LMFDB - Embedded newform 192.2.s.a.11.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [192,2,Mod(11,192)] 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("192.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(192, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 5, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.s (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			11.11
Character	$\chi$	$=$	192.11
Dual form			192.2.s.a.35.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.640805 + 1.26070i) q^{2} +(0.585574 - 1.63006i) q^{3} +(-1.17874 - 1.61573i) q^{4} +(-3.57797 + 2.39072i) q^{5} +(1.67978 + 1.78279i) q^{6} +(-0.994439 + 2.40079i) q^{7} +(2.79229 - 0.450669i) q^{8} +(-2.31421 - 1.90904i) q^{9} +(-0.721207 - 6.04274i) q^{10} +(-0.714367 + 3.59136i) q^{11} +(-3.32398 + 0.975288i) q^{12} +(-1.38986 + 2.08008i) q^{13} +(-2.38944 - 2.79213i) q^{14} +(1.80186 + 7.23226i) q^{15} +(-1.22116 + 3.80904i) q^{16} +(-0.951204 - 0.951204i) q^{17} +(3.88969 - 1.69420i) q^{18} +(-0.214739 + 0.321380i) q^{19} +(8.08025 + 2.96299i) q^{20} +(3.33112 + 3.02684i) q^{21} +(-4.06987 - 3.20197i) q^{22} +(-1.14288 - 2.75916i) q^{23} +(0.900474 - 4.81551i) q^{24} +(5.17290 - 12.4885i) q^{25} +(-1.73173 - 3.08513i) q^{26} +(-4.46700 + 2.65442i) q^{27} +(5.05121 - 1.22316i) q^{28} +(-2.53398 + 0.504039i) q^{29} +(-10.2724 - 2.36286i) q^{30} +2.03735 q^{31} +(-4.01954 - 3.98037i) q^{32} +(5.43583 + 3.26747i) q^{33} +(1.80872 - 0.589648i) q^{34} +(-2.18155 - 10.9674i) q^{35} +(-0.356653 + 5.98939i) q^{36} +(4.28668 - 2.86427i) q^{37} +(-0.267558 - 0.476664i) q^{38} +(2.57679 + 3.48361i) q^{39} +(-8.91331 + 8.28808i) q^{40} +(4.29457 - 1.77887i) q^{41} +(-5.95054 + 2.25993i) q^{42} +(-1.88124 + 9.45763i) q^{43} +(6.64472 - 3.07905i) q^{44} +(12.8442 + 1.29787i) q^{45} +(4.21083 + 0.327251i) q^{46} +(-5.57116 + 5.57116i) q^{47} +(5.49389 + 4.22103i) q^{48} +(0.174869 + 0.174869i) q^{49} +(12.4294 + 14.5242i) q^{50} +(-2.10752 + 0.993522i) q^{51} +(4.99913 - 0.206223i) q^{52} +(1.47041 + 0.292483i) q^{53} +(-0.483953 - 7.33252i) q^{54} +(-6.02998 - 14.5576i) q^{55} +(-1.69480 + 7.15187i) q^{56} +(0.398124 + 0.538230i) q^{57} +(0.988343 - 3.51758i) q^{58} +(3.66506 + 5.48515i) q^{59} +(9.56144 - 11.4363i) q^{60} +(-4.09381 + 0.814309i) q^{61} +(-1.30554 + 2.56849i) q^{62} +(6.88455 - 3.65750i) q^{63} +(7.59380 - 2.51680i) q^{64} -10.7652i q^{65} +(-7.60262 + 4.75915i) q^{66} +(1.50936 + 7.58806i) q^{67} +(-0.415668 + 2.65811i) q^{68} +(-5.16684 + 0.247277i) q^{69} +(15.2245 + 4.27767i) q^{70} +(6.27514 + 2.59925i) q^{71} +(-7.32229 - 4.28767i) q^{72} +(-15.4732 + 6.40920i) q^{73} +(0.864060 + 7.23966i) q^{74} +(-17.3279 - 15.7451i) q^{75} +(0.772384 - 0.0318623i) q^{76} +(-7.91171 - 5.28644i) q^{77} +(-6.04301 + 1.01625i) q^{78} +(2.31400 - 2.31400i) q^{79} +(-4.73710 - 16.5481i) q^{80} +(1.71111 + 8.83584i) q^{81} +(-0.509359 + 6.55408i) q^{82} +(-1.62719 - 1.08726i) q^{83} +(0.964032 - 8.95003i) q^{84} +(5.67744 + 1.12931i) q^{85} +(-10.7177 - 8.43218i) q^{86} +(-0.662214 + 4.42569i) q^{87} +(-0.376205 + 10.3501i) q^{88} +(4.04231 + 1.67438i) q^{89} +(-9.86683 + 15.3610i) q^{90} +(-3.61170 - 5.40528i) q^{91} +(-3.11089 + 5.09890i) q^{92} +(1.19302 - 3.32101i) q^{93} +(-3.45354 - 10.5936i) q^{94} -1.66327i q^{95} +(-8.84198 + 4.22130i) q^{96} +1.86899i q^{97} +(-0.332515 + 0.108401i) q^{98} +(8.50926 - 6.94740i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{16}\right)$

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 $

$2$	−0.640805	+	1.26070i	−0.453118	+	0.891451i
$2$	−0.640805	+	1.26070i	−0.453118	+	0.891451i
$3$	0.585574	−	1.63006i	0.338081	−	0.941117i
$3$	0.585574	−	1.63006i	0.338081	−	0.941117i
$4$	−1.17874	−	1.61573i	−0.589369	−	0.807864i
$5$	−3.57797	+	2.39072i	−1.60012	+	1.06916i	−0.648796	+	0.760963i	$0.724727\pi$
$5$	−3.57797	+	2.39072i	−1.60012	+	1.06916i	−0.951321	+	0.308201i	$0.900273\pi$
$6$	1.67978	+	1.78279i	0.685769	+	0.727819i
$7$	−0.994439	+	2.40079i	−0.375863	+	0.907413i	0.616869	+	0.787066i	$0.288401\pi$
$7$	−0.994439	+	2.40079i	−0.375863	+	0.907413i	−0.992732	+	0.120347i	$0.961599\pi$
$8$	2.79229	−	0.450669i	0.987224	−	0.159336i
$9$	−2.31421	−	1.90904i	−0.771402	−	0.636348i
$10$	−0.721207	−	6.04274i	−0.228066	−	1.91088i
$11$	−0.714367	+	3.59136i	−0.215390	+	1.08284i	0.710111	+	0.704090i	$0.248645\pi$
$11$	−0.714367	+	3.59136i	−0.215390	+	1.08284i	−0.925500	+	0.378747i	$0.876355\pi$
$12$	−3.32398	+	0.975288i	−0.959549	+	0.281541i
$13$	−1.38986	+	2.08008i	−0.385479	+	0.576910i	−0.972570	−	0.232611i	$-0.925273\pi$
$13$	−1.38986	+	2.08008i	−0.385479	+	0.576910i	0.587091	+	0.809521i	$0.300273\pi$
$14$	−2.38944	−	2.79213i	−0.638604	−	0.746228i
$15$	1.80186	+	7.23226i	0.465239	+	1.86736i
$16$	−1.22116	+	3.80904i	−0.305289	+	0.952260i
$17$	−0.951204	−	0.951204i	−0.230701	−	0.230701i	0.582284	−	0.812985i	$-0.302159\pi$
$17$	−0.951204	−	0.951204i	−0.230701	−	0.230701i	−0.812985	+	0.582284i	$0.802159\pi$
$18$	3.88969	−	1.69420i	0.916809	−	0.399327i
$19$	−0.214739	+	0.321380i	−0.0492646	+	0.0737297i	−0.855284	−	0.518159i	$-0.826618\pi$
$19$	−0.214739	+	0.321380i	−0.0492646	+	0.0737297i	0.806020	+	0.591889i	$0.201618\pi$
$20$	8.08025	+	2.96299i	1.80680	+	0.662545i
$21$	3.33112	+	3.02684i	0.726910	+	0.660510i
$22$	−4.06987	−	3.20197i	−0.867699	−	0.682662i
$23$	−1.14288	−	2.75916i	−0.238307	−	0.575324i	0.758801	−	0.651322i	$-0.225785\pi$
$23$	−1.14288	−	2.75916i	−0.238307	−	0.575324i	−0.997108	+	0.0759988i	$0.975785\pi$
$24$	0.900474	−	4.81551i	0.183809	−	0.982962i
$25$	5.17290	−	12.4885i	1.03458	−	2.49769i
$26$	−1.73173	−	3.08513i	−0.339620	−	0.605044i
$27$	−4.46700	+	2.65442i	−0.859674	+	0.510843i
$28$	5.05121	−	1.22316i	0.954588	−	0.231155i
$29$	−2.53398	+	0.504039i	−0.470548	+	0.0935978i	−0.424668	−	0.905349i	$-0.639609\pi$
$29$	−2.53398	+	0.504039i	−0.470548	+	0.0935978i	−0.0458799	+	0.998947i	$0.514609\pi$
$30$	−10.2724	−	2.36286i	−1.87547	−	0.431397i
$31$	2.03735			0.365919			0.182959	−	0.983120i	$-0.441432\pi$
$31$	2.03735			0.365919			0.182959	+	0.983120i	$0.441432\pi$
$32$	−4.01954	−	3.98037i	−0.710561	−	0.703636i
$33$	5.43583	+	3.26747i	0.946257	+	0.568794i
$34$	1.80872	−	0.589648i	0.310193	−	0.101124i
$35$	−2.18155	−	10.9674i	−0.368749	−	1.85383i
$36$	−0.356653	+	5.98939i	−0.0594421	+	0.998232i
$37$	4.28668	−	2.86427i	0.704726	−	0.470883i	−0.150852	−	0.988556i	$-0.548202\pi$
$37$	4.28668	−	2.86427i	0.704726	−	0.470883i	0.855578	+	0.517674i	$0.173202\pi$
$38$	−0.267558	−	0.476664i	−0.0434037	−	0.0773252i
$39$	2.57679	+	3.48361i	0.412617	+	0.557823i
$40$	−8.91331	+	8.28808i	−1.40932	+	1.31046i
$41$	4.29457	−	1.77887i	0.670699	−	0.277813i	−0.0212338	−	0.999775i	$-0.506759\pi$
$41$	4.29457	−	1.77887i	0.670699	−	0.277813i	0.691933	+	0.721962i	$0.256759\pi$
$42$	−5.95054	+	2.25993i	−0.918188	+	0.348715i
$43$	−1.88124	+	9.45763i	−0.286886	+	1.44228i	0.521312	+	0.853366i	$0.325443\pi$
$43$	−1.88124	+	9.45763i	−0.286886	+	1.44228i	−0.808199	+	0.588910i	$0.799557\pi$
$44$	6.64472	−	3.07905i	1.00173	−	0.464185i
$45$	12.8442	+	1.29787i	1.91469	+	0.193475i
$46$	4.21083	+	0.327251i	0.620854	+	0.0482505i
$47$	−5.57116	+	5.57116i	−0.812637	+	0.812637i	−0.985028	−	0.172392i	$-0.944850\pi$
$47$	−5.57116	+	5.57116i	−0.812637	+	0.812637i	0.172392	+	0.985028i	$0.444850\pi$
$48$	5.49389	+	4.22103i	0.792975	+	0.609254i
$49$	0.174869	+	0.174869i	0.0249813	+	0.0249813i
$50$	12.4294	+	14.5242i	1.75779	+	2.05403i
$51$	−2.10752	+	0.993522i	−0.295112	+	0.139121i
$52$	4.99913	−	0.206223i	0.693254	−	0.0285981i
$53$	1.47041	+	0.292483i	0.201977	+	0.0401757i	0.295042	−	0.955484i	$-0.404666\pi$
$53$	1.47041	+	0.292483i	0.201977	+	0.0401757i	−0.0930650	+	0.995660i	$0.529666\pi$
$54$	−0.483953	−	7.33252i	−0.0658576	−	0.997829i
$55$	−6.02998	−	14.5576i	−0.813082	−	1.96295i
$56$	−1.69480	+	7.15187i	−0.226478	+	0.955709i
$57$	0.398124	+	0.538230i	0.0527328	+	0.0712903i
$58$	0.988343	−	3.51758i	0.129776	−	0.461881i
$59$	3.66506	+	5.48515i	0.477150	+	0.714105i	0.989478	−	0.144685i	$-0.0462167\pi$
$59$	3.66506	+	5.48515i	0.477150	+	0.714105i	−0.512328	+	0.858790i	$0.671217\pi$
$60$	9.56144	−	11.4363i	1.23438	−	1.47641i
$61$	−4.09381	+	0.814309i	−0.524158	+	0.104262i	−0.450075	−	0.892991i	$-0.648603\pi$
$61$	−4.09381	+	0.814309i	−0.524158	+	0.104262i	−0.0740827	+	0.997252i	$0.523603\pi$
$62$	−1.30554	+	2.56849i	−0.165804	+	0.326199i
$63$	6.88455	−	3.65750i	0.867372	−	0.460801i
$64$	7.59380	−	2.51680i	0.949224	−	0.314600i
$65$		−	10.7652i		−	1.33526i
$66$	−7.60262	+	4.75915i	−0.935817	+	0.585811i
$67$	1.50936	+	7.58806i	0.184398	+	0.927029i	0.956545	+	0.291585i	$0.0941827\pi$
$67$	1.50936	+	7.58806i	0.184398	+	0.927029i	−0.772147	+	0.635444i	$0.780817\pi$
$68$	−0.415668	+	2.65811i	−0.0504071	+	0.322343i
$69$	−5.16684	+	0.247277i	−0.622014	+	0.0297686i
$70$	15.2245	+	4.27767i	1.81968	+	0.511280i
$71$	6.27514	+	2.59925i	0.744722	+	0.308474i	0.722586	−	0.691281i	$-0.242953\pi$
$71$	6.27514	+	2.59925i	0.744722	+	0.308474i	0.0221361	+	0.999755i	$0.492953\pi$
$72$	−7.32229	−	4.28767i	−0.862940	−	0.505306i
$73$	−15.4732	+	6.40920i	−1.81100	+	0.750140i	−0.829543	+	0.558443i	$0.811399\pi$
$73$	−15.4732	+	6.40920i	−1.81100	+	0.750140i	−0.981454	+	0.191697i	$0.938601\pi$
$74$	0.864060	+	7.23966i	0.100445	+	0.841593i
$75$	−17.3279	−	15.7451i	−2.00085	−	1.81808i
$76$	0.772384	−	0.0318623i	0.0885985	−	0.00365486i
$77$	−7.91171	−	5.28644i	−0.901623	−	0.602446i
$78$	−6.04301	+	1.01625i	−0.684236	+	0.115068i
$79$	2.31400	−	2.31400i	0.260345	−	0.260345i	−0.564849	−	0.825194i	$-0.691066\pi$
$79$	2.31400	−	2.31400i	0.260345	−	0.260345i	0.825194	+	0.564849i	$0.191066\pi$
$80$	−4.73710	−	16.5481i	−0.529623	−	1.85013i
$81$	1.71111	+	8.83584i	0.190123	+	0.981760i
$82$	−0.509359	+	6.55408i	−0.0562493	+	0.723777i
$83$	−1.62719	−	1.08726i	−0.178608	−	0.119342i	0.463053	−	0.886331i	$-0.346754\pi$
$83$	−1.62719	−	1.08726i	−0.178608	−	0.119342i	−0.641660	+	0.766989i	$0.721754\pi$
$84$	0.964032	−	8.95003i	0.105185	−	0.976528i
$85$	5.67744	+	1.12931i	0.615805	+	0.122491i
$86$	−10.7177	−	8.43218i	−1.15572	−	0.909266i
$87$	−0.662214	+	4.42569i	−0.0709968	+	0.474484i
$88$	−0.376205	+	10.3501i	−0.0401036	+	1.10332i
$89$	4.04231	+	1.67438i	0.428484	+	0.177484i	0.586494	−	0.809954i	$-0.300508\pi$
$89$	4.04231	+	1.67438i	0.428484	+	0.177484i	−0.158010	+	0.987438i	$0.550508\pi$
$90$	−9.86683	+	15.3610i	−1.04006	+	1.61919i
$91$	−3.61170	−	5.40528i	−0.378609	−	0.566628i
$92$	−3.11089	+	5.09890i	−0.324333	+	0.531597i
$93$	1.19302	−	3.32101i	0.123710	−	0.344372i
$94$	−3.45354	−	10.5936i	−0.356205	−	1.09265i
$95$		−	1.66327i		−	0.170648i
$96$	−8.84198	+	4.22130i	−0.902431	+	0.430835i
$97$			1.86899i			0.189767i	0.995488	+	0.0948834i	$0.0302478\pi$
$97$			1.86899i			0.189767i	−0.995488	+	0.0948834i	$0.969752\pi$
$98$	−0.332515	+	0.108401i	−0.0335891	+	0.0109501i
$99$	8.50926	−	6.94740i	0.855213	−	0.698240i
$100$	−26.2755	+	6.36264i	−2.62755	+	0.636264i
$101$	−7.63182	−	11.4218i	−0.759395	−	1.13651i	−0.986678	−	0.162686i	$-0.947984\pi$
$101$	−7.63182	−	11.4218i	−0.759395	−	1.13651i	0.227283	−	0.973829i	$-0.427016\pi$
$102$	0.0979762	−	3.29361i	0.00970109	−	0.326116i
$103$	13.4251	+	5.56087i	1.32282	+	0.547929i	0.928598	−	0.371087i	$-0.121015\pi$
$103$	13.4251	+	5.56087i	1.32282	+	0.547929i	0.394220	+	0.919016i	$0.371015\pi$
$104$	−2.94348	+	6.43456i	−0.288632	+	0.630960i
$105$	−19.1550	−	2.86615i	−1.86933	−	0.279708i
$106$	−1.31098	+	1.66633i	−0.127334	+	0.161848i
$107$	2.15026	+	0.427713i	0.207874	+	0.0413486i	0.297929	−	0.954588i	$-0.403704\pi$
$107$	2.15026	+	0.427713i	0.207874	+	0.0413486i	−0.0900550	+	0.995937i	$0.528704\pi$
$108$	9.55423	+	4.08859i	0.919357	+	0.393425i
$109$	−14.2766	−	9.53929i	−1.36745	−	0.913698i	−0.367579	−	0.929992i	$-0.619813\pi$
$109$	−14.2766	−	9.53929i	−1.36745	−	0.913698i	−0.999867	+	0.0162943i	$0.994813\pi$
$110$	22.2169	+	1.72662i	2.11830	+	0.164626i
$111$	−2.15877	−	8.66479i	−0.204901	−	0.822426i
$112$	−7.93033	−	6.71960i	−0.749346	−	0.634942i
$113$	8.95069	−	8.95069i	0.842010	−	0.842010i	−0.147110	−	0.989120i	$-0.546997\pi$
$113$	8.95069	−	8.95069i	0.842010	−	0.842010i	0.989120	+	0.147110i	$0.0469971\pi$
$114$	−0.933668	+	0.157015i	−0.0874460	+	0.0147058i
$115$	10.6856	+	7.13987i	0.996434	+	0.665796i
$116$	3.80128	+	3.50009i	0.352940	+	0.324975i
$117$	7.18740	−	2.16042i	0.664475	−	0.199731i
$118$	−9.26372	+	1.10563i	−0.852795	+	0.101782i
$119$	3.22955	−	1.33773i	0.296053	−	0.122629i
$120$	8.29068	+	19.3825i	0.756832	+	1.76938i
$121$	−2.22490	−	0.921585i	−0.202264	−	0.0837805i
$122$	1.59673	−	5.68288i	0.144561	−	0.514504i
$123$	−0.384881	−	8.04207i	−0.0347036	−	0.725129i
$124$	−2.40150	−	3.29180i	−0.215661	−	0.295613i
$125$	7.15047	+	35.9478i	0.639557	+	3.21527i
$126$	0.199356	+	11.0231i	0.0177601	+	0.982016i
$127$			17.0863i			1.51617i	0.652158	+	0.758083i	$0.273864\pi$
$127$			17.0863i			1.51617i	−0.652158	+	0.758083i	$0.726136\pi$
$128$	−1.69321	+	11.1863i	−0.149660	+	0.988737i
$129$	14.3149	+	8.60468i	1.26036	+	0.757600i
$130$	13.5718	+	6.89842i	1.19032	+	0.605032i
$131$	−1.56358	+	0.311016i	−0.136611	+	0.0271736i	−0.262922	−	0.964817i	$-0.584686\pi$
$131$	−1.56358	+	0.311016i	−0.136611	+	0.0271736i	0.126311	+	0.991991i	$0.459686\pi$
$132$	−1.12808	−	12.6343i	−0.0981864	−	1.09968i
$133$	−0.558021	−	0.835137i	−0.0483865	−	0.0724155i
$134$	−10.5335	−	2.95962i	−0.909954	−	0.255672i
$135$	9.63681	−	20.1768i	0.829404	−	1.73654i
$136$	−3.08472	−	2.22736i	−0.264512	−	0.190995i
$137$	−5.56434	−	13.4335i	−0.475393	−	1.14770i	−0.961747	−	0.273939i	$-0.911673\pi$
$137$	−5.56434	−	13.4335i	−0.475393	−	1.14770i	0.486354	−	0.873762i	$-0.338327\pi$
$138$	2.99919	−	6.67229i	0.255308	−	0.567983i
$139$	−4.94256	−	0.983137i	−0.419223	−	0.0833886i	−0.0190285	−	0.999819i	$-0.506057\pi$
$139$	−4.94256	−	0.983137i	−0.419223	−	0.0833886i	−0.400194	+	0.916430i	$0.631057\pi$
$140$	−15.1488	+	16.4524i	−1.28031	+	1.39049i
$141$	5.81901	+	12.3437i	0.490049	+	1.03952i
$142$	−7.29802	+	6.24547i	−0.612436	+	0.524108i
$143$	−6.47745	−	6.47745i	−0.541672	−	0.541672i
$144$	10.0976	−	6.48366i	0.841469	−	0.540305i
$145$	7.86148	−	7.86148i	0.652860	−	0.652860i
$146$	1.83520	−	23.6141i	0.151882	−	1.95432i
$147$	0.387446	−	0.182649i	0.0319560	−	0.0150646i
$148$	−9.68075	−	3.54989i	−0.795752	−	0.291799i
$149$	−0.473681	+	2.38135i	−0.0388054	+	0.195088i	−0.995325	−	0.0965790i	$-0.969210\pi$
$149$	−0.473681	+	2.38135i	−0.0388054	+	0.195088i	0.956520	+	0.291667i	$0.0942100\pi$
$150$	30.9536	−	11.7558i	2.52735	−	0.959855i
$151$	−1.17767	+	0.487807i	−0.0958374	+	0.0396972i	−0.430087	−	0.902787i	$-0.641517\pi$
$151$	−1.17767	+	0.487807i	−0.0958374	+	0.0396972i	0.334250	+	0.942485i	$0.391517\pi$
$152$	−0.454779	+	0.994164i	−0.0368874	+	0.0806373i
$153$	0.385394	+	4.01717i	0.0311572	+	0.324769i
$154$	11.7345	−	6.58673i	0.945592	−	0.530774i
$155$	−7.28958	+	4.87074i	−0.585513	+	0.391227i
$156$	2.59120	−	8.26965i	0.207462	−	0.662102i
$157$	2.08481	+	10.4811i	0.166386	+	0.836479i	0.970332	+	0.241777i	$0.0777302\pi$
$157$	2.08481	+	10.4811i	0.166386	+	0.836479i	−0.803946	+	0.594703i	$0.797270\pi$
$158$	1.43444	+	4.40008i	0.114118	+	0.350052i
$159$	1.33780	−	2.22559i	0.106094	−	0.176501i
$160$	23.8977	+	4.63203i	1.88928	+	0.366194i
$161$	7.76067			0.611627
$162$	−12.2358	−	3.50485i	−0.961339	−	0.275367i
$163$	−7.80064	+	1.55164i	−0.610993	+	0.121534i	−0.490882	−	0.871226i	$-0.663325\pi$
$163$	−7.80064	+	1.55164i	−0.610993	+	0.121534i	−0.120112	+	0.992760i	$0.538325\pi$
$164$	−7.93634	−	4.84204i	−0.619724	−	0.378100i
$165$	−27.2609	+	1.30466i	−2.12226	+	0.101568i
$166$	2.41342	−	1.35469i	0.187318	−	0.105144i
$167$	−6.86336	+	16.5696i	−0.531103	+	1.28220i	0.399691	+	0.916650i	$0.369118\pi$
$167$	−6.86336	+	16.5696i	−0.531103	+	1.28220i	−0.930793	+	0.365545i	$0.880882\pi$
$168$	10.6656	+	6.95058i	0.822866	+	0.536249i
$169$	2.57988	+	6.22838i	0.198452	+	0.479106i
$170$	−5.06186	+	6.43389i	−0.388227	+	0.493457i
$171$	1.11048	−	0.333794i	0.0849205	−	0.0255258i
$172$	17.4985	−	8.10849i	1.33424	−	0.618267i
$173$	−7.24199	+	10.8384i	−0.550598	+	0.824029i	−0.997508	−	0.0705503i	$-0.977524\pi$
$173$	−7.24199	+	10.8384i	−0.550598	+	0.824029i	0.446910	+	0.894579i	$0.352524\pi$
$174$	−5.15513	−	3.67086i	−0.390809	−	0.278287i
$175$	24.8381	+	24.8381i	1.87758	+	1.87758i
$176$	−12.8073	−	7.10667i	−0.965386	−	0.535685i
$177$	11.0873	−	2.76232i	0.833372	−	0.207628i
$178$	−4.70122	+	4.02319i	−0.352372	+	0.301551i
$179$	3.45085	−	5.16456i	0.257929	−	0.386018i	−0.679794	−	0.733404i	$-0.737931\pi$
$179$	3.45085	−	5.16456i	0.257929	−	0.386018i	0.937722	+	0.347386i	$0.112931\pi$
$180$	−13.0429	−	22.2825i	−0.972159	−	1.66084i
$181$	2.65101	−	13.3275i	0.197048	−	0.990627i	−0.748001	−	0.663698i	$-0.768986\pi$
$181$	2.65101	−	13.3275i	0.197048	−	0.990627i	0.945049	−	0.326929i	$-0.106014\pi$
$182$	9.12884	−	1.08954i	0.676675	−	0.0807618i
$183$	−1.06985	+	7.15000i	−0.0790856	+	0.528543i
$184$	−4.43472	−	7.18931i	−0.326932	−	0.530003i
$185$	−8.48994	+	20.4965i	−0.624193	+	1.50693i
$186$	3.42231	+	3.63216i	0.250936	+	0.266323i
$187$	4.09563	−	2.73661i	0.299502	−	0.200121i
$188$	15.5684	+	2.43455i	1.13544	+	0.177557i
$189$	−1.93054	−	13.3640i	−0.140426	−	0.972086i
$190$	2.09689	+	1.06583i	0.152124	+	0.0773236i
$191$	13.5497			0.980420			0.490210	−	0.871604i	$-0.336920\pi$
$191$	13.5497			0.980420			0.490210	+	0.871604i	$0.336920\pi$
$192$	0.344186	−	13.8521i	0.0248395	−	0.999691i
$193$	−20.6394			−1.48566			−0.742830	−	0.669480i	$-0.766517\pi$
$193$	−20.6394			−1.48566			−0.742830	+	0.669480i	$0.766517\pi$
$194$	−2.35623	−	1.19766i	−0.169168	−	0.0859867i
$195$	−17.5480	−	6.30384i	−1.25664	−	0.451427i
$196$	0.0764163	−	0.488666i	0.00545830	−	0.0349047i
$197$	2.97611	−	1.98857i	0.212039	−	0.141680i	−0.445016	−	0.895523i	$-0.646802\pi$
$197$	2.97611	−	1.98857i	0.212039	−	0.141680i	0.657055	+	0.753843i	$0.271802\pi$
$198$	3.30582	+	15.1796i	0.234935	+	1.07877i
$199$	5.60732	−	13.5373i	0.397492	−	0.959631i	−0.590767	−	0.806842i	$-0.701175\pi$
$199$	5.60732	−	13.5373i	0.397492	−	0.959631i	0.988259	−	0.152788i	$-0.0488253\pi$
$200$	8.81607	−	37.2027i	0.623390	−	2.63063i
$201$	13.2529	+	1.98302i	0.934784	+	0.139871i
$202$	19.2900	−	2.30228i	1.35724	−	0.161988i
$203$	1.30979	−	6.58478i	0.0919295	−	0.462161i
$204$	4.08948	+	2.23408i	0.286321	+	0.156417i
$205$	−11.1131	+	16.6319i	−0.776169	+	1.16162i
$206$	−15.6135	+	13.3617i	−1.08784	+	0.930951i
$207$	−2.62249	+	8.56706i	−0.182275	+	0.595452i
$208$	−6.22586	−	7.83415i	−0.431686	−	0.543201i
$209$	−1.00079	−	1.00079i	−0.0692261	−	0.0692261i
$210$	15.8880	−	22.3121i	1.09637	−	1.53968i
$211$	10.2740	−	15.3761i	0.707289	−	1.05853i	−0.287619	−	0.957745i	$-0.592864\pi$
$211$	10.2740	−	15.3761i	0.707289	−	1.05853i	0.994908	−	0.100788i	$-0.0321362\pi$
$212$	−1.26066	−	2.72055i	−0.0865823	−	0.186848i
$213$	7.91149	−	8.70682i	0.542087	−	0.596581i
$214$	−1.91712	+	2.43676i	−0.131051	+	0.166573i
$215$	−15.8796	−	38.3367i	−1.08298	−	2.61454i
$216$	−11.2769	+	9.42505i	−0.767296	+	0.641293i
$217$	−2.02602	+	4.89125i	−0.137535	+	0.332040i
$218$	21.1747	−	11.8856i	1.43413	−	0.804998i
$219$	1.38671	+	28.9753i	0.0937053	+	1.95797i
$220$	−16.4134	+	26.9024i	−1.10659	+	1.81376i
$221$	3.30062	−	0.656535i	0.222024	−	0.0441633i
$222$	12.3071	+	2.83088i	0.825996	+	0.189996i
$223$	−19.2274			−1.28756			−0.643782	−	0.765209i	$-0.722636\pi$
$223$	−19.2274			−1.28756			−0.643782	+	0.765209i	$0.722636\pi$
$224$	13.5532	−	5.69183i	0.905562	−	0.380301i
$225$	−35.8122	+	19.0256i	−2.38748	+	1.26838i
$226$	5.54850	+	17.0198i	0.369081	+	1.13214i
$227$	1.97234	+	9.91561i	0.130909	+	0.658122i	0.989391	+	0.145279i	$0.0464079\pi$
$227$	1.97234	+	9.91561i	0.130909	+	0.658122i	−0.858482	+	0.512844i	$0.828592\pi$
$228$	0.400350	−	1.27769i	0.0265138	−	0.0846172i
$229$	14.4937	−	9.68436i	0.957768	−	0.639960i	0.0247136	−	0.999695i	$-0.492133\pi$
$229$	14.4937	−	9.68436i	0.957768	−	0.639960i	0.933055	+	0.359734i	$0.117133\pi$
$230$	−15.8486	+	8.89605i	−1.04503	+	0.586588i
$231$	−13.2501	+	9.80099i	−0.871794	+	0.644858i
$232$	−6.84845	+	2.54941i	−0.449623	+	0.167377i
$233$	7.39105	−	3.06147i	0.484203	−	0.200564i	−0.127209	−	0.991876i	$-0.540602\pi$
$233$	7.39105	−	3.06147i	0.484203	−	0.200564i	0.611412	+	0.791312i	$0.290602\pi$
$234$	−1.88207	+	10.4456i	−0.123035	+	0.682848i
$235$	6.61434	−	33.2525i	0.431472	−	2.16916i
$236$	4.54237	−	12.3873i	0.295683	−	0.806344i
$237$	−2.41694	−	5.12698i	−0.156997	−	0.333033i
$238$	−0.383043	+	4.92873i	−0.0248290	+	0.319482i
$239$	8.30613	−	8.30613i	0.537279	−	0.537279i	−0.385450	−	0.922729i	$-0.625954\pi$
$239$	8.30613	−	8.30613i	0.537279	−	0.537279i	0.922729	+	0.385450i	$0.125954\pi$
$240$	−29.7483	−	1.96835i	−1.92025	−	0.127057i
$241$	3.01268	+	3.01268i	0.194063	+	0.194063i	0.797449	−	0.603386i	$-0.206182\pi$
$241$	3.01268	+	3.01268i	0.194063	+	0.194063i	−0.603386	+	0.797449i	$0.706182\pi$
$242$	2.58757	−	2.21438i	0.166336	−	0.142346i
$243$	15.4050	+	2.38482i	0.988228	+	0.152986i
$244$	6.14122	+	5.65462i	0.393152	+	0.362000i
$245$	−1.04374	−	0.207613i	−0.0666821	−	0.0132639i
$246$	10.3853	+	4.66818i	0.662142	+	0.297632i
$247$	−0.370038	−	0.893350i	−0.0235449	−	0.0568425i
$248$	5.68888	−	0.918170i	0.361244	−	0.0583039i
$249$	−2.72514	+	2.01576i	−0.172698	+	0.127743i
$250$	−49.9015	−	14.0209i	−3.15605	−	0.886763i
$251$	7.23109	+	10.8221i	0.456422	+	0.683085i	0.986295	−	0.164993i	$-0.0527601\pi$
$251$	7.23109	+	10.8221i	0.456422	+	0.683085i	−0.529872	+	0.848077i	$0.677760\pi$
$252$	−14.0246	−	6.81233i	−0.883466	−	0.429137i
$253$	10.7256	−	2.13345i	0.674311	−	0.134129i
$254$	−21.5408	−	10.9490i	−1.35159	−	0.687002i
$255$	5.16541	−	8.59329i	0.323471	−	0.538133i
$256$	−13.0176	−	9.30287i	−0.813597	−	0.581429i
$257$			27.8550i			1.73755i	0.495210	+	0.868773i	$0.335091\pi$
$257$			27.8550i			1.73755i	−0.495210	+	0.868773i	$0.664909\pi$
$258$	−20.0210	+	12.5329i	−1.24645	+	0.780266i
$259$	2.61366	+	13.1398i	0.162405	+	0.816464i
$260$	−17.3937	+	12.6894i	−1.07871	+	0.786963i
$261$	6.82638	+	3.67102i	0.422542	+	0.227230i
$262$	0.609854	−	2.17051i	0.0376769	−	0.134095i
$263$	−10.8728	−	4.50368i	−0.670448	−	0.277709i	0.0213794	−	0.999771i	$-0.493194\pi$
$263$	−10.8728	−	4.50368i	−0.670448	−	0.277709i	−0.691828	+	0.722063i	$0.743194\pi$
$264$	16.6510	+	6.67397i	1.02480	+	0.410755i
$265$	−5.96034	+	2.46885i	−0.366141	+	0.151660i
$266$	1.41044	−	0.168337i	0.0864797	−	0.0103214i
$267$	5.09641	−	5.60874i	0.311895	−	0.343249i
$268$	10.4811	−	11.3830i	0.640235	−	0.695330i
$269$	3.40585	+	2.27572i	0.207658	+	0.138753i	0.655051	−	0.755585i	$-0.272647\pi$
$269$	3.40585	+	2.27572i	0.207658	+	0.138753i	−0.447392	+	0.894338i	$0.647647\pi$
$270$	19.2616	+	25.0785i	1.17222	+	1.52623i
$271$	−1.68641	+	1.68641i	−0.102442	+	0.102442i	−0.756470	−	0.654028i	$-0.773078\pi$
$271$	−1.68641	+	1.68641i	−0.102442	+	0.102442i	0.654028	+	0.756470i	$0.273078\pi$
$272$	4.78474	−	2.46160i	0.290118	−	0.149257i
$273$	−10.9259	+	2.72210i	−0.661263	+	0.164749i
$274$	20.5013	+	1.59329i	1.23853	+	0.0962540i
$275$	41.1553	+	27.4991i	2.48176	+	1.65826i
$276$	6.48987	+	8.05673i	0.390644	+	0.484958i
$277$	3.18127	+	0.632795i	0.191144	+	0.0380210i	0.289734	−	0.957107i	$-0.406433\pi$
$277$	3.18127	+	0.632795i	0.191144	+	0.0380210i	−0.0985898	+	0.995128i	$0.531433\pi$
$278$	4.40666	−	5.60110i	0.264294	−	0.335931i
$279$	−4.71485	−	3.88939i	−0.282271	−	0.232852i
$280$	−11.0342	−	29.6410i	−0.659418	−	1.77139i
$281$	22.6232	+	9.37084i	1.34959	+	0.559018i	0.936178	−	0.351527i	$-0.114338\pi$
$281$	22.6232	+	9.37084i	1.34959	+	0.559018i	0.413410	+	0.910545i	$0.364338\pi$
$282$	−19.2905	−	0.573842i	−1.14873	−	0.0341718i
$283$	1.43456	+	2.14698i	0.0852760	+	0.127625i	0.871655	−	0.490119i	$-0.163047\pi$
$283$	1.43456	+	2.14698i	0.0852760	+	0.127625i	−0.786379	+	0.617744i	$0.788047\pi$
$284$	−3.19706	−	13.2028i	−0.189711	−	0.783439i
$285$	−2.71123	−	0.973967i	−0.160600	−	0.0576928i
$286$	12.3169	−	4.01535i	0.728314	−	0.237433i
$287$			12.0793i			0.713020i
$288$	1.70335	+	16.8849i	0.100371	+	0.994950i
$289$		−	15.1904i		−	0.893554i
$290$	4.87330	+	14.9487i	0.286170	+	0.877815i
$291$	3.04656	+	1.09443i	0.178593	+	0.0641565i
$292$	28.5943	+	17.4457i	1.67336	+	1.02093i
$293$	9.50218	+	14.2210i	0.555123	+	0.830800i	0.997828	−	0.0658668i	$-0.0209812\pi$
$293$	9.50218	+	14.2210i	0.555123	+	0.830800i	−0.442705	+	0.896667i	$0.645981\pi$
$294$	−0.0180119	+	0.605497i	−0.00105048	+	0.0353133i
$295$	−26.2269	−	10.8636i	−1.52699	−	0.632500i
$296$	10.6788	−	9.92975i	0.620694	−	0.577155i
$297$	−6.34190	−	17.9388i	−0.367995	−	1.04092i
$298$	−2.69864	−	2.12315i	−0.156328	−	0.122991i
$299$	7.32771	+	1.45757i	0.423772	+	0.0842936i
$300$	−5.01472	+	46.5564i	−0.289525	+	2.68794i
$301$	−20.8350	−	13.9215i	−1.20091	−	0.802422i
$302$	0.139678	−	1.79728i	0.00803757	−	0.103422i
$303$	−23.0873	+	5.75203i	−1.32633	+	0.330445i
$304$	−0.961919	−	1.21041i	−0.0551698	−	0.0694215i
$305$	12.7007	−	12.7007i	0.727242	−	0.727242i
$306$	−5.31142	−	2.08836i	−0.303634	−	0.119383i
$307$	−6.85681	−	4.58157i	−0.391339	−	0.261484i	0.344298	−	0.938860i	$-0.388117\pi$
$307$	−6.85681	−	4.58157i	−0.391339	−	0.261484i	−0.735637	+	0.677376i	$0.763117\pi$
$308$	0.784384	+	19.0145i	0.0446944	+	1.08345i
$309$	16.9260	−	18.6275i	0.962885	−	1.05968i
$310$	−1.46935	−	12.3112i	−0.0834535	−	0.699228i
$311$	−30.1840	+	12.5026i	−1.71157	+	0.708958i	−0.711595	+	0.702590i	$0.752027\pi$
$311$	−30.1840	+	12.5026i	−1.71157	+	0.708958i	−0.999980	+	0.00636791i	$0.997973\pi$
$312$	8.76511	+	8.56597i	0.496227	+	0.484952i
$313$	−6.61643	−	2.74061i	−0.373982	−	0.154909i	0.187772	−	0.982213i	$-0.439873\pi$
$313$	−6.61643	−	2.74061i	−0.373982	−	0.154909i	−0.561754	+	0.827304i	$0.689873\pi$
$314$	−14.5494	−	4.08799i	−0.821073	−	0.230699i
$315$	−15.8886	+	29.5455i	−0.895224	+	1.66470i
$316$	−6.46639	−	1.01120i	−0.363763	−	0.0568842i
$317$	−3.68607	−	18.5311i	−0.207031	−	1.04081i	−0.934850	−	0.355044i	$-0.884466\pi$
$317$	−3.68607	−	18.5311i	−0.207031	−	1.04081i	0.727819	−	0.685769i	$-0.240534\pi$
$318$	1.94854	+	3.11274i	0.109269	+	0.174554i
$319$		−	9.46050i		−	0.529687i
$320$	−21.1534	+	27.1597i	−1.18251	+	1.51827i
$321$	1.95634	−	3.25460i	0.109192	−	0.181654i
$322$	−4.97308	+	9.78389i	−0.277139	+	0.545235i
$323$	0.509959	−	0.101437i	0.0283749	−	0.00564411i
$324$	12.2594	−	13.1798i	0.681076	−	0.732213i
$325$	18.7874	+	28.1173i	1.04214	+	1.55967i
$326$	3.04253	−	10.8286i	0.168510	−	0.599740i
$327$	−23.9096	+	17.6857i	−1.32220	+	0.978023i
$328$	11.1900	−	6.90255i	0.617865	−	0.381130i
$329$	−7.83499	−	18.9153i	−0.431957	−	1.04284i
$330$	15.8241	−	35.2039i	0.871089	−	1.93791i
$331$	19.6169	+	3.90204i	1.07824	+	0.214476i	0.702094	−	0.712084i	$-0.252249\pi$
$331$	19.6169	+	3.90204i	1.07824	+	0.214476i	0.376147	+	0.926560i	$0.377249\pi$
$332$	0.161323	+	3.91069i	0.00885377	+	0.214627i
$333$	−15.3883	−	1.55495i	−0.843272	−	0.0852105i
$334$	−16.4913	−	19.2705i	−0.902362	−	1.05444i
$335$	−23.5414	−	23.5414i	−1.28620	−	1.28620i
$336$	−15.5972	+	8.99212i	−0.850895	+	0.490560i
$337$	3.84192	−	3.84192i	0.209283	−	0.209283i	−0.594680	−	0.803963i	$-0.702721\pi$
$337$	3.84192	−	3.84192i	0.209283	−	0.209283i	0.803963	+	0.594680i	$0.202721\pi$
$338$	−9.50532	−	0.738720i	−0.517021	−	0.0401811i
$339$	−9.34890	−	19.8315i	−0.507762	−	1.07710i
$340$	−4.86755	−	10.5044i	−0.263980	−	0.569680i
$341$	−1.45542	+	7.31687i	−0.0788152	+	0.396231i
$342$	−0.290787	+	1.61388i	−0.0157240	+	0.0872686i
$343$	−17.3992	+	7.20700i	−0.939471	+	0.389142i
$344$	−0.990712	+	27.2563i	−0.0534156	+	1.46956i
$345$	17.8956	−	13.2372i	0.963467	−	0.712668i
$346$	−9.02329	−	16.0753i	−0.485095	−	0.864213i
$347$	14.6437	−	9.78460i	0.786114	−	0.525265i	−0.0965168	−	0.995331i	$-0.530770\pi$
$347$	14.6437	−	9.78460i	0.786114	−	0.525265i	0.882631	+	0.470067i	$0.155770\pi$
$348$	7.93130	−	4.14677i	0.425162	−	0.222290i
$349$	−0.173660	−	0.873047i	−0.00929580	−	0.0467332i	0.975859	−	0.218402i	$-0.0700842\pi$
$349$	−0.173660	−	0.873047i	−0.00929580	−	0.0467332i	−0.985155	+	0.171668i	$0.945084\pi$
$350$	−47.2297	+	15.3970i	−2.52454	+	0.823006i
$351$	0.687124	−	12.9810i	0.0366760	−	0.692874i
$352$	17.1664	−	11.5922i	0.914971	−	0.617866i
$353$	−33.0774			−1.76053			−0.880266	−	0.474481i	$-0.842636\pi$
$353$	−33.0774			−1.76053			−0.880266	+	0.474481i	$0.842636\pi$
$354$	−3.62234	+	15.7479i	−0.192525	+	0.836990i
$355$	−28.6663	+	5.70209i	−1.52145	+	0.302636i
$356$	−2.05948	−	8.50492i	−0.109152	−	0.450760i
$357$	−0.289434	−	6.04771i	−0.0153185	−	0.320079i
$358$	4.29965	+	7.65997i	0.227244	+	0.404842i
$359$	4.91221	−	11.8591i	0.259257	−	0.625901i	−0.739633	−	0.673010i	$-0.765001\pi$
$359$	4.91221	−	11.8591i	0.259257	−	0.625901i	0.998890	+	0.0471093i	$0.0150009\pi$
$360$	36.4496	−	2.16443i	1.92106	−	0.114075i
$361$	7.21381	+	17.4157i	0.379674	+	0.916615i
$362$	15.1032	+	11.8825i	0.793809	+	0.624529i
$363$	−2.80509	+	3.08708i	−0.147229	+	0.162030i
$364$	−4.47623	+	12.2069i	−0.234618	+	0.639817i
$365$	40.0399	−	59.9240i	2.09579	−	3.13656i
$366$	−8.32845	−	5.93052i	−0.435335	−	0.309993i
$367$	0.647822	+	0.647822i	0.0338161	+	0.0338161i	0.723813	−	0.689997i	$-0.242388\pi$
$367$	0.647822	+	0.647822i	0.0338161	+	0.0338161i	−0.689997	+	0.723813i	$0.742388\pi$
$368$	11.9054	−	0.983912i	0.620610	−	0.0512899i
$369$	−13.3345	−	4.08185i	−0.694164	−	0.212492i
$370$	−20.3996	−	23.8376i	−1.06053	−	1.23926i
$371$	−2.16443	+	3.23929i	−0.112371	+	0.168176i
$372$	−6.77210	+	1.98700i	−0.351117	+	0.103021i
$373$	3.01645	−	15.1647i	0.156186	−	0.785200i	−0.820687	−	0.571378i	$-0.806409\pi$
$373$	3.01645	−	15.1647i	0.156186	−	0.785200i	0.976873	−	0.213821i	$-0.0685911\pi$
$374$	0.825550	+	6.91700i	0.0426882	+	0.357670i
$375$	62.7843	+	9.39439i	3.24217	+	0.485124i
$376$	−13.0456	+	18.0670i	−0.672773	+	0.931737i
$377$	2.47344	−	5.97142i	0.127389	−	0.307544i
$378$	18.0851	+	6.12987i	0.930196	+	0.315287i
$379$	−2.79369	+	1.86669i	−0.143502	+	0.0958852i	−0.625249	−	0.780425i	$-0.715003\pi$
$379$	−2.79369	+	1.86669i	−0.143502	+	0.0958852i	0.481747	+	0.876311i	$0.340003\pi$
$380$	−2.68739	+	1.96056i	−0.137860	+	0.100575i
$381$	27.8518	+	10.0053i	1.42689	+	0.512587i
$382$	−8.68271	+	17.0821i	−0.444246	+	0.873996i
$383$	23.3643			1.19386			0.596931	−	0.802293i	$-0.296387\pi$
$383$	23.3643			1.19386			0.596931	+	0.802293i	$0.296387\pi$
$384$	17.2428	+	9.31043i	0.879920	+	0.475121i
$385$	40.9463			2.08682
$386$	13.2259	−	26.0202i	0.673179	−	1.32439i
$387$	22.4086	−	18.2956i	1.13909	−	0.930015i
$388$	3.01977	−	2.20304i	0.153306	−	0.111843i
$389$	−10.1512	+	6.78284i	−0.514688	+	0.343904i	−0.785635	−	0.618691i	$-0.787663\pi$
$389$	−10.1512	+	6.78284i	−0.514688	+	0.343904i	0.270946	+	0.962594i	$0.412663\pi$
$390$	19.1921	−	18.0833i	0.971831	−	0.915683i
$391$	−1.53741	+	3.71163i	−0.0777501	+	0.187705i
$392$	0.567094	+	0.409478i	0.0286426	+	0.0206817i
$393$	−0.408617	+	2.73086i	−0.0206120	+	0.137754i
$394$	0.599890	+	5.02627i	0.0302220	+	0.253220i
$395$	−2.74729	+	13.8115i	−0.138231	+	0.694934i
$396$	−21.2553	−	5.55949i	−1.06812	−	0.279375i
$397$	15.0250	−	22.4865i	0.754083	−	1.12856i	−0.233636	−	0.972324i	$-0.575062\pi$
$397$	15.0250	−	22.4865i	0.754083	−	1.12856i	0.987719	−	0.156241i	$-0.0499376\pi$
$398$	13.4732	+	15.7439i	0.675353	+	0.789170i
$399$	−1.68809	+	0.420574i	−0.0845101	+	0.0210551i
$400$	41.2522	+	34.9541i	2.06261	+	1.74771i
$401$	−1.77953	−	1.77953i	−0.0888656	−	0.0888656i	0.661277	−	0.750142i	$-0.270015\pi$
$401$	−1.77953	−	1.77953i	−0.0888656	−	0.0888656i	−0.750142	+	0.661277i	$0.770015\pi$
$402$	−10.9925	+	15.4372i	−0.548256	+	0.769936i
$403$	−2.83164	+	4.23785i	−0.141054	+	0.211102i
$404$	−9.45866	+	25.7943i	−0.470586	+	1.28331i
$405$	−27.2464	−	27.5236i	−1.35388	−	1.36766i
$406$	7.46212	+	5.87082i	0.370339	+	0.291364i
$407$	7.22437	+	17.4412i	0.358099	+	0.864526i
$408$	−5.43707	+	3.72400i	−0.269175	+	0.184365i
$409$	−7.30266	+	17.6302i	−0.361093	+	0.871756i	0.634048	+	0.773294i	$0.281392\pi$
$409$	−7.30266	+	17.6302i	−0.361093	+	0.871756i	−0.995141	+	0.0984620i	$0.968608\pi$
$410$	−13.8465	−	24.6680i	−0.683831	−	1.21827i
$411$	−25.1558	+	1.20392i	−1.24084	+	0.0593848i
$412$	−6.83985	−	28.2462i	−0.336975	−	1.39159i
$413$	−16.8134	+	3.34439i	−0.827331	+	0.164566i
$414$	−9.12001	−	8.79599i	−0.448224	−	0.432299i
$415$	8.42137			0.413389
$416$	13.8661	−	2.82879i	0.679841	−	0.138693i
$417$	−4.49681	+	7.48099i	−0.220210	+	0.366345i
$418$	1.90301	−	0.620386i	0.0930793	−	0.0303441i
$419$	−2.89265	−	14.5424i	−0.141315	−	0.710440i	−0.984856	−	0.173375i	$-0.944533\pi$
$419$	−2.89265	−	14.5424i	−0.141315	−	0.710440i	0.843541	−	0.537066i	$-0.180467\pi$
$420$	17.9478	+	34.3277i	0.875761	+	1.67502i
$421$	−9.40305	+	6.28291i	−0.458276	+	0.306211i	−0.763195	−	0.646168i	$-0.776371\pi$
$421$	−9.40305	+	6.28291i	−0.458276	+	0.306211i	0.304919	+	0.952378i	$0.401371\pi$
$422$	12.8010	+	22.8055i	0.623144	+	1.11015i
$423$	23.5284	−	2.25723i	1.14399	−	0.109750i
$424$	4.23764	+	0.154030i	0.205798	+	0.00748034i
$425$	−16.7996	+	6.95861i	−0.814898	+	0.337542i
$426$	5.90698	+	15.5534i	0.286194	+	0.753565i
$427$	2.11606	−	10.6381i	0.102403	−	0.514816i
$428$	−1.84352	−	3.97840i	−0.0891101	−	0.192303i
$429$	−14.3517	+	6.76562i	−0.692905	+	0.326647i
$430$	58.5068	+	4.54694i	2.82145	+	0.219273i
$431$	−0.840930	+	0.840930i	−0.0405062	+	0.0405062i	−0.727070	−	0.686564i	$-0.759118\pi$
$431$	−0.840930	+	0.840930i	−0.0405062	+	0.0405062i	0.686564	+	0.727070i	$0.259118\pi$
$432$	−4.65587	−	20.2564i	−0.224006	−	0.974588i
$433$	0.498959	+	0.498959i	0.0239785	+	0.0239785i	0.718994	−	0.695016i	$-0.244603\pi$
$433$	0.498959	+	0.498959i	0.0239785	+	0.0239785i	−0.695016	+	0.718994i	$0.744603\pi$
$434$	−4.86812	−	5.68854i	−0.233677	−	0.273059i
$435$	−8.21122	−	17.4182i	−0.393698	−	0.835137i
$436$	1.41541	+	34.3113i	0.0677857	+	1.64322i
$437$	1.13216	+	0.225200i	0.0541585	+	0.0107728i
$438$	−37.4178	−	16.8193i	−1.78789	−	0.803657i
$439$	−5.55530	−	13.4117i	−0.265140	−	0.640105i	0.734102	−	0.679040i	$-0.237604\pi$
$439$	−5.55530	−	13.4117i	−0.265140	−	0.640105i	−0.999242	+	0.0389347i	$0.987604\pi$
$440$	−23.3981	−	37.9317i	−1.11546	−	1.80832i
$441$	−0.0708507	−	0.738516i	−0.00337384	−	0.0351674i
$442$	−1.28736	+	4.58181i	−0.0612336	+	0.217935i
$443$	1.97447	+	2.95500i	0.0938100	+	0.140397i	0.875406	−	0.483388i	$-0.160594\pi$
$443$	1.97447	+	2.95500i	0.0938100	+	0.140397i	−0.781596	+	0.623785i	$0.785594\pi$
$444$	−11.4553	+	13.7015i	−0.543646	+	0.650244i
$445$	−18.4662	+	3.67316i	−0.875383	+	0.174125i
$446$	12.3210	−	24.2400i	0.583418	−	1.14780i
$447$	3.60438	+	2.16659i	0.170481	+	0.102476i
$448$	−1.50927	+	20.7339i	−0.0713061	+	0.979585i
$449$		−	5.09669i		−	0.240527i	−0.992742	−	0.120264i	$-0.961626\pi$
$449$		−	5.09669i		−	0.240527i	0.992742	−	0.120264i	$-0.0383740\pi$
$450$	−1.03702	−	57.3402i	−0.0488854	−	2.70304i
$451$	3.32067	+	16.6941i	0.156364	+	0.786096i
$452$	−25.0124	−	3.91137i	−1.17648	−	0.183975i
$453$	0.105543	+	2.20532i	0.00495885	+	0.103615i
$454$	−13.7645	−	3.86745i	−0.646001	−	0.181508i
$455$	25.8451	+	10.7054i	1.21164	+	0.501876i
$456$	1.35424	+	1.32347i	0.0634182	+	0.0619774i
$457$	32.8641	−	13.6128i	1.53732	−	0.636779i	0.556351	−	0.830947i	$-0.312201\pi$
$457$	32.8641	−	13.6128i	1.53732	−	0.636779i	0.980968	+	0.194169i	$0.0622009\pi$
$458$	2.92147	+	24.4780i	0.136511	+	1.14378i
$459$	6.77392	+	1.72413i	0.316179	+	0.0804757i
$460$	−1.05939	−	25.6810i	−0.0493943	−	1.19738i
$461$	−8.02408	−	5.36152i	−0.373719	−	0.249711i	0.354500	−	0.935056i	$-0.384651\pi$
$461$	−8.02408	−	5.36152i	−0.373719	−	0.249711i	−0.728218	+	0.685345i	$0.759651\pi$
$462$	−3.86538	−	22.9850i	−0.179834	−	1.06936i
$463$	−13.9676	+	13.9676i	−0.649129	+	0.649129i	−0.952782	−	0.303654i	$-0.901793\pi$
$463$	−13.9676	+	13.9676i	−0.649129	+	0.649129i	0.303654	+	0.952782i	$0.401793\pi$
$464$	1.17448	−	10.2675i	0.0545237	−	0.476658i
$465$	3.67103	+	14.7346i	0.170240	+	0.683303i
$466$	−0.876619	+	11.2797i	−0.0406086	+	0.522522i
$467$	26.7190	+	17.8531i	1.23641	+	0.826141i	0.989729	−	0.142957i	$-0.0456610\pi$
$467$	26.7190	+	17.8531i	1.23641	+	0.826141i	0.246678	+	0.969097i	$0.420661\pi$
$468$	−11.9627	−	9.06631i	−0.552976	−	0.419090i
$469$	−19.7183	−	3.92221i	−0.910506	−	0.181111i
$470$	37.6830	+	29.6471i	1.73819	+	1.36752i
$471$	18.3056	+	2.73906i	0.843477	+	0.126209i
$472$	12.7059	+	13.6644i	0.584836	+	0.628955i
$473$	−32.6219	−	13.5124i	−1.49996	−	0.621303i
$474$	8.01238	+	0.238347i	0.368021	+	0.0109476i
$475$	2.90272	+	4.34423i	0.133186	+	0.199327i
$476$	−5.96820	−	3.64126i	−0.273552	−	0.166897i
$477$	−2.84448	−	3.48395i	−0.130240	−	0.159519i
$478$	5.14894	+	15.7942i	0.235507	+	0.722408i
$479$			6.21762i			0.284090i	0.989860	+	0.142045i	$0.0453678\pi$
$479$			6.21762i			0.284090i	−0.989860	+	0.142045i	$0.954632\pi$
$480$	21.5444	−	36.2424i	0.983362	−	1.65423i
$481$			12.8976i			0.588079i
$482$	−5.72862	+	1.86755i	−0.260932	+	0.0850644i
$483$	4.54445	−	12.6504i	0.206779	−	0.575612i
$484$	1.13355	+	4.68115i	0.0515248	+	0.212779i
$485$	−4.46823	−	6.68717i	−0.202892	−	0.303649i
$486$	−12.8781	+	17.8928i	−0.584163	+	0.811636i
$487$	1.30351	+	0.539930i	0.0590676	+	0.0244666i	0.412022	−	0.911174i	$-0.364823\pi$
$487$	1.30351	+	0.539930i	0.0590676	+	0.0244666i	−0.352954	+	0.935641i	$0.614823\pi$
$488$	−11.0641	+	4.11874i	−0.500849	+	0.186447i
$489$	−2.03857	+	13.6241i	−0.0921874	+	0.616105i
$490$	0.930572	−	1.18281i	0.0420390	−	0.0534337i
$491$	−10.3424	−	2.05722i	−0.466744	−	0.0928411i	−0.0438848	−	0.999037i	$-0.513973\pi$
$491$	−10.3424	−	2.05722i	−0.466744	−	0.0928411i	−0.422859	+	0.906195i	$0.638973\pi$
$492$	−12.5401	+	10.1014i	−0.565353	+	0.455404i
$493$	2.88977	+	1.93088i	0.130149	+	0.0869627i
$494$	1.36337	+	0.105956i	0.0613409	+	0.00476719i
$495$	−13.8366	+	45.2009i	−0.621907	+	2.03163i
$496$	−2.48792	+	7.76034i	−0.111711	+	0.348450i
$497$	−12.4805	+	12.4805i	−0.559827	+	0.559827i
$498$	−0.794988	−	4.72729i	−0.0356243	−	0.211835i
$499$	−10.5229	−	7.03120i	−0.471071	−	0.314760i	0.297277	−	0.954791i	$-0.403921\pi$
$499$	−10.5229	−	7.03120i	−0.471071	−	0.314760i	−0.768349	+	0.640031i	$0.778921\pi$
$500$	49.6534	−	53.9263i	2.22057	−	2.41166i
$501$	22.9905	+	20.8904i	1.02714	+	0.933316i
$502$	−18.2772	+	2.18140i	−0.815749	+	0.0973604i
$503$	−6.66908	+	2.76242i	−0.297360	+	0.123170i	−0.526375	−	0.850252i	$-0.676449\pi$
$503$	−6.66908	+	2.76242i	−0.297360	+	0.123170i	0.229016	+	0.973423i	$0.426449\pi$
$504$	17.5754	−	13.3154i	0.782868	−	0.593117i
$505$	54.6129	+	22.6214i	2.43024	+	1.00664i
$506$	−4.18336	+	14.8889i	−0.185973	+	0.661891i
$507$	11.6634	−	0.558190i	0.517988	−	0.0247901i
$508$	27.6069	−	20.1403i	1.22486	−	0.893581i
$509$	1.85153	+	9.30829i	0.0820678	+	0.412583i	0.999879	+	0.0155653i	$0.00495480\pi$
$509$	1.85153	+	9.30829i	0.0820678	+	0.412583i	−0.917811	+	0.397018i	$0.870045\pi$
$510$	7.52355	+	12.0187i	0.333149	+	0.532196i
$511$		−	43.5214i		−	1.92527i
$512$	20.0699	−	10.4499i	0.886971	−	0.461826i
$513$	0.106163	−	2.00561i	0.00468722	−	0.0885499i
$514$	−35.1168	−	17.8496i	−1.54894	−	0.787313i
$515$	−61.3293	+	12.1991i	−2.70249	+	0.537559i
$516$	−2.97072	−	33.2717i	−0.130778	−	1.46470i
$517$	−16.0282	−	23.9879i	−0.704920	−	1.05499i
$518$	−18.2402	−	5.12498i	−0.801426	−	0.225179i
$519$	13.4266	+	18.1516i	0.589361	+	0.796766i
$520$	−4.85156	−	30.0597i	−0.212755	−	1.31821i
$521$	−6.13573	−	14.8130i	−0.268811	−	0.648968i	0.730617	−	0.682788i	$-0.239233\pi$
$521$	−6.13573	−	14.8130i	−0.268811	−	0.648968i	−0.999428	+	0.0338199i	$0.989233\pi$
$522$	−9.00244	+	6.25362i	−0.394026	+	0.273714i
$523$	−31.6109	−	6.28780i	−1.38225	−	0.274946i	−0.552699	−	0.833381i	$-0.686402\pi$
$523$	−31.6109	−	6.28780i	−1.38225	−	0.274946i	−0.829548	+	0.558435i	$0.811402\pi$
$524$	2.34557	+	2.15972i	0.102467	+	0.0943477i
$525$	55.0321	−	25.9431i	2.40180	−	1.13225i
$526$	12.6452	−	10.8214i	0.551356	−	0.471837i
$527$	−1.93794	−	1.93794i	−0.0844178	−	0.0844178i
$528$	−19.0839	+	16.7152i	−0.830521	+	0.727436i
$529$	9.95669	−	9.95669i	0.432900	−	0.432900i
$530$	0.706929	−	9.09626i	0.0307070	−	0.395116i
$531$	1.98968	−	19.6905i	0.0863447	−	0.854496i
$532$	−0.691595	+	1.88602i	−0.0299844	+	0.0817692i
$533$	−2.26868	+	11.4054i	−0.0982675	+	0.494024i
$534$	3.80514	+	10.0192i	0.164665	+	0.433572i
$535$	−8.71611	+	3.61033i	−0.376830	+	0.156088i
$536$	7.63427	+	20.5079i	0.329750	+	0.885805i
$537$	−6.39783	−	8.64933i	−0.276087	−	0.373246i
$538$	−5.05149	+	2.83547i	−0.217785	+	0.122246i
$539$	−0.752940	+	0.503098i	−0.0324314	+	0.0216700i
$540$	−43.9595	+	8.21266i	−1.89171	+	0.353417i
$541$	5.30294	+	26.6597i	0.227991	+	1.14619i	0.909924	+	0.414774i	$0.136139\pi$
$541$	5.30294	+	26.6597i	0.227991	+	1.14619i	−0.681933	+	0.731414i	$0.738861\pi$
$542$	−1.04540	−	3.20673i	−0.0449039	−	0.137741i
$543$	−20.1723	−	12.1256i	−0.865678	−	0.520357i
$544$	0.0372604	+	7.60954i	0.00159753	+	0.326256i
$545$	73.8869			3.16497
$546$	3.56960	−	15.5186i	0.152765	−	0.664134i
$547$	2.89843	−	0.576533i	0.123928	−	0.0246508i	−0.132737	−	0.991151i	$-0.542376\pi$
$547$	2.89843	−	0.576533i	0.123928	−	0.0246508i	0.256664	+	0.966501i	$0.417376\pi$
$548$	−15.1460	+	24.8250i	−0.647005	+	1.06047i
$549$	11.0285	+	5.93077i	0.470683	+	0.253119i
$550$	−61.0407	+	34.2630i	−2.60278	+	1.46098i
$551$	0.382156	−	0.922607i	0.0162804	−	0.0393044i
$552$	−14.3159	+	3.01900i	−0.609324	+	0.128497i
$553$	3.25429	+	7.85655i	0.138386	+	0.334095i
$554$	−2.83634	+	3.60514i	−0.120505	+	0.153168i
$555$	28.4391	+	25.8414i	1.20717	+	1.09690i
$556$	4.23750	+	9.14470i	0.179710	+	0.387822i
$557$	−9.09602	+	13.6132i	−0.385411	+	0.576808i	−0.972555	−	0.232675i	$-0.925252\pi$
$557$	−9.09602	+	13.6132i	−0.385411	+	0.576808i	0.587144	+	0.809483i	$0.300252\pi$
$558$	7.92466	−	3.45168i	0.335478	−	0.146121i
$559$	−17.0580	−	17.0580i	−0.721475	−	0.721475i
$560$	44.4392	+	5.08329i	1.87790	+	0.214808i
$561$	−2.06256	−	8.27862i	−0.0870812	−	0.349524i
$562$	−26.3109	+	22.5162i	−1.10986	+	0.949790i
$563$	−19.5452	+	29.2515i	−0.823732	+	1.23280i	0.146159	+	0.989261i	$0.453309\pi$
$563$	−19.5452	+	29.2515i	−0.823732	+	1.23280i	−0.969891	+	0.243541i	$0.921691\pi$
$564$	13.0849	−	23.9519i	0.550974	−	1.00856i
$565$	−10.6267	+	53.4239i	−0.447068	+	2.24756i
$566$	−3.62598	+	0.432764i	−0.152411	+	0.0181904i
$567$	−22.9146	−	4.67870i	−0.962322	−	0.196487i
$568$	18.6934	+	4.42985i	0.784359	+	0.185872i
$569$	−7.42318	+	17.9211i	−0.311196	+	0.751293i	0.688465	+	0.725269i	$0.258285\pi$
$569$	−7.42318	+	17.9211i	−0.311196	+	0.751293i	−0.999661	+	0.0260241i	$0.991715\pi$
$570$	2.96526	−	2.79394i	0.124201	−	0.117025i
$571$	25.4369	−	16.9964i	1.06450	−	0.711277i	0.105426	−	0.994427i	$-0.466379\pi$
$571$	25.4369	−	16.9964i	1.06450	−	0.711277i	0.959076	+	0.283150i	$0.0913794\pi$
$572$	−2.83059	+	18.1010i	−0.118353	+	0.756841i
$573$	7.93433	−	22.0868i	0.331462	−	0.922690i
$574$	−15.2284	−	7.74050i	−0.635622	−	0.323082i
$575$	−40.3696			−1.68353
$576$	−22.3783	−	8.67249i	−0.932429	−	0.361354i
$577$	−13.6429			−0.567963			−0.283982	−	0.958830i	$-0.591655\pi$
$577$	−13.6429			−0.567963			−0.283982	+	0.958830i	$0.591655\pi$
$578$	19.1506	+	9.73410i	0.796560	+	0.404885i
$579$	−12.0859	+	33.6436i	−0.502273	+	1.39818i
$580$	−21.9686	−	3.43539i	−0.912198	−	0.142647i
$581$	4.22842	−	2.82534i	0.175424	−	0.117215i
$582$	−3.33200	+	3.13949i	−0.138116	+	0.130136i
$583$	−2.10083	+	5.07185i	−0.0870074	+	0.210054i
$584$	−40.3172	+	24.8696i	−1.66834	+	1.02911i
$585$	−20.5513	+	24.9130i	−0.849692	+	1.03003i
$586$	−24.0175	+	2.86651i	−0.992154	+	0.118414i
$587$	4.83875	−	24.3260i	0.199717	−	1.00404i	−0.742706	−	0.669618i	$-0.766458\pi$
$587$	4.83875	−	24.3260i	0.199717	−	1.00404i	0.942422	−	0.334425i	$-0.108542\pi$
$588$	−0.751808	−	0.410713i	−0.0310041	−	0.0169375i
$589$	−0.437499	+	0.654764i	−0.0180268	+	0.0269791i
$590$	30.5021	−	26.1029i	1.25575	−	1.07464i
$591$	−1.49877	−	6.01569i	−0.0616510	−	0.247453i
$592$	5.67540	+	19.8258i	0.233257	+	0.814837i
$593$	−9.31734	−	9.31734i	−0.382617	−	0.382617i	0.489427	−	0.872044i	$-0.337206\pi$
$593$	−9.31734	−	9.31734i	−0.382617	−	0.382617i	−0.872044	+	0.489427i	$0.837206\pi$
$594$	26.6795	+	3.50006i	1.09467	+	0.143609i
$595$	−8.35712	+	12.5073i	−0.342608	+	0.512750i
$596$	4.40597	−	2.04165i	0.180475	−	0.0836293i
$597$	−18.7831	−	17.0673i	−0.768740	−	0.698520i
$598$	−6.53320	+	8.30404i	−0.267162	+	0.339577i
$599$	−0.450558	−	1.08774i	−0.0184093	−	0.0444440i	0.914408	−	0.404795i	$-0.132657\pi$
$599$	−0.450558	−	1.08774i	−0.0184093	−	0.0444440i	−0.932817	+	0.360351i	$0.882657\pi$
$600$	−55.4803	−	36.1557i	−2.26497	−	1.47605i
$601$	−9.25984	+	22.3552i	−0.377717	+	0.911889i	0.614676	+	0.788780i	$0.289287\pi$
$601$	−9.25984	+	22.3552i	−0.377717	+	0.911889i	−0.992393	+	0.123110i	$0.960713\pi$
$602$	30.9020	−	17.3458i	1.25947	−	0.706960i
$603$	10.9930	−	20.4418i	0.447668	−	0.832453i
$604$	2.17633	+	1.32780i	0.0885535	+	0.0540274i
$605$	10.1639	−	2.02172i	0.413221	−	0.0821948i
$606$	7.54287	−	32.7921i	0.306408	−	1.33209i
$607$	47.3452			1.92168			0.960840	−	0.277103i	$-0.0893743\pi$
$607$	47.3452			1.92168			0.960840	+	0.277103i	$0.0893743\pi$
$608$	2.14236	−	0.437058i	0.0868843	−	0.0177251i
$609$	−9.96662	−	5.99092i	−0.403868	−	0.242764i
$610$	7.87314	+	24.1505i	0.318774	+	0.977826i
$611$	−3.84529	−	19.3316i	−0.155564	−	0.782073i
$612$	6.03638	−	5.35788i	0.244006	−	0.216580i
$613$	0.532520	−	0.355818i	0.0215083	−	0.0143714i	−0.544770	−	0.838586i	$-0.683383\pi$
$613$	0.532520	−	0.355818i	0.0215083	−	0.0143714i	0.566278	+	0.824214i	$0.308383\pi$
$614$	10.1699	−	5.70850i	0.410423	−	0.230376i
$615$	20.6035	+	27.8542i	0.830812	+	1.12319i
$616$	−24.4743	−	11.1957i	−0.986096	−	0.451088i
$617$	15.4604	−	6.40389i	0.622411	−	0.257811i	−0.0491140	−	0.998793i	$-0.515640\pi$
$617$	15.4604	−	6.40389i	0.622411	−	0.257811i	0.671525	+	0.740982i	$0.265640\pi$
$618$	12.6375	+	33.2752i	0.508354	+	1.33853i
$619$	−8.36961	+	42.0769i	−0.336403	+	1.69121i	0.328678	+	0.944442i	$0.393397\pi$
$619$	−8.36961	+	42.0769i	−0.336403	+	1.69121i	−0.665081	+	0.746771i	$0.731603\pi$
$620$	16.4623	+	6.03665i	0.661141	+	0.242438i
$621$	12.4292	+	9.29146i	0.498766	+	0.372854i
$622$	3.57998	−	46.0647i	0.143544	−	1.84703i
$623$	−8.03966	+	8.03966i	−0.322102	+	0.322102i
$624$	−16.4159	+	5.56107i	−0.657160	+	0.222621i
$625$	−63.7341	−	63.7341i	−2.54937	−	2.54937i
$626$	7.69494	−	6.58514i	0.307551	−	0.263195i
$627$	−2.21739	+	1.04531i	−0.0885539	+	0.0417458i
$628$	14.4771	−	15.7229i	0.577699	−	0.627412i
$629$	−6.80201	−	1.35300i	−0.271214	−	0.0539478i
$630$	−27.0665	−	38.9637i	−1.07835	−	1.55235i
$631$	8.07387	+	19.4920i	0.321416	+	0.775966i	0.999172	+	0.0406796i	$0.0129523\pi$
$631$	8.07387	+	19.4920i	0.321416	+	0.775966i	−0.677757	+	0.735286i	$0.737048\pi$
$632$	5.41851	−	7.50421i	0.215537	−	0.298501i
$633$	−19.0478	−	25.7510i	−0.757082	−	1.02351i
$634$	25.7243	+	7.22782i	1.02164	+	0.287053i
$635$	−40.8487	−	61.1344i	−1.62103	−	2.42604i
$636$	−5.17287	+	0.461868i	−0.205118	+	0.0183143i
$637$	−0.606786	+	0.120697i	−0.0240417	+	0.00478220i
$638$	11.9269	+	6.06234i	0.472189	+	0.240010i
$639$	−9.55990	−	17.9947i	−0.378184	−	0.711860i
$640$	−20.6851	−	44.0722i	−0.817649	−	1.74211i
$641$			37.3054i			1.47347i	0.676180	+	0.736736i	$0.263634\pi$
$641$			37.3054i			1.47347i	−0.676180	+	0.736736i	$0.736366\pi$
$642$	2.84945	+	4.55192i	0.112459	+	0.179650i
$643$	−0.437593	−	2.19993i	−0.0172570	−	0.0867567i	0.971197	−	0.238278i	$-0.0765829\pi$
$643$	−0.437593	−	2.19993i	−0.0172570	−	0.0867567i	−0.988454	+	0.151521i	$0.951583\pi$
$644$	−9.14780	−	12.5391i	−0.360474	−	0.494111i
$645$	−71.7898	+	3.43575i	−2.82672	+	0.135282i
$646$	−0.198902	+	0.707907i	−0.00782571	+	0.0278522i
$647$	13.8914	+	5.75400i	0.546126	+	0.226213i	0.638650	−	0.769498i	$-0.279493\pi$
$647$	13.8914	+	5.75400i	0.546126	+	0.226213i	−0.0925234	+	0.995711i	$0.529493\pi$
$648$	8.75996	+	23.9011i	0.344124	+	0.938924i
$649$	−22.3174	+	9.24415i	−0.876033	+	0.362865i
$650$	−47.4866	+	5.66757i	−1.86258	+	0.222300i
$651$	6.78665	+	6.16673i	0.265990	+	0.241693i
$652$	11.7019	+	10.7747i	0.458283	+	0.421971i
$653$	−20.8375	−	13.9232i	−0.815433	−	0.544855i	0.0764751	−	0.997071i	$-0.475633\pi$
$653$	−20.8375	−	13.9232i	−0.815433	−	0.544855i	−0.891908	+	0.452216i	$0.850633\pi$
$654$	−6.97501	−	41.4760i	−0.272745	−	1.62184i
$655$	4.85090	−	4.85090i	0.189540	−	0.189540i
$656$	1.53144	+	18.5305i	0.0597926	+	0.723493i
$657$	48.0435	+	14.7067i	1.87436	+	0.573764i
$658$	28.8673	+	2.24346i	1.12537	+	0.0874593i
$659$	−24.4240	−	16.3196i	−0.951426	−	0.635722i	−0.0200567	−	0.999799i	$-0.506385\pi$
$659$	−24.4240	−	16.3196i	−0.951426	−	0.635722i	−0.931369	+	0.364076i	$0.881385\pi$
$660$	34.2414	+	42.5083i	1.33284	+	1.65463i
$661$	37.5355	+	7.46628i	1.45996	+	0.290405i	0.860275	−	0.509830i	$-0.170292\pi$
$661$	37.5355	+	7.46628i	1.45996	+	0.290405i	0.599687	+	0.800235i	$0.295292\pi$
$662$	−17.4899	+	22.2306i	−0.679765	+	0.864016i
$663$	0.862565	−	5.76467i	0.0334993	−	0.223881i
$664$	−5.03359	−	2.30261i	−0.195341	−	0.0893586i
$665$	3.99316	+	1.65402i	0.154848	+	0.0641402i
$666$	11.8212	−	18.4036i	0.458063	−	0.713125i
$667$	4.28675	+	6.41558i	0.165984	+	0.248412i
$668$	34.8621	−	8.44190i	1.34886	−	0.326627i
$669$	−11.2591	+	31.3419i	−0.435301	+	1.21175i
$670$	44.7641	−	14.5932i	1.72939	−	0.563785i
$671$		−	15.2841i		−	0.590035i
$672$	−1.34164	−	25.4256i	−0.0517548	−	0.980812i
$673$			17.2901i			0.666486i	0.942841	+	0.333243i	$0.108143\pi$
$673$			17.2901i			0.666486i	−0.942841	+	0.333243i	$0.891857\pi$
$674$	2.38159	+	7.30544i	0.0917356	+	0.281395i
$675$	10.0423	+	69.5170i	0.386529	+	2.67571i
$676$	7.02237	−	11.5100i	0.270091	−	0.442692i
$677$	0.0350577	+	0.0524676i	0.00134738	+	0.00201649i	0.832143	−	0.554562i	$-0.187114\pi$
$677$	0.0350577	+	0.0524676i	0.00134738	+	0.00201649i	−0.830795	+	0.556578i	$0.812114\pi$
$678$	30.9924	+	0.921942i	1.19026	+	0.0354070i
$679$	−4.48704	−	1.85859i	−0.172197	−	0.0713263i
$680$	16.3620	+	0.594727i	0.627455	+	0.0228067i
$681$	17.3180	+	2.59129i	0.663628	+	0.0992983i
$682$	−8.29175	−	6.52353i	−0.317507	−	0.249799i
$683$	25.4364	+	5.05961i	0.973297	+	0.193601i	0.656029	−	0.754735i	$-0.272235\pi$
$683$	25.4364	+	5.05961i	0.973297	+	0.193601i	0.317267	+	0.948336i	$0.397235\pi$
$684$	−1.84828	−	1.40078i	−0.0706709	−	0.0535601i
$685$	52.0248	+	34.7619i	1.98777	+	1.32818i
$686$	2.06365	−	26.5535i	0.0787904	−	1.01382i
$687$	−7.29900	−	29.2965i	−0.278474	−	1.11773i
$688$	−33.7272	−	18.7150i	−1.28584	−	0.713502i
$689$	−2.65206	+	2.65206i	−0.101036	+	0.101036i
$690$	5.22058	+	31.0435i	0.198744	+	1.18181i
$691$	−31.0818	−	20.7682i	−1.18241	−	0.790059i	−0.200550	−	0.979683i	$-0.564273\pi$
$691$	−31.0818	−	20.7682i	−1.18241	−	0.790059i	−0.981857	+	0.189624i	$0.939273\pi$
$692$	26.0483	−	1.07454i	0.990209	−	0.0408480i
$693$	8.21731	+	27.3377i	0.312150	+	1.03847i
$694$	2.95171	+	24.7313i	0.112045	+	0.938789i
$695$	20.0347	−	8.29866i	0.759961	−	0.314786i
$696$	0.145426	+	12.6563i	0.00551236	+	0.479735i
$697$	−5.77708	−	2.39294i	−0.218822	−	0.0906392i
$698$	1.21193	+	0.340520i	0.0458724	+	0.0128889i
$699$	−0.662388	−	13.8406i	−0.0250538	−	0.523499i
$700$	10.8540	−	69.4091i	0.410243	−	2.62342i
$701$	6.43348	+	32.3433i	0.242989	+	1.22159i	0.888873	+	0.458154i	$0.151489\pi$
$701$	6.43348	+	32.3433i	0.242989	+	1.22159i	−0.645884	+	0.763436i	$0.723511\pi$
$702$	15.9248	+	9.18454i	0.601044	+	0.346648i
$703$			1.99272i			0.0751570i
$704$	3.61399	+	29.0700i	0.136207	+	1.09562i
$705$	−50.3305	−	30.2536i	−1.89556	−	1.13942i
$706$	21.1962	−	41.7007i	0.797728	−	1.56943i
$707$	35.0108	−	6.96408i	1.31672	−	0.261911i
$708$	−17.5322	−	14.6580i	−0.658899	−	0.550882i
$709$	13.2204	+	19.7857i	0.496502	+	0.743067i	0.992095	−	0.125487i	$-0.0400494\pi$
$709$	13.2204	+	19.7857i	0.496502	+	0.743067i	−0.495593	+	0.868555i	$0.665049\pi$
$710$	11.1809	−	39.7936i	0.419612	−	1.49343i
$711$	−9.77259	+	0.937549i	−0.366501	+	0.0351608i
$712$	12.0419	+	2.85361i	0.451289	+	0.106944i
$713$	−2.32845	−	5.62136i	−0.0872010	−	0.210522i
$714$	7.80983	+	3.51052i	0.292276	+	0.131378i
$715$	38.6619	+	7.69033i	1.44587	+	0.287602i
$716$	−12.4122	+	0.512026i	−0.463865	+	0.0191353i
$717$	−8.67566	−	18.4034i	−0.323999	−	0.687286i
$718$	11.8031	+	13.7922i	0.440486	+	0.514722i
$719$	17.8047	+	17.8047i	0.664002	+	0.664002i	0.956321	−	0.292319i	$-0.0944270\pi$
$719$	17.8047	+	17.8047i	0.664002	+	0.664002i	−0.292319	+	0.956321i	$0.594427\pi$
$720$	−20.6284	+	47.3390i	−0.768774	+	1.76422i
$721$	−26.7010	+	26.7010i	−0.994396	+	0.994396i
$722$	−26.5786	−	2.06560i	−0.989154	−	0.0768735i
$723$	6.67499	−	3.14671i	0.248246	−	0.117027i
$724$	−24.6585	+	11.4263i	−0.916426	+	0.424656i
$725$	−6.81332	+	34.2529i	−0.253040	+	1.27212i
$726$	−2.09437	−	5.51459i	−0.0777293	−	0.204666i
$727$	22.6315	−	9.37426i	0.839355	−	0.347672i	0.0787556	−	0.996894i	$-0.474905\pi$
$727$	22.6315	−	9.37426i	0.839355	−	0.347672i	0.760599	+	0.649222i	$0.224905\pi$
$728$	−12.5209	−	13.4655i	−0.464056	−	0.499063i
$729$	12.9081	−	23.7146i	0.478079	−	0.878317i
$730$	49.8885	+	88.8780i	1.84645	+	3.28952i
$731$	10.7856	−	7.20670i	0.398919	−	0.266549i
$732$	12.8135	−	6.69938i	0.473602	−	0.247616i
$733$	−9.77199	−	49.1271i	−0.360937	−	1.81455i	−0.553015	−	0.833171i	$-0.686523\pi$
$733$	−9.77199	−	49.1271i	−0.360937	−	1.81455i	0.192078	−	0.981380i	$-0.438477\pi$
$734$	−1.23184	+	0.401583i	−0.0454680	+	0.0148227i
$735$	−0.949609	+	1.57979i	−0.0350268	+	0.0582714i
$736$	−6.38860	+	15.6396i	−0.235487	+	0.576484i
$737$	−28.3297			−1.04354
$738$	13.6908	−	14.1951i	0.503965	−	0.522529i
$739$	28.8194	−	5.73254i	1.06014	−	0.210875i	0.365926	−	0.930644i	$-0.380752\pi$
$739$	28.8194	−	5.73254i	1.06014	−	0.210875i	0.694214	+	0.719769i	$0.255752\pi$
$740$	43.1242	−	10.4426i	1.58528	−	0.383877i
$741$	−1.67290	+	0.0800624i	−0.0614555	+	0.00294116i
$742$	−2.69681	−	4.80445i	−0.0990029	−	0.176377i
$743$	15.3189	−	36.9832i	0.561997	−	1.35678i	−0.346169	−	0.938172i	$-0.612518\pi$
$743$	15.3189	−	36.9832i	0.561997	−	1.35678i	0.908166	−	0.418609i	$-0.137482\pi$
$744$	1.83458	−	9.81088i	0.0672590	−	0.359684i
$745$	−3.99834	−	9.65285i	−0.146488	−	0.353653i
$746$	17.1852	+	13.5205i	0.629196	+	0.495020i
$747$	1.69004	+	5.62252i	0.0618355	+	0.205717i
$748$	−9.24929	−	3.39168i	−0.338188	−	0.124012i
$749$	−3.16515	+	4.73699i	−0.115652	+	0.173086i
$750$	−52.0760	+	73.1323i	−1.90155	+	2.67042i
$751$	−0.644925	−	0.644925i	−0.0235337	−	0.0235337i	0.695242	−	0.718776i	$-0.255297\pi$
$751$	−0.644925	−	0.644925i	−0.0235337	−	0.0235337i	−0.718776	+	0.695242i	$0.755297\pi$
$752$	−14.4175	−	28.0240i	−0.525752	−	1.02193i
$753$	21.8750	−	5.45000i	0.797170	−	0.198609i
$754$	5.94318	+	6.94479i	0.216438	+	0.252914i
$755$	3.04746	−	4.56084i	0.110908	−	0.165986i
$756$	−19.3170	+	18.8718i	−0.702551	+	0.686362i
$757$	2.74459	−	13.7980i	0.0997538	−	0.501496i	−0.898314	−	0.439355i	$-0.855207\pi$
$757$	2.74459	−	13.7980i	0.0997538	−	0.501496i	0.998067	−	0.0621412i	$-0.0197929\pi$
$758$	−0.563121	−	4.71820i	−0.0204535	−	0.171373i
$759$	2.80296	−	18.7326i	0.101741	−	0.679952i
$760$	−0.749584	−	4.64434i	−0.0271903	−	0.168468i
$761$	−0.456572	+	1.10226i	−0.0165507	+	0.0399570i	−0.931939	−	0.362615i	$-0.881884\pi$
$761$	−0.456572	+	1.10226i	−0.0165507	+	0.0399570i	0.915388	+	0.402572i	$0.131884\pi$
$762$	−30.4613	+	28.7013i	−1.10350	+	1.03974i
$763$	37.0990	−	24.7888i	1.34307	−	0.897413i
$764$	−15.9715	−	21.8926i	−0.577829	−	0.792047i
$765$	−10.9829	−	13.4520i	−0.397087	−	0.486356i
$766$	−14.9720	+	29.4555i	−0.540960	+	1.06427i
$767$	−16.5035			−0.595906
$768$	−22.7870	+	15.7719i	−0.822255	+	0.569120i
$769$	17.8345			0.643128			0.321564	−	0.946888i	$-0.395792\pi$
$769$	17.8345			0.643128			0.321564	+	0.946888i	$0.395792\pi$
$770$	−26.2386	+	51.6210i	−0.945573	+	1.86029i
$771$	45.4054	+	16.3111i	1.63523	+	0.587431i
$772$	24.3285	+	33.3477i	0.875601	+	1.20021i
$773$	30.0410	−	20.0728i	1.08050	−	0.721968i	0.117937	−	0.993021i	$-0.462372\pi$
$773$	30.0410	−	20.0728i	1.08050	−	0.721968i	0.962564	+	0.271053i	$0.0873720\pi$
$774$	8.70568	+	39.9745i	0.312919	+	1.43685i
$775$	10.5390	−	25.4434i	0.378572	−	0.913954i
$776$	0.842294	+	5.21875i	0.0302366	+	0.187342i
$777$	22.9491	+	3.43386i	0.823295	+	0.123189i
$778$	−2.04617	−	17.1442i	−0.0733588	−	0.614648i
$779$	−0.350520	+	1.76218i	−0.0125587	+	0.0631367i
$780$	10.4992	+	35.7834i	0.375932	+	1.28125i
$781$	−13.8176	+	20.6795i	−0.494433	+	0.739971i
$782$	−3.69408	−	4.31665i	−0.132100	−	0.154363i
$783$	9.98134	−	8.97778i	0.356704	−	0.320840i
$784$	−0.879626	+	0.452541i	−0.0314152	+	0.0161622i
$785$	−32.5167	−	32.5167i	−1.16057	−	1.16057i
$786$	−3.18096	−	2.26509i	−0.113461	−	0.0807932i
$787$	−28.9404	+	43.3124i	−1.03161	+	1.54392i	−0.206906	+	0.978361i	$0.566339\pi$
$787$	−28.9404	+	43.3124i	−1.03161	+	1.54392i	−0.824708	+	0.565558i	$0.808661\pi$
$788$	−6.72104	−	2.46458i	−0.239427	−	0.0877969i
$789$	−13.7081	+	15.0862i	−0.488022	+	0.537082i
$790$	−15.6518	−	12.3140i	−0.556865	−	0.438113i
$791$	12.5878	+	30.3896i	0.447571	+	1.08053i
$792$	20.6294	−	23.2340i	0.733033	−	0.825586i
$793$	3.99601	−	9.64722i	0.141902	−	0.342583i
$794$	18.7207	+	33.3515i	0.664372	+	1.18360i
$795$	0.534168	+	11.1614i	0.0189450	+	0.395855i
$796$	−28.4821	+	6.89697i	−1.00952	+	0.244457i
$797$	−16.5418	+	3.29037i	−0.585942	+	0.116551i	−0.479154	−	0.877731i	$-0.659056\pi$
$797$	−16.5418	+	3.29037i	−0.585942	+	0.116551i	−0.106788	+	0.994282i	$0.534056\pi$
$798$	0.551516	−	2.39768i	0.0195235	−	0.0848770i
$799$	10.5986			0.374952
$800$	−70.5013	+	29.6079i	−2.49260	+	1.04680i
$801$	−6.15828	−	11.5918i	−0.217592	−	0.409576i
$802$	3.38379	−	1.10313i	0.119486	−	0.0389527i
$803$	−11.9642	−	60.1483i	−0.422209	−	2.12259i
$804$	−12.4176	−	23.7505i	−0.437935	−	0.837614i
$805$	−27.7675	+	18.5536i	−0.978674	+	0.653929i
$806$	−3.52813	−	6.28549i	−0.124273	−	0.221397i
$807$	5.70394	−	4.21915i	0.200788	−	0.148521i
$808$	−26.4577	−	28.4537i	−0.930780	−	1.00100i
$809$	39.8340	−	16.4998i	1.40049	−	0.580102i	0.450611	−	0.892721i	$-0.351206\pi$
$809$	39.8340	−	16.4998i	1.40049	−	0.580102i	0.949879	+	0.312619i	$0.101206\pi$
$810$	52.1586	−	16.7123i	1.83267	−	0.587209i
$811$	9.67058	−	48.6173i	0.339580	−	1.70718i	−0.313243	−	0.949673i	$-0.601416\pi$
$811$	9.67058	−	48.6173i	0.339580	−	1.70718i	0.652823	−	0.757510i	$-0.273584\pi$
$812$	−12.1831	+	5.64546i	−0.427544	+	0.198117i
$813$	1.76144	+	3.73648i	0.0617765	+	0.131044i
$814$	−26.6175	−	2.06862i	−0.932943	−	0.0725050i
$815$	24.2009	−	24.2009i	0.847721	−	0.847721i
$816$	−1.21075	−	9.24088i	−0.0423847	−	0.323495i
$817$	−2.63552	−	2.63552i	−0.0922051	−	0.0922051i
$818$	−17.5468	−	20.5040i	−0.613510	−	0.716905i
$819$	−1.96071	+	19.4038i	−0.0685127	+	0.678025i
$820$	39.9719	−	1.64892i	1.39588	−	0.0575827i
$821$	−17.9426	−	3.56901i	−0.626203	−	0.124559i	−0.128219	−	0.991746i	$-0.540926\pi$
$821$	−17.9426	−	3.56901i	−0.626203	−	0.124559i	−0.497984	+	0.867186i	$0.665926\pi$
$822$	14.6022	−	32.4854i	0.509309	−	1.13306i
$823$	5.19727	+	12.5473i	0.181165	+	0.437372i	0.988207	−	0.153122i	$-0.0489329\pi$
$823$	5.19727	+	12.5473i	0.181165	+	0.437372i	−0.807042	+	0.590494i	$0.798933\pi$
$824$	39.9930	+	9.47730i	1.39322	+	0.330157i
$825$	68.9247	−	50.9830i	2.39965	−	1.77500i
$826$	6.55782	−	23.3397i	0.228176	−	0.812093i
$827$	16.4642	+	24.6404i	0.572516	+	0.856831i	0.998860	−	0.0477298i	$-0.0151986\pi$
$827$	16.4642	+	24.6404i	0.572516	+	0.856831i	−0.426344	+	0.904561i	$0.640199\pi$
$828$	16.9333	−	5.86109i	0.588472	−	0.203687i
$829$	−16.2671	+	3.23572i	−0.564979	+	0.112381i	−0.469312	−	0.883032i	$-0.655498\pi$
$829$	−16.2671	+	3.23572i	−0.564979	+	0.112381i	−0.0956663	+	0.995413i	$0.530498\pi$
$830$	−5.39646	+	10.6168i	−0.187314	+	0.368516i
$831$	2.89436	−	4.81513i	0.100404	−	0.167035i
$832$	−5.31921	+	19.2937i	−0.184410	+	0.668889i
$833$		−	0.332672i		−	0.0115264i
$834$	−6.54971	−	10.4630i	−0.226798	−	0.362304i
$835$	−15.0565	−	75.6940i	−0.521051	−	2.61950i
$836$	−0.437336	+	2.79667i	−0.0151256	+	0.0967250i
$837$	−9.10084	+	5.40798i	−0.314571	+	0.186927i
$838$	20.1872	+	5.67204i	0.697355	+	0.195937i
$839$	45.1745	+	18.7119i	1.55960	+	0.646006i	0.985019	−	0.172444i	$-0.0551662\pi$
$839$	45.1745	+	18.7119i	1.55960	+	0.646006i	0.574578	+	0.818450i	$0.305166\pi$
$840$	−54.7780	+	0.629423i	−1.89002	+	0.0217171i
$841$	−20.6255	+	8.54337i	−0.711225	+	0.294599i
$842$	−1.89536	−	15.8806i	−0.0653184	−	0.547280i
$843$	28.5226	−	31.3899i	0.982371	−	1.08113i
$844$	−36.9539	+	1.52442i	−1.27200	+	0.0524726i
$845$	−24.1211	−	16.1172i	−0.829789	−	0.554448i
$846$	−12.2314	+	31.1087i	−0.420525	+	1.06954i
$847$	4.42506	−	4.42506i	0.152047	−	0.152047i
$848$	−2.90968	+	5.24369i	−0.0999190	+	0.180069i
$849$	4.33975	−	1.08122i	0.148940	−	0.0371073i
$850$	1.99252	−	25.6383i	0.0683429	−	0.879388i
$851$	−12.8021	−	8.55410i	−0.438851	−	0.293231i
$852$	−23.3934	−	2.51977i	−0.801446	−	0.0863259i
$853$	25.6899	+	5.11004i	0.879606	+	0.174965i	0.614179	−	0.789166i	$-0.289487\pi$
$853$	25.6899	+	5.11004i	0.879606	+	0.174965i	0.265427	+	0.964131i	$0.414487\pi$
$854$	12.0555	+	9.48470i	0.412532	+	0.324560i
$855$	−3.17526	+	3.84915i	−0.108591	+	0.131638i
$856$	6.19691	+	0.225245i	0.211806	+	0.00769873i
$857$	30.8971	+	12.7980i	1.05543	+	0.437172i	0.841826	−	0.539749i	$-0.181481\pi$
$857$	30.8971	+	12.7980i	1.05543	+	0.437172i	0.213600	+	0.976921i	$0.431481\pi$
$858$	0.667192	−	22.4286i	0.0227776	−	0.765701i
$859$	16.0686	+	24.0483i	0.548252	+	0.820517i	0.997334	−	0.0729736i	$-0.0232489\pi$
$859$	16.0686	+	24.0483i	0.548252	+	0.820517i	−0.449082	+	0.893491i	$0.648249\pi$
$860$	−43.2238	+	70.8459i	−1.47392	+	2.41583i
$861$	19.6901	+	7.07334i	0.671036	+	0.241059i
$862$	−0.521290	−	1.59904i	−0.0177552	−	0.0544634i
$863$			44.8567i			1.52694i	0.645843	+	0.763470i	$0.276506\pi$
$863$			44.8567i			1.52694i	−0.645843	+	0.763470i	$0.723494\pi$
$864$	28.5208	+	7.11076i	0.970298	+	0.241913i
$865$		−	56.0931i		−	1.90722i
$866$	−0.948775	+	0.309303i	−0.0322407	+	0.0105105i
$867$	−24.7613	−	8.89511i	−0.840939	−	0.302094i
$868$	10.2911	−	2.49200i	0.349302	−	0.0845839i
$869$	6.65737	+	9.96345i	0.225836	+	0.337987i
$870$	27.2209	+	0.809750i	0.922875	+	0.0274531i
$871$	−17.8816	−	7.40679i	−0.605894	−	0.250969i
$872$	−44.1634	−	20.2025i	−1.49556	−	0.684142i
$873$	3.56797	−	4.32522i	0.120758	−	0.146387i
$874$	−1.00940	+	1.28300i	−0.0341436	+	0.0433983i
$875$	−93.4139	−	18.5812i	−3.15796	−	0.628158i
$876$	45.1816	−	36.3948i	1.52655	−	1.22967i
$877$	−16.5425	−	11.0534i	−0.558602	−	0.373246i	0.243987	−	0.969779i	$-0.421545\pi$
$877$	−16.5425	−	11.0534i	−0.558602	−	0.373246i	−0.802589	+	0.596533i	$0.796545\pi$
$878$	20.4680	+	1.59070i	0.690762	+	0.0536835i
$879$	28.7454	−	7.16169i	0.969557	−	0.241558i
$880$	62.8142	−	5.19124i	2.11747	−	0.174997i
$881$	−29.6126	+	29.6126i	−0.997673	+	0.997673i	−0.999997	−	0.00232406i	$-0.999260\pi$
$881$	−29.6126	+	29.6126i	−0.997673	+	0.997673i	0.00232406	+	0.999997i	$0.499260\pi$
$882$	0.976450	+	0.383923i	0.0328788	+	0.0129274i
$883$	−34.3003	−	22.9187i	−1.15430	−	0.771277i	−0.177222	−	0.984171i	$-0.556711\pi$
$883$	−34.3003	−	22.9187i	−1.15430	−	0.771277i	−0.977075	+	0.212894i	$0.931711\pi$
$884$	−4.95135	−	4.55903i	−0.166532	−	0.153337i
$885$	−33.0661	+	36.3901i	−1.11150	+	1.22324i
$886$	−4.99063	+	0.595636i	−0.167664	+	0.0200108i
$887$	−17.2802	+	7.15771i	−0.580214	+	0.240332i	−0.653434	−	0.756983i	$-0.726672\pi$
$887$	−17.2802	+	7.15771i	−0.580214	+	0.240332i	0.0732204	+	0.997316i	$0.476672\pi$
$888$	−9.93287	−	23.2217i	−0.333325	−	0.779271i
$889$	−41.0207	−	16.9913i	−1.37579	−	0.569871i
$890$	7.20250	−	25.6342i	0.241428	−	0.859260i
$891$	−32.9551	−	0.166813i	−1.10404	−	0.00558845i
$892$	22.6641	+	31.0663i	0.758850	+	1.04018i
$893$	−0.594112	−	2.98680i	−0.0198812	−	0.0999496i
$894$	−5.04113	+	3.15569i	−0.168600	+	0.105542i
$895$			26.7287i			0.893441i
$896$	−25.1721	−	15.1891i	−0.840942	−	0.507433i
$897$	6.66685	−	11.0911i	0.222600	−	0.370321i
$898$	6.42540	+	3.26598i	0.214418	+	0.108987i
$899$	−5.16260	+	1.02690i	−0.172182	+	0.0342492i
$900$	72.9534	+	35.4365i	2.43178	+	1.18122i
$901$	−1.12045	−	1.67687i	−0.0373276	−	0.0558648i
$902$	−23.1742	−	6.51131i	−0.771617	−	0.216803i
$903$	−34.8934	+	25.8103i	−1.16118	+	0.858913i
$904$	20.9592	−	29.0267i	0.697091	−	0.965415i
$905$	22.3772	+	54.0233i	0.743843	+	1.79580i
$906$	−2.84789	−	1.28012i	−0.0946147	−	0.0425293i
$907$	−6.74321	−	1.34131i	−0.223905	−	0.0445374i	0.0818628	−	0.996644i	$-0.473913\pi$
$907$	−6.74321	−	1.34131i	−0.223905	−	0.0445374i	−0.305768	+	0.952106i	$0.598913\pi$
$908$	13.6961	−	14.8747i	0.454520	−	0.493633i
$909$	−4.14315	+	41.0020i	−0.137419	+	1.35995i
$910$	−30.0580	+	25.7229i	−0.996411	+	0.852705i
$911$	7.04481	+	7.04481i	0.233405	+	0.233405i	0.814112	−	0.580707i	$-0.197224\pi$
$911$	7.04481	+	7.04481i	0.233405	+	0.233405i	−0.580707	+	0.814112i	$0.697224\pi$
$912$	−2.53631	+	0.859206i	−0.0839857	+	0.0284512i
$913$	5.06714	−	5.06714i	0.167698	−	0.167698i
$914$	−3.89787	+	50.1550i	−0.128930	+	1.65898i
$915$	−13.2658	−	28.1402i	−0.438553	−	0.930286i
$916$	−32.7315	−	12.0025i	−1.08148	−	0.396574i
$917$	0.808204	−	4.06312i	0.0266893	−	0.134176i
$918$	−6.51438	+	7.43506i	−0.215007	+	0.245393i
$919$	−47.5960	+	19.7149i	−1.57005	+	0.650335i	−0.986798	−	0.161959i	$-0.948219\pi$
$919$	−47.5960	+	19.7149i	−1.57005	+	0.650335i	−0.583249	+	0.812293i	$0.698219\pi$
$920$	33.0549	+	15.1209i	1.08979	+	0.498523i
$921$	−11.4834	+	8.49418i	−0.378392	+	0.279893i
$922$	11.9011	−	6.68028i	0.391943	−	0.220003i
$923$	−14.1282	+	9.44019i	−0.465037	+	0.310728i
$924$	31.4541	+	9.85580i	1.03477	+	0.324232i
$925$	−13.5958	−	68.3506i	−0.447027	−	2.24735i
$926$	−8.65846	−	26.5595i	−0.284534	−	0.872798i
$927$	−20.4526	−	38.4982i	−0.671752	−	1.26445i
$928$	12.1917	+	8.06015i	0.400211	+	0.264587i
$929$	−2.02612			−0.0664748			−0.0332374	−	0.999447i	$-0.510582\pi$
$929$	−2.02612			−0.0664748			−0.0332374	+	0.999447i	$0.510582\pi$
$930$	−20.9284	−	4.81397i	−0.686269	−	0.157856i
$931$	−0.0937507	+	0.0186482i	−0.00307256	+	0.000611169i
$932$	−13.6586	−	8.33325i	−0.447403	−	0.272965i
$933$	2.70510	+	56.5229i	0.0885609	+	1.85048i
$934$	−39.6290	+	22.2443i	−1.29670	+	0.727857i
$935$	−8.11156	+	19.5830i	−0.265276	+	0.640433i
$936$	19.0957	−	9.27167i	0.624162	−	0.303054i
$937$	−0.987795	−	2.38475i	−0.0322699	−	0.0779063i	0.906923	−	0.421296i	$-0.138425\pi$
$937$	−0.987795	−	2.38475i	−0.0322699	−	0.0779063i	−0.939193	+	0.343390i	$0.888425\pi$
$938$	17.5803	−	22.3455i	0.574018	−	0.729607i
$939$	−8.34177	+	9.18036i	−0.272224	+	0.299590i
$940$	−61.5236	+	28.5090i	−2.00668	+	0.929862i
$941$	−2.09080	+	3.12910i	−0.0681580	+	0.102006i	−0.863983	−	0.503521i	$-0.832038\pi$
$941$	−2.09080	+	3.12910i	−0.0681580	+	0.102006i	0.795825	+	0.605527i	$0.207038\pi$
$942$	−15.1834	+	21.3227i	−0.494703	+	0.694731i
$943$	−9.81635	−	9.81635i	−0.319664	−	0.319664i
$944$	−25.3687	+	7.26212i	−0.825682	+	0.236362i
$945$	38.8570	+	43.2005i	1.26402	+	1.40531i
$946$	37.9395	−	32.4677i	1.23352	−	1.05561i
$947$	16.2924	−	24.3833i	0.529432	−	0.792352i	−0.466301	−	0.884626i	$-0.654414\pi$
$947$	16.2924	−	24.3833i	0.529432	−	0.792352i	0.995734	+	0.0922743i	$0.0294137\pi$
$948$	−5.43486	+	9.94849i	−0.176516	+	0.323112i
$949$	8.17397	−	41.0933i	0.265338	−	1.33395i
$950$	−7.33686	+	0.875661i	−0.238039	+	0.0284102i
$951$	−32.3654	−	4.84282i	−1.04952	−	0.157039i
$952$	8.41499	−	5.19078i	0.272731	−	0.168234i
$953$	12.0888	−	29.1848i	0.391593	−	0.945389i	−0.598000	−	0.801496i	$-0.704038\pi$
$953$	12.0888	−	29.1848i	0.391593	−	0.945389i	0.989593	−	0.143893i	$-0.0459622\pi$
$954$	6.21497	−	1.35350i	0.201217	−	0.0438213i
$955$	−48.4803	+	32.3935i	−1.56879	+	1.04823i
$956$	−23.2112	−	3.62971i	−0.750704	−	0.117393i
$957$	−15.4212	−	5.53982i	−0.498497	−	0.179077i
$958$	−7.83856	−	3.98428i	−0.253253	−	0.128726i
$959$	37.7844			1.22012
$960$	31.8851	+	50.3854i	1.02909	+	1.62618i
$961$	−26.8492			−0.866103
$962$	−16.2600	−	8.26483i	−0.524243	−	0.266469i
$963$	−4.15963	−	5.09476i	−0.134042	−	0.164176i
$964$	1.31651	−	8.41882i	0.0424020	−	0.271152i
$965$	73.8473	−	49.3432i	2.37723	−	1.58841i
$966$	13.0363	+	13.8356i	0.419435	+	0.445154i
$967$	−16.2050	+	39.1222i	−0.521116	+	1.25809i	0.416094	+	0.909321i	$0.363399\pi$
$967$	−16.2050	+	39.1222i	−0.521116	+	1.25809i	−0.937210	+	0.348764i	$0.886601\pi$
$968$	−6.62791	−	1.57064i	−0.213029	−	0.0504823i
$969$	0.133270	−	0.890664i	0.00428124	−	0.0286122i
$970$	11.2938	−	1.34793i	0.362622	−	0.0432793i
$971$	−8.80545	+	44.2680i	−0.282580	+	1.42063i	0.535019	+	0.844840i	$0.320304\pi$
$971$	−8.80545	+	44.2680i	−0.282580	+	1.42063i	−0.817600	+	0.575787i	$0.804696\pi$
$972$	−14.3052	−	27.7013i	−0.458839	−	0.888520i
$973$	7.27538	−	10.8884i	0.233238	−	0.349065i
$974$	−1.51599	+	1.29734i	−0.0485753	+	0.0415696i
$975$	56.8344	−	14.1599i	1.82016	−	0.453479i
$976$	1.89744	−	16.5879i	0.0607357	−	0.530965i
$977$	8.81730	+	8.81730i	0.282090	+	0.282090i	0.833942	−	0.551852i	$-0.186079\pi$
$977$	8.81730	+	8.81730i	0.282090	+	0.282090i	−0.551852	+	0.833942i	$0.686079\pi$
$978$	−15.8696	−	11.3004i	−0.507455	−	0.361349i
$979$	−8.90099	+	13.3213i	−0.284477	+	0.425750i
$980$	0.894850	+	1.93112i	0.0285849	+	0.0616874i
$981$	14.8280	+	49.3304i	0.473421	+	1.57500i
$982$	9.22098	−	11.7203i	0.294253	−	0.374011i
$983$	−16.0320	−	38.7047i	−0.511341	−	1.23449i	−0.943103	−	0.332500i	$-0.892108\pi$
$983$	−16.0320	−	38.7047i	−0.511341	−	1.23449i	0.431762	−	0.901988i	$-0.357892\pi$
$984$	−4.69901	−	22.2824i	−0.149799	−	0.710336i
$985$	−5.89430	+	14.2301i	−0.187808	+	0.453408i
$986$	−4.28605	+	2.40582i	−0.136496	+	0.0766169i
$987$	−35.4212	+	1.69520i	−1.12747	+	0.0539588i
$988$	−1.00723	+	1.65090i	−0.0320444	+	0.0525223i
$989$	28.2451	−	5.61830i	0.898142	−	0.178652i
$990$	−48.1183	−	46.4087i	−1.52930	−	1.47497i
$991$	30.3970			0.965592			0.482796	−	0.875733i	$-0.339621\pi$
$991$	30.3970			0.965592			0.482796	+	0.875733i	$0.339621\pi$
$992$	−8.18921	−	8.10940i	−0.260008	−	0.257474i
$993$	17.8477	−	29.6918i	0.566380	−	0.942241i
$994$	−7.73661	−	23.7317i	−0.245390	−	0.752725i
$995$	12.3010	+	61.8414i	0.389969	+	1.96051i
$996$	6.46914	+	2.02703i	0.204982	+	0.0642289i
$997$	−2.67064	+	1.78447i	−0.0845801	+	0.0565146i	−0.597141	−	0.802136i	$-0.703697\pi$
$997$	−2.67064	+	1.78447i	−0.0845801	+	0.0565146i	0.512561	+	0.858651i	$0.328697\pi$
$998$	15.6074	−	8.76065i	0.494044	−	0.277314i
$999$	−11.5456	+	24.1733i	−0.365287	+	0.764810i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.s.a.11.11	✓	240
3.2	odd	2	inner	192.2.s.a.11.20	yes	240
4.3	odd	2		768.2.s.a.719.12		240
12.11	even	2		768.2.s.a.719.23		240
64.29	even	16		768.2.s.a.47.23		240
64.35	odd	16	inner	192.2.s.a.35.20	yes	240
192.29	odd	16		768.2.s.a.47.12		240
192.35	even	16	inner	192.2.s.a.35.11	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.11.11	✓	240	1.1	even	1	trivial
192.2.s.a.11.20	yes	240	3.2	odd	2	inner
192.2.s.a.35.11	yes	240	192.35	even	16	inner
192.2.s.a.35.20	yes	240	64.35	odd	16	inner
768.2.s.a.47.12		240	192.29	odd	16
768.2.s.a.47.23		240	64.29	even	16
768.2.s.a.719.12		240	4.3	odd	2
768.2.s.a.719.23		240	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.640805 + 1.26070i) q^{2} +(0.585574 - 1.63006i) q^{3} +(-1.17874 - 1.61573i) q^{4} +(-3.57797 + 2.39072i) q^{5} +(1.67978 + 1.78279i) q^{6} +(-0.994439 + 2.40079i) q^{7} +(2.79229 - 0.450669i) q^{8} +(-2.31421 - 1.90904i) q^{9} +(-0.721207 - 6.04274i) q^{10} +(-0.714367 + 3.59136i) q^{11} +(-3.32398 + 0.975288i) q^{12} +(-1.38986 + 2.08008i) q^{13} +(-2.38944 - 2.79213i) q^{14} +(1.80186 + 7.23226i) q^{15} +(-1.22116 + 3.80904i) q^{16} +(-0.951204 - 0.951204i) q^{17} +(3.88969 - 1.69420i) q^{18} +(-0.214739 + 0.321380i) q^{19} +(8.08025 + 2.96299i) q^{20} +(3.33112 + 3.02684i) q^{21} +(-4.06987 - 3.20197i) q^{22} +(-1.14288 - 2.75916i) q^{23} +(0.900474 - 4.81551i) q^{24} +(5.17290 - 12.4885i) q^{25} +(-1.73173 - 3.08513i) q^{26} +(-4.46700 + 2.65442i) q^{27} +(5.05121 - 1.22316i) q^{28} +(-2.53398 + 0.504039i) q^{29} +(-10.2724 - 2.36286i) q^{30} +2.03735 q^{31} +(-4.01954 - 3.98037i) q^{32} +(5.43583 + 3.26747i) q^{33} +(1.80872 - 0.589648i) q^{34} +(-2.18155 - 10.9674i) q^{35} +(-0.356653 + 5.98939i) q^{36} +(4.28668 - 2.86427i) q^{37} +(-0.267558 - 0.476664i) q^{38} +(2.57679 + 3.48361i) q^{39} +(-8.91331 + 8.28808i) q^{40} +(4.29457 - 1.77887i) q^{41} +(-5.95054 + 2.25993i) q^{42} +(-1.88124 + 9.45763i) q^{43} +(6.64472 - 3.07905i) q^{44} +(12.8442 + 1.29787i) q^{45} +(4.21083 + 0.327251i) q^{46} +(-5.57116 + 5.57116i) q^{47} +(5.49389 + 4.22103i) q^{48} +(0.174869 + 0.174869i) q^{49} +(12.4294 + 14.5242i) q^{50} +(-2.10752 + 0.993522i) q^{51} +(4.99913 - 0.206223i) q^{52} +(1.47041 + 0.292483i) q^{53} +(-0.483953 - 7.33252i) q^{54} +(-6.02998 - 14.5576i) q^{55} +(-1.69480 + 7.15187i) q^{56} +(0.398124 + 0.538230i) q^{57} +(0.988343 - 3.51758i) q^{58} +(3.66506 + 5.48515i) q^{59} +(9.56144 - 11.4363i) q^{60} +(-4.09381 + 0.814309i) q^{61} +(-1.30554 + 2.56849i) q^{62} +(6.88455 - 3.65750i) q^{63} +(7.59380 - 2.51680i) q^{64} -10.7652i q^{65} +(-7.60262 + 4.75915i) q^{66} +(1.50936 + 7.58806i) q^{67} +(-0.415668 + 2.65811i) q^{68} +(-5.16684 + 0.247277i) q^{69} +(15.2245 + 4.27767i) q^{70} +(6.27514 + 2.59925i) q^{71} +(-7.32229 - 4.28767i) q^{72} +(-15.4732 + 6.40920i) q^{73} +(0.864060 + 7.23966i) q^{74} +(-17.3279 - 15.7451i) q^{75} +(0.772384 - 0.0318623i) q^{76} +(-7.91171 - 5.28644i) q^{77} +(-6.04301 + 1.01625i) q^{78} +(2.31400 - 2.31400i) q^{79} +(-4.73710 - 16.5481i) q^{80} +(1.71111 + 8.83584i) q^{81} +(-0.509359 + 6.55408i) q^{82} +(-1.62719 - 1.08726i) q^{83} +(0.964032 - 8.95003i) q^{84} +(5.67744 + 1.12931i) q^{85} +(-10.7177 - 8.43218i) q^{86} +(-0.662214 + 4.42569i) q^{87} +(-0.376205 + 10.3501i) q^{88} +(4.04231 + 1.67438i) q^{89} +(-9.86683 + 15.3610i) q^{90} +(-3.61170 - 5.40528i) q^{91} +(-3.11089 + 5.09890i) q^{92} +(1.19302 - 3.32101i) q^{93} +(-3.45354 - 10.5936i) q^{94} -1.66327i q^{95} +(-8.84198 + 4.22130i) q^{96} +1.86899i q^{97} +(-0.332515 + 0.108401i) q^{98} +(8.50926 - 6.94740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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