LMFDB - Embedded newform 201.3.c.a.68.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(68,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("201.68");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.c (of order $2$, degree $1$, 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:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			68.3
Character	$\chi$	$=$	201.68
Dual form			201.3.c.a.68.42

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.74856i q^{2} +(-2.69559 + 1.31674i) q^{3} -10.0517 q^{4} -4.74753i q^{5} +(4.93589 + 10.1046i) q^{6} -4.78098 q^{7} +22.6851i q^{8} +(5.53237 - 7.09880i) q^{9} +O(q^{10})$	\(q-3.74856i q^{2} +(-2.69559 + 1.31674i) q^{3} -10.0517 q^{4} -4.74753i q^{5} +(4.93589 + 10.1046i) q^{6} -4.78098 q^{7} +22.6851i q^{8} +(5.53237 - 7.09880i) q^{9} -17.7964 q^{10} +18.6817i q^{11} +(27.0952 - 13.2355i) q^{12} -4.14209 q^{13} +17.9218i q^{14} +(6.25129 + 12.7974i) q^{15} +44.8297 q^{16} -26.7489i q^{17} +(-26.6102 - 20.7384i) q^{18} +9.76095 q^{19} +47.7207i q^{20} +(12.8875 - 6.29533i) q^{21} +70.0296 q^{22} +28.7876i q^{23} +(-29.8705 - 61.1496i) q^{24} +2.46094 q^{25} +15.5269i q^{26} +(-5.56568 + 26.4201i) q^{27} +48.0569 q^{28} +22.6205i q^{29} +(47.9717 - 23.4333i) q^{30} -41.0405 q^{31} -77.3062i q^{32} +(-24.5991 - 50.3582i) q^{33} -100.270 q^{34} +22.6979i q^{35} +(-55.6096 + 71.3549i) q^{36} -24.6432 q^{37} -36.5895i q^{38} +(11.1654 - 5.45407i) q^{39} +107.698 q^{40} +51.5187i q^{41} +(-23.5984 - 48.3097i) q^{42} -68.1944 q^{43} -187.783i q^{44} +(-33.7018 - 26.2651i) q^{45} +107.912 q^{46} -29.5942i q^{47} +(-120.842 + 59.0292i) q^{48} -26.1422 q^{49} -9.22497i q^{50} +(35.2214 + 72.1039i) q^{51} +41.6350 q^{52} +52.1743i q^{53} +(99.0374 + 20.8633i) q^{54} +88.6922 q^{55} -108.457i q^{56} +(-26.3115 + 12.8527i) q^{57} +84.7944 q^{58} +32.9581i q^{59} +(-62.8360 - 128.635i) q^{60} -72.5580 q^{61} +153.843i q^{62} +(-26.4501 + 33.9392i) q^{63} -110.468 q^{64} +19.6647i q^{65} +(-188.771 + 92.2111i) q^{66} -8.18535 q^{67} +268.871i q^{68} +(-37.9059 - 77.5995i) q^{69} +85.0842 q^{70} -48.2206i q^{71} +(161.037 + 125.502i) q^{72} -6.54622 q^{73} +92.3764i q^{74} +(-6.63367 + 3.24043i) q^{75} -98.1140 q^{76} -89.3170i q^{77} +(-20.4449 - 41.8540i) q^{78} +93.9919 q^{79} -212.830i q^{80} +(-19.7858 - 78.5463i) q^{81} +193.121 q^{82} -38.8283i q^{83} +(-129.542 + 63.2787i) q^{84} -126.991 q^{85} +255.631i q^{86} +(-29.7855 - 60.9756i) q^{87} -423.797 q^{88} -33.5856i q^{89} +(-98.4562 + 126.333i) q^{90} +19.8032 q^{91} -289.364i q^{92} +(110.628 - 54.0399i) q^{93} -110.935 q^{94} -46.3404i q^{95} +(101.793 + 208.386i) q^{96} +87.5412 q^{97} +97.9957i q^{98} +(132.618 + 103.354i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$68$	$136$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	3.74856i		−	1.87428i	−0.348955	−	0.937140i	$-0.613463\pi$
$2$		−	3.74856i		−	1.87428i	0.348955	−	0.937140i	$-0.386537\pi$
$3$	−2.69559	+	1.31674i	−0.898529	+	0.438915i
$3$	−2.69559	+	1.31674i	−0.898529	+	0.438915i
$4$	−10.0517			−2.51292
$5$		−	4.74753i		−	0.949506i	−0.880119	−	0.474753i	$-0.842537\pi$
$5$		−	4.74753i		−	0.949506i	0.880119	−	0.474753i	$-0.157463\pi$
$6$	4.93589	+	10.1046i	0.822649	+	1.68409i
$7$	−4.78098			−0.682997			−0.341498	−	0.939882i	$-0.610934\pi$
$7$	−4.78098			−0.682997			−0.341498	+	0.939882i	$0.610934\pi$
$8$			22.6851i			2.83564i
$9$	5.53237	−	7.09880i	0.614708	−	0.788755i
$10$	−17.7964			−1.77964
$11$			18.6817i			1.69834i	0.528120	+	0.849170i	$0.322897\pi$
$11$			18.6817i			1.69834i	−0.528120	+	0.849170i	$0.677103\pi$
$12$	27.0952	−	13.2355i	2.25793	−	1.10296i
$13$	−4.14209			−0.318622			−0.159311	−	0.987228i	$-0.550927\pi$
$13$	−4.14209			−0.318622			−0.159311	+	0.987228i	$0.550927\pi$
$14$			17.9218i			1.28013i
$15$	6.25129	+	12.7974i	0.416752	+	0.853159i
$16$	44.8297			2.80185
$17$		−	26.7489i		−	1.57346i	−0.617295	−	0.786732i	$-0.711772\pi$
$17$		−	26.7489i		−	1.57346i	0.617295	−	0.786732i	$-0.288228\pi$
$18$	−26.6102	−	20.7384i	−1.47835	−	1.15213i
$19$	9.76095			0.513734			0.256867	−	0.966447i	$-0.417310\pi$
$19$	9.76095			0.513734			0.256867	+	0.966447i	$0.417310\pi$
$20$			47.7207i			2.38604i
$21$	12.8875	−	6.29533i	0.613692	−	0.299777i
$22$	70.0296			3.18316
$23$			28.7876i			1.25164i	0.779969	+	0.625818i	$0.215235\pi$
$23$			28.7876i			1.25164i	−0.779969	+	0.625818i	$0.784765\pi$
$24$	−29.8705	−	61.1496i	−1.24460	−	2.54790i
$25$	2.46094			0.0984376
$26$			15.5269i			0.597187i
$27$	−5.56568	+	26.4201i	−0.206136	+	0.978523i
$28$	48.0569			1.71632
$29$			22.6205i			0.780018i	0.920811	+	0.390009i	$0.127528\pi$
$29$			22.6205i			0.780018i	−0.920811	+	0.390009i	$0.872472\pi$
$30$	47.9717	−	23.4333i	1.59906	−	0.781110i
$31$	−41.0405			−1.32389			−0.661944	−	0.749553i	$-0.730268\pi$
$31$	−41.0405			−1.32389			−0.661944	+	0.749553i	$0.730268\pi$
$32$		−	77.3062i		−	2.41582i
$33$	−24.5991	−	50.3582i	−0.745427	−	1.52601i
$34$	−100.270			−2.94911
$35$			22.6979i			0.648510i
$36$	−55.6096	+	71.3549i	−1.54471	+	1.98208i
$37$	−24.6432			−0.666032			−0.333016	−	0.942921i	$-0.608066\pi$
$37$	−24.6432			−0.666032			−0.333016	+	0.942921i	$0.608066\pi$
$38$		−	36.5895i		−	0.962881i
$39$	11.1654	−	5.45407i	0.286291	−	0.139848i
$40$	107.698			2.69246
$41$			51.5187i			1.25655i	0.777990	+	0.628276i	$0.216239\pi$
$41$			51.5187i			1.25655i	−0.777990	+	0.628276i	$0.783761\pi$
$42$	−23.5984	−	48.3097i	−0.561867	−	1.15023i
$43$	−68.1944			−1.58592			−0.792958	−	0.609276i	$-0.791460\pi$
$43$	−68.1944			−1.58592			−0.792958	+	0.609276i	$0.791460\pi$
$44$		−	187.783i		−	4.26780i
$45$	−33.7018	−	26.2651i	−0.748928	−	0.583669i
$46$	107.912			2.34591
$47$		−	29.5942i		−	0.629663i	−0.949148	−	0.314832i	$-0.898052\pi$
$47$		−	29.5942i		−	0.629663i	0.949148	−	0.314832i	$-0.101948\pi$
$48$	−120.842	+	59.0292i	−2.51755	+	1.22978i
$49$	−26.1422			−0.533515
$50$		−	9.22497i		−	0.184499i
$51$	35.2214	+	72.1039i	0.690616	+	1.41380i
$52$	41.6350			0.800672
$53$			52.1743i			0.984420i	0.870476	+	0.492210i	$0.163811\pi$
$53$			52.1743i			0.984420i	−0.870476	+	0.492210i	$0.836189\pi$
$54$	99.0374	+	20.8633i	1.83403	+	0.386357i
$55$	88.6922			1.61258
$56$		−	108.457i		−	1.93673i
$57$	−26.3115	+	12.8527i	−0.461605	+	0.225486i
$58$	84.7944			1.46197
$59$			32.9581i			0.558612i	0.960202	+	0.279306i	$0.0901044\pi$
$59$			32.9581i			0.558612i	−0.960202	+	0.279306i	$0.909896\pi$
$60$	−62.8360	−	128.635i	−1.04727	−	2.14392i
$61$	−72.5580			−1.18948			−0.594738	−	0.803920i	$-0.702744\pi$
$61$	−72.5580			−1.18948			−0.594738	+	0.803920i	$0.702744\pi$
$62$			153.843i			2.48133i
$63$	−26.4501	+	33.9392i	−0.419843	+	0.538717i
$64$	−110.468			−1.72607
$65$			19.6647i			0.302534i
$66$	−188.771	+	92.2111i	−2.86016	+	1.39714i
$67$	−8.18535			−0.122169
$67$	−8.18535			−0.122169
$68$			268.871i			3.95399i
$69$	−37.9059	−	77.5995i	−0.549361	−	1.12463i
$70$	85.0842			1.21549
$71$		−	48.2206i		−	0.679164i	−0.940576	−	0.339582i	$-0.889714\pi$
$71$		−	48.2206i		−	0.679164i	0.940576	−	0.339582i	$-0.110286\pi$
$72$	161.037	+	125.502i	2.23662	+	1.74309i
$73$	−6.54622			−0.0896743			−0.0448372	−	0.998994i	$-0.514277\pi$
$73$	−6.54622			−0.0896743			−0.0448372	+	0.998994i	$0.514277\pi$
$74$			92.3764i			1.24833i
$75$	−6.63367	+	3.24043i	−0.0884490	+	0.0432057i
$76$	−98.1140			−1.29097
$77$		−	89.3170i		−	1.15996i
$78$	−20.4449	−	41.8540i	−0.262114	−	0.536589i
$79$	93.9919			1.18977			0.594885	−	0.803811i	$-0.297197\pi$
$79$	93.9919			1.18977			0.594885	+	0.803811i	$0.297197\pi$
$80$		−	212.830i		−	2.66038i
$81$	−19.7858	−	78.5463i	−0.244269	−	0.969707i
$82$	193.121			2.35513
$83$		−	38.8283i		−	0.467811i	−0.972259	−	0.233906i	$-0.924849\pi$
$83$		−	38.8283i		−	0.467811i	0.972259	−	0.233906i	$-0.0751507\pi$
$84$	−129.542	+	63.2787i	−1.54216	+	0.753317i
$85$	−126.991			−1.49401
$86$			255.631i			2.97245i
$87$	−29.7855	−	60.9756i	−0.342362	−	0.700869i
$88$	−423.797			−4.81588
$89$		−	33.5856i		−	0.377366i	−0.982038	−	0.188683i	$-0.939578\pi$
$89$		−	33.5856i		−	0.377366i	0.982038	−	0.188683i	$-0.0604219\pi$
$90$	−98.4562	+	126.333i	−1.09396	+	1.40370i
$91$	19.8032			0.217618
$92$		−	289.364i		−	3.14526i
$93$	110.628	−	54.0399i	1.18955	−	0.581074i
$94$	−110.935			−1.18016
$95$		−	46.3404i		−	0.487794i
$96$	101.793	+	208.386i	1.06034	+	2.17068i
$97$	87.5412			0.902487			0.451244	−	0.892401i	$-0.350981\pi$
$97$	87.5412			0.902487			0.451244	+	0.892401i	$0.350981\pi$
$98$			97.9957i			0.999956i
$99$	132.618	+	103.354i	1.33957	+	1.04398i
$100$	−24.7366			−0.247366
$101$			37.3190i			0.369495i	0.982786	+	0.184747i	$0.0591467\pi$
$101$			37.3190i			0.369495i	−0.982786	+	0.184747i	$0.940853\pi$
$102$	270.286	−	132.030i	2.64986	−	1.29441i
$103$	−108.628			−1.05464			−0.527318	−	0.849668i	$-0.676802\pi$
$103$	−108.628			−1.05464			−0.527318	+	0.849668i	$0.676802\pi$
$104$		−	93.9637i		−	0.903497i
$105$	−29.8873	−	61.1840i	−0.284641	−	0.582705i
$106$	195.578			1.84508
$107$		−	156.424i		−	1.46191i	−0.682428	−	0.730953i	$-0.739076\pi$
$107$		−	156.424i		−	1.46191i	0.682428	−	0.730953i	$-0.260924\pi$
$108$	55.9444	−	265.567i	0.518004	−	2.45895i
$109$	47.8098			0.438622			0.219311	−	0.975655i	$-0.429619\pi$
$109$	47.8098			0.438622			0.219311	+	0.975655i	$0.429619\pi$
$110$		−	332.468i		−	3.02243i
$111$	66.4278	−	32.4488i	0.598449	−	0.292331i
$112$	−214.330			−1.91366
$113$			84.2095i			0.745217i	0.927989	+	0.372608i	$0.121537\pi$
$113$			84.2095i			0.745217i	−0.927989	+	0.372608i	$0.878463\pi$
$114$	48.1790	+	98.6301i	0.422623	+	0.865176i
$115$	136.670			1.18844
$116$		−	227.375i		−	1.96013i
$117$	−22.9156	+	29.4038i	−0.195859	+	0.251315i
$118$	123.545			1.04699
$119$			127.886i			1.07467i
$120$	−290.310	+	141.811i	−2.41925	+	1.18176i
$121$	−228.007			−1.88436
$122$			271.988i			2.22941i
$123$	−67.8369	−	138.873i	−0.551520	−	1.12905i
$124$	412.526			3.32683
$125$		−	130.372i		−	1.04297i
$126$	127.223	+	99.1499i	1.00971	+	0.786904i
$127$	−131.167			−1.03281			−0.516405	−	0.856344i	$-0.672730\pi$
$127$	−131.167			−1.03281			−0.516405	+	0.856344i	$0.672730\pi$
$128$			104.871i			0.819309i
$129$	183.824	−	89.7946i	1.42499	−	0.696082i
$130$	73.7142			0.567033
$131$			18.2054i			0.138973i	0.997583	+	0.0694863i	$0.0221360\pi$
$131$			18.2054i			0.138973i	−0.997583	+	0.0694863i	$0.977864\pi$
$132$	247.262	+	506.185i	1.87320	+	3.83474i
$133$	−46.6669			−0.350879
$134$			30.6833i			0.228980i
$135$	125.430	+	26.4232i	0.929114	+	0.195728i
$136$	606.801			4.46177
$137$		−	153.735i		−	1.12215i	−0.827765	−	0.561075i	$-0.810388\pi$
$137$		−	153.735i		−	1.12215i	0.827765	−	0.561075i	$-0.189612\pi$
$138$	−290.886	+	142.093i	−2.10787	+	1.02966i
$139$	45.6408			0.328351			0.164175	−	0.986431i	$-0.447504\pi$
$139$	45.6408			0.328351			0.164175	+	0.986431i	$0.447504\pi$
$140$		−	228.152i		−	1.62965i
$141$	38.9680	+	79.7736i	0.276369	+	0.565771i
$142$	−180.758			−1.27294
$143$		−	77.3814i		−	0.541129i
$144$	248.014	−	318.237i	1.72232	−	2.20998i
$145$	107.392			0.740633
$146$			24.5389i			0.168075i
$147$	70.4687	−	34.4226i	0.479379	−	0.234168i
$148$	247.705			1.67369
$149$			272.331i			1.82772i	0.406026	+	0.913862i	$0.366914\pi$
$149$			272.331i			1.82772i	−0.406026	+	0.913862i	$0.633086\pi$
$150$	12.1469	+	24.8667i	0.0809796	+	0.165778i
$151$	−236.939			−1.56913			−0.784565	−	0.620047i	$-0.787114\pi$
$151$	−236.939			−1.56913			−0.784565	+	0.620047i	$0.787114\pi$
$152$			221.428i			1.45676i
$153$	−189.885	−	147.985i	−1.24108	−	0.967220i
$154$	−334.810			−2.17409
$155$			194.841i			1.25704i
$156$	−112.231	+	54.8226i	−0.719427	+	0.351427i
$157$	−24.2266			−0.154309			−0.0771547	−	0.997019i	$-0.524584\pi$
$157$	−24.2266			−0.154309			−0.0771547	+	0.997019i	$0.524584\pi$
$158$		−	352.334i		−	2.22996i
$159$	−68.7002	−	140.640i	−0.432077	−	0.884530i
$160$	−367.014			−2.29384
$161$		−	137.633i		−	0.854863i
$162$	−294.435	+	74.1682i	−1.81750	+	0.457828i
$163$	−166.767			−1.02311			−0.511554	−	0.859251i	$-0.670930\pi$
$163$	−166.767			−1.02311			−0.511554	+	0.859251i	$0.670930\pi$
$164$		−	517.850i		−	3.15762i
$165$	−239.077	+	116.785i	−1.44895	+	0.707787i
$166$	−145.550			−0.876809
$167$			114.931i			0.688212i	0.938931	+	0.344106i	$0.111818\pi$
$167$			114.931i			0.688212i	−0.938931	+	0.344106i	$0.888182\pi$
$168$	142.810	+	292.355i	0.850060	+	1.74021i
$169$	−151.843			−0.898480
$170$			476.034i			2.80020i
$171$	54.0012	−	69.2910i	0.315796	−	0.405210i
$172$	685.469			3.98528
$173$		−	18.1994i		−	0.105199i	−0.998616	−	0.0525995i	$-0.983249\pi$
$173$		−	18.1994i		−	0.105199i	0.998616	−	0.0525995i	$-0.0167507\pi$
$174$	−228.571	+	111.653i	−1.31362	+	0.641681i
$175$	−11.7657			−0.0672326
$176$			837.496i			4.75850i
$177$	−43.3974	−	88.8414i	−0.245183	−	0.501929i
$178$	−125.898			−0.707290
$179$			154.257i			0.861769i	0.902407	+	0.430884i	$0.141798\pi$
$179$			154.257i			0.861769i	−0.902407	+	0.430884i	$0.858202\pi$
$180$	338.760	+	264.009i	1.88200	+	1.46671i
$181$	251.971			1.39210			0.696052	−	0.717991i	$-0.254938\pi$
$181$	251.971			1.39210			0.696052	+	0.717991i	$0.254938\pi$
$182$		−	74.2336i		−	0.407877i
$183$	195.586	−	95.5404i	1.06878	−	0.522078i
$184$	−653.050			−3.54918
$185$			116.994i			0.632401i
$186$	−202.572	−	414.696i	−1.08909	−	2.22955i
$187$	499.716			2.67228
$188$			297.471i			1.58229i
$189$	26.6094	−	126.314i	0.140790	−	0.668328i
$190$	−173.710			−0.914262
$191$			274.239i			1.43580i	0.696144	+	0.717902i	$0.254897\pi$
$191$			274.239i			1.43580i	−0.696144	+	0.717902i	$0.745103\pi$
$192$	297.776	−	145.458i	1.55092	−	0.757596i
$193$	137.363			0.711728			0.355864	−	0.934538i	$-0.384187\pi$
$193$	137.363			0.711728			0.355864	+	0.934538i	$0.384187\pi$
$194$		−	328.153i		−	1.69151i
$195$	−25.8934	−	53.0079i	−0.132787	−	0.271835i
$196$	262.774			1.34068
$197$			24.2886i			0.123293i	0.998098	+	0.0616463i	$0.0196351\pi$
$197$			24.2886i			0.123293i	−0.998098	+	0.0616463i	$0.980365\pi$
$198$	387.430	−	497.126i	1.95671	−	2.51074i
$199$	−285.024			−1.43228			−0.716140	−	0.697957i	$-0.754093\pi$
$199$	−285.024			−1.43228			−0.716140	+	0.697957i	$0.754093\pi$
$200$			55.8267i			0.279133i
$201$	22.0643	−	10.7780i	0.109773	−	0.0536220i
$202$	139.892			0.692537
$203$		−	108.148i		−	0.532750i
$204$	−354.035	−	724.766i	−1.73547	−	3.55277i
$205$	244.587			1.19311
$206$			407.197i			1.97668i
$207$	204.357	+	159.264i	0.987233	+	0.769390i
$208$	−185.688			−0.892733
$209$			182.352i			0.872495i
$210$	−229.352	+	112.034i	−1.09215	+	0.533496i
$211$	291.237			1.38027			0.690135	−	0.723681i	$-0.257551\pi$
$211$	291.237			1.38027			0.690135	+	0.723681i	$0.257551\pi$
$212$		−	524.439i		−	2.47377i
$213$	63.4942	+	129.983i	0.298095	+	0.610248i
$214$	−586.364			−2.74002
$215$			323.755i			1.50584i
$216$	−599.343	−	126.258i	−2.77474	−	0.584528i
$217$	196.214			0.904211
$218$		−	179.218i		−	0.822101i
$219$	17.6459	−	8.61970i	0.0805749	−	0.0393594i
$220$	−891.506			−4.05230
$221$			110.796i			0.501340i
$222$	−121.636	−	249.008i	−0.547910	−	1.12166i
$223$	185.542			0.832027			0.416013	−	0.909359i	$-0.363427\pi$
$223$	185.542			0.832027			0.416013	+	0.909359i	$0.363427\pi$
$224$			369.599i			1.65000i
$225$	13.6148	−	17.4697i	0.0605103	−	0.0776431i
$226$	315.664			1.39674
$227$		−	136.350i		−	0.600659i	−0.953836	−	0.300329i	$-0.902903\pi$
$227$		−	136.350i		−	0.600659i	0.953836	−	0.300329i	$-0.0970966\pi$
$228$	264.475	−	129.191i	1.15998	−	0.566628i
$229$	−222.402			−0.971188			−0.485594	−	0.874184i	$-0.661397\pi$
$229$	−222.402			−0.971188			−0.485594	+	0.874184i	$0.661397\pi$
$230$		−	512.316i		−	2.22746i
$231$	117.608	+	240.762i	0.509124	+	1.04226i
$232$	−513.149			−2.21185
$233$			3.81658i			0.0163802i	0.999966	+	0.00819009i	$0.00260702\pi$
$233$			3.81658i			0.0163802i	−0.999966	+	0.00819009i	$0.997393\pi$
$234$	110.222	+	85.9003i	0.471034	+	0.367095i
$235$	−140.499			−0.597869
$236$		−	331.285i		−	1.40375i
$237$	−253.363	+	123.763i	−1.06904	+	0.522208i
$238$	479.387			2.01423
$239$		−	80.4046i		−	0.336421i	−0.985751	−	0.168210i	$-0.946201\pi$
$239$		−	80.4046i		−	0.336421i	0.985751	−	0.168210i	$-0.0537988\pi$
$240$	280.243	+	573.702i	1.16768	+	2.39043i
$241$	−347.572			−1.44221			−0.721105	−	0.692826i	$-0.756365\pi$
$241$	−347.572			−1.44221			−0.721105	+	0.692826i	$0.756365\pi$
$242$			854.699i			3.53181i
$243$	156.760	+	185.675i	0.645102	+	0.764097i
$244$	729.330			2.98906
$245$			124.111i			0.506576i
$246$	−520.574	+	254.291i	−2.11615	+	1.03370i
$247$	−40.4307			−0.163687
$248$		−	931.008i		−	3.75407i
$249$	51.1270	+	104.665i	0.205329	+	0.420342i
$250$	−488.706			−1.95482
$251$		−	10.9620i		−	0.0436734i	−0.999762	−	0.0218367i	$-0.993049\pi$
$251$		−	10.9620i		−	0.0436734i	0.999762	−	0.0218367i	$-0.00695139\pi$
$252$	265.869	−	341.146i	1.05503	−	1.35375i
$253$	−537.803			−2.12570
$254$			491.687i			1.93578i
$255$	342.316	−	167.215i	1.34241	−	0.655745i
$256$	−48.7559			−0.190453
$257$		−	385.051i		−	1.49825i	−0.662428	−	0.749126i	$-0.730474\pi$
$257$		−	385.051i		−	1.49825i	0.662428	−	0.749126i	$-0.269526\pi$
$258$	−336.600	−	689.074i	−1.30465	−	2.67083i
$259$	117.818			0.454898
$260$		−	197.663i		−	0.760244i
$261$	160.579	+	125.145i	0.615244	+	0.479483i
$262$	68.2441			0.260474
$263$		−	256.382i		−	0.974836i	−0.873169	−	0.487418i	$-0.837939\pi$
$263$		−	256.382i		−	0.974836i	0.873169	−	0.487418i	$-0.162061\pi$
$264$	1142.38	−	558.033i	4.32720	−	2.11376i
$265$	247.699			0.934713
$266$			174.934i			0.657645i
$267$	44.2237	+	90.5329i	0.165632	+	0.339075i
$268$	82.2766			0.307002
$269$		−	327.314i		−	1.21678i	−0.793638	−	0.608391i	$-0.791815\pi$
$269$		−	327.314i		−	1.21678i	0.793638	−	0.608391i	$-0.208185\pi$
$270$	99.0490	−	470.183i	0.366848	−	1.74142i
$271$	−180.927			−0.667629			−0.333814	−	0.942639i	$-0.608336\pi$
$271$	−180.927			−0.667629			−0.333814	+	0.942639i	$0.608336\pi$
$272$		−	1199.14i		−	4.40862i
$273$	−53.3813	+	26.0758i	−0.195536	+	0.0955157i
$274$	−576.283			−2.10322
$275$			45.9746i			0.167180i
$276$	381.018	+	780.006i	1.38050	+	2.82611i
$277$	−256.101			−0.924554			−0.462277	−	0.886736i	$-0.652967\pi$
$277$	−256.101			−0.924554			−0.462277	+	0.886736i	$0.652967\pi$
$278$		−	171.087i		−	0.615421i
$279$	−227.051	+	291.338i	−0.813804	+	1.04422i
$280$	−514.903			−1.83894
$281$		−	390.164i		−	1.38848i	−0.719742	−	0.694241i	$-0.755740\pi$
$281$		−	390.164i		−	1.38848i	0.719742	−	0.694241i	$-0.244260\pi$
$282$	299.036	−	146.074i	1.06041	−	0.517992i
$283$	434.492			1.53531			0.767653	−	0.640866i	$-0.221425\pi$
$283$	434.492			1.53531			0.767653	+	0.640866i	$0.221425\pi$
$284$			484.699i			1.70669i
$285$	61.0185	+	124.915i	0.214100	+	0.438297i
$286$	−290.069			−1.01423
$287$		−	246.310i		−	0.858222i
$288$	−548.781	−	427.687i	−1.90549	−	1.48502i
$289$	−426.503			−1.47579
$290$		−	402.564i		−	1.38815i
$291$	−235.975	+	115.269i	−0.810911	+	0.396115i
$292$	65.8006			0.225345
$293$			356.908i			1.21812i	0.793125	+	0.609059i	$0.208453\pi$
$293$			356.908i			1.21812i	−0.793125	+	0.609059i	$0.791547\pi$
$294$	−129.035	−	264.156i	−0.438896	−	0.898489i
$295$	156.470			0.530406
$296$		−	559.033i		−	1.88862i
$297$	−493.574	−	103.977i	−1.66187	−	0.350089i
$298$	1020.85			3.42566
$299$		−	119.241i		−	0.398799i
$300$	66.6796	−	32.5718i	0.222265	−	0.108573i
$301$	326.036			1.08318
$302$			888.178i			2.94099i
$303$	−49.1396	−	100.597i	−0.162177	−	0.332002i
$304$	437.580			1.43941
$305$			344.471i			1.12941i
$306$	−554.729	+	711.794i	−1.81284	+	2.32613i
$307$	9.58144			0.0312099			0.0156050	−	0.999878i	$-0.495033\pi$
$307$	9.58144			0.0312099			0.0156050	+	0.999878i	$0.495033\pi$
$308$			897.787i			2.91489i
$309$	292.815	−	143.035i	0.947621	−	0.462895i
$310$	730.373			2.35604
$311$			169.507i			0.545040i	0.962150	+	0.272520i	$0.0878570\pi$
$311$			169.507i			0.545040i	−0.962150	+	0.272520i	$0.912143\pi$
$312$	123.726	+	253.287i	0.396558	+	0.811818i
$313$	601.899			1.92300			0.961500	−	0.274805i	$-0.0886133\pi$
$313$	601.899			1.92300			0.961500	+	0.274805i	$0.0886133\pi$
$314$			90.8147i			0.289219i
$315$	161.127	+	125.573i	0.511516	+	0.398644i
$316$	−944.777			−2.98980
$317$			52.4412i			0.165430i	0.996573	+	0.0827148i	$0.0263590\pi$
$317$			52.4412i			0.165430i	−0.996573	+	0.0827148i	$0.973641\pi$
$318$	−527.198	+	257.527i	−1.65786	+	0.809832i
$319$	−422.591			−1.32474
$320$			524.451i			1.63891i
$321$	205.970	+	421.654i	0.641652	+	1.31356i
$322$	−515.925			−1.60225
$323$		−	261.094i		−	0.808342i
$324$	198.881	+	789.523i	0.613829	+	2.43680i
$325$	−10.1934			−0.0313644
$326$			625.134i			1.91759i
$327$	−128.876	+	62.9533i	−0.394115	+	0.192518i
$328$	−1168.71			−3.56313
$329$			141.489i			0.430058i
$330$	437.775	+	896.195i	1.32659	+	2.71574i
$331$	−248.469			−0.750661			−0.375330	−	0.926891i	$-0.622471\pi$
$331$	−248.469			−0.750661			−0.375330	+	0.926891i	$0.622471\pi$
$332$			390.290i			1.17557i
$333$	−136.335	+	174.937i	−0.409415	+	0.525336i
$334$	430.827			1.28990
$335$			38.8602i			0.116001i
$336$	577.744	−	282.217i	1.71948	−	0.839933i
$337$	−344.345			−1.02180			−0.510898	−	0.859642i	$-0.670687\pi$
$337$	−344.345			−1.02180			−0.510898	+	0.859642i	$0.670687\pi$
$338$			569.193i			1.68400i
$339$	−110.882	−	226.994i	−0.327087	−	0.669599i
$340$	1276.48			3.75434
$341$		−	766.708i		−	2.24841i
$342$	−259.741	−	202.427i	−0.759477	−	0.591890i
$343$	359.253			1.04739
$344$		−	1547.00i		−	4.49708i
$345$	−368.406	+	179.960i	−1.06784	+	0.521622i
$346$	−68.2216			−0.197172
$347$			294.239i			0.847951i	0.905674	+	0.423976i	$0.139366\pi$
$347$			294.239i			0.847951i	−0.905674	+	0.423976i	$0.860634\pi$
$348$	299.394	+	612.908i	0.860328	+	1.76123i
$349$	157.942			0.452556			0.226278	−	0.974063i	$-0.427344\pi$
$349$	157.942			0.452556			0.226278	+	0.974063i	$0.427344\pi$
$350$			44.1044i			0.126013i
$351$	23.0535	−	109.434i	0.0656795	−	0.311779i
$352$	1444.21			4.10288
$353$			33.2784i			0.0942730i	0.998888	+	0.0471365i	$0.0150096\pi$
$353$			33.2784i			0.0942730i	−0.998888	+	0.0471365i	$0.984990\pi$
$354$	−333.027	+	162.678i	−0.940755	+	0.459541i
$355$	−228.929			−0.644870
$356$			337.592i			0.948292i
$357$	−168.393	−	344.727i	−0.471689	−	0.965623i
$358$	578.240			1.61520
$359$			361.759i			1.00769i	0.863795	+	0.503843i	$0.168081\pi$
$359$			361.759i			1.00769i	−0.863795	+	0.503843i	$0.831919\pi$
$360$	595.826	−	764.528i	1.65507	−	2.12369i
$361$	−265.724			−0.736077
$362$		−	944.528i		−	2.60919i
$363$	614.614	−	300.228i	1.69315	−	0.827073i
$364$	−199.056			−0.546857
$365$			31.0784i			0.0851463i
$366$	−358.139	−	733.167i	−0.978521	−	2.00319i
$367$	−465.878			−1.26942			−0.634712	−	0.772749i	$-0.718881\pi$
$367$	−465.878			−1.26942			−0.634712	+	0.772749i	$0.718881\pi$
$368$			1290.54i			3.50690i
$369$	365.721	+	285.020i	0.991112	+	0.772413i
$370$	438.560			1.18530
$371$		−	249.444i		−	0.672356i
$372$	−1112.00	+	543.192i	−2.98925	+	1.46019i
$373$	−94.7081			−0.253909			−0.126955	−	0.991909i	$-0.540520\pi$
$373$	−94.7081			−0.253909			−0.126955	+	0.991909i	$0.540520\pi$
$374$		−	1873.21i		−	5.00859i
$375$	171.666	+	351.428i	0.457777	+	0.937142i
$376$	671.347			1.78550
$377$		−	93.6962i		−	0.248531i
$378$	−473.496	−	99.7468i	−1.25263	−	0.263880i
$379$	43.1484			0.113848			0.0569240	−	0.998379i	$-0.481871\pi$
$379$	43.1484			0.113848			0.0569240	+	0.998379i	$0.481871\pi$
$380$			465.799i			1.22579i
$381$	353.572	−	172.713i	0.928010	−	0.453316i
$382$	1028.00			2.69110
$383$			451.872i			1.17982i	0.807468	+	0.589912i	$0.200837\pi$
$383$			451.872i			1.17982i	−0.807468	+	0.589912i	$0.799163\pi$
$384$	−138.089	−	282.690i	−0.359607	−	0.736172i
$385$	−424.035			−1.10139
$386$		−	514.915i		−	1.33398i
$387$	−377.277	+	484.098i	−0.974875	+	1.25090i
$388$	−879.937			−2.26788
$389$			602.116i			1.54786i	0.633274	+	0.773928i	$0.281711\pi$
$389$			602.116i			1.54786i	−0.633274	+	0.773928i	$0.718289\pi$
$390$	−198.703	+	97.0628i	−0.509495	+	0.248879i
$391$	770.036			1.96940
$392$		−	593.039i		−	1.51286i
$393$	−23.9719	−	49.0743i	−0.0609972	−	0.124871i
$394$	91.0473			0.231085
$395$		−	446.230i		−	1.12969i
$396$	−1333.03	−	1038.88i	−3.36625	−	2.62345i
$397$	−59.3971			−0.149615			−0.0748074	−	0.997198i	$-0.523834\pi$
$397$	−59.3971			−0.149615			−0.0748074	+	0.997198i	$0.523834\pi$
$398$			1068.43i			2.68449i
$399$	125.795	−	61.4484i	0.315275	−	0.154006i
$400$	110.323			0.275808
$401$			119.281i			0.297458i	0.988878	+	0.148729i	$0.0475182\pi$
$401$			119.281i			0.297458i	−0.988878	+	0.148729i	$0.952482\pi$
$402$	−40.4020	−	82.7094i	−0.100503	−	0.205745i
$403$	169.993			0.421820
$404$		−	375.119i		−	0.928512i
$405$	−372.901	+	93.9337i	−0.920743	+	0.231935i
$406$	−405.400			−0.998523
$407$		−	460.377i		−	1.13115i
$408$	−1635.68	+	799.002i	−4.00903	+	1.95834i
$409$	211.454			0.517003			0.258501	−	0.966011i	$-0.416771\pi$
$409$	211.454			0.517003			0.258501	+	0.966011i	$0.416771\pi$
$410$		−	916.847i		−	2.23621i
$411$	202.429	+	414.405i	0.492529	+	1.00828i
$412$	1091.89			2.65022
$413$		−	157.572i		−	0.381530i
$414$	597.009	−	766.045i	1.44205	−	1.85035i
$415$	−184.339			−0.444190
$416$			320.209i			0.769733i
$417$	−123.029	+	60.0972i	−0.295033	+	0.144118i
$418$	683.555			1.63530
$419$		−	299.296i		−	0.714310i	−0.934045	−	0.357155i	$-0.883747\pi$
$419$		−	299.296i		−	0.714310i	0.934045	−	0.357155i	$-0.116253\pi$
$420$	300.417	+	615.003i	0.715280	+	1.46429i
$421$	317.332			0.753757			0.376879	−	0.926263i	$-0.376997\pi$
$421$	317.332			0.753757			0.376879	+	0.926263i	$0.376997\pi$
$422$		−	1091.72i		−	2.58701i
$423$	−210.083	−	163.726i	−0.496650	−	0.387059i
$424$	−1183.58			−2.79146
$425$		−	65.8274i		−	0.154888i
$426$	487.248	−	238.012i	1.14378	−	0.558713i
$427$	346.898			0.812408
$428$			1572.32i			3.67366i
$429$	101.892	+	208.588i	0.237509	+	0.486220i
$430$	1213.61			2.82236
$431$			16.6461i			0.0386219i	0.999814	+	0.0193110i	$0.00614725\pi$
$431$			16.6461i			0.0386219i	−0.999814	+	0.0193110i	$0.993853\pi$
$432$	−249.507	+	1184.41i	−0.577564	+	2.74168i
$433$	181.809			0.419883			0.209941	−	0.977714i	$-0.432673\pi$
$433$	181.809			0.419883			0.209941	+	0.977714i	$0.432673\pi$
$434$		−	735.519i		−	1.69474i
$435$	−289.484	+	141.407i	−0.665480	+	0.325075i
$436$	−480.570			−1.10222
$437$			280.994i			0.643008i
$438$	−32.3115	−	66.1467i	−0.0737705	−	0.151020i
$439$	−228.059			−0.519495			−0.259748	−	0.965677i	$-0.583639\pi$
$439$	−228.059			−0.519495			−0.259748	+	0.965677i	$0.583639\pi$
$440$			2011.99i			4.57271i
$441$	−144.629	+	185.578i	−0.327956	+	0.420813i
$442$	415.326			0.939651
$443$		−	812.059i		−	1.83309i	−0.399931	−	0.916545i	$-0.630966\pi$
$443$		−	812.059i		−	1.83309i	0.399931	−	0.916545i	$-0.369034\pi$
$444$	−667.711	+	326.165i	−1.50385	+	0.734605i
$445$	−159.449			−0.358312
$446$		−	695.515i		−	1.55945i
$447$	−358.590	−	734.091i	−0.802215	−	1.64226i
$448$	528.146			1.17890
$449$		−	173.469i		−	0.386345i	−0.981165	−	0.193172i	$-0.938122\pi$
$449$		−	173.469i		−	0.386345i	0.981165	−	0.193172i	$-0.0618777\pi$
$450$	−65.4862	−	51.0360i	−0.145525	−	0.113413i
$451$	−962.458			−2.13405
$452$		−	846.448i		−	1.87267i
$453$	638.688	−	311.988i	1.40991	−	0.688714i
$454$	−511.114			−1.12580
$455$		−	94.0165i		−	0.206630i
$456$	−291.564	−	596.879i	−0.639395	−	1.30894i
$457$	−257.422			−0.563287			−0.281644	−	0.959519i	$-0.590880\pi$
$457$	−257.422			−0.563287			−0.281644	+	0.959519i	$0.590880\pi$
$458$			833.687i			1.82028i
$459$	706.709	+	148.876i	1.53967	+	0.324348i
$460$	−1373.76			−2.98645
$461$		−	533.038i		−	1.15627i	−0.815943	−	0.578133i	$-0.803782\pi$
$461$		−	533.038i		−	1.15627i	0.815943	−	0.578133i	$-0.196218\pi$
$462$	902.509	−	440.859i	1.95348	−	0.954241i
$463$	318.394			0.687676			0.343838	−	0.939029i	$-0.388273\pi$
$463$	318.394			0.687676			0.343838	+	0.939029i	$0.388273\pi$
$464$			1014.07i			2.18550i
$465$	−256.556	−	525.211i	−0.551733	−	1.12949i
$466$	14.3067			0.0307010
$467$		−	140.874i		−	0.301658i	−0.988560	−	0.150829i	$-0.951806\pi$
$467$		−	140.874i		−	0.301658i	0.988560	−	0.150829i	$-0.0481943\pi$
$468$	230.340	−	295.558i	0.492179	−	0.631534i
$469$	39.1340			0.0834414
$470$			526.670i			1.12057i
$471$	65.3048	−	31.9002i	0.138651	−	0.0677286i
$472$	−747.658			−1.58402
$473$		−	1273.99i		−	2.69343i
$474$	463.934	+	949.747i	0.978764	+	2.00369i
$475$	24.0211			0.0505708
$476$		−	1285.47i		−	2.70056i
$477$	370.374	+	288.647i	0.776466	+	0.605131i
$478$	−301.401			−0.630547
$479$			299.572i			0.625411i	0.949850	+	0.312705i	$0.101235\pi$
$479$			299.572i			0.625411i	−0.949850	+	0.312705i	$0.898765\pi$
$480$	989.317	−	483.263i	2.06108	−	1.00680i
$481$	102.074			0.212212
$482$			1302.90i			2.70310i
$483$	181.227	+	371.001i	0.375212	+	0.768119i
$484$	2291.86			4.73525
$485$		−	415.605i		−	0.856917i
$486$	696.015	−	587.623i	1.43213	−	1.20910i
$487$	−403.948			−0.829463			−0.414731	−	0.909944i	$-0.636124\pi$
$487$	−403.948			−0.829463			−0.414731	+	0.909944i	$0.636124\pi$
$488$		−	1645.99i		−	3.37292i
$489$	449.534	−	219.589i	0.919291	−	0.449057i
$490$	465.238			0.949465
$491$			294.173i			0.599130i	0.954076	+	0.299565i	$0.0968416\pi$
$491$			294.173i			0.599130i	−0.954076	+	0.299565i	$0.903158\pi$
$492$	681.876	+	1395.91i	1.38593	+	2.83721i
$493$	605.074			1.22733
$494$			151.557i			0.306795i
$495$	490.678	−	629.608i	0.991268	−	1.27193i
$496$	−1839.83			−3.70934
$497$			230.542i			0.463867i
$498$	392.343	−	191.653i	0.787838	−	0.384844i
$499$	−658.423			−1.31949			−0.659743	−	0.751492i	$-0.729335\pi$
$499$	−658.423			−1.31949			−0.659743	+	0.751492i	$0.729335\pi$
$500$			1310.46i			2.62091i
$501$	−151.335	−	309.808i	−0.302067	−	0.618379i
$502$	−41.0918			−0.0818561
$503$		−	584.271i		−	1.16157i	−0.814056	−	0.580786i	$-0.802745\pi$
$503$		−	584.271i		−	1.16157i	0.814056	−	0.580786i	$-0.197255\pi$
$504$	−769.914	−	600.024i	−1.52761	−	1.19052i
$505$	177.173			0.350838
$506$			2015.98i			3.98416i
$507$	409.306	−	199.939i	0.807310	−	0.394356i
$508$	1318.45			2.59537
$509$			293.802i			0.577213i	0.957448	+	0.288607i	$0.0931920\pi$
$509$			293.802i			0.577213i	−0.957448	+	0.288607i	$0.906808\pi$
$510$	−626.815	−	1283.19i	−1.22905	−	2.51606i
$511$	31.2974			0.0612473
$512$			602.250i			1.17627i
$513$	−54.3263	+	257.886i	−0.105899	+	0.502701i
$514$	−1443.38			−2.80814
$515$			515.713i			1.00138i
$516$	−1847.74	+	902.587i	−3.58089	+	1.74920i
$517$	552.871			1.06938
$518$		−	441.649i		−	0.852605i
$519$	23.9640	+	49.0581i	0.0461734	+	0.0945242i
$520$	−446.095			−0.857876
$521$			553.151i			1.06171i	0.847463	+	0.530855i	$0.178129\pi$
$521$			553.151i			1.06171i	−0.847463	+	0.530855i	$0.821871\pi$
$522$	469.114	−	601.938i	0.898685	−	1.15314i
$523$	408.355			0.780794			0.390397	−	0.920647i	$-0.372338\pi$
$523$	408.355			0.780794			0.390397	+	0.920647i	$0.372338\pi$
$524$		−	182.995i		−	0.349227i
$525$	31.7155	−	15.4924i	0.0604104	−	0.0295094i
$526$	−961.062			−1.82711
$527$			1097.79i			2.08309i
$528$	−1102.77	−	2257.54i	−2.08858	−	4.27565i
$529$	−299.726			−0.566590
$530$		−	928.514i		−	1.75191i
$531$	233.963	+	182.336i	0.440608	+	0.343383i
$532$	469.081			0.881731
$533$		−	213.395i		−	0.400365i
$534$	339.368	−	165.775i	0.635520	−	0.310440i
$535$	−742.628			−1.38809
$536$		−	185.686i		−	0.346428i
$537$	−203.117	−	415.812i	−0.378243	−	0.774324i
$538$	−1226.96			−2.28059
$539$		−	488.383i		−	0.906090i
$540$	−1260.79	−	265.598i	−2.33479	−	0.491848i
$541$	399.590			0.738614			0.369307	−	0.929307i	$-0.379595\pi$
$541$	399.590			0.738614			0.369307	+	0.929307i	$0.379595\pi$
$542$			678.217i			1.25132i
$543$	−679.209	+	331.781i	−1.25085	+	0.611015i
$544$	−2067.85			−3.80120
$545$		−	226.979i		−	0.416475i
$546$	97.7466	+	200.103i	0.179023	+	0.366489i
$547$	−20.2170			−0.0369598			−0.0184799	−	0.999829i	$-0.505883\pi$
$547$	−20.2170			−0.0369598			−0.0184799	+	0.999829i	$0.505883\pi$
$548$			1545.29i			2.81988i
$549$	−401.418	+	515.075i	−0.731180	+	0.938205i
$550$	172.339			0.313343
$551$			220.798i			0.400722i
$552$	1760.35	−	859.900i	3.18904	−	1.55779i
$553$	−449.373			−0.812610
$554$			960.011i			1.73287i
$555$	−154.052	−	315.368i	−0.277570	−	0.568231i
$556$	−458.767			−0.825120
$557$		−	69.0429i		−	0.123955i	−0.998078	−	0.0619775i	$-0.980259\pi$
$557$		−	69.0429i		−	0.123955i	0.998078	−	0.0619775i	$-0.0197407\pi$
$558$	1092.10	+	851.115i	1.95717	+	1.52530i
$559$	282.467			0.505308
$560$			1017.54i			1.81703i
$561$	−1347.03	+	657.998i	−2.40112	+	1.17290i
$562$	−1462.55			−2.60240
$563$		−	200.381i		−	0.355916i	−0.984038	−	0.177958i	$-0.943051\pi$
$563$		−	200.381i		−	0.355916i	0.984038	−	0.177958i	$-0.0569491\pi$
$564$	−391.694	−	801.860i	−0.694493	−	1.42174i
$565$	399.787			0.707588
$566$		−	1628.72i		−	2.87759i
$567$	94.5955	+	375.528i	0.166835	+	0.662307i
$568$	1093.89			1.92586
$569$		−	1017.55i		−	1.78831i	−0.447754	−	0.894157i	$-0.647776\pi$
$569$		−	1017.55i		−	1.78831i	0.447754	−	0.894157i	$-0.352224\pi$
$570$	468.250	−	228.731i	0.821491	−	0.401283i
$571$	758.717			1.32875			0.664375	−	0.747399i	$-0.268698\pi$
$571$	758.717			1.32875			0.664375	+	0.747399i	$0.268698\pi$
$572$			777.814i			1.35981i
$573$	−361.102	−	739.234i	−0.630196	−	1.29011i
$574$	−923.306			−1.60855
$575$			70.8446i			0.123208i
$576$	−611.151	+	784.191i	−1.06103	+	1.36144i
$577$	223.052			0.386572			0.193286	−	0.981142i	$-0.438085\pi$
$577$	223.052			0.386572			0.193286	+	0.981142i	$0.438085\pi$
$578$			1598.77i			2.76604i
$579$	−370.275	+	180.873i	−0.639508	+	0.312388i
$580$	−1079.47			−1.86115
$581$			185.637i			0.319514i
$582$	432.094	+	884.566i	0.742430	+	1.51987i
$583$	−974.706			−1.67188
$584$		−	148.502i		−	0.254284i
$585$	139.596	+	108.792i	0.238625	+	0.185970i
$586$	1337.89			2.28309
$587$			631.782i			1.07629i	0.842852	+	0.538145i	$0.180875\pi$
$587$			631.782i			1.07629i	−0.842852	+	0.538145i	$0.819125\pi$
$588$	−708.329	+	346.006i	−1.20464	+	0.588445i
$589$	−400.594			−0.680126
$590$		−	586.536i		−	0.994128i
$591$	−31.9819	−	65.4721i	−0.0541149	−	0.110782i
$592$	−1104.75			−1.86612
$593$		−	724.745i		−	1.22217i	−0.791566	−	0.611083i	$-0.790734\pi$
$593$		−	724.745i		−	1.22217i	0.791566	−	0.611083i	$-0.209266\pi$
$594$	−389.762	+	1850.19i	−0.656165	+	3.11480i
$595$	607.142			1.02041
$596$		−	2737.38i		−	4.59293i
$597$	768.306	−	375.303i	1.28694	−	0.628649i
$598$	−446.981			−0.747460
$599$		−	497.117i		−	0.829912i	−0.909841	−	0.414956i	$-0.863797\pi$
$599$		−	497.117i		−	0.829912i	0.909841	−	0.414956i	$-0.136203\pi$
$600$	−73.5094	−	150.486i	−0.122516	−	0.250809i
$601$	−549.008			−0.913491			−0.456746	−	0.889597i	$-0.650985\pi$
$601$	−549.008			−0.913491			−0.456746	+	0.889597i	$0.650985\pi$
$602$		−	1222.16i		−	2.03017i
$603$	−45.2844	+	58.1061i	−0.0750985	+	0.0963618i
$604$	2381.63			3.94310
$605$			1082.47i			1.78921i
$606$	−377.092	+	184.203i	−0.622264	+	0.303965i
$607$	193.641			0.319013			0.159507	−	0.987197i	$-0.449010\pi$
$607$	193.641			0.319013			0.159507	+	0.987197i	$0.449010\pi$
$608$		−	754.582i		−	1.24109i
$609$	142.404	+	291.523i	0.233832	+	0.478691i
$610$	1291.27			2.11684
$611$			122.582i			0.200625i
$612$	1908.66	+	1487.50i	3.11873	+	2.43055i
$613$	235.206			0.383697			0.191848	−	0.981425i	$-0.438552\pi$
$613$	235.206			0.383697			0.191848	+	0.981425i	$0.438552\pi$
$614$		−	35.9166i		−	0.0584961i
$615$	−659.304	+	322.058i	−1.07204	+	0.523671i
$616$	2026.17			3.28923
$617$		−	110.949i		−	0.179820i	−0.995950	−	0.0899102i	$-0.971342\pi$
$617$		−	110.949i		−	0.179820i	0.995950	−	0.0899102i	$-0.0286580\pi$
$618$	−536.174	−	1097.63i	−0.867595	−	1.77611i
$619$	622.204			1.00518			0.502588	−	0.864526i	$-0.332381\pi$
$619$	622.204			1.00518			0.502588	+	0.864526i	$0.332381\pi$
$620$		−	1958.48i		−	3.15884i
$621$	−760.572	−	160.223i	−1.22475	−	0.258007i
$622$	635.408			1.02156
$623$			160.572i			0.257740i
$624$	500.539	−	244.504i	0.802146	−	0.391834i
$625$	−557.420			−0.891872
$626$		−	2256.25i		−	3.60424i
$627$	−240.110	−	491.544i	−0.382951	−	0.783962i
$628$	243.518			0.387767
$629$			659.177i			1.04798i
$630$	470.717	−	603.995i	0.747170	−	0.958723i
$631$	785.382			1.24466			0.622331	−	0.782754i	$-0.286186\pi$
$631$	785.382			1.24466			0.622331	+	0.782754i	$0.286186\pi$
$632$			2132.22i			3.37376i
$633$	−785.054	+	383.485i	−1.24021	+	0.605821i
$634$	196.579			0.310061
$635$			622.719i			0.980660i
$636$	690.553	+	1413.67i	1.08577	+	2.22275i
$637$	108.283			0.169990
$638$			1584.11i			2.48293i
$639$	−342.308	−	266.774i	−0.535694	−	0.417487i
$640$	497.881			0.777939
$641$			215.659i			0.336442i	0.985749	+	0.168221i	$0.0538022\pi$
$641$			215.659i			0.336442i	−0.985749	+	0.168221i	$0.946198\pi$
$642$	1580.60	−	772.092i	2.46199	−	1.20264i
$643$	−608.300			−0.946034			−0.473017	−	0.881053i	$-0.656835\pi$
$643$	−608.300			−0.946034			−0.473017	+	0.881053i	$0.656835\pi$
$644$			1383.44i			2.14820i
$645$	−426.303	−	872.710i	−0.660934	−	1.35304i
$646$	−978.728			−1.51506
$647$		−	36.2809i		−	0.0560756i	−0.999607	−	0.0280378i	$-0.991074\pi$
$647$		−	36.2809i		−	0.0560756i	0.999607	−	0.0280378i	$-0.00892587\pi$
$648$	1781.83	−	448.843i	2.74974	−	0.692659i
$649$	−615.715			−0.948713
$650$			38.2106i			0.0587856i
$651$	−528.911	+	258.363i	−0.812460	+	0.396872i
$652$	1676.29			2.57099
$653$			221.083i			0.338566i	0.985567	+	0.169283i	$0.0541452\pi$
$653$			221.083i			0.338566i	−0.985567	+	0.169283i	$0.945855\pi$
$654$	235.984	+	483.097i	0.360832	+	0.738681i
$655$	86.4308			0.131955
$656$			2309.57i			3.52068i
$657$	−36.2161	+	46.4703i	−0.0551235	+	0.0707311i
$658$	530.380			0.806049
$659$			812.142i			1.23238i	0.787596	+	0.616192i	$0.211326\pi$
$659$			812.142i			1.23238i	−0.787596	+	0.616192i	$0.788674\pi$
$660$	2403.13	−	1173.89i	3.64111	−	1.77861i
$661$	583.597			0.882900			0.441450	−	0.897286i	$-0.354464\pi$
$661$	583.597			0.882900			0.441450	+	0.897286i	$0.354464\pi$
$662$			931.399i			1.40695i
$663$	−145.890	−	298.661i	−0.220046	−	0.450469i
$664$	880.825			1.32654
$665$			221.553i			0.333162i
$666$	655.761	+	511.060i	0.984626	+	0.767358i
$667$	−651.191			−0.976298
$668$		−	1155.26i		−	1.72942i
$669$	−500.144	+	244.311i	−0.747600	+	0.365189i
$670$	145.670			0.217418
$671$		−	1355.51i		−	2.02013i
$672$	−486.668	−	996.287i	−0.724208	−	1.48257i
$673$	907.322			1.34818			0.674088	−	0.738651i	$-0.264537\pi$
$673$	907.322			1.34818			0.674088	+	0.738651i	$0.264537\pi$
$674$			1290.80i			1.91513i
$675$	−13.6968	+	65.0183i	−0.0202915	+	0.0963235i
$676$	1526.28			2.25781
$677$			626.494i			0.925398i	0.886516	+	0.462699i	$0.153119\pi$
$677$			626.494i			0.925398i	−0.886516	+	0.462699i	$0.846881\pi$
$678$	−850.900	+	415.649i	−1.25501	+	0.613052i
$679$	−418.533			−0.616396
$680$		−	2880.81i		−	4.23648i
$681$	179.538	+	367.542i	0.263638	+	0.539709i
$682$	−2874.05			−4.21415
$683$		−	98.4053i		−	0.144078i	−0.997402	−	0.0720390i	$-0.977049\pi$
$683$		−	98.4053i		−	0.144078i	0.997402	−	0.0720390i	$-0.0229506\pi$
$684$	−542.803	+	696.491i	−0.793572	+	1.01826i
$685$	−729.860			−1.06549
$686$		−	1346.68i		−	1.96309i
$687$	599.504	−	292.847i	0.872640	−	0.426269i
$688$	−3057.13			−4.44351
$689$		−	216.110i		−	0.313658i
$690$	674.589	+	1380.99i	0.977665	+	2.00144i
$691$	818.088			1.18392			0.591960	−	0.805968i	$-0.298355\pi$
$691$	818.088			1.18392			0.591960	+	0.805968i	$0.298355\pi$
$692$			182.935i			0.264357i
$693$	−634.043	−	494.135i	−0.914925	−	0.713037i
$694$	1102.97			1.58930
$695$		−	216.681i		−	0.311771i
$696$	1383.24	−	675.686i	1.98741	−	0.970814i
$697$	1378.07			1.97714
$698$		−	592.055i		−	0.848216i
$699$	−5.02547	−	10.2879i	−0.00718951	−	0.0147181i
$700$	118.265			0.168950
$701$		−	537.982i		−	0.767450i	−0.923447	−	0.383725i	$-0.874641\pi$
$701$		−	537.982i		−	0.767450i	0.923447	−	0.383725i	$-0.125359\pi$
$702$	−410.221	−	86.4174i	−0.584361	−	0.123102i
$703$	−240.541			−0.342163
$704$		−	2063.74i		−	2.93145i
$705$	378.728	−	185.002i	0.537203	−	0.262414i
$706$	124.746			0.176694
$707$		−	178.421i		−	0.252364i
$708$	436.217	+	893.006i	0.616126	+	1.26131i
$709$	226.020			0.318786			0.159393	−	0.987215i	$-0.449046\pi$
$709$	226.020			0.318786			0.159393	+	0.987215i	$0.449046\pi$
$710$			858.154i			1.20867i
$711$	519.998	−	667.229i	0.731361	−	0.938438i
$712$	761.893			1.07007
$713$		−	1181.46i		−	1.65702i
$714$	−1292.23	+	631.231i	−1.80985	+	0.884077i
$715$	−367.371			−0.513805
$716$		−	1550.54i		−	2.16556i
$717$	105.872	+	216.737i	0.147660	+	0.302284i
$718$	1356.08			1.88869
$719$			715.751i			0.995481i	0.867326	+	0.497740i	$0.165837\pi$
$719$			715.751i			0.995481i	−0.867326	+	0.497740i	$0.834163\pi$
$720$	−1510.84	−	1177.46i	−2.09839	−	1.63536i
$721$	519.346			0.720313
$722$			996.081i			1.37961i
$723$	936.911	−	457.664i	1.29587	−	0.633007i
$724$	−2532.73			−3.49825
$725$			55.6678i			0.0767831i
$726$	−1125.42	−	2303.92i	−1.55017	−	3.17344i
$727$	−1112.34			−1.53005			−0.765024	−	0.644002i	$-0.777273\pi$
$727$	−1112.34			−1.53005			−0.765024	+	0.644002i	$0.777273\pi$
$728$			449.238i			0.617086i
$729$	−667.046	−	294.092i	−0.915016	−	0.403418i
$730$	116.499			0.159588
$731$			1824.12i			2.49538i
$732$	−1965.97	+	960.342i	−2.68576	+	1.31194i
$733$	−682.229			−0.930735			−0.465368	−	0.885118i	$-0.654078\pi$
$733$	−682.229			−0.930735			−0.465368	+	0.885118i	$0.654078\pi$
$734$			1746.37i			2.37925i
$735$	−163.423	−	334.552i	−0.222344	−	0.455173i
$736$	2225.46			3.02372
$737$		−	152.917i		−	0.207485i
$738$	1068.42	−	1370.92i	1.44772	−	1.85762i
$739$	546.695			0.739777			0.369889	−	0.929076i	$-0.379396\pi$
$739$	546.695			0.739777			0.369889	+	0.929076i	$0.379396\pi$
$740$		−	1175.99i		−	1.58918i
$741$	108.984	−	53.2369i	0.147078	−	0.0718447i
$742$	−935.056			−1.26018
$743$		−	610.581i		−	0.821778i	−0.911685	−	0.410889i	$-0.865218\pi$
$743$		−	610.581i		−	0.821778i	0.911685	−	0.410889i	$-0.134782\pi$
$744$	1225.90	+	2509.61i	1.64771	+	3.37314i
$745$	1292.90			1.73543
$746$			355.019i			0.475896i
$747$	−275.634	−	214.813i	−0.368989	−	0.287567i
$748$	−5022.99			−6.71522
$749$			747.860i			0.998477i
$750$	1317.35	−	643.501i	1.75646	−	0.858001i
$751$	−1217.35			−1.62097			−0.810487	−	0.585756i	$-0.800798\pi$
$751$	−1217.35			−1.62097			−0.810487	+	0.585756i	$0.800798\pi$
$752$		−	1326.70i		−	1.76423i
$753$	14.4342	+	29.5491i	0.0191689	+	0.0392418i
$754$	−351.226			−0.465817
$755$			1124.87i			1.48990i
$756$	−267.469	+	1269.67i	−0.353795	+	1.67946i
$757$	−562.259			−0.742746			−0.371373	−	0.928484i	$-0.621113\pi$
$757$	−562.259			−0.742746			−0.371373	+	0.928484i	$0.621113\pi$
$758$		−	161.744i		−	0.213383i
$759$	1449.69	−	708.149i	1.91000	−	0.933002i
$760$	1051.24			1.38321
$761$		−	522.049i		−	0.686003i	−0.939335	−	0.343002i	$-0.888556\pi$
$761$		−	522.049i		−	0.686003i	0.939335	−	0.343002i	$-0.111444\pi$
$762$	−647.426	−	1325.38i	−0.849640	−	1.73935i
$763$	−228.578			−0.299578
$764$		−	2756.56i		−	3.60806i
$765$	−702.562	+	901.484i	−0.918382	+	1.17841i
$766$	1693.87			2.21132
$767$		−	136.515i		−	0.177986i
$768$	131.426	−	64.1990i	0.171127	−	0.0835924i
$769$	−131.569			−0.171091			−0.0855456	−	0.996334i	$-0.527263\pi$
$769$	−131.569			−0.171091			−0.0855456	+	0.996334i	$0.527263\pi$
$770$			1589.52i			2.06431i
$771$	507.013	+	1037.94i	0.657605	+	1.34622i
$772$	−1380.73			−1.78852
$773$			838.779i			1.08510i	0.840025	+	0.542548i	$0.182540\pi$
$773$			838.779i			1.08510i	−0.840025	+	0.542548i	$0.817460\pi$
$774$	1814.67	+	1414.24i	2.34453	+	1.82719i
$775$	−100.998			−0.130320
$776$			1985.88i			2.55913i
$777$	−317.590	+	155.137i	−0.408739	+	0.199661i
$778$	2257.07			2.90111
$779$			502.871i			0.645534i
$780$	260.272	+	532.818i	0.333682	+	0.683101i
$781$	900.845			1.15345
$782$		−	2886.53i		−	3.69121i
$783$	−597.637	−	125.899i	−0.763266	−	0.160790i
$784$	−1171.95			−1.49483
$785$			115.016i			0.146518i
$786$	−183.958	+	89.8600i	−0.234043	+	0.114326i
$787$	−145.154			−0.184440			−0.0922199	−	0.995739i	$-0.529396\pi$
$787$	−145.154			−0.184440			−0.0922199	+	0.995739i	$0.529396\pi$
$788$		−	244.142i		−	0.309824i
$789$	337.589	+	691.099i	0.427870	+	0.875918i
$790$	−1672.72			−2.11736
$791$		−	402.604i		−	0.508981i
$792$	−2344.60	+	3008.45i	−2.96036	+	3.79855i
$793$	300.542			0.378993
$794$			222.653i			0.280420i
$795$	−667.694	+	326.156i	−0.839867	+	0.410259i
$796$	2864.97			3.59921
$797$		−	339.615i		−	0.426117i	−0.977039	−	0.213058i	$-0.931658\pi$
$797$		−	339.615i		−	0.426117i	0.977039	−	0.213058i	$-0.0683424\pi$
$798$	−230.343	−	471.548i	−0.288650	−	0.590913i
$799$	−791.611			−0.990752
$800$		−	190.246i		−	0.237807i
$801$	−238.417	−	185.808i	−0.297650	−	0.231970i
$802$	447.130			0.557519
$803$		−	122.295i		−	0.152297i
$804$	−221.784	+	108.337i	−0.275850	+	0.134748i
$805$	−653.417			−0.811698
$806$		−	637.230i		−	0.790608i
$807$	430.989	+	882.303i	0.534063	+	1.09331i
$808$	−846.585			−1.04775
$809$			444.196i			0.549068i	0.961577	+	0.274534i	$0.0885235\pi$
$809$			444.196i			0.549068i	−0.961577	+	0.274534i	$0.911476\pi$
$810$	352.116	+	1397.84i	0.434711	+	1.72573i
$811$	−686.566			−0.846568			−0.423284	−	0.905997i	$-0.639123\pi$
$811$	−686.566			−0.846568			−0.423284	+	0.905997i	$0.639123\pi$
$812$			1087.07i			1.33876i
$813$	487.705	−	238.235i	0.599884	−	0.293032i
$814$	−1725.75			−2.12009
$815$			791.729i			0.971447i
$816$	1578.97	+	3232.39i	1.93501	+	3.96127i
$817$	−665.642			−0.814739
$818$		−	792.648i		−	0.969007i
$819$	109.559	−	140.579i	0.133771	−	0.171647i
$820$	−2458.51			−2.99818
$821$			794.313i			0.967495i	0.875208	+	0.483747i	$0.160725\pi$
$821$			794.313i			0.967495i	−0.875208	+	0.483747i	$0.839275\pi$
$822$	1553.42	−	758.818i	1.88981	−	0.923136i
$823$	876.112			1.06453			0.532267	−	0.846576i	$-0.321340\pi$
$823$	876.112			1.06453			0.532267	+	0.846576i	$0.321340\pi$
$824$		−	2464.23i		−	2.99057i
$825$	−60.5368	−	123.929i	−0.0733780	−	0.150216i
$826$	−590.668			−0.715094
$827$		−	329.558i		−	0.398499i	−0.979949	−	0.199249i	$-0.936150\pi$
$827$		−	329.558i		−	0.398499i	0.979949	−	0.199249i	$-0.0638504\pi$
$828$	−2054.14	−	1600.87i	−2.48084	−	1.93342i
$829$	−251.246			−0.303071			−0.151535	−	0.988452i	$-0.548422\pi$
$829$	−251.246			−0.303071			−0.151535	+	0.988452i	$0.548422\pi$
$830$			691.005i			0.832536i
$831$	690.343	−	337.220i	0.830738	−	0.405800i
$832$	457.569			0.549962
$833$			699.276i			0.839467i
$834$	225.278	+	461.180i	0.270117	+	0.552973i
$835$	545.641			0.653462
$836$		−	1832.94i		−	2.19251i
$837$	228.418	−	1084.30i	0.272901	−	1.29545i
$838$	−1121.93			−1.33882
$839$		−	891.350i		−	1.06240i	−0.847248	−	0.531198i	$-0.821742\pi$
$839$		−	891.350i		−	1.06240i	0.847248	−	0.531198i	$-0.178258\pi$
$840$	1387.97	−	677.996i	1.65234	−	0.807138i
$841$	329.311			0.391571
$842$		−	1189.54i		−	1.41275i
$843$	513.746	+	1051.72i	0.609426	+	1.24759i
$844$	−2927.42			−3.46851
$845$			720.880i			0.853113i
$846$	−613.736	+	787.508i	−0.725456	+	0.930861i
$847$	1090.10			1.28701
$848$			2338.96i			2.75820i
$849$	−1171.21	+	572.114i	−1.37952	+	0.673868i
$850$	−246.758			−0.290303
$851$		−	709.418i		−	0.833629i
$852$	−638.224	−	1306.55i	−0.749090	−	1.53351i
$853$	−888.636			−1.04178			−0.520888	−	0.853625i	$-0.674399\pi$
$853$	−888.636			−1.04178			−0.520888	+	0.853625i	$0.674399\pi$
$854$		−	1300.37i		−	1.52268i
$855$	−328.961	−	256.372i	−0.384750	−	0.299851i
$856$	3548.49			4.14544
$857$			380.108i			0.443533i	0.975100	+	0.221767i	$0.0711824\pi$
$857$			380.108i			0.443533i	−0.975100	+	0.221767i	$0.928818\pi$
$858$	781.905	−	381.946i	0.911311	−	0.445159i
$859$	1068.81			1.24425			0.622124	−	0.782919i	$-0.286270\pi$
$859$	1068.81			1.24425			0.622124	+	0.782919i	$0.286270\pi$
$860$		−	3254.28i		−	3.78405i
$861$	324.327	+	663.949i	0.376686	+	0.771137i
$862$	62.3987			0.0723883
$863$		−	339.531i		−	0.393432i	−0.980461	−	0.196716i	$-0.936972\pi$
$863$		−	339.531i		−	0.393432i	0.980461	−	0.196716i	$-0.0630276\pi$
$864$	2042.44	+	430.261i	2.36394	+	0.497988i
$865$	−86.4023			−0.0998870
$866$		−	681.523i		−	0.786977i
$867$	1149.67	−	561.595i	1.32604	−	0.647745i
$868$	−1972.28			−2.27221
$869$			1755.93i			2.02064i
$870$	530.074	+	1085.15i	0.609280	+	1.24729i
$871$	33.9044			0.0389259
$872$			1084.57i			1.24377i
$873$	484.310	−	621.437i	0.554766	−	0.711841i
$874$	1053.32			1.20518
$875$			623.304i			0.712348i
$876$	−177.371	+	86.6426i	−0.202479	+	0.0989070i
$877$	437.044			0.498340			0.249170	−	0.968460i	$-0.419842\pi$
$877$	437.044			0.498340			0.249170	+	0.968460i	$0.419842\pi$
$878$			854.891i			0.973679i
$879$	−469.957	−	962.077i	−0.534650	−	1.09451i
$880$	3976.04			4.51823
$881$			526.587i			0.597715i	0.954298	+	0.298858i	$0.0966056\pi$
$881$			526.587i			0.597715i	−0.954298	+	0.298858i	$0.903394\pi$
$882$	695.652	+	542.148i	0.788721	+	0.614681i
$883$	−646.034			−0.731635			−0.365818	−	0.930687i	$-0.619211\pi$
$883$	−646.034			−0.731635			−0.365818	+	0.930687i	$0.619211\pi$
$884$		−	1113.69i		−	1.25983i
$885$	−421.777	+	206.031i	−0.476585	+	0.232803i
$886$	−3044.05			−3.43572
$887$		−	28.0552i		−	0.0316293i	−0.999875	−	0.0158146i	$-0.994966\pi$
$887$		−	28.0552i		−	0.0316293i	0.999875	−	0.0158146i	$-0.00503417\pi$
$888$	736.103	+	1506.92i	0.828945	+	1.69698i
$889$	627.106			0.705406
$890$			597.703i			0.671576i
$891$	1467.38	−	369.633i	1.64689	−	0.414852i
$892$	−1865.01			−2.09082
$893$		−	288.867i		−	0.323480i
$894$	−2751.78	+	1344.20i	−3.07806	+	1.50357i
$895$	732.338			0.818255
$896$		−	501.388i		−	0.559585i
$897$	157.010	+	321.424i	0.175039	+	0.358332i
$898$	−650.258			−0.724118
$899$		−	928.358i		−	1.03266i
$900$	−136.852	+	175.600i	−0.152058	+	0.195111i
$901$	1395.60			1.54895
$902$			3607.83i			3.99981i
$903$	−878.858	+	429.306i	−0.973265	+	0.475422i
$904$	−1910.30			−2.11316
$905$		−	1196.24i		−	1.32181i
$906$	−1169.50	−	2394.16i	−1.29084	−	2.64256i
$907$	513.015			0.565617			0.282809	−	0.959176i	$-0.408734\pi$
$907$	513.015			0.565617			0.282809	+	0.959176i	$0.408734\pi$
$908$			1370.54i			1.50941i
$909$	264.920	+	206.462i	0.291441	+	0.227131i
$910$	−352.426			−0.387282
$911$		−	355.004i		−	0.389686i	−0.980834	−	0.194843i	$-0.937580\pi$
$911$		−	355.004i		−	0.389686i	0.980834	−	0.194843i	$-0.0624198\pi$
$912$	−1179.54	+	576.181i	−1.29335	+	0.631778i
$913$	725.381			0.794503
$914$			964.963i			1.05576i
$915$	−453.581	−	928.553i	−0.495717	−	1.01481i
$916$	2235.52			2.44052
$917$		−	87.0397i		−	0.0949179i
$918$	558.069	−	2649.14i	0.607918	−	2.88577i
$919$	162.274			0.176576			0.0882882	−	0.996095i	$-0.471860\pi$
$919$	162.274			0.176576			0.0882882	+	0.996095i	$0.471860\pi$
$920$			3100.37i			3.36997i
$921$	−25.8276	+	12.6163i	−0.0280430	+	0.0136985i
$922$	−1998.13			−2.16716
$923$			199.734i			0.216397i
$924$	−1182.16	−	2420.06i	−1.27939	−	2.61911i
$925$	−60.6454			−0.0655626
$926$		−	1193.52i		−	1.28890i
$927$	−600.968	+	771.125i	−0.648293	+	0.831850i
$928$	1748.71			1.88438
$929$		−	173.262i		−	0.186504i	−0.995643	−	0.0932519i	$-0.970274\pi$
$929$		−	173.262i		−	0.186504i	0.995643	−	0.0932519i	$-0.0297262\pi$
$930$	−1968.78	+	961.715i	−2.11697	+	1.03410i
$931$	−255.173			−0.274085
$932$		−	38.3631i		−	0.0411621i
$933$	−223.198	−	456.922i	−0.239226	−	0.489734i
$934$	−528.076			−0.565392
$935$		−	2372.42i		−	2.53734i
$936$	−667.029	−	519.842i	−0.712638	−	0.555386i
$937$	941.002			1.00427			0.502135	−	0.864789i	$-0.332548\pi$
$937$	941.002			1.00427			0.502135	+	0.864789i	$0.332548\pi$
$938$		−	146.696i		−	0.156392i
$939$	−1622.47	+	792.547i	−1.72787	+	0.844033i
$940$	1412.26			1.50240
$941$			888.247i			0.943940i	0.881615	+	0.471970i	$0.156457\pi$
$941$			888.247i			0.943940i	−0.881615	+	0.471970i	$0.843543\pi$
$942$	−119.580	−	244.799i	−0.126942	−	0.259871i
$943$	−1483.10			−1.57275
$944$			1477.50i			1.56515i
$945$	−599.680	−	126.329i	−0.634582	−	0.133681i
$946$	−4775.63			−5.04823
$947$			289.593i			0.305800i	0.988242	+	0.152900i	$0.0488613\pi$
$947$			289.593i			0.305800i	−0.988242	+	0.152900i	$0.951139\pi$
$948$	2546.73	−	1244.03i	2.68642	−	1.31227i
$949$	27.1150			0.0285722
$950$		−	90.0445i		−	0.0947837i
$951$	−69.0516	−	141.360i	−0.0726095	−	0.148643i
$952$	−2901.10			−3.04738
$953$			1203.73i			1.26310i	0.775336	+	0.631549i	$0.217580\pi$
$953$			1203.73i			1.26310i	−0.775336	+	0.631549i	$0.782420\pi$
$954$	1082.01	−	1388.37i	1.13418	−	1.45531i
$955$	1301.96			1.36331
$956$			808.202i			0.845399i
$957$	1139.13	−	556.444i	1.19031	−	0.581446i
$958$	1122.96			1.17219
$959$			735.002i			0.766426i
$960$	−690.568	−	1413.70i	−0.719342	−	1.47261i
$961$	723.324			0.752678
$962$		−	382.631i		−	0.397745i
$963$	−1110.42	−	865.395i	−1.15309	−	0.898645i
$964$	3493.69			3.62416
$965$		−	652.137i		−	0.675790i
$966$	1390.72	−	679.341i	1.43967	−	0.703252i
$967$	−1236.75			−1.27896			−0.639479	−	0.768809i	$-0.720850\pi$
$967$	−1236.75			−1.27896			−0.639479	+	0.768809i	$0.720850\pi$
$968$		−	5172.37i		−	5.34336i
$969$	343.795	+	703.803i	0.354793	+	0.726319i
$970$	−1557.92			−1.60610
$971$		−	989.704i		−	1.01926i	−0.860393	−	0.509631i	$-0.829782\pi$
$971$		−	989.704i		−	1.01926i	0.860393	−	0.509631i	$-0.170218\pi$
$972$	−1575.70	−	1866.35i	−1.62109	−	1.92012i
$973$	−218.207			−0.224263
$974$			1514.22i			1.55465i
$975$	27.4773	−	13.4221i	0.0281818	−	0.0137663i
$976$	−3252.75			−3.33274
$977$		−	1576.87i		−	1.61399i	−0.590560	−	0.806994i	$-0.701093\pi$
$977$		−	1576.87i		−	1.61399i	0.590560	−	0.806994i	$-0.298907\pi$
$978$	−823.142	−	1685.10i	−0.841658	−	1.72301i
$979$	627.438			0.640897
$980$		−	1247.53i		−	1.27299i
$981$	264.502	−	339.392i	0.269625	−	0.345966i
$982$	1102.72			1.12294
$983$			1243.92i			1.26543i	0.774384	+	0.632716i	$0.218060\pi$
$983$			1243.92i			1.26543i	−0.774384	+	0.632716i	$0.781940\pi$
$984$	3150.35	−	1538.89i	3.20157	−	1.56391i
$985$	115.311			0.117067
$986$		−	2268.15i		−	2.30036i
$987$	−186.305	−	381.396i	−0.188759	−	0.386420i
$988$	406.397			0.411333
$989$		−	1963.15i		−	1.98499i
$990$	−2360.12	−	1839.33i	−2.38396	−	1.85791i
$991$	−108.963			−0.109952			−0.0549762	−	0.998488i	$-0.517508\pi$
$991$	−108.963			−0.109952			−0.0549762	+	0.998488i	$0.517508\pi$
$992$			3172.69i			3.19827i
$993$	669.769	−	327.170i	0.674490	−	0.329476i
$994$	864.199			0.869416
$995$			1353.16i			1.35996i
$996$	−513.913	−	1052.06i	−0.515977	−	1.05629i
$997$	−227.748			−0.228433			−0.114217	−	0.993456i	$-0.536436\pi$
$997$	−227.748			−0.228433			−0.114217	+	0.993456i	$0.536436\pi$
$998$			2468.14i			2.47308i
$999$	137.156	−	651.076i	0.137293	−	0.651728i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.c.a.68.3	✓	44
3.2	odd	2	inner	201.3.c.a.68.42	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.c.a.68.3	✓	44	1.1	even	1	trivial
201.3.c.a.68.42	yes	44	3.2	odd	2	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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.74856i q^{2} +(-2.69559 + 1.31674i) q^{3} -10.0517 q^{4} -4.74753i q^{5} +(4.93589 + 10.1046i) q^{6} -4.78098 q^{7} +22.6851i q^{8} +(5.53237 - 7.09880i) q^{9} +O(q^{10})\)	\(q-3.74856i q^{2} +(-2.69559 + 1.31674i) q^{3} -10.0517 q^{4} -4.74753i q^{5} +(4.93589 + 10.1046i) q^{6} -4.78098 q^{7} +22.6851i q^{8} +(5.53237 - 7.09880i) q^{9} -17.7964 q^{10} +18.6817i q^{11} +(27.0952 - 13.2355i) q^{12} -4.14209 q^{13} +17.9218i q^{14} +(6.25129 + 12.7974i) q^{15} +44.8297 q^{16} -26.7489i q^{17} +(-26.6102 - 20.7384i) q^{18} +9.76095 q^{19} +47.7207i q^{20} +(12.8875 - 6.29533i) q^{21} +70.0296 q^{22} +28.7876i q^{23} +(-29.8705 - 61.1496i) q^{24} +2.46094 q^{25} +15.5269i q^{26} +(-5.56568 + 26.4201i) q^{27} +48.0569 q^{28} +22.6205i q^{29} +(47.9717 - 23.4333i) q^{30} -41.0405 q^{31} -77.3062i q^{32} +(-24.5991 - 50.3582i) q^{33} -100.270 q^{34} +22.6979i q^{35} +(-55.6096 + 71.3549i) q^{36} -24.6432 q^{37} -36.5895i q^{38} +(11.1654 - 5.45407i) q^{39} +107.698 q^{40} +51.5187i q^{41} +(-23.5984 - 48.3097i) q^{42} -68.1944 q^{43} -187.783i q^{44} +(-33.7018 - 26.2651i) q^{45} +107.912 q^{46} -29.5942i q^{47} +(-120.842 + 59.0292i) q^{48} -26.1422 q^{49} -9.22497i q^{50} +(35.2214 + 72.1039i) q^{51} +41.6350 q^{52} +52.1743i q^{53} +(99.0374 + 20.8633i) q^{54} +88.6922 q^{55} -108.457i q^{56} +(-26.3115 + 12.8527i) q^{57} +84.7944 q^{58} +32.9581i q^{59} +(-62.8360 - 128.635i) q^{60} -72.5580 q^{61} +153.843i q^{62} +(-26.4501 + 33.9392i) q^{63} -110.468 q^{64} +19.6647i q^{65} +(-188.771 + 92.2111i) q^{66} -8.18535 q^{67} +268.871i q^{68} +(-37.9059 - 77.5995i) q^{69} +85.0842 q^{70} -48.2206i q^{71} +(161.037 + 125.502i) q^{72} -6.54622 q^{73} +92.3764i q^{74} +(-6.63367 + 3.24043i) q^{75} -98.1140 q^{76} -89.3170i q^{77} +(-20.4449 - 41.8540i) q^{78} +93.9919 q^{79} -212.830i q^{80} +(-19.7858 - 78.5463i) q^{81} +193.121 q^{82} -38.8283i q^{83} +(-129.542 + 63.2787i) q^{84} -126.991 q^{85} +255.631i q^{86} +(-29.7855 - 60.9756i) q^{87} -423.797 q^{88} -33.5856i q^{89} +(-98.4562 + 126.333i) q^{90} +19.8032 q^{91} -289.364i q^{92} +(110.628 - 54.0399i) q^{93} -110.935 q^{94} -46.3404i q^{95} +(101.793 + 208.386i) q^{96} +87.5412 q^{97} +97.9957i q^{98} +(132.618 + 103.354i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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