LMFDB - Embedded newform 60.3.l.a.23.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,3,Mod(23,60)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			23.3
Character	$\chi$	$=$	60.23
Dual form			60.3.l.a.47.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.81610 - 0.837725i) q^{2} +(2.69303 + 1.32197i) q^{3} +(2.59643 + 3.04278i) q^{4} +(-3.21472 + 3.82956i) q^{5} +(-3.78336 - 4.65685i) q^{6} +(3.54241 + 3.54241i) q^{7} +(-2.16636 - 7.70110i) q^{8} +(5.50478 + 7.12021i) q^{9} +O(q^{10})$	\(q+(-1.81610 - 0.837725i) q^{2} +(2.69303 + 1.32197i) q^{3} +(2.59643 + 3.04278i) q^{4} +(-3.21472 + 3.82956i) q^{5} +(-3.78336 - 4.65685i) q^{6} +(3.54241 + 3.54241i) q^{7} +(-2.16636 - 7.70110i) q^{8} +(5.50478 + 7.12021i) q^{9} +(9.04638 - 4.26182i) q^{10} +16.8337 q^{11} +(2.96979 + 11.6267i) 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} +(-4.03246 - 17.5425i) q^{18} -4.78419 q^{19} +(-19.9993 + 0.161503i) q^{20} +(4.85684 + 14.2228i) q^{21} +(-30.5716 - 14.1020i) q^{22} +(-13.5716 - 13.5716i) q^{23} +(4.34655 - 23.6031i) q^{24} +(-4.33113 - 24.6220i) q^{25} +(8.45895 + 22.9448i) q^{26} +(5.41182 + 26.4521i) q^{27} +(-1.58116 + 19.9764i) q^{28} +14.8741 q^{29} +(29.9961 + 0.481867i) q^{30} -14.0641i q^{31} +(17.8080 - 26.5872i) q^{32} +(45.3336 + 22.2536i) q^{33} +(9.51674 + 25.8140i) q^{34} +(-24.9537 + 2.17802i) q^{35} +(-7.37245 + 35.2370i) q^{36} +(-10.1182 + 10.1182i) q^{37} +(8.68857 + 4.00784i) q^{38} +(-11.8540 - 34.7134i) q^{39} +(36.4561 + 16.4607i) q^{40} -6.08509i q^{41} +(3.09427 - 29.8987i) 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} +(-27.6667 + 39.2244i) q^{48} -23.9027i q^{49} +(-12.7607 + 48.3442i) q^{50} +(-13.3364 - 39.0543i) q^{51} +(3.85911 - 48.7562i) q^{52} +(-16.2015 + 16.2015i) q^{53} +(12.3312 - 52.5732i) q^{54} +(-54.1156 + 64.4657i) q^{55} +(19.6063 - 34.9546i) q^{56} +(-12.8840 - 6.32456i) q^{57} +(-27.0128 - 12.4604i) q^{58} +4.37150i q^{59} +(-54.0723 - 26.0036i) q^{60} +8.52269 q^{61} +(-11.7818 + 25.5418i) q^{62} +(-5.72249 + 44.7229i) q^{63} +(-54.6137 + 33.3667i) q^{64} +(60.9043 - 5.31588i) q^{65} +(-63.6878 - 78.3919i) q^{66} +(53.9714 + 53.9714i) q^{67} +(4.34170 - 54.8532i) q^{68} +(-18.6074 - 54.4900i) q^{69} +(47.1431 + 16.9489i) q^{70} +36.6679 q^{71} +(42.9080 - 57.8178i) 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} +(-7.55214 + 72.9733i) q^{78} -88.4346 q^{79} +(-52.4184 - 60.4344i) q^{80} +(-20.3947 + 78.3904i) q^{81} +(-5.09763 + 11.0511i) q^{82} +(63.7372 + 63.7372i) q^{83} +(-30.6663 + 51.7068i) q^{84} +(68.5205 - 5.98063i) q^{85} +(-151.896 + 55.9988i) q^{86} +(40.0563 + 19.6631i) q^{87} +(-36.4679 - 129.638i) q^{88} -115.022 q^{89} +(80.1434 + 40.9517i) q^{90} -61.2548i q^{91} +(6.05770 - 76.5332i) q^{92} +(18.5923 - 37.8749i) q^{93} +(46.7728 - 17.2435i) q^{94} +(15.3798 - 18.3214i) q^{95} +(83.1047 - 48.0583i) q^{96} +(-85.3544 + 85.3544i) q^{97} +(-20.0239 + 43.4096i) q^{98} +(92.6658 + 119.859i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{6}+O(q^{10}) $ 40 * q - 4 * q^6	$ 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$	−1.81610	−	0.837725i	−0.908050	−	0.418863i
$2$	−1.81610	−	0.837725i	−0.908050	−	0.418863i
$3$	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
$6$	−3.78336	−	4.65685i	−0.630559	−	0.776141i
$7$	3.54241	+	3.54241i	0.506059	+	0.506059i	0.913314	−	0.407256i	$-0.133514\pi$
$7$	3.54241	+	3.54241i	0.506059	+	0.506059i	−0.407256	+	0.913314i	$0.633514\pi$
$8$	−2.16636	−	7.70110i	−0.270795	−	0.962637i
$9$	5.50478	+	7.12021i	0.611643	+	0.791134i
$10$	9.04638	−	4.26182i	0.904638	−	0.426182i
$11$	16.8337			1.53034			0.765168	−	0.643831i	$-0.222656\pi$
$11$	16.8337			1.53034			0.765168	+	0.643831i	$0.222656\pi$
$12$	2.96979	+	11.6267i	0.247483	+	0.968892i
$13$	−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	$0.882587\pi$
$18$	−4.03246	−	17.5425i	−0.224025	−	0.974583i
$19$	−4.78419			−0.251800			−0.125900	−	0.992043i	$-0.540182\pi$
$19$	−4.78419			−0.251800			−0.125900	+	0.992043i	$0.540182\pi$
$20$	−19.9993	+	0.161503i	−0.999967	+	0.00807515i
$21$	4.85684	+	14.2228i	0.231278	+	0.677275i
$22$	−30.5716	−	14.1020i	−1.38962	−	0.641000i
$23$	−13.5716	−	13.5716i	−0.590070	−	0.590070i	0.347580	−	0.937650i	$-0.387003\pi$
$23$	−13.5716	−	13.5716i	−0.590070	−	0.590070i	−0.937650	+	0.347580i	$0.887003\pi$
$24$	4.34655	−	23.6031i	0.181106	−	0.983464i
$25$	−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
$28$	−1.58116	+	19.9764i	−0.0564699	+	0.713444i
$29$	14.8741			0.512899			0.256449	−	0.966558i	$-0.417447\pi$
$29$	14.8741			0.512899			0.256449	+	0.966558i	$0.417447\pi$
$30$	29.9961	+	0.481867i	0.999871	+	0.0160622i
$31$		−	14.0641i		−	0.453680i	−0.973932	−	0.226840i	$-0.927161\pi$
$31$		−	14.0641i		−	0.453680i	0.973932	−	0.226840i	$-0.0728395\pi$
$32$	17.8080	−	26.5872i	0.556498	−	0.830849i
$33$	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
$36$	−7.37245	+	35.2370i	−0.204790	+	0.978806i
$37$	−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	$0.311941\pi$
$38$	8.68857	+	4.00784i	0.228647	+	0.105469i
$39$	−11.8540	−	34.7134i	−0.303950	−	0.890086i
$40$	36.4561	+	16.4607i	0.911402	+	0.411516i
$41$		−	6.08509i		−	0.148417i	−0.997243	−	0.0742084i	$-0.976357\pi$
$41$		−	6.08509i		−	0.148417i	0.997243	−	0.0742084i	$-0.0236430\pi$
$42$	3.09427	−	29.8987i	0.0736730	−	0.711873i
$43$	57.2366	−	57.2366i	1.33108	−	1.33108i	0.426683	−	0.904401i	$-0.359682\pi$
$43$	57.2366	−	57.2366i	1.33108	−	1.33108i	0.904401	−	0.426683i	$-0.140318\pi$
$44$	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	−0.869292	−	0.494299i	$-0.835425\pi$
$47$	−17.6247	+	17.6247i	−0.374993	+	0.374993i	0.494299	+	0.869292i	$0.335425\pi$
$48$	−27.6667	+	39.2244i	−0.576390	+	0.817175i
$49$		−	23.9027i		−	0.487809i
$50$	−12.7607	+	48.3442i	−0.255214	+	0.966885i
$51$	−13.3364	−	39.0543i	−0.261498	−	0.765770i
$52$	3.85911	−	48.7562i	0.0742137	−	0.937620i
$53$	−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	$0.319351\pi$
$54$	12.3312	−	52.5732i	0.228355	−	0.973578i
$55$	−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
$58$	−27.0128	−	12.4604i	−0.465738	−	0.214834i
$59$			4.37150i			0.0740931i	0.999314	+	0.0370466i	$0.0117950\pi$
$59$			4.37150i			0.0740931i	−0.999314	+	0.0370466i	$0.988205\pi$
$60$	−54.0723	−	26.0036i	−0.901205	−	0.433394i
$61$	8.52269			0.139716			0.0698582	−	0.997557i	$-0.477745\pi$
$61$	8.52269			0.139716			0.0698582	+	0.997557i	$0.477745\pi$
$62$	−11.7818	+	25.5418i	−0.190030	+	0.411964i
$63$	−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
$66$	−63.6878	−	78.3919i	−0.964967	−	1.18776i
$67$	53.9714	+	53.9714i	0.805543	+	0.805543i	0.983956	−	0.178413i	$-0.0570963\pi$
$67$	53.9714	+	53.9714i	0.805543	+	0.805543i	−0.178413	+	0.983956i	$0.557096\pi$
$68$	4.34170	−	54.8532i	0.0638485	−	0.806665i
$69$	−18.6074	−	54.4900i	−0.269673	−	0.789710i
$70$	47.1431	+	16.9489i	0.673472	+	0.242127i
$71$	36.6679			0.516449			0.258225	−	0.966085i	$-0.416863\pi$
$71$	36.6679			0.516449			0.258225	+	0.966085i	$0.416863\pi$
$72$	42.9080	−	57.8178i	0.595945	−	0.803025i
$73$	−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
$78$	−7.55214	+	72.9733i	−0.0968223	+	0.935555i
$79$	−88.4346			−1.11943			−0.559713	−	0.828687i	$-0.689088\pi$
$79$	−88.4346			−1.11943			−0.559713	+	0.828687i	$0.689088\pi$
$80$	−52.4184	−	60.4344i	−0.655230	−	0.755430i
$81$	−20.3947	+	78.3904i	−0.251786	+	0.967783i
$82$	−5.09763	+	11.0511i	−0.0621663	+	0.134770i
$83$	63.7372	+	63.7372i	0.767918	+	0.767918i	0.977740	−	0.209822i	$-0.0672884\pi$
$83$	63.7372	+	63.7372i	0.767918	+	0.767918i	−0.209822	+	0.977740i	$0.567288\pi$
$84$	−30.6663	+	51.7068i	−0.365076	+	0.615557i
$85$	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
$88$	−36.4679	−	129.638i	−0.414408	−	1.47316i
$89$	−115.022			−1.29238			−0.646190	−	0.763177i	$-0.723639\pi$
$89$	−115.022			−1.29238			−0.646190	+	0.763177i	$0.723639\pi$
$90$	80.1434	+	40.9517i	0.890482	+	0.455019i
$91$		−	61.2548i		−	0.673130i
$92$	6.05770	−	76.5332i	0.0658445	−	0.831883i
$93$	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
$96$	83.1047	−	48.0583i	0.865674	−	0.500607i
$97$	−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	$0.463766\pi$
$98$	−20.0239	+	43.4096i	−0.204325	+	0.442955i
$99$	92.6658	+	119.859i	0.936018	+	1.21070i
$100$	63.6739	−	77.1080i	0.636739	−	0.771080i
$101$		−	158.917i		−	1.57343i	−0.617313	−	0.786717i	$-0.711779\pi$
$101$		−	158.917i		−	1.57343i	0.617313	−	0.786717i	$-0.288221\pi$
$102$	−8.49654	+	82.0987i	−0.0832994	+	0.804889i
$103$	−28.6266	+	28.6266i	−0.277928	+	0.277928i	−0.832282	−	0.554353i	$-0.812966\pi$
$103$	−28.6266	+	28.6266i	−0.277928	+	0.277928i	0.554353	+	0.832282i	$0.312966\pi$
$104$	−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	−0.563050	−	0.826423i	$-0.690372\pi$
$107$	28.1808	−	28.1808i	0.263372	−	0.263372i	0.826423	+	0.563050i	$0.190372\pi$
$108$	−66.4365	+	85.1480i	−0.615153	+	0.788408i
$109$			159.944i			1.46737i	0.679489	+	0.733686i	$0.262202\pi$
$109$			159.944i			1.46737i	−0.679489	+	0.733686i	$0.737798\pi$
$110$	152.284	−	71.7421i	1.38440	−	0.652201i
$111$	−40.6245	+	13.8726i	−0.365986	+	0.124978i
$112$	−64.8893	+	47.0563i	−0.579369	+	0.420146i
$113$	−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	$0.468442\pi$
$114$	18.1003	+	22.2793i	0.158775	+	0.195432i
$115$	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
$118$	3.66211	−	7.93907i	0.0310348	−	0.0672803i
$119$		−	68.9147i		−	0.579115i
$120$	76.4167	+	92.5229i	0.636806	+	0.771024i
$121$	162.373			1.34193
$122$	−15.4781	−	7.13968i	−0.126869	−	0.0585219i
$123$	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
$126$	47.8581	−	76.4273i	0.379826	−	0.606566i
$127$	−94.0845	−	94.0845i	−0.740823	−	0.740823i	0.231914	−	0.972736i	$-0.425501\pi$
$127$	−94.0845	−	94.0845i	−0.740823	−	0.740823i	−0.972736	+	0.231914i	$0.925501\pi$
$128$	127.136	−	14.8460i	0.993251	−	0.115985i
$129$	229.805	−	78.4746i	1.78143	−	0.608330i
$130$	−115.062	−	41.3669i	−0.885089	−	0.318207i
$131$	−145.148			−1.10800			−0.554002	−	0.832515i	$-0.686900\pi$
$131$	−145.148			−1.10800			−0.554002	+	0.832515i	$0.686900\pi$
$132$	49.9925	+	195.720i	0.378731	+	1.48273i
$133$	−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	$0.850399\pi$
$138$	−11.8547	+	114.547i	−0.0859035	+	0.830051i
$139$	12.5985			0.0906366			0.0453183	−	0.998973i	$-0.485570\pi$
$139$	12.5985			0.0906366			0.0453183	+	0.998973i	$0.485570\pi$
$140$	−71.4180	−	70.2738i	−0.510129	−	0.501956i
$141$	−70.7630	+	24.1644i	−0.501865	+	0.171379i
$142$	−66.5925	−	30.7176i	−0.468961	−	0.216321i
$143$	−145.543	−	145.543i	−1.01778	−	1.01778i
$144$	−126.361	+	69.0578i	−0.877505	+	0.479568i
$145$	−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
$148$	−57.0587	−	4.51626i	−0.385531	−	0.0305153i
$149$	−25.9233			−0.173982			−0.0869911	−	0.996209i	$-0.527725\pi$
$149$	−25.9233			−0.173982			−0.0869911	+	0.996209i	$0.527725\pi$
$150$	−98.2746	+	113.323i	−0.655164	+	0.755487i
$151$			200.379i			1.32701i	0.748171	+	0.663506i	$0.230932\pi$
$151$			200.379i			1.32701i	−0.748171	+	0.663506i	$0.769068\pi$
$152$	10.3643	+	36.8435i	0.0681862	+	0.242392i
$153$	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
$156$	74.8470	−	126.200i	0.479789	−	0.808976i
$157$	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	$0.0328486\pi$
$158$	160.606	+	74.0839i	1.01649	+	0.468885i
$159$	−65.0489	+	22.2131i	−0.409113	+	0.139705i
$160$	44.5696	+	153.667i	0.278560	+	0.960419i
$161$		−	96.1524i		−	0.597220i
$162$	102.708	−	125.280i	0.634003	−	0.773331i
$163$	−58.6324	+	58.6324i	−0.359708	+	0.359708i	−0.863705	−	0.503997i	$-0.831862\pi$
$163$	−58.6324	+	58.6324i	−0.359708	+	0.359708i	0.503997	+	0.863705i	$0.331862\pi$
$164$	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	−0.912841	−	0.408316i	$-0.866116\pi$
$167$	−84.2556	+	84.2556i	−0.504524	+	0.504524i	0.408316	+	0.912841i	$0.366116\pi$
$168$	99.0092	−	68.2147i	0.589341	−	0.406040i
$169$		−	19.4961i		−	0.115361i
$170$	−129.450	−	46.5399i	−0.761471	−	0.273764i
$171$	−26.3359	−	34.0644i	−0.154011	−	0.199207i
$172$	322.770	+	25.5476i	1.87657	+	0.148533i
$173$	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	$0.182846\pi$
$174$	−56.2739	−	69.2663i	−0.323413	−	0.398082i
$175$	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
$178$	208.891	+	96.3566i	1.17354	+	0.541329i
$179$		−	27.2276i		−	0.152109i	−0.997104	−	0.0760547i	$-0.975768\pi$
$179$		−	27.2276i		−	0.152109i	0.997104	−	0.0760547i	$-0.0242324\pi$
$180$	−111.242	−	141.510i	−0.618011	−	0.786169i
$181$	−276.624			−1.52831			−0.764155	−	0.645033i	$-0.776844\pi$
$181$	−276.624			−1.52831			−0.764155	+	0.645033i	$0.776844\pi$
$182$	−51.3147	+	111.245i	−0.281949	+	0.611235i
$183$	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
$186$	−65.4943	+	53.2094i	−0.352120	+	0.286072i
$187$	−163.743	−	163.743i	−0.875630	−	0.875630i
$188$	−99.3894	−	7.86679i	−0.528667	−	0.0418446i
$189$	−74.5332	+	112.875i	−0.394356	+	0.597222i
$190$	−43.2796	+	20.3893i	−0.227787	+	0.107312i
$191$	340.010			1.78016			0.890078	−	0.455807i	$-0.150649\pi$
$191$	340.010			1.78016			0.890078	+	0.455807i	$0.150649\pi$
$192$	−191.186	+	17.6597i	−0.995761	+	0.0919779i
$193$	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	$0.449626\pi$
$198$	−67.8811	−	295.305i	−0.342834	−	1.49144i
$199$	286.672			1.44056			0.720281	−	0.693682i	$-0.244013\pi$
$199$	286.672			1.44056			0.720281	+	0.693682i	$0.244013\pi$
$200$	−180.233	+	86.6945i	−0.901167	+	0.433473i
$201$	73.9977	+	216.695i	0.368148	+	1.07808i
$202$	−133.129	+	288.609i	−0.659053	+	1.42876i
$203$	52.6900	+	52.6900i	0.259557	+	0.259557i
$204$	84.2067	−	141.982i	0.412778	−	0.695988i
$205$	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
$208$	158.375	−	114.850i	0.761416	−	0.552163i
$209$	−80.5356			−0.385338
$210$	104.552	+	107.966i	0.497865	+	0.514122i
$211$			183.842i			0.871288i	0.900119	+	0.435644i	$0.143479\pi$
$211$			183.842i			0.871288i	−0.900119	+	0.435644i	$0.856521\pi$
$212$	−91.3637	−	7.23155i	−0.430961	−	0.0341111i
$213$	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
$216$	191.986	−	98.9818i	0.888824	−	0.458249i
$217$	49.8207	−	49.8207i	0.229589	−	0.229589i
$218$	133.989	−	290.473i	0.614627	−	1.33245i
$219$	−17.3850	−	50.9103i	−0.0793836	−	0.232467i
$220$	−336.663	+	2.71869i	−1.53029	+	0.0123577i
$221$			168.199i			0.761083i
$222$	85.3995	+	8.83816i	0.384683	+	0.0398115i
$223$	−7.02165	+	7.02165i	−0.0314872	+	0.0314872i	−0.722675	−	0.691188i	$-0.757088\pi$
$223$	−7.02165	+	7.02165i	−0.0314872	+	0.0314872i	0.691188	+	0.722675i	$0.257088\pi$
$224$	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	−0.621711	−	0.783246i	$-0.713562\pi$
$227$	36.6684	−	36.6684i	0.161535	−	0.161535i	0.783246	+	0.621711i	$0.213562\pi$
$228$	−14.2081	−	55.6244i	−0.0623160	−	0.243967i
$229$		−	270.126i		−	1.17959i	−0.807554	−	0.589794i	$-0.799209\pi$
$229$		−	270.126i		−	1.17959i	0.807554	−	0.589794i	$-0.200791\pi$
$230$	−180.613	−	64.9342i	−0.785276	−	0.282322i
$231$	81.7585	+	239.422i	0.353933	+	1.03646i
$232$	−32.2226	−	114.547i	−0.138891	−	0.493735i
$233$	−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	$0.303589\pi$
$234$	−116.807	+	186.535i	−0.499174	+	0.797160i
$235$	−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
$238$	−57.7316	+	125.156i	−0.242570	+	0.525865i
$239$		−	46.1374i		−	0.193044i	−0.995331	−	0.0965218i	$-0.969228\pi$
$239$		−	46.1374i		−	0.193044i	0.995331	−	0.0965218i	$-0.0307718\pi$
$240$	−61.2716	−	232.047i	−0.255298	−	0.966862i
$241$	−212.165			−0.880351			−0.440176	−	0.897912i	$-0.645084\pi$
$241$	−212.165			−0.880351			−0.440176	+	0.897912i	$0.645084\pi$
$242$	−294.885	−	136.024i	−1.21853	−	0.562082i
$243$	−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
$246$	−28.3373	+	23.0221i	−0.115192	+	0.0935856i
$247$	41.3638	+	41.3638i	0.167465	+	0.167465i
$248$	−108.309	+	30.4679i	−0.436729	+	0.122855i
$249$	87.3872	+	255.905i	0.350953	+	1.02773i
$250$	−144.115	−	204.281i	−0.576461	−	0.817125i
$251$	−159.687			−0.636203			−0.318101	−	0.948057i	$-0.603045\pi$
$251$	−159.687			−0.636203			−0.318101	+	0.948057i	$0.603045\pi$
$252$	−150.940	+	98.7077i	−0.598969	+	0.391697i
$253$	−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	$0.836983\pi$
$258$	−483.089	−	49.9957i	−1.87244	−	0.193782i
$259$	−71.6855			−0.276778
$260$	174.309	+	171.516i	0.670420	+	0.659679i
$261$	81.8785	+	105.906i	0.313711	+	0.405772i
$262$	263.604	+	121.595i	1.00612	+	0.464101i
$263$	−141.919	−	141.919i	−0.539614	−	0.539614i	0.383802	−	0.923416i	$-0.374615\pi$
$263$	−141.919	−	141.919i	−0.539614	−	0.539614i	−0.923416	+	0.383802i	$0.874615\pi$
$264$	73.1685	−	397.328i	0.277153	−	1.50503i
$265$	−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
$268$	−24.0902	+	304.356i	−0.0898887	+	1.13566i
$269$	−0.543377			−0.00201999			−0.00100999	−	0.999999i	$-0.500321\pi$
$269$	−0.543377			−0.00201999			−0.00100999	+	0.999999i	$0.500321\pi$
$270$	161.691	+	216.231i	0.598856	+	0.800856i
$271$		−	362.830i		−	1.33886i	−0.742877	−	0.669428i	$-0.766539\pi$
$271$		−	362.830i		−	1.33886i	0.742877	−	0.669428i	$-0.233461\pi$
$272$	178.179	−	129.212i	0.655071	−	0.475044i
$273$	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
$276$	117.488	−	198.098i	0.425682	−	0.717746i
$277$	−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	$0.314823\pi$
$278$	−22.8801	−	10.5541i	−0.0823025	−	0.0379643i
$279$	100.139	−	77.4197i	0.358922	−	0.277490i
$280$	70.8321	+	187.453i	0.252972	+	0.669474i
$281$		−	318.753i		−	1.13435i	−0.823597	−	0.567176i	$-0.808036\pi$
$281$		−	318.753i		−	1.13435i	0.823597	−	0.567176i	$-0.191964\pi$
$282$	148.756	+	15.3950i	0.527503	+	0.0545922i
$283$	−223.036	+	223.036i	−0.788112	+	0.788112i	−0.981185	−	0.193072i	$-0.938155\pi$
$283$	−223.036	+	223.036i	−0.788112	+	0.788112i	0.193072	+	0.981185i	$0.438155\pi$
$284$	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
$288$	287.335	−	19.5603i	0.997691	−	0.0679176i
$289$		−	99.7672i		−	0.345215i
$290$	134.556	−	63.3905i	0.463988	−	0.218588i
$291$	−342.698	+	117.026i	−1.17765	+	0.402150i
$292$	5.65974	−	71.5054i	0.0193827	−	0.244881i
$293$	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	$0.191827\pi$
$294$	−111.311	+	90.4323i	−0.378609	+	0.307593i
$295$	−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
$298$	47.0794	+	21.7166i	0.157984	+	0.0728746i
$299$			234.678i			0.784876i
$300$	273.410	−	123.479i	0.911366	−	0.411596i
$301$	405.511			1.34721
$302$	167.862	−	363.908i	0.555836	−	1.20499i
$303$	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
$306$	−131.413	+	209.862i	−0.429456	+	0.685823i
$307$	330.497	+	330.497i	1.07654	+	1.07654i	0.996817	+	0.0797218i	$0.0254032\pi$
$307$	330.497	+	330.497i	1.07654	+	1.07654i	0.0797218	+	0.996817i	$0.474597\pi$
$308$	−26.6167	+	336.277i	−0.0864179	+	1.09181i
$309$	−114.936	+	39.2487i	−0.371961	+	0.127018i
$310$	−59.9385	−	127.229i	−0.193350	−	0.410416i
$311$	−26.5302			−0.0853063			−0.0426531	−	0.999090i	$-0.513581\pi$
$311$	−26.5302			−0.0853063			−0.0426531	+	0.999090i	$0.513581\pi$
$312$	−241.651	+	166.491i	−0.774522	+	0.533624i
$313$	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	$0.797470\pi$
$318$	136.744	+	14.1519i	0.430012	+	0.0445027i
$319$	250.385			0.784907
$320$	47.7879	−	316.412i	0.149337	−	0.988786i
$321$	113.146	−	38.6375i	0.352480	−	0.120366i
$322$	−80.5492	+	174.622i	−0.250153	+	0.542305i
$323$	46.5363	+	46.5363i	0.144075	+	0.144075i
$324$	−291.479	+	141.479i	−0.899625	+	0.436663i
$325$	−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
$328$	−46.8619	+	13.1825i	−0.142872	+	0.0401906i
$329$	−124.868			−0.379537
$330$	504.945	+	8.11159i	1.53014	+	0.0245806i
$331$		−	284.948i		−	0.860871i	−0.902621	−	0.430436i	$-0.858360\pi$
$331$		−	284.948i		−	0.860871i	0.902621	−	0.430436i	$-0.141640\pi$
$332$	−28.4491	+	359.428i	−0.0856902	+	1.08261i
$333$	−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
$336$	−236.956	+	40.9421i	−0.705225	+	0.121852i
$337$	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	$0.0382564\pi$
$338$	−16.3324	+	35.4068i	−0.0483206	+	0.104754i
$339$	−406.561	+	138.834i	−1.19929	+	0.409539i
$340$	196.107	+	192.965i	0.576784	+	0.567543i
$341$		−	236.750i		−	0.694283i
$342$	19.2921	+	83.9267i	0.0564095	+	0.245400i
$343$	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	−0.191679	−	0.981458i	$-0.561393\pi$
$347$	274.053	−	274.053i	0.789779	−	0.789779i	0.981458	+	0.191679i	$0.0613932\pi$
$348$	44.1729	+	172.936i	0.126934	+	0.496944i
$349$			129.175i			0.370128i	0.982726	+	0.185064i	$0.0592492\pi$
$349$			129.175i			0.370128i	−0.982726	+	0.185064i	$0.940751\pi$
$350$	−216.459	+	126.051i	−0.618453	+	0.360147i
$351$	181.912	−	275.493i	0.518269	−	0.784880i
$352$	299.773	−	447.560i	0.851629	−	1.27148i
$353$	−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	$0.972893\pi$
$354$	20.3574	−	16.5389i	0.0575067	−	0.0467201i
$355$	−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
$358$	−22.8092	+	49.4480i	−0.0637129	+	0.138123i
$359$		−	209.720i		−	0.584178i	−0.956391	−	0.292089i	$-0.905650\pi$
$359$		−	209.720i		−	0.584178i	0.956391	−	0.292089i	$-0.0943503\pi$
$360$	83.4797	+	350.187i	0.231888	+	0.972742i
$361$	−338.112			−0.936597
$362$	502.377	+	231.735i	1.38778	+	0.640151i
$363$	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
$366$	−32.2444	−	39.6889i	−0.0880994	−	0.108440i
$367$	4.27652	+	4.27652i	0.0116527	+	0.0116527i	0.712909	−	0.701256i	$-0.247377\pi$
$367$	4.27652	+	4.27652i	0.0116527	+	0.0116527i	−0.701256	+	0.712909i	$0.747377\pi$
$368$	248.602	−	180.281i	0.675550	−	0.489894i
$369$	43.3271	−	33.4971i	0.117418	−	0.0907781i
$370$	−48.4111	+	134.655i	−0.130841	+	0.363932i
$371$	−114.785			−0.309393
$372$	163.519	−	41.7674i	0.439567	−	0.112278i
$373$	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
$378$	229.918	−	142.554i	0.608248	−	0.377127i
$379$	−732.379			−1.93240			−0.966199	−	0.257796i	$-0.917004\pi$
$379$	−732.379			−1.93240			−0.966199	+	0.257796i	$0.917004\pi$
$380$	95.6807	−	0.772662i	0.251791	−	0.00203332i
$381$	−128.995	−	377.749i	−0.338570	−	0.991467i
$382$	−617.492	−	284.835i	−1.61647	−	0.745641i
$383$	343.246	+	343.246i	0.896203	+	0.896203i	0.995098	−	0.0988948i	$-0.0315307\pi$
$383$	343.246	+	343.246i	0.896203	+	0.896203i	−0.0988948	+	0.995098i	$0.531531\pi$
$384$	362.007	+	128.090i	0.942727	+	0.333567i
$385$	−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
$388$	−481.332	−	38.0980i	−1.24055	−	0.0981907i
$389$	600.575			1.54389			0.771947	−	0.635687i	$-0.219283\pi$
$389$	600.575			1.54389			0.771947	+	0.635687i	$0.219283\pi$
$390$	−255.178	−	263.510i	−0.654303	−	0.675668i
$391$			264.025i			0.675255i
$392$	−184.077	+	51.7819i	−0.469583	+	0.132097i
$393$	−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
$396$	−124.105	+	593.169i	−0.313398	+	1.49790i
$397$	−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	$0.426287\pi$
$398$	−520.625	−	240.152i	−1.30810	−	0.603398i
$399$	−23.2361	−	68.0445i	−0.0582357	−	0.170537i
$400$	399.948	−	6.45991i	0.999870	−	0.0161498i
$401$			300.412i			0.749157i	0.927195	+	0.374578i	$0.122213\pi$
$401$			300.412i			0.749157i	−0.927195	+	0.374578i	$0.877787\pi$
$402$	47.1436	−	455.529i	0.117273	−	1.13316i
$403$	−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
$408$	−271.869	+	187.311i	−0.666346	+	0.459094i
$409$		−	53.8159i		−	0.131579i	−0.997834	−	0.0657896i	$-0.979043\pi$
$409$		−	53.8159i		−	0.131579i	0.997834	−	0.0657896i	$-0.0209566\pi$
$410$	−25.9335	−	55.0480i	−0.0632525	−	0.134263i
$411$	−82.4035	−	241.310i	−0.200495	−	0.587130i
$412$	−161.432	−	12.7775i	−0.391825	−	0.0310134i
$413$	−15.4856	+	15.4856i	−0.0374955	+	0.0374955i
$414$	−183.353	+	292.807i	−0.442881	+	0.707263i
$415$	−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
$418$	146.261	+	67.4667i	0.349906	+	0.161404i
$419$			582.593i			1.39044i	0.718799	+	0.695218i	$0.244692\pi$
$419$			582.593i			1.39044i	−0.718799	+	0.695218i	$0.755308\pi$
$420$	−99.4307	−	283.662i	−0.236740	−	0.675385i
$421$	486.678			1.15600			0.578002	−	0.816035i	$-0.303833\pi$
$421$	486.678			1.15600			0.578002	+	0.816035i	$0.303833\pi$
$422$	154.009	−	333.875i	0.364950	−	0.791173i
$423$	−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
$426$	−138.728	−	170.757i	−0.325652	−	0.400837i
$427$	30.1909	+	30.1909i	0.0707046	+	0.0707046i
$428$	158.918	+	12.5785i	0.371304	+	0.0293891i
$429$	−199.547	−	584.354i	−0.465145	−	1.36213i
$430$	273.852	−	761.716i	0.636865	−	1.77143i
$431$	554.639			1.28686			0.643432	−	0.765503i	$-0.277510\pi$
$431$	554.639			1.28686			0.643432	+	0.765503i	$0.277510\pi$
$432$	−431.585	+	18.9292i	−0.999040	+	0.0438177i
$433$	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
$438$	−11.0759	+	107.022i	−0.0252874	+	0.244342i
$439$	218.824			0.498461			0.249231	−	0.968444i	$-0.419822\pi$
$439$	218.824			0.498461			0.249231	+	0.968444i	$0.419822\pi$
$440$	613.690	+	277.093i	1.39475	+	0.629758i
$441$	170.192	−	131.579i	0.385923	−	0.298365i
$442$	140.905	−	305.467i	0.318789	−	0.691101i
$443$	−39.9964	−	39.9964i	−0.0902853	−	0.0902853i	0.660522	−	0.750807i	$-0.270335\pi$
$443$	−39.9964	−	39.9964i	−0.0902853	−	0.0902853i	−0.750807	+	0.660522i	$0.770335\pi$
$444$	−147.690	−	87.5923i	−0.332635	−	0.197280i
$445$	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
$448$	−311.663	−	75.2655i	−0.695676	−	0.168003i
$449$	−236.471			−0.526660			−0.263330	−	0.964706i	$-0.584821\pi$
$449$	−236.471			−0.526660			−0.263330	+	0.964706i	$0.584821\pi$
$450$	−414.466	+	175.266i	−0.921035	+	0.389480i
$451$		−	102.435i		−	0.227128i
$452$	−571.030	−	45.1977i	−1.26334	−	0.0999949i
$453$	−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
$456$	−20.7947	+	112.922i	−0.0456025	+	0.247636i
$457$	−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	$0.372594\pi$
$458$	−226.291	+	490.575i	−0.494085	+	1.07112i
$459$	204.661	−	309.943i	0.445884	−	0.675257i
$460$	273.615	+	269.231i	0.594815	+	0.585286i
$461$			640.776i			1.38997i	0.719024	+	0.694985i	$0.244589\pi$
$461$			640.776i			1.38997i	−0.719024	+	0.694985i	$0.755411\pi$
$462$	52.0879	−	503.305i	0.112744	−	1.08940i
$463$	162.780	−	162.780i	0.351577	−	0.351577i	−0.509119	−	0.860696i	$-0.670029\pi$
$463$	162.780	−	162.780i	0.351577	−	0.351577i	0.860696	+	0.509119i	$0.170029\pi$
$464$	−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	−0.996270	−	0.0862867i	$-0.972500\pi$
$467$	−424.962	+	424.962i	−0.909984	+	0.909984i	0.0862867	+	0.996270i	$0.472500\pi$
$468$	368.398	−	240.915i	0.787175	−	0.514775i
$469$			382.377i			0.815304i
$470$	−84.3263	+	234.553i	−0.179418	+	0.499048i
$471$	562.066	−	191.936i	1.19335	−	0.407508i
$472$	33.6653	−	9.47025i	0.0713248	−	0.0200641i
$473$	963.503	−	963.503i	2.03700	−	2.03700i
$474$	334.579	+	411.826i	0.705864	+	0.868832i
$475$	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
$478$	−38.6505	+	83.7902i	−0.0808588	+	0.175293i
$479$		−	439.071i		−	0.916641i	−0.888787	−	0.458321i	$-0.848451\pi$
$479$		−	439.071i		−	0.916641i	0.888787	−	0.458321i	$-0.151549\pi$
$480$	−83.1162	+	472.749i	−0.173159	+	0.984894i
$481$	174.962			0.363747
$482$	385.312	+	177.736i	0.799403	+	0.368746i
$483$	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
$486$	442.213	−	201.604i	0.909902	−	0.414823i
$487$	308.231	+	308.231i	0.632918	+	0.632918i	0.948799	−	0.315881i	$-0.102300\pi$
$487$	308.231	+	308.231i	0.632918	+	0.632918i	−0.315881	+	0.948799i	$0.602300\pi$
$488$	−18.4633	−	65.6341i	−0.0378345	−	0.134496i
$489$	−235.409	+	80.3883i	−0.481409	+	0.164393i
$490$	−101.869	−	216.233i	−0.207895	−	0.441291i
$491$	−751.660			−1.53088			−0.765438	−	0.643509i	$-0.777478\pi$
$491$	−751.660			−1.53088			−0.765438	+	0.643509i	$0.777478\pi$
$492$	70.7496	−	18.0714i	0.143800	−	0.0367306i
$493$	−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
$498$	55.6739	−	537.955i	0.111795	−	1.08023i
$499$	304.485			0.610191			0.305096	−	0.952322i	$-0.401312\pi$
$499$	304.485			0.610191			0.305096	+	0.952322i	$0.401312\pi$
$500$	90.5962	+	491.724i	0.181192	+	0.983448i
$501$	−338.286	+	115.519i	−0.675221	+	0.230577i
$502$	290.007	+	133.774i	0.577704	+	0.266481i
$503$	−230.058	−	230.058i	−0.457372	−	0.457372i	0.440420	−	0.897792i	$-0.354830\pi$
$503$	−230.058	−	230.058i	−0.457372	−	0.457372i	−0.897792	+	0.440420i	$0.854830\pi$
$504$	356.812	−	52.8166i	0.707961	−	0.104795i
$505$	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
$508$	41.9947	−	530.563i	0.0826667	−	1.04442i
$509$	−98.9386			−0.194378			−0.0971892	−	0.995266i	$-0.530985\pi$
$509$	−98.9386			−0.194378			−0.0971892	+	0.995266i	$0.530985\pi$
$510$	−287.088	−	296.462i	−0.562918	−	0.581299i
$511$		−	89.8357i		−	0.175804i
$512$	375.274	+	348.301i	0.732956	+	0.680276i
$513$	−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
$516$	835.454	+	495.493i	1.61910	+	0.960257i
$517$	−296.688	+	296.688i	−0.573865	+	0.573865i
$518$	130.188	+	60.0528i	0.251328	+	0.115932i
$519$	205.705	−	70.2448i	0.396349	−	0.135346i
$520$	−172.879	−	457.514i	−0.332460	−	0.879835i
$521$			485.997i			0.932816i	0.884570	+	0.466408i	$0.154452\pi$
$521$			485.997i			0.932816i	−0.884570	+	0.466408i	$0.845548\pi$
$522$	−59.9791	−	260.928i	−0.114902	−	0.499863i
$523$	303.922	−	303.922i	0.581112	−	0.581112i	−0.354096	−	0.935209i	$-0.615212\pi$
$523$	303.922	−	303.922i	0.581112	−	0.581112i	0.935209	+	0.354096i	$0.115212\pi$
$524$	−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
$528$	−465.733	+	660.291i	−0.882069	+	1.25055i
$529$		−	160.623i		−	0.303636i
$530$	−77.5170	+	215.613i	−0.146259	+	0.406816i
$531$	−31.1260	+	24.0641i	−0.0586176	+	0.0453185i
$532$	7.56456	−	95.5710i	0.0142191	−	0.179645i
$533$	−52.6112	+	52.6112i	−0.0987077	+	0.0987077i
$534$	435.168	+	535.639i	0.814922	+	1.00307i
$535$	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
$538$	0.986826	+	0.455200i	0.00183425	+	0.000846097i
$539$		−	402.370i		−	0.746512i
$540$	−112.505	−	528.150i	−0.208343	−	0.978056i
$541$	−388.275			−0.717700			−0.358850	−	0.933395i	$-0.616831\pi$
$541$	−388.275			−0.717700			−0.358850	+	0.933395i	$0.616831\pi$
$542$	−303.952	+	658.936i	−0.560797	+	1.21575i
$543$	−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
$546$	−285.254	+	231.749i	−0.522444	+	0.424448i
$547$	−169.325	−	169.325i	−0.309551	−	0.309551i	0.535184	−	0.844735i	$-0.320242\pi$
$547$	−169.325	−	169.325i	−0.309551	−	0.309551i	−0.844735	+	0.535184i	$0.820242\pi$
$548$	26.8267	−	338.929i	0.0489538	−	0.618484i
$549$	46.9156	+	60.6834i	0.0854565	+	0.110534i
$550$	−214.809	+	813.812i	−0.390563	+	1.47966i
$551$	−71.1604			−0.129148
$552$	−379.322	+	261.343i	−0.687177	+	0.473447i
$553$	−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	$0.878962\pi$
$558$	−246.719	+	56.7128i	−0.442149	+	0.101636i
$559$	−989.727			−1.77053
$560$	28.3959	−	399.771i	0.0507069	−	0.713876i
$561$	−224.501	−	657.427i	−0.400179	−	1.17188i
$562$	−267.027	+	578.887i	−0.475137	+	1.03005i
$563$	234.187	+	234.187i	0.415962	+	0.415962i	0.883809	−	0.467847i	$-0.154970\pi$
$563$	234.187	+	234.187i	0.415962	+	0.415962i	−0.467847	+	0.883809i	$0.654970\pi$
$564$	−257.259	−	152.575i	−0.456132	−	0.270524i
$565$	−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
$568$	−79.4360	−	282.383i	−0.139852	−	0.497153i
$569$	386.708			0.679627			0.339813	−	0.940493i	$-0.389636\pi$
$569$	386.708			0.679627			0.339813	+	0.940493i	$0.389636\pi$
$570$	−143.507	−	2.30534i	−0.251767	−	0.00404446i
$571$		−	556.152i		−	0.973996i	−0.873403	−	0.486998i	$-0.838092\pi$
$571$		−	556.152i		−	0.973996i	0.873403	−	0.486998i	$-0.161908\pi$
$572$	64.9631	−	820.747i	0.113572	−	1.43487i
$573$	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
$576$	−538.215	−	205.184i	−0.934401	−	0.356223i
$577$	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	$-0.0750277\pi$
$578$	−83.5775	+	181.187i	−0.144598	+	0.313473i
$579$	138.451	+	405.440i	0.239121	+	0.700242i
$580$	−297.472	+	2.40221i	−0.512882	+	0.00414174i
$581$			451.566i			0.777223i
$582$	720.408	+	74.5563i	1.23781	+	0.128104i
$583$	−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	−0.470604	−	0.882344i	$-0.655964\pi$
$587$	241.691	−	241.691i	0.411740	−	0.411740i	0.882344	+	0.470604i	$0.155964\pi$
$588$	277.909	−	70.9859i	0.472635	−	0.120724i
$589$			67.2853i			0.114236i
$590$	18.6305	+	39.5462i	0.0315771	+	0.0670274i
$591$	309.289	+	905.721i	0.523331	+	1.53252i
$592$	−134.407	−	185.343i	−0.227039	−	0.313080i
$593$	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	$0.208330\pi$
$594$	207.579	−	885.001i	0.349459	−	1.48990i
$595$	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
$598$	196.596	−	426.199i	0.328755	−	0.712707i
$599$		−	527.412i		−	0.880487i	−0.897878	−	0.440243i	$-0.854892\pi$
$599$		−	527.412i		−	0.880487i	0.897878	−	0.440243i	$-0.145108\pi$
$600$	−599.981	−	4.79255i	−0.999968	−	0.00798759i
$601$	−133.338			−0.221861			−0.110930	−	0.993828i	$-0.535383\pi$
$601$	−133.338			−0.221861			−0.110930	+	0.993828i	$0.535383\pi$
$602$	−736.448	−	339.707i	−1.22334	−	0.564297i
$603$	−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
$606$	−740.052	+	601.239i	−1.22121	+	0.992144i
$607$	−401.515	−	401.515i	−0.661475	−	0.661475i	0.294253	−	0.955728i	$-0.404929\pi$
$607$	−401.515	−	401.515i	−0.661475	−	0.661475i	−0.955728	+	0.294253i	$0.904929\pi$
$608$	−85.1967	+	127.198i	−0.140126	+	0.209207i
$609$	72.2410	+	211.550i	0.118622	+	0.347373i
$610$	77.0995	−	36.3222i	0.126393	−	0.0595445i
$611$	304.763			0.498794
$612$	414.466	−	271.041i	0.677233	−	0.442878i
$613$	−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	$0.768829\pi$
$618$	241.615	+	25.0051i	0.390962	+	0.0404614i
$619$	1063.63			1.71831			0.859155	−	0.511716i	$-0.170990\pi$
$619$	1063.63			1.71831			0.859155	+	0.511716i	$0.170990\pi$
$620$	2.27139	+	281.272i	0.00366354	+	0.453665i
$621$	285.550	−	432.444i	0.459823	−	0.696367i
$622$	48.1816	+	22.2251i	0.0774623	+	0.0357316i
$623$	−407.454	−	407.454i	−0.654020	−	0.654020i
$624$	578.335	−	99.9270i	0.926819	−	0.160139i
$625$	−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
$628$	789.443	+	62.4854i	1.25707	+	0.0994990i
$629$	196.841			0.312943
$630$	138.833	+	428.968i	0.220370	+	0.680902i
$631$			834.260i			1.32212i	0.750331	+	0.661062i	$0.229894\pi$
$631$			834.260i			1.32212i	−0.750331	+	0.661062i	$0.770106\pi$
$632$	191.581	+	681.043i	0.303135	+	1.07760i
$633$	−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
$636$	−236.485	−	140.255i	−0.371832	−	0.220527i
$637$	−206.661	+	206.661i	−0.324428	+	0.324428i
$638$	−454.725	−	209.754i	−0.712735	−	0.328768i
$639$	201.849	+	261.083i	0.315882	+	0.408581i
$640$	−351.854	+	534.602i	−0.549771	+	0.835315i
$641$		−	104.566i		−	0.163130i	−0.996668	−	0.0815648i	$-0.974008\pi$
$641$		−	104.566i		−	0.163130i	0.996668	−	0.0815648i	$-0.0259918\pi$
$642$	−237.852	−	24.6157i	−0.370486	−	0.0383423i
$643$	357.160	−	357.160i	0.555459	−	0.555459i	−0.372552	−	0.928011i	$-0.621517\pi$
$643$	357.160	−	357.160i	0.555459	−	0.555459i	0.928011	+	0.372552i	$0.121517\pi$
$644$	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	−0.293266	−	0.956031i	$-0.594742\pi$
$647$	428.808	−	428.808i	0.662764	−	0.662764i	0.956031	+	0.293266i	$0.0947423\pi$
$648$	647.874	−	12.7606i	0.999806	−	0.0196923i
$649$			73.5884i			0.113387i
$650$	528.308	−	307.653i	0.812782	−	0.473312i
$651$	200.030	−	68.3070i	0.307266	−	0.104926i
$652$	−330.641	−	26.1706i	−0.507118	−	0.0401390i
$653$	−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	$0.325274\pi$
$654$	744.833	−	605.123i	1.13889	−	0.925265i
$655$	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
$658$	226.772	+	104.605i	0.344638	+	0.158974i
$659$			862.678i			1.30907i	0.756031	+	0.654535i	$0.227136\pi$
$659$			862.678i			1.30907i	−0.756031	+	0.654535i	$0.772864\pi$
$660$	−910.236	−	437.737i	−1.37915	−	0.663238i
$661$	56.1770			0.0849879			0.0424939	−	0.999097i	$-0.486470\pi$
$661$	56.1770			0.0849879			0.0424939	+	0.999097i	$0.486470\pi$
$662$	−238.708	+	517.494i	−0.360587	+	0.781714i
$663$	−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
$666$	218.299	+	136.697i	0.327777	+	0.205251i
$667$	−201.865	−	201.865i	−0.302646	−	0.302646i
$668$	−475.135	−	37.6075i	−0.711281	−	0.0562987i
$669$	−28.1919	+	9.62707i	−0.0421404	+	0.0143902i
$670$	718.261	+	258.229i	1.07203	+	0.385417i
$671$	143.468			0.213813
$672$	464.633	+	124.149i	0.691419	+	0.184745i
$673$	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	$-0.539174\pi$
$678$	854.659	+	88.4502i	1.26056	+	0.130458i
$679$	−604.720			−0.890604
$680$	−194.498	−	514.726i	−0.286026	−	0.756950i
$681$	147.224	−	50.2744i	0.216187	−	0.0738244i
$682$	−198.332	+	429.962i	−0.290809	+	0.630443i
$683$	848.561	+	848.561i	1.24240	+	1.24240i	0.959002	+	0.283401i	$0.0914626\pi$
$683$	848.561	+	848.561i	1.24240	+	1.24240i	0.283401	+	0.959002i	$0.408537\pi$
$684$	35.2712	−	168.581i	0.0515661	−	0.246463i
$685$	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
$688$	760.314	+	1048.45i	1.10511	+	1.52391i
$689$	280.154			0.406609
$690$	−400.556	−	413.635i	−0.580516	−	0.599471i
$691$			973.366i			1.40863i	0.709886	+	0.704317i	$0.248747\pi$
$691$			973.366i			1.40863i	−0.709886	+	0.704317i	$0.751253\pi$
$692$	288.920	+	22.8684i	0.417515	+	0.0330468i
$693$	−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
$696$	64.6509	−	351.074i	0.0928892	−	0.504417i
$697$	−59.1903	+	59.1903i	−0.0849215	+	0.0849215i
$698$	108.213	−	234.594i	0.155033	−	0.336094i
$699$	−221.682	+	75.7008i	−0.317142	+	0.108299i
$700$	498.707	−	47.5892i	0.712438	−	0.0679845i
$701$			8.02635i			0.0114499i	0.999984	+	0.00572493i	$0.00182231\pi$
$701$			8.02635i			0.0114499i	−0.999984	+	0.00572493i	$0.998178\pi$
$702$	−561.158	+	347.930i	−0.799371	+	0.495626i
$703$	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
$708$	−50.8261	+	12.9824i	−0.0717883	+	0.0183368i
$709$		−	378.225i		−	0.533463i	−0.963771	−	0.266731i	$-0.914056\pi$
$709$		−	378.225i		−	0.533463i	0.963771	−	0.266731i	$-0.0859437\pi$
$710$	331.712	−	156.272i	0.467199	−	0.220101i
$711$	−486.813	−	629.673i	−0.684688	−	0.885615i
$712$	249.179	+	885.794i	0.349970	+	1.24409i
$713$	−190.872	+	190.872i	−0.267703	+	0.267703i
$714$	−320.925	+	260.729i	−0.449475	+	0.365166i
$715$	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
$718$	−175.688	+	380.872i	−0.244690	+	0.530463i
$719$			901.949i			1.25445i	0.778838	+	0.627225i	$0.215809\pi$
$719$			901.949i			1.25445i	−0.778838	+	0.627225i	$0.784191\pi$
$720$	141.753	−	705.908i	0.196880	−	0.980428i
$721$	−202.815			−0.281296
$722$	614.044	+	283.245i	0.850477	+	0.392305i
$723$	−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
$726$	−614.315	−	756.146i	−0.846163	−	1.04152i
$727$	−647.476	−	647.476i	−0.890613	−	0.890613i	0.103967	−	0.994581i	$-0.466846\pi$
$727$	−647.476	−	647.476i	−0.890613	−	0.890613i	−0.994581	+	0.103967i	$0.966846\pi$
$728$	−471.729	+	132.700i	−0.647979	+	0.182280i
$729$	−670.424	+	286.308i	−0.919649	+	0.392740i
$730$	−168.748	−	60.6683i	−0.231162	−	0.0831073i
$731$	−1113.49			−1.52325
$732$	25.3106	+	99.0909i	0.0345773	+	0.135370i
$733$	−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
$738$	−106.748	+	24.5379i	−0.144645	+	0.0332492i
$739$	605.307			0.819090			0.409545	−	0.912290i	$-0.365687\pi$
$739$	605.307			0.819090			0.409545	+	0.912290i	$0.365687\pi$
$740$	200.723	−	203.991i	0.271247	−	0.275664i
$741$	56.7120	+	166.075i	0.0765344	+	0.224123i
$742$	208.460	+	96.1580i	0.280944	+	0.129593i
$743$	−149.548	−	149.548i	−0.201275	−	0.201275i	0.599271	−	0.800546i	$-0.295457\pi$
$743$	−149.548	−	149.548i	−0.201275	−	0.201275i	−0.800546	+	0.599271i	$0.795457\pi$
$744$	−331.956	−	61.1303i	−0.446178	−	0.0821643i
$745$	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
$748$	73.0868	−	923.382i	0.0977096	−	1.23447i
$749$	199.656			0.266564
$750$	−118.052	−	740.651i	−0.157403	−	0.987534i
$751$			988.027i			1.31562i	0.753186	+	0.657808i	$0.228516\pi$
$751$			988.027i			1.31562i	−0.753186	+	0.657808i	$0.771484\pi$
$752$	−234.121	−	322.846i	−0.311331	−	0.429316i
$753$	−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
$756$	−536.975	+	66.2839i	−0.710284	+	0.0876771i
$757$	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	$0.0639866\pi$
$758$	1330.07	+	613.532i	1.75471	+	0.809410i
$759$	−313.231	−	917.267i	−0.412690	−	1.20852i
$760$	−174.413	−	78.7509i	−0.229491	−	0.103620i
$761$		−	354.692i		−	0.466087i	−0.972466	−	0.233043i	$-0.925132\pi$
$761$		−	354.692i		−	0.466087i	0.972466	−	0.233043i	$-0.0748684\pi$
$762$	−82.1820	+	794.092i	−0.107850	+	1.04212i
$763$	−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
$768$	−550.137	−	535.886i	−0.716324	−	0.697768i
$769$			262.078i			0.340804i	0.985375	+	0.170402i	$0.0545067\pi$
$769$			262.078i			0.340804i	−0.985375	+	0.170402i	$0.945493\pi$
$770$	793.592	+	285.312i	1.03064	+	0.370535i
$771$	−134.484	−	393.822i	−0.174428	−	0.510794i
$772$	−45.0732	+	569.456i	−0.0583849	+	0.737638i
$773$	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	$0.0591115\pi$
$774$	−1234.88	−	773.269i	−1.59545	−	0.999056i
$775$	−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
$778$	−1090.70	−	503.117i	−1.40193	−	0.646679i
$779$			29.1122i			0.0373713i
$780$	242.679	+	692.330i	0.311127	+	0.887603i
$781$	617.256			0.790340
$782$	221.180	−	479.495i	0.282839	−	0.613165i
$783$	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
$786$	549.148	+	675.934i	0.698662	+	0.859967i
$787$	−471.258	−	471.258i	−0.598803	−	0.598803i	0.341191	−	0.939994i	$-0.389170\pi$
$787$	−471.258	−	471.258i	−0.598803	−	0.598803i	−0.939994	+	0.341191i	$0.889170\pi$
$788$	−100.690	+	1272.12i	−0.127779	+	1.61437i
$789$	−194.578	−	569.802i	−0.246614	−	0.722183i
$790$	−800.012	+	376.892i	−1.01267	+	0.477078i
$791$	−717.412			−0.906969
$792$	722.300	−	973.287i	0.911995	−	1.22890i
$793$	−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	$0.608189\pi$
$798$	−14.8036	+	143.041i	−0.0185508	+	0.179249i
$799$	342.874			0.429129
$800$	−731.757	−	323.315i	−0.914696	−	0.404143i
$801$	−633.170	−	818.979i	−0.790474	−	1.02245i
$802$	251.663	−	545.578i	0.313794	−	0.680271i
$803$	−213.451	−	213.451i	−0.265818	−	0.265818i
$804$	−467.226	+	787.793i	−0.581127	+	0.979842i
$805$	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
$808$	−1223.83	+	344.272i	−1.51465	+	0.426079i
$809$	183.688			0.227056			0.113528	−	0.993535i	$-0.463785\pi$
$809$	183.688			0.227056			0.113528	+	0.993535i	$0.463785\pi$
$810$	149.587	+	796.068i	0.184676	+	0.982800i
$811$		−	1332.68i		−	1.64325i	−0.570027	−	0.821626i	$-0.693067\pi$
$811$		−	1332.68i		−	1.64325i	0.570027	−	0.821626i	$-0.306933\pi$
$812$	−23.5182	+	297.131i	−0.0289634	+	0.365924i
$813$	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
$816$	650.656	−	112.423i	0.797373	−	0.137773i
$817$	−273.831	+	273.831i	−0.335166	+	0.335166i
$818$	−45.0829	+	97.7350i	−0.0551136	+	0.119480i
$819$	436.147	−	337.194i	0.532536	−	0.411715i
$820$	0.982761	+	121.698i	0.00119849	+	0.148412i
$821$		−	1157.86i		−	1.41030i	−0.709057	−	0.705152i	$-0.750879\pi$
$821$		−	1157.86i		−	1.41030i	0.709057	−	0.705152i	$-0.249121\pi$
$822$	−52.4988	+	507.275i	−0.0638672	+	0.617123i
$823$	−420.085	+	420.085i	−0.510432	+	0.510432i	−0.914659	−	0.404227i	$-0.867541\pi$
$823$	−420.085	+	420.085i	−0.510432	+	0.510432i	0.404227	+	0.914659i	$0.367541\pi$
$824$	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	−0.924959	−	0.380066i	$-0.875901\pi$
$827$	−450.627	+	450.627i	−0.544893	+	0.544893i	0.380066	+	0.924959i	$0.375901\pi$
$828$	578.279	−	378.167i	0.698404	−	0.456723i
$829$			1059.56i			1.27812i	0.769155	+	0.639062i	$0.220677\pi$
$829$			1059.56i			1.27812i	−0.769155	+	0.639062i	$0.779323\pi$
$830$	848.227	+	304.954i	1.02196	+	0.367415i
$831$	−318.094	+	108.624i	−0.382785	+	0.130715i
$832$	760.672	+	183.700i	0.914270	+	0.220793i
$833$	−232.504	+	232.504i	−0.279116	+	0.279116i
$834$	−47.6646	−	58.6692i	−0.0571517	−	0.0703468i
$835$	−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
$838$	488.053	−	1058.05i	0.582402	−	1.26259i
$839$			425.692i			0.507380i	0.967286	+	0.253690i	$0.0816443\pi$
$839$			425.692i			0.507380i	−0.967286	+	0.253690i	$0.918356\pi$
$840$	−57.0546	+	598.453i	−0.0679221	+	0.712444i
$841$	−619.762			−0.736935
$842$	−883.855	−	407.702i	−1.04971	−	0.484207i
$843$	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
$846$	380.252	+	238.110i	0.449470	+	0.281454i
$847$	575.192	+	575.192i	0.679093	+	0.679093i
$848$	−215.216	−	296.776i	−0.253792	−	0.349972i
$849$	−895.488	+	305.794i	−1.05476	+	0.360182i
$850$	594.373	−	346.125i	0.699263	−	0.407205i
$851$	274.640			0.322726
$852$	108.896	+	426.327i	0.127812	+	0.500384i
$853$	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	$0.907447\pi$
$858$	−127.130	+	1228.41i	−0.148171	+	1.43171i
$859$	−730.948			−0.850929			−0.425465	−	0.904975i	$-0.639889\pi$
$859$	−730.948			−0.850929			−0.425465	+	0.904975i	$0.639889\pi$
$860$	−1135.45	+	1153.94i	−1.32029	+	1.34179i
$861$	86.5468	−	29.5543i	0.100519	−	0.0343256i
$862$	−1007.28	−	464.635i	−1.16854	−	0.539019i
$863$	−503.710	−	503.710i	−0.583673	−	0.583673i	0.352238	−	0.935911i	$-0.385421\pi$
$863$	−503.710	−	503.710i	−0.583673	−	0.583673i	−0.935911	+	0.352238i	$0.885421\pi$
$864$	799.659	+	327.172i	0.925531	+	0.378672i
$865$	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
$868$	280.950	+	22.2375i	0.323675	+	0.0256193i
$869$	−1488.68			−1.71310
$870$	446.164	+	7.16732i	0.512833	+	0.00823830i
$871$		−	933.264i		−	1.07149i
$872$	1231.74	−	346.496i	1.41255	−	0.397358i
$873$	−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
$876$	109.770	−	185.084i	0.125308	−	0.211283i
$877$	−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	$0.950273\pi$
$878$	−397.407	−	183.315i	−0.452627	−	0.208787i
$879$	302.356	−	103.249i	0.343977	−	0.117462i
$880$	−882.395	−	1017.33i	−1.00272	−	1.15606i
$881$			1337.17i			1.51779i	0.651213	+	0.758895i	$0.274261\pi$
$881$			1337.17i			1.51779i	−0.651213	+	0.758895i	$0.725739\pi$
$882$	−419.312	+	96.3865i	−0.475411	+	0.109282i
$883$	29.5709	−	29.5709i	0.0334891	−	0.0334891i	−0.690164	−	0.723653i	$-0.742462\pi$
$883$	29.5709	−	29.5709i	0.0334891	−	0.0334891i	0.723653	+	0.690164i	$0.242462\pi$
$884$	−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	−0.996950	−	0.0780457i	$-0.975132\pi$
$887$	−815.068	+	815.068i	−0.918904	+	0.918904i	0.0780457	+	0.996950i	$0.475132\pi$
$888$	194.842	+	282.800i	0.219416	+	0.318469i
$889$		−	666.572i		−	0.749799i
$890$	−1040.53	+	490.202i	−1.16914	+	0.550788i
$891$	−343.318	+	1319.60i	−0.385318	+	1.48103i
$892$	−39.5966	−	3.13412i	−0.0443908	−	0.00351359i
$893$	84.3198	−	84.3198i	0.0944231	−	0.0944231i
$894$	98.0772	+	120.721i	0.109706	+	0.135035i
$895$	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
$898$	429.454	+	198.097i	0.478234	+	0.220598i
$899$		−	209.190i		−	0.232692i
$900$	899.536	+	28.9083i	0.999484	+	0.0321203i
$901$	315.187			0.349819
$902$	−85.8120	+	186.031i	−0.0951352	+	0.206243i
$903$	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
$906$	933.134	−	758.104i	1.02995	−	0.836760i
$907$	551.789	+	551.789i	0.608367	+	0.608367i	0.942519	−	0.334152i	$-0.108450\pi$
$907$	551.789	+	551.789i	0.608367	+	0.608367i	−0.334152	+	0.942519i	$0.608450\pi$
$908$	206.781	+	16.3670i	0.227733	+	0.0180253i
$909$	1131.52	−	874.803i	1.24480	−	0.962380i
$910$	−261.057	−	554.134i	−0.286875	−	0.608938i
$911$	1547.30			1.69846			0.849231	−	0.528022i	$-0.177066\pi$
$911$	1547.30			1.69846			0.849231	+	0.528022i	$0.177066\pi$
$912$	132.363	−	187.657i	0.145135	−	0.205764i
$913$	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
$918$	−631.331	+	391.438i	−0.687725	+	0.426403i
$919$	1012.94			1.10222			0.551109	−	0.834433i	$-0.314205\pi$
$919$	1012.94			1.10222			0.551109	+	0.834433i	$0.314205\pi$
$920$	−271.370	−	718.165i	−0.294968	−	0.780614i
$921$	453.130	+	1326.95i	0.491998	+	1.44077i
$922$	536.794	−	1163.71i	0.582207	−	1.26216i
$923$	−317.028	−	317.028i	−0.343475	−	0.343475i
$924$	−516.228	+	870.416i	−0.558688	+	0.942008i
$925$	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
$928$	264.877	−	395.459i	0.285427	−	0.426141i
$929$	1529.05			1.64591			0.822955	−	0.568106i	$-0.192324\pi$
$929$	1529.05			1.64591			0.822955	+	0.568106i	$0.192324\pi$
$930$	6.77702	−	421.868i	0.00728711	−	0.453622i
$931$			114.355i			0.122830i
$932$	−311.361	−	24.6446i	−0.334079	−	0.0264427i
$933$	−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
$936$	−870.868	+	128.909i	−0.930414	+	0.137723i
$937$	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	$0.0833328\pi$
$938$	320.327	−	694.435i	0.341500	−	0.740336i
$939$	180.774	+	529.380i	0.192518	+	0.563769i
$940$	349.636	−	355.328i	0.371953	−	0.378009i
$941$			961.186i			1.02145i	0.859744	+	0.510726i	$0.170623\pi$
$941$			961.186i			1.02145i	−0.859744	+	0.510726i	$0.829377\pi$
$942$	−1181.56	−	122.281i	−1.25431	−	0.129811i
$943$	−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	$-0.360555\pi$
$947$	1259.29	−	1259.29i	1.32977	−	1.32977i	0.905568	−	0.424202i	$-0.139445\pi$
$948$	−262.632	−	1028.20i	−0.277038	−	1.08460i
$949$			219.261i			0.231044i
$950$	61.0496	−	231.288i	0.0642627	−	0.243461i
$951$	−91.3247	−	267.435i	−0.0960302	−	0.281215i
$952$	−530.719	+	149.294i	−0.557478	+	0.156822i
$953$	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	$0.235307\pi$
$954$	349.546	+	218.883i	0.366401	+	0.229437i
$955$	−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
$958$	−367.821	+	797.397i	−0.383947	+	0.832356i
$959$		−	425.813i		−	0.444018i
$960$	546.981	−	788.931i	0.569772	−	0.821803i
$961$	763.202			0.794174
$962$	−317.749	−	146.570i	−0.330300	−	0.152360i
$963$	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
$966$	−447.767	+	363.779i	−0.463527	+	0.376582i
$967$	−1.17333	−	1.17333i	−0.00121337	−	0.00121337i	0.706500	−	0.707713i	$-0.250273\pi$
$967$	−1.17333	−	1.17333i	−0.00121337	−	0.00121337i	−0.707713	+	0.706500i	$0.750273\pi$
$968$	−351.759	−	1250.45i	−0.363387	−	1.29179i
$969$	63.8038	+	186.843i	0.0658450	+	0.192821i
$970$	−408.383	+	1135.91i	−0.421014	+	1.17104i
$971$	570.125			0.587153			0.293576	−	0.955936i	$-0.405154\pi$
$971$	570.125			0.587153			0.293576	+	0.955936i	$0.405154\pi$
$972$	−971.990	−	4.32014i	−0.999990	−	0.00444459i
$973$	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	$0.649212\pi$
$978$	494.869	+	51.2149i	0.506001	+	0.0523670i
$979$	−1936.24			−1.97777
$980$	3.86035	+	478.038i	0.00393914	+	0.487794i
$981$	−1138.83	+	880.455i	−1.16089	+	0.897507i
$982$	1365.09	+	629.685i	1.39011	+	0.641227i
$983$	876.585	+	876.585i	0.891745	+	0.891745i	0.994687	−	0.102942i	$-0.0328257\pi$
$983$	876.585	+	876.585i	0.891745	+	0.891745i	−0.102942	+	0.994687i	$0.532826\pi$
$984$	−143.627	−	26.4492i	−0.145963	−	0.0268792i
$985$	−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
$988$	−18.4627	+	233.259i	−0.0186870	+	0.236092i
$989$	−1553.59			−1.57086
$990$	1349.11	+	689.368i	1.36274	+	0.696331i
$991$		−	183.991i		−	0.185662i	−0.995682	−	0.0928310i	$-0.970408\pi$
$991$		−	183.991i		−	0.185662i	0.995682	−	0.0928310i	$-0.0295916\pi$
$992$	−373.924	−	250.453i	−0.376939	−	0.252472i
$993$	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
$996$	−551.768	+	930.340i	−0.553983	+	0.934076i
$997$	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	$0.187208\pi$
$998$	−552.976	−	255.075i	−0.554084	−	0.255586i
$999$	−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.23.3	✓	40
3.2	odd	2	inner	60.3.l.a.23.18	yes	40
4.3	odd	2	inner	60.3.l.a.23.8	yes	40
5.2	odd	4	inner	60.3.l.a.47.13	yes	40
5.3	odd	4		300.3.l.g.107.8		40
5.4	even	2		300.3.l.g.143.18		40
12.11	even	2	inner	60.3.l.a.23.13	yes	40
15.2	even	4	inner	60.3.l.a.47.8	yes	40
15.8	even	4		300.3.l.g.107.13		40
15.14	odd	2		300.3.l.g.143.3		40
20.3	even	4		300.3.l.g.107.3		40
20.7	even	4	inner	60.3.l.a.47.18	yes	40
20.19	odd	2		300.3.l.g.143.13		40
60.23	odd	4		300.3.l.g.107.18		40
60.47	odd	4	inner	60.3.l.a.47.3	yes	40
60.59	even	2		300.3.l.g.143.8		40

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.81610 - 0.837725i) q^{2} +(2.69303 + 1.32197i) q^{3} +(2.59643 + 3.04278i) q^{4} +(-3.21472 + 3.82956i) q^{5} +(-3.78336 - 4.65685i) q^{6} +(3.54241 + 3.54241i) q^{7} +(-2.16636 - 7.70110i) q^{8} +(5.50478 + 7.12021i) q^{9} +O(q^{10})\)	\(q+(-1.81610 - 0.837725i) q^{2} +(2.69303 + 1.32197i) q^{3} +(2.59643 + 3.04278i) q^{4} +(-3.21472 + 3.82956i) q^{5} +(-3.78336 - 4.65685i) q^{6} +(3.54241 + 3.54241i) q^{7} +(-2.16636 - 7.70110i) q^{8} +(5.50478 + 7.12021i) q^{9} +(9.04638 - 4.26182i) q^{10} +16.8337 q^{11} +(2.96979 + 11.6267i) 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} +(-4.03246 - 17.5425i) q^{18} -4.78419 q^{19} +(-19.9993 + 0.161503i) q^{20} +(4.85684 + 14.2228i) q^{21} +(-30.5716 - 14.1020i) q^{22} +(-13.5716 - 13.5716i) q^{23} +(4.34655 - 23.6031i) q^{24} +(-4.33113 - 24.6220i) q^{25} +(8.45895 + 22.9448i) q^{26} +(5.41182 + 26.4521i) q^{27} +(-1.58116 + 19.9764i) q^{28} +14.8741 q^{29} +(29.9961 + 0.481867i) q^{30} -14.0641i q^{31} +(17.8080 - 26.5872i) q^{32} +(45.3336 + 22.2536i) q^{33} +(9.51674 + 25.8140i) q^{34} +(-24.9537 + 2.17802i) q^{35} +(-7.37245 + 35.2370i) q^{36} +(-10.1182 + 10.1182i) q^{37} +(8.68857 + 4.00784i) q^{38} +(-11.8540 - 34.7134i) q^{39} +(36.4561 + 16.4607i) q^{40} -6.08509i q^{41} +(3.09427 - 29.8987i) 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} +(-27.6667 + 39.2244i) q^{48} -23.9027i q^{49} +(-12.7607 + 48.3442i) q^{50} +(-13.3364 - 39.0543i) q^{51} +(3.85911 - 48.7562i) q^{52} +(-16.2015 + 16.2015i) q^{53} +(12.3312 - 52.5732i) q^{54} +(-54.1156 + 64.4657i) q^{55} +(19.6063 - 34.9546i) q^{56} +(-12.8840 - 6.32456i) q^{57} +(-27.0128 - 12.4604i) q^{58} +4.37150i q^{59} +(-54.0723 - 26.0036i) q^{60} +8.52269 q^{61} +(-11.7818 + 25.5418i) q^{62} +(-5.72249 + 44.7229i) q^{63} +(-54.6137 + 33.3667i) q^{64} +(60.9043 - 5.31588i) q^{65} +(-63.6878 - 78.3919i) q^{66} +(53.9714 + 53.9714i) q^{67} +(4.34170 - 54.8532i) q^{68} +(-18.6074 - 54.4900i) q^{69} +(47.1431 + 16.9489i) q^{70} +36.6679 q^{71} +(42.9080 - 57.8178i) 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} +(-7.55214 + 72.9733i) q^{78} -88.4346 q^{79} +(-52.4184 - 60.4344i) q^{80} +(-20.3947 + 78.3904i) q^{81} +(-5.09763 + 11.0511i) q^{82} +(63.7372 + 63.7372i) q^{83} +(-30.6663 + 51.7068i) q^{84} +(68.5205 - 5.98063i) q^{85} +(-151.896 + 55.9988i) q^{86} +(40.0563 + 19.6631i) q^{87} +(-36.4679 - 129.638i) q^{88} -115.022 q^{89} +(80.1434 + 40.9517i) q^{90} -61.2548i q^{91} +(6.05770 - 76.5332i) q^{92} +(18.5923 - 37.8749i) q^{93} +(46.7728 - 17.2435i) q^{94} +(15.3798 - 18.3214i) q^{95} +(83.1047 - 48.0583i) q^{96} +(-85.3544 + 85.3544i) q^{97} +(-20.0239 + 43.4096i) q^{98} +(92.6658 + 119.859i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{6}+O(q^{10}) \) 40 * q - 4 * q^6	\( 40 q - 4 q^{6} - 12 q^{10} - 20 q^{12} - 8 q^{13} - 36 q^{16} - 24 q^{18} - 24 q^{21} - 76 q^{22} - 8 q^{25} - 84 q^{28} + 68 q^{30} - 40 q^{33} + 172 q^{36} - 40 q^{37} + 104 q^{40} + 236 q^{42} - 104 q^{45} + 240 q^{46} + 196 q^{48} + 304 q^{52} - 72 q^{57} + 180 q^{58} - 284 q^{60} + 48 q^{61} - 552 q^{66} - 372 q^{70} - 600 q^{72} + 104 q^{73} - 736 q^{76} - 408 q^{78} + 72 q^{81} - 720 q^{82} + 216 q^{85} - 580 q^{88} + 528 q^{90} + 368 q^{93} + 884 q^{96} + 72 q^{97}+O(q^{100}) \) 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

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