Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6525,2,Mod(1,6525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6525, 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("6525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6525 = 3^{2} \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6525.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: | \(52.1023873189\) |
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: | \( x^{8} - 2x^{7} - 12x^{6} + 23x^{5} + 36x^{4} - 62x^{3} - 15x^{2} + 14x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2175) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.57789\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.57789 | −1.82285 | −0.911423 | − | 0.411471i | \(-0.865015\pi\) | ||||
−0.911423 | + | 0.411471i | \(0.865015\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.64553 | 2.32277 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.69867 | 1.77593 | 0.887966 | − | 0.459909i | \(-0.152118\pi\) | ||||
0.887966 | + | 0.459909i | \(0.152118\pi\) | |||||||
\(8\) | −6.81989 | −2.41120 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.11503 | 0.939218 | 0.469609 | − | 0.882875i | \(-0.344395\pi\) | ||||
0.469609 | + | 0.882875i | \(0.344395\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.07945 | −1.40879 | −0.704393 | − | 0.709810i | \(-0.748781\pi\) | ||||
−0.704393 | + | 0.709810i | \(0.748781\pi\) | |||||||
\(14\) | −12.1127 | −3.23725 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 8.28989 | 2.07247 | ||||||||
\(17\) | −1.40020 | −0.339599 | −0.169799 | − | 0.985479i | \(-0.554312\pi\) | ||||
−0.169799 | + | 0.985479i | \(0.554312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.76514 | −0.863783 | −0.431892 | − | 0.901925i | \(-0.642154\pi\) | ||||
−0.431892 | + | 0.901925i | \(0.642154\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.03022 | −1.71205 | ||||||||
\(23\) | −5.71483 | −1.19162 | −0.595812 | − | 0.803124i | \(-0.703170\pi\) | ||||
−0.595812 | + | 0.803124i | \(0.703170\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 13.0943 | 2.56800 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 21.8278 | 4.12507 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.23218 | −0.400911 | −0.200456 | − | 0.979703i | \(-0.564242\pi\) | ||||
−0.200456 | + | 0.979703i | \(0.564242\pi\) | |||||||
\(32\) | −7.73067 | −1.36660 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.60957 | 0.619036 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.79088 | 0.952015 | 0.476008 | − | 0.879441i | \(-0.342083\pi\) | ||||
0.476008 | + | 0.879441i | \(0.342083\pi\) | |||||||
\(38\) | 9.70614 | 1.57454 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.6968 | 1.67055 | 0.835276 | − | 0.549830i | \(-0.185308\pi\) | ||||
0.835276 | + | 0.549830i | \(0.185308\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.89527 | −1.35652 | −0.678258 | − | 0.734824i | \(-0.737265\pi\) | ||||
−0.678258 | + | 0.734824i | \(0.737265\pi\) | |||||||
\(44\) | 14.4710 | 2.18158 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.7322 | 2.17215 | ||||||||
\(47\) | −3.62785 | −0.529176 | −0.264588 | − | 0.964362i | \(-0.585236\pi\) | ||||
−0.264588 | + | 0.964362i | \(0.585236\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.0775 | 2.15393 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −23.5967 | −3.27228 | ||||||||
\(53\) | 0.948260 | 0.130254 | 0.0651268 | − | 0.997877i | \(-0.479255\pi\) | ||||
0.0651268 | + | 0.997877i | \(0.479255\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −32.0445 | −4.28212 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.57789 | 0.338494 | ||||||||
\(59\) | 8.53886 | 1.11166 | 0.555832 | − | 0.831294i | \(-0.312400\pi\) | ||||
0.555832 | + | 0.831294i | \(0.312400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.21467 | −0.795707 | −0.397853 | − | 0.917449i | \(-0.630245\pi\) | ||||
−0.397853 | + | 0.917449i | \(0.630245\pi\) | |||||||
\(62\) | 5.75432 | 0.730799 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.34905 | 0.418631 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.9099 | −1.69937 | −0.849685 | − | 0.527291i | \(-0.823208\pi\) | ||||
−0.849685 | + | 0.527291i | \(0.823208\pi\) | |||||||
\(68\) | −6.50468 | −0.788808 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.88726 | −0.698690 | −0.349345 | − | 0.936994i | \(-0.613596\pi\) | ||||
−0.349345 | + | 0.936994i | \(0.613596\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.08398 | 0.829117 | 0.414559 | − | 0.910023i | \(-0.363936\pi\) | ||||
0.414559 | + | 0.910023i | \(0.363936\pi\) | |||||||
\(74\) | −14.9283 | −1.73538 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −17.4911 | −2.00637 | ||||||||
\(77\) | 14.6365 | 1.66799 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.31672 | 0.823195 | 0.411598 | − | 0.911366i | \(-0.364971\pi\) | ||||
0.411598 | + | 0.911366i | \(0.364971\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −27.5751 | −3.04516 | ||||||||
\(83\) | −13.6579 | −1.49915 | −0.749577 | − | 0.661917i | \(-0.769743\pi\) | ||||
−0.749577 | + | 0.661917i | \(0.769743\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 22.9311 | 2.47272 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −21.2442 | −2.26464 | ||||||||
\(89\) | 7.98017 | 0.845897 | 0.422948 | − | 0.906154i | \(-0.360995\pi\) | ||||
0.422948 | + | 0.906154i | \(0.360995\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −23.8667 | −2.50191 | ||||||||
\(92\) | −26.5484 | −2.76786 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.35221 | 0.964607 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.8343 | −1.40466 | −0.702329 | − | 0.711853i | \(-0.747856\pi\) | ||||
−0.702329 | + | 0.711853i | \(0.747856\pi\) | |||||||
\(98\) | −38.8683 | −3.92629 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.7461 | −1.26829 | −0.634144 | − | 0.773215i | \(-0.718647\pi\) | ||||
−0.634144 | + | 0.773215i | \(0.718647\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.20406 | 0.808370 | 0.404185 | − | 0.914677i | \(-0.367555\pi\) | ||||
0.404185 | + | 0.914677i | \(0.367555\pi\) | |||||||
\(104\) | 34.6413 | 3.39686 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.44451 | −0.237432 | ||||||||
\(107\) | −3.28873 | −0.317933 | −0.158967 | − | 0.987284i | \(-0.550816\pi\) | ||||
−0.158967 | + | 0.987284i | \(0.550816\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.246732 | −0.0236326 | −0.0118163 | − | 0.999930i | \(-0.503761\pi\) | ||||
−0.0118163 | + | 0.999930i | \(0.503761\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 38.9515 | 3.68057 | ||||||||
\(113\) | −14.4273 | −1.35721 | −0.678603 | − | 0.734505i | \(-0.737414\pi\) | ||||
−0.678603 | + | 0.734505i | \(0.737414\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.64553 | −0.431327 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −22.0123 | −2.02639 | ||||||||
\(119\) | −6.57909 | −0.603104 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.29657 | −0.117870 | ||||||||
\(122\) | 16.0207 | 1.45045 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.3697 | −0.931223 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.1707 | 1.87860 | 0.939299 | − | 0.343101i | \(-0.111477\pi\) | ||||
0.939299 | + | 0.343101i | \(0.111477\pi\) | |||||||
\(128\) | 6.82785 | 0.603503 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.18994 | 0.715559 | 0.357779 | − | 0.933806i | \(-0.383534\pi\) | ||||
0.357779 | + | 0.933806i | \(0.383534\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.6912 | −1.53402 | ||||||||
\(134\) | 35.8583 | 3.09769 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.54923 | 0.818840 | ||||||||
\(137\) | 17.4054 | 1.48704 | 0.743520 | − | 0.668714i | \(-0.233155\pi\) | ||||
0.743520 | + | 0.668714i | \(0.233155\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.81900 | −0.578380 | −0.289190 | − | 0.957272i | \(-0.593386\pi\) | ||||
−0.289190 | + | 0.957272i | \(0.593386\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.1767 | 1.27360 | ||||||||
\(143\) | −15.8226 | −1.32316 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −18.2617 | −1.51135 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 26.9017 | 2.21131 | ||||||||
\(149\) | −23.7335 | −1.94432 | −0.972162 | − | 0.234311i | \(-0.924717\pi\) | ||||
−0.972162 | + | 0.234311i | \(0.924717\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.3095 | −1.40863 | −0.704315 | − | 0.709888i | \(-0.748746\pi\) | ||||
−0.704315 | + | 0.709888i | \(0.748746\pi\) | |||||||
\(152\) | 25.6779 | 2.08275 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −37.7314 | −3.04048 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0537 | −0.802375 | −0.401188 | − | 0.915996i | \(-0.631402\pi\) | ||||
−0.401188 | + | 0.915996i | \(0.631402\pi\) | |||||||
\(158\) | −18.8617 | −1.50056 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −26.8521 | −2.11624 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.2602 | −0.960291 | −0.480145 | − | 0.877189i | \(-0.659416\pi\) | ||||
−0.480145 | + | 0.877189i | \(0.659416\pi\) | |||||||
\(164\) | 49.6921 | 3.88030 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 35.2087 | 2.73273 | ||||||||
\(167\) | −13.5990 | −1.05232 | −0.526160 | − | 0.850386i | \(-0.676369\pi\) | ||||
−0.526160 | + | 0.850386i | \(0.676369\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8008 | 0.984677 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −41.3233 | −3.15087 | ||||||||
\(173\) | 8.35226 | 0.635011 | 0.317505 | − | 0.948256i | \(-0.397155\pi\) | ||||
0.317505 | + | 0.948256i | \(0.397155\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 25.8233 | 1.94650 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −20.5720 | −1.54194 | ||||||||
\(179\) | −26.5865 | −1.98717 | −0.993583 | − | 0.113109i | \(-0.963919\pi\) | ||||
−0.993583 | + | 0.113109i | \(0.963919\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.72547 | 0.276912 | 0.138456 | − | 0.990369i | \(-0.455786\pi\) | ||||
0.138456 | + | 0.990369i | \(0.455786\pi\) | |||||||
\(182\) | 61.5257 | 4.56059 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 38.9745 | 2.87324 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.36167 | −0.318957 | ||||||||
\(188\) | −16.8533 | −1.22915 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.76433 | −0.489450 | −0.244725 | − | 0.969593i | \(-0.578698\pi\) | ||||
−0.244725 | + | 0.969593i | \(0.578698\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.140715 | −0.0101289 | −0.00506444 | − | 0.999987i | \(-0.501612\pi\) | ||||
−0.00506444 | + | 0.999987i | \(0.501612\pi\) | |||||||
\(194\) | 35.6633 | 2.56047 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 70.0431 | 5.00308 | ||||||||
\(197\) | −1.48273 | −0.105640 | −0.0528200 | − | 0.998604i | \(-0.516821\pi\) | ||||
−0.0528200 | + | 0.998604i | \(0.516821\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.8626 | 1.83335 | 0.916677 | − | 0.399628i | \(-0.130861\pi\) | ||||
0.916677 | + | 0.399628i | \(0.130861\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 32.8582 | 2.31189 | ||||||||
\(203\) | −4.69867 | −0.329782 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −21.1492 | −1.47353 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −42.1081 | −2.91967 | ||||||||
\(209\) | −11.7285 | −0.811281 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.3428 | 1.60698 | 0.803491 | − | 0.595317i | \(-0.202974\pi\) | ||||
0.803491 | + | 0.595317i | \(0.202974\pi\) | |||||||
\(212\) | 4.40517 | 0.302548 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.47799 | 0.579543 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.4883 | −0.711991 | ||||||||
\(218\) | 0.636049 | 0.0430787 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.11225 | 0.478422 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.4256 | −1.50173 | −0.750865 | − | 0.660455i | \(-0.770363\pi\) | ||||
−0.750865 | + | 0.660455i | \(0.770363\pi\) | |||||||
\(224\) | −36.3239 | −2.42699 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 37.1920 | 2.47398 | ||||||||
\(227\) | −4.07327 | −0.270353 | −0.135176 | − | 0.990822i | \(-0.543160\pi\) | ||||
−0.135176 | + | 0.990822i | \(0.543160\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.7170 | −1.03861 | −0.519303 | − | 0.854590i | \(-0.673808\pi\) | ||||
−0.519303 | + | 0.854590i | \(0.673808\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.81989 | 0.447748 | ||||||||
\(233\) | 16.4568 | 1.07812 | 0.539059 | − | 0.842268i | \(-0.318780\pi\) | ||||
0.539059 | + | 0.842268i | \(0.318780\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 39.6675 | 2.58214 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 16.9602 | 1.09937 | ||||||||
\(239\) | −3.18702 | −0.206151 | −0.103075 | − | 0.994674i | \(-0.532868\pi\) | ||||
−0.103075 | + | 0.994674i | \(0.532868\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.1482 | 0.718118 | 0.359059 | − | 0.933315i | \(-0.383098\pi\) | ||||
0.359059 | + | 0.933315i | \(0.383098\pi\) | |||||||
\(242\) | 3.34243 | 0.214859 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −28.8704 | −1.84824 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.1249 | 1.21689 | ||||||||
\(248\) | 15.2232 | 0.966676 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.23388 | 0.204121 | 0.102060 | − | 0.994778i | \(-0.467457\pi\) | ||||
0.102060 | + | 0.994778i | \(0.467457\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.8019 | −1.11919 | ||||||||
\(254\) | −54.5758 | −3.42439 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −24.2996 | −1.51872 | ||||||||
\(257\) | 3.96761 | 0.247493 | 0.123746 | − | 0.992314i | \(-0.460509\pi\) | ||||
0.123746 | + | 0.992314i | \(0.460509\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27.2095 | 1.69071 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −21.1128 | −1.30435 | ||||||||
\(263\) | 16.6865 | 1.02893 | 0.514467 | − | 0.857510i | \(-0.327990\pi\) | ||||
0.514467 | + | 0.857510i | \(0.327990\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 45.6060 | 2.79628 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −64.6191 | −3.94724 | ||||||||
\(269\) | −7.94329 | −0.484311 | −0.242155 | − | 0.970237i | \(-0.577854\pi\) | ||||
−0.242155 | + | 0.970237i | \(0.577854\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.3087 | −1.05143 | −0.525714 | − | 0.850662i | \(-0.676202\pi\) | ||||
−0.525714 | + | 0.850662i | \(0.676202\pi\) | |||||||
\(272\) | −11.6075 | −0.703810 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −44.8691 | −2.71064 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.2791 | −0.617612 | −0.308806 | − | 0.951125i | \(-0.599929\pi\) | ||||
−0.308806 | + | 0.951125i | \(0.599929\pi\) | |||||||
\(278\) | 17.5786 | 1.05430 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.57869 | −0.273142 | −0.136571 | − | 0.990630i | \(-0.543608\pi\) | ||||
−0.136571 | + | 0.990630i | \(0.543608\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.2431 | −1.14388 | −0.571941 | − | 0.820294i | \(-0.693810\pi\) | ||||
−0.571941 | + | 0.820294i | \(0.693810\pi\) | |||||||
\(284\) | −27.3495 | −1.62289 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 40.7891 | 2.41191 | ||||||||
\(287\) | 50.2606 | 2.96679 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0394 | −0.884673 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 32.9089 | 1.92584 | ||||||||
\(293\) | 14.6045 | 0.853203 | 0.426602 | − | 0.904440i | \(-0.359711\pi\) | ||||
0.426602 | + | 0.904440i | \(0.359711\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −39.4932 | −2.29550 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 61.1824 | 3.54420 | ||||||||
\(299\) | 29.0282 | 1.67874 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −41.7960 | −2.40908 | ||||||||
\(302\) | 44.6221 | 2.56771 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −31.2127 | −1.79017 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.3324 | −0.703850 | −0.351925 | − | 0.936028i | \(-0.614473\pi\) | ||||
−0.351925 | + | 0.936028i | \(0.614473\pi\) | |||||||
\(308\) | 67.9944 | 3.87434 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.3084 | −0.697943 | −0.348971 | − | 0.937133i | \(-0.613469\pi\) | ||||
−0.348971 | + | 0.937133i | \(0.613469\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.7306 | −0.945672 | −0.472836 | − | 0.881150i | \(-0.656770\pi\) | ||||
−0.472836 | + | 0.881150i | \(0.656770\pi\) | |||||||
\(314\) | 25.9174 | 1.46261 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 33.9901 | 1.91209 | ||||||||
\(317\) | −10.9429 | −0.614617 | −0.307308 | − | 0.951610i | \(-0.599428\pi\) | ||||
−0.307308 | + | 0.951610i | \(0.599428\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.11503 | −0.174408 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 69.2219 | 3.85759 | ||||||||
\(323\) | 5.27196 | 0.293340 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 31.6054 | 1.75046 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −72.9508 | −4.02803 | ||||||||
\(329\) | −17.0461 | −0.939781 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.1431 | −1.05220 | −0.526099 | − | 0.850423i | \(-0.676346\pi\) | ||||
−0.526099 | + | 0.850423i | \(0.676346\pi\) | |||||||
\(332\) | −63.4484 | −3.48218 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 35.0567 | 1.91822 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.0294 | 0.927650 | 0.463825 | − | 0.885927i | \(-0.346477\pi\) | ||||
0.463825 | + | 0.885927i | \(0.346477\pi\) | |||||||
\(338\) | −32.9991 | −1.79491 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.95331 | −0.376543 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 37.9537 | 2.04931 | ||||||||
\(344\) | 60.6648 | 3.27083 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −21.5312 | −1.15753 | ||||||||
\(347\) | −17.2564 | −0.926373 | −0.463186 | − | 0.886261i | \(-0.653294\pi\) | ||||
−0.463186 | + | 0.886261i | \(0.653294\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.3969 | 0.717118 | 0.358559 | − | 0.933507i | \(-0.383268\pi\) | ||||
0.358559 | + | 0.933507i | \(0.383268\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −24.0813 | −1.28354 | ||||||||
\(353\) | 2.04594 | 0.108894 | 0.0544472 | − | 0.998517i | \(-0.482660\pi\) | ||||
0.0544472 | + | 0.998517i | \(0.482660\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 37.0721 | 1.96482 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 68.5370 | 3.62229 | ||||||||
\(359\) | 25.2336 | 1.33178 | 0.665889 | − | 0.746051i | \(-0.268053\pi\) | ||||
0.665889 | + | 0.746051i | \(0.268053\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.82368 | −0.253878 | ||||||||
\(362\) | −9.60387 | −0.504768 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −110.873 | −5.81134 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.13285 | 0.476731 | 0.238366 | − | 0.971176i | \(-0.423388\pi\) | ||||
0.238366 | + | 0.971176i | \(0.423388\pi\) | |||||||
\(368\) | −47.3753 | −2.46961 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.45557 | 0.231321 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.41148 | −0.280196 | −0.140098 | − | 0.990138i | \(-0.544742\pi\) | ||||
−0.140098 | + | 0.990138i | \(0.544742\pi\) | |||||||
\(374\) | 11.2439 | 0.581410 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 24.7416 | 1.27595 | ||||||||
\(377\) | 5.07945 | 0.261605 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.8284 | 1.01852 | 0.509258 | − | 0.860614i | \(-0.329920\pi\) | ||||
0.509258 | + | 0.860614i | \(0.329920\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 17.4377 | 0.892191 | ||||||||
\(383\) | 14.8919 | 0.760941 | 0.380470 | − | 0.924793i | \(-0.375762\pi\) | ||||
0.380470 | + | 0.924793i | \(0.375762\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.362748 | 0.0184634 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −64.2675 | −3.26269 | ||||||||
\(389\) | 15.7680 | 0.799470 | 0.399735 | − | 0.916631i | \(-0.369102\pi\) | ||||
0.399735 | + | 0.916631i | \(0.369102\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00192 | 0.404674 | ||||||||
\(392\) | −102.827 | −5.19356 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.82232 | 0.192566 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.5318 | 1.33159 | 0.665796 | − | 0.746134i | \(-0.268092\pi\) | ||||
0.665796 | + | 0.746134i | \(0.268092\pi\) | |||||||
\(398\) | −66.6711 | −3.34192 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.71205 | −0.484997 | −0.242498 | − | 0.970152i | \(-0.577967\pi\) | ||||
−0.242498 | + | 0.970152i | \(0.577967\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.3382 | 0.564798 | ||||||||
\(404\) | −59.2126 | −2.94593 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.1127 | 0.601142 | ||||||||
\(407\) | 18.0388 | 0.894150 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.4468 | −0.862691 | −0.431346 | − | 0.902187i | \(-0.641961\pi\) | ||||
−0.431346 | + | 0.902187i | \(0.641961\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 38.1122 | 1.87765 | ||||||||
\(413\) | 40.1213 | 1.97424 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 39.2675 | 1.92525 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 30.2349 | 1.47884 | ||||||||
\(419\) | −26.0588 | −1.27306 | −0.636529 | − | 0.771253i | \(-0.719630\pi\) | ||||
−0.636529 | + | 0.771253i | \(0.719630\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.66465 | 0.129867 | 0.0649337 | − | 0.997890i | \(-0.479316\pi\) | ||||
0.0649337 | + | 0.997890i | \(0.479316\pi\) | |||||||
\(422\) | −60.1751 | −2.92928 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.46704 | −0.314067 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −29.2007 | −1.41312 | ||||||||
\(428\) | −15.2779 | −0.738485 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.150532 | 0.00725086 | 0.00362543 | − | 0.999993i | \(-0.498846\pi\) | ||||
0.00362543 | + | 0.999993i | \(0.498846\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.2461 | 1.59770 | 0.798852 | − | 0.601527i | \(-0.205441\pi\) | ||||
0.798852 | + | 0.601527i | \(0.205441\pi\) | |||||||
\(434\) | 27.0377 | 1.29785 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.14620 | −0.0548931 | ||||||||
\(437\) | 21.5172 | 1.02931 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.1320 | 0.865391 | 0.432695 | − | 0.901540i | \(-0.357563\pi\) | ||||
0.432695 | + | 0.901540i | \(0.357563\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −18.3346 | −0.872089 | ||||||||
\(443\) | 34.8312 | 1.65488 | 0.827440 | − | 0.561554i | \(-0.189796\pi\) | ||||
0.827440 | + | 0.561554i | \(0.189796\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 57.8108 | 2.73742 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 15.7361 | 0.743460 | ||||||||
\(449\) | −36.1516 | −1.70610 | −0.853049 | − | 0.521830i | \(-0.825249\pi\) | ||||
−0.853049 | + | 0.521830i | \(0.825249\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.3207 | 1.56901 | ||||||||
\(452\) | −67.0225 | −3.15247 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.5005 | 0.492811 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.93775 | 0.418090 | 0.209045 | − | 0.977906i | \(-0.432964\pi\) | ||||
0.209045 | + | 0.977906i | \(0.432964\pi\) | |||||||
\(458\) | 40.5166 | 1.89322 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.6733 | −1.61490 | −0.807449 | − | 0.589937i | \(-0.799152\pi\) | ||||
−0.807449 | + | 0.589937i | \(0.799152\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.9412 | −1.43796 | −0.718981 | − | 0.695030i | \(-0.755391\pi\) | ||||
−0.718981 | + | 0.695030i | \(0.755391\pi\) | |||||||
\(464\) | −8.28989 | −0.384849 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −42.4237 | −1.96524 | ||||||||
\(467\) | 5.40920 | 0.250308 | 0.125154 | − | 0.992137i | \(-0.460057\pi\) | ||||
0.125154 | + | 0.992137i | \(0.460057\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −65.3583 | −3.01797 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −58.2341 | −2.68044 | ||||||||
\(473\) | −27.7091 | −1.27406 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −30.5634 | −1.40087 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.21578 | 0.375781 | ||||||||
\(479\) | −13.4270 | −0.613494 | −0.306747 | − | 0.951791i | \(-0.599241\pi\) | ||||
−0.306747 | + | 0.951791i | \(0.599241\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29.4145 | −1.34119 | ||||||||
\(482\) | −28.7389 | −1.30902 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.02327 | −0.273785 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.8746 | 1.12718 | 0.563589 | − | 0.826055i | \(-0.309420\pi\) | ||||
0.563589 | + | 0.826055i | \(0.309420\pi\) | |||||||
\(488\) | 42.3834 | 1.91861 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.6717 | −0.932902 | −0.466451 | − | 0.884547i | \(-0.654468\pi\) | ||||
−0.466451 | + | 0.884547i | \(0.654468\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.40020 | 0.0630619 | ||||||||
\(494\) | −49.3018 | −2.21819 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −18.5045 | −0.830878 | ||||||||
\(497\) | −27.6623 | −1.24083 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.2182 | 0.949856 | 0.474928 | − | 0.880025i | \(-0.342474\pi\) | ||||
0.474928 | + | 0.880025i | \(0.342474\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.33660 | −0.372081 | ||||||||
\(503\) | −35.9602 | −1.60339 | −0.801693 | − | 0.597736i | \(-0.796067\pi\) | ||||
−0.801693 | + | 0.597736i | \(0.796067\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 45.8913 | 2.04012 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 98.3492 | 4.36354 | ||||||||
\(509\) | −21.3861 | −0.947924 | −0.473962 | − | 0.880545i | \(-0.657177\pi\) | ||||
−0.473962 | + | 0.880545i | \(0.657177\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 33.2853 | 1.47246 | ||||||||
\(512\) | 48.9860 | 2.16489 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.2281 | −0.451141 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.3009 | −0.497012 | ||||||||
\(518\) | −70.1431 | −3.08191 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.56775 | 0.287738 | 0.143869 | − | 0.989597i | \(-0.454046\pi\) | ||||
0.143869 | + | 0.989597i | \(0.454046\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.1811 | 0.926184 | 0.463092 | − | 0.886310i | \(-0.346740\pi\) | ||||
0.463092 | + | 0.886310i | \(0.346740\pi\) | |||||||
\(524\) | 38.0466 | 1.66207 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −43.0160 | −1.87559 | ||||||||
\(527\) | 3.12550 | 0.136149 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.65929 | 0.419969 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −82.1850 | −3.56317 | ||||||||
\(533\) | −54.3336 | −2.35345 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 94.8643 | 4.09752 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20.4769 | 0.882824 | ||||||||
\(539\) | 46.9670 | 2.02301 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.98542 | −0.429307 | −0.214653 | − | 0.976690i | \(-0.568862\pi\) | ||||
−0.214653 | + | 0.976690i | \(0.568862\pi\) | |||||||
\(542\) | 44.6199 | 1.91659 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.8245 | 0.464097 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.01143 | 0.0432457 | 0.0216228 | − | 0.999766i | \(-0.493117\pi\) | ||||
0.0216228 | + | 0.999766i | \(0.493117\pi\) | |||||||
\(548\) | 80.8571 | 3.45404 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.76514 | 0.160401 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 34.3789 | 1.46194 | ||||||||
\(554\) | 26.4985 | 1.12581 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −31.6779 | −1.34344 | ||||||||
\(557\) | 30.4618 | 1.29071 | 0.645353 | − | 0.763885i | \(-0.276710\pi\) | ||||
0.645353 | + | 0.763885i | \(0.276710\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 45.1831 | 1.91104 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.8034 | 0.497895 | ||||||||
\(563\) | 2.49954 | 0.105343 | 0.0526716 | − | 0.998612i | \(-0.483226\pi\) | ||||
0.0526716 | + | 0.998612i | \(0.483226\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 49.6066 | 2.08512 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 40.1505 | 1.68468 | ||||||||
\(569\) | 0.611166 | 0.0256214 | 0.0128107 | − | 0.999918i | \(-0.495922\pi\) | ||||
0.0128107 | + | 0.999918i | \(0.495922\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.527376 | −0.0220700 | −0.0110350 | − | 0.999939i | \(-0.503513\pi\) | ||||
−0.0110350 | + | 0.999939i | \(0.503513\pi\) | |||||||
\(572\) | −73.5046 | −3.07338 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −129.566 | −5.40800 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.3938 | −1.01553 | −0.507764 | − | 0.861496i | \(-0.669528\pi\) | ||||
−0.507764 | + | 0.861496i | \(0.669528\pi\) | |||||||
\(578\) | 38.7700 | 1.61262 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −64.1742 | −2.66239 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.95386 | 0.122336 | ||||||||
\(584\) | −48.3120 | −1.99917 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −37.6488 | −1.55526 | ||||||||
\(587\) | 28.4529 | 1.17438 | 0.587188 | − | 0.809450i | \(-0.300235\pi\) | ||||
0.587188 | + | 0.809450i | \(0.300235\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.40448 | 0.346301 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 48.0058 | 1.97303 | ||||||||
\(593\) | −2.96753 | −0.121862 | −0.0609310 | − | 0.998142i | \(-0.519407\pi\) | ||||
−0.0609310 | + | 0.998142i | \(0.519407\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −110.255 | −4.51621 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −74.8316 | −3.06009 | ||||||||
\(599\) | −21.9546 | −0.897040 | −0.448520 | − | 0.893773i | \(-0.648049\pi\) | ||||
−0.448520 | + | 0.893773i | \(0.648049\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.4446 | −0.874745 | −0.437372 | − | 0.899280i | \(-0.644091\pi\) | ||||
−0.437372 | + | 0.899280i | \(0.644091\pi\) | |||||||
\(602\) | 107.746 | 4.39138 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −80.4120 | −3.27192 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 48.0114 | 1.94872 | 0.974361 | − | 0.224988i | \(-0.0722344\pi\) | ||||
0.974361 | + | 0.224988i | \(0.0722344\pi\) | |||||||
\(608\) | 29.1071 | 1.18045 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.4275 | 0.745496 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.9093 | 1.53114 | 0.765571 | − | 0.643351i | \(-0.222456\pi\) | ||||
0.765571 | + | 0.643351i | \(0.222456\pi\) | |||||||
\(614\) | 31.7917 | 1.28301 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −99.8195 | −4.02184 | ||||||||
\(617\) | −8.29772 | −0.334054 | −0.167027 | − | 0.985952i | \(-0.553417\pi\) | ||||
−0.167027 | + | 0.985952i | \(0.553417\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.6135 | −0.627559 | −0.313779 | − | 0.949496i | \(-0.601595\pi\) | ||||
−0.313779 | + | 0.949496i | \(0.601595\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 31.7296 | 1.27224 | ||||||||
\(623\) | 37.4962 | 1.50225 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 43.1298 | 1.72381 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −46.7049 | −1.86373 | ||||||||
\(629\) | −8.10841 | −0.323303 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.7848 | 0.429336 | 0.214668 | − | 0.976687i | \(-0.431133\pi\) | ||||
0.214668 | + | 0.976687i | \(0.431133\pi\) | |||||||
\(632\) | −49.8993 | −1.98489 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 28.2097 | 1.12035 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −76.5856 | −3.03443 | ||||||||
\(638\) | 8.03022 | 0.317919 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.1226 | −0.636805 | −0.318403 | − | 0.947956i | \(-0.603146\pi\) | ||||
−0.318403 | + | 0.947956i | \(0.603146\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.0313 | −0.987137 | −0.493569 | − | 0.869707i | \(-0.664308\pi\) | ||||
−0.493569 | + | 0.869707i | \(0.664308\pi\) | |||||||
\(644\) | −124.742 | −4.91554 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.5906 | −0.534713 | ||||||||
\(647\) | −34.9798 | −1.37520 | −0.687599 | − | 0.726091i | \(-0.741335\pi\) | ||||
−0.687599 | + | 0.726091i | \(0.741335\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.5988 | 1.04409 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −56.9550 | −2.23053 | ||||||||
\(653\) | −22.0250 | −0.861904 | −0.430952 | − | 0.902375i | \(-0.641822\pi\) | ||||
−0.430952 | + | 0.902375i | \(0.641822\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 88.6750 | 3.46218 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 43.9430 | 1.71308 | ||||||||
\(659\) | 32.9279 | 1.28269 | 0.641345 | − | 0.767253i | \(-0.278377\pi\) | ||||
0.641345 | + | 0.767253i | \(0.278377\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.78801 | 0.380710 | 0.190355 | − | 0.981715i | \(-0.439036\pi\) | ||||
0.190355 | + | 0.981715i | \(0.439036\pi\) | |||||||
\(662\) | 49.3488 | 1.91799 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 93.1457 | 3.61475 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.71483 | 0.221279 | ||||||||
\(668\) | −63.1745 | −2.44429 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.3589 | −0.747342 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.3634 | −0.977689 | −0.488844 | − | 0.872371i | \(-0.662581\pi\) | ||||
−0.488844 | + | 0.872371i | \(0.662581\pi\) | |||||||
\(674\) | −43.8999 | −1.69096 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 59.4665 | 2.28717 | ||||||||
\(677\) | 19.7896 | 0.760578 | 0.380289 | − | 0.924868i | \(-0.375825\pi\) | ||||
0.380289 | + | 0.924868i | \(0.375825\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −65.0027 | −2.49458 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 17.9249 | 0.686380 | ||||||||
\(683\) | −44.9656 | −1.72056 | −0.860281 | − | 0.509820i | \(-0.829712\pi\) | ||||
−0.860281 | + | 0.509820i | \(0.829712\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −97.8406 | −3.73557 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −73.7409 | −2.81134 | ||||||||
\(689\) | −4.81664 | −0.183499 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.7758 | −1.17077 | −0.585384 | − | 0.810756i | \(-0.699056\pi\) | ||||
−0.585384 | + | 0.810756i | \(0.699056\pi\) | |||||||
\(692\) | 38.8007 | 1.47498 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 44.4852 | 1.68863 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.9776 | −0.567318 | ||||||||
\(698\) | −34.5357 | −1.30720 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.2459 | 0.877984 | 0.438992 | − | 0.898491i | \(-0.355336\pi\) | ||||
0.438992 | + | 0.898491i | \(0.355336\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.8035 | −0.822335 | ||||||||
\(704\) | 10.4324 | 0.393186 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.27422 | −0.198498 | ||||||||
\(707\) | −59.8899 | −2.25239 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.86251 | 0.295283 | 0.147641 | − | 0.989041i | \(-0.452832\pi\) | ||||
0.147641 | + | 0.989041i | \(0.452832\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −54.4239 | −2.03962 | ||||||||
\(713\) | 12.7565 | 0.477736 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −123.508 | −4.61572 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −65.0495 | −2.42762 | ||||||||
\(719\) | −35.0267 | −1.30628 | −0.653138 | − | 0.757239i | \(-0.726548\pi\) | ||||
−0.653138 | + | 0.757239i | \(0.726548\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38.5482 | 1.43561 | ||||||||
\(722\) | 12.4349 | 0.462781 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 17.3068 | 0.643202 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.4518 | 0.832691 | 0.416346 | − | 0.909206i | \(-0.363311\pi\) | ||||
0.416346 | + | 0.909206i | \(0.363311\pi\) | |||||||
\(728\) | 162.768 | 6.03259 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.4552 | 0.460671 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.0028 | −0.554140 | −0.277070 | − | 0.960850i | \(-0.589363\pi\) | ||||
−0.277070 | + | 0.960850i | \(0.589363\pi\) | |||||||
\(734\) | −23.5435 | −0.869007 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 44.1795 | 1.62848 | ||||||||
\(737\) | −43.3299 | −1.59608 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.4801 | −1.23159 | −0.615793 | − | 0.787908i | \(-0.711164\pi\) | ||||
−0.615793 | + | 0.787908i | \(0.711164\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.4860 | −0.421663 | ||||||||
\(743\) | −6.75081 | −0.247663 | −0.123832 | − | 0.992303i | \(-0.539518\pi\) | ||||
−0.123832 | + | 0.992303i | \(0.539518\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 13.9502 | 0.510754 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −20.2623 | −0.740863 | ||||||||
\(749\) | −15.4527 | −0.564628 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.0482 | 1.02349 | 0.511747 | − | 0.859136i | \(-0.328999\pi\) | ||||
0.511747 | + | 0.859136i | \(0.328999\pi\) | |||||||
\(752\) | −30.0745 | −1.09670 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −13.0943 | −0.476865 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.1698 | 1.20558 | 0.602789 | − | 0.797901i | \(-0.294056\pi\) | ||||
0.602789 | + | 0.797901i | \(0.294056\pi\) | |||||||
\(758\) | −51.1155 | −1.85660 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.0982 | 0.438560 | 0.219280 | − | 0.975662i | \(-0.429629\pi\) | ||||
0.219280 | + | 0.975662i | \(0.429629\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.15931 | −0.0419700 | ||||||||
\(764\) | −31.4239 | −1.13688 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −38.3897 | −1.38708 | ||||||||
\(767\) | −43.3727 | −1.56610 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.5811 | −1.53551 | −0.767756 | − | 0.640742i | \(-0.778627\pi\) | ||||
−0.767756 | + | 0.640742i | \(0.778627\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.653695 | −0.0235270 | ||||||||
\(773\) | −6.87342 | −0.247220 | −0.123610 | − | 0.992331i | \(-0.539447\pi\) | ||||
−0.123610 | + | 0.992331i | \(0.539447\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 94.3483 | 3.38691 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −40.6482 | −1.45731 | ||||||||
\(779\) | −40.2748 | −1.44300 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.3390 | −0.656222 | ||||||||
\(782\) | −20.6281 | −0.737659 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 124.991 | 4.46397 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.51935 | −0.161097 | −0.0805487 | − | 0.996751i | \(-0.525667\pi\) | ||||
−0.0805487 | + | 0.996751i | \(0.525667\pi\) | |||||||
\(788\) | −6.88806 | −0.245377 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −67.7892 | −2.41031 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.5671 | 1.12098 | ||||||||
\(794\) | −68.3961 | −2.42729 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 120.146 | 4.25845 | ||||||||
\(797\) | −13.9670 | −0.494736 | −0.247368 | − | 0.968922i | \(-0.579566\pi\) | ||||
−0.247368 | + | 0.968922i | \(0.579566\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.07972 | 0.179708 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 25.0366 | 0.884074 | ||||||||
\(803\) | 22.0668 | 0.778722 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −29.2288 | −1.02954 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 86.9273 | 3.05809 | ||||||||
\(809\) | −8.18148 | −0.287646 | −0.143823 | − | 0.989603i | \(-0.545940\pi\) | ||||
−0.143823 | + | 0.989603i | \(0.545940\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.4011 | −1.55913 | −0.779566 | − | 0.626320i | \(-0.784560\pi\) | ||||
−0.779566 | + | 0.626320i | \(0.784560\pi\) | |||||||
\(812\) | −21.8278 | −0.766007 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −46.5021 | −1.62990 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.4920 | 1.17174 | ||||||||
\(818\) | 44.9761 | 1.57255 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.73119 | −0.304721 | −0.152360 | − | 0.988325i | \(-0.548687\pi\) | ||||
−0.152360 | + | 0.988325i | \(0.548687\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.1844 | −1.36588 | −0.682942 | − | 0.730473i | \(-0.739300\pi\) | ||||
−0.682942 | + | 0.730473i | \(0.739300\pi\) | |||||||
\(824\) | −55.9508 | −1.94914 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −103.428 | −3.59873 | ||||||||
\(827\) | −6.33428 | −0.220264 | −0.110132 | − | 0.993917i | \(-0.535127\pi\) | ||||
−0.110132 | + | 0.993917i | \(0.535127\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.36706 | 0.0474798 | 0.0237399 | − | 0.999718i | \(-0.492443\pi\) | ||||
0.0237399 | + | 0.999718i | \(0.492443\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −17.0113 | −0.589762 | ||||||||
\(833\) | −21.1116 | −0.731473 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −54.4853 | −1.88441 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 67.1769 | 2.32059 | ||||||||
\(839\) | 55.7902 | 1.92609 | 0.963046 | − | 0.269339i | \(-0.0868051\pi\) | ||||
0.963046 | + | 0.269339i | \(0.0868051\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −6.86919 | −0.236728 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 108.439 | 3.73264 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.09218 | −0.209330 | ||||||||
\(848\) | 7.86098 | 0.269947 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33.0939 | −1.13444 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.42812 | 0.220095 | 0.110047 | − | 0.993926i | \(-0.464900\pi\) | ||||
0.110047 | + | 0.993926i | \(0.464900\pi\) | |||||||
\(854\) | 75.2762 | 2.57590 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22.4288 | 0.766600 | ||||||||
\(857\) | −35.0274 | −1.19651 | −0.598257 | − | 0.801304i | \(-0.704140\pi\) | ||||
−0.598257 | + | 0.801304i | \(0.704140\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.4412 | 0.629207 | 0.314603 | − | 0.949223i | \(-0.398128\pi\) | ||||
0.314603 | + | 0.949223i | \(0.398128\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.388055 | −0.0132172 | ||||||||
\(863\) | −7.23911 | −0.246422 | −0.123211 | − | 0.992380i | \(-0.539319\pi\) | ||||
−0.123211 | + | 0.992380i | \(0.539319\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −85.7048 | −2.91237 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −48.7237 | −1.65379 | ||||||||
\(869\) | 22.7918 | 0.773160 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 70.6549 | 2.39405 | ||||||||
\(872\) | 1.68269 | 0.0569830 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −55.4689 | −1.87626 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.6324 | 0.831777 | 0.415889 | − | 0.909416i | \(-0.363471\pi\) | ||||
0.415889 | + | 0.909416i | \(0.363471\pi\) | |||||||
\(878\) | −46.7422 | −1.57747 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.2145 | −0.883190 | −0.441595 | − | 0.897214i | \(-0.645587\pi\) | ||||
−0.441595 | + | 0.897214i | \(0.645587\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.7656 | 0.362290 | 0.181145 | − | 0.983456i | \(-0.442020\pi\) | ||||
0.181145 | + | 0.983456i | \(0.442020\pi\) | |||||||
\(884\) | 33.0402 | 1.11126 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −89.7911 | −3.01659 | ||||||||
\(887\) | 6.27796 | 0.210793 | 0.105397 | − | 0.994430i | \(-0.466389\pi\) | ||||
0.105397 | + | 0.994430i | \(0.466389\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 99.4743 | 3.33626 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −104.179 | −3.48817 | ||||||||
\(893\) | 13.6594 | 0.457094 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 32.0818 | 1.07178 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 93.1949 | 3.10995 | ||||||||
\(899\) | 2.23218 | 0.0744474 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.32776 | −0.0442340 | ||||||||
\(902\) | −85.8973 | −2.86007 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 98.3927 | 3.27249 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.7954 | −0.723704 | −0.361852 | − | 0.932235i | \(-0.617855\pi\) | ||||
−0.361852 | + | 0.932235i | \(0.617855\pi\) | |||||||
\(908\) | −18.9225 | −0.627966 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.56422 | 0.184351 | 0.0921753 | − | 0.995743i | \(-0.470618\pi\) | ||||
0.0921753 | + | 0.995743i | \(0.470618\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42.5449 | −1.40803 | ||||||||
\(914\) | −23.0406 | −0.762114 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −73.0136 | −2.41244 | ||||||||
\(917\) | 38.4819 | 1.27078 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.76705 | −0.256211 | −0.128106 | − | 0.991761i | \(-0.540890\pi\) | ||||
−0.128106 | + | 0.991761i | \(0.540890\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 89.3841 | 2.94371 | ||||||||
\(923\) | 29.9041 | 0.984304 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 79.7632 | 2.62118 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.73067 | 0.253772 | ||||||||
\(929\) | 11.3588 | 0.372672 | 0.186336 | − | 0.982486i | \(-0.440339\pi\) | ||||
0.186336 | + | 0.982486i | \(0.440339\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −56.7691 | −1.86053 | ||||||||
\(932\) | 76.4503 | 2.50421 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13.9443 | −0.456273 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.7813 | −1.07092 | −0.535460 | − | 0.844561i | \(-0.679862\pi\) | ||||
−0.535460 | + | 0.844561i | \(0.679862\pi\) | |||||||
\(938\) | 168.487 | 5.50128 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.3074 | 0.433808 | 0.216904 | − | 0.976193i | \(-0.430404\pi\) | ||||
0.216904 | + | 0.976193i | \(0.430404\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −61.1302 | −1.99067 | ||||||||
\(944\) | 70.7862 | 2.30390 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 71.4310 | 2.32242 | ||||||||
\(947\) | 31.9463 | 1.03811 | 0.519057 | − | 0.854740i | \(-0.326283\pi\) | ||||
0.519057 | + | 0.854740i | \(0.326283\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35.9827 | −1.16805 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 44.8687 | 1.45420 | ||||||||
\(953\) | −53.5304 | −1.73402 | −0.867009 | − | 0.498292i | \(-0.833961\pi\) | ||||
−0.867009 | + | 0.498292i | \(0.833961\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.8054 | −0.478840 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 34.6133 | 1.11831 | ||||||||
\(959\) | 81.7821 | 2.64088 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.0174 | −0.839270 | ||||||||
\(962\) | 75.8274 | 2.44477 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 51.7893 | 1.66802 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.9490 | −0.545044 | −0.272522 | − | 0.962150i | \(-0.587858\pi\) | ||||
−0.272522 | + | 0.962150i | \(0.587858\pi\) | |||||||
\(968\) | 8.84250 | 0.284209 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.5476 | 0.916135 | 0.458067 | − | 0.888917i | \(-0.348542\pi\) | ||||
0.458067 | + | 0.888917i | \(0.348542\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.0402 | −1.02716 | ||||||||
\(974\) | −64.1242 | −2.05467 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −51.5189 | −1.64908 | ||||||||
\(977\) | −30.8519 | −0.987040 | −0.493520 | − | 0.869734i | \(-0.664290\pi\) | ||||
−0.493520 | + | 0.869734i | \(0.664290\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.8585 | 0.794481 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 53.2895 | 1.70054 | ||||||||
\(983\) | 25.9915 | 0.829000 | 0.414500 | − | 0.910049i | \(-0.363956\pi\) | ||||
0.414500 | + | 0.910049i | \(0.363956\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.60957 | −0.114952 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 88.8451 | 2.82654 | ||||||||
\(989\) | 50.8350 | 1.61646 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.17860 | −0.100972 | −0.0504858 | − | 0.998725i | \(-0.516077\pi\) | ||||
−0.0504858 | + | 0.998725i | \(0.516077\pi\) | |||||||
\(992\) | 17.2562 | 0.547886 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 71.3105 | 2.26183 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.6331 | −1.00183 | −0.500916 | − | 0.865496i | \(-0.667003\pi\) | ||||
−0.500916 | + | 0.865496i | \(0.667003\pi\) | |||||||
\(998\) | −54.6982 | −1.73144 | ||||||||
\(999\) | 0 | 0 |
(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 | 6525.2.a.by.1.2 | 8 | ||
3.2 | odd | 2 | 2175.2.a.bd.1.7 | yes | 8 | ||
5.4 | even | 2 | 6525.2.a.bz.1.7 | 8 | |||
15.2 | even | 4 | 2175.2.c.p.349.14 | 16 | |||
15.8 | even | 4 | 2175.2.c.p.349.3 | 16 | |||
15.14 | odd | 2 | 2175.2.a.bc.1.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2175.2.a.bc.1.2 | ✓ | 8 | 15.14 | odd | 2 | ||
2175.2.a.bd.1.7 | yes | 8 | 3.2 | odd | 2 | ||
2175.2.c.p.349.3 | 16 | 15.8 | even | 4 | |||
2175.2.c.p.349.14 | 16 | 15.2 | even | 4 | |||
6525.2.a.by.1.2 | 8 | 1.1 | even | 1 | trivial | ||
6525.2.a.bz.1.7 | 8 | 5.4 | even | 2 |