LMFDB - Embedded newform 343.3.l.a.10.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [343,3,Mod(3,343)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(343, base_ring=CyclotomicField(294))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("343.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 343 = 7^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	343.l (of order $294$, degree $84$, 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:	$9.34607306756$
Analytic rank:	$0$
Dimension:	$5376$
Relative dimension:	$64$ over $\Q(\zeta_{294})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{294}]$

Embedding invariants

Embedding label			10.23
Character	$\chi$	$=$	343.10
Dual form			343.3.l.a.103.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21275 - 0.616298i) q^{2} +(-3.55216 + 3.36726i) q^{3} +(-1.26710 - 1.73620i) q^{4} +(6.29980 - 0.0673203i) q^{5} +(6.38313 - 1.89448i) q^{6} +(-4.48629 - 5.37338i) q^{7} +(1.33512 + 8.25821i) q^{8} +(0.798710 - 14.9349i) q^{9} +(-7.68160 - 3.80091i) q^{10} +(-9.13348 + 8.11840i) q^{11} +(10.3472 + 1.90059i) q^{12} +(20.4627 + 12.4046i) q^{13} +(2.12917 + 9.28148i) q^{14} +(-22.1512 + 21.4522i) q^{15} +(0.848507 - 2.64992i) q^{16} +(-1.27051 + 0.150031i) q^{17} +(-10.1730 + 17.6202i) q^{18} +(-5.06767 + 2.92582i) q^{19} +(-8.09936 - 10.8524i) q^{20} +(34.0296 + 3.98054i) q^{21} +(16.0800 - 4.21668i) q^{22} +(-10.3909 - 30.2124i) q^{23} +(-32.5501 - 24.8387i) q^{24} +(14.6886 - 0.313964i) q^{25} +(-17.1713 - 27.6549i) q^{26} +(18.8978 + 22.1985i) q^{27} +(-3.64467 + 14.5977i) q^{28} +(-34.2562 + 6.67139i) q^{29} +(40.0849 - 12.3646i) q^{30} +(16.6324 - 6.52773i) q^{31} +(20.8721 - 21.0963i) q^{32} +(5.10675 - 59.5927i) q^{33} +(1.63328 + 0.601062i) q^{34} +(-28.6245 - 33.5492i) q^{35} +(-26.9421 + 17.5373i) q^{36} +(-65.4989 - 28.1613i) q^{37} +(7.94902 - 0.425108i) q^{38} +(-114.456 + 24.8402i) q^{39} +(8.96696 + 51.9352i) q^{40} +(9.85557 - 6.87482i) q^{41} +(-38.8163 - 25.7998i) q^{42} +(-0.842330 + 5.21011i) q^{43} +(25.6682 + 5.57072i) q^{44} +(4.02629 - 94.1408i) q^{45} +(-6.01819 + 43.0441i) q^{46} +(-82.0239 - 20.5750i) q^{47} +(5.90896 + 12.2701i) q^{48} +(-8.74636 + 48.2131i) q^{49} +(-18.0072 - 8.67182i) q^{50} +(4.00785 - 4.81107i) q^{51} +(-4.39143 - 51.2452i) q^{52} +(11.3347 - 41.4153i) q^{53} +(-9.23757 - 38.5680i) q^{54} +(-56.9926 + 51.7591i) q^{55} +(38.3847 - 44.2229i) q^{56} +(8.14914 - 27.4572i) q^{57} +(45.6559 + 13.0212i) q^{58} +(-35.0922 + 16.4399i) q^{59} +(65.3131 + 11.2767i) q^{60} +(-3.67501 - 85.9274i) q^{61} +(-24.1940 - 2.33397i) q^{62} +(-83.8343 + 62.7107i) q^{63} +(-48.8772 + 16.2283i) q^{64} +(129.746 + 76.7690i) q^{65} +(-42.9201 + 69.1240i) q^{66} +(77.7165 - 11.7139i) q^{67} +(1.87035 + 2.01575i) q^{68} +(138.643 + 72.3300i) q^{69} +(14.0382 + 58.3281i) q^{70} +(-72.8634 - 14.1901i) q^{71} +(124.402 - 13.3441i) q^{72} +(6.80809 - 1.70775i) q^{73} +(62.0783 + 74.5195i) q^{74} +(-51.1192 + 50.5758i) q^{75} +(11.5011 + 5.09118i) q^{76} +(84.5987 + 12.6561i) q^{77} +(154.116 + 40.4141i) q^{78} +(5.07560 + 67.7291i) q^{79} +(5.16703 - 16.7511i) q^{80} +(-8.03756 - 0.862152i) q^{81} +(-16.1893 + 2.26350i) q^{82} +(-108.143 + 10.4324i) q^{83} +(-36.2079 - 64.1259i) q^{84} +(-7.99385 + 1.03069i) q^{85} +(4.23252 - 5.79946i) q^{86} +(99.2189 - 139.047i) q^{87} +(-79.2378 - 64.5872i) q^{88} +(-96.0130 + 40.0707i) q^{89} +(-62.9017 + 111.688i) q^{90} +(-25.1470 - 165.604i) q^{91} +(-39.2884 + 56.3228i) q^{92} +(-37.1002 + 79.1931i) q^{93} +(86.7945 + 75.5036i) q^{94} +(-31.7283 + 18.7732i) q^{95} +(-3.10401 + 145.219i) q^{96} +(-98.4697 - 78.5269i) q^{97} +(40.3208 - 53.0803i) q^{98} +(113.953 + 142.892i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5376 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 112 q^{6} - 84 q^{7} - 84 q^{8} - 28 q^{9} - 84 q^{10} - 119 q^{11} - 119 q^{12} - 84 q^{13} + 21 q^{14} - 168 q^{15} - 84 q^{16} - 35 q^{17} - 42 q^{18}+ \cdots + 42 q^{99}+O(q^{100}) $ 5376 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 112 * q^6 - 84 * q^7 - 84 * q^8 - 28 * q^9 - 84 * q^10 - 119 * q^11 - 119 * q^12 - 84 * q^13 + 21 * q^14 - 168 * q^15 - 84 * q^16 - 35 * q^17 - 42 * q^18 - 126 * q^19 - 420 * q^20 - 84 * q^21 + 28 * q^22 - 147 * q^23 - 210 * q^24 - 84 * q^25 - 196 * q^26 + 21 * q^27 + 126 * q^28 - 336 * q^29 - 91 * q^30 - 77 * q^31 - 84 * q^33 - 616 * q^34 + 56 * q^35 + 420 * q^36 - 539 * q^37 - 532 * q^38 - 441 * q^39 - 364 * q^40 - 280 * q^41 - 700 * q^42 - 84 * q^43 - 112 * q^44 - 315 * q^45 - 252 * q^46 - 7 * q^47 - 98 * q^48 - 28 * q^49 + 56 * q^50 + 84 * q^51 + 84 * q^52 + 371 * q^53 + 798 * q^54 + 1267 * q^55 - 42 * q^56 - 735 * q^57 - 868 * q^58 + 1400 * q^59 + 406 * q^60 + 637 * q^61 + 336 * q^62 + 735 * q^63 - 420 * q^64 - 84 * q^65 + 1372 * q^66 - 91 * q^67 - 77 * q^68 + 84 * q^69 - 1078 * q^70 + 679 * q^71 + 273 * q^72 + 294 * q^73 - 1428 * q^74 - 1344 * q^75 - 231 * q^76 - 714 * q^77 + 5040 * q^78 - 91 * q^79 - 1148 * q^80 - 784 * q^81 - 224 * q^82 - 1414 * q^83 - 1246 * q^84 + 364 * q^85 - 1582 * q^86 - 952 * q^87 - 1974 * q^88 - 910 * q^89 - 287 * q^90 + 1456 * q^91 - 6384 * q^92 - 154 * q^93 - 770 * q^94 - 1358 * q^95 - 4284 * q^96 + 3430 * q^97 + 7 * q^98 + 42 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/343\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{223}{294}\right)$

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 $

$2$	−1.21275	−	0.616298i	−0.606377	−	0.308149i	0.122845	−	0.992426i	$-0.460798\pi$
$2$	−1.21275	−	0.616298i	−0.606377	−	0.308149i	−0.729222	+	0.684277i	$0.760118\pi$
$3$	−3.55216	+	3.36726i	−1.18405	+	1.12242i	−0.194105	+	0.980981i	$0.562180\pi$
$3$	−3.55216	+	3.36726i	−1.18405	+	1.12242i	−0.989947	+	0.141441i	$0.954827\pi$
$4$	−1.26710	−	1.73620i	−0.316775	−	0.434050i
$5$	6.29980	−	0.0673203i	1.25996	−	0.0134641i	0.621682	−	0.783270i	$-0.286450\pi$
$5$	6.29980	−	0.0673203i	1.25996	−	0.0134641i	0.638278	+	0.769806i	$0.279647\pi$
$6$	6.38313	−	1.89448i	1.06386	−	0.315747i
$7$	−4.48629	−	5.37338i	−0.640899	−	0.767625i
$7$	−4.48629	−	5.37338i	−0.640899	−	0.767625i
$8$	1.33512	+	8.25821i	0.166890	+	1.03228i
$9$	0.798710	−	14.9349i	0.0887456	−	1.65944i
$10$	−7.68160	−	3.80091i	−0.768160	−	0.380091i
$11$	−9.13348	+	8.11840i	−0.830317	+	0.738036i	−0.967598	−	0.252496i	$-0.918749\pi$
$11$	−9.13348	+	8.11840i	−0.830317	+	0.738036i	0.137281	+	0.990532i	$0.456164\pi$
$12$	10.3472	+	1.90059i	0.862265	+	0.158382i
$13$	20.4627	+	12.4046i	1.57405	+	0.954201i	0.989773	+	0.142649i	$0.0455619\pi$
$13$	20.4627	+	12.4046i	1.57405	+	0.954201i	0.584280	+	0.811552i	$0.301377\pi$
$14$	2.12917	+	9.28148i	0.152084	+	0.662963i
$15$	−22.1512	+	21.4522i	−1.47675	+	1.43015i
$16$	0.848507	−	2.64992i	0.0530317	−	0.165620i
$17$	−1.27051	+	0.150031i	−0.0747358	+	0.00882533i	−0.154557	−	0.987984i	$-0.549395\pi$
$17$	−1.27051	+	0.150031i	−0.0747358	+	0.00882533i	0.0798211	+	0.996809i	$0.474565\pi$
$18$	−10.1730	+	17.6202i	−0.565167	+	0.978898i
$19$	−5.06767	+	2.92582i	−0.266719	+	0.153991i	−0.627396	−	0.778700i	$-0.715879\pi$
$19$	−5.06767	+	2.92582i	−0.266719	+	0.153991i	0.360676	+	0.932691i	$0.382546\pi$
$20$	−8.09936	−	10.8524i	−0.404968	−	0.542620i
$21$	34.0296	+	3.98054i	1.62046	+	0.189549i
$22$	16.0800	−	4.21668i	0.730910	−	0.191667i
$23$	−10.3909	−	30.2124i	−0.451779	−	1.31358i	−0.906221	−	0.422805i	$-0.861046\pi$
$23$	−10.3909	−	30.2124i	−0.451779	−	1.31358i	0.454442	−	0.890776i	$-0.349839\pi$
$24$	−32.5501	−	24.8387i	−1.35626	−	1.03495i
$25$	14.6886	−	0.313964i	0.587546	−	0.0125586i
$26$	−17.1713	−	27.6549i	−0.660435	−	1.06365i
$27$	18.8978	+	22.1985i	0.699920	+	0.822166i
$28$	−3.64467	+	14.5977i	−0.130167	+	0.521347i
$29$	−34.2562	+	6.67139i	−1.18125	+	0.230048i	−0.743303	−	0.668955i	$-0.766742\pi$
$29$	−34.2562	+	6.67139i	−1.18125	+	0.230048i	−0.437944	+	0.899002i	$0.644293\pi$
$30$	40.0849	−	12.3646i	1.33616	−	0.412152i
$31$	16.6324	−	6.52773i	0.536528	−	0.210572i	−0.0815770	−	0.996667i	$-0.525996\pi$
$31$	16.6324	−	6.52773i	0.536528	−	0.210572i	0.618106	+	0.786095i	$0.287900\pi$
$32$	20.8721	−	21.0963i	0.652254	−	0.659261i
$33$	5.10675	−	59.5927i	0.154750	−	1.80584i
$34$	1.63328	+	0.601062i	0.0480376	+	0.0176783i
$35$	−28.6245	−	33.5492i	−0.817842	−	0.958548i
$36$	−26.9421	+	17.5373i	−0.748391	+	0.487148i
$37$	−65.4989	−	28.1613i	−1.77024	−	0.761115i	−0.990914	−	0.134497i	$-0.957058\pi$
$37$	−65.4989	−	28.1613i	−1.77024	−	0.761115i	−0.779326	−	0.626618i	$-0.784439\pi$
$38$	7.94902	−	0.425108i	0.209185	−	0.0111871i
$39$	−114.456	+	24.8402i	−2.93478	+	0.636929i
$40$	8.96696	+	51.9352i	0.224174	+	1.29838i
$41$	9.85557	−	6.87482i	0.240380	−	0.167679i	−0.445750	−	0.895157i	$-0.647063\pi$
$41$	9.85557	−	6.87482i	0.240380	−	0.167679i	0.686130	+	0.727479i	$0.259308\pi$
$42$	−38.8163	−	25.7998i	−0.924199	−	0.614280i
$43$	−0.842330	+	5.21011i	−0.0195891	+	0.121165i	−0.995116	−	0.0987164i	$-0.968526\pi$
$43$	−0.842330	+	5.21011i	−0.0195891	+	0.121165i	0.975527	+	0.219882i	$0.0705672\pi$
$44$	25.6682	+	5.57072i	0.583368	+	0.126607i
$45$	4.02629	−	94.1408i	0.0894731	−	2.09202i
$46$	−6.01819	+	43.0441i	−0.130830	+	0.935741i
$47$	−82.0239	−	20.5750i	−1.74519	−	0.437767i	−0.766354	−	0.642418i	$-0.777931\pi$
$47$	−82.0239	−	20.5750i	−1.74519	−	0.437767i	−0.978835	+	0.204652i	$0.934394\pi$
$48$	5.90896	+	12.2701i	0.123103	+	0.255627i
$49$	−8.74636	+	48.2131i	−0.178497	+	0.983940i
$50$	−18.0072	−	8.67182i	−0.360144	−	0.173436i
$51$	4.00785	−	4.81107i	0.0785854	−	0.0943347i
$52$	−4.39143	−	51.2452i	−0.0844505	−	0.985485i
$53$	11.3347	−	41.4153i	0.213862	−	0.781421i	−0.774920	−	0.632059i	$-0.782210\pi$
$53$	11.3347	−	41.4153i	0.213862	−	0.781421i	0.988783	−	0.149362i	$-0.0477220\pi$
$54$	−9.23757	−	38.5680i	−0.171066	−	0.714223i
$55$	−56.9926	+	51.7591i	−1.03623	+	0.941075i
$56$	38.3847	−	44.2229i	0.685442	−	0.789694i
$57$	8.14914	−	27.4572i	0.142967	−	0.481704i
$58$	45.6559	+	13.0212i	0.787170	+	0.224504i
$59$	−35.0922	+	16.4399i	−0.594782	+	0.278642i	−0.698093	−	0.716007i	$-0.745968\pi$
$59$	−35.0922	+	16.4399i	−0.594782	+	0.278642i	0.103311	+	0.994649i	$0.467056\pi$
$60$	65.3131	+	11.2767i	1.08855	+	0.187946i
$61$	−3.67501	−	85.9274i	−0.0602461	−	1.40865i	−0.738716	−	0.674017i	$-0.764567\pi$
$61$	−3.67501	−	85.9274i	−0.0602461	−	1.40865i	0.678470	−	0.734629i	$-0.262644\pi$
$62$	−24.1940	−	2.33397i	−0.390226	−	0.0376447i
$63$	−83.8343	+	62.7107i	−1.33070	+	0.995408i
$64$	−48.8772	+	16.2283i	−0.763706	+	0.253568i
$65$	129.746	+	76.7690i	1.99609	+	1.18106i
$66$	−42.9201	+	69.1240i	−0.650304	+	1.04733i
$67$	77.7165	−	11.7139i	1.15995	−	0.174834i	0.459260	−	0.888302i	$-0.348115\pi$
$67$	77.7165	−	11.7139i	1.15995	−	0.174834i	0.700688	+	0.713468i	$0.252877\pi$
$68$	1.87035	+	2.01575i	0.0275051	+	0.0296434i
$69$	138.643	+	72.3300i	2.00932	+	1.04826i
$70$	14.0382	+	58.3281i	0.200545	+	0.833259i
$71$	−72.8634	−	14.1901i	−1.02624	−	0.199861i	−0.350164	−	0.936688i	$-0.613874\pi$
$71$	−72.8634	−	14.1901i	−1.02624	−	0.199861i	−0.676081	+	0.736827i	$0.736323\pi$
$72$	124.402	−	13.3441i	1.72781	−	0.185334i
$73$	6.80809	−	1.70775i	0.0932615	−	0.0233939i	−0.196392	−	0.980525i	$-0.562923\pi$
$73$	6.80809	−	1.70775i	0.0932615	−	0.0233939i	0.289654	+	0.957132i	$0.406460\pi$
$74$	62.0783	+	74.5195i	0.838897	+	1.00702i
$75$	−51.1192	+	50.5758i	−0.681589	+	0.674344i
$76$	11.5011	+	5.09118i	0.151330	+	0.0669892i
$77$	84.5987	+	12.6561i	1.09868	+	0.164365i
$78$	154.116	+	40.4141i	1.97585	+	0.518129i
$79$	5.07560	+	67.7291i	0.0642480	+	0.857331i	0.932491	+	0.361192i	$0.117630\pi$
$79$	5.07560	+	67.7291i	0.0642480	+	0.857331i	−0.868243	+	0.496139i	$0.834751\pi$
$80$	5.16703	−	16.7511i	0.0645879	−	0.209389i
$81$	−8.03756	−	0.862152i	−0.0992291	−	0.0106439i
$82$	−16.1893	+	2.26350i	−0.197431	+	0.0276037i
$83$	−108.143	+	10.4324i	−1.30293	+	0.125692i	−0.724063	−	0.689734i	$-0.757728\pi$
$83$	−108.143	+	10.4324i	−1.30293	+	0.125692i	−0.578862	+	0.815425i	$0.696503\pi$
$84$	−36.2079	−	64.1259i	−0.431047	−	0.763404i
$85$	−7.99385	+	1.03069i	−0.0940453	+	0.0121258i
$86$	4.23252	−	5.79946i	0.0492154	−	0.0674356i
$87$	99.2189	−	139.047i	1.14045	−	1.59825i
$88$	−79.2378	−	64.5872i	−0.900429	−	0.733945i
$89$	−96.0130	+	40.0707i	−1.07880	+	0.450233i	−0.851910	−	0.523688i	$-0.824556\pi$
$89$	−96.0130	+	40.0707i	−1.07880	+	0.450233i	−0.226887	+	0.973921i	$0.572855\pi$
$90$	−62.9017	+	111.688i	−0.698908	+	1.24098i
$91$	−25.1470	−	165.604i	−0.276341	−	1.81983i
$92$	−39.2884	+	56.3228i	−0.427047	+	0.612205i
$93$	−37.1002	+	79.1931i	−0.398927	+	0.851539i
$94$	86.7945	+	75.5036i	0.923346	+	0.803230i
$95$	−31.7283	+	18.7732i	−0.333982	+	0.197613i
$96$	−3.10401	+	145.219i	−0.0323335	+	1.51270i
$97$	−98.4697	−	78.5269i	−1.01515	−	0.809556i	−0.0333454	−	0.999444i	$-0.510616\pi$
$97$	−98.4697	−	78.5269i	−1.01515	−	0.809556i	−0.981806	+	0.189888i	$0.939188\pi$
$98$	40.3208	−	53.0803i	0.411437	−	0.541635i
$99$	113.953	+	142.892i	1.15104	+	1.44336i
$100$	−19.1571	−	25.1046i	−0.191571	−	0.251046i
$101$	86.4338	+	57.5864i	0.855780	+	0.570162i	0.903446	−	0.428701i	$-0.141029\pi$
$101$	86.4338	+	57.5864i	0.855780	+	0.570162i	−0.0476662	+	0.998863i	$0.515178\pi$
$102$	−7.82560	+	3.36462i	−0.0767215	+	0.0329865i
$103$	−47.3408	+	23.4246i	−0.459620	+	0.227423i	−0.658470	−	0.752607i	$-0.728796\pi$
$103$	−47.3408	+	23.4246i	−0.459620	+	0.227423i	0.198851	+	0.980030i	$0.436279\pi$
$104$	−75.1196	+	185.547i	−0.722304	+	1.78411i
$105$	214.648	+	22.7857i	2.04426	+	0.217007i
$106$	−39.2704	+	43.2411i	−0.370476	+	0.407935i
$107$	52.1128	−	94.8888i	0.487035	−	0.886811i	−0.512568	−	0.858647i	$-0.671306\pi$
$107$	52.1128	−	94.8888i	0.487035	−	0.886811i	0.999603	−	0.0281649i	$-0.00896634\pi$
$108$	14.5955	−	60.9382i	0.135144	−	0.564242i
$109$	−19.9188	−	36.2689i	−0.182741	−	0.332742i	0.769208	−	0.638999i	$-0.220651\pi$
$109$	−19.9188	−	36.2689i	−0.182741	−	0.332742i	−0.951949	+	0.306257i	$0.900923\pi$
$110$	101.017	−	27.6467i	0.918337	−	0.251334i
$111$	327.489	−	120.519i	2.95035	−	1.08576i
$112$	−18.0457	+	7.32898i	−0.161122	+	0.0654373i
$113$	−98.4378	−	12.6921i	−0.871131	−	0.112320i	−0.320680	−	0.947188i	$-0.603911\pi$
$113$	−98.4378	−	12.6921i	−0.871131	−	0.112320i	−0.550451	+	0.834868i	$0.685544\pi$
$114$	−26.8047	+	28.2765i	−0.235129	+	0.248039i
$115$	−67.4946	−	189.632i	−0.586909	−	1.64898i
$116$	54.9889	+	51.0222i	0.474042	+	0.439847i
$117$	201.606	−	295.701i	1.72313	−	2.52736i
$118$	52.6900	+	1.68967i	0.446526	+	0.0143192i
$119$	6.50605	+	6.15384i	0.0546727	+	0.0517130i
$120$	−206.732	−	154.288i	−1.72276	−	1.28573i
$121$	3.32219	−	28.1334i	0.0274561	−	0.232507i
$122$	−48.5000	+	106.474i	−0.397541	+	0.872736i
$123$	−11.8592	+	57.6067i	−0.0964161	+	0.468347i
$124$	−32.4083	−	20.6058i	−0.261358	−	0.166176i
$125$	−64.9087	+	2.08149i	−0.519269	+	0.0166520i
$126$	140.319	−	24.3858i	1.11364	−	0.193538i
$127$	125.433	+	106.783i	0.987662	+	0.840809i	0.987248	−	0.159191i	$-0.0508885\pi$
$127$	125.433	+	106.783i	0.987662	+	0.840809i	0.000414401		1.00000i	$0.499868\pi$
$128$	−48.1030	−	7.25037i	−0.375805	−	0.0566435i
$129$	−14.5517	−	21.3435i	−0.112804	−	0.165453i
$130$	−110.037	−	173.064i	−0.846442	−	1.33126i
$131$	60.0012	+	157.819i	0.458025	+	1.20472i	0.943764	+	0.330620i	$0.107258\pi$
$131$	60.0012	+	157.819i	0.458025	+	1.20472i	−0.485739	+	0.874104i	$0.661450\pi$
$132$	−109.936	+	66.6436i	−0.832845	+	0.504875i
$133$	38.4566	+	14.1044i	0.289147	+	0.106048i
$134$	−101.470	−	33.6904i	−0.757241	−	0.251421i
$135$	120.547	+	138.574i	0.892941	+	1.02647i
$136$	−2.93527	−	10.2918i	−0.0215829	−	0.0756752i
$137$	−1.72754	+	161.662i	−0.0126098	+	1.18002i	0.801021	+	0.598636i	$0.204290\pi$
$137$	−1.72754	+	161.662i	−0.0126098	+	1.18002i	−0.813631	+	0.581381i	$0.802512\pi$
$138$	−123.563	−	173.164i	−0.895386	−	1.25481i
$139$	6.32809	−	98.5651i	0.0455258	−	0.709102i	−0.910076	−	0.414441i	$-0.863977\pi$
$139$	6.32809	−	98.5651i	0.0455258	−	0.709102i	0.955602	−	0.294661i	$-0.0952066\pi$
$140$	−21.9780	+	92.2080i	−0.156985	+	0.658629i
$141$	360.643	−	203.110i	2.55775	−	1.44050i
$142$	79.6200	+	62.1147i	0.560705	+	0.437427i
$143$	−287.601	+	52.8271i	−2.01120	+	0.369420i
$144$	−38.8987	−	14.7889i	−0.270130	−	0.102701i
$145$	−215.358	+	44.3345i	−1.48523	+	0.305755i
$146$	−9.30903	−	2.12472i	−0.0637605	−	0.0145529i
$147$	−131.278	−	200.712i	−0.893046	−	1.36539i
$148$	34.1001	+	149.402i	0.230406	+	1.00948i
$149$	130.369	−	59.3846i	0.874961	−	0.398555i	0.0739909	−	0.997259i	$-0.476426\pi$
$149$	130.369	−	59.3846i	0.874961	−	0.398555i	0.800970	+	0.598704i	$0.204318\pi$
$150$	93.1647	−	29.8314i	0.621098	−	0.198876i
$151$	−77.7021	−	41.5994i	−0.514584	−	0.275493i	0.194146	−	0.980973i	$-0.437806\pi$
$151$	−77.7021	−	41.5994i	−0.514584	−	0.275493i	−0.708730	+	0.705480i	$0.750732\pi$
$152$	−30.9280	−	37.9436i	−0.203474	−	0.249629i
$153$	1.22593	+	19.0948i	0.00801259	+	0.124803i
$154$	−94.7975	−	67.4868i	−0.615568	−	0.438226i
$155$	104.341	−	42.2431i	0.673169	−	0.272536i
$156$	188.155	+	167.244i	1.20612	+	1.07208i
$157$	−16.8582	−	21.6092i	−0.107377	−	0.137638i	0.731751	−	0.681572i	$-0.238703\pi$
$157$	−16.8582	−	21.6092i	−0.107377	−	0.137638i	−0.839129	+	0.543933i	$0.816934\pi$
$158$	35.5859	−	85.2669i	0.225227	−	0.539664i
$159$	99.1937	+	185.281i	0.623860	+	1.16529i
$160$	130.070	−	134.308i	0.812937	−	0.839424i
$161$	−115.726	+	191.376i	−0.718793	+	1.18867i
$162$	9.21624	+	5.99911i	0.0568904	+	0.0370315i
$163$	−109.295	−	164.045i	−0.670521	−	1.00641i	−0.998102	−	0.0615897i	$-0.980383\pi$
$163$	−109.295	−	164.045i	−0.670521	−	1.00641i	0.327581	−	0.944823i	$-0.393767\pi$
$164$	−24.4241	−	8.40015i	−0.148927	−	0.0512204i
$165$	28.1597	−	375.766i	0.170665	−	2.27737i
$166$	137.580	+	53.9962i	0.828796	+	0.325278i
$167$	26.3246	−	11.6531i	0.157632	−	0.0697792i	−0.324461	−	0.945899i	$-0.605183\pi$
$167$	26.3246	−	11.6531i	0.157632	−	0.0697792i	0.482093	+	0.876120i	$0.339877\pi$
$168$	12.5616	+	286.338i	0.0747714	+	1.70439i
$169$	186.679	+	357.828i	1.10461	+	2.11733i
$170$	10.3298	+	3.67662i	0.0607635	+	0.0216272i
$171$	39.6493	+	78.0222i	0.231867	+	0.456270i
$172$	10.1131	−	5.13928i	0.0587972	−	0.0298796i
$173$	−43.8059	+	123.077i	−0.253213	+	0.711426i	0.745764	+	0.666210i	$0.232085\pi$
$173$	−43.8059	+	123.077i	−0.253213	+	0.711426i	−0.998977	+	0.0452156i	$0.985603\pi$
$174$	−206.023	+	107.482i	−1.18404	+	0.617712i
$175$	−67.5846	−	77.5191i	−0.386198	−	0.442966i
$176$	13.7633	+	31.0915i	0.0782005	+	0.176656i
$177$	69.2953	−	176.562i	0.391499	−	0.997523i
$178$	141.136	+	10.5767i	0.792897	+	0.0594194i
$179$	8.28921	−	24.1015i	0.0463084	−	0.134645i	−0.920081	−	0.391729i	$-0.871877\pi$
$179$	8.28921	−	24.1015i	0.0463084	−	0.134645i	0.966389	+	0.257083i	$0.0827615\pi$
$180$	−168.549	+	112.295i	−0.936383	+	0.623864i
$181$	112.339	−	172.583i	0.620659	−	0.953499i	−0.378947	−	0.925419i	$-0.623714\pi$
$181$	112.339	−	172.583i	0.620659	−	0.953499i	0.999606	−	0.0280804i	$-0.00893944\pi$
$182$	−71.5645	+	216.336i	−0.393212	+	1.18866i
$183$	302.394	+	292.853i	1.65243	+	1.60029i
$184$	235.627	−	126.148i	1.28058	−	0.685585i
$185$	−414.526	−	173.001i	−2.24068	−	0.935140i
$186$	93.8000	−	73.1771i	0.504301	−	0.393425i
$187$	10.3862	−	11.6848i	0.0555410	−	0.0624856i
$188$	68.2102	+	168.480i	0.362820	+	0.896173i
$189$	34.4996	−	201.134i	0.182537	−	1.06420i
$190$	50.0486	−	3.21323i	0.263414	−	0.0169117i
$191$	−54.4828	+	44.4092i	−0.285250	+	0.232509i	−0.763646	−	0.645635i	$-0.776593\pi$
$191$	−54.4828	+	44.4092i	−0.285250	+	0.232509i	0.478396	+	0.878144i	$0.341218\pi$
$192$	118.974	−	222.228i	0.619658	−	1.15744i
$193$	−65.1735	−	203.540i	−0.337687	−	1.05461i	−0.961911	−	0.273364i	$-0.911864\pi$
$193$	−65.1735	−	203.540i	−0.337687	−	1.05461i	0.624224	−	0.781246i	$-0.285415\pi$
$194$	71.0236	+	155.921i	0.366101	+	0.803714i
$195$	−719.379	+	164.194i	−3.68912	+	0.842019i
$196$	94.7901	−	45.9054i	0.483623	−	0.234211i
$197$	−37.0023	+	162.118i	−0.187829	+	0.822932i	0.789929	+	0.613198i	$0.210117\pi$
$197$	−37.0023	+	162.118i	−0.187829	+	0.822932i	−0.977758	+	0.209735i	$0.932740\pi$
$198$	−50.1325	−	243.522i	−0.253195	−	1.22991i
$199$	40.2581	−	105.889i	0.202302	−	0.532108i	−0.794910	−	0.606728i	$-0.792482\pi$
$199$	40.2581	−	105.889i	0.202302	−	0.532108i	0.997212	+	0.0746200i	$0.0237744\pi$
$200$	22.2039	+	120.883i	0.111020	+	0.604414i
$201$	−236.617	+	303.301i	−1.17720	+	1.50896i
$202$	−69.3326	−	123.107i	−0.343231	−	0.609441i
$203$	189.531	+	154.141i	0.933650	+	0.759318i
$204$	−13.4313	−	0.862320i	−0.0658399	−	0.00422706i
$205$	61.6253	−	43.9735i	0.300611	−	0.214505i
$206$	71.8493	+	0.767789i	0.348783	+	0.00372713i
$207$	−459.519	+	131.057i	−2.21990	+	0.633124i
$208$	50.2340	−	43.6991i	0.241509	−	0.210092i
$209$	22.5325	−	67.8643i	0.107811	−	0.324710i
$210$	−246.272	−	159.920i	−1.17272	−	0.761525i
$211$	−123.391	−	203.546i	−0.584791	−	0.964674i	−0.998526	−	0.0542765i	$-0.982715\pi$
$211$	−123.391	−	203.546i	−0.584791	−	0.964674i	0.413735	−	0.910397i	$-0.364224\pi$
$212$	−86.2675	+	32.7981i	−0.406922	+	0.154708i
$213$	306.604	−	194.945i	1.43946	−	0.915233i
$214$	−121.680	+	82.9599i	−0.568597	+	0.387663i
$215$	−4.95577	+	32.8794i	−0.0230501	+	0.152927i
$216$	−158.089	+	185.700i	−0.731893	+	0.859723i
$217$	−109.694	−	60.0868i	−0.505501	−	0.276898i
$218$	1.80419	+	56.2612i	0.00827609	+	0.258079i
$219$	−18.4329	+	28.9908i	−0.0841686	+	0.132378i
$220$	162.080	+	33.3664i	0.736725	+	0.151666i
$221$	−27.8591	−	12.6901i	−0.126059	−	0.0574214i
$222$	−471.439	−	55.6708i	−2.12360	−	0.250769i
$223$	183.714	−	246.160i	0.823829	−	1.10386i	−0.169153	−	0.985590i	$-0.554103\pi$
$223$	183.714	−	246.160i	0.823829	−	1.10386i	0.992982	−	0.118266i	$-0.0377335\pi$
$224$	−206.997	−	17.5094i	−0.924094	−	0.0781668i
$225$	7.04294	−	219.625i	0.0313019	−	0.976110i
$226$	111.559	+	76.0595i	0.493623	+	0.336546i
$227$	181.773	−	195.905i	0.800764	−	0.863018i	−0.192210	−	0.981354i	$-0.561565\pi$
$227$	181.773	−	195.905i	0.800764	−	0.863018i	0.992974	+	0.118336i	$0.0377558\pi$
$228$	−57.9969	+	20.6424i	−0.254372	+	0.0905371i
$229$	197.348	+	187.076i	0.861782	+	0.816926i	0.984476	−	0.175518i	$-0.0561602\pi$
$229$	197.348	+	187.076i	0.861782	+	0.816926i	−0.122694	+	0.992445i	$0.539153\pi$
$230$	−35.0156	+	271.574i	−0.152242	+	1.18076i
$231$	−343.124	+	239.910i	−1.48539	+	1.03857i
$232$	−100.830	−	273.988i	−0.434612	−	1.18098i
$233$	−50.8596	−	185.833i	−0.218282	−	0.797568i	−0.987371	−	0.158427i	$-0.949358\pi$
$233$	−50.8596	−	185.833i	−0.218282	−	0.797568i	0.769089	−	0.639141i	$-0.220710\pi$
$234$	−426.738	+	234.364i	−1.82367	+	1.00156i
$235$	−518.119	−	124.097i	−2.20476	−	0.528071i
$236$	73.0082	+	40.0960i	0.309357	+	0.169898i
$237$	−246.091	−	223.493i	−1.03836	−	0.943010i
$238$	−4.09764	−	11.4728i	−0.0172170	−	0.0482049i
$239$	−78.3753	−	31.7307i	−0.327930	−	0.132764i	0.205384	−	0.978681i	$-0.434156\pi$
$239$	−78.3753	−	31.7307i	−0.327930	−	0.132764i	−0.533314	+	0.845917i	$0.679054\pi$
$240$	38.0513	+	76.9012i	0.158547	+	0.320422i
$241$	6.44369	+	14.9871i	0.0267373	+	0.0621870i	0.931528	−	0.363669i	$-0.118476\pi$
$241$	6.44369	+	14.9871i	0.0267373	+	0.0621870i	−0.904791	+	0.425856i	$0.859973\pi$
$242$	−21.3675	+	32.0715i	−0.0882957	+	0.132527i
$243$	−177.130	+	135.167i	−0.728932	+	0.556241i
$244$	−144.530	+	115.259i	−0.592338	+	0.472374i
$245$	−51.8546	+	304.322i	−0.211651	+	1.24213i
$246$	49.8852	−	62.5541i	0.202785	−	0.254285i
$247$	−139.992	−	2.99227i	−0.566769	−	0.0121145i
$248$	76.1137	+	128.638i	0.306910	+	0.518703i
$249$	349.011	−	401.203i	1.40165	−	1.61126i
$250$	80.0011	+	37.4787i	0.320004	+	0.149915i
$251$	198.303	+	138.328i	0.790053	+	0.551106i	0.896412	−	0.443221i	$-0.146164\pi$
$251$	198.303	+	138.328i	0.790053	+	0.551106i	−0.106360	+	0.994328i	$0.533919\pi$
$252$	215.105	+	66.0922i	0.853590	+	0.262271i
$253$	340.181	+	191.587i	1.34459	+	0.757259i
$254$	−86.3096	−	206.805i	−0.339802	−	0.814195i
$255$	24.9248	−	30.5786i	0.0977443	−	0.119916i
$256$	221.558	+	158.095i	0.865461	+	0.617560i
$257$	−79.2056	−	57.8053i	−0.308193	−	0.224923i	0.424590	−	0.905386i	$-0.360418\pi$
$257$	−79.2056	−	57.8053i	−0.308193	−	0.224923i	−0.732783	+	0.680463i	$0.761779\pi$
$258$	4.49375	+	34.8526i	0.0174176	+	0.135088i
$259$	142.526	+	478.290i	0.550294	+	1.84668i
$260$	−31.1149	−	322.539i	−0.119673	−	1.24053i
$261$	72.2760	+	516.942i	0.276919	+	1.98062i
$262$	24.4967	−	228.374i	0.0934987	−	0.871657i
$263$	−224.585	−	69.2754i	−0.853937	−	0.263405i	−0.163273	−	0.986581i	$-0.552205\pi$
$263$	−224.585	−	69.2754i	−0.853937	−	0.263405i	−0.690664	+	0.723176i	$0.742681\pi$
$264$	498.947	−	37.3909i	1.88995	−	0.141632i
$265$	68.6183	−	261.671i	0.258937	−	0.987439i
$266$	−37.9459	−	40.8059i	−0.142654	−	0.153406i
$267$	206.124	−	465.638i	0.772001	−	1.74396i
$268$	−118.812	−	120.089i	−0.443329	−	0.448092i
$269$	−50.4207	+	42.0028i	−0.187437	+	0.156144i	−0.728994	−	0.684520i	$-0.760012\pi$
$269$	−50.4207	+	42.0028i	−0.187437	+	0.156144i	0.541557	+	0.840664i	$0.317835\pi$
$270$	−60.7913	−	242.349i	−0.225153	−	0.897589i
$271$	8.69392	+	81.0505i	0.0320809	+	0.299079i	0.999027	+	0.0440991i	$0.0140417\pi$
$271$	8.69392	+	81.0505i	0.0320809	+	0.299079i	−0.966946	+	0.254980i	$0.917931\pi$
$272$	−0.680466	+	3.49405i	−0.00250172	+	0.0128458i
$273$	646.960	+	503.576i	2.36982	+	1.84460i
$274$	101.727	−	194.992i	0.371267	−	0.711650i
$275$	−131.610	+	122.116i	−0.478580	+	0.444058i
$276$	−50.0955	−	332.362i	−0.181505	−	1.20421i
$277$	103.840	+	64.4757i	0.374874	+	0.232764i	0.701939	−	0.712238i	$-0.252318\pi$
$277$	103.840	+	64.4757i	0.374874	+	0.232764i	−0.327065	+	0.945002i	$0.606060\pi$
$278$	−68.4199	+	115.635i	−0.246115	+	0.415954i
$279$	−84.2067	−	253.617i	−0.301816	−	0.909023i
$280$	238.839	−	281.179i	0.852996	−	1.00421i
$281$	−0.846492	+	8.77478i	−0.00301243	+	0.0312270i	−0.996763	−	0.0803977i	$-0.974381\pi$
$281$	−0.846492	+	8.77478i	−0.00301243	+	0.0312270i	0.993750	+	0.111625i	$0.0356054\pi$
$282$	−562.548	+	24.0595i	−1.99485	+	0.0853174i
$283$	−89.8781	+	520.560i	−0.317590	+	1.83943i	0.195004	+	0.980802i	$0.437528\pi$
$283$	−89.8781	+	520.560i	−0.317590	+	1.83943i	−0.512594	+	0.858631i	$0.671316\pi$
$284$	67.6883	+	144.486i	0.238339	+	0.508753i
$285$	49.4895	−	173.523i	0.173647	−	0.608853i
$286$	381.347	+	113.182i	1.33338	+	0.395740i
$287$	−81.1560	−	22.1152i	−0.282773	−	0.0770566i
$288$	−298.402	−	328.574i	−1.03612	−	1.14088i
$289$	−279.459	+	66.9343i	−0.966987	+	0.231607i
$290$	288.499	+	78.9577i	0.994826	+	0.272268i
$291$	614.201	−	52.6335i	2.11065	−	0.180871i
$292$	−11.5915	−	9.65631i	−0.0396971	−	0.0330695i
$293$	170.955	−	354.992i	0.583465	−	1.21158i	−0.375174	−	0.926954i	$-0.622417\pi$
$293$	170.955	−	354.992i	0.583465	−	1.21158i	0.958639	−	0.284624i	$-0.0918686\pi$
$294$	35.5096	+	324.320i	0.120781	+	1.10313i
$295$	−219.967	+	105.930i	−0.745650	+	0.359086i
$296$	145.113	−	578.502i	0.490245	−	1.95440i
$297$	−352.819	−	49.3292i	−1.18794	−	0.166092i
$298$	−194.704	−	8.32728i	−0.653371	−	0.0279439i
$299$	162.146	−	747.122i	0.542296	−	2.49873i
$300$	152.583	+	24.6684i	0.508609	+	0.0822280i
$301$	31.7748	−	18.8479i	0.105564	−	0.0626177i
$302$	68.5960	+	98.3375i	0.227139	+	0.325621i
$303$	−500.935	+	86.4897i	−1.65325	+	0.285445i
$304$	3.45324	+	15.9115i	0.0113594	+	0.0523405i
$305$	−28.9365	−	541.078i	−0.0948737	−	1.77403i
$306$	10.2813	−	23.9128i	0.0335991	−	0.0781465i
$307$	−80.4087	−	123.529i	−0.261918	−	0.402376i	0.682623	−	0.730771i	$-0.260839\pi$
$307$	−80.4087	−	123.529i	−0.261918	−	0.402376i	−0.944540	+	0.328395i	$0.893492\pi$
$308$	−85.2215	−	162.917i	−0.276693	−	0.528951i
$309$	89.2852	−	242.617i	0.288949	−	0.785168i
$310$	−152.575	−	13.0748i	−0.492176	−	0.0421767i
$311$	158.239	+	156.557i	0.508807	+	0.503398i	0.911141	−	0.412094i	$-0.135203\pi$
$311$	158.239	+	156.557i	0.508807	+	0.503398i	−0.402335	+	0.915493i	$0.631801\pi$
$312$	−357.949	−	912.039i	−1.14727	−	2.92320i
$313$	−134.053	−	434.590i	−0.428285	−	1.38847i	−0.870770	−	0.491690i	$-0.836379\pi$
$313$	−134.053	−	434.590i	−0.428285	−	1.38847i	0.442485	−	0.896776i	$-0.354097\pi$
$314$	7.12714	+	36.5964i	0.0226979	+	0.116549i
$315$	−523.917	+	400.709i	−1.66323	+	1.27209i
$316$	111.160	−	94.6319i	0.351772	−	0.299468i
$317$	−31.4791	+	19.5458i	−0.0993032	+	0.0616587i	−0.576251	−	0.817273i	$-0.695485\pi$
$317$	−31.4791	+	19.5458i	−0.0993032	+	0.0616587i	0.476947	+	0.878932i	$0.341743\pi$
$318$	−6.10957	−	285.833i	−0.0192125	−	0.898846i
$319$	258.717	−	339.038i	0.811025	−	1.06282i
$320$	−306.824	+	105.526i	−0.958825	+	0.329768i
$321$	134.403	+	512.537i	0.418701	+	1.59669i
$322$	258.291	−	160.770i	0.802147	−	0.499287i
$323$	5.99956	−	4.47759i	0.0185745	−	0.0138625i
$324$	8.68753	+	15.0472i	0.0268134	+	0.0464421i
$325$	304.464	+	175.782i	0.936812	+	0.540869i
$326$	31.4471	+	266.305i	0.0964636	+	0.816886i
$327$	192.882	+	61.7608i	0.589852	+	0.188871i
$328$	69.9321	+	72.2107i	0.213208	+	0.220154i
$329$	257.426	+	533.051i	0.782449	+	1.62022i
$330$	−265.734	+	438.357i	−0.805256	+	1.32835i
$331$	23.1420	−	125.990i	0.0699155	−	0.380634i	−0.929999	−	0.367562i	$-0.880193\pi$
$331$	23.1420	−	125.990i	0.0699155	−	0.380634i	0.999915	−	0.0130722i	$-0.00416112\pi$
$332$	155.141	+	174.539i	0.467291	+	0.525719i
$333$	−472.901	+	955.729i	−1.42012	+	2.87006i
$334$	−39.1071	−	2.09142i	−0.117087	−	0.00626174i
$335$	488.810	−	79.0269i	1.45913	−	0.235901i
$336$	39.4224	−	86.7982i	0.117329	−	0.258328i
$337$	177.188	+	597.006i	0.525781	+	1.77153i	0.629582	+	0.776934i	$0.283226\pi$
$337$	177.188	+	597.006i	0.525781	+	1.77153i	−0.103800	+	0.994598i	$0.533100\pi$
$338$	−5.86675	−	549.008i	−0.0173572	−	1.62428i
$339$	392.404	−	286.382i	1.15753	−	0.844783i
$340$	11.9185	+	12.5729i	0.0350544	+	0.0369792i
$341$	−98.9169	+	194.649i	−0.290079	+	0.570819i
$342$		−	119.058i		−	0.348122i
$343$	298.306	−	169.301i	0.869696	−	0.493587i
$344$	−44.1508			−0.128345
$345$	878.293	+	446.331i	2.54578	+	1.29371i
$346$	128.978	−	122.264i	0.372768	−	0.353365i
$347$	−34.2707	−	46.9582i	−0.0987628	−	0.135326i	0.755539	−	0.655104i	$-0.227375\pi$
$347$	−34.2707	−	46.9582i	−0.0987628	−	0.135326i	−0.854301	+	0.519778i	$0.826015\pi$
$348$	−367.134	+	3.92323i	−1.05498	+	0.0112737i
$349$	−514.645	+	152.744i	−1.47463	+	0.437662i	−0.919162	−	0.393879i	$-0.871133\pi$
$349$	−514.645	+	152.744i	−1.47463	+	0.437662i	−0.555465	+	0.831540i	$0.687460\pi$
$350$	34.1887	+	135.664i	0.0976820	+	0.387611i
$351$	111.337	+	688.661i	0.317201	+	1.96200i
$352$	−19.3665	+	362.131i	−0.0550186	+	1.02878i
$353$	47.5682	+	23.5371i	0.134754	+	0.0666773i	0.509608	−	0.860406i	$-0.329790\pi$
$353$	47.5682	+	23.5371i	0.134754	+	0.0666773i	−0.374854	+	0.927084i	$0.622307\pi$
$354$	−192.853	+	171.419i	−0.544782	+	0.484235i
$355$	−459.980	−	84.4899i	−1.29572	−	0.238000i
$356$	191.229	+	115.924i	0.537160	+	0.325629i
$357$	−43.8321	+	0.0481693i	−0.122779	+	0.000134928i
$358$	−24.9065	+	24.1206i	−0.0695711	+	0.0673759i
$359$	−176.767	+	552.051i	−0.492387	+	1.53775i	0.315803	+	0.948825i	$0.397726\pi$
$359$	−176.767	+	552.051i	−0.492387	+	1.53775i	−0.808190	+	0.588921i	$0.799553\pi$
$360$	782.811	−	92.4397i	2.17447	−	0.256777i
$361$	−163.379	+	282.981i	−0.452574	+	0.783881i
$362$	−242.603	+	140.067i	−0.670173	+	0.386925i
$363$	82.9317	+	111.121i	0.228462	+	0.306118i
$364$	−255.659	+	253.498i	−0.702359	+	0.696423i
$365$	42.7746	−	11.2168i	0.117191	−	0.0307310i
$366$	−186.246	−	541.523i	−0.508868	−	1.47957i
$367$	108.500	+	82.7956i	0.295641	+	0.225601i	0.743881	−	0.668312i	$-0.232983\pi$
$367$	108.500	+	82.7956i	0.295641	+	0.225601i	−0.448240	+	0.893913i	$0.647949\pi$
$368$	−88.8772	+	1.89972i	−0.241514	+	0.00516227i
$369$	−94.8032	−	152.683i	−0.256919	−	0.413776i
$370$	396.098	+	465.279i	1.07053	+	1.25751i
$371$	−273.391	+	124.896i	−0.736903	+	0.336646i
$372$	184.505	−	35.9323i	0.495981	−	0.0965922i
$373$	175.448	−	54.1186i	0.470370	−	0.145090i	−0.0505031	−	0.998724i	$-0.516082\pi$
$373$	175.448	−	54.1186i	0.470370	−	0.145090i	0.520874	+	0.853634i	$0.325606\pi$
$374$	−19.7972	+	7.76982i	−0.0529337	+	0.0207749i
$375$	223.557	−	225.958i	0.596151	−	0.602556i
$376$	60.4009	−	704.841i	0.160641	−	1.87458i
$377$	−783.729	−	288.420i	−2.07886	−	0.765039i
$378$	−165.798	+	222.664i	−0.438619	+	0.589059i
$379$	−263.985	+	171.835i	−0.696531	+	0.453391i	−0.844468	−	0.535605i	$-0.820083\pi$
$379$	−263.985	+	171.835i	−0.696531	+	0.453391i	0.147938	+	0.988997i	$0.452736\pi$
$380$	72.7971	+	31.2991i	0.191571	+	0.0823662i
$381$	−805.124	+	43.0575i	−2.11319	+	0.113012i
$382$	93.4436	−	20.2799i	0.244617	−	0.0530887i
$383$	59.4146	+	344.120i	0.155129	+	0.898485i	0.954624	+	0.297813i	$0.0962571\pi$
$383$	59.4146	+	344.120i	0.155129	+	0.898485i	−0.799495	+	0.600673i	$0.794899\pi$
$384$	195.283	−	136.221i	0.508550	−	0.354743i
$385$	533.807	+	74.0359i	1.38651	+	0.192301i
$386$	−46.4015	+	287.010i	−0.120211	+	0.743549i
$387$	77.1399	+	16.7415i	0.199328	+	0.0432597i
$388$	−11.5674	+	270.465i	−0.0298130	+	0.697074i
$389$	1.97248	−	14.1079i	0.00507065	−	0.0362670i	−0.987666	−	0.156578i	$-0.949954\pi$
$389$	1.97248	−	14.1079i	0.00507065	−	0.0362670i	0.992736	+	0.120311i	$0.0383891\pi$
$390$	973.623	+	244.225i	2.49647	+	0.626219i
$391$	17.7345	+	36.8261i	0.0453569	+	0.0941845i
$392$	−409.831	−	7.85886i	−1.04549	−	0.0200481i
$393$	−744.551	−	358.557i	−1.89453	−	0.912359i
$394$	144.788	−	173.805i	0.367481	−	0.441128i
$395$	36.5348	+	426.338i	0.0924931	+	1.07934i
$396$	103.700	−	378.903i	0.261868	−	0.956827i
$397$	−38.5618	−	161.000i	−0.0971330	−	0.405543i	0.902554	−	0.430578i	$-0.141690\pi$
$397$	−38.5618	−	161.000i	−0.0971330	−	0.405543i	−0.999687	+	0.0250350i	$0.992030\pi$
$398$	−114.083	+	103.607i	−0.286640	+	0.260319i
$399$	−184.097	+	79.3924i	−0.461396	+	0.198979i
$400$	11.6314	−	39.1902i	0.0290786	−	0.0979754i
$401$	512.354	+	146.125i	1.27769	+	0.364402i	0.843846	−	0.536586i	$-0.180286\pi$
$401$	512.354	+	146.125i	1.27769	+	0.364402i	0.433844	+	0.900988i	$0.357157\pi$
$402$	473.883	−	222.003i	1.17881	−	0.552247i
$403$	421.317	+	72.7432i	1.04545	+	0.180504i
$404$	−9.53890	−	223.034i	−0.0236111	−	0.552065i
$405$	−50.6930	−	4.89030i	−0.125168	−	0.0120748i
$406$	−134.858	−	303.743i	−0.332162	−	0.748136i
$407$	826.857	−	274.536i	2.03159	−	0.674535i
$408$	45.0818	+	26.6743i	0.110495	+	0.0653783i
$409$	87.4152	−	140.785i	0.213729	−	0.344217i	−0.725074	−	0.688671i	$-0.758194\pi$
$409$	87.4152	−	140.785i	0.213729	−	0.344217i	0.938803	+	0.344454i	$0.111936\pi$
$410$	−101.837	+	15.3495i	−0.248383	+	0.0374378i
$411$	−538.223	−	580.067i	−1.30955	−	1.41135i
$412$	100.655	+	52.5118i	0.244309	+	0.127456i
$413$	245.771	+	114.809i	0.595088	+	0.277988i
$414$	638.054	+	124.261i	1.54119	+	0.300147i
$415$	−680.576	+	73.0023i	−1.63994	+	0.175909i
$416$	688.792	−	172.778i	1.65575	−	0.415331i
$417$	309.416	+	371.427i	0.742006	+	0.890712i
$418$	−69.1510	+	68.4160i	−0.165433	+	0.163675i
$419$	83.6975	+	37.0504i	0.199755	+	0.0884258i	0.502239	−	0.864729i	$-0.332510\pi$
$419$	83.6975	+	37.0504i	0.199755	+	0.0884258i	−0.302484	+	0.953155i	$0.597816\pi$
$420$	−232.420	−	401.543i	−0.553380	−	0.956054i
$421$	100.482	+	26.3495i	0.238675	+	0.0625880i	0.371054	−	0.928611i	$-0.378996\pi$
$421$	100.482	+	26.3495i	0.238675	+	0.0625880i	−0.132379	+	0.991199i	$0.542262\pi$
$422$	24.1978	+	322.897i	0.0573407	+	0.765159i
$423$	−372.800	+	1208.59i	−0.881324	+	2.85718i
$424$	357.150	+	38.3098i	0.842335	+	0.0903534i
$425$	−18.6150	+	2.60264i	−0.0437999	+	0.00612386i
$426$	−491.979	+	47.4607i	−1.15488	+	0.111410i
$427$	−445.233	+	405.243i	−1.04270	+	0.949046i
$428$	−230.778	+	29.7555i	−0.539201	+	0.0695223i
$429$	843.721	−	1156.08i	1.96672	−	2.69482i
$430$	26.2736	−	36.8204i	0.0611014	−	0.0856288i
$431$	422.744	+	344.581i	0.980845	+	0.799492i	0.979692	−	0.200507i	$-0.0642590\pi$
$431$	422.744	+	344.581i	0.980845	+	0.799492i	0.00115244	+	0.999999i	$0.499633\pi$
$432$	74.8592	−	31.2422i	0.173285	−	0.0723200i
$433$	10.5050	−	18.6526i	0.0242609	−	0.0430777i	−0.858922	−	0.512106i	$-0.828865\pi$
$433$	10.5050	−	18.6526i	0.0242609	−	0.0430777i	0.883183	+	0.469029i	$0.155396\pi$
$434$	96.0002	+	140.474i	0.221199	+	0.323674i
$435$	615.698	−	882.650i	1.41540	−	2.02908i
$436$	−37.7309	+	80.5394i	−0.0865388	+	0.184723i
$437$	141.054	+	122.704i	0.322777	+	0.280788i
$438$	40.2216	−	23.7986i	0.0918302	−	0.0543347i
$439$	−2.74861	+	128.592i	−0.00626106	+	0.292920i	0.985855	+	0.167599i	$0.0536015\pi$
$439$	−2.74861	+	128.592i	−0.00626106	+	0.292920i	−0.992116	+	0.125321i	$0.960004\pi$
$440$	−503.530	−	401.552i	−1.14439	−	0.912618i
$441$	713.073	+	169.135i	1.61695	+	0.383525i
$442$	25.9654	+	32.5595i	0.0587452	+	0.0736641i
$443$	17.3941	+	22.7943i	0.0392643	+	0.0514543i	0.814193	−	0.580595i	$-0.197180\pi$
$443$	17.3941	+	22.7943i	0.0392643	+	0.0514543i	−0.774928	+	0.632049i	$0.782214\pi$
$444$	−624.206	−	415.876i	−1.40587	−	0.936658i
$445$	−602.165	+	258.901i	−1.35318	+	0.581800i
$446$	−374.508	+	185.309i	−0.839703	+	0.415491i
$447$	−263.128	+	649.931i	−0.588653	+	1.45398i
$448$	306.478	+	189.831i	0.684104	+	0.423729i
$449$	−244.085	+	268.765i	−0.543620	+	0.598586i	−0.948888	−	0.315612i	$-0.897790\pi$
$449$	−244.085	+	268.765i	−0.543620	+	0.598586i	0.405269	+	0.914198i	$0.367178\pi$
$450$	−143.896	+	262.010i	−0.319768	+	0.582245i
$451$	−34.2032	+	142.802i	−0.0758385	+	0.316635i
$452$	102.695	+	186.990i	0.227200	+	0.413694i
$453$	416.086	−	113.876i	0.918513	−	0.251382i
$454$	−341.183	+	125.558i	−0.751503	+	0.276560i
$455$	−169.570	−	1041.58i	−0.372681	−	2.28919i
$456$	237.627	+	30.6386i	0.521112	+	0.0671900i
$457$	386.978	−	408.227i	0.846780	−	0.893275i	−0.148638	−	0.988892i	$-0.547489\pi$
$457$	386.978	−	408.227i	0.846780	−	0.893275i	0.995418	+	0.0956165i	$0.0304822\pi$
$458$	−124.040	−	348.503i	−0.270830	−	0.760923i
$459$	−27.3403	−	25.3681i	−0.0595650	−	0.0552683i
$460$	−243.717	+	357.467i	−0.529820	+	0.777103i
$461$	−639.940	−	20.5216i	−1.38816	−	0.0445155i	−0.671015	−	0.741444i	$-0.734141\pi$
$461$	−639.940	−	20.5216i	−1.38816	−	0.0445155i	−0.717141	+	0.696928i	$0.754550\pi$
$462$	563.981	−	79.4847i	1.22074	−	0.172045i
$463$	−113.660	−	84.8264i	−0.245485	−	0.183210i	0.468311	−	0.883564i	$-0.344863\pi$
$463$	−113.660	−	84.8264i	−0.245485	−	0.183210i	−0.713796	+	0.700353i	$0.753026\pi$
$464$	−11.3879	+	96.4369i	−0.0245430	+	0.207838i
$465$	−228.393	+	501.398i	−0.491167	+	1.07828i
$466$	−52.8485	+	256.715i	−0.113409	+	0.550890i
$467$	197.183	+	125.372i	0.422232	+	0.268463i	0.730602	−	0.682803i	$-0.239239\pi$
$467$	197.183	+	125.372i	0.422232	+	0.268463i	−0.308370	+	0.951266i	$0.599784\pi$
$468$	−768.851	+	24.6556i	−1.64284	+	0.0526828i
$469$	−411.602	−	365.048i	−0.877616	−	0.778354i
$470$	551.871	+	469.815i	1.17419	+	0.999605i
$471$	132.647	+	19.9933i	0.281628	+	0.0424486i
$472$	−182.616	−	267.849i	−0.386899	−	0.567477i
$473$	−34.6043	−	54.4248i	−0.0731593	−	0.115063i
$474$	160.710	+	422.708i	0.339050	+	0.891789i
$475$	−73.5186	+	44.5674i	−0.154776	+	0.0938261i
$476$	2.44048	−	19.0933i	0.00512707	−	0.0401121i
$477$	−609.482	−	202.362i	−1.27774	−	0.424239i
$478$	75.4945	+	86.7841i	0.157938	+	0.181557i
$479$	71.8348	+	251.872i	0.149968	+	0.525828i	1.00000		0.000904293i	$-0.000287845\pi$
$479$	71.8348	+	251.872i	0.149968	+	0.525828i	−0.850031	+	0.526732i	$0.823417\pi$
$480$	−9.77844	+	915.062i	−0.0203718	+	1.90638i
$481$	−990.954	−	1388.74i	−2.06020	−	2.88720i
$482$	1.42188	−	22.1469i	0.00294995	−	0.0459479i
$483$	−233.337	−	1069.48i	−0.483100	−	2.21424i
$484$	−53.0547	+	29.8799i	−0.109617	+	0.0617353i
$485$	−625.626	−	488.075i	−1.28995	−	1.00634i
$486$	298.119	−	54.7589i	0.613413	−	0.112673i
$487$	404.327	+	153.721i	0.830240	+	0.315649i	0.733525	−	0.679663i	$-0.237874\pi$
$487$	404.327	+	153.721i	0.830240	+	0.315649i	0.0967152	+	0.995312i	$0.469166\pi$
$488$	704.700	−	145.073i	1.44406	−	0.297280i
$489$	940.616	+	214.690i	1.92355	+	0.439038i
$490$	250.440	−	337.109i	0.511101	−	0.687979i
$491$	9.17020	+	40.1773i	0.0186766	+	0.0818274i	0.983407	−	0.181411i	$-0.0580665\pi$
$491$	9.17020	+	40.1773i	0.0186766	+	0.0818274i	−0.964731	+	0.263239i	$0.915209\pi$
$492$	115.044	−	52.4036i	0.233828	−	0.106511i
$493$	42.5219	−	13.6155i	0.0862512	−	0.0276177i
$494$	167.932	+	89.9056i	0.339943	+	0.181995i
$495$	727.499	+	892.521i	1.46969	+	1.80307i
$496$	−3.18528	−	49.6133i	−0.00642194	−	0.100027i
$497$	250.637	+	455.184i	0.504301	+	0.915862i
$498$	−670.526	+	271.466i	−1.34644	+	0.545112i
$499$	315.669	+	280.586i	0.632604	+	0.562297i	0.918232	−	0.396044i	$-0.129617\pi$
$499$	315.669	+	280.586i	0.632604	+	0.562297i	−0.285628	+	0.958341i	$0.592202\pi$
$500$	85.8597	+	110.057i	0.171719	+	0.220114i
$501$	−54.2699	+	130.036i	−0.108323	+	0.259552i
$502$	−155.242	−	289.971i	−0.309247	−	0.577632i
$503$	429.391	−	443.381i	0.853659	−	0.881473i	−0.140424	−	0.990091i	$-0.544847\pi$
$503$	429.391	−	443.381i	0.853659	−	0.881473i	0.994084	+	0.108618i	$0.0346426\pi$
$504$	−629.807	−	608.595i	−1.24962	−	1.20753i
$505$	548.392	+	356.964i	1.08593	+	0.706859i
$506$	−294.482	−	442.000i	−0.581980	−	0.873519i
$507$	−1868.01	−	642.465i	−3.68445	−	1.26719i
$508$	26.4598	−	353.081i	0.0520862	−	0.695042i
$509$	−66.6335	−	26.1517i	−0.130911	−	0.0513786i	0.298981	−	0.954259i	$-0.403353\pi$
$509$	−66.6335	−	26.1517i	−0.130911	−	0.0513786i	−0.429892	+	0.902880i	$0.641448\pi$
$510$	−49.0732	+	21.7232i	−0.0962219	+	0.0425946i
$511$	−39.7195	−	28.9210i	−0.0777289	−	0.0565968i
$512$	−81.2585	−	155.757i	−0.158708	−	0.304214i
$513$	−160.717	−	57.2029i	−0.313288	−	0.111507i
$514$	60.4317	+	118.918i	0.117571	+	0.231358i
$515$	−296.661	+	150.757i	−0.576040	+	0.292732i
$516$	−18.6180	+	52.3091i	−0.0360814	+	0.101374i
$517$	916.200	−	477.981i	1.77215	−	0.924528i
$518$	121.920	−	667.887i	0.235367	−	1.28936i
$519$	−258.826	−	584.693i	−0.498702	−	1.12658i
$520$	−460.748	+	1173.97i	−0.886053	+	2.25763i
$521$	−573.073	−	42.9459i	−1.09995	−	0.0824298i	−0.487637	−	0.873046i	$-0.662141\pi$
$521$	−573.073	−	42.9459i	−1.09995	−	0.0824298i	−0.612312	+	0.790617i	$0.709760\pi$
$522$	230.937	−	671.467i	0.442409	−	1.28634i
$523$	479.902	−	319.734i	0.917595	−	0.611346i	−0.00379200	−	0.999993i	$-0.501207\pi$
$523$	479.902	−	319.734i	0.917595	−	0.611346i	0.921387	+	0.388647i	$0.127057\pi$
$524$	197.977	−	304.146i	0.377819	−	0.580432i
$525$	501.098	+	47.7846i	0.954473	+	0.0910183i
$526$	229.673	+	222.426i	0.436640	+	0.422862i
$527$	−20.1522	+	10.7889i	−0.0382395	+	0.0204723i
$528$	−153.583	−	64.0973i	−0.290876	−	0.121396i
$529$	−387.726	+	302.480i	−0.732942	+	0.571797i
$530$	−244.485	+	275.054i	−0.461292	+	0.518970i
$531$	217.500	+	537.230i	0.409605	+	1.01173i
$532$	−24.2403	−	84.6400i	−0.0455645	−	0.159098i
$533$	286.951	−	18.4229i	0.538370	−	0.0345645i
$534$	−536.950	+	437.671i	−1.00552	+	0.819609i
$535$	321.912	−	601.289i	0.601705	−	1.12390i
$536$	200.497	+	626.159i	0.374061	+	1.16821i
$537$	51.7115	+	113.524i	0.0962971	+	0.211404i
$538$	87.0342	−	19.8650i	0.161774	−	0.0369238i
$539$	−311.528	−	511.360i	−0.577975	−	0.948719i
$540$	87.8465	−	384.881i	0.162679	−	0.712742i
$541$	11.6353	+	56.5194i	0.0215071	+	0.104472i	0.988820	−	0.149113i	$-0.0476419\pi$
$541$	11.6353	+	56.5194i	0.0215071	+	0.104472i	−0.967313	+	0.253585i	$0.918390\pi$
$542$	39.4076	−	103.652i	0.0727078	−	0.191241i
$543$	182.087	+	991.319i	0.335335	+	1.82563i
$544$	−23.3531	+	29.9346i	−0.0429285	+	0.0550268i
$545$	−127.926	−	227.146i	−0.234727	−	0.416781i
$546$	−474.251	−	1009.43i	−0.868592	−	1.84878i
$547$	102.484	+	6.57970i	0.187357	+	0.0120287i	0.157466	−	0.987524i	$-0.449668\pi$
$547$	102.484	+	6.57970i	0.187357	+	0.0120287i	0.0298911	+	0.999553i	$0.490484\pi$
$548$	282.867	−	201.843i	0.516181	−	0.368327i
$549$	−1286.25	−	13.7450i	−2.34291	−	0.0250365i
$550$	234.870	−	66.9859i	0.427036	−	0.121792i
$551$	154.080	−	134.036i	0.279636	−	0.243259i
$552$	−412.211	+	1241.51i	−0.746759	+	2.24912i
$553$	341.163	−	331.126i	0.616932	−	0.598781i
$554$	−86.1962	−	142.190i	−0.155589	−	0.256660i
$555$	2055.00	−	781.291i	3.70270	−	1.40773i
$556$	−179.147	+	113.905i	−0.322207	+	0.204865i
$557$	367.526	−	250.575i	0.659831	−	0.449865i	−0.186548	−	0.982446i	$-0.559730\pi$
$557$	367.526	−	250.575i	0.659831	−	0.449865i	0.846379	+	0.532581i	$0.178778\pi$
$558$	−54.1817	+	359.472i	−0.0970998	+	0.644215i
$559$	−81.8657	+	96.1642i	−0.146450	+	0.172029i
$560$	−113.191	+	47.3859i	−0.202126	+	0.0846177i
$561$	2.45254	+	76.4792i	0.00437173	+	0.136327i
$562$	6.43446	−	10.1200i	0.0114492	−	0.0180070i
$563$	−687.306	−	141.492i	−1.22079	−	0.251318i	−0.452703	−	0.891661i	$-0.649540\pi$
$563$	−687.306	−	141.492i	−1.22079	−	0.251318i	−0.768089	+	0.640344i	$0.778792\pi$
$564$	−809.611	−	368.787i	−1.43548	−	0.653878i
$565$	−620.993	−	73.3311i	−1.09910	−	0.129790i
$566$	429.820	−	575.919i	0.759399	−	1.01753i
$567$	31.4262	+	47.0567i	0.0554253	+	0.0829924i
$568$	19.9036	−	620.667i	0.0350415	−	1.09272i
$569$	−73.8689	−	50.3630i	−0.129822	−	0.0885114i	0.496668	−	0.867941i	$-0.334557\pi$
$569$	−73.8689	−	50.3630i	−0.129822	−	0.0885114i	−0.626490	+	0.779429i	$0.715509\pi$
$570$	−166.961	+	179.941i	−0.292913	+	0.315685i
$571$	−402.800	+	143.366i	−0.705429	+	0.251079i	−0.663645	−	0.748048i	$-0.730991\pi$
$571$	−402.800	+	143.366i	−0.705429	+	0.251079i	−0.0417841	+	0.999127i	$0.513304\pi$
$572$	456.138	+	432.396i	0.797444	+	0.755937i
$573$	43.9937	−	341.206i	0.0767778	−	0.595474i
$574$	84.7927	+	76.8366i	0.147722	+	0.133862i
$575$	−162.114	−	440.516i	−0.281938	−	0.766115i
$576$	203.331	+	742.939i	0.353004	+	1.28983i
$577$	196.018	−	107.653i	0.339719	−	0.186573i	−0.302394	−	0.953183i	$-0.597786\pi$
$577$	196.018	−	107.653i	0.339719	−	0.186573i	0.642113	+	0.766610i	$0.278058\pi$
$578$	380.167	+	91.0552i	0.657728	+	0.157535i
$579$	916.878	+	503.548i	1.58356	+	0.869686i
$580$	349.854	+	317.728i	0.603196	+	0.547807i
$581$	541.217	+	534.289i	0.931527	+	0.919603i
$582$	−777.312	−	314.699i	−1.33559	−	0.540720i
$583$	232.701	+	470.286i	0.399144	+	0.806665i
$584$	23.1926	+	53.9426i	0.0397134	+	0.0923674i
$585$	1250.17	−	1876.43i	2.13704	−	3.20757i
$586$	−426.108	+	325.159i	−0.727147	+	0.554879i
$587$	−357.594	+	285.172i	−0.609190	+	0.485813i	−0.878821	−	0.477151i	$-0.841670\pi$
$587$	−357.594	+	285.172i	−0.609190	+	0.485813i	0.269632	+	0.962964i	$0.413098\pi$
$588$	−182.133	+	482.246i	−0.309751	+	0.820147i
$589$	−65.1885	+	81.7437i	−0.110677	+	0.138784i
$590$	332.050	+	7.09746i	0.562797	+	0.0120296i
$591$	−414.455	−	700.464i	−0.701278	−	1.18522i
$592$	−130.201	+	149.672i	−0.219935	+	0.252824i
$593$	−789.547	−	369.885i	−1.33144	−	0.623752i	−0.378136	−	0.925750i	$-0.623435\pi$
$593$	−789.547	−	369.885i	−1.33144	−	0.623752i	−0.953309	+	0.301998i	$0.902346\pi$
$594$	397.482	+	277.266i	0.669161	+	0.466778i
$595$	41.4011	+	38.3300i	0.0695816	+	0.0644202i
$596$	−268.294	−	151.101i	−0.450159	−	0.253525i
$597$	213.554	+	511.695i	0.357713	+	0.857111i
$598$	−657.093	+	806.145i	−1.09882	+	1.34807i
$599$	148.055	+	105.646i	0.247170	+	0.176371i	0.697700	−	0.716390i	$-0.254207\pi$
$599$	148.055	+	105.646i	0.247170	+	0.176371i	−0.450529	+	0.892762i	$0.648765\pi$
$600$	−485.916	−	354.628i	−0.809860	−	0.591046i
$601$	−18.0237	−	139.788i	−0.0299894	−	0.232592i	0.969953	−	0.243291i	$-0.0782270\pi$
$601$	−18.0237	−	139.788i	−0.0299894	−	0.232592i	−0.999943	+	0.0106989i	$0.996594\pi$
$602$	−50.1510	+	3.27515i	−0.0833073	+	0.00544044i
$603$	−112.873	−	1170.05i	−0.187186	−	1.94037i
$604$	26.2316	+	187.617i	0.0434298	+	0.310624i
$605$	19.0352	−	177.458i	0.0314631	−	0.293320i
$606$	660.814	+	203.834i	1.09045	+	0.336360i
$607$	54.9451	−	4.11756i	0.0905190	−	0.00678346i	−0.0293936	−	0.999568i	$-0.509358\pi$
$607$	54.9451	−	4.11756i	0.0905190	−	0.00678346i	0.119913	+	0.992784i	$0.461739\pi$
$608$	−44.0489	+	167.977i	−0.0724488	+	0.276279i
$609$	−1192.28	+	90.6667i	−1.95776	+	0.148878i
$610$	−298.372	+	674.028i	−0.489135	+	1.10496i
$611$	−1423.20	−	1438.49i	−2.32930	−	2.35433i
$612$	31.5990	−	26.3235i	0.0516324	−	0.0430122i
$613$	78.5243	+	313.043i	0.128098	+	0.510674i	0.999787	+	0.0206146i	$0.00656228\pi$
$613$	78.5243	+	313.043i	0.128098	+	0.510674i	−0.871689	+	0.490059i	$0.836975\pi$
$614$	21.3851	+	199.366i	0.0348292	+	0.324701i
$615$	−70.8324	+	363.709i	−0.115175	+	0.591397i
$616$	8.43267	+	715.531i	0.0136894	+	1.16158i
$617$	−265.575	+	509.057i	−0.430429	+	0.825052i	0.569566	+	0.821945i	$0.307111\pi$
$617$	−265.575	+	509.057i	−0.430429	+	0.825052i	−0.999995	+	0.00310632i	$0.999011\pi$
$618$	−257.805	+	239.208i	−0.417161	+	0.387069i
$619$	−12.7641	−	84.6843i	−0.0206205	−	0.136808i	0.976152	−	0.217089i	$-0.0696563\pi$
$619$	−12.7641	−	84.6843i	−0.0206205	−	0.136808i	−0.996772	+	0.0802811i	$0.974418\pi$
$620$	−205.553	−	127.631i	−0.331538	−	0.205856i
$621$	474.303	−	801.611i	0.763773	−	1.29084i
$622$	−95.4192	−	287.387i	−0.153407	−	0.462038i
$623$	646.057	+	336.145i	1.03701	+	0.539558i
$624$	−31.2923	+	324.377i	−0.0501479	+	0.519835i
$625$	−775.736	+	33.1773i	−1.24118	+	0.0530837i
$626$	−105.263	+	609.668i	−0.168152	+	0.973910i
$627$	148.478	+	316.937i	0.236807	+	0.505482i
$628$	−16.1569	+	56.6503i	−0.0257275	+	0.0902075i
$629$	87.4420	+	25.9523i	0.139017	+	0.0412597i
$630$	882.339	−	163.072i	1.40054	−	0.258844i
$631$	464.794	+	511.790i	0.736599	+	0.811078i	0.987614	−	0.156906i	$-0.0501519\pi$
$631$	464.794	+	511.790i	0.736599	+	0.811078i	−0.251014	+	0.967983i	$0.580764\pi$
$632$	−552.545	+	132.342i	−0.874280	+	0.209402i
$633$	1123.70	+	307.538i	1.77519	+	0.485842i
$634$	50.2225	−	4.30378i	0.0792153	−	0.00678830i
$635$	797.392	+	664.266i	1.25574	+	1.04609i
$636$	195.996	−	406.989i	0.308169	−	0.639920i
$637$	−777.038	+	878.075i	−1.21984	+	1.37845i
$638$	−522.709	+	251.723i	−0.819293	+	0.394551i
$639$	−270.126	+	1076.88i	−0.422732	+	1.68525i
$640$	−303.528	−	42.4375i	−0.474262	−	0.0663087i
$641$	−681.867	−	29.1626i	−1.06375	−	0.0454955i	−0.495706	−	0.868490i	$-0.665091\pi$
$641$	−681.867	−	29.1626i	−1.06375	−	0.0454955i	−0.568049	+	0.822995i	$0.692301\pi$
$642$	152.878	−	704.414i	0.238127	−	1.09722i
$643$	−801.525	−	129.584i	−1.24654	−	0.201531i	−0.499502	−	0.866313i	$-0.666484\pi$
$643$	−801.525	−	129.584i	−1.24654	−	0.201531i	−0.747037	+	0.664782i	$0.768524\pi$
$644$	478.903	−	41.5695i	0.743638	−	0.0645489i
$645$	−93.1099	−	133.480i	−0.144356	−	0.206946i
$646$	−10.0355	+	1.73270i	−0.0155349	+	0.00268220i
$647$	−31.2817	−	144.137i	−0.0483488	−	0.222777i	0.946707	−	0.322097i	$-0.104388\pi$
$647$	−31.2817	−	144.137i	−0.0483488	−	0.222777i	−0.995056	+	0.0993200i	$0.968333\pi$
$648$	−3.61130	−	67.5269i	−0.00557299	−	0.104208i
$649$	187.048	−	435.045i	0.288210	−	0.670332i
$650$	−260.906	−	400.821i	−0.401394	−	0.616648i
$651$	591.977	−	155.930i	0.909335	−	0.239524i
$652$	−146.328	+	397.620i	−0.224429	+	0.609846i
$653$	−630.382	−	54.0201i	−0.965362	−	0.0827261i	−0.407988	−	0.912987i	$-0.633769\pi$
$653$	−630.382	−	54.0201i	−0.965362	−	0.0827261i	−0.557374	+	0.830261i	$0.688191\pi$
$654$	−195.855	−	193.773i	−0.299473	−	0.296289i
$655$	388.620	+	990.188i	0.593313	+	1.51174i
$656$	−9.85521	−	31.9498i	−0.0150232	−	0.0487040i
$657$	−20.0675	−	103.042i	−0.0305441	−	0.156838i
$658$	16.3238	−	805.111i	0.0248082	−	1.22357i
$659$	−734.193	+	625.028i	−1.11410	+	0.948449i	−0.998991	−	0.0449035i	$-0.985702\pi$
$659$	−734.193	+	625.028i	−1.11410	+	0.948449i	−0.115111	+	0.993353i	$0.536722\pi$
$660$	−688.085	+	427.242i	−1.04255	+	0.647336i
$661$	−4.60330	−	215.363i	−0.00696414	−	0.325814i	−0.989892	−	0.141823i	$-0.954704\pi$
$661$	−4.60330	−	215.363i	−0.00696414	−	0.325814i	0.982928	−	0.183991i	$-0.0589017\pi$
$662$	−105.713	+	138.532i	−0.159687	+	0.209263i
$663$	141.691	−	48.7317i	0.213712	−	0.0735018i
$664$	−230.537	−	879.138i	−0.347194	−	1.32400i
$665$	243.218	+	86.2661i	0.365742	+	0.129723i
$666$	1162.53	−	867.616i	1.74554	−	1.30273i
$667$	557.511	+	965.638i	0.835849	+	1.44773i
$668$	−53.5881	−	30.9391i	−0.0802217	−	0.0463160i
$669$	176.305	+	1493.01i	0.263535	+	2.23171i
$670$	−641.510	−	205.412i	−0.957478	−	0.306585i
$671$	731.158	+	754.981i	1.08965	+	1.12516i
$672$	794.244	−	634.818i	1.18191	−	0.944669i
$673$	−196.068	+	323.435i	−0.291334	+	0.480586i	−0.966355	−	0.257213i	$-0.917196\pi$
$673$	−196.068	+	323.435i	−0.291334	+	0.480586i	0.675021	+	0.737799i	$0.264135\pi$
$674$	153.048	−	833.223i	0.227074	−	1.23624i
$675$	284.553	+	320.132i	0.421561	+	0.474270i
$676$	384.720	−	777.516i	0.569113	−	1.15017i
$677$	−1105.34	−	59.1128i	−1.63270	−	0.0873158i	−0.785596	−	0.618740i	$-0.787644\pi$
$677$	−1105.34	−	59.1128i	−1.63270	−	0.0873158i	−0.847106	+	0.531424i	$0.821657\pi$
$678$	−652.386	+	105.473i	−0.962222	+	0.155565i
$679$	19.8089	+	881.409i	0.0291736	+	1.29810i
$680$	−19.1845	−	64.6388i	−0.0282124	−	0.0950571i
$681$	13.9770	+	1307.96i	0.0205243	+	1.92065i
$682$	239.924	−	175.099i	0.351794	−	0.256744i
$683$	−421.860	−	445.023i	−0.617657	−	0.651571i	0.339682	−	0.940541i	$-0.389681\pi$
$683$	−421.860	−	445.023i	−0.617657	−	0.651571i	−0.957338	+	0.288969i	$0.906688\pi$
$684$	85.2224	−	167.701i	0.124594	−	0.245177i
$685$			1018.56i			1.48694i
$686$	−466.111	+	21.4748i	−0.679462	+	0.0313043i
$687$	−1330.95			−1.93733
$688$	13.0917	+	6.65292i	0.0190286	+	0.00966995i
$689$	745.680	−	706.867i	1.08226	−	1.02593i
$690$	−790.081	−	1082.58i	−1.14505	−	1.56896i
$691$	533.280	−	5.69868i	0.771751	−	0.00824700i	0.376018	−	0.926613i	$-0.377293\pi$
$691$	533.280	−	5.69868i	0.771751	−	0.00824700i	0.395733	+	0.918366i	$0.370491\pi$
$692$	269.192	−	79.8948i	0.389006	−	0.115455i
$693$	256.588	−	1253.37i	0.370257	−	1.80861i
$694$	12.6217	+	78.0698i	0.0181869	+	0.112492i
$695$	33.2303	−	621.367i	0.0478133	−	0.894053i
$696$	1280.75	+	633.725i	1.84016	+	0.910525i
$697$	−11.4902	+	10.2132i	−0.0164852	+	0.0146530i
$698$	718.274	+	131.934i	1.02905	+	0.189017i
$699$	806.411	+	488.851i	1.15366	+	0.699358i
$700$	−48.9521	+	215.565i	−0.0699316	+	0.307950i
$701$	−865.055	+	837.759i	−1.23403	+	1.19509i	−0.260767	+	0.965402i	$0.583975\pi$
$701$	−865.055	+	837.759i	−1.23403	+	1.19509i	−0.973264	+	0.229690i	$0.926229\pi$
$702$	289.396	−	903.794i	0.412244	−	1.28746i
$703$	414.322	−	48.9260i	0.589362	−	0.0695960i
$704$	314.671	−	545.026i	0.446976	−	0.774185i
$705$	2258.31	−	1303.83i	3.20327	−	1.84941i
$706$	−43.1827	−	57.8609i	−0.0611653	−	0.0819559i
$707$	−78.3340	−	722.791i	−0.110798	−	1.02233i
$708$	−394.350	+	103.411i	−0.556992	+	0.146060i
$709$	−421.682	−	1226.07i	−0.594756	−	1.72930i	−0.680272	−	0.732959i	$-0.738139\pi$
$709$	−421.682	−	1226.07i	−0.594756	−	1.72930i	0.0855169	−	0.996337i	$-0.472746\pi$
$710$	505.772	+	385.950i	0.712355	+	0.543592i
$711$	1015.58	−	21.7077i	1.42839	−	0.0305313i
$712$	−459.101	−	739.396i	−0.644805	−	1.03848i
$713$	−370.044	−	434.675i	−0.518996	−	0.609642i
$714$	53.1873	+	26.9552i	0.0744920	+	0.0377524i
$715$	−1808.27	+	352.161i	−2.52905	+	0.492533i
$716$	−52.3483	+	16.1473i	−0.0731121	+	0.0225521i
$717$	385.247	−	151.198i	0.537304	−	0.210876i
$718$	554.603	−	560.561i	0.772427	−	0.780726i
$719$	−43.0224	+	502.044i	−0.0598364	+	0.698253i	0.903259	+	0.429095i	$0.141167\pi$
$719$	−43.0224	+	502.044i	−0.0598364	+	0.698253i	−0.963096	+	0.269159i	$0.913254\pi$
$720$	−246.049	−	90.5485i	−0.341735	−	0.125762i
$721$	338.254	+	149.291i	0.469145	+	0.207060i
$722$	372.539	−	242.496i	0.515983	−	0.335867i
$723$	−73.3544	−	31.5388i	−0.101458	−	0.0436221i
$724$	−441.984	+	23.6370i	−0.610476	+	0.0326478i
$725$	−501.082	+	108.749i	−0.691148	+	0.149998i
$726$	−32.0922	−	185.873i	−0.0442041	−	0.256023i
$727$	−265.986	+	185.540i	−0.365868	+	0.255214i	−0.740638	−	0.671904i	$-0.765477\pi$
$727$	−265.986	+	185.540i	−0.365868	+	0.255214i	0.374770	+	0.927118i	$0.377722\pi$
$728$	1334.02	−	428.772i	1.83245	−	0.588972i
$729$	185.664	−	1148.40i	0.254683	−	1.57531i
$730$	−58.7880	−	12.7587i	−0.0805316	−	0.0174776i
$731$	0.288513	−	6.74587i	0.000394682	−	0.00922828i
$732$	125.286	−	896.091i	0.171156	−	1.22417i
$733$	−570.879	−	143.200i	−0.778826	−	0.195362i	−0.166578	−	0.986028i	$-0.553272\pi$
$733$	−570.879	−	143.200i	−0.778826	−	0.195362i	−0.612248	+	0.790666i	$0.709734\pi$
$734$	−80.5574	−	167.279i	−0.109751	−	0.227901i
$735$	−840.535	−	1255.61i	−1.14359	−	1.70831i
$736$	−854.251	−	411.386i	−1.16067	−	0.558948i
$737$	−614.724	+	737.922i	−0.834090	+	1.00125i
$738$	20.8747	+	243.594i	0.0282855	+	0.330074i
$739$	77.1412	−	281.862i	0.104386	−	0.381410i	−0.893295	−	0.449470i	$-0.851613\pi$
$739$	77.1412	−	281.862i	0.104386	−	0.381410i	0.997681	+	0.0680597i	$0.0216808\pi$
$740$	224.882	+	938.909i	0.303894	+	1.26880i
$741$	507.349	−	460.761i	0.684681	−	0.621809i
$742$	408.529	+	17.0226i	0.550578	+	0.0229414i
$743$	−293.183	+	987.830i	−0.394593	+	1.32952i	0.493458	+	0.869770i	$0.335733\pi$
$743$	−293.183	+	987.830i	−0.394593	+	1.32952i	−0.888051	+	0.459745i	$0.847941\pi$
$744$	−703.527	−	200.649i	−0.945601	−	0.269689i
$745$	817.302	−	382.888i	1.09705	−	0.513943i
$746$	−246.129	−	42.4958i	−0.329931	−	0.0569648i
$747$	69.4325	+	1623.44i	0.0929485	+	2.17328i
$748$	−33.4475	−	3.22664i	−0.0447159	−	0.00431369i
$749$	−743.667	+	145.677i	−0.992879	+	0.194496i
$750$	−410.377	+	136.255i	−0.547169	+	0.181673i
$751$	787.195	+	465.773i	1.04820	+	0.620204i	0.928013	−	0.372548i	$-0.121516\pi$
$751$	787.195	+	465.773i	1.04820	+	0.620204i	0.120183	+	0.992752i	$0.461652\pi$
$752$	−124.120	+	199.899i	−0.165053	+	0.265823i
$753$	−1170.19	+	176.378i	−1.55404	+	0.234233i
$754$	772.719	+	832.793i	1.02483	+	1.10450i
$755$	−492.308	−	256.837i	−0.652064	−	0.340181i
$756$	−392.924	+	194.959i	−0.519740	+	0.257882i
$757$	1098.99	+	214.028i	1.45177	+	0.282732i	0.854560	−	0.519353i	$-0.173827\pi$
$757$	1098.99	+	214.028i	1.45177	+	0.282732i	0.597209	+	0.802085i	$0.296276\pi$
$758$	426.051	−	45.7005i	0.562072	−	0.0602910i
$759$	−1853.50	+	464.935i	−2.44203	+	0.612563i
$760$	−197.395	−	236.955i	−0.259730	−	0.311783i
$761$	343.681	−	340.028i	0.451618	−	0.446818i	−0.441083	−	0.897466i	$-0.645406\pi$
$761$	343.681	−	340.028i	0.451618	−	0.446818i	0.892702	+	0.450648i	$0.148807\pi$
$762$	1002.95	+	443.978i	1.31621	+	0.582648i
$763$	−105.525	+	269.744i	−0.138303	+	0.353531i
$764$	146.139	+	38.3220i	0.191281	+	0.0501597i
$765$	9.00856	+	120.211i	0.0117759	+	0.157138i
$766$	140.025	−	453.950i	0.182800	−	0.592624i
$767$	−922.010	−	98.8999i	−1.20210	−	0.128944i
$768$	−1319.36	+	184.465i	−1.71791	+	0.240189i
$769$	−236.150	+	22.7811i	−0.307087	+	0.0296243i	−0.248417	−	0.968653i	$-0.579910\pi$
$769$	−236.150	+	22.7811i	−0.307087	+	0.0296243i	−0.0586696	+	0.998277i	$0.518686\pi$
$770$	−601.748	−	418.771i	−0.781491	−	0.543859i
$771$	475.996	−	61.3729i	0.617375	−	0.0796017i
$772$	−270.804	+	371.060i	−0.350782	+	0.480647i
$773$	−833.391	+	1167.93i	−1.07812	+	1.51091i	−0.235902	+	0.971777i	$0.575804\pi$
$773$	−833.391	+	1167.93i	−1.07812	+	1.51091i	−0.842223	+	0.539129i	$0.818753\pi$
$774$	−83.2340	−	67.8445i	−0.107537	−	0.0876544i
$775$	242.258	−	101.105i	0.312591	−	0.130459i
$776$	517.023	−	918.027i	0.666267	−	1.18302i
$777$	−2116.80	−	1219.04i	−2.72433	−	1.56890i
$778$	−11.0868	+	15.8937i	−0.0142504	+	0.0204290i
$779$	−29.8303	+	63.6750i	−0.0382931	+	0.0817393i
$780$	1196.60	+	1040.94i	1.53410	+	1.33453i
$781$	780.698	−	461.928i	0.999613	−	0.591458i
$782$	1.18823	−	55.5908i	0.00151948	−	0.0710880i
$783$	−795.462	−	634.360i	−1.01592	−	0.810166i
$784$	120.340	+	64.0863i	0.153494	+	0.0817427i
$785$	−107.658	−	134.999i	−0.137144	−	0.171973i
$786$	681.980	+	893.707i	0.867659	+	1.13703i
$787$	−977.284	−	651.114i	−1.24178	−	0.827337i	−0.251699	−	0.967806i	$-0.580989\pi$
$787$	−977.284	−	651.114i	−1.24178	−	0.827337i	−0.990085	+	0.140469i	$0.955139\pi$
$788$	328.354	−	141.176i	0.416693	−	0.179157i
$789$	1031.03	−	510.161i	1.30676	−	0.646592i
$790$	218.444	−	539.560i	0.276511	−	0.682987i
$791$	373.421	+	585.884i	0.472087	+	0.740688i
$792$	−1027.89	+	1131.82i	−1.29784	+	1.42907i
$793$	990.695	−	1803.89i	1.24930	−	2.27477i
$794$	−52.4582	+	219.020i	−0.0660683	+	0.275843i
$795$	637.374	+	1160.55i	0.801728	+	1.45982i
$796$	−234.856	+	64.2764i	−0.295046	+	0.0807492i
$797$	750.380	−	276.147i	0.941506	−	0.346483i	0.171981	−	0.985100i	$-0.444983\pi$
$797$	750.380	−	276.147i	0.941506	−	0.346483i	0.769524	+	0.638617i	$0.220493\pi$
$798$	272.194	+	17.1751i	0.341095	+	0.0215227i
$799$	107.299	+	13.8347i	0.134292	+	0.0173150i
$800$	299.960	−	316.430i	0.374950	−	0.395537i
$801$	521.767	+	1465.95i	0.651394	+	1.83015i
$802$	−531.302	−	492.977i	−0.662472	−	0.614684i
$803$	−48.3173	+	70.8685i	−0.0601710	+	0.0882547i
$804$	826.410	+	26.5013i	1.02787	+	0.0329619i
$805$	−716.165	+	1213.42i	−0.889646	+	1.50735i
$806$	−466.123	−	347.877i	−0.578316	−	0.431609i
$807$	37.6674	−	318.980i	0.0466758	−	0.395267i
$808$	−360.161	+	790.673i	−0.445743	+	0.978556i
$809$	82.8091	−	402.250i	0.102360	−	0.497219i	−0.896204	−	0.443642i	$-0.853686\pi$
$809$	82.8091	−	402.250i	0.102360	−	0.497219i	0.998564	−	0.0535770i	$-0.0170622\pi$
$810$	58.4643	+	37.1727i	0.0721782	+	0.0458923i
$811$	674.045	−	21.6153i	0.831128	−	0.0266526i	0.386414	−	0.922325i	$-0.373714\pi$
$811$	674.045	−	21.6153i	0.831128	−	0.0266526i	0.444714	+	0.895673i	$0.353305\pi$
$812$	27.4654	−	524.377i	0.0338244	−	0.645784i
$813$	−303.801	−	258.629i	−0.373678	−	0.318117i
$814$	−1171.97	−	176.646i	−1.43977	−	0.217010i
$815$	−699.580	−	1026.09i	−0.858380	−	1.25901i
$816$	−9.34827	−	14.7027i	−0.0114562	−	0.0180180i
$817$	−10.9752	−	28.8676i	−0.0134335	−	0.0353337i
$818$	−192.778	+	116.863i	−0.235671	+	0.142865i
$819$	−2493.38	+	243.299i	−3.04442	+	0.297068i
$820$	−154.432	−	51.2750i	−0.188332	−	0.0625305i
$821$	467.174	+	537.035i	0.569030	+	0.654123i	0.964415	−	0.264392i	$-0.0851712\pi$
$821$	467.174	+	537.035i	0.569030	+	0.654123i	−0.395385	+	0.918515i	$0.629389\pi$
$822$	295.239	+	1035.18i	0.359171	+	1.25935i
$823$	7.00880	−	655.881i	0.00851617	−	0.796939i	−0.912861	−	0.408270i	$-0.866132\pi$
$823$	7.00880	−	655.881i	0.00851617	−	0.796939i	0.921377	−	0.388669i	$-0.127065\pi$
$824$	−256.651	−	359.676i	−0.311470	−	0.436500i
$825$	56.3013	−	876.939i	0.0682440	−	1.06296i
$826$	−227.304	−	290.704i	−0.275186	−	0.351942i
$827$	1188.81	−	669.525i	1.43750	−	0.809583i	0.441354	−	0.897333i	$-0.354498\pi$
$827$	1188.81	−	669.525i	1.43750	−	0.809583i	0.996143	+	0.0877500i	$0.0279677\pi$
$828$	809.797	+	631.755i	0.978016	+	0.762989i
$829$	1007.27	−	185.016i	1.21504	−	0.223180i	0.465443	−	0.885078i	$-0.345895\pi$
$829$	1007.27	−	185.016i	1.21504	−	0.223180i	0.749594	+	0.661898i	$0.230249\pi$
$830$	870.362	+	330.903i	1.04863	+	0.398679i
$831$	−585.963	+	120.629i	−0.705129	+	0.145161i
$832$	−1201.47	−	274.227i	−1.44407	−	0.329599i
$833$	3.87890	−	62.5674i	0.00465654	−	0.0751109i
$834$	−146.337	−	641.143i	−0.175464	−	0.768756i
$835$	165.055	−	75.1845i	0.197671	−	0.0900413i
$836$	−146.377	+	46.8700i	−0.175092	+	0.0560646i
$837$	459.222	+	245.854i	0.548652	+	0.293732i
$838$	−78.6704	−	96.5156i	−0.0938788	−	0.115174i
$839$	44.2405	+	689.082i	0.0527301	+	0.821313i	0.935901	+	0.352263i	$0.114588\pi$
$839$	44.2405	+	689.082i	0.0527301	+	0.821313i	−0.883171	+	0.469051i	$0.844596\pi$
$840$	98.4119	+	1803.03i	0.117157	+	2.14646i
$841$	349.440	−	141.473i	0.415506	−	0.168220i
$842$	−105.621	−	93.8825i	−0.125441	−	0.111499i
$843$	−26.5401	−	34.0197i	−0.0314829	−	0.0403556i
$844$	−197.048	+	472.145i	−0.233469	+	0.559413i
$845$	1200.13	+	2241.68i	1.42027	+	2.65287i
$846$	1196.96	−	1235.96i	1.41485	−	1.46095i
$847$	−166.076	+	108.363i	−0.196075	+	0.127938i
$848$	−100.130	−	65.1773i	−0.118078	−	0.0768600i
$849$	−1433.60	−	2151.75i	−1.68858	−	2.53445i
$850$	24.1794	+	8.31600i	0.0284463	+	0.00978352i
$851$	−170.225	+	2271.50i	−0.200030	+	2.66921i
$852$	−726.961	−	285.311i	−0.853241	−	0.334872i
$853$	891.845	−	394.793i	1.04554	−	0.462829i	0.190660	−	0.981656i	$-0.438937\pi$
$853$	891.845	−	394.793i	1.04554	−	0.462829i	0.854879	+	0.518827i	$0.173631\pi$
$854$	789.709	−	217.064i	0.924717	−	0.254173i
$855$	255.035	+	488.855i	0.298287	+	0.571760i
$856$	853.189	+	303.670i	0.996716	+	0.354755i
$857$	−463.279	−	911.643i	−0.540582	−	1.06376i	−0.985735	−	0.168306i	$-0.946170\pi$
$857$	−463.279	−	911.643i	−0.540582	−	1.06376i	0.445152	−	0.895455i	$-0.353150\pi$
$858$	−1735.72	+	882.057i	−2.02298	+	1.02804i
$859$	41.9311	−	117.809i	0.0488139	−	0.137147i	−0.915199	−	0.403001i	$-0.867967\pi$
$859$	41.9311	−	117.809i	0.0488139	−	0.137147i	0.964013	+	0.265854i	$0.0856540\pi$
$860$	63.3646	−	33.0573i	0.0736798	−	0.0384387i
$861$	362.746	−	194.717i	0.421308	−	0.226152i
$862$	−300.320	−	678.429i	−0.348399	−	0.787040i
$863$	304.733	−	776.448i	0.353109	−	0.899707i	−0.638404	−	0.769701i	$-0.720405\pi$
$863$	304.733	−	776.448i	0.353109	−	0.899707i	0.991513	−	0.130006i	$-0.0414997\pi$
$864$	862.745	+	64.6538i	0.998548	+	0.0748308i
$865$	−267.683	+	778.307i	−0.309460	+	0.899777i
$866$	−24.2355	+	16.1469i	−0.0279856	+	0.0186454i
$867$	767.297	−	1178.77i	0.885002	−	1.35960i
$868$	34.6704	+	266.586i	0.0399428	+	0.307127i
$869$	−596.210	−	577.397i	−0.686087	−	0.664438i
$870$	−1290.67	+	690.984i	−1.48352	+	0.794235i
$871$	1735.59	+	724.345i	1.99265	+	0.831624i
$872$	272.922	−	212.917i	0.312984	−	0.244171i
$873$	−1251.44	+	1407.92i	−1.43350	+	1.61273i
$874$	−95.4411	−	235.741i	−0.109200	−	0.269727i
$875$	302.384	+	339.440i	0.345582	+	0.387932i
$876$	73.6903	−	4.73107i	0.0841213	−	0.00540077i
$877$	−1014.97	+	827.310i	−1.15732	+	0.943341i	−0.999029	−	0.0440505i	$-0.985974\pi$
$877$	−1014.97	+	827.310i	−1.15732	+	0.943341i	−0.158295	+	0.987392i	$0.550600\pi$
$878$	82.5843	−	154.256i	0.0940596	−	0.175691i
$879$	588.093	+	1836.64i	0.669048	+	2.08946i
$880$	88.7991	+	194.944i	0.100908	+	0.221527i
$881$	−297.394	+	67.8783i	−0.337564	+	0.0770468i	−0.387943	−	0.921683i	$-0.626814\pi$
$881$	−297.394	+	67.8783i	−0.337564	+	0.0770468i	0.0503788	+	0.998730i	$0.483957\pi$
$882$	−760.546	−	644.584i	−0.862297	−	0.730821i
$883$	227.650	−	997.398i	0.257814	−	1.12956i	−0.665769	−	0.746158i	$-0.731897\pi$
$883$	227.650	−	997.398i	0.257814	−	1.12956i	0.923583	−	0.383398i	$-0.125246\pi$
$884$	13.2677	+	64.4487i	0.0150087	+	0.0729057i
$885$	424.660	−	1116.97i	0.479842	−	1.26211i
$886$	−7.04673	−	38.3638i	−0.00795341	−	0.0433000i
$887$	826.653	−	1059.62i	0.931965	−	1.19461i	−0.0486790	−	0.998814i	$-0.515501\pi$
$887$	826.653	−	1059.62i	0.931965	−	1.19461i	0.980644	−	0.195799i	$-0.0627302\pi$
$888$	1432.51	+	2543.56i	1.61318	+	2.86437i
$889$	11.0544	−	1153.06i	0.0124347	−	1.29703i
$890$	889.838	+	57.1295i	0.999818	+	0.0641905i
$891$	80.4102	−	57.3776i	0.0902471	−	0.0643969i
$892$	−660.167	−	7.05460i	−0.740097	−	0.00790875i
$893$	475.869	−	135.720i	0.532888	−	0.151982i
$894$	719.661	−	626.042i	0.804989	−	0.700270i
$895$	50.5978	−	152.393i	0.0565339	−	0.170271i
$896$	176.845	+	291.003i	0.197372	+	0.324780i
$897$	1939.79	+	3199.88i	2.16253	+	3.56732i
$898$	461.655	−	175.517i	0.514092	−	0.195453i
$899$	−526.213	+	334.576i	−0.585331	+	0.372165i
$900$	−390.236	+	266.059i	−0.433596	+	0.295621i
$901$	−8.18729	+	54.3191i	−0.00908689	+	0.0602876i
$902$	129.489	−	152.105i	0.143558	−	0.168631i
$903$	−49.4032	+	173.945i	−0.0547101	+	0.192630i
$904$	−26.6122	−	829.866i	−0.0294382	−	0.917993i
$905$	696.097	−	1094.80i	0.769167	−	1.20973i
$906$	−574.792	−	118.329i	−0.634428	−	0.130606i
$907$	961.243	+	437.857i	1.05980	+	0.482753i	0.866909	−	0.498466i	$-0.166103\pi$
$907$	961.243	+	437.857i	1.05980	+	0.482753i	0.192896	+	0.981219i	$0.438212\pi$
$908$	−570.456	−	67.3634i	−0.628255	−	0.0741887i
$909$	929.084	−	1244.89i	1.02209	−	1.36951i
$910$	−436.278	+	1367.69i	−0.479427	+	1.50295i
$911$	0.0237897	−	0.741851i	2.61138e−5	−	0.000814326i	−0.999473	−	0.0324587i	$-0.989666\pi$
$911$	0.0237897	−	0.741851i	2.61138e−5	−	0.000814326i	0.999499	+	0.0316444i	$0.0100744\pi$
$912$	−65.8447	−	44.8922i	−0.0721981	−	0.0492239i
$913$	903.026	−	973.230i	0.989075	−	1.06597i
$914$	−720.899	+	256.585i	−0.788730	+	0.280727i
$915$	1924.74	+	1824.56i	2.10354	+	1.99405i
$916$	74.7415	−	579.680i	0.0815955	−	0.632838i
$917$	578.837	−	1030.43i	0.631229	−	1.12370i
$918$	17.5228	+	47.6151i	0.0190880	+	0.0518683i
$919$	231.677	+	846.513i	0.252097	+	0.921124i	0.973515	+	0.228624i	$0.0734227\pi$
$919$	231.677	+	846.513i	0.252097	+	0.921124i	−0.721418	+	0.692500i	$0.756509\pi$
$920$	1475.91	−	810.567i	1.60425	−	0.881051i
$921$	701.580	+	168.038i	0.761759	+	0.182452i
$922$	763.443	+	419.281i	0.828029	+	0.454752i
$923$	−1314.96	−	1194.21i	−1.42466	−	1.29384i
$924$	851.304	+	291.742i	0.921325	+	0.315739i
$925$	−970.932	−	393.087i	−1.04966	−	0.424959i
$926$	85.5629	+	172.922i	0.0924005	+	0.186741i
$927$	312.033	+	725.742i	0.336605	+	0.782893i
$928$	−574.257	+	861.926i	−0.618811	+	0.928800i
$929$	897.608	−	684.957i	0.966209	−	0.737305i	0.00132941	−	0.999999i	$-0.499577\pi$
$929$	897.608	−	684.957i	0.966209	−	0.737305i	0.964879	+	0.262694i	$0.0846108\pi$
$930$	585.995	−	467.315i	0.630102	−	0.502490i
$931$	−96.7392	−	269.918i	−0.103909	−	0.289923i
$932$	−258.200	+	323.772i	−0.277038	+	0.347395i
$933$	−1089.26	−	23.2825i	−1.16748	−	0.0249544i
$934$	−161.867	−	273.569i	−0.173305	−	0.292901i
$935$	64.6441	−	74.3111i	0.0691381	−	0.0794771i
$936$	2711.13	+	1270.11i	2.89651	+	1.35695i
$937$	320.012	+	223.226i	0.341528	+	0.238235i	0.730343	−	0.683081i	$-0.239360\pi$
$937$	320.012	+	223.226i	0.341528	+	0.238235i	−0.388815	+	0.921316i	$0.627115\pi$
$938$	274.194	+	696.383i	0.292317	+	0.742413i
$939$	1939.56	+	1092.34i	2.06556	+	1.16330i
$940$	441.053	+	1056.80i	0.469205	+	1.12426i
$941$	−473.105	+	580.422i	−0.502768	+	0.616814i	−0.962512	−	0.271238i	$-0.912567\pi$
$941$	−473.105	+	580.422i	−0.502768	+	0.616814i	0.459744	+	0.888051i	$0.347941\pi$
$942$	−148.546	−	105.997i	−0.157693	−	0.112523i
$943$	−310.113	−	226.324i	−0.328858	−	0.240005i
$944$	13.7885	+	106.941i	0.0146065	+	0.113285i
$945$	203.800	−	1269.43i	0.215661	−	1.34331i
$946$	8.42467	+	87.3306i	0.00890557	+	0.0923156i
$947$	110.428	+	789.819i	0.116608	+	0.834022i	0.956596	+	0.291417i	$0.0941267\pi$
$947$	110.428	+	789.819i	0.116608	+	0.834022i	−0.839988	+	0.542605i	$0.817438\pi$
$948$	−76.2070	+	710.452i	−0.0803871	+	0.749422i
$949$	160.496	+	49.5064i	0.169121	+	0.0521669i
$950$	116.627	−	8.73997i	0.122765	−	0.00919997i
$951$	46.0027	−	175.428i	0.0483730	−	0.184467i
$952$	−42.1334	+	61.9445i	−0.0442577	+	0.0650677i
$953$	−90.3927	+	204.199i	−0.0948507	+	0.214269i	−0.955540	−	0.294861i	$-0.904727\pi$
$953$	−90.3927	+	204.199i	−0.0948507	+	0.214269i	0.860690	+	0.509130i	$0.170033\pi$
$954$	614.437	+	621.038i	0.644064	+	0.650983i
$955$	−340.241	+	283.437i	−0.356273	+	0.296793i
$956$	44.2187	+	176.281i	0.0462539	+	0.184395i
$957$	222.628	+	2075.48i	0.232631	+	2.16874i
$958$	68.1099	−	349.730i	0.0710959	−	0.365063i
$959$	876.423	−	715.982i	0.913893	−	0.746592i
$960$	734.554	−	1408.00i	0.765160	−	1.46667i
$961$	−470.438	+	436.503i	−0.489530	+	0.454217i
$962$	345.905	+	2294.93i	0.359568	+	2.38558i
$963$	−1375.54	−	854.089i	−1.42839	−	0.886905i
$964$	17.8557	−	30.1777i	0.0185225	−	0.0313046i
$965$	−424.283	−	1277.87i	−0.439671	−	1.32422i
$966$	−376.135	+	1440.82i	−0.389374	+	1.49153i
$967$	168.137	−	1742.91i	0.173875	−	1.80239i	−0.335702	−	0.941968i	$-0.608974\pi$
$967$	168.137	−	1742.91i	0.173875	−	1.80239i	0.509577	−	0.860425i	$-0.329802\pi$
$968$	236.767	−	10.1262i	0.244594	−	0.0104610i
$969$	−6.23414	+	36.1072i	−0.00643359	+	0.0372623i
$970$	457.931	+	977.487i	0.472094	+	1.00772i
$971$	48.2043	−	169.017i	0.0496440	−	0.174065i	−0.932885	−	0.360174i	$-0.882717\pi$
$971$	48.2043	−	169.017i	0.0496440	−	0.174065i	0.982529	+	0.186110i	$0.0595879\pi$
$972$	459.118	+	136.264i	0.472344	+	0.140189i
$973$	−558.017	+	408.189i	−0.573502	+	0.419516i
$974$	−395.611	−	435.612i	−0.406172	−	0.447240i
$975$	−1673.41	+	400.804i	−1.71632	+	0.411081i
$976$	−230.819	−	63.1715i	−0.236495	−	0.0647249i
$977$	−1233.84	+	105.733i	−1.26289	+	0.108222i	−0.697488	−	0.716597i	$-0.745699\pi$
$977$	−1233.84	+	105.733i	−1.26289	+	0.108222i	−0.565397	+	0.824819i	$0.691277\pi$
$978$	−1008.42	−	840.066i	−1.03111	−	0.858963i
$979$	551.623	−	1145.46i	0.563455	−	1.17003i
$980$	594.068	−	295.576i	0.606192	−	0.301608i
$981$	−557.583	+	268.518i	−0.568382	+	0.273718i
$982$	13.6400	−	54.3767i	0.0138900	−	0.0553734i
$983$	1572.71	+	219.888i	1.59991	+	0.223691i	0.881588	−	0.472020i	$-0.156475\pi$
$983$	1572.71	+	219.888i	1.59991	+	0.223691i	0.718322	+	0.695710i	$0.244910\pi$
$984$	−491.562	−	21.0235i	−0.499555	−	0.0213654i
$985$	−222.193	+	1023.80i	−0.225577	+	1.03939i
$986$	−59.9598	−	9.69384i	−0.0608112	−	0.00983148i
$987$	−2709.34	−	1026.66i	−2.74502	−	1.04018i
$988$	172.189	+	246.845i	0.174280	+	0.249843i
$989$	166.162	−	28.6890i	0.168010	−	0.0290081i
$990$	−332.219	−	1530.76i	−0.335575	−	1.54623i
$991$	−82.7299	−	1546.95i	−0.0834812	−	1.56100i	−0.664612	−	0.747189i	$-0.731403\pi$
$991$	−82.7299	−	1546.95i	−0.0834812	−	1.56100i	0.581130	−	0.813811i	$-0.302611\pi$
$992$	209.442	−	487.130i	0.211131	−	0.491059i
$993$	342.037	+	525.461i	0.344448	+	0.529165i
$994$	−23.4331	−	706.493i	−0.0235745	−	0.710758i
$995$	246.490	−	669.792i	0.247728	−	0.673158i
$996$	−1138.80	−	97.5888i	−1.14337	−	0.0979807i
$997$	310.672	+	307.370i	0.311607	+	0.308295i	0.842022	−	0.539443i	$-0.181365\pi$
$997$	310.672	+	307.370i	0.311607	+	0.308295i	−0.530415	+	0.847738i	$0.677964\pi$
$998$	−209.905	−	534.829i	−0.210325	−	0.535900i
$999$	−612.650	−	1986.16i	−0.613264	−	1.98815i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	343.3.l.a.10.23	✓	5376
343.103	odd	294	inner	343.3.l.a.103.23	yes	5376

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
343.3.l.a.10.23	✓	5376	1.1	even	1	trivial
343.3.l.a.103.23	yes	5376	343.103	odd	294	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:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	343.l (of order \(294\), degree \(84\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21275 - 0.616298i) q^{2} +(-3.55216 + 3.36726i) q^{3} +(-1.26710 - 1.73620i) q^{4} +(6.29980 - 0.0673203i) q^{5} +(6.38313 - 1.89448i) q^{6} +(-4.48629 - 5.37338i) q^{7} +(1.33512 + 8.25821i) q^{8} +(0.798710 - 14.9349i) q^{9} +(-7.68160 - 3.80091i) q^{10} +(-9.13348 + 8.11840i) q^{11} +(10.3472 + 1.90059i) q^{12} +(20.4627 + 12.4046i) q^{13} +(2.12917 + 9.28148i) q^{14} +(-22.1512 + 21.4522i) q^{15} +(0.848507 - 2.64992i) q^{16} +(-1.27051 + 0.150031i) q^{17} +(-10.1730 + 17.6202i) q^{18} +(-5.06767 + 2.92582i) q^{19} +(-8.09936 - 10.8524i) q^{20} +(34.0296 + 3.98054i) q^{21} +(16.0800 - 4.21668i) q^{22} +(-10.3909 - 30.2124i) q^{23} +(-32.5501 - 24.8387i) q^{24} +(14.6886 - 0.313964i) q^{25} +(-17.1713 - 27.6549i) q^{26} +(18.8978 + 22.1985i) q^{27} +(-3.64467 + 14.5977i) q^{28} +(-34.2562 + 6.67139i) q^{29} +(40.0849 - 12.3646i) q^{30} +(16.6324 - 6.52773i) q^{31} +(20.8721 - 21.0963i) q^{32} +(5.10675 - 59.5927i) q^{33} +(1.63328 + 0.601062i) q^{34} +(-28.6245 - 33.5492i) q^{35} +(-26.9421 + 17.5373i) q^{36} +(-65.4989 - 28.1613i) q^{37} +(7.94902 - 0.425108i) q^{38} +(-114.456 + 24.8402i) q^{39} +(8.96696 + 51.9352i) q^{40} +(9.85557 - 6.87482i) q^{41} +(-38.8163 - 25.7998i) q^{42} +(-0.842330 + 5.21011i) q^{43} +(25.6682 + 5.57072i) q^{44} +(4.02629 - 94.1408i) q^{45} +(-6.01819 + 43.0441i) q^{46} +(-82.0239 - 20.5750i) q^{47} +(5.90896 + 12.2701i) q^{48} +(-8.74636 + 48.2131i) q^{49} +(-18.0072 - 8.67182i) q^{50} +(4.00785 - 4.81107i) q^{51} +(-4.39143 - 51.2452i) q^{52} +(11.3347 - 41.4153i) q^{53} +(-9.23757 - 38.5680i) q^{54} +(-56.9926 + 51.7591i) q^{55} +(38.3847 - 44.2229i) q^{56} +(8.14914 - 27.4572i) q^{57} +(45.6559 + 13.0212i) q^{58} +(-35.0922 + 16.4399i) q^{59} +(65.3131 + 11.2767i) q^{60} +(-3.67501 - 85.9274i) q^{61} +(-24.1940 - 2.33397i) q^{62} +(-83.8343 + 62.7107i) q^{63} +(-48.8772 + 16.2283i) q^{64} +(129.746 + 76.7690i) q^{65} +(-42.9201 + 69.1240i) q^{66} +(77.7165 - 11.7139i) q^{67} +(1.87035 + 2.01575i) q^{68} +(138.643 + 72.3300i) q^{69} +(14.0382 + 58.3281i) q^{70} +(-72.8634 - 14.1901i) q^{71} +(124.402 - 13.3441i) q^{72} +(6.80809 - 1.70775i) q^{73} +(62.0783 + 74.5195i) q^{74} +(-51.1192 + 50.5758i) q^{75} +(11.5011 + 5.09118i) q^{76} +(84.5987 + 12.6561i) q^{77} +(154.116 + 40.4141i) q^{78} +(5.07560 + 67.7291i) q^{79} +(5.16703 - 16.7511i) q^{80} +(-8.03756 - 0.862152i) q^{81} +(-16.1893 + 2.26350i) q^{82} +(-108.143 + 10.4324i) q^{83} +(-36.2079 - 64.1259i) q^{84} +(-7.99385 + 1.03069i) q^{85} +(4.23252 - 5.79946i) q^{86} +(99.2189 - 139.047i) q^{87} +(-79.2378 - 64.5872i) q^{88} +(-96.0130 + 40.0707i) q^{89} +(-62.9017 + 111.688i) q^{90} +(-25.1470 - 165.604i) q^{91} +(-39.2884 + 56.3228i) q^{92} +(-37.1002 + 79.1931i) q^{93} +(86.7945 + 75.5036i) q^{94} +(-31.7283 + 18.7732i) q^{95} +(-3.10401 + 145.219i) q^{96} +(-98.4697 - 78.5269i) q^{97} +(40.3208 - 53.0803i) q^{98} +(113.953 + 142.892i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5376 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 112 q^{6} - 84 q^{7} - 84 q^{8} - 28 q^{9} - 84 q^{10} - 119 q^{11} - 119 q^{12} - 84 q^{13} + 21 q^{14} - 168 q^{15} - 84 q^{16} - 35 q^{17} - 42 q^{18}+ \cdots + 42 q^{99}+O(q^{100}) \) 5376 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 112 * q^6 - 84 * q^7 - 84 * q^8 - 28 * q^9 - 84 * q^10 - 119 * q^11 - 119 * q^12 - 84 * q^13 + 21 * q^14 - 168 * q^15 - 84 * q^16 - 35 * q^17 - 42 * q^18 - 126 * q^19 - 420 * q^20 - 84 * q^21 + 28 * q^22 - 147 * q^23 - 210 * q^24 - 84 * q^25 - 196 * q^26 + 21 * q^27 + 126 * q^28 - 336 * q^29 - 91 * q^30 - 77 * q^31 - 84 * q^33 - 616 * q^34 + 56 * q^35 + 420 * q^36 - 539 * q^37 - 532 * q^38 - 441 * q^39 - 364 * q^40 - 280 * q^41 - 700 * q^42 - 84 * q^43 - 112 * q^44 - 315 * q^45 - 252 * q^46 - 7 * q^47 - 98 * q^48 - 28 * q^49 + 56 * q^50 + 84 * q^51 + 84 * q^52 + 371 * q^53 + 798 * q^54 + 1267 * q^55 - 42 * q^56 - 735 * q^57 - 868 * q^58 + 1400 * q^59 + 406 * q^60 + 637 * q^61 + 336 * q^62 + 735 * q^63 - 420 * q^64 - 84 * q^65 + 1372 * q^66 - 91 * q^67 - 77 * q^68 + 84 * q^69 - 1078 * q^70 + 679 * q^71 + 273 * q^72 + 294 * q^73 - 1428 * q^74 - 1344 * q^75 - 231 * q^76 - 714 * q^77 + 5040 * q^78 - 91 * q^79 - 1148 * q^80 - 784 * q^81 - 224 * q^82 - 1414 * q^83 - 1246 * q^84 + 364 * q^85 - 1582 * q^86 - 952 * q^87 - 1974 * q^88 - 910 * q^89 - 287 * q^90 + 1456 * q^91 - 6384 * q^92 - 154 * q^93 - 770 * q^94 - 1358 * q^95 - 4284 * q^96 + 3430 * q^97 + 7 * q^98 + 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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