Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 17x^{6} + 37x^{5} + 105x^{4} - 117x^{3} - 238x^{2} + 42x + 90 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.36472\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.85158 | −1.72248 | −0.861240 | − | 0.508198i | \(-0.830312\pi\) | ||||
−0.861240 | + | 0.508198i | \(0.830312\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 4.10228 | 1.55052 | 0.775259 | − | 0.631644i | \(-0.217619\pi\) | ||||
0.775259 | + | 0.631644i | \(0.217619\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.85158 | 1.21798 | ||||||||
\(11\) | −2.03357 | −0.613144 | −0.306572 | − | 0.951848i | \(-0.599182\pi\) | ||||
−0.306572 | + | 0.951848i | \(0.599182\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 3.36769 | 0.934029 | 0.467014 | − | 0.884250i | \(-0.345330\pi\) | ||||
0.467014 | + | 0.884250i | \(0.345330\pi\) | |||||||
\(14\) | −4.10228 | −1.09638 | ||||||||
\(15\) | 3.85158 | 0.994474 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −6.19110 | −1.42034 | −0.710168 | − | 0.704033i | \(-0.751381\pi\) | ||||
−0.710168 | + | 0.704033i | \(0.751381\pi\) | |||||||
\(20\) | −3.85158 | −0.861240 | ||||||||
\(21\) | −4.10228 | −0.895192 | ||||||||
\(22\) | 2.03357 | 0.433558 | ||||||||
\(23\) | 0.906308 | 0.188978 | 0.0944891 | − | 0.995526i | \(-0.469878\pi\) | ||||
0.0944891 | + | 0.995526i | \(0.469878\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 9.83469 | 1.96694 | ||||||||
\(26\) | −3.36769 | −0.660458 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.10228 | 0.775259 | ||||||||
\(29\) | −2.02807 | −0.376603 | −0.188301 | − | 0.982111i | \(-0.560298\pi\) | ||||
−0.188301 | + | 0.982111i | \(0.560298\pi\) | |||||||
\(30\) | −3.85158 | −0.703200 | ||||||||
\(31\) | 6.66369 | 1.19683 | 0.598417 | − | 0.801185i | \(-0.295797\pi\) | ||||
0.598417 | + | 0.801185i | \(0.295797\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.03357 | 0.353999 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | −15.8003 | −2.67074 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.914678 | 0.150372 | 0.0751860 | − | 0.997170i | \(-0.476045\pi\) | ||||
0.0751860 | + | 0.997170i | \(0.476045\pi\) | |||||||
\(38\) | 6.19110 | 1.00433 | ||||||||
\(39\) | −3.36769 | −0.539262 | ||||||||
\(40\) | 3.85158 | 0.608989 | ||||||||
\(41\) | 4.76289 | 0.743839 | 0.371919 | − | 0.928265i | \(-0.378700\pi\) | ||||
0.371919 | + | 0.928265i | \(0.378700\pi\) | |||||||
\(42\) | 4.10228 | 0.632996 | ||||||||
\(43\) | −2.58915 | −0.394842 | −0.197421 | − | 0.980319i | \(-0.563257\pi\) | ||||
−0.197421 | + | 0.980319i | \(0.563257\pi\) | |||||||
\(44\) | −2.03357 | −0.306572 | ||||||||
\(45\) | −3.85158 | −0.574160 | ||||||||
\(46\) | −0.906308 | −0.133628 | ||||||||
\(47\) | 7.74937 | 1.13036 | 0.565181 | − | 0.824967i | \(-0.308806\pi\) | ||||
0.565181 | + | 0.824967i | \(0.308806\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 9.82874 | 1.40411 | ||||||||
\(50\) | −9.83469 | −1.39084 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 3.36769 | 0.467014 | ||||||||
\(53\) | −8.72500 | −1.19847 | −0.599236 | − | 0.800573i | \(-0.704529\pi\) | ||||
−0.599236 | + | 0.800573i | \(0.704529\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 7.83245 | 1.05613 | ||||||||
\(56\) | −4.10228 | −0.548191 | ||||||||
\(57\) | 6.19110 | 0.820031 | ||||||||
\(58\) | 2.02807 | 0.266298 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 3.85158 | 0.497237 | ||||||||
\(61\) | −10.5221 | −1.34721 | −0.673606 | − | 0.739090i | \(-0.735256\pi\) | ||||
−0.673606 | + | 0.739090i | \(0.735256\pi\) | |||||||
\(62\) | −6.66369 | −0.846289 | ||||||||
\(63\) | 4.10228 | 0.516839 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −12.9709 | −1.60885 | ||||||||
\(66\) | −2.03357 | −0.250315 | ||||||||
\(67\) | 5.05990 | 0.618165 | 0.309083 | − | 0.951035i | \(-0.399978\pi\) | ||||
0.309083 | + | 0.951035i | \(0.399978\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | −0.906308 | −0.109107 | ||||||||
\(70\) | 15.8003 | 1.88850 | ||||||||
\(71\) | 7.71254 | 0.915311 | 0.457655 | − | 0.889130i | \(-0.348689\pi\) | ||||
0.457655 | + | 0.889130i | \(0.348689\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −2.79488 | −0.327116 | −0.163558 | − | 0.986534i | \(-0.552297\pi\) | ||||
−0.163558 | + | 0.986534i | \(0.552297\pi\) | |||||||
\(74\) | −0.914678 | −0.106329 | ||||||||
\(75\) | −9.83469 | −1.13561 | ||||||||
\(76\) | −6.19110 | −0.710168 | ||||||||
\(77\) | −8.34227 | −0.950690 | ||||||||
\(78\) | 3.36769 | 0.381316 | ||||||||
\(79\) | 0.640835 | 0.0720996 | 0.0360498 | − | 0.999350i | \(-0.488523\pi\) | ||||
0.0360498 | + | 0.999350i | \(0.488523\pi\) | |||||||
\(80\) | −3.85158 | −0.430620 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.76289 | −0.525974 | ||||||||
\(83\) | −6.57742 | −0.721966 | −0.360983 | − | 0.932572i | \(-0.617559\pi\) | ||||
−0.360983 | + | 0.932572i | \(0.617559\pi\) | |||||||
\(84\) | −4.10228 | −0.447596 | ||||||||
\(85\) | 3.85158 | 0.417763 | ||||||||
\(86\) | 2.58915 | 0.279195 | ||||||||
\(87\) | 2.02807 | 0.217432 | ||||||||
\(88\) | 2.03357 | 0.216779 | ||||||||
\(89\) | 12.8278 | 1.35975 | 0.679874 | − | 0.733329i | \(-0.262034\pi\) | ||||
0.679874 | + | 0.733329i | \(0.262034\pi\) | |||||||
\(90\) | 3.85158 | 0.405992 | ||||||||
\(91\) | 13.8152 | 1.44823 | ||||||||
\(92\) | 0.906308 | 0.0944891 | ||||||||
\(93\) | −6.66369 | −0.690992 | ||||||||
\(94\) | −7.74937 | −0.799286 | ||||||||
\(95\) | 23.8455 | 2.44650 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −5.13805 | −0.521690 | −0.260845 | − | 0.965381i | \(-0.584001\pi\) | ||||
−0.260845 | + | 0.965381i | \(0.584001\pi\) | |||||||
\(98\) | −9.82874 | −0.992853 | ||||||||
\(99\) | −2.03357 | −0.204381 | ||||||||
\(100\) | 9.83469 | 0.983469 | ||||||||
\(101\) | 6.29084 | 0.625962 | 0.312981 | − | 0.949759i | \(-0.398672\pi\) | ||||
0.312981 | + | 0.949759i | \(0.398672\pi\) | |||||||
\(102\) | −1.00000 | −0.0990148 | ||||||||
\(103\) | −8.32588 | −0.820374 | −0.410187 | − | 0.912001i | \(-0.634537\pi\) | ||||
−0.410187 | + | 0.912001i | \(0.634537\pi\) | |||||||
\(104\) | −3.36769 | −0.330229 | ||||||||
\(105\) | 15.8003 | 1.54195 | ||||||||
\(106\) | 8.72500 | 0.847447 | ||||||||
\(107\) | −8.96644 | −0.866819 | −0.433409 | − | 0.901197i | \(-0.642690\pi\) | ||||
−0.433409 | + | 0.901197i | \(0.642690\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −2.10396 | −0.201523 | −0.100761 | − | 0.994911i | \(-0.532128\pi\) | ||||
−0.100761 | + | 0.994911i | \(0.532128\pi\) | |||||||
\(110\) | −7.83245 | −0.746795 | ||||||||
\(111\) | −0.914678 | −0.0868174 | ||||||||
\(112\) | 4.10228 | 0.387629 | ||||||||
\(113\) | 2.72031 | 0.255905 | 0.127953 | − | 0.991780i | \(-0.459159\pi\) | ||||
0.127953 | + | 0.991780i | \(0.459159\pi\) | |||||||
\(114\) | −6.19110 | −0.579849 | ||||||||
\(115\) | −3.49072 | −0.325511 | ||||||||
\(116\) | −2.02807 | −0.188301 | ||||||||
\(117\) | 3.36769 | 0.311343 | ||||||||
\(118\) | −1.00000 | −0.0920575 | ||||||||
\(119\) | −4.10228 | −0.376056 | ||||||||
\(120\) | −3.85158 | −0.351600 | ||||||||
\(121\) | −6.86460 | −0.624055 | ||||||||
\(122\) | 10.5221 | 0.952623 | ||||||||
\(123\) | −4.76289 | −0.429456 | ||||||||
\(124\) | 6.66369 | 0.598417 | ||||||||
\(125\) | −18.6212 | −1.66553 | ||||||||
\(126\) | −4.10228 | −0.365461 | ||||||||
\(127\) | −17.3191 | −1.53682 | −0.768410 | − | 0.639958i | \(-0.778952\pi\) | ||||
−0.768410 | + | 0.639958i | \(0.778952\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.58915 | 0.227962 | ||||||||
\(130\) | 12.9709 | 1.13763 | ||||||||
\(131\) | −13.5534 | −1.18416 | −0.592081 | − | 0.805878i | \(-0.701694\pi\) | ||||
−0.592081 | + | 0.805878i | \(0.701694\pi\) | |||||||
\(132\) | 2.03357 | 0.176999 | ||||||||
\(133\) | −25.3976 | −2.20226 | ||||||||
\(134\) | −5.05990 | −0.437109 | ||||||||
\(135\) | 3.85158 | 0.331491 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −2.68219 | −0.229155 | −0.114578 | − | 0.993414i | \(-0.536551\pi\) | ||||
−0.114578 | + | 0.993414i | \(0.536551\pi\) | |||||||
\(138\) | 0.906308 | 0.0771501 | ||||||||
\(139\) | 14.7398 | 1.25022 | 0.625108 | − | 0.780538i | \(-0.285055\pi\) | ||||
0.625108 | + | 0.780538i | \(0.285055\pi\) | |||||||
\(140\) | −15.8003 | −1.33537 | ||||||||
\(141\) | −7.74937 | −0.652615 | ||||||||
\(142\) | −7.71254 | −0.647222 | ||||||||
\(143\) | −6.84842 | −0.572694 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 7.81127 | 0.648691 | ||||||||
\(146\) | 2.79488 | 0.231306 | ||||||||
\(147\) | −9.82874 | −0.810661 | ||||||||
\(148\) | 0.914678 | 0.0751860 | ||||||||
\(149\) | 3.89820 | 0.319353 | 0.159677 | − | 0.987169i | \(-0.448955\pi\) | ||||
0.159677 | + | 0.987169i | \(0.448955\pi\) | |||||||
\(150\) | 9.83469 | 0.802999 | ||||||||
\(151\) | −10.0378 | −0.816869 | −0.408434 | − | 0.912788i | \(-0.633925\pi\) | ||||
−0.408434 | + | 0.912788i | \(0.633925\pi\) | |||||||
\(152\) | 6.19110 | 0.502164 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 8.34227 | 0.672239 | ||||||||
\(155\) | −25.6657 | −2.06152 | ||||||||
\(156\) | −3.36769 | −0.269631 | ||||||||
\(157\) | 10.9642 | 0.875041 | 0.437521 | − | 0.899208i | \(-0.355857\pi\) | ||||
0.437521 | + | 0.899208i | \(0.355857\pi\) | |||||||
\(158\) | −0.640835 | −0.0509821 | ||||||||
\(159\) | 8.72500 | 0.691938 | ||||||||
\(160\) | 3.85158 | 0.304494 | ||||||||
\(161\) | 3.71793 | 0.293014 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 24.7990 | 1.94241 | 0.971205 | − | 0.238245i | \(-0.0765721\pi\) | ||||
0.971205 | + | 0.238245i | \(0.0765721\pi\) | |||||||
\(164\) | 4.76289 | 0.371919 | ||||||||
\(165\) | −7.83245 | −0.609756 | ||||||||
\(166\) | 6.57742 | 0.510507 | ||||||||
\(167\) | −9.47876 | −0.733488 | −0.366744 | − | 0.930322i | \(-0.619528\pi\) | ||||
−0.366744 | + | 0.930322i | \(0.619528\pi\) | |||||||
\(168\) | 4.10228 | 0.316498 | ||||||||
\(169\) | −1.65868 | −0.127591 | ||||||||
\(170\) | −3.85158 | −0.295403 | ||||||||
\(171\) | −6.19110 | −0.473445 | ||||||||
\(172\) | −2.58915 | −0.197421 | ||||||||
\(173\) | −4.53051 | −0.344448 | −0.172224 | − | 0.985058i | \(-0.555095\pi\) | ||||
−0.172224 | + | 0.985058i | \(0.555095\pi\) | |||||||
\(174\) | −2.02807 | −0.153747 | ||||||||
\(175\) | 40.3447 | 3.04977 | ||||||||
\(176\) | −2.03357 | −0.153286 | ||||||||
\(177\) | −1.00000 | −0.0751646 | ||||||||
\(178\) | −12.8278 | −0.961487 | ||||||||
\(179\) | 1.28226 | 0.0958406 | 0.0479203 | − | 0.998851i | \(-0.484741\pi\) | ||||
0.0479203 | + | 0.998851i | \(0.484741\pi\) | |||||||
\(180\) | −3.85158 | −0.287080 | ||||||||
\(181\) | 2.18692 | 0.162553 | 0.0812763 | − | 0.996692i | \(-0.474100\pi\) | ||||
0.0812763 | + | 0.996692i | \(0.474100\pi\) | |||||||
\(182\) | −13.8152 | −1.02405 | ||||||||
\(183\) | 10.5221 | 0.777814 | ||||||||
\(184\) | −0.906308 | −0.0668139 | ||||||||
\(185\) | −3.52296 | −0.259013 | ||||||||
\(186\) | 6.66369 | 0.488605 | ||||||||
\(187\) | 2.03357 | 0.148709 | ||||||||
\(188\) | 7.74937 | 0.565181 | ||||||||
\(189\) | −4.10228 | −0.298397 | ||||||||
\(190\) | −23.8455 | −1.72994 | ||||||||
\(191\) | −7.49899 | −0.542608 | −0.271304 | − | 0.962494i | \(-0.587455\pi\) | ||||
−0.271304 | + | 0.962494i | \(0.587455\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 4.84547 | 0.348784 | 0.174392 | − | 0.984676i | \(-0.444204\pi\) | ||||
0.174392 | + | 0.984676i | \(0.444204\pi\) | |||||||
\(194\) | 5.13805 | 0.368891 | ||||||||
\(195\) | 12.9709 | 0.928868 | ||||||||
\(196\) | 9.82874 | 0.702053 | ||||||||
\(197\) | 15.3061 | 1.09052 | 0.545258 | − | 0.838268i | \(-0.316432\pi\) | ||||
0.545258 | + | 0.838268i | \(0.316432\pi\) | |||||||
\(198\) | 2.03357 | 0.144519 | ||||||||
\(199\) | 6.62692 | 0.469770 | 0.234885 | − | 0.972023i | \(-0.424529\pi\) | ||||
0.234885 | + | 0.972023i | \(0.424529\pi\) | |||||||
\(200\) | −9.83469 | −0.695418 | ||||||||
\(201\) | −5.05990 | −0.356898 | ||||||||
\(202\) | −6.29084 | −0.442622 | ||||||||
\(203\) | −8.31971 | −0.583929 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | −18.3447 | −1.28125 | ||||||||
\(206\) | 8.32588 | 0.580092 | ||||||||
\(207\) | 0.906308 | 0.0629928 | ||||||||
\(208\) | 3.36769 | 0.233507 | ||||||||
\(209\) | 12.5900 | 0.870869 | ||||||||
\(210\) | −15.8003 | −1.09032 | ||||||||
\(211\) | 16.6354 | 1.14522 | 0.572612 | − | 0.819826i | \(-0.305930\pi\) | ||||
0.572612 | + | 0.819826i | \(0.305930\pi\) | |||||||
\(212\) | −8.72500 | −0.599236 | ||||||||
\(213\) | −7.71254 | −0.528455 | ||||||||
\(214\) | 8.96644 | 0.612933 | ||||||||
\(215\) | 9.97232 | 0.680107 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 27.3363 | 1.85571 | ||||||||
\(218\) | 2.10396 | 0.142498 | ||||||||
\(219\) | 2.79488 | 0.188860 | ||||||||
\(220\) | 7.83245 | 0.528064 | ||||||||
\(221\) | −3.36769 | −0.226535 | ||||||||
\(222\) | 0.914678 | 0.0613891 | ||||||||
\(223\) | −1.93856 | −0.129815 | −0.0649076 | − | 0.997891i | \(-0.520675\pi\) | ||||
−0.0649076 | + | 0.997891i | \(0.520675\pi\) | |||||||
\(224\) | −4.10228 | −0.274095 | ||||||||
\(225\) | 9.83469 | 0.655646 | ||||||||
\(226\) | −2.72031 | −0.180952 | ||||||||
\(227\) | −9.70323 | −0.644026 | −0.322013 | − | 0.946735i | \(-0.604359\pi\) | ||||
−0.322013 | + | 0.946735i | \(0.604359\pi\) | |||||||
\(228\) | 6.19110 | 0.410015 | ||||||||
\(229\) | −21.2594 | −1.40486 | −0.702431 | − | 0.711752i | \(-0.747902\pi\) | ||||
−0.702431 | + | 0.711752i | \(0.747902\pi\) | |||||||
\(230\) | 3.49072 | 0.230171 | ||||||||
\(231\) | 8.34227 | 0.548881 | ||||||||
\(232\) | 2.02807 | 0.133149 | ||||||||
\(233\) | 9.13446 | 0.598418 | 0.299209 | − | 0.954188i | \(-0.403277\pi\) | ||||
0.299209 | + | 0.954188i | \(0.403277\pi\) | |||||||
\(234\) | −3.36769 | −0.220153 | ||||||||
\(235\) | −29.8473 | −1.94703 | ||||||||
\(236\) | 1.00000 | 0.0650945 | ||||||||
\(237\) | −0.640835 | −0.0416267 | ||||||||
\(238\) | 4.10228 | 0.265912 | ||||||||
\(239\) | −14.6133 | −0.945253 | −0.472626 | − | 0.881263i | \(-0.656694\pi\) | ||||
−0.472626 | + | 0.881263i | \(0.656694\pi\) | |||||||
\(240\) | 3.85158 | 0.248619 | ||||||||
\(241\) | −16.3402 | −1.05257 | −0.526283 | − | 0.850309i | \(-0.676415\pi\) | ||||
−0.526283 | + | 0.850309i | \(0.676415\pi\) | |||||||
\(242\) | 6.86460 | 0.441273 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −10.5221 | −0.673606 | ||||||||
\(245\) | −37.8562 | −2.41854 | ||||||||
\(246\) | 4.76289 | 0.303671 | ||||||||
\(247\) | −20.8497 | −1.32663 | ||||||||
\(248\) | −6.66369 | −0.423145 | ||||||||
\(249\) | 6.57742 | 0.416827 | ||||||||
\(250\) | 18.6212 | 1.17771 | ||||||||
\(251\) | −7.29327 | −0.460347 | −0.230174 | − | 0.973150i | \(-0.573929\pi\) | ||||
−0.230174 | + | 0.973150i | \(0.573929\pi\) | |||||||
\(252\) | 4.10228 | 0.258420 | ||||||||
\(253\) | −1.84304 | −0.115871 | ||||||||
\(254\) | 17.3191 | 1.08670 | ||||||||
\(255\) | −3.85158 | −0.241195 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.3591 | 0.770937 | 0.385469 | − | 0.922721i | \(-0.374040\pi\) | ||||
0.385469 | + | 0.922721i | \(0.374040\pi\) | |||||||
\(258\) | −2.58915 | −0.161193 | ||||||||
\(259\) | 3.75227 | 0.233155 | ||||||||
\(260\) | −12.9709 | −0.804423 | ||||||||
\(261\) | −2.02807 | −0.125534 | ||||||||
\(262\) | 13.5534 | 0.837329 | ||||||||
\(263\) | 20.2388 | 1.24798 | 0.623988 | − | 0.781434i | \(-0.285512\pi\) | ||||
0.623988 | + | 0.781434i | \(0.285512\pi\) | |||||||
\(264\) | −2.03357 | −0.125157 | ||||||||
\(265\) | 33.6051 | 2.06434 | ||||||||
\(266\) | 25.3976 | 1.55723 | ||||||||
\(267\) | −12.8278 | −0.785051 | ||||||||
\(268\) | 5.05990 | 0.309083 | ||||||||
\(269\) | 28.6320 | 1.74572 | 0.872862 | − | 0.487968i | \(-0.162262\pi\) | ||||
0.872862 | + | 0.487968i | \(0.162262\pi\) | |||||||
\(270\) | −3.85158 | −0.234400 | ||||||||
\(271\) | 0.0160069 | 0.000972353 0 | 0.000486176 | − | 1.00000i | \(-0.499845\pi\) | ||||
0.000486176 | 1.00000i | \(0.499845\pi\) | ||||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | −13.8152 | −0.836135 | ||||||||
\(274\) | 2.68219 | 0.162037 | ||||||||
\(275\) | −19.9995 | −1.20602 | ||||||||
\(276\) | −0.906308 | −0.0545533 | ||||||||
\(277\) | 26.2831 | 1.57920 | 0.789598 | − | 0.613624i | \(-0.210289\pi\) | ||||
0.789598 | + | 0.613624i | \(0.210289\pi\) | |||||||
\(278\) | −14.7398 | −0.884037 | ||||||||
\(279\) | 6.66369 | 0.398945 | ||||||||
\(280\) | 15.8003 | 0.944248 | ||||||||
\(281\) | 30.6341 | 1.82748 | 0.913740 | − | 0.406300i | \(-0.133181\pi\) | ||||
0.913740 | + | 0.406300i | \(0.133181\pi\) | |||||||
\(282\) | 7.74937 | 0.461468 | ||||||||
\(283\) | 0.234324 | 0.0139291 | 0.00696455 | − | 0.999976i | \(-0.497783\pi\) | ||||
0.00696455 | + | 0.999976i | \(0.497783\pi\) | |||||||
\(284\) | 7.71254 | 0.457655 | ||||||||
\(285\) | −23.8455 | −1.41249 | ||||||||
\(286\) | 6.84842 | 0.404956 | ||||||||
\(287\) | 19.5387 | 1.15334 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −7.81127 | −0.458694 | ||||||||
\(291\) | 5.13805 | 0.301198 | ||||||||
\(292\) | −2.79488 | −0.163558 | ||||||||
\(293\) | −3.63443 | −0.212326 | −0.106163 | − | 0.994349i | \(-0.533856\pi\) | ||||
−0.106163 | + | 0.994349i | \(0.533856\pi\) | |||||||
\(294\) | 9.82874 | 0.573224 | ||||||||
\(295\) | −3.85158 | −0.224248 | ||||||||
\(296\) | −0.914678 | −0.0531646 | ||||||||
\(297\) | 2.03357 | 0.118000 | ||||||||
\(298\) | −3.89820 | −0.225817 | ||||||||
\(299\) | 3.05216 | 0.176511 | ||||||||
\(300\) | −9.83469 | −0.567806 | ||||||||
\(301\) | −10.6214 | −0.612209 | ||||||||
\(302\) | 10.0378 | 0.577613 | ||||||||
\(303\) | −6.29084 | −0.361399 | ||||||||
\(304\) | −6.19110 | −0.355084 | ||||||||
\(305\) | 40.5266 | 2.32055 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | 15.7695 | 0.900011 | 0.450005 | − | 0.893026i | \(-0.351422\pi\) | ||||
0.450005 | + | 0.893026i | \(0.351422\pi\) | |||||||
\(308\) | −8.34227 | −0.475345 | ||||||||
\(309\) | 8.32588 | 0.473643 | ||||||||
\(310\) | 25.6657 | 1.45772 | ||||||||
\(311\) | 31.5974 | 1.79173 | 0.895863 | − | 0.444331i | \(-0.146559\pi\) | ||||
0.895863 | + | 0.444331i | \(0.146559\pi\) | |||||||
\(312\) | 3.36769 | 0.190658 | ||||||||
\(313\) | 12.5346 | 0.708497 | 0.354249 | − | 0.935151i | \(-0.384737\pi\) | ||||
0.354249 | + | 0.935151i | \(0.384737\pi\) | |||||||
\(314\) | −10.9642 | −0.618748 | ||||||||
\(315\) | −15.8003 | −0.890245 | ||||||||
\(316\) | 0.640835 | 0.0360498 | ||||||||
\(317\) | 8.78766 | 0.493564 | 0.246782 | − | 0.969071i | \(-0.420627\pi\) | ||||
0.246782 | + | 0.969071i | \(0.420627\pi\) | |||||||
\(318\) | −8.72500 | −0.489274 | ||||||||
\(319\) | 4.12421 | 0.230912 | ||||||||
\(320\) | −3.85158 | −0.215310 | ||||||||
\(321\) | 8.96644 | 0.500458 | ||||||||
\(322\) | −3.71793 | −0.207192 | ||||||||
\(323\) | 6.19110 | 0.344482 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 33.1202 | 1.83718 | ||||||||
\(326\) | −24.7990 | −1.37349 | ||||||||
\(327\) | 2.10396 | 0.116349 | ||||||||
\(328\) | −4.76289 | −0.262987 | ||||||||
\(329\) | 31.7901 | 1.75265 | ||||||||
\(330\) | 7.83245 | 0.431162 | ||||||||
\(331\) | 28.1629 | 1.54797 | 0.773987 | − | 0.633202i | \(-0.218260\pi\) | ||||
0.773987 | + | 0.633202i | \(0.218260\pi\) | |||||||
\(332\) | −6.57742 | −0.360983 | ||||||||
\(333\) | 0.914678 | 0.0501240 | ||||||||
\(334\) | 9.47876 | 0.518655 | ||||||||
\(335\) | −19.4886 | −1.06478 | ||||||||
\(336\) | −4.10228 | −0.223798 | ||||||||
\(337\) | −28.0093 | −1.52576 | −0.762882 | − | 0.646537i | \(-0.776217\pi\) | ||||
−0.762882 | + | 0.646537i | \(0.776217\pi\) | |||||||
\(338\) | 1.65868 | 0.0902201 | ||||||||
\(339\) | −2.72031 | −0.147747 | ||||||||
\(340\) | 3.85158 | 0.208881 | ||||||||
\(341\) | −13.5511 | −0.733831 | ||||||||
\(342\) | 6.19110 | 0.334776 | ||||||||
\(343\) | 11.6043 | 0.626573 | ||||||||
\(344\) | 2.58915 | 0.139598 | ||||||||
\(345\) | 3.49072 | 0.187934 | ||||||||
\(346\) | 4.53051 | 0.243562 | ||||||||
\(347\) | 29.5665 | 1.58721 | 0.793607 | − | 0.608431i | \(-0.208201\pi\) | ||||
0.793607 | + | 0.608431i | \(0.208201\pi\) | |||||||
\(348\) | 2.02807 | 0.108716 | ||||||||
\(349\) | 28.6964 | 1.53608 | 0.768042 | − | 0.640399i | \(-0.221231\pi\) | ||||
0.768042 | + | 0.640399i | \(0.221231\pi\) | |||||||
\(350\) | −40.3447 | −2.15652 | ||||||||
\(351\) | −3.36769 | −0.179754 | ||||||||
\(352\) | 2.03357 | 0.108390 | ||||||||
\(353\) | −5.29416 | −0.281780 | −0.140890 | − | 0.990025i | \(-0.544996\pi\) | ||||
−0.140890 | + | 0.990025i | \(0.544996\pi\) | |||||||
\(354\) | 1.00000 | 0.0531494 | ||||||||
\(355\) | −29.7055 | −1.57660 | ||||||||
\(356\) | 12.8278 | 0.679874 | ||||||||
\(357\) | 4.10228 | 0.217116 | ||||||||
\(358\) | −1.28226 | −0.0677696 | ||||||||
\(359\) | 1.73252 | 0.0914391 | 0.0457195 | − | 0.998954i | \(-0.485442\pi\) | ||||
0.0457195 | + | 0.998954i | \(0.485442\pi\) | |||||||
\(360\) | 3.85158 | 0.202996 | ||||||||
\(361\) | 19.3297 | 1.01735 | ||||||||
\(362\) | −2.18692 | −0.114942 | ||||||||
\(363\) | 6.86460 | 0.360298 | ||||||||
\(364\) | 13.8152 | 0.724114 | ||||||||
\(365\) | 10.7647 | 0.563451 | ||||||||
\(366\) | −10.5221 | −0.549997 | ||||||||
\(367\) | −28.1227 | −1.46799 | −0.733996 | − | 0.679153i | \(-0.762347\pi\) | ||||
−0.733996 | + | 0.679153i | \(0.762347\pi\) | |||||||
\(368\) | 0.906308 | 0.0472446 | ||||||||
\(369\) | 4.76289 | 0.247946 | ||||||||
\(370\) | 3.52296 | 0.183150 | ||||||||
\(371\) | −35.7924 | −1.85825 | ||||||||
\(372\) | −6.66369 | −0.345496 | ||||||||
\(373\) | −12.4392 | −0.644079 | −0.322040 | − | 0.946726i | \(-0.604368\pi\) | ||||
−0.322040 | + | 0.946726i | \(0.604368\pi\) | |||||||
\(374\) | −2.03357 | −0.105153 | ||||||||
\(375\) | 18.6212 | 0.961595 | ||||||||
\(376\) | −7.74937 | −0.399643 | ||||||||
\(377\) | −6.82990 | −0.351758 | ||||||||
\(378\) | 4.10228 | 0.210999 | ||||||||
\(379\) | −6.21140 | −0.319058 | −0.159529 | − | 0.987193i | \(-0.550998\pi\) | ||||
−0.159529 | + | 0.987193i | \(0.550998\pi\) | |||||||
\(380\) | 23.8455 | 1.22325 | ||||||||
\(381\) | 17.3191 | 0.887283 | ||||||||
\(382\) | 7.49899 | 0.383682 | ||||||||
\(383\) | −5.50310 | −0.281195 | −0.140598 | − | 0.990067i | \(-0.544902\pi\) | ||||
−0.140598 | + | 0.990067i | \(0.544902\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 32.1310 | 1.63755 | ||||||||
\(386\) | −4.84547 | −0.246628 | ||||||||
\(387\) | −2.58915 | −0.131614 | ||||||||
\(388\) | −5.13805 | −0.260845 | ||||||||
\(389\) | 24.9539 | 1.26522 | 0.632608 | − | 0.774473i | \(-0.281985\pi\) | ||||
0.632608 | + | 0.774473i | \(0.281985\pi\) | |||||||
\(390\) | −12.9709 | −0.656809 | ||||||||
\(391\) | −0.906308 | −0.0458340 | ||||||||
\(392\) | −9.82874 | −0.496426 | ||||||||
\(393\) | 13.5534 | 0.683677 | ||||||||
\(394\) | −15.3061 | −0.771111 | ||||||||
\(395\) | −2.46823 | −0.124190 | ||||||||
\(396\) | −2.03357 | −0.102191 | ||||||||
\(397\) | −12.0760 | −0.606075 | −0.303037 | − | 0.952979i | \(-0.598001\pi\) | ||||
−0.303037 | + | 0.952979i | \(0.598001\pi\) | |||||||
\(398\) | −6.62692 | −0.332177 | ||||||||
\(399\) | 25.3976 | 1.27147 | ||||||||
\(400\) | 9.83469 | 0.491735 | ||||||||
\(401\) | 39.3071 | 1.96290 | 0.981452 | − | 0.191711i | \(-0.0614035\pi\) | ||||
0.981452 | + | 0.191711i | \(0.0614035\pi\) | |||||||
\(402\) | 5.05990 | 0.252365 | ||||||||
\(403\) | 22.4412 | 1.11788 | ||||||||
\(404\) | 6.29084 | 0.312981 | ||||||||
\(405\) | −3.85158 | −0.191387 | ||||||||
\(406\) | 8.31971 | 0.412900 | ||||||||
\(407\) | −1.86006 | −0.0921997 | ||||||||
\(408\) | −1.00000 | −0.0495074 | ||||||||
\(409\) | 28.9306 | 1.43053 | 0.715263 | − | 0.698856i | \(-0.246307\pi\) | ||||
0.715263 | + | 0.698856i | \(0.246307\pi\) | |||||||
\(410\) | 18.3447 | 0.905979 | ||||||||
\(411\) | 2.68219 | 0.132303 | ||||||||
\(412\) | −8.32588 | −0.410187 | ||||||||
\(413\) | 4.10228 | 0.201860 | ||||||||
\(414\) | −0.906308 | −0.0445426 | ||||||||
\(415\) | 25.3335 | 1.24357 | ||||||||
\(416\) | −3.36769 | −0.165114 | ||||||||
\(417\) | −14.7398 | −0.721813 | ||||||||
\(418\) | −12.5900 | −0.615798 | ||||||||
\(419\) | 16.0554 | 0.784360 | 0.392180 | − | 0.919889i | \(-0.371721\pi\) | ||||
0.392180 | + | 0.919889i | \(0.371721\pi\) | |||||||
\(420\) | 15.8003 | 0.770975 | ||||||||
\(421\) | 19.7480 | 0.962461 | 0.481231 | − | 0.876594i | \(-0.340190\pi\) | ||||
0.481231 | + | 0.876594i | \(0.340190\pi\) | |||||||
\(422\) | −16.6354 | −0.809796 | ||||||||
\(423\) | 7.74937 | 0.376787 | ||||||||
\(424\) | 8.72500 | 0.423724 | ||||||||
\(425\) | −9.83469 | −0.477053 | ||||||||
\(426\) | 7.71254 | 0.373674 | ||||||||
\(427\) | −43.1645 | −2.08888 | ||||||||
\(428\) | −8.96644 | −0.433409 | ||||||||
\(429\) | 6.84842 | 0.330645 | ||||||||
\(430\) | −9.97232 | −0.480908 | ||||||||
\(431\) | 20.4445 | 0.984778 | 0.492389 | − | 0.870375i | \(-0.336124\pi\) | ||||
0.492389 | + | 0.870375i | \(0.336124\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 9.91123 | 0.476303 | 0.238152 | − | 0.971228i | \(-0.423458\pi\) | ||||
0.238152 | + | 0.971228i | \(0.423458\pi\) | |||||||
\(434\) | −27.3363 | −1.31219 | ||||||||
\(435\) | −7.81127 | −0.374522 | ||||||||
\(436\) | −2.10396 | −0.100761 | ||||||||
\(437\) | −5.61104 | −0.268412 | ||||||||
\(438\) | −2.79488 | −0.133545 | ||||||||
\(439\) | −16.4570 | −0.785452 | −0.392726 | − | 0.919656i | \(-0.628468\pi\) | ||||
−0.392726 | + | 0.919656i | \(0.628468\pi\) | |||||||
\(440\) | −7.83245 | −0.373398 | ||||||||
\(441\) | 9.82874 | 0.468035 | ||||||||
\(442\) | 3.36769 | 0.160185 | ||||||||
\(443\) | −22.6158 | −1.07451 | −0.537254 | − | 0.843420i | \(-0.680538\pi\) | ||||
−0.537254 | + | 0.843420i | \(0.680538\pi\) | |||||||
\(444\) | −0.914678 | −0.0434087 | ||||||||
\(445\) | −49.4075 | −2.34214 | ||||||||
\(446\) | 1.93856 | 0.0917933 | ||||||||
\(447\) | −3.89820 | −0.184379 | ||||||||
\(448\) | 4.10228 | 0.193815 | ||||||||
\(449\) | −12.8141 | −0.604734 | −0.302367 | − | 0.953192i | \(-0.597777\pi\) | ||||
−0.302367 | + | 0.953192i | \(0.597777\pi\) | |||||||
\(450\) | −9.83469 | −0.463612 | ||||||||
\(451\) | −9.68566 | −0.456080 | ||||||||
\(452\) | 2.72031 | 0.127953 | ||||||||
\(453\) | 10.0378 | 0.471619 | ||||||||
\(454\) | 9.70323 | 0.455395 | ||||||||
\(455\) | −53.2104 | −2.49454 | ||||||||
\(456\) | −6.19110 | −0.289925 | ||||||||
\(457\) | 30.5625 | 1.42966 | 0.714828 | − | 0.699301i | \(-0.246505\pi\) | ||||
0.714828 | + | 0.699301i | \(0.246505\pi\) | |||||||
\(458\) | 21.2594 | 0.993387 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −3.49072 | −0.162756 | ||||||||
\(461\) | −8.23817 | −0.383690 | −0.191845 | − | 0.981425i | \(-0.561447\pi\) | ||||
−0.191845 | + | 0.981425i | \(0.561447\pi\) | |||||||
\(462\) | −8.34227 | −0.388118 | ||||||||
\(463\) | −14.1573 | −0.657946 | −0.328973 | − | 0.944339i | \(-0.606703\pi\) | ||||
−0.328973 | + | 0.944339i | \(0.606703\pi\) | |||||||
\(464\) | −2.02807 | −0.0941507 | ||||||||
\(465\) | 25.6657 | 1.19022 | ||||||||
\(466\) | −9.13446 | −0.423146 | ||||||||
\(467\) | −9.80450 | −0.453698 | −0.226849 | − | 0.973930i | \(-0.572842\pi\) | ||||
−0.226849 | + | 0.973930i | \(0.572842\pi\) | |||||||
\(468\) | 3.36769 | 0.155671 | ||||||||
\(469\) | 20.7572 | 0.958477 | ||||||||
\(470\) | 29.8473 | 1.37675 | ||||||||
\(471\) | −10.9642 | −0.505205 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | 5.26521 | 0.242095 | ||||||||
\(474\) | 0.640835 | 0.0294345 | ||||||||
\(475\) | −60.8875 | −2.79371 | ||||||||
\(476\) | −4.10228 | −0.188028 | ||||||||
\(477\) | −8.72500 | −0.399490 | ||||||||
\(478\) | 14.6133 | 0.668395 | ||||||||
\(479\) | 37.7151 | 1.72325 | 0.861624 | − | 0.507547i | \(-0.169448\pi\) | ||||
0.861624 | + | 0.507547i | \(0.169448\pi\) | |||||||
\(480\) | −3.85158 | −0.175800 | ||||||||
\(481\) | 3.08035 | 0.140452 | ||||||||
\(482\) | 16.3402 | 0.744277 | ||||||||
\(483\) | −3.71793 | −0.169172 | ||||||||
\(484\) | −6.86460 | −0.312027 | ||||||||
\(485\) | 19.7896 | 0.898601 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 25.9042 | 1.17383 | 0.586915 | − | 0.809648i | \(-0.300342\pi\) | ||||
0.586915 | + | 0.809648i | \(0.300342\pi\) | |||||||
\(488\) | 10.5221 | 0.476312 | ||||||||
\(489\) | −24.7990 | −1.12145 | ||||||||
\(490\) | 37.8562 | 1.71017 | ||||||||
\(491\) | 9.43153 | 0.425639 | 0.212819 | − | 0.977092i | \(-0.431735\pi\) | ||||
0.212819 | + | 0.977092i | \(0.431735\pi\) | |||||||
\(492\) | −4.76289 | −0.214728 | ||||||||
\(493\) | 2.02807 | 0.0913396 | ||||||||
\(494\) | 20.8497 | 0.938072 | ||||||||
\(495\) | 7.83245 | 0.352043 | ||||||||
\(496\) | 6.66369 | 0.299208 | ||||||||
\(497\) | 31.6391 | 1.41921 | ||||||||
\(498\) | −6.57742 | −0.294741 | ||||||||
\(499\) | 15.0782 | 0.674994 | 0.337497 | − | 0.941327i | \(-0.390420\pi\) | ||||
0.337497 | + | 0.941327i | \(0.390420\pi\) | |||||||
\(500\) | −18.6212 | −0.832766 | ||||||||
\(501\) | 9.47876 | 0.423480 | ||||||||
\(502\) | 7.29327 | 0.325515 | ||||||||
\(503\) | −6.89424 | −0.307399 | −0.153699 | − | 0.988118i | \(-0.549119\pi\) | ||||
−0.153699 | + | 0.988118i | \(0.549119\pi\) | |||||||
\(504\) | −4.10228 | −0.182730 | ||||||||
\(505\) | −24.2297 | −1.07821 | ||||||||
\(506\) | 1.84304 | 0.0819330 | ||||||||
\(507\) | 1.65868 | 0.0736644 | ||||||||
\(508\) | −17.3191 | −0.768410 | ||||||||
\(509\) | −15.3575 | −0.680707 | −0.340354 | − | 0.940298i | \(-0.610547\pi\) | ||||
−0.340354 | + | 0.940298i | \(0.610547\pi\) | |||||||
\(510\) | 3.85158 | 0.170551 | ||||||||
\(511\) | −11.4654 | −0.507199 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 6.19110 | 0.273344 | ||||||||
\(514\) | −12.3591 | −0.545135 | ||||||||
\(515\) | 32.0678 | 1.41308 | ||||||||
\(516\) | 2.58915 | 0.113981 | ||||||||
\(517\) | −15.7589 | −0.693074 | ||||||||
\(518\) | −3.75227 | −0.164865 | ||||||||
\(519\) | 4.53051 | 0.198867 | ||||||||
\(520\) | 12.9709 | 0.568813 | ||||||||
\(521\) | −43.0445 | −1.88581 | −0.942907 | − | 0.333057i | \(-0.891920\pi\) | ||||
−0.942907 | + | 0.333057i | \(0.891920\pi\) | |||||||
\(522\) | 2.02807 | 0.0887661 | ||||||||
\(523\) | 37.4999 | 1.63976 | 0.819878 | − | 0.572538i | \(-0.194041\pi\) | ||||
0.819878 | + | 0.572538i | \(0.194041\pi\) | |||||||
\(524\) | −13.5534 | −0.592081 | ||||||||
\(525\) | −40.3447 | −1.76079 | ||||||||
\(526\) | −20.2388 | −0.882452 | ||||||||
\(527\) | −6.66369 | −0.290275 | ||||||||
\(528\) | 2.03357 | 0.0884997 | ||||||||
\(529\) | −22.1786 | −0.964287 | ||||||||
\(530\) | −33.6051 | −1.45971 | ||||||||
\(531\) | 1.00000 | 0.0433963 | ||||||||
\(532\) | −25.3976 | −1.10113 | ||||||||
\(533\) | 16.0399 | 0.694767 | ||||||||
\(534\) | 12.8278 | 0.555115 | ||||||||
\(535\) | 34.5350 | 1.49308 | ||||||||
\(536\) | −5.05990 | −0.218554 | ||||||||
\(537\) | −1.28226 | −0.0553336 | ||||||||
\(538\) | −28.6320 | −1.23441 | ||||||||
\(539\) | −19.9874 | −0.860919 | ||||||||
\(540\) | 3.85158 | 0.165746 | ||||||||
\(541\) | −26.7279 | −1.14912 | −0.574561 | − | 0.818461i | \(-0.694827\pi\) | ||||
−0.574561 | + | 0.818461i | \(0.694827\pi\) | |||||||
\(542\) | −0.0160069 | −0.000687557 0 | ||||||||
\(543\) | −2.18692 | −0.0938498 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 8.10357 | 0.347119 | ||||||||
\(546\) | 13.8152 | 0.591237 | ||||||||
\(547\) | 29.7929 | 1.27385 | 0.636926 | − | 0.770925i | \(-0.280206\pi\) | ||||
0.636926 | + | 0.770925i | \(0.280206\pi\) | |||||||
\(548\) | −2.68219 | −0.114578 | ||||||||
\(549\) | −10.5221 | −0.449071 | ||||||||
\(550\) | 19.9995 | 0.852782 | ||||||||
\(551\) | 12.5560 | 0.534902 | ||||||||
\(552\) | 0.906308 | 0.0385750 | ||||||||
\(553\) | 2.62889 | 0.111792 | ||||||||
\(554\) | −26.2831 | −1.11666 | ||||||||
\(555\) | 3.52296 | 0.149541 | ||||||||
\(556\) | 14.7398 | 0.625108 | ||||||||
\(557\) | 19.5006 | 0.826265 | 0.413133 | − | 0.910671i | \(-0.364435\pi\) | ||||
0.413133 | + | 0.910671i | \(0.364435\pi\) | |||||||
\(558\) | −6.66369 | −0.282096 | ||||||||
\(559\) | −8.71945 | −0.368793 | ||||||||
\(560\) | −15.8003 | −0.667684 | ||||||||
\(561\) | −2.03357 | −0.0858573 | ||||||||
\(562\) | −30.6341 | −1.29222 | ||||||||
\(563\) | 43.2795 | 1.82401 | 0.912006 | − | 0.410177i | \(-0.134533\pi\) | ||||
0.912006 | + | 0.410177i | \(0.134533\pi\) | |||||||
\(564\) | −7.74937 | −0.326307 | ||||||||
\(565\) | −10.4775 | −0.440792 | ||||||||
\(566\) | −0.234324 | −0.00984937 | ||||||||
\(567\) | 4.10228 | 0.172280 | ||||||||
\(568\) | −7.71254 | −0.323611 | ||||||||
\(569\) | −3.79414 | −0.159059 | −0.0795293 | − | 0.996833i | \(-0.525342\pi\) | ||||
−0.0795293 | + | 0.996833i | \(0.525342\pi\) | |||||||
\(570\) | 23.8455 | 0.998779 | ||||||||
\(571\) | −45.4622 | −1.90254 | −0.951268 | − | 0.308366i | \(-0.900218\pi\) | ||||
−0.951268 | + | 0.308366i | \(0.900218\pi\) | |||||||
\(572\) | −6.84842 | −0.286347 | ||||||||
\(573\) | 7.49899 | 0.313275 | ||||||||
\(574\) | −19.5387 | −0.815531 | ||||||||
\(575\) | 8.91326 | 0.371709 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 16.7057 | 0.695469 | 0.347735 | − | 0.937593i | \(-0.386951\pi\) | ||||
0.347735 | + | 0.937593i | \(0.386951\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | −4.84547 | −0.201371 | ||||||||
\(580\) | 7.81127 | 0.324345 | ||||||||
\(581\) | −26.9825 | −1.11942 | ||||||||
\(582\) | −5.13805 | −0.212979 | ||||||||
\(583\) | 17.7429 | 0.734835 | ||||||||
\(584\) | 2.79488 | 0.115653 | ||||||||
\(585\) | −12.9709 | −0.536282 | ||||||||
\(586\) | 3.63443 | 0.150137 | ||||||||
\(587\) | 1.65489 | 0.0683045 | 0.0341522 | − | 0.999417i | \(-0.489127\pi\) | ||||
0.0341522 | + | 0.999417i | \(0.489127\pi\) | |||||||
\(588\) | −9.82874 | −0.405330 | ||||||||
\(589\) | −41.2555 | −1.69991 | ||||||||
\(590\) | 3.85158 | 0.158567 | ||||||||
\(591\) | −15.3061 | −0.629610 | ||||||||
\(592\) | 0.914678 | 0.0375930 | ||||||||
\(593\) | −15.5054 | −0.636729 | −0.318364 | − | 0.947968i | \(-0.603134\pi\) | ||||
−0.318364 | + | 0.947968i | \(0.603134\pi\) | |||||||
\(594\) | −2.03357 | −0.0834383 | ||||||||
\(595\) | 15.8003 | 0.647749 | ||||||||
\(596\) | 3.89820 | 0.159677 | ||||||||
\(597\) | −6.62692 | −0.271222 | ||||||||
\(598\) | −3.05216 | −0.124812 | ||||||||
\(599\) | 13.5626 | 0.554152 | 0.277076 | − | 0.960848i | \(-0.410635\pi\) | ||||
0.277076 | + | 0.960848i | \(0.410635\pi\) | |||||||
\(600\) | 9.83469 | 0.401500 | ||||||||
\(601\) | 33.5262 | 1.36756 | 0.683782 | − | 0.729687i | \(-0.260334\pi\) | ||||
0.683782 | + | 0.729687i | \(0.260334\pi\) | |||||||
\(602\) | 10.6214 | 0.432897 | ||||||||
\(603\) | 5.05990 | 0.206055 | ||||||||
\(604\) | −10.0378 | −0.408434 | ||||||||
\(605\) | 26.4396 | 1.07492 | ||||||||
\(606\) | 6.29084 | 0.255548 | ||||||||
\(607\) | −0.334109 | −0.0135611 | −0.00678053 | − | 0.999977i | \(-0.502158\pi\) | ||||
−0.00678053 | + | 0.999977i | \(0.502158\pi\) | |||||||
\(608\) | 6.19110 | 0.251082 | ||||||||
\(609\) | 8.31971 | 0.337132 | ||||||||
\(610\) | −40.5266 | −1.64087 | ||||||||
\(611\) | 26.0975 | 1.05579 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | −3.86596 | −0.156145 | −0.0780723 | − | 0.996948i | \(-0.524876\pi\) | ||||
−0.0780723 | + | 0.996948i | \(0.524876\pi\) | |||||||
\(614\) | −15.7695 | −0.636404 | ||||||||
\(615\) | 18.3447 | 0.739729 | ||||||||
\(616\) | 8.34227 | 0.336120 | ||||||||
\(617\) | 8.72380 | 0.351207 | 0.175603 | − | 0.984461i | \(-0.443812\pi\) | ||||
0.175603 | + | 0.984461i | \(0.443812\pi\) | |||||||
\(618\) | −8.32588 | −0.334916 | ||||||||
\(619\) | 26.7813 | 1.07643 | 0.538215 | − | 0.842807i | \(-0.319099\pi\) | ||||
0.538215 | + | 0.842807i | \(0.319099\pi\) | |||||||
\(620\) | −25.6657 | −1.03076 | ||||||||
\(621\) | −0.906308 | −0.0363689 | ||||||||
\(622\) | −31.5974 | −1.26694 | ||||||||
\(623\) | 52.6234 | 2.10831 | ||||||||
\(624\) | −3.36769 | −0.134815 | ||||||||
\(625\) | 22.5477 | 0.901908 | ||||||||
\(626\) | −12.5346 | −0.500983 | ||||||||
\(627\) | −12.5900 | −0.502797 | ||||||||
\(628\) | 10.9642 | 0.437521 | ||||||||
\(629\) | −0.914678 | −0.0364706 | ||||||||
\(630\) | 15.8003 | 0.629499 | ||||||||
\(631\) | −32.8906 | −1.30935 | −0.654677 | − | 0.755909i | \(-0.727195\pi\) | ||||
−0.654677 | + | 0.755909i | \(0.727195\pi\) | |||||||
\(632\) | −0.640835 | −0.0254911 | ||||||||
\(633\) | −16.6354 | −0.661196 | ||||||||
\(634\) | −8.78766 | −0.349003 | ||||||||
\(635\) | 66.7059 | 2.64714 | ||||||||
\(636\) | 8.72500 | 0.345969 | ||||||||
\(637\) | 33.1001 | 1.31147 | ||||||||
\(638\) | −4.12421 | −0.163279 | ||||||||
\(639\) | 7.71254 | 0.305104 | ||||||||
\(640\) | 3.85158 | 0.152247 | ||||||||
\(641\) | 1.52225 | 0.0601253 | 0.0300626 | − | 0.999548i | \(-0.490429\pi\) | ||||
0.0300626 | + | 0.999548i | \(0.490429\pi\) | |||||||
\(642\) | −8.96644 | −0.353877 | ||||||||
\(643\) | −0.936604 | −0.0369360 | −0.0184680 | − | 0.999829i | \(-0.505879\pi\) | ||||
−0.0184680 | + | 0.999829i | \(0.505879\pi\) | |||||||
\(644\) | 3.71793 | 0.146507 | ||||||||
\(645\) | −9.97232 | −0.392660 | ||||||||
\(646\) | −6.19110 | −0.243585 | ||||||||
\(647\) | −8.74507 | −0.343804 | −0.171902 | − | 0.985114i | \(-0.554991\pi\) | ||||
−0.171902 | + | 0.985114i | \(0.554991\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −2.03357 | −0.0798245 | ||||||||
\(650\) | −33.1202 | −1.29908 | ||||||||
\(651\) | −27.3363 | −1.07140 | ||||||||
\(652\) | 24.7990 | 0.971205 | ||||||||
\(653\) | 46.5279 | 1.82078 | 0.910390 | − | 0.413752i | \(-0.135782\pi\) | ||||
0.910390 | + | 0.413752i | \(0.135782\pi\) | |||||||
\(654\) | −2.10396 | −0.0822713 | ||||||||
\(655\) | 52.2019 | 2.03970 | ||||||||
\(656\) | 4.76289 | 0.185960 | ||||||||
\(657\) | −2.79488 | −0.109039 | ||||||||
\(658\) | −31.7901 | −1.23931 | ||||||||
\(659\) | 1.76409 | 0.0687192 | 0.0343596 | − | 0.999410i | \(-0.489061\pi\) | ||||
0.0343596 | + | 0.999410i | \(0.489061\pi\) | |||||||
\(660\) | −7.83245 | −0.304878 | ||||||||
\(661\) | −16.6486 | −0.647555 | −0.323777 | − | 0.946133i | \(-0.604953\pi\) | ||||
−0.323777 | + | 0.946133i | \(0.604953\pi\) | |||||||
\(662\) | −28.1629 | −1.09458 | ||||||||
\(663\) | 3.36769 | 0.130790 | ||||||||
\(664\) | 6.57742 | 0.255254 | ||||||||
\(665\) | 97.8211 | 3.79334 | ||||||||
\(666\) | −0.914678 | −0.0354430 | ||||||||
\(667\) | −1.83805 | −0.0711697 | ||||||||
\(668\) | −9.47876 | −0.366744 | ||||||||
\(669\) | 1.93856 | 0.0749489 | ||||||||
\(670\) | 19.4886 | 0.752912 | ||||||||
\(671\) | 21.3973 | 0.826035 | ||||||||
\(672\) | 4.10228 | 0.158249 | ||||||||
\(673\) | −17.2731 | −0.665827 | −0.332914 | − | 0.942957i | \(-0.608032\pi\) | ||||
−0.332914 | + | 0.942957i | \(0.608032\pi\) | |||||||
\(674\) | 28.0093 | 1.07888 | ||||||||
\(675\) | −9.83469 | −0.378537 | ||||||||
\(676\) | −1.65868 | −0.0637953 | ||||||||
\(677\) | 27.4725 | 1.05586 | 0.527928 | − | 0.849289i | \(-0.322969\pi\) | ||||
0.527928 | + | 0.849289i | \(0.322969\pi\) | |||||||
\(678\) | 2.72031 | 0.104473 | ||||||||
\(679\) | −21.0778 | −0.808890 | ||||||||
\(680\) | −3.85158 | −0.147701 | ||||||||
\(681\) | 9.70323 | 0.371828 | ||||||||
\(682\) | 13.5511 | 0.518897 | ||||||||
\(683\) | −27.1264 | −1.03796 | −0.518981 | − | 0.854786i | \(-0.673688\pi\) | ||||
−0.518981 | + | 0.854786i | \(0.673688\pi\) | |||||||
\(684\) | −6.19110 | −0.236723 | ||||||||
\(685\) | 10.3307 | 0.394715 | ||||||||
\(686\) | −11.6043 | −0.443054 | ||||||||
\(687\) | 21.2594 | 0.811097 | ||||||||
\(688\) | −2.58915 | −0.0987104 | ||||||||
\(689\) | −29.3831 | −1.11941 | ||||||||
\(690\) | −3.49072 | −0.132889 | ||||||||
\(691\) | −26.3483 | −1.00234 | −0.501168 | − | 0.865350i | \(-0.667096\pi\) | ||||
−0.501168 | + | 0.865350i | \(0.667096\pi\) | |||||||
\(692\) | −4.53051 | −0.172224 | ||||||||
\(693\) | −8.34227 | −0.316897 | ||||||||
\(694\) | −29.5665 | −1.12233 | ||||||||
\(695\) | −56.7717 | −2.15347 | ||||||||
\(696\) | −2.02807 | −0.0768737 | ||||||||
\(697\) | −4.76289 | −0.180407 | ||||||||
\(698\) | −28.6964 | −1.08618 | ||||||||
\(699\) | −9.13446 | −0.345497 | ||||||||
\(700\) | 40.3447 | 1.52489 | ||||||||
\(701\) | 17.7786 | 0.671488 | 0.335744 | − | 0.941953i | \(-0.391012\pi\) | ||||
0.335744 | + | 0.941953i | \(0.391012\pi\) | |||||||
\(702\) | 3.36769 | 0.127105 | ||||||||
\(703\) | −5.66286 | −0.213579 | ||||||||
\(704\) | −2.03357 | −0.0766430 | ||||||||
\(705\) | 29.8473 | 1.12412 | ||||||||
\(706\) | 5.29416 | 0.199248 | ||||||||
\(707\) | 25.8068 | 0.970565 | ||||||||
\(708\) | −1.00000 | −0.0375823 | ||||||||
\(709\) | −13.8529 | −0.520258 | −0.260129 | − | 0.965574i | \(-0.583765\pi\) | ||||
−0.260129 | + | 0.965574i | \(0.583765\pi\) | |||||||
\(710\) | 29.7055 | 1.11483 | ||||||||
\(711\) | 0.640835 | 0.0240332 | ||||||||
\(712\) | −12.8278 | −0.480744 | ||||||||
\(713\) | 6.03935 | 0.226176 | ||||||||
\(714\) | −4.10228 | −0.153524 | ||||||||
\(715\) | 26.3773 | 0.986454 | ||||||||
\(716\) | 1.28226 | 0.0479203 | ||||||||
\(717\) | 14.6133 | 0.545742 | ||||||||
\(718\) | −1.73252 | −0.0646572 | ||||||||
\(719\) | −8.30614 | −0.309767 | −0.154883 | − | 0.987933i | \(-0.549500\pi\) | ||||
−0.154883 | + | 0.987933i | \(0.549500\pi\) | |||||||
\(720\) | −3.85158 | −0.143540 | ||||||||
\(721\) | −34.1551 | −1.27200 | ||||||||
\(722\) | −19.3297 | −0.719377 | ||||||||
\(723\) | 16.3402 | 0.607700 | ||||||||
\(724\) | 2.18692 | 0.0812763 | ||||||||
\(725\) | −19.9454 | −0.740754 | ||||||||
\(726\) | −6.86460 | −0.254769 | ||||||||
\(727\) | 7.62966 | 0.282968 | 0.141484 | − | 0.989941i | \(-0.454813\pi\) | ||||
0.141484 | + | 0.989941i | \(0.454813\pi\) | |||||||
\(728\) | −13.8152 | −0.512026 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −10.7647 | −0.398420 | ||||||||
\(731\) | 2.58915 | 0.0957632 | ||||||||
\(732\) | 10.5221 | 0.388907 | ||||||||
\(733\) | −9.68544 | −0.357740 | −0.178870 | − | 0.983873i | \(-0.557244\pi\) | ||||
−0.178870 | + | 0.983873i | \(0.557244\pi\) | |||||||
\(734\) | 28.1227 | 1.03803 | ||||||||
\(735\) | 37.8562 | 1.39635 | ||||||||
\(736\) | −0.906308 | −0.0334070 | ||||||||
\(737\) | −10.2897 | −0.379024 | ||||||||
\(738\) | −4.76289 | −0.175325 | ||||||||
\(739\) | 52.2739 | 1.92293 | 0.961463 | − | 0.274935i | \(-0.0886563\pi\) | ||||
0.961463 | + | 0.274935i | \(0.0886563\pi\) | |||||||
\(740\) | −3.52296 | −0.129506 | ||||||||
\(741\) | 20.8497 | 0.765932 | ||||||||
\(742\) | 35.7924 | 1.31398 | ||||||||
\(743\) | −1.96054 | −0.0719251 | −0.0359626 | − | 0.999353i | \(-0.511450\pi\) | ||||
−0.0359626 | + | 0.999353i | \(0.511450\pi\) | |||||||
\(744\) | 6.66369 | 0.244303 | ||||||||
\(745\) | −15.0142 | −0.550079 | ||||||||
\(746\) | 12.4392 | 0.455433 | ||||||||
\(747\) | −6.57742 | −0.240655 | ||||||||
\(748\) | 2.03357 | 0.0743546 | ||||||||
\(749\) | −36.7829 | −1.34402 | ||||||||
\(750\) | −18.6212 | −0.679951 | ||||||||
\(751\) | 17.7692 | 0.648407 | 0.324203 | − | 0.945987i | \(-0.394904\pi\) | ||||
0.324203 | + | 0.945987i | \(0.394904\pi\) | |||||||
\(752\) | 7.74937 | 0.282590 | ||||||||
\(753\) | 7.29327 | 0.265782 | ||||||||
\(754\) | 6.82990 | 0.248730 | ||||||||
\(755\) | 38.6616 | 1.40704 | ||||||||
\(756\) | −4.10228 | −0.149199 | ||||||||
\(757\) | 20.9295 | 0.760697 | 0.380348 | − | 0.924843i | \(-0.375804\pi\) | ||||
0.380348 | + | 0.924843i | \(0.375804\pi\) | |||||||
\(758\) | 6.21140 | 0.225608 | ||||||||
\(759\) | 1.84304 | 0.0668981 | ||||||||
\(760\) | −23.8455 | −0.864968 | ||||||||
\(761\) | −53.7044 | −1.94678 | −0.973391 | − | 0.229151i | \(-0.926405\pi\) | ||||
−0.973391 | + | 0.229151i | \(0.926405\pi\) | |||||||
\(762\) | −17.3191 | −0.627404 | ||||||||
\(763\) | −8.63104 | −0.312465 | ||||||||
\(764\) | −7.49899 | −0.271304 | ||||||||
\(765\) | 3.85158 | 0.139254 | ||||||||
\(766\) | 5.50310 | 0.198835 | ||||||||
\(767\) | 3.36769 | 0.121600 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −11.0674 | −0.399100 | −0.199550 | − | 0.979888i | \(-0.563948\pi\) | ||||
−0.199550 | + | 0.979888i | \(0.563948\pi\) | |||||||
\(770\) | −32.1310 | −1.15792 | ||||||||
\(771\) | −12.3591 | −0.445101 | ||||||||
\(772\) | 4.84547 | 0.174392 | ||||||||
\(773\) | −18.8995 | −0.679767 | −0.339883 | − | 0.940468i | \(-0.610388\pi\) | ||||
−0.339883 | + | 0.940468i | \(0.610388\pi\) | |||||||
\(774\) | 2.58915 | 0.0930651 | ||||||||
\(775\) | 65.5353 | 2.35410 | ||||||||
\(776\) | 5.13805 | 0.184445 | ||||||||
\(777\) | −3.75227 | −0.134612 | ||||||||
\(778\) | −24.9539 | −0.894642 | ||||||||
\(779\) | −29.4875 | −1.05650 | ||||||||
\(780\) | 12.9709 | 0.464434 | ||||||||
\(781\) | −15.6840 | −0.561217 | ||||||||
\(782\) | 0.906308 | 0.0324095 | ||||||||
\(783\) | 2.02807 | 0.0724772 | ||||||||
\(784\) | 9.82874 | 0.351026 | ||||||||
\(785\) | −42.2297 | −1.50724 | ||||||||
\(786\) | −13.5534 | −0.483432 | ||||||||
\(787\) | 36.5777 | 1.30385 | 0.651927 | − | 0.758282i | \(-0.273961\pi\) | ||||
0.651927 | + | 0.758282i | \(0.273961\pi\) | |||||||
\(788\) | 15.3061 | 0.545258 | ||||||||
\(789\) | −20.2388 | −0.720519 | ||||||||
\(790\) | 2.46823 | 0.0878157 | ||||||||
\(791\) | 11.1595 | 0.396786 | ||||||||
\(792\) | 2.03357 | 0.0722597 | ||||||||
\(793\) | −35.4350 | −1.25834 | ||||||||
\(794\) | 12.0760 | 0.428559 | ||||||||
\(795\) | −33.6051 | −1.19185 | ||||||||
\(796\) | 6.62692 | 0.234885 | ||||||||
\(797\) | −38.4484 | −1.36191 | −0.680956 | − | 0.732324i | \(-0.738435\pi\) | ||||
−0.680956 | + | 0.732324i | \(0.738435\pi\) | |||||||
\(798\) | −25.3976 | −0.899067 | ||||||||
\(799\) | −7.74937 | −0.274153 | ||||||||
\(800\) | −9.83469 | −0.347709 | ||||||||
\(801\) | 12.8278 | 0.453249 | ||||||||
\(802\) | −39.3071 | −1.38798 | ||||||||
\(803\) | 5.68358 | 0.200569 | ||||||||
\(804\) | −5.05990 | −0.178449 | ||||||||
\(805\) | −14.3199 | −0.504711 | ||||||||
\(806\) | −22.4412 | −0.790458 | ||||||||
\(807\) | −28.6320 | −1.00789 | ||||||||
\(808\) | −6.29084 | −0.221311 | ||||||||
\(809\) | 49.6867 | 1.74689 | 0.873446 | − | 0.486921i | \(-0.161880\pi\) | ||||
0.873446 | + | 0.486921i | \(0.161880\pi\) | |||||||
\(810\) | 3.85158 | 0.135331 | ||||||||
\(811\) | 23.5153 | 0.825733 | 0.412867 | − | 0.910792i | \(-0.364528\pi\) | ||||
0.412867 | + | 0.910792i | \(0.364528\pi\) | |||||||
\(812\) | −8.31971 | −0.291965 | ||||||||
\(813\) | −0.0160069 | −0.000561388 0 | ||||||||
\(814\) | 1.86006 | 0.0651950 | ||||||||
\(815\) | −95.5155 | −3.34576 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | 16.0297 | 0.560807 | ||||||||
\(818\) | −28.9306 | −1.01153 | ||||||||
\(819\) | 13.8152 | 0.482743 | ||||||||
\(820\) | −18.3447 | −0.640624 | ||||||||
\(821\) | 25.6672 | 0.895791 | 0.447896 | − | 0.894086i | \(-0.352174\pi\) | ||||
0.447896 | + | 0.894086i | \(0.352174\pi\) | |||||||
\(822\) | −2.68219 | −0.0935522 | ||||||||
\(823\) | −6.25093 | −0.217894 | −0.108947 | − | 0.994048i | \(-0.534748\pi\) | ||||
−0.108947 | + | 0.994048i | \(0.534748\pi\) | |||||||
\(824\) | 8.32588 | 0.290046 | ||||||||
\(825\) | 19.9995 | 0.696293 | ||||||||
\(826\) | −4.10228 | −0.142737 | ||||||||
\(827\) | 37.4425 | 1.30200 | 0.651002 | − | 0.759076i | \(-0.274349\pi\) | ||||
0.651002 | + | 0.759076i | \(0.274349\pi\) | |||||||
\(828\) | 0.906308 | 0.0314964 | ||||||||
\(829\) | −54.0389 | −1.87685 | −0.938424 | − | 0.345485i | \(-0.887714\pi\) | ||||
−0.938424 | + | 0.345485i | \(0.887714\pi\) | |||||||
\(830\) | −25.3335 | −0.879338 | ||||||||
\(831\) | −26.2831 | −0.911750 | ||||||||
\(832\) | 3.36769 | 0.116754 | ||||||||
\(833\) | −9.82874 | −0.340546 | ||||||||
\(834\) | 14.7398 | 0.510399 | ||||||||
\(835\) | 36.5082 | 1.26342 | ||||||||
\(836\) | 12.5900 | 0.435435 | ||||||||
\(837\) | −6.66369 | −0.230331 | ||||||||
\(838\) | −16.0554 | −0.554626 | ||||||||
\(839\) | −11.7778 | −0.406614 | −0.203307 | − | 0.979115i | \(-0.565169\pi\) | ||||
−0.203307 | + | 0.979115i | \(0.565169\pi\) | |||||||
\(840\) | −15.8003 | −0.545162 | ||||||||
\(841\) | −24.8869 | −0.858170 | ||||||||
\(842\) | −19.7480 | −0.680563 | ||||||||
\(843\) | −30.6341 | −1.05510 | ||||||||
\(844\) | 16.6354 | 0.572612 | ||||||||
\(845\) | 6.38853 | 0.219772 | ||||||||
\(846\) | −7.74937 | −0.266429 | ||||||||
\(847\) | −28.1606 | −0.967608 | ||||||||
\(848\) | −8.72500 | −0.299618 | ||||||||
\(849\) | −0.234324 | −0.00804198 | ||||||||
\(850\) | 9.83469 | 0.337327 | ||||||||
\(851\) | 0.828980 | 0.0284171 | ||||||||
\(852\) | −7.71254 | −0.264227 | ||||||||
\(853\) | 46.2275 | 1.58280 | 0.791399 | − | 0.611300i | \(-0.209353\pi\) | ||||
0.791399 | + | 0.611300i | \(0.209353\pi\) | |||||||
\(854\) | 43.1645 | 1.47706 | ||||||||
\(855\) | 23.8455 | 0.815500 | ||||||||
\(856\) | 8.96644 | 0.306467 | ||||||||
\(857\) | 42.8968 | 1.46533 | 0.732663 | − | 0.680591i | \(-0.238277\pi\) | ||||
0.732663 | + | 0.680591i | \(0.238277\pi\) | |||||||
\(858\) | −6.84842 | −0.233801 | ||||||||
\(859\) | −6.90108 | −0.235462 | −0.117731 | − | 0.993046i | \(-0.537562\pi\) | ||||
−0.117731 | + | 0.993046i | \(0.537562\pi\) | |||||||
\(860\) | 9.97232 | 0.340053 | ||||||||
\(861\) | −19.5387 | −0.665879 | ||||||||
\(862\) | −20.4445 | −0.696343 | ||||||||
\(863\) | −32.3405 | −1.10088 | −0.550442 | − | 0.834874i | \(-0.685541\pi\) | ||||
−0.550442 | + | 0.834874i | \(0.685541\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 17.4496 | 0.593306 | ||||||||
\(866\) | −9.91123 | −0.336797 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 27.3363 | 0.927856 | ||||||||
\(869\) | −1.30318 | −0.0442074 | ||||||||
\(870\) | 7.81127 | 0.264827 | ||||||||
\(871\) | 17.0402 | 0.577384 | ||||||||
\(872\) | 2.10396 | 0.0712491 | ||||||||
\(873\) | −5.13805 | −0.173897 | ||||||||
\(874\) | 5.61104 | 0.189796 | ||||||||
\(875\) | −76.3895 | −2.58244 | ||||||||
\(876\) | 2.79488 | 0.0944302 | ||||||||
\(877\) | 47.7667 | 1.61297 | 0.806484 | − | 0.591256i | \(-0.201368\pi\) | ||||
0.806484 | + | 0.591256i | \(0.201368\pi\) | |||||||
\(878\) | 16.4570 | 0.555399 | ||||||||
\(879\) | 3.63443 | 0.122586 | ||||||||
\(880\) | 7.83245 | 0.264032 | ||||||||
\(881\) | −22.6017 | −0.761470 | −0.380735 | − | 0.924684i | \(-0.624329\pi\) | ||||
−0.380735 | + | 0.924684i | \(0.624329\pi\) | |||||||
\(882\) | −9.82874 | −0.330951 | ||||||||
\(883\) | −12.5773 | −0.423261 | −0.211630 | − | 0.977350i | \(-0.567877\pi\) | ||||
−0.211630 | + | 0.977350i | \(0.567877\pi\) | |||||||
\(884\) | −3.36769 | −0.113268 | ||||||||
\(885\) | 3.85158 | 0.129470 | ||||||||
\(886\) | 22.6158 | 0.759792 | ||||||||
\(887\) | 5.72503 | 0.192228 | 0.0961139 | − | 0.995370i | \(-0.469359\pi\) | ||||
0.0961139 | + | 0.995370i | \(0.469359\pi\) | |||||||
\(888\) | 0.914678 | 0.0306946 | ||||||||
\(889\) | −71.0478 | −2.38287 | ||||||||
\(890\) | 49.4075 | 1.65614 | ||||||||
\(891\) | −2.03357 | −0.0681271 | ||||||||
\(892\) | −1.93856 | −0.0649076 | ||||||||
\(893\) | −47.9771 | −1.60549 | ||||||||
\(894\) | 3.89820 | 0.130375 | ||||||||
\(895\) | −4.93873 | −0.165084 | ||||||||
\(896\) | −4.10228 | −0.137048 | ||||||||
\(897\) | −3.05216 | −0.101909 | ||||||||
\(898\) | 12.8141 | 0.427612 | ||||||||
\(899\) | −13.5144 | −0.450731 | ||||||||
\(900\) | 9.83469 | 0.327823 | ||||||||
\(901\) | 8.72500 | 0.290672 | ||||||||
\(902\) | 9.68566 | 0.322497 | ||||||||
\(903\) | 10.6214 | 0.353459 | ||||||||
\(904\) | −2.72031 | −0.0904762 | ||||||||
\(905\) | −8.42311 | −0.279994 | ||||||||
\(906\) | −10.0378 | −0.333485 | ||||||||
\(907\) | 40.0786 | 1.33079 | 0.665394 | − | 0.746492i | \(-0.268264\pi\) | ||||
0.665394 | + | 0.746492i | \(0.268264\pi\) | |||||||
\(908\) | −9.70323 | −0.322013 | ||||||||
\(909\) | 6.29084 | 0.208654 | ||||||||
\(910\) | 53.2104 | 1.76391 | ||||||||
\(911\) | −17.3584 | −0.575109 | −0.287555 | − | 0.957764i | \(-0.592842\pi\) | ||||
−0.287555 | + | 0.957764i | \(0.592842\pi\) | |||||||
\(912\) | 6.19110 | 0.205008 | ||||||||
\(913\) | 13.3756 | 0.442669 | ||||||||
\(914\) | −30.5625 | −1.01092 | ||||||||
\(915\) | −40.5266 | −1.33977 | ||||||||
\(916\) | −21.2594 | −0.702431 | ||||||||
\(917\) | −55.5997 | −1.83607 | ||||||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | 26.3032 | 0.867664 | 0.433832 | − | 0.900994i | \(-0.357161\pi\) | ||||
0.433832 | + | 0.900994i | \(0.357161\pi\) | |||||||
\(920\) | 3.49072 | 0.115086 | ||||||||
\(921\) | −15.7695 | −0.519622 | ||||||||
\(922\) | 8.23817 | 0.271310 | ||||||||
\(923\) | 25.9734 | 0.854926 | ||||||||
\(924\) | 8.34227 | 0.274441 | ||||||||
\(925\) | 8.99557 | 0.295773 | ||||||||
\(926\) | 14.1573 | 0.465238 | ||||||||
\(927\) | −8.32588 | −0.273458 | ||||||||
\(928\) | 2.02807 | 0.0665746 | ||||||||
\(929\) | −1.21778 | −0.0399539 | −0.0199770 | − | 0.999800i | \(-0.506359\pi\) | ||||
−0.0199770 | + | 0.999800i | \(0.506359\pi\) | |||||||
\(930\) | −25.6657 | −0.841613 | ||||||||
\(931\) | −60.8507 | −1.99430 | ||||||||
\(932\) | 9.13446 | 0.299209 | ||||||||
\(933\) | −31.5974 | −1.03445 | ||||||||
\(934\) | 9.80450 | 0.320813 | ||||||||
\(935\) | −7.83245 | −0.256149 | ||||||||
\(936\) | −3.36769 | −0.110076 | ||||||||
\(937\) | 47.8832 | 1.56427 | 0.782137 | − | 0.623106i | \(-0.214129\pi\) | ||||
0.782137 | + | 0.623106i | \(0.214129\pi\) | |||||||
\(938\) | −20.7572 | −0.677745 | ||||||||
\(939\) | −12.5346 | −0.409051 | ||||||||
\(940\) | −29.8473 | −0.973513 | ||||||||
\(941\) | −15.8978 | −0.518255 | −0.259127 | − | 0.965843i | \(-0.583435\pi\) | ||||
−0.259127 | + | 0.965843i | \(0.583435\pi\) | |||||||
\(942\) | 10.9642 | 0.357234 | ||||||||
\(943\) | 4.31665 | 0.140569 | ||||||||
\(944\) | 1.00000 | 0.0325472 | ||||||||
\(945\) | 15.8003 | 0.513983 | ||||||||
\(946\) | −5.26521 | −0.171187 | ||||||||
\(947\) | 40.0018 | 1.29988 | 0.649942 | − | 0.759984i | \(-0.274793\pi\) | ||||
0.649942 | + | 0.759984i | \(0.274793\pi\) | |||||||
\(948\) | −0.640835 | −0.0208134 | ||||||||
\(949\) | −9.41228 | −0.305536 | ||||||||
\(950\) | 60.8875 | 1.97545 | ||||||||
\(951\) | −8.78766 | −0.284959 | ||||||||
\(952\) | 4.10228 | 0.132956 | ||||||||
\(953\) | −30.1726 | −0.977386 | −0.488693 | − | 0.872456i | \(-0.662526\pi\) | ||||
−0.488693 | + | 0.872456i | \(0.662526\pi\) | |||||||
\(954\) | 8.72500 | 0.282482 | ||||||||
\(955\) | 28.8830 | 0.934631 | ||||||||
\(956\) | −14.6133 | −0.472626 | ||||||||
\(957\) | −4.12421 | −0.133317 | ||||||||
\(958\) | −37.7151 | −1.21852 | ||||||||
\(959\) | −11.0031 | −0.355309 | ||||||||
\(960\) | 3.85158 | 0.124309 | ||||||||
\(961\) | 13.4047 | 0.432411 | ||||||||
\(962\) | −3.08035 | −0.0993144 | ||||||||
\(963\) | −8.96644 | −0.288940 | ||||||||
\(964\) | −16.3402 | −0.526283 | ||||||||
\(965\) | −18.6627 | −0.600774 | ||||||||
\(966\) | 3.71793 | 0.119623 | ||||||||
\(967\) | 20.8432 | 0.670271 | 0.335135 | − | 0.942170i | \(-0.391218\pi\) | ||||
0.335135 | + | 0.942170i | \(0.391218\pi\) | |||||||
\(968\) | 6.86460 | 0.220637 | ||||||||
\(969\) | −6.19110 | −0.198887 | ||||||||
\(970\) | −19.7896 | −0.635407 | ||||||||
\(971\) | −20.0708 | −0.644102 | −0.322051 | − | 0.946722i | \(-0.604372\pi\) | ||||
−0.322051 | + | 0.946722i | \(0.604372\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 60.4670 | 1.93848 | ||||||||
\(974\) | −25.9042 | −0.830024 | ||||||||
\(975\) | −33.1202 | −1.06069 | ||||||||
\(976\) | −10.5221 | −0.336803 | ||||||||
\(977\) | −38.2031 | −1.22223 | −0.611113 | − | 0.791543i | \(-0.709278\pi\) | ||||
−0.611113 | + | 0.791543i | \(0.709278\pi\) | |||||||
\(978\) | 24.7990 | 0.792986 | ||||||||
\(979\) | −26.0863 | −0.833721 | ||||||||
\(980\) | −37.8562 | −1.20927 | ||||||||
\(981\) | −2.10396 | −0.0671743 | ||||||||
\(982\) | −9.43153 | −0.300972 | ||||||||
\(983\) | 49.6362 | 1.58315 | 0.791574 | − | 0.611073i | \(-0.209262\pi\) | ||||
0.791574 | + | 0.611073i | \(0.209262\pi\) | |||||||
\(984\) | 4.76289 | 0.151835 | ||||||||
\(985\) | −58.9528 | −1.87839 | ||||||||
\(986\) | −2.02807 | −0.0645868 | ||||||||
\(987\) | −31.7901 | −1.01189 | ||||||||
\(988\) | −20.8497 | −0.663317 | ||||||||
\(989\) | −2.34657 | −0.0746165 | ||||||||
\(990\) | −7.83245 | −0.248932 | ||||||||
\(991\) | 60.5667 | 1.92397 | 0.961983 | − | 0.273109i | \(-0.0880520\pi\) | ||||
0.961983 | + | 0.273109i | \(0.0880520\pi\) | |||||||
\(992\) | −6.66369 | −0.211572 | ||||||||
\(993\) | −28.1629 | −0.893723 | ||||||||
\(994\) | −31.6391 | −1.00353 | ||||||||
\(995\) | −25.5241 | −0.809169 | ||||||||
\(996\) | 6.57742 | 0.208414 | ||||||||
\(997\) | −9.71941 | −0.307817 | −0.153908 | − | 0.988085i | \(-0.549186\pi\) | ||||
−0.153908 | + | 0.988085i | \(0.549186\pi\) | |||||||
\(998\) | −15.0782 | −0.477293 | ||||||||
\(999\) | −0.914678 | −0.0289391 |
(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 | 6018.2.a.s.1.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.s.1.1 | ✓ | 8 | 1.1 | even | 1 | trivial |