Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2415,2,Mod(1,2415)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2415, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2415.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2415.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: | \(19.2838720881\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 16x^{8} + 30x^{7} + 83x^{6} - 137x^{5} - 164x^{4} + 208x^{3} + 108x^{2} - 83x - 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.13650\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2415.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.13650 | −1.51074 | −0.755369 | − | 0.655300i | \(-0.772542\pi\) | ||||
−0.755369 | + | 0.655300i | \(0.772542\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.56465 | 1.28233 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.13650 | −0.872224 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.20638 | −0.426521 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.13650 | −0.675622 | ||||||||
\(11\) | 1.78663 | 0.538690 | 0.269345 | − | 0.963044i | \(-0.413193\pi\) | ||||
0.269345 | + | 0.963044i | \(0.413193\pi\) | |||||||
\(12\) | 2.56465 | 0.740351 | ||||||||
\(13\) | 4.29660 | 1.19166 | 0.595831 | − | 0.803110i | \(-0.296823\pi\) | ||||
0.595831 | + | 0.803110i | \(0.296823\pi\) | |||||||
\(14\) | 2.13650 | 0.571005 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −2.55186 | −0.637965 | ||||||||
\(17\) | −0.0943613 | −0.0228860 | −0.0114430 | − | 0.999935i | \(-0.503642\pi\) | ||||
−0.0114430 | + | 0.999935i | \(0.503642\pi\) | |||||||
\(18\) | −2.13650 | −0.503579 | ||||||||
\(19\) | 6.77795 | 1.55497 | 0.777484 | − | 0.628903i | \(-0.216496\pi\) | ||||
0.777484 | + | 0.628903i | \(0.216496\pi\) | |||||||
\(20\) | 2.56465 | 0.573474 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −3.81715 | −0.813819 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.20638 | −0.246252 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −9.17970 | −1.80029 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.56465 | −0.484674 | ||||||||
\(29\) | −2.21636 | −0.411569 | −0.205784 | − | 0.978597i | \(-0.565975\pi\) | ||||
−0.205784 | + | 0.978597i | \(0.565975\pi\) | |||||||
\(30\) | −2.13650 | −0.390071 | ||||||||
\(31\) | −0.792668 | −0.142367 | −0.0711837 | − | 0.997463i | \(-0.522678\pi\) | ||||
−0.0711837 | + | 0.997463i | \(0.522678\pi\) | |||||||
\(32\) | 7.86483 | 1.39032 | ||||||||
\(33\) | 1.78663 | 0.311013 | ||||||||
\(34\) | 0.201603 | 0.0345747 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 2.56465 | 0.427442 | ||||||||
\(37\) | 6.35324 | 1.04447 | 0.522233 | − | 0.852803i | \(-0.325099\pi\) | ||||
0.522233 | + | 0.852803i | \(0.325099\pi\) | |||||||
\(38\) | −14.4811 | −2.34915 | ||||||||
\(39\) | 4.29660 | 0.688006 | ||||||||
\(40\) | −1.20638 | −0.190746 | ||||||||
\(41\) | 7.49896 | 1.17114 | 0.585571 | − | 0.810621i | \(-0.300871\pi\) | ||||
0.585571 | + | 0.810621i | \(0.300871\pi\) | |||||||
\(42\) | 2.13650 | 0.329670 | ||||||||
\(43\) | −8.14100 | −1.24149 | −0.620745 | − | 0.784012i | \(-0.713170\pi\) | ||||
−0.620745 | + | 0.784012i | \(0.713170\pi\) | |||||||
\(44\) | 4.58209 | 0.690777 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −2.13650 | −0.315010 | ||||||||
\(47\) | −10.7203 | −1.56372 | −0.781858 | − | 0.623456i | \(-0.785728\pi\) | ||||
−0.781858 | + | 0.623456i | \(0.785728\pi\) | |||||||
\(48\) | −2.55186 | −0.368330 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.13650 | −0.302147 | ||||||||
\(51\) | −0.0943613 | −0.0132132 | ||||||||
\(52\) | 11.0193 | 1.52810 | ||||||||
\(53\) | −10.3783 | −1.42557 | −0.712785 | − | 0.701383i | \(-0.752566\pi\) | ||||
−0.712785 | + | 0.701383i | \(0.752566\pi\) | |||||||
\(54\) | −2.13650 | −0.290741 | ||||||||
\(55\) | 1.78663 | 0.240910 | ||||||||
\(56\) | 1.20638 | 0.161210 | ||||||||
\(57\) | 6.77795 | 0.897761 | ||||||||
\(58\) | 4.73527 | 0.621772 | ||||||||
\(59\) | 3.09238 | 0.402594 | 0.201297 | − | 0.979530i | \(-0.435484\pi\) | ||||
0.201297 | + | 0.979530i | \(0.435484\pi\) | |||||||
\(60\) | 2.56465 | 0.331095 | ||||||||
\(61\) | −5.84740 | −0.748683 | −0.374341 | − | 0.927291i | \(-0.622131\pi\) | ||||
−0.374341 | + | 0.927291i | \(0.622131\pi\) | |||||||
\(62\) | 1.69354 | 0.215080 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −11.6995 | −1.46244 | ||||||||
\(65\) | 4.29660 | 0.532927 | ||||||||
\(66\) | −3.81715 | −0.469859 | ||||||||
\(67\) | 13.5810 | 1.65918 | 0.829589 | − | 0.558374i | \(-0.188575\pi\) | ||||
0.829589 | + | 0.558374i | \(0.188575\pi\) | |||||||
\(68\) | −0.242004 | −0.0293473 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 2.13650 | 0.255361 | ||||||||
\(71\) | 5.24064 | 0.621950 | 0.310975 | − | 0.950418i | \(-0.399345\pi\) | ||||
0.310975 | + | 0.950418i | \(0.399345\pi\) | |||||||
\(72\) | −1.20638 | −0.142174 | ||||||||
\(73\) | 11.5241 | 1.34879 | 0.674397 | − | 0.738369i | \(-0.264404\pi\) | ||||
0.674397 | + | 0.738369i | \(0.264404\pi\) | |||||||
\(74\) | −13.5737 | −1.57791 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 17.3831 | 1.99398 | ||||||||
\(77\) | −1.78663 | −0.203606 | ||||||||
\(78\) | −9.17970 | −1.03940 | ||||||||
\(79\) | 11.7510 | 1.32209 | 0.661047 | − | 0.750345i | \(-0.270112\pi\) | ||||
0.661047 | + | 0.750345i | \(0.270112\pi\) | |||||||
\(80\) | −2.55186 | −0.285307 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −16.0216 | −1.76929 | ||||||||
\(83\) | −9.22806 | −1.01291 | −0.506455 | − | 0.862266i | \(-0.669045\pi\) | ||||
−0.506455 | + | 0.862266i | \(0.669045\pi\) | |||||||
\(84\) | −2.56465 | −0.279827 | ||||||||
\(85\) | −0.0943613 | −0.0102349 | ||||||||
\(86\) | 17.3933 | 1.87557 | ||||||||
\(87\) | −2.21636 | −0.237619 | ||||||||
\(88\) | −2.15536 | −0.229763 | ||||||||
\(89\) | 5.11100 | 0.541765 | 0.270883 | − | 0.962612i | \(-0.412684\pi\) | ||||
0.270883 | + | 0.962612i | \(0.412684\pi\) | |||||||
\(90\) | −2.13650 | −0.225207 | ||||||||
\(91\) | −4.29660 | −0.450406 | ||||||||
\(92\) | 2.56465 | 0.267384 | ||||||||
\(93\) | −0.792668 | −0.0821959 | ||||||||
\(94\) | 22.9040 | 2.36236 | ||||||||
\(95\) | 6.77795 | 0.695403 | ||||||||
\(96\) | 7.86483 | 0.802701 | ||||||||
\(97\) | 5.36007 | 0.544233 | 0.272116 | − | 0.962264i | \(-0.412276\pi\) | ||||
0.272116 | + | 0.962264i | \(0.412276\pi\) | |||||||
\(98\) | −2.13650 | −0.215820 | ||||||||
\(99\) | 1.78663 | 0.179563 | ||||||||
\(100\) | 2.56465 | 0.256465 | ||||||||
\(101\) | −8.27803 | −0.823695 | −0.411848 | − | 0.911253i | \(-0.635116\pi\) | ||||
−0.411848 | + | 0.911253i | \(0.635116\pi\) | |||||||
\(102\) | 0.201603 | 0.0199617 | ||||||||
\(103\) | −17.5937 | −1.73356 | −0.866778 | − | 0.498695i | \(-0.833813\pi\) | ||||
−0.866778 | + | 0.498695i | \(0.833813\pi\) | |||||||
\(104\) | −5.18334 | −0.508269 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | 22.1733 | 2.15366 | ||||||||
\(107\) | −12.9655 | −1.25342 | −0.626709 | − | 0.779253i | \(-0.715599\pi\) | ||||
−0.626709 | + | 0.779253i | \(0.715599\pi\) | |||||||
\(108\) | 2.56465 | 0.246784 | ||||||||
\(109\) | 13.0849 | 1.25331 | 0.626653 | − | 0.779299i | \(-0.284424\pi\) | ||||
0.626653 | + | 0.779299i | \(0.284424\pi\) | |||||||
\(110\) | −3.81715 | −0.363951 | ||||||||
\(111\) | 6.35324 | 0.603023 | ||||||||
\(112\) | 2.55186 | 0.241128 | ||||||||
\(113\) | 3.26165 | 0.306830 | 0.153415 | − | 0.988162i | \(-0.450973\pi\) | ||||
0.153415 | + | 0.988162i | \(0.450973\pi\) | |||||||
\(114\) | −14.4811 | −1.35628 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | −5.68421 | −0.527765 | ||||||||
\(117\) | 4.29660 | 0.397221 | ||||||||
\(118\) | −6.60689 | −0.608213 | ||||||||
\(119\) | 0.0943613 | 0.00865009 | ||||||||
\(120\) | −1.20638 | −0.110127 | ||||||||
\(121\) | −7.80794 | −0.709813 | ||||||||
\(122\) | 12.4930 | 1.13106 | ||||||||
\(123\) | 7.49896 | 0.676159 | ||||||||
\(124\) | −2.03292 | −0.182561 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.13650 | 0.190335 | ||||||||
\(127\) | 11.9605 | 1.06133 | 0.530664 | − | 0.847583i | \(-0.321943\pi\) | ||||
0.530664 | + | 0.847583i | \(0.321943\pi\) | |||||||
\(128\) | 9.26643 | 0.819045 | ||||||||
\(129\) | −8.14100 | −0.716775 | ||||||||
\(130\) | −9.17970 | −0.805113 | ||||||||
\(131\) | −10.3525 | −0.904503 | −0.452251 | − | 0.891891i | \(-0.649379\pi\) | ||||
−0.452251 | + | 0.891891i | \(0.649379\pi\) | |||||||
\(132\) | 4.58209 | 0.398820 | ||||||||
\(133\) | −6.77795 | −0.587723 | ||||||||
\(134\) | −29.0158 | −2.50658 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0.113836 | 0.00976135 | ||||||||
\(137\) | −7.09215 | −0.605924 | −0.302962 | − | 0.953003i | \(-0.597975\pi\) | ||||
−0.302962 | + | 0.953003i | \(0.597975\pi\) | |||||||
\(138\) | −2.13650 | −0.181871 | ||||||||
\(139\) | 12.1235 | 1.02830 | 0.514149 | − | 0.857701i | \(-0.328108\pi\) | ||||
0.514149 | + | 0.857701i | \(0.328108\pi\) | |||||||
\(140\) | −2.56465 | −0.216753 | ||||||||
\(141\) | −10.7203 | −0.902812 | ||||||||
\(142\) | −11.1967 | −0.939602 | ||||||||
\(143\) | 7.67644 | 0.641936 | ||||||||
\(144\) | −2.55186 | −0.212655 | ||||||||
\(145\) | −2.21636 | −0.184059 | ||||||||
\(146\) | −24.6213 | −2.03767 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 16.2939 | 1.33935 | ||||||||
\(149\) | −1.94223 | −0.159114 | −0.0795570 | − | 0.996830i | \(-0.525351\pi\) | ||||
−0.0795570 | + | 0.996830i | \(0.525351\pi\) | |||||||
\(150\) | −2.13650 | −0.174445 | ||||||||
\(151\) | 7.56553 | 0.615674 | 0.307837 | − | 0.951439i | \(-0.400395\pi\) | ||||
0.307837 | + | 0.951439i | \(0.400395\pi\) | |||||||
\(152\) | −8.17680 | −0.663226 | ||||||||
\(153\) | −0.0943613 | −0.00762866 | ||||||||
\(154\) | 3.81715 | 0.307595 | ||||||||
\(155\) | −0.792668 | −0.0636686 | ||||||||
\(156\) | 11.0193 | 0.882248 | ||||||||
\(157\) | −21.3972 | −1.70768 | −0.853840 | − | 0.520535i | \(-0.825733\pi\) | ||||
−0.853840 | + | 0.520535i | \(0.825733\pi\) | |||||||
\(158\) | −25.1061 | −1.99734 | ||||||||
\(159\) | −10.3783 | −0.823053 | ||||||||
\(160\) | 7.86483 | 0.621770 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | −2.13650 | −0.167860 | ||||||||
\(163\) | 0.103163 | 0.00808033 | 0.00404016 | − | 0.999992i | \(-0.498714\pi\) | ||||
0.00404016 | + | 0.999992i | \(0.498714\pi\) | |||||||
\(164\) | 19.2322 | 1.50179 | ||||||||
\(165\) | 1.78663 | 0.139089 | ||||||||
\(166\) | 19.7158 | 1.53024 | ||||||||
\(167\) | −15.7873 | −1.22166 | −0.610830 | − | 0.791762i | \(-0.709164\pi\) | ||||
−0.610830 | + | 0.791762i | \(0.709164\pi\) | |||||||
\(168\) | 1.20638 | 0.0930745 | ||||||||
\(169\) | 5.46074 | 0.420057 | ||||||||
\(170\) | 0.201603 | 0.0154623 | ||||||||
\(171\) | 6.77795 | 0.518323 | ||||||||
\(172\) | −20.8788 | −1.59200 | ||||||||
\(173\) | −7.26997 | −0.552726 | −0.276363 | − | 0.961053i | \(-0.589129\pi\) | ||||
−0.276363 | + | 0.961053i | \(0.589129\pi\) | |||||||
\(174\) | 4.73527 | 0.358980 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −4.55924 | −0.343666 | ||||||||
\(177\) | 3.09238 | 0.232438 | ||||||||
\(178\) | −10.9197 | −0.818465 | ||||||||
\(179\) | 18.3495 | 1.37150 | 0.685752 | − | 0.727835i | \(-0.259473\pi\) | ||||
0.685752 | + | 0.727835i | \(0.259473\pi\) | |||||||
\(180\) | 2.56465 | 0.191158 | ||||||||
\(181\) | 21.1377 | 1.57115 | 0.785576 | − | 0.618765i | \(-0.212367\pi\) | ||||
0.785576 | + | 0.618765i | \(0.212367\pi\) | |||||||
\(182\) | 9.17970 | 0.680445 | ||||||||
\(183\) | −5.84740 | −0.432252 | ||||||||
\(184\) | −1.20638 | −0.0889358 | ||||||||
\(185\) | 6.35324 | 0.467100 | ||||||||
\(186\) | 1.69354 | 0.124176 | ||||||||
\(187\) | −0.168589 | −0.0123285 | ||||||||
\(188\) | −27.4938 | −2.00519 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −14.4811 | −1.05057 | ||||||||
\(191\) | −4.75992 | −0.344416 | −0.172208 | − | 0.985061i | \(-0.555090\pi\) | ||||
−0.172208 | + | 0.985061i | \(0.555090\pi\) | |||||||
\(192\) | −11.6995 | −0.844341 | ||||||||
\(193\) | 6.70344 | 0.482524 | 0.241262 | − | 0.970460i | \(-0.422439\pi\) | ||||
0.241262 | + | 0.970460i | \(0.422439\pi\) | |||||||
\(194\) | −11.4518 | −0.822192 | ||||||||
\(195\) | 4.29660 | 0.307686 | ||||||||
\(196\) | 2.56465 | 0.183189 | ||||||||
\(197\) | 21.1463 | 1.50661 | 0.753306 | − | 0.657670i | \(-0.228458\pi\) | ||||
0.753306 | + | 0.657670i | \(0.228458\pi\) | |||||||
\(198\) | −3.81715 | −0.271273 | ||||||||
\(199\) | 24.0722 | 1.70643 | 0.853216 | − | 0.521557i | \(-0.174649\pi\) | ||||
0.853216 | + | 0.521557i | \(0.174649\pi\) | |||||||
\(200\) | −1.20638 | −0.0853042 | ||||||||
\(201\) | 13.5810 | 0.957927 | ||||||||
\(202\) | 17.6861 | 1.24439 | ||||||||
\(203\) | 2.21636 | 0.155558 | ||||||||
\(204\) | −0.242004 | −0.0169437 | ||||||||
\(205\) | 7.49896 | 0.523750 | ||||||||
\(206\) | 37.5890 | 2.61895 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −10.9643 | −0.760239 | ||||||||
\(209\) | 12.1097 | 0.837646 | ||||||||
\(210\) | 2.13650 | 0.147433 | ||||||||
\(211\) | −0.851389 | −0.0586121 | −0.0293060 | − | 0.999570i | \(-0.509330\pi\) | ||||
−0.0293060 | + | 0.999570i | \(0.509330\pi\) | |||||||
\(212\) | −26.6168 | −1.82805 | ||||||||
\(213\) | 5.24064 | 0.359083 | ||||||||
\(214\) | 27.7008 | 1.89359 | ||||||||
\(215\) | −8.14100 | −0.555211 | ||||||||
\(216\) | −1.20638 | −0.0820840 | ||||||||
\(217\) | 0.792668 | 0.0538098 | ||||||||
\(218\) | −27.9559 | −1.89341 | ||||||||
\(219\) | 11.5241 | 0.778726 | ||||||||
\(220\) | 4.58209 | 0.308925 | ||||||||
\(221\) | −0.405433 | −0.0272724 | ||||||||
\(222\) | −13.5737 | −0.911009 | ||||||||
\(223\) | 6.49348 | 0.434835 | 0.217418 | − | 0.976079i | \(-0.430237\pi\) | ||||
0.217418 | + | 0.976079i | \(0.430237\pi\) | |||||||
\(224\) | −7.86483 | −0.525491 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −6.96854 | −0.463540 | ||||||||
\(227\) | 14.7385 | 0.978228 | 0.489114 | − | 0.872220i | \(-0.337320\pi\) | ||||
0.489114 | + | 0.872220i | \(0.337320\pi\) | |||||||
\(228\) | 17.3831 | 1.15122 | ||||||||
\(229\) | −17.0305 | −1.12541 | −0.562703 | − | 0.826659i | \(-0.690239\pi\) | ||||
−0.562703 | + | 0.826659i | \(0.690239\pi\) | |||||||
\(230\) | −2.13650 | −0.140877 | ||||||||
\(231\) | −1.78663 | −0.117552 | ||||||||
\(232\) | 2.67379 | 0.175543 | ||||||||
\(233\) | −4.08268 | −0.267465 | −0.133733 | − | 0.991017i | \(-0.542696\pi\) | ||||
−0.133733 | + | 0.991017i | \(0.542696\pi\) | |||||||
\(234\) | −9.17970 | −0.600096 | ||||||||
\(235\) | −10.7203 | −0.699315 | ||||||||
\(236\) | 7.93089 | 0.516257 | ||||||||
\(237\) | 11.7510 | 0.763311 | ||||||||
\(238\) | −0.201603 | −0.0130680 | ||||||||
\(239\) | −23.2202 | −1.50199 | −0.750994 | − | 0.660309i | \(-0.770425\pi\) | ||||
−0.750994 | + | 0.660309i | \(0.770425\pi\) | |||||||
\(240\) | −2.55186 | −0.164722 | ||||||||
\(241\) | 27.0592 | 1.74304 | 0.871520 | − | 0.490361i | \(-0.163135\pi\) | ||||
0.871520 | + | 0.490361i | \(0.163135\pi\) | |||||||
\(242\) | 16.6817 | 1.07234 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −14.9965 | −0.960056 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −16.0216 | −1.02150 | ||||||||
\(247\) | 29.1221 | 1.85300 | ||||||||
\(248\) | 0.956262 | 0.0607227 | ||||||||
\(249\) | −9.22806 | −0.584804 | ||||||||
\(250\) | −2.13650 | −0.135124 | ||||||||
\(251\) | 26.1630 | 1.65139 | 0.825695 | − | 0.564116i | \(-0.190783\pi\) | ||||
0.825695 | + | 0.564116i | \(0.190783\pi\) | |||||||
\(252\) | −2.56465 | −0.161558 | ||||||||
\(253\) | 1.78663 | 0.112325 | ||||||||
\(254\) | −25.5538 | −1.60339 | ||||||||
\(255\) | −0.0943613 | −0.00590914 | ||||||||
\(256\) | 3.60128 | 0.225080 | ||||||||
\(257\) | 23.5375 | 1.46823 | 0.734113 | − | 0.679027i | \(-0.237598\pi\) | ||||
0.734113 | + | 0.679027i | \(0.237598\pi\) | |||||||
\(258\) | 17.3933 | 1.08286 | ||||||||
\(259\) | −6.35324 | −0.394771 | ||||||||
\(260\) | 11.0193 | 0.683387 | ||||||||
\(261\) | −2.21636 | −0.137190 | ||||||||
\(262\) | 22.1182 | 1.36647 | ||||||||
\(263\) | −18.4727 | −1.13907 | −0.569537 | − | 0.821966i | \(-0.692877\pi\) | ||||
−0.569537 | + | 0.821966i | \(0.692877\pi\) | |||||||
\(264\) | −2.15536 | −0.132654 | ||||||||
\(265\) | −10.3783 | −0.637534 | ||||||||
\(266\) | 14.4811 | 0.887894 | ||||||||
\(267\) | 5.11100 | 0.312788 | ||||||||
\(268\) | 34.8305 | 2.12761 | ||||||||
\(269\) | 14.3774 | 0.876606 | 0.438303 | − | 0.898827i | \(-0.355580\pi\) | ||||
0.438303 | + | 0.898827i | \(0.355580\pi\) | |||||||
\(270\) | −2.13650 | −0.130024 | ||||||||
\(271\) | −18.0079 | −1.09390 | −0.546951 | − | 0.837165i | \(-0.684211\pi\) | ||||
−0.546951 | + | 0.837165i | \(0.684211\pi\) | |||||||
\(272\) | 0.240797 | 0.0146005 | ||||||||
\(273\) | −4.29660 | −0.260042 | ||||||||
\(274\) | 15.1524 | 0.915391 | ||||||||
\(275\) | 1.78663 | 0.107738 | ||||||||
\(276\) | 2.56465 | 0.154374 | ||||||||
\(277\) | 5.94604 | 0.357263 | 0.178631 | − | 0.983916i | \(-0.442833\pi\) | ||||
0.178631 | + | 0.983916i | \(0.442833\pi\) | |||||||
\(278\) | −25.9018 | −1.55349 | ||||||||
\(279\) | −0.792668 | −0.0474558 | ||||||||
\(280\) | 1.20638 | 0.0720952 | ||||||||
\(281\) | −17.9816 | −1.07269 | −0.536347 | − | 0.843998i | \(-0.680196\pi\) | ||||
−0.536347 | + | 0.843998i | \(0.680196\pi\) | |||||||
\(282\) | 22.9040 | 1.36391 | ||||||||
\(283\) | −10.0103 | −0.595049 | −0.297524 | − | 0.954714i | \(-0.596161\pi\) | ||||
−0.297524 | + | 0.954714i | \(0.596161\pi\) | |||||||
\(284\) | 13.4404 | 0.797542 | ||||||||
\(285\) | 6.77795 | 0.401491 | ||||||||
\(286\) | −16.4008 | −0.969797 | ||||||||
\(287\) | −7.49896 | −0.442650 | ||||||||
\(288\) | 7.86483 | 0.463440 | ||||||||
\(289\) | −16.9911 | −0.999476 | ||||||||
\(290\) | 4.73527 | 0.278065 | ||||||||
\(291\) | 5.36007 | 0.314213 | ||||||||
\(292\) | 29.5553 | 1.72959 | ||||||||
\(293\) | 28.8258 | 1.68402 | 0.842011 | − | 0.539460i | \(-0.181371\pi\) | ||||
0.842011 | + | 0.539460i | \(0.181371\pi\) | |||||||
\(294\) | −2.13650 | −0.124603 | ||||||||
\(295\) | 3.09238 | 0.180045 | ||||||||
\(296\) | −7.66444 | −0.445487 | ||||||||
\(297\) | 1.78663 | 0.103671 | ||||||||
\(298\) | 4.14959 | 0.240379 | ||||||||
\(299\) | 4.29660 | 0.248479 | ||||||||
\(300\) | 2.56465 | 0.148070 | ||||||||
\(301\) | 8.14100 | 0.469239 | ||||||||
\(302\) | −16.1638 | −0.930122 | ||||||||
\(303\) | −8.27803 | −0.475561 | ||||||||
\(304\) | −17.2964 | −0.992016 | ||||||||
\(305\) | −5.84740 | −0.334821 | ||||||||
\(306\) | 0.201603 | 0.0115249 | ||||||||
\(307\) | −21.9082 | −1.25037 | −0.625184 | − | 0.780478i | \(-0.714976\pi\) | ||||
−0.625184 | + | 0.780478i | \(0.714976\pi\) | |||||||
\(308\) | −4.58209 | −0.261089 | ||||||||
\(309\) | −17.5937 | −1.00087 | ||||||||
\(310\) | 1.69354 | 0.0961866 | ||||||||
\(311\) | 31.9210 | 1.81008 | 0.905038 | − | 0.425331i | \(-0.139842\pi\) | ||||
0.905038 | + | 0.425331i | \(0.139842\pi\) | |||||||
\(312\) | −5.18334 | −0.293449 | ||||||||
\(313\) | −0.0950302 | −0.00537142 | −0.00268571 | − | 0.999996i | \(-0.500855\pi\) | ||||
−0.00268571 | + | 0.999996i | \(0.500855\pi\) | |||||||
\(314\) | 45.7152 | 2.57986 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | 30.1373 | 1.69536 | ||||||||
\(317\) | 9.58935 | 0.538591 | 0.269296 | − | 0.963058i | \(-0.413209\pi\) | ||||
0.269296 | + | 0.963058i | \(0.413209\pi\) | |||||||
\(318\) | 22.1733 | 1.24342 | ||||||||
\(319\) | −3.95983 | −0.221708 | ||||||||
\(320\) | −11.6995 | −0.654023 | ||||||||
\(321\) | −12.9655 | −0.723662 | ||||||||
\(322\) | 2.13650 | 0.119063 | ||||||||
\(323\) | −0.639576 | −0.0355870 | ||||||||
\(324\) | 2.56465 | 0.142481 | ||||||||
\(325\) | 4.29660 | 0.238332 | ||||||||
\(326\) | −0.220408 | −0.0122072 | ||||||||
\(327\) | 13.0849 | 0.723596 | ||||||||
\(328\) | −9.04662 | −0.499516 | ||||||||
\(329\) | 10.7203 | 0.591029 | ||||||||
\(330\) | −3.81715 | −0.210127 | ||||||||
\(331\) | 4.28108 | 0.235309 | 0.117655 | − | 0.993055i | \(-0.462462\pi\) | ||||
0.117655 | + | 0.993055i | \(0.462462\pi\) | |||||||
\(332\) | −23.6668 | −1.29888 | ||||||||
\(333\) | 6.35324 | 0.348155 | ||||||||
\(334\) | 33.7297 | 1.84561 | ||||||||
\(335\) | 13.5810 | 0.742007 | ||||||||
\(336\) | 2.55186 | 0.139215 | ||||||||
\(337\) | 36.2564 | 1.97501 | 0.987507 | − | 0.157576i | \(-0.0503680\pi\) | ||||
0.987507 | + | 0.157576i | \(0.0503680\pi\) | |||||||
\(338\) | −11.6669 | −0.634596 | ||||||||
\(339\) | 3.26165 | 0.177149 | ||||||||
\(340\) | −0.242004 | −0.0131245 | ||||||||
\(341\) | −1.41621 | −0.0766919 | ||||||||
\(342\) | −14.4811 | −0.783049 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 9.82116 | 0.529522 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | 15.5323 | 0.835023 | ||||||||
\(347\) | 18.9656 | 1.01812 | 0.509062 | − | 0.860730i | \(-0.329992\pi\) | ||||
0.509062 | + | 0.860730i | \(0.329992\pi\) | |||||||
\(348\) | −5.68421 | −0.304705 | ||||||||
\(349\) | −4.03031 | −0.215738 | −0.107869 | − | 0.994165i | \(-0.534403\pi\) | ||||
−0.107869 | + | 0.994165i | \(0.534403\pi\) | |||||||
\(350\) | 2.13650 | 0.114201 | ||||||||
\(351\) | 4.29660 | 0.229335 | ||||||||
\(352\) | 14.0516 | 0.748951 | ||||||||
\(353\) | 3.50110 | 0.186345 | 0.0931723 | − | 0.995650i | \(-0.470299\pi\) | ||||
0.0931723 | + | 0.995650i | \(0.470299\pi\) | |||||||
\(354\) | −6.60689 | −0.351152 | ||||||||
\(355\) | 5.24064 | 0.278144 | ||||||||
\(356\) | 13.1079 | 0.694720 | ||||||||
\(357\) | 0.0943613 | 0.00499413 | ||||||||
\(358\) | −39.2037 | −2.07198 | ||||||||
\(359\) | 7.71988 | 0.407440 | 0.203720 | − | 0.979029i | \(-0.434697\pi\) | ||||
0.203720 | + | 0.979029i | \(0.434697\pi\) | |||||||
\(360\) | −1.20638 | −0.0635820 | ||||||||
\(361\) | 26.9406 | 1.41793 | ||||||||
\(362\) | −45.1608 | −2.37360 | ||||||||
\(363\) | −7.80794 | −0.409811 | ||||||||
\(364\) | −11.0193 | −0.577567 | ||||||||
\(365\) | 11.5241 | 0.603199 | ||||||||
\(366\) | 12.4930 | 0.653019 | ||||||||
\(367\) | −3.63482 | −0.189736 | −0.0948680 | − | 0.995490i | \(-0.530243\pi\) | ||||
−0.0948680 | + | 0.995490i | \(0.530243\pi\) | |||||||
\(368\) | −2.55186 | −0.133025 | ||||||||
\(369\) | 7.49896 | 0.390380 | ||||||||
\(370\) | −13.5737 | −0.705665 | ||||||||
\(371\) | 10.3783 | 0.538815 | ||||||||
\(372\) | −2.03292 | −0.105402 | ||||||||
\(373\) | 9.22651 | 0.477730 | 0.238865 | − | 0.971053i | \(-0.423225\pi\) | ||||
0.238865 | + | 0.971053i | \(0.423225\pi\) | |||||||
\(374\) | 0.360192 | 0.0186251 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 12.9328 | 0.666958 | ||||||||
\(377\) | −9.52283 | −0.490451 | ||||||||
\(378\) | 2.13650 | 0.109890 | ||||||||
\(379\) | 22.1036 | 1.13539 | 0.567693 | − | 0.823240i | \(-0.307836\pi\) | ||||
0.567693 | + | 0.823240i | \(0.307836\pi\) | |||||||
\(380\) | 17.3831 | 0.891733 | ||||||||
\(381\) | 11.9605 | 0.612758 | ||||||||
\(382\) | 10.1696 | 0.520322 | ||||||||
\(383\) | −22.7321 | −1.16156 | −0.580778 | − | 0.814062i | \(-0.697252\pi\) | ||||
−0.580778 | + | 0.814062i | \(0.697252\pi\) | |||||||
\(384\) | 9.26643 | 0.472876 | ||||||||
\(385\) | −1.78663 | −0.0910553 | ||||||||
\(386\) | −14.3219 | −0.728967 | ||||||||
\(387\) | −8.14100 | −0.413830 | ||||||||
\(388\) | 13.7467 | 0.697884 | ||||||||
\(389\) | 35.4091 | 1.79531 | 0.897655 | − | 0.440698i | \(-0.145269\pi\) | ||||
0.897655 | + | 0.440698i | \(0.145269\pi\) | |||||||
\(390\) | −9.17970 | −0.464832 | ||||||||
\(391\) | −0.0943613 | −0.00477206 | ||||||||
\(392\) | −1.20638 | −0.0609316 | ||||||||
\(393\) | −10.3525 | −0.522215 | ||||||||
\(394\) | −45.1792 | −2.27610 | ||||||||
\(395\) | 11.7510 | 0.591258 | ||||||||
\(396\) | 4.58209 | 0.230259 | ||||||||
\(397\) | −35.9923 | −1.80640 | −0.903200 | − | 0.429219i | \(-0.858789\pi\) | ||||
−0.903200 | + | 0.429219i | \(0.858789\pi\) | |||||||
\(398\) | −51.4304 | −2.57797 | ||||||||
\(399\) | −6.77795 | −0.339322 | ||||||||
\(400\) | −2.55186 | −0.127593 | ||||||||
\(401\) | 16.8014 | 0.839024 | 0.419512 | − | 0.907750i | \(-0.362201\pi\) | ||||
0.419512 | + | 0.907750i | \(0.362201\pi\) | |||||||
\(402\) | −29.0158 | −1.44718 | ||||||||
\(403\) | −3.40578 | −0.169654 | ||||||||
\(404\) | −21.2303 | −1.05625 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −4.73527 | −0.235008 | ||||||||
\(407\) | 11.3509 | 0.562644 | ||||||||
\(408\) | 0.113836 | 0.00563572 | ||||||||
\(409\) | −15.2505 | −0.754087 | −0.377044 | − | 0.926196i | \(-0.623059\pi\) | ||||
−0.377044 | + | 0.926196i | \(0.623059\pi\) | |||||||
\(410\) | −16.0216 | −0.791249 | ||||||||
\(411\) | −7.09215 | −0.349830 | ||||||||
\(412\) | −45.1216 | −2.22298 | ||||||||
\(413\) | −3.09238 | −0.152166 | ||||||||
\(414\) | −2.13650 | −0.105003 | ||||||||
\(415\) | −9.22806 | −0.452987 | ||||||||
\(416\) | 33.7920 | 1.65679 | ||||||||
\(417\) | 12.1235 | 0.593688 | ||||||||
\(418\) | −25.8725 | −1.26546 | ||||||||
\(419\) | 20.7184 | 1.01216 | 0.506080 | − | 0.862486i | \(-0.331094\pi\) | ||||
0.506080 | + | 0.862486i | \(0.331094\pi\) | |||||||
\(420\) | −2.56465 | −0.125142 | ||||||||
\(421\) | −2.34883 | −0.114475 | −0.0572374 | − | 0.998361i | \(-0.518229\pi\) | ||||
−0.0572374 | + | 0.998361i | \(0.518229\pi\) | |||||||
\(422\) | 1.81900 | 0.0885474 | ||||||||
\(423\) | −10.7203 | −0.521239 | ||||||||
\(424\) | 12.5202 | 0.608035 | ||||||||
\(425\) | −0.0943613 | −0.00457720 | ||||||||
\(426\) | −11.1967 | −0.542480 | ||||||||
\(427\) | 5.84740 | 0.282975 | ||||||||
\(428\) | −33.2519 | −1.60729 | ||||||||
\(429\) | 7.67644 | 0.370622 | ||||||||
\(430\) | 17.3933 | 0.838778 | ||||||||
\(431\) | −16.4999 | −0.794774 | −0.397387 | − | 0.917651i | \(-0.630083\pi\) | ||||
−0.397387 | + | 0.917651i | \(0.630083\pi\) | |||||||
\(432\) | −2.55186 | −0.122777 | ||||||||
\(433\) | −21.5192 | −1.03415 | −0.517074 | − | 0.855941i | \(-0.672979\pi\) | ||||
−0.517074 | + | 0.855941i | \(0.672979\pi\) | |||||||
\(434\) | −1.69354 | −0.0812925 | ||||||||
\(435\) | −2.21636 | −0.106267 | ||||||||
\(436\) | 33.5582 | 1.60715 | ||||||||
\(437\) | 6.77795 | 0.324233 | ||||||||
\(438\) | −24.6213 | −1.17645 | ||||||||
\(439\) | −18.2234 | −0.869754 | −0.434877 | − | 0.900490i | \(-0.643208\pi\) | ||||
−0.434877 | + | 0.900490i | \(0.643208\pi\) | |||||||
\(440\) | −2.15536 | −0.102753 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0.866209 | 0.0412014 | ||||||||
\(443\) | 18.3345 | 0.871099 | 0.435550 | − | 0.900165i | \(-0.356554\pi\) | ||||
0.435550 | + | 0.900165i | \(0.356554\pi\) | |||||||
\(444\) | 16.2939 | 0.773272 | ||||||||
\(445\) | 5.11100 | 0.242285 | ||||||||
\(446\) | −13.8733 | −0.656922 | ||||||||
\(447\) | −1.94223 | −0.0918645 | ||||||||
\(448\) | 11.6995 | 0.552751 | ||||||||
\(449\) | −25.7028 | −1.21299 | −0.606495 | − | 0.795087i | \(-0.707425\pi\) | ||||
−0.606495 | + | 0.795087i | \(0.707425\pi\) | |||||||
\(450\) | −2.13650 | −0.100716 | ||||||||
\(451\) | 13.3979 | 0.630882 | ||||||||
\(452\) | 8.36501 | 0.393457 | ||||||||
\(453\) | 7.56553 | 0.355460 | ||||||||
\(454\) | −31.4889 | −1.47785 | ||||||||
\(455\) | −4.29660 | −0.201428 | ||||||||
\(456\) | −8.17680 | −0.382914 | ||||||||
\(457\) | −31.0069 | −1.45044 | −0.725220 | − | 0.688517i | \(-0.758262\pi\) | ||||
−0.725220 | + | 0.688517i | \(0.758262\pi\) | |||||||
\(458\) | 36.3857 | 1.70019 | ||||||||
\(459\) | −0.0943613 | −0.00440441 | ||||||||
\(460\) | 2.56465 | 0.119578 | ||||||||
\(461\) | −4.01677 | −0.187079 | −0.0935397 | − | 0.995616i | \(-0.529818\pi\) | ||||
−0.0935397 | + | 0.995616i | \(0.529818\pi\) | |||||||
\(462\) | 3.81715 | 0.177590 | ||||||||
\(463\) | −2.90641 | −0.135072 | −0.0675361 | − | 0.997717i | \(-0.521514\pi\) | ||||
−0.0675361 | + | 0.997717i | \(0.521514\pi\) | |||||||
\(464\) | 5.65586 | 0.262567 | ||||||||
\(465\) | −0.792668 | −0.0367591 | ||||||||
\(466\) | 8.72267 | 0.404070 | ||||||||
\(467\) | −13.8420 | −0.640532 | −0.320266 | − | 0.947328i | \(-0.603772\pi\) | ||||
−0.320266 | + | 0.947328i | \(0.603772\pi\) | |||||||
\(468\) | 11.0193 | 0.509366 | ||||||||
\(469\) | −13.5810 | −0.627111 | ||||||||
\(470\) | 22.9040 | 1.05648 | ||||||||
\(471\) | −21.3972 | −0.985930 | ||||||||
\(472\) | −3.73060 | −0.171715 | ||||||||
\(473\) | −14.5450 | −0.668779 | ||||||||
\(474\) | −25.1061 | −1.15316 | ||||||||
\(475\) | 6.77795 | 0.310994 | ||||||||
\(476\) | 0.242004 | 0.0110922 | ||||||||
\(477\) | −10.3783 | −0.475190 | ||||||||
\(478\) | 49.6100 | 2.26911 | ||||||||
\(479\) | −24.5487 | −1.12166 | −0.560829 | − | 0.827931i | \(-0.689518\pi\) | ||||
−0.560829 | + | 0.827931i | \(0.689518\pi\) | |||||||
\(480\) | 7.86483 | 0.358979 | ||||||||
\(481\) | 27.2973 | 1.24465 | ||||||||
\(482\) | −57.8122 | −2.63327 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | −20.0247 | −0.910212 | ||||||||
\(485\) | 5.36007 | 0.243388 | ||||||||
\(486\) | −2.13650 | −0.0969138 | ||||||||
\(487\) | −25.2374 | −1.14362 | −0.571808 | − | 0.820388i | \(-0.693758\pi\) | ||||
−0.571808 | + | 0.820388i | \(0.693758\pi\) | |||||||
\(488\) | 7.05420 | 0.319329 | ||||||||
\(489\) | 0.103163 | 0.00466518 | ||||||||
\(490\) | −2.13650 | −0.0965174 | ||||||||
\(491\) | −20.3759 | −0.919553 | −0.459777 | − | 0.888035i | \(-0.652071\pi\) | ||||
−0.459777 | + | 0.888035i | \(0.652071\pi\) | |||||||
\(492\) | 19.2322 | 0.867056 | ||||||||
\(493\) | 0.209139 | 0.00941915 | ||||||||
\(494\) | −62.2195 | −2.79939 | ||||||||
\(495\) | 1.78663 | 0.0803032 | ||||||||
\(496\) | 2.02278 | 0.0908255 | ||||||||
\(497\) | −5.24064 | −0.235075 | ||||||||
\(498\) | 19.7158 | 0.883486 | ||||||||
\(499\) | 1.90564 | 0.0853081 | 0.0426541 | − | 0.999090i | \(-0.486419\pi\) | ||||
0.0426541 | + | 0.999090i | \(0.486419\pi\) | |||||||
\(500\) | 2.56465 | 0.114695 | ||||||||
\(501\) | −15.7873 | −0.705325 | ||||||||
\(502\) | −55.8973 | −2.49482 | ||||||||
\(503\) | −34.3617 | −1.53211 | −0.766057 | − | 0.642773i | \(-0.777784\pi\) | ||||
−0.766057 | + | 0.642773i | \(0.777784\pi\) | |||||||
\(504\) | 1.20638 | 0.0537366 | ||||||||
\(505\) | −8.27803 | −0.368368 | ||||||||
\(506\) | −3.81715 | −0.169693 | ||||||||
\(507\) | 5.46074 | 0.242520 | ||||||||
\(508\) | 30.6747 | 1.36097 | ||||||||
\(509\) | 21.8470 | 0.968353 | 0.484176 | − | 0.874970i | \(-0.339119\pi\) | ||||
0.484176 | + | 0.874970i | \(0.339119\pi\) | |||||||
\(510\) | 0.201603 | 0.00892715 | ||||||||
\(511\) | −11.5241 | −0.509796 | ||||||||
\(512\) | −26.2270 | −1.15908 | ||||||||
\(513\) | 6.77795 | 0.299254 | ||||||||
\(514\) | −50.2879 | −2.21810 | ||||||||
\(515\) | −17.5937 | −0.775270 | ||||||||
\(516\) | −20.8788 | −0.919139 | ||||||||
\(517\) | −19.1532 | −0.842359 | ||||||||
\(518\) | 13.5737 | 0.596395 | ||||||||
\(519\) | −7.26997 | −0.319116 | ||||||||
\(520\) | −5.18334 | −0.227305 | ||||||||
\(521\) | 10.5180 | 0.460804 | 0.230402 | − | 0.973096i | \(-0.425996\pi\) | ||||
0.230402 | + | 0.973096i | \(0.425996\pi\) | |||||||
\(522\) | 4.73527 | 0.207257 | ||||||||
\(523\) | −12.0486 | −0.526849 | −0.263425 | − | 0.964680i | \(-0.584852\pi\) | ||||
−0.263425 | + | 0.964680i | \(0.584852\pi\) | |||||||
\(524\) | −26.5506 | −1.15987 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 39.4669 | 1.72084 | ||||||||
\(527\) | 0.0747972 | 0.00325822 | ||||||||
\(528\) | −4.55924 | −0.198416 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 22.1733 | 0.963147 | ||||||||
\(531\) | 3.09238 | 0.134198 | ||||||||
\(532\) | −17.3831 | −0.753652 | ||||||||
\(533\) | 32.2200 | 1.39560 | ||||||||
\(534\) | −10.9197 | −0.472541 | ||||||||
\(535\) | −12.9655 | −0.560546 | ||||||||
\(536\) | −16.3838 | −0.707674 | ||||||||
\(537\) | 18.3495 | 0.791838 | ||||||||
\(538\) | −30.7174 | −1.32432 | ||||||||
\(539\) | 1.78663 | 0.0769558 | ||||||||
\(540\) | 2.56465 | 0.110365 | ||||||||
\(541\) | 31.6201 | 1.35945 | 0.679726 | − | 0.733466i | \(-0.262099\pi\) | ||||
0.679726 | + | 0.733466i | \(0.262099\pi\) | |||||||
\(542\) | 38.4739 | 1.65260 | ||||||||
\(543\) | 21.1377 | 0.907105 | ||||||||
\(544\) | −0.742136 | −0.0318188 | ||||||||
\(545\) | 13.0849 | 0.560495 | ||||||||
\(546\) | 9.17970 | 0.392855 | ||||||||
\(547\) | −36.1537 | −1.54582 | −0.772911 | − | 0.634514i | \(-0.781200\pi\) | ||||
−0.772911 | + | 0.634514i | \(0.781200\pi\) | |||||||
\(548\) | −18.1889 | −0.776992 | ||||||||
\(549\) | −5.84740 | −0.249561 | ||||||||
\(550\) | −3.81715 | −0.162764 | ||||||||
\(551\) | −15.0224 | −0.639976 | ||||||||
\(552\) | −1.20638 | −0.0513471 | ||||||||
\(553\) | −11.7510 | −0.499705 | ||||||||
\(554\) | −12.7037 | −0.539730 | ||||||||
\(555\) | 6.35324 | 0.269680 | ||||||||
\(556\) | 31.0925 | 1.31861 | ||||||||
\(557\) | 15.4602 | 0.655070 | 0.327535 | − | 0.944839i | \(-0.393782\pi\) | ||||
0.327535 | + | 0.944839i | \(0.393782\pi\) | |||||||
\(558\) | 1.69354 | 0.0716932 | ||||||||
\(559\) | −34.9786 | −1.47944 | ||||||||
\(560\) | 2.55186 | 0.107836 | ||||||||
\(561\) | −0.168589 | −0.00711784 | ||||||||
\(562\) | 38.4178 | 1.62056 | ||||||||
\(563\) | −30.2491 | −1.27485 | −0.637425 | − | 0.770513i | \(-0.720000\pi\) | ||||
−0.637425 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(564\) | −27.4938 | −1.15770 | ||||||||
\(565\) | 3.26165 | 0.137219 | ||||||||
\(566\) | 21.3870 | 0.898962 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −6.32222 | −0.265275 | ||||||||
\(569\) | −3.54282 | −0.148523 | −0.0742613 | − | 0.997239i | \(-0.523660\pi\) | ||||
−0.0742613 | + | 0.997239i | \(0.523660\pi\) | |||||||
\(570\) | −14.4811 | −0.606547 | ||||||||
\(571\) | −17.3304 | −0.725256 | −0.362628 | − | 0.931934i | \(-0.618121\pi\) | ||||
−0.362628 | + | 0.931934i | \(0.618121\pi\) | |||||||
\(572\) | 19.6874 | 0.823172 | ||||||||
\(573\) | −4.75992 | −0.198849 | ||||||||
\(574\) | 16.0216 | 0.668727 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | −11.6995 | −0.487480 | ||||||||
\(577\) | −12.0064 | −0.499833 | −0.249917 | − | 0.968267i | \(-0.580403\pi\) | ||||
−0.249917 | + | 0.968267i | \(0.580403\pi\) | |||||||
\(578\) | 36.3016 | 1.50995 | ||||||||
\(579\) | 6.70344 | 0.278585 | ||||||||
\(580\) | −5.68421 | −0.236024 | ||||||||
\(581\) | 9.22806 | 0.382844 | ||||||||
\(582\) | −11.4518 | −0.474693 | ||||||||
\(583\) | −18.5422 | −0.767941 | ||||||||
\(584\) | −13.9025 | −0.575289 | ||||||||
\(585\) | 4.29660 | 0.177642 | ||||||||
\(586\) | −61.5865 | −2.54412 | ||||||||
\(587\) | 3.28838 | 0.135726 | 0.0678629 | − | 0.997695i | \(-0.478382\pi\) | ||||
0.0678629 | + | 0.997695i | \(0.478382\pi\) | |||||||
\(588\) | 2.56465 | 0.105764 | ||||||||
\(589\) | −5.37266 | −0.221377 | ||||||||
\(590\) | −6.60689 | −0.272001 | ||||||||
\(591\) | 21.1463 | 0.869843 | ||||||||
\(592\) | −16.2126 | −0.666334 | ||||||||
\(593\) | 32.4005 | 1.33053 | 0.665265 | − | 0.746607i | \(-0.268318\pi\) | ||||
0.665265 | + | 0.746607i | \(0.268318\pi\) | |||||||
\(594\) | −3.81715 | −0.156620 | ||||||||
\(595\) | 0.0943613 | 0.00386844 | ||||||||
\(596\) | −4.98115 | −0.204036 | ||||||||
\(597\) | 24.0722 | 0.985209 | ||||||||
\(598\) | −9.17970 | −0.375386 | ||||||||
\(599\) | 8.30020 | 0.339137 | 0.169568 | − | 0.985518i | \(-0.445763\pi\) | ||||
0.169568 | + | 0.985518i | \(0.445763\pi\) | |||||||
\(600\) | −1.20638 | −0.0492504 | ||||||||
\(601\) | −6.31789 | −0.257712 | −0.128856 | − | 0.991663i | \(-0.541131\pi\) | ||||
−0.128856 | + | 0.991663i | \(0.541131\pi\) | |||||||
\(602\) | −17.3933 | −0.708897 | ||||||||
\(603\) | 13.5810 | 0.553060 | ||||||||
\(604\) | 19.4030 | 0.789495 | ||||||||
\(605\) | −7.80794 | −0.317438 | ||||||||
\(606\) | 17.6861 | 0.718447 | ||||||||
\(607\) | 32.3279 | 1.31215 | 0.656075 | − | 0.754695i | \(-0.272215\pi\) | ||||
0.656075 | + | 0.754695i | \(0.272215\pi\) | |||||||
\(608\) | 53.3074 | 2.16190 | ||||||||
\(609\) | 2.21636 | 0.0898116 | ||||||||
\(610\) | 12.4930 | 0.505827 | ||||||||
\(611\) | −46.0608 | −1.86342 | ||||||||
\(612\) | −0.242004 | −0.00978244 | ||||||||
\(613\) | 1.22597 | 0.0495165 | 0.0247583 | − | 0.999693i | \(-0.492118\pi\) | ||||
0.0247583 | + | 0.999693i | \(0.492118\pi\) | |||||||
\(614\) | 46.8070 | 1.88898 | ||||||||
\(615\) | 7.49896 | 0.302387 | ||||||||
\(616\) | 2.15536 | 0.0868421 | ||||||||
\(617\) | −38.3230 | −1.54282 | −0.771412 | − | 0.636336i | \(-0.780449\pi\) | ||||
−0.771412 | + | 0.636336i | \(0.780449\pi\) | |||||||
\(618\) | 37.5890 | 1.51205 | ||||||||
\(619\) | −14.6750 | −0.589838 | −0.294919 | − | 0.955522i | \(-0.595293\pi\) | ||||
−0.294919 | + | 0.955522i | \(0.595293\pi\) | |||||||
\(620\) | −2.03292 | −0.0816440 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −68.1994 | −2.73455 | ||||||||
\(623\) | −5.11100 | −0.204768 | ||||||||
\(624\) | −10.9643 | −0.438924 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0.203032 | 0.00811481 | ||||||||
\(627\) | 12.1097 | 0.483615 | ||||||||
\(628\) | −54.8763 | −2.18980 | ||||||||
\(629\) | −0.599500 | −0.0239036 | ||||||||
\(630\) | 2.13650 | 0.0851204 | ||||||||
\(631\) | −6.56327 | −0.261280 | −0.130640 | − | 0.991430i | \(-0.541703\pi\) | ||||
−0.130640 | + | 0.991430i | \(0.541703\pi\) | |||||||
\(632\) | −14.1762 | −0.563901 | ||||||||
\(633\) | −0.851389 | −0.0338397 | ||||||||
\(634\) | −20.4877 | −0.813670 | ||||||||
\(635\) | 11.9605 | 0.474640 | ||||||||
\(636\) | −26.6168 | −1.05542 | ||||||||
\(637\) | 4.29660 | 0.170237 | ||||||||
\(638\) | 8.46020 | 0.334943 | ||||||||
\(639\) | 5.24064 | 0.207317 | ||||||||
\(640\) | 9.26643 | 0.366288 | ||||||||
\(641\) | −26.0757 | −1.02993 | −0.514965 | − | 0.857211i | \(-0.672195\pi\) | ||||
−0.514965 | + | 0.857211i | \(0.672195\pi\) | |||||||
\(642\) | 27.7008 | 1.09326 | ||||||||
\(643\) | 3.55563 | 0.140220 | 0.0701102 | − | 0.997539i | \(-0.477665\pi\) | ||||
0.0701102 | + | 0.997539i | \(0.477665\pi\) | |||||||
\(644\) | −2.56465 | −0.101061 | ||||||||
\(645\) | −8.14100 | −0.320551 | ||||||||
\(646\) | 1.36646 | 0.0537626 | ||||||||
\(647\) | −8.95614 | −0.352102 | −0.176051 | − | 0.984381i | \(-0.556332\pi\) | ||||
−0.176051 | + | 0.984381i | \(0.556332\pi\) | |||||||
\(648\) | −1.20638 | −0.0473912 | ||||||||
\(649\) | 5.52495 | 0.216873 | ||||||||
\(650\) | −9.17970 | −0.360057 | ||||||||
\(651\) | 0.792668 | 0.0310671 | ||||||||
\(652\) | 0.264576 | 0.0103616 | ||||||||
\(653\) | 18.6879 | 0.731312 | 0.365656 | − | 0.930750i | \(-0.380845\pi\) | ||||
0.365656 | + | 0.930750i | \(0.380845\pi\) | |||||||
\(654\) | −27.9559 | −1.09316 | ||||||||
\(655\) | −10.3525 | −0.404506 | ||||||||
\(656\) | −19.1363 | −0.747148 | ||||||||
\(657\) | 11.5241 | 0.449598 | ||||||||
\(658\) | −22.9040 | −0.892890 | ||||||||
\(659\) | −40.3803 | −1.57299 | −0.786496 | − | 0.617596i | \(-0.788107\pi\) | ||||
−0.786496 | + | 0.617596i | \(0.788107\pi\) | |||||||
\(660\) | 4.58209 | 0.178358 | ||||||||
\(661\) | −19.6916 | −0.765916 | −0.382958 | − | 0.923766i | \(-0.625095\pi\) | ||||
−0.382958 | + | 0.923766i | \(0.625095\pi\) | |||||||
\(662\) | −9.14655 | −0.355491 | ||||||||
\(663\) | −0.405433 | −0.0157457 | ||||||||
\(664\) | 11.1326 | 0.432028 | ||||||||
\(665\) | −6.77795 | −0.262838 | ||||||||
\(666\) | −13.5737 | −0.525971 | ||||||||
\(667\) | −2.21636 | −0.0858180 | ||||||||
\(668\) | −40.4890 | −1.56657 | ||||||||
\(669\) | 6.49348 | 0.251052 | ||||||||
\(670\) | −29.0158 | −1.12098 | ||||||||
\(671\) | −10.4472 | −0.403308 | ||||||||
\(672\) | −7.86483 | −0.303392 | ||||||||
\(673\) | −23.6121 | −0.910180 | −0.455090 | − | 0.890445i | \(-0.650393\pi\) | ||||
−0.455090 | + | 0.890445i | \(0.650393\pi\) | |||||||
\(674\) | −77.4620 | −2.98373 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 14.0049 | 0.538650 | ||||||||
\(677\) | 12.1823 | 0.468205 | 0.234103 | − | 0.972212i | \(-0.424785\pi\) | ||||
0.234103 | + | 0.972212i | \(0.424785\pi\) | |||||||
\(678\) | −6.96854 | −0.267625 | ||||||||
\(679\) | −5.36007 | −0.205701 | ||||||||
\(680\) | 0.113836 | 0.00436541 | ||||||||
\(681\) | 14.7385 | 0.564780 | ||||||||
\(682\) | 3.02573 | 0.115861 | ||||||||
\(683\) | 11.7118 | 0.448139 | 0.224069 | − | 0.974573i | \(-0.428066\pi\) | ||||
0.224069 | + | 0.974573i | \(0.428066\pi\) | |||||||
\(684\) | 17.3831 | 0.664659 | ||||||||
\(685\) | −7.09215 | −0.270977 | ||||||||
\(686\) | 2.13650 | 0.0815721 | ||||||||
\(687\) | −17.0305 | −0.649754 | ||||||||
\(688\) | 20.7747 | 0.792028 | ||||||||
\(689\) | −44.5914 | −1.69880 | ||||||||
\(690\) | −2.13650 | −0.0813353 | ||||||||
\(691\) | −0.455045 | −0.0173107 | −0.00865535 | − | 0.999963i | \(-0.502755\pi\) | ||||
−0.00865535 | + | 0.999963i | \(0.502755\pi\) | |||||||
\(692\) | −18.6450 | −0.708775 | ||||||||
\(693\) | −1.78663 | −0.0678686 | ||||||||
\(694\) | −40.5200 | −1.53812 | ||||||||
\(695\) | 12.1235 | 0.459869 | ||||||||
\(696\) | 2.67379 | 0.101350 | ||||||||
\(697\) | −0.707612 | −0.0268027 | ||||||||
\(698\) | 8.61078 | 0.325923 | ||||||||
\(699\) | −4.08268 | −0.154421 | ||||||||
\(700\) | −2.56465 | −0.0969348 | ||||||||
\(701\) | −11.7366 | −0.443285 | −0.221642 | − | 0.975128i | \(-0.571142\pi\) | ||||
−0.221642 | + | 0.975128i | \(0.571142\pi\) | |||||||
\(702\) | −9.17970 | −0.346465 | ||||||||
\(703\) | 43.0619 | 1.62411 | ||||||||
\(704\) | −20.9028 | −0.787803 | ||||||||
\(705\) | −10.7203 | −0.403750 | ||||||||
\(706\) | −7.48011 | −0.281518 | ||||||||
\(707\) | 8.27803 | 0.311327 | ||||||||
\(708\) | 7.93089 | 0.298061 | ||||||||
\(709\) | 43.9572 | 1.65085 | 0.825424 | − | 0.564513i | \(-0.190936\pi\) | ||||
0.825424 | + | 0.564513i | \(0.190936\pi\) | |||||||
\(710\) | −11.1967 | −0.420203 | ||||||||
\(711\) | 11.7510 | 0.440698 | ||||||||
\(712\) | −6.16583 | −0.231074 | ||||||||
\(713\) | −0.792668 | −0.0296857 | ||||||||
\(714\) | −0.201603 | −0.00754482 | ||||||||
\(715\) | 7.67644 | 0.287083 | ||||||||
\(716\) | 47.0600 | 1.75872 | ||||||||
\(717\) | −23.2202 | −0.867173 | ||||||||
\(718\) | −16.4936 | −0.615534 | ||||||||
\(719\) | −25.9590 | −0.968106 | −0.484053 | − | 0.875039i | \(-0.660836\pi\) | ||||
−0.484053 | + | 0.875039i | \(0.660836\pi\) | |||||||
\(720\) | −2.55186 | −0.0951023 | ||||||||
\(721\) | 17.5937 | 0.655222 | ||||||||
\(722\) | −57.5587 | −2.14211 | ||||||||
\(723\) | 27.0592 | 1.00634 | ||||||||
\(724\) | 54.2108 | 2.01473 | ||||||||
\(725\) | −2.21636 | −0.0823137 | ||||||||
\(726\) | 16.6817 | 0.619116 | ||||||||
\(727\) | 33.0098 | 1.22427 | 0.612133 | − | 0.790755i | \(-0.290312\pi\) | ||||
0.612133 | + | 0.790755i | \(0.290312\pi\) | |||||||
\(728\) | 5.18334 | 0.192107 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −24.6213 | −0.911275 | ||||||||
\(731\) | 0.768195 | 0.0284127 | ||||||||
\(732\) | −14.9965 | −0.554288 | ||||||||
\(733\) | −11.4160 | −0.421659 | −0.210830 | − | 0.977523i | \(-0.567617\pi\) | ||||
−0.210830 | + | 0.977523i | \(0.567617\pi\) | |||||||
\(734\) | 7.76581 | 0.286641 | ||||||||
\(735\) | 1.00000 | 0.0368856 | ||||||||
\(736\) | 7.86483 | 0.289902 | ||||||||
\(737\) | 24.2642 | 0.893783 | ||||||||
\(738\) | −16.0216 | −0.589762 | ||||||||
\(739\) | −10.8797 | −0.400215 | −0.200107 | − | 0.979774i | \(-0.564129\pi\) | ||||
−0.200107 | + | 0.979774i | \(0.564129\pi\) | |||||||
\(740\) | 16.2939 | 0.598974 | ||||||||
\(741\) | 29.1221 | 1.06983 | ||||||||
\(742\) | −22.1733 | −0.814008 | ||||||||
\(743\) | −33.1400 | −1.21579 | −0.607895 | − | 0.794017i | \(-0.707986\pi\) | ||||
−0.607895 | + | 0.794017i | \(0.707986\pi\) | |||||||
\(744\) | 0.956262 | 0.0350583 | ||||||||
\(745\) | −1.94223 | −0.0711579 | ||||||||
\(746\) | −19.7125 | −0.721725 | ||||||||
\(747\) | −9.22806 | −0.337637 | ||||||||
\(748\) | −0.432373 | −0.0158091 | ||||||||
\(749\) | 12.9655 | 0.473748 | ||||||||
\(750\) | −2.13650 | −0.0780141 | ||||||||
\(751\) | −18.8474 | −0.687752 | −0.343876 | − | 0.939015i | \(-0.611740\pi\) | ||||
−0.343876 | + | 0.939015i | \(0.611740\pi\) | |||||||
\(752\) | 27.3567 | 0.997597 | ||||||||
\(753\) | 26.1630 | 0.953431 | ||||||||
\(754\) | 20.3456 | 0.740942 | ||||||||
\(755\) | 7.56553 | 0.275338 | ||||||||
\(756\) | −2.56465 | −0.0932755 | ||||||||
\(757\) | 1.55270 | 0.0564338 | 0.0282169 | − | 0.999602i | \(-0.491017\pi\) | ||||
0.0282169 | + | 0.999602i | \(0.491017\pi\) | |||||||
\(758\) | −47.2245 | −1.71527 | ||||||||
\(759\) | 1.78663 | 0.0648507 | ||||||||
\(760\) | −8.17680 | −0.296604 | ||||||||
\(761\) | −23.2767 | −0.843781 | −0.421890 | − | 0.906647i | \(-0.638633\pi\) | ||||
−0.421890 | + | 0.906647i | \(0.638633\pi\) | |||||||
\(762\) | −25.5538 | −0.925715 | ||||||||
\(763\) | −13.0849 | −0.473705 | ||||||||
\(764\) | −12.2076 | −0.441654 | ||||||||
\(765\) | −0.0943613 | −0.00341164 | ||||||||
\(766\) | 48.5673 | 1.75481 | ||||||||
\(767\) | 13.2867 | 0.479756 | ||||||||
\(768\) | 3.60128 | 0.129950 | ||||||||
\(769\) | −27.4213 | −0.988839 | −0.494419 | − | 0.869224i | \(-0.664619\pi\) | ||||
−0.494419 | + | 0.869224i | \(0.664619\pi\) | |||||||
\(770\) | 3.81715 | 0.137561 | ||||||||
\(771\) | 23.5375 | 0.847681 | ||||||||
\(772\) | 17.1920 | 0.618754 | ||||||||
\(773\) | −49.0281 | −1.76342 | −0.881708 | − | 0.471795i | \(-0.843606\pi\) | ||||
−0.881708 | + | 0.471795i | \(0.843606\pi\) | |||||||
\(774\) | 17.3933 | 0.625189 | ||||||||
\(775\) | −0.792668 | −0.0284735 | ||||||||
\(776\) | −6.46630 | −0.232127 | ||||||||
\(777\) | −6.35324 | −0.227921 | ||||||||
\(778\) | −75.6516 | −2.71224 | ||||||||
\(779\) | 50.8276 | 1.82109 | ||||||||
\(780\) | 11.0193 | 0.394553 | ||||||||
\(781\) | 9.36310 | 0.335038 | ||||||||
\(782\) | 0.201603 | 0.00720933 | ||||||||
\(783\) | −2.21636 | −0.0792064 | ||||||||
\(784\) | −2.55186 | −0.0911379 | ||||||||
\(785\) | −21.3972 | −0.763698 | ||||||||
\(786\) | 22.1182 | 0.788929 | ||||||||
\(787\) | −16.1608 | −0.576069 | −0.288034 | − | 0.957620i | \(-0.593002\pi\) | ||||
−0.288034 | + | 0.957620i | \(0.593002\pi\) | |||||||
\(788\) | 54.2330 | 1.93197 | ||||||||
\(789\) | −18.4727 | −0.657644 | ||||||||
\(790\) | −25.1061 | −0.893236 | ||||||||
\(791\) | −3.26165 | −0.115971 | ||||||||
\(792\) | −2.15536 | −0.0765876 | ||||||||
\(793\) | −25.1239 | −0.892176 | ||||||||
\(794\) | 76.8977 | 2.72900 | ||||||||
\(795\) | −10.3783 | −0.368081 | ||||||||
\(796\) | 61.7368 | 2.18820 | ||||||||
\(797\) | 20.1299 | 0.713038 | 0.356519 | − | 0.934288i | \(-0.383963\pi\) | ||||
0.356519 | + | 0.934288i | \(0.383963\pi\) | |||||||
\(798\) | 14.4811 | 0.512626 | ||||||||
\(799\) | 1.01158 | 0.0357872 | ||||||||
\(800\) | 7.86483 | 0.278064 | ||||||||
\(801\) | 5.11100 | 0.180588 | ||||||||
\(802\) | −35.8963 | −1.26754 | ||||||||
\(803\) | 20.5893 | 0.726582 | ||||||||
\(804\) | 34.8305 | 1.22838 | ||||||||
\(805\) | −1.00000 | −0.0352454 | ||||||||
\(806\) | 7.27646 | 0.256302 | ||||||||
\(807\) | 14.3774 | 0.506109 | ||||||||
\(808\) | 9.98648 | 0.351323 | ||||||||
\(809\) | −10.0935 | −0.354868 | −0.177434 | − | 0.984133i | \(-0.556780\pi\) | ||||
−0.177434 | + | 0.984133i | \(0.556780\pi\) | |||||||
\(810\) | −2.13650 | −0.0750691 | ||||||||
\(811\) | 7.27148 | 0.255336 | 0.127668 | − | 0.991817i | \(-0.459251\pi\) | ||||
0.127668 | + | 0.991817i | \(0.459251\pi\) | |||||||
\(812\) | 5.68421 | 0.199477 | ||||||||
\(813\) | −18.0079 | −0.631564 | ||||||||
\(814\) | −24.2513 | −0.850007 | ||||||||
\(815\) | 0.103163 | 0.00361363 | ||||||||
\(816\) | 0.240797 | 0.00842959 | ||||||||
\(817\) | −55.1793 | −1.93048 | ||||||||
\(818\) | 32.5827 | 1.13923 | ||||||||
\(819\) | −4.29660 | −0.150135 | ||||||||
\(820\) | 19.2322 | 0.671619 | ||||||||
\(821\) | −55.1620 | −1.92517 | −0.962584 | − | 0.270984i | \(-0.912651\pi\) | ||||
−0.962584 | + | 0.270984i | \(0.912651\pi\) | |||||||
\(822\) | 15.1524 | 0.528501 | ||||||||
\(823\) | 22.5494 | 0.786024 | 0.393012 | − | 0.919533i | \(-0.371433\pi\) | ||||
0.393012 | + | 0.919533i | \(0.371433\pi\) | |||||||
\(824\) | 21.2247 | 0.739398 | ||||||||
\(825\) | 1.78663 | 0.0622026 | ||||||||
\(826\) | 6.60689 | 0.229883 | ||||||||
\(827\) | −12.2478 | −0.425898 | −0.212949 | − | 0.977063i | \(-0.568307\pi\) | ||||
−0.212949 | + | 0.977063i | \(0.568307\pi\) | |||||||
\(828\) | 2.56465 | 0.0891278 | ||||||||
\(829\) | −17.4614 | −0.606460 | −0.303230 | − | 0.952917i | \(-0.598065\pi\) | ||||
−0.303230 | + | 0.952917i | \(0.598065\pi\) | |||||||
\(830\) | 19.7158 | 0.684345 | ||||||||
\(831\) | 5.94604 | 0.206266 | ||||||||
\(832\) | −50.2681 | −1.74273 | ||||||||
\(833\) | −0.0943613 | −0.00326943 | ||||||||
\(834\) | −25.9018 | −0.896907 | ||||||||
\(835\) | −15.7873 | −0.546343 | ||||||||
\(836\) | 31.0572 | 1.07414 | ||||||||
\(837\) | −0.792668 | −0.0273986 | ||||||||
\(838\) | −44.2650 | −1.52911 | ||||||||
\(839\) | 34.6725 | 1.19703 | 0.598514 | − | 0.801113i | \(-0.295758\pi\) | ||||
0.598514 | + | 0.801113i | \(0.295758\pi\) | |||||||
\(840\) | 1.20638 | 0.0416242 | ||||||||
\(841\) | −24.0877 | −0.830611 | ||||||||
\(842\) | 5.01828 | 0.172941 | ||||||||
\(843\) | −17.9816 | −0.619320 | ||||||||
\(844\) | −2.18352 | −0.0751598 | ||||||||
\(845\) | 5.46074 | 0.187855 | ||||||||
\(846\) | 22.9040 | 0.787455 | ||||||||
\(847\) | 7.80794 | 0.268284 | ||||||||
\(848\) | 26.4840 | 0.909464 | ||||||||
\(849\) | −10.0103 | −0.343552 | ||||||||
\(850\) | 0.201603 | 0.00691494 | ||||||||
\(851\) | 6.35324 | 0.217786 | ||||||||
\(852\) | 13.4404 | 0.460461 | ||||||||
\(853\) | 42.7465 | 1.46361 | 0.731807 | − | 0.681512i | \(-0.238677\pi\) | ||||
0.731807 | + | 0.681512i | \(0.238677\pi\) | |||||||
\(854\) | −12.4930 | −0.427502 | ||||||||
\(855\) | 6.77795 | 0.231801 | ||||||||
\(856\) | 15.6413 | 0.534609 | ||||||||
\(857\) | 46.8484 | 1.60031 | 0.800155 | − | 0.599793i | \(-0.204750\pi\) | ||||
0.800155 | + | 0.599793i | \(0.204750\pi\) | |||||||
\(858\) | −16.4008 | −0.559913 | ||||||||
\(859\) | 4.28101 | 0.146066 | 0.0730331 | − | 0.997330i | \(-0.476732\pi\) | ||||
0.0730331 | + | 0.997330i | \(0.476732\pi\) | |||||||
\(860\) | −20.8788 | −0.711962 | ||||||||
\(861\) | −7.49896 | −0.255564 | ||||||||
\(862\) | 35.2522 | 1.20069 | ||||||||
\(863\) | 15.1862 | 0.516943 | 0.258472 | − | 0.966019i | \(-0.416781\pi\) | ||||
0.258472 | + | 0.966019i | \(0.416781\pi\) | |||||||
\(864\) | 7.86483 | 0.267567 | ||||||||
\(865\) | −7.26997 | −0.247187 | ||||||||
\(866\) | 45.9759 | 1.56233 | ||||||||
\(867\) | −16.9911 | −0.577048 | ||||||||
\(868\) | 2.03292 | 0.0690018 | ||||||||
\(869\) | 20.9948 | 0.712199 | ||||||||
\(870\) | 4.73527 | 0.160541 | ||||||||
\(871\) | 58.3519 | 1.97718 | ||||||||
\(872\) | −15.7854 | −0.534561 | ||||||||
\(873\) | 5.36007 | 0.181411 | ||||||||
\(874\) | −14.4811 | −0.489831 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 29.5553 | 0.998581 | ||||||||
\(877\) | −22.9270 | −0.774190 | −0.387095 | − | 0.922040i | \(-0.626521\pi\) | ||||
−0.387095 | + | 0.922040i | \(0.626521\pi\) | |||||||
\(878\) | 38.9343 | 1.31397 | ||||||||
\(879\) | 28.8258 | 0.972271 | ||||||||
\(880\) | −4.55924 | −0.153692 | ||||||||
\(881\) | −27.7091 | −0.933542 | −0.466771 | − | 0.884378i | \(-0.654583\pi\) | ||||
−0.466771 | + | 0.884378i | \(0.654583\pi\) | |||||||
\(882\) | −2.13650 | −0.0719399 | ||||||||
\(883\) | 45.3010 | 1.52450 | 0.762249 | − | 0.647283i | \(-0.224095\pi\) | ||||
0.762249 | + | 0.647283i | \(0.224095\pi\) | |||||||
\(884\) | −1.03979 | −0.0349721 | ||||||||
\(885\) | 3.09238 | 0.103949 | ||||||||
\(886\) | −39.1718 | −1.31600 | ||||||||
\(887\) | 42.9145 | 1.44093 | 0.720464 | − | 0.693492i | \(-0.243929\pi\) | ||||
0.720464 | + | 0.693492i | \(0.243929\pi\) | |||||||
\(888\) | −7.66444 | −0.257202 | ||||||||
\(889\) | −11.9605 | −0.401144 | ||||||||
\(890\) | −10.9197 | −0.366029 | ||||||||
\(891\) | 1.78663 | 0.0598545 | ||||||||
\(892\) | 16.6535 | 0.557601 | ||||||||
\(893\) | −72.6616 | −2.43153 | ||||||||
\(894\) | 4.14959 | 0.138783 | ||||||||
\(895\) | 18.3495 | 0.613355 | ||||||||
\(896\) | −9.26643 | −0.309570 | ||||||||
\(897\) | 4.29660 | 0.143459 | ||||||||
\(898\) | 54.9142 | 1.83251 | ||||||||
\(899\) | 1.75684 | 0.0585940 | ||||||||
\(900\) | 2.56465 | 0.0854884 | ||||||||
\(901\) | 0.979311 | 0.0326256 | ||||||||
\(902\) | −28.6247 | −0.953097 | ||||||||
\(903\) | 8.14100 | 0.270915 | ||||||||
\(904\) | −3.93480 | −0.130870 | ||||||||
\(905\) | 21.1377 | 0.702641 | ||||||||
\(906\) | −16.1638 | −0.537006 | ||||||||
\(907\) | −1.29413 | −0.0429707 | −0.0214854 | − | 0.999769i | \(-0.506840\pi\) | ||||
−0.0214854 | + | 0.999769i | \(0.506840\pi\) | |||||||
\(908\) | 37.7991 | 1.25441 | ||||||||
\(909\) | −8.27803 | −0.274565 | ||||||||
\(910\) | 9.17970 | 0.304304 | ||||||||
\(911\) | 8.05207 | 0.266777 | 0.133388 | − | 0.991064i | \(-0.457414\pi\) | ||||
0.133388 | + | 0.991064i | \(0.457414\pi\) | |||||||
\(912\) | −17.2964 | −0.572741 | ||||||||
\(913\) | −16.4872 | −0.545645 | ||||||||
\(914\) | 66.2464 | 2.19123 | ||||||||
\(915\) | −5.84740 | −0.193309 | ||||||||
\(916\) | −43.6773 | −1.44314 | ||||||||
\(917\) | 10.3525 | 0.341870 | ||||||||
\(918\) | 0.201603 | 0.00665391 | ||||||||
\(919\) | −48.3126 | −1.59369 | −0.796843 | − | 0.604186i | \(-0.793498\pi\) | ||||
−0.796843 | + | 0.604186i | \(0.793498\pi\) | |||||||
\(920\) | −1.20638 | −0.0397733 | ||||||||
\(921\) | −21.9082 | −0.721900 | ||||||||
\(922\) | 8.58184 | 0.282628 | ||||||||
\(923\) | 22.5169 | 0.741153 | ||||||||
\(924\) | −4.58209 | −0.150740 | ||||||||
\(925\) | 6.35324 | 0.208893 | ||||||||
\(926\) | 6.20956 | 0.204059 | ||||||||
\(927\) | −17.5937 | −0.577852 | ||||||||
\(928\) | −17.4313 | −0.572212 | ||||||||
\(929\) | 16.2587 | 0.533432 | 0.266716 | − | 0.963775i | \(-0.414061\pi\) | ||||
0.266716 | + | 0.963775i | \(0.414061\pi\) | |||||||
\(930\) | 1.69354 | 0.0555333 | ||||||||
\(931\) | 6.77795 | 0.222138 | ||||||||
\(932\) | −10.4707 | −0.342978 | ||||||||
\(933\) | 31.9210 | 1.04505 | ||||||||
\(934\) | 29.5735 | 0.967675 | ||||||||
\(935\) | −0.168589 | −0.00551345 | ||||||||
\(936\) | −5.18334 | −0.169423 | ||||||||
\(937\) | 0.0791510 | 0.00258575 | 0.00129287 | − | 0.999999i | \(-0.499588\pi\) | ||||
0.00129287 | + | 0.999999i | \(0.499588\pi\) | |||||||
\(938\) | 29.0158 | 0.947399 | ||||||||
\(939\) | −0.0950302 | −0.00310119 | ||||||||
\(940\) | −27.4938 | −0.896750 | ||||||||
\(941\) | −30.3413 | −0.989098 | −0.494549 | − | 0.869150i | \(-0.664667\pi\) | ||||
−0.494549 | + | 0.869150i | \(0.664667\pi\) | |||||||
\(942\) | 45.7152 | 1.48948 | ||||||||
\(943\) | 7.49896 | 0.244200 | ||||||||
\(944\) | −7.89133 | −0.256841 | ||||||||
\(945\) | −1.00000 | −0.0325300 | ||||||||
\(946\) | 31.0754 | 1.01035 | ||||||||
\(947\) | −26.3732 | −0.857015 | −0.428507 | − | 0.903538i | \(-0.640960\pi\) | ||||
−0.428507 | + | 0.903538i | \(0.640960\pi\) | |||||||
\(948\) | 30.1373 | 0.978814 | ||||||||
\(949\) | 49.5144 | 1.60731 | ||||||||
\(950\) | −14.4811 | −0.469830 | ||||||||
\(951\) | 9.58935 | 0.310956 | ||||||||
\(952\) | −0.113836 | −0.00368944 | ||||||||
\(953\) | 8.93301 | 0.289368 | 0.144684 | − | 0.989478i | \(-0.453783\pi\) | ||||
0.144684 | + | 0.989478i | \(0.453783\pi\) | |||||||
\(954\) | 22.1733 | 0.717887 | ||||||||
\(955\) | −4.75992 | −0.154028 | ||||||||
\(956\) | −59.5517 | −1.92604 | ||||||||
\(957\) | −3.95983 | −0.128003 | ||||||||
\(958\) | 52.4484 | 1.69453 | ||||||||
\(959\) | 7.09215 | 0.229018 | ||||||||
\(960\) | −11.6995 | −0.377601 | ||||||||
\(961\) | −30.3717 | −0.979732 | ||||||||
\(962\) | −58.3208 | −1.88034 | ||||||||
\(963\) | −12.9655 | −0.417806 | ||||||||
\(964\) | 69.3976 | 2.23514 | ||||||||
\(965\) | 6.70344 | 0.215791 | ||||||||
\(966\) | 2.13650 | 0.0687409 | ||||||||
\(967\) | −2.58674 | −0.0831840 | −0.0415920 | − | 0.999135i | \(-0.513243\pi\) | ||||
−0.0415920 | + | 0.999135i | \(0.513243\pi\) | |||||||
\(968\) | 9.41937 | 0.302750 | ||||||||
\(969\) | −0.639576 | −0.0205462 | ||||||||
\(970\) | −11.4518 | −0.367696 | ||||||||
\(971\) | −16.5154 | −0.530005 | −0.265003 | − | 0.964248i | \(-0.585373\pi\) | ||||
−0.265003 | + | 0.964248i | \(0.585373\pi\) | |||||||
\(972\) | 2.56465 | 0.0822613 | ||||||||
\(973\) | −12.1235 | −0.388660 | ||||||||
\(974\) | 53.9198 | 1.72770 | ||||||||
\(975\) | 4.29660 | 0.137601 | ||||||||
\(976\) | 14.9218 | 0.477634 | ||||||||
\(977\) | 35.6320 | 1.13997 | 0.569984 | − | 0.821656i | \(-0.306949\pi\) | ||||
0.569984 | + | 0.821656i | \(0.306949\pi\) | |||||||
\(978\) | −0.220408 | −0.00704786 | ||||||||
\(979\) | 9.13149 | 0.291844 | ||||||||
\(980\) | 2.56465 | 0.0819248 | ||||||||
\(981\) | 13.0849 | 0.417768 | ||||||||
\(982\) | 43.5333 | 1.38920 | ||||||||
\(983\) | −23.3567 | −0.744964 | −0.372482 | − | 0.928039i | \(-0.621493\pi\) | ||||
−0.372482 | + | 0.928039i | \(0.621493\pi\) | |||||||
\(984\) | −9.04662 | −0.288396 | ||||||||
\(985\) | 21.1463 | 0.673778 | ||||||||
\(986\) | −0.446827 | −0.0142299 | ||||||||
\(987\) | 10.7203 | 0.341231 | ||||||||
\(988\) | 74.6881 | 2.37615 | ||||||||
\(989\) | −8.14100 | −0.258869 | ||||||||
\(990\) | −3.81715 | −0.121317 | ||||||||
\(991\) | −4.68461 | −0.148812 | −0.0744058 | − | 0.997228i | \(-0.523706\pi\) | ||||
−0.0744058 | + | 0.997228i | \(0.523706\pi\) | |||||||
\(992\) | −6.23420 | −0.197936 | ||||||||
\(993\) | 4.28108 | 0.135856 | ||||||||
\(994\) | 11.1967 | 0.355136 | ||||||||
\(995\) | 24.0722 | 0.763140 | ||||||||
\(996\) | −23.6668 | −0.749910 | ||||||||
\(997\) | 15.2149 | 0.481862 | 0.240931 | − | 0.970542i | \(-0.422547\pi\) | ||||
0.240931 | + | 0.970542i | \(0.422547\pi\) | |||||||
\(998\) | −4.07141 | −0.128878 | ||||||||
\(999\) | 6.35324 | 0.201008 |
(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 | 2415.2.a.v.1.2 | ✓ | 10 | |
3.2 | odd | 2 | 7245.2.a.bu.1.9 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2415.2.a.v.1.2 | ✓ | 10 | 1.1 | even | 1 | trivial | |
7245.2.a.bu.1.9 | 10 | 3.2 | odd | 2 |