Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("245.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(14.4554679514\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{11}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 11 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.31662\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.31662 | 1.52616 | 0.763079 | − | 0.646306i | \(-0.223687\pi\) | ||||
0.763079 | + | 0.646306i | \(0.223687\pi\) | |||||||
\(3\) | 5.00000 | 0.962250 | 0.481125 | − | 0.876652i | \(-0.340228\pi\) | ||||
0.481125 | + | 0.876652i | \(0.340228\pi\) | |||||||
\(4\) | 10.6332 | 1.32916 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 21.5831 | 1.46855 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 11.3668 | 0.502344 | ||||||||
\(9\) | −2.00000 | −0.0740741 | ||||||||
\(10\) | 21.5831 | 0.682518 | ||||||||
\(11\) | 19.7335 | 0.540898 | 0.270449 | − | 0.962734i | \(-0.412828\pi\) | ||||
0.270449 | + | 0.962734i | \(0.412828\pi\) | |||||||
\(12\) | 53.1662 | 1.27898 | ||||||||
\(13\) | 71.3325 | 1.52185 | 0.760926 | − | 0.648839i | \(-0.224745\pi\) | ||||
0.760926 | + | 0.648839i | \(0.224745\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 25.0000 | 0.430331 | ||||||||
\(16\) | −36.0000 | −0.562500 | ||||||||
\(17\) | −31.3325 | −0.447014 | −0.223507 | − | 0.974702i | \(-0.571751\pi\) | ||||
−0.223507 | + | 0.974702i | \(0.571751\pi\) | |||||||
\(18\) | −8.63325 | −0.113049 | ||||||||
\(19\) | 136.332 | 1.64615 | 0.823074 | − | 0.567934i | \(-0.192257\pi\) | ||||
0.823074 | + | 0.567934i | \(0.192257\pi\) | |||||||
\(20\) | 53.1662 | 0.594417 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 85.1821 | 0.825495 | ||||||||
\(23\) | −100.865 | −0.914431 | −0.457215 | − | 0.889356i | \(-0.651153\pi\) | ||||
−0.457215 | + | 0.889356i | \(0.651153\pi\) | |||||||
\(24\) | 56.8338 | 0.483381 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 307.916 | 2.32259 | ||||||||
\(27\) | −145.000 | −1.03353 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −288.198 | −1.84541 | −0.922707 | − | 0.385501i | \(-0.874029\pi\) | ||||
−0.922707 | + | 0.385501i | \(0.874029\pi\) | |||||||
\(30\) | 107.916 | 0.656754 | ||||||||
\(31\) | −208.997 | −1.21087 | −0.605436 | − | 0.795894i | \(-0.707001\pi\) | ||||
−0.605436 | + | 0.795894i | \(0.707001\pi\) | |||||||
\(32\) | −246.332 | −1.36081 | ||||||||
\(33\) | 98.6675 | 0.520479 | ||||||||
\(34\) | −135.251 | −0.682214 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −21.2665 | −0.0984560 | ||||||||
\(37\) | 309.931 | 1.37709 | 0.688546 | − | 0.725192i | \(-0.258249\pi\) | ||||
0.688546 | + | 0.725192i | \(0.258249\pi\) | |||||||
\(38\) | 588.496 | 2.51228 | ||||||||
\(39\) | 356.662 | 1.46440 | ||||||||
\(40\) | 56.8338 | 0.224655 | ||||||||
\(41\) | −181.662 | −0.691973 | −0.345987 | − | 0.938239i | \(-0.612456\pi\) | ||||
−0.345987 | + | 0.938239i | \(0.612456\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −18.2005 | −0.0645477 | −0.0322738 | − | 0.999479i | \(-0.510275\pi\) | ||||
−0.0322738 | + | 0.999479i | \(0.510275\pi\) | |||||||
\(44\) | 209.831 | 0.718937 | ||||||||
\(45\) | −10.0000 | −0.0331269 | ||||||||
\(46\) | −435.398 | −1.39557 | ||||||||
\(47\) | −147.665 | −0.458280 | −0.229140 | − | 0.973393i | \(-0.573591\pi\) | ||||
−0.229140 | + | 0.973393i | \(0.573591\pi\) | |||||||
\(48\) | −180.000 | −0.541266 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 107.916 | 0.305231 | ||||||||
\(51\) | −156.662 | −0.430140 | ||||||||
\(52\) | 758.496 | 2.02278 | ||||||||
\(53\) | −127.995 | −0.331726 | −0.165863 | − | 0.986149i | \(-0.553041\pi\) | ||||
−0.165863 | + | 0.986149i | \(0.553041\pi\) | |||||||
\(54\) | −625.911 | −1.57733 | ||||||||
\(55\) | 98.6675 | 0.241897 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 681.662 | 1.58401 | ||||||||
\(58\) | −1244.04 | −2.81639 | ||||||||
\(59\) | 322.665 | 0.711990 | 0.355995 | − | 0.934488i | \(-0.384142\pi\) | ||||
0.355995 | + | 0.934488i | \(0.384142\pi\) | |||||||
\(60\) | 265.831 | 0.571978 | ||||||||
\(61\) | 341.003 | 0.715752 | 0.357876 | − | 0.933769i | \(-0.383501\pi\) | ||||
0.357876 | + | 0.933769i | \(0.383501\pi\) | |||||||
\(62\) | −902.164 | −1.84798 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −775.325 | −1.51431 | ||||||||
\(65\) | 356.662 | 0.680593 | ||||||||
\(66\) | 425.911 | 0.794333 | ||||||||
\(67\) | −84.3960 | −0.153890 | −0.0769449 | − | 0.997035i | \(-0.524517\pi\) | ||||
−0.0769449 | + | 0.997035i | \(0.524517\pi\) | |||||||
\(68\) | −333.166 | −0.594152 | ||||||||
\(69\) | −504.327 | −0.879911 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −315.736 | −0.527760 | −0.263880 | − | 0.964555i | \(-0.585002\pi\) | ||||
−0.263880 | + | 0.964555i | \(0.585002\pi\) | |||||||
\(72\) | −22.7335 | −0.0372107 | ||||||||
\(73\) | −1093.32 | −1.75293 | −0.876466 | − | 0.481464i | \(-0.840105\pi\) | ||||
−0.876466 | + | 0.481464i | \(0.840105\pi\) | |||||||
\(74\) | 1337.86 | 2.10166 | ||||||||
\(75\) | 125.000 | 0.192450 | ||||||||
\(76\) | 1449.66 | 2.18799 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1539.58 | 2.23491 | ||||||||
\(79\) | 1233.19 | 1.75626 | 0.878128 | − | 0.478426i | \(-0.158793\pi\) | ||||
0.878128 | + | 0.478426i | \(0.158793\pi\) | |||||||
\(80\) | −180.000 | −0.251558 | ||||||||
\(81\) | −671.000 | −0.920439 | ||||||||
\(82\) | −784.169 | −1.05606 | ||||||||
\(83\) | −643.325 | −0.850772 | −0.425386 | − | 0.905012i | \(-0.639862\pi\) | ||||
−0.425386 | + | 0.905012i | \(0.639862\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −156.662 | −0.199911 | ||||||||
\(86\) | −78.5647 | −0.0985099 | ||||||||
\(87\) | −1440.99 | −1.77575 | ||||||||
\(88\) | 224.306 | 0.271717 | ||||||||
\(89\) | 1140.32 | 1.35813 | 0.679064 | − | 0.734079i | \(-0.262386\pi\) | ||||
0.679064 | + | 0.734079i | \(0.262386\pi\) | |||||||
\(90\) | −43.1662 | −0.0505569 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1072.53 | −1.21542 | ||||||||
\(93\) | −1044.99 | −1.16516 | ||||||||
\(94\) | −637.414 | −0.699407 | ||||||||
\(95\) | 681.662 | 0.736180 | ||||||||
\(96\) | −1231.66 | −1.30944 | ||||||||
\(97\) | 1411.99 | 1.47800 | 0.739001 | − | 0.673705i | \(-0.235298\pi\) | ||||
0.739001 | + | 0.673705i | \(0.235298\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −39.4670 | −0.0400665 | ||||||||
\(100\) | 265.831 | 0.265831 | ||||||||
\(101\) | −545.673 | −0.537589 | −0.268794 | − | 0.963198i | \(-0.586625\pi\) | ||||
−0.268794 | + | 0.963198i | \(0.586625\pi\) | |||||||
\(102\) | −676.253 | −0.656461 | ||||||||
\(103\) | 780.990 | 0.747119 | 0.373559 | − | 0.927606i | \(-0.378137\pi\) | ||||
0.373559 | + | 0.927606i | \(0.378137\pi\) | |||||||
\(104\) | 810.819 | 0.764493 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −552.506 | −0.506266 | ||||||||
\(107\) | −620.660 | −0.560761 | −0.280381 | − | 0.959889i | \(-0.590461\pi\) | ||||
−0.280381 | + | 0.959889i | \(0.590461\pi\) | |||||||
\(108\) | −1541.82 | −1.37372 | ||||||||
\(109\) | 4.18794 | 0.00368011 | 0.00184005 | − | 0.999998i | \(-0.499414\pi\) | ||||
0.00184005 | + | 0.999998i | \(0.499414\pi\) | |||||||
\(110\) | 425.911 | 0.369173 | ||||||||
\(111\) | 1549.66 | 1.32511 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1413.53 | 1.17676 | 0.588379 | − | 0.808585i | \(-0.299766\pi\) | ||||
0.588379 | + | 0.808585i | \(0.299766\pi\) | |||||||
\(114\) | 2942.48 | 2.41744 | ||||||||
\(115\) | −504.327 | −0.408946 | ||||||||
\(116\) | −3064.48 | −2.45284 | ||||||||
\(117\) | −142.665 | −0.112730 | ||||||||
\(118\) | 1392.82 | 1.08661 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 284.169 | 0.216175 | ||||||||
\(121\) | −941.589 | −0.707430 | ||||||||
\(122\) | 1471.98 | 1.09235 | ||||||||
\(123\) | −908.312 | −0.665852 | ||||||||
\(124\) | −2222.32 | −1.60944 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2046.26 | −1.42974 | −0.714868 | − | 0.699259i | \(-0.753513\pi\) | ||||
−0.714868 | + | 0.699259i | \(0.753513\pi\) | |||||||
\(128\) | −1376.13 | −0.950262 | ||||||||
\(129\) | −91.0025 | −0.0621110 | ||||||||
\(130\) | 1539.58 | 1.03869 | ||||||||
\(131\) | 1140.32 | 0.760534 | 0.380267 | − | 0.924877i | \(-0.375832\pi\) | ||||
0.380267 | + | 0.924877i | \(0.375832\pi\) | |||||||
\(132\) | 1049.16 | 0.691798 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −364.306 | −0.234860 | ||||||||
\(135\) | −725.000 | −0.462208 | ||||||||
\(136\) | −356.149 | −0.224555 | ||||||||
\(137\) | −490.343 | −0.305787 | −0.152893 | − | 0.988243i | \(-0.548859\pi\) | ||||
−0.152893 | + | 0.988243i | \(0.548859\pi\) | |||||||
\(138\) | −2176.99 | −1.34288 | ||||||||
\(139\) | 2800.00 | 1.70858 | 0.854291 | − | 0.519795i | \(-0.173992\pi\) | ||||
0.854291 | + | 0.519795i | \(0.173992\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −738.325 | −0.440980 | ||||||||
\(142\) | −1362.91 | −0.805445 | ||||||||
\(143\) | 1407.64 | 0.823166 | ||||||||
\(144\) | 72.0000 | 0.0416667 | ||||||||
\(145\) | −1440.99 | −0.825294 | ||||||||
\(146\) | −4719.47 | −2.67525 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3295.58 | 1.83037 | ||||||||
\(149\) | 1166.12 | 0.641154 | 0.320577 | − | 0.947222i | \(-0.396123\pi\) | ||||
0.320577 | + | 0.947222i | \(0.396123\pi\) | |||||||
\(150\) | 539.578 | 0.293709 | ||||||||
\(151\) | 959.581 | 0.517150 | 0.258575 | − | 0.965991i | \(-0.416747\pi\) | ||||
0.258575 | + | 0.965991i | \(0.416747\pi\) | |||||||
\(152\) | 1549.66 | 0.826933 | ||||||||
\(153\) | 62.6650 | 0.0331122 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1044.99 | −0.541519 | ||||||||
\(156\) | 3792.48 | 1.94642 | ||||||||
\(157\) | −1020.66 | −0.518838 | −0.259419 | − | 0.965765i | \(-0.583531\pi\) | ||||
−0.259419 | + | 0.965765i | \(0.583531\pi\) | |||||||
\(158\) | 5323.20 | 2.68032 | ||||||||
\(159\) | −639.975 | −0.319203 | ||||||||
\(160\) | −1231.66 | −0.608572 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2896.46 | −1.40473 | ||||||||
\(163\) | −1566.02 | −0.752514 | −0.376257 | − | 0.926515i | \(-0.622789\pi\) | ||||
−0.376257 | + | 0.926515i | \(0.622789\pi\) | |||||||
\(164\) | −1931.66 | −0.919741 | ||||||||
\(165\) | 493.338 | 0.232765 | ||||||||
\(166\) | −2776.99 | −1.29841 | ||||||||
\(167\) | −1130.30 | −0.523746 | −0.261873 | − | 0.965102i | \(-0.584340\pi\) | ||||
−0.261873 | + | 0.965102i | \(0.584340\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2891.32 | 1.31603 | ||||||||
\(170\) | −676.253 | −0.305096 | ||||||||
\(171\) | −272.665 | −0.121937 | ||||||||
\(172\) | −193.530 | −0.0857940 | ||||||||
\(173\) | 2543.34 | 1.11772 | 0.558862 | − | 0.829260i | \(-0.311238\pi\) | ||||
0.558862 | + | 0.829260i | \(0.311238\pi\) | |||||||
\(174\) | −6220.21 | −2.71008 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −710.406 | −0.304255 | ||||||||
\(177\) | 1613.32 | 0.685113 | ||||||||
\(178\) | 4922.32 | 2.07272 | ||||||||
\(179\) | −1210.65 | −0.505521 | −0.252760 | − | 0.967529i | \(-0.581338\pi\) | ||||
−0.252760 | + | 0.967529i | \(0.581338\pi\) | |||||||
\(180\) | −106.332 | −0.0440309 | ||||||||
\(181\) | −3031.32 | −1.24484 | −0.622421 | − | 0.782683i | \(-0.713851\pi\) | ||||
−0.622421 | + | 0.782683i | \(0.713851\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1705.01 | 0.688733 | ||||||||
\(184\) | −1146.51 | −0.459359 | ||||||||
\(185\) | 1549.66 | 0.615854 | ||||||||
\(186\) | −4510.82 | −1.77822 | ||||||||
\(187\) | −618.300 | −0.241789 | ||||||||
\(188\) | −1570.16 | −0.609125 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2942.48 | 1.12353 | ||||||||
\(191\) | −2168.64 | −0.821555 | −0.410778 | − | 0.911736i | \(-0.634743\pi\) | ||||
−0.410778 | + | 0.911736i | \(0.634743\pi\) | |||||||
\(192\) | −3876.62 | −1.45714 | ||||||||
\(193\) | 1490.48 | 0.555892 | 0.277946 | − | 0.960597i | \(-0.410346\pi\) | ||||
0.277946 | + | 0.960597i | \(0.410346\pi\) | |||||||
\(194\) | 6095.04 | 2.25566 | ||||||||
\(195\) | 1783.31 | 0.654901 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3380.57 | 1.22262 | 0.611308 | − | 0.791393i | \(-0.290644\pi\) | ||||
0.611308 | + | 0.791393i | \(0.290644\pi\) | |||||||
\(198\) | −170.364 | −0.0611478 | ||||||||
\(199\) | 4595.33 | 1.63696 | 0.818478 | − | 0.574538i | \(-0.194818\pi\) | ||||
0.818478 | + | 0.574538i | \(0.194818\pi\) | |||||||
\(200\) | 284.169 | 0.100469 | ||||||||
\(201\) | −421.980 | −0.148080 | ||||||||
\(202\) | −2355.46 | −0.820445 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1665.83 | −0.571723 | ||||||||
\(205\) | −908.312 | −0.309460 | ||||||||
\(206\) | 3371.24 | 1.14022 | ||||||||
\(207\) | 201.731 | 0.0677356 | ||||||||
\(208\) | −2567.97 | −0.856042 | ||||||||
\(209\) | 2690.32 | 0.890398 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4988.66 | −1.62765 | −0.813824 | − | 0.581112i | \(-0.802618\pi\) | ||||
−0.813824 | + | 0.581112i | \(0.802618\pi\) | |||||||
\(212\) | −1361.00 | −0.440915 | ||||||||
\(213\) | −1578.68 | −0.507837 | ||||||||
\(214\) | −2679.16 | −0.855810 | ||||||||
\(215\) | −91.0025 | −0.0288666 | ||||||||
\(216\) | −1648.18 | −0.519187 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 18.0778 | 0.00561643 | ||||||||
\(219\) | −5466.62 | −1.68676 | ||||||||
\(220\) | 1049.16 | 0.321519 | ||||||||
\(221\) | −2235.03 | −0.680290 | ||||||||
\(222\) | 6689.29 | 2.02232 | ||||||||
\(223\) | 3792.97 | 1.13900 | 0.569498 | − | 0.821993i | \(-0.307138\pi\) | ||||
0.569498 | + | 0.821993i | \(0.307138\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −50.0000 | −0.0148148 | ||||||||
\(226\) | 6101.68 | 1.79592 | ||||||||
\(227\) | 3910.96 | 1.14352 | 0.571762 | − | 0.820420i | \(-0.306260\pi\) | ||||
0.571762 | + | 0.820420i | \(0.306260\pi\) | |||||||
\(228\) | 7248.29 | 2.10539 | ||||||||
\(229\) | 354.327 | 0.102247 | 0.0511236 | − | 0.998692i | \(-0.483720\pi\) | ||||
0.0511236 | + | 0.998692i | \(0.483720\pi\) | |||||||
\(230\) | −2176.99 | −0.624116 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3275.87 | −0.927033 | ||||||||
\(233\) | 6492.48 | 1.82548 | 0.912739 | − | 0.408543i | \(-0.133963\pi\) | ||||
0.912739 | + | 0.408543i | \(0.133963\pi\) | |||||||
\(234\) | −615.831 | −0.172043 | ||||||||
\(235\) | −738.325 | −0.204949 | ||||||||
\(236\) | 3430.98 | 0.946346 | ||||||||
\(237\) | 6165.93 | 1.68996 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −342.688 | −0.0927474 | −0.0463737 | − | 0.998924i | \(-0.514766\pi\) | ||||
−0.0463737 | + | 0.998924i | \(0.514766\pi\) | |||||||
\(240\) | −900.000 | −0.242061 | ||||||||
\(241\) | 2313.67 | 0.618408 | 0.309204 | − | 0.950996i | \(-0.399937\pi\) | ||||
0.309204 | + | 0.950996i | \(0.399937\pi\) | |||||||
\(242\) | −4064.49 | −1.07965 | ||||||||
\(243\) | 560.000 | 0.147835 | ||||||||
\(244\) | 3625.96 | 0.951347 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3920.84 | −1.01619 | ||||||||
\(247\) | 9724.94 | 2.50519 | ||||||||
\(248\) | −2375.62 | −0.608275 | ||||||||
\(249\) | −3216.62 | −0.818656 | ||||||||
\(250\) | 539.578 | 0.136504 | ||||||||
\(251\) | 3989.29 | 1.00319 | 0.501597 | − | 0.865101i | \(-0.332746\pi\) | ||||
0.501597 | + | 0.865101i | \(0.332746\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1990.43 | −0.494614 | ||||||||
\(254\) | −8832.95 | −2.18200 | ||||||||
\(255\) | −783.312 | −0.192364 | ||||||||
\(256\) | 262.376 | 0.0640566 | ||||||||
\(257\) | 2291.32 | 0.556142 | 0.278071 | − | 0.960560i | \(-0.410305\pi\) | ||||
0.278071 | + | 0.960560i | \(0.410305\pi\) | |||||||
\(258\) | −392.824 | −0.0947912 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3792.48 | 0.904614 | ||||||||
\(261\) | 576.396 | 0.136697 | ||||||||
\(262\) | 4922.32 | 1.16070 | ||||||||
\(263\) | 6360.47 | 1.49127 | 0.745634 | − | 0.666356i | \(-0.232147\pi\) | ||||
0.745634 | + | 0.666356i | \(0.232147\pi\) | |||||||
\(264\) | 1121.53 | 0.261460 | ||||||||
\(265\) | −639.975 | −0.148352 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5701.59 | 1.30686 | ||||||||
\(268\) | −897.404 | −0.204543 | ||||||||
\(269\) | −991.345 | −0.224697 | −0.112348 | − | 0.993669i | \(-0.535837\pi\) | ||||
−0.112348 | + | 0.993669i | \(0.535837\pi\) | |||||||
\(270\) | −3129.55 | −0.705402 | ||||||||
\(271\) | 730.977 | 0.163851 | 0.0819257 | − | 0.996638i | \(-0.473893\pi\) | ||||
0.0819257 | + | 0.996638i | \(0.473893\pi\) | |||||||
\(272\) | 1127.97 | 0.251446 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2116.62 | −0.466679 | ||||||||
\(275\) | 493.338 | 0.108180 | ||||||||
\(276\) | −5362.64 | −1.16954 | ||||||||
\(277\) | −3538.63 | −0.767566 | −0.383783 | − | 0.923423i | \(-0.625379\pi\) | ||||
−0.383783 | + | 0.923423i | \(0.625379\pi\) | |||||||
\(278\) | 12086.5 | 2.60756 | ||||||||
\(279\) | 417.995 | 0.0896943 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4663.20 | −0.989975 | −0.494988 | − | 0.868900i | \(-0.664827\pi\) | ||||
−0.494988 | + | 0.868900i | \(0.664827\pi\) | |||||||
\(282\) | −3187.07 | −0.673005 | ||||||||
\(283\) | −2104.95 | −0.442142 | −0.221071 | − | 0.975258i | \(-0.570955\pi\) | ||||
−0.221071 | + | 0.975258i | \(0.570955\pi\) | |||||||
\(284\) | −3357.30 | −0.701476 | ||||||||
\(285\) | 3408.31 | 0.708389 | ||||||||
\(286\) | 6076.25 | 1.25628 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 492.665 | 0.100801 | ||||||||
\(289\) | −3931.27 | −0.800178 | ||||||||
\(290\) | −6220.21 | −1.25953 | ||||||||
\(291\) | 7059.96 | 1.42221 | ||||||||
\(292\) | −11625.6 | −2.32992 | ||||||||
\(293\) | −6594.66 | −1.31489 | −0.657447 | − | 0.753501i | \(-0.728364\pi\) | ||||
−0.657447 | + | 0.753501i | \(0.728364\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1613.32 | 0.318412 | ||||||||
\(296\) | 3522.91 | 0.691774 | ||||||||
\(297\) | −2861.36 | −0.559033 | ||||||||
\(298\) | 5033.69 | 0.978503 | ||||||||
\(299\) | −7194.99 | −1.39163 | ||||||||
\(300\) | 1329.16 | 0.255796 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4142.15 | 0.789252 | ||||||||
\(303\) | −2728.36 | −0.517295 | ||||||||
\(304\) | −4907.97 | −0.925958 | ||||||||
\(305\) | 1705.01 | 0.320094 | ||||||||
\(306\) | 270.501 | 0.0505344 | ||||||||
\(307\) | −2672.97 | −0.496920 | −0.248460 | − | 0.968642i | \(-0.579924\pi\) | ||||
−0.248460 | + | 0.968642i | \(0.579924\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3904.95 | 0.718915 | ||||||||
\(310\) | −4510.82 | −0.826443 | ||||||||
\(311\) | −855.698 | −0.156020 | −0.0780099 | − | 0.996953i | \(-0.524857\pi\) | ||||
−0.0780099 | + | 0.996953i | \(0.524857\pi\) | |||||||
\(312\) | 4054.09 | 0.735634 | ||||||||
\(313\) | −3349.99 | −0.604960 | −0.302480 | − | 0.953156i | \(-0.597815\pi\) | ||||
−0.302480 | + | 0.953156i | \(0.597815\pi\) | |||||||
\(314\) | −4405.81 | −0.791828 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13112.8 | 2.33434 | ||||||||
\(317\) | 7633.05 | 1.35241 | 0.676206 | − | 0.736712i | \(-0.263623\pi\) | ||||
0.676206 | + | 0.736712i | \(0.263623\pi\) | |||||||
\(318\) | −2762.53 | −0.487154 | ||||||||
\(319\) | −5687.16 | −0.998180 | ||||||||
\(320\) | −3876.62 | −0.677218 | ||||||||
\(321\) | −3103.30 | −0.539593 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4271.64 | −0.735852 | ||||||||
\(324\) | −7134.91 | −1.22341 | ||||||||
\(325\) | 1783.31 | 0.304370 | ||||||||
\(326\) | −6759.90 | −1.14845 | ||||||||
\(327\) | 20.9397 | 0.00354119 | ||||||||
\(328\) | −2064.91 | −0.347609 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2129.55 | 0.355236 | ||||||||
\(331\) | −3321.70 | −0.551593 | −0.275796 | − | 0.961216i | \(-0.588942\pi\) | ||||
−0.275796 | + | 0.961216i | \(0.588942\pi\) | |||||||
\(332\) | −6840.63 | −1.13081 | ||||||||
\(333\) | −619.863 | −0.102007 | ||||||||
\(334\) | −4879.10 | −0.799319 | ||||||||
\(335\) | −421.980 | −0.0688216 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2233.98 | −0.361107 | −0.180553 | − | 0.983565i | \(-0.557789\pi\) | ||||
−0.180553 | + | 0.983565i | \(0.557789\pi\) | |||||||
\(338\) | 12480.8 | 2.00847 | ||||||||
\(339\) | 7067.65 | 1.13234 | ||||||||
\(340\) | −1665.83 | −0.265713 | ||||||||
\(341\) | −4124.25 | −0.654958 | ||||||||
\(342\) | −1176.99 | −0.186095 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −206.881 | −0.0324252 | ||||||||
\(345\) | −2521.64 | −0.393508 | ||||||||
\(346\) | 10978.6 | 1.70582 | ||||||||
\(347\) | 2528.61 | 0.391190 | 0.195595 | − | 0.980685i | \(-0.437336\pi\) | ||||
0.195595 | + | 0.980685i | \(0.437336\pi\) | |||||||
\(348\) | −15322.4 | −2.36025 | ||||||||
\(349\) | 1291.00 | 0.198011 | 0.0990054 | − | 0.995087i | \(-0.468434\pi\) | ||||
0.0990054 | + | 0.995087i | \(0.468434\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10343.2 | −1.57288 | ||||||||
\(352\) | −4861.00 | −0.736058 | ||||||||
\(353\) | −7768.64 | −1.17134 | −0.585670 | − | 0.810550i | \(-0.699169\pi\) | ||||
−0.585670 | + | 0.810550i | \(0.699169\pi\) | |||||||
\(354\) | 6964.12 | 1.04559 | ||||||||
\(355\) | −1578.68 | −0.236022 | ||||||||
\(356\) | 12125.3 | 1.80516 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5225.92 | −0.771504 | ||||||||
\(359\) | −2284.14 | −0.335800 | −0.167900 | − | 0.985804i | \(-0.553699\pi\) | ||||
−0.167900 | + | 0.985804i | \(0.553699\pi\) | |||||||
\(360\) | −113.668 | −0.0166411 | ||||||||
\(361\) | 11727.5 | 1.70980 | ||||||||
\(362\) | −13085.1 | −1.89982 | ||||||||
\(363\) | −4707.94 | −0.680725 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5466.62 | −0.783935 | ||||||||
\(366\) | 7359.90 | 1.05112 | ||||||||
\(367\) | 10707.0 | 1.52289 | 0.761446 | − | 0.648229i | \(-0.224490\pi\) | ||||
0.761446 | + | 0.648229i | \(0.224490\pi\) | |||||||
\(368\) | 3631.16 | 0.514367 | ||||||||
\(369\) | 363.325 | 0.0512573 | ||||||||
\(370\) | 6689.29 | 0.939891 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −11111.6 | −1.54868 | ||||||||
\(373\) | −830.429 | −0.115276 | −0.0576381 | − | 0.998338i | \(-0.518357\pi\) | ||||
−0.0576381 | + | 0.998338i | \(0.518357\pi\) | |||||||
\(374\) | −2668.97 | −0.369008 | ||||||||
\(375\) | 625.000 | 0.0860663 | ||||||||
\(376\) | −1678.47 | −0.230214 | ||||||||
\(377\) | −20557.9 | −2.80845 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5253.17 | 0.711972 | 0.355986 | − | 0.934491i | \(-0.384145\pi\) | ||||
0.355986 | + | 0.934491i | \(0.384145\pi\) | |||||||
\(380\) | 7248.29 | 0.978498 | ||||||||
\(381\) | −10231.3 | −1.37576 | ||||||||
\(382\) | −9361.19 | −1.25382 | ||||||||
\(383\) | −11243.9 | −1.50010 | −0.750048 | − | 0.661383i | \(-0.769970\pi\) | ||||
−0.750048 | + | 0.661383i | \(0.769970\pi\) | |||||||
\(384\) | −6880.63 | −0.914390 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6433.84 | 0.848378 | ||||||||
\(387\) | 36.4010 | 0.00478131 | ||||||||
\(388\) | 15014.1 | 1.96449 | ||||||||
\(389\) | −8506.85 | −1.10878 | −0.554389 | − | 0.832258i | \(-0.687048\pi\) | ||||
−0.554389 | + | 0.832258i | \(0.687048\pi\) | |||||||
\(390\) | 7697.89 | 0.999482 | ||||||||
\(391\) | 3160.37 | 0.408764 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5701.59 | 0.731824 | ||||||||
\(394\) | 14592.6 | 1.86590 | ||||||||
\(395\) | 6165.93 | 0.785421 | ||||||||
\(396\) | −419.662 | −0.0532546 | ||||||||
\(397\) | 3123.24 | 0.394838 | 0.197419 | − | 0.980319i | \(-0.436744\pi\) | ||||
0.197419 | + | 0.980319i | \(0.436744\pi\) | |||||||
\(398\) | 19836.3 | 2.49825 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −900.000 | −0.112500 | ||||||||
\(401\) | −11255.3 | −1.40166 | −0.700828 | − | 0.713330i | \(-0.747186\pi\) | ||||
−0.700828 | + | 0.713330i | \(0.747186\pi\) | |||||||
\(402\) | −1821.53 | −0.225994 | ||||||||
\(403\) | −14908.3 | −1.84277 | ||||||||
\(404\) | −5802.27 | −0.714539 | ||||||||
\(405\) | −3355.00 | −0.411633 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6116.03 | 0.744866 | ||||||||
\(408\) | −1780.74 | −0.216078 | ||||||||
\(409\) | −7919.92 | −0.957494 | −0.478747 | − | 0.877953i | \(-0.658909\pi\) | ||||
−0.478747 | + | 0.877953i | \(0.658909\pi\) | |||||||
\(410\) | −3920.84 | −0.472285 | ||||||||
\(411\) | −2451.71 | −0.294243 | ||||||||
\(412\) | 8304.46 | 0.993037 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 870.797 | 0.103375 | ||||||||
\(415\) | −3216.62 | −0.380477 | ||||||||
\(416\) | −17571.5 | −2.07095 | ||||||||
\(417\) | 14000.0 | 1.64408 | ||||||||
\(418\) | 11613.1 | 1.35889 | ||||||||
\(419\) | −5257.28 | −0.612972 | −0.306486 | − | 0.951875i | \(-0.599153\pi\) | ||||
−0.306486 | + | 0.951875i | \(0.599153\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1457.36 | 0.168711 | 0.0843556 | − | 0.996436i | \(-0.473117\pi\) | ||||
0.0843556 | + | 0.996436i | \(0.473117\pi\) | |||||||
\(422\) | −21534.2 | −2.48405 | ||||||||
\(423\) | 295.330 | 0.0339467 | ||||||||
\(424\) | −1454.89 | −0.166640 | ||||||||
\(425\) | −783.312 | −0.0894029 | ||||||||
\(426\) | −6814.57 | −0.775040 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6599.63 | −0.745339 | ||||||||
\(429\) | 7038.20 | 0.792092 | ||||||||
\(430\) | −392.824 | −0.0440550 | ||||||||
\(431\) | −15291.2 | −1.70893 | −0.854467 | − | 0.519506i | \(-0.826116\pi\) | ||||
−0.854467 | + | 0.519506i | \(0.826116\pi\) | |||||||
\(432\) | 5220.00 | 0.581360 | ||||||||
\(433\) | 187.260 | 0.0207832 | 0.0103916 | − | 0.999946i | \(-0.496692\pi\) | ||||
0.0103916 | + | 0.999946i | \(0.496692\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7204.95 | −0.794140 | ||||||||
\(436\) | 44.5314 | 0.00489144 | ||||||||
\(437\) | −13751.2 | −1.50529 | ||||||||
\(438\) | −23597.4 | −2.57426 | ||||||||
\(439\) | 3587.92 | 0.390073 | 0.195037 | − | 0.980796i | \(-0.437517\pi\) | ||||
0.195037 | + | 0.980796i | \(0.437517\pi\) | |||||||
\(440\) | 1121.53 | 0.121515 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9647.76 | −1.03823 | ||||||||
\(443\) | 4915.65 | 0.527200 | 0.263600 | − | 0.964632i | \(-0.415090\pi\) | ||||
0.263600 | + | 0.964632i | \(0.415090\pi\) | |||||||
\(444\) | 16477.9 | 1.76128 | ||||||||
\(445\) | 5701.59 | 0.607373 | ||||||||
\(446\) | 16372.8 | 1.73829 | ||||||||
\(447\) | 5830.58 | 0.616951 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7091.12 | 0.745324 | 0.372662 | − | 0.927967i | \(-0.378445\pi\) | ||||
0.372662 | + | 0.927967i | \(0.378445\pi\) | |||||||
\(450\) | −215.831 | −0.0226097 | ||||||||
\(451\) | −3584.84 | −0.374287 | ||||||||
\(452\) | 15030.4 | 1.56410 | ||||||||
\(453\) | 4797.91 | 0.497628 | ||||||||
\(454\) | 16882.2 | 1.74520 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7748.29 | 0.795717 | ||||||||
\(457\) | 5051.81 | 0.517098 | 0.258549 | − | 0.965998i | \(-0.416756\pi\) | ||||
0.258549 | + | 0.965998i | \(0.416756\pi\) | |||||||
\(458\) | 1529.50 | 0.156045 | ||||||||
\(459\) | 4543.21 | 0.462002 | ||||||||
\(460\) | −5362.64 | −0.543553 | ||||||||
\(461\) | −16681.3 | −1.68531 | −0.842653 | − | 0.538456i | \(-0.819008\pi\) | ||||
−0.842653 | + | 0.538456i | \(0.819008\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15569.6 | 1.56280 | 0.781402 | − | 0.624027i | \(-0.214505\pi\) | ||||
0.781402 | + | 0.624027i | \(0.214505\pi\) | |||||||
\(464\) | 10375.1 | 1.03805 | ||||||||
\(465\) | −5224.94 | −0.521077 | ||||||||
\(466\) | 28025.6 | 2.78597 | ||||||||
\(467\) | 3328.35 | 0.329802 | 0.164901 | − | 0.986310i | \(-0.447269\pi\) | ||||
0.164901 | + | 0.986310i | \(0.447269\pi\) | |||||||
\(468\) | −1516.99 | −0.149835 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3187.07 | −0.312784 | ||||||||
\(471\) | −5103.30 | −0.499252 | ||||||||
\(472\) | 3667.65 | 0.357664 | ||||||||
\(473\) | −359.160 | −0.0349137 | ||||||||
\(474\) | 26616.0 | 2.57914 | ||||||||
\(475\) | 3408.31 | 0.329230 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 255.990 | 0.0245723 | ||||||||
\(478\) | −1479.25 | −0.141547 | ||||||||
\(479\) | −14607.5 | −1.39339 | −0.696695 | − | 0.717367i | \(-0.745347\pi\) | ||||
−0.696695 | + | 0.717367i | \(0.745347\pi\) | |||||||
\(480\) | −6158.31 | −0.585598 | ||||||||
\(481\) | 22108.2 | 2.09573 | ||||||||
\(482\) | 9987.23 | 0.943789 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10012.2 | −0.940285 | ||||||||
\(485\) | 7059.96 | 0.660982 | ||||||||
\(486\) | 2417.31 | 0.225620 | ||||||||
\(487\) | −1879.49 | −0.174882 | −0.0874412 | − | 0.996170i | \(-0.527869\pi\) | ||||
−0.0874412 | + | 0.996170i | \(0.527869\pi\) | |||||||
\(488\) | 3876.09 | 0.359554 | ||||||||
\(489\) | −7830.08 | −0.724107 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3221.13 | 0.296064 | 0.148032 | − | 0.988983i | \(-0.452706\pi\) | ||||
0.148032 | + | 0.988983i | \(0.452706\pi\) | |||||||
\(492\) | −9658.31 | −0.885021 | ||||||||
\(493\) | 9029.96 | 0.824927 | ||||||||
\(494\) | 41978.9 | 3.82332 | ||||||||
\(495\) | −197.335 | −0.0179183 | ||||||||
\(496\) | 7523.91 | 0.681116 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −13885.0 | −1.24940 | ||||||||
\(499\) | 9713.81 | 0.871443 | 0.435721 | − | 0.900082i | \(-0.356493\pi\) | ||||
0.435721 | + | 0.900082i | \(0.356493\pi\) | |||||||
\(500\) | 1329.16 | 0.118883 | ||||||||
\(501\) | −5651.52 | −0.503975 | ||||||||
\(502\) | 17220.3 | 1.53103 | ||||||||
\(503\) | 2078.32 | 0.184230 | 0.0921152 | − | 0.995748i | \(-0.470637\pi\) | ||||
0.0921152 | + | 0.995748i | \(0.470637\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2728.36 | −0.240417 | ||||||||
\(506\) | −8591.94 | −0.754858 | ||||||||
\(507\) | 14456.6 | 1.26635 | ||||||||
\(508\) | −21758.4 | −1.90034 | ||||||||
\(509\) | −18974.5 | −1.65232 | −0.826158 | − | 0.563439i | \(-0.809478\pi\) | ||||
−0.826158 | + | 0.563439i | \(0.809478\pi\) | |||||||
\(510\) | −3381.27 | −0.293578 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 12141.6 | 1.04802 | ||||||||
\(513\) | −19768.2 | −1.70134 | ||||||||
\(514\) | 9890.77 | 0.848761 | ||||||||
\(515\) | 3904.95 | 0.334122 | ||||||||
\(516\) | −967.652 | −0.0825553 | ||||||||
\(517\) | −2913.95 | −0.247883 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12716.7 | 1.07553 | ||||||||
\(520\) | 4054.09 | 0.341892 | ||||||||
\(521\) | 17523.6 | 1.47355 | 0.736777 | − | 0.676136i | \(-0.236347\pi\) | ||||
0.736777 | + | 0.676136i | \(0.236347\pi\) | |||||||
\(522\) | 2488.09 | 0.208622 | ||||||||
\(523\) | 15218.6 | 1.27239 | 0.636197 | − | 0.771527i | \(-0.280507\pi\) | ||||
0.636197 | + | 0.771527i | \(0.280507\pi\) | |||||||
\(524\) | 12125.3 | 1.01087 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27455.8 | 2.27591 | ||||||||
\(527\) | 6548.41 | 0.541278 | ||||||||
\(528\) | −3552.03 | −0.292769 | ||||||||
\(529\) | −1993.15 | −0.163816 | ||||||||
\(530\) | −2762.53 | −0.226409 | ||||||||
\(531\) | −645.330 | −0.0527400 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12958.4 | −1.05308 | ||||||||
\(534\) | 24611.6 | 1.99447 | ||||||||
\(535\) | −3103.30 | −0.250780 | ||||||||
\(536\) | −959.308 | −0.0773056 | ||||||||
\(537\) | −6053.25 | −0.486438 | ||||||||
\(538\) | −4279.26 | −0.342922 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7709.11 | −0.614346 | ||||||||
\(541\) | −15559.3 | −1.23650 | −0.618249 | − | 0.785983i | \(-0.712158\pi\) | ||||
−0.618249 | + | 0.785983i | \(0.712158\pi\) | |||||||
\(542\) | 3155.36 | 0.250063 | ||||||||
\(543\) | −15156.6 | −1.19785 | ||||||||
\(544\) | 7718.21 | 0.608301 | ||||||||
\(545\) | 20.9397 | 0.00164579 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8690.70 | −0.679319 | −0.339660 | − | 0.940548i | \(-0.610312\pi\) | ||||
−0.339660 | + | 0.940548i | \(0.610312\pi\) | |||||||
\(548\) | −5213.93 | −0.406438 | ||||||||
\(549\) | −682.005 | −0.0530187 | ||||||||
\(550\) | 2129.55 | 0.165099 | ||||||||
\(551\) | −39290.8 | −3.03783 | ||||||||
\(552\) | −5732.56 | −0.442018 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −15274.9 | −1.17143 | ||||||||
\(555\) | 7748.29 | 0.592606 | ||||||||
\(556\) | 29773.1 | 2.27097 | ||||||||
\(557\) | −7376.26 | −0.561117 | −0.280559 | − | 0.959837i | \(-0.590520\pi\) | ||||
−0.280559 | + | 0.959837i | \(0.590520\pi\) | |||||||
\(558\) | 1804.33 | 0.136888 | ||||||||
\(559\) | −1298.29 | −0.0982320 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3091.50 | −0.232662 | ||||||||
\(562\) | −20129.3 | −1.51086 | ||||||||
\(563\) | 12875.4 | 0.963825 | 0.481913 | − | 0.876219i | \(-0.339942\pi\) | ||||
0.481913 | + | 0.876219i | \(0.339942\pi\) | |||||||
\(564\) | −7850.79 | −0.586131 | ||||||||
\(565\) | 7067.65 | 0.526263 | ||||||||
\(566\) | −9086.28 | −0.674779 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3588.89 | −0.265117 | ||||||||
\(569\) | −12064.6 | −0.888882 | −0.444441 | − | 0.895808i | \(-0.646598\pi\) | ||||
−0.444441 | + | 0.895808i | \(0.646598\pi\) | |||||||
\(570\) | 14712.4 | 1.08111 | ||||||||
\(571\) | 23745.6 | 1.74032 | 0.870158 | − | 0.492772i | \(-0.164016\pi\) | ||||
0.870158 | + | 0.492772i | \(0.164016\pi\) | |||||||
\(572\) | 14967.8 | 1.09412 | ||||||||
\(573\) | −10843.2 | −0.790542 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2521.64 | −0.182886 | ||||||||
\(576\) | 1550.65 | 0.112171 | ||||||||
\(577\) | −9846.08 | −0.710394 | −0.355197 | − | 0.934791i | \(-0.615586\pi\) | ||||
−0.355197 | + | 0.934791i | \(0.615586\pi\) | |||||||
\(578\) | −16969.8 | −1.22120 | ||||||||
\(579\) | 7452.40 | 0.534907 | ||||||||
\(580\) | −15322.4 | −1.09695 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 30475.2 | 2.17051 | ||||||||
\(583\) | −2525.79 | −0.179430 | ||||||||
\(584\) | −12427.6 | −0.880575 | ||||||||
\(585\) | −713.325 | −0.0504143 | ||||||||
\(586\) | −28466.7 | −2.00674 | ||||||||
\(587\) | 10074.7 | 0.708392 | 0.354196 | − | 0.935171i | \(-0.384755\pi\) | ||||
0.354196 | + | 0.935171i | \(0.384755\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28493.1 | −1.99328 | ||||||||
\(590\) | 6964.12 | 0.485946 | ||||||||
\(591\) | 16902.8 | 1.17646 | ||||||||
\(592\) | −11157.5 | −0.774615 | ||||||||
\(593\) | −7387.25 | −0.511565 | −0.255782 | − | 0.966734i | \(-0.582333\pi\) | ||||
−0.255782 | + | 0.966734i | \(0.582333\pi\) | |||||||
\(594\) | −12351.4 | −0.853172 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12399.6 | 0.852194 | ||||||||
\(597\) | 22976.6 | 1.57516 | ||||||||
\(598\) | −31058.1 | −2.12384 | ||||||||
\(599\) | 1252.73 | 0.0854510 | 0.0427255 | − | 0.999087i | \(-0.486396\pi\) | ||||
0.0427255 | + | 0.999087i | \(0.486396\pi\) | |||||||
\(600\) | 1420.84 | 0.0966762 | ||||||||
\(601\) | −1800.81 | −0.122224 | −0.0611120 | − | 0.998131i | \(-0.519465\pi\) | ||||
−0.0611120 | + | 0.998131i | \(0.519465\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 168.792 | 0.0113992 | ||||||||
\(604\) | 10203.5 | 0.687373 | ||||||||
\(605\) | −4707.94 | −0.316372 | ||||||||
\(606\) | −11777.3 | −0.789473 | ||||||||
\(607\) | 2497.06 | 0.166973 | 0.0834863 | − | 0.996509i | \(-0.473395\pi\) | ||||
0.0834863 | + | 0.996509i | \(0.473395\pi\) | |||||||
\(608\) | −33583.1 | −2.24009 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7359.90 | 0.488514 | ||||||||
\(611\) | −10533.3 | −0.697434 | ||||||||
\(612\) | 666.332 | 0.0440113 | ||||||||
\(613\) | −19750.8 | −1.30135 | −0.650674 | − | 0.759357i | \(-0.725513\pi\) | ||||
−0.650674 | + | 0.759357i | \(0.725513\pi\) | |||||||
\(614\) | −11538.2 | −0.758378 | ||||||||
\(615\) | −4541.56 | −0.297778 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16797.4 | 1.09601 | 0.548004 | − | 0.836476i | \(-0.315388\pi\) | ||||
0.548004 | + | 0.836476i | \(0.315388\pi\) | |||||||
\(618\) | 16856.2 | 1.09718 | ||||||||
\(619\) | 26547.4 | 1.72379 | 0.861897 | − | 0.507084i | \(-0.169277\pi\) | ||||
0.861897 | + | 0.507084i | \(0.169277\pi\) | |||||||
\(620\) | −11111.6 | −0.719763 | ||||||||
\(621\) | 14625.5 | 0.945090 | ||||||||
\(622\) | −3693.73 | −0.238111 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −12839.8 | −0.823727 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −14460.6 | −0.923264 | ||||||||
\(627\) | 13451.6 | 0.856786 | ||||||||
\(628\) | −10852.9 | −0.689616 | ||||||||
\(629\) | −9710.93 | −0.615580 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5394.86 | 0.340358 | 0.170179 | − | 0.985413i | \(-0.445565\pi\) | ||||
0.170179 | + | 0.985413i | \(0.445565\pi\) | |||||||
\(632\) | 14017.3 | 0.882245 | ||||||||
\(633\) | −24943.3 | −1.56620 | ||||||||
\(634\) | 32949.0 | 2.06399 | ||||||||
\(635\) | −10231.3 | −0.639398 | ||||||||
\(636\) | −6805.01 | −0.424271 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −24549.3 | −1.52338 | ||||||||
\(639\) | 631.472 | 0.0390933 | ||||||||
\(640\) | −6880.63 | −0.424970 | ||||||||
\(641\) | 2452.41 | 0.151114 | 0.0755572 | − | 0.997141i | \(-0.475926\pi\) | ||||
0.0755572 | + | 0.997141i | \(0.475926\pi\) | |||||||
\(642\) | −13395.8 | −0.823504 | ||||||||
\(643\) | 7074.97 | 0.433919 | 0.216959 | − | 0.976181i | \(-0.430386\pi\) | ||||
0.216959 | + | 0.976181i | \(0.430386\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −455.013 | −0.0277769 | ||||||||
\(646\) | −18439.1 | −1.12303 | ||||||||
\(647\) | 3341.37 | 0.203034 | 0.101517 | − | 0.994834i | \(-0.467630\pi\) | ||||
0.101517 | + | 0.994834i | \(0.467630\pi\) | |||||||
\(648\) | −7627.09 | −0.462377 | ||||||||
\(649\) | 6367.31 | 0.385114 | ||||||||
\(650\) | 7697.89 | 0.464517 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16651.8 | −1.00021 | ||||||||
\(653\) | −23061.6 | −1.38204 | −0.691019 | − | 0.722837i | \(-0.742838\pi\) | ||||
−0.691019 | + | 0.722837i | \(0.742838\pi\) | |||||||
\(654\) | 90.3888 | 0.00540441 | ||||||||
\(655\) | 5701.59 | 0.340121 | ||||||||
\(656\) | 6539.85 | 0.389235 | ||||||||
\(657\) | 2186.65 | 0.129847 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1742.64 | 0.103010 | 0.0515049 | − | 0.998673i | \(-0.483598\pi\) | ||||
0.0515049 | + | 0.998673i | \(0.483598\pi\) | |||||||
\(660\) | 5245.78 | 0.309381 | ||||||||
\(661\) | −12576.5 | −0.740046 | −0.370023 | − | 0.929023i | \(-0.620650\pi\) | ||||
−0.370023 | + | 0.929023i | \(0.620650\pi\) | |||||||
\(662\) | −14338.5 | −0.841817 | ||||||||
\(663\) | −11175.1 | −0.654609 | ||||||||
\(664\) | −7312.51 | −0.427380 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2675.72 | −0.155679 | ||||||||
\(667\) | 29069.2 | 1.68750 | ||||||||
\(668\) | −12018.8 | −0.696141 | ||||||||
\(669\) | 18964.8 | 1.09600 | ||||||||
\(670\) | −1821.53 | −0.105033 | ||||||||
\(671\) | 6729.17 | 0.387149 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10680.8 | −0.611760 | −0.305880 | − | 0.952070i | \(-0.598951\pi\) | ||||
−0.305880 | + | 0.952070i | \(0.598951\pi\) | |||||||
\(674\) | −9643.27 | −0.551105 | ||||||||
\(675\) | −3625.00 | −0.206706 | ||||||||
\(676\) | 30744.2 | 1.74921 | ||||||||
\(677\) | −29559.1 | −1.67806 | −0.839032 | − | 0.544082i | \(-0.816878\pi\) | ||||
−0.839032 | + | 0.544082i | \(0.816878\pi\) | |||||||
\(678\) | 30508.4 | 1.72812 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1780.74 | −0.100424 | ||||||||
\(681\) | 19554.8 | 1.10036 | ||||||||
\(682\) | −17802.8 | −0.999569 | ||||||||
\(683\) | 10250.4 | 0.574263 | 0.287132 | − | 0.957891i | \(-0.407298\pi\) | ||||
0.287132 | + | 0.957891i | \(0.407298\pi\) | |||||||
\(684\) | −2899.31 | −0.162073 | ||||||||
\(685\) | −2451.71 | −0.136752 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1771.64 | 0.0983875 | ||||||||
\(688\) | 655.218 | 0.0363081 | ||||||||
\(689\) | −9130.20 | −0.504837 | ||||||||
\(690\) | −10885.0 | −0.600556 | ||||||||
\(691\) | −8874.04 | −0.488544 | −0.244272 | − | 0.969707i | \(-0.578549\pi\) | ||||
−0.244272 | + | 0.969707i | \(0.578549\pi\) | |||||||
\(692\) | 27043.9 | 1.48563 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10915.1 | 0.597018 | ||||||||
\(695\) | 14000.0 | 0.764101 | ||||||||
\(696\) | −16379.4 | −0.892038 | ||||||||
\(697\) | 5691.94 | 0.309322 | ||||||||
\(698\) | 5572.77 | 0.302196 | ||||||||
\(699\) | 32462.4 | 1.75657 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22086.2 | −1.18999 | −0.594996 | − | 0.803729i | \(-0.702846\pi\) | ||||
−0.594996 | + | 0.803729i | \(0.702846\pi\) | |||||||
\(702\) | −44647.8 | −2.40046 | ||||||||
\(703\) | 42253.7 | 2.26690 | ||||||||
\(704\) | −15299.9 | −0.819085 | ||||||||
\(705\) | −3691.62 | −0.197212 | ||||||||
\(706\) | −33534.3 | −1.78765 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 17154.9 | 0.910622 | ||||||||
\(709\) | −27878.9 | −1.47675 | −0.738373 | − | 0.674392i | \(-0.764406\pi\) | ||||
−0.738373 | + | 0.674392i | \(0.764406\pi\) | |||||||
\(710\) | −6814.57 | −0.360206 | ||||||||
\(711\) | −2466.37 | −0.130093 | ||||||||
\(712\) | 12961.7 | 0.682248 | ||||||||
\(713\) | 21080.6 | 1.10726 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7038.20 | 0.368131 | ||||||||
\(716\) | −12873.1 | −0.671916 | ||||||||
\(717\) | −1713.44 | −0.0892462 | ||||||||
\(718\) | −9859.76 | −0.512483 | ||||||||
\(719\) | 25863.3 | 1.34150 | 0.670750 | − | 0.741684i | \(-0.265973\pi\) | ||||
0.670750 | + | 0.741684i | \(0.265973\pi\) | |||||||
\(720\) | 360.000 | 0.0186339 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 50623.4 | 2.60943 | ||||||||
\(723\) | 11568.3 | 0.595064 | ||||||||
\(724\) | −32232.8 | −1.65459 | ||||||||
\(725\) | −7204.95 | −0.369083 | ||||||||
\(726\) | −20322.4 | −1.03889 | ||||||||
\(727\) | 29157.0 | 1.48744 | 0.743722 | − | 0.668489i | \(-0.233059\pi\) | ||||
0.743722 | + | 0.668489i | \(0.233059\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20917.0 | 1.06269 | ||||||||
\(730\) | −23597.4 | −1.19641 | ||||||||
\(731\) | 570.267 | 0.0288538 | ||||||||
\(732\) | 18129.8 | 0.915434 | ||||||||
\(733\) | 11006.1 | 0.554595 | 0.277297 | − | 0.960784i | \(-0.410561\pi\) | ||||
0.277297 | + | 0.960784i | \(0.410561\pi\) | |||||||
\(734\) | 46218.1 | 2.32417 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 24846.4 | 1.24436 | ||||||||
\(737\) | −1665.43 | −0.0832386 | ||||||||
\(738\) | 1568.34 | 0.0782267 | ||||||||
\(739\) | −37214.4 | −1.85244 | −0.926221 | − | 0.376982i | \(-0.876962\pi\) | ||||
−0.926221 | + | 0.376982i | \(0.876962\pi\) | |||||||
\(740\) | 16477.9 | 0.818567 | ||||||||
\(741\) | 48624.7 | 2.41062 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11214.5 | 0.553730 | 0.276865 | − | 0.960909i | \(-0.410704\pi\) | ||||
0.276865 | + | 0.960909i | \(0.410704\pi\) | |||||||
\(744\) | −11878.1 | −0.585313 | ||||||||
\(745\) | 5830.58 | 0.286733 | ||||||||
\(746\) | −3584.65 | −0.175930 | ||||||||
\(747\) | 1286.65 | 0.0630202 | ||||||||
\(748\) | −6574.54 | −0.321375 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2697.89 | 0.131351 | ||||||||
\(751\) | 6965.26 | 0.338437 | 0.169218 | − | 0.985579i | \(-0.445876\pi\) | ||||
0.169218 | + | 0.985579i | \(0.445876\pi\) | |||||||
\(752\) | 5315.94 | 0.257782 | ||||||||
\(753\) | 19946.4 | 0.965324 | ||||||||
\(754\) | −88740.7 | −4.28613 | ||||||||
\(755\) | 4797.91 | 0.231276 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19352.8 | −0.929180 | −0.464590 | − | 0.885526i | \(-0.653798\pi\) | ||||
−0.464590 | + | 0.885526i | \(0.653798\pi\) | |||||||
\(758\) | 22676.0 | 1.08658 | ||||||||
\(759\) | −9952.15 | −0.475942 | ||||||||
\(760\) | 7748.29 | 0.369816 | ||||||||
\(761\) | 32383.6 | 1.54258 | 0.771291 | − | 0.636483i | \(-0.219612\pi\) | ||||
0.771291 | + | 0.636483i | \(0.219612\pi\) | |||||||
\(762\) | −44164.8 | −2.09963 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −23059.7 | −1.09198 | ||||||||
\(765\) | 313.325 | 0.0148082 | ||||||||
\(766\) | −48535.7 | −2.28938 | ||||||||
\(767\) | 23016.5 | 1.08354 | ||||||||
\(768\) | 1311.88 | 0.0616385 | ||||||||
\(769\) | −25353.9 | −1.18893 | −0.594463 | − | 0.804123i | \(-0.702635\pi\) | ||||
−0.594463 | + | 0.804123i | \(0.702635\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11456.6 | 0.535148 | ||||||||
\(772\) | 15848.6 | 0.738867 | ||||||||
\(773\) | 26117.0 | 1.21522 | 0.607610 | − | 0.794236i | \(-0.292128\pi\) | ||||
0.607610 | + | 0.794236i | \(0.292128\pi\) | |||||||
\(774\) | 157.129 | 0.00729703 | ||||||||
\(775\) | −5224.94 | −0.242175 | ||||||||
\(776\) | 16049.8 | 0.742465 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −36720.9 | −1.69217 | ||||||||
\(779\) | −24766.5 | −1.13909 | ||||||||
\(780\) | 18962.4 | 0.870465 | ||||||||
\(781\) | −6230.58 | −0.285464 | ||||||||
\(782\) | 13642.1 | 0.623838 | ||||||||
\(783\) | 41788.7 | 1.90729 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5103.30 | −0.232031 | ||||||||
\(786\) | 24611.6 | 1.11688 | ||||||||
\(787\) | −2273.38 | −0.102970 | −0.0514849 | − | 0.998674i | \(-0.516395\pi\) | ||||
−0.0514849 | + | 0.998674i | \(0.516395\pi\) | |||||||
\(788\) | 35946.4 | 1.62505 | ||||||||
\(789\) | 31802.4 | 1.43497 | ||||||||
\(790\) | 26616.0 | 1.19868 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −448.612 | −0.0201272 | ||||||||
\(793\) | 24324.6 | 1.08927 | ||||||||
\(794\) | 13481.8 | 0.602585 | ||||||||
\(795\) | −3199.87 | −0.142752 | ||||||||
\(796\) | 48863.3 | 2.17577 | ||||||||
\(797\) | 2937.42 | 0.130551 | 0.0652753 | − | 0.997867i | \(-0.479207\pi\) | ||||
0.0652753 | + | 0.997867i | \(0.479207\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4626.71 | 0.204858 | ||||||||
\(800\) | −6158.31 | −0.272162 | ||||||||
\(801\) | −2280.63 | −0.100602 | ||||||||
\(802\) | −48585.0 | −2.13915 | ||||||||
\(803\) | −21575.1 | −0.948157 | ||||||||
\(804\) | −4487.02 | −0.196822 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −64353.6 | −2.81236 | ||||||||
\(807\) | −4956.73 | −0.216214 | ||||||||
\(808\) | −6202.52 | −0.270054 | ||||||||
\(809\) | −4317.51 | −0.187634 | −0.0938169 | − | 0.995589i | \(-0.529907\pi\) | ||||
−0.0938169 | + | 0.995589i | \(0.529907\pi\) | |||||||
\(810\) | −14482.3 | −0.628216 | ||||||||
\(811\) | 1286.12 | 0.0556863 | 0.0278432 | − | 0.999612i | \(-0.491136\pi\) | ||||
0.0278432 | + | 0.999612i | \(0.491136\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3654.89 | 0.157666 | ||||||||
\(814\) | 26400.6 | 1.13678 | ||||||||
\(815\) | −7830.08 | −0.336534 | ||||||||
\(816\) | 5639.85 | 0.241954 | ||||||||
\(817\) | −2481.32 | −0.106255 | ||||||||
\(818\) | −34187.3 | −1.46129 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9658.31 | −0.411321 | ||||||||
\(821\) | 26350.2 | 1.12013 | 0.560066 | − | 0.828448i | \(-0.310776\pi\) | ||||
0.560066 | + | 0.828448i | \(0.310776\pi\) | |||||||
\(822\) | −10583.1 | −0.449062 | ||||||||
\(823\) | 9820.05 | 0.415924 | 0.207962 | − | 0.978137i | \(-0.433317\pi\) | ||||
0.207962 | + | 0.978137i | \(0.433317\pi\) | |||||||
\(824\) | 8877.32 | 0.375311 | ||||||||
\(825\) | 2466.69 | 0.104096 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30370.7 | −1.27702 | −0.638509 | − | 0.769615i | \(-0.720448\pi\) | ||||
−0.638509 | + | 0.769615i | \(0.720448\pi\) | |||||||
\(828\) | 2145.06 | 0.0900312 | ||||||||
\(829\) | −30817.7 | −1.29112 | −0.645562 | − | 0.763708i | \(-0.723377\pi\) | ||||
−0.645562 | + | 0.763708i | \(0.723377\pi\) | |||||||
\(830\) | −13885.0 | −0.580668 | ||||||||
\(831\) | −17693.1 | −0.738590 | ||||||||
\(832\) | −55305.9 | −2.30455 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 60432.7 | 2.50913 | ||||||||
\(835\) | −5651.52 | −0.234226 | ||||||||
\(836\) | 28606.8 | 1.18348 | ||||||||
\(837\) | 30304.6 | 1.25147 | ||||||||
\(838\) | −22693.7 | −0.935491 | ||||||||
\(839\) | −24746.0 | −1.01827 | −0.509134 | − | 0.860688i | \(-0.670034\pi\) | ||||
−0.509134 | + | 0.860688i | \(0.670034\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58669.1 | 2.40556 | ||||||||
\(842\) | 6290.88 | 0.257480 | ||||||||
\(843\) | −23316.0 | −0.952604 | ||||||||
\(844\) | −53045.7 | −2.16340 | ||||||||
\(845\) | 14456.6 | 0.588548 | ||||||||
\(846\) | 1274.83 | 0.0518079 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4607.82 | 0.186596 | ||||||||
\(849\) | −10524.7 | −0.425452 | ||||||||
\(850\) | −3381.27 | −0.136443 | ||||||||
\(851\) | −31261.4 | −1.25926 | ||||||||
\(852\) | −16786.5 | −0.674995 | ||||||||
\(853\) | −11812.1 | −0.474135 | −0.237067 | − | 0.971493i | \(-0.576186\pi\) | ||||
−0.237067 | + | 0.971493i | \(0.576186\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1363.32 | −0.0545318 | ||||||||
\(856\) | −7054.89 | −0.281695 | ||||||||
\(857\) | −23440.6 | −0.934322 | −0.467161 | − | 0.884172i | \(-0.654723\pi\) | ||||
−0.467161 | + | 0.884172i | \(0.654723\pi\) | |||||||
\(858\) | 30381.3 | 1.20886 | ||||||||
\(859\) | 8945.58 | 0.355319 | 0.177660 | − | 0.984092i | \(-0.443147\pi\) | ||||
0.177660 | + | 0.984092i | \(0.443147\pi\) | |||||||
\(860\) | −967.652 | −0.0383682 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −66006.3 | −2.60810 | ||||||||
\(863\) | 19313.5 | 0.761806 | 0.380903 | − | 0.924615i | \(-0.375613\pi\) | ||||
0.380903 | + | 0.924615i | \(0.375613\pi\) | |||||||
\(864\) | 35718.2 | 1.40643 | ||||||||
\(865\) | 12716.7 | 0.499862 | ||||||||
\(866\) | 808.330 | 0.0317184 | ||||||||
\(867\) | −19656.4 | −0.769972 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24335.1 | 0.949955 | ||||||||
\(870\) | −31101.1 | −1.21198 | ||||||||
\(871\) | −6020.18 | −0.234197 | ||||||||
\(872\) | 47.6033 | 0.00184868 | ||||||||
\(873\) | −2823.98 | −0.109482 | ||||||||
\(874\) | −59359.0 | −2.29731 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −58128.0 | −2.24197 | ||||||||
\(877\) | −12154.8 | −0.468001 | −0.234001 | − | 0.972236i | \(-0.575182\pi\) | ||||
−0.234001 | + | 0.972236i | \(0.575182\pi\) | |||||||
\(878\) | 15487.7 | 0.595313 | ||||||||
\(879\) | −32973.3 | −1.26526 | ||||||||
\(880\) | −3552.03 | −0.136067 | ||||||||
\(881\) | −29390.4 | −1.12394 | −0.561968 | − | 0.827159i | \(-0.689956\pi\) | ||||
−0.561968 | + | 0.827159i | \(0.689956\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4180.02 | 0.159308 | 0.0796540 | − | 0.996823i | \(-0.474618\pi\) | ||||
0.0796540 | + | 0.996823i | \(0.474618\pi\) | |||||||
\(884\) | −23765.6 | −0.904211 | ||||||||
\(885\) | 8066.62 | 0.306392 | ||||||||
\(886\) | 21219.0 | 0.804590 | ||||||||
\(887\) | 21825.8 | 0.826198 | 0.413099 | − | 0.910686i | \(-0.364446\pi\) | ||||
0.413099 | + | 0.910686i | \(0.364446\pi\) | |||||||
\(888\) | 17614.6 | 0.665660 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 24611.6 | 0.926947 | ||||||||
\(891\) | −13241.2 | −0.497863 | ||||||||
\(892\) | 40331.6 | 1.51390 | ||||||||
\(893\) | −20131.5 | −0.754397 | ||||||||
\(894\) | 25168.4 | 0.941565 | ||||||||
\(895\) | −6053.25 | −0.226076 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −35974.9 | −1.33909 | ||||||||
\(898\) | 30609.7 | 1.13748 | ||||||||
\(899\) | 60232.7 | 2.23456 | ||||||||
\(900\) | −531.662 | −0.0196912 | ||||||||
\(901\) | 4010.40 | 0.148286 | ||||||||
\(902\) | −15474.4 | −0.571221 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16067.2 | 0.591138 | ||||||||
\(905\) | −15156.6 | −0.556710 | ||||||||
\(906\) | 20710.8 | 0.759458 | ||||||||
\(907\) | −8356.11 | −0.305910 | −0.152955 | − | 0.988233i | \(-0.548879\pi\) | ||||
−0.152955 | + | 0.988233i | \(0.548879\pi\) | |||||||
\(908\) | 41586.3 | 1.51992 | ||||||||
\(909\) | 1091.35 | 0.0398214 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4419.80 | −0.160740 | −0.0803701 | − | 0.996765i | \(-0.525610\pi\) | ||||
−0.0803701 | + | 0.996765i | \(0.525610\pi\) | |||||||
\(912\) | −24539.8 | −0.891004 | ||||||||
\(913\) | −12695.1 | −0.460181 | ||||||||
\(914\) | 21806.8 | 0.789173 | ||||||||
\(915\) | 8525.06 | 0.308011 | ||||||||
\(916\) | 3767.65 | 0.135903 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 19611.3 | 0.705088 | ||||||||
\(919\) | −39257.6 | −1.40913 | −0.704563 | − | 0.709641i | \(-0.748857\pi\) | ||||
−0.704563 | + | 0.709641i | \(0.748857\pi\) | |||||||
\(920\) | −5732.56 | −0.205432 | ||||||||
\(921\) | −13364.8 | −0.478162 | ||||||||
\(922\) | −72007.0 | −2.57204 | ||||||||
\(923\) | −22522.2 | −0.803173 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7748.29 | 0.275419 | ||||||||
\(926\) | 67207.9 | 2.38509 | ||||||||
\(927\) | −1561.98 | −0.0553421 | ||||||||
\(928\) | 70992.5 | 2.51125 | ||||||||
\(929\) | −13399.9 | −0.473235 | −0.236618 | − | 0.971603i | \(-0.576039\pi\) | ||||
−0.236618 | + | 0.971603i | \(0.576039\pi\) | |||||||
\(930\) | −22554.1 | −0.795245 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 69036.1 | 2.42635 | ||||||||
\(933\) | −4278.49 | −0.150130 | ||||||||
\(934\) | 14367.2 | 0.503330 | ||||||||
\(935\) | −3091.50 | −0.108131 | ||||||||
\(936\) | −1621.64 | −0.0566291 | ||||||||
\(937\) | 27539.8 | 0.960176 | 0.480088 | − | 0.877220i | \(-0.340605\pi\) | ||||
0.480088 | + | 0.877220i | \(0.340605\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16749.9 | −0.582123 | ||||||||
\(940\) | −7850.79 | −0.272409 | ||||||||
\(941\) | 14363.8 | 0.497605 | 0.248802 | − | 0.968554i | \(-0.419963\pi\) | ||||
0.248802 | + | 0.968554i | \(0.419963\pi\) | |||||||
\(942\) | −22029.0 | −0.761937 | ||||||||
\(943\) | 18323.5 | 0.632762 | ||||||||
\(944\) | −11615.9 | −0.400494 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1550.36 | −0.0532838 | ||||||||
\(947\) | −6372.12 | −0.218655 | −0.109327 | − | 0.994006i | \(-0.534870\pi\) | ||||
−0.109327 | + | 0.994006i | \(0.534870\pi\) | |||||||
\(948\) | 65563.8 | 2.24622 | ||||||||
\(949\) | −77989.6 | −2.66770 | ||||||||
\(950\) | 14712.4 | 0.502456 | ||||||||
\(951\) | 38165.3 | 1.30136 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 958.776 | 0.0325895 | 0.0162948 | − | 0.999867i | \(-0.494813\pi\) | ||||
0.0162948 | + | 0.999867i | \(0.494813\pi\) | |||||||
\(954\) | 1105.01 | 0.0375012 | ||||||||
\(955\) | −10843.2 | −0.367411 | ||||||||
\(956\) | −3643.88 | −0.123276 | ||||||||
\(957\) | −28435.8 | −0.960500 | ||||||||
\(958\) | −63055.1 | −2.12653 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −19383.1 | −0.651654 | ||||||||
\(961\) | 13888.9 | 0.466213 | ||||||||
\(962\) | 95432.7 | 3.19842 | ||||||||
\(963\) | 1241.32 | 0.0415379 | ||||||||
\(964\) | 24601.8 | 0.821961 | ||||||||
\(965\) | 7452.40 | 0.248602 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40104.5 | −1.33369 | −0.666843 | − | 0.745198i | \(-0.732355\pi\) | ||||
−0.666843 | + | 0.745198i | \(0.732355\pi\) | |||||||
\(968\) | −10702.8 | −0.355373 | ||||||||
\(969\) | −21358.2 | −0.708074 | ||||||||
\(970\) | 30475.2 | 1.00876 | ||||||||
\(971\) | 12397.4 | 0.409732 | 0.204866 | − | 0.978790i | \(-0.434324\pi\) | ||||
0.204866 | + | 0.978790i | \(0.434324\pi\) | |||||||
\(972\) | 5954.62 | 0.196496 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −8113.05 | −0.266898 | ||||||||
\(975\) | 8916.56 | 0.292881 | ||||||||
\(976\) | −12276.1 | −0.402611 | ||||||||
\(977\) | 44982.9 | 1.47301 | 0.736506 | − | 0.676432i | \(-0.236475\pi\) | ||||
0.736506 | + | 0.676432i | \(0.236475\pi\) | |||||||
\(978\) | −33799.5 | −1.10510 | ||||||||
\(979\) | 22502.5 | 0.734608 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.37588 | −0.000272601 0 | ||||||||
\(982\) | 13904.4 | 0.451841 | ||||||||
\(983\) | −7895.76 | −0.256191 | −0.128095 | − | 0.991762i | \(-0.540886\pi\) | ||||
−0.128095 | + | 0.991762i | \(0.540886\pi\) | |||||||
\(984\) | −10324.6 | −0.334487 | ||||||||
\(985\) | 16902.8 | 0.546771 | ||||||||
\(986\) | 38979.0 | 1.25897 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 103408. | 3.32979 | ||||||||
\(989\) | 1835.80 | 0.0590244 | ||||||||
\(990\) | −851.821 | −0.0273461 | ||||||||
\(991\) | 54534.9 | 1.74809 | 0.874046 | − | 0.485844i | \(-0.161488\pi\) | ||||
0.874046 | + | 0.485844i | \(0.161488\pi\) | |||||||
\(992\) | 51482.9 | 1.64776 | ||||||||
\(993\) | −16608.5 | −0.530770 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22976.6 | 0.732069 | ||||||||
\(996\) | −34203.2 | −1.08812 | ||||||||
\(997\) | −6028.06 | −0.191485 | −0.0957425 | − | 0.995406i | \(-0.530523\pi\) | ||||
−0.0957425 | + | 0.995406i | \(0.530523\pi\) | |||||||
\(998\) | 41930.9 | 1.32996 | ||||||||
\(999\) | −44940.1 | −1.42326 |
(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 | 245.4.a.j.1.2 | yes | 2 | |
3.2 | odd | 2 | 2205.4.a.w.1.1 | 2 | |||
5.4 | even | 2 | 1225.4.a.p.1.1 | 2 | |||
7.2 | even | 3 | 245.4.e.j.116.1 | 4 | |||
7.3 | odd | 6 | 245.4.e.k.226.1 | 4 | |||
7.4 | even | 3 | 245.4.e.j.226.1 | 4 | |||
7.5 | odd | 6 | 245.4.e.k.116.1 | 4 | |||
7.6 | odd | 2 | 245.4.a.i.1.2 | ✓ | 2 | ||
21.20 | even | 2 | 2205.4.a.x.1.1 | 2 | |||
35.34 | odd | 2 | 1225.4.a.q.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.4.a.i.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
245.4.a.j.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
245.4.e.j.116.1 | 4 | 7.2 | even | 3 | |||
245.4.e.j.226.1 | 4 | 7.4 | even | 3 | |||
245.4.e.k.116.1 | 4 | 7.5 | odd | 6 | |||
245.4.e.k.226.1 | 4 | 7.3 | odd | 6 | |||
1225.4.a.p.1.1 | 2 | 5.4 | even | 2 | |||
1225.4.a.q.1.1 | 2 | 35.34 | odd | 2 | |||
2205.4.a.w.1.1 | 2 | 3.2 | odd | 2 | |||
2205.4.a.x.1.1 | 2 | 21.20 | even | 2 |