LMFDB - Embedded newform 201.3.k.a.14.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(14,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 8]))

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

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

chi := DirichletCharacter("201.14");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.k (of order $22$, degree $10$, 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:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$44$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			14.6
Character	$\chi$	$=$	201.14
Dual form			201.3.k.a.158.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.89089 + 1.32022i) q^{2} +(0.926782 + 2.85326i) q^{3} +(3.99480 - 4.61025i) q^{4} +(1.94917 - 0.280248i) q^{5} +(-6.44616 - 7.02489i) q^{6} +(-0.497027 - 1.08834i) q^{7} +(-1.88048 + 6.40434i) q^{8} +(-7.28215 + 5.28870i) q^{9} +O(q^{10})$	\(q+(-2.89089 + 1.32022i) q^{2} +(0.926782 + 2.85326i) q^{3} +(3.99480 - 4.61025i) q^{4} +(1.94917 - 0.280248i) q^{5} +(-6.44616 - 7.02489i) q^{6} +(-0.497027 - 1.08834i) q^{7} +(-1.88048 + 6.40434i) q^{8} +(-7.28215 + 5.28870i) q^{9} +(-5.26484 + 3.38351i) q^{10} +(-4.00294 + 0.575536i) q^{11} +(16.8565 + 7.12550i) q^{12} +(-19.7600 + 5.80205i) q^{13} +(2.87370 + 2.49007i) q^{14} +(2.60608 + 5.30175i) q^{15} +(0.453716 + 3.15566i) q^{16} +(-12.0105 + 10.4071i) q^{17} +(14.0696 - 24.9031i) q^{18} +(-0.794782 + 1.74033i) q^{19} +(6.49453 - 10.1057i) q^{20} +(2.64467 - 2.42680i) q^{21} +(10.8122 - 6.94859i) q^{22} +(8.74103 - 13.6013i) q^{23} +(-20.0160 + 0.569925i) q^{24} +(-20.2666 + 5.95081i) q^{25} +(49.4638 - 42.8606i) q^{26} +(-21.8390 - 15.8764i) q^{27} +(-7.00302 - 2.05627i) q^{28} -16.7084i q^{29} +(-14.5334 - 11.8862i) q^{30} +(-13.8311 - 4.06119i) q^{31} +(-19.9123 - 30.9842i) q^{32} +(-5.35200 - 10.8880i) q^{33} +(20.9812 - 45.9423i) q^{34} +(-1.27379 - 1.98206i) q^{35} +(-4.70855 + 54.6998i) q^{36} -13.4489 q^{37} -6.08039i q^{38} +(-34.8679 - 51.0030i) q^{39} +(-1.87058 + 13.0101i) q^{40} +(2.05699 - 1.78239i) q^{41} +(-4.44153 + 10.5072i) q^{42} +(22.3911 + 25.8407i) q^{43} +(-13.3376 + 20.7537i) q^{44} +(-12.7120 + 12.3494i) q^{45} +(-7.31256 + 50.8600i) q^{46} +(-25.4790 + 39.6461i) q^{47} +(-8.58343 + 4.21918i) q^{48} +(31.1507 - 35.9499i) q^{49} +(50.7321 - 43.9596i) q^{50} +(-40.8253 - 24.6238i) q^{51} +(-52.1882 + 114.276i) q^{52} +(45.3907 + 39.3313i) q^{53} +(84.0944 + 17.0645i) q^{54} +(-7.64111 + 2.24363i) q^{55} +(7.90473 - 1.13653i) q^{56} +(-5.70220 - 0.654811i) q^{57} +(22.0589 + 48.3022i) q^{58} +(-5.94552 + 20.2486i) q^{59} +(34.8531 + 9.16479i) q^{60} +(10.7882 - 75.0334i) q^{61} +(45.3459 - 6.51976i) q^{62} +(9.37530 + 5.29681i) q^{63} +(87.7423 + 56.3885i) q^{64} +(-36.8895 + 16.8469i) q^{65} +(29.8467 + 24.4102i) q^{66} +(-28.2074 + 60.7729i) q^{67} +96.9455i q^{68} +(46.9090 + 12.3349i) q^{69} +(6.29916 + 4.04822i) q^{70} +(33.0016 + 28.5961i) q^{71} +(-20.1766 - 56.5826i) q^{72} +(-10.1712 + 70.7422i) q^{73} +(38.8792 - 17.7555i) q^{74} +(-35.7619 - 52.3107i) q^{75} +(4.84835 + 10.6164i) q^{76} +(2.61594 + 4.07049i) q^{77} +(168.135 + 101.411i) q^{78} +(-22.8701 + 6.71528i) q^{79} +(1.76874 + 6.02377i) q^{80} +(25.0594 - 77.0261i) q^{81} +(-3.59337 + 7.86838i) q^{82} +(-163.570 + 23.5178i) q^{83} +(-0.623202 - 21.8871i) q^{84} +(-20.4938 + 23.6511i) q^{85} +(-98.8458 - 45.1414i) q^{86} +(47.6735 - 15.4851i) q^{87} +(3.84153 - 26.7185i) q^{88} +(27.6402 + 43.0090i) q^{89} +(20.4450 - 52.4833i) q^{90} +(16.1358 + 18.6217i) q^{91} +(-27.7867 - 94.6328i) q^{92} +(-1.23084 - 43.2276i) q^{93} +(21.3152 - 148.250i) q^{94} +(-1.06144 + 3.61493i) q^{95} +(69.9514 - 85.5305i) q^{96} +31.4504 q^{97} +(-42.5914 + 145.053i) q^{98} +(26.1062 - 25.3615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 11 q^{3} + 70 q^{4} - 17 q^{6} - 30 q^{7} - 15 q^{9}+O(q^{10}) $ 440 * q - 11 * q^3 + 70 * q^4 - 17 * q^6 - 30 * q^7 - 15 * q^9	$ 440 q - 11 q^{3} + 70 q^{4} - 17 q^{6} - 30 q^{7} - 15 q^{9} - 34 q^{10} - 123 q^{12} + 10 q^{13} + 19 q^{15} - 226 q^{16} - 33 q^{18} - 100 q^{19} + 85 q^{21} - 454 q^{22} - 251 q^{24} + 142 q^{25} - 53 q^{27} + 642 q^{28} - 80 q^{30} - 130 q^{31} + 104 q^{33} + 26 q^{34} + 67 q^{36} - 144 q^{37} + 117 q^{39} - 182 q^{40} + 193 q^{42} - 156 q^{43} + 341 q^{45} - 746 q^{46} - 485 q^{48} - 354 q^{49} - 125 q^{51} + 1130 q^{52} + 272 q^{54} - 590 q^{55} + 15 q^{57} - 274 q^{58} - 217 q^{60} - 1134 q^{61} + 279 q^{63} + 58 q^{64} + 1288 q^{66} - 87 q^{69} + 1038 q^{70} - 977 q^{72} + 1208 q^{73} - 751 q^{75} + 1126 q^{76} - 11 q^{78} + 678 q^{79} + 125 q^{81} + 510 q^{82} + 191 q^{84} + 166 q^{85} + 1080 q^{87} + 62 q^{88} - 105 q^{90} + 550 q^{91} + 635 q^{93} + 986 q^{94} - 1632 q^{96} - 112 q^{97} - 500 q^{99}+O(q^{100}) $ 440 * q - 11 * q^3 + 70 * q^4 - 17 * q^6 - 30 * q^7 - 15 * q^9 - 34 * q^10 - 123 * q^12 + 10 * q^13 + 19 * q^15 - 226 * q^16 - 33 * q^18 - 100 * q^19 + 85 * q^21 - 454 * q^22 - 251 * q^24 + 142 * q^25 - 53 * q^27 + 642 * q^28 - 80 * q^30 - 130 * q^31 + 104 * q^33 + 26 * q^34 + 67 * q^36 - 144 * q^37 + 117 * q^39 - 182 * q^40 + 193 * q^42 - 156 * q^43 + 341 * q^45 - 746 * q^46 - 485 * q^48 - 354 * q^49 - 125 * q^51 + 1130 * q^52 + 272 * q^54 - 590 * q^55 + 15 * q^57 - 274 * q^58 - 217 * q^60 - 1134 * q^61 + 279 * q^63 + 58 * q^64 + 1288 * q^66 - 87 * q^69 + 1038 * q^70 - 977 * q^72 + 1208 * q^73 - 751 * q^75 + 1126 * q^76 - 11 * q^78 + 678 * q^79 + 125 * q^81 + 510 * q^82 + 191 * q^84 + 166 * q^85 + 1080 * q^87 + 62 * q^88 - 105 * q^90 + 550 * q^91 + 635 * q^93 + 986 * q^94 - 1632 * q^96 - 112 * q^97 - 500 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−2.89089	+	1.32022i	−1.44544	+	0.660112i	−0.974977	−	0.222305i	$-0.928642\pi$
$2$	−2.89089	+	1.32022i	−1.44544	+	0.660112i	−0.470467	+	0.882417i	$0.655915\pi$
$3$	0.926782	+	2.85326i	0.308927	+	0.951086i
$3$	0.926782	+	2.85326i	0.308927	+	0.951086i
$4$	3.99480	−	4.61025i	0.998700	−	1.15256i
$5$	1.94917	−	0.280248i	0.389834	−	0.0560496i	0.0553887	−	0.998465i	$-0.482360\pi$
$5$	1.94917	−	0.280248i	0.389834	−	0.0560496i	0.334445	+	0.942415i	$0.391451\pi$
$6$	−6.44616	−	7.02489i	−1.07436	−	1.17081i
$7$	−0.497027	−	1.08834i	−0.0710038	−	0.155477i	0.870802	−	0.491634i	$-0.163600\pi$
$7$	−0.497027	−	1.08834i	−0.0710038	−	0.155477i	−0.941806	+	0.336157i	$0.890873\pi$
$8$	−1.88048	+	6.40434i	−0.235060	+	0.800542i
$9$	−7.28215	+	5.28870i	−0.809128	+	0.587633i
$10$	−5.26484	+	3.38351i	−0.526484	+	0.338351i
$11$	−4.00294	+	0.575536i	−0.363904	+	0.0523214i	−0.321841	−	0.946794i	$-0.604302\pi$
$11$	−4.00294	+	0.575536i	−0.363904	+	0.0523214i	−0.0420621	+	0.999115i	$0.513393\pi$
$12$	16.8565	+	7.12550i	1.40471	+	0.593792i
$13$	−19.7600	+	5.80205i	−1.52000	+	0.446311i	−0.931972	−	0.362531i	$-0.881913\pi$
$13$	−19.7600	+	5.80205i	−1.52000	+	0.446311i	−0.588025	+	0.808843i	$0.700094\pi$
$14$	2.87370	+	2.49007i	0.205264	+	0.177862i
$15$	2.60608	+	5.30175i	0.173738	+	0.353450i
$16$	0.453716	+	3.15566i	0.0283573	+	0.197229i
$17$	−12.0105	+	10.4071i	−0.706497	+	0.612183i	−0.932170	−	0.362020i	$-0.882087\pi$
$17$	−12.0105	+	10.4071i	−0.706497	+	0.612183i	0.225673	+	0.974203i	$0.427542\pi$
$18$	14.0696	−	24.9031i	0.781645	−	1.38351i
$19$	−0.794782	+	1.74033i	−0.0418306	+	0.0915963i	−0.929394	−	0.369090i	$-0.879669\pi$
$19$	−0.794782	+	1.74033i	−0.0418306	+	0.0915963i	0.887563	+	0.460686i	$0.152397\pi$
$20$	6.49453	−	10.1057i	0.324726	−	0.505284i
$21$	2.64467	−	2.42680i	0.125937	−	0.115562i
$22$	10.8122	−	6.94859i	0.491464	−	0.315845i
$23$	8.74103	−	13.6013i	0.380045	−	0.591361i	−0.597557	−	0.801827i	$-0.703862\pi$
$23$	8.74103	−	13.6013i	0.380045	−	0.591361i	0.977601	+	0.210466i	$0.0674980\pi$
$24$	−20.0160	+	0.569925i	−0.834001	+	0.0237469i
$25$	−20.2666	+	5.95081i	−0.810664	+	0.238032i
$26$	49.4638	−	42.8606i	1.90245	−	1.64849i
$27$	−21.8390	−	15.8764i	−0.808851	−	0.588014i
$28$	−7.00302	−	2.05627i	−0.250108	−	0.0734383i
$29$		−	16.7084i		−	0.576153i	−0.957607	−	0.288077i	$-0.906984\pi$
$29$		−	16.7084i		−	0.576153i	0.957607	−	0.288077i	$-0.0930158\pi$
$30$	−14.5334	−	11.8862i	−0.484446	−	0.396206i
$31$	−13.8311	−	4.06119i	−0.446166	−	0.131006i	0.0509292	−	0.998702i	$-0.483782\pi$
$31$	−13.8311	−	4.06119i	−0.446166	−	0.131006i	−0.497095	+	0.867696i	$0.665600\pi$
$32$	−19.9123	−	30.9842i	−0.622260	−	0.968255i
$33$	−5.35200	−	10.8880i	−0.162182	−	0.329940i
$34$	20.9812	−	45.9423i	0.617093	−	1.35124i
$35$	−1.27379	−	1.98206i	−0.0363941	−	0.0566303i
$36$	−4.70855	+	54.6998i	−0.130793	+	1.51944i
$37$	−13.4489			−0.363483			−0.181741	−	0.983346i	$-0.558173\pi$
$37$	−13.4489			−0.363483			−0.181741	+	0.983346i	$0.558173\pi$
$38$		−	6.08039i		−	0.160010i
$39$	−34.8679	−	51.0030i	−0.894049	−	1.30777i
$40$	−1.87058	+	13.0101i	−0.0467644	+	0.325254i
$41$	2.05699	−	1.78239i	0.0501705	−	0.0434730i	−0.629415	−	0.777070i	$-0.716705\pi$
$41$	2.05699	−	1.78239i	0.0501705	−	0.0434730i	0.679585	+	0.733597i	$0.262160\pi$
$42$	−4.44153	+	10.5072i	−0.105751	+	0.250170i
$43$	22.3911	+	25.8407i	0.520724	+	0.600947i	0.953812	−	0.300404i	$-0.0971216\pi$
$43$	22.3911	+	25.8407i	0.520724	+	0.600947i	−0.433088	+	0.901352i	$0.642576\pi$
$44$	−13.3376	+	20.7537i	−0.303127	+	0.471675i
$45$	−12.7120	+	12.3494i	−0.282489	+	0.274430i
$46$	−7.31256	+	50.8600i	−0.158969	+	1.10565i
$47$	−25.4790	+	39.6461i	−0.542106	+	0.843534i	−0.998941	−	0.0460178i	$-0.985347\pi$
$47$	−25.4790	+	39.6461i	−0.542106	+	0.843534i	0.456834	+	0.889552i	$0.348983\pi$
$48$	−8.58343	+	4.21918i	−0.178821	+	0.0878996i
$49$	31.1507	−	35.9499i	0.635729	−	0.733671i
$50$	50.7321	−	43.9596i	1.01464	−	0.879192i
$51$	−40.8253	−	24.6238i	−0.800495	−	0.482819i
$52$	−52.1882	+	114.276i	−1.00362	+	2.19762i
$53$	45.3907	+	39.3313i	0.856428	+	0.742099i	0.967811	−	0.251678i	$-0.0809825\pi$
$53$	45.3907	+	39.3313i	0.856428	+	0.742099i	−0.111383	+	0.993778i	$0.535528\pi$
$54$	84.0944	+	17.0645i	1.55730	+	0.316009i
$55$	−7.64111	+	2.24363i	−0.138929	+	0.0407933i
$56$	7.90473	−	1.13653i	0.141156	−	0.0202951i
$57$	−5.70220	−	0.654811i	−0.100039	−	0.0114879i
$58$	22.0589	+	48.3022i	0.380326	+	0.832797i
$59$	−5.94552	+	20.2486i	−0.100772	+	0.343196i	−0.994410	−	0.105592i	$-0.966326\pi$
$59$	−5.94552	+	20.2486i	−0.100772	+	0.343196i	0.893638	+	0.448789i	$0.148144\pi$
$60$	34.8531	+	9.16479i	0.580886	+	0.152747i
$61$	10.7882	−	75.0334i	0.176855	−	1.23006i	−0.687128	−	0.726536i	$-0.741129\pi$
$61$	10.7882	−	75.0334i	0.176855	−	1.23006i	0.863984	−	0.503520i	$-0.167962\pi$
$62$	45.3459	−	6.51976i	0.731386	−	0.105157i
$63$	9.37530	+	5.29681i	0.148814	+	0.0840763i
$64$	87.7423	+	56.3885i	1.37097	+	0.881071i
$65$	−36.8895	+	16.8469i	−0.567531	+	0.259183i
$66$	29.8467	+	24.4102i	0.452222	+	0.369851i
$67$	−28.2074	+	60.7729i	−0.421006	+	0.907058i
$67$	−28.2074	+	60.7729i	−0.421006	+	0.907058i
$68$			96.9455i			1.42567i
$69$	46.9090	+	12.3349i	0.679841	+	0.178767i
$70$	6.29916	+	4.04822i	0.0899880	+	0.0578318i
$71$	33.0016	+	28.5961i	0.464811	+	0.402761i	0.855534	−	0.517747i	$-0.173229\pi$
$71$	33.0016	+	28.5961i	0.464811	+	0.402761i	−0.390722	+	0.920509i	$0.627775\pi$
$72$	−20.1766	−	56.5826i	−0.280231	−	0.785870i
$73$	−10.1712	+	70.7422i	−0.139331	+	0.969071i	0.793452	+	0.608633i	$0.208282\pi$
$73$	−10.1712	+	70.7422i	−0.139331	+	0.969071i	−0.932783	+	0.360438i	$0.882627\pi$
$74$	38.8792	−	17.7555i	0.525394	−	0.239940i
$75$	−35.7619	−	52.3107i	−0.476826	−	0.697476i
$76$	4.84835	+	10.6164i	0.0637941	+	0.139690i
$77$	2.61594	+	4.07049i	0.0339733	+	0.0528635i
$78$	168.135	+	101.411i	2.15557	+	1.30013i
$79$	−22.8701	+	6.71528i	−0.289495	+	0.0850035i	−0.423256	−	0.906010i	$-0.639113\pi$
$79$	−22.8701	+	6.71528i	−0.289495	+	0.0850035i	0.133761	+	0.991014i	$0.457295\pi$
$80$	1.76874	+	6.02377i	0.0221092	+	0.0752971i
$81$	25.0594	−	77.0261i	0.309375	−	0.950940i
$82$	−3.59337	+	7.86838i	−0.0438216	+	0.0959559i
$83$	−163.570	+	23.5178i	−1.97072	+	0.283347i	−0.971862	+	0.235552i	$0.924310\pi$
$83$	−163.570	+	23.5178i	−1.97072	+	0.283347i	−0.998857	+	0.0477949i	$0.984781\pi$
$84$	−0.623202	−	21.8871i	−0.00741908	−	0.260561i
$85$	−20.4938	+	23.6511i	−0.241104	+	0.278249i
$86$	−98.8458	−	45.1414i	−1.14937	−	0.524900i
$87$	47.6735	−	15.4851i	0.547971	−	0.177989i
$88$	3.84153	−	26.7185i	0.0436538	−	0.303619i
$89$	27.6402	+	43.0090i	0.310564	+	0.483247i	0.961089	−	0.276237i	$-0.0890876\pi$
$89$	27.6402	+	43.0090i	0.310564	+	0.483247i	−0.650525	+	0.759485i	$0.725451\pi$
$90$	20.4450	−	52.4833i	0.227167	−	0.583148i
$91$	16.1358	+	18.6217i	0.177317	+	0.204634i
$92$	−27.7867	−	94.6328i	−0.302029	−	1.02862i
$93$	−1.23084	−	43.2276i	−0.0132348	−	0.464813i
$94$	21.3152	−	148.250i	0.226757	−	1.57713i
$95$	−1.06144	+	3.61493i	−0.0111731	+	0.0380519i
$96$	69.9514	−	85.5305i	0.728660	−	0.890943i
$97$	31.4504			0.324231			0.162115	−	0.986772i	$-0.448168\pi$
$97$	31.4504			0.324231			0.162115	+	0.986772i	$0.448168\pi$
$98$	−42.5914	+	145.053i	−0.434606	+	1.48013i
$99$	26.1062	−	25.3615i	0.263699	−	0.256176i
$100$	−53.5263	+	117.206i	−0.535263	+	1.17206i
$101$	−57.4160	−	26.2210i	−0.568476	−	0.259614i	0.110376	−	0.993890i	$-0.464795\pi$
$101$	−57.4160	−	26.2210i	−0.568476	−	0.259614i	−0.678851	+	0.734276i	$0.737522\pi$
$102$	150.530	+	17.2861i	1.47579	+	0.169471i
$103$	−99.6259	−	29.2528i	−0.967241	−	0.284008i	−0.240293	−	0.970700i	$-0.577244\pi$
$103$	−99.6259	−	29.2528i	−0.967241	−	0.284008i	−0.726948	+	0.686693i	$0.759062\pi$
$104$		−	137.460i		−	1.32173i
$105$	4.47480	−	5.47140i	0.0426171	−	0.0521086i
$106$	−183.146	−	53.7764i	−1.72779	−	0.507324i
$107$	−29.3006	−	4.21278i	−0.273837	−	0.0393718i	0.00402825	−	0.999992i	$-0.498718\pi$
$107$	−29.3006	−	4.21278i	−0.273837	−	0.0393718i	−0.277865	+	0.960620i	$0.589627\pi$
$108$	−160.436	+	37.2601i	−1.48552	+	0.345001i
$109$	89.1759	−	26.1844i	0.818127	−	0.240224i	0.154218	−	0.988037i	$-0.450714\pi$
$109$	89.1759	−	26.1844i	0.818127	−	0.240224i	0.663909	+	0.747813i	$0.268896\pi$
$110$	19.1275	−	16.5741i	0.173886	−	0.150673i
$111$	−12.4642	−	38.3731i	−0.112290	−	0.345703i
$112$	3.20892	−	2.06225i	0.0286510	−	0.0184129i
$113$	199.475	+	28.6802i	1.76527	+	0.253807i	0.947046	−	0.321098i	$-0.104052\pi$
$113$	199.475	+	28.6802i	1.76527	+	0.253807i	0.818220	+	0.574905i	$0.194961\pi$
$114$	17.3489	−	5.63520i	0.152184	−	0.0494316i
$115$	13.2260	−	28.9609i	0.115009	−	0.251834i
$116$	−77.0300	−	66.7469i	−0.664052	−	0.575404i
$117$	113.210	−	146.756i	0.967604	−	1.25432i
$118$	−9.54484	−	66.3858i	−0.0808885	−	0.562592i
$119$	17.2960	+	7.89880i	0.145344	+	0.0663765i
$120$	−38.8549	+	6.72033i	−0.323791	+	0.0560028i
$121$	−100.406	+	29.4820i	−0.829805	+	0.243653i
$122$	67.8736	+	231.156i	0.556341	+	1.89472i
$123$	6.99200	+	4.21723i	0.0568455	+	0.0342864i
$124$	−73.9757	+	47.5413i	−0.596578	+	0.383398i
$125$	−82.6168	+	37.7298i	−0.660934	+	0.301839i
$126$	−34.0959	−	2.93497i	−0.270603	−	0.0232934i
$127$	31.4177	+	68.7953i	0.247384	+	0.541695i	0.992065	−	0.125725i	$-0.0401258\pi$
$127$	31.4177	+	68.7953i	0.247384	+	0.541695i	−0.744681	+	0.667420i	$0.767399\pi$
$128$	−182.274	−	26.2071i	−1.42402	−	0.204743i
$129$	−52.9785	+	87.8364i	−0.410686	+	0.680902i
$130$	84.4017	−	97.4048i	0.649244	−	0.749268i
$131$	−78.1491	+	121.602i	−0.596558	+	0.928263i	0.403354	+	0.915044i	$0.367844\pi$
$131$	−78.1491	+	121.602i	−0.596558	+	0.928263i	−0.999913	+	0.0132190i	$0.995792\pi$
$132$	−71.5766	−	18.8214i	−0.542247	−	0.142586i
$133$	2.28909			0.0172112
$134$	1.31073	−	212.928i	0.00978154	−	1.58901i
$135$	−47.0172	−	24.8254i	−0.348275	−	0.183892i
$136$	−44.0652	−	96.4894i	−0.324009	−	0.709481i
$137$	−57.6647	+	89.7281i	−0.420910	+	0.654949i	−0.985354	−	0.170522i	$-0.945455\pi$
$137$	−57.6647	+	89.7281i	−0.420910	+	0.654949i	0.564443	+	0.825472i	$0.309091\pi$
$138$	−151.894	+	26.2715i	−1.10068	+	0.190373i
$139$	−18.5263	−	128.853i	−0.133283	−	0.927000i	−0.941235	−	0.337753i	$-0.890333\pi$
$139$	−18.5263	−	128.853i	−0.133283	−	0.927000i	0.807952	−	0.589248i	$-0.200576\pi$
$140$	−14.2263	−	2.04544i	−0.101617	−	0.0146103i
$141$	−136.734	−	35.9548i	−0.969745	−	0.254999i
$142$	−133.157	−	39.0985i	−0.937727	−	0.275341i
$143$	75.7586	−	34.5978i	0.529780	−	0.241943i
$144$	−19.9934	−	20.5805i	−0.138843	−	0.142920i
$145$	−4.68251	−	32.5676i	−0.0322932	−	0.224604i
$146$	−63.9918	−	217.936i	−0.438300	−	1.49271i
$147$	131.444	+	55.5633i	0.894178	+	0.377982i
$148$	−53.7256	+	62.0026i	−0.363011	+	0.418936i
$149$	185.688	+	84.8008i	1.24623	+	0.569133i	0.925755	−	0.378125i	$-0.123431\pi$
$149$	185.688	+	84.8008i	1.24623	+	0.569133i	0.320473	+	0.947258i	$0.396158\pi$
$150$	172.446	+	104.011i	1.14964	+	0.693405i
$151$	−121.278	−	139.962i	−0.803165	−	0.926902i	0.195385	−	0.980727i	$-0.437404\pi$
$151$	−121.278	−	139.962i	−0.803165	−	0.926902i	−0.998550	+	0.0538244i	$0.982859\pi$
$152$	−9.65109	−	8.36272i	−0.0634940	−	0.0550179i
$153$	32.4218	−	139.306i	0.211907	−	0.910496i
$154$	−12.9364	−	8.31369i	−0.0840023	−	0.0539850i
$155$	−28.0974	−	4.03979i	−0.181273	−	0.0260632i
$156$	−374.427	−	42.9972i	−2.40017	−	0.275623i
$157$	212.968	+	136.866i	1.35649	+	0.871760i	0.998088	−	0.0618091i	$-0.0196870\pi$
$157$	212.968	+	136.866i	1.35649	+	0.871760i	0.358397	+	0.933569i	$0.383323\pi$
$158$	57.2493	−	49.6068i	0.362338	−	0.313967i
$159$	−70.1549	+	165.963i	−0.441226	+	1.04379i
$160$	−47.4957	−	54.8130i	−0.296848	−	0.342581i
$161$	−19.1473	−	2.75297i	−0.118927	−	0.0170992i
$162$	29.2479	+	255.758i	0.180543	+	1.57875i
$163$	166.938			1.02416			0.512078	−	0.858939i	$-0.328876\pi$
$163$	166.938			1.02416			0.512078	+	0.858939i	$0.328876\pi$
$164$		−	16.6035i		−	0.101241i
$165$	−13.4833	−	19.7227i	−0.0817170	−	0.119531i
$166$	441.813	−	283.936i	2.66152	−	1.71046i
$167$	37.2376	+	17.0058i	0.222979	+	0.101831i	0.523773	−	0.851858i	$-0.324524\pi$
$167$	37.2376	+	17.0058i	0.222979	+	0.101831i	−0.300793	+	0.953689i	$0.597251\pi$
$168$	10.5688	+	21.5009i	0.0629093	+	0.127982i
$169$	214.620	−	137.928i	1.26994	−	0.816142i
$170$	28.0206	−	95.4293i	0.164827	−	0.561349i
$171$	−3.41636	−	16.8767i	−0.0199787	−	0.0986942i
$172$	208.580			1.21268
$173$	−23.8023	+	81.0632i	−0.137586	+	0.468573i	−0.999242	−	0.0389179i	$-0.987609\pi$
$173$	−23.8023	+	81.0632i	−0.137586	+	0.468573i	0.861657	+	0.507491i	$0.169427\pi$
$174$	−117.375	+	107.705i	−0.674568	+	0.618996i
$175$	16.5495	+	19.0992i	0.0945687	+	0.109138i
$176$	−3.63240	−	12.3708i	−0.0206386	−	0.0702887i
$177$	−63.2846	+	1.80193i	−0.357540	+	0.0101804i
$178$	−136.686	−	87.8430i	−0.767901	−	0.493500i
$179$	87.4029	+	136.002i	0.488285	+	0.759786i	0.994735	−	0.102484i	$-0.0326790\pi$
$179$	87.4029	+	136.002i	0.488285	+	0.759786i	−0.506450	+	0.862269i	$0.669043\pi$
$180$	6.15176	+	107.939i	0.0341765	+	0.599659i
$181$	163.804	+	105.270i	0.904992	+	0.581603i	0.908267	−	0.418391i	$-0.137406\pi$
$181$	163.804	+	105.270i	0.904992	+	0.581603i	−0.00327453	+	0.999995i	$0.501042\pi$
$182$	−71.2317	−	32.5304i	−0.391383	−	0.178738i
$183$	224.088	−	38.7582i	1.22452	−	0.211794i
$184$	70.6700	+	81.5575i	0.384076	+	0.443247i
$185$	−26.2141	+	3.76902i	−0.141698	+	0.0203731i
$186$	60.6284	+	123.341i	0.325959	+	0.663125i
$187$	42.0874	−	48.5715i	0.225067	−	0.259741i
$188$	80.9947	+	275.843i	0.430823	+	1.46725i
$189$	−6.42428	+	31.6591i	−0.0339909	+	0.167509i
$190$	−1.70402	−	11.8517i	−0.00896852	−	0.0623774i
$191$	−146.031	−	227.228i	−0.764559	−	1.18968i	−0.977153	−	0.212537i	$-0.931827\pi$
$191$	−146.031	−	227.228i	−0.764559	−	1.18968i	0.212594	−	0.977141i	$-0.431809\pi$
$192$	−79.5730	+	302.611i	−0.414443	+	1.57610i
$193$	−8.38402	−	2.46177i	−0.0434405	−	0.0127553i	0.259940	−	0.965625i	$-0.416297\pi$
$193$	−8.38402	−	2.46177i	−0.0434405	−	0.0127553i	−0.303381	+	0.952869i	$0.598115\pi$
$194$	−90.9196	+	41.5216i	−0.468658	+	0.214029i
$195$	−82.2569	−	89.6418i	−0.421830	−	0.459702i
$196$	−41.2967	−	287.225i	−0.210698	−	1.46543i
$197$	31.7361	+	27.4995i	0.161097	+	0.139591i	0.731679	−	0.681649i	$-0.238737\pi$
$197$	31.7361	+	27.4995i	0.161097	+	0.139591i	−0.570582	+	0.821240i	$0.693282\pi$
$198$	−41.9872	+	107.783i	−0.212056	+	0.544359i
$199$	141.089	+	308.942i	0.708990	+	1.55247i	0.828719	+	0.559665i	$0.189070\pi$
$199$	141.089	+	308.942i	0.708990	+	1.55247i	−0.119729	+	0.992807i	$0.538203\pi$
$200$		−	140.985i		−	0.704923i
$201$	−199.543	−	24.1598i	−0.992750	−	0.120198i
$202$	200.601			0.993074
$203$	−18.1844	+	8.30454i	−0.0895784	+	0.0409091i
$204$	−276.610	+	89.8474i	−1.35593	+	0.440428i
$205$	3.50991	−	4.05065i	0.0171215	−	0.0197593i
$206$	326.627	−	46.9619i	1.58557	−	0.227971i
$207$	8.27970	+	145.275i	0.0399985	+	0.701813i
$208$	−27.2747	−	59.7233i	−0.131128	−	0.287131i
$209$	2.17984	−	7.42386i	0.0104299	−	0.0355209i
$210$	−5.71267	+	21.7249i	−0.0272032	+	0.103452i
$211$	−302.444	+	194.369i	−1.43338	+	0.921178i	−0.433583	+	0.901114i	$0.642751\pi$
$211$	−302.444	+	194.369i	−1.43338	+	0.921178i	−0.999799	+	0.0200649i	$0.993613\pi$
$212$	362.654	−	52.1417i	1.71063	−	0.245952i
$213$	−51.0066	+	120.664i	−0.239468	+	0.566499i
$214$	90.2665	−	26.5046i	0.421806	−	0.123853i
$215$	50.8859	+	44.0929i	0.236679	+	0.205083i
$216$	142.745	−	110.009i	0.660859	−	0.509301i
$217$	2.45450	+	17.0714i	0.0113111	+	0.0786703i
$218$	−223.228	+	193.428i	−1.02398	+	0.887286i
$219$	−211.272	+	36.5416i	−0.964713	+	0.166857i
$220$	−20.1810	+	44.1903i	−0.0917319	+	0.200865i
$221$	176.943	−	275.329i	0.800649	−	1.24583i
$222$	86.6936	+	94.4768i	0.390512	+	0.425571i
$223$	−250.087	+	160.721i	−1.12147	+	0.720723i	−0.963762	−	0.266763i	$-0.914046\pi$
$223$	−250.087	+	160.721i	−1.12147	+	0.720723i	−0.157705	+	0.987486i	$0.550410\pi$
$224$	−23.8242	+	37.0713i	−0.106358	+	0.165497i
$225$	116.112	−	150.519i	0.516055	−	0.668972i
$226$	−614.525	+	180.441i	−2.71914	+	0.798410i
$227$	199.560	−	172.920i	0.879118	−	0.761760i	−0.0931445	−	0.995653i	$-0.529692\pi$
$227$	199.560	−	172.920i	0.879118	−	0.761760i	0.972262	+	0.233893i	$0.0751464\pi$
$228$	−25.7980	+	23.6727i	−0.113149	+	0.103828i
$229$	93.8028	+	27.5430i	0.409619	+	0.120275i	0.480049	−	0.877242i	$-0.340619\pi$
$229$	93.8028	+	27.5430i	0.409619	+	0.120275i	−0.0704298	+	0.997517i	$0.522437\pi$
$230$			101.184i			0.439931i
$231$	−9.18974	+	11.2364i	−0.0397824	+	0.0486425i
$232$	107.006	+	31.4199i	0.461235	+	0.135431i
$233$	−78.9730	−	122.884i	−0.338940	−	0.527401i	0.629385	−	0.777093i	$-0.283307\pi$
$233$	−78.9730	−	122.884i	−0.338940	−	0.527401i	−0.968325	+	0.249693i	$0.919670\pi$
$234$	−133.526	+	573.717i	−0.570624	+	2.45178i
$235$	−38.5521	+	84.4174i	−0.164052	+	0.359223i
$236$	69.5998	+	108.299i	0.294914	+	0.458896i
$237$	−40.3560	−	59.0308i	−0.170279	−	0.249075i
$238$	−60.4289			−0.253903
$239$			334.652i			1.40022i	0.714037	+	0.700108i	$0.246865\pi$
$239$			334.652i			1.40022i	−0.714037	+	0.700108i	$0.753135\pi$
$240$	−15.5481	+	10.6294i	−0.0647839	+	0.0442891i
$241$	−17.7177	+	123.229i	−0.0735175	+	0.511325i	0.919475	+	0.393148i	$0.128614\pi$
$241$	−17.7177	+	123.229i	−0.0735175	+	0.511325i	−0.992993	+	0.118177i	$0.962295\pi$
$242$	251.341	−	217.788i	1.03860	−	0.899951i
$243$	243.000	+	0.114413i	1.00000	+	0.000470836i
$244$	−302.826	−	349.480i	−1.24109	−	1.43229i
$245$	50.6432	−	78.8023i	0.206707	−	0.321642i
$246$	−25.7808	−	2.96053i	−0.104800	−	0.0120347i
$247$	5.60738	−	39.0002i	0.0227020	−	0.157896i
$248$	52.0184	−	80.9423i	0.209752	−	0.326380i
$249$	−218.696	−	444.910i	−0.878296	−	1.78679i
$250$	189.024	−	218.145i	0.756097	−	0.872582i
$251$	241.264	−	209.056i	0.961210	−	0.832893i	−0.0247807	−	0.999693i	$-0.507889\pi$
$251$	241.264	−	209.056i	0.961210	−	0.832893i	0.985991	+	0.166800i	$0.0533433\pi$
$252$	61.8721	−	22.0628i	0.245524	−	0.0875507i
$253$	−27.1618	+	59.4760i	−0.107359	+	0.235083i
$254$	−181.650	−	157.401i	−0.715159	−	0.619689i
$255$	−86.4761	−	36.5547i	−0.339122	−	0.143352i
$256$	161.236	−	47.3432i	0.629828	−	0.184934i
$257$	−407.722	+	58.6216i	−1.58647	+	0.228099i	−0.878358	−	0.478004i	$-0.841360\pi$
$257$	−407.722	+	58.6216i	−1.58647	+	0.228099i	−0.708109	+	0.706103i	$0.750451\pi$
$258$	37.1914	−	323.869i	0.144153	−	1.25531i
$259$	6.68445	+	14.6369i	0.0258087	+	0.0565131i
$260$	−69.6980	+	237.369i	−0.268069	+	0.912959i
$261$	88.3659	+	121.673i	0.338566	+	0.466181i
$262$	65.3779	−	454.714i	0.249534	−	1.73555i
$263$	111.316	−	16.0049i	0.423256	−	0.0608551i	0.0726041	−	0.997361i	$-0.476869\pi$
$263$	111.316	−	16.0049i	0.423256	−	0.0608551i	0.350652	+	0.936506i	$0.385960\pi$
$264$	79.7949	−	13.8013i	0.302253	−	0.0522777i
$265$	99.4967	+	63.9426i	0.375459	+	0.241293i
$266$	−6.61751	+	3.02212i	−0.0248779	+	0.0113613i
$267$	−97.0993	+	118.725i	−0.363668	+	0.444661i
$268$	167.495	+	372.819i	0.624980	+	1.39111i
$269$		−	374.997i		−	1.39404i	−0.717051	−	0.697021i	$-0.754508\pi$
$269$		−	374.997i		−	1.39404i	0.717051	−	0.697021i	$-0.245492\pi$
$270$	168.697	+	9.69423i	0.624802	+	0.0359046i
$271$	−335.894	−	215.866i	−1.23946	−	0.796553i	−0.254124	−	0.967172i	$-0.581787\pi$
$271$	−335.894	−	215.866i	−1.23946	−	0.796553i	−0.985337	+	0.170619i	$0.945423\pi$
$272$	−38.2907	−	33.1791i	−0.140775	−	0.121982i
$273$	−38.1781	+	63.2979i	−0.139847	+	0.231860i
$274$	48.2411	−	335.524i	0.176062	−	1.22454i
$275$	77.7011	−	35.4849i	0.282549	−	0.129036i
$276$	244.259	−	166.987i	0.884998	−	0.605024i
$277$	179.201	+	392.395i	0.646934	+	1.41659i	0.894212	+	0.447643i	$0.147737\pi$
$277$	179.201	+	392.395i	0.646934	+	1.41659i	−0.247278	+	0.968945i	$0.579536\pi$
$278$	223.672	+	348.041i	0.804577	+	1.25195i
$279$	122.199	−	43.5745i	0.437988	−	0.156181i
$280$	15.0891	−	4.43057i	0.0538898	−	0.0158235i
$281$	−124.176	−	422.903i	−0.441906	−	1.50499i	−0.816248	−	0.577702i	$-0.803949\pi$
$281$	−124.176	−	422.903i	−0.441906	−	1.50499i	0.374342	−	0.927291i	$-0.377869\pi$
$282$	442.751	−	76.5782i	1.57004	−	0.271554i
$283$	44.4036	−	97.2303i	0.156903	−	0.343570i	−0.814812	−	0.579725i	$-0.803160\pi$
$283$	44.4036	−	97.2303i	0.156903	−	0.343570i	0.971715	+	0.236155i	$0.0758873\pi$
$284$	263.670	−	37.9100i	0.928415	−	0.133486i
$285$	−11.2981	+	0.321695i	−0.0396423	+	0.00112875i
$286$	−173.333	+	200.037i	−0.606059	+	0.699429i
$287$	−2.96222	−	1.35280i	−0.0103213	−	0.00471359i
$288$	308.870	+	120.321i	1.07247	+	0.417782i
$289$	−5.18608	+	36.0700i	−0.0179449	+	0.124810i
$290$	56.5331	+	87.9673i	0.194942	+	0.303335i
$291$	29.1477	+	89.7360i	0.100164	+	0.308371i
$292$	285.507	+	329.493i	0.977764	+	1.12840i
$293$	−86.0146	−	292.939i	−0.293565	−	0.999791i	−0.965764	−	0.259421i	$-0.916468\pi$
$293$	−86.0146	−	292.939i	−0.293565	−	0.999791i	0.672199	−	0.740370i	$-0.265350\pi$
$294$	−453.346	+	12.9083i	−1.54199	+	0.0439059i
$295$	−5.91419	+	41.1341i	−0.0200481	+	0.139438i
$296$	25.2904	−	86.1311i	0.0854405	−	0.290983i
$297$	96.5575	+	50.9830i	0.325109	+	0.171660i
$298$	−648.759			−2.17704
$299$	−93.8069	+	319.477i	−0.313736	+	1.06849i
$300$	−384.027	−	44.0996i	−1.28009	−	0.146999i
$301$	16.9944	−	37.2126i	0.0564599	−	0.123630i
$302$	535.383	+	244.501i	1.77279	+	0.809606i
$303$	21.6032	−	188.124i	0.0712975	−	0.620871i
$304$	−5.85251	−	1.71845i	−0.0192517	−	0.00565280i
$305$		−	149.276i		−	0.489430i
$306$	90.1871	+	445.522i	0.294729	+	1.45595i
$307$	−478.134	−	140.393i	−1.55744	−	0.457306i	−0.614126	−	0.789208i	$-0.710491\pi$
$307$	−478.134	−	140.393i	−1.55744	−	0.457306i	−0.943314	+	0.331902i	$0.892310\pi$
$308$	29.2161	+	4.20064i	0.0948576	+	0.0136385i
$309$	−8.86576	−	311.369i	−0.0286918	−	1.00767i
$310$	86.5598	−	25.4162i	0.279225	−	0.0819879i
$311$	98.8461	−	85.6507i	0.317833	−	0.275404i	−0.481303	−	0.876554i	$-0.659836\pi$
$311$	98.8461	−	85.6507i	0.317833	−	0.275404i	0.799136	+	0.601150i	$0.205291\pi$
$312$	392.209	−	127.396i	1.25708	−	0.408319i
$313$	110.419	−	70.9623i	0.352778	−	0.226716i	−0.352234	−	0.935912i	$-0.614578\pi$
$313$	110.419	−	70.9623i	0.352778	−	0.226716i	0.705012	+	0.709195i	$0.250942\pi$
$314$	−796.362	−	114.500i	−2.53618	−	0.364648i
$315$	19.7585	+	7.69696i	0.0627253	+	0.0244348i
$316$	−60.4025	+	132.263i	−0.191147	+	0.418554i
$317$	−271.993	−	235.683i	−0.858022	−	0.743480i	0.110110	−	0.993919i	$-0.464880\pi$
$317$	−271.993	−	235.683i	−0.858022	−	0.743480i	−0.968132	+	0.250439i	$0.919425\pi$
$318$	−16.2982	−	572.400i	−0.0512523	−	1.80000i
$319$	9.61630	+	66.8829i	0.0301452	+	0.209664i
$320$	186.827	+	85.3212i	0.583835	+	0.266629i
$321$	−15.1351	−	87.5063i	−0.0471498	−	0.272605i
$322$	58.9873	−	17.3202i	0.183190	−	0.0537896i
$323$	−8.56613	−	29.1736i	−0.0265205	−	0.0903206i
$324$	−255.002	−	423.234i	−0.787044	−	1.30628i
$325$	365.940	−	235.176i	1.12597	−	0.723617i
$326$	−482.598	+	220.395i	−1.48036	+	0.676058i
$327$	157.357	+	230.174i	0.481215	+	0.703897i
$328$	7.54690	+	16.5254i	0.0230088	+	0.0503823i
$329$	55.8120	+	8.02456i	0.169641	+	0.0243908i
$330$	65.0171	+	39.2151i	0.197022	+	0.118834i
$331$	−184.205	+	212.584i	−0.556512	+	0.642249i	−0.962388	−	0.271679i	$-0.912421\pi$
$331$	−184.205	+	212.584i	−0.556512	+	0.642249i	0.405876	+	0.913928i	$0.366966\pi$
$332$	−545.006	+	848.045i	−1.64158	+	2.55435i
$333$	97.9367	−	71.1270i	0.294104	−	0.213595i
$334$	−130.101			−0.389524
$335$	−37.9496	+	126.362i	−0.113282	+	0.377199i
$336$	8.85808	+	7.24461i	0.0263633	+	0.0215613i
$337$	176.496	+	386.472i	0.523727	+	1.14680i	0.968009	+	0.250915i	$0.0807314\pi$
$337$	176.496	+	386.472i	0.523727	+	1.14680i	−0.444283	+	0.895887i	$0.646541\pi$
$338$	−438.347	+	682.082i	−1.29689	+	2.01799i
$339$	103.038	+	595.734i	0.303947	+	1.75733i
$340$	27.1688	+	188.963i	0.0799083	+	0.555774i
$341$	57.7025	+	8.29637i	0.169216	+	0.0243295i
$342$	32.1573	+	44.2783i	0.0940273	+	0.129469i
$343$	−110.860	−	32.5514i	−0.323207	−	0.0949021i
$344$	−207.599	+	94.8072i	−0.603485	+	0.275602i
$345$	94.8905	+	10.8967i	0.275045	+	0.0315847i
$346$	−38.2118	−	265.769i	−0.110439	−	0.768119i
$347$	143.258	+	487.892i	0.412848	+	1.40603i	0.859414	+	0.511280i	$0.170828\pi$
$347$	143.258	+	487.892i	0.412848	+	1.40603i	−0.446567	+	0.894750i	$0.647353\pi$
$348$	119.056	−	281.646i	0.342115	−	0.809328i
$349$	321.358	−	370.866i	0.920795	−	1.06265i	−0.0770488	−	0.997027i	$-0.524550\pi$
$349$	321.358	−	370.866i	0.920795	−	1.06265i	0.997844	−	0.0656273i	$-0.0209048\pi$
$350$	−73.0580	−	33.3645i	−0.208737	−	0.0953271i
$351$	523.653	+	187.006i	1.49189	+	0.532780i
$352$	97.5403	+	112.567i	0.277103	+	0.319794i
$353$	−228.712	−	198.180i	−0.647910	−	0.561417i	0.267691	−	0.963505i	$-0.413739\pi$
$353$	−228.712	−	198.180i	−0.647910	−	0.561417i	−0.915601	+	0.402087i	$0.868285\pi$
$354$	180.570	−	88.7591i	0.510084	−	0.250732i
$355$	72.3397	+	46.4899i	0.203774	+	0.130957i
$356$	308.699	+	44.3842i	0.867133	+	0.124675i
$357$	−6.50772	+	56.6703i	−0.0182289	+	0.158740i
$358$	−432.225	−	277.774i	−1.20733	−	0.775905i
$359$	−6.34911	+	5.50153i	−0.0176855	+	0.0153246i	−0.663659	−	0.748036i	$-0.730997\pi$
$359$	−6.34911	+	5.50153i	−0.0176855	+	0.0153246i	0.645973	+	0.763360i	$0.276452\pi$
$360$	−55.1849	−	104.635i	−0.153291	−	0.290652i
$361$	234.008	+	270.059i	0.648221	+	0.748087i
$362$	−612.518	−	88.0668i	−1.69204	−	0.243279i
$363$	−177.174	−	259.162i	−0.488084	−	0.713944i
$364$	150.310			0.412940
$365$			140.739i			0.385586i
$366$	−596.644	+	407.892i	−1.63017	+	1.11446i
$367$	415.337	−	266.921i	1.13171	−	0.727305i	0.165793	−	0.986161i	$-0.446982\pi$
$367$	415.337	−	266.921i	1.13171	−	0.727305i	0.965916	+	0.258855i	$0.0833452\pi$
$368$	46.8871	+	21.4126i	0.127411	+	0.0581865i
$369$	−5.55278	+	23.8584i	−0.0150482	+	0.0646570i
$370$	70.8062	−	45.5043i	0.191368	−	0.122985i
$371$	20.2453	−	68.9490i	0.0545695	−	0.185846i
$372$	−204.207	−	167.011i	−0.548943	−	0.448955i
$373$	309.455			0.829639			0.414819	−	0.909904i	$-0.363845\pi$
$373$	309.455			0.829639			0.414819	+	0.909904i	$0.363845\pi$
$374$	−57.5448	+	195.980i	−0.153863	+	0.524010i
$375$	−184.221	−	200.760i	−0.491255	−	0.535359i
$376$	−205.994	−	237.730i	−0.547857	−	0.632261i
$377$	96.9431	+	330.158i	0.257144	+	0.875751i
$378$	−23.2253	−	100.005i	−0.0614425	−	0.264562i
$379$	−59.0701	−	37.9621i	−0.155858	−	0.100164i	0.460387	−	0.887718i	$-0.347711\pi$
$379$	−59.0701	−	37.9621i	−0.155858	−	0.100164i	−0.616245	+	0.787554i	$0.711347\pi$
$380$	12.4255	+	19.3344i	0.0326987	+	0.0508801i
$381$	−167.173	+	153.401i	−0.438775	+	0.402628i
$382$	722.151	+	464.098i	1.89045	+	1.21492i
$383$	−445.162	−	203.299i	−1.16230	−	0.530806i	−0.261573	−	0.965184i	$-0.584241\pi$
$383$	−445.162	−	203.299i	−1.16230	−	0.530806i	−0.900731	+	0.434378i	$0.856968\pi$
$384$	−94.1531	−	544.364i	−0.245190	−	1.41761i
$385$	6.23966	+	7.20096i	0.0162069	+	0.0187038i
$386$	27.4874	−	3.95209i	0.0712108	−	0.0102386i
$387$	−299.719	−	69.7562i	−0.774468	−	0.180249i
$388$	125.638	−	144.994i	0.323809	−	0.373696i
$389$	67.6694	+	230.461i	0.173957	+	0.592444i	0.999601	+	0.0282519i	$0.00899407\pi$
$389$	67.6694	+	230.461i	0.173957	+	0.592444i	−0.825644	+	0.564192i	$0.809188\pi$
$390$	356.143	+	150.547i	0.913187	+	0.386017i
$391$	36.5667	+	254.327i	0.0935209	+	0.650452i
$392$	171.657	+	267.103i	0.437900	+	0.681385i
$393$	−419.390	−	110.281i	−1.06715	−	0.280612i
$394$	−128.051	−	37.5992i	−0.325003	−	0.0954294i
$395$	−42.6958	+	19.4985i	−0.108091	+	0.0493634i
$396$	−12.6337	−	221.670i	−0.0319032	−	0.559772i
$397$	−96.1526	−	668.756i	−0.242198	−	1.68452i	−0.641043	−	0.767505i	$-0.721498\pi$
$397$	−96.1526	−	668.756i	−0.242198	−	1.68452i	0.398845	−	0.917019i	$-0.369411\pi$
$398$	−815.745	−	706.847i	−2.04961	−	1.77600i
$399$	2.12149	+	6.53137i	0.00531702	+	0.0163694i
$400$	−27.9741	−	61.2546i	−0.0699351	−	0.153137i
$401$		−	424.723i		−	1.05916i	−0.848260	−	0.529580i	$-0.822350\pi$
$401$		−	424.723i		−	1.05916i	0.848260	−	0.529580i	$-0.177650\pi$
$402$	608.752	−	193.598i	1.51431	−	0.481587i
$403$	296.866			0.736640
$404$	−350.251	+	159.954i	−0.866958	+	0.395926i
$405$	27.2586	−	157.160i	0.0673051	−	0.388049i
$406$	41.6052	−	48.0150i	0.102476	−	0.118264i
$407$	53.8350	−	7.74030i	0.132273	−	0.0190179i
$408$	234.470	−	215.154i	0.574682	−	0.527339i
$409$	−263.916	−	577.896i	−0.645272	−	1.41295i	−0.895632	−	0.444796i	$-0.853276\pi$
$409$	−263.916	−	577.896i	−0.645272	−	1.41295i	0.250359	−	0.968153i	$-0.419451\pi$
$410$	−4.79898	+	16.3438i	−0.0117048	+	0.0398630i
$411$	−309.460	−	81.3739i	−0.752944	−	0.197990i
$412$	−532.848	+	342.441i	−1.29332	+	0.831167i
$413$	24.9923	−	3.59336i	0.0605142	−	0.00870062i
$414$	−215.732	−	409.044i	−0.521091	−	0.988029i
$415$	−312.234	+	91.6802i	−0.752371	+	0.220916i
$416$	573.238	+	496.714i	1.37798	+	1.19402i
$417$	350.481	−	172.279i	0.840482	−	0.413139i
$418$	3.49948	+	24.3394i	0.00837197	+	0.0582283i
$419$	241.439	−	209.208i	0.576227	−	0.499304i	−0.317292	−	0.948328i	$-0.602774\pi$
$419$	241.439	−	209.208i	0.576227	−	0.499304i	0.893520	+	0.449024i	$0.148228\pi$
$420$	−7.34856	−	42.4871i	−0.0174966	−	0.101160i
$421$	−340.633	+	745.882i	−0.809104	+	1.77169i	−0.197891	+	0.980224i	$0.563409\pi$
$421$	−340.633	+	745.882i	−0.809104	+	1.77169i	−0.611213	+	0.791466i	$0.709318\pi$
$422$	617.720	−	961.192i	1.46379	−	2.27771i
$423$	−24.1343	−	423.460i	−0.0570550	−	1.00109i
$424$	−337.247	+	216.736i	−0.795394	+	0.511169i
$425$	181.480	−	282.389i	0.427012	−	0.664444i
$426$	−11.8497	−	416.167i	−0.0278163	−	0.976919i
$427$	−87.0236	+	25.5524i	−0.203802	+	0.0598418i
$428$	−136.472	+	118.254i	−0.318859	+	0.276293i
$429$	168.928	+	184.094i	0.393772	+	0.429124i
$430$	−205.318	−	60.2868i	−0.477484	−	0.140202i
$431$			148.571i			0.344711i	0.985035	+	0.172356i	$0.0551378\pi$
$431$			148.571i			0.344711i	−0.985035	+	0.172356i	$0.944862\pi$
$432$	40.1918	−	76.1199i	0.0930366	−	0.176203i
$433$	−300.472	−	88.2264i	−0.693930	−	0.203756i	−0.0842976	−	0.996441i	$-0.526865\pi$
$433$	−300.472	−	88.2264i	−0.693930	−	0.203756i	−0.609632	+	0.792684i	$0.708683\pi$
$434$	−29.6338	−	46.1112i	−0.0682807	−	0.106247i
$435$	88.5840	−	43.5435i	0.203641	−	0.100100i
$436$	235.523	−	515.724i	0.540191	−	1.18285i
$437$	16.7236	+	26.0224i	0.0382690	+	0.0595477i
$438$	562.521	−	384.564i	1.28430	−	0.878001i
$439$	−15.8936			−0.0362042			−0.0181021	−	0.999836i	$-0.505762\pi$
$439$	−15.8936			−0.0362042			−0.0181021	+	0.999836i	$0.505762\pi$
$440$		−	53.1554i		−	0.120808i
$441$	−36.7164	+	426.539i	−0.0832571	+	0.967209i
$442$	−148.027	+	1029.55i	−0.334903	+	2.32930i
$443$	−357.454	+	309.736i	−0.806894	+	0.699178i	−0.957189	−	0.289463i	$-0.906523\pi$
$443$	−357.454	+	309.736i	−0.806894	+	0.699178i	0.150295	+	0.988641i	$0.451978\pi$
$444$	−226.701	−	95.8299i	−0.510588	−	0.215833i
$445$	65.9286	+	76.0857i	0.148154	+	0.170979i
$446$	510.786	−	794.799i	1.14526	−	1.78206i
$447$	−69.8662	+	608.407i	−0.156300	+	1.36109i
$448$	17.7595	−	123.520i	0.0396416	−	0.275714i
$449$	−93.7839	+	145.931i	−0.208873	+	0.325012i	−0.929845	−	0.367952i	$-0.880059\pi$
$449$	−93.7839	+	145.931i	−0.208873	+	0.325012i	0.720972	+	0.692964i	$0.243696\pi$
$450$	−136.950	+	588.427i	−0.304333	+	1.30762i
$451$	−7.20817	+	8.31867i	−0.0159826	+	0.0184450i
$452$	929.086	−	805.058i	2.05550	−	1.78110i
$453$	286.950	−	475.752i	0.633444	−	1.05022i
$454$	−348.612	+	763.355i	−0.767869	+	1.68140i
$455$	36.6701	+	31.7748i	0.0805937	+	0.0698348i
$456$	14.9165	−	35.2875i	0.0327117	−	0.0773848i
$457$	−281.597	+	82.6843i	−0.616186	+	0.180929i	−0.574906	−	0.818219i	$-0.694962\pi$
$457$	−281.597	+	82.6843i	−0.616186	+	0.180929i	−0.0412795	+	0.999148i	$0.513143\pi$
$458$	−307.536	+	44.2170i	−0.671477	+	0.0965438i
$459$	427.523	−	36.5983i	0.931423	−	0.0797349i
$460$	−80.6817	−	176.668i	−0.175395	−	0.384061i
$461$	−89.2566	+	303.980i	−0.193615	+	0.659392i	0.804262	+	0.594274i	$0.202561\pi$
$461$	−89.2566	+	303.980i	−0.193615	+	0.659392i	−0.997878	+	0.0651182i	$0.979258\pi$
$462$	11.7319	−	44.6157i	0.0253938	−	0.0965709i
$463$	−16.1734	+	112.488i	−0.0349317	+	0.242955i	−0.999805	−	0.0197615i	$-0.993709\pi$
$463$	−16.1734	+	112.488i	−0.0349317	+	0.242955i	0.964873	+	0.262716i	$0.0846184\pi$
$464$	52.7262	−	7.58089i	0.113634	−	0.0163381i
$465$	−14.5136	−	83.9130i	−0.0312120	−	0.180458i
$466$	390.537	+	250.983i	0.838062	+	0.538590i
$467$	544.767	−	248.787i	1.16652	−	0.532734i	0.264486	−	0.964389i	$-0.414798\pi$
$467$	544.767	−	248.787i	1.16652	−	0.532734i	0.902039	+	0.431655i	$0.142070\pi$
$468$	−224.330	−	1108.18i	−0.479338	−	2.36792i
$469$	80.1612	+	0.493451i	0.170919	+	0.00105213i
$470$		−	294.939i		−	0.627529i
$471$	−193.140	+	734.498i	−0.410063	+	1.55944i
$472$	−118.498	−	76.1542i	−0.251056	−	0.161344i
$473$	−104.503	−	90.5520i	−0.220936	−	0.191442i
$474$	194.599	+	117.372i	0.410546	+	0.247621i
$475$	5.75116	−	40.0002i	0.0121077	−	0.0842109i
$476$	105.509	−	48.1845i	0.221658	−	0.101228i
$477$	−538.553	−	46.3585i	−1.12904	−	0.0971877i
$478$	−441.815	−	967.440i	−0.924300	−	2.02393i
$479$	431.489	+	671.411i	0.900813	+	1.40169i	0.915726	+	0.401803i	$0.131616\pi$
$479$	431.489	+	671.411i	0.900813	+	1.40169i	−0.0149132	+	0.999889i	$0.504747\pi$
$480$	112.377	−	186.317i	0.234119	−	0.388161i
$481$	265.749	−	78.0310i	0.552493	−	0.162227i
$482$	−111.471	−	379.634i	−0.231267	−	0.787622i
$483$	−9.89047	−	57.1836i	−0.0204772	−	0.118393i
$484$	−265.184	+	580.673i	−0.547902	+	1.19974i
$485$	61.3021	−	8.81392i	0.126396	−	0.0181730i
$486$	−702.637	+	320.484i	−1.44575	+	0.659432i
$487$	−584.054	+	674.035i	−1.19929	+	1.38405i	−0.295909	+	0.955216i	$0.595623\pi$
$487$	−584.054	+	674.035i	−1.19929	+	1.38405i	−0.903381	+	0.428839i	$0.858923\pi$
$488$	460.253	+	210.190i	0.943140	+	0.430718i
$489$	154.715	+	476.316i	0.316390	+	0.974061i
$490$	−42.3670	+	294.669i	−0.0864633	+	0.601365i
$491$	−290.845	−	452.563i	−0.592352	−	0.921718i	−0.999963	−	0.00856227i	$-0.997275\pi$
$491$	−290.845	−	452.563i	−0.592352	−	0.921718i	0.407611	−	0.913156i	$-0.366362\pi$
$492$	47.3741	−	15.3879i	0.0962888	−	0.0312761i
$493$	173.887	+	200.676i	0.352711	+	0.407051i
$494$	35.2787	+	120.148i	0.0714144	+	0.243215i
$495$	43.7778	−	56.7500i	0.0884401	−	0.114646i
$496$	6.54034	−	45.4891i	0.0131862	−	0.0917118i
$497$	14.7195	−	50.1299i	0.0296166	−	0.100865i
$498$	1219.61	+	997.459i	2.44901	+	2.00293i
$499$	174.053			0.348804			0.174402	−	0.984675i	$-0.444201\pi$
$499$	174.053			0.348804			0.174402	+	0.984675i	$0.444201\pi$
$500$	−156.094	+	531.607i	−0.312188	+	1.06321i
$501$	−14.0109	+	122.009i	−0.0279658	+	0.243531i
$502$	−421.465	+	922.881i	−0.839573	+	1.83841i
$503$	299.111	+	136.599i	0.594653	+	0.271569i	0.689923	−	0.723882i	$-0.257644\pi$
$503$	299.111	+	136.599i	0.594653	+	0.271569i	−0.0952700	+	0.995451i	$0.530371\pi$
$504$	−51.5526	+	50.0821i	−0.102287	+	0.0993692i
$505$	−119.262	−	35.0185i	−0.236162	−	0.0693435i
$506$		−	207.798i		−	0.410668i
$507$	592.450	+	484.537i	1.16854	+	0.955695i
$508$	442.671	+	129.980i	0.871399	+	0.255866i
$509$	450.059	+	64.7088i	0.884203	+	0.127129i	0.569432	−	0.822038i	$-0.307163\pi$
$509$	450.059	+	64.7088i	0.884203	+	0.127129i	0.314771	+	0.949168i	$0.398072\pi$
$510$	298.253	−	8.49230i	0.584810	−	0.0166516i
$511$	82.0467	−	24.0911i	0.160561	−	0.0471450i
$512$	153.070	−	132.636i	0.298964	−	0.259054i
$513$	44.9874	−	25.3888i	0.0876947	−	0.0494908i
$514$	1101.28	−	707.753i	2.14258	−	1.37695i
$515$	−202.386	−	29.0987i	−0.392982	−	0.0565023i
$516$	193.308	+	595.133i	0.374629	+	1.15336i
$517$	79.1731	−	173.365i	0.153140	−	0.335329i
$518$	−38.6480	−	33.4887i	−0.0746100	−	0.0646499i
$519$	−253.354	+	7.21386i	−0.488157	+	0.0138995i
$520$	−38.5229	−	267.933i	−0.0740826	−	0.515256i
$521$	197.868	+	90.3633i	0.379785	+	0.173442i	0.596155	−	0.802869i	$-0.296694\pi$
$521$	197.868	+	90.3633i	0.379785	+	0.173442i	−0.216370	+	0.976311i	$0.569422\pi$
$522$	−416.092	−	235.081i	−0.797111	−	0.450347i
$523$	−170.338	+	50.0156i	−0.325693	+	0.0956322i	−0.440492	−	0.897757i	$-0.645196\pi$
$523$	−170.338	+	50.0156i	−0.325693	+	0.0956322i	0.114799	+	0.993389i	$0.463378\pi$
$524$	248.427	+	846.064i	0.474097	+	1.61463i
$525$	−39.1570	+	64.9208i	−0.0745848	+	0.123659i
$526$	−300.673	+	193.231i	−0.571622	+	0.367359i
$527$	208.383	−	95.1655i	0.395415	−	0.180580i
$528$	31.9306	−	21.8292i	0.0604747	−	0.0413432i
$529$	111.165	+	243.417i	0.210141	+	0.460145i
$530$	−372.052	−	53.4931i	−0.701986	−	0.100930i
$531$	−63.7924	−	178.897i	−0.120136	−	0.336906i
$532$	9.14447	−	10.5533i	0.0171889	−	0.0198370i
$533$	−30.3045	+	47.1547i	−0.0568565	+	0.0884704i
$534$	123.960	−	471.412i	0.232135	−	0.882795i
$535$	−58.2924			−0.108958
$536$	−336.166	−	294.932i	−0.627176	−	0.550247i
$537$	−307.044	+	375.427i	−0.571777	+	0.699119i
$538$	495.081	+	1084.08i	0.920224	+	2.01501i
$539$	−104.004	+	161.833i	−0.192957	+	0.300248i
$540$	−302.275	+	117.588i	−0.559769	+	0.217756i
$541$	−91.7061	−	637.830i	−0.169512	−	1.17898i	−0.879895	−	0.475168i	$-0.842387\pi$
$541$	−91.7061	−	637.830i	−0.169512	−	1.17898i	0.710383	−	0.703815i	$-0.248522\pi$
$542$	1256.02	+	180.589i	2.31739	+	0.333190i
$543$	−148.553	+	564.936i	−0.273578	+	1.04040i
$544$	561.612	+	164.904i	1.03237	+	0.303133i
$545$	166.481	−	76.0292i	0.305469	−	0.139503i
$546$	26.8014	−	233.391i	0.0490868	−	0.427456i
$547$	−143.844	−	1000.46i	−0.262969	−	1.82899i	−0.510226	−	0.860040i	$-0.670438\pi$
$547$	−143.844	−	1000.46i	−0.262969	−	1.82899i	0.247257	−	0.968950i	$-0.420471\pi$
$548$	183.309	+	624.294i	0.334506	+	1.13922i
$549$	318.268	+	603.460i	0.579723	+	1.09920i
$550$	−177.777	+	205.166i	−0.323231	+	0.373029i
$551$	29.0782	+	13.2796i	0.0527735	+	0.0241009i
$552$	−167.209	+	277.226i	−0.302915	+	0.502221i
$553$	18.6755	+	21.5527i	0.0337713	+	0.0389742i
$554$	−1036.10	−	897.785i	−1.87021	−	1.62055i
$555$	−35.0488	−	71.3026i	−0.0631509	−	0.128473i
$556$	−668.053	−	429.332i	−1.20153	−	0.772179i
$557$	153.910	+	22.1290i	0.276320	+	0.0397289i	0.279082	−	0.960267i	$-0.409970\pi$
$557$	153.910	+	22.1290i	0.276320	+	0.0397289i	−0.00276150	+	0.999996i	$0.500879\pi$
$558$	−295.735	+	287.299i	−0.529991	+	0.514872i
$559$	−592.377	−	380.697i	−1.05971	−	0.681033i
$560$	5.67678	−	4.91896i	0.0101371	−	0.00878385i
$561$	177.593	+	75.0711i	0.316565	+	0.133817i
$562$	917.305	+	1058.63i	1.63221	+	1.88368i
$563$	−847.644	−	121.873i	−1.50558	−	0.216470i	−0.660387	−	0.750925i	$-0.729608\pi$
$563$	−847.644	−	121.873i	−1.50558	−	0.216470i	−0.845197	+	0.534455i	$0.820517\pi$
$564$	−711.986	+	486.745i	−1.26239	+	0.863023i
$565$	396.848			0.702386
$566$			339.705i			0.600185i
$567$	−96.2856	+	11.0110i	−0.169816	+	0.0194197i
$568$	−245.198	+	157.579i	−0.431686	+	0.277428i
$569$	−889.388	−	406.170i	−1.56307	−	0.713831i	−0.568978	−	0.822353i	$-0.692661\pi$
$569$	−889.388	−	406.170i	−1.56307	−	0.713831i	−0.994094	+	0.108522i	$0.965388\pi$
$570$	32.2367	−	15.8460i	0.0565557	−	0.0277999i
$571$	244.711	−	157.266i	0.428565	−	0.275422i	−0.308525	−	0.951216i	$-0.599836\pi$
$571$	244.711	−	157.266i	0.428565	−	0.275422i	0.737090	+	0.675794i	$0.236199\pi$
$572$	143.136	−	487.477i	0.250238	−	0.852233i
$573$	513.002	−	627.255i	0.895292	−	1.09469i
$574$	10.3494			0.0180304
$575$	−96.2121	+	327.668i	−0.167325	+	0.569858i
$576$	−937.174	+	53.4125i	−1.62704	+	0.0927300i
$577$	176.372	+	203.544i	0.305670	+	0.352762i	0.887714	−	0.460395i	$-0.152292\pi$
$577$	176.372	+	203.544i	0.305670	+	0.352762i	−0.582044	+	0.813157i	$0.697747\pi$
$578$	−32.6281	−	111.121i	−0.0564500	−	0.192251i
$579$	−0.746098	−	26.2033i	−0.00128860	−	0.0452561i
$580$	−168.850	−	108.513i	−0.291121	−	0.187092i
$581$	106.894	+	166.330i	0.183982	+	0.286282i
$582$	−202.734	−	220.935i	−0.348341	−	0.379614i
$583$	−204.333	−	131.317i	−0.350485	−	0.225243i
$584$	−433.930	−	198.169i	−0.743031	−	0.339331i
$585$	179.537	−	317.779i	0.306900	−	0.543211i
$586$	635.403	+	733.295i	1.08431	+	1.25136i
$587$	−453.467	+	65.1987i	−0.772516	+	0.111071i	−0.517290	−	0.855810i	$-0.673059\pi$
$587$	−453.467	+	65.1987i	−0.772516	+	0.111071i	−0.255226	+	0.966881i	$0.582150\pi$
$588$	781.254	−	384.025i	1.32866	−	0.653104i
$589$	18.0605	−	20.8430i	0.0306631	−	0.0353871i
$590$	−37.2090	−	126.722i	−0.0630661	−	0.214783i
$591$	−49.0506	+	116.037i	−0.0829960	+	0.196341i
$592$	−6.10197	−	42.4401i	−0.0103074	−	0.0716894i
$593$	314.473	+	489.330i	0.530309	+	0.825177i	0.998284	−	0.0585651i	$-0.0186525\pi$
$593$	314.473	+	489.330i	0.530309	+	0.825177i	−0.467975	+	0.883742i	$0.655016\pi$
$594$	−346.446	−	19.9087i	−0.583242	−	0.0335163i
$595$	35.9264	+	10.5489i	0.0603805	+	0.0177293i
$596$	1132.74	−	517.304i	1.90057	−	0.867960i
$597$	−750.732	+	688.885i	−1.25751	+	1.15391i
$598$	−150.596	−	1047.42i	−0.251833	−	1.75154i
$599$	439.181	+	380.553i	0.733191	+	0.635313i	0.939253	−	0.343225i	$-0.111519\pi$
$599$	439.181	+	380.553i	0.733191	+	0.635313i	−0.206062	+	0.978539i	$0.566065\pi$
$600$	402.265	−	130.662i	0.670442	−	0.217770i
$601$	−299.350	−	655.486i	−0.498087	−	1.09066i	−0.977086	−	0.212843i	$-0.931728\pi$
$601$	−299.350	−	655.486i	−0.498087	−	1.09066i	0.478999	−	0.877815i	$-0.341000\pi$
$602$			130.014i			0.215970i
$603$	−115.998	−	591.738i	−0.192369	−	0.981323i
$604$	−1129.74			−1.87043
$605$	−187.447	+	85.6041i	−0.309829	+	0.141494i
$606$	185.913	+	572.366i	0.306788	+	0.944499i
$607$	−116.923	+	134.936i	−0.192624	+	0.222301i	−0.843844	−	0.536589i	$-0.819712\pi$
$607$	−116.923	+	134.936i	−0.192624	+	0.222301i	0.651219	+	0.758890i	$0.274258\pi$
$608$	69.7486	−	10.0283i	0.114718	−	0.0164940i
$609$	−40.5480	−	44.1883i	−0.0665812	−	0.0725588i
$610$	197.078	+	431.541i	0.323079	+	0.707444i
$611$	273.435	−	931.236i	0.447521	−	1.52412i
$612$	−512.715	−	705.972i	−0.837770	−	1.15355i
$613$	304.346	−	195.591i	0.496486	−	0.319072i	−0.268323	−	0.963329i	$-0.586470\pi$
$613$	304.346	−	195.591i	0.496486	−	0.319072i	0.764809	+	0.644257i	$0.222833\pi$
$614$	1567.58	−	225.384i	2.55307	−	0.367075i
$615$	14.8105	+	6.26060i	0.0240821	+	0.0101798i
$616$	−30.9880	+	9.09890i	−0.0503052	+	0.0147709i
$617$	8.98958	+	7.78952i	0.0145698	+	0.0126248i	0.662115	−	0.749402i	$-0.269659\pi$
$617$	8.98958	+	7.78952i	0.0145698	+	0.0126248i	−0.647545	+	0.762027i	$0.724204\pi$
$618$	436.707	+	888.429i	0.706646	+	1.43759i
$619$	−149.271	−	1038.20i	−0.241149	−	1.67723i	−0.646382	−	0.763014i	$-0.723719\pi$
$619$	−149.271	−	1038.20i	−0.241149	−	1.67723i	0.405234	−	0.914213i	$-0.367190\pi$
$620$	−130.868	+	113.398i	−0.211077	+	0.182899i
$621$	−406.834	+	158.263i	−0.655128	+	0.254851i
$622$	−172.675	+	378.106i	−0.277613	+	0.607887i
$623$	33.0703	−	51.4585i	0.0530824	−	0.0825979i
$624$	145.128	−	133.172i	0.232577	−	0.213417i
$625$	293.768	−	188.793i	0.470028	−	0.302069i
$626$	−225.524	+	350.922i	−0.360262	+	0.560579i
$627$	23.2024	−	0.660653i	0.0370055	−	0.00105367i
$628$	1481.75	−	435.082i	2.35948	−	0.692806i
$629$	161.527	−	139.964i	0.256800	−	0.222518i
$630$	−67.2813	+	3.83457i	−0.106796	+	0.00608662i
$631$	230.473	+	67.6731i	0.365251	+	0.107247i	0.459208	−	0.888329i	$-0.348133\pi$
$631$	230.473	+	67.6731i	0.365251	+	0.107247i	−0.0939568	+	0.995576i	$0.529952\pi$
$632$		−	159.096i		−	0.251734i
$633$	−834.883	−	682.812i	−1.31893	−	1.07869i
$634$	1097.46	+	322.242i	1.73100	+	0.508268i
$635$	80.5182	+	125.289i	0.126800	+	0.197305i
$636$	484.875	+	986.420i	0.762382	+	1.55097i
$637$	−406.954	+	891.106i	−0.638861	+	1.39891i
$638$	−116.100	−	180.655i	−0.181975	−	0.283159i
$639$	−391.558	−	33.7053i	−0.612768	−	0.0527469i
$640$	−362.628			−0.566607
$641$			882.295i			1.37644i	0.725504	+	0.688218i	$0.241607\pi$
$641$			882.295i			1.37644i	−0.725504	+	0.688218i	$0.758393\pi$
$642$	159.282	+	232.989i	0.248103	+	0.362912i
$643$	−25.8185	+	179.571i	−0.0401532	+	0.279271i	−0.999999	−	0.00125595i	$-0.999600\pi$
$643$	−25.8185	+	179.571i	−0.0401532	+	0.279271i	0.959846	+	0.280527i	$0.0905093\pi$
$644$	−89.1816	+	77.2763i	−0.138481	+	0.119994i
$645$	−78.6482	+	186.055i	−0.121935	+	0.288457i
$646$	63.2794	+	73.0283i	0.0979557	+	0.113047i
$647$	325.385	−	506.309i	0.502913	−	0.782548i	−0.493266	−	0.869878i	$-0.664197\pi$
$647$	325.385	−	506.309i	0.502913	−	0.782548i	0.996179	+	0.0873301i	$0.0278335\pi$
$648$	446.178	+	305.335i	0.688546	+	0.471196i
$649$	12.1458	−	84.4757i	0.0187146	−	0.130163i
$650$	−747.408	+	1162.99i	−1.14986	+	1.78921i
$651$	−46.4344	+	22.8248i	−0.0713279	+	0.0350612i
$652$	666.882	−	769.623i	1.02283	−	1.18040i
$653$	54.3020	−	47.0529i	0.0831577	−	0.0720565i	−0.612290	−	0.790633i	$-0.709752\pi$
$653$	54.3020	−	47.0529i	0.0831577	−	0.0720565i	0.695448	+	0.718577i	$0.255206\pi$
$654$	−758.785	−	457.662i	−1.16022	−	0.699788i
$655$	−118.247	+	258.925i	−0.180530	+	0.395305i
$656$	6.55792	+	5.68247i	0.00999683	+	0.00866230i
$657$	−300.066	−	568.948i	−0.456721	−	0.865978i
$658$	−171.941	+	50.4863i	−0.261308	+	0.0767269i
$659$	−617.888	+	88.8389i	−0.937615	+	0.134809i	−0.594148	−	0.804356i	$-0.702510\pi$
$659$	−617.888	+	88.8389i	−0.937615	+	0.134809i	−0.343467	+	0.939165i	$0.611601\pi$
$660$	−144.790	−	16.6269i	−0.219378	−	0.0251922i
$661$	−231.833	−	507.643i	−0.350730	−	0.767992i	−0.999973	−	0.00741057i	$-0.997641\pi$
$661$	−231.833	−	507.643i	−0.350730	−	0.767992i	0.649242	−	0.760582i	$-0.275086\pi$
$662$	251.858	−	857.750i	0.380450	−	1.29570i
$663$	949.574	+	249.695i	1.43224	+	0.376613i
$664$	156.974	−	1091.78i	0.236407	−	1.64425i
$665$	4.46183	−	0.641514i	0.00670952	−	0.000964683i
$666$	−189.220	+	334.919i	−0.284115	+	0.502881i
$667$	−227.257	−	146.049i	−0.340715	−	0.218964i
$668$	227.158	−	103.739i	0.340056	−	0.155299i
$669$	−690.356	−	564.610i	−1.03192	−	0.843960i
$670$	−57.1178	−	415.399i	−0.0852504	−	0.619999i
$671$			306.563i			0.456875i
$672$	−127.854	−	33.6197i	−0.190258	−	0.0500293i
$673$	−713.233	−	458.367i	−1.05978	−	0.681081i	−0.109981	−	0.993934i	$-0.535079\pi$
$673$	−713.233	−	458.367i	−1.05978	−	0.681081i	−0.949802	+	0.312853i	$0.898715\pi$
$674$	−1020.46	−	884.233i	−1.51404	−	1.31192i
$675$	537.079	+	191.801i	0.795673	+	0.284149i
$676$	221.483	−	1540.45i	0.327637	−	2.27877i
$677$	535.378	−	244.499i	0.790809	−	0.361151i	0.0212895	−	0.999773i	$-0.493223\pi$
$677$	535.378	−	244.499i	0.790809	−	0.361151i	0.769520	+	0.638623i	$0.220496\pi$
$678$	−1084.37	−	1586.17i	−1.59937	−	2.33948i
$679$	−15.6317	−	34.2286i	−0.0230216	−	0.0504103i
$680$	−112.932	−	175.725i	−0.166076	−	0.258419i
$681$	678.332	+	409.137i	0.996083	+	0.600788i
$682$	−177.765	+	52.1964i	−0.260652	+	0.0765343i
$683$	−143.742	−	489.542i	−0.210457	−	0.716752i	−0.995281	−	0.0970329i	$-0.969065\pi$
$683$	−143.742	−	489.542i	−0.210457	−	0.716752i	0.784824	−	0.619719i	$-0.212753\pi$
$684$	−91.4534	−	51.6689i	−0.133704	−	0.0755393i
$685$	−87.2522	+	191.056i	−0.127375	+	0.278913i
$686$	363.459	−	52.2575i	0.529824	−	0.0761771i
$687$	8.34756	+	293.170i	0.0121507	+	0.426739i
$688$	−71.3855	+	82.3832i	−0.103758	+	0.119743i
$689$	−1125.12	−	513.825i	−1.63298	−	0.745755i
$690$	−288.704	+	93.7756i	−0.418412	+	0.135907i
$691$	69.5476	−	483.714i	0.100648	−	0.700020i	−0.875548	−	0.483130i	$-0.839500\pi$
$691$	69.5476	−	483.714i	0.100648	−	0.700020i	0.976196	−	0.216890i	$-0.0695912\pi$
$692$	278.636	+	433.566i	0.402653	+	0.626540i
$693$	−40.5773	−	15.8070i	−0.0585531	−	0.0228095i
$694$	−1058.27	−	1221.31i	−1.52489	−	1.75981i
$695$	−72.2217	−	245.964i	−0.103916	−	0.353906i
$696$	9.52256	+	334.436i	0.0136818	+	0.480512i
$697$	−6.15582	+	42.8146i	−0.00883188	+	0.0614270i
$698$	−439.382	+	1496.40i	−0.629487	+	2.14384i
$699$	277.430	−	339.217i	0.396895	−	0.485289i
$700$	154.164			0.220234
$701$	125.308	−	426.760i	0.178756	−	0.608788i	−0.820551	−	0.571573i	$-0.806333\pi$
$701$	125.308	−	426.760i	0.178756	−	0.608788i	0.999307	−	0.0372146i	$-0.0118485\pi$
$702$	−1760.71	+	150.727i	−2.50814	+	0.214710i
$703$	10.6889	−	23.4055i	0.0152047	−	0.0332937i
$704$	−383.681	−	175.221i	−0.545001	−	0.248894i
$705$	−276.594	−	31.7626i	−0.392332	−	0.0450533i
$706$	922.824	+	270.966i	1.30712	+	0.383804i
$707$			75.5205i			0.106818i
$708$	−244.502	+	298.956i	−0.345342	+	0.422254i
$709$	1240.84	+	364.344i	1.75013	+	0.513884i	0.990624	−	0.136618i	$-0.0436233\pi$
$709$	1240.84	+	364.344i	1.75013	+	0.513884i	0.759505	+	0.650502i	$0.225441\pi$
$710$	−270.503	−	38.8925i	−0.380990	−	0.0547781i
$711$	131.029	−	169.855i	0.184288	−	0.238896i
$712$	−327.421	+	96.1395i	−0.459861	+	0.135027i
$713$	−176.136	+	152.623i	−0.247035	+	0.214057i
$714$	−56.0044	−	172.419i	−0.0784376	−	0.241483i
$715$	137.970	−	88.6682i	0.192966	−	0.124011i
$716$	976.158	+	140.350i	1.36335	+	0.196020i
$717$	−954.847	+	310.149i	−1.33173	+	0.432565i
$718$	11.0913	−	24.2866i	0.0154475	−	0.0338253i
$719$	−156.850	−	135.912i	−0.218151	−	0.189029i	0.538929	−	0.842351i	$-0.318829\pi$
$719$	−156.850	−	135.912i	−0.218151	−	0.189029i	−0.757080	+	0.653323i	$0.773375\pi$
$720$	−44.7381	−	34.5117i	−0.0621363	−	0.0479329i
$721$	17.6798	+	122.966i	0.0245213	+	0.170549i
$722$	−1033.03	−	471.768i	−1.43079	−	0.653419i
$723$	−368.026	+	63.6537i	−0.509026	+	0.0880410i
$724$	1139.68	−	334.641i	1.57415	−	0.462212i
$725$	99.4288	+	338.623i	0.137143	+	0.467067i
$726$	854.343	+	515.298i	1.17678	+	0.709777i
$727$	−681.308	+	437.850i	−0.937149	+	0.602269i	−0.917585	−	0.397539i	$-0.869864\pi$
$727$	−681.308	+	437.850i	−0.937149	+	0.602269i	−0.0195643	+	0.999809i	$0.506228\pi$
$728$	−149.603	+	68.3213i	−0.205498	+	0.0938480i
$729$	224.882	+	693.447i	0.308480	+	0.951231i
$730$	−185.807	−	406.861i	−0.254530	−	0.557344i
$731$	−537.855	−	77.3319i	−0.735780	−	0.105789i
$732$	716.502	−	1187.93i	0.978828	−	1.62286i
$733$	−471.722	+	544.396i	−0.643550	+	0.742696i	−0.979998	−	0.199006i	$-0.936229\pi$
$733$	−471.722	+	544.396i	−0.643550	+	0.742696i	0.336449	+	0.941702i	$0.390774\pi$
$734$	−848.298	+	1319.98i	−1.15572	+	1.79833i
$735$	271.778	+	71.4654i	0.369767	+	0.0972318i
$736$	−595.479			−0.809075
$737$	77.9357	−	259.504i	0.105747	−	0.352109i
$738$	−15.4460	−	76.3030i	−0.0209296	−	0.103392i
$739$	−49.9515	−	109.378i	−0.0675933	−	0.148009i	0.872820	−	0.488042i	$-0.162289\pi$
$739$	−49.9515	−	109.378i	−0.0675933	−	0.148009i	−0.940413	+	0.340034i	$0.889562\pi$
$740$	−87.3441	+	135.910i	−0.118033	+	0.183662i
$741$	116.474	−	20.1454i	0.157186	−	0.0271868i
$742$	32.5014	+	226.052i	0.0438024	+	0.304653i
$743$	146.702	+	21.0925i	0.197445	+	0.0283883i	0.240328	−	0.970692i	$-0.422745\pi$
$743$	146.702	+	21.0925i	0.197445	+	0.0283883i	−0.0428828	+	0.999080i	$0.513654\pi$
$744$	279.159	+	73.4061i	0.375213	+	0.0986641i
$745$	385.702	+	113.252i	0.517721	+	0.152017i
$746$	−894.601	+	408.550i	−1.19920	+	0.547655i
$747$	1066.76	−	1036.33i	1.42806	−	1.38732i
$748$	−55.7956	−	388.067i	−0.0745931	−	0.518806i
$749$	9.97823	+	33.9827i	0.0133221	+	0.0453708i
$750$	797.609	+	337.161i	1.06348	+	0.449548i
$751$	334.134	−	385.611i	0.444919	−	0.513464i	−0.488347	−	0.872649i	$-0.662400\pi$
$751$	334.134	−	385.611i	0.444919	−	0.513464i	0.933266	+	0.359186i	$0.116945\pi$
$752$	−136.670	−	62.4151i	−0.181742	−	0.0829988i
$753$	820.090	+	494.638i	1.08910	+	0.656890i
$754$	−716.135	−	826.463i	−0.949781	−	1.09611i
$755$	−275.615	−	238.822i	−0.365054	−	0.316321i
$756$	120.293	+	156.089i	0.159117	+	0.206468i
$757$	−564.657	−	362.883i	−0.745914	−	0.479370i	0.111650	−	0.993748i	$-0.464387\pi$
$757$	−564.657	−	362.883i	−0.745914	−	0.479370i	−0.857564	+	0.514378i	$0.828023\pi$
$758$	220.884	+	31.7583i	0.291403	+	0.0418975i
$759$	−194.873	−	22.3782i	−0.256750	−	0.0294838i
$760$	−21.1552	−	13.5956i	−0.0278358	−	0.0178890i
$761$	−462.422	+	400.691i	−0.607650	+	0.526532i	−0.903436	−	0.428722i	$-0.858964\pi$
$761$	−462.422	+	400.691i	−0.607650	+	0.526532i	0.295786	+	0.955254i	$0.404418\pi$
$762$	280.755	−	664.172i	0.368445	−	0.871616i
$763$	−72.8202	−	84.0390i	−0.0954394	−	0.110143i
$764$	−1630.94	−	234.494i	−2.13474	−	0.306930i
$765$	24.1554	−	280.617i	0.0315757	−	0.366819i
$766$	1555.31			2.03044
$767$		−	434.607i		−	0.566633i
$768$	284.513	+	416.171i	0.370460	+	0.541889i
$769$	−384.693	+	247.227i	−0.500251	+	0.321492i	−0.766317	−	0.642463i	$-0.777913\pi$
$769$	−384.693	+	247.227i	−0.500251	+	0.321492i	0.266065	+	0.963955i	$0.414276\pi$
$770$	−27.5451	−	12.5794i	−0.0357728	−	0.0163369i
$771$	−545.132	−	1109.01i	−0.707045	−	1.43840i
$772$	−44.8419	+	28.8181i	−0.0580853	+	0.0373292i
$773$	−281.435	+	958.479i	−0.364081	+	1.23995i	0.550257	+	0.834995i	$0.314530\pi$
$773$	−281.435	+	958.479i	−0.364081	+	1.23995i	−0.914338	+	0.404951i	$0.867288\pi$
$774$	958.549	−	194.039i	1.23844	−	0.250697i
$775$	304.477			0.392874
$776$	−59.1419	+	201.419i	−0.0762138	+	0.259560i
$777$	−35.5678	+	32.6377i	−0.0457758	+	0.0420047i
$778$	−499.885	−	576.898i	−0.642525	−	0.741513i
$779$	1.46709	+	4.99645i	0.00188330	+	0.00641393i
$780$	−741.871	+	21.1236i	−0.951117	+	0.0270816i
$781$	−148.561	−	95.4747i	−0.190220	−	0.122247i
$782$	−441.479	−	686.954i	−0.564551	−	0.878458i
$783$	−265.269	+	364.895i	−0.338786	+	0.466022i
$784$	127.579	+	81.9902i	0.162729	+	0.104579i
$785$	453.468	+	207.092i	0.577666	+	0.263811i
$786$	1358.01	−	234.880i	1.72774	−	0.298830i
$787$	−520.604	−	600.809i	−0.661505	−	0.763417i	0.321518	−	0.946904i	$-0.395807\pi$
$787$	−520.604	−	600.809i	−0.661505	−	0.763417i	−0.983022	+	0.183487i	$0.941262\pi$
$788$	253.559	−	36.4563i	0.321775	−	0.0462643i
$789$	148.832	+	302.781i	0.188634	+	0.383753i
$790$	97.6864	−	112.736i	0.123654	−	0.142704i
$791$	−67.9307	−	231.351i	−0.0858796	−	0.292479i
$792$	113.331	+	214.885i	0.143095	+	0.271319i
$793$	222.174	+	1545.25i	0.280168	+	1.94861i
$794$	1160.87	+	1806.36i	1.46206	+	2.27501i
$795$	−90.2330	+	343.150i	−0.113501	+	0.431636i
$796$	1987.92	+	583.706i	2.49739	+	0.733299i
$797$	−780.636	+	356.504i	−0.979468	+	0.447308i	−0.839803	−	0.542891i	$-0.817330\pi$
$797$	−780.636	+	356.504i	−0.979468	+	0.447308i	−0.139664	+	0.990199i	$0.544602\pi$
$798$	−14.7559	−	16.0806i	−0.0184911	−	0.0201512i
$799$	−106.587	−	741.331i	−0.133401	−	0.927823i
$800$	587.936	+	509.449i	0.734920	+	0.636812i
$801$	−428.742	−	167.017i	−0.535258	−	0.208511i
$802$	560.730	+	1227.83i	0.699164	+	1.53096i
$803$		−	289.031i		−	0.359939i
$804$	−908.516	+	823.427i	−1.13000	+	1.02416i
$805$	−38.0929			−0.0473204
$806$	−858.206	+	391.930i	−1.06477	+	0.486265i
$807$	1069.96	−	347.541i	1.32585	−	0.430658i
$808$	275.898	−	318.404i	0.341458	−	0.394064i
$809$	421.243	−	60.5656i	0.520696	−	0.0748648i	0.123044	−	0.992401i	$-0.460734\pi$
$809$	421.243	−	60.5656i	0.520696	−	0.0748648i	0.397652	+	0.917536i	$0.369825\pi$
$810$	128.685	+	490.319i	0.158870	+	0.605332i
$811$	134.155	+	293.759i	0.165419	+	0.362218i	0.974130	−	0.225989i	$-0.0725614\pi$
$811$	134.155	+	293.759i	0.165419	+	0.362218i	−0.808711	+	0.588207i	$0.799834\pi$
$812$	−34.3571	+	117.010i	−0.0423117	+	0.144100i
$813$	304.620	−	1158.45i	0.374687	−	1.42491i
$814$	−145.412	+	93.4507i	−0.178639	+	0.114804i
$815$	325.390	−	46.7840i	0.399251	−	0.0574036i
$816$	59.1813	−	140.003i	0.0725261	−	0.171572i
$817$	−62.7675	+	18.4302i	−0.0768268	+	0.0225584i
$818$	1525.91	+	1322.20i	1.86541	+	1.61639i
$819$	−215.988	−	50.2687i	−0.263721	−	0.0613782i
$820$	−4.65311	−	32.3631i	−0.00567452	−	0.0394672i
$821$	−559.570	+	484.870i	−0.681571	+	0.590585i	−0.925290	−	0.379261i	$-0.876178\pi$
$821$	−559.570	+	484.870i	−0.681571	+	0.590585i	0.243719	+	0.969846i	$0.421633\pi$
$822$	1002.05	−	173.314i	1.21903	−	0.210844i
$823$	−580.564	+	1271.26i	−0.705424	+	1.54466i	0.127845	+	0.991794i	$0.459194\pi$
$823$	−580.564	+	1271.26i	−0.705424	+	1.54466i	−0.833269	+	0.552868i	$0.813533\pi$
$824$	374.690	−	583.028i	0.454720	−	0.707559i
$825$	173.259	+	188.814i	0.210011	+	0.228866i
$826$	−67.5061	+	43.3835i	−0.0817265	+	0.0525224i
$827$	392.557	−	610.831i	0.474677	−	0.738611i	−0.518519	−	0.855066i	$-0.673517\pi$
$827$	392.557	−	610.831i	0.474677	−	0.738611i	0.993196	+	0.116455i	$0.0371530\pi$
$828$	702.831	+	542.175i	0.848830	+	0.654800i
$829$	−135.490	+	39.7834i	−0.163437	+	0.0479896i	−0.362428	−	0.932012i	$-0.618052\pi$
$829$	−135.490	+	39.7834i	−0.163437	+	0.0479896i	0.198990	+	0.980001i	$0.436234\pi$
$830$	781.596	−	677.257i	0.941682	−	0.815972i
$831$	−953.523	+	874.970i	−1.14744	+	1.05291i
$832$	−2060.95	−	605.150i	−2.47711	−	0.727344i
$833$			755.964i			0.907519i
$834$	−785.755	+	960.753i	−0.942152	+	1.15198i
$835$	77.3482	+	22.7115i	0.0926325	+	0.0271994i
$836$	−25.5178	−	39.7065i	−0.0305237	−	0.0474958i
$837$	237.581	+	308.280i	0.283848	+	0.368316i
$838$	−421.772	+	923.552i	−0.503308	+	1.10209i
$839$	858.808	+	1336.33i	1.02361	+	1.59277i	0.782878	+	0.622175i	$0.213751\pi$
$839$	858.808	+	1336.33i	1.02361	+	1.59277i	0.240731	+	0.970592i	$0.422613\pi$
$840$	26.6259	+	38.9470i	0.0316975	+	0.0463655i
$841$	561.828			0.668048
$842$		−	2605.97i		−	3.09498i
$843$	1091.57	−	746.244i	1.29486	−	0.885224i
$844$	−312.114	+	2170.80i	−0.369804	+	2.57204i
$845$	379.677	−	328.992i	0.449322	−	0.389340i
$846$	628.831	+	1192.31i	0.743299	+	1.40935i
$847$	81.9910	+	94.6226i	0.0968016	+	0.111715i
$848$	−103.522	+	161.083i	−0.122078	+	0.189956i
$849$	318.576	+	36.5835i	0.375236	+	0.0430901i
$850$	−151.823	+	1055.95i	−0.178615	+	1.24229i
$851$	−117.557	+	182.922i	−0.138140	+	0.214950i
$852$	352.531	+	717.183i	0.413769	+	0.841764i
$853$	−405.083	+	467.491i	−0.474892	+	0.548055i	−0.941766	−	0.336269i	$-0.890835\pi$
$853$	−405.083	+	467.491i	−0.474892	+	0.548055i	0.466874	+	0.884324i	$0.345380\pi$
$854$	217.841	−	188.760i	0.255083	−	0.221030i
$855$	−11.3887	−	31.9381i	−0.0133201	−	0.0373545i
$856$	82.0793	−	179.729i	0.0958870	−	0.209963i
$857$	1124.43	+	974.327i	1.31206	+	1.13690i	0.981151	+	0.193241i	$0.0618999\pi$
$857$	1124.43	+	974.327i	1.31206	+	1.13690i	0.330906	+	0.943664i	$0.392646\pi$
$858$	−731.398	−	309.173i	−0.852445	−	0.360341i
$859$	−187.970	+	55.1929i	−0.218824	+	0.0642525i	−0.389307	−	0.921108i	$-0.627285\pi$
$859$	−187.970	+	55.1929i	−0.218824	+	0.0642525i	0.170483	+	0.985361i	$0.445467\pi$
$860$	406.558	−	58.4542i	0.472742	−	0.0679700i
$861$	1.11455	−	9.70572i	0.00129449	−	0.0112726i
$862$	−196.146	−	429.501i	−0.227548	−	0.498261i
$863$	−182.322	+	620.931i	−0.211265	+	0.719503i	0.783865	+	0.620932i	$0.213246\pi$
$863$	−182.322	+	620.931i	−0.211265	+	0.719503i	−0.995130	+	0.0985716i	$0.968573\pi$
$864$	−57.0516	+	992.798i	−0.0660320	+	1.14907i
$865$	−23.6769	+	164.676i	−0.0273721	+	0.190377i
$866$	985.108	−	141.637i	1.13754	−	0.163553i
$867$	−107.723	+	18.6318i	−0.124248	+	0.0214900i
$868$	88.5088	+	56.8812i	0.101969	+	0.0655313i
$869$	87.6829	−	40.0434i	0.100901	−	0.0460799i
$870$	−198.599	+	242.830i	−0.228275	+	0.279115i
$871$	204.771	−	1364.53i	0.235098	−	1.56662i
$872$			620.352i			0.711413i
$873$	−229.026	+	166.332i	−0.262344	+	0.190529i
$874$	−82.7013	−	53.1489i	−0.0946239	−	0.0608111i
$875$	82.1255	+	71.1622i	0.0938577	+	0.0813282i
$876$	−675.525	+	1119.99i	−0.771147	+	1.27853i
$877$	84.8875	−	590.406i	0.0967931	−	0.673211i	−0.882433	−	0.470438i	$-0.844096\pi$
$877$	84.8875	−	590.406i	0.0967931	−	0.673211i	0.979226	−	0.202772i	$-0.0649951\pi$
$878$	45.9467	−	20.9832i	0.0523311	−	0.0238988i
$879$	756.113	−	516.912i	0.860196	−	0.588068i
$880$	−10.5470	−	23.0948i	−0.0119853	−	0.0262441i
$881$	−13.3467	−	20.7679i	−0.0151495	−	0.0235731i	0.833596	−	0.552374i	$-0.186278\pi$
$881$	−13.3467	−	20.7679i	−0.0151495	−	0.0235731i	−0.848746	+	0.528801i	$0.822642\pi$
$882$	−456.984	−	1281.55i	−0.518123	−	1.45301i
$883$	1480.22	−	434.632i	1.67635	−	0.492222i	0.701054	−	0.713109i	$-0.252713\pi$
$883$	1480.22	−	434.632i	1.67635	−	0.492222i	0.975299	+	0.220887i	$0.0708951\pi$
$884$	−562.482	−	1915.64i	−0.636292	−	2.16701i
$885$	−122.847	+	21.2477i	−0.138811	+	0.0240087i
$886$	624.439	−	1367.33i	0.704785	−	1.54326i
$887$	−1127.30	+	162.081i	−1.27091	+	0.182729i	−0.744569	−	0.667545i	$-0.767345\pi$
$887$	−1127.30	+	162.081i	−1.27091	+	0.182729i	−0.526340	+	0.850274i	$0.676436\pi$
$888$	269.193	−	7.66485i	0.303145	−	0.00863159i
$889$	59.2569	−	68.3862i	0.0666557	−	0.0769248i
$890$	−291.043	−	132.915i	−0.327014	−	0.149342i
$891$	−55.9799	+	322.754i	−0.0628282	+	0.362237i
$892$	−258.084	+	1795.01i	−0.289332	+	2.01235i
$893$	−48.7471	−	75.8519i	−0.0545880	−	0.0849405i
$894$	−601.258	−	1851.08i	−0.672548	−	2.07055i
$895$	208.477	+	240.596i	0.232936	+	0.268822i
$896$	62.0731	+	211.402i	0.0692780	+	0.235939i
$897$	−998.489	+	28.4304i	−1.11314	+	0.0316950i
$898$	78.4576	−	545.685i	0.0873693	−	0.607667i
$899$	−67.8561	+	231.097i	−0.0754795	+	0.257060i
$900$	−230.082	−	1136.60i	−0.255647	−	1.26289i
$901$	−954.488			−1.05937
$902$	9.85550	−	33.5648i	0.0109263	−	0.0372115i
$903$	121.927	+	14.0015i	0.135025	+	0.0155055i
$904$	−558.787	+	1223.57i	−0.618127	+	1.35351i
$905$	348.783	+	159.284i	0.385395	+	0.176004i
$906$	−201.441	+	1754.18i	−0.222341	+	1.93618i
$907$	193.823	+	56.9116i	0.213697	+	0.0627471i	0.386829	−	0.922152i	$-0.373570\pi$
$907$	193.823	+	56.9116i	0.213697	+	0.0627471i	−0.173132	+	0.984899i	$0.555389\pi$
$908$		−	1610.80i		−	1.77401i
$909$	556.787	−	112.711i	0.612527	−	0.123994i
$910$	−147.959	−	43.4447i	−0.162592	−	0.0477415i
$911$	−186.370	−	26.7960i	−0.204577	−	0.0294138i	0.0392642	−	0.999229i	$-0.487499\pi$
$911$	−186.370	−	26.7960i	−0.204577	−	0.0294138i	−0.243842	+	0.969815i	$0.578408\pi$
$912$	−0.520817	−	18.2913i	−0.000571072	−	0.0200563i
$913$	641.224	−	188.280i	0.702327	−	0.206222i
$914$	704.904	−	610.802i	0.771229	−	0.668274i
$915$	425.923	−	138.347i	0.465490	−	0.151198i
$916$	501.703	−	322.425i	0.547711	−	0.351993i
$917$	171.187	+	24.6129i	0.186681	+	0.0268407i
$918$	−1187.60	+	670.228i	−1.29369	+	0.730096i
$919$	−502.551	+	1100.43i	−0.546845	+	1.19742i	0.411394	+	0.911458i	$0.365042\pi$
$919$	−502.551	+	1100.43i	−0.546845	+	1.19742i	−0.958240	+	0.285967i	$0.907685\pi$
$920$	160.604	+	139.164i	0.174570	+	0.151266i
$921$	−42.5494	−	1494.35i	−0.0461991	−	1.62253i
$922$	−143.291	−	996.611i	−0.155413	−	1.08092i
$923$	−818.026	−	373.580i	−0.886269	−	0.404745i
$924$	15.0915	+	87.2542i	0.0163328	+	0.0944310i
$925$	272.563	−	80.0317i	0.294663	−	0.0865207i
$926$	−101.754	−	346.543i	−0.109886	−	0.374237i
$927$	880.199	−	313.868i	0.949514	−	0.338584i
$928$	−517.697	+	332.704i	−0.557863	+	0.358517i
$929$	600.103	−	274.058i	0.645967	−	0.295003i	−0.0653631	−	0.997862i	$-0.520821\pi$
$929$	600.103	−	274.058i	0.645967	−	0.295003i	0.711330	+	0.702858i	$0.248093\pi$
$930$	152.741	+	223.422i	0.164238	+	0.240239i
$931$	37.8066	+	82.7849i	0.0406086	+	0.0889204i
$932$	−882.009	−	126.814i	−0.946361	−	0.136066i
$933$	335.992	+	202.654i	0.360120	+	0.217207i
$934$	−1246.41	+	1438.43i	−1.33448	+	1.54007i
$935$	68.4235	−	106.469i	0.0731802	−	0.113871i
$936$	726.985	+	1001.00i	0.776693	+	1.06945i
$937$	1655.01			1.76629			0.883144	−	0.469102i	$-0.155422\pi$
$937$	1655.01			1.76629			0.883144	+	0.469102i	$0.155422\pi$
$938$	−232.388	+	104.404i	−0.247749	+	0.111305i
$939$	304.808	+	249.288i	0.324610	+	0.265483i
$940$	235.177	+	514.966i	0.250188	+	0.547836i
$941$	−16.9473	+	26.3704i	−0.0180098	+	0.0280238i	−0.850142	−	0.526554i	$-0.823484\pi$
$941$	−16.9473	+	26.3704i	−0.0180098	+	0.0280238i	0.832132	+	0.554578i	$0.187120\pi$
$942$	−411.357	−	2378.34i	−0.436685	−	2.52478i
$943$	−6.26265	−	43.5577i	−0.00664119	−	0.0461905i
$944$	−66.5953	−	9.57496i	−0.0705459	−	0.0101430i
$945$	−3.64960	+	63.5094i	−0.00386201	+	0.0672057i
$946$	421.654	+	123.809i	0.445723	+	0.130876i
$947$	529.374	−	241.757i	0.559001	−	0.255287i	−0.115818	−	0.993270i	$-0.536949\pi$
$947$	529.374	−	241.757i	0.559001	−	0.255287i	0.674819	+	0.737983i	$0.264222\pi$
$948$	−433.361	−	49.7649i	−0.457132	−	0.0524946i
$949$	−209.467	−	1456.88i	−0.220724	−	1.53517i
$950$	36.1833	+	123.229i	0.0380877	+	0.129715i
$951$	420.387	−	994.493i	0.442047	−	1.04573i
$952$	−83.1114	+	95.9156i	−0.0873019	+	0.100752i
$953$	996.669	+	455.163i	1.04582	+	0.477611i	0.862825	−	0.505502i	$-0.168693\pi$
$953$	996.669	+	455.163i	1.04582	+	0.477611i	0.182997	+	0.983113i	$0.441420\pi$
$954$	1618.10	−	576.994i	1.69612	−	0.604815i
$955$	−348.319	−	401.982i	−0.364732	−	0.420923i
$956$	1542.83	+	1336.87i	1.61383	+	1.39840i
$957$	−181.922	+	89.4236i	−0.190096	+	0.0934416i
$958$	−2133.80	−	1371.31i	−2.22735	−	1.43143i
$959$	126.315	+	18.1614i	0.131716	+	0.0189378i
$960$	−70.2950	+	612.141i	−0.0732239	+	0.637646i
$961$	−633.638	−	407.214i	−0.659352	−	0.423740i
$962$	−665.233	+	576.427i	−0.691510	+	0.599197i
$963$	235.651	−	124.284i	0.244705	−	0.129059i
$964$	497.339	+	573.960i	0.515912	+	0.595394i
$965$	−17.0318	−	2.44880i	−0.0176495	−	0.00253762i
$966$	104.087	+	152.254i	0.107751	+	0.157613i
$967$	−695.393			−0.719124			−0.359562	−	0.933121i	$-0.617074\pi$
$967$	−695.393			−0.719124			−0.359562	+	0.933121i	$0.617074\pi$
$968$		−	698.477i		−	0.721567i
$969$	75.3007	−	51.4789i	0.0777097	−	0.0531258i
$970$	−165.581	+	106.413i	−0.170702	+	0.109704i
$971$	−541.919	−	247.486i	−0.558104	−	0.254878i	0.116332	−	0.993210i	$-0.462886\pi$
$971$	−541.919	−	247.486i	−0.558104	−	0.254878i	−0.674437	+	0.738333i	$0.735613\pi$
$972$	971.264	−	1119.83i	0.999243	−	1.15209i
$973$	−131.027	+	84.2062i	−0.134663	+	0.0865429i
$974$	798.559	−	2719.64i	0.819876	−	2.79224i
$975$	1010.16	+	826.165i	1.03606	+	0.847349i
$976$	241.675			0.247618
$977$	190.358	−	648.300i	0.194839	−	0.663562i	−0.802885	−	0.596134i	$-0.796703\pi$
$977$	190.358	−	648.300i	0.194839	−	0.663562i	0.997724	−	0.0674277i	$-0.0214792\pi$
$978$	−1076.11	−	1172.72i	−1.10031	−	1.19910i
$979$	−135.395	−	156.254i	−0.138300	−	0.159606i
$980$	−160.989	−	548.277i	−0.164274	−	0.559466i
$981$	−510.911	+	662.303i	−0.520806	+	0.675130i
$982$	1438.29	+	924.330i	1.46465	+	0.941273i
$983$	−515.418	−	802.006i	−0.524331	−	0.815876i	0.473561	−	0.880761i	$-0.342968\pi$
$983$	−515.418	−	802.006i	−0.524331	−	0.815876i	−0.997893	+	0.0648852i	$0.979332\pi$
$984$	−40.1569	+	36.8487i	−0.0408099	+	0.0374479i
$985$	69.5657	+	44.7072i	0.0706251	+	0.0453880i
$986$	−767.624	−	350.562i	−0.778524	−	0.355540i
$987$	28.8295	+	166.683i	0.0292092	+	0.168879i
$988$	−157.400	−	181.650i	−0.159312	−	0.183856i
$989$	547.189	−	78.6739i	0.553275	−	0.0795490i
$990$	−51.6341	+	221.854i	−0.0521556	+	0.224095i
$991$	597.654	−	689.730i	0.603082	−	0.695994i	−0.369321	−	0.929302i	$-0.620410\pi$
$991$	597.654	−	689.730i	0.603082	−	0.695994i	0.972403	+	0.233308i	$0.0749551\pi$
$992$	149.577	+	509.414i	0.150784	+	0.513522i
$993$	−777.276	−	328.566i	−0.782755	−	0.330882i
$994$	23.6304	+	164.353i	0.0237730	+	0.165345i
$995$	361.587	+	562.640i	0.363404	+	0.565467i
$996$	−2924.79	−	769.088i	−2.93654	−	0.772176i
$997$	1612.92	+	473.595i	1.61777	+	0.475020i	0.960418	−	0.278564i	$-0.0898584\pi$
$997$	1612.92	+	473.595i	1.61777	+	0.475020i	0.657352	+	0.753584i	$0.271677\pi$
$998$	−503.169	+	229.789i	−0.504177	+	0.230250i
$999$	293.710	+	213.519i	0.294004	+	0.213733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.k.a.14.6	✓	440
3.2	odd	2	inner	201.3.k.a.14.39	yes	440
67.24	even	11	inner	201.3.k.a.158.39	yes	440
201.158	odd	22	inner	201.3.k.a.158.6	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.k.a.14.6	✓	440	1.1	even	1	trivial
201.3.k.a.14.39	yes	440	3.2	odd	2	inner
201.3.k.a.158.6	yes	440	201.158	odd	22	inner
201.3.k.a.158.39	yes	440	67.24	even	11	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.89089 + 1.32022i) q^{2} +(0.926782 + 2.85326i) q^{3} +(3.99480 - 4.61025i) q^{4} +(1.94917 - 0.280248i) q^{5} +(-6.44616 - 7.02489i) q^{6} +(-0.497027 - 1.08834i) q^{7} +(-1.88048 + 6.40434i) q^{8} +(-7.28215 + 5.28870i) q^{9} +O(q^{10})\)	\(q+(-2.89089 + 1.32022i) q^{2} +(0.926782 + 2.85326i) q^{3} +(3.99480 - 4.61025i) q^{4} +(1.94917 - 0.280248i) q^{5} +(-6.44616 - 7.02489i) q^{6} +(-0.497027 - 1.08834i) q^{7} +(-1.88048 + 6.40434i) q^{8} +(-7.28215 + 5.28870i) q^{9} +(-5.26484 + 3.38351i) q^{10} +(-4.00294 + 0.575536i) q^{11} +(16.8565 + 7.12550i) q^{12} +(-19.7600 + 5.80205i) q^{13} +(2.87370 + 2.49007i) q^{14} +(2.60608 + 5.30175i) q^{15} +(0.453716 + 3.15566i) q^{16} +(-12.0105 + 10.4071i) q^{17} +(14.0696 - 24.9031i) q^{18} +(-0.794782 + 1.74033i) q^{19} +(6.49453 - 10.1057i) q^{20} +(2.64467 - 2.42680i) q^{21} +(10.8122 - 6.94859i) q^{22} +(8.74103 - 13.6013i) q^{23} +(-20.0160 + 0.569925i) q^{24} +(-20.2666 + 5.95081i) q^{25} +(49.4638 - 42.8606i) q^{26} +(-21.8390 - 15.8764i) q^{27} +(-7.00302 - 2.05627i) q^{28} -16.7084i q^{29} +(-14.5334 - 11.8862i) q^{30} +(-13.8311 - 4.06119i) q^{31} +(-19.9123 - 30.9842i) q^{32} +(-5.35200 - 10.8880i) q^{33} +(20.9812 - 45.9423i) q^{34} +(-1.27379 - 1.98206i) q^{35} +(-4.70855 + 54.6998i) q^{36} -13.4489 q^{37} -6.08039i q^{38} +(-34.8679 - 51.0030i) q^{39} +(-1.87058 + 13.0101i) q^{40} +(2.05699 - 1.78239i) q^{41} +(-4.44153 + 10.5072i) q^{42} +(22.3911 + 25.8407i) q^{43} +(-13.3376 + 20.7537i) q^{44} +(-12.7120 + 12.3494i) q^{45} +(-7.31256 + 50.8600i) q^{46} +(-25.4790 + 39.6461i) q^{47} +(-8.58343 + 4.21918i) q^{48} +(31.1507 - 35.9499i) q^{49} +(50.7321 - 43.9596i) q^{50} +(-40.8253 - 24.6238i) q^{51} +(-52.1882 + 114.276i) q^{52} +(45.3907 + 39.3313i) q^{53} +(84.0944 + 17.0645i) q^{54} +(-7.64111 + 2.24363i) q^{55} +(7.90473 - 1.13653i) q^{56} +(-5.70220 - 0.654811i) q^{57} +(22.0589 + 48.3022i) q^{58} +(-5.94552 + 20.2486i) q^{59} +(34.8531 + 9.16479i) q^{60} +(10.7882 - 75.0334i) q^{61} +(45.3459 - 6.51976i) q^{62} +(9.37530 + 5.29681i) q^{63} +(87.7423 + 56.3885i) q^{64} +(-36.8895 + 16.8469i) q^{65} +(29.8467 + 24.4102i) q^{66} +(-28.2074 + 60.7729i) q^{67} +96.9455i q^{68} +(46.9090 + 12.3349i) q^{69} +(6.29916 + 4.04822i) q^{70} +(33.0016 + 28.5961i) q^{71} +(-20.1766 - 56.5826i) q^{72} +(-10.1712 + 70.7422i) q^{73} +(38.8792 - 17.7555i) q^{74} +(-35.7619 - 52.3107i) q^{75} +(4.84835 + 10.6164i) q^{76} +(2.61594 + 4.07049i) q^{77} +(168.135 + 101.411i) q^{78} +(-22.8701 + 6.71528i) q^{79} +(1.76874 + 6.02377i) q^{80} +(25.0594 - 77.0261i) q^{81} +(-3.59337 + 7.86838i) q^{82} +(-163.570 + 23.5178i) q^{83} +(-0.623202 - 21.8871i) q^{84} +(-20.4938 + 23.6511i) q^{85} +(-98.8458 - 45.1414i) q^{86} +(47.6735 - 15.4851i) q^{87} +(3.84153 - 26.7185i) q^{88} +(27.6402 + 43.0090i) q^{89} +(20.4450 - 52.4833i) q^{90} +(16.1358 + 18.6217i) q^{91} +(-27.7867 - 94.6328i) q^{92} +(-1.23084 - 43.2276i) q^{93} +(21.3152 - 148.250i) q^{94} +(-1.06144 + 3.61493i) q^{95} +(69.9514 - 85.5305i) q^{96} +31.4504 q^{97} +(-42.5914 + 145.053i) q^{98} +(26.1062 - 25.3615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 11 q^{3} + 70 q^{4} - 17 q^{6} - 30 q^{7} - 15 q^{9}+O(q^{10}) \) 440 * q - 11 * q^3 + 70 * q^4 - 17 * q^6 - 30 * q^7 - 15 * q^9	\( 440 q - 11 q^{3} + 70 q^{4} - 17 q^{6} - 30 q^{7} - 15 q^{9} - 34 q^{10} - 123 q^{12} + 10 q^{13} + 19 q^{15} - 226 q^{16} - 33 q^{18} - 100 q^{19} + 85 q^{21} - 454 q^{22} - 251 q^{24} + 142 q^{25} - 53 q^{27} + 642 q^{28} - 80 q^{30} - 130 q^{31} + 104 q^{33} + 26 q^{34} + 67 q^{36} - 144 q^{37} + 117 q^{39} - 182 q^{40} + 193 q^{42} - 156 q^{43} + 341 q^{45} - 746 q^{46} - 485 q^{48} - 354 q^{49} - 125 q^{51} + 1130 q^{52} + 272 q^{54} - 590 q^{55} + 15 q^{57} - 274 q^{58} - 217 q^{60} - 1134 q^{61} + 279 q^{63} + 58 q^{64} + 1288 q^{66} - 87 q^{69} + 1038 q^{70} - 977 q^{72} + 1208 q^{73} - 751 q^{75} + 1126 q^{76} - 11 q^{78} + 678 q^{79} + 125 q^{81} + 510 q^{82} + 191 q^{84} + 166 q^{85} + 1080 q^{87} + 62 q^{88} - 105 q^{90} + 550 q^{91} + 635 q^{93} + 986 q^{94} - 1632 q^{96} - 112 q^{97} - 500 q^{99}+O(q^{100}) \) 440 * q - 11 * q^3 + 70 * q^4 - 17 * q^6 - 30 * q^7 - 15 * q^9 - 34 * q^10 - 123 * q^12 + 10 * q^13 + 19 * q^15 - 226 * q^16 - 33 * q^18 - 100 * q^19 + 85 * q^21 - 454 * q^22 - 251 * q^24 + 142 * q^25 - 53 * q^27 + 642 * q^28 - 80 * q^30 - 130 * q^31 + 104 * q^33 + 26 * q^34 + 67 * q^36 - 144 * q^37 + 117 * q^39 - 182 * q^40 + 193 * q^42 - 156 * q^43 + 341 * q^45 - 746 * q^46 - 485 * q^48 - 354 * q^49 - 125 * q^51 + 1130 * q^52 + 272 * q^54 - 590 * q^55 + 15 * q^57 - 274 * q^58 - 217 * q^60 - 1134 * q^61 + 279 * q^63 + 58 * q^64 + 1288 * q^66 - 87 * q^69 + 1038 * q^70 - 977 * q^72 + 1208 * q^73 - 751 * q^75 + 1126 * q^76 - 11 * q^78 + 678 * q^79 + 125 * q^81 + 510 * q^82 + 191 * q^84 + 166 * q^85 + 1080 * q^87 + 62 * q^88 - 105 * q^90 + 550 * q^91 + 635 * q^93 + 986 * q^94 - 1632 * q^96 - 112 * q^97 - 500 * q^99

Introduction

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