Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.a (trivial) |
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: | yes |
Analytic conductor: | \(47.9182262530\) |
Analytic rank: | \(0\) |
Dimension: | \(121\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.15090 | −1.52091 | −0.760457 | − | 0.649388i | \(-0.775025\pi\) | ||||
−0.760457 | + | 0.649388i | \(0.775025\pi\) | |||||||
\(3\) | 0.00192410 | 0.00111088 | 0.000555439 | − | 1.00000i | \(-0.499823\pi\) | ||||
0.000555439 | 1.00000i | \(0.499823\pi\) | ||||||||
\(4\) | 2.62636 | 1.31318 | ||||||||
\(5\) | −2.18392 | −0.976677 | −0.488338 | − | 0.872654i | \(-0.662397\pi\) | ||||
−0.488338 | + | 0.872654i | \(0.662397\pi\) | |||||||
\(6\) | −0.00413853 | −0.00168955 | ||||||||
\(7\) | −0.0660171 | −0.0249521 | −0.0124761 | − | 0.999922i | \(-0.503971\pi\) | ||||
−0.0124761 | + | 0.999922i | \(0.503971\pi\) | |||||||
\(8\) | −1.34723 | −0.476318 | ||||||||
\(9\) | −3.00000 | −0.999999 | ||||||||
\(10\) | 4.69738 | 1.48544 | ||||||||
\(11\) | −1.22409 | −0.369078 | −0.184539 | − | 0.982825i | \(-0.559079\pi\) | ||||
−0.184539 | + | 0.982825i | \(0.559079\pi\) | |||||||
\(12\) | 0.00505337 | 0.00145878 | ||||||||
\(13\) | 4.00583 | 1.11102 | 0.555509 | − | 0.831511i | \(-0.312524\pi\) | ||||
0.555509 | + | 0.831511i | \(0.312524\pi\) | |||||||
\(14\) | 0.141996 | 0.0379500 | ||||||||
\(15\) | −0.00420207 | −0.00108497 | ||||||||
\(16\) | −2.35496 | −0.588740 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 6.45268 | 1.52091 | ||||||||
\(19\) | 3.51056 | 0.805378 | 0.402689 | − | 0.915337i | \(-0.368076\pi\) | ||||
0.402689 | + | 0.915337i | \(0.368076\pi\) | |||||||
\(20\) | −5.73574 | −1.28255 | ||||||||
\(21\) | −0.000127023 0 | −2.77187e−5 0 | ||||||||
\(22\) | 2.63290 | 0.561336 | ||||||||
\(23\) | 6.94081 | 1.44726 | 0.723629 | − | 0.690189i | \(-0.242472\pi\) | ||||
0.723629 | + | 0.690189i | \(0.242472\pi\) | |||||||
\(24\) | −0.00259220 | −0.000529131 0 | ||||||||
\(25\) | −0.230514 | −0.0461028 | ||||||||
\(26\) | −8.61613 | −1.68976 | ||||||||
\(27\) | −0.0115446 | −0.00222175 | ||||||||
\(28\) | −0.173384 | −0.0327666 | ||||||||
\(29\) | 2.17980 | 0.404778 | 0.202389 | − | 0.979305i | \(-0.435129\pi\) | ||||
0.202389 | + | 0.979305i | \(0.435129\pi\) | |||||||
\(30\) | 0.00903821 | 0.00165014 | ||||||||
\(31\) | −4.00292 | −0.718946 | −0.359473 | − | 0.933156i | \(-0.617043\pi\) | ||||
−0.359473 | + | 0.933156i | \(0.617043\pi\) | |||||||
\(32\) | 7.75974 | 1.37174 | ||||||||
\(33\) | −0.00235528 | −0.000410001 0 | ||||||||
\(34\) | −2.15090 | −0.368876 | ||||||||
\(35\) | 0.144176 | 0.0243701 | ||||||||
\(36\) | −7.87906 | −1.31318 | ||||||||
\(37\) | 1.73156 | 0.284667 | 0.142333 | − | 0.989819i | \(-0.454539\pi\) | ||||
0.142333 | + | 0.989819i | \(0.454539\pi\) | |||||||
\(38\) | −7.55085 | −1.22491 | ||||||||
\(39\) | 0.00770761 | 0.00123420 | ||||||||
\(40\) | 2.94224 | 0.465208 | ||||||||
\(41\) | −0.957973 | −0.149610 | −0.0748051 | − | 0.997198i | \(-0.523833\pi\) | ||||
−0.0748051 | + | 0.997198i | \(0.523833\pi\) | |||||||
\(42\) | 0.000273214 0 | 4.21578e−5 0 | ||||||||
\(43\) | 0.963143 | 0.146878 | 0.0734390 | − | 0.997300i | \(-0.476603\pi\) | ||||
0.0734390 | + | 0.997300i | \(0.476603\pi\) | |||||||
\(44\) | −3.21491 | −0.484666 | ||||||||
\(45\) | 6.55174 | 0.976675 | ||||||||
\(46\) | −14.9290 | −2.20116 | ||||||||
\(47\) | 7.86225 | 1.14683 | 0.573413 | − | 0.819266i | \(-0.305619\pi\) | ||||
0.573413 | + | 0.819266i | \(0.305619\pi\) | |||||||
\(48\) | −0.00453118 | −0.000654019 0 | ||||||||
\(49\) | −6.99564 | −0.999377 | ||||||||
\(50\) | 0.495812 | 0.0701184 | ||||||||
\(51\) | 0.00192410 | 0.000269428 0 | ||||||||
\(52\) | 10.5207 | 1.45896 | ||||||||
\(53\) | 11.0535 | 1.51831 | 0.759155 | − | 0.650910i | \(-0.225613\pi\) | ||||
0.759155 | + | 0.650910i | \(0.225613\pi\) | |||||||
\(54\) | 0.0248312 | 0.00337910 | ||||||||
\(55\) | 2.67332 | 0.360470 | ||||||||
\(56\) | 0.0889402 | 0.0118851 | ||||||||
\(57\) | 0.00675466 | 0.000894677 0 | ||||||||
\(58\) | −4.68852 | −0.615633 | ||||||||
\(59\) | −8.58175 | −1.11725 | −0.558625 | − | 0.829421i | \(-0.688671\pi\) | ||||
−0.558625 | + | 0.829421i | \(0.688671\pi\) | |||||||
\(60\) | −0.0110361 | −0.00142476 | ||||||||
\(61\) | −5.45989 | −0.699067 | −0.349533 | − | 0.936924i | \(-0.613660\pi\) | ||||
−0.349533 | + | 0.936924i | \(0.613660\pi\) | |||||||
\(62\) | 8.60987 | 1.09345 | ||||||||
\(63\) | 0.198051 | 0.0249521 | ||||||||
\(64\) | −11.9805 | −1.49756 | ||||||||
\(65\) | −8.74839 | −1.08510 | ||||||||
\(66\) | 0.00506596 | 0.000623576 0 | ||||||||
\(67\) | 2.72843 | 0.333331 | 0.166666 | − | 0.986013i | \(-0.446700\pi\) | ||||
0.166666 | + | 0.986013i | \(0.446700\pi\) | |||||||
\(68\) | 2.62636 | 0.318493 | ||||||||
\(69\) | 0.0133548 | 0.00160773 | ||||||||
\(70\) | −0.310107 | −0.0370649 | ||||||||
\(71\) | −3.68059 | −0.436805 | −0.218403 | − | 0.975859i | \(-0.570085\pi\) | ||||
−0.218403 | + | 0.975859i | \(0.570085\pi\) | |||||||
\(72\) | 4.04169 | 0.476317 | ||||||||
\(73\) | −6.56518 | −0.768397 | −0.384198 | − | 0.923251i | \(-0.625522\pi\) | ||||
−0.384198 | + | 0.923251i | \(0.625522\pi\) | |||||||
\(74\) | −3.72441 | −0.432954 | ||||||||
\(75\) | −0.000443531 0 | −5.12146e−5 0 | ||||||||
\(76\) | 9.21999 | 1.05761 | ||||||||
\(77\) | 0.0808111 | 0.00920928 | ||||||||
\(78\) | −0.0165783 | −0.00187712 | ||||||||
\(79\) | −15.3460 | −1.72656 | −0.863280 | − | 0.504726i | \(-0.831594\pi\) | ||||
−0.863280 | + | 0.504726i | \(0.831594\pi\) | |||||||
\(80\) | 5.14304 | 0.575009 | ||||||||
\(81\) | 8.99997 | 0.999996 | ||||||||
\(82\) | 2.06050 | 0.227544 | ||||||||
\(83\) | −1.95438 | −0.214522 | −0.107261 | − | 0.994231i | \(-0.534208\pi\) | ||||
−0.107261 | + | 0.994231i | \(0.534208\pi\) | |||||||
\(84\) | −0.000333608 0 | −3.63997e−5 0 | ||||||||
\(85\) | −2.18392 | −0.236879 | ||||||||
\(86\) | −2.07162 | −0.223389 | ||||||||
\(87\) | 0.00419414 | 0.000449659 0 | ||||||||
\(88\) | 1.64914 | 0.175799 | ||||||||
\(89\) | 2.65682 | 0.281623 | 0.140811 | − | 0.990036i | \(-0.455029\pi\) | ||||
0.140811 | + | 0.990036i | \(0.455029\pi\) | |||||||
\(90\) | −14.0921 | −1.48544 | ||||||||
\(91\) | −0.264453 | −0.0277222 | ||||||||
\(92\) | 18.2290 | 1.90051 | ||||||||
\(93\) | −0.00770201 | −0.000798661 0 | ||||||||
\(94\) | −16.9109 | −1.74422 | ||||||||
\(95\) | −7.66677 | −0.786594 | ||||||||
\(96\) | 0.0149305 | 0.00152384 | ||||||||
\(97\) | −14.0058 | −1.42207 | −0.711036 | − | 0.703155i | \(-0.751774\pi\) | ||||
−0.711036 | + | 0.703155i | \(0.751774\pi\) | |||||||
\(98\) | 15.0469 | 1.51997 | ||||||||
\(99\) | 3.67228 | 0.369078 | ||||||||
\(100\) | −0.605412 | −0.0605412 | ||||||||
\(101\) | −1.04744 | −0.104224 | −0.0521120 | − | 0.998641i | \(-0.516595\pi\) | ||||
−0.0521120 | + | 0.998641i | \(0.516595\pi\) | |||||||
\(102\) | −0.00413853 | −0.000409776 0 | ||||||||
\(103\) | −1.96651 | −0.193766 | −0.0968828 | − | 0.995296i | \(-0.530887\pi\) | ||||
−0.0968828 | + | 0.995296i | \(0.530887\pi\) | |||||||
\(104\) | −5.39678 | −0.529197 | ||||||||
\(105\) | 0.000277408 0 | 2.70723e−5 0 | ||||||||
\(106\) | −23.7748 | −2.30922 | ||||||||
\(107\) | 13.8145 | 1.33550 | 0.667751 | − | 0.744385i | \(-0.267257\pi\) | ||||
0.667751 | + | 0.744385i | \(0.267257\pi\) | |||||||
\(108\) | −0.0303202 | −0.00291756 | ||||||||
\(109\) | 8.54786 | 0.818737 | 0.409368 | − | 0.912369i | \(-0.365749\pi\) | ||||
0.409368 | + | 0.912369i | \(0.365749\pi\) | |||||||
\(110\) | −5.75003 | −0.548244 | ||||||||
\(111\) | 0.00333169 | 0.000316230 0 | ||||||||
\(112\) | 0.155468 | 0.0146903 | ||||||||
\(113\) | −2.66162 | −0.250384 | −0.125192 | − | 0.992133i | \(-0.539955\pi\) | ||||
−0.125192 | + | 0.992133i | \(0.539955\pi\) | |||||||
\(114\) | −0.0145286 | −0.00136073 | ||||||||
\(115\) | −15.1581 | −1.41350 | ||||||||
\(116\) | 5.72493 | 0.531546 | ||||||||
\(117\) | −12.0175 | −1.11102 | ||||||||
\(118\) | 18.4585 | 1.69924 | ||||||||
\(119\) | −0.0660171 | −0.00605178 | ||||||||
\(120\) | 0.00566115 | 0.000516790 0 | ||||||||
\(121\) | −9.50159 | −0.863781 | ||||||||
\(122\) | 11.7437 | 1.06322 | ||||||||
\(123\) | −0.00184323 | −0.000166199 0 | ||||||||
\(124\) | −10.5131 | −0.944104 | ||||||||
\(125\) | 11.4230 | 1.02170 | ||||||||
\(126\) | −0.425987 | −0.0379500 | ||||||||
\(127\) | −10.2995 | −0.913934 | −0.456967 | − | 0.889484i | \(-0.651064\pi\) | ||||
−0.456967 | + | 0.889484i | \(0.651064\pi\) | |||||||
\(128\) | 10.2493 | 0.905918 | ||||||||
\(129\) | 0.00185318 | 0.000163163 0 | ||||||||
\(130\) | 18.8169 | 1.65035 | ||||||||
\(131\) | 2.97846 | 0.260229 | 0.130115 | − | 0.991499i | \(-0.458465\pi\) | ||||
0.130115 | + | 0.991499i | \(0.458465\pi\) | |||||||
\(132\) | −0.00618580 | −0.000538405 0 | ||||||||
\(133\) | −0.231757 | −0.0200959 | ||||||||
\(134\) | −5.86858 | −0.506968 | ||||||||
\(135\) | 0.0252124 | 0.00216994 | ||||||||
\(136\) | −1.34723 | −0.115524 | ||||||||
\(137\) | 18.0870 | 1.54528 | 0.772639 | − | 0.634846i | \(-0.218936\pi\) | ||||
0.772639 | + | 0.634846i | \(0.218936\pi\) | |||||||
\(138\) | −0.0287248 | −0.00244522 | ||||||||
\(139\) | 22.5177 | 1.90993 | 0.954964 | − | 0.296722i | \(-0.0958936\pi\) | ||||
0.954964 | + | 0.296722i | \(0.0958936\pi\) | |||||||
\(140\) | 0.378657 | 0.0320023 | ||||||||
\(141\) | 0.0151277 | 0.00127398 | ||||||||
\(142\) | 7.91656 | 0.664343 | ||||||||
\(143\) | −4.90352 | −0.410053 | ||||||||
\(144\) | 7.06488 | 0.588740 | ||||||||
\(145\) | −4.76050 | −0.395338 | ||||||||
\(146\) | 14.1210 | 1.16867 | ||||||||
\(147\) | −0.0134603 | −0.00111019 | ||||||||
\(148\) | 4.54770 | 0.373819 | ||||||||
\(149\) | −11.5854 | −0.949110 | −0.474555 | − | 0.880226i | \(-0.657391\pi\) | ||||
−0.474555 | + | 0.880226i | \(0.657391\pi\) | |||||||
\(150\) | 0.000953990 0 | 7.78929e−5 0 | ||||||||
\(151\) | −12.4322 | −1.01172 | −0.505859 | − | 0.862616i | \(-0.668824\pi\) | ||||
−0.505859 | + | 0.862616i | \(0.668824\pi\) | |||||||
\(152\) | −4.72953 | −0.383616 | ||||||||
\(153\) | −3.00000 | −0.242535 | ||||||||
\(154\) | −0.173816 | −0.0140065 | ||||||||
\(155\) | 8.74204 | 0.702177 | ||||||||
\(156\) | 0.0202429 | 0.00162073 | ||||||||
\(157\) | 2.80771 | 0.224080 | 0.112040 | − | 0.993704i | \(-0.464262\pi\) | ||||
0.112040 | + | 0.993704i | \(0.464262\pi\) | |||||||
\(158\) | 33.0077 | 2.62595 | ||||||||
\(159\) | 0.0212679 | 0.00168666 | ||||||||
\(160\) | −16.9466 | −1.33975 | ||||||||
\(161\) | −0.458212 | −0.0361122 | ||||||||
\(162\) | −19.3580 | −1.52091 | ||||||||
\(163\) | −11.3378 | −0.888041 | −0.444021 | − | 0.896017i | \(-0.646448\pi\) | ||||
−0.444021 | + | 0.896017i | \(0.646448\pi\) | |||||||
\(164\) | −2.51598 | −0.196465 | ||||||||
\(165\) | 0.00514373 | 0.000400438 0 | ||||||||
\(166\) | 4.20368 | 0.326269 | ||||||||
\(167\) | 3.19854 | 0.247511 | 0.123755 | − | 0.992313i | \(-0.460506\pi\) | ||||
0.123755 | + | 0.992313i | \(0.460506\pi\) | |||||||
\(168\) | 0.000171130 0 | 1.32029e−5 0 | ||||||||
\(169\) | 3.04668 | 0.234360 | ||||||||
\(170\) | 4.69738 | 0.360272 | ||||||||
\(171\) | −10.5317 | −0.805377 | ||||||||
\(172\) | 2.52956 | 0.192877 | ||||||||
\(173\) | −4.75516 | −0.361528 | −0.180764 | − | 0.983526i | \(-0.557857\pi\) | ||||
−0.180764 | + | 0.983526i | \(0.557857\pi\) | |||||||
\(174\) | −0.00902117 | −0.000683893 0 | ||||||||
\(175\) | 0.0152179 | 0.00115036 | ||||||||
\(176\) | 2.88270 | 0.217291 | ||||||||
\(177\) | −0.0165121 | −0.00124113 | ||||||||
\(178\) | −5.71455 | −0.428324 | ||||||||
\(179\) | −14.0034 | −1.04667 | −0.523333 | − | 0.852128i | \(-0.675312\pi\) | ||||
−0.523333 | + | 0.852128i | \(0.675312\pi\) | |||||||
\(180\) | 17.2072 | 1.28255 | ||||||||
\(181\) | 1.84346 | 0.137023 | 0.0685115 | − | 0.997650i | \(-0.478175\pi\) | ||||
0.0685115 | + | 0.997650i | \(0.478175\pi\) | |||||||
\(182\) | 0.568812 | 0.0421631 | ||||||||
\(183\) | −0.0105054 | −0.000776578 0 | ||||||||
\(184\) | −9.35087 | −0.689355 | ||||||||
\(185\) | −3.78158 | −0.278028 | ||||||||
\(186\) | 0.0165662 | 0.00121469 | ||||||||
\(187\) | −1.22409 | −0.0895147 | ||||||||
\(188\) | 20.6491 | 1.50599 | ||||||||
\(189\) | 0.000762139 0 | 5.54375e−5 0 | ||||||||
\(190\) | 16.4904 | 1.19634 | ||||||||
\(191\) | −1.02605 | −0.0742421 | −0.0371211 | − | 0.999311i | \(-0.511819\pi\) | ||||
−0.0371211 | + | 0.999311i | \(0.511819\pi\) | |||||||
\(192\) | −0.0230516 | −0.00166361 | ||||||||
\(193\) | 18.0690 | 1.30064 | 0.650319 | − | 0.759662i | \(-0.274635\pi\) | ||||
0.650319 | + | 0.759662i | \(0.274635\pi\) | |||||||
\(194\) | 30.1250 | 2.16285 | ||||||||
\(195\) | −0.0168328 | −0.00120542 | ||||||||
\(196\) | −18.3731 | −1.31236 | ||||||||
\(197\) | 22.7681 | 1.62216 | 0.811080 | − | 0.584935i | \(-0.198880\pi\) | ||||
0.811080 | + | 0.584935i | \(0.198880\pi\) | |||||||
\(198\) | −7.89869 | −0.561336 | ||||||||
\(199\) | −0.940724 | −0.0666862 | −0.0333431 | − | 0.999444i | \(-0.510615\pi\) | ||||
−0.0333431 | + | 0.999444i | \(0.510615\pi\) | |||||||
\(200\) | 0.310555 | 0.0219596 | ||||||||
\(201\) | 0.00524977 | 0.000370290 0 | ||||||||
\(202\) | 2.25293 | 0.158516 | ||||||||
\(203\) | −0.143904 | −0.0101001 | ||||||||
\(204\) | 0.00505337 | 0.000353806 0 | ||||||||
\(205\) | 2.09213 | 0.146121 | ||||||||
\(206\) | 4.22975 | 0.294701 | ||||||||
\(207\) | −20.8224 | −1.44726 | ||||||||
\(208\) | −9.43358 | −0.654101 | ||||||||
\(209\) | −4.29726 | −0.297248 | ||||||||
\(210\) | −0.000596676 0 | −4.11746e−5 0 | ||||||||
\(211\) | 27.0996 | 1.86561 | 0.932805 | − | 0.360381i | \(-0.117353\pi\) | ||||
0.932805 | + | 0.360381i | \(0.117353\pi\) | |||||||
\(212\) | 29.0303 | 1.99381 | ||||||||
\(213\) | −0.00708181 | −0.000485237 0 | ||||||||
\(214\) | −29.7136 | −2.03118 | ||||||||
\(215\) | −2.10342 | −0.143452 | ||||||||
\(216\) | 0.0155532 | 0.00105826 | ||||||||
\(217\) | 0.264261 | 0.0179392 | ||||||||
\(218\) | −18.3856 | −1.24523 | ||||||||
\(219\) | −0.0126321 | −0.000853595 0 | ||||||||
\(220\) | 7.02109 | 0.473362 | ||||||||
\(221\) | 4.00583 | 0.269461 | ||||||||
\(222\) | −0.00716613 | −0.000480959 0 | ||||||||
\(223\) | −3.89565 | −0.260872 | −0.130436 | − | 0.991457i | \(-0.541638\pi\) | ||||
−0.130436 | + | 0.991457i | \(0.541638\pi\) | |||||||
\(224\) | −0.512275 | −0.0342278 | ||||||||
\(225\) | 0.691541 | 0.0461027 | ||||||||
\(226\) | 5.72488 | 0.380813 | ||||||||
\(227\) | 19.7182 | 1.30874 | 0.654370 | − | 0.756174i | \(-0.272934\pi\) | ||||
0.654370 | + | 0.756174i | \(0.272934\pi\) | |||||||
\(228\) | 0.0177402 | 0.00117487 | ||||||||
\(229\) | −16.5887 | −1.09621 | −0.548106 | − | 0.836409i | \(-0.684651\pi\) | ||||
−0.548106 | + | 0.836409i | \(0.684651\pi\) | |||||||
\(230\) | 32.6036 | 2.14982 | ||||||||
\(231\) | 0.000155488 0 | 1.02304e−5 0 | ||||||||
\(232\) | −2.93669 | −0.192803 | ||||||||
\(233\) | −21.3086 | −1.39597 | −0.697986 | − | 0.716111i | \(-0.745920\pi\) | ||||
−0.697986 | + | 0.716111i | \(0.745920\pi\) | |||||||
\(234\) | 25.8484 | 1.68976 | ||||||||
\(235\) | −17.1705 | −1.12008 | ||||||||
\(236\) | −22.5388 | −1.46715 | ||||||||
\(237\) | −0.0295272 | −0.00191800 | ||||||||
\(238\) | 0.141996 | 0.00920423 | ||||||||
\(239\) | −25.1268 | −1.62532 | −0.812660 | − | 0.582738i | \(-0.801981\pi\) | ||||
−0.812660 | + | 0.582738i | \(0.801981\pi\) | |||||||
\(240\) | 0.00989570 | 0.000638765 0 | ||||||||
\(241\) | 26.6567 | 1.71711 | 0.858554 | − | 0.512723i | \(-0.171363\pi\) | ||||
0.858554 | + | 0.512723i | \(0.171363\pi\) | |||||||
\(242\) | 20.4369 | 1.31374 | ||||||||
\(243\) | 0.0519505 | 0.00333263 | ||||||||
\(244\) | −14.3396 | −0.918000 | ||||||||
\(245\) | 15.2779 | 0.976069 | ||||||||
\(246\) | 0.00396460 | 0.000252774 0 | ||||||||
\(247\) | 14.0627 | 0.894789 | ||||||||
\(248\) | 5.39285 | 0.342447 | ||||||||
\(249\) | −0.00376043 | −0.000238307 0 | ||||||||
\(250\) | −24.5697 | −1.55392 | ||||||||
\(251\) | 6.07268 | 0.383304 | 0.191652 | − | 0.981463i | \(-0.438615\pi\) | ||||
0.191652 | + | 0.981463i | \(0.438615\pi\) | |||||||
\(252\) | 0.520153 | 0.0327665 | ||||||||
\(253\) | −8.49621 | −0.534152 | ||||||||
\(254\) | 22.1532 | 1.39001 | ||||||||
\(255\) | −0.00420207 | −0.000263144 0 | ||||||||
\(256\) | 1.91579 | 0.119737 | ||||||||
\(257\) | 26.4315 | 1.64875 | 0.824374 | − | 0.566045i | \(-0.191527\pi\) | ||||
0.824374 | + | 0.566045i | \(0.191527\pi\) | |||||||
\(258\) | −0.00398600 | −0.000248158 0 | ||||||||
\(259\) | −0.114313 | −0.00710304 | ||||||||
\(260\) | −22.9764 | −1.42494 | ||||||||
\(261\) | −6.53939 | −0.404778 | ||||||||
\(262\) | −6.40636 | −0.395786 | ||||||||
\(263\) | −9.51496 | −0.586717 | −0.293359 | − | 0.956002i | \(-0.594773\pi\) | ||||
−0.293359 | + | 0.956002i | \(0.594773\pi\) | |||||||
\(264\) | 0.00317310 | 0.000195291 0 | ||||||||
\(265\) | −24.1398 | −1.48290 | ||||||||
\(266\) | 0.498485 | 0.0305641 | ||||||||
\(267\) | 0.00511199 | 0.000312849 0 | ||||||||
\(268\) | 7.16584 | 0.437723 | ||||||||
\(269\) | 3.92078 | 0.239054 | 0.119527 | − | 0.992831i | \(-0.461862\pi\) | ||||
0.119527 | + | 0.992831i | \(0.461862\pi\) | |||||||
\(270\) | −0.0542292 | −0.00330029 | ||||||||
\(271\) | −0.360394 | −0.0218924 | −0.0109462 | − | 0.999940i | \(-0.503484\pi\) | ||||
−0.0109462 | + | 0.999940i | \(0.503484\pi\) | |||||||
\(272\) | −2.35496 | −0.142791 | ||||||||
\(273\) | −0.000508834 0 | −3.07960e−5 0 | ||||||||
\(274\) | −38.9033 | −2.35023 | ||||||||
\(275\) | 0.282171 | 0.0170155 | ||||||||
\(276\) | 0.0350745 | 0.00211123 | ||||||||
\(277\) | −24.2096 | −1.45461 | −0.727306 | − | 0.686314i | \(-0.759228\pi\) | ||||
−0.727306 | + | 0.686314i | \(0.759228\pi\) | |||||||
\(278\) | −48.4333 | −2.90484 | ||||||||
\(279\) | 12.0087 | 0.718945 | ||||||||
\(280\) | −0.194238 | −0.0116079 | ||||||||
\(281\) | −9.77843 | −0.583332 | −0.291666 | − | 0.956520i | \(-0.594210\pi\) | ||||
−0.291666 | + | 0.956520i | \(0.594210\pi\) | |||||||
\(282\) | −0.0325382 | −0.00193762 | ||||||||
\(283\) | 19.3972 | 1.15305 | 0.576523 | − | 0.817081i | \(-0.304409\pi\) | ||||
0.576523 | + | 0.817081i | \(0.304409\pi\) | |||||||
\(284\) | −9.66653 | −0.573603 | ||||||||
\(285\) | −0.0147516 | −0.000873810 0 | ||||||||
\(286\) | 10.5470 | 0.623655 | ||||||||
\(287\) | 0.0632425 | 0.00373309 | ||||||||
\(288\) | −23.2792 | −1.37174 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 10.2393 | 0.601274 | ||||||||
\(291\) | −0.0269485 | −0.00157975 | ||||||||
\(292\) | −17.2425 | −1.00904 | ||||||||
\(293\) | −5.92616 | −0.346210 | −0.173105 | − | 0.984903i | \(-0.555380\pi\) | ||||
−0.173105 | + | 0.984903i | \(0.555380\pi\) | |||||||
\(294\) | 0.0289517 | 0.00168850 | ||||||||
\(295\) | 18.7418 | 1.09119 | ||||||||
\(296\) | −2.33281 | −0.135592 | ||||||||
\(297\) | 0.0141317 | 0.000820002 0 | ||||||||
\(298\) | 24.9189 | 1.44351 | ||||||||
\(299\) | 27.8037 | 1.60793 | ||||||||
\(300\) | −0.00116487 | −6.72539e−5 0 | ||||||||
\(301\) | −0.0635839 | −0.00366491 | ||||||||
\(302\) | 26.7404 | 1.53874 | ||||||||
\(303\) | −0.00201537 | −0.000115780 0 | ||||||||
\(304\) | −8.26724 | −0.474158 | ||||||||
\(305\) | 11.9239 | 0.682762 | ||||||||
\(306\) | 6.45268 | 0.368875 | ||||||||
\(307\) | 28.0133 | 1.59880 | 0.799402 | − | 0.600797i | \(-0.205150\pi\) | ||||
0.799402 | + | 0.600797i | \(0.205150\pi\) | |||||||
\(308\) | 0.212239 | 0.0120934 | ||||||||
\(309\) | −0.00378375 | −0.000215250 0 | ||||||||
\(310\) | −18.8032 | −1.06795 | ||||||||
\(311\) | −17.1756 | −0.973939 | −0.486970 | − | 0.873419i | \(-0.661898\pi\) | ||||
−0.486970 | + | 0.873419i | \(0.661898\pi\) | |||||||
\(312\) | −0.0103839 | −0.000587874 0 | ||||||||
\(313\) | 0.972274 | 0.0549562 | 0.0274781 | − | 0.999622i | \(-0.491252\pi\) | ||||
0.0274781 | + | 0.999622i | \(0.491252\pi\) | |||||||
\(314\) | −6.03910 | −0.340806 | ||||||||
\(315\) | −0.432527 | −0.0243701 | ||||||||
\(316\) | −40.3041 | −2.26728 | ||||||||
\(317\) | 2.10893 | 0.118449 | 0.0592247 | − | 0.998245i | \(-0.481137\pi\) | ||||
0.0592247 | + | 0.998245i | \(0.481137\pi\) | |||||||
\(318\) | −0.0457451 | −0.00256526 | ||||||||
\(319\) | −2.66828 | −0.149395 | ||||||||
\(320\) | 26.1643 | 1.46263 | ||||||||
\(321\) | 0.0265805 | 0.00148358 | ||||||||
\(322\) | 0.985567 | 0.0549235 | ||||||||
\(323\) | 3.51056 | 0.195333 | ||||||||
\(324\) | 23.6371 | 1.31317 | ||||||||
\(325\) | −0.923400 | −0.0512210 | ||||||||
\(326\) | 24.3863 | 1.35063 | ||||||||
\(327\) | 0.0164469 | 0.000909516 0 | ||||||||
\(328\) | 1.29061 | 0.0712620 | ||||||||
\(329\) | −0.519043 | −0.0286157 | ||||||||
\(330\) | −0.0110636 | −0.000609032 0 | ||||||||
\(331\) | −18.8176 | −1.03431 | −0.517154 | − | 0.855892i | \(-0.673009\pi\) | ||||
−0.517154 | + | 0.855892i | \(0.673009\pi\) | |||||||
\(332\) | −5.13291 | −0.281705 | ||||||||
\(333\) | −5.19468 | −0.284667 | ||||||||
\(334\) | −6.87973 | −0.376442 | ||||||||
\(335\) | −5.95867 | −0.325557 | ||||||||
\(336\) | 0.000299135 0 | 1.63191e−5 0 | ||||||||
\(337\) | 27.1204 | 1.47734 | 0.738670 | − | 0.674067i | \(-0.235454\pi\) | ||||
0.738670 | + | 0.674067i | \(0.235454\pi\) | |||||||
\(338\) | −6.55308 | −0.356441 | ||||||||
\(339\) | −0.00512122 | −0.000278147 0 | ||||||||
\(340\) | −5.73574 | −0.311064 | ||||||||
\(341\) | 4.89995 | 0.265347 | ||||||||
\(342\) | 22.6525 | 1.22491 | ||||||||
\(343\) | 0.923951 | 0.0498887 | ||||||||
\(344\) | −1.29758 | −0.0699606 | ||||||||
\(345\) | −0.0291657 | −0.00157023 | ||||||||
\(346\) | 10.2279 | 0.549853 | ||||||||
\(347\) | 3.04343 | 0.163380 | 0.0816900 | − | 0.996658i | \(-0.473968\pi\) | ||||
0.0816900 | + | 0.996658i | \(0.473968\pi\) | |||||||
\(348\) | 0.0110153 | 0.000590483 0 | ||||||||
\(349\) | 17.9538 | 0.961045 | 0.480523 | − | 0.876982i | \(-0.340447\pi\) | ||||
0.480523 | + | 0.876982i | \(0.340447\pi\) | |||||||
\(350\) | −0.0327320 | −0.00174960 | ||||||||
\(351\) | −0.0462456 | −0.00246841 | ||||||||
\(352\) | −9.49866 | −0.506280 | ||||||||
\(353\) | −1.00000 | −0.0532246 | ||||||||
\(354\) | 0.0355159 | 0.00188765 | ||||||||
\(355\) | 8.03809 | 0.426617 | ||||||||
\(356\) | 6.97777 | 0.369821 | ||||||||
\(357\) | −0.000127023 0 | −6.72278e−6 0 | ||||||||
\(358\) | 30.1199 | 1.59189 | ||||||||
\(359\) | 28.0790 | 1.48195 | 0.740977 | − | 0.671531i | \(-0.234363\pi\) | ||||
0.740977 | + | 0.671531i | \(0.234363\pi\) | |||||||
\(360\) | −8.82670 | −0.465208 | ||||||||
\(361\) | −6.67596 | −0.351367 | ||||||||
\(362\) | −3.96509 | −0.208400 | ||||||||
\(363\) | −0.0182820 | −0.000959555 0 | ||||||||
\(364\) | −0.694549 | −0.0364042 | ||||||||
\(365\) | 14.3378 | 0.750475 | ||||||||
\(366\) | 0.0225959 | 0.00118111 | ||||||||
\(367\) | −14.8703 | −0.776221 | −0.388111 | − | 0.921613i | \(-0.626872\pi\) | ||||
−0.388111 | + | 0.921613i | \(0.626872\pi\) | |||||||
\(368\) | −16.3453 | −0.852060 | ||||||||
\(369\) | 2.87391 | 0.149610 | ||||||||
\(370\) | 8.13380 | 0.422856 | ||||||||
\(371\) | −0.729717 | −0.0378850 | ||||||||
\(372\) | −0.0202282 | −0.00104878 | ||||||||
\(373\) | −10.0753 | −0.521680 | −0.260840 | − | 0.965382i | \(-0.583999\pi\) | ||||
−0.260840 | + | 0.965382i | \(0.583999\pi\) | |||||||
\(374\) | 2.63290 | 0.136144 | ||||||||
\(375\) | 0.0219790 | 0.00113499 | ||||||||
\(376\) | −10.5923 | −0.546254 | ||||||||
\(377\) | 8.73190 | 0.449716 | ||||||||
\(378\) | −0.00163928 | −8.43156e−5 0 | ||||||||
\(379\) | 7.24287 | 0.372041 | 0.186021 | − | 0.982546i | \(-0.440441\pi\) | ||||
0.186021 | + | 0.982546i | \(0.440441\pi\) | |||||||
\(380\) | −20.1357 | −1.03294 | ||||||||
\(381\) | −0.0198173 | −0.00101527 | ||||||||
\(382\) | 2.20692 | 0.112916 | ||||||||
\(383\) | 8.85020 | 0.452224 | 0.226112 | − | 0.974101i | \(-0.427398\pi\) | ||||
0.226112 | + | 0.974101i | \(0.427398\pi\) | |||||||
\(384\) | 0.0197206 | 0.00100636 | ||||||||
\(385\) | −0.176485 | −0.00899449 | ||||||||
\(386\) | −38.8646 | −1.97816 | ||||||||
\(387\) | −2.88943 | −0.146878 | ||||||||
\(388\) | −36.7842 | −1.86744 | ||||||||
\(389\) | 5.22915 | 0.265128 | 0.132564 | − | 0.991174i | \(-0.457679\pi\) | ||||
0.132564 | + | 0.991174i | \(0.457679\pi\) | |||||||
\(390\) | 0.0362055 | 0.00183334 | ||||||||
\(391\) | 6.94081 | 0.351012 | ||||||||
\(392\) | 9.42474 | 0.476021 | ||||||||
\(393\) | 0.00573084 | 0.000289083 0 | ||||||||
\(394\) | −48.9719 | −2.46717 | ||||||||
\(395\) | 33.5144 | 1.68629 | ||||||||
\(396\) | 9.64472 | 0.484665 | ||||||||
\(397\) | −2.35073 | −0.117980 | −0.0589899 | − | 0.998259i | \(-0.518788\pi\) | ||||
−0.0589899 | + | 0.998259i | \(0.518788\pi\) | |||||||
\(398\) | 2.02340 | 0.101424 | ||||||||
\(399\) | −0.000445923 0 | −2.23241e−5 0 | ||||||||
\(400\) | 0.542851 | 0.0271426 | ||||||||
\(401\) | 3.02122 | 0.150872 | 0.0754362 | − | 0.997151i | \(-0.475965\pi\) | ||||
0.0754362 | + | 0.997151i | \(0.475965\pi\) | |||||||
\(402\) | −0.0112917 | −0.000563180 0 | ||||||||
\(403\) | −16.0350 | −0.798761 | ||||||||
\(404\) | −2.75095 | −0.136865 | ||||||||
\(405\) | −19.6552 | −0.976673 | ||||||||
\(406\) | 0.309522 | 0.0153613 | ||||||||
\(407\) | −2.11960 | −0.105064 | ||||||||
\(408\) | −0.00259220 | −0.000128333 0 | ||||||||
\(409\) | −25.0321 | −1.23776 | −0.618879 | − | 0.785486i | \(-0.712413\pi\) | ||||
−0.618879 | + | 0.785486i | \(0.712413\pi\) | |||||||
\(410\) | −4.49996 | −0.222237 | ||||||||
\(411\) | 0.0348012 | 0.00171662 | ||||||||
\(412\) | −5.16475 | −0.254449 | ||||||||
\(413\) | 0.566542 | 0.0278777 | ||||||||
\(414\) | 44.7868 | 2.20115 | ||||||||
\(415\) | 4.26821 | 0.209518 | ||||||||
\(416\) | 31.0842 | 1.52403 | ||||||||
\(417\) | 0.0433263 | 0.00212170 | ||||||||
\(418\) | 9.24296 | 0.452088 | ||||||||
\(419\) | −20.4178 | −0.997474 | −0.498737 | − | 0.866753i | \(-0.666203\pi\) | ||||
−0.498737 | + | 0.866753i | \(0.666203\pi\) | |||||||
\(420\) | 0.000728573 0 | 3.55507e−5 0 | ||||||||
\(421\) | 27.6799 | 1.34904 | 0.674518 | − | 0.738258i | \(-0.264351\pi\) | ||||
0.674518 | + | 0.738258i | \(0.264351\pi\) | |||||||
\(422\) | −58.2884 | −2.83743 | ||||||||
\(423\) | −23.5867 | −1.14683 | ||||||||
\(424\) | −14.8916 | −0.723198 | ||||||||
\(425\) | −0.230514 | −0.0111816 | ||||||||
\(426\) | 0.0152322 | 0.000738004 0 | ||||||||
\(427\) | 0.360446 | 0.0174432 | ||||||||
\(428\) | 36.2819 | 1.75375 | ||||||||
\(429\) | −0.00943484 | −0.000455518 0 | ||||||||
\(430\) | 4.52425 | 0.218178 | ||||||||
\(431\) | 34.2033 | 1.64751 | 0.823757 | − | 0.566943i | \(-0.191874\pi\) | ||||
0.823757 | + | 0.566943i | \(0.191874\pi\) | |||||||
\(432\) | 0.0271870 | 0.00130804 | ||||||||
\(433\) | 8.54142 | 0.410474 | 0.205237 | − | 0.978712i | \(-0.434203\pi\) | ||||
0.205237 | + | 0.978712i | \(0.434203\pi\) | |||||||
\(434\) | −0.568398 | −0.0272840 | ||||||||
\(435\) | −0.00915966 | −0.000439172 0 | ||||||||
\(436\) | 22.4497 | 1.07515 | ||||||||
\(437\) | 24.3661 | 1.16559 | ||||||||
\(438\) | 0.0271702 | 0.00129824 | ||||||||
\(439\) | −14.0159 | −0.668941 | −0.334470 | − | 0.942406i | \(-0.608557\pi\) | ||||
−0.334470 | + | 0.942406i | \(0.608557\pi\) | |||||||
\(440\) | −3.60158 | −0.171698 | ||||||||
\(441\) | 20.9869 | 0.999376 | ||||||||
\(442\) | −8.61613 | −0.409827 | ||||||||
\(443\) | −16.7385 | −0.795268 | −0.397634 | − | 0.917544i | \(-0.630169\pi\) | ||||
−0.397634 | + | 0.917544i | \(0.630169\pi\) | |||||||
\(444\) | 0.00875022 | 0.000415267 0 | ||||||||
\(445\) | −5.80228 | −0.275054 | ||||||||
\(446\) | 8.37914 | 0.396764 | ||||||||
\(447\) | −0.0222914 | −0.00105434 | ||||||||
\(448\) | 0.790916 | 0.0373673 | ||||||||
\(449\) | 24.5082 | 1.15661 | 0.578306 | − | 0.815820i | \(-0.303714\pi\) | ||||
0.578306 | + | 0.815820i | \(0.303714\pi\) | |||||||
\(450\) | −1.48743 | −0.0701183 | ||||||||
\(451\) | 1.17265 | 0.0552179 | ||||||||
\(452\) | −6.99037 | −0.328800 | ||||||||
\(453\) | −0.0239208 | −0.00112390 | ||||||||
\(454\) | −42.4117 | −1.99048 | ||||||||
\(455\) | 0.577543 | 0.0270756 | ||||||||
\(456\) | −0.00910008 | −0.000426150 0 | ||||||||
\(457\) | 29.3567 | 1.37325 | 0.686625 | − | 0.727012i | \(-0.259092\pi\) | ||||
0.686625 | + | 0.727012i | \(0.259092\pi\) | |||||||
\(458\) | 35.6806 | 1.66724 | ||||||||
\(459\) | −0.0115446 | −0.000538855 0 | ||||||||
\(460\) | −39.8107 | −1.85618 | ||||||||
\(461\) | 7.82734 | 0.364556 | 0.182278 | − | 0.983247i | \(-0.441653\pi\) | ||||
0.182278 | + | 0.983247i | \(0.441653\pi\) | |||||||
\(462\) | −0.000334440 0 | −1.55595e−5 0 | ||||||||
\(463\) | −20.1106 | −0.934618 | −0.467309 | − | 0.884094i | \(-0.654776\pi\) | ||||
−0.467309 | + | 0.884094i | \(0.654776\pi\) | |||||||
\(464\) | −5.13334 | −0.238309 | ||||||||
\(465\) | 0.0168205 | 0.000780034 0 | ||||||||
\(466\) | 45.8326 | 2.12315 | ||||||||
\(467\) | −39.4279 | −1.82451 | −0.912253 | − | 0.409627i | \(-0.865659\pi\) | ||||
−0.912253 | + | 0.409627i | \(0.865659\pi\) | |||||||
\(468\) | −31.5622 | −1.45896 | ||||||||
\(469\) | −0.180123 | −0.00831732 | ||||||||
\(470\) | 36.9319 | 1.70354 | ||||||||
\(471\) | 0.00540231 | 0.000248925 0 | ||||||||
\(472\) | 11.5616 | 0.532166 | ||||||||
\(473\) | −1.17898 | −0.0542095 | ||||||||
\(474\) | 0.0635099 | 0.00291711 | ||||||||
\(475\) | −0.809233 | −0.0371302 | ||||||||
\(476\) | −0.173384 | −0.00794706 | ||||||||
\(477\) | −33.1603 | −1.51831 | ||||||||
\(478\) | 54.0452 | 2.47197 | ||||||||
\(479\) | −10.2907 | −0.470196 | −0.235098 | − | 0.971972i | \(-0.575541\pi\) | ||||
−0.235098 | + | 0.971972i | \(0.575541\pi\) | |||||||
\(480\) | −0.0326069 | −0.00148830 | ||||||||
\(481\) | 6.93634 | 0.316270 | ||||||||
\(482\) | −57.3358 | −2.61157 | ||||||||
\(483\) | −0.000881644 0 | −4.01162e−5 0 | ||||||||
\(484\) | −24.9546 | −1.13430 | ||||||||
\(485\) | 30.5875 | 1.38890 | ||||||||
\(486\) | −0.111740 | −0.00506864 | ||||||||
\(487\) | −5.09851 | −0.231036 | −0.115518 | − | 0.993305i | \(-0.536853\pi\) | ||||
−0.115518 | + | 0.993305i | \(0.536853\pi\) | |||||||
\(488\) | 7.35572 | 0.332978 | ||||||||
\(489\) | −0.0218149 | −0.000986506 0 | ||||||||
\(490\) | −32.8612 | −1.48452 | ||||||||
\(491\) | 28.4709 | 1.28488 | 0.642438 | − | 0.766338i | \(-0.277923\pi\) | ||||
0.642438 | + | 0.766338i | \(0.277923\pi\) | |||||||
\(492\) | −0.00484099 | −0.000218249 0 | ||||||||
\(493\) | 2.17980 | 0.0981732 | ||||||||
\(494\) | −30.2474 | −1.36090 | ||||||||
\(495\) | −8.01995 | −0.360470 | ||||||||
\(496\) | 9.42672 | 0.423272 | ||||||||
\(497\) | 0.242982 | 0.0108992 | ||||||||
\(498\) | 0.00808829 | 0.000362445 0 | ||||||||
\(499\) | −16.0159 | −0.716972 | −0.358486 | − | 0.933535i | \(-0.616707\pi\) | ||||
−0.358486 | + | 0.933535i | \(0.616707\pi\) | |||||||
\(500\) | 30.0009 | 1.34168 | ||||||||
\(501\) | 0.00615430 | 0.000274954 0 | ||||||||
\(502\) | −13.0617 | −0.582972 | ||||||||
\(503\) | 33.9449 | 1.51353 | 0.756764 | − | 0.653689i | \(-0.226779\pi\) | ||||
0.756764 | + | 0.653689i | \(0.226779\pi\) | |||||||
\(504\) | −0.266820 | −0.0118851 | ||||||||
\(505\) | 2.28752 | 0.101793 | ||||||||
\(506\) | 18.2745 | 0.812399 | ||||||||
\(507\) | 0.00586210 | 0.000260345 0 | ||||||||
\(508\) | −27.0502 | −1.20016 | ||||||||
\(509\) | −36.3553 | −1.61142 | −0.805709 | − | 0.592311i | \(-0.798216\pi\) | ||||
−0.805709 | + | 0.592311i | \(0.798216\pi\) | |||||||
\(510\) | 0.00903821 | 0.000400219 0 | ||||||||
\(511\) | 0.433414 | 0.0191731 | ||||||||
\(512\) | −24.6192 | −1.08803 | ||||||||
\(513\) | −0.0405279 | −0.00178935 | ||||||||
\(514\) | −56.8513 | −2.50760 | ||||||||
\(515\) | 4.29468 | 0.189246 | ||||||||
\(516\) | 0.00486712 | 0.000214263 0 | ||||||||
\(517\) | −9.62414 | −0.423269 | ||||||||
\(518\) | 0.245875 | 0.0108031 | ||||||||
\(519\) | −0.00914939 | −0.000401614 0 | ||||||||
\(520\) | 11.7861 | 0.516855 | ||||||||
\(521\) | 20.0091 | 0.876614 | 0.438307 | − | 0.898825i | \(-0.355578\pi\) | ||||
0.438307 | + | 0.898825i | \(0.355578\pi\) | |||||||
\(522\) | 14.0655 | 0.615632 | ||||||||
\(523\) | 12.9235 | 0.565103 | 0.282552 | − | 0.959252i | \(-0.408819\pi\) | ||||
0.282552 | + | 0.959252i | \(0.408819\pi\) | |||||||
\(524\) | 7.82250 | 0.341727 | ||||||||
\(525\) | 2.92806e−5 0 | 1.27791e−6 0 | ||||||||
\(526\) | 20.4657 | 0.892347 | ||||||||
\(527\) | −4.00292 | −0.174370 | ||||||||
\(528\) | 0.00554659 | 0.000241384 0 | ||||||||
\(529\) | 25.1748 | 1.09456 | ||||||||
\(530\) | 51.9223 | 2.25536 | ||||||||
\(531\) | 25.7452 | 1.11725 | ||||||||
\(532\) | −0.608677 | −0.0263895 | ||||||||
\(533\) | −3.83748 | −0.166220 | ||||||||
\(534\) | −0.0109954 | −0.000475816 0 | ||||||||
\(535\) | −30.1698 | −1.30435 | ||||||||
\(536\) | −3.67583 | −0.158772 | ||||||||
\(537\) | −0.0269440 | −0.00116272 | ||||||||
\(538\) | −8.43319 | −0.363581 | ||||||||
\(539\) | 8.56333 | 0.368849 | ||||||||
\(540\) | 0.0662167 | 0.00284951 | ||||||||
\(541\) | 15.7378 | 0.676622 | 0.338311 | − | 0.941034i | \(-0.390144\pi\) | ||||
0.338311 | + | 0.941034i | \(0.390144\pi\) | |||||||
\(542\) | 0.775170 | 0.0332964 | ||||||||
\(543\) | 0.00354699 | 0.000152216 0 | ||||||||
\(544\) | 7.75974 | 0.332696 | ||||||||
\(545\) | −18.6678 | −0.799641 | ||||||||
\(546\) | 0.00109445 | 4.68381e−5 0 | ||||||||
\(547\) | −18.9470 | −0.810115 | −0.405057 | − | 0.914291i | \(-0.632748\pi\) | ||||
−0.405057 | + | 0.914291i | \(0.632748\pi\) | |||||||
\(548\) | 47.5030 | 2.02923 | ||||||||
\(549\) | 16.3796 | 0.699066 | ||||||||
\(550\) | −0.606920 | −0.0258792 | ||||||||
\(551\) | 7.65231 | 0.326000 | ||||||||
\(552\) | −0.0179920 | −0.000765789 0 | ||||||||
\(553\) | 1.01310 | 0.0430813 | ||||||||
\(554\) | 52.0723 | 2.21234 | ||||||||
\(555\) | −0.00727613 | −0.000308855 0 | ||||||||
\(556\) | 59.1396 | 2.50808 | ||||||||
\(557\) | −2.18886 | −0.0927451 | −0.0463725 | − | 0.998924i | \(-0.514766\pi\) | ||||
−0.0463725 | + | 0.998924i | \(0.514766\pi\) | |||||||
\(558\) | −25.8296 | −1.09345 | ||||||||
\(559\) | 3.85819 | 0.163184 | ||||||||
\(560\) | −0.339528 | −0.0143477 | ||||||||
\(561\) | −0.00235528 | −9.94399e−5 0 | ||||||||
\(562\) | 21.0324 | 0.887198 | ||||||||
\(563\) | 4.44828 | 0.187473 | 0.0937363 | − | 0.995597i | \(-0.470119\pi\) | ||||
0.0937363 | + | 0.995597i | \(0.470119\pi\) | |||||||
\(564\) | 0.0397308 | 0.00167297 | ||||||||
\(565\) | 5.81276 | 0.244545 | ||||||||
\(566\) | −41.7215 | −1.75368 | ||||||||
\(567\) | −0.594151 | −0.0249520 | ||||||||
\(568\) | 4.95860 | 0.208058 | ||||||||
\(569\) | 30.2155 | 1.26670 | 0.633351 | − | 0.773865i | \(-0.281679\pi\) | ||||
0.633351 | + | 0.773865i | \(0.281679\pi\) | |||||||
\(570\) | 0.0317292 | 0.00132899 | ||||||||
\(571\) | 21.0723 | 0.881848 | 0.440924 | − | 0.897544i | \(-0.354651\pi\) | ||||
0.440924 | + | 0.897544i | \(0.354651\pi\) | |||||||
\(572\) | −12.8784 | −0.538472 | ||||||||
\(573\) | −0.00197421 | −8.24739e−5 0 | ||||||||
\(574\) | −0.136028 | −0.00567771 | ||||||||
\(575\) | −1.59995 | −0.0667227 | ||||||||
\(576\) | 35.9414 | 1.49756 | ||||||||
\(577\) | 18.2837 | 0.761161 | 0.380581 | − | 0.924748i | \(-0.375724\pi\) | ||||
0.380581 | + | 0.924748i | \(0.375724\pi\) | |||||||
\(578\) | −2.15090 | −0.0894655 | ||||||||
\(579\) | 0.0347666 | 0.00144485 | ||||||||
\(580\) | −12.5028 | −0.519149 | ||||||||
\(581\) | 0.129023 | 0.00535276 | ||||||||
\(582\) | 0.0579634 | 0.00240266 | ||||||||
\(583\) | −13.5305 | −0.560375 | ||||||||
\(584\) | 8.84481 | 0.366001 | ||||||||
\(585\) | 26.2451 | 1.08510 | ||||||||
\(586\) | 12.7466 | 0.526555 | ||||||||
\(587\) | 11.7756 | 0.486030 | 0.243015 | − | 0.970022i | \(-0.421864\pi\) | ||||
0.243015 | + | 0.970022i | \(0.421864\pi\) | |||||||
\(588\) | −0.0353515 | −0.00145787 | ||||||||
\(589\) | −14.0525 | −0.579023 | ||||||||
\(590\) | −40.3117 | −1.65961 | ||||||||
\(591\) | 0.0438081 | 0.00180202 | ||||||||
\(592\) | −4.07776 | −0.167595 | ||||||||
\(593\) | −5.47969 | −0.225024 | −0.112512 | − | 0.993650i | \(-0.535890\pi\) | ||||
−0.112512 | + | 0.993650i | \(0.535890\pi\) | |||||||
\(594\) | −0.0303957 | −0.00124715 | ||||||||
\(595\) | 0.144176 | 0.00591063 | ||||||||
\(596\) | −30.4273 | −1.24635 | ||||||||
\(597\) | −0.00181004 | −7.40802e−5 0 | ||||||||
\(598\) | −59.8029 | −2.44552 | ||||||||
\(599\) | 34.6462 | 1.41560 | 0.707802 | − | 0.706411i | \(-0.249687\pi\) | ||||
0.707802 | + | 0.706411i | \(0.249687\pi\) | |||||||
\(600\) | 0.000597539 0 | 2.43944e−5 0 | ||||||||
\(601\) | −28.4667 | −1.16118 | −0.580591 | − | 0.814195i | \(-0.697179\pi\) | ||||
−0.580591 | + | 0.814195i | \(0.697179\pi\) | |||||||
\(602\) | 0.136762 | 0.00557402 | ||||||||
\(603\) | −8.18529 | −0.333331 | ||||||||
\(604\) | −32.6514 | −1.32857 | ||||||||
\(605\) | 20.7507 | 0.843635 | ||||||||
\(606\) | 0.00433486 | 0.000176092 0 | ||||||||
\(607\) | 29.8214 | 1.21041 | 0.605206 | − | 0.796069i | \(-0.293091\pi\) | ||||
0.605206 | + | 0.796069i | \(0.293091\pi\) | |||||||
\(608\) | 27.2410 | 1.10477 | ||||||||
\(609\) | −0.000276885 0 | −1.12200e−5 0 | ||||||||
\(610\) | −25.6471 | −1.03842 | ||||||||
\(611\) | 31.4948 | 1.27414 | ||||||||
\(612\) | −7.87906 | −0.318492 | ||||||||
\(613\) | 17.6244 | 0.711842 | 0.355921 | − | 0.934516i | \(-0.384167\pi\) | ||||
0.355921 | + | 0.934516i | \(0.384167\pi\) | |||||||
\(614\) | −60.2537 | −2.43164 | ||||||||
\(615\) | 0.00402546 | 0.000162322 0 | ||||||||
\(616\) | −0.108871 | −0.00438655 | ||||||||
\(617\) | 20.8462 | 0.839238 | 0.419619 | − | 0.907700i | \(-0.362164\pi\) | ||||
0.419619 | + | 0.907700i | \(0.362164\pi\) | |||||||
\(618\) | 0.00813845 | 0.000327377 0 | ||||||||
\(619\) | 32.5000 | 1.30629 | 0.653144 | − | 0.757234i | \(-0.273450\pi\) | ||||
0.653144 | + | 0.757234i | \(0.273450\pi\) | |||||||
\(620\) | 22.9597 | 0.922085 | ||||||||
\(621\) | −0.0801287 | −0.00321545 | ||||||||
\(622\) | 36.9429 | 1.48128 | ||||||||
\(623\) | −0.175396 | −0.00702708 | ||||||||
\(624\) | −0.0181511 | −0.000726626 0 | ||||||||
\(625\) | −23.7943 | −0.951772 | ||||||||
\(626\) | −2.09126 | −0.0835836 | ||||||||
\(627\) | −0.00826834 | −0.000330206 0 | ||||||||
\(628\) | 7.37406 | 0.294257 | ||||||||
\(629\) | 1.73156 | 0.0690419 | ||||||||
\(630\) | 0.930320 | 0.0370648 | ||||||||
\(631\) | −16.0987 | −0.640878 | −0.320439 | − | 0.947269i | \(-0.603830\pi\) | ||||
−0.320439 | + | 0.947269i | \(0.603830\pi\) | |||||||
\(632\) | 20.6746 | 0.822391 | ||||||||
\(633\) | 0.0521422 | 0.00207247 | ||||||||
\(634\) | −4.53609 | −0.180151 | ||||||||
\(635\) | 22.4933 | 0.892618 | ||||||||
\(636\) | 0.0558572 | 0.00221488 | ||||||||
\(637\) | −28.0234 | −1.11033 | ||||||||
\(638\) | 5.73919 | 0.227217 | ||||||||
\(639\) | 11.0417 | 0.436805 | ||||||||
\(640\) | −22.3836 | −0.884789 | ||||||||
\(641\) | −12.9469 | −0.511373 | −0.255686 | − | 0.966760i | \(-0.582301\pi\) | ||||
−0.255686 | + | 0.966760i | \(0.582301\pi\) | |||||||
\(642\) | −0.0571719 | −0.00225640 | ||||||||
\(643\) | 44.1599 | 1.74150 | 0.870748 | − | 0.491730i | \(-0.163635\pi\) | ||||
0.870748 | + | 0.491730i | \(0.163635\pi\) | |||||||
\(644\) | −1.20343 | −0.0474217 | ||||||||
\(645\) | −0.00404719 | −0.000159358 0 | ||||||||
\(646\) | −7.55085 | −0.297084 | ||||||||
\(647\) | 16.1624 | 0.635409 | 0.317705 | − | 0.948190i | \(-0.397088\pi\) | ||||
0.317705 | + | 0.948190i | \(0.397088\pi\) | |||||||
\(648\) | −12.1250 | −0.476316 | ||||||||
\(649\) | 10.5049 | 0.412353 | ||||||||
\(650\) | 1.98614 | 0.0779027 | ||||||||
\(651\) | 0.000508464 0 | 1.99283e−5 0 | ||||||||
\(652\) | −29.7770 | −1.16616 | ||||||||
\(653\) | −38.6017 | −1.51060 | −0.755301 | − | 0.655378i | \(-0.772509\pi\) | ||||
−0.755301 | + | 0.655378i | \(0.772509\pi\) | |||||||
\(654\) | −0.0353756 | −0.00138330 | ||||||||
\(655\) | −6.50470 | −0.254160 | ||||||||
\(656\) | 2.25599 | 0.0880816 | ||||||||
\(657\) | 19.6955 | 0.768396 | ||||||||
\(658\) | 1.11641 | 0.0435221 | ||||||||
\(659\) | 33.4201 | 1.30186 | 0.650931 | − | 0.759137i | \(-0.274379\pi\) | ||||
0.650931 | + | 0.759137i | \(0.274379\pi\) | |||||||
\(660\) | 0.0135093 | 0.000525847 0 | ||||||||
\(661\) | 4.36077 | 0.169614 | 0.0848071 | − | 0.996397i | \(-0.472973\pi\) | ||||
0.0848071 | + | 0.996397i | \(0.472973\pi\) | |||||||
\(662\) | 40.4747 | 1.57309 | ||||||||
\(663\) | 0.00770761 | 0.000299339 0 | ||||||||
\(664\) | 2.63301 | 0.102180 | ||||||||
\(665\) | 0.506138 | 0.0196272 | ||||||||
\(666\) | 11.1732 | 0.432953 | ||||||||
\(667\) | 15.1296 | 0.585819 | ||||||||
\(668\) | 8.40051 | 0.325026 | ||||||||
\(669\) | −0.00749561 | −0.000289797 0 | ||||||||
\(670\) | 12.8165 | 0.495144 | ||||||||
\(671\) | 6.68342 | 0.258010 | ||||||||
\(672\) | −0.000985668 0 | −3.80229e−5 0 | ||||||||
\(673\) | 47.4623 | 1.82954 | 0.914769 | − | 0.403977i | \(-0.132372\pi\) | ||||
0.914769 | + | 0.403977i | \(0.132372\pi\) | |||||||
\(674\) | −58.3331 | −2.24691 | ||||||||
\(675\) | 0.00266119 | 0.000102429 0 | ||||||||
\(676\) | 8.00166 | 0.307756 | ||||||||
\(677\) | −6.69512 | −0.257314 | −0.128657 | − | 0.991689i | \(-0.541067\pi\) | ||||
−0.128657 | + | 0.991689i | \(0.541067\pi\) | |||||||
\(678\) | 0.0110152 | 0.000423037 0 | ||||||||
\(679\) | 0.924621 | 0.0354837 | ||||||||
\(680\) | 2.94224 | 0.112830 | ||||||||
\(681\) | 0.0379397 | 0.00145385 | ||||||||
\(682\) | −10.5393 | −0.403570 | ||||||||
\(683\) | −34.2662 | −1.31116 | −0.655579 | − | 0.755127i | \(-0.727575\pi\) | ||||
−0.655579 | + | 0.755127i | \(0.727575\pi\) | |||||||
\(684\) | −27.6599 | −1.05760 | ||||||||
\(685\) | −39.5005 | −1.50924 | ||||||||
\(686\) | −1.98732 | −0.0758764 | ||||||||
\(687\) | −0.0319183 | −0.00121776 | ||||||||
\(688\) | −2.26817 | −0.0864730 | ||||||||
\(689\) | 44.2783 | 1.68687 | ||||||||
\(690\) | 0.0627325 | 0.00238819 | ||||||||
\(691\) | 37.6204 | 1.43115 | 0.715574 | − | 0.698537i | \(-0.246165\pi\) | ||||
0.715574 | + | 0.698537i | \(0.246165\pi\) | |||||||
\(692\) | −12.4887 | −0.474751 | ||||||||
\(693\) | −0.242433 | −0.00920927 | ||||||||
\(694\) | −6.54611 | −0.248487 | ||||||||
\(695\) | −49.1768 | −1.86538 | ||||||||
\(696\) | −0.00565048 | −0.000214181 0 | ||||||||
\(697\) | −0.957973 | −0.0362858 | ||||||||
\(698\) | −38.6168 | −1.46167 | ||||||||
\(699\) | −0.0409998 | −0.00155075 | ||||||||
\(700\) | 0.0399675 | 0.00151063 | ||||||||
\(701\) | 22.8514 | 0.863084 | 0.431542 | − | 0.902093i | \(-0.357970\pi\) | ||||
0.431542 | + | 0.902093i | \(0.357970\pi\) | |||||||
\(702\) | 0.0994695 | 0.00375424 | ||||||||
\(703\) | 6.07875 | 0.229264 | ||||||||
\(704\) | 14.6652 | 0.552717 | ||||||||
\(705\) | −0.0330377 | −0.00124427 | ||||||||
\(706\) | 2.15090 | 0.0809501 | ||||||||
\(707\) | 0.0691488 | 0.00260061 | ||||||||
\(708\) | −0.0433667 | −0.00162982 | ||||||||
\(709\) | 28.5678 | 1.07289 | 0.536444 | − | 0.843936i | \(-0.319767\pi\) | ||||
0.536444 | + | 0.843936i | \(0.319767\pi\) | |||||||
\(710\) | −17.2891 | −0.648848 | ||||||||
\(711\) | 46.0379 | 1.72656 | ||||||||
\(712\) | −3.57935 | −0.134142 | ||||||||
\(713\) | −27.7835 | −1.04050 | ||||||||
\(714\) | 0.000273214 0 | 1.02248e−5 0 | ||||||||
\(715\) | 10.7089 | 0.400489 | ||||||||
\(716\) | −36.7780 | −1.37446 | ||||||||
\(717\) | −0.0483465 | −0.00180553 | ||||||||
\(718\) | −60.3950 | −2.25392 | ||||||||
\(719\) | −17.5267 | −0.653634 | −0.326817 | − | 0.945088i | \(-0.605976\pi\) | ||||
−0.326817 | + | 0.945088i | \(0.605976\pi\) | |||||||
\(720\) | −15.4291 | −0.575008 | ||||||||
\(721\) | 0.129823 | 0.00483486 | ||||||||
\(722\) | 14.3593 | 0.534398 | ||||||||
\(723\) | 0.0512901 | 0.00190750 | ||||||||
\(724\) | 4.84158 | 0.179936 | ||||||||
\(725\) | −0.502474 | −0.0186614 | ||||||||
\(726\) | 0.0393227 | 0.00145940 | ||||||||
\(727\) | 34.3346 | 1.27340 | 0.636699 | − | 0.771112i | \(-0.280299\pi\) | ||||
0.636699 | + | 0.771112i | \(0.280299\pi\) | |||||||
\(728\) | 0.356279 | 0.0132046 | ||||||||
\(729\) | −26.9998 | −0.999993 | ||||||||
\(730\) | −30.8391 | −1.14141 | ||||||||
\(731\) | 0.963143 | 0.0356231 | ||||||||
\(732\) | −0.0275908 | −0.00101979 | ||||||||
\(733\) | 6.02979 | 0.222715 | 0.111358 | − | 0.993780i | \(-0.464480\pi\) | ||||
0.111358 | + | 0.993780i | \(0.464480\pi\) | |||||||
\(734\) | 31.9844 | 1.18057 | ||||||||
\(735\) | 0.0293961 | 0.00108429 | ||||||||
\(736\) | 53.8589 | 1.98526 | ||||||||
\(737\) | −3.33986 | −0.123025 | ||||||||
\(738\) | −6.18149 | −0.227544 | ||||||||
\(739\) | −49.2832 | −1.81291 | −0.906457 | − | 0.422299i | \(-0.861223\pi\) | ||||
−0.906457 | + | 0.422299i | \(0.861223\pi\) | |||||||
\(740\) | −9.93179 | −0.365100 | ||||||||
\(741\) | 0.0270580 | 0.000994001 0 | ||||||||
\(742\) | 1.56955 | 0.0576198 | ||||||||
\(743\) | 41.4348 | 1.52010 | 0.760048 | − | 0.649867i | \(-0.225175\pi\) | ||||
0.760048 | + | 0.649867i | \(0.225175\pi\) | |||||||
\(744\) | 0.0103764 | 0.000380416 0 | ||||||||
\(745\) | 25.3014 | 0.926973 | ||||||||
\(746\) | 21.6710 | 0.793430 | ||||||||
\(747\) | 5.86315 | 0.214521 | ||||||||
\(748\) | −3.21491 | −0.117549 | ||||||||
\(749\) | −0.911995 | −0.0333236 | ||||||||
\(750\) | −0.0472745 | −0.00172622 | ||||||||
\(751\) | −7.13645 | −0.260413 | −0.130206 | − | 0.991487i | \(-0.541564\pi\) | ||||
−0.130206 | + | 0.991487i | \(0.541564\pi\) | |||||||
\(752\) | −18.5153 | −0.675183 | ||||||||
\(753\) | 0.0116844 | 0.000425804 0 | ||||||||
\(754\) | −18.7814 | −0.683979 | ||||||||
\(755\) | 27.1509 | 0.988122 | ||||||||
\(756\) | 0.00200165 | 7.27993e−5 0 | ||||||||
\(757\) | 39.6273 | 1.44028 | 0.720140 | − | 0.693829i | \(-0.244078\pi\) | ||||
0.720140 | + | 0.693829i | \(0.244078\pi\) | |||||||
\(758\) | −15.5787 | −0.565843 | ||||||||
\(759\) | −0.0163475 | −0.000593378 0 | ||||||||
\(760\) | 10.3289 | 0.374669 | ||||||||
\(761\) | 34.1137 | 1.23662 | 0.618310 | − | 0.785935i | \(-0.287818\pi\) | ||||
0.618310 | + | 0.785935i | \(0.287818\pi\) | |||||||
\(762\) | 0.0426249 | 0.00154414 | ||||||||
\(763\) | −0.564305 | −0.0204292 | ||||||||
\(764\) | −2.69476 | −0.0974931 | ||||||||
\(765\) | 6.55174 | 0.236879 | ||||||||
\(766\) | −19.0359 | −0.687794 | ||||||||
\(767\) | −34.3770 | −1.24128 | ||||||||
\(768\) | 0.00368616 | 0.000133013 0 | ||||||||
\(769\) | 14.9781 | 0.540122 | 0.270061 | − | 0.962843i | \(-0.412956\pi\) | ||||
0.270061 | + | 0.962843i | \(0.412956\pi\) | |||||||
\(770\) | 0.379600 | 0.0136798 | ||||||||
\(771\) | 0.0508567 | 0.00183156 | ||||||||
\(772\) | 47.4557 | 1.70797 | ||||||||
\(773\) | 24.0200 | 0.863940 | 0.431970 | − | 0.901888i | \(-0.357819\pi\) | ||||
0.431970 | + | 0.901888i | \(0.357819\pi\) | |||||||
\(774\) | 6.21486 | 0.223388 | ||||||||
\(775\) | 0.922729 | 0.0331454 | ||||||||
\(776\) | 18.8690 | 0.677358 | ||||||||
\(777\) | −0.000219949 0 | −7.89061e−6 0 | ||||||||
\(778\) | −11.2474 | −0.403237 | ||||||||
\(779\) | −3.36302 | −0.120493 | ||||||||
\(780\) | −0.0442088 | −0.00158293 | ||||||||
\(781\) | 4.50539 | 0.161215 | ||||||||
\(782\) | −14.9290 | −0.533859 | ||||||||
\(783\) | −0.0251649 | −0.000899318 0 | ||||||||
\(784\) | 16.4745 | 0.588374 | ||||||||
\(785\) | −6.13181 | −0.218854 | ||||||||
\(786\) | −0.0123265 | −0.000439670 0 | ||||||||
\(787\) | 24.4061 | 0.869982 | 0.434991 | − | 0.900435i | \(-0.356751\pi\) | ||||
0.434991 | + | 0.900435i | \(0.356751\pi\) | |||||||
\(788\) | 59.7972 | 2.13019 | ||||||||
\(789\) | −0.0183077 | −0.000651772 0 | ||||||||
\(790\) | −72.0859 | −2.56470 | ||||||||
\(791\) | 0.175713 | 0.00624762 | ||||||||
\(792\) | −4.94741 | −0.175798 | ||||||||
\(793\) | −21.8714 | −0.776675 | ||||||||
\(794\) | 5.05618 | 0.179437 | ||||||||
\(795\) | −0.0464474 | −0.00164732 | ||||||||
\(796\) | −2.47068 | −0.0875709 | ||||||||
\(797\) | −20.5525 | −0.728008 | −0.364004 | − | 0.931397i | \(-0.618591\pi\) | ||||
−0.364004 | + | 0.931397i | \(0.618591\pi\) | |||||||
\(798\) | 0.000959134 0 | 3.39530e−5 0 | ||||||||
\(799\) | 7.86225 | 0.278146 | ||||||||
\(800\) | −1.78873 | −0.0632411 | ||||||||
\(801\) | −7.97046 | −0.281622 | ||||||||
\(802\) | −6.49833 | −0.229464 | ||||||||
\(803\) | 8.03641 | 0.283599 | ||||||||
\(804\) | 0.0137878 | 0.000486257 0 | ||||||||
\(805\) | 1.00070 | 0.0352699 | ||||||||
\(806\) | 34.4897 | 1.21485 | ||||||||
\(807\) | 0.00754396 | 0.000265560 0 | ||||||||
\(808\) | 1.41114 | 0.0496437 | ||||||||
\(809\) | 23.9840 | 0.843232 | 0.421616 | − | 0.906774i | \(-0.361463\pi\) | ||||
0.421616 | + | 0.906774i | \(0.361463\pi\) | |||||||
\(810\) | 42.2762 | 1.48544 | ||||||||
\(811\) | −27.4895 | −0.965288 | −0.482644 | − | 0.875817i | \(-0.660324\pi\) | ||||
−0.482644 | + | 0.875817i | \(0.660324\pi\) | |||||||
\(812\) | −0.377943 | −0.0132632 | ||||||||
\(813\) | −0.000693433 0 | −2.43198e−5 0 | ||||||||
\(814\) | 4.55903 | 0.159794 | ||||||||
\(815\) | 24.7607 | 0.867329 | ||||||||
\(816\) | −0.00453118 | −0.000158623 0 | ||||||||
\(817\) | 3.38117 | 0.118292 | ||||||||
\(818\) | 53.8415 | 1.88252 | ||||||||
\(819\) | 0.793359 | 0.0277222 | ||||||||
\(820\) | 5.49468 | 0.191883 | ||||||||
\(821\) | 37.1874 | 1.29785 | 0.648925 | − | 0.760852i | \(-0.275219\pi\) | ||||
0.648925 | + | 0.760852i | \(0.275219\pi\) | |||||||
\(822\) | −0.0748537 | −0.00261082 | ||||||||
\(823\) | 17.9888 | 0.627050 | 0.313525 | − | 0.949580i | \(-0.398490\pi\) | ||||
0.313525 | + | 0.949580i | \(0.398490\pi\) | |||||||
\(824\) | 2.64934 | 0.0922940 | ||||||||
\(825\) | 0.000542924 0 | 1.89022e−5 0 | ||||||||
\(826\) | −1.21857 | −0.0423996 | ||||||||
\(827\) | 1.31666 | 0.0457848 | 0.0228924 | − | 0.999738i | \(-0.492712\pi\) | ||||
0.0228924 | + | 0.999738i | \(0.492712\pi\) | |||||||
\(828\) | −54.6871 | −1.90051 | ||||||||
\(829\) | 20.6743 | 0.718049 | 0.359025 | − | 0.933328i | \(-0.383109\pi\) | ||||
0.359025 | + | 0.933328i | \(0.383109\pi\) | |||||||
\(830\) | −9.18048 | −0.318659 | ||||||||
\(831\) | −0.0465815 | −0.00161590 | ||||||||
\(832\) | −47.9918 | −1.66381 | ||||||||
\(833\) | −6.99564 | −0.242385 | ||||||||
\(834\) | −0.0931903 | −0.00322692 | ||||||||
\(835\) | −6.98534 | −0.241738 | ||||||||
\(836\) | −11.2861 | −0.390339 | ||||||||
\(837\) | 0.0462120 | 0.00159732 | ||||||||
\(838\) | 43.9166 | 1.51707 | ||||||||
\(839\) | −4.26481 | −0.147238 | −0.0736189 | − | 0.997286i | \(-0.523455\pi\) | ||||
−0.0736189 | + | 0.997286i | \(0.523455\pi\) | |||||||
\(840\) | −0.000373732 0 | −1.28950e−5 0 | ||||||||
\(841\) | −24.2485 | −0.836154 | ||||||||
\(842\) | −59.5367 | −2.05177 | ||||||||
\(843\) | −0.0188146 | −0.000648011 0 | ||||||||
\(844\) | 71.1731 | 2.44988 | ||||||||
\(845\) | −6.65368 | −0.228894 | ||||||||
\(846\) | 50.7326 | 1.74422 | ||||||||
\(847\) | 0.627267 | 0.0215532 | ||||||||
\(848\) | −26.0305 | −0.893890 | ||||||||
\(849\) | 0.0373222 | 0.00128089 | ||||||||
\(850\) | 0.495812 | 0.0170062 | ||||||||
\(851\) | 12.0184 | 0.411987 | ||||||||
\(852\) | −0.0185994 | −0.000637203 0 | ||||||||
\(853\) | 13.4613 | 0.460908 | 0.230454 | − | 0.973083i | \(-0.425979\pi\) | ||||
0.230454 | + | 0.973083i | \(0.425979\pi\) | |||||||
\(854\) | −0.775282 | −0.0265296 | ||||||||
\(855\) | 23.0003 | 0.786593 | ||||||||
\(856\) | −18.6114 | −0.636123 | ||||||||
\(857\) | −32.8656 | −1.12267 | −0.561335 | − | 0.827589i | \(-0.689712\pi\) | ||||
−0.561335 | + | 0.827589i | \(0.689712\pi\) | |||||||
\(858\) | 0.0202934 | 0.000692804 0 | ||||||||
\(859\) | 48.3685 | 1.65031 | 0.825157 | − | 0.564904i | \(-0.191087\pi\) | ||||
0.825157 | + | 0.564904i | \(0.191087\pi\) | |||||||
\(860\) | −5.52434 | −0.188378 | ||||||||
\(861\) | 0.000121685 0 | 4.14701e−6 0 | ||||||||
\(862\) | −73.5678 | −2.50573 | ||||||||
\(863\) | 30.6660 | 1.04388 | 0.521942 | − | 0.852981i | \(-0.325208\pi\) | ||||
0.521942 | + | 0.852981i | \(0.325208\pi\) | |||||||
\(864\) | −0.0895829 | −0.00304767 | ||||||||
\(865\) | 10.3849 | 0.353096 | ||||||||
\(866\) | −18.3717 | −0.624296 | ||||||||
\(867\) | 0.00192410 | 6.53458e−5 0 | ||||||||
\(868\) | 0.694044 | 0.0235574 | ||||||||
\(869\) | 18.7850 | 0.637236 | ||||||||
\(870\) | 0.0197015 | 0.000667943 0 | ||||||||
\(871\) | 10.9296 | 0.370337 | ||||||||
\(872\) | −11.5159 | −0.389979 | ||||||||
\(873\) | 42.0173 | 1.42207 | ||||||||
\(874\) | −52.4090 | −1.77276 | ||||||||
\(875\) | −0.754113 | −0.0254937 | ||||||||
\(876\) | −0.0331763 | −0.00112092 | ||||||||
\(877\) | 30.8966 | 1.04330 | 0.521652 | − | 0.853159i | \(-0.325316\pi\) | ||||
0.521652 | + | 0.853159i | \(0.325316\pi\) | |||||||
\(878\) | 30.1467 | 1.01740 | ||||||||
\(879\) | −0.0114025 | −0.000384597 0 | ||||||||
\(880\) | −6.29556 | −0.212223 | ||||||||
\(881\) | 21.6270 | 0.728631 | 0.364315 | − | 0.931276i | \(-0.381303\pi\) | ||||
0.364315 | + | 0.931276i | \(0.381303\pi\) | |||||||
\(882\) | −45.1407 | −1.51996 | ||||||||
\(883\) | 12.8697 | 0.433098 | 0.216549 | − | 0.976272i | \(-0.430520\pi\) | ||||
0.216549 | + | 0.976272i | \(0.430520\pi\) | |||||||
\(884\) | 10.5207 | 0.353851 | ||||||||
\(885\) | 0.0360611 | 0.00121218 | ||||||||
\(886\) | 36.0027 | 1.20953 | ||||||||
\(887\) | 2.89962 | 0.0973598 | 0.0486799 | − | 0.998814i | \(-0.484499\pi\) | ||||
0.0486799 | + | 0.998814i | \(0.484499\pi\) | |||||||
\(888\) | −0.00448856 | −0.000150626 0 | ||||||||
\(889\) | 0.679944 | 0.0228046 | ||||||||
\(890\) | 12.4801 | 0.418334 | ||||||||
\(891\) | −11.0168 | −0.369077 | ||||||||
\(892\) | −10.2314 | −0.342571 | ||||||||
\(893\) | 27.6009 | 0.923629 | ||||||||
\(894\) | 0.0479464 | 0.00160357 | ||||||||
\(895\) | 30.5823 | 1.02225 | ||||||||
\(896\) | −0.676628 | −0.0226046 | ||||||||
\(897\) | 0.0534970 | 0.00178621 | ||||||||
\(898\) | −52.7145 | −1.75911 | ||||||||
\(899\) | −8.72556 | −0.291014 | ||||||||
\(900\) | 1.81623 | 0.0605411 | ||||||||
\(901\) | 11.0535 | 0.368244 | ||||||||
\(902\) | −2.52225 | −0.0839817 | ||||||||
\(903\) | −0.000122342 0 | −4.07127e−6 0 | ||||||||
\(904\) | 3.58582 | 0.119263 | ||||||||
\(905\) | −4.02595 | −0.133827 | ||||||||
\(906\) | 0.0514511 | 0.00170935 | ||||||||
\(907\) | −12.8277 | −0.425937 | −0.212969 | − | 0.977059i | \(-0.568313\pi\) | ||||
−0.212969 | + | 0.977059i | \(0.568313\pi\) | |||||||
\(908\) | 51.7870 | 1.71861 | ||||||||
\(909\) | 3.14231 | 0.104224 | ||||||||
\(910\) | −1.24224 | −0.0411797 | ||||||||
\(911\) | 33.5315 | 1.11095 | 0.555474 | − | 0.831534i | \(-0.312537\pi\) | ||||
0.555474 | + | 0.831534i | \(0.312537\pi\) | |||||||
\(912\) | −0.0159070 | −0.000526732 0 | ||||||||
\(913\) | 2.39235 | 0.0791753 | ||||||||
\(914\) | −63.1433 | −2.08859 | ||||||||
\(915\) | 0.0229428 | 0.000758466 0 | ||||||||
\(916\) | −43.5678 | −1.43952 | ||||||||
\(917\) | −0.196629 | −0.00649327 | ||||||||
\(918\) | 0.0248312 | 0.000819551 0 | ||||||||
\(919\) | 15.3195 | 0.505344 | 0.252672 | − | 0.967552i | \(-0.418691\pi\) | ||||
0.252672 | + | 0.967552i | \(0.418691\pi\) | |||||||
\(920\) | 20.4215 | 0.673277 | ||||||||
\(921\) | 0.0539003 | 0.00177608 | ||||||||
\(922\) | −16.8358 | −0.554458 | ||||||||
\(923\) | −14.7438 | −0.485298 | ||||||||
\(924\) | 0.000408368 0 | 1.34343e−5 0 | ||||||||
\(925\) | −0.399149 | −0.0131239 | ||||||||
\(926\) | 43.2558 | 1.42147 | ||||||||
\(927\) | 5.89951 | 0.193765 | ||||||||
\(928\) | 16.9147 | 0.555251 | ||||||||
\(929\) | −41.9901 | −1.37765 | −0.688825 | − | 0.724928i | \(-0.741873\pi\) | ||||
−0.688825 | + | 0.724928i | \(0.741873\pi\) | |||||||
\(930\) | −0.0361792 | −0.00118636 | ||||||||
\(931\) | −24.5586 | −0.804876 | ||||||||
\(932\) | −55.9640 | −1.83316 | ||||||||
\(933\) | −0.0330475 | −0.00108193 | ||||||||
\(934\) | 84.8054 | 2.77492 | ||||||||
\(935\) | 2.67332 | 0.0874269 | ||||||||
\(936\) | 16.1903 | 0.529197 | ||||||||
\(937\) | 47.7920 | 1.56130 | 0.780648 | − | 0.624971i | \(-0.214889\pi\) | ||||
0.780648 | + | 0.624971i | \(0.214889\pi\) | |||||||
\(938\) | 0.387426 | 0.0126499 | ||||||||
\(939\) | 0.00187075 | 6.10496e−5 0 | ||||||||
\(940\) | −45.0958 | −1.47086 | ||||||||
\(941\) | −11.4752 | −0.374082 | −0.187041 | − | 0.982352i | \(-0.559890\pi\) | ||||
−0.187041 | + | 0.982352i | \(0.559890\pi\) | |||||||
\(942\) | −0.0116198 | −0.000378594 0 | ||||||||
\(943\) | −6.64911 | −0.216525 | ||||||||
\(944\) | 20.2097 | 0.657770 | ||||||||
\(945\) | −0.00166445 | −5.41445e−5 0 | ||||||||
\(946\) | 2.53586 | 0.0824479 | ||||||||
\(947\) | −1.57913 | −0.0513148 | −0.0256574 | − | 0.999671i | \(-0.508168\pi\) | ||||
−0.0256574 | + | 0.999671i | \(0.508168\pi\) | |||||||
\(948\) | −0.0775489 | −0.00251867 | ||||||||
\(949\) | −26.2990 | −0.853702 | ||||||||
\(950\) | 1.74058 | 0.0564718 | ||||||||
\(951\) | 0.00405779 | 0.000131583 0 | ||||||||
\(952\) | 0.0889402 | 0.00288257 | ||||||||
\(953\) | 6.81875 | 0.220881 | 0.110440 | − | 0.993883i | \(-0.464774\pi\) | ||||
0.110440 | + | 0.993883i | \(0.464774\pi\) | |||||||
\(954\) | 71.3245 | 2.30921 | ||||||||
\(955\) | 2.24080 | 0.0725105 | ||||||||
\(956\) | −65.9921 | −2.13434 | ||||||||
\(957\) | −0.00513403 | −0.000165960 0 | ||||||||
\(958\) | 22.1343 | 0.715127 | ||||||||
\(959\) | −1.19405 | −0.0385579 | ||||||||
\(960\) | 0.0503427 | 0.00162481 | ||||||||
\(961\) | −14.9766 | −0.483117 | ||||||||
\(962\) | −14.9194 | −0.481019 | ||||||||
\(963\) | −41.4435 | −1.33550 | ||||||||
\(964\) | 70.0100 | 2.25487 | ||||||||
\(965\) | −39.4612 | −1.27030 | ||||||||
\(966\) | 0.00189633 | 6.10133e−5 0 | ||||||||
\(967\) | −44.4238 | −1.42857 | −0.714286 | − | 0.699854i | \(-0.753249\pi\) | ||||
−0.714286 | + | 0.699854i | \(0.753249\pi\) | |||||||
\(968\) | 12.8008 | 0.411434 | ||||||||
\(969\) | 0.00675466 | 0.000216991 0 | ||||||||
\(970\) | −65.7905 | −2.11240 | ||||||||
\(971\) | 15.3517 | 0.492660 | 0.246330 | − | 0.969186i | \(-0.420775\pi\) | ||||
0.246330 | + | 0.969186i | \(0.420775\pi\) | |||||||
\(972\) | 0.136441 | 0.00437634 | ||||||||
\(973\) | −1.48655 | −0.0476567 | ||||||||
\(974\) | 10.9664 | 0.351385 | ||||||||
\(975\) | −0.00177671 | −5.69003e−5 0 | ||||||||
\(976\) | 12.8578 | 0.411569 | ||||||||
\(977\) | −46.0827 | −1.47432 | −0.737158 | − | 0.675720i | \(-0.763833\pi\) | ||||
−0.737158 | + | 0.675720i | \(0.763833\pi\) | |||||||
\(978\) | 0.0469217 | 0.00150039 | ||||||||
\(979\) | −3.25220 | −0.103941 | ||||||||
\(980\) | 40.1252 | 1.28175 | ||||||||
\(981\) | −25.6435 | −0.818736 | ||||||||
\(982\) | −61.2380 | −1.95418 | ||||||||
\(983\) | −34.8750 | −1.11234 | −0.556170 | − | 0.831069i | \(-0.687730\pi\) | ||||
−0.556170 | + | 0.831069i | \(0.687730\pi\) | |||||||
\(984\) | 0.00248326 | 7.91634e−5 0 | ||||||||
\(985\) | −49.7236 | −1.58433 | ||||||||
\(986\) | −4.68852 | −0.149313 | ||||||||
\(987\) | −0.000998688 0 | −3.17886e−5 0 | ||||||||
\(988\) | 36.9337 | 1.17502 | ||||||||
\(989\) | 6.68499 | 0.212570 | ||||||||
\(990\) | 17.2501 | 0.548244 | ||||||||
\(991\) | −7.12912 | −0.226464 | −0.113232 | − | 0.993569i | \(-0.536120\pi\) | ||||
−0.113232 | + | 0.993569i | \(0.536120\pi\) | |||||||
\(992\) | −31.0616 | −0.986207 | ||||||||
\(993\) | −0.0362069 | −0.00114899 | ||||||||
\(994\) | −0.522628 | −0.0165768 | ||||||||
\(995\) | 2.05446 | 0.0651308 | ||||||||
\(996\) | −0.00987622 | −0.000312940 0 | ||||||||
\(997\) | 48.2534 | 1.52820 | 0.764101 | − | 0.645097i | \(-0.223183\pi\) | ||||
0.764101 | + | 0.645097i | \(0.223183\pi\) | |||||||
\(998\) | 34.4486 | 1.09045 | ||||||||
\(999\) | −0.0199901 | −0.000632460 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6001.2.a.d.1.17 | ✓ | 121 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.d.1.17 | ✓ | 121 | 1.1 | even | 1 | trivial |