Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, 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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.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: | \(32.0200112105\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 12x^{8} + 34x^{7} + 46x^{6} - 104x^{5} - 90x^{4} + 89x^{3} + 82x^{2} + 12x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.54628\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.74362 | −1.00668 | −0.503341 | − | 0.864088i | \(-0.667896\pi\) | ||||
−0.503341 | + | 0.864088i | \(0.667896\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.74362 | 0.711831 | ||||||||
\(7\) | 2.79885 | 1.05786 | 0.528932 | − | 0.848664i | \(-0.322593\pi\) | ||||
0.528932 | + | 0.848664i | \(0.322593\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.0402221 | 0.0134074 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 2.90568 | 0.876097 | 0.438048 | − | 0.898951i | \(-0.355670\pi\) | ||||
0.438048 | + | 0.898951i | \(0.355670\pi\) | |||||||
\(12\) | −1.74362 | −0.503341 | ||||||||
\(13\) | 3.29780 | 0.914645 | 0.457322 | − | 0.889301i | \(-0.348809\pi\) | ||||
0.457322 | + | 0.889301i | \(0.348809\pi\) | |||||||
\(14\) | −2.79885 | −0.748023 | ||||||||
\(15\) | −1.74362 | −0.450202 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.26503 | −1.03442 | −0.517210 | − | 0.855858i | \(-0.673030\pi\) | ||||
−0.517210 | + | 0.855858i | \(0.673030\pi\) | |||||||
\(18\) | −0.0402221 | −0.00948044 | ||||||||
\(19\) | −0.133159 | −0.0305488 | −0.0152744 | − | 0.999883i | \(-0.504862\pi\) | ||||
−0.0152744 | + | 0.999883i | \(0.504862\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −4.88013 | −1.06493 | ||||||||
\(22\) | −2.90568 | −0.619494 | ||||||||
\(23\) | −1.71130 | −0.356831 | −0.178415 | − | 0.983955i | \(-0.557097\pi\) | ||||
−0.178415 | + | 0.983955i | \(0.557097\pi\) | |||||||
\(24\) | 1.74362 | 0.355916 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.29780 | −0.646751 | ||||||||
\(27\) | 5.16074 | 0.993184 | ||||||||
\(28\) | 2.79885 | 0.528932 | ||||||||
\(29\) | −2.64609 | −0.491366 | −0.245683 | − | 0.969350i | \(-0.579012\pi\) | ||||
−0.245683 | + | 0.969350i | \(0.579012\pi\) | |||||||
\(30\) | 1.74362 | 0.318341 | ||||||||
\(31\) | −9.13104 | −1.63998 | −0.819992 | − | 0.572375i | \(-0.806022\pi\) | ||||
−0.819992 | + | 0.572375i | \(0.806022\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.06642 | −0.881950 | ||||||||
\(34\) | 4.26503 | 0.731446 | ||||||||
\(35\) | 2.79885 | 0.473091 | ||||||||
\(36\) | 0.0402221 | 0.00670368 | ||||||||
\(37\) | −11.8979 | −1.95600 | −0.978001 | − | 0.208598i | \(-0.933110\pi\) | ||||
−0.978001 | + | 0.208598i | \(0.933110\pi\) | |||||||
\(38\) | 0.133159 | 0.0216012 | ||||||||
\(39\) | −5.75012 | −0.920756 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −5.26369 | −0.822050 | −0.411025 | − | 0.911624i | \(-0.634829\pi\) | ||||
−0.411025 | + | 0.911624i | \(0.634829\pi\) | |||||||
\(42\) | 4.88013 | 0.753021 | ||||||||
\(43\) | −4.56873 | −0.696724 | −0.348362 | − | 0.937360i | \(-0.613262\pi\) | ||||
−0.348362 | + | 0.937360i | \(0.613262\pi\) | |||||||
\(44\) | 2.90568 | 0.438048 | ||||||||
\(45\) | 0.0402221 | 0.00599596 | ||||||||
\(46\) | 1.71130 | 0.252317 | ||||||||
\(47\) | 6.49550 | 0.947466 | 0.473733 | − | 0.880668i | \(-0.342906\pi\) | ||||
0.473733 | + | 0.880668i | \(0.342906\pi\) | |||||||
\(48\) | −1.74362 | −0.251670 | ||||||||
\(49\) | 0.833534 | 0.119076 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 7.43660 | 1.04133 | ||||||||
\(52\) | 3.29780 | 0.457322 | ||||||||
\(53\) | 4.03808 | 0.554673 | 0.277336 | − | 0.960773i | \(-0.410548\pi\) | ||||
0.277336 | + | 0.960773i | \(0.410548\pi\) | |||||||
\(54\) | −5.16074 | −0.702287 | ||||||||
\(55\) | 2.90568 | 0.391802 | ||||||||
\(56\) | −2.79885 | −0.374011 | ||||||||
\(57\) | 0.232179 | 0.0307529 | ||||||||
\(58\) | 2.64609 | 0.347448 | ||||||||
\(59\) | −6.96517 | −0.906788 | −0.453394 | − | 0.891310i | \(-0.649787\pi\) | ||||
−0.453394 | + | 0.891310i | \(0.649787\pi\) | |||||||
\(60\) | −1.74362 | −0.225101 | ||||||||
\(61\) | −5.75525 | −0.736885 | −0.368442 | − | 0.929651i | \(-0.620109\pi\) | ||||
−0.368442 | + | 0.929651i | \(0.620109\pi\) | |||||||
\(62\) | 9.13104 | 1.15964 | ||||||||
\(63\) | 0.112575 | 0.0141832 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.29780 | 0.409041 | ||||||||
\(66\) | 5.06642 | 0.623633 | ||||||||
\(67\) | −1.15003 | −0.140499 | −0.0702494 | − | 0.997529i | \(-0.522380\pi\) | ||||
−0.0702494 | + | 0.997529i | \(0.522380\pi\) | |||||||
\(68\) | −4.26503 | −0.517210 | ||||||||
\(69\) | 2.98386 | 0.359215 | ||||||||
\(70\) | −2.79885 | −0.334526 | ||||||||
\(71\) | −0.443856 | −0.0526760 | −0.0263380 | − | 0.999653i | \(-0.508385\pi\) | ||||
−0.0263380 | + | 0.999653i | \(0.508385\pi\) | |||||||
\(72\) | −0.0402221 | −0.00474022 | ||||||||
\(73\) | −0.955975 | −0.111888 | −0.0559442 | − | 0.998434i | \(-0.517817\pi\) | ||||
−0.0559442 | + | 0.998434i | \(0.517817\pi\) | |||||||
\(74\) | 11.8979 | 1.38310 | ||||||||
\(75\) | −1.74362 | −0.201336 | ||||||||
\(76\) | −0.133159 | −0.0152744 | ||||||||
\(77\) | 8.13256 | 0.926791 | ||||||||
\(78\) | 5.75012 | 0.651073 | ||||||||
\(79\) | −14.5373 | −1.63557 | −0.817785 | − | 0.575523i | \(-0.804798\pi\) | ||||
−0.817785 | + | 0.575523i | \(0.804798\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −9.11905 | −1.01323 | ||||||||
\(82\) | 5.26369 | 0.581277 | ||||||||
\(83\) | 16.8564 | 1.85023 | 0.925115 | − | 0.379688i | \(-0.123969\pi\) | ||||
0.925115 | + | 0.379688i | \(0.123969\pi\) | |||||||
\(84\) | −4.88013 | −0.532466 | ||||||||
\(85\) | −4.26503 | −0.462607 | ||||||||
\(86\) | 4.56873 | 0.492658 | ||||||||
\(87\) | 4.61378 | 0.494649 | ||||||||
\(88\) | −2.90568 | −0.309747 | ||||||||
\(89\) | −13.2086 | −1.40011 | −0.700054 | − | 0.714090i | \(-0.746841\pi\) | ||||
−0.700054 | + | 0.714090i | \(0.746841\pi\) | |||||||
\(90\) | −0.0402221 | −0.00423978 | ||||||||
\(91\) | 9.23003 | 0.967570 | ||||||||
\(92\) | −1.71130 | −0.178415 | ||||||||
\(93\) | 15.9211 | 1.65094 | ||||||||
\(94\) | −6.49550 | −0.669960 | ||||||||
\(95\) | −0.133159 | −0.0136618 | ||||||||
\(96\) | 1.74362 | 0.177958 | ||||||||
\(97\) | −8.57086 | −0.870239 | −0.435120 | − | 0.900373i | \(-0.643294\pi\) | ||||
−0.435120 | + | 0.900373i | \(0.643294\pi\) | |||||||
\(98\) | −0.833534 | −0.0841997 | ||||||||
\(99\) | 0.116873 | 0.0117462 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 13.3505 | 1.32842 | 0.664211 | − | 0.747545i | \(-0.268768\pi\) | ||||
0.664211 | + | 0.747545i | \(0.268768\pi\) | |||||||
\(102\) | −7.43660 | −0.736333 | ||||||||
\(103\) | −16.0085 | −1.57737 | −0.788684 | − | 0.614799i | \(-0.789237\pi\) | ||||
−0.788684 | + | 0.614799i | \(0.789237\pi\) | |||||||
\(104\) | −3.29780 | −0.323376 | ||||||||
\(105\) | −4.88013 | −0.476252 | ||||||||
\(106\) | −4.03808 | −0.392213 | ||||||||
\(107\) | −10.8925 | −1.05302 | −0.526511 | − | 0.850168i | \(-0.676500\pi\) | ||||
−0.526511 | + | 0.850168i | \(0.676500\pi\) | |||||||
\(108\) | 5.16074 | 0.496592 | ||||||||
\(109\) | 10.3384 | 0.990235 | 0.495117 | − | 0.868826i | \(-0.335125\pi\) | ||||
0.495117 | + | 0.868826i | \(0.335125\pi\) | |||||||
\(110\) | −2.90568 | −0.277046 | ||||||||
\(111\) | 20.7455 | 1.96907 | ||||||||
\(112\) | 2.79885 | 0.264466 | ||||||||
\(113\) | 11.1906 | 1.05272 | 0.526360 | − | 0.850262i | \(-0.323557\pi\) | ||||
0.526360 | + | 0.850262i | \(0.323557\pi\) | |||||||
\(114\) | −0.232179 | −0.0217456 | ||||||||
\(115\) | −1.71130 | −0.159580 | ||||||||
\(116\) | −2.64609 | −0.245683 | ||||||||
\(117\) | 0.132644 | 0.0122630 | ||||||||
\(118\) | 6.96517 | 0.641196 | ||||||||
\(119\) | −11.9371 | −1.09428 | ||||||||
\(120\) | 1.74362 | 0.159170 | ||||||||
\(121\) | −2.55700 | −0.232455 | ||||||||
\(122\) | 5.75525 | 0.521056 | ||||||||
\(123\) | 9.17789 | 0.827542 | ||||||||
\(124\) | −9.13104 | −0.819992 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.112575 | −0.0100290 | ||||||||
\(127\) | −0.0819637 | −0.00727310 | −0.00363655 | − | 0.999993i | \(-0.501158\pi\) | ||||
−0.00363655 | + | 0.999993i | \(0.501158\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 7.96614 | 0.701379 | ||||||||
\(130\) | −3.29780 | −0.289236 | ||||||||
\(131\) | 3.94983 | 0.345098 | 0.172549 | − | 0.985001i | \(-0.444800\pi\) | ||||
0.172549 | + | 0.985001i | \(0.444800\pi\) | |||||||
\(132\) | −5.06642 | −0.440975 | ||||||||
\(133\) | −0.372691 | −0.0323164 | ||||||||
\(134\) | 1.15003 | 0.0993477 | ||||||||
\(135\) | 5.16074 | 0.444166 | ||||||||
\(136\) | 4.26503 | 0.365723 | ||||||||
\(137\) | 17.4396 | 1.48996 | 0.744981 | − | 0.667085i | \(-0.232458\pi\) | ||||
0.744981 | + | 0.667085i | \(0.232458\pi\) | |||||||
\(138\) | −2.98386 | −0.254003 | ||||||||
\(139\) | −6.57556 | −0.557732 | −0.278866 | − | 0.960330i | \(-0.589958\pi\) | ||||
−0.278866 | + | 0.960330i | \(0.589958\pi\) | |||||||
\(140\) | 2.79885 | 0.236546 | ||||||||
\(141\) | −11.3257 | −0.953797 | ||||||||
\(142\) | 0.443856 | 0.0372476 | ||||||||
\(143\) | 9.58236 | 0.801317 | ||||||||
\(144\) | 0.0402221 | 0.00335184 | ||||||||
\(145\) | −2.64609 | −0.219746 | ||||||||
\(146\) | 0.955975 | 0.0791170 | ||||||||
\(147\) | −1.45337 | −0.119872 | ||||||||
\(148\) | −11.8979 | −0.978001 | ||||||||
\(149\) | 6.75074 | 0.553042 | 0.276521 | − | 0.961008i | \(-0.410818\pi\) | ||||
0.276521 | + | 0.961008i | \(0.410818\pi\) | |||||||
\(150\) | 1.74362 | 0.142366 | ||||||||
\(151\) | 9.75498 | 0.793849 | 0.396925 | − | 0.917851i | \(-0.370077\pi\) | ||||
0.396925 | + | 0.917851i | \(0.370077\pi\) | |||||||
\(152\) | 0.133159 | 0.0108006 | ||||||||
\(153\) | −0.171548 | −0.0138689 | ||||||||
\(154\) | −8.13256 | −0.655340 | ||||||||
\(155\) | −9.13104 | −0.733423 | ||||||||
\(156\) | −5.75012 | −0.460378 | ||||||||
\(157\) | 16.8599 | 1.34557 | 0.672784 | − | 0.739839i | \(-0.265098\pi\) | ||||
0.672784 | + | 0.739839i | \(0.265098\pi\) | |||||||
\(158\) | 14.5373 | 1.15652 | ||||||||
\(159\) | −7.04089 | −0.558379 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −4.78967 | −0.377478 | ||||||||
\(162\) | 9.11905 | 0.716460 | ||||||||
\(163\) | 1.37041 | 0.107339 | 0.0536693 | − | 0.998559i | \(-0.482908\pi\) | ||||
0.0536693 | + | 0.998559i | \(0.482908\pi\) | |||||||
\(164\) | −5.26369 | −0.411025 | ||||||||
\(165\) | −5.06642 | −0.394420 | ||||||||
\(166\) | −16.8564 | −1.30831 | ||||||||
\(167\) | −16.5346 | −1.27949 | −0.639743 | − | 0.768589i | \(-0.720959\pi\) | ||||
−0.639743 | + | 0.768589i | \(0.720959\pi\) | |||||||
\(168\) | 4.88013 | 0.376510 | ||||||||
\(169\) | −2.12453 | −0.163425 | ||||||||
\(170\) | 4.26503 | 0.327113 | ||||||||
\(171\) | −0.00535593 | −0.000409579 0 | ||||||||
\(172\) | −4.56873 | −0.348362 | ||||||||
\(173\) | 16.2885 | 1.23840 | 0.619198 | − | 0.785235i | \(-0.287458\pi\) | ||||
0.619198 | + | 0.785235i | \(0.287458\pi\) | |||||||
\(174\) | −4.61378 | −0.349770 | ||||||||
\(175\) | 2.79885 | 0.211573 | ||||||||
\(176\) | 2.90568 | 0.219024 | ||||||||
\(177\) | 12.1446 | 0.912846 | ||||||||
\(178\) | 13.2086 | 0.990026 | ||||||||
\(179\) | −4.16912 | −0.311614 | −0.155807 | − | 0.987787i | \(-0.549798\pi\) | ||||
−0.155807 | + | 0.987787i | \(0.549798\pi\) | |||||||
\(180\) | 0.0402221 | 0.00299798 | ||||||||
\(181\) | 0.834483 | 0.0620266 | 0.0310133 | − | 0.999519i | \(-0.490127\pi\) | ||||
0.0310133 | + | 0.999519i | \(0.490127\pi\) | |||||||
\(182\) | −9.23003 | −0.684175 | ||||||||
\(183\) | 10.0350 | 0.741808 | ||||||||
\(184\) | 1.71130 | 0.126159 | ||||||||
\(185\) | −11.8979 | −0.874751 | ||||||||
\(186\) | −15.9211 | −1.16739 | ||||||||
\(187\) | −12.3928 | −0.906253 | ||||||||
\(188\) | 6.49550 | 0.473733 | ||||||||
\(189\) | 14.4441 | 1.05065 | ||||||||
\(190\) | 0.133159 | 0.00966037 | ||||||||
\(191\) | 17.5122 | 1.26714 | 0.633569 | − | 0.773686i | \(-0.281589\pi\) | ||||
0.633569 | + | 0.773686i | \(0.281589\pi\) | |||||||
\(192\) | −1.74362 | −0.125835 | ||||||||
\(193\) | −3.27577 | −0.235795 | −0.117897 | − | 0.993026i | \(-0.537615\pi\) | ||||
−0.117897 | + | 0.993026i | \(0.537615\pi\) | |||||||
\(194\) | 8.57086 | 0.615352 | ||||||||
\(195\) | −5.75012 | −0.411774 | ||||||||
\(196\) | 0.833534 | 0.0595382 | ||||||||
\(197\) | −16.3680 | −1.16617 | −0.583087 | − | 0.812410i | \(-0.698155\pi\) | ||||
−0.583087 | + | 0.812410i | \(0.698155\pi\) | |||||||
\(198\) | −0.116873 | −0.00830578 | ||||||||
\(199\) | 5.25004 | 0.372166 | 0.186083 | − | 0.982534i | \(-0.440421\pi\) | ||||
0.186083 | + | 0.982534i | \(0.440421\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 2.00522 | 0.141438 | ||||||||
\(202\) | −13.3505 | −0.939336 | ||||||||
\(203\) | −7.40599 | −0.519798 | ||||||||
\(204\) | 7.43660 | 0.520666 | ||||||||
\(205\) | −5.26369 | −0.367632 | ||||||||
\(206\) | 16.0085 | 1.11537 | ||||||||
\(207\) | −0.0688321 | −0.00478416 | ||||||||
\(208\) | 3.29780 | 0.228661 | ||||||||
\(209\) | −0.386918 | −0.0267637 | ||||||||
\(210\) | 4.88013 | 0.336761 | ||||||||
\(211\) | −18.6119 | −1.28130 | −0.640648 | − | 0.767835i | \(-0.721334\pi\) | ||||
−0.640648 | + | 0.767835i | \(0.721334\pi\) | |||||||
\(212\) | 4.03808 | 0.277336 | ||||||||
\(213\) | 0.773917 | 0.0530280 | ||||||||
\(214\) | 10.8925 | 0.744599 | ||||||||
\(215\) | −4.56873 | −0.311584 | ||||||||
\(216\) | −5.16074 | −0.351144 | ||||||||
\(217\) | −25.5564 | −1.73488 | ||||||||
\(218\) | −10.3384 | −0.700202 | ||||||||
\(219\) | 1.66686 | 0.112636 | ||||||||
\(220\) | 2.90568 | 0.195901 | ||||||||
\(221\) | −14.0652 | −0.946127 | ||||||||
\(222\) | −20.7455 | −1.39234 | ||||||||
\(223\) | −5.61665 | −0.376118 | −0.188059 | − | 0.982158i | \(-0.560220\pi\) | ||||
−0.188059 | + | 0.982158i | \(0.560220\pi\) | |||||||
\(224\) | −2.79885 | −0.187006 | ||||||||
\(225\) | 0.0402221 | 0.00268147 | ||||||||
\(226\) | −11.1906 | −0.744385 | ||||||||
\(227\) | −19.0382 | −1.26361 | −0.631806 | − | 0.775127i | \(-0.717686\pi\) | ||||
−0.631806 | + | 0.775127i | \(0.717686\pi\) | |||||||
\(228\) | 0.232179 | 0.0153764 | ||||||||
\(229\) | −18.2529 | −1.20618 | −0.603092 | − | 0.797672i | \(-0.706065\pi\) | ||||
−0.603092 | + | 0.797672i | \(0.706065\pi\) | |||||||
\(230\) | 1.71130 | 0.112840 | ||||||||
\(231\) | −14.1801 | −0.932983 | ||||||||
\(232\) | 2.64609 | 0.173724 | ||||||||
\(233\) | 17.9389 | 1.17522 | 0.587609 | − | 0.809145i | \(-0.300069\pi\) | ||||
0.587609 | + | 0.809145i | \(0.300069\pi\) | |||||||
\(234\) | −0.132644 | −0.00867123 | ||||||||
\(235\) | 6.49550 | 0.423720 | ||||||||
\(236\) | −6.96517 | −0.453394 | ||||||||
\(237\) | 25.3475 | 1.64650 | ||||||||
\(238\) | 11.9371 | 0.773770 | ||||||||
\(239\) | −27.5765 | −1.78378 | −0.891889 | − | 0.452254i | \(-0.850620\pi\) | ||||
−0.891889 | + | 0.452254i | \(0.850620\pi\) | |||||||
\(240\) | −1.74362 | −0.112550 | ||||||||
\(241\) | 9.60993 | 0.619030 | 0.309515 | − | 0.950895i | \(-0.399833\pi\) | ||||
0.309515 | + | 0.950895i | \(0.399833\pi\) | |||||||
\(242\) | 2.55700 | 0.164370 | ||||||||
\(243\) | 0.417972 | 0.0268129 | ||||||||
\(244\) | −5.75525 | −0.368442 | ||||||||
\(245\) | 0.833534 | 0.0532525 | ||||||||
\(246\) | −9.17789 | −0.585161 | ||||||||
\(247\) | −0.439131 | −0.0279413 | ||||||||
\(248\) | 9.13104 | 0.579822 | ||||||||
\(249\) | −29.3912 | −1.86259 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −27.8466 | −1.75766 | −0.878832 | − | 0.477131i | \(-0.841677\pi\) | ||||
−0.878832 | + | 0.477131i | \(0.841677\pi\) | |||||||
\(252\) | 0.112575 | 0.00709159 | ||||||||
\(253\) | −4.97250 | −0.312618 | ||||||||
\(254\) | 0.0819637 | 0.00514286 | ||||||||
\(255\) | 7.43660 | 0.465698 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.46595 | 0.0914436 | 0.0457218 | − | 0.998954i | \(-0.485441\pi\) | ||||
0.0457218 | + | 0.998954i | \(0.485441\pi\) | |||||||
\(258\) | −7.96614 | −0.495950 | ||||||||
\(259\) | −33.3004 | −2.06919 | ||||||||
\(260\) | 3.29780 | 0.204521 | ||||||||
\(261\) | −0.106431 | −0.00658792 | ||||||||
\(262\) | −3.94983 | −0.244021 | ||||||||
\(263\) | 24.0201 | 1.48114 | 0.740570 | − | 0.671979i | \(-0.234556\pi\) | ||||
0.740570 | + | 0.671979i | \(0.234556\pi\) | |||||||
\(264\) | 5.06642 | 0.311816 | ||||||||
\(265\) | 4.03808 | 0.248057 | ||||||||
\(266\) | 0.372691 | 0.0228512 | ||||||||
\(267\) | 23.0308 | 1.40946 | ||||||||
\(268\) | −1.15003 | −0.0702494 | ||||||||
\(269\) | 15.2572 | 0.930250 | 0.465125 | − | 0.885245i | \(-0.346009\pi\) | ||||
0.465125 | + | 0.885245i | \(0.346009\pi\) | |||||||
\(270\) | −5.16074 | −0.314072 | ||||||||
\(271\) | −7.93860 | −0.482235 | −0.241118 | − | 0.970496i | \(-0.577514\pi\) | ||||
−0.241118 | + | 0.970496i | \(0.577514\pi\) | |||||||
\(272\) | −4.26503 | −0.258605 | ||||||||
\(273\) | −16.0937 | −0.974034 | ||||||||
\(274\) | −17.4396 | −1.05356 | ||||||||
\(275\) | 2.90568 | 0.175219 | ||||||||
\(276\) | 2.98386 | 0.179607 | ||||||||
\(277\) | 4.90642 | 0.294798 | 0.147399 | − | 0.989077i | \(-0.452910\pi\) | ||||
0.147399 | + | 0.989077i | \(0.452910\pi\) | |||||||
\(278\) | 6.57556 | 0.394376 | ||||||||
\(279\) | −0.367270 | −0.0219879 | ||||||||
\(280\) | −2.79885 | −0.167263 | ||||||||
\(281\) | −29.6156 | −1.76672 | −0.883360 | − | 0.468695i | \(-0.844724\pi\) | ||||
−0.883360 | + | 0.468695i | \(0.844724\pi\) | |||||||
\(282\) | 11.3257 | 0.674436 | ||||||||
\(283\) | 2.32408 | 0.138152 | 0.0690762 | − | 0.997611i | \(-0.477995\pi\) | ||||
0.0690762 | + | 0.997611i | \(0.477995\pi\) | |||||||
\(284\) | −0.443856 | −0.0263380 | ||||||||
\(285\) | 0.232179 | 0.0137531 | ||||||||
\(286\) | −9.58236 | −0.566617 | ||||||||
\(287\) | −14.7322 | −0.869617 | ||||||||
\(288\) | −0.0402221 | −0.00237011 | ||||||||
\(289\) | 1.19045 | 0.0700267 | ||||||||
\(290\) | 2.64609 | 0.155384 | ||||||||
\(291\) | 14.9444 | 0.876054 | ||||||||
\(292\) | −0.955975 | −0.0559442 | ||||||||
\(293\) | −24.9104 | −1.45528 | −0.727641 | − | 0.685958i | \(-0.759384\pi\) | ||||
−0.727641 | + | 0.685958i | \(0.759384\pi\) | |||||||
\(294\) | 1.45337 | 0.0847622 | ||||||||
\(295\) | −6.96517 | −0.405528 | ||||||||
\(296\) | 11.8979 | 0.691551 | ||||||||
\(297\) | 14.9955 | 0.870126 | ||||||||
\(298\) | −6.75074 | −0.391060 | ||||||||
\(299\) | −5.64352 | −0.326373 | ||||||||
\(300\) | −1.74362 | −0.100668 | ||||||||
\(301\) | −12.7872 | −0.737039 | ||||||||
\(302\) | −9.75498 | −0.561336 | ||||||||
\(303\) | −23.2782 | −1.33730 | ||||||||
\(304\) | −0.133159 | −0.00763719 | ||||||||
\(305\) | −5.75525 | −0.329545 | ||||||||
\(306\) | 0.171548 | 0.00980677 | ||||||||
\(307\) | 21.2022 | 1.21008 | 0.605038 | − | 0.796197i | \(-0.293158\pi\) | ||||
0.605038 | + | 0.796197i | \(0.293158\pi\) | |||||||
\(308\) | 8.13256 | 0.463396 | ||||||||
\(309\) | 27.9128 | 1.58791 | ||||||||
\(310\) | 9.13104 | 0.518608 | ||||||||
\(311\) | 5.00671 | 0.283904 | 0.141952 | − | 0.989874i | \(-0.454662\pi\) | ||||
0.141952 | + | 0.989874i | \(0.454662\pi\) | |||||||
\(312\) | 5.75012 | 0.325536 | ||||||||
\(313\) | 23.1915 | 1.31086 | 0.655431 | − | 0.755255i | \(-0.272487\pi\) | ||||
0.655431 | + | 0.755255i | \(0.272487\pi\) | |||||||
\(314\) | −16.8599 | −0.951460 | ||||||||
\(315\) | 0.112575 | 0.00634291 | ||||||||
\(316\) | −14.5373 | −0.817785 | ||||||||
\(317\) | 16.0766 | 0.902952 | 0.451476 | − | 0.892283i | \(-0.350898\pi\) | ||||
0.451476 | + | 0.892283i | \(0.350898\pi\) | |||||||
\(318\) | 7.04089 | 0.394833 | ||||||||
\(319\) | −7.68869 | −0.430484 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 18.9925 | 1.06006 | ||||||||
\(322\) | 4.78967 | 0.266918 | ||||||||
\(323\) | 0.567927 | 0.0316003 | ||||||||
\(324\) | −9.11905 | −0.506614 | ||||||||
\(325\) | 3.29780 | 0.182929 | ||||||||
\(326\) | −1.37041 | −0.0758999 | ||||||||
\(327\) | −18.0262 | −0.996851 | ||||||||
\(328\) | 5.26369 | 0.290639 | ||||||||
\(329\) | 18.1799 | 1.00229 | ||||||||
\(330\) | 5.06642 | 0.278897 | ||||||||
\(331\) | 3.88676 | 0.213636 | 0.106818 | − | 0.994279i | \(-0.465934\pi\) | ||||
0.106818 | + | 0.994279i | \(0.465934\pi\) | |||||||
\(332\) | 16.8564 | 0.925115 | ||||||||
\(333\) | −0.478559 | −0.0262249 | ||||||||
\(334\) | 16.5346 | 0.904733 | ||||||||
\(335\) | −1.15003 | −0.0628330 | ||||||||
\(336\) | −4.88013 | −0.266233 | ||||||||
\(337\) | 9.32872 | 0.508168 | 0.254084 | − | 0.967182i | \(-0.418226\pi\) | ||||
0.254084 | + | 0.967182i | \(0.418226\pi\) | |||||||
\(338\) | 2.12453 | 0.115559 | ||||||||
\(339\) | −19.5121 | −1.05975 | ||||||||
\(340\) | −4.26503 | −0.231304 | ||||||||
\(341\) | −26.5319 | −1.43678 | ||||||||
\(342\) | 0.00535593 | 0.000289616 0 | ||||||||
\(343\) | −17.2590 | −0.931897 | ||||||||
\(344\) | 4.56873 | 0.246329 | ||||||||
\(345\) | 2.98386 | 0.160646 | ||||||||
\(346\) | −16.2885 | −0.875678 | ||||||||
\(347\) | −34.2218 | −1.83712 | −0.918560 | − | 0.395282i | \(-0.870647\pi\) | ||||
−0.918560 | + | 0.395282i | \(0.870647\pi\) | |||||||
\(348\) | 4.61378 | 0.247324 | ||||||||
\(349\) | −33.0131 | −1.76715 | −0.883576 | − | 0.468288i | \(-0.844871\pi\) | ||||
−0.883576 | + | 0.468288i | \(0.844871\pi\) | |||||||
\(350\) | −2.79885 | −0.149605 | ||||||||
\(351\) | 17.0191 | 0.908411 | ||||||||
\(352\) | −2.90568 | −0.154873 | ||||||||
\(353\) | 11.6475 | 0.619934 | 0.309967 | − | 0.950747i | \(-0.399682\pi\) | ||||
0.309967 | + | 0.950747i | \(0.399682\pi\) | |||||||
\(354\) | −12.1446 | −0.645480 | ||||||||
\(355\) | −0.443856 | −0.0235574 | ||||||||
\(356\) | −13.2086 | −0.700054 | ||||||||
\(357\) | 20.8139 | 1.10159 | ||||||||
\(358\) | 4.16912 | 0.220345 | ||||||||
\(359\) | −11.8552 | −0.625695 | −0.312848 | − | 0.949803i | \(-0.601283\pi\) | ||||
−0.312848 | + | 0.949803i | \(0.601283\pi\) | |||||||
\(360\) | −0.0402221 | −0.00211989 | ||||||||
\(361\) | −18.9823 | −0.999067 | ||||||||
\(362\) | −0.834483 | −0.0438594 | ||||||||
\(363\) | 4.45845 | 0.234008 | ||||||||
\(364\) | 9.23003 | 0.483785 | ||||||||
\(365\) | −0.955975 | −0.0500380 | ||||||||
\(366\) | −10.0350 | −0.524538 | ||||||||
\(367\) | −21.3941 | −1.11676 | −0.558382 | − | 0.829584i | \(-0.688578\pi\) | ||||
−0.558382 | + | 0.829584i | \(0.688578\pi\) | |||||||
\(368\) | −1.71130 | −0.0892077 | ||||||||
\(369\) | −0.211717 | −0.0110215 | ||||||||
\(370\) | 11.8979 | 0.618542 | ||||||||
\(371\) | 11.3020 | 0.586768 | ||||||||
\(372\) | 15.9211 | 0.825471 | ||||||||
\(373\) | −22.1828 | −1.14858 | −0.574291 | − | 0.818651i | \(-0.694722\pi\) | ||||
−0.574291 | + | 0.818651i | \(0.694722\pi\) | |||||||
\(374\) | 12.3928 | 0.640817 | ||||||||
\(375\) | −1.74362 | −0.0900403 | ||||||||
\(376\) | −6.49550 | −0.334980 | ||||||||
\(377\) | −8.72626 | −0.449425 | ||||||||
\(378\) | −14.4441 | −0.742925 | ||||||||
\(379\) | 21.7483 | 1.11714 | 0.558569 | − | 0.829458i | \(-0.311351\pi\) | ||||
0.558569 | + | 0.829458i | \(0.311351\pi\) | |||||||
\(380\) | −0.133159 | −0.00683091 | ||||||||
\(381\) | 0.142914 | 0.00732169 | ||||||||
\(382\) | −17.5122 | −0.896002 | ||||||||
\(383\) | 15.3907 | 0.786429 | 0.393214 | − | 0.919447i | \(-0.371363\pi\) | ||||
0.393214 | + | 0.919447i | \(0.371363\pi\) | |||||||
\(384\) | 1.74362 | 0.0889789 | ||||||||
\(385\) | 8.13256 | 0.414474 | ||||||||
\(386\) | 3.27577 | 0.166732 | ||||||||
\(387\) | −0.183764 | −0.00934124 | ||||||||
\(388\) | −8.57086 | −0.435120 | ||||||||
\(389\) | 21.0759 | 1.06859 | 0.534296 | − | 0.845297i | \(-0.320577\pi\) | ||||
0.534296 | + | 0.845297i | \(0.320577\pi\) | |||||||
\(390\) | 5.75012 | 0.291168 | ||||||||
\(391\) | 7.29874 | 0.369113 | ||||||||
\(392\) | −0.833534 | −0.0420998 | ||||||||
\(393\) | −6.88701 | −0.347404 | ||||||||
\(394\) | 16.3680 | 0.824610 | ||||||||
\(395\) | −14.5373 | −0.731450 | ||||||||
\(396\) | 0.116873 | 0.00587308 | ||||||||
\(397\) | −35.7748 | −1.79549 | −0.897744 | − | 0.440518i | \(-0.854795\pi\) | ||||
−0.897744 | + | 0.440518i | \(0.854795\pi\) | |||||||
\(398\) | −5.25004 | −0.263161 | ||||||||
\(399\) | 0.649833 | 0.0325324 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | −2.00522 | −0.100011 | ||||||||
\(403\) | −30.1123 | −1.50000 | ||||||||
\(404\) | 13.3505 | 0.664211 | ||||||||
\(405\) | −9.11905 | −0.453129 | ||||||||
\(406\) | 7.40599 | 0.367553 | ||||||||
\(407\) | −34.5715 | −1.71365 | ||||||||
\(408\) | −7.43660 | −0.368167 | ||||||||
\(409\) | −33.6239 | −1.66259 | −0.831297 | − | 0.555828i | \(-0.812401\pi\) | ||||
−0.831297 | + | 0.555828i | \(0.812401\pi\) | |||||||
\(410\) | 5.26369 | 0.259955 | ||||||||
\(411\) | −30.4080 | −1.49992 | ||||||||
\(412\) | −16.0085 | −0.788684 | ||||||||
\(413\) | −19.4944 | −0.959258 | ||||||||
\(414\) | 0.0688321 | 0.00338291 | ||||||||
\(415\) | 16.8564 | 0.827448 | ||||||||
\(416\) | −3.29780 | −0.161688 | ||||||||
\(417\) | 11.4653 | 0.561458 | ||||||||
\(418\) | 0.386918 | 0.0189248 | ||||||||
\(419\) | −5.91594 | −0.289012 | −0.144506 | − | 0.989504i | \(-0.546159\pi\) | ||||
−0.144506 | + | 0.989504i | \(0.546159\pi\) | |||||||
\(420\) | −4.88013 | −0.238126 | ||||||||
\(421\) | −15.9075 | −0.775284 | −0.387642 | − | 0.921810i | \(-0.626710\pi\) | ||||
−0.387642 | + | 0.921810i | \(0.626710\pi\) | |||||||
\(422\) | 18.6119 | 0.906013 | ||||||||
\(423\) | 0.261263 | 0.0127030 | ||||||||
\(424\) | −4.03808 | −0.196106 | ||||||||
\(425\) | −4.26503 | −0.206884 | ||||||||
\(426\) | −0.773917 | −0.0374964 | ||||||||
\(427\) | −16.1081 | −0.779524 | ||||||||
\(428\) | −10.8925 | −0.526511 | ||||||||
\(429\) | −16.7080 | −0.806671 | ||||||||
\(430\) | 4.56873 | 0.220324 | ||||||||
\(431\) | 21.9256 | 1.05612 | 0.528059 | − | 0.849208i | \(-0.322920\pi\) | ||||
0.528059 | + | 0.849208i | \(0.322920\pi\) | |||||||
\(432\) | 5.16074 | 0.248296 | ||||||||
\(433\) | 31.5732 | 1.51731 | 0.758656 | − | 0.651491i | \(-0.225856\pi\) | ||||
0.758656 | + | 0.651491i | \(0.225856\pi\) | |||||||
\(434\) | 25.5564 | 1.22675 | ||||||||
\(435\) | 4.61378 | 0.221214 | ||||||||
\(436\) | 10.3384 | 0.495117 | ||||||||
\(437\) | 0.227875 | 0.0109007 | ||||||||
\(438\) | −1.66686 | −0.0796456 | ||||||||
\(439\) | 5.12336 | 0.244525 | 0.122262 | − | 0.992498i | \(-0.460985\pi\) | ||||
0.122262 | + | 0.992498i | \(0.460985\pi\) | |||||||
\(440\) | −2.90568 | −0.138523 | ||||||||
\(441\) | 0.0335265 | 0.00159650 | ||||||||
\(442\) | 14.0652 | 0.669013 | ||||||||
\(443\) | −35.2770 | −1.67606 | −0.838030 | − | 0.545625i | \(-0.816292\pi\) | ||||
−0.838030 | + | 0.545625i | \(0.816292\pi\) | |||||||
\(444\) | 20.7455 | 0.984536 | ||||||||
\(445\) | −13.2086 | −0.626148 | ||||||||
\(446\) | 5.61665 | 0.265956 | ||||||||
\(447\) | −11.7708 | −0.556737 | ||||||||
\(448\) | 2.79885 | 0.132233 | ||||||||
\(449\) | −13.7311 | −0.648009 | −0.324005 | − | 0.946056i | \(-0.605029\pi\) | ||||
−0.324005 | + | 0.946056i | \(0.605029\pi\) | |||||||
\(450\) | −0.0402221 | −0.00189609 | ||||||||
\(451\) | −15.2946 | −0.720195 | ||||||||
\(452\) | 11.1906 | 0.526360 | ||||||||
\(453\) | −17.0090 | −0.799153 | ||||||||
\(454\) | 19.0382 | 0.893508 | ||||||||
\(455\) | 9.23003 | 0.432710 | ||||||||
\(456\) | −0.232179 | −0.0108728 | ||||||||
\(457\) | 32.3369 | 1.51265 | 0.756327 | − | 0.654194i | \(-0.226992\pi\) | ||||
0.756327 | + | 0.654194i | \(0.226992\pi\) | |||||||
\(458\) | 18.2529 | 0.852900 | ||||||||
\(459\) | −22.0107 | −1.02737 | ||||||||
\(460\) | −1.71130 | −0.0797898 | ||||||||
\(461\) | 0.219374 | 0.0102173 | 0.00510864 | − | 0.999987i | \(-0.498374\pi\) | ||||
0.00510864 | + | 0.999987i | \(0.498374\pi\) | |||||||
\(462\) | 14.1801 | 0.659719 | ||||||||
\(463\) | −7.36374 | −0.342222 | −0.171111 | − | 0.985252i | \(-0.554736\pi\) | ||||
−0.171111 | + | 0.985252i | \(0.554736\pi\) | |||||||
\(464\) | −2.64609 | −0.122841 | ||||||||
\(465\) | 15.9211 | 0.738323 | ||||||||
\(466\) | −17.9389 | −0.831005 | ||||||||
\(467\) | −13.1656 | −0.609232 | −0.304616 | − | 0.952475i | \(-0.598528\pi\) | ||||
−0.304616 | + | 0.952475i | \(0.598528\pi\) | |||||||
\(468\) | 0.132644 | 0.00613149 | ||||||||
\(469\) | −3.21876 | −0.148629 | ||||||||
\(470\) | −6.49550 | −0.299615 | ||||||||
\(471\) | −29.3974 | −1.35456 | ||||||||
\(472\) | 6.96517 | 0.320598 | ||||||||
\(473\) | −13.2753 | −0.610398 | ||||||||
\(474\) | −25.3475 | −1.16425 | ||||||||
\(475\) | −0.133159 | −0.00610975 | ||||||||
\(476\) | −11.9371 | −0.547138 | ||||||||
\(477\) | 0.162420 | 0.00743670 | ||||||||
\(478\) | 27.5765 | 1.26132 | ||||||||
\(479\) | −28.8129 | −1.31650 | −0.658249 | − | 0.752801i | \(-0.728702\pi\) | ||||
−0.658249 | + | 0.752801i | \(0.728702\pi\) | |||||||
\(480\) | 1.74362 | 0.0795851 | ||||||||
\(481\) | −39.2369 | −1.78905 | ||||||||
\(482\) | −9.60993 | −0.437720 | ||||||||
\(483\) | 8.35137 | 0.380001 | ||||||||
\(484\) | −2.55700 | −0.116227 | ||||||||
\(485\) | −8.57086 | −0.389183 | ||||||||
\(486\) | −0.417972 | −0.0189596 | ||||||||
\(487\) | −2.51157 | −0.113810 | −0.0569051 | − | 0.998380i | \(-0.518123\pi\) | ||||
−0.0569051 | + | 0.998380i | \(0.518123\pi\) | |||||||
\(488\) | 5.75525 | 0.260528 | ||||||||
\(489\) | −2.38947 | −0.108056 | ||||||||
\(490\) | −0.833534 | −0.0376552 | ||||||||
\(491\) | −11.0188 | −0.497272 | −0.248636 | − | 0.968597i | \(-0.579982\pi\) | ||||
−0.248636 | + | 0.968597i | \(0.579982\pi\) | |||||||
\(492\) | 9.17789 | 0.413771 | ||||||||
\(493\) | 11.2856 | 0.508279 | ||||||||
\(494\) | 0.439131 | 0.0197575 | ||||||||
\(495\) | 0.116873 | 0.00525304 | ||||||||
\(496\) | −9.13104 | −0.409996 | ||||||||
\(497\) | −1.24228 | −0.0557241 | ||||||||
\(498\) | 29.3912 | 1.31705 | ||||||||
\(499\) | 18.0283 | 0.807058 | 0.403529 | − | 0.914967i | \(-0.367783\pi\) | ||||
0.403529 | + | 0.914967i | \(0.367783\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 28.8301 | 1.28803 | ||||||||
\(502\) | 27.8466 | 1.24286 | ||||||||
\(503\) | 30.9924 | 1.38188 | 0.690941 | − | 0.722911i | \(-0.257196\pi\) | ||||
0.690941 | + | 0.722911i | \(0.257196\pi\) | |||||||
\(504\) | −0.112575 | −0.00501451 | ||||||||
\(505\) | 13.3505 | 0.594088 | ||||||||
\(506\) | 4.97250 | 0.221055 | ||||||||
\(507\) | 3.70438 | 0.164517 | ||||||||
\(508\) | −0.0819637 | −0.00363655 | ||||||||
\(509\) | 10.7138 | 0.474880 | 0.237440 | − | 0.971402i | \(-0.423692\pi\) | ||||
0.237440 | + | 0.971402i | \(0.423692\pi\) | |||||||
\(510\) | −7.43660 | −0.329298 | ||||||||
\(511\) | −2.67562 | −0.118363 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.687198 | −0.0303406 | ||||||||
\(514\) | −1.46595 | −0.0646604 | ||||||||
\(515\) | −16.0085 | −0.705420 | ||||||||
\(516\) | 7.96614 | 0.350690 | ||||||||
\(517\) | 18.8739 | 0.830072 | ||||||||
\(518\) | 33.3004 | 1.46313 | ||||||||
\(519\) | −28.4011 | −1.24667 | ||||||||
\(520\) | −3.29780 | −0.144618 | ||||||||
\(521\) | 37.4207 | 1.63943 | 0.819715 | − | 0.572772i | \(-0.194132\pi\) | ||||
0.819715 | + | 0.572772i | \(0.194132\pi\) | |||||||
\(522\) | 0.106431 | 0.00465837 | ||||||||
\(523\) | 18.2035 | 0.795982 | 0.397991 | − | 0.917389i | \(-0.369708\pi\) | ||||
0.397991 | + | 0.917389i | \(0.369708\pi\) | |||||||
\(524\) | 3.94983 | 0.172549 | ||||||||
\(525\) | −4.88013 | −0.212986 | ||||||||
\(526\) | −24.0201 | −1.04732 | ||||||||
\(527\) | 38.9441 | 1.69643 | ||||||||
\(528\) | −5.06642 | −0.220488 | ||||||||
\(529\) | −20.0715 | −0.872672 | ||||||||
\(530\) | −4.03808 | −0.175403 | ||||||||
\(531\) | −0.280154 | −0.0121576 | ||||||||
\(532\) | −0.372691 | −0.0161582 | ||||||||
\(533\) | −17.3586 | −0.751883 | ||||||||
\(534\) | −23.0308 | −0.996641 | ||||||||
\(535\) | −10.8925 | −0.470926 | ||||||||
\(536\) | 1.15003 | 0.0496738 | ||||||||
\(537\) | 7.26937 | 0.313696 | ||||||||
\(538\) | −15.2572 | −0.657786 | ||||||||
\(539\) | 2.42199 | 0.104322 | ||||||||
\(540\) | 5.16074 | 0.222083 | ||||||||
\(541\) | 12.4127 | 0.533662 | 0.266831 | − | 0.963743i | \(-0.414023\pi\) | ||||
0.266831 | + | 0.963743i | \(0.414023\pi\) | |||||||
\(542\) | 7.93860 | 0.340992 | ||||||||
\(543\) | −1.45502 | −0.0624410 | ||||||||
\(544\) | 4.26503 | 0.182862 | ||||||||
\(545\) | 10.3384 | 0.442846 | ||||||||
\(546\) | 16.0937 | 0.688746 | ||||||||
\(547\) | 36.2153 | 1.54845 | 0.774227 | − | 0.632908i | \(-0.218139\pi\) | ||||
0.774227 | + | 0.632908i | \(0.218139\pi\) | |||||||
\(548\) | 17.4396 | 0.744981 | ||||||||
\(549\) | −0.231488 | −0.00987969 | ||||||||
\(550\) | −2.90568 | −0.123899 | ||||||||
\(551\) | 0.352350 | 0.0150106 | ||||||||
\(552\) | −2.98386 | −0.127002 | ||||||||
\(553\) | −40.6876 | −1.73021 | ||||||||
\(554\) | −4.90642 | −0.208454 | ||||||||
\(555\) | 20.7455 | 0.880596 | ||||||||
\(556\) | −6.57556 | −0.278866 | ||||||||
\(557\) | 10.1921 | 0.431854 | 0.215927 | − | 0.976410i | \(-0.430723\pi\) | ||||
0.215927 | + | 0.976410i | \(0.430723\pi\) | |||||||
\(558\) | 0.367270 | 0.0155478 | ||||||||
\(559\) | −15.0667 | −0.637255 | ||||||||
\(560\) | 2.79885 | 0.118273 | ||||||||
\(561\) | 21.6084 | 0.912308 | ||||||||
\(562\) | 29.6156 | 1.24926 | ||||||||
\(563\) | 0.952127 | 0.0401274 | 0.0200637 | − | 0.999799i | \(-0.493613\pi\) | ||||
0.0200637 | + | 0.999799i | \(0.493613\pi\) | |||||||
\(564\) | −11.3257 | −0.476898 | ||||||||
\(565\) | 11.1906 | 0.470790 | ||||||||
\(566\) | −2.32408 | −0.0976885 | ||||||||
\(567\) | −25.5228 | −1.07186 | ||||||||
\(568\) | 0.443856 | 0.0186238 | ||||||||
\(569\) | −1.70621 | −0.0715282 | −0.0357641 | − | 0.999360i | \(-0.511386\pi\) | ||||
−0.0357641 | + | 0.999360i | \(0.511386\pi\) | |||||||
\(570\) | −0.232179 | −0.00972491 | ||||||||
\(571\) | 1.32147 | 0.0553017 | 0.0276508 | − | 0.999618i | \(-0.491197\pi\) | ||||
0.0276508 | + | 0.999618i | \(0.491197\pi\) | |||||||
\(572\) | 9.58236 | 0.400659 | ||||||||
\(573\) | −30.5347 | −1.27560 | ||||||||
\(574\) | 14.7322 | 0.614912 | ||||||||
\(575\) | −1.71130 | −0.0713662 | ||||||||
\(576\) | 0.0402221 | 0.00167592 | ||||||||
\(577\) | −23.1428 | −0.963448 | −0.481724 | − | 0.876323i | \(-0.659989\pi\) | ||||
−0.481724 | + | 0.876323i | \(0.659989\pi\) | |||||||
\(578\) | −1.19045 | −0.0495164 | ||||||||
\(579\) | 5.71170 | 0.237370 | ||||||||
\(580\) | −2.64609 | −0.109873 | ||||||||
\(581\) | 47.1784 | 1.95729 | ||||||||
\(582\) | −14.9444 | −0.619464 | ||||||||
\(583\) | 11.7334 | 0.485947 | ||||||||
\(584\) | 0.955975 | 0.0395585 | ||||||||
\(585\) | 0.132644 | 0.00548417 | ||||||||
\(586\) | 24.9104 | 1.02904 | ||||||||
\(587\) | 37.1775 | 1.53448 | 0.767240 | − | 0.641360i | \(-0.221629\pi\) | ||||
0.767240 | + | 0.641360i | \(0.221629\pi\) | |||||||
\(588\) | −1.45337 | −0.0599360 | ||||||||
\(589\) | 1.21588 | 0.0500995 | ||||||||
\(590\) | 6.96517 | 0.286751 | ||||||||
\(591\) | 28.5397 | 1.17397 | ||||||||
\(592\) | −11.8979 | −0.489001 | ||||||||
\(593\) | 20.3523 | 0.835769 | 0.417885 | − | 0.908500i | \(-0.362772\pi\) | ||||
0.417885 | + | 0.908500i | \(0.362772\pi\) | |||||||
\(594\) | −14.9955 | −0.615272 | ||||||||
\(595\) | −11.9371 | −0.489375 | ||||||||
\(596\) | 6.75074 | 0.276521 | ||||||||
\(597\) | −9.15410 | −0.374652 | ||||||||
\(598\) | 5.64352 | 0.230781 | ||||||||
\(599\) | −41.5364 | −1.69713 | −0.848566 | − | 0.529089i | \(-0.822534\pi\) | ||||
−0.848566 | + | 0.529089i | \(0.822534\pi\) | |||||||
\(600\) | 1.74362 | 0.0711831 | ||||||||
\(601\) | 26.1358 | 1.06610 | 0.533050 | − | 0.846084i | \(-0.321046\pi\) | ||||
0.533050 | + | 0.846084i | \(0.321046\pi\) | |||||||
\(602\) | 12.7872 | 0.521166 | ||||||||
\(603\) | −0.0462567 | −0.00188372 | ||||||||
\(604\) | 9.75498 | 0.396925 | ||||||||
\(605\) | −2.55700 | −0.103957 | ||||||||
\(606\) | 23.2782 | 0.945612 | ||||||||
\(607\) | −6.25162 | −0.253745 | −0.126873 | − | 0.991919i | \(-0.540494\pi\) | ||||
−0.126873 | + | 0.991919i | \(0.540494\pi\) | |||||||
\(608\) | 0.133159 | 0.00540031 | ||||||||
\(609\) | 12.9133 | 0.523271 | ||||||||
\(610\) | 5.75525 | 0.233023 | ||||||||
\(611\) | 21.4209 | 0.866595 | ||||||||
\(612\) | −0.171548 | −0.00693443 | ||||||||
\(613\) | 4.38076 | 0.176937 | 0.0884685 | − | 0.996079i | \(-0.471803\pi\) | ||||
0.0884685 | + | 0.996079i | \(0.471803\pi\) | |||||||
\(614\) | −21.2022 | −0.855653 | ||||||||
\(615\) | 9.17789 | 0.370088 | ||||||||
\(616\) | −8.13256 | −0.327670 | ||||||||
\(617\) | −35.3261 | −1.42217 | −0.711087 | − | 0.703104i | \(-0.751797\pi\) | ||||
−0.711087 | + | 0.703104i | \(0.751797\pi\) | |||||||
\(618\) | −27.9128 | −1.12282 | ||||||||
\(619\) | −13.5824 | −0.545922 | −0.272961 | − | 0.962025i | \(-0.588003\pi\) | ||||
−0.272961 | + | 0.962025i | \(0.588003\pi\) | |||||||
\(620\) | −9.13104 | −0.366712 | ||||||||
\(621\) | −8.83157 | −0.354399 | ||||||||
\(622\) | −5.00671 | −0.200751 | ||||||||
\(623\) | −36.9688 | −1.48112 | ||||||||
\(624\) | −5.75012 | −0.230189 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −23.1915 | −0.926920 | ||||||||
\(627\) | 0.674639 | 0.0269425 | ||||||||
\(628\) | 16.8599 | 0.672784 | ||||||||
\(629\) | 50.7449 | 2.02333 | ||||||||
\(630\) | −0.112575 | −0.00448511 | ||||||||
\(631\) | 8.62253 | 0.343257 | 0.171629 | − | 0.985162i | \(-0.445097\pi\) | ||||
0.171629 | + | 0.985162i | \(0.445097\pi\) | |||||||
\(632\) | 14.5373 | 0.578262 | ||||||||
\(633\) | 32.4521 | 1.28986 | ||||||||
\(634\) | −16.0766 | −0.638483 | ||||||||
\(635\) | −0.0819637 | −0.00325263 | ||||||||
\(636\) | −7.04089 | −0.279189 | ||||||||
\(637\) | 2.74883 | 0.108913 | ||||||||
\(638\) | 7.68869 | 0.304398 | ||||||||
\(639\) | −0.0178528 | −0.000706247 0 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 4.17080 | 0.164737 | 0.0823683 | − | 0.996602i | \(-0.473752\pi\) | ||||
0.0823683 | + | 0.996602i | \(0.473752\pi\) | |||||||
\(642\) | −18.9925 | −0.749574 | ||||||||
\(643\) | 31.3917 | 1.23797 | 0.618984 | − | 0.785403i | \(-0.287544\pi\) | ||||
0.618984 | + | 0.785403i | \(0.287544\pi\) | |||||||
\(644\) | −4.78967 | −0.188739 | ||||||||
\(645\) | 7.96614 | 0.313666 | ||||||||
\(646\) | −0.567927 | −0.0223448 | ||||||||
\(647\) | 16.0835 | 0.632309 | 0.316154 | − | 0.948708i | \(-0.397608\pi\) | ||||
0.316154 | + | 0.948708i | \(0.397608\pi\) | |||||||
\(648\) | 9.11905 | 0.358230 | ||||||||
\(649\) | −20.2386 | −0.794434 | ||||||||
\(650\) | −3.29780 | −0.129350 | ||||||||
\(651\) | 44.5607 | 1.74647 | ||||||||
\(652\) | 1.37041 | 0.0536693 | ||||||||
\(653\) | −14.8296 | −0.580328 | −0.290164 | − | 0.956977i | \(-0.593710\pi\) | ||||
−0.290164 | + | 0.956977i | \(0.593710\pi\) | |||||||
\(654\) | 18.0262 | 0.704880 | ||||||||
\(655\) | 3.94983 | 0.154332 | ||||||||
\(656\) | −5.26369 | −0.205512 | ||||||||
\(657\) | −0.0384513 | −0.00150013 | ||||||||
\(658\) | −18.1799 | −0.708726 | ||||||||
\(659\) | −45.1202 | −1.75763 | −0.878817 | − | 0.477159i | \(-0.841667\pi\) | ||||
−0.878817 | + | 0.477159i | \(0.841667\pi\) | |||||||
\(660\) | −5.06642 | −0.197210 | ||||||||
\(661\) | 22.9207 | 0.891513 | 0.445757 | − | 0.895154i | \(-0.352935\pi\) | ||||
0.445757 | + | 0.895154i | \(0.352935\pi\) | |||||||
\(662\) | −3.88676 | −0.151063 | ||||||||
\(663\) | 24.5244 | 0.952449 | ||||||||
\(664\) | −16.8564 | −0.654155 | ||||||||
\(665\) | −0.372691 | −0.0144523 | ||||||||
\(666\) | 0.478559 | 0.0185438 | ||||||||
\(667\) | 4.52825 | 0.175335 | ||||||||
\(668\) | −16.5346 | −0.639743 | ||||||||
\(669\) | 9.79331 | 0.378631 | ||||||||
\(670\) | 1.15003 | 0.0444296 | ||||||||
\(671\) | −16.7229 | −0.645582 | ||||||||
\(672\) | 4.88013 | 0.188255 | ||||||||
\(673\) | 22.9161 | 0.883352 | 0.441676 | − | 0.897175i | \(-0.354384\pi\) | ||||
0.441676 | + | 0.897175i | \(0.354384\pi\) | |||||||
\(674\) | −9.32872 | −0.359329 | ||||||||
\(675\) | 5.16074 | 0.198637 | ||||||||
\(676\) | −2.12453 | −0.0817127 | ||||||||
\(677\) | −22.9572 | −0.882317 | −0.441158 | − | 0.897429i | \(-0.645432\pi\) | ||||
−0.441158 | + | 0.897429i | \(0.645432\pi\) | |||||||
\(678\) | 19.5121 | 0.749358 | ||||||||
\(679\) | −23.9885 | −0.920595 | ||||||||
\(680\) | 4.26503 | 0.163556 | ||||||||
\(681\) | 33.1955 | 1.27205 | ||||||||
\(682\) | 26.5319 | 1.01596 | ||||||||
\(683\) | 3.83965 | 0.146920 | 0.0734600 | − | 0.997298i | \(-0.476596\pi\) | ||||
0.0734600 | + | 0.997298i | \(0.476596\pi\) | |||||||
\(684\) | −0.00535593 | −0.000204789 0 | ||||||||
\(685\) | 17.4396 | 0.666331 | ||||||||
\(686\) | 17.2590 | 0.658951 | ||||||||
\(687\) | 31.8261 | 1.21424 | ||||||||
\(688\) | −4.56873 | −0.174181 | ||||||||
\(689\) | 13.3168 | 0.507328 | ||||||||
\(690\) | −2.98386 | −0.113594 | ||||||||
\(691\) | −22.2790 | −0.847533 | −0.423767 | − | 0.905771i | \(-0.639292\pi\) | ||||
−0.423767 | + | 0.905771i | \(0.639292\pi\) | |||||||
\(692\) | 16.2885 | 0.619198 | ||||||||
\(693\) | 0.327109 | 0.0124258 | ||||||||
\(694\) | 34.2218 | 1.29904 | ||||||||
\(695\) | −6.57556 | −0.249425 | ||||||||
\(696\) | −4.61378 | −0.174885 | ||||||||
\(697\) | 22.4498 | 0.850346 | ||||||||
\(698\) | 33.0131 | 1.24956 | ||||||||
\(699\) | −31.2787 | −1.18307 | ||||||||
\(700\) | 2.79885 | 0.105786 | ||||||||
\(701\) | 45.8891 | 1.73321 | 0.866603 | − | 0.498997i | \(-0.166298\pi\) | ||||
0.866603 | + | 0.498997i | \(0.166298\pi\) | |||||||
\(702\) | −17.0191 | −0.642343 | ||||||||
\(703\) | 1.58431 | 0.0597535 | ||||||||
\(704\) | 2.90568 | 0.109512 | ||||||||
\(705\) | −11.3257 | −0.426551 | ||||||||
\(706\) | −11.6475 | −0.438359 | ||||||||
\(707\) | 37.3659 | 1.40529 | ||||||||
\(708\) | 12.1446 | 0.456423 | ||||||||
\(709\) | 24.5503 | 0.922006 | 0.461003 | − | 0.887398i | \(-0.347490\pi\) | ||||
0.461003 | + | 0.887398i | \(0.347490\pi\) | |||||||
\(710\) | 0.443856 | 0.0166576 | ||||||||
\(711\) | −0.584720 | −0.0219287 | ||||||||
\(712\) | 13.2086 | 0.495013 | ||||||||
\(713\) | 15.6260 | 0.585197 | ||||||||
\(714\) | −20.8139 | −0.778940 | ||||||||
\(715\) | 9.58236 | 0.358360 | ||||||||
\(716\) | −4.16912 | −0.155807 | ||||||||
\(717\) | 48.0831 | 1.79570 | ||||||||
\(718\) | 11.8552 | 0.442433 | ||||||||
\(719\) | −19.2846 | −0.719193 | −0.359597 | − | 0.933108i | \(-0.617086\pi\) | ||||
−0.359597 | + | 0.933108i | \(0.617086\pi\) | |||||||
\(720\) | 0.0402221 | 0.00149899 | ||||||||
\(721\) | −44.8054 | −1.66864 | ||||||||
\(722\) | 18.9823 | 0.706447 | ||||||||
\(723\) | −16.7561 | −0.623166 | ||||||||
\(724\) | 0.834483 | 0.0310133 | ||||||||
\(725\) | −2.64609 | −0.0982732 | ||||||||
\(726\) | −4.45845 | −0.165468 | ||||||||
\(727\) | 6.33098 | 0.234803 | 0.117402 | − | 0.993085i | \(-0.462544\pi\) | ||||
0.117402 | + | 0.993085i | \(0.462544\pi\) | |||||||
\(728\) | −9.23003 | −0.342088 | ||||||||
\(729\) | 26.6284 | 0.986236 | ||||||||
\(730\) | 0.955975 | 0.0353822 | ||||||||
\(731\) | 19.4857 | 0.720706 | ||||||||
\(732\) | 10.0350 | 0.370904 | ||||||||
\(733\) | 39.5562 | 1.46104 | 0.730521 | − | 0.682890i | \(-0.239277\pi\) | ||||
0.730521 | + | 0.682890i | \(0.239277\pi\) | |||||||
\(734\) | 21.3941 | 0.789671 | ||||||||
\(735\) | −1.45337 | −0.0536083 | ||||||||
\(736\) | 1.71130 | 0.0630794 | ||||||||
\(737\) | −3.34163 | −0.123091 | ||||||||
\(738\) | 0.211717 | 0.00779340 | ||||||||
\(739\) | −2.00932 | −0.0739141 | −0.0369571 | − | 0.999317i | \(-0.511766\pi\) | ||||
−0.0369571 | + | 0.999317i | \(0.511766\pi\) | |||||||
\(740\) | −11.8979 | −0.437376 | ||||||||
\(741\) | 0.765680 | 0.0281279 | ||||||||
\(742\) | −11.3020 | −0.414908 | ||||||||
\(743\) | −39.4729 | −1.44812 | −0.724060 | − | 0.689737i | \(-0.757726\pi\) | ||||
−0.724060 | + | 0.689737i | \(0.757726\pi\) | |||||||
\(744\) | −15.9211 | −0.583696 | ||||||||
\(745\) | 6.75074 | 0.247328 | ||||||||
\(746\) | 22.1828 | 0.812170 | ||||||||
\(747\) | 0.678000 | 0.0248067 | ||||||||
\(748\) | −12.3928 | −0.453126 | ||||||||
\(749\) | −30.4865 | −1.11395 | ||||||||
\(750\) | 1.74362 | 0.0636681 | ||||||||
\(751\) | 0.749562 | 0.0273519 | 0.0136760 | − | 0.999906i | \(-0.495647\pi\) | ||||
0.0136760 | + | 0.999906i | \(0.495647\pi\) | |||||||
\(752\) | 6.49550 | 0.236867 | ||||||||
\(753\) | 48.5541 | 1.76941 | ||||||||
\(754\) | 8.72626 | 0.317792 | ||||||||
\(755\) | 9.75498 | 0.355020 | ||||||||
\(756\) | 14.4441 | 0.525327 | ||||||||
\(757\) | 13.3021 | 0.483472 | 0.241736 | − | 0.970342i | \(-0.422283\pi\) | ||||
0.241736 | + | 0.970342i | \(0.422283\pi\) | |||||||
\(758\) | −21.7483 | −0.789935 | ||||||||
\(759\) | 8.67016 | 0.314707 | ||||||||
\(760\) | 0.133159 | 0.00483018 | ||||||||
\(761\) | −30.1643 | −1.09345 | −0.546727 | − | 0.837311i | \(-0.684126\pi\) | ||||
−0.546727 | + | 0.837311i | \(0.684126\pi\) | |||||||
\(762\) | −0.142914 | −0.00517722 | ||||||||
\(763\) | 28.9355 | 1.04753 | ||||||||
\(764\) | 17.5122 | 0.633569 | ||||||||
\(765\) | −0.171548 | −0.00620234 | ||||||||
\(766\) | −15.3907 | −0.556089 | ||||||||
\(767\) | −22.9697 | −0.829388 | ||||||||
\(768\) | −1.74362 | −0.0629176 | ||||||||
\(769\) | −31.2458 | −1.12675 | −0.563377 | − | 0.826200i | \(-0.690498\pi\) | ||||
−0.563377 | + | 0.826200i | \(0.690498\pi\) | |||||||
\(770\) | −8.13256 | −0.293077 | ||||||||
\(771\) | −2.55607 | −0.0920546 | ||||||||
\(772\) | −3.27577 | −0.117897 | ||||||||
\(773\) | 5.49037 | 0.197475 | 0.0987375 | − | 0.995114i | \(-0.468520\pi\) | ||||
0.0987375 | + | 0.995114i | \(0.468520\pi\) | |||||||
\(774\) | 0.183764 | 0.00660525 | ||||||||
\(775\) | −9.13104 | −0.327997 | ||||||||
\(776\) | 8.57086 | 0.307676 | ||||||||
\(777\) | 58.0633 | 2.08301 | ||||||||
\(778\) | −21.0759 | −0.755609 | ||||||||
\(779\) | 0.700907 | 0.0251126 | ||||||||
\(780\) | −5.75012 | −0.205887 | ||||||||
\(781\) | −1.28971 | −0.0461493 | ||||||||
\(782\) | −7.29874 | −0.261003 | ||||||||
\(783\) | −13.6558 | −0.488017 | ||||||||
\(784\) | 0.833534 | 0.0297691 | ||||||||
\(785\) | 16.8599 | 0.601756 | ||||||||
\(786\) | 6.88701 | 0.245651 | ||||||||
\(787\) | −19.4370 | −0.692854 | −0.346427 | − | 0.938077i | \(-0.612605\pi\) | ||||
−0.346427 | + | 0.938077i | \(0.612605\pi\) | |||||||
\(788\) | −16.3680 | −0.583087 | ||||||||
\(789\) | −41.8819 | −1.49104 | ||||||||
\(790\) | 14.5373 | 0.517213 | ||||||||
\(791\) | 31.3206 | 1.11363 | ||||||||
\(792\) | −0.116873 | −0.00415289 | ||||||||
\(793\) | −18.9797 | −0.673988 | ||||||||
\(794\) | 35.7748 | 1.26960 | ||||||||
\(795\) | −7.04089 | −0.249715 | ||||||||
\(796\) | 5.25004 | 0.186083 | ||||||||
\(797\) | −8.35740 | −0.296034 | −0.148017 | − | 0.988985i | \(-0.547289\pi\) | ||||
−0.148017 | + | 0.988985i | \(0.547289\pi\) | |||||||
\(798\) | −0.649833 | −0.0230038 | ||||||||
\(799\) | −27.7035 | −0.980079 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −0.531278 | −0.0187718 | ||||||||
\(802\) | −1.00000 | −0.0353112 | ||||||||
\(803\) | −2.77776 | −0.0980250 | ||||||||
\(804\) | 2.00522 | 0.0707188 | ||||||||
\(805\) | −4.78967 | −0.168814 | ||||||||
\(806\) | 30.1123 | 1.06066 | ||||||||
\(807\) | −26.6029 | −0.936465 | ||||||||
\(808\) | −13.3505 | −0.469668 | ||||||||
\(809\) | 46.6245 | 1.63923 | 0.819615 | − | 0.572914i | \(-0.194187\pi\) | ||||
0.819615 | + | 0.572914i | \(0.194187\pi\) | |||||||
\(810\) | 9.11905 | 0.320411 | ||||||||
\(811\) | 25.6122 | 0.899368 | 0.449684 | − | 0.893188i | \(-0.351537\pi\) | ||||
0.449684 | + | 0.893188i | \(0.351537\pi\) | |||||||
\(812\) | −7.40599 | −0.259899 | ||||||||
\(813\) | 13.8419 | 0.485457 | ||||||||
\(814\) | 34.5715 | 1.21173 | ||||||||
\(815\) | 1.37041 | 0.0480033 | ||||||||
\(816\) | 7.43660 | 0.260333 | ||||||||
\(817\) | 0.608367 | 0.0212841 | ||||||||
\(818\) | 33.6239 | 1.17563 | ||||||||
\(819\) | 0.371251 | 0.0129726 | ||||||||
\(820\) | −5.26369 | −0.183816 | ||||||||
\(821\) | 27.8303 | 0.971285 | 0.485643 | − | 0.874157i | \(-0.338586\pi\) | ||||
0.485643 | + | 0.874157i | \(0.338586\pi\) | |||||||
\(822\) | 30.4080 | 1.06060 | ||||||||
\(823\) | −3.07396 | −0.107151 | −0.0535757 | − | 0.998564i | \(-0.517062\pi\) | ||||
−0.0535757 | + | 0.998564i | \(0.517062\pi\) | |||||||
\(824\) | 16.0085 | 0.557684 | ||||||||
\(825\) | −5.06642 | −0.176390 | ||||||||
\(826\) | 19.4944 | 0.678298 | ||||||||
\(827\) | 39.3794 | 1.36935 | 0.684677 | − | 0.728846i | \(-0.259943\pi\) | ||||
0.684677 | + | 0.728846i | \(0.259943\pi\) | |||||||
\(828\) | −0.0688321 | −0.00239208 | ||||||||
\(829\) | −35.6968 | −1.23980 | −0.619900 | − | 0.784680i | \(-0.712827\pi\) | ||||
−0.619900 | + | 0.784680i | \(0.712827\pi\) | |||||||
\(830\) | −16.8564 | −0.585094 | ||||||||
\(831\) | −8.55495 | −0.296768 | ||||||||
\(832\) | 3.29780 | 0.114331 | ||||||||
\(833\) | −3.55505 | −0.123175 | ||||||||
\(834\) | −11.4653 | −0.397011 | ||||||||
\(835\) | −16.5346 | −0.572203 | ||||||||
\(836\) | −0.386918 | −0.0133818 | ||||||||
\(837\) | −47.1229 | −1.62881 | ||||||||
\(838\) | 5.91594 | 0.204363 | ||||||||
\(839\) | −40.1386 | −1.38574 | −0.692869 | − | 0.721063i | \(-0.743654\pi\) | ||||
−0.692869 | + | 0.721063i | \(0.743654\pi\) | |||||||
\(840\) | 4.88013 | 0.168381 | ||||||||
\(841\) | −21.9982 | −0.758560 | ||||||||
\(842\) | 15.9075 | 0.548209 | ||||||||
\(843\) | 51.6385 | 1.77852 | ||||||||
\(844\) | −18.6119 | −0.640648 | ||||||||
\(845\) | −2.12453 | −0.0730860 | ||||||||
\(846\) | −0.261263 | −0.00898240 | ||||||||
\(847\) | −7.15665 | −0.245905 | ||||||||
\(848\) | 4.03808 | 0.138668 | ||||||||
\(849\) | −4.05232 | −0.139075 | ||||||||
\(850\) | 4.26503 | 0.146289 | ||||||||
\(851\) | 20.3609 | 0.697962 | ||||||||
\(852\) | 0.773917 | 0.0265140 | ||||||||
\(853\) | −29.0724 | −0.995421 | −0.497711 | − | 0.867343i | \(-0.665826\pi\) | ||||
−0.497711 | + | 0.867343i | \(0.665826\pi\) | |||||||
\(854\) | 16.1081 | 0.551207 | ||||||||
\(855\) | −0.00535593 | −0.000183169 0 | ||||||||
\(856\) | 10.8925 | 0.372299 | ||||||||
\(857\) | 51.8740 | 1.77198 | 0.885990 | − | 0.463704i | \(-0.153480\pi\) | ||||
0.885990 | + | 0.463704i | \(0.153480\pi\) | |||||||
\(858\) | 16.7080 | 0.570403 | ||||||||
\(859\) | 27.4459 | 0.936443 | 0.468222 | − | 0.883611i | \(-0.344895\pi\) | ||||
0.468222 | + | 0.883611i | \(0.344895\pi\) | |||||||
\(860\) | −4.56873 | −0.155792 | ||||||||
\(861\) | 25.6875 | 0.875427 | ||||||||
\(862\) | −21.9256 | −0.746788 | ||||||||
\(863\) | −44.1100 | −1.50152 | −0.750761 | − | 0.660574i | \(-0.770313\pi\) | ||||
−0.750761 | + | 0.660574i | \(0.770313\pi\) | |||||||
\(864\) | −5.16074 | −0.175572 | ||||||||
\(865\) | 16.2885 | 0.553827 | ||||||||
\(866\) | −31.5732 | −1.07290 | ||||||||
\(867\) | −2.07570 | −0.0704946 | ||||||||
\(868\) | −25.5564 | −0.867440 | ||||||||
\(869\) | −42.2407 | −1.43292 | ||||||||
\(870\) | −4.61378 | −0.156422 | ||||||||
\(871\) | −3.79257 | −0.128506 | ||||||||
\(872\) | −10.3384 | −0.350101 | ||||||||
\(873\) | −0.344738 | −0.0116676 | ||||||||
\(874\) | −0.227875 | −0.00770799 | ||||||||
\(875\) | 2.79885 | 0.0946182 | ||||||||
\(876\) | 1.66686 | 0.0563180 | ||||||||
\(877\) | 13.0104 | 0.439331 | 0.219666 | − | 0.975575i | \(-0.429503\pi\) | ||||
0.219666 | + | 0.975575i | \(0.429503\pi\) | |||||||
\(878\) | −5.12336 | −0.172905 | ||||||||
\(879\) | 43.4344 | 1.46501 | ||||||||
\(880\) | 2.90568 | 0.0979506 | ||||||||
\(881\) | 47.0400 | 1.58482 | 0.792408 | − | 0.609991i | \(-0.208827\pi\) | ||||
0.792408 | + | 0.609991i | \(0.208827\pi\) | |||||||
\(882\) | −0.0335265 | −0.00112890 | ||||||||
\(883\) | −52.3454 | −1.76156 | −0.880782 | − | 0.473522i | \(-0.842982\pi\) | ||||
−0.880782 | + | 0.473522i | \(0.842982\pi\) | |||||||
\(884\) | −14.0652 | −0.473064 | ||||||||
\(885\) | 12.1446 | 0.408237 | ||||||||
\(886\) | 35.2770 | 1.18515 | ||||||||
\(887\) | 29.3491 | 0.985447 | 0.492723 | − | 0.870186i | \(-0.336001\pi\) | ||||
0.492723 | + | 0.870186i | \(0.336001\pi\) | |||||||
\(888\) | −20.7455 | −0.696172 | ||||||||
\(889\) | −0.229404 | −0.00769395 | ||||||||
\(890\) | 13.2086 | 0.442753 | ||||||||
\(891\) | −26.4971 | −0.887685 | ||||||||
\(892\) | −5.61665 | −0.188059 | ||||||||
\(893\) | −0.864934 | −0.0289439 | ||||||||
\(894\) | 11.7708 | 0.393673 | ||||||||
\(895\) | −4.16912 | −0.139358 | ||||||||
\(896\) | −2.79885 | −0.0935029 | ||||||||
\(897\) | 9.84018 | 0.328554 | ||||||||
\(898\) | 13.7311 | 0.458212 | ||||||||
\(899\) | 24.1615 | 0.805832 | ||||||||
\(900\) | 0.0402221 | 0.00134074 | ||||||||
\(901\) | −17.2225 | −0.573765 | ||||||||
\(902\) | 15.2946 | 0.509255 | ||||||||
\(903\) | 22.2960 | 0.741964 | ||||||||
\(904\) | −11.1906 | −0.372192 | ||||||||
\(905\) | 0.834483 | 0.0277392 | ||||||||
\(906\) | 17.0090 | 0.565087 | ||||||||
\(907\) | −10.7838 | −0.358069 | −0.179034 | − | 0.983843i | \(-0.557297\pi\) | ||||
−0.179034 | + | 0.983843i | \(0.557297\pi\) | |||||||
\(908\) | −19.0382 | −0.631806 | ||||||||
\(909\) | 0.536984 | 0.0178106 | ||||||||
\(910\) | −9.23003 | −0.305972 | ||||||||
\(911\) | 24.3801 | 0.807747 | 0.403874 | − | 0.914815i | \(-0.367664\pi\) | ||||
0.403874 | + | 0.914815i | \(0.367664\pi\) | |||||||
\(912\) | 0.232179 | 0.00768822 | ||||||||
\(913\) | 48.9793 | 1.62098 | ||||||||
\(914\) | −32.3369 | −1.06961 | ||||||||
\(915\) | 10.0350 | 0.331747 | ||||||||
\(916\) | −18.2529 | −0.603092 | ||||||||
\(917\) | 11.0550 | 0.365067 | ||||||||
\(918\) | 22.0107 | 0.726461 | ||||||||
\(919\) | −37.3006 | −1.23043 | −0.615216 | − | 0.788358i | \(-0.710931\pi\) | ||||
−0.615216 | + | 0.788358i | \(0.710931\pi\) | |||||||
\(920\) | 1.71130 | 0.0564199 | ||||||||
\(921\) | −36.9687 | −1.21816 | ||||||||
\(922\) | −0.219374 | −0.00722470 | ||||||||
\(923\) | −1.46375 | −0.0481798 | ||||||||
\(924\) | −14.1801 | −0.466492 | ||||||||
\(925\) | −11.8979 | −0.391201 | ||||||||
\(926\) | 7.36374 | 0.241988 | ||||||||
\(927\) | −0.643897 | −0.0211483 | ||||||||
\(928\) | 2.64609 | 0.0868620 | ||||||||
\(929\) | 42.9751 | 1.40997 | 0.704984 | − | 0.709223i | \(-0.250954\pi\) | ||||
0.704984 | + | 0.709223i | \(0.250954\pi\) | |||||||
\(930\) | −15.9211 | −0.522073 | ||||||||
\(931\) | −0.110993 | −0.00363763 | ||||||||
\(932\) | 17.9389 | 0.587609 | ||||||||
\(933\) | −8.72981 | −0.285801 | ||||||||
\(934\) | 13.1656 | 0.430792 | ||||||||
\(935\) | −12.3928 | −0.405289 | ||||||||
\(936\) | −0.132644 | −0.00433562 | ||||||||
\(937\) | 11.9642 | 0.390853 | 0.195426 | − | 0.980718i | \(-0.437391\pi\) | ||||
0.195426 | + | 0.980718i | \(0.437391\pi\) | |||||||
\(938\) | 3.21876 | 0.105096 | ||||||||
\(939\) | −40.4373 | −1.31962 | ||||||||
\(940\) | 6.49550 | 0.211860 | ||||||||
\(941\) | −6.91846 | −0.225535 | −0.112768 | − | 0.993621i | \(-0.535972\pi\) | ||||
−0.112768 | + | 0.993621i | \(0.535972\pi\) | |||||||
\(942\) | 29.3974 | 0.957817 | ||||||||
\(943\) | 9.00775 | 0.293333 | ||||||||
\(944\) | −6.96517 | −0.226697 | ||||||||
\(945\) | 14.4441 | 0.469867 | ||||||||
\(946\) | 13.2753 | 0.431616 | ||||||||
\(947\) | −9.80580 | −0.318646 | −0.159323 | − | 0.987227i | \(-0.550931\pi\) | ||||
−0.159323 | + | 0.987227i | \(0.550931\pi\) | |||||||
\(948\) | 25.3475 | 0.823249 | ||||||||
\(949\) | −3.15261 | −0.102338 | ||||||||
\(950\) | 0.133159 | 0.00432025 | ||||||||
\(951\) | −28.0315 | −0.908985 | ||||||||
\(952\) | 11.9371 | 0.386885 | ||||||||
\(953\) | 22.4361 | 0.726776 | 0.363388 | − | 0.931638i | \(-0.381620\pi\) | ||||
0.363388 | + | 0.931638i | \(0.381620\pi\) | |||||||
\(954\) | −0.162420 | −0.00525854 | ||||||||
\(955\) | 17.5122 | 0.566681 | ||||||||
\(956\) | −27.5765 | −0.891889 | ||||||||
\(957\) | 13.4062 | 0.433360 | ||||||||
\(958\) | 28.8129 | 0.930904 | ||||||||
\(959\) | 48.8106 | 1.57618 | ||||||||
\(960\) | −1.74362 | −0.0562752 | ||||||||
\(961\) | 52.3759 | 1.68955 | ||||||||
\(962\) | 39.2369 | 1.26505 | ||||||||
\(963\) | −0.438121 | −0.0141182 | ||||||||
\(964\) | 9.60993 | 0.309515 | ||||||||
\(965\) | −3.27577 | −0.105451 | ||||||||
\(966\) | −8.35137 | −0.268701 | ||||||||
\(967\) | −52.4073 | −1.68531 | −0.842653 | − | 0.538457i | \(-0.819008\pi\) | ||||
−0.842653 | + | 0.538457i | \(0.819008\pi\) | |||||||
\(968\) | 2.55700 | 0.0821851 | ||||||||
\(969\) | −0.990250 | −0.0318114 | ||||||||
\(970\) | 8.57086 | 0.275194 | ||||||||
\(971\) | −13.7733 | −0.442005 | −0.221002 | − | 0.975273i | \(-0.570933\pi\) | ||||
−0.221002 | + | 0.975273i | \(0.570933\pi\) | |||||||
\(972\) | 0.417972 | 0.0134065 | ||||||||
\(973\) | −18.4040 | −0.590004 | ||||||||
\(974\) | 2.51157 | 0.0804760 | ||||||||
\(975\) | −5.75012 | −0.184151 | ||||||||
\(976\) | −5.75525 | −0.184221 | ||||||||
\(977\) | 2.88069 | 0.0921616 | 0.0460808 | − | 0.998938i | \(-0.485327\pi\) | ||||
0.0460808 | + | 0.998938i | \(0.485327\pi\) | |||||||
\(978\) | 2.38947 | 0.0764070 | ||||||||
\(979\) | −38.3800 | −1.22663 | ||||||||
\(980\) | 0.833534 | 0.0266263 | ||||||||
\(981\) | 0.415830 | 0.0132764 | ||||||||
\(982\) | 11.0188 | 0.351624 | ||||||||
\(983\) | 16.0515 | 0.511963 | 0.255981 | − | 0.966682i | \(-0.417601\pi\) | ||||
0.255981 | + | 0.966682i | \(0.417601\pi\) | |||||||
\(984\) | −9.17789 | −0.292580 | ||||||||
\(985\) | −16.3680 | −0.521529 | ||||||||
\(986\) | −11.2856 | −0.359408 | ||||||||
\(987\) | −31.6989 | −1.00899 | ||||||||
\(988\) | −0.439131 | −0.0139706 | ||||||||
\(989\) | 7.81846 | 0.248613 | ||||||||
\(990\) | −0.116873 | −0.00371446 | ||||||||
\(991\) | 28.2981 | 0.898920 | 0.449460 | − | 0.893301i | \(-0.351616\pi\) | ||||
0.449460 | + | 0.893301i | \(0.351616\pi\) | |||||||
\(992\) | 9.13104 | 0.289911 | ||||||||
\(993\) | −6.77705 | −0.215063 | ||||||||
\(994\) | 1.24228 | 0.0394029 | ||||||||
\(995\) | 5.25004 | 0.166438 | ||||||||
\(996\) | −29.3912 | −0.931296 | ||||||||
\(997\) | −39.4637 | −1.24983 | −0.624913 | − | 0.780694i | \(-0.714866\pi\) | ||||
−0.624913 | + | 0.780694i | \(0.714866\pi\) | |||||||
\(998\) | −18.0283 | −0.570676 | ||||||||
\(999\) | −61.4019 | −1.94267 |
(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 | 4010.2.a.i.1.3 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.i.1.3 | ✓ | 10 | 1.1 | even | 1 | trivial |