Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1397868136\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.2147108.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 9x^{3} + 17x^{2} + 16x - 27 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 161) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.69017\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.69017 | −1.90224 | −0.951119 | − | 0.308825i | \(-0.900064\pi\) | ||||
−0.951119 | + | 0.308825i | \(0.900064\pi\) | |||||||
\(3\) | 0.269842 | 0.155793 | 0.0778967 | − | 0.996961i | \(-0.475180\pi\) | ||||
0.0778967 | + | 0.996961i | \(0.475180\pi\) | |||||||
\(4\) | 5.23702 | 2.61851 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.725921 | −0.296356 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −8.70812 | −3.07879 | ||||||||
\(9\) | −2.92719 | −0.975728 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.78810 | −1.14215 | −0.571077 | − | 0.820896i | \(-0.693474\pi\) | ||||
−0.571077 | + | 0.820896i | \(0.693474\pi\) | |||||||
\(12\) | 1.41317 | 0.407946 | ||||||||
\(13\) | −1.24125 | −0.344261 | −0.172131 | − | 0.985074i | \(-0.555065\pi\) | ||||
−0.172131 | + | 0.985074i | \(0.555065\pi\) | |||||||
\(14\) | 2.69017 | 0.718978 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.9523 | 3.23807 | ||||||||
\(17\) | −5.98512 | −1.45161 | −0.725803 | − | 0.687903i | \(-0.758532\pi\) | ||||
−0.725803 | + | 0.687903i | \(0.758532\pi\) | |||||||
\(18\) | 7.87463 | 1.85607 | ||||||||
\(19\) | −3.38034 | −0.775503 | −0.387752 | − | 0.921764i | \(-0.626748\pi\) | ||||
−0.387752 | + | 0.921764i | \(0.626748\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.269842 | −0.0588844 | ||||||||
\(22\) | 10.1906 | 2.17265 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −2.34982 | −0.479655 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.33918 | 0.654867 | ||||||||
\(27\) | −1.59940 | −0.307805 | ||||||||
\(28\) | −5.23702 | −0.989703 | ||||||||
\(29\) | −7.02088 | −1.30374 | −0.651872 | − | 0.758329i | \(-0.726016\pi\) | ||||
−0.651872 | + | 0.758329i | \(0.726016\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.26984 | 1.12610 | 0.563048 | − | 0.826424i | \(-0.309628\pi\) | ||||
0.563048 | + | 0.826424i | \(0.309628\pi\) | |||||||
\(32\) | −17.4276 | −3.08080 | ||||||||
\(33\) | −1.02219 | −0.177940 | ||||||||
\(34\) | 16.1010 | 2.76130 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −15.3297 | −2.55495 | ||||||||
\(37\) | −4.84066 | −0.795799 | −0.397899 | − | 0.917429i | \(-0.630261\pi\) | ||||
−0.397899 | + | 0.917429i | \(0.630261\pi\) | |||||||
\(38\) | 9.09369 | 1.47519 | ||||||||
\(39\) | −0.334942 | −0.0536336 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.78094 | −0.278135 | −0.139068 | − | 0.990283i | \(-0.544411\pi\) | ||||
−0.139068 | + | 0.990283i | \(0.544411\pi\) | |||||||
\(42\) | 0.725921 | 0.112012 | ||||||||
\(43\) | −3.02219 | −0.460879 | −0.230440 | − | 0.973087i | \(-0.574016\pi\) | ||||
−0.230440 | + | 0.973087i | \(0.574016\pi\) | |||||||
\(44\) | −19.8383 | −2.99074 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.69017 | −0.396644 | ||||||||
\(47\) | −3.90322 | −0.569343 | −0.284671 | − | 0.958625i | \(-0.591884\pi\) | ||||
−0.284671 | + | 0.958625i | \(0.591884\pi\) | |||||||
\(48\) | 3.49508 | 0.504471 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.61504 | −0.226151 | ||||||||
\(52\) | −6.50046 | −0.901451 | ||||||||
\(53\) | 2.47403 | 0.339834 | 0.169917 | − | 0.985458i | \(-0.445650\pi\) | ||||
0.169917 | + | 0.985458i | \(0.445650\pi\) | |||||||
\(54\) | 4.30267 | 0.585519 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.70812 | 1.16367 | ||||||||
\(57\) | −0.912158 | −0.120818 | ||||||||
\(58\) | 18.8873 | 2.48003 | ||||||||
\(59\) | −2.89143 | −0.376433 | −0.188216 | − | 0.982128i | \(-0.560271\pi\) | ||||
−0.188216 | + | 0.982128i | \(0.560271\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.3518 | −1.32541 | −0.662703 | − | 0.748882i | \(-0.730591\pi\) | ||||
−0.662703 | + | 0.748882i | \(0.730591\pi\) | |||||||
\(62\) | −16.8669 | −2.14210 | ||||||||
\(63\) | 2.92719 | 0.368791 | ||||||||
\(64\) | 20.9787 | 2.62234 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.74986 | 0.338484 | ||||||||
\(67\) | −11.4466 | −1.39843 | −0.699213 | − | 0.714913i | \(-0.746466\pi\) | ||||
−0.699213 | + | 0.714913i | \(0.746466\pi\) | |||||||
\(68\) | −31.3442 | −3.80104 | ||||||||
\(69\) | 0.269842 | 0.0324852 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.70157 | 0.320617 | 0.160309 | − | 0.987067i | \(-0.448751\pi\) | ||||
0.160309 | + | 0.987067i | \(0.448751\pi\) | |||||||
\(72\) | 25.4903 | 3.00406 | ||||||||
\(73\) | 14.1893 | 1.66073 | 0.830367 | − | 0.557217i | \(-0.188131\pi\) | ||||
0.830367 | + | 0.557217i | \(0.188131\pi\) | |||||||
\(74\) | 13.0222 | 1.51380 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −17.7029 | −2.03066 | ||||||||
\(77\) | 3.78810 | 0.431694 | ||||||||
\(78\) | 0.901051 | 0.102024 | ||||||||
\(79\) | 3.31407 | 0.372862 | 0.186431 | − | 0.982468i | \(-0.440308\pi\) | ||||
0.186431 | + | 0.982468i | \(0.440308\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.34997 | 0.927774 | ||||||||
\(82\) | 4.79102 | 0.529080 | ||||||||
\(83\) | −7.02219 | −0.770785 | −0.385393 | − | 0.922753i | \(-0.625934\pi\) | ||||
−0.385393 | + | 0.922753i | \(0.625934\pi\) | |||||||
\(84\) | −1.41317 | −0.154189 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.13020 | 0.876702 | ||||||||
\(87\) | −1.89453 | −0.203115 | ||||||||
\(88\) | 32.9872 | 3.51645 | ||||||||
\(89\) | −1.59107 | −0.168653 | −0.0843265 | − | 0.996438i | \(-0.526874\pi\) | ||||
−0.0843265 | + | 0.996438i | \(0.526874\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.24125 | 0.130119 | ||||||||
\(92\) | 5.23702 | 0.545997 | ||||||||
\(93\) | 1.69187 | 0.175438 | ||||||||
\(94\) | 10.5003 | 1.08302 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.70271 | −0.479968 | ||||||||
\(97\) | 11.6270 | 1.18054 | 0.590270 | − | 0.807206i | \(-0.299021\pi\) | ||||
0.590270 | + | 0.807206i | \(0.299021\pi\) | |||||||
\(98\) | −2.69017 | −0.271748 | ||||||||
\(99\) | 11.0885 | 1.11443 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.366626 | −0.0364806 | −0.0182403 | − | 0.999834i | \(-0.505806\pi\) | ||||
−0.0182403 | + | 0.999834i | \(0.505806\pi\) | |||||||
\(102\) | 4.34473 | 0.430192 | ||||||||
\(103\) | 0.474030 | 0.0467076 | 0.0233538 | − | 0.999727i | \(-0.492566\pi\) | ||||
0.0233538 | + | 0.999727i | \(0.492566\pi\) | |||||||
\(104\) | 10.8090 | 1.05991 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.65556 | −0.646445 | ||||||||
\(107\) | 5.74697 | 0.555580 | 0.277790 | − | 0.960642i | \(-0.410398\pi\) | ||||
0.277790 | + | 0.960642i | \(0.410398\pi\) | |||||||
\(108\) | −8.37610 | −0.805991 | ||||||||
\(109\) | 15.4877 | 1.48346 | 0.741728 | − | 0.670700i | \(-0.234006\pi\) | ||||
0.741728 | + | 0.670700i | \(0.234006\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.30621 | −0.123980 | ||||||||
\(112\) | −12.9523 | −1.22388 | ||||||||
\(113\) | 4.48250 | 0.421678 | 0.210839 | − | 0.977521i | \(-0.432380\pi\) | ||||
0.210839 | + | 0.977521i | \(0.432380\pi\) | |||||||
\(114\) | 2.45386 | 0.229825 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −36.7684 | −3.41386 | ||||||||
\(117\) | 3.63337 | 0.335906 | ||||||||
\(118\) | 7.77845 | 0.716064 | ||||||||
\(119\) | 5.98512 | 0.548655 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.34968 | 0.304516 | ||||||||
\(122\) | 27.8480 | 2.52124 | ||||||||
\(123\) | −0.480572 | −0.0433317 | ||||||||
\(124\) | 32.8353 | 2.94869 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −7.87463 | −0.701527 | ||||||||
\(127\) | 2.13061 | 0.189061 | 0.0945307 | − | 0.995522i | \(-0.469865\pi\) | ||||
0.0945307 | + | 0.995522i | \(0.469865\pi\) | |||||||
\(128\) | −21.5811 | −1.90751 | ||||||||
\(129\) | −0.815514 | −0.0718020 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.1242 | −1.58352 | −0.791760 | − | 0.610832i | \(-0.790835\pi\) | ||||
−0.791760 | + | 0.610832i | \(0.790835\pi\) | |||||||
\(132\) | −5.35321 | −0.465937 | ||||||||
\(133\) | 3.38034 | 0.293113 | ||||||||
\(134\) | 30.7933 | 2.66014 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 52.1192 | 4.46918 | ||||||||
\(137\) | 15.3062 | 1.30770 | 0.653849 | − | 0.756625i | \(-0.273153\pi\) | ||||
0.653849 | + | 0.756625i | \(0.273153\pi\) | |||||||
\(138\) | −0.725921 | −0.0617945 | ||||||||
\(139\) | 13.5273 | 1.14737 | 0.573687 | − | 0.819074i | \(-0.305512\pi\) | ||||
0.573687 | + | 0.819074i | \(0.305512\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.05325 | −0.0886998 | ||||||||
\(142\) | −7.26768 | −0.609890 | ||||||||
\(143\) | 4.70198 | 0.393200 | ||||||||
\(144\) | −37.9138 | −3.15948 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −38.1717 | −3.15911 | ||||||||
\(147\) | 0.269842 | 0.0222562 | ||||||||
\(148\) | −25.3506 | −2.08381 | ||||||||
\(149\) | 5.75773 | 0.471691 | 0.235846 | − | 0.971791i | \(-0.424214\pi\) | ||||
0.235846 | + | 0.971791i | \(0.424214\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.57813 | −0.779457 | −0.389728 | − | 0.920930i | \(-0.627431\pi\) | ||||
−0.389728 | + | 0.920930i | \(0.627431\pi\) | |||||||
\(152\) | 29.4364 | 2.38761 | ||||||||
\(153\) | 17.5196 | 1.41637 | ||||||||
\(154\) | −10.1906 | −0.821184 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.75410 | −0.140440 | ||||||||
\(157\) | 5.03706 | 0.402001 | 0.201001 | − | 0.979591i | \(-0.435581\pi\) | ||||
0.201001 | + | 0.979591i | \(0.435581\pi\) | |||||||
\(158\) | −8.91540 | −0.709271 | ||||||||
\(159\) | 0.667598 | 0.0529439 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | −22.4628 | −1.76485 | ||||||||
\(163\) | 7.35713 | 0.576255 | 0.288127 | − | 0.957592i | \(-0.406967\pi\) | ||||
0.288127 | + | 0.957592i | \(0.406967\pi\) | |||||||
\(164\) | −9.32679 | −0.728300 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 18.8909 | 1.46622 | ||||||||
\(167\) | −20.9904 | −1.62428 | −0.812142 | − | 0.583460i | \(-0.801698\pi\) | ||||
−0.812142 | + | 0.583460i | \(0.801698\pi\) | |||||||
\(168\) | 2.34982 | 0.181292 | ||||||||
\(169\) | −11.4593 | −0.881484 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.89488 | 0.756681 | ||||||||
\(172\) | −15.8272 | −1.20682 | ||||||||
\(173\) | 12.3369 | 0.937955 | 0.468978 | − | 0.883210i | \(-0.344622\pi\) | ||||
0.468978 | + | 0.883210i | \(0.344622\pi\) | |||||||
\(174\) | 5.09660 | 0.386372 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −49.0646 | −3.69838 | ||||||||
\(177\) | −0.780231 | −0.0586457 | ||||||||
\(178\) | 4.28025 | 0.320818 | ||||||||
\(179\) | −12.9082 | −0.964807 | −0.482404 | − | 0.875949i | \(-0.660236\pi\) | ||||
−0.482404 | + | 0.875949i | \(0.660236\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.86925 | −0.436258 | −0.218129 | − | 0.975920i | \(-0.569995\pi\) | ||||
−0.218129 | + | 0.975920i | \(0.569995\pi\) | |||||||
\(182\) | −3.33918 | −0.247516 | ||||||||
\(183\) | −2.79334 | −0.206489 | ||||||||
\(184\) | −8.70812 | −0.641971 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.55141 | −0.333726 | ||||||||
\(187\) | 22.6722 | 1.65796 | ||||||||
\(188\) | −20.4412 | −1.49083 | ||||||||
\(189\) | 1.59940 | 0.116340 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.9343 | 0.863539 | 0.431769 | − | 0.901984i | \(-0.357889\pi\) | ||||
0.431769 | + | 0.901984i | \(0.357889\pi\) | |||||||
\(192\) | 5.66094 | 0.408543 | ||||||||
\(193\) | −0.752900 | −0.0541949 | −0.0270975 | − | 0.999633i | \(-0.508626\pi\) | ||||
−0.0270975 | + | 0.999633i | \(0.508626\pi\) | |||||||
\(194\) | −31.2785 | −2.24567 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.23702 | 0.374073 | ||||||||
\(197\) | −25.4074 | −1.81020 | −0.905100 | − | 0.425200i | \(-0.860204\pi\) | ||||
−0.905100 | + | 0.425200i | \(0.860204\pi\) | |||||||
\(198\) | −29.8298 | −2.11991 | ||||||||
\(199\) | 15.1988 | 1.07741 | 0.538707 | − | 0.842493i | \(-0.318913\pi\) | ||||
0.538707 | + | 0.842493i | \(0.318913\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.08878 | −0.217866 | ||||||||
\(202\) | 0.986286 | 0.0693948 | ||||||||
\(203\) | 7.02088 | 0.492769 | ||||||||
\(204\) | −8.45798 | −0.592177 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.27522 | −0.0888489 | ||||||||
\(207\) | −2.92719 | −0.203453 | ||||||||
\(208\) | −16.0771 | −1.11474 | ||||||||
\(209\) | 12.8051 | 0.885744 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.2797 | −1.67148 | −0.835742 | − | 0.549123i | \(-0.814962\pi\) | ||||
−0.835742 | + | 0.549123i | \(0.814962\pi\) | |||||||
\(212\) | 12.9565 | 0.889858 | ||||||||
\(213\) | 0.728997 | 0.0499500 | ||||||||
\(214\) | −15.4603 | −1.05685 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 13.9278 | 0.947667 | ||||||||
\(217\) | −6.26984 | −0.425625 | ||||||||
\(218\) | −41.6647 | −2.82189 | ||||||||
\(219\) | 3.82887 | 0.258731 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.42905 | 0.499732 | ||||||||
\(222\) | 3.51393 | 0.235840 | ||||||||
\(223\) | −17.7344 | −1.18758 | −0.593791 | − | 0.804619i | \(-0.702369\pi\) | ||||
−0.593791 | + | 0.804619i | \(0.702369\pi\) | |||||||
\(224\) | 17.4276 | 1.16443 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.0587 | −0.802133 | ||||||||
\(227\) | 15.7087 | 1.04263 | 0.521313 | − | 0.853366i | \(-0.325442\pi\) | ||||
0.521313 | + | 0.853366i | \(0.325442\pi\) | |||||||
\(228\) | −4.77699 | −0.316364 | ||||||||
\(229\) | −4.51633 | −0.298448 | −0.149224 | − | 0.988803i | \(-0.547678\pi\) | ||||
−0.149224 | + | 0.988803i | \(0.547678\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.02219 | 0.0672550 | ||||||||
\(232\) | 61.1386 | 4.01395 | ||||||||
\(233\) | 16.2641 | 1.06549 | 0.532747 | − | 0.846275i | \(-0.321160\pi\) | ||||
0.532747 | + | 0.846275i | \(0.321160\pi\) | |||||||
\(234\) | −9.77439 | −0.638972 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −15.1425 | −0.985692 | ||||||||
\(237\) | 0.894275 | 0.0580894 | ||||||||
\(238\) | −16.1010 | −1.04367 | ||||||||
\(239\) | 2.14756 | 0.138914 | 0.0694571 | − | 0.997585i | \(-0.477873\pi\) | ||||
0.0694571 | + | 0.997585i | \(0.477873\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.4676 | 0.803111 | 0.401555 | − | 0.915835i | \(-0.368470\pi\) | ||||
0.401555 | + | 0.915835i | \(0.368470\pi\) | |||||||
\(242\) | −9.01121 | −0.579262 | ||||||||
\(243\) | 7.05139 | 0.452347 | ||||||||
\(244\) | −54.2123 | −3.47059 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.29282 | 0.0824271 | ||||||||
\(247\) | 4.19585 | 0.266976 | ||||||||
\(248\) | −54.5985 | −3.46701 | ||||||||
\(249\) | −1.89488 | −0.120083 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.91478 | 0.310218 | 0.155109 | − | 0.987897i | \(-0.450427\pi\) | ||||
0.155109 | + | 0.987897i | \(0.450427\pi\) | |||||||
\(252\) | 15.3297 | 0.965681 | ||||||||
\(253\) | −3.78810 | −0.238156 | ||||||||
\(254\) | −5.73172 | −0.359640 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0993 | 1.00620 | ||||||||
\(257\) | −28.4782 | −1.77642 | −0.888212 | − | 0.459433i | \(-0.848052\pi\) | ||||
−0.888212 | + | 0.459433i | \(0.848052\pi\) | |||||||
\(258\) | 2.19387 | 0.136584 | ||||||||
\(259\) | 4.84066 | 0.300784 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.5514 | 1.27210 | ||||||||
\(262\) | 48.7572 | 3.01223 | ||||||||
\(263\) | −1.89322 | −0.116741 | −0.0583703 | − | 0.998295i | \(-0.518590\pi\) | ||||
−0.0583703 | + | 0.998295i | \(0.518590\pi\) | |||||||
\(264\) | 8.90134 | 0.547839 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.09369 | −0.557570 | ||||||||
\(267\) | −0.429338 | −0.0262750 | ||||||||
\(268\) | −59.9461 | −3.66179 | ||||||||
\(269\) | −2.51156 | −0.153133 | −0.0765663 | − | 0.997064i | \(-0.524396\pi\) | ||||
−0.0765663 | + | 0.997064i | \(0.524396\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.1098 | 1.52531 | 0.762656 | − | 0.646804i | \(-0.223895\pi\) | ||||
0.762656 | + | 0.646804i | \(0.223895\pi\) | |||||||
\(272\) | −77.5211 | −4.70041 | ||||||||
\(273\) | 0.334942 | 0.0202716 | ||||||||
\(274\) | −41.1763 | −2.48755 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.41317 | 0.0850627 | ||||||||
\(277\) | −9.48643 | −0.569984 | −0.284992 | − | 0.958530i | \(-0.591991\pi\) | ||||
−0.284992 | + | 0.958530i | \(0.591991\pi\) | |||||||
\(278\) | −36.3909 | −2.18258 | ||||||||
\(279\) | −18.3530 | −1.09876 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.71197 | 0.519713 | 0.259856 | − | 0.965647i | \(-0.416325\pi\) | ||||
0.259856 | + | 0.965647i | \(0.416325\pi\) | |||||||
\(282\) | 2.83343 | 0.168728 | ||||||||
\(283\) | −30.5543 | −1.81627 | −0.908133 | − | 0.418683i | \(-0.862492\pi\) | ||||
−0.908133 | + | 0.418683i | \(0.862492\pi\) | |||||||
\(284\) | 14.1482 | 0.839538 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.6491 | −0.747959 | ||||||||
\(287\) | 1.78094 | 0.105125 | ||||||||
\(288\) | 51.0139 | 3.00602 | ||||||||
\(289\) | 18.8217 | 1.10716 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.13745 | 0.183920 | ||||||||
\(292\) | 74.3096 | 4.34864 | ||||||||
\(293\) | −12.7063 | −0.742312 | −0.371156 | − | 0.928570i | \(-0.621039\pi\) | ||||
−0.371156 | + | 0.928570i | \(0.621039\pi\) | |||||||
\(294\) | −0.725921 | −0.0423366 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 42.1530 | 2.45009 | ||||||||
\(297\) | 6.05870 | 0.351561 | ||||||||
\(298\) | −15.4893 | −0.897269 | ||||||||
\(299\) | −1.24125 | −0.0717835 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.02219 | 0.174196 | ||||||||
\(302\) | 25.7668 | 1.48271 | ||||||||
\(303\) | −0.0989310 | −0.00568344 | ||||||||
\(304\) | −43.7832 | −2.51114 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −47.1306 | −2.69428 | ||||||||
\(307\) | −22.1153 | −1.26219 | −0.631094 | − | 0.775706i | \(-0.717394\pi\) | ||||
−0.631094 | + | 0.775706i | \(0.717394\pi\) | |||||||
\(308\) | 19.8383 | 1.13039 | ||||||||
\(309\) | 0.127913 | 0.00727673 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.3945 | 1.21317 | 0.606586 | − | 0.795018i | \(-0.292539\pi\) | ||||
0.606586 | + | 0.795018i | \(0.292539\pi\) | |||||||
\(312\) | 2.91672 | 0.165127 | ||||||||
\(313\) | 29.9051 | 1.69034 | 0.845169 | − | 0.534498i | \(-0.179499\pi\) | ||||
0.845169 | + | 0.534498i | \(0.179499\pi\) | |||||||
\(314\) | −13.5506 | −0.764702 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.3558 | 0.976341 | ||||||||
\(317\) | −7.06103 | −0.396587 | −0.198294 | − | 0.980143i | \(-0.563540\pi\) | ||||
−0.198294 | + | 0.980143i | \(0.563540\pi\) | |||||||
\(318\) | −1.79595 | −0.100712 | ||||||||
\(319\) | 26.5958 | 1.48908 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.55077 | 0.0865557 | ||||||||
\(322\) | 2.69017 | 0.149917 | ||||||||
\(323\) | 20.2318 | 1.12573 | ||||||||
\(324\) | 43.7289 | 2.42938 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −19.7919 | −1.09617 | ||||||||
\(327\) | 4.17925 | 0.231113 | ||||||||
\(328\) | 15.5086 | 0.856320 | ||||||||
\(329\) | 3.90322 | 0.215191 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.2063 | 0.890777 | 0.445388 | − | 0.895338i | \(-0.353066\pi\) | ||||
0.445388 | + | 0.895338i | \(0.353066\pi\) | |||||||
\(332\) | −36.7753 | −2.01831 | ||||||||
\(333\) | 14.1695 | 0.776484 | ||||||||
\(334\) | 56.4677 | 3.08977 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.49508 | −0.190672 | ||||||||
\(337\) | −5.21804 | −0.284245 | −0.142122 | − | 0.989849i | \(-0.545393\pi\) | ||||
−0.142122 | + | 0.989849i | \(0.545393\pi\) | |||||||
\(338\) | 30.8274 | 1.67679 | ||||||||
\(339\) | 1.20957 | 0.0656947 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.7508 | −1.28618 | ||||||||
\(342\) | −26.6189 | −1.43939 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 26.3176 | 1.41895 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −33.1883 | −1.78421 | ||||||||
\(347\) | −4.19094 | −0.224982 | −0.112491 | − | 0.993653i | \(-0.535883\pi\) | ||||
−0.112491 | + | 0.993653i | \(0.535883\pi\) | |||||||
\(348\) | −9.92167 | −0.531857 | ||||||||
\(349\) | −18.6611 | −0.998903 | −0.499452 | − | 0.866342i | \(-0.666465\pi\) | ||||
−0.499452 | + | 0.866342i | \(0.666465\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.98526 | 0.105966 | ||||||||
\(352\) | 66.0176 | 3.51875 | ||||||||
\(353\) | 11.5781 | 0.616241 | 0.308121 | − | 0.951347i | \(-0.400300\pi\) | ||||
0.308121 | + | 0.951347i | \(0.400300\pi\) | |||||||
\(354\) | 2.09895 | 0.111558 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8.33246 | −0.441619 | ||||||||
\(357\) | 1.61504 | 0.0854769 | ||||||||
\(358\) | 34.7254 | 1.83529 | ||||||||
\(359\) | 29.4910 | 1.55647 | 0.778237 | − | 0.627970i | \(-0.216114\pi\) | ||||
0.778237 | + | 0.627970i | \(0.216114\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.57330 | −0.398595 | ||||||||
\(362\) | 15.7893 | 0.829866 | ||||||||
\(363\) | 0.903884 | 0.0474416 | ||||||||
\(364\) | 6.50046 | 0.340716 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.51455 | 0.392792 | ||||||||
\(367\) | 24.7858 | 1.29381 | 0.646903 | − | 0.762572i | \(-0.276064\pi\) | ||||
0.646903 | + | 0.762572i | \(0.276064\pi\) | |||||||
\(368\) | 12.9523 | 0.675185 | ||||||||
\(369\) | 5.21313 | 0.271385 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.47403 | −0.128445 | ||||||||
\(372\) | 8.86033 | 0.459387 | ||||||||
\(373\) | −17.1524 | −0.888117 | −0.444058 | − | 0.895998i | \(-0.646462\pi\) | ||||
−0.444058 | + | 0.895998i | \(0.646462\pi\) | |||||||
\(374\) | −60.9922 | −3.15383 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 33.9897 | 1.75288 | ||||||||
\(377\) | 8.71467 | 0.448829 | ||||||||
\(378\) | −4.30267 | −0.221305 | ||||||||
\(379\) | 32.8211 | 1.68591 | 0.842953 | − | 0.537986i | \(-0.180815\pi\) | ||||
0.842953 | + | 0.537986i | \(0.180815\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.574930 | 0.0294545 | ||||||||
\(382\) | −32.1054 | −1.64266 | ||||||||
\(383\) | 8.42609 | 0.430553 | 0.215277 | − | 0.976553i | \(-0.430935\pi\) | ||||
0.215277 | + | 0.976553i | \(0.430935\pi\) | |||||||
\(384\) | −5.82348 | −0.297178 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.02543 | 0.103092 | ||||||||
\(387\) | 8.84650 | 0.449693 | ||||||||
\(388\) | 60.8906 | 3.09125 | ||||||||
\(389\) | −25.3004 | −1.28278 | −0.641390 | − | 0.767215i | \(-0.721642\pi\) | ||||
−0.641390 | + | 0.767215i | \(0.721642\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.98512 | −0.302681 | ||||||||
\(392\) | −8.70812 | −0.439827 | ||||||||
\(393\) | −4.89068 | −0.246702 | ||||||||
\(394\) | 68.3501 | 3.44343 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 58.0704 | 2.91815 | ||||||||
\(397\) | −20.3650 | −1.02209 | −0.511045 | − | 0.859554i | \(-0.670741\pi\) | ||||
−0.511045 | + | 0.859554i | \(0.670741\pi\) | |||||||
\(398\) | −40.8874 | −2.04950 | ||||||||
\(399\) | 0.912158 | 0.0456650 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.10277 | 0.204883 | 0.102441 | − | 0.994739i | \(-0.467335\pi\) | ||||
0.102441 | + | 0.994739i | \(0.467335\pi\) | |||||||
\(402\) | 8.30934 | 0.414432 | ||||||||
\(403\) | −7.78245 | −0.387672 | ||||||||
\(404\) | −1.92002 | −0.0955248 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.8873 | −0.937363 | ||||||||
\(407\) | 18.3369 | 0.908925 | ||||||||
\(408\) | 14.0640 | 0.696269 | ||||||||
\(409\) | −26.8449 | −1.32739 | −0.663697 | − | 0.748002i | \(-0.731013\pi\) | ||||
−0.663697 | + | 0.748002i | \(0.731013\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.13026 | 0.203731 | ||||||||
\(412\) | 2.48250 | 0.122304 | ||||||||
\(413\) | 2.89143 | 0.142278 | ||||||||
\(414\) | 7.87463 | 0.387017 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 21.6321 | 1.06060 | ||||||||
\(417\) | 3.65025 | 0.178753 | ||||||||
\(418\) | −34.4478 | −1.68490 | ||||||||
\(419\) | 0.149494 | 0.00730327 | 0.00365163 | − | 0.999993i | \(-0.498838\pi\) | ||||
0.00365163 | + | 0.999993i | \(0.498838\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.5269 | −0.513049 | −0.256524 | − | 0.966538i | \(-0.582577\pi\) | ||||
−0.256524 | + | 0.966538i | \(0.582577\pi\) | |||||||
\(422\) | 65.3165 | 3.17956 | ||||||||
\(423\) | 11.4254 | 0.555524 | ||||||||
\(424\) | −21.5442 | −1.04628 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.96113 | −0.0950168 | ||||||||
\(427\) | 10.3518 | 0.500956 | ||||||||
\(428\) | 30.0969 | 1.45479 | ||||||||
\(429\) | 1.26879 | 0.0612579 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.28665 | −0.110144 | −0.0550720 | − | 0.998482i | \(-0.517539\pi\) | ||||
−0.0550720 | + | 0.998482i | \(0.517539\pi\) | |||||||
\(432\) | −20.7160 | −0.996697 | ||||||||
\(433\) | 20.4569 | 0.983094 | 0.491547 | − | 0.870851i | \(-0.336432\pi\) | ||||
0.491547 | + | 0.870851i | \(0.336432\pi\) | |||||||
\(434\) | 16.8669 | 0.809639 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 81.1096 | 3.88444 | ||||||||
\(437\) | −3.38034 | −0.161704 | ||||||||
\(438\) | −10.3003 | −0.492168 | ||||||||
\(439\) | 8.93821 | 0.426597 | 0.213299 | − | 0.976987i | \(-0.431579\pi\) | ||||
0.213299 | + | 0.976987i | \(0.431579\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.92719 | −0.139390 | ||||||||
\(442\) | −19.9854 | −0.950609 | ||||||||
\(443\) | 6.71589 | 0.319082 | 0.159541 | − | 0.987191i | \(-0.448999\pi\) | ||||
0.159541 | + | 0.987191i | \(0.448999\pi\) | |||||||
\(444\) | −6.84066 | −0.324643 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 47.7085 | 2.25906 | ||||||||
\(447\) | 1.55368 | 0.0734864 | ||||||||
\(448\) | −20.9787 | −0.991151 | ||||||||
\(449\) | 39.7178 | 1.87440 | 0.937200 | − | 0.348792i | \(-0.113408\pi\) | ||||
0.937200 | + | 0.348792i | \(0.113408\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.74636 | 0.317674 | ||||||||
\(452\) | 23.4749 | 1.10417 | ||||||||
\(453\) | −2.58458 | −0.121434 | ||||||||
\(454\) | −42.2592 | −1.98332 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.94318 | 0.371974 | ||||||||
\(457\) | 35.7388 | 1.67179 | 0.835895 | − | 0.548889i | \(-0.184949\pi\) | ||||
0.835895 | + | 0.548889i | \(0.184949\pi\) | |||||||
\(458\) | 12.1497 | 0.567719 | ||||||||
\(459\) | 9.57263 | 0.446812 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.3516 | −0.854720 | −0.427360 | − | 0.904082i | \(-0.640556\pi\) | ||||
−0.427360 | + | 0.904082i | \(0.640556\pi\) | |||||||
\(462\) | −2.74986 | −0.127935 | ||||||||
\(463\) | −11.1821 | −0.519678 | −0.259839 | − | 0.965652i | \(-0.583670\pi\) | ||||
−0.259839 | + | 0.965652i | \(0.583670\pi\) | |||||||
\(464\) | −90.9365 | −4.22162 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −43.7531 | −2.02682 | ||||||||
\(467\) | −31.7231 | −1.46797 | −0.733984 | − | 0.679167i | \(-0.762341\pi\) | ||||
−0.733984 | + | 0.679167i | \(0.762341\pi\) | |||||||
\(468\) | 19.0280 | 0.879571 | ||||||||
\(469\) | 11.4466 | 0.528556 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.35921 | 0.0626292 | ||||||||
\(472\) | 25.1790 | 1.15896 | ||||||||
\(473\) | 11.4483 | 0.526395 | ||||||||
\(474\) | −2.40575 | −0.110500 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 31.3442 | 1.43666 | ||||||||
\(477\) | −7.24194 | −0.331586 | ||||||||
\(478\) | −5.77731 | −0.264248 | ||||||||
\(479\) | −9.81725 | −0.448562 | −0.224281 | − | 0.974525i | \(-0.572003\pi\) | ||||
−0.224281 | + | 0.974525i | \(0.572003\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.00847 | 0.273963 | ||||||||
\(482\) | −33.5400 | −1.52771 | ||||||||
\(483\) | −0.269842 | −0.0122782 | ||||||||
\(484\) | 17.5423 | 0.797378 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −18.9694 | −0.860471 | ||||||||
\(487\) | 36.2778 | 1.64390 | 0.821952 | − | 0.569557i | \(-0.192885\pi\) | ||||
0.821952 | + | 0.569557i | \(0.192885\pi\) | |||||||
\(488\) | 90.1443 | 4.08064 | ||||||||
\(489\) | 1.98526 | 0.0897767 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.6053 | −0.794514 | −0.397257 | − | 0.917707i | \(-0.630038\pi\) | ||||
−0.397257 | + | 0.917707i | \(0.630038\pi\) | |||||||
\(492\) | −2.51676 | −0.113464 | ||||||||
\(493\) | 42.0208 | 1.89252 | ||||||||
\(494\) | −11.2876 | −0.507851 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 81.2089 | 3.64639 | ||||||||
\(497\) | −2.70157 | −0.121182 | ||||||||
\(498\) | 5.09755 | 0.228427 | ||||||||
\(499\) | 12.1142 | 0.542308 | 0.271154 | − | 0.962536i | \(-0.412595\pi\) | ||||
0.271154 | + | 0.962536i | \(0.412595\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.66408 | −0.253053 | ||||||||
\(502\) | −13.2216 | −0.590109 | ||||||||
\(503\) | −10.2723 | −0.458020 | −0.229010 | − | 0.973424i | \(-0.573549\pi\) | ||||
−0.229010 | + | 0.973424i | \(0.573549\pi\) | |||||||
\(504\) | −25.4903 | −1.13543 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.1906 | 0.453029 | ||||||||
\(507\) | −3.09220 | −0.137329 | ||||||||
\(508\) | 11.1581 | 0.495059 | ||||||||
\(509\) | −6.45082 | −0.285928 | −0.142964 | − | 0.989728i | \(-0.545663\pi\) | ||||
−0.142964 | + | 0.989728i | \(0.545663\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.1893 | −0.627698 | ||||||||
\(512\) | −0.147625 | −0.00652419 | ||||||||
\(513\) | 5.40653 | 0.238704 | ||||||||
\(514\) | 76.6113 | 3.37918 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.27086 | −0.188014 | ||||||||
\(517\) | 14.7858 | 0.650277 | ||||||||
\(518\) | −13.0222 | −0.572162 | ||||||||
\(519\) | 3.32901 | 0.146127 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.4858 | 1.51085 | 0.755425 | − | 0.655235i | \(-0.227430\pi\) | ||||
0.755425 | + | 0.655235i | \(0.227430\pi\) | |||||||
\(522\) | −55.2868 | −2.41984 | ||||||||
\(523\) | 25.7852 | 1.12751 | 0.563753 | − | 0.825943i | \(-0.309357\pi\) | ||||
0.563753 | + | 0.825943i | \(0.309357\pi\) | |||||||
\(524\) | −94.9168 | −4.14646 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.09307 | 0.222068 | ||||||||
\(527\) | −37.5258 | −1.63465 | ||||||||
\(528\) | −13.2397 | −0.576183 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.46376 | 0.367296 | ||||||||
\(532\) | 17.7029 | 0.767518 | ||||||||
\(533\) | 2.21059 | 0.0957513 | ||||||||
\(534\) | 1.15499 | 0.0499814 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 99.6785 | 4.30546 | ||||||||
\(537\) | −3.48319 | −0.150311 | ||||||||
\(538\) | 6.75653 | 0.291295 | ||||||||
\(539\) | −3.78810 | −0.163165 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.1475 | −0.909203 | −0.454601 | − | 0.890695i | \(-0.650218\pi\) | ||||
−0.454601 | + | 0.890695i | \(0.650218\pi\) | |||||||
\(542\) | −67.5496 | −2.90151 | ||||||||
\(543\) | −1.58377 | −0.0679661 | ||||||||
\(544\) | 104.307 | 4.47211 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.901051 | −0.0385614 | ||||||||
\(547\) | 3.97188 | 0.169825 | 0.0849126 | − | 0.996388i | \(-0.472939\pi\) | ||||
0.0849126 | + | 0.996388i | \(0.472939\pi\) | |||||||
\(548\) | 80.1589 | 3.42422 | ||||||||
\(549\) | 30.3015 | 1.29324 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.7329 | 1.01106 | ||||||||
\(552\) | −2.34982 | −0.100015 | ||||||||
\(553\) | −3.31407 | −0.140928 | ||||||||
\(554\) | 25.5201 | 1.08425 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 70.8429 | 3.00441 | ||||||||
\(557\) | 13.5585 | 0.574491 | 0.287246 | − | 0.957857i | \(-0.407260\pi\) | ||||
0.287246 | + | 0.957857i | \(0.407260\pi\) | |||||||
\(558\) | 49.3727 | 2.09011 | ||||||||
\(559\) | 3.75130 | 0.158663 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.11792 | 0.258299 | ||||||||
\(562\) | −23.4367 | −0.988617 | ||||||||
\(563\) | 32.4740 | 1.36862 | 0.684309 | − | 0.729193i | \(-0.260104\pi\) | ||||
0.684309 | + | 0.729193i | \(0.260104\pi\) | |||||||
\(564\) | −5.51590 | −0.232261 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 82.1963 | 3.45497 | ||||||||
\(567\) | −8.34997 | −0.350666 | ||||||||
\(568\) | −23.5256 | −0.987111 | ||||||||
\(569\) | −26.7707 | −1.12228 | −0.561142 | − | 0.827719i | \(-0.689638\pi\) | ||||
−0.561142 | + | 0.827719i | \(0.689638\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.30884 | 0.222168 | 0.111084 | − | 0.993811i | \(-0.464568\pi\) | ||||
0.111084 | + | 0.993811i | \(0.464568\pi\) | |||||||
\(572\) | 24.6244 | 1.02960 | ||||||||
\(573\) | 3.22039 | 0.134534 | ||||||||
\(574\) | −4.79102 | −0.199973 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −61.4086 | −2.55869 | ||||||||
\(577\) | −43.9737 | −1.83065 | −0.915325 | − | 0.402717i | \(-0.868066\pi\) | ||||
−0.915325 | + | 0.402717i | \(0.868066\pi\) | |||||||
\(578\) | −50.6336 | −2.10608 | ||||||||
\(579\) | −0.203164 | −0.00844321 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.02219 | 0.291329 | ||||||||
\(582\) | −8.44026 | −0.349860 | ||||||||
\(583\) | −9.37187 | −0.388143 | ||||||||
\(584\) | −123.562 | −5.11304 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 34.1822 | 1.41205 | ||||||||
\(587\) | 34.5314 | 1.42526 | 0.712631 | − | 0.701539i | \(-0.247503\pi\) | ||||
0.712631 | + | 0.701539i | \(0.247503\pi\) | |||||||
\(588\) | 1.41317 | 0.0582780 | ||||||||
\(589\) | −21.1942 | −0.873292 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.85597 | −0.282017 | ||||||||
\(592\) | −62.6976 | −2.57686 | ||||||||
\(593\) | −2.06074 | −0.0846245 | −0.0423123 | − | 0.999104i | \(-0.513472\pi\) | ||||
−0.0423123 | + | 0.999104i | \(0.513472\pi\) | |||||||
\(594\) | −16.2989 | −0.668753 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 30.1533 | 1.23513 | ||||||||
\(597\) | 4.10128 | 0.167854 | ||||||||
\(598\) | 3.33918 | 0.136549 | ||||||||
\(599\) | −28.2627 | −1.15478 | −0.577392 | − | 0.816467i | \(-0.695930\pi\) | ||||
−0.577392 | + | 0.816467i | \(0.695930\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.0036 | −1.01992 | −0.509959 | − | 0.860199i | \(-0.670340\pi\) | ||||
−0.509959 | + | 0.860199i | \(0.670340\pi\) | |||||||
\(602\) | −8.13020 | −0.331362 | ||||||||
\(603\) | 33.5064 | 1.36448 | ||||||||
\(604\) | −50.1608 | −2.04101 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.266141 | 0.0108113 | ||||||||
\(607\) | 29.0255 | 1.17811 | 0.589054 | − | 0.808093i | \(-0.299500\pi\) | ||||
0.589054 | + | 0.808093i | \(0.299500\pi\) | |||||||
\(608\) | 58.9114 | 2.38917 | ||||||||
\(609\) | 1.89453 | 0.0767701 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.84487 | 0.196003 | ||||||||
\(612\) | 91.7502 | 3.70878 | ||||||||
\(613\) | 25.2180 | 1.01855 | 0.509274 | − | 0.860605i | \(-0.329914\pi\) | ||||
0.509274 | + | 0.860605i | \(0.329914\pi\) | |||||||
\(614\) | 59.4940 | 2.40098 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −32.9872 | −1.32909 | ||||||||
\(617\) | −41.7462 | −1.68064 | −0.840319 | − | 0.542093i | \(-0.817632\pi\) | ||||
−0.840319 | + | 0.542093i | \(0.817632\pi\) | |||||||
\(618\) | −0.344109 | −0.0138421 | ||||||||
\(619\) | −0.503782 | −0.0202487 | −0.0101243 | − | 0.999949i | \(-0.503223\pi\) | ||||
−0.0101243 | + | 0.999949i | \(0.503223\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.59940 | −0.0641819 | ||||||||
\(622\) | −57.5549 | −2.30774 | ||||||||
\(623\) | 1.59107 | 0.0637449 | ||||||||
\(624\) | −4.33827 | −0.173670 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −80.4499 | −3.21543 | ||||||||
\(627\) | 3.45534 | 0.137993 | ||||||||
\(628\) | 26.3792 | 1.05264 | ||||||||
\(629\) | 28.9719 | 1.15519 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.6868 | −0.704102 | −0.352051 | − | 0.935981i | \(-0.614516\pi\) | ||||
−0.352051 | + | 0.935981i | \(0.614516\pi\) | |||||||
\(632\) | −28.8593 | −1.14796 | ||||||||
\(633\) | −6.55168 | −0.260406 | ||||||||
\(634\) | 18.9954 | 0.754403 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.49622 | 0.138634 | ||||||||
\(637\) | −1.24125 | −0.0491802 | ||||||||
\(638\) | −71.5471 | −2.83258 | ||||||||
\(639\) | −7.90799 | −0.312835 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.4714 | −1.48003 | −0.740015 | − | 0.672590i | \(-0.765182\pi\) | ||||
−0.740015 | + | 0.672590i | \(0.765182\pi\) | |||||||
\(642\) | −4.17184 | −0.164650 | ||||||||
\(643\) | −0.178907 | −0.00705539 | −0.00352770 | − | 0.999994i | \(-0.501123\pi\) | ||||
−0.00352770 | + | 0.999994i | \(0.501123\pi\) | |||||||
\(644\) | −5.23702 | −0.206367 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −54.4269 | −2.14140 | ||||||||
\(647\) | −2.94235 | −0.115676 | −0.0578379 | − | 0.998326i | \(-0.518421\pi\) | ||||
−0.0578379 | + | 0.998326i | \(0.518421\pi\) | |||||||
\(648\) | −72.7125 | −2.85642 | ||||||||
\(649\) | 10.9530 | 0.429944 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.69187 | −0.0663095 | ||||||||
\(652\) | 38.5294 | 1.50893 | ||||||||
\(653\) | −44.1719 | −1.72858 | −0.864290 | − | 0.502994i | \(-0.832232\pi\) | ||||
−0.864290 | + | 0.502994i | \(0.832232\pi\) | |||||||
\(654\) | −11.2429 | −0.439631 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −23.0672 | −0.900623 | ||||||||
\(657\) | −41.5347 | −1.62042 | ||||||||
\(658\) | −10.5003 | −0.409345 | ||||||||
\(659\) | 13.9282 | 0.542564 | 0.271282 | − | 0.962500i | \(-0.412552\pi\) | ||||
0.271282 | + | 0.962500i | \(0.412552\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.15327 | −0.0837525 | −0.0418763 | − | 0.999123i | \(-0.513334\pi\) | ||||
−0.0418763 | + | 0.999123i | \(0.513334\pi\) | |||||||
\(662\) | −43.5976 | −1.69447 | ||||||||
\(663\) | 2.00467 | 0.0778549 | ||||||||
\(664\) | 61.1501 | 2.37308 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −38.1184 | −1.47706 | ||||||||
\(667\) | −7.02088 | −0.271849 | ||||||||
\(668\) | −109.927 | −4.25320 | ||||||||
\(669\) | −4.78548 | −0.185017 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.2134 | 1.51382 | ||||||||
\(672\) | 4.70271 | 0.181411 | ||||||||
\(673\) | 2.96276 | 0.114206 | 0.0571030 | − | 0.998368i | \(-0.481814\pi\) | ||||
0.0571030 | + | 0.998368i | \(0.481814\pi\) | |||||||
\(674\) | 14.0374 | 0.540701 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −60.0125 | −2.30817 | ||||||||
\(677\) | −9.59927 | −0.368930 | −0.184465 | − | 0.982839i | \(-0.559055\pi\) | ||||
−0.184465 | + | 0.982839i | \(0.559055\pi\) | |||||||
\(678\) | −3.25394 | −0.124967 | ||||||||
\(679\) | −11.6270 | −0.446202 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.23888 | 0.162434 | ||||||||
\(682\) | 63.8936 | 2.44661 | ||||||||
\(683\) | 24.1908 | 0.925636 | 0.462818 | − | 0.886453i | \(-0.346838\pi\) | ||||
0.462818 | + | 0.886453i | \(0.346838\pi\) | |||||||
\(684\) | 51.8196 | 1.98137 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.69017 | 0.102711 | ||||||||
\(687\) | −1.21870 | −0.0464962 | ||||||||
\(688\) | −39.1443 | −1.49236 | ||||||||
\(689\) | −3.07089 | −0.116992 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.4784 | 1.15945 | 0.579726 | − | 0.814811i | \(-0.303159\pi\) | ||||
0.579726 | + | 0.814811i | \(0.303159\pi\) | |||||||
\(692\) | 64.6084 | 2.45604 | ||||||||
\(693\) | −11.0885 | −0.421216 | ||||||||
\(694\) | 11.2743 | 0.427968 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 16.4978 | 0.625347 | ||||||||
\(697\) | 10.6591 | 0.403743 | ||||||||
\(698\) | 50.2014 | 1.90015 | ||||||||
\(699\) | 4.38873 | 0.165997 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.4101 | 0.657570 | 0.328785 | − | 0.944405i | \(-0.393361\pi\) | ||||
0.328785 | + | 0.944405i | \(0.393361\pi\) | |||||||
\(702\) | −5.34070 | −0.201572 | ||||||||
\(703\) | 16.3631 | 0.617145 | ||||||||
\(704\) | −79.4694 | −2.99512 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −31.1471 | −1.17224 | ||||||||
\(707\) | 0.366626 | 0.0137884 | ||||||||
\(708\) | −4.08608 | −0.153564 | ||||||||
\(709\) | 13.6465 | 0.512504 | 0.256252 | − | 0.966610i | \(-0.417512\pi\) | ||||
0.256252 | + | 0.966610i | \(0.417512\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.70089 | −0.363812 | ||||||||
\(712\) | 13.8552 | 0.519247 | ||||||||
\(713\) | 6.26984 | 0.234807 | ||||||||
\(714\) | −4.34473 | −0.162597 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −67.6007 | −2.52636 | ||||||||
\(717\) | 0.579503 | 0.0216419 | ||||||||
\(718\) | −79.3358 | −2.96078 | ||||||||
\(719\) | −29.8264 | −1.11234 | −0.556169 | − | 0.831069i | \(-0.687729\pi\) | ||||
−0.556169 | + | 0.831069i | \(0.687729\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.474030 | −0.0176538 | ||||||||
\(722\) | 20.3735 | 0.758222 | ||||||||
\(723\) | 3.36429 | 0.125119 | ||||||||
\(724\) | −30.7373 | −1.14234 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.43160 | −0.0902452 | ||||||||
\(727\) | −6.92789 | −0.256941 | −0.128471 | − | 0.991713i | \(-0.541007\pi\) | ||||
−0.128471 | + | 0.991713i | \(0.541007\pi\) | |||||||
\(728\) | −10.8090 | −0.400607 | ||||||||
\(729\) | −23.1471 | −0.857302 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.0882 | 0.669015 | ||||||||
\(732\) | −14.6288 | −0.540694 | ||||||||
\(733\) | 10.8092 | 0.399246 | 0.199623 | − | 0.979873i | \(-0.436028\pi\) | ||||
0.199623 | + | 0.979873i | \(0.436028\pi\) | |||||||
\(734\) | −66.6779 | −2.46113 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.4276 | −0.642391 | ||||||||
\(737\) | 43.3609 | 1.59722 | ||||||||
\(738\) | −14.0242 | −0.516238 | ||||||||
\(739\) | 34.5455 | 1.27078 | 0.635388 | − | 0.772193i | \(-0.280840\pi\) | ||||
0.635388 | + | 0.772193i | \(0.280840\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.13222 | 0.0415931 | ||||||||
\(742\) | 6.65556 | 0.244333 | ||||||||
\(743\) | −19.7750 | −0.725475 | −0.362737 | − | 0.931891i | \(-0.618158\pi\) | ||||
−0.362737 | + | 0.931891i | \(0.618158\pi\) | |||||||
\(744\) | −14.7330 | −0.540137 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 46.1428 | 1.68941 | ||||||||
\(747\) | 20.5552 | 0.752077 | ||||||||
\(748\) | 118.735 | 4.34137 | ||||||||
\(749\) | −5.74697 | −0.209990 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.0704 | −1.13378 | −0.566888 | − | 0.823795i | \(-0.691853\pi\) | ||||
−0.566888 | + | 0.823795i | \(0.691853\pi\) | |||||||
\(752\) | −50.5556 | −1.84357 | ||||||||
\(753\) | 1.32622 | 0.0483300 | ||||||||
\(754\) | −23.4440 | −0.853779 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.37610 | 0.304636 | ||||||||
\(757\) | −8.32104 | −0.302433 | −0.151217 | − | 0.988501i | \(-0.548319\pi\) | ||||
−0.151217 | + | 0.988501i | \(0.548319\pi\) | |||||||
\(758\) | −88.2944 | −3.20700 | ||||||||
\(759\) | −1.02219 | −0.0371031 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.82034 | −0.138487 | −0.0692436 | − | 0.997600i | \(-0.522059\pi\) | ||||
−0.0692436 | + | 0.997600i | \(0.522059\pi\) | |||||||
\(762\) | −1.54666 | −0.0560295 | ||||||||
\(763\) | −15.4877 | −0.560694 | ||||||||
\(764\) | 62.5004 | 2.26118 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.6676 | −0.819014 | ||||||||
\(767\) | 3.58900 | 0.129591 | ||||||||
\(768\) | 4.34426 | 0.156760 | ||||||||
\(769\) | 8.05891 | 0.290612 | 0.145306 | − | 0.989387i | \(-0.453583\pi\) | ||||
0.145306 | + | 0.989387i | \(0.453583\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.68463 | −0.276755 | ||||||||
\(772\) | −3.94295 | −0.141910 | ||||||||
\(773\) | 20.3254 | 0.731054 | 0.365527 | − | 0.930801i | \(-0.380889\pi\) | ||||
0.365527 | + | 0.930801i | \(0.380889\pi\) | |||||||
\(774\) | −23.7986 | −0.855423 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −101.249 | −3.63463 | ||||||||
\(777\) | 1.30621 | 0.0468601 | ||||||||
\(778\) | 68.0623 | 2.44015 | ||||||||
\(779\) | 6.02017 | 0.215695 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.2338 | −0.366194 | ||||||||
\(782\) | 16.1010 | 0.575771 | ||||||||
\(783\) | 11.2292 | 0.401299 | ||||||||
\(784\) | 12.9523 | 0.462582 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 13.1567 | 0.469286 | ||||||||
\(787\) | 47.7951 | 1.70371 | 0.851856 | − | 0.523775i | \(-0.175477\pi\) | ||||
0.851856 | + | 0.523775i | \(0.175477\pi\) | |||||||
\(788\) | −133.059 | −4.74002 | ||||||||
\(789\) | −0.510869 | −0.0181874 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.48250 | −0.159379 | ||||||||
\(792\) | −96.5597 | −3.43110 | ||||||||
\(793\) | 12.8491 | 0.456286 | ||||||||
\(794\) | 54.7853 | 1.94426 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 79.5964 | 2.82122 | ||||||||
\(797\) | 7.57090 | 0.268175 | 0.134088 | − | 0.990969i | \(-0.457190\pi\) | ||||
0.134088 | + | 0.990969i | \(0.457190\pi\) | |||||||
\(798\) | −2.45386 | −0.0868657 | ||||||||
\(799\) | 23.3612 | 0.826461 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.65736 | 0.164560 | ||||||||
\(802\) | −11.0372 | −0.389735 | ||||||||
\(803\) | −53.7505 | −1.89681 | ||||||||
\(804\) | −16.1760 | −0.570483 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20.9361 | 0.737444 | ||||||||
\(807\) | −0.677725 | −0.0238571 | ||||||||
\(808\) | 3.19262 | 0.112316 | ||||||||
\(809\) | 8.55279 | 0.300700 | 0.150350 | − | 0.988633i | \(-0.451960\pi\) | ||||
0.150350 | + | 0.988633i | \(0.451960\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45.0023 | −1.58024 | −0.790122 | − | 0.612950i | \(-0.789983\pi\) | ||||
−0.790122 | + | 0.612950i | \(0.789983\pi\) | |||||||
\(812\) | 36.7684 | 1.29032 | ||||||||
\(813\) | 6.77568 | 0.237634 | ||||||||
\(814\) | −49.3293 | −1.72899 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −20.9185 | −0.732293 | ||||||||
\(817\) | 10.2160 | 0.357413 | ||||||||
\(818\) | 72.2173 | 2.52502 | ||||||||
\(819\) | −3.63337 | −0.126960 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.4358 | 1.44612 | 0.723060 | − | 0.690785i | \(-0.242735\pi\) | ||||
0.723060 | + | 0.690785i | \(0.242735\pi\) | |||||||
\(822\) | −11.1111 | −0.387544 | ||||||||
\(823\) | 19.1508 | 0.667553 | 0.333777 | − | 0.942652i | \(-0.391677\pi\) | ||||
0.333777 | + | 0.942652i | \(0.391677\pi\) | |||||||
\(824\) | −4.12791 | −0.143803 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.77845 | −0.270647 | ||||||||
\(827\) | 32.2820 | 1.12256 | 0.561278 | − | 0.827627i | \(-0.310310\pi\) | ||||
0.561278 | + | 0.827627i | \(0.310310\pi\) | |||||||
\(828\) | −15.3297 | −0.532744 | ||||||||
\(829\) | 9.85700 | 0.342348 | 0.171174 | − | 0.985241i | \(-0.445244\pi\) | ||||
0.171174 | + | 0.985241i | \(0.445244\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.55984 | −0.0887998 | ||||||||
\(832\) | −26.0399 | −0.902770 | ||||||||
\(833\) | −5.98512 | −0.207372 | ||||||||
\(834\) | −9.81979 | −0.340031 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 67.0603 | 2.31933 | ||||||||
\(837\) | −10.0280 | −0.346619 | ||||||||
\(838\) | −0.402165 | −0.0138925 | ||||||||
\(839\) | 11.7098 | 0.404267 | 0.202133 | − | 0.979358i | \(-0.435213\pi\) | ||||
0.202133 | + | 0.979358i | \(0.435213\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.2927 | 0.699748 | ||||||||
\(842\) | 28.3191 | 0.975941 | ||||||||
\(843\) | 2.35086 | 0.0809678 | ||||||||
\(844\) | −127.153 | −4.37679 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −30.7364 | −1.05674 | ||||||||
\(847\) | −3.34968 | −0.115096 | ||||||||
\(848\) | 32.0444 | 1.10041 | ||||||||
\(849\) | −8.24484 | −0.282962 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.84066 | −0.165936 | ||||||||
\(852\) | 3.81777 | 0.130795 | ||||||||
\(853\) | 29.2441 | 1.00130 | 0.500650 | − | 0.865650i | \(-0.333094\pi\) | ||||
0.500650 | + | 0.865650i | \(0.333094\pi\) | |||||||
\(854\) | −27.8480 | −0.952938 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −50.0453 | −1.71051 | ||||||||
\(857\) | −38.6873 | −1.32153 | −0.660766 | − | 0.750592i | \(-0.729768\pi\) | ||||
−0.660766 | + | 0.750592i | \(0.729768\pi\) | |||||||
\(858\) | −3.41327 | −0.116527 | ||||||||
\(859\) | −49.3913 | −1.68521 | −0.842604 | − | 0.538534i | \(-0.818979\pi\) | ||||
−0.842604 | + | 0.538534i | \(0.818979\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.480572 | 0.0163778 | ||||||||
\(862\) | 6.15148 | 0.209520 | ||||||||
\(863\) | 2.32156 | 0.0790267 | 0.0395134 | − | 0.999219i | \(-0.487419\pi\) | ||||
0.0395134 | + | 0.999219i | \(0.487419\pi\) | |||||||
\(864\) | 27.8738 | 0.948287 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −55.0325 | −1.87008 | ||||||||
\(867\) | 5.07889 | 0.172488 | ||||||||
\(868\) | −32.8353 | −1.11450 | ||||||||
\(869\) | −12.5540 | −0.425865 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.2081 | 0.481424 | ||||||||
\(872\) | −134.869 | −4.56725 | ||||||||
\(873\) | −34.0343 | −1.15189 | ||||||||
\(874\) | 9.09369 | 0.307599 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20.0519 | 0.677490 | ||||||||
\(877\) | −36.2775 | −1.22500 | −0.612502 | − | 0.790469i | \(-0.709837\pi\) | ||||
−0.612502 | + | 0.790469i | \(0.709837\pi\) | |||||||
\(878\) | −24.0453 | −0.811490 | ||||||||
\(879\) | −3.42871 | −0.115647 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.1252 | 1.01494 | 0.507472 | − | 0.861668i | \(-0.330580\pi\) | ||||
0.507472 | + | 0.861668i | \(0.330580\pi\) | |||||||
\(882\) | 7.87463 | 0.265152 | ||||||||
\(883\) | −1.94158 | −0.0653394 | −0.0326697 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326697 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(884\) | 38.9060 | 1.30855 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.0669 | −0.606969 | ||||||||
\(887\) | −52.3596 | −1.75806 | −0.879031 | − | 0.476765i | \(-0.841809\pi\) | ||||
−0.879031 | + | 0.476765i | \(0.841809\pi\) | |||||||
\(888\) | 11.3747 | 0.381709 | ||||||||
\(889\) | −2.13061 | −0.0714585 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −31.6305 | −1.05966 | ||||||||
\(892\) | −92.8752 | −3.10969 | ||||||||
\(893\) | 13.1942 | 0.441527 | ||||||||
\(894\) | −4.17965 | −0.139789 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 21.5811 | 0.720972 | ||||||||
\(897\) | −0.334942 | −0.0111834 | ||||||||
\(898\) | −106.848 | −3.56555 | ||||||||
\(899\) | −44.0198 | −1.46814 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.8074 | −0.493305 | ||||||||
\(902\) | −18.1489 | −0.604291 | ||||||||
\(903\) | 0.815514 | 0.0271386 | ||||||||
\(904\) | −39.0342 | −1.29826 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.95296 | 0.230997 | ||||||||
\(907\) | −9.62846 | −0.319708 | −0.159854 | − | 0.987141i | \(-0.551102\pi\) | ||||
−0.159854 | + | 0.987141i | \(0.551102\pi\) | |||||||
\(908\) | 82.2669 | 2.73012 | ||||||||
\(909\) | 1.07318 | 0.0355952 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.6036 | −0.815154 | −0.407577 | − | 0.913171i | \(-0.633626\pi\) | ||||
−0.407577 | + | 0.913171i | \(0.633626\pi\) | |||||||
\(912\) | −11.8145 | −0.391219 | ||||||||
\(913\) | 26.6007 | 0.880356 | ||||||||
\(914\) | −96.1434 | −3.18014 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −23.6521 | −0.781488 | ||||||||
\(917\) | 18.1242 | 0.598514 | ||||||||
\(918\) | −25.7520 | −0.849943 | ||||||||
\(919\) | 18.4685 | 0.609220 | 0.304610 | − | 0.952477i | \(-0.401474\pi\) | ||||
0.304610 | + | 0.952477i | \(0.401474\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.96765 | −0.196641 | ||||||||
\(922\) | 49.3690 | 1.62588 | ||||||||
\(923\) | −3.35333 | −0.110376 | ||||||||
\(924\) | 5.35321 | 0.176108 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 30.0819 | 0.988551 | ||||||||
\(927\) | −1.38757 | −0.0455739 | ||||||||
\(928\) | 122.357 | 4.01657 | ||||||||
\(929\) | 21.6032 | 0.708778 | 0.354389 | − | 0.935098i | \(-0.384689\pi\) | ||||
0.354389 | + | 0.935098i | \(0.384689\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.38034 | −0.110786 | ||||||||
\(932\) | 85.1751 | 2.79000 | ||||||||
\(933\) | 5.77314 | 0.189004 | ||||||||
\(934\) | 85.3404 | 2.79242 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −31.6399 | −1.03418 | ||||||||
\(937\) | −4.95446 | −0.161855 | −0.0809276 | − | 0.996720i | \(-0.525788\pi\) | ||||
−0.0809276 | + | 0.996720i | \(0.525788\pi\) | |||||||
\(938\) | −30.7933 | −1.00544 | ||||||||
\(939\) | 8.06967 | 0.263344 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37.1398 | −1.21072 | −0.605361 | − | 0.795951i | \(-0.706971\pi\) | ||||
−0.605361 | + | 0.795951i | \(0.706971\pi\) | |||||||
\(942\) | −3.65651 | −0.119136 | ||||||||
\(943\) | −1.78094 | −0.0579953 | ||||||||
\(944\) | −37.4507 | −1.21892 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −30.7980 | −1.00133 | ||||||||
\(947\) | 11.0644 | 0.359543 | 0.179772 | − | 0.983708i | \(-0.442464\pi\) | ||||
0.179772 | + | 0.983708i | \(0.442464\pi\) | |||||||
\(948\) | 4.68333 | 0.152107 | ||||||||
\(949\) | −17.6125 | −0.571726 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.90536 | −0.0617857 | ||||||||
\(952\) | −52.1192 | −1.68919 | ||||||||
\(953\) | −19.3888 | −0.628065 | −0.314033 | − | 0.949412i | \(-0.601680\pi\) | ||||
−0.314033 | + | 0.949412i | \(0.601680\pi\) | |||||||
\(954\) | 19.4821 | 0.630755 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.2468 | 0.363748 | ||||||||
\(957\) | 7.17665 | 0.231988 | ||||||||
\(958\) | 26.4101 | 0.853271 | ||||||||
\(959\) | −15.3062 | −0.494263 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.31092 | 0.268094 | ||||||||
\(962\) | −16.1638 | −0.521142 | ||||||||
\(963\) | −16.8224 | −0.542095 | ||||||||
\(964\) | 65.2932 | 2.10295 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.725921 | 0.0233561 | ||||||||
\(967\) | 32.5154 | 1.04563 | 0.522813 | − | 0.852448i | \(-0.324883\pi\) | ||||
0.522813 | + | 0.852448i | \(0.324883\pi\) | |||||||
\(968\) | −29.1694 | −0.937540 | ||||||||
\(969\) | 5.45938 | 0.175381 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.32316 | 0.0424622 | 0.0212311 | − | 0.999775i | \(-0.493241\pi\) | ||||
0.0212311 | + | 0.999775i | \(0.493241\pi\) | |||||||
\(972\) | 36.9282 | 1.18447 | ||||||||
\(973\) | −13.5273 | −0.433667 | ||||||||
\(974\) | −97.5934 | −3.12709 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −134.079 | −4.29176 | ||||||||
\(977\) | 31.6195 | 1.01160 | 0.505799 | − | 0.862651i | \(-0.331198\pi\) | ||||
0.505799 | + | 0.862651i | \(0.331198\pi\) | |||||||
\(978\) | −5.34070 | −0.170777 | ||||||||
\(979\) | 6.02713 | 0.192628 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −45.3355 | −1.44745 | ||||||||
\(982\) | 47.3611 | 1.51135 | ||||||||
\(983\) | 12.1696 | 0.388149 | 0.194074 | − | 0.980987i | \(-0.437830\pi\) | ||||
0.194074 | + | 0.980987i | \(0.437830\pi\) | |||||||
\(984\) | 4.18488 | 0.133409 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −113.043 | −3.60003 | ||||||||
\(987\) | 1.05325 | 0.0335254 | ||||||||
\(988\) | 21.9737 | 0.699078 | ||||||||
\(989\) | −3.02219 | −0.0961000 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.18738 | 0.0694844 | 0.0347422 | − | 0.999396i | \(-0.488939\pi\) | ||||
0.0347422 | + | 0.999396i | \(0.488939\pi\) | |||||||
\(992\) | −109.269 | −3.46928 | ||||||||
\(993\) | 4.37313 | 0.138777 | ||||||||
\(994\) | 7.26768 | 0.230517 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −9.92353 | −0.314439 | ||||||||
\(997\) | 3.78052 | 0.119730 | 0.0598652 | − | 0.998206i | \(-0.480933\pi\) | ||||
0.0598652 | + | 0.998206i | \(0.480933\pi\) | |||||||
\(998\) | −32.5894 | −1.03160 | ||||||||
\(999\) | 7.74216 | 0.244951 |
(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 | 4025.2.a.p.1.1 | 5 | ||
5.4 | even | 2 | 161.2.a.d.1.5 | ✓ | 5 | ||
15.14 | odd | 2 | 1449.2.a.r.1.1 | 5 | |||
20.19 | odd | 2 | 2576.2.a.bd.1.3 | 5 | |||
35.34 | odd | 2 | 1127.2.a.h.1.5 | 5 | |||
115.114 | odd | 2 | 3703.2.a.j.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
161.2.a.d.1.5 | ✓ | 5 | 5.4 | even | 2 | ||
1127.2.a.h.1.5 | 5 | 35.34 | odd | 2 | |||
1449.2.a.r.1.1 | 5 | 15.14 | odd | 2 | |||
2576.2.a.bd.1.3 | 5 | 20.19 | odd | 2 | |||
3703.2.a.j.1.5 | 5 | 115.114 | odd | 2 | |||
4025.2.a.p.1.1 | 5 | 1.1 | even | 1 | trivial |