Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,4,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, 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("1875.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.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: | \(110.628581261\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 81 x^{12} - 7 x^{11} + 2512 x^{10} + 517 x^{9} - 36970 x^{8} - 12987 x^{7} + 257291 x^{6} + \cdots + 42064 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 5^{3} \) |
Twist minimal: | no (minimal twist has level 75) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.65416\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.65416 | −1.64549 | −0.822747 | − | 0.568407i | \(-0.807560\pi\) | ||||
−0.822747 | + | 0.568407i | \(0.807560\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 13.6612 | 1.70765 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 13.9625 | 0.950027 | ||||||||
\(7\) | 26.0445 | 1.40627 | 0.703136 | − | 0.711056i | \(-0.251783\pi\) | ||||
0.703136 | + | 0.711056i | \(0.251783\pi\) | |||||||
\(8\) | −26.3483 | −1.16444 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.51593 | 0.0689621 | 0.0344810 | − | 0.999405i | \(-0.489022\pi\) | ||||
0.0344810 | + | 0.999405i | \(0.489022\pi\) | |||||||
\(12\) | −40.9837 | −0.985914 | ||||||||
\(13\) | −39.6201 | −0.845281 | −0.422640 | − | 0.906298i | \(-0.638897\pi\) | ||||
−0.422640 | + | 0.906298i | \(0.638897\pi\) | |||||||
\(14\) | −121.215 | −2.31401 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.3393 | 0.208426 | ||||||||
\(17\) | 84.9913 | 1.21255 | 0.606277 | − | 0.795253i | \(-0.292662\pi\) | ||||
0.606277 | + | 0.795253i | \(0.292662\pi\) | |||||||
\(18\) | −41.8875 | −0.548498 | ||||||||
\(19\) | −142.827 | −1.72457 | −0.862284 | − | 0.506425i | \(-0.830967\pi\) | ||||
−0.862284 | + | 0.506425i | \(0.830967\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −78.1335 | −0.811911 | ||||||||
\(22\) | −11.7096 | −0.113477 | ||||||||
\(23\) | −157.199 | −1.42514 | −0.712571 | − | 0.701600i | \(-0.752469\pi\) | ||||
−0.712571 | + | 0.701600i | \(0.752469\pi\) | |||||||
\(24\) | 79.0448 | 0.672289 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 184.399 | 1.39090 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 355.800 | 2.40142 | ||||||||
\(29\) | −100.233 | −0.641821 | −0.320911 | − | 0.947109i | \(-0.603989\pi\) | ||||
−0.320911 | + | 0.947109i | \(0.603989\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −173.361 | −1.00441 | −0.502203 | − | 0.864750i | \(-0.667477\pi\) | ||||
−0.502203 | + | 0.864750i | \(0.667477\pi\) | |||||||
\(32\) | 148.703 | 0.821476 | ||||||||
\(33\) | −7.54780 | −0.0398153 | ||||||||
\(34\) | −395.563 | −1.99525 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 122.951 | 0.569218 | ||||||||
\(37\) | 59.3956 | 0.263907 | 0.131954 | − | 0.991256i | \(-0.457875\pi\) | ||||
0.131954 | + | 0.991256i | \(0.457875\pi\) | |||||||
\(38\) | 664.741 | 2.83777 | ||||||||
\(39\) | 118.860 | 0.488023 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −355.427 | −1.35386 | −0.676930 | − | 0.736047i | \(-0.736690\pi\) | ||||
−0.676930 | + | 0.736047i | \(0.736690\pi\) | |||||||
\(42\) | 363.646 | 1.33600 | ||||||||
\(43\) | −109.742 | −0.389198 | −0.194599 | − | 0.980883i | \(-0.562341\pi\) | ||||
−0.194599 | + | 0.980883i | \(0.562341\pi\) | |||||||
\(44\) | 34.3707 | 0.117763 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 731.630 | 2.34506 | ||||||||
\(47\) | 58.1116 | 0.180350 | 0.0901750 | − | 0.995926i | \(-0.471257\pi\) | ||||
0.0901750 | + | 0.995926i | \(0.471257\pi\) | |||||||
\(48\) | −40.0178 | −0.120335 | ||||||||
\(49\) | 335.317 | 0.977600 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −254.974 | −0.700069 | ||||||||
\(52\) | −541.260 | −1.44345 | ||||||||
\(53\) | 390.876 | 1.01304 | 0.506518 | − | 0.862229i | \(-0.330932\pi\) | ||||
0.506518 | + | 0.862229i | \(0.330932\pi\) | |||||||
\(54\) | 125.662 | 0.316676 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −686.228 | −1.63752 | ||||||||
\(57\) | 428.481 | 0.995680 | ||||||||
\(58\) | 466.501 | 1.05611 | ||||||||
\(59\) | 412.549 | 0.910327 | 0.455163 | − | 0.890408i | \(-0.349581\pi\) | ||||
0.455163 | + | 0.890408i | \(0.349581\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 358.635 | 0.752763 | 0.376381 | − | 0.926465i | \(-0.377168\pi\) | ||||
0.376381 | + | 0.926465i | \(0.377168\pi\) | |||||||
\(62\) | 806.851 | 1.65274 | ||||||||
\(63\) | 234.401 | 0.468757 | ||||||||
\(64\) | −798.802 | −1.56016 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 35.1287 | 0.0655158 | ||||||||
\(67\) | −351.010 | −0.640041 | −0.320020 | − | 0.947411i | \(-0.603690\pi\) | ||||
−0.320020 | + | 0.947411i | \(0.603690\pi\) | |||||||
\(68\) | 1161.09 | 2.07062 | ||||||||
\(69\) | 471.597 | 0.822806 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 170.828 | 0.285543 | 0.142771 | − | 0.989756i | \(-0.454399\pi\) | ||||
0.142771 | + | 0.989756i | \(0.454399\pi\) | |||||||
\(72\) | −237.134 | −0.388146 | ||||||||
\(73\) | 932.891 | 1.49571 | 0.747853 | − | 0.663864i | \(-0.231085\pi\) | ||||
0.747853 | + | 0.663864i | \(0.231085\pi\) | |||||||
\(74\) | −276.437 | −0.434258 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1951.19 | −2.94496 | ||||||||
\(77\) | 65.5263 | 0.0969794 | ||||||||
\(78\) | −553.196 | −0.803039 | ||||||||
\(79\) | −1313.26 | −1.87029 | −0.935147 | − | 0.354261i | \(-0.884733\pi\) | ||||
−0.935147 | + | 0.354261i | \(0.884733\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1654.21 | 2.22777 | ||||||||
\(83\) | 653.900 | 0.864757 | 0.432378 | − | 0.901692i | \(-0.357674\pi\) | ||||
0.432378 | + | 0.901692i | \(0.357674\pi\) | |||||||
\(84\) | −1067.40 | −1.38646 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 510.757 | 0.640423 | ||||||||
\(87\) | 300.699 | 0.370556 | ||||||||
\(88\) | −66.2905 | −0.0803021 | ||||||||
\(89\) | 1059.65 | 1.26205 | 0.631025 | − | 0.775763i | \(-0.282635\pi\) | ||||
0.631025 | + | 0.775763i | \(0.282635\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1031.89 | −1.18869 | ||||||||
\(92\) | −2147.53 | −2.43365 | ||||||||
\(93\) | 520.083 | 0.579894 | ||||||||
\(94\) | −270.461 | −0.296765 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −446.109 | −0.474279 | ||||||||
\(97\) | −641.500 | −0.671489 | −0.335745 | − | 0.941953i | \(-0.608988\pi\) | ||||
−0.335745 | + | 0.941953i | \(0.608988\pi\) | |||||||
\(98\) | −1560.62 | −1.60864 | ||||||||
\(99\) | 22.6434 | 0.0229874 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 864.030 | 0.851229 | 0.425615 | − | 0.904904i | \(-0.360058\pi\) | ||||
0.425615 | + | 0.904904i | \(0.360058\pi\) | |||||||
\(102\) | 1186.69 | 1.15196 | ||||||||
\(103\) | −1832.11 | −1.75265 | −0.876324 | − | 0.481722i | \(-0.840012\pi\) | ||||
−0.876324 | + | 0.481722i | \(0.840012\pi\) | |||||||
\(104\) | 1043.92 | 0.984278 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1819.20 | −1.66695 | ||||||||
\(107\) | 1037.99 | 0.937816 | 0.468908 | − | 0.883247i | \(-0.344648\pi\) | ||||
0.468908 | + | 0.883247i | \(0.344648\pi\) | |||||||
\(108\) | −368.853 | −0.328638 | ||||||||
\(109\) | 1557.03 | 1.36823 | 0.684113 | − | 0.729376i | \(-0.260189\pi\) | ||||
0.684113 | + | 0.729376i | \(0.260189\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −178.187 | −0.152367 | ||||||||
\(112\) | 347.415 | 0.293104 | ||||||||
\(113\) | 975.199 | 0.811850 | 0.405925 | − | 0.913906i | \(-0.366949\pi\) | ||||
0.405925 | + | 0.913906i | \(0.366949\pi\) | |||||||
\(114\) | −1994.22 | −1.63839 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1369.31 | −1.09601 | ||||||||
\(117\) | −356.581 | −0.281760 | ||||||||
\(118\) | −1920.07 | −1.49794 | ||||||||
\(119\) | 2213.56 | 1.70518 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1324.67 | −0.995244 | ||||||||
\(122\) | −1669.15 | −1.23867 | ||||||||
\(123\) | 1066.28 | 0.781652 | ||||||||
\(124\) | −2368.33 | −1.71518 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1090.94 | −0.771338 | ||||||||
\(127\) | 1028.89 | 0.718894 | 0.359447 | − | 0.933166i | \(-0.382965\pi\) | ||||
0.359447 | + | 0.933166i | \(0.382965\pi\) | |||||||
\(128\) | 2528.13 | 1.74576 | ||||||||
\(129\) | 329.226 | 0.224704 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2669.90 | −1.78069 | −0.890346 | − | 0.455285i | \(-0.849537\pi\) | ||||
−0.890346 | + | 0.455285i | \(0.849537\pi\) | |||||||
\(132\) | −103.112 | −0.0679907 | ||||||||
\(133\) | −3719.86 | −2.42521 | ||||||||
\(134\) | 1633.66 | 1.05318 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2239.37 | −1.41195 | ||||||||
\(137\) | 1219.42 | 0.760454 | 0.380227 | − | 0.924893i | \(-0.375846\pi\) | ||||
0.380227 | + | 0.924893i | \(0.375846\pi\) | |||||||
\(138\) | −2194.89 | −1.35392 | ||||||||
\(139\) | 875.292 | 0.534110 | 0.267055 | − | 0.963681i | \(-0.413949\pi\) | ||||
0.267055 | + | 0.963681i | \(0.413949\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −174.335 | −0.104125 | ||||||||
\(142\) | −795.061 | −0.469859 | ||||||||
\(143\) | −99.6816 | −0.0582923 | ||||||||
\(144\) | 120.053 | 0.0694753 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4341.82 | −2.46118 | ||||||||
\(147\) | −1005.95 | −0.564417 | ||||||||
\(148\) | 811.416 | 0.450662 | ||||||||
\(149\) | −819.633 | −0.450650 | −0.225325 | − | 0.974284i | \(-0.572344\pi\) | ||||
−0.225325 | + | 0.974284i | \(0.572344\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 567.457 | 0.305821 | 0.152911 | − | 0.988240i | \(-0.451135\pi\) | ||||
0.152911 | + | 0.988240i | \(0.451135\pi\) | |||||||
\(152\) | 3763.25 | 2.00815 | ||||||||
\(153\) | 764.922 | 0.404185 | ||||||||
\(154\) | −304.970 | −0.159579 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1623.78 | 0.833374 | ||||||||
\(157\) | 1643.63 | 0.835516 | 0.417758 | − | 0.908558i | \(-0.362816\pi\) | ||||
0.417758 | + | 0.908558i | \(0.362816\pi\) | |||||||
\(158\) | 6112.12 | 3.07756 | ||||||||
\(159\) | −1172.63 | −0.584877 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4094.17 | −2.00414 | ||||||||
\(162\) | −376.987 | −0.182833 | ||||||||
\(163\) | 1280.29 | 0.615217 | 0.307608 | − | 0.951513i | \(-0.400471\pi\) | ||||
0.307608 | + | 0.951513i | \(0.400471\pi\) | |||||||
\(164\) | −4855.56 | −2.31192 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3043.36 | −1.42295 | ||||||||
\(167\) | 1576.61 | 0.730547 | 0.365274 | − | 0.930900i | \(-0.380975\pi\) | ||||
0.365274 | + | 0.930900i | \(0.380975\pi\) | |||||||
\(168\) | 2058.68 | 0.945422 | ||||||||
\(169\) | −627.245 | −0.285501 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1285.44 | −0.574856 | ||||||||
\(172\) | −1499.21 | −0.664615 | ||||||||
\(173\) | −2221.62 | −0.976337 | −0.488169 | − | 0.872749i | \(-0.662335\pi\) | ||||
−0.488169 | + | 0.872749i | \(0.662335\pi\) | |||||||
\(174\) | −1399.50 | −0.609747 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 33.5607 | 0.0143735 | ||||||||
\(177\) | −1237.65 | −0.525577 | ||||||||
\(178\) | −4931.77 | −2.07670 | ||||||||
\(179\) | 3015.07 | 1.25898 | 0.629489 | − | 0.777010i | \(-0.283264\pi\) | ||||
0.629489 | + | 0.777010i | \(0.283264\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2472.66 | 1.01542 | 0.507710 | − | 0.861528i | \(-0.330492\pi\) | ||||
0.507710 | + | 0.861528i | \(0.330492\pi\) | |||||||
\(182\) | 4802.57 | 1.95599 | ||||||||
\(183\) | −1075.91 | −0.434608 | ||||||||
\(184\) | 4141.92 | 1.65949 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2420.55 | −0.954212 | ||||||||
\(187\) | 213.833 | 0.0836203 | ||||||||
\(188\) | 793.876 | 0.307975 | ||||||||
\(189\) | −703.202 | −0.270637 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −640.945 | −0.242812 | −0.121406 | − | 0.992603i | \(-0.538740\pi\) | ||||
−0.121406 | + | 0.992603i | \(0.538740\pi\) | |||||||
\(192\) | 2396.41 | 0.900759 | ||||||||
\(193\) | 658.953 | 0.245764 | 0.122882 | − | 0.992421i | \(-0.460786\pi\) | ||||
0.122882 | + | 0.992421i | \(0.460786\pi\) | |||||||
\(194\) | 2985.65 | 1.10493 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4580.84 | 1.66940 | ||||||||
\(197\) | −2802.27 | −1.01347 | −0.506734 | − | 0.862102i | \(-0.669147\pi\) | ||||
−0.506734 | + | 0.862102i | \(0.669147\pi\) | |||||||
\(198\) | −105.386 | −0.0378256 | ||||||||
\(199\) | −2715.89 | −0.967459 | −0.483729 | − | 0.875218i | \(-0.660718\pi\) | ||||
−0.483729 | + | 0.875218i | \(0.660718\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1053.03 | 0.369528 | ||||||||
\(202\) | −4021.33 | −1.40069 | ||||||||
\(203\) | −2610.52 | −0.902575 | ||||||||
\(204\) | −3483.26 | −1.19547 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8526.92 | 2.88397 | ||||||||
\(207\) | −1414.79 | −0.475047 | ||||||||
\(208\) | −528.503 | −0.176178 | ||||||||
\(209\) | −359.344 | −0.118930 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1733.25 | −0.565507 | −0.282753 | − | 0.959193i | \(-0.591248\pi\) | ||||
−0.282753 | + | 0.959193i | \(0.591248\pi\) | |||||||
\(212\) | 5339.84 | 1.72991 | ||||||||
\(213\) | −512.484 | −0.164858 | ||||||||
\(214\) | −4830.97 | −1.54317 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 711.403 | 0.224096 | ||||||||
\(217\) | −4515.11 | −1.41247 | ||||||||
\(218\) | −7246.68 | −2.25141 | ||||||||
\(219\) | −2798.67 | −0.863547 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3367.37 | −1.02495 | ||||||||
\(222\) | 829.310 | 0.250719 | ||||||||
\(223\) | −4377.14 | −1.31442 | −0.657208 | − | 0.753709i | \(-0.728263\pi\) | ||||
−0.657208 | + | 0.753709i | \(0.728263\pi\) | |||||||
\(224\) | 3872.90 | 1.15522 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4538.74 | −1.33589 | ||||||||
\(227\) | 2248.73 | 0.657503 | 0.328752 | − | 0.944416i | \(-0.393372\pi\) | ||||
0.328752 | + | 0.944416i | \(0.393372\pi\) | |||||||
\(228\) | 5853.58 | 1.70028 | ||||||||
\(229\) | 2245.32 | 0.647926 | 0.323963 | − | 0.946070i | \(-0.394985\pi\) | ||||
0.323963 | + | 0.946070i | \(0.394985\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −196.579 | −0.0559911 | ||||||||
\(232\) | 2640.97 | 0.747362 | ||||||||
\(233\) | −708.378 | −0.199173 | −0.0995866 | − | 0.995029i | \(-0.531752\pi\) | ||||
−0.0995866 | + | 0.995029i | \(0.531752\pi\) | |||||||
\(234\) | 1659.59 | 0.463635 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5635.92 | 1.55452 | ||||||||
\(237\) | 3939.78 | 1.07981 | ||||||||
\(238\) | −10302.3 | −2.80587 | ||||||||
\(239\) | 5452.75 | 1.47577 | 0.737885 | − | 0.674927i | \(-0.235825\pi\) | ||||
0.737885 | + | 0.674927i | \(0.235825\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5720.73 | 1.52906 | 0.764532 | − | 0.644585i | \(-0.222970\pi\) | ||||
0.764532 | + | 0.644585i | \(0.222970\pi\) | |||||||
\(242\) | 6165.23 | 1.63767 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 4899.39 | 1.28546 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4962.64 | −1.28620 | ||||||||
\(247\) | 5658.83 | 1.45774 | ||||||||
\(248\) | 4567.76 | 1.16957 | ||||||||
\(249\) | −1961.70 | −0.499268 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2045.23 | 0.514319 | 0.257159 | − | 0.966369i | \(-0.417213\pi\) | ||||
0.257159 | + | 0.966369i | \(0.417213\pi\) | |||||||
\(252\) | 3202.20 | 0.800475 | ||||||||
\(253\) | −395.502 | −0.0982807 | ||||||||
\(254\) | −4788.64 | −1.18294 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5375.91 | −1.31248 | ||||||||
\(257\) | −407.547 | −0.0989186 | −0.0494593 | − | 0.998776i | \(-0.515750\pi\) | ||||
−0.0494593 | + | 0.998776i | \(0.515750\pi\) | |||||||
\(258\) | −1532.27 | −0.369748 | ||||||||
\(259\) | 1546.93 | 0.371125 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −902.098 | −0.213940 | ||||||||
\(262\) | 12426.2 | 2.93012 | ||||||||
\(263\) | 887.485 | 0.208079 | 0.104039 | − | 0.994573i | \(-0.466823\pi\) | ||||
0.104039 | + | 0.994573i | \(0.466823\pi\) | |||||||
\(264\) | 198.871 | 0.0463625 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 17312.8 | 3.99067 | ||||||||
\(267\) | −3178.94 | −0.728645 | ||||||||
\(268\) | −4795.23 | −1.09297 | ||||||||
\(269\) | 6033.48 | 1.36754 | 0.683769 | − | 0.729699i | \(-0.260340\pi\) | ||||
0.683769 | + | 0.729699i | \(0.260340\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6534.92 | 1.46483 | 0.732413 | − | 0.680860i | \(-0.238394\pi\) | ||||
0.732413 | + | 0.680860i | \(0.238394\pi\) | |||||||
\(272\) | 1133.72 | 0.252728 | ||||||||
\(273\) | 3095.66 | 0.686293 | ||||||||
\(274\) | −5675.39 | −1.25132 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6442.59 | 1.40507 | ||||||||
\(277\) | 5506.53 | 1.19442 | 0.597212 | − | 0.802084i | \(-0.296275\pi\) | ||||
0.597212 | + | 0.802084i | \(0.296275\pi\) | |||||||
\(278\) | −4073.75 | −0.878875 | ||||||||
\(279\) | −1560.25 | −0.334802 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7519.12 | −1.59627 | −0.798137 | − | 0.602476i | \(-0.794181\pi\) | ||||
−0.798137 | + | 0.602476i | \(0.794181\pi\) | |||||||
\(282\) | 811.382 | 0.171337 | ||||||||
\(283\) | −4480.16 | −0.941052 | −0.470526 | − | 0.882386i | \(-0.655936\pi\) | ||||
−0.470526 | + | 0.882386i | \(0.655936\pi\) | |||||||
\(284\) | 2333.72 | 0.487608 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 463.934 | 0.0959197 | ||||||||
\(287\) | −9256.91 | −1.90390 | ||||||||
\(288\) | 1338.33 | 0.273825 | ||||||||
\(289\) | 2310.53 | 0.470289 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1924.50 | 0.387685 | ||||||||
\(292\) | 12744.4 | 2.55415 | ||||||||
\(293\) | 6672.17 | 1.33035 | 0.665174 | − | 0.746688i | \(-0.268357\pi\) | ||||
0.665174 | + | 0.746688i | \(0.268357\pi\) | |||||||
\(294\) | 4681.85 | 0.928746 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1564.97 | −0.307304 | ||||||||
\(297\) | −67.9302 | −0.0132718 | ||||||||
\(298\) | 3814.70 | 0.741543 | ||||||||
\(299\) | 6228.25 | 1.20464 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2858.18 | −0.547318 | ||||||||
\(302\) | −2641.04 | −0.503227 | ||||||||
\(303\) | −2592.09 | −0.491458 | ||||||||
\(304\) | −1905.21 | −0.359445 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3560.07 | −0.665084 | ||||||||
\(307\) | −5433.28 | −1.01008 | −0.505039 | − | 0.863097i | \(-0.668522\pi\) | ||||
−0.505039 | + | 0.863097i | \(0.668522\pi\) | |||||||
\(308\) | 895.169 | 0.165607 | ||||||||
\(309\) | 5496.32 | 1.01189 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 513.012 | 0.0935377 | 0.0467689 | − | 0.998906i | \(-0.485108\pi\) | ||||
0.0467689 | + | 0.998906i | \(0.485108\pi\) | |||||||
\(312\) | −3131.76 | −0.568273 | ||||||||
\(313\) | 996.467 | 0.179948 | 0.0899739 | − | 0.995944i | \(-0.471322\pi\) | ||||
0.0899739 | + | 0.995944i | \(0.471322\pi\) | |||||||
\(314\) | −7649.72 | −1.37484 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17940.7 | −3.19381 | ||||||||
\(317\) | −4280.57 | −0.758425 | −0.379213 | − | 0.925310i | \(-0.623805\pi\) | ||||
−0.379213 | + | 0.925310i | \(0.623805\pi\) | |||||||
\(318\) | 5457.60 | 0.962411 | ||||||||
\(319\) | −252.180 | −0.0442613 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3113.97 | −0.541448 | ||||||||
\(322\) | 19054.9 | 3.29780 | ||||||||
\(323\) | −12139.1 | −2.09113 | ||||||||
\(324\) | 1106.56 | 0.189739 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5958.70 | −1.01234 | ||||||||
\(327\) | −4671.10 | −0.789946 | ||||||||
\(328\) | 9364.87 | 1.57649 | ||||||||
\(329\) | 1513.49 | 0.253621 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2972.75 | −0.493647 | −0.246823 | − | 0.969060i | \(-0.579387\pi\) | ||||
−0.246823 | + | 0.969060i | \(0.579387\pi\) | |||||||
\(332\) | 8933.07 | 1.47670 | ||||||||
\(333\) | 534.560 | 0.0879691 | ||||||||
\(334\) | −7337.78 | −1.20211 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1042.24 | −0.169223 | ||||||||
\(337\) | −1542.78 | −0.249379 | −0.124690 | − | 0.992196i | \(-0.539794\pi\) | ||||
−0.124690 | + | 0.992196i | \(0.539794\pi\) | |||||||
\(338\) | 2919.30 | 0.469790 | ||||||||
\(339\) | −2925.60 | −0.468722 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −436.165 | −0.0692659 | ||||||||
\(342\) | 5982.67 | 0.945922 | ||||||||
\(343\) | −200.108 | −0.0315009 | ||||||||
\(344\) | 2891.51 | 0.453197 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10339.8 | 1.60656 | ||||||||
\(347\) | 5624.32 | 0.870114 | 0.435057 | − | 0.900403i | \(-0.356728\pi\) | ||||
0.435057 | + | 0.900403i | \(0.356728\pi\) | |||||||
\(348\) | 4107.92 | 0.632780 | ||||||||
\(349\) | 3546.44 | 0.543945 | 0.271972 | − | 0.962305i | \(-0.412324\pi\) | ||||
0.271972 | + | 0.962305i | \(0.412324\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1069.74 | 0.162674 | ||||||||
\(352\) | 374.127 | 0.0566506 | ||||||||
\(353\) | 1916.05 | 0.288898 | 0.144449 | − | 0.989512i | \(-0.453859\pi\) | ||||
0.144449 | + | 0.989512i | \(0.453859\pi\) | |||||||
\(354\) | 5760.21 | 0.864835 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14476.1 | 2.15514 | ||||||||
\(357\) | −6640.67 | −0.984487 | ||||||||
\(358\) | −14032.6 | −2.07164 | ||||||||
\(359\) | 2633.09 | 0.387101 | 0.193550 | − | 0.981090i | \(-0.438000\pi\) | ||||
0.193550 | + | 0.981090i | \(0.438000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13540.6 | 1.97413 | ||||||||
\(362\) | −11508.1 | −1.67087 | ||||||||
\(363\) | 3974.01 | 0.574605 | ||||||||
\(364\) | −14096.8 | −2.02988 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5007.44 | 0.715145 | ||||||||
\(367\) | 6802.59 | 0.967554 | 0.483777 | − | 0.875191i | \(-0.339265\pi\) | ||||
0.483777 | + | 0.875191i | \(0.339265\pi\) | |||||||
\(368\) | −2096.92 | −0.297037 | ||||||||
\(369\) | −3198.84 | −0.451287 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10180.2 | 1.42460 | ||||||||
\(372\) | 7104.98 | 0.990258 | ||||||||
\(373\) | 6705.12 | 0.930772 | 0.465386 | − | 0.885108i | \(-0.345916\pi\) | ||||
0.465386 | + | 0.885108i | \(0.345916\pi\) | |||||||
\(374\) | −995.212 | −0.137597 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1531.14 | −0.210007 | ||||||||
\(377\) | 3971.25 | 0.542519 | ||||||||
\(378\) | 3272.82 | 0.445332 | ||||||||
\(379\) | 3890.69 | 0.527312 | 0.263656 | − | 0.964617i | \(-0.415072\pi\) | ||||
0.263656 | + | 0.964617i | \(0.415072\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3086.68 | −0.415054 | ||||||||
\(382\) | 2983.06 | 0.399547 | ||||||||
\(383\) | 5642.19 | 0.752748 | 0.376374 | − | 0.926468i | \(-0.377171\pi\) | ||||
0.376374 | + | 0.926468i | \(0.377171\pi\) | |||||||
\(384\) | −7584.39 | −1.00791 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3066.87 | −0.404403 | ||||||||
\(387\) | −987.679 | −0.129733 | ||||||||
\(388\) | −8763.68 | −1.14667 | ||||||||
\(389\) | −4678.95 | −0.609852 | −0.304926 | − | 0.952376i | \(-0.598632\pi\) | ||||
−0.304926 | + | 0.952376i | \(0.598632\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13360.6 | −1.72806 | ||||||||
\(392\) | −8835.01 | −1.13836 | ||||||||
\(393\) | 8009.71 | 1.02808 | ||||||||
\(394\) | 13042.2 | 1.66766 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 309.337 | 0.0392544 | ||||||||
\(397\) | −8379.25 | −1.05930 | −0.529650 | − | 0.848216i | \(-0.677677\pi\) | ||||
−0.529650 | + | 0.848216i | \(0.677677\pi\) | |||||||
\(398\) | 12640.2 | 1.59195 | ||||||||
\(399\) | 11159.6 | 1.40020 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6042.30 | 0.752464 | 0.376232 | − | 0.926525i | \(-0.377220\pi\) | ||||
0.376232 | + | 0.926525i | \(0.377220\pi\) | |||||||
\(402\) | −4900.98 | −0.608056 | ||||||||
\(403\) | 6868.59 | 0.849005 | ||||||||
\(404\) | 11803.7 | 1.45360 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12149.8 | 1.48518 | ||||||||
\(407\) | 149.435 | 0.0181996 | ||||||||
\(408\) | 6718.12 | 0.815188 | ||||||||
\(409\) | 6539.69 | 0.790628 | 0.395314 | − | 0.918546i | \(-0.370636\pi\) | ||||
0.395314 | + | 0.918546i | \(0.370636\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3658.27 | −0.439049 | ||||||||
\(412\) | −25028.8 | −2.99292 | ||||||||
\(413\) | 10744.6 | 1.28017 | ||||||||
\(414\) | 6584.67 | 0.781688 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5891.63 | −0.694377 | ||||||||
\(417\) | −2625.88 | −0.308368 | ||||||||
\(418\) | 1672.44 | 0.195698 | ||||||||
\(419\) | 13109.1 | 1.52846 | 0.764228 | − | 0.644946i | \(-0.223120\pi\) | ||||
0.764228 | + | 0.644946i | \(0.223120\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3413.16 | 0.395124 | 0.197562 | − | 0.980290i | \(-0.436698\pi\) | ||||
0.197562 | + | 0.980290i | \(0.436698\pi\) | |||||||
\(422\) | 8066.83 | 0.930538 | ||||||||
\(423\) | 523.004 | 0.0601167 | ||||||||
\(424\) | −10298.9 | −1.17962 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2385.18 | 0.271273 | ||||||||
\(427\) | 9340.48 | 1.05859 | ||||||||
\(428\) | 14180.2 | 1.60146 | ||||||||
\(429\) | 299.045 | 0.0336551 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1511.82 | −0.168960 | −0.0844801 | − | 0.996425i | \(-0.526923\pi\) | ||||
−0.0844801 | + | 0.996425i | \(0.526923\pi\) | |||||||
\(432\) | −360.160 | −0.0401116 | ||||||||
\(433\) | 8624.67 | 0.957218 | 0.478609 | − | 0.878028i | \(-0.341141\pi\) | ||||
0.478609 | + | 0.878028i | \(0.341141\pi\) | |||||||
\(434\) | 21014.0 | 2.32421 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 21271.0 | 2.33646 | ||||||||
\(437\) | 22452.3 | 2.45775 | ||||||||
\(438\) | 13025.5 | 1.42096 | ||||||||
\(439\) | −3528.80 | −0.383645 | −0.191823 | − | 0.981430i | \(-0.561440\pi\) | ||||
−0.191823 | + | 0.981430i | \(0.561440\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3017.85 | 0.325867 | ||||||||
\(442\) | 15672.3 | 1.68655 | ||||||||
\(443\) | 9589.40 | 1.02846 | 0.514228 | − | 0.857653i | \(-0.328078\pi\) | ||||
0.514228 | + | 0.857653i | \(0.328078\pi\) | |||||||
\(444\) | −2434.25 | −0.260190 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 20371.9 | 2.16286 | ||||||||
\(447\) | 2458.90 | 0.260183 | ||||||||
\(448\) | −20804.4 | −2.19401 | ||||||||
\(449\) | −9820.81 | −1.03223 | −0.516117 | − | 0.856518i | \(-0.672623\pi\) | ||||
−0.516117 | + | 0.856518i | \(0.672623\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −894.230 | −0.0933650 | ||||||||
\(452\) | 13322.4 | 1.38636 | ||||||||
\(453\) | −1702.37 | −0.176566 | ||||||||
\(454\) | −10465.9 | −1.08192 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11289.7 | −1.15941 | ||||||||
\(457\) | −1597.23 | −0.163491 | −0.0817455 | − | 0.996653i | \(-0.526049\pi\) | ||||
−0.0817455 | + | 0.996653i | \(0.526049\pi\) | |||||||
\(458\) | −10450.1 | −1.06616 | ||||||||
\(459\) | −2294.77 | −0.233356 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3903.07 | −0.394325 | −0.197163 | − | 0.980371i | \(-0.563173\pi\) | ||||
−0.197163 | + | 0.980371i | \(0.563173\pi\) | |||||||
\(462\) | 914.910 | 0.0921330 | ||||||||
\(463\) | 15661.9 | 1.57208 | 0.786039 | − | 0.618177i | \(-0.212129\pi\) | ||||
0.786039 | + | 0.618177i | \(0.212129\pi\) | |||||||
\(464\) | −1337.04 | −0.133772 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3296.90 | 0.327739 | ||||||||
\(467\) | 6397.32 | 0.633903 | 0.316951 | − | 0.948442i | \(-0.397341\pi\) | ||||
0.316951 | + | 0.948442i | \(0.397341\pi\) | |||||||
\(468\) | −4871.34 | −0.481149 | ||||||||
\(469\) | −9141.89 | −0.900071 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4930.89 | −0.482385 | ||||||||
\(472\) | −10869.9 | −1.06002 | ||||||||
\(473\) | −276.104 | −0.0268399 | ||||||||
\(474\) | −18336.4 | −1.77683 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 30239.9 | 2.91186 | ||||||||
\(477\) | 3517.88 | 0.337679 | ||||||||
\(478\) | −25378.0 | −2.42837 | ||||||||
\(479\) | −10285.8 | −0.981153 | −0.490576 | − | 0.871398i | \(-0.663214\pi\) | ||||
−0.490576 | + | 0.871398i | \(0.663214\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2353.26 | −0.223076 | ||||||||
\(482\) | −26625.2 | −2.51607 | ||||||||
\(483\) | 12282.5 | 1.15709 | ||||||||
\(484\) | −18096.6 | −1.69953 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1130.96 | 0.105559 | ||||||||
\(487\) | −2083.46 | −0.193861 | −0.0969306 | − | 0.995291i | \(-0.530902\pi\) | ||||
−0.0969306 | + | 0.995291i | \(0.530902\pi\) | |||||||
\(488\) | −9449.41 | −0.876546 | ||||||||
\(489\) | −3840.88 | −0.355196 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17704.5 | 1.62727 | 0.813636 | − | 0.581374i | \(-0.197485\pi\) | ||||
0.813636 | + | 0.581374i | \(0.197485\pi\) | |||||||
\(492\) | 14566.7 | 1.33479 | ||||||||
\(493\) | −8518.94 | −0.778243 | ||||||||
\(494\) | −26337.1 | −2.39871 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2312.51 | −0.209344 | ||||||||
\(497\) | 4449.13 | 0.401551 | ||||||||
\(498\) | 9130.07 | 0.821542 | ||||||||
\(499\) | 5018.92 | 0.450256 | 0.225128 | − | 0.974329i | \(-0.427720\pi\) | ||||
0.225128 | + | 0.974329i | \(0.427720\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4729.82 | −0.421782 | ||||||||
\(502\) | −9518.85 | −0.846309 | ||||||||
\(503\) | 10061.9 | 0.891924 | 0.445962 | − | 0.895052i | \(-0.352862\pi\) | ||||
0.445962 | + | 0.895052i | \(0.352862\pi\) | |||||||
\(504\) | −6176.05 | −0.545839 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1840.73 | 0.161720 | ||||||||
\(507\) | 1881.73 | 0.164834 | ||||||||
\(508\) | 14055.9 | 1.22762 | ||||||||
\(509\) | −5317.01 | −0.463011 | −0.231505 | − | 0.972834i | \(-0.574365\pi\) | ||||
−0.231505 | + | 0.972834i | \(0.574365\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24296.7 | 2.10337 | ||||||||
\(512\) | 4795.32 | 0.413916 | ||||||||
\(513\) | 3856.33 | 0.331893 | ||||||||
\(514\) | 1896.79 | 0.162770 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4497.63 | 0.383716 | ||||||||
\(517\) | 146.205 | 0.0124373 | ||||||||
\(518\) | −7199.66 | −0.610685 | ||||||||
\(519\) | 6664.85 | 0.563689 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6274.02 | −0.527582 | −0.263791 | − | 0.964580i | \(-0.584973\pi\) | ||||
−0.263791 | + | 0.964580i | \(0.584973\pi\) | |||||||
\(522\) | 4198.51 | 0.352038 | ||||||||
\(523\) | −14059.6 | −1.17549 | −0.587746 | − | 0.809045i | \(-0.699985\pi\) | ||||
−0.587746 | + | 0.809045i | \(0.699985\pi\) | |||||||
\(524\) | −36474.1 | −3.04080 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4130.50 | −0.342392 | ||||||||
\(527\) | −14734.2 | −1.21790 | ||||||||
\(528\) | −100.682 | −0.00829853 | ||||||||
\(529\) | 12544.5 | 1.03103 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3712.94 | 0.303442 | ||||||||
\(532\) | −50817.9 | −4.14142 | ||||||||
\(533\) | 14082.0 | 1.14439 | ||||||||
\(534\) | 14795.3 | 1.19898 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9248.51 | 0.745289 | ||||||||
\(537\) | −9045.21 | −0.726871 | ||||||||
\(538\) | −28080.8 | −2.25028 | ||||||||
\(539\) | 843.635 | 0.0674173 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20130.6 | −1.59978 | −0.799891 | − | 0.600145i | \(-0.795110\pi\) | ||||
−0.799891 | + | 0.600145i | \(0.795110\pi\) | |||||||
\(542\) | −30414.6 | −2.41036 | ||||||||
\(543\) | −7417.97 | −0.586253 | ||||||||
\(544\) | 12638.5 | 0.996084 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −14407.7 | −1.12929 | ||||||||
\(547\) | 13220.8 | 1.03342 | 0.516711 | − | 0.856160i | \(-0.327156\pi\) | ||||
0.516711 | + | 0.856160i | \(0.327156\pi\) | |||||||
\(548\) | 16658.8 | 1.29859 | ||||||||
\(549\) | 3227.72 | 0.250921 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14316.0 | 1.10686 | ||||||||
\(552\) | −12425.8 | −0.958108 | ||||||||
\(553\) | −34203.2 | −2.63014 | ||||||||
\(554\) | −25628.3 | −1.96542 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11957.6 | 0.912074 | ||||||||
\(557\) | 14165.4 | 1.07757 | 0.538786 | − | 0.842442i | \(-0.318883\pi\) | ||||
0.538786 | + | 0.842442i | \(0.318883\pi\) | |||||||
\(558\) | 7261.66 | 0.550915 | ||||||||
\(559\) | 4348.00 | 0.328981 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −641.498 | −0.0482782 | ||||||||
\(562\) | 34995.2 | 2.62666 | ||||||||
\(563\) | −11266.9 | −0.843413 | −0.421707 | − | 0.906732i | \(-0.638569\pi\) | ||||
−0.421707 | + | 0.906732i | \(0.638569\pi\) | |||||||
\(564\) | −2381.63 | −0.177810 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 20851.4 | 1.54850 | ||||||||
\(567\) | 2109.61 | 0.156252 | ||||||||
\(568\) | −4501.02 | −0.332497 | ||||||||
\(569\) | −7401.52 | −0.545322 | −0.272661 | − | 0.962110i | \(-0.587904\pi\) | ||||
−0.272661 | + | 0.962110i | \(0.587904\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13070.2 | −0.957919 | −0.478959 | − | 0.877837i | \(-0.658986\pi\) | ||||
−0.478959 | + | 0.877837i | \(0.658986\pi\) | |||||||
\(572\) | −1361.77 | −0.0995430 | ||||||||
\(573\) | 1922.84 | 0.140188 | ||||||||
\(574\) | 43083.2 | 3.13285 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7189.22 | −0.520053 | ||||||||
\(577\) | −8216.81 | −0.592843 | −0.296421 | − | 0.955057i | \(-0.595793\pi\) | ||||
−0.296421 | + | 0.955057i | \(0.595793\pi\) | |||||||
\(578\) | −10753.6 | −0.773857 | ||||||||
\(579\) | −1976.86 | −0.141892 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17030.5 | 1.21608 | ||||||||
\(582\) | −8956.94 | −0.637933 | ||||||||
\(583\) | 983.417 | 0.0698610 | ||||||||
\(584\) | −24580.0 | −1.74166 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −31053.3 | −2.18908 | ||||||||
\(587\) | −19965.0 | −1.40382 | −0.701911 | − | 0.712265i | \(-0.747669\pi\) | ||||
−0.701911 | + | 0.712265i | \(0.747669\pi\) | |||||||
\(588\) | −13742.5 | −0.963829 | ||||||||
\(589\) | 24760.7 | 1.73217 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8406.80 | 0.585126 | ||||||||
\(592\) | 792.293 | 0.0550051 | ||||||||
\(593\) | 14429.9 | 0.999267 | 0.499634 | − | 0.866237i | \(-0.333468\pi\) | ||||
0.499634 | + | 0.866237i | \(0.333468\pi\) | |||||||
\(594\) | 316.158 | 0.0218386 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11197.2 | −0.769555 | ||||||||
\(597\) | 8147.67 | 0.558563 | ||||||||
\(598\) | −28987.3 | −1.98224 | ||||||||
\(599\) | −7838.61 | −0.534686 | −0.267343 | − | 0.963601i | \(-0.586146\pi\) | ||||
−0.267343 | + | 0.963601i | \(0.586146\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25163.3 | −1.70787 | −0.853937 | − | 0.520376i | \(-0.825792\pi\) | ||||
−0.853937 | + | 0.520376i | \(0.825792\pi\) | |||||||
\(602\) | 13302.4 | 0.900609 | ||||||||
\(603\) | −3159.09 | −0.213347 | ||||||||
\(604\) | 7752.16 | 0.522237 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 12064.0 | 0.808691 | ||||||||
\(607\) | 563.698 | 0.0376932 | 0.0188466 | − | 0.999822i | \(-0.494001\pi\) | ||||
0.0188466 | + | 0.999822i | \(0.494001\pi\) | |||||||
\(608\) | −21238.8 | −1.41669 | ||||||||
\(609\) | 7831.56 | 0.521102 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2302.39 | −0.152446 | ||||||||
\(612\) | 10449.8 | 0.690208 | ||||||||
\(613\) | 6736.20 | 0.443838 | 0.221919 | − | 0.975065i | \(-0.428768\pi\) | ||||
0.221919 | + | 0.975065i | \(0.428768\pi\) | |||||||
\(614\) | 25287.4 | 1.66208 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1726.50 | −0.112927 | ||||||||
\(617\) | 10198.6 | 0.665448 | 0.332724 | − | 0.943024i | \(-0.392032\pi\) | ||||
0.332724 | + | 0.943024i | \(0.392032\pi\) | |||||||
\(618\) | −25580.8 | −1.66506 | ||||||||
\(619\) | 7579.25 | 0.492142 | 0.246071 | − | 0.969252i | \(-0.420860\pi\) | ||||
0.246071 | + | 0.969252i | \(0.420860\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4244.37 | 0.274269 | ||||||||
\(622\) | −2387.64 | −0.153916 | ||||||||
\(623\) | 27598.0 | 1.77478 | ||||||||
\(624\) | 1585.51 | 0.101717 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4637.72 | −0.296103 | ||||||||
\(627\) | 1078.03 | 0.0686641 | ||||||||
\(628\) | 22454.0 | 1.42677 | ||||||||
\(629\) | 5048.11 | 0.320002 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4575.59 | 0.288671 | 0.144335 | − | 0.989529i | \(-0.453896\pi\) | ||||
0.144335 | + | 0.989529i | \(0.453896\pi\) | |||||||
\(632\) | 34602.1 | 2.17784 | ||||||||
\(633\) | 5199.75 | 0.326495 | ||||||||
\(634\) | 19922.5 | 1.24799 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −16019.5 | −0.998766 | ||||||||
\(637\) | −13285.3 | −0.826346 | ||||||||
\(638\) | 1173.69 | 0.0728317 | ||||||||
\(639\) | 1537.45 | 0.0951809 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17713.6 | −1.09149 | −0.545745 | − | 0.837951i | \(-0.683753\pi\) | ||||
−0.545745 | + | 0.837951i | \(0.683753\pi\) | |||||||
\(642\) | 14492.9 | 0.890950 | ||||||||
\(643\) | 13212.2 | 0.810323 | 0.405162 | − | 0.914245i | \(-0.367215\pi\) | ||||
0.405162 | + | 0.914245i | \(0.367215\pi\) | |||||||
\(644\) | −55931.4 | −3.42237 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 56497.2 | 3.44095 | ||||||||
\(647\) | −4215.72 | −0.256163 | −0.128081 | − | 0.991764i | \(-0.540882\pi\) | ||||
−0.128081 | + | 0.991764i | \(0.540882\pi\) | |||||||
\(648\) | −2134.21 | −0.129382 | ||||||||
\(649\) | 1037.95 | 0.0627780 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13545.3 | 0.815488 | ||||||||
\(652\) | 17490.4 | 1.05058 | ||||||||
\(653\) | −26191.1 | −1.56958 | −0.784792 | − | 0.619759i | \(-0.787230\pi\) | ||||
−0.784792 | + | 0.619759i | \(0.787230\pi\) | |||||||
\(654\) | 21740.1 | 1.29985 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4741.13 | −0.282180 | ||||||||
\(657\) | 8396.02 | 0.498569 | ||||||||
\(658\) | −7044.02 | −0.417332 | ||||||||
\(659\) | −12868.3 | −0.760665 | −0.380332 | − | 0.924850i | \(-0.624190\pi\) | ||||
−0.380332 | + | 0.924850i | \(0.624190\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21599.8 | −1.27101 | −0.635503 | − | 0.772099i | \(-0.719207\pi\) | ||||
−0.635503 | + | 0.772099i | \(0.719207\pi\) | |||||||
\(662\) | 13835.7 | 0.812293 | ||||||||
\(663\) | 10102.1 | 0.591755 | ||||||||
\(664\) | −17229.1 | −1.00696 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2487.93 | −0.144753 | ||||||||
\(667\) | 15756.5 | 0.914686 | ||||||||
\(668\) | 21538.4 | 1.24752 | ||||||||
\(669\) | 13131.4 | 0.758878 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 902.302 | 0.0519121 | ||||||||
\(672\) | −11618.7 | −0.666965 | ||||||||
\(673\) | −10572.3 | −0.605546 | −0.302773 | − | 0.953063i | \(-0.597912\pi\) | ||||
−0.302773 | + | 0.953063i | \(0.597912\pi\) | |||||||
\(674\) | 7180.37 | 0.410352 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8568.93 | −0.487536 | ||||||||
\(677\) | 15661.0 | 0.889070 | 0.444535 | − | 0.895762i | \(-0.353369\pi\) | ||||
0.444535 | + | 0.895762i | \(0.353369\pi\) | |||||||
\(678\) | 13616.2 | 0.771279 | ||||||||
\(679\) | −16707.6 | −0.944296 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6746.18 | −0.379610 | ||||||||
\(682\) | 2029.98 | 0.113977 | ||||||||
\(683\) | −23697.9 | −1.32763 | −0.663817 | − | 0.747895i | \(-0.731065\pi\) | ||||
−0.663817 | + | 0.747895i | \(0.731065\pi\) | |||||||
\(684\) | −17560.7 | −0.981655 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 931.335 | 0.0518346 | ||||||||
\(687\) | −6735.97 | −0.374080 | ||||||||
\(688\) | −1463.88 | −0.0811189 | ||||||||
\(689\) | −15486.5 | −0.856300 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4426.30 | 0.243682 | 0.121841 | − | 0.992550i | \(-0.461120\pi\) | ||||
0.121841 | + | 0.992550i | \(0.461120\pi\) | |||||||
\(692\) | −30350.0 | −1.66725 | ||||||||
\(693\) | 589.736 | 0.0323265 | ||||||||
\(694\) | −26176.5 | −1.43177 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7922.90 | −0.431490 | ||||||||
\(697\) | −30208.2 | −1.64163 | ||||||||
\(698\) | −16505.7 | −0.895059 | ||||||||
\(699\) | 2125.13 | 0.114993 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5192.49 | 0.279768 | 0.139884 | − | 0.990168i | \(-0.455327\pi\) | ||||
0.139884 | + | 0.990168i | \(0.455327\pi\) | |||||||
\(702\) | −4978.76 | −0.267680 | ||||||||
\(703\) | −8483.30 | −0.455126 | ||||||||
\(704\) | −2009.73 | −0.107592 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8917.59 | −0.475379 | ||||||||
\(707\) | 22503.2 | 1.19706 | ||||||||
\(708\) | −16907.8 | −0.897504 | ||||||||
\(709\) | −1120.17 | −0.0593356 | −0.0296678 | − | 0.999560i | \(-0.509445\pi\) | ||||
−0.0296678 | + | 0.999560i | \(0.509445\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11819.3 | −0.623431 | ||||||||
\(712\) | −27919.9 | −1.46958 | ||||||||
\(713\) | 27252.2 | 1.43142 | ||||||||
\(714\) | 30906.8 | 1.61997 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 41189.5 | 2.14990 | ||||||||
\(717\) | −16358.2 | −0.852036 | ||||||||
\(718\) | −12254.8 | −0.636973 | ||||||||
\(719\) | 22785.4 | 1.18185 | 0.590927 | − | 0.806725i | \(-0.298762\pi\) | ||||
0.590927 | + | 0.806725i | \(0.298762\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −47716.3 | −2.46470 | ||||||||
\(722\) | −63020.1 | −3.24843 | ||||||||
\(723\) | −17162.2 | −0.882806 | ||||||||
\(724\) | 33779.5 | 1.73399 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −18495.7 | −0.945509 | ||||||||
\(727\) | −32028.6 | −1.63394 | −0.816970 | − | 0.576680i | \(-0.804348\pi\) | ||||
−0.816970 | + | 0.576680i | \(0.804348\pi\) | |||||||
\(728\) | 27188.4 | 1.38416 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9327.13 | −0.471924 | ||||||||
\(732\) | −14698.2 | −0.742159 | ||||||||
\(733\) | −21723.1 | −1.09463 | −0.547313 | − | 0.836928i | \(-0.684349\pi\) | ||||
−0.547313 | + | 0.836928i | \(0.684349\pi\) | |||||||
\(734\) | −31660.4 | −1.59211 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −23376.0 | −1.17072 | ||||||||
\(737\) | −883.119 | −0.0441385 | ||||||||
\(738\) | 14887.9 | 0.742590 | ||||||||
\(739\) | 30000.0 | 1.49332 | 0.746662 | − | 0.665203i | \(-0.231655\pi\) | ||||
0.746662 | + | 0.665203i | \(0.231655\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16976.5 | −0.841629 | ||||||||
\(742\) | −47380.2 | −2.34418 | ||||||||
\(743\) | 5551.03 | 0.274088 | 0.137044 | − | 0.990565i | \(-0.456240\pi\) | ||||
0.137044 | + | 0.990565i | \(0.456240\pi\) | |||||||
\(744\) | −13703.3 | −0.675251 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −31206.7 | −1.53158 | ||||||||
\(747\) | 5885.10 | 0.288252 | ||||||||
\(748\) | 2921.21 | 0.142794 | ||||||||
\(749\) | 27033.9 | 1.31882 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5337.87 | 0.259363 | 0.129682 | − | 0.991556i | \(-0.458604\pi\) | ||||
0.129682 | + | 0.991556i | \(0.458604\pi\) | |||||||
\(752\) | 775.166 | 0.0375896 | ||||||||
\(753\) | −6135.70 | −0.296942 | ||||||||
\(754\) | −18482.8 | −0.892712 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −9606.60 | −0.462154 | ||||||||
\(757\) | 17462.2 | 0.838409 | 0.419205 | − | 0.907892i | \(-0.362309\pi\) | ||||
0.419205 | + | 0.907892i | \(0.362309\pi\) | |||||||
\(758\) | −18107.9 | −0.867690 | ||||||||
\(759\) | 1186.51 | 0.0567424 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13611.2 | 0.648367 | 0.324183 | − | 0.945994i | \(-0.394911\pi\) | ||||
0.324183 | + | 0.945994i | \(0.394911\pi\) | |||||||
\(762\) | 14365.9 | 0.682969 | ||||||||
\(763\) | 40552.2 | 1.92410 | ||||||||
\(764\) | −8756.10 | −0.414639 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26259.7 | −1.23864 | ||||||||
\(767\) | −16345.2 | −0.769481 | ||||||||
\(768\) | 16127.7 | 0.757759 | ||||||||
\(769\) | −23956.9 | −1.12342 | −0.561709 | − | 0.827335i | \(-0.689856\pi\) | ||||
−0.561709 | + | 0.827335i | \(0.689856\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1222.64 | 0.0571107 | ||||||||
\(772\) | 9002.10 | 0.419680 | ||||||||
\(773\) | 35279.7 | 1.64156 | 0.820779 | − | 0.571246i | \(-0.193540\pi\) | ||||
0.820779 | + | 0.571246i | \(0.193540\pi\) | |||||||
\(774\) | 4596.82 | 0.213474 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 16902.4 | 0.781909 | ||||||||
\(777\) | −4640.79 | −0.214269 | ||||||||
\(778\) | 21776.6 | 1.00351 | ||||||||
\(779\) | 50764.5 | 2.33482 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 429.792 | 0.0196916 | ||||||||
\(782\) | 62182.2 | 2.84352 | ||||||||
\(783\) | 2706.29 | 0.123519 | ||||||||
\(784\) | 4472.88 | 0.203757 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −37278.5 | −1.69170 | ||||||||
\(787\) | 3904.96 | 0.176870 | 0.0884351 | − | 0.996082i | \(-0.471813\pi\) | ||||
0.0884351 | + | 0.996082i | \(0.471813\pi\) | |||||||
\(788\) | −38282.4 | −1.73065 | ||||||||
\(789\) | −2662.46 | −0.120134 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25398.6 | 1.14168 | ||||||||
\(792\) | −596.614 | −0.0267674 | ||||||||
\(793\) | −14209.2 | −0.636296 | ||||||||
\(794\) | 38998.4 | 1.74307 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −37102.4 | −1.65208 | ||||||||
\(797\) | −6743.01 | −0.299686 | −0.149843 | − | 0.988710i | \(-0.547877\pi\) | ||||
−0.149843 | + | 0.988710i | \(0.547877\pi\) | |||||||
\(798\) | −51938.5 | −2.30402 | ||||||||
\(799\) | 4938.98 | 0.218684 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9536.83 | 0.420683 | ||||||||
\(802\) | −28121.8 | −1.23818 | ||||||||
\(803\) | 2347.09 | 0.103147 | ||||||||
\(804\) | 14385.7 | 0.631025 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −31967.5 | −1.39703 | ||||||||
\(807\) | −18100.4 | −0.789548 | ||||||||
\(808\) | −22765.7 | −0.991205 | ||||||||
\(809\) | 13083.1 | 0.568577 | 0.284288 | − | 0.958739i | \(-0.408243\pi\) | ||||
0.284288 | + | 0.958739i | \(0.408243\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7501.06 | 0.324782 | 0.162391 | − | 0.986727i | \(-0.448079\pi\) | ||||
0.162391 | + | 0.986727i | \(0.448079\pi\) | |||||||
\(812\) | −35662.9 | −1.54128 | ||||||||
\(813\) | −19604.8 | −0.845718 | ||||||||
\(814\) | −695.496 | −0.0299473 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3401.17 | −0.145913 | ||||||||
\(817\) | 15674.1 | 0.671198 | ||||||||
\(818\) | −30436.8 | −1.30097 | ||||||||
\(819\) | −9286.98 | −0.396231 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23440.2 | −0.996431 | −0.498215 | − | 0.867053i | \(-0.666011\pi\) | ||||
−0.498215 | + | 0.867053i | \(0.666011\pi\) | |||||||
\(822\) | 17026.2 | 0.722452 | ||||||||
\(823\) | 6213.94 | 0.263189 | 0.131594 | − | 0.991304i | \(-0.457990\pi\) | ||||
0.131594 | + | 0.991304i | \(0.457990\pi\) | |||||||
\(824\) | 48272.8 | 2.04085 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −50007.3 | −2.10651 | ||||||||
\(827\) | 589.434 | 0.0247843 | 0.0123922 | − | 0.999923i | \(-0.496055\pi\) | ||||
0.0123922 | + | 0.999923i | \(0.496055\pi\) | |||||||
\(828\) | −19327.8 | −0.811216 | ||||||||
\(829\) | 39666.0 | 1.66183 | 0.830916 | − | 0.556398i | \(-0.187817\pi\) | ||||
0.830916 | + | 0.556398i | \(0.187817\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16519.6 | −0.689601 | ||||||||
\(832\) | 31648.6 | 1.31877 | ||||||||
\(833\) | 28499.0 | 1.18539 | ||||||||
\(834\) | 12221.2 | 0.507419 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4909.07 | −0.203091 | ||||||||
\(837\) | 4680.75 | 0.193298 | ||||||||
\(838\) | −61012.0 | −2.51507 | ||||||||
\(839\) | −6048.43 | −0.248885 | −0.124443 | − | 0.992227i | \(-0.539714\pi\) | ||||
−0.124443 | + | 0.992227i | \(0.539714\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14342.3 | −0.588066 | ||||||||
\(842\) | −15885.4 | −0.650174 | ||||||||
\(843\) | 22557.4 | 0.921610 | ||||||||
\(844\) | −23678.3 | −0.965689 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2434.15 | −0.0989216 | ||||||||
\(847\) | −34500.4 | −1.39958 | ||||||||
\(848\) | 5213.99 | 0.211143 | ||||||||
\(849\) | 13440.5 | 0.543317 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9336.93 | −0.376105 | ||||||||
\(852\) | −7001.16 | −0.281521 | ||||||||
\(853\) | 31051.4 | 1.24640 | 0.623200 | − | 0.782063i | \(-0.285832\pi\) | ||||
0.623200 | + | 0.782063i | \(0.285832\pi\) | |||||||
\(854\) | −43472.1 | −1.74190 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −27349.2 | −1.09203 | ||||||||
\(857\) | −10170.1 | −0.405371 | −0.202685 | − | 0.979244i | \(-0.564967\pi\) | ||||
−0.202685 | + | 0.979244i | \(0.564967\pi\) | |||||||
\(858\) | −1391.80 | −0.0553792 | ||||||||
\(859\) | −41323.5 | −1.64137 | −0.820687 | − | 0.571378i | \(-0.806409\pi\) | ||||
−0.820687 | + | 0.571378i | \(0.806409\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27770.7 | 1.09921 | ||||||||
\(862\) | 7036.26 | 0.278023 | ||||||||
\(863\) | −30910.9 | −1.21926 | −0.609628 | − | 0.792688i | \(-0.708681\pi\) | ||||
−0.609628 | + | 0.792688i | \(0.708681\pi\) | |||||||
\(864\) | −4014.98 | −0.158093 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −40140.6 | −1.57510 | ||||||||
\(867\) | −6931.58 | −0.271521 | ||||||||
\(868\) | −61681.9 | −2.41200 | ||||||||
\(869\) | −3304.07 | −0.128979 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13907.1 | 0.541014 | ||||||||
\(872\) | −41025.1 | −1.59322 | ||||||||
\(873\) | −5773.50 | −0.223830 | ||||||||
\(874\) | −104497. | −4.04422 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −38233.3 | −1.47464 | ||||||||
\(877\) | 10750.3 | 0.413923 | 0.206961 | − | 0.978349i | \(-0.433643\pi\) | ||||
0.206961 | + | 0.978349i | \(0.433643\pi\) | |||||||
\(878\) | 16423.6 | 0.631286 | ||||||||
\(879\) | −20016.5 | −0.768077 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20982.9 | −0.802419 | −0.401209 | − | 0.915986i | \(-0.631410\pi\) | ||||
−0.401209 | + | 0.915986i | \(0.631410\pi\) | |||||||
\(882\) | −14045.6 | −0.536212 | ||||||||
\(883\) | 30286.5 | 1.15427 | 0.577136 | − | 0.816648i | \(-0.304170\pi\) | ||||
0.577136 | + | 0.816648i | \(0.304170\pi\) | |||||||
\(884\) | −46002.4 | −1.75026 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −44630.6 | −1.69232 | ||||||||
\(887\) | −18397.5 | −0.696423 | −0.348212 | − | 0.937416i | \(-0.613211\pi\) | ||||
−0.348212 | + | 0.937416i | \(0.613211\pi\) | |||||||
\(888\) | 4694.91 | 0.177422 | ||||||||
\(889\) | 26797.0 | 1.01096 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 203.791 | 0.00766245 | ||||||||
\(892\) | −59797.0 | −2.24457 | ||||||||
\(893\) | −8299.91 | −0.311026 | ||||||||
\(894\) | −11444.1 | −0.428130 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 65843.9 | 2.45501 | ||||||||
\(897\) | −18684.7 | −0.695502 | ||||||||
\(898\) | 45707.6 | 1.69853 | ||||||||
\(899\) | 17376.5 | 0.644649 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33221.1 | 1.22836 | ||||||||
\(902\) | 4161.89 | 0.153632 | ||||||||
\(903\) | 8574.54 | 0.315994 | ||||||||
\(904\) | −25694.8 | −0.945350 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7923.12 | 0.290539 | ||||||||
\(907\) | 22143.3 | 0.810648 | 0.405324 | − | 0.914173i | \(-0.367159\pi\) | ||||
0.405324 | + | 0.914173i | \(0.367159\pi\) | |||||||
\(908\) | 30720.4 | 1.12279 | ||||||||
\(909\) | 7776.27 | 0.283743 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42399.1 | 1.54198 | 0.770991 | − | 0.636846i | \(-0.219761\pi\) | ||||
0.770991 | + | 0.636846i | \(0.219761\pi\) | |||||||
\(912\) | 5715.63 | 0.207526 | ||||||||
\(913\) | 1645.17 | 0.0596354 | ||||||||
\(914\) | 7433.78 | 0.269024 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 30673.9 | 1.10643 | ||||||||
\(917\) | −69536.3 | −2.50414 | ||||||||
\(918\) | 10680.2 | 0.383986 | ||||||||
\(919\) | 11557.8 | 0.414859 | 0.207429 | − | 0.978250i | \(-0.433490\pi\) | ||||
0.207429 | + | 0.978250i | \(0.433490\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16299.9 | 0.583169 | ||||||||
\(922\) | 18165.5 | 0.648860 | ||||||||
\(923\) | −6768.22 | −0.241364 | ||||||||
\(924\) | −2685.51 | −0.0956133 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −72893.2 | −2.58685 | ||||||||
\(927\) | −16489.0 | −0.584216 | ||||||||
\(928\) | −14905.0 | −0.527240 | ||||||||
\(929\) | −16273.9 | −0.574735 | −0.287367 | − | 0.957820i | \(-0.592780\pi\) | ||||
−0.287367 | + | 0.957820i | \(0.592780\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −47892.3 | −1.68594 | ||||||||
\(932\) | −9677.31 | −0.340119 | ||||||||
\(933\) | −1539.04 | −0.0540040 | ||||||||
\(934\) | −29774.2 | −1.04308 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9395.29 | 0.328093 | ||||||||
\(937\) | 39685.9 | 1.38365 | 0.691825 | − | 0.722065i | \(-0.256807\pi\) | ||||
0.691825 | + | 0.722065i | \(0.256807\pi\) | |||||||
\(938\) | 42547.8 | 1.48106 | ||||||||
\(939\) | −2989.40 | −0.103893 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21618.8 | −0.748940 | −0.374470 | − | 0.927239i | \(-0.622175\pi\) | ||||
−0.374470 | + | 0.927239i | \(0.622175\pi\) | |||||||
\(942\) | 22949.2 | 0.793762 | ||||||||
\(943\) | 55872.7 | 1.92944 | ||||||||
\(944\) | 5503.10 | 0.189736 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1285.03 | 0.0441649 | ||||||||
\(947\) | −3083.65 | −0.105813 | −0.0529066 | − | 0.998599i | \(-0.516849\pi\) | ||||
−0.0529066 | + | 0.998599i | \(0.516849\pi\) | |||||||
\(948\) | 53822.2 | 1.84395 | ||||||||
\(949\) | −36961.2 | −1.26429 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12841.7 | 0.437877 | ||||||||
\(952\) | −58323.4 | −1.98558 | ||||||||
\(953\) | −35749.5 | −1.21515 | −0.607576 | − | 0.794261i | \(-0.707858\pi\) | ||||
−0.607576 | + | 0.794261i | \(0.707858\pi\) | |||||||
\(954\) | −16372.8 | −0.555649 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 74491.2 | 2.52010 | ||||||||
\(957\) | 756.539 | 0.0255543 | ||||||||
\(958\) | 47872.0 | 1.61448 | ||||||||
\(959\) | 31759.3 | 1.06941 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 263.073 | 0.00883061 | ||||||||
\(962\) | 10952.5 | 0.367070 | ||||||||
\(963\) | 9341.91 | 0.312605 | ||||||||
\(964\) | 78152.2 | 2.61111 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −57164.8 | −1.90398 | ||||||||
\(967\) | 23629.2 | 0.785796 | 0.392898 | − | 0.919582i | \(-0.371473\pi\) | ||||
0.392898 | + | 0.919582i | \(0.371473\pi\) | |||||||
\(968\) | 34902.7 | 1.15890 | ||||||||
\(969\) | 36417.2 | 1.20732 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15734.9 | 0.520039 | 0.260019 | − | 0.965603i | \(-0.416271\pi\) | ||||
0.260019 | + | 0.965603i | \(0.416271\pi\) | |||||||
\(972\) | −3319.68 | −0.109546 | ||||||||
\(973\) | 22796.5 | 0.751104 | ||||||||
\(974\) | 9696.74 | 0.318997 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4783.93 | 0.156895 | ||||||||
\(977\) | 4163.71 | 0.136345 | 0.0681724 | − | 0.997674i | \(-0.478283\pi\) | ||||
0.0681724 | + | 0.997674i | \(0.478283\pi\) | |||||||
\(978\) | 17876.1 | 0.584473 | ||||||||
\(979\) | 2666.00 | 0.0870335 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14013.3 | 0.456076 | ||||||||
\(982\) | −82399.4 | −2.67767 | ||||||||
\(983\) | 40241.6 | 1.30571 | 0.652853 | − | 0.757485i | \(-0.273572\pi\) | ||||
0.652853 | + | 0.757485i | \(0.273572\pi\) | |||||||
\(984\) | −28094.6 | −0.910186 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 39648.5 | 1.28060 | ||||||||
\(987\) | −4540.47 | −0.146428 | ||||||||
\(988\) | 77306.5 | 2.48932 | ||||||||
\(989\) | 17251.3 | 0.554662 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52220.5 | 1.67390 | 0.836952 | − | 0.547276i | \(-0.184335\pi\) | ||||
0.836952 | + | 0.547276i | \(0.184335\pi\) | |||||||
\(992\) | −25779.3 | −0.825095 | ||||||||
\(993\) | 8918.25 | 0.285007 | ||||||||
\(994\) | −20707.0 | −0.660750 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −26799.2 | −0.852576 | ||||||||
\(997\) | 57238.6 | 1.81822 | 0.909109 | − | 0.416558i | \(-0.136764\pi\) | ||||
0.909109 | + | 0.416558i | \(0.136764\pi\) | |||||||
\(998\) | −23358.9 | −0.740894 | ||||||||
\(999\) | −1603.68 | −0.0507890 |
(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 | 1875.4.a.f.1.2 | 14 | ||
5.4 | even | 2 | 1875.4.a.g.1.13 | 14 | |||
25.4 | even | 10 | 75.4.g.b.16.1 | ✓ | 28 | ||
25.19 | even | 10 | 75.4.g.b.61.1 | yes | 28 | ||
75.29 | odd | 10 | 225.4.h.a.91.7 | 28 | |||
75.44 | odd | 10 | 225.4.h.a.136.7 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.g.b.16.1 | ✓ | 28 | 25.4 | even | 10 | ||
75.4.g.b.61.1 | yes | 28 | 25.19 | even | 10 | ||
225.4.h.a.91.7 | 28 | 75.29 | odd | 10 | |||
225.4.h.a.136.7 | 28 | 75.44 | odd | 10 | |||
1875.4.a.f.1.2 | 14 | 1.1 | even | 1 | trivial | ||
1875.4.a.g.1.13 | 14 | 5.4 | even | 2 |