Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(1,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 672) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.876894 | 0.0784318 | 0.0392159 | − | 0.999231i | \(-0.487514\pi\) | ||||
0.0392159 | + | 0.999231i | \(0.487514\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 56.3542 | 1.54467 | 0.772337 | − | 0.635213i | \(-0.219088\pi\) | ||||
0.772337 | + | 0.635213i | \(0.219088\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.75379 | 0.0800857 | 0.0400428 | − | 0.999198i | \(-0.487251\pi\) | ||||
0.0400428 | + | 0.999198i | \(0.487251\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.63068 | −0.0452826 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −29.6458 | −0.422951 | −0.211476 | − | 0.977383i | \(-0.567827\pi\) | ||||
−0.211476 | + | 0.977383i | \(0.567827\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −135.939 | −1.64140 | −0.820701 | − | 0.571358i | \(-0.806417\pi\) | ||||
−0.820701 | + | 0.571358i | \(0.806417\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −177.062 | −1.60522 | −0.802610 | − | 0.596504i | \(-0.796556\pi\) | ||||
−0.802610 | + | 0.596504i | \(0.796556\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.231 | −0.993848 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 149.939 | 0.960105 | 0.480052 | − | 0.877240i | \(-0.340618\pi\) | ||||
0.480052 | + | 0.877240i | \(0.340618\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −38.4621 | −0.222839 | −0.111419 | − | 0.993773i | \(-0.535540\pi\) | ||||
−0.111419 | + | 0.993773i | \(0.535540\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −169.062 | −0.891818 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.13826 | 0.0296444 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −86.2765 | −0.383345 | −0.191673 | − | 0.981459i | \(-0.561391\pi\) | ||||
−0.191673 | + | 0.981459i | \(0.561391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.2614 | −0.0462375 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 58.5094 | 0.222869 | 0.111435 | − | 0.993772i | \(-0.464455\pi\) | ||||
0.111435 | + | 0.993772i | \(0.464455\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 485.356 | 1.72130 | 0.860652 | − | 0.509193i | \(-0.170056\pi\) | ||||
0.860652 | + | 0.509193i | \(0.170056\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.89205 | 0.0261439 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 315.542 | 0.979287 | 0.489643 | − | 0.871923i | \(-0.337127\pi\) | ||||
0.489643 | + | 0.871923i | \(0.337127\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 88.9375 | 0.244191 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −154.216 | −0.399683 | −0.199841 | − | 0.979828i | \(-0.564043\pi\) | ||||
−0.199841 | + | 0.979828i | \(0.564043\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 49.4166 | 0.121152 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 407.818 | 0.947664 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 727.663 | 1.60565 | 0.802827 | − | 0.596211i | \(-0.203328\pi\) | ||||
0.802827 | + | 0.596211i | \(0.203328\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −688.220 | −1.44455 | −0.722275 | − | 0.691606i | \(-0.756903\pi\) | ||||
−0.722275 | + | 0.691606i | \(0.756903\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.29168 | 0.00628126 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 710.739 | 1.29598 | 0.647989 | − | 0.761650i | \(-0.275610\pi\) | ||||
0.647989 | + | 0.761650i | \(0.275610\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 531.187 | 0.926775 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −777.771 | −1.30006 | −0.650031 | − | 0.759908i | \(-0.725244\pi\) | ||||
−0.650031 | + | 0.759908i | \(0.725244\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −853.913 | −1.36908 | −0.684541 | − | 0.728975i | \(-0.739997\pi\) | ||||
−0.684541 | + | 0.728975i | \(0.739997\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 372.693 | 0.573799 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 394.479 | 0.583832 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 231.049 | 0.329051 | 0.164526 | − | 0.986373i | \(-0.447391\pi\) | ||||
0.164526 | + | 0.986373i | \(0.447391\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −444.189 | −0.587423 | −0.293712 | − | 0.955894i | \(-0.594891\pi\) | ||||
−0.293712 | + | 0.955894i | \(0.594891\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −25.9963 | −0.0331728 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −449.818 | −0.554317 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1083.28 | −1.29019 | −0.645097 | − | 0.764101i | \(-0.723183\pi\) | ||||
−0.645097 | + | 0.764101i | \(0.723183\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 26.2765 | 0.0302695 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 115.386 | 0.128656 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −119.204 | −0.128738 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 634.155 | 0.663801 | 0.331901 | − | 0.943314i | \(-0.392310\pi\) | ||||
0.331901 | + | 0.943314i | \(0.392310\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 507.187 | 0.514891 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1960.64 | −1.93160 | −0.965798 | − | 0.259296i | \(-0.916509\pi\) | ||||
−0.965798 | + | 0.259296i | \(0.916509\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1806.65 | −1.72830 | −0.864149 | − | 0.503236i | \(-0.832143\pi\) | ||||
−0.864149 | + | 0.503236i | \(0.832143\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −18.4148 | −0.0171152 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 120.718 | 0.109068 | 0.0545338 | − | 0.998512i | \(-0.482633\pi\) | ||||
0.0545338 | + | 0.998512i | \(0.482633\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1219.17 | −1.07133 | −0.535665 | − | 0.844431i | \(-0.679939\pi\) | ||||
−0.535665 | + | 0.844431i | \(0.679939\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 258.830 | 0.221324 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −608.212 | −0.506334 | −0.253167 | − | 0.967423i | \(-0.581472\pi\) | ||||
−0.253167 | + | 0.967423i | \(0.581472\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −155.265 | −0.125900 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 33.7841 | 0.0266952 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −207.521 | −0.159861 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1844.79 | 1.38602 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −175.528 | −0.128674 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −218.549 | −0.156381 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1356.77 | −0.947982 | −0.473991 | − | 0.880530i | \(-0.657187\pi\) | ||||
−0.473991 | + | 0.880530i | \(0.657187\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1456.07 | −0.993796 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1782.23 | 1.18866 | 0.594328 | − | 0.804223i | \(-0.297418\pi\) | ||||
0.594328 | + | 0.804223i | \(0.297418\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −951.576 | −0.620392 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −23.6761 | −0.0150942 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −979.701 | −0.610960 | −0.305480 | − | 0.952199i | \(-0.598817\pi\) | ||||
−0.305480 | + | 0.952199i | \(0.598817\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 636.257 | 0.388249 | 0.194125 | − | 0.980977i | \(-0.437813\pi\) | ||||
0.194125 | + | 0.980977i | \(0.437813\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −946.625 | −0.565391 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 211.542 | 0.123706 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 131.481 | 0.0753028 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 903.269 | 0.496635 | 0.248318 | − | 0.968679i | \(-0.420122\pi\) | ||||
0.248318 | + | 0.968679i | \(0.420122\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1373.30 | 0.740118 | 0.370059 | − | 0.929008i | \(-0.379337\pi\) | ||||
0.370059 | + | 0.929008i | \(0.379337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −266.813 | −0.140984 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −33.7272 | −0.0174776 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 347.060 | 0.176423 | 0.0882116 | − | 0.996102i | \(-0.471885\pi\) | ||||
0.0882116 | + | 0.996102i | \(0.471885\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 462.648 | 0.230757 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1239.44 | −0.606716 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2667.49 | 1.28180 | 0.640901 | − | 0.767623i | \(-0.278561\pi\) | ||||
0.640901 | + | 0.767623i | \(0.278561\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −148.250 | −0.0699469 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2333.51 | −1.08127 | −0.540636 | − | 0.841256i | \(-0.681816\pi\) | ||||
−0.540636 | + | 0.841256i | \(0.681816\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2182.91 | −0.993586 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1223.45 | −0.547134 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2511.35 | −1.10367 | −0.551833 | − | 0.833955i | \(-0.686071\pi\) | ||||
−0.551833 | + | 0.833955i | \(0.686071\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −869.617 | −0.375639 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2182.99 | −0.927025 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1799.61 | −0.751449 | −0.375724 | − | 0.926731i | \(-0.622606\pi\) | ||||
−0.375724 | + | 0.926731i | \(0.622606\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1567.89 | −0.643869 | −0.321935 | − | 0.946762i | \(-0.604333\pi\) | ||||
−0.321935 | + | 0.946762i | \(0.604333\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2064.66 | 0.834011 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −75.6554 | −0.0300665 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1670.67 | −0.653322 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3768.49 | −1.42764 | −0.713818 | − | 0.700331i | \(-0.753036\pi\) | ||||
−0.713818 | + | 0.700331i | \(0.753036\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2440.06 | 0.910050 | 0.455025 | − | 0.890479i | \(-0.349630\pi\) | ||||
0.455025 | + | 0.890479i | \(0.349630\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.87503 | −0.00362649 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2543.70 | 0.919955 | 0.459978 | − | 0.887931i | \(-0.347857\pi\) | ||||
0.459978 | + | 0.887931i | \(0.347857\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1080.43 | 0.384873 | 0.192437 | − | 0.981309i | \(-0.438361\pi\) | ||||
0.192437 | + | 0.981309i | \(0.438361\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2132.22 | −0.748233 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1049.58 | 0.362886 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 51.3066 | 0.0174800 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1593.56 | −0.535074 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7660.75 | −2.53543 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3766.55 | −1.22891 | −0.614454 | − | 0.788953i | \(-0.710624\pi\) | ||||
−0.614454 | + | 0.788953i | \(0.710624\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2333.31 | 0.750591 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 425.606 | 0.135005 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −269.235 | −0.0842251 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2561.74 | 0.790439 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −111.284 | −0.0338723 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5461.86 | 1.64015 | 0.820074 | − | 0.572258i | \(-0.193932\pi\) | ||||
0.820074 | + | 0.572258i | \(0.193932\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1118.08 | −0.331283 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3480.41 | −1.01763 | −0.508816 | − | 0.860875i | \(-0.669917\pi\) | ||||
−0.508816 | + | 0.860875i | \(0.669917\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3465.22 | −0.999949 | −0.499975 | − | 0.866040i | \(-0.666657\pi\) | ||||
−0.499975 | + | 0.866040i | \(0.666657\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1183.44 | −0.337076 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4469.14 | 1.25658 | 0.628290 | − | 0.777979i | \(-0.283755\pi\) | ||||
0.628290 | + | 0.777979i | \(0.283755\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 276.697 | 0.0768072 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −693.148 | −0.189978 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2879.32 | 0.779278 | 0.389639 | − | 0.920968i | \(-0.372600\pi\) | ||||
0.389639 | + | 0.920968i | \(0.372600\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1014.11 | 0.271056 | 0.135528 | − | 0.990774i | \(-0.456727\pi\) | ||||
0.135528 | + | 0.990774i | \(0.456727\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 42.9678 | 0.0112045 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −510.288 | −0.131453 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1332.57 | 0.339149 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7235.24 | −1.81946 | −0.909729 | − | 0.415201i | \(-0.863711\pi\) | ||||
−0.909729 | + | 0.415201i | \(0.863711\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9978.21 | −2.47954 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 77.9888 | 0.0191523 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 719.449 | 0.174622 | 0.0873112 | − | 0.996181i | \(-0.472173\pi\) | ||||
0.0873112 | + | 0.996181i | \(0.472173\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −603.936 | −0.144891 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1349.45 | 0.320035 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1340.74 | 0.314348 | 0.157174 | − | 0.987571i | \(-0.449762\pi\) | ||||
0.157174 | + | 0.987571i | \(0.449762\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −135.231 | −0.0313478 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3249.84 | 0.744894 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1189.06 | 0.269510 | 0.134755 | − | 0.990879i | \(-0.456975\pi\) | ||||
0.134755 | + | 0.990879i | \(0.456975\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2661.82 | −0.596656 | −0.298328 | − | 0.954463i | \(-0.596429\pi\) | ||||
−0.298328 | + | 0.954463i | \(0.596429\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −78.8296 | −0.0174761 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7000.94 | −1.53517 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8638.72 | −1.87383 | −0.936914 | − | 0.349559i | \(-0.886331\pi\) | ||||
−0.936914 | + | 0.349559i | \(0.886331\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −346.159 | −0.0742796 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6951.67 | −1.47581 | −0.737904 | − | 0.674906i | \(-0.764184\pi\) | ||||
−0.737904 | + | 0.674906i | \(0.764184\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3231.21 | 0.678712 | 0.339356 | − | 0.940658i | \(-0.389791\pi\) | ||||
0.339356 | + | 0.940658i | \(0.389791\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 357.613 | 0.0743270 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 409.566 | 0.0842367 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4034.12 | −0.821112 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1902.47 | −0.383246 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4270.89 | 0.851563 | 0.425781 | − | 0.904826i | \(-0.359999\pi\) | ||||
0.425781 | + | 0.904826i | \(0.359999\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 638.083 | 0.125934 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1521.56 | −0.297273 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −664.655 | −0.128555 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3397.49 | 0.650592 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5881.93 | 1.11521 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −603.496 | −0.113299 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −285.402 | −0.0530578 | −0.0265289 | − | 0.999648i | \(-0.508445\pi\) | ||||
−0.0265289 | + | 0.999648i | \(0.508445\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5419.95 | 0.997833 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1366.10 | 0.249082 | 0.124541 | − | 0.992214i | \(-0.460254\pi\) | ||||
0.124541 | + | 0.992214i | \(0.460254\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 753.970 | 0.136156 | 0.0680781 | − | 0.997680i | \(-0.478313\pi\) | ||||
0.0680781 | + | 0.997680i | \(0.478313\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 55.2443 | 0.00988148 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5379.11 | −0.953063 | −0.476531 | − | 0.879157i | \(-0.658106\pi\) | ||||
−0.476531 | + | 0.879157i | \(0.658106\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8449.71 | 1.48305 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −362.154 | −0.0629702 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4030.04 | 0.694233 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −466.337 | −0.0795930 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3657.50 | 0.618533 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2208.79 | 0.370136 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8010.26 | −1.33016 | −0.665081 | − | 0.746771i | \(-0.731603\pi\) | ||||
−0.665081 | + | 0.746771i | \(0.731603\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −776.489 | −0.127782 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 623.243 | 0.101646 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5653.31 | 0.913814 | 0.456907 | − | 0.889514i | \(-0.348957\pi\) | ||||
0.456907 | + | 0.889514i | \(0.348957\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1824.64 | 0.292332 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2167.50 | −0.344213 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 465.795 | 0.0726886 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −770.445 | −0.119192 | −0.0595961 | − | 0.998223i | \(-0.518981\pi\) | ||||
−0.0595961 | + | 0.998223i | \(0.518981\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −904.811 | −0.138778 | −0.0693889 | − | 0.997590i | \(-0.522105\pi\) | ||||
−0.0693889 | + | 0.997590i | \(0.522105\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −101.352 | −0.0154125 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −409.934 | −0.0618090 | −0.0309045 | − | 0.999522i | \(-0.509839\pi\) | ||||
−0.0309045 | + | 0.999522i | \(0.509839\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −682.023 | −0.101966 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 622.563 | 0.0922955 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2446.32 | −0.359642 | −0.179821 | − | 0.983699i | \(-0.557552\pi\) | ||||
−0.179821 | + | 0.983699i | \(0.557552\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11620.5 | 1.69420 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5534.37 | −0.800219 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −748.791 | −0.107380 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8076.32 | 1.14872 | 0.574360 | − | 0.818603i | \(-0.305251\pi\) | ||||
0.574360 | + | 0.818603i | \(0.305251\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 526.585 | 0.0742898 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1079.51 | −0.151066 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8458.38 | −1.17415 | −0.587075 | − | 0.809532i | \(-0.699721\pi\) | ||||
−0.587075 | + | 0.809532i | \(0.699721\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 655.648 | 0.0902867 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 562.841 | 0.0768906 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11138.6 | 1.50963 | 0.754817 | − | 0.655936i | \(-0.227726\pi\) | ||||
0.754817 | + | 0.655936i | \(0.227726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4070.31 | 0.547318 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 499.363 | 0.0666221 | 0.0333110 | − | 0.999445i | \(-0.489395\pi\) | ||||
0.0333110 | + | 0.999445i | \(0.489395\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 345.917 | 0.0457910 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4368.20 | 0.573768 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −227.788 | −0.0296897 | −0.0148449 | − | 0.999890i | \(-0.504725\pi\) | ||||
−0.0148449 | + | 0.999890i | \(0.504725\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5249.17 | 0.678930 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5346.68 | −0.686271 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 202.606 | 0.0258081 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7979.71 | −1.00879 | −0.504396 | − | 0.863473i | \(-0.668285\pi\) | ||||
−0.504396 | + | 0.863473i | \(0.668285\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2854.73 | 0.358183 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12358.0 | −1.53898 | −0.769489 | − | 0.638660i | \(-0.779489\pi\) | ||||
−0.769489 | + | 0.638660i | \(0.779489\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −144.379 | −0.0178462 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 71.0284 | 0.00871465 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4862.04 | −0.592144 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 372.125 | 0.0449887 | 0.0224944 | − | 0.999747i | \(-0.492839\pi\) | ||||
0.0224944 | + | 0.999747i | \(0.492839\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2939.10 | 0.352738 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5093.64 | 0.606880 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −389.507 | −0.0460727 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1908.77 | −0.224156 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8281.97 | −0.965635 | −0.482817 | − | 0.875721i | \(-0.660386\pi\) | ||||
−0.482817 | + | 0.875721i | \(0.660386\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12771.4 | 1.47848 | 0.739242 | − | 0.673440i | \(-0.235184\pi\) | ||||
0.739242 | + | 0.673440i | \(0.235184\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2839.87 | 0.326429 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3682.93 | 0.420349 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4817.54 | −0.545988 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −634.625 | −0.0714219 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9372.55 | −1.04747 | −0.523735 | − | 0.851881i | \(-0.675462\pi\) | ||||
−0.523735 | + | 0.851881i | \(0.675462\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7381.75 | −0.819271 | −0.409635 | − | 0.912249i | \(-0.634344\pi\) | ||||
−0.409635 | + | 0.912249i | \(0.634344\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −394.443 | −0.0434761 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24069.8 | 2.63481 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1508.09 | 0.163957 | 0.0819786 | − | 0.996634i | \(-0.473876\pi\) | ||||
0.0819786 | + | 0.996634i | \(0.473876\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9229.84 | 0.989894 | 0.494947 | − | 0.868923i | \(-0.335187\pi\) | ||||
0.494947 | + | 0.868923i | \(0.335187\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −949.921 | −0.101192 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2709.81 | −0.286733 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1747.05 | −0.183627 | −0.0918136 | − | 0.995776i | \(-0.529266\pi\) | ||||
−0.0918136 | + | 0.995776i | \(0.529266\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3297.25 | 0.344260 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4119.91 | −0.427307 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 23.0417 | 0.00237409 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14462.8 | 1.48040 | 0.740198 | − | 0.672388i | \(-0.234732\pi\) | ||||
0.740198 | + | 0.672388i | \(0.234732\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 800.438 | 0.0813970 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 712.086 | 0.0719417 | 0.0359709 | − | 0.999353i | \(-0.488548\pi\) | ||||
0.0359709 | + | 0.999353i | \(0.488548\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3749.73 | −0.376382 | −0.188191 | − | 0.982132i | \(-0.560262\pi\) | ||||
−0.188191 | + | 0.982132i | \(0.560262\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 101.182 | 0.0100907 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17963.3 | −1.77997 | −0.889983 | − | 0.455994i | \(-0.849284\pi\) | ||||
−0.889983 | + | 0.455994i | \(0.849284\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4975.17 | 0.489834 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1041.18 | −0.101858 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27351.8 | 2.65886 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16887.9 | 1.63130 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1387.94 | −0.133228 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7260.06 | −0.692527 | −0.346264 | − | 0.938137i | \(-0.612550\pi\) | ||||
−0.346264 | + | 0.938137i | \(0.612550\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −323.864 | −0.0307005 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3718.31 | 0.350288 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 556.087 | 0.0520631 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3182.75 | −0.296148 | −0.148074 | − | 0.988976i | \(-0.547307\pi\) | ||||
−0.148074 | + | 0.988976i | \(0.547307\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8002.47 | −0.740049 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12187.9 | −1.12022 | −0.560112 | − | 0.828417i | \(-0.689242\pi\) | ||||
−0.560112 | + | 0.828417i | \(0.689242\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4445.08 | −0.406078 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 444.750 | 0.0403839 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5444.40 | −0.491377 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 368.606 | 0.0330683 | 0.0165341 | − | 0.999863i | \(-0.494737\pi\) | ||||
0.0165341 | + | 0.999863i | \(0.494737\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7000.53 | 0.624273 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12794.1 | −1.13412 | −0.567060 | − | 0.823677i | \(-0.691919\pi\) | ||||
−0.567060 | + | 0.823677i | \(0.691919\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1719.28 | −0.151499 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6548.73 | 0.573647 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −603.881 | −0.0525866 | −0.0262933 | − | 0.999654i | \(-0.508370\pi\) | ||||
−0.0262933 | + | 0.999654i | \(0.508370\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5977.39 | −0.517464 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3670.36 | 0.315888 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1584.24 | −0.135554 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17782.1 | 1.51268 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7534.04 | 0.637202 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11964.9 | −1.00613 | −0.503064 | − | 0.864249i | \(-0.667794\pi\) | ||||
−0.503064 | + | 0.864249i | \(0.667794\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4926.73 | 0.411913 | 0.205957 | − | 0.978561i | \(-0.433969\pi\) | ||||
0.205957 | + | 0.978561i | \(0.433969\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2608.85 | 0.216876 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1140.24 | 0.0942499 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19184.1 | 1.57673 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6548.97 | 0.535218 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 219.632 | 0.0178486 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 105.857 | 0.00855437 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5398.84 | 0.433849 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2761.35 | 0.220668 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2094.84 | 0.166477 | 0.0832385 | − | 0.996530i | \(-0.473474\pi\) | ||||
0.0832385 | + | 0.996530i | \(0.473474\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4703.67 | 0.371738 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1069.08 | −0.0840264 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8445.47 | 0.660150 | 0.330075 | − | 0.943955i | \(-0.392926\pi\) | ||||
0.330075 | + | 0.943955i | \(0.392926\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6193.98 | −0.481516 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20382.7 | −1.57592 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1617.34 | 0.124370 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 226.966 | 0.0173589 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18621.4 | −1.41654 | −0.708271 | − | 0.705940i | \(-0.750525\pi\) | ||||
−0.708271 | + | 0.705940i | \(0.750525\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1821.92 | 0.137852 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5012.00 | 0.377196 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8094.87 | 0.605964 | 0.302982 | − | 0.952996i | \(-0.402018\pi\) | ||||
0.302982 | + | 0.952996i | \(0.402018\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −533.338 | −0.0397127 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8187.82 | 0.603254 | 0.301627 | − | 0.953426i | \(-0.402470\pi\) | ||||
0.301627 | + | 0.953426i | \(0.402470\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11758.0 | 0.861744 | 0.430872 | − | 0.902413i | \(-0.358206\pi\) | ||||
0.430872 | + | 0.902413i | \(0.358206\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11305.5 | 0.824246 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21996.7 | 1.59535 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9198.93 | −0.663703 | −0.331851 | − | 0.943332i | \(-0.607673\pi\) | ||||
−0.331851 | + | 0.943332i | \(0.607673\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7320.19 | −0.525418 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3109.33 | −0.222025 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8690.71 | −0.617380 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 29.6251 | 0.00209375 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 106.239 | 0.00747009 | 0.00373504 | − | 0.999993i | \(-0.498811\pi\) | ||||
0.00373504 | + | 0.999993i | \(0.498811\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5228.52 | 0.365768 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7631.10 | −0.531136 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11280.0 | −0.781136 | −0.390568 | − | 0.920574i | \(-0.627721\pi\) | ||||
−0.390568 | + | 0.920574i | \(0.627721\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −181.974 | −0.0125382 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3241.30 | −0.222207 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12945.7 | −0.883053 | −0.441527 | − | 0.897248i | \(-0.645563\pi\) | ||||
−0.441527 | + | 0.897248i | \(0.645563\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3077.87 | −0.208900 | −0.104450 | − | 0.994530i | \(-0.533308\pi\) | ||||
−0.104450 | + | 0.994530i | \(0.533308\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6396.65 | 0.431993 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1617.69 | 0.108708 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16004.8 | −1.07020 | −0.535102 | − | 0.844787i | \(-0.679727\pi\) | ||||
−0.535102 | + | 0.844787i | \(0.679727\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3148.73 | −0.209512 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1184.48 | 0.0784268 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11740.7 | 0.773578 | 0.386789 | − | 0.922168i | \(-0.373584\pi\) | ||||
0.386789 | + | 0.922168i | \(0.373584\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −153.920 | −0.0100921 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.63255 | −0.000237019 0 | −0.000118510 | − | 1.00000i | \(-0.500038\pi\) | ||||
−0.000118510 | 1.00000i | \(0.500038\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6041.73 | −0.392307 | −0.196153 | − | 0.980573i | \(-0.562845\pi\) | ||||
−0.196153 | + | 0.980573i | \(0.562845\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4780.69 | 0.308925 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7582.95 | −0.487648 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15337.2 | 0.981583 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 22982.2 | 1.46383 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2557.74 | 0.162136 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26746.9 | 1.68745 | 0.843723 | − | 0.536779i | \(-0.180359\pi\) | ||||
0.843723 | + | 0.536779i | \(0.180359\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11299.6 | 0.709511 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1189.74 | −0.0743520 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 183.936 | 0.0114408 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6999.94 | −0.433354 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23798.5 | 1.46643 | 0.733217 | − | 0.679994i | \(-0.238018\pi\) | ||||
0.733217 | + | 0.679994i | \(0.238018\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12067.9 | 0.740140 | 0.370070 | − | 0.929004i | \(-0.379334\pi\) | ||||
0.370070 | + | 0.929004i | \(0.379334\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1276.82 | −0.0779452 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6510.14 | −0.395580 | −0.197790 | − | 0.980244i | \(-0.563376\pi\) | ||||
−0.197790 | + | 0.980244i | \(0.563376\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 41006.8 | 2.48021 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 807.704 | 0.0486274 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29875.2 | 1.79036 | 0.895181 | − | 0.445703i | \(-0.147046\pi\) | ||||
0.895181 | + | 0.445703i | \(0.147046\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1562.82 | 0.0932284 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7685.22 | −0.456360 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16941.0 | 1.00141 | 0.500705 | − | 0.865618i | \(-0.333074\pi\) | ||||
0.500705 | + | 0.865618i | \(0.333074\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31618.1 | 1.86052 | 0.930259 | − | 0.366905i | \(-0.119583\pi\) | ||||
0.930259 | + | 0.366905i | \(0.119583\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 333.853 | 0.0195562 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −834.431 | −0.0486584 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26548.6 | −1.54118 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16385.6 | −0.946940 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38784.0 | −2.23136 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27915.4 | −1.59890 | −0.799449 | − | 0.600734i | \(-0.794875\pi\) | ||||
−0.799449 | + | 0.600734i | \(0.794875\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3354.24 | 0.191266 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14052.2 | −0.797741 | −0.398871 | − | 0.917007i | \(-0.630598\pi\) | ||||
−0.398871 | + | 0.917007i | \(0.630598\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4439.09 | 0.250893 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10441.2 | 0.587530 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9826.72 | −0.550526 | −0.275263 | − | 0.961369i | \(-0.588765\pi\) | ||||
−0.275263 | + | 0.961369i | \(0.588765\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −859.094 | −0.0479187 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10395.7 | 0.577321 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −578.894 | −0.0320089 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28241.2 | 1.55477 | 0.777386 | − | 0.629024i | \(-0.216545\pi\) | ||||
0.777386 | + | 0.629024i | \(0.216545\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3550.31 | 0.194611 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 557.931 | 0.0304511 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1734.56 | −0.0942628 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13407.4 | −0.725487 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13561.0 | −0.730658 | −0.365329 | − | 0.930879i | \(-0.619043\pi\) | ||||
−0.365329 | + | 0.930879i | \(0.619043\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11728.4 | 0.629223 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −830.090 | −0.0443447 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13724.5 | −0.730075 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12419.2 | 0.657848 | 0.328924 | − | 0.944356i | \(-0.393314\pi\) | ||||
0.328924 | + | 0.944356i | \(0.393314\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2079.44 | 0.109684 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6810.20 | 0.357705 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 185.500 | 0.00970251 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8637.95 | −0.449916 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23656.1 | −1.22702 | −0.613508 | − | 0.789688i | \(-0.710242\pi\) | ||||
−0.613508 | + | 0.789688i | \(0.710242\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12646.6 | −0.653235 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3042.33 | −0.156494 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18627.1 | −0.954199 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32584.6 | −1.66231 | −0.831153 | − | 0.556044i | \(-0.812319\pi\) | ||||
−0.831153 | + | 0.556044i | \(0.812319\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14388.8 | −0.728028 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27826.8 | −1.40219 | −0.701095 | − | 0.713068i | \(-0.747305\pi\) | ||||
−0.701095 | + | 0.713068i | \(0.747305\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −128.903 | −0.00646895 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 40053.1 | 2.00186 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17634.8 | −0.877818 | −0.438909 | − | 0.898531i | \(-0.644635\pi\) | ||||
−0.438909 | + | 0.898531i | \(0.644635\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1530.86 | 0.0758943 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17572.6 | −0.867669 | −0.433834 | − | 0.900993i | \(-0.642840\pi\) | ||||
−0.433834 | + | 0.900993i | \(0.642840\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 792.071 | 0.0389520 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3997.70 | −0.195808 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 845.025 | 0.0412237 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8719.41 | −0.423669 | −0.211835 | − | 0.977306i | \(-0.567944\pi\) | ||||
−0.211835 | + | 0.977306i | \(0.567944\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21705.7 | 1.05047 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1204.24 | 0.0580488 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37363.8 | 1.79394 | 0.896969 | − | 0.442093i | \(-0.145764\pi\) | ||||
0.896969 | + | 0.442093i | \(0.145764\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 29934.6 | 1.43157 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19533.4 | 0.930468 | 0.465234 | − | 0.885188i | \(-0.345970\pi\) | ||||
0.465234 | + | 0.885188i | \(0.345970\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8534.17 | −0.404925 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −233.966 | −0.0110576 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2731.49 | 0.128590 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22424.6 | −1.05156 | −0.525781 | − | 0.850620i | \(-0.676227\pi\) | ||||
−0.525781 | + | 0.850620i | \(0.676227\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2158.35 | −0.100818 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34994.7 | 1.62830 | 0.814148 | − | 0.580658i | \(-0.197205\pi\) | ||||
0.814148 | + | 0.580658i | \(0.197205\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4778.19 | 0.221468 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1811.81 | 0.0836528 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7953.74 | −0.365818 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43830.6 | −2.00817 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4048.36 | −0.184772 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 304.335 | 0.0138372 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30981.7 | 1.40328 | 0.701639 | − | 0.712532i | \(-0.252452\pi\) | ||||
0.701639 | + | 0.712532i | \(0.252452\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4022.22 | −0.181489 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4257.49 | −0.191376 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2583.43 | −0.115688 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 405.693 | 0.0180987 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38915.7 | 1.72957 | 0.864784 | − | 0.502144i | \(-0.167455\pi\) | ||||
0.864784 | + | 0.502144i | \(0.167455\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9354.50 | −0.414191 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9749.51 | −0.430065 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −48121.5 | −2.11478 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1086.86 | −0.0475859 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3567.18 | −0.155602 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3956.52 | 0.171946 | 0.0859728 | − | 0.996297i | \(-0.472600\pi\) | ||||
0.0859728 | + | 0.996297i | \(0.472600\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21542.7 | −0.932759 | −0.466379 | − | 0.884585i | \(-0.654442\pi\) | ||||
−0.466379 | + | 0.884585i | \(0.654442\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7985.45 | 0.344480 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2339.11 | 0.100534 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −65979.0 | −2.82535 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 236.489 | 0.0100898 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3362.75 | 0.142948 | 0.0714742 | − | 0.997442i | \(-0.477230\pi\) | ||||
0.0714742 | + | 0.997442i | \(0.477230\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35734.9 | 1.51354 | 0.756768 | − | 0.653683i | \(-0.226777\pi\) | ||||
0.756768 | + | 0.653683i | \(0.226777\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21002.8 | 0.886332 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3687.52 | 0.155052 | 0.0775258 | − | 0.996990i | \(-0.475298\pi\) | ||||
0.0775258 | + | 0.996990i | \(0.475298\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8365.15 | 0.350463 | 0.175231 | − | 0.984527i | \(-0.443933\pi\) | ||||
0.175231 | + | 0.984527i | \(0.443933\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25916.2 | 1.08186 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1452.65 | −0.0604216 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2046.24 | −0.0848062 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1038.48 | 0.0428853 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33414.8 | 1.37498 | 0.687490 | − | 0.726194i | \(-0.258713\pi\) | ||||
0.687490 | + | 0.726194i | \(0.258713\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1907.18 | −0.0781985 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20855.0 | 0.852058 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1914.18 | −0.0779288 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12913.5 | 0.523866 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9693.64 | −0.391855 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15276.3 | 0.615354 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22959.6 | 0.921597 | 0.460798 | − | 0.887505i | \(-0.347563\pi\) | ||||
0.460798 | + | 0.887505i | \(0.347563\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1072.84 | −0.0429127 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1835.34 | 0.0731553 | 0.0365777 | − | 0.999331i | \(-0.488354\pi\) | ||||
0.0365777 | + | 0.999331i | \(0.488354\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15520.2 | −0.616463 | −0.308232 | − | 0.951311i | \(-0.599737\pi\) | ||||
−0.308232 | + | 0.951311i | \(0.599737\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1228.70 | −0.0486341 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3343.74 | −0.131891 | −0.0659456 | − | 0.997823i | \(-0.521006\pi\) | ||||
−0.0659456 | + | 0.997823i | \(0.521006\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2202.19 | −0.0865625 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12102.4 | 0.474069 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13020.6 | 0.508277 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2667.96 | 0.103789 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5707.40 | 0.221267 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1529.85 | −0.0591065 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12103.7 | 0.466035 | 0.233017 | − | 0.972473i | \(-0.425140\pi\) | ||||
0.233017 | + | 0.972473i | \(0.425140\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12812.7 | −0.491650 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30396.5 | −1.16241 | −0.581206 | − | 0.813757i | \(-0.697419\pi\) | ||||
−0.581206 | + | 0.813757i | \(0.697419\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48003.3 | 1.82949 | 0.914746 | − | 0.404030i | \(-0.132391\pi\) | ||||
0.914746 | + | 0.404030i | \(0.132391\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1914.25 | −0.0727083 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46162.9 | 1.74746 | 0.873730 | − | 0.486411i | \(-0.161694\pi\) | ||||
0.873730 | + | 0.486411i | \(0.161694\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9497.38 | −0.358304 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4564.69 | 0.171630 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −42894.5 | −1.60740 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1578.07 | −0.0589375 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1993.97 | 0.0742214 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5766.99 | −0.213949 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4571.86 | 0.169046 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10192.5 | −0.375619 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1374.87 | −0.0504998 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33924.6 | 1.24195 | 0.620975 | − | 0.783830i | \(-0.286737\pi\) | ||||
0.620975 | + | 0.783830i | \(0.286737\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17645.8 | −0.643865 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53863.4 | 1.95892 | 0.979459 | − | 0.201644i | \(-0.0646284\pi\) | ||||
0.979459 | + | 0.201644i | \(0.0646284\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25031.9 | −0.907377 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1810.49 | 0.0654130 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12475.6 | 0.449270 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42709.2 | 1.53302 | 0.766511 | − | 0.642231i | \(-0.221991\pi\) | ||||
0.766511 | + | 0.642231i | \(0.221991\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 856.205 | 0.0306329 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2919.59 | −0.104116 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10718.2 | 0.380987 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16259.9 | −0.576099 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27676.5 | 0.977434 | 0.488717 | − | 0.872442i | \(-0.337465\pi\) | ||||
0.488717 | + | 0.872442i | \(0.337465\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6661.03 | −0.234486 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4098.31 | −0.143808 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1465.00 | −0.0512412 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1942.63 | 0.0677298 | 0.0338649 | − | 0.999426i | \(-0.489218\pi\) | ||||
0.0338649 | + | 0.999426i | \(0.489218\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2261.91 | −0.0786099 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38950.3 | −1.34936 | −0.674679 | − | 0.738112i | \(-0.735718\pi\) | ||||
−0.674679 | + | 0.738112i | \(0.735718\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10359.8 | −0.357754 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −165.733 | −0.00570508 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36704.5 | −1.25949 | −0.629744 | − | 0.776803i | \(-0.716840\pi\) | ||||
−0.629744 | + | 0.776803i | \(0.716840\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3205.41 | −0.109644 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16137.3 | 0.550251 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21115.4 | 0.717729 | 0.358865 | − | 0.933390i | \(-0.383164\pi\) | ||||
0.358865 | + | 0.933390i | \(0.383164\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3304.57 | −0.111972 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −25349.1 | −0.856239 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6857.90 | −0.230921 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28311.7 | −0.950343 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1086.46 | 0.0363559 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2139.68 | 0.0713769 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48141.5 | 1.60096 | 0.800479 | − | 0.599360i | \(-0.204578\pi\) | ||||
0.800479 | + | 0.599360i | \(0.204578\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12090.1 | −0.400816 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23997.8 | −0.793128 | −0.396564 | − | 0.918007i | \(-0.629798\pi\) | ||||
−0.396564 | + | 0.918007i | \(0.629798\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4453.80 | 0.146744 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1399.01 | 0.0459530 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16720.0 | −0.547513 | −0.273756 | − | 0.961799i | \(-0.588266\pi\) | ||||
−0.273756 | + | 0.961799i | \(0.588266\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −61047.2 | −1.99293 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10972.5 | −0.357110 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29992.3 | −0.973150 | −0.486575 | − | 0.873639i | \(-0.661754\pi\) | ||||
−0.486575 | + | 0.873639i | \(0.661754\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2230.56 | 0.0721538 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6626.37 | −0.213698 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −85938.3 | −2.76307 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10445.9 | −0.334838 | −0.167419 | − | 0.985886i | \(-0.553543\pi\) | ||||
−0.167419 | + | 0.985886i | \(0.553543\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24030.8 | 0.767969 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 947.425 | 0.0301863 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1464.38 | −0.0465168 | −0.0232584 | − | 0.999729i | \(-0.507404\pi\) | ||||
−0.0232584 | + | 0.999729i | \(0.507404\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2329.47 | 0.0737748 |
(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 | 1344.4.a.bj.1.1 | 2 | ||
4.3 | odd | 2 | 1344.4.a.br.1.1 | 2 | |||
8.3 | odd | 2 | 672.4.a.e.1.2 | ✓ | 2 | ||
8.5 | even | 2 | 672.4.a.j.1.2 | yes | 2 | ||
24.5 | odd | 2 | 2016.4.a.r.1.1 | 2 | |||
24.11 | even | 2 | 2016.4.a.q.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.a.e.1.2 | ✓ | 2 | 8.3 | odd | 2 | ||
672.4.a.j.1.2 | yes | 2 | 8.5 | even | 2 | ||
1344.4.a.bj.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1344.4.a.br.1.1 | 2 | 4.3 | odd | 2 | |||
2016.4.a.q.1.1 | 2 | 24.11 | even | 2 | |||
2016.4.a.r.1.1 | 2 | 24.5 | odd | 2 |