Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8049,2,Mod(1,8049)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8049, 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("8049.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8049 = 3 \cdot 2683 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8049.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: | \(64.2715885869\) |
Analytic rank: | \(1\) |
Dimension: | \(104\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8049.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.49098 | −1.76139 | −0.880694 | − | 0.473685i | \(-0.842923\pi\) | ||||
−0.880694 | + | 0.473685i | \(0.842923\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.20498 | 2.10249 | ||||||||
\(5\) | −3.30007 | −1.47584 | −0.737919 | − | 0.674889i | \(-0.764191\pi\) | ||||
−0.737919 | + | 0.674889i | \(0.764191\pi\) | |||||||
\(6\) | 2.49098 | 1.01694 | ||||||||
\(7\) | −0.252788 | −0.0955447 | −0.0477724 | − | 0.998858i | \(-0.515212\pi\) | ||||
−0.0477724 | + | 0.998858i | \(0.515212\pi\) | |||||||
\(8\) | −5.49255 | −1.94191 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 8.22041 | 2.59952 | ||||||||
\(11\) | 0.866258 | 0.261187 | 0.130593 | − | 0.991436i | \(-0.458312\pi\) | ||||
0.130593 | + | 0.991436i | \(0.458312\pi\) | |||||||
\(12\) | −4.20498 | −1.21387 | ||||||||
\(13\) | −1.69541 | −0.470222 | −0.235111 | − | 0.971969i | \(-0.575545\pi\) | ||||
−0.235111 | + | 0.971969i | \(0.575545\pi\) | |||||||
\(14\) | 0.629689 | 0.168291 | ||||||||
\(15\) | 3.30007 | 0.852075 | ||||||||
\(16\) | 5.27188 | 1.31797 | ||||||||
\(17\) | 6.53809 | 1.58572 | 0.792860 | − | 0.609404i | \(-0.208591\pi\) | ||||
0.792860 | + | 0.609404i | \(0.208591\pi\) | |||||||
\(18\) | −2.49098 | −0.587129 | ||||||||
\(19\) | 8.58286 | 1.96904 | 0.984522 | − | 0.175261i | \(-0.0560768\pi\) | ||||
0.984522 | + | 0.175261i | \(0.0560768\pi\) | |||||||
\(20\) | −13.8767 | −3.10293 | ||||||||
\(21\) | 0.252788 | 0.0551628 | ||||||||
\(22\) | −2.15783 | −0.460051 | ||||||||
\(23\) | −0.330861 | −0.0689894 | −0.0344947 | − | 0.999405i | \(-0.510982\pi\) | ||||
−0.0344947 | + | 0.999405i | \(0.510982\pi\) | |||||||
\(24\) | 5.49255 | 1.12116 | ||||||||
\(25\) | 5.89049 | 1.17810 | ||||||||
\(26\) | 4.22323 | 0.828244 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.06297 | −0.200882 | ||||||||
\(29\) | −6.30189 | −1.17023 | −0.585116 | − | 0.810950i | \(-0.698951\pi\) | ||||
−0.585116 | + | 0.810950i | \(0.698951\pi\) | |||||||
\(30\) | −8.22041 | −1.50084 | ||||||||
\(31\) | −0.392200 | −0.0704412 | −0.0352206 | − | 0.999380i | \(-0.511213\pi\) | ||||
−0.0352206 | + | 0.999380i | \(0.511213\pi\) | |||||||
\(32\) | −2.14704 | −0.379546 | ||||||||
\(33\) | −0.866258 | −0.150796 | ||||||||
\(34\) | −16.2862 | −2.79307 | ||||||||
\(35\) | 0.834218 | 0.141009 | ||||||||
\(36\) | 4.20498 | 0.700830 | ||||||||
\(37\) | −4.11920 | −0.677193 | −0.338596 | − | 0.940932i | \(-0.609952\pi\) | ||||
−0.338596 | + | 0.940932i | \(0.609952\pi\) | |||||||
\(38\) | −21.3797 | −3.46825 | ||||||||
\(39\) | 1.69541 | 0.271483 | ||||||||
\(40\) | 18.1258 | 2.86595 | ||||||||
\(41\) | −5.47986 | −0.855810 | −0.427905 | − | 0.903824i | \(-0.640748\pi\) | ||||
−0.427905 | + | 0.903824i | \(0.640748\pi\) | |||||||
\(42\) | −0.629689 | −0.0971631 | ||||||||
\(43\) | 3.91004 | 0.596275 | 0.298138 | − | 0.954523i | \(-0.403635\pi\) | ||||
0.298138 | + | 0.954523i | \(0.403635\pi\) | |||||||
\(44\) | 3.64259 | 0.549142 | ||||||||
\(45\) | −3.30007 | −0.491946 | ||||||||
\(46\) | 0.824169 | 0.121517 | ||||||||
\(47\) | −5.33816 | −0.778651 | −0.389325 | − | 0.921100i | \(-0.627292\pi\) | ||||
−0.389325 | + | 0.921100i | \(0.627292\pi\) | |||||||
\(48\) | −5.27188 | −0.760930 | ||||||||
\(49\) | −6.93610 | −0.990871 | ||||||||
\(50\) | −14.6731 | −2.07509 | ||||||||
\(51\) | −6.53809 | −0.915516 | ||||||||
\(52\) | −7.12916 | −0.988637 | ||||||||
\(53\) | −5.15842 | −0.708564 | −0.354282 | − | 0.935139i | \(-0.615275\pi\) | ||||
−0.354282 | + | 0.935139i | \(0.615275\pi\) | |||||||
\(54\) | 2.49098 | 0.338979 | ||||||||
\(55\) | −2.85871 | −0.385469 | ||||||||
\(56\) | 1.38845 | 0.185539 | ||||||||
\(57\) | −8.58286 | −1.13683 | ||||||||
\(58\) | 15.6979 | 2.06123 | ||||||||
\(59\) | −9.03502 | −1.17626 | −0.588129 | − | 0.808767i | \(-0.700135\pi\) | ||||
−0.588129 | + | 0.808767i | \(0.700135\pi\) | |||||||
\(60\) | 13.8767 | 1.79148 | ||||||||
\(61\) | −2.97621 | −0.381064 | −0.190532 | − | 0.981681i | \(-0.561021\pi\) | ||||
−0.190532 | + | 0.981681i | \(0.561021\pi\) | |||||||
\(62\) | 0.976961 | 0.124074 | ||||||||
\(63\) | −0.252788 | −0.0318482 | ||||||||
\(64\) | −5.19553 | −0.649442 | ||||||||
\(65\) | 5.59498 | 0.693972 | ||||||||
\(66\) | 2.15783 | 0.265610 | ||||||||
\(67\) | 15.5848 | 1.90398 | 0.951992 | − | 0.306122i | \(-0.0990315\pi\) | ||||
0.951992 | + | 0.306122i | \(0.0990315\pi\) | |||||||
\(68\) | 27.4925 | 3.33396 | ||||||||
\(69\) | 0.330861 | 0.0398310 | ||||||||
\(70\) | −2.07802 | −0.248371 | ||||||||
\(71\) | −12.4476 | −1.47725 | −0.738627 | − | 0.674114i | \(-0.764526\pi\) | ||||
−0.738627 | + | 0.674114i | \(0.764526\pi\) | |||||||
\(72\) | −5.49255 | −0.647304 | ||||||||
\(73\) | −3.53769 | −0.414055 | −0.207028 | − | 0.978335i | \(-0.566379\pi\) | ||||
−0.207028 | + | 0.978335i | \(0.566379\pi\) | |||||||
\(74\) | 10.2608 | 1.19280 | ||||||||
\(75\) | −5.89049 | −0.680175 | ||||||||
\(76\) | 36.0908 | 4.13989 | ||||||||
\(77\) | −0.218979 | −0.0249550 | ||||||||
\(78\) | −4.22323 | −0.478187 | ||||||||
\(79\) | 10.0125 | 1.12650 | 0.563249 | − | 0.826287i | \(-0.309551\pi\) | ||||
0.563249 | + | 0.826287i | \(0.309551\pi\) | |||||||
\(80\) | −17.3976 | −1.94511 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 13.6502 | 1.50741 | ||||||||
\(83\) | 0.830870 | 0.0911998 | 0.0455999 | − | 0.998960i | \(-0.485480\pi\) | ||||
0.0455999 | + | 0.998960i | \(0.485480\pi\) | |||||||
\(84\) | 1.06297 | 0.115979 | ||||||||
\(85\) | −21.5762 | −2.34027 | ||||||||
\(86\) | −9.73983 | −1.05027 | ||||||||
\(87\) | 6.30189 | 0.675634 | ||||||||
\(88\) | −4.75797 | −0.507201 | ||||||||
\(89\) | 9.43735 | 1.00036 | 0.500178 | − | 0.865922i | \(-0.333268\pi\) | ||||
0.500178 | + | 0.865922i | \(0.333268\pi\) | |||||||
\(90\) | 8.22041 | 0.866508 | ||||||||
\(91\) | 0.428579 | 0.0449273 | ||||||||
\(92\) | −1.39126 | −0.145049 | ||||||||
\(93\) | 0.392200 | 0.0406692 | ||||||||
\(94\) | 13.2973 | 1.37151 | ||||||||
\(95\) | −28.3241 | −2.90599 | ||||||||
\(96\) | 2.14704 | 0.219131 | ||||||||
\(97\) | 4.48288 | 0.455167 | 0.227584 | − | 0.973759i | \(-0.426918\pi\) | ||||
0.227584 | + | 0.973759i | \(0.426918\pi\) | |||||||
\(98\) | 17.2777 | 1.74531 | ||||||||
\(99\) | 0.866258 | 0.0870622 | ||||||||
\(100\) | 24.7694 | 2.47694 | ||||||||
\(101\) | −9.49629 | −0.944917 | −0.472458 | − | 0.881353i | \(-0.656633\pi\) | ||||
−0.472458 | + | 0.881353i | \(0.656633\pi\) | |||||||
\(102\) | 16.2862 | 1.61258 | ||||||||
\(103\) | 5.02397 | 0.495026 | 0.247513 | − | 0.968885i | \(-0.420387\pi\) | ||||
0.247513 | + | 0.968885i | \(0.420387\pi\) | |||||||
\(104\) | 9.31213 | 0.913129 | ||||||||
\(105\) | −0.834218 | −0.0814113 | ||||||||
\(106\) | 12.8495 | 1.24806 | ||||||||
\(107\) | 14.2898 | 1.38145 | 0.690725 | − | 0.723118i | \(-0.257292\pi\) | ||||
0.690725 | + | 0.723118i | \(0.257292\pi\) | |||||||
\(108\) | −4.20498 | −0.404624 | ||||||||
\(109\) | 10.5485 | 1.01036 | 0.505182 | − | 0.863013i | \(-0.331425\pi\) | ||||
0.505182 | + | 0.863013i | \(0.331425\pi\) | |||||||
\(110\) | 7.12100 | 0.678960 | ||||||||
\(111\) | 4.11920 | 0.390977 | ||||||||
\(112\) | −1.33267 | −0.125925 | ||||||||
\(113\) | 3.77217 | 0.354856 | 0.177428 | − | 0.984134i | \(-0.443222\pi\) | ||||
0.177428 | + | 0.984134i | \(0.443222\pi\) | |||||||
\(114\) | 21.3797 | 2.00240 | ||||||||
\(115\) | 1.09187 | 0.101817 | ||||||||
\(116\) | −26.4993 | −2.46040 | ||||||||
\(117\) | −1.69541 | −0.156741 | ||||||||
\(118\) | 22.5060 | 2.07185 | ||||||||
\(119\) | −1.65275 | −0.151507 | ||||||||
\(120\) | −18.1258 | −1.65465 | ||||||||
\(121\) | −10.2496 | −0.931782 | ||||||||
\(122\) | 7.41367 | 0.671202 | ||||||||
\(123\) | 5.47986 | 0.494102 | ||||||||
\(124\) | −1.64919 | −0.148102 | ||||||||
\(125\) | −2.93867 | −0.262843 | ||||||||
\(126\) | 0.629689 | 0.0560971 | ||||||||
\(127\) | −1.64141 | −0.145652 | −0.0728258 | − | 0.997345i | \(-0.523202\pi\) | ||||
−0.0728258 | + | 0.997345i | \(0.523202\pi\) | |||||||
\(128\) | 17.2360 | 1.52347 | ||||||||
\(129\) | −3.91004 | −0.344260 | ||||||||
\(130\) | −13.9370 | −1.22235 | ||||||||
\(131\) | 11.2097 | 0.979400 | 0.489700 | − | 0.871891i | \(-0.337106\pi\) | ||||
0.489700 | + | 0.871891i | \(0.337106\pi\) | |||||||
\(132\) | −3.64259 | −0.317047 | ||||||||
\(133\) | −2.16964 | −0.188132 | ||||||||
\(134\) | −38.8214 | −3.35366 | ||||||||
\(135\) | 3.30007 | 0.284025 | ||||||||
\(136\) | −35.9108 | −3.07933 | ||||||||
\(137\) | −7.67703 | −0.655893 | −0.327947 | − | 0.944696i | \(-0.606357\pi\) | ||||
−0.327947 | + | 0.944696i | \(0.606357\pi\) | |||||||
\(138\) | −0.824169 | −0.0701579 | ||||||||
\(139\) | −7.14740 | −0.606234 | −0.303117 | − | 0.952953i | \(-0.598027\pi\) | ||||
−0.303117 | + | 0.952953i | \(0.598027\pi\) | |||||||
\(140\) | 3.50787 | 0.296469 | ||||||||
\(141\) | 5.33816 | 0.449554 | ||||||||
\(142\) | 31.0066 | 2.60202 | ||||||||
\(143\) | −1.46866 | −0.122816 | ||||||||
\(144\) | 5.27188 | 0.439323 | ||||||||
\(145\) | 20.7967 | 1.72707 | ||||||||
\(146\) | 8.81231 | 0.729312 | ||||||||
\(147\) | 6.93610 | 0.572080 | ||||||||
\(148\) | −17.3212 | −1.42379 | ||||||||
\(149\) | −6.68129 | −0.547352 | −0.273676 | − | 0.961822i | \(-0.588240\pi\) | ||||
−0.273676 | + | 0.961822i | \(0.588240\pi\) | |||||||
\(150\) | 14.6731 | 1.19805 | ||||||||
\(151\) | −14.6051 | −1.18855 | −0.594273 | − | 0.804263i | \(-0.702560\pi\) | ||||
−0.594273 | + | 0.804263i | \(0.702560\pi\) | |||||||
\(152\) | −47.1418 | −3.82371 | ||||||||
\(153\) | 6.53809 | 0.528573 | ||||||||
\(154\) | 0.545473 | 0.0439554 | ||||||||
\(155\) | 1.29429 | 0.103960 | ||||||||
\(156\) | 7.12916 | 0.570790 | ||||||||
\(157\) | 15.5162 | 1.23833 | 0.619166 | − | 0.785260i | \(-0.287471\pi\) | ||||
0.619166 | + | 0.785260i | \(0.287471\pi\) | |||||||
\(158\) | −24.9410 | −1.98420 | ||||||||
\(159\) | 5.15842 | 0.409089 | ||||||||
\(160\) | 7.08538 | 0.560149 | ||||||||
\(161\) | 0.0836377 | 0.00659157 | ||||||||
\(162\) | −2.49098 | −0.195710 | ||||||||
\(163\) | 24.1841 | 1.89425 | 0.947123 | − | 0.320870i | \(-0.103975\pi\) | ||||
0.947123 | + | 0.320870i | \(0.103975\pi\) | |||||||
\(164\) | −23.0427 | −1.79933 | ||||||||
\(165\) | 2.85871 | 0.222551 | ||||||||
\(166\) | −2.06968 | −0.160638 | ||||||||
\(167\) | 6.18236 | 0.478405 | 0.239203 | − | 0.970970i | \(-0.423114\pi\) | ||||
0.239203 | + | 0.970970i | \(0.423114\pi\) | |||||||
\(168\) | −1.38845 | −0.107121 | ||||||||
\(169\) | −10.1256 | −0.778891 | ||||||||
\(170\) | 53.7458 | 4.12212 | ||||||||
\(171\) | 8.58286 | 0.656348 | ||||||||
\(172\) | 16.4416 | 1.25366 | ||||||||
\(173\) | −11.3238 | −0.860935 | −0.430467 | − | 0.902606i | \(-0.641651\pi\) | ||||
−0.430467 | + | 0.902606i | \(0.641651\pi\) | |||||||
\(174\) | −15.6979 | −1.19005 | ||||||||
\(175\) | −1.48904 | −0.112561 | ||||||||
\(176\) | 4.56681 | 0.344236 | ||||||||
\(177\) | 9.03502 | 0.679113 | ||||||||
\(178\) | −23.5082 | −1.76202 | ||||||||
\(179\) | −4.52948 | −0.338549 | −0.169274 | − | 0.985569i | \(-0.554142\pi\) | ||||
−0.169274 | + | 0.985569i | \(0.554142\pi\) | |||||||
\(180\) | −13.8767 | −1.03431 | ||||||||
\(181\) | 5.61638 | 0.417462 | 0.208731 | − | 0.977973i | \(-0.433067\pi\) | ||||
0.208731 | + | 0.977973i | \(0.433067\pi\) | |||||||
\(182\) | −1.06758 | −0.0791343 | ||||||||
\(183\) | 2.97621 | 0.220008 | ||||||||
\(184\) | 1.81727 | 0.133971 | ||||||||
\(185\) | 13.5937 | 0.999427 | ||||||||
\(186\) | −0.976961 | −0.0716343 | ||||||||
\(187\) | 5.66367 | 0.414169 | ||||||||
\(188\) | −22.4469 | −1.63710 | ||||||||
\(189\) | 0.252788 | 0.0183876 | ||||||||
\(190\) | 70.5547 | 5.11858 | ||||||||
\(191\) | 2.52502 | 0.182704 | 0.0913521 | − | 0.995819i | \(-0.470881\pi\) | ||||
0.0913521 | + | 0.995819i | \(0.470881\pi\) | |||||||
\(192\) | 5.19553 | 0.374955 | ||||||||
\(193\) | −2.24897 | −0.161884 | −0.0809420 | − | 0.996719i | \(-0.525793\pi\) | ||||
−0.0809420 | + | 0.996719i | \(0.525793\pi\) | |||||||
\(194\) | −11.1667 | −0.801726 | ||||||||
\(195\) | −5.59498 | −0.400665 | ||||||||
\(196\) | −29.1661 | −2.08330 | ||||||||
\(197\) | 1.39271 | 0.0992266 | 0.0496133 | − | 0.998769i | \(-0.484201\pi\) | ||||
0.0496133 | + | 0.998769i | \(0.484201\pi\) | |||||||
\(198\) | −2.15783 | −0.153350 | ||||||||
\(199\) | 10.1436 | 0.719063 | 0.359531 | − | 0.933133i | \(-0.382937\pi\) | ||||
0.359531 | + | 0.933133i | \(0.382937\pi\) | |||||||
\(200\) | −32.3538 | −2.28776 | ||||||||
\(201\) | −15.5848 | −1.09927 | ||||||||
\(202\) | 23.6551 | 1.66437 | ||||||||
\(203\) | 1.59304 | 0.111809 | ||||||||
\(204\) | −27.4925 | −1.92486 | ||||||||
\(205\) | 18.0839 | 1.26304 | ||||||||
\(206\) | −12.5146 | −0.871933 | ||||||||
\(207\) | −0.330861 | −0.0229965 | ||||||||
\(208\) | −8.93800 | −0.619739 | ||||||||
\(209\) | 7.43497 | 0.514288 | ||||||||
\(210\) | 2.07802 | 0.143397 | ||||||||
\(211\) | −1.50575 | −0.103660 | −0.0518302 | − | 0.998656i | \(-0.516505\pi\) | ||||
−0.0518302 | + | 0.998656i | \(0.516505\pi\) | |||||||
\(212\) | −21.6910 | −1.48975 | ||||||||
\(213\) | 12.4476 | 0.852893 | ||||||||
\(214\) | −35.5957 | −2.43327 | ||||||||
\(215\) | −12.9034 | −0.880006 | ||||||||
\(216\) | 5.49255 | 0.373721 | ||||||||
\(217\) | 0.0991432 | 0.00673028 | ||||||||
\(218\) | −26.2761 | −1.77964 | ||||||||
\(219\) | 3.53769 | 0.239055 | ||||||||
\(220\) | −12.0208 | −0.810444 | ||||||||
\(221\) | −11.0847 | −0.745641 | ||||||||
\(222\) | −10.2608 | −0.688663 | ||||||||
\(223\) | 16.5754 | 1.10997 | 0.554984 | − | 0.831861i | \(-0.312724\pi\) | ||||
0.554984 | + | 0.831861i | \(0.312724\pi\) | |||||||
\(224\) | 0.542745 | 0.0362636 | ||||||||
\(225\) | 5.89049 | 0.392699 | ||||||||
\(226\) | −9.39641 | −0.625040 | ||||||||
\(227\) | 2.28245 | 0.151491 | 0.0757457 | − | 0.997127i | \(-0.475866\pi\) | ||||
0.0757457 | + | 0.997127i | \(0.475866\pi\) | |||||||
\(228\) | −36.0908 | −2.39017 | ||||||||
\(229\) | −0.491074 | −0.0324511 | −0.0162255 | − | 0.999868i | \(-0.505165\pi\) | ||||
−0.0162255 | + | 0.999868i | \(0.505165\pi\) | |||||||
\(230\) | −2.71982 | −0.179339 | ||||||||
\(231\) | 0.218979 | 0.0144078 | ||||||||
\(232\) | 34.6135 | 2.27249 | ||||||||
\(233\) | 9.77908 | 0.640649 | 0.320325 | − | 0.947308i | \(-0.396208\pi\) | ||||
0.320325 | + | 0.947308i | \(0.396208\pi\) | |||||||
\(234\) | 4.22323 | 0.276081 | ||||||||
\(235\) | 17.6163 | 1.14916 | ||||||||
\(236\) | −37.9920 | −2.47307 | ||||||||
\(237\) | −10.0125 | −0.650384 | ||||||||
\(238\) | 4.11696 | 0.266863 | ||||||||
\(239\) | 13.0928 | 0.846901 | 0.423451 | − | 0.905919i | \(-0.360819\pi\) | ||||
0.423451 | + | 0.905919i | \(0.360819\pi\) | |||||||
\(240\) | 17.3976 | 1.12301 | ||||||||
\(241\) | −25.4302 | −1.63810 | −0.819052 | − | 0.573719i | \(-0.805500\pi\) | ||||
−0.819052 | + | 0.573719i | \(0.805500\pi\) | |||||||
\(242\) | 25.5315 | 1.64123 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −12.5149 | −0.801184 | ||||||||
\(245\) | 22.8896 | 1.46237 | ||||||||
\(246\) | −13.6502 | −0.870306 | ||||||||
\(247\) | −14.5515 | −0.925888 | ||||||||
\(248\) | 2.15418 | 0.136790 | ||||||||
\(249\) | −0.830870 | −0.0526543 | ||||||||
\(250\) | 7.32016 | 0.462968 | ||||||||
\(251\) | −24.2725 | −1.53207 | −0.766034 | − | 0.642801i | \(-0.777772\pi\) | ||||
−0.766034 | + | 0.642801i | \(0.777772\pi\) | |||||||
\(252\) | −1.06297 | −0.0669606 | ||||||||
\(253\) | −0.286611 | −0.0180191 | ||||||||
\(254\) | 4.08872 | 0.256549 | ||||||||
\(255\) | 21.5762 | 1.35115 | ||||||||
\(256\) | −32.5436 | −2.03397 | ||||||||
\(257\) | −2.97237 | −0.185411 | −0.0927056 | − | 0.995694i | \(-0.529552\pi\) | ||||
−0.0927056 | + | 0.995694i | \(0.529552\pi\) | |||||||
\(258\) | 9.73983 | 0.606375 | ||||||||
\(259\) | 1.04128 | 0.0647022 | ||||||||
\(260\) | 23.5268 | 1.45907 | ||||||||
\(261\) | −6.30189 | −0.390077 | ||||||||
\(262\) | −27.9232 | −1.72510 | ||||||||
\(263\) | 13.7085 | 0.845300 | 0.422650 | − | 0.906293i | \(-0.361100\pi\) | ||||
0.422650 | + | 0.906293i | \(0.361100\pi\) | |||||||
\(264\) | 4.75797 | 0.292833 | ||||||||
\(265\) | 17.0232 | 1.04572 | ||||||||
\(266\) | 5.40453 | 0.331373 | ||||||||
\(267\) | −9.43735 | −0.577556 | ||||||||
\(268\) | 65.5337 | 4.00311 | ||||||||
\(269\) | 11.7569 | 0.716833 | 0.358417 | − | 0.933562i | \(-0.383317\pi\) | ||||
0.358417 | + | 0.933562i | \(0.383317\pi\) | |||||||
\(270\) | −8.22041 | −0.500279 | ||||||||
\(271\) | −12.4951 | −0.759023 | −0.379511 | − | 0.925187i | \(-0.623908\pi\) | ||||
−0.379511 | + | 0.925187i | \(0.623908\pi\) | |||||||
\(272\) | 34.4680 | 2.08993 | ||||||||
\(273\) | −0.428579 | −0.0259388 | ||||||||
\(274\) | 19.1233 | 1.15528 | ||||||||
\(275\) | 5.10268 | 0.307703 | ||||||||
\(276\) | 1.39126 | 0.0837443 | ||||||||
\(277\) | −30.6336 | −1.84059 | −0.920297 | − | 0.391221i | \(-0.872053\pi\) | ||||
−0.920297 | + | 0.391221i | \(0.872053\pi\) | |||||||
\(278\) | 17.8040 | 1.06781 | ||||||||
\(279\) | −0.392200 | −0.0234804 | ||||||||
\(280\) | −4.58198 | −0.273826 | ||||||||
\(281\) | −12.9428 | −0.772104 | −0.386052 | − | 0.922477i | \(-0.626162\pi\) | ||||
−0.386052 | + | 0.922477i | \(0.626162\pi\) | |||||||
\(282\) | −13.2973 | −0.791840 | ||||||||
\(283\) | 23.2299 | 1.38087 | 0.690436 | − | 0.723394i | \(-0.257419\pi\) | ||||
0.690436 | + | 0.723394i | \(0.257419\pi\) | |||||||
\(284\) | −52.3417 | −3.10591 | ||||||||
\(285\) | 28.3241 | 1.67777 | ||||||||
\(286\) | 3.65841 | 0.216326 | ||||||||
\(287\) | 1.38524 | 0.0817682 | ||||||||
\(288\) | −2.14704 | −0.126515 | ||||||||
\(289\) | 25.7466 | 1.51451 | ||||||||
\(290\) | −51.8042 | −3.04205 | ||||||||
\(291\) | −4.48288 | −0.262791 | ||||||||
\(292\) | −14.8759 | −0.870547 | ||||||||
\(293\) | 16.3329 | 0.954177 | 0.477088 | − | 0.878855i | \(-0.341692\pi\) | ||||
0.477088 | + | 0.878855i | \(0.341692\pi\) | |||||||
\(294\) | −17.2777 | −1.00765 | ||||||||
\(295\) | 29.8162 | 1.73597 | ||||||||
\(296\) | 22.6249 | 1.31505 | ||||||||
\(297\) | −0.866258 | −0.0502654 | ||||||||
\(298\) | 16.6429 | 0.964100 | ||||||||
\(299\) | 0.560946 | 0.0324403 | ||||||||
\(300\) | −24.7694 | −1.43006 | ||||||||
\(301\) | −0.988409 | −0.0569710 | ||||||||
\(302\) | 36.3810 | 2.09349 | ||||||||
\(303\) | 9.49629 | 0.545548 | ||||||||
\(304\) | 45.2478 | 2.59514 | ||||||||
\(305\) | 9.82171 | 0.562389 | ||||||||
\(306\) | −16.2862 | −0.931023 | ||||||||
\(307\) | −5.52388 | −0.315264 | −0.157632 | − | 0.987498i | \(-0.550386\pi\) | ||||
−0.157632 | + | 0.987498i | \(0.550386\pi\) | |||||||
\(308\) | −0.920803 | −0.0524676 | ||||||||
\(309\) | −5.02397 | −0.285803 | ||||||||
\(310\) | −3.22404 | −0.183113 | ||||||||
\(311\) | 0.610266 | 0.0346050 | 0.0173025 | − | 0.999850i | \(-0.494492\pi\) | ||||
0.0173025 | + | 0.999850i | \(0.494492\pi\) | |||||||
\(312\) | −9.31213 | −0.527196 | ||||||||
\(313\) | 24.6675 | 1.39429 | 0.697146 | − | 0.716929i | \(-0.254453\pi\) | ||||
0.697146 | + | 0.716929i | \(0.254453\pi\) | |||||||
\(314\) | −38.6506 | −2.18118 | ||||||||
\(315\) | 0.834218 | 0.0470028 | ||||||||
\(316\) | 42.1025 | 2.36845 | ||||||||
\(317\) | −29.2000 | −1.64003 | −0.820016 | − | 0.572340i | \(-0.806036\pi\) | ||||
−0.820016 | + | 0.572340i | \(0.806036\pi\) | |||||||
\(318\) | −12.8495 | −0.720565 | ||||||||
\(319\) | −5.45906 | −0.305649 | ||||||||
\(320\) | 17.1456 | 0.958471 | ||||||||
\(321\) | −14.2898 | −0.797580 | ||||||||
\(322\) | −0.208340 | −0.0116103 | ||||||||
\(323\) | 56.1155 | 3.12235 | ||||||||
\(324\) | 4.20498 | 0.233610 | ||||||||
\(325\) | −9.98679 | −0.553967 | ||||||||
\(326\) | −60.2421 | −3.33650 | ||||||||
\(327\) | −10.5485 | −0.583334 | ||||||||
\(328\) | 30.0984 | 1.66191 | ||||||||
\(329\) | 1.34942 | 0.0743960 | ||||||||
\(330\) | −7.12100 | −0.391998 | ||||||||
\(331\) | −21.1649 | −1.16333 | −0.581665 | − | 0.813429i | \(-0.697598\pi\) | ||||
−0.581665 | + | 0.813429i | \(0.697598\pi\) | |||||||
\(332\) | 3.49379 | 0.191747 | ||||||||
\(333\) | −4.11920 | −0.225731 | ||||||||
\(334\) | −15.4001 | −0.842657 | ||||||||
\(335\) | −51.4309 | −2.80997 | ||||||||
\(336\) | 1.33267 | 0.0727029 | ||||||||
\(337\) | −33.1359 | −1.80503 | −0.902513 | − | 0.430662i | \(-0.858280\pi\) | ||||
−0.902513 | + | 0.430662i | \(0.858280\pi\) | |||||||
\(338\) | 25.2226 | 1.37193 | ||||||||
\(339\) | −3.77217 | −0.204876 | ||||||||
\(340\) | −90.7273 | −4.92038 | ||||||||
\(341\) | −0.339746 | −0.0183983 | ||||||||
\(342\) | −21.3797 | −1.15608 | ||||||||
\(343\) | 3.52287 | 0.190217 | ||||||||
\(344\) | −21.4761 | −1.15791 | ||||||||
\(345\) | −1.09187 | −0.0587841 | ||||||||
\(346\) | 28.2074 | 1.51644 | ||||||||
\(347\) | 10.1332 | 0.543980 | 0.271990 | − | 0.962300i | \(-0.412318\pi\) | ||||
0.271990 | + | 0.962300i | \(0.412318\pi\) | |||||||
\(348\) | 26.4993 | 1.42051 | ||||||||
\(349\) | −22.4799 | −1.20332 | −0.601660 | − | 0.798752i | \(-0.705494\pi\) | ||||
−0.601660 | + | 0.798752i | \(0.705494\pi\) | |||||||
\(350\) | 3.70917 | 0.198264 | ||||||||
\(351\) | 1.69541 | 0.0904943 | ||||||||
\(352\) | −1.85989 | −0.0991324 | ||||||||
\(353\) | −32.6651 | −1.73859 | −0.869293 | − | 0.494297i | \(-0.835425\pi\) | ||||
−0.869293 | + | 0.494297i | \(0.835425\pi\) | |||||||
\(354\) | −22.5060 | −1.19618 | ||||||||
\(355\) | 41.0779 | 2.18019 | ||||||||
\(356\) | 39.6838 | 2.10324 | ||||||||
\(357\) | 1.65275 | 0.0874727 | ||||||||
\(358\) | 11.2828 | 0.596316 | ||||||||
\(359\) | 6.08836 | 0.321331 | 0.160666 | − | 0.987009i | \(-0.448636\pi\) | ||||
0.160666 | + | 0.987009i | \(0.448636\pi\) | |||||||
\(360\) | 18.1258 | 0.955315 | ||||||||
\(361\) | 54.6656 | 2.87713 | ||||||||
\(362\) | −13.9903 | −0.735313 | ||||||||
\(363\) | 10.2496 | 0.537964 | ||||||||
\(364\) | 1.80216 | 0.0944590 | ||||||||
\(365\) | 11.6746 | 0.611078 | ||||||||
\(366\) | −7.41367 | −0.387519 | ||||||||
\(367\) | −8.13070 | −0.424419 | −0.212210 | − | 0.977224i | \(-0.568066\pi\) | ||||
−0.212210 | + | 0.977224i | \(0.568066\pi\) | |||||||
\(368\) | −1.74426 | −0.0909259 | ||||||||
\(369\) | −5.47986 | −0.285270 | ||||||||
\(370\) | −33.8616 | −1.76038 | ||||||||
\(371\) | 1.30398 | 0.0676995 | ||||||||
\(372\) | 1.64919 | 0.0855066 | ||||||||
\(373\) | −16.8537 | −0.872651 | −0.436326 | − | 0.899789i | \(-0.643720\pi\) | ||||
−0.436326 | + | 0.899789i | \(0.643720\pi\) | |||||||
\(374\) | −14.1081 | −0.729512 | ||||||||
\(375\) | 2.93867 | 0.151752 | ||||||||
\(376\) | 29.3201 | 1.51207 | ||||||||
\(377\) | 10.6843 | 0.550269 | ||||||||
\(378\) | −0.629689 | −0.0323877 | ||||||||
\(379\) | −12.4834 | −0.641229 | −0.320614 | − | 0.947210i | \(-0.603889\pi\) | ||||
−0.320614 | + | 0.947210i | \(0.603889\pi\) | |||||||
\(380\) | −119.102 | −6.10981 | ||||||||
\(381\) | 1.64141 | 0.0840919 | ||||||||
\(382\) | −6.28978 | −0.321813 | ||||||||
\(383\) | −7.27147 | −0.371555 | −0.185777 | − | 0.982592i | \(-0.559480\pi\) | ||||
−0.185777 | + | 0.982592i | \(0.559480\pi\) | |||||||
\(384\) | −17.2360 | −0.879573 | ||||||||
\(385\) | 0.722648 | 0.0368295 | ||||||||
\(386\) | 5.60213 | 0.285141 | ||||||||
\(387\) | 3.91004 | 0.198758 | ||||||||
\(388\) | 18.8504 | 0.956983 | ||||||||
\(389\) | 12.4577 | 0.631633 | 0.315816 | − | 0.948820i | \(-0.397722\pi\) | ||||
0.315816 | + | 0.948820i | \(0.397722\pi\) | |||||||
\(390\) | 13.9370 | 0.705726 | ||||||||
\(391\) | −2.16320 | −0.109398 | ||||||||
\(392\) | 38.0969 | 1.92418 | ||||||||
\(393\) | −11.2097 | −0.565457 | ||||||||
\(394\) | −3.46922 | −0.174777 | ||||||||
\(395\) | −33.0421 | −1.66253 | ||||||||
\(396\) | 3.64259 | 0.183047 | ||||||||
\(397\) | −28.0490 | −1.40774 | −0.703870 | − | 0.710329i | \(-0.748546\pi\) | ||||
−0.703870 | + | 0.710329i | \(0.748546\pi\) | |||||||
\(398\) | −25.2676 | −1.26655 | ||||||||
\(399\) | 2.16964 | 0.108618 | ||||||||
\(400\) | 31.0539 | 1.55270 | ||||||||
\(401\) | 28.9364 | 1.44502 | 0.722509 | − | 0.691362i | \(-0.242989\pi\) | ||||
0.722509 | + | 0.691362i | \(0.242989\pi\) | |||||||
\(402\) | 38.8214 | 1.93623 | ||||||||
\(403\) | 0.664939 | 0.0331230 | ||||||||
\(404\) | −39.9317 | −1.98668 | ||||||||
\(405\) | −3.30007 | −0.163982 | ||||||||
\(406\) | −3.96823 | −0.196940 | ||||||||
\(407\) | −3.56829 | −0.176874 | ||||||||
\(408\) | 35.9108 | 1.77785 | ||||||||
\(409\) | 15.1959 | 0.751387 | 0.375694 | − | 0.926744i | \(-0.377405\pi\) | ||||
0.375694 | + | 0.926744i | \(0.377405\pi\) | |||||||
\(410\) | −45.0467 | −2.22470 | ||||||||
\(411\) | 7.67703 | 0.378680 | ||||||||
\(412\) | 21.1257 | 1.04079 | ||||||||
\(413\) | 2.28394 | 0.112385 | ||||||||
\(414\) | 0.824169 | 0.0405057 | ||||||||
\(415\) | −2.74193 | −0.134596 | ||||||||
\(416\) | 3.64011 | 0.178471 | ||||||||
\(417\) | 7.14740 | 0.350010 | ||||||||
\(418\) | −18.5204 | −0.905860 | ||||||||
\(419\) | −13.6956 | −0.669076 | −0.334538 | − | 0.942382i | \(-0.608580\pi\) | ||||
−0.334538 | + | 0.942382i | \(0.608580\pi\) | |||||||
\(420\) | −3.50787 | −0.171166 | ||||||||
\(421\) | 29.3738 | 1.43159 | 0.715796 | − | 0.698310i | \(-0.246064\pi\) | ||||
0.715796 | + | 0.698310i | \(0.246064\pi\) | |||||||
\(422\) | 3.75080 | 0.182586 | ||||||||
\(423\) | −5.33816 | −0.259550 | ||||||||
\(424\) | 28.3329 | 1.37597 | ||||||||
\(425\) | 38.5125 | 1.86813 | ||||||||
\(426\) | −31.0066 | −1.50228 | ||||||||
\(427\) | 0.752349 | 0.0364087 | ||||||||
\(428\) | 60.0884 | 2.90448 | ||||||||
\(429\) | 1.46866 | 0.0709077 | ||||||||
\(430\) | 32.1421 | 1.55003 | ||||||||
\(431\) | 0.295952 | 0.0142555 | 0.00712776 | − | 0.999975i | \(-0.497731\pi\) | ||||
0.00712776 | + | 0.999975i | \(0.497731\pi\) | |||||||
\(432\) | −5.27188 | −0.253643 | ||||||||
\(433\) | 13.6064 | 0.653882 | 0.326941 | − | 0.945045i | \(-0.393982\pi\) | ||||
0.326941 | + | 0.945045i | \(0.393982\pi\) | |||||||
\(434\) | −0.246964 | −0.0118546 | ||||||||
\(435\) | −20.7967 | −0.997126 | ||||||||
\(436\) | 44.3563 | 2.12428 | ||||||||
\(437\) | −2.83974 | −0.135843 | ||||||||
\(438\) | −8.81231 | −0.421069 | ||||||||
\(439\) | −10.0809 | −0.481136 | −0.240568 | − | 0.970632i | \(-0.577334\pi\) | ||||
−0.240568 | + | 0.970632i | \(0.577334\pi\) | |||||||
\(440\) | 15.7016 | 0.748546 | ||||||||
\(441\) | −6.93610 | −0.330290 | ||||||||
\(442\) | 27.6119 | 1.31336 | ||||||||
\(443\) | 4.17952 | 0.198575 | 0.0992874 | − | 0.995059i | \(-0.468344\pi\) | ||||
0.0992874 | + | 0.995059i | \(0.468344\pi\) | |||||||
\(444\) | 17.3212 | 0.822026 | ||||||||
\(445\) | −31.1439 | −1.47636 | ||||||||
\(446\) | −41.2889 | −1.95508 | ||||||||
\(447\) | 6.68129 | 0.316014 | ||||||||
\(448\) | 1.31337 | 0.0620507 | ||||||||
\(449\) | 36.3050 | 1.71334 | 0.856669 | − | 0.515866i | \(-0.172530\pi\) | ||||
0.856669 | + | 0.515866i | \(0.172530\pi\) | |||||||
\(450\) | −14.6731 | −0.691696 | ||||||||
\(451\) | −4.74697 | −0.223526 | ||||||||
\(452\) | 15.8619 | 0.746081 | ||||||||
\(453\) | 14.6051 | 0.686207 | ||||||||
\(454\) | −5.68553 | −0.266835 | ||||||||
\(455\) | −1.41434 | −0.0663053 | ||||||||
\(456\) | 47.1418 | 2.20762 | ||||||||
\(457\) | −8.42188 | −0.393959 | −0.196980 | − | 0.980408i | \(-0.563113\pi\) | ||||
−0.196980 | + | 0.980408i | \(0.563113\pi\) | |||||||
\(458\) | 1.22325 | 0.0571589 | ||||||||
\(459\) | −6.53809 | −0.305172 | ||||||||
\(460\) | 4.59128 | 0.214069 | ||||||||
\(461\) | 16.6185 | 0.774000 | 0.387000 | − | 0.922080i | \(-0.373511\pi\) | ||||
0.387000 | + | 0.922080i | \(0.373511\pi\) | |||||||
\(462\) | −0.545473 | −0.0253777 | ||||||||
\(463\) | −12.3387 | −0.573429 | −0.286715 | − | 0.958016i | \(-0.592563\pi\) | ||||
−0.286715 | + | 0.958016i | \(0.592563\pi\) | |||||||
\(464\) | −33.2228 | −1.54233 | ||||||||
\(465\) | −1.29429 | −0.0600212 | ||||||||
\(466\) | −24.3595 | −1.12843 | ||||||||
\(467\) | 6.44956 | 0.298450 | 0.149225 | − | 0.988803i | \(-0.452322\pi\) | ||||
0.149225 | + | 0.988803i | \(0.452322\pi\) | |||||||
\(468\) | −7.12916 | −0.329546 | ||||||||
\(469\) | −3.93964 | −0.181916 | ||||||||
\(470\) | −43.8819 | −2.02412 | ||||||||
\(471\) | −15.5162 | −0.714951 | ||||||||
\(472\) | 49.6253 | 2.28419 | ||||||||
\(473\) | 3.38710 | 0.155739 | ||||||||
\(474\) | 24.9410 | 1.14558 | ||||||||
\(475\) | 50.5572 | 2.31973 | ||||||||
\(476\) | −6.94977 | −0.318542 | ||||||||
\(477\) | −5.15842 | −0.236188 | ||||||||
\(478\) | −32.6138 | −1.49172 | ||||||||
\(479\) | −3.46978 | −0.158539 | −0.0792693 | − | 0.996853i | \(-0.525259\pi\) | ||||
−0.0792693 | + | 0.996853i | \(0.525259\pi\) | |||||||
\(480\) | −7.08538 | −0.323402 | ||||||||
\(481\) | 6.98374 | 0.318431 | ||||||||
\(482\) | 63.3462 | 2.88534 | ||||||||
\(483\) | −0.0836377 | −0.00380565 | ||||||||
\(484\) | −43.0993 | −1.95906 | ||||||||
\(485\) | −14.7938 | −0.671753 | ||||||||
\(486\) | 2.49098 | 0.112993 | ||||||||
\(487\) | 33.8636 | 1.53451 | 0.767254 | − | 0.641343i | \(-0.221623\pi\) | ||||
0.767254 | + | 0.641343i | \(0.221623\pi\) | |||||||
\(488\) | 16.3470 | 0.739993 | ||||||||
\(489\) | −24.1841 | −1.09364 | ||||||||
\(490\) | −57.0176 | −2.57579 | ||||||||
\(491\) | 25.5921 | 1.15495 | 0.577477 | − | 0.816407i | \(-0.304037\pi\) | ||||
0.577477 | + | 0.816407i | \(0.304037\pi\) | |||||||
\(492\) | 23.0427 | 1.03884 | ||||||||
\(493\) | −41.2023 | −1.85566 | ||||||||
\(494\) | 36.2474 | 1.63085 | ||||||||
\(495\) | −2.85871 | −0.128490 | ||||||||
\(496\) | −2.06763 | −0.0928393 | ||||||||
\(497\) | 3.14659 | 0.141144 | ||||||||
\(498\) | 2.06968 | 0.0927446 | ||||||||
\(499\) | −0.369851 | −0.0165568 | −0.00827841 | − | 0.999966i | \(-0.502635\pi\) | ||||
−0.00827841 | + | 0.999966i | \(0.502635\pi\) | |||||||
\(500\) | −12.3570 | −0.552623 | ||||||||
\(501\) | −6.18236 | −0.276207 | ||||||||
\(502\) | 60.4623 | 2.69857 | ||||||||
\(503\) | −5.14909 | −0.229587 | −0.114793 | − | 0.993389i | \(-0.536621\pi\) | ||||
−0.114793 | + | 0.993389i | \(0.536621\pi\) | |||||||
\(504\) | 1.38845 | 0.0618464 | ||||||||
\(505\) | 31.3385 | 1.39454 | ||||||||
\(506\) | 0.713943 | 0.0317386 | ||||||||
\(507\) | 10.1256 | 0.449693 | ||||||||
\(508\) | −6.90209 | −0.306231 | ||||||||
\(509\) | 38.5337 | 1.70798 | 0.853988 | − | 0.520293i | \(-0.174177\pi\) | ||||
0.853988 | + | 0.520293i | \(0.174177\pi\) | |||||||
\(510\) | −53.7458 | −2.37990 | ||||||||
\(511\) | 0.894284 | 0.0395608 | ||||||||
\(512\) | 46.5932 | 2.05915 | ||||||||
\(513\) | −8.58286 | −0.378943 | ||||||||
\(514\) | 7.40410 | 0.326581 | ||||||||
\(515\) | −16.5795 | −0.730578 | ||||||||
\(516\) | −16.4416 | −0.723802 | ||||||||
\(517\) | −4.62422 | −0.203373 | ||||||||
\(518\) | −2.59382 | −0.113966 | ||||||||
\(519\) | 11.3238 | 0.497061 | ||||||||
\(520\) | −30.7307 | −1.34763 | ||||||||
\(521\) | 5.61476 | 0.245987 | 0.122993 | − | 0.992407i | \(-0.460751\pi\) | ||||
0.122993 | + | 0.992407i | \(0.460751\pi\) | |||||||
\(522\) | 15.6979 | 0.687078 | ||||||||
\(523\) | −24.0678 | −1.05241 | −0.526205 | − | 0.850358i | \(-0.676386\pi\) | ||||
−0.526205 | + | 0.850358i | \(0.676386\pi\) | |||||||
\(524\) | 47.1367 | 2.05918 | ||||||||
\(525\) | 1.48904 | 0.0649871 | ||||||||
\(526\) | −34.1475 | −1.48890 | ||||||||
\(527\) | −2.56424 | −0.111700 | ||||||||
\(528\) | −4.56681 | −0.198745 | ||||||||
\(529\) | −22.8905 | −0.995240 | ||||||||
\(530\) | −42.4044 | −1.84193 | ||||||||
\(531\) | −9.03502 | −0.392086 | ||||||||
\(532\) | −9.12329 | −0.395545 | ||||||||
\(533\) | 9.29061 | 0.402421 | ||||||||
\(534\) | 23.5082 | 1.01730 | ||||||||
\(535\) | −47.1575 | −2.03880 | ||||||||
\(536\) | −85.6003 | −3.69737 | ||||||||
\(537\) | 4.52948 | 0.195461 | ||||||||
\(538\) | −29.2863 | −1.26262 | ||||||||
\(539\) | −6.00845 | −0.258802 | ||||||||
\(540\) | 13.8767 | 0.597160 | ||||||||
\(541\) | −4.40018 | −0.189179 | −0.0945893 | − | 0.995516i | \(-0.530154\pi\) | ||||
−0.0945893 | + | 0.995516i | \(0.530154\pi\) | |||||||
\(542\) | 31.1250 | 1.33693 | ||||||||
\(543\) | −5.61638 | −0.241022 | ||||||||
\(544\) | −14.0375 | −0.601854 | ||||||||
\(545\) | −34.8109 | −1.49113 | ||||||||
\(546\) | 1.06758 | 0.0456882 | ||||||||
\(547\) | 38.0465 | 1.62675 | 0.813375 | − | 0.581740i | \(-0.197628\pi\) | ||||
0.813375 | + | 0.581740i | \(0.197628\pi\) | |||||||
\(548\) | −32.2817 | −1.37901 | ||||||||
\(549\) | −2.97621 | −0.127021 | ||||||||
\(550\) | −12.7107 | −0.541985 | ||||||||
\(551\) | −54.0883 | −2.30424 | ||||||||
\(552\) | −1.81727 | −0.0773483 | ||||||||
\(553\) | −2.53104 | −0.107631 | ||||||||
\(554\) | 76.3076 | 3.24200 | ||||||||
\(555\) | −13.5937 | −0.577019 | ||||||||
\(556\) | −30.0546 | −1.27460 | ||||||||
\(557\) | −7.37486 | −0.312483 | −0.156241 | − | 0.987719i | \(-0.549938\pi\) | ||||
−0.156241 | + | 0.987719i | \(0.549938\pi\) | |||||||
\(558\) | 0.976961 | 0.0413581 | ||||||||
\(559\) | −6.62912 | −0.280382 | ||||||||
\(560\) | 4.39790 | 0.185845 | ||||||||
\(561\) | −5.66367 | −0.239120 | ||||||||
\(562\) | 32.2403 | 1.35998 | ||||||||
\(563\) | −13.1356 | −0.553600 | −0.276800 | − | 0.960928i | \(-0.589274\pi\) | ||||
−0.276800 | + | 0.960928i | \(0.589274\pi\) | |||||||
\(564\) | 22.4469 | 0.945183 | ||||||||
\(565\) | −12.4485 | −0.523710 | ||||||||
\(566\) | −57.8651 | −2.43225 | ||||||||
\(567\) | −0.252788 | −0.0106161 | ||||||||
\(568\) | 68.3689 | 2.86870 | ||||||||
\(569\) | 27.5793 | 1.15618 | 0.578092 | − | 0.815972i | \(-0.303797\pi\) | ||||
0.578092 | + | 0.815972i | \(0.303797\pi\) | |||||||
\(570\) | −70.5547 | −2.95521 | ||||||||
\(571\) | 36.0366 | 1.50808 | 0.754042 | − | 0.656826i | \(-0.228102\pi\) | ||||
0.754042 | + | 0.656826i | \(0.228102\pi\) | |||||||
\(572\) | −6.17569 | −0.258219 | ||||||||
\(573\) | −2.52502 | −0.105484 | ||||||||
\(574\) | −3.45061 | −0.144026 | ||||||||
\(575\) | −1.94893 | −0.0812762 | ||||||||
\(576\) | −5.19553 | −0.216481 | ||||||||
\(577\) | −26.5890 | −1.10691 | −0.553457 | − | 0.832878i | \(-0.686692\pi\) | ||||
−0.553457 | + | 0.832878i | \(0.686692\pi\) | |||||||
\(578\) | −64.1343 | −2.66763 | ||||||||
\(579\) | 2.24897 | 0.0934638 | ||||||||
\(580\) | 87.4497 | 3.63115 | ||||||||
\(581\) | −0.210034 | −0.00871367 | ||||||||
\(582\) | 11.1667 | 0.462877 | ||||||||
\(583\) | −4.46852 | −0.185067 | ||||||||
\(584\) | 19.4309 | 0.804058 | ||||||||
\(585\) | 5.59498 | 0.231324 | ||||||||
\(586\) | −40.6849 | −1.68068 | ||||||||
\(587\) | 9.91669 | 0.409306 | 0.204653 | − | 0.978835i | \(-0.434393\pi\) | ||||
0.204653 | + | 0.978835i | \(0.434393\pi\) | |||||||
\(588\) | 29.1661 | 1.20279 | ||||||||
\(589\) | −3.36620 | −0.138702 | ||||||||
\(590\) | −74.2716 | −3.05771 | ||||||||
\(591\) | −1.39271 | −0.0572885 | ||||||||
\(592\) | −21.7159 | −0.892520 | ||||||||
\(593\) | −46.1857 | −1.89662 | −0.948310 | − | 0.317344i | \(-0.897209\pi\) | ||||
−0.948310 | + | 0.317344i | \(0.897209\pi\) | |||||||
\(594\) | 2.15783 | 0.0885368 | ||||||||
\(595\) | 5.45419 | 0.223600 | ||||||||
\(596\) | −28.0947 | −1.15080 | ||||||||
\(597\) | −10.1436 | −0.415151 | ||||||||
\(598\) | −1.39730 | −0.0571400 | ||||||||
\(599\) | 23.0878 | 0.943342 | 0.471671 | − | 0.881775i | \(-0.343651\pi\) | ||||
0.471671 | + | 0.881775i | \(0.343651\pi\) | |||||||
\(600\) | 32.3538 | 1.32084 | ||||||||
\(601\) | −13.2257 | −0.539488 | −0.269744 | − | 0.962932i | \(-0.586939\pi\) | ||||
−0.269744 | + | 0.962932i | \(0.586939\pi\) | |||||||
\(602\) | 2.46211 | 0.100348 | ||||||||
\(603\) | 15.5848 | 0.634662 | ||||||||
\(604\) | −61.4141 | −2.49890 | ||||||||
\(605\) | 33.8244 | 1.37516 | ||||||||
\(606\) | −23.6551 | −0.960922 | ||||||||
\(607\) | −38.3276 | −1.55567 | −0.777834 | − | 0.628470i | \(-0.783682\pi\) | ||||
−0.777834 | + | 0.628470i | \(0.783682\pi\) | |||||||
\(608\) | −18.4277 | −0.747343 | ||||||||
\(609\) | −1.59304 | −0.0645532 | ||||||||
\(610\) | −24.4657 | −0.990586 | ||||||||
\(611\) | 9.05037 | 0.366139 | ||||||||
\(612\) | 27.4925 | 1.11132 | ||||||||
\(613\) | −36.9493 | −1.49237 | −0.746184 | − | 0.665740i | \(-0.768116\pi\) | ||||
−0.746184 | + | 0.665740i | \(0.768116\pi\) | |||||||
\(614\) | 13.7599 | 0.555303 | ||||||||
\(615\) | −18.0839 | −0.729215 | ||||||||
\(616\) | 1.20275 | 0.0484604 | ||||||||
\(617\) | −34.6841 | −1.39633 | −0.698164 | − | 0.715938i | \(-0.745999\pi\) | ||||
−0.698164 | + | 0.715938i | \(0.745999\pi\) | |||||||
\(618\) | 12.5146 | 0.503411 | ||||||||
\(619\) | −18.4086 | −0.739906 | −0.369953 | − | 0.929050i | \(-0.620626\pi\) | ||||
−0.369953 | + | 0.929050i | \(0.620626\pi\) | |||||||
\(620\) | 5.44245 | 0.218574 | ||||||||
\(621\) | 0.330861 | 0.0132770 | ||||||||
\(622\) | −1.52016 | −0.0609529 | ||||||||
\(623\) | −2.38564 | −0.0955788 | ||||||||
\(624\) | 8.93800 | 0.357806 | ||||||||
\(625\) | −19.7546 | −0.790184 | ||||||||
\(626\) | −61.4463 | −2.45589 | ||||||||
\(627\) | −7.43497 | −0.296924 | ||||||||
\(628\) | 65.2455 | 2.60358 | ||||||||
\(629\) | −26.9317 | −1.07384 | ||||||||
\(630\) | −2.07802 | −0.0827903 | ||||||||
\(631\) | 5.93731 | 0.236360 | 0.118180 | − | 0.992992i | \(-0.462294\pi\) | ||||
0.118180 | + | 0.992992i | \(0.462294\pi\) | |||||||
\(632\) | −54.9943 | −2.18756 | ||||||||
\(633\) | 1.50575 | 0.0598483 | ||||||||
\(634\) | 72.7365 | 2.88873 | ||||||||
\(635\) | 5.41677 | 0.214958 | ||||||||
\(636\) | 21.6910 | 0.860106 | ||||||||
\(637\) | 11.7595 | 0.465930 | ||||||||
\(638\) | 13.5984 | 0.538366 | ||||||||
\(639\) | −12.4476 | −0.492418 | ||||||||
\(640\) | −56.8802 | −2.24839 | ||||||||
\(641\) | −15.1781 | −0.599498 | −0.299749 | − | 0.954018i | \(-0.596903\pi\) | ||||
−0.299749 | + | 0.954018i | \(0.596903\pi\) | |||||||
\(642\) | 35.5957 | 1.40485 | ||||||||
\(643\) | 2.38802 | 0.0941745 | 0.0470873 | − | 0.998891i | \(-0.485006\pi\) | ||||
0.0470873 | + | 0.998891i | \(0.485006\pi\) | |||||||
\(644\) | 0.351694 | 0.0138587 | ||||||||
\(645\) | 12.9034 | 0.508072 | ||||||||
\(646\) | −139.783 | −5.49967 | ||||||||
\(647\) | 19.6234 | 0.771475 | 0.385737 | − | 0.922609i | \(-0.373947\pi\) | ||||
0.385737 | + | 0.922609i | \(0.373947\pi\) | |||||||
\(648\) | −5.49255 | −0.215768 | ||||||||
\(649\) | −7.82665 | −0.307223 | ||||||||
\(650\) | 24.8769 | 0.975752 | ||||||||
\(651\) | −0.0991432 | −0.00388573 | ||||||||
\(652\) | 101.694 | 3.98263 | ||||||||
\(653\) | −0.817489 | −0.0319908 | −0.0159954 | − | 0.999872i | \(-0.505092\pi\) | ||||
−0.0159954 | + | 0.999872i | \(0.505092\pi\) | |||||||
\(654\) | 26.2761 | 1.02748 | ||||||||
\(655\) | −36.9930 | −1.44544 | ||||||||
\(656\) | −28.8892 | −1.12793 | ||||||||
\(657\) | −3.53769 | −0.138018 | ||||||||
\(658\) | −3.36138 | −0.131040 | ||||||||
\(659\) | −20.6687 | −0.805138 | −0.402569 | − | 0.915390i | \(-0.631883\pi\) | ||||
−0.402569 | + | 0.915390i | \(0.631883\pi\) | |||||||
\(660\) | 12.0208 | 0.467910 | ||||||||
\(661\) | 3.44613 | 0.134039 | 0.0670195 | − | 0.997752i | \(-0.478651\pi\) | ||||
0.0670195 | + | 0.997752i | \(0.478651\pi\) | |||||||
\(662\) | 52.7214 | 2.04907 | ||||||||
\(663\) | 11.0847 | 0.430496 | ||||||||
\(664\) | −4.56360 | −0.177102 | ||||||||
\(665\) | 7.15998 | 0.277652 | ||||||||
\(666\) | 10.2608 | 0.397600 | ||||||||
\(667\) | 2.08505 | 0.0807336 | ||||||||
\(668\) | 25.9967 | 1.00584 | ||||||||
\(669\) | −16.5754 | −0.640840 | ||||||||
\(670\) | 128.113 | 4.94945 | ||||||||
\(671\) | −2.57816 | −0.0995289 | ||||||||
\(672\) | −0.542745 | −0.0209368 | ||||||||
\(673\) | 40.1017 | 1.54581 | 0.772903 | − | 0.634524i | \(-0.218804\pi\) | ||||
0.772903 | + | 0.634524i | \(0.218804\pi\) | |||||||
\(674\) | 82.5408 | 3.17935 | ||||||||
\(675\) | −5.89049 | −0.226725 | ||||||||
\(676\) | −42.5779 | −1.63761 | ||||||||
\(677\) | 23.4290 | 0.900450 | 0.450225 | − | 0.892915i | \(-0.351344\pi\) | ||||
0.450225 | + | 0.892915i | \(0.351344\pi\) | |||||||
\(678\) | 9.39641 | 0.360867 | ||||||||
\(679\) | −1.13322 | −0.0434888 | ||||||||
\(680\) | 118.508 | 4.54459 | ||||||||
\(681\) | −2.28245 | −0.0874636 | ||||||||
\(682\) | 0.846300 | 0.0324065 | ||||||||
\(683\) | 25.6193 | 0.980294 | 0.490147 | − | 0.871640i | \(-0.336943\pi\) | ||||
0.490147 | + | 0.871640i | \(0.336943\pi\) | |||||||
\(684\) | 36.0908 | 1.37996 | ||||||||
\(685\) | 25.3348 | 0.967992 | ||||||||
\(686\) | −8.77540 | −0.335046 | ||||||||
\(687\) | 0.491074 | 0.0187356 | ||||||||
\(688\) | 20.6133 | 0.785873 | ||||||||
\(689\) | 8.74564 | 0.333182 | ||||||||
\(690\) | 2.71982 | 0.103542 | ||||||||
\(691\) | 1.82421 | 0.0693962 | 0.0346981 | − | 0.999398i | \(-0.488953\pi\) | ||||
0.0346981 | + | 0.999398i | \(0.488953\pi\) | |||||||
\(692\) | −47.6164 | −1.81011 | ||||||||
\(693\) | −0.218979 | −0.00831833 | ||||||||
\(694\) | −25.2416 | −0.958159 | ||||||||
\(695\) | 23.5869 | 0.894704 | ||||||||
\(696\) | −34.6135 | −1.31202 | ||||||||
\(697\) | −35.8278 | −1.35708 | ||||||||
\(698\) | 55.9969 | 2.11951 | ||||||||
\(699\) | −9.77908 | −0.369879 | ||||||||
\(700\) | −6.26139 | −0.236658 | ||||||||
\(701\) | −26.8568 | −1.01437 | −0.507184 | − | 0.861838i | \(-0.669314\pi\) | ||||
−0.507184 | + | 0.861838i | \(0.669314\pi\) | |||||||
\(702\) | −4.22323 | −0.159396 | ||||||||
\(703\) | −35.3546 | −1.33342 | ||||||||
\(704\) | −4.50067 | −0.169625 | ||||||||
\(705\) | −17.6163 | −0.663469 | ||||||||
\(706\) | 81.3680 | 3.06232 | ||||||||
\(707\) | 2.40055 | 0.0902818 | ||||||||
\(708\) | 37.9920 | 1.42783 | ||||||||
\(709\) | 15.1296 | 0.568205 | 0.284102 | − | 0.958794i | \(-0.408304\pi\) | ||||
0.284102 | + | 0.958794i | \(0.408304\pi\) | |||||||
\(710\) | −102.324 | −3.84016 | ||||||||
\(711\) | 10.0125 | 0.375499 | ||||||||
\(712\) | −51.8351 | −1.94260 | ||||||||
\(713\) | 0.129764 | 0.00485969 | ||||||||
\(714\) | −4.11696 | −0.154073 | ||||||||
\(715\) | 4.84669 | 0.181256 | ||||||||
\(716\) | −19.0463 | −0.711795 | ||||||||
\(717\) | −13.0928 | −0.488959 | ||||||||
\(718\) | −15.1660 | −0.565989 | ||||||||
\(719\) | −6.29821 | −0.234884 | −0.117442 | − | 0.993080i | \(-0.537469\pi\) | ||||
−0.117442 | + | 0.993080i | \(0.537469\pi\) | |||||||
\(720\) | −17.3976 | −0.648370 | ||||||||
\(721\) | −1.27000 | −0.0472971 | ||||||||
\(722\) | −136.171 | −5.06775 | ||||||||
\(723\) | 25.4302 | 0.945760 | ||||||||
\(724\) | 23.6168 | 0.877710 | ||||||||
\(725\) | −37.1212 | −1.37865 | ||||||||
\(726\) | −25.5315 | −0.947564 | ||||||||
\(727\) | −15.4988 | −0.574819 | −0.287410 | − | 0.957808i | \(-0.592794\pi\) | ||||
−0.287410 | + | 0.957808i | \(0.592794\pi\) | |||||||
\(728\) | −2.35399 | −0.0872447 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −29.0813 | −1.07635 | ||||||||
\(731\) | 25.5642 | 0.945526 | ||||||||
\(732\) | 12.5149 | 0.462564 | ||||||||
\(733\) | −14.8320 | −0.547831 | −0.273915 | − | 0.961754i | \(-0.588319\pi\) | ||||
−0.273915 | + | 0.961754i | \(0.588319\pi\) | |||||||
\(734\) | 20.2534 | 0.747567 | ||||||||
\(735\) | −22.8896 | −0.844297 | ||||||||
\(736\) | 0.710372 | 0.0261847 | ||||||||
\(737\) | 13.5004 | 0.497295 | ||||||||
\(738\) | 13.6502 | 0.502471 | ||||||||
\(739\) | −32.7803 | −1.20584 | −0.602922 | − | 0.797800i | \(-0.705997\pi\) | ||||
−0.602922 | + | 0.797800i | \(0.705997\pi\) | |||||||
\(740\) | 57.1611 | 2.10128 | ||||||||
\(741\) | 14.5515 | 0.534562 | ||||||||
\(742\) | −3.24820 | −0.119245 | ||||||||
\(743\) | −48.3011 | −1.77199 | −0.885997 | − | 0.463691i | \(-0.846525\pi\) | ||||
−0.885997 | + | 0.463691i | \(0.846525\pi\) | |||||||
\(744\) | −2.15418 | −0.0789760 | ||||||||
\(745\) | 22.0487 | 0.807803 | ||||||||
\(746\) | 41.9822 | 1.53708 | ||||||||
\(747\) | 0.830870 | 0.0303999 | ||||||||
\(748\) | 23.8156 | 0.870785 | ||||||||
\(749\) | −3.61229 | −0.131990 | ||||||||
\(750\) | −7.32016 | −0.267295 | ||||||||
\(751\) | −48.0579 | −1.75366 | −0.876830 | − | 0.480801i | \(-0.840346\pi\) | ||||
−0.876830 | + | 0.480801i | \(0.840346\pi\) | |||||||
\(752\) | −28.1422 | −1.02624 | ||||||||
\(753\) | 24.2725 | 0.884539 | ||||||||
\(754\) | −26.6143 | −0.969237 | ||||||||
\(755\) | 48.1979 | 1.75410 | ||||||||
\(756\) | 1.06297 | 0.0386597 | ||||||||
\(757\) | 47.1476 | 1.71361 | 0.856805 | − | 0.515640i | \(-0.172446\pi\) | ||||
0.856805 | + | 0.515640i | \(0.172446\pi\) | |||||||
\(758\) | 31.0959 | 1.12945 | ||||||||
\(759\) | 0.286611 | 0.0104033 | ||||||||
\(760\) | 155.572 | 5.64317 | ||||||||
\(761\) | −12.6815 | −0.459703 | −0.229852 | − | 0.973226i | \(-0.573824\pi\) | ||||
−0.229852 | + | 0.973226i | \(0.573824\pi\) | |||||||
\(762\) | −4.08872 | −0.148119 | ||||||||
\(763\) | −2.66653 | −0.0965350 | ||||||||
\(764\) | 10.6177 | 0.384134 | ||||||||
\(765\) | −21.5762 | −0.780088 | ||||||||
\(766\) | 18.1131 | 0.654452 | ||||||||
\(767\) | 15.3181 | 0.553103 | ||||||||
\(768\) | 32.5436 | 1.17431 | ||||||||
\(769\) | −52.7162 | −1.90100 | −0.950498 | − | 0.310730i | \(-0.899427\pi\) | ||||
−0.950498 | + | 0.310730i | \(0.899427\pi\) | |||||||
\(770\) | −1.80010 | −0.0648711 | ||||||||
\(771\) | 2.97237 | 0.107047 | ||||||||
\(772\) | −9.45685 | −0.340359 | ||||||||
\(773\) | 9.27871 | 0.333732 | 0.166866 | − | 0.985980i | \(-0.446635\pi\) | ||||
0.166866 | + | 0.985980i | \(0.446635\pi\) | |||||||
\(774\) | −9.73983 | −0.350091 | ||||||||
\(775\) | −2.31025 | −0.0829865 | ||||||||
\(776\) | −24.6224 | −0.883894 | ||||||||
\(777\) | −1.04128 | −0.0373558 | ||||||||
\(778\) | −31.0320 | −1.11255 | ||||||||
\(779\) | −47.0329 | −1.68513 | ||||||||
\(780\) | −23.5268 | −0.842393 | ||||||||
\(781\) | −10.7828 | −0.385839 | ||||||||
\(782\) | 5.38849 | 0.192692 | ||||||||
\(783\) | 6.30189 | 0.225211 | ||||||||
\(784\) | −36.5663 | −1.30594 | ||||||||
\(785\) | −51.2047 | −1.82758 | ||||||||
\(786\) | 27.9232 | 0.995989 | ||||||||
\(787\) | 40.2522 | 1.43483 | 0.717417 | − | 0.696644i | \(-0.245324\pi\) | ||||
0.717417 | + | 0.696644i | \(0.245324\pi\) | |||||||
\(788\) | 5.85632 | 0.208623 | ||||||||
\(789\) | −13.7085 | −0.488034 | ||||||||
\(790\) | 82.3071 | 2.92836 | ||||||||
\(791\) | −0.953559 | −0.0339047 | ||||||||
\(792\) | −4.75797 | −0.169067 | ||||||||
\(793\) | 5.04589 | 0.179185 | ||||||||
\(794\) | 69.8695 | 2.47958 | ||||||||
\(795\) | −17.0232 | −0.603750 | ||||||||
\(796\) | 42.6537 | 1.51182 | ||||||||
\(797\) | 7.09151 | 0.251194 | 0.125597 | − | 0.992081i | \(-0.459915\pi\) | ||||
0.125597 | + | 0.992081i | \(0.459915\pi\) | |||||||
\(798\) | −5.40453 | −0.191318 | ||||||||
\(799\) | −34.9014 | −1.23472 | ||||||||
\(800\) | −12.6471 | −0.447142 | ||||||||
\(801\) | 9.43735 | 0.333452 | ||||||||
\(802\) | −72.0801 | −2.54524 | ||||||||
\(803\) | −3.06455 | −0.108146 | ||||||||
\(804\) | −65.5337 | −2.31119 | ||||||||
\(805\) | −0.276010 | −0.00972809 | ||||||||
\(806\) | −1.65635 | −0.0583425 | ||||||||
\(807\) | −11.7569 | −0.413864 | ||||||||
\(808\) | 52.1589 | 1.83494 | ||||||||
\(809\) | −27.8915 | −0.980614 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(810\) | 8.22041 | 0.288836 | ||||||||
\(811\) | −13.8111 | −0.484972 | −0.242486 | − | 0.970155i | \(-0.577963\pi\) | ||||
−0.242486 | + | 0.970155i | \(0.577963\pi\) | |||||||
\(812\) | 6.69870 | 0.235078 | ||||||||
\(813\) | 12.4951 | 0.438222 | ||||||||
\(814\) | 8.88854 | 0.311543 | ||||||||
\(815\) | −79.8094 | −2.79560 | ||||||||
\(816\) | −34.4680 | −1.20662 | ||||||||
\(817\) | 33.5593 | 1.17409 | ||||||||
\(818\) | −37.8526 | −1.32348 | ||||||||
\(819\) | 0.428579 | 0.0149758 | ||||||||
\(820\) | 76.0426 | 2.65552 | ||||||||
\(821\) | −11.3110 | −0.394757 | −0.197378 | − | 0.980327i | \(-0.563243\pi\) | ||||
−0.197378 | + | 0.980327i | \(0.563243\pi\) | |||||||
\(822\) | −19.1233 | −0.667003 | ||||||||
\(823\) | −5.22466 | −0.182120 | −0.0910602 | − | 0.995845i | \(-0.529026\pi\) | ||||
−0.0910602 | + | 0.995845i | \(0.529026\pi\) | |||||||
\(824\) | −27.5944 | −0.961296 | ||||||||
\(825\) | −5.10268 | −0.177652 | ||||||||
\(826\) | −5.68925 | −0.197954 | ||||||||
\(827\) | 4.38009 | 0.152311 | 0.0761553 | − | 0.997096i | \(-0.475736\pi\) | ||||
0.0761553 | + | 0.997096i | \(0.475736\pi\) | |||||||
\(828\) | −1.39126 | −0.0483498 | ||||||||
\(829\) | −8.16601 | −0.283617 | −0.141809 | − | 0.989894i | \(-0.545292\pi\) | ||||
−0.141809 | + | 0.989894i | \(0.545292\pi\) | |||||||
\(830\) | 6.83010 | 0.237076 | ||||||||
\(831\) | 30.6336 | 1.06267 | ||||||||
\(832\) | 8.80856 | 0.305382 | ||||||||
\(833\) | −45.3488 | −1.57124 | ||||||||
\(834\) | −17.8040 | −0.616503 | ||||||||
\(835\) | −20.4022 | −0.706048 | ||||||||
\(836\) | 31.2639 | 1.08128 | ||||||||
\(837\) | 0.392200 | 0.0135564 | ||||||||
\(838\) | 34.1156 | 1.17850 | ||||||||
\(839\) | 2.42446 | 0.0837015 | 0.0418508 | − | 0.999124i | \(-0.486675\pi\) | ||||
0.0418508 | + | 0.999124i | \(0.486675\pi\) | |||||||
\(840\) | 4.58198 | 0.158094 | ||||||||
\(841\) | 10.7138 | 0.369443 | ||||||||
\(842\) | −73.1695 | −2.52159 | ||||||||
\(843\) | 12.9428 | 0.445775 | ||||||||
\(844\) | −6.33166 | −0.217945 | ||||||||
\(845\) | 33.4152 | 1.14952 | ||||||||
\(846\) | 13.2973 | 0.457169 | ||||||||
\(847\) | 2.59097 | 0.0890268 | ||||||||
\(848\) | −27.1946 | −0.933866 | ||||||||
\(849\) | −23.2299 | −0.797246 | ||||||||
\(850\) | −95.9339 | −3.29051 | ||||||||
\(851\) | 1.36289 | 0.0467191 | ||||||||
\(852\) | 52.3417 | 1.79320 | ||||||||
\(853\) | 3.56887 | 0.122196 | 0.0610978 | − | 0.998132i | \(-0.480540\pi\) | ||||
0.0610978 | + | 0.998132i | \(0.480540\pi\) | |||||||
\(854\) | −1.87408 | −0.0641299 | ||||||||
\(855\) | −28.3241 | −0.968663 | ||||||||
\(856\) | −78.4876 | −2.68265 | ||||||||
\(857\) | 22.7608 | 0.777494 | 0.388747 | − | 0.921345i | \(-0.372908\pi\) | ||||
0.388747 | + | 0.921345i | \(0.372908\pi\) | |||||||
\(858\) | −3.65841 | −0.124896 | ||||||||
\(859\) | −11.2838 | −0.384998 | −0.192499 | − | 0.981297i | \(-0.561659\pi\) | ||||
−0.192499 | + | 0.981297i | \(0.561659\pi\) | |||||||
\(860\) | −54.2586 | −1.85020 | ||||||||
\(861\) | −1.38524 | −0.0472089 | ||||||||
\(862\) | −0.737211 | −0.0251095 | ||||||||
\(863\) | 0.930016 | 0.0316581 | 0.0158291 | − | 0.999875i | \(-0.494961\pi\) | ||||
0.0158291 | + | 0.999875i | \(0.494961\pi\) | |||||||
\(864\) | 2.14704 | 0.0730437 | ||||||||
\(865\) | 37.3695 | 1.27060 | ||||||||
\(866\) | −33.8932 | −1.15174 | ||||||||
\(867\) | −25.7466 | −0.874401 | ||||||||
\(868\) | 0.416895 | 0.0141503 | ||||||||
\(869\) | 8.67343 | 0.294226 | ||||||||
\(870\) | 51.8042 | 1.75633 | ||||||||
\(871\) | −26.4226 | −0.895296 | ||||||||
\(872\) | −57.9383 | −1.96204 | ||||||||
\(873\) | 4.48288 | 0.151722 | ||||||||
\(874\) | 7.07373 | 0.239272 | ||||||||
\(875\) | 0.742859 | 0.0251132 | ||||||||
\(876\) | 14.8759 | 0.502610 | ||||||||
\(877\) | 35.3390 | 1.19331 | 0.596656 | − | 0.802497i | \(-0.296496\pi\) | ||||
0.596656 | + | 0.802497i | \(0.296496\pi\) | |||||||
\(878\) | 25.1114 | 0.847468 | ||||||||
\(879\) | −16.3329 | −0.550894 | ||||||||
\(880\) | −15.0708 | −0.508036 | ||||||||
\(881\) | 1.24826 | 0.0420549 | 0.0210274 | − | 0.999779i | \(-0.493306\pi\) | ||||
0.0210274 | + | 0.999779i | \(0.493306\pi\) | |||||||
\(882\) | 17.2777 | 0.581770 | ||||||||
\(883\) | 10.2014 | 0.343305 | 0.171652 | − | 0.985158i | \(-0.445089\pi\) | ||||
0.171652 | + | 0.985158i | \(0.445089\pi\) | |||||||
\(884\) | −46.6111 | −1.56770 | ||||||||
\(885\) | −29.8162 | −1.00226 | ||||||||
\(886\) | −10.4111 | −0.349767 | ||||||||
\(887\) | 32.0112 | 1.07483 | 0.537416 | − | 0.843317i | \(-0.319401\pi\) | ||||
0.537416 | + | 0.843317i | \(0.319401\pi\) | |||||||
\(888\) | −22.6249 | −0.759243 | ||||||||
\(889\) | 0.414928 | 0.0139162 | ||||||||
\(890\) | 77.5789 | 2.60045 | ||||||||
\(891\) | 0.866258 | 0.0290207 | ||||||||
\(892\) | 69.6990 | 2.33370 | ||||||||
\(893\) | −45.8167 | −1.53320 | ||||||||
\(894\) | −16.6429 | −0.556623 | ||||||||
\(895\) | 14.9476 | 0.499643 | ||||||||
\(896\) | −4.35706 | −0.145559 | ||||||||
\(897\) | −0.560946 | −0.0187294 | ||||||||
\(898\) | −90.4350 | −3.01785 | ||||||||
\(899\) | 2.47160 | 0.0824325 | ||||||||
\(900\) | 24.7694 | 0.825645 | ||||||||
\(901\) | −33.7262 | −1.12358 | ||||||||
\(902\) | 11.8246 | 0.393716 | ||||||||
\(903\) | 0.988409 | 0.0328922 | ||||||||
\(904\) | −20.7189 | −0.689099 | ||||||||
\(905\) | −18.5345 | −0.616107 | ||||||||
\(906\) | −36.3810 | −1.20868 | ||||||||
\(907\) | 29.3494 | 0.974531 | 0.487266 | − | 0.873254i | \(-0.337994\pi\) | ||||
0.487266 | + | 0.873254i | \(0.337994\pi\) | |||||||
\(908\) | 9.59764 | 0.318509 | ||||||||
\(909\) | −9.49629 | −0.314972 | ||||||||
\(910\) | 3.52309 | 0.116789 | ||||||||
\(911\) | −18.3068 | −0.606532 | −0.303266 | − | 0.952906i | \(-0.598077\pi\) | ||||
−0.303266 | + | 0.952906i | \(0.598077\pi\) | |||||||
\(912\) | −45.2478 | −1.49831 | ||||||||
\(913\) | 0.719748 | 0.0238202 | ||||||||
\(914\) | 20.9787 | 0.693915 | ||||||||
\(915\) | −9.82171 | −0.324696 | ||||||||
\(916\) | −2.06495 | −0.0682280 | ||||||||
\(917\) | −2.83368 | −0.0935765 | ||||||||
\(918\) | 16.2862 | 0.537526 | ||||||||
\(919\) | −29.3278 | −0.967436 | −0.483718 | − | 0.875224i | \(-0.660714\pi\) | ||||
−0.483718 | + | 0.875224i | \(0.660714\pi\) | |||||||
\(920\) | −5.99714 | −0.197720 | ||||||||
\(921\) | 5.52388 | 0.182018 | ||||||||
\(922\) | −41.3963 | −1.36331 | ||||||||
\(923\) | 21.1037 | 0.694638 | ||||||||
\(924\) | 0.920803 | 0.0302922 | ||||||||
\(925\) | −24.2641 | −0.797799 | ||||||||
\(926\) | 30.7355 | 1.01003 | ||||||||
\(927\) | 5.02397 | 0.165009 | ||||||||
\(928\) | 13.5304 | 0.444157 | ||||||||
\(929\) | 24.8575 | 0.815547 | 0.407773 | − | 0.913083i | \(-0.366305\pi\) | ||||
0.407773 | + | 0.913083i | \(0.366305\pi\) | |||||||
\(930\) | 3.22404 | 0.105721 | ||||||||
\(931\) | −59.5316 | −1.95107 | ||||||||
\(932\) | 41.1208 | 1.34696 | ||||||||
\(933\) | −0.610266 | −0.0199792 | ||||||||
\(934\) | −16.0657 | −0.525686 | ||||||||
\(935\) | −18.6905 | −0.611246 | ||||||||
\(936\) | 9.31213 | 0.304376 | ||||||||
\(937\) | 36.9219 | 1.20619 | 0.603093 | − | 0.797671i | \(-0.293935\pi\) | ||||
0.603093 | + | 0.797671i | \(0.293935\pi\) | |||||||
\(938\) | 9.81356 | 0.320424 | ||||||||
\(939\) | −24.6675 | −0.804995 | ||||||||
\(940\) | 74.0763 | 2.41610 | ||||||||
\(941\) | 4.92014 | 0.160392 | 0.0801959 | − | 0.996779i | \(-0.474445\pi\) | ||||
0.0801959 | + | 0.996779i | \(0.474445\pi\) | |||||||
\(942\) | 38.6506 | 1.25931 | ||||||||
\(943\) | 1.81307 | 0.0590418 | ||||||||
\(944\) | −47.6315 | −1.55027 | ||||||||
\(945\) | −0.834218 | −0.0271371 | ||||||||
\(946\) | −8.43720 | −0.274317 | ||||||||
\(947\) | −37.9354 | −1.23274 | −0.616368 | − | 0.787458i | \(-0.711397\pi\) | ||||
−0.616368 | + | 0.787458i | \(0.711397\pi\) | |||||||
\(948\) | −42.1025 | −1.36742 | ||||||||
\(949\) | 5.99784 | 0.194698 | ||||||||
\(950\) | −125.937 | −4.08594 | ||||||||
\(951\) | 29.2000 | 0.946873 | ||||||||
\(952\) | 9.07781 | 0.294213 | ||||||||
\(953\) | 53.1225 | 1.72081 | 0.860404 | − | 0.509612i | \(-0.170211\pi\) | ||||
0.860404 | + | 0.509612i | \(0.170211\pi\) | |||||||
\(954\) | 12.8495 | 0.416019 | ||||||||
\(955\) | −8.33276 | −0.269642 | ||||||||
\(956\) | 55.0548 | 1.78060 | ||||||||
\(957\) | 5.45906 | 0.176466 | ||||||||
\(958\) | 8.64316 | 0.279248 | ||||||||
\(959\) | 1.94066 | 0.0626671 | ||||||||
\(960\) | −17.1456 | −0.553373 | ||||||||
\(961\) | −30.8462 | −0.995038 | ||||||||
\(962\) | −17.3963 | −0.560881 | ||||||||
\(963\) | 14.2898 | 0.460483 | ||||||||
\(964\) | −106.934 | −3.44410 | ||||||||
\(965\) | 7.42175 | 0.238915 | ||||||||
\(966\) | 0.208340 | 0.00670322 | ||||||||
\(967\) | −46.1959 | −1.48556 | −0.742780 | − | 0.669535i | \(-0.766493\pi\) | ||||
−0.742780 | + | 0.669535i | \(0.766493\pi\) | |||||||
\(968\) | 56.2965 | 1.80944 | ||||||||
\(969\) | −56.1155 | −1.80269 | ||||||||
\(970\) | 36.8511 | 1.18322 | ||||||||
\(971\) | −50.4578 | −1.61927 | −0.809633 | − | 0.586936i | \(-0.800334\pi\) | ||||
−0.809633 | + | 0.586936i | \(0.800334\pi\) | |||||||
\(972\) | −4.20498 | −0.134875 | ||||||||
\(973\) | 1.80677 | 0.0579225 | ||||||||
\(974\) | −84.3536 | −2.70286 | ||||||||
\(975\) | 9.98679 | 0.319833 | ||||||||
\(976\) | −15.6902 | −0.502231 | ||||||||
\(977\) | −56.3159 | −1.80170 | −0.900852 | − | 0.434125i | \(-0.857057\pi\) | ||||
−0.900852 | + | 0.434125i | \(0.857057\pi\) | |||||||
\(978\) | 60.2421 | 1.92633 | ||||||||
\(979\) | 8.17518 | 0.261280 | ||||||||
\(980\) | 96.2504 | 3.07461 | ||||||||
\(981\) | 10.5485 | 0.336788 | ||||||||
\(982\) | −63.7493 | −2.03432 | ||||||||
\(983\) | 18.2181 | 0.581067 | 0.290534 | − | 0.956865i | \(-0.406167\pi\) | ||||
0.290534 | + | 0.956865i | \(0.406167\pi\) | |||||||
\(984\) | −30.0984 | −0.959503 | ||||||||
\(985\) | −4.59605 | −0.146442 | ||||||||
\(986\) | 102.634 | 3.26854 | ||||||||
\(987\) | −1.34942 | −0.0429526 | ||||||||
\(988\) | −61.1886 | −1.94667 | ||||||||
\(989\) | −1.29368 | −0.0411367 | ||||||||
\(990\) | 7.12100 | 0.226320 | ||||||||
\(991\) | −18.2555 | −0.579906 | −0.289953 | − | 0.957041i | \(-0.593640\pi\) | ||||
−0.289953 | + | 0.957041i | \(0.593640\pi\) | |||||||
\(992\) | 0.842068 | 0.0267357 | ||||||||
\(993\) | 21.1649 | 0.671648 | ||||||||
\(994\) | −7.83809 | −0.248609 | ||||||||
\(995\) | −33.4747 | −1.06122 | ||||||||
\(996\) | −3.49379 | −0.110705 | ||||||||
\(997\) | −23.0943 | −0.731403 | −0.365701 | − | 0.930732i | \(-0.619171\pi\) | ||||
−0.365701 | + | 0.930732i | \(0.619171\pi\) | |||||||
\(998\) | 0.921292 | 0.0291630 | ||||||||
\(999\) | 4.11920 | 0.130326 |
(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 | 8049.2.a.b.1.10 | ✓ | 104 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8049.2.a.b.1.10 | ✓ | 104 | 1.1 | even | 1 | trivial |