Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 3 x^{12} - 17 x^{11} + 51 x^{10} + 106 x^{9} - 316 x^{8} - 288 x^{7} + 852 x^{6} + 309 x^{5} + \cdots - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 705) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(2.74237\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.74237 | 1.93915 | 0.969574 | − | 0.244799i | \(-0.0787219\pi\) | ||||
0.969574 | + | 0.244799i | \(0.0787219\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 5.52059 | 2.76029 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.74237 | 1.11957 | ||||||||
\(7\) | 1.18262 | 0.446987 | 0.223493 | − | 0.974705i | \(-0.428254\pi\) | ||||
0.223493 | + | 0.974705i | \(0.428254\pi\) | |||||||
\(8\) | 9.65475 | 3.41347 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.47841 | −1.04878 | −0.524390 | − | 0.851478i | \(-0.675707\pi\) | ||||
−0.524390 | + | 0.851478i | \(0.675707\pi\) | |||||||
\(12\) | 5.52059 | 1.59366 | ||||||||
\(13\) | −5.63132 | −1.56185 | −0.780923 | − | 0.624627i | \(-0.785251\pi\) | ||||
−0.780923 | + | 0.624627i | \(0.785251\pi\) | |||||||
\(14\) | 3.24317 | 0.866773 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.4357 | 3.85893 | ||||||||
\(17\) | 4.27384 | 1.03656 | 0.518279 | − | 0.855212i | \(-0.326573\pi\) | ||||
0.518279 | + | 0.855212i | \(0.326573\pi\) | |||||||
\(18\) | 2.74237 | 0.646383 | ||||||||
\(19\) | 8.18104 | 1.87686 | 0.938430 | − | 0.345470i | \(-0.112280\pi\) | ||||
0.938430 | + | 0.345470i | \(0.112280\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.18262 | 0.258068 | ||||||||
\(22\) | −9.53909 | −2.03374 | ||||||||
\(23\) | −6.05477 | −1.26251 | −0.631253 | − | 0.775577i | \(-0.717459\pi\) | ||||
−0.631253 | + | 0.775577i | \(0.717459\pi\) | |||||||
\(24\) | 9.65475 | 1.97077 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −15.4432 | −3.02865 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 6.52874 | 1.23381 | ||||||||
\(29\) | 4.15942 | 0.772385 | 0.386193 | − | 0.922418i | \(-0.373790\pi\) | ||||
0.386193 | + | 0.922418i | \(0.373790\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.98011 | −0.535244 | −0.267622 | − | 0.963524i | \(-0.586238\pi\) | ||||
−0.267622 | + | 0.963524i | \(0.586238\pi\) | |||||||
\(32\) | 23.0209 | 4.06956 | ||||||||
\(33\) | −3.47841 | −0.605514 | ||||||||
\(34\) | 11.7204 | 2.01004 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.52059 | 0.920098 | ||||||||
\(37\) | 6.90639 | 1.13540 | 0.567702 | − | 0.823234i | \(-0.307833\pi\) | ||||
0.567702 | + | 0.823234i | \(0.307833\pi\) | |||||||
\(38\) | 22.4354 | 3.63951 | ||||||||
\(39\) | −5.63132 | −0.901732 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.34896 | 1.14772 | 0.573858 | − | 0.818955i | \(-0.305446\pi\) | ||||
0.573858 | + | 0.818955i | \(0.305446\pi\) | |||||||
\(42\) | 3.24317 | 0.500432 | ||||||||
\(43\) | 2.62207 | 0.399862 | 0.199931 | − | 0.979810i | \(-0.435928\pi\) | ||||
0.199931 | + | 0.979810i | \(0.435928\pi\) | |||||||
\(44\) | −19.2029 | −2.89494 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −16.6044 | −2.44819 | ||||||||
\(47\) | 1.00000 | 0.145865 | ||||||||
\(48\) | 15.4357 | 2.22795 | ||||||||
\(49\) | −5.60142 | −0.800203 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.27384 | 0.598457 | ||||||||
\(52\) | −31.0882 | −4.31116 | ||||||||
\(53\) | −1.77644 | −0.244013 | −0.122006 | − | 0.992529i | \(-0.538933\pi\) | ||||
−0.122006 | + | 0.992529i | \(0.538933\pi\) | |||||||
\(54\) | 2.74237 | 0.373189 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 11.4179 | 1.52578 | ||||||||
\(57\) | 8.18104 | 1.08361 | ||||||||
\(58\) | 11.4067 | 1.49777 | ||||||||
\(59\) | 2.60332 | 0.338923 | 0.169462 | − | 0.985537i | \(-0.445797\pi\) | ||||
0.169462 | + | 0.985537i | \(0.445797\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.07880 | −1.16242 | −0.581211 | − | 0.813753i | \(-0.697421\pi\) | ||||
−0.581211 | + | 0.813753i | \(0.697421\pi\) | |||||||
\(62\) | −8.17257 | −1.03792 | ||||||||
\(63\) | 1.18262 | 0.148996 | ||||||||
\(64\) | 32.2604 | 4.03256 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.53909 | −1.17418 | ||||||||
\(67\) | −12.8586 | −1.57093 | −0.785463 | − | 0.618908i | \(-0.787575\pi\) | ||||
−0.785463 | + | 0.618908i | \(0.787575\pi\) | |||||||
\(68\) | 23.5941 | 2.86120 | ||||||||
\(69\) | −6.05477 | −0.728908 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.83113 | 0.217315 | 0.108657 | − | 0.994079i | \(-0.465345\pi\) | ||||
0.108657 | + | 0.994079i | \(0.465345\pi\) | |||||||
\(72\) | 9.65475 | 1.13782 | ||||||||
\(73\) | −1.43456 | −0.167902 | −0.0839510 | − | 0.996470i | \(-0.526754\pi\) | ||||
−0.0839510 | + | 0.996470i | \(0.526754\pi\) | |||||||
\(74\) | 18.9399 | 2.20172 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 45.1642 | 5.18068 | ||||||||
\(77\) | −4.11362 | −0.468791 | ||||||||
\(78\) | −15.4432 | −1.74859 | ||||||||
\(79\) | −2.99071 | −0.336481 | −0.168241 | − | 0.985746i | \(-0.553809\pi\) | ||||
−0.168241 | + | 0.985746i | \(0.553809\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 20.1536 | 2.22559 | ||||||||
\(83\) | −6.78713 | −0.744984 | −0.372492 | − | 0.928035i | \(-0.621497\pi\) | ||||
−0.372492 | + | 0.928035i | \(0.621497\pi\) | |||||||
\(84\) | 6.52874 | 0.712343 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.19069 | 0.775392 | ||||||||
\(87\) | 4.15942 | 0.445937 | ||||||||
\(88\) | −33.5832 | −3.57998 | ||||||||
\(89\) | −11.7281 | −1.24318 | −0.621590 | − | 0.783343i | \(-0.713513\pi\) | ||||
−0.621590 | + | 0.783343i | \(0.713513\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.65969 | −0.698125 | ||||||||
\(92\) | −33.4259 | −3.48489 | ||||||||
\(93\) | −2.98011 | −0.309023 | ||||||||
\(94\) | 2.74237 | 0.282854 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 23.0209 | 2.34956 | ||||||||
\(97\) | −14.9476 | −1.51770 | −0.758850 | − | 0.651266i | \(-0.774238\pi\) | ||||
−0.758850 | + | 0.651266i | \(0.774238\pi\) | |||||||
\(98\) | −15.3612 | −1.55171 | ||||||||
\(99\) | −3.47841 | −0.349593 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.9891 | −1.29246 | −0.646230 | − | 0.763142i | \(-0.723655\pi\) | ||||
−0.646230 | + | 0.763142i | \(0.723655\pi\) | |||||||
\(102\) | 11.7204 | 1.16050 | ||||||||
\(103\) | 3.89453 | 0.383740 | 0.191870 | − | 0.981420i | \(-0.438545\pi\) | ||||
0.191870 | + | 0.981420i | \(0.438545\pi\) | |||||||
\(104\) | −54.3690 | −5.33132 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.87166 | −0.473177 | ||||||||
\(107\) | 10.4948 | 1.01457 | 0.507286 | − | 0.861778i | \(-0.330649\pi\) | ||||
0.507286 | + | 0.861778i | \(0.330649\pi\) | |||||||
\(108\) | 5.52059 | 0.531219 | ||||||||
\(109\) | −5.81961 | −0.557418 | −0.278709 | − | 0.960376i | \(-0.589906\pi\) | ||||
−0.278709 | + | 0.960376i | \(0.589906\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.90639 | 0.655526 | ||||||||
\(112\) | 18.2545 | 1.72489 | ||||||||
\(113\) | −15.1609 | −1.42621 | −0.713107 | − | 0.701055i | \(-0.752713\pi\) | ||||
−0.713107 | + | 0.701055i | \(0.752713\pi\) | |||||||
\(114\) | 22.4354 | 2.10127 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 22.9625 | 2.13201 | ||||||||
\(117\) | −5.63132 | −0.520615 | ||||||||
\(118\) | 7.13926 | 0.657222 | ||||||||
\(119\) | 5.05431 | 0.463328 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.09934 | 0.0999399 | ||||||||
\(122\) | −24.8974 | −2.25411 | ||||||||
\(123\) | 7.34896 | 0.662634 | ||||||||
\(124\) | −16.4520 | −1.47743 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.24317 | 0.288924 | ||||||||
\(127\) | −9.51162 | −0.844020 | −0.422010 | − | 0.906591i | \(-0.638675\pi\) | ||||
−0.422010 | + | 0.906591i | \(0.638675\pi\) | |||||||
\(128\) | 42.4282 | 3.75016 | ||||||||
\(129\) | 2.62207 | 0.230860 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.8032 | 0.943878 | 0.471939 | − | 0.881631i | \(-0.343554\pi\) | ||||
0.471939 | + | 0.881631i | \(0.343554\pi\) | |||||||
\(132\) | −19.2029 | −1.67140 | ||||||||
\(133\) | 9.67503 | 0.838931 | ||||||||
\(134\) | −35.2630 | −3.04626 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 41.2628 | 3.53826 | ||||||||
\(137\) | −2.10628 | −0.179952 | −0.0899759 | − | 0.995944i | \(-0.528679\pi\) | ||||
−0.0899759 | + | 0.995944i | \(0.528679\pi\) | |||||||
\(138\) | −16.6044 | −1.41346 | ||||||||
\(139\) | −1.89352 | −0.160607 | −0.0803033 | − | 0.996770i | \(-0.525589\pi\) | ||||
−0.0803033 | + | 0.996770i | \(0.525589\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.00000 | 0.0842152 | ||||||||
\(142\) | 5.02163 | 0.421405 | ||||||||
\(143\) | 19.5880 | 1.63803 | ||||||||
\(144\) | 15.4357 | 1.28631 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.93408 | −0.325587 | ||||||||
\(147\) | −5.60142 | −0.461997 | ||||||||
\(148\) | 38.1273 | 3.13405 | ||||||||
\(149\) | 6.21102 | 0.508827 | 0.254413 | − | 0.967096i | \(-0.418118\pi\) | ||||
0.254413 | + | 0.967096i | \(0.418118\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.8462 | −1.28955 | −0.644773 | − | 0.764374i | \(-0.723048\pi\) | ||||
−0.644773 | + | 0.764374i | \(0.723048\pi\) | |||||||
\(152\) | 78.9859 | 6.40660 | ||||||||
\(153\) | 4.27384 | 0.345519 | ||||||||
\(154\) | −11.2811 | −0.909055 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −31.0882 | −2.48905 | ||||||||
\(157\) | 13.7455 | 1.09701 | 0.548505 | − | 0.836147i | \(-0.315197\pi\) | ||||
0.548505 | + | 0.836147i | \(0.315197\pi\) | |||||||
\(158\) | −8.20164 | −0.652487 | ||||||||
\(159\) | −1.77644 | −0.140881 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.16046 | −0.564324 | ||||||||
\(162\) | 2.74237 | 0.215461 | ||||||||
\(163\) | −5.87563 | −0.460215 | −0.230107 | − | 0.973165i | \(-0.573908\pi\) | ||||
−0.230107 | + | 0.973165i | \(0.573908\pi\) | |||||||
\(164\) | 40.5706 | 3.16803 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.6128 | −1.44463 | ||||||||
\(167\) | −6.92563 | −0.535921 | −0.267961 | − | 0.963430i | \(-0.586350\pi\) | ||||
−0.267961 | + | 0.963430i | \(0.586350\pi\) | |||||||
\(168\) | 11.4179 | 0.880907 | ||||||||
\(169\) | 18.7117 | 1.43936 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.18104 | 0.625620 | ||||||||
\(172\) | 14.4754 | 1.10374 | ||||||||
\(173\) | −5.58431 | −0.424567 | −0.212284 | − | 0.977208i | \(-0.568090\pi\) | ||||
−0.212284 | + | 0.977208i | \(0.568090\pi\) | |||||||
\(174\) | 11.4067 | 0.864737 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −53.6918 | −4.04717 | ||||||||
\(177\) | 2.60332 | 0.195678 | ||||||||
\(178\) | −32.1629 | −2.41071 | ||||||||
\(179\) | −10.2242 | −0.764191 | −0.382096 | − | 0.924123i | \(-0.624797\pi\) | ||||
−0.382096 | + | 0.924123i | \(0.624797\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.13256 | −0.530159 | −0.265080 | − | 0.964227i | \(-0.585398\pi\) | ||||
−0.265080 | + | 0.964227i | \(0.585398\pi\) | |||||||
\(182\) | −18.2633 | −1.35377 | ||||||||
\(183\) | −9.07880 | −0.671124 | ||||||||
\(184\) | −58.4573 | −4.30953 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −8.17257 | −0.599242 | ||||||||
\(187\) | −14.8662 | −1.08712 | ||||||||
\(188\) | 5.52059 | 0.402630 | ||||||||
\(189\) | 1.18262 | 0.0860226 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.25306 | 0.669528 | 0.334764 | − | 0.942302i | \(-0.391343\pi\) | ||||
0.334764 | + | 0.942302i | \(0.391343\pi\) | |||||||
\(192\) | 32.2604 | 2.32820 | ||||||||
\(193\) | −1.96214 | −0.141238 | −0.0706191 | − | 0.997503i | \(-0.522497\pi\) | ||||
−0.0706191 | + | 0.997503i | \(0.522497\pi\) | |||||||
\(194\) | −40.9919 | −2.94304 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −30.9231 | −2.20880 | ||||||||
\(197\) | 8.01414 | 0.570984 | 0.285492 | − | 0.958381i | \(-0.407843\pi\) | ||||
0.285492 | + | 0.958381i | \(0.407843\pi\) | |||||||
\(198\) | −9.53909 | −0.677913 | ||||||||
\(199\) | 19.8368 | 1.40619 | 0.703096 | − | 0.711095i | \(-0.251800\pi\) | ||||
0.703096 | + | 0.711095i | \(0.251800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.8586 | −0.906975 | ||||||||
\(202\) | −35.6208 | −2.50627 | ||||||||
\(203\) | 4.91900 | 0.345246 | ||||||||
\(204\) | 23.5941 | 1.65192 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.6803 | 0.744128 | ||||||||
\(207\) | −6.05477 | −0.420835 | ||||||||
\(208\) | −86.9234 | −6.02705 | ||||||||
\(209\) | −28.4570 | −1.96841 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.65052 | −0.182470 | −0.0912348 | − | 0.995829i | \(-0.529081\pi\) | ||||
−0.0912348 | + | 0.995829i | \(0.529081\pi\) | |||||||
\(212\) | −9.80700 | −0.673547 | ||||||||
\(213\) | 1.83113 | 0.125467 | ||||||||
\(214\) | 28.7807 | 1.96741 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.65475 | 0.656923 | ||||||||
\(217\) | −3.52433 | −0.239247 | ||||||||
\(218\) | −15.9595 | −1.08091 | ||||||||
\(219\) | −1.43456 | −0.0969383 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.0673 | −1.61894 | ||||||||
\(222\) | 18.9399 | 1.27116 | ||||||||
\(223\) | 0.118378 | 0.00792715 | 0.00396358 | − | 0.999992i | \(-0.498738\pi\) | ||||
0.00396358 | + | 0.999992i | \(0.498738\pi\) | |||||||
\(224\) | 27.2249 | 1.81904 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −41.5767 | −2.76564 | ||||||||
\(227\) | 1.63231 | 0.108340 | 0.0541702 | − | 0.998532i | \(-0.482749\pi\) | ||||
0.0541702 | + | 0.998532i | \(0.482749\pi\) | |||||||
\(228\) | 45.1642 | 2.99107 | ||||||||
\(229\) | −15.2328 | −1.00661 | −0.503307 | − | 0.864107i | \(-0.667884\pi\) | ||||
−0.503307 | + | 0.864107i | \(0.667884\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.11362 | −0.270657 | ||||||||
\(232\) | 40.1582 | 2.63651 | ||||||||
\(233\) | 16.1791 | 1.05993 | 0.529964 | − | 0.848020i | \(-0.322205\pi\) | ||||
0.529964 | + | 0.848020i | \(0.322205\pi\) | |||||||
\(234\) | −15.4432 | −1.00955 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 14.3719 | 0.935528 | ||||||||
\(237\) | −2.99071 | −0.194268 | ||||||||
\(238\) | 13.8608 | 0.898461 | ||||||||
\(239\) | −11.7407 | −0.759445 | −0.379723 | − | 0.925100i | \(-0.623981\pi\) | ||||
−0.379723 | + | 0.925100i | \(0.623981\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.5789 | 1.90534 | 0.952672 | − | 0.304002i | \(-0.0983228\pi\) | ||||
0.952672 | + | 0.304002i | \(0.0983228\pi\) | |||||||
\(242\) | 3.01479 | 0.193798 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −50.1203 | −3.20862 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 20.1536 | 1.28494 | ||||||||
\(247\) | −46.0700 | −2.93137 | ||||||||
\(248\) | −28.7723 | −1.82704 | ||||||||
\(249\) | −6.78713 | −0.430117 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.6905 | 1.05349 | 0.526746 | − | 0.850023i | \(-0.323412\pi\) | ||||
0.526746 | + | 0.850023i | \(0.323412\pi\) | |||||||
\(252\) | 6.52874 | 0.411272 | ||||||||
\(253\) | 21.0610 | 1.32409 | ||||||||
\(254\) | −26.0844 | −1.63668 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 51.8329 | 3.23956 | ||||||||
\(257\) | 20.6039 | 1.28524 | 0.642618 | − | 0.766187i | \(-0.277848\pi\) | ||||
0.642618 | + | 0.766187i | \(0.277848\pi\) | |||||||
\(258\) | 7.19069 | 0.447673 | ||||||||
\(259\) | 8.16761 | 0.507510 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.15942 | 0.257462 | ||||||||
\(262\) | 29.6263 | 1.83032 | ||||||||
\(263\) | −5.57321 | −0.343659 | −0.171829 | − | 0.985127i | \(-0.554968\pi\) | ||||
−0.171829 | + | 0.985127i | \(0.554968\pi\) | |||||||
\(264\) | −33.5832 | −2.06690 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 26.5325 | 1.62681 | ||||||||
\(267\) | −11.7281 | −0.717751 | ||||||||
\(268\) | −70.9870 | −4.33622 | ||||||||
\(269\) | 11.0853 | 0.675885 | 0.337943 | − | 0.941167i | \(-0.390269\pi\) | ||||
0.337943 | + | 0.941167i | \(0.390269\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.20390 | 0.498352 | 0.249176 | − | 0.968458i | \(-0.419840\pi\) | ||||
0.249176 | + | 0.968458i | \(0.419840\pi\) | |||||||
\(272\) | 65.9697 | 4.00000 | ||||||||
\(273\) | −6.65969 | −0.403062 | ||||||||
\(274\) | −5.77620 | −0.348953 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −33.4259 | −2.01200 | ||||||||
\(277\) | −12.0691 | −0.725163 | −0.362582 | − | 0.931952i | \(-0.618105\pi\) | ||||
−0.362582 | + | 0.931952i | \(0.618105\pi\) | |||||||
\(278\) | −5.19274 | −0.311440 | ||||||||
\(279\) | −2.98011 | −0.178415 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.3492 | 1.45255 | 0.726276 | − | 0.687403i | \(-0.241249\pi\) | ||||
0.726276 | + | 0.687403i | \(0.241249\pi\) | |||||||
\(282\) | 2.74237 | 0.163306 | ||||||||
\(283\) | −23.0077 | −1.36767 | −0.683834 | − | 0.729638i | \(-0.739689\pi\) | ||||
−0.683834 | + | 0.729638i | \(0.739689\pi\) | |||||||
\(284\) | 10.1089 | 0.599853 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 53.7176 | 3.17639 | ||||||||
\(287\) | 8.69100 | 0.513013 | ||||||||
\(288\) | 23.0209 | 1.35652 | ||||||||
\(289\) | 1.26568 | 0.0744518 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.9476 | −0.876244 | ||||||||
\(292\) | −7.91959 | −0.463459 | ||||||||
\(293\) | −24.7312 | −1.44481 | −0.722406 | − | 0.691469i | \(-0.756964\pi\) | ||||
−0.722406 | + | 0.691469i | \(0.756964\pi\) | |||||||
\(294\) | −15.3612 | −0.895881 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 66.6795 | 3.87567 | ||||||||
\(297\) | −3.47841 | −0.201838 | ||||||||
\(298\) | 17.0329 | 0.986690 | ||||||||
\(299\) | 34.0963 | 1.97184 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.10090 | 0.178733 | ||||||||
\(302\) | −43.4562 | −2.50062 | ||||||||
\(303\) | −12.9891 | −0.746202 | ||||||||
\(304\) | 126.280 | 7.24267 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 11.7204 | 0.670013 | ||||||||
\(307\) | 9.37703 | 0.535176 | 0.267588 | − | 0.963533i | \(-0.413773\pi\) | ||||
0.267588 | + | 0.963533i | \(0.413773\pi\) | |||||||
\(308\) | −22.7096 | −1.29400 | ||||||||
\(309\) | 3.89453 | 0.221552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.1338 | 1.36850 | 0.684251 | − | 0.729246i | \(-0.260129\pi\) | ||||
0.684251 | + | 0.729246i | \(0.260129\pi\) | |||||||
\(312\) | −54.3690 | −3.07804 | ||||||||
\(313\) | 30.6656 | 1.73332 | 0.866660 | − | 0.498900i | \(-0.166262\pi\) | ||||
0.866660 | + | 0.498900i | \(0.166262\pi\) | |||||||
\(314\) | 37.6953 | 2.12727 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.5105 | −0.928787 | ||||||||
\(317\) | 12.2027 | 0.685372 | 0.342686 | − | 0.939450i | \(-0.388663\pi\) | ||||
0.342686 | + | 0.939450i | \(0.388663\pi\) | |||||||
\(318\) | −4.87166 | −0.273189 | ||||||||
\(319\) | −14.4682 | −0.810062 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.4948 | 0.585764 | ||||||||
\(322\) | −19.6366 | −1.09431 | ||||||||
\(323\) | 34.9644 | 1.94547 | ||||||||
\(324\) | 5.52059 | 0.306699 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −16.1132 | −0.892425 | ||||||||
\(327\) | −5.81961 | −0.321825 | ||||||||
\(328\) | 70.9524 | 3.91769 | ||||||||
\(329\) | 1.18262 | 0.0651997 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.92128 | 0.160568 | 0.0802841 | − | 0.996772i | \(-0.474417\pi\) | ||||
0.0802841 | + | 0.996772i | \(0.474417\pi\) | |||||||
\(332\) | −37.4689 | −2.05638 | ||||||||
\(333\) | 6.90639 | 0.378468 | ||||||||
\(334\) | −18.9926 | −1.03923 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 18.2545 | 0.995866 | ||||||||
\(337\) | 7.60845 | 0.414459 | 0.207229 | − | 0.978292i | \(-0.433555\pi\) | ||||
0.207229 | + | 0.978292i | \(0.433555\pi\) | |||||||
\(338\) | 51.3145 | 2.79114 | ||||||||
\(339\) | −15.1609 | −0.823425 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.3661 | 0.561354 | ||||||||
\(342\) | 22.4354 | 1.21317 | ||||||||
\(343\) | −14.9026 | −0.804667 | ||||||||
\(344\) | 25.3154 | 1.36492 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.3142 | −0.823298 | ||||||||
\(347\) | 11.8416 | 0.635691 | 0.317846 | − | 0.948142i | \(-0.397041\pi\) | ||||
0.317846 | + | 0.948142i | \(0.397041\pi\) | |||||||
\(348\) | 22.9625 | 1.23092 | ||||||||
\(349\) | 15.7616 | 0.843697 | 0.421848 | − | 0.906666i | \(-0.361381\pi\) | ||||
0.421848 | + | 0.906666i | \(0.361381\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.63132 | −0.300577 | ||||||||
\(352\) | −80.0762 | −4.26808 | ||||||||
\(353\) | 16.7000 | 0.888851 | 0.444426 | − | 0.895816i | \(-0.353408\pi\) | ||||
0.444426 | + | 0.895816i | \(0.353408\pi\) | |||||||
\(354\) | 7.13926 | 0.379448 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −64.7462 | −3.43154 | ||||||||
\(357\) | 5.05431 | 0.267502 | ||||||||
\(358\) | −28.0385 | −1.48188 | ||||||||
\(359\) | 24.5406 | 1.29520 | 0.647602 | − | 0.761979i | \(-0.275772\pi\) | ||||
0.647602 | + | 0.761979i | \(0.275772\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 47.9294 | 2.52260 | ||||||||
\(362\) | −19.5601 | −1.02806 | ||||||||
\(363\) | 1.09934 | 0.0577003 | ||||||||
\(364\) | −36.7654 | −1.92703 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −24.8974 | −1.30141 | ||||||||
\(367\) | −17.9776 | −0.938425 | −0.469213 | − | 0.883085i | \(-0.655462\pi\) | ||||
−0.469213 | + | 0.883085i | \(0.655462\pi\) | |||||||
\(368\) | −93.4597 | −4.87192 | ||||||||
\(369\) | 7.34896 | 0.382572 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.10085 | −0.109071 | ||||||||
\(372\) | −16.4520 | −0.852996 | ||||||||
\(373\) | −36.5447 | −1.89221 | −0.946105 | − | 0.323859i | \(-0.895020\pi\) | ||||
−0.946105 | + | 0.323859i | \(0.895020\pi\) | |||||||
\(374\) | −40.7685 | −2.10809 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.65475 | 0.497906 | ||||||||
\(377\) | −23.4230 | −1.20635 | ||||||||
\(378\) | 3.24317 | 0.166811 | ||||||||
\(379\) | 16.8696 | 0.866531 | 0.433265 | − | 0.901266i | \(-0.357361\pi\) | ||||
0.433265 | + | 0.901266i | \(0.357361\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.51162 | −0.487295 | ||||||||
\(382\) | 25.3753 | 1.29831 | ||||||||
\(383\) | −16.2560 | −0.830645 | −0.415322 | − | 0.909674i | \(-0.636331\pi\) | ||||
−0.415322 | + | 0.909674i | \(0.636331\pi\) | |||||||
\(384\) | 42.4282 | 2.16515 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.38092 | −0.273882 | ||||||||
\(387\) | 2.62207 | 0.133287 | ||||||||
\(388\) | −82.5196 | −4.18930 | ||||||||
\(389\) | −14.3181 | −0.725959 | −0.362979 | − | 0.931797i | \(-0.618240\pi\) | ||||
−0.362979 | + | 0.931797i | \(0.618240\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.8771 | −1.30866 | ||||||||
\(392\) | −54.0803 | −2.73147 | ||||||||
\(393\) | 10.8032 | 0.544948 | ||||||||
\(394\) | 21.9777 | 1.10722 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −19.2029 | −0.964981 | ||||||||
\(397\) | 11.6416 | 0.584275 | 0.292138 | − | 0.956376i | \(-0.405633\pi\) | ||||
0.292138 | + | 0.956376i | \(0.405633\pi\) | |||||||
\(398\) | 54.3998 | 2.72681 | ||||||||
\(399\) | 9.67503 | 0.484357 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.8760 | 0.892684 | 0.446342 | − | 0.894862i | \(-0.352726\pi\) | ||||
0.446342 | + | 0.894862i | \(0.352726\pi\) | |||||||
\(402\) | −35.2630 | −1.75876 | ||||||||
\(403\) | 16.7820 | 0.835969 | ||||||||
\(404\) | −71.7073 | −3.56757 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.4897 | 0.669483 | ||||||||
\(407\) | −24.0233 | −1.19079 | ||||||||
\(408\) | 41.2628 | 2.04281 | ||||||||
\(409\) | 1.48293 | 0.0733264 | 0.0366632 | − | 0.999328i | \(-0.488327\pi\) | ||||
0.0366632 | + | 0.999328i | \(0.488327\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.10628 | −0.103895 | ||||||||
\(412\) | 21.5001 | 1.05924 | ||||||||
\(413\) | 3.07873 | 0.151494 | ||||||||
\(414\) | −16.6044 | −0.816062 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −129.638 | −6.35603 | ||||||||
\(417\) | −1.89352 | −0.0927263 | ||||||||
\(418\) | −78.0396 | −3.81704 | ||||||||
\(419\) | 40.3031 | 1.96893 | 0.984467 | − | 0.175570i | \(-0.0561767\pi\) | ||||
0.984467 | + | 0.175570i | \(0.0561767\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.56293 | 0.417332 | 0.208666 | − | 0.977987i | \(-0.433088\pi\) | ||||
0.208666 | + | 0.977987i | \(0.433088\pi\) | |||||||
\(422\) | −7.26871 | −0.353835 | ||||||||
\(423\) | 1.00000 | 0.0486217 | ||||||||
\(424\) | −17.1511 | −0.832931 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.02163 | 0.243299 | ||||||||
\(427\) | −10.7367 | −0.519587 | ||||||||
\(428\) | 57.9376 | 2.80052 | ||||||||
\(429\) | 19.5880 | 0.945719 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.03240 | 0.0497290 | 0.0248645 | − | 0.999691i | \(-0.492085\pi\) | ||||
0.0248645 | + | 0.999691i | \(0.492085\pi\) | |||||||
\(432\) | 15.4357 | 0.742651 | ||||||||
\(433\) | 21.1914 | 1.01839 | 0.509196 | − | 0.860651i | \(-0.329943\pi\) | ||||
0.509196 | + | 0.860651i | \(0.329943\pi\) | |||||||
\(434\) | −9.66502 | −0.463936 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −32.1277 | −1.53864 | ||||||||
\(437\) | −49.5343 | −2.36955 | ||||||||
\(438\) | −3.93408 | −0.187978 | ||||||||
\(439\) | 7.72254 | 0.368577 | 0.184288 | − | 0.982872i | \(-0.441002\pi\) | ||||
0.184288 | + | 0.982872i | \(0.441002\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.60142 | −0.266734 | ||||||||
\(442\) | −66.0015 | −3.13937 | ||||||||
\(443\) | −30.0193 | −1.42626 | −0.713131 | − | 0.701031i | \(-0.752724\pi\) | ||||
−0.713131 | + | 0.701031i | \(0.752724\pi\) | |||||||
\(444\) | 38.1273 | 1.80944 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.324635 | 0.0153719 | ||||||||
\(447\) | 6.21102 | 0.293771 | ||||||||
\(448\) | 38.1517 | 1.80250 | ||||||||
\(449\) | 20.5004 | 0.967473 | 0.483736 | − | 0.875214i | \(-0.339279\pi\) | ||||
0.483736 | + | 0.875214i | \(0.339279\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.5627 | −1.20370 | ||||||||
\(452\) | −83.6969 | −3.93677 | ||||||||
\(453\) | −15.8462 | −0.744520 | ||||||||
\(454\) | 4.47641 | 0.210088 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 78.9859 | 3.69885 | ||||||||
\(457\) | −14.3886 | −0.673073 | −0.336536 | − | 0.941670i | \(-0.609255\pi\) | ||||
−0.336536 | + | 0.941670i | \(0.609255\pi\) | |||||||
\(458\) | −41.7741 | −1.95197 | ||||||||
\(459\) | 4.27384 | 0.199486 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.15305 | −0.193427 | −0.0967135 | − | 0.995312i | \(-0.530833\pi\) | ||||
−0.0967135 | + | 0.995312i | \(0.530833\pi\) | |||||||
\(462\) | −11.2811 | −0.524843 | ||||||||
\(463\) | 14.6304 | 0.679930 | 0.339965 | − | 0.940438i | \(-0.389585\pi\) | ||||
0.339965 | + | 0.940438i | \(0.389585\pi\) | |||||||
\(464\) | 64.2036 | 2.98058 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 44.3691 | 2.05536 | ||||||||
\(467\) | 27.2159 | 1.25940 | 0.629701 | − | 0.776838i | \(-0.283177\pi\) | ||||
0.629701 | + | 0.776838i | \(0.283177\pi\) | |||||||
\(468\) | −31.0882 | −1.43705 | ||||||||
\(469\) | −15.2068 | −0.702184 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.7455 | 0.633359 | ||||||||
\(472\) | 25.1344 | 1.15690 | ||||||||
\(473\) | −9.12064 | −0.419367 | ||||||||
\(474\) | −8.20164 | −0.376714 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 27.9027 | 1.27892 | ||||||||
\(477\) | −1.77644 | −0.0813376 | ||||||||
\(478\) | −32.1974 | −1.47268 | ||||||||
\(479\) | 11.5282 | 0.526736 | 0.263368 | − | 0.964695i | \(-0.415167\pi\) | ||||
0.263368 | + | 0.964695i | \(0.415167\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −38.8921 | −1.77333 | ||||||||
\(482\) | 81.1162 | 3.69474 | ||||||||
\(483\) | −7.16046 | −0.325812 | ||||||||
\(484\) | 6.06900 | 0.275863 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.74237 | 0.124396 | ||||||||
\(487\) | −10.7084 | −0.485243 | −0.242621 | − | 0.970121i | \(-0.578007\pi\) | ||||
−0.242621 | + | 0.970121i | \(0.578007\pi\) | |||||||
\(488\) | −87.6536 | −3.96789 | ||||||||
\(489\) | −5.87563 | −0.265705 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.6363 | −1.06669 | −0.533346 | − | 0.845897i | \(-0.679066\pi\) | ||||
−0.533346 | + | 0.845897i | \(0.679066\pi\) | |||||||
\(492\) | 40.5706 | 1.82906 | ||||||||
\(493\) | 17.7767 | 0.800622 | ||||||||
\(494\) | −126.341 | −5.68435 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −46.0002 | −2.06547 | ||||||||
\(497\) | 2.16552 | 0.0971368 | ||||||||
\(498\) | −18.6128 | −0.834060 | ||||||||
\(499\) | 20.8755 | 0.934514 | 0.467257 | − | 0.884121i | \(-0.345242\pi\) | ||||
0.467257 | + | 0.884121i | \(0.345242\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.92563 | −0.309414 | ||||||||
\(502\) | 45.7714 | 2.04288 | ||||||||
\(503\) | −25.7847 | −1.14968 | −0.574842 | − | 0.818264i | \(-0.694937\pi\) | ||||
−0.574842 | + | 0.818264i | \(0.694937\pi\) | |||||||
\(504\) | 11.4179 | 0.508592 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 57.7569 | 2.56761 | ||||||||
\(507\) | 18.7117 | 0.831017 | ||||||||
\(508\) | −52.5098 | −2.32974 | ||||||||
\(509\) | −20.8904 | −0.925951 | −0.462976 | − | 0.886371i | \(-0.653218\pi\) | ||||
−0.462976 | + | 0.886371i | \(0.653218\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.69653 | −0.0750500 | ||||||||
\(512\) | 57.2885 | 2.53182 | ||||||||
\(513\) | 8.18104 | 0.361202 | ||||||||
\(514\) | 56.5035 | 2.49226 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 14.4754 | 0.637243 | ||||||||
\(517\) | −3.47841 | −0.152980 | ||||||||
\(518\) | 22.3986 | 0.984138 | ||||||||
\(519\) | −5.58431 | −0.245124 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.8480 | 0.738124 | 0.369062 | − | 0.929405i | \(-0.379679\pi\) | ||||
0.369062 | + | 0.929405i | \(0.379679\pi\) | |||||||
\(522\) | 11.4067 | 0.499256 | ||||||||
\(523\) | 1.30328 | 0.0569885 | 0.0284942 | − | 0.999594i | \(-0.490929\pi\) | ||||
0.0284942 | + | 0.999594i | \(0.490929\pi\) | |||||||
\(524\) | 59.6399 | 2.60538 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.2838 | −0.666405 | ||||||||
\(527\) | −12.7365 | −0.554812 | ||||||||
\(528\) | −53.6918 | −2.33663 | ||||||||
\(529\) | 13.6602 | 0.593922 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.60332 | 0.112974 | ||||||||
\(532\) | 53.4119 | 2.31570 | ||||||||
\(533\) | −41.3843 | −1.79255 | ||||||||
\(534\) | −32.1629 | −1.39182 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −124.146 | −5.36231 | ||||||||
\(537\) | −10.2242 | −0.441206 | ||||||||
\(538\) | 30.4001 | 1.31064 | ||||||||
\(539\) | 19.4840 | 0.839237 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.3500 | 0.659950 | 0.329975 | − | 0.943990i | \(-0.392960\pi\) | ||||
0.329975 | + | 0.943990i | \(0.392960\pi\) | |||||||
\(542\) | 22.4981 | 0.966377 | ||||||||
\(543\) | −7.13256 | −0.306087 | ||||||||
\(544\) | 98.3877 | 4.21834 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −18.2633 | −0.781598 | ||||||||
\(547\) | −35.5735 | −1.52101 | −0.760507 | − | 0.649330i | \(-0.775050\pi\) | ||||
−0.760507 | + | 0.649330i | \(0.775050\pi\) | |||||||
\(548\) | −11.6279 | −0.496720 | ||||||||
\(549\) | −9.07880 | −0.387474 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.0284 | 1.44966 | ||||||||
\(552\) | −58.4573 | −2.48811 | ||||||||
\(553\) | −3.53686 | −0.150403 | ||||||||
\(554\) | −33.0980 | −1.40620 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.4534 | −0.443321 | ||||||||
\(557\) | 7.76343 | 0.328947 | 0.164474 | − | 0.986381i | \(-0.447407\pi\) | ||||
0.164474 | + | 0.986381i | \(0.447407\pi\) | |||||||
\(558\) | −8.17257 | −0.345973 | ||||||||
\(559\) | −14.7657 | −0.624523 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.8662 | −0.627650 | ||||||||
\(562\) | 66.7745 | 2.81671 | ||||||||
\(563\) | 18.1505 | 0.764954 | 0.382477 | − | 0.923965i | \(-0.375071\pi\) | ||||
0.382477 | + | 0.923965i | \(0.375071\pi\) | |||||||
\(564\) | 5.52059 | 0.232459 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −63.0957 | −2.65211 | ||||||||
\(567\) | 1.18262 | 0.0496652 | ||||||||
\(568\) | 17.6791 | 0.741797 | ||||||||
\(569\) | −21.5551 | −0.903635 | −0.451818 | − | 0.892110i | \(-0.649224\pi\) | ||||
−0.451818 | + | 0.892110i | \(0.649224\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.55294 | 0.274232 | 0.137116 | − | 0.990555i | \(-0.456217\pi\) | ||||
0.137116 | + | 0.990555i | \(0.456217\pi\) | |||||||
\(572\) | 108.137 | 4.52145 | ||||||||
\(573\) | 9.25306 | 0.386552 | ||||||||
\(574\) | 23.8339 | 0.994809 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 32.2604 | 1.34419 | ||||||||
\(577\) | 15.6852 | 0.652981 | 0.326491 | − | 0.945200i | \(-0.394134\pi\) | ||||
0.326491 | + | 0.945200i | \(0.394134\pi\) | |||||||
\(578\) | 3.47097 | 0.144373 | ||||||||
\(579\) | −1.96214 | −0.0815439 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.02657 | −0.332998 | ||||||||
\(582\) | −40.9919 | −1.69917 | ||||||||
\(583\) | 6.17919 | 0.255916 | ||||||||
\(584\) | −13.8503 | −0.573129 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −67.8221 | −2.80170 | ||||||||
\(587\) | −19.0872 | −0.787815 | −0.393907 | − | 0.919150i | \(-0.628877\pi\) | ||||
−0.393907 | + | 0.919150i | \(0.628877\pi\) | |||||||
\(588\) | −30.9231 | −1.27525 | ||||||||
\(589\) | −24.3804 | −1.00458 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.01414 | 0.329657 | ||||||||
\(592\) | 106.605 | 4.38144 | ||||||||
\(593\) | −9.57363 | −0.393142 | −0.196571 | − | 0.980490i | \(-0.562981\pi\) | ||||
−0.196571 | + | 0.980490i | \(0.562981\pi\) | |||||||
\(594\) | −9.53909 | −0.391393 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 34.2885 | 1.40451 | ||||||||
\(597\) | 19.8368 | 0.811865 | ||||||||
\(598\) | 93.5047 | 3.82369 | ||||||||
\(599\) | 31.9147 | 1.30400 | 0.652001 | − | 0.758218i | \(-0.273930\pi\) | ||||
0.652001 | + | 0.758218i | \(0.273930\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.1866 | −1.14976 | −0.574878 | − | 0.818239i | \(-0.694950\pi\) | ||||
−0.574878 | + | 0.818239i | \(0.694950\pi\) | |||||||
\(602\) | 8.50382 | 0.346590 | ||||||||
\(603\) | −12.8586 | −0.523642 | ||||||||
\(604\) | −87.4804 | −3.55953 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −35.6208 | −1.44700 | ||||||||
\(607\) | 24.3726 | 0.989253 | 0.494627 | − | 0.869106i | \(-0.335305\pi\) | ||||
0.494627 | + | 0.869106i | \(0.335305\pi\) | |||||||
\(608\) | 188.335 | 7.63800 | ||||||||
\(609\) | 4.91900 | 0.199328 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.63132 | −0.227819 | ||||||||
\(612\) | 23.5941 | 0.953735 | ||||||||
\(613\) | −26.0517 | −1.05222 | −0.526109 | − | 0.850417i | \(-0.676350\pi\) | ||||
−0.526109 | + | 0.850417i | \(0.676350\pi\) | |||||||
\(614\) | 25.7153 | 1.03778 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −39.7160 | −1.60020 | ||||||||
\(617\) | −41.6712 | −1.67762 | −0.838810 | − | 0.544424i | \(-0.816748\pi\) | ||||
−0.838810 | + | 0.544424i | \(0.816748\pi\) | |||||||
\(618\) | 10.6803 | 0.429623 | ||||||||
\(619\) | −14.0162 | −0.563358 | −0.281679 | − | 0.959509i | \(-0.590891\pi\) | ||||
−0.281679 | + | 0.959509i | \(0.590891\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.05477 | −0.242969 | ||||||||
\(622\) | 66.1838 | 2.65373 | ||||||||
\(623\) | −13.8699 | −0.555685 | ||||||||
\(624\) | −86.9234 | −3.47972 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 84.0963 | 3.36116 | ||||||||
\(627\) | −28.4570 | −1.13646 | ||||||||
\(628\) | 75.8833 | 3.02807 | ||||||||
\(629\) | 29.5168 | 1.17691 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.8924 | −0.553048 | −0.276524 | − | 0.961007i | \(-0.589183\pi\) | ||||
−0.276524 | + | 0.961007i | \(0.589183\pi\) | |||||||
\(632\) | −28.8746 | −1.14857 | ||||||||
\(633\) | −2.65052 | −0.105349 | ||||||||
\(634\) | 33.4643 | 1.32904 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −9.80700 | −0.388873 | ||||||||
\(637\) | 31.5434 | 1.24979 | ||||||||
\(638\) | −39.6771 | −1.57083 | ||||||||
\(639\) | 1.83113 | 0.0724383 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.7776 | −1.57112 | −0.785561 | − | 0.618785i | \(-0.787625\pi\) | ||||
−0.785561 | + | 0.618785i | \(0.787625\pi\) | |||||||
\(642\) | 28.7807 | 1.13588 | ||||||||
\(643\) | 28.8715 | 1.13858 | 0.569290 | − | 0.822137i | \(-0.307218\pi\) | ||||
0.569290 | + | 0.822137i | \(0.307218\pi\) | |||||||
\(644\) | −39.5300 | −1.55770 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 95.8854 | 3.77256 | ||||||||
\(647\) | −26.7367 | −1.05113 | −0.525564 | − | 0.850754i | \(-0.676146\pi\) | ||||
−0.525564 | + | 0.850754i | \(0.676146\pi\) | |||||||
\(648\) | 9.65475 | 0.379274 | ||||||||
\(649\) | −9.05541 | −0.355456 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.52433 | −0.138129 | ||||||||
\(652\) | −32.4369 | −1.27033 | ||||||||
\(653\) | 6.84567 | 0.267892 | 0.133946 | − | 0.990989i | \(-0.457235\pi\) | ||||
0.133946 | + | 0.990989i | \(0.457235\pi\) | |||||||
\(654\) | −15.9595 | −0.624067 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 113.436 | 4.42895 | ||||||||
\(657\) | −1.43456 | −0.0559673 | ||||||||
\(658\) | 3.24317 | 0.126432 | ||||||||
\(659\) | −4.14255 | −0.161371 | −0.0806854 | − | 0.996740i | \(-0.525711\pi\) | ||||
−0.0806854 | + | 0.996740i | \(0.525711\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.8061 | −1.04264 | −0.521319 | − | 0.853362i | \(-0.674560\pi\) | ||||
−0.521319 | + | 0.853362i | \(0.674560\pi\) | |||||||
\(662\) | 8.01124 | 0.311366 | ||||||||
\(663\) | −24.0673 | −0.934698 | ||||||||
\(664\) | −65.5281 | −2.54298 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 18.9399 | 0.733905 | ||||||||
\(667\) | −25.1843 | −0.975141 | ||||||||
\(668\) | −38.2336 | −1.47930 | ||||||||
\(669\) | 0.118378 | 0.00457674 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.5798 | 1.21912 | ||||||||
\(672\) | 27.2249 | 1.05022 | ||||||||
\(673\) | −26.4223 | −1.01850 | −0.509252 | − | 0.860617i | \(-0.670078\pi\) | ||||
−0.509252 | + | 0.860617i | \(0.670078\pi\) | |||||||
\(674\) | 20.8652 | 0.803696 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 103.300 | 3.97307 | ||||||||
\(677\) | 1.48733 | 0.0571626 | 0.0285813 | − | 0.999591i | \(-0.490901\pi\) | ||||
0.0285813 | + | 0.999591i | \(0.490901\pi\) | |||||||
\(678\) | −41.5767 | −1.59674 | ||||||||
\(679\) | −17.6773 | −0.678392 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.63231 | 0.0625504 | ||||||||
\(682\) | 28.4276 | 1.08855 | ||||||||
\(683\) | 1.53579 | 0.0587655 | 0.0293828 | − | 0.999568i | \(-0.490646\pi\) | ||||
0.0293828 | + | 0.999568i | \(0.490646\pi\) | |||||||
\(684\) | 45.1642 | 1.72689 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −40.8685 | −1.56037 | ||||||||
\(687\) | −15.2328 | −0.581169 | ||||||||
\(688\) | 40.4735 | 1.54304 | ||||||||
\(689\) | 10.0037 | 0.381111 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.1681 | 0.729188 | 0.364594 | − | 0.931167i | \(-0.381208\pi\) | ||||
0.364594 | + | 0.931167i | \(0.381208\pi\) | |||||||
\(692\) | −30.8287 | −1.17193 | ||||||||
\(693\) | −4.11362 | −0.156264 | ||||||||
\(694\) | 32.4741 | 1.23270 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 40.1582 | 1.52219 | ||||||||
\(697\) | 31.4083 | 1.18967 | ||||||||
\(698\) | 43.2240 | 1.63605 | ||||||||
\(699\) | 16.1791 | 0.611950 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.52069 | −0.0952052 | −0.0476026 | − | 0.998866i | \(-0.515158\pi\) | ||||
−0.0476026 | + | 0.998866i | \(0.515158\pi\) | |||||||
\(702\) | −15.4432 | −0.582864 | ||||||||
\(703\) | 56.5015 | 2.13099 | ||||||||
\(704\) | −112.215 | −4.22926 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 45.7976 | 1.72361 | ||||||||
\(707\) | −15.3611 | −0.577713 | ||||||||
\(708\) | 14.3719 | 0.540127 | ||||||||
\(709\) | 36.8532 | 1.38405 | 0.692025 | − | 0.721873i | \(-0.256719\pi\) | ||||
0.692025 | + | 0.721873i | \(0.256719\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.99071 | −0.112160 | ||||||||
\(712\) | −113.232 | −4.24356 | ||||||||
\(713\) | 18.0439 | 0.675749 | ||||||||
\(714\) | 13.8608 | 0.518727 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −56.4435 | −2.10939 | ||||||||
\(717\) | −11.7407 | −0.438466 | ||||||||
\(718\) | 67.2994 | 2.51159 | ||||||||
\(719\) | 35.6166 | 1.32828 | 0.664138 | − | 0.747610i | \(-0.268799\pi\) | ||||
0.664138 | + | 0.747610i | \(0.268799\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.60574 | 0.171527 | ||||||||
\(722\) | 131.440 | 4.89170 | ||||||||
\(723\) | 29.5789 | 1.10005 | ||||||||
\(724\) | −39.3759 | −1.46339 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.01479 | 0.111889 | ||||||||
\(727\) | 4.53503 | 0.168195 | 0.0840975 | − | 0.996458i | \(-0.473199\pi\) | ||||
0.0840975 | + | 0.996458i | \(0.473199\pi\) | |||||||
\(728\) | −64.2976 | −2.38303 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.2063 | 0.414480 | ||||||||
\(732\) | −50.1203 | −1.85250 | ||||||||
\(733\) | −39.5305 | −1.46009 | −0.730047 | − | 0.683397i | \(-0.760502\pi\) | ||||
−0.730047 | + | 0.683397i | \(0.760502\pi\) | |||||||
\(734\) | −49.3013 | −1.81975 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −139.386 | −5.13785 | ||||||||
\(737\) | 44.7275 | 1.64756 | ||||||||
\(738\) | 20.1536 | 0.741863 | ||||||||
\(739\) | −51.9928 | −1.91259 | −0.956293 | − | 0.292409i | \(-0.905543\pi\) | ||||
−0.956293 | + | 0.292409i | \(0.905543\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −46.0700 | −1.69243 | ||||||||
\(742\) | −5.76130 | −0.211504 | ||||||||
\(743\) | −35.8825 | −1.31640 | −0.658201 | − | 0.752842i | \(-0.728682\pi\) | ||||
−0.658201 | + | 0.752842i | \(0.728682\pi\) | |||||||
\(744\) | −28.7723 | −1.05484 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −100.219 | −3.66928 | ||||||||
\(747\) | −6.78713 | −0.248328 | ||||||||
\(748\) | −82.0699 | −3.00077 | ||||||||
\(749\) | 12.4113 | 0.453500 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.8687 | −1.12641 | −0.563207 | − | 0.826316i | \(-0.690433\pi\) | ||||
−0.563207 | + | 0.826316i | \(0.690433\pi\) | |||||||
\(752\) | 15.4357 | 0.562883 | ||||||||
\(753\) | 16.6905 | 0.608234 | ||||||||
\(754\) | −64.2346 | −2.33929 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 6.52874 | 0.237448 | ||||||||
\(757\) | 3.12622 | 0.113625 | 0.0568123 | − | 0.998385i | \(-0.481906\pi\) | ||||
0.0568123 | + | 0.998385i | \(0.481906\pi\) | |||||||
\(758\) | 46.2626 | 1.68033 | ||||||||
\(759\) | 21.0610 | 0.764465 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.7431 | 1.04194 | 0.520968 | − | 0.853576i | \(-0.325571\pi\) | ||||
0.520968 | + | 0.853576i | \(0.325571\pi\) | |||||||
\(762\) | −26.0844 | −0.944937 | ||||||||
\(763\) | −6.88236 | −0.249158 | ||||||||
\(764\) | 51.0824 | 1.84809 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −44.5801 | −1.61074 | ||||||||
\(767\) | −14.6601 | −0.529346 | ||||||||
\(768\) | 51.8329 | 1.87036 | ||||||||
\(769\) | 43.3401 | 1.56288 | 0.781441 | − | 0.623979i | \(-0.214485\pi\) | ||||
0.781441 | + | 0.623979i | \(0.214485\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.6039 | 0.742032 | ||||||||
\(772\) | −10.8322 | −0.389859 | ||||||||
\(773\) | 32.0671 | 1.15337 | 0.576686 | − | 0.816966i | \(-0.304346\pi\) | ||||
0.576686 | + | 0.816966i | \(0.304346\pi\) | |||||||
\(774\) | 7.19069 | 0.258464 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −144.315 | −5.18062 | ||||||||
\(777\) | 8.16761 | 0.293011 | ||||||||
\(778\) | −39.2656 | −1.40774 | ||||||||
\(779\) | 60.1222 | 2.15410 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.36941 | −0.227915 | ||||||||
\(782\) | −70.9645 | −2.53769 | ||||||||
\(783\) | 4.15942 | 0.148646 | ||||||||
\(784\) | −86.4619 | −3.08793 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 29.6263 | 1.05674 | ||||||||
\(787\) | 25.1775 | 0.897483 | 0.448741 | − | 0.893662i | \(-0.351872\pi\) | ||||
0.448741 | + | 0.893662i | \(0.351872\pi\) | |||||||
\(788\) | 44.2427 | 1.57608 | ||||||||
\(789\) | −5.57321 | −0.198411 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.9295 | −0.637499 | ||||||||
\(792\) | −33.5832 | −1.19333 | ||||||||
\(793\) | 51.1256 | 1.81552 | ||||||||
\(794\) | 31.9256 | 1.13300 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 109.511 | 3.88150 | ||||||||
\(797\) | 47.5905 | 1.68574 | 0.842871 | − | 0.538116i | \(-0.180864\pi\) | ||||
0.842871 | + | 0.538116i | \(0.180864\pi\) | |||||||
\(798\) | 26.5325 | 0.939240 | ||||||||
\(799\) | 4.27384 | 0.151197 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.7281 | −0.414393 | ||||||||
\(802\) | 49.0225 | 1.73105 | ||||||||
\(803\) | 4.98997 | 0.176092 | ||||||||
\(804\) | −70.9870 | −2.50352 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 46.0224 | 1.62107 | ||||||||
\(807\) | 11.0853 | 0.390222 | ||||||||
\(808\) | −125.406 | −4.41178 | ||||||||
\(809\) | −7.72930 | −0.271748 | −0.135874 | − | 0.990726i | \(-0.543384\pi\) | ||||
−0.135874 | + | 0.990726i | \(0.543384\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.0007 | 1.58019 | 0.790095 | − | 0.612985i | \(-0.210031\pi\) | ||||
0.790095 | + | 0.612985i | \(0.210031\pi\) | |||||||
\(812\) | 27.1558 | 0.952980 | ||||||||
\(813\) | 8.20390 | 0.287723 | ||||||||
\(814\) | −65.8806 | −2.30912 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 65.9697 | 2.30940 | ||||||||
\(817\) | 21.4513 | 0.750485 | ||||||||
\(818\) | 4.06675 | 0.142191 | ||||||||
\(819\) | −6.65969 | −0.232708 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.1851 | 1.33267 | 0.666335 | − | 0.745652i | \(-0.267862\pi\) | ||||
0.666335 | + | 0.745652i | \(0.267862\pi\) | |||||||
\(822\) | −5.77620 | −0.201468 | ||||||||
\(823\) | −7.04124 | −0.245442 | −0.122721 | − | 0.992441i | \(-0.539162\pi\) | ||||
−0.122721 | + | 0.992441i | \(0.539162\pi\) | |||||||
\(824\) | 37.6008 | 1.30988 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.44301 | 0.293770 | ||||||||
\(827\) | −2.26867 | −0.0788895 | −0.0394447 | − | 0.999222i | \(-0.512559\pi\) | ||||
−0.0394447 | + | 0.999222i | \(0.512559\pi\) | |||||||
\(828\) | −33.4259 | −1.16163 | ||||||||
\(829\) | −3.91186 | −0.135864 | −0.0679322 | − | 0.997690i | \(-0.521640\pi\) | ||||
−0.0679322 | + | 0.997690i | \(0.521640\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.0691 | −0.418673 | ||||||||
\(832\) | −181.669 | −6.29823 | ||||||||
\(833\) | −23.9396 | −0.829456 | ||||||||
\(834\) | −5.19274 | −0.179810 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −157.099 | −5.43340 | ||||||||
\(837\) | −2.98011 | −0.103008 | ||||||||
\(838\) | 110.526 | 3.81805 | ||||||||
\(839\) | 29.5413 | 1.01988 | 0.509939 | − | 0.860210i | \(-0.329668\pi\) | ||||
0.509939 | + | 0.860210i | \(0.329668\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.6992 | −0.403421 | ||||||||
\(842\) | 23.4827 | 0.809268 | ||||||||
\(843\) | 24.3492 | 0.838632 | ||||||||
\(844\) | −14.6325 | −0.503670 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.74237 | 0.0942846 | ||||||||
\(847\) | 1.30010 | 0.0446718 | ||||||||
\(848\) | −27.4206 | −0.941629 | ||||||||
\(849\) | −23.0077 | −0.789623 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −41.8166 | −1.43345 | ||||||||
\(852\) | 10.1089 | 0.346325 | ||||||||
\(853\) | −34.1490 | −1.16924 | −0.584620 | − | 0.811308i | \(-0.698756\pi\) | ||||
−0.584620 | + | 0.811308i | \(0.698756\pi\) | |||||||
\(854\) | −29.4441 | −1.00756 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 101.325 | 3.46321 | ||||||||
\(857\) | −13.1307 | −0.448535 | −0.224267 | − | 0.974528i | \(-0.571999\pi\) | ||||
−0.224267 | + | 0.974528i | \(0.571999\pi\) | |||||||
\(858\) | 53.7176 | 1.83389 | ||||||||
\(859\) | 22.8736 | 0.780437 | 0.390219 | − | 0.920722i | \(-0.372399\pi\) | ||||
0.390219 | + | 0.920722i | \(0.372399\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.69100 | 0.296188 | ||||||||
\(862\) | 2.83123 | 0.0964319 | ||||||||
\(863\) | −25.6058 | −0.871630 | −0.435815 | − | 0.900036i | \(-0.643540\pi\) | ||||
−0.435815 | + | 0.900036i | \(0.643540\pi\) | |||||||
\(864\) | 23.0209 | 0.783188 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 58.1145 | 1.97481 | ||||||||
\(867\) | 1.26568 | 0.0429848 | ||||||||
\(868\) | −19.4564 | −0.660393 | ||||||||
\(869\) | 10.4029 | 0.352895 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 72.4108 | 2.45355 | ||||||||
\(872\) | −56.1869 | −1.90273 | ||||||||
\(873\) | −14.9476 | −0.505900 | ||||||||
\(874\) | −135.841 | −4.59490 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.91959 | −0.267578 | ||||||||
\(877\) | −23.2851 | −0.786283 | −0.393141 | − | 0.919478i | \(-0.628612\pi\) | ||||
−0.393141 | + | 0.919478i | \(0.628612\pi\) | |||||||
\(878\) | 21.1781 | 0.714725 | ||||||||
\(879\) | −24.7312 | −0.834162 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.1682 | −0.409959 | −0.204979 | − | 0.978766i | \(-0.565713\pi\) | ||||
−0.204979 | + | 0.978766i | \(0.565713\pi\) | |||||||
\(882\) | −15.3612 | −0.517237 | ||||||||
\(883\) | −19.9941 | −0.672855 | −0.336427 | − | 0.941709i | \(-0.609219\pi\) | ||||
−0.336427 | + | 0.941709i | \(0.609219\pi\) | |||||||
\(884\) | −132.866 | −4.46876 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −82.3241 | −2.76573 | ||||||||
\(887\) | 6.65494 | 0.223451 | 0.111726 | − | 0.993739i | \(-0.464362\pi\) | ||||
0.111726 | + | 0.993739i | \(0.464362\pi\) | |||||||
\(888\) | 66.6795 | 2.23762 | ||||||||
\(889\) | −11.2486 | −0.377266 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.47841 | −0.116531 | ||||||||
\(892\) | 0.653514 | 0.0218813 | ||||||||
\(893\) | 8.18104 | 0.273768 | ||||||||
\(894\) | 17.0329 | 0.569666 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 50.1763 | 1.67627 | ||||||||
\(897\) | 34.0963 | 1.13844 | ||||||||
\(898\) | 56.2196 | 1.87607 | ||||||||
\(899\) | −12.3956 | −0.413415 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.59222 | −0.252933 | ||||||||
\(902\) | −70.1024 | −2.33415 | ||||||||
\(903\) | 3.10090 | 0.103192 | ||||||||
\(904\) | −146.374 | −4.86834 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −43.4562 | −1.44373 | ||||||||
\(907\) | 0.194434 | 0.00645608 | 0.00322804 | − | 0.999995i | \(-0.498972\pi\) | ||||
0.00322804 | + | 0.999995i | \(0.498972\pi\) | |||||||
\(908\) | 9.01133 | 0.299051 | ||||||||
\(909\) | −12.9891 | −0.430820 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.6508 | −0.783585 | −0.391793 | − | 0.920054i | \(-0.628145\pi\) | ||||
−0.391793 | + | 0.920054i | \(0.628145\pi\) | |||||||
\(912\) | 126.280 | 4.18156 | ||||||||
\(913\) | 23.6084 | 0.781325 | ||||||||
\(914\) | −39.4590 | −1.30519 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −84.0943 | −2.77855 | ||||||||
\(917\) | 12.7760 | 0.421901 | ||||||||
\(918\) | 11.7204 | 0.386832 | ||||||||
\(919\) | −4.37513 | −0.144322 | −0.0721612 | − | 0.997393i | \(-0.522990\pi\) | ||||
−0.0721612 | + | 0.997393i | \(0.522990\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.37703 | 0.308984 | ||||||||
\(922\) | −11.3892 | −0.375083 | ||||||||
\(923\) | −10.3117 | −0.339412 | ||||||||
\(924\) | −22.7096 | −0.747092 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 40.1218 | 1.31849 | ||||||||
\(927\) | 3.89453 | 0.127913 | ||||||||
\(928\) | 95.7537 | 3.14327 | ||||||||
\(929\) | −32.4233 | −1.06377 | −0.531886 | − | 0.846816i | \(-0.678517\pi\) | ||||
−0.531886 | + | 0.846816i | \(0.678517\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45.8254 | −1.50187 | ||||||||
\(932\) | 89.3182 | 2.92572 | ||||||||
\(933\) | 24.1338 | 0.790105 | ||||||||
\(934\) | 74.6361 | 2.44217 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −54.3690 | −1.77711 | ||||||||
\(937\) | 27.8464 | 0.909702 | 0.454851 | − | 0.890567i | \(-0.349692\pi\) | ||||
0.454851 | + | 0.890567i | \(0.349692\pi\) | |||||||
\(938\) | −41.7026 | −1.36164 | ||||||||
\(939\) | 30.6656 | 1.00073 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.0603 | 0.882141 | 0.441070 | − | 0.897473i | \(-0.354599\pi\) | ||||
0.441070 | + | 0.897473i | \(0.354599\pi\) | |||||||
\(942\) | 37.6953 | 1.22818 | ||||||||
\(943\) | −44.4963 | −1.44900 | ||||||||
\(944\) | 40.1841 | 1.30788 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −25.0122 | −0.813215 | ||||||||
\(947\) | 17.1707 | 0.557973 | 0.278986 | − | 0.960295i | \(-0.410002\pi\) | ||||
0.278986 | + | 0.960295i | \(0.410002\pi\) | |||||||
\(948\) | −16.5105 | −0.536236 | ||||||||
\(949\) | 8.07844 | 0.262237 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.2027 | 0.395700 | ||||||||
\(952\) | 48.7981 | 1.58155 | ||||||||
\(953\) | 13.1959 | 0.427459 | 0.213729 | − | 0.976893i | \(-0.431439\pi\) | ||||
0.213729 | + | 0.976893i | \(0.431439\pi\) | |||||||
\(954\) | −4.87166 | −0.157726 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −64.8158 | −2.09629 | ||||||||
\(957\) | −14.4682 | −0.467690 | ||||||||
\(958\) | 31.6145 | 1.02142 | ||||||||
\(959\) | −2.49092 | −0.0804361 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.1189 | −0.713513 | ||||||||
\(962\) | −106.656 | −3.43874 | ||||||||
\(963\) | 10.4948 | 0.338191 | ||||||||
\(964\) | 163.293 | 5.25931 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −19.6366 | −0.631798 | ||||||||
\(967\) | −12.2492 | −0.393906 | −0.196953 | − | 0.980413i | \(-0.563105\pi\) | ||||
−0.196953 | + | 0.980413i | \(0.563105\pi\) | |||||||
\(968\) | 10.6138 | 0.341142 | ||||||||
\(969\) | 34.9644 | 1.12322 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 54.7498 | 1.75700 | 0.878502 | − | 0.477738i | \(-0.158543\pi\) | ||||
0.878502 | + | 0.477738i | \(0.158543\pi\) | |||||||
\(972\) | 5.52059 | 0.177073 | ||||||||
\(973\) | −2.23931 | −0.0717890 | ||||||||
\(974\) | −29.3663 | −0.940957 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −140.138 | −4.48570 | ||||||||
\(977\) | −42.0218 | −1.34440 | −0.672198 | − | 0.740372i | \(-0.734650\pi\) | ||||
−0.672198 | + | 0.740372i | \(0.734650\pi\) | |||||||
\(978\) | −16.1132 | −0.515242 | ||||||||
\(979\) | 40.7953 | 1.30382 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.81961 | −0.185806 | ||||||||
\(982\) | −64.8196 | −2.06848 | ||||||||
\(983\) | 18.6630 | 0.595259 | 0.297629 | − | 0.954682i | \(-0.403804\pi\) | ||||
0.297629 | + | 0.954682i | \(0.403804\pi\) | |||||||
\(984\) | 70.9524 | 2.26188 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 48.7502 | 1.55252 | ||||||||
\(987\) | 1.18262 | 0.0376431 | ||||||||
\(988\) | −254.334 | −8.09143 | ||||||||
\(989\) | −15.8760 | −0.504828 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.9705 | 0.539085 | 0.269542 | − | 0.962989i | \(-0.413128\pi\) | ||||
0.269542 | + | 0.962989i | \(0.413128\pi\) | |||||||
\(992\) | −68.6050 | −2.17821 | ||||||||
\(993\) | 2.92128 | 0.0927041 | ||||||||
\(994\) | 5.93865 | 0.188363 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −37.4689 | −1.18725 | ||||||||
\(997\) | 38.4006 | 1.21616 | 0.608079 | − | 0.793876i | \(-0.291940\pi\) | ||||
0.608079 | + | 0.793876i | \(0.291940\pi\) | |||||||
\(998\) | 57.2482 | 1.81216 | ||||||||
\(999\) | 6.90639 | 0.218509 |
(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 | 3525.2.a.bi.1.13 | 13 | ||
5.2 | odd | 4 | 705.2.c.c.424.26 | yes | 26 | ||
5.3 | odd | 4 | 705.2.c.c.424.1 | ✓ | 26 | ||
5.4 | even | 2 | 3525.2.a.bh.1.1 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
705.2.c.c.424.1 | ✓ | 26 | 5.3 | odd | 4 | ||
705.2.c.c.424.26 | yes | 26 | 5.2 | odd | 4 | ||
3525.2.a.bh.1.1 | 13 | 5.4 | even | 2 | |||
3525.2.a.bi.1.13 | 13 | 1.1 | even | 1 | trivial |