Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6422,2,Mod(1,6422)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, 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("6422.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6422 = 2 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6422.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: | \(51.2799281781\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 4x^{6} + 22x^{5} + 3x^{4} - 28x^{3} + 7x^{2} + 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 494) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.40354\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6422.1 |
$q$-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 | ||||||||
\(3\) | 1.40354 | 0.810335 | 0.405168 | − | 0.914242i | \(-0.367213\pi\) | ||||
0.405168 | + | 0.914242i | \(0.367213\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.425845 | 0.190444 | 0.0952218 | − | 0.995456i | \(-0.469644\pi\) | ||||
0.0952218 | + | 0.995456i | \(0.469644\pi\) | |||||||
\(6\) | −1.40354 | −0.572993 | ||||||||
\(7\) | −2.92512 | −1.10559 | −0.552795 | − | 0.833317i | \(-0.686439\pi\) | ||||
−0.552795 | + | 0.833317i | \(0.686439\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.03007 | −0.343357 | ||||||||
\(10\) | −0.425845 | −0.134664 | ||||||||
\(11\) | 6.25275 | 1.88527 | 0.942637 | − | 0.333820i | \(-0.108338\pi\) | ||||
0.942637 | + | 0.333820i | \(0.108338\pi\) | |||||||
\(12\) | 1.40354 | 0.405168 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.92512 | 0.781770 | ||||||||
\(15\) | 0.597691 | 0.154323 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.36685 | −1.05912 | −0.529559 | − | 0.848273i | \(-0.677642\pi\) | ||||
−0.529559 | + | 0.848273i | \(0.677642\pi\) | |||||||
\(18\) | 1.03007 | 0.242790 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0.425845 | 0.0952218 | ||||||||
\(21\) | −4.10552 | −0.895898 | ||||||||
\(22\) | −6.25275 | −1.33309 | ||||||||
\(23\) | 2.24450 | 0.468011 | 0.234005 | − | 0.972235i | \(-0.424817\pi\) | ||||
0.234005 | + | 0.972235i | \(0.424817\pi\) | |||||||
\(24\) | −1.40354 | −0.286497 | ||||||||
\(25\) | −4.81866 | −0.963731 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65637 | −1.08857 | ||||||||
\(28\) | −2.92512 | −0.552795 | ||||||||
\(29\) | 0.394227 | 0.0732061 | 0.0366031 | − | 0.999330i | \(-0.488346\pi\) | ||||
0.0366031 | + | 0.999330i | \(0.488346\pi\) | |||||||
\(30\) | −0.597691 | −0.109123 | ||||||||
\(31\) | 4.46367 | 0.801698 | 0.400849 | − | 0.916144i | \(-0.368715\pi\) | ||||
0.400849 | + | 0.916144i | \(0.368715\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 8.77599 | 1.52770 | ||||||||
\(34\) | 4.36685 | 0.748909 | ||||||||
\(35\) | −1.24565 | −0.210553 | ||||||||
\(36\) | −1.03007 | −0.171679 | ||||||||
\(37\) | 6.38774 | 1.05014 | 0.525069 | − | 0.851060i | \(-0.324040\pi\) | ||||
0.525069 | + | 0.851060i | \(0.324040\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.425845 | −0.0673320 | ||||||||
\(41\) | −4.52838 | −0.707214 | −0.353607 | − | 0.935394i | \(-0.615045\pi\) | ||||
−0.353607 | + | 0.935394i | \(0.615045\pi\) | |||||||
\(42\) | 4.10552 | 0.633496 | ||||||||
\(43\) | −8.90193 | −1.35753 | −0.678766 | − | 0.734355i | \(-0.737485\pi\) | ||||
−0.678766 | + | 0.734355i | \(0.737485\pi\) | |||||||
\(44\) | 6.25275 | 0.942637 | ||||||||
\(45\) | −0.438651 | −0.0653902 | ||||||||
\(46\) | −2.24450 | −0.330934 | ||||||||
\(47\) | −7.29953 | −1.06475 | −0.532373 | − | 0.846510i | \(-0.678699\pi\) | ||||
−0.532373 | + | 0.846510i | \(0.678699\pi\) | |||||||
\(48\) | 1.40354 | 0.202584 | ||||||||
\(49\) | 1.55630 | 0.222329 | ||||||||
\(50\) | 4.81866 | 0.681461 | ||||||||
\(51\) | −6.12906 | −0.858240 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.60396 | −0.632402 | −0.316201 | − | 0.948692i | \(-0.602407\pi\) | ||||
−0.316201 | + | 0.948692i | \(0.602407\pi\) | |||||||
\(54\) | 5.65637 | 0.769735 | ||||||||
\(55\) | 2.66270 | 0.359038 | ||||||||
\(56\) | 2.92512 | 0.390885 | ||||||||
\(57\) | 1.40354 | 0.185904 | ||||||||
\(58\) | −0.394227 | −0.0517646 | ||||||||
\(59\) | −1.02166 | −0.133008 | −0.0665042 | − | 0.997786i | \(-0.521185\pi\) | ||||
−0.0665042 | + | 0.997786i | \(0.521185\pi\) | |||||||
\(60\) | 0.597691 | 0.0771616 | ||||||||
\(61\) | −3.65403 | −0.467850 | −0.233925 | − | 0.972255i | \(-0.575157\pi\) | ||||
−0.233925 | + | 0.972255i | \(0.575157\pi\) | |||||||
\(62\) | −4.46367 | −0.566886 | ||||||||
\(63\) | 3.01308 | 0.379612 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.77599 | −1.08025 | ||||||||
\(67\) | −8.23193 | −1.00569 | −0.502845 | − | 0.864377i | \(-0.667713\pi\) | ||||
−0.502845 | + | 0.864377i | \(0.667713\pi\) | |||||||
\(68\) | −4.36685 | −0.529559 | ||||||||
\(69\) | 3.15025 | 0.379246 | ||||||||
\(70\) | 1.24565 | 0.148883 | ||||||||
\(71\) | 4.91483 | 0.583283 | 0.291642 | − | 0.956528i | \(-0.405798\pi\) | ||||
0.291642 | + | 0.956528i | \(0.405798\pi\) | |||||||
\(72\) | 1.03007 | 0.121395 | ||||||||
\(73\) | 10.5155 | 1.23075 | 0.615373 | − | 0.788236i | \(-0.289005\pi\) | ||||
0.615373 | + | 0.788236i | \(0.289005\pi\) | |||||||
\(74\) | −6.38774 | −0.742560 | ||||||||
\(75\) | −6.76318 | −0.780945 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −18.2900 | −2.08434 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.39511 | 0.832014 | 0.416007 | − | 0.909361i | \(-0.363429\pi\) | ||||
0.416007 | + | 0.909361i | \(0.363429\pi\) | |||||||
\(80\) | 0.425845 | 0.0476109 | ||||||||
\(81\) | −4.84874 | −0.538749 | ||||||||
\(82\) | 4.52838 | 0.500076 | ||||||||
\(83\) | −9.79541 | −1.07519 | −0.537593 | − | 0.843205i | \(-0.680666\pi\) | ||||
−0.537593 | + | 0.843205i | \(0.680666\pi\) | |||||||
\(84\) | −4.10552 | −0.447949 | ||||||||
\(85\) | −1.85960 | −0.201702 | ||||||||
\(86\) | 8.90193 | 0.959920 | ||||||||
\(87\) | 0.553314 | 0.0593215 | ||||||||
\(88\) | −6.25275 | −0.666545 | ||||||||
\(89\) | 0.552500 | 0.0585649 | 0.0292824 | − | 0.999571i | \(-0.490678\pi\) | ||||
0.0292824 | + | 0.999571i | \(0.490678\pi\) | |||||||
\(90\) | 0.438651 | 0.0462378 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.24450 | 0.234005 | ||||||||
\(93\) | 6.26494 | 0.649644 | ||||||||
\(94\) | 7.29953 | 0.752889 | ||||||||
\(95\) | 0.425845 | 0.0436908 | ||||||||
\(96\) | −1.40354 | −0.143248 | ||||||||
\(97\) | 4.87829 | 0.495316 | 0.247658 | − | 0.968848i | \(-0.420339\pi\) | ||||
0.247658 | + | 0.968848i | \(0.420339\pi\) | |||||||
\(98\) | −1.55630 | −0.157210 | ||||||||
\(99\) | −6.44077 | −0.647322 | ||||||||
\(100\) | −4.81866 | −0.481866 | ||||||||
\(101\) | −7.74682 | −0.770838 | −0.385419 | − | 0.922742i | \(-0.625943\pi\) | ||||
−0.385419 | + | 0.922742i | \(0.625943\pi\) | |||||||
\(102\) | 6.12906 | 0.606867 | ||||||||
\(103\) | −5.07181 | −0.499740 | −0.249870 | − | 0.968279i | \(-0.580388\pi\) | ||||
−0.249870 | + | 0.968279i | \(0.580388\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.74832 | −0.170618 | ||||||||
\(106\) | 4.60396 | 0.447176 | ||||||||
\(107\) | −9.71994 | −0.939662 | −0.469831 | − | 0.882756i | \(-0.655685\pi\) | ||||
−0.469831 | + | 0.882756i | \(0.655685\pi\) | |||||||
\(108\) | −5.65637 | −0.544285 | ||||||||
\(109\) | −8.51312 | −0.815409 | −0.407705 | − | 0.913114i | \(-0.633671\pi\) | ||||
−0.407705 | + | 0.913114i | \(0.633671\pi\) | |||||||
\(110\) | −2.66270 | −0.253879 | ||||||||
\(111\) | 8.96546 | 0.850963 | ||||||||
\(112\) | −2.92512 | −0.276397 | ||||||||
\(113\) | 20.8886 | 1.96503 | 0.982517 | − | 0.186174i | \(-0.0596089\pi\) | ||||
0.982517 | + | 0.186174i | \(0.0596089\pi\) | |||||||
\(114\) | −1.40354 | −0.131454 | ||||||||
\(115\) | 0.955809 | 0.0891297 | ||||||||
\(116\) | 0.394227 | 0.0366031 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.02166 | 0.0940512 | ||||||||
\(119\) | 12.7735 | 1.17095 | ||||||||
\(120\) | −0.597691 | −0.0545615 | ||||||||
\(121\) | 28.0968 | 2.55426 | ||||||||
\(122\) | 3.65403 | 0.330820 | ||||||||
\(123\) | −6.35577 | −0.573080 | ||||||||
\(124\) | 4.46367 | 0.400849 | ||||||||
\(125\) | −4.18123 | −0.373980 | ||||||||
\(126\) | −3.01308 | −0.268426 | ||||||||
\(127\) | −15.4402 | −1.37009 | −0.685046 | − | 0.728500i | \(-0.740218\pi\) | ||||
−0.685046 | + | 0.728500i | \(0.740218\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −12.4942 | −1.10006 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.5021 | 1.70390 | 0.851952 | − | 0.523619i | \(-0.175419\pi\) | ||||
0.851952 | + | 0.523619i | \(0.175419\pi\) | |||||||
\(132\) | 8.77599 | 0.763852 | ||||||||
\(133\) | −2.92512 | −0.253640 | ||||||||
\(134\) | 8.23193 | 0.711130 | ||||||||
\(135\) | −2.40874 | −0.207311 | ||||||||
\(136\) | 4.36685 | 0.374454 | ||||||||
\(137\) | 8.34116 | 0.712633 | 0.356317 | − | 0.934365i | \(-0.384032\pi\) | ||||
0.356317 | + | 0.934365i | \(0.384032\pi\) | |||||||
\(138\) | −3.15025 | −0.268167 | ||||||||
\(139\) | −8.64283 | −0.733075 | −0.366538 | − | 0.930403i | \(-0.619457\pi\) | ||||
−0.366538 | + | 0.930403i | \(0.619457\pi\) | |||||||
\(140\) | −1.24565 | −0.105276 | ||||||||
\(141\) | −10.2452 | −0.862801 | ||||||||
\(142\) | −4.91483 | −0.412444 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.03007 | −0.0858393 | ||||||||
\(145\) | 0.167880 | 0.0139416 | ||||||||
\(146\) | −10.5155 | −0.870269 | ||||||||
\(147\) | 2.18433 | 0.180161 | ||||||||
\(148\) | 6.38774 | 0.525069 | ||||||||
\(149\) | −7.29288 | −0.597456 | −0.298728 | − | 0.954338i | \(-0.596562\pi\) | ||||
−0.298728 | + | 0.954338i | \(0.596562\pi\) | |||||||
\(150\) | 6.76318 | 0.552212 | ||||||||
\(151\) | −0.0688467 | −0.00560267 | −0.00280133 | − | 0.999996i | \(-0.500892\pi\) | ||||
−0.00280133 | + | 0.999996i | \(0.500892\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 4.49817 | 0.363655 | ||||||||
\(154\) | 18.2900 | 1.47385 | ||||||||
\(155\) | 1.90083 | 0.152678 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.5441 | −0.841510 | −0.420755 | − | 0.907174i | \(-0.638235\pi\) | ||||
−0.420755 | + | 0.907174i | \(0.638235\pi\) | |||||||
\(158\) | −7.39511 | −0.588323 | ||||||||
\(159\) | −6.46185 | −0.512458 | ||||||||
\(160\) | −0.425845 | −0.0336660 | ||||||||
\(161\) | −6.56542 | −0.517428 | ||||||||
\(162\) | 4.84874 | 0.380953 | ||||||||
\(163\) | −6.02314 | −0.471769 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(164\) | −4.52838 | −0.353607 | ||||||||
\(165\) | 3.73721 | 0.290941 | ||||||||
\(166\) | 9.79541 | 0.760271 | ||||||||
\(167\) | 9.32561 | 0.721637 | 0.360819 | − | 0.932636i | \(-0.382497\pi\) | ||||
0.360819 | + | 0.932636i | \(0.382497\pi\) | |||||||
\(168\) | 4.10552 | 0.316748 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.85960 | 0.142625 | ||||||||
\(171\) | −1.03007 | −0.0787715 | ||||||||
\(172\) | −8.90193 | −0.678766 | ||||||||
\(173\) | −18.6618 | −1.41883 | −0.709414 | − | 0.704792i | \(-0.751040\pi\) | ||||
−0.709414 | + | 0.704792i | \(0.751040\pi\) | |||||||
\(174\) | −0.553314 | −0.0419466 | ||||||||
\(175\) | 14.0951 | 1.06549 | ||||||||
\(176\) | 6.25275 | 0.471319 | ||||||||
\(177\) | −1.43394 | −0.107781 | ||||||||
\(178\) | −0.552500 | −0.0414116 | ||||||||
\(179\) | −24.4248 | −1.82560 | −0.912799 | − | 0.408409i | \(-0.866084\pi\) | ||||
−0.912799 | + | 0.408409i | \(0.866084\pi\) | |||||||
\(180\) | −0.438651 | −0.0326951 | ||||||||
\(181\) | 26.4469 | 1.96579 | 0.982893 | − | 0.184179i | \(-0.0589626\pi\) | ||||
0.982893 | + | 0.184179i | \(0.0589626\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.12858 | −0.379115 | ||||||||
\(184\) | −2.24450 | −0.165467 | ||||||||
\(185\) | 2.72019 | 0.199992 | ||||||||
\(186\) | −6.26494 | −0.459368 | ||||||||
\(187\) | −27.3048 | −1.99673 | ||||||||
\(188\) | −7.29953 | −0.532373 | ||||||||
\(189\) | 16.5455 | 1.20351 | ||||||||
\(190\) | −0.425845 | −0.0308940 | ||||||||
\(191\) | −15.4036 | −1.11456 | −0.557281 | − | 0.830324i | \(-0.688155\pi\) | ||||
−0.557281 | + | 0.830324i | \(0.688155\pi\) | |||||||
\(192\) | 1.40354 | 0.101292 | ||||||||
\(193\) | 9.64505 | 0.694266 | 0.347133 | − | 0.937816i | \(-0.387155\pi\) | ||||
0.347133 | + | 0.937816i | \(0.387155\pi\) | |||||||
\(194\) | −4.87829 | −0.350241 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.55630 | 0.111164 | ||||||||
\(197\) | −8.84308 | −0.630044 | −0.315022 | − | 0.949084i | \(-0.602012\pi\) | ||||
−0.315022 | + | 0.949084i | \(0.602012\pi\) | |||||||
\(198\) | 6.44077 | 0.457726 | ||||||||
\(199\) | −15.2687 | −1.08237 | −0.541184 | − | 0.840904i | \(-0.682024\pi\) | ||||
−0.541184 | + | 0.840904i | \(0.682024\pi\) | |||||||
\(200\) | 4.81866 | 0.340730 | ||||||||
\(201\) | −11.5539 | −0.814946 | ||||||||
\(202\) | 7.74682 | 0.545065 | ||||||||
\(203\) | −1.15316 | −0.0809360 | ||||||||
\(204\) | −6.12906 | −0.429120 | ||||||||
\(205\) | −1.92839 | −0.134684 | ||||||||
\(206\) | 5.07181 | 0.353370 | ||||||||
\(207\) | −2.31200 | −0.160695 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.25275 | 0.432512 | ||||||||
\(210\) | 1.74832 | 0.120645 | ||||||||
\(211\) | 16.8320 | 1.15876 | 0.579382 | − | 0.815056i | \(-0.303294\pi\) | ||||
0.579382 | + | 0.815056i | \(0.303294\pi\) | |||||||
\(212\) | −4.60396 | −0.316201 | ||||||||
\(213\) | 6.89817 | 0.472655 | ||||||||
\(214\) | 9.71994 | 0.664441 | ||||||||
\(215\) | −3.79084 | −0.258533 | ||||||||
\(216\) | 5.65637 | 0.384867 | ||||||||
\(217\) | −13.0567 | −0.886349 | ||||||||
\(218\) | 8.51312 | 0.576581 | ||||||||
\(219\) | 14.7589 | 0.997317 | ||||||||
\(220\) | 2.66270 | 0.179519 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −8.96546 | −0.601722 | ||||||||
\(223\) | −1.32645 | −0.0888254 | −0.0444127 | − | 0.999013i | \(-0.514142\pi\) | ||||
−0.0444127 | + | 0.999013i | \(0.514142\pi\) | |||||||
\(224\) | 2.92512 | 0.195443 | ||||||||
\(225\) | 4.96356 | 0.330904 | ||||||||
\(226\) | −20.8886 | −1.38949 | ||||||||
\(227\) | −22.4672 | −1.49120 | −0.745599 | − | 0.666395i | \(-0.767837\pi\) | ||||
−0.745599 | + | 0.666395i | \(0.767837\pi\) | |||||||
\(228\) | 1.40354 | 0.0929518 | ||||||||
\(229\) | −19.4946 | −1.28824 | −0.644119 | − | 0.764925i | \(-0.722776\pi\) | ||||
−0.644119 | + | 0.764925i | \(0.722776\pi\) | |||||||
\(230\) | −0.955809 | −0.0630242 | ||||||||
\(231\) | −25.6708 | −1.68901 | ||||||||
\(232\) | −0.394227 | −0.0258823 | ||||||||
\(233\) | −18.1804 | −1.19103 | −0.595517 | − | 0.803342i | \(-0.703053\pi\) | ||||
−0.595517 | + | 0.803342i | \(0.703053\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.10847 | −0.202774 | ||||||||
\(236\) | −1.02166 | −0.0665042 | ||||||||
\(237\) | 10.3793 | 0.674210 | ||||||||
\(238\) | −12.7735 | −0.827986 | ||||||||
\(239\) | −28.3307 | −1.83256 | −0.916279 | − | 0.400541i | \(-0.868822\pi\) | ||||
−0.916279 | + | 0.400541i | \(0.868822\pi\) | |||||||
\(240\) | 0.597691 | 0.0385808 | ||||||||
\(241\) | 9.76218 | 0.628837 | 0.314419 | − | 0.949284i | \(-0.398190\pi\) | ||||
0.314419 | + | 0.949284i | \(0.398190\pi\) | |||||||
\(242\) | −28.0968 | −1.80613 | ||||||||
\(243\) | 10.1637 | 0.652002 | ||||||||
\(244\) | −3.65403 | −0.233925 | ||||||||
\(245\) | 0.662743 | 0.0423411 | ||||||||
\(246\) | 6.35577 | 0.405229 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −4.46367 | −0.283443 | ||||||||
\(249\) | −13.7483 | −0.871261 | ||||||||
\(250\) | 4.18123 | 0.264444 | ||||||||
\(251\) | −16.7474 | −1.05709 | −0.528544 | − | 0.848906i | \(-0.677262\pi\) | ||||
−0.528544 | + | 0.848906i | \(0.677262\pi\) | |||||||
\(252\) | 3.01308 | 0.189806 | ||||||||
\(253\) | 14.0343 | 0.882329 | ||||||||
\(254\) | 15.4402 | 0.968801 | ||||||||
\(255\) | −2.61003 | −0.163446 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.9082 | −1.17946 | −0.589732 | − | 0.807599i | \(-0.700767\pi\) | ||||
−0.589732 | + | 0.807599i | \(0.700767\pi\) | |||||||
\(258\) | 12.4942 | 0.777857 | ||||||||
\(259\) | −18.6849 | −1.16102 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.406082 | −0.0251358 | ||||||||
\(262\) | −19.5021 | −1.20484 | ||||||||
\(263\) | 17.1653 | 1.05846 | 0.529228 | − | 0.848480i | \(-0.322482\pi\) | ||||
0.529228 | + | 0.848480i | \(0.322482\pi\) | |||||||
\(264\) | −8.77599 | −0.540125 | ||||||||
\(265\) | −1.96057 | −0.120437 | ||||||||
\(266\) | 2.92512 | 0.179350 | ||||||||
\(267\) | 0.775457 | 0.0474572 | ||||||||
\(268\) | −8.23193 | −0.502845 | ||||||||
\(269\) | 23.8294 | 1.45290 | 0.726451 | − | 0.687218i | \(-0.241168\pi\) | ||||
0.726451 | + | 0.687218i | \(0.241168\pi\) | |||||||
\(270\) | 2.40874 | 0.146591 | ||||||||
\(271\) | −12.4715 | −0.757589 | −0.378795 | − | 0.925481i | \(-0.623661\pi\) | ||||
−0.378795 | + | 0.925481i | \(0.623661\pi\) | |||||||
\(272\) | −4.36685 | −0.264779 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.34116 | −0.503908 | ||||||||
\(275\) | −30.1298 | −1.81690 | ||||||||
\(276\) | 3.15025 | 0.189623 | ||||||||
\(277\) | −16.3303 | −0.981193 | −0.490597 | − | 0.871387i | \(-0.663221\pi\) | ||||
−0.490597 | + | 0.871387i | \(0.663221\pi\) | |||||||
\(278\) | 8.64283 | 0.518363 | ||||||||
\(279\) | −4.59789 | −0.275269 | ||||||||
\(280\) | 1.24565 | 0.0744416 | ||||||||
\(281\) | −19.6635 | −1.17302 | −0.586512 | − | 0.809940i | \(-0.699499\pi\) | ||||
−0.586512 | + | 0.809940i | \(0.699499\pi\) | |||||||
\(282\) | 10.2452 | 0.610092 | ||||||||
\(283\) | 17.4667 | 1.03828 | 0.519142 | − | 0.854688i | \(-0.326251\pi\) | ||||
0.519142 | + | 0.854688i | \(0.326251\pi\) | |||||||
\(284\) | 4.91483 | 0.291642 | ||||||||
\(285\) | 0.597691 | 0.0354042 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.2460 | 0.781888 | ||||||||
\(288\) | 1.03007 | 0.0606975 | ||||||||
\(289\) | 2.06939 | 0.121729 | ||||||||
\(290\) | −0.167880 | −0.00985823 | ||||||||
\(291\) | 6.84689 | 0.401372 | ||||||||
\(292\) | 10.5155 | 0.615373 | ||||||||
\(293\) | −5.83845 | −0.341086 | −0.170543 | − | 0.985350i | \(-0.554552\pi\) | ||||
−0.170543 | + | 0.985350i | \(0.554552\pi\) | |||||||
\(294\) | −2.18433 | −0.127393 | ||||||||
\(295\) | −0.435068 | −0.0253306 | ||||||||
\(296\) | −6.38774 | −0.371280 | ||||||||
\(297\) | −35.3679 | −2.05225 | ||||||||
\(298\) | 7.29288 | 0.422465 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −6.76318 | −0.390473 | ||||||||
\(301\) | 26.0392 | 1.50087 | ||||||||
\(302\) | 0.0688467 | 0.00396168 | ||||||||
\(303\) | −10.8730 | −0.624637 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −1.55605 | −0.0890991 | ||||||||
\(306\) | −4.49817 | −0.257143 | ||||||||
\(307\) | −9.68903 | −0.552982 | −0.276491 | − | 0.961017i | \(-0.589172\pi\) | ||||
−0.276491 | + | 0.961017i | \(0.589172\pi\) | |||||||
\(308\) | −18.2900 | −1.04217 | ||||||||
\(309\) | −7.11850 | −0.404957 | ||||||||
\(310\) | −1.90083 | −0.107960 | ||||||||
\(311\) | −1.67689 | −0.0950877 | −0.0475439 | − | 0.998869i | \(-0.515139\pi\) | ||||
−0.0475439 | + | 0.998869i | \(0.515139\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.1187 | −0.684991 | −0.342496 | − | 0.939519i | \(-0.611272\pi\) | ||||
−0.342496 | + | 0.939519i | \(0.611272\pi\) | |||||||
\(314\) | 10.5441 | 0.595038 | ||||||||
\(315\) | 1.28310 | 0.0722947 | ||||||||
\(316\) | 7.39511 | 0.416007 | ||||||||
\(317\) | −10.1049 | −0.567549 | −0.283775 | − | 0.958891i | \(-0.591587\pi\) | ||||
−0.283775 | + | 0.958891i | \(0.591587\pi\) | |||||||
\(318\) | 6.46185 | 0.362362 | ||||||||
\(319\) | 2.46500 | 0.138014 | ||||||||
\(320\) | 0.425845 | 0.0238055 | ||||||||
\(321\) | −13.6423 | −0.761441 | ||||||||
\(322\) | 6.56542 | 0.365877 | ||||||||
\(323\) | −4.36685 | −0.242978 | ||||||||
\(324\) | −4.84874 | −0.269374 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.02314 | 0.333591 | ||||||||
\(327\) | −11.9485 | −0.660755 | ||||||||
\(328\) | 4.52838 | 0.250038 | ||||||||
\(329\) | 21.3520 | 1.17717 | ||||||||
\(330\) | −3.73721 | −0.205727 | ||||||||
\(331\) | −35.5859 | −1.95598 | −0.977989 | − | 0.208655i | \(-0.933091\pi\) | ||||
−0.977989 | + | 0.208655i | \(0.933091\pi\) | |||||||
\(332\) | −9.79541 | −0.537593 | ||||||||
\(333\) | −6.57982 | −0.360572 | ||||||||
\(334\) | −9.32561 | −0.510275 | ||||||||
\(335\) | −3.50553 | −0.191527 | ||||||||
\(336\) | −4.10552 | −0.223975 | ||||||||
\(337\) | −22.9814 | −1.25188 | −0.625939 | − | 0.779872i | \(-0.715284\pi\) | ||||
−0.625939 | + | 0.779872i | \(0.715284\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 29.3180 | 1.59234 | ||||||||
\(340\) | −1.85960 | −0.100851 | ||||||||
\(341\) | 27.9102 | 1.51142 | ||||||||
\(342\) | 1.03007 | 0.0556999 | ||||||||
\(343\) | 15.9234 | 0.859785 | ||||||||
\(344\) | 8.90193 | 0.479960 | ||||||||
\(345\) | 1.34152 | 0.0722249 | ||||||||
\(346\) | 18.6618 | 1.00326 | ||||||||
\(347\) | 7.20555 | 0.386814 | 0.193407 | − | 0.981119i | \(-0.438046\pi\) | ||||
0.193407 | + | 0.981119i | \(0.438046\pi\) | |||||||
\(348\) | 0.553314 | 0.0296608 | ||||||||
\(349\) | 29.5472 | 1.58163 | 0.790814 | − | 0.612057i | \(-0.209658\pi\) | ||||
0.790814 | + | 0.612057i | \(0.209658\pi\) | |||||||
\(350\) | −14.0951 | −0.753416 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.25275 | −0.333273 | ||||||||
\(353\) | −1.41643 | −0.0753892 | −0.0376946 | − | 0.999289i | \(-0.512001\pi\) | ||||
−0.0376946 | + | 0.999289i | \(0.512001\pi\) | |||||||
\(354\) | 1.43394 | 0.0762130 | ||||||||
\(355\) | 2.09296 | 0.111083 | ||||||||
\(356\) | 0.552500 | 0.0292824 | ||||||||
\(357\) | 17.9282 | 0.948861 | ||||||||
\(358\) | 24.4248 | 1.29089 | ||||||||
\(359\) | 2.06385 | 0.108926 | 0.0544629 | − | 0.998516i | \(-0.482655\pi\) | ||||
0.0544629 | + | 0.998516i | \(0.482655\pi\) | |||||||
\(360\) | 0.438651 | 0.0231189 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −26.4469 | −1.39002 | ||||||||
\(363\) | 39.4351 | 2.06981 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.47797 | 0.234388 | ||||||||
\(366\) | 5.12858 | 0.268075 | ||||||||
\(367\) | −28.1446 | −1.46913 | −0.734567 | − | 0.678536i | \(-0.762615\pi\) | ||||
−0.734567 | + | 0.678536i | \(0.762615\pi\) | |||||||
\(368\) | 2.24450 | 0.117003 | ||||||||
\(369\) | 4.66455 | 0.242827 | ||||||||
\(370\) | −2.72019 | −0.141416 | ||||||||
\(371\) | 13.4671 | 0.699177 | ||||||||
\(372\) | 6.26494 | 0.324822 | ||||||||
\(373\) | −30.4016 | −1.57413 | −0.787067 | − | 0.616867i | \(-0.788401\pi\) | ||||
−0.787067 | + | 0.616867i | \(0.788401\pi\) | |||||||
\(374\) | 27.3048 | 1.41190 | ||||||||
\(375\) | −5.86852 | −0.303049 | ||||||||
\(376\) | 7.29953 | 0.376444 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −16.5455 | −0.851011 | ||||||||
\(379\) | 4.93867 | 0.253682 | 0.126841 | − | 0.991923i | \(-0.459516\pi\) | ||||
0.126841 | + | 0.991923i | \(0.459516\pi\) | |||||||
\(380\) | 0.425845 | 0.0218454 | ||||||||
\(381\) | −21.6709 | −1.11023 | ||||||||
\(382\) | 15.4036 | 0.788115 | ||||||||
\(383\) | 14.2852 | 0.729940 | 0.364970 | − | 0.931019i | \(-0.381079\pi\) | ||||
0.364970 | + | 0.931019i | \(0.381079\pi\) | |||||||
\(384\) | −1.40354 | −0.0716242 | ||||||||
\(385\) | −7.78871 | −0.396949 | ||||||||
\(386\) | −9.64505 | −0.490920 | ||||||||
\(387\) | 9.16962 | 0.466118 | ||||||||
\(388\) | 4.87829 | 0.247658 | ||||||||
\(389\) | 5.81026 | 0.294592 | 0.147296 | − | 0.989092i | \(-0.452943\pi\) | ||||
0.147296 | + | 0.989092i | \(0.452943\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.80140 | −0.495678 | ||||||||
\(392\) | −1.55630 | −0.0786051 | ||||||||
\(393\) | 27.3720 | 1.38073 | ||||||||
\(394\) | 8.84308 | 0.445508 | ||||||||
\(395\) | 3.14917 | 0.158452 | ||||||||
\(396\) | −6.44077 | −0.323661 | ||||||||
\(397\) | 15.5364 | 0.779751 | 0.389876 | − | 0.920868i | \(-0.372518\pi\) | ||||
0.389876 | + | 0.920868i | \(0.372518\pi\) | |||||||
\(398\) | 15.2687 | 0.765350 | ||||||||
\(399\) | −4.10552 | −0.205533 | ||||||||
\(400\) | −4.81866 | −0.240933 | ||||||||
\(401\) | 3.79901 | 0.189714 | 0.0948568 | − | 0.995491i | \(-0.469761\pi\) | ||||
0.0948568 | + | 0.995491i | \(0.469761\pi\) | |||||||
\(402\) | 11.5539 | 0.576254 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −7.74682 | −0.385419 | ||||||||
\(405\) | −2.06481 | −0.102601 | ||||||||
\(406\) | 1.15316 | 0.0572304 | ||||||||
\(407\) | 39.9409 | 1.97980 | ||||||||
\(408\) | 6.12906 | 0.303434 | ||||||||
\(409\) | −21.9275 | −1.08424 | −0.542122 | − | 0.840300i | \(-0.682379\pi\) | ||||
−0.542122 | + | 0.840300i | \(0.682379\pi\) | |||||||
\(410\) | 1.92839 | 0.0952362 | ||||||||
\(411\) | 11.7072 | 0.577472 | ||||||||
\(412\) | −5.07181 | −0.249870 | ||||||||
\(413\) | 2.98847 | 0.147053 | ||||||||
\(414\) | 2.31200 | 0.113628 | ||||||||
\(415\) | −4.17133 | −0.204762 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.1306 | −0.594037 | ||||||||
\(418\) | −6.25275 | −0.305832 | ||||||||
\(419\) | 19.8371 | 0.969104 | 0.484552 | − | 0.874762i | \(-0.338983\pi\) | ||||
0.484552 | + | 0.874762i | \(0.338983\pi\) | |||||||
\(420\) | −1.74832 | −0.0853091 | ||||||||
\(421\) | 15.5001 | 0.755428 | 0.377714 | − | 0.925922i | \(-0.376710\pi\) | ||||
0.377714 | + | 0.925922i | \(0.376710\pi\) | |||||||
\(422\) | −16.8320 | −0.819370 | ||||||||
\(423\) | 7.51903 | 0.365588 | ||||||||
\(424\) | 4.60396 | 0.223588 | ||||||||
\(425\) | 21.0424 | 1.02070 | ||||||||
\(426\) | −6.89817 | −0.334218 | ||||||||
\(427\) | 10.6884 | 0.517250 | ||||||||
\(428\) | −9.71994 | −0.469831 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.79084 | 0.182811 | ||||||||
\(431\) | 30.6034 | 1.47411 | 0.737057 | − | 0.675831i | \(-0.236215\pi\) | ||||
0.737057 | + | 0.675831i | \(0.236215\pi\) | |||||||
\(432\) | −5.65637 | −0.272142 | ||||||||
\(433\) | 4.32019 | 0.207615 | 0.103808 | − | 0.994597i | \(-0.466897\pi\) | ||||
0.103808 | + | 0.994597i | \(0.466897\pi\) | |||||||
\(434\) | 13.0567 | 0.626743 | ||||||||
\(435\) | 0.235626 | 0.0112974 | ||||||||
\(436\) | −8.51312 | −0.407705 | ||||||||
\(437\) | 2.24450 | 0.107369 | ||||||||
\(438\) | −14.7589 | −0.705210 | ||||||||
\(439\) | −19.0722 | −0.910269 | −0.455134 | − | 0.890423i | \(-0.650409\pi\) | ||||
−0.455134 | + | 0.890423i | \(0.650409\pi\) | |||||||
\(440\) | −2.66270 | −0.126939 | ||||||||
\(441\) | −1.60310 | −0.0763381 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.5646 | 0.882032 | 0.441016 | − | 0.897499i | \(-0.354618\pi\) | ||||
0.441016 | + | 0.897499i | \(0.354618\pi\) | |||||||
\(444\) | 8.96546 | 0.425482 | ||||||||
\(445\) | 0.235279 | 0.0111533 | ||||||||
\(446\) | 1.32645 | 0.0628090 | ||||||||
\(447\) | −10.2359 | −0.484139 | ||||||||
\(448\) | −2.92512 | −0.138199 | ||||||||
\(449\) | 2.64242 | 0.124703 | 0.0623517 | − | 0.998054i | \(-0.480140\pi\) | ||||
0.0623517 | + | 0.998054i | \(0.480140\pi\) | |||||||
\(450\) | −4.96356 | −0.233984 | ||||||||
\(451\) | −28.3148 | −1.33329 | ||||||||
\(452\) | 20.8886 | 0.982517 | ||||||||
\(453\) | −0.0966292 | −0.00454004 | ||||||||
\(454\) | 22.4672 | 1.05444 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.40354 | −0.0657269 | ||||||||
\(457\) | 39.2950 | 1.83814 | 0.919071 | − | 0.394093i | \(-0.128941\pi\) | ||||
0.919071 | + | 0.394093i | \(0.128941\pi\) | |||||||
\(458\) | 19.4946 | 0.910922 | ||||||||
\(459\) | 24.7005 | 1.15292 | ||||||||
\(460\) | 0.955809 | 0.0445648 | ||||||||
\(461\) | 32.1567 | 1.49769 | 0.748844 | − | 0.662746i | \(-0.230609\pi\) | ||||
0.748844 | + | 0.662746i | \(0.230609\pi\) | |||||||
\(462\) | 25.6708 | 1.19431 | ||||||||
\(463\) | −10.9509 | −0.508933 | −0.254466 | − | 0.967082i | \(-0.581900\pi\) | ||||
−0.254466 | + | 0.967082i | \(0.581900\pi\) | |||||||
\(464\) | 0.394227 | 0.0183015 | ||||||||
\(465\) | 2.66789 | 0.123721 | ||||||||
\(466\) | 18.1804 | 0.842189 | ||||||||
\(467\) | 36.2880 | 1.67921 | 0.839604 | − | 0.543199i | \(-0.182787\pi\) | ||||
0.839604 | + | 0.543199i | \(0.182787\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.0793 | 1.11188 | ||||||||
\(470\) | 3.10847 | 0.143383 | ||||||||
\(471\) | −14.7991 | −0.681905 | ||||||||
\(472\) | 1.02166 | 0.0470256 | ||||||||
\(473\) | −55.6615 | −2.55932 | ||||||||
\(474\) | −10.3793 | −0.476739 | ||||||||
\(475\) | −4.81866 | −0.221095 | ||||||||
\(476\) | 12.7735 | 0.585474 | ||||||||
\(477\) | 4.74240 | 0.217140 | ||||||||
\(478\) | 28.3307 | 1.29581 | ||||||||
\(479\) | −8.63902 | −0.394727 | −0.197363 | − | 0.980330i | \(-0.563238\pi\) | ||||
−0.197363 | + | 0.980330i | \(0.563238\pi\) | |||||||
\(480\) | −0.597691 | −0.0272807 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −9.76218 | −0.444655 | ||||||||
\(483\) | −9.21485 | −0.419290 | ||||||||
\(484\) | 28.0968 | 1.27713 | ||||||||
\(485\) | 2.07740 | 0.0943297 | ||||||||
\(486\) | −10.1637 | −0.461035 | ||||||||
\(487\) | 35.4068 | 1.60443 | 0.802217 | − | 0.597032i | \(-0.203653\pi\) | ||||
0.802217 | + | 0.597032i | \(0.203653\pi\) | |||||||
\(488\) | 3.65403 | 0.165410 | ||||||||
\(489\) | −8.45372 | −0.382291 | ||||||||
\(490\) | −0.662743 | −0.0299397 | ||||||||
\(491\) | 38.0024 | 1.71502 | 0.857512 | − | 0.514464i | \(-0.172009\pi\) | ||||
0.857512 | + | 0.514464i | \(0.172009\pi\) | |||||||
\(492\) | −6.35577 | −0.286540 | ||||||||
\(493\) | −1.72153 | −0.0775339 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.74277 | −0.123278 | ||||||||
\(496\) | 4.46367 | 0.200424 | ||||||||
\(497\) | −14.3765 | −0.644872 | ||||||||
\(498\) | 13.7483 | 0.616074 | ||||||||
\(499\) | −5.50496 | −0.246436 | −0.123218 | − | 0.992380i | \(-0.539321\pi\) | ||||
−0.123218 | + | 0.992380i | \(0.539321\pi\) | |||||||
\(500\) | −4.18123 | −0.186990 | ||||||||
\(501\) | 13.0889 | 0.584768 | ||||||||
\(502\) | 16.7474 | 0.747475 | ||||||||
\(503\) | −13.8524 | −0.617650 | −0.308825 | − | 0.951119i | \(-0.599936\pi\) | ||||
−0.308825 | + | 0.951119i | \(0.599936\pi\) | |||||||
\(504\) | −3.01308 | −0.134213 | ||||||||
\(505\) | −3.29895 | −0.146801 | ||||||||
\(506\) | −14.0343 | −0.623901 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.4402 | −0.685046 | ||||||||
\(509\) | 11.0775 | 0.491002 | 0.245501 | − | 0.969396i | \(-0.421048\pi\) | ||||
0.245501 | + | 0.969396i | \(0.421048\pi\) | |||||||
\(510\) | 2.61003 | 0.115574 | ||||||||
\(511\) | −30.7591 | −1.36070 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.65637 | −0.249735 | ||||||||
\(514\) | 18.9082 | 0.834007 | ||||||||
\(515\) | −2.15981 | −0.0951724 | ||||||||
\(516\) | −12.4942 | −0.550028 | ||||||||
\(517\) | −45.6421 | −2.00734 | ||||||||
\(518\) | 18.6849 | 0.820966 | ||||||||
\(519\) | −26.1926 | −1.14973 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.7563 | −1.04078 | −0.520392 | − | 0.853927i | \(-0.674214\pi\) | ||||
−0.520392 | + | 0.853927i | \(0.674214\pi\) | |||||||
\(522\) | 0.406082 | 0.0177737 | ||||||||
\(523\) | −15.6082 | −0.682499 | −0.341250 | − | 0.939973i | \(-0.610850\pi\) | ||||
−0.341250 | + | 0.939973i | \(0.610850\pi\) | |||||||
\(524\) | 19.5021 | 0.851952 | ||||||||
\(525\) | 19.7831 | 0.863405 | ||||||||
\(526\) | −17.1653 | −0.748441 | ||||||||
\(527\) | −19.4922 | −0.849092 | ||||||||
\(528\) | 8.77599 | 0.381926 | ||||||||
\(529\) | −17.9622 | −0.780966 | ||||||||
\(530\) | 1.96057 | 0.0851618 | ||||||||
\(531\) | 1.05238 | 0.0456694 | ||||||||
\(532\) | −2.92512 | −0.126820 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.775457 | −0.0335573 | ||||||||
\(535\) | −4.13919 | −0.178953 | ||||||||
\(536\) | 8.23193 | 0.355565 | ||||||||
\(537\) | −34.2813 | −1.47935 | ||||||||
\(538\) | −23.8294 | −1.02736 | ||||||||
\(539\) | 9.73116 | 0.419151 | ||||||||
\(540\) | −2.40874 | −0.103656 | ||||||||
\(541\) | −22.2684 | −0.957395 | −0.478697 | − | 0.877980i | \(-0.658891\pi\) | ||||
−0.478697 | + | 0.877980i | \(0.658891\pi\) | |||||||
\(542\) | 12.4715 | 0.535696 | ||||||||
\(543\) | 37.1194 | 1.59294 | ||||||||
\(544\) | 4.36685 | 0.187227 | ||||||||
\(545\) | −3.62527 | −0.155290 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.3856 | −1.17093 | −0.585463 | − | 0.810699i | \(-0.699087\pi\) | ||||
−0.585463 | + | 0.810699i | \(0.699087\pi\) | |||||||
\(548\) | 8.34116 | 0.356317 | ||||||||
\(549\) | 3.76391 | 0.160640 | ||||||||
\(550\) | 30.1298 | 1.28474 | ||||||||
\(551\) | 0.394227 | 0.0167946 | ||||||||
\(552\) | −3.15025 | −0.134084 | ||||||||
\(553\) | −21.6315 | −0.919867 | ||||||||
\(554\) | 16.3303 | 0.693808 | ||||||||
\(555\) | 3.81789 | 0.162061 | ||||||||
\(556\) | −8.64283 | −0.366538 | ||||||||
\(557\) | −29.9692 | −1.26983 | −0.634917 | − | 0.772580i | \(-0.718966\pi\) | ||||
−0.634917 | + | 0.772580i | \(0.718966\pi\) | |||||||
\(558\) | 4.59789 | 0.194644 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.24565 | −0.0526381 | ||||||||
\(561\) | −38.3234 | −1.61802 | ||||||||
\(562\) | 19.6635 | 0.829454 | ||||||||
\(563\) | −36.7770 | −1.54997 | −0.774983 | − | 0.631982i | \(-0.782241\pi\) | ||||
−0.774983 | + | 0.631982i | \(0.782241\pi\) | |||||||
\(564\) | −10.2452 | −0.431400 | ||||||||
\(565\) | 8.89530 | 0.374228 | ||||||||
\(566\) | −17.4667 | −0.734178 | ||||||||
\(567\) | 14.1831 | 0.595635 | ||||||||
\(568\) | −4.91483 | −0.206222 | ||||||||
\(569\) | 14.0998 | 0.591092 | 0.295546 | − | 0.955328i | \(-0.404498\pi\) | ||||
0.295546 | + | 0.955328i | \(0.404498\pi\) | |||||||
\(570\) | −0.597691 | −0.0250345 | ||||||||
\(571\) | 17.8101 | 0.745330 | 0.372665 | − | 0.927966i | \(-0.378444\pi\) | ||||
0.372665 | + | 0.927966i | \(0.378444\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.6195 | −0.903169 | ||||||||
\(574\) | −13.2460 | −0.552878 | ||||||||
\(575\) | −10.8155 | −0.451037 | ||||||||
\(576\) | −1.03007 | −0.0429196 | ||||||||
\(577\) | −20.4540 | −0.851512 | −0.425756 | − | 0.904838i | \(-0.639992\pi\) | ||||
−0.425756 | + | 0.904838i | \(0.639992\pi\) | |||||||
\(578\) | −2.06939 | −0.0860753 | ||||||||
\(579\) | 13.5372 | 0.562588 | ||||||||
\(580\) | 0.167880 | 0.00697082 | ||||||||
\(581\) | 28.6527 | 1.18871 | ||||||||
\(582\) | −6.84689 | −0.283813 | ||||||||
\(583\) | −28.7874 | −1.19225 | ||||||||
\(584\) | −10.5155 | −0.435135 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.83845 | 0.241184 | ||||||||
\(587\) | 39.4733 | 1.62924 | 0.814620 | − | 0.579995i | \(-0.196946\pi\) | ||||
0.814620 | + | 0.579995i | \(0.196946\pi\) | |||||||
\(588\) | 2.18433 | 0.0900804 | ||||||||
\(589\) | 4.46367 | 0.183922 | ||||||||
\(590\) | 0.435068 | 0.0179114 | ||||||||
\(591\) | −12.4116 | −0.510547 | ||||||||
\(592\) | 6.38774 | 0.262534 | ||||||||
\(593\) | 10.4284 | 0.428243 | 0.214122 | − | 0.976807i | \(-0.431311\pi\) | ||||
0.214122 | + | 0.976807i | \(0.431311\pi\) | |||||||
\(594\) | 35.3679 | 1.45116 | ||||||||
\(595\) | 5.43955 | 0.223000 | ||||||||
\(596\) | −7.29288 | −0.298728 | ||||||||
\(597\) | −21.4302 | −0.877081 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.1621 | −0.742085 | −0.371043 | − | 0.928616i | \(-0.621000\pi\) | ||||
−0.371043 | + | 0.928616i | \(0.621000\pi\) | |||||||
\(600\) | 6.76318 | 0.276106 | ||||||||
\(601\) | −36.8943 | −1.50495 | −0.752474 | − | 0.658622i | \(-0.771140\pi\) | ||||
−0.752474 | + | 0.658622i | \(0.771140\pi\) | |||||||
\(602\) | −26.0392 | −1.06128 | ||||||||
\(603\) | 8.47947 | 0.345311 | ||||||||
\(604\) | −0.0688467 | −0.00280133 | ||||||||
\(605\) | 11.9649 | 0.486442 | ||||||||
\(606\) | 10.8730 | 0.441685 | ||||||||
\(607\) | −19.1434 | −0.777005 | −0.388502 | − | 0.921448i | \(-0.627007\pi\) | ||||
−0.388502 | + | 0.921448i | \(0.627007\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −1.61851 | −0.0655853 | ||||||||
\(610\) | 1.55605 | 0.0630026 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.49817 | 0.181828 | ||||||||
\(613\) | −36.5355 | −1.47566 | −0.737828 | − | 0.674989i | \(-0.764148\pi\) | ||||
−0.737828 | + | 0.674989i | \(0.764148\pi\) | |||||||
\(614\) | 9.68903 | 0.391017 | ||||||||
\(615\) | −2.70657 | −0.109139 | ||||||||
\(616\) | 18.2900 | 0.736925 | ||||||||
\(617\) | −6.76760 | −0.272454 | −0.136227 | − | 0.990678i | \(-0.543498\pi\) | ||||
−0.136227 | + | 0.990678i | \(0.543498\pi\) | |||||||
\(618\) | 7.11850 | 0.286348 | ||||||||
\(619\) | 16.1044 | 0.647289 | 0.323644 | − | 0.946179i | \(-0.395092\pi\) | ||||
0.323644 | + | 0.946179i | \(0.395092\pi\) | |||||||
\(620\) | 1.90083 | 0.0763391 | ||||||||
\(621\) | −12.6957 | −0.509462 | ||||||||
\(622\) | 1.67689 | 0.0672372 | ||||||||
\(623\) | −1.61613 | −0.0647487 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.3127 | 0.892509 | ||||||||
\(626\) | 12.1187 | 0.484362 | ||||||||
\(627\) | 8.77599 | 0.350479 | ||||||||
\(628\) | −10.5441 | −0.420755 | ||||||||
\(629\) | −27.8943 | −1.11222 | ||||||||
\(630\) | −1.28310 | −0.0511201 | ||||||||
\(631\) | 24.2721 | 0.966258 | 0.483129 | − | 0.875549i | \(-0.339500\pi\) | ||||
0.483129 | + | 0.875549i | \(0.339500\pi\) | |||||||
\(632\) | −7.39511 | −0.294162 | ||||||||
\(633\) | 23.6244 | 0.938987 | ||||||||
\(634\) | 10.1049 | 0.401318 | ||||||||
\(635\) | −6.57511 | −0.260925 | ||||||||
\(636\) | −6.46185 | −0.256229 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.46500 | −0.0975904 | ||||||||
\(639\) | −5.06263 | −0.200274 | ||||||||
\(640\) | −0.425845 | −0.0168330 | ||||||||
\(641\) | 13.7304 | 0.542320 | 0.271160 | − | 0.962534i | \(-0.412593\pi\) | ||||
0.271160 | + | 0.962534i | \(0.412593\pi\) | |||||||
\(642\) | 13.6423 | 0.538420 | ||||||||
\(643\) | −15.1056 | −0.595705 | −0.297852 | − | 0.954612i | \(-0.596270\pi\) | ||||
−0.297852 | + | 0.954612i | \(0.596270\pi\) | |||||||
\(644\) | −6.56542 | −0.258714 | ||||||||
\(645\) | −5.32061 | −0.209499 | ||||||||
\(646\) | 4.36685 | 0.171811 | ||||||||
\(647\) | 37.4397 | 1.47191 | 0.735953 | − | 0.677032i | \(-0.236734\pi\) | ||||
0.735953 | + | 0.677032i | \(0.236734\pi\) | |||||||
\(648\) | 4.84874 | 0.190477 | ||||||||
\(649\) | −6.38816 | −0.250757 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.3257 | −0.718240 | ||||||||
\(652\) | −6.02314 | −0.235884 | ||||||||
\(653\) | −28.4606 | −1.11375 | −0.556874 | − | 0.830597i | \(-0.687999\pi\) | ||||
−0.556874 | + | 0.830597i | \(0.687999\pi\) | |||||||
\(654\) | 11.9485 | 0.467224 | ||||||||
\(655\) | 8.30486 | 0.324498 | ||||||||
\(656\) | −4.52838 | −0.176803 | ||||||||
\(657\) | −10.8317 | −0.422585 | ||||||||
\(658\) | −21.3520 | −0.832386 | ||||||||
\(659\) | 11.6888 | 0.455333 | 0.227666 | − | 0.973739i | \(-0.426890\pi\) | ||||
0.227666 | + | 0.973739i | \(0.426890\pi\) | |||||||
\(660\) | 3.73721 | 0.145471 | ||||||||
\(661\) | 13.4492 | 0.523113 | 0.261556 | − | 0.965188i | \(-0.415764\pi\) | ||||
0.261556 | + | 0.965188i | \(0.415764\pi\) | |||||||
\(662\) | 35.5859 | 1.38309 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.79541 | 0.380136 | ||||||||
\(665\) | −1.24565 | −0.0483041 | ||||||||
\(666\) | 6.57982 | 0.254963 | ||||||||
\(667\) | 0.884843 | 0.0342613 | ||||||||
\(668\) | 9.32561 | 0.360819 | ||||||||
\(669\) | −1.86172 | −0.0719783 | ||||||||
\(670\) | 3.50553 | 0.135430 | ||||||||
\(671\) | −22.8477 | −0.882026 | ||||||||
\(672\) | 4.10552 | 0.158374 | ||||||||
\(673\) | 25.6200 | 0.987579 | 0.493790 | − | 0.869581i | \(-0.335611\pi\) | ||||
0.493790 | + | 0.869581i | \(0.335611\pi\) | |||||||
\(674\) | 22.9814 | 0.885211 | ||||||||
\(675\) | 27.2561 | 1.04909 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.2260 | −1.23855 | −0.619274 | − | 0.785175i | \(-0.712573\pi\) | ||||
−0.619274 | + | 0.785175i | \(0.712573\pi\) | |||||||
\(678\) | −29.3180 | −1.12595 | ||||||||
\(679\) | −14.2696 | −0.547616 | ||||||||
\(680\) | 1.85960 | 0.0713125 | ||||||||
\(681\) | −31.5336 | −1.20837 | ||||||||
\(682\) | −27.9102 | −1.06874 | ||||||||
\(683\) | 9.93578 | 0.380182 | 0.190091 | − | 0.981766i | \(-0.439122\pi\) | ||||
0.190091 | + | 0.981766i | \(0.439122\pi\) | |||||||
\(684\) | −1.03007 | −0.0393858 | ||||||||
\(685\) | 3.55204 | 0.135717 | ||||||||
\(686\) | −15.9234 | −0.607960 | ||||||||
\(687\) | −27.3615 | −1.04391 | ||||||||
\(688\) | −8.90193 | −0.339383 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.34152 | −0.0510707 | ||||||||
\(691\) | 27.9932 | 1.06491 | 0.532455 | − | 0.846458i | \(-0.321270\pi\) | ||||
0.532455 | + | 0.846458i | \(0.321270\pi\) | |||||||
\(692\) | −18.6618 | −0.709414 | ||||||||
\(693\) | 18.8400 | 0.715673 | ||||||||
\(694\) | −7.20555 | −0.273519 | ||||||||
\(695\) | −3.68051 | −0.139610 | ||||||||
\(696\) | −0.553314 | −0.0209733 | ||||||||
\(697\) | 19.7747 | 0.749022 | ||||||||
\(698\) | −29.5472 | −1.11838 | ||||||||
\(699\) | −25.5169 | −0.965137 | ||||||||
\(700\) | 14.0951 | 0.532746 | ||||||||
\(701\) | −32.6718 | −1.23400 | −0.616999 | − | 0.786964i | \(-0.711652\pi\) | ||||
−0.616999 | + | 0.786964i | \(0.711652\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.38774 | 0.240918 | ||||||||
\(704\) | 6.25275 | 0.235659 | ||||||||
\(705\) | −4.36286 | −0.164315 | ||||||||
\(706\) | 1.41643 | 0.0533082 | ||||||||
\(707\) | 22.6604 | 0.852230 | ||||||||
\(708\) | −1.43394 | −0.0538907 | ||||||||
\(709\) | −45.9336 | −1.72507 | −0.862536 | − | 0.505995i | \(-0.831125\pi\) | ||||
−0.862536 | + | 0.505995i | \(0.831125\pi\) | |||||||
\(710\) | −2.09296 | −0.0785473 | ||||||||
\(711\) | −7.61748 | −0.285678 | ||||||||
\(712\) | −0.552500 | −0.0207058 | ||||||||
\(713\) | 10.0187 | 0.375203 | ||||||||
\(714\) | −17.9282 | −0.670946 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.4248 | −0.912799 | ||||||||
\(717\) | −39.7633 | −1.48499 | ||||||||
\(718\) | −2.06385 | −0.0770222 | ||||||||
\(719\) | −14.1325 | −0.527054 | −0.263527 | − | 0.964652i | \(-0.584886\pi\) | ||||
−0.263527 | + | 0.964652i | \(0.584886\pi\) | |||||||
\(720\) | −0.438651 | −0.0163475 | ||||||||
\(721\) | 14.8356 | 0.552508 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 13.7016 | 0.509569 | ||||||||
\(724\) | 26.4469 | 0.982893 | ||||||||
\(725\) | −1.89965 | −0.0705510 | ||||||||
\(726\) | −39.4351 | −1.46357 | ||||||||
\(727\) | 15.2232 | 0.564598 | 0.282299 | − | 0.959326i | \(-0.408903\pi\) | ||||
0.282299 | + | 0.959326i | \(0.408903\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.8114 | 1.06709 | ||||||||
\(730\) | −4.47797 | −0.165737 | ||||||||
\(731\) | 38.8734 | 1.43779 | ||||||||
\(732\) | −5.12858 | −0.189558 | ||||||||
\(733\) | −6.19770 | −0.228917 | −0.114459 | − | 0.993428i | \(-0.536513\pi\) | ||||
−0.114459 | + | 0.993428i | \(0.536513\pi\) | |||||||
\(734\) | 28.1446 | 1.03883 | ||||||||
\(735\) | 0.930187 | 0.0343105 | ||||||||
\(736\) | −2.24450 | −0.0827334 | ||||||||
\(737\) | −51.4722 | −1.89600 | ||||||||
\(738\) | −4.66455 | −0.171704 | ||||||||
\(739\) | 32.3924 | 1.19158 | 0.595788 | − | 0.803142i | \(-0.296840\pi\) | ||||
0.595788 | + | 0.803142i | \(0.296840\pi\) | |||||||
\(740\) | 2.72019 | 0.0999960 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13.4671 | −0.494393 | ||||||||
\(743\) | 3.82612 | 0.140367 | 0.0701834 | − | 0.997534i | \(-0.477642\pi\) | ||||
0.0701834 | + | 0.997534i | \(0.477642\pi\) | |||||||
\(744\) | −6.26494 | −0.229684 | ||||||||
\(745\) | −3.10564 | −0.113782 | ||||||||
\(746\) | 30.4016 | 1.11308 | ||||||||
\(747\) | 10.0900 | 0.369173 | ||||||||
\(748\) | −27.3048 | −0.998363 | ||||||||
\(749\) | 28.4319 | 1.03888 | ||||||||
\(750\) | 5.86852 | 0.214288 | ||||||||
\(751\) | 20.7881 | 0.758568 | 0.379284 | − | 0.925280i | \(-0.376170\pi\) | ||||
0.379284 | + | 0.925280i | \(0.376170\pi\) | |||||||
\(752\) | −7.29953 | −0.266186 | ||||||||
\(753\) | −23.5057 | −0.856596 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.0293180 | −0.00106699 | ||||||||
\(756\) | 16.5455 | 0.601756 | ||||||||
\(757\) | −29.5267 | −1.07317 | −0.536584 | − | 0.843847i | \(-0.680285\pi\) | ||||
−0.536584 | + | 0.843847i | \(0.680285\pi\) | |||||||
\(758\) | −4.93867 | −0.179381 | ||||||||
\(759\) | 19.6977 | 0.714982 | ||||||||
\(760\) | −0.425845 | −0.0154470 | ||||||||
\(761\) | −16.8275 | −0.609996 | −0.304998 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304998 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(762\) | 21.6709 | 0.785054 | ||||||||
\(763\) | 24.9019 | 0.901508 | ||||||||
\(764\) | −15.4036 | −0.557281 | ||||||||
\(765\) | 1.91552 | 0.0692558 | ||||||||
\(766\) | −14.2852 | −0.516145 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.40354 | 0.0506459 | ||||||||
\(769\) | 7.82739 | 0.282263 | 0.141131 | − | 0.989991i | \(-0.454926\pi\) | ||||
0.141131 | + | 0.989991i | \(0.454926\pi\) | |||||||
\(770\) | 7.78871 | 0.280686 | ||||||||
\(771\) | −26.5385 | −0.955761 | ||||||||
\(772\) | 9.64505 | 0.347133 | ||||||||
\(773\) | 20.3217 | 0.730919 | 0.365460 | − | 0.930827i | \(-0.380912\pi\) | ||||
0.365460 | + | 0.930827i | \(0.380912\pi\) | |||||||
\(774\) | −9.16962 | −0.329595 | ||||||||
\(775\) | −21.5089 | −0.772621 | ||||||||
\(776\) | −4.87829 | −0.175121 | ||||||||
\(777\) | −26.2250 | −0.940817 | ||||||||
\(778\) | −5.81026 | −0.208308 | ||||||||
\(779\) | −4.52838 | −0.162246 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.7312 | 1.09965 | ||||||||
\(782\) | 9.80140 | 0.350497 | ||||||||
\(783\) | −2.22990 | −0.0796900 | ||||||||
\(784\) | 1.55630 | 0.0555822 | ||||||||
\(785\) | −4.49015 | −0.160260 | ||||||||
\(786\) | −27.3720 | −0.976326 | ||||||||
\(787\) | 32.4595 | 1.15706 | 0.578528 | − | 0.815663i | \(-0.303627\pi\) | ||||
0.578528 | + | 0.815663i | \(0.303627\pi\) | |||||||
\(788\) | −8.84308 | −0.315022 | ||||||||
\(789\) | 24.0922 | 0.857704 | ||||||||
\(790\) | −3.14917 | −0.112042 | ||||||||
\(791\) | −61.1015 | −2.17252 | ||||||||
\(792\) | 6.44077 | 0.228863 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −15.5364 | −0.551367 | ||||||||
\(795\) | −2.75174 | −0.0975943 | ||||||||
\(796\) | −15.2687 | −0.541184 | ||||||||
\(797\) | −3.01437 | −0.106775 | −0.0533873 | − | 0.998574i | \(-0.517002\pi\) | ||||
−0.0533873 | + | 0.998574i | \(0.517002\pi\) | |||||||
\(798\) | 4.10552 | 0.145334 | ||||||||
\(799\) | 31.8759 | 1.12769 | ||||||||
\(800\) | 4.81866 | 0.170365 | ||||||||
\(801\) | −0.569114 | −0.0201087 | ||||||||
\(802\) | −3.79901 | −0.134148 | ||||||||
\(803\) | 65.7508 | 2.32029 | ||||||||
\(804\) | −11.5539 | −0.407473 | ||||||||
\(805\) | −2.79585 | −0.0985409 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 33.4455 | 1.17734 | ||||||||
\(808\) | 7.74682 | 0.272532 | ||||||||
\(809\) | 22.2551 | 0.782449 | 0.391224 | − | 0.920295i | \(-0.372052\pi\) | ||||
0.391224 | + | 0.920295i | \(0.372052\pi\) | |||||||
\(810\) | 2.06481 | 0.0725501 | ||||||||
\(811\) | 3.31086 | 0.116260 | 0.0581300 | − | 0.998309i | \(-0.481486\pi\) | ||||
0.0581300 | + | 0.998309i | \(0.481486\pi\) | |||||||
\(812\) | −1.15316 | −0.0404680 | ||||||||
\(813\) | −17.5043 | −0.613901 | ||||||||
\(814\) | −39.9409 | −1.39993 | ||||||||
\(815\) | −2.56492 | −0.0898453 | ||||||||
\(816\) | −6.12906 | −0.214560 | ||||||||
\(817\) | −8.90193 | −0.311439 | ||||||||
\(818\) | 21.9275 | 0.766676 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.92839 | −0.0673422 | ||||||||
\(821\) | −29.8984 | −1.04346 | −0.521731 | − | 0.853110i | \(-0.674713\pi\) | ||||
−0.521731 | + | 0.853110i | \(0.674713\pi\) | |||||||
\(822\) | −11.7072 | −0.408334 | ||||||||
\(823\) | −32.6938 | −1.13963 | −0.569817 | − | 0.821772i | \(-0.692986\pi\) | ||||
−0.569817 | + | 0.821772i | \(0.692986\pi\) | |||||||
\(824\) | 5.07181 | 0.176685 | ||||||||
\(825\) | −42.2885 | −1.47230 | ||||||||
\(826\) | −2.98847 | −0.103982 | ||||||||
\(827\) | 6.15194 | 0.213924 | 0.106962 | − | 0.994263i | \(-0.465888\pi\) | ||||
0.106962 | + | 0.994263i | \(0.465888\pi\) | |||||||
\(828\) | −2.31200 | −0.0803474 | ||||||||
\(829\) | −27.1186 | −0.941869 | −0.470935 | − | 0.882168i | \(-0.656083\pi\) | ||||
−0.470935 | + | 0.882168i | \(0.656083\pi\) | |||||||
\(830\) | 4.17133 | 0.144789 | ||||||||
\(831\) | −22.9203 | −0.795095 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.79614 | −0.235472 | ||||||||
\(834\) | 12.1306 | 0.420047 | ||||||||
\(835\) | 3.97126 | 0.137431 | ||||||||
\(836\) | 6.25275 | 0.216256 | ||||||||
\(837\) | −25.2482 | −0.872704 | ||||||||
\(838\) | −19.8371 | −0.685260 | ||||||||
\(839\) | −33.8084 | −1.16720 | −0.583598 | − | 0.812043i | \(-0.698356\pi\) | ||||
−0.583598 | + | 0.812043i | \(0.698356\pi\) | |||||||
\(840\) | 1.74832 | 0.0603226 | ||||||||
\(841\) | −28.8446 | −0.994641 | ||||||||
\(842\) | −15.5001 | −0.534168 | ||||||||
\(843\) | −27.5985 | −0.950543 | ||||||||
\(844\) | 16.8320 | 0.579382 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.51903 | −0.258510 | ||||||||
\(847\) | −82.1865 | −2.82396 | ||||||||
\(848\) | −4.60396 | −0.158101 | ||||||||
\(849\) | 24.5152 | 0.841359 | ||||||||
\(850\) | −21.0424 | −0.721747 | ||||||||
\(851\) | 14.3373 | 0.491476 | ||||||||
\(852\) | 6.89817 | 0.236328 | ||||||||
\(853\) | −33.3895 | −1.14323 | −0.571617 | − | 0.820521i | \(-0.693684\pi\) | ||||
−0.571617 | + | 0.820521i | \(0.693684\pi\) | |||||||
\(854\) | −10.6884 | −0.365751 | ||||||||
\(855\) | −0.438651 | −0.0150015 | ||||||||
\(856\) | 9.71994 | 0.332221 | ||||||||
\(857\) | 34.2122 | 1.16867 | 0.584333 | − | 0.811514i | \(-0.301356\pi\) | ||||
0.584333 | + | 0.811514i | \(0.301356\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.0118 | 1.80874 | 0.904370 | − | 0.426750i | \(-0.140341\pi\) | ||||
0.904370 | + | 0.426750i | \(0.140341\pi\) | |||||||
\(860\) | −3.79084 | −0.129267 | ||||||||
\(861\) | 18.5913 | 0.633591 | ||||||||
\(862\) | −30.6034 | −1.04236 | ||||||||
\(863\) | 27.2945 | 0.929115 | 0.464557 | − | 0.885543i | \(-0.346213\pi\) | ||||
0.464557 | + | 0.885543i | \(0.346213\pi\) | |||||||
\(864\) | 5.65637 | 0.192434 | ||||||||
\(865\) | −7.94702 | −0.270207 | ||||||||
\(866\) | −4.32019 | −0.146806 | ||||||||
\(867\) | 2.90448 | 0.0986412 | ||||||||
\(868\) | −13.0567 | −0.443175 | ||||||||
\(869\) | 46.2397 | 1.56858 | ||||||||
\(870\) | −0.235626 | −0.00798847 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.51312 | 0.288291 | ||||||||
\(873\) | −5.02499 | −0.170070 | ||||||||
\(874\) | −2.24450 | −0.0759214 | ||||||||
\(875\) | 12.2306 | 0.413469 | ||||||||
\(876\) | 14.7589 | 0.498659 | ||||||||
\(877\) | −35.2315 | −1.18968 | −0.594842 | − | 0.803843i | \(-0.702785\pi\) | ||||
−0.594842 | + | 0.803843i | \(0.702785\pi\) | |||||||
\(878\) | 19.0722 | 0.643657 | ||||||||
\(879\) | −8.19451 | −0.276394 | ||||||||
\(880\) | 2.66270 | 0.0897596 | ||||||||
\(881\) | 16.8108 | 0.566372 | 0.283186 | − | 0.959065i | \(-0.408609\pi\) | ||||
0.283186 | + | 0.959065i | \(0.408609\pi\) | |||||||
\(882\) | 1.60310 | 0.0539792 | ||||||||
\(883\) | 22.5292 | 0.758168 | 0.379084 | − | 0.925362i | \(-0.376239\pi\) | ||||
0.379084 | + | 0.925362i | \(0.376239\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.610635 | −0.0205263 | ||||||||
\(886\) | −18.5646 | −0.623691 | ||||||||
\(887\) | 37.4171 | 1.25634 | 0.628171 | − | 0.778075i | \(-0.283804\pi\) | ||||
0.628171 | + | 0.778075i | \(0.283804\pi\) | |||||||
\(888\) | −8.96546 | −0.300861 | ||||||||
\(889\) | 45.1642 | 1.51476 | ||||||||
\(890\) | −0.235279 | −0.00788658 | ||||||||
\(891\) | −30.3179 | −1.01569 | ||||||||
\(892\) | −1.32645 | −0.0444127 | ||||||||
\(893\) | −7.29953 | −0.244269 | ||||||||
\(894\) | 10.2359 | 0.342338 | ||||||||
\(895\) | −10.4012 | −0.347674 | ||||||||
\(896\) | 2.92512 | 0.0977213 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.64242 | −0.0881786 | ||||||||
\(899\) | 1.75970 | 0.0586892 | ||||||||
\(900\) | 4.96356 | 0.165452 | ||||||||
\(901\) | 20.1048 | 0.669788 | ||||||||
\(902\) | 28.3148 | 0.942780 | ||||||||
\(903\) | 36.5471 | 1.21621 | ||||||||
\(904\) | −20.8886 | −0.694744 | ||||||||
\(905\) | 11.2623 | 0.374371 | ||||||||
\(906\) | 0.0966292 | 0.00321029 | ||||||||
\(907\) | −50.7929 | −1.68655 | −0.843276 | − | 0.537481i | \(-0.819376\pi\) | ||||
−0.843276 | + | 0.537481i | \(0.819376\pi\) | |||||||
\(908\) | −22.4672 | −0.745599 | ||||||||
\(909\) | 7.97978 | 0.264673 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.7232 | 1.77993 | 0.889964 | − | 0.456031i | \(-0.150729\pi\) | ||||
0.889964 | + | 0.456031i | \(0.150729\pi\) | |||||||
\(912\) | 1.40354 | 0.0464759 | ||||||||
\(913\) | −61.2482 | −2.02702 | ||||||||
\(914\) | −39.2950 | −1.29976 | ||||||||
\(915\) | −2.18398 | −0.0722001 | ||||||||
\(916\) | −19.4946 | −0.644119 | ||||||||
\(917\) | −57.0458 | −1.88382 | ||||||||
\(918\) | −24.7005 | −0.815239 | ||||||||
\(919\) | −6.33546 | −0.208988 | −0.104494 | − | 0.994526i | \(-0.533322\pi\) | ||||
−0.104494 | + | 0.994526i | \(0.533322\pi\) | |||||||
\(920\) | −0.955809 | −0.0315121 | ||||||||
\(921\) | −13.5989 | −0.448101 | ||||||||
\(922\) | −32.1567 | −1.05903 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −25.6708 | −0.844507 | ||||||||
\(925\) | −30.7803 | −1.01205 | ||||||||
\(926\) | 10.9509 | 0.359870 | ||||||||
\(927\) | 5.22433 | 0.171589 | ||||||||
\(928\) | −0.394227 | −0.0129411 | ||||||||
\(929\) | 46.3899 | 1.52200 | 0.761002 | − | 0.648750i | \(-0.224708\pi\) | ||||
0.761002 | + | 0.648750i | \(0.224708\pi\) | |||||||
\(930\) | −2.66789 | −0.0874837 | ||||||||
\(931\) | 1.55630 | 0.0510057 | ||||||||
\(932\) | −18.1804 | −0.595517 | ||||||||
\(933\) | −2.35358 | −0.0770529 | ||||||||
\(934\) | −36.2880 | −1.18738 | ||||||||
\(935\) | −11.6276 | −0.380264 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.8813 | 1.59688 | 0.798441 | − | 0.602072i | \(-0.205658\pi\) | ||||
0.798441 | + | 0.602072i | \(0.205658\pi\) | |||||||
\(938\) | −24.0793 | −0.786219 | ||||||||
\(939\) | −17.0091 | −0.555073 | ||||||||
\(940\) | −3.10847 | −0.101387 | ||||||||
\(941\) | −0.310622 | −0.0101260 | −0.00506300 | − | 0.999987i | \(-0.501612\pi\) | ||||
−0.00506300 | + | 0.999987i | \(0.501612\pi\) | |||||||
\(942\) | 14.7991 | 0.482180 | ||||||||
\(943\) | −10.1639 | −0.330984 | ||||||||
\(944\) | −1.02166 | −0.0332521 | ||||||||
\(945\) | 7.04584 | 0.229201 | ||||||||
\(946\) | 55.6615 | 1.80971 | ||||||||
\(947\) | −43.4871 | −1.41314 | −0.706570 | − | 0.707643i | \(-0.749759\pi\) | ||||
−0.706570 | + | 0.707643i | \(0.749759\pi\) | |||||||
\(948\) | 10.3793 | 0.337105 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4.81866 | 0.156338 | ||||||||
\(951\) | −14.1827 | −0.459905 | ||||||||
\(952\) | −12.7735 | −0.413993 | ||||||||
\(953\) | 39.4689 | 1.27852 | 0.639262 | − | 0.768989i | \(-0.279240\pi\) | ||||
0.639262 | + | 0.768989i | \(0.279240\pi\) | |||||||
\(954\) | −4.74240 | −0.153541 | ||||||||
\(955\) | −6.55953 | −0.212261 | ||||||||
\(956\) | −28.3307 | −0.916279 | ||||||||
\(957\) | 3.45973 | 0.111837 | ||||||||
\(958\) | 8.63902 | 0.279114 | ||||||||
\(959\) | −24.3989 | −0.787880 | ||||||||
\(960\) | 0.597691 | 0.0192904 | ||||||||
\(961\) | −11.0757 | −0.357280 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.0122 | 0.322639 | ||||||||
\(964\) | 9.76218 | 0.314419 | ||||||||
\(965\) | 4.10730 | 0.132219 | ||||||||
\(966\) | 9.21485 | 0.296483 | ||||||||
\(967\) | −43.8685 | −1.41072 | −0.705358 | − | 0.708851i | \(-0.749214\pi\) | ||||
−0.705358 | + | 0.708851i | \(0.749214\pi\) | |||||||
\(968\) | −28.0968 | −0.903067 | ||||||||
\(969\) | −6.12906 | −0.196894 | ||||||||
\(970\) | −2.07740 | −0.0667012 | ||||||||
\(971\) | 10.5724 | 0.339284 | 0.169642 | − | 0.985506i | \(-0.445739\pi\) | ||||
0.169642 | + | 0.985506i | \(0.445739\pi\) | |||||||
\(972\) | 10.1637 | 0.326001 | ||||||||
\(973\) | 25.2813 | 0.810481 | ||||||||
\(974\) | −35.4068 | −1.13451 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.65403 | −0.116963 | ||||||||
\(977\) | 7.55789 | 0.241798 | 0.120899 | − | 0.992665i | \(-0.461422\pi\) | ||||
0.120899 | + | 0.992665i | \(0.461422\pi\) | |||||||
\(978\) | 8.45372 | 0.270320 | ||||||||
\(979\) | 3.45464 | 0.110411 | ||||||||
\(980\) | 0.662743 | 0.0211705 | ||||||||
\(981\) | 8.76912 | 0.279976 | ||||||||
\(982\) | −38.0024 | −1.21270 | ||||||||
\(983\) | −6.75818 | −0.215553 | −0.107776 | − | 0.994175i | \(-0.534373\pi\) | ||||
−0.107776 | + | 0.994175i | \(0.534373\pi\) | |||||||
\(984\) | 6.35577 | 0.202614 | ||||||||
\(985\) | −3.76578 | −0.119988 | ||||||||
\(986\) | 1.72153 | 0.0548247 | ||||||||
\(987\) | 29.9684 | 0.953903 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.9804 | −0.635340 | ||||||||
\(990\) | 2.74277 | 0.0871710 | ||||||||
\(991\) | −59.3782 | −1.88621 | −0.943105 | − | 0.332496i | \(-0.892109\pi\) | ||||
−0.943105 | + | 0.332496i | \(0.892109\pi\) | |||||||
\(992\) | −4.46367 | −0.141722 | ||||||||
\(993\) | −49.9463 | −1.58500 | ||||||||
\(994\) | 14.3765 | 0.455994 | ||||||||
\(995\) | −6.50209 | −0.206130 | ||||||||
\(996\) | −13.7483 | −0.435630 | ||||||||
\(997\) | −46.0862 | −1.45956 | −0.729782 | − | 0.683680i | \(-0.760378\pi\) | ||||
−0.729782 | + | 0.683680i | \(0.760378\pi\) | |||||||
\(998\) | 5.50496 | 0.174256 | ||||||||
\(999\) | −36.1314 | −1.14315 |
(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 | 6422.2.a.bg.1.7 | 8 | ||
13.2 | odd | 12 | 494.2.m.a.381.1 | yes | 16 | ||
13.7 | odd | 12 | 494.2.m.a.153.1 | ✓ | 16 | ||
13.12 | even | 2 | 6422.2.a.bh.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
494.2.m.a.153.1 | ✓ | 16 | 13.7 | odd | 12 | ||
494.2.m.a.381.1 | yes | 16 | 13.2 | odd | 12 | ||
6422.2.a.bg.1.7 | 8 | 1.1 | even | 1 | trivial | ||
6422.2.a.bh.1.7 | 8 | 13.12 | even | 2 |