Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.31 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.823784 | 0.475612 | 0.237806 | − | 0.971313i | \(-0.423572\pi\) | ||||
0.237806 | + | 0.971313i | \(0.423572\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.53384 | −0.685955 | −0.342978 | − | 0.939344i | \(-0.611436\pi\) | ||||
−0.342978 | + | 0.939344i | \(0.611436\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.257976 | 0.0975059 | 0.0487530 | − | 0.998811i | \(-0.484475\pi\) | ||||
0.0487530 | + | 0.998811i | \(0.484475\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.32138 | −0.773793 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.07385 | 0.323778 | 0.161889 | − | 0.986809i | \(-0.448241\pi\) | ||||
0.161889 | + | 0.986809i | \(0.448241\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.44368 | −1.78716 | −0.893578 | − | 0.448908i | \(-0.851813\pi\) | ||||
−0.893578 | + | 0.448908i | \(0.851813\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.26356 | −0.326249 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.61157 | 0.875935 | 0.437967 | − | 0.898991i | \(-0.355699\pi\) | ||||
0.437967 | + | 0.898991i | \(0.355699\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.46432 | −0.565354 | −0.282677 | − | 0.959215i | \(-0.591222\pi\) | ||||
−0.282677 | + | 0.959215i | \(0.591222\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.212517 | 0.0463750 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.43274 | 1.34132 | 0.670659 | − | 0.741765i | \(-0.266011\pi\) | ||||
0.670659 | + | 0.741765i | \(0.266011\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.64733 | −0.529465 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.38367 | −0.843637 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.41256 | 1.19078 | 0.595391 | − | 0.803436i | \(-0.296997\pi\) | ||||
0.595391 | + | 0.803436i | \(0.296997\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.45048 | −0.799329 | −0.399665 | − | 0.916661i | \(-0.630873\pi\) | ||||
−0.399665 | + | 0.916661i | \(0.630873\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.884621 | 0.153993 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.395695 | −0.0668847 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.37506 | −0.883654 | −0.441827 | − | 0.897100i | \(-0.645670\pi\) | ||||
−0.441827 | + | 0.897100i | \(0.645670\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.30820 | −0.849993 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.12753 | −0.176091 | −0.0880456 | − | 0.996116i | \(-0.528062\pi\) | ||||
−0.0880456 | + | 0.996116i | \(0.528062\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.77360 | 0.880466 | 0.440233 | − | 0.897883i | \(-0.354896\pi\) | ||||
0.440233 | + | 0.897883i | \(0.354896\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.56063 | 0.530788 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.2174 | 1.49037 | 0.745183 | − | 0.666860i | \(-0.232362\pi\) | ||||
0.745183 | + | 0.666860i | \(0.232362\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.93345 | −0.990493 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.97515 | 0.416605 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.86551 | −0.530968 | −0.265484 | − | 0.964115i | \(-0.585532\pi\) | ||||
−0.265484 | + | 0.964115i | \(0.585532\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.64712 | −0.222097 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.03007 | −0.268889 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.8763 | 1.67635 | 0.838174 | − | 0.545402i | \(-0.183623\pi\) | ||||
0.838174 | + | 0.545402i | \(0.183623\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.43728 | 0.696173 | 0.348086 | − | 0.937462i | \(-0.386832\pi\) | ||||
0.348086 | + | 0.937462i | \(0.386832\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.598861 | −0.0754494 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.88360 | 1.22591 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.75113 | −0.458274 | −0.229137 | − | 0.973394i | \(-0.573590\pi\) | ||||
−0.229137 | + | 0.973394i | \(0.573590\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.29919 | 0.637947 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.92554 | 0.228520 | 0.114260 | − | 0.993451i | \(-0.463550\pi\) | ||||
0.114260 | + | 0.993451i | \(0.463550\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.39270 | −1.09933 | −0.549666 | − | 0.835384i | \(-0.685245\pi\) | ||||
−0.549666 | + | 0.835384i | \(0.685245\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.18083 | −0.251820 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.277028 | 0.0315703 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.75356 | −0.422309 | −0.211154 | − | 0.977453i | \(-0.567722\pi\) | ||||
−0.211154 | + | 0.977453i | \(0.567722\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.35294 | 0.372549 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.37289 | 0.809280 | 0.404640 | − | 0.914476i | \(-0.367397\pi\) | ||||
0.404640 | + | 0.914476i | \(0.367397\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.53958 | −0.600852 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.28256 | 0.566350 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.01587 | −0.213681 | −0.106841 | − | 0.994276i | \(-0.534073\pi\) | ||||
−0.106841 | + | 0.994276i | \(0.534073\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.66232 | −0.174258 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.66623 | −0.380171 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.77988 | 0.387808 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.889947 | 0.0903604 | 0.0451802 | − | 0.998979i | \(-0.485614\pi\) | ||||
0.0451802 | + | 0.998979i | \(0.485614\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.49281 | −0.250537 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.90622 | 0.388683 | 0.194342 | − | 0.980934i | \(-0.437743\pi\) | ||||
0.194342 | + | 0.980934i | \(0.437743\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.5639 | 1.53355 | 0.766777 | − | 0.641914i | \(-0.221859\pi\) | ||||
0.766777 | + | 0.641914i | \(0.221859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.325968 | −0.0318112 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.6240 | 1.22041 | 0.610205 | − | 0.792244i | \(-0.291087\pi\) | ||||
0.610205 | + | 0.792244i | \(0.291087\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.46925 | 0.428076 | 0.214038 | − | 0.976825i | \(-0.431338\pi\) | ||||
0.214038 | + | 0.976825i | \(0.431338\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.42789 | −0.420277 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.68554 | −0.440779 | −0.220389 | − | 0.975412i | \(-0.570733\pi\) | ||||
−0.220389 | + | 0.975412i | \(0.570733\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.86681 | −0.920085 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.9582 | 1.38289 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.931700 | 0.0854088 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.84685 | −0.895168 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.928844 | −0.0837511 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.7298 | 1.04914 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.5313 | 0.934500 | 0.467250 | − | 0.884125i | \(-0.345245\pi\) | ||||
0.467250 | + | 0.884125i | \(0.345245\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.75620 | 0.418760 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2390 | 0.894588 | 0.447294 | − | 0.894387i | \(-0.352388\pi\) | ||||
0.447294 | + | 0.894387i | \(0.352388\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.635737 | −0.0551254 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.72386 | 0.578698 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.7184 | −1.00117 | −0.500587 | − | 0.865686i | \(-0.666883\pi\) | ||||
−0.500587 | + | 0.865686i | \(0.666883\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.10083 | 0.263009 | 0.131505 | − | 0.991316i | \(-0.458019\pi\) | ||||
0.131505 | + | 0.991316i | \(0.458019\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.41696 | 0.708836 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.91955 | −0.578642 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.83586 | −0.816823 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.71167 | −0.471090 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.6141 | 1.68877 | 0.844385 | − | 0.535737i | \(-0.179966\pi\) | ||||
0.844385 | + | 0.535737i | \(0.179966\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.3683 | 1.33203 | 0.666015 | − | 0.745939i | \(-0.267999\pi\) | ||||
0.666015 | + | 0.745939i | \(0.267999\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.38383 | −0.677792 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.82633 | 0.548304 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.49065 | 0.198775 | 0.0993876 | − | 0.995049i | \(-0.468312\pi\) | ||||
0.0993876 | + | 0.995049i | \(0.468312\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.18434 | −0.252535 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.65950 | 0.130787 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.7014 | 1.30816 | 0.654078 | − | 0.756427i | \(-0.273057\pi\) | ||||
0.654078 | + | 0.756427i | \(0.273057\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.35687 | −0.105632 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.32144 | 0.179638 | 0.0898192 | − | 0.995958i | \(-0.471371\pi\) | ||||
0.0898192 | + | 0.995958i | \(0.471371\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.5210 | 2.19393 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.72062 | 0.437467 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.2380 | −0.778384 | −0.389192 | − | 0.921157i | \(-0.627246\pi\) | ||||
−0.389192 | + | 0.921157i | \(0.627246\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.682948 | −0.0516260 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.6073 | 0.797292 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.2142 | −1.13716 | −0.568581 | − | 0.822627i | \(-0.692508\pi\) | ||||
−0.568581 | + | 0.822627i | \(0.692508\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.7594 | 1.61736 | 0.808682 | − | 0.588246i | \(-0.200181\pi\) | ||||
0.808682 | + | 0.588246i | \(0.200181\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.47915 | 0.331108 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.24450 | 0.606148 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.87829 | 0.283608 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.13088 | −0.0822597 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.6361 | −1.71025 | −0.855125 | − | 0.518422i | \(-0.826520\pi\) | ||||
−0.855125 | + | 0.518422i | \(0.826520\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.5693 | 1.12070 | 0.560352 | − | 0.828255i | \(-0.310666\pi\) | ||||
0.560352 | + | 0.828255i | \(0.310666\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.14195 | 0.583057 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.41782 | −0.243510 | −0.121755 | − | 0.992560i | \(-0.538852\pi\) | ||||
−0.121755 | + | 0.992560i | \(0.538852\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.46278 | −0.103694 | −0.0518469 | − | 0.998655i | \(-0.516511\pi\) | ||||
−0.0518469 | + | 0.998655i | \(0.516511\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.09012 | −0.217961 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.65429 | 0.116108 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.72946 | 0.120791 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.9328 | −1.03790 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.64631 | −0.183049 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.0346 | −0.897342 | −0.448671 | − | 0.893697i | \(-0.648102\pi\) | ||||
−0.448671 | + | 0.893697i | \(0.648102\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.58623 | 0.108687 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.85580 | −0.603961 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.14812 | −0.0779393 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.73756 | −0.522856 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.2718 | −1.56543 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.7395 | −1.65668 | −0.828339 | − | 0.560227i | \(-0.810714\pi\) | ||||
−0.828339 | + | 0.560227i | \(0.810714\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.14545 | 0.409697 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.05729 | 0.601154 | 0.300577 | − | 0.953758i | \(-0.402821\pi\) | ||||
0.300577 | + | 0.953758i | \(0.402821\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.4397 | 1.02028 | 0.510141 | − | 0.860091i | \(-0.329593\pi\) | ||||
0.510141 | + | 0.860091i | \(0.329593\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.228211 | 0.0150152 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.5932 | 1.48013 | 0.740063 | − | 0.672537i | \(-0.234795\pi\) | ||||
0.740063 | + | 0.672537i | \(0.234795\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.6719 | −1.02232 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.09213 | −0.200855 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.04908 | 0.261913 | 0.130957 | − | 0.991388i | \(-0.458195\pi\) | ||||
0.130957 | + | 0.991388i | \(0.458195\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.2685 | −0.983534 | −0.491767 | − | 0.870727i | \(-0.663649\pi\) | ||||
−0.491767 | + | 0.870727i | \(0.663649\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.9131 | 1.02083 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.6348 | 0.679434 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.8793 | 1.01038 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.07367 | 0.384903 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.99522 | 0.125937 | 0.0629687 | − | 0.998016i | \(-0.479943\pi\) | ||||
0.0629687 | + | 0.998016i | \(0.479943\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.90780 | 0.434290 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.56342 | −0.285772 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.3723 | −0.834144 | −0.417072 | − | 0.908873i | \(-0.636944\pi\) | ||||
−0.417072 | + | 0.908873i | \(0.636944\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.38664 | −0.0861616 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.8860 | −0.921419 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.82422 | −0.112486 | −0.0562430 | − | 0.998417i | \(-0.517912\pi\) | ||||
−0.0562430 | + | 0.998417i | \(0.517912\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.92908 | 0.364220 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.66064 | −0.101629 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.9092 | 1.45777 | 0.728886 | − | 0.684635i | \(-0.240038\pi\) | ||||
0.728886 | + | 0.684635i | \(0.240038\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.3306 | −1.35649 | −0.678244 | − | 0.734837i | \(-0.737259\pi\) | ||||
−0.678244 | + | 0.734837i | \(0.737259\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.36939 | −0.0828793 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.84283 | −0.171429 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.64305 | 0.459226 | 0.229613 | − | 0.973282i | \(-0.426254\pi\) | ||||
0.229613 | + | 0.973282i | \(0.426254\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.3312 | 0.618515 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.0867 | 0.959653 | 0.479827 | − | 0.877363i | \(-0.340700\pi\) | ||||
0.479827 | + | 0.877363i | \(0.340700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.06827 | −0.122946 | −0.0614730 | − | 0.998109i | \(-0.519580\pi\) | ||||
−0.0614730 | + | 0.998109i | \(0.519580\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.11381 | 0.184446 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.290877 | −0.0171699 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.95656 | −0.232739 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.733124 | 0.0429765 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.2292 | 1.35706 | 0.678531 | − | 0.734572i | \(-0.262617\pi\) | ||||
0.678531 | + | 0.734572i | \(0.262617\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.7502 | −1.14990 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.70740 | −0.273151 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −41.4505 | −2.39715 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.48945 | 0.0858507 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.21788 | 0.184862 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.33994 | −0.477544 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.5329 | −1.34309 | −0.671546 | − | 0.740962i | \(-0.734370\pi\) | ||||
−0.671546 | + | 0.740962i | \(0.734370\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.8213 | 0.729376 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.3627 | 1.32478 | 0.662389 | − | 0.749160i | \(-0.269543\pi\) | ||||
0.662389 | + | 0.749160i | \(0.269543\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.8635 | −1.51841 | −0.759207 | − | 0.650849i | \(-0.774413\pi\) | ||||
−0.759207 | + | 0.650849i | \(0.774413\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.918559 | 0.0517550 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.8629 | 1.05944 | 0.529722 | − | 0.848171i | \(-0.322296\pi\) | ||||
0.529722 | + | 0.848171i | \(0.322296\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.88613 | 0.385549 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.3995 | 0.580442 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.90007 | −0.495213 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.0585 | 0.946237 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.68169 | 0.203598 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.63586 | 0.145320 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.3505 | 1.94304 | 0.971520 | − | 0.236958i | \(-0.0761503\pi\) | ||||
0.971520 | + | 0.236958i | \(0.0761503\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.4776 | 0.683766 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.75365 | 0.314355 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.63805 | 0.198177 | 0.0990887 | − | 0.995079i | \(-0.468407\pi\) | ||||
0.0990887 | + | 0.995079i | \(0.468407\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.85988 | −0.209640 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.77915 | −0.258805 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.59450 | −0.194085 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.12812 | −0.437603 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.69117 | 0.251835 | 0.125918 | − | 0.992041i | \(-0.459812\pi\) | ||||
0.125918 | + | 0.992041i | \(0.459812\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.5269 | 0.777609 | 0.388805 | − | 0.921320i | \(-0.372888\pi\) | ||||
0.388805 | + | 0.921320i | \(0.372888\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 28.2470 | 1.50771 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.7680 | −1.69084 | −0.845419 | − | 0.534104i | \(-0.820649\pi\) | ||||
−0.845419 | + | 0.534104i | \(0.820649\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.95348 | −0.156754 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.767520 | 0.0406215 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.82780 | −0.149246 | −0.0746229 | − | 0.997212i | \(-0.523775\pi\) | ||||
−0.0746229 | + | 0.997212i | \(0.523775\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.9271 | −0.680375 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.11168 | −0.425753 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.4069 | 0.754093 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.7407 | 1.13486 | 0.567428 | − | 0.823423i | \(-0.307938\pi\) | ||||
0.567428 | + | 0.823423i | \(0.307938\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.61743 | 0.136258 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.997209 | −0.0517725 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.7736 | −1.02384 | −0.511918 | − | 0.859034i | \(-0.671065\pi\) | ||||
−0.511918 | + | 0.859034i | \(0.671065\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.66282 | 0.498986 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −41.3205 | −2.12811 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.0301 | −0.515212 | −0.257606 | − | 0.966250i | \(-0.582934\pi\) | ||||
−0.257606 | + | 0.966250i | \(0.582934\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.67550 | 0.444459 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.37137 | 0.274464 | 0.137232 | − | 0.990539i | \(-0.456179\pi\) | ||||
0.137232 | + | 0.990539i | \(0.456179\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.424918 | −0.0216558 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.4027 | −0.681299 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.9092 | −1.16154 | −0.580771 | − | 0.814067i | \(-0.697249\pi\) | ||||
−0.580771 | + | 0.814067i | \(0.697249\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.2323 | 1.17491 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.43475 | 0.425477 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.75738 | 0.289685 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.4109 | 1.67684 | 0.838421 | − | 0.545022i | \(-0.183479\pi\) | ||||
0.838421 | + | 0.545022i | \(0.183479\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.523710 | −0.0262183 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.1166 | 0.854761 | 0.427380 | − | 0.904072i | \(-0.359437\pi\) | ||||
0.427380 | + | 0.904072i | \(0.359437\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.6775 | 1.42853 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.14289 | −0.255552 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.77201 | −0.286108 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.3132 | 1.69668 | 0.848338 | − | 0.529455i | \(-0.177603\pi\) | ||||
0.848338 | + | 0.529455i | \(0.177603\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.65347 | −0.476171 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.32178 | 0.163454 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.3089 | −0.555130 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.55442 | 0.125090 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.9327 | 0.534098 | 0.267049 | − | 0.963683i | \(-0.413951\pi\) | ||||
0.267049 | + | 0.963683i | \(0.413951\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.85783 | 0.0905450 | 0.0452725 | − | 0.998975i | \(-0.485584\pi\) | ||||
0.0452725 | + | 0.998975i | \(0.485584\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −23.7185 | −1.15324 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.56100 | −0.463777 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.40269 | 0.0678810 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.70022 | −0.275209 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.8740 | −0.957298 | −0.478649 | − | 0.878006i | \(-0.658873\pi\) | ||||
−0.478649 | + | 0.878006i | \(0.658873\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.0400 | 0.963060 | 0.481530 | − | 0.876430i | \(-0.340081\pi\) | ||||
0.481530 | + | 0.876430i | \(0.340081\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.10262 | −0.388491 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.8523 | −0.758320 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.9388 | 1.33345 | 0.666723 | − | 0.745306i | \(-0.267697\pi\) | ||||
0.666723 | + | 0.745306i | \(0.267697\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.0952 | 0.766436 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.10720 | −0.385185 | −0.192592 | − | 0.981279i | \(-0.561689\pi\) | ||||
−0.192592 | + | 0.981279i | \(0.561689\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.09202 | 0.146576 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.9815 | 0.803199 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.5796 | −0.499282 | −0.249641 | − | 0.968338i | \(-0.580313\pi\) | ||||
−0.249641 | + | 0.968338i | \(0.580313\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.21080 | −0.0570145 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.4839 | 0.633529 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.54974 | 0.119533 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.23297 | −0.291566 | −0.145783 | − | 0.989317i | \(-0.546570\pi\) | ||||
−0.145783 | + | 0.989317i | \(0.546570\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.8319 | −0.738971 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.7819 | −0.828187 | −0.414094 | − | 0.910234i | \(-0.635901\pi\) | ||||
−0.414094 | + | 0.910234i | \(0.635901\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.6781 | 1.05394 | 0.526970 | − | 0.849884i | \(-0.323328\pi\) | ||||
0.526970 | + | 0.849884i | \(0.323328\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.62342 | 0.260780 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.0419 | −0.973704 | −0.486852 | − | 0.873485i | \(-0.661855\pi\) | ||||
−0.486852 | + | 0.873485i | \(0.661855\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.967704 | −0.0446844 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.05175 | 0.0945399 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.19999 | 0.285076 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.52386 | 0.299335 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.97331 | 0.410859 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 42.1448 | 1.92564 | 0.962822 | − | 0.270137i | \(-0.0870689\pi\) | ||||
0.962822 | + | 0.270137i | \(0.0870689\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.6352 | 1.57923 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.36707 | 0.0622037 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.36504 | −0.0619832 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.9964 | −1.81241 | −0.906205 | − | 0.422838i | \(-0.861034\pi\) | ||||
−0.906205 | + | 0.422838i | \(0.861034\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.7584 | 0.622175 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.7596 | −0.666093 | −0.333047 | − | 0.942910i | \(-0.608077\pi\) | ||||
−0.333047 | + | 0.942910i | \(0.608077\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.1594 | 1.04305 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.82359 | 0.171857 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.496745 | 0.0222820 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.9064 | −1.38356 | −0.691780 | − | 0.722108i | \(-0.743173\pi\) | ||||
−0.691780 | + | 0.722108i | \(0.743173\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.91237 | 0.0854382 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.3279 | −0.995550 | −0.497775 | − | 0.867306i | \(-0.665849\pi\) | ||||
−0.497775 | + | 0.867306i | \(0.665849\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.99152 | −0.266619 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.4952 | 1.04346 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.9159 | −0.528163 | −0.264082 | − | 0.964500i | \(-0.585069\pi\) | ||||
−0.264082 | + | 0.964500i | \(0.585069\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.42310 | −0.107191 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.8028 | 0.476954 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −23.8725 | −1.05195 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.9720 | 0.482548 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.43394 | −0.370209 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.80323 | −0.254244 | −0.127122 | − | 0.991887i | \(-0.540574\pi\) | ||||
−0.127122 | + | 0.991887i | \(0.540574\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.65408 | 0.116055 | 0.0580275 | − | 0.998315i | \(-0.481519\pi\) | ||||
0.0580275 | + | 0.998315i | \(0.481519\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.562602 | −0.0245539 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.0732 | −0.700160 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.3801 | 0.799136 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −29.8907 | −1.29715 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.26547 | 0.314702 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.3633 | −0.837147 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.5332 | −0.540848 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.44549 | −0.320700 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.4325 | −1.60935 | −0.804675 | − | 0.593716i | \(-0.797660\pi\) | ||||
−0.804675 | + | 0.593716i | \(0.797660\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.9251 | 0.769238 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.85512 | −0.293641 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.2642 | 0.481620 | 0.240810 | − | 0.970572i | \(-0.422587\pi\) | ||||
0.240810 | + | 0.970572i | \(0.422587\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.6220 | −0.538694 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.8026 | −0.673213 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.968331 | −0.0411776 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.79169 | 0.288291 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.3468 | 1.28583 | 0.642917 | − | 0.765936i | \(-0.277724\pi\) | ||||
0.642917 | + | 0.765936i | \(0.277724\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −37.2033 | −1.57353 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.19487 | 0.134888 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.47156 | −0.230599 | −0.115299 | − | 0.993331i | \(-0.536783\pi\) | ||||
−0.115299 | + | 0.993331i | \(0.536783\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.18689 | 0.302355 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.864980 | 0.0363258 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.9163 | 1.54761 | 0.773806 | − | 0.633423i | \(-0.218351\pi\) | ||||
0.773806 | + | 0.633423i | \(0.218351\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.66161 | 0.0695360 | 0.0347680 | − | 0.999395i | \(-0.488931\pi\) | ||||
0.0347680 | + | 0.999395i | \(0.488931\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.4711 | −0.813415 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.0296 | −0.710181 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.2836 | 1.21909 | 0.609546 | − | 0.792751i | \(-0.291352\pi\) | ||||
0.609546 | + | 0.792751i | \(0.291352\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.8258 | 0.533020 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.90203 | 0.0789096 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.15097 | −0.171916 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22.9436 | −0.948600 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.51689 | 0.268981 | 0.134490 | − | 0.990915i | \(-0.457060\pi\) | ||||
0.134490 | + | 0.990915i | \(0.457060\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.9674 | 0.451904 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.81555 | −0.115816 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.5789 | −1.25573 | −0.627863 | − | 0.778324i | \(-0.716070\pi\) | ||||
−0.627863 | + | 0.778324i | \(0.716070\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.42908 | −0.0585866 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.20502 | −0.0493180 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.6196 | 1.16936 | 0.584682 | − | 0.811263i | \(-0.301219\pi\) | ||||
0.584682 | + | 0.811263i | \(0.301219\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.77277 | −0.398640 | −0.199320 | − | 0.979935i | \(-0.563873\pi\) | ||||
−0.199320 | + | 0.979935i | \(0.563873\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.70780 | 0.354609 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.1035 | 0.614045 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.1220 | 1.18203 | 0.591013 | − | 0.806662i | \(-0.298728\pi\) | ||||
0.591013 | + | 0.806662i | \(0.298728\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.36278 | 0.0552225 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −65.8379 | −2.66352 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.8416 | −1.24568 | −0.622839 | − | 0.782350i | \(-0.714021\pi\) | ||||
−0.622839 | + | 0.782350i | \(0.714021\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.42470 | 0.0574495 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.1505 | 0.650195 | 0.325097 | − | 0.945681i | \(-0.394603\pi\) | ||||
0.325097 | + | 0.945681i | \(0.394603\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.53909 | 0.182442 | 0.0912208 | − | 0.995831i | \(-0.470923\pi\) | ||||
0.0912208 | + | 0.995831i | \(0.470923\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.1990 | −1.13159 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.520046 | −0.0208352 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.75504 | −0.190202 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.17999 | −0.0870604 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.4124 | −0.774023 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.0968 | 0.879659 | 0.439830 | − | 0.898081i | \(-0.355039\pi\) | ||||
0.439830 | + | 0.898081i | \(0.355039\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.7377 | −0.426787 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.1533 | −0.641025 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 44.6769 | 1.77016 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.46992 | −0.176827 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.0606 | −0.989835 | −0.494917 | − | 0.868940i | \(-0.664802\pi\) | ||||
−0.494917 | + | 0.868940i | \(0.664802\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.2678 | −0.483797 | −0.241898 | − | 0.970302i | \(-0.577770\pi\) | ||||
−0.241898 | + | 0.970302i | \(0.577770\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.29527 | −0.287251 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.0505 | 1.49592 | 0.747961 | − | 0.663743i | \(-0.231033\pi\) | ||||
0.747961 | + | 0.663743i | \(0.231033\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.8272 | 0.542765 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.945802 | −0.0370689 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.7831 | −0.500242 | −0.250121 | − | 0.968215i | \(-0.580470\pi\) | ||||
−0.250121 | + | 0.968215i | \(0.580470\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.7051 | −0.613648 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 21.8040 | 0.850656 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.5002 | −1.18812 | −0.594060 | − | 0.804421i | \(-0.702476\pi\) | ||||
−0.594060 | + | 0.804421i | \(0.702476\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.42832 | 0.0555552 | 0.0277776 | − | 0.999614i | \(-0.491157\pi\) | ||||
0.0277776 | + | 0.999614i | \(0.491157\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.1709 | −0.744538 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.975120 | 0.0378135 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 41.2503 | 1.59722 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.3800 | −0.787936 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.83883 | 0.225406 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.6743 | −0.912575 | −0.456288 | − | 0.889832i | \(-0.650821\pi\) | ||||
−0.456288 | + | 0.889832i | \(0.650821\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11.6050 | 0.446677 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.8887 | 1.26401 | 0.632007 | − | 0.774963i | \(-0.282231\pi\) | ||||
0.632007 | + | 0.774963i | \(0.282231\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.229585 | 0.00881068 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.46125 | 0.285916 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.2987 | −0.968027 | −0.484013 | − | 0.875061i | \(-0.660821\pi\) | ||||
−0.484013 | + | 0.875061i | \(0.660821\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.9743 | 0.686761 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.7190 | 0.485259 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.9081 | 0.948922 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.8372 | 1.47744 | 0.738718 | − | 0.674015i | \(-0.235432\pi\) | ||||
0.738718 | + | 0.674015i | \(0.235432\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.643087 | −0.0244289 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.75619 | −0.180413 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.07217 | −0.154244 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.6119 | 0.703966 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.71520 | 0.0647824 | 0.0323912 | − | 0.999475i | \(-0.489688\pi\) | ||||
0.0323912 | + | 0.999475i | \(0.489688\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.2459 | 0.499577 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.9103 | −0.486230 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.00771 | 0.0378989 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.1255 | −1.31917 | −0.659583 | − | 0.751632i | \(-0.729267\pi\) | ||||
−0.659583 | + | 0.751632i | \(0.729267\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.71345 | 0.326780 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.6288 | −1.07216 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.6135 | 0.396923 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.33557 | 0.124569 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.1608 | −0.975632 | −0.487816 | − | 0.872946i | \(-0.662206\pi\) | ||||
−0.487816 | + | 0.872946i | \(0.662206\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.01511 | 0.149531 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.5780 | −0.467780 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.9761 | −0.630478 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.2843 | −1.60533 | −0.802663 | − | 0.596433i | \(-0.796584\pi\) | ||||
−0.802663 | + | 0.596433i | \(0.796584\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.05014 | 0.112968 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.8518 | 0.771231 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.7171 | 0.839077 | 0.419538 | − | 0.907738i | \(-0.362192\pi\) | ||||
0.419538 | + | 0.907738i | \(0.362192\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.76080 | 0.323147 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.02816 | −0.148379 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.3423 | −0.454018 | −0.227009 | − | 0.973893i | \(-0.572895\pi\) | ||||
−0.227009 | + | 0.973893i | \(0.572895\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.0811 | 0.480547 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.4100 | 0.565339 | 0.282670 | − | 0.959217i | \(-0.408780\pi\) | ||||
0.282670 | + | 0.959217i | \(0.408780\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31.6187 | −1.15842 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17.1153 | −0.626216 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.25670 | 0.118997 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.64363 | 0.0598973 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.1063 | −0.913713 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.1285 | −1.05869 | −0.529347 | − | 0.848405i | \(-0.677563\pi\) | ||||
−0.529347 | + | 0.848405i | \(0.677563\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.69054 | 0.206553 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.20326 | −0.0798680 | −0.0399340 | − | 0.999202i | \(-0.512715\pi\) | ||||
−0.0399340 | + | 0.999202i | \(0.512715\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.15296 | 0.0417400 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.8595 | 0.464935 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −82.9706 | −2.99590 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.54002 | −0.307961 | −0.153981 | − | 0.988074i | \(-0.549209\pi\) | ||||
−0.153981 | + | 0.988074i | \(0.549209\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.0159 | −0.396729 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.58639 | 0.200929 | 0.100464 | − | 0.994941i | \(-0.467967\pi\) | ||||
0.100464 | + | 0.994941i | \(0.467967\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.7819 | 0.423217 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.14229 | −0.0409795 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.77860 | 0.0995538 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.06775 | 0.0739897 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −28.1105 | −1.00459 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.82026 | −0.136351 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.1750 | 1.71725 | 0.858627 | − | 0.512602i | \(-0.171318\pi\) | ||||
0.858627 | + | 0.512602i | \(0.171318\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.50276 | −0.0534997 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.20876 | −0.0429785 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.0361 | −1.24417 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.88428 | 0.173228 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.6833 | 0.520108 | 0.260054 | − | 0.965594i | \(-0.416260\pi\) | ||||
0.260054 | + | 0.965594i | \(0.416260\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.9010 | 1.30546 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.67959 | 0.165345 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.0864 | −0.355940 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.54541 | −0.0897137 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.6961 | 0.693334 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.0743 | 1.23315 | 0.616573 | − | 0.787298i | \(-0.288521\pi\) | ||||
0.616573 | + | 0.787298i | \(0.288521\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.2328 | 0.359323 | 0.179662 | − | 0.983728i | \(-0.442500\pi\) | ||||
0.179662 | + | 0.983728i | \(0.442500\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.3956 | −0.645162 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.6174 | −0.897337 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.2280 | −0.497775 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.85887 | 0.134840 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.0226 | 0.663893 | 0.331946 | − | 0.943298i | \(-0.392295\pi\) | ||||
0.331946 | + | 0.943298i | \(0.392295\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.6733 | −0.825199 | −0.412599 | − | 0.910913i | \(-0.635379\pi\) | ||||
−0.412599 | + | 0.910913i | \(0.635379\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.34188 | −0.0815338 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.62961 | 0.230534 | 0.115267 | − | 0.993335i | \(-0.463228\pi\) | ||||
0.115267 | + | 0.993335i | \(0.463228\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.9608 | 1.35316 | 0.676582 | − | 0.736368i | \(-0.263461\pi\) | ||||
0.676582 | + | 0.736368i | \(0.263461\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.29622 | 0.218414 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.0406 | −0.867607 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.56072 | −0.123224 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.5094 | 0.674344 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.5794 | −0.434290 | −0.217145 | − | 0.976139i | \(-0.569675\pi\) | ||||
−0.217145 | + | 0.976139i | \(0.569675\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.1209 | 0.417962 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.2520 | 0.456423 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −43.7468 | −1.50494 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.54025 | −0.0872842 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.70381 | −0.0584746 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.5764 | −1.18526 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 57.6697 | 1.97457 | 0.987287 | − | 0.158946i | \(-0.0508096\pi\) | ||||
0.987287 | + | 0.158946i | \(0.0508096\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.77454 | −0.300083 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −47.8245 | −1.63365 | −0.816827 | − | 0.576883i | \(-0.804269\pi\) | ||||
−0.816827 | + | 0.576883i | \(0.804269\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.5829 | −1.52115 | −0.760574 | − | 0.649251i | \(-0.775083\pi\) | ||||
−0.760574 | + | 0.649251i | \(0.775083\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.239620 | −0.00816623 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.84737 | 0.130966 | 0.0654830 | − | 0.997854i | \(-0.479141\pi\) | ||||
0.0654830 | + | 0.997854i | \(0.479141\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.7035 | 0.533937 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.25935 | −0.110693 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.03077 | −0.136734 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.1711 | 0.819007 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.06590 | −0.0699203 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.02601 | 0.102298 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.56099 | −0.154014 | −0.0770068 | − | 0.997031i | \(-0.524536\pi\) | ||||
−0.0770068 | + | 0.997031i | \(0.524536\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.1358 | 0.645435 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.6292 | 0.863470 | 0.431735 | − | 0.902001i | \(-0.357902\pi\) | ||||
0.431735 | + | 0.902001i | \(0.357902\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.0678 | 0.641681 | 0.320841 | − | 0.947133i | \(-0.396035\pi\) | ||||
0.320841 | + | 0.947133i | \(0.396035\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.2699 | −0.546907 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.112708 | 0.00378437 | 0.00189219 | − | 0.999998i | \(-0.499398\pi\) | ||||
0.00189219 | + | 0.999998i | \(0.499398\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.71682 | 0.0911193 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.60056 | 0.120623 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.1790 | −0.842584 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.3362 | 0.780043 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −34.1463 | −1.14011 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.5389 | −0.951827 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.9605 | −0.465093 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.22699 | 0.0408316 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33.3755 | −1.10944 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.52667 | −0.249919 | −0.124960 | − | 0.992162i | \(-0.539880\pi\) | ||||
−0.124960 | + | 0.992162i | \(0.539880\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.06781 | −0.300760 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.4119 | −1.30577 | −0.652887 | − | 0.757456i | \(-0.726442\pi\) | ||||
−0.652887 | + | 0.757456i | \(0.726442\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.91739 | 0.262027 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.87031 | −0.227125 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.64143 | 0.0872277 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.9443 | −0.987770 | −0.493885 | − | 0.869527i | \(-0.664424\pi\) | ||||
−0.493885 | + | 0.869527i | \(0.664424\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.3860 | −0.638791 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.4076 | −0.408401 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.2295 | 0.467864 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −36.1296 | −1.18665 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.8317 | 1.40526 | 0.702632 | − | 0.711554i | \(-0.252008\pi\) | ||||
0.702632 | + | 0.711554i | \(0.252008\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.0862 | 0.559979 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.2458 | 0.630080 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.94868 | −0.194543 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.8023 | 1.49630 | 0.748148 | − | 0.663532i | \(-0.230943\pi\) | ||||
0.748148 | + | 0.663532i | \(0.230943\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.1297 | −0.722176 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.0046 | 1.46711 | 0.733554 | − | 0.679631i | \(-0.237860\pi\) | ||||
0.733554 | + | 0.679631i | \(0.237860\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.25313 | −0.236194 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.73460 | 0.0564265 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.69868 | −0.0876952 | −0.0438476 | − | 0.999038i | \(-0.513962\pi\) | ||||
−0.0438476 | + | 0.999038i | \(0.513962\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 60.5236 | 1.96468 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.5389 | 0.503884 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 50.0779 | 1.62218 | 0.811091 | − | 0.584920i | \(-0.198874\pi\) | ||||
0.811091 | + | 0.584920i | \(0.198874\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36.2541 | 1.17316 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.67268 | 0.183372 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.02308 | −0.0976205 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.1933 | −0.361073 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −29.3051 | −0.944345 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.8809 | −0.768753 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.1810 | −0.584661 | −0.292330 | − | 0.956317i | \(-0.594431\pi\) | ||||
−0.292330 | + | 0.956317i | \(0.594431\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.33173 | −0.235529 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.4217 | −0.880003 | −0.440002 | − | 0.897997i | \(-0.645022\pi\) | ||||
−0.440002 | + | 0.897997i | \(0.645022\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.799942 | 0.0256450 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.0525 | 0.450042 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 51.9065 | 1.66064 | 0.830318 | − | 0.557290i | \(-0.188159\pi\) | ||||
0.830318 | + | 0.557290i | \(0.188159\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.16474 | −0.0691853 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.3748 | −0.331242 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53.8609 | 1.71790 | 0.858948 | − | 0.512063i | \(-0.171119\pi\) | ||||
0.858948 | + | 0.512063i | \(0.171119\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.24240 | 0.167037 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.17138 | 0.0691157 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37.1401 | 1.18099 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.5246 | −0.810816 | −0.405408 | − | 0.914136i | \(-0.632870\pi\) | ||||
−0.405408 | + | 0.914136i | \(0.632870\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29.1212 | 0.924133 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.24367 | 0.0711293 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.3414 | −1.34097 | −0.670483 | − | 0.741925i | \(-0.733913\pi\) | ||||
−0.670483 | + | 0.741925i | \(0.733913\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 23.5625 | 0.745484 |
(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 | 6008.2.a.e.1.31 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.e.1.31 | ✓ | 50 | 1.1 | even | 1 | trivial |