LMFDB - Embedded newform 60.3.l.a.23.13

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			23.13
Character	$\chi$	$=$	60.23
Dual form			60.3.l.a.47.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.837725 + 1.81610i) q^{2} +(1.32197 + 2.69303i) q^{3} +(-2.59643 + 3.04278i) q^{4} +(3.21472 - 3.82956i) q^{5} +(-3.78336 + 4.65685i) q^{6} +(-3.54241 - 3.54241i) q^{7} +(-7.70110 - 2.16636i) q^{8} +(-5.50478 + 7.12021i) q^{9} +O(q^{10})$	\(q+(0.837725 + 1.81610i) q^{2} +(1.32197 + 2.69303i) 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} +(-7.70110 - 2.16636i) q^{8} +(-5.50478 + 7.12021i) q^{9} +(9.64792 + 2.63013i) q^{10} +16.8337 q^{11} +(-11.6267 - 2.96979i) q^{12} +(-8.64592 - 8.64592i) q^{13} +(3.46580 - 9.40093i) q^{14} +(14.5629 + 3.59476i) q^{15} +(-2.51707 - 15.8008i) q^{16} +(9.72710 + 9.72710i) q^{17} +(-17.5425 - 4.03246i) 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} +(-4.34655 - 23.6031i) q^{24} +(-4.33113 - 24.6220i) q^{25} +(8.45895 - 22.9448i) q^{26} +(-26.4521 - 5.41182i) q^{27} +(19.9764 - 1.58116i) q^{28} -14.8741 q^{29} +(5.67126 + 29.4591i) q^{30} +14.0641i q^{31} +(26.5872 - 17.8080i) q^{32} +(22.2536 + 45.3336i) 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} +(4.00784 + 8.68857i) q^{38} +(11.8540 - 34.7134i) q^{39} +(-33.0531 + 22.5276i) q^{40} +6.08509i q^{41} +(29.8987 - 3.09427i) q^{42} +(-57.2366 + 57.2366i) q^{43} +(-43.7075 + 51.2213i) q^{44} +(9.57094 + 43.9704i) q^{45} +(13.2781 - 36.0167i) q^{46} +(-17.6247 + 17.6247i) q^{47} +(39.2244 - 27.6667i) 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} +(-12.3312 - 52.5732i) q^{54} +(54.1156 - 64.4657i) q^{55} +(19.6063 + 34.9546i) q^{56} +(6.32456 + 12.8840i) q^{57} +(-12.4604 - 27.0128i) q^{58} +4.37150i q^{59} +(-48.7496 + 34.9782i) q^{60} +8.52269 q^{61} +(-25.5418 + 11.7818i) q^{62} +(44.7229 - 5.72249i) 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} +(-54.8532 + 4.34170i) q^{68} +(18.6074 - 54.4900i) q^{69} +(-24.8599 - 43.4939i) q^{70} +36.6679 q^{71} +(57.8178 - 42.9080i) q^{72} +(-12.6800 - 12.6800i) q^{73} +(-26.8519 - 9.89937i) q^{74} +(60.5820 - 44.2134i) q^{75} +(-12.4218 + 14.5573i) q^{76} +(-59.6318 - 59.6318i) q^{77} +(72.9733 - 7.55214i) 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} +(30.6663 + 51.7068i) q^{84} +(68.5205 - 5.98063i) q^{85} +(-151.896 - 55.9988i) q^{86} +(-19.6631 - 40.0563i) q^{87} +(-129.638 - 36.4679i) q^{88} +115.022 q^{89} +(-71.8368 + 54.2169i) q^{90} +61.2548i q^{91} +(76.5332 - 6.05770i) q^{92} +(-37.8749 + 18.5923i) 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} +(43.4096 - 20.0239i) 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 $

$2$	0.837725	+	1.81610i	0.418863	+	0.908050i
$2$	0.837725	+	1.81610i	0.418863	+	0.908050i
$3$	1.32197	+	2.69303i	0.440657	+	0.897676i
$3$	1.32197	+	2.69303i	0.440657	+	0.897676i
$4$	−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	0.407256	−	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	$-0.222656\pi$
$11$	16.8337			1.53034			0.765168	+	0.643831i	$0.222656\pi$
$12$	−11.6267	−	2.96979i	−0.968892	−	0.247483i
$13$	−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
$15$	14.5629	+	3.59476i	0.970859	+	0.239651i
$16$	−2.51707	−	15.8008i	−0.157317	−	0.987548i
$17$	9.72710	+	9.72710i	0.572182	+	0.572182i	0.932738	−	0.360556i	$-0.117413\pi$
$17$	9.72710	+	9.72710i	0.572182	+	0.572182i	−0.360556	+	0.932738i	$0.617413\pi$
$18$	−17.5425	−	4.03246i	−0.974583	−	0.224025i
$19$	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	0.347580	−	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
$27$	−26.4521	−	5.41182i	−0.979706	−	0.200438i
$28$	19.9764	−	1.58116i	0.713444	−	0.0564699i
$29$	−14.8741			−0.512899			−0.256449	−	0.966558i	$-0.582553\pi$
$29$	−14.8741			−0.512899			−0.256449	+	0.966558i	$0.582553\pi$
$30$	5.67126	+	29.4591i	0.189042	+	0.981969i
$31$			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
$33$	22.2536	+	45.3336i	0.674353	+	1.37374i
$34$	−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	$0.311941\pi$
$38$	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	$0.0236430\pi$
$41$			6.08509i			0.148417i	−0.997243	+	0.0742084i	$0.976357\pi$
$42$	29.8987	−	3.09427i	0.711873	−	0.0736730i
$43$	−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
$45$	9.57094	+	43.9704i	0.212688	+	0.977120i
$46$	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	$0.335425\pi$
$48$	39.2244	−	27.6667i	0.817175	−	0.576390i
$49$		−	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	−0.537546	−	0.843234i	$-0.680649\pi$
$53$	16.2015	−	16.2015i	0.305688	−	0.305688i	0.843234	+	0.537546i	$0.180649\pi$
$54$	−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
$57$	6.32456	+	12.8840i	0.110957	+	0.226034i
$58$	−12.4604	−	27.0128i	−0.214834	−	0.465738i
$59$			4.37150i			0.0740931i	0.999314	+	0.0370466i	$0.0117950\pi$
$59$			4.37150i			0.0740931i	−0.999314	+	0.0370466i	$0.988205\pi$
$60$	−48.7496	+	34.9782i	−0.812494	+	0.582970i
$61$	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
$63$	44.7229	−	5.72249i	0.709887	−	0.0908332i
$64$	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	0.178413	−	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	$-0.416863\pi$
$71$	36.6679			0.516449			0.258225	+	0.966085i	$0.416863\pi$
$72$	57.8178	−	42.9080i	0.803025	−	0.595945i
$73$	−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
$75$	60.5820	−	44.2134i	0.807760	−	0.589512i
$76$	−12.4218	+	14.5573i	−0.163445	+	0.191543i
$77$	−59.6318	−	59.6318i	−0.774439	−	0.774439i
$78$	72.9733	−	7.55214i	0.935555	−	0.0968223i
$79$	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	0.977740	−	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
$87$	−19.6631	−	40.0563i	−0.226013	−	0.460417i
$88$	−129.638	−	36.4679i	−1.47316	−	0.414408i
$89$	115.022			1.29238			0.646190	−	0.763177i	$-0.276361\pi$
$89$	115.022			1.29238			0.646190	+	0.763177i	$0.276361\pi$
$90$	−71.8368	+	54.2169i	−0.798187	+	0.602410i
$91$			61.2548i			0.673130i
$92$	76.5332	−	6.05770i	0.831883	−	0.0658445i
$93$	−37.8749	+	18.5923i	−0.407258	+	0.199917i
$94$	−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	$0.463766\pi$
$98$	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	$0.288221\pi$
$101$			158.917i			1.57343i	−0.617313	+	0.786717i	$0.711779\pi$
$102$	−82.0987	+	8.49654i	−0.804889	+	0.0832994i
$103$	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
$105$	−38.8536	−	64.3218i	−0.370034	−	0.612589i
$106$	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	$0.190372\pi$
$108$	85.1480	−	66.4365i	0.788408	−	0.615153i
$109$			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	−0.0989792	−	0.995089i	$-0.531558\pi$
$113$	101.260	−	101.260i	0.896110	−	0.896110i	0.995089	+	0.0989792i	$0.0315577\pi$
$114$	−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
$117$	109.155	−	13.9668i	0.932946	−	0.119375i
$118$	−7.93907	+	3.66211i	−0.0672803	+	0.0310348i
$119$		−	68.9147i		−	0.579115i
$120$	−104.363	−	59.2321i	−0.869689	−	0.493601i
$121$	162.373			1.34193
$122$	7.13968	+	15.4781i	0.0585219	+	0.126869i
$123$	−16.3873	+	8.04432i	−0.133230	+	0.0654009i
$124$	−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	0.972736	−	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	$-0.686900\pi$
$131$	−145.148			−1.10800			−0.554002	+	0.832515i	$0.686900\pi$
$132$	−195.720	−	49.9925i	−1.48273	−	0.378731i
$133$	−16.9476	−	16.9476i	−0.127425	−	0.127425i
$134$	52.8042	−	143.231i	0.394061	−	1.06888i
$135$	−105.761	+	83.9024i	−0.783415	+	0.621499i
$136$	−53.8369	−	95.9817i	−0.395859	−	0.705748i
$137$	60.1022	+	60.1022i	0.438702	+	0.438702i	0.891575	−	0.452873i	$-0.149601\pi$
$137$	60.1022	+	60.1022i	0.438702	+	0.438702i	−0.452873	+	0.891575i	$0.649601\pi$
$138$	114.547	−	11.8547i	0.830051	−	0.0859035i
$139$	−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
$144$	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
$147$	64.3705	−	31.5986i	0.437895	−	0.214957i
$148$	−4.51626	−	57.0587i	−0.0305153	−	0.385531i
$149$	25.9233			0.173982			0.0869911	−	0.996209i	$-0.472275\pi$
$149$	25.9233			0.173982			0.0869911	+	0.996209i	$0.472275\pi$
$150$	131.047	+	72.9843i	0.873646	+	0.486562i
$151$		−	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
$153$	−122.805	+	15.7134i	−0.802644	+	0.102702i
$154$	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	$0.0328486\pi$
$158$	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
$162$	125.280	−	102.708i	0.773331	−	0.634003i
$163$	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
$165$	245.147	+	60.5130i	1.48574	+	0.366746i
$166$	−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	$0.366116\pi$
$168$	−68.2147	+	99.0092i	−0.406040	+	0.589341i
$169$		−	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	−0.839504	−	0.543353i	$-0.817154\pi$
$173$	−51.2341	+	51.2341i	−0.296151	+	0.296151i	0.543353	+	0.839504i	$0.317154\pi$
$174$	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
$177$	−11.7726	+	5.77899i	−0.0665116	+	0.0326497i
$178$	96.3566	+	208.891i	0.541329	+	1.17354i
$179$		−	27.2276i		−	0.152109i	−0.997104	−	0.0760547i	$-0.975768\pi$
$179$		−	27.2276i		−	0.152109i	0.997104	−	0.0760547i	$-0.0242324\pi$
$180$	−158.643	−	85.0439i	−0.881349	−	0.472466i
$181$	−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
$183$	11.2668	+	22.9518i	0.0615670	+	0.125420i
$184$	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
$188$	−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	$-0.150649\pi$
$191$	340.010			1.78016			0.890078	+	0.455807i	$0.150649\pi$
$192$	−17.6597	+	191.186i	−0.0919779	+	0.995761i
$193$	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
$195$	−94.8296	−	156.990i	−0.486306	−	0.805075i
$196$	72.7306	+	62.0617i	0.371075	+	0.316641i
$197$	−225.584	−	225.584i	−1.14510	−	1.14510i	−0.987504	−	0.157595i	$-0.949626\pi$
$197$	−225.584	−	225.584i	−1.14510	−	1.14510i	−0.157595	−	0.987504i	$-0.550374\pi$
$198$	−295.305	−	67.8811i	−1.49144	−	0.342834i
$199$	−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
$204$	−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
$207$	171.341	−	21.9239i	0.827736	−	0.105912i
$208$	−114.850	+	158.375i	−0.552163	+	0.761416i
$209$	80.5356			0.385338
$210$	84.2662	−	124.446i	0.401267	−	0.592600i
$211$		−	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
$213$	48.4739	+	98.7476i	0.227577	+	0.463604i
$214$	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
$218$	−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
$222$	−8.83816	−	85.3995i	−0.0398115	−	0.384683i
$223$	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
$225$	199.155	+	104.700i	0.885135	+	0.465334i
$226$	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	$0.213562\pi$
$228$	−55.6244	−	14.2081i	−0.243967	−	0.0623160i
$229$		−	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	−0.578625	−	0.815593i	$-0.696411\pi$
$233$	55.2135	−	55.2135i	0.236968	−	0.236968i	0.815593	+	0.578625i	$0.196411\pi$
$234$	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
$237$	116.908	+	238.157i	0.493283	+	1.00488i
$238$	125.156	−	57.7316i	0.525865	−	0.242570i
$239$		−	46.1374i		−	0.193044i	−0.995331	−	0.0965218i	$-0.969228\pi$
$239$		−	46.1374i		−	0.193044i	0.995331	−	0.0965218i	$-0.0307718\pi$
$240$	20.1441	−	239.153i	0.0839339	−	0.996471i
$241$	−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
$243$	184.146	−	158.553i	0.757803	−	0.652483i
$244$	−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
$248$	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	$-0.603045\pi$
$251$	−159.687			−0.636203			−0.318101	+	0.948057i	$0.603045\pi$
$252$	−98.7077	+	150.940i	−0.391697	+	0.598969i
$253$	−228.460	−	228.460i	−0.903004	−	0.903004i
$254$	−92.0498	+	249.684i	−0.362401	+	0.983007i
$255$	106.688	+	176.621i	0.418385	+	0.692632i
$256$	−243.329	+	79.5433i	−0.950503	+	0.310716i
$257$	98.0877	+	98.0877i	0.381664	+	0.381664i	0.871701	−	0.490037i	$-0.163017\pi$
$257$	98.0877	+	98.0877i	0.381664	+	0.381664i	−0.490037	+	0.871701i	$0.663017\pi$
$258$	−49.9957	−	483.089i	−0.193782	−	1.87244i
$259$	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	0.383802	−	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
$267$	152.055	+	309.757i	0.569496	+	1.16014i
$268$	304.356	−	24.0902i	1.13566	−	0.0898887i
$269$	0.543377			0.00201999			0.00100999	−	0.999999i	$-0.499679\pi$
$269$	0.543377			0.00201999			0.00100999	+	0.999999i	$0.499679\pi$
$270$	−240.974	−	121.785i	−0.892495	−	0.451057i
$271$			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
$273$	−164.961	+	80.9771i	−0.604252	+	0.296619i
$274$	−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	$0.314823\pi$
$278$	−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	$0.191964\pi$
$281$			318.753i			1.13435i	−0.823597	+	0.567176i	$0.808036\pi$
$282$	−15.3950	−	148.756i	−0.0545922	−	0.527503i
$283$	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
$285$	69.6717	+	17.1980i	0.244462	+	0.0603439i
$286$	142.395	−	386.245i	0.497885	−	1.35051i
$287$	21.5559	−	21.5559i	0.0751076	−	0.0751076i
$288$	−19.5603	+	287.335i	−0.0679176	+	0.997691i
$289$		−	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	−0.823841	−	0.566822i	$-0.808173\pi$
$293$	−75.3066	+	75.3066i	−0.257019	+	0.257019i	0.566822	+	0.823841i	$0.308173\pi$
$294$	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
$297$	−445.286	−	91.1009i	−1.49928	−	0.306737i
$298$	21.7166	+	47.0794i	0.0728746	+	0.157984i
$299$			234.678i			0.784876i
$300$	−22.7654	+	299.135i	−0.0758845	+	0.997117i
$301$	405.511			1.34721
$302$	363.908	−	167.862i	1.20499	−	0.555836i
$303$	−427.967	+	210.084i	−1.41243	+	0.693345i
$304$	−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	$-0.974597\pi$
$307$	−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	$-0.513581\pi$
$311$	−26.5302			−0.0853063			−0.0426531	+	0.999090i	$0.513581\pi$
$312$	−166.491	+	241.651i	−0.533624	+	0.774522i
$313$	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
$315$	121.857	−	189.665i	0.386848	−	0.602112i
$316$	−229.614	+	269.087i	−0.726628	+	0.851542i
$317$	66.6091	+	66.6091i	0.210123	+	0.210123i	0.804320	−	0.594197i	$-0.202530\pi$
$317$	66.6091	+	66.6091i	0.210123	+	0.210123i	−0.594197	+	0.804320i	$0.702530\pi$
$318$	14.1519	+	136.744i	0.0445027	+	0.430012i
$319$	−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
$324$	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
$327$	−430.732	+	211.441i	−1.31722	+	0.646608i
$328$	13.1825	−	46.8619i	0.0401906	−	0.142872i
$329$	124.868			0.379537
$330$	95.4682	+	495.905i	0.289298	+	1.50274i
$331$			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
$333$	−16.3452	−	127.742i	−0.0490845	−	0.383610i
$334$	−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	$0.0382564\pi$
$338$	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
$342$	−83.9267	−	19.2921i	−0.245400	−	0.0564095i
$343$	−258.251	+	258.251i	−0.752919	+	0.752919i
$344$	564.780	−	316.789i	1.64180	−	0.920899i
$345$	−148.855	−	246.428i	−0.431464	−	0.714285i
$346$	−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	$0.0613932\pi$
$348$	172.936	+	44.1729i	0.496944	+	0.126934i
$349$			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	$-0.472893\pi$
$353$	381.746	−	381.746i	1.08143	−	1.08143i	0.996376	−	0.0850569i	$-0.0271072\pi$
$354$	−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
$357$	185.589	−	91.1033i	0.519858	−	0.255191i
$358$	49.4480	−	22.8092i	0.138123	−	0.0637129i
$359$		−	209.720i		−	0.584178i	−0.956391	−	0.292089i	$-0.905650\pi$
$359$		−	209.720i		−	0.584178i	0.956391	−	0.292089i	$-0.0943503\pi$
$360$	21.5492	−	359.354i	0.0598588	−	0.998207i
$361$	−338.112			−0.936597
$362$	−231.735	−	502.377i	−0.640151	−	1.38778i
$363$	214.652	+	437.275i	0.591329	+	1.20461i
$364$	−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	0.701256	−	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
$372$	41.7674	−	163.519i	0.112278	−	0.439567i
$373$	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
$375$	25.4363	−	374.136i	0.0678302	−	0.997697i
$376$	173.911	−	97.5478i	0.462529	−	0.259436i
$377$	128.600	+	128.600i	0.341114	+	0.341114i
$378$	−142.554	+	229.918i	−0.377127	+	0.608248i
$379$	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	0.995098	−	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
$387$	−92.4613	−	722.612i	−0.238918	−	1.86721i
$388$	−38.0980	−	481.332i	−0.0981907	−	1.24055i
$389$	−600.575			−1.54389			−0.771947	−	0.635687i	$-0.780717\pi$
$389$	−600.575			−1.54389			−0.771947	+	0.635687i	$0.780717\pi$
$390$	205.668	−	303.734i	0.527353	−	0.778805i
$391$		−	264.025i		−	0.675255i
$392$	−51.7819	+	184.077i	−0.132097	+	0.469583i
$393$	−191.882	−	390.889i	−0.488250	−	0.994628i
$394$	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	$0.426287\pi$
$398$	−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	$-0.877787\pi$
$401$		−	300.412i		−	0.749157i	0.927195	−	0.374578i	$-0.122213\pi$
$402$	455.529	−	47.1436i	1.13316	−	0.117273i
$403$	121.597	−	121.597i	0.301729	−	0.301729i
$404$	−483.550	−	412.617i	−1.19691	−	1.02133i
$405$	−365.764	−	173.901i	−0.903122	−	0.429384i
$406$	−51.5506	+	139.830i	−0.126972	+	0.344409i
$407$	−170.326	+	170.326i	−0.418492	+	0.418492i
$408$	187.311	−	271.869i	0.459094	−	0.666346i
$409$		−	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
$414$	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
$417$	−16.6548	−	33.9281i	−0.0399397	−	0.0813623i
$418$	67.4667	+	146.261i	0.161404	+	0.349906i
$419$			582.593i			1.39044i	0.718799	+	0.695218i	$0.244692\pi$
$419$			582.593i			1.39044i	−0.718799	+	0.695218i	$0.755308\pi$
$420$	296.598	+	48.7842i	0.706186	+	0.116153i
$421$	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
$423$	−28.4713	−	222.511i	−0.0673080	−	0.526032i
$424$	−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
$428$	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	$-0.277510\pi$
$431$	554.639			1.28686			0.643432	+	0.765503i	$0.277510\pi$
$432$	−18.9292	+	431.585i	−0.0438177	+	0.999040i
$433$	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
$435$	−216.609	−	53.4687i	−0.497953	−	0.122916i
$436$	−486.674	−	415.283i	−1.11622	−	0.952483i
$437$	−64.9292	−	64.9292i	−0.148579	−	0.148579i
$438$	107.022	−	11.0759i	0.244342	−	0.0252874i
$439$	−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	0.660522	−	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
$447$	34.2699	+	69.8122i	0.0766665	+	0.156180i
$448$	−75.2655	−	311.663i	−0.168003	−	0.695676i
$449$	236.471			0.526660			0.263330	−	0.964706i	$-0.415179\pi$
$449$	236.471			0.526660			0.263330	+	0.964706i	$0.415179\pi$
$450$	−23.3083	+	449.396i	−0.0517962	+	0.998658i
$451$			102.435i			0.227128i
$452$	45.1977	+	571.030i	0.0999949	+	1.26334i
$453$	539.626	−	264.895i	1.19123	−	0.584757i
$454$	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	$0.372594\pi$
$458$	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	$-0.755411\pi$
$461$		−	640.776i		−	1.38997i	0.719024	−	0.694985i	$-0.244589\pi$
$462$	503.305	−	52.0879i	1.08940	−	0.112744i
$463$	−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
$465$	−50.5570	+	204.814i	−0.108725	+	0.440460i
$466$	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	$0.472500\pi$
$468$	−240.915	+	368.398i	−0.514775	+	0.787175i
$469$			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
$474$	−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
$477$	26.1723	+	204.544i	0.0548685	+	0.428813i
$478$	83.7902	−	38.6505i	0.175293	−	0.0808588i
$479$		−	439.071i		−	0.916641i	−0.888787	−	0.458321i	$-0.848451\pi$
$479$		−	439.071i		−	0.916641i	0.888787	−	0.458321i	$-0.151549\pi$
$480$	451.201	−	163.761i	0.940002	−	0.341168i
$481$	174.962			0.363747
$482$	−177.736	−	385.312i	−0.368746	−	0.799403i
$483$	−258.941	+	127.111i	−0.536109	+	0.263169i
$484$	−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	0.315881	−	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	$-0.777478\pi$
$491$	−751.660			−1.53088			−0.765438	+	0.643509i	$0.777478\pi$
$492$	18.0714	−	70.7496i	0.0367306	−	0.143800i
$493$	−144.681	−	144.681i	−0.293472	−	0.293472i
$494$	40.4692	−	109.772i	0.0819215	−	0.222211i
$495$	161.114	+	740.184i	0.325483	+	1.49532i
$496$	222.223	−	35.4003i	0.448031	−	0.0713715i
$497$	−129.893	−	129.893i	−0.261353	−	0.261353i
$498$	−537.955	+	55.6739i	−1.08023	+	0.111795i
$499$	−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	0.440420	−	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
$507$	52.5035	−	25.7733i	0.103557	−	0.0508348i
$508$	−530.563	+	41.9947i	−1.04442	+	0.0826667i
$509$	98.9386			0.194378			0.0971892	−	0.995266i	$-0.469015\pi$
$509$	98.9386			0.194378			0.0971892	+	0.995266i	$0.469015\pi$
$510$	−231.386	+	341.716i	−0.453699	+	0.670032i
$511$			89.8357i			0.175804i
$512$	−348.301	−	375.274i	−0.680276	−	0.732956i
$513$	−126.552	−	25.8912i	−0.246690	−	0.0504702i
$514$	−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
$518$	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	$-0.845548\pi$
$521$		−	485.997i		−	0.932816i	0.884570	−	0.466408i	$-0.154452\pi$
$522$	260.928	+	59.9791i	0.499863	+	0.114902i
$523$	−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
$525$	−371.228	−	57.9844i	−0.707101	−	0.110446i
$526$	138.849	−	376.627i	0.263972	−	0.716021i
$527$	−136.803	+	136.803i	−0.259588	+	0.259588i
$528$	660.291	−	465.733i	1.25055	−	0.882069i
$529$		−	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
$534$	−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
$537$	73.3246	−	35.9941i	0.136545	−	0.0670281i
$538$	0.455200	+	0.986826i	0.000846097	+	0.00183425i
$539$		−	402.370i		−	0.746512i
$540$	19.3044	−	539.655i	0.0357489	−	0.999361i
$541$	−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
$543$	−365.689	−	744.956i	−0.673460	−	1.37193i
$544$	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	0.844735	−	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
$552$	−261.343	+	379.322i	−0.473447	+	0.687177i
$553$	−313.272	−	313.272i	−0.566495	−	0.566495i
$554$	−210.253	−	77.5132i	−0.379519	−	0.139916i
$555$	−183.722	+	110.978i	−0.331031	+	0.199960i
$556$	32.7111	−	38.3345i	0.0588330	−	0.0689469i
$557$	310.481	+	310.481i	0.557417	+	0.557417i	0.928571	−	0.371155i	$-0.121038\pi$
$557$	310.481	+	310.481i	0.557417	+	0.557417i	−0.371155	+	0.928571i	$0.621038\pi$
$558$	56.7128	−	246.719i	0.101636	−	0.442149i
$559$	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	0.883809	−	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
$567$	−205.445	+	349.937i	−0.362336	+	0.617173i
$568$	−282.383	−	79.4360i	−0.497153	−	0.139852i
$569$	−386.708			−0.679627			−0.339813	−	0.940493i	$-0.610364\pi$
$569$	−386.708			−0.679627			−0.339813	+	0.940493i	$0.610364\pi$
$570$	27.1324	+	140.938i	0.0476007	+	0.247259i
$571$			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
$573$	449.483	+	915.656i	0.784439	+	1.59800i
$574$	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	$-0.0750277\pi$
$578$	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
$582$	−74.5563	−	720.408i	−0.128104	−	1.23781i
$583$	272.731	−	272.731i	0.467806	−	0.467806i
$584$	70.1805	+	125.120i	0.120172	+	0.214246i
$585$	297.415	−	462.914i	0.508402	−	0.791307i
$586$	−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	$0.155964\pi$
$588$	−70.9859	+	277.909i	−0.120724	+	0.472635i
$589$			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	−0.793359	−	0.608754i	$-0.791670\pi$
$593$	−109.471	+	109.471i	−0.184605	+	0.184605i	0.608754	+	0.793359i	$0.291670\pi$
$594$	−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
$597$	−378.972	−	772.015i	−0.634794	−	1.29316i
$598$	−426.199	+	196.596i	−0.712707	+	0.328755i
$599$		−	527.412i		−	0.880487i	−0.897878	−	0.440243i	$-0.854892\pi$
$599$		−	527.412i		−	0.880487i	0.897878	−	0.440243i	$-0.145108\pi$
$600$	−562.330	+	209.249i	−0.937217	+	0.348748i
$601$	−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
$603$	681.388	−	87.1866i	1.13000	−	0.144588i
$604$	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	0.955728	−	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
$612$	271.041	−	414.466i	0.442878	−	0.677233i
$613$	−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
$615$	−21.8744	+	88.6165i	−0.0355682	+	0.144092i
$616$	330.046	+	588.414i	0.535789	+	0.955218i
$617$	51.5846	+	51.5846i	0.0836055	+	0.0836055i	0.747673	−	0.664067i	$-0.231171\pi$
$617$	51.5846	+	51.5846i	0.0836055	+	0.0836055i	−0.664067	+	0.747673i	$0.731171\pi$
$618$	25.0051	+	241.615i	0.0404614	+	0.390962i
$619$	−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
$624$	−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
$627$	106.466	+	216.884i	0.169802	+	0.345908i
$628$	62.4854	+	789.443i	0.0994990	+	1.25707i
$629$	−196.841			−0.312943
$630$	446.534	+	62.4170i	0.708784	+	0.0990746i
$631$		−	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
$633$	495.091	−	243.034i	0.782134	−	0.383939i
$634$	−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
$638$	−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	$0.0259918\pi$
$641$			104.566i			0.163130i	−0.996668	+	0.0815648i	$0.974008\pi$
$642$	24.6157	+	237.852i	0.0383423	+	0.370486i
$643$	−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
$645$	−1039.28	+	627.779i	−1.61129	+	0.973300i
$646$	−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	$0.0947423\pi$
$648$	−12.7606	+	647.874i	−0.0196923	+	0.999806i
$649$			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	−0.521763	−	0.853090i	$-0.674726\pi$
$653$	216.356	−	216.356i	0.331327	−	0.331327i	0.853090	+	0.521763i	$0.174726\pi$
$654$	−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
$657$	160.085	−	20.4836i	0.243661	−	0.0311775i
$658$	104.605	+	226.772i	0.158974	+	0.344638i
$659$			862.678i			1.30907i	0.756031	+	0.654535i	$0.227136\pi$
$659$			862.678i			1.30907i	−0.756031	+	0.654535i	$0.772864\pi$
$660$	−820.636	+	588.812i	−1.24339	+	0.892139i
$661$	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
$663$	452.966	−	222.355i	0.683206	−	0.335377i
$664$	−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
$668$	−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
$672$	−124.149	−	464.633i	−0.184745	−	0.691419i
$673$	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
$675$	−18.6824	+	674.741i	−0.0276777	+	0.999617i
$676$	59.3223	+	50.6203i	0.0877550	+	0.0748820i
$677$	754.987	+	754.987i	1.11520	+	1.11520i	0.992437	+	0.122759i	$0.0391742\pi$
$677$	754.987	+	754.987i	1.11520	+	1.11520i	0.122759	+	0.992437i	$0.460826\pi$
$678$	88.4502	+	854.659i	0.130458	+	1.26056i
$679$	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	$0.0914626\pi$
$683$	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
$687$	727.455	−	357.098i	1.05889	−	0.519794i
$688$	1048.45	+	760.314i	1.52391	+	1.10511i
$689$	−280.154			−0.406609
$690$	322.839	−	476.775i	0.467882	−	0.690978i
$691$		−	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
$693$	752.851	−	96.3306i	1.08637	−	0.139005i
$694$	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
$698$	−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	$-0.998178\pi$
$701$		−	8.02635i		−	0.0114499i	0.999984	−	0.00572493i	$-0.00182231\pi$
$702$	−347.930	+	561.158i	−0.495626	+	0.799371i
$703$	−48.4074	+	48.4074i	−0.0688583	+	0.0688583i
$704$	919.350	+	561.685i	1.30590	+	0.797848i
$705$	−320.023	+	193.310i	−0.453933	+	0.274198i
$706$	1013.09	+	373.490i	1.43497	+	0.529023i
$707$	562.949	−	562.949i	0.796250	−	0.796250i
$708$	12.9824	−	50.8261i	0.0183368	−	0.0717883i
$709$		−	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
$714$	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
$717$	124.249	−	60.9924i	0.173291	−	0.0850660i
$718$	380.872	−	175.688i	0.530463	−	0.244690i
$719$			901.949i			1.25445i	0.778838	+	0.627225i	$0.215809\pi$
$719$			901.949i			1.25445i	−0.778838	+	0.627225i	$0.784191\pi$
$720$	670.676	−	261.905i	0.931494	−	0.363757i
$721$	−202.815			−0.281296
$722$	−283.245	−	614.044i	−0.392305	−	0.850477i
$723$	−280.476	−	571.365i	−0.387933	−	0.790270i
$724$	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	0.994581	−	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
$732$	−99.0909	−	25.3106i	−0.135370	−	0.0345773i
$733$	−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
$735$	85.9243	−	348.092i	0.116904	−	0.473594i
$736$	−602.513	−	119.148i	−0.818631	−	0.161886i
$737$	−908.537	−	908.537i	−1.23275	−	1.23275i
$738$	24.5379	−	106.748i	0.0332492	−	0.144645i
$739$	−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	0.599271	−	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
$747$	−804.681	+	102.963i	−1.07722	+	0.137835i
$748$	−923.382	+	73.0868i	−1.23447	+	0.0977096i
$749$	−199.656			−0.266564
$750$	700.777	−	267.229i	0.934370	−	0.356305i
$751$		−	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
$753$	−211.101	−	430.041i	−0.280347	−	0.571103i
$754$	−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	$0.0639866\pi$
$758$	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	$0.0748684\pi$
$761$			354.692i			0.466087i	−0.972466	+	0.233043i	$0.925132\pi$
$762$	−794.092	+	82.1820i	−1.04212	+	0.107850i
$763$	566.586	−	566.586i	0.742576	−	0.742576i
$764$	−882.813	+	1034.58i	−1.15551	+	1.35416i
$765$	−334.607	+	520.802i	−0.437395	+	0.680787i
$766$	−335.823	+	910.914i	−0.438411	+	1.18918i
$767$	37.7956	−	37.7956i	0.0492772	−	0.0492772i
$768$	−535.886	−	550.137i	−0.697768	−	0.716324i
$769$			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	−0.982806	−	0.184639i	$-0.940888\pi$
$773$	−616.984	+	616.984i	−0.798168	+	0.798168i	0.184639	+	0.982806i	$0.440888\pi$
$774$	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
$777$	94.7662	+	193.051i	0.121964	+	0.248457i
$778$	−503.117	−	1090.70i	−0.646679	−	1.40193i
$779$			29.1122i			0.0373713i
$780$	723.904	+	119.067i	0.928082	+	0.152650i
$781$	617.256			0.790340
$782$	479.495	−	221.180i	0.613165	−	0.282839i
$783$	393.450	+	80.4958i	0.502490	+	0.102804i
$784$	−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	0.939994	−	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
$792$	973.287	−	722.300i	1.22890	−	0.911995i
$793$	−73.6865	−	73.6865i	−0.0929212	−	0.0929212i
$794$	−783.636	−	288.900i	−0.986947	−	0.363853i
$795$	294.181	−	177.700i	0.370039	−	0.223522i
$796$	744.324	−	872.281i	0.935081	−	1.09583i
$797$	−485.701	−	485.701i	−0.609411	−	0.609411i	0.333381	−	0.942792i	$-0.391811\pi$
$797$	−485.701	−	485.701i	−0.609411	−	0.609411i	−0.942792	+	0.333381i	$0.891811\pi$
$798$	143.041	−	14.8036i	0.179249	−	0.0185508i
$799$	−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
$804$	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
$807$	0.718328	+	1.46333i	0.000890122	+	0.00181329i
$808$	344.272	−	1223.83i	0.426079	−	1.51465i
$809$	−183.688			−0.227056			−0.113528	−	0.993535i	$-0.536215\pi$
$809$	−183.688			−0.227056			−0.113528	+	0.993535i	$0.536215\pi$
$810$	9.41062	−	809.945i	0.0116181	−	0.999933i
$811$			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
$813$	−977.111	+	479.651i	−1.20186	+	0.589977i
$814$	−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
$818$	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	$0.249121\pi$
$821$			1157.86i			1.41030i	−0.709057	+	0.705152i	$0.750879\pi$
$822$	−507.275	+	52.4988i	−0.617123	+	0.0638672i
$823$	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
$825$	1019.82	−	744.274i	1.23614	−	0.902150i
$826$	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	$0.375901\pi$
$828$	−378.167	+	578.279i	−0.456723	+	0.698404i
$829$			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
$834$	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
$837$	76.1123	−	372.024i	0.0909346	−	0.444473i
$838$	−1058.05	+	488.053i	−1.26259	+	0.582402i
$839$			425.692i			0.507380i	0.967286	+	0.253690i	$0.0816443\pi$
$839$			425.692i			0.507380i	−0.967286	+	0.253690i	$0.918356\pi$
$840$	159.871	+	579.520i	0.190323	+	0.689904i
$841$	−619.762			−0.736935
$842$	407.702	+	883.855i	0.484207	+	1.04971i
$843$	−858.410	+	421.382i	−1.01828	+	0.499860i
$844$	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
$848$	−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
$852$	−426.327	−	108.896i	−0.500384	−	0.127812i
$853$	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
$855$	45.7892	+	210.363i	0.0535546	+	0.246039i
$856$	−278.073	+	155.973i	−0.324852	+	0.182212i
$857$	575.339	+	575.339i	0.671340	+	0.671340i	0.958025	−	0.286685i	$-0.0925532\pi$
$857$	575.339	+	575.339i	0.671340	+	0.671340i	−0.286685	+	0.958025i	$0.592553\pi$
$858$	1228.41	−	127.130i	1.43171	−	0.148171i
$859$	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	0.352238	−	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
$867$	268.676	−	131.889i	0.309891	−	0.152122i
$868$	22.2375	+	280.950i	0.0256193	+	0.323675i
$869$	1488.68			1.71310
$870$	−84.3547	−	438.176i	−0.0969594	−	0.503651i
$871$			933.264i			1.07149i
$872$	346.496	−	1231.74i	0.397358	−	1.41255i
$873$	−137.883	−	1077.60i	−0.157942	−	1.23436i
$874$	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	$0.950273\pi$
$878$	−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	$-0.725739\pi$
$881$		−	1337.17i		−	1.51779i	0.651213	−	0.758895i	$-0.274261\pi$
$882$	−96.3865	+	419.312i	−0.109282	+	0.475411i
$883$	−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
$885$	−15.7145	+	63.6616i	−0.0177565	+	0.0719340i
$886$	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	$0.475132\pi$
$888$	282.800	+	194.842i	0.318469	+	0.219416i
$889$		−	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
$894$	−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
$897$	−631.994	+	310.238i	−0.704564	+	0.345861i
$898$	198.097	+	429.454i	0.220598	+	0.478234i
$899$		−	209.190i		−	0.232692i
$900$	−835.674	+	334.140i	−0.928526	+	0.371267i
$901$	315.187			0.349819
$902$	−186.031	+	85.8120i	−0.206243	+	0.0951352i
$903$	536.074	+	1092.05i	0.593659	+	1.20936i
$904$	−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	0.334152	−	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	$-0.177066\pi$
$911$	1547.30			1.69846			0.849231	+	0.528022i	$0.177066\pi$
$912$	187.657	−	132.363i	0.205764	−	0.145135i
$913$	1072.93	+	1072.93i	1.17517	+	1.17517i
$914$	−644.364	−	237.555i	−0.704993	−	0.259907i
$915$	124.115	+	30.6370i	0.135645	+	0.0334831i
$916$	821.934	+	701.363i	0.897307	+	0.765680i
$917$	514.175	+	514.175i	0.560715	+	0.560715i
$918$	391.438	−	631.331i	0.426403	−	0.687725i
$919$	−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
$924$	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
$927$	46.2441	+	361.411i	0.0498858	+	0.389872i
$928$	−395.459	+	264.877i	−0.426141	+	0.285427i
$929$	−1529.05			−1.64591			−0.822955	−	0.568106i	$-0.807676\pi$
$929$	−1529.05			−1.64591			−0.822955	+	0.568106i	$0.807676\pi$
$930$	−414.315	+	79.7611i	−0.445500	+	0.0857646i
$931$		−	114.355i		−	0.122830i
$932$	24.6446	+	311.361i	0.0264427	+	0.334079i
$933$	−35.0722	−	71.4467i	−0.0375908	−	0.0765773i
$934$	−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	$0.0833328\pi$
$938$	−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	$-0.829377\pi$
$941$		−	961.186i		−	1.02145i	0.859744	−	0.510726i	$-0.170623\pi$
$942$	122.281	+	1181.56i	0.129811	+	1.25431i
$943$	82.5844	−	82.5844i	0.0875763	−	0.0875763i
$944$	69.0730	−	11.0034i	0.0731706	−	0.0116561i
$945$	671.865	+	77.4320i	0.710969	+	0.0819386i
$946$	−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	$-0.139445\pi$
$948$	−1028.20	−	262.632i	−1.08460	−	0.277038i
$949$			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	−0.738981	−	0.673726i	$-0.764693\pi$
$953$	−62.1880	+	62.1880i	−0.0652550	+	0.0652550i	0.673726	+	0.738981i	$0.264693\pi$
$954$	−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
$957$	−331.002	−	674.295i	−0.345875	−	0.704592i
$958$	797.397	−	367.821i	0.832356	−	0.383947i
$959$		−	425.813i		−	0.444018i
$960$	675.388	+	682.239i	0.703530	+	0.710666i
$961$	763.202			0.794174
$962$	146.570	+	317.749i	0.152360	+	0.330300i
$963$	45.5240	+	355.783i	0.0472731	+	0.369453i
$964$	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	0.707713	−	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	$-0.405154\pi$
$971$	570.125			0.587153			0.293576	+	0.955936i	$0.405154\pi$
$972$	4.32014	+	971.990i	0.00444459	+	0.999990i
$973$	44.6290	+	44.6290i	0.0458674	+	0.0458674i
$974$	301.565	−	817.991i	0.309615	−	0.839827i
$975$	−906.053	−	141.522i	−0.929285	−	0.145151i
$976$	−21.4522	−	134.665i	−0.0219797	−	0.137977i
$977$	−430.216	−	430.216i	−0.440344	−	0.440344i	0.451784	−	0.892128i	$-0.350788\pi$
$977$	−430.216	−	430.216i	−0.440344	−	0.440344i	−0.892128	+	0.451784i	$0.850788\pi$
$978$	51.2149	+	494.869i	0.0523670	+	0.506001i
$979$	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	0.994687	−	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
$987$	165.071	+	336.272i	0.167246	+	0.340701i
$988$	233.259	−	18.4627i	0.236092	−	0.0186870i
$989$	1553.59			1.57086
$990$	−1209.28	+	912.670i	−1.22149	+	0.921889i
$991$			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
$993$	−767.373	+	376.693i	−0.772783	+	0.379349i
$994$	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	$0.187208\pi$
$998$	−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.23.13	yes	40
3.2	odd	2	inner	60.3.l.a.23.8	yes	40
4.3	odd	2	inner	60.3.l.a.23.18	yes	40
5.2	odd	4	inner	60.3.l.a.47.3	yes	40
5.3	odd	4		300.3.l.g.107.18		40
5.4	even	2		300.3.l.g.143.8		40
12.11	even	2	inner	60.3.l.a.23.3	✓	40
15.2	even	4	inner	60.3.l.a.47.18	yes	40
15.8	even	4		300.3.l.g.107.3		40
15.14	odd	2		300.3.l.g.143.13		40
20.3	even	4		300.3.l.g.107.13		40
20.7	even	4	inner	60.3.l.a.47.8	yes	40
20.19	odd	2		300.3.l.g.143.3		40
60.23	odd	4		300.3.l.g.107.8		40
60.47	odd	4	inner	60.3.l.a.47.13	yes	40
60.59	even	2		300.3.l.g.143.18		40

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

\(f(q)\)	\(=\)	\(q+(0.837725 + 1.81610i) q^{2} +(1.32197 + 2.69303i) q^{3} +(-2.59643 + 3.04278i) q^{4} +(3.21472 - 3.82956i) q^{5} +(-3.78336 + 4.65685i) q^{6} +(-3.54241 - 3.54241i) q^{7} +(-7.70110 - 2.16636i) q^{8} +(-5.50478 + 7.12021i) q^{9} +O(q^{10})\)	\(q+(0.837725 + 1.81610i) q^{2} +(1.32197 + 2.69303i) 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} +(-7.70110 - 2.16636i) q^{8} +(-5.50478 + 7.12021i) q^{9} +(9.64792 + 2.63013i) q^{10} +16.8337 q^{11} +(-11.6267 - 2.96979i) q^{12} +(-8.64592 - 8.64592i) q^{13} +(3.46580 - 9.40093i) q^{14} +(14.5629 + 3.59476i) q^{15} +(-2.51707 - 15.8008i) q^{16} +(9.72710 + 9.72710i) q^{17} +(-17.5425 - 4.03246i) 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} +(-4.34655 - 23.6031i) q^{24} +(-4.33113 - 24.6220i) q^{25} +(8.45895 - 22.9448i) q^{26} +(-26.4521 - 5.41182i) q^{27} +(19.9764 - 1.58116i) q^{28} -14.8741 q^{29} +(5.67126 + 29.4591i) q^{30} +14.0641i q^{31} +(26.5872 - 17.8080i) q^{32} +(22.2536 + 45.3336i) 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} +(4.00784 + 8.68857i) q^{38} +(11.8540 - 34.7134i) q^{39} +(-33.0531 + 22.5276i) q^{40} +6.08509i q^{41} +(29.8987 - 3.09427i) q^{42} +(-57.2366 + 57.2366i) q^{43} +(-43.7075 + 51.2213i) q^{44} +(9.57094 + 43.9704i) q^{45} +(13.2781 - 36.0167i) q^{46} +(-17.6247 + 17.6247i) q^{47} +(39.2244 - 27.6667i) 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} +(-12.3312 - 52.5732i) q^{54} +(54.1156 - 64.4657i) q^{55} +(19.6063 + 34.9546i) q^{56} +(6.32456 + 12.8840i) q^{57} +(-12.4604 - 27.0128i) q^{58} +4.37150i q^{59} +(-48.7496 + 34.9782i) q^{60} +8.52269 q^{61} +(-25.5418 + 11.7818i) q^{62} +(44.7229 - 5.72249i) 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} +(-54.8532 + 4.34170i) q^{68} +(18.6074 - 54.4900i) q^{69} +(-24.8599 - 43.4939i) q^{70} +36.6679 q^{71} +(57.8178 - 42.9080i) q^{72} +(-12.6800 - 12.6800i) q^{73} +(-26.8519 - 9.89937i) q^{74} +(60.5820 - 44.2134i) q^{75} +(-12.4218 + 14.5573i) q^{76} +(-59.6318 - 59.6318i) q^{77} +(72.9733 - 7.55214i) 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} +(30.6663 + 51.7068i) q^{84} +(68.5205 - 5.98063i) q^{85} +(-151.896 - 55.9988i) q^{86} +(-19.6631 - 40.0563i) q^{87} +(-129.638 - 36.4679i) q^{88} +115.022 q^{89} +(-71.8368 + 54.2169i) q^{90} +61.2548i q^{91} +(76.5332 - 6.05770i) q^{92} +(-37.8749 + 18.5923i) 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} +(43.4096 - 20.0239i) 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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