LMFDB - Embedded newform 500.2.l.e.107.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [500,2,Mod(7,500)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("500.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(500, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 500 = 2^{2} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	500.l (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,10,0,-6,0,30,20,0,0,0,0,10,0,-14,0,20,0,0,-12,-50,0,0, 0,-12,0,-40,20,0,0,-50,0,60] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(34)] == traces)

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

Self dual:	no
Analytic conductor:	$3.99252010106$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 100)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			107.7
Character	$\chi$	$=$	500.107
Dual form			500.2.l.e.243.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.238186 - 1.39401i) q^{2} +(0.745599 + 0.118091i) q^{3} +(-1.88654 + 0.664067i) q^{4} +(-0.0129704 - 1.06750i) q^{6} +(-2.75590 + 2.75590i) q^{7} +(1.37506 + 2.47168i) q^{8} +(-2.31120 - 0.750953i) q^{9} +(0.712633 - 0.231549i) q^{11} +(-1.48502 + 0.272345i) q^{12} +(0.753078 + 1.47800i) q^{13} +(4.49817 + 3.18534i) q^{14} +(3.11803 - 2.50557i) q^{16} +(0.715035 + 4.51455i) q^{17} +(-0.496343 + 3.40070i) q^{18} +(2.96269 + 2.15252i) q^{19} +(-2.38025 + 1.72935i) q^{21} +(-0.492520 - 0.938267i) q^{22} +(-4.00635 + 7.86291i) q^{23} +(0.733362 + 2.00527i) q^{24} +(1.88097 - 1.40184i) q^{26} +(-3.65239 - 1.86099i) q^{27} +(3.36900 - 7.02921i) q^{28} +(-0.00370724 - 0.00510258i) q^{29} +(-1.08939 + 1.49941i) q^{31} +(-4.23547 - 3.74978i) q^{32} +(0.558683 - 0.0884866i) q^{33} +(6.12303 - 2.07207i) q^{34} +(4.85884 - 0.118090i) q^{36} +(3.22426 - 1.64284i) q^{37} +(2.29497 - 4.64273i) q^{38} +(0.386956 + 1.19093i) q^{39} +(-1.93115 + 5.94348i) q^{41} +(2.97767 + 2.90618i) q^{42} +(-6.10648 - 6.10648i) q^{43} +(-1.19064 + 0.910061i) q^{44} +(11.9152 + 3.71207i) q^{46} +(-0.184694 + 1.16611i) q^{47} +(2.62069 - 1.49994i) q^{48} -8.18997i q^{49} +3.45049i q^{51} +(-2.40220 - 2.28820i) q^{52} +(-1.44300 + 9.11077i) q^{53} +(-1.72429 + 5.53473i) q^{54} +(-10.6012 - 3.02217i) q^{56} +(1.95479 + 1.95479i) q^{57} +(-0.00623004 + 0.00638330i) q^{58} +(4.58114 - 14.0993i) q^{59} +(-0.569042 - 1.75133i) q^{61} +(2.34967 + 1.16148i) q^{62} +(8.43898 - 4.29987i) q^{63} +(-4.21840 + 6.79743i) q^{64} +(-0.256422 - 0.757734i) q^{66} +(5.08652 - 0.805626i) q^{67} +(-4.34691 - 8.04203i) q^{68} +(-3.91567 + 5.38946i) q^{69} +(-6.26883 - 8.62831i) q^{71} +(-1.32192 - 6.74515i) q^{72} +(6.26568 + 3.19252i) q^{73} +(-3.05811 - 4.10335i) q^{74} +(-7.01865 - 2.09338i) q^{76} +(-1.32582 + 2.60207i) q^{77} +(1.56800 - 0.823082i) q^{78} +(-2.90976 + 2.11406i) q^{79} +(3.39461 + 2.46633i) q^{81} +(8.74525 + 1.27640i) q^{82} +(-0.308214 - 1.94599i) q^{83} +(3.34201 - 4.84312i) q^{84} +(-7.05803 + 9.96698i) q^{86} +(-0.00216155 - 0.00424227i) q^{87} +(1.55223 + 1.44301i) q^{88} +(-3.79225 + 1.23218i) q^{89} +(-6.14862 - 1.99781i) q^{91} +(2.33662 - 17.4941i) q^{92} +(-0.989314 + 0.989314i) q^{93} +(1.66956 - 0.0202857i) q^{94} +(-2.71514 - 3.29600i) q^{96} +(6.43432 + 1.01910i) q^{97} +(-11.4169 + 1.95073i) q^{98} -1.82092 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 10 q^{4} - 6 q^{6} + 30 q^{8} + 20 q^{9} + 10 q^{14} - 14 q^{16} + 20 q^{18} - 12 q^{21} - 50 q^{22} - 12 q^{26} - 40 q^{28} + 20 q^{29} - 50 q^{32} + 60 q^{34} - 10 q^{36} - 40 q^{37} + 70 q^{38}+ \cdots - 70 q^{98}+O(q^{100}) $ 96 * q + 10 * q^4 - 6 * q^6 + 30 * q^8 + 20 * q^9 + 10 * q^14 - 14 * q^16 + 20 * q^18 - 12 * q^21 - 50 * q^22 - 12 * q^26 - 40 * q^28 + 20 * q^29 - 50 * q^32 + 60 * q^34 - 10 * q^36 - 40 * q^37 + 70 * q^38 - 28 * q^41 + 60 * q^42 - 60 * q^44 - 6 * q^46 - 100 * q^52 - 80 * q^53 - 120 * q^54 - 6 * q^56 - 20 * q^57 - 120 * q^58 + 12 * q^61 - 20 * q^64 - 30 * q^66 - 10 * q^68 + 20 * q^69 + 150 * q^72 + 140 * q^77 + 130 * q^78 - 36 * q^81 - 50 * q^82 + 90 * q^84 - 6 * q^86 - 110 * q^88 - 160 * q^89 - 90 * q^92 + 60 * q^93 + 170 * q^94 + 14 * q^96 - 70 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/500\mathbb{Z}\right)^\times$.

$n$	$251$	$377$
$\chi(n)$	$-1$	$e\left(\frac{13}{20}\right)$

Coefficient data

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

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

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

$2$	−0.238186	−	1.39401i	−0.168423	−	0.985715i
$2$	−0.238186	−	1.39401i	−0.168423	−	0.985715i
$3$	0.745599	+	0.118091i	0.430472	+	0.0681801i	0.367911	−	0.929861i	$-0.380073\pi$
$3$	0.745599	+	0.118091i	0.430472	+	0.0681801i	0.0625612	+	0.998041i	$0.480073\pi$
$4$	−1.88654	+	0.664067i	−0.943268	+	0.332034i
$5$		0			0
$5$		0			0
$6$	−0.0129704	−	1.06750i	−0.00529516	−	0.435806i
$7$	−2.75590	+	2.75590i	−1.04163	+	1.04163i	−0.0425375	+	0.999095i	$0.513544\pi$
$7$	−2.75590	+	2.75590i	−1.04163	+	1.04163i	−0.999095	+	0.0425375i	$0.986456\pi$
$8$	1.37506	+	2.47168i	0.486158	+	0.873871i
$9$	−2.31120	−	0.750953i	−0.770399	−	0.250318i
$10$		0			0
$11$	0.712633	−	0.231549i	0.214867	−	0.0698145i	−0.199606	−	0.979876i	$-0.563966\pi$
$11$	0.712633	−	0.231549i	0.214867	−	0.0698145i	0.414473	+	0.910062i	$0.363966\pi$
$12$	−1.48502	+	0.272345i	−0.428688	+	0.0786191i
$13$	0.753078	+	1.47800i	0.208866	+	0.409923i	0.971545	−	0.236854i	$-0.0761164\pi$
$13$	0.753078	+	1.47800i	0.208866	+	0.409923i	−0.762679	+	0.646777i	$0.776116\pi$
$14$	4.49817	+	3.18534i	1.20219	+	0.851318i
$15$		0			0
$16$	3.11803	−	2.50557i	0.779507	−	0.626393i
$17$	0.715035	+	4.51455i	0.173421	+	1.09494i	0.908784	+	0.417266i	$0.137012\pi$
$17$	0.715035	+	4.51455i	0.173421	+	1.09494i	−0.735363	+	0.677674i	$0.762988\pi$
$18$	−0.496343	+	3.40070i	−0.116989	+	0.801553i
$19$	2.96269	+	2.15252i	0.679689	+	0.493823i	0.873254	−	0.487265i	$-0.162005\pi$
$19$	2.96269	+	2.15252i	0.679689	+	0.493823i	−0.193566	+	0.981087i	$0.562005\pi$
$20$		0			0
$21$	−2.38025	+	1.72935i	−0.519412	+	0.377375i
$22$	−0.492520	−	0.938267i	−0.105006	−	0.200039i
$23$	−4.00635	+	7.86291i	−0.835382	+	1.63953i	−0.0685797	+	0.997646i	$0.521847\pi$
$23$	−4.00635	+	7.86291i	−0.835382	+	1.63953i	−0.766802	+	0.641884i	$0.778153\pi$
$24$	0.733362	+	2.00527i	0.149697	+	0.409323i
$25$		0			0
$26$	1.88097	−	1.40184i	0.368889	−	0.274923i
$27$	−3.65239	−	1.86099i	−0.702903	−	0.358147i
$28$	3.36900	−	7.02921i	0.636681	−	1.32839i
$29$	−0.00370724	−	0.00510258i	−0.000688418	−	0.000947526i	0.808673	−	0.588259i	$-0.200186\pi$
$29$	−0.00370724	−	0.00510258i	−0.000688418	−	0.000947526i	−0.809361	+	0.587311i	$0.800186\pi$
$30$		0			0
$31$	−1.08939	+	1.49941i	−0.195660	+	0.269302i	−0.895563	−	0.444936i	$-0.853227\pi$
$31$	−1.08939	+	1.49941i	−0.195660	+	0.269302i	0.699903	+	0.714238i	$0.253227\pi$
$32$	−4.23547	−	3.74978i	−0.748732	−	0.662873i
$33$	0.558683	−	0.0884866i	0.0972542	−	0.0154035i
$34$	6.12303	−	2.07207i	1.05009	−	0.355357i
$35$		0			0
$36$	4.85884	−	0.118090i	0.809806	−	0.0196816i
$37$	3.22426	−	1.64284i	0.530065	−	0.270082i	−0.168409	−	0.985717i	$-0.553863\pi$
$37$	3.22426	−	1.64284i	0.530065	−	0.270082i	0.698474	+	0.715636i	$0.253863\pi$
$38$	2.29497	−	4.64273i	0.372293	−	0.753150i
$39$	0.386956	+	1.19093i	0.0619625	+	0.190701i
$40$		0			0
$41$	−1.93115	+	5.94348i	−0.301595	+	0.928215i	0.679330	+	0.733832i	$0.262270\pi$
$41$	−1.93115	+	5.94348i	−0.301595	+	0.928215i	−0.980926	+	0.194383i	$0.937730\pi$
$42$	2.97767	+	2.90618i	0.459465	+	0.448434i
$43$	−6.10648	−	6.10648i	−0.931230	−	0.931230i	0.0665532	−	0.997783i	$-0.478800\pi$
$43$	−6.10648	−	6.10648i	−0.931230	−	0.931230i	−0.997783	+	0.0665532i	$0.978800\pi$
$44$	−1.19064	+	0.910061i	−0.179496	+	0.137197i
$45$		0			0
$46$	11.9152	+	3.71207i	1.75681	+	0.547314i
$47$	−0.184694	+	1.16611i	−0.0269404	+	0.170095i	−0.997490	−	0.0708061i	$-0.977443\pi$
$47$	−0.184694	+	1.16611i	−0.0269404	+	0.170095i	0.970550	+	0.240901i	$0.0774429\pi$
$48$	2.62069	−	1.49994i	0.378264	−	0.216498i
$49$		−	8.18997i		−	1.17000i
$50$		0			0
$51$			3.45049i			0.483165i
$52$	−2.40220	−	2.28820i	−0.333125	−	0.317316i
$53$	−1.44300	+	9.11077i	−0.198212	+	1.25146i	0.665086	+	0.746767i	$0.268395\pi$
$53$	−1.44300	+	9.11077i	−0.198212	+	1.25146i	−0.863298	+	0.504694i	$0.831605\pi$
$54$	−1.72429	+	5.53473i	−0.234646	+	0.753182i
$55$		0			0
$56$	−10.6012	−	3.02217i	−1.41665	−	0.403854i
$57$	1.95479	+	1.95479i	0.258918	+	0.258918i
$58$	−0.00623004	+	0.00638330i	−0.000818045	+	0.000838168i
$59$	4.58114	−	14.0993i	0.596413	−	1.83557i	0.0488499	−	0.998806i	$-0.484444\pi$
$59$	4.58114	−	14.0993i	0.596413	−	1.83557i	0.547563	−	0.836764i	$-0.315556\pi$
$60$		0			0
$61$	−0.569042	−	1.75133i	−0.0728583	−	0.224235i	0.907996	−	0.418980i	$-0.137612\pi$
$61$	−0.569042	−	1.75133i	−0.0728583	−	0.224235i	−0.980854	+	0.194745i	$0.937612\pi$
$62$	2.34967	+	1.16148i	0.298409	+	0.147508i
$63$	8.43898	−	4.29987i	1.06321	−	0.541733i
$64$	−4.21840	+	6.79743i	−0.527301	+	0.849679i
$65$		0			0
$66$	−0.256422	−	0.757734i	−0.0315633	−	0.0932706i
$67$	5.08652	−	0.805626i	0.621417	−	0.0984228i	0.162216	−	0.986755i	$-0.448136\pi$
$67$	5.08652	−	0.805626i	0.621417	−	0.0984228i	0.459201	+	0.888332i	$0.348136\pi$
$68$	−4.34691	−	8.04203i	−0.527140	−	0.975240i
$69$	−3.91567	+	5.38946i	−0.471392	+	0.648815i
$70$		0			0
$71$	−6.26883	−	8.62831i	−0.743973	−	1.02399i	−0.998380	−	0.0568943i	$-0.981880\pi$
$71$	−6.26883	−	8.62831i	−0.743973	−	1.02399i	0.254407	−	0.967097i	$-0.418120\pi$
$72$	−1.32192	−	6.74515i	−0.155790	−	0.794923i
$73$	6.26568	+	3.19252i	0.733342	+	0.373656i	0.780437	−	0.625234i	$-0.214996\pi$
$73$	6.26568	+	3.19252i	0.733342	+	0.373656i	−0.0470953	+	0.998890i	$0.514996\pi$
$74$	−3.05811	−	4.10335i	−0.355498	−	0.477005i
$75$		0			0
$76$	−7.01865	−	2.09338i	−0.805094	−	0.240127i
$77$	−1.32582	+	2.60207i	−0.151091	+	0.296533i
$78$	1.56800	−	0.823082i	0.177541	−	0.0931957i
$79$	−2.90976	+	2.11406i	−0.327373	+	0.237851i	−0.739315	−	0.673359i	$-0.764851\pi$
$79$	−2.90976	+	2.11406i	−0.327373	+	0.237851i	0.411942	+	0.911210i	$0.364851\pi$
$80$		0			0
$81$	3.39461	+	2.46633i	0.377179	+	0.274036i
$82$	8.74525	+	1.27640i	0.965751	+	0.140955i
$83$	−0.308214	−	1.94599i	−0.0338309	−	0.213600i	0.964982	−	0.262317i	$-0.0844867\pi$
$83$	−0.308214	−	1.94599i	−0.0338309	−	0.213600i	−0.998813	+	0.0487173i	$0.984487\pi$
$84$	3.34201	−	4.84312i	0.364643	−	0.528428i
$85$		0			0
$86$	−7.05803	+	9.96698i	−0.761087	+	1.07477i
$87$	−0.00216155	−	0.00424227i	−0.000231742	−	0.000454820i
$88$	1.55223	+	1.44301i	0.165468	+	0.153825i
$89$	−3.79225	+	1.23218i	−0.401978	+	0.130611i	−0.503027	−	0.864271i	$-0.667780\pi$
$89$	−3.79225	+	1.23218i	−0.401978	+	0.130611i	0.101049	+	0.994881i	$0.467780\pi$
$90$		0			0
$91$	−6.14862	−	1.99781i	−0.644551	−	0.209427i
$92$	2.33662	−	17.4941i	0.243610	−	1.82389i
$93$	−0.989314	+	0.989314i	−0.102587	+	0.102587i
$94$	1.66956	−	0.0202857i	0.172202	−	0.00209231i
$95$		0			0
$96$	−2.71514	−	3.29600i	−0.277113	−	0.336397i
$97$	6.43432	+	1.01910i	0.653306	+	0.103474i	0.474285	−	0.880372i	$-0.342707\pi$
$97$	6.43432	+	1.01910i	0.653306	+	0.103474i	0.179022	+	0.983845i	$0.442707\pi$
$98$	−11.4169	+	1.95073i	−1.15328	+	0.197054i
$99$	−1.82092			−0.183009
$100$		0			0
$101$	8.26277			0.822176			0.411088	−	0.911596i	$-0.365149\pi$
$101$	8.26277			0.822176			0.411088	+	0.911596i	$0.365149\pi$
$102$	4.81002	−	0.821857i	0.476263	−	0.0813760i
$103$	−5.57914	−	0.883649i	−0.549729	−	0.0870685i	−0.124610	−	0.992206i	$-0.539768\pi$
$103$	−5.57914	−	0.883649i	−0.549729	−	0.0870685i	−0.425119	+	0.905137i	$0.639768\pi$
$104$	−2.61761	+	3.89371i	−0.256678	+	0.381809i
$105$		0			0
$106$	13.0442	−	0.158491i	1.26697	−	0.0153940i
$107$	−2.63780	+	2.63780i	−0.255005	+	0.255005i	−0.823019	−	0.568014i	$-0.807712\pi$
$107$	−2.63780	+	2.63780i	−0.255005	+	0.255005i	0.568014	+	0.823019i	$0.307712\pi$
$108$	8.12618	+	1.08538i	0.781942	+	0.104441i
$109$	2.78468	+	0.904799i	0.266724	+	0.0866640i	0.439326	−	0.898328i	$-0.355217\pi$
$109$	2.78468	+	0.904799i	0.266724	+	0.0866640i	−0.172602	+	0.984992i	$0.555217\pi$
$110$		0			0
$111$	2.59801	−	0.844145i	0.246592	−	0.0801227i
$112$	−1.68787	+	15.4981i	−0.159489	+	1.46443i
$113$	−6.81465	−	13.3745i	−0.641068	−	1.25817i	−0.951523	−	0.307579i	$-0.900481\pi$
$113$	−6.81465	−	13.3745i	−0.641068	−	1.25817i	0.310455	−	0.950588i	$-0.399519\pi$
$114$	2.25939	−	3.19060i	0.211612	−	0.298827i
$115$		0			0
$116$	0.0103823	+	0.00716434i	0.000963972	+	0.000665192i
$117$	−0.630603	−	3.98147i	−0.0582993	−	0.368087i
$118$	−20.7457	−	3.02791i	−1.90980	−	0.278741i
$119$	−14.4122	−	10.4711i	−1.32117	−	0.959884i
$120$		0			0
$121$	−8.44496	+	6.13562i	−0.767723	+	0.557784i
$122$	−2.30584	+	1.21039i	−0.208761	+	0.109584i
$123$	−2.14174	+	4.20340i	−0.193114	+	0.379008i
$124$	1.05946	−	3.55212i	0.0951420	−	0.318990i
$125$		0			0
$126$	−8.00412	−	10.7399i	−0.713064	−	0.956783i
$127$	10.0005	+	5.09550i	0.887400	+	0.452153i	0.837396	−	0.546596i	$-0.184077\pi$
$127$	10.0005	+	5.09550i	0.887400	+	0.452153i	0.0500037	+	0.998749i	$0.484077\pi$
$128$	10.4805	+	4.26145i	0.926350	+	0.376663i
$129$	−3.83187	−	5.27411i	−0.337377	−	0.464360i
$130$		0			0
$131$	0.647820	−	0.891647i	0.0566003	−	0.0779036i	−0.779779	−	0.626055i	$-0.784668\pi$
$131$	0.647820	−	0.891647i	0.0566003	−	0.0779036i	0.836379	+	0.548152i	$0.184668\pi$
$132$	−0.995213	+	0.537936i	−0.0866222	+	0.0468213i
$133$	−14.0970	+	2.23275i	−1.22237	+	0.193604i
$134$	−2.33459	−	6.89878i	−0.201678	−	0.595964i
$135$		0			0
$136$	−10.1753	+	7.97513i	−0.872526	+	0.683862i
$137$	−6.71304	+	3.42046i	−0.573534	+	0.292230i	−0.716601	−	0.697483i	$-0.754303\pi$
$137$	−6.71304	+	3.42046i	−0.573534	+	0.292230i	0.143068	+	0.989713i	$0.454303\pi$
$138$	8.44563	+	4.17480i	0.718940	+	0.355383i
$139$	3.91451	+	12.0476i	0.332024	+	1.02187i	0.968169	+	0.250296i	$0.0805280\pi$
$139$	3.91451	+	12.0476i	0.332024	+	1.02187i	−0.636145	+	0.771570i	$0.719472\pi$
$140$		0			0
$141$	−0.275415	+	0.847641i	−0.0231941	+	0.0713842i
$142$	−10.5348	+	10.7940i	−0.884062	+	0.905809i
$143$	0.878896	+	0.878896i	0.0734970	+	0.0734970i
$144$	−9.08795	+	3.44937i	−0.757329	+	0.287448i
$145$		0			0
$146$	2.95802	−	9.49484i	0.244807	−	0.785798i
$147$	0.967165	−	6.10644i	0.0797704	−	0.503651i
$148$	−4.99172	+	5.24040i	−0.410317	+	0.430759i
$149$			15.6649i			1.28332i	0.766990	+	0.641659i	$0.221753\pi$
$149$			15.6649i			1.28332i	−0.766990	+	0.641659i	$0.778247\pi$
$150$		0			0
$151$			13.1571i			1.07071i	0.844628	+	0.535353i	$0.179821\pi$
$151$			13.1571i			1.07071i	−0.844628	+	0.535353i	$0.820179\pi$
$152$	−1.24646	+	10.2827i	−0.101101	+	0.834036i
$153$	1.73763	−	10.9710i	0.140479	−	0.886951i
$154$	3.94311	+	1.22843i	0.317745	+	0.0989900i
$155$		0			0
$156$	−1.52086	−	1.98976i	−0.121766	−	0.159308i
$157$	−10.7749	−	10.7749i	−0.859930	−	0.859930i	0.131400	−	0.991329i	$-0.458053\pi$
$157$	−10.7749	−	10.7749i	−0.859930	−	0.859930i	−0.991329	+	0.131400i	$0.958053\pi$
$158$	3.64009	+	3.55270i	0.289590	+	0.282637i
$159$	−2.15181	+	6.62258i	−0.170649	+	0.525205i
$160$		0			0
$161$	−10.6283	−	32.7105i	−0.837626	−	2.57795i
$162$	2.62954	−	5.31957i	0.206596	−	0.417945i
$163$	10.0328	−	5.11197i	0.785830	−	0.400401i	−0.0145493	−	0.999894i	$-0.504631\pi$
$163$	10.0328	−	5.11197i	0.785830	−	0.400401i	0.800380	+	0.599494i	$0.204631\pi$
$164$	−0.303680	−	12.4950i	−0.0237134	−	0.975695i
$165$		0			0
$166$	−2.63932	+	0.893160i	−0.204851	+	0.0693227i
$167$	−4.33254	+	0.686207i	−0.335262	+	0.0531003i	−0.321796	−	0.946809i	$-0.604286\pi$
$167$	−4.33254	+	0.686207i	−0.335262	+	0.0531003i	−0.0134660	+	0.999909i	$0.504286\pi$
$168$	−7.54739	−	3.50524i	−0.582293	−	0.270435i
$169$	6.02386	−	8.29113i	0.463374	−	0.637779i
$170$		0			0
$171$	−5.23092	−	7.19975i	−0.400019	−	0.550579i
$172$	15.5752	+	7.46498i	1.18760	+	0.569199i
$173$	14.5877	+	7.43280i	1.10908	+	0.565105i	0.909888	−	0.414855i	$-0.136168\pi$
$173$	14.5877	+	7.43280i	1.10908	+	0.565105i	0.199194	+	0.979960i	$0.436168\pi$
$174$	−0.00539893	+	0.00402367i	−0.000409292	+	0.000305034i
$175$		0			0
$176$	1.64185	−	2.50753i	0.123759	−	0.189012i
$177$	5.08070	−	9.97143i	0.381888	−	0.749498i
$178$	2.62093	+	4.99296i	0.196447	+	0.374238i
$179$	−10.7676	+	7.82314i	−0.804811	+	0.584729i	−0.912321	−	0.409475i	$-0.865712\pi$
$179$	−10.7676	+	7.82314i	−0.804811	+	0.584729i	0.107511	+	0.994204i	$0.465712\pi$
$180$		0			0
$181$	12.3668	+	8.98499i	0.919215	+	0.667849i	0.943329	−	0.331860i	$-0.107676\pi$
$181$	12.3668	+	8.98499i	0.919215	+	0.667849i	−0.0241132	+	0.999709i	$0.507676\pi$
$182$	−1.32045	+	9.04710i	−0.0978786	+	0.670616i
$183$	−0.217460	−	1.37299i	−0.0160751	−	0.101494i
$184$	−24.9436	+	0.909572i	−1.83886	+	0.0670545i
$185$		0			0
$186$	1.61476	+	1.14347i	0.118400	+	0.0838436i
$187$	1.55490	+	3.05166i	0.113705	+	0.223159i
$188$	−0.425945	−	2.32256i	−0.0310652	−	0.169390i
$189$	15.1943	−	4.93693i	1.10522	−	0.359109i
$190$		0			0
$191$	9.06811	+	2.94641i	0.656145	+	0.213194i	0.618122	−	0.786082i	$-0.287894\pi$
$191$	9.06811	+	2.94641i	0.656145	+	0.213194i	0.0380234	+	0.999277i	$0.487894\pi$
$192$	−3.94796	+	4.57000i	−0.284919	+	0.329812i
$193$	6.86588	−	6.86588i	0.494217	−	0.494217i	−0.415415	−	0.909632i	$-0.636364\pi$
$193$	6.86588	−	6.86588i	0.494217	−	0.494217i	0.909632	+	0.415415i	$0.136364\pi$
$194$	−0.111931	−	9.21225i	−0.00803620	−	0.661401i
$195$		0			0
$196$	5.43869	+	15.4507i	0.388478	+	1.10362i
$197$	−13.0003	−	2.05905i	−0.926237	−	0.146701i	−0.324947	−	0.945732i	$-0.605346\pi$
$197$	−13.0003	−	2.05905i	−0.926237	−	0.146701i	−0.601290	+	0.799031i	$0.705346\pi$
$198$	0.433716	+	2.53838i	0.0308229	+	0.180395i
$199$	25.8172			1.83013			0.915067	−	0.403302i	$-0.132137\pi$
$199$	25.8172			1.83013			0.915067	+	0.403302i	$0.132137\pi$
$200$		0			0
$201$	3.88764			0.274213
$202$	−1.96807	−	11.5184i	−0.138473	−	0.810431i
$203$	0.0242790	+	0.00384542i	0.00170405	+	0.000269895i
$204$	−2.29136	−	6.50947i	−0.160427	−	0.455754i
$205$		0			0
$206$	0.0970547	+	7.98786i	0.00676212	+	0.556541i
$207$	15.1641	−	15.1641i	1.05398	−	1.05398i
$208$	6.05135	+	2.72155i	0.419586	+	0.188706i
$209$	2.60973	+	0.847952i	0.180519	+	0.0586540i
$210$		0			0
$211$	23.5520	−	7.65252i	1.62139	−	0.526821i	0.649120	−	0.760686i	$-0.275137\pi$
$211$	23.5520	−	7.65252i	1.62139	−	0.526821i	0.972269	+	0.233865i	$0.0751373\pi$
$212$	−3.32789	−	18.1460i	−0.228560	−	1.24628i
$213$	−3.65511	−	7.17356i	−0.250444	−	0.491524i
$214$	4.30540	+	3.04883i	0.294311	+	0.208414i
$215$		0			0
$216$	−0.422504	−	11.5865i	−0.0287478	−	0.788362i
$217$	−1.12999	−	7.13447i	−0.0767087	−	0.484320i
$218$	0.598028	−	4.09739i	0.0405036	−	0.277510i
$219$	4.29468	+	3.12027i	0.290207	+	0.210848i
$220$		0			0
$221$	−6.13403	+	4.45663i	−0.412619	+	0.299785i
$222$	−1.79556	−	3.42059i	−0.120510	−	0.229575i
$223$	−0.350575	+	0.688042i	−0.0234762	+	0.0460747i	−0.902447	−	0.430801i	$-0.858231\pi$
$223$	−0.350575	+	0.688042i	−0.0234762	+	0.0460747i	0.878971	+	0.476876i	$0.158231\pi$
$224$	22.0065	−	1.33851i	1.47037	−	0.0894329i
$225$		0			0
$226$	−17.0210	+	12.6853i	−1.13222	+	0.843814i
$227$	−7.51174	−	3.82742i	−0.498572	−	0.254035i	0.186574	−	0.982441i	$-0.440262\pi$
$227$	−7.51174	−	3.82742i	−0.498572	−	0.254035i	−0.685146	+	0.728406i	$0.740262\pi$
$228$	−4.98589	−	2.38967i	−0.330198	−	0.158260i
$229$	13.8017	+	18.9964i	0.912042	+	1.25532i	0.966465	+	0.256800i	$0.0826682\pi$
$229$	13.8017	+	18.9964i	0.912042	+	1.25532i	−0.0544226	+	0.998518i	$0.517332\pi$
$230$		0			0
$231$	−1.29581	+	1.78353i	−0.0852583	+	0.117348i
$232$	0.00751426	−	0.0161795i	0.000493335	−	0.00106224i
$233$	2.19561	−	0.347751i	0.143839	−	0.0227819i	−0.0840996	−	0.996457i	$-0.526801\pi$
$233$	2.19561	−	0.347751i	0.143839	−	0.0227819i	0.227939	+	0.973675i	$0.426801\pi$
$234$	−5.40001	+	1.82740i	−0.353010	+	0.119461i
$235$		0			0
$236$	0.720398	+	29.6410i	0.0468939	+	1.92946i
$237$	−2.41917	+	1.23263i	−0.157142	+	0.0800677i
$238$	−11.1640	+	22.5849i	−0.723657	+	1.46396i
$239$	−0.258139	−	0.794470i	−0.0166976	−	0.0513900i	0.942361	−	0.334599i	$-0.108601\pi$
$239$	−0.258139	−	0.794470i	−0.0166976	−	0.0513900i	−0.959058	+	0.283209i	$0.908601\pi$
$240$		0			0
$241$	3.75910	−	11.5693i	0.242145	−	0.745245i	−0.753948	−	0.656934i	$-0.771853\pi$
$241$	3.75910	−	11.5693i	0.242145	−	0.745245i	0.996093	−	0.0883110i	$-0.0281469\pi$
$242$	10.5646	+	10.3109i	0.679118	+	0.662813i
$243$	10.9354	+	10.9354i	0.701508	+	0.701508i
$244$	2.23652	+	2.92606i	0.143178	+	0.187322i
$245$		0			0
$246$	6.36972	+	1.98442i	0.406118	+	0.126522i
$247$	−0.950287	+	5.99987i	−0.0604653	+	0.381763i
$248$	−5.20404	−	0.630830i	−0.330457	−	0.0400577i
$249$		−	1.48732i		−	0.0942554i
$250$		0			0
$251$			5.53474i			0.349350i	0.984626	+	0.174675i	$0.0558875\pi$
$251$			5.53474i			0.349350i	−0.984626	+	0.174675i	$0.944113\pi$
$252$	−13.0650	+	13.7159i	−0.823019	+	0.864021i
$253$	−1.03441	+	6.53103i	−0.0650330	+	0.410602i
$254$	4.72122	−	15.1545i	0.296236	−	0.950876i
$255$		0			0
$256$	3.44422	−	15.6249i	0.215264	−	0.976556i
$257$	13.0870	+	13.0870i	0.816347	+	0.816347i	0.985577	−	0.169230i	$-0.0541280\pi$
$257$	13.0870	+	13.0870i	0.816347	+	0.816347i	−0.169230	+	0.985577i	$0.554128\pi$
$258$	−6.43948	+	6.59788i	−0.400904	+	0.410766i
$259$	−4.35823	+	13.4132i	−0.270807	+	0.833459i
$260$		0			0
$261$	0.00473637	+	0.0145770i	0.000293174	+	0.000902296i
$262$	−1.39727	−	0.690690i	−0.0863235	−	0.0426710i
$263$	10.4335	−	5.31614i	0.643358	−	0.327807i	−0.101692	−	0.994816i	$-0.532426\pi$
$263$	10.4335	−	5.31614i	0.643358	−	0.327807i	0.745050	+	0.667009i	$0.232426\pi$
$264$	0.986934	+	1.25921i	0.0607416	+	0.0774990i
$265$		0			0
$266$	6.47019	+	19.1196i	0.396713	+	1.17230i
$267$	−2.97301	+	0.470879i	−0.181945	+	0.0288173i
$268$	−9.06091	+	4.89763i	−0.553483	+	0.299171i
$269$	−2.93900	+	4.04519i	−0.179194	+	0.246640i	−0.889160	−	0.457597i	$-0.848710\pi$
$269$	−2.93900	+	4.04519i	−0.179194	+	0.246640i	0.709966	+	0.704236i	$0.248710\pi$
$270$		0			0
$271$	14.8746	+	20.4731i	0.903565	+	1.24365i	0.969317	+	0.245815i	$0.0790556\pi$
$271$	14.8746	+	20.4731i	0.903565	+	1.24365i	−0.0657513	+	0.997836i	$0.520944\pi$
$272$	13.5410	+	12.2849i	0.821046	+	0.744884i
$273$	−4.34849	−	2.21566i	−0.263182	−	0.134098i
$274$	6.36712	+	8.54335i	0.384652	+	0.516122i
$275$		0			0
$276$	3.80809	−	12.7677i	0.229220	−	0.768524i
$277$	−6.96028	+	13.6603i	−0.418203	+	0.820769i	0.581770	+	0.813354i	$0.302360\pi$
$277$	−6.96028	+	13.6603i	−0.418203	+	0.820769i	−0.999973	+	0.00741564i	$0.997640\pi$
$278$	15.8621	−	8.32644i	0.951348	−	0.499387i
$279$	3.64378	−	2.64736i	0.218147	−	0.158493i
$280$		0			0
$281$	−17.8125	−	12.9415i	−1.06260	−	0.772026i	−0.0880347	−	0.996117i	$-0.528059\pi$
$281$	−17.8125	−	12.9415i	−1.06260	−	0.772026i	−0.974568	+	0.224091i	$0.928059\pi$
$282$	1.24722	+	0.182036i	0.0742709	+	0.0108401i
$283$	0.402261	+	2.53977i	0.0239119	+	0.150974i	0.996755	−	0.0804900i	$-0.0256485\pi$
$283$	0.402261	+	2.53977i	0.0239119	+	0.150974i	−0.972844	+	0.231464i	$0.925649\pi$
$284$	17.5561	+	12.1147i	1.04177	+	0.718874i
$285$		0			0
$286$	1.01585	−	1.43453i	0.0600685	−	0.0848257i
$287$	−11.0576	−	21.7017i	−0.652707	−	1.28101i
$288$	6.97309	+	11.8471i	0.410893	+	0.698098i
$289$	−3.70196	+	1.20284i	−0.217763	+	0.0707554i
$290$		0			0
$291$	4.67708	+	1.51967i	0.274175	+	0.0890849i
$292$	−13.9405	−	1.86198i	−0.815804	−	0.108964i
$293$	12.9784	−	12.9784i	0.758205	−	0.758205i	−0.217790	−	0.975996i	$-0.569885\pi$
$293$	12.9784	−	12.9784i	0.758205	−	0.758205i	0.975996	+	0.217790i	$0.0698849\pi$
$294$	−8.74281	+	0.106228i	−0.509891	+	0.00619532i
$295$		0			0
$296$	8.49414	+	5.71033i	0.493712	+	0.331906i
$297$	−3.03372	−	0.480494i	−0.176034	−	0.0278811i
$298$	21.8370	−	3.73115i	1.26498	−	0.216140i
$299$	−14.6385			−0.846564
$300$		0			0
$301$	33.6577			1.94000
$302$	18.3411	−	3.13382i	1.05541	−	0.180331i
$303$	6.16071	+	0.975761i	0.353924	+	0.0560560i
$304$	14.6311	−	0.711611i	0.839149	−	0.0408137i
$305$		0			0
$306$	−15.7076	+	0.190851i	−0.897941	+	0.0109102i
$307$	−5.84355	+	5.84355i	−0.333509	+	0.333509i	−0.853917	−	0.520409i	$-0.825780\pi$
$307$	−5.84355	+	5.84355i	−0.333509	+	0.333509i	0.520409	+	0.853917i	$0.325780\pi$
$308$	0.773259	−	5.78933i	0.0440605	−	0.329878i
$309$	−4.05545	−	1.31770i	−0.230707	−	0.0749611i
$310$		0			0
$311$	14.5346	−	4.72259i	0.824184	−	0.267794i	0.133590	−	0.991037i	$-0.457349\pi$
$311$	14.5346	−	4.72259i	0.824184	−	0.267794i	0.690594	+	0.723243i	$0.257349\pi$
$312$	−2.41150	+	2.59403i	−0.136524	+	0.146858i
$313$	−12.1792	−	23.9030i	−0.688408	−	1.35108i	−0.925186	−	0.379513i	$-0.876092\pi$
$313$	−12.1792	−	23.9030i	−0.688408	−	1.35108i	0.236778	−	0.971564i	$-0.423908\pi$
$314$	−12.4539	+	17.5867i	−0.702814	+	0.992477i
$315$		0			0
$316$	4.08548	−	5.92053i	0.229826	−	0.333056i
$317$	−0.573817	−	3.62294i	−0.0322288	−	0.203484i	0.966320	−	0.257345i	$-0.0828475\pi$
$317$	−0.573817	−	3.62294i	−0.0322288	−	0.203484i	−0.998548	+	0.0538600i	$0.982848\pi$
$318$	9.74448	+	1.42224i	0.546443	+	0.0797552i
$319$	−0.00382340	−	0.00277786i	−0.000214069	−	0.000155530i
$320$		0			0
$321$	−2.27824	+	1.65524i	−0.127159	+	0.0923864i
$322$	−43.0673	+	22.6071i	−2.40005	+	1.25985i
$323$	−7.59925	+	14.9144i	−0.422834	+	0.829858i
$324$	−8.04186	−	2.39857i	−0.446770	−	0.133254i
$325$		0			0
$326$	−9.51582	−	12.7683i	−0.527032	−	0.707168i
$327$	1.96941	+	1.00346i	0.108909	+	0.0554917i
$328$	−17.3458	+	3.39946i	−0.957763	+	0.187704i
$329$	−2.70469	−	3.72268i	−0.149114	−	0.205238i
$330$		0			0
$331$	−8.96644	+	12.3412i	−0.492840	+	0.678336i	−0.980909	−	0.194469i	$-0.937702\pi$
$331$	−8.96644	+	12.3412i	−0.492840	+	0.678336i	0.488069	+	0.872805i	$0.337702\pi$
$332$	1.87372	+	3.46650i	0.102834	+	0.190249i
$333$	−8.68560	+	1.37566i	−0.475968	+	0.0753859i
$334$	1.98853	+	5.87616i	0.108807	+	0.321529i
$335$		0			0
$336$	−3.08867	+	11.3560i	−0.168501	+	0.619523i
$337$	26.0429	−	13.2695i	1.41865	−	0.722838i	0.434581	−	0.900633i	$-0.356896\pi$
$337$	26.0429	−	13.2695i	1.41865	−	0.722838i	0.984068	+	0.177795i	$0.0568964\pi$
$338$	−12.9927	−	6.42250i	−0.706711	−	0.349338i
$339$	−3.50158	−	10.7768i	−0.190180	−	0.585314i
$340$		0			0
$341$	−0.429146	+	1.32078i	−0.0232396	+	0.0715241i
$342$	−8.79060	+	9.00684i	−0.475341	+	0.487034i
$343$	3.27944	+	3.27944i	0.177073	+	0.177073i
$344$	6.69647	−	23.4901i	0.361050	−	1.26650i
$345$		0			0
$346$	6.88683	−	22.1058i	0.370238	−	1.18842i
$347$	−0.393873	+	2.48682i	−0.0211442	+	0.133499i	−0.996002	−	0.0893271i	$-0.971528\pi$
$347$	−0.393873	+	2.48682i	−0.0211442	+	0.133499i	0.974858	+	0.222827i	$0.0715284\pi$
$348$	0.00689499	+	0.00656779i	0.000369610	+	0.000352070i
$349$		−	18.8483i		−	1.00893i	−0.863434	−	0.504463i	$-0.831691\pi$
$349$		−	18.8483i		−	1.00893i	0.863434	−	0.504463i	$-0.168309\pi$
$350$		0			0
$351$		−	6.79969i		−	0.362941i
$352$	−3.88659	−	1.69150i	−0.207156	−	0.0901572i
$353$	−3.50250	+	22.1139i	−0.186419	+	1.17700i	0.700008	+	0.714135i	$0.253180\pi$
$353$	−3.50250	+	22.1139i	−0.186419	+	1.17700i	−0.886427	+	0.462869i	$0.846820\pi$
$354$	−15.1104	−	4.70750i	−0.803110	−	0.250201i
$355$		0			0
$356$	6.33597	−	4.84286i	0.335806	−	0.256671i
$357$	−9.50920	−	9.50920i	−0.503280	−	0.503280i
$358$	13.4702	+	13.1468i	0.711925	+	0.694832i
$359$	−7.71491	+	23.7440i	−0.407177	+	1.25316i	0.511886	+	0.859053i	$0.328947\pi$
$359$	−7.71491	+	23.7440i	−0.407177	+	1.25316i	−0.919063	+	0.394110i	$0.871053\pi$
$360$		0			0
$361$	−1.72712	−	5.31554i	−0.0909013	−	0.279765i
$362$	9.57959	−	19.3795i	0.503492	−	1.01857i
$363$	−7.02112	+	3.57744i	−0.368513	+	0.187767i
$364$	12.9263	−	0.314162i	0.677521	−	0.0164666i
$365$		0			0
$366$	−1.86217	+	0.630168i	−0.0973370	+	0.0329394i
$367$	−7.60906	+	1.20516i	−0.397190	+	0.0629087i	−0.351834	−	0.936062i	$-0.614442\pi$
$367$	−7.60906	+	1.20516i	−0.397190	+	0.0629087i	−0.0453553	+	0.998971i	$0.514442\pi$
$368$	7.20916	+	34.5550i	0.375803	+	1.80130i
$369$	8.92655	−	12.2863i	0.464697	−	0.639601i
$370$		0			0
$371$	−21.1316	−	29.0852i	−1.09710	−	1.51003i
$372$	1.20940	−	2.52335i	0.0627047	−	0.130829i
$373$	−8.54114	−	4.35193i	−0.442243	−	0.225334i	0.218666	−	0.975800i	$-0.429829\pi$
$373$	−8.54114	−	4.35193i	−0.442243	−	0.225334i	−0.660910	+	0.750465i	$0.729829\pi$
$374$	3.88369	−	2.89440i	0.200821	−	0.149666i
$375$		0			0
$376$	−3.13622	+	1.14697i	−0.161738	+	0.0591505i
$377$	0.00474976	−	0.00932194i	0.000244625	−	0.000480104i
$378$	−10.5012	−	20.0051i	−0.540124	−	1.02895i
$379$	14.7902	−	10.7457i	0.759723	−	0.551971i	−0.139102	−	0.990278i	$-0.544422\pi$
$379$	14.7902	−	10.7457i	0.759723	−	0.551971i	0.898825	+	0.438307i	$0.144422\pi$
$380$		0			0
$381$	6.85463	+	4.98018i	0.351173	+	0.255142i
$382$	1.94743	−	13.3428i	0.0996392	−	0.682679i
$383$	−2.50325	−	15.8049i	−0.127910	−	0.807591i	−0.965330	−	0.261032i	$-0.915937\pi$
$383$	−2.50325	−	15.8049i	−0.127910	−	0.807591i	0.837420	−	0.546559i	$-0.184063\pi$
$384$	7.31098	+	4.41499i	0.373087	+	0.225301i
$385$		0			0
$386$	−11.2065	−	7.93576i	−0.570394	−	0.403919i
$387$	9.52760	+	18.6990i	0.484315	+	0.950522i
$388$	−12.8153	+	2.35026i	−0.650599	+	0.119316i
$389$	−14.5768	+	4.73629i	−0.739073	+	0.240139i	−0.654273	−	0.756259i	$-0.727025\pi$
$389$	−14.5768	+	4.73629i	−0.739073	+	0.240139i	−0.0848002	+	0.996398i	$0.527025\pi$
$390$		0			0
$391$	−38.3622	−	12.4646i	−1.94006	−	0.630364i
$392$	20.2430	−	11.2617i	1.02243	−	0.568803i
$393$	0.588310	−	0.588310i	0.0296763	−	0.0296763i
$394$	0.226154	+	18.6131i	0.0113935	+	0.937713i
$395$		0			0
$396$	3.43522	−	1.20921i	0.172627	−	0.0607651i
$397$	−11.0132	−	1.74431i	−0.552734	−	0.0875445i	−0.126182	−	0.992007i	$-0.540272\pi$
$397$	−11.0132	−	1.74431i	−0.552734	−	0.0875445i	−0.426553	+	0.904463i	$0.640272\pi$
$398$	−6.14929	−	35.9895i	−0.308236	−	1.80399i
$399$	−10.7744			−0.539395
$400$		0			0
$401$	−10.1423			−0.506483			−0.253242	−	0.967403i	$-0.581497\pi$
$401$	−10.1423			−0.506483			−0.253242	+	0.967403i	$0.581497\pi$
$402$	−0.925981	−	5.41942i	−0.0461837	−	0.270296i
$403$	−3.03652	−	0.480938i	−0.151260	−	0.0239572i
$404$	−15.5880	+	5.48703i	−0.775532	+	0.272990i
$405$		0			0
$406$	−0.000422357	−	0.0347611i	−2.09612e−5	−	0.00172517i
$407$	1.91732	−	1.91732i	0.0950378	−	0.0950378i
$408$	−8.52850	+	4.74464i	−0.422224	+	0.234895i
$409$	1.08325	+	0.351968i	0.0535630	+	0.0174037i	0.335676	−	0.941978i	$-0.391035\pi$
$409$	1.08325	+	0.351968i	0.0535630	+	0.0174037i	−0.282113	+	0.959381i	$0.591035\pi$
$410$		0			0
$411$	−5.40917	+	1.75754i	−0.266814	+	0.0866933i
$412$	11.1120	−	2.03789i	0.547451	−	0.100400i
$413$	26.2311	+	51.4814i	1.29075	+	2.53323i
$414$	−24.7509	−	17.5271i	−1.21644	−	0.861410i
$415$		0			0
$416$	2.35253	−	9.08388i	0.115342	−	0.445374i
$417$	1.49594	+	9.44497i	0.0732563	+	0.462522i
$418$	0.560455	−	3.83996i	0.0274127	−	0.187819i
$419$	6.31833	+	4.59053i	0.308670	+	0.224262i	0.731326	−	0.682028i	$-0.238902\pi$
$419$	6.31833	+	4.59053i	0.308670	+	0.224262i	−0.422655	+	0.906291i	$0.638902\pi$
$420$		0			0
$421$	−15.8211	+	11.4947i	−0.771074	+	0.560218i	−0.902287	−	0.431136i	$-0.858113\pi$
$421$	−15.8211	+	11.4947i	−0.771074	+	0.560218i	0.131213	+	0.991354i	$0.458113\pi$
$422$	−16.2775	−	31.0091i	−0.792374	−	1.50950i
$423$	1.30256	−	2.55642i	0.0633326	−	0.124297i
$424$	−24.5031	+	8.96124i	−1.18998	+	0.435196i
$425$		0			0
$426$	−9.12942	+	6.80390i	−0.442322	+	0.329650i
$427$	6.39471	+	3.25827i	0.309462	+	0.157679i
$428$	3.22462	−	6.72797i	0.155868	−	0.325209i
$429$	0.551515	+	0.759095i	0.0266274	+	0.0366494i
$430$		0			0
$431$	9.49241	−	13.0652i	0.457233	−	0.629328i	−0.516699	−	0.856167i	$-0.672839\pi$
$431$	9.49241	−	13.0652i	0.457233	−	0.629328i	0.973932	+	0.226840i	$0.0728393\pi$
$432$	−16.0511	+	3.34872i	−0.772259	+	0.161115i
$433$	6.22123	−	0.985346i	0.298973	−	0.0473527i	−0.00514584	−	0.999987i	$-0.501638\pi$
$433$	6.22123	−	0.985346i	0.298973	−	0.0473527i	0.304119	+	0.952634i	$0.401638\pi$
$434$	−9.67639	+	3.27455i	−0.464481	+	0.157183i
$435$		0			0
$436$	−5.85425	+	0.142283i	−0.280368	+	0.00681410i
$437$	−28.7947	+	14.6716i	−1.37744	+	0.701839i
$438$	3.32675	−	6.73003i	0.158958	−	0.321573i
$439$	−9.07012	−	27.9149i	−0.432893	−	1.33231i	−0.895230	−	0.445604i	$-0.852989\pi$
$439$	−9.07012	−	27.9149i	−0.432893	−	1.33231i	0.462337	−	0.886704i	$-0.347011\pi$
$440$		0			0
$441$	−6.15029	+	18.9286i	−0.292871	+	0.901364i
$442$	7.67363	+	7.48940i	0.364997	+	0.356234i
$443$	−1.81845	−	1.81845i	−0.0863972	−	0.0863972i	0.662587	−	0.748985i	$-0.269458\pi$
$443$	−1.81845	−	1.81845i	−0.0863972	−	0.0863972i	−0.748985	+	0.662587i	$0.769458\pi$
$444$	−4.34067	+	3.31776i	−0.205999	+	0.157454i
$445$		0			0
$446$	1.04264	+	0.324824i	0.0493705	+	0.0153808i
$447$	−1.84989	+	11.6797i	−0.0874967	+	0.552432i
$448$	−7.10754	−	30.3585i	−0.335800	−	1.43431i
$449$			19.3249i			0.911999i	0.889980	+	0.455999i	$0.150718\pi$
$449$			19.3249i			0.911999i	−0.889980	+	0.455999i	$0.849282\pi$
$450$		0			0
$451$			4.68267i			0.220498i
$452$	21.7376	+	20.7061i	1.02245	+	0.973932i
$453$	−1.55373	+	9.80989i	−0.0730008	+	0.460909i
$454$	−3.54628	+	11.3831i	−0.166435	+	0.534235i
$455$		0			0
$456$	−2.14365	+	7.51957i	−0.100386	+	0.352136i
$457$	15.9424	+	15.9424i	0.745755	+	0.745755i	0.973679	−	0.227924i	$-0.0731937\pi$
$457$	15.9424	+	15.9424i	0.745755	+	0.745755i	−0.227924	+	0.973679i	$0.573194\pi$
$458$	23.1938	−	23.7644i	1.08378	−	1.11044i
$459$	5.78993	−	17.8196i	0.270251	−	0.831747i
$460$		0			0
$461$	5.16980	+	15.9110i	0.240782	+	0.741049i	0.996302	+	0.0859240i	$0.0273842\pi$
$461$	5.16980	+	15.9110i	0.240782	+	0.741049i	−0.755520	+	0.655125i	$0.772616\pi$
$462$	2.79491	+	1.38157i	0.130031	+	0.0642763i
$463$	−24.6825	+	12.5764i	−1.14710	+	0.584474i	−0.920974	−	0.389625i	$-0.872605\pi$
$463$	−24.6825	+	12.5764i	−1.14710	+	0.584474i	−0.226122	+	0.974099i	$0.572605\pi$
$464$	−0.0243442	−	0.00662124i	−0.00113015	−	0.000307383i
$465$		0			0
$466$	−1.00773	−	2.97788i	−0.0466823	−	0.137947i
$467$	10.2246	−	1.61942i	0.473139	−	0.0749378i	0.0846885	−	0.996407i	$-0.473010\pi$
$467$	10.2246	−	1.61942i	0.473139	−	0.0749378i	0.388450	+	0.921470i	$0.373010\pi$
$468$	3.83362	+	7.09242i	0.177209	+	0.327847i
$469$	−11.7977	+	16.2382i	−0.544768	+	0.749809i
$470$		0			0
$471$	−6.76133	−	9.30617i	−0.311546	−	0.428806i
$472$	41.1483	−	8.06430i	1.89400	−	0.371190i
$473$	−5.76563	−	2.93773i	−0.265104	−	0.135077i
$474$	2.29451	+	3.07875i	0.105390	+	0.141412i
$475$		0			0
$476$	34.1427	+	10.1834i	1.56493	+	0.466756i
$477$	10.1768	−	19.9732i	0.465965	−	0.914508i
$478$	−1.04601	+	0.549080i	−0.0478436	+	0.0251143i
$479$	19.2530	−	13.9881i	0.879693	−	0.639134i	−0.0534775	−	0.998569i	$-0.517031\pi$
$479$	19.2530	−	13.9881i	0.879693	−	0.639134i	0.933170	+	0.359435i	$0.117031\pi$
$480$		0			0
$481$	4.85624	+	3.52826i	0.221425	+	0.160875i
$482$	−17.0231	−	2.48458i	−0.775382	−	0.113169i
$483$	−4.06161	−	25.6440i	−0.184810	−	1.16684i
$484$	11.8572	−	17.1831i	0.538966	−	0.781049i
$485$		0			0
$486$	12.6394	−	17.8488i	0.573337	−	0.809637i
$487$	11.0199	+	21.6278i	0.499360	+	0.980049i	0.993836	+	0.110858i	$0.0353598\pi$
$487$	11.0199	+	21.6278i	0.499360	+	0.980049i	−0.494477	+	0.869191i	$0.664640\pi$
$488$	3.54626	−	3.81468i	0.160532	−	0.172682i
$489$	8.08414	−	2.62670i	0.365577	−	0.118783i
$490$		0			0
$491$	20.7954	+	6.75684i	0.938484	+	0.304932i	0.738028	−	0.674771i	$-0.235757\pi$
$491$	20.7954	+	6.75684i	0.938484	+	0.304932i	0.200457	+	0.979703i	$0.435757\pi$
$492$	1.24913	−	9.35212i	0.0563150	−	0.421626i
$493$	0.0203851	−	0.0203851i	0.000918097	−	0.000918097i
$494$	8.59024	−	0.104374i	0.386493	−	0.00469600i
$495$		0			0
$496$	0.360145	+	7.40475i	0.0161710	+	0.332483i
$497$	41.0550	+	6.50248i	1.84157	+	0.291676i
$498$	−2.07335	+	0.354259i	−0.0929089	+	0.0158747i
$499$	−9.81690			−0.439465			−0.219732	−	0.975560i	$-0.570518\pi$
$499$	−9.81690			−0.439465			−0.219732	+	0.975560i	$0.570518\pi$
$500$		0			0
$501$	−3.31137			−0.147941
$502$	7.71549	−	1.31830i	0.344359	−	0.0588385i
$503$	−32.8952	−	5.21009i	−1.46673	−	0.232306i	−0.628576	−	0.777748i	$-0.716362\pi$
$503$	−32.8952	−	5.21009i	−1.46673	−	0.232306i	−0.838149	+	0.545442i	$0.816362\pi$
$504$	22.2320	+	14.9459i	0.990294	+	0.665742i
$505$		0			0
$506$	9.35071	−	0.113614i	0.415690	−	0.00505075i
$507$	5.47049	−	5.47049i	0.242953	−	0.242953i
$508$	−22.2500	−	2.97185i	−0.987186	−	0.131855i
$509$	−17.4707	−	5.67657i	−0.774375	−	0.251610i	−0.104938	−	0.994479i	$-0.533464\pi$
$509$	−17.4707	−	5.67657i	−0.774375	−	0.251610i	−0.669437	+	0.742869i	$0.733464\pi$
$510$		0			0
$511$	−26.0659	+	8.46931i	−1.15309	+	0.374660i
$512$	−22.6016	−	1.07965i	−0.998861	−	0.0477144i
$513$	−6.81510	−	13.3754i	−0.300894	−	0.590538i
$514$	15.1263	−	21.3606i	0.667194	−	0.942176i
$515$		0			0
$516$	10.7313	+	7.40518i	0.472420	+	0.325995i
$517$	0.138392	+	0.873775i	0.00608649	+	0.0384286i
$518$	19.7363	+	2.88058i	0.867163	+	0.126565i
$519$	9.99883	+	7.26457i	0.438900	+	0.318879i
$520$		0			0
$521$	−10.3305	+	7.50555i	−0.452587	+	0.328824i	−0.790617	−	0.612312i	$-0.790240\pi$
$521$	−10.3305	+	7.50555i	−0.452587	+	0.328824i	0.338029	+	0.941136i	$0.390240\pi$
$522$	0.0191924	−	0.0100746i	0.000840029	−	0.000440953i
$523$	19.1488	−	37.5817i	0.837321	−	1.64333i	0.0740511	−	0.997254i	$-0.476407\pi$
$523$	19.1488	−	37.5817i	0.837321	−	1.64333i	0.763270	−	0.646080i	$-0.223593\pi$
$524$	−0.630021	+	2.11232i	−0.0275226	+	0.0922771i
$525$		0			0
$526$	−9.89587	−	13.2782i	−0.431480	−	0.578957i
$527$	−7.54813	−	3.84596i	−0.328802	−	0.167533i
$528$	1.52028	−	1.67572i	0.0661617	−	0.0729265i
$529$	−32.2554	−	44.3957i	−1.40241	−	1.93025i
$530$		0			0
$531$	−21.1758	+	29.1460i	−0.918952	+	1.26483i
$532$	25.1118	−	13.5735i	1.08874	−	0.588487i
$533$	−10.2388	+	1.62166i	−0.443490	+	0.0702419i
$534$	1.36454	+	4.03226i	0.0590494	+	0.174493i
$535$		0			0
$536$	8.98553	+	11.4645i	0.388116	+	0.495189i
$537$	−8.95219	+	4.56137i	−0.386315	+	0.196837i
$538$	6.33907	+	3.13350i	0.273297	+	0.135095i
$539$	−1.89638	−	5.83644i	−0.0816827	−	0.251393i
$540$		0			0
$541$	−7.07714	+	21.7812i	−0.304270	+	0.936447i	0.675678	+	0.737197i	$0.263851\pi$
$541$	−7.07714	+	21.7812i	−0.304270	+	0.936447i	−0.979949	+	0.199251i	$0.936149\pi$
$542$	24.9968	−	25.6117i	1.07370	−	1.10012i
$543$	8.15961	+	8.15961i	0.350163	+	0.350163i
$544$	13.9001	−	21.8025i	0.595960	−	0.934773i
$545$		0			0
$546$	−2.05291	+	6.58958i	−0.0878566	+	0.282008i
$547$	3.85178	−	24.3192i	0.164690	−	1.03981i	−0.757432	−	0.652914i	$-0.773546\pi$
$547$	3.85178	−	24.3192i	0.164690	−	1.03981i	0.922122	−	0.386899i	$-0.126454\pi$
$548$	10.3930	−	10.9107i	0.443966	−	0.466084i
$549$			4.47499i			0.190988i
$550$		0			0
$551$		−	0.0230973i		−	0.000983978i
$552$	−18.7053	−	2.26744i	−0.796151	−	0.0965088i
$553$	2.19286	−	13.8451i	0.0932497	−	0.588756i
$554$	20.7005	+	6.44902i	0.879479	+	0.273993i
$555$		0			0
$556$	−15.3853	−	20.1288i	−0.652482	−	0.853650i
$557$	2.83685	+	2.83685i	0.120201	+	0.120201i	0.764649	−	0.644447i	$-0.222913\pi$
$557$	2.83685	+	2.83685i	0.120201	+	0.120201i	−0.644447	+	0.764649i	$0.722913\pi$
$558$	−4.55834	−	4.44890i	−0.192970	−	0.188337i
$559$	4.42671	−	13.6240i	0.187230	−	0.576235i
$560$		0			0
$561$	0.798955	+	2.45893i	0.0337319	+	0.103816i
$562$	−13.7979	+	27.9133i	−0.582031	+	1.17745i
$563$	−19.6112	+	9.99243i	−0.826515	+	0.421131i	−0.815464	−	0.578808i	$-0.803518\pi$
$563$	−19.6112	+	9.99243i	−0.826515	+	0.421131i	−0.0110516	+	0.999939i	$0.503518\pi$
$564$	−0.0433099	−	1.78200i	−0.00182368	−	0.0750357i
$565$		0			0
$566$	3.44466	−	1.16569i	0.144790	−	0.0489977i
$567$	−16.1522	+	2.55825i	−0.678327	+	0.107436i
$568$	12.7064	−	27.3590i	0.533148	−	1.14796i
$569$	−2.34646	+	3.22963i	−0.0983688	+	0.135393i	−0.855364	−	0.518027i	$-0.826667\pi$
$569$	−2.34646	+	3.22963i	−0.0983688	+	0.135393i	0.756995	+	0.653420i	$0.226667\pi$
$570$		0			0
$571$	13.9597	+	19.2139i	0.584197	+	0.804078i	0.994148	−	0.108029i	$-0.0344541\pi$
$571$	13.9597	+	19.2139i	0.584197	+	0.804078i	−0.409951	+	0.912108i	$0.634454\pi$
$572$	−2.24171	−	1.07442i	−0.0937308	−	0.0449239i
$573$	6.41323	+	3.26770i	0.267917	+	0.136510i
$574$	−27.6186	+	20.5834i	−1.15278	+	0.859135i
$575$		0			0
$576$	14.8541	−	12.5424i	0.618921	−	0.522599i
$577$	−5.57748	+	10.9464i	−0.232194	+	0.455706i	−0.977477	−	0.211042i	$-0.932314\pi$
$577$	−5.57748	+	10.9464i	−0.232194	+	0.455706i	0.745283	+	0.666748i	$0.232314\pi$
$578$	2.55853	+	4.87408i	0.106421	+	0.202735i
$579$	5.93000	−	4.30839i	0.246442	−	0.179051i
$580$		0			0
$581$	6.21235	+	4.51354i	0.257732	+	0.187253i
$582$	1.00443	−	6.88187i	0.0416350	−	0.285262i
$583$	1.08125	+	6.82676i	0.0447809	+	0.282736i
$584$	0.724806	+	19.8767i	0.0299927	+	0.822502i
$585$		0			0
$586$	−21.1833	−	15.0007i	−0.875073	−	0.619675i
$587$	−8.67508	−	17.0258i	−0.358059	−	0.702730i	0.639772	−	0.768565i	$-0.279029\pi$
$587$	−8.67508	−	17.0258i	−0.358059	−	0.702730i	−0.997831	+	0.0658352i	$0.979029\pi$
$588$	2.23049	+	12.1623i	0.0919840	+	0.501564i
$589$	−6.45504	+	2.09737i	−0.265975	+	0.0864206i
$590$		0			0
$591$	−9.44990	−	3.07046i	−0.388717	−	0.126302i
$592$	5.93708	−	13.2010i	0.244012	−	0.542560i
$593$	−19.5284	+	19.5284i	−0.801936	+	0.801936i	−0.983398	−	0.181462i	$-0.941917\pi$
$593$	−19.5284	+	19.5284i	−0.801936	+	0.801936i	0.181462	+	0.983398i	$0.441917\pi$
$594$	0.0527746	+	4.34349i	0.00216537	+	0.178216i
$595$		0			0
$596$	−10.4025	−	29.5524i	−0.426104	−	1.21051i
$597$	19.2493	+	3.04879i	0.787822	+	0.124779i
$598$	3.48667	+	20.4062i	0.142581	+	0.834470i
$599$	−13.5371			−0.553109			−0.276555	−	0.960998i	$-0.589193\pi$
$599$	−13.5371			−0.553109			−0.276555	+	0.960998i	$0.589193\pi$
$600$		0			0
$601$	−20.0981			−0.819819			−0.409910	−	0.912126i	$-0.634440\pi$
$601$	−20.0981			−0.819819			−0.409910	+	0.912126i	$0.634440\pi$
$602$	−8.01678	−	46.9192i	−0.326740	−	1.91228i
$603$	−12.3609	−	1.95778i	−0.503376	−	0.0797270i
$604$	−8.73717	−	24.8212i	−0.355510	−	1.00996i
$605$		0			0
$606$	−0.107172	−	8.82052i	−0.00435355	−	0.358309i
$607$	−13.9387	+	13.9387i	−0.565753	+	0.565753i	−0.930936	−	0.365182i	$-0.881007\pi$
$607$	−13.9387	+	13.9387i	−0.565753	+	0.565753i	0.365182	+	0.930936i	$0.381007\pi$
$608$	−4.47691	−	20.2264i	−0.181562	−	0.820288i
$609$	0.0176483	+	0.00573428i	0.000715145	+	0.000232365i
$610$		0			0
$611$	−1.86260	+	0.605195i	−0.0753527	+	0.0244836i
$612$	4.00736	+	21.8510i	0.161988	+	0.883276i
$613$	7.55485	+	14.8272i	0.305137	+	0.598866i	0.991754	−	0.128153i	$-0.0409050\pi$
$613$	7.55485	+	14.8272i	0.305137	+	0.598866i	−0.686617	+	0.727019i	$0.740905\pi$
$614$	9.53782	+	6.75412i	0.384915	+	0.272574i
$615$		0			0
$616$	−8.25457	+	0.301004i	−0.332586	+	0.0121278i
$617$	2.57536	+	16.2602i	0.103680	+	0.654610i	0.983720	+	0.179710i	$0.0575159\pi$
$617$	2.57536	+	16.2602i	0.103680	+	0.654610i	−0.880040	+	0.474900i	$0.842484\pi$
$618$	−0.870933	+	5.96720i	−0.0350341	+	0.240036i
$619$	2.41281	+	1.75301i	0.0969790	+	0.0704593i	0.635218	−	0.772333i	$-0.280910\pi$
$619$	2.41281	+	1.75301i	0.0969790	+	0.0704593i	−0.538239	+	0.842792i	$0.680910\pi$
$620$		0			0
$621$	29.2655	−	21.2626i	1.17438	−	0.853240i
$622$	−10.0453	−	19.1366i	−0.402779	−	0.767308i
$623$	7.05531	−	13.8468i	0.282665	−	0.554762i
$624$	4.19049	+	2.74380i	0.167754	+	0.109840i
$625$		0			0
$626$	−30.4201	+	22.6713i	−1.21583	+	0.906126i
$627$	1.84568	+	0.940418i	0.0737092	+	0.0375567i
$628$	27.4825	+	13.1720i	1.09667	+	0.525618i
$629$	9.72216	+	13.3814i	0.387648	+	0.533552i
$630$		0			0
$631$	10.9928	−	15.1303i	0.437618	−	0.602329i	−0.532063	−	0.846705i	$-0.678583\pi$
$631$	10.9928	−	15.1303i	0.437618	−	0.602329i	0.969681	+	0.244376i	$0.0785830\pi$
$632$	−9.22639	−	4.28502i	−0.367006	−	0.170449i
$633$	18.4641	−	2.92442i	0.733881	−	0.116235i
$634$	−4.91374	+	1.66284i	−0.195150	+	0.0660398i
$635$		0			0
$636$	−0.338379	−	13.9227i	−0.0134176	−	0.552070i
$637$	12.1048	−	6.16769i	0.479608	−	0.244373i
$638$	−0.00296169	+	0.00599151i	−0.000117254	+	0.000237206i
$639$	8.00905	+	24.6493i	0.316833	+	0.975112i
$640$		0			0
$641$	6.50379	−	20.0166i	0.256884	−	0.790608i	−0.736568	−	0.676363i	$-0.763555\pi$
$641$	6.50379	−	20.0166i	0.256884	−	0.790608i	0.993453	−	0.114245i	$-0.0364449\pi$
$642$	2.85006	+	2.78164i	0.112483	+	0.109782i
$643$	16.6982	+	16.6982i	0.658511	+	0.658511i	0.955028	−	0.296516i	$-0.0958250\pi$
$643$	16.6982	+	16.6982i	0.658511	+	0.658511i	−0.296516	+	0.955028i	$0.595825\pi$
$644$	41.7726	+	54.6516i	1.64607	+	2.15357i
$645$		0			0
$646$	22.6008	+	7.04105i	0.889218	+	0.277027i
$647$	−0.900819	+	5.68755i	−0.0354149	+	0.223601i	−0.999048	−	0.0436287i	$-0.986108\pi$
$647$	−0.900819	+	5.68755i	−0.0354149	+	0.223601i	0.963633	+	0.267229i	$0.0861081\pi$
$648$	−1.42817	+	11.7817i	−0.0561039	+	0.462831i
$649$		−	11.1084i		−	0.436042i
$650$		0			0
$651$		−	5.45290i		−	0.213716i
$652$	−15.5326	+	16.3064i	−0.608302	+	0.638607i
$653$	0.646208	−	4.08000i	0.0252881	−	0.159663i	−0.971813	−	0.235754i	$-0.924244\pi$
$653$	0.646208	−	4.08000i	0.0252881	−	0.159663i	0.997101	+	0.0760913i	$0.0242440\pi$
$654$	0.929756	−	2.98439i	0.0363563	−	0.116699i
$655$		0			0
$656$	8.87042	+	23.3706i	0.346332	+	0.912468i
$657$	−12.0838	−	12.0838i	−0.471433	−	0.471433i
$658$	−4.54524	+	4.65706i	−0.177192	+	0.181551i
$659$	8.02901	−	24.7107i	0.312766	−	0.962594i	−0.663899	−	0.747823i	$-0.731099\pi$
$659$	8.02901	−	24.7107i	0.312766	−	0.962594i	0.976664	−	0.214771i	$-0.0689006\pi$
$660$		0			0
$661$	0.665910	+	2.04946i	0.0259009	+	0.0797148i	0.963171	−	0.268888i	$-0.0866562\pi$
$661$	0.665910	+	2.04946i	0.0259009	+	0.0797148i	−0.937271	+	0.348603i	$0.886656\pi$
$662$	19.3395	+	9.55981i	0.751652	+	0.371553i
$663$	−5.09982	+	2.59849i	−0.198060	+	0.100917i
$664$	4.38604	−	3.43766i	0.170212	−	0.133407i
$665$		0			0
$666$	3.98648	+	11.7802i	0.154473	+	0.456472i
$667$	0.0549736	−	0.00870697i	0.00212859	−	0.000337135i
$668$	7.71780	−	4.17165i	0.298611	−	0.161406i
$669$	−0.342640	+	0.471604i	−0.0132472	+	0.0182333i
$670$		0			0
$671$	−0.811036	−	1.11629i	−0.0313097	−	0.0430941i
$672$	16.5661	+	1.60079i	0.639052	+	0.0617518i
$673$	23.7755	+	12.1142i	0.916479	+	0.466969i	0.847588	−	0.530655i	$-0.178054\pi$
$673$	23.7755	+	12.1142i	0.916479	+	0.466969i	0.0688909	+	0.997624i	$0.478054\pi$
$674$	−24.7009	−	33.1435i	−0.951444	−	1.27664i
$675$		0			0
$676$	−5.85835	+	19.6417i	−0.225321	+	0.755452i
$677$	−4.53364	+	8.89777i	−0.174242	+	0.341969i	−0.961568	−	0.274568i	$-0.911465\pi$
$677$	−4.53364	+	8.89777i	−0.174242	+	0.341969i	0.787326	+	0.616537i	$0.211465\pi$
$678$	−14.1889	+	7.44812i	−0.544922	+	0.286043i
$679$	−20.5409	+	14.9238i	−0.788286	+	0.572723i
$680$		0			0
$681$	−5.14876	−	3.74080i	−0.197301	−	0.143348i
$682$	1.94339	+	0.283645i	0.0744164	+	0.0108613i
$683$	6.26839	+	39.5771i	0.239853	+	1.51437i	0.754116	+	0.656741i	$0.228066\pi$
$683$	6.26839	+	39.5771i	0.239853	+	1.51437i	−0.514263	+	0.857633i	$0.671934\pi$
$684$	14.6494	+	10.1089i	0.560135	+	0.386523i
$685$		0			0
$686$	3.79047	−	5.35270i	0.144721	−	0.204367i
$687$	8.04723	+	15.7936i	0.307021	+	0.602562i
$688$	−34.3404	−	3.73996i	−1.30922	−	0.142585i
$689$	−14.5524	+	4.72836i	−0.554402	+	0.180136i
$690$		0			0
$691$	−10.3709	−	3.36971i	−0.394528	−	0.128190i	0.105033	−	0.994469i	$-0.466505\pi$
$691$	−10.3709	−	3.36971i	−0.394528	−	0.128190i	−0.499561	+	0.866279i	$0.666505\pi$
$692$	−32.4561	−	4.33503i	−1.23379	−	0.164793i
$693$	5.01827	−	5.01827i	0.190628	−	0.190628i
$694$	3.56047	−	0.0432607i	0.135154	−	0.00164215i
$695$		0			0
$696$	0.00751328	−	0.0111760i	0.000284790	−	0.000423627i
$697$	−28.2130	−	4.46850i	−1.06864	−	0.169256i
$698$	−26.2747	+	4.48939i	−0.994513	+	0.169926i
$699$	1.67811			0.0634720
$700$		0			0
$701$	−11.2244			−0.423940			−0.211970	−	0.977276i	$-0.567988\pi$
$701$	−11.2244			−0.423940			−0.211970	+	0.977276i	$0.567988\pi$
$702$	−9.47885	+	1.61959i	−0.357756	+	0.0611275i
$703$	13.0888	+	2.07305i	0.493652	+	0.0781867i
$704$	−1.43224	+	5.82084i	−0.0539796	+	0.219381i
$705$		0			0
$706$	31.6613	−	0.384693i	1.19159	−	0.0144781i
$707$	−22.7714	+	22.7714i	−0.856405	+	0.856405i
$708$	−2.96321	+	22.1854i	−0.111364	+	0.833777i
$709$	40.0107	+	13.0003i	1.50263	+	0.488235i	0.940784	−	0.339006i	$-0.110091\pi$
$709$	40.0107	+	13.0003i	1.50263	+	0.488235i	0.561848	+	0.827240i	$0.310091\pi$
$710$		0			0
$711$	8.31258	−	2.70092i	0.311746	−	0.101293i
$712$	−8.26014	−	7.67892i	−0.309562	−	0.287780i
$713$	−7.42527	−	14.5729i	−0.278079	−	0.545760i
$714$	−10.9910	+	15.5209i	−0.411327	+	0.580855i
$715$		0			0
$716$	15.1184	−	21.9091i	0.565002	−	0.818780i
$717$	−0.0986482	−	0.622840i	−0.00368408	−	0.0232604i
$718$	34.9371	+	5.09918i	1.30384	+	0.190300i
$719$	15.1605	+	11.0147i	0.565391	+	0.410781i	0.833428	−	0.552628i	$-0.186375\pi$
$719$	15.1605	+	11.0147i	0.565391	+	0.410781i	−0.268037	+	0.963409i	$0.586375\pi$
$720$		0			0
$721$	17.8108	−	12.9403i	0.663309	−	0.481922i
$722$	−6.99855	+	3.67372i	−0.260459	+	0.136722i
$723$	4.16902	−	8.18215i	0.155047	−	0.304298i
$724$	−29.2970	−	8.73813i	−1.08881	−	0.324750i
$725$		0			0
$726$	6.65932	+	8.93542i	0.247151	+	0.331625i
$727$	−30.9449	−	15.7672i	−1.14768	−	0.584773i	−0.226540	−	0.974002i	$-0.572742\pi$
$727$	−30.9449	−	15.7672i	−1.14768	−	0.584773i	−0.921141	+	0.389229i	$0.872742\pi$
$728$	−3.51680	−	17.9445i	−0.130341	−	0.665069i
$729$	−0.536916	−	0.739001i	−0.0198858	−	0.0273704i
$730$		0			0
$731$	23.2017	−	31.9344i	0.858146	−	1.18114i
$732$	1.32200	+	2.44578i	0.0488627	+	0.0903988i
$733$	−30.1255	+	4.77141i	−1.11271	+	0.176236i	−0.685611	−	0.727968i	$-0.740465\pi$
$733$	−30.1255	+	4.77141i	−1.11271	+	0.176236i	−0.427100	+	0.904204i	$0.640465\pi$
$734$	3.49237	+	10.3201i	0.128906	+	0.380921i
$735$		0			0
$736$	46.4529	−	18.2801i	1.71228	−	0.673815i
$737$	3.43828	−	1.75189i	0.126651	−	0.0645318i
$738$	−19.2535	−	9.51728i	−0.708730	−	0.350336i
$739$	2.21800	+	6.82631i	0.0815905	+	0.251110i	0.983528	−	0.180757i	$-0.0578549\pi$
$739$	2.21800	+	6.82631i	0.0815905	+	0.251110i	−0.901937	+	0.431867i	$0.857855\pi$
$740$		0			0
$741$	−1.41707	+	4.36128i	−0.0520572	+	0.160216i
$742$	−35.5118	+	36.3854i	−1.30368	+	1.33575i
$743$	29.7687	+	29.7687i	1.09211	+	1.09211i	0.995303	+	0.0968046i	$0.0308622\pi$
$743$	29.7687	+	29.7687i	1.09211	+	1.09211i	0.0968046	+	0.995303i	$0.469138\pi$
$744$	−3.80564	−	1.08490i	−0.139521	−	0.0397743i
$745$		0			0
$746$	−4.03226	+	12.9430i	−0.147632	+	0.473877i
$747$	−0.749002	+	4.72901i	−0.0274046	+	0.173026i
$748$	−4.95987	−	4.72450i	−0.181351	−	0.172745i
$749$		−	14.5390i		−	0.531244i
$750$		0			0
$751$		−	31.2660i		−	1.14091i	−0.821327	−	0.570457i	$-0.806766\pi$
$751$		−	31.2660i		−	1.14091i	0.821327	−	0.570457i	$-0.193234\pi$
$752$	2.34589	+	4.09873i	0.0855460	+	0.149465i
$753$	−0.653605	+	4.12670i	−0.0238187	+	0.150385i
$754$	−0.0141262	−	0.00440087i	−0.000514446	−	0.000160270i
$755$		0			0
$756$	−25.3862	+	19.4037i	−0.923286	+	0.705707i
$757$	4.53335	+	4.53335i	0.164767	+	0.164767i	0.784675	−	0.619908i	$-0.212830\pi$
$757$	4.53335	+	4.53335i	0.164767	+	0.164767i	−0.619908	+	0.784675i	$0.712830\pi$
$758$	−18.5025	−	18.0583i	−0.672041	−	0.655906i
$759$	−1.54252	+	4.74738i	−0.0559898	+	0.172319i
$760$		0			0
$761$	8.99353	+	27.6792i	0.326015	+	1.00337i	0.970980	+	0.239159i	$0.0768718\pi$
$761$	8.99353	+	27.6792i	0.326015	+	1.00337i	−0.644965	+	0.764212i	$0.723128\pi$
$762$	5.30975	−	10.7416i	0.192352	−	0.389128i
$763$	−10.1678	+	5.18078i	−0.368101	+	0.187557i
$764$	−19.0639	+	0.463332i	−0.689708	+	0.0167628i
$765$		0			0
$766$	−21.4359	+	7.25405i	−0.774512	+	0.262099i
$767$	24.2887	−	3.84695i	0.877013	−	0.138905i
$768$	4.41317	−	11.2432i	0.159247	−	0.405703i
$769$	21.5371	−	29.6433i	0.776649	−	1.06897i	−0.218994	−	0.975726i	$-0.570278\pi$
$769$	21.5371	−	29.6433i	0.776649	−	1.06897i	0.995644	−	0.0932401i	$-0.0297224\pi$
$770$		0			0
$771$	8.21222	+	11.3031i	0.295756	+	0.407073i
$772$	−8.39332	+	17.5121i	−0.302082	+	0.630275i
$773$	−21.7496	−	11.0820i	−0.782279	−	0.398591i	0.0167684	−	0.999859i	$-0.494662\pi$
$773$	−21.7496	−	11.0820i	−0.782279	−	0.398591i	−0.799047	+	0.601268i	$0.794662\pi$
$774$	23.7972	−	17.7354i	0.855374	−	0.637486i
$775$		0			0
$776$	6.32871	+	17.3049i	0.227188	+	0.621210i
$777$	−4.83348	+	9.48624i	−0.173400	+	0.340317i
$778$	10.0744	+	19.1921i	0.361186	+	0.688070i
$779$	−18.5149	+	13.4518i	−0.663364	+	0.481962i
$780$		0			0
$781$	−6.46525	−	4.69728i	−0.231345	−	0.168082i
$782$	−8.23851	+	56.4462i	−0.294609	+	2.01851i
$783$	0.00404446	+	0.0255357i	0.000144537	+	0.000912573i
$784$	−20.5206	−	25.5366i	−0.732877	−	0.912021i
$785$		0			0
$786$	−0.960237	−	0.679983i	−0.0342505	−	0.0242542i
$787$	−1.57397	−	3.08909i	−0.0561060	−	0.110114i	0.861251	−	0.508180i	$-0.169682\pi$
$787$	−1.57397	−	3.08909i	−0.0561060	−	0.110114i	−0.917357	+	0.398066i	$0.869682\pi$
$788$	25.8930	−	4.74863i	0.922399	−	0.169163i
$789$	8.40701	−	2.73160i	0.299297	−	0.0972476i
$790$		0			0
$791$	55.6393	+	18.0783i	1.97830	+	0.642790i
$792$	−2.50388	−	4.50072i	−0.0889713	−	0.159926i
$793$	2.15993	−	2.15993i	0.0767014	−	0.0767014i
$794$	0.191585	+	15.7679i	0.00679909	+	0.559583i
$795$		0			0
$796$	−48.7051	+	17.1444i	−1.72631	+	0.607666i
$797$	−12.2116	−	1.93413i	−0.432557	−	0.0685103i	−0.0636405	−	0.997973i	$-0.520271\pi$
$797$	−12.2116	−	1.93413i	−0.432557	−	0.0685103i	−0.368916	+	0.929463i	$0.620271\pi$
$798$	2.56631	+	15.0196i	0.0908463	+	0.531689i
$799$	−5.39653			−0.190916
$800$		0			0
$801$	9.68995			0.342378
$802$	2.41575	+	14.1385i	0.0853033	+	0.499248i
$803$	5.20435	+	0.824288i	0.183658	+	0.0290885i
$804$	−7.33418	+	2.58166i	−0.258656	+	0.0910480i
$805$		0			0
$806$	0.0528233	+	4.34750i	0.00186062	+	0.153134i
$807$	−2.66902	+	2.66902i	−0.0939540	+	0.0939540i
$808$	11.3618	+	20.4229i	0.399707	+	0.718476i
$809$	13.3278	+	4.33048i	0.468582	+	0.152251i	0.533784	−	0.845621i	$-0.320769\pi$
$809$	13.3278	+	4.33048i	0.468582	+	0.152251i	−0.0652027	+	0.997872i	$0.520769\pi$
$810$		0			0
$811$	−15.0031	+	4.87481i	−0.526831	+	0.171178i	−0.560343	−	0.828261i	$-0.689331\pi$
$811$	−15.0031	+	4.87481i	−0.526831	+	0.171178i	0.0335122	+	0.999438i	$0.489331\pi$
$812$	−0.0483568	+	0.00886837i	−0.00169699	+	0.000311219i
$813$	8.67277	+	17.0213i	0.304167	+	0.596962i
$814$	−3.12944	−	2.21608i	−0.109687	−	0.0776737i
$815$		0			0
$816$	8.64545	+	10.7587i	0.302651	+	0.376631i
$817$	−4.94729	−	31.2360i	−0.173084	−	1.09281i
$818$	0.232634	−	1.59389i	0.00813384	−	0.0557291i
$819$	12.7104	+	9.23466i	0.444138	+	0.322685i
$820$		0			0
$821$	6.24060	−	4.53406i	0.217798	−	0.158240i	−0.473537	−	0.880774i	$-0.657023\pi$
$821$	6.24060	−	4.53406i	0.217798	−	0.158240i	0.691335	+	0.722534i	$0.257023\pi$
$822$	3.73842	+	7.12182i	0.130392	+	0.248402i
$823$	−3.19071	+	6.26212i	−0.111221	+	0.218284i	−0.939907	−	0.341430i	$-0.889089\pi$
$823$	−3.19071	+	6.26212i	−0.111221	+	0.218284i	0.828686	+	0.559714i	$0.189089\pi$
$824$	−5.48757	−	15.0049i	−0.191169	−	0.522721i
$825$		0			0
$826$	65.5178	−	48.8285i	2.27965	−	1.69896i
$827$	12.1390	+	6.18514i	0.422115	+	0.215078i	0.652128	−	0.758109i	$-0.273877\pi$
$827$	12.1390	+	6.18514i	0.422115	+	0.215078i	−0.230012	+	0.973188i	$0.573877\pi$
$828$	−18.5377	+	38.6777i	−0.644229	+	1.34414i
$829$	21.4059	+	29.4626i	0.743456	+	1.02328i	0.998412	+	0.0563271i	$0.0179390\pi$
$829$	21.4059	+	29.4626i	0.743456	+	1.02328i	−0.254956	+	0.966953i	$0.582061\pi$
$830$		0			0
$831$	−6.80275	+	9.36318i	−0.235985	+	0.324805i
$832$	−13.2234	−	1.11580i	−0.458438	−	0.0386835i
$833$	36.9741	−	5.85612i	1.28108	−	0.202902i
$834$	12.8101	−	4.33501i	0.443577	−	0.150109i
$835$		0			0
$836$	−5.48644	+	0.133343i	−0.189752	+	0.00461177i
$837$	6.76925	−	3.44911i	0.233980	−	0.119219i
$838$	4.89432	−	9.90122i	0.169071	−	0.342032i
$839$	6.64845	+	20.4618i	0.229530	+	0.706420i	0.997800	+	0.0662946i	$0.0211177\pi$
$839$	6.64845	+	20.4618i	0.229530	+	0.706420i	−0.768270	+	0.640126i	$0.778882\pi$
$840$		0			0
$841$	8.96148	−	27.5806i	0.309017	−	0.951055i
$842$	19.7921	+	19.3169i	0.682081	+	0.665705i
$843$	−11.7527	−	11.7527i	−0.404784	−	0.404784i
$844$	−39.3500	+	30.0769i	−1.35448	+	1.03529i
$845$		0			0
$846$	−3.87392	−	1.20688i	−0.133188	−	0.0414934i
$847$	6.36430	−	40.1826i	0.218680	−	1.38069i
$848$	18.3284	+	32.0232i	0.629399	+	1.09968i
$849$			1.94116i			0.0666203i
$850$		0			0
$851$			31.9339i			1.09468i
$852$	11.6592	+	11.1059i	0.399438	+	0.380483i
$853$	5.12879	−	32.3819i	0.175606	−	1.10873i	−0.729635	−	0.683837i	$-0.760310\pi$
$853$	5.12879	−	32.3819i	0.175606	−	1.10873i	0.905241	−	0.424898i	$-0.139690\pi$
$854$	3.01893	−	9.69038i	0.103306	−	0.331598i
$855$		0			0
$856$	−10.1469	−	2.89265i	−0.346815	−	0.0988688i
$857$	−9.60872	−	9.60872i	−0.328228	−	0.328228i	0.523685	−	0.851912i	$-0.324557\pi$
$857$	−9.60872	−	9.60872i	−0.328228	−	0.328228i	−0.851912	+	0.523685i	$0.824557\pi$
$858$	0.926824	−	0.949623i	0.0316412	−	0.0324196i
$859$	−17.0359	+	52.4310i	−0.581256	+	1.78892i	0.0325570	+	0.999470i	$0.489635\pi$
$859$	−17.0359	+	52.4310i	−0.581256	+	1.78892i	−0.613813	+	0.789452i	$0.710365\pi$
$860$		0			0
$861$	−5.68173	−	17.4866i	−0.193633	−	0.595941i
$862$	−20.4740	−	10.1206i	−0.697346	−	0.344709i
$863$	−2.70712	+	1.37935i	−0.0921515	+	0.0469535i	−0.499459	−	0.866338i	$-0.666468\pi$
$863$	−2.70712	+	1.37935i	−0.0921515	+	0.0469535i	0.407307	+	0.913291i	$0.366468\pi$
$864$	8.49129	+	21.5778i	0.288880	+	0.734091i
$865$		0			0
$866$	−2.85539	−	8.43777i	−0.0970301	−	0.286727i
$867$	−2.90223	+	0.459668i	−0.0985648	+	0.0156111i
$868$	6.86953	+	12.7090i	0.233167	+	0.431373i
$869$	−1.58408	+	2.18030i	−0.0537363	+	0.0739616i
$870$		0			0
$871$	5.02126	+	6.91117i	0.170139	+	0.234176i
$872$	1.59274	+	8.12700i	0.0539371	+	0.275215i
$873$	−14.1057	−	7.18720i	−0.477405	−	0.243250i
$874$	27.3109	+	36.6455i	0.923804	+	1.23955i
$875$		0			0
$876$	−10.1741	−	3.03454i	−0.343752	−	0.102527i
$877$	12.3371	−	24.2129i	0.416595	−	0.817613i	−0.583391	−	0.812192i	$-0.698274\pi$
$877$	12.3371	−	24.2129i	0.416595	−	0.817613i	0.999985	−	0.00542141i	$-0.00172570\pi$
$878$	−36.7534	+	19.2928i	−1.24037	+	0.651100i
$879$	11.2093	−	8.14404i	0.378081	−	0.274692i
$880$		0			0
$881$	−4.42541	−	3.21525i	−0.149096	−	0.108325i	0.510737	−	0.859737i	$-0.329373\pi$
$881$	−4.42541	−	3.21525i	−0.149096	−	0.108325i	−0.659832	+	0.751413i	$0.729373\pi$
$882$	27.8516	+	4.06504i	0.937814	+	0.136877i
$883$	3.58180	+	22.6146i	0.120537	+	0.761041i	0.971714	+	0.236162i	$0.0758895\pi$
$883$	3.58180	+	22.6146i	0.120537	+	0.761041i	−0.851177	+	0.524879i	$0.824110\pi$
$884$	8.61255	−	12.4810i	0.289672	−	0.419781i
$885$		0			0
$886$	−2.10181	+	2.96807i	−0.0706118	+	0.0997143i
$887$	−21.2791	−	41.7627i	−0.714484	−	1.40225i	−0.907073	−	0.420974i	$-0.861688\pi$
$887$	−21.2791	−	41.7627i	−0.714484	−	1.40225i	0.192589	−	0.981279i	$-0.438312\pi$
$888$	5.65889	+	5.26070i	0.189900	+	0.176538i
$889$	−41.6031	+	13.5177i	−1.39532	+	0.453368i
$890$		0			0
$891$	2.99019	+	0.971570i	0.100175	+	0.0325488i
$892$	0.204466	−	1.53082i	0.00684602	−	0.0512557i
$893$	−3.05727	+	3.05727i	−0.102308	+	0.102308i
$894$	16.7223	−	0.203180i	0.559277	−	0.00679537i
$895$		0			0
$896$	−40.6272	+	17.1390i	−1.35726	+	0.572572i
$897$	−10.9144	−	1.72867i	−0.364422	−	0.0577188i
$898$	26.9391	−	4.60292i	0.898971	−	0.153601i
$899$	0.0116895			0.000389866
$900$		0			0
$901$	−42.1629			−1.40465
$902$	6.52770	−	1.11535i	0.217349	−	0.0371369i
$903$	25.0952	+	3.97468i	0.835115	+	0.132269i
$904$	23.6869	−	35.2344i	0.787815	−	1.17188i
$905$		0			0
$906$	14.0452	−	0.170653i	0.466620	−	0.00566956i
$907$	37.7459	−	37.7459i	1.25333	−	1.25333i	0.299114	−	0.954217i	$-0.403309\pi$
$907$	37.7459	−	37.7459i	1.25333	−	1.25333i	0.954217	−	0.299114i	$-0.0966911\pi$
$908$	16.7128	+	2.23227i	0.554635	+	0.0740804i
$909$	−19.0969	−	6.20495i	−0.633403	−	0.205805i
$910$		0			0
$911$	−38.7405	+	12.5875i	−1.28353	+	0.417044i	−0.869822	−	0.493366i	$-0.835766\pi$
$911$	−38.7405	+	12.5875i	−1.28353	+	0.417044i	−0.413707	+	0.910410i	$0.635766\pi$
$912$	10.9930	+	1.19723i	0.364013	+	0.0396441i
$913$	−0.670234	−	1.31541i	−0.0221815	−	0.0435337i
$914$	18.4267	−	26.0212i	0.609500	−	0.860704i
$915$		0			0
$916$	−38.6523	−	26.6721i	−1.27711	−	0.881272i
$917$	0.671964	+	4.24262i	0.0221902	+	0.140104i
$918$	−26.2198	−	3.82686i	−0.865382	−	0.126305i
$919$	0.445380	+	0.323588i	0.0146917	+	0.0106742i	0.595107	−	0.803647i	$-0.297110\pi$
$919$	0.445380	+	0.323588i	0.0146917	+	0.0106742i	−0.580415	+	0.814321i	$0.697110\pi$
$920$		0			0
$921$	−5.04702	+	3.66687i	−0.166305	+	0.120828i
$922$	20.9488	−	10.9965i	0.689910	−	0.362152i
$923$	8.03170	−	15.7631i	0.264367	−	0.518849i
$924$	1.26021	−	4.22521i	0.0414579	−	0.138999i
$925$		0			0
$926$	23.4107	+	31.4122i	0.769322	+	1.03227i
$927$	12.2309	+	6.23196i	0.401716	+	0.204684i
$928$	−0.00343165	+	0.0355131i	−0.000112649	+	0.00116578i
$929$	−0.175529	−	0.241595i	−0.00575892	−	0.00792648i	0.806128	−	0.591741i	$-0.201559\pi$
$929$	−0.175529	−	0.241595i	−0.00575892	−	0.00792648i	−0.811887	+	0.583815i	$0.801559\pi$
$930$		0			0
$931$	17.6291	−	24.2644i	0.577771	−	0.795233i
$932$	−3.91117	+	2.11408i	−0.128115	+	0.0692489i
$933$	11.3947	−	1.80475i	0.373046	−	0.0590847i
$934$	−4.69285	−	13.8675i	−0.153555	−	0.453759i
$935$		0			0
$936$	8.97380	−	7.03342i	0.293318	−	0.229895i
$937$	4.66050	−	2.37464i	0.152252	−	0.0775762i	−0.376205	−	0.926537i	$-0.622771\pi$
$937$	4.66050	−	2.37464i	0.152252	−	0.0775762i	0.528456	+	0.848960i	$0.322771\pi$
$938$	25.4462	+	12.5785i	0.830849	+	0.410701i
$939$	−6.25805	−	19.2603i	−0.204224	−	0.628536i
$940$		0			0
$941$	17.5386	−	53.9783i	0.571743	−	1.75964i	−0.0752692	−	0.997163i	$-0.523982\pi$
$941$	17.5386	−	53.9783i	0.571743	−	1.75964i	0.647012	−	0.762480i	$-0.276018\pi$
$942$	−11.3625	+	11.6420i	−0.370209	+	0.379316i
$943$	−38.9961	−	38.9961i	−1.26989	−	1.26989i
$944$	−21.0427	−	55.4404i	−0.684880	−	1.80443i
$945$		0			0
$946$	−2.72194	+	8.73708i	−0.0884980	+	0.284067i
$947$	−8.15849	+	51.5107i	−0.265115	+	1.67387i	0.391911	+	0.920003i	$0.371814\pi$
$947$	−8.15849	+	51.5107i	−0.265115	+	1.67387i	−0.657026	+	0.753868i	$0.728186\pi$
$948$	3.74530	−	3.93188i	0.121642	−	0.127702i
$949$			11.6649i			0.378658i
$950$		0			0
$951$		−	2.76902i		−	0.0897917i
$952$	6.06348	−	50.0208i	0.196519	−	1.62118i
$953$	7.71129	−	48.6871i	0.249793	−	1.57713i	−0.469824	−	0.882760i	$-0.655683\pi$
$953$	7.71129	−	48.6871i	0.249793	−	1.57713i	0.719617	−	0.694371i	$-0.244317\pi$
$954$	−30.2668	−	9.42930i	−0.979923	−	0.305285i
$955$		0			0
$956$	1.01457	+	1.32737i	0.0328135	+	0.0429303i
$957$	−0.00252268	−	0.00252268i	−8.15467e−5	−	8.15467e-5i
$958$	−24.0854	−	23.5071i	−0.778164	−	0.759481i
$959$	9.07401	−	27.9269i	0.293015	−	0.901807i
$960$		0			0
$961$	8.51805	+	26.2159i	0.274776	+	0.845673i
$962$	3.76175	−	7.61003i	0.121284	−	0.245357i
$963$	8.07732	−	4.11560i	0.260288	−	0.132623i
$964$	0.591130	+	24.3222i	0.0190390	+	0.783365i
$965$		0			0
$966$	−34.7806	+	11.7700i	−1.11905	+	0.378693i
$967$	42.4644	−	6.72570i	1.36556	−	0.216284i	0.569746	−	0.821821i	$-0.307041\pi$
$967$	42.4644	−	6.72570i	1.36556	−	0.216284i	0.795817	+	0.605537i	$0.207041\pi$
$968$	−26.7776	−	12.4364i	−0.860666	−	0.399720i
$969$	−7.42726	+	10.2227i	−0.238598	+	0.328402i
$970$		0			0
$971$	21.5829	+	29.7063i	0.692627	+	0.953319i	0.999999	+	0.00172953i	$0.000550527\pi$
$971$	21.5829	+	29.7063i	0.692627	+	0.953319i	−0.307372	+	0.951590i	$0.599449\pi$
$972$	−27.8919	−	13.3682i	−0.894634	−	0.428786i
$973$	−43.9900	−	22.4140i	−1.41026	−	0.718561i
$974$	27.5246	−	20.5133i	0.881945	−	0.657289i
$975$		0			0
$976$	−6.16237	−	4.03492i	−0.197253	−	0.129155i
$977$	1.15632	−	2.26941i	0.0369940	−	0.0726048i	−0.871770	−	0.489916i	$-0.837027\pi$
$977$	1.15632	−	2.26941i	0.0369940	−	0.0726048i	0.908764	+	0.417311i	$0.137027\pi$
$978$	−5.58717	−	10.6437i	−0.178658	−	0.340349i
$979$	−2.41718	+	1.75618i	−0.0772533	+	0.0561278i
$980$		0			0
$981$	−5.75649	−	4.18234i	−0.183791	−	0.133532i
$982$	4.46594	−	30.5984i	0.142514	−	0.976435i
$983$	−5.62969	−	35.5444i	−0.179559	−	1.13369i	−0.898615	−	0.438739i	$-0.855425\pi$
$983$	−5.62969	−	35.5444i	−0.179559	−	1.13369i	0.719055	−	0.694953i	$-0.244575\pi$
$984$	−13.3345	+	0.486244i	−0.425088	+	0.0155009i
$985$		0			0
$986$	−0.0332725	−	0.0235616i	−0.00105961	−	0.000750354i
$987$	−1.57700	−	3.09503i	−0.0501964	−	0.0985159i
$988$	−2.19157	−	11.9500i	−0.0697231	−	0.380181i
$989$	72.4794	−	23.5500i	2.30471	−	0.748846i
$990$		0			0
$991$	14.2120	+	4.61776i	0.451459	+	0.146688i	0.525916	−	0.850536i	$-0.323722\pi$
$991$	14.2120	+	4.61776i	0.451459	+	0.146688i	−0.0744574	+	0.997224i	$0.523722\pi$
$992$	10.2365	−	2.26575i	0.325010	−	0.0719377i
$993$	−8.14277	+	8.14277i	−0.258403	+	0.258403i
$994$	−0.714193	−	58.7800i	−0.0226528	−	1.86439i
$995$		0			0
$996$	0.987683	+	2.80589i	0.0312959	+	0.0889080i
$997$	−25.8603	−	4.09586i	−0.819003	−	0.129717i	−0.267146	−	0.963656i	$-0.586081\pi$
$997$	−25.8603	−	4.09586i	−0.819003	−	0.129717i	−0.551857	+	0.833939i	$0.686081\pi$
$998$	2.33825	+	13.6849i	0.0740159	+	0.433187i
$999$	−14.8336			−0.469313

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	500.2.l.e.107.7		96
4.3	odd	2	inner	500.2.l.e.107.10		96
5.2	odd	4		500.2.l.f.143.12		96
5.3	odd	4		100.2.l.b.83.1	yes	96
5.4	even	2		500.2.l.d.107.6		96
15.8	even	4		900.2.bj.d.883.12		96
20.3	even	4		100.2.l.b.83.4	yes	96
20.7	even	4		500.2.l.f.143.9		96
20.19	odd	2		500.2.l.d.107.3		96
25.3	odd	20	inner	500.2.l.e.243.10		96
25.4	even	10		500.2.l.f.7.9		96
25.21	even	5		100.2.l.b.47.4	yes	96
25.22	odd	20		500.2.l.d.243.3		96
60.23	odd	4		900.2.bj.d.883.9		96
75.71	odd	10		900.2.bj.d.847.9		96
100.3	even	20	inner	500.2.l.e.243.7		96
100.47	even	20		500.2.l.d.243.6		96
100.71	odd	10		100.2.l.b.47.1	✓	96
100.79	odd	10		500.2.l.f.7.12		96
300.71	even	10		900.2.bj.d.847.12		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.l.b.47.1	✓	96	100.71	odd	10
100.2.l.b.47.4	yes	96	25.21	even	5
100.2.l.b.83.1	yes	96	5.3	odd	4
100.2.l.b.83.4	yes	96	20.3	even	4
500.2.l.d.107.3		96	20.19	odd	2
500.2.l.d.107.6		96	5.4	even	2
500.2.l.d.243.3		96	25.22	odd	20
500.2.l.d.243.6		96	100.47	even	20
500.2.l.e.107.7		96	1.1	even	1	trivial
500.2.l.e.107.10		96	4.3	odd	2	inner
500.2.l.e.243.7		96	100.3	even	20	inner
500.2.l.e.243.10		96	25.3	odd	20	inner
500.2.l.f.7.9		96	25.4	even	10
500.2.l.f.7.12		96	100.79	odd	10
500.2.l.f.143.9		96	20.7	even	4
500.2.l.f.143.12		96	5.2	odd	4
900.2.bj.d.847.9		96	75.71	odd	10
900.2.bj.d.847.12		96	300.71	even	10
900.2.bj.d.883.9		96	60.23	odd	4
900.2.bj.d.883.12		96	15.8	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 500 = 2^{2} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	500.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.238186 - 1.39401i) q^{2} +(0.745599 + 0.118091i) q^{3} +(-1.88654 + 0.664067i) q^{4} +(-0.0129704 - 1.06750i) q^{6} +(-2.75590 + 2.75590i) q^{7} +(1.37506 + 2.47168i) q^{8} +(-2.31120 - 0.750953i) q^{9} +(0.712633 - 0.231549i) q^{11} +(-1.48502 + 0.272345i) q^{12} +(0.753078 + 1.47800i) q^{13} +(4.49817 + 3.18534i) q^{14} +(3.11803 - 2.50557i) q^{16} +(0.715035 + 4.51455i) q^{17} +(-0.496343 + 3.40070i) q^{18} +(2.96269 + 2.15252i) q^{19} +(-2.38025 + 1.72935i) q^{21} +(-0.492520 - 0.938267i) q^{22} +(-4.00635 + 7.86291i) q^{23} +(0.733362 + 2.00527i) q^{24} +(1.88097 - 1.40184i) q^{26} +(-3.65239 - 1.86099i) q^{27} +(3.36900 - 7.02921i) q^{28} +(-0.00370724 - 0.00510258i) q^{29} +(-1.08939 + 1.49941i) q^{31} +(-4.23547 - 3.74978i) q^{32} +(0.558683 - 0.0884866i) q^{33} +(6.12303 - 2.07207i) q^{34} +(4.85884 - 0.118090i) q^{36} +(3.22426 - 1.64284i) q^{37} +(2.29497 - 4.64273i) q^{38} +(0.386956 + 1.19093i) q^{39} +(-1.93115 + 5.94348i) q^{41} +(2.97767 + 2.90618i) q^{42} +(-6.10648 - 6.10648i) q^{43} +(-1.19064 + 0.910061i) q^{44} +(11.9152 + 3.71207i) q^{46} +(-0.184694 + 1.16611i) q^{47} +(2.62069 - 1.49994i) q^{48} -8.18997i q^{49} +3.45049i q^{51} +(-2.40220 - 2.28820i) q^{52} +(-1.44300 + 9.11077i) q^{53} +(-1.72429 + 5.53473i) q^{54} +(-10.6012 - 3.02217i) q^{56} +(1.95479 + 1.95479i) q^{57} +(-0.00623004 + 0.00638330i) q^{58} +(4.58114 - 14.0993i) q^{59} +(-0.569042 - 1.75133i) q^{61} +(2.34967 + 1.16148i) q^{62} +(8.43898 - 4.29987i) q^{63} +(-4.21840 + 6.79743i) q^{64} +(-0.256422 - 0.757734i) q^{66} +(5.08652 - 0.805626i) q^{67} +(-4.34691 - 8.04203i) q^{68} +(-3.91567 + 5.38946i) q^{69} +(-6.26883 - 8.62831i) q^{71} +(-1.32192 - 6.74515i) q^{72} +(6.26568 + 3.19252i) q^{73} +(-3.05811 - 4.10335i) q^{74} +(-7.01865 - 2.09338i) q^{76} +(-1.32582 + 2.60207i) q^{77} +(1.56800 - 0.823082i) q^{78} +(-2.90976 + 2.11406i) q^{79} +(3.39461 + 2.46633i) q^{81} +(8.74525 + 1.27640i) q^{82} +(-0.308214 - 1.94599i) q^{83} +(3.34201 - 4.84312i) q^{84} +(-7.05803 + 9.96698i) q^{86} +(-0.00216155 - 0.00424227i) q^{87} +(1.55223 + 1.44301i) q^{88} +(-3.79225 + 1.23218i) q^{89} +(-6.14862 - 1.99781i) q^{91} +(2.33662 - 17.4941i) q^{92} +(-0.989314 + 0.989314i) q^{93} +(1.66956 - 0.0202857i) q^{94} +(-2.71514 - 3.29600i) q^{96} +(6.43432 + 1.01910i) q^{97} +(-11.4169 + 1.95073i) q^{98} -1.82092 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 10 q^{4} - 6 q^{6} + 30 q^{8} + 20 q^{9} + 10 q^{14} - 14 q^{16} + 20 q^{18} - 12 q^{21} - 50 q^{22} - 12 q^{26} - 40 q^{28} + 20 q^{29} - 50 q^{32} + 60 q^{34} - 10 q^{36} - 40 q^{37} + 70 q^{38}+ \cdots - 70 q^{98}+O(q^{100}) \) 96 * q + 10 * q^4 - 6 * q^6 + 30 * q^8 + 20 * q^9 + 10 * q^14 - 14 * q^16 + 20 * q^18 - 12 * q^21 - 50 * q^22 - 12 * q^26 - 40 * q^28 + 20 * q^29 - 50 * q^32 + 60 * q^34 - 10 * q^36 - 40 * q^37 + 70 * q^38 - 28 * q^41 + 60 * q^42 - 60 * q^44 - 6 * q^46 - 100 * q^52 - 80 * q^53 - 120 * q^54 - 6 * q^56 - 20 * q^57 - 120 * q^58 + 12 * q^61 - 20 * q^64 - 30 * q^66 - 10 * q^68 + 20 * q^69 + 150 * q^72 + 140 * q^77 + 130 * q^78 - 36 * q^81 - 50 * q^82 + 90 * q^84 - 6 * q^86 - 110 * q^88 - 160 * q^89 - 90 * q^92 + 60 * q^93 + 170 * q^94 + 14 * q^96 - 70 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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