Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.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: | \(32.0759064919\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.491539 | −0.347571 | −0.173785 | − | 0.984784i | \(-0.555600\pi\) | ||||
−0.173785 | + | 0.984784i | \(0.555600\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.75839 | −0.879195 | ||||||||
\(5\) | −1.95668 | −0.875053 | −0.437526 | − | 0.899206i | \(-0.644145\pi\) | ||||
−0.437526 | + | 0.899206i | \(0.644145\pi\) | |||||||
\(6\) | 0.491539 | 0.200670 | ||||||||
\(7\) | −2.76715 | −1.04589 | −0.522943 | − | 0.852368i | \(-0.675166\pi\) | ||||
−0.522943 | + | 0.852368i | \(0.675166\pi\) | |||||||
\(8\) | 1.84740 | 0.653153 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.961784 | 0.304143 | ||||||||
\(11\) | 0.480495 | 0.144875 | 0.0724373 | − | 0.997373i | \(-0.476922\pi\) | ||||
0.0724373 | + | 0.997373i | \(0.476922\pi\) | |||||||
\(12\) | 1.75839 | 0.507603 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 1.36017 | 0.363519 | ||||||||
\(15\) | 1.95668 | 0.505212 | ||||||||
\(16\) | 2.60871 | 0.652178 | ||||||||
\(17\) | −2.47905 | −0.601258 | −0.300629 | − | 0.953741i | \(-0.597197\pi\) | ||||
−0.300629 | + | 0.953741i | \(0.597197\pi\) | |||||||
\(18\) | −0.491539 | −0.115857 | ||||||||
\(19\) | −0.387464 | −0.0888904 | −0.0444452 | − | 0.999012i | \(-0.514152\pi\) | ||||
−0.0444452 | + | 0.999012i | \(0.514152\pi\) | |||||||
\(20\) | 3.44060 | 0.769342 | ||||||||
\(21\) | 2.76715 | 0.603843 | ||||||||
\(22\) | −0.236182 | −0.0503542 | ||||||||
\(23\) | −2.25159 | −0.469490 | −0.234745 | − | 0.972057i | \(-0.575425\pi\) | ||||
−0.234745 | + | 0.972057i | \(0.575425\pi\) | |||||||
\(24\) | −1.84740 | −0.377098 | ||||||||
\(25\) | −1.17141 | −0.234283 | ||||||||
\(26\) | −0.491539 | −0.0963988 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.86573 | 0.919537 | ||||||||
\(29\) | −10.3692 | −1.92551 | −0.962757 | − | 0.270369i | \(-0.912854\pi\) | ||||
−0.962757 | + | 0.270369i | \(0.912854\pi\) | |||||||
\(30\) | −0.961784 | −0.175597 | ||||||||
\(31\) | −4.61906 | −0.829607 | −0.414804 | − | 0.909911i | \(-0.636150\pi\) | ||||
−0.414804 | + | 0.909911i | \(0.636150\pi\) | |||||||
\(32\) | −4.97708 | −0.879831 | ||||||||
\(33\) | −0.480495 | −0.0836434 | ||||||||
\(34\) | 1.21855 | 0.208980 | ||||||||
\(35\) | 5.41443 | 0.915205 | ||||||||
\(36\) | −1.75839 | −0.293065 | ||||||||
\(37\) | −8.05406 | −1.32408 | −0.662039 | − | 0.749469i | \(-0.730309\pi\) | ||||
−0.662039 | + | 0.749469i | \(0.730309\pi\) | |||||||
\(38\) | 0.190454 | 0.0308957 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −3.61476 | −0.571543 | ||||||||
\(41\) | 11.4803 | 1.79293 | 0.896463 | − | 0.443118i | \(-0.146128\pi\) | ||||
0.896463 | + | 0.443118i | \(0.146128\pi\) | |||||||
\(42\) | −1.36017 | −0.209878 | ||||||||
\(43\) | 0.735128 | 0.112106 | 0.0560530 | − | 0.998428i | \(-0.482148\pi\) | ||||
0.0560530 | + | 0.998428i | \(0.482148\pi\) | |||||||
\(44\) | −0.844897 | −0.127373 | ||||||||
\(45\) | −1.95668 | −0.291684 | ||||||||
\(46\) | 1.10675 | 0.163181 | ||||||||
\(47\) | 6.95910 | 1.01509 | 0.507544 | − | 0.861626i | \(-0.330553\pi\) | ||||
0.507544 | + | 0.861626i | \(0.330553\pi\) | |||||||
\(48\) | −2.60871 | −0.376535 | ||||||||
\(49\) | 0.657144 | 0.0938777 | ||||||||
\(50\) | 0.575796 | 0.0814299 | ||||||||
\(51\) | 2.47905 | 0.347136 | ||||||||
\(52\) | −1.75839 | −0.243845 | ||||||||
\(53\) | −4.35675 | −0.598446 | −0.299223 | − | 0.954183i | \(-0.596727\pi\) | ||||
−0.299223 | + | 0.954183i | \(0.596727\pi\) | |||||||
\(54\) | 0.491539 | 0.0668900 | ||||||||
\(55\) | −0.940173 | −0.126773 | ||||||||
\(56\) | −5.11203 | −0.683124 | ||||||||
\(57\) | 0.387464 | 0.0513209 | ||||||||
\(58\) | 5.09687 | 0.669252 | ||||||||
\(59\) | −13.8126 | −1.79824 | −0.899122 | − | 0.437697i | \(-0.855794\pi\) | ||||
−0.899122 | + | 0.437697i | \(0.855794\pi\) | |||||||
\(60\) | −3.44060 | −0.444180 | ||||||||
\(61\) | −5.00479 | −0.640797 | −0.320399 | − | 0.947283i | \(-0.603817\pi\) | ||||
−0.320399 | + | 0.947283i | \(0.603817\pi\) | |||||||
\(62\) | 2.27045 | 0.288347 | ||||||||
\(63\) | −2.76715 | −0.348629 | ||||||||
\(64\) | −2.77099 | −0.346374 | ||||||||
\(65\) | −1.95668 | −0.242696 | ||||||||
\(66\) | 0.236182 | 0.0290720 | ||||||||
\(67\) | −6.94438 | −0.848391 | −0.424196 | − | 0.905571i | \(-0.639443\pi\) | ||||
−0.424196 | + | 0.905571i | \(0.639443\pi\) | |||||||
\(68\) | 4.35913 | 0.528623 | ||||||||
\(69\) | 2.25159 | 0.271060 | ||||||||
\(70\) | −2.66140 | −0.318099 | ||||||||
\(71\) | −6.52869 | −0.774813 | −0.387406 | − | 0.921909i | \(-0.626629\pi\) | ||||
−0.387406 | + | 0.921909i | \(0.626629\pi\) | |||||||
\(72\) | 1.84740 | 0.217718 | ||||||||
\(73\) | −4.41024 | −0.516180 | −0.258090 | − | 0.966121i | \(-0.583093\pi\) | ||||
−0.258090 | + | 0.966121i | \(0.583093\pi\) | |||||||
\(74\) | 3.95888 | 0.460211 | ||||||||
\(75\) | 1.17141 | 0.135263 | ||||||||
\(76\) | 0.681313 | 0.0781520 | ||||||||
\(77\) | −1.32960 | −0.151522 | ||||||||
\(78\) | 0.491539 | 0.0556559 | ||||||||
\(79\) | 1.22535 | 0.137862 | 0.0689311 | − | 0.997621i | \(-0.478041\pi\) | ||||
0.0689311 | + | 0.997621i | \(0.478041\pi\) | |||||||
\(80\) | −5.10440 | −0.570690 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.64303 | −0.623169 | ||||||||
\(83\) | −14.8793 | −1.63321 | −0.816605 | − | 0.577197i | \(-0.804146\pi\) | ||||
−0.816605 | + | 0.577197i | \(0.804146\pi\) | |||||||
\(84\) | −4.86573 | −0.530895 | ||||||||
\(85\) | 4.85070 | 0.526132 | ||||||||
\(86\) | −0.361344 | −0.0389647 | ||||||||
\(87\) | 10.3692 | 1.11170 | ||||||||
\(88\) | 0.887664 | 0.0946253 | ||||||||
\(89\) | −9.52671 | −1.00983 | −0.504915 | − | 0.863169i | \(-0.668476\pi\) | ||||
−0.504915 | + | 0.863169i | \(0.668476\pi\) | |||||||
\(90\) | 0.961784 | 0.101381 | ||||||||
\(91\) | −2.76715 | −0.290077 | ||||||||
\(92\) | 3.95918 | 0.412773 | ||||||||
\(93\) | 4.61906 | 0.478974 | ||||||||
\(94\) | −3.42067 | −0.352815 | ||||||||
\(95\) | 0.758143 | 0.0777838 | ||||||||
\(96\) | 4.97708 | 0.507971 | ||||||||
\(97\) | 8.28494 | 0.841208 | 0.420604 | − | 0.907244i | \(-0.361818\pi\) | ||||
0.420604 | + | 0.907244i | \(0.361818\pi\) | |||||||
\(98\) | −0.323012 | −0.0326291 | ||||||||
\(99\) | 0.480495 | 0.0482915 | ||||||||
\(100\) | 2.05980 | 0.205980 | ||||||||
\(101\) | 10.1155 | 1.00653 | 0.503265 | − | 0.864132i | \(-0.332132\pi\) | ||||
0.503265 | + | 0.864132i | \(0.332132\pi\) | |||||||
\(102\) | −1.21855 | −0.120654 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 1.84740 | 0.181152 | ||||||||
\(105\) | −5.41443 | −0.528394 | ||||||||
\(106\) | 2.14152 | 0.208002 | ||||||||
\(107\) | −6.81812 | −0.659132 | −0.329566 | − | 0.944133i | \(-0.606902\pi\) | ||||
−0.329566 | + | 0.944133i | \(0.606902\pi\) | |||||||
\(108\) | 1.75839 | 0.169201 | ||||||||
\(109\) | −5.37639 | −0.514965 | −0.257482 | − | 0.966283i | \(-0.582893\pi\) | ||||
−0.257482 | + | 0.966283i | \(0.582893\pi\) | |||||||
\(110\) | 0.462132 | 0.0440626 | ||||||||
\(111\) | 8.05406 | 0.764457 | ||||||||
\(112\) | −7.21871 | −0.682104 | ||||||||
\(113\) | 3.35708 | 0.315807 | 0.157904 | − | 0.987455i | \(-0.449526\pi\) | ||||
0.157904 | + | 0.987455i | \(0.449526\pi\) | |||||||
\(114\) | −0.190454 | −0.0178376 | ||||||||
\(115\) | 4.40564 | 0.410828 | ||||||||
\(116\) | 18.2331 | 1.69290 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 6.78943 | 0.625017 | ||||||||
\(119\) | 6.85991 | 0.628847 | ||||||||
\(120\) | 3.61476 | 0.329981 | ||||||||
\(121\) | −10.7691 | −0.979011 | ||||||||
\(122\) | 2.46005 | 0.222722 | ||||||||
\(123\) | −11.4803 | −1.03515 | ||||||||
\(124\) | 8.12210 | 0.729386 | ||||||||
\(125\) | 12.0755 | 1.08006 | ||||||||
\(126\) | 1.36017 | 0.121173 | ||||||||
\(127\) | 16.7237 | 1.48399 | 0.741995 | − | 0.670405i | \(-0.233880\pi\) | ||||
0.741995 | + | 0.670405i | \(0.233880\pi\) | |||||||
\(128\) | 11.3162 | 1.00022 | ||||||||
\(129\) | −0.735128 | −0.0647244 | ||||||||
\(130\) | 0.961784 | 0.0843540 | ||||||||
\(131\) | 10.0919 | 0.881736 | 0.440868 | − | 0.897572i | \(-0.354671\pi\) | ||||
0.440868 | + | 0.897572i | \(0.354671\pi\) | |||||||
\(132\) | 0.844897 | 0.0735388 | ||||||||
\(133\) | 1.07217 | 0.0929692 | ||||||||
\(134\) | 3.41344 | 0.294876 | ||||||||
\(135\) | 1.95668 | 0.168404 | ||||||||
\(136\) | −4.57979 | −0.392713 | ||||||||
\(137\) | 3.29098 | 0.281168 | 0.140584 | − | 0.990069i | \(-0.455102\pi\) | ||||
0.140584 | + | 0.990069i | \(0.455102\pi\) | |||||||
\(138\) | −1.10675 | −0.0942125 | ||||||||
\(139\) | 10.0889 | 0.855726 | 0.427863 | − | 0.903844i | \(-0.359267\pi\) | ||||
0.427863 | + | 0.903844i | \(0.359267\pi\) | |||||||
\(140\) | −9.52067 | −0.804644 | ||||||||
\(141\) | −6.95910 | −0.586062 | ||||||||
\(142\) | 3.20911 | 0.269302 | ||||||||
\(143\) | 0.480495 | 0.0401810 | ||||||||
\(144\) | 2.60871 | 0.217393 | ||||||||
\(145\) | 20.2892 | 1.68493 | ||||||||
\(146\) | 2.16781 | 0.179409 | ||||||||
\(147\) | −0.657144 | −0.0542003 | ||||||||
\(148\) | 14.1622 | 1.16412 | ||||||||
\(149\) | −15.3939 | −1.26112 | −0.630558 | − | 0.776142i | \(-0.717174\pi\) | ||||
−0.630558 | + | 0.776142i | \(0.717174\pi\) | |||||||
\(150\) | −0.575796 | −0.0470136 | ||||||||
\(151\) | 16.5159 | 1.34405 | 0.672023 | − | 0.740530i | \(-0.265426\pi\) | ||||
0.672023 | + | 0.740530i | \(0.265426\pi\) | |||||||
\(152\) | −0.715800 | −0.0580590 | ||||||||
\(153\) | −2.47905 | −0.200419 | ||||||||
\(154\) | 0.653552 | 0.0526647 | ||||||||
\(155\) | 9.03801 | 0.725950 | ||||||||
\(156\) | 1.75839 | 0.140784 | ||||||||
\(157\) | 20.8104 | 1.66085 | 0.830425 | − | 0.557130i | \(-0.188098\pi\) | ||||
0.830425 | + | 0.557130i | \(0.188098\pi\) | |||||||
\(158\) | −0.602306 | −0.0479169 | ||||||||
\(159\) | 4.35675 | 0.345513 | ||||||||
\(160\) | 9.73853 | 0.769898 | ||||||||
\(161\) | 6.23051 | 0.491033 | ||||||||
\(162\) | −0.491539 | −0.0386190 | ||||||||
\(163\) | −17.6077 | −1.37914 | −0.689572 | − | 0.724217i | \(-0.742201\pi\) | ||||
−0.689572 | + | 0.724217i | \(0.742201\pi\) | |||||||
\(164\) | −20.1869 | −1.57633 | ||||||||
\(165\) | 0.940173 | 0.0731924 | ||||||||
\(166\) | 7.31374 | 0.567656 | ||||||||
\(167\) | 12.4143 | 0.960647 | 0.480324 | − | 0.877091i | \(-0.340519\pi\) | ||||
0.480324 | + | 0.877091i | \(0.340519\pi\) | |||||||
\(168\) | 5.11203 | 0.394402 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −2.38431 | −0.182868 | ||||||||
\(171\) | −0.387464 | −0.0296301 | ||||||||
\(172\) | −1.29264 | −0.0985629 | ||||||||
\(173\) | −0.962096 | −0.0731468 | −0.0365734 | − | 0.999331i | \(-0.511644\pi\) | ||||
−0.0365734 | + | 0.999331i | \(0.511644\pi\) | |||||||
\(174\) | −5.09687 | −0.386393 | ||||||||
\(175\) | 3.24148 | 0.245033 | ||||||||
\(176\) | 1.25347 | 0.0944840 | ||||||||
\(177\) | 13.8126 | 1.03822 | ||||||||
\(178\) | 4.68275 | 0.350987 | ||||||||
\(179\) | −16.7816 | −1.25431 | −0.627157 | − | 0.778893i | \(-0.715782\pi\) | ||||
−0.627157 | + | 0.778893i | \(0.715782\pi\) | |||||||
\(180\) | 3.44060 | 0.256447 | ||||||||
\(181\) | −16.9505 | −1.25992 | −0.629960 | − | 0.776627i | \(-0.716929\pi\) | ||||
−0.629960 | + | 0.776627i | \(0.716929\pi\) | |||||||
\(182\) | 1.36017 | 0.100822 | ||||||||
\(183\) | 5.00479 | 0.369965 | ||||||||
\(184\) | −4.15958 | −0.306649 | ||||||||
\(185\) | 15.7592 | 1.15864 | ||||||||
\(186\) | −2.27045 | −0.166477 | ||||||||
\(187\) | −1.19117 | −0.0871070 | ||||||||
\(188\) | −12.2368 | −0.892460 | ||||||||
\(189\) | 2.76715 | 0.201281 | ||||||||
\(190\) | −0.372657 | −0.0270354 | ||||||||
\(191\) | −7.04770 | −0.509953 | −0.254977 | − | 0.966947i | \(-0.582068\pi\) | ||||
−0.254977 | + | 0.966947i | \(0.582068\pi\) | |||||||
\(192\) | 2.77099 | 0.199979 | ||||||||
\(193\) | 6.44544 | 0.463953 | 0.231977 | − | 0.972721i | \(-0.425481\pi\) | ||||
0.231977 | + | 0.972721i | \(0.425481\pi\) | |||||||
\(194\) | −4.07237 | −0.292379 | ||||||||
\(195\) | 1.95668 | 0.140121 | ||||||||
\(196\) | −1.15551 | −0.0825368 | ||||||||
\(197\) | 25.7287 | 1.83309 | 0.916547 | − | 0.399927i | \(-0.130965\pi\) | ||||
0.916547 | + | 0.399927i | \(0.130965\pi\) | |||||||
\(198\) | −0.236182 | −0.0167847 | ||||||||
\(199\) | −19.2453 | −1.36427 | −0.682133 | − | 0.731228i | \(-0.738947\pi\) | ||||
−0.682133 | + | 0.731228i | \(0.738947\pi\) | |||||||
\(200\) | −2.16407 | −0.153023 | ||||||||
\(201\) | 6.94438 | 0.489819 | ||||||||
\(202\) | −4.97216 | −0.349840 | ||||||||
\(203\) | 28.6932 | 2.01387 | ||||||||
\(204\) | −4.35913 | −0.305200 | ||||||||
\(205\) | −22.4633 | −1.56891 | ||||||||
\(206\) | 0.491539 | 0.0342472 | ||||||||
\(207\) | −2.25159 | −0.156497 | ||||||||
\(208\) | 2.60871 | 0.180882 | ||||||||
\(209\) | −0.186175 | −0.0128780 | ||||||||
\(210\) | 2.66140 | 0.183654 | ||||||||
\(211\) | 16.2268 | 1.11710 | 0.558548 | − | 0.829472i | \(-0.311359\pi\) | ||||
0.558548 | + | 0.829472i | \(0.311359\pi\) | |||||||
\(212\) | 7.66087 | 0.526151 | ||||||||
\(213\) | 6.52869 | 0.447338 | ||||||||
\(214\) | 3.35137 | 0.229095 | ||||||||
\(215\) | −1.43841 | −0.0980986 | ||||||||
\(216\) | −1.84740 | −0.125699 | ||||||||
\(217\) | 12.7816 | 0.867675 | ||||||||
\(218\) | 2.64271 | 0.178987 | ||||||||
\(219\) | 4.41024 | 0.298016 | ||||||||
\(220\) | 1.65319 | 0.111458 | ||||||||
\(221\) | −2.47905 | −0.166759 | ||||||||
\(222\) | −3.95888 | −0.265703 | ||||||||
\(223\) | −21.9279 | −1.46840 | −0.734201 | − | 0.678932i | \(-0.762443\pi\) | ||||
−0.734201 | + | 0.678932i | \(0.762443\pi\) | |||||||
\(224\) | 13.7723 | 0.920203 | ||||||||
\(225\) | −1.17141 | −0.0780943 | ||||||||
\(226\) | −1.65013 | −0.109765 | ||||||||
\(227\) | 15.2201 | 1.01019 | 0.505096 | − | 0.863063i | \(-0.331457\pi\) | ||||
0.505096 | + | 0.863063i | \(0.331457\pi\) | |||||||
\(228\) | −0.681313 | −0.0451211 | ||||||||
\(229\) | −10.1190 | −0.668683 | −0.334342 | − | 0.942452i | \(-0.608514\pi\) | ||||
−0.334342 | + | 0.942452i | \(0.608514\pi\) | |||||||
\(230\) | −2.16555 | −0.142792 | ||||||||
\(231\) | 1.32960 | 0.0874815 | ||||||||
\(232\) | −19.1560 | −1.25765 | ||||||||
\(233\) | −9.06953 | −0.594165 | −0.297082 | − | 0.954852i | \(-0.596014\pi\) | ||||
−0.297082 | + | 0.954852i | \(0.596014\pi\) | |||||||
\(234\) | −0.491539 | −0.0321329 | ||||||||
\(235\) | −13.6167 | −0.888256 | ||||||||
\(236\) | 24.2879 | 1.58101 | ||||||||
\(237\) | −1.22535 | −0.0795948 | ||||||||
\(238\) | −3.37192 | −0.218569 | ||||||||
\(239\) | 25.2699 | 1.63458 | 0.817288 | − | 0.576229i | \(-0.195476\pi\) | ||||
0.817288 | + | 0.576229i | \(0.195476\pi\) | |||||||
\(240\) | 5.10440 | 0.329488 | ||||||||
\(241\) | −18.6914 | −1.20402 | −0.602009 | − | 0.798490i | \(-0.705633\pi\) | ||||
−0.602009 | + | 0.798490i | \(0.705633\pi\) | |||||||
\(242\) | 5.29345 | 0.340276 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 8.80036 | 0.563386 | ||||||||
\(245\) | −1.28582 | −0.0821479 | ||||||||
\(246\) | 5.64303 | 0.359787 | ||||||||
\(247\) | −0.387464 | −0.0246538 | ||||||||
\(248\) | −8.53323 | −0.541861 | ||||||||
\(249\) | 14.8793 | 0.942934 | ||||||||
\(250\) | −5.93557 | −0.375398 | ||||||||
\(251\) | 17.3227 | 1.09340 | 0.546698 | − | 0.837330i | \(-0.315884\pi\) | ||||
0.546698 | + | 0.837330i | \(0.315884\pi\) | |||||||
\(252\) | 4.86573 | 0.306512 | ||||||||
\(253\) | −1.08188 | −0.0680171 | ||||||||
\(254\) | −8.22037 | −0.515792 | ||||||||
\(255\) | −4.85070 | −0.303763 | ||||||||
\(256\) | −0.0203706 | −0.00127316 | ||||||||
\(257\) | 2.03321 | 0.126828 | 0.0634141 | − | 0.997987i | \(-0.479801\pi\) | ||||
0.0634141 | + | 0.997987i | \(0.479801\pi\) | |||||||
\(258\) | 0.361344 | 0.0224963 | ||||||||
\(259\) | 22.2868 | 1.38484 | ||||||||
\(260\) | 3.44060 | 0.213377 | ||||||||
\(261\) | −10.3692 | −0.641838 | ||||||||
\(262\) | −4.96058 | −0.306466 | ||||||||
\(263\) | 13.7493 | 0.847819 | 0.423909 | − | 0.905705i | \(-0.360657\pi\) | ||||
0.423909 | + | 0.905705i | \(0.360657\pi\) | |||||||
\(264\) | −0.887664 | −0.0546319 | ||||||||
\(265\) | 8.52476 | 0.523672 | ||||||||
\(266\) | −0.527015 | −0.0323134 | ||||||||
\(267\) | 9.52671 | 0.583025 | ||||||||
\(268\) | 12.2109 | 0.745901 | ||||||||
\(269\) | 24.6331 | 1.50191 | 0.750954 | − | 0.660355i | \(-0.229594\pi\) | ||||
0.750954 | + | 0.660355i | \(0.229594\pi\) | |||||||
\(270\) | −0.961784 | −0.0585323 | ||||||||
\(271\) | 15.7442 | 0.956393 | 0.478196 | − | 0.878253i | \(-0.341291\pi\) | ||||
0.478196 | + | 0.878253i | \(0.341291\pi\) | |||||||
\(272\) | −6.46712 | −0.392127 | ||||||||
\(273\) | 2.76715 | 0.167476 | ||||||||
\(274\) | −1.61765 | −0.0977256 | ||||||||
\(275\) | −0.562858 | −0.0339416 | ||||||||
\(276\) | −3.95918 | −0.238315 | ||||||||
\(277\) | −4.02082 | −0.241587 | −0.120794 | − | 0.992678i | \(-0.538544\pi\) | ||||
−0.120794 | + | 0.992678i | \(0.538544\pi\) | |||||||
\(278\) | −4.95907 | −0.297425 | ||||||||
\(279\) | −4.61906 | −0.276536 | ||||||||
\(280\) | 10.0026 | 0.597769 | ||||||||
\(281\) | 18.1106 | 1.08039 | 0.540194 | − | 0.841541i | \(-0.318351\pi\) | ||||
0.540194 | + | 0.841541i | \(0.318351\pi\) | |||||||
\(282\) | 3.42067 | 0.203698 | ||||||||
\(283\) | −0.376343 | −0.0223713 | −0.0111856 | − | 0.999937i | \(-0.503561\pi\) | ||||
−0.0111856 | + | 0.999937i | \(0.503561\pi\) | |||||||
\(284\) | 11.4800 | 0.681211 | ||||||||
\(285\) | −0.758143 | −0.0449085 | ||||||||
\(286\) | −0.236182 | −0.0139657 | ||||||||
\(287\) | −31.7678 | −1.87520 | ||||||||
\(288\) | −4.97708 | −0.293277 | ||||||||
\(289\) | −10.8543 | −0.638489 | ||||||||
\(290\) | −9.97293 | −0.585631 | ||||||||
\(291\) | −8.28494 | −0.485672 | ||||||||
\(292\) | 7.75492 | 0.453822 | ||||||||
\(293\) | 21.4651 | 1.25400 | 0.627001 | − | 0.779018i | \(-0.284282\pi\) | ||||
0.627001 | + | 0.779018i | \(0.284282\pi\) | |||||||
\(294\) | 0.323012 | 0.0188384 | ||||||||
\(295\) | 27.0268 | 1.57356 | ||||||||
\(296\) | −14.8790 | −0.864826 | ||||||||
\(297\) | −0.480495 | −0.0278811 | ||||||||
\(298\) | 7.56669 | 0.438327 | ||||||||
\(299\) | −2.25159 | −0.130213 | ||||||||
\(300\) | −2.05980 | −0.118923 | ||||||||
\(301\) | −2.03421 | −0.117250 | ||||||||
\(302\) | −8.11822 | −0.467151 | ||||||||
\(303\) | −10.1155 | −0.581120 | ||||||||
\(304\) | −1.01078 | −0.0579723 | ||||||||
\(305\) | 9.79275 | 0.560731 | ||||||||
\(306\) | 1.21855 | 0.0696599 | ||||||||
\(307\) | −26.7164 | −1.52479 | −0.762394 | − | 0.647114i | \(-0.775976\pi\) | ||||
−0.762394 | + | 0.647114i | \(0.775976\pi\) | |||||||
\(308\) | 2.33796 | 0.133218 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −4.44253 | −0.252319 | ||||||||
\(311\) | 10.4602 | 0.593142 | 0.296571 | − | 0.955011i | \(-0.404157\pi\) | ||||
0.296571 | + | 0.955011i | \(0.404157\pi\) | |||||||
\(312\) | −1.84740 | −0.104588 | ||||||||
\(313\) | −11.1601 | −0.630806 | −0.315403 | − | 0.948958i | \(-0.602140\pi\) | ||||
−0.315403 | + | 0.948958i | \(0.602140\pi\) | |||||||
\(314\) | −10.2291 | −0.577263 | ||||||||
\(315\) | 5.41443 | 0.305068 | ||||||||
\(316\) | −2.15464 | −0.121208 | ||||||||
\(317\) | 27.1428 | 1.52449 | 0.762247 | − | 0.647287i | \(-0.224096\pi\) | ||||
0.762247 | + | 0.647287i | \(0.224096\pi\) | |||||||
\(318\) | −2.14152 | −0.120090 | ||||||||
\(319\) | −4.98235 | −0.278958 | ||||||||
\(320\) | 5.42194 | 0.303096 | ||||||||
\(321\) | 6.81812 | 0.380550 | ||||||||
\(322\) | −3.06254 | −0.170669 | ||||||||
\(323\) | 0.960543 | 0.0534460 | ||||||||
\(324\) | −1.75839 | −0.0976883 | ||||||||
\(325\) | −1.17141 | −0.0649784 | ||||||||
\(326\) | 8.65490 | 0.479350 | ||||||||
\(327\) | 5.37639 | 0.297315 | ||||||||
\(328\) | 21.2087 | 1.17106 | ||||||||
\(329\) | −19.2569 | −1.06167 | ||||||||
\(330\) | −0.462132 | −0.0254395 | ||||||||
\(331\) | −17.7149 | −0.973700 | −0.486850 | − | 0.873485i | \(-0.661854\pi\) | ||||
−0.486850 | + | 0.873485i | \(0.661854\pi\) | |||||||
\(332\) | 26.1635 | 1.43591 | ||||||||
\(333\) | −8.05406 | −0.441360 | ||||||||
\(334\) | −6.10211 | −0.333893 | ||||||||
\(335\) | 13.5879 | 0.742387 | ||||||||
\(336\) | 7.21871 | 0.393813 | ||||||||
\(337\) | −30.4798 | −1.66034 | −0.830171 | − | 0.557509i | \(-0.811757\pi\) | ||||
−0.830171 | + | 0.557509i | \(0.811757\pi\) | |||||||
\(338\) | −0.491539 | −0.0267362 | ||||||||
\(339\) | −3.35708 | −0.182331 | ||||||||
\(340\) | −8.52942 | −0.462573 | ||||||||
\(341\) | −2.21943 | −0.120189 | ||||||||
\(342\) | 0.190454 | 0.0102986 | ||||||||
\(343\) | 17.5517 | 0.947701 | ||||||||
\(344\) | 1.35807 | 0.0732223 | ||||||||
\(345\) | −4.40564 | −0.237192 | ||||||||
\(346\) | 0.472908 | 0.0254237 | ||||||||
\(347\) | −15.9376 | −0.855575 | −0.427788 | − | 0.903879i | \(-0.640707\pi\) | ||||
−0.427788 | + | 0.903879i | \(0.640707\pi\) | |||||||
\(348\) | −18.2331 | −0.977397 | ||||||||
\(349\) | −16.5775 | −0.887373 | −0.443687 | − | 0.896182i | \(-0.646330\pi\) | ||||
−0.443687 | + | 0.896182i | \(0.646330\pi\) | |||||||
\(350\) | −1.59332 | −0.0851664 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −2.39146 | −0.127465 | ||||||||
\(353\) | −12.3502 | −0.657333 | −0.328667 | − | 0.944446i | \(-0.606599\pi\) | ||||
−0.328667 | + | 0.944446i | \(0.606599\pi\) | |||||||
\(354\) | −6.78943 | −0.360854 | ||||||||
\(355\) | 12.7745 | 0.678002 | ||||||||
\(356\) | 16.7517 | 0.887837 | ||||||||
\(357\) | −6.85991 | −0.363065 | ||||||||
\(358\) | 8.24881 | 0.435963 | ||||||||
\(359\) | 8.07523 | 0.426195 | 0.213097 | − | 0.977031i | \(-0.431645\pi\) | ||||
0.213097 | + | 0.977031i | \(0.431645\pi\) | |||||||
\(360\) | −3.61476 | −0.190514 | ||||||||
\(361\) | −18.8499 | −0.992098 | ||||||||
\(362\) | 8.33184 | 0.437912 | ||||||||
\(363\) | 10.7691 | 0.565232 | ||||||||
\(364\) | 4.86573 | 0.255034 | ||||||||
\(365\) | 8.62942 | 0.451684 | ||||||||
\(366\) | −2.46005 | −0.128589 | ||||||||
\(367\) | 18.9159 | 0.987401 | 0.493701 | − | 0.869632i | \(-0.335644\pi\) | ||||
0.493701 | + | 0.869632i | \(0.335644\pi\) | |||||||
\(368\) | −5.87376 | −0.306191 | ||||||||
\(369\) | 11.4803 | 0.597642 | ||||||||
\(370\) | −7.74626 | −0.402709 | ||||||||
\(371\) | 12.0558 | 0.625906 | ||||||||
\(372\) | −8.12210 | −0.421111 | ||||||||
\(373\) | −10.8347 | −0.561001 | −0.280500 | − | 0.959854i | \(-0.590500\pi\) | ||||
−0.280500 | + | 0.959854i | \(0.590500\pi\) | |||||||
\(374\) | 0.585507 | 0.0302758 | ||||||||
\(375\) | −12.0755 | −0.623574 | ||||||||
\(376\) | 12.8562 | 0.663008 | ||||||||
\(377\) | −10.3692 | −0.534041 | ||||||||
\(378\) | −1.36017 | −0.0699593 | ||||||||
\(379\) | −17.4704 | −0.897396 | −0.448698 | − | 0.893683i | \(-0.648112\pi\) | ||||
−0.448698 | + | 0.893683i | \(0.648112\pi\) | |||||||
\(380\) | −1.33311 | −0.0683871 | ||||||||
\(381\) | −16.7237 | −0.856782 | ||||||||
\(382\) | 3.46422 | 0.177245 | ||||||||
\(383\) | −14.4202 | −0.736836 | −0.368418 | − | 0.929660i | \(-0.620100\pi\) | ||||
−0.368418 | + | 0.929660i | \(0.620100\pi\) | |||||||
\(384\) | −11.3162 | −0.577478 | ||||||||
\(385\) | 2.60160 | 0.132590 | ||||||||
\(386\) | −3.16819 | −0.161257 | ||||||||
\(387\) | 0.735128 | 0.0373686 | ||||||||
\(388\) | −14.5681 | −0.739586 | ||||||||
\(389\) | −29.3126 | −1.48621 | −0.743105 | − | 0.669175i | \(-0.766647\pi\) | ||||
−0.743105 | + | 0.669175i | \(0.766647\pi\) | |||||||
\(390\) | −0.961784 | −0.0487018 | ||||||||
\(391\) | 5.58181 | 0.282284 | ||||||||
\(392\) | 1.21400 | 0.0613165 | ||||||||
\(393\) | −10.0919 | −0.509070 | ||||||||
\(394\) | −12.6467 | −0.637130 | ||||||||
\(395\) | −2.39761 | −0.120637 | ||||||||
\(396\) | −0.844897 | −0.0424577 | ||||||||
\(397\) | 10.8183 | 0.542954 | 0.271477 | − | 0.962445i | \(-0.412488\pi\) | ||||
0.271477 | + | 0.962445i | \(0.412488\pi\) | |||||||
\(398\) | 9.45984 | 0.474179 | ||||||||
\(399\) | −1.07217 | −0.0536758 | ||||||||
\(400\) | −3.05588 | −0.152794 | ||||||||
\(401\) | 19.1319 | 0.955400 | 0.477700 | − | 0.878523i | \(-0.341471\pi\) | ||||
0.477700 | + | 0.878523i | \(0.341471\pi\) | |||||||
\(402\) | −3.41344 | −0.170247 | ||||||||
\(403\) | −4.61906 | −0.230092 | ||||||||
\(404\) | −17.7870 | −0.884935 | ||||||||
\(405\) | −1.95668 | −0.0972281 | ||||||||
\(406\) | −14.1038 | −0.699961 | ||||||||
\(407\) | −3.86993 | −0.191825 | ||||||||
\(408\) | 4.57979 | 0.226733 | ||||||||
\(409\) | −29.1543 | −1.44159 | −0.720793 | − | 0.693150i | \(-0.756222\pi\) | ||||
−0.720793 | + | 0.693150i | \(0.756222\pi\) | |||||||
\(410\) | 11.0416 | 0.545305 | ||||||||
\(411\) | −3.29098 | −0.162332 | ||||||||
\(412\) | 1.75839 | 0.0866296 | ||||||||
\(413\) | 38.2215 | 1.88076 | ||||||||
\(414\) | 1.10675 | 0.0543936 | ||||||||
\(415\) | 29.1139 | 1.42914 | ||||||||
\(416\) | −4.97708 | −0.244021 | ||||||||
\(417\) | −10.0889 | −0.494053 | ||||||||
\(418\) | 0.0915121 | 0.00447600 | ||||||||
\(419\) | 21.5025 | 1.05047 | 0.525233 | − | 0.850958i | \(-0.323978\pi\) | ||||
0.525233 | + | 0.850958i | \(0.323978\pi\) | |||||||
\(420\) | 9.52067 | 0.464561 | ||||||||
\(421\) | 22.1443 | 1.07925 | 0.539623 | − | 0.841907i | \(-0.318567\pi\) | ||||
0.539623 | + | 0.841907i | \(0.318567\pi\) | |||||||
\(422\) | −7.97609 | −0.388270 | ||||||||
\(423\) | 6.95910 | 0.338363 | ||||||||
\(424\) | −8.04865 | −0.390877 | ||||||||
\(425\) | 2.90399 | 0.140864 | ||||||||
\(426\) | −3.20911 | −0.155482 | ||||||||
\(427\) | 13.8490 | 0.670201 | ||||||||
\(428\) | 11.9889 | 0.579505 | ||||||||
\(429\) | −0.480495 | −0.0231985 | ||||||||
\(430\) | 0.707034 | 0.0340962 | ||||||||
\(431\) | 28.9147 | 1.39277 | 0.696386 | − | 0.717667i | \(-0.254790\pi\) | ||||
0.696386 | + | 0.717667i | \(0.254790\pi\) | |||||||
\(432\) | −2.60871 | −0.125512 | ||||||||
\(433\) | −14.9288 | −0.717432 | −0.358716 | − | 0.933447i | \(-0.616785\pi\) | ||||
−0.358716 | + | 0.933447i | \(0.616785\pi\) | |||||||
\(434\) | −6.28268 | −0.301578 | ||||||||
\(435\) | −20.2892 | −0.972792 | ||||||||
\(436\) | 9.45378 | 0.452754 | ||||||||
\(437\) | 0.872412 | 0.0417331 | ||||||||
\(438\) | −2.16781 | −0.103582 | ||||||||
\(439\) | −21.3339 | −1.01821 | −0.509106 | − | 0.860704i | \(-0.670024\pi\) | ||||
−0.509106 | + | 0.860704i | \(0.670024\pi\) | |||||||
\(440\) | −1.73687 | −0.0828021 | ||||||||
\(441\) | 0.657144 | 0.0312926 | ||||||||
\(442\) | 1.21855 | 0.0579605 | ||||||||
\(443\) | 9.47183 | 0.450020 | 0.225010 | − | 0.974356i | \(-0.427759\pi\) | ||||
0.225010 | + | 0.974356i | \(0.427759\pi\) | |||||||
\(444\) | −14.1622 | −0.672107 | ||||||||
\(445\) | 18.6407 | 0.883654 | ||||||||
\(446\) | 10.7784 | 0.510374 | ||||||||
\(447\) | 15.3939 | 0.728105 | ||||||||
\(448\) | 7.66777 | 0.362268 | ||||||||
\(449\) | −12.4659 | −0.588300 | −0.294150 | − | 0.955759i | \(-0.595037\pi\) | ||||
−0.294150 | + | 0.955759i | \(0.595037\pi\) | |||||||
\(450\) | 0.575796 | 0.0271433 | ||||||||
\(451\) | 5.51624 | 0.259749 | ||||||||
\(452\) | −5.90305 | −0.277656 | ||||||||
\(453\) | −16.5159 | −0.775985 | ||||||||
\(454\) | −7.48127 | −0.351113 | ||||||||
\(455\) | 5.41443 | 0.253832 | ||||||||
\(456\) | 0.715800 | 0.0335204 | ||||||||
\(457\) | 19.7556 | 0.924126 | 0.462063 | − | 0.886847i | \(-0.347109\pi\) | ||||
0.462063 | + | 0.886847i | \(0.347109\pi\) | |||||||
\(458\) | 4.97389 | 0.232415 | ||||||||
\(459\) | 2.47905 | 0.115712 | ||||||||
\(460\) | −7.74683 | −0.361198 | ||||||||
\(461\) | −3.14897 | −0.146662 | −0.0733310 | − | 0.997308i | \(-0.523363\pi\) | ||||
−0.0733310 | + | 0.997308i | \(0.523363\pi\) | |||||||
\(462\) | −0.653552 | −0.0304060 | ||||||||
\(463\) | −3.25643 | −0.151339 | −0.0756695 | − | 0.997133i | \(-0.524109\pi\) | ||||
−0.0756695 | + | 0.997133i | \(0.524109\pi\) | |||||||
\(464\) | −27.0503 | −1.25578 | ||||||||
\(465\) | −9.03801 | −0.419127 | ||||||||
\(466\) | 4.45803 | 0.206514 | ||||||||
\(467\) | −26.9886 | −1.24888 | −0.624442 | − | 0.781071i | \(-0.714674\pi\) | ||||
−0.624442 | + | 0.781071i | \(0.714674\pi\) | |||||||
\(468\) | −1.75839 | −0.0812816 | ||||||||
\(469\) | 19.2162 | 0.887320 | ||||||||
\(470\) | 6.69314 | 0.308732 | ||||||||
\(471\) | −20.8104 | −0.958893 | ||||||||
\(472\) | −25.5173 | −1.17453 | ||||||||
\(473\) | 0.353225 | 0.0162413 | ||||||||
\(474\) | 0.602306 | 0.0276648 | ||||||||
\(475\) | 0.453881 | 0.0208255 | ||||||||
\(476\) | −12.0624 | −0.552879 | ||||||||
\(477\) | −4.35675 | −0.199482 | ||||||||
\(478\) | −12.4212 | −0.568131 | ||||||||
\(479\) | 39.1301 | 1.78790 | 0.893949 | − | 0.448168i | \(-0.147923\pi\) | ||||
0.893949 | + | 0.448168i | \(0.147923\pi\) | |||||||
\(480\) | −9.73853 | −0.444501 | ||||||||
\(481\) | −8.05406 | −0.367233 | ||||||||
\(482\) | 9.18754 | 0.418481 | ||||||||
\(483\) | −6.23051 | −0.283498 | ||||||||
\(484\) | 18.9363 | 0.860741 | ||||||||
\(485\) | −16.2110 | −0.736101 | ||||||||
\(486\) | 0.491539 | 0.0222967 | ||||||||
\(487\) | 18.5749 | 0.841709 | 0.420855 | − | 0.907128i | \(-0.361730\pi\) | ||||
0.420855 | + | 0.907128i | \(0.361730\pi\) | |||||||
\(488\) | −9.24582 | −0.418539 | ||||||||
\(489\) | 17.6077 | 0.796249 | ||||||||
\(490\) | 0.632030 | 0.0285522 | ||||||||
\(491\) | −28.4496 | −1.28391 | −0.641956 | − | 0.766742i | \(-0.721877\pi\) | ||||
−0.641956 | + | 0.766742i | \(0.721877\pi\) | |||||||
\(492\) | 20.1869 | 0.910095 | ||||||||
\(493\) | 25.7058 | 1.15773 | ||||||||
\(494\) | 0.190454 | 0.00856893 | ||||||||
\(495\) | −0.940173 | −0.0422576 | ||||||||
\(496\) | −12.0498 | −0.541051 | ||||||||
\(497\) | 18.0659 | 0.810366 | ||||||||
\(498\) | −7.31374 | −0.327736 | ||||||||
\(499\) | 44.1140 | 1.97482 | 0.987408 | − | 0.158197i | \(-0.0505682\pi\) | ||||
0.987408 | + | 0.158197i | \(0.0505682\pi\) | |||||||
\(500\) | −21.2334 | −0.949585 | ||||||||
\(501\) | −12.4143 | −0.554630 | ||||||||
\(502\) | −8.51477 | −0.380033 | ||||||||
\(503\) | 28.3813 | 1.26546 | 0.632730 | − | 0.774372i | \(-0.281934\pi\) | ||||
0.632730 | + | 0.774372i | \(0.281934\pi\) | |||||||
\(504\) | −5.11203 | −0.227708 | ||||||||
\(505\) | −19.7928 | −0.880766 | ||||||||
\(506\) | 0.531786 | 0.0236408 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −29.4068 | −1.30472 | ||||||||
\(509\) | −19.8630 | −0.880411 | −0.440205 | − | 0.897897i | \(-0.645094\pi\) | ||||
−0.440205 | + | 0.897897i | \(0.645094\pi\) | |||||||
\(510\) | 2.38431 | 0.105579 | ||||||||
\(511\) | 12.2038 | 0.539865 | ||||||||
\(512\) | −22.6224 | −0.999778 | ||||||||
\(513\) | 0.387464 | 0.0171070 | ||||||||
\(514\) | −0.999402 | −0.0440818 | ||||||||
\(515\) | 1.95668 | 0.0862215 | ||||||||
\(516\) | 1.29264 | 0.0569053 | ||||||||
\(517\) | 3.34381 | 0.147061 | ||||||||
\(518\) | −10.9548 | −0.481328 | ||||||||
\(519\) | 0.962096 | 0.0422313 | ||||||||
\(520\) | −3.61476 | −0.158518 | ||||||||
\(521\) | −40.0692 | −1.75547 | −0.877733 | − | 0.479151i | \(-0.840945\pi\) | ||||
−0.877733 | + | 0.479151i | \(0.840945\pi\) | |||||||
\(522\) | 5.09687 | 0.223084 | ||||||||
\(523\) | −8.18749 | −0.358014 | −0.179007 | − | 0.983848i | \(-0.557288\pi\) | ||||
−0.179007 | + | 0.983848i | \(0.557288\pi\) | |||||||
\(524\) | −17.7455 | −0.775217 | ||||||||
\(525\) | −3.24148 | −0.141470 | ||||||||
\(526\) | −6.75833 | −0.294677 | ||||||||
\(527\) | 11.4509 | 0.498808 | ||||||||
\(528\) | −1.25347 | −0.0545504 | ||||||||
\(529\) | −17.9303 | −0.779579 | ||||||||
\(530\) | −4.19025 | −0.182013 | ||||||||
\(531\) | −13.8126 | −0.599415 | ||||||||
\(532\) | −1.88530 | −0.0817381 | ||||||||
\(533\) | 11.4803 | 0.497268 | ||||||||
\(534\) | −4.68275 | −0.202643 | ||||||||
\(535\) | 13.3409 | 0.576775 | ||||||||
\(536\) | −12.8290 | −0.554129 | ||||||||
\(537\) | 16.7816 | 0.724179 | ||||||||
\(538\) | −12.1081 | −0.522019 | ||||||||
\(539\) | 0.315754 | 0.0136005 | ||||||||
\(540\) | −3.44060 | −0.148060 | ||||||||
\(541\) | −20.8714 | −0.897330 | −0.448665 | − | 0.893700i | \(-0.648100\pi\) | ||||
−0.448665 | + | 0.893700i | \(0.648100\pi\) | |||||||
\(542\) | −7.73890 | −0.332414 | ||||||||
\(543\) | 16.9505 | 0.727416 | ||||||||
\(544\) | 12.3384 | 0.529005 | ||||||||
\(545\) | 10.5199 | 0.450621 | ||||||||
\(546\) | −1.36017 | −0.0582097 | ||||||||
\(547\) | 42.6030 | 1.82157 | 0.910786 | − | 0.412878i | \(-0.135477\pi\) | ||||
0.910786 | + | 0.412878i | \(0.135477\pi\) | |||||||
\(548\) | −5.78683 | −0.247201 | ||||||||
\(549\) | −5.00479 | −0.213599 | ||||||||
\(550\) | 0.276667 | 0.0117971 | ||||||||
\(551\) | 4.01770 | 0.171160 | ||||||||
\(552\) | 4.15958 | 0.177044 | ||||||||
\(553\) | −3.39072 | −0.144188 | ||||||||
\(554\) | 1.97639 | 0.0839687 | ||||||||
\(555\) | −15.7592 | −0.668940 | ||||||||
\(556\) | −17.7401 | −0.752349 | ||||||||
\(557\) | 18.9148 | 0.801446 | 0.400723 | − | 0.916199i | \(-0.368759\pi\) | ||||
0.400723 | + | 0.916199i | \(0.368759\pi\) | |||||||
\(558\) | 2.27045 | 0.0961157 | ||||||||
\(559\) | 0.735128 | 0.0310926 | ||||||||
\(560\) | 14.1247 | 0.596877 | ||||||||
\(561\) | 1.19117 | 0.0502912 | ||||||||
\(562\) | −8.90207 | −0.375511 | ||||||||
\(563\) | 5.08678 | 0.214382 | 0.107191 | − | 0.994238i | \(-0.465814\pi\) | ||||
0.107191 | + | 0.994238i | \(0.465814\pi\) | |||||||
\(564\) | 12.2368 | 0.515262 | ||||||||
\(565\) | −6.56872 | −0.276348 | ||||||||
\(566\) | 0.184987 | 0.00777560 | ||||||||
\(567\) | −2.76715 | −0.116210 | ||||||||
\(568\) | −12.0611 | −0.506071 | ||||||||
\(569\) | 40.8836 | 1.71393 | 0.856965 | − | 0.515374i | \(-0.172347\pi\) | ||||
0.856965 | + | 0.515374i | \(0.172347\pi\) | |||||||
\(570\) | 0.372657 | 0.0156089 | ||||||||
\(571\) | 44.4352 | 1.85956 | 0.929778 | − | 0.368120i | \(-0.119998\pi\) | ||||
0.929778 | + | 0.368120i | \(0.119998\pi\) | |||||||
\(572\) | −0.844897 | −0.0353269 | ||||||||
\(573\) | 7.04770 | 0.294422 | ||||||||
\(574\) | 15.6151 | 0.651764 | ||||||||
\(575\) | 2.63755 | 0.109993 | ||||||||
\(576\) | −2.77099 | −0.115458 | ||||||||
\(577\) | −34.5205 | −1.43711 | −0.718553 | − | 0.695473i | \(-0.755195\pi\) | ||||
−0.718553 | + | 0.695473i | \(0.755195\pi\) | |||||||
\(578\) | 5.33532 | 0.221920 | ||||||||
\(579\) | −6.44544 | −0.267863 | ||||||||
\(580\) | −35.6763 | −1.48138 | ||||||||
\(581\) | 41.1732 | 1.70815 | ||||||||
\(582\) | 4.07237 | 0.168805 | ||||||||
\(583\) | −2.09340 | −0.0866996 | ||||||||
\(584\) | −8.14746 | −0.337144 | ||||||||
\(585\) | −1.95668 | −0.0808986 | ||||||||
\(586\) | −10.5509 | −0.435855 | ||||||||
\(587\) | 22.8267 | 0.942159 | 0.471080 | − | 0.882091i | \(-0.343864\pi\) | ||||
0.471080 | + | 0.882091i | \(0.343864\pi\) | |||||||
\(588\) | 1.15551 | 0.0476526 | ||||||||
\(589\) | 1.78972 | 0.0737441 | ||||||||
\(590\) | −13.2847 | −0.546923 | ||||||||
\(591\) | −25.7287 | −1.05834 | ||||||||
\(592\) | −21.0107 | −0.863535 | ||||||||
\(593\) | 43.7769 | 1.79770 | 0.898850 | − | 0.438256i | \(-0.144404\pi\) | ||||
0.898850 | + | 0.438256i | \(0.144404\pi\) | |||||||
\(594\) | 0.236182 | 0.00969066 | ||||||||
\(595\) | −13.4226 | −0.550274 | ||||||||
\(596\) | 27.0684 | 1.10877 | ||||||||
\(597\) | 19.2453 | 0.787659 | ||||||||
\(598\) | 1.10675 | 0.0452582 | ||||||||
\(599\) | −29.2432 | −1.19484 | −0.597422 | − | 0.801927i | \(-0.703808\pi\) | ||||
−0.597422 | + | 0.801927i | \(0.703808\pi\) | |||||||
\(600\) | 2.16407 | 0.0883476 | ||||||||
\(601\) | −39.3488 | −1.60507 | −0.802536 | − | 0.596603i | \(-0.796517\pi\) | ||||
−0.802536 | + | 0.596603i | \(0.796517\pi\) | |||||||
\(602\) | 0.999895 | 0.0407527 | ||||||||
\(603\) | −6.94438 | −0.282797 | ||||||||
\(604\) | −29.0414 | −1.18168 | ||||||||
\(605\) | 21.0717 | 0.856686 | ||||||||
\(606\) | 4.97216 | 0.201980 | ||||||||
\(607\) | 28.7010 | 1.16494 | 0.582470 | − | 0.812852i | \(-0.302087\pi\) | ||||
0.582470 | + | 0.812852i | \(0.302087\pi\) | |||||||
\(608\) | 1.92844 | 0.0782085 | ||||||||
\(609\) | −28.6932 | −1.16271 | ||||||||
\(610\) | −4.81352 | −0.194894 | ||||||||
\(611\) | 6.95910 | 0.281535 | ||||||||
\(612\) | 4.35913 | 0.176208 | ||||||||
\(613\) | 24.7941 | 1.00143 | 0.500713 | − | 0.865613i | \(-0.333071\pi\) | ||||
0.500713 | + | 0.865613i | \(0.333071\pi\) | |||||||
\(614\) | 13.1322 | 0.529971 | ||||||||
\(615\) | 22.4633 | 0.905808 | ||||||||
\(616\) | −2.45630 | −0.0989673 | ||||||||
\(617\) | −18.3698 | −0.739539 | −0.369770 | − | 0.929123i | \(-0.620563\pi\) | ||||
−0.369770 | + | 0.929123i | \(0.620563\pi\) | |||||||
\(618\) | −0.491539 | −0.0197726 | ||||||||
\(619\) | 19.7081 | 0.792137 | 0.396069 | − | 0.918221i | \(-0.370374\pi\) | ||||
0.396069 | + | 0.918221i | \(0.370374\pi\) | |||||||
\(620\) | −15.8923 | −0.638251 | ||||||||
\(621\) | 2.25159 | 0.0903533 | ||||||||
\(622\) | −5.14159 | −0.206159 | ||||||||
\(623\) | 26.3619 | 1.05617 | ||||||||
\(624\) | −2.60871 | −0.104432 | ||||||||
\(625\) | −17.7707 | −0.710829 | ||||||||
\(626\) | 5.48563 | 0.219250 | ||||||||
\(627\) | 0.186175 | 0.00743509 | ||||||||
\(628\) | −36.5928 | −1.46021 | ||||||||
\(629\) | 19.9664 | 0.796113 | ||||||||
\(630\) | −2.66140 | −0.106033 | ||||||||
\(631\) | −20.0553 | −0.798387 | −0.399194 | − | 0.916867i | \(-0.630710\pi\) | ||||
−0.399194 | + | 0.916867i | \(0.630710\pi\) | |||||||
\(632\) | 2.26370 | 0.0900451 | ||||||||
\(633\) | −16.2268 | −0.644956 | ||||||||
\(634\) | −13.3418 | −0.529869 | ||||||||
\(635\) | −32.7229 | −1.29857 | ||||||||
\(636\) | −7.66087 | −0.303773 | ||||||||
\(637\) | 0.657144 | 0.0260370 | ||||||||
\(638\) | 2.44902 | 0.0969576 | ||||||||
\(639\) | −6.52869 | −0.258271 | ||||||||
\(640\) | −22.1422 | −0.875246 | ||||||||
\(641\) | −28.3837 | −1.12109 | −0.560544 | − | 0.828125i | \(-0.689408\pi\) | ||||
−0.560544 | + | 0.828125i | \(0.689408\pi\) | |||||||
\(642\) | −3.35137 | −0.132268 | ||||||||
\(643\) | 22.4343 | 0.884722 | 0.442361 | − | 0.896837i | \(-0.354141\pi\) | ||||
0.442361 | + | 0.896837i | \(0.354141\pi\) | |||||||
\(644\) | −10.9557 | −0.431713 | ||||||||
\(645\) | 1.43841 | 0.0566373 | ||||||||
\(646\) | −0.472145 | −0.0185763 | ||||||||
\(647\) | 37.1338 | 1.45988 | 0.729940 | − | 0.683511i | \(-0.239548\pi\) | ||||
0.729940 | + | 0.683511i | \(0.239548\pi\) | |||||||
\(648\) | 1.84740 | 0.0725726 | ||||||||
\(649\) | −6.63687 | −0.260520 | ||||||||
\(650\) | 0.575796 | 0.0225846 | ||||||||
\(651\) | −12.7816 | −0.500952 | ||||||||
\(652\) | 30.9613 | 1.21254 | ||||||||
\(653\) | 21.2042 | 0.829786 | 0.414893 | − | 0.909870i | \(-0.363819\pi\) | ||||
0.414893 | + | 0.909870i | \(0.363819\pi\) | |||||||
\(654\) | −2.64271 | −0.103338 | ||||||||
\(655\) | −19.7466 | −0.771565 | ||||||||
\(656\) | 29.9489 | 1.16931 | ||||||||
\(657\) | −4.41024 | −0.172060 | ||||||||
\(658\) | 9.46552 | 0.369004 | ||||||||
\(659\) | −36.1974 | −1.41005 | −0.705026 | − | 0.709181i | \(-0.749065\pi\) | ||||
−0.705026 | + | 0.709181i | \(0.749065\pi\) | |||||||
\(660\) | −1.65319 | −0.0643503 | ||||||||
\(661\) | −39.3570 | −1.53081 | −0.765405 | − | 0.643548i | \(-0.777462\pi\) | ||||
−0.765405 | + | 0.643548i | \(0.777462\pi\) | |||||||
\(662\) | 8.70758 | 0.338430 | ||||||||
\(663\) | 2.47905 | 0.0962783 | ||||||||
\(664\) | −27.4879 | −1.06674 | ||||||||
\(665\) | −2.09790 | −0.0813530 | ||||||||
\(666\) | 3.95888 | 0.153404 | ||||||||
\(667\) | 23.3472 | 0.904009 | ||||||||
\(668\) | −21.8292 | −0.844596 | ||||||||
\(669\) | 21.9279 | 0.847782 | ||||||||
\(670\) | −6.67899 | −0.258032 | ||||||||
\(671\) | −2.40477 | −0.0928353 | ||||||||
\(672\) | −13.7723 | −0.531279 | ||||||||
\(673\) | −16.1827 | −0.623799 | −0.311899 | − | 0.950115i | \(-0.600965\pi\) | ||||
−0.311899 | + | 0.950115i | \(0.600965\pi\) | |||||||
\(674\) | 14.9820 | 0.577086 | ||||||||
\(675\) | 1.17141 | 0.0450878 | ||||||||
\(676\) | −1.75839 | −0.0676304 | ||||||||
\(677\) | −7.72257 | −0.296802 | −0.148401 | − | 0.988927i | \(-0.547413\pi\) | ||||
−0.148401 | + | 0.988927i | \(0.547413\pi\) | |||||||
\(678\) | 1.65013 | 0.0633730 | ||||||||
\(679\) | −22.9257 | −0.879808 | ||||||||
\(680\) | 8.96116 | 0.343645 | ||||||||
\(681\) | −15.2201 | −0.583235 | ||||||||
\(682\) | 1.09094 | 0.0417742 | ||||||||
\(683\) | −47.3126 | −1.81037 | −0.905184 | − | 0.425020i | \(-0.860267\pi\) | ||||
−0.905184 | + | 0.425020i | \(0.860267\pi\) | |||||||
\(684\) | 0.681313 | 0.0260507 | ||||||||
\(685\) | −6.43939 | −0.246036 | ||||||||
\(686\) | −8.62733 | −0.329393 | ||||||||
\(687\) | 10.1190 | 0.386065 | ||||||||
\(688\) | 1.91774 | 0.0731130 | ||||||||
\(689\) | −4.35675 | −0.165979 | ||||||||
\(690\) | 2.16555 | 0.0824409 | ||||||||
\(691\) | 13.3320 | 0.507172 | 0.253586 | − | 0.967313i | \(-0.418390\pi\) | ||||
0.253586 | + | 0.967313i | \(0.418390\pi\) | |||||||
\(692\) | 1.69174 | 0.0643103 | ||||||||
\(693\) | −1.32960 | −0.0505074 | ||||||||
\(694\) | 7.83396 | 0.297373 | ||||||||
\(695\) | −19.7406 | −0.748805 | ||||||||
\(696\) | 19.1560 | 0.726107 | ||||||||
\(697\) | −28.4603 | −1.07801 | ||||||||
\(698\) | 8.14849 | 0.308425 | ||||||||
\(699\) | 9.06953 | 0.343041 | ||||||||
\(700\) | −5.69979 | −0.215432 | ||||||||
\(701\) | −5.88540 | −0.222289 | −0.111144 | − | 0.993804i | \(-0.535452\pi\) | ||||
−0.111144 | + | 0.993804i | \(0.535452\pi\) | |||||||
\(702\) | 0.491539 | 0.0185520 | ||||||||
\(703\) | 3.12066 | 0.117698 | ||||||||
\(704\) | −1.33145 | −0.0501808 | ||||||||
\(705\) | 13.6167 | 0.512835 | ||||||||
\(706\) | 6.07059 | 0.228470 | ||||||||
\(707\) | −27.9911 | −1.05271 | ||||||||
\(708\) | −24.2879 | −0.912795 | ||||||||
\(709\) | 22.1855 | 0.833195 | 0.416598 | − | 0.909091i | \(-0.363222\pi\) | ||||
0.416598 | + | 0.909091i | \(0.363222\pi\) | |||||||
\(710\) | −6.27918 | −0.235654 | ||||||||
\(711\) | 1.22535 | 0.0459541 | ||||||||
\(712\) | −17.5996 | −0.659573 | ||||||||
\(713\) | 10.4002 | 0.389492 | ||||||||
\(714\) | 3.37192 | 0.126191 | ||||||||
\(715\) | −0.940173 | −0.0351605 | ||||||||
\(716\) | 29.5086 | 1.10279 | ||||||||
\(717\) | −25.2699 | −0.943723 | ||||||||
\(718\) | −3.96929 | −0.148133 | ||||||||
\(719\) | 13.4460 | 0.501451 | 0.250726 | − | 0.968058i | \(-0.419331\pi\) | ||||
0.250726 | + | 0.968058i | \(0.419331\pi\) | |||||||
\(720\) | −5.10440 | −0.190230 | ||||||||
\(721\) | 2.76715 | 0.103054 | ||||||||
\(722\) | 9.26545 | 0.344824 | ||||||||
\(723\) | 18.6914 | 0.695140 | ||||||||
\(724\) | 29.8056 | 1.10772 | ||||||||
\(725\) | 12.1466 | 0.451115 | ||||||||
\(726\) | −5.29345 | −0.196458 | ||||||||
\(727\) | −17.2018 | −0.637980 | −0.318990 | − | 0.947758i | \(-0.603344\pi\) | ||||
−0.318990 | + | 0.947758i | \(0.603344\pi\) | |||||||
\(728\) | −5.11203 | −0.189464 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.24170 | −0.156992 | ||||||||
\(731\) | −1.82242 | −0.0674046 | ||||||||
\(732\) | −8.80036 | −0.325271 | ||||||||
\(733\) | 8.65637 | 0.319730 | 0.159865 | − | 0.987139i | \(-0.448894\pi\) | ||||
0.159865 | + | 0.987139i | \(0.448894\pi\) | |||||||
\(734\) | −9.29790 | −0.343192 | ||||||||
\(735\) | 1.28582 | 0.0474281 | ||||||||
\(736\) | 11.2064 | 0.413072 | ||||||||
\(737\) | −3.33674 | −0.122910 | ||||||||
\(738\) | −5.64303 | −0.207723 | ||||||||
\(739\) | −32.7796 | −1.20582 | −0.602909 | − | 0.797810i | \(-0.705992\pi\) | ||||
−0.602909 | + | 0.797810i | \(0.705992\pi\) | |||||||
\(740\) | −27.7108 | −1.01867 | ||||||||
\(741\) | 0.387464 | 0.0142339 | ||||||||
\(742\) | −5.92590 | −0.217547 | ||||||||
\(743\) | 30.7713 | 1.12889 | 0.564444 | − | 0.825471i | \(-0.309091\pi\) | ||||
0.564444 | + | 0.825471i | \(0.309091\pi\) | |||||||
\(744\) | 8.53323 | 0.312843 | ||||||||
\(745\) | 30.1208 | 1.10354 | ||||||||
\(746\) | 5.32569 | 0.194988 | ||||||||
\(747\) | −14.8793 | −0.544403 | ||||||||
\(748\) | 2.09454 | 0.0765840 | ||||||||
\(749\) | 18.8668 | 0.689377 | ||||||||
\(750\) | 5.93557 | 0.216736 | ||||||||
\(751\) | −1.52787 | −0.0557529 | −0.0278764 | − | 0.999611i | \(-0.508874\pi\) | ||||
−0.0278764 | + | 0.999611i | \(0.508874\pi\) | |||||||
\(752\) | 18.1543 | 0.662018 | ||||||||
\(753\) | −17.3227 | −0.631273 | ||||||||
\(754\) | 5.09687 | 0.185617 | ||||||||
\(755\) | −32.3163 | −1.17611 | ||||||||
\(756\) | −4.86573 | −0.176965 | ||||||||
\(757\) | 8.97197 | 0.326092 | 0.163046 | − | 0.986618i | \(-0.447868\pi\) | ||||
0.163046 | + | 0.986618i | \(0.447868\pi\) | |||||||
\(758\) | 8.58741 | 0.311909 | ||||||||
\(759\) | 1.08188 | 0.0392697 | ||||||||
\(760\) | 1.40059 | 0.0508047 | ||||||||
\(761\) | 21.9966 | 0.797376 | 0.398688 | − | 0.917087i | \(-0.369466\pi\) | ||||
0.398688 | + | 0.917087i | \(0.369466\pi\) | |||||||
\(762\) | 8.22037 | 0.297793 | ||||||||
\(763\) | 14.8773 | 0.538594 | ||||||||
\(764\) | 12.3926 | 0.448348 | ||||||||
\(765\) | 4.85070 | 0.175377 | ||||||||
\(766\) | 7.08807 | 0.256103 | ||||||||
\(767\) | −13.8126 | −0.498743 | ||||||||
\(768\) | 0.0203706 | 0.000735062 0 | ||||||||
\(769\) | 6.77796 | 0.244420 | 0.122210 | − | 0.992504i | \(-0.461002\pi\) | ||||
0.122210 | + | 0.992504i | \(0.461002\pi\) | |||||||
\(770\) | −1.27879 | −0.0460844 | ||||||||
\(771\) | −2.03321 | −0.0732243 | ||||||||
\(772\) | −11.3336 | −0.407905 | ||||||||
\(773\) | 3.43558 | 0.123569 | 0.0617847 | − | 0.998090i | \(-0.480321\pi\) | ||||
0.0617847 | + | 0.998090i | \(0.480321\pi\) | |||||||
\(774\) | −0.361344 | −0.0129882 | ||||||||
\(775\) | 5.41083 | 0.194363 | ||||||||
\(776\) | 15.3056 | 0.549438 | ||||||||
\(777\) | −22.2868 | −0.799535 | ||||||||
\(778\) | 14.4083 | 0.516563 | ||||||||
\(779\) | −4.44822 | −0.159374 | ||||||||
\(780\) | −3.44060 | −0.123193 | ||||||||
\(781\) | −3.13700 | −0.112251 | ||||||||
\(782\) | −2.74368 | −0.0981138 | ||||||||
\(783\) | 10.3692 | 0.370565 | ||||||||
\(784\) | 1.71430 | 0.0612249 | ||||||||
\(785\) | −40.7192 | −1.45333 | ||||||||
\(786\) | 4.96058 | 0.176938 | ||||||||
\(787\) | −28.2237 | −1.00607 | −0.503033 | − | 0.864267i | \(-0.667782\pi\) | ||||
−0.503033 | + | 0.864267i | \(0.667782\pi\) | |||||||
\(788\) | −45.2411 | −1.61165 | ||||||||
\(789\) | −13.7493 | −0.489489 | ||||||||
\(790\) | 1.17852 | 0.0419298 | ||||||||
\(791\) | −9.28955 | −0.330298 | ||||||||
\(792\) | 0.887664 | 0.0315418 | ||||||||
\(793\) | −5.00479 | −0.177725 | ||||||||
\(794\) | −5.31761 | −0.188715 | ||||||||
\(795\) | −8.52476 | −0.302342 | ||||||||
\(796\) | 33.8408 | 1.19946 | ||||||||
\(797\) | −25.0026 | −0.885636 | −0.442818 | − | 0.896611i | \(-0.646021\pi\) | ||||
−0.442818 | + | 0.896611i | \(0.646021\pi\) | |||||||
\(798\) | 0.527015 | 0.0186561 | ||||||||
\(799\) | −17.2519 | −0.610330 | ||||||||
\(800\) | 5.83022 | 0.206129 | ||||||||
\(801\) | −9.52671 | −0.336610 | ||||||||
\(802\) | −9.40407 | −0.332069 | ||||||||
\(803\) | −2.11910 | −0.0747813 | ||||||||
\(804\) | −12.2109 | −0.430646 | ||||||||
\(805\) | −12.1911 | −0.429680 | ||||||||
\(806\) | 2.27045 | 0.0799731 | ||||||||
\(807\) | −24.6331 | −0.867127 | ||||||||
\(808\) | 18.6873 | 0.657418 | ||||||||
\(809\) | 35.9696 | 1.26462 | 0.632312 | − | 0.774714i | \(-0.282106\pi\) | ||||
0.632312 | + | 0.774714i | \(0.282106\pi\) | |||||||
\(810\) | 0.961784 | 0.0337936 | ||||||||
\(811\) | 5.62271 | 0.197440 | 0.0987201 | − | 0.995115i | \(-0.468525\pi\) | ||||
0.0987201 | + | 0.995115i | \(0.468525\pi\) | |||||||
\(812\) | −50.4538 | −1.77058 | ||||||||
\(813\) | −15.7442 | −0.552174 | ||||||||
\(814\) | 1.90222 | 0.0666729 | ||||||||
\(815\) | 34.4527 | 1.20682 | ||||||||
\(816\) | 6.46712 | 0.226395 | ||||||||
\(817\) | −0.284836 | −0.00996514 | ||||||||
\(818\) | 14.3305 | 0.501053 | ||||||||
\(819\) | −2.76715 | −0.0966922 | ||||||||
\(820\) | 39.4992 | 1.37937 | ||||||||
\(821\) | −4.03037 | −0.140661 | −0.0703304 | − | 0.997524i | \(-0.522405\pi\) | ||||
−0.0703304 | + | 0.997524i | \(0.522405\pi\) | |||||||
\(822\) | 1.61765 | 0.0564219 | ||||||||
\(823\) | 43.3982 | 1.51276 | 0.756382 | − | 0.654130i | \(-0.226965\pi\) | ||||
0.756382 | + | 0.654130i | \(0.226965\pi\) | |||||||
\(824\) | −1.84740 | −0.0643571 | ||||||||
\(825\) | 0.562858 | 0.0195962 | ||||||||
\(826\) | −18.7874 | −0.653697 | ||||||||
\(827\) | −44.5844 | −1.55035 | −0.775176 | − | 0.631746i | \(-0.782339\pi\) | ||||
−0.775176 | + | 0.631746i | \(0.782339\pi\) | |||||||
\(828\) | 3.95918 | 0.137591 | ||||||||
\(829\) | −4.66154 | −0.161902 | −0.0809510 | − | 0.996718i | \(-0.525796\pi\) | ||||
−0.0809510 | + | 0.996718i | \(0.525796\pi\) | |||||||
\(830\) | −14.3106 | −0.496729 | ||||||||
\(831\) | 4.02082 | 0.139481 | ||||||||
\(832\) | −2.77099 | −0.0960669 | ||||||||
\(833\) | −1.62909 | −0.0564447 | ||||||||
\(834\) | 4.95907 | 0.171719 | ||||||||
\(835\) | −24.2908 | −0.840617 | ||||||||
\(836\) | 0.327367 | 0.0113222 | ||||||||
\(837\) | 4.61906 | 0.159658 | ||||||||
\(838\) | −10.5693 | −0.365111 | ||||||||
\(839\) | 41.3981 | 1.42922 | 0.714610 | − | 0.699523i | \(-0.246604\pi\) | ||||
0.714610 | + | 0.699523i | \(0.246604\pi\) | |||||||
\(840\) | −10.0026 | −0.345122 | ||||||||
\(841\) | 78.5204 | 2.70760 | ||||||||
\(842\) | −10.8848 | −0.375114 | ||||||||
\(843\) | −18.1106 | −0.623762 | ||||||||
\(844\) | −28.5330 | −0.982145 | ||||||||
\(845\) | −1.95668 | −0.0673117 | ||||||||
\(846\) | −3.42067 | −0.117605 | ||||||||
\(847\) | 29.7998 | 1.02393 | ||||||||
\(848\) | −11.3655 | −0.390293 | ||||||||
\(849\) | 0.376343 | 0.0129161 | ||||||||
\(850\) | −1.42743 | −0.0489603 | ||||||||
\(851\) | 18.1345 | 0.621641 | ||||||||
\(852\) | −11.4800 | −0.393297 | ||||||||
\(853\) | 47.5696 | 1.62875 | 0.814376 | − | 0.580338i | \(-0.197079\pi\) | ||||
0.814376 | + | 0.580338i | \(0.197079\pi\) | |||||||
\(854\) | −6.80734 | −0.232942 | ||||||||
\(855\) | 0.758143 | 0.0259279 | ||||||||
\(856\) | −12.5958 | −0.430514 | ||||||||
\(857\) | 6.16085 | 0.210451 | 0.105225 | − | 0.994448i | \(-0.466444\pi\) | ||||
0.105225 | + | 0.994448i | \(0.466444\pi\) | |||||||
\(858\) | 0.236182 | 0.00806312 | ||||||||
\(859\) | −3.59898 | −0.122796 | −0.0613979 | − | 0.998113i | \(-0.519556\pi\) | ||||
−0.0613979 | + | 0.998113i | \(0.519556\pi\) | |||||||
\(860\) | 2.52928 | 0.0862478 | ||||||||
\(861\) | 31.7678 | 1.08265 | ||||||||
\(862\) | −14.2127 | −0.484087 | ||||||||
\(863\) | −24.7634 | −0.842955 | −0.421477 | − | 0.906839i | \(-0.638488\pi\) | ||||
−0.421477 | + | 0.906839i | \(0.638488\pi\) | |||||||
\(864\) | 4.97708 | 0.169324 | ||||||||
\(865\) | 1.88251 | 0.0640073 | ||||||||
\(866\) | 7.33808 | 0.249358 | ||||||||
\(867\) | 10.8543 | 0.368632 | ||||||||
\(868\) | −22.4751 | −0.762855 | ||||||||
\(869\) | 0.588772 | 0.0199727 | ||||||||
\(870\) | 9.97293 | 0.338114 | ||||||||
\(871\) | −6.94438 | −0.235301 | ||||||||
\(872\) | −9.93232 | −0.336351 | ||||||||
\(873\) | 8.28494 | 0.280403 | ||||||||
\(874\) | −0.428825 | −0.0145052 | ||||||||
\(875\) | −33.4147 | −1.12962 | ||||||||
\(876\) | −7.75492 | −0.262014 | ||||||||
\(877\) | 40.8347 | 1.37889 | 0.689444 | − | 0.724339i | \(-0.257855\pi\) | ||||
0.689444 | + | 0.724339i | \(0.257855\pi\) | |||||||
\(878\) | 10.4865 | 0.353901 | ||||||||
\(879\) | −21.4651 | −0.723999 | ||||||||
\(880\) | −2.45264 | −0.0826785 | ||||||||
\(881\) | −29.0234 | −0.977825 | −0.488912 | − | 0.872333i | \(-0.662606\pi\) | ||||
−0.488912 | + | 0.872333i | \(0.662606\pi\) | |||||||
\(882\) | −0.323012 | −0.0108764 | ||||||||
\(883\) | −29.5256 | −0.993616 | −0.496808 | − | 0.867860i | \(-0.665495\pi\) | ||||
−0.496808 | + | 0.867860i | \(0.665495\pi\) | |||||||
\(884\) | 4.35913 | 0.146614 | ||||||||
\(885\) | −27.0268 | −0.908495 | ||||||||
\(886\) | −4.65577 | −0.156414 | ||||||||
\(887\) | −39.9619 | −1.34179 | −0.670895 | − | 0.741553i | \(-0.734090\pi\) | ||||
−0.670895 | + | 0.741553i | \(0.734090\pi\) | |||||||
\(888\) | 14.8790 | 0.499308 | ||||||||
\(889\) | −46.2771 | −1.55209 | ||||||||
\(890\) | −9.16264 | −0.307132 | ||||||||
\(891\) | 0.480495 | 0.0160972 | ||||||||
\(892\) | 38.5578 | 1.29101 | ||||||||
\(893\) | −2.69640 | −0.0902316 | ||||||||
\(894\) | −7.56669 | −0.253068 | ||||||||
\(895\) | 32.8361 | 1.09759 | ||||||||
\(896\) | −31.3137 | −1.04612 | ||||||||
\(897\) | 2.25159 | 0.0751785 | ||||||||
\(898\) | 6.12746 | 0.204476 | ||||||||
\(899\) | 47.8960 | 1.59742 | ||||||||
\(900\) | 2.05980 | 0.0686601 | ||||||||
\(901\) | 10.8006 | 0.359820 | ||||||||
\(902\) | −2.71145 | −0.0902813 | ||||||||
\(903\) | 2.03421 | 0.0676943 | ||||||||
\(904\) | 6.20185 | 0.206270 | ||||||||
\(905\) | 33.1667 | 1.10250 | ||||||||
\(906\) | 8.11822 | 0.269710 | ||||||||
\(907\) | −34.6869 | −1.15176 | −0.575881 | − | 0.817534i | \(-0.695341\pi\) | ||||
−0.575881 | + | 0.817534i | \(0.695341\pi\) | |||||||
\(908\) | −26.7628 | −0.888155 | ||||||||
\(909\) | 10.1155 | 0.335510 | ||||||||
\(910\) | −2.66140 | −0.0882247 | ||||||||
\(911\) | 2.80043 | 0.0927825 | 0.0463912 | − | 0.998923i | \(-0.485228\pi\) | ||||
0.0463912 | + | 0.998923i | \(0.485228\pi\) | |||||||
\(912\) | 1.01078 | 0.0334703 | ||||||||
\(913\) | −7.14940 | −0.236611 | ||||||||
\(914\) | −9.71064 | −0.321199 | ||||||||
\(915\) | −9.79275 | −0.323738 | ||||||||
\(916\) | 17.7932 | 0.587903 | ||||||||
\(917\) | −27.9259 | −0.922195 | ||||||||
\(918\) | −1.21855 | −0.0402181 | ||||||||
\(919\) | −27.9650 | −0.922481 | −0.461241 | − | 0.887275i | \(-0.652595\pi\) | ||||
−0.461241 | + | 0.887275i | \(0.652595\pi\) | |||||||
\(920\) | 8.13896 | 0.268334 | ||||||||
\(921\) | 26.7164 | 0.880336 | ||||||||
\(922\) | 1.54784 | 0.0509754 | ||||||||
\(923\) | −6.52869 | −0.214894 | ||||||||
\(924\) | −2.33796 | −0.0769132 | ||||||||
\(925\) | 9.43464 | 0.310209 | ||||||||
\(926\) | 1.60066 | 0.0526010 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 51.6083 | 1.69413 | ||||||||
\(929\) | 17.5222 | 0.574884 | 0.287442 | − | 0.957798i | \(-0.407195\pi\) | ||||
0.287442 | + | 0.957798i | \(0.407195\pi\) | |||||||
\(930\) | 4.44253 | 0.145676 | ||||||||
\(931\) | −0.254620 | −0.00834483 | ||||||||
\(932\) | 15.9478 | 0.522386 | ||||||||
\(933\) | −10.4602 | −0.342451 | ||||||||
\(934\) | 13.2660 | 0.434076 | ||||||||
\(935\) | 2.33074 | 0.0762232 | ||||||||
\(936\) | 1.84740 | 0.0603840 | ||||||||
\(937\) | 10.5990 | 0.346254 | 0.173127 | − | 0.984899i | \(-0.444613\pi\) | ||||
0.173127 | + | 0.984899i | \(0.444613\pi\) | |||||||
\(938\) | −9.44550 | −0.308407 | ||||||||
\(939\) | 11.1601 | 0.364196 | ||||||||
\(940\) | 23.9435 | 0.780950 | ||||||||
\(941\) | −58.8341 | −1.91794 | −0.958968 | − | 0.283515i | \(-0.908500\pi\) | ||||
−0.958968 | + | 0.283515i | \(0.908500\pi\) | |||||||
\(942\) | 10.2291 | 0.333283 | ||||||||
\(943\) | −25.8490 | −0.841761 | ||||||||
\(944\) | −36.0330 | −1.17278 | ||||||||
\(945\) | −5.41443 | −0.176131 | ||||||||
\(946\) | −0.173624 | −0.00564500 | ||||||||
\(947\) | 41.2002 | 1.33883 | 0.669413 | − | 0.742891i | \(-0.266546\pi\) | ||||
0.669413 | + | 0.742891i | \(0.266546\pi\) | |||||||
\(948\) | 2.15464 | 0.0699793 | ||||||||
\(949\) | −4.41024 | −0.143162 | ||||||||
\(950\) | −0.223100 | −0.00723833 | ||||||||
\(951\) | −27.1428 | −0.880167 | ||||||||
\(952\) | 12.6730 | 0.410733 | ||||||||
\(953\) | 2.86744 | 0.0928854 | 0.0464427 | − | 0.998921i | \(-0.485212\pi\) | ||||
0.0464427 | + | 0.998921i | \(0.485212\pi\) | |||||||
\(954\) | 2.14152 | 0.0693341 | ||||||||
\(955\) | 13.7901 | 0.446236 | ||||||||
\(956\) | −44.4344 | −1.43711 | ||||||||
\(957\) | 4.98235 | 0.161056 | ||||||||
\(958\) | −19.2340 | −0.621421 | ||||||||
\(959\) | −9.10665 | −0.294069 | ||||||||
\(960\) | −5.42194 | −0.174992 | ||||||||
\(961\) | −9.66430 | −0.311752 | ||||||||
\(962\) | 3.95888 | 0.127640 | ||||||||
\(963\) | −6.81812 | −0.219711 | ||||||||
\(964\) | 32.8667 | 1.05857 | ||||||||
\(965\) | −12.6117 | −0.405983 | ||||||||
\(966\) | 3.06254 | 0.0985356 | ||||||||
\(967\) | −6.63065 | −0.213227 | −0.106614 | − | 0.994301i | \(-0.534001\pi\) | ||||
−0.106614 | + | 0.994301i | \(0.534001\pi\) | |||||||
\(968\) | −19.8948 | −0.639444 | ||||||||
\(969\) | −0.960543 | −0.0308571 | ||||||||
\(970\) | 7.96832 | 0.255847 | ||||||||
\(971\) | 24.9652 | 0.801171 | 0.400585 | − | 0.916259i | \(-0.368807\pi\) | ||||
0.400585 | + | 0.916259i | \(0.368807\pi\) | |||||||
\(972\) | 1.75839 | 0.0564004 | ||||||||
\(973\) | −27.9174 | −0.894992 | ||||||||
\(974\) | −9.13029 | −0.292554 | ||||||||
\(975\) | 1.17141 | 0.0375153 | ||||||||
\(976\) | −13.0560 | −0.417914 | ||||||||
\(977\) | 54.4994 | 1.74359 | 0.871795 | − | 0.489871i | \(-0.162956\pi\) | ||||
0.871795 | + | 0.489871i | \(0.162956\pi\) | |||||||
\(978\) | −8.65490 | −0.276753 | ||||||||
\(979\) | −4.57753 | −0.146299 | ||||||||
\(980\) | 2.26097 | 0.0722240 | ||||||||
\(981\) | −5.37639 | −0.171655 | ||||||||
\(982\) | 13.9841 | 0.446250 | ||||||||
\(983\) | −26.3143 | −0.839296 | −0.419648 | − | 0.907687i | \(-0.637846\pi\) | ||||
−0.419648 | + | 0.907687i | \(0.637846\pi\) | |||||||
\(984\) | −21.2087 | −0.676109 | ||||||||
\(985\) | −50.3428 | −1.60405 | ||||||||
\(986\) | −12.6354 | −0.402393 | ||||||||
\(987\) | 19.2569 | 0.612954 | ||||||||
\(988\) | 0.681313 | 0.0216755 | ||||||||
\(989\) | −1.65521 | −0.0526326 | ||||||||
\(990\) | 0.462132 | 0.0146875 | ||||||||
\(991\) | 49.7884 | 1.58158 | 0.790791 | − | 0.612086i | \(-0.209670\pi\) | ||||
0.790791 | + | 0.612086i | \(0.209670\pi\) | |||||||
\(992\) | 22.9894 | 0.729914 | ||||||||
\(993\) | 17.7149 | 0.562166 | ||||||||
\(994\) | −8.88009 | −0.281659 | ||||||||
\(995\) | 37.6569 | 1.19380 | ||||||||
\(996\) | −26.1635 | −0.829023 | ||||||||
\(997\) | −46.8119 | −1.48255 | −0.741275 | − | 0.671202i | \(-0.765778\pi\) | ||||
−0.741275 | + | 0.671202i | \(0.765778\pi\) | |||||||
\(998\) | −21.6838 | −0.686388 | ||||||||
\(999\) | 8.05406 | 0.254819 |
(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 | 4017.2.a.j.1.10 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.j.1.10 | ✓ | 25 | 1.1 | even | 1 | trivial |