−	0.851995i
$5$	−1.22676	+	1.86951i	−0.548623	+	0.836070i
$5$	−1.22676	+	1.86951i	−0.548623	+	0.836070i
$6$	−3.92228	+	1.10881i	−1.60127	+	0.452670i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	2.82604	−	0.116271i	0.999155	−	0.0411078i
$9$			5.30689i			1.76896i
$10$	−1.46080	−	2.80465i	−0.461946	−	0.886908i
$11$	−1.33341			−0.402037			−0.201019	−	0.979587i	$-0.564425\pi$
$11$	−1.33341			−0.402037			−0.201019	+	0.979587i	$0.564425\pi$
$12$	1.33874	−	5.60672i	0.386462	−	1.61852i
$13$	−2.58476	+	2.58476i	−0.716884	+	0.716884i	−0.967966	−	0.251082i	$-0.919214\pi$
$13$	−2.58476	+	2.58476i	−0.716884	+	0.716884i	0.251082	+	0.967966i	$0.419214\pi$
$14$	1.36088	−	0.384714i	0.363711	−	0.102819i
$15$	−6.31019	+	1.30993i	−1.62928	+	0.338221i
$16$	−1.80717	+	3.56849i	−0.451792	+	0.892123i
$17$	3.37680	−	3.37680i	0.818993	−	0.818993i	−0.166969	−	0.985962i	$-0.553398\pi$
$17$	3.37680	−	3.37680i	0.818993	−	0.818993i	0.985962	+	0.166969i	$0.0533979\pi$
$18$	−6.55040	−	3.66310i	−1.54394	−	0.863401i
$19$			6.20644i			1.42386i	0.702253	+	0.711928i	$0.252178\pi$
$19$			6.20644i			1.42386i	−0.702253	+	0.711928i	$0.747822\pi$
$20$	4.47016	+	0.132823i	0.999559	+	0.0297002i
$21$		−	2.88217i		−	0.628940i
$22$	0.920389	−	1.64585i	0.196228	−	0.350897i
$23$	4.26143	−	4.26143i	0.888569	−	0.888569i	−0.105817	−	0.994386i	$-0.533746\pi$
$23$	4.26143	−	4.26143i	0.888569	−	0.888569i	0.994386	+	0.105817i	$0.0337456\pi$
$24$	5.99642	+	5.52250i	1.22401	+	1.12728i
$25$	−1.99013	−	4.58687i	−0.398026	−	0.917374i
$26$	−1.40629	−	4.97457i	−0.275795	−	0.975594i
$27$	−4.70143	+	4.70143i	−0.904791	+	0.904791i
$28$	−0.464492	+	1.94531i	−0.0877808	+	0.367630i
$29$	8.84843			1.64311			0.821556	−	0.570128i	$-0.193106\pi$
$29$	8.84843			1.64311			0.821556	+	0.570128i	$0.193106\pi$
$30$	2.73877	−	8.69299i	0.500028	−	1.58712i
$31$			2.87458i			0.516290i	0.966106	+	0.258145i	$0.0831112\pi$
$31$			2.87458i			0.516290i	−0.966106	+	0.258145i	$0.916889\pi$
$32$	−3.15726	−	4.69379i	−0.558131	−	0.829753i
$33$	−2.71748	−	2.71748i	−0.473053	−	0.473053i
$34$	1.83720	+	6.49890i	0.315078	+	1.11455i
$35$	2.18939	−	0.454494i	0.370075	−	0.0768234i
$36$	9.04288	−	5.55684i	1.50715	−	0.926139i
$37$	−3.25361	−	3.25361i	−0.534890	−	0.534890i	0.387133	−	0.922024i	$-0.373465\pi$
$37$	−3.25361	−	3.25361i	−0.534890	−	0.534890i	−0.922024	+	0.387133i	$0.873465\pi$
$38$	−7.66074	−	4.28402i	−1.24274	−	0.694960i
$39$	−10.5355			−1.68703
$40$	−3.24949	+	5.42594i	−0.513790	+	0.857916i
$41$	−4.30135			−0.671758			−0.335879	−	0.941905i	$-0.609033\pi$
$41$	−4.30135			−0.671758			−0.335879	+	0.941905i	$0.609033\pi$
$42$	3.55752	+	1.98943i	0.548937	+	0.306975i
$43$	0.490171	+	0.490171i	0.0747504	+	0.0747504i	0.743494	−	0.668743i	$-0.233167\pi$
$43$	0.490171	+	0.490171i	0.0747504	+	0.0747504i	−0.668743	+	0.743494i	$0.733167\pi$
$44$	1.39621	+	2.27211i	0.210486	+	0.342534i
$45$	−9.92127	−	6.51027i	−1.47898	−	0.970493i
$46$	2.31850	+	8.20144i	0.341845	+	1.20924i
$47$	8.38536	+	8.38536i	1.22313	+	1.22313i	0.966513	+	0.256618i	$0.0826081\pi$
$47$	8.38536	+	8.38536i	1.22313	+	1.22313i	0.256618	+	0.966513i	$0.417392\pi$
$48$	−10.9556	+	3.58958i	−1.58130	+	0.518112i
$49$			1.00000i			0.142857i
$50$	7.03537	+	0.709648i	0.994951	+	0.100359i
$51$	13.7638			1.92732
$52$	7.11091	+	1.69791i	0.986106	+	0.235458i
$53$	1.22630	−	1.22630i	0.168446	−	0.168446i	−0.617850	−	0.786296i	$-0.711996\pi$
$53$	1.22630	−	1.22630i	0.168446	−	0.168446i	0.786296	+	0.617850i	$0.211996\pi$
$54$	−2.55790	−	9.04826i	−0.348086	−	1.23131i
$55$	1.63577	−	2.49282i	0.220567	−	0.336131i
$56$	−2.08053	−	1.91609i	−0.278022	−	0.256049i
$57$	−12.6487	+	12.6487i	−1.67536	+	1.67536i
$58$	−6.10766	+	10.9218i	−0.801975	+	1.43410i
$59$		−	3.35433i		−	0.436696i	−0.975871	−	0.218348i	$-0.929933\pi$
$59$		−	3.35433i		−	0.436696i	0.975871	−	0.218348i	$-0.0700668\pi$
$60$	8.83950	+	9.38089i	1.14117	+	1.21107i
$61$		−	0.498207i		−	0.0637889i	−0.999491	−	0.0318944i	$-0.989846\pi$
$61$		−	0.498207i		−	0.0637889i	0.999491	−	0.0318944i	$-0.0101540\pi$
$62$	−3.54815	−	1.98419i	−0.450616	−	0.251992i
$63$	3.75254	−	3.75254i	0.472775	−	0.472775i
$64$	7.97296	−	0.657170i	0.996620	−	0.0821462i
$65$	−1.66136	−	8.00312i	−0.206066	−	0.992664i
$66$	5.23000	−	1.47849i	0.643768	−	0.181990i
$67$	7.16083	−	7.16083i	0.874834	−	0.874834i	−0.118160	−	0.992995i	$-0.537700\pi$
$67$	7.16083	−	7.16083i	0.874834	−	0.874834i	0.992995	+	0.118160i	$0.0376997\pi$
$68$	−9.28987	−	2.21819i	−1.12656	−	0.268995i
$69$	17.3696			2.09105
$70$	−0.950245	+	3.01613i	−0.113576	+	0.360496i
$71$			8.65751i			1.02746i	0.857953	+	0.513729i	$0.171736\pi$
$71$			8.65751i			1.02746i	−0.857953	+	0.513729i	$0.828264\pi$
$72$	0.617035	+	14.9975i	0.0727182	+	1.76747i
$73$	−2.32039	−	2.32039i	−0.271581	−	0.271581i	0.558156	−	0.829736i	$-0.311509\pi$
$73$	−2.32039	−	2.32039i	−0.271581	−	0.271581i	−0.829736	+	0.558156i	$0.811509\pi$
$74$	6.26182	−	1.77018i	0.727922	−	0.205780i
$75$	5.29216	−	13.4039i	0.611086	−	1.54775i
$76$	10.5757	−	6.49876i	1.21312	−	0.745459i
$77$	0.942861	+	0.942861i	0.107449	+	0.107449i
$78$	7.27216	−	13.0042i	0.823411	−	1.47243i
$79$	0.155109			0.0174511			0.00872554	−	0.999962i	$-0.497223\pi$
$79$	0.155109			0.0174511			0.00872554	+	0.999962i	$0.497223\pi$
$80$	−4.45437	−	7.75619i	−0.498014	−	0.867169i
$81$	−3.24238			−0.360265
$82$	2.96902	−	5.30925i	0.327874	−	0.586308i
$83$	11.3004	+	11.3004i	1.24038	+	1.24038i	0.959844	+	0.280534i	$0.0905115\pi$
$83$	11.3004	+	11.3004i	1.24038	+	1.24038i	0.280534	+	0.959844i	$0.409489\pi$
$84$	−4.91119	+	3.01791i	−0.535854	+	0.329281i
$85$	2.17044	+	10.4555i	0.235417	+	1.13405i
$86$	−0.943372	+	0.266686i	−0.101726	+	0.0287575i
$87$	18.0331	+	18.0331i	1.93335	+	1.93335i
$88$	−3.76826	+	0.155036i	−0.401697	+	0.0165269i
$89$		−	4.54563i		−	0.481836i	−0.970546	−	0.240918i	$-0.922552\pi$
$89$		−	4.54563i		−	0.481836i	0.970546	−	0.240918i	$-0.0774484\pi$
$90$	14.8840	−	7.75230i	1.56891	−	0.817164i
$91$	3.65541			0.383191
$92$	−11.7236	−	2.79930i	−1.22227	−	0.291847i
$93$	−5.85839	+	5.85839i	−0.607487	+	0.607487i
$94$	−16.1383	+	4.56220i	−1.66453	+	0.470555i
$95$	−11.6030	−	7.61380i	−1.19044	−	0.781160i
$96$	3.13145	−	16.0005i	0.319602	−	1.63304i
$97$	4.05986	−	4.05986i	0.412216	−	0.412216i	−0.470294	−	0.882510i	$-0.655852\pi$
$97$	4.05986	−	4.05986i	0.412216	−	0.412216i	0.882510	+	0.470294i	$0.155852\pi$
$98$	−1.23432	−	0.690254i	−0.124685	−	0.0697262i
$99$		−	7.07624i		−	0.711189i
$100$	−5.73212	+	8.19407i	−0.573212	+	0.819407i
$101$		−	8.26856i		−	0.822752i	−0.911466	−	0.411376i	$-0.865048\pi$
$101$		−	8.26856i		−	0.822752i	0.911466	−	0.411376i	$-0.134952\pi$
$102$	−9.50053	+	16.9890i	−0.940693	+	1.68216i
$103$	−0.724640	+	0.724640i	−0.0714009	+	0.0714009i	−0.741905	−	0.670505i	$-0.766078\pi$
$103$	−0.724640	+	0.724640i	−0.0714009	+	0.0714009i	0.670505	+	0.741905i	$0.266078\pi$
$104$	−7.00410	+	7.60517i	−0.686809	+	0.745748i
$105$	5.38824	+	3.53572i	0.525838	+	0.345051i
$106$	0.667191	+	2.36011i	0.0648034	+	0.229234i
$107$	−4.81637	+	4.81637i	−0.465616	+	0.465616i	−0.900491	−	0.434875i	$-0.856793\pi$
$107$	−4.81637	+	4.81637i	−0.465616	+	0.465616i	0.434875	+	0.900491i	$0.356793\pi$
$108$	12.9341	+	3.08833i	1.24458	+	0.297175i
$109$	−7.12093			−0.682061			−0.341031	−	0.940052i	$-0.610776\pi$
$109$	−7.12093			−0.682061			−0.341031	+	0.940052i	$0.610776\pi$
$110$	1.94784	+	3.73974i	0.185719	+	0.356570i
$111$		−	13.2617i		−	1.25875i
$112$	3.80117	−	1.24545i	0.359176	−	0.117684i
$113$	−11.4151	−	11.4151i	−1.07384	−	1.07384i	−0.997047	−	0.0767956i	$-0.975531\pi$
$113$	−11.4151	−	11.4151i	−1.07384	−	1.07384i	−0.0767956	−	0.997047i	$-0.524469\pi$
$114$	−6.88176	−	24.3434i	−0.644536	−	2.27997i
$115$	2.73904	+	13.1945i	0.255416	+	1.23040i
$116$	−9.26518	−	15.0776i	−0.860250	−	1.39992i
$117$	−13.7170	−	13.7170i	−1.26814	−	1.26814i
$118$	4.14032	+	2.31534i	0.381147	+	0.213144i
$119$	−4.77551			−0.437770
$120$	−17.6805	+	4.43559i	−1.61400	+	0.404912i
$121$	−9.22203			−0.838366
$122$	0.614948	+	0.343889i	0.0556748	+	0.0311343i
$123$	−8.76615	−	8.76615i	−0.790417	−	0.790417i
$124$	4.89826	−	3.00997i	0.439876	−	0.270303i
$125$	11.0166	+	1.90642i	0.985355	+	0.170515i
$126$	2.04163	+	7.22204i	0.181883	+	0.643390i
$127$	−6.16353	−	6.16353i	−0.546924	−	0.546924i	0.378625	−	0.925550i	$-0.376397\pi$
$127$	−6.16353	−	6.16353i	−0.546924	−	0.546924i	−0.925550	+	0.378625i	$0.876397\pi$
$128$	−4.69221	+	10.2948i	−0.414737	+	0.909941i
$129$			1.99794i			0.175909i
$130$	11.0252	+	3.47353i	0.966972	+	0.304649i
$131$	−8.27017			−0.722568			−0.361284	−	0.932456i	$-0.617662\pi$
$131$	−8.27017			−0.722568			−0.361284	+	0.932456i	$0.617662\pi$
$132$	−1.78509	+	7.47604i	−0.155372	+	0.650705i
$133$	4.38862	−	4.38862i	0.380541	−	0.380541i
$134$	3.89597	+	13.7815i	0.336561	+	1.19054i
$135$	−3.02185	−	14.5569i	−0.260079	−	1.25286i
$136$	9.15033	−	9.93557i	0.784634	−	0.851968i
$137$	13.1746	−	13.1746i	1.12559	−	1.12559i	0.134700	−	0.990886i	$-0.456993\pi$
$137$	13.1746	−	13.1746i	1.12559	−	1.12559i	0.990886	−	0.134700i	$-0.0430070\pi$
$138$	−11.9894	+	21.4396i	−1.02061	+	1.82506i
$139$		−	2.56009i		−	0.217144i	−0.994089	−	0.108572i	$-0.965372\pi$
$139$		−	2.56009i		−	0.217144i	0.994089	−	0.108572i	$-0.0346277\pi$
$140$	−3.06696	−	3.25480i	−0.259206	−	0.275081i
$141$			34.1787i			2.87837i
$142$	−10.6862	−	5.97588i	−0.896762	−	0.501485i
$143$	3.44654	−	3.44654i	0.288214	−	0.288214i
$144$	−18.9376	−	9.59043i	−1.57813	−	0.799203i
$145$	−10.8549	+	16.5422i	−0.901449	+	1.37376i
$146$	4.46576	−	1.26245i	0.369589	−	0.104481i
$147$	−2.03800	+	2.03800i	−0.168091	+	0.168091i
$148$	−2.13727	+	8.95097i	−0.175682	+	0.735765i
$149$	7.71168			0.631765			0.315883	−	0.948798i	$-0.397699\pi$
$149$	7.71168			0.631765			0.315883	+	0.948798i	$0.397699\pi$
$150$	12.8918	+	15.7843i	1.05261	+	1.28879i
$151$			8.38739i			0.682556i	0.939962	+	0.341278i	$0.110860\pi$
$151$			8.38739i			0.682556i	−0.939962	+	0.341278i	$0.889140\pi$
$152$	0.721626	+	17.5396i	0.0585316	+	1.42265i
$153$	17.9203	+	17.9203i	1.44877	+	1.44877i
$154$	−1.81461	+	0.512980i	−0.146225	+	0.0413371i
$155$	−5.37405	−	3.52641i	−0.431654	−	0.283248i
$156$	11.0317	+	17.9524i	0.883243	+	1.43734i
$157$	−13.8063	−	13.8063i	−1.10186	−	1.10186i	−0.994186	−	0.107673i	$-0.965660\pi$
$157$	−13.8063	−	13.8063i	−1.10186	−	1.10186i	−0.107673	−	0.994186i	$-0.534340\pi$
$158$	−0.107064	+	0.191454i	−0.00851758	+	0.0152313i
$159$	4.99841			0.396400
$160$	12.6483	−	0.144385i	0.999935	−	0.0114146i
$161$	−6.02657			−0.474960
$162$	2.23807	−	4.00214i	0.175839	−	0.314438i
$163$	−8.76593	−	8.76593i	−0.686601	−	0.686601i	0.274878	−	0.961479i	$-0.411362\pi$
$163$	−8.76593	−	8.76593i	−0.686601	−	0.686601i	−0.961479	+	0.274878i	$0.911362\pi$
$164$	4.50394	+	7.32946i	0.351698	+	0.572334i
$165$	8.41405	−	1.74666i	0.655033	−	0.135978i
$166$	−21.7484	+	6.14817i	−1.68801	+	0.477191i
$167$	−14.5461	−	14.5461i	−1.12561	−	1.12561i	−0.990882	−	0.134732i	$-0.956983\pi$
$167$	−14.5461	−	14.5461i	−1.12561	−	1.12561i	−0.134732	−	0.990882i	$-0.543017\pi$
$168$	−0.335111	−	8.14511i	−0.0258544	−	0.628409i
$169$		−	0.361997i		−	0.0278459i
$170$	−14.4036	−	4.53791i	−1.10470	−	0.348041i
$171$	−32.9369			−2.51875
$172$	0.321989	−	1.34851i	0.0245515	−	0.102823i
$173$	9.87078	−	9.87078i	0.750462	−	0.750462i	−0.224104	−	0.974565i	$-0.571945\pi$
$173$	9.87078	−	9.87078i	0.750462	−	0.750462i	0.974565	+	0.224104i	$0.0719454\pi$
$174$	−34.7061	+	9.81122i	−2.63106	+	0.743787i
$175$	−1.83617	+	4.65064i	−0.138802	+	0.351555i
$176$	2.40969	−	4.75825i	0.181637	−	0.358667i
$177$	6.83612	−	6.83612i	0.513834	−	0.513834i
$178$	5.61077	+	3.13764i	0.420545	+	0.235176i
$179$			12.3951i			0.926451i	0.886241	+	0.463225i	$0.153308\pi$
$179$			12.3951i			0.926451i	−0.886241	+	0.463225i	$0.846692\pi$
$180$	−0.704878	+	23.7226i	−0.0525385	+	1.76818i
$181$		−	6.00083i		−	0.446038i	−0.974814	−	0.223019i	$-0.928409\pi$
$181$		−	6.00083i		−	0.446038i	0.974814	−	0.223019i	$-0.0715912\pi$
$182$	−2.52316	+	4.51195i	−0.187029	+	0.334448i
$183$	1.01535	−	1.01535i	0.0750565	−	0.0750565i
$184$	11.5475	−	12.5384i	0.851291	−	0.924345i
$185$	10.0740	−	2.09126i	0.740659	−	0.153753i
$186$	−3.18736	−	11.2749i	−0.233709	−	0.826717i
$187$	−4.50264	+	4.50264i	−0.329266	+	0.329266i
$188$	5.50827	−	23.0689i	0.401732	−	1.68247i
$189$	6.64883			0.483631
$190$	17.4069	−	9.06637i	1.26283	−	0.657744i
$191$		−	0.931261i		−	0.0673837i	−0.999432	−	0.0336918i	$-0.989274\pi$
$191$		−	0.931261i		−	0.0673837i	0.999432	−	0.0336918i	$-0.0107265\pi$
$192$	17.5882	+	14.9096i	1.26932	+	1.07601i
$193$	−6.99323	−	6.99323i	−0.503384	−	0.503384i	0.409104	−	0.912488i	$-0.365841\pi$
$193$	−6.99323	−	6.99323i	−0.503384	−	0.503384i	−0.912488	+	0.409104i	$0.865841\pi$
$194$	2.20884	+	7.81351i	0.158585	+	0.560977i
$195$	12.9245	−	19.6962i	0.925543	−	1.41047i
$196$	1.70399	−	1.04710i	0.121714	−	0.0747928i
$197$	−13.9407	−	13.9407i	−0.993237	−	0.993237i	0.00674053	−	0.999977i	$-0.497854\pi$
$197$	−13.9407	−	13.9407i	−0.993237	−	0.993237i	−0.999977	+	0.00674053i	$0.997854\pi$
$198$	8.73435	+	4.88440i	0.620723	+	0.347119i
$199$	26.0806			1.84880			0.924402	−	0.381419i	$-0.124565\pi$
$199$	26.0806			1.84880			0.924402	+	0.381419i	$0.124565\pi$
$200$	−6.15749	−	12.7313i	−0.435401	−	0.900237i
$201$	29.1875			2.05873
$202$	10.2061	+	5.70741i	0.718096	+	0.401572i
$203$	−6.25678	−	6.25678i	−0.439140	−	0.439140i
$204$	−14.4121	−	23.4534i	−1.00905	−	1.64207i
$205$	5.27671	−	8.04141i	0.368542	−	0.561636i
$206$	−0.394253	−	1.39462i	−0.0274689	−	0.0971681i
$207$	22.6149	+	22.6149i	1.57184	+	1.57184i
$208$	−4.55261	−	13.8948i	−0.315667	−	0.963432i
$209$		−	8.27571i		−	0.572443i
$210$	−8.08347	+	4.21027i	−0.557812	+	0.290536i
$211$	−13.9610			−0.961116			−0.480558	−	0.876963i	$-0.659566\pi$
$211$	−13.9610			−0.961116			−0.480558	+	0.876963i	$0.659566\pi$
$212$	−3.37367	−	0.805548i	−0.231704	−	0.0553252i
$213$	−17.6440	+	17.6440i	−1.20895	+	1.20895i
$214$	−2.62043	−	9.26947i	−0.179129	−	0.633648i
$215$	−1.51770	+	0.315058i	−0.103506	+	0.0214868i
$216$	−12.7398	+	13.8331i	−0.866832	+	0.941221i
$217$	2.03263	−	2.03263i	0.137984	−	0.137984i
$218$	4.91525	−	8.78951i	0.332903	−	0.595301i
$219$		−	9.45789i		−	0.639105i
$220$	−5.96054	−	0.177107i	−0.401860	−	0.0119406i
$221$			17.4564i			1.17425i
$222$	16.3692	+	9.15395i	1.09863	+	0.614373i
$223$	8.58204	−	8.58204i	0.574696	−	0.574696i	−0.358741	−	0.933437i	$-0.616794\pi$
$223$	8.58204	−	8.58204i	0.574696	−	0.574696i	0.933437	+	0.358741i	$0.116794\pi$
$224$	−1.08649	+	5.55153i	−0.0725942	+	0.370928i
$225$	24.3420	−	10.5614i	1.62280	−	0.704092i
$226$	21.9692	−	6.21059i	1.46137	−	0.413122i
$227$	−4.17660	+	4.17660i	−0.277211	+	0.277211i	−0.831995	−	0.554784i	$-0.812801\pi$
$227$	−4.17660	+	4.17660i	−0.277211	+	0.277211i	0.554784	+	0.831995i	$0.312801\pi$
$228$	34.7978	+	8.30884i	2.30454	+	0.550266i
$229$	11.8903			0.785731			0.392866	−	0.919596i	$-0.371484\pi$
$229$	11.8903			0.785731			0.392866	+	0.919596i	$0.371484\pi$
$230$	−18.1769	−	5.72672i	−1.19855	−	0.377609i
$231$			3.84310i			0.252857i
$232$	25.0060	−	1.02881i	1.64172	−	0.0675448i
$233$	11.8799	+	11.8799i	0.778276	+	0.778276i	0.979538	−	0.201261i	$-0.0645040\pi$
$233$	11.8799	+	11.8799i	0.778276	+	0.778276i	−0.201261	+	0.979538i	$0.564504\pi$
$234$	26.3995	−	7.46300i	1.72579	−	0.487871i
$235$	−25.9633	+	5.38970i	−1.69366	+	0.351585i
$236$	−5.71574	+	3.51231i	−0.372063	+	0.228632i
$237$	0.316111	+	0.316111i	0.0205336	+	0.0205336i
$238$	3.29631	−	5.89452i	0.213668	−	0.382085i
$239$	−18.7459			−1.21257			−0.606287	−	0.795246i	$-0.707342\pi$
$239$	−18.7459			−1.21257			−0.606287	+	0.795246i	$0.707342\pi$
$240$	6.72911	−	24.8851i	0.434362	−	1.60633i
$241$	−16.5390			−1.06537			−0.532684	−	0.846314i	$-0.678817\pi$
$241$	−16.5390			−1.06537			−0.532684	+	0.846314i	$0.678817\pi$
$242$	6.36554	−	11.3829i	0.409192	−	0.731723i
$243$	7.49633	+	7.49633i	0.480890	+	0.480890i
$244$	−0.848940	+	0.521672i	−0.0543478	+	0.0333966i
$245$	−1.86951	−	1.22676i	−0.119439	−	0.0783747i
$246$	16.8711	−	4.76938i	1.07566	−	0.304084i
$247$	−16.0422	−	16.0422i	−1.02074	−	1.02074i
$248$	0.334229	+	8.12366i	0.0212236	+	0.515853i
$249$			46.0603i			2.91896i
$250$	−9.95739	+	12.2821i	−0.629761	+	0.776789i
$251$	−7.08287			−0.447067			−0.223533	−	0.974696i	$-0.571759\pi$
$251$	−7.08287			−0.447067			−0.223533	+	0.974696i	$0.571759\pi$
$252$	−10.3236	−	2.46501i	−0.650323	−	0.155281i
$253$	−5.68222	+	5.68222i	−0.357238	+	0.357238i
$254$	11.8622	−	3.35337i	0.744299	−	0.210409i
$255$	−16.8849	+	25.7316i	−1.05737	+	1.61137i
$256$	−9.46829	−	12.8977i	−0.591768	−	0.806108i
$257$	13.6375	−	13.6375i	0.850686	−	0.850686i	−0.139532	−	0.990218i	$-0.544560\pi$
$257$	13.6375	−	13.6375i	0.850686	−	0.850686i	0.990218	+	0.139532i	$0.0445597\pi$
$258$	−2.46610	−	1.37908i	−0.153533	−	0.0858581i
$259$			4.60130i			0.285911i
$260$	−11.8976	+	11.2110i	−0.737860	+	0.695276i
$261$			46.9576i			2.90660i
$262$	5.70852	−	10.2080i	0.352673	−	0.630655i
$263$	3.41130	−	3.41130i	0.210350	−	0.210350i	−0.594066	−	0.804416i	$-0.702478\pi$
$263$	3.41130	−	3.41130i	0.210350	−	0.210350i	0.804416	+	0.594066i	$0.202478\pi$
$264$	−7.99567	−	7.36374i	−0.492099	−	0.453207i
$265$	0.788207	+	3.79696i	0.0484192	+	0.233245i
$266$	2.38770	+	8.44622i	0.146400	+	0.517871i
$267$	9.26399	−	9.26399i	0.566947	−	0.566947i
$268$	−19.7001	−	4.70389i	−1.20337	−	0.287336i
$269$	−10.2171			−0.622949			−0.311474	−	0.950255i	$-0.600823\pi$
$269$	−10.2171			−0.622949			−0.311474	+	0.950255i	$0.600823\pi$
$270$	20.0537	+	6.31802i	1.22043	+	0.384502i
$271$		−	0.157881i		−	0.00959058i	−0.999989	−	0.00479529i	$-0.998474\pi$
$271$		−	0.157881i		−	0.00959058i	0.999989	−	0.00479529i	$-0.00152639\pi$
$272$	5.94764	+	18.1525i	0.360629	+	1.10066i
$273$	7.44972	+	7.44972i	0.450877	+	0.450877i
$274$	7.16790	+	25.3556i	0.433029	+	1.53179i
$275$	2.65365	+	6.11616i	0.160021	+	0.368819i
$276$	−18.1877	−	29.5976i	−1.09477	−	1.78157i
$277$	2.04434	+	2.04434i	0.122832	+	0.122832i	0.765851	−	0.643018i	$-0.222318\pi$
$277$	2.04434	+	2.04434i	0.122832	+	0.122832i	−0.643018	+	0.765851i	$0.722318\pi$
$278$	3.15997	+	1.76711i	0.189522	+	0.105984i
$279$	−15.2551			−0.913297
$280$	6.13446	−	1.53898i	0.366604	−	0.0919715i
$281$	17.6519			1.05302			0.526511	−	0.850168i	$-0.323500\pi$
$281$	17.6519			1.05302			0.526511	+	0.850168i	$0.323500\pi$
$282$	−42.1875	−	23.5920i	−2.51223	−	1.40488i
$283$	14.2491	+	14.2491i	0.847019	+	0.847019i	0.989760	−	0.142741i	$-0.0455915\pi$
$283$	14.2491	+	14.2491i	0.847019	+	0.847019i	−0.142741	+	0.989760i	$0.545592\pi$
$284$	14.7523	−	9.06527i	0.875389	−	0.537925i
$285$	−8.12998	−	39.1638i	−0.481578	−	2.31987i
$286$	1.87515	+	6.63313i	0.110880	+	0.392225i
$287$	3.04151	+	3.04151i	0.179535	+	0.179535i
$288$	24.9094	−	16.7552i	1.46780	−	0.987312i
$289$		−	5.80550i		−	0.341500i
$290$	−12.9258	−	24.8167i	−0.759028	−	1.45729i
$291$	16.5480			0.970060
$292$	−1.52424	+	6.38359i	−0.0891995	+	0.373571i
$293$	−13.0978	+	13.0978i	−0.765180	+	0.765180i	−0.977254	−	0.212073i	$-0.931978\pi$
$293$	−13.0978	+	13.0978i	−0.765180	+	0.765180i	0.212073	+	0.977254i	$0.431978\pi$
$294$	−1.10881	−	3.92228i	−0.0646671	−	0.228752i
$295$	6.27095	+	4.11495i	0.365109	+	0.239582i
$296$	−9.57312	−	8.81652i	−0.556426	−	0.512450i
$297$	6.26892	−	6.26892i	0.363760	−	0.363760i
$298$	−5.32302	+	9.51869i	−0.308354	+	0.551403i
$299$			22.0296i			1.27400i
$300$	−28.3816	+	5.01744i	−1.63861	+	0.289682i
$301$		−	0.693207i		−	0.0399558i
$302$	−10.3527	−	5.78943i	−0.595733	−	0.333144i
$303$	16.8513	−	16.8513i	0.968083	−	0.968083i
$304$	−22.1476	−	11.2161i	−1.27025	−	0.643286i
$305$	0.931403	+	0.611180i	0.0533320	+	0.0349961i
$306$	−34.4889	+	9.74984i	−1.97160	+	0.557361i
$307$	5.22780	−	5.22780i	0.298366	−	0.298366i	−0.542007	−	0.840374i	$-0.682336\pi$
$307$	5.22780	−	5.22780i	0.298366	−	0.298366i	0.840374	+	0.542007i	$0.182336\pi$
$308$	0.619357	−	2.59389i	0.0352912	−	0.147801i
$309$	−2.95363			−0.168026
$310$	8.06219	−	4.19919i	0.457901	−	0.238498i
$311$			2.81480i			0.159613i	0.996810	+	0.0798064i	$0.0254302\pi$
$311$			2.81480i			0.159613i	−0.996810	+	0.0798064i	$0.974570\pi$
$312$	−29.7737	+	1.22497i	−1.68560	+	0.0693501i
$313$	15.5659	+	15.5659i	0.879837	+	0.879837i	0.993517	−	0.113681i	$-0.0362641\pi$
$313$	15.5659	+	15.5659i	0.879837	+	0.879837i	−0.113681	+	0.993517i	$0.536264\pi$
$314$	26.5712	−	7.51153i	1.49950	−	0.423900i
$315$	2.41195	+	11.6189i	0.135898	+	0.654648i
$316$	−0.162414	−	0.264304i	−0.00913651	−	0.0148682i
$317$	15.3904	+	15.3904i	0.864409	+	0.864409i	0.991847	−	0.127437i	$-0.0406752\pi$
$317$	15.3904	+	15.3904i	0.864409	+	0.864409i	−0.127437	+	0.991847i	$0.540675\pi$
$318$	−3.45017	+	6.16964i	−0.193476	+	0.345976i
$319$	−11.7986			−0.660592
$320$	−8.55231	+	15.7117i	−0.478089	+	0.878312i
$321$	−19.6315			−1.09572
$322$	4.15986	−	7.43872i	0.231820	−	0.414544i
$323$	20.9579	+	20.9579i	1.16613	+	1.16613i
$324$	3.39510	+	5.52499i	0.188616	+	0.306944i
$325$	17.0000	+	6.71196i	0.942989	+	0.372313i
$326$	16.8707	−	4.76926i	0.934382	−	0.264145i
$327$	−14.5124	−	14.5124i	−0.802540	−	0.802540i
$328$	−12.1558	+	0.500120i	−0.671190	+	0.0276145i
$329$		−	11.8587i		−	0.653791i
$330$	−3.65189	+	11.5913i	−0.201030	+	0.638079i
$331$	13.4192			0.737583			0.368792	−	0.929512i	$-0.379772\pi$
$331$	13.4192			0.737583			0.368792	+	0.929512i	$0.379772\pi$
$332$	7.42312	−	31.0884i	0.407397	−	1.70620i
$333$	17.2665	−	17.2665i	0.946200	−	0.946200i
$334$	27.9951	−	7.91408i	1.53183	−	0.433039i
$335$	4.60263	+	22.1718i	0.251468	+	1.21138i
$336$	10.2850	+	5.20856i	0.561092	+	0.284150i
$337$	−21.6903	+	21.6903i	−1.18155	+	1.18155i	−0.202203	+	0.979344i	$0.564810\pi$
$337$	−21.6903	+	21.6903i	−1.18155	+	1.18155i	−0.979344	+	0.202203i	$0.935190\pi$
$338$	0.446820	+	0.249870i	0.0243038	+	0.0135911i
$339$		−	46.5279i		−	2.52705i
$340$	15.5433	−	14.6463i	0.842956	−	0.794308i
$341$		−	3.83298i		−	0.207568i
$342$	22.7348	−	40.6547i	1.22936	−	2.19835i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	1.44223	+	1.32825i	0.0777601	+	0.0716144i
$345$	−21.3083	+	32.4726i	−1.14720	+	1.74827i
$346$	5.37037	+	18.9971i	0.288713	+	1.02129i
$347$	8.65855	−	8.65855i	0.464816	−	0.464816i	−0.435415	−	0.900230i	$-0.643398\pi$
$347$	8.65855	−	8.65855i	0.464816	−	0.464816i	0.900230	+	0.435415i	$0.143398\pi$
$348$	11.8458	−	49.6107i	0.635001	−	2.65941i
$349$	−15.3875			−0.823672			−0.411836	−	0.911258i	$-0.635112\pi$
$349$	−15.3875			−0.823672			−0.411836	+	0.911258i	$0.635112\pi$
$350$	−4.47296	−	5.47655i	−0.239090	−	0.292734i
$351$		−	24.3042i		−	1.29726i
$352$	4.20992	+	6.25873i	0.224389	+	0.333592i
$353$	−2.21654	−	2.21654i	−0.117974	−	0.117974i	0.645655	−	0.763629i	$-0.276584\pi$
$353$	−2.21654	−	2.21654i	−0.117974	−	0.117974i	−0.763629	+	0.645655i	$0.776584\pi$
$354$	3.71931	+	13.1566i	0.197679	+	0.699267i
$355$	−16.1853	−	10.6207i	−0.859027	−	0.563687i
$356$	−7.74571	+	4.75972i	−0.410522	+	0.252265i
$357$	−9.73249	−	9.73249i	−0.515098	−	0.515098i
$358$	−15.2995	−	8.55574i	−0.808604	−	0.452185i
$359$	7.35177			0.388012			0.194006	−	0.981000i	$-0.437852\pi$
$359$	7.35177			0.388012			0.194006	+	0.981000i	$0.437852\pi$
$360$	−28.7948	−	17.2447i	−1.51762	−	0.908875i
$361$	−19.5199			−1.02736
$362$	7.40695	+	4.14210i	0.389301	+	0.217704i
$363$	−18.7945	−	18.7945i	−0.986455	−	0.986455i
$364$	−3.82757	−	6.22878i	−0.200619	−	0.326477i
$365$	7.18453	−	1.49143i	0.376056	−	0.0780650i
$366$	0.552417	+	1.95411i	0.0288753	+	0.102143i
$367$	0.372057	+	0.372057i	0.0194212	+	0.0194212i	0.716751	−	0.697329i	$-0.245629\pi$
$367$	0.372057	+	0.372057i	0.0194212	+	0.0194212i	−0.697329	+	0.716751i	$0.745629\pi$
$368$	7.50576	+	22.9080i	0.391265	+	1.19416i
$369$		−	22.8268i		−	1.18831i
$370$	−4.37236	+	13.8781i	−0.227308	+	0.721489i
$371$	−1.73425			−0.0900380
$372$	16.1170	+	3.84833i	0.835625	+	0.199526i
$373$	−1.30146	+	1.30146i	−0.0673872	+	0.0673872i	−0.739997	−	0.672610i	$-0.765173\pi$
$373$	−1.30146	+	1.30146i	−0.0673872	+	0.0673872i	0.672610	+	0.739997i	$0.265173\pi$
$374$	−2.44974	−	8.66567i	−0.126673	−	0.448091i
$375$	18.5666	+	26.3371i	0.958773	+	1.36004i
$376$	24.6723	+	22.7224i	1.27238	+	1.17182i
$377$	−22.8711	+	22.8711i	−1.17792	+	1.17792i
$378$	−4.58938	+	8.20680i	−0.236052	+	0.422112i
$379$		−	17.6885i		−	0.908597i	−0.890849	−	0.454299i	$-0.849890\pi$
$379$		−	17.6885i		−	0.908597i	0.890849	−	0.454299i	$-0.150110\pi$
$380$	−0.824360	+	27.7438i	−0.0422888	+	1.42323i
$381$		−	25.1225i		−	1.28707i
$382$	1.14948	+	0.642806i	0.0588123	+	0.0328888i
$383$	20.0504	−	20.0504i	1.02453	−	1.02453i	0.0248364	−	0.999692i	$-0.492094\pi$
$383$	20.0504	−	20.0504i	1.02453	−	1.02453i	0.999692	−	0.0248364i	$-0.00790648\pi$
$384$	−30.5435	+	11.4181i	−1.55867	+	0.582678i
$385$	−2.91935	+	0.606025i	−0.148784	+	0.0308859i
$386$	13.4590	−	3.80479i	0.685045	−	0.193659i
$387$	−2.60128	+	2.60128i	−0.132231	+	0.132231i
$388$	−11.1690	−	2.66689i	−0.567022	−	0.135391i
$389$	−39.1547			−1.98522			−0.992610	−	0.121345i	$-0.961279\pi$
$389$	−39.1547			−1.98522			−0.992610	+	0.121345i	$0.961279\pi$
$390$	15.3903	+	29.5484i	0.779316	+	1.49624i
$391$		−	28.7799i		−	1.45546i
$392$	0.116271	+	2.82604i	0.00587255	+	0.142736i
$393$	−16.8546	−	16.8546i	−0.850202	−	0.850202i
$394$	26.8300	−	7.58471i	1.35168	−	0.382112i
$395$	−0.190281	+	0.289977i	−0.00957407	+	0.0145903i
$396$	−12.0578	+	7.40952i	−0.605929	+	0.372342i
$397$	−5.60643	−	5.60643i	−0.281379	−	0.281379i	0.552280	−	0.833659i	$-0.313758\pi$
$397$	−5.60643	−	5.60643i	−0.281379	−	0.281379i	−0.833659	+	0.552280i	$0.813758\pi$
$398$	−18.0022	+	32.1918i	−0.902370	+	1.61363i
$399$	17.8880			0.895520
$400$	19.9647	+	1.18748i	0.998236	+	0.0593742i
$401$	10.6689			0.532778			0.266389	−	0.963866i	$-0.414169\pi$
$401$	10.6689			0.532778			0.266389	+	0.963866i	$0.414169\pi$
$402$	−20.1468	+	36.0268i	−1.00483	+	1.79685i
$403$	−7.43010	−	7.43010i	−0.370120	−	0.370120i
$404$	−14.0895	+	8.65800i	−0.700981	+	0.430752i
$405$	3.97762	−	6.06166i	0.197650	−	0.301207i
$406$	12.0417	−	3.40411i	0.597617	−	0.168943i
$407$	4.33838	+	4.33838i	0.215046	+	0.215046i
$408$	38.8970	−	1.60033i	1.92569	−	0.0792280i
$409$			33.1345i			1.63839i	0.573512	+	0.819197i	$0.305581\pi$
$409$			33.1345i			1.63839i	−0.573512	+	0.819197i	$0.694419\pi$
$410$	6.28341	+	12.0638i	0.310316	+	0.595788i
$411$	53.6999			2.64882
$412$	1.99355	+	0.476010i	0.0982152	+	0.0234513i
$413$	−2.37187	+	2.37187i	−0.116712	+	0.116712i
$414$	−43.5241	+	12.3040i	−2.13909	+	0.604711i
$415$	−34.9890	+	7.26333i	−1.71754	+	0.356543i
$416$	20.2931	+	3.97156i	0.994952	+	0.194722i
$417$	5.21745	−	5.21745i	0.255500	−	0.255500i
$418$	10.2149	+	5.71234i	0.499626	+	0.279400i
$419$			16.9010i			0.825667i	0.910806	+	0.412834i	$0.135461\pi$
$419$			16.9010i			0.825667i	−0.910806	+	0.412834i	$0.864539\pi$
$420$	0.382819	−	12.8838i	0.0186797	−	0.628663i
$421$		−	16.3868i		−	0.798643i	−0.916811	−	0.399321i	$-0.869246\pi$
$421$		−	16.3868i		−	0.798643i	0.916811	−	0.399321i	$-0.130754\pi$
$422$	9.63664	−	17.2324i	0.469104	−	0.838859i
$423$	−44.5002	+	44.5002i	−2.16367	+	2.16367i
$424$	3.32299	−	3.60816i	0.161379	−	0.175228i
$425$	−22.2092	−	8.76867i	−1.07730	−	0.425343i
$426$	−9.59953	−	33.9572i	−0.465099	−	1.64523i
$427$	−0.352286	+	0.352286i	−0.0170483	+	0.0170483i
$428$	13.2503	+	3.16383i	0.640476	+	0.152930i
$429$	14.0481			0.678248
$430$	0.658717	−	2.09080i	0.0317661	−	0.100827i
$431$		−	13.0706i		−	0.629588i	−0.949160	−	0.314794i	$-0.898065\pi$
$431$		−	13.0706i		−	0.629588i	0.949160	−	0.314794i	$-0.101935\pi$
$432$	−8.28076	−	25.2733i	−0.398408	−	1.21596i
$433$	−0.997219	−	0.997219i	−0.0479233	−	0.0479233i	0.682739	−	0.730662i	$-0.260789\pi$
$433$	−0.997219	−	0.997219i	−0.0479233	−	0.0479233i	−0.730662	+	0.682739i	$0.760789\pi$
$434$	1.10589	+	3.91196i	0.0530844	+	0.187780i
$435$	−55.8353	+	11.5908i	−2.67710	+	0.555736i
$436$	7.45632	+	12.1340i	0.357093	+	0.581113i
$437$	26.4483	+	26.4483i	1.26519	+	1.26519i
$438$	11.6741	+	6.52835i	0.557809	+	0.311936i
$439$	3.29846			0.157427			0.0787135	−	0.996897i	$-0.474919\pi$
$439$	3.29846			0.157427			0.0787135	+	0.996897i	$0.474919\pi$
$440$	4.33290	−	7.23498i	0.206563	−	0.344914i
$441$	−5.30689			−0.252709
$442$	−21.5468	−	12.0494i	−1.02488	−	0.573130i
$443$	8.39638	+	8.39638i	0.398924	+	0.398924i	0.877853	−	0.478929i	$-0.158975\pi$
$443$	8.39638	+	8.39638i	0.398924	+	0.398924i	−0.478929	+	0.877853i	$0.658975\pi$
$444$	−22.5978	+	13.8863i	−1.07245	+	0.659016i
$445$	8.49810	+	5.57639i	0.402848	+	0.264346i
$446$	4.66921	+	16.5168i	0.221093	+	0.782092i
$447$	15.7164	+	15.7164i	0.743360	+	0.743360i
$448$	−6.10242	−	5.17305i	−0.288312	−	0.244403i
$449$		−	23.7944i		−	1.12293i	−0.827502	−	0.561463i	$-0.810239\pi$
$449$		−	23.7944i		−	1.12293i	0.827502	−	0.561463i	$-0.189761\pi$
$450$	−3.76602	+	37.3359i	−0.177532	+	1.76003i
$451$	5.73545			0.270072
$452$	−7.49848	+	31.4040i	−0.352699	+	1.47712i
$453$	−17.0935	+	17.0935i	−0.803122	+	0.803122i
$454$	−2.27235	−	8.03819i	−0.106647	−	0.377251i
$455$	−4.48430	+	6.83382i	−0.210227	+	0.320374i
$456$	−34.2751	+	37.2164i	−1.60508	+	1.74282i
$457$	13.8185	−	13.8185i	0.646402	−	0.646402i	−0.305720	−	0.952122i	$-0.598897\pi$
$457$	13.8185	−	13.8185i	0.646402	−	0.646402i	0.952122	+	0.305720i	$0.0988971\pi$
$458$	−8.20731	+	14.6764i	−0.383502	+	0.685784i
$459$			31.7516i			1.48204i
$460$	19.6153	−	18.4833i	0.914568	−	0.861786i
$461$			30.0394i			1.39908i	0.714596	+	0.699538i	$0.246611\pi$
$461$			30.0394i			1.39908i	−0.714596	+	0.699538i	$0.753389\pi$
$462$	−4.74362	−	2.65272i	−0.220693	−	0.123415i
$463$	−18.1411	+	18.1411i	−0.843089	+	0.843089i	−0.989259	−	0.146170i	$-0.953305\pi$
$463$	−18.1411	+	18.1411i	−0.843089	+	0.843089i	0.146170	+	0.989259i	$0.453305\pi$
$464$	−15.9906	+	31.5756i	−0.742345	+	1.46586i
$465$	−3.76549	−	18.1391i	−0.174620	−	0.841183i
$466$	−22.8637	+	6.46345i	−1.05914	+	0.299414i
$467$	−16.8527	+	16.8527i	−0.779851	+	0.779851i	−0.979805	−	0.199954i	$-0.935921\pi$
$467$	−16.8527	+	16.8527i	−0.779851	+	0.779851i	0.199954	+	0.979805i	$0.435921\pi$
$468$	−9.01061	+	37.7368i	−0.416516	+	1.74438i
$469$	−10.1269			−0.467618
$470$	11.2687	−	35.7673i	0.519785	−	1.64982i
$471$		−	56.2743i		−	2.59298i
$472$	−0.390010	−	9.47945i	−0.0179516	−	0.436327i
$473$	−0.653598	−	0.653598i	−0.0300525	−	0.0300525i
$474$	−0.608380	+	0.171986i	−0.0279438	+	0.00789958i
$475$	28.4681	−	12.3516i	1.30621	−	0.566731i
$476$	5.00043	+	8.13742i	0.229194	+	0.372978i
$477$	6.50785	+	6.50785i	0.297974	+	0.297974i
$478$	12.9395	−	23.1385i	0.591837	−	1.05833i
$479$	−17.7401			−0.810566			−0.405283	−	0.914191i	$-0.632827\pi$
$479$	−17.7401			−0.810566			−0.405283	+	0.914191i	$0.632827\pi$
$480$	26.0715	+	25.4829i	1.18999	+	1.16313i
$481$	16.8196			0.766909
$482$	11.4161	−	20.4144i	0.519989	−	0.929851i
$483$	−12.2821	−	12.2821i	−0.558857	−	0.558857i
$484$	9.65638	+	15.7142i	0.438926	+	0.714284i
$485$	2.60948	+	12.5704i	0.118490	+	0.570793i
$486$	−14.4272	+	4.07851i	−0.654433	+	0.185005i
$487$	5.94559	+	5.94559i	0.269421	+	0.269421i	0.828867	−	0.559446i	$-0.188986\pi$
$487$	5.94559	+	5.94559i	0.269421	+	0.269421i	−0.559446	+	0.828867i	$0.688986\pi$
$488$	−0.0579268	−	1.40795i	−0.00262222	−	0.0637350i
$489$		−	35.7299i		−	1.61576i
$490$	2.80465	−	1.46080i	0.126701	−	0.0659922i
$491$	7.87942			0.355593			0.177797	−	0.984067i	$-0.443103\pi$
$491$	7.87942			0.355593			0.177797	+	0.984067i	$0.443103\pi$
$492$	−5.75841	+	24.1165i	−0.259609	+	1.08725i
$493$	29.8793	−	29.8793i	1.34570	−	1.34570i
$494$	30.8744	−	8.72803i	1.38910	−	0.392693i
$495$	13.2291	+	8.68083i	0.594603	+	0.390174i
$496$	−10.2579	−	5.19485i	−0.460594	−	0.233255i
$497$	6.12179	−	6.12179i	0.274600	−	0.274600i
$498$	−56.8533	−	31.7933i	−2.54766	−	1.42469i
$499$			25.3277i			1.13382i	0.823778	+	0.566912i	$0.191862\pi$
$499$			25.3277i			1.13382i	−0.823778	+	0.566912i	$0.808138\pi$
$500$	−8.28696	−	20.7684i	−0.370604	−	0.928791i
$501$		−	59.2900i		−	2.64888i
$502$	4.88898	−	8.74254i	0.218206	−	0.390198i
$503$	1.77722	−	1.77722i	0.0792425	−	0.0792425i	−0.666375	−	0.745617i	$-0.732155\pi$
$503$	1.77722	−	1.77722i	0.0792425	−	0.0792425i	0.745617	+	0.666375i	$0.232155\pi$
$504$	10.1685	−	11.0411i	0.452941	−	0.491810i
$505$	15.4581	+	10.1435i	0.687878	+	0.451381i
$506$	−3.09151	−	10.9359i	−0.137434	−	0.486158i
$507$	0.737749	−	0.737749i	0.0327646	−	0.0327646i
$508$	−4.04877	+	16.9564i	−0.179635	+	0.752319i
$509$	−12.2036			−0.540915			−0.270458	−	0.962732i	$-0.587175\pi$
$509$	−12.2036			−0.540915			−0.270458	+	0.962732i	$0.587175\pi$
$510$	−20.1062	−	38.6027i	−0.890317	−	1.70936i
$511$			3.28152i			0.145166i
$512$	22.4555	−	2.78421i	0.992401	−	0.123046i
$513$	−29.1792	−	29.1792i	−1.28829	−	1.28829i
$514$	7.41974	+	26.2465i	0.327271	+	1.15768i
$515$	−0.465763	−	2.24368i	−0.0205240	−	0.0988683i
$516$	3.40447	−	2.09204i	0.149873	−	0.0920969i
$517$	−11.1811	−	11.1811i	−0.491744	−	0.491744i
$518$	−5.67948	−	3.17607i	−0.249542	−	0.139548i
$519$	40.2333			1.76605
$520$	−5.62559	−	22.4239i	−0.246698	−	0.983354i
$521$	26.2863			1.15163			0.575813	−	0.817582i	$-0.304686\pi$
$521$	26.2863			1.15163			0.575813	+	0.817582i	$0.304686\pi$
$522$	−57.9608	−	32.4127i	−2.53687	−	1.41866i
$523$	−25.8186	−	25.8186i	−1.12897	−	1.12897i	−0.990345	−	0.138624i	$-0.955732\pi$
$523$	−25.8186	−	25.8186i	−1.12897	−	1.12897i	−0.138624	−	0.990345i	$-0.544268\pi$
$524$	8.65969	+	14.0923i	0.378300	+	0.615625i
$525$	−13.2201	+	5.73588i	−0.576974	+	0.250334i
$526$	1.85598	+	6.56531i	0.0809245	+	0.286261i
$527$	9.70687	+	9.70687i	0.422838	+	0.422838i
$528$	14.6083	−	4.78637i	0.635743	−	0.208300i
$529$		−	13.3195i		−	0.579110i
$530$	−5.23073	−	1.64797i	−0.227209	−	0.0715831i
$531$	17.8010			0.772499
$532$	−12.0735	−	2.88285i	−0.523452	−	0.124987i
$533$	11.1180	−	11.1180i	0.481573	−	0.481573i
$534$	5.04024	+	17.8293i	0.218112	+	0.771547i
$535$	−3.09573	−	14.9128i	−0.133840	−	0.644735i
$536$	19.4042	−	21.0693i	0.838132	−	0.910057i
$537$	−25.2611	+	25.2611i	−1.09010	+	1.09010i
$538$	7.05241	−	12.6112i	0.304051	−	0.543708i
$539$		−	1.33341i		−	0.0574339i
$540$	−21.6406	+	20.3917i	−0.931265	+	0.877520i
$541$		−	11.1861i		−	0.480928i	−0.970658	−	0.240464i	$-0.922700\pi$
$541$		−	11.1861i		−	0.480928i	0.970658	−	0.240464i	$-0.0772995\pi$
$542$	0.194876	+	0.108978i	0.00837063	+	0.00468100i
$543$	12.2297	−	12.2297i	0.524826	−	0.524826i
$544$	−26.5114	−	5.18854i	−1.13667	−	0.222457i
$545$	8.73566	−	13.3126i	0.374194	−	0.570251i
$546$	−14.3375	+	4.05315i	−0.613590	+	0.173459i
$547$	−3.45209	+	3.45209i	−0.147601	+	0.147601i	−0.777045	−	0.629445i	$-0.783282\pi$
$547$	−3.45209	+	3.45209i	−0.147601	+	0.147601i	0.629445	+	0.777045i	$0.283282\pi$
$548$	−36.2446	−	8.65432i	−1.54829	−	0.369694i
$549$	2.64393			0.112840
$550$	−9.38101	−	0.946249i	−0.400007	−	0.0403482i
$551$			54.9172i			2.33955i
$552$	49.0871	−	2.01957i	2.08928	−	0.0859586i
$553$	−0.109678	−	0.109678i	−0.00466400	−	0.00466400i
$554$	−3.93449	+	1.11226i	−0.167160	+	0.0472553i
$555$	24.7929	+	16.2689i	1.05240	+	0.690577i
$556$	−4.36236	+	2.68066i	−0.185005	+	0.113685i
$557$	−6.62772	−	6.62772i	−0.280826	−	0.280826i	0.552613	−	0.833438i	$-0.313631\pi$
$557$	−6.62772	−	6.62772i	−0.280826	−	0.280826i	−0.833438	+	0.552613i	$0.813631\pi$
$558$	10.5299	−	18.8297i	0.445765	−	0.797123i
$559$	−2.53395			−0.107175
$560$	−2.33474	+	8.63418i	−0.0986608	+	0.364861i
$561$	−18.3528			−0.774854
$562$	−12.1843	+	21.7881i	−0.513963	+	0.919075i
$563$	−2.91471	−	2.91471i	−0.122840	−	0.122840i	0.643014	−	0.765854i	$-0.277684\pi$
$563$	−2.91471	−	2.91471i	−0.122840	−	0.122840i	−0.765854	+	0.643014i	$0.777684\pi$
$564$	58.2402	−	35.7885i	2.45236	−	1.50697i
$565$	35.3442	−	7.33707i	1.48694	−	0.308673i
$566$	−27.4234	+	7.75246i	−1.15269	+	0.325860i
$567$	2.29271	+	2.29271i	0.0962848	+	0.0962848i
$568$	1.00661	+	24.4664i	0.0422366	+	1.02659i
$569$		−	2.91062i		−	0.122020i	−0.998137	−	0.0610098i	$-0.980568\pi$
$569$		−	2.91062i		−	0.122020i	0.998137	−	0.0610098i	$-0.0194321\pi$
$570$	53.9525	+	16.9980i	2.25982	+	0.711967i
$571$	−3.76468			−0.157547			−0.0787734	−	0.996893i	$-0.525100\pi$
$571$	−3.76468			−0.157547			−0.0787734	+	0.996893i	$0.525100\pi$
$572$	−9.48174	−	2.26400i	−0.396451	−	0.0946627i
$573$	1.89791	−	1.89791i	0.0792863	−	0.0792863i
$574$	−5.85362	+	1.65479i	−0.244325	+	0.0690695i
$575$	−28.0274	−	11.0658i	−1.16882	−	0.461477i
$576$	3.48752	+	42.3116i	0.145314	+	1.76298i
$577$	5.16677	−	5.16677i	0.215096	−	0.215096i	−0.591332	−	0.806428i	$-0.701398\pi$
$577$	5.16677	−	5.16677i	0.215096	−	0.215096i	0.806428	+	0.591332i	$0.201398\pi$
$578$	7.16585	+	4.00727i	0.298060	+	0.166680i
$579$		−	28.5044i		−	1.18460i
$580$	39.5539	+	1.17528i	1.64239	+	0.0488007i
$581$		−	15.9812i		−	0.663010i
$582$	−11.4223	+	20.4255i	−0.473470	+	0.846666i
$583$	−1.63516	+	1.63516i	−0.0677214	+	0.0677214i
$584$	−6.82729	−	6.28770i	−0.282515	−	0.260187i
$585$	42.4716	−	8.81664i	1.75599	−	0.364523i
$586$	−7.12608	−	25.2077i	−0.294375	−	1.04132i
$587$	−22.1414	+	22.1414i	−0.913873	+	0.913873i	−0.996574	−	0.0827018i	$-0.973645\pi$
$587$	−22.1414	+	22.1414i	−0.913873	+	0.913873i	0.0827018	+	0.996574i	$0.473645\pi$
$588$	5.60672	+	1.33874i	0.231217	+	0.0552089i
$589$	−17.8409			−0.735122
$590$	−9.40771	+	4.90000i	−0.387309	+	0.201730i
$591$		−	56.8225i		−	2.33736i
$592$	17.4903	−	5.73067i	0.718847	−	0.235529i
$593$	18.9925	+	18.9925i	0.779928	+	0.779928i	0.979818	−	0.199890i	$-0.0640584\pi$
$593$	18.9925	+	18.9925i	0.779928	+	0.779928i	−0.199890	+	0.979818i	$0.564058\pi$
$594$	3.41072	+	12.0650i	0.139943	+	0.495034i
$595$	5.85840	−	8.92786i	0.240171	−	0.366007i
$596$	−8.07489	−	13.1406i	−0.330760	−	0.538261i
$597$	53.1522	+	53.1522i	2.17538	+	2.17538i
$598$	−27.1916	−	15.2060i	−1.11195	−	0.621819i
$599$	31.9227			1.30433			0.652163	−	0.758079i	$-0.273862\pi$
$599$	31.9227			1.30433			0.652163	+	0.758079i	$0.273862\pi$
$600$	13.3974	−	38.4953i	0.546945	−	1.57156i
$601$	−15.6688			−0.639143			−0.319571	−	0.947562i	$-0.603539\pi$
$601$	−15.6688			−0.639143			−0.319571	+	0.947562i	$0.603539\pi$
$602$	0.855640	+	0.478489i	0.0348733	+	0.0195018i
$603$	38.0017	+	38.0017i	1.54755	+	1.54755i
$604$	14.2920	−	8.78242i	0.581534	−	0.357352i
$605$	11.3132	−	17.2407i	0.459947	−	0.700933i
$606$	9.16826	+	32.4316i	0.372435	+	1.31745i
$607$	16.9887	+	16.9887i	0.689551	+	0.689551i	0.962133	−	0.272582i	$-0.0878776\pi$
$607$	16.9887	+	16.9887i	0.689551	+	0.689551i	−0.272582	+	0.962133i	$0.587878\pi$
$608$	29.1317	−	19.5954i	1.18145	−	0.794697i
$609$		−	25.5026i		−	1.03342i
$610$	−1.39730	+	0.727781i	−0.0565749	+	0.0294670i
$611$	−43.3483			−1.75369
$612$	11.7717	−	49.3003i	0.475842	−	1.99285i
$613$	−13.8037	+	13.8037i	−0.557526	+	0.557526i	−0.928602	−	0.371077i	$-0.878989\pi$
$613$	−13.8037	+	13.8037i	−0.557526	+	0.557526i	0.371077	+	0.928602i	$0.378989\pi$
$614$	2.84428	+	10.0613i	0.114786	+	0.406041i
$615$	27.1423	−	5.63445i	1.09448	−	0.227203i
$616$	2.77419	+	2.55493i	0.111775	+	0.102941i
$617$	0.832413	−	0.832413i	0.0335117	−	0.0335117i	−0.690152	−	0.723664i	$-0.742457\pi$
$617$	0.832413	−	0.832413i	0.0335117	−	0.0335117i	0.723664	+	0.690152i	$0.242457\pi$
$618$	2.03876	−	3.64573i	0.0820108	−	0.146653i
$619$		−	25.1335i		−	1.01020i	−0.863061	−	0.505100i	$-0.831455\pi$
$619$		−	25.1335i		−	1.01020i	0.863061	−	0.505100i	$-0.168545\pi$
$620$	−0.381811	+	12.8498i	−0.0153339	+	0.516062i
$621$			40.0696i			1.60794i
$622$	−3.47437	−	1.94293i	−0.139310	−	0.0779043i
$623$	−3.21425	+	3.21425i	−0.128776	+	0.128776i
$624$	19.0394	−	37.5958i	0.762186	−	1.50504i
$625$	−17.0788	+	18.2569i	−0.683151	+	0.730277i
$626$	−29.9577	+	8.46890i	−1.19735	+	0.338485i
$627$	16.8659	−	16.8659i	0.673559	−	0.673559i
$628$	−9.06921	+	37.9822i	−0.361901	+	1.51566i
$629$	−21.9736			−0.876143
$630$	−16.0063	−	5.04284i	−0.637704	−	0.200912i
$631$			22.5410i			0.897342i	0.893697	+	0.448671i	$0.148102\pi$
$631$			22.5410i			0.897342i	−0.893697	+	0.448671i	$0.851898\pi$
$632$	0.438343	−	0.0180346i	0.0174363	−	0.000717377i
$633$	−28.4525	−	28.4525i	−1.13089	−	1.13089i
$634$	−29.6199	+	8.37340i	−1.17636	+	0.332550i
$635$	19.0839	−	3.96161i	0.757322	−	0.157212i
$636$	−5.23383	−	8.51724i	−0.207535	−	0.337731i
$637$	−2.58476	−	2.58476i	−0.102412	−	0.102412i
$638$	8.14400	−	14.5632i	0.322424	−	0.576563i
$639$	−45.9444			−1.81753
$640$	−13.4900	−	21.4014i	−0.533241	−	0.845964i
$641$	19.0683			0.753153			0.376577	−	0.926385i	$-0.377101\pi$
$641$	19.0683			0.753153			0.376577	+	0.926385i	$0.377101\pi$
$642$	13.5507	−	24.2316i	0.534805	−	0.956345i
$643$	−8.72257	−	8.72257i	−0.343984	−	0.343984i	0.513879	−	0.857863i	$-0.328208\pi$
$643$	−8.72257	−	8.72257i	−0.343984	−	0.343984i	−0.857863	+	0.513879i	$0.828208\pi$
$644$	6.31041	+	10.2692i	0.248665	+	0.404664i
$645$	−3.73516	−	2.45099i	−0.147072	−	0.0965075i
$646$	−40.3350	+	11.4025i	−1.58696	+	0.448626i
$647$	−26.9653	−	26.9653i	−1.06011	−	1.06011i	−0.998074	−	0.0620401i	$-0.980239\pi$
$647$	−26.9653	−	26.9653i	−1.06011	−	1.06011i	−0.0620401	−	0.998074i	$-0.519761\pi$
$648$	−9.16309	+	0.376994i	−0.359960	+	0.0148097i
$649$			4.47268i			0.175568i
$650$	−20.0190	+	16.3505i	−0.785211	+	0.641319i
$651$	8.28502			0.324715
$652$	−5.75827	+	24.1159i	−0.225511	+	0.944450i
$653$	10.0850	−	10.0850i	0.394657	−	0.394657i	−0.481686	−	0.876344i	$-0.659976\pi$
$653$	10.0850	−	10.0850i	0.394657	−	0.394657i	0.876344	+	0.481686i	$0.159976\pi$
$654$	27.9303	−	7.89575i	1.09216	−	0.308748i
$655$	10.1455	−	15.4612i	0.396417	−	0.604117i
$656$	7.77326	−	15.3493i	0.303495	−	0.599291i
$657$	12.3140	−	12.3140i	0.480416	−	0.480416i
$658$	14.6374	+	8.18551i	0.570627	+	0.319104i
$659$		−	45.1570i		−	1.75907i	−0.475835	−	0.879534i	$-0.657854\pi$
$659$		−	45.1570i		−	1.75907i	0.475835	−	0.879534i	$-0.342146\pi$
$660$	−11.7866	−	12.5085i	−0.458794	−	0.486894i
$661$			49.7982i			1.93692i	0.249162	+	0.968462i	$0.419845\pi$
$661$			49.7982i			1.93692i	−0.249162	+	0.968462i	$0.580155\pi$
$662$	−9.26262	+	16.5635i	−0.360002	+	0.643761i
$663$	−35.5762	+	35.5762i	−1.38167	+	1.38167i
$664$	33.2492	+	30.6214i	1.29032	+	1.18834i
$665$	2.82079	+	13.5883i	0.109385	+	0.526933i
$666$	9.39416	+	33.2308i	0.364016	+	1.28767i
$667$	37.7069	−	37.7069i	1.46002	−	1.46002i
$668$	−9.55523	+	40.0177i	−0.369703	+	1.54833i
$669$	34.9804			1.35242
$670$	−30.5441	−	9.62307i	−1.18002	−	0.371772i
$671$			0.664313i			0.0256455i
$672$	−13.5283	+	9.09976i	−0.521865	+	0.351031i
$673$	−13.1816	−	13.1816i	−0.508112	−	0.508112i	0.405835	−	0.913946i	$-0.366981\pi$
$673$	−13.1816	−	13.1816i	−0.508112	−	0.508112i	−0.913946	+	0.405835i	$0.866981\pi$
$674$	−11.8010	−	41.7446i	−0.454557	−	1.60794i
$675$	30.9213	+	12.2084i	1.19016	+	0.469902i
$676$	−0.616839	+	0.379046i	−0.0237246	+	0.0145787i
$677$	21.6756	+	21.6756i	0.833061	+	0.833061i	0.987934	−	0.154874i	$-0.0494970\pi$
$677$	21.6756	+	21.6756i	0.833061	+	0.833061i	−0.154874	+	0.987934i	$0.549497\pi$
$678$	57.4304	+	32.1161i	2.20560	+	1.23341i
$679$	−5.74151			−0.220339
$680$	7.34940	+	29.2952i	0.281837	+	1.12342i
$681$	−17.0238			−0.652355
$682$	4.73113	+	2.64573i	0.181164	+	0.101310i
$683$	29.5924	+	29.5924i	1.13232	+	1.13232i	0.989791	+	0.142530i	$0.0455236\pi$
$683$	29.5924	+	29.5924i	1.13232	+	1.13232i	0.142530	+	0.989791i	$0.454476\pi$
$684$	34.4882	+	56.1241i	1.31869	+	2.14596i
$685$	8.46802	+	40.7922i	0.323546	+	1.55859i
$686$	0.384714	+	1.36088i	0.0146884	+	0.0519587i
$687$	24.2324	+	24.2324i	0.924523	+	0.924523i
$688$	−2.63500	+	0.863352i	−0.100458	+	0.0329150i
$689$			6.33940i			0.241512i
$690$	−25.3735	−	48.7156i	−0.965952	−	1.85457i
$691$	−9.96801			−0.379201			−0.189600	−	0.981861i	$-0.560719\pi$
$691$	−9.96801			−0.379201			−0.189600	+	0.981861i	$0.560719\pi$
$692$	−27.1554	−	6.48403i	−1.03229	−	0.246486i
$693$	−5.00365	+	5.00365i	−0.190073	+	0.190073i
$694$	4.71084	+	16.6640i	0.178821	+	0.632558i
$695$	4.78610	+	3.14061i	0.181547	+	0.119130i
$696$	53.0589	+	48.8655i	2.01119	+	1.85224i
$697$	−14.5248	+	14.5248i	−0.550165	+	0.550165i
$698$	10.6213	−	18.9931i	0.402020	−	0.718898i
$699$			48.4224i			1.83150i
$700$	9.84730	−	1.74086i	0.372193	−	0.0657982i
$701$			2.71613i			0.102587i	0.998684	+	0.0512934i	$0.0163343\pi$
$701$			2.71613i			0.102587i	−0.998684	+	0.0512934i	$0.983666\pi$
$702$	29.9992	+	16.7761i	1.13225	+	0.633171i
$703$	20.1933	−	20.1933i	0.761606	−	0.761606i
$704$	−10.6312	+	0.876274i	−0.400678	+	0.0330258i
$705$	−63.8974	−	41.9290i	−2.40652	−	1.57914i
$706$	4.26590	−	1.20595i	0.160549	−	0.0453864i
$707$	−5.84675	+	5.84675i	−0.219890	+	0.219890i
$708$	−18.8068	−	4.49059i	−0.706802	−	0.168767i
$709$	−5.73081			−0.215225			−0.107613	−	0.994193i	$-0.534321\pi$
$709$	−5.73081			−0.215225			−0.107613	+	0.994193i	$0.534321\pi$
$710$	24.2813	−	12.6469i	0.911261	−	0.474630i
$711$			0.823144i			0.0308703i
$712$	−0.528523	−	12.8461i	−0.0198072	−	0.481428i
$713$	12.2498	+	12.2498i	0.458759	+	0.458759i
$714$	18.7309	−	5.29513i	0.700987	−	0.198165i
$715$	2.21527	+	10.6714i	0.0828463	+	0.399088i
$716$	21.1211	−	12.9789i	0.789332	−	0.485043i
$717$	−38.2042	−	38.2042i	−1.42676	−	1.42676i
$718$	−5.07459	+	9.07445i	−0.189382	+	0.338655i
$719$	−32.5582			−1.21422			−0.607108	−	0.794619i	$-0.707671\pi$
$719$	−32.5582			−1.21422			−0.607108	+	0.794619i	$0.707671\pi$
$720$	41.1612	−	23.6389i	1.53399	−	0.880968i
$721$	1.02480			0.0381654
$722$	13.4737	−	24.0938i	0.501439	−	0.896680i
$723$	−33.7064	−	33.7064i	−1.25356	−	1.25356i
$724$	−10.2254	+	6.28346i	−0.380022	+	0.233523i
$725$	−17.6095	−	40.5866i	−0.654001	−	1.50735i
$726$	36.1714	−	10.2255i	1.34245	−	0.379503i
$727$	−2.97096	−	2.97096i	−0.110187	−	0.110187i	0.649864	−	0.760051i	$-0.274826\pi$
$727$	−2.97096	−	2.97096i	−0.110187	−	0.110187i	−0.760051	+	0.649864i	$0.774826\pi$
$728$	10.3303	−	0.425016i	0.382867	−	0.0157521i
$729$			40.2822i			1.49193i
$730$	−3.11825	+	9.89749i	−0.115412	+	0.366323i
$731$	3.31042			0.122440
$732$	−2.79331	−	0.666972i	−0.103244	−	0.0246520i
$733$	−12.0537	+	12.0537i	−0.445214	+	0.445214i	−0.893760	−	0.448546i	$-0.851942\pi$
$733$	−12.0537	+	12.0537i	−0.445214	+	0.445214i	0.448546	+	0.893760i	$0.351942\pi$
$734$	−0.716052	+	0.202424i	−0.0264300	+	0.00747162i
$735$	−1.30993	−	6.31019i	−0.0483174	−	0.232755i
$736$	−33.4567	−	6.54781i	−1.23323	−	0.241355i
$737$	−9.54829	+	9.54829i	−0.351716	+	0.351716i
$738$	28.1756	+	15.7563i	1.03716	+	0.579996i
$739$			28.4589i			1.04688i	0.852063	+	0.523439i	$0.175351\pi$
$739$			28.4589i			1.04688i	−0.852063	+	0.523439i	$0.824649\pi$
$740$	−14.1120	−	14.9763i	−0.518768	−	0.550541i
$741$		−	65.3879i		−	2.40208i
$742$	1.19708	−	2.14063i	0.0439460	−	0.0785849i
$743$	25.4577	−	25.4577i	0.933952	−	0.933952i	−0.0639979	−	0.997950i	$-0.520385\pi$
$743$	25.4577	−	25.4577i	0.933952	−	0.933952i	0.997950	+	0.0639979i	$0.0203851\pi$
$744$	−15.8749	+	17.2372i	−0.582001	+	0.631946i
$745$	−9.46036	+	14.4171i	−0.346601	+	0.528200i
$746$	−0.708084	−	2.50477i	−0.0259248	−	0.0917060i
$747$	−59.9698	+	59.9698i	−2.19418	+	2.19418i
$748$	12.3872	+	2.95775i	0.452920	+	0.108146i
$749$	6.81138			0.248882
$750$	−45.3241	+	4.73780i	−1.65500	+	0.173000i
$751$		−	2.50885i		−	0.0915493i	−0.998952	−	0.0457747i	$-0.985424\pi$
$751$		−	2.50885i		−	0.0915493i	0.998952	−	0.0457747i	$-0.0145756\pi$
$752$	−45.0769	+	14.7694i	−1.64378	+	0.538583i
$753$	−14.4349	−	14.4349i	−0.526036	−	0.526036i
$754$	−12.4434	−	44.0171i	−0.453162	−	1.60301i
$755$	−15.6803	−	10.2893i	−0.570664	−	0.374466i
$756$	−6.96198	−	11.3295i	−0.253205	−	0.412052i
$757$	−27.4238	−	27.4238i	−0.996734	−	0.996734i	0.00326060	−	0.999995i	$-0.498962\pi$
$757$	−27.4238	−	27.4238i	−0.996734	−	0.996734i	−0.999995	+	0.00326060i	$0.998962\pi$
$758$	21.8333	+	12.2096i	0.793021	+	0.443471i
$759$	−23.1607			−0.840680
$760$	−33.6758	−	20.1678i	−1.22155	−	0.731563i
$761$	−48.5336			−1.75934			−0.879671	−	0.475582i	$-0.842237\pi$
$761$	−48.5336			−1.75934			−0.879671	+	0.475582i	$0.842237\pi$
$762$	31.0093	+	17.3409i	1.12335	+	0.628195i
$763$	5.03526	+	5.03526i	0.182289	+	0.182289i
$764$	−1.58686	+	0.975122i	−0.0574106	+	0.0352787i
$765$	−55.4859	+	11.5183i	−2.00610	+	0.416444i
$766$	10.9088	+	38.5885i	0.394150	+	1.39426i
$767$	8.67014	+	8.67014i	0.313061	+	0.313061i
$768$	6.98920	−	45.5819i	0.252201	−	1.64480i
$769$			10.6754i			0.384966i	0.981300	+	0.192483i	$0.0616541\pi$
$769$			10.6754i			0.384966i	−0.981300	+	0.192483i	$0.938346\pi$
$770$	1.26706	−	4.02173i	0.0456618	−	0.144933i
$771$	55.5866			2.00190
$772$	−4.59380	+	19.2390i	−0.165334	+	0.692427i
$773$	19.0729	−	19.0729i	0.686003	−	0.686003i	−0.275343	−	0.961346i	$-0.588791\pi$
$773$	19.0729	−	19.0729i	0.686003	−	0.686003i	0.961346	+	0.275343i	$0.0887913\pi$
$774$	−1.41527	−	5.00637i	−0.0508710	−	0.179950i
$775$	13.1853	−	5.72078i	0.473631	−	0.205497i
$776$	11.0013	−	11.9454i	0.394923	−	0.428813i
$777$	−9.37745	+	9.37745i	−0.336414	+	0.336414i
$778$	27.0267	−	48.3295i	0.968953	−	1.73269i
$779$		−	26.6961i		−	0.956486i
$780$	−47.0954	−	1.39936i	−1.68628	−	0.0501051i
$781$		−	11.5440i		−	0.413076i
$782$	35.5237	+	19.8655i	1.27032	+	0.710388i
$783$	−41.6003	+	41.6003i	−1.48667	+	1.48667i
$784$	−3.56849	−	1.80717i	−0.127446	−	0.0645417i
$785$	42.7479	−	8.87398i	1.52574	−	0.316726i
$786$	32.4380	−	9.17004i	1.15702	−	0.327085i
$787$	−14.7559	+	14.7559i	−0.525991	+	0.525991i	−0.919375	−	0.393383i	$-0.871305\pi$
$787$	−14.7559	+	14.7559i	−0.525991	+	0.525991i	0.393383	+	0.919375i	$0.371305\pi$
$788$	−9.15756	+	38.3522i	−0.326224	+	1.36624i
$789$	13.9045			0.495012
$790$	−0.226583	−	0.435026i	−0.00806146	−	0.0154775i
$791$			16.1434i			0.573993i
$792$	−0.822758	−	19.9977i	−0.0292354	−	0.710587i
$793$	1.28775	+	1.28775i	0.0457292	+	0.0457292i
$794$	10.7900	−	3.05028i	0.382922	−	0.108250i
$795$	−6.13184	+	9.34457i	−0.217474	+	0.331418i
$796$	−27.3090	−	44.4411i	−0.967941	−	1.57517i
$797$	29.8444	+	29.8444i	1.05714	+	1.05714i	0.998265	+	0.0588769i	$0.0187520\pi$
$797$	29.8444	+	29.8444i	1.05714	+	1.05714i	0.0588769	+	0.998265i	$0.481248\pi$
$798$	−12.3473	+	22.0795i	−0.437088	+	0.781607i
$799$	56.6313			2.00347
$800$	−15.2465	+	23.8232i	−0.539044	+	0.842278i
$801$	24.1231			0.852349
$802$	−7.36423	+	13.1688i	−0.260040	+	0.465007i
$803$	3.09402	+	3.09402i	0.109185	+	0.109185i
$804$	−30.5622	−	49.7353i	−1.07785	−	1.75403i
$805$	7.39314	−	11.2667i	0.260574	−	0.397100i
$806$	14.2998	−	4.04248i	0.503689	−	0.142390i
$807$	−20.8225	−	20.8225i	−0.732987	−	0.732987i
$808$	−0.961390	−	23.3672i	−0.0338216	−	0.822057i
$809$		−	42.5866i		−	1.49727i	−0.662984	−	0.748633i	$-0.730710\pi$
$809$		−	42.5866i		−	1.49727i	0.662984	−	0.748633i	$-0.269290\pi$
$810$	4.73647	+	9.09375i	0.166423	+	0.319522i
$811$	−3.38353			−0.118812			−0.0594059	−	0.998234i	$-0.518921\pi$
$811$	−3.38353			−0.118812			−0.0594059	+	0.998234i	$0.518921\pi$
$812$	−4.11003	+	17.2130i	−0.144234	+	0.604057i
$813$	0.321761	−	0.321761i	0.0112847	−	0.0112847i
$814$	−8.34955	+	2.36037i	−0.292652	+	0.0827311i
$815$	27.1417	−	5.63431i	0.950731	−	0.197361i
$816$	−24.8735	+	49.1161i	−0.870748	+	1.71941i
$817$	−3.04222	+	3.04222i	−0.106434	+	0.106434i
$818$	−40.8986	−	22.8712i	−1.42999	−	0.799673i
$819$			19.3988i			0.677850i
$820$	−19.2277	−	0.571319i	−0.671461	−	0.0199513i
$821$		−	32.1262i		−	1.12121i	−0.828083	−	0.560606i	$-0.810568\pi$
$821$		−	32.1262i		−	1.12121i	0.828083	−	0.560606i	$-0.189432\pi$
$822$	−37.0665	+	66.2829i	−1.29284	+	2.31188i
$823$	−23.1436	+	23.1436i	−0.806734	+	0.806734i	−0.984138	−	0.177404i	$-0.943230\pi$
$823$	−23.1436	+	23.1436i	−0.806734	+	0.806734i	0.177404	+	0.984138i	$0.443230\pi$
$824$	−1.96360	+	2.13211i	−0.0684054	+	0.0742757i
$825$	−7.05660	+	17.8729i	−0.245679	+	0.622254i
$826$	−1.29046	−	4.56484i	−0.0449007	−	0.158831i
$827$	18.7899	−	18.7899i	0.653390	−	0.653390i	−0.300417	−	0.953808i	$-0.597126\pi$
$827$	18.7899	−	18.7899i	0.653390	−	0.653390i	0.953808	+	0.300417i	$0.0971260\pi$
$828$	14.8555	−	62.2156i	0.516266	−	2.16214i
$829$	12.0791			0.419524			0.209762	−	0.977752i	$-0.432731\pi$
$829$	12.0791			0.419524			0.209762	+	0.977752i	$0.432731\pi$
$830$	15.1860	−	48.2012i	0.527114	−	1.67309i
$831$			8.33273i			0.289059i
$832$	−18.9096	+	22.3068i	−0.655572	+	0.773351i
$833$	3.37680	+	3.37680i	0.116999	+	0.116999i
$834$	2.83865	+	10.0414i	0.0982943	+	0.347705i
$835$	45.0387	−	9.34954i	1.55863	−	0.323554i
$836$	−14.1017	+	8.66549i	−0.487719	+	0.299702i
$837$	−13.5146	−	13.5146i	−0.467134	−	0.467134i
$838$	−20.8612	−	11.6660i	−0.720640	−	0.402994i
$839$	−7.99422			−0.275991			−0.137996	−	0.990433i	$-0.544066\pi$
$839$	−7.99422			−0.275991			−0.137996	+	0.990433i	$0.544066\pi$
$840$	15.6385	+	9.36559i	0.539578	+	0.323143i
$841$	49.2947			1.69982
$842$	20.2266	+	11.3110i	0.697053	+	0.389804i
$843$	35.9745	+	35.9745i	1.23903	+	1.23903i
$844$	14.6186	+	23.7894i	0.503192	+	0.818866i
$845$	0.676756	+	0.444083i	0.0232811	+	0.0152769i
$846$	−24.2111	−	85.6439i	−0.832394	−	2.94450i
$847$	6.52096	+	6.52096i	0.224063	+	0.224063i
$848$	2.15992	+	6.59219i	0.0741719	+	0.226377i
$849$			58.0792i			1.99327i
$850$	26.1533	−	21.3607i	0.897052	−	0.732665i
$851$	−27.7300			−0.950574
$852$	48.5403	+	11.5902i	1.66296	+	0.397074i
$853$	−38.9616	+	38.9616i	−1.33402	+	1.33402i	−0.432283	+	0.901738i	$0.642292\pi$
$853$	−38.9616	+	38.9616i	−1.33402	+	1.33402i	−0.901738	+	0.432283i	$0.857708\pi$
$854$	−0.191667	−	0.678000i	−0.00655872	−	0.0232007i
$855$	40.4056	−	61.5758i	1.38184	−	2.10585i
$856$	−13.0512	+	14.1712i	−0.446082	+	0.484363i
$857$	−7.16261	+	7.16261i	−0.244670	+	0.244670i	−0.818779	−	0.574109i	$-0.805349\pi$
$857$	−7.16261	+	7.16261i	−0.244670	+	0.244670i	0.574109	+	0.818779i	$0.305349\pi$
$858$	−9.69675	+	17.3399i	−0.331042	+	0.591973i
$859$		−	23.0106i		−	0.785112i	−0.919728	−	0.392556i	$-0.871591\pi$
$859$		−	23.0106i		−	0.785112i	0.919728	−	0.392556i	$-0.128409\pi$
$860$	2.12604	+	2.25625i	0.0724974	+	0.0769376i
$861$			12.3972i			0.422496i
$862$	16.1333	+	9.02202i	0.549503	+	0.307291i
$863$	−7.26769	+	7.26769i	−0.247395	+	0.247395i	−0.819901	−	0.572506i	$-0.805971\pi$
$863$	−7.26769	+	7.26769i	−0.247395	+	0.247395i	0.572506	+	0.819901i	$0.305971\pi$
$864$	36.9112	+	7.22389i	1.25575	+	0.245762i
$865$	6.34446	+	30.5626i	0.215718	+	1.03916i
$866$	1.91922	−	0.542554i	0.0652179	−	0.0184368i
$867$	11.8316	−	11.8316i	0.401822	−	0.401822i
$868$	−5.59196	−	1.33522i	−0.189803	−	0.0453203i
$869$	−0.206823			−0.00701599
$870$	24.2338	−	76.9193i	0.821602	−	2.60781i
$871$			37.0181i			1.25431i
$872$	−20.1240	+	0.827954i	−0.681485	+	0.0280381i
$873$	21.5452	+	21.5452i	0.729195	+	0.729195i
$874$	−50.9017	+	14.3897i	−1.72178	+	0.486738i
$875$	−6.44187	−	9.13796i	−0.217775	−	0.308919i
$876$	−16.1162	+	9.90335i	−0.544514	+	0.334603i
$877$	−39.5313	−	39.5313i	−1.33488	−	1.33488i	−0.900945	−	0.433934i	$-0.857125\pi$
$877$	−39.5313	−	39.5313i	−1.33488	−	1.33488i	−0.433934	−	0.900945i	$-0.642875\pi$
$878$	−2.27678	+	4.07136i	−0.0768374	+	0.137402i
$879$	−53.3865			−1.80068
$880$	5.93949	+	10.3422i	0.200220	+	0.348634i
$881$	−24.4761			−0.824621			−0.412311	−	0.911043i	$-0.635278\pi$
$881$	−24.4761			−0.824621			−0.412311	+	0.911043i	$0.635278\pi$
$882$	3.66310	−	6.55040i	0.123343	−	0.220564i
$883$	−16.6605	−	16.6605i	−0.560670	−	0.560670i	0.368828	−	0.929498i	$-0.379759\pi$
$883$	−16.6605	−	16.6605i	−0.560670	−	0.560670i	−0.929498	+	0.368828i	$0.879759\pi$
$884$	29.7456	−	18.2786i	1.00045	−	0.614776i
$885$	4.39392	+	21.1665i	0.147700	+	0.711502i
$886$	−16.1595	+	4.56820i	−0.542888	+	0.153472i
$887$	−18.0113	−	18.0113i	−0.604760	−	0.604760i	0.336812	−	0.941572i	$-0.390651\pi$
$887$	−18.0113	−	18.0113i	−0.604760	−	0.604760i	−0.941572	+	0.336812i	$0.890651\pi$
$888$	−1.54195	−	37.4781i	−0.0517443	−	1.25768i
$889$			8.71654i			0.292343i
$890$	−12.7489	+	6.64026i	−0.427344	+	0.222582i
$891$	4.32341			0.144840
$892$	−23.6100	−	5.63747i	−0.790520	−	0.188756i
$893$	−52.0432	+	52.0432i	−1.74156	+	1.74156i
$894$	−30.2474	+	8.55078i	−1.01162	+	0.285981i
$895$	−23.1727	−	15.2057i	−0.774578	−	0.508272i
$896$	10.5974	−	3.96164i	0.354035	−	0.132349i
$897$	−44.8962	+	44.8962i	−1.49904	+	1.49904i
$898$	29.3699	+	16.4241i	0.980086	+	0.548081i
$899$			25.4355i			0.848322i
$900$	−43.4850	−	30.4197i	−1.44950	−	1.01399i
$901$		−	8.28195i		−	0.275912i
$902$	−3.95891	+	7.07938i	−0.131817	+	0.235718i
$903$	1.41276	−	1.41276i	0.0470136	−	0.0470136i
$904$	−33.5867	−	30.9323i	−1.11708	−	1.02879i
$905$	11.2186	+	7.36157i	0.372919	+	0.244707i
$906$	−9.30001	−	32.8977i	−0.308972	−	1.09295i
$907$	38.2461	−	38.2461i	1.26994	−	1.26994i	0.323821	−	0.946118i	$-0.395032\pi$
$907$	38.2461	−	38.2461i	1.26994	−	1.26994i	0.946118	−	0.323821i	$-0.104968\pi$
$908$	11.4902	+	2.74357i	0.381316	+	0.0910487i
$909$	43.8803			1.45542
$910$	−5.33982	−	10.2521i	−0.177013	−	0.339855i
$911$			5.44507i			0.180403i	0.995924	+	0.0902016i	$0.0287511\pi$
$911$			5.44507i			0.180403i	−0.995924	+	0.0902016i	$0.971249\pi$
$912$	−22.2785	−	67.9953i	−0.737716	−	2.25155i
$913$	−15.0680	−	15.0680i	−0.498678	−	0.498678i
$914$	7.51819	+	26.5947i	0.248680	+	0.879675i
$915$	0.652615	+	3.14378i	0.0215748	+	0.103930i
$916$	−12.4503	−	20.2609i	−0.411369	−	0.669439i
$917$	5.84789	+	5.84789i	0.193114	+	0.193114i
$918$	−39.1916	−	21.9166i	−1.29352	−	0.723357i
$919$	−1.19184			−0.0393153			−0.0196576	−	0.999807i	$-0.506258\pi$
$919$	−1.19184			−0.0393153			−0.0196576	+	0.999807i	$0.506258\pi$
$920$	9.27475	+	36.9697i	0.305779	+	1.21886i
$921$	21.3085			0.702139
$922$	−37.0783	−	20.7348i	−1.22111	−	0.682865i
$923$	−22.3776	−	22.3776i	−0.736568	−	0.736568i
$924$	6.54861	−	4.02411i	0.215433	−	0.132383i
$925$	−8.44879	+	21.3990i	−0.277794	+	0.703595i
$926$	−9.86999	−	34.9139i	−0.324348	−	1.14734i
$927$	−3.84558	−	3.84558i	−0.126306	−	0.126306i
$928$	−27.9368	−	41.5327i	−0.917071	−	1.36338i
$929$			5.33831i			0.175144i	0.996158	+	0.0875721i	$0.0279108\pi$
$929$			5.33831i			0.175144i	−0.996158	+	0.0875721i	$0.972089\pi$
$930$	24.9887	+	7.87280i	0.819411	+	0.258159i
$931$	−6.20644			−0.203408
$932$	7.80379	−	32.6826i	0.255622	−	1.07055i
$933$	−5.73657	+	5.73657i	−0.187807	+	0.187807i
$934$	−9.16902	−	32.4343i	−0.300020	−	1.06128i
$935$	−2.89408	−	13.9414i	−0.0946464	−	0.455932i
$936$	−40.3597	−	37.1700i	−1.31920	−	1.21494i
$937$	37.3665	−	37.3665i	1.22071	−	1.22071i	0.253329	−	0.967380i	$-0.418475\pi$
$937$	37.3665	−	37.3665i	1.22071	−	1.22071i	0.967380	−	0.253329i	$-0.0815255\pi$
$938$	6.99016	−	12.4999i	0.228237	−	0.408136i
$939$			63.4466i			2.07050i
$940$	36.3702	+	38.5977i	1.18626	+	1.25892i
$941$		−	38.4488i		−	1.25340i	−0.779262	−	0.626698i	$-0.784406\pi$
$941$		−	38.4488i		−	1.25340i	0.779262	−	0.626698i	$-0.215594\pi$
$942$	69.4606	+	38.8435i	2.26315	+	1.26559i
$943$	−18.3299	+	18.3299i	−0.596903	+	0.596903i
$944$	11.9699	+	6.06183i	0.389587	+	0.197296i
$945$	−8.15651	+	12.4301i	−0.265331	+	0.404350i
$946$	1.25790	−	0.355601i	0.0408978	−	0.0115616i
$947$	−8.59827	+	8.59827i	−0.279406	+	0.279406i	−0.832872	−	0.553466i	$-0.813305\pi$
$947$	−8.59827	+	8.59827i	−0.279406	+	0.279406i	0.553466	+	0.832872i	$0.313305\pi$
$948$	0.207651	−	0.869651i	0.00674419	−	0.0282449i
$949$	11.9953			0.389384
$950$	−4.40439	+	43.6646i	−0.142897	+	1.41667i
$951$			62.7311i			2.03420i
$952$	−13.4958	+	0.555251i	−0.437400	+	0.0179958i
$953$	6.05673	+	6.05673i	0.196197	+	0.196197i	0.798367	−	0.602171i	$-0.205697\pi$
$953$	6.05673	+	6.05673i	0.196197	+	0.196197i	−0.602171	+	0.798367i	$0.705697\pi$
$954$	−12.5248	+	3.54071i	−0.405507	+	0.114635i
$955$	1.74100	+	1.14243i	0.0563374	+	0.0369682i
$956$	19.6288	+	31.9429i	0.634842	+	1.03311i
$957$	−24.0454	−	24.0454i	−0.777279	−	0.777279i
$958$	12.2452	−	21.8970i	0.395624	−	0.707460i
$959$	−18.6318			−0.601651
$960$	−49.4501	+	14.5909i	−1.59599	+	0.470918i
$961$	22.7368			0.733445
$962$	−11.6098	+	20.7608i	−0.374315	+	0.669356i
$963$	−25.5599	−	25.5599i	−0.823657	−	0.823657i
$964$	17.3179	+	28.1822i	0.557773	+	0.907689i
$965$	21.6529	−	4.49491i	0.697032	−	0.144696i
$966$	23.6379	−	6.68232i	0.760537	−	0.215000i
$967$	−34.7672	−	34.7672i	−1.11804	−	1.11804i	−0.992029	−	0.126010i	$-0.959783\pi$
$967$	−34.7672	−	34.7672i	−1.11804	−	1.11804i	−0.126010	−	0.992029i	$-0.540217\pi$
$968$	−26.0618	+	1.07225i	−0.837657	+	0.0344634i
$969$			85.4243i			2.74422i
$970$	−17.3171	−	5.45584i	−0.556020	−	0.175176i
$971$	38.8822			1.24779			0.623895	−	0.781508i	$-0.285549\pi$
$971$	38.8822			1.24779			0.623895	+	0.781508i	$0.285549\pi$
$972$	4.92427	−	20.6231i	0.157946	−	0.661485i
$973$	−1.81025	+	1.81025i	−0.0580341	+	0.0580341i
$974$	−11.4427	+	3.23480i	−0.366649	+	0.103650i
$975$	20.9670	+	48.3249i	0.671481	+	1.54764i
$976$	1.77785	+	0.900344i	0.0569076	+	0.0288193i
$977$	−6.86387	+	6.86387i	−0.219595	+	0.219595i	−0.808328	−	0.588733i	$-0.799627\pi$
$977$	−6.86387	+	6.86387i	−0.219595	+	0.219595i	0.588733	+	0.808328i	$0.299627\pi$
$978$	44.1022	+	24.6627i	1.41023	+	0.788627i
$979$			6.06117i			0.193716i
$980$	−0.132823	+	4.47016i	−0.00424289	+	0.142794i
$981$		−	37.7900i		−	1.20654i
$982$	−5.43880	+	9.72574i	−0.173559	+	0.310361i
$983$	15.3348	−	15.3348i	0.489103	−	0.489103i	−0.418920	−	0.908023i	$-0.637591\pi$
$983$	15.3348	−	15.3348i	0.489103	−	0.489103i	0.908023	+	0.418920i	$0.137591\pi$
$984$	−25.7927	−	23.7542i	−0.822241	−	0.757256i
$985$	43.1643	−	8.96042i	1.37533	−	0.285503i
$986$	16.2564	+	57.5050i	0.517708	+	1.83133i
$987$	24.1680	−	24.1680i	0.769276	−	0.769276i
$988$	−10.5380	+	44.1335i	−0.335258	+	1.40407i
$989$	4.17766			0.132842
$990$	−19.8464	+	10.3370i	−0.630759	+	0.328530i
$991$			4.21261i			0.133818i	0.997759	+	0.0669089i	$0.0213137\pi$
$991$			4.21261i			0.133818i	−0.997759	+	0.0669089i	$0.978686\pi$
$992$	13.4927	−	9.07580i	0.428393	−	0.288157i
$993$	27.3482	+	27.3482i	0.867870	+	0.867870i
$994$	3.33067	+	11.7818i	0.105642	+	0.373697i
$995$	−31.9946	+	48.7579i	−1.01430	+	1.54573i
$996$	78.4864	−	48.2297i	2.48694	−	1.52822i
$997$	41.6694	+	41.6694i	1.31968	+	1.31968i	0.914024	+	0.405660i	$0.132958\pi$
$997$	41.6694	+	41.6694i	1.31968	+	1.31968i	0.405660	+	0.914024i	$0.367042\pi$
$998$	−31.2625	−	17.4826i	−0.989598	−	0.553400i
$999$	30.5933			0.967928

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.w.a.43.13	yes	72
4.3	odd	2		1120.2.bi.a.463.4		72
5.2	odd	4	inner	280.2.w.a.267.7	yes	72
8.3	odd	2	inner	280.2.w.a.43.7	✓	72
8.5	even	2		1120.2.bi.a.463.3		72
20.7	even	4		1120.2.bi.a.687.3		72
40.27	even	4	inner	280.2.w.a.267.13	yes	72
40.37	odd	4		1120.2.bi.a.687.4		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.w.a.43.7	✓	72	8.3	odd	2	inner
280.2.w.a.43.13	yes	72	1.1	even	1	trivial
280.2.w.a.267.7	yes	72	5.2	odd	4	inner
280.2.w.a.267.13	yes	72	40.27	even	4	inner
1120.2.bi.a.463.3		72	8.5	even	2
1120.2.bi.a.463.4		72	4.3	odd	2
1120.2.bi.a.687.3		72	20.7	even	4
1120.2.bi.a.687.4		72	40.37	odd	4

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.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.690254 + 1.23432i) q^{2} +(2.03800 + 2.03800i) q^{3} +(-1.04710 - 1.70399i) q^{4} +(-1.22676 + 1.86951i) q^{5} +(-3.92228 + 1.10881i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(2.82604 - 0.116271i) q^{8} +5.30689i q^{9} +O(q^{10})\)	\(q+(-0.690254 + 1.23432i) q^{2} +(2.03800 + 2.03800i) q^{3} +(-1.04710 - 1.70399i) q^{4} +(-1.22676 + 1.86951i) q^{5} +(-3.92228 + 1.10881i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(2.82604 - 0.116271i) q^{8} +5.30689i q^{9} +(-1.46080 - 2.80465i) q^{10} -1.33341 q^{11} +(1.33874 - 5.60672i) q^{12} +(-2.58476 + 2.58476i) q^{13} +(1.36088 - 0.384714i) q^{14} +(-6.31019 + 1.30993i) q^{15} +(-1.80717 + 3.56849i) q^{16} +(3.37680 - 3.37680i) q^{17} +(-6.55040 - 3.66310i) q^{18} +6.20644i q^{19} +(4.47016 + 0.132823i) q^{20} -2.88217i q^{21} +(0.920389 - 1.64585i) q^{22} +(4.26143 - 4.26143i) q^{23} +(5.99642 + 5.52250i) q^{24} +(-1.99013 - 4.58687i) q^{25} +(-1.40629 - 4.97457i) q^{26} +(-4.70143 + 4.70143i) q^{27} +(-0.464492 + 1.94531i) q^{28} +8.84843 q^{29} +(2.73877 - 8.69299i) q^{30} +2.87458i q^{31} +(-3.15726 - 4.69379i) q^{32} +(-2.71748 - 2.71748i) q^{33} +(1.83720 + 6.49890i) q^{34} +(2.18939 - 0.454494i) q^{35} +(9.04288 - 5.55684i) q^{36} +(-3.25361 - 3.25361i) q^{37} +(-7.66074 - 4.28402i) q^{38} -10.5355 q^{39} +(-3.24949 + 5.42594i) q^{40} -4.30135 q^{41} +(3.55752 + 1.98943i) q^{42} +(0.490171 + 0.490171i) q^{43} +(1.39621 + 2.27211i) q^{44} +(-9.92127 - 6.51027i) q^{45} +(2.31850 + 8.20144i) q^{46} +(8.38536 + 8.38536i) q^{47} +(-10.9556 + 3.58958i) q^{48} +1.00000i q^{49} +(7.03537 + 0.709648i) q^{50} +13.7638 q^{51} +(7.11091 + 1.69791i) q^{52} +(1.22630 - 1.22630i) q^{53} +(-2.55790 - 9.04826i) q^{54} +(1.63577 - 2.49282i) q^{55} +(-2.08053 - 1.91609i) q^{56} +(-12.6487 + 12.6487i) q^{57} +(-6.10766 + 10.9218i) q^{58} -3.35433i q^{59} +(8.83950 + 9.38089i) q^{60} -0.498207i q^{61} +(-3.54815 - 1.98419i) q^{62} +(3.75254 - 3.75254i) q^{63} +(7.97296 - 0.657170i) q^{64} +(-1.66136 - 8.00312i) q^{65} +(5.23000 - 1.47849i) q^{66} +(7.16083 - 7.16083i) q^{67} +(-9.28987 - 2.21819i) q^{68} +17.3696 q^{69} +(-0.950245 + 3.01613i) q^{70} +8.65751i q^{71} +(0.617035 + 14.9975i) q^{72} +(-2.32039 - 2.32039i) q^{73} +(6.26182 - 1.77018i) q^{74} +(5.29216 - 13.4039i) q^{75} +(10.5757 - 6.49876i) q^{76} +(0.942861 + 0.942861i) q^{77} +(7.27216 - 13.0042i) q^{78} +0.155109 q^{79} +(-4.45437 - 7.75619i) q^{80} -3.24238 q^{81} +(2.96902 - 5.30925i) q^{82} +(11.3004 + 11.3004i) q^{83} +(-4.91119 + 3.01791i) q^{84} +(2.17044 + 10.4555i) q^{85} +(-0.943372 + 0.266686i) q^{86} +(18.0331 + 18.0331i) q^{87} +(-3.76826 + 0.155036i) q^{88} -4.54563i q^{89} +(14.8840 - 7.75230i) q^{90} +3.65541 q^{91} +(-11.7236 - 2.79930i) q^{92} +(-5.85839 + 5.85839i) q^{93} +(-16.1383 + 4.56220i) q^{94} +(-11.6030 - 7.61380i) q^{95} +(3.13145 - 16.0005i) q^{96} +(4.05986 - 4.05986i) q^{97} +(-1.23432 - 0.690254i) q^{98} -7.07624i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 8 q^{6}+O(q^{10}) \) 72 * q + 8 * q^6	\( 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) \) 72 * q + 8 * q^6 + 16 * q^10 - 16 * q^12 - 8 * q^16 + 8 * q^17 - 28 * q^18 - 20 * q^20 - 36 * q^22 - 8 * q^25 - 32 * q^26 - 4 * q^30 + 40 * q^32 + 64 * q^36 - 4 * q^40 + 20 * q^42 - 64 * q^43 + 48 * q^46 - 80 * q^48 - 32 * q^51 + 16 * q^52 - 24 * q^56 + 4 * q^58 - 80 * q^60 - 40 * q^62 - 8 * q^65 + 32 * q^66 - 24 * q^68 + 40 * q^72 - 40 * q^73 + 112 * q^75 - 8 * q^76 + 28 * q^78 - 20 * q^80 - 72 * q^81 + 24 * q^82 + 80 * q^83 + 8 * q^86 - 88 * q^88 + 136 * q^90 - 96 * q^92 - 56 * q^96 - 8 * q^97

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