LMFDB - Embedded newform 357.2.bl.a.10.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(10,357)] 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("357.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([0, 8, 9])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$357 = 3 \cdot 7 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	357.bl (of order $48$ , degree $16$ , 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$24$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			10.23
Character	$\chi$	$=$	357.10
Dual form			357.2.bl.a.250.23

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.53902 - 0.334268i) q^{2} +(0.442289 + 0.896873i) q^{3} +(4.40301 - 1.17978i) q^{4} +(-2.60989 + 2.28881i) q^{5} +(1.42277 + 2.12933i) q^{6} +(1.31783 - 2.29419i) q^{7} +(6.05298 - 2.50723i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(-5.86148 + 6.68374i) q^{10} +(0.897223 - 0.0588071i) q^{11} +(3.00552 + 3.42714i) q^{12} +(-0.424382 - 0.424382i) q^{13} +(2.57913 - 6.26549i) q^{14} +(-3.20710 - 1.32842i) q^{15} +(6.63526 - 3.83087i) q^{16} +(0.161598 + 4.11994i) q^{17} +(-1.28046 + 2.21783i) q^{18} +(-0.871576 - 6.62028i) q^{19} +(-8.79108 + 13.1568i) q^{20} +(2.64046 + 0.167236i) q^{21} +(2.25840 - 0.449225i) q^{22} +(-6.64578 - 3.27734i) q^{23} +(4.92583 + 4.31983i) q^{24} +(0.920237 - 6.98989i) q^{25} +(-1.21937 - 0.935654i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(3.09579 - 11.6561i) q^{28} +(0.763391 + 3.83783i) q^{29} +(-8.58693 - 2.30086i) q^{30} +(-4.51208 + 2.22511i) q^{31} +(5.17086 - 3.96774i) q^{32} +(0.449574 + 0.778685i) q^{33} +(1.78746 + 10.4066i) q^{34} +(1.81157 + 9.00387i) q^{35} +(-1.74440 + 4.21135i) q^{36} +(-0.105032 + 1.60248i) q^{37} +(-4.42589 - 16.5177i) q^{38} +(0.192917 - 0.568315i) q^{39} +(-10.0591 + 20.3977i) q^{40} +(0.823123 - 4.13812i) q^{41} +(6.76007 - 0.458007i) q^{42} +(-1.94442 - 4.69425i) q^{43} +(3.88110 - 1.31746i) q^{44} +(-0.227037 - 3.46391i) q^{45} +(-17.9693 - 6.09974i) q^{46} +(3.08056 - 11.4968i) q^{47} +(6.37050 + 4.25663i) q^{48} +(-3.52662 - 6.04673i) q^{49} -18.0550i q^{50} +(-3.62359 + 1.96713i) q^{51} +(-2.36924 - 1.36788i) q^{52} +(6.26017 + 8.15841i) q^{53} +(-2.55544 - 0.167492i) q^{54} +(-2.20706 + 2.20706i) q^{55} +(2.22477 - 17.1908i) q^{56} +(5.55206 - 3.70977i) q^{57} +(3.22112 + 9.48912i) q^{58} +(-1.96500 - 0.258697i) q^{59} +(-15.6882 - 2.06539i) q^{60} +(3.82900 + 11.2799i) q^{61} +(-10.7125 + 7.15784i) q^{62} +(1.01786 + 2.44212i) q^{63} +(0.967281 - 0.967281i) q^{64} +(2.07892 + 0.136260i) q^{65} +(1.40176 + 1.82681i) q^{66} +(7.92783 + 4.57713i) q^{67} +(5.57215 + 17.9495i) q^{68} -7.40995i q^{69} +(7.60930 + 22.2554i) q^{70} +(2.59668 + 1.73505i) q^{71} +(-1.69570 + 6.32845i) q^{72} +(10.8738 + 3.69116i) q^{73} +(0.268979 + 4.10383i) q^{74} +(6.67605 - 2.26622i) q^{75} +(-11.6481 - 28.1209i) q^{76} +(1.04748 - 2.13590i) q^{77} +(0.299850 - 1.50745i) q^{78} +(-3.59325 + 7.28639i) q^{79} +(-8.54916 + 25.1850i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(0.706682 - 10.7819i) q^{82} +(-2.24675 + 5.42414i) q^{83} +(11.8233 - 2.37883i) q^{84} +(-9.85152 - 10.3827i) q^{85} +(-6.50605 - 11.2688i) q^{86} +(-3.10440 + 2.38209i) q^{87} +(5.28343 - 2.60550i) q^{88} +(15.3524 + 4.11366i) q^{89} +(-1.73432 - 8.71903i) q^{90} +(-1.53288 + 0.414347i) q^{91} +(-33.1280 - 6.58957i) q^{92} +(-3.99129 - 3.06262i) q^{93} +(3.97857 - 30.2203i) q^{94} +(17.4273 + 15.2833i) q^{95} +(5.84557 + 2.88272i) q^{96} +(-3.62847 + 0.721749i) q^{97} +(-10.9754 - 14.1739i) q^{98} +(-0.499540 + 0.747614i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100})$ 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$ .

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{16}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	2.53902	−	0.334268i	1.79535	−	0.236363i	0.842268	−	0.539059i	$-0.181220\pi$
$2$	2.53902	−	0.334268i	1.79535	−	0.236363i	0.953087	+	0.302696i	$0.0978868\pi$
$3$	0.442289	+	0.896873i	0.255355	+	0.517810i
$3$	0.442289	+	0.896873i	0.255355	+	0.517810i
$4$	4.40301	−	1.17978i	2.20151	−	0.589892i
$5$	−2.60989	+	2.28881i	−1.16718	+	1.02359i	−0.167893	+	0.985805i	$0.553696\pi$
$5$	−2.60989	+	2.28881i	−1.16718	+	1.02359i	−0.999286	+	0.0377836i	$0.987970\pi$
$6$	1.42277	+	2.12933i	0.580845	+	0.869296i
$7$	1.31783	−	2.29419i	0.498095	−	0.867123i
$7$	1.31783	−	2.29419i	0.498095	−	0.867123i
$8$	6.05298	−	2.50723i	2.14005	−	0.886438i
$9$	−0.608761	+	0.793353i	−0.202920	+	0.264451i
$10$	−5.86148	+	6.68374i	−1.85356	+	2.11358i
$11$	0.897223	−	0.0588071i	0.270523	−	0.0177310i	0.0704619	−	0.997514i	$-0.477553\pi$
$11$	0.897223	−	0.0588071i	0.270523	−	0.0177310i	0.200061	+	0.979783i	$0.435886\pi$
$12$	3.00552	+	3.42714i	0.867618	+	0.989329i
$13$	−0.424382	−	0.424382i	−0.117702	−	0.117702i	0.645802	−	0.763505i	$-0.276523\pi$
$13$	−0.424382	−	0.424382i	−0.117702	−	0.117702i	−0.763505	+	0.645802i	$0.776523\pi$
$14$	2.57913	−	6.26549i	0.689301	−	1.67452i
$15$	−3.20710	−	1.32842i	−0.828070	−	0.342998i
$16$	6.63526	−	3.83087i	1.65881	−	0.957717i
$17$	0.161598	+	4.11994i	0.0391932	+	0.999232i
$17$	0.161598	+	4.11994i	0.0391932	+	0.999232i
$18$	−1.28046	+	2.21783i	−0.301808	+	0.522746i
$19$	−0.871576	−	6.62028i	−0.199953	−	1.51880i	−0.737376	−	0.675483i	$-0.763935\pi$
$19$	−0.871576	−	6.62028i	−0.199953	−	1.51880i	0.537422	−	0.843313i	$-0.319398\pi$
$20$	−8.79108	+	13.1568i	−1.96575	+	2.94195i
$21$	2.64046	+	0.167236i	0.576196	+	0.0364938i
$22$	2.25840	−	0.449225i	0.481493	−	0.0957750i
$23$	−6.64578	−	3.27734i	−1.38574	−	0.683372i	−0.412033	−	0.911169i	$-0.635181\pi$
$23$	−6.64578	−	3.27734i	−1.38574	−	0.683372i	−0.973709	+	0.227797i	$0.926848\pi$
$24$	4.92583	+	4.31983i	1.00548	+	0.881783i
$25$	0.920237	−	6.98989i	0.184047	−	1.39798i
$26$	−1.21937	−	0.935654i	−0.239138	−	0.183497i
$27$	−0.980785	−	0.195090i	−0.188752	−	0.0375451i
$28$	3.09579	−	11.6561i	0.585050	−	2.20280i
$29$	0.763391	+	3.83783i	0.141758	+	0.712666i	0.984644	+	0.174574i	$0.0558548\pi$
$29$	0.763391	+	3.83783i	0.141758	+	0.712666i	−0.842886	+	0.538092i	$0.819145\pi$
$30$	−8.58693	−	2.30086i	−1.56775	−	0.420078i
$31$	−4.51208	+	2.22511i	−0.810394	+	0.399642i	−0.799774	−	0.600302i	$-0.795047\pi$
$31$	−4.51208	+	2.22511i	−0.810394	+	0.399642i	−0.0106202	+	0.999944i	$0.503381\pi$
$32$	5.17086	−	3.96774i	0.914088	−	0.701404i
$33$	0.449574	+	0.778685i	0.0782608	+	0.135552i
$34$	1.78746	+	10.4066i	0.306547	+	1.78471i
$35$	1.81157	+	9.00387i	0.306211	+	1.52193i
$36$	−1.74440	+	4.21135i	−0.290733	+	0.701892i
$37$	−0.105032	+	1.60248i	−0.0172672	+	0.263446i	0.980493	+	0.196554i	$0.0629750\pi$
$37$	−0.105032	+	1.60248i	−0.0172672	+	0.263446i	−0.997760	+	0.0668923i	$0.978692\pi$
$38$	−4.42589	−	16.5177i	−0.717974	−	2.67952i
$39$	0.192917	−	0.568315i	0.0308915	−	0.0910033i
$40$	−10.0591	+	20.3977i	−1.59048	+	3.22517i
$41$	0.823123	−	4.13812i	0.128550	−	0.646265i	−0.861751	−	0.507331i	$-0.830632\pi$
$41$	0.823123	−	4.13812i	0.128550	−	0.646265i	0.990302	−	0.138935i	$-0.0443678\pi$
$42$	6.76007	−	0.458007i	1.04310	−	0.0706720i
$43$	−1.94442	−	4.69425i	−0.296521	−	0.715866i	−0.999987	−	0.00513653i	$-0.998365\pi$
$43$	−1.94442	−	4.69425i	−0.296521	−	0.715866i	0.703465	−	0.710730i	$-0.251635\pi$
$44$	3.88110	−	1.31746i	0.585098	−	0.198614i
$45$	−0.227037	−	3.46391i	−0.0338446	−	0.516369i
$46$	−17.9693	−	6.09974i	−2.64942	−	0.899357i
$47$	3.08056	−	11.4968i	0.449345	−	1.67698i	−0.254856	−	0.966979i	$-0.582028\pi$
$47$	3.08056	−	11.4968i	0.449345	−	1.67698i	0.704201	−	0.710001i	$-0.251305\pi$
$48$	6.37050	+	4.25663i	0.919503	+	0.614392i
$49$	−3.52662	−	6.04673i	−0.503803	−	0.863818i
$50$		−	18.0550i		−	2.55337i
$51$	−3.62359	+	1.96713i	−0.507404	+	0.275454i
$52$	−2.36924	−	1.36788i	−0.328554	−	0.189691i
$53$	6.26017	+	8.15841i	0.859901	+	1.12064i	0.991598	+	0.129354i	$0.0412905\pi$
$53$	6.26017	+	8.15841i	0.859901	+	1.12064i	−0.131698	+	0.991290i	$0.542043\pi$
$54$	−2.55544	−	0.167492i	−0.347751	−	0.0227928i
$55$	−2.20706	+	2.20706i	−0.297599	+	0.297599i
$56$	2.22477	−	17.1908i	0.297298	−	2.29722i
$57$	5.55206	−	3.70977i	0.735388	−	0.491371i
$58$	3.22112	+	9.48912i	0.422954	+	1.24598i
$59$	−1.96500	−	0.258697i	−0.255821	−	0.0336794i	0.00152505	−	0.999999i	$-0.499515\pi$
$59$	−1.96500	−	0.258697i	−0.255821	−	0.0336794i	−0.257346	+	0.966319i	$0.582848\pi$
$60$	−15.6882	−	2.06539i	−2.02533	−	0.266640i
$61$	3.82900	+	11.2799i	0.490253	+	1.44424i	0.857679	+	0.514186i	$0.171906\pi$
$61$	3.82900	+	11.2799i	0.490253	+	1.44424i	−0.367426	+	0.930053i	$0.619761\pi$
$62$	−10.7125	+	7.15784i	−1.36048	+	0.909046i
$63$	1.01786	+	2.44212i	0.128238	+	0.307679i
$64$	0.967281	−	0.967281i	0.120910	−	0.120910i
$65$	2.07892	+	0.136260i	0.257858	+	0.0169009i
$66$	1.40176	+	1.82681i	0.172545	+	0.224865i
$67$	7.92783	+	4.57713i	0.968538	+	0.559186i	0.898790	−	0.438379i	$-0.144447\pi$
$67$	7.92783	+	4.57713i	0.968538	+	0.559186i	0.0697480	+	0.997565i	$0.477780\pi$
$68$	5.57215	+	17.9495i	0.675722	+	2.17669i
$69$		−	7.40995i		−	0.892053i
$70$	7.60930	+	22.2554i	0.909486	+	2.66003i
$71$	2.59668	+	1.73505i	0.308170	+	0.205912i	0.700032	−	0.714111i	$-0.253169\pi$
$71$	2.59668	+	1.73505i	0.308170	+	0.205912i	−0.391862	+	0.920024i	$0.628169\pi$
$72$	−1.69570	+	6.32845i	−0.199841	+	0.745815i
$73$	10.8738	+	3.69116i	1.27268	+	0.432018i	0.874383	−	0.485236i	$-0.161266\pi$
$73$	10.8738	+	3.69116i	1.27268	+	0.432018i	0.398301	+	0.917255i	$0.369600\pi$
$74$	0.268979	+	4.10383i	0.0312682	+	0.477061i
$75$	6.67605	−	2.26622i	0.770884	−	0.261680i
$76$	−11.6481	−	28.1209i	−1.33612	−	3.22569i
$77$	1.04748	−	2.13590i	0.119371	−	0.243408i
$78$	0.299850	−	1.50745i	0.0339513	−	0.170685i
$79$	−3.59325	+	7.28639i	−0.404272	+	0.819782i	0.595592	+	0.803287i	$0.296918\pi$
$79$	−3.59325	+	7.28639i	−0.404272	+	0.819782i	−0.999864	+	0.0164953i	$0.994749\pi$
$80$	−8.54916	+	25.1850i	−0.955826	+	2.81577i
$81$	−0.258819	−	0.965926i	−0.0287577	−	0.107325i
$82$	0.706682	−	10.7819i	0.0780400	−	1.19066i
$83$	−2.24675	+	5.42414i	−0.246613	+	0.595377i	−0.997912	−	0.0645849i	$-0.979428\pi$
$83$	−2.24675	+	5.42414i	−0.246613	+	0.595377i	0.751299	+	0.659962i	$0.229428\pi$
$84$	11.8233	−	2.37883i	1.29003	−	0.259552i
$85$	−9.85152	−	10.3827i	−1.06855	−	1.12616i
$86$	−6.50605	−	11.2688i	−0.701565	−	1.21515i
$87$	−3.10440	+	2.38209i	−0.332827	+	0.255387i
$88$	5.28343	−	2.60550i	0.563215	−	0.277747i
$89$	15.3524	+	4.11366i	1.62735	+	0.436047i	0.953149	−	0.302502i	$-0.0978220\pi$
$89$	15.3524	+	4.11366i	1.62735	+	0.436047i	0.674200	+	0.738549i	$0.264489\pi$
$90$	−1.73432	−	8.71903i	−0.182814	−	0.919066i
$91$	−1.53288	+	0.414347i	−0.160689	+	0.0434354i
$92$	−33.1280	−	6.58957i	−3.45383	−	0.687010i
$93$	−3.99129	−	3.06262i	−0.413877	−	0.317579i
$94$	3.97857	−	30.2203i	0.410359	−	3.11698i
$95$	17.4273	+	15.2833i	1.78800	+	1.56804i
$96$	5.84557	+	2.88272i	0.596611	+	0.294216i
$97$	−3.62847	+	0.721749i	−0.368416	+	0.0732825i	−0.375826	−	0.926690i	$-0.622641\pi$
$97$	−3.62847	+	0.721749i	−0.368416	+	0.0732825i	0.00741061	+	0.999973i	$0.497641\pi$
$98$	−10.9754	−	14.1739i	−1.10868	−	1.43178i
$99$	−0.499540	+	0.747614i	−0.0502056	+	0.0751380i
$100$	−4.19475	−	31.8623i	−0.419475	−	3.18623i
$101$	−5.76342	+	9.98254i	−0.573482	+	0.993299i	0.422723	+	0.906259i	$0.361074\pi$
$101$	−5.76342	+	9.98254i	−0.573482	+	0.993299i	−0.996205	+	0.0870405i	$0.972259\pi$
$102$	−8.54279	+	6.20583i	−0.845863	+	0.614469i
$103$	−0.0230596	+	0.0133135i	−0.00227213	+	0.00131181i	−0.501136	−	0.865369i	$-0.667084\pi$
$103$	−0.0230596	+	0.0133135i	−0.00227213	+	0.00131181i	0.498864	+	0.866681i	$0.333751\pi$
$104$	−3.63279	−	1.50475i	−0.356225	−	0.147553i
$105$	−7.27409	+	5.60706i	−0.709878	+	0.547193i
$106$	18.6218	+	18.6218i	1.80871	+	1.80871i
$107$	0.251397	+	0.286663i	0.0243035	+	0.0277128i	0.763864	−	0.645377i	$-0.223300\pi$
$107$	0.251397	+	0.286663i	0.0243035	+	0.0277128i	−0.739560	+	0.673090i	$0.764967\pi$
$108$	−4.54857	+	0.298129i	−0.437687	+	0.0286875i
$109$	3.01133	−	3.43377i	0.288433	−	0.328895i	−0.589418	−	0.807828i	$-0.700643\pi$
$109$	3.01133	−	3.43377i	0.288433	−	0.328895i	0.877852	+	0.478933i	$0.158976\pi$
$110$	−4.86600	+	6.34150i	−0.463955	+	0.604638i
$111$	−1.48368	+	0.614558i	−0.140824	+	0.0583313i
$112$	−0.0445678	−	20.2710i	−0.00421126	−	1.91543i
$113$	−4.83150	−	7.23085i	−0.454509	−	0.680221i	0.531472	−	0.847076i	$-0.321639\pi$
$113$	−4.83150	−	7.23085i	−0.454509	−	0.680221i	−0.985982	+	0.166855i	$0.946639\pi$
$114$	12.8567	−	11.2750i	1.20414	−	1.05600i
$115$	24.8460	−	6.65746i	2.31690	−	0.620812i
$116$	7.88902	+	15.9974i	0.732477	+	1.48532i
$117$	0.595032	−	0.0783374i	0.0550107	−	0.00724230i
$118$	−5.07563			−0.467249
$119$	9.66488	+	5.05866i	0.885978	+	0.463727i
$120$	−22.7432			−2.07616
$121$	−10.1043	+	1.33026i	−0.918577	+	0.120933i
$122$	13.4924	+	27.3598i	1.22154	+	2.47704i
$123$	4.07542	−	1.09201i	0.367469	−	0.0984629i
$124$	−17.2416	+	15.1205i	−1.54834	+	1.35786i
$125$	3.95398	+	5.91755i	0.353655	+	0.529281i
$126$	3.40068	+	5.86035i	0.302956	+	0.522082i
$127$	−4.36836	+	1.80943i	−0.387629	+	0.160561i	−0.567982	−	0.823041i	$-0.692276\pi$
$127$	−4.36836	+	1.80943i	−0.387629	+	0.160561i	0.180353	+	0.983602i	$0.442276\pi$
$128$	−5.80288	+	7.56245i	−0.512907	+	0.668433i
$129$	3.35015	−	3.82011i	0.294964	−	0.336342i
$130$	5.32396	−	0.348951i	0.466942	−	0.0306050i
$131$	−7.93346	−	9.04638i	−0.693150	−	0.790386i	0.293023	−	0.956105i	$-0.405339\pi$
$131$	−7.93346	−	9.04638i	−0.693150	−	0.790386i	−0.986173	+	0.165719i	$0.947005\pi$
$132$	2.89816	+	2.89816i	0.252252	+	0.252252i
$133$	−16.3368	−	6.72487i	−1.41658	−	0.583120i
$134$	21.6589	+	8.97140i	1.87104	+	0.775011i
$135$	3.00627	−	1.73567i	0.258738	−	0.149383i
$136$	11.3078	+	24.5327i	0.969633	+	2.10366i
$137$	−9.89744	+	17.1429i	−0.845596	+	1.46461i	0.0395072	+	0.999219i	$0.487421\pi$
$137$	−9.89744	+	17.1429i	−0.845596	+	1.46461i	−0.885103	+	0.465395i	$0.845912\pi$
$138$	−2.47691	−	18.8140i	−0.210848	−	1.60155i
$139$	6.07969	−	9.09890i	0.515672	−	0.771758i	−0.478668	−	0.877996i	$-0.658880\pi$
$139$	6.07969	−	9.09890i	0.515672	−	0.771758i	0.994341	+	0.106237i	$0.0338804\pi$
$140$	18.5990	+	37.5069i	1.57190	+	3.16991i
$141$	11.6737	−	2.32203i	0.983099	−	0.195551i
$142$	7.17299	+	3.53733i	0.601944	+	0.296846i
$143$	−0.405721	−	0.355808i	−0.0339281	−	0.0297542i
$144$	−1.00006	+	7.59619i	−0.0833381	+	0.633016i
$145$	−10.7764	−	8.26905i	−0.894934	−	0.686707i
$146$	28.8426	+	5.73716i	2.38703	+	0.474810i
$147$	3.86336	−	5.83733i	0.318645	−	0.481455i
$148$	1.42812	+	7.17965i	0.117391	+	0.590164i
$149$	15.7191	+	4.21193i	1.28776	+	0.345054i	0.836810	−	0.547494i	$-0.184418\pi$
$149$	15.7191	+	4.21193i	1.28776	+	0.345054i	0.450951	+	0.892549i	$0.351085\pi$
$150$	16.1931	−	7.98554i	1.32216	−	0.652017i
$151$	−2.55000	+	1.95668i	−0.207516	+	0.159233i	−0.707291	−	0.706923i	$-0.750083\pi$
$151$	−2.55000	+	1.95668i	−0.207516	+	0.159233i	0.499775	+	0.866155i	$0.333416\pi$
$152$	−21.8742	−	37.8872i	−1.77423	−	3.07306i
$153$	−3.36694	−	2.37986i	−0.272201	−	0.192400i
$154$	1.94560	−	5.77321i	0.156781	−	0.465219i
$155$	6.68318	−	16.1346i	0.536806	−	1.29596i
$156$	0.178927	−	2.72990i	0.0143256	−	0.218567i
$157$	1.81737	+	6.78251i	0.145042	+	0.541303i	0.999754	+	0.0222002i	$0.00706713\pi$
$157$	1.81737	+	6.78251i	0.145042	+	0.541303i	−0.854712	+	0.519103i	$0.826266\pi$
$158$	−6.68771	+	19.7014i	−0.532045	+	1.56736i
$159$	−4.54826	+	9.22295i	−0.360700	+	0.731428i
$160$	−4.41397	+	22.1905i	−0.348955	+	1.75432i
$161$	−16.2769	+	10.9277i	−1.28280	+	0.861224i
$162$	−0.980023	−	2.36599i	−0.0769979	−	0.185889i
$163$	19.0972	−	6.48263i	1.49581	−	0.507758i	0.550753	−	0.834669i	$-0.314341\pi$
$163$	19.0972	−	6.48263i	1.49581	−	0.507758i	0.945055	+	0.326910i	$0.106007\pi$
$164$	−1.25786	−	19.1913i	−0.0982226	−	1.49859i
$165$	−2.95560	−	1.00329i	−0.230093	−	0.0781062i
$166$	−3.89143	+	14.5230i	−0.302033	+	1.12720i
$167$	−8.34831	−	5.57816i	−0.646012	−	0.431651i	0.188929	−	0.981991i	$-0.439498\pi$
$167$	−8.34831	−	5.57816i	−0.646012	−	0.431651i	−0.834941	+	0.550339i	$0.814498\pi$
$168$	16.4020	−	5.60796i	1.26544	−	0.432663i
$169$		−	12.6398i		−	0.972292i
$170$	−28.4838	−	23.0689i	−2.18461	−	1.76930i
$171$	5.78280	+	3.33870i	0.442222	+	0.255317i
$172$	−14.0995	−	18.3748i	−1.07508	−	1.40107i
$173$	−15.8502	−	1.03888i	−1.20507	−	0.0789845i	−0.550401	−	0.834900i	$-0.685525\pi$
$173$	−15.8502	−	1.03888i	−1.20507	−	0.0789845i	−0.654669	+	0.755916i	$0.727192\pi$
$174$	−7.08587	+	7.08587i	−0.537178	+	0.537178i
$175$	−14.8234	−	11.3227i	−1.12055	−	0.855917i
$176$	5.72802	−	3.82734i	0.431766	−	0.288497i
$177$	−0.637077	−	1.87677i	−0.0478857	−	0.141067i
$178$	40.3550	+	5.31283i	3.02473	+	0.398214i
$179$	6.81951	+	0.897806i	0.509714	+	0.0671051i	0.380997	−	0.924576i	$-0.375581\pi$
$179$	6.81951	+	0.897806i	0.509714	+	0.0671051i	0.128717	+	0.991681i	$0.458914\pi$
$180$	−5.08631	−	14.9838i	−0.379111	−	1.11682i
$181$	−11.0097	+	7.35646i	−0.818346	+	0.546801i	−0.892816	−	0.450422i	$-0.851274\pi$
$181$	−11.0097	+	7.35646i	−0.818346	+	0.546801i	0.0744698	+	0.997223i	$0.476274\pi$
$182$	−3.75350	+	1.56443i	−0.278228	+	0.115963i
$183$	−8.42308	+	8.42308i	−0.622652	+	0.622652i
$184$	−48.4438	−	3.17518i	−3.57133	−	0.234077i
$185$	−3.39366	−	4.42270i	−0.249507	−	0.325163i
$186$	−11.1577	−	6.44188i	−0.818120	−	0.472342i
$187$	0.387270	+	3.68700i	0.0283200	+	0.269620i
$188$		−	54.2549i		−	3.95695i
$189$	−1.74009	+	1.99301i	−0.126573	+	0.144970i
$190$	49.3569	+	32.9792i	3.58073	+	2.39257i
$191$	2.20810	−	8.24076i	0.159773	−	0.596280i	−0.838876	−	0.544322i	$-0.816787\pi$
$191$	2.20810	−	8.24076i	0.159773	−	0.596280i	0.998649	−	0.0519584i	$-0.0165463\pi$
$192$	1.29534	+	0.439710i	0.0934835	+	0.0317334i
$193$	−1.35886	−	20.7322i	−0.0978128	−	1.49233i	−0.711444	−	0.702742i	$-0.751959\pi$
$193$	−1.35886	−	20.7322i	−0.0978128	−	1.49233i	0.613632	−	0.789593i	$-0.289708\pi$
$194$	−8.97150	+	3.04541i	−0.644116	+	0.218648i
$195$	0.797276	+	1.92479i	0.0570941	+	0.137837i
$196$	−22.6616	−	22.4632i	−1.61869	−	1.60451i
$197$	0.921449	−	4.63244i	0.0656505	−	0.330047i	−0.933977	−	0.357333i	$-0.883686\pi$
$197$	0.921449	−	4.63244i	0.0656505	−	0.330047i	0.999628	+	0.0272853i	$0.00868624\pi$
$198$	−1.01844	+	2.06518i	−0.0723771	+	0.146766i
$199$	2.74620	−	8.09003i	0.194673	−	0.573487i	−0.805135	−	0.593091i	$-0.797907\pi$
$199$	2.74620	−	8.09003i	0.194673	−	0.573487i	0.999808	+	0.0196043i	$0.00624064\pi$
$200$	−11.9551	−	44.6169i	−0.845351	−	3.15489i
$201$	−0.598718	+	9.13467i	−0.0422303	+	0.644310i
$202$	−11.2966	+	27.2723i	−0.794824	+	1.91887i
$203$	9.81073	+	3.30626i	0.688578	+	0.232054i
$204$	−13.6339	+	12.9364i	−0.954564	+	0.905727i
$205$	7.32312	+	12.6840i	0.511469	+	0.885890i
$206$	−0.0540984	+	0.0415111i	−0.00376921	+	0.00289222i
$207$	6.64578	−	3.27734i	0.461914	−	0.227791i
$208$	−4.44163	−	1.19013i	−0.307972	−	0.0825208i
$209$	−1.17132	−	5.88861i	−0.0810217	−	0.407324i
$210$	−16.5948	+	16.6679i	−1.14515	+	1.15019i
$211$	−0.731409	−	0.145486i	−0.0503523	−	0.0100157i	0.169850	−	0.985470i	$-0.445672\pi$
$211$	−0.731409	−	0.145486i	−0.0503523	−	0.0100157i	−0.220202	+	0.975454i	$0.570672\pi$
$212$	37.1888	+	28.5359i	2.55414	+	1.95986i
$213$	−0.407634	+	3.09629i	−0.0279306	+	0.212154i
$214$	0.734123	+	0.643809i	0.0501836	+	0.0440099i
$215$	15.8190	+	7.80106i	1.07885	+	0.532028i
$216$	−6.42581	+	1.27817i	−0.437221	+	0.0869686i
$217$	−0.841346	+	13.2839i	−0.0571143	+	0.901771i
$218$	6.49802	−	9.72498i	0.440102	−	0.658659i
$219$	1.49886	+	11.3850i	0.101284	+	0.769327i
$220$	−7.11385	+	12.3215i	−0.479615	+	0.830718i
$221$	1.67985	−	1.81700i	0.112999	−	0.122225i
$222$	−3.56165	+	2.05632i	−0.239042	+	0.138011i
$223$	16.3616	+	6.77719i	1.09565	+	0.453834i	0.855974	−	0.517019i	$-0.172958\pi$
$223$	16.3616	+	6.77719i	1.09565	+	0.453834i	0.239678	+	0.970852i	$0.422958\pi$
$224$	−2.28842	−	17.0918i	−0.152901	−	1.14199i
$225$	4.98525	+	4.98525i	0.332350	+	0.332350i
$226$	−14.6843	−	16.7442i	−0.976784	−	1.11381i
$227$	4.63658	−	0.303898i	0.307741	−	0.0201704i	0.0892494	−	0.996009i	$-0.471553\pi$
$227$	4.63658	−	0.303898i	0.307741	−	0.0201704i	0.218491	+	0.975839i	$0.429887\pi$
$228$	20.0691	−	22.8844i	1.32911	−	1.51556i
$229$	8.05852	−	10.5021i	0.532522	−	0.693996i	−0.447182	−	0.894443i	$-0.647573\pi$
$229$	8.05852	−	10.5021i	0.532522	−	0.693996i	0.979705	+	0.200446i	$0.0642392\pi$
$230$	60.8590	−	25.2086i	4.01292	−	1.66221i
$231$	2.37892	−	0.00523028i	0.156521	−	0.000344127i
$232$	14.2431	+	21.3163i	0.935104	+	1.39948i
$233$	5.87598	−	5.15310i	0.384949	−	0.337591i	−0.444899	−	0.895581i	$-0.646761\pi$
$233$	5.87598	−	5.15310i	0.384949	−	0.337591i	0.829848	+	0.557990i	$0.188427\pi$
$234$	1.48461	−	0.397800i	0.0970519	−	0.0260050i
$235$	18.2741	+	37.0562i	1.19207	+	2.41728i
$236$	−8.95710	+	1.17923i	−0.583058	+	0.0767610i
$237$	−8.12421			−0.527724
$238$	26.2302	+	9.61336i	1.70025	+	0.623142i
$239$	−20.9725			−1.35660			−0.678299	−	0.734786i	$-0.737283\pi$
$239$	−20.9725			−1.35660			−0.678299	+	0.734786i	$0.737283\pi$
$240$	−26.3690	+	3.47154i	−1.70211	+	0.224087i
$241$	−6.07959	−	12.3282i	−0.391621	−	0.794129i	−1.00000		0.000482056i	$-0.999847\pi$
$241$	−6.07959	−	12.3282i	−0.391621	−	0.794129i	0.608379	−	0.793647i	$-0.291820\pi$
$242$	−25.2104	+	6.75511i	−1.62059	+	0.434235i
$243$	0.751840	−	0.659346i	0.0482305	−	0.0422971i
$244$	30.1669	+	45.1480i	1.93124	+	2.89030i
$245$	23.0439	+	7.70953i	1.47222	+	0.492544i
$246$	9.98254	−	4.13490i	0.636463	−	0.263632i
$247$	−2.43964	+	3.17941i	−0.155231	+	0.202301i
$248$	−21.7327	+	24.7814i	−1.38003	+	1.57362i
$249$	−5.85848	+	0.383985i	−0.371266	+	0.0243341i
$250$	12.0173	+	13.7031i	0.760038	+	0.866657i
$251$	−4.70285	−	4.70285i	−0.296841	−	0.296841i	0.542934	−	0.839775i	$-0.317313\pi$
$251$	−4.70285	−	4.70285i	−0.296841	−	0.296841i	−0.839775	+	0.542934i	$0.817313\pi$
$252$	7.36281	+	9.55185i	0.463814	+	0.601710i
$253$	−6.15548	−	2.54968i	−0.386992	−	0.160297i
$254$	−10.4865	+	6.05438i	−0.657981	+	0.379886i
$255$	4.95477	−	13.4277i	0.310280	−	0.840877i
$256$	−13.5736	+	23.5102i	−0.848353	+	1.46939i
$257$	−1.70666	−	12.9633i	−0.106458	−	0.808631i	−0.958487	−	0.285136i	$-0.907961\pi$
$257$	−1.70666	−	12.9633i	−0.106458	−	0.808631i	0.852029	−	0.523495i	$-0.175372\pi$
$258$	7.22914	−	10.8192i	0.450066	−	0.673572i
$259$	3.53798	+	2.35277i	0.219839	+	0.146194i
$260$	9.31427	−	1.85272i	0.577646	−	0.114901i
$261$	−3.50947	−	1.73068i	−0.217231	−	0.107126i
$262$	−23.1671	−	20.3170i	−1.43127	−	1.25519i
$263$	−0.146623	+	1.11371i	−0.00904116	+	0.0686744i	−0.995371	−	0.0961107i	$-0.969360\pi$
$263$	−0.146623	+	1.11371i	−0.00904116	+	0.0686744i	0.986329	+	0.164785i	$0.0526931\pi$
$264$	4.67360	+	3.58618i	0.287640	+	0.220714i
$265$	−35.0115	−	6.96421i	−2.15074	−	0.427808i
$266$	−43.7272	−	11.6137i	−2.68109	−	0.712081i
$267$	3.10076	+	15.5886i	0.189763	+	0.954004i
$268$	40.3063	+	10.8001i	2.46210	+	0.659718i
$269$	11.1488	−	5.49799i	0.679755	−	0.335218i	−0.0694225	−	0.997587i	$-0.522116\pi$
$269$	11.1488	−	5.49799i	0.679755	−	0.335218i	0.749178	+	0.662369i	$0.230449\pi$
$270$	7.05279	−	5.41179i	0.429219	−	0.329351i
$271$	−2.51828	−	4.36179i	−0.152975	−	0.264960i	0.779345	−	0.626595i	$-0.215552\pi$
$271$	−2.51828	−	4.36179i	−0.152975	−	0.264960i	−0.932320	+	0.361635i	$0.882219\pi$
$272$	16.8552	+	26.7178i	1.02200	+	1.62000i
$273$	−1.04959	−	1.19153i	−0.0635241	−	0.0721149i
$274$	−19.3995	+	46.8344i	−1.17196	+	2.82937i
$275$	0.414602	−	6.32561i	0.0250014	−	0.381448i
$276$	−8.74214	−	32.6261i	−0.526215	−	1.96386i
$277$	8.35036	−	24.5994i	0.501724	−	1.47803i	−0.341195	−	0.939992i	$-0.610832\pi$
$277$	8.35036	−	24.5994i	0.501724	−	1.47803i	0.842920	−	0.538040i	$-0.180835\pi$
$278$	12.3950	−	25.1345i	0.743400	−	1.50747i
$279$	0.981481	−	4.93424i	0.0587597	−	0.295405i
$280$	33.5401	+	49.9582i	2.00441	+	2.98558i
$281$	8.59256	+	20.7443i	0.512589	+	1.23750i	0.942372	+	0.334567i	$0.108590\pi$
$281$	8.59256	+	20.7443i	0.512589	+	1.23750i	−0.429783	+	0.902932i	$0.641410\pi$
$282$	28.8634	−	9.79781i	1.71879	−	0.583451i
$283$	−1.17392	−	17.9105i	−0.0697822	−	1.06467i	−0.878894	−	0.477016i	$-0.841718\pi$
$283$	−1.17392	−	17.9105i	−0.0697822	−	1.06467i	0.809112	−	0.587654i	$-0.199948\pi$
$284$	13.4802	+	4.57592i	0.799904	+	0.271531i
$285$	−5.99931	+	22.3897i	−0.355368	+	1.32625i
$286$	−1.14907	−	0.767783i	−0.0679458	−	0.0453999i
$287$	−8.40889	−	7.34176i	−0.496361	−	0.433370i
$288$			6.51773i			0.384061i
$289$	−16.9478	+	1.33154i	−0.996928	+	0.0783261i
$290$	−30.1256	−	17.3930i	−1.76904	−	1.02135i
$291$	−2.25215	−	2.93506i	−0.132023	−	0.172056i
$292$	52.2323	+	3.42349i	3.05667	+	0.200344i
$293$	−7.30316	+	7.30316i	−0.426655	+	0.426655i	−0.887487	−	0.460832i	$-0.847551\pi$
$293$	−7.30316	+	7.30316i	−0.426655	+	0.426655i	0.460832	+	0.887487i	$0.347551\pi$
$294$	7.85790	−	16.1125i	0.458282	−	0.939698i
$295$	5.72053	−	3.82234i	0.333062	−	0.222545i
$296$	3.38202	+	9.96312i	0.196576	+	0.579094i
$297$	−0.891455	−	0.117362i	−0.0517275	−	0.00681005i
$298$	41.3190	+	5.43975i	2.39355	+	0.315116i
$299$	1.42951	+	4.21119i	0.0826705	+	0.243539i
$300$	26.7211	−	17.8545i	1.54274	−	1.03083i
$301$	−13.3319	−	1.72537i	−0.768439	−	0.0994487i
$302$	−5.82043	+	5.82043i	−0.334928	+	0.334928i
$303$	−11.5022	−	0.753891i	−0.660782	−	0.0433099i
$304$	−31.1445	−	40.5884i	−1.78626	−	2.32790i
$305$	−35.8108	−	20.6754i	−2.05052	−	1.18387i
$306$	−9.34422	−	4.91703i	−0.534174	−	0.281088i
$307$			20.9888i			1.19789i	0.800789	+	0.598946i	$0.204414\pi$
$307$			20.9888i			1.19789i	−0.800789	+	0.598946i	$0.795586\pi$
$308$	2.09215	−	10.6402i	0.119212	−	0.606280i
$309$	−0.0221395	−	0.0147931i	−0.00125947	−	0.000841551i
$310$	11.5754	−	43.2000i	0.657439	−	2.45360i
$311$	17.3953	+	5.90492i	0.986400	+	0.334838i	0.767598	−	0.640932i	$-0.221452\pi$
$311$	17.3953	+	5.90492i	0.986400	+	0.334838i	0.218802	+	0.975769i	$0.429785\pi$
$312$	−0.257172	−	3.92369i	−0.0145595	−	0.222135i
$313$	5.83741	−	1.98153i	0.329950	−	0.112003i	−0.151549	−	0.988450i	$-0.548426\pi$
$313$	5.83741	−	1.98153i	0.329950	−	0.112003i	0.481499	+	0.876447i	$0.340093\pi$
$314$	6.88150	+	16.6134i	0.388345	+	0.937548i
$315$	−8.24606	−	4.04399i	−0.464613	−	0.227853i
$316$	−7.22476	+	36.3213i	−0.406424	+	2.04323i
$317$	−6.99231	+	14.1790i	−0.392727	+	0.796373i	0.607271	+	0.794495i	$0.292264\pi$
$317$	−6.99231	+	14.1790i	−0.392727	+	0.796373i	−0.999998	+	0.00187761i	$0.999402\pi$
$318$	−8.46516	+	24.9375i	−0.474702	+	1.39843i
$319$	0.910623	+	3.39849i	0.0509851	+	0.190279i
$320$	−0.310573	+	4.73842i	−0.0173615	+	0.264886i
$321$	−0.145911	+	0.352259i	−0.00814393	+	0.0196612i
$322$	−37.6745	+	33.1864i	−2.09952	+	1.84941i
$323$	27.1343	−	4.66066i	1.50979	−	0.259326i
$324$	−2.27917	−	3.94763i	−0.126620	−	0.219313i
$325$	−3.35691	+	2.57585i	−0.186208	+	0.142882i
$326$	46.3211	−	22.8431i	2.56549	−	1.26516i
$327$	4.41153	+	1.18207i	0.243958	+	0.0653684i
$328$	−5.39285	−	27.1117i	−0.297770	−	1.49699i
$329$	−22.3162	−	22.2183i	−1.23033	−	1.22493i
$330$	−7.83969	−	1.55941i	−0.431561	−	0.0858428i
$331$	9.32437	+	7.15484i	0.512514	+	0.393266i	0.832387	−	0.554195i	$-0.186974\pi$
$331$	9.32437	+	7.15484i	0.512514	+	0.393266i	−0.319873	+	0.947460i	$0.603640\pi$
$332$	−3.49317	+	26.5333i	−0.191713	+	1.45620i
$333$	−1.20739	−	1.05886i	−0.0661647	−	0.0580249i
$334$	−23.0611	−	11.3725i	−1.26185	−	0.622274i
$335$	−31.1670	+	6.19950i	−1.70283	+	0.338715i
$336$	18.1608	−	9.00561i	0.990753	−	0.491296i
$337$	−2.89024	+	4.32555i	−0.157441	+	0.235628i	−0.901801	−	0.432151i	$-0.857755\pi$
$337$	−2.89024	+	4.32555i	−0.157441	+	0.235628i	0.744360	+	0.667779i	$0.232755\pi$
$338$	−4.22508	−	32.0926i	−0.229814	−	1.74561i
$339$	4.34823	−	7.53136i	0.236164	−	0.409047i
$340$	−55.6257	−	34.0926i	−3.01673	−	1.84893i
$341$	−3.91749	+	2.26176i	−0.212144	+	0.122481i
$342$	15.7986	+	6.54401i	0.854293	+	0.353860i
$343$	−18.5199	+	0.122155i	−0.999978	+	0.00659574i
$344$	−23.5391	−	23.5391i	−1.26914	−	1.26914i
$345$	16.9600	+	19.3392i	0.913096	+	1.04119i
$346$	−40.5912	+	2.66049i	−2.18220	+	0.143029i
$347$	12.4095	−	14.1504i	0.666179	−	0.759632i	−0.315758	−	0.948840i	$-0.602259\pi$
$347$	12.4095	−	14.1504i	0.666179	−	0.759632i	0.981937	+	0.189208i	$0.0605920\pi$
$348$	−10.8584	+	14.1509i	−0.582070	+	0.758568i
$349$	6.64268	−	2.75149i	0.355574	−	0.147284i	−0.197744	−	0.980254i	$-0.563361\pi$
$349$	6.64268	−	2.75149i	0.355574	−	0.147284i	0.553318	+	0.832970i	$0.313361\pi$
$350$	−41.4217	−	23.7936i	−2.21408	−	1.27182i
$351$	0.333434	+	0.499020i	0.0177974	+	0.0266357i
$352$	4.40608	−	3.86403i	0.234845	−	0.205954i
$353$	−4.97339	+	1.33261i	−0.264707	+	0.0709279i	−0.388731	−	0.921351i	$-0.627087\pi$
$353$	−4.97339	+	1.33261i	−0.264707	+	0.0709279i	0.124025	+	0.992279i	$0.460420\pi$
$354$	−2.24489	−	4.55219i	−0.119315	−	0.241946i
$355$	−10.7483	+	1.41504i	−0.570459	+	0.0751024i
$356$	72.4499			3.83984
$357$	−0.262308	+	10.9056i	−0.0138828	+	0.577183i
$358$	17.6150			0.930979
$359$	−34.6327	+	4.55949i	−1.82785	+	0.240641i	−0.964521	−	0.264007i	$-0.914956\pi$
$359$	−34.6327	+	4.55949i	−1.82785	+	0.240641i	−0.863326	+	0.504647i	$0.831623\pi$
$360$	−10.0591	−	20.3977i	−0.530159	−	1.07506i
$361$	−24.7159	+	6.62259i	−1.30083	+	0.348558i
$362$	−25.4948	+	22.3584i	−1.33998	+	1.17513i
$363$	−5.66211	−	8.47395i	−0.297184	−	0.444767i
$364$	−6.26044	+	3.63284i	−0.328136	+	0.190413i
$365$	−36.8279	+	15.2546i	−1.92766	+	0.798463i
$366$	−18.5708	+	24.2019i	−0.970710	+	1.26505i
$367$	−17.4245	+	19.8688i	−0.909552	+	1.03715i	0.0896001	+	0.995978i	$0.471441\pi$
$367$	−17.4245	+	19.8688i	−0.909552	+	1.03715i	−0.999152	+	0.0411676i	$0.986892\pi$
$368$	−56.6515	+	3.71314i	−2.95317	+	0.193561i
$369$	2.78190	+	3.17215i	0.144820	+	0.165136i
$370$	−10.0949	−	10.0949i	−0.524809	−	0.524809i
$371$	26.9668	−	3.61058i	1.40005	−	0.187452i
$372$	−21.1869	−	8.77591i	−1.09849	−	0.455010i
$373$	11.7240	−	6.76886i	0.607046	−	0.350478i	−0.164762	−	0.986333i	$-0.552686\pi$
$373$	11.7240	−	6.76886i	0.607046	−	0.350478i	0.771808	+	0.635855i	$0.219352\pi$
$374$	2.21573	+	9.23189i	0.114573	+	0.477370i
$375$	−3.55849	+	6.16348i	−0.183759	+	0.318281i
$376$	−10.1785	−	77.3135i	−0.524917	−	3.98714i
$377$	1.30473	−	1.95267i	0.0671972	−	0.100568i
$378$	−3.75191	+	5.64194i	−0.192977	+	0.290190i
$379$	−1.80153	+	0.358346i	−0.0925383	+	0.0184070i	−0.241142	−	0.970490i	$-0.577522\pi$
$379$	−1.80153	+	0.358346i	−0.0925383	+	0.0184070i	0.148604	+	0.988897i	$0.452522\pi$
$380$	94.7637	+	46.7323i	4.86127	+	2.39732i
$381$	−3.55491	−	3.11757i	−0.182123	−	0.159718i
$382$	2.85179	−	21.6615i	0.145910	−	1.10830i
$383$	−24.3263	−	18.6662i	−1.24302	−	0.953800i	−0.243148	−	0.969989i	$-0.578180\pi$
$383$	−24.3263	−	18.6662i	−1.24302	−	0.953800i	−0.999869	+	0.0161887i	$0.994847\pi$
$384$	−9.34911	−	1.85965i	−0.477095	−	0.0949000i
$385$	2.15487	+	7.97194i	0.109822	+	0.406288i
$386$	−10.3803	−	52.1851i	−0.528341	−	2.65615i
$387$	4.90789	+	1.31506i	0.249482	+	0.0668485i
$388$	−15.1247	+	7.45868i	−0.767841	+	0.378657i
$389$	6.09675	−	4.67820i	0.309117	−	0.237194i	−0.442539	−	0.896749i	$-0.645922\pi$
$389$	6.09675	−	4.67820i	0.309117	−	0.237194i	0.751656	+	0.659555i	$0.229255\pi$
$390$	2.66769	+	4.62058i	0.135084	+	0.233972i
$391$	12.4285	−	27.9098i	0.628535	−	1.41146i
$392$	−36.5071	−	27.7587i	−1.84389	−	1.40203i
$393$	4.60457	−	11.1164i	0.232270	−	0.560749i
$394$	0.791099	−	12.0698i	0.0398550	−	0.608070i
$395$	−7.29919	−	27.2410i	−0.367262	−	1.37064i
$396$	−1.31746	+	3.88110i	−0.0662047	+	0.195033i
$397$	1.41350	−	2.86629i	0.0709414	−	0.143855i	−0.858513	−	0.512791i	$-0.828611\pi$
$397$	1.41350	−	2.86629i	0.0709414	−	0.143855i	0.929455	+	0.368937i	$0.120278\pi$
$398$	4.26840	−	21.4587i	0.213955	−	1.07563i
$399$	−1.19422	−	17.6263i	−0.0597856	−	0.882421i
$400$	−20.6713	−	49.9050i	−1.03357	−	2.49525i
$401$	−9.67316	+	3.28360i	−0.483055	+	0.163975i	−0.552335	−	0.833622i	$-0.686263\pi$
$401$	−9.67316	+	3.28360i	−0.483055	+	0.163975i	0.0692803	+	0.997597i	$0.477930\pi$
$402$	1.53327	+	23.3932i	0.0764726	+	1.16675i
$403$	2.85914	+	0.970548i	0.142424	+	0.0483464i
$404$	−13.5992	+	50.7528i	−0.676584	+	2.52505i
$405$	2.88631	+	1.92857i	0.143422	+	0.0958316i
$406$	26.0148	+	5.11522i	1.29109	+	0.253864i
$407$			1.44396i			0.0715743i
$408$	−17.0014	+	20.9922i	−0.841697	+	1.03927i
$409$	6.46282	+	3.73131i	0.319566	+	0.184502i	0.651199	−	0.758907i	$-0.274266\pi$
$409$	6.46282	+	3.73131i	0.319566	+	0.184502i	−0.331633	+	0.943408i	$0.607600\pi$
$410$	22.8334	+	29.7570i	1.12766	+	1.46960i
$411$	−19.7525	−	1.29465i	−0.974319	−	0.0638603i
$412$	−0.0858246	+	0.0858246i	−0.00422828	+	0.00422828i
$413$	−3.18304	+	4.16715i	−0.156627	+	0.205052i
$414$	15.7782	−	10.5427i	0.775458	−	0.518144i
$415$	−6.55107	−	19.2988i	−0.321579	−	0.947342i
$416$	−3.87826	−	0.510582i	−0.190147	−	0.0250333i
$417$	10.8495	+	1.42837i	0.531304	+	0.0699475i
$418$	−4.94236	−	14.5597i	−0.241739	−	0.712140i
$419$	−16.6822	+	11.1467i	−0.814981	+	0.544553i	−0.891767	−	0.452495i	$-0.850534\pi$
$419$	−16.6822	+	11.1467i	−0.814981	+	0.544553i	0.0767862	+	0.997048i	$0.475534\pi$
$420$	−25.4128	+	33.2698i	−1.24002	+	1.62340i
$421$	5.08109	−	5.08109i	0.247637	−	0.247637i	−0.572363	−	0.820000i	$-0.693973\pi$
$421$	5.08109	−	5.08109i	0.247637	−	0.247637i	0.820000	+	0.572363i	$0.193973\pi$
$422$	−1.90569	−	0.124906i	−0.0927676	−	0.00608031i
$423$	7.24570	+	9.44278i	0.352298	+	0.459123i
$424$	58.3477	+	33.6870i	2.83361	+	1.63599i
$425$	28.9466	+	2.66177i	1.40412	+	0.129115i
$426$			7.99778i			0.387494i
$427$	30.9241	+	6.08055i	1.49652	+	0.294258i
$428$	1.44511	+	0.965588i	0.0698518	+	0.0466735i
$429$	0.139669	−	0.521250i	0.00674326	−	0.0251662i
$430$	42.7723	+	14.5192i	2.06266	+	0.700180i
$431$	2.59867	+	39.6481i	0.125174	+	1.90978i	0.352252	+	0.935905i	$0.385416\pi$
$431$	2.59867	+	39.6481i	0.125174	+	1.90978i	−0.227079	+	0.973876i	$0.572917\pi$
$432$	−7.25513	+	2.46278i	−0.349063	+	0.118491i
$433$	8.54106	+	20.6199i	0.410457	+	0.990931i	0.985015	+	0.172467i	$0.0551739\pi$
$433$	8.54106	+	20.6199i	0.410457	+	0.990931i	−0.574558	+	0.818464i	$0.694826\pi$
$434$	2.30419	+	34.0093i	0.110605	+	1.63250i
$435$	2.64999	−	13.3224i	0.127057	−	0.638760i
$436$	9.20783	−	18.6716i	0.440975	−	0.894209i
$437$	−15.9046	+	46.8534i	−0.760819	+	2.24130i
$438$	7.61127	+	28.4057i	0.363681	+	1.35727i
$439$	−1.53868	+	23.4757i	−0.0734371	+	1.12043i	0.789042	+	0.614340i	$0.210578\pi$
$439$	−1.53868	+	23.4757i	−0.0734371	+	1.12043i	−0.862479	+	0.506093i	$0.831089\pi$
$440$	−7.82568	+	18.8929i	−0.373074	+	0.900681i
$441$	6.94406	+	0.883158i	0.330670	+	0.0420551i
$442$	3.65779	−	5.17492i	0.173983	−	0.246146i
$443$	−10.7955	−	18.6983i	−0.512907	−	0.888382i	−0.999888	−	0.0149690i	$-0.995235\pi$
$443$	−10.7955	−	18.6983i	−0.512907	−	0.888382i	0.486980	−	0.873413i	$-0.338098\pi$
$444$	−5.80759	+	4.45632i	−0.275616	+	0.211488i
$445$	−49.4834	+	24.4025i	−2.34574	+	1.15679i
$446$	43.8077	+	11.7382i	2.07435	+	0.555821i
$447$	3.17483	+	15.9609i	0.150164	+	0.754927i
$448$	−0.944410	−	3.49384i	−0.0446192	−	0.165069i
$449$	−13.8741	−	2.75972i	−0.654758	−	0.130239i	−0.143478	−	0.989654i	$-0.545828\pi$
$449$	−13.8741	−	2.75972i	−0.654758	−	0.130239i	−0.511280	+	0.859414i	$0.670828\pi$
$450$	14.3240	+	10.9912i	0.675241	+	0.518131i
$451$	0.495174	−	3.76122i	0.0233168	−	0.177109i
$452$	−29.8040	−	26.1374i	−1.40186	−	1.22940i
$453$	−2.88273	−	1.42161i	−0.135442	−	0.0667928i
$454$	11.6708	−	2.32146i	0.547736	−	0.108951i
$455$	3.05228	−	4.58987i	0.143093	−	0.215177i
$456$	24.3053	−	36.3754i	1.13820	−	1.70344i
$457$	0.554399	+	4.21108i	0.0259337	+	0.196986i	0.999507	−	0.0313876i	$-0.00999262\pi$
$457$	0.554399	+	4.21108i	0.0259337	+	0.196986i	−0.973574	+	0.228373i	$0.926659\pi$
$458$	16.9502	−	29.3586i	0.792031	−	1.37184i
$459$	0.645268	−	4.07230i	0.0301185	−	0.190079i
$460$	101.543	−	58.6258i	4.73446	−	2.73344i
$461$	0.0223573	+	0.00926068i	0.00104128	+	0.000431313i	0.383204	−	0.923664i	$-0.374821\pi$
$461$	0.0223573	+	0.00926068i	0.00104128	+	0.000431313i	−0.382163	+	0.924095i	$0.624821\pi$
$462$	6.03835	−	0.808474i	0.280930	−	0.0376136i
$463$	−19.2904	−	19.2904i	−0.896500	−	0.896500i	0.0986247	−	0.995125i	$-0.468556\pi$
$463$	−19.2904	−	19.2904i	−0.896500	−	0.896500i	−0.995125	+	0.0986247i	$0.968556\pi$
$464$	19.7675	+	22.5405i	0.917683	+	1.04642i
$465$	17.4266	−	1.14220i	0.808139	−	0.0529682i
$466$	13.1967	−	15.0480i	0.611325	−	0.697083i
$467$	22.7993	−	29.7126i	1.05502	−	1.37493i	0.131534	−	0.991312i	$-0.458010\pi$
$467$	22.7993	−	29.7126i	1.05502	−	1.37493i	0.923490	−	0.383623i	$-0.125324\pi$
$468$	2.52751	−	1.04693i	0.116834	−	0.0483943i
$469$	20.9484	−	12.1560i	0.967307	−	0.561314i
$470$	58.7849	+	87.9779i	2.71155	+	4.05812i
$471$	−5.27924	+	4.62977i	−0.243255	+	0.213329i
$472$	−12.5427	+	3.36080i	−0.577324	+	0.154693i
$473$	−2.02063	−	4.09744i	−0.0929088	−	0.188400i
$474$	−20.6275	+	2.71566i	−0.947453	+	0.124734i
$475$	−47.0771			−2.16005
$476$	48.5227	+	10.8709i	2.22403	+	0.498266i
$477$	−10.2835			−0.470847
$478$	−53.2495	+	7.01043i	−2.43557	+	0.320650i
$479$	−12.6264	−	25.6038i	−0.576915	−	1.16987i	−0.968335	−	0.249655i	$-0.919683\pi$
$479$	−12.6264	−	25.6038i	−0.576915	−	1.16987i	0.391420	−	0.920212i	$-0.371984\pi$
$480$	−21.8543	+	5.85585i	−0.997509	+	0.267282i
$481$	0.724637	−	0.635489i	0.0330406	−	0.0289758i
$482$	−19.5571	−	29.2693i	−0.890801	−	1.33318i
$483$	−16.9998	−	9.76509i	−0.773520	−	0.444327i
$484$	−42.9201	+	17.7781i	−1.95091	+	0.808095i
$485$	7.81798	−	10.1886i	0.354996	−	0.462640i
$486$	1.68853	−	1.92540i	0.0765935	−	0.0873381i
$487$	11.4643	−	0.751409i	0.519497	−	0.0340496i	0.196600	−	0.980484i	$-0.437010\pi$
$487$	11.4643	−	0.751409i	0.519497	−	0.0340496i	0.322897	+	0.946434i	$0.395343\pi$
$488$	51.4580	+	58.6766i	2.32940	+	2.65617i
$489$	14.2606	+	14.2606i	0.644885	+	0.644885i
$490$	61.0860	+	11.8718i	2.75958	+	0.536312i
$491$	23.8090	+	9.86199i	1.07448	+	0.445066i	0.848571	−	0.529082i	$-0.177464\pi$
$491$	23.8090	+	9.86199i	1.07448	+	0.445066i	0.225913	+	0.974148i	$0.427464\pi$
$492$	16.6558	−	9.61623i	0.750902	−	0.433533i
$493$	−15.6882	+	3.76531i	−0.706563	+	0.169581i
$494$	−5.13152	+	8.88805i	−0.230878	+	0.399892i
$495$	−0.407405	−	3.09455i	−0.0183115	−	0.139089i
$496$	−21.4147	+	32.0494i	−0.961549	+	1.43906i
$497$	7.40254	−	3.67078i	0.332049	−	0.164657i
$498$	−14.7464	+	2.93324i	−0.660803	+	0.131442i
$499$	−1.87099	−	0.922671i	−0.0837571	−	0.0413044i	0.399928	−	0.916547i	$-0.369035\pi$
$499$	−1.87099	−	0.922671i	−0.0837571	−	0.0413044i	−0.483685	+	0.875242i	$0.660702\pi$
$500$	24.3908	+	21.3902i	1.09079	+	0.956598i
$501$	1.31054	−	9.95453i	0.0585506	−	0.444736i
$502$	−13.5126	−	10.3686i	−0.603097	−	0.462773i
$503$	−3.29825	−	0.656062i	−0.147062	−	0.0292524i	0.121011	−	0.992651i	$-0.461387\pi$
$503$	−3.29825	−	0.656062i	−0.147062	−	0.0292524i	−0.268072	+	0.963399i	$0.586387\pi$
$504$	12.2840	+	12.2301i	0.547174	+	0.544773i
$505$	−7.80626	−	39.2447i	−0.347374	−	1.74637i
$506$	−16.4811	−	4.41610i	−0.732675	−	0.196320i
$507$	11.3363	−	5.59044i	0.503462	−	0.248280i
$508$	−17.0992	+	13.1207i	−0.758654	+	0.582136i
$509$	−4.42943	−	7.67199i	−0.196331	−	0.340055i	0.751005	−	0.660296i	$-0.229569\pi$
$509$	−4.42943	−	7.67199i	−0.196331	−	0.340055i	−0.947336	+	0.320241i	$0.896236\pi$
$510$	8.09177	−	35.7494i	0.358310	−	1.58301i
$511$	22.7981	−	20.0823i	1.00853	−	0.888387i
$512$	−19.3093	+	46.6168i	−0.853359	+	2.06019i
$513$	−0.436723	+	6.66311i	−0.0192818	+	0.294183i
$514$	−8.66645	−	32.3436i	−0.382261	−	1.42662i
$515$	0.0297110	−	0.0875258i	0.00130922	−	0.00385685i
$516$	10.2438	−	20.7724i	0.450960	−	0.914456i
$517$	2.08785	−	10.4963i	0.0918236	−	0.461629i
$518$	9.76944	+	4.79108i	0.429245	+	0.210508i
$519$	−6.07863	−	14.6751i	−0.266822	−	0.644166i
$520$	12.9253	−	4.38755i	0.566812	−	0.192407i
$521$	0.640120	+	9.76635i	0.0280442	+	0.427871i	0.988678	+	0.150053i	$0.0479445\pi$
$521$	0.640120	+	9.76635i	0.0280442	+	0.427871i	−0.960634	+	0.277818i	$0.910389\pi$
$522$	−9.48912	−	3.22112i	−0.415328	−	0.140985i
$523$	−1.25831	+	4.69609i	−0.0550222	+	0.205345i	−0.987965	−	0.154680i	$-0.950565\pi$
$523$	−1.25831	+	4.69609i	−0.0550222	+	0.205345i	0.932942	+	0.360025i	$0.117232\pi$
$524$	−45.6039	−	30.4716i	−1.99222	−	1.33116i
$525$	3.59881	−	18.3026i	0.157065	−	0.798793i
$526$			2.87674i			0.125432i
$527$	−9.89647	−	18.2299i	−0.431097	−	0.794108i
$528$	5.96608	+	3.44452i	0.259640	+	0.149903i
$529$	19.4240	+	25.3138i	0.844521	+	1.10060i
$530$	−91.2226	−	5.97904i	−3.96245	−	0.259713i
$531$	1.40145	−	1.40145i	0.0608178	−	0.0608178i
$532$	−79.8649	−	10.3358i	−3.46258	−	0.448115i
$533$	−2.10546	+	1.40682i	−0.0911976	+	0.0609363i
$534$	13.0836	+	38.5431i	0.566183	+	1.66792i
$535$	−1.31224	−	0.172759i	−0.0567330	−	0.00746904i
$536$	59.4629	+	7.82844i	2.56841	+	0.338137i
$537$	2.21098	+	6.51332i	0.0954106	+	0.281071i
$538$	26.4692	−	17.6862i	1.14117	−	0.762504i
$539$	−3.51976	−	5.21787i	−0.151607	−	0.224750i
$540$	11.1889	−	11.1889i	0.481495	−	0.481495i
$541$	−17.7999	−	1.16667i	−0.765277	−	0.0501589i	−0.322235	−	0.946660i	$-0.604434\pi$
$541$	−17.7999	−	1.16667i	−0.765277	−	0.0501589i	−0.443042	+	0.896501i	$0.646101\pi$
$542$	−7.85197	−	10.2329i	−0.337271	−	0.439540i
$543$	−11.4673	−	6.62064i	−0.492108	−	0.284119i
$544$	17.1825	+	20.6625i	0.736692	+	0.885895i
$545$			15.8541i			0.679117i
$546$	−3.06322	−	2.67448i	−0.131094	−	0.114457i
$547$	22.5405	+	15.0611i	0.963764	+	0.643967i	0.934635	−	0.355609i	$-0.115727\pi$
$547$	22.5405	+	15.0611i	0.963764	+	0.643967i	0.0291292	+	0.999576i	$0.490727\pi$
$548$	−23.3537	+	87.1571i	−0.997620	+	3.72317i
$549$	−11.2799	−	3.82900i	−0.481413	−	0.163418i
$550$	−1.06176	−	16.1994i	−0.0452738	−	0.690745i
$551$	24.7421	−	8.39882i	1.05405	−	0.357802i
$552$	−18.5784	−	44.8523i	−0.790750	−	1.90904i
$553$	11.9811	+	17.8458i	0.509486	+	0.758883i
$554$	12.9789	−	65.2494i	0.551421	−	2.77218i
$555$	2.46562	−	4.99979i	0.104660	−	0.212229i
$556$	16.0342	−	47.2353i	0.680002	−	2.00322i
$557$	4.31205	+	16.0928i	0.182708	+	0.681874i	0.995110	+	0.0987762i	$0.0314928\pi$
$557$	4.31205	+	16.0928i	0.182708	+	0.681874i	−0.812402	+	0.583098i	$0.801841\pi$
$558$	0.842639	−	12.8562i	0.0356717	−	0.544246i
$559$	−1.16698	+	2.81733i	−0.0493578	+	0.119160i
$560$	46.5129	+	52.8031i	1.96553	+	2.23134i
$561$	−3.13548	+	1.97805i	−0.132380	+	0.0835133i
$562$	28.7508	+	49.7978i	1.21278	+	2.10059i
$563$	4.82390	−	3.70151i	0.203303	−	0.156000i	−0.502092	−	0.864814i	$-0.667436\pi$
$563$	4.82390	−	3.70151i	0.203303	−	0.156000i	0.705395	+	0.708814i	$0.250769\pi$
$564$	48.6598	−	23.9963i	2.04895	−	1.01043i
$565$	29.1598	+	7.81333i	1.22676	+	0.328709i
$566$	−8.96751	−	45.0827i	−0.376932	−	1.89497i
$567$	−2.55710	−	0.679150i	−0.107388	−	0.0285216i
$568$	20.0678	+	3.99174i	0.842028	+	0.167490i
$569$	−19.7198	−	15.1316i	−0.826699	−	0.634348i	0.106257	−	0.994339i	$-0.466113\pi$
$569$	−19.7198	−	15.1316i	−0.826699	−	0.634348i	−0.932956	+	0.359990i	$0.882780\pi$
$570$	−7.74818	+	58.8532i	−0.324535	+	2.46509i
$571$	14.6998	+	12.8913i	0.615166	+	0.539486i	0.909227	−	0.416301i	$-0.136674\pi$
$571$	14.6998	+	12.8913i	0.615166	+	0.539486i	−0.294061	+	0.955787i	$0.595007\pi$
$572$	−2.20617	−	1.08796i	−0.0922447	−	0.0454901i
$573$	8.36753	−	1.66441i	0.349559	−	0.0695315i
$574$	−23.8044	−	15.8300i	−0.993577	−	0.660732i
$575$	−29.0239	+	43.4374i	−1.21038	+	1.81146i
$576$	0.178552	+	1.35624i	0.00743967	+	0.0565099i
$577$	3.67118	−	6.35867i	0.152833	−	0.264715i	−0.779435	−	0.626483i	$-0.784494\pi$
$577$	3.67118	−	6.35867i	0.152833	−	0.264715i	0.932268	+	0.361769i	$0.117827\pi$
$578$	−42.5856	+	9.04590i	−1.77133	+	0.376260i
$579$	17.9931	−	10.3883i	0.747769	−	0.431724i
$580$	−57.2045	−	23.6949i	−2.37529	−	0.983876i
$581$	9.48317	+	12.3026i	0.393428	+	0.510398i
$582$	−6.69934	−	6.69934i	−0.277697	−	0.277697i
$583$	6.09654	+	6.95177i	0.252493	+	0.287913i
$584$	75.0736	−	4.92058i	3.10657	−	0.203615i
$585$	−1.37367	+	1.56637i	−0.0567942	+	0.0647614i
$586$	−16.1016	+	20.9840i	−0.665152	+	0.866843i
$587$	−15.2046	+	6.29795i	−0.627561	+	0.259944i	−0.673716	−	0.738990i	$-0.735303\pi$
$587$	−15.2046	+	6.29795i	−0.627561	+	0.259944i	0.0461553	+	0.998934i	$0.485303\pi$
$588$	10.1236	−	30.2598i	0.417492	−	1.24789i
$589$	18.6635	+	27.9319i	0.769016	+	1.15091i
$590$	13.2468	−	11.6172i	0.545364	−	0.478271i
$591$	4.56225	−	1.22245i	0.187666	−	0.0502849i
$592$	5.44197	+	11.0352i	0.223664	+	0.453545i
$593$	44.7964	−	5.89755i	1.83957	−	0.242183i	0.871060	−	0.491176i	$-0.163433\pi$
$593$	44.7964	−	5.89755i	1.83957	−	0.242183i	0.968505	+	0.248992i	$0.0800994\pi$
$594$	−2.30265			−0.0944788
$595$	−36.8026	+	8.91856i	−1.50876	+	0.365625i
$596$	74.1806			3.03856
$597$	8.47034	−	1.11514i	0.346668	−	0.0456397i
$598$	5.03720	+	10.2144i	0.205987	+	0.417699i
$599$	2.43634	−	0.652814i	0.0995460	−	0.0266733i	−0.208702	−	0.977979i	$-0.566924\pi$
$599$	2.43634	−	0.652814i	0.0995460	−	0.0266733i	0.308248	+	0.951306i	$0.400257\pi$
$600$	34.7281	−	30.4557i	1.41777	−	1.24335i
$601$	2.37073	+	3.54805i	0.0967040	+	0.144728i	0.876667	−	0.481098i	$-0.159762\pi$
$601$	2.37073	+	3.54805i	0.0967040	+	0.144728i	−0.779963	+	0.625826i	$0.784762\pi$
$602$	−34.4267	+	0.0756905i	−1.40313	+	0.00308491i
$603$	−8.45744	+	3.50319i	−0.344414	+	0.142661i
$604$	−8.91921	+	11.6237i	−0.362918	+	0.472963i
$605$	23.3265	−	26.5988i	0.948358	−	1.08140i
$606$	−29.4562	+	1.93066i	−1.19657	+	0.0784276i
$607$	−0.956953	−	1.09120i	−0.0388415	−	0.0442903i	0.732093	−	0.681205i	$-0.238544\pi$
$607$	−0.956953	−	1.09120i	−0.0388415	−	0.0442903i	−0.770934	+	0.636915i	$0.780210\pi$
$608$	−30.7744	−	30.7744i	−1.24807	−	1.24807i
$609$	1.37388	+	10.2613i	0.0556726	+	0.415809i
$610$	−97.8352	−	40.5247i	−3.96123	−	1.64080i
$611$	−6.18636	+	3.57170i	−0.250273	+	0.144495i
$612$	−17.6324	−	6.50627i	−0.712747	−	0.263000i
$613$	−0.347586	+	0.602037i	−0.0140389	+	0.0243161i	−0.872960	−	0.487793i	$-0.837802\pi$
$613$	−0.347586	+	0.602037i	−0.0140389	+	0.0243161i	0.858921	+	0.512109i	$0.171136\pi$
$614$	7.01587	+	53.2908i	0.283137	+	2.15064i
$615$	−8.13702	+	12.1779i	−0.328116	+	0.491061i
$616$	0.985175	−	15.5548i	0.0396938	−	0.626721i
$617$	14.8971	−	2.96322i	0.599736	−	0.119295i	0.114120	−	0.993467i	$-0.463595\pi$
$617$	14.8971	−	2.96322i	0.599736	−	0.119295i	0.485616	+	0.874172i	$0.338595\pi$
$618$	−0.0611573	−	0.0301594i	−0.00246011	−	0.00121319i
$619$	36.8168	+	32.2874i	1.47979	+	1.29774i	0.856958	+	0.515386i	$0.172352\pi$
$619$	36.8168	+	32.2874i	1.47979	+	1.29774i	0.622833	+	0.782355i	$0.285982\pi$
$620$	10.3908	−	78.9256i	0.417303	−	3.16973i
$621$	5.87871	+	4.51089i	0.235904	+	0.181016i
$622$	46.1409	+	9.17799i	1.85008	+	0.368004i
$623$	29.6694	−	29.8002i	1.18868	−	1.19392i
$624$	−0.897087	−	4.50996i	−0.0359122	−	0.180543i
$625$	10.1863	+	2.72940i	0.407451	+	0.109176i
$626$	14.1589	−	6.98240i	0.565904	−	0.279073i
$627$	4.76327	−	3.65499i	0.190227	−	0.145966i
$628$	16.0038	+	27.7194i	0.638620	+	1.10612i
$629$	−6.61909	−	0.173769i	−0.263920	−	0.00692862i
$630$	−22.2887	−	7.51137i	−0.888001	−	0.299260i
$631$	−1.30540	+	3.15152i	−0.0519673	+	0.125460i	−0.947731	−	0.319070i	$-0.896629\pi$
$631$	−1.30540	+	3.15152i	−0.0519673	+	0.125460i	0.895764	+	0.444530i	$0.146629\pi$
$632$	−3.48124	+	53.1134i	−0.138476	+	2.11274i
$633$	−0.193011	−	0.720328i	−0.00767151	−	0.0286305i
$634$	−13.0140	+	38.3380i	−0.516852	+	1.52260i
$635$	7.25949	−	14.7208i	0.288084	−	0.584177i
$636$	−9.14494	+	45.9747i	−0.362620	+	1.82302i
$637$	−1.06949	+	4.06275i	−0.0423746	+	0.160972i
$638$	3.44809	+	8.32443i	0.136511	+	0.329567i
$639$	−2.95727	+	1.00386i	−0.116988	+	0.0397120i
$640$	−2.16417	−	33.0189i	−0.0855464	−	1.30519i
$641$	0.261096	+	0.0886300i	0.0103127	+	0.00350068i	0.326591	−	0.945166i	$-0.394100\pi$
$641$	0.261096	+	0.0886300i	0.0103127	+	0.00350068i	−0.316278	+	0.948666i	$0.602433\pi$
$642$	−0.252720	+	0.943165i	−0.00997407	+	0.0372237i
$643$	29.3408	+	19.6049i	1.15709	+	0.773140i	0.977569	−	0.210614i	$-0.0675465\pi$
$643$	29.3408	+	19.6049i	1.15709	+	0.773140i	0.179517	+	0.983755i	$0.442546\pi$
$644$	−58.7750	+	67.3180i	−2.31606	+	2.65270i
$645$			17.6379i			0.694493i
$646$	67.3365	−	20.9036i	2.64932	−	0.822441i
$647$	−10.4425	−	6.02895i	−0.410535	−	0.237023i	0.280484	−	0.959859i	$-0.409505\pi$
$647$	−10.4425	−	6.02895i	−0.410535	−	0.237023i	−0.691020	+	0.722836i	$0.742838\pi$
$648$	−3.98842	−	5.19781i	−0.156680	−	0.204189i
$649$	−1.77825	−	0.116553i	−0.0698025	−	0.00457510i
$650$	−7.66223	+	7.66223i	−0.300537	+	0.300537i
$651$	−12.2861	+	5.12074i	−0.481530	+	0.200698i
$652$	76.4371	−	51.0736i	2.99351	−	2.00020i
$653$	−4.01281	−	11.8214i	−0.157033	−	0.462606i	0.839729	−	0.543005i	$-0.182714\pi$
$653$	−4.01281	−	11.8214i	−0.157033	−	0.462606i	−0.996763	+	0.0803997i	$0.974380\pi$
$654$	11.5961	+	1.52665i	0.453442	+	0.0596968i
$655$	41.4110	+	5.45186i	1.61806	+	0.213022i
$656$	−10.3910	−	30.6108i	−0.405699	−	1.19515i
$657$	−9.54796	+	6.37974i	−0.372501	+	0.248897i
$658$	−64.0880	−	48.9529i	−2.49841	−	1.90838i
$659$	−8.68356	+	8.68356i	−0.338263	+	0.338263i	−0.855713	−	0.517450i	$-0.826881\pi$
$659$	−8.68356	+	8.68356i	−0.338263	+	0.338263i	0.517450	+	0.855713i	$0.326881\pi$
$660$	−14.1972	−	0.930535i	−0.552626	−	0.0362210i
$661$	18.4584	+	24.0554i	0.717948	+	0.935648i	0.999716	−	0.0238342i	$-0.00758739\pi$
$661$	18.4584	+	24.0554i	0.717948	+	0.935648i	−0.281768	+	0.959483i	$0.590921\pi$
$662$	26.0664	+	15.0494i	1.01310	+	0.584912i
$663$	2.37260	+	0.702968i	0.0921441	+	0.0273010i
$664$			38.4654i			1.49275i
$665$	58.0292	−	19.8407i	2.25028	−	0.769388i
$666$	−3.41953	−	2.28486i	−0.132504	−	0.0885364i
$667$	7.50452	−	28.0072i	0.290576	−	1.08444i
$668$	−43.3388	−	14.7115i	−1.67683	−	0.569206i
$669$	1.15827	+	17.6717i	0.0447811	+	0.683228i
$670$	−77.0612	+	26.1587i	−2.97713	+	1.01060i
$671$	4.09880	+	9.89538i	0.158232	+	0.382007i
$672$	14.3170	−	9.61192i	0.552291	−	0.370788i
$673$	6.36286	−	31.9883i	0.245270	−	1.23306i	−0.640144	−	0.768255i	$-0.721125\pi$
$673$	6.36286	−	31.9883i	0.245270	−	1.23306i	0.885415	−	0.464802i	$-0.153875\pi$
$674$	−5.89247	+	11.9488i	−0.226970	+	0.460249i
$675$	−2.26622	+	6.67605i	−0.0872267	+	0.256961i
$676$	−14.9122	−	55.6532i	−0.573547	−	2.14051i
$677$	1.79107	−	27.3265i	0.0688366	−	1.05024i	−0.814092	−	0.580736i	$-0.802765\pi$
$677$	1.79107	−	27.3265i	0.0688366	−	1.05024i	0.882929	−	0.469507i	$-0.155568\pi$
$678$	8.52274	−	20.5757i	0.327314	−	0.790206i
$679$	−3.12590	+	9.27556i	−0.119961	+	0.355963i
$680$	−85.6629	−	38.1464i	−3.28502	−	1.46285i
$681$	2.32326	+	4.02401i	0.0890277	+	0.154200i
$682$	−9.19053	+	7.05214i	−0.351924	+	0.270041i
$683$	−22.6835	+	11.1863i	−0.867959	+	0.428030i	−0.821041	−	0.570869i	$-0.806607\pi$
$683$	−22.6835	+	11.1863i	−0.867959	+	0.428030i	−0.0469177	+	0.998899i	$0.514940\pi$
$684$	29.4007	+	7.87789i	1.12416	+	0.301219i
$685$	−13.4056	−	67.3945i	−0.512201	−	2.57501i
$686$	−46.9814	+	6.50074i	−1.79376	+	0.248200i
$687$	12.9832	+	2.58252i	0.495341	+	0.0985294i
$688$	−30.8848	−	23.6987i	−1.17747	−	0.903505i
$689$	0.805579	−	6.11898i	0.0306901	−	0.233115i
$690$	49.5262	+	43.4333i	1.88543	+	1.65348i
$691$	6.12760	+	3.02180i	0.233105	+	0.114955i	0.555091	−	0.831790i	$-0.312684\pi$
$691$	6.12760	+	3.02180i	0.233105	+	0.114955i	−0.321986	+	0.946745i	$0.604350\pi$
$692$	−71.0144	+	14.1256i	−2.69956	+	0.536976i
$693$	1.05686	+	2.13127i	0.0401467	+	0.0809603i
$694$	26.7780	−	40.0761i	1.01648	−	1.52127i
$695$	4.95835	+	37.6624i	0.188081	+	1.42862i
$696$	−12.8184	+	22.2022i	−0.485882	+	0.841572i
$697$	17.1818	+	2.72251i	0.650807	+	0.103122i
$698$	15.9461	−	9.20650i	0.603570	−	0.348471i
$699$	7.22056	+	2.99085i	0.273107	+	0.113124i
$700$	−78.6261	−	32.3656i	−2.97179	−	1.22331i
$701$	−30.6174	−	30.6174i	−1.15640	−	1.15640i	−0.985244	−	0.171158i	$-0.945249\pi$
$701$	−30.6174	−	30.6174i	−1.15640	−	1.15640i	−0.171158	−	0.985244i	$-0.554751\pi$
$702$	1.01340	+	1.15556i	0.0382484	+	0.0436139i
$703$	10.7004	−	0.701342i	0.403574	−	0.0264516i
$704$	0.810983	−	0.924749i	0.0305651	−	0.0348528i
$705$	−25.1523	+	32.7791i	−0.947290	+	1.23453i
$706$	−12.1821	+	5.04597i	−0.458478	+	0.189908i
$707$	15.3066	+	26.3777i	0.575664	+	0.992036i
$708$	−5.01924	−	7.51182i	−0.188635	−	0.282312i
$709$	−6.87764	+	6.03153i	−0.258295	+	0.226519i	−0.778693	−	0.627405i	$-0.784117\pi$
$709$	−6.87764	+	6.03153i	−0.258295	+	0.226519i	0.520398	+	0.853924i	$0.325784\pi$
$710$	−26.8170	+	7.18560i	−1.00643	+	0.269671i
$711$	−3.59325	−	7.28639i	−0.134757	−	0.273261i
$712$	103.241	−	13.5920i	3.86914	−	0.509382i
$713$	37.2788			1.39610
$714$	2.97937	+	27.7771i	0.111500	+	1.03953i
$715$	1.87327			0.0700562
$716$	31.0856	−	4.09250i	1.16172	−	0.152944i
$717$	−9.27590	−	18.8097i	−0.346415	−	0.702460i
$718$	−86.4090	+	23.1532i	−3.22475	+	0.864070i
$719$	−9.55497	+	8.37949i	−0.356340	+	0.312502i	−0.818734	−	0.574172i	$-0.805324\pi$
$719$	−9.55497	+	8.37949i	−0.356340	+	0.312502i	0.462394	+	0.886675i	$0.346991\pi$
$720$	−14.7762	−	22.1142i	−0.550677	−	0.824147i
$721$	0.000154887		0.0704480i	5.76829e−6		0.00262362i
$722$	−60.5402	+	25.0766i	−2.25307	+	0.933254i
$723$	8.36789	−	10.9052i	0.311205	−	0.405570i
$724$	−39.7969	+	45.3797i	−1.47904	+	1.68652i
$725$	27.5285	−	1.80431i	1.02238	−	0.0670105i
$726$	−17.2088	−	19.6228i	−0.638677	−	0.728271i
$727$	5.53824	+	5.53824i	0.205402	+	0.205402i	0.802310	−	0.596908i	$-0.203604\pi$
$727$	5.53824	+	5.53824i	0.205402	+	0.205402i	−0.596908	+	0.802310i	$0.703604\pi$
$728$	−8.23961	+	6.35131i	−0.305380	+	0.235395i
$729$	0.923880	+	0.382683i	0.0342178	+	0.0141735i
$730$	−88.4075	+	51.0421i	−3.27211	+	1.88915i
$731$	19.0258	−	8.76947i	0.703694	−	0.324351i
$732$	−27.1495	+	47.0243i	−1.00347	+	1.73807i
$733$	4.75679	+	36.1314i	0.175696	+	1.33454i	0.821136	+	0.570733i	$0.193341\pi$
$733$	4.75679	+	36.1314i	0.175696	+	1.33454i	−0.645439	+	0.763812i	$0.723326\pi$
$734$	−37.5996	+	56.2718i	−1.38783	+	2.07703i
$735$	3.27761	+	24.0773i	0.120896	+	0.888105i
$736$	−47.3681	+	9.42209i	−1.74601	+	0.347303i
$737$	7.38219	+	3.64050i	0.271927	+	0.134099i
$738$	8.12365	+	7.12425i	0.299036	+	0.262247i
$739$	1.93877	−	14.7264i	0.0713188	−	0.541720i	−0.918069	−	0.396421i	$-0.870252\pi$
$739$	1.93877	−	14.7264i	0.0713188	−	0.541720i	0.989388	−	0.145299i	$-0.0464145\pi$
$740$	−20.1601	−	15.4694i	−0.741101	−	0.568667i
$741$	−3.93055	−	0.781835i	−0.144392	−	0.0287214i
$742$	67.2623	−	18.1815i	2.46928	−	0.667463i
$743$	−7.66441	−	38.5316i	−0.281180	−	1.41359i	−0.820577	−	0.571535i	$-0.806348\pi$
$743$	−7.66441	−	38.5316i	−0.281180	−	1.41359i	0.539398	−	0.842051i	$-0.318652\pi$
$744$	−31.8379	−	8.53093i	−1.16723	−	0.312759i
$745$	−50.6655	+	24.9855i	−1.85624	+	0.915397i
$746$	27.5048	−	21.1052i	1.00702	−	0.772716i
$747$	−2.93553	−	5.08448i	−0.107405	−	0.186031i
$748$	6.05502	+	15.7770i	0.221393	+	0.576864i
$749$	0.988960	−	0.198978i	0.0361358	−	0.00727049i
$750$	−6.97480	+	16.8387i	−0.254684	+	0.614861i
$751$	−3.15514	+	48.1382i	−0.115133	+	1.75659i	0.416061	+	0.909337i	$0.363410\pi$
$751$	−3.15514	+	48.1382i	−0.115133	+	1.75659i	−0.531194	+	0.847250i	$0.678256\pi$
$752$	−23.6024	−	88.0854i	−0.860691	−	3.21214i
$753$	2.13784	−	6.29787i	0.0779072	−	0.229507i
$754$	2.66002	−	5.39399i	0.0968723	−	0.196438i
$755$	2.17674	−	10.9432i	0.0792196	−	0.398264i
$756$	−5.31030	+	10.8282i	−0.193134	+	0.393817i
$757$	−10.5680	−	25.5134i	−0.384101	−	0.927301i	−0.991163	−	0.132647i	$-0.957652\pi$
$757$	−10.5680	−	25.5134i	−0.384101	−	0.927301i	0.607063	−	0.794654i	$-0.292348\pi$
$758$	−4.45432	+	1.51204i	−0.161788	+	0.0549197i
$759$	−0.435758	−	6.64837i	−0.0158170	−	0.241321i
$760$	143.806	+	48.8155i	5.21639	+	1.77073i
$761$	0.754444	−	2.81562i	0.0273486	−	0.102066i	−0.950902	−	0.309491i	$-0.899841\pi$
$761$	0.754444	−	2.81562i	0.0273486	−	0.102066i	0.978251	+	0.207424i	$0.0665081\pi$
$762$	−10.0681	−	6.72727i	−0.364727	−	0.243703i
$763$	−3.90928	−	11.4337i	−0.141525	−	0.413928i
$764$		−	38.8892i		−	1.40696i
$765$	14.2344	−	1.49514i	0.514646	−	0.0540567i
$766$	−68.0044	−	39.2624i	−2.45710	−	1.41861i
$767$	0.724122	+	0.943694i	0.0261465	+	0.0340748i
$768$	−27.0892	−	1.77552i	−0.977496	−	0.0640685i
$769$	−10.2063	+	10.2063i	−0.368050	+	0.368050i	−0.866766	−	0.498716i	$-0.833805\pi$
$769$	−10.2063	+	10.2063i	−0.368050	+	0.368050i	0.498716	+	0.866766i	$0.333805\pi$
$770$	8.13602	+	19.5206i	0.293202	+	0.703473i
$771$	10.8716	−	7.26419i	0.391532	−	0.261613i
$772$	−30.4426	−	89.6809i	−1.09565	−	3.22769i
$773$	40.5068	+	5.33282i	1.45693	+	0.191808i	0.817005	−	0.576631i	$-0.195633\pi$
$773$	40.5068	+	5.33282i	1.45693	+	0.191808i	0.639923	+	0.768439i	$0.278966\pi$
$774$	12.9008	+	1.69842i	0.463709	+	0.0610484i
$775$	11.4011	+	33.5866i	0.409540	+	1.20647i
$776$	−20.1535	+	13.4661i	−0.723468	+	0.483406i
$777$	−0.545325	+	4.21372i	−0.0195634	+	0.151166i
$778$	13.9160	−	13.9160i	0.498911	−	0.498911i
$779$	−28.1129	−	1.84262i	−1.00725	−	0.0660186i
$780$	5.78125	+	7.53428i	0.207002	+	0.269770i
$781$	2.43184	+	1.40402i	0.0870180	+	0.0502399i
$782$	22.2268	−	75.0179i	0.794827	−	2.68263i
$783$		−	3.91301i		−	0.139840i
$784$	−46.5643	−	26.6116i	−1.66301	−	0.950414i
$785$	−20.2670	−	13.5420i	−0.723361	−	0.483335i
$786$	7.97522	−	29.7639i	0.284467	−	1.06164i
$787$	−42.1824	−	14.3190i	−1.50364	−	0.510417i	−0.556392	−	0.830920i	$-0.687815\pi$
$787$	−42.1824	−	14.3190i	−1.50364	−	0.510417i	−0.947247	+	0.320504i	$0.896148\pi$
$788$	−1.40812	−	21.4838i	−0.0501623	−	0.765328i
$789$	−1.06371	+	0.361080i	−0.0378690	+	0.0128548i
$790$	−27.6385	−	66.7253i	−0.983335	−	2.37398i
$791$	−22.9561	+	1.55532i	−0.816224	+	0.0553006i
$792$	−1.14927	+	5.77775i	−0.0408374	+	0.205303i
$793$	3.16201	−	6.41192i	0.112286	−	0.227694i
$794$	2.63078	−	7.75004i	0.0933630	−	0.275038i
$795$	−9.23916	−	34.4810i	−0.327679	−	1.22292i
$796$	2.54705	−	38.8604i	0.0902777	−	1.37737i
$797$	−1.92150	+	4.63892i	−0.0680631	+	0.164319i	−0.954251	−	0.299008i	$-0.903344\pi$
$797$	−1.92150	+	4.63892i	−0.0680631	+	0.164319i	0.886188	+	0.463327i	$0.153344\pi$
$798$	−8.92405	−	44.3544i	−0.315908	−	1.57013i
$799$	47.8639	+	10.8338i	1.69330	+	0.383274i
$800$	−22.9757	−	39.7950i	−0.812313	−	1.40697i
$801$	−12.6095	+	9.67562i	−0.445535	+	0.341871i
$802$	−23.4627	+	11.5705i	−0.828497	+	0.408569i
$803$	9.97330	+	2.67234i	0.351950	+	0.0943048i
$804$	8.14077	+	40.9264i	0.287103	+	1.44336i
$805$	17.4694	−	65.7749i	0.615716	−	2.31826i
$806$	7.58383	+	1.50852i	0.267129	+	0.0531352i
$807$	9.86199	+	7.56737i	0.347158	+	0.266384i
$808$	−9.85739	+	74.8743i	−0.346782	+	2.63407i
$809$	−33.4042	−	29.2947i	−1.17443	−	1.02995i	−0.998966	−	0.0454622i	$-0.985524\pi$
$809$	−33.4042	−	29.2947i	−1.17443	−	1.02995i	−0.175464	−	0.984486i	$-0.556143\pi$
$810$	7.97306	+	3.93188i	0.280145	+	0.138152i
$811$	−6.42944	+	1.27889i	−0.225768	+	0.0449081i	−0.306678	−	0.951813i	$-0.599217\pi$
$811$	−6.42944	+	1.27889i	−0.225768	+	0.0449081i	0.0809098	+	0.996721i	$0.474217\pi$
$812$	47.0974	+	2.98295i	1.65280	+	0.104681i
$813$	2.79817	−	4.18775i	0.0981360	−	0.146871i
$814$	0.482668	+	3.66623i	0.0169175	+	0.128501i
$815$	−35.0041	+	60.6289i	−1.22614	+	2.12374i
$816$	−16.5076	+	26.9339i	−0.577882	+	0.942876i
$817$	−29.3825	+	16.9640i	−1.02796	+	0.593495i
$818$	17.6565	+	7.31355i	0.617344	+	0.255712i
$819$	0.604433	−	1.46835i	0.0211206	−	0.0513084i
$820$	47.2082	+	47.2082i	1.64858	+	1.64858i
$821$	−4.62534	−	5.27419i	−0.161425	−	0.184070i	0.665473	−	0.746422i	$-0.268230\pi$
$821$	−4.62534	−	5.27419i	−0.161425	−	0.184070i	−0.826898	+	0.562352i	$0.809897\pi$
$822$	−50.5847	+	3.31549i	−1.76434	+	0.115641i
$823$	15.5075	−	17.6829i	0.540558	−	0.616388i	−0.415490	−	0.909598i	$-0.636390\pi$
$823$	15.5075	−	17.6829i	0.540558	−	0.616388i	0.956048	+	0.293209i	$0.0947233\pi$
$824$	−0.106199	+	0.138402i	−0.00369963	+	0.00482145i
$825$	5.85664	−	2.42590i	0.203902	−	0.0844589i
$826$	−6.68884	+	11.6445i	−0.232734	+	0.405162i
$827$	−25.4699	−	38.1184i	−0.885675	−	1.32551i	−0.944933	−	0.327264i	$-0.893873\pi$
$827$	−25.4699	−	38.1184i	−0.885675	−	1.32551i	0.0592577	−	0.998243i	$-0.481127\pi$
$828$	25.3949	−	22.2707i	0.882534	−	0.773962i
$829$	−21.1734	+	5.67339i	−0.735382	+	0.197045i	−0.607025	−	0.794683i	$-0.707637\pi$
$829$	−21.1734	+	5.67339i	−0.735382	+	0.197045i	−0.128357	+	0.991728i	$0.540970\pi$
$830$	−23.0842	−	46.8102i	−0.801266	−	1.62481i
$831$	25.7558	−	3.39081i	0.893457	−	0.117626i
$832$	−0.820992			−0.0284628
$833$	24.3423	−	15.5066i	0.843409	−	0.537272i
$834$	28.0246			0.970412
$835$	34.5556	−	4.54933i	1.19585	−	0.157436i
$836$	−12.1046	−	24.5457i	−0.418647	−	0.848931i
$837$	4.85948	−	1.30209i	0.167968	−	0.0450070i
$838$	−38.6305	+	33.8780i	−1.33447	+	1.17030i
$839$	5.81427	+	8.70167i	0.200731	+	0.300415i	0.918155	−	0.396222i	$-0.129679\pi$
$839$	5.81427	+	8.70167i	0.200731	+	0.300415i	−0.717424	+	0.696637i	$0.754679\pi$
$840$	−29.9718	+	52.1772i	−1.03412	+	1.80028i
$841$	12.6464	−	5.23830i	0.436082	−	0.180631i
$842$	11.2025	−	14.5994i	0.386064	−	0.503128i
$843$	−14.8046	+	16.8814i	−0.509897	+	0.581426i
$844$	−3.39205	+	0.222326i	−0.116759	+	0.00765279i
$845$	28.9302	+	32.9885i	0.995228	+	1.13484i
$846$	21.5533	+	21.5533i	0.741019	+	0.741019i
$847$	−10.2640	+	24.9344i	−0.352675	+	0.856755i
$848$	72.7917	+	30.1513i	2.49968	+	1.03540i
$849$	15.5443	−	8.97448i	0.533477	−	0.308003i
$850$	74.3857	−	2.91765i	2.55141	−	0.100075i
$851$	5.94989	−	10.3055i	0.203960	−	0.353268i
$852$	1.85813	+	14.1139i	0.0636586	+	0.483535i
$853$	24.1690	−	36.1715i	0.827532	−	1.23849i	−0.141101	−	0.989995i	$-0.545064\pi$
$853$	24.1690	−	36.1715i	0.827532	−	1.23849i	0.968633	−	0.248494i	$-0.0799357\pi$
$854$	80.5494	+	5.10166i	2.75634	+	0.174575i
$855$	−22.7342	+	4.52211i	−0.777492	+	0.154653i
$856$	2.24043	+	1.10486i	0.0765764	+	0.0377633i
$857$	−5.68951	−	4.98956i	−0.194350	−	0.170440i	0.556640	−	0.830754i	$-0.312090\pi$
$857$	−5.68951	−	4.98956i	−0.194350	−	0.170440i	−0.750990	+	0.660313i	$0.770423\pi$
$858$	0.180384	−	1.37015i	0.00615819	−	0.0467761i
$859$	−20.1814	−	15.4857i	−0.688580	−	0.528366i	0.204160	−	0.978937i	$-0.434554\pi$
$859$	−20.1814	−	15.4857i	−0.688580	−	0.528366i	−0.892740	+	0.450571i	$0.851220\pi$
$860$	78.8548	+	15.6852i	2.68893	+	0.534860i
$861$	2.86546	−	10.7889i	0.0976548	−	0.367684i
$862$	19.8511	+	99.7985i	0.676133	+	3.39915i
$863$	4.20692	+	1.12724i	0.143205	+	0.0383718i	0.329710	−	0.944082i	$-0.393049\pi$
$863$	4.20692	+	1.12724i	0.143205	+	0.0383718i	−0.186504	+	0.982454i	$0.559716\pi$
$864$	−5.84557	+	2.88272i	−0.198870	+	0.0980721i
$865$	43.7452	−	33.5669i	1.48738	−	1.14131i
$866$	28.5785	+	49.4993i	0.971135	+	1.68206i
$867$	−8.69003	−	14.6111i	−0.295129	−	0.496218i
$868$	11.9677	+	59.4818i	0.406210	+	2.01894i
$869$	−2.79545	+	6.74882i	−0.0948292	+	0.228938i
$870$	2.27512	−	34.7116i	0.0771337	−	1.17683i
$871$	−1.42197	−	5.30688i	−0.0481817	−	0.179817i
$872$	9.61831	−	28.3346i	0.325717	−	0.959531i
$873$	1.63627	−	3.31804i	0.0553795	−	0.112298i
$874$	−24.7204	+	124.278i	−0.836180	+	4.20376i
$875$	18.7867	−	1.27283i	0.635105	−	0.0430295i
$876$	20.0313	+	48.3599i	0.676796	+	1.63393i
$877$	35.3897	−	12.0132i	1.19502	−	0.405656i	0.348144	−	0.937441i	$-0.386812\pi$
$877$	35.3897	−	12.0132i	1.19502	−	0.405656i	0.846879	+	0.531785i	$0.178479\pi$
$878$	3.94044	+	60.1194i	0.132983	+	2.02893i
$879$	−9.78011	−	3.31990i	−0.329875	−	0.111977i
$880$	−6.18945	+	23.0993i	−0.208646	+	0.778678i
$881$	39.6523	+	26.4948i	1.33592	+	0.892633i	0.998807	−	0.0488316i	$-0.0155498\pi$
$881$	39.6523	+	26.4948i	1.33592	+	0.892633i	0.337112	+	0.941464i	$0.390550\pi$
$882$	17.9263	−	0.0788258i	0.603610	−	0.00265420i
$883$			7.00336i			0.235682i	0.993032	+	0.117841i	$0.0375973\pi$
$883$			7.00336i			0.235682i	−0.993032	+	0.117841i	$0.962403\pi$
$884$	5.25271	−	9.98215i	0.176668	−	0.335736i
$885$	5.95828	+	3.44001i	0.200285	+	0.115635i
$886$	−33.6601	−	43.8666i	−1.13083	−	1.47373i
$887$	−0.987130	−	0.0646999i	−0.0331446	−	0.00217241i	0.0488218	−	0.998808i	$-0.484453\pi$
$887$	−0.987130	−	0.0646999i	−0.0331446	−	0.00217241i	−0.0819664	+	0.996635i	$0.526120\pi$
$888$	−7.43982	+	7.43982i	−0.249664	+	0.249664i
$889$	−1.60559	+	12.4064i	−0.0538497	+	0.416097i
$890$	−117.482	+	78.4991i	−3.93801	+	2.63130i
$891$	−0.289022	−	0.851430i	−0.00968259	−	0.0285240i
$892$	80.0358	+	10.5369i	2.67980	+	0.352802i
$893$	−78.7969	−	10.3738i	−2.63684	−	0.347146i
$894$	13.3962	+	39.4638i	0.448035	+	1.31987i
$895$	−19.8531	+	13.2654i	−0.663616	+	0.443414i
$896$	9.70248	+	23.2790i	0.324137	+	0.777696i
$897$	−3.14465	+	3.14465i	−0.104997	+	0.104997i
$898$	−36.1489	−	2.36933i	−1.20631	−	0.0790655i
$899$	−11.9841	−	15.6180i	−0.399691	−	0.520888i
$900$	27.8316	+	16.0686i	0.927721	+	0.535620i
$901$	−32.6005	+	27.1099i	−1.08608	+	0.903162i
$902$		−	9.71531i		−	0.323485i
$903$	−4.34912	−	12.7202i	−0.144730	−	0.423300i
$904$	−47.3743	−	31.6545i	−1.57565	−	1.05281i
$905$	11.8966	−	44.3988i	0.395457	−	1.47586i
$906$	−7.79449	−	2.64587i	−0.258955	−	0.0879033i
$907$	−3.33635	−	50.9028i	−0.110782	−	1.69020i	−0.585983	−	0.810323i	$-0.699292\pi$
$907$	−3.33635	−	50.9028i	−0.110782	−	1.69020i	0.475202	−	0.879877i	$-0.342375\pi$
$908$	20.0564	−	6.80823i	0.665594	−	0.225939i
$909$	−4.41113	−	10.6494i	−0.146308	−	0.353219i
$910$	6.21554	−	12.6740i	0.206043	−	0.420140i
$911$	−2.11966	+	10.6562i	−0.0702274	+	0.353057i	−0.999882	−	0.0153759i	$-0.995106\pi$
$911$	−2.11966	+	10.6562i	−0.0702274	+	0.353057i	0.929654	+	0.368433i	$0.120106\pi$
$912$	22.6277	−	45.8845i	0.749279	−	1.51939i
$913$	−1.69686	+	4.99879i	−0.0561579	+	0.165436i
$914$	2.81525	+	10.5067i	0.0931203	+	0.347530i
$915$	2.70447	−	41.2622i	0.0894069	−	1.36409i
$916$	23.0916	−	55.7481i	0.762968	−	1.84197i
$917$	−31.2091	+	6.27924i	−1.03062	+	0.207359i
$918$	0.277106	−	10.5553i	0.00914585	−	0.348378i
$919$	−3.89271	−	6.74237i	−0.128409	−	0.222410i	0.794652	−	0.607066i	$-0.207654\pi$
$919$	−3.89271	−	6.74237i	−0.128409	−	0.222410i	−0.923060	+	0.384655i	$0.874320\pi$
$920$	133.701	−	102.592i	4.40798	−	3.38236i
$921$	−18.8243	+	9.28309i	−0.620280	+	0.305888i
$922$	0.0598610	+	0.0160397i	0.00197142	+	0.000528239i
$923$	−0.365662	−	1.83831i	−0.0120359	−	0.0605086i
$924$	10.4682	−	2.82963i	0.344379	−	0.0930881i
$925$	11.1045	+	2.20882i	0.365114	+	0.0726257i
$926$	−55.4267	−	42.5304i	−1.82144	−	1.39764i
$927$	0.00347551	−	0.0263991i	0.000114151	−	0.000867061i
$928$	19.1749	+	16.8159i	0.629447	+	0.552010i
$929$	−23.9699	−	11.8207i	−0.786427	−	0.387823i	0.00430065	−	0.999991i	$-0.498631\pi$
$929$	−23.9699	−	11.8207i	−0.786427	−	0.387823i	−0.790728	+	0.612168i	$0.790298\pi$
$930$	43.8646	−	8.72521i	1.43838	−	0.286111i
$931$	−36.9573	+	28.6174i	−1.21123	+	0.937898i
$932$	19.7925	−	29.6215i	0.648324	−	0.970286i
$933$	2.39780	+	18.2131i	0.0785004	+	0.596270i
$934$	47.9557	−	83.0618i	1.56916	−	2.71786i
$935$	−9.44959	−	8.73628i	−0.309035	−	0.285707i
$936$	3.40530	−	1.96605i	0.111306	−	0.0642625i
$937$	30.8148	+	12.7639i	1.00668	+	0.416979i	0.824241	−	0.566239i	$-0.191602\pi$
$937$	30.8148	+	12.7639i	1.00668	+	0.416979i	0.182435	+	0.983218i	$0.441602\pi$
$938$	49.1249	−	37.8667i	1.60398	−	1.23639i
$939$	4.35900	+	4.35900i	0.142251	+	0.142251i
$940$	124.179	+	141.599i	4.05029	+	4.61847i
$941$	−14.2973	+	0.937092i	−0.466077	+	0.0305483i	−0.296633	−	0.954991i	$-0.595864\pi$
$941$	−14.2973	+	0.937092i	−0.466077	+	0.0305483i	−0.169444	+	0.985540i	$0.554197\pi$
$942$	−11.8565	+	13.5197i	−0.386306	+	0.440497i
$943$	−19.0323	+	24.8034i	−0.619777	+	0.807709i
$944$	−14.0293	+	5.81112i	−0.456614	+	0.189136i
$945$	−0.0201925	−	9.18428i	−0.000656864	−	0.298765i
$946$	−6.50006	−	9.72803i	−0.211335	−	0.316285i
$947$	−1.13142	+	0.992226i	−0.0367661	+	0.0322430i	−0.677532	−	0.735494i	$-0.736950\pi$
$947$	−1.13142	+	0.992226i	−0.0367661	+	0.0322430i	0.640766	+	0.767737i	$0.278617\pi$
$948$	−35.7710	+	9.58481i	−1.16179	+	0.311300i
$949$	−3.04819	−	6.18111i	−0.0989483	−	0.200647i
$950$	−119.529	+	15.7364i	−3.87805	+	0.510555i
$951$	−15.8094			−0.512655
$952$	71.1845	+	6.38793i	2.30710	+	0.207034i
$953$	33.5754			1.08761			0.543807	−	0.839211i	$-0.316982\pi$
$953$	33.5754			1.08761			0.543807	+	0.839211i	$0.316982\pi$
$954$	−26.1099	+	3.43743i	−0.845338	+	0.111291i
$955$	13.0986	+	26.5614i	0.423862	+	0.859508i
$956$	−92.3422	+	24.7430i	−2.98656	+	0.800246i
$957$	−2.64526	+	2.31983i	−0.0855090	+	0.0749894i
$958$	−40.6171	−	60.7878i	−1.31228	−	1.96397i
$959$	26.2858	+	45.2981i	0.848814	+	1.46275i
$960$	−4.38713	+	1.81721i	−0.141594	+	0.0586501i
$961$	−3.46384	+	4.51417i	−0.111737	+	0.145618i
$962$	1.62744	−	1.85574i	0.0524708	−	0.0598314i
$963$	−0.380466	+	0.0249371i	−0.0122604	+	0.000803586i
$964$	−41.3131	−	47.1086i	−1.33061	−	1.51727i
$965$	50.9986	+	50.9986i	1.64170	+	1.64170i
$966$	−46.4270	−	19.1112i	−1.49376	−	0.614893i
$967$	−28.6360	−	11.8614i	−0.920872	−	0.381438i	−0.128664	−	0.991688i	$-0.541069\pi$
$967$	−28.6360	−	11.8614i	−0.920872	−	0.381438i	−0.792208	+	0.610251i	$0.791069\pi$
$968$	−57.8261	+	33.3859i	−1.85860	+	1.07306i
$969$	16.1812	+	22.2747i	0.519815	+	0.715565i
$970$	16.4443	−	28.4823i	0.527993	−	0.914511i
$971$	2.40127	+	18.2395i	0.0770605	+	0.585332i	0.985794	+	0.167957i	$0.0537168\pi$
$971$	2.40127	+	18.2395i	0.0770605	+	0.585332i	−0.908734	+	0.417376i	$0.862950\pi$
$972$	2.53247	−	3.79012i	0.0812292	−	0.121568i
$973$	−12.8626	−	25.9388i	−0.412355	−	0.831560i
$974$	28.8568	−	5.73998i	0.924633	−	0.183921i
$975$	−3.79493	−	1.87145i	−0.121535	−	0.0599345i
$976$	68.6181	+	60.1764i	2.19641	+	1.92620i
$977$	3.78740	−	28.7681i	0.121170	−	0.920374i	−0.817590	−	0.575801i	$-0.804690\pi$
$977$	3.78740	−	28.7681i	0.121170	−	0.920374i	0.938760	−	0.344573i	$-0.111976\pi$
$978$	40.9746	+	31.4409i	1.31022	+	1.00537i
$979$	14.0164	+	2.78804i	0.447966	+	0.0891061i
$980$	110.558	+	6.75828i	3.53166	+	0.215885i
$981$	0.891007	+	4.47940i	0.0284477	+	0.143016i
$982$	63.7479	+	17.0812i	2.03428	+	0.545083i
$983$	21.3837	−	10.5453i	0.682034	−	0.336342i	−0.0680522	−	0.997682i	$-0.521678\pi$
$983$	21.3837	−	10.5453i	0.682034	−	0.336342i	0.750087	+	0.661340i	$0.230012\pi$
$984$	21.9305	−	16.8279i	0.699120	−	0.536454i
$985$	8.19790	+	14.1992i	0.261207	+	0.452424i
$986$	−38.5741	+	14.8042i	−1.22845	+	0.471463i
$987$	10.0568	−	29.8417i	0.320110	−	0.949870i
$988$	−6.99077	+	16.8772i	−0.222406	+	0.536936i
$989$	−2.46243	+	37.5695i	−0.0783008	+	1.19464i
$990$	−2.06881	−	7.72092i	−0.0657512	−	0.245387i
$991$	−14.4686	+	42.6232i	−0.459612	+	1.35397i	0.432287	+	0.901736i	$0.357707\pi$
$991$	−14.4686	+	42.6232i	−0.459612	+	1.35397i	−0.891898	+	0.452236i	$0.850627\pi$
$992$	−14.5027	+	29.4085i	−0.460461	+	0.933722i
$993$	−2.29292	+	11.5273i	−0.0727636	+	0.365807i
$994$	17.5681	−	11.7946i	0.557227	−	0.374102i
$995$	11.3493	+	27.3996i	0.359797	+	0.868627i
$996$	−25.3419	+	8.60243i	−0.802990	+	0.272578i
$997$	2.13753	+	32.6125i	0.0676964	+	1.03285i	0.887680	+	0.460460i	$0.152316\pi$
$997$	2.13753	+	32.6125i	0.0676964	+	1.03285i	−0.819984	+	0.572387i	$0.806018\pi$
$998$	−5.05890	−	1.71726i	−0.160137	−	0.0543591i
$999$	0.415642	−	1.55120i	0.0131503	−	0.0490777i

Display

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bl.a.10.23	✓	384
7.5	odd	6	inner	357.2.bl.a.61.2	yes	384
17.12	odd	16	inner	357.2.bl.a.199.2	yes	384
119.12	even	48	inner	357.2.bl.a.250.23	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bl.a.10.23	✓	384	1.1	even	1	trivial
357.2.bl.a.61.2	yes	384	7.5	odd	6	inner
357.2.bl.a.199.2	yes	384	17.12	odd	16	inner
357.2.bl.a.250.23	yes	384	119.12	even	48	inner

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

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$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	357.2.bl.a.10.23

Level	$357$
Weight	$2$
Character	357.10
Analytic conductor	$2.851$
Analytic rank	$0$
Dimension	$384$
Inner twists	$4$