Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [931,2,Mod(1,931)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(931, 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("931.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 931 = 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 931.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: | \(7.43407242818\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 6x^{5} + 18x^{4} + 4x^{3} - 12x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 133) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-2.29398\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 931.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.59421 | 1.83438 | 0.917190 | − | 0.398449i | \(-0.130452\pi\) | ||||
0.917190 | + | 0.398449i | \(0.130452\pi\) | |||||||
\(3\) | 2.89925 | 1.67389 | 0.836943 | − | 0.547291i | \(-0.184341\pi\) | ||||
0.836943 | + | 0.547291i | \(0.184341\pi\) | |||||||
\(4\) | 4.72991 | 2.36495 | ||||||||
\(5\) | −1.85806 | −0.830949 | −0.415475 | − | 0.909605i | \(-0.636384\pi\) | ||||
−0.415475 | + | 0.909605i | \(0.636384\pi\) | |||||||
\(6\) | 7.52126 | 3.07054 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 7.08194 | 2.50384 | ||||||||
\(9\) | 5.40568 | 1.80189 | ||||||||
\(10\) | −4.82019 | −1.52428 | ||||||||
\(11\) | −3.51514 | −1.05985 | −0.529927 | − | 0.848043i | \(-0.677781\pi\) | ||||
−0.529927 | + | 0.848043i | \(0.677781\pi\) | |||||||
\(12\) | 13.7132 | 3.95866 | ||||||||
\(13\) | −3.68871 | −1.02306 | −0.511532 | − | 0.859264i | \(-0.670922\pi\) | ||||
−0.511532 | + | 0.859264i | \(0.670922\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.38698 | −1.39091 | ||||||||
\(16\) | 8.91219 | 2.22805 | ||||||||
\(17\) | −4.85806 | −1.17825 | −0.589126 | − | 0.808041i | \(-0.700528\pi\) | ||||
−0.589126 | + | 0.808041i | \(0.700528\pi\) | |||||||
\(18\) | 14.0234 | 3.30536 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −8.78844 | −1.96516 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.11899 | −1.94418 | ||||||||
\(23\) | 1.71956 | 0.358553 | 0.179276 | − | 0.983799i | \(-0.442624\pi\) | ||||
0.179276 | + | 0.983799i | \(0.442624\pi\) | |||||||
\(24\) | 20.5323 | 4.19115 | ||||||||
\(25\) | −1.54762 | −0.309524 | ||||||||
\(26\) | −9.56927 | −1.87669 | ||||||||
\(27\) | 6.97467 | 1.34228 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.20098 | 0.594407 | 0.297203 | − | 0.954814i | \(-0.403946\pi\) | ||||
0.297203 | + | 0.954814i | \(0.403946\pi\) | |||||||
\(30\) | −13.9749 | −2.55146 | ||||||||
\(31\) | −0.627857 | −0.112766 | −0.0563832 | − | 0.998409i | \(-0.517957\pi\) | ||||
−0.0563832 | + | 0.998409i | \(0.517957\pi\) | |||||||
\(32\) | 8.95619 | 1.58325 | ||||||||
\(33\) | −10.1913 | −1.77407 | ||||||||
\(34\) | −12.6028 | −2.16136 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 25.5683 | 4.26139 | ||||||||
\(37\) | 1.62286 | 0.266797 | 0.133398 | − | 0.991063i | \(-0.457411\pi\) | ||||
0.133398 | + | 0.991063i | \(0.457411\pi\) | |||||||
\(38\) | −2.59421 | −0.420836 | ||||||||
\(39\) | −10.6945 | −1.71249 | ||||||||
\(40\) | −13.1587 | −2.08057 | ||||||||
\(41\) | 5.18841 | 0.810294 | 0.405147 | − | 0.914252i | \(-0.367220\pi\) | ||||
0.405147 | + | 0.914252i | \(0.367220\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.18419 | 0.943080 | 0.471540 | − | 0.881845i | \(-0.343698\pi\) | ||||
0.471540 | + | 0.881845i | \(0.343698\pi\) | |||||||
\(44\) | −16.6263 | −2.50650 | ||||||||
\(45\) | −10.0441 | −1.49728 | ||||||||
\(46\) | 4.46089 | 0.657722 | ||||||||
\(47\) | 5.43568 | 0.792875 | 0.396437 | − | 0.918062i | \(-0.370246\pi\) | ||||
0.396437 | + | 0.918062i | \(0.370246\pi\) | |||||||
\(48\) | 25.8387 | 3.72950 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.01484 | −0.567784 | ||||||||
\(51\) | −14.0847 | −1.97226 | ||||||||
\(52\) | −17.4472 | −2.41950 | ||||||||
\(53\) | 5.81446 | 0.798677 | 0.399338 | − | 0.916804i | \(-0.369240\pi\) | ||||
0.399338 | + | 0.916804i | \(0.369240\pi\) | |||||||
\(54\) | 18.0937 | 2.46224 | ||||||||
\(55\) | 6.53133 | 0.880685 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.89925 | −0.384016 | ||||||||
\(58\) | 8.30400 | 1.09037 | ||||||||
\(59\) | 4.88969 | 0.636583 | 0.318292 | − | 0.947993i | \(-0.396891\pi\) | ||||
0.318292 | + | 0.947993i | \(0.396891\pi\) | |||||||
\(60\) | −25.4799 | −3.28944 | ||||||||
\(61\) | 7.36829 | 0.943413 | 0.471707 | − | 0.881756i | \(-0.343638\pi\) | ||||
0.471707 | + | 0.881756i | \(0.343638\pi\) | |||||||
\(62\) | −1.62879 | −0.206856 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.40982 | 0.676227 | ||||||||
\(65\) | 6.85384 | 0.850114 | ||||||||
\(66\) | −26.4383 | −3.25433 | ||||||||
\(67\) | −0.0879948 | −0.0107503 | −0.00537514 | − | 0.999986i | \(-0.501711\pi\) | ||||
−0.00537514 | + | 0.999986i | \(0.501711\pi\) | |||||||
\(68\) | −22.9782 | −2.78651 | ||||||||
\(69\) | 4.98544 | 0.600176 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.7990 | 1.87499 | 0.937496 | − | 0.347995i | \(-0.113137\pi\) | ||||
0.937496 | + | 0.347995i | \(0.113137\pi\) | |||||||
\(72\) | 38.2827 | 4.51165 | ||||||||
\(73\) | −3.01818 | −0.353251 | −0.176626 | − | 0.984278i | \(-0.556518\pi\) | ||||
−0.176626 | + | 0.984278i | \(0.556518\pi\) | |||||||
\(74\) | 4.21003 | 0.489406 | ||||||||
\(75\) | −4.48694 | −0.518107 | ||||||||
\(76\) | −4.72991 | −0.542557 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −27.7438 | −3.14136 | ||||||||
\(79\) | −14.7534 | −1.65988 | −0.829942 | − | 0.557850i | \(-0.811627\pi\) | ||||
−0.829942 | + | 0.557850i | \(0.811627\pi\) | |||||||
\(80\) | −16.5594 | −1.85139 | ||||||||
\(81\) | 4.00431 | 0.444924 | ||||||||
\(82\) | 13.4598 | 1.48639 | ||||||||
\(83\) | 4.03094 | 0.442454 | 0.221227 | − | 0.975222i | \(-0.428994\pi\) | ||||
0.221227 | + | 0.975222i | \(0.428994\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.02656 | 0.979068 | ||||||||
\(86\) | 16.0431 | 1.72997 | ||||||||
\(87\) | 9.28045 | 0.994969 | ||||||||
\(88\) | −24.8940 | −2.65371 | ||||||||
\(89\) | 1.32673 | 0.140633 | 0.0703163 | − | 0.997525i | \(-0.477599\pi\) | ||||
0.0703163 | + | 0.997525i | \(0.477599\pi\) | |||||||
\(90\) | −26.0564 | −2.74658 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.13335 | 0.847960 | ||||||||
\(93\) | −1.82032 | −0.188758 | ||||||||
\(94\) | 14.1013 | 1.45443 | ||||||||
\(95\) | 1.85806 | 0.190633 | ||||||||
\(96\) | 25.9663 | 2.65017 | ||||||||
\(97\) | 4.69587 | 0.476793 | 0.238397 | − | 0.971168i | \(-0.423378\pi\) | ||||
0.238397 | + | 0.971168i | \(0.423378\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −19.0017 | −1.90974 | ||||||||
\(100\) | −7.32009 | −0.732009 | ||||||||
\(101\) | −0.569938 | −0.0567110 | −0.0283555 | − | 0.999598i | \(-0.509027\pi\) | ||||
−0.0283555 | + | 0.999598i | \(0.509027\pi\) | |||||||
\(102\) | −36.5387 | −3.61787 | ||||||||
\(103\) | 12.2276 | 1.20482 | 0.602409 | − | 0.798188i | \(-0.294208\pi\) | ||||
0.602409 | + | 0.798188i | \(0.294208\pi\) | |||||||
\(104\) | −26.1232 | −2.56159 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 15.0839 | 1.46508 | ||||||||
\(107\) | −18.3739 | −1.77627 | −0.888136 | − | 0.459580i | \(-0.848000\pi\) | ||||
−0.888136 | + | 0.459580i | \(0.848000\pi\) | |||||||
\(108\) | 32.9895 | 3.17442 | ||||||||
\(109\) | −13.9624 | −1.33735 | −0.668677 | − | 0.743553i | \(-0.733139\pi\) | ||||
−0.668677 | + | 0.743553i | \(0.733139\pi\) | |||||||
\(110\) | 16.9436 | 1.61551 | ||||||||
\(111\) | 4.70508 | 0.446587 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.2840 | −1.81409 | −0.907044 | − | 0.421035i | \(-0.861667\pi\) | ||||
−0.907044 | + | 0.421035i | \(0.861667\pi\) | |||||||
\(114\) | −7.52126 | −0.704431 | ||||||||
\(115\) | −3.19504 | −0.297939 | ||||||||
\(116\) | 15.1403 | 1.40574 | ||||||||
\(117\) | −19.9400 | −1.84345 | ||||||||
\(118\) | 12.6849 | 1.16774 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −38.1503 | −3.48263 | ||||||||
\(121\) | 1.35620 | 0.123291 | ||||||||
\(122\) | 19.1149 | 1.73058 | ||||||||
\(123\) | 15.0425 | 1.35634 | ||||||||
\(124\) | −2.96970 | −0.266687 | ||||||||
\(125\) | 12.1659 | 1.08815 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.98199 | −0.530816 | −0.265408 | − | 0.964136i | \(-0.585507\pi\) | ||||
−0.265408 | + | 0.964136i | \(0.585507\pi\) | |||||||
\(128\) | −3.87820 | −0.342788 | ||||||||
\(129\) | 17.9295 | 1.57861 | ||||||||
\(130\) | 17.7803 | 1.55943 | ||||||||
\(131\) | −18.5645 | −1.62198 | −0.810992 | − | 0.585057i | \(-0.801072\pi\) | ||||
−0.810992 | + | 0.585057i | \(0.801072\pi\) | |||||||
\(132\) | −48.2038 | −4.19560 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.228277 | −0.0197201 | ||||||||
\(135\) | −12.9593 | −1.11536 | ||||||||
\(136\) | −34.4045 | −2.95016 | ||||||||
\(137\) | −0.392832 | −0.0335619 | −0.0167810 | − | 0.999859i | \(-0.505342\pi\) | ||||
−0.0167810 | + | 0.999859i | \(0.505342\pi\) | |||||||
\(138\) | 12.9333 | 1.10095 | ||||||||
\(139\) | −2.20935 | −0.187395 | −0.0936973 | − | 0.995601i | \(-0.529869\pi\) | ||||
−0.0936973 | + | 0.995601i | \(0.529869\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.7594 | 1.32718 | ||||||||
\(142\) | 40.9858 | 3.43945 | ||||||||
\(143\) | 12.9663 | 1.08430 | ||||||||
\(144\) | 48.1764 | 4.01470 | ||||||||
\(145\) | −5.94761 | −0.493922 | ||||||||
\(146\) | −7.82978 | −0.647997 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.67597 | 0.630961 | ||||||||
\(149\) | 14.7422 | 1.20772 | 0.603862 | − | 0.797089i | \(-0.293628\pi\) | ||||
0.603862 | + | 0.797089i | \(0.293628\pi\) | |||||||
\(150\) | −11.6400 | −0.950406 | ||||||||
\(151\) | −8.64356 | −0.703403 | −0.351701 | − | 0.936112i | \(-0.614397\pi\) | ||||
−0.351701 | + | 0.936112i | \(0.614397\pi\) | |||||||
\(152\) | −7.08194 | −0.574421 | ||||||||
\(153\) | −26.2611 | −2.12308 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.16659 | 0.0937031 | ||||||||
\(156\) | −50.5840 | −4.04996 | ||||||||
\(157\) | −23.0605 | −1.84043 | −0.920213 | − | 0.391417i | \(-0.871985\pi\) | ||||
−0.920213 | + | 0.391417i | \(0.871985\pi\) | |||||||
\(158\) | −38.2733 | −3.04486 | ||||||||
\(159\) | 16.8576 | 1.33689 | ||||||||
\(160\) | −16.6411 | −1.31560 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 10.3880 | 0.816159 | ||||||||
\(163\) | −1.56192 | −0.122339 | −0.0611694 | − | 0.998127i | \(-0.519483\pi\) | ||||
−0.0611694 | + | 0.998127i | \(0.519483\pi\) | |||||||
\(164\) | 24.5407 | 1.91631 | ||||||||
\(165\) | 18.9360 | 1.47417 | ||||||||
\(166\) | 10.4571 | 0.811628 | ||||||||
\(167\) | 15.6485 | 1.21092 | 0.605458 | − | 0.795877i | \(-0.292990\pi\) | ||||
0.605458 | + | 0.795877i | \(0.292990\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.606574 | 0.0466595 | ||||||||
\(170\) | 23.4167 | 1.79598 | ||||||||
\(171\) | −5.40568 | −0.413382 | ||||||||
\(172\) | 29.2506 | 2.23034 | ||||||||
\(173\) | 9.98245 | 0.758952 | 0.379476 | − | 0.925202i | \(-0.376104\pi\) | ||||
0.379476 | + | 0.925202i | \(0.376104\pi\) | |||||||
\(174\) | 24.0754 | 1.82515 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −31.3276 | −2.36141 | ||||||||
\(177\) | 14.1764 | 1.06557 | ||||||||
\(178\) | 3.44180 | 0.257974 | ||||||||
\(179\) | 15.6761 | 1.17169 | 0.585845 | − | 0.810423i | \(-0.300763\pi\) | ||||
0.585845 | + | 0.810423i | \(0.300763\pi\) | |||||||
\(180\) | −47.5075 | −3.54100 | ||||||||
\(181\) | 14.0629 | 1.04529 | 0.522645 | − | 0.852550i | \(-0.324945\pi\) | ||||
0.522645 | + | 0.852550i | \(0.324945\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.3626 | 1.57917 | ||||||||
\(184\) | 12.1778 | 0.897759 | ||||||||
\(185\) | −3.01537 | −0.221694 | ||||||||
\(186\) | −4.72228 | −0.346254 | ||||||||
\(187\) | 17.0767 | 1.24878 | ||||||||
\(188\) | 25.7102 | 1.87511 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.82019 | 0.349693 | ||||||||
\(191\) | 14.2579 | 1.03166 | 0.515832 | − | 0.856690i | \(-0.327483\pi\) | ||||
0.515832 | + | 0.856690i | \(0.327483\pi\) | |||||||
\(192\) | 15.6844 | 1.13193 | ||||||||
\(193\) | −6.26005 | −0.450608 | −0.225304 | − | 0.974288i | \(-0.572338\pi\) | ||||
−0.225304 | + | 0.974288i | \(0.572338\pi\) | |||||||
\(194\) | 12.1821 | 0.874620 | ||||||||
\(195\) | 19.8710 | 1.42299 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.46741 | −0.318290 | −0.159145 | − | 0.987255i | \(-0.550874\pi\) | ||||
−0.159145 | + | 0.987255i | \(0.550874\pi\) | |||||||
\(198\) | −49.2943 | −3.50320 | ||||||||
\(199\) | −15.8836 | −1.12596 | −0.562980 | − | 0.826471i | \(-0.690345\pi\) | ||||
−0.562980 | + | 0.826471i | \(0.690345\pi\) | |||||||
\(200\) | −10.9601 | −0.774999 | ||||||||
\(201\) | −0.255119 | −0.0179947 | ||||||||
\(202\) | −1.47854 | −0.104030 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −66.6195 | −4.66430 | ||||||||
\(205\) | −9.64037 | −0.673313 | ||||||||
\(206\) | 31.7208 | 2.21009 | ||||||||
\(207\) | 9.29538 | 0.646073 | ||||||||
\(208\) | −32.8745 | −2.27944 | ||||||||
\(209\) | 3.51514 | 0.243147 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.71958 | 0.600281 | 0.300140 | − | 0.953895i | \(-0.402966\pi\) | ||||
0.300140 | + | 0.953895i | \(0.402966\pi\) | |||||||
\(212\) | 27.5018 | 1.88883 | ||||||||
\(213\) | 45.8052 | 3.13852 | ||||||||
\(214\) | −47.6657 | −3.25836 | ||||||||
\(215\) | −11.4906 | −0.783652 | ||||||||
\(216\) | 49.3942 | 3.36085 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −36.2213 | −2.45322 | ||||||||
\(219\) | −8.75047 | −0.591302 | ||||||||
\(220\) | 30.8926 | 2.08278 | ||||||||
\(221\) | 17.9200 | 1.20543 | ||||||||
\(222\) | 12.2060 | 0.819210 | ||||||||
\(223\) | 5.10334 | 0.341745 | 0.170872 | − | 0.985293i | \(-0.445341\pi\) | ||||
0.170872 | + | 0.985293i | \(0.445341\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.36593 | −0.557728 | ||||||||
\(226\) | −50.0267 | −3.32773 | ||||||||
\(227\) | 2.16600 | 0.143763 | 0.0718813 | − | 0.997413i | \(-0.477100\pi\) | ||||
0.0718813 | + | 0.997413i | \(0.477100\pi\) | |||||||
\(228\) | −13.7132 | −0.908179 | ||||||||
\(229\) | −24.2488 | −1.60240 | −0.801202 | − | 0.598394i | \(-0.795806\pi\) | ||||
−0.801202 | + | 0.598394i | \(0.795806\pi\) | |||||||
\(230\) | −8.28859 | −0.546534 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 22.6691 | 1.48830 | ||||||||
\(233\) | 2.79368 | 0.183020 | 0.0915101 | − | 0.995804i | \(-0.470831\pi\) | ||||
0.0915101 | + | 0.995804i | \(0.470831\pi\) | |||||||
\(234\) | −51.7284 | −3.38159 | ||||||||
\(235\) | −10.0998 | −0.658838 | ||||||||
\(236\) | 23.1278 | 1.50549 | ||||||||
\(237\) | −42.7738 | −2.77846 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.1576 | 1.82136 | 0.910682 | − | 0.413109i | \(-0.135557\pi\) | ||||
0.910682 | + | 0.413109i | \(0.135557\pi\) | |||||||
\(240\) | −48.0098 | −3.09902 | ||||||||
\(241\) | −17.2881 | −1.11362 | −0.556812 | − | 0.830639i | \(-0.687975\pi\) | ||||
−0.556812 | + | 0.830639i | \(0.687975\pi\) | |||||||
\(242\) | 3.51825 | 0.226162 | ||||||||
\(243\) | −9.31449 | −0.597525 | ||||||||
\(244\) | 34.8513 | 2.23113 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 39.0234 | 2.48804 | ||||||||
\(247\) | 3.68871 | 0.234707 | ||||||||
\(248\) | −4.44644 | −0.282349 | ||||||||
\(249\) | 11.6867 | 0.740617 | ||||||||
\(250\) | 31.5607 | 1.99608 | ||||||||
\(251\) | −3.30974 | −0.208909 | −0.104455 | − | 0.994530i | \(-0.533310\pi\) | ||||
−0.104455 | + | 0.994530i | \(0.533310\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.04448 | −0.380013 | ||||||||
\(254\) | −15.5185 | −0.973718 | ||||||||
\(255\) | 26.1703 | 1.63885 | ||||||||
\(256\) | −20.8805 | −1.30503 | ||||||||
\(257\) | 2.20124 | 0.137310 | 0.0686548 | − | 0.997640i | \(-0.478129\pi\) | ||||
0.0686548 | + | 0.997640i | \(0.478129\pi\) | |||||||
\(258\) | 46.5129 | 2.89577 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 32.4180 | 2.01048 | ||||||||
\(261\) | 17.3035 | 1.07106 | ||||||||
\(262\) | −48.1600 | −2.97534 | ||||||||
\(263\) | 1.42703 | 0.0879945 | 0.0439972 | − | 0.999032i | \(-0.485991\pi\) | ||||
0.0439972 | + | 0.999032i | \(0.485991\pi\) | |||||||
\(264\) | −72.1740 | −4.44200 | ||||||||
\(265\) | −10.8036 | −0.663660 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.84652 | 0.235403 | ||||||||
\(268\) | −0.416207 | −0.0254239 | ||||||||
\(269\) | 2.26935 | 0.138365 | 0.0691823 | − | 0.997604i | \(-0.477961\pi\) | ||||
0.0691823 | + | 0.997604i | \(0.477961\pi\) | |||||||
\(270\) | −33.6192 | −2.04600 | ||||||||
\(271\) | −3.43963 | −0.208943 | −0.104471 | − | 0.994528i | \(-0.533315\pi\) | ||||
−0.104471 | + | 0.994528i | \(0.533315\pi\) | |||||||
\(272\) | −43.2959 | −2.62520 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.01909 | −0.0615653 | ||||||||
\(275\) | 5.44009 | 0.328050 | ||||||||
\(276\) | 23.5806 | 1.41939 | ||||||||
\(277\) | 5.91649 | 0.355487 | 0.177744 | − | 0.984077i | \(-0.443120\pi\) | ||||
0.177744 | + | 0.984077i | \(0.443120\pi\) | |||||||
\(278\) | −5.73151 | −0.343753 | ||||||||
\(279\) | −3.39399 | −0.203193 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.4540 | −1.45880 | −0.729402 | − | 0.684086i | \(-0.760201\pi\) | ||||
−0.729402 | + | 0.684086i | \(0.760201\pi\) | |||||||
\(282\) | 40.8831 | 2.43456 | ||||||||
\(283\) | 23.6926 | 1.40838 | 0.704188 | − | 0.710013i | \(-0.251311\pi\) | ||||
0.704188 | + | 0.710013i | \(0.251311\pi\) | |||||||
\(284\) | 74.7276 | 4.43427 | ||||||||
\(285\) | 5.38698 | 0.319097 | ||||||||
\(286\) | 33.6373 | 1.98902 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 48.4143 | 2.85284 | ||||||||
\(289\) | 6.60073 | 0.388278 | ||||||||
\(290\) | −15.4293 | −0.906041 | ||||||||
\(291\) | 13.6145 | 0.798097 | ||||||||
\(292\) | −14.2757 | −0.835423 | ||||||||
\(293\) | −14.8606 | −0.868164 | −0.434082 | − | 0.900873i | \(-0.642927\pi\) | ||||
−0.434082 | + | 0.900873i | \(0.642927\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.08533 | −0.528968 | ||||||||
\(296\) | 11.4930 | 0.668017 | ||||||||
\(297\) | −24.5169 | −1.42262 | ||||||||
\(298\) | 38.2442 | 2.21543 | ||||||||
\(299\) | −6.34295 | −0.366822 | ||||||||
\(300\) | −21.2228 | −1.22530 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −22.4232 | −1.29031 | ||||||||
\(303\) | −1.65240 | −0.0949277 | ||||||||
\(304\) | −8.91219 | −0.511149 | ||||||||
\(305\) | −13.6907 | −0.783928 | ||||||||
\(306\) | −68.1267 | −3.89454 | ||||||||
\(307\) | −23.0610 | −1.31616 | −0.658080 | − | 0.752948i | \(-0.728631\pi\) | ||||
−0.658080 | + | 0.752948i | \(0.728631\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 35.4508 | 2.01673 | ||||||||
\(310\) | 3.02639 | 0.171887 | ||||||||
\(311\) | −7.36533 | −0.417650 | −0.208825 | − | 0.977953i | \(-0.566964\pi\) | ||||
−0.208825 | + | 0.977953i | \(0.566964\pi\) | |||||||
\(312\) | −75.7378 | −4.28781 | ||||||||
\(313\) | 6.60341 | 0.373247 | 0.186623 | − | 0.982432i | \(-0.440246\pi\) | ||||
0.186623 | + | 0.982432i | \(0.440246\pi\) | |||||||
\(314\) | −59.8236 | −3.37604 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −69.7820 | −3.92555 | ||||||||
\(317\) | −19.7434 | −1.10890 | −0.554451 | − | 0.832217i | \(-0.687072\pi\) | ||||
−0.554451 | + | 0.832217i | \(0.687072\pi\) | |||||||
\(318\) | 43.7321 | 2.45237 | ||||||||
\(319\) | −11.2519 | −0.629985 | ||||||||
\(320\) | −10.0518 | −0.561910 | ||||||||
\(321\) | −53.2706 | −2.97328 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.85806 | 0.270310 | ||||||||
\(324\) | 18.9400 | 1.05222 | ||||||||
\(325\) | 5.70871 | 0.316662 | ||||||||
\(326\) | −4.05194 | −0.224416 | ||||||||
\(327\) | −40.4805 | −2.23858 | ||||||||
\(328\) | 36.7440 | 2.02885 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 49.1239 | 2.70418 | ||||||||
\(331\) | 34.9018 | 1.91838 | 0.959189 | − | 0.282765i | \(-0.0912516\pi\) | ||||
0.959189 | + | 0.282765i | \(0.0912516\pi\) | |||||||
\(332\) | 19.0660 | 1.04638 | ||||||||
\(333\) | 8.77266 | 0.480739 | ||||||||
\(334\) | 40.5954 | 2.22128 | ||||||||
\(335\) | 0.163500 | 0.00893293 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.4312 | −1.22191 | −0.610953 | − | 0.791667i | \(-0.709213\pi\) | ||||
−0.610953 | + | 0.791667i | \(0.709213\pi\) | |||||||
\(338\) | 1.57358 | 0.0855914 | ||||||||
\(339\) | −55.9093 | −3.03658 | ||||||||
\(340\) | 42.6948 | 2.31545 | ||||||||
\(341\) | 2.20700 | 0.119516 | ||||||||
\(342\) | −14.0234 | −0.758301 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 43.7960 | 2.36132 | ||||||||
\(345\) | −9.26323 | −0.498716 | ||||||||
\(346\) | 25.8965 | 1.39221 | ||||||||
\(347\) | 3.43777 | 0.184549 | 0.0922745 | − | 0.995734i | \(-0.470586\pi\) | ||||
0.0922745 | + | 0.995734i | \(0.470586\pi\) | |||||||
\(348\) | 43.8957 | 2.35305 | ||||||||
\(349\) | 15.9690 | 0.854802 | 0.427401 | − | 0.904062i | \(-0.359429\pi\) | ||||
0.427401 | + | 0.904062i | \(0.359429\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.7275 | −1.37323 | ||||||||
\(352\) | −31.4822 | −1.67801 | ||||||||
\(353\) | −23.4843 | −1.24994 | −0.624970 | − | 0.780648i | \(-0.714889\pi\) | ||||
−0.624970 | + | 0.780648i | \(0.714889\pi\) | |||||||
\(354\) | 36.7766 | 1.95466 | ||||||||
\(355\) | −29.3554 | −1.55802 | ||||||||
\(356\) | 6.27529 | 0.332590 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 40.6671 | 2.14933 | ||||||||
\(359\) | −7.48850 | −0.395228 | −0.197614 | − | 0.980280i | \(-0.563319\pi\) | ||||
−0.197614 | + | 0.980280i | \(0.563319\pi\) | |||||||
\(360\) | −71.1314 | −3.74896 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 36.4822 | 1.91746 | ||||||||
\(363\) | 3.93196 | 0.206374 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.60796 | 0.293534 | ||||||||
\(366\) | 55.4189 | 2.89679 | ||||||||
\(367\) | 1.32190 | 0.0690027 | 0.0345013 | − | 0.999405i | \(-0.489016\pi\) | ||||
0.0345013 | + | 0.999405i | \(0.489016\pi\) | |||||||
\(368\) | 15.3250 | 0.798873 | ||||||||
\(369\) | 28.0469 | 1.46006 | ||||||||
\(370\) | −7.82249 | −0.406672 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8.60992 | −0.446404 | ||||||||
\(373\) | 16.0606 | 0.831588 | 0.415794 | − | 0.909459i | \(-0.363504\pi\) | ||||
0.415794 | + | 0.909459i | \(0.363504\pi\) | |||||||
\(374\) | 44.3006 | 2.29073 | ||||||||
\(375\) | 35.2719 | 1.82143 | ||||||||
\(376\) | 38.4951 | 1.98523 | ||||||||
\(377\) | −11.8075 | −0.608116 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.7184 | 1.52653 | 0.763265 | − | 0.646085i | \(-0.223595\pi\) | ||||
0.763265 | + | 0.646085i | \(0.223595\pi\) | |||||||
\(380\) | 8.78844 | 0.450837 | ||||||||
\(381\) | −17.3433 | −0.888525 | ||||||||
\(382\) | 36.9879 | 1.89247 | ||||||||
\(383\) | 8.81894 | 0.450627 | 0.225313 | − | 0.974286i | \(-0.427659\pi\) | ||||
0.225313 | + | 0.974286i | \(0.427659\pi\) | |||||||
\(384\) | −11.2439 | −0.573787 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.2399 | −0.826587 | ||||||||
\(387\) | 33.4297 | 1.69933 | ||||||||
\(388\) | 22.2110 | 1.12759 | ||||||||
\(389\) | −2.69383 | −0.136583 | −0.0682913 | − | 0.997665i | \(-0.521755\pi\) | ||||
−0.0682913 | + | 0.997665i | \(0.521755\pi\) | |||||||
\(390\) | 51.5495 | 2.61031 | ||||||||
\(391\) | −8.35371 | −0.422465 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −53.8231 | −2.71502 | ||||||||
\(394\) | −11.5894 | −0.583864 | ||||||||
\(395\) | 27.4126 | 1.37928 | ||||||||
\(396\) | −89.8762 | −4.51645 | ||||||||
\(397\) | 12.6488 | 0.634824 | 0.317412 | − | 0.948288i | \(-0.397186\pi\) | ||||
0.317412 | + | 0.948288i | \(0.397186\pi\) | |||||||
\(398\) | −41.2054 | −2.06544 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.7927 | −0.689634 | ||||||||
\(401\) | 14.0325 | 0.700750 | 0.350375 | − | 0.936610i | \(-0.386054\pi\) | ||||
0.350375 | + | 0.936610i | \(0.386054\pi\) | |||||||
\(402\) | −0.661832 | −0.0330092 | ||||||||
\(403\) | 2.31598 | 0.115367 | ||||||||
\(404\) | −2.69575 | −0.134119 | ||||||||
\(405\) | −7.44025 | −0.369709 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.70458 | −0.282765 | ||||||||
\(408\) | −99.7473 | −4.93823 | ||||||||
\(409\) | 19.1589 | 0.947345 | 0.473672 | − | 0.880701i | \(-0.342928\pi\) | ||||
0.473672 | + | 0.880701i | \(0.342928\pi\) | |||||||
\(410\) | −25.0091 | −1.23511 | ||||||||
\(411\) | −1.13892 | −0.0561788 | ||||||||
\(412\) | 57.8352 | 2.84934 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 24.1141 | 1.18514 | ||||||||
\(415\) | −7.48973 | −0.367656 | ||||||||
\(416\) | −33.0368 | −1.61976 | ||||||||
\(417\) | −6.40547 | −0.313677 | ||||||||
\(418\) | 9.11899 | 0.446025 | ||||||||
\(419\) | 19.9035 | 0.972350 | 0.486175 | − | 0.873861i | \(-0.338392\pi\) | ||||
0.486175 | + | 0.873861i | \(0.338392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.62383 | −0.0791408 | −0.0395704 | − | 0.999217i | \(-0.512599\pi\) | ||||
−0.0395704 | + | 0.999217i | \(0.512599\pi\) | |||||||
\(422\) | 22.6204 | 1.10114 | ||||||||
\(423\) | 29.3835 | 1.42867 | ||||||||
\(424\) | 41.1776 | 1.99976 | ||||||||
\(425\) | 7.51842 | 0.364697 | ||||||||
\(426\) | 118.828 | 5.75725 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −86.9068 | −4.20080 | ||||||||
\(429\) | 37.5927 | 1.81499 | ||||||||
\(430\) | −29.8090 | −1.43752 | ||||||||
\(431\) | −9.50653 | −0.457913 | −0.228957 | − | 0.973437i | \(-0.573531\pi\) | ||||
−0.228957 | + | 0.973437i | \(0.573531\pi\) | |||||||
\(432\) | 62.1596 | 2.99065 | ||||||||
\(433\) | −32.9746 | −1.58466 | −0.792328 | − | 0.610095i | \(-0.791131\pi\) | ||||
−0.792328 | + | 0.610095i | \(0.791131\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.2436 | −0.826769 | ||||||||
\(436\) | −66.0407 | −3.16278 | ||||||||
\(437\) | −1.71956 | −0.0822576 | ||||||||
\(438\) | −22.7005 | −1.08467 | ||||||||
\(439\) | 28.5020 | 1.36032 | 0.680162 | − | 0.733061i | \(-0.261909\pi\) | ||||
0.680162 | + | 0.733061i | \(0.261909\pi\) | |||||||
\(440\) | 46.2545 | 2.20510 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 46.4881 | 2.21121 | ||||||||
\(443\) | −4.93266 | −0.234358 | −0.117179 | − | 0.993111i | \(-0.537385\pi\) | ||||
−0.117179 | + | 0.993111i | \(0.537385\pi\) | |||||||
\(444\) | 22.2546 | 1.05616 | ||||||||
\(445\) | −2.46513 | −0.116859 | ||||||||
\(446\) | 13.2391 | 0.626890 | ||||||||
\(447\) | 42.7413 | 2.02159 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.8243 | 1.12434 | 0.562170 | − | 0.827022i | \(-0.309967\pi\) | ||||
0.562170 | + | 0.827022i | \(0.309967\pi\) | |||||||
\(450\) | −21.7029 | −1.02309 | ||||||||
\(451\) | −18.2380 | −0.858793 | ||||||||
\(452\) | −91.2116 | −4.29023 | ||||||||
\(453\) | −25.0599 | −1.17742 | ||||||||
\(454\) | 5.61905 | 0.263715 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −20.5323 | −0.961515 | ||||||||
\(457\) | 16.5346 | 0.773455 | 0.386727 | − | 0.922194i | \(-0.373605\pi\) | ||||
0.386727 | + | 0.922194i | \(0.373605\pi\) | |||||||
\(458\) | −62.9063 | −2.93942 | ||||||||
\(459\) | −33.8834 | −1.58154 | ||||||||
\(460\) | −15.1122 | −0.704612 | ||||||||
\(461\) | 28.5520 | 1.32980 | 0.664899 | − | 0.746933i | \(-0.268475\pi\) | ||||
0.664899 | + | 0.746933i | \(0.268475\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.7870 | −1.10548 | −0.552739 | − | 0.833355i | \(-0.686417\pi\) | ||||
−0.552739 | + | 0.833355i | \(0.686417\pi\) | |||||||
\(464\) | 28.5277 | 1.32437 | ||||||||
\(465\) | 3.38225 | 0.156848 | ||||||||
\(466\) | 7.24739 | 0.335729 | ||||||||
\(467\) | −24.0932 | −1.11490 | −0.557451 | − | 0.830210i | \(-0.688220\pi\) | ||||
−0.557451 | + | 0.830210i | \(0.688220\pi\) | |||||||
\(468\) | −94.3142 | −4.35967 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −26.2010 | −1.20856 | ||||||||
\(471\) | −66.8582 | −3.08066 | ||||||||
\(472\) | 34.6285 | 1.59390 | ||||||||
\(473\) | −21.7383 | −0.999527 | ||||||||
\(474\) | −110.964 | −5.09674 | ||||||||
\(475\) | 1.54762 | 0.0710096 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.4311 | 1.43913 | ||||||||
\(478\) | 73.0466 | 3.34107 | ||||||||
\(479\) | −21.5096 | −0.982797 | −0.491398 | − | 0.870935i | \(-0.663514\pi\) | ||||
−0.491398 | + | 0.870935i | \(0.663514\pi\) | |||||||
\(480\) | −48.2469 | −2.20216 | ||||||||
\(481\) | −5.98626 | −0.272950 | ||||||||
\(482\) | −44.8489 | −2.04281 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.41468 | 0.291576 | ||||||||
\(485\) | −8.72520 | −0.396191 | ||||||||
\(486\) | −24.1637 | −1.09609 | ||||||||
\(487\) | −30.8062 | −1.39596 | −0.697982 | − | 0.716115i | \(-0.745918\pi\) | ||||
−0.697982 | + | 0.716115i | \(0.745918\pi\) | |||||||
\(488\) | 52.1818 | 2.36216 | ||||||||
\(489\) | −4.52840 | −0.204781 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.1395 | 0.773495 | 0.386747 | − | 0.922186i | \(-0.373599\pi\) | ||||
0.386747 | + | 0.922186i | \(0.373599\pi\) | |||||||
\(492\) | 71.1497 | 3.20768 | ||||||||
\(493\) | −15.5505 | −0.700361 | ||||||||
\(494\) | 9.56927 | 0.430542 | ||||||||
\(495\) | 35.3063 | 1.58690 | ||||||||
\(496\) | −5.59558 | −0.251249 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 30.3178 | 1.35857 | ||||||||
\(499\) | −23.9337 | −1.07142 | −0.535711 | − | 0.844402i | \(-0.679956\pi\) | ||||
−0.535711 | + | 0.844402i | \(0.679956\pi\) | |||||||
\(500\) | 57.5434 | 2.57342 | ||||||||
\(501\) | 45.3689 | 2.02694 | ||||||||
\(502\) | −8.58615 | −0.383219 | ||||||||
\(503\) | −6.98088 | −0.311262 | −0.155631 | − | 0.987815i | \(-0.549741\pi\) | ||||
−0.155631 | + | 0.987815i | \(0.549741\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.05898 | 0.0471239 | ||||||||
\(506\) | −15.6806 | −0.697089 | ||||||||
\(507\) | 1.75861 | 0.0781027 | ||||||||
\(508\) | −28.2942 | −1.25535 | ||||||||
\(509\) | 10.4918 | 0.465039 | 0.232520 | − | 0.972592i | \(-0.425303\pi\) | ||||
0.232520 | + | 0.972592i | \(0.425303\pi\) | |||||||
\(510\) | 67.8911 | 3.00627 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −46.4119 | −2.05113 | ||||||||
\(513\) | −6.97467 | −0.307939 | ||||||||
\(514\) | 5.71047 | 0.251878 | ||||||||
\(515\) | −22.7195 | −1.00114 | ||||||||
\(516\) | 84.8050 | 3.73333 | ||||||||
\(517\) | −19.1071 | −0.840331 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 28.9417 | 1.27040 | ||||||||
\(520\) | 48.5384 | 2.12855 | ||||||||
\(521\) | −1.21564 | −0.0532580 | −0.0266290 | − | 0.999645i | \(-0.508477\pi\) | ||||
−0.0266290 | + | 0.999645i | \(0.508477\pi\) | |||||||
\(522\) | 44.8887 | 1.96473 | ||||||||
\(523\) | 4.25228 | 0.185939 | 0.0929697 | − | 0.995669i | \(-0.470364\pi\) | ||||
0.0929697 | + | 0.995669i | \(0.470364\pi\) | |||||||
\(524\) | −87.8081 | −3.83592 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.70201 | 0.161415 | ||||||||
\(527\) | 3.05016 | 0.132867 | ||||||||
\(528\) | −90.8266 | −3.95272 | ||||||||
\(529\) | −20.0431 | −0.871440 | ||||||||
\(530\) | −28.0268 | −1.21740 | ||||||||
\(531\) | 26.4321 | 1.14705 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.1385 | −0.828982 | ||||||||
\(534\) | 9.97866 | 0.431819 | ||||||||
\(535\) | 34.1398 | 1.47599 | ||||||||
\(536\) | −0.623174 | −0.0269170 | ||||||||
\(537\) | 45.4491 | 1.96127 | ||||||||
\(538\) | 5.88716 | 0.253813 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −61.2965 | −2.63778 | ||||||||
\(541\) | 32.2316 | 1.38575 | 0.692873 | − | 0.721060i | \(-0.256345\pi\) | ||||
0.692873 | + | 0.721060i | \(0.256345\pi\) | |||||||
\(542\) | −8.92310 | −0.383280 | ||||||||
\(543\) | 40.7721 | 1.74970 | ||||||||
\(544\) | −43.5097 | −1.86546 | ||||||||
\(545\) | 25.9429 | 1.11127 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.39956 | −0.0598407 | −0.0299204 | − | 0.999552i | \(-0.509525\pi\) | ||||
−0.0299204 | + | 0.999552i | \(0.509525\pi\) | |||||||
\(548\) | −1.85806 | −0.0793723 | ||||||||
\(549\) | 39.8306 | 1.69993 | ||||||||
\(550\) | 14.1127 | 0.601768 | ||||||||
\(551\) | −3.20098 | −0.136366 | ||||||||
\(552\) | 35.3065 | 1.50275 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 15.3486 | 0.652099 | ||||||||
\(555\) | −8.74232 | −0.371091 | ||||||||
\(556\) | −10.4500 | −0.443179 | ||||||||
\(557\) | 26.4429 | 1.12042 | 0.560212 | − | 0.828349i | \(-0.310720\pi\) | ||||
0.560212 | + | 0.828349i | \(0.310720\pi\) | |||||||
\(558\) | −8.80471 | −0.372733 | ||||||||
\(559\) | −22.8117 | −0.964831 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 49.5098 | 2.09031 | ||||||||
\(562\) | −63.4387 | −2.67600 | ||||||||
\(563\) | −27.1771 | −1.14538 | −0.572689 | − | 0.819772i | \(-0.694100\pi\) | ||||
−0.572689 | + | 0.819772i | \(0.694100\pi\) | |||||||
\(564\) | 74.5405 | 3.13872 | ||||||||
\(565\) | 35.8308 | 1.50742 | ||||||||
\(566\) | 61.4634 | 2.58350 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 111.887 | 4.69469 | ||||||||
\(569\) | −16.2384 | −0.680748 | −0.340374 | − | 0.940290i | \(-0.610554\pi\) | ||||
−0.340374 | + | 0.940290i | \(0.610554\pi\) | |||||||
\(570\) | 13.9749 | 0.585346 | ||||||||
\(571\) | −22.8445 | −0.956011 | −0.478005 | − | 0.878357i | \(-0.658640\pi\) | ||||
−0.478005 | + | 0.878357i | \(0.658640\pi\) | |||||||
\(572\) | 61.3295 | 2.56431 | ||||||||
\(573\) | 41.3372 | 1.72689 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.66122 | −0.110981 | ||||||||
\(576\) | 29.2437 | 1.21849 | ||||||||
\(577\) | 47.6337 | 1.98302 | 0.991509 | − | 0.130041i | \(-0.0415109\pi\) | ||||
0.991509 | + | 0.130041i | \(0.0415109\pi\) | |||||||
\(578\) | 17.1237 | 0.712250 | ||||||||
\(579\) | −18.1495 | −0.754267 | ||||||||
\(580\) | −28.1316 | −1.16810 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 35.3189 | 1.46401 | ||||||||
\(583\) | −20.4386 | −0.846481 | ||||||||
\(584\) | −21.3746 | −0.884486 | ||||||||
\(585\) | 37.0496 | 1.53181 | ||||||||
\(586\) | −38.5514 | −1.59254 | ||||||||
\(587\) | 21.9802 | 0.907221 | 0.453611 | − | 0.891200i | \(-0.350136\pi\) | ||||
0.453611 | + | 0.891200i | \(0.350136\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.627857 | 0.0258704 | ||||||||
\(590\) | −23.5692 | −0.970329 | ||||||||
\(591\) | −12.9522 | −0.532780 | ||||||||
\(592\) | 14.4632 | 0.594436 | ||||||||
\(593\) | 9.04871 | 0.371586 | 0.185793 | − | 0.982589i | \(-0.440515\pi\) | ||||
0.185793 | + | 0.982589i | \(0.440515\pi\) | |||||||
\(594\) | −63.6020 | −2.60962 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 69.7290 | 2.85621 | ||||||||
\(597\) | −46.0506 | −1.88473 | ||||||||
\(598\) | −16.4549 | −0.672892 | ||||||||
\(599\) | 3.14651 | 0.128563 | 0.0642814 | − | 0.997932i | \(-0.479524\pi\) | ||||
0.0642814 | + | 0.997932i | \(0.479524\pi\) | |||||||
\(600\) | −31.7762 | −1.29726 | ||||||||
\(601\) | −34.2901 | −1.39872 | −0.699361 | − | 0.714769i | \(-0.746532\pi\) | ||||
−0.699361 | + | 0.714769i | \(0.746532\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.475672 | −0.0193708 | ||||||||
\(604\) | −40.8832 | −1.66351 | ||||||||
\(605\) | −2.51989 | −0.102448 | ||||||||
\(606\) | −4.28666 | −0.174134 | ||||||||
\(607\) | 3.90479 | 0.158491 | 0.0792454 | − | 0.996855i | \(-0.474749\pi\) | ||||
0.0792454 | + | 0.996855i | \(0.474749\pi\) | |||||||
\(608\) | −8.95619 | −0.363221 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −35.5165 | −1.43802 | ||||||||
\(611\) | −20.0506 | −0.811161 | ||||||||
\(612\) | −124.212 | −5.02099 | ||||||||
\(613\) | −17.5869 | −0.710330 | −0.355165 | − | 0.934804i | \(-0.615575\pi\) | ||||
−0.355165 | + | 0.934804i | \(0.615575\pi\) | |||||||
\(614\) | −59.8250 | −2.41434 | ||||||||
\(615\) | −27.9499 | −1.12705 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 43.3913 | 1.74687 | 0.873434 | − | 0.486943i | \(-0.161888\pi\) | ||||
0.873434 | + | 0.486943i | \(0.161888\pi\) | |||||||
\(618\) | 91.9667 | 3.69944 | ||||||||
\(619\) | 26.8786 | 1.08034 | 0.540172 | − | 0.841555i | \(-0.318359\pi\) | ||||
0.540172 | + | 0.841555i | \(0.318359\pi\) | |||||||
\(620\) | 5.51788 | 0.221603 | ||||||||
\(621\) | 11.9934 | 0.481277 | ||||||||
\(622\) | −19.1072 | −0.766128 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −95.3115 | −3.81551 | ||||||||
\(625\) | −14.8668 | −0.594671 | ||||||||
\(626\) | 17.1306 | 0.684677 | ||||||||
\(627\) | 10.1913 | 0.407001 | ||||||||
\(628\) | −109.074 | −4.35252 | ||||||||
\(629\) | −7.88395 | −0.314354 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.5102 | −1.17478 | −0.587391 | − | 0.809303i | \(-0.699845\pi\) | ||||
−0.587391 | + | 0.809303i | \(0.699845\pi\) | |||||||
\(632\) | −104.482 | −4.15609 | ||||||||
\(633\) | 25.2803 | 1.00480 | ||||||||
\(634\) | −51.2185 | −2.03415 | ||||||||
\(635\) | 11.1149 | 0.441081 | ||||||||
\(636\) | 79.7348 | 3.16169 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −29.1897 | −1.15563 | ||||||||
\(639\) | 85.4041 | 3.37854 | ||||||||
\(640\) | 7.20592 | 0.284839 | ||||||||
\(641\) | −11.1538 | −0.440548 | −0.220274 | − | 0.975438i | \(-0.570695\pi\) | ||||
−0.220274 | + | 0.975438i | \(0.570695\pi\) | |||||||
\(642\) | −138.195 | −5.45412 | ||||||||
\(643\) | 30.3635 | 1.19742 | 0.598710 | − | 0.800966i | \(-0.295680\pi\) | ||||
0.598710 | + | 0.800966i | \(0.295680\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −33.3141 | −1.31174 | ||||||||
\(646\) | 12.6028 | 0.495851 | ||||||||
\(647\) | 11.1611 | 0.438790 | 0.219395 | − | 0.975636i | \(-0.429592\pi\) | ||||
0.219395 | + | 0.975636i | \(0.429592\pi\) | |||||||
\(648\) | 28.3583 | 1.11402 | ||||||||
\(649\) | −17.1879 | −0.674685 | ||||||||
\(650\) | 14.8096 | 0.580880 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.38773 | −0.289326 | ||||||||
\(653\) | 40.0307 | 1.56652 | 0.783262 | − | 0.621692i | \(-0.213554\pi\) | ||||
0.783262 | + | 0.621692i | \(0.213554\pi\) | |||||||
\(654\) | −105.015 | −4.10640 | ||||||||
\(655\) | 34.4938 | 1.34779 | ||||||||
\(656\) | 46.2401 | 1.80537 | ||||||||
\(657\) | −16.3153 | −0.636521 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.9271 | −0.776248 | −0.388124 | − | 0.921607i | \(-0.626877\pi\) | ||||
−0.388124 | + | 0.921607i | \(0.626877\pi\) | |||||||
\(660\) | 89.5655 | 3.48633 | ||||||||
\(661\) | 22.4030 | 0.871375 | 0.435687 | − | 0.900098i | \(-0.356505\pi\) | ||||
0.435687 | + | 0.900098i | \(0.356505\pi\) | |||||||
\(662\) | 90.5426 | 3.51904 | ||||||||
\(663\) | 51.9545 | 2.01775 | ||||||||
\(664\) | 28.5469 | 1.10783 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 22.7581 | 0.881858 | ||||||||
\(667\) | 5.50427 | 0.213126 | ||||||||
\(668\) | 74.0159 | 2.86376 | ||||||||
\(669\) | 14.7959 | 0.572041 | ||||||||
\(670\) | 0.424151 | 0.0163864 | ||||||||
\(671\) | −25.9006 | −0.999880 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.4386 | 0.826399 | 0.413200 | − | 0.910640i | \(-0.364411\pi\) | ||||
0.413200 | + | 0.910640i | \(0.364411\pi\) | |||||||
\(674\) | −58.1912 | −2.24144 | ||||||||
\(675\) | −10.7941 | −0.415466 | ||||||||
\(676\) | 2.86904 | 0.110348 | ||||||||
\(677\) | −1.63459 | −0.0628223 | −0.0314111 | − | 0.999507i | \(-0.510000\pi\) | ||||
−0.0314111 | + | 0.999507i | \(0.510000\pi\) | |||||||
\(678\) | −145.040 | −5.57024 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 63.9255 | 2.45143 | ||||||||
\(681\) | 6.27979 | 0.240642 | ||||||||
\(682\) | 5.72542 | 0.219238 | ||||||||
\(683\) | −32.3500 | −1.23784 | −0.618920 | − | 0.785454i | \(-0.712430\pi\) | ||||
−0.618920 | + | 0.785454i | \(0.712430\pi\) | |||||||
\(684\) | −25.5683 | −0.977630 | ||||||||
\(685\) | 0.729905 | 0.0278882 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −70.3034 | −2.68224 | ||||||||
\(688\) | 55.1147 | 2.10123 | ||||||||
\(689\) | −21.4478 | −0.817098 | ||||||||
\(690\) | −24.0307 | −0.914834 | ||||||||
\(691\) | −25.5852 | −0.973308 | −0.486654 | − | 0.873595i | \(-0.661783\pi\) | ||||
−0.486654 | + | 0.873595i | \(0.661783\pi\) | |||||||
\(692\) | 47.2161 | 1.79489 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.91828 | 0.338533 | ||||||||
\(695\) | 4.10510 | 0.155715 | ||||||||
\(696\) | 65.7236 | 2.49125 | ||||||||
\(697\) | −25.2056 | −0.954731 | ||||||||
\(698\) | 41.4269 | 1.56803 | ||||||||
\(699\) | 8.09960 | 0.306355 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.2978 | 1.03102 | 0.515511 | − | 0.856883i | \(-0.327602\pi\) | ||||
0.515511 | + | 0.856883i | \(0.327602\pi\) | |||||||
\(702\) | −66.7425 | −2.51903 | ||||||||
\(703\) | −1.62286 | −0.0612073 | ||||||||
\(704\) | −19.0163 | −0.716702 | ||||||||
\(705\) | −29.2819 | −1.10282 | ||||||||
\(706\) | −60.9230 | −2.29287 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 67.0533 | 2.52002 | ||||||||
\(709\) | 25.8953 | 0.972520 | 0.486260 | − | 0.873814i | \(-0.338361\pi\) | ||||
0.486260 | + | 0.873814i | \(0.338361\pi\) | |||||||
\(710\) | −76.1540 | −2.85801 | ||||||||
\(711\) | −79.7520 | −2.99093 | ||||||||
\(712\) | 9.39579 | 0.352122 | ||||||||
\(713\) | −1.07964 | −0.0404327 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.0922 | −0.900997 | ||||||||
\(716\) | 74.1467 | 2.77099 | ||||||||
\(717\) | 81.6360 | 3.04875 | ||||||||
\(718\) | −19.4267 | −0.724998 | ||||||||
\(719\) | 7.38755 | 0.275509 | 0.137755 | − | 0.990466i | \(-0.456011\pi\) | ||||
0.137755 | + | 0.990466i | \(0.456011\pi\) | |||||||
\(720\) | −89.5146 | −3.33601 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.59421 | 0.0965464 | ||||||||
\(723\) | −50.1226 | −1.86408 | ||||||||
\(724\) | 66.5164 | 2.47206 | ||||||||
\(725\) | −4.95389 | −0.183983 | ||||||||
\(726\) | 10.2003 | 0.378569 | ||||||||
\(727\) | 29.7644 | 1.10390 | 0.551950 | − | 0.833877i | \(-0.313884\pi\) | ||||
0.551950 | + | 0.833877i | \(0.313884\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −39.0180 | −1.44511 | ||||||||
\(730\) | 14.5482 | 0.538453 | ||||||||
\(731\) | −30.0432 | −1.11119 | ||||||||
\(732\) | 101.043 | 3.73465 | ||||||||
\(733\) | 45.3928 | 1.67662 | 0.838312 | − | 0.545191i | \(-0.183543\pi\) | ||||
0.838312 | + | 0.545191i | \(0.183543\pi\) | |||||||
\(734\) | 3.42928 | 0.126577 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.4007 | 0.567677 | ||||||||
\(737\) | 0.309314 | 0.0113937 | ||||||||
\(738\) | 72.7594 | 2.67831 | ||||||||
\(739\) | 48.1394 | 1.77084 | 0.885418 | − | 0.464796i | \(-0.153872\pi\) | ||||
0.885418 | + | 0.464796i | \(0.153872\pi\) | |||||||
\(740\) | −14.2624 | −0.524297 | ||||||||
\(741\) | 10.6945 | 0.392873 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.43426 | −0.272737 | −0.136368 | − | 0.990658i | \(-0.543543\pi\) | ||||
−0.136368 | + | 0.990658i | \(0.543543\pi\) | |||||||
\(744\) | −12.8914 | −0.472620 | ||||||||
\(745\) | −27.3918 | −1.00356 | ||||||||
\(746\) | 41.6646 | 1.52545 | ||||||||
\(747\) | 21.7900 | 0.797254 | ||||||||
\(748\) | 80.7714 | 2.95329 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 91.5026 | 3.34120 | ||||||||
\(751\) | −16.1586 | −0.589636 | −0.294818 | − | 0.955553i | \(-0.595259\pi\) | ||||
−0.294818 | + | 0.955553i | \(0.595259\pi\) | |||||||
\(752\) | 48.4438 | 1.76656 | ||||||||
\(753\) | −9.59578 | −0.349690 | ||||||||
\(754\) | −30.6310 | −1.11552 | ||||||||
\(755\) | 16.0602 | 0.584492 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.5836 | 1.22062 | 0.610308 | − | 0.792164i | \(-0.291046\pi\) | ||||
0.610308 | + | 0.792164i | \(0.291046\pi\) | |||||||
\(758\) | 77.0956 | 2.80024 | ||||||||
\(759\) | −17.5245 | −0.636099 | ||||||||
\(760\) | 13.1587 | 0.477314 | ||||||||
\(761\) | −29.4504 | −1.06757 | −0.533787 | − | 0.845619i | \(-0.679232\pi\) | ||||
−0.533787 | + | 0.845619i | \(0.679232\pi\) | |||||||
\(762\) | −44.9921 | −1.62989 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 67.4385 | 2.43984 | ||||||||
\(765\) | 48.7947 | 1.76417 | ||||||||
\(766\) | 22.8781 | 0.826621 | ||||||||
\(767\) | −18.0366 | −0.651265 | ||||||||
\(768\) | −60.5378 | −2.18447 | ||||||||
\(769\) | 38.9622 | 1.40501 | 0.702506 | − | 0.711678i | \(-0.252064\pi\) | ||||
0.702506 | + | 0.711678i | \(0.252064\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.38196 | 0.229841 | ||||||||
\(772\) | −29.6094 | −1.06567 | ||||||||
\(773\) | −9.94169 | −0.357578 | −0.178789 | − | 0.983887i | \(-0.557218\pi\) | ||||
−0.178789 | + | 0.983887i | \(0.557218\pi\) | |||||||
\(774\) | 86.7236 | 3.11722 | ||||||||
\(775\) | 0.971682 | 0.0349039 | ||||||||
\(776\) | 33.2558 | 1.19382 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.98835 | −0.250545 | ||||||||
\(779\) | −5.18841 | −0.185894 | ||||||||
\(780\) | 93.9880 | 3.36531 | ||||||||
\(781\) | −55.5356 | −1.98722 | ||||||||
\(782\) | −21.6713 | −0.774963 | ||||||||
\(783\) | 22.3258 | 0.797858 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 42.8477 | 1.52930 | ||||||||
\(786\) | −139.628 | −4.98037 | ||||||||
\(787\) | −48.5087 | −1.72915 | −0.864575 | − | 0.502505i | \(-0.832412\pi\) | ||||
−0.864575 | + | 0.502505i | \(0.832412\pi\) | |||||||
\(788\) | −21.1304 | −0.752740 | ||||||||
\(789\) | 4.13732 | 0.147293 | ||||||||
\(790\) | 71.1140 | 2.53012 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −134.569 | −4.78170 | ||||||||
\(793\) | −27.1795 | −0.965172 | ||||||||
\(794\) | 32.8135 | 1.16451 | ||||||||
\(795\) | −31.3224 | −1.11089 | ||||||||
\(796\) | −75.1280 | −2.66284 | ||||||||
\(797\) | 33.5790 | 1.18943 | 0.594715 | − | 0.803936i | \(-0.297265\pi\) | ||||
0.594715 | + | 0.803936i | \(0.297265\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.4068 | −0.934206 | ||||||||
\(800\) | −13.8608 | −0.490052 | ||||||||
\(801\) | 7.17185 | 0.253405 | ||||||||
\(802\) | 36.4032 | 1.28544 | ||||||||
\(803\) | 10.6093 | 0.374395 | ||||||||
\(804\) | −1.20669 | −0.0425567 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.00813 | 0.211627 | ||||||||
\(807\) | 6.57942 | 0.231606 | ||||||||
\(808\) | −4.03627 | −0.141995 | ||||||||
\(809\) | 53.5849 | 1.88395 | 0.941973 | − | 0.335689i | \(-0.108969\pi\) | ||||
0.941973 | + | 0.335689i | \(0.108969\pi\) | |||||||
\(810\) | −19.3015 | −0.678187 | ||||||||
\(811\) | −44.4587 | −1.56116 | −0.780579 | − | 0.625057i | \(-0.785076\pi\) | ||||
−0.780579 | + | 0.625057i | \(0.785076\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.97236 | −0.349746 | ||||||||
\(814\) | −14.7988 | −0.518699 | ||||||||
\(815\) | 2.90214 | 0.101657 | ||||||||
\(816\) | −125.526 | −4.39429 | ||||||||
\(817\) | −6.18419 | −0.216357 | ||||||||
\(818\) | 49.7020 | 1.73779 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −45.5981 | −1.59235 | ||||||||
\(821\) | 0.257745 | 0.00899535 | 0.00449767 | − | 0.999990i | \(-0.498568\pi\) | ||||
0.00449767 | + | 0.999990i | \(0.498568\pi\) | |||||||
\(822\) | −2.95459 | −0.103053 | ||||||||
\(823\) | 9.75380 | 0.339996 | 0.169998 | − | 0.985444i | \(-0.445624\pi\) | ||||
0.169998 | + | 0.985444i | \(0.445624\pi\) | |||||||
\(824\) | 86.5948 | 3.01667 | ||||||||
\(825\) | 15.7722 | 0.549118 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.5627 | 1.02800 | 0.513998 | − | 0.857791i | \(-0.328164\pi\) | ||||
0.513998 | + | 0.857791i | \(0.328164\pi\) | |||||||
\(828\) | 43.9662 | 1.52793 | ||||||||
\(829\) | −40.7861 | −1.41656 | −0.708280 | − | 0.705931i | \(-0.750529\pi\) | ||||
−0.708280 | + | 0.705931i | \(0.750529\pi\) | |||||||
\(830\) | −19.4299 | −0.674422 | ||||||||
\(831\) | 17.1534 | 0.595045 | ||||||||
\(832\) | −19.9552 | −0.691823 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −16.6171 | −0.575403 | ||||||||
\(835\) | −29.0758 | −1.00621 | ||||||||
\(836\) | 16.6263 | 0.575032 | ||||||||
\(837\) | −4.37909 | −0.151364 | ||||||||
\(838\) | 51.6338 | 1.78366 | ||||||||
\(839\) | −13.7643 | −0.475195 | −0.237597 | − | 0.971364i | \(-0.576360\pi\) | ||||
−0.237597 | + | 0.971364i | \(0.576360\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.7537 | −0.646680 | ||||||||
\(842\) | −4.21256 | −0.145174 | ||||||||
\(843\) | −70.8984 | −2.44187 | ||||||||
\(844\) | 41.2428 | 1.41964 | ||||||||
\(845\) | −1.12705 | −0.0387717 | ||||||||
\(846\) | 76.2269 | 2.62073 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 51.8195 | 1.77949 | ||||||||
\(849\) | 68.6908 | 2.35746 | ||||||||
\(850\) | 19.5043 | 0.668993 | ||||||||
\(851\) | 2.79060 | 0.0956606 | ||||||||
\(852\) | 216.654 | 7.42246 | ||||||||
\(853\) | 11.6913 | 0.400303 | 0.200152 | − | 0.979765i | \(-0.435857\pi\) | ||||
0.200152 | + | 0.979765i | \(0.435857\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.0441 | 0.343500 | ||||||||
\(856\) | −130.123 | −4.44751 | ||||||||
\(857\) | −3.07531 | −0.105051 | −0.0525253 | − | 0.998620i | \(-0.516727\pi\) | ||||
−0.0525253 | + | 0.998620i | \(0.516727\pi\) | |||||||
\(858\) | 97.5231 | 3.32938 | ||||||||
\(859\) | −52.3984 | −1.78781 | −0.893906 | − | 0.448255i | \(-0.852046\pi\) | ||||
−0.893906 | + | 0.448255i | \(0.852046\pi\) | |||||||
\(860\) | −54.3494 | −1.85330 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.6619 | −0.839987 | ||||||||
\(863\) | 29.0479 | 0.988802 | 0.494401 | − | 0.869234i | \(-0.335388\pi\) | ||||
0.494401 | + | 0.869234i | \(0.335388\pi\) | |||||||
\(864\) | 62.4665 | 2.12515 | ||||||||
\(865\) | −18.5480 | −0.630650 | ||||||||
\(866\) | −85.5428 | −2.90686 | ||||||||
\(867\) | 19.1372 | 0.649934 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 51.8601 | 1.75923 | ||||||||
\(870\) | −44.7335 | −1.51661 | ||||||||
\(871\) | 0.324587 | 0.0109982 | ||||||||
\(872\) | −98.8807 | −3.34852 | ||||||||
\(873\) | 25.3844 | 0.859130 | ||||||||
\(874\) | −4.46089 | −0.150892 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −41.3889 | −1.39840 | ||||||||
\(877\) | −37.2859 | −1.25906 | −0.629528 | − | 0.776978i | \(-0.716752\pi\) | ||||
−0.629528 | + | 0.776978i | \(0.716752\pi\) | |||||||
\(878\) | 73.9400 | 2.49535 | ||||||||
\(879\) | −43.0846 | −1.45321 | ||||||||
\(880\) | 58.2085 | 1.96221 | ||||||||
\(881\) | −13.6326 | −0.459295 | −0.229648 | − | 0.973274i | \(-0.573757\pi\) | ||||
−0.229648 | + | 0.973274i | \(0.573757\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.2253 | −1.58926 | −0.794629 | − | 0.607096i | \(-0.792335\pi\) | ||||
−0.794629 | + | 0.607096i | \(0.792335\pi\) | |||||||
\(884\) | 84.7597 | 2.85078 | ||||||||
\(885\) | −26.3407 | −0.885432 | ||||||||
\(886\) | −12.7963 | −0.429901 | ||||||||
\(887\) | −47.8778 | −1.60758 | −0.803789 | − | 0.594914i | \(-0.797186\pi\) | ||||
−0.803789 | + | 0.594914i | \(0.797186\pi\) | |||||||
\(888\) | 33.3211 | 1.11818 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6.39507 | −0.214363 | ||||||||
\(891\) | −14.0757 | −0.471554 | ||||||||
\(892\) | 24.1383 | 0.808210 | ||||||||
\(893\) | −5.43568 | −0.181898 | ||||||||
\(894\) | 110.880 | 3.70837 | ||||||||
\(895\) | −29.1272 | −0.973615 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.3898 | −0.614018 | ||||||||
\(898\) | 61.8052 | 2.06247 | ||||||||
\(899\) | −2.00976 | −0.0670291 | ||||||||
\(900\) | −39.5700 | −1.31900 | ||||||||
\(901\) | −28.2470 | −0.941043 | ||||||||
\(902\) | −47.3131 | −1.57535 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −136.568 | −4.54219 | ||||||||
\(905\) | −26.1298 | −0.868583 | ||||||||
\(906\) | −65.0105 | −2.15983 | ||||||||
\(907\) | 4.27946 | 0.142097 | 0.0710485 | − | 0.997473i | \(-0.477365\pi\) | ||||
0.0710485 | + | 0.997473i | \(0.477365\pi\) | |||||||
\(908\) | 10.2450 | 0.339991 | ||||||||
\(909\) | −3.08090 | −0.102187 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.50426 | −0.0829697 | −0.0414848 | − | 0.999139i | \(-0.513209\pi\) | ||||
−0.0414848 | + | 0.999139i | \(0.513209\pi\) | |||||||
\(912\) | −25.8387 | −0.855605 | ||||||||
\(913\) | −14.1693 | −0.468936 | ||||||||
\(914\) | 42.8941 | 1.41881 | ||||||||
\(915\) | −39.6929 | −1.31221 | ||||||||
\(916\) | −114.694 | −3.78961 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −87.9004 | −2.90115 | ||||||||
\(919\) | 7.25451 | 0.239304 | 0.119652 | − | 0.992816i | \(-0.461822\pi\) | ||||
0.119652 | + | 0.992816i | \(0.461822\pi\) | |||||||
\(920\) | −22.6271 | −0.745992 | ||||||||
\(921\) | −66.8597 | −2.20310 | ||||||||
\(922\) | 74.0697 | 2.43936 | ||||||||
\(923\) | −58.2778 | −1.91824 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.51157 | −0.0825799 | ||||||||
\(926\) | −61.7085 | −2.02787 | ||||||||
\(927\) | 66.0982 | 2.17095 | ||||||||
\(928\) | 28.6686 | 0.941092 | ||||||||
\(929\) | −8.75357 | −0.287195 | −0.143598 | − | 0.989636i | \(-0.545867\pi\) | ||||
−0.143598 | + | 0.989636i | \(0.545867\pi\) | |||||||
\(930\) | 8.77426 | 0.287719 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 13.2139 | 0.432834 | ||||||||
\(933\) | −21.3540 | −0.699098 | ||||||||
\(934\) | −62.5028 | −2.04515 | ||||||||
\(935\) | −31.7296 | −1.03767 | ||||||||
\(936\) | −141.214 | −4.61571 | ||||||||
\(937\) | −28.4821 | −0.930469 | −0.465235 | − | 0.885187i | \(-0.654030\pi\) | ||||
−0.465235 | + | 0.885187i | \(0.654030\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.1450 | 0.624772 | ||||||||
\(940\) | −47.7711 | −1.55812 | ||||||||
\(941\) | −31.6167 | −1.03068 | −0.515338 | − | 0.856987i | \(-0.672334\pi\) | ||||
−0.515338 | + | 0.856987i | \(0.672334\pi\) | |||||||
\(942\) | −173.444 | −5.65111 | ||||||||
\(943\) | 8.92178 | 0.290533 | ||||||||
\(944\) | 43.5778 | 1.41834 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −56.3936 | −1.83351 | ||||||||
\(947\) | 16.1626 | 0.525215 | 0.262607 | − | 0.964903i | \(-0.415418\pi\) | ||||
0.262607 | + | 0.964903i | \(0.415418\pi\) | |||||||
\(948\) | −202.316 | −6.57091 | ||||||||
\(949\) | 11.1332 | 0.361399 | ||||||||
\(950\) | 4.01484 | 0.130259 | ||||||||
\(951\) | −57.2412 | −1.85617 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.5802 | 1.02298 | 0.511492 | − | 0.859288i | \(-0.329093\pi\) | ||||
0.511492 | + | 0.859288i | \(0.329093\pi\) | |||||||
\(954\) | 81.5387 | 2.63991 | ||||||||
\(955\) | −26.4920 | −0.857261 | ||||||||
\(956\) | 133.183 | 4.30744 | ||||||||
\(957\) | −32.6221 | −1.05452 | ||||||||
\(958\) | −55.8002 | −1.80282 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −29.1426 | −0.940573 | ||||||||
\(961\) | −30.6058 | −0.987284 | ||||||||
\(962\) | −15.5296 | −0.500694 | ||||||||
\(963\) | −99.3234 | −3.20065 | ||||||||
\(964\) | −81.7710 | −2.63367 | ||||||||
\(965\) | 11.6315 | 0.374432 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.3998 | −1.52427 | −0.762137 | − | 0.647415i | \(-0.775850\pi\) | ||||
−0.762137 | + | 0.647415i | \(0.775850\pi\) | |||||||
\(968\) | 9.60450 | 0.308700 | ||||||||
\(969\) | 14.0847 | 0.452467 | ||||||||
\(970\) | −22.6350 | −0.726765 | ||||||||
\(971\) | −27.0996 | −0.869669 | −0.434835 | − | 0.900510i | \(-0.643193\pi\) | ||||
−0.434835 | + | 0.900510i | \(0.643193\pi\) | |||||||
\(972\) | −44.0566 | −1.41312 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −79.9177 | −2.56073 | ||||||||
\(975\) | 16.5510 | 0.530057 | ||||||||
\(976\) | 65.6676 | 2.10197 | ||||||||
\(977\) | 29.9068 | 0.956804 | 0.478402 | − | 0.878141i | \(-0.341216\pi\) | ||||
0.478402 | + | 0.878141i | \(0.341216\pi\) | |||||||
\(978\) | −11.7476 | −0.375647 | ||||||||
\(979\) | −4.66363 | −0.149050 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −75.4761 | −2.40977 | ||||||||
\(982\) | 44.4634 | 1.41888 | ||||||||
\(983\) | 17.8375 | 0.568928 | 0.284464 | − | 0.958687i | \(-0.408184\pi\) | ||||
0.284464 | + | 0.958687i | \(0.408184\pi\) | |||||||
\(984\) | 106.530 | 3.39606 | ||||||||
\(985\) | 8.30071 | 0.264483 | ||||||||
\(986\) | −40.3413 | −1.28473 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17.4472 | 0.555071 | ||||||||
\(989\) | 10.6341 | 0.338144 | ||||||||
\(990\) | 91.5917 | 2.91098 | ||||||||
\(991\) | −27.9506 | −0.887881 | −0.443940 | − | 0.896056i | \(-0.646420\pi\) | ||||
−0.443940 | + | 0.896056i | \(0.646420\pi\) | |||||||
\(992\) | −5.62320 | −0.178537 | ||||||||
\(993\) | 101.189 | 3.21115 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 29.5127 | 0.935615 | ||||||||
\(996\) | 55.2771 | 1.75152 | ||||||||
\(997\) | −29.8690 | −0.945960 | −0.472980 | − | 0.881073i | \(-0.656822\pi\) | ||||
−0.472980 | + | 0.881073i | \(0.656822\pi\) | |||||||
\(998\) | −62.0891 | −1.96539 | ||||||||
\(999\) | 11.3189 | 0.358115 |
(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 | 931.2.a.o.1.6 | 7 | ||
3.2 | odd | 2 | 8379.2.a.ck.1.2 | 7 | |||
7.2 | even | 3 | 931.2.f.p.704.2 | 14 | |||
7.3 | odd | 6 | 133.2.f.d.58.2 | yes | 14 | ||
7.4 | even | 3 | 931.2.f.p.324.2 | 14 | |||
7.5 | odd | 6 | 133.2.f.d.39.2 | ✓ | 14 | ||
7.6 | odd | 2 | 931.2.a.n.1.6 | 7 | |||
21.5 | even | 6 | 1197.2.j.l.172.6 | 14 | |||
21.17 | even | 6 | 1197.2.j.l.856.6 | 14 | |||
21.20 | even | 2 | 8379.2.a.cl.1.2 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
133.2.f.d.39.2 | ✓ | 14 | 7.5 | odd | 6 | ||
133.2.f.d.58.2 | yes | 14 | 7.3 | odd | 6 | ||
931.2.a.n.1.6 | 7 | 7.6 | odd | 2 | |||
931.2.a.o.1.6 | 7 | 1.1 | even | 1 | trivial | ||
931.2.f.p.324.2 | 14 | 7.4 | even | 3 | |||
931.2.f.p.704.2 | 14 | 7.2 | even | 3 | |||
1197.2.j.l.172.6 | 14 | 21.5 | even | 6 | |||
1197.2.j.l.856.6 | 14 | 21.17 | even | 6 | |||
8379.2.a.ck.1.2 | 7 | 3.2 | odd | 2 | |||
8379.2.a.cl.1.2 | 7 | 21.20 | even | 2 |