LMFDB - Embedded newform 201.3.k.a.14.18

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			14.18
Character	$\chi$	$=$	201.14
Dual form			201.3.k.a.158.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.912928 + 0.416920i) q^{2} +(-0.305710 + 2.98438i) q^{3} +(-1.95983 + 2.26176i) q^{4} +(-6.49262 + 0.933498i) q^{5} +(-0.965159 - 2.85198i) q^{6} +(4.87674 + 10.6786i) q^{7} +(1.97722 - 6.73380i) q^{8} +(-8.81308 - 1.82471i) q^{9} +O(q^{10})$	\(q+(-0.912928 + 0.416920i) q^{2} +(-0.305710 + 2.98438i) q^{3} +(-1.95983 + 2.26176i) q^{4} +(-6.49262 + 0.933498i) q^{5} +(-0.965159 - 2.85198i) q^{6} +(4.87674 + 10.6786i) q^{7} +(1.97722 - 6.73380i) q^{8} +(-8.81308 - 1.82471i) q^{9} +(5.53810 - 3.55912i) q^{10} +(9.70154 - 1.39487i) q^{11} +(-6.15082 - 6.54032i) q^{12} +(-9.96353 + 2.92556i) q^{13} +(-8.90424 - 7.71556i) q^{14} +(-0.801059 - 19.6618i) q^{15} +(-0.701249 - 4.87729i) q^{16} +(-4.91437 + 4.25832i) q^{17} +(8.80647 - 2.00853i) q^{18} +(11.5967 - 25.3933i) q^{19} +(10.6131 - 16.5143i) q^{20} +(-33.3598 + 11.2895i) q^{21} +(-8.27526 + 5.31819i) q^{22} +(-4.00510 + 6.23206i) q^{23} +(19.4918 + 7.95937i) q^{24} +(17.2954 - 5.07838i) q^{25} +(7.87627 - 6.82482i) q^{26} +(8.13987 - 25.7438i) q^{27} +(-33.7100 - 9.89814i) q^{28} +23.6126i q^{29} +(8.92873 + 17.6159i) q^{30} +(13.9838 + 4.10601i) q^{31} +(17.8507 + 27.7762i) q^{32} +(1.19698 + 29.3795i) q^{33} +(2.71108 - 5.93645i) q^{34} +(-41.6313 - 64.7795i) q^{35} +(21.3992 - 16.3570i) q^{36} -50.1270 q^{37} +28.0172i q^{38} +(-5.68504 - 30.6294i) q^{39} +(-6.55136 + 45.5657i) q^{40} +(30.1287 - 26.1067i) q^{41} +(25.7483 - 24.2149i) q^{42} +(-19.3826 - 22.3687i) q^{43} +(-15.8585 + 24.6763i) q^{44} +(58.9234 + 3.62015i) q^{45} +(1.05810 - 7.35923i) q^{46} +(-43.4804 + 67.6568i) q^{47} +(14.7701 - 0.601760i) q^{48} +(-58.1613 + 67.1217i) q^{49} +(-13.6722 + 11.8470i) q^{50} +(-11.2061 - 15.9682i) q^{51} +(12.9099 - 28.2687i) q^{52} +(-42.7164 - 37.0140i) q^{53} +(3.30199 + 26.8959i) q^{54} +(-61.6863 + 18.1127i) q^{55} +(81.5498 - 11.7251i) q^{56} +(72.2381 + 42.3721i) q^{57} +(-9.84458 - 21.5566i) q^{58} +(5.76364 - 19.6292i) q^{59} +(46.0403 + 36.7220i) q^{60} +(-11.5132 + 80.0761i) q^{61} +(-14.4781 + 2.08163i) q^{62} +(-23.4939 - 103.010i) q^{63} +(-11.2959 - 7.25945i) q^{64} +(61.9584 - 28.2955i) q^{65} +(-13.3417 - 26.3224i) q^{66} +(12.7478 + 65.7761i) q^{67} -19.4607i q^{68} +(-17.3744 - 13.8580i) q^{69} +(65.0143 + 41.7821i) q^{70} +(52.6087 + 45.5857i) q^{71} +(-29.7126 + 55.7377i) q^{72} +(2.24030 - 15.5817i) q^{73} +(45.7623 - 20.8990i) q^{74} +(9.86847 + 53.1685i) q^{75} +(34.7060 + 75.9955i) q^{76} +(62.2072 + 96.7963i) q^{77} +(17.9600 + 25.5922i) q^{78} +(35.1021 - 10.3069i) q^{79} +(9.10588 + 31.0118i) q^{80} +(74.3409 + 32.1626i) q^{81} +(-16.6210 + 36.3948i) q^{82} +(41.9879 - 6.03694i) q^{83} +(39.8453 - 97.5775i) q^{84} +(27.9320 - 32.2352i) q^{85} +(27.0208 + 12.3400i) q^{86} +(-70.4690 - 7.21860i) q^{87} +(9.78932 - 68.0862i) q^{88} +(-35.6608 - 55.4892i) q^{89} +(-55.3021 + 21.2614i) q^{90} +(-79.8304 - 92.1292i) q^{91} +(-6.24612 - 21.2723i) q^{92} +(-16.5289 + 40.4777i) q^{93} +(11.4870 - 79.8937i) q^{94} +(-51.5886 + 175.695i) q^{95} +(-88.3519 + 44.7818i) q^{96} -184.345 q^{97} +(25.1127 - 85.5259i) q^{98} +(-88.0458 - 5.40937i) 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 $

$2$	−0.912928	+	0.416920i	−0.456464	+	0.208460i	−0.630359	−	0.776304i	$-0.717092\pi$
$2$	−0.912928	+	0.416920i	−0.456464	+	0.208460i	0.173894	+	0.984764i	$0.444365\pi$
$3$	−0.305710	+	2.98438i	−0.101903	+	0.994794i
$3$	−0.305710	+	2.98438i	−0.101903	+	0.994794i
$4$	−1.95983	+	2.26176i	−0.489957	+	0.565440i
$5$	−6.49262	+	0.933498i	−1.29852	+	0.186700i	−0.756683	−	0.653782i	$-0.773182\pi$
$5$	−6.49262	+	0.933498i	−1.29852	+	0.186700i	−0.541841	+	0.840481i	$0.682272\pi$
$6$	−0.965159	−	2.85198i	−0.160860	−	0.475331i
$7$	4.87674	+	10.6786i	0.696678	+	1.52551i	0.843954	+	0.536416i	$0.180222\pi$
$7$	4.87674	+	10.6786i	0.696678	+	1.52551i	−0.147276	+	0.989095i	$0.547051\pi$
$8$	1.97722	−	6.73380i	0.247153	−	0.841725i
$9$	−8.81308	−	1.82471i	−0.979231	−	0.202745i
$10$	5.53810	−	3.55912i	0.553810	−	0.355912i
$11$	9.70154	−	1.39487i	0.881959	−	0.126806i	0.313568	−	0.949566i	$-0.398476\pi$
$11$	9.70154	−	1.39487i	0.881959	−	0.126806i	0.568390	+	0.822759i	$0.307566\pi$
$12$	−6.15082	−	6.54032i	−0.512569	−	0.545026i
$13$	−9.96353	+	2.92556i	−0.766426	+	0.225043i	−0.641500	−	0.767123i	$-0.721687\pi$
$13$	−9.96353	+	2.92556i	−0.766426	+	0.225043i	−0.124926	+	0.992166i	$0.539869\pi$
$14$	−8.90424	−	7.71556i	−0.636017	−	0.551112i
$15$	−0.801059	−	19.6618i	−0.0534039	−	1.31079i
$16$	−0.701249	−	4.87729i	−0.0438280	−	0.304831i
$17$	−4.91437	+	4.25832i	−0.289081	+	0.250490i	−0.787313	−	0.616554i	$-0.788528\pi$
$17$	−4.91437	+	4.25832i	−0.289081	+	0.250490i	0.498232	+	0.867044i	$0.333983\pi$
$18$	8.80647	−	2.00853i	0.489248	−	0.111585i
$19$	11.5967	−	25.3933i	0.610354	−	1.33649i	−0.311977	−	0.950090i	$-0.600991\pi$
$19$	11.5967	−	25.3933i	0.610354	−	1.33649i	0.922331	−	0.386400i	$-0.126282\pi$
$20$	10.6131	−	16.5143i	0.530653	−	0.825713i
$21$	−33.3598	+	11.2895i	−1.58856	+	0.537597i
$22$	−8.27526	+	5.31819i	−0.376148	+	0.241736i
$23$	−4.00510	+	6.23206i	−0.174135	+	0.270959i	−0.917340	−	0.398104i	$-0.869668\pi$
$23$	−4.00510	+	6.23206i	−0.174135	+	0.270959i	0.743205	+	0.669063i	$0.233305\pi$
$24$	19.4918	+	7.95937i	0.812157	+	0.331641i
$25$	17.2954	−	5.07838i	0.691815	−	0.203135i
$26$	7.87627	−	6.82482i	0.302933	−	0.262493i
$27$	8.13987	−	25.7438i	0.301477	−	0.953474i
$28$	−33.7100	−	9.89814i	−1.20393	−	0.353505i
$29$			23.6126i			0.814228i	0.913377	+	0.407114i	$0.133465\pi$
$29$			23.6126i			0.814228i	−0.913377	+	0.407114i	$0.866535\pi$
$30$	8.92873	+	17.6159i	0.297624	+	0.587196i
$31$	13.9838	+	4.10601i	0.451090	+	0.132452i	0.499383	−	0.866381i	$-0.333560\pi$
$31$	13.9838	+	4.10601i	0.451090	+	0.132452i	−0.0482934	+	0.998833i	$0.515378\pi$
$32$	17.8507	+	27.7762i	0.557834	+	0.868006i
$33$	1.19698	+	29.3795i	0.0362720	+	0.890289i
$34$	2.71108	−	5.93645i	0.0797378	−	0.174601i
$35$	−41.6313	−	64.7795i	−1.18947	−	1.85084i
$36$	21.3992	−	16.3570i	0.594422	−	0.454361i
$37$	−50.1270			−1.35478			−0.677391	−	0.735623i	$-0.736890\pi$
$37$	−50.1270			−1.35478			−0.677391	+	0.735623i	$0.736890\pi$
$38$			28.0172i			0.737294i
$39$	−5.68504	−	30.6294i	−0.145770	−	0.785369i
$40$	−6.55136	+	45.5657i	−0.163784	+	1.13914i
$41$	30.1287	−	26.1067i	0.734847	−	0.636748i	−0.204836	−	0.978796i	$-0.565666\pi$
$41$	30.1287	−	26.1067i	0.734847	−	0.636748i	0.939682	+	0.342048i	$0.111121\pi$
$42$	25.7483	−	24.2149i	0.613055	−	0.576546i
$43$	−19.3826	−	22.3687i	−0.450757	−	0.520201i	0.484202	−	0.874956i	$-0.339110\pi$
$43$	−19.3826	−	22.3687i	−0.450757	−	0.520201i	−0.934959	+	0.354755i	$0.884564\pi$
$44$	−15.8585	+	24.6763i	−0.360420	+	0.560825i
$45$	58.9234	+	3.62015i	1.30941	+	0.0804477i
$46$	1.05810	−	7.35923i	0.0230021	−	0.159983i
$47$	−43.4804	+	67.6568i	−0.925115	+	1.43951i	−0.0270546	+	0.999634i	$0.508613\pi$
$47$	−43.4804	+	67.6568i	−0.925115	+	1.43951i	−0.898060	+	0.439873i	$0.855024\pi$
$48$	14.7701	−	0.601760i	0.307710	−	0.0125367i
$49$	−58.1613	+	67.1217i	−1.18696	+	1.36983i
$50$	−13.6722	+	11.8470i	−0.273443	+	0.236940i
$51$	−11.2061	−	15.9682i	−0.219728	−	0.313101i
$52$	12.9099	−	28.2687i	0.248267	−	0.543629i
$53$	−42.7164	−	37.0140i	−0.805971	−	0.698378i	0.151009	−	0.988532i	$-0.451748\pi$
$53$	−42.7164	−	37.0140i	−0.805971	−	0.698378i	−0.956980	+	0.290155i	$0.906293\pi$
$54$	3.30199	+	26.8959i	0.0611479	+	0.498072i
$55$	−61.6863	+	18.1127i	−1.12157	+	0.329323i
$56$	81.5498	−	11.7251i	1.45625	−	0.209377i
$57$	72.2381	+	42.3721i	1.26734	+	0.743370i
$58$	−9.84458	−	21.5566i	−0.169734	−	0.371666i
$59$	5.76364	−	19.6292i	0.0976888	−	0.332697i	−0.896118	−	0.443815i	$-0.853625\pi$
$59$	5.76364	−	19.6292i	0.0976888	−	0.332697i	0.993807	+	0.111117i	$0.0354430\pi$
$60$	46.0403	+	36.7220i	0.767339	+	0.612034i
$61$	−11.5132	+	80.0761i	−0.188741	+	1.31272i	0.646531	+	0.762887i	$0.276219\pi$
$61$	−11.5132	+	80.0761i	−0.188741	+	1.31272i	−0.835272	+	0.549836i	$0.814690\pi$
$62$	−14.4781	+	2.08163i	−0.233517	+	0.0335747i
$63$	−23.4939	−	103.010i	−0.372918	−	1.63508i
$64$	−11.2959	−	7.25945i	−0.176499	−	0.113429i
$65$	61.9584	−	28.2955i	0.953207	−	0.435315i
$66$	−13.3417	−	26.3224i	−0.202147	−	0.398824i
$67$	12.7478	+	65.7761i	0.190266	+	0.981733i
$67$	12.7478	+	65.7761i	0.190266	+	0.981733i
$68$		−	19.4607i		−	0.286187i
$69$	−17.3744	−	13.8580i	−0.251804	−	0.200840i
$70$	65.0143	+	41.7821i	0.928775	+	0.596888i
$71$	52.6087	+	45.5857i	0.740967	+	0.642052i	0.941259	−	0.337684i	$-0.109644\pi$
$71$	52.6087	+	45.5857i	0.740967	+	0.642052i	−0.200292	+	0.979736i	$0.564189\pi$
$72$	−29.7126	+	55.7377i	−0.412676	+	0.774134i
$73$	2.24030	−	15.5817i	0.0306891	−	0.213447i	−0.968707	−	0.248209i	$-0.920158\pi$
$73$	2.24030	−	15.5817i	0.0306891	−	0.213447i	0.999396	+	0.0347615i	$0.0110672\pi$
$74$	45.7623	−	20.8990i	0.618410	−	0.282418i
$75$	9.86847	+	53.1685i	0.131580	+	0.708914i
$76$	34.7060	+	75.9955i	0.456658	+	0.999941i
$77$	62.2072	+	96.7963i	0.807886	+	1.25709i
$78$	17.9600	+	25.5922i	0.230257	+	0.328105i
$79$	35.1021	−	10.3069i	0.444330	−	0.130467i	−0.0519112	−	0.998652i	$-0.516531\pi$
$79$	35.1021	−	10.3069i	0.444330	−	0.130467i	0.496241	+	0.868185i	$0.334713\pi$
$80$	9.10588	+	31.0118i	0.113824	+	0.387647i
$81$	74.3409	+	32.1626i	0.917789	+	0.397069i
$82$	−16.6210	+	36.3948i	−0.202695	+	0.443839i
$83$	41.9879	−	6.03694i	0.505878	−	0.0727343i	0.115349	−	0.993325i	$-0.463201\pi$
$83$	41.9879	−	6.03694i	0.505878	−	0.0727343i	0.390529	+	0.920591i	$0.372292\pi$
$84$	39.8453	−	97.5775i	0.474349	−	1.16164i
$85$	27.9320	−	32.2352i	0.328612	−	0.379238i
$86$	27.0208	+	12.3400i	0.314196	+	0.143488i
$87$	−70.4690	−	7.21860i	−0.809989	−	0.0829724i
$88$	9.78932	−	68.0862i	0.111242	−	0.773707i
$89$	−35.6608	−	55.4892i	−0.400683	−	0.623475i	0.581021	−	0.813889i	$-0.302653\pi$
$89$	−35.6608	−	55.4892i	−0.400683	−	0.623475i	−0.981704	+	0.190414i	$0.939017\pi$
$90$	−55.3021	+	21.2614i	−0.614468	+	0.236238i
$91$	−79.8304	−	92.1292i	−0.877257	−	1.01241i
$92$	−6.24612	−	21.2723i	−0.0678926	−	0.231221i
$93$	−16.5289	+	40.4777i	−0.177730	+	0.435244i
$94$	11.4870	−	79.8937i	0.122202	−	0.849933i
$95$	−51.5886	+	175.695i	−0.543038	+	1.84942i
$96$	−88.3519	+	44.7818i	−0.920332	+	0.466477i
$97$	−184.345			−1.90046			−0.950229	−	0.311551i	$-0.899151\pi$
$97$	−184.345			−1.90046			−0.950229	+	0.311551i	$0.899151\pi$
$98$	25.1127	−	85.5259i	0.256252	−	0.872713i
$99$	−88.0458	−	5.40937i	−0.889351	−	0.0546401i
$100$	−22.4099	+	49.0708i	−0.224099	+	0.490708i
$101$	−154.088	−	70.3697i	−1.52563	−	0.696730i	−0.536514	−	0.843892i	$-0.680259\pi$
$101$	−154.088	−	70.3697i	−1.52563	−	0.696730i	−0.989112	+	0.147162i	$0.952986\pi$
$102$	16.8878	+	9.90574i	0.165567	+	0.0971151i
$103$	−129.984	−	38.1666i	−1.26198	−	0.370550i	−0.418746	−	0.908103i	$-0.637530\pi$
$103$	−129.984	−	38.1666i	−1.26198	−	0.370550i	−0.843230	+	0.537554i	$0.819349\pi$
$104$			72.8769i			0.700739i
$105$	206.054	−	104.440i	1.96242	−	0.994666i
$106$	54.4290	+	15.9818i	0.513481	+	0.150772i
$107$	82.5086	+	11.8629i	0.771109	+	0.110869i	0.516629	−	0.856209i	$-0.327187\pi$
$107$	82.5086	+	11.8629i	0.771109	+	0.110869i	0.254480	+	0.967078i	$0.418096\pi$
$108$	42.2736	+	68.8638i	0.391422	+	0.637628i
$109$	179.458	−	52.6937i	1.64641	−	0.483429i	0.678471	−	0.734627i	$-0.262643\pi$
$109$	179.458	−	52.6937i	1.64641	−	0.483429i	0.967936	+	0.251199i	$0.0808248\pi$
$110$	48.7636	−	42.2539i	0.443306	−	0.384127i
$111$	15.3243	−	149.598i	0.138057	−	1.34773i
$112$	48.6627	−	31.2736i	0.434489	−	0.279229i
$113$	−215.960	−	31.0504i	−1.91115	−	0.274782i	−0.918464	−	0.395504i	$-0.870570\pi$
$113$	−215.960	−	31.0504i	−1.91115	−	0.274782i	−0.992686	+	0.120722i	$0.961479\pi$
$114$	−83.6140	−	8.56512i	−0.733456	−	0.0751326i
$115$	20.1860	−	44.2011i	0.175530	−	0.384358i
$116$	−53.4061	−	46.2766i	−0.460397	−	0.398936i
$117$	93.1477	−	7.60264i	0.796135	−	0.0649798i
$118$	2.92200	+	20.3230i	0.0247627	+	0.172229i
$119$	−69.4390	−	31.7117i	−0.583521	−	0.266485i
$120$	−133.983	−	33.4817i	−1.11652	−	0.279014i
$121$	−23.9244	+	7.02482i	−0.197722	+	0.0580564i
$122$	−22.8746	−	77.9039i	−0.187497	−	0.638556i
$123$	68.7017	+	97.8967i	0.558550	+	0.795908i
$124$	−36.6926	+	23.5809i	−0.295908	+	0.190169i
$125$	41.6140	−	19.0045i	0.332912	−	0.152036i
$126$	64.3951	+	84.2455i	0.511072	+	0.668615i
$127$	44.2715	+	96.9411i	0.348595	+	0.763316i	0.999990	+	0.00457706i	$0.00145693\pi$
$127$	44.2715	+	96.9411i	0.348595	+	0.763316i	−0.651395	+	0.758739i	$0.725816\pi$
$128$	−117.387	−	16.8777i	−0.917088	−	0.131857i
$129$	72.6821	−	51.0067i	0.563427	−	0.395400i
$130$	−44.7667	+	51.6635i	−0.344359	+	0.397411i
$131$	5.68733	−	8.84966i	0.0434147	−	0.0675547i	−0.818868	−	0.573982i	$-0.805398\pi$
$131$	5.68733	−	8.84966i	0.0434147	−	0.0675547i	0.862283	+	0.506428i	$0.169034\pi$
$132$	−68.7954	−	54.8716i	−0.521177	−	0.415694i
$133$	327.719			2.46405
$134$	−39.0613	−	54.7340i	−0.291502	−	0.408463i
$135$	−28.8173	+	174.743i	−0.213462	+	1.29439i
$136$	18.9579	+	41.5120i	0.139396	+	0.305235i
$137$	−16.2143	+	25.2300i	−0.118353	+	0.184161i	−0.895375	−	0.445312i	$-0.853093\pi$
$137$	−16.2143	+	25.2300i	−0.118353	+	0.184161i	0.777023	+	0.629473i	$0.216729\pi$
$138$	21.6393	+	5.40755i	0.156806	+	0.0391852i
$139$	−0.122513	−	0.852096i	−0.000881388	−	0.00613019i	0.989376	−	0.145379i	$-0.0464402\pi$
$139$	−0.122513	−	0.852096i	−0.000881388	−	0.00613019i	−0.990257	+	0.139249i	$0.955531\pi$
$140$	228.106	+	32.7967i	1.62933	+	0.234262i
$141$	−188.621	−	150.445i	−1.33774	−	1.06699i
$142$	−67.0336	−	19.6828i	−0.472067	−	0.138611i
$143$	−92.5809	+	42.2803i	−0.647419	+	0.295666i
$144$	−2.71947	+	44.2636i	−0.0188852	+	0.307386i
$145$	−22.0423	−	153.308i	−0.152016	−	1.05729i
$146$	4.45107	+	15.1590i	0.0304868	+	0.103829i
$147$	−182.536	−	194.095i	−1.24174	−	1.32038i
$148$	98.2402	−	113.375i	0.663785	−	0.766049i
$149$	−117.503	−	53.6616i	−0.788607	−	0.360145i	−0.0199462	−	0.999801i	$-0.506350\pi$
$149$	−117.503	−	53.6616i	−0.788607	−	0.360145i	−0.768661	+	0.639656i	$0.779077\pi$
$150$	−31.1763	−	44.4247i	−0.207842	−	0.296165i
$151$	89.1344	+	102.867i	0.590294	+	0.681236i	0.969785	−	0.243959i	$-0.0784464\pi$
$151$	89.1344	+	102.867i	0.590294	+	0.681236i	−0.379491	+	0.925195i	$0.623901\pi$
$152$	−148.064	−	128.298i	−0.974106	−	0.844067i
$153$	51.0809	−	28.5617i	0.333862	−	0.186678i
$154$	−97.1471	−	62.4326i	−0.630825	−	0.405407i
$155$	−94.6243	−	13.6049i	−0.610479	−	0.0877737i
$156$	80.4180	+	47.1701i	0.515500	+	0.302372i
$157$	57.0400	+	36.6574i	0.363312	+	0.233487i	0.709542	−	0.704663i	$-0.248902\pi$
$157$	57.0400	+	36.6574i	0.363312	+	0.233487i	−0.346230	+	0.938150i	$0.612538\pi$
$158$	−27.7485	+	24.0442i	−0.175624	+	0.152179i
$159$	123.523	−	116.167i	0.776873	−	0.730608i
$160$	−141.827	−	163.677i	−0.886417	−	1.02298i
$161$	−86.0814	−	12.3766i	−0.534667	−	0.0768735i
$162$	−81.2771	+	1.63206i	−0.501711	+	0.0100745i
$163$	81.2524			0.498481			0.249240	−	0.968442i	$-0.419819\pi$
$163$	81.2524			0.498481			0.249240	+	0.968442i	$0.419819\pi$
$164$			119.309i			0.727491i
$165$	−35.1973	−	189.633i	−0.213317	−	1.14929i
$166$	−35.8150	+	23.0169i	−0.215753	+	0.138656i
$167$	112.070	+	51.1808i	0.671079	+	0.306472i	0.721659	−	0.692248i	$-0.243380\pi$
$167$	112.070	+	51.1808i	0.671079	+	0.306472i	−0.0505801	+	0.998720i	$0.516107\pi$
$168$	10.0616	+	246.960i	0.0598905	+	1.47000i
$169$	−51.4587	+	33.0705i	−0.304489	+	0.195684i
$170$	−12.0604	+	41.0739i	−0.0709434	+	0.241611i
$171$	−148.538	+	202.633i	−0.868645	+	1.18499i
$172$	88.5790			0.514994
$173$	−11.4967	+	39.1541i	−0.0664547	+	0.226324i	−0.986024	−	0.166604i	$-0.946720\pi$
$173$	−11.4967	+	39.1541i	−0.0664547	+	0.226324i	0.919569	+	0.392928i	$0.128538\pi$
$174$	67.3428	−	22.7899i	0.387027	−	0.130977i
$175$	138.575	+	159.924i	0.791857	+	0.913852i
$176$	−13.6064	−	46.3391i	−0.0773090	−	0.263290i
$177$	56.8189	+	23.2017i	0.321011	+	0.131083i
$178$	55.6903	+	35.7900i	0.312867	+	0.201067i
$179$	132.404	+	206.024i	0.739685	+	1.15097i	0.983457	+	0.181140i	$0.0579786\pi$
$179$	132.404	+	206.024i	0.739685	+	1.15097i	−0.243772	+	0.969832i	$0.578385\pi$
$180$	−123.668	+	126.176i	−0.687042	+	0.700976i
$181$	−205.365	−	131.980i	−1.13462	−	0.729173i	−0.168097	−	0.985771i	$-0.553762\pi$
$181$	−205.365	−	131.980i	−1.13462	−	0.729173i	−0.966518	+	0.256598i	$0.917398\pi$
$182$	111.290	+	50.8244i	0.611483	+	0.279255i
$183$	−235.458	−	58.8399i	−1.28666	−	0.321529i
$184$	34.0464	+	39.2917i	0.185035	+	0.213542i
$185$	325.455	−	46.7934i	1.75922	−	0.252937i
$186$	−1.78630	−	43.8445i	−0.00960378	−	0.235723i
$187$	−41.7372	+	48.1672i	−0.223193	+	0.257579i
$188$	−67.8095	−	230.938i	−0.360689	−	1.22839i
$189$	314.603	−	38.6236i	1.66457	−	0.204357i
$190$	−26.1540	−	181.905i	−0.137653	−	0.957394i
$191$	27.7477	+	43.1763i	0.145276	+	0.226054i	0.906264	−	0.422712i	$-0.138922\pi$
$191$	27.7477	+	43.1763i	0.145276	+	0.226054i	−0.760988	+	0.648766i	$0.775285\pi$
$192$	25.1182	−	31.4921i	0.130824	−	0.164021i
$193$	224.569	+	65.9393i	1.16357	+	0.341654i	0.805818	−	0.592163i	$-0.201726\pi$
$193$	224.569	+	65.9393i	1.16357	+	0.341654i	0.357750	+	0.933818i	$0.383544\pi$
$194$	168.293	−	76.8570i	0.867491	−	0.396170i
$195$	65.5032	+	193.558i	0.335914	+	0.992605i
$196$	−37.8272	−	263.094i	−0.192996	−	1.34232i
$197$	158.944	+	137.726i	0.806822	+	0.699115i	0.957173	−	0.289518i	$-0.0934948\pi$
$197$	158.944	+	137.726i	0.806822	+	0.699115i	−0.150351	+	0.988633i	$0.548040\pi$
$198$	82.6347	−	31.7697i	0.417347	−	0.160453i
$199$	−66.5134	−	145.644i	−0.334238	−	0.731880i	0.665658	−	0.746257i	$-0.268151\pi$
$199$	−66.5134	−	145.644i	−0.334238	−	0.731880i	−0.999897	+	0.0143769i	$0.995424\pi$
$200$		−	126.505i		−	0.632523i
$201$	−200.198	+	17.9361i	−0.996011	+	0.0892341i
$202$	170.010			0.841634
$203$	−252.149	+	115.153i	−1.24211	+	0.567254i
$204$	58.0782	+	5.94933i	0.284697	+	0.0291634i
$205$	−171.244	+	197.626i	−0.835336	+	0.964029i
$206$	134.578	−	19.3494i	0.653292	−	0.0939292i
$207$	46.6690	−	47.6155i	0.225454	−	0.230027i
$208$	21.2557	+	46.5435i	0.102191	+	0.223767i
$209$	77.0858	−	262.530i	0.368832	−	1.25613i
$210$	−144.569	+	181.254i	−0.688426	+	0.863116i
$211$	−13.0452	+	8.38364i	−0.0618256	+	0.0397329i	−0.571188	−	0.820819i	$-0.693517\pi$
$211$	−13.0452	+	8.38364i	−0.0618256	+	0.0397329i	0.509363	+	0.860552i	$0.329881\pi$
$212$	167.434	−	24.0733i	0.789782	−	0.113553i
$213$	−152.128	+	143.068i	−0.714216	+	0.671683i
$214$	−80.2704	+	23.5695i	−0.375095	+	0.110138i
$215$	146.725	+	127.138i	0.682440	+	0.591338i
$216$	−157.259	−	105.713i	−0.728051	−	0.489414i
$217$	24.3490	+	169.351i	0.112207	+	0.780419i
$218$	−141.863	+	122.925i	−0.650750	+	0.563878i
$219$	45.8168	+	11.4494i	0.209209	+	0.0522803i
$220$	79.9279	−	175.018i	0.363309	−	0.795535i
$221$	36.5065	−	56.8052i	0.165188	−	0.257037i
$222$	48.3805	+	142.961i	0.217930	+	0.643970i
$223$	−231.244	+	148.611i	−1.03697	+	0.666419i	−0.944235	−	0.329272i	$-0.893197\pi$
$223$	−231.244	+	148.611i	−1.03697	+	0.666419i	−0.0927331	+	0.995691i	$0.529560\pi$
$224$	−209.557	+	326.077i	−0.935523	+	1.45570i
$225$	−161.692	+	13.1972i	−0.718632	+	0.0586541i
$226$	210.102	−	61.6914i	0.929653	−	0.272971i
$227$	−166.556	+	144.322i	−0.733729	+	0.635780i	−0.939393	−	0.342843i	$-0.888610\pi$
$227$	−166.556	+	144.322i	−0.733729	+	0.635780i	0.205664	+	0.978623i	$0.434065\pi$
$228$	−237.410	+	80.3434i	−1.04127	+	0.352383i
$229$	169.922	+	49.8937i	0.742019	+	0.217876i	0.630828	−	0.775923i	$-0.282715\pi$
$229$	169.922	+	49.8937i	0.742019	+	0.217876i	0.111191	+	0.993799i	$0.464533\pi$
$230$			48.7684i			0.212037i
$231$	−307.895	+	156.059i	−1.33288	+	0.675578i
$232$	159.002	+	46.6873i	0.685356	+	0.201239i
$233$	110.379	+	171.753i	0.473729	+	0.737136i	0.993082	−	0.117423i	$-0.0374635\pi$
$233$	110.379	+	171.753i	0.473729	+	0.737136i	−0.519353	+	0.854560i	$0.673827\pi$
$234$	−81.8675	+	45.7759i	−0.349861	+	0.195623i
$235$	219.144	−	479.859i	0.932528	−	2.04195i
$236$	33.1007	+	51.5057i	0.140257	+	0.218245i
$237$	20.0287	+	107.909i	0.0845093	+	0.455312i
$238$	76.6141			0.321908
$239$		−	276.108i		−	1.15527i	−0.816297	−	0.577633i	$-0.803977\pi$
$239$		−	276.108i		−	1.15527i	0.816297	−	0.577633i	$-0.196023\pi$
$240$	−95.3348	+	17.6948i	−0.397228	+	0.0737285i
$241$	−67.2949	+	468.047i	−0.279232	+	1.94210i	0.0522348	+	0.998635i	$0.483366\pi$
$241$	−67.2949	+	468.047i	−0.279232	+	1.94210i	−0.331467	+	0.943467i	$0.607543\pi$
$242$	18.9124	−	16.3877i	0.0781505	−	0.0677178i
$243$	−118.712	+	212.029i	−0.488528	+	0.872548i
$244$	−158.549	−	182.976i	−0.649792	−	0.749900i
$245$	314.961	−	490.089i	1.28556	−	2.00036i
$246$	−103.535	−	60.7295i	−0.420873	−	0.246868i
$247$	−41.2549	+	286.934i	−0.167024	+	1.16168i
$248$	55.2981	−	86.0454i	0.222976	−	0.346957i
$249$	5.18046	+	127.153i	0.0208051	+	0.510656i
$250$	−30.0673	+	34.6995i	−0.120269	+	0.138798i
$251$	−37.4509	+	32.4513i	−0.149207	+	0.129288i	−0.726266	−	0.687414i	$-0.758746\pi$
$251$	−37.4509	+	32.4513i	−0.149207	+	0.129288i	0.577059	+	0.816702i	$0.304200\pi$
$252$	279.028	+	148.744i	1.10725	+	0.590254i
$253$	−30.1627	+	66.0472i	−0.119220	+	0.261056i
$254$	−80.8335	−	70.0426i	−0.318242	−	0.275758i
$255$	87.6632	+	93.2144i	0.343777	+	0.365547i
$256$	165.737	−	48.6648i	0.647411	−	0.190097i
$257$	388.806	−	55.9018i	1.51286	−	0.217517i	0.664643	−	0.747161i	$-0.268584\pi$
$257$	388.806	−	55.9018i	1.51286	−	0.217517i	0.848220	+	0.529644i	$0.177675\pi$
$258$	−45.0878	+	76.8681i	−0.174759	+	0.297938i
$259$	−244.456	−	535.285i	−0.943847	−	2.06674i
$260$	−57.4302	+	195.589i	−0.220886	+	0.752267i
$261$	43.0861	−	208.100i	0.165081	−	0.797317i
$262$	−1.50252	+	10.4503i	−0.00573482	+	0.0398865i
$263$	49.4779	−	7.11385i	0.188129	−	0.0270489i	−0.0476062	−	0.998866i	$-0.515159\pi$
$263$	49.4779	−	7.11385i	0.188129	−	0.0270489i	0.235735	+	0.971817i	$0.424250\pi$
$264$	200.203	+	50.0297i	0.758343	+	0.189506i
$265$	311.894	+	200.442i	1.17696	+	0.756386i
$266$	−299.184	+	136.633i	−1.12475	+	0.513656i
$267$	176.503	−	89.4618i	0.661060	−	0.335063i
$268$	−173.753	−	100.077i	−0.648333	−	0.373422i
$269$		−	220.987i		−	0.821512i	−0.911745	−	0.410756i	$-0.865265\pi$
$269$		−	220.987i		−	0.821512i	0.911745	−	0.410756i	$-0.134735\pi$
$270$	−46.5458	−	171.543i	−0.172392	−	0.635343i
$271$	51.4853	+	33.0876i	0.189983	+	0.122094i	0.632174	−	0.774826i	$-0.282163\pi$
$271$	51.4853	+	33.0876i	0.189983	+	0.122094i	−0.442192	+	0.896921i	$0.645799\pi$
$272$	24.2153	+	20.9827i	0.0890268	+	0.0771422i
$273$	299.354	−	210.080i	1.09653	−	0.769523i
$274$	4.28363	−	29.7933i	0.0156337	−	0.108735i
$275$	160.708	−	73.3930i	0.584393	−	0.266884i
$276$	65.3943	−	12.1377i	0.236936	−	0.0439770i
$277$	−4.01662	−	8.79517i	−0.0145004	−	0.0317515i	0.902243	−	0.431227i	$-0.141919\pi$
$277$	−4.01662	−	8.79517i	−0.0145004	−	0.0317515i	−0.916744	+	0.399476i	$0.869192\pi$
$278$	0.467102	+	0.726824i	0.00168022	+	0.00261448i
$279$	−115.748	−	61.7029i	−0.414867	−	0.221157i
$280$	−518.527	+	152.253i	−1.85188	+	0.543761i
$281$	61.2732	+	208.677i	0.218054	+	0.742625i	0.993761	+	0.111531i	$0.0355754\pi$
$281$	61.2732	+	208.677i	0.218054	+	0.742625i	−0.775707	+	0.631094i	$0.782606\pi$
$282$	234.922	+	58.7058i	0.833056	+	0.208177i
$283$	−32.5072	+	71.1808i	−0.114866	+	0.251522i	−0.958330	−	0.285665i	$-0.907786\pi$
$283$	−32.5072	+	71.1808i	−0.114866	+	0.251522i	0.843463	+	0.537187i	$0.180513\pi$
$284$	−206.208	+	29.6482i	−0.726084	+	0.104395i
$285$	−508.569	−	207.672i	−1.78445	−	0.728672i
$286$	66.8922	−	77.1977i	0.233889	−	0.269922i
$287$	425.712	+	194.416i	1.48332	+	0.677409i
$288$	−106.636	−	277.366i	−0.370264	−	0.963077i
$289$	−35.1113	+	244.204i	−0.121492	+	0.844998i
$290$	84.0401	+	130.769i	0.289794	+	0.450928i
$291$	56.3559	−	550.155i	0.193663	−	1.89057i
$292$	30.8514	+	35.6044i	0.105655	+	0.121933i
$293$	50.8346	+	173.127i	0.173497	+	0.590877i	0.999625	+	0.0273937i	$0.00872077\pi$
$293$	50.8346	+	173.127i	0.173497	+	0.590877i	−0.826128	+	0.563483i	$0.809461\pi$
$294$	247.565	+	101.092i	0.842057	+	0.343850i
$295$	−19.0973	+	132.825i	−0.0647368	+	0.450254i
$296$	−99.1121	+	337.545i	−0.334838	+	1.14035i
$297$	43.0601	−	261.109i	0.144983	−	0.879153i
$298$	129.644			0.435047
$299$	21.6727	−	73.8105i	0.0724840	−	0.246858i
$300$	−139.595	−	81.8810i	−0.465317	−	0.272937i
$301$	144.342	−	316.064i	0.479541	−	1.05005i
$302$	−124.261	−	56.7479i	−0.411459	−	0.187907i
$303$	257.116	−	438.346i	0.848569	−	1.44669i
$304$	−131.983	−	38.7536i	−0.434154	−	0.127479i
$305$		−	530.652i		−	1.73984i
$306$	−34.7253	+	47.3715i	−0.113481	+	0.154809i
$307$	436.417	+	128.143i	1.42155	+	0.417405i	0.900028	−	0.435831i	$-0.143546\pi$
$307$	436.417	+	128.143i	1.42155	+	0.417405i	0.521524	+	0.853237i	$0.325364\pi$
$308$	−340.845	−	49.0062i	−1.10664	−	0.159111i
$309$	153.641	−	376.253i	0.497220	−	1.21765i
$310$	92.0574	−	27.0305i	0.296959	−	0.0871951i
$311$	−411.989	+	356.991i	−1.32472	+	1.14788i	−0.347028	+	0.937855i	$0.612809\pi$
$311$	−411.989	+	356.991i	−1.32472	+	1.14788i	−0.977696	+	0.210025i	$0.932645\pi$
$312$	−217.493	−	22.2792i	−0.697092	−	0.0714076i
$313$	101.566	−	65.2727i	0.324493	−	0.208539i	−0.368244	−	0.929729i	$-0.620041\pi$
$313$	101.566	−	65.2727i	0.324493	−	0.208539i	0.692737	+	0.721190i	$0.256405\pi$
$314$	−67.3567	−	9.68443i	−0.214512	−	0.0308421i
$315$	248.696	+	646.872i	0.789512	+	2.05356i
$316$	−45.4823	+	99.5923i	−0.143931	+	0.315166i
$317$	−77.1242	−	66.8285i	−0.243294	−	0.210815i	0.524675	−	0.851303i	$-0.324187\pi$
$317$	−77.1242	−	66.8285i	−0.243294	−	0.210815i	−0.767969	+	0.640487i	$0.778732\pi$
$318$	−64.3352	+	157.551i	−0.202312	+	0.495444i
$319$	32.9365	+	229.079i	0.103249	+	0.718115i
$320$	80.1168	+	36.5881i	0.250365	+	0.114338i
$321$	−60.6272	+	242.611i	−0.188870	+	0.755797i
$322$	83.7462	−	24.5901i	0.260081	−	0.0763668i
$323$	51.1423	+	174.175i	0.158335	+	0.539241i
$324$	−218.439	+	105.108i	−0.674196	+	0.324408i
$325$	−157.466	+	101.197i	−0.484511	+	0.311376i
$326$	−74.1776	+	33.8758i	−0.227539	+	0.103913i
$327$	102.396	+	551.681i	0.313138	+	1.68710i
$328$	−116.226	−	254.499i	−0.354348	−	0.775913i
$329$	−934.521	−	134.364i	−2.84049	−	0.408401i
$330$	111.194	+	158.447i	0.336953	+	0.480142i
$331$	7.85061	−	9.06009i	0.0237179	−	0.0273719i	−0.743767	−	0.668439i	$-0.766963\pi$
$331$	7.85061	−	9.06009i	0.0237179	−	0.0273719i	0.767485	+	0.641067i	$0.221508\pi$
$332$	−68.6348	+	106.798i	−0.206731	+	0.321680i
$333$	441.773	+	91.4671i	1.32665	+	0.274676i
$334$	−123.650			−0.370211
$335$	−144.169	−	415.159i	−0.430354	−	1.23928i
$336$	78.4559	+	154.789i	0.233500	+	0.460681i
$337$	129.498	+	283.560i	0.384266	+	0.841425i	0.998626	+	0.0523992i	$0.0166868\pi$
$337$	129.498	+	283.560i	0.384266	+	0.841425i	−0.614360	+	0.789026i	$0.710586\pi$
$338$	33.1904	−	51.6452i	0.0981963	−	0.152796i
$339$	158.687	−	635.015i	0.468104	−	1.87320i
$340$	18.1665	+	126.351i	0.0534310	+	0.371621i
$341$	141.392	+	20.3290i	0.414638	+	0.0596160i
$342$	51.1232	−	246.918i	0.149483	−	0.721982i
$343$	−448.470	−	131.683i	−1.30749	−	0.383914i
$344$	−188.950	+	86.2904i	−0.549272	+	0.250844i
$345$	125.742	+	73.7554i	0.364470	+	0.213784i
$346$	−5.82849	−	40.5381i	−0.0168454	−	0.117162i
$347$	−53.7277	−	182.980i	−0.154835	−	0.527319i	0.845139	−	0.534546i	$-0.179518\pi$
$347$	−53.7277	−	182.980i	−0.154835	−	0.527319i	−0.999974	+	0.00722761i	$0.997699\pi$
$348$	154.434	−	145.237i	0.443776	−	0.417348i
$349$	17.4242	−	20.1086i	0.0499261	−	0.0576178i	−0.730237	−	0.683194i	$-0.760590\pi$
$349$	17.4242	−	20.1086i	0.0499261	−	0.0576178i	0.780163	+	0.625576i	$0.215136\pi$
$350$	−193.185	−	88.2245i	−0.551956	−	0.252070i
$351$	−5.78698	+	280.313i	−0.0164871	+	0.798612i
$352$	211.923	+	244.573i	0.602055	+	0.694808i
$353$	−124.251	−	107.664i	−0.351985	−	0.304997i	0.460864	−	0.887471i	$-0.347539\pi$
$353$	−124.251	−	107.664i	−0.351985	−	0.304997i	−0.812849	+	0.582474i	$0.802085\pi$
$354$	−61.5449	+	2.50745i	−0.173856	+	0.00708319i
$355$	−384.122	−	246.860i	−1.08203	−	0.695381i
$356$	195.392	+	28.0932i	0.548855	+	0.0789134i
$357$	115.868	−	197.538i	0.324560	−	0.553328i
$358$	−206.771	−	132.883i	−0.577572	−	0.371183i
$359$	−61.3405	+	53.1518i	−0.170865	+	0.148055i	−0.736096	−	0.676878i	$-0.763333\pi$
$359$	−61.3405	+	53.1518i	−0.170865	+	0.148055i	0.565231	+	0.824933i	$0.308787\pi$
$360$	140.882	−	389.620i	0.391339	−	1.08228i
$361$	−273.931	−	316.133i	−0.758811	−	0.875715i
$362$	242.509	+	34.8675i	0.669915	+	0.0963192i
$363$	−13.6509	−	73.5470i	−0.0376057	−	0.202609i
$364$	364.828			1.00227
$365$			103.257i			0.282896i
$366$	239.488	−	44.4507i	0.654339	−	0.121450i
$367$	−267.265	+	171.761i	−0.728242	+	0.468013i	−0.851495	−	0.524363i	$-0.824304\pi$
$367$	−267.265	+	171.761i	−0.728242	+	0.468013i	0.123253	+	0.992375i	$0.460667\pi$
$368$	33.2041	+	15.1638i	0.0902286	+	0.0412060i
$369$	−313.164	+	175.104i	−0.848683	+	0.474537i
$370$	−277.608	+	178.408i	−0.750293	+	0.482184i
$371$	186.940	−	636.659i	0.503881	−	1.71606i
$372$	−59.1572	−	116.714i	−0.159025	−	0.313746i
$373$	538.807			1.44452			0.722261	−	0.691621i	$-0.243103\pi$
$373$	538.807			1.44452			0.722261	+	0.691621i	$0.243103\pi$
$374$	18.0211	−	61.3743i	0.0481848	−	0.164102i
$375$	43.9949	+	130.002i	0.117320	+	0.346672i
$376$	369.617	+	426.561i	0.983024	+	1.13447i
$377$	−69.0800	−	235.265i	−0.183236	−	0.624045i
$378$	−271.107	+	166.425i	−0.717215	+	0.440278i
$379$	−325.167	−	208.972i	−0.857960	−	0.551377i	0.0360880	−	0.999349i	$-0.488510\pi$
$379$	−325.167	−	208.972i	−0.857960	−	0.551377i	−0.894048	+	0.447971i	$0.852147\pi$
$380$	−296.275	−	461.012i	−0.779670	−	1.21319i
$381$	−302.844	+	102.487i	−0.794865	+	0.268996i
$382$	−43.3328	−	27.8483i	−0.113437	−	0.0729012i
$383$	265.545	+	121.271i	0.693330	+	0.316633i	0.730730	−	0.682667i	$-0.239180\pi$
$383$	265.545	+	121.271i	0.693330	+	0.316633i	−0.0373993	+	0.999300i	$0.511907\pi$
$384$	86.2560	−	345.169i	0.224625	−	0.898877i
$385$	−494.247	−	570.391i	−1.28376	−	1.48154i
$386$	−232.506	+	33.4294i	−0.602348	+	0.0866046i
$387$	130.004	+	232.504i	0.335927	+	0.600787i
$388$	361.283	−	416.943i	0.931143	−	1.07460i
$389$	181.763	+	619.027i	0.467256	+	1.59133i	0.769860	+	0.638213i	$0.220326\pi$
$389$	181.763	+	619.027i	0.467256	+	1.59133i	−0.302604	+	0.953116i	$0.597856\pi$
$390$	−140.498	−	149.395i	−0.360251	−	0.383064i
$391$	−6.85559	−	47.6816i	−0.0175335	−	0.121948i
$392$	336.986	+	524.361i	0.859658	+	1.33765i
$393$	24.6721	+	19.6786i	0.0627789	+	0.0500728i
$394$	−202.525	−	59.4667i	−0.514023	−	0.150931i
$395$	−218.283	+	99.6865i	−0.552615	+	0.252371i
$396$	184.789	−	188.537i	0.466639	−	0.476104i
$397$	−22.9504	−	159.624i	−0.0578097	−	0.402075i	−0.998095	−	0.0616890i	$-0.980351\pi$
$397$	−22.9504	−	159.624i	−0.0578097	−	0.402075i	0.940286	−	0.340386i	$-0.110558\pi$
$398$	121.444	+	105.232i	0.305136	+	0.264401i
$399$	−100.187	+	978.038i	−0.251095	+	2.45122i
$400$	−36.8971	−	80.7934i	−0.0922428	−	0.201983i
$401$		−	625.029i		−	1.55867i	−0.626605	−	0.779337i	$-0.715556\pi$
$401$		−	625.029i		−	1.55867i	0.626605	−	0.779337i	$-0.284444\pi$
$402$	175.289	−	99.8410i	0.436041	−	0.248361i
$403$	−151.340			−0.375534
$404$	461.146	−	210.598i	1.14145	−	0.521283i
$405$	−512.691	−	139.423i	−1.26590	−	0.344253i
$406$	182.185	−	210.252i	0.448730	−	0.517862i
$407$	−486.309	+	69.9207i	−1.19486	+	0.171795i
$408$	−129.683	+	43.8870i	−0.317851	+	0.107566i
$409$	296.992	+	650.322i	0.726142	+	1.59003i	0.805091	+	0.593151i	$0.202116\pi$
$409$	296.992	+	650.322i	0.726142	+	1.59003i	−0.0789491	+	0.996879i	$0.525156\pi$
$410$	73.9391	−	251.813i	0.180339	−	0.614179i
$411$	−70.3392	−	56.1029i	−0.171142	−	0.136503i
$412$	341.069	−	219.192i	0.827837	−	0.532019i
$413$	237.719	−	34.1789i	0.575591	−	0.0827576i
$414$	−22.7536	+	62.9268i	−0.0549603	+	0.151997i
$415$	−266.976	+	78.3912i	−0.643315	+	0.188894i
$416$	−259.117	−	224.526i	−0.622877	−	0.539726i
$417$	2.58043	−	0.105132i	0.00618809	−	0.000252114i
$418$	39.0804	+	271.810i	0.0934937	+	0.650263i
$419$	−202.980	+	175.883i	−0.484440	+	0.419769i	−0.862535	−	0.505997i	$-0.831125\pi$
$419$	−202.980	+	175.883i	−0.484440	+	0.419769i	0.378095	+	0.925767i	$0.376579\pi$
$420$	−167.612	+	670.729i	−0.399076	+	1.59697i
$421$	77.5118	−	169.727i	0.184114	−	0.403153i	−0.794959	−	0.606663i	$-0.792508\pi$
$421$	77.5118	−	169.727i	0.184114	−	0.403153i	0.979073	+	0.203510i	$0.0652351\pi$
$422$	8.41402	−	13.0925i	0.0199384	−	0.0310248i
$423$	506.650	−	516.926i	1.19775	−	1.22205i
$424$	−333.705	+	214.459i	−0.787040	+	0.505800i
$425$	−63.3705	+	98.6064i	−0.149107	+	0.232015i
$426$	79.2339	−	194.037i	0.185995	−	0.455485i
$427$	−911.247	+	267.566i	−2.13407	+	0.626619i
$428$	−188.534	+	163.365i	−0.440500	+	0.381695i
$429$	−97.8777	−	289.222i	−0.228153	−	0.674178i
$430$	−186.955	−	54.8951i	−0.434780	−	0.127663i
$431$			381.559i			0.885288i	0.896697	+	0.442644i	$0.145959\pi$
$431$			381.559i			0.885288i	−0.896697	+	0.442644i	$0.854041\pi$
$432$	−131.268	−	21.6477i	−0.303861	−	0.0501105i
$433$	−617.823	−	181.409i	−1.42684	−	0.418959i	−0.525029	−	0.851084i	$-0.675946\pi$
$433$	−617.823	−	181.409i	−1.42684	−	0.418959i	−0.901814	+	0.432125i	$0.857764\pi$
$434$	−92.8347	−	144.454i	−0.213905	−	0.332842i
$435$	464.267	−	18.9151i	1.06728	−	0.0434830i
$436$	−232.527	+	509.162i	−0.533318	+	1.16780i
$437$	111.806	+	173.974i	0.255850	+	0.398110i
$438$	−46.6009	+	8.64947i	−0.106395	+	0.0197477i
$439$	433.028			0.986395			0.493198	−	0.869917i	$-0.335828\pi$
$439$	433.028			0.986395			0.493198	+	0.869917i	$0.335828\pi$
$440$			451.196i			1.02545i
$441$	635.058	−	485.422i	1.44004	−	1.10073i
$442$	−9.64456	+	67.0794i	−0.0218203	+	0.151763i
$443$	−466.964	+	404.627i	−1.05410	+	0.913379i	−0.996385	−	0.0849547i	$-0.972925\pi$
$443$	−466.964	+	404.627i	−1.05410	+	0.913379i	−0.0577103	+	0.998333i	$0.518380\pi$
$444$	308.322	+	327.846i	0.694419	+	0.738392i
$445$	283.331	+	326.981i	0.636699	+	0.734790i
$446$	149.150	−	232.082i	0.334417	−	0.520363i
$447$	196.068	−	334.268i	0.438632	−	0.747802i
$448$	22.4333	−	156.027i	0.0500743	−	0.348274i
$449$	−4.98637	+	7.75895i	−0.0111055	+	0.0172805i	−0.846762	−	0.531972i	$-0.821451\pi$
$449$	−4.98637	+	7.75895i	−0.0111055	+	0.0172805i	0.835656	+	0.549253i	$0.185088\pi$
$450$	142.111	−	79.4608i	0.315803	−	0.176580i
$451$	255.880	−	295.301i	0.567361	−	0.654769i
$452$	493.473	−	427.597i	1.09175	−	0.946010i
$453$	−334.243	+	234.564i	−0.737843	+	0.517801i
$454$	91.8833	−	201.196i	0.202386	−	0.443164i
$455$	604.311	+	523.638i	1.32816	+	1.15085i
$456$	428.156	−	402.658i	0.938938	−	0.883022i
$457$	−190.868	+	56.0438i	−0.417654	+	0.122634i	−0.483806	−	0.875175i	$-0.660746\pi$
$457$	−190.868	+	56.0438i	−0.417654	+	0.122634i	0.0661522	+	0.997810i	$0.478928\pi$
$458$	−175.929	+	25.2947i	−0.384124	+	0.0552286i
$459$	69.6231	+	161.177i	0.151684	+	0.351147i
$460$	60.4114	+	132.282i	0.131329	+	0.287571i
$461$	218.537	−	744.268i	0.474050	−	1.61447i	−0.281629	−	0.959523i	$-0.590875\pi$
$461$	218.537	−	744.268i	0.474050	−	1.61447i	0.755679	−	0.654942i	$-0.227307\pi$
$462$	216.022	−	270.838i	0.467579	−	0.586229i
$463$	−27.7415	+	192.946i	−0.0599169	+	0.416731i	0.937683	+	0.347491i	$0.112966\pi$
$463$	−27.7415	+	192.946i	−0.0599169	+	0.416731i	−0.997600	+	0.0692397i	$0.977943\pi$
$464$	115.166	−	16.5583i	0.248202	−	0.0356860i
$465$	69.5298	−	278.236i	0.149527	−	0.598357i
$466$	−172.375	−	110.779i	−0.369904	−	0.237723i
$467$	374.017	−	170.808i	0.800892	−	0.365755i	0.0274507	−	0.999623i	$-0.491261\pi$
$467$	374.017	−	170.808i	0.800892	−	0.365755i	0.773441	+	0.633868i	$0.218534\pi$
$468$	−165.358	+	225.578i	−0.353329	+	0.482004i
$469$	−640.227	+	456.902i	−1.36509	+	0.974205i
$470$			529.442i			1.12647i
$471$	−126.837	+	159.023i	−0.269294	+	0.337628i
$472$	−120.783	−	77.6224i	−0.255896	−	0.164454i
$473$	−219.242	−	189.974i	−0.463514	−	0.401637i
$474$	−63.2742	−	90.1628i	−0.133490	−	0.190217i
$475$	71.6130	−	498.079i	0.150764	−	1.04859i
$476$	207.813	−	94.9049i	0.436581	−	0.199380i
$477$	308.924	+	404.153i	0.647639	+	0.847280i
$478$	115.115	+	252.067i	0.240827	+	0.527337i
$479$	−136.702	−	212.713i	−0.285391	−	0.444078i	0.668727	−	0.743508i	$-0.266840\pi$
$479$	−136.702	−	212.713i	−0.285391	−	0.444078i	−0.954118	+	0.299431i	$0.903203\pi$
$480$	531.832	−	373.228i	1.10798	−	0.777557i
$481$	499.442	−	146.649i	1.03834	−	0.304884i
$482$	−133.703	−	455.350i	−0.277391	−	0.944709i
$483$	63.2525	−	253.116i	0.130958	−	0.524050i
$484$	30.9991	−	67.8786i	0.0640478	−	0.140245i
$485$	1196.88	−	172.085i	2.46779	−	0.354815i
$486$	19.9765	−	243.061i	0.0411039	−	0.500126i
$487$	−313.088	+	361.323i	−0.642891	+	0.741936i	−0.979883	−	0.199572i	$-0.936045\pi$
$487$	−313.088	+	361.323i	−0.642891	+	0.741936i	0.336992	+	0.941507i	$0.390590\pi$
$488$	516.452	+	235.856i	1.05830	+	0.483311i
$489$	−24.8396	+	242.488i	−0.0507968	+	0.495886i
$490$	−83.2088	+	578.730i	−0.169814	+	1.18108i
$491$	−28.7564	−	44.7459i	−0.0585671	−	0.0911321i	0.810735	−	0.585413i	$-0.199068\pi$
$491$	−28.7564	−	44.7459i	−0.0585671	−	0.0911321i	−0.869302	+	0.494281i	$0.835431\pi$
$492$	−356.062	−	36.4738i	−0.723704	−	0.0741337i
$493$	−100.550	−	116.041i	−0.203956	−	0.235377i
$494$	−81.9659	−	279.150i	−0.165923	−	0.565081i
$495$	576.697	−	47.0695i	1.16505	−	0.0950899i
$496$	10.2201	−	71.0823i	0.0206050	−	0.143311i
$497$	−230.231	+	784.096i	−0.463242	+	1.57766i
$498$	−57.7422	−	113.922i	−0.115948	−	0.228759i
$499$	766.379			1.53583			0.767915	−	0.640551i	$-0.221294\pi$
$499$	766.379			1.53583			0.767915	+	0.640551i	$0.221294\pi$
$500$	−38.5727	+	131.366i	−0.0771454	+	0.262733i
$501$	−187.004	+	318.814i	−0.373261	+	0.636355i
$502$	20.6603	−	45.2398i	0.0411560	−	0.0901191i
$503$	43.7545	+	19.9820i	0.0869870	+	0.0397256i	0.458433	−	0.888729i	$-0.348411\pi$
$503$	43.7545	+	19.9820i	0.0869870	+	0.0397256i	−0.371446	+	0.928454i	$0.621138\pi$
$504$	−740.100	−	45.4704i	−1.46845	−	0.0902191i
$505$	1066.13	+	313.043i	2.11114	+	0.619887i
$506$		−	72.8718i		−	0.144015i
$507$	−82.9637	−	163.683i	−0.163636	−	0.322845i
$508$	−306.022	−	89.8563i	−0.602406	−	0.176882i
$509$	−817.505	−	117.539i	−1.60610	−	0.230922i	−0.719850	−	0.694130i	$-0.755789\pi$
$509$	−817.505	−	117.539i	−1.60610	−	0.230922i	−0.886250	+	0.463207i	$0.846698\pi$
$510$	−118.893	−	48.5495i	−0.233124	−	0.0951950i
$511$	177.315	−	52.0645i	0.346997	−	0.101887i
$512$	227.494	−	197.124i	0.444324	−	0.385009i
$513$	−559.324	−	505.242i	−1.09030	−	0.984877i
$514$	−331.645	+	213.135i	−0.645224	+	0.414660i
$515$	879.562	+	126.462i	1.70789	+	0.245557i
$516$	−27.0795	+	264.354i	−0.0524796	+	0.512313i
$517$	−327.454	+	717.025i	−0.633374	+	1.38690i
$518$	446.342	+	386.758i	0.861665	+	0.746637i
$519$	−113.336	−	46.2802i	−0.218374	−	0.0891719i
$520$	−68.0304	−	473.162i	−0.130828	−	0.909927i
$521$	−65.6380	−	29.9759i	−0.125985	−	0.0575353i	0.351425	−	0.936216i	$-0.385697\pi$
$521$	−65.6380	−	29.9759i	−0.125985	−	0.0575353i	−0.477410	+	0.878681i	$0.658424\pi$
$522$	47.4265	+	207.944i	0.0908554	+	0.398360i
$523$	107.773	−	31.6451i	0.206068	−	0.0605069i	−0.177070	−	0.984198i	$-0.556662\pi$
$523$	107.773	−	31.6451i	0.206068	−	0.0605069i	0.383137	+	0.923691i	$0.374844\pi$
$524$	8.86963	+	30.2072i	0.0169268	+	0.0576473i
$525$	−519.638	+	364.671i	−0.989788	+	0.694611i
$526$	−42.2039	+	27.1228i	−0.0802356	+	0.0515643i
$527$	−86.2062	+	39.3690i	−0.163579	+	0.0747040i
$528$	142.453	−	26.4404i	0.269798	−	0.0500765i
$529$	196.957	+	431.275i	0.372319	+	0.815265i
$530$	−368.305	−	52.9543i	−0.694916	−	0.0999138i
$531$	−86.6129	+	162.476i	−0.163113	+	0.305982i
$532$	−642.272	+	741.222i	−1.20728	+	1.39327i
$533$	−223.812	+	348.258i	−0.419910	+	0.653392i
$534$	−123.836	+	155.260i	−0.231903	+	0.290749i
$535$	−546.771			−1.02200
$536$	468.128	+	44.2125i	0.873373	+	0.0824860i
$537$	−655.332	+	332.160i	−1.22036	+	0.618547i
$538$	92.1339	+	201.745i	0.171253	+	0.374991i
$539$	−470.628	+	732.311i	−0.873150	+	1.35865i
$540$	−338.750	−	407.644i	−0.627316	−	0.754897i
$541$	−54.3608	−	378.088i	−0.100482	−	0.698868i	−0.976331	−	0.216282i	$-0.930607\pi$
$541$	−54.3608	−	378.088i	−0.100482	−	0.698868i	0.875849	−	0.482586i	$-0.160302\pi$
$542$	−60.7973	−	8.74133i	−0.112172	−	0.0161279i
$543$	456.662	−	572.541i	0.840998	−	1.05440i
$544$	−206.005	−	60.4885i	−0.378685	−	0.111192i
$545$	−1115.97	+	509.644i	−2.04764	+	0.935127i
$546$	−185.702	+	316.594i	−0.340114	+	0.579843i
$547$	−104.083	−	723.910i	−0.190279	−	1.32342i	−0.831269	−	0.555870i	$-0.812385\pi$
$547$	−104.083	−	723.910i	−0.190279	−	1.32342i	0.640991	−	0.767549i	$-0.278524\pi$
$548$	−25.2870	−	86.1195i	−0.0461441	−	0.157152i
$549$	247.583	−	684.710i	0.450970	−	1.24719i
$550$	−116.116	+	134.005i	−0.211120	+	0.243646i
$551$	599.602	+	273.829i	1.08821	+	0.496967i
$552$	−127.670	+	89.5958i	−0.231286	+	0.162311i
$553$	281.247	+	324.576i	0.508584	+	0.586937i
$554$	7.33377	+	6.35475i	0.0132379	+	0.0114707i
$555$	40.1547	+	985.588i	0.0723507	+	1.77584i
$556$	2.16734	+	1.39287i	0.00389810	+	0.00250515i
$557$	833.348	+	119.817i	1.49614	+	0.215112i	0.841263	−	0.540626i	$-0.181813\pi$
$557$	833.348	+	119.817i	1.49614	+	0.215112i	0.654874	+	0.755738i	$0.272722\pi$
$558$	131.395	+	8.07266i	0.235474	+	0.0144671i
$559$	258.560	+	166.166i	0.462539	+	0.297256i
$560$	−286.755	+	248.474i	−0.512062	+	0.443704i
$561$	−130.990	−	139.285i	−0.233494	−	0.248280i
$562$	−142.940	−	164.962i	−0.254342	−	0.293526i
$563$	−845.807	−	121.609i	−1.50232	−	0.216001i	−0.658481	−	0.752597i	$-0.728801\pi$
$563$	−845.807	−	121.609i	−1.50232	−	0.216001i	−0.843839	+	0.536596i	$0.819710\pi$
$564$	709.937	−	131.770i	1.25875	−	0.233634i
$565$	1431.13			2.53298
$566$		−	78.5359i		−	0.138756i
$567$	19.0903	+	950.704i	0.0336690	+	1.67673i
$568$	410.984	−	264.123i	0.723563	−	0.465006i
$569$	−496.274	−	226.641i	−0.872186	−	0.398314i	−0.0715303	−	0.997438i	$-0.522788\pi$
$569$	−496.274	−	226.641i	−0.872186	−	0.398314i	−0.800656	+	0.599124i	$0.795516\pi$
$570$	550.869	−	22.4434i	0.966438	−	0.0393744i
$571$	169.174	−	108.721i	0.296276	−	0.190405i	−0.384055	−	0.923310i	$-0.625473\pi$
$571$	169.174	−	108.721i	0.296276	−	0.190405i	0.680331	+	0.732905i	$0.261836\pi$
$572$	85.8147	−	292.258i	0.150026	−	0.510940i
$573$	−137.337	+	69.6104i	−0.239681	+	0.121484i
$574$	−469.701			−0.818294
$575$	−37.6210	+	128.125i	−0.0654277	+	0.222826i
$576$	86.3055	+	84.5899i	0.149836	+	0.146857i
$577$	−677.651	−	782.051i	−1.17444	−	1.35537i	−0.921730	−	0.387833i	$-0.873224\pi$
$577$	−677.651	−	782.051i	−1.17444	−	1.35537i	−0.252709	−	0.967542i	$-0.581322\pi$
$578$	−69.7597	−	237.580i	−0.120692	−	0.411038i
$579$	−265.441	+	650.040i	−0.458447	+	1.12269i
$580$	389.944	+	250.602i	0.672318	+	0.432073i
$581$	269.230	+	418.930i	0.463391	+	0.721050i
$582$	177.922	+	525.748i	0.305708	+	0.903346i
$583$	−466.045	−	299.509i	−0.799392	−	0.513738i
$584$	−100.494	−	45.8942i	−0.172079	−	0.0785859i
$585$	−597.676	+	136.314i	−1.02167	+	0.233016i
$586$	−118.588	−	136.858i	−0.202369	−	0.233547i
$587$	−845.231	+	121.526i	−1.43992	+	0.207029i	−0.817622	−	0.575755i	$-0.804708\pi$
$587$	−845.231	+	121.526i	−1.43992	+	0.207029i	−0.622294	+	0.782784i	$0.713799\pi$
$588$	796.737	−	32.4605i	1.35499	−	0.0552049i
$589$	266.431	−	307.478i	0.452345	−	0.522034i
$590$	−37.9429	−	129.222i	−0.0643100	−	0.219020i
$591$	−459.617	+	432.245i	−0.777694	+	0.731380i
$592$	35.1515	+	244.484i	0.0593775	+	0.412979i
$593$	−471.716	−	734.005i	−0.795474	−	1.23778i	−0.967545	−	0.252698i	$-0.918682\pi$
$593$	−471.716	−	734.005i	−0.795474	−	1.23778i	0.172071	−	0.985085i	$-0.444954\pi$
$594$	69.5507	+	256.326i	0.117089	+	0.431525i
$595$	480.444	+	141.071i	0.807469	+	0.237094i
$596$	351.654	−	160.595i	0.590024	−	0.269455i
$597$	454.991	−	153.977i	0.762130	−	0.257917i
$598$	10.9875	+	76.4195i	0.0183737	+	0.127792i
$599$	482.796	+	418.345i	0.806004	+	0.698406i	0.956987	−	0.290130i	$-0.0936985\pi$
$599$	482.796	+	418.345i	0.806004	+	0.698406i	−0.150983	+	0.988536i	$0.548244\pi$
$600$	377.538	+	38.6737i	0.629231	+	0.0644561i
$601$	−32.5304	−	71.2316i	−0.0541271	−	0.118522i	0.880636	−	0.473793i	$-0.157116\pi$
$601$	−32.5304	−	71.2316i	−0.0541271	−	0.118522i	−0.934763	+	0.355272i	$0.884388\pi$
$602$			348.723i			0.579274i
$603$	7.67440	−	602.951i	0.0127270	−	0.999919i
$604$	−407.348			−0.674417
$605$	148.774	−	67.9428i	0.245908	−	0.112302i
$606$	−51.9737	+	507.375i	−0.0857652	+	0.837253i
$607$	486.435	−	561.376i	0.801376	−	0.924837i	−0.197080	−	0.980387i	$-0.563146\pi$
$607$	486.435	−	561.376i	0.801376	−	0.924837i	0.998456	+	0.0555501i	$0.0176913\pi$
$608$	912.339	−	131.174i	1.50056	−	0.215748i
$609$	−266.575	−	787.713i	−0.437726	−	1.29345i
$610$	221.239	+	484.447i	0.362688	+	0.794175i
$611$	235.284	−	801.305i	0.385081	−	1.31147i
$612$	−35.5101	+	171.509i	−0.0580231	+	0.280243i
$613$	−282.827	+	181.762i	−0.461382	+	0.296512i	−0.750607	−	0.660749i	$-0.770239\pi$
$613$	−282.827	+	181.762i	−0.461382	+	0.296512i	0.289225	+	0.957261i	$0.406602\pi$
$614$	−451.843	+	64.9652i	−0.735900	+	0.105806i
$615$	−537.440	−	571.473i	−0.873887	−	0.929225i
$616$	774.804	−	227.503i	1.25780	−	0.369323i
$617$	562.583	+	487.481i	0.911804	+	0.790083i	0.978190	−	0.207711i	$-0.0666014\pi$
$617$	562.583	+	487.481i	0.911804	+	0.790083i	−0.0663859	+	0.997794i	$0.521147\pi$
$618$	16.6042	+	407.548i	0.0268677	+	0.659462i
$619$	−7.51878	−	52.2943i	−0.0121467	−	0.0844819i	0.982846	−	0.184426i	$-0.0590426\pi$
$619$	−7.51878	−	52.2943i	−0.0121467	−	0.0844819i	−0.994993	+	0.0999442i	$0.968134\pi$
$620$	216.218	−	187.354i	0.348739	−	0.302184i
$621$	127.836	+	153.835i	0.205855	+	0.247721i
$622$	227.280	−	497.674i	0.365402	−	0.800118i
$623$	418.638	−	651.413i	0.671971	−	1.04561i
$624$	−145.402	+	49.2064i	−0.233016	+	0.0788564i
$625$	−631.545	+	405.869i	−1.01047	+	0.649390i
$626$	−65.5093	+	101.934i	−0.104647	+	0.162834i
$627$	759.925	+	310.312i	1.21200	+	0.494915i
$628$	−194.699	+	57.1688i	−0.310030	+	0.0910331i
$629$	246.342	−	213.457i	0.391641	−	0.339359i
$630$	−496.736	−	486.862i	−0.788470	−	0.772796i
$631$	−869.104	−	255.192i	−1.37734	−	0.404425i	−0.492500	−	0.870313i	$-0.663917\pi$
$631$	−869.104	−	255.192i	−1.37734	−	0.404425i	−0.884844	+	0.465888i	$0.845735\pi$
$632$		−	256.749i		−	0.406249i
$633$	−21.0319	−	41.4948i	−0.0332258	−	0.0655526i
$634$	98.2710	+	28.8550i	0.155002	+	0.0455126i
$635$	−377.933	−	588.075i	−0.595169	−	0.926102i
$636$	20.6580	+	507.046i	0.0324811	+	0.797242i
$637$	383.123	−	838.923i	0.601450	−	1.31699i
$638$	−125.576	−	195.401i	−0.196828	−	0.306270i
$639$	−380.464	−	497.746i	−0.595405	−	0.778945i
$640$	777.906			1.21548
$641$		−	10.6629i		−	0.0166347i	−0.999965	−	0.00831736i	$-0.997352\pi$
$641$		−	10.6629i		−	0.0166347i	0.999965	−	0.00831736i	$-0.00264753\pi$
$642$	−45.8010	−	246.763i	−0.0713411	−	0.384366i
$643$	11.8721	−	82.5723i	0.0184636	−	0.128417i	−0.978505	−	0.206224i	$-0.933883\pi$
$643$	11.8721	−	82.5723i	0.0184636	−	0.128417i	0.996968	+	0.0778064i	$0.0247916\pi$
$644$	196.698	−	170.439i	0.305431	−	0.264658i
$645$	−424.283	+	399.015i	−0.657802	+	0.618629i
$646$	−119.306	−	137.687i	−0.184685	−	0.213137i
$647$	−363.097	+	564.991i	−0.561202	+	0.873247i	−0.999675	−	0.0254975i	$-0.991883\pi$
$647$	−363.097	+	564.991i	−0.561202	+	0.873247i	0.438473	+	0.898744i	$0.355519\pi$
$648$	363.565	−	437.004i	0.561057	−	0.674389i
$649$	28.5361	−	198.473i	0.0439693	−	0.305813i
$650$	101.564	−	158.037i	0.156252	−	0.243133i
$651$	−512.851	+	20.8945i	−0.787790	+	0.0320960i
$652$	−159.241	+	183.774i	−0.244234	+	0.281861i
$653$	570.294	−	494.162i	0.873344	−	0.756757i	−0.0978114	−	0.995205i	$-0.531184\pi$
$653$	570.294	−	494.162i	0.873344	−	0.756757i	0.971155	+	0.238448i	$0.0766387\pi$
$654$	−323.487	−	460.954i	−0.494629	−	0.704823i
$655$	−28.6645	+	62.7666i	−0.0437627	+	0.0958269i
$656$	−148.458	−	128.639i	−0.226307	−	0.196096i
$657$	−48.1760	+	133.235i	−0.0733272	+	0.202792i
$658$	909.170	−	266.956i	1.38172	−	0.405709i
$659$	51.9704	−	7.47221i	0.0788625	−	0.0113387i	−0.102771	−	0.994705i	$-0.532771\pi$
$659$	51.9704	−	7.47221i	0.0788625	−	0.0113387i	0.181633	+	0.983366i	$0.441862\pi$
$660$	497.885	+	292.040i	0.754371	+	0.442485i
$661$	253.436	+	554.948i	0.383413	+	0.839558i	0.998686	+	0.0512436i	$0.0163185\pi$
$661$	253.436	+	554.948i	0.383413	+	0.839558i	−0.615273	+	0.788314i	$0.710954\pi$
$662$	−3.38971	+	11.5443i	−0.00512041	+	0.0174385i
$663$	158.368	+	126.315i	0.238866	+	0.190521i
$664$	42.3678	−	294.674i	0.0638069	−	0.443786i
$665$	−2127.75	+	305.925i	−3.19963	+	0.460037i
$666$	−441.442	+	100.681i	−0.662825	+	0.151173i
$667$	−147.155	−	94.5708i	−0.220622	−	0.141785i
$668$	−335.397	+	153.171i	−0.502091	+	0.229297i
$669$	−372.820	−	735.552i	−0.557280	−	1.09948i
$670$	304.704	+	318.904i	0.454782	+	0.475975i
$671$			792.922i			1.18170i
$672$	−909.076	−	725.084i	−1.35279	−	1.07899i
$673$	349.106	+	224.357i	0.518732	+	0.333369i	0.773670	−	0.633589i	$-0.218419\pi$
$673$	349.106	+	224.357i	0.518732	+	0.333369i	−0.254938	+	0.966957i	$0.582055\pi$
$674$	−236.444	−	204.880i	−0.350807	−	0.303976i
$675$	10.0454	−	486.586i	0.0148821	−	0.720868i
$676$	26.0526	−	181.200i	0.0385394	−	0.268047i
$677$	1101.51	−	503.044i	1.62705	−	0.743049i	0.627679	−	0.778472i	$-0.284005\pi$
$677$	1101.51	−	503.044i	1.62705	−	0.743049i	0.999372	+	0.0354230i	$0.0112778\pi$
$678$	119.881	+	645.883i	0.176815	+	0.952630i
$679$	−899.001	−	1968.54i	−1.32401	−	2.89917i
$680$	−161.838	−	251.825i	−0.237997	−	0.370330i
$681$	−379.794	−	541.189i	−0.557701	−	0.794697i
$682$	−137.556	+	40.3901i	−0.201695	+	0.0592230i
$683$	−167.764	−	571.351i	−0.245628	−	0.836531i	−0.986342	−	0.164711i	$-0.947331\pi$
$683$	−167.764	−	571.351i	−0.245628	−	0.836531i	0.740714	−	0.671820i	$-0.234487\pi$
$684$	−167.197	−	733.083i	−0.244440	−	1.07176i
$685$	81.7214	−	178.945i	0.119301	−	0.261234i
$686$	464.322	−	66.7594i	0.676854	−	0.0973169i
$687$	−200.849	+	491.860i	−0.292356	+	0.715954i
$688$	−95.5065	+	110.220i	−0.138818	+	0.160204i
$689$	533.893	+	243.821i	0.774882	+	0.353877i
$690$	−145.544	−	14.9090i	−0.210933	−	0.0216072i
$691$	62.2434	−	432.912i	0.0900773	−	0.626501i	−0.893908	−	0.448251i	$-0.852047\pi$
$691$	62.2434	−	432.912i	0.0900773	−	0.626501i	0.983985	−	0.178250i	$-0.0570437\pi$
$692$	−66.0257	−	102.738i	−0.0954128	−	0.148465i
$693$	−371.612	−	966.584i	−0.536237	−	1.39478i
$694$	125.337	+	144.647i	0.180602	+	0.208425i
$695$	1.59086	+	5.41797i	0.00228901	+	0.00779564i
$696$	−187.941	+	460.252i	−0.270031	+	0.661281i
$697$	−36.8929	+	256.596i	−0.0529310	+	0.368143i
$698$	−7.52337	+	25.6222i	−0.0107785	+	0.0367081i
$699$	−546.320	+	276.906i	−0.781573	+	0.396146i
$700$	−633.293			−0.904705
$701$	−280.867	+	956.545i	−0.400666	+	1.36454i	0.474301	+	0.880363i	$0.342701\pi$
$701$	−280.867	+	956.545i	−0.400666	+	1.36454i	−0.874968	+	0.484181i	$0.839117\pi$
$702$	−111.585	−	258.318i	−0.158953	−	0.367975i
$703$	−581.309	+	1272.89i	−0.826897	+	1.81065i
$704$	−119.714	−	54.6715i	−0.170048	−	0.0776584i
$705$	1365.09	+	800.708i	1.93630	+	1.13576i
$706$	158.319	+	46.4867i	0.224248	+	0.0658452i
$707$		−	1988.62i		−	2.81276i
$708$	−163.832	+	83.0394i	−0.231401	+	0.117287i
$709$	−61.0307	−	17.9202i	−0.0860800	−	0.0252754i	0.238409	−	0.971165i	$-0.423374\pi$
$709$	−61.0307	−	17.9202i	−0.0860800	−	0.0252754i	−0.324489	+	0.945889i	$0.605192\pi$
$710$	453.597	+	65.2174i	0.638869	+	0.0918556i
$711$	−328.165	+	26.7845i	−0.461554	+	0.0376716i
$712$	−444.163	+	130.418i	−0.623824	+	0.183171i
$713$	−81.5953	+	70.7027i	−0.114439	+	0.0991623i
$714$	−23.4217	+	228.646i	−0.0328034	+	0.320232i
$715$	561.624	−	360.934i	0.785488	−	0.504803i
$716$	−725.465	−	104.306i	−1.01322	−	0.145679i
$717$	824.013	+	84.4090i	1.14925	+	0.117725i
$718$	33.8394	−	74.0979i	0.0471300	−	0.103200i
$719$	−457.453	−	396.386i	−0.636236	−	0.551301i	0.275902	−	0.961186i	$-0.411024\pi$
$719$	−457.453	−	396.386i	−0.636236	−	0.551301i	−0.912137	+	0.409884i	$0.865569\pi$
$720$	−23.6634	−	289.925i	−0.0328659	−	0.402674i
$721$	−226.331	−	1574.17i	−0.313913	−	2.18331i
$722$	381.882	+	174.399i	0.528922	+	0.241551i
$723$	−1376.26	−	343.920i	−1.90354	−	0.475685i
$724$	700.989	−	205.829i	0.968216	−	0.284294i
$725$	119.914	+	408.389i	0.165398	+	0.563295i
$726$	43.1255	+	61.4518i	0.0594015	+	0.0846444i
$727$	−220.337	+	141.602i	−0.303078	+	0.194776i	−0.683336	−	0.730104i	$-0.739471\pi$
$727$	−220.337	+	141.602i	−0.303078	+	0.194776i	0.380258	+	0.924880i	$0.375835\pi$
$728$	−778.222	+	355.402i	−1.06899	+	0.488190i
$729$	−596.485	−	419.102i	−0.818224	−	0.574900i
$730$	−43.0500	−	94.2664i	−0.0589726	−	0.129132i
$731$	190.506	+	27.3906i	0.260610	+	0.0374701i
$732$	594.539	−	417.234i	0.812212	−	0.569992i
$733$	116.136	−	134.029i	0.158440	−	0.182849i	−0.670979	−	0.741476i	$-0.734126\pi$
$733$	116.136	−	134.029i	0.158440	−	0.182849i	0.829419	+	0.558627i	$0.188672\pi$
$734$	172.383	−	268.233i	0.234854	−	0.365441i
$735$	1366.33	+	1089.79i	1.85895	+	1.48271i
$736$	−244.597			−0.332332
$737$	215.423	+	620.348i	0.292297	+	0.841720i
$738$	212.892	−	290.422i	0.288471	−	0.393526i
$739$	256.835	+	562.390i	0.347544	+	0.761015i	0.999995	+	0.00318426i	$0.00101358\pi$
$739$	256.835	+	562.390i	0.347544	+	0.761015i	−0.652451	+	0.757831i	$0.726259\pi$
$740$	−532.001	+	827.809i	−0.718920	+	1.11866i
$741$	−843.709	−	210.839i	−1.13861	−	0.284533i
$742$	94.7733	+	659.163i	0.127727	+	0.888360i
$743$	238.768	+	34.3297i	0.321357	+	0.0462042i	0.301106	−	0.953591i	$-0.402644\pi$
$743$	238.768	+	34.3297i	0.321357	+	0.0462042i	0.0202513	+	0.999795i	$0.493553\pi$
$744$	239.887	+	191.335i	0.322429	+	0.257171i
$745$	812.992	+	238.716i	1.09126	+	0.320424i
$746$	−491.892	+	224.639i	−0.659372	+	0.301125i
$747$	−381.058	−	23.4115i	−0.510118	−	0.0313407i
$748$	−27.1452	−	188.799i	−0.0362904	−	0.252405i
$749$	275.694	+	938.927i	0.368083	+	1.25357i
$750$	−94.3646	−	100.340i	−0.125820	−	0.133787i
$751$	220.731	−	254.737i	0.293916	−	0.339198i	−0.589516	−	0.807757i	$-0.700681\pi$
$751$	220.731	−	254.737i	0.293916	−	0.339198i	0.883432	+	0.468559i	$0.155227\pi$
$752$	360.473	+	164.622i	0.479352	+	0.218913i
$753$	−85.3982	−	121.688i	−0.113411	−	0.161605i
$754$	161.152	+	185.979i	0.213729	+	0.246657i
$755$	−674.742	−	584.667i	−0.893698	−	0.774394i
$756$	−529.211	+	787.253i	−0.700014	+	1.04134i
$757$	33.2046	+	21.3393i	0.0438634	+	0.0281893i	0.562389	−	0.826873i	$-0.309882\pi$
$757$	33.2046	+	21.3393i	0.0438634	+	0.0281893i	−0.518525	+	0.855062i	$0.673519\pi$
$758$	383.979	+	55.2078i	0.506568	+	0.0728335i
$759$	−187.889	−	110.208i	−0.247548	−	0.145202i
$760$	1081.09	+	694.774i	1.42249	+	0.914177i
$761$	−492.019	+	426.337i	−0.646542	+	0.560232i	−0.915198	−	0.403004i	$-0.867966\pi$
$761$	−492.019	+	426.337i	−0.646542	+	0.560232i	0.268656	+	0.963236i	$0.413421\pi$
$762$	233.746	−	219.825i	0.306753	−	0.288485i
$763$	1437.87	+	1659.39i	1.88449	+	2.17482i
$764$	−152.035	−	21.8594i	−0.198999	−	0.0286117i
$765$	−304.987	+	233.124i	−0.398676	+	0.304737i
$766$	−292.984			−0.382486
$767$			212.438i			0.276972i
$768$	94.5670	+	509.500i	0.123134	+	0.663412i
$769$	122.928	−	79.0011i	0.159854	−	0.102732i	−0.458268	−	0.888814i	$-0.651530\pi$
$769$	122.928	−	79.0011i	0.159854	−	0.102732i	0.618122	+	0.786082i	$0.287894\pi$
$770$	689.020	+	314.665i	0.894831	+	0.408655i
$771$	47.9708	+	1177.43i	0.0622190	+	1.52715i
$772$	−589.254	+	378.691i	−0.763283	+	0.490532i
$773$	−80.5709	+	274.399i	−0.104231	+	0.354979i	−0.995049	−	0.0993806i	$-0.968314\pi$
$773$	−80.5709	+	274.399i	−0.104231	+	0.354979i	0.890818	+	0.454360i	$0.150132\pi$
$774$	−215.620	−	158.059i	−0.278579	−	0.204210i
$775$	262.707			0.338976
$776$	−364.490	+	1241.34i	−0.469703	+	1.59966i
$777$	1672.23	−	565.910i	2.15216	−	0.728327i
$778$	−424.021	−	489.347i	−0.545015	−	0.628980i
$779$	−313.540	−	1067.82i	−0.402491	−	1.37076i
$780$	−566.157	−	231.187i	−0.725842	−	0.296394i
$781$	573.972	+	368.869i	0.734919	+	0.472304i
$782$	26.1381	+	40.6717i	0.0334247	+	0.0520098i
$783$	607.878	+	192.204i	0.776345	+	0.245471i
$784$	368.157	+	236.600i	0.469589	+	0.301786i
$785$	−404.559	−	184.756i	−0.515362	−	0.235358i
$786$	−30.7283	−	7.67885i	−0.0390945	−	0.00976953i
$787$	−358.148	−	413.325i	−0.455081	−	0.525191i	0.481121	−	0.876654i	$-0.340230\pi$
$787$	−358.148	−	413.325i	−0.455081	−	0.525191i	−0.936202	+	0.351463i	$0.885684\pi$
$788$	−623.005	+	89.5746i	−0.790616	+	0.113673i
$789$	6.10459	+	149.836i	0.00773712	+	0.189906i
$790$	157.715	−	182.013i	0.199640	−	0.230397i
$791$	−721.608	−	2457.57i	−0.912273	−	3.10692i
$792$	−210.512	+	582.187i	−0.265797	+	0.735084i
$793$	−119.555	−	831.524i	−0.150763	−	1.04858i
$794$	87.5025	+	136.157i	0.110205	+	0.171482i
$795$	−693.545	+	869.535i	−0.872384	+	1.09375i
$796$	459.767	+	135.000i	0.577597	+	0.169598i
$797$	−792.878	+	362.095i	−0.994828	+	0.454323i	−0.845217	−	0.534423i	$-0.820529\pi$
$797$	−792.878	+	362.095i	−0.994828	+	0.454323i	−0.149610	+	0.988745i	$0.547802\pi$
$798$	−316.301	−	934.649i	−0.396367	−	1.17124i
$799$	−74.4260	−	517.644i	−0.0931489	−	0.647865i
$800$	449.792	+	389.747i	0.562240	+	0.487184i
$801$	213.030	+	554.102i	0.265955	+	0.691763i
$802$	260.587	+	570.606i	0.324922	+	0.711479i
$803$		−	154.291i		−	0.192143i
$804$	351.787	−	487.952i	0.437546	−	0.606906i
$805$	570.447			0.708630
$806$	138.163	−	63.0968i	0.171418	−	0.0782839i
$807$	659.509	+	67.5578i	0.817236	+	0.0837147i
$808$	−778.522	+	898.462i	−0.963518	+	1.11196i
$809$	793.277	−	114.056i	0.980565	−	0.140984i	0.366652	−	0.930358i	$-0.380504\pi$
$809$	793.277	−	114.056i	0.980565	−	0.140984i	0.613913	+	0.789374i	$0.289595\pi$
$810$	526.178	−	86.4684i	0.649603	−	0.106751i
$811$	−182.951	−	400.606i	−0.225587	−	0.493966i	0.762666	−	0.646792i	$-0.223890\pi$
$811$	−182.951	−	400.606i	−0.225587	−	0.493966i	−0.988253	+	0.152826i	$0.951163\pi$
$812$	233.721	−	795.980i	0.287834	−	0.980271i
$813$	−114.486	+	143.537i	−0.140819	+	0.176552i
$814$	414.814	−	266.585i	0.509599	−	0.327500i
$815$	−527.541	+	75.8489i	−0.647289	+	0.0930662i
$816$	−70.0232	+	65.8531i	−0.0858127	+	0.0807023i
$817$	−792.788	+	232.784i	−0.970365	+	0.284925i
$818$	−542.265	−	469.875i	−0.662916	−	0.574420i
$819$	535.443	+	957.610i	0.653777	+	1.16924i
$820$	−111.374	−	774.625i	−0.135822	−	0.944665i
$821$	−737.326	+	638.897i	−0.898083	+	0.778193i	−0.975773	−	0.218784i	$-0.929791\pi$
$821$	−737.326	+	638.897i	−0.898083	+	0.778193i	0.0776902	+	0.996978i	$0.475246\pi$
$822$	87.6050	+	21.8921i	0.106575	+	0.0266327i
$823$	−154.246	+	337.753i	−0.187420	+	0.410392i	−0.979896	−	0.199511i	$-0.936065\pi$
$823$	−154.246	+	337.753i	−0.187420	+	0.410392i	0.792476	+	0.609903i	$0.208792\pi$
$824$	−514.012	+	799.819i	−0.623802	+	0.970654i
$825$	169.903	+	502.052i	0.205943	+	0.608547i
$826$	−202.771	+	130.313i	−0.245485	+	0.157764i
$827$	−68.5794	+	106.712i	−0.0829255	+	0.129035i	−0.880239	−	0.474531i	$-0.842618\pi$
$827$	−68.5794	+	106.712i	−0.0829255	+	0.129035i	0.797313	+	0.603566i	$0.206254\pi$
$828$	16.2318	+	198.872i	0.0196036	+	0.240184i
$829$	−100.101	+	29.3924i	−0.120749	+	0.0354552i	−0.341549	−	0.939864i	$-0.610952\pi$
$829$	−100.101	+	29.3924i	−0.120749	+	0.0354552i	0.220800	+	0.975319i	$0.429133\pi$
$830$	211.047	−	182.873i	0.254273	−	0.220329i
$831$	27.4761	−	9.29836i	0.0330639	−	0.0111894i
$832$	133.785	+	39.2829i	0.160800	+	0.0472150i
$833$		−	577.530i		−	0.693314i
$834$	−2.31192	+	1.17181i	−0.00277209	+	0.00140505i
$835$	−775.407	−	227.680i	−0.928631	−	0.272671i
$836$	442.706	+	688.864i	0.529552	+	0.824000i
$837$	219.530	−	326.573i	0.262282	−	0.390171i
$838$	111.977	−	245.196i	0.133624	−	0.292596i
$839$	601.947	+	936.647i	0.717457	+	1.11639i	0.988116	+	0.153710i	$0.0491221\pi$
$839$	601.947	+	936.647i	0.717457	+	1.11639i	−0.270659	+	0.962675i	$0.587242\pi$
$840$	−295.863	−	1594.03i	−0.352218	−	1.89765i
$841$	283.445			0.337033
$842$			187.265i			0.222405i
$843$	−641.505	+	119.068i	−0.760979	+	0.141243i
$844$	6.60454	−	45.9356i	0.00782529	−	0.0544261i
$845$	303.231	−	262.751i	0.358853	−	0.310948i
$846$	−247.018	+	683.149i	−0.291984	+	0.807505i
$847$	−191.688	−	221.220i	−0.226314	−	0.261180i
$848$	−150.573	+	234.297i	−0.177563	+	0.276293i
$849$	−202.493	−	118.775i	−0.238508	−	0.139899i
$850$	16.7417	−	116.441i	0.0196961	−	0.136989i
$851$	200.763	−	312.394i	0.235915	−	0.367091i
$852$	−25.4419	−	624.467i	−0.0298614	−	0.732943i
$853$	484.387	−	559.012i	0.567863	−	0.655349i	−0.397088	−	0.917781i	$-0.629979\pi$
$853$	484.387	−	559.012i	0.567863	−	0.655349i	0.964950	+	0.262432i	$0.0845246\pi$
$854$	720.349	−	624.186i	0.843500	−	0.730897i
$855$	775.246	−	1454.28i	0.906720	−	1.70091i
$856$	243.020	−	532.141i	0.283902	−	0.621660i
$857$	371.160	+	321.612i	0.433092	+	0.375277i	0.843949	−	0.536423i	$-0.180225\pi$
$857$	371.160	+	321.612i	0.433092	+	0.375277i	−0.410857	+	0.911700i	$0.634770\pi$
$858$	209.938	+	223.232i	0.244683	+	0.260177i
$859$	616.383	−	180.986i	0.717559	−	0.210694i	0.0974843	−	0.995237i	$-0.468920\pi$
$859$	616.383	−	180.986i	0.717559	−	0.210694i	0.620075	+	0.784543i	$0.287102\pi$
$860$	−575.110	+	82.6883i	−0.668733	+	0.0961492i
$861$	−710.357	+	1211.05i	−0.825037	+	1.40657i
$862$	−159.080	−	348.336i	−0.184547	−	0.404102i
$863$	−34.9009	+	118.861i	−0.0404413	+	0.137731i	−0.977239	−	0.212141i	$-0.931956\pi$
$863$	−34.9009	+	118.861i	−0.0404413	+	0.137731i	0.936798	+	0.349871i	$0.113775\pi$
$864$	860.366	−	233.449i	0.995795	−	0.270196i
$865$	38.0933	−	264.945i	0.0440385	−	0.306294i
$866$	639.661	−	91.9694i	0.738639	−	0.106200i
$867$	−718.066	−	179.441i	−0.828219	−	0.206968i
$868$	−430.751	−	276.827i	−0.496257	−	0.318925i
$869$	326.168	−	148.956i	0.375337	−	0.171411i
$870$	−415.957	+	210.831i	−0.478111	+	0.242334i
$871$	−319.445	−	618.068i	−0.366757	−	0.709607i
$872$		−	1312.62i		−	1.50530i
$873$	1624.64	+	336.375i	1.86099	+	0.385309i
$874$	−174.605	−	112.212i	−0.199777	−	0.128389i
$875$	405.882	+	351.699i	0.463865	+	0.401941i
$876$	−115.689	+	81.1878i	−0.132065	+	0.0926801i
$877$	−223.350	+	1553.43i	−0.254675	+	1.77130i	0.314667	+	0.949202i	$0.398107\pi$
$877$	−223.350	+	1553.43i	−0.254675	+	1.77130i	−0.569342	+	0.822101i	$0.692802\pi$
$878$	−395.323	+	180.538i	−0.450254	+	0.205624i
$879$	−532.217	+	98.7835i	−0.605481	+	0.112382i
$880$	131.599	+	288.161i	0.149544	+	0.327455i
$881$	562.187	+	874.781i	0.638124	+	0.992941i	0.998197	+	0.0600165i	$0.0191153\pi$
$881$	562.187	+	874.781i	0.638124	+	0.992941i	−0.360073	+	0.932924i	$0.617248\pi$
$882$	−377.380	+	707.924i	−0.427868	+	0.802634i
$883$	594.747	−	174.633i	0.673552	−	0.197773i	0.0729680	−	0.997334i	$-0.476753\pi$
$883$	594.747	−	174.633i	0.673552	−	0.197773i	0.600584	+	0.799562i	$0.294935\pi$
$884$	56.9334	+	193.897i	0.0644043	+	0.219341i
$885$	−390.562	−	97.5997i	−0.441313	−	0.110282i
$886$	257.608	−	564.082i	0.290754	−	0.636661i
$887$	1636.98	−	235.362i	1.84552	−	0.265346i	0.871267	−	0.490809i	$-0.163299\pi$
$887$	1636.98	−	235.362i	1.84552	−	0.265346i	0.974252	+	0.225463i	$0.0723895\pi$
$888$	−977.063	−	398.979i	−1.10030	−	0.449301i
$889$	−819.293	+	945.514i	−0.921589	+	1.06357i
$890$	−394.986	−	180.384i	−0.443805	−	0.202679i
$891$	766.084	+	208.331i	0.859803	+	0.233817i
$892$	117.075	−	814.271i	0.131249	−	0.912860i
$893$	1213.80	+	1888.71i	1.35924	+	2.11502i
$894$	−39.6334	+	386.907i	−0.0443327	+	0.432782i
$895$	−1051.97	−	1214.04i	−1.17538	−	1.35647i
$896$	−392.237	−	1335.84i	−0.437765	−	1.49089i
$897$	213.653	+	87.2442i	0.238186	+	0.0972622i
$898$	1.31734	−	9.16228i	0.00146697	−	0.0102030i
$899$	−96.9535	+	330.193i	−0.107846	+	0.367290i
$900$	287.040	−	391.573i	0.318933	−	0.435081i
$901$	367.542			0.407927
$902$	−110.483	+	376.270i	−0.122487	+	0.417151i
$903$	899.131	+	527.395i	0.995715	+	0.584048i
$904$	−636.088	+	1392.84i	−0.703637	+	1.54075i
$905$	1456.56	+	665.190i	1.60946	+	0.735016i
$906$	207.345	−	353.493i	0.228858	−	0.390169i
$907$	1020.90	+	299.763i	1.12558	+	0.330499i	0.790967	−	0.611858i	$-0.209578\pi$
$907$	1020.90	+	299.763i	1.12558	+	0.330499i	0.334609	+	0.942357i	$0.391396\pi$
$908$		−	659.557i		−	0.726385i
$909$	1229.59	+	901.341i	1.35268	+	0.991574i
$910$	−770.008	−	226.095i	−0.846163	−	0.248456i
$911$	646.526	+	92.9564i	0.709688	+	0.102038i	0.487700	−	0.873011i	$-0.337836\pi$
$911$	646.526	+	92.9564i	0.709688	+	0.102038i	0.221989	+	0.975049i	$0.428745\pi$
$912$	156.004	−	382.040i	0.171057	−	0.418903i
$913$	398.926	−	117.135i	0.436940	−	0.128297i
$914$	150.883	−	130.741i	0.165080	−	0.143042i
$915$	1583.67	+	162.225i	1.73078	+	0.177295i
$916$	−445.866	+	286.541i	−0.486754	+	0.312817i
$917$	122.237	+	17.5751i	0.133301	+	0.0191659i
$918$	−130.759	−	118.115i	−0.142439	−	0.128666i
$919$	28.1198	−	61.5737i	0.0305982	−	0.0670008i	−0.893716	−	0.448634i	$-0.851911\pi$
$919$	28.1198	−	61.5737i	0.0305982	−	0.0670008i	0.924314	+	0.381633i	$0.124638\pi$
$920$	−257.729	−	223.324i	−0.280141	−	0.242743i
$921$	−515.846	+	1263.26i	−0.560093	+	1.37162i
$922$	110.792	+	770.576i	0.120165	+	0.835766i
$923$	−657.532	−	300.285i	−0.712386	−	0.325336i
$924$	250.453	−	1002.23i	0.271053	−	1.08467i
$925$	−866.965	+	254.564i	−0.937259	+	0.275204i
$926$	−55.1173	−	187.712i	−0.0595219	−	0.202713i
$927$	1075.91	+	573.548i	1.16064	+	0.618714i
$928$	−655.868	+	421.501i	−0.706754	+	0.454203i
$929$	−562.090	+	256.698i	−0.605048	+	0.276316i	−0.694292	−	0.719693i	$-0.744282\pi$
$929$	−562.090	+	256.698i	−0.605048	+	0.276316i	0.0892435	+	0.996010i	$0.471555\pi$
$930$	52.5265	+	282.998i	0.0564801	+	0.304299i
$931$	1029.96	+	2255.30i	1.10629	+	2.42245i
$932$	−604.787	−	86.9553i	−0.648913	−	0.0932996i
$933$	−939.448	−	1338.67i	−1.00691	−	1.43480i
$934$	−270.237	+	311.870i	−0.289333	+	0.333908i
$935$	226.019	−	351.693i	0.241732	−	0.376142i
$936$	132.979	−	642.270i	0.142072	−	0.686186i
$937$	449.242			0.479447			0.239724	−	0.970841i	$-0.422943\pi$
$937$	449.242			0.479447			0.239724	+	0.970841i	$0.422943\pi$
$938$	393.990	−	684.042i	0.420032	−	0.729256i
$939$	163.749	+	323.067i	0.174387	+	0.344055i
$940$	655.841	+	1436.09i	0.697704	+	1.52776i
$941$	−240.110	+	373.619i	−0.255165	+	0.397044i	−0.945076	−	0.326849i	$-0.894013\pi$
$941$	−240.110	+	373.619i	−0.255165	+	0.397044i	0.689912	+	0.723894i	$0.257649\pi$
$942$	49.4936	−	198.058i	0.0525410	−	0.210252i
$943$	42.0298	+	292.324i	0.0445703	+	0.309993i
$944$	−99.7788	−	14.3460i	−0.105698	−	0.0151971i
$945$	−2006.54	+	544.450i	−2.12333	+	0.576137i
$946$	279.357	+	82.0265i	0.295303	+	0.0867087i
$947$	639.334	−	291.974i	0.675115	−	0.308315i	−0.0481952	−	0.998838i	$-0.515347\pi$
$947$	639.334	−	291.974i	0.675115	−	0.308315i	0.723310	+	0.690523i	$0.242620\pi$
$948$	−283.317	−	166.183i	−0.298858	−	0.175298i
$949$	23.2637	+	161.803i	0.0245139	+	0.170498i
$950$	142.282	+	484.568i	0.149770	+	0.510071i
$951$	223.019	−	209.738i	0.234510	−	0.220545i
$952$	−350.837	+	404.887i	−0.368526	+	0.425301i
$953$	943.240	+	430.763i	0.989759	+	0.452008i	0.843436	−	0.537229i	$-0.180529\pi$
$953$	943.240	+	430.763i	0.989759	+	0.452008i	0.146323	+	0.989237i	$0.453256\pi$
$954$	−450.525	−	240.166i	−0.472248	−	0.251746i
$955$	−220.460	−	254.425i	−0.230849	−	0.266413i
$956$	624.491	+	541.125i	0.653234	+	0.566030i
$957$	−693.728	+	28.2637i	−0.724898	+	0.0295337i
$958$	213.484	+	137.198i	0.222843	+	0.143213i
$959$	−348.494	−	50.1059i	−0.363393	−	0.0522480i
$960$	−133.685	+	227.914i	−0.139256	+	0.237410i
$961$	−629.758	−	404.721i	−0.655315	−	0.421146i
$962$	−394.813	+	342.108i	−0.410409	+	0.355621i
$963$	−705.509	−	255.103i	−0.732616	−	0.264905i
$964$	−926.723	−	1069.50i	−0.961331	−	1.10944i
$965$	−1519.59	−	218.484i	−1.57471	−	0.226409i
$966$	47.7843	+	257.448i	0.0494661	+	0.266509i
$967$	358.428			0.370660			0.185330	−	0.982676i	$-0.440665\pi$
$967$	358.428			0.370660			0.185330	+	0.982676i	$0.440665\pi$
$968$			174.991i			0.180776i
$969$	−535.439	+	99.3814i	−0.552568	+	0.102561i
$970$	−1020.92	+	656.105i	−1.05249	+	0.676397i
$971$	1511.35	+	690.210i	1.55649	+	0.710824i	0.993306	−	0.115509i	$-0.0368498\pi$
$971$	1511.35	+	690.210i	1.55649	+	0.710824i	0.563182	+	0.826333i	$0.309577\pi$
$972$	−246.904	−	684.040i	−0.254016	−	0.703744i
$973$	8.50171	−	5.46372i	0.00873762	−	0.00561533i
$974$	135.184	−	460.395i	0.138793	−	0.472684i
$975$	−253.872	−	500.876i	−0.260382	−	0.513719i
$976$	398.628			0.408431
$977$	432.194	−	1471.92i	0.442369	−	1.50657i	−0.373113	−	0.927786i	$-0.621710\pi$
$977$	432.194	−	1471.92i	0.442369	−	1.50657i	0.815481	−	0.578783i	$-0.196472\pi$
$978$	−78.4215	−	231.731i	−0.0801856	−	0.236943i
$979$	−423.365	−	488.589i	−0.432446	−	0.499070i
$980$	491.195	+	1672.86i	0.501219	+	1.70700i
$981$	−1677.73	+	136.935i	−1.71023	+	0.139587i
$982$	44.9080	+	28.8606i	0.0457312	+	0.0293897i
$983$	−137.699	−	214.264i	−0.140080	−	0.217969i	0.764124	−	0.645069i	$-0.223172\pi$
$983$	−137.699	−	214.264i	−0.140080	−	0.217969i	−0.904204	+	0.427100i	$0.859535\pi$
$984$	795.055	−	269.060i	0.807983	−	0.273435i
$985$	−1160.53	−	745.827i	−1.17820	−	0.757185i
$986$	140.175	+	64.0157i	0.142165	+	0.0649247i
$987$	686.685	−	2747.89i	0.695730	−	2.78409i
$988$	−568.124	−	655.650i	−0.575024	−	0.663613i
$989$	217.032	−	31.2045i	0.219446	−	0.0315515i
$990$	−506.859	+	283.408i	−0.511979	+	0.286271i
$991$	−950.745	+	1097.22i	−0.959380	+	1.10718i	0.0347943	+	0.999394i	$0.488922\pi$
$991$	−950.745	+	1097.22i	−0.959380	+	1.10718i	−0.994174	+	0.107789i	$0.965623\pi$
$992$	135.571	+	461.711i	0.136664	+	0.465435i
$993$	24.6388	+	26.1990i	0.0248124	+	0.0263837i
$994$	−116.721	−	811.811i	−0.117425	−	0.816712i
$995$	567.805	+	883.521i	0.570658	+	0.887961i
$996$	−297.744	−	237.482i	−0.298939	−	0.238436i
$997$	−657.099	−	192.942i	−0.659076	−	0.193522i	−0.0649432	−	0.997889i	$-0.520687\pi$
$997$	−657.099	−	192.942i	−0.659076	−	0.193522i	−0.594133	+	0.804367i	$0.702505\pi$
$998$	−699.649	+	319.519i	−0.701052	+	0.320160i
$999$	−408.027	+	1290.46i	−0.408435	+	1.29175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.k.a.14.18	✓	440
3.2	odd	2	inner	201.3.k.a.14.27	yes	440
67.24	even	11	inner	201.3.k.a.158.27	yes	440
201.158	odd	22	inner	201.3.k.a.158.18	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.k.a.14.18	✓	440	1.1	even	1	trivial
201.3.k.a.14.27	yes	440	3.2	odd	2	inner
201.3.k.a.158.18	yes	440	201.158	odd	22	inner
201.3.k.a.158.27	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)

\(f(q)\)	\(=\)	\(q+(-0.912928 + 0.416920i) q^{2} +(-0.305710 + 2.98438i) q^{3} +(-1.95983 + 2.26176i) q^{4} +(-6.49262 + 0.933498i) q^{5} +(-0.965159 - 2.85198i) q^{6} +(4.87674 + 10.6786i) q^{7} +(1.97722 - 6.73380i) q^{8} +(-8.81308 - 1.82471i) q^{9} +O(q^{10})\)	\(q+(-0.912928 + 0.416920i) q^{2} +(-0.305710 + 2.98438i) q^{3} +(-1.95983 + 2.26176i) q^{4} +(-6.49262 + 0.933498i) q^{5} +(-0.965159 - 2.85198i) q^{6} +(4.87674 + 10.6786i) q^{7} +(1.97722 - 6.73380i) q^{8} +(-8.81308 - 1.82471i) q^{9} +(5.53810 - 3.55912i) q^{10} +(9.70154 - 1.39487i) q^{11} +(-6.15082 - 6.54032i) q^{12} +(-9.96353 + 2.92556i) q^{13} +(-8.90424 - 7.71556i) q^{14} +(-0.801059 - 19.6618i) q^{15} +(-0.701249 - 4.87729i) q^{16} +(-4.91437 + 4.25832i) q^{17} +(8.80647 - 2.00853i) q^{18} +(11.5967 - 25.3933i) q^{19} +(10.6131 - 16.5143i) q^{20} +(-33.3598 + 11.2895i) q^{21} +(-8.27526 + 5.31819i) q^{22} +(-4.00510 + 6.23206i) q^{23} +(19.4918 + 7.95937i) q^{24} +(17.2954 - 5.07838i) q^{25} +(7.87627 - 6.82482i) q^{26} +(8.13987 - 25.7438i) q^{27} +(-33.7100 - 9.89814i) q^{28} +23.6126i q^{29} +(8.92873 + 17.6159i) q^{30} +(13.9838 + 4.10601i) q^{31} +(17.8507 + 27.7762i) q^{32} +(1.19698 + 29.3795i) q^{33} +(2.71108 - 5.93645i) q^{34} +(-41.6313 - 64.7795i) q^{35} +(21.3992 - 16.3570i) q^{36} -50.1270 q^{37} +28.0172i q^{38} +(-5.68504 - 30.6294i) q^{39} +(-6.55136 + 45.5657i) q^{40} +(30.1287 - 26.1067i) q^{41} +(25.7483 - 24.2149i) q^{42} +(-19.3826 - 22.3687i) q^{43} +(-15.8585 + 24.6763i) q^{44} +(58.9234 + 3.62015i) q^{45} +(1.05810 - 7.35923i) q^{46} +(-43.4804 + 67.6568i) q^{47} +(14.7701 - 0.601760i) q^{48} +(-58.1613 + 67.1217i) q^{49} +(-13.6722 + 11.8470i) q^{50} +(-11.2061 - 15.9682i) q^{51} +(12.9099 - 28.2687i) q^{52} +(-42.7164 - 37.0140i) q^{53} +(3.30199 + 26.8959i) q^{54} +(-61.6863 + 18.1127i) q^{55} +(81.5498 - 11.7251i) q^{56} +(72.2381 + 42.3721i) q^{57} +(-9.84458 - 21.5566i) q^{58} +(5.76364 - 19.6292i) q^{59} +(46.0403 + 36.7220i) q^{60} +(-11.5132 + 80.0761i) q^{61} +(-14.4781 + 2.08163i) q^{62} +(-23.4939 - 103.010i) q^{63} +(-11.2959 - 7.25945i) q^{64} +(61.9584 - 28.2955i) q^{65} +(-13.3417 - 26.3224i) q^{66} +(12.7478 + 65.7761i) q^{67} -19.4607i q^{68} +(-17.3744 - 13.8580i) q^{69} +(65.0143 + 41.7821i) q^{70} +(52.6087 + 45.5857i) q^{71} +(-29.7126 + 55.7377i) q^{72} +(2.24030 - 15.5817i) q^{73} +(45.7623 - 20.8990i) q^{74} +(9.86847 + 53.1685i) q^{75} +(34.7060 + 75.9955i) q^{76} +(62.2072 + 96.7963i) q^{77} +(17.9600 + 25.5922i) q^{78} +(35.1021 - 10.3069i) q^{79} +(9.10588 + 31.0118i) q^{80} +(74.3409 + 32.1626i) q^{81} +(-16.6210 + 36.3948i) q^{82} +(41.9879 - 6.03694i) q^{83} +(39.8453 - 97.5775i) q^{84} +(27.9320 - 32.2352i) q^{85} +(27.0208 + 12.3400i) q^{86} +(-70.4690 - 7.21860i) q^{87} +(9.78932 - 68.0862i) q^{88} +(-35.6608 - 55.4892i) q^{89} +(-55.3021 + 21.2614i) q^{90} +(-79.8304 - 92.1292i) q^{91} +(-6.24612 - 21.2723i) q^{92} +(-16.5289 + 40.4777i) q^{93} +(11.4870 - 79.8937i) q^{94} +(-51.5886 + 175.695i) q^{95} +(-88.3519 + 44.7818i) q^{96} -184.345 q^{97} +(25.1127 - 85.5259i) q^{98} +(-88.0458 - 5.40937i) 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

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