Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,4,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2013.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(118.770844842\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.79323 | −1.69466 | −0.847332 | − | 0.531064i | \(-0.821793\pi\) | ||||
−0.847332 | + | 0.531064i | \(0.821793\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 14.9751 | 1.87189 | ||||||||
\(5\) | −18.8616 | −1.68703 | −0.843517 | − | 0.537103i | \(-0.819519\pi\) | ||||
−0.843517 | + | 0.537103i | \(0.819519\pi\) | |||||||
\(6\) | 14.3797 | 0.978415 | ||||||||
\(7\) | −18.5258 | −1.00030 | −0.500151 | − | 0.865938i | \(-0.666722\pi\) | ||||
−0.500151 | + | 0.865938i | \(0.666722\pi\) | |||||||
\(8\) | −33.4332 | −1.47755 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 90.4081 | 2.85896 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | −44.9253 | −1.08073 | ||||||||
\(13\) | 58.9290 | 1.25723 | 0.628614 | − | 0.777718i | \(-0.283623\pi\) | ||||
0.628614 | + | 0.777718i | \(0.283623\pi\) | |||||||
\(14\) | 88.7987 | 1.69517 | ||||||||
\(15\) | 56.5848 | 0.974009 | ||||||||
\(16\) | 40.4525 | 0.632070 | ||||||||
\(17\) | −109.455 | −1.56157 | −0.780784 | − | 0.624801i | \(-0.785180\pi\) | ||||
−0.780784 | + | 0.624801i | \(0.785180\pi\) | |||||||
\(18\) | −43.1391 | −0.564888 | ||||||||
\(19\) | 9.97788 | 0.120478 | 0.0602390 | − | 0.998184i | \(-0.480814\pi\) | ||||
0.0602390 | + | 0.998184i | \(0.480814\pi\) | |||||||
\(20\) | −282.454 | −3.15793 | ||||||||
\(21\) | 55.5775 | 0.577524 | ||||||||
\(22\) | 52.7256 | 0.510960 | ||||||||
\(23\) | 22.2452 | 0.201671 | 0.100836 | − | 0.994903i | \(-0.467848\pi\) | ||||
0.100836 | + | 0.994903i | \(0.467848\pi\) | |||||||
\(24\) | 100.300 | 0.853066 | ||||||||
\(25\) | 230.760 | 1.84608 | ||||||||
\(26\) | −282.460 | −2.13058 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −277.426 | −1.87245 | ||||||||
\(29\) | 23.1129 | 0.147999 | 0.0739993 | − | 0.997258i | \(-0.476424\pi\) | ||||
0.0739993 | + | 0.997258i | \(0.476424\pi\) | |||||||
\(30\) | −271.224 | −1.65062 | ||||||||
\(31\) | 40.4720 | 0.234484 | 0.117242 | − | 0.993103i | \(-0.462595\pi\) | ||||
0.117242 | + | 0.993103i | \(0.462595\pi\) | |||||||
\(32\) | 73.5674 | 0.406406 | ||||||||
\(33\) | 33.0000 | 0.174078 | ||||||||
\(34\) | 524.642 | 2.64633 | ||||||||
\(35\) | 349.427 | 1.68754 | ||||||||
\(36\) | 134.776 | 0.623962 | ||||||||
\(37\) | 96.3869 | 0.428268 | 0.214134 | − | 0.976804i | \(-0.431307\pi\) | ||||
0.214134 | + | 0.976804i | \(0.431307\pi\) | |||||||
\(38\) | −47.8263 | −0.204170 | ||||||||
\(39\) | −176.787 | −0.725861 | ||||||||
\(40\) | 630.604 | 2.49268 | ||||||||
\(41\) | −78.4205 | −0.298713 | −0.149356 | − | 0.988783i | \(-0.547720\pi\) | ||||
−0.149356 | + | 0.988783i | \(0.547720\pi\) | |||||||
\(42\) | −266.396 | −0.978710 | ||||||||
\(43\) | −29.9808 | −0.106326 | −0.0531631 | − | 0.998586i | \(-0.516930\pi\) | ||||
−0.0531631 | + | 0.998586i | \(0.516930\pi\) | |||||||
\(44\) | −164.726 | −0.564395 | ||||||||
\(45\) | −169.754 | −0.562345 | ||||||||
\(46\) | −106.626 | −0.341765 | ||||||||
\(47\) | 173.214 | 0.537572 | 0.268786 | − | 0.963200i | \(-0.413378\pi\) | ||||
0.268786 | + | 0.963200i | \(0.413378\pi\) | |||||||
\(48\) | −121.358 | −0.364926 | ||||||||
\(49\) | 0.206858 | 0.000603085 0 | ||||||||
\(50\) | −1106.09 | −3.12849 | ||||||||
\(51\) | 328.364 | 0.901571 | ||||||||
\(52\) | 882.467 | 2.35339 | ||||||||
\(53\) | −132.685 | −0.343880 | −0.171940 | − | 0.985107i | \(-0.555003\pi\) | ||||
−0.171940 | + | 0.985107i | \(0.555003\pi\) | |||||||
\(54\) | 129.417 | 0.326138 | ||||||||
\(55\) | 207.478 | 0.508660 | ||||||||
\(56\) | 619.378 | 1.47800 | ||||||||
\(57\) | −29.9336 | −0.0695580 | ||||||||
\(58\) | −110.786 | −0.250808 | ||||||||
\(59\) | −309.354 | −0.682618 | −0.341309 | − | 0.939951i | \(-0.610870\pi\) | ||||
−0.341309 | + | 0.939951i | \(0.610870\pi\) | |||||||
\(60\) | 847.363 | 1.82323 | ||||||||
\(61\) | −61.0000 | −0.128037 | ||||||||
\(62\) | −193.992 | −0.397371 | ||||||||
\(63\) | −166.733 | −0.333434 | ||||||||
\(64\) | −676.246 | −1.32079 | ||||||||
\(65\) | −1111.50 | −2.12099 | ||||||||
\(66\) | −158.177 | −0.295003 | ||||||||
\(67\) | 103.354 | 0.188458 | 0.0942290 | − | 0.995551i | \(-0.469961\pi\) | ||||
0.0942290 | + | 0.995551i | \(0.469961\pi\) | |||||||
\(68\) | −1639.09 | −2.92308 | ||||||||
\(69\) | −66.7355 | −0.116435 | ||||||||
\(70\) | −1674.89 | −2.85982 | ||||||||
\(71\) | −489.246 | −0.817787 | −0.408893 | − | 0.912582i | \(-0.634085\pi\) | ||||
−0.408893 | + | 0.912582i | \(0.634085\pi\) | |||||||
\(72\) | −300.899 | −0.492518 | ||||||||
\(73\) | 79.7769 | 0.127906 | 0.0639532 | − | 0.997953i | \(-0.479629\pi\) | ||||
0.0639532 | + | 0.997953i | \(0.479629\pi\) | |||||||
\(74\) | −462.005 | −0.725770 | ||||||||
\(75\) | −692.281 | −1.06584 | ||||||||
\(76\) | 149.420 | 0.225521 | ||||||||
\(77\) | 203.784 | 0.301602 | ||||||||
\(78\) | 847.381 | 1.23009 | ||||||||
\(79\) | −337.338 | −0.480424 | −0.240212 | − | 0.970720i | \(-0.577217\pi\) | ||||
−0.240212 | + | 0.970720i | \(0.577217\pi\) | |||||||
\(80\) | −762.999 | −1.06632 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 375.888 | 0.506218 | ||||||||
\(83\) | −640.928 | −0.847602 | −0.423801 | − | 0.905755i | \(-0.639304\pi\) | ||||
−0.423801 | + | 0.905755i | \(0.639304\pi\) | |||||||
\(84\) | 832.278 | 1.08106 | ||||||||
\(85\) | 2064.49 | 2.63442 | ||||||||
\(86\) | 143.705 | 0.180187 | ||||||||
\(87\) | −69.3387 | −0.0854470 | ||||||||
\(88\) | 367.765 | 0.445499 | ||||||||
\(89\) | 219.386 | 0.261291 | 0.130646 | − | 0.991429i | \(-0.458295\pi\) | ||||
0.130646 | + | 0.991429i | \(0.458295\pi\) | |||||||
\(90\) | 813.673 | 0.952985 | ||||||||
\(91\) | −1091.71 | −1.25761 | ||||||||
\(92\) | 333.123 | 0.377505 | ||||||||
\(93\) | −121.416 | −0.135379 | ||||||||
\(94\) | −830.256 | −0.911003 | ||||||||
\(95\) | −188.199 | −0.203250 | ||||||||
\(96\) | −220.702 | −0.234639 | ||||||||
\(97\) | 43.0051 | 0.0450155 | 0.0225078 | − | 0.999747i | \(-0.492835\pi\) | ||||
0.0225078 | + | 0.999747i | \(0.492835\pi\) | |||||||
\(98\) | −0.991519 | −0.00102203 | ||||||||
\(99\) | −99.0000 | −0.100504 | ||||||||
\(100\) | 3455.66 | 3.45566 | ||||||||
\(101\) | −1294.03 | −1.27486 | −0.637429 | − | 0.770509i | \(-0.720002\pi\) | ||||
−0.637429 | + | 0.770509i | \(0.720002\pi\) | |||||||
\(102\) | −1573.92 | −1.52786 | ||||||||
\(103\) | −691.875 | −0.661869 | −0.330934 | − | 0.943654i | \(-0.607364\pi\) | ||||
−0.330934 | + | 0.943654i | \(0.607364\pi\) | |||||||
\(104\) | −1970.19 | −1.85762 | ||||||||
\(105\) | −1048.28 | −0.974303 | ||||||||
\(106\) | 635.988 | 0.582760 | ||||||||
\(107\) | 976.022 | 0.881828 | 0.440914 | − | 0.897549i | \(-0.354654\pi\) | ||||
0.440914 | + | 0.897549i | \(0.354654\pi\) | |||||||
\(108\) | −404.327 | −0.360245 | ||||||||
\(109\) | −863.019 | −0.758369 | −0.379184 | − | 0.925321i | \(-0.623795\pi\) | ||||
−0.379184 | + | 0.925321i | \(0.623795\pi\) | |||||||
\(110\) | −994.489 | −0.862007 | ||||||||
\(111\) | −289.161 | −0.247261 | ||||||||
\(112\) | −749.417 | −0.632261 | ||||||||
\(113\) | −1057.91 | −0.880706 | −0.440353 | − | 0.897825i | \(-0.645147\pi\) | ||||
−0.440353 | + | 0.897825i | \(0.645147\pi\) | |||||||
\(114\) | 143.479 | 0.117877 | ||||||||
\(115\) | −419.580 | −0.340226 | ||||||||
\(116\) | 346.118 | 0.277036 | ||||||||
\(117\) | 530.361 | 0.419076 | ||||||||
\(118\) | 1482.80 | 1.15681 | ||||||||
\(119\) | 2027.74 | 1.56204 | ||||||||
\(120\) | −1891.81 | −1.43915 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 292.387 | 0.216979 | ||||||||
\(123\) | 235.261 | 0.172462 | ||||||||
\(124\) | 606.072 | 0.438926 | ||||||||
\(125\) | −1994.81 | −1.42737 | ||||||||
\(126\) | 799.188 | 0.565058 | ||||||||
\(127\) | 562.287 | 0.392873 | 0.196437 | − | 0.980517i | \(-0.437063\pi\) | ||||
0.196437 | + | 0.980517i | \(0.437063\pi\) | |||||||
\(128\) | 2652.86 | 1.83189 | ||||||||
\(129\) | 89.9423 | 0.0613874 | ||||||||
\(130\) | 5327.66 | 3.59436 | ||||||||
\(131\) | 52.1834 | 0.0348037 | 0.0174018 | − | 0.999849i | \(-0.494461\pi\) | ||||
0.0174018 | + | 0.999849i | \(0.494461\pi\) | |||||||
\(132\) | 494.178 | 0.325853 | ||||||||
\(133\) | −184.849 | −0.120514 | ||||||||
\(134\) | −495.399 | −0.319373 | ||||||||
\(135\) | 509.263 | 0.324670 | ||||||||
\(136\) | 3659.42 | 2.30730 | ||||||||
\(137\) | 438.281 | 0.273320 | 0.136660 | − | 0.990618i | \(-0.456363\pi\) | ||||
0.136660 | + | 0.990618i | \(0.456363\pi\) | |||||||
\(138\) | 319.879 | 0.197318 | ||||||||
\(139\) | −989.299 | −0.603678 | −0.301839 | − | 0.953359i | \(-0.597600\pi\) | ||||
−0.301839 | + | 0.953359i | \(0.597600\pi\) | |||||||
\(140\) | 5232.70 | 3.15889 | ||||||||
\(141\) | −519.642 | −0.310367 | ||||||||
\(142\) | 2345.07 | 1.38587 | ||||||||
\(143\) | −648.219 | −0.379068 | ||||||||
\(144\) | 364.073 | 0.210690 | ||||||||
\(145\) | −435.946 | −0.249679 | ||||||||
\(146\) | −382.389 | −0.216759 | ||||||||
\(147\) | −0.620574 | −0.000348191 0 | ||||||||
\(148\) | 1443.40 | 0.801669 | ||||||||
\(149\) | −2484.38 | −1.36596 | −0.682981 | − | 0.730436i | \(-0.739317\pi\) | ||||
−0.682981 | + | 0.730436i | \(0.739317\pi\) | |||||||
\(150\) | 3318.26 | 1.80623 | ||||||||
\(151\) | −2543.02 | −1.37052 | −0.685258 | − | 0.728300i | \(-0.740311\pi\) | ||||
−0.685258 | + | 0.728300i | \(0.740311\pi\) | |||||||
\(152\) | −333.593 | −0.178013 | ||||||||
\(153\) | −985.092 | −0.520522 | ||||||||
\(154\) | −976.786 | −0.511114 | ||||||||
\(155\) | −763.368 | −0.395582 | ||||||||
\(156\) | −2647.40 | −1.35873 | ||||||||
\(157\) | −136.047 | −0.0691576 | −0.0345788 | − | 0.999402i | \(-0.511009\pi\) | ||||
−0.0345788 | + | 0.999402i | \(0.511009\pi\) | |||||||
\(158\) | 1616.94 | 0.814157 | ||||||||
\(159\) | 398.054 | 0.198539 | ||||||||
\(160\) | −1387.60 | −0.685621 | ||||||||
\(161\) | −412.110 | −0.201732 | ||||||||
\(162\) | −388.252 | −0.188296 | ||||||||
\(163\) | −2537.25 | −1.21922 | −0.609611 | − | 0.792701i | \(-0.708674\pi\) | ||||
−0.609611 | + | 0.792701i | \(0.708674\pi\) | |||||||
\(164\) | −1174.35 | −0.559156 | ||||||||
\(165\) | −622.433 | −0.293675 | ||||||||
\(166\) | 3072.12 | 1.43640 | ||||||||
\(167\) | −406.687 | −0.188446 | −0.0942228 | − | 0.995551i | \(-0.530037\pi\) | ||||
−0.0942228 | + | 0.995551i | \(0.530037\pi\) | |||||||
\(168\) | −1858.14 | −0.853323 | ||||||||
\(169\) | 1275.63 | 0.580622 | ||||||||
\(170\) | −9895.58 | −4.46445 | ||||||||
\(171\) | 89.8009 | 0.0401593 | ||||||||
\(172\) | −448.964 | −0.199030 | ||||||||
\(173\) | 3353.97 | 1.47398 | 0.736988 | − | 0.675906i | \(-0.236247\pi\) | ||||
0.736988 | + | 0.675906i | \(0.236247\pi\) | |||||||
\(174\) | 332.357 | 0.144804 | ||||||||
\(175\) | −4275.03 | −1.84664 | ||||||||
\(176\) | −444.978 | −0.190576 | ||||||||
\(177\) | 928.061 | 0.394109 | ||||||||
\(178\) | −1051.57 | −0.442801 | ||||||||
\(179\) | −4696.73 | −1.96117 | −0.980587 | − | 0.196087i | \(-0.937177\pi\) | ||||
−0.980587 | + | 0.196087i | \(0.937177\pi\) | |||||||
\(180\) | −2542.09 | −1.05264 | ||||||||
\(181\) | 1335.68 | 0.548510 | 0.274255 | − | 0.961657i | \(-0.411569\pi\) | ||||
0.274255 | + | 0.961657i | \(0.411569\pi\) | |||||||
\(182\) | 5232.82 | 2.13122 | ||||||||
\(183\) | 183.000 | 0.0739221 | ||||||||
\(184\) | −743.727 | −0.297980 | ||||||||
\(185\) | −1818.01 | −0.722503 | ||||||||
\(186\) | 581.976 | 0.229422 | ||||||||
\(187\) | 1204.00 | 0.470830 | ||||||||
\(188\) | 2593.90 | 1.00627 | ||||||||
\(189\) | 500.198 | 0.192508 | ||||||||
\(190\) | 902.081 | 0.344441 | ||||||||
\(191\) | −1041.63 | −0.394605 | −0.197303 | − | 0.980343i | \(-0.563218\pi\) | ||||
−0.197303 | + | 0.980343i | \(0.563218\pi\) | |||||||
\(192\) | 2028.74 | 0.762560 | ||||||||
\(193\) | −2512.80 | −0.937178 | −0.468589 | − | 0.883416i | \(-0.655237\pi\) | ||||
−0.468589 | + | 0.883416i | \(0.655237\pi\) | |||||||
\(194\) | −206.133 | −0.0762862 | ||||||||
\(195\) | 3334.49 | 1.22455 | ||||||||
\(196\) | 3.09772 | 0.00112891 | ||||||||
\(197\) | −3428.63 | −1.24000 | −0.620000 | − | 0.784602i | \(-0.712867\pi\) | ||||
−0.620000 | + | 0.784602i | \(0.712867\pi\) | |||||||
\(198\) | 474.530 | 0.170320 | ||||||||
\(199\) | −3527.37 | −1.25652 | −0.628262 | − | 0.778002i | \(-0.716233\pi\) | ||||
−0.628262 | + | 0.778002i | \(0.716233\pi\) | |||||||
\(200\) | −7715.06 | −2.72769 | ||||||||
\(201\) | −310.062 | −0.108806 | ||||||||
\(202\) | 6202.59 | 2.16046 | ||||||||
\(203\) | −428.186 | −0.148043 | ||||||||
\(204\) | 4917.28 | 1.68764 | ||||||||
\(205\) | 1479.14 | 0.503938 | ||||||||
\(206\) | 3316.32 | 1.12165 | ||||||||
\(207\) | 200.206 | 0.0672237 | ||||||||
\(208\) | 2383.83 | 0.794656 | ||||||||
\(209\) | −109.757 | −0.0363255 | ||||||||
\(210\) | 5024.66 | 1.65112 | ||||||||
\(211\) | 772.916 | 0.252179 | 0.126089 | − | 0.992019i | \(-0.459757\pi\) | ||||
0.126089 | + | 0.992019i | \(0.459757\pi\) | |||||||
\(212\) | −1986.96 | −0.643703 | ||||||||
\(213\) | 1467.74 | 0.472149 | ||||||||
\(214\) | −4678.30 | −1.49440 | ||||||||
\(215\) | 565.485 | 0.179376 | ||||||||
\(216\) | 902.697 | 0.284355 | ||||||||
\(217\) | −749.778 | −0.234554 | ||||||||
\(218\) | 4136.65 | 1.28518 | ||||||||
\(219\) | −239.331 | −0.0738468 | ||||||||
\(220\) | 3107.00 | 0.952153 | ||||||||
\(221\) | −6450.05 | −1.96325 | ||||||||
\(222\) | 1386.02 | 0.419024 | ||||||||
\(223\) | 5306.49 | 1.59349 | 0.796746 | − | 0.604314i | \(-0.206553\pi\) | ||||
0.796746 | + | 0.604314i | \(0.206553\pi\) | |||||||
\(224\) | −1362.90 | −0.406529 | ||||||||
\(225\) | 2076.84 | 0.615361 | ||||||||
\(226\) | 5070.81 | 1.49250 | ||||||||
\(227\) | −1625.41 | −0.475251 | −0.237626 | − | 0.971357i | \(-0.576369\pi\) | ||||
−0.237626 | + | 0.971357i | \(0.576369\pi\) | |||||||
\(228\) | −448.259 | −0.130205 | ||||||||
\(229\) | −2780.64 | −0.802402 | −0.401201 | − | 0.915990i | \(-0.631407\pi\) | ||||
−0.401201 | + | 0.915990i | \(0.631407\pi\) | |||||||
\(230\) | 2011.14 | 0.576569 | ||||||||
\(231\) | −611.353 | −0.174130 | ||||||||
\(232\) | −772.738 | −0.218676 | ||||||||
\(233\) | −4367.06 | −1.22788 | −0.613939 | − | 0.789353i | \(-0.710416\pi\) | ||||
−0.613939 | + | 0.789353i | \(0.710416\pi\) | |||||||
\(234\) | −2542.14 | −0.710193 | ||||||||
\(235\) | −3267.10 | −0.906902 | ||||||||
\(236\) | −4632.60 | −1.27778 | ||||||||
\(237\) | 1012.01 | 0.277373 | ||||||||
\(238\) | −9719.43 | −2.64713 | ||||||||
\(239\) | 1421.27 | 0.384663 | 0.192331 | − | 0.981330i | \(-0.438395\pi\) | ||||
0.192331 | + | 0.981330i | \(0.438395\pi\) | |||||||
\(240\) | 2289.00 | 0.615642 | ||||||||
\(241\) | 910.885 | 0.243466 | 0.121733 | − | 0.992563i | \(-0.461155\pi\) | ||||
0.121733 | + | 0.992563i | \(0.461155\pi\) | |||||||
\(242\) | −579.981 | −0.154060 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −913.480 | −0.239670 | ||||||||
\(245\) | −3.90168 | −0.00101742 | ||||||||
\(246\) | −1127.66 | −0.292265 | ||||||||
\(247\) | 587.986 | 0.151468 | ||||||||
\(248\) | −1353.11 | −0.346462 | ||||||||
\(249\) | 1922.78 | 0.489363 | ||||||||
\(250\) | 9561.59 | 2.41891 | ||||||||
\(251\) | −3620.98 | −0.910574 | −0.455287 | − | 0.890345i | \(-0.650463\pi\) | ||||
−0.455287 | + | 0.890345i | \(0.650463\pi\) | |||||||
\(252\) | −2496.83 | −0.624150 | ||||||||
\(253\) | −244.697 | −0.0608061 | ||||||||
\(254\) | −2695.17 | −0.665788 | ||||||||
\(255\) | −6193.47 | −1.52098 | ||||||||
\(256\) | −7305.83 | −1.78365 | ||||||||
\(257\) | −7784.06 | −1.88932 | −0.944662 | − | 0.328046i | \(-0.893610\pi\) | ||||
−0.944662 | + | 0.328046i | \(0.893610\pi\) | |||||||
\(258\) | −431.114 | −0.104031 | ||||||||
\(259\) | −1785.65 | −0.428397 | ||||||||
\(260\) | −16644.7 | −3.97024 | ||||||||
\(261\) | 208.016 | 0.0493328 | ||||||||
\(262\) | −250.127 | −0.0589805 | ||||||||
\(263\) | 692.609 | 0.162388 | 0.0811941 | − | 0.996698i | \(-0.474127\pi\) | ||||
0.0811941 | + | 0.996698i | \(0.474127\pi\) | |||||||
\(264\) | −1103.30 | −0.257209 | ||||||||
\(265\) | 2502.64 | 0.580136 | ||||||||
\(266\) | 886.023 | 0.204231 | ||||||||
\(267\) | −658.159 | −0.150856 | ||||||||
\(268\) | 1547.73 | 0.352772 | ||||||||
\(269\) | −4169.68 | −0.945093 | −0.472547 | − | 0.881306i | \(-0.656665\pi\) | ||||
−0.472547 | + | 0.881306i | \(0.656665\pi\) | |||||||
\(270\) | −2441.02 | −0.550206 | ||||||||
\(271\) | 5151.66 | 1.15476 | 0.577382 | − | 0.816474i | \(-0.304074\pi\) | ||||
0.577382 | + | 0.816474i | \(0.304074\pi\) | |||||||
\(272\) | −4427.71 | −0.987020 | ||||||||
\(273\) | 3275.13 | 0.726080 | ||||||||
\(274\) | −2100.78 | −0.463186 | ||||||||
\(275\) | −2538.36 | −0.556615 | ||||||||
\(276\) | −999.369 | −0.217953 | ||||||||
\(277\) | 1033.41 | 0.224158 | 0.112079 | − | 0.993699i | \(-0.464249\pi\) | ||||
0.112079 | + | 0.993699i | \(0.464249\pi\) | |||||||
\(278\) | 4741.94 | 1.02303 | ||||||||
\(279\) | 364.248 | 0.0781612 | ||||||||
\(280\) | −11682.5 | −2.49343 | ||||||||
\(281\) | 6683.56 | 1.41889 | 0.709444 | − | 0.704762i | \(-0.248946\pi\) | ||||
0.709444 | + | 0.704762i | \(0.248946\pi\) | |||||||
\(282\) | 2490.77 | 0.525968 | ||||||||
\(283\) | 7916.57 | 1.66287 | 0.831434 | − | 0.555624i | \(-0.187521\pi\) | ||||
0.831434 | + | 0.555624i | \(0.187521\pi\) | |||||||
\(284\) | −7326.51 | −1.53080 | ||||||||
\(285\) | 564.597 | 0.117347 | ||||||||
\(286\) | 3107.06 | 0.642394 | ||||||||
\(287\) | 1452.81 | 0.298803 | ||||||||
\(288\) | 662.107 | 0.135469 | ||||||||
\(289\) | 7067.31 | 1.43849 | ||||||||
\(290\) | 2089.59 | 0.423121 | ||||||||
\(291\) | −129.015 | −0.0259897 | ||||||||
\(292\) | 1194.67 | 0.239426 | ||||||||
\(293\) | −6375.73 | −1.27124 | −0.635622 | − | 0.772001i | \(-0.719256\pi\) | ||||
−0.635622 | + | 0.772001i | \(0.719256\pi\) | |||||||
\(294\) | 2.97456 | 0.000590067 0 | ||||||||
\(295\) | 5834.91 | 1.15160 | ||||||||
\(296\) | −3222.53 | −0.632789 | ||||||||
\(297\) | 297.000 | 0.0580259 | ||||||||
\(298\) | 11908.2 | 2.31485 | ||||||||
\(299\) | 1310.88 | 0.253547 | ||||||||
\(300\) | −10367.0 | −1.99512 | ||||||||
\(301\) | 555.419 | 0.106358 | ||||||||
\(302\) | 12189.3 | 2.32256 | ||||||||
\(303\) | 3882.09 | 0.736040 | ||||||||
\(304\) | 403.630 | 0.0761506 | ||||||||
\(305\) | 1150.56 | 0.216003 | ||||||||
\(306\) | 4721.77 | 0.882111 | ||||||||
\(307\) | −4931.49 | −0.916792 | −0.458396 | − | 0.888748i | \(-0.651576\pi\) | ||||
−0.458396 | + | 0.888748i | \(0.651576\pi\) | |||||||
\(308\) | 3051.69 | 0.564565 | ||||||||
\(309\) | 2075.63 | 0.382130 | ||||||||
\(310\) | 3659.00 | 0.670378 | ||||||||
\(311\) | 4864.56 | 0.886958 | 0.443479 | − | 0.896285i | \(-0.353744\pi\) | ||||
0.443479 | + | 0.896285i | \(0.353744\pi\) | |||||||
\(312\) | 5910.56 | 1.07250 | ||||||||
\(313\) | 6219.53 | 1.12316 | 0.561579 | − | 0.827423i | \(-0.310194\pi\) | ||||
0.561579 | + | 0.827423i | \(0.310194\pi\) | |||||||
\(314\) | 652.106 | 0.117199 | ||||||||
\(315\) | 3144.84 | 0.562514 | ||||||||
\(316\) | −5051.66 | −0.899298 | ||||||||
\(317\) | 7094.59 | 1.25701 | 0.628505 | − | 0.777806i | \(-0.283667\pi\) | ||||
0.628505 | + | 0.777806i | \(0.283667\pi\) | |||||||
\(318\) | −1907.96 | −0.336457 | ||||||||
\(319\) | −254.242 | −0.0446232 | ||||||||
\(320\) | 12755.1 | 2.22822 | ||||||||
\(321\) | −2928.07 | −0.509124 | ||||||||
\(322\) | 1975.34 | 0.341868 | ||||||||
\(323\) | −1092.12 | −0.188135 | ||||||||
\(324\) | 1212.98 | 0.207987 | ||||||||
\(325\) | 13598.5 | 2.32095 | ||||||||
\(326\) | 12161.7 | 2.06617 | ||||||||
\(327\) | 2589.06 | 0.437844 | ||||||||
\(328\) | 2621.85 | 0.441364 | ||||||||
\(329\) | −3208.94 | −0.537734 | ||||||||
\(330\) | 2983.47 | 0.497680 | ||||||||
\(331\) | 6.12699 | 0.00101743 | 0.000508715 | − | 1.00000i | \(-0.499838\pi\) | ||||
0.000508715 | 1.00000i | \(0.499838\pi\) | ||||||||
\(332\) | −9597.95 | −1.58661 | ||||||||
\(333\) | 867.483 | 0.142756 | ||||||||
\(334\) | 1949.35 | 0.319352 | ||||||||
\(335\) | −1949.42 | −0.317935 | ||||||||
\(336\) | 2248.25 | 0.365036 | ||||||||
\(337\) | −9683.53 | −1.56527 | −0.782634 | − | 0.622482i | \(-0.786124\pi\) | ||||
−0.782634 | + | 0.622482i | \(0.786124\pi\) | |||||||
\(338\) | −6114.37 | −0.983959 | ||||||||
\(339\) | 3173.73 | 0.508476 | ||||||||
\(340\) | 30915.9 | 4.93133 | ||||||||
\(341\) | −445.192 | −0.0706995 | ||||||||
\(342\) | −430.437 | −0.0680566 | ||||||||
\(343\) | 6350.53 | 0.999698 | ||||||||
\(344\) | 1002.35 | 0.157102 | ||||||||
\(345\) | 1258.74 | 0.196430 | ||||||||
\(346\) | −16076.4 | −2.49789 | ||||||||
\(347\) | 7814.64 | 1.20897 | 0.604484 | − | 0.796617i | \(-0.293379\pi\) | ||||
0.604484 | + | 0.796617i | \(0.293379\pi\) | |||||||
\(348\) | −1038.35 | −0.159947 | ||||||||
\(349\) | −388.966 | −0.0596587 | −0.0298293 | − | 0.999555i | \(-0.509496\pi\) | ||||
−0.0298293 | + | 0.999555i | \(0.509496\pi\) | |||||||
\(350\) | 20491.2 | 3.12943 | ||||||||
\(351\) | −1591.08 | −0.241954 | ||||||||
\(352\) | −809.242 | −0.122536 | ||||||||
\(353\) | −7425.41 | −1.11959 | −0.559794 | − | 0.828632i | \(-0.689120\pi\) | ||||
−0.559794 | + | 0.828632i | \(0.689120\pi\) | |||||||
\(354\) | −4448.41 | −0.667883 | ||||||||
\(355\) | 9227.97 | 1.37963 | ||||||||
\(356\) | 3285.33 | 0.489107 | ||||||||
\(357\) | −6083.22 | −0.901843 | ||||||||
\(358\) | 22512.5 | 3.32353 | ||||||||
\(359\) | 1652.68 | 0.242967 | 0.121484 | − | 0.992593i | \(-0.461235\pi\) | ||||
0.121484 | + | 0.992593i | \(0.461235\pi\) | |||||||
\(360\) | 5675.44 | 0.830894 | ||||||||
\(361\) | −6759.44 | −0.985485 | ||||||||
\(362\) | −6402.23 | −0.929541 | ||||||||
\(363\) | −363.000 | −0.0524864 | ||||||||
\(364\) | −16348.4 | −2.35410 | ||||||||
\(365\) | −1504.72 | −0.215783 | ||||||||
\(366\) | −877.162 | −0.125273 | ||||||||
\(367\) | 4307.76 | 0.612706 | 0.306353 | − | 0.951918i | \(-0.400891\pi\) | ||||
0.306353 | + | 0.951918i | \(0.400891\pi\) | |||||||
\(368\) | 899.872 | 0.127470 | ||||||||
\(369\) | −705.784 | −0.0995709 | ||||||||
\(370\) | 8714.16 | 1.22440 | ||||||||
\(371\) | 2458.09 | 0.343983 | ||||||||
\(372\) | −1818.22 | −0.253414 | ||||||||
\(373\) | 4742.18 | 0.658286 | 0.329143 | − | 0.944280i | \(-0.393240\pi\) | ||||
0.329143 | + | 0.944280i | \(0.393240\pi\) | |||||||
\(374\) | −5771.06 | −0.797899 | ||||||||
\(375\) | 5984.43 | 0.824092 | ||||||||
\(376\) | −5791.10 | −0.794291 | ||||||||
\(377\) | 1362.02 | 0.186068 | ||||||||
\(378\) | −2397.56 | −0.326237 | ||||||||
\(379\) | −8767.91 | −1.18833 | −0.594165 | − | 0.804343i | \(-0.702518\pi\) | ||||
−0.594165 | + | 0.804343i | \(0.702518\pi\) | |||||||
\(380\) | −2818.29 | −0.380462 | ||||||||
\(381\) | −1686.86 | −0.226825 | ||||||||
\(382\) | 4992.77 | 0.668724 | ||||||||
\(383\) | 11781.3 | 1.57179 | 0.785895 | − | 0.618360i | \(-0.212202\pi\) | ||||
0.785895 | + | 0.618360i | \(0.212202\pi\) | |||||||
\(384\) | −7958.59 | −1.05764 | ||||||||
\(385\) | −3843.70 | −0.508813 | ||||||||
\(386\) | 12044.4 | 1.58820 | ||||||||
\(387\) | −269.827 | −0.0354420 | ||||||||
\(388\) | 644.005 | 0.0842639 | ||||||||
\(389\) | 1332.13 | 0.173629 | 0.0868143 | − | 0.996225i | \(-0.472331\pi\) | ||||
0.0868143 | + | 0.996225i | \(0.472331\pi\) | |||||||
\(390\) | −15983.0 | −2.07520 | ||||||||
\(391\) | −2434.84 | −0.314923 | ||||||||
\(392\) | −6.91593 | −0.000891090 0 | ||||||||
\(393\) | −156.550 | −0.0200939 | ||||||||
\(394\) | 16434.2 | 2.10138 | ||||||||
\(395\) | 6362.74 | 0.810491 | ||||||||
\(396\) | −1482.53 | −0.188132 | ||||||||
\(397\) | −11017.4 | −1.39282 | −0.696409 | − | 0.717645i | \(-0.745220\pi\) | ||||
−0.696409 | + | 0.717645i | \(0.745220\pi\) | |||||||
\(398\) | 16907.5 | 2.12939 | ||||||||
\(399\) | 554.546 | 0.0695790 | ||||||||
\(400\) | 9334.83 | 1.16685 | ||||||||
\(401\) | 13120.1 | 1.63388 | 0.816940 | − | 0.576722i | \(-0.195669\pi\) | ||||
0.816940 | + | 0.576722i | \(0.195669\pi\) | |||||||
\(402\) | 1486.20 | 0.184390 | ||||||||
\(403\) | 2384.98 | 0.294799 | ||||||||
\(404\) | −19378.2 | −2.38639 | ||||||||
\(405\) | −1527.79 | −0.187448 | ||||||||
\(406\) | 2052.39 | 0.250883 | ||||||||
\(407\) | −1060.26 | −0.129128 | ||||||||
\(408\) | −10978.3 | −1.33212 | ||||||||
\(409\) | −4856.51 | −0.587137 | −0.293569 | − | 0.955938i | \(-0.594843\pi\) | ||||
−0.293569 | + | 0.955938i | \(0.594843\pi\) | |||||||
\(410\) | −7089.85 | −0.854006 | ||||||||
\(411\) | −1314.84 | −0.157801 | ||||||||
\(412\) | −10360.9 | −1.23894 | ||||||||
\(413\) | 5731.04 | 0.682823 | ||||||||
\(414\) | −959.636 | −0.113922 | ||||||||
\(415\) | 12088.9 | 1.42993 | ||||||||
\(416\) | 4335.25 | 0.510945 | ||||||||
\(417\) | 2967.90 | 0.348534 | ||||||||
\(418\) | 526.089 | 0.0615595 | ||||||||
\(419\) | 4568.10 | 0.532617 | 0.266308 | − | 0.963888i | \(-0.414196\pi\) | ||||
0.266308 | + | 0.963888i | \(0.414196\pi\) | |||||||
\(420\) | −15698.1 | −1.82378 | ||||||||
\(421\) | 5706.02 | 0.660557 | 0.330278 | − | 0.943884i | \(-0.392857\pi\) | ||||
0.330278 | + | 0.943884i | \(0.392857\pi\) | |||||||
\(422\) | −3704.76 | −0.427358 | ||||||||
\(423\) | 1558.93 | 0.179191 | ||||||||
\(424\) | 4436.07 | 0.508100 | ||||||||
\(425\) | −25257.8 | −2.88278 | ||||||||
\(426\) | −7035.22 | −0.800134 | ||||||||
\(427\) | 1130.08 | 0.128075 | ||||||||
\(428\) | 14616.0 | 1.65068 | ||||||||
\(429\) | 1944.66 | 0.218855 | ||||||||
\(430\) | −2710.50 | −0.303982 | ||||||||
\(431\) | 312.058 | 0.0348754 | 0.0174377 | − | 0.999848i | \(-0.494449\pi\) | ||||
0.0174377 | + | 0.999848i | \(0.494449\pi\) | |||||||
\(432\) | −1092.22 | −0.121642 | ||||||||
\(433\) | 15365.2 | 1.70533 | 0.852664 | − | 0.522460i | \(-0.174986\pi\) | ||||
0.852664 | + | 0.522460i | \(0.174986\pi\) | |||||||
\(434\) | 3593.86 | 0.397491 | ||||||||
\(435\) | 1307.84 | 0.144152 | ||||||||
\(436\) | −12923.8 | −1.41958 | ||||||||
\(437\) | 221.960 | 0.0242969 | ||||||||
\(438\) | 1147.17 | 0.125146 | ||||||||
\(439\) | −13092.4 | −1.42339 | −0.711693 | − | 0.702491i | \(-0.752071\pi\) | ||||
−0.711693 | + | 0.702491i | \(0.752071\pi\) | |||||||
\(440\) | −6936.65 | −0.751572 | ||||||||
\(441\) | 1.86172 | 0.000201028 0 | ||||||||
\(442\) | 30916.6 | 3.32704 | ||||||||
\(443\) | 7799.41 | 0.836481 | 0.418241 | − | 0.908336i | \(-0.362647\pi\) | ||||
0.418241 | + | 0.908336i | \(0.362647\pi\) | |||||||
\(444\) | −4330.21 | −0.462844 | ||||||||
\(445\) | −4137.98 | −0.440807 | ||||||||
\(446\) | −25435.2 | −2.70043 | ||||||||
\(447\) | 7453.14 | 0.788639 | ||||||||
\(448\) | 12528.0 | 1.32119 | ||||||||
\(449\) | 16633.3 | 1.74828 | 0.874138 | − | 0.485677i | \(-0.161427\pi\) | ||||
0.874138 | + | 0.485677i | \(0.161427\pi\) | |||||||
\(450\) | −9954.79 | −1.04283 | ||||||||
\(451\) | 862.625 | 0.0900653 | ||||||||
\(452\) | −15842.3 | −1.64858 | ||||||||
\(453\) | 7629.06 | 0.791268 | ||||||||
\(454\) | 7790.95 | 0.805391 | ||||||||
\(455\) | 20591.4 | 2.12163 | ||||||||
\(456\) | 1000.78 | 0.102776 | ||||||||
\(457\) | −5873.50 | −0.601205 | −0.300603 | − | 0.953749i | \(-0.597188\pi\) | ||||
−0.300603 | + | 0.953749i | \(0.597188\pi\) | |||||||
\(458\) | 13328.3 | 1.35980 | ||||||||
\(459\) | 2955.27 | 0.300524 | ||||||||
\(460\) | −6283.24 | −0.636864 | ||||||||
\(461\) | −3848.23 | −0.388785 | −0.194393 | − | 0.980924i | \(-0.562274\pi\) | ||||
−0.194393 | + | 0.980924i | \(0.562274\pi\) | |||||||
\(462\) | 2930.36 | 0.295092 | ||||||||
\(463\) | −12000.7 | −1.20458 | −0.602291 | − | 0.798277i | \(-0.705745\pi\) | ||||
−0.602291 | + | 0.798277i | \(0.705745\pi\) | |||||||
\(464\) | 934.975 | 0.0935455 | ||||||||
\(465\) | 2290.10 | 0.228389 | ||||||||
\(466\) | 20932.3 | 2.08084 | ||||||||
\(467\) | −5908.05 | −0.585422 | −0.292711 | − | 0.956201i | \(-0.594557\pi\) | ||||
−0.292711 | + | 0.956201i | \(0.594557\pi\) | |||||||
\(468\) | 7942.20 | 0.784462 | ||||||||
\(469\) | −1914.72 | −0.188515 | ||||||||
\(470\) | 15660.0 | 1.53689 | ||||||||
\(471\) | 408.141 | 0.0399282 | ||||||||
\(472\) | 10342.7 | 1.00860 | ||||||||
\(473\) | 329.788 | 0.0320585 | ||||||||
\(474\) | −4850.82 | −0.470054 | ||||||||
\(475\) | 2302.50 | 0.222412 | ||||||||
\(476\) | 30365.6 | 2.92396 | ||||||||
\(477\) | −1194.16 | −0.114627 | ||||||||
\(478\) | −6812.48 | −0.651874 | ||||||||
\(479\) | −18102.6 | −1.72679 | −0.863393 | − | 0.504531i | \(-0.831665\pi\) | ||||
−0.863393 | + | 0.504531i | \(0.831665\pi\) | |||||||
\(480\) | 4162.80 | 0.395844 | ||||||||
\(481\) | 5679.99 | 0.538430 | ||||||||
\(482\) | −4366.09 | −0.412593 | ||||||||
\(483\) | 1236.33 | 0.116470 | ||||||||
\(484\) | 1811.99 | 0.170171 | ||||||||
\(485\) | −811.145 | −0.0759427 | ||||||||
\(486\) | 1164.76 | 0.108713 | ||||||||
\(487\) | −7731.38 | −0.719388 | −0.359694 | − | 0.933070i | \(-0.617119\pi\) | ||||
−0.359694 | + | 0.933070i | \(0.617119\pi\) | |||||||
\(488\) | 2039.43 | 0.189181 | ||||||||
\(489\) | 7611.76 | 0.703918 | ||||||||
\(490\) | 18.7016 | 0.00172419 | ||||||||
\(491\) | −11164.5 | −1.02616 | −0.513080 | − | 0.858341i | \(-0.671496\pi\) | ||||
−0.513080 | + | 0.858341i | \(0.671496\pi\) | |||||||
\(492\) | 3523.06 | 0.322829 | ||||||||
\(493\) | −2529.81 | −0.231110 | ||||||||
\(494\) | −2818.36 | −0.256688 | ||||||||
\(495\) | 1867.30 | 0.169553 | ||||||||
\(496\) | 1637.19 | 0.148210 | ||||||||
\(497\) | 9063.70 | 0.818033 | ||||||||
\(498\) | −9216.35 | −0.829306 | ||||||||
\(499\) | 4923.93 | 0.441734 | 0.220867 | − | 0.975304i | \(-0.429111\pi\) | ||||
0.220867 | + | 0.975304i | \(0.429111\pi\) | |||||||
\(500\) | −29872.4 | −2.67187 | ||||||||
\(501\) | 1220.06 | 0.108799 | ||||||||
\(502\) | 17356.2 | 1.54312 | ||||||||
\(503\) | 16329.3 | 1.44749 | 0.723744 | − | 0.690068i | \(-0.242420\pi\) | ||||
0.723744 | + | 0.690068i | \(0.242420\pi\) | |||||||
\(504\) | 5574.41 | 0.492666 | ||||||||
\(505\) | 24407.5 | 2.15073 | ||||||||
\(506\) | 1172.89 | 0.103046 | ||||||||
\(507\) | −3826.88 | −0.335222 | ||||||||
\(508\) | 8420.29 | 0.735414 | ||||||||
\(509\) | 2997.63 | 0.261037 | 0.130518 | − | 0.991446i | \(-0.458336\pi\) | ||||
0.130518 | + | 0.991446i | \(0.458336\pi\) | |||||||
\(510\) | 29686.8 | 2.57755 | ||||||||
\(511\) | −1477.93 | −0.127945 | ||||||||
\(512\) | 13795.6 | 1.19080 | ||||||||
\(513\) | −269.403 | −0.0231860 | ||||||||
\(514\) | 37310.8 | 3.20177 | ||||||||
\(515\) | 13049.9 | 1.11659 | ||||||||
\(516\) | 1346.89 | 0.114910 | ||||||||
\(517\) | −1905.35 | −0.162084 | ||||||||
\(518\) | 8559.03 | 0.725989 | ||||||||
\(519\) | −10061.9 | −0.851001 | ||||||||
\(520\) | 37160.9 | 3.13387 | ||||||||
\(521\) | 12999.6 | 1.09313 | 0.546567 | − | 0.837416i | \(-0.315935\pi\) | ||||
0.546567 | + | 0.837416i | \(0.315935\pi\) | |||||||
\(522\) | −997.070 | −0.0836026 | ||||||||
\(523\) | 747.484 | 0.0624956 | 0.0312478 | − | 0.999512i | \(-0.490052\pi\) | ||||
0.0312478 | + | 0.999512i | \(0.490052\pi\) | |||||||
\(524\) | 781.450 | 0.0651485 | ||||||||
\(525\) | 12825.1 | 1.06616 | ||||||||
\(526\) | −3319.84 | −0.275193 | ||||||||
\(527\) | −4429.85 | −0.366162 | ||||||||
\(528\) | 1334.93 | 0.110029 | ||||||||
\(529\) | −11672.2 | −0.959329 | ||||||||
\(530\) | −11995.8 | −0.983136 | ||||||||
\(531\) | −2784.18 | −0.227539 | ||||||||
\(532\) | −2768.12 | −0.225589 | ||||||||
\(533\) | −4621.24 | −0.375550 | ||||||||
\(534\) | 3154.71 | 0.255651 | ||||||||
\(535\) | −18409.3 | −1.48767 | ||||||||
\(536\) | −3455.45 | −0.278457 | ||||||||
\(537\) | 14090.2 | 1.13228 | ||||||||
\(538\) | 19986.3 | 1.60162 | ||||||||
\(539\) | −2.27544 | −0.000181837 0 | ||||||||
\(540\) | 7626.26 | 0.607745 | ||||||||
\(541\) | 15587.5 | 1.23874 | 0.619370 | − | 0.785099i | \(-0.287388\pi\) | ||||
0.619370 | + | 0.785099i | \(0.287388\pi\) | |||||||
\(542\) | −24693.1 | −1.95694 | ||||||||
\(543\) | −4007.04 | −0.316683 | ||||||||
\(544\) | −8052.29 | −0.634631 | ||||||||
\(545\) | 16277.9 | 1.27939 | ||||||||
\(546\) | −15698.5 | −1.23046 | ||||||||
\(547\) | −1789.45 | −0.139874 | −0.0699371 | − | 0.997551i | \(-0.522280\pi\) | ||||
−0.0699371 | + | 0.997551i | \(0.522280\pi\) | |||||||
\(548\) | 6563.29 | 0.511624 | ||||||||
\(549\) | −549.000 | −0.0426790 | ||||||||
\(550\) | 12167.0 | 0.943275 | ||||||||
\(551\) | 230.618 | 0.0178306 | ||||||||
\(552\) | 2231.18 | 0.172039 | ||||||||
\(553\) | 6249.47 | 0.480569 | ||||||||
\(554\) | −4953.38 | −0.379872 | ||||||||
\(555\) | 5454.04 | 0.417137 | ||||||||
\(556\) | −14814.8 | −1.13002 | ||||||||
\(557\) | 7793.66 | 0.592869 | 0.296434 | − | 0.955053i | \(-0.404202\pi\) | ||||
0.296434 | + | 0.955053i | \(0.404202\pi\) | |||||||
\(558\) | −1745.93 | −0.132457 | ||||||||
\(559\) | −1766.74 | −0.133676 | ||||||||
\(560\) | 14135.2 | 1.06665 | ||||||||
\(561\) | −3612.00 | −0.271834 | ||||||||
\(562\) | −32035.9 | −2.40454 | ||||||||
\(563\) | −1845.05 | −0.138116 | −0.0690581 | − | 0.997613i | \(-0.521999\pi\) | ||||
−0.0690581 | + | 0.997613i | \(0.521999\pi\) | |||||||
\(564\) | −7781.69 | −0.580972 | ||||||||
\(565\) | 19953.9 | 1.48578 | ||||||||
\(566\) | −37946.0 | −2.81800 | ||||||||
\(567\) | −1500.59 | −0.111145 | ||||||||
\(568\) | 16357.1 | 1.20832 | ||||||||
\(569\) | −8875.38 | −0.653911 | −0.326955 | − | 0.945040i | \(-0.606023\pi\) | ||||
−0.326955 | + | 0.945040i | \(0.606023\pi\) | |||||||
\(570\) | −2706.24 | −0.198863 | ||||||||
\(571\) | −8181.61 | −0.599632 | −0.299816 | − | 0.953997i | \(-0.596925\pi\) | ||||
−0.299816 | + | 0.953997i | \(0.596925\pi\) | |||||||
\(572\) | −9707.13 | −0.709573 | ||||||||
\(573\) | 3124.89 | 0.227826 | ||||||||
\(574\) | −6963.64 | −0.506370 | ||||||||
\(575\) | 5133.30 | 0.372302 | ||||||||
\(576\) | −6086.21 | −0.440264 | ||||||||
\(577\) | 25816.5 | 1.86266 | 0.931330 | − | 0.364176i | \(-0.118650\pi\) | ||||
0.931330 | + | 0.364176i | \(0.118650\pi\) | |||||||
\(578\) | −33875.3 | −2.43776 | ||||||||
\(579\) | 7538.40 | 0.541080 | ||||||||
\(580\) | −6528.34 | −0.467370 | ||||||||
\(581\) | 11873.7 | 0.847857 | ||||||||
\(582\) | 618.400 | 0.0440438 | ||||||||
\(583\) | 1459.53 | 0.103684 | ||||||||
\(584\) | −2667.20 | −0.188989 | ||||||||
\(585\) | −10003.5 | −0.706995 | ||||||||
\(586\) | 30560.4 | 2.15433 | ||||||||
\(587\) | −8100.43 | −0.569575 | −0.284788 | − | 0.958591i | \(-0.591923\pi\) | ||||
−0.284788 | + | 0.958591i | \(0.591923\pi\) | |||||||
\(588\) | −9.29315 | −0.000651774 0 | ||||||||
\(589\) | 403.825 | 0.0282501 | ||||||||
\(590\) | −27968.1 | −1.95157 | ||||||||
\(591\) | 10285.9 | 0.715914 | ||||||||
\(592\) | 3899.09 | 0.270696 | ||||||||
\(593\) | −156.409 | −0.0108313 | −0.00541564 | − | 0.999985i | \(-0.501724\pi\) | ||||
−0.00541564 | + | 0.999985i | \(0.501724\pi\) | |||||||
\(594\) | −1423.59 | −0.0983344 | ||||||||
\(595\) | −38246.4 | −2.63521 | ||||||||
\(596\) | −37203.8 | −2.55693 | ||||||||
\(597\) | 10582.1 | 0.725455 | ||||||||
\(598\) | −6283.38 | −0.429676 | ||||||||
\(599\) | −6206.03 | −0.423325 | −0.211662 | − | 0.977343i | \(-0.567888\pi\) | ||||
−0.211662 | + | 0.977343i | \(0.567888\pi\) | |||||||
\(600\) | 23145.2 | 1.57483 | ||||||||
\(601\) | −1228.88 | −0.0834058 | −0.0417029 | − | 0.999130i | \(-0.513278\pi\) | ||||
−0.0417029 | + | 0.999130i | \(0.513278\pi\) | |||||||
\(602\) | −2662.25 | −0.180241 | ||||||||
\(603\) | 930.185 | 0.0628193 | ||||||||
\(604\) | −38081.9 | −2.56545 | ||||||||
\(605\) | −2282.25 | −0.153367 | ||||||||
\(606\) | −18607.8 | −1.24734 | ||||||||
\(607\) | 13556.4 | 0.906484 | 0.453242 | − | 0.891388i | \(-0.350267\pi\) | ||||
0.453242 | + | 0.891388i | \(0.350267\pi\) | |||||||
\(608\) | 734.047 | 0.0489630 | ||||||||
\(609\) | 1284.56 | 0.0854728 | ||||||||
\(610\) | −5514.89 | −0.366052 | ||||||||
\(611\) | 10207.3 | 0.675850 | ||||||||
\(612\) | −14751.8 | −0.974359 | ||||||||
\(613\) | 3560.47 | 0.234594 | 0.117297 | − | 0.993097i | \(-0.462577\pi\) | ||||
0.117297 | + | 0.993097i | \(0.462577\pi\) | |||||||
\(614\) | 23637.8 | 1.55365 | ||||||||
\(615\) | −4437.41 | −0.290949 | ||||||||
\(616\) | −6813.16 | −0.445633 | ||||||||
\(617\) | 10574.1 | 0.689949 | 0.344974 | − | 0.938612i | \(-0.387888\pi\) | ||||
0.344974 | + | 0.938612i | \(0.387888\pi\) | |||||||
\(618\) | −9948.96 | −0.647582 | ||||||||
\(619\) | −8415.44 | −0.546438 | −0.273219 | − | 0.961952i | \(-0.588088\pi\) | ||||
−0.273219 | + | 0.961952i | \(0.588088\pi\) | |||||||
\(620\) | −11431.5 | −0.740484 | ||||||||
\(621\) | −600.619 | −0.0388116 | ||||||||
\(622\) | −23317.0 | −1.50310 | ||||||||
\(623\) | −4064.32 | −0.261370 | ||||||||
\(624\) | −7151.48 | −0.458795 | ||||||||
\(625\) | 8780.29 | 0.561938 | ||||||||
\(626\) | −29811.6 | −1.90338 | ||||||||
\(627\) | 329.270 | 0.0209725 | ||||||||
\(628\) | −2037.32 | −0.129455 | ||||||||
\(629\) | −10550.0 | −0.668769 | ||||||||
\(630\) | −15074.0 | −0.953272 | ||||||||
\(631\) | −5319.98 | −0.335634 | −0.167817 | − | 0.985818i | \(-0.553672\pi\) | ||||
−0.167817 | + | 0.985818i | \(0.553672\pi\) | |||||||
\(632\) | 11278.3 | 0.709852 | ||||||||
\(633\) | −2318.75 | −0.145595 | ||||||||
\(634\) | −34006.0 | −2.13021 | ||||||||
\(635\) | −10605.6 | −0.662790 | ||||||||
\(636\) | 5960.89 | 0.371642 | ||||||||
\(637\) | 12.1899 | 0.000758215 0 | ||||||||
\(638\) | 1218.64 | 0.0756214 | ||||||||
\(639\) | −4403.22 | −0.272596 | ||||||||
\(640\) | −50037.3 | −3.09047 | ||||||||
\(641\) | −4860.98 | −0.299528 | −0.149764 | − | 0.988722i | \(-0.547851\pi\) | ||||
−0.149764 | + | 0.988722i | \(0.547851\pi\) | |||||||
\(642\) | 14034.9 | 0.862793 | ||||||||
\(643\) | 14243.1 | 0.873552 | 0.436776 | − | 0.899570i | \(-0.356120\pi\) | ||||
0.436776 | + | 0.899570i | \(0.356120\pi\) | |||||||
\(644\) | −6171.39 | −0.377619 | ||||||||
\(645\) | −1696.46 | −0.103563 | ||||||||
\(646\) | 5234.81 | 0.318825 | ||||||||
\(647\) | −3965.55 | −0.240961 | −0.120481 | − | 0.992716i | \(-0.538444\pi\) | ||||
−0.120481 | + | 0.992716i | \(0.538444\pi\) | |||||||
\(648\) | −2708.09 | −0.164173 | ||||||||
\(649\) | 3402.89 | 0.205817 | ||||||||
\(650\) | −65180.7 | −3.93322 | ||||||||
\(651\) | 2249.34 | 0.135420 | ||||||||
\(652\) | −37995.6 | −2.28224 | ||||||||
\(653\) | −10569.8 | −0.633430 | −0.316715 | − | 0.948521i | \(-0.602580\pi\) | ||||
−0.316715 | + | 0.948521i | \(0.602580\pi\) | |||||||
\(654\) | −12409.9 | −0.741999 | ||||||||
\(655\) | −984.262 | −0.0587150 | ||||||||
\(656\) | −3172.30 | −0.188807 | ||||||||
\(657\) | 717.992 | 0.0426355 | ||||||||
\(658\) | 15381.2 | 0.911278 | ||||||||
\(659\) | 10893.7 | 0.643946 | 0.321973 | − | 0.946749i | \(-0.395654\pi\) | ||||
0.321973 | + | 0.946749i | \(0.395654\pi\) | |||||||
\(660\) | −9320.99 | −0.549726 | ||||||||
\(661\) | 7773.81 | 0.457437 | 0.228719 | − | 0.973493i | \(-0.426546\pi\) | ||||
0.228719 | + | 0.973493i | \(0.426546\pi\) | |||||||
\(662\) | −29.3681 | −0.00172420 | ||||||||
\(663\) | 19350.2 | 1.13348 | ||||||||
\(664\) | 21428.3 | 1.25238 | ||||||||
\(665\) | 3486.54 | 0.203312 | ||||||||
\(666\) | −4158.05 | −0.241923 | ||||||||
\(667\) | 514.150 | 0.0298470 | ||||||||
\(668\) | −6090.18 | −0.352749 | ||||||||
\(669\) | −15919.5 | −0.920004 | ||||||||
\(670\) | 9344.03 | 0.538793 | ||||||||
\(671\) | 671.000 | 0.0386046 | ||||||||
\(672\) | 4088.69 | 0.234710 | ||||||||
\(673\) | −14506.9 | −0.830907 | −0.415454 | − | 0.909614i | \(-0.636377\pi\) | ||||
−0.415454 | + | 0.909614i | \(0.636377\pi\) | |||||||
\(674\) | 46415.4 | 2.65260 | ||||||||
\(675\) | −6230.53 | −0.355279 | ||||||||
\(676\) | 19102.6 | 1.08686 | ||||||||
\(677\) | −8803.40 | −0.499767 | −0.249883 | − | 0.968276i | \(-0.580392\pi\) | ||||
−0.249883 | + | 0.968276i | \(0.580392\pi\) | |||||||
\(678\) | −15212.4 | −0.861695 | ||||||||
\(679\) | −796.706 | −0.0450291 | ||||||||
\(680\) | −69022.5 | −3.89249 | ||||||||
\(681\) | 4876.22 | 0.274386 | ||||||||
\(682\) | 2133.91 | 0.119812 | ||||||||
\(683\) | 10311.0 | 0.577657 | 0.288829 | − | 0.957381i | \(-0.406734\pi\) | ||||
0.288829 | + | 0.957381i | \(0.406734\pi\) | |||||||
\(684\) | 1344.78 | 0.0751737 | ||||||||
\(685\) | −8266.68 | −0.461100 | ||||||||
\(686\) | −30439.6 | −1.69415 | ||||||||
\(687\) | 8341.93 | 0.463267 | ||||||||
\(688\) | −1212.80 | −0.0672056 | ||||||||
\(689\) | −7818.96 | −0.432335 | ||||||||
\(690\) | −6033.43 | −0.332882 | ||||||||
\(691\) | 21715.5 | 1.19551 | 0.597755 | − | 0.801679i | \(-0.296059\pi\) | ||||
0.597755 | + | 0.801679i | \(0.296059\pi\) | |||||||
\(692\) | 50226.0 | 2.75912 | ||||||||
\(693\) | 1834.06 | 0.100534 | ||||||||
\(694\) | −37457.4 | −2.04879 | ||||||||
\(695\) | 18659.8 | 1.01842 | ||||||||
\(696\) | 2318.22 | 0.126252 | ||||||||
\(697\) | 8583.48 | 0.466460 | ||||||||
\(698\) | 1864.41 | 0.101101 | ||||||||
\(699\) | 13101.2 | 0.708916 | ||||||||
\(700\) | −64018.9 | −3.45670 | ||||||||
\(701\) | −20905.0 | −1.12635 | −0.563175 | − | 0.826338i | \(-0.690420\pi\) | ||||
−0.563175 | + | 0.826338i | \(0.690420\pi\) | |||||||
\(702\) | 7626.43 | 0.410030 | ||||||||
\(703\) | 961.737 | 0.0515969 | ||||||||
\(704\) | 7438.70 | 0.398234 | ||||||||
\(705\) | 9801.29 | 0.523600 | ||||||||
\(706\) | 35591.7 | 1.89733 | ||||||||
\(707\) | 23973.0 | 1.27524 | ||||||||
\(708\) | 13897.8 | 0.737728 | ||||||||
\(709\) | 35474.1 | 1.87907 | 0.939533 | − | 0.342459i | \(-0.111260\pi\) | ||||
0.939533 | + | 0.342459i | \(0.111260\pi\) | |||||||
\(710\) | −44231.8 | −2.33802 | ||||||||
\(711\) | −3036.04 | −0.160141 | ||||||||
\(712\) | −7334.79 | −0.386071 | ||||||||
\(713\) | 900.307 | 0.0472886 | ||||||||
\(714\) | 29158.3 | 1.52832 | ||||||||
\(715\) | 12226.5 | 0.639501 | ||||||||
\(716\) | −70333.9 | −3.67109 | ||||||||
\(717\) | −4263.81 | −0.222085 | ||||||||
\(718\) | −7921.70 | −0.411748 | ||||||||
\(719\) | 35219.3 | 1.82679 | 0.913393 | − | 0.407078i | \(-0.133452\pi\) | ||||
0.913393 | + | 0.407078i | \(0.133452\pi\) | |||||||
\(720\) | −6866.99 | −0.355441 | ||||||||
\(721\) | 12817.6 | 0.662068 | ||||||||
\(722\) | 32399.6 | 1.67007 | ||||||||
\(723\) | −2732.66 | −0.140565 | ||||||||
\(724\) | 20001.9 | 1.02675 | ||||||||
\(725\) | 5333.54 | 0.273218 | ||||||||
\(726\) | 1739.94 | 0.0889468 | ||||||||
\(727\) | 24680.5 | 1.25908 | 0.629538 | − | 0.776970i | \(-0.283244\pi\) | ||||
0.629538 | + | 0.776970i | \(0.283244\pi\) | |||||||
\(728\) | 36499.3 | 1.85818 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 7212.47 | 0.365679 | ||||||||
\(731\) | 3281.53 | 0.166035 | ||||||||
\(732\) | 2740.44 | 0.138374 | ||||||||
\(733\) | −30881.4 | −1.55611 | −0.778055 | − | 0.628196i | \(-0.783794\pi\) | ||||
−0.778055 | + | 0.628196i | \(0.783794\pi\) | |||||||
\(734\) | −20648.1 | −1.03833 | ||||||||
\(735\) | 11.7050 | 0.000587410 0 | ||||||||
\(736\) | 1636.52 | 0.0819604 | ||||||||
\(737\) | −1136.89 | −0.0568222 | ||||||||
\(738\) | 3382.99 | 0.168739 | ||||||||
\(739\) | −26058.9 | −1.29715 | −0.648575 | − | 0.761151i | \(-0.724635\pi\) | ||||
−0.648575 | + | 0.761151i | \(0.724635\pi\) | |||||||
\(740\) | −27224.9 | −1.35244 | ||||||||
\(741\) | −1763.96 | −0.0874503 | ||||||||
\(742\) | −11782.2 | −0.582936 | ||||||||
\(743\) | −4982.23 | −0.246003 | −0.123001 | − | 0.992406i | \(-0.539252\pi\) | ||||
−0.123001 | + | 0.992406i | \(0.539252\pi\) | |||||||
\(744\) | 4059.33 | 0.200030 | ||||||||
\(745\) | 46859.4 | 2.30443 | ||||||||
\(746\) | −22730.4 | −1.11557 | ||||||||
\(747\) | −5768.35 | −0.282534 | ||||||||
\(748\) | 18030.0 | 0.881340 | ||||||||
\(749\) | −18081.6 | −0.882094 | ||||||||
\(750\) | −28684.8 | −1.39656 | ||||||||
\(751\) | −13658.8 | −0.663671 | −0.331835 | − | 0.943337i | \(-0.607668\pi\) | ||||
−0.331835 | + | 0.943337i | \(0.607668\pi\) | |||||||
\(752\) | 7006.94 | 0.339783 | ||||||||
\(753\) | 10862.9 | 0.525720 | ||||||||
\(754\) | −6528.48 | −0.315323 | ||||||||
\(755\) | 47965.4 | 2.31211 | ||||||||
\(756\) | 7490.50 | 0.360353 | ||||||||
\(757\) | −22713.8 | −1.09055 | −0.545275 | − | 0.838257i | \(-0.683575\pi\) | ||||
−0.545275 | + | 0.838257i | \(0.683575\pi\) | |||||||
\(758\) | 42026.6 | 2.01382 | ||||||||
\(759\) | 734.090 | 0.0351064 | ||||||||
\(760\) | 6292.09 | 0.300313 | ||||||||
\(761\) | −34502.3 | −1.64351 | −0.821754 | − | 0.569843i | \(-0.807004\pi\) | ||||
−0.821754 | + | 0.569843i | \(0.807004\pi\) | |||||||
\(762\) | 8085.52 | 0.384393 | ||||||||
\(763\) | 15988.1 | 0.758597 | ||||||||
\(764\) | −15598.5 | −0.738656 | ||||||||
\(765\) | 18580.4 | 0.878139 | ||||||||
\(766\) | −56470.5 | −2.66366 | ||||||||
\(767\) | −18229.9 | −0.858206 | ||||||||
\(768\) | 21917.5 | 1.02979 | ||||||||
\(769\) | −24960.0 | −1.17046 | −0.585229 | − | 0.810868i | \(-0.698995\pi\) | ||||
−0.585229 | + | 0.810868i | \(0.698995\pi\) | |||||||
\(770\) | 18423.7 | 0.862267 | ||||||||
\(771\) | 23352.2 | 1.09080 | ||||||||
\(772\) | −37629.4 | −1.75429 | ||||||||
\(773\) | 26785.9 | 1.24634 | 0.623172 | − | 0.782085i | \(-0.285844\pi\) | ||||
0.623172 | + | 0.782085i | \(0.285844\pi\) | |||||||
\(774\) | 1293.34 | 0.0600623 | ||||||||
\(775\) | 9339.34 | 0.432876 | ||||||||
\(776\) | −1437.80 | −0.0665128 | ||||||||
\(777\) | 5356.95 | 0.247335 | ||||||||
\(778\) | −6385.20 | −0.294242 | ||||||||
\(779\) | −782.470 | −0.0359883 | ||||||||
\(780\) | 49934.2 | 2.29222 | ||||||||
\(781\) | 5381.71 | 0.246572 | ||||||||
\(782\) | 11670.7 | 0.533689 | ||||||||
\(783\) | −624.048 | −0.0284823 | ||||||||
\(784\) | 8.36793 | 0.000381192 0 | ||||||||
\(785\) | 2566.07 | 0.116671 | ||||||||
\(786\) | 750.381 | 0.0340524 | ||||||||
\(787\) | −11184.1 | −0.506570 | −0.253285 | − | 0.967392i | \(-0.581511\pi\) | ||||
−0.253285 | + | 0.967392i | \(0.581511\pi\) | |||||||
\(788\) | −51344.1 | −2.32114 | ||||||||
\(789\) | −2077.83 | −0.0937549 | ||||||||
\(790\) | −30498.1 | −1.37351 | ||||||||
\(791\) | 19598.7 | 0.880971 | ||||||||
\(792\) | 3309.89 | 0.148500 | ||||||||
\(793\) | −3594.67 | −0.160972 | ||||||||
\(794\) | 52809.1 | 2.36036 | ||||||||
\(795\) | −7507.93 | −0.334942 | ||||||||
\(796\) | −52822.6 | −2.35207 | ||||||||
\(797\) | 991.876 | 0.0440829 | 0.0220414 | − | 0.999757i | \(-0.492983\pi\) | ||||
0.0220414 | + | 0.999757i | \(0.492983\pi\) | |||||||
\(798\) | −2658.07 | −0.117913 | ||||||||
\(799\) | −18959.1 | −0.839454 | ||||||||
\(800\) | 16976.4 | 0.750260 | ||||||||
\(801\) | 1974.48 | 0.0870970 | ||||||||
\(802\) | −62887.6 | −2.76888 | ||||||||
\(803\) | −877.545 | −0.0385653 | ||||||||
\(804\) | −4643.20 | −0.203673 | ||||||||
\(805\) | 7773.06 | 0.340329 | ||||||||
\(806\) | −11431.7 | −0.499586 | ||||||||
\(807\) | 12509.0 | 0.545650 | ||||||||
\(808\) | 43263.6 | 1.88367 | ||||||||
\(809\) | −26801.0 | −1.16474 | −0.582369 | − | 0.812925i | \(-0.697874\pi\) | ||||
−0.582369 | + | 0.812925i | \(0.697874\pi\) | |||||||
\(810\) | 7323.06 | 0.317662 | ||||||||
\(811\) | 19912.1 | 0.862157 | 0.431078 | − | 0.902315i | \(-0.358133\pi\) | ||||
0.431078 | + | 0.902315i | \(0.358133\pi\) | |||||||
\(812\) | −6412.12 | −0.277120 | ||||||||
\(813\) | −15455.0 | −0.666704 | ||||||||
\(814\) | 5082.06 | 0.218828 | ||||||||
\(815\) | 47856.7 | 2.05687 | ||||||||
\(816\) | 13283.1 | 0.569857 | ||||||||
\(817\) | −299.144 | −0.0128100 | ||||||||
\(818\) | 23278.4 | 0.995001 | ||||||||
\(819\) | −9825.38 | −0.419202 | ||||||||
\(820\) | 22150.2 | 0.943315 | ||||||||
\(821\) | 13978.8 | 0.594233 | 0.297116 | − | 0.954841i | \(-0.403975\pi\) | ||||
0.297116 | + | 0.954841i | \(0.403975\pi\) | |||||||
\(822\) | 6302.35 | 0.267420 | ||||||||
\(823\) | −45931.2 | −1.94540 | −0.972699 | − | 0.232070i | \(-0.925450\pi\) | ||||
−0.972699 | + | 0.232070i | \(0.925450\pi\) | |||||||
\(824\) | 23131.6 | 0.977946 | ||||||||
\(825\) | 7615.09 | 0.321362 | ||||||||
\(826\) | −27470.2 | −1.15716 | ||||||||
\(827\) | 21005.1 | 0.883215 | 0.441607 | − | 0.897208i | \(-0.354408\pi\) | ||||
0.441607 | + | 0.897208i | \(0.354408\pi\) | |||||||
\(828\) | 2998.11 | 0.125835 | ||||||||
\(829\) | −8843.43 | −0.370501 | −0.185250 | − | 0.982691i | \(-0.559310\pi\) | ||||
−0.185250 | + | 0.982691i | \(0.559310\pi\) | |||||||
\(830\) | −57945.1 | −2.42326 | ||||||||
\(831\) | −3100.24 | −0.129418 | ||||||||
\(832\) | −39850.5 | −1.66054 | ||||||||
\(833\) | −22.6416 | −0.000941757 0 | ||||||||
\(834\) | −14225.8 | −0.590647 | ||||||||
\(835\) | 7670.78 | 0.317914 | ||||||||
\(836\) | −1643.62 | −0.0679972 | ||||||||
\(837\) | −1092.74 | −0.0451264 | ||||||||
\(838\) | −21896.0 | −0.902607 | ||||||||
\(839\) | −2322.54 | −0.0955695 | −0.0477848 | − | 0.998858i | \(-0.515216\pi\) | ||||
−0.0477848 | + | 0.998858i | \(0.515216\pi\) | |||||||
\(840\) | 35047.4 | 1.43958 | ||||||||
\(841\) | −23854.8 | −0.978096 | ||||||||
\(842\) | −27350.3 | −1.11942 | ||||||||
\(843\) | −20050.7 | −0.819196 | ||||||||
\(844\) | 11574.5 | 0.472050 | ||||||||
\(845\) | −24060.4 | −0.979529 | ||||||||
\(846\) | −7472.30 | −0.303668 | ||||||||
\(847\) | −2241.63 | −0.0909365 | ||||||||
\(848\) | −5367.42 | −0.217356 | ||||||||
\(849\) | −23749.7 | −0.960057 | ||||||||
\(850\) | 121066. | 4.88535 | ||||||||
\(851\) | 2144.14 | 0.0863693 | ||||||||
\(852\) | 21979.5 | 0.883810 | ||||||||
\(853\) | −34381.4 | −1.38007 | −0.690033 | − | 0.723778i | \(-0.742404\pi\) | ||||
−0.690033 | + | 0.723778i | \(0.742404\pi\) | |||||||
\(854\) | −5416.72 | −0.217045 | ||||||||
\(855\) | −1693.79 | −0.0677502 | ||||||||
\(856\) | −32631.5 | −1.30295 | ||||||||
\(857\) | −27698.0 | −1.10402 | −0.552010 | − | 0.833837i | \(-0.686139\pi\) | ||||
−0.552010 | + | 0.833837i | \(0.686139\pi\) | |||||||
\(858\) | −9321.19 | −0.370886 | ||||||||
\(859\) | −34147.7 | −1.35635 | −0.678174 | − | 0.734901i | \(-0.737229\pi\) | ||||
−0.678174 | + | 0.734901i | \(0.737229\pi\) | |||||||
\(860\) | 8468.19 | 0.335771 | ||||||||
\(861\) | −4358.42 | −0.172514 | ||||||||
\(862\) | −1495.77 | −0.0591022 | ||||||||
\(863\) | 19295.6 | 0.761102 | 0.380551 | − | 0.924760i | \(-0.375734\pi\) | ||||
0.380551 | + | 0.924760i | \(0.375734\pi\) | |||||||
\(864\) | −1986.32 | −0.0782129 | ||||||||
\(865\) | −63261.3 | −2.48665 | ||||||||
\(866\) | −73649.2 | −2.88996 | ||||||||
\(867\) | −21201.9 | −0.830514 | ||||||||
\(868\) | −11228.0 | −0.439059 | ||||||||
\(869\) | 3710.72 | 0.144853 | ||||||||
\(870\) | −6268.78 | −0.244289 | ||||||||
\(871\) | 6090.54 | 0.236935 | ||||||||
\(872\) | 28853.5 | 1.12053 | ||||||||
\(873\) | 387.046 | 0.0150052 | ||||||||
\(874\) | −1063.90 | −0.0411751 | ||||||||
\(875\) | 36955.5 | 1.42780 | ||||||||
\(876\) | −3584.00 | −0.138233 | ||||||||
\(877\) | 44076.1 | 1.69709 | 0.848544 | − | 0.529125i | \(-0.177480\pi\) | ||||
0.848544 | + | 0.529125i | \(0.177480\pi\) | |||||||
\(878\) | 62754.9 | 2.41216 | ||||||||
\(879\) | 19127.2 | 0.733953 | ||||||||
\(880\) | 8392.99 | 0.321509 | ||||||||
\(881\) | 29485.7 | 1.12758 | 0.563791 | − | 0.825917i | \(-0.309342\pi\) | ||||
0.563791 | + | 0.825917i | \(0.309342\pi\) | |||||||
\(882\) | −8.92367 | −0.000340675 0 | ||||||||
\(883\) | −24782.6 | −0.944510 | −0.472255 | − | 0.881462i | \(-0.656560\pi\) | ||||
−0.472255 | + | 0.881462i | \(0.656560\pi\) | |||||||
\(884\) | −96590.1 | −3.67497 | ||||||||
\(885\) | −17504.7 | −0.664876 | ||||||||
\(886\) | −37384.4 | −1.41755 | ||||||||
\(887\) | 6772.25 | 0.256358 | 0.128179 | − | 0.991751i | \(-0.459087\pi\) | ||||
0.128179 | + | 0.991751i | \(0.459087\pi\) | |||||||
\(888\) | 9667.58 | 0.365341 | ||||||||
\(889\) | −10416.8 | −0.392992 | ||||||||
\(890\) | 19834.3 | 0.747019 | ||||||||
\(891\) | −891.000 | −0.0335013 | ||||||||
\(892\) | 79465.2 | 2.98284 | ||||||||
\(893\) | 1728.31 | 0.0647656 | ||||||||
\(894\) | −35724.7 | −1.33648 | ||||||||
\(895\) | 88587.9 | 3.30857 | ||||||||
\(896\) | −49146.6 | −1.83245 | ||||||||
\(897\) | −3932.65 | −0.146385 | ||||||||
\(898\) | −79727.5 | −2.96274 | ||||||||
\(899\) | 935.426 | 0.0347032 | ||||||||
\(900\) | 31100.9 | 1.15189 | ||||||||
\(901\) | 14522.9 | 0.536991 | ||||||||
\(902\) | −4134.76 | −0.152630 | ||||||||
\(903\) | −1666.26 | −0.0614059 | ||||||||
\(904\) | 35369.3 | 1.30129 | ||||||||
\(905\) | −25193.1 | −0.925355 | ||||||||
\(906\) | −36567.9 | −1.34093 | ||||||||
\(907\) | −25557.1 | −0.935624 | −0.467812 | − | 0.883828i | \(-0.654957\pi\) | ||||
−0.467812 | + | 0.883828i | \(0.654957\pi\) | |||||||
\(908\) | −24340.6 | −0.889616 | ||||||||
\(909\) | −11646.3 | −0.424953 | ||||||||
\(910\) | −98699.4 | −3.59544 | ||||||||
\(911\) | −25703.4 | −0.934788 | −0.467394 | − | 0.884049i | \(-0.654807\pi\) | ||||
−0.467394 | + | 0.884049i | \(0.654807\pi\) | |||||||
\(912\) | −1210.89 | −0.0439656 | ||||||||
\(913\) | 7050.20 | 0.255562 | ||||||||
\(914\) | 28153.1 | 1.01884 | ||||||||
\(915\) | −3451.67 | −0.124709 | ||||||||
\(916\) | −41640.4 | −1.50201 | ||||||||
\(917\) | −966.741 | −0.0348142 | ||||||||
\(918\) | −14165.3 | −0.509287 | ||||||||
\(919\) | −46893.9 | −1.68323 | −0.841614 | − | 0.540079i | \(-0.818394\pi\) | ||||
−0.841614 | + | 0.540079i | \(0.818394\pi\) | |||||||
\(920\) | 14027.9 | 0.502702 | ||||||||
\(921\) | 14794.5 | 0.529310 | ||||||||
\(922\) | 18445.5 | 0.658860 | ||||||||
\(923\) | −28830.8 | −1.02814 | ||||||||
\(924\) | −9155.06 | −0.325952 | ||||||||
\(925\) | 22242.3 | 0.790618 | ||||||||
\(926\) | 57522.3 | 2.04136 | ||||||||
\(927\) | −6226.88 | −0.220623 | ||||||||
\(928\) | 1700.36 | 0.0601475 | ||||||||
\(929\) | −38581.3 | −1.36255 | −0.681277 | − | 0.732026i | \(-0.738575\pi\) | ||||
−0.681277 | + | 0.732026i | \(0.738575\pi\) | |||||||
\(930\) | −10977.0 | −0.387043 | ||||||||
\(931\) | 2.06400 | 7.26585e−5 0 | ||||||||
\(932\) | −65397.1 | −2.29845 | ||||||||
\(933\) | −14593.7 | −0.512085 | ||||||||
\(934\) | 28318.7 | 0.992093 | ||||||||
\(935\) | −22709.4 | −0.794307 | ||||||||
\(936\) | −17731.7 | −0.619207 | ||||||||
\(937\) | 43555.9 | 1.51858 | 0.759290 | − | 0.650752i | \(-0.225546\pi\) | ||||
0.759290 | + | 0.650752i | \(0.225546\pi\) | |||||||
\(938\) | 9177.69 | 0.319469 | ||||||||
\(939\) | −18658.6 | −0.648456 | ||||||||
\(940\) | −48925.0 | −1.69762 | ||||||||
\(941\) | 13064.7 | 0.452599 | 0.226300 | − | 0.974058i | \(-0.427337\pi\) | ||||
0.226300 | + | 0.974058i | \(0.427337\pi\) | |||||||
\(942\) | −1956.32 | −0.0676648 | ||||||||
\(943\) | −1744.48 | −0.0602417 | ||||||||
\(944\) | −12514.1 | −0.431462 | ||||||||
\(945\) | −9434.53 | −0.324768 | ||||||||
\(946\) | −1580.75 | −0.0543284 | ||||||||
\(947\) | 26424.6 | 0.906741 | 0.453370 | − | 0.891322i | \(-0.350222\pi\) | ||||
0.453370 | + | 0.891322i | \(0.350222\pi\) | |||||||
\(948\) | 15155.0 | 0.519210 | ||||||||
\(949\) | 4701.17 | 0.160808 | ||||||||
\(950\) | −11036.4 | −0.376914 | ||||||||
\(951\) | −21283.8 | −0.725735 | ||||||||
\(952\) | −67793.8 | −2.30799 | ||||||||
\(953\) | 11812.2 | 0.401505 | 0.200752 | − | 0.979642i | \(-0.435661\pi\) | ||||
0.200752 | + | 0.979642i | \(0.435661\pi\) | |||||||
\(954\) | 5723.89 | 0.194253 | ||||||||
\(955\) | 19646.8 | 0.665713 | ||||||||
\(956\) | 21283.7 | 0.720045 | ||||||||
\(957\) | 762.726 | 0.0257632 | ||||||||
\(958\) | 86770.2 | 2.92632 | ||||||||
\(959\) | −8119.52 | −0.273403 | ||||||||
\(960\) | −38265.3 | −1.28646 | ||||||||
\(961\) | −28153.0 | −0.945017 | ||||||||
\(962\) | −27225.5 | −0.912459 | ||||||||
\(963\) | 8784.20 | 0.293943 | ||||||||
\(964\) | 13640.6 | 0.455740 | ||||||||
\(965\) | 47395.5 | 1.58105 | ||||||||
\(966\) | −5926.02 | −0.197377 | ||||||||
\(967\) | −20141.3 | −0.669805 | −0.334903 | − | 0.942253i | \(-0.608703\pi\) | ||||
−0.334903 | + | 0.942253i | \(0.608703\pi\) | |||||||
\(968\) | −4045.42 | −0.134323 | ||||||||
\(969\) | 3276.37 | 0.108620 | ||||||||
\(970\) | 3888.01 | 0.128697 | ||||||||
\(971\) | −29399.5 | −0.971652 | −0.485826 | − | 0.874055i | \(-0.661481\pi\) | ||||
−0.485826 | + | 0.874055i | \(0.661481\pi\) | |||||||
\(972\) | −3638.95 | −0.120082 | ||||||||
\(973\) | 18327.6 | 0.603860 | ||||||||
\(974\) | 37058.3 | 1.21912 | ||||||||
\(975\) | −40795.4 | −1.34000 | ||||||||
\(976\) | −2467.60 | −0.0809283 | ||||||||
\(977\) | 23697.1 | 0.775986 | 0.387993 | − | 0.921662i | \(-0.373168\pi\) | ||||
0.387993 | + | 0.921662i | \(0.373168\pi\) | |||||||
\(978\) | −36485.0 | −1.19290 | ||||||||
\(979\) | −2413.25 | −0.0787822 | ||||||||
\(980\) | −58.4279 | −0.00190450 | ||||||||
\(981\) | −7767.17 | −0.252790 | ||||||||
\(982\) | 53513.8 | 1.73900 | ||||||||
\(983\) | 18025.7 | 0.584872 | 0.292436 | − | 0.956285i | \(-0.405534\pi\) | ||||
0.292436 | + | 0.956285i | \(0.405534\pi\) | |||||||
\(984\) | −7865.55 | −0.254822 | ||||||||
\(985\) | 64669.5 | 2.09192 | ||||||||
\(986\) | 12126.0 | 0.391653 | ||||||||
\(987\) | 9626.81 | 0.310461 | ||||||||
\(988\) | 8805.15 | 0.283531 | ||||||||
\(989\) | −666.927 | −0.0214429 | ||||||||
\(990\) | −8950.40 | −0.287336 | ||||||||
\(991\) | 5295.79 | 0.169754 | 0.0848771 | − | 0.996391i | \(-0.472950\pi\) | ||||
0.0848771 | + | 0.996391i | \(0.472950\pi\) | |||||||
\(992\) | 2977.42 | 0.0952956 | ||||||||
\(993\) | −18.3810 | −0.000587414 0 | ||||||||
\(994\) | −43444.4 | −1.38629 | ||||||||
\(995\) | 66531.8 | 2.11980 | ||||||||
\(996\) | 28793.8 | 0.916032 | ||||||||
\(997\) | −55027.5 | −1.74798 | −0.873990 | − | 0.485943i | \(-0.838476\pi\) | ||||
−0.873990 | + | 0.485943i | \(0.838476\pi\) | |||||||
\(998\) | −23601.6 | −0.748591 | ||||||||
\(999\) | −2602.45 | −0.0824202 |
(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 | 2013.4.a.e.1.4 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.4.a.e.1.4 | ✓ | 38 | 1.1 | even | 1 | trivial |