LMFDB - Embedded newform 60.3.l.a.23.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [60,3,Mod(23,60)] 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("60.23"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(60, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	60.l (of order $4$, degree $2$, 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:	$1.63488158616$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.8
Character	$\chi$	$=$	60.23
Dual form			60.3.l.a.47.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.837725 - 1.81610i) q^{2} +(-2.69303 - 1.32197i) q^{3} +(-2.59643 + 3.04278i) q^{4} +(-3.21472 + 3.82956i) q^{5} +(-0.144815 + 5.99825i) q^{6} +(-3.54241 - 3.54241i) q^{7} +(7.70110 + 2.16636i) q^{8} +(5.50478 + 7.12021i) q^{9} +(9.64792 + 2.63013i) q^{10} -16.8337 q^{11} +(11.0147 - 4.76189i) q^{12} +(-8.64592 - 8.64592i) q^{13} +(-3.46580 + 9.40093i) q^{14} +(13.7199 - 6.06335i) q^{15} +(-2.51707 - 15.8008i) q^{16} +(-9.72710 - 9.72710i) q^{17} +(8.31951 - 15.9620i) q^{18} +4.78419 q^{19} +(-3.30573 - 19.7249i) q^{20} +(4.85684 + 14.2228i) q^{21} +(14.1020 + 30.5716i) q^{22} +(13.5716 + 13.5716i) q^{23} +(-17.8754 - 16.0147i) q^{24} +(-4.33113 - 24.6220i) q^{25} +(-8.45895 + 22.9448i) q^{26} +(-5.41182 - 26.4521i) q^{27} +(19.9764 - 1.58116i) q^{28} +14.8741 q^{29} +(-22.5052 - 19.8373i) q^{30} +14.0641i q^{31} +(-26.5872 + 17.8080i) q^{32} +(45.3336 + 22.2536i) q^{33} +(-9.51674 + 25.8140i) q^{34} +(24.9537 - 2.17802i) q^{35} +(-35.9581 - 1.73727i) q^{36} +(-10.1182 + 10.1182i) q^{37} +(-4.00784 - 8.68857i) q^{38} +(11.8540 + 34.7134i) q^{39} +(-33.0531 + 22.5276i) q^{40} -6.08509i q^{41} +(21.7613 - 20.7353i) q^{42} +(-57.2366 + 57.2366i) q^{43} +(43.7075 - 51.2213i) q^{44} +(-44.9636 - 1.80856i) q^{45} +(13.2781 - 36.0167i) q^{46} +(17.6247 - 17.6247i) q^{47} +(-14.1096 + 45.8794i) q^{48} -23.9027i q^{49} +(-41.0876 + 28.4922i) q^{50} +(13.3364 + 39.0543i) q^{51} +(48.7562 - 3.85911i) q^{52} +(-16.2015 + 16.2015i) q^{53} +(-43.5060 + 31.9880i) q^{54} +(54.1156 - 64.4657i) q^{55} +(-19.6063 - 34.9546i) q^{56} +(-12.8840 - 6.32456i) q^{57} +(-12.4604 - 27.0128i) q^{58} -4.37150i q^{59} +(-17.1734 + 57.4898i) q^{60} +8.52269 q^{61} +(25.5418 - 11.7818i) q^{62} +(5.72249 - 44.7229i) q^{63} +(54.6137 + 33.3667i) q^{64} +(60.9043 - 5.31588i) q^{65} +(2.43777 - 100.973i) q^{66} +(-53.9714 - 53.9714i) q^{67} +(54.8532 - 4.34170i) q^{68} +(-18.6074 - 54.4900i) q^{69} +(-24.8599 - 43.4939i) q^{70} -36.6679 q^{71} +(26.9679 + 66.7588i) q^{72} +(-12.6800 - 12.6800i) q^{73} +(26.8519 + 9.89937i) q^{74} +(-20.8857 + 72.0332i) q^{75} +(-12.4218 + 14.5573i) q^{76} +(59.6318 + 59.6318i) q^{77} +(53.1125 - 50.6084i) q^{78} +88.4346 q^{79} +(68.6017 + 41.1558i) q^{80} +(-20.3947 + 78.3904i) q^{81} +(-11.0511 + 5.09763i) q^{82} +(-63.7372 - 63.7372i) q^{83} +(-55.8873 - 22.1502i) q^{84} +(68.5205 - 5.98063i) q^{85} +(151.896 + 55.9988i) q^{86} +(-40.0563 - 19.6631i) q^{87} +(-129.638 - 36.4679i) q^{88} -115.022 q^{89} +(34.3826 + 83.1735i) q^{90} +61.2548i q^{91} +(-76.5332 + 6.05770i) q^{92} +(18.5923 - 37.8749i) q^{93} +(-46.7728 - 17.2435i) q^{94} +(-15.3798 + 18.3214i) q^{95} +(95.1415 - 12.8098i) q^{96} +(-85.3544 + 85.3544i) q^{97} +(-43.4096 + 20.0239i) q^{98} +(-92.6658 - 119.859i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{6} - 12 q^{10} - 20 q^{12} - 8 q^{13} - 36 q^{16} - 24 q^{18} - 24 q^{21} - 76 q^{22} - 8 q^{25} - 84 q^{28} + 68 q^{30} - 40 q^{33} + 172 q^{36} - 40 q^{37} + 104 q^{40} + 236 q^{42} - 104 q^{45}+ \cdots + 72 q^{97}+O(q^{100}) $ 40 * q - 4 * q^6 - 12 * q^10 - 20 * q^12 - 8 * q^13 - 36 * q^16 - 24 * q^18 - 24 * q^21 - 76 * q^22 - 8 * q^25 - 84 * q^28 + 68 * q^30 - 40 * q^33 + 172 * q^36 - 40 * q^37 + 104 * q^40 + 236 * q^42 - 104 * q^45 + 240 * q^46 + 196 * q^48 + 304 * q^52 - 72 * q^57 + 180 * q^58 - 284 * q^60 + 48 * q^61 - 552 * q^66 - 372 * q^70 - 600 * q^72 + 104 * q^73 - 736 * q^76 - 408 * q^78 + 72 * q^81 - 720 * q^82 + 216 * q^85 - 580 * q^88 + 528 * q^90 + 368 * q^93 + 884 * q^96 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.837725	−	1.81610i	−0.418863	−	0.908050i
$2$	−0.837725	−	1.81610i	−0.418863	−	0.908050i
$3$	−2.69303	−	1.32197i	−0.897676	−	0.440657i
$3$	−2.69303	−	1.32197i	−0.897676	−	0.440657i
$4$	−2.59643	+	3.04278i	−0.649108	+	0.760696i
$5$	−3.21472	+	3.82956i	−0.642944	+	0.765913i
$5$	−3.21472	+	3.82956i	−0.642944	+	0.765913i
$6$	−0.144815	+	5.99825i	−0.0241358	+	0.999709i
$7$	−3.54241	−	3.54241i	−0.506059	−	0.506059i	0.407256	−	0.913314i	$-0.366486\pi$
$7$	−3.54241	−	3.54241i	−0.506059	−	0.506059i	−0.913314	+	0.407256i	$0.866486\pi$
$8$	7.70110	+	2.16636i	0.962637	+	0.270795i
$9$	5.50478	+	7.12021i	0.611643	+	0.791134i
$10$	9.64792	+	2.63013i	0.964792	+	0.263013i
$11$	−16.8337			−1.53034			−0.765168	−	0.643831i	$-0.777344\pi$
$11$	−16.8337			−1.53034			−0.765168	+	0.643831i	$0.777344\pi$
$12$	11.0147	−	4.76189i	0.917895	−	0.396824i
$13$	−8.64592	−	8.64592i	−0.665071	−	0.665071i	0.291500	−	0.956571i	$-0.405846\pi$
$13$	−8.64592	−	8.64592i	−0.665071	−	0.665071i	−0.956571	+	0.291500i	$0.905846\pi$
$14$	−3.46580	+	9.40093i	−0.247557	+	0.671495i
$15$	13.7199	−	6.06335i	0.914660	−	0.404223i
$16$	−2.51707	−	15.8008i	−0.157317	−	0.987548i
$17$	−9.72710	−	9.72710i	−0.572182	−	0.572182i	0.360556	−	0.932738i	$-0.382587\pi$
$17$	−9.72710	−	9.72710i	−0.572182	−	0.572182i	−0.932738	+	0.360556i	$0.882587\pi$
$18$	8.31951	−	15.9620i	0.462195	−	0.886778i
$19$	4.78419			0.251800			0.125900	−	0.992043i	$-0.459818\pi$
$19$	4.78419			0.251800			0.125900	+	0.992043i	$0.459818\pi$
$20$	−3.30573	−	19.7249i	−0.165286	−	0.986246i
$21$	4.85684	+	14.2228i	0.231278	+	0.677275i
$22$	14.1020	+	30.5716i	0.641000	+	1.38962i
$23$	13.5716	+	13.5716i	0.590070	+	0.590070i	0.937650	−	0.347580i	$-0.112997\pi$
$23$	13.5716	+	13.5716i	0.590070	+	0.590070i	−0.347580	+	0.937650i	$0.612997\pi$
$24$	−17.8754	−	16.0147i	−0.744808	−	0.667279i
$25$	−4.33113	−	24.6220i	−0.173245	−	0.984879i
$26$	−8.45895	+	22.9448i	−0.325344	+	0.882491i
$27$	−5.41182	−	26.4521i	−0.200438	−	0.979706i
$28$	19.9764	−	1.58116i	0.713444	−	0.0564699i
$29$	14.8741			0.512899			0.256449	−	0.966558i	$-0.417447\pi$
$29$	14.8741			0.512899			0.256449	+	0.966558i	$0.417447\pi$
$30$	−22.5052	−	19.8373i	−0.750172	−	0.661243i
$31$			14.0641i			0.453680i	0.973932	+	0.226840i	$0.0728395\pi$
$31$			14.0641i			0.453680i	−0.973932	+	0.226840i	$0.927161\pi$
$32$	−26.5872	+	17.8080i	−0.830849	+	0.556498i
$33$	45.3336	+	22.2536i	1.37374	+	0.674353i
$34$	−9.51674	+	25.8140i	−0.279904	+	0.759235i
$35$	24.9537	−	2.17802i	0.712964	−	0.0622292i
$36$	−35.9581	−	1.73727i	−0.998835	−	0.0482576i
$37$	−10.1182	+	10.1182i	−0.273465	+	0.273465i	−0.830493	−	0.557029i	$-0.811941\pi$
$37$	−10.1182	+	10.1182i	−0.273465	+	0.273465i	0.557029	+	0.830493i	$0.311941\pi$
$38$	−4.00784	−	8.68857i	−0.105469	−	0.228647i
$39$	11.8540	+	34.7134i	0.303950	+	0.890086i
$40$	−33.0531	+	22.5276i	−0.826328	+	0.563190i
$41$		−	6.08509i		−	0.148417i	−0.997243	−	0.0742084i	$-0.976357\pi$
$41$		−	6.08509i		−	0.148417i	0.997243	−	0.0742084i	$-0.0236430\pi$
$42$	21.7613	−	20.7353i	0.518125	−	0.493697i
$43$	−57.2366	+	57.2366i	−1.33108	+	1.33108i	−0.426683	+	0.904401i	$0.640318\pi$
$43$	−57.2366	+	57.2366i	−1.33108	+	1.33108i	−0.904401	+	0.426683i	$0.859682\pi$
$44$	43.7075	−	51.2213i	0.993353	−	1.16412i
$45$	−44.9636	−	1.80856i	−0.999192	−	0.0401903i
$46$	13.2781	−	36.0167i	0.288654	−	0.782971i
$47$	17.6247	−	17.6247i	0.374993	−	0.374993i	−0.494299	−	0.869292i	$-0.664575\pi$
$47$	17.6247	−	17.6247i	0.374993	−	0.374993i	0.869292	+	0.494299i	$0.164575\pi$
$48$	−14.1096	+	45.8794i	−0.293951	+	0.955821i
$49$		−	23.9027i		−	0.487809i
$50$	−41.0876	+	28.4922i	−0.821753	+	0.569844i
$51$	13.3364	+	39.0543i	0.261498	+	0.765770i
$52$	48.7562	−	3.85911i	0.937620	−	0.0742137i
$53$	−16.2015	+	16.2015i	−0.305688	+	0.305688i	−0.843234	−	0.537546i	$-0.819351\pi$
$53$	−16.2015	+	16.2015i	−0.305688	+	0.305688i	0.537546	+	0.843234i	$0.319351\pi$
$54$	−43.5060	+	31.9880i	−0.805666	+	0.592370i
$55$	54.1156	−	64.4657i	0.983920	−	1.17210i
$56$	−19.6063	−	34.9546i	−0.350112	−	0.624189i
$57$	−12.8840	−	6.32456i	−0.226034	−	0.110957i
$58$	−12.4604	−	27.0128i	−0.214834	−	0.465738i
$59$		−	4.37150i		−	0.0740931i	−0.999314	−	0.0370466i	$-0.988205\pi$
$59$		−	4.37150i		−	0.0740931i	0.999314	−	0.0370466i	$-0.0117950\pi$
$60$	−17.1734	+	57.4898i	−0.286223	+	0.958163i
$61$	8.52269			0.139716			0.0698582	−	0.997557i	$-0.477745\pi$
$61$	8.52269			0.139716			0.0698582	+	0.997557i	$0.477745\pi$
$62$	25.5418	−	11.7818i	0.411964	−	0.190030i
$63$	5.72249	−	44.7229i	0.0908332	−	0.709887i
$64$	54.6137	+	33.3667i	0.853340	+	0.521355i
$65$	60.9043	−	5.31588i	0.936990	−	0.0817828i
$66$	2.43777	−	100.973i	0.0369359	−	1.52989i
$67$	−53.9714	−	53.9714i	−0.805543	−	0.805543i	0.178413	−	0.983956i	$-0.442904\pi$
$67$	−53.9714	−	53.9714i	−0.805543	−	0.805543i	−0.983956	+	0.178413i	$0.942904\pi$
$68$	54.8532	−	4.34170i	0.806665	−	0.0638485i
$69$	−18.6074	−	54.4900i	−0.269673	−	0.789710i
$70$	−24.8599	−	43.4939i	−0.355141	−	0.621341i
$71$	−36.6679			−0.516449			−0.258225	−	0.966085i	$-0.583137\pi$
$71$	−36.6679			−0.516449			−0.258225	+	0.966085i	$0.583137\pi$
$72$	26.9679	+	66.7588i	0.374554	+	0.927205i
$73$	−12.6800	−	12.6800i	−0.173699	−	0.173699i	0.614903	−	0.788602i	$-0.289195\pi$
$73$	−12.6800	−	12.6800i	−0.173699	−	0.173699i	−0.788602	+	0.614903i	$0.789195\pi$
$74$	26.8519	+	9.89937i	0.362863	+	0.133775i
$75$	−20.8857	+	72.0332i	−0.278476	+	0.960443i
$76$	−12.4218	+	14.5573i	−0.163445	+	0.191543i
$77$	59.6318	+	59.6318i	0.774439	+	0.774439i
$78$	53.1125	−	50.6084i	0.680929	−	0.648825i
$79$	88.4346			1.11943			0.559713	−	0.828687i	$-0.310912\pi$
$79$	88.4346			1.11943			0.559713	+	0.828687i	$0.310912\pi$
$80$	68.6017	+	41.1558i	0.857522	+	0.514448i
$81$	−20.3947	+	78.3904i	−0.251786	+	0.967783i
$82$	−11.0511	+	5.09763i	−0.134770	+	0.0621663i
$83$	−63.7372	−	63.7372i	−0.767918	−	0.767918i	0.209822	−	0.977740i	$-0.432712\pi$
$83$	−63.7372	−	63.7372i	−0.767918	−	0.767918i	−0.977740	+	0.209822i	$0.932712\pi$
$84$	−55.8873	−	22.1502i	−0.665325	−	0.263692i
$85$	68.5205	−	5.98063i	0.806123	−	0.0703604i
$86$	151.896	+	55.9988i	1.76623	+	0.651149i
$87$	−40.0563	−	19.6631i	−0.460417	−	0.226013i
$88$	−129.638	−	36.4679i	−1.47316	−	0.414408i
$89$	−115.022			−1.29238			−0.646190	−	0.763177i	$-0.723639\pi$
$89$	−115.022			−1.29238			−0.646190	+	0.763177i	$0.723639\pi$
$90$	34.3826	+	83.1735i	0.382029	+	0.924150i
$91$			61.2548i			0.673130i
$92$	−76.5332	+	6.05770i	−0.831883	+	0.0658445i
$93$	18.5923	−	37.8749i	0.199917	−	0.407258i
$94$	−46.7728	−	17.2435i	−0.497583	−	0.183442i
$95$	−15.3798	+	18.3214i	−0.161893	+	0.192857i
$96$	95.1415	−	12.8098i	0.991057	−	0.133436i
$97$	−85.3544	+	85.3544i	−0.879942	+	0.879942i	−0.993528	−	0.113586i	$-0.963766\pi$
$97$	−85.3544	+	85.3544i	−0.879942	+	0.879942i	0.113586	+	0.993528i	$0.463766\pi$
$98$	−43.4096	+	20.0239i	−0.442955	+	0.204325i
$99$	−92.6658	−	119.859i	−0.936018	−	1.21070i
$100$	86.1648	+	50.7506i	0.861648	+	0.507506i
$101$		−	158.917i		−	1.57343i	−0.617313	−	0.786717i	$-0.711779\pi$
$101$		−	158.917i		−	1.57343i	0.617313	−	0.786717i	$-0.288221\pi$
$102$	59.7542	−	56.9369i	0.585826	−	0.558205i
$103$	28.6266	−	28.6266i	0.277928	−	0.277928i	−0.554353	−	0.832282i	$-0.687034\pi$
$103$	28.6266	−	28.6266i	0.277928	−	0.277928i	0.832282	+	0.554353i	$0.187034\pi$
$104$	−47.8529	−	85.3133i	−0.460124	−	0.820320i
$105$	−70.0804	−	27.1227i	−0.667432	−	0.258311i
$106$	42.9959	+	15.8511i	0.405622	+	0.149539i
$107$	−28.1808	+	28.1808i	−0.263372	+	0.263372i	−0.826423	−	0.563050i	$-0.809628\pi$
$107$	−28.1808	+	28.1808i	−0.263372	+	0.263372i	0.563050	+	0.826423i	$0.309628\pi$
$108$	94.5394	+	52.2140i	0.875365	+	0.483463i
$109$			159.944i			1.46737i	0.679489	+	0.733686i	$0.262202\pi$
$109$			159.944i			1.46737i	−0.679489	+	0.733686i	$0.737798\pi$
$110$	−162.410	−	44.2748i	−1.47646	−	0.402498i
$111$	40.6245	−	13.8726i	0.365986	−	0.124978i
$112$	−47.0563	+	64.8893i	−0.420146	+	0.579369i
$113$	−101.260	+	101.260i	−0.896110	+	0.896110i	−0.995089	−	0.0989792i	$-0.968442\pi$
$113$	−101.260	+	101.260i	−0.896110	+	0.896110i	0.0989792	+	0.995089i	$0.468442\pi$
$114$	−0.692822	+	28.6968i	−0.00607739	+	0.251726i
$115$	−95.6023	+	8.34440i	−0.831324	+	0.0725600i
$116$	−38.6195	+	45.2586i	−0.332927	+	0.390160i
$117$	13.9668	−	109.155i	0.119375	−	0.932946i
$118$	−7.93907	+	3.66211i	−0.0672803	+	0.0310348i
$119$			68.9147i			0.579115i
$120$	118.794	−	16.9721i	0.989948	−	0.141434i
$121$	162.373			1.34193
$122$	−7.13968	−	15.4781i	−0.0585219	−	0.126869i
$123$	−8.04432	+	16.3873i	−0.0654009	+	0.133230i
$124$	−42.7940	−	36.5165i	−0.345113	−	0.294488i
$125$	108.215	+	62.5665i	0.865718	+	0.500532i
$126$	−86.0151	+	27.0729i	−0.682659	+	0.214864i
$127$	94.0845	+	94.0845i	0.740823	+	0.740823i	0.972736	−	0.231914i	$-0.0744987\pi$
$127$	94.0845	+	94.0845i	0.740823	+	0.740823i	−0.231914	+	0.972736i	$0.574499\pi$
$128$	14.8460	−	127.136i	0.115985	−	0.993251i
$129$	229.805	−	78.4746i	1.78143	−	0.608330i
$130$	−60.6753	−	106.155i	−0.466733	−	0.816578i
$131$	145.148			1.10800			0.554002	−	0.832515i	$-0.313100\pi$
$131$	145.148			1.10800			0.554002	+	0.832515i	$0.313100\pi$
$132$	−185.419	+	80.1601i	−1.40469	+	0.607274i
$133$	−16.9476	−	16.9476i	−0.127425	−	0.127425i
$134$	−52.8042	+	143.231i	−0.394061	+	1.06888i
$135$	118.697	+	64.3111i	0.879240	+	0.476379i
$136$	−53.8369	−	95.9817i	−0.395859	−	0.705748i
$137$	−60.1022	−	60.1022i	−0.438702	−	0.438702i	0.452873	−	0.891575i	$-0.350399\pi$
$137$	−60.1022	−	60.1022i	−0.438702	−	0.438702i	−0.891575	+	0.452873i	$0.850399\pi$
$138$	−83.3713	+	79.4405i	−0.604140	+	0.575656i
$139$	−12.5985			−0.0906366			−0.0453183	−	0.998973i	$-0.514430\pi$
$139$	−12.5985			−0.0906366			−0.0453183	+	0.998973i	$0.514430\pi$
$140$	−58.1635	+	81.5840i	−0.415453	+	0.582743i
$141$	−70.7630	+	24.1644i	−0.501865	+	0.171379i
$142$	30.7176	+	66.5925i	0.216321	+	0.468961i
$143$	145.543	+	145.543i	1.01778	+	1.01778i
$144$	98.6488	−	104.902i	0.685061	−	0.728485i
$145$	−47.8160	+	56.9612i	−0.329765	+	0.392836i
$146$	−12.4058	+	33.6506i	−0.0849713	+	0.230483i
$147$	−31.5986	+	64.3705i	−0.214957	+	0.437895i
$148$	−4.51626	−	57.0587i	−0.0305153	−	0.385531i
$149$	−25.9233			−0.173982			−0.0869911	−	0.996209i	$-0.527725\pi$
$149$	−25.9233			−0.173982			−0.0869911	+	0.996209i	$0.527725\pi$
$150$	148.316	−	22.4136i	0.988773	−	0.149424i
$151$		−	200.379i		−	1.32701i	−0.748171	−	0.663506i	$-0.769068\pi$
$151$		−	200.379i		−	1.32701i	0.748171	−	0.663506i	$-0.230932\pi$
$152$	36.8435	+	10.3643i	0.242392	+	0.0681862i
$153$	15.7134	−	122.805i	0.102702	−	0.802644i
$154$	58.3422	−	158.252i	0.378846	−	1.02761i
$155$	−53.8593	−	45.2121i	−0.347479	−	0.291691i
$156$	−136.403	−	54.0616i	−0.874381	−	0.346549i
$157$	139.992	−	139.992i	0.891666	−	0.891666i	−0.103014	−	0.994680i	$-0.532849\pi$
$157$	139.992	−	139.992i	0.891666	−	0.891666i	0.994680	+	0.103014i	$0.0328486\pi$
$158$	−74.0839	−	160.606i	−0.468885	−	1.01649i
$159$	65.0489	−	22.2131i	0.409113	−	0.139705i
$160$	17.2736	−	159.065i	0.107960	−	0.994155i
$161$		−	96.1524i		−	0.597220i
$162$	159.450	−	28.6308i	0.984259	−	0.176733i
$163$	58.6324	−	58.6324i	0.359708	−	0.359708i	−0.503997	−	0.863705i	$-0.668138\pi$
$163$	58.6324	−	58.6324i	0.359708	−	0.359708i	0.863705	+	0.503997i	$0.168138\pi$
$164$	18.5156	+	15.7995i	0.112900	+	0.0963386i
$165$	−230.957	+	102.069i	−1.39974	+	0.618597i
$166$	−62.3588	+	169.147i	−0.375655	+	1.01896i
$167$	84.2556	−	84.2556i	0.504524	−	0.504524i	−0.408316	−	0.912841i	$-0.633884\pi$
$167$	84.2556	−	84.2556i	0.504524	−	0.504524i	0.912841	+	0.408316i	$0.133884\pi$
$168$	6.59130	+	120.053i	0.0392339	+	0.714599i
$169$		−	19.4961i		−	0.115361i
$170$	−68.2627	−	119.430i	−0.401545	−	0.702528i
$171$	26.3359	+	34.0644i	0.154011	+	0.199207i
$172$	−25.5476	−	322.770i	−0.148533	−	1.87657i
$173$	51.2341	−	51.2341i	0.296151	−	0.296151i	−0.543353	−	0.839504i	$-0.682846\pi$
$173$	51.2341	−	51.2341i	0.296151	−	0.296151i	0.839504	+	0.543353i	$0.182846\pi$
$174$	−2.15399	+	89.2184i	−0.0123792	+	0.512749i
$175$	−71.8785	+	102.564i	−0.410734	+	0.586078i
$176$	42.3716	+	265.985i	0.240747	+	1.51128i
$177$	−5.77899	+	11.7726i	−0.0326497	+	0.0665116i
$178$	96.3566	+	208.891i	0.541329	+	1.17354i
$179$			27.2276i			0.152109i	0.997104	+	0.0760547i	$0.0242324\pi$
$179$			27.2276i			0.152109i	−0.997104	+	0.0760547i	$0.975768\pi$
$180$	122.248	−	132.119i	0.679156	−	0.733994i
$181$	−276.624			−1.52831			−0.764155	−	0.645033i	$-0.776844\pi$
$181$	−276.624			−1.52831			−0.764155	+	0.645033i	$0.776844\pi$
$182$	111.245	−	51.3147i	0.611235	−	0.281949i
$183$	−22.9518	−	11.2668i	−0.125420	−	0.0615670i
$184$	75.1152	+	133.917i	0.408235	+	0.727811i
$185$	−6.22109	−	71.2754i	−0.0336275	−	0.385272i
$186$	−84.3599	−	2.03669i	−0.453548	−	0.0109499i
$187$	163.743	+	163.743i	0.875630	+	0.875630i
$188$	7.86679	+	99.3894i	0.0418446	+	0.528667i
$189$	−74.5332	+	112.875i	−0.394356	+	0.597222i
$190$	46.1575	+	12.5831i	0.242934	+	0.0662266i
$191$	−340.010			−1.78016			−0.890078	−	0.455807i	$-0.849351\pi$
$191$	−340.010			−1.78016			−0.890078	+	0.455807i	$0.849351\pi$
$192$	−102.966	−	162.055i	−0.536283	−	0.844038i
$193$	100.981	+	100.981i	0.523220	+	0.523220i	0.918542	−	0.395322i	$-0.129367\pi$
$193$	100.981	+	100.981i	0.523220	+	0.523220i	−0.395322	+	0.918542i	$0.629367\pi$
$194$	226.515	+	83.5085i	1.16761	+	0.430456i
$195$	−171.044	−	66.1980i	−0.877151	−	0.339477i
$196$	72.7306	+	62.0617i	0.371075	+	0.316641i
$197$	225.584	+	225.584i	1.14510	+	1.14510i	0.987504	+	0.157595i	$0.0503741\pi$
$197$	225.584	+	225.584i	1.14510	+	1.14510i	0.157595	+	0.987504i	$0.449626\pi$
$198$	−140.048	+	268.699i	−0.707313	+	1.35707i
$199$	−286.672			−1.44056			−0.720281	−	0.693682i	$-0.755987\pi$
$199$	−286.672			−1.44056			−0.720281	+	0.693682i	$0.755987\pi$
$200$	19.9857	−	198.999i	0.0999286	−	0.994995i
$201$	73.9977	+	216.695i	0.368148	+	1.07808i
$202$	−288.609	+	133.129i	−1.42876	+	0.659053i
$203$	−52.6900	−	52.6900i	−0.259557	−	0.259557i
$204$	−153.461	−	60.8221i	−0.752259	−	0.298147i
$205$	23.3032	+	19.5619i	0.113674	+	0.0954238i
$206$	−75.9701	−	28.0076i	−0.368787	−	0.135959i
$207$	−21.9239	+	171.341i	−0.105912	+	0.827736i
$208$	−114.850	+	158.375i	−0.552163	+	0.761416i
$209$	−80.5356			−0.385338
$210$	9.45066	+	149.994i	0.0450031	+	0.714259i
$211$		−	183.842i		−	0.871288i	−0.900119	−	0.435644i	$-0.856521\pi$
$211$		−	183.842i		−	0.871288i	0.900119	−	0.435644i	$-0.143479\pi$
$212$	−7.23155	−	91.3637i	−0.0341111	−	0.430961i
$213$	98.7476	+	48.4739i	0.463604	+	0.227577i
$214$	74.7870	+	27.5714i	0.349472	+	0.128838i
$215$	−35.1915	−	403.191i	−0.163681	−	1.87531i
$216$	15.6279	−	215.434i	0.0723512	−	0.997379i
$217$	49.8207	−	49.8207i	0.229589	−	0.229589i
$218$	290.473	−	133.989i	1.33245	−	0.614627i
$219$	17.3850	+	50.9103i	0.0793836	+	0.232467i
$220$	55.6476	+	332.043i	0.252943	+	1.50929i
$221$			168.199i			0.761083i
$222$	−59.2262	−	62.1567i	−0.266785	−	0.279985i
$223$	7.02165	−	7.02165i	0.0314872	−	0.0314872i	−0.691188	−	0.722675i	$-0.742912\pi$
$223$	7.02165	−	7.02165i	0.0314872	−	0.0314872i	0.722675	+	0.691188i	$0.242912\pi$
$224$	157.266	+	31.0995i	0.702079	+	0.138837i
$225$	151.472	−	166.377i	0.673207	−	0.739454i
$226$	268.727	+	99.0706i	1.18906	+	0.438366i
$227$	−36.6684	+	36.6684i	−0.161535	+	0.161535i	−0.783246	−	0.621711i	$-0.786438\pi$
$227$	−36.6684	+	36.6684i	−0.161535	+	0.161535i	0.621711	+	0.783246i	$0.286438\pi$
$228$	52.6966	−	22.7818i	0.231126	−	0.0999201i
$229$		−	270.126i		−	1.17959i	−0.807554	−	0.589794i	$-0.799209\pi$
$229$		−	270.126i		−	1.17959i	0.807554	−	0.589794i	$-0.200791\pi$
$230$	95.2427	+	166.633i	0.414099	+	0.724491i
$231$	−81.7585	−	239.422i	−0.353933	−	1.03646i
$232$	114.547	+	32.2226i	0.493735	+	0.138891i
$233$	−55.2135	+	55.2135i	−0.236968	+	0.236968i	−0.815593	−	0.578625i	$-0.803589\pi$
$233$	−55.2135	+	55.2135i	−0.236968	+	0.236968i	0.578625	+	0.815593i	$0.303589\pi$
$234$	−209.936	+	66.0765i	−0.897163	+	0.282378i
$235$	10.8364	+	124.153i	0.0461123	+	0.528312i
$236$	13.3015	+	11.3503i	0.0563624	+	0.0480945i
$237$	−238.157	−	116.908i	−1.00488	−	0.493283i
$238$	125.156	−	57.7316i	0.525865	−	0.242570i
$239$			46.1374i			0.193044i	0.995331	+	0.0965218i	$0.0307718\pi$
$239$			46.1374i			0.193044i	−0.995331	+	0.0965218i	$0.969228\pi$
$240$	−130.340	−	201.523i	−0.543081	−	0.839680i
$241$	−212.165			−0.880351			−0.440176	−	0.897912i	$-0.645084\pi$
$241$	−212.165			−0.880351			−0.440176	+	0.897912i	$0.645084\pi$
$242$	−136.024	−	294.885i	−0.562082	−	1.21853i
$243$	158.553	−	184.146i	0.652483	−	0.757803i
$244$	−22.1286	+	25.9327i	−0.0906910	+	0.106282i
$245$	91.5368	+	76.8404i	0.373620	+	0.313634i
$246$	36.4999	+	0.881212i	0.148374	+	0.00358216i
$247$	−41.3638	−	41.3638i	−0.167465	−	0.167465i
$248$	−30.4679	+	108.309i	−0.122855	+	0.436729i
$249$	87.3872	+	255.905i	0.350953	+	1.02773i
$250$	22.9727	−	248.942i	0.0918907	−	0.995769i
$251$	159.687			0.636203			0.318101	−	0.948057i	$-0.396955\pi$
$251$	159.687			0.636203			0.318101	+	0.948057i	$0.396955\pi$
$252$	121.224	+	133.532i	0.481048	+	0.529890i
$253$	−228.460	−	228.460i	−0.903004	−	0.903004i
$254$	92.0498	−	249.684i	0.362401	−	0.983007i
$255$	−192.434	−	74.4761i	−0.754642	−	0.292063i
$256$	−243.329	+	79.5433i	−0.950503	+	0.310716i
$257$	−98.0877	−	98.0877i	−0.381664	−	0.381664i	0.490037	−	0.871701i	$-0.336983\pi$
$257$	−98.0877	−	98.0877i	−0.381664	−	0.381664i	−0.871701	+	0.490037i	$0.836983\pi$
$258$	−335.031	−	351.608i	−1.29857	−	1.36282i
$259$	71.6855			0.276778
$260$	−141.959	+	199.121i	−0.545996	+	0.765850i
$261$	81.8785	+	105.906i	0.313711	+	0.405772i
$262$	−121.595	−	263.604i	−0.464101	−	1.00612i
$263$	141.919	+	141.919i	0.539614	+	0.539614i	0.923416	−	0.383802i	$-0.125385\pi$
$263$	141.919	+	141.919i	0.539614	+	0.539614i	−0.383802	+	0.923416i	$0.625385\pi$
$264$	300.909	+	269.586i	1.13981	+	1.02116i
$265$	−9.96136	−	114.128i	−0.0375900	−	0.430671i
$266$	−16.5811	+	44.9759i	−0.0623348	+	0.169082i
$267$	309.757	+	152.055i	1.16014	+	0.569496i
$268$	304.356	−	24.0902i	1.13566	−	0.0898887i
$269$	−0.543377			−0.00201999			−0.00100999	−	0.999999i	$-0.500321\pi$
$269$	−0.543377			−0.00201999			−0.00100999	+	0.999999i	$0.500321\pi$
$270$	17.3596	−	269.441i	0.0642949	−	0.997931i
$271$			362.830i			1.33886i	0.742877	+	0.669428i	$0.233461\pi$
$271$			362.830i			1.33886i	−0.742877	+	0.669428i	$0.766539\pi$
$272$	−129.212	+	178.179i	−0.475044	+	0.655071i
$273$	80.9771	−	164.961i	0.296619	−	0.604252i
$274$	−58.8025	+	159.501i	−0.214608	+	0.582120i
$275$	72.9088	+	414.478i	0.265123	+	1.50719i
$276$	214.114	+	84.8612i	0.775776	+	0.307468i
$277$	−79.2266	+	79.2266i	−0.286016	+	0.286016i	−0.835503	−	0.549486i	$-0.814823\pi$
$277$	−79.2266	+	79.2266i	−0.286016	+	0.286016i	0.549486	+	0.835503i	$0.314823\pi$
$278$	10.5541	+	22.8801i	0.0379643	+	0.0823025i
$279$	−100.139	+	77.4197i	−0.358922	+	0.277490i
$280$	196.890	+	37.2857i	0.703177	+	0.133163i
$281$		−	318.753i		−	1.13435i	−0.823597	−	0.567176i	$-0.808036\pi$
$281$		−	318.753i		−	1.13435i	0.823597	−	0.567176i	$-0.191964\pi$
$282$	103.165	+	108.270i	0.365833	+	0.383935i
$283$	223.036	−	223.036i	0.788112	−	0.788112i	−0.193072	−	0.981185i	$-0.561845\pi$
$283$	223.036	−	223.036i	0.788112	−	0.788112i	0.981185	+	0.193072i	$0.0618451\pi$
$284$	95.2057	−	111.572i	0.335231	−	0.392861i
$285$	65.6387	−	29.0082i	0.230311	−	0.101783i
$286$	142.395	−	386.245i	0.497885	−	1.35051i
$287$	−21.5559	+	21.5559i	−0.0751076	+	0.0751076i
$288$	−273.153	−	91.2771i	−0.948447	−	0.316934i
$289$		−	99.7672i		−	0.345215i
$290$	143.504	+	39.1208i	0.494841	+	0.134899i
$291$	342.698	−	117.026i	1.17765	−	0.402150i
$292$	71.5054	−	5.65974i	0.244881	−	0.0193827i
$293$	75.3066	−	75.3066i	0.257019	−	0.257019i	−0.566822	−	0.823841i	$-0.691827\pi$
$293$	75.3066	−	75.3066i	0.257019	−	0.257019i	0.823841	+	0.566822i	$0.191827\pi$
$294$	143.374	+	3.46146i	0.487667	+	0.0117737i
$295$	16.7409	+	14.0531i	0.0567489	+	0.0476378i
$296$	−99.8408	+	56.0015i	−0.337300	+	0.189194i
$297$	91.1009	+	445.286i	0.306737	+	1.49928i
$298$	21.7166	+	47.0794i	0.0728746	+	0.157984i
$299$		−	234.678i		−	0.784876i
$300$	−164.953	−	250.580i	−0.549844	−	0.835267i
$301$	405.511			1.34721
$302$	−363.908	+	167.862i	−1.20499	+	0.555836i
$303$	−210.084	+	427.967i	−0.693345	+	1.41243i
$304$	−12.0421	−	75.5939i	−0.0396123	−	0.248664i
$305$	−27.3981	+	32.6382i	−0.0898298	+	0.107011i
$306$	−236.189	+	74.3394i	−0.771858	+	0.242939i
$307$	−330.497	−	330.497i	−1.07654	−	1.07654i	−0.996817	−	0.0797218i	$-0.974597\pi$
$307$	−330.497	−	330.497i	−1.07654	−	1.07654i	−0.0797218	−	0.996817i	$-0.525403\pi$
$308$	−336.277	+	26.6167i	−1.09181	+	0.0864179i
$309$	−114.936	+	39.2487i	−0.371961	+	0.127018i
$310$	−36.9904	+	135.689i	−0.119324	+	0.437707i
$311$	26.5302			0.0853063			0.0426531	−	0.999090i	$-0.486419\pi$
$311$	26.5302			0.0853063			0.0426531	+	0.999090i	$0.486419\pi$
$312$	16.0873	+	293.011i	0.0515619	+	0.939138i
$313$	131.851	+	131.851i	0.421248	+	0.421248i	0.885633	−	0.464385i	$-0.153725\pi$
$313$	131.851	+	131.851i	0.421248	+	0.421248i	−0.464385	+	0.885633i	$0.653725\pi$
$314$	−371.513	−	136.964i	−1.18316	−	0.436191i
$315$	152.873	+	165.686i	0.485311	+	0.525988i
$316$	−229.614	+	269.087i	−0.726628	+	0.851542i
$317$	−66.6091	−	66.6091i	−0.210123	−	0.210123i	0.594197	−	0.804320i	$-0.297470\pi$
$317$	−66.6091	−	66.6091i	−0.210123	−	0.210123i	−0.804320	+	0.594197i	$0.797470\pi$
$318$	−94.8344	−	99.5268i	−0.298221	−	0.312977i
$319$	−250.385			−0.784907
$320$	−303.348	+	101.882i	−0.947963	+	0.318381i
$321$	113.146	−	38.6375i	0.352480	−	0.120366i
$322$	−174.622	+	80.5492i	−0.542305	+	0.250153i
$323$	−46.5363	−	46.5363i	−0.144075	−	0.144075i
$324$	−185.572	−	265.592i	−0.572752	−	0.819729i
$325$	−175.433	+	250.326i	−0.539794	+	0.770234i
$326$	−155.600	−	57.3644i	−0.477301	−	0.175965i
$327$	211.441	−	430.732i	0.646608	−	1.31722i
$328$	13.1825	−	46.8619i	0.0401906	−	0.142872i
$329$	−124.868			−0.379537
$330$	378.845	+	333.935i	1.14801	+	1.01192i
$331$			284.948i			0.860871i	0.902621	+	0.430436i	$0.141640\pi$
$331$			284.948i			0.860871i	−0.902621	+	0.430436i	$0.858360\pi$
$332$	359.428	−	28.4491i	1.08261	−	0.0856902i
$333$	−127.742	−	16.3452i	−0.383610	−	0.0490845i
$334$	−223.599	−	82.4335i	−0.669460	−	0.246807i
$335$	380.190	−	33.1839i	1.13489	−	0.0990564i
$336$	212.506	−	112.542i	0.632457	−	0.334945i
$337$	294.164	−	294.164i	0.872889	−	0.872889i	−0.119897	−	0.992786i	$-0.538256\pi$
$337$	294.164	−	294.164i	0.872889	−	0.872889i	0.992786	+	0.119897i	$0.0382564\pi$
$338$	−35.4068	+	16.3324i	−0.104754	+	0.0483206i
$339$	406.561	−	138.834i	1.19929	−	0.409539i
$340$	−159.711	+	224.021i	−0.469738	+	0.658886i
$341$		−	236.750i		−	0.694283i
$342$	39.8021	−	76.3653i	0.116380	−	0.223290i
$343$	−258.251	+	258.251i	−0.752919	+	0.752919i
$344$	−564.780	+	316.789i	−1.64180	+	0.920899i
$345$	268.490	+	103.912i	0.778233	+	0.301193i
$346$	−135.966	−	50.1262i	−0.392966	−	0.144873i
$347$	−274.053	+	274.053i	−0.789779	+	0.789779i	−0.981458	−	0.191679i	$-0.938607\pi$
$347$	−274.053	+	274.053i	−0.789779	+	0.789779i	0.191679	+	0.981458i	$0.438607\pi$
$348$	163.834	−	70.8287i	0.470787	−	0.203531i
$349$			129.175i			0.370128i	0.982726	+	0.185064i	$0.0592492\pi$
$349$			129.175i			0.370128i	−0.982726	+	0.185064i	$0.940751\pi$
$350$	246.480	+	44.6182i	0.704229	+	0.127481i
$351$	−181.912	+	275.493i	−0.518269	+	0.784880i
$352$	447.560	−	299.773i	1.27148	−	0.851629i
$353$	−381.746	+	381.746i	−1.08143	+	1.08143i	−0.0850569	+	0.996376i	$0.527107\pi$
$353$	−381.746	+	381.746i	−1.08143	+	1.08143i	−0.996376	+	0.0850569i	$0.972893\pi$
$354$	26.2213	+	0.633058i	0.0740716	+	0.00178830i
$355$	117.877	−	140.422i	0.332048	−	0.395555i
$356$	298.646	−	349.986i	0.838894	−	0.983108i
$357$	91.1033	−	185.589i	0.255191	−	0.519858i
$358$	49.4480	−	22.8092i	0.138123	−	0.0637129i
$359$			209.720i			0.584178i	0.956391	+	0.292089i	$0.0943503\pi$
$359$			209.720i			0.584178i	−0.956391	+	0.292089i	$0.905650\pi$
$360$	−342.351	−	111.336i	−0.950976	−	0.309265i
$361$	−338.112			−0.936597
$362$	231.735	+	502.377i	0.640151	+	1.38778i
$363$	−437.275	−	214.652i	−1.20461	−	0.591329i
$364$	−186.385	−	159.044i	−0.512047	−	0.436934i
$365$	89.3217	−	7.79621i	0.244717	−	0.0213595i
$366$	−1.23421	+	51.1213i	−0.00337217	+	0.139676i
$367$	−4.27652	−	4.27652i	−0.0116527	−	0.0116527i	0.701256	−	0.712909i	$-0.252623\pi$
$367$	−4.27652	−	4.27652i	−0.0116527	−	0.0116527i	−0.712909	+	0.701256i	$0.752623\pi$
$368$	180.281	−	248.602i	0.489894	−	0.675550i
$369$	43.3271	−	33.4971i	0.117418	−	0.0907781i
$370$	−124.232	+	71.0073i	−0.335761	+	0.191912i
$371$	114.785			0.309393
$372$	66.9716	+	154.912i	0.180031	+	0.416431i
$373$	363.822	+	363.822i	0.975394	+	0.975394i	0.999704	−	0.0243109i	$-0.00773917\pi$
$373$	363.822	+	363.822i	0.975394	+	0.975394i	−0.0243109	+	0.999704i	$0.507739\pi$
$374$	160.202	−	434.545i	0.428347	−	1.16188i
$375$	−208.714	−	311.550i	−0.556571	−	0.830800i
$376$	173.911	−	97.5478i	0.462529	−	0.259436i
$377$	−128.600	−	128.600i	−0.341114	−	0.341114i
$378$	267.430	+	40.8015i	0.707488	+	0.107940i
$379$	732.379			1.93240			0.966199	−	0.257796i	$-0.0829962\pi$
$379$	732.379			1.93240			0.966199	+	0.257796i	$0.0829962\pi$
$380$	−15.8152	−	94.3678i	−0.0416190	−	0.248336i
$381$	−128.995	−	377.749i	−0.338570	−	0.991467i
$382$	284.835	+	617.492i	0.745641	+	1.61647i
$383$	−343.246	−	343.246i	−0.896203	−	0.896203i	0.0988948	−	0.995098i	$-0.468469\pi$
$383$	−343.246	−	343.246i	−0.896203	−	0.896203i	−0.995098	+	0.0988948i	$0.968469\pi$
$384$	−208.051	+	322.755i	−0.541800	+	0.840508i
$385$	−420.064	+	36.6642i	−1.09107	+	0.0952316i
$386$	98.7977	−	267.987i	0.255952	−	0.694267i
$387$	−722.612	−	92.4613i	−1.86721	−	0.238918i
$388$	−38.0980	−	481.332i	−0.0981907	−	1.24055i
$389$	600.575			1.54389			0.771947	−	0.635687i	$-0.219283\pi$
$389$	600.575			1.54389			0.771947	+	0.635687i	$0.219283\pi$
$390$	23.0661	+	366.089i	0.0591439	+	0.938691i
$391$		−	264.025i		−	0.675255i
$392$	51.7819	−	184.077i	0.132097	−	0.469583i
$393$	−390.889	−	191.882i	−0.994628	−	0.488250i
$394$	220.706	−	598.662i	0.560168	−	1.51945i
$395$	−284.293	+	338.666i	−0.719728	+	0.857382i
$396$	605.307	+	29.2447i	1.52855	+	0.0738503i
$397$	−295.285	+	295.285i	−0.743792	+	0.743792i	−0.973306	−	0.229513i	$-0.926287\pi$
$397$	−295.285	+	295.285i	−0.743792	+	0.743792i	0.229513	+	0.973306i	$0.426287\pi$
$398$	240.152	+	520.625i	0.603398	+	1.30810i
$399$	23.2361	+	68.0445i	0.0582357	+	0.170537i
$400$	−378.144	+	130.410i	−0.945361	+	0.326026i
$401$			300.412i			0.749157i	0.927195	+	0.374578i	$0.122213\pi$
$401$			300.412i			0.749157i	−0.927195	+	0.374578i	$0.877787\pi$
$402$	331.550	−	315.918i	0.824751	−	0.785866i
$403$	121.597	−	121.597i	0.301729	−	0.301729i
$404$	483.550	+	412.617i	1.19691	+	1.02133i
$405$	−234.638	−	330.106i	−0.579353	−	0.815077i
$406$	−51.5506	+	139.830i	−0.126972	+	0.344409i
$407$	170.326	−	170.326i	0.418492	−	0.418492i
$408$	18.0990	+	329.652i	0.0443604	+	0.807971i
$409$		−	53.8159i		−	0.131579i	−0.997834	−	0.0657896i	$-0.979043\pi$
$409$		−	53.8159i		−	0.131579i	0.997834	−	0.0657896i	$-0.0209566\pi$
$410$	16.0046	−	58.7085i	0.0390356	−	0.143191i
$411$	82.4035	+	241.310i	0.200495	+	0.587130i
$412$	12.7775	+	161.432i	0.0310134	+	0.391825i
$413$	−15.4856	+	15.4856i	−0.0374955	+	0.0374955i
$414$	329.539	−	103.721i	0.795988	−	0.250534i
$415$	448.983	−	39.1883i	1.08189	−	0.0944297i
$416$	383.837	+	75.9043i	0.922684	+	0.182462i
$417$	33.9281	+	16.6548i	0.0813623	+	0.0399397i
$418$	67.4667	+	146.261i	0.161404	+	0.349906i
$419$		−	582.593i		−	1.39044i	−0.718799	−	0.695218i	$-0.755308\pi$
$419$		−	582.593i		−	1.39044i	0.718799	−	0.695218i	$-0.244692\pi$
$420$	264.487	−	142.817i	0.629732	−	0.340041i
$421$	486.678			1.15600			0.578002	−	0.816035i	$-0.303833\pi$
$421$	486.678			1.15600			0.578002	+	0.816035i	$0.303833\pi$
$422$	−333.875	+	154.009i	−0.791173	+	0.364950i
$423$	222.511	+	28.4713i	0.526032	+	0.0673080i
$424$	−159.868	+	89.6709i	−0.377046	+	0.211488i
$425$	−197.371	+	281.630i	−0.464402	+	0.662658i
$426$	5.31006	−	219.943i	0.0124649	−	0.516299i
$427$	−30.1909	−	30.1909i	−0.0707046	−	0.0707046i
$428$	−12.5785	−	158.918i	−0.0293891	−	0.371304i
$429$	−199.547	−	584.354i	−0.465145	−	1.36213i
$430$	−702.754	+	401.675i	−1.63431	+	0.934127i
$431$	−554.639			−1.28686			−0.643432	−	0.765503i	$-0.722490\pi$
$431$	−554.639			−1.28686			−0.643432	+	0.765503i	$0.722490\pi$
$432$	−404.341	+	152.093i	−0.935975	+	0.352066i
$433$	152.907	+	152.907i	0.353135	+	0.353135i	0.861275	−	0.508140i	$-0.169667\pi$
$433$	152.907	+	152.907i	0.353135	+	0.353135i	−0.508140	+	0.861275i	$0.669667\pi$
$434$	−132.216	−	48.7433i	−0.304644	−	0.112312i
$435$	204.071	−	90.1867i	0.469128	−	0.207326i
$436$	−486.674	−	415.283i	−1.11622	−	0.952483i
$437$	64.9292	+	64.9292i	0.148579	+	0.148579i
$438$	77.8942	−	74.2217i	0.177841	−	0.169456i
$439$	−218.824			−0.498461			−0.249231	−	0.968444i	$-0.580178\pi$
$439$	−218.824			−0.498461			−0.249231	+	0.968444i	$0.580178\pi$
$440$	556.406	−	379.222i	1.26456	−	0.861869i
$441$	170.192	−	131.579i	0.385923	−	0.298365i
$442$	305.467	−	140.905i	0.691101	−	0.318789i
$443$	39.9964	+	39.9964i	0.0902853	+	0.0902853i	0.750807	−	0.660522i	$-0.229665\pi$
$443$	39.9964	+	39.9964i	0.0902853	+	0.0902853i	−0.660522	+	0.750807i	$0.729665\pi$
$444$	−63.2675	+	159.631i	−0.142494	+	0.359529i
$445$	369.763	−	440.483i	0.830928	−	0.989850i
$446$	−18.6342	−	6.86980i	−0.0417808	−	0.0154031i
$447$	69.8122	+	34.2699i	0.156180	+	0.0766665i
$448$	−75.2655	−	311.663i	−0.168003	−	0.695676i
$449$	−236.471			−0.526660			−0.263330	−	0.964706i	$-0.584821\pi$
$449$	−236.471			−0.526660			−0.263330	+	0.964706i	$0.584821\pi$
$450$	−429.049	−	135.709i	−0.953442	−	0.301576i
$451$			102.435i			0.227128i
$452$	−45.1977	−	571.030i	−0.0999949	−	1.26334i
$453$	−264.895	+	539.626i	−0.584757	+	1.19123i
$454$	97.3115	+	35.8754i	0.214343	+	0.0790208i
$455$	−234.579	−	196.917i	−0.515559	−	0.432785i
$456$	−85.5193	−	76.6174i	−0.187542	−	0.168021i
$457$	−242.806	+	242.806i	−0.531304	+	0.531304i	−0.920960	−	0.389657i	$-0.872594\pi$
$457$	−242.806	+	242.806i	−0.531304	+	0.531304i	0.389657	+	0.920960i	$0.372594\pi$
$458$	−490.575	+	226.291i	−1.07112	+	0.494085i
$459$	−204.661	+	309.943i	−0.445884	+	0.675257i
$460$	222.835	−	312.563i	0.484423	−	0.679484i
$461$			640.776i			1.38997i	0.719024	+	0.694985i	$0.244589\pi$
$461$			640.776i			1.38997i	−0.719024	+	0.694985i	$0.755411\pi$
$462$	−366.322	+	349.051i	−0.792905	+	0.755522i
$463$	−162.780	+	162.780i	−0.351577	+	0.351577i	−0.860696	−	0.509119i	$-0.829971\pi$
$463$	−162.780	+	162.780i	−0.351577	+	0.351577i	0.509119	+	0.860696i	$0.329971\pi$
$464$	−37.4391	−	235.022i	−0.0806876	−	0.506512i
$465$	85.2754	+	192.958i	0.183388	+	0.414963i
$466$	146.527	+	54.0195i	0.314436	+	0.115922i
$467$	424.962	−	424.962i	0.909984	−	0.909984i	−0.0862867	−	0.996270i	$-0.527500\pi$
$467$	424.962	−	424.962i	0.909984	−	0.909984i	0.996270	+	0.0862867i	$0.0275001\pi$
$468$	295.870	+	325.911i	0.632201	+	0.696391i
$469$			382.377i			0.815304i
$470$	216.397	−	123.686i	0.460419	−	0.263162i
$471$	−562.066	+	191.936i	−1.19335	+	0.407508i
$472$	9.47025	−	33.6653i	0.0200641	−	0.0713248i
$473$	963.503	−	963.503i	2.03700	−	2.03700i
$474$	−12.8066	+	530.453i	−0.0270182	+	1.11910i
$475$	−20.7209	−	117.796i	−0.0436230	−	0.247992i
$476$	−209.693	−	178.932i	−0.440531	−	0.375909i
$477$	−204.544	−	26.1723i	−0.428813	−	0.0548685i
$478$	83.7902	−	38.6505i	0.175293	−	0.0808588i
$479$			439.071i			0.916641i	0.888787	+	0.458321i	$0.151549\pi$
$479$			439.071i			0.916641i	−0.888787	+	0.458321i	$0.848451\pi$
$480$	−256.797	+	405.531i	−0.534995	+	0.844855i
$481$	174.962			0.363747
$482$	177.736	+	385.312i	0.368746	+	0.799403i
$483$	−127.111	+	258.941i	−0.263169	+	0.536109i
$484$	−421.591	+	494.066i	−0.871055	+	1.02080i
$485$	−52.4795	−	601.261i	−0.108205	−	1.23971i
$486$	−467.252	−	133.685i	−0.961424	−	0.275071i
$487$	−308.231	−	308.231i	−0.632918	−	0.632918i	0.315881	−	0.948799i	$-0.397700\pi$
$487$	−308.231	−	308.231i	−0.632918	−	0.632918i	−0.948799	+	0.315881i	$0.897700\pi$
$488$	65.6341	+	18.4633i	0.134496	+	0.0378345i
$489$	−235.409	+	80.3883i	−0.481409	+	0.164393i
$490$	62.8672	−	230.611i	0.128300	−	0.470635i
$491$	751.660			1.53088			0.765438	−	0.643509i	$-0.222522\pi$
$491$	751.660			1.53088			0.765438	+	0.643509i	$0.222522\pi$
$492$	−28.9765	−	67.0257i	−0.0588954	−	0.136231i
$493$	−144.681	−	144.681i	−0.293472	−	0.293472i
$494$	−40.4692	+	109.772i	−0.0819215	+	0.222211i
$495$	756.904	+	30.4448i	1.52910	+	0.0615046i
$496$	222.223	−	35.4003i	0.448031	−	0.0713715i
$497$	129.893	+	129.893i	0.261353	+	0.261353i
$498$	391.542	−	373.082i	0.786228	−	0.749160i
$499$	−304.485			−0.610191			−0.305096	−	0.952322i	$-0.598688\pi$
$499$	−304.485			−0.610191			−0.305096	+	0.952322i	$0.598688\pi$
$500$	−471.349	+	166.825i	−0.942697	+	0.333649i
$501$	−338.286	+	115.519i	−0.675221	+	0.230577i
$502$	−133.774	−	290.007i	−0.266481	−	0.577704i
$503$	230.058	+	230.058i	0.457372	+	0.457372i	0.897792	−	0.440420i	$-0.145170\pi$
$503$	230.058	+	230.058i	0.457372	+	0.457372i	−0.440420	+	0.897792i	$0.645170\pi$
$504$	140.955	−	332.018i	0.279674	−	0.658766i
$505$	608.582	+	510.874i	1.20511	+	1.01163i
$506$	−223.519	+	606.293i	−0.441738	+	1.19821i
$507$	−25.7733	+	52.5035i	−0.0508348	+	0.103557i
$508$	−530.563	+	41.9947i	−1.04442	+	0.0826667i
$509$	−98.9386			−0.194378			−0.0971892	−	0.995266i	$-0.530985\pi$
$509$	−98.9386			−0.194378			−0.0971892	+	0.995266i	$0.530985\pi$
$510$	25.9505	+	411.869i	0.0508834	+	0.807586i
$511$			89.8357i			0.175804i
$512$	348.301	+	375.274i	0.680276	+	0.732956i
$513$	−25.8912	−	126.552i	−0.0504702	−	0.246690i
$514$	−95.9665	+	260.307i	−0.186705	+	0.506435i
$515$	17.6009	+	201.654i	0.0341764	+	0.391562i
$516$	−357.892	+	903.001i	−0.693589	+	1.75000i
$517$	−296.688	+	296.688i	−0.573865	+	0.573865i
$518$	−60.0528	−	130.188i	−0.115932	−	0.251328i
$519$	−205.705	+	70.2448i	−0.396349	+	0.135346i
$520$	480.546	+	91.0029i	0.924128	+	0.175006i
$521$			485.997i			0.932816i	0.884570	+	0.466408i	$0.154452\pi$
$521$			485.997i			0.932816i	−0.884570	+	0.466408i	$0.845548\pi$
$522$	123.745	−	237.420i	0.237059	−	0.454828i
$523$	−303.922	+	303.922i	−0.581112	+	0.581112i	−0.935209	−	0.354096i	$-0.884788\pi$
$523$	−303.922	+	303.922i	−0.581112	+	0.581112i	0.354096	+	0.935209i	$0.384788\pi$
$524$	−376.868	+	441.655i	−0.719214	+	0.842854i
$525$	329.157	−	181.186i	0.626966	−	0.345115i
$526$	138.849	−	376.627i	0.263972	−	0.716021i
$527$	136.803	−	136.803i	0.259588	−	0.259588i
$528$	237.517	−	772.319i	0.449843	−	1.46273i
$529$		−	160.623i		−	0.303636i
$530$	−198.923	+	113.699i	−0.375326	+	0.214526i
$531$	31.1260	−	24.0641i	0.0586176	−	0.0453185i
$532$	95.5710	−	7.56456i	0.179645	−	0.0142191i
$533$	−52.6112	+	52.6112i	−0.0987077	+	0.0987077i
$534$	16.6569	−	689.930i	0.0311926	−	1.29200i
$535$	−17.3268	−	198.514i	−0.0323865	−	0.371054i
$536$	−298.717	−	532.560i	−0.557308	−	0.993583i
$537$	35.9941	−	73.3246i	0.0670281	−	0.136545i
$538$	0.455200	+	0.986826i	0.000846097	+	0.00183425i
$539$			402.370i			0.746512i
$540$	−503.875	+	194.191i	−0.933102	+	0.359613i
$541$	−388.275			−0.717700			−0.358850	−	0.933395i	$-0.616831\pi$
$541$	−388.275			−0.717700			−0.358850	+	0.933395i	$0.616831\pi$
$542$	658.936	−	303.952i	1.21575	−	0.560797i
$543$	744.956	+	365.689i	1.37193	+	0.673460i
$544$	431.835	+	85.3962i	0.793815	+	0.156978i
$545$	−612.514	−	514.174i	−1.12388	−	0.943439i
$546$	−367.422	−	8.87061i	−0.672934	−	0.0162465i
$547$	169.325	+	169.325i	0.309551	+	0.309551i	0.844735	−	0.535184i	$-0.179758\pi$
$547$	169.325	+	169.325i	0.309551	+	0.309551i	−0.535184	+	0.844735i	$0.679758\pi$
$548$	338.929	−	26.8267i	0.618484	−	0.0489538i
$549$	46.9156	+	60.6834i	0.0854565	+	0.110534i
$550$	691.657	−	479.629i	1.25756	−	0.872052i
$551$	71.1604			0.129148
$552$	−25.2524	−	459.943i	−0.0457472	−	0.833230i
$553$	−313.272	−	313.272i	−0.566495	−	0.566495i
$554$	210.253	+	77.5132i	0.379519	+	0.139916i
$555$	−77.4705	+	200.171i	−0.139586	+	0.360668i
$556$	32.7111	−	38.3345i	0.0588330	−	0.0689469i
$557$	−310.481	−	310.481i	−0.557417	−	0.557417i	0.371155	−	0.928571i	$-0.378962\pi$
$557$	−310.481	−	310.481i	−0.557417	−	0.557417i	−0.928571	+	0.371155i	$0.878962\pi$
$558$	224.491	+	117.006i	0.402314	+	0.209689i
$559$	989.727			1.77053
$560$	−97.2248	−	388.806i	−0.173616	−	0.694297i
$561$	−224.501	−	657.427i	−0.400179	−	1.17188i
$562$	−578.887	+	267.027i	−1.03005	+	0.475137i
$563$	−234.187	−	234.187i	−0.415962	−	0.415962i	0.467847	−	0.883809i	$-0.345030\pi$
$563$	−234.187	−	234.187i	−0.415962	−	0.415962i	−0.883809	+	0.467847i	$0.845030\pi$
$564$	110.204	−	278.058i	0.195398	−	0.493010i
$565$	−62.2592	−	713.308i	−0.110193	−	1.26249i
$566$	−591.898	−	218.212i	−1.04576	−	0.385534i
$567$	349.937	−	205.445i	0.617173	−	0.362336i
$568$	−282.383	−	79.4360i	−0.497153	−	0.139852i
$569$	386.708			0.679627			0.339813	−	0.940493i	$-0.389636\pi$
$569$	386.708			0.679627			0.339813	+	0.940493i	$0.389636\pi$
$570$	−107.669	−	94.9054i	−0.188893	−	0.166501i
$571$			556.152i			0.973996i	0.873403	+	0.486998i	$0.161908\pi$
$571$			556.152i			0.973996i	−0.873403	+	0.486998i	$0.838092\pi$
$572$	−820.747	+	64.9631i	−1.43487	+	0.113572i
$573$	915.656	+	449.483i	1.59800	+	0.784439i
$574$	57.2055	+	21.0897i	0.0996612	+	0.0367417i
$575$	275.379	−	392.940i	0.478920	−	0.683374i
$576$	63.0587	+	572.538i	0.109477	+	0.993989i
$577$	695.792	−	695.792i	1.20588	−	1.20588i	0.233530	−	0.972350i	$-0.424972\pi$
$577$	695.792	−	695.792i	1.20588	−	1.20588i	0.972350	−	0.233530i	$-0.0750277\pi$
$578$	−181.187	+	83.5775i	−0.313473	+	0.144598i
$579$	−138.451	−	405.440i	−0.239121	−	0.700242i
$580$	−49.1696	−	293.390i	−0.0847752	−	0.505844i
$581$			451.566i			0.777223i
$582$	−499.616	−	524.338i	−0.858447	−	0.900924i
$583$	272.731	−	272.731i	0.467806	−	0.467806i
$584$	−70.1805	−	125.120i	−0.120172	−	0.214246i
$585$	373.115	+	404.389i	0.637804	+	0.691263i
$586$	−199.850	−	73.6780i	−0.341042	−	0.125730i
$587$	−241.691	+	241.691i	−0.411740	+	0.411740i	−0.882344	−	0.470604i	$-0.844036\pi$
$587$	−241.691	+	241.691i	−0.411740	+	0.411740i	0.470604	+	0.882344i	$0.344036\pi$
$588$	−113.822	−	263.282i	−0.193575	−	0.447758i
$589$			67.2853i			0.114236i
$590$	11.4976	−	42.1758i	0.0194875	−	0.0714845i
$591$	−309.289	−	905.721i	−0.523331	−	1.53252i
$592$	185.343	+	134.407i	0.313080	+	0.227039i
$593$	109.471	−	109.471i	0.184605	−	0.184605i	−0.608754	−	0.793359i	$-0.708330\pi$
$593$	109.471	−	109.471i	0.184605	−	0.184605i	0.793359	+	0.608754i	$0.208330\pi$
$594$	732.366	−	538.475i	1.23294	−	0.906524i
$595$	−263.913	−	221.542i	−0.443552	−	0.372339i
$596$	67.3082	−	78.8791i	0.112933	−	0.132348i
$597$	772.015	+	378.972i	1.29316	+	0.634794i
$598$	−426.199	+	196.596i	−0.712707	+	0.328755i
$599$			527.412i			0.880487i	0.897878	+	0.440243i	$0.145108\pi$
$599$			527.412i			0.880487i	−0.897878	+	0.440243i	$0.854892\pi$
$600$	−316.893	+	509.489i	−0.528155	+	0.849148i
$601$	−133.338			−0.221861			−0.110930	−	0.993828i	$-0.535383\pi$
$601$	−133.338			−0.221861			−0.110930	+	0.993828i	$0.535383\pi$
$602$	−339.707	−	736.448i	−0.564297	−	1.22334i
$603$	87.1866	−	681.388i	0.144588	−	1.13000i
$604$	609.710	+	520.270i	1.00945	+	0.861375i
$605$	−521.984	+	621.818i	−0.862783	+	1.02780i
$606$	953.224	+	23.0135i	1.57298	+	0.0379761i
$607$	401.515	+	401.515i	0.661475	+	0.661475i	0.955728	−	0.294253i	$-0.0950707\pi$
$607$	401.515	+	401.515i	0.661475	+	0.661475i	−0.294253	+	0.955728i	$0.595071\pi$
$608$	−127.198	+	85.1967i	−0.209207	+	0.140126i
$609$	72.2410	+	211.550i	0.118622	+	0.347373i
$610$	82.2263	+	22.4158i	0.134797	+	0.0367472i
$611$	−304.763			−0.498794
$612$	332.869	+	366.666i	0.543903	+	0.599128i
$613$	−604.618	−	604.618i	−0.986326	−	0.986326i	0.0135821	−	0.999908i	$-0.495677\pi$
$613$	−604.618	−	604.618i	−0.986326	−	0.986326i	−0.999908	+	0.0135821i	$0.995677\pi$
$614$	−323.350	+	877.082i	−0.526629	+	1.42847i
$615$	−36.8960	−	83.4869i	−0.0599935	−	0.135751i
$616$	330.046	+	588.414i	0.535789	+	0.955218i
$617$	−51.5846	−	51.5846i	−0.0836055	−	0.0836055i	0.664067	−	0.747673i	$-0.268829\pi$
$617$	−51.5846	−	51.5846i	−0.0836055	−	0.0836055i	−0.747673	+	0.664067i	$0.768829\pi$
$618$	167.564	+	175.855i	0.271139	+	0.284556i
$619$	−1063.63			−1.71831			−0.859155	−	0.511716i	$-0.829010\pi$
$619$	−1063.63			−1.71831			−0.859155	+	0.511716i	$0.829010\pi$
$620$	277.413	−	46.4920i	0.447440	−	0.0749871i
$621$	285.550	−	432.444i	0.459823	−	0.696367i
$622$	−22.2251	−	48.1816i	−0.0357316	−	0.0774623i
$623$	407.454	+	407.454i	0.654020	+	0.654020i
$624$	518.660	−	274.679i	0.831186	−	0.440190i
$625$	−587.483	+	213.282i	−0.939972	+	0.341251i
$626$	128.999	−	349.908i	0.206069	−	0.558959i
$627$	216.884	+	106.466i	0.345908	+	0.169802i
$628$	62.4854	+	789.443i	0.0994990	+	1.25707i
$629$	196.841			0.312943
$630$	172.837	−	416.432i	0.274345	−	0.661003i
$631$		−	834.260i		−	1.32212i	−0.750331	−	0.661062i	$-0.770106\pi$
$631$		−	834.260i		−	1.32212i	0.750331	−	0.661062i	$-0.229894\pi$
$632$	681.043	+	191.581i	1.07760	+	0.303135i
$633$	−243.034	+	495.091i	−0.383939	+	0.782134i
$634$	−65.1686	+	176.769i	−0.102790	+	0.278815i
$635$	−662.758	+	57.8471i	−1.04371	+	0.0910978i
$636$	−101.305	+	255.605i	−0.159285	+	0.401894i
$637$	−206.661	+	206.661i	−0.324428	+	0.324428i
$638$	209.754	+	454.725i	0.328768	+	0.712735i
$639$	−201.849	−	261.083i	−0.315882	−	0.408581i
$640$	439.150	+	465.561i	0.686172	+	0.727439i
$641$		−	104.566i		−	0.163130i	−0.996668	−	0.0815648i	$-0.974008\pi$
$641$		−	104.566i		−	0.163130i	0.996668	−	0.0815648i	$-0.0259918\pi$
$642$	−164.955	−	173.117i	−0.256939	−	0.269652i
$643$	−357.160	+	357.160i	−0.555459	+	0.555459i	−0.928011	−	0.372552i	$-0.878483\pi$
$643$	−357.160	+	357.160i	−0.555459	+	0.555459i	0.372552	+	0.928011i	$0.378483\pi$
$644$	292.571	+	249.653i	0.454303	+	0.387660i
$645$	−438.235	+	1132.33i	−0.679435	+	1.75554i
$646$	−45.5299	+	123.499i	−0.0704797	+	0.191175i
$647$	−428.808	+	428.808i	−0.662764	+	0.662764i	−0.956031	−	0.293266i	$-0.905258\pi$
$647$	−428.808	+	428.808i	−0.662764	+	0.662764i	0.293266	+	0.956031i	$0.405258\pi$
$648$	−326.884	+	559.510i	−0.504450	+	0.863441i
$649$			73.5884i			0.113387i
$650$	601.582	+	108.899i	0.925511	+	0.167537i
$651$	−200.030	+	68.3070i	−0.307266	+	0.104926i
$652$	26.1706	+	330.641i	0.0401390	+	0.507118i
$653$	−216.356	+	216.356i	−0.331327	+	0.331327i	−0.853090	−	0.521763i	$-0.825274\pi$
$653$	−216.356	+	216.356i	−0.331327	+	0.331327i	0.521763	+	0.853090i	$0.325274\pi$
$654$	−959.382	−	23.1622i	−1.46694	−	0.0354162i
$655$	−466.612	+	555.855i	−0.712385	+	0.848634i
$656$	−96.1491	+	15.3166i	−0.146569	+	0.0233485i
$657$	20.4836	−	160.085i	0.0311775	−	0.243661i
$658$	104.605	+	226.772i	0.158974	+	0.344638i
$659$		−	862.678i		−	1.30907i	−0.756031	−	0.654535i	$-0.772864\pi$
$659$		−	862.678i		−	1.30907i	0.756031	−	0.654535i	$-0.227136\pi$
$660$	289.091	−	967.765i	0.438017	−	1.46631i
$661$	56.1770			0.0849879			0.0424939	−	0.999097i	$-0.486470\pi$
$661$	56.1770			0.0849879			0.0424939	+	0.999097i	$0.486470\pi$
$662$	517.494	−	238.708i	0.781714	−	0.360587i
$663$	222.355	−	452.966i	0.335377	−	0.683206i
$664$	−352.768	−	628.924i	−0.531277	−	0.947175i
$665$	119.384	−	10.4201i	0.179524	−	0.0156693i
$666$	77.3283	+	245.685i	0.116109	+	0.368896i
$667$	201.865	+	201.865i	0.302646	+	0.302646i
$668$	37.6075	+	475.135i	0.0562987	+	0.711281i
$669$	−28.1919	+	9.62707i	−0.0421404	+	0.0143902i
$670$	−378.760	−	662.663i	−0.565313	−	0.989050i
$671$	−143.468			−0.213813
$672$	−382.408	−	291.653i	−0.569059	−	0.434007i
$673$	236.472	+	236.472i	0.351371	+	0.351371i	0.860619	−	0.509249i	$-0.170077\pi$
$673$	236.472	+	236.472i	0.351371	+	0.351371i	−0.509249	+	0.860619i	$0.670077\pi$
$674$	−780.659	−	287.802i	−1.15825	−	0.427006i
$675$	−627.863	+	247.817i	−0.930167	+	0.367136i
$676$	59.3223	+	50.6203i	0.0877550	+	0.0748820i
$677$	−754.987	−	754.987i	−1.11520	−	1.11520i	−0.992437	−	0.122759i	$-0.960826\pi$
$677$	−754.987	−	754.987i	−1.11520	−	1.11520i	−0.122759	−	0.992437i	$-0.539174\pi$
$678$	−592.722	−	622.050i	−0.874221	−	0.917478i
$679$	604.720			0.890604
$680$	540.639	+	102.383i	0.795057	+	0.150563i
$681$	147.224	−	50.2744i	0.216187	−	0.0738244i
$682$	−429.962	+	198.332i	−0.630443	+	0.290809i
$683$	−848.561	−	848.561i	−1.24240	−	1.24240i	−0.959002	−	0.283401i	$-0.908537\pi$
$683$	−848.561	−	848.561i	−1.24240	−	1.24240i	−0.283401	−	0.959002i	$-0.591463\pi$
$684$	−172.030	−	8.31145i	−0.251506	−	0.0121512i
$685$	423.377	−	36.9534i	0.618069	−	0.0539466i
$686$	685.353	+	252.666i	0.999057	+	0.368318i
$687$	−357.098	+	727.455i	−0.519794	+	1.05889i
$688$	1048.45	+	760.314i	1.52391	+	1.10511i
$689$	280.154			0.406609
$690$	−36.2072	−	574.655i	−0.0524741	−	0.832833i
$691$		−	973.366i		−	1.40863i	−0.709886	−	0.704317i	$-0.751253\pi$
$691$		−	973.366i		−	1.40863i	0.709886	−	0.704317i	$-0.248747\pi$
$692$	22.8684	+	288.920i	0.0330468	+	0.417515i
$693$	−96.3306	+	752.851i	−0.139005	+	1.08637i
$694$	727.289	+	268.127i	1.04797	+	0.386350i
$695$	40.5006	−	48.2467i	0.0582743	−	0.0694197i
$696$	−265.880	−	238.204i	−0.382011	−	0.342247i
$697$	−59.1903	+	59.1903i	−0.0849215	+	0.0849215i
$698$	234.594	−	108.213i	0.336094	−	0.155033i
$699$	221.682	−	75.7008i	0.317142	−	0.108299i
$700$	−125.452	−	485.011i	−0.179217	−	0.692872i
$701$			8.02635i			0.0114499i	0.999984	+	0.00572493i	$0.00182231\pi$
$701$			8.02635i			0.0114499i	−0.999984	+	0.00572493i	$0.998178\pi$
$702$	652.715	+	99.5837i	0.929793	+	0.141857i
$703$	−48.4074	+	48.4074i	−0.0688583	+	0.0688583i
$704$	−919.350	−	561.685i	−1.30590	−	0.797848i
$705$	134.944	−	348.673i	0.191410	−	0.494572i
$706$	1013.09	+	373.490i	1.43497	+	0.529023i
$707$	−562.949	+	562.949i	−0.796250	+	0.796250i
$708$	−20.8166	−	48.1509i	−0.0294019	−	0.0680097i
$709$		−	378.225i		−	0.533463i	−0.963771	−	0.266731i	$-0.914056\pi$
$709$		−	378.225i		−	0.533463i	0.963771	−	0.266731i	$-0.0859437\pi$
$710$	−353.769	−	96.4414i	−0.498266	−	0.135833i
$711$	486.813	+	629.673i	0.684688	+	0.885615i
$712$	−885.794	−	249.179i	−1.24409	−	0.349970i
$713$	−190.872	+	190.872i	−0.267703	+	0.267703i
$714$	−413.368	−	9.97988i	−0.578947	−	0.0139774i
$715$	−1025.24	+	89.4858i	−1.43391	+	0.125155i
$716$	−82.8476	−	70.6946i	−0.115709	−	0.0987354i
$717$	60.9924	−	124.249i	0.0850660	−	0.173291i
$718$	380.872	−	175.688i	0.530463	−	0.244690i
$719$		−	901.949i		−	1.25445i	−0.778838	−	0.627225i	$-0.784191\pi$
$719$		−	901.949i		−	1.25445i	0.778838	−	0.627225i	$-0.215809\pi$
$720$	84.6000	+	715.012i	0.117500	+	0.993073i
$721$	−202.815			−0.281296
$722$	283.245	+	614.044i	0.392305	+	0.850477i
$723$	571.365	+	280.476i	0.790270	+	0.387933i
$724$	718.236	−	841.707i	0.992038	−	1.16258i
$725$	−64.4215	−	366.229i	−0.0888572	−	0.505143i
$726$	−23.5140	+	973.954i	−0.0323885	+	1.34153i
$727$	647.476	+	647.476i	0.890613	+	0.890613i	0.994581	−	0.103967i	$-0.0331537\pi$
$727$	647.476	+	647.476i	0.890613	+	0.890613i	−0.103967	+	0.994581i	$0.533154\pi$
$728$	−132.700	+	471.729i	−0.182280	+	0.647979i
$729$	−670.424	+	286.308i	−0.919649	+	0.392740i
$730$	−88.9857	−	155.686i	−0.121898	−	0.213268i
$731$	1113.49			1.52325
$732$	93.8752	−	40.5841i	0.128245	−	0.0554428i
$733$	−664.993	−	664.993i	−0.907221	−	0.907221i	0.0888262	−	0.996047i	$-0.471688\pi$
$733$	−664.993	−	664.993i	−0.907221	−	0.907221i	−0.996047	+	0.0888262i	$0.971688\pi$
$734$	−4.18404	+	11.3491i	−0.00570033	+	0.0154620i
$735$	−144.930	−	327.942i	−0.197184	−	0.446180i
$736$	−602.513	−	119.148i	−0.818631	−	0.161886i
$737$	908.537	+	908.537i	1.23275	+	1.23275i
$738$	−97.1303	−	50.6250i	−0.131613	−	0.0685975i
$739$	−605.307			−0.819090			−0.409545	−	0.912290i	$-0.634313\pi$
$739$	−605.307			−0.819090			−0.409545	+	0.912290i	$0.634313\pi$
$740$	233.028	+	166.132i	0.314903	+	0.224503i
$741$	56.7120	+	166.075i	0.0765344	+	0.224123i
$742$	−96.1580	−	208.460i	−0.129593	−	0.280944i
$743$	149.548	+	149.548i	0.201275	+	0.201275i	0.800546	−	0.599271i	$-0.204543\pi$
$743$	149.548	+	149.548i	0.201275	+	0.201275i	−0.599271	+	0.800546i	$0.704543\pi$
$744$	225.232	−	251.401i	0.302731	−	0.337904i
$745$	83.3363	−	99.2751i	0.111861	−	0.133255i
$746$	355.954	−	965.519i	0.477150	−	1.29426i
$747$	102.963	−	804.681i	0.137835	−	1.07722i
$748$	−923.382	+	73.0868i	−1.23447	+	0.0977096i
$749$	199.656			0.266564
$750$	−390.961	+	640.039i	−0.521281	+	0.853385i
$751$		−	988.027i		−	1.31562i	−0.753186	−	0.657808i	$-0.771484\pi$
$751$		−	988.027i		−	1.31562i	0.753186	−	0.657808i	$-0.228516\pi$
$752$	−322.846	−	234.121i	−0.429316	−	0.311331i
$753$	−430.041	−	211.101i	−0.571103	−	0.280347i
$754$	−125.819	+	341.282i	−0.166869	+	0.452629i
$755$	767.364	+	644.162i	1.01638	+	0.853195i
$756$	−149.934	−	519.861i	−0.198325	−	0.687646i
$757$	590.607	−	590.607i	0.780195	−	0.780195i	−0.199669	−	0.979863i	$-0.563987\pi$
$757$	590.607	−	590.607i	0.780195	−	0.780195i	0.979863	+	0.199669i	$0.0639866\pi$
$758$	−613.532	−	1330.07i	−0.809410	−	1.75471i
$759$	313.231	+	917.267i	0.412690	+	1.20852i
$760$	−158.132	+	107.776i	−0.208069	+	0.141811i
$761$		−	354.692i		−	0.466087i	−0.972466	−	0.233043i	$-0.925132\pi$
$761$		−	354.692i		−	0.466087i	0.972466	−	0.233043i	$-0.0748684\pi$
$762$	−577.967	+	550.718i	−0.758487	+	0.722727i
$763$	566.586	−	566.586i	0.742576	−	0.742576i
$764$	882.813	−	1034.58i	1.15551	−	1.35416i
$765$	419.774	+	454.958i	0.548724	+	0.594716i
$766$	−335.823	+	910.914i	−0.438411	+	1.18918i
$767$	−37.7956	+	37.7956i	−0.0492772	+	0.0492772i
$768$	760.445	+	107.461i	0.990162	+	0.139924i
$769$			262.078i			0.340804i	0.985375	+	0.170402i	$0.0545067\pi$
$769$			262.078i			0.340804i	−0.985375	+	0.170402i	$0.945493\pi$
$770$	418.484	+	732.163i	0.543485	+	0.950861i
$771$	134.484	+	393.822i	0.174428	+	0.510794i
$772$	−569.456	+	45.0732i	−0.737638	+	0.0583849i
$773$	616.984	−	616.984i	0.798168	−	0.798168i	−0.184639	−	0.982806i	$-0.559112\pi$
$773$	616.984	−	616.984i	0.798168	−	0.798168i	0.982806	+	0.184639i	$0.0591115\pi$
$774$	437.431	+	1389.79i	0.565156	+	1.79560i
$775$	346.285	−	60.9133i	0.446820	−	0.0785978i
$776$	−842.231	+	472.413i	−1.08535	+	0.608780i
$777$	−193.051	−	94.7662i	−0.248457	−	0.121964i
$778$	−503.117	−	1090.70i	−0.646679	−	1.40193i
$779$		−	29.1122i		−	0.0373713i
$780$	645.532	−	348.573i	0.827605	−	0.446888i
$781$	617.256			0.790340
$782$	−479.495	+	221.180i	−0.613165	+	0.282839i
$783$	−80.4958	−	393.450i	−0.102804	−	0.502490i
$784$	−377.681	+	60.1647i	−0.481735	+	0.0767407i
$785$	86.0727	+	986.141i	0.109647	+	1.25623i
$786$	−21.0197	+	870.637i	−0.0267426	+	1.10768i
$787$	471.258	+	471.258i	0.598803	+	0.598803i	0.939994	−	0.341191i	$-0.110830\pi$
$787$	471.258	+	471.258i	0.598803	+	0.598803i	−0.341191	+	0.939994i	$0.610830\pi$
$788$	−1272.12	+	100.690i	−1.61437	+	0.127779i
$789$	−194.578	−	569.802i	−0.246614	−	0.722183i
$790$	853.210	+	232.595i	1.08001	+	0.294424i
$791$	717.412			0.906969
$792$	−453.969	−	1123.80i	−0.573194	−	1.41893i
$793$	−73.6865	−	73.6865i	−0.0929212	−	0.0929212i
$794$	783.636	+	288.900i	0.986947	+	0.363853i
$795$	−124.048	+	320.518i	−0.156035	+	0.403168i
$796$	744.324	−	872.281i	0.935081	−	1.09583i
$797$	485.701	+	485.701i	0.609411	+	0.609411i	0.942792	−	0.333381i	$-0.108189\pi$
$797$	485.701	+	485.701i	0.609411	+	0.609411i	−0.333381	+	0.942792i	$0.608189\pi$
$798$	104.110	−	99.2015i	0.130464	−	0.124313i
$799$	−342.874			−0.429129
$800$	553.619	+	577.500i	0.692024	+	0.721875i
$801$	−633.170	−	818.979i	−0.790474	−	1.02245i
$802$	545.578	−	251.663i	0.680271	−	0.313794i
$803$	213.451	+	213.451i	0.265818	+	0.265818i
$804$	−851.486	−	337.475i	−1.05906	−	0.419745i
$805$	368.222	+	309.103i	0.457418	+	0.383979i
$806$	−322.697	−	118.967i	−0.400368	−	0.147602i
$807$	1.46333	+	0.718328i	0.00181329	+	0.000890122i
$808$	344.272	−	1223.83i	0.426079	−	1.51465i
$809$	183.688			0.227056			0.113528	−	0.993535i	$-0.463785\pi$
$809$	183.688			0.227056			0.113528	+	0.993535i	$0.463785\pi$
$810$	−402.944	+	702.664i	−0.497461	+	0.867486i
$811$			1332.68i			1.64325i	0.570027	+	0.821626i	$0.306933\pi$
$811$			1332.68i			1.64325i	−0.570027	+	0.821626i	$0.693067\pi$
$812$	297.131	−	23.5182i	0.365924	−	0.0289634i
$813$	479.651	−	977.111i	0.589977	−	1.20186i
$814$	−452.016	−	166.643i	−0.555303	−	0.204721i
$815$	36.0497	+	413.023i	0.0442327	+	0.506777i
$816$	583.519	−	309.028i	0.715097	−	0.378710i
$817$	−273.831	+	273.831i	−0.335166	+	0.335166i
$818$	−97.7350	+	45.0829i	−0.119480	+	0.0551136i
$819$	−436.147	+	337.194i	−0.532536	+	0.411715i
$820$	−120.028	+	20.1156i	−0.146375	+	0.0245313i
$821$		−	1157.86i		−	1.41030i	−0.709057	−	0.705152i	$-0.750879\pi$
$821$		−	1157.86i		−	1.41030i	0.709057	−	0.705152i	$-0.249121\pi$
$822$	369.212	−	351.805i	0.449163	−	0.427986i
$823$	420.085	−	420.085i	0.510432	−	0.510432i	−0.404227	−	0.914659i	$-0.632459\pi$
$823$	420.085	−	420.085i	0.510432	−	0.510432i	0.914659	+	0.404227i	$0.132459\pi$
$824$	282.472	−	158.441i	0.342806	−	0.192282i
$825$	351.583	−	1212.58i	0.426162	−	1.46980i
$826$	41.0961	+	15.1507i	0.0497532	+	0.0183423i
$827$	450.627	−	450.627i	0.544893	−	0.544893i	−0.380066	−	0.924959i	$-0.624099\pi$
$827$	450.627	−	450.627i	0.544893	−	0.544893i	0.924959	+	0.380066i	$0.124099\pi$
$828$	−464.431	−	511.586i	−0.560907	−	0.617858i
$829$			1059.56i			1.27812i	0.769155	+	0.639062i	$0.220677\pi$
$829$			1059.56i			1.27812i	−0.769155	+	0.639062i	$0.779323\pi$
$830$	−447.294	−	782.569i	−0.538909	−	0.942854i
$831$	318.094	−	108.624i	0.382785	−	0.130715i
$832$	−183.700	−	760.672i	−0.220793	−	0.914270i
$833$	−232.504	+	232.504i	−0.279116	+	0.279116i
$834$	1.82445	−	75.5689i	0.00218759	−	0.0906102i
$835$	51.8039	+	593.520i	0.0620406	+	0.710803i
$836$	209.105	−	245.052i	0.250126	−	0.293125i
$837$	372.024	−	76.1123i	0.444473	−	0.0909346i
$838$	−1058.05	+	488.053i	−1.26259	+	0.582402i
$839$		−	425.692i		−	0.507380i	−0.967286	−	0.253690i	$-0.918356\pi$
$839$		−	425.692i		−	0.507380i	0.967286	−	0.253690i	$-0.0816443\pi$
$840$	−480.938	−	360.694i	−0.572546	−	0.429397i
$841$	−619.762			−0.736935
$842$	−407.702	−	883.855i	−0.484207	−	1.04971i
$843$	−421.382	+	858.410i	−0.499860	+	1.01828i
$844$	559.391	+	477.333i	0.662786	+	0.565560i
$845$	74.6615	+	62.6745i	0.0883568	+	0.0741710i
$846$	−134.697	−	427.954i	−0.159216	−	0.505856i
$847$	−575.192	−	575.192i	−0.679093	−	0.679093i
$848$	296.776	+	215.216i	0.349972	+	0.253792i
$849$	−895.488	+	305.794i	−1.05476	+	0.360182i
$850$	676.810	+	122.517i	0.796247	+	0.144138i
$851$	−274.640			−0.322726
$852$	−403.887	+	174.608i	−0.474046	+	0.204939i
$853$	533.860	+	533.860i	0.625861	+	0.625861i	0.947024	−	0.321163i	$-0.104074\pi$
$853$	533.860	+	533.860i	0.625861	+	0.625861i	−0.321163	+	0.947024i	$0.604074\pi$
$854$	−29.5380	+	80.1213i	−0.0345878	+	0.0938188i
$855$	−215.115	−	8.65251i	−0.251596	−	0.0101199i
$856$	−278.073	+	155.973i	−0.324852	+	0.182212i
$857$	−575.339	−	575.339i	−0.671340	−	0.671340i	0.286685	−	0.958025i	$-0.407447\pi$
$857$	−575.339	−	575.339i	−0.671340	−	0.671340i	−0.958025	+	0.286685i	$0.907447\pi$
$858$	−894.079	+	851.925i	−1.04205	+	0.992920i
$859$	730.948			0.850929			0.425465	−	0.904975i	$-0.360111\pi$
$859$	730.948			0.850929			0.425465	+	0.904975i	$0.360111\pi$
$860$	1318.20	+	939.779i	1.53279	+	1.09277i
$861$	86.5468	−	29.5543i	0.100519	−	0.0343256i
$862$	464.635	+	1007.28i	0.539019	+	1.16854i
$863$	503.710	+	503.710i	0.583673	+	0.583673i	0.935911	−	0.352238i	$-0.114579\pi$
$863$	503.710	+	503.710i	0.583673	+	0.583673i	−0.352238	+	0.935911i	$0.614579\pi$
$864$	614.942	+	606.912i	0.711739	+	0.702444i
$865$	31.5009	+	360.908i	0.0364172	+	0.417235i
$866$	149.601	−	405.789i	0.172749	−	0.468579i
$867$	−131.889	+	268.676i	−0.152122	+	0.309891i
$868$	22.2375	+	280.950i	0.0256193	+	0.323675i
$869$	−1488.68			−1.71310
$870$	−334.743	−	295.061i	−0.384762	−	0.339151i
$871$			933.264i			1.07149i
$872$	−346.496	+	1231.74i	−0.397358	+	1.41255i
$873$	−1077.60	−	137.883i	−1.23436	−	0.157942i
$874$	63.5250	−	172.311i	0.0726831	−	0.197152i
$875$	−161.705	−	604.977i	−0.184806	−	0.691402i
$876$	−200.048	−	79.2862i	−0.228365	−	0.0905094i
$877$	−1002.77	+	1002.77i	−1.14341	+	1.14341i	−0.155586	+	0.987822i	$0.549727\pi$
$877$	−1002.77	+	1002.77i	−1.14341	+	1.14341i	−0.987822	+	0.155586i	$0.950273\pi$
$878$	183.315	+	397.407i	0.208787	+	0.452627i
$879$	−302.356	+	103.249i	−0.343977	+	0.117462i
$880$	−1154.82	−	692.804i	−1.31230	−	0.787277i
$881$			1337.17i			1.51779i	0.651213	+	0.758895i	$0.274261\pi$
$881$			1337.17i			1.51779i	−0.651213	+	0.758895i	$0.725739\pi$
$882$	−381.535	−	198.858i	−0.432579	−	0.225463i
$883$	−29.5709	+	29.5709i	−0.0334891	+	0.0334891i	−0.723653	−	0.690164i	$-0.757538\pi$
$883$	−29.5709	+	29.5709i	−0.0334891	+	0.0334891i	0.690164	+	0.723653i	$0.257538\pi$
$884$	−511.795	−	436.719i	−0.578953	−	0.494026i
$885$	−26.5059	−	59.9765i	−0.0299502	−	0.0677701i
$886$	39.1314	−	106.143i	0.0441664	−	0.119801i
$887$	815.068	−	815.068i	0.918904	−	0.918904i	−0.0780457	−	0.996950i	$-0.524868\pi$
$887$	815.068	−	815.068i	0.918904	−	0.918904i	0.996950	+	0.0780457i	$0.0248680\pi$
$888$	342.906	−	18.8267i	0.386156	−	0.0212013i
$889$		−	666.572i		−	0.749799i
$890$	−1109.72	−	302.522i	−1.24688	−	0.339913i
$891$	343.318	−	1319.60i	0.385318	−	1.48103i
$892$	3.13412	+	39.5966i	0.00351359	+	0.0443908i
$893$	84.3198	−	84.3198i	0.0944231	−	0.0944231i
$894$	3.75409	−	155.495i	0.00419920	−	0.173931i
$895$	−104.270	−	87.5291i	−0.116502	−	0.0977978i
$896$	−502.959	+	397.778i	−0.561338	+	0.443948i
$897$	−310.238	+	631.994i	−0.345861	+	0.704564i
$898$	198.097	+	429.454i	0.220598	+	0.478234i
$899$			209.190i			0.232692i
$900$	112.964	+	892.883i	0.125515	+	0.992092i
$901$	315.187			0.349819
$902$	186.031	−	85.8120i	0.206243	−	0.0951352i
$903$	−1092.05	−	536.074i	−1.20936	−	0.593659i
$904$	−999.183	+	560.449i	−1.10529	+	0.619966i
$905$	889.269	−	1059.35i	0.982618	−	1.17055i
$906$	1201.92	+	29.0178i	1.32663	+	0.0320285i
$907$	−551.789	−	551.789i	−0.608367	−	0.608367i	0.334152	−	0.942519i	$-0.391550\pi$
$907$	−551.789	−	551.789i	−0.608367	−	0.608367i	−0.942519	+	0.334152i	$0.891550\pi$
$908$	−16.3670	−	206.781i	−0.0180253	−	0.227733i
$909$	1131.52	−	874.803i	1.24480	−	0.962380i
$910$	−161.108	+	590.982i	−0.177042	+	0.649430i
$911$	−1547.30			−1.69846			−0.849231	−	0.528022i	$-0.822934\pi$
$911$	−1547.30			−1.69846			−0.849231	+	0.528022i	$0.822934\pi$
$912$	−67.5032	+	219.496i	−0.0740166	+	0.240675i
$913$	1072.93	+	1072.93i	1.17517	+	1.17517i
$914$	644.364	+	237.555i	0.704993	+	0.259907i
$915$	116.931	−	51.6761i	0.127793	−	0.0564766i
$916$	821.934	+	701.363i	0.897307	+	0.765680i
$917$	−514.175	−	514.175i	−0.560715	−	0.560715i
$918$	734.337	+	112.037i	0.799931	+	0.122044i
$919$	−1012.94			−1.10222			−0.551109	−	0.834433i	$-0.685795\pi$
$919$	−1012.94			−1.10222			−0.551109	+	0.834433i	$0.685795\pi$
$920$	−754.319	−	142.848i	−0.819912	−	0.155270i
$921$	453.130	+	1326.95i	0.491998	+	1.44077i
$922$	1163.71	−	536.794i	1.26216	−	0.582207i
$923$	317.028	+	317.028i	0.343475	+	0.343475i
$924$	940.789	+	372.869i	1.01817	+	0.403538i
$925$	292.953	+	205.307i	0.316706	+	0.221953i
$926$	431.990	+	159.260i	0.466512	+	0.171987i
$927$	361.411	+	46.2441i	0.389872	+	0.0498858i
$928$	−395.459	+	264.877i	−0.426141	+	0.285427i
$929$	1529.05			1.64591			0.822955	−	0.568106i	$-0.192324\pi$
$929$	1529.05			1.64591			0.822955	+	0.568106i	$0.192324\pi$
$930$	278.993	−	316.514i	0.299993	−	0.340338i
$931$		−	114.355i		−	0.122830i
$932$	−24.6446	−	311.361i	−0.0264427	−	0.334079i
$933$	−71.4467	−	35.0722i	−0.0765773	−	0.0375908i
$934$	−1127.78	−	415.772i	−1.20747	−	0.445152i
$935$	−1153.45	+	100.676i	−1.23364	+	0.107675i
$936$	344.029	−	810.353i	0.367552	−	0.865762i
$937$	662.561	−	662.561i	0.707109	−	0.707109i	−0.258818	−	0.965926i	$-0.583333\pi$
$937$	662.561	−	662.561i	0.707109	−	0.707109i	0.965926	+	0.258818i	$0.0833328\pi$
$938$	694.435	−	320.327i	0.740336	−	0.341500i
$939$	−180.774	−	529.380i	−0.192518	−	0.563769i
$940$	−405.908	−	289.383i	−0.431817	−	0.307854i
$941$			961.186i			1.02145i	0.859744	+	0.510726i	$0.170623\pi$
$941$			961.186i			1.02145i	−0.859744	+	0.510726i	$0.829377\pi$
$942$	819.432	+	859.978i	0.869885	+	0.912927i
$943$	82.5844	−	82.5844i	0.0875763	−	0.0875763i
$944$	−69.0730	+	11.0034i	−0.0731706	+	0.0116561i
$945$	−192.658	−	648.291i	−0.203871	−	0.686023i
$946$	−2556.97	−	942.667i	−2.70293	−	0.996476i
$947$	−1259.29	+	1259.29i	−1.32977	+	1.32977i	−0.424202	+	0.905568i	$0.639445\pi$
$947$	−1259.29	+	1259.29i	−1.32977	+	1.32977i	−0.905568	+	0.424202i	$0.860555\pi$
$948$	974.084	−	421.116i	1.02751	−	0.444215i
$949$			219.261i			0.231044i
$950$	−196.571	+	136.312i	−0.206917	+	0.143486i
$951$	91.3247	+	267.435i	0.0960302	+	0.281215i
$952$	−149.294	+	530.719i	−0.156822	+	0.557478i
$953$	62.1880	−	62.1880i	0.0652550	−	0.0652550i	−0.673726	−	0.738981i	$-0.735307\pi$
$953$	62.1880	−	62.1880i	0.0652550	−	0.0652550i	0.738981	+	0.673726i	$0.235307\pi$
$954$	123.820	+	393.397i	0.129790	+	0.412366i
$955$	1093.04	−	1302.09i	1.14454	−	1.36345i
$956$	−140.386	−	119.793i	−0.146848	−	0.125306i
$957$	674.295	+	331.002i	0.704592	+	0.345875i
$958$	797.397	−	367.821i	0.832356	−	0.383947i
$959$			425.813i			0.444018i
$960$	951.610	+	126.646i	0.991260	+	0.131923i
$961$	763.202			0.794174
$962$	−146.570	−	317.749i	−0.152360	−	0.330300i
$963$	−355.783	−	45.5240i	−0.369453	−	0.0472731i
$964$	550.871	−	645.571i	0.571443	−	0.669680i
$965$	−711.342	+	62.0877i	−0.737142	+	0.0643396i
$966$	576.746	+	13.9243i	0.597046	+	0.0144144i
$967$	1.17333	+	1.17333i	0.00121337	+	0.00121337i	0.707713	−	0.706500i	$-0.249727\pi$
$967$	1.17333	+	1.17333i	0.00121337	+	0.00121337i	−0.706500	+	0.707713i	$0.749727\pi$
$968$	1250.45	+	351.759i	1.29179	+	0.363387i
$969$	63.8038	+	186.843i	0.0658450	+	0.192821i
$970$	−1047.99	+	598.999i	−1.08040	+	0.617525i
$971$	−570.125			−0.587153			−0.293576	−	0.955936i	$-0.594846\pi$
$971$	−570.125			−0.587153			−0.293576	+	0.955936i	$0.594846\pi$
$972$	148.644	+	960.567i	0.152926	+	0.988238i
$973$	44.6290	+	44.6290i	0.0458674	+	0.0458674i
$974$	−301.565	+	817.991i	−0.309615	+	0.839827i
$975$	803.370	−	442.218i	0.823969	−	0.453557i
$976$	−21.4522	−	134.665i	−0.0219797	−	0.137977i
$977$	430.216	+	430.216i	0.440344	+	0.440344i	0.892128	−	0.451784i	$-0.149212\pi$
$977$	430.216	+	430.216i	0.440344	+	0.440344i	−0.451784	+	0.892128i	$0.649212\pi$
$978$	343.201	+	360.183i	0.350921	+	0.368285i
$979$	1936.24			1.97777
$980$	−471.478	+	79.0157i	−0.481100	+	0.0806282i
$981$	−1138.83	+	880.455i	−1.16089	+	0.897507i
$982$	−629.685	−	1365.09i	−0.641227	−	1.39011i
$983$	−876.585	−	876.585i	−0.891745	−	0.891745i	0.102942	−	0.994687i	$-0.467174\pi$
$983$	−876.585	−	876.585i	−0.891745	−	0.891745i	−0.994687	+	0.102942i	$0.967174\pi$
$984$	−97.4509	+	108.773i	−0.0990355	+	0.110542i
$985$	−1589.08	+	138.699i	−1.61328	+	0.140811i
$986$	−141.553	+	383.959i	−0.143563	+	0.389411i
$987$	336.272	+	165.071i	0.340701	+	0.167246i
$988$	233.259	−	18.4627i	0.236092	−	0.0186870i
$989$	−1553.59			−1.57086
$990$	−578.787	−	1400.12i	−0.584633	−	1.41426i
$991$			183.991i			0.185662i	0.995682	+	0.0928310i	$0.0295916\pi$
$991$			183.991i			0.185662i	−0.995682	+	0.0928310i	$0.970408\pi$
$992$	−250.453	−	373.924i	−0.252472	−	0.376939i
$993$	376.693	−	767.373i	0.379349	−	0.772783i
$994$	127.084	−	344.712i	0.127851	−	0.346793i
$995$	921.571	−	1097.83i	0.926202	−	1.10335i
$996$	−1005.56	−	398.539i	−1.00960	−	0.400139i
$997$	276.341	−	276.341i	0.277172	−	0.277172i	−0.554807	−	0.831979i	$-0.687208\pi$
$997$	276.341	−	276.341i	0.277172	−	0.277172i	0.831979	+	0.554807i	$0.187208\pi$
$998$	255.075	+	552.976i	0.255586	+	0.554084i
$999$	322.405	+	212.889i	0.322728	+	0.213102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.3.l.a.23.8	yes	40
3.2	odd	2	inner	60.3.l.a.23.13	yes	40
4.3	odd	2	inner	60.3.l.a.23.3	✓	40
5.2	odd	4	inner	60.3.l.a.47.18	yes	40
5.3	odd	4		300.3.l.g.107.3		40
5.4	even	2		300.3.l.g.143.13		40
12.11	even	2	inner	60.3.l.a.23.18	yes	40
15.2	even	4	inner	60.3.l.a.47.3	yes	40
15.8	even	4		300.3.l.g.107.18		40
15.14	odd	2		300.3.l.g.143.8		40
20.3	even	4		300.3.l.g.107.8		40
20.7	even	4	inner	60.3.l.a.47.13	yes	40
20.19	odd	2		300.3.l.g.143.18		40
60.23	odd	4		300.3.l.g.107.13		40
60.47	odd	4	inner	60.3.l.a.47.8	yes	40
60.59	even	2		300.3.l.g.143.3		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.3.l.a.23.3	✓	40	4.3	odd	2	inner
60.3.l.a.23.8	yes	40	1.1	even	1	trivial
60.3.l.a.23.13	yes	40	3.2	odd	2	inner
60.3.l.a.23.18	yes	40	12.11	even	2	inner
60.3.l.a.47.3	yes	40	15.2	even	4	inner
60.3.l.a.47.8	yes	40	60.47	odd	4	inner
60.3.l.a.47.13	yes	40	20.7	even	4	inner
60.3.l.a.47.18	yes	40	5.2	odd	4	inner
300.3.l.g.107.3		40	5.3	odd	4
300.3.l.g.107.8		40	20.3	even	4
300.3.l.g.107.13		40	60.23	odd	4
300.3.l.g.107.18		40	15.8	even	4
300.3.l.g.143.3		40	60.59	even	2
300.3.l.g.143.8		40	15.14	odd	2
300.3.l.g.143.13		40	5.4	even	2
300.3.l.g.143.18		40	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	60.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.837725 - 1.81610i) q^{2} +(-2.69303 - 1.32197i) q^{3} +(-2.59643 + 3.04278i) q^{4} +(-3.21472 + 3.82956i) q^{5} +(-0.144815 + 5.99825i) q^{6} +(-3.54241 - 3.54241i) q^{7} +(7.70110 + 2.16636i) q^{8} +(5.50478 + 7.12021i) q^{9} +(9.64792 + 2.63013i) q^{10} -16.8337 q^{11} +(11.0147 - 4.76189i) q^{12} +(-8.64592 - 8.64592i) q^{13} +(-3.46580 + 9.40093i) q^{14} +(13.7199 - 6.06335i) q^{15} +(-2.51707 - 15.8008i) q^{16} +(-9.72710 - 9.72710i) q^{17} +(8.31951 - 15.9620i) q^{18} +4.78419 q^{19} +(-3.30573 - 19.7249i) q^{20} +(4.85684 + 14.2228i) q^{21} +(14.1020 + 30.5716i) q^{22} +(13.5716 + 13.5716i) q^{23} +(-17.8754 - 16.0147i) q^{24} +(-4.33113 - 24.6220i) q^{25} +(-8.45895 + 22.9448i) q^{26} +(-5.41182 - 26.4521i) q^{27} +(19.9764 - 1.58116i) q^{28} +14.8741 q^{29} +(-22.5052 - 19.8373i) q^{30} +14.0641i q^{31} +(-26.5872 + 17.8080i) q^{32} +(45.3336 + 22.2536i) q^{33} +(-9.51674 + 25.8140i) q^{34} +(24.9537 - 2.17802i) q^{35} +(-35.9581 - 1.73727i) q^{36} +(-10.1182 + 10.1182i) q^{37} +(-4.00784 - 8.68857i) q^{38} +(11.8540 + 34.7134i) q^{39} +(-33.0531 + 22.5276i) q^{40} -6.08509i q^{41} +(21.7613 - 20.7353i) q^{42} +(-57.2366 + 57.2366i) q^{43} +(43.7075 - 51.2213i) q^{44} +(-44.9636 - 1.80856i) q^{45} +(13.2781 - 36.0167i) q^{46} +(17.6247 - 17.6247i) q^{47} +(-14.1096 + 45.8794i) q^{48} -23.9027i q^{49} +(-41.0876 + 28.4922i) q^{50} +(13.3364 + 39.0543i) q^{51} +(48.7562 - 3.85911i) q^{52} +(-16.2015 + 16.2015i) q^{53} +(-43.5060 + 31.9880i) q^{54} +(54.1156 - 64.4657i) q^{55} +(-19.6063 - 34.9546i) q^{56} +(-12.8840 - 6.32456i) q^{57} +(-12.4604 - 27.0128i) q^{58} -4.37150i q^{59} +(-17.1734 + 57.4898i) q^{60} +8.52269 q^{61} +(25.5418 - 11.7818i) q^{62} +(5.72249 - 44.7229i) q^{63} +(54.6137 + 33.3667i) q^{64} +(60.9043 - 5.31588i) q^{65} +(2.43777 - 100.973i) q^{66} +(-53.9714 - 53.9714i) q^{67} +(54.8532 - 4.34170i) q^{68} +(-18.6074 - 54.4900i) q^{69} +(-24.8599 - 43.4939i) q^{70} -36.6679 q^{71} +(26.9679 + 66.7588i) q^{72} +(-12.6800 - 12.6800i) q^{73} +(26.8519 + 9.89937i) q^{74} +(-20.8857 + 72.0332i) q^{75} +(-12.4218 + 14.5573i) q^{76} +(59.6318 + 59.6318i) q^{77} +(53.1125 - 50.6084i) q^{78} +88.4346 q^{79} +(68.6017 + 41.1558i) q^{80} +(-20.3947 + 78.3904i) q^{81} +(-11.0511 + 5.09763i) q^{82} +(-63.7372 - 63.7372i) q^{83} +(-55.8873 - 22.1502i) q^{84} +(68.5205 - 5.98063i) q^{85} +(151.896 + 55.9988i) q^{86} +(-40.0563 - 19.6631i) q^{87} +(-129.638 - 36.4679i) q^{88} -115.022 q^{89} +(34.3826 + 83.1735i) q^{90} +61.2548i q^{91} +(-76.5332 + 6.05770i) q^{92} +(18.5923 - 37.8749i) q^{93} +(-46.7728 - 17.2435i) q^{94} +(-15.3798 + 18.3214i) q^{95} +(95.1415 - 12.8098i) q^{96} +(-85.3544 + 85.3544i) q^{97} +(-43.4096 + 20.0239i) q^{98} +(-92.6658 - 119.859i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{6} - 12 q^{10} - 20 q^{12} - 8 q^{13} - 36 q^{16} - 24 q^{18} - 24 q^{21} - 76 q^{22} - 8 q^{25} - 84 q^{28} + 68 q^{30} - 40 q^{33} + 172 q^{36} - 40 q^{37} + 104 q^{40} + 236 q^{42} - 104 q^{45}+ \cdots + 72 q^{97}+O(q^{100}) \) 40 * q - 4 * q^6 - 12 * q^10 - 20 * q^12 - 8 * q^13 - 36 * q^16 - 24 * q^18 - 24 * q^21 - 76 * q^22 - 8 * q^25 - 84 * q^28 + 68 * q^30 - 40 * q^33 + 172 * q^36 - 40 * q^37 + 104 * q^40 + 236 * q^42 - 104 * q^45 + 240 * q^46 + 196 * q^48 + 304 * q^52 - 72 * q^57 + 180 * q^58 - 284 * q^60 + 48 * q^61 - 552 * q^66 - 372 * q^70 - 600 * q^72 + 104 * q^73 - 736 * q^76 - 408 * q^78 + 72 * q^81 - 720 * q^82 + 216 * q^85 - 580 * q^88 + 528 * q^90 + 368 * q^93 + 884 * q^96 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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