LMFDB - Embedded newform 169.3.j.a.5.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,3,Mod(5,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(52))

chi = DirichletCharacter(H, H._module([3]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("169.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	169.j (of order $52$, degree $24$, 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:	$4.60491646769$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$30$ over $\Q(\zeta_{52})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{52}]$

Embedding invariants

Embedding label			5.12
Character	$\chi$	$=$	169.5
Dual form			169.3.j.a.34.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.992467 - 0.181876i) q^{2} +(3.21951 + 1.68973i) q^{3} +(-2.78815 - 1.05741i) q^{4} +(0.233707 - 3.86364i) q^{5} +(-2.88794 - 2.26255i) q^{6} +(-10.1385 - 6.12897i) q^{7} +(6.02875 + 3.64450i) q^{8} +(2.39748 + 3.47334i) q^{9} +(-0.934651 + 3.79203i) q^{10} +(-13.2706 + 2.43193i) q^{11} +(-7.18976 - 8.11556i) q^{12} +(-9.18947 - 9.19530i) q^{13} +(8.94746 + 7.92676i) q^{14} +(7.28092 - 12.0441i) q^{15} +(3.60754 + 3.19601i) q^{16} +(2.54300 + 10.3173i) q^{17} +(-1.74770 - 3.88322i) q^{18} +(13.6988 - 13.6988i) q^{19} +(-4.73705 + 10.5253i) q^{20} +(-22.2849 - 36.8637i) q^{21} +13.6129 q^{22} -12.5412i q^{23} +(13.2514 + 21.9205i) q^{24} +(9.94464 + 1.20750i) q^{25} +(7.44784 + 10.7974i) q^{26} +(-2.09474 - 17.2518i) q^{27} +(21.7870 + 27.8091i) q^{28} +(2.72253 + 3.94426i) q^{29} +(-9.41662 + 10.6292i) q^{30} +(-29.6221 - 23.2075i) q^{31} +(-20.3776 - 26.0100i) q^{32} +(-46.8341 - 14.5941i) q^{33} +(-0.647360 - 10.7021i) q^{34} +(-26.0496 + 37.7393i) q^{35} +(-3.01179 - 12.2193i) q^{36} +(-39.1642 + 49.9895i) q^{37} +(-16.0871 + 11.1041i) q^{38} +(-14.0480 - 45.1321i) q^{39} +(15.4900 - 22.4412i) q^{40} +(34.6006 - 10.7820i) q^{41} +(15.4124 + 40.6391i) q^{42} +(42.4978 + 5.16017i) q^{43} +(39.5720 + 7.25184i) q^{44} +(13.9801 - 8.45124i) q^{45} +(-2.28094 + 12.4467i) q^{46} +(23.2581 - 51.6774i) q^{47} +(6.21414 + 16.3853i) q^{48} +(42.4545 + 80.8903i) q^{49} +(-9.65011 - 3.00710i) q^{50} +(-9.24631 + 37.5137i) q^{51} +(15.8985 + 35.3549i) q^{52} +(-11.7884 + 2.90558i) q^{53} +(-1.05872 + 17.5028i) q^{54} +(6.29466 + 51.8412i) q^{55} +(-38.7857 - 73.9000i) q^{56} +(67.2505 - 20.9561i) q^{57} +(-1.98465 - 4.40971i) q^{58} +(71.6597 + 4.33461i) q^{59} +(-33.0359 + 25.8820i) q^{60} +(-67.5946 - 16.6606i) q^{61} +(25.1781 + 28.4202i) q^{62} +(-3.01892 - 49.9087i) q^{63} +(6.53427 + 12.4500i) q^{64} +(-37.6750 + 33.3558i) q^{65} +(43.8270 + 23.0022i) q^{66} +(70.5766 + 31.7640i) q^{67} +(3.81937 - 31.4553i) q^{68} +(21.1912 - 40.3764i) q^{69} +(32.7172 - 32.7172i) q^{70} +(-32.0539 + 9.98839i) q^{71} +(1.79516 + 29.6775i) q^{72} +(-107.554 + 19.7099i) q^{73} +(47.9611 - 42.4898i) q^{74} +(29.9765 + 20.6913i) q^{75} +(-52.6794 + 23.7091i) q^{76} +(149.450 + 56.6789i) q^{77} +(5.73376 + 47.3471i) q^{78} +(28.0551 + 73.9751i) q^{79} +(13.1913 - 13.1913i) q^{80} +(35.8760 - 94.5973i) q^{81} +(-36.3010 + 4.40774i) q^{82} +(21.1457 - 67.8590i) q^{83} +(23.1537 + 126.346i) q^{84} +(40.4568 - 7.41398i) q^{85} +(-41.2392 - 12.8506i) q^{86} +(2.10047 + 17.2989i) q^{87} +(-88.8683 - 33.7033i) q^{88} +(-68.3280 - 68.3280i) q^{89} +(-15.4118 + 5.84493i) q^{90} +(36.8103 + 149.549i) q^{91} +(-13.2611 + 34.9667i) q^{92} +(-56.1544 - 124.770i) q^{93} +(-32.4818 + 47.0581i) q^{94} +(-49.7256 - 56.1286i) q^{95} +(-21.6558 - 118.172i) q^{96} +(34.4808 - 2.08570i) q^{97} +(-27.4227 - 88.0024i) q^{98} +(-40.2629 - 40.2629i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - 22 q^{2} - 22 q^{3} - 26 q^{4} - 34 q^{5} - 10 q^{6} - 14 q^{7} - 62 q^{8} - 202 q^{9} - 26 q^{10} - 22 q^{11} - 26 q^{12} - 34 q^{13} - 38 q^{14} + 2 q^{15} + 242 q^{16} - 26 q^{17} - 58 q^{18}+ \cdots - 178 q^{99}+O(q^{100}) $ 720 * q - 22 * q^2 - 22 * q^3 - 26 * q^4 - 34 * q^5 - 10 * q^6 - 14 * q^7 - 62 * q^8 - 202 * q^9 - 26 * q^10 - 22 * q^11 - 26 * q^12 - 34 * q^13 - 38 * q^14 + 2 * q^15 + 242 * q^16 - 26 * q^17 - 58 * q^18 - 26 * q^19 - 42 * q^20 - 58 * q^21 - 108 * q^22 + 262 * q^24 - 26 * q^25 + 62 * q^26 + 2 * q^27 - 30 * q^28 - 54 * q^29 - 858 * q^30 - 66 * q^31 - 696 * q^32 + 50 * q^33 + 82 * q^34 - 2 * q^35 - 26 * q^36 - 66 * q^37 + 884 * q^38 + 922 * q^39 - 522 * q^40 - 58 * q^41 - 106 * q^42 - 26 * q^43 + 42 * q^44 - 212 * q^45 - 54 * q^46 + 368 * q^47 + 94 * q^48 - 26 * q^49 + 102 * q^50 - 26 * q^51 - 1276 * q^52 + 620 * q^53 - 178 * q^54 - 834 * q^55 - 26 * q^56 + 14 * q^57 + 114 * q^58 - 82 * q^59 + 1338 * q^60 + 254 * q^61 + 1404 * q^62 - 1392 * q^63 - 26 * q^64 - 82 * q^65 - 304 * q^66 - 358 * q^67 - 434 * q^68 + 208 * q^69 + 838 * q^70 - 310 * q^71 + 22 * q^72 - 26 * q^73 - 1308 * q^74 + 1664 * q^75 - 106 * q^76 - 26 * q^77 - 574 * q^78 - 78 * q^79 + 62 * q^80 - 262 * q^81 + 1274 * q^82 + 26 * q^83 + 158 * q^84 + 1522 * q^85 - 1562 * q^86 - 122 * q^87 - 442 * q^88 - 616 * q^89 - 26 * q^90 - 182 * q^91 + 646 * q^92 + 544 * q^93 - 2394 * q^94 - 26 * q^95 - 4064 * q^96 + 1914 * q^97 - 250 * q^98 - 178 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{52}\right)$

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 $

$2$	−0.992467	−	0.181876i	−0.496233	−	0.0909382i	−0.0736907	−	0.997281i	$-0.523478\pi$
$2$	−0.992467	−	0.181876i	−0.496233	−	0.0909382i	−0.422543	+	0.906343i	$0.638862\pi$
$3$	3.21951	+	1.68973i	1.07317	+	0.563243i	0.906256	−	0.422729i	$-0.138928\pi$
$3$	3.21951	+	1.68973i	1.07317	+	0.563243i	0.166914	+	0.985972i	$0.446620\pi$
$4$	−2.78815	−	1.05741i	−0.697038	−	0.264352i
$5$	0.233707	−	3.86364i	0.0467414	−	0.772728i	−0.896997	−	0.442036i	$-0.854256\pi$
$5$	0.233707	−	3.86364i	0.0467414	−	0.772728i	0.943739	−	0.330692i	$-0.107282\pi$
$6$	−2.88794	−	2.26255i	−0.481323	−	0.377092i
$7$	−10.1385	−	6.12897i	−1.44836	−	0.875567i	−0.448530	−	0.893768i	$-0.648052\pi$
$7$	−10.1385	−	6.12897i	−1.44836	−	0.875567i	−0.999834	+	0.0182012i	$0.994206\pi$
$8$	6.02875	+	3.64450i	0.753593	+	0.455563i
$9$	2.39748	+	3.47334i	0.266386	+	0.385927i
$10$	−0.934651	+	3.79203i	−0.0934651	+	0.379203i
$11$	−13.2706	+	2.43193i	−1.20642	+	0.221084i	−0.745590	−	0.666405i	$-0.767832\pi$
$11$	−13.2706	+	2.43193i	−1.20642	+	0.221084i	−0.460828	+	0.887489i	$0.652448\pi$
$12$	−7.18976	−	8.11556i	−0.599146	−	0.676296i
$13$	−9.18947	−	9.19530i	−0.706883	−	0.707331i
$13$	−9.18947	−	9.19530i	−0.706883	−	0.707331i
$14$	8.94746	+	7.92676i	0.639104	+	0.566197i
$15$	7.28092	−	12.0441i	0.485395	−	0.802941i
$16$	3.60754	+	3.19601i	0.225472	+	0.199750i
$17$	2.54300	+	10.3173i	0.149588	+	0.606902i	0.997098	+	0.0761235i	$0.0242543\pi$
$17$	2.54300	+	10.3173i	0.149588	+	0.606902i	−0.847510	+	0.530779i	$0.821900\pi$
$18$	−1.74770	−	3.88322i	−0.0970943	−	0.215735i
$19$	13.6988	−	13.6988i	0.720988	−	0.720988i	−0.247819	−	0.968806i	$-0.579714\pi$
$19$	13.6988	−	13.6988i	0.720988	−	0.720988i	0.968806	+	0.247819i	$0.0797137\pi$
$20$	−4.73705	+	10.5253i	−0.236852	+	0.526265i
$21$	−22.2849	−	36.8637i	−1.06118	−	1.75541i
$22$	13.6129			0.618770
$23$		−	12.5412i		−	0.545268i	−0.962118	−	0.272634i	$-0.912105\pi$
$23$		−	12.5412i		−	0.545268i	0.962118	−	0.272634i	$-0.0878949\pi$
$24$	13.2514	+	21.9205i	0.552141	+	0.913353i
$25$	9.94464	+	1.20750i	0.397786	+	0.0482999i
$26$	7.44784	+	10.7974i	0.286455	+	0.415284i
$27$	−2.09474	−	17.2518i	−0.0775831	−	0.638955i
$28$	21.7870	+	27.8091i	0.778108	+	0.993181i
$29$	2.72253	+	3.94426i	0.0938803	+	0.136009i	0.867110	−	0.498118i	$-0.165975\pi$
$29$	2.72253	+	3.94426i	0.0938803	+	0.136009i	−0.773229	+	0.634127i	$0.781360\pi$
$30$	−9.41662	+	10.6292i	−0.313887	+	0.354305i
$31$	−29.6221	−	23.2075i	−0.955553	−	0.748628i	0.0123575	−	0.999924i	$-0.496066\pi$
$31$	−29.6221	−	23.2075i	−0.955553	−	0.748628i	−0.967910	+	0.251296i	$0.919143\pi$
$32$	−20.3776	−	26.0100i	−0.636799	−	0.812814i
$33$	−46.8341	−	14.5941i	−1.41922	−	0.442246i
$34$	−0.647360	−	10.7021i	−0.0190400	−	0.314769i
$35$	−26.0496	+	37.7393i	−0.744273	+	1.07827i
$36$	−3.01179	−	12.2193i	−0.0836609	−	0.339426i
$37$	−39.1642	+	49.9895i	−1.05849	+	1.35107i	−0.125127	+	0.992141i	$0.539934\pi$
$37$	−39.1642	+	49.9895i	−1.05849	+	1.35107i	−0.933366	+	0.358926i	$0.883143\pi$
$38$	−16.0871	+	11.1041i	−0.423344	+	0.292213i
$39$	−14.0480	−	45.1321i	−0.360206	−	1.15723i
$40$	15.4900	−	22.4412i	0.387250	−	0.561029i
$41$	34.6006	−	10.7820i	0.843918	−	0.262976i	0.155090	−	0.987900i	$-0.450433\pi$
$41$	34.6006	−	10.7820i	0.843918	−	0.262976i	0.688828	+	0.724925i	$0.258126\pi$
$42$	15.4124	+	40.6391i	0.366961	+	0.967597i
$43$	42.4978	+	5.16017i	0.988321	+	0.120004i	0.598702	−	0.800972i	$-0.295683\pi$
$43$	42.4978	+	5.16017i	0.988321	+	0.120004i	0.389619	+	0.920976i	$0.372607\pi$
$44$	39.5720	+	7.25184i	0.899364	+	0.164815i
$45$	13.9801	−	8.45124i	0.310668	−	0.187805i
$46$	−2.28094	+	12.4467i	−0.0495857	+	0.270580i
$47$	23.2581	−	51.6774i	0.494854	−	1.09952i	−0.480121	−	0.877203i	$-0.659407\pi$
$47$	23.2581	−	51.6774i	0.494854	−	1.09952i	0.974974	−	0.222318i	$-0.0713622\pi$
$48$	6.21414	+	16.3853i	0.129461	+	0.341361i
$49$	42.4545	+	80.8903i	0.866419	+	1.65082i
$50$	−9.65011	−	3.00710i	−0.193002	−	0.0601419i
$51$	−9.24631	+	37.5137i	−0.181300	+	0.735564i
$52$	15.8985	+	35.3549i	0.305740	+	0.679902i
$53$	−11.7884	+	2.90558i	−0.222423	+	0.0548222i	−0.348952	−	0.937141i	$-0.613462\pi$
$53$	−11.7884	+	2.90558i	−0.222423	+	0.0548222i	0.126529	+	0.991963i	$0.459616\pi$
$54$	−1.05872	+	17.5028i	−0.0196060	+	0.324126i
$55$	6.29466	+	51.8412i	0.114448	+	0.942567i
$56$	−38.7857	−	73.9000i	−0.692602	−	1.31964i
$57$	67.2505	−	20.9561i	1.17983	−	0.367651i
$58$	−1.98465	−	4.40971i	−0.0342181	−	0.0760295i
$59$	71.6597	+	4.33461i	1.21457	+	0.0734680i	0.655204	−	0.755452i	$-0.272583\pi$
$59$	71.6597	+	4.33461i	1.21457	+	0.0734680i	0.559367	+	0.828920i	$0.311044\pi$
$60$	−33.0359	+	25.8820i	−0.550598	+	0.431366i
$61$	−67.5946	−	16.6606i	−1.10811	−	0.273124i	−0.357528	−	0.933903i	$-0.616380\pi$
$61$	−67.5946	−	16.6606i	−1.10811	−	0.273124i	−0.750581	+	0.660778i	$0.770226\pi$
$62$	25.1781	+	28.4202i	0.406098	+	0.458390i
$63$	−3.01892	−	49.9087i	−0.0479194	−	0.792202i
$64$	6.53427	+	12.4500i	0.102098	+	0.194531i
$65$	−37.6750	+	33.3558i	−0.579615	+	0.513166i
$66$	43.8270	+	23.0022i	0.664046	+	0.348518i
$67$	70.5766	+	31.7640i	1.05338	+	0.474089i	0.861726	−	0.507373i	$-0.169383\pi$
$67$	70.5766	+	31.7640i	1.05338	+	0.474089i	0.191656	+	0.981462i	$0.438614\pi$
$68$	3.81937	−	31.4553i	0.0561671	−	0.462578i
$69$	21.1912	−	40.3764i	0.307119	−	0.585166i
$70$	32.7172	−	32.7172i	0.467389	−	0.467389i
$71$	−32.0539	+	9.98839i	−0.451463	+	0.140682i	−0.514799	−	0.857311i	$-0.672134\pi$
$71$	−32.0539	+	9.98839i	−0.451463	+	0.140682i	0.0633364	+	0.997992i	$0.479826\pi$
$72$	1.79516	+	29.6775i	0.0249328	+	0.412188i
$73$	−107.554	+	19.7099i	−1.47334	+	0.269999i	−0.856114	−	0.516788i	$-0.827128\pi$
$73$	−107.554	+	19.7099i	−1.47334	+	0.269999i	−0.617225	+	0.786787i	$0.711743\pi$
$74$	47.9611	−	42.4898i	0.648123	−	0.574187i
$75$	29.9765	+	20.6913i	0.399687	+	0.275884i
$76$	−52.6794	+	23.7091i	−0.693150	+	0.311962i
$77$	149.450	+	56.6789i	1.94091	+	0.736089i
$78$	5.73376	+	47.3471i	0.0735097	+	0.607014i
$79$	28.0551	+	73.9751i	0.355127	+	0.936394i	0.986913	+	0.161251i	$0.0515529\pi$
$79$	28.0551	+	73.9751i	0.355127	+	0.936394i	−0.631786	+	0.775143i	$0.717678\pi$
$80$	13.1913	−	13.1913i	0.164892	−	0.164892i
$81$	35.8760	−	94.5973i	0.442914	−	1.16787i
$82$	−36.3010	+	4.40774i	−0.442695	+	0.0537529i
$83$	21.1457	−	67.8590i	0.254768	−	0.817578i	−0.735393	−	0.677641i	$-0.763002\pi$
$83$	21.1457	−	67.8590i	0.254768	−	0.817578i	0.990160	−	0.139937i	$-0.0446900\pi$
$84$	23.1537	+	126.346i	0.275639	+	1.50412i
$85$	40.4568	−	7.41398i	0.475962	−	0.0872233i
$86$	−41.2392	−	12.8506i	−0.479525	−	0.149426i
$87$	2.10047	+	17.2989i	0.0241433	+	0.198838i
$88$	−88.8683	−	33.7033i	−1.00987	−	0.382992i
$89$	−68.3280	−	68.3280i	−0.767730	−	0.767730i	0.209976	−	0.977706i	$-0.432661\pi$
$89$	−68.3280	−	68.3280i	−0.767730	−	0.767730i	−0.977706	+	0.209976i	$0.932661\pi$
$90$	−15.4118	+	5.84493i	−0.171242	+	0.0649437i
$91$	36.8103	+	149.549i	0.404508	+	1.64340i
$92$	−13.2611	+	34.9667i	−0.144143	+	0.380073i
$93$	−56.1544	−	124.770i	−0.603811	−	1.34161i
$94$	−32.4818	+	47.0581i	−0.345551	+	0.500618i
$95$	−49.7256	−	56.1286i	−0.523427	−	0.590827i
$96$	−21.6558	−	118.172i	−0.225582	−	1.23096i
$97$	34.4808	−	2.08570i	0.355472	−	0.0215021i	0.118322	−	0.992975i	$-0.462248\pi$
$97$	34.4808	−	2.08570i	0.355472	−	0.0215021i	0.237150	+	0.971473i	$0.423787\pi$
$98$	−27.4227	−	88.0024i	−0.279823	−	0.897984i
$99$	−40.2629	−	40.2629i	−0.406696	−	0.406696i
$100$	−26.4504	−	13.8822i	−0.264504	−	0.138822i
$101$	−173.456	−	21.0614i	−1.71739	−	0.208529i	−0.798212	−	0.602377i	$-0.794220\pi$
$101$	−173.456	−	21.0614i	−1.71739	−	0.208529i	−0.919175	+	0.393849i	$0.871143\pi$
$102$	15.9995	−	35.5495i	0.156858	−	0.348524i
$103$	32.5998	−	62.1137i	0.316503	−	0.603046i	−0.674285	−	0.738472i	$-0.735548\pi$
$103$	32.5998	−	62.1137i	0.316503	−	0.603046i	0.990788	+	0.135426i	$0.0432402\pi$
$104$	−21.8887	−	88.9272i	−0.210468	−	0.855069i
$105$	−147.636	+	77.4854i	−1.40606	+	0.737956i
$106$	12.2280	−	0.739661i	0.115359	−	0.00697793i
$107$	17.4837	−	15.4892i	0.163399	−	0.144759i	−0.577461	−	0.816418i	$-0.695957\pi$
$107$	17.4837	−	15.4892i	0.163399	−	0.144759i	0.740860	+	0.671659i	$0.234418\pi$
$108$	−12.4017	+	50.3156i	−0.114830	+	0.465885i
$109$	−59.2481	−	75.6246i	−0.543560	−	0.693804i	0.434843	−	0.900506i	$-0.356804\pi$
$109$	−59.2481	−	75.6246i	−0.543560	−	0.693804i	−0.978404	+	0.206702i	$0.933727\pi$
$110$	3.18144	−	52.5955i	0.0289222	−	0.478141i
$111$	−210.558	+	94.7646i	−1.89692	+	0.853735i
$112$	−16.9871	−	54.5134i	−0.151670	−	0.486727i
$113$	95.9425	−	50.3545i	0.849049	−	0.445615i	0.0166955	−	0.999861i	$-0.494685\pi$
$113$	95.9425	−	50.3545i	0.849049	−	0.445615i	0.832353	+	0.554245i	$0.186993\pi$
$114$	−70.5553	+	8.56697i	−0.618906	+	0.0751489i
$115$	−48.4546	−	2.93096i	−0.421344	−	0.0254866i
$116$	−3.42013	−	13.8760i	−0.0294839	−	0.119621i
$117$	9.90689	−	53.9637i	0.0846743	−	0.461228i
$118$	−70.3315	−	17.3352i	−0.596030	−	0.146908i
$119$	37.4523	−	120.189i	0.314726	−	1.00999i
$120$	87.7897	−	46.0756i	0.731581	−	0.383963i
$121$	57.0577	−	21.6391i	0.471551	−	0.178836i
$122$	64.0553	+	28.8289i	0.525043	+	0.236303i
$123$	129.616	+	23.7530i	1.05379	+	0.193114i
$124$	58.0513	+	96.0286i	0.468156	+	0.774424i
$125$	24.4323	−	133.323i	0.195458	−	1.06658i
$126$	−6.08103	+	50.0818i	−0.0482622	+	0.397475i
$127$	−32.9233	+	12.4861i	−0.259238	+	0.0983161i	−0.480800	−	0.876830i	$-0.659654\pi$
$127$	−32.9233	+	12.4861i	−0.259238	+	0.0983161i	0.221562	+	0.975146i	$0.428885\pi$
$128$	35.0996	+	112.638i	0.274215	+	0.879988i
$129$	128.103	+	88.4230i	0.993045	+	0.685450i
$130$	43.4578	−	26.2523i	0.334291	−	0.201941i
$131$	−64.0712	−	92.8232i	−0.489093	−	0.708574i	0.498274	−	0.867019i	$-0.333967\pi$
$131$	−64.0712	−	92.8232i	−0.489093	−	0.708574i	−0.987368	+	0.158445i	$0.949352\pi$
$132$	115.149	+	90.2134i	0.872340	+	0.683435i
$133$	−222.845	+	54.9263i	−1.67553	+	0.412980i
$134$	−64.2679	−	44.3609i	−0.479611	−	0.331051i
$135$	−67.1442	+	4.06147i	−0.497364	+	0.0300850i
$136$	−22.2705	+	71.4686i	−0.163754	+	0.525504i
$137$	−93.8118	+	73.4969i	−0.684758	+	0.536473i	−0.897709	−	0.440589i	$-0.854769\pi$
$137$	−93.8118	+	73.4969i	−0.684758	+	0.536473i	0.212951	+	0.977063i	$0.431693\pi$
$138$	−28.3751	+	36.2181i	−0.205616	+	0.262450i
$139$	−36.9920	−	32.7720i	−0.266129	−	0.235770i	0.519496	−	0.854473i	$-0.326120\pi$
$139$	−36.9920	−	32.7720i	−0.266129	−	0.235770i	−0.785625	+	0.618703i	$0.787658\pi$
$140$	112.536	−	77.6780i	0.803828	−	0.554843i
$141$	162.201	−	127.076i	1.15036	−	0.901249i
$142$	33.6291	−	4.08331i	0.236824	−	0.0287557i
$143$	144.312	+	99.6791i	1.00918	+	0.697056i
$144$	−2.45182	+	20.1926i	−0.0170266	+	0.140226i
$145$	15.8755	−	9.59706i	0.109486	−	0.0661866i
$146$	110.328			0.755673
$147$			332.164i			2.25962i
$148$	162.055	−	97.9657i	1.09497	−	0.661931i
$149$	115.144	+	51.8222i	0.772780	+	0.347800i	0.758139	−	0.652093i	$-0.226109\pi$
$149$	115.144	+	51.8222i	0.772780	+	0.347800i	0.0146408	+	0.999893i	$0.495340\pi$
$150$	−25.9874	−	25.9874i	−0.173250	−	0.173250i
$151$	168.554	−	75.8599i	1.11625	−	0.502383i	0.233561	−	0.972342i	$-0.424962\pi$
$151$	168.554	−	75.8599i	1.11625	−	0.502383i	0.882688	+	0.469959i	$0.155731\pi$
$152$	132.512	−	32.6612i	0.871787	−	0.214876i
$153$	−29.7389	+	33.5683i	−0.194372	+	0.219400i
$154$	−138.016	−	83.4333i	−0.896205	−	0.541775i
$155$	−96.5882	+	109.025i	−0.623149	+	0.703390i
$156$	−8.55490	+	140.690i	−0.0548391	+	0.901857i
$157$	5.18810	−	4.59626i	0.0330452	−	0.0292755i	−0.646438	−	0.762966i	$-0.723742\pi$
$157$	5.18810	−	4.59626i	0.0330452	−	0.0292755i	0.679484	+	0.733691i	$0.262204\pi$
$158$	−14.3894	−	78.5204i	−0.0910722	−	0.496965i
$159$	−42.8625	−	10.5647i	−0.269575	−	0.0664444i
$160$	−105.256	+	72.6528i	−0.657848	+	0.454080i
$161$	−76.8644	+	127.149i	−0.477419	+	0.789747i
$162$	−52.8108	+	87.3597i	−0.325992	+	0.539257i
$163$	166.436	−	212.440i	1.02108	−	1.30331i	0.0689510	−	0.997620i	$-0.478035\pi$
$163$	166.436	−	212.440i	1.02108	−	1.30331i	0.952130	−	0.305694i	$-0.0988883\pi$
$164$	−107.873	−	6.52511i	−0.657761	−	0.0397872i
$165$	−67.3318	+	177.539i	−0.408072	+	1.07600i
$166$	−33.3284	+	63.5019i	−0.200773	+	0.382542i
$167$	42.5632	−	232.260i	0.254869	−	1.39078i	−0.568225	−	0.822873i	$-0.692370\pi$
$167$	42.5632	−	232.260i	0.254869	−	1.39078i	0.823095	−	0.567904i	$-0.192246\pi$
$168$		−	303.459i		−	1.80630i
$169$	−0.107104	+	169.000i	−0.000633753	+	1.00000i
$170$	−41.5005			−0.244120
$171$	80.4230	+	14.7381i	0.470310	+	0.0861875i
$172$	−113.034	−	59.3248i	−0.657175	−	0.344912i
$173$	−135.512	−	51.3928i	−0.783305	−	0.297068i	−0.0696554	−	0.997571i	$-0.522190\pi$
$173$	−135.512	−	51.3928i	−0.783305	−	0.297068i	−0.713650	+	0.700503i	$0.752959\pi$
$174$	1.06162	−	17.5506i	0.00610125	−	0.100866i
$175$	−93.4235	−	73.1926i	−0.533849	−	0.418244i
$176$	−55.6468	−	33.6396i	−0.316175	−	0.191134i
$177$	223.385	+	135.041i	1.26206	+	0.762943i
$178$	55.3860	+	80.2405i	0.311157	+	0.450789i
$179$	−10.9194	+	44.3016i	−0.0610020	+	0.247495i	−0.993525	−	0.113617i	$-0.963756\pi$
$179$	−10.9194	+	44.3016i	−0.0610020	+	0.247495i	0.932523	+	0.361111i	$0.117603\pi$
$180$	−47.9149	+	8.78074i	−0.266194	+	0.0487819i
$181$	113.499	+	128.114i	0.627068	+	0.707813i	0.973093	−	0.230412i	$-0.0740073\pi$
$181$	113.499	+	128.114i	0.627068	+	0.707813i	−0.346025	+	0.938225i	$0.612469\pi$
$182$	−9.33354	−	155.117i	−0.0512832	−	0.852293i
$183$	−189.470	−	167.856i	−1.03535	−	0.917243i
$184$	45.7064	−	75.6075i	0.248404	−	0.410911i
$185$	183.988	+	162.999i	0.994531	+	0.881078i
$186$	33.0387	+	134.043i	0.177627	+	0.720663i
$187$	−58.8381	−	130.733i	−0.314642	−	0.699107i
$188$	−119.491	+	119.491i	−0.635592	+	0.635592i
$189$	−84.4979	+	187.747i	−0.447079	+	0.993368i
$190$	39.1425	+	64.7497i	0.206013	+	0.340788i
$191$	273.628			1.43261			0.716304	−	0.697788i	$-0.245832\pi$
$191$	273.628			1.43261			0.716304	+	0.697788i	$0.245832\pi$
$192$			51.1241i			0.266271i
$193$	−9.25756	−	15.3139i	−0.0479666	−	0.0793465i	0.830878	−	0.556455i	$-0.187839\pi$
$193$	−9.25756	−	15.3139i	−0.0479666	−	0.0793465i	−0.878844	+	0.477108i	$0.841685\pi$
$194$	−34.6004	−	4.20125i	−0.178353	−	0.0216559i
$195$	−177.657	+	43.7289i	−0.911062	+	0.224251i
$196$	−32.8357	−	270.426i	−0.167529	−	1.37973i
$197$	−106.122	−	135.455i	−0.538690	−	0.687587i	0.438796	−	0.898587i	$-0.355405\pi$
$197$	−106.122	−	135.455i	−0.538690	−	0.687587i	−0.977486	+	0.211000i	$0.932328\pi$
$198$	32.6367	+	47.2824i	0.164832	+	0.238800i
$199$	−11.6991	+	13.2056i	−0.0587896	+	0.0663598i	−0.777170	−	0.629291i	$-0.783345\pi$
$199$	−11.6991	+	13.2056i	−0.0587896	+	0.0663598i	0.718380	+	0.695651i	$0.244884\pi$
$200$	55.5530	+	43.5230i	0.277765	+	0.217615i
$201$	173.550	+	221.520i	0.863431	+	1.10209i
$202$	168.319	+	52.4503i	0.833262	+	0.259655i
$203$	−3.42823	−	56.6754i	−0.0168878	−	0.279189i
$204$	65.4474	−	94.8170i	0.320821	−	0.464789i
$205$	−33.5713	−	136.204i	−0.163763	−	0.664411i
$206$	−43.6513	+	55.7167i	−0.211899	+	0.270469i
$207$	43.5598	−	30.0672i	0.210434	−	0.145252i
$208$	−3.76321	−	62.5421i	−0.0180923	−	0.300683i
$209$	−148.477	+	215.105i	−0.710414	+	1.02921i
$210$	160.617	−	50.0502i	0.764841	−	0.238334i
$211$	−20.9456	−	55.2289i	−0.0992681	−	0.261748i	0.876178	−	0.481988i	$-0.160085\pi$
$211$	−20.9456	−	55.2289i	−0.0992681	−	0.261748i	−0.975446	+	0.220240i	$0.929316\pi$
$212$	35.9402	+	4.36393i	0.169529	+	0.0205846i
$213$	−120.075	−	22.0046i	−0.563734	−	0.103308i
$214$	−20.1691	+	12.1926i	−0.0942481	+	0.0569749i
$215$	29.8691	−	162.990i	0.138926	−	0.758094i
$216$	50.2455	−	111.641i	0.232618	−	0.516856i
$217$	158.088	+	416.843i	0.728515	+	1.92094i
$218$	45.0474	+	85.8307i	0.206640	+	0.393719i
$219$	−379.575	−	118.280i	−1.73322	−	0.540092i
$220$	37.2668	−	151.197i	0.169394	−	0.687260i
$221$	71.5022	−	118.195i	0.323540	−	0.534817i
$222$	226.208	−	55.7552i	1.01895	−	0.251149i
$223$	−19.8718	+	328.520i	−0.0891112	+	1.47318i	0.629082	+	0.777339i	$0.283431\pi$
$223$	−19.8718	+	328.520i	−0.0891112	+	1.47318i	−0.718193	+	0.695844i	$0.755030\pi$
$224$	47.1843	+	388.597i	0.210644	+	1.73481i
$225$	19.6480	+	37.4361i	0.0873243	+	0.166383i
$226$	−104.378	+	32.5255i	−0.461850	+	0.143918i
$227$	−163.379	−	363.014i	−0.719732	−	1.59918i	−0.798293	−	0.602270i	$-0.794263\pi$
$227$	−163.379	−	363.014i	−0.719732	−	1.59918i	0.0785605	−	0.996909i	$-0.474968\pi$
$228$	−209.664	−	12.6823i	−0.919579	−	0.0556243i
$229$	217.215	−	170.177i	0.948536	−	0.743130i	−0.0179530	−	0.999839i	$-0.505715\pi$
$229$	217.215	−	170.177i	0.948536	−	0.743130i	0.966489	+	0.256708i	$0.0826380\pi$
$230$	47.5565	+	11.7216i	0.206767	+	0.0509636i
$231$	385.383	+	435.008i	1.66833	+	1.88315i
$232$	2.03855	+	33.7012i	0.00878685	+	0.145264i
$233$	−103.174	−	196.581i	−0.442805	−	0.843694i	−0.999912	−	0.0132535i	$-0.995781\pi$
$233$	−103.174	−	196.581i	−0.442805	−	0.843694i	0.557107	−	0.830440i	$-0.311911\pi$
$234$	−19.6470	+	51.7554i	−0.0839615	+	0.221177i
$235$	−194.227	−	101.938i	−0.826499	−	0.433780i
$236$	−195.215	−	87.8591i	−0.827181	−	0.372284i
$237$	−34.6744	+	285.569i	−0.146305	+	1.20493i
$238$	−59.0297	+	112.472i	−0.248024	+	0.472570i
$239$	−182.120	+	182.120i	−0.762007	+	0.762007i	−0.976685	−	0.214678i	$-0.931130\pi$
$239$	−182.120	+	182.120i	−0.762007	+	0.762007i	0.214678	+	0.976685i	$0.431130\pi$
$240$	64.7593	−	20.1798i	0.269831	−	0.0840826i
$241$	20.0094	+	330.794i	0.0830264	+	1.37259i	0.766326	+	0.642452i	$0.222083\pi$
$241$	20.0094	+	330.794i	0.0830264	+	1.37259i	−0.683299	+	0.730138i	$0.739456\pi$
$242$	−60.5635	+	11.0987i	−0.250263	+	0.0458623i
$243$	158.275	−	140.220i	0.651338	−	0.577036i
$244$	170.847	+	117.927i	0.700193	+	0.483309i
$245$	322.453	−	145.124i	1.31613	−	0.592344i
$246$	−124.319	−	47.1481i	−0.505363	−	0.191659i
$247$	−251.849	−	0.0798050i	−1.01963	−	0.000323097i
$248$	−94.0047	−	247.870i	−0.379051	−	0.999476i
$249$	182.742	−	182.742i	0.733904	−	0.733904i
$250$	−48.4965	+	127.875i	−0.193986	+	0.511499i
$251$	192.418	−	23.3638i	0.766607	−	0.0930830i	0.272115	−	0.962265i	$-0.412277\pi$
$251$	192.418	−	23.3638i	0.766607	−	0.0930830i	0.494493	+	0.869182i	$0.335354\pi$
$252$	−44.3566	+	142.345i	−0.176018	+	0.564863i
$253$	30.4992	+	166.429i	0.120550	+	0.657822i
$254$	34.9462	−	6.40413i	0.137583	−	0.0252131i
$255$	142.779	+	44.4916i	0.559916	+	0.174477i
$256$	−21.1281	−	174.006i	−0.0825318	−	0.679711i
$257$	−256.078	−	97.1176i	−0.996413	−	0.377890i	−0.198132	−	0.980175i	$-0.563488\pi$
$257$	−256.078	−	97.1176i	−0.996413	−	0.377890i	−0.798281	+	0.602286i	$0.794257\pi$
$258$	−111.056	−	111.056i	−0.430449	−	0.430449i
$259$	703.452	−	266.784i	2.71603	−	1.03006i
$260$	140.314	−	53.1633i	0.539670	−	0.204474i
$261$	−7.17258	+	18.9125i	−0.0274812	+	0.0724619i
$262$	46.7062	+	103.777i	0.178268	+	0.396096i
$263$	149.459	−	216.529i	0.568285	−	0.823303i	−0.428491	−	0.903546i	$-0.640954\pi$
$263$	149.459	−	216.529i	0.568285	−	0.823303i	0.996775	+	0.0802437i	$0.0255699\pi$
$264$	−229.163	−	258.671i	−0.868041	−	0.979816i
$265$	8.47107	+	46.2251i	0.0319663	+	0.174435i
$266$	231.156	−	13.9824i	0.869008	−	0.0525653i
$267$	−104.527	−	335.438i	−0.391486	−	1.25632i
$268$	−163.191	−	163.191i	−0.608922	−	0.608922i
$269$	368.518	+	193.413i	1.36996	+	0.719008i	0.979468	−	0.201600i	$-0.0646141\pi$
$269$	368.518	+	193.413i	1.36996	+	0.719008i	0.390488	+	0.920608i	$0.372306\pi$
$270$	67.3771	+	8.18106i	0.249545	+	0.0303002i
$271$	−16.2194	+	36.0380i	−0.0598502	+	0.132982i	−0.939398	−	0.342830i	$-0.888615\pi$
$271$	−16.2194	+	36.0380i	−0.0598502	+	0.132982i	0.879547	+	0.475811i	$0.157845\pi$
$272$	−23.8003	+	45.3477i	−0.0875011	+	0.166719i
$273$	−134.186	+	543.674i	−0.491525	+	1.99148i
$274$	106.472	−	55.8811i	0.388586	−	0.203945i
$275$	−134.908	+	8.16043i	−0.490574	+	0.0296743i
$276$	−101.779	+	90.1680i	−0.368763	+	0.326695i
$277$	−6.88152	+	27.9194i	−0.0248430	+	0.100792i	−0.982055	−	0.188597i	$-0.939606\pi$
$277$	−6.88152	+	27.9194i	−0.0248430	+	0.100792i	0.957212	+	0.289389i	$0.0934522\pi$
$278$	30.7529	+	39.2531i	0.110622	+	0.141198i
$279$	9.58913	−	158.527i	0.0343696	−	0.568198i
$280$	−294.587	+	132.583i	−1.05210	+	0.473511i
$281$	−13.5872	−	43.6029i	−0.0483531	−	0.155171i	0.927387	−	0.374104i	$-0.122050\pi$
$281$	−13.5872	−	43.6029i	−0.0483531	−	0.155171i	−0.975740	+	0.218934i	$0.929742\pi$
$282$	−184.091	+	96.6184i	−0.652805	+	0.342618i
$283$	−239.750	+	29.1109i	−0.847173	+	0.102865i	−0.532599	−	0.846368i	$-0.678785\pi$
$283$	−239.750	+	29.1109i	−0.847173	+	0.102865i	−0.314574	+	0.949233i	$0.601862\pi$
$284$	99.9329	+	6.04483i	0.351876	+	0.0212846i
$285$	−65.2499	−	264.729i	−0.228947	−	0.928875i
$286$	−125.096	−	125.175i	−0.437398	−	0.437675i
$287$	−416.883	−	102.752i	−1.45255	−	0.358022i
$288$	41.4871	−	133.137i	0.144052	−	0.462280i
$289$	155.916	−	81.8311i	0.539502	−	0.283153i
$290$	−17.5014	+	6.63739i	−0.0603495	+	0.0228876i
$291$	114.536	+	51.5483i	0.393593	+	0.177142i
$292$	320.718	+	58.7737i	1.09835	+	0.201280i
$293$	260.715	+	431.275i	0.889813	+	1.47193i	0.881618	+	0.471963i	$0.156455\pi$
$293$	260.715	+	431.275i	0.889813	+	1.47193i	0.00819443	+	0.999966i	$0.497392\pi$
$294$	60.4127	−	329.662i	0.205485	−	1.12130i
$295$	33.4948	−	275.854i	0.113542	−	0.935099i
$296$	−418.298	+	158.640i	−1.41317	+	0.535944i
$297$	69.7536	+	223.847i	0.234861	+	0.753694i
$298$	−104.852	−	72.3738i	−0.351851	−	0.242865i
$299$	−115.320	+	115.247i	−0.385685	+	0.385441i
$300$	−61.7000	−	89.3879i	−0.205667	−	0.297960i
$301$	−399.240	−	312.784i	−1.32638	−	1.03915i
$302$	−181.081	+	44.6325i	−0.599606	+	0.147790i
$303$	−522.856	−	360.901i	−1.72560	−	1.19109i
$304$	93.2003	−	5.63758i	0.306580	−	0.0185447i
$305$	−80.1678	+	257.268i	−0.262845	+	0.843500i
$306$	35.6201	−	27.9066i	0.116406	−	0.0911980i
$307$	−348.442	+	444.753i	−1.13499	+	1.44871i	−0.259322	+	0.965791i	$0.583499\pi$
$307$	−348.442	+	444.753i	−1.13499	+	1.44871i	−0.875667	+	0.482916i	$0.839578\pi$
$308$	−356.757	−	316.059i	−1.15830	−	1.02616i
$309$	209.911	−	144.891i	0.679323	−	0.468903i
$310$	115.690	−	90.6371i	0.373193	−	0.292378i
$311$	30.5429	−	3.70858i	0.0982086	−	0.0119247i	−0.0712848	−	0.997456i	$-0.522710\pi$
$311$	30.5429	−	3.70858i	0.0982086	−	0.0119247i	0.169493	+	0.985531i	$0.445787\pi$
$312$	79.7920	−	323.288i	0.255744	−	1.03618i
$313$	−1.75232	+	14.4317i	−0.00559847	+	0.0461076i	−0.995240	−	0.0974504i	$-0.968931\pi$
$313$	−1.75232	+	14.4317i	−0.00559847	+	0.0461076i	0.989642	+	0.143558i	$0.0458543\pi$
$314$	−5.98497	+	3.61804i	−0.0190604	+	0.0115224i
$315$	−193.535			−0.614396
$316$		−	235.920i		−	0.746581i
$317$	408.481	−	246.935i	1.28858	−	0.778976i	0.303796	−	0.952737i	$-0.401746\pi$
$317$	408.481	−	246.935i	1.28858	−	0.778976i	0.984788	+	0.173761i	$0.0555920\pi$
$318$	40.6181	+	18.2807i	0.127730	+	0.0574866i
$319$	−45.7218	−	45.7218i	−0.143328	−	0.143328i
$320$	49.6294	−	22.3364i	0.155092	−	0.0698013i
$321$	82.4614	−	20.3249i	0.256889	−	0.0633175i
$322$	99.4108	−	112.212i	0.308729	−	0.348483i
$323$	176.171	+	106.499i	0.545420	+	0.329718i
$324$	−200.056	+	225.816i	−0.617456	+	0.696964i
$325$	−80.2827	−	102.540i	−0.247024	−	0.315508i
$326$	−203.820	+	180.569i	−0.625216	+	0.553893i
$327$	−62.9647	−	343.587i	−0.192553	−	1.05073i
$328$	247.894	+	61.1003i	0.755773	+	0.186281i
$329$	−552.533	+	381.386i	−1.67943	+	1.15923i
$330$	99.1148	−	163.956i	0.300348	−	0.496836i
$331$	−144.486	+	239.010i	−0.436515	+	0.722084i	−0.994151	−	0.108002i	$-0.965555\pi$
$331$	−144.486	+	239.010i	−0.436515	+	0.722084i	0.557636	+	0.830086i	$0.311709\pi$
$332$	−130.712	+	166.842i	−0.393711	+	0.502535i
$333$	−267.526	−	16.1823i	−0.803381	−	0.0485956i
$334$	−84.4851	+	222.769i	−0.252949	+	0.666973i
$335$	139.219	−	265.259i	0.415578	−	0.791818i
$336$	37.4229	−	204.210i	0.111378	−	0.607768i
$337$			184.888i			0.548630i	0.961640	+	0.274315i	$0.0884511\pi$
$337$			184.888i			0.548630i	−0.961640	+	0.274315i	$0.911549\pi$
$338$	30.8434	−	167.707i	0.0912526	−	0.496176i
$339$	393.973			1.16216
$340$	−120.639	−	22.1080i	−0.354822	−	0.0650235i
$341$	449.543	+	235.938i	1.31831	+	0.691901i
$342$	−77.1367	−	29.2541i	−0.225546	−	0.0855382i
$343$	30.2966	−	500.863i	0.0883283	−	1.46024i
$344$	237.402	+	185.993i	0.690123	+	0.540677i
$345$	−151.047	−	91.3113i	−0.437818	−	0.264670i
$346$	125.144	+	75.6521i	0.361687	+	0.218648i
$347$	−27.1102	−	39.2759i	−0.0781273	−	0.113187i	0.781972	−	0.623314i	$-0.214214\pi$
$347$	−27.1102	−	39.2759i	−0.0781273	−	0.113187i	−0.860099	+	0.510127i	$0.829599\pi$
$348$	12.4356	−	50.4531i	0.0357344	−	0.144980i
$349$	−413.775	+	75.8271i	−1.18560	+	0.217270i	−0.736642	−	0.676283i	$-0.763590\pi$
$349$	−413.775	+	75.8271i	−1.18560	+	0.217270i	−0.448959	+	0.893552i	$0.648205\pi$
$350$	79.4077	+	89.6328i	0.226879	+	0.256094i
$351$	−139.386	+	177.797i	−0.397110	+	0.506543i
$352$	333.677	+	295.612i	0.947946	+	0.839807i
$353$	−244.582	+	404.588i	−0.692866	+	1.14614i	0.289139	+	0.957287i	$0.406631\pi$
$353$	−244.582	+	404.588i	−0.692866	+	1.14614i	−0.982005	+	0.188853i	$0.939523\pi$
$354$	−197.141	−	174.652i	−0.556896	−	0.493367i
$355$	31.1003	+	126.179i	0.0876065	+	0.355434i
$356$	118.258	+	262.759i	0.332187	+	0.738088i
$357$	323.665	−	323.665i	0.906624	−	0.906624i
$358$	18.8945	−	41.9819i	0.0527780	−	0.117268i
$359$	144.763	+	239.467i	0.403240	+	0.667040i	0.989735	−	0.142913i	$-0.0456468\pi$
$359$	144.763	+	239.467i	0.403240	+	0.667040i	−0.586496	+	0.809952i	$0.699493\pi$
$360$	115.083			0.319674
$361$		−	14.3124i		−	0.0396467i
$362$	−89.3434	−	147.792i	−0.246805	−	0.408265i
$363$	220.262	+	26.7447i	0.606783	+	0.0736768i
$364$	55.5015	−	455.889i	0.152477	−	1.25244i
$365$	51.0160	+	420.155i	0.139770	+	1.15111i
$366$	157.514	+	201.051i	0.430365	+	0.549320i
$367$	−80.9720	−	117.308i	−0.220632	−	0.319641i	0.697000	−	0.717071i	$-0.254518\pi$
$367$	−80.9720	−	117.308i	−0.220632	−	0.319641i	−0.917633	+	0.397430i	$0.869902\pi$
$368$	40.0817	−	45.2428i	0.108918	−	0.122942i
$369$	120.404	+	94.3303i	0.326298	+	0.255638i
$370$	−152.957	−	195.235i	−0.413396	−	0.527661i
$371$	137.325	+	42.7923i	0.370149	+	0.115343i
$372$	24.6345	+	407.256i	0.0662217	+	1.09477i
$373$	389.008	−	563.575i	1.04292	−	1.51092i	0.194993	−	0.980805i	$-0.437532\pi$
$373$	389.008	−	563.575i	1.04292	−	1.51092i	0.847923	−	0.530120i	$-0.177853\pi$
$374$	34.6177	+	140.449i	0.0925606	+	0.375533i
$375$	303.939	−	387.950i	0.810505	−	1.03453i
$376$	328.556	−	226.786i	0.873819	−	0.603154i
$377$	11.2501	−	61.2802i	0.0298411	−	0.162547i
$378$	118.008	−	170.964i	0.312190	−	0.452286i
$379$	8.42867	−	2.62648i	0.0222392	−	0.00693002i	−0.286363	−	0.958121i	$-0.592446\pi$
$379$	8.42867	−	2.62648i	0.0222392	−	0.00693002i	0.308602	+	0.951191i	$0.400139\pi$
$380$	79.2918	+	209.075i	0.208663	+	0.550198i
$381$	−127.095	−	15.4321i	−0.333583	−	0.0405043i
$382$	−271.567	−	49.7665i	−0.710908	−	0.130279i
$383$	79.9467	−	48.3295i	0.208738	−	0.126187i	−0.409107	−	0.912486i	$-0.634160\pi$
$383$	79.9467	−	48.3295i	0.208738	−	0.126187i	0.617845	+	0.786300i	$0.288006\pi$
$384$	−77.3251	+	421.949i	−0.201367	+	1.09883i
$385$	253.914	−	564.174i	0.659517	−	1.46539i
$386$	6.40259	+	16.8822i	0.0165870	+	0.0437364i
$387$	83.9645	+	159.981i	0.216962	+	0.413387i
$388$	−98.3432	−	30.6450i	−0.253462	−	0.0789819i
$389$	−177.352	+	719.543i	−0.455916	+	1.84973i	0.0676031	+	0.997712i	$0.478465\pi$
$389$	−177.352	+	719.543i	−0.455916	+	1.84973i	−0.523520	+	0.852014i	$0.675381\pi$
$390$	184.272	−	11.0878i	0.472493	−	0.0284303i
$391$	129.392	−	31.8921i	0.330925	−	0.0815656i
$392$	−38.8576	+	642.393i	−0.0991266	+	1.63876i
$393$	−49.4319	−	407.108i	−0.125781	−	1.03590i
$394$	80.6865	+	153.735i	0.204788	+	0.390191i
$395$	292.370	−	91.1061i	0.740177	−	0.230648i
$396$	69.6848	+	154.833i	0.175972	+	0.390993i
$397$	−563.034	−	34.0573i	−1.41822	−	0.0857866i	−0.666617	−	0.745401i	$-0.732258\pi$
$397$	−563.034	−	34.0573i	−1.41822	−	0.0857866i	−0.751605	+	0.659614i	$0.770720\pi$
$398$	14.0128	−	10.9783i	0.0352080	−	0.0275837i
$399$	−810.262	−	199.712i	−2.03073	−	0.500530i
$400$	32.0166	+	36.1392i	0.0800414	+	0.0903481i
$401$	−14.1269	−	233.546i	−0.0352292	−	0.582408i	−0.972368	−	0.233452i	$-0.924998\pi$
$401$	−14.1269	−	233.546i	−0.0352292	−	0.582408i	0.937139	−	0.348956i	$-0.113464\pi$
$402$	−131.953	−	251.416i	−0.328242	−	0.625412i
$403$	58.8123	+	485.649i	0.145936	+	1.20508i
$404$	461.352	+	242.136i	1.14196	+	0.599347i
$405$	−357.105	−	160.720i	−0.881742	−	0.396840i
$406$	−6.90551	+	56.8720i	−0.0170086	+	0.140079i
$407$	398.162	−	758.635i	0.978286	−	1.86397i
$408$	−192.463	+	192.463i	−0.471722	+	0.471722i
$409$	−260.014	+	81.0238i	−0.635732	+	0.198102i	−0.598396	−	0.801201i	$-0.704195\pi$
$409$	−260.014	+	81.0238i	−0.635732	+	0.198102i	−0.0373363	+	0.999303i	$0.511887\pi$
$410$	8.54611	+	141.284i	0.0208442	+	0.344595i
$411$	−426.218	+	78.1073i	−1.03703	+	0.190042i
$412$	−156.573	+	138.711i	−0.380031	+	0.336678i
$413$	−699.959	−	483.147i	−1.69482	−	1.16985i
$414$	−48.7002	+	21.9182i	−0.117633	+	0.0529424i
$415$	−257.241	−	97.5585i	−0.619857	−	0.235081i
$416$	−51.9110	+	426.396i	−0.124786	+	1.02499i
$417$	−63.7202	−	168.016i	−0.152806	−	0.402917i
$418$	186.481	−	186.481i	0.446126	−	0.446126i
$419$	160.235	−	422.506i	0.382423	−	1.00837i	−0.596223	−	0.802819i	$-0.703333\pi$
$419$	160.235	−	422.506i	0.382423	−	1.00837i	0.978647	−	0.205549i	$-0.0658980\pi$
$420$	493.565	−	59.9297i	1.17516	−	0.142690i
$421$	−97.7160	+	313.582i	−0.232104	+	0.744850i	0.763033	+	0.646359i	$0.223709\pi$
$421$	−97.7160	+	313.582i	−0.232104	+	0.744850i	−0.995138	+	0.0984906i	$0.968599\pi$
$422$	10.7429	+	58.6224i	0.0254572	+	0.138916i
$423$	235.254	−	43.1120i	0.556157	−	0.101920i
$424$	−81.6586	−	25.4459i	−0.192591	−	0.0600138i
$425$	12.8310	+	105.673i	0.0301906	+	0.248642i
$426$	115.169	+	43.6778i	0.270349	+	0.102530i
$427$	583.199	+	583.199i	1.36581	+	1.36581i
$428$	−65.1255	+	24.6989i	−0.152162	+	0.0577076i
$429$	296.184	+	564.766i	0.690405	+	1.31647i
$430$	−59.2881	+	156.330i	−0.137879	+	0.363558i
$431$	208.372	+	462.985i	0.483463	+	1.07421i	0.978671	+	0.205436i	$0.0658611\pi$
$431$	208.372	+	462.985i	0.483463	+	1.07421i	−0.495208	+	0.868775i	$0.664908\pi$
$432$	47.5799	−	68.9314i	0.110139	−	0.159563i
$433$	−237.835	−	268.460i	−0.549272	−	0.620000i	0.406663	−	0.913578i	$-0.366692\pi$
$433$	−237.835	−	268.460i	−0.549272	−	0.620000i	−0.955935	+	0.293578i	$0.905154\pi$
$434$	−81.0830	−	442.455i	−0.186827	−	1.01948i
$435$	67.3277	−	4.07257i	0.154776	−	0.00936224i
$436$	85.2268	+	273.502i	0.195474	+	0.627299i
$437$	−171.799	−	171.799i	−0.393132	−	0.393132i
$438$	355.203	+	186.425i	0.810966	+	0.425628i
$439$	331.918	+	40.3022i	0.756078	+	0.0918045i	0.489493	−	0.872007i	$-0.337182\pi$
$439$	331.918	+	40.3022i	0.756078	+	0.0918045i	0.266585	+	0.963812i	$0.414105\pi$
$440$	−150.987	+	335.478i	−0.343151	+	0.762451i
$441$	−179.176	+	341.392i	−0.406295	+	0.774131i
$442$	−92.4604	+	104.300i	−0.209186	+	0.235972i
$443$	123.180	−	64.6496i	0.278058	−	0.145936i	−0.319930	−	0.947441i	$-0.603659\pi$
$443$	123.180	−	64.6496i	0.278058	−	0.145936i	0.597988	+	0.801505i	$0.295967\pi$
$444$	687.274	−	41.5724i	1.54791	−	0.0936315i
$445$	−279.963	+	248.026i	−0.629131	+	0.557362i
$446$	79.4721	−	322.431i	0.178189	−	0.722939i
$447$	283.142	+	361.405i	0.633428	+	0.808511i
$448$	10.0577	−	166.273i	0.0224502	−	0.371146i
$449$	−62.6003	+	28.1741i	−0.139422	+	0.0627486i	−0.478923	−	0.877857i	$-0.658973\pi$
$449$	−62.6003	+	28.1741i	−0.139422	+	0.0627486i	0.339501	+	0.940606i	$0.389742\pi$
$450$	−12.6912	−	40.7276i	−0.0282027	−	0.0905058i
$451$	−432.950	+	227.230i	−0.959979	+	0.503836i
$452$	−320.748	+	38.9458i	−0.709619	+	0.0861633i
$453$	670.843	+	40.5785i	1.48089	+	0.0895773i
$454$	96.1249	+	389.994i	0.211729	+	0.859017i
$455$	586.406	−	107.271i	1.28880	−	0.235760i
$456$	481.811	+	118.756i	1.05660	+	0.260429i
$457$	134.470	−	431.529i	0.294245	−	0.944266i	−0.682686	−	0.730712i	$-0.739188\pi$
$457$	134.470	−	431.529i	0.294245	−	0.944266i	0.976931	−	0.213554i	$-0.0685039\pi$
$458$	−246.530	+	129.389i	−0.538274	+	0.282508i
$459$	172.665	−	65.4834i	0.376177	−	0.142665i
$460$	131.999	+	59.4082i	0.286955	+	0.129148i
$461$	312.910	+	57.3428i	0.678763	+	0.124388i	0.508567	−	0.861022i	$-0.330175\pi$
$461$	312.910	+	57.3428i	0.678763	+	0.124388i	0.170196	+	0.985410i	$0.445560\pi$
$462$	−303.363	−	501.823i	−0.656629	−	1.08620i
$463$	−51.8001	+	282.664i	−0.111879	+	0.610505i	0.879116	+	0.476608i	$0.158134\pi$
$463$	−51.8001	+	282.664i	−0.111879	+	0.610505i	−0.990995	+	0.133897i	$0.957251\pi$
$464$	−2.78424	+	22.9303i	−0.00600053	+	0.0494188i
$465$	−495.190	+	187.801i	−1.06492	+	0.403873i
$466$	66.6429	+	213.865i	0.143011	+	0.458937i
$467$	−328.731	−	226.907i	−0.703921	−	0.485882i	0.161534	−	0.986867i	$-0.448356\pi$
$467$	−328.731	−	226.907i	−0.703921	−	0.485882i	−0.865456	+	0.500985i	$0.832971\pi$
$468$	−84.6836	+	139.984i	−0.180948	+	0.299110i
$469$	−520.864	−	754.602i	−1.11058	−	1.60896i
$470$	174.224	+	136.496i	0.370690	+	0.290417i
$471$	24.4696	−	6.03121i	0.0519524	−	0.0128051i
$472$	416.221	+	287.296i	0.881824	+	0.608679i
$473$	−576.521	+	34.8731i	−1.21886	+	0.0737275i
$474$	86.3514	−	277.111i	0.182176	−	0.584623i
$475$	152.771	−	119.688i	0.321622	−	0.251975i
$476$	−231.511	+	295.502i	−0.486368	+	0.620803i
$477$	−38.3545	−	33.9791i	−0.0804077	−	0.0712350i
$478$	213.871	−	147.625i	0.447429	−	0.308838i
$479$	−634.981	+	497.476i	−1.32564	+	1.03857i	−0.330126	+	0.943937i	$0.607091\pi$
$479$	−634.981	+	497.476i	−1.32564	+	1.03857i	−0.995512	+	0.0946340i	$0.969832\pi$
$480$	−461.635	+	56.0527i	−0.961740	+	0.116776i
$481$	819.567	−	99.2499i	1.70388	−	0.206341i
$482$	40.3050	−	331.942i	0.0836204	−	0.688676i
$483$	−462.314	+	279.478i	−0.957171	+	0.578630i
$484$	−181.967			−0.375965
$485$		−	133.709i		−	0.275688i
$486$	−182.586	+	110.377i	−0.375690	+	0.227113i
$487$	105.239	+	47.3641i	0.216096	+	0.0972568i	0.515570	−	0.856848i	$-0.327580\pi$
$487$	105.239	+	47.3641i	0.216096	+	0.0972568i	−0.299474	+	0.954105i	$0.596811\pi$
$488$	−346.791	−	346.791i	−0.710638	−	0.710638i
$489$	894.809	−	402.721i	1.82988	−	0.823560i
$490$	−346.418	+	85.3845i	−0.706976	+	0.174254i
$491$	216.971	−	244.909i	0.441896	−	0.498797i	−0.484792	−	0.874629i	$-0.661105\pi$
$491$	216.971	−	244.909i	0.441896	−	0.498797i	0.926688	+	0.375832i	$0.122643\pi$
$492$	−336.272	−	203.284i	−0.683480	−	0.413178i
$493$	−33.7709	+	38.1195i	−0.0685008	+	0.0773215i
$494$	249.937	+	45.8845i	0.505945	+	0.0928837i
$495$	−164.971	+	146.152i	−0.333275	+	0.295256i
$496$	−32.6920	−	178.395i	−0.0659113	−	0.359666i
$497$	386.198	+	95.1893i	0.777059	+	0.191528i
$498$	−214.602	+	148.129i	−0.430928	+	0.297448i
$499$	−6.72543	+	11.1252i	−0.0134778	+	0.0222950i	−0.862448	−	0.506146i	$-0.831070\pi$
$499$	−6.72543	+	11.1252i	−0.0134778	+	0.0222950i	0.848970	+	0.528441i	$0.177223\pi$
$500$	−209.097	+	345.889i	−0.418195	+	0.691779i
$501$	529.489	−	675.842i	1.05686	−	1.34899i
$502$	−195.218	−	11.8085i	−0.388881	−	0.0235230i
$503$	293.840	−	774.793i	0.584175	−	1.54034i	−0.238092	−	0.971243i	$-0.576522\pi$
$503$	293.840	−	774.793i	0.584175	−	1.54034i	0.822268	−	0.569101i	$-0.192709\pi$
$504$	163.692	−	311.889i	0.324786	−	0.618828i
$505$	−121.911	+	665.249i	−0.241409	+	1.31733i
$506$		−	170.722i		−	0.337396i
$507$	−285.909	+	543.916i	−0.563923	+	1.07281i
$508$	104.998			0.206689
$509$	586.815	+	107.538i	1.15288	+	0.211273i	0.722497	−	0.691375i	$-0.242995\pi$
$509$	586.815	+	107.538i	1.15288	+	0.211273i	0.430381	+	0.902647i	$0.358379\pi$
$510$	−133.611	−	70.1245i	−0.261983	−	0.137499i
$511$	1211.24	+	459.363i	2.37033	+	0.898949i
$512$	17.8154	−	294.523i	0.0347957	−	0.575241i
$513$	−265.023	−	207.633i	−0.516615	−	0.404742i
$514$	236.486	+	142.961i	0.460089	+	0.278133i
$515$	−232.366	−	140.470i	−0.451197	−	0.272758i
$516$	−263.671	−	381.994i	−0.510991	−	0.740298i
$517$	−182.974	+	742.353i	−0.353914	+	1.43589i
$518$	−746.675	+	136.833i	−1.44146	+	0.264157i
$519$	−349.442	−	394.438i	−0.673298	−	0.759996i
$520$	−348.698	+	63.7871i	−0.670573	+	0.122668i
$521$	−100.186	−	88.7574i	−0.192296	−	0.170360i	0.561481	−	0.827490i	$-0.310232\pi$
$521$	−100.186	−	88.7574i	−0.192296	−	0.170360i	−0.753777	+	0.657130i	$0.771770\pi$
$522$	10.5583	−	17.4656i	0.0202266	−	0.0334589i
$523$	−172.642	−	152.948i	−0.330100	−	0.292443i	0.481750	−	0.876309i	$-0.340001\pi$
$523$	−172.642	−	152.948i	−0.330100	−	0.292443i	−0.811851	+	0.583865i	$0.801540\pi$
$524$	80.4885	+	326.555i	0.153604	+	0.623196i
$525$	−177.102	−	393.505i	−0.337337	−	0.749533i
$526$	−187.714	+	187.714i	−0.356872	+	0.356872i
$527$	164.110	−	364.638i	0.311405	−	0.691913i
$528$	−122.313	−	202.331i	−0.231654	−	0.383203i
$529$	371.719			0.702682
$530$		−	47.4176i		−	0.0894672i
$531$	156.747	+	259.291i	0.295192	+	0.488307i
$532$	679.405	+	82.4947i	1.27708	+	0.155065i
$533$	−417.105	−	219.082i	−0.782562	−	0.411036i
$534$	42.7311	+	351.923i	0.0800208	+	0.659031i
$535$	−55.7585	−	71.1705i	−0.104222	−	0.133029i
$536$	309.725	+	448.714i	0.577845	+	0.837152i
$537$	−110.013	+	124.179i	−0.204865	+	0.231245i
$538$	−330.565	−	258.981i	−0.614433	−	0.481377i
$539$	−760.117	−	970.217i	−1.41023	−	1.80003i
$540$	191.503	+	59.6747i	0.354635	+	0.110509i
$541$	28.8107	+	476.298i	0.0532545	+	0.880402i	0.922494	+	0.386011i	$0.126147\pi$
$541$	28.8107	+	476.298i	0.0532545	+	0.880402i	−0.869240	+	0.494391i	$0.835391\pi$
$542$	22.6517	−	32.8166i	0.0417928	−	0.0605473i
$543$	148.934	+	604.248i	0.274280	+	1.11280i
$544$	216.534	−	276.386i	0.398041	−	0.508062i
$545$	−306.033	+	211.239i	−0.561528	+	0.387595i
$546$	232.057	−	515.173i	0.425013	−	0.943540i
$547$	162.529	−	235.464i	0.297128	−	0.430464i	−0.645777	−	0.763526i	$-0.723466\pi$
$547$	162.529	−	235.464i	0.297128	−	0.430464i	0.942905	+	0.333062i	$0.108082\pi$
$548$	339.278	−	105.723i	0.619120	−	0.192926i
$549$	−104.189	−	274.723i	−0.189779	−	0.500406i
$550$	135.376	+	16.4376i	0.246138	+	0.0298865i
$551$	91.3268	+	16.7363i	0.165747	+	0.0303743i
$552$	274.908	−	166.188i	0.498022	−	0.301065i
$553$	168.953	−	921.949i	0.305522	−	1.66718i
$554$	11.9076	−	26.4575i	0.0214938	−	0.0477573i
$555$	316.927	+	835.668i	0.571040	+	1.50571i
$556$	68.4859	+	130.489i	0.123176	+	0.234692i
$557$	−20.3078	−	6.32816i	−0.0364592	−	0.0113612i	0.279219	−	0.960227i	$-0.409924\pi$
$557$	−20.3078	−	6.32816i	−0.0364592	−	0.0113612i	−0.315678	+	0.948866i	$0.602232\pi$
$558$	−38.3492	+	155.589i	−0.0687262	+	0.278833i
$559$	−343.083	−	438.199i	−0.613745	−	0.783899i
$560$	−214.590	+	52.8917i	−0.383196	+	0.0944494i
$561$	31.4734	−	520.317i	0.0561022	−	0.927480i
$562$	5.55453	+	45.7456i	0.00988350	+	0.0813979i
$563$	−158.598	−	302.183i	−0.281702	−	0.536738i	0.702956	−	0.711233i	$-0.251863\pi$
$563$	−158.598	−	302.183i	−0.281702	−	0.536738i	−0.984658	+	0.174495i	$0.944171\pi$
$564$	−586.611	+	182.796i	−1.04009	+	0.324106i
$565$	−172.129	−	382.455i	−0.304653	−	0.676912i
$566$	243.238	+	14.7132i	0.429750	+	0.0259951i
$567$	−943.515	+	739.197i	−1.66405	+	1.30370i
$568$	−229.647	−	56.6030i	−0.404309	−	0.0996532i
$569$	374.057	+	422.224i	0.657394	+	0.742045i	0.978782	−	0.204903i	$-0.0656878\pi$
$569$	374.057	+	422.224i	0.657394	+	0.742045i	−0.321388	+	0.946948i	$0.604149\pi$
$570$	16.6104	+	274.602i	0.0291410	+	0.481759i
$571$	−5.31487	−	10.1266i	−0.00930800	−	0.0177349i	0.880758	−	0.473567i	$-0.157034\pi$
$571$	−5.31487	−	10.1266i	−0.00930800	−	0.0177349i	−0.890066	+	0.455832i	$0.849342\pi$
$572$	−296.963	−	430.517i	−0.519166	−	0.752653i
$573$	880.949	+	462.358i	1.53743	+	0.806907i
$574$	395.054	+	177.799i	0.688248	+	0.309755i
$575$	15.1434	−	124.717i	0.0263364	−	0.216900i
$576$	−27.5774	+	52.5444i	−0.0478775	+	0.0912229i
$577$	442.527	−	442.527i	0.766945	−	0.766945i	−0.210622	−	0.977568i	$-0.567549\pi$
$577$	442.527	−	442.527i	0.766945	−	0.766945i	0.977568	+	0.210622i	$0.0675490\pi$
$578$	−169.625	+	52.8572i	−0.293468	+	0.0914485i
$579$	−3.92850	−	64.9459i	−0.00678498	−	0.112169i
$580$	−54.4113	+	9.97123i	−0.0938125	+	0.0171918i
$581$	−630.292	+	558.390i	−1.08484	+	0.961085i
$582$	−104.297	−	71.9913i	−0.179205	−	0.123696i
$583$	149.373	−	67.2273i	0.256214	−	0.115313i
$584$	−720.247	−	273.154i	−1.23330	−	0.467729i
$585$	−206.181	−	50.8884i	−0.352446	−	0.0869886i
$586$	−180.312	−	475.445i	−0.307700	−	0.811339i
$587$	−463.715	+	463.715i	−0.789974	+	0.789974i	−0.981490	−	0.191516i	$-0.938660\pi$
$587$	−463.715	+	463.715i	−0.789974	+	0.789974i	0.191516	+	0.981490i	$0.438660\pi$
$588$	351.232	−	926.124i	0.597334	−	1.57504i
$589$	−723.700	+	87.8731i	−1.22869	+	0.149190i
$590$	−83.4138	+	267.684i	−0.141379	+	0.453702i
$591$	−112.779	−	615.415i	−0.190827	−	1.04131i
$592$	−301.053	+	55.1701i	−0.508536	+	0.0931927i
$593$	524.924	+	163.573i	0.885201	+	0.275840i	0.706203	−	0.708009i	$-0.250407\pi$
$593$	524.924	+	163.573i	0.885201	+	0.275840i	0.178998	+	0.983849i	$0.442714\pi$
$594$	−28.5156	−	234.847i	−0.0480061	−	0.395366i
$595$	−455.613	−	172.791i	−0.765736	−	0.290406i
$596$	−266.243	−	266.243i	−0.446716	−	0.446716i
$597$	−59.9794	+	22.7472i	−0.100468	+	0.0381025i
$598$	135.412	−	93.4047i	0.226441	−	0.156195i
$599$	−129.546	+	341.586i	−0.216271	+	0.570260i	−0.998616	−	0.0525850i	$-0.983254\pi$
$599$	−129.546	+	341.586i	−0.216271	+	0.570260i	0.782345	+	0.622845i	$0.214023\pi$
$600$	105.311	+	233.992i	0.175519	+	0.389987i
$601$	421.935	−	611.279i	0.702056	−	1.01710i	−0.296025	−	0.955180i	$-0.595661\pi$
$601$	421.935	−	611.279i	0.702056	−	1.01710i	0.998081	−	0.0619231i	$-0.0197233\pi$
$602$	339.344	+	383.040i	0.563695	+	0.636280i
$603$	58.8786	+	321.290i	0.0976428	+	0.532820i
$604$	−550.168	+	33.2791i	−0.910875	+	0.0550978i
$605$	−70.2710	−	225.508i	−0.116150	−	0.372740i
$606$	453.277	+	453.277i	0.747983	+	0.747983i
$607$	−535.198	−	280.893i	−0.881709	−	0.462757i	−0.0378265	−	0.999284i	$-0.512043\pi$
$607$	−535.198	−	280.893i	−0.881709	−	0.462757i	−0.843883	+	0.536528i	$0.819736\pi$
$608$	−635.453	−	77.1579i	−1.04515	−	0.126905i
$609$	84.7288	−	188.260i	0.139128	−	0.309129i
$610$	126.355	−	240.749i	0.207139	−	0.394670i
$611$	−688.920	+	261.023i	−1.12753	+	0.427206i
$612$	118.412	−	62.1474i	0.193484	−	0.101548i
$613$	25.0514	−	1.51533i	0.0408669	−	0.00247199i	−0.0399324	−	0.999202i	$-0.512714\pi$
$613$	25.0514	−	1.51533i	0.0408669	−	0.00247199i	0.0807993	+	0.996730i	$0.474253\pi$
$614$	426.707	−	378.029i	0.694962	−	0.615683i
$615$	122.065	−	495.237i	0.198480	−	0.805264i
$616$	694.429	+	886.373i	1.12732	+	1.43892i
$617$	49.0613	−	811.080i	0.0795158	−	1.31455i	−0.711469	−	0.702718i	$-0.751970\pi$
$617$	49.0613	−	811.080i	0.0795158	−	1.31455i	0.790985	−	0.611836i	$-0.209569\pi$
$618$	−234.682	+	105.622i	−0.379744	+	0.170909i
$619$	−276.968	−	888.820i	−0.447443	−	1.43590i	−0.853041	−	0.521845i	$-0.825244\pi$
$619$	−276.968	−	888.820i	−0.447443	−	1.43590i	0.405597	−	0.914052i	$-0.367064\pi$
$620$	384.587	−	201.847i	0.620301	−	0.325559i
$621$	−216.357	+	26.2705i	−0.348402	+	0.0423036i
$622$	−30.9873	−	1.87439i	−0.0498188	−	0.00301348i
$623$	273.967	+	1111.53i	0.439754	+	1.78415i
$624$	93.5635	−	207.714i	0.149941	−	0.332874i
$625$	−266.236	−	65.6214i	−0.425978	−	0.104994i
$626$	4.36390	−	14.0042i	0.00697109	−	0.0223710i
$627$	−841.491	+	441.649i	−1.34209	+	0.704384i
$628$	−19.3253	+	7.32913i	−0.0307728	+	0.0116706i
$629$	−615.353	−	276.948i	−0.978303	−	0.440299i
$630$	192.077	+	35.1994i	0.304884	+	0.0558721i
$631$	−53.7910	−	88.9812i	−0.0852472	−	0.141016i	0.810248	−	0.586087i	$-0.199332\pi$
$631$	−53.7910	−	88.9812i	−0.0852472	−	0.141016i	−0.895495	+	0.445071i	$0.853178\pi$
$632$	−100.466	+	548.224i	−0.158965	+	0.867443i
$633$	25.8875	−	213.202i	0.0408964	−	0.336813i
$634$	−450.316	+	170.782i	−0.710277	+	0.269373i
$635$	40.5476	+	130.122i	0.0638544	+	0.204916i
$636$	108.336	+	74.7790i	0.170340	+	0.117577i
$637$	353.676	−	1133.72i	0.555221	−	1.77978i
$638$	37.0616	+	53.6930i	0.0580903	+	0.0841584i
$639$	−111.542	−	87.3872i	−0.174556	−	0.136756i
$640$	443.397	−	109.288i	0.692808	−	0.170762i
$641$	124.981	+	86.2684i	0.194979	+	0.134584i	0.661554	−	0.749897i	$-0.269897\pi$
$641$	124.981	+	86.2684i	0.194979	+	0.134584i	−0.466576	+	0.884481i	$0.654512\pi$
$642$	−85.5368	+	5.17402i	−0.133235	+	0.00805923i
$643$	−140.322	+	450.308i	−0.218230	+	0.700323i	0.779074	+	0.626932i	$0.215690\pi$
$643$	−140.322	+	450.308i	−0.218230	+	0.700323i	−0.997303	+	0.0733909i	$0.976618\pi$
$644$	348.758	−	273.235i	0.541550	−	0.424277i
$645$	371.573	−	474.278i	0.576082	−	0.735315i
$646$	−155.474	−	137.738i	−0.240672	−	0.213217i
$647$	1042.05	−	719.277i	1.61059	−	1.11171i	0.688156	−	0.725563i	$-0.258420\pi$
$647$	1042.05	−	719.277i	1.61059	−	1.11171i	0.922436	−	0.386149i	$-0.126195\pi$
$648$	561.048	−	439.553i	0.865815	−	0.678322i
$649$	−961.509	+	116.748i	−1.48152	+	0.179890i
$650$	61.0283	+	116.369i	0.0938897	+	0.179030i
$651$	−195.387	+	1609.16i	−0.300133	+	2.47182i
$652$	−688.685	+	416.325i	−1.05627	+	0.638535i
$653$	−97.2552			−0.148936			−0.0744680	−	0.997223i	$-0.523726\pi$
$653$	−97.2552			−0.148936			−0.0744680	+	0.997223i	$0.523726\pi$
$654$			352.451i			0.538916i
$655$	−373.609	+	225.855i	−0.570396	+	0.344816i
$656$	159.283	+	71.6873i	0.242809	+	0.109279i
$657$	−326.317	−	326.317i	−0.496677	−	0.496677i
$658$	617.736	−	278.020i	0.938808	−	0.422523i
$659$	−329.280	+	81.1603i	−0.499667	+	0.123157i	−0.481091	−	0.876671i	$-0.659759\pi$
$659$	−329.280	+	81.1603i	−0.499667	+	0.123157i	−0.0185757	+	0.999827i	$0.505913\pi$
$660$	375.463	−	423.810i	0.568883	−	0.642136i
$661$	315.554	+	190.759i	0.477389	+	0.288592i	0.735501	−	0.677523i	$-0.236947\pi$
$661$	315.554	+	190.759i	0.477389	+	0.288592i	−0.258113	+	0.966115i	$0.583101\pi$
$662$	186.868	−	210.931i	0.282278	−	0.318626i
$663$	429.919	−	259.709i	0.648445	−	0.391718i
$664$	374.795	−	332.039i	0.564450	−	0.500059i
$665$	160.135	+	873.829i	0.240805	+	1.31403i
$666$	262.567	+	64.7171i	0.394245	+	0.0971728i
$667$	49.4657	−	34.1437i	0.0741614	−	0.0511899i
$668$	−364.266	+	602.569i	−0.545308	+	0.902050i
$669$	−619.087	+	1024.10i	−0.925392	+	1.53079i
$670$	−186.414	+	237.940i	−0.278230	+	0.355135i
$671$	937.539	+	56.7107i	1.39723	+	0.0845166i
$672$	−504.714	+	1330.82i	−0.751063	+	1.98039i
$673$	402.098	−	766.135i	0.597472	−	1.13839i	−0.379535	−	0.925178i	$-0.623916\pi$
$673$	402.098	−	766.135i	0.597472	−	1.13839i	0.977006	−	0.213210i	$-0.0683918\pi$
$674$	33.6268	−	183.496i	0.0498914	−	0.272249i
$675$		−	174.092i		−	0.257914i
$676$	179.000	−	471.085i	0.264793	−	0.696871i
$677$	−204.844			−0.302576			−0.151288	−	0.988490i	$-0.548342\pi$
$677$	−204.844			−0.302576			−0.151288	+	0.988490i	$0.548342\pi$
$678$	−391.006	−	71.6544i	−0.576704	−	0.105685i
$679$	−362.369	−	190.186i	−0.533680	−	0.280097i
$680$	270.924	+	102.748i	0.398418	+	0.151100i
$681$	87.3939	−	1444.79i	0.128332	−	2.12158i
$682$	−403.245	−	315.922i	−0.591268	−	0.463229i
$683$	624.027	+	377.238i	0.913656	+	0.552325i	0.894290	−	0.447488i	$-0.147681\pi$
$683$	624.027	+	377.238i	0.913656	+	0.552325i	0.0193664	+	0.999812i	$0.493835\pi$
$684$	−208.648	−	126.132i	−0.305040	−	0.184403i
$685$	262.041	+	379.632i	0.382541	+	0.554207i
$686$	−121.163	+	491.579i	−0.176623	+	0.716588i
$687$	986.878	−	180.852i	1.43650	−	0.263249i
$688$	136.821	+	154.439i	0.198868	+	0.224475i
$689$	135.047	+	81.6971i	0.196004	+	0.118573i
$690$	133.302	+	118.095i	0.193192	+	0.171153i
$691$	2.54184	−	4.20472i	0.00367850	−	0.00608498i	−0.853937	−	0.520377i	$-0.825791\pi$
$691$	2.54184	−	4.20472i	0.00367850	−	0.00608498i	0.857615	+	0.514292i	$0.171945\pi$
$692$	323.485	+	286.582i	0.467463	+	0.414136i
$693$	161.437	+	654.977i	0.232954	+	0.945133i
$694$	19.7626	+	43.9107i	0.0284764	+	0.0632719i
$695$	−135.265	+	135.265i	−0.194625	+	0.194625i
$696$	−50.3828	+	111.946i	−0.0723891	+	0.160842i
$697$	199.231	+	329.568i	0.285840	+	0.472838i
$698$	424.449			0.608093
$699$		−	807.229i		−	1.15483i
$700$	183.085	+	302.859i	0.261549	+	0.432656i
$701$	1034.62	+	125.626i	1.47592	+	0.179209i	0.818583	−	0.574388i	$-0.194760\pi$
$701$	1034.62	+	125.626i	1.47592	+	0.179209i	0.657337	+	0.753597i	$0.271683\pi$
$702$	170.673	−	151.106i	0.243123	−	0.215251i
$703$	148.292	+	1221.30i	0.210942	+	1.73726i
$704$	−116.991	−	149.328i	−0.166181	−	0.212114i
$705$	−453.069	−	656.383i	−0.642651	−	0.931040i
$706$	316.324	−	357.056i	0.448051	−	0.505745i
$707$	1629.51	+	1276.64i	2.30482	+	1.80571i
$708$	−480.038	−	612.723i	−0.678020	−	0.865428i
$709$	910.019	+	283.573i	1.28352	+	0.399962i	0.862025	−	0.506866i	$-0.169196\pi$
$709$	910.019	+	283.573i	1.28352	+	0.399962i	0.421500	+	0.906829i	$0.361504\pi$
$710$	−7.91707	−	130.885i	−0.0111508	−	0.184345i
$711$	−189.680	+	274.798i	−0.266779	+	0.386496i
$712$	−162.910	−	660.954i	−0.228807	−	0.928306i
$713$	−291.049	+	371.496i	−0.408203	+	0.521033i
$714$	−380.093	+	262.360i	−0.532344	+	0.367450i
$715$	418.851	−	534.274i	0.585805	−	0.747237i
$716$	77.2897	−	111.973i	0.107946	−	0.156387i
$717$	−894.069	+	278.603i	−1.24696	+	0.388568i
$718$	−100.119	−	263.992i	−0.139442	−	0.367677i
$719$	821.772	+	99.7812i	1.14294	+	0.138778i	0.670030	−	0.742334i	$-0.266281\pi$
$719$	821.772	+	99.7812i	1.14294	+	0.138778i	0.472908	+	0.881112i	$0.343204\pi$
$720$	77.4439	+	14.1921i	0.107561	+	0.0197113i
$721$	−711.208	+	429.940i	−0.986419	+	0.596311i
$722$	−2.60309	+	14.2046i	−0.00360539	+	0.0196740i
$723$	−494.532	+	1098.81i	−0.684001	+	1.51979i
$724$	−180.985	−	477.217i	−0.249979	−	0.659140i
$725$	22.3119	+	42.5117i	0.0307750	+	0.0586368i
$726$	−213.739	−	66.6037i	−0.294406	−	0.0917406i
$727$	−50.1250	+	203.365i	−0.0689478	+	0.279732i	−0.995289	−	0.0969536i	$-0.969090\pi$
$727$	−50.1250	+	203.365i	−0.0689478	+	0.279732i	0.926341	+	0.376686i	$0.122936\pi$
$728$	−323.112	+	1035.75i	−0.443836	+	1.42273i
$729$	−137.586	+	33.9119i	−0.188732	+	0.0465183i
$730$	25.7845	−	426.269i	0.0353212	−	0.583929i
$731$	54.8325	+	451.587i	0.0750103	+	0.617766i
$732$	350.779	+	668.354i	0.479206	+	0.913051i
$733$	377.808	−	117.730i	0.515427	−	0.160614i	−0.0287456	−	0.999587i	$-0.509151\pi$
$733$	377.808	−	117.730i	0.515427	−	0.160614i	0.544173	+	0.838973i	$0.316844\pi$
$734$	59.0265	+	131.151i	0.0804175	+	0.178680i
$735$	1283.36	+	77.6290i	1.74607	+	0.105618i
$736$	−326.196	+	255.558i	−0.443201	+	0.347226i
$737$	−1013.84	−	249.890i	−1.37563	−	0.339063i
$738$	−102.340	−	115.518i	−0.138673	−	0.156529i
$739$	74.6391	+	1233.93i	0.101000	+	1.66973i	0.597632	+	0.801771i	$0.296109\pi$
$739$	74.6391	+	1233.93i	0.101000	+	1.66973i	−0.496631	+	0.867962i	$0.665430\pi$
$740$	−340.631	−	649.018i	−0.460312	−	0.877051i
$741$	−810.695	−	425.813i	−1.09405	−	0.574647i
$742$	−128.508	−	67.4462i	−0.173191	−	0.0908979i
$743$	−438.912	−	197.538i	−0.590729	−	0.265866i	0.0929235	−	0.995673i	$-0.470379\pi$
$743$	−438.912	−	197.538i	−0.590729	−	0.265866i	−0.683652	+	0.729808i	$0.739610\pi$
$744$	116.184	−	956.862i	0.156161	−	1.28610i
$745$	227.132	−	432.764i	0.304876	−	0.580892i
$746$	−488.578	+	488.578i	−0.654930	+	0.654930i
$747$	286.394	−	89.2440i	0.383392	−	0.119470i
$748$	25.8118	+	426.719i	0.0345077	+	0.570480i
$749$	−272.192	+	49.8810i	−0.363407	+	0.0665968i
$750$	−372.209	+	329.748i	−0.496278	+	0.439664i
$751$	86.2063	+	59.5039i	0.114789	+	0.0792329i	0.624076	−	0.781364i	$-0.285476\pi$
$751$	86.2063	+	59.5039i	0.114789	+	0.0792329i	−0.509287	+	0.860597i	$0.670091\pi$
$752$	249.066	−	112.096i	0.331205	−	0.149063i
$753$	658.972	+	249.915i	0.875128	+	0.331892i
$754$	−22.3107	+	58.7724i	−0.0295898	+	0.0779475i
$755$	−253.703	−	668.960i	−0.336030	−	0.886039i
$756$	434.118	−	434.118i	0.574230	−	0.574230i
$757$	−321.819	+	848.566i	−0.425124	+	1.12096i	0.535848	+	0.844314i	$0.319992\pi$
$757$	−321.819	+	848.566i	−0.425124	+	1.12096i	−0.960972	+	0.276645i	$0.910777\pi$
$758$	−8.84287	+	1.07372i	−0.0116660	+	0.00141651i
$759$	−183.027	+	587.355i	−0.241143	+	0.773854i
$760$	−95.2221	−	519.610i	−0.125292	−	0.683698i
$761$	−299.664	+	54.9155i	−0.393777	+	0.0721623i	−0.373495	−	0.927632i	$-0.621841\pi$
$761$	−299.664	+	54.9155i	−0.393777	+	0.0721623i	−0.0202815	+	0.999794i	$0.506456\pi$
$762$	123.331	+	38.4314i	0.161852	+	0.0504350i
$763$	137.189	+	1129.85i	0.179802	+	1.48080i
$764$	−762.917	−	289.336i	−0.998583	−	0.378713i
$765$	122.745	+	122.745i	0.160452	+	0.160452i
$766$	−88.1345	+	33.4250i	−0.115058	+	0.0436358i
$767$	−618.657	−	698.765i	−0.806593	−	0.911037i
$768$	226.001	−	595.915i	0.294272	−	0.775931i
$769$	−131.182	−	291.475i	−0.170588	−	0.379031i	0.806695	−	0.590967i	$-0.201254\pi$
$769$	−131.182	−	291.475i	−0.170588	−	0.379031i	−0.977283	+	0.211936i	$0.932023\pi$
$770$	−354.611	+	513.743i	−0.460534	+	0.667199i
$771$	−660.343	−	745.374i	−0.856477	−	0.966762i
$772$	9.61849	+	52.4864i	0.0124592	+	0.0679876i
$773$	939.877	−	56.8521i	1.21588	−	0.0735473i	0.560053	−	0.828457i	$-0.310781\pi$
$773$	939.877	−	56.8521i	1.21588	−	0.0735473i	0.655829	+	0.754909i	$0.272319\pi$
$774$	−54.2352	−	174.047i	−0.0700713	−	0.224867i
$775$	−266.558	−	266.558i	−0.343946	−	0.343946i
$776$	215.477	+	113.091i	0.277677	+	0.145736i
$777$	2715.56	+	329.729i	3.49494	+	0.424362i
$778$	306.883	−	681.867i	0.394452	−	0.876436i
$779$	326.286	−	621.686i	0.418852	−	0.798057i
$780$	541.575	+	65.9332i	0.694326	+	0.0845298i
$781$	401.083	−	210.505i	0.513551	−	0.269532i
$782$	−134.217	+	8.11865i	−0.171633	+	0.0103819i
$783$	62.3425	−	55.2306i	0.0796201	−	0.0705372i
$784$	−105.369	+	427.500i	−0.134400	+	0.545281i
$785$	−16.5458	−	21.1191i	−0.0210774	−	0.0269033i
$786$	−24.9838	+	413.032i	−0.0317861	+	0.525486i
$787$	277.632	−	124.952i	0.352773	−	0.158770i	−0.226276	−	0.974063i	$-0.572655\pi$
$787$	277.632	−	124.952i	0.352773	−	0.158770i	0.579048	+	0.815293i	$0.303424\pi$
$788$	152.654	+	489.882i	0.193723	+	0.621678i
$789$	847.059	−	444.571i	1.07359	−	0.563461i
$790$	−306.737	+	37.2447i	−0.388275	+	0.0471451i
$791$	−1281.34	−	77.5067i	−1.61990	−	0.0979858i
$792$	−95.9965	−	389.473i	−0.121208	−	0.491759i
$793$	467.960	+	774.655i	0.590114	+	0.976866i
$794$	552.598	+	136.203i	0.695968	+	0.171541i
$795$	−50.8353	+	163.136i	−0.0639437	+	0.205203i
$796$	46.5827	−	24.4485i	0.0585210	−	0.0307142i
$797$	595.479	−	225.835i	0.747151	−	0.283357i	0.0485032	−	0.998823i	$-0.484555\pi$
$797$	595.479	−	225.835i	0.747151	−	0.283357i	0.698647	+	0.715466i	$0.253786\pi$
$798$	767.835	+	345.575i	0.962200	+	0.433051i
$799$	592.319	+	108.546i	0.741325	+	0.135853i
$800$	−171.240	−	283.266i	−0.214050	−	0.354083i
$801$	73.5119	−	401.141i	0.0917751	−	0.500801i
$802$	−28.4559	+	234.356i	−0.0354812	+	0.292214i
$803$	1379.37	−	523.126i	1.71777	−	0.651464i
$804$	−249.646	−	801.144i	−0.310506	−	0.996447i
$805$	473.295	+	326.692i	0.587944	+	0.405829i
$806$	29.9588	−	492.687i	0.0371697	−	0.611274i
$807$	859.632	+	1245.39i	1.06522	+	1.54324i
$808$	−968.965	−	759.135i	−1.19921	−	0.939524i
$809$	−1231.01	+	303.417i	−1.52164	+	0.375051i	−0.909503	−	0.415697i	$-0.863538\pi$
$809$	−1231.01	+	303.417i	−1.52164	+	0.375051i	−0.612141	+	0.790749i	$0.709691\pi$
$810$	325.184	+	224.458i	0.401462	+	0.277109i
$811$	−1511.30	+	91.4170i	−1.86351	+	0.112721i	−0.953410	−	0.301677i	$-0.902454\pi$
$811$	−1511.30	+	91.4170i	−1.86351	+	0.112721i	−0.910096	+	0.414398i	$0.863992\pi$
$812$	−50.3705	+	161.645i	−0.0620327	+	0.199070i
$813$	−113.113	+	88.6184i	−0.139130	+	0.109002i
$814$	−533.141	+	680.504i	−0.654964	+	0.836000i
$815$	−781.895	−	692.698i	−0.959380	−	0.849936i
$816$	−153.251	+	105.781i	−0.187807	+	0.129634i
$817$	652.856	−	511.480i	0.799089	−	0.626046i
$818$	272.792	−	33.1229i	0.333487	−	0.0404926i
$819$	−431.183	+	486.395i	−0.526475	+	0.593889i
$820$	−50.4213	+	415.257i	−0.0614894	+	0.506411i
$821$	−860.780	+	520.360i	−1.04845	+	0.633812i	−0.933139	−	0.359517i	$-0.882941\pi$
$821$	−860.780	+	520.360i	−1.04845	+	0.633812i	−0.115315	+	0.993329i	$0.536788\pi$
$822$	437.213			0.531889
$823$		−	275.323i		−	0.334536i	−0.985911	−	0.167268i	$-0.946506\pi$
$823$		−	275.323i		−	0.334536i	0.985911	−	0.167268i	$-0.0534945\pi$
$824$	422.910	−	255.658i	0.513240	−	0.310264i
$825$	−448.126	−	201.685i	−0.543183	−	0.244467i
$826$	606.813	+	606.813i	0.734641	+	0.734641i
$827$	577.461	−	259.894i	0.698260	−	0.314261i	−0.0300118	−	0.999550i	$-0.509554\pi$
$827$	577.461	−	259.894i	0.698260	−	0.314261i	0.728272	+	0.685288i	$0.240324\pi$
$828$	−153.245	+	37.7714i	−0.185078	+	0.0456176i
$829$	−435.092	+	491.117i	−0.524839	+	0.592421i	−0.949826	−	0.312778i	$-0.898740\pi$
$829$	−435.092	+	491.117i	−0.524839	+	0.592421i	0.424987	+	0.905200i	$0.360279\pi$
$830$	237.559	+	143.610i	0.286216	+	0.173024i
$831$	−69.3314	+	78.2590i	−0.0834313	+	0.0941745i
$832$	54.4351	−	174.494i	0.0654268	−	0.209728i
$833$	−726.611	+	643.721i	−0.872282	+	0.772775i
$834$	32.6820	+	178.340i	0.0391870	+	0.213837i
$835$	−887.420	−	218.729i	−1.06278	−	0.261951i
$836$	641.429	−	442.747i	0.767260	−	0.529601i
$837$	−338.319	+	559.648i	−0.404204	+	0.668636i
$838$	−235.872	+	390.180i	−0.281470	+	0.465609i
$839$	356.760	−	455.370i	0.425220	−	0.542754i	−0.526316	−	0.850289i	$-0.676427\pi$
$839$	356.760	−	455.370i	0.425220	−	0.542754i	0.951537	+	0.307535i	$0.0995042\pi$
$840$	−1172.46	−	70.9205i	−1.39578	−	0.0844292i
$841$	290.078	−	764.872i	0.344920	−	0.909479i
$842$	154.013	−	293.447i	0.182913	−	0.348512i
$843$	29.9329	−	163.339i	0.0355076	−	0.193759i
$844$			176.135i			0.208690i
$845$	652.930	+	39.9103i	0.772698	+	0.0472311i
$846$	−241.323			−0.285252
$847$	−711.108	−	130.315i	−0.839561	−	0.153855i
$848$	−51.8134	−	27.1938i	−0.0611007	−	0.0320681i
$849$	−821.067	−	311.390i	−0.967099	−	0.366772i
$850$	6.48504	−	107.210i	0.00762946	−	0.126130i
$851$	626.926	+	491.165i	0.736694	+	0.577163i
$852$	311.521	+	188.321i	0.365635	+	0.221034i
$853$	−691.289	−	417.899i	−0.810421	−	0.489917i	0.0504582	−	0.998726i	$-0.483932\pi$
$853$	−691.289	−	417.899i	−0.810421	−	0.489917i	−0.860879	+	0.508810i	$0.830086\pi$
$854$	−472.736	−	684.876i	−0.553555	−	0.801963i
$855$	75.7380	−	307.281i	0.0885824	−	0.359393i
$856$	161.855	−	29.6610i	0.189083	−	0.0346507i
$857$	411.972	+	465.020i	0.480714	+	0.542614i	0.937968	−	0.346723i	$-0.112705\pi$
$857$	411.972	+	465.020i	0.480714	+	0.542614i	−0.457254	+	0.889336i	$0.651167\pi$
$858$	−191.235	−	614.381i	−0.222885	−	0.716061i
$859$	−416.313	−	368.821i	−0.484648	−	0.429361i	0.385086	−	0.922881i	$-0.374172\pi$
$859$	−416.313	−	368.821i	−0.484648	−	0.429361i	−0.869735	+	0.493519i	$0.835710\pi$
$860$	−255.627	+	422.858i	−0.297240	+	0.491695i
$861$	−1168.53	−	1035.23i	−1.35718	−	1.20236i
$862$	−122.597	−	497.395i	−0.142224	−	0.577024i
$863$	−225.191	−	500.355i	−0.260940	−	0.579785i	0.734124	−	0.679015i	$-0.237593\pi$
$863$	−225.191	−	500.355i	−0.260940	−	0.579785i	−0.995065	+	0.0992297i	$0.968362\pi$
$864$	−406.033	+	406.033i	−0.469946	+	0.469946i
$865$	−230.233	+	511.558i	−0.266166	+	0.591396i
$866$	187.217	+	309.694i	0.216185	+	0.357614i
$867$	640.246			0.738461
$868$		−	1329.39i		−	1.53155i
$869$	−552.210	−	913.467i	−0.635454	−	1.05117i
$870$	−67.5612	−	8.20342i	−0.0776566	−	0.00942921i
$871$	−356.483	−	940.867i	−0.409280	−	1.08022i
$872$	−81.5775	−	671.851i	−0.0935522	−	0.770472i
$873$	89.9113	+	114.763i	0.102991	+	0.131458i
$874$	139.258	+	201.751i	0.159334	+	0.230836i
$875$	−1064.84	+	1201.95i	−1.21696	+	1.37366i
$876$	933.242	+	731.148i	1.06534	+	0.834644i
$877$	797.101	+	1017.42i	0.908895	+	1.16012i	0.986602	+	0.163143i	$0.0521632\pi$
$877$	797.101	+	1017.42i	0.908895	+	1.16012i	−0.0777072	+	0.996976i	$0.524760\pi$
$878$	−322.088	−	100.367i	−0.366843	−	0.114313i
$879$	110.636	+	1829.03i	0.125866	+	2.08081i
$880$	−142.976	+	207.137i	−0.162473	+	0.235383i
$881$	−363.893	−	1476.37i	−0.413045	−	1.67579i	−0.697094	−	0.716980i	$-0.745524\pi$
$881$	−363.893	−	1476.37i	−0.413045	−	1.67579i	0.284049	−	0.958810i	$-0.408322\pi$
$882$	239.918	−	306.232i	0.272015	−	0.347202i
$883$	−1188.04	+	820.042i	−1.34545	+	0.928700i	−0.999953	−	0.00971835i	$-0.996907\pi$
$883$	−1188.04	+	820.042i	−1.34545	+	0.928700i	−0.345501	+	0.938418i	$0.612291\pi$
$884$	−324.339	+	253.938i	−0.366899	+	0.287260i
$885$	573.956	−	831.518i	0.648537	−	0.939569i
$886$	−134.010	+	41.7592i	−0.151253	+	0.0471322i
$887$	−309.668	−	816.527i	−0.349118	−	0.920549i	−0.988440	−	0.151610i	$-0.951554\pi$
$887$	−309.668	−	816.527i	−0.349118	−	0.920549i	0.639322	−	0.768939i	$-0.279215\pi$
$888$	−1614.77	−	196.069i	−1.81844	−	0.220798i
$889$	410.321	+	75.1942i	0.461554	+	0.0845829i
$890$	322.964	−	195.239i	0.362881	−	0.219369i
$891$	−246.043	+	1342.61i	−0.276142	+	1.50686i
$892$	402.785	−	894.951i	0.451553	−	1.00331i
$893$	−389.310	−	1026.52i	−0.435957	−	1.14952i
$894$	−215.279	−	410.179i	−0.240804	−	0.458813i
$895$	168.613	+	52.5421i	0.188395	+	0.0587062i
$896$	334.499	−	1357.11i	0.373325	−	1.51464i
$897$	−566.009	+	176.179i	−0.631002	+	0.196409i
$898$	67.2530	−	16.5764i	0.0748920	−	0.0184592i
$899$	10.8892	−	180.020i	0.0121126	−	0.200245i
$900$	−15.1964	−	125.153i	−0.0168849	−	0.139059i
$901$	−59.9557	−	114.236i	−0.0665435	−	0.126788i
$902$	471.017	−	146.775i	0.522191	−	0.162721i
$903$	−756.835	−	1681.62i	−0.838134	−	1.86226i
$904$	761.930	+	46.0883i	0.842843	+	0.0509826i
$905$	521.513	−	408.579i	0.576257	−	0.451469i
$906$	−658.409	−	162.283i	−0.726721	−	0.179121i
$907$	829.764	+	936.610i	0.914845	+	1.03265i	0.999344	+	0.0362226i	$0.0115325\pi$
$907$	829.764	+	936.610i	0.914845	+	1.03265i	−0.0844991	+	0.996424i	$0.526929\pi$
$908$	71.6730	+	1184.90i	0.0789350	+	1.30495i
$909$	−342.703	−	652.967i	−0.377011	−	0.718335i
$910$	−601.499	−	0.190601i	−0.660988	−	0.000209451i
$911$	339.062	+	177.954i	0.372187	+	0.195339i	0.640437	−	0.768010i	$-0.278753\pi$
$911$	339.062	+	177.954i	0.372187	+	0.195339i	−0.268250	+	0.963349i	$0.586445\pi$
$912$	309.585	+	139.333i	0.339457	+	0.152777i
$913$	−115.588	+	951.955i	−0.126603	+	1.04267i
$914$	−211.942	+	403.822i	−0.231884	+	0.441818i
$915$	−692.814	+	692.814i	−0.757173	+	0.757173i
$916$	−785.574	+	244.795i	−0.857614	+	0.267243i
$917$	80.6790	+	1333.78i	0.0879815	+	1.45451i
$918$	−183.275	+	33.5863i	−0.199646	+	0.0365864i
$919$	519.329	−	460.085i	0.565102	−	0.500637i	−0.331511	−	0.943451i	$-0.607559\pi$
$919$	519.329	−	460.085i	0.565102	−	0.500637i	0.896613	+	0.442815i	$0.146020\pi$
$920$	−281.438	−	194.263i	−0.305911	−	0.211155i
$921$	−1873.32	+	843.114i	−2.03401	+	0.915434i
$922$	−300.123	−	113.822i	−0.325513	−	0.123451i
$923$	386.405	+	202.957i	0.418640	+	0.219888i
$924$	−614.528	−	1620.38i	−0.665073	−	1.75365i
$925$	−449.836	+	449.836i	−0.486310	+	0.486310i
$926$	102.820	−	271.113i	0.111036	−	0.292779i
$927$	293.900	−	35.6859i	0.317044	−	0.0384961i
$928$	47.1119	−	151.187i	0.0507672	−	0.162918i
$929$	172.250	+	939.940i	0.185415	+	1.01178i	0.936263	+	0.351301i	$0.114261\pi$
$929$	172.250	+	939.940i	0.185415	+	1.01178i	−0.750848	+	0.660475i	$0.770355\pi$
$930$	525.616	−	96.3228i	0.565179	−	0.103573i
$931$	1689.67	+	526.523i	1.81490	+	0.565546i
$932$	79.7977	+	657.194i	0.0856199	+	0.705143i
$933$	104.600	+	39.6694i	0.112111	+	0.0425181i
$934$	284.986	+	284.986i	0.305124	+	0.305124i
$935$	−518.856	+	196.776i	−0.554926	+	0.210456i
$936$	256.397	−	289.228i	0.273929	−	0.309004i
$937$	38.1388	−	100.564i	0.0407030	−	0.107325i	−0.913124	−	0.407683i	$-0.866337\pi$
$937$	38.1388	−	100.564i	0.0407030	−	0.107325i	0.953827	+	0.300358i	$0.0971061\pi$
$938$	379.696	+	843.651i	0.404794	+	0.899414i
$939$	−30.0272	+	43.5020i	−0.0319779	+	0.0463280i
$940$	433.745	+	489.597i	0.461431	+	0.520848i
$941$	−279.109	−	1523.05i	−0.296609	−	1.61854i	−0.707400	−	0.706813i	$-0.750132\pi$
$941$	−279.109	−	1523.05i	−0.296609	−	1.61854i	0.410791	−	0.911729i	$-0.365252\pi$
$942$	−25.3822	+	1.53534i	−0.0269450	+	0.00162987i
$943$	−135.219	−	433.933i	−0.143392	−	0.460162i
$944$	244.662	+	244.662i	0.259176	+	0.259176i
$945$	705.637	+	370.347i	0.746706	+	0.391901i
$946$	578.520	+	70.2451i	0.611544	+	0.0742549i
$947$	86.8245	−	192.916i	0.0916838	−	0.203713i	−0.860352	−	0.509701i	$-0.829756\pi$
$947$	86.8245	−	192.916i	0.0916838	−	0.203713i	0.952035	+	0.305988i	$0.0989868\pi$
$948$	398.640	−	759.545i	0.420507	−	0.801208i
$949$	1169.60	+	807.865i	1.23246	+	0.851280i
$950$	−173.388	+	91.0011i	−0.182514	+	0.0957906i
$951$	1732.36	−	104.789i	1.82162	−	0.110188i
$952$	663.819	−	588.093i	0.697289	−	0.617744i
$953$	266.774	−	1082.35i	0.279931	−	1.13572i	−0.647601	−	0.761980i	$-0.724228\pi$
$953$	266.774	−	1082.35i	0.279931	−	1.13572i	0.927532	−	0.373744i	$-0.121926\pi$
$954$	31.8855	+	40.6989i	0.0334230	+	0.0426613i
$955$	63.9489	−	1057.20i	0.0669621	−	1.10702i
$956$	700.352	−	315.203i	0.732586	−	0.329710i
$957$	−69.9443	−	224.459i	−0.0730870	−	0.234544i
$958$	720.676	−	378.240i	0.752272	−	0.394823i
$959$	1401.58	−	170.182i	1.46150	−	0.177458i
$960$	197.525	+	11.9481i	0.205755	+	0.0124459i
$961$	108.902	+	441.834i	0.113322	+	0.459765i
$962$	−831.444	−	50.5575i	−0.864287	−	0.0525546i
$963$	95.7159	+	23.5919i	0.0993935	+	0.0244983i
$964$	293.995	−	943.463i	0.304974	−	0.978696i
$965$	−61.3308	+	32.1889i	−0.0635552	+	0.0333564i
$966$	509.661	−	193.289i	0.527600	−	0.200092i
$967$	−684.959	−	308.275i	−0.708335	−	0.318795i	0.0240272	−	0.999711i	$-0.492351\pi$
$967$	−684.959	−	308.275i	−0.708335	−	0.318795i	−0.732362	+	0.680916i	$0.761582\pi$
$968$	422.850	+	77.4902i	0.436829	+	0.0800519i
$969$	387.229	+	640.555i	0.399617	+	0.661048i
$970$	−24.3185	+	132.702i	−0.0250706	+	0.136806i
$971$	−41.6534	+	343.046i	−0.0428974	+	0.353292i	0.955417	+	0.295259i	$0.0954059\pi$
$971$	−41.6534	+	343.046i	−0.0428974	+	0.353292i	−0.998315	+	0.0580329i	$0.981517\pi$
$972$	−589.565	+	223.592i	−0.606548	+	0.230033i
$973$	174.186	+	558.983i	0.179020	+	0.574495i
$974$	−95.8314	−	66.1477i	−0.0983896	−	0.0679134i
$975$	−85.2058	−	465.785i	−0.0873905	−	0.477728i
$976$	−190.603	−	276.137i	−0.195290	−	0.282927i
$977$	1009.88	+	791.192i	1.03366	+	0.809818i	0.982006	−	0.188847i	$-0.0604751\pi$
$977$	1009.88	+	791.192i	1.03366	+	0.809818i	0.0516500	+	0.998665i	$0.483552\pi$
$978$	−961.314	+	236.943i	−0.982939	+	0.242273i
$979$	1072.92	+	740.585i	1.09594	+	0.756471i
$980$	−1052.50	+	63.6647i	−1.07398	+	0.0649640i
$981$	120.624	−	387.097i	0.122961	−	0.394594i
$982$	−259.880	+	203.603i	−0.264643	+	0.207335i
$983$	1003.51	−	1280.88i	1.02086	−	1.30304i	0.0686365	−	0.997642i	$-0.478135\pi$
$983$	1003.51	−	1280.88i	1.02086	−	1.30304i	0.952226	−	0.305393i	$-0.0987879\pi$
$984$	694.853	+	615.586i	0.706151	+	0.625595i
$985$	−548.149	+	378.360i	−0.556497	+	0.384122i
$986$	40.4496	−	31.6902i	0.0410239	−	0.0321402i
$987$	−2423.32	+	294.245i	−2.45524	+	0.298120i
$988$	702.109	+	266.529i	0.710636	+	0.269766i
$989$	64.7146	−	532.972i	0.0654343	−	0.538900i
$990$	190.310	−	115.046i	0.192232	−	0.116208i
$991$	−368.799			−0.372148			−0.186074	−	0.982536i	$-0.559576\pi$
$991$	−368.799			−0.372148			−0.186074	+	0.982536i	$0.559576\pi$
$992$			1243.38i			1.25341i
$993$	−869.038	+	525.352i	−0.875164	+	0.529055i
$994$	−365.976	−	164.713i	−0.368185	−	0.165707i
$995$	48.2875	+	48.2875i	0.0485301	+	0.0485301i
$996$	−702.746	+	316.280i	−0.705568	+	0.317550i
$997$	−297.585	+	73.3481i	−0.298480	+	0.0735688i	−0.385712	−	0.922619i	$-0.626044\pi$
$997$	−297.585	+	73.3481i	−0.298480	+	0.0735688i	0.0872316	+	0.996188i	$0.472198\pi$
$998$	8.69819	−	9.81822i	0.00871562	−	0.00983790i
$999$	944.446	+	570.937i	0.945391	+	0.571509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.3.j.a.5.12	✓	720
169.34	odd	52	inner	169.3.j.a.34.12	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.3.j.a.5.12	✓	720	1.1	even	1	trivial
169.3.j.a.34.12	yes	720	169.34	odd	52	inner

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	169.j (of order \(52\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.992467 - 0.181876i) q^{2} +(3.21951 + 1.68973i) q^{3} +(-2.78815 - 1.05741i) q^{4} +(0.233707 - 3.86364i) q^{5} +(-2.88794 - 2.26255i) q^{6} +(-10.1385 - 6.12897i) q^{7} +(6.02875 + 3.64450i) q^{8} +(2.39748 + 3.47334i) q^{9} +(-0.934651 + 3.79203i) q^{10} +(-13.2706 + 2.43193i) q^{11} +(-7.18976 - 8.11556i) q^{12} +(-9.18947 - 9.19530i) q^{13} +(8.94746 + 7.92676i) q^{14} +(7.28092 - 12.0441i) q^{15} +(3.60754 + 3.19601i) q^{16} +(2.54300 + 10.3173i) q^{17} +(-1.74770 - 3.88322i) q^{18} +(13.6988 - 13.6988i) q^{19} +(-4.73705 + 10.5253i) q^{20} +(-22.2849 - 36.8637i) q^{21} +13.6129 q^{22} -12.5412i q^{23} +(13.2514 + 21.9205i) q^{24} +(9.94464 + 1.20750i) q^{25} +(7.44784 + 10.7974i) q^{26} +(-2.09474 - 17.2518i) q^{27} +(21.7870 + 27.8091i) q^{28} +(2.72253 + 3.94426i) q^{29} +(-9.41662 + 10.6292i) q^{30} +(-29.6221 - 23.2075i) q^{31} +(-20.3776 - 26.0100i) q^{32} +(-46.8341 - 14.5941i) q^{33} +(-0.647360 - 10.7021i) q^{34} +(-26.0496 + 37.7393i) q^{35} +(-3.01179 - 12.2193i) q^{36} +(-39.1642 + 49.9895i) q^{37} +(-16.0871 + 11.1041i) q^{38} +(-14.0480 - 45.1321i) q^{39} +(15.4900 - 22.4412i) q^{40} +(34.6006 - 10.7820i) q^{41} +(15.4124 + 40.6391i) q^{42} +(42.4978 + 5.16017i) q^{43} +(39.5720 + 7.25184i) q^{44} +(13.9801 - 8.45124i) q^{45} +(-2.28094 + 12.4467i) q^{46} +(23.2581 - 51.6774i) q^{47} +(6.21414 + 16.3853i) q^{48} +(42.4545 + 80.8903i) q^{49} +(-9.65011 - 3.00710i) q^{50} +(-9.24631 + 37.5137i) q^{51} +(15.8985 + 35.3549i) q^{52} +(-11.7884 + 2.90558i) q^{53} +(-1.05872 + 17.5028i) q^{54} +(6.29466 + 51.8412i) q^{55} +(-38.7857 - 73.9000i) q^{56} +(67.2505 - 20.9561i) q^{57} +(-1.98465 - 4.40971i) q^{58} +(71.6597 + 4.33461i) q^{59} +(-33.0359 + 25.8820i) q^{60} +(-67.5946 - 16.6606i) q^{61} +(25.1781 + 28.4202i) q^{62} +(-3.01892 - 49.9087i) q^{63} +(6.53427 + 12.4500i) q^{64} +(-37.6750 + 33.3558i) q^{65} +(43.8270 + 23.0022i) q^{66} +(70.5766 + 31.7640i) q^{67} +(3.81937 - 31.4553i) q^{68} +(21.1912 - 40.3764i) q^{69} +(32.7172 - 32.7172i) q^{70} +(-32.0539 + 9.98839i) q^{71} +(1.79516 + 29.6775i) q^{72} +(-107.554 + 19.7099i) q^{73} +(47.9611 - 42.4898i) q^{74} +(29.9765 + 20.6913i) q^{75} +(-52.6794 + 23.7091i) q^{76} +(149.450 + 56.6789i) q^{77} +(5.73376 + 47.3471i) q^{78} +(28.0551 + 73.9751i) q^{79} +(13.1913 - 13.1913i) q^{80} +(35.8760 - 94.5973i) q^{81} +(-36.3010 + 4.40774i) q^{82} +(21.1457 - 67.8590i) q^{83} +(23.1537 + 126.346i) q^{84} +(40.4568 - 7.41398i) q^{85} +(-41.2392 - 12.8506i) q^{86} +(2.10047 + 17.2989i) q^{87} +(-88.8683 - 33.7033i) q^{88} +(-68.3280 - 68.3280i) q^{89} +(-15.4118 + 5.84493i) q^{90} +(36.8103 + 149.549i) q^{91} +(-13.2611 + 34.9667i) q^{92} +(-56.1544 - 124.770i) q^{93} +(-32.4818 + 47.0581i) q^{94} +(-49.7256 - 56.1286i) q^{95} +(-21.6558 - 118.172i) q^{96} +(34.4808 - 2.08570i) q^{97} +(-27.4227 - 88.0024i) q^{98} +(-40.2629 - 40.2629i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 22 q^{2} - 22 q^{3} - 26 q^{4} - 34 q^{5} - 10 q^{6} - 14 q^{7} - 62 q^{8} - 202 q^{9} - 26 q^{10} - 22 q^{11} - 26 q^{12} - 34 q^{13} - 38 q^{14} + 2 q^{15} + 242 q^{16} - 26 q^{17} - 58 q^{18}+ \cdots - 178 q^{99}+O(q^{100}) \) 720 * q - 22 * q^2 - 22 * q^3 - 26 * q^4 - 34 * q^5 - 10 * q^6 - 14 * q^7 - 62 * q^8 - 202 * q^9 - 26 * q^10 - 22 * q^11 - 26 * q^12 - 34 * q^13 - 38 * q^14 + 2 * q^15 + 242 * q^16 - 26 * q^17 - 58 * q^18 - 26 * q^19 - 42 * q^20 - 58 * q^21 - 108 * q^22 + 262 * q^24 - 26 * q^25 + 62 * q^26 + 2 * q^27 - 30 * q^28 - 54 * q^29 - 858 * q^30 - 66 * q^31 - 696 * q^32 + 50 * q^33 + 82 * q^34 - 2 * q^35 - 26 * q^36 - 66 * q^37 + 884 * q^38 + 922 * q^39 - 522 * q^40 - 58 * q^41 - 106 * q^42 - 26 * q^43 + 42 * q^44 - 212 * q^45 - 54 * q^46 + 368 * q^47 + 94 * q^48 - 26 * q^49 + 102 * q^50 - 26 * q^51 - 1276 * q^52 + 620 * q^53 - 178 * q^54 - 834 * q^55 - 26 * q^56 + 14 * q^57 + 114 * q^58 - 82 * q^59 + 1338 * q^60 + 254 * q^61 + 1404 * q^62 - 1392 * q^63 - 26 * q^64 - 82 * q^65 - 304 * q^66 - 358 * q^67 - 434 * q^68 + 208 * q^69 + 838 * q^70 - 310 * q^71 + 22 * q^72 - 26 * q^73 - 1308 * q^74 + 1664 * q^75 - 106 * q^76 - 26 * q^77 - 574 * q^78 - 78 * q^79 + 62 * q^80 - 262 * q^81 + 1274 * q^82 + 26 * q^83 + 158 * q^84 + 1522 * q^85 - 1562 * q^86 - 122 * q^87 - 442 * q^88 - 616 * q^89 - 26 * q^90 - 182 * q^91 + 646 * q^92 + 544 * q^93 - 2394 * q^94 - 26 * q^95 - 4064 * q^96 + 1914 * q^97 - 250 * q^98 - 178 * q^99

Introduction

L-functions

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