Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.59175 | −1.12554 | −0.562769 | − | 0.826614i | \(-0.690264\pi\) | ||||
−0.562769 | + | 0.826614i | \(0.690264\pi\) | |||||||
\(3\) | 0.0342835 | 0.0197936 | 0.00989678 | − | 0.999951i | \(-0.496850\pi\) | ||||
0.00989678 | + | 0.999951i | \(0.496850\pi\) | |||||||
\(4\) | 0.533671 | 0.266836 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.0545707 | −0.0222784 | ||||||||
\(7\) | −1.01795 | −0.384749 | −0.192375 | − | 0.981322i | \(-0.561619\pi\) | ||||
−0.192375 | + | 0.981322i | \(0.561619\pi\) | |||||||
\(8\) | 2.33403 | 0.825204 | ||||||||
\(9\) | −2.99882 | −0.999608 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.74092 | 1.73095 | 0.865477 | − | 0.500949i | \(-0.167016\pi\) | ||||
0.865477 | + | 0.500949i | \(0.167016\pi\) | |||||||
\(12\) | 0.0182961 | 0.00528163 | ||||||||
\(13\) | 4.77625 | 1.32469 | 0.662347 | − | 0.749197i | \(-0.269561\pi\) | ||||
0.662347 | + | 0.749197i | \(0.269561\pi\) | |||||||
\(14\) | 1.62032 | 0.433050 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.78254 | −1.19563 | ||||||||
\(17\) | −2.20671 | −0.535206 | −0.267603 | − | 0.963529i | \(-0.586232\pi\) | ||||
−0.267603 | + | 0.963529i | \(0.586232\pi\) | |||||||
\(18\) | 4.77338 | 1.12510 | ||||||||
\(19\) | 7.81958 | 1.79393 | 0.896967 | − | 0.442097i | \(-0.145765\pi\) | ||||
0.896967 | + | 0.442097i | \(0.145765\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0348989 | −0.00761556 | ||||||||
\(22\) | −9.13812 | −1.94825 | ||||||||
\(23\) | −3.98508 | −0.830947 | −0.415474 | − | 0.909605i | \(-0.636384\pi\) | ||||
−0.415474 | + | 0.909605i | \(0.636384\pi\) | |||||||
\(24\) | 0.0800186 | 0.0163337 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.60260 | −1.49099 | ||||||||
\(27\) | −0.205661 | −0.0395794 | ||||||||
\(28\) | −0.543251 | −0.102665 | ||||||||
\(29\) | 0.409391 | 0.0760220 | 0.0380110 | − | 0.999277i | \(-0.487898\pi\) | ||||
0.0380110 | + | 0.999277i | \(0.487898\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.04105 | −1.62382 | −0.811911 | − | 0.583782i | \(-0.801572\pi\) | ||||
−0.811911 | + | 0.583782i | \(0.801572\pi\) | |||||||
\(32\) | 2.94455 | 0.520528 | ||||||||
\(33\) | 0.196819 | 0.0342617 | ||||||||
\(34\) | 3.51253 | 0.602395 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.60039 | −0.266731 | ||||||||
\(37\) | −7.42508 | −1.22067 | −0.610337 | − | 0.792142i | \(-0.708966\pi\) | ||||
−0.610337 | + | 0.792142i | \(0.708966\pi\) | |||||||
\(38\) | −12.4468 | −2.01914 | ||||||||
\(39\) | 0.163746 | 0.0262204 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.1893 | −1.90365 | −0.951827 | − | 0.306635i | \(-0.900797\pi\) | ||||
−0.951827 | + | 0.306635i | \(0.900797\pi\) | |||||||
\(42\) | 0.0555503 | 0.00857160 | ||||||||
\(43\) | −0.457663 | −0.0697929 | −0.0348965 | − | 0.999391i | \(-0.511110\pi\) | ||||
−0.0348965 | + | 0.999391i | \(0.511110\pi\) | |||||||
\(44\) | 3.06377 | 0.461880 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.34326 | 0.935263 | ||||||||
\(47\) | −6.21788 | −0.906971 | −0.453486 | − | 0.891264i | \(-0.649820\pi\) | ||||
−0.453486 | + | 0.891264i | \(0.649820\pi\) | |||||||
\(48\) | −0.163962 | −0.0236659 | ||||||||
\(49\) | −5.96378 | −0.851968 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0756537 | −0.0105936 | ||||||||
\(52\) | 2.54895 | 0.353476 | ||||||||
\(53\) | −2.25459 | −0.309692 | −0.154846 | − | 0.987939i | \(-0.549488\pi\) | ||||
−0.154846 | + | 0.987939i | \(0.549488\pi\) | |||||||
\(54\) | 0.327360 | 0.0445481 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.37593 | −0.317497 | ||||||||
\(57\) | 0.268082 | 0.0355084 | ||||||||
\(58\) | −0.651649 | −0.0855656 | ||||||||
\(59\) | 8.50068 | 1.10669 | 0.553347 | − | 0.832951i | \(-0.313350\pi\) | ||||
0.553347 | + | 0.832951i | \(0.313350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.47487 | 0.316874 | 0.158437 | − | 0.987369i | \(-0.449355\pi\) | ||||
0.158437 | + | 0.987369i | \(0.449355\pi\) | |||||||
\(62\) | 14.3911 | 1.82767 | ||||||||
\(63\) | 3.05266 | 0.384599 | ||||||||
\(64\) | 4.87809 | 0.609761 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.313286 | −0.0385629 | ||||||||
\(67\) | 3.16911 | 0.387169 | 0.193584 | − | 0.981084i | \(-0.437989\pi\) | ||||
0.193584 | + | 0.981084i | \(0.437989\pi\) | |||||||
\(68\) | −1.17766 | −0.142812 | ||||||||
\(69\) | −0.136622 | −0.0164474 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.46327 | 0.173658 | 0.0868288 | − | 0.996223i | \(-0.472327\pi\) | ||||
0.0868288 | + | 0.996223i | \(0.472327\pi\) | |||||||
\(72\) | −6.99935 | −0.824881 | ||||||||
\(73\) | −10.8698 | −1.27222 | −0.636109 | − | 0.771599i | \(-0.719457\pi\) | ||||
−0.636109 | + | 0.771599i | \(0.719457\pi\) | |||||||
\(74\) | 11.8189 | 1.37392 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.17308 | 0.478686 | ||||||||
\(77\) | −5.84398 | −0.665983 | ||||||||
\(78\) | −0.260644 | −0.0295121 | ||||||||
\(79\) | 16.2231 | 1.82524 | 0.912621 | − | 0.408806i | \(-0.134055\pi\) | ||||
0.912621 | + | 0.408806i | \(0.134055\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.98942 | 0.998825 | ||||||||
\(82\) | 19.4024 | 2.14264 | ||||||||
\(83\) | −2.52675 | −0.277347 | −0.138674 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138674 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(84\) | −0.0186245 | −0.00203210 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.728485 | 0.0785546 | ||||||||
\(87\) | 0.0140353 | 0.00150475 | ||||||||
\(88\) | 13.3995 | 1.42839 | ||||||||
\(89\) | −11.5557 | −1.22491 | −0.612453 | − | 0.790507i | \(-0.709817\pi\) | ||||
−0.612453 | + | 0.790507i | \(0.709817\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.86199 | −0.509675 | ||||||||
\(92\) | −2.12672 | −0.221726 | ||||||||
\(93\) | −0.309959 | −0.0321412 | ||||||||
\(94\) | 9.89732 | 1.02083 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.100949 | 0.0103031 | ||||||||
\(97\) | −13.1176 | −1.33189 | −0.665945 | − | 0.746001i | \(-0.731972\pi\) | ||||
−0.665945 | + | 0.746001i | \(0.731972\pi\) | |||||||
\(98\) | 9.49285 | 0.958922 | ||||||||
\(99\) | −17.2160 | −1.73028 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.7144 | 1.86216 | 0.931078 | − | 0.364821i | \(-0.118870\pi\) | ||||
0.931078 | + | 0.364821i | \(0.118870\pi\) | |||||||
\(102\) | 0.120422 | 0.0119235 | ||||||||
\(103\) | 16.5410 | 1.62983 | 0.814915 | − | 0.579581i | \(-0.196784\pi\) | ||||
0.814915 | + | 0.579581i | \(0.196784\pi\) | |||||||
\(104\) | 11.1479 | 1.09314 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.58875 | 0.348570 | ||||||||
\(107\) | 9.75782 | 0.943324 | 0.471662 | − | 0.881779i | \(-0.343654\pi\) | ||||
0.471662 | + | 0.881779i | \(0.343654\pi\) | |||||||
\(108\) | −0.109755 | −0.0105612 | ||||||||
\(109\) | 2.29356 | 0.219683 | 0.109841 | − | 0.993949i | \(-0.464966\pi\) | ||||
0.109841 | + | 0.993949i | \(0.464966\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.254557 | −0.0241615 | ||||||||
\(112\) | 4.86839 | 0.460020 | ||||||||
\(113\) | −10.0532 | −0.945727 | −0.472864 | − | 0.881136i | \(-0.656780\pi\) | ||||
−0.472864 | + | 0.881136i | \(0.656780\pi\) | |||||||
\(114\) | −0.426720 | −0.0399660 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.218480 | 0.0202854 | ||||||||
\(117\) | −14.3231 | −1.32417 | ||||||||
\(118\) | −13.5310 | −1.24563 | ||||||||
\(119\) | 2.24632 | 0.205920 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.9582 | 1.99620 | ||||||||
\(122\) | −3.93937 | −0.356654 | ||||||||
\(123\) | −0.417893 | −0.0376801 | ||||||||
\(124\) | −4.82495 | −0.433293 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.85907 | −0.432880 | ||||||||
\(127\) | −17.5071 | −1.55350 | −0.776750 | − | 0.629809i | \(-0.783133\pi\) | ||||
−0.776750 | + | 0.629809i | \(0.783133\pi\) | |||||||
\(128\) | −13.6538 | −1.20684 | ||||||||
\(129\) | −0.0156903 | −0.00138145 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.80696 | 0.856838 | 0.428419 | − | 0.903580i | \(-0.359071\pi\) | ||||
0.428419 | + | 0.903580i | \(0.359071\pi\) | |||||||
\(132\) | 0.105037 | 0.00914226 | ||||||||
\(133\) | −7.95995 | −0.690215 | ||||||||
\(134\) | −5.04444 | −0.435773 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.15053 | −0.441654 | ||||||||
\(137\) | −1.80059 | −0.153835 | −0.0769175 | − | 0.997037i | \(-0.524508\pi\) | ||||
−0.0769175 | + | 0.997037i | \(0.524508\pi\) | |||||||
\(138\) | 0.217469 | 0.0185122 | ||||||||
\(139\) | −4.92304 | −0.417566 | −0.208783 | − | 0.977962i | \(-0.566950\pi\) | ||||
−0.208783 | + | 0.977962i | \(0.566950\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.213171 | −0.0179522 | ||||||||
\(142\) | −2.32915 | −0.195458 | ||||||||
\(143\) | 27.4201 | 2.29298 | ||||||||
\(144\) | 14.3420 | 1.19517 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 17.3021 | 1.43193 | ||||||||
\(147\) | −0.204459 | −0.0168635 | ||||||||
\(148\) | −3.96255 | −0.325720 | ||||||||
\(149\) | 7.29802 | 0.597877 | 0.298938 | − | 0.954272i | \(-0.403367\pi\) | ||||
0.298938 | + | 0.954272i | \(0.403367\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.96990 | −0.567202 | −0.283601 | − | 0.958942i | \(-0.591529\pi\) | ||||
−0.283601 | + | 0.958942i | \(0.591529\pi\) | |||||||
\(152\) | 18.2511 | 1.48036 | ||||||||
\(153\) | 6.61754 | 0.534996 | ||||||||
\(154\) | 9.30216 | 0.749589 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.0873868 | 0.00699654 | ||||||||
\(157\) | −21.5262 | −1.71798 | −0.858991 | − | 0.511991i | \(-0.828908\pi\) | ||||
−0.858991 | + | 0.511991i | \(0.828908\pi\) | |||||||
\(158\) | −25.8232 | −2.05438 | ||||||||
\(159\) | −0.0772953 | −0.00612992 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.05662 | 0.319706 | ||||||||
\(162\) | −14.3089 | −1.12422 | ||||||||
\(163\) | 3.55531 | 0.278473 | 0.139237 | − | 0.990259i | \(-0.455535\pi\) | ||||
0.139237 | + | 0.990259i | \(0.455535\pi\) | |||||||
\(164\) | −6.50510 | −0.507963 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.02196 | 0.312165 | ||||||||
\(167\) | −11.9448 | −0.924317 | −0.462158 | − | 0.886797i | \(-0.652925\pi\) | ||||
−0.462158 | + | 0.886797i | \(0.652925\pi\) | |||||||
\(168\) | −0.0814551 | −0.00628439 | ||||||||
\(169\) | 9.81257 | 0.754813 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −23.4495 | −1.79323 | ||||||||
\(172\) | −0.244241 | −0.0186232 | ||||||||
\(173\) | −4.86182 | −0.369637 | −0.184819 | − | 0.982773i | \(-0.559170\pi\) | ||||
−0.184819 | + | 0.982773i | \(0.559170\pi\) | |||||||
\(174\) | −0.0223408 | −0.00169365 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −27.4562 | −2.06959 | ||||||||
\(177\) | 0.291433 | 0.0219054 | ||||||||
\(178\) | 18.3939 | 1.37868 | ||||||||
\(179\) | 1.77821 | 0.132910 | 0.0664548 | − | 0.997789i | \(-0.478831\pi\) | ||||
0.0664548 | + | 0.997789i | \(0.478831\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.10703 | 0.676921 | 0.338460 | − | 0.940981i | \(-0.390094\pi\) | ||||
0.338460 | + | 0.940981i | \(0.390094\pi\) | |||||||
\(182\) | 7.73908 | 0.573659 | ||||||||
\(183\) | 0.0848470 | 0.00627207 | ||||||||
\(184\) | −9.30131 | −0.685701 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.493377 | 0.0361762 | ||||||||
\(187\) | −12.6686 | −0.926417 | ||||||||
\(188\) | −3.31831 | −0.242012 | ||||||||
\(189\) | 0.209352 | 0.0152281 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.97595 | 0.432405 | 0.216202 | − | 0.976349i | \(-0.430633\pi\) | ||||
0.216202 | + | 0.976349i | \(0.430633\pi\) | |||||||
\(192\) | 0.167238 | 0.0120693 | ||||||||
\(193\) | −20.2480 | −1.45749 | −0.728743 | − | 0.684788i | \(-0.759895\pi\) | ||||
−0.728743 | + | 0.684788i | \(0.759895\pi\) | |||||||
\(194\) | 20.8800 | 1.49909 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.18270 | −0.227335 | ||||||||
\(197\) | −5.59926 | −0.398931 | −0.199465 | − | 0.979905i | \(-0.563921\pi\) | ||||
−0.199465 | + | 0.979905i | \(0.563921\pi\) | |||||||
\(198\) | 27.4036 | 1.94749 | ||||||||
\(199\) | −11.8854 | −0.842532 | −0.421266 | − | 0.906937i | \(-0.638414\pi\) | ||||
−0.421266 | + | 0.906937i | \(0.638414\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.108648 | 0.00766345 | ||||||||
\(202\) | −29.7887 | −2.09593 | ||||||||
\(203\) | −0.416740 | −0.0292494 | ||||||||
\(204\) | −0.0403742 | −0.00282676 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −26.3291 | −1.83444 | ||||||||
\(207\) | 11.9506 | 0.830622 | ||||||||
\(208\) | −22.8426 | −1.58385 | ||||||||
\(209\) | 44.8916 | 3.10522 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.99471 | 0.343850 | 0.171925 | − | 0.985110i | \(-0.445001\pi\) | ||||
0.171925 | + | 0.985110i | \(0.445001\pi\) | |||||||
\(212\) | −1.20321 | −0.0826369 | ||||||||
\(213\) | 0.0501658 | 0.00343730 | ||||||||
\(214\) | −15.5320 | −1.06175 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.480018 | −0.0326611 | ||||||||
\(217\) | 9.20335 | 0.624764 | ||||||||
\(218\) | −3.65077 | −0.247261 | ||||||||
\(219\) | −0.372656 | −0.0251817 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.5398 | −0.708984 | ||||||||
\(222\) | 0.405192 | 0.0271947 | ||||||||
\(223\) | 9.69650 | 0.649325 | 0.324663 | − | 0.945830i | \(-0.394749\pi\) | ||||
0.324663 | + | 0.945830i | \(0.394749\pi\) | |||||||
\(224\) | −2.99741 | −0.200273 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.0022 | 1.06445 | ||||||||
\(227\) | −13.8085 | −0.916504 | −0.458252 | − | 0.888822i | \(-0.651524\pi\) | ||||
−0.458252 | + | 0.888822i | \(0.651524\pi\) | |||||||
\(228\) | 0.143068 | 0.00947490 | ||||||||
\(229\) | −8.18876 | −0.541128 | −0.270564 | − | 0.962702i | \(-0.587210\pi\) | ||||
−0.270564 | + | 0.962702i | \(0.587210\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.200352 | −0.0131822 | ||||||||
\(232\) | 0.955531 | 0.0627337 | ||||||||
\(233\) | −16.0598 | −1.05211 | −0.526055 | − | 0.850450i | \(-0.676329\pi\) | ||||
−0.526055 | + | 0.850450i | \(0.676329\pi\) | |||||||
\(234\) | 22.7989 | 1.49041 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.53657 | 0.295306 | ||||||||
\(237\) | 0.556184 | 0.0361281 | ||||||||
\(238\) | −3.57559 | −0.231771 | ||||||||
\(239\) | −21.1719 | −1.36950 | −0.684749 | − | 0.728779i | \(-0.740088\pi\) | ||||
−0.684749 | + | 0.728779i | \(0.740088\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | −34.9520 | −2.24680 | ||||||||
\(243\) | 0.925170 | 0.0593497 | ||||||||
\(244\) | 1.32076 | 0.0845533 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.665181 | 0.0424104 | ||||||||
\(247\) | 37.3483 | 2.37641 | ||||||||
\(248\) | −21.1021 | −1.33998 | ||||||||
\(249\) | −0.0866259 | −0.00548969 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.5406 | −0.728436 | −0.364218 | − | 0.931314i | \(-0.618664\pi\) | ||||
−0.364218 | + | 0.931314i | \(0.618664\pi\) | |||||||
\(252\) | 1.62912 | 0.102625 | ||||||||
\(253\) | −22.8781 | −1.43833 | ||||||||
\(254\) | 27.8669 | 1.74852 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.9773 | 0.748580 | ||||||||
\(257\) | 31.1018 | 1.94008 | 0.970039 | − | 0.242948i | \(-0.0781145\pi\) | ||||
0.970039 | + | 0.242948i | \(0.0781145\pi\) | |||||||
\(258\) | 0.0249750 | 0.00155488 | ||||||||
\(259\) | 7.55836 | 0.469654 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.22769 | −0.0759922 | ||||||||
\(262\) | −15.6102 | −0.964404 | ||||||||
\(263\) | −3.93805 | −0.242831 | −0.121415 | − | 0.992602i | \(-0.538743\pi\) | ||||
−0.121415 | + | 0.992602i | \(0.538743\pi\) | |||||||
\(264\) | 0.459381 | 0.0282729 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 12.6703 | 0.776863 | ||||||||
\(267\) | −0.396171 | −0.0242453 | ||||||||
\(268\) | 1.69126 | 0.103310 | ||||||||
\(269\) | −29.5233 | −1.80007 | −0.900034 | − | 0.435821i | \(-0.856458\pi\) | ||||
−0.900034 | + | 0.435821i | \(0.856458\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.87037 | −0.174362 | −0.0871812 | − | 0.996192i | \(-0.527786\pi\) | ||||
−0.0871812 | + | 0.996192i | \(0.527786\pi\) | |||||||
\(272\) | 10.5537 | 0.639911 | ||||||||
\(273\) | −0.166686 | −0.0100883 | ||||||||
\(274\) | 2.86610 | 0.173147 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.0729115 | −0.00438876 | ||||||||
\(277\) | −14.7589 | −0.886777 | −0.443389 | − | 0.896330i | \(-0.646224\pi\) | ||||
−0.443389 | + | 0.896330i | \(0.646224\pi\) | |||||||
\(278\) | 7.83625 | 0.469987 | ||||||||
\(279\) | 27.1125 | 1.62319 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.6731 | −1.47187 | −0.735937 | − | 0.677050i | \(-0.763258\pi\) | ||||
−0.735937 | + | 0.677050i | \(0.763258\pi\) | |||||||
\(282\) | 0.339315 | 0.0202059 | ||||||||
\(283\) | −9.54548 | −0.567420 | −0.283710 | − | 0.958910i | \(-0.591565\pi\) | ||||
−0.283710 | + | 0.958910i | \(0.591565\pi\) | |||||||
\(284\) | 0.780903 | 0.0463381 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −43.6460 | −2.58084 | ||||||||
\(287\) | 12.4081 | 0.732430 | ||||||||
\(288\) | −8.83019 | −0.520324 | ||||||||
\(289\) | −12.1304 | −0.713555 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.449717 | −0.0263629 | ||||||||
\(292\) | −5.80092 | −0.339473 | ||||||||
\(293\) | 21.8810 | 1.27830 | 0.639151 | − | 0.769082i | \(-0.279286\pi\) | ||||
0.639151 | + | 0.769082i | \(0.279286\pi\) | |||||||
\(294\) | 0.325448 | 0.0189805 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −17.3304 | −1.00731 | ||||||||
\(297\) | −1.18068 | −0.0685101 | ||||||||
\(298\) | −11.6166 | −0.672933 | ||||||||
\(299\) | −19.0338 | −1.10075 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.465878 | 0.0268528 | ||||||||
\(302\) | 11.0943 | 0.638408 | ||||||||
\(303\) | 0.641596 | 0.0368587 | ||||||||
\(304\) | −37.3974 | −2.14489 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −10.5335 | −0.602159 | ||||||||
\(307\) | −1.80394 | −0.102957 | −0.0514783 | − | 0.998674i | \(-0.516393\pi\) | ||||
−0.0514783 | + | 0.998674i | \(0.516393\pi\) | |||||||
\(308\) | −3.11876 | −0.177708 | ||||||||
\(309\) | 0.567082 | 0.0322601 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.7668 | −1.51781 | −0.758904 | − | 0.651203i | \(-0.774265\pi\) | ||||
−0.758904 | + | 0.651203i | \(0.774265\pi\) | |||||||
\(312\) | 0.382189 | 0.0216372 | ||||||||
\(313\) | 10.1814 | 0.575488 | 0.287744 | − | 0.957707i | \(-0.407095\pi\) | ||||
0.287744 | + | 0.957707i | \(0.407095\pi\) | |||||||
\(314\) | 34.2644 | 1.93365 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.65781 | 0.487040 | ||||||||
\(317\) | 7.59564 | 0.426614 | 0.213307 | − | 0.976985i | \(-0.431577\pi\) | ||||
0.213307 | + | 0.976985i | \(0.431577\pi\) | |||||||
\(318\) | 0.123035 | 0.00689945 | ||||||||
\(319\) | 2.35028 | 0.131591 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.334532 | 0.0186718 | ||||||||
\(322\) | −6.45713 | −0.359842 | ||||||||
\(323\) | −17.2555 | −0.960124 | ||||||||
\(324\) | 4.79740 | 0.266522 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.65917 | −0.313432 | ||||||||
\(327\) | 0.0786310 | 0.00434831 | ||||||||
\(328\) | −28.4503 | −1.57090 | ||||||||
\(329\) | 6.32950 | 0.348957 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.5457 | −0.744540 | −0.372270 | − | 0.928125i | \(-0.621420\pi\) | ||||
−0.372270 | + | 0.928125i | \(0.621420\pi\) | |||||||
\(332\) | −1.34846 | −0.0740061 | ||||||||
\(333\) | 22.2665 | 1.22020 | ||||||||
\(334\) | 19.0132 | 1.04035 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.166905 | 0.00910543 | ||||||||
\(337\) | 18.7266 | 1.02010 | 0.510051 | − | 0.860144i | \(-0.329626\pi\) | ||||
0.510051 | + | 0.860144i | \(0.329626\pi\) | |||||||
\(338\) | −15.6192 | −0.849571 | ||||||||
\(339\) | −0.344659 | −0.0187193 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −51.9040 | −2.81076 | ||||||||
\(342\) | 37.3258 | 2.01835 | ||||||||
\(343\) | 13.1965 | 0.712543 | ||||||||
\(344\) | −1.06820 | −0.0575934 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.73880 | 0.416041 | ||||||||
\(347\) | −24.5071 | −1.31561 | −0.657805 | − | 0.753189i | \(-0.728515\pi\) | ||||
−0.657805 | + | 0.753189i | \(0.728515\pi\) | |||||||
\(348\) | 0.00749026 | 0.000401520 0 | ||||||||
\(349\) | 28.7644 | 1.53972 | 0.769860 | − | 0.638213i | \(-0.220326\pi\) | ||||
0.769860 | + | 0.638213i | \(0.220326\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.982286 | −0.0524306 | ||||||||
\(352\) | 16.9044 | 0.901009 | ||||||||
\(353\) | −3.86101 | −0.205501 | −0.102750 | − | 0.994707i | \(-0.532764\pi\) | ||||
−0.102750 | + | 0.994707i | \(0.532764\pi\) | |||||||
\(354\) | −0.463888 | −0.0246554 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.16697 | −0.326849 | ||||||||
\(357\) | 0.0770118 | 0.00407589 | ||||||||
\(358\) | −2.83046 | −0.149595 | ||||||||
\(359\) | −9.19684 | −0.485391 | −0.242695 | − | 0.970103i | \(-0.578032\pi\) | ||||
−0.242695 | + | 0.970103i | \(0.578032\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 42.1458 | 2.21820 | ||||||||
\(362\) | −14.4961 | −0.761900 | ||||||||
\(363\) | 0.752803 | 0.0395119 | ||||||||
\(364\) | −2.59470 | −0.135999 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.135055 | −0.00705945 | ||||||||
\(367\) | 25.7878 | 1.34611 | 0.673057 | − | 0.739590i | \(-0.264981\pi\) | ||||
0.673057 | + | 0.739590i | \(0.264981\pi\) | |||||||
\(368\) | 19.0588 | 0.993509 | ||||||||
\(369\) | 36.5537 | 1.90291 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.29507 | 0.119154 | ||||||||
\(372\) | −0.165416 | −0.00857642 | ||||||||
\(373\) | −24.5838 | −1.27290 | −0.636450 | − | 0.771318i | \(-0.719598\pi\) | ||||
−0.636450 | + | 0.771318i | \(0.719598\pi\) | |||||||
\(374\) | 20.1652 | 1.04272 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14.5127 | −0.748437 | ||||||||
\(377\) | 1.95535 | 0.100706 | ||||||||
\(378\) | −0.333237 | −0.0171399 | ||||||||
\(379\) | 13.3858 | 0.687584 | 0.343792 | − | 0.939046i | \(-0.388288\pi\) | ||||
0.343792 | + | 0.939046i | \(0.388288\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.600202 | −0.0307493 | ||||||||
\(382\) | −9.51223 | −0.486688 | ||||||||
\(383\) | 5.75124 | 0.293875 | 0.146937 | − | 0.989146i | \(-0.453058\pi\) | ||||
0.146937 | + | 0.989146i | \(0.453058\pi\) | |||||||
\(384\) | −0.468100 | −0.0238876 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 32.2298 | 1.64046 | ||||||||
\(387\) | 1.37245 | 0.0697656 | ||||||||
\(388\) | −7.00049 | −0.355396 | ||||||||
\(389\) | −11.5104 | −0.583598 | −0.291799 | − | 0.956480i | \(-0.594254\pi\) | ||||
−0.291799 | + | 0.956480i | \(0.594254\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.79393 | 0.444728 | ||||||||
\(392\) | −13.9196 | −0.703048 | ||||||||
\(393\) | 0.336217 | 0.0169599 | ||||||||
\(394\) | 8.91262 | 0.449012 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −9.18770 | −0.461699 | ||||||||
\(397\) | 11.7261 | 0.588518 | 0.294259 | − | 0.955726i | \(-0.404927\pi\) | ||||
0.294259 | + | 0.955726i | \(0.404927\pi\) | |||||||
\(398\) | 18.9186 | 0.948301 | ||||||||
\(399\) | −0.272895 | −0.0136618 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.795398 | −0.0397203 | −0.0198602 | − | 0.999803i | \(-0.506322\pi\) | ||||
−0.0198602 | + | 0.999803i | \(0.506322\pi\) | |||||||
\(402\) | −0.172941 | −0.00862550 | ||||||||
\(403\) | −43.1823 | −2.15107 | ||||||||
\(404\) | 9.98735 | 0.496889 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.663346 | 0.0329213 | ||||||||
\(407\) | −42.6268 | −2.11293 | ||||||||
\(408\) | −0.176578 | −0.00874191 | ||||||||
\(409\) | 2.98099 | 0.147401 | 0.0737004 | − | 0.997280i | \(-0.476519\pi\) | ||||
0.0737004 | + | 0.997280i | \(0.476519\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0617306 | −0.00304494 | ||||||||
\(412\) | 8.82744 | 0.434897 | ||||||||
\(413\) | −8.65328 | −0.425800 | ||||||||
\(414\) | −19.0223 | −0.934896 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 14.0639 | 0.689540 | ||||||||
\(417\) | −0.168779 | −0.00826513 | ||||||||
\(418\) | −71.4562 | −3.49504 | ||||||||
\(419\) | 24.7131 | 1.20731 | 0.603656 | − | 0.797245i | \(-0.293710\pi\) | ||||
0.603656 | + | 0.797245i | \(0.293710\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.7598 | 0.914298 | 0.457149 | − | 0.889390i | \(-0.348871\pi\) | ||||
0.457149 | + | 0.889390i | \(0.348871\pi\) | |||||||
\(422\) | −7.95033 | −0.387016 | ||||||||
\(423\) | 18.6463 | 0.906616 | ||||||||
\(424\) | −5.26229 | −0.255559 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.0798515 | −0.00386882 | ||||||||
\(427\) | −2.51929 | −0.121917 | ||||||||
\(428\) | 5.20747 | 0.251713 | ||||||||
\(429\) | 0.940056 | 0.0453863 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.10510 | −0.0532307 | −0.0266154 | − | 0.999646i | \(-0.508473\pi\) | ||||
−0.0266154 | + | 0.999646i | \(0.508473\pi\) | |||||||
\(432\) | 0.983579 | 0.0473225 | ||||||||
\(433\) | 32.9637 | 1.58413 | 0.792066 | − | 0.610435i | \(-0.209005\pi\) | ||||
0.792066 | + | 0.610435i | \(0.209005\pi\) | |||||||
\(434\) | −14.6494 | −0.703196 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.22400 | 0.0586192 | ||||||||
\(437\) | −31.1617 | −1.49067 | ||||||||
\(438\) | 0.593175 | 0.0283430 | ||||||||
\(439\) | 3.06090 | 0.146089 | 0.0730444 | − | 0.997329i | \(-0.476729\pi\) | ||||
0.0730444 | + | 0.997329i | \(0.476729\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.8843 | 0.851634 | ||||||||
\(442\) | 16.7767 | 0.797988 | ||||||||
\(443\) | 25.7992 | 1.22576 | 0.612879 | − | 0.790177i | \(-0.290011\pi\) | ||||
0.612879 | + | 0.790177i | \(0.290011\pi\) | |||||||
\(444\) | −0.135850 | −0.00644715 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −15.4344 | −0.730840 | ||||||||
\(447\) | 0.250201 | 0.0118341 | ||||||||
\(448\) | −4.96565 | −0.234605 | ||||||||
\(449\) | −33.3883 | −1.57569 | −0.787846 | − | 0.615872i | \(-0.788804\pi\) | ||||
−0.787846 | + | 0.615872i | \(0.788804\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −69.9780 | −3.29514 | ||||||||
\(452\) | −5.36511 | −0.252354 | ||||||||
\(453\) | −0.238952 | −0.0112270 | ||||||||
\(454\) | 21.9797 | 1.03156 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.625712 | 0.0293017 | ||||||||
\(457\) | −1.59727 | −0.0747172 | −0.0373586 | − | 0.999302i | \(-0.511894\pi\) | ||||
−0.0373586 | + | 0.999302i | \(0.511894\pi\) | |||||||
\(458\) | 13.0345 | 0.609060 | ||||||||
\(459\) | 0.453833 | 0.0211831 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.6226 | 0.587892 | 0.293946 | − | 0.955822i | \(-0.405031\pi\) | ||||
0.293946 | + | 0.955822i | \(0.405031\pi\) | |||||||
\(462\) | 0.318910 | 0.0148370 | ||||||||
\(463\) | 5.97980 | 0.277905 | 0.138953 | − | 0.990299i | \(-0.455626\pi\) | ||||
0.138953 | + | 0.990299i | \(0.455626\pi\) | |||||||
\(464\) | −1.95793 | −0.0908945 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 25.5632 | 1.18419 | ||||||||
\(467\) | 10.4848 | 0.485180 | 0.242590 | − | 0.970129i | \(-0.422003\pi\) | ||||
0.242590 | + | 0.970129i | \(0.422003\pi\) | |||||||
\(468\) | −7.64385 | −0.353337 | ||||||||
\(469\) | −3.22600 | −0.148963 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.737994 | −0.0340050 | ||||||||
\(472\) | 19.8408 | 0.913249 | ||||||||
\(473\) | −2.62741 | −0.120808 | ||||||||
\(474\) | −0.885307 | −0.0406635 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.19880 | 0.0549468 | ||||||||
\(477\) | 6.76113 | 0.309571 | ||||||||
\(478\) | 33.7004 | 1.54142 | ||||||||
\(479\) | 2.88134 | 0.131652 | 0.0658258 | − | 0.997831i | \(-0.479032\pi\) | ||||
0.0658258 | + | 0.997831i | \(0.479032\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −35.4640 | −1.61702 | ||||||||
\(482\) | 1.59175 | 0.0725023 | ||||||||
\(483\) | 0.139075 | 0.00632813 | ||||||||
\(484\) | 11.7185 | 0.532657 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.47264 | −0.0668003 | ||||||||
\(487\) | −18.2911 | −0.828850 | −0.414425 | − | 0.910083i | \(-0.636017\pi\) | ||||
−0.414425 | + | 0.910083i | \(0.636017\pi\) | |||||||
\(488\) | 5.77641 | 0.261486 | ||||||||
\(489\) | 0.121888 | 0.00551198 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.0482 | 0.904762 | 0.452381 | − | 0.891825i | \(-0.350575\pi\) | ||||
0.452381 | + | 0.891825i | \(0.350575\pi\) | |||||||
\(492\) | −0.223017 | −0.0100544 | ||||||||
\(493\) | −0.903407 | −0.0406874 | ||||||||
\(494\) | −59.4491 | −2.67474 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 43.2392 | 1.94150 | ||||||||
\(497\) | −1.48953 | −0.0668147 | ||||||||
\(498\) | 0.137887 | 0.00617885 | ||||||||
\(499\) | 5.02273 | 0.224848 | 0.112424 | − | 0.993660i | \(-0.464138\pi\) | ||||
0.112424 | + | 0.993660i | \(0.464138\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.409509 | −0.0182955 | ||||||||
\(502\) | 18.3698 | 0.819882 | ||||||||
\(503\) | 12.6546 | 0.564242 | 0.282121 | − | 0.959379i | \(-0.408962\pi\) | ||||
0.282121 | + | 0.959379i | \(0.408962\pi\) | |||||||
\(504\) | 7.12499 | 0.317372 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 36.4162 | 1.61890 | ||||||||
\(507\) | 0.336409 | 0.0149405 | ||||||||
\(508\) | −9.34301 | −0.414529 | ||||||||
\(509\) | −7.20912 | −0.319539 | −0.159769 | − | 0.987154i | \(-0.551075\pi\) | ||||
−0.159769 | + | 0.987154i | \(0.551075\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.0650 | 0.489485 | ||||||||
\(512\) | 8.24276 | 0.364282 | ||||||||
\(513\) | −1.60818 | −0.0710028 | ||||||||
\(514\) | −49.5064 | −2.18363 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.00837344 | −0.000368620 0 | ||||||||
\(517\) | −35.6964 | −1.56993 | ||||||||
\(518\) | −12.0310 | −0.528613 | ||||||||
\(519\) | −0.166680 | −0.00731644 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.53657 | 0.111129 | 0.0555647 | − | 0.998455i | \(-0.482304\pi\) | ||||
0.0555647 | + | 0.998455i | \(0.482304\pi\) | |||||||
\(522\) | 1.95418 | 0.0855321 | ||||||||
\(523\) | −4.55695 | −0.199262 | −0.0996308 | − | 0.995024i | \(-0.531766\pi\) | ||||
−0.0996308 | + | 0.995024i | \(0.531766\pi\) | |||||||
\(524\) | 5.23369 | 0.228635 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.26840 | 0.273315 | ||||||||
\(527\) | 19.9510 | 0.869079 | ||||||||
\(528\) | −0.941293 | −0.0409645 | ||||||||
\(529\) | −7.11911 | −0.309526 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −25.4921 | −1.10626 | ||||||||
\(532\) | −4.24800 | −0.184174 | ||||||||
\(533\) | −58.2193 | −2.52176 | ||||||||
\(534\) | 0.630606 | 0.0272890 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.39680 | 0.319493 | ||||||||
\(537\) | 0.0609631 | 0.00263075 | ||||||||
\(538\) | 46.9937 | 2.02604 | ||||||||
\(539\) | −34.2376 | −1.47472 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.9491 | −1.41659 | −0.708296 | − | 0.705915i | \(-0.750536\pi\) | ||||
−0.708296 | + | 0.705915i | \(0.750536\pi\) | |||||||
\(542\) | 4.56891 | 0.196252 | ||||||||
\(543\) | 0.312221 | 0.0133987 | ||||||||
\(544\) | −6.49777 | −0.278589 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.265322 | 0.0113548 | ||||||||
\(547\) | 5.31970 | 0.227454 | 0.113727 | − | 0.993512i | \(-0.463721\pi\) | ||||
0.113727 | + | 0.993512i | \(0.463721\pi\) | |||||||
\(548\) | −0.960925 | −0.0410487 | ||||||||
\(549\) | −7.42169 | −0.316750 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.20127 | 0.136378 | ||||||||
\(552\) | −0.318881 | −0.0135725 | ||||||||
\(553\) | −16.5143 | −0.702261 | ||||||||
\(554\) | 23.4925 | 0.998101 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.62728 | −0.111422 | ||||||||
\(557\) | −34.5349 | −1.46329 | −0.731644 | − | 0.681687i | \(-0.761247\pi\) | ||||
−0.731644 | + | 0.681687i | \(0.761247\pi\) | |||||||
\(558\) | −43.1564 | −1.82696 | ||||||||
\(559\) | −2.18591 | −0.0924542 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.434322 | −0.0183371 | ||||||||
\(562\) | 39.2734 | 1.65665 | ||||||||
\(563\) | −3.85041 | −0.162275 | −0.0811377 | − | 0.996703i | \(-0.525855\pi\) | ||||
−0.0811377 | + | 0.996703i | \(0.525855\pi\) | |||||||
\(564\) | −0.113763 | −0.00479029 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15.1940 | 0.638653 | ||||||||
\(567\) | −9.15079 | −0.384297 | ||||||||
\(568\) | 3.41531 | 0.143303 | ||||||||
\(569\) | −42.1707 | −1.76789 | −0.883943 | − | 0.467595i | \(-0.845121\pi\) | ||||
−0.883943 | + | 0.467595i | \(0.845121\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.9479 | 1.00219 | 0.501094 | − | 0.865393i | \(-0.332931\pi\) | ||||
0.501094 | + | 0.865393i | \(0.332931\pi\) | |||||||
\(572\) | 14.6333 | 0.611850 | ||||||||
\(573\) | 0.204876 | 0.00855883 | ||||||||
\(574\) | −19.7507 | −0.824378 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −14.6285 | −0.609522 | ||||||||
\(577\) | −32.2352 | −1.34197 | −0.670984 | − | 0.741472i | \(-0.734128\pi\) | ||||
−0.670984 | + | 0.741472i | \(0.734128\pi\) | |||||||
\(578\) | 19.3086 | 0.803133 | ||||||||
\(579\) | −0.694173 | −0.0288488 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.57211 | 0.106709 | ||||||||
\(582\) | 0.715837 | 0.0296724 | ||||||||
\(583\) | −12.9434 | −0.536063 | ||||||||
\(584\) | −25.3705 | −1.04984 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −34.8291 | −1.43878 | ||||||||
\(587\) | −18.8703 | −0.778863 | −0.389431 | − | 0.921056i | \(-0.627328\pi\) | ||||
−0.389431 | + | 0.921056i | \(0.627328\pi\) | |||||||
\(588\) | −0.109114 | −0.00449978 | ||||||||
\(589\) | −70.6972 | −2.91303 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.191962 | −0.00789626 | ||||||||
\(592\) | 35.5107 | 1.45948 | ||||||||
\(593\) | 36.3745 | 1.49372 | 0.746860 | − | 0.664981i | \(-0.231560\pi\) | ||||
0.746860 | + | 0.664981i | \(0.231560\pi\) | |||||||
\(594\) | 1.87935 | 0.0771107 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.89474 | 0.159535 | ||||||||
\(597\) | −0.407472 | −0.0166767 | ||||||||
\(598\) | 30.2970 | 1.23894 | ||||||||
\(599\) | 9.75093 | 0.398412 | 0.199206 | − | 0.979958i | \(-0.436164\pi\) | ||||
0.199206 | + | 0.979958i | \(0.436164\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.19087 | −0.374903 | −0.187452 | − | 0.982274i | \(-0.560023\pi\) | ||||
−0.187452 | + | 0.982274i | \(0.560023\pi\) | |||||||
\(602\) | −0.741562 | −0.0302238 | ||||||||
\(603\) | −9.50361 | −0.387017 | ||||||||
\(604\) | −3.71964 | −0.151350 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.02126 | −0.0414859 | ||||||||
\(607\) | −6.58402 | −0.267237 | −0.133618 | − | 0.991033i | \(-0.542660\pi\) | ||||
−0.133618 | + | 0.991033i | \(0.542660\pi\) | |||||||
\(608\) | 23.0251 | 0.933792 | ||||||||
\(609\) | −0.0142873 | −0.000578950 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.6982 | −1.20146 | ||||||||
\(612\) | 3.53159 | 0.142756 | ||||||||
\(613\) | −37.4431 | −1.51231 | −0.756156 | − | 0.654392i | \(-0.772925\pi\) | ||||
−0.756156 | + | 0.654392i | \(0.772925\pi\) | |||||||
\(614\) | 2.87143 | 0.115881 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.6400 | −0.549572 | ||||||||
\(617\) | −34.9827 | −1.40835 | −0.704175 | − | 0.710026i | \(-0.748683\pi\) | ||||
−0.704175 | + | 0.710026i | \(0.748683\pi\) | |||||||
\(618\) | −0.902653 | −0.0363100 | ||||||||
\(619\) | 5.12303 | 0.205912 | 0.102956 | − | 0.994686i | \(-0.467170\pi\) | ||||
0.102956 | + | 0.994686i | \(0.467170\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.819574 | 0.0328884 | ||||||||
\(622\) | 42.6061 | 1.70835 | ||||||||
\(623\) | 11.7632 | 0.471282 | ||||||||
\(624\) | −0.783124 | −0.0313500 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −16.2063 | −0.647734 | ||||||||
\(627\) | 1.53904 | 0.0614633 | ||||||||
\(628\) | −11.4879 | −0.458419 | ||||||||
\(629\) | 16.3850 | 0.653312 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.57742 | −0.261843 | −0.130922 | − | 0.991393i | \(-0.541794\pi\) | ||||
−0.130922 | + | 0.991393i | \(0.541794\pi\) | |||||||
\(632\) | 37.8652 | 1.50620 | ||||||||
\(633\) | 0.171236 | 0.00680601 | ||||||||
\(634\) | −12.0904 | −0.480170 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.0412503 | −0.00163568 | ||||||||
\(637\) | −28.4845 | −1.12860 | ||||||||
\(638\) | −3.74106 | −0.148110 | ||||||||
\(639\) | −4.38808 | −0.173590 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.14309 | −0.321633 | −0.160816 | − | 0.986984i | \(-0.551413\pi\) | ||||
−0.160816 | + | 0.986984i | \(0.551413\pi\) | |||||||
\(642\) | −0.532492 | −0.0210158 | ||||||||
\(643\) | −9.93346 | −0.391737 | −0.195869 | − | 0.980630i | \(-0.562753\pi\) | ||||
−0.195869 | + | 0.980630i | \(0.562753\pi\) | |||||||
\(644\) | 2.16490 | 0.0853091 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 27.4665 | 1.08066 | ||||||||
\(647\) | −33.9129 | −1.33325 | −0.666627 | − | 0.745391i | \(-0.732263\pi\) | ||||
−0.666627 | + | 0.745391i | \(0.732263\pi\) | |||||||
\(648\) | 20.9816 | 0.824234 | ||||||||
\(649\) | 48.8018 | 1.91564 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.315523 | 0.0123663 | ||||||||
\(652\) | 1.89737 | 0.0743066 | ||||||||
\(653\) | 6.12347 | 0.239630 | 0.119815 | − | 0.992796i | \(-0.461770\pi\) | ||||
0.119815 | + | 0.992796i | \(0.461770\pi\) | |||||||
\(654\) | −0.125161 | −0.00489418 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 58.2960 | 2.27607 | ||||||||
\(657\) | 32.5967 | 1.27172 | ||||||||
\(658\) | −10.0750 | −0.392764 | ||||||||
\(659\) | −18.4602 | −0.719106 | −0.359553 | − | 0.933125i | \(-0.617071\pi\) | ||||
−0.359553 | + | 0.933125i | \(0.617071\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.1393 | 0.705536 | 0.352768 | − | 0.935711i | \(-0.385240\pi\) | ||||
0.352768 | + | 0.935711i | \(0.385240\pi\) | |||||||
\(662\) | 21.5614 | 0.838008 | ||||||||
\(663\) | −0.361341 | −0.0140333 | ||||||||
\(664\) | −5.89752 | −0.228868 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −35.4427 | −1.37338 | ||||||||
\(667\) | −1.63146 | −0.0631703 | ||||||||
\(668\) | −6.37460 | −0.246641 | ||||||||
\(669\) | 0.332429 | 0.0128525 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.2080 | 0.548494 | ||||||||
\(672\) | −0.102761 | −0.00396411 | ||||||||
\(673\) | 39.1328 | 1.50846 | 0.754229 | − | 0.656611i | \(-0.228011\pi\) | ||||
0.754229 | + | 0.656611i | \(0.228011\pi\) | |||||||
\(674\) | −29.8081 | −1.14816 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.23669 | 0.201411 | ||||||||
\(677\) | −11.9755 | −0.460256 | −0.230128 | − | 0.973160i | \(-0.573915\pi\) | ||||
−0.230128 | + | 0.973160i | \(0.573915\pi\) | |||||||
\(678\) | 0.548612 | 0.0210693 | ||||||||
\(679\) | 13.3531 | 0.512444 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.473404 | −0.0181409 | ||||||||
\(682\) | 82.6182 | 3.16362 | ||||||||
\(683\) | 19.4941 | 0.745923 | 0.372961 | − | 0.927847i | \(-0.378342\pi\) | ||||
0.372961 | + | 0.927847i | \(0.378342\pi\) | |||||||
\(684\) | −12.5143 | −0.478498 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −21.0055 | −0.801995 | ||||||||
\(687\) | −0.280739 | −0.0107109 | ||||||||
\(688\) | 2.18879 | 0.0834468 | ||||||||
\(689\) | −10.7685 | −0.410247 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0515 | 0.762795 | 0.381397 | − | 0.924411i | \(-0.375443\pi\) | ||||
0.381397 | + | 0.924411i | \(0.375443\pi\) | |||||||
\(692\) | −2.59461 | −0.0986324 | ||||||||
\(693\) | 17.5251 | 0.665722 | ||||||||
\(694\) | 39.0092 | 1.48077 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.0327589 | 0.00124172 | ||||||||
\(697\) | 26.8983 | 1.01885 | ||||||||
\(698\) | −45.7857 | −1.73301 | ||||||||
\(699\) | −0.550585 | −0.0208250 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.4415 | 0.583217 | 0.291609 | − | 0.956538i | \(-0.405810\pi\) | ||||
0.291609 | + | 0.956538i | \(0.405810\pi\) | |||||||
\(702\) | 1.56356 | 0.0590126 | ||||||||
\(703\) | −58.0610 | −2.18981 | ||||||||
\(704\) | 28.0047 | 1.05547 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.14576 | 0.231299 | ||||||||
\(707\) | −19.0504 | −0.716463 | ||||||||
\(708\) | 0.155529 | 0.00584515 | ||||||||
\(709\) | 7.99965 | 0.300433 | 0.150216 | − | 0.988653i | \(-0.452003\pi\) | ||||
0.150216 | + | 0.988653i | \(0.452003\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −48.6503 | −1.82453 | ||||||||
\(712\) | −26.9715 | −1.01080 | ||||||||
\(713\) | 36.0294 | 1.34931 | ||||||||
\(714\) | −0.122584 | −0.00458757 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.948979 | 0.0354650 | ||||||||
\(717\) | −0.725847 | −0.0271072 | ||||||||
\(718\) | 14.6391 | 0.546326 | ||||||||
\(719\) | −32.7769 | −1.22237 | −0.611187 | − | 0.791487i | \(-0.709307\pi\) | ||||
−0.611187 | + | 0.791487i | \(0.709307\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.8379 | −0.627076 | ||||||||
\(722\) | −67.0856 | −2.49667 | ||||||||
\(723\) | −0.0342835 | −0.00127502 | ||||||||
\(724\) | 4.86016 | 0.180627 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.19828 | −0.0444722 | ||||||||
\(727\) | 42.1467 | 1.56313 | 0.781567 | − | 0.623821i | \(-0.214420\pi\) | ||||
0.781567 | + | 0.623821i | \(0.214420\pi\) | |||||||
\(728\) | −11.3480 | −0.420586 | ||||||||
\(729\) | −26.9366 | −0.997650 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.00993 | 0.0373536 | ||||||||
\(732\) | 0.0452804 | 0.00167361 | ||||||||
\(733\) | −47.9618 | −1.77151 | −0.885755 | − | 0.464153i | \(-0.846359\pi\) | ||||
−0.885755 | + | 0.464153i | \(0.846359\pi\) | |||||||
\(734\) | −41.0478 | −1.51510 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.7343 | −0.432531 | ||||||||
\(737\) | 18.1936 | 0.670171 | ||||||||
\(738\) | −58.1844 | −2.14180 | ||||||||
\(739\) | −20.8420 | −0.766686 | −0.383343 | − | 0.923606i | \(-0.625227\pi\) | ||||
−0.383343 | + | 0.923606i | \(0.625227\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.28043 | 0.0470377 | ||||||||
\(742\) | −3.65317 | −0.134112 | ||||||||
\(743\) | 7.06747 | 0.259280 | 0.129640 | − | 0.991561i | \(-0.458618\pi\) | ||||
0.129640 | + | 0.991561i | \(0.458618\pi\) | |||||||
\(744\) | −0.723453 | −0.0265231 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 39.1312 | 1.43270 | ||||||||
\(747\) | 7.57729 | 0.277239 | ||||||||
\(748\) | −6.76084 | −0.247201 | ||||||||
\(749\) | −9.93298 | −0.362943 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.09920 | 0.295544 | 0.147772 | − | 0.989021i | \(-0.452790\pi\) | ||||
0.147772 | + | 0.989021i | \(0.452790\pi\) | |||||||
\(752\) | 29.7373 | 1.08441 | ||||||||
\(753\) | −0.395652 | −0.0144183 | ||||||||
\(754\) | −3.11244 | −0.113348 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.111725 | 0.00406341 | ||||||||
\(757\) | −3.77993 | −0.137384 | −0.0686919 | − | 0.997638i | \(-0.521883\pi\) | ||||
−0.0686919 | + | 0.997638i | \(0.521883\pi\) | |||||||
\(758\) | −21.3069 | −0.773902 | ||||||||
\(759\) | −0.784339 | −0.0284697 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.6997 | −0.786614 | −0.393307 | − | 0.919407i | \(-0.628669\pi\) | ||||
−0.393307 | + | 0.919407i | \(0.628669\pi\) | |||||||
\(762\) | 0.955373 | 0.0346095 | ||||||||
\(763\) | −2.33473 | −0.0845228 | ||||||||
\(764\) | 3.18920 | 0.115381 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.15455 | −0.330767 | ||||||||
\(767\) | 40.6014 | 1.46603 | ||||||||
\(768\) | 0.410622 | 0.0148171 | ||||||||
\(769\) | 12.8260 | 0.462519 | 0.231260 | − | 0.972892i | \(-0.425715\pi\) | ||||
0.231260 | + | 0.972892i | \(0.425715\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.06628 | 0.0384011 | ||||||||
\(772\) | −10.8058 | −0.388909 | ||||||||
\(773\) | −32.0226 | −1.15177 | −0.575887 | − | 0.817529i | \(-0.695343\pi\) | ||||
−0.575887 | + | 0.817529i | \(0.695343\pi\) | |||||||
\(774\) | −2.18460 | −0.0785238 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −30.6169 | −1.09908 | ||||||||
\(777\) | 0.259127 | 0.00929613 | ||||||||
\(778\) | 18.3216 | 0.656862 | ||||||||
\(779\) | −95.3155 | −3.41503 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.40049 | 0.300593 | ||||||||
\(782\) | −13.9977 | −0.500558 | ||||||||
\(783\) | −0.0841956 | −0.00300890 | ||||||||
\(784\) | 28.5220 | 1.01864 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.535173 | −0.0190890 | ||||||||
\(787\) | 30.4017 | 1.08370 | 0.541851 | − | 0.840474i | \(-0.317724\pi\) | ||||
0.541851 | + | 0.840474i | \(0.317724\pi\) | |||||||
\(788\) | −2.98816 | −0.106449 | ||||||||
\(789\) | −0.135010 | −0.00480648 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.2337 | 0.363868 | ||||||||
\(792\) | −40.1827 | −1.42783 | ||||||||
\(793\) | 11.8206 | 0.419761 | ||||||||
\(794\) | −18.6651 | −0.662399 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.34288 | −0.224817 | ||||||||
\(797\) | −6.52493 | −0.231125 | −0.115562 | − | 0.993300i | \(-0.536867\pi\) | ||||
−0.115562 | + | 0.993300i | \(0.536867\pi\) | |||||||
\(798\) | 0.434380 | 0.0153769 | ||||||||
\(799\) | 13.7211 | 0.485417 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 34.6537 | 1.22443 | ||||||||
\(802\) | 1.26608 | 0.0447067 | ||||||||
\(803\) | −62.4029 | −2.20215 | ||||||||
\(804\) | 0.0579824 | 0.00204488 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 68.7355 | 2.42111 | ||||||||
\(807\) | −1.01216 | −0.0356298 | ||||||||
\(808\) | 43.6800 | 1.53666 | ||||||||
\(809\) | 39.8132 | 1.39976 | 0.699878 | − | 0.714262i | \(-0.253238\pi\) | ||||
0.699878 | + | 0.714262i | \(0.253238\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.57329 | 0.0903604 | 0.0451802 | − | 0.998979i | \(-0.485614\pi\) | ||||
0.0451802 | + | 0.998979i | \(0.485614\pi\) | |||||||
\(812\) | −0.222402 | −0.00780479 | ||||||||
\(813\) | −0.0984062 | −0.00345126 | ||||||||
\(814\) | 67.8512 | 2.37818 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.361817 | 0.0126661 | ||||||||
\(817\) | −3.57873 | −0.125204 | ||||||||
\(818\) | −4.74500 | −0.165905 | ||||||||
\(819\) | 14.5803 | 0.509475 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.14063 | 0.0398081 | 0.0199041 | − | 0.999802i | \(-0.493664\pi\) | ||||
0.0199041 | + | 0.999802i | \(0.493664\pi\) | |||||||
\(822\) | 0.0982597 | 0.00342720 | ||||||||
\(823\) | 17.9025 | 0.624041 | 0.312020 | − | 0.950075i | \(-0.398994\pi\) | ||||
0.312020 | + | 0.950075i | \(0.398994\pi\) | |||||||
\(824\) | 38.6071 | 1.34494 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.7739 | 0.479254 | ||||||||
\(827\) | −19.4059 | −0.674809 | −0.337405 | − | 0.941360i | \(-0.609549\pi\) | ||||
−0.337405 | + | 0.941360i | \(0.609549\pi\) | |||||||
\(828\) | 6.37768 | 0.221640 | ||||||||
\(829\) | −23.7397 | −0.824512 | −0.412256 | − | 0.911068i | \(-0.635259\pi\) | ||||
−0.412256 | + | 0.911068i | \(0.635259\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.505987 | −0.0175525 | ||||||||
\(832\) | 23.2990 | 0.807746 | ||||||||
\(833\) | 13.1603 | 0.455978 | ||||||||
\(834\) | 0.268654 | 0.00930272 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 23.9574 | 0.828583 | ||||||||
\(837\) | 1.85939 | 0.0642698 | ||||||||
\(838\) | −39.3370 | −1.35888 | ||||||||
\(839\) | 4.72509 | 0.163128 | 0.0815642 | − | 0.996668i | \(-0.474008\pi\) | ||||
0.0815642 | + | 0.996668i | \(0.474008\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8324 | −0.994221 | ||||||||
\(842\) | −29.8610 | −1.02908 | ||||||||
\(843\) | −0.845879 | −0.0291336 | ||||||||
\(844\) | 2.66553 | 0.0917514 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −29.6803 | −1.02043 | ||||||||
\(847\) | −22.3524 | −0.768037 | ||||||||
\(848\) | 10.7827 | 0.370279 | ||||||||
\(849\) | −0.327252 | −0.0112313 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.5895 | 1.01432 | ||||||||
\(852\) | 0.0267721 | 0.000917196 0 | ||||||||
\(853\) | −58.2448 | −1.99426 | −0.997132 | − | 0.0756804i | \(-0.975887\pi\) | ||||
−0.997132 | + | 0.0756804i | \(0.975887\pi\) | |||||||
\(854\) | 4.01009 | 0.137222 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22.7750 | 0.778435 | ||||||||
\(857\) | −55.0013 | −1.87881 | −0.939404 | − | 0.342812i | \(-0.888621\pi\) | ||||
−0.939404 | + | 0.342812i | \(0.888621\pi\) | |||||||
\(858\) | −1.49633 | −0.0510840 | ||||||||
\(859\) | 48.6222 | 1.65897 | 0.829483 | − | 0.558532i | \(-0.188635\pi\) | ||||
0.829483 | + | 0.558532i | \(0.188635\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.425394 | 0.0144974 | ||||||||
\(862\) | 1.75904 | 0.0599132 | ||||||||
\(863\) | −57.3980 | −1.95385 | −0.976926 | − | 0.213579i | \(-0.931488\pi\) | ||||
−0.976926 | + | 0.213579i | \(0.931488\pi\) | |||||||
\(864\) | −0.605577 | −0.0206022 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −52.4699 | −1.78300 | ||||||||
\(867\) | −0.415873 | −0.0141238 | ||||||||
\(868\) | 4.91156 | 0.166709 | ||||||||
\(869\) | 93.1356 | 3.15941 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.1365 | 0.512880 | ||||||||
\(872\) | 5.35323 | 0.181283 | ||||||||
\(873\) | 39.3374 | 1.33137 | ||||||||
\(874\) | 49.6016 | 1.67780 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.198876 | −0.00671939 | ||||||||
\(877\) | 25.2704 | 0.853320 | 0.426660 | − | 0.904412i | \(-0.359690\pi\) | ||||
0.426660 | + | 0.904412i | \(0.359690\pi\) | |||||||
\(878\) | −4.87219 | −0.164428 | ||||||||
\(879\) | 0.750156 | 0.0253021 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.5670 | −1.16459 | −0.582297 | − | 0.812976i | \(-0.697846\pi\) | ||||
−0.582297 | + | 0.812976i | \(0.697846\pi\) | |||||||
\(882\) | −28.4674 | −0.958547 | ||||||||
\(883\) | 38.6836 | 1.30181 | 0.650904 | − | 0.759160i | \(-0.274390\pi\) | ||||
0.650904 | + | 0.759160i | \(0.274390\pi\) | |||||||
\(884\) | −5.62479 | −0.189182 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −41.0659 | −1.37964 | ||||||||
\(887\) | −26.4989 | −0.889746 | −0.444873 | − | 0.895594i | \(-0.646751\pi\) | ||||
−0.444873 | + | 0.895594i | \(0.646751\pi\) | |||||||
\(888\) | −0.594145 | −0.0199382 | ||||||||
\(889\) | 17.8213 | 0.597708 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 51.6076 | 1.72892 | ||||||||
\(892\) | 5.17474 | 0.173263 | ||||||||
\(893\) | −48.6212 | −1.62705 | ||||||||
\(894\) | −0.398258 | −0.0133198 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 13.8989 | 0.464330 | ||||||||
\(897\) | −0.652543 | −0.0217878 | ||||||||
\(898\) | 53.1459 | 1.77350 | ||||||||
\(899\) | −3.70133 | −0.123446 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.97524 | 0.165749 | ||||||||
\(902\) | 111.388 | 3.70880 | ||||||||
\(903\) | 0.0159719 | 0.000531512 0 | ||||||||
\(904\) | −23.4645 | −0.780418 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.380353 | 0.0126364 | ||||||||
\(907\) | 47.6929 | 1.58362 | 0.791809 | − | 0.610769i | \(-0.209140\pi\) | ||||
0.791809 | + | 0.610769i | \(0.209140\pi\) | |||||||
\(908\) | −7.36921 | −0.244556 | ||||||||
\(909\) | −56.1213 | −1.86143 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.1515 | −1.49594 | −0.747969 | − | 0.663734i | \(-0.768971\pi\) | ||||
−0.747969 | + | 0.663734i | \(0.768971\pi\) | |||||||
\(912\) | −1.28211 | −0.0424550 | ||||||||
\(913\) | −14.5059 | −0.480075 | ||||||||
\(914\) | 2.54246 | 0.0840971 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.37010 | −0.144392 | ||||||||
\(917\) | −9.98300 | −0.329668 | ||||||||
\(918\) | −0.722389 | −0.0238424 | ||||||||
\(919\) | −30.2152 | −0.996706 | −0.498353 | − | 0.866974i | \(-0.666062\pi\) | ||||
−0.498353 | + | 0.866974i | \(0.666062\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.0618455 | −0.00203788 | ||||||||
\(922\) | −20.0920 | −0.661695 | ||||||||
\(923\) | 6.98892 | 0.230043 | ||||||||
\(924\) | −0.106922 | −0.00351748 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9.51836 | −0.312793 | ||||||||
\(927\) | −49.6035 | −1.62919 | ||||||||
\(928\) | 1.20547 | 0.0395715 | ||||||||
\(929\) | −49.6981 | −1.63054 | −0.815270 | − | 0.579081i | \(-0.803412\pi\) | ||||
−0.815270 | + | 0.579081i | \(0.803412\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −46.6342 | −1.52837 | ||||||||
\(932\) | −8.57064 | −0.280741 | ||||||||
\(933\) | −0.917659 | −0.0300428 | ||||||||
\(934\) | −16.6892 | −0.546088 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −33.4306 | −1.09271 | ||||||||
\(937\) | −0.189215 | −0.00618140 | −0.00309070 | − | 0.999995i | \(-0.500984\pi\) | ||||
−0.00309070 | + | 0.999995i | \(0.500984\pi\) | |||||||
\(938\) | 5.13499 | 0.167663 | ||||||||
\(939\) | 0.349055 | 0.0113910 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.7887 | 0.482098 | 0.241049 | − | 0.970513i | \(-0.422508\pi\) | ||||
0.241049 | + | 0.970513i | \(0.422508\pi\) | |||||||
\(942\) | 1.17470 | 0.0382739 | ||||||||
\(943\) | 48.5755 | 1.58184 | ||||||||
\(944\) | −40.6548 | −1.32320 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.18218 | 0.135974 | ||||||||
\(947\) | 6.06365 | 0.197042 | 0.0985211 | − | 0.995135i | \(-0.468589\pi\) | ||||
0.0985211 | + | 0.995135i | \(0.468589\pi\) | |||||||
\(948\) | 0.296820 | 0.00964026 | ||||||||
\(949\) | −51.9171 | −1.68530 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.260405 | 0.00844421 | ||||||||
\(952\) | 5.24299 | 0.169926 | ||||||||
\(953\) | 48.1276 | 1.55900 | 0.779502 | − | 0.626400i | \(-0.215472\pi\) | ||||
0.779502 | + | 0.626400i | \(0.215472\pi\) | |||||||
\(954\) | −10.7620 | −0.348434 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −11.2988 | −0.365431 | ||||||||
\(957\) | 0.0805758 | 0.00260465 | ||||||||
\(958\) | −4.58637 | −0.148179 | ||||||||
\(959\) | 1.83292 | 0.0591879 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 50.7407 | 1.63680 | ||||||||
\(962\) | 56.4499 | 1.82002 | ||||||||
\(963\) | −29.2620 | −0.942955 | ||||||||
\(964\) | −0.533671 | −0.0171884 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.221373 | −0.00712255 | ||||||||
\(967\) | 25.6884 | 0.826083 | 0.413042 | − | 0.910712i | \(-0.364466\pi\) | ||||
0.413042 | + | 0.910712i | \(0.364466\pi\) | |||||||
\(968\) | 51.2511 | 1.64727 | ||||||||
\(969\) | −0.591580 | −0.0190043 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.8393 | 1.02177 | 0.510886 | − | 0.859649i | \(-0.329318\pi\) | ||||
0.510886 | + | 0.859649i | \(0.329318\pi\) | |||||||
\(972\) | 0.493737 | 0.0158366 | ||||||||
\(973\) | 5.01141 | 0.160658 | ||||||||
\(974\) | 29.1149 | 0.932903 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.8361 | −0.378866 | ||||||||
\(977\) | −16.9361 | −0.541834 | −0.270917 | − | 0.962603i | \(-0.587327\pi\) | ||||
−0.270917 | + | 0.962603i | \(0.587327\pi\) | |||||||
\(978\) | −0.194016 | −0.00620394 | ||||||||
\(979\) | −66.3407 | −2.12026 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.87797 | −0.219597 | ||||||||
\(982\) | −31.9117 | −1.01834 | ||||||||
\(983\) | 12.8294 | 0.409194 | 0.204597 | − | 0.978846i | \(-0.434412\pi\) | ||||
0.204597 | + | 0.978846i | \(0.434412\pi\) | |||||||
\(984\) | −0.975374 | −0.0310938 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.43800 | 0.0457952 | ||||||||
\(987\) | 0.216997 | 0.00690710 | ||||||||
\(988\) | 19.9317 | 0.634112 | ||||||||
\(989\) | 1.82382 | 0.0579942 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.11578 | −0.0354438 | −0.0177219 | − | 0.999843i | \(-0.505641\pi\) | ||||
−0.0177219 | + | 0.999843i | \(0.505641\pi\) | |||||||
\(992\) | −26.6218 | −0.845244 | ||||||||
\(993\) | −0.464394 | −0.0147371 | ||||||||
\(994\) | 2.37097 | 0.0752024 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.0462297 | −0.00146485 | ||||||||
\(997\) | 18.4505 | 0.584334 | 0.292167 | − | 0.956367i | \(-0.405624\pi\) | ||||
0.292167 | + | 0.956367i | \(0.405624\pi\) | |||||||
\(998\) | −7.99494 | −0.253075 | ||||||||
\(999\) | 1.52704 | 0.0483136 |
(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 | 6025.2.a.l.1.12 | ✓ | 40 | |
5.4 | even | 2 | 6025.2.a.o.1.29 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6025.2.a.l.1.12 | ✓ | 40 | 1.1 | even | 1 | trivial | |
6025.2.a.o.1.29 | yes | 40 | 5.4 | even | 2 |