LMFDB - Embedded newform 60.3.l.a.23.18

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			23.18
Character	$\chi$	$=$	60.23
Dual form			60.3.l.a.47.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.81610 + 0.837725i) q^{2} +(-1.32197 - 2.69303i) q^{3} +(2.59643 + 3.04278i) q^{4} +(3.21472 - 3.82956i) q^{5} +(-0.144815 - 5.99825i) q^{6} +(3.54241 + 3.54241i) q^{7} +(2.16636 + 7.70110i) q^{8} +(-5.50478 + 7.12021i) q^{9} +O(q^{10})$	\(q+(1.81610 + 0.837725i) q^{2} +(-1.32197 - 2.69303i) q^{3} +(2.59643 + 3.04278i) q^{4} +(3.21472 - 3.82956i) q^{5} +(-0.144815 - 5.99825i) q^{6} +(3.54241 + 3.54241i) q^{7} +(2.16636 + 7.70110i) q^{8} +(-5.50478 + 7.12021i) q^{9} +(9.04638 - 4.26182i) q^{10} -16.8337 q^{11} +(4.76189 - 11.0147i) 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} +(-15.9620 + 8.31951i) 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} +(17.8754 - 16.0147i) q^{24} +(-4.33113 - 24.6220i) q^{25} +(-8.45895 - 22.9448i) q^{26} +(26.4521 + 5.41182i) q^{27} +(-1.58116 + 19.9764i) q^{28} -14.8741 q^{29} +(-23.4362 - 18.7281i) q^{30} -14.0641i q^{31} +(-17.8080 + 26.5872i) q^{32} +(22.2536 + 45.3336i) q^{33} +(9.51674 + 25.8140i) q^{34} +(24.9537 - 2.17802i) q^{35} +(-35.9581 + 1.73727i) q^{36} +(-10.1182 + 10.1182i) q^{37} +(-8.68857 - 4.00784i) q^{38} +(-11.8540 + 34.7134i) q^{39} +(36.4561 + 16.4607i) q^{40} +6.08509i q^{41} +(20.7353 - 21.7613i) 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} +(45.8794 - 14.1096i) 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} +(43.5060 + 31.9880i) q^{54} +(-54.1156 + 64.4657i) q^{55} +(-19.6063 + 34.9546i) q^{56} +(6.32456 + 12.8840i) q^{57} +(-27.0128 - 12.4604i) q^{58} -4.37150i q^{59} +(-26.8735 - 53.6453i) q^{60} +8.52269 q^{61} +(11.7818 - 25.5418i) q^{62} +(-44.7229 + 5.72249i) q^{63} +(-54.6137 + 33.3667i) q^{64} +(-60.9043 + 5.31588i) q^{65} +(2.43777 + 100.973i) q^{66} +(53.9714 + 53.9714i) q^{67} +(-4.34170 + 54.8532i) q^{68} +(18.6074 - 54.4900i) q^{69} +(47.1431 + 16.9489i) q^{70} -36.6679 q^{71} +(-66.7588 - 26.9679i) 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} +(-50.6084 + 53.1125i) 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} +(55.8873 - 22.1502i) q^{84} +(68.5205 - 5.98063i) q^{85} +(151.896 - 55.9988i) q^{86} +(19.6631 + 40.0563i) q^{87} +(-36.4679 - 129.638i) q^{88} +115.022 q^{89} +(-19.4533 + 87.8725i) q^{90} -61.2548i q^{91} +(-6.05770 + 76.5332i) q^{92} +(-37.8749 + 18.5923i) q^{93} +(46.7728 - 17.2435i) q^{94} +(-15.3798 + 18.3214i) q^{95} +(95.1415 + 12.8098i) q^{96} +(-85.3544 + 85.3544i) q^{97} +(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
$3$	−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
$6$	−0.144815	−	5.99825i	−0.0241358	−	0.999709i
$7$	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	$-0.777344\pi$
$11$	−16.8337			−1.53034			−0.765168	+	0.643831i	$0.777344\pi$
$12$	4.76189	−	11.0147i	0.396824	−	0.917895i
$13$	−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	$0.617413\pi$
$18$	−15.9620	+	8.31951i	−0.886778	+	0.462195i
$19$	−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	0.937650	−	0.347580i	$-0.112997\pi$
$23$	13.5716	+	13.5716i	0.590070	+	0.590070i	−0.347580	+	0.937650i	$0.612997\pi$
$24$	17.8754	−	16.0147i	0.744808	−	0.667279i
$25$	−4.33113	−	24.6220i	−0.173245	−	0.984879i
$26$	−8.45895	−	22.9448i	−0.325344	−	0.882491i
$27$	26.4521	+	5.41182i	0.979706	+	0.200438i
$28$	−1.58116	+	19.9764i	−0.0564699	+	0.713444i
$29$	−14.8741			−0.512899			−0.256449	−	0.966558i	$-0.582553\pi$
$29$	−14.8741			−0.512899			−0.256449	+	0.966558i	$0.582553\pi$
$30$	−23.4362	−	18.7281i	−0.781208	−	0.624271i
$31$		−	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
$33$	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
$36$	−35.9581	+	1.73727i	−0.998835	+	0.0482576i
$37$	−10.1182	+	10.1182i	−0.273465	+	0.273465i	−0.830493	−	0.557029i	$-0.811941\pi$
$37$	−10.1182	+	10.1182i	−0.273465	+	0.273465i	0.557029	+	0.830493i	$0.311941\pi$
$38$	−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	$0.0236430\pi$
$41$			6.08509i			0.148417i	−0.997243	+	0.0742084i	$0.976357\pi$
$42$	20.7353	−	21.7613i	0.493697	−	0.518125i
$43$	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
$45$	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	−0.494299	−	0.869292i	$-0.664575\pi$
$47$	17.6247	−	17.6247i	0.374993	−	0.374993i	0.869292	+	0.494299i	$0.164575\pi$
$48$	45.8794	−	14.1096i	0.955821	−	0.293951i
$49$		−	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	−0.537546	−	0.843234i	$-0.680649\pi$
$53$	16.2015	−	16.2015i	0.305688	−	0.305688i	0.843234	+	0.537546i	$0.180649\pi$
$54$	43.5060	+	31.9880i	0.805666	+	0.592370i
$55$	−54.1156	+	64.4657i	−0.983920	+	1.17210i
$56$	−19.6063	+	34.9546i	−0.350112	+	0.624189i
$57$	6.32456	+	12.8840i	0.110957	+	0.226034i
$58$	−27.0128	−	12.4604i	−0.465738	−	0.214834i
$59$		−	4.37150i		−	0.0740931i	−0.999314	−	0.0370466i	$-0.988205\pi$
$59$		−	4.37150i		−	0.0740931i	0.999314	−	0.0370466i	$-0.0117950\pi$
$60$	−26.8735	−	53.6453i	−0.447892	−	0.894088i
$61$	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
$63$	−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
$66$	2.43777	+	100.973i	0.0369359	+	1.52989i
$67$	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	$-0.583137\pi$
$71$	−36.6679			−0.516449			−0.258225	+	0.966085i	$0.583137\pi$
$72$	−66.7588	−	26.9679i	−0.927205	−	0.374554i
$73$	−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
$78$	−50.6084	+	53.1125i	−0.648825	+	0.680929i
$79$	−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	0.209822	−	0.977740i	$-0.432712\pi$
$83$	−63.7372	−	63.7372i	−0.767918	−	0.767918i	−0.977740	+	0.209822i	$0.932712\pi$
$84$	55.8873	−	22.1502i	0.665325	−	0.263692i
$85$	68.5205	−	5.98063i	0.806123	−	0.0703604i
$86$	151.896	−	55.9988i	1.76623	−	0.651149i
$87$	19.6631	+	40.0563i	0.226013	+	0.460417i
$88$	−36.4679	−	129.638i	−0.414408	−	1.47316i
$89$	115.022			1.29238			0.646190	−	0.763177i	$-0.276361\pi$
$89$	115.022			1.29238			0.646190	+	0.763177i	$0.276361\pi$
$90$	−19.4533	+	87.8725i	−0.216148	+	0.976361i
$91$		−	61.2548i		−	0.673130i
$92$	−6.05770	+	76.5332i	−0.0658445	+	0.831883i
$93$	−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
$96$	95.1415	+	12.8098i	0.991057	+	0.133436i
$97$	−85.3544	+	85.3544i	−0.879942	+	0.879942i	−0.993528	−	0.113586i	$-0.963766\pi$
$97$	−85.3544	+	85.3544i	−0.879942	+	0.879942i	0.113586	+	0.993528i	$0.463766\pi$
$98$	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	$0.288221\pi$
$101$			158.917i			1.57343i	−0.617313	+	0.786717i	$0.711779\pi$
$102$	56.9369	−	59.7542i	0.558205	−	0.585826i
$103$	−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
$105$	−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	−0.826423	−	0.563050i	$-0.809628\pi$
$107$	−28.1808	+	28.1808i	−0.263372	+	0.263372i	0.563050	+	0.826423i	$0.309628\pi$
$108$	52.2140	+	94.5394i	0.483463	+	0.875365i
$109$			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	−0.0989792	−	0.995089i	$-0.531558\pi$
$113$	101.260	−	101.260i	0.896110	−	0.896110i	0.995089	+	0.0989792i	$0.0315577\pi$
$114$	0.692822	+	28.6968i	0.00607739	+	0.251726i
$115$	95.6023	−	8.34440i	0.831324	−	0.0725600i
$116$	−38.6195	−	45.2586i	−0.332927	−	0.390160i
$117$	109.155	−	13.9668i	0.932946	−	0.119375i
$118$	3.66211	−	7.93907i	0.0310348	−	0.0672803i
$119$			68.9147i			0.579115i
$120$	−3.86494	−	119.938i	−0.0322078	−	0.999481i
$121$	162.373			1.34193
$122$	15.4781	+	7.13968i	0.126869	+	0.0585219i
$123$	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
$126$	−86.0151	−	27.0729i	−0.682659	−	0.214864i
$127$	−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	$-0.313100\pi$
$131$	145.148			1.10800			0.554002	+	0.832515i	$0.313100\pi$
$132$	−80.1601	+	185.419i	−0.607274	+	1.40469i
$133$	−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	$0.649601\pi$
$138$	79.4405	−	83.3713i	0.575656	−	0.604140i
$139$	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
$144$	−98.6488	−	104.902i	−0.685061	−	0.728485i
$145$	−47.8160	+	56.9612i	−0.329765	+	0.392836i
$146$	−12.4058	−	33.6506i	−0.0849713	−	0.230483i
$147$	−64.3705	+	31.5986i	−0.437895	+	0.214957i
$148$	−57.0587	−	4.51626i	−0.385531	−	0.0305153i
$149$	25.9233			0.173982			0.0869911	−	0.996209i	$-0.472275\pi$
$149$	25.9233			0.173982			0.0869911	+	0.996209i	$0.472275\pi$
$150$	−147.062	+	29.5448i	−0.980410	+	0.196965i
$151$			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
$153$	−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
$156$	−136.403	+	54.0616i	−0.874381	+	0.346549i
$157$	139.992	−	139.992i	0.891666	−	0.891666i	−0.103014	−	0.994680i	$-0.532849\pi$
$157$	139.992	−	139.992i	0.891666	−	0.891666i	0.994680	+	0.103014i	$0.0328486\pi$
$158$	−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
$162$	28.6308	−	159.450i	0.176733	−	0.984259i
$163$	−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
$165$	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	−0.408316	−	0.912841i	$-0.633884\pi$
$167$	84.2556	−	84.2556i	0.504524	−	0.504524i	0.912841	+	0.408316i	$0.133884\pi$
$168$	120.053	+	6.59130i	0.714599	+	0.0392339i
$169$		−	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	−0.839504	−	0.543353i	$-0.817154\pi$
$173$	−51.2341	+	51.2341i	−0.296151	+	0.296151i	0.543353	+	0.839504i	$0.317154\pi$
$174$	2.15399	+	89.2184i	0.0123792	+	0.512749i
$175$	71.8785	−	102.564i	0.410734	−	0.586078i
$176$	42.3716	−	265.985i	0.240747	−	1.51128i
$177$	−11.7726	+	5.77899i	−0.0665116	+	0.0326497i
$178$	208.891	+	96.3566i	1.17354	+	0.541329i
$179$			27.2276i			0.152109i	0.997104	+	0.0760547i	$0.0242324\pi$
$179$			27.2276i			0.152109i	−0.997104	+	0.0760547i	$0.975768\pi$
$180$	−108.942	+	143.289i	−0.605234	+	0.796047i
$181$	−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
$183$	−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
$186$	−84.3599	+	2.03669i	−0.453548	+	0.0109499i
$187$	−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	$-0.849351\pi$
$191$	−340.010			−1.78016			−0.890078	+	0.455807i	$0.849351\pi$
$192$	162.055	+	102.966i	0.844038	+	0.536283i
$193$	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	$-0.550374\pi$
$198$	268.699	−	140.048i	1.35707	−	0.707313i
$199$	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
$204$	153.461	−	60.8221i	0.752259	−	0.298147i
$205$	23.3032	+	19.5619i	0.113674	+	0.0954238i
$206$	−75.9701	+	28.0076i	−0.368787	+	0.135959i
$207$	−171.341	+	21.9239i	−0.827736	+	0.105912i
$208$	158.375	−	114.850i	0.761416	−	0.552163i
$209$	80.5356			0.385338
$210$	−16.6780	−	149.363i	−0.0794191	−	0.711255i
$211$			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
$213$	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
$216$	15.6279	+	215.434i	0.0723512	+	0.997379i
$217$	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
$222$	62.1567	+	59.2262i	0.279985	+	0.266785i
$223$	−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
$225$	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	−0.783246	−	0.621711i	$-0.786438\pi$
$227$	−36.6684	+	36.6684i	−0.161535	+	0.161535i	0.621711	+	0.783246i	$0.286438\pi$
$228$	−22.7818	+	52.6966i	−0.0999201	+	0.231126i
$229$		−	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	−0.578625	−	0.815593i	$-0.696411\pi$
$233$	55.2135	−	55.2135i	0.236968	−	0.236968i	0.815593	+	0.578625i	$0.196411\pi$
$234$	209.936	+	66.0765i	0.897163	+	0.282378i
$235$	−10.8364	−	124.153i	−0.0461123	−	0.528312i
$236$	13.3015	−	11.3503i	0.0563624	−	0.0480945i
$237$	116.908	+	238.157i	0.493283	+	1.00488i
$238$	−57.7316	+	125.156i	−0.242570	+	0.525865i
$239$			46.1374i			0.193044i	0.995331	+	0.0965218i	$0.0307718\pi$
$239$			46.1374i			0.193044i	−0.995331	+	0.0965218i	$0.969228\pi$
$240$	93.4557	−	221.057i	0.389399	−	0.921069i
$241$	−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
$243$	−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
$246$	36.4999	−	0.881212i	0.148374	−	0.00358216i
$247$	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	$-0.396955\pi$
$251$	159.687			0.636203			0.318101	+	0.948057i	$0.396955\pi$
$252$	−133.532	−	121.224i	−0.529890	−	0.481048i
$253$	−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	$0.663017\pi$
$258$	−351.608	−	335.031i	−1.36282	−	1.29857i
$259$	−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	0.923416	−	0.383802i	$-0.125385\pi$
$263$	141.919	+	141.919i	0.539614	+	0.539614i	−0.383802	+	0.923416i	$0.625385\pi$
$264$	−300.909	+	269.586i	−1.13981	+	1.02116i
$265$	−9.96136	−	114.128i	−0.0375900	−	0.430671i
$266$	−16.5811	−	44.9759i	−0.0623348	−	0.169082i
$267$	−152.055	−	309.757i	−0.569496	−	1.16014i
$268$	−24.0902	+	304.356i	−0.0898887	+	1.13566i
$269$	0.543377			0.00201999			0.00100999	−	0.999999i	$-0.499679\pi$
$269$	0.543377			0.00201999			0.00100999	+	0.999999i	$0.499679\pi$
$270$	262.360	−	63.7765i	0.971702	−	0.236209i
$271$		−	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
$273$	−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
$276$	214.114	−	84.8612i	0.775776	−	0.307468i
$277$	−79.2266	+	79.2266i	−0.286016	+	0.286016i	−0.835503	−	0.549486i	$-0.814823\pi$
$277$	−79.2266	+	79.2266i	−0.286016	+	0.286016i	0.549486	+	0.835503i	$0.314823\pi$
$278$	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	$0.191964\pi$
$281$			318.753i			1.13435i	−0.823597	+	0.567176i	$0.808036\pi$
$282$	−108.270	−	103.165i	−0.383935	−	0.365833i
$283$	−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
$285$	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
$288$	−91.2771	−	273.153i	−0.316934	−	0.948447i
$289$		−	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	−0.823841	−	0.566822i	$-0.808173\pi$
$293$	−75.3066	+	75.3066i	−0.257019	+	0.257019i	0.566822	+	0.823841i	$0.308173\pi$
$294$	−143.374	+	3.46146i	−0.487667	+	0.0117737i
$295$	−16.7409	−	14.0531i	−0.0567489	−	0.0476378i
$296$	−99.8408	−	56.0015i	−0.337300	−	0.189194i
$297$	−445.286	−	91.1009i	−1.49928	−	0.306737i
$298$	47.0794	+	21.7166i	0.157984	+	0.0728746i
$299$		−	234.678i		−	0.784876i
$300$	−291.829	−	69.5409i	−0.972763	−	0.231803i
$301$	405.511			1.34721
$302$	−167.862	+	363.908i	−0.555836	+	1.20499i
$303$	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
$306$	−236.189	−	74.3394i	−0.771858	−	0.242939i
$307$	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	$-0.486419\pi$
$311$	26.5302			0.0853063			0.0426531	+	0.999090i	$0.486419\pi$
$312$	−293.011	−	16.0873i	−0.939138	−	0.0515619i
$313$	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	$0.702530\pi$
$318$	−99.5268	−	94.8344i	−0.312977	−	0.298221i
$319$	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
$324$	185.572	−	265.592i	0.572752	−	0.819729i
$325$	−175.433	+	250.326i	−0.539794	+	0.770234i
$326$	−155.600	+	57.3644i	−0.477301	+	0.175965i
$327$	430.732	−	211.441i	1.31722	−	0.646608i
$328$	−46.8619	+	13.1825i	−0.142872	+	0.0401906i
$329$	124.868			0.379537
$330$	394.518	+	315.264i	1.19551	+	0.955344i
$331$		−	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
$333$	−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
$336$	212.506	+	112.542i	0.632457	+	0.334945i
$337$	294.164	−	294.164i	0.872889	−	0.872889i	−0.119897	−	0.992786i	$-0.538256\pi$
$337$	294.164	−	294.164i	0.872889	−	0.872889i	0.992786	+	0.119897i	$0.0382564\pi$
$338$	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
$342$	76.3653	−	39.8021i	0.223290	−	0.116380i
$343$	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	−0.981458	−	0.191679i	$-0.938607\pi$
$347$	−274.053	+	274.053i	−0.789779	+	0.789779i	0.191679	+	0.981458i	$0.438607\pi$
$348$	−70.8287	+	163.834i	−0.203531	+	0.470787i
$349$			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	$-0.472893\pi$
$353$	381.746	−	381.746i	1.08143	−	1.08143i	0.996376	−	0.0850569i	$-0.0271072\pi$
$354$	−26.2213	+	0.633058i	−0.0740716	+	0.00178830i
$355$	−117.877	+	140.422i	−0.332048	+	0.395555i
$356$	298.646	+	349.986i	0.838894	+	0.983108i
$357$	185.589	−	91.1033i	0.519858	−	0.255191i
$358$	−22.8092	+	49.4480i	−0.0637129	+	0.138123i
$359$			209.720i			0.584178i	0.956391	+	0.292089i	$0.0943503\pi$
$359$			209.720i			0.584178i	−0.956391	+	0.292089i	$0.905650\pi$
$360$	−317.886	+	168.963i	−0.883017	+	0.469341i
$361$	−338.112			−0.936597
$362$	−502.377	−	231.735i	−1.38778	−	0.640151i
$363$	−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
$366$	−1.23421	−	51.1213i	−0.00337217	−	0.139676i
$367$	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
$372$	−154.912	−	66.9716i	−0.416431	−	0.180031i
$373$	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
$378$	40.8015	+	267.430i	0.107940	+	0.707488i
$379$	−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	0.0988948	−	0.995098i	$-0.468469\pi$
$383$	−343.246	−	343.246i	−0.896203	−	0.896203i	−0.995098	+	0.0988948i	$0.968469\pi$
$384$	208.051	+	322.755i	0.541800	+	0.840508i
$385$	−420.064	+	36.6642i	−1.09107	+	0.0952316i
$386$	98.7977	+	267.987i	0.255952	+	0.694267i
$387$	92.4613	+	722.612i	0.238918	+	1.86721i
$388$	−481.332	−	38.0980i	−1.24055	−	0.0981907i
$389$	−600.575			−1.54389			−0.771947	−	0.635687i	$-0.780717\pi$
$389$	−600.575			−1.54389			−0.771947	+	0.635687i	$0.780717\pi$
$390$	40.7058	+	364.550i	0.104374	+	0.934743i
$391$			264.025i			0.675255i
$392$	184.077	−	51.7819i	0.469583	−	0.132097i
$393$	−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
$396$	605.307	−	29.2447i	1.52855	−	0.0738503i
$397$	−295.285	+	295.285i	−0.743792	+	0.743792i	−0.973306	−	0.229513i	$-0.926287\pi$
$397$	−295.285	+	295.285i	−0.743792	+	0.743792i	0.229513	+	0.973306i	$0.426287\pi$
$398$	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	$-0.877787\pi$
$401$		−	300.412i		−	0.749157i	0.927195	−	0.374578i	$-0.122213\pi$
$402$	315.918	−	331.550i	0.785866	−	0.824751i
$403$	−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
$408$	329.652	+	18.0990i	0.807971	+	0.0443604i
$409$		−	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
$414$	−329.539	−	103.721i	−0.795988	−	0.250534i
$415$	−448.983	+	39.1883i	−1.08189	+	0.0944297i
$416$	383.837	−	75.9043i	0.922684	−	0.182462i
$417$	−16.6548	−	33.9281i	−0.0399397	−	0.0813623i
$418$	146.261	+	67.4667i	0.349906	+	0.161404i
$419$		−	582.593i		−	1.39044i	−0.718799	−	0.695218i	$-0.755308\pi$
$419$		−	582.593i		−	1.39044i	0.718799	−	0.695218i	$-0.244692\pi$
$420$	94.8366	−	285.230i	0.225801	−	0.679120i
$421$	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
$423$	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
$426$	5.31006	+	219.943i	0.0124649	+	0.516299i
$427$	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	$-0.722490\pi$
$431$	−554.639			−1.28686			−0.643432	+	0.765503i	$0.722490\pi$
$432$	−152.093	+	404.341i	−0.352066	+	0.935975i
$433$	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
$438$	−74.2217	+	77.8942i	−0.169456	+	0.177841i
$439$	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	0.750807	−	0.660522i	$-0.229665\pi$
$443$	39.9964	+	39.9964i	0.0902853	+	0.0902853i	−0.660522	+	0.750807i	$0.729665\pi$
$444$	63.2675	+	159.631i	0.142494	+	0.359529i
$445$	369.763	−	440.483i	0.830928	−	0.989850i
$446$	−18.6342	+	6.86980i	−0.0417808	+	0.0154031i
$447$	−34.2699	−	69.8122i	−0.0766665	−	0.156180i
$448$	−311.663	−	75.2655i	−0.695676	−	0.168003i
$449$	236.471			0.526660			0.263330	−	0.964706i	$-0.415179\pi$
$449$	236.471			0.526660			0.263330	+	0.964706i	$0.415179\pi$
$450$	273.976	+	356.983i	0.608836	+	0.793296i
$451$		−	102.435i		−	0.227128i
$452$	571.030	+	45.1977i	1.26334	+	0.0999949i
$453$	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
$456$	−85.5193	+	76.6174i	−0.187542	+	0.168021i
$457$	−242.806	+	242.806i	−0.531304	+	0.531304i	−0.920960	−	0.389657i	$-0.872594\pi$
$457$	−242.806	+	242.806i	−0.531304	+	0.531304i	0.389657	+	0.920960i	$0.372594\pi$
$458$	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	$-0.755411\pi$
$461$		−	640.776i		−	1.38997i	0.719024	−	0.694985i	$-0.244589\pi$
$462$	−349.051	+	366.322i	−0.755522	+	0.792905i
$463$	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
$465$	−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	−0.0862867	−	0.996270i	$-0.527500\pi$
$467$	424.962	−	424.962i	0.909984	−	0.909984i	0.996270	+	0.0862867i	$0.0275001\pi$
$468$	325.911	+	295.870i	0.696391	+	0.632201i
$469$			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
$474$	12.8066	+	530.453i	0.0270182	+	1.11910i
$475$	20.7209	+	117.796i	0.0436230	+	0.247992i
$476$	−209.693	+	178.932i	−0.440531	+	0.375909i
$477$	26.1723	+	204.544i	0.0548685	+	0.428813i
$478$	−38.6505	+	83.7902i	−0.0808588	+	0.175293i
$479$			439.071i			0.916641i	0.888787	+	0.458321i	$0.151549\pi$
$479$			439.071i			0.916641i	−0.888787	+	0.458321i	$0.848451\pi$
$480$	354.910	−	323.171i	0.739395	−	0.673272i
$481$	174.962			0.363747
$482$	−385.312	−	177.736i	−0.799403	−	0.368746i
$483$	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
$486$	−467.252	+	133.685i	−0.961424	+	0.275071i
$487$	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	$-0.222522\pi$
$491$	751.660			1.53088			0.765438	+	0.643509i	$0.222522\pi$
$492$	67.0257	+	28.9765i	0.136231	+	0.0588954i
$493$	−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
$498$	−373.082	+	391.542i	−0.749160	+	0.786228i
$499$	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	0.897792	−	0.440420i	$-0.145170\pi$
$503$	230.058	+	230.058i	0.457372	+	0.457372i	−0.440420	+	0.897792i	$0.645170\pi$
$504$	−140.955	−	332.018i	−0.279674	−	0.658766i
$505$	608.582	+	510.874i	1.20511	+	1.01163i
$506$	−223.519	−	606.293i	−0.441738	−	1.19821i
$507$	−52.5035	+	25.7733i	−0.103557	+	0.0508348i
$508$	41.9947	−	530.563i	0.0826667	−	1.04442i
$509$	98.9386			0.194378			0.0971892	−	0.995266i	$-0.469015\pi$
$509$	98.9386			0.194378			0.0971892	+	0.995266i	$0.469015\pi$
$510$	−45.7961	−	410.137i	−0.0897963	−	0.804190i
$511$		−	89.8357i		−	0.175804i
$512$	−375.274	−	348.301i	−0.732956	−	0.680276i
$513$	−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
$516$	−357.892	−	903.001i	−0.693589	−	1.75000i
$517$	−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	$-0.845548\pi$
$521$		−	485.997i		−	0.932816i	0.884570	−	0.466408i	$-0.154452\pi$
$522$	237.420	−	123.745i	0.454828	−	0.237059i
$523$	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
$525$	−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
$528$	−772.319	+	237.517i	−1.46273	+	0.449843i
$529$		−	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
$534$	−16.6569	−	689.930i	−0.0311926	−	1.29200i
$535$	17.3268	+	198.514i	0.0323865	+	0.371054i
$536$	−298.717	+	532.560i	−0.557308	+	0.993583i
$537$	73.3246	−	35.9941i	0.136545	−	0.0670281i
$538$	0.986826	+	0.455200i	0.00183425	+	0.000846097i
$539$			402.370i			0.746512i
$540$	529.898	+	103.961i	0.981293	+	0.192520i
$541$	−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
$543$	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
$546$	−367.422	+	8.87061i	−0.672934	+	0.0162465i
$547$	−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
$552$	459.943	+	25.2524i	0.833230	+	0.0457472i
$553$	−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	$0.621038\pi$
$558$	117.006	+	224.491i	0.209689	+	0.402314i
$559$	−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	0.467847	−	0.883809i	$-0.345030\pi$
$563$	−234.187	−	234.187i	−0.415962	−	0.415962i	−0.883809	+	0.467847i	$0.845030\pi$
$564$	−110.204	−	278.058i	−0.195398	−	0.493010i
$565$	−62.2592	−	713.308i	−0.110193	−	1.26249i
$566$	−591.898	+	218.212i	−1.04576	+	0.385534i
$567$	205.445	−	349.937i	0.362336	−	0.617173i
$568$	−79.4360	−	282.383i	−0.139852	−	0.497153i
$569$	−386.708			−0.679627			−0.339813	−	0.940493i	$-0.610364\pi$
$569$	−386.708			−0.679627			−0.339813	+	0.940493i	$0.610364\pi$
$570$	112.123	+	89.5990i	0.196708	+	0.157191i
$571$		−	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
$573$	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
$576$	63.0587	−	572.538i	0.109477	−	0.993989i
$577$	695.792	−	695.792i	1.20588	−	1.20588i	0.233530	−	0.972350i	$-0.424972\pi$
$577$	695.792	−	695.792i	1.20588	−	1.20588i	0.972350	−	0.233530i	$-0.0750277\pi$
$578$	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
$582$	524.338	+	499.616i	0.900924	+	0.858447i
$583$	−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	−0.882344	−	0.470604i	$-0.844036\pi$
$587$	−241.691	+	241.691i	−0.411740	+	0.411740i	0.470604	+	0.882344i	$0.344036\pi$
$588$	−263.282	−	113.822i	−0.447758	−	0.193575i
$589$			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	−0.793359	−	0.608754i	$-0.791670\pi$
$593$	−109.471	+	109.471i	−0.184605	+	0.184605i	0.608754	+	0.793359i	$0.291670\pi$
$594$	−732.366	−	538.475i	−1.23294	−	0.906524i
$595$	263.913	+	221.542i	0.443552	+	0.372339i
$596$	67.3082	+	78.8791i	0.112933	+	0.132348i
$597$	−378.972	−	772.015i	−0.634794	−	1.29316i
$598$	196.596	−	426.199i	0.328755	−	0.712707i
$599$			527.412i			0.880487i	0.897878	+	0.440243i	$0.145108\pi$
$599$			527.412i			0.880487i	−0.897878	+	0.440243i	$0.854892\pi$
$600$	−471.734	−	370.765i	−0.786223	−	0.617942i
$601$	−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
$603$	−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
$606$	953.224	−	23.0135i	1.57298	−	0.0379761i
$607$	−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
$612$	−366.666	−	332.869i	−0.599128	−	0.543903i
$613$	−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	$0.731171\pi$
$618$	175.855	+	167.564i	0.284556	+	0.271139i
$619$	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
$624$	−518.660	−	274.679i	−0.831186	−	0.440190i
$625$	−587.483	+	213.282i	−0.939972	+	0.341251i
$626$	128.999	+	349.908i	0.206069	+	0.558959i
$627$	−106.466	−	216.884i	−0.169802	−	0.345908i
$628$	789.443	+	62.4854i	1.25707	+	0.0994990i
$629$	−196.841			−0.312943
$630$	−380.192	+	242.369i	−0.603479	+	0.384712i
$631$			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
$633$	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
$636$	−101.305	−	255.605i	−0.159285	−	0.401894i
$637$	−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	$0.0259918\pi$
$641$			104.566i			0.163130i	−0.996668	+	0.0815648i	$0.974008\pi$
$642$	173.117	+	164.955i	0.269652	+	0.256939i
$643$	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
$645$	−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	−0.956031	−	0.293266i	$-0.905258\pi$
$647$	−428.808	+	428.808i	−0.662764	+	0.662764i	0.293266	+	0.956031i	$0.405258\pi$
$648$	559.510	−	326.884i	0.863441	−	0.504450i
$649$			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	−0.521763	−	0.853090i	$-0.674726\pi$
$653$	216.356	−	216.356i	0.331327	−	0.331327i	0.853090	+	0.521763i	$0.174726\pi$
$654$	959.382	−	23.1622i	1.46694	−	0.0354162i
$655$	466.612	−	555.855i	0.712385	−	0.848634i
$656$	−96.1491	−	15.3166i	−0.146569	−	0.0233485i
$657$	160.085	−	20.4836i	0.243661	−	0.0311775i
$658$	226.772	+	104.605i	0.344638	+	0.158974i
$659$		−	862.678i		−	1.30907i	−0.756031	−	0.654535i	$-0.772864\pi$
$659$		−	862.678i		−	1.30907i	0.756031	−	0.654535i	$-0.227136\pi$
$660$	452.380	+	903.048i	0.685424	+	1.36825i
$661$	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
$663$	−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
$666$	77.3283	−	245.685i	0.116109	−	0.368896i
$667$	−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
$672$	291.653	+	382.408i	0.434007	+	0.569059i
$673$	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	$0.460826\pi$
$678$	−622.050	−	592.722i	−0.917478	−	0.874221i
$679$	−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	$-0.908537\pi$
$683$	−848.561	−	848.561i	−1.24240	−	1.24240i	−0.283401	−	0.959002i	$-0.591463\pi$
$684$	172.030	−	8.31145i	0.251506	−	0.0121512i
$685$	423.377	−	36.9534i	0.618069	−	0.0539466i
$686$	685.353	−	252.666i	0.999057	−	0.368318i
$687$	−727.455	+	357.098i	−1.05889	+	0.519794i
$688$	760.314	+	1048.45i	1.10511	+	1.52391i
$689$	−280.154			−0.406609
$690$	−63.8964	−	572.238i	−0.0926035	−	0.829330i
$691$			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
$693$	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
$696$	−265.880	+	238.204i	−0.382011	+	0.342247i
$697$	−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	$-0.998178\pi$
$701$		−	8.02635i		−	0.0114499i	0.999984	−	0.00572493i	$-0.00182231\pi$
$702$	−99.5837	−	652.715i	−0.141857	−	0.929793i
$703$	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
$708$	−48.1509	−	20.8166i	−0.0680097	−	0.0294019i
$709$		−	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
$714$	413.368	−	9.97988i	0.578947	−	0.0139774i
$715$	1025.24	−	89.4858i	1.43391	−	0.125155i
$716$	−82.8476	+	70.6946i	−0.115709	+	0.0987354i
$717$	124.249	−	60.9924i	0.173291	−	0.0850660i
$718$	−175.688	+	380.872i	−0.244690	+	0.530463i
$719$		−	901.949i		−	1.25445i	−0.778838	−	0.627225i	$-0.784191\pi$
$719$		−	901.949i		−	1.25445i	0.778838	−	0.627225i	$-0.215809\pi$
$720$	−718.857	+	40.5517i	−0.998413	+	0.0563217i
$721$	−202.815			−0.281296
$722$	−614.044	−	283.245i	−0.850477	−	0.392305i
$723$	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
$726$	−23.5140	−	973.954i	−0.0323885	−	1.34153i
$727$	−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
$732$	40.5841	−	93.8752i	0.0554428	−	0.128245i
$733$	−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
$738$	−50.6250	−	97.1303i	−0.0685975	−	0.131613i
$739$	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	0.800546	−	0.599271i	$-0.204543\pi$
$743$	149.548	+	149.548i	0.201275	+	0.201275i	−0.599271	+	0.800546i	$0.704543\pi$
$744$	−225.232	−	251.401i	−0.302731	−	0.337904i
$745$	83.3363	−	99.2751i	0.111861	−	0.133255i
$746$	355.954	+	965.519i	0.477150	+	1.29426i
$747$	804.681	−	102.963i	1.07722	−	0.137835i
$748$	73.0868	−	923.382i	0.0977096	−	1.23447i
$749$	−199.656			−0.266564
$750$	−359.618	+	658.160i	−0.479491	+	0.877547i
$751$			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
$753$	−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
$756$	−149.934	+	519.861i	−0.198325	+	0.687646i
$757$	590.607	−	590.607i	0.780195	−	0.780195i	−0.199669	−	0.979863i	$-0.563987\pi$
$757$	590.607	−	590.607i	0.780195	−	0.780195i	0.979863	+	0.199669i	$0.0639866\pi$
$758$	−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	$0.0748684\pi$
$761$			354.692i			0.466087i	−0.972466	+	0.233043i	$0.925132\pi$
$762$	−550.718	+	577.967i	−0.722727	+	0.758487i
$763$	−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
$768$	107.461	+	760.445i	0.139924	+	0.990162i
$769$			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	−0.982806	−	0.184639i	$-0.940888\pi$
$773$	−616.984	+	616.984i	−0.798168	+	0.798168i	0.184639	+	0.982806i	$0.440888\pi$
$774$	−437.431	+	1389.79i	−0.565156	+	1.79560i
$775$	−346.285	+	60.9133i	−0.446820	+	0.0785978i
$776$	−842.231	−	472.413i	−1.08535	−	0.608780i
$777$	94.7662	+	193.051i	0.121964	+	0.248457i
$778$	−1090.70	−	503.117i	−1.40193	−	0.646679i
$779$		−	29.1122i		−	0.0373713i
$780$	−231.467	+	696.159i	−0.296752	+	0.892511i
$781$	617.256			0.790340
$782$	−221.180	+	479.495i	−0.282839	+	0.613165i
$783$	−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
$786$	−21.0197	−	870.637i	−0.0267426	−	1.10768i
$787$	−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
$792$	1123.80	+	453.969i	1.41893	+	0.573194i
$793$	−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	$0.891811\pi$
$798$	−99.2015	+	104.110i	−0.124313	+	0.130464i
$799$	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
$804$	851.486	−	337.475i	1.05906	−	0.419745i
$805$	368.222	+	309.103i	0.457418	+	0.383979i
$806$	−322.697	+	118.967i	−0.400368	+	0.147602i
$807$	−0.718328	−	1.46333i	−0.000890122	−	0.00181329i
$808$	−1223.83	+	344.272i	−1.51465	+	0.426079i
$809$	−183.688			−0.227056			−0.113528	−	0.993535i	$-0.536215\pi$
$809$	−183.688			−0.227056			−0.113528	+	0.993535i	$0.536215\pi$
$810$	−518.584	−	622.231i	−0.640227	−	0.768186i
$811$		−	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
$813$	−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
$816$	583.519	+	309.028i	0.715097	+	0.378710i
$817$	−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	$0.249121\pi$
$821$			1157.86i			1.41030i	−0.709057	+	0.705152i	$0.750879\pi$
$822$	351.805	−	369.212i	0.427986	−	0.449163i
$823$	−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
$825$	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	−0.380066	−	0.924959i	$-0.624099\pi$
$827$	450.627	−	450.627i	0.544893	−	0.544893i	0.924959	+	0.380066i	$0.124099\pi$
$828$	−511.586	−	464.431i	−0.617858	−	0.560907i
$829$			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
$834$	−1.82445	−	75.5689i	−0.00218759	−	0.0906102i
$835$	−51.8039	−	593.520i	−0.0620406	−	0.710803i
$836$	209.105	+	245.052i	0.250126	+	0.293125i
$837$	76.1123	−	372.024i	0.0909346	−	0.444473i
$838$	488.053	−	1058.05i	0.582402	−	1.26259i
$839$		−	425.692i		−	0.507380i	−0.967286	−	0.253690i	$-0.918356\pi$
$839$		−	425.692i		−	0.507380i	0.967286	−	0.253690i	$-0.0816443\pi$
$840$	411.177	−	438.560i	0.489497	−	0.522095i
$841$	−619.762			−0.736935
$842$	883.855	+	407.702i	1.04971	+	0.484207i
$843$	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
$846$	−134.697	+	427.954i	−0.159216	+	0.505856i
$847$	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
$852$	−174.608	+	403.887i	−0.204939	+	0.474046i
$853$	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	$0.592553\pi$
$858$	851.925	−	894.079i	0.992920	−	1.04205i
$859$	−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	0.935911	−	0.352238i	$-0.114579\pi$
$863$	503.710	+	503.710i	0.583673	+	0.583673i	−0.352238	+	0.935911i	$0.614579\pi$
$864$	−614.942	+	606.912i	−0.711739	+	0.702444i
$865$	31.5009	+	360.908i	0.0364172	+	0.417235i
$866$	149.601	+	405.789i	0.172749	+	0.468579i
$867$	−268.676	+	131.889i	−0.309891	+	0.152122i
$868$	280.950	+	22.2375i	0.323675	+	0.0256193i
$869$	1488.68			1.71310
$870$	348.592	+	278.564i	0.400681	+	0.320188i
$871$		−	933.264i		−	1.07149i
$872$	−1231.74	+	346.496i	−1.41255	+	0.397358i
$873$	−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
$876$	−200.048	+	79.2862i	−0.228365	+	0.0905094i
$877$	−1002.77	+	1002.77i	−1.14341	+	1.14341i	−0.155586	+	0.987822i	$0.549727\pi$
$877$	−1002.77	+	1002.77i	−1.14341	+	1.14341i	−0.987822	+	0.155586i	$0.950273\pi$
$878$	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	$-0.725739\pi$
$881$		−	1337.17i		−	1.51779i	0.651213	−	0.758895i	$-0.274261\pi$
$882$	198.858	+	381.535i	0.225463	+	0.432579i
$883$	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
$885$	−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	−0.0780457	−	0.996950i	$-0.524868\pi$
$887$	815.068	−	815.068i	0.918904	−	0.918904i	0.996950	+	0.0780457i	$0.0248680\pi$
$888$	−18.8267	+	342.906i	−0.0212013	+	0.386156i
$889$		−	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
$894$	−3.75409	−	155.495i	−0.00419920	−	0.173931i
$895$	104.270	+	87.5291i	0.116502	+	0.0977978i
$896$	−502.959	−	397.778i	−0.561338	−	0.443948i
$897$	−631.994	+	310.238i	−0.704564	+	0.345861i
$898$	429.454	+	198.097i	0.478234	+	0.220598i
$899$			209.190i			0.232692i
$900$	198.514	+	877.834i	0.220571	+	0.975371i
$901$	315.187			0.349819
$902$	85.8120	−	186.031i	0.0951352	−	0.206243i
$903$	−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
$906$	1201.92	−	29.0178i	1.32663	−	0.0320285i
$907$	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	$-0.822934\pi$
$911$	−1547.30			−1.69846			−0.849231	+	0.528022i	$0.822934\pi$
$912$	−219.496	+	67.5032i	−0.240675	+	0.0740166i
$913$	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
$918$	112.037	+	734.337i	0.122044	+	0.799931i
$919$	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
$924$	−940.789	+	372.869i	−1.01817	+	0.403538i
$925$	292.953	+	205.307i	0.316706	+	0.221953i
$926$	431.990	−	159.260i	0.466512	−	0.171987i
$927$	−46.2441	−	361.411i	−0.0498858	−	0.389872i
$928$	264.877	−	395.459i	0.285427	−	0.426141i
$929$	−1529.05			−1.64591			−0.822955	−	0.568106i	$-0.807676\pi$
$929$	−1529.05			−1.64591			−0.822955	+	0.568106i	$0.807676\pi$
$930$	−263.394	+	329.609i	−0.283219	+	0.354418i
$931$			114.355i			0.122830i
$932$	311.361	+	24.6446i	0.334079	+	0.0264427i
$933$	−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
$936$	344.029	+	810.353i	0.367552	+	0.865762i
$937$	662.561	−	662.561i	0.707109	−	0.707109i	−0.258818	−	0.965926i	$-0.583333\pi$
$937$	662.561	−	662.561i	0.707109	−	0.707109i	0.965926	+	0.258818i	$0.0833328\pi$
$938$	−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	$-0.829377\pi$
$941$		−	961.186i		−	1.02145i	0.859744	−	0.510726i	$-0.170623\pi$
$942$	−859.978	−	819.432i	−0.912927	−	0.869885i
$943$	−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	$0.639445\pi$
$947$	−1259.29	+	1259.29i	−1.32977	+	1.32977i	−0.905568	+	0.424202i	$0.860555\pi$
$948$	−421.116	+	974.084i	−0.444215	+	1.02751i
$949$			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	−0.738981	−	0.673726i	$-0.764693\pi$
$953$	−62.1880	+	62.1880i	−0.0652550	+	0.0652550i	0.673726	+	0.738981i	$0.264693\pi$
$954$	−123.820	+	393.397i	−0.129790	+	0.412366i
$955$	−1093.04	+	1302.09i	−1.14454	+	1.36345i
$956$	−140.386	+	119.793i	−0.146848	+	0.125306i
$957$	−331.002	−	674.295i	−0.345875	−	0.704592i
$958$	−367.821	+	797.397i	−0.383947	+	0.832356i
$959$			425.813i			0.444018i
$960$	915.279	−	289.593i	0.953416	−	0.301659i
$961$	763.202			0.794174
$962$	317.749	+	146.570i	0.330300	+	0.152360i
$963$	−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
$966$	576.746	−	13.9243i	0.597046	−	0.0144144i
$967$	−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	$-0.594846\pi$
$971$	−570.125			−0.587153			−0.293576	+	0.955936i	$0.594846\pi$
$972$	−960.567	−	148.644i	−0.988238	−	0.152926i
$973$	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	$0.850788\pi$
$978$	360.183	+	343.201i	0.368285	+	0.350921i
$979$	−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	0.102942	−	0.994687i	$-0.467174\pi$
$983$	−876.585	−	876.585i	−0.891745	−	0.891745i	−0.994687	+	0.102942i	$0.967174\pi$
$984$	97.4509	+	108.773i	0.0990355	+	0.110542i
$985$	−1589.08	+	138.699i	−1.61328	+	0.140811i
$986$	−141.553	−	383.959i	−0.143563	−	0.389411i
$987$	−165.071	−	336.272i	−0.167246	−	0.340701i
$988$	−18.4627	+	233.259i	−0.0186870	+	0.236092i
$989$	1553.59			1.57086
$990$	327.471	−	1479.22i	0.330779	−	1.49416i
$991$		−	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
$993$	−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
$996$	−1005.56	+	398.539i	−1.00960	+	0.400139i
$997$	276.341	−	276.341i	0.277172	−	0.277172i	−0.554807	−	0.831979i	$-0.687208\pi$
$997$	276.341	−	276.341i	0.277172	−	0.277172i	0.831979	+	0.554807i	$0.187208\pi$
$998$	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.23.18	yes	40
3.2	odd	2	inner	60.3.l.a.23.3	✓	40
4.3	odd	2	inner	60.3.l.a.23.13	yes	40
5.2	odd	4	inner	60.3.l.a.47.8	yes	40
5.3	odd	4		300.3.l.g.107.13		40
5.4	even	2		300.3.l.g.143.3		40
12.11	even	2	inner	60.3.l.a.23.8	yes	40
15.2	even	4	inner	60.3.l.a.47.13	yes	40
15.8	even	4		300.3.l.g.107.8		40
15.14	odd	2		300.3.l.g.143.18		40
20.3	even	4		300.3.l.g.107.18		40
20.7	even	4	inner	60.3.l.a.47.3	yes	40
20.19	odd	2		300.3.l.g.143.8		40
60.23	odd	4		300.3.l.g.107.3		40
60.47	odd	4	inner	60.3.l.a.47.18	yes	40
60.59	even	2		300.3.l.g.143.13		40

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.81610 + 0.837725i) q^{2} +(-1.32197 - 2.69303i) q^{3} +(2.59643 + 3.04278i) q^{4} +(3.21472 - 3.82956i) q^{5} +(-0.144815 - 5.99825i) q^{6} +(3.54241 + 3.54241i) q^{7} +(2.16636 + 7.70110i) q^{8} +(-5.50478 + 7.12021i) q^{9} +O(q^{10})\)	\(q+(1.81610 + 0.837725i) q^{2} +(-1.32197 - 2.69303i) q^{3} +(2.59643 + 3.04278i) q^{4} +(3.21472 - 3.82956i) q^{5} +(-0.144815 - 5.99825i) q^{6} +(3.54241 + 3.54241i) q^{7} +(2.16636 + 7.70110i) q^{8} +(-5.50478 + 7.12021i) q^{9} +(9.04638 - 4.26182i) q^{10} -16.8337 q^{11} +(4.76189 - 11.0147i) 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} +(-15.9620 + 8.31951i) 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} +(17.8754 - 16.0147i) q^{24} +(-4.33113 - 24.6220i) q^{25} +(-8.45895 - 22.9448i) q^{26} +(26.4521 + 5.41182i) q^{27} +(-1.58116 + 19.9764i) q^{28} -14.8741 q^{29} +(-23.4362 - 18.7281i) q^{30} -14.0641i q^{31} +(-17.8080 + 26.5872i) q^{32} +(22.2536 + 45.3336i) q^{33} +(9.51674 + 25.8140i) q^{34} +(24.9537 - 2.17802i) q^{35} +(-35.9581 + 1.73727i) q^{36} +(-10.1182 + 10.1182i) q^{37} +(-8.68857 - 4.00784i) q^{38} +(-11.8540 + 34.7134i) q^{39} +(36.4561 + 16.4607i) q^{40} +6.08509i q^{41} +(20.7353 - 21.7613i) 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} +(45.8794 - 14.1096i) 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} +(43.5060 + 31.9880i) q^{54} +(-54.1156 + 64.4657i) q^{55} +(-19.6063 + 34.9546i) q^{56} +(6.32456 + 12.8840i) q^{57} +(-27.0128 - 12.4604i) q^{58} -4.37150i q^{59} +(-26.8735 - 53.6453i) q^{60} +8.52269 q^{61} +(11.7818 - 25.5418i) q^{62} +(-44.7229 + 5.72249i) q^{63} +(-54.6137 + 33.3667i) q^{64} +(-60.9043 + 5.31588i) q^{65} +(2.43777 + 100.973i) q^{66} +(53.9714 + 53.9714i) q^{67} +(-4.34170 + 54.8532i) q^{68} +(18.6074 - 54.4900i) q^{69} +(47.1431 + 16.9489i) q^{70} -36.6679 q^{71} +(-66.7588 - 26.9679i) 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} +(-50.6084 + 53.1125i) 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} +(55.8873 - 22.1502i) q^{84} +(68.5205 - 5.98063i) q^{85} +(151.896 - 55.9988i) q^{86} +(19.6631 + 40.0563i) q^{87} +(-36.4679 - 129.638i) q^{88} +115.022 q^{89} +(-19.4533 + 87.8725i) q^{90} -61.2548i q^{91} +(-6.05770 + 76.5332i) q^{92} +(-37.8749 + 18.5923i) q^{93} +(46.7728 - 17.2435i) q^{94} +(-15.3798 + 18.3214i) q^{95} +(95.1415 + 12.8098i) q^{96} +(-85.3544 + 85.3544i) q^{97} +(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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more