Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,4,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(61.6569959560\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} - 105 x^{18} + 103 x^{17} + 4500 x^{16} - 4345 x^{15} - 101844 x^{14} + 95592 x^{13} + 1317797 x^{12} - 1160501 x^{11} - 9914845 x^{10} + 7570653 x^{9} + \cdots + 150528 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.01989\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.01989 | −0.714140 | −0.357070 | − | 0.934078i | \(-0.616224\pi\) | ||||
−0.357070 | + | 0.934078i | \(0.616224\pi\) | |||||||
\(3\) | 7.09682 | 1.36578 | 0.682892 | − | 0.730519i | \(-0.260722\pi\) | ||||
0.682892 | + | 0.730519i | \(0.260722\pi\) | |||||||
\(4\) | −3.92003 | −0.490004 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | −14.3348 | −0.975361 | ||||||||
\(7\) | −8.46588 | −0.457114 | −0.228557 | − | 0.973530i | \(-0.573401\pi\) | ||||
−0.228557 | + | 0.973530i | \(0.573401\pi\) | |||||||
\(8\) | 24.0772 | 1.06407 | ||||||||
\(9\) | 23.3649 | 0.865365 | ||||||||
\(10\) | 10.0995 | 0.319373 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | −27.8198 | −0.669240 | ||||||||
\(13\) | −33.6704 | −0.718346 | −0.359173 | − | 0.933271i | \(-0.616941\pi\) | ||||
−0.359173 | + | 0.933271i | \(0.616941\pi\) | |||||||
\(14\) | 17.1002 | 0.326444 | ||||||||
\(15\) | −35.4841 | −0.610797 | ||||||||
\(16\) | −17.2731 | −0.269892 | ||||||||
\(17\) | 98.1464 | 1.40023 | 0.700117 | − | 0.714028i | \(-0.253131\pi\) | ||||
0.700117 | + | 0.714028i | \(0.253131\pi\) | |||||||
\(18\) | −47.1945 | −0.617992 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | 19.6002 | 0.219137 | ||||||||
\(21\) | −60.0808 | −0.624319 | ||||||||
\(22\) | 22.2188 | 0.215321 | ||||||||
\(23\) | 90.8592 | 0.823716 | 0.411858 | − | 0.911248i | \(-0.364880\pi\) | ||||
0.411858 | + | 0.911248i | \(0.364880\pi\) | |||||||
\(24\) | 170.871 | 1.45329 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 68.0106 | 0.512999 | ||||||||
\(27\) | −25.7979 | −0.183882 | ||||||||
\(28\) | 33.1865 | 0.223988 | ||||||||
\(29\) | −142.201 | −0.910554 | −0.455277 | − | 0.890350i | \(-0.650460\pi\) | ||||
−0.455277 | + | 0.890350i | \(0.650460\pi\) | |||||||
\(30\) | 71.6741 | 0.436195 | ||||||||
\(31\) | 38.3284 | 0.222064 | 0.111032 | − | 0.993817i | \(-0.464584\pi\) | ||||
0.111032 | + | 0.993817i | \(0.464584\pi\) | |||||||
\(32\) | −157.728 | −0.871331 | ||||||||
\(33\) | −78.0650 | −0.411799 | ||||||||
\(34\) | −198.245 | −0.999964 | ||||||||
\(35\) | 42.3294 | 0.204428 | ||||||||
\(36\) | −91.5910 | −0.424033 | ||||||||
\(37\) | −66.4096 | −0.295072 | −0.147536 | − | 0.989057i | \(-0.547134\pi\) | ||||
−0.147536 | + | 0.989057i | \(0.547134\pi\) | |||||||
\(38\) | −38.3780 | −0.163835 | ||||||||
\(39\) | −238.953 | −0.981105 | ||||||||
\(40\) | −120.386 | −0.475867 | ||||||||
\(41\) | 501.764 | 1.91128 | 0.955639 | − | 0.294540i | \(-0.0951663\pi\) | ||||
0.955639 | + | 0.294540i | \(0.0951663\pi\) | |||||||
\(42\) | 121.357 | 0.445851 | ||||||||
\(43\) | −249.116 | −0.883483 | −0.441741 | − | 0.897142i | \(-0.645639\pi\) | ||||
−0.441741 | + | 0.897142i | \(0.645639\pi\) | |||||||
\(44\) | 43.1204 | 0.147742 | ||||||||
\(45\) | −116.824 | −0.387003 | ||||||||
\(46\) | −183.526 | −0.588248 | ||||||||
\(47\) | 269.945 | 0.837776 | 0.418888 | − | 0.908038i | \(-0.362420\pi\) | ||||
0.418888 | + | 0.908038i | \(0.362420\pi\) | |||||||
\(48\) | −122.584 | −0.368614 | ||||||||
\(49\) | −271.329 | −0.791046 | ||||||||
\(50\) | −50.4973 | −0.142828 | ||||||||
\(51\) | 696.527 | 1.91242 | ||||||||
\(52\) | 131.989 | 0.351992 | ||||||||
\(53\) | −252.766 | −0.655097 | −0.327548 | − | 0.944834i | \(-0.606222\pi\) | ||||
−0.327548 | + | 0.944834i | \(0.606222\pi\) | |||||||
\(54\) | 52.1091 | 0.131318 | ||||||||
\(55\) | 55.0000 | 0.134840 | ||||||||
\(56\) | −203.835 | −0.486402 | ||||||||
\(57\) | 134.840 | 0.313332 | ||||||||
\(58\) | 287.231 | 0.650263 | ||||||||
\(59\) | −669.048 | −1.47632 | −0.738158 | − | 0.674628i | \(-0.764304\pi\) | ||||
−0.738158 | + | 0.674628i | \(0.764304\pi\) | |||||||
\(60\) | 139.099 | 0.299293 | ||||||||
\(61\) | −546.193 | −1.14644 | −0.573220 | − | 0.819402i | \(-0.694306\pi\) | ||||
−0.573220 | + | 0.819402i | \(0.694306\pi\) | |||||||
\(62\) | −77.4193 | −0.158585 | ||||||||
\(63\) | −197.804 | −0.395571 | ||||||||
\(64\) | 456.778 | 0.892144 | ||||||||
\(65\) | 168.352 | 0.321254 | ||||||||
\(66\) | 157.683 | 0.294082 | ||||||||
\(67\) | 648.266 | 1.18206 | 0.591032 | − | 0.806648i | \(-0.298721\pi\) | ||||
0.591032 | + | 0.806648i | \(0.298721\pi\) | |||||||
\(68\) | −384.737 | −0.686121 | ||||||||
\(69\) | 644.812 | 1.12502 | ||||||||
\(70\) | −85.5008 | −0.145990 | ||||||||
\(71\) | 773.047 | 1.29217 | 0.646083 | − | 0.763267i | \(-0.276406\pi\) | ||||
0.646083 | + | 0.763267i | \(0.276406\pi\) | |||||||
\(72\) | 562.560 | 0.920810 | ||||||||
\(73\) | −685.480 | −1.09903 | −0.549516 | − | 0.835483i | \(-0.685188\pi\) | ||||
−0.549516 | + | 0.835483i | \(0.685188\pi\) | |||||||
\(74\) | 134.140 | 0.210723 | ||||||||
\(75\) | 177.421 | 0.273157 | ||||||||
\(76\) | −74.4806 | −0.112415 | ||||||||
\(77\) | 93.1247 | 0.137825 | ||||||||
\(78\) | 482.659 | 0.700646 | ||||||||
\(79\) | −1258.69 | −1.79258 | −0.896290 | − | 0.443468i | \(-0.853748\pi\) | ||||
−0.896290 | + | 0.443468i | \(0.853748\pi\) | |||||||
\(80\) | 86.3654 | 0.120699 | ||||||||
\(81\) | −813.935 | −1.11651 | ||||||||
\(82\) | −1013.51 | −1.36492 | ||||||||
\(83\) | −1290.53 | −1.70668 | −0.853338 | − | 0.521358i | \(-0.825426\pi\) | ||||
−0.853338 | + | 0.521358i | \(0.825426\pi\) | |||||||
\(84\) | 235.519 | 0.305919 | ||||||||
\(85\) | −490.732 | −0.626204 | ||||||||
\(86\) | 503.187 | 0.630930 | ||||||||
\(87\) | −1009.18 | −1.24362 | ||||||||
\(88\) | −264.849 | −0.320830 | ||||||||
\(89\) | −734.991 | −0.875381 | −0.437690 | − | 0.899126i | \(-0.644203\pi\) | ||||
−0.437690 | + | 0.899126i | \(0.644203\pi\) | |||||||
\(90\) | 235.973 | 0.276374 | ||||||||
\(91\) | 285.050 | 0.328366 | ||||||||
\(92\) | −356.171 | −0.403624 | ||||||||
\(93\) | 272.010 | 0.303292 | ||||||||
\(94\) | −545.260 | −0.598290 | ||||||||
\(95\) | −95.0000 | −0.102598 | ||||||||
\(96\) | −1119.37 | −1.19005 | ||||||||
\(97\) | −1006.26 | −1.05330 | −0.526650 | − | 0.850082i | \(-0.676552\pi\) | ||||
−0.526650 | + | 0.850082i | \(0.676552\pi\) | |||||||
\(98\) | 548.055 | 0.564918 | ||||||||
\(99\) | −257.013 | −0.260917 | ||||||||
\(100\) | −98.0008 | −0.0980008 | ||||||||
\(101\) | 1207.14 | 1.18925 | 0.594626 | − | 0.804002i | \(-0.297300\pi\) | ||||
0.594626 | + | 0.804002i | \(0.297300\pi\) | |||||||
\(102\) | −1406.91 | −1.36573 | ||||||||
\(103\) | −696.236 | −0.666041 | −0.333020 | − | 0.942920i | \(-0.608068\pi\) | ||||
−0.333020 | + | 0.942920i | \(0.608068\pi\) | |||||||
\(104\) | −810.689 | −0.764371 | ||||||||
\(105\) | 300.404 | 0.279204 | ||||||||
\(106\) | 510.561 | 0.467831 | ||||||||
\(107\) | 611.211 | 0.552224 | 0.276112 | − | 0.961125i | \(-0.410954\pi\) | ||||
0.276112 | + | 0.961125i | \(0.410954\pi\) | |||||||
\(108\) | 101.129 | 0.0901030 | ||||||||
\(109\) | 1109.55 | 0.975006 | 0.487503 | − | 0.873121i | \(-0.337908\pi\) | ||||
0.487503 | + | 0.873121i | \(0.337908\pi\) | |||||||
\(110\) | −111.094 | −0.0962946 | ||||||||
\(111\) | −471.297 | −0.403005 | ||||||||
\(112\) | 146.232 | 0.123371 | ||||||||
\(113\) | −801.022 | −0.666848 | −0.333424 | − | 0.942777i | \(-0.608204\pi\) | ||||
−0.333424 | + | 0.942777i | \(0.608204\pi\) | |||||||
\(114\) | −272.362 | −0.223763 | ||||||||
\(115\) | −454.296 | −0.368377 | ||||||||
\(116\) | 557.433 | 0.446175 | ||||||||
\(117\) | −786.705 | −0.621631 | ||||||||
\(118\) | 1351.40 | 1.05430 | ||||||||
\(119\) | −830.895 | −0.640068 | ||||||||
\(120\) | −854.357 | −0.649932 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 1103.25 | 0.818719 | ||||||||
\(123\) | 3560.93 | 2.61039 | ||||||||
\(124\) | −150.249 | −0.108812 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 399.543 | 0.282493 | ||||||||
\(127\) | −1926.14 | −1.34581 | −0.672904 | − | 0.739729i | \(-0.734953\pi\) | ||||
−0.672904 | + | 0.739729i | \(0.734953\pi\) | |||||||
\(128\) | 339.180 | 0.234215 | ||||||||
\(129\) | −1767.93 | −1.20665 | ||||||||
\(130\) | −340.053 | −0.229420 | ||||||||
\(131\) | −2340.12 | −1.56074 | −0.780370 | − | 0.625318i | \(-0.784969\pi\) | ||||
−0.780370 | + | 0.625318i | \(0.784969\pi\) | |||||||
\(132\) | 306.017 | 0.201783 | ||||||||
\(133\) | −160.852 | −0.104869 | ||||||||
\(134\) | −1309.43 | −0.844159 | ||||||||
\(135\) | 128.990 | 0.0822346 | ||||||||
\(136\) | 2363.09 | 1.48995 | ||||||||
\(137\) | −351.320 | −0.219090 | −0.109545 | − | 0.993982i | \(-0.534939\pi\) | ||||
−0.109545 | + | 0.993982i | \(0.534939\pi\) | |||||||
\(138\) | −1302.45 | −0.803420 | ||||||||
\(139\) | 544.833 | 0.332461 | 0.166231 | − | 0.986087i | \(-0.446840\pi\) | ||||
0.166231 | + | 0.986087i | \(0.446840\pi\) | |||||||
\(140\) | −165.933 | −0.100170 | ||||||||
\(141\) | 1915.75 | 1.14422 | ||||||||
\(142\) | −1561.47 | −0.922788 | ||||||||
\(143\) | 370.375 | 0.216589 | ||||||||
\(144\) | −403.583 | −0.233555 | ||||||||
\(145\) | 711.005 | 0.407212 | ||||||||
\(146\) | 1384.60 | 0.784863 | ||||||||
\(147\) | −1925.57 | −1.08040 | ||||||||
\(148\) | 260.328 | 0.144587 | ||||||||
\(149\) | 2517.27 | 1.38405 | 0.692024 | − | 0.721875i | \(-0.256719\pi\) | ||||
0.692024 | + | 0.721875i | \(0.256719\pi\) | |||||||
\(150\) | −358.370 | −0.195072 | ||||||||
\(151\) | 2695.70 | 1.45280 | 0.726400 | − | 0.687272i | \(-0.241192\pi\) | ||||
0.726400 | + | 0.687272i | \(0.241192\pi\) | |||||||
\(152\) | 457.467 | 0.244115 | ||||||||
\(153\) | 2293.18 | 1.21171 | ||||||||
\(154\) | −188.102 | −0.0984265 | ||||||||
\(155\) | −191.642 | −0.0993101 | ||||||||
\(156\) | 936.703 | 0.480745 | ||||||||
\(157\) | −2298.33 | −1.16832 | −0.584162 | − | 0.811637i | \(-0.698577\pi\) | ||||
−0.584162 | + | 0.811637i | \(0.698577\pi\) | |||||||
\(158\) | 2542.42 | 1.28015 | ||||||||
\(159\) | −1793.84 | −0.894721 | ||||||||
\(160\) | 788.639 | 0.389671 | ||||||||
\(161\) | −769.203 | −0.376532 | ||||||||
\(162\) | 1644.06 | 0.797343 | ||||||||
\(163\) | −3635.99 | −1.74720 | −0.873598 | − | 0.486649i | \(-0.838219\pi\) | ||||
−0.873598 | + | 0.486649i | \(0.838219\pi\) | |||||||
\(164\) | −1966.93 | −0.936534 | ||||||||
\(165\) | 390.325 | 0.184162 | ||||||||
\(166\) | 2606.73 | 1.21881 | ||||||||
\(167\) | 4033.97 | 1.86921 | 0.934604 | − | 0.355689i | \(-0.115754\pi\) | ||||
0.934604 | + | 0.355689i | \(0.115754\pi\) | |||||||
\(168\) | −1446.58 | −0.664320 | ||||||||
\(169\) | −1063.30 | −0.483979 | ||||||||
\(170\) | 991.226 | 0.447197 | ||||||||
\(171\) | 443.932 | 0.198528 | ||||||||
\(172\) | 976.541 | 0.432910 | ||||||||
\(173\) | −985.837 | −0.433247 | −0.216624 | − | 0.976255i | \(-0.569504\pi\) | ||||
−0.216624 | + | 0.976255i | \(0.569504\pi\) | |||||||
\(174\) | 2038.43 | 0.888119 | ||||||||
\(175\) | −211.647 | −0.0914229 | ||||||||
\(176\) | 190.004 | 0.0813754 | ||||||||
\(177\) | −4748.11 | −2.01633 | ||||||||
\(178\) | 1484.60 | 0.625144 | ||||||||
\(179\) | −1643.02 | −0.686063 | −0.343032 | − | 0.939324i | \(-0.611454\pi\) | ||||
−0.343032 | + | 0.939324i | \(0.611454\pi\) | |||||||
\(180\) | 457.955 | 0.189633 | ||||||||
\(181\) | 896.230 | 0.368046 | 0.184023 | − | 0.982922i | \(-0.441088\pi\) | ||||
0.184023 | + | 0.982922i | \(0.441088\pi\) | |||||||
\(182\) | −575.770 | −0.234499 | ||||||||
\(183\) | −3876.23 | −1.56579 | ||||||||
\(184\) | 2187.64 | 0.876492 | ||||||||
\(185\) | 332.048 | 0.131960 | ||||||||
\(186\) | −549.431 | −0.216593 | ||||||||
\(187\) | −1079.61 | −0.422187 | ||||||||
\(188\) | −1058.19 | −0.410514 | ||||||||
\(189\) | 218.402 | 0.0840552 | ||||||||
\(190\) | 191.890 | 0.0732692 | ||||||||
\(191\) | 2241.19 | 0.849041 | 0.424521 | − | 0.905418i | \(-0.360443\pi\) | ||||
0.424521 | + | 0.905418i | \(0.360443\pi\) | |||||||
\(192\) | 3241.67 | 1.21848 | ||||||||
\(193\) | 3670.91 | 1.36911 | 0.684553 | − | 0.728963i | \(-0.259997\pi\) | ||||
0.684553 | + | 0.728963i | \(0.259997\pi\) | |||||||
\(194\) | 2032.53 | 0.752203 | ||||||||
\(195\) | 1194.76 | 0.438763 | ||||||||
\(196\) | 1063.62 | 0.387616 | ||||||||
\(197\) | −3468.41 | −1.25439 | −0.627193 | − | 0.778864i | \(-0.715796\pi\) | ||||
−0.627193 | + | 0.778864i | \(0.715796\pi\) | |||||||
\(198\) | 519.140 | 0.186332 | ||||||||
\(199\) | 999.241 | 0.355951 | 0.177976 | − | 0.984035i | \(-0.443045\pi\) | ||||
0.177976 | + | 0.984035i | \(0.443045\pi\) | |||||||
\(200\) | 601.930 | 0.212814 | ||||||||
\(201\) | 4600.63 | 1.61444 | ||||||||
\(202\) | −2438.29 | −0.849293 | ||||||||
\(203\) | 1203.86 | 0.416227 | ||||||||
\(204\) | −2730.41 | −0.937093 | ||||||||
\(205\) | −2508.82 | −0.854750 | ||||||||
\(206\) | 1406.32 | 0.475646 | ||||||||
\(207\) | 2122.91 | 0.712815 | ||||||||
\(208\) | 581.592 | 0.193876 | ||||||||
\(209\) | −209.000 | −0.0691714 | ||||||||
\(210\) | −606.784 | −0.199391 | ||||||||
\(211\) | −5828.82 | −1.90176 | −0.950882 | − | 0.309553i | \(-0.899821\pi\) | ||||
−0.950882 | + | 0.309553i | \(0.899821\pi\) | |||||||
\(212\) | 990.853 | 0.321000 | ||||||||
\(213\) | 5486.18 | 1.76482 | ||||||||
\(214\) | −1234.58 | −0.394365 | ||||||||
\(215\) | 1245.58 | 0.395106 | ||||||||
\(216\) | −621.142 | −0.195664 | ||||||||
\(217\) | −324.484 | −0.101509 | ||||||||
\(218\) | −2241.17 | −0.696291 | ||||||||
\(219\) | −4864.73 | −1.50104 | ||||||||
\(220\) | −215.602 | −0.0660721 | ||||||||
\(221\) | −3304.63 | −1.00585 | ||||||||
\(222\) | 951.970 | 0.287802 | ||||||||
\(223\) | −4403.88 | −1.32245 | −0.661223 | − | 0.750190i | \(-0.729962\pi\) | ||||
−0.661223 | + | 0.750190i | \(0.729962\pi\) | |||||||
\(224\) | 1335.30 | 0.398298 | ||||||||
\(225\) | 584.121 | 0.173073 | ||||||||
\(226\) | 1617.98 | 0.476223 | ||||||||
\(227\) | −5588.56 | −1.63403 | −0.817017 | − | 0.576614i | \(-0.804374\pi\) | ||||
−0.817017 | + | 0.576614i | \(0.804374\pi\) | |||||||
\(228\) | −528.576 | −0.153534 | ||||||||
\(229\) | −5112.12 | −1.47519 | −0.737595 | − | 0.675243i | \(-0.764039\pi\) | ||||
−0.737595 | + | 0.675243i | \(0.764039\pi\) | |||||||
\(230\) | 917.630 | 0.263073 | ||||||||
\(231\) | 660.889 | 0.188239 | ||||||||
\(232\) | −3423.80 | −0.968895 | ||||||||
\(233\) | −3928.08 | −1.10445 | −0.552225 | − | 0.833695i | \(-0.686221\pi\) | ||||
−0.552225 | + | 0.833695i | \(0.686221\pi\) | |||||||
\(234\) | 1589.06 | 0.443932 | ||||||||
\(235\) | −1349.72 | −0.374665 | ||||||||
\(236\) | 2622.69 | 0.723401 | ||||||||
\(237\) | −8932.71 | −2.44828 | ||||||||
\(238\) | 1678.32 | 0.457098 | ||||||||
\(239\) | 4642.18 | 1.25639 | 0.628196 | − | 0.778055i | \(-0.283794\pi\) | ||||
0.628196 | + | 0.778055i | \(0.283794\pi\) | |||||||
\(240\) | 612.919 | 0.164849 | ||||||||
\(241\) | −3635.15 | −0.971620 | −0.485810 | − | 0.874064i | \(-0.661475\pi\) | ||||
−0.485810 | + | 0.874064i | \(0.661475\pi\) | |||||||
\(242\) | −244.407 | −0.0649218 | ||||||||
\(243\) | −5079.80 | −1.34103 | ||||||||
\(244\) | 2141.09 | 0.561760 | ||||||||
\(245\) | 1356.64 | 0.353767 | ||||||||
\(246\) | −7192.70 | −1.86419 | ||||||||
\(247\) | −639.738 | −0.164800 | ||||||||
\(248\) | 922.841 | 0.236292 | ||||||||
\(249\) | −9158.66 | −2.33095 | ||||||||
\(250\) | 252.487 | 0.0638746 | ||||||||
\(251\) | −1114.30 | −0.280214 | −0.140107 | − | 0.990136i | \(-0.544745\pi\) | ||||
−0.140107 | + | 0.990136i | \(0.544745\pi\) | |||||||
\(252\) | 775.398 | 0.193831 | ||||||||
\(253\) | −999.452 | −0.248360 | ||||||||
\(254\) | 3890.61 | 0.961096 | ||||||||
\(255\) | −3482.64 | −0.855259 | ||||||||
\(256\) | −4339.33 | −1.05941 | ||||||||
\(257\) | −1864.36 | −0.452512 | −0.226256 | − | 0.974068i | \(-0.572649\pi\) | ||||
−0.226256 | + | 0.974068i | \(0.572649\pi\) | |||||||
\(258\) | 3571.02 | 0.861714 | ||||||||
\(259\) | 562.216 | 0.134882 | ||||||||
\(260\) | −659.946 | −0.157416 | ||||||||
\(261\) | −3322.51 | −0.787962 | ||||||||
\(262\) | 4726.78 | 1.11459 | ||||||||
\(263\) | −2985.71 | −0.700025 | −0.350012 | − | 0.936745i | \(-0.613823\pi\) | ||||
−0.350012 | + | 0.936745i | \(0.613823\pi\) | |||||||
\(264\) | −1879.59 | −0.438184 | ||||||||
\(265\) | 1263.83 | 0.292968 | ||||||||
\(266\) | 324.903 | 0.0748913 | ||||||||
\(267\) | −5216.10 | −1.19558 | ||||||||
\(268\) | −2541.22 | −0.579216 | ||||||||
\(269\) | 2454.88 | 0.556419 | 0.278210 | − | 0.960520i | \(-0.410259\pi\) | ||||
0.278210 | + | 0.960520i | \(0.410259\pi\) | |||||||
\(270\) | −260.545 | −0.0587270 | ||||||||
\(271\) | 4937.48 | 1.10676 | 0.553378 | − | 0.832930i | \(-0.313339\pi\) | ||||
0.553378 | + | 0.832930i | \(0.313339\pi\) | |||||||
\(272\) | −1695.29 | −0.377912 | ||||||||
\(273\) | 2022.95 | 0.448477 | ||||||||
\(274\) | 709.629 | 0.156461 | ||||||||
\(275\) | −275.000 | −0.0603023 | ||||||||
\(276\) | −2527.68 | −0.551263 | ||||||||
\(277\) | 8417.50 | 1.82584 | 0.912921 | − | 0.408135i | \(-0.133821\pi\) | ||||
0.912921 | + | 0.408135i | \(0.133821\pi\) | |||||||
\(278\) | −1100.50 | −0.237424 | ||||||||
\(279\) | 895.538 | 0.192167 | ||||||||
\(280\) | 1019.17 | 0.217526 | ||||||||
\(281\) | −3428.72 | −0.727902 | −0.363951 | − | 0.931418i | \(-0.618572\pi\) | ||||
−0.363951 | + | 0.931418i | \(0.618572\pi\) | |||||||
\(282\) | −3869.61 | −0.817134 | ||||||||
\(283\) | 3319.00 | 0.697153 | 0.348576 | − | 0.937280i | \(-0.386665\pi\) | ||||
0.348576 | + | 0.937280i | \(0.386665\pi\) | |||||||
\(284\) | −3030.37 | −0.633167 | ||||||||
\(285\) | −674.198 | −0.140126 | ||||||||
\(286\) | −748.117 | −0.154675 | ||||||||
\(287\) | −4247.88 | −0.873673 | ||||||||
\(288\) | −3685.29 | −0.754019 | ||||||||
\(289\) | 4719.71 | 0.960658 | ||||||||
\(290\) | −1436.15 | −0.290806 | ||||||||
\(291\) | −7141.24 | −1.43858 | ||||||||
\(292\) | 2687.11 | 0.538531 | ||||||||
\(293\) | −3387.73 | −0.675473 | −0.337736 | − | 0.941241i | \(-0.609661\pi\) | ||||
−0.337736 | + | 0.941241i | \(0.609661\pi\) | |||||||
\(294\) | 3889.45 | 0.771556 | ||||||||
\(295\) | 3345.24 | 0.660228 | ||||||||
\(296\) | −1598.96 | −0.313978 | ||||||||
\(297\) | 283.777 | 0.0554425 | ||||||||
\(298\) | −5084.62 | −0.988404 | ||||||||
\(299\) | −3059.27 | −0.591713 | ||||||||
\(300\) | −695.494 | −0.133848 | ||||||||
\(301\) | 2108.98 | 0.403853 | ||||||||
\(302\) | −5445.02 | −1.03750 | ||||||||
\(303\) | 8566.83 | 1.62426 | ||||||||
\(304\) | −328.188 | −0.0619174 | ||||||||
\(305\) | 2730.96 | 0.512704 | ||||||||
\(306\) | −4631.97 | −0.865334 | ||||||||
\(307\) | −282.993 | −0.0526100 | −0.0263050 | − | 0.999654i | \(-0.508374\pi\) | ||||
−0.0263050 | + | 0.999654i | \(0.508374\pi\) | |||||||
\(308\) | −365.052 | −0.0675349 | ||||||||
\(309\) | −4941.06 | −0.909667 | ||||||||
\(310\) | 387.097 | 0.0709213 | ||||||||
\(311\) | −1137.96 | −0.207484 | −0.103742 | − | 0.994604i | \(-0.533082\pi\) | ||||
−0.103742 | + | 0.994604i | \(0.533082\pi\) | |||||||
\(312\) | −5753.31 | −1.04397 | ||||||||
\(313\) | 6864.16 | 1.23957 | 0.619784 | − | 0.784772i | \(-0.287220\pi\) | ||||
0.619784 | + | 0.784772i | \(0.287220\pi\) | |||||||
\(314\) | 4642.39 | 0.834347 | ||||||||
\(315\) | 989.020 | 0.176905 | ||||||||
\(316\) | 4934.11 | 0.878372 | ||||||||
\(317\) | −7369.52 | −1.30572 | −0.652861 | − | 0.757478i | \(-0.726431\pi\) | ||||
−0.652861 | + | 0.757478i | \(0.726431\pi\) | |||||||
\(318\) | 3623.36 | 0.638956 | ||||||||
\(319\) | 1564.21 | 0.274542 | ||||||||
\(320\) | −2283.89 | −0.398979 | ||||||||
\(321\) | 4337.66 | 0.754219 | ||||||||
\(322\) | 1553.71 | 0.268897 | ||||||||
\(323\) | 1864.78 | 0.321236 | ||||||||
\(324\) | 3190.65 | 0.547094 | ||||||||
\(325\) | −841.761 | −0.143669 | ||||||||
\(326\) | 7344.31 | 1.24774 | ||||||||
\(327\) | 7874.28 | 1.33165 | ||||||||
\(328\) | 12081.1 | 2.03374 | ||||||||
\(329\) | −2285.32 | −0.382960 | ||||||||
\(330\) | −788.415 | −0.131518 | ||||||||
\(331\) | −3486.74 | −0.578998 | −0.289499 | − | 0.957178i | \(-0.593489\pi\) | ||||
−0.289499 | + | 0.957178i | \(0.593489\pi\) | |||||||
\(332\) | 5058.92 | 0.836278 | ||||||||
\(333\) | −1551.65 | −0.255345 | ||||||||
\(334\) | −8148.18 | −1.33488 | ||||||||
\(335\) | −3241.33 | −0.528635 | ||||||||
\(336\) | 1037.78 | 0.168499 | ||||||||
\(337\) | 8742.45 | 1.41315 | 0.706575 | − | 0.707638i | \(-0.250239\pi\) | ||||
0.706575 | + | 0.707638i | \(0.250239\pi\) | |||||||
\(338\) | 2147.76 | 0.345629 | ||||||||
\(339\) | −5684.71 | −0.910771 | ||||||||
\(340\) | 1923.69 | 0.306843 | ||||||||
\(341\) | −421.613 | −0.0669549 | ||||||||
\(342\) | −896.696 | −0.141777 | ||||||||
\(343\) | 5200.83 | 0.818713 | ||||||||
\(344\) | −5998.00 | −0.940089 | ||||||||
\(345\) | −3224.06 | −0.503123 | ||||||||
\(346\) | 1991.28 | 0.309399 | ||||||||
\(347\) | −2887.00 | −0.446635 | −0.223318 | − | 0.974746i | \(-0.571689\pi\) | ||||
−0.223318 | + | 0.974746i | \(0.571689\pi\) | |||||||
\(348\) | 3956.00 | 0.609379 | ||||||||
\(349\) | −3735.62 | −0.572961 | −0.286480 | − | 0.958086i | \(-0.592485\pi\) | ||||
−0.286480 | + | 0.958086i | \(0.592485\pi\) | |||||||
\(350\) | 427.504 | 0.0652887 | ||||||||
\(351\) | 868.628 | 0.132091 | ||||||||
\(352\) | 1735.01 | 0.262716 | ||||||||
\(353\) | 1311.14 | 0.197690 | 0.0988452 | − | 0.995103i | \(-0.468485\pi\) | ||||
0.0988452 | + | 0.995103i | \(0.468485\pi\) | |||||||
\(354\) | 9590.68 | 1.43994 | ||||||||
\(355\) | −3865.24 | −0.577874 | ||||||||
\(356\) | 2881.19 | 0.428940 | ||||||||
\(357\) | −5896.71 | −0.874194 | ||||||||
\(358\) | 3318.73 | 0.489945 | ||||||||
\(359\) | 567.020 | 0.0833598 | 0.0416799 | − | 0.999131i | \(-0.486729\pi\) | ||||
0.0416799 | + | 0.999131i | \(0.486729\pi\) | |||||||
\(360\) | −2812.80 | −0.411799 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | −1810.29 | −0.262836 | ||||||||
\(363\) | 858.715 | 0.124162 | ||||||||
\(364\) | −1117.40 | −0.160901 | ||||||||
\(365\) | 3427.40 | 0.491502 | ||||||||
\(366\) | 7829.58 | 1.11819 | ||||||||
\(367\) | −8364.22 | −1.18967 | −0.594835 | − | 0.803848i | \(-0.702782\pi\) | ||||
−0.594835 | + | 0.803848i | \(0.702782\pi\) | |||||||
\(368\) | −1569.42 | −0.222314 | ||||||||
\(369\) | 11723.7 | 1.65395 | ||||||||
\(370\) | −670.702 | −0.0942381 | ||||||||
\(371\) | 2139.89 | 0.299454 | ||||||||
\(372\) | −1066.29 | −0.148614 | ||||||||
\(373\) | 11870.5 | 1.64780 | 0.823899 | − | 0.566736i | \(-0.191794\pi\) | ||||
0.823899 | + | 0.566736i | \(0.191794\pi\) | |||||||
\(374\) | 2180.70 | 0.301500 | ||||||||
\(375\) | −887.103 | −0.122159 | ||||||||
\(376\) | 6499.51 | 0.891454 | ||||||||
\(377\) | 4787.97 | 0.654093 | ||||||||
\(378\) | −441.149 | −0.0600271 | ||||||||
\(379\) | −9903.32 | −1.34222 | −0.671108 | − | 0.741360i | \(-0.734181\pi\) | ||||
−0.671108 | + | 0.741360i | \(0.734181\pi\) | |||||||
\(380\) | 372.403 | 0.0502734 | ||||||||
\(381\) | −13669.5 | −1.83808 | ||||||||
\(382\) | −4526.96 | −0.606334 | ||||||||
\(383\) | 8875.98 | 1.18418 | 0.592090 | − | 0.805872i | \(-0.298303\pi\) | ||||
0.592090 | + | 0.805872i | \(0.298303\pi\) | |||||||
\(384\) | 2407.10 | 0.319888 | ||||||||
\(385\) | −465.623 | −0.0616373 | ||||||||
\(386\) | −7414.84 | −0.977734 | ||||||||
\(387\) | −5820.55 | −0.764535 | ||||||||
\(388\) | 3944.57 | 0.516121 | ||||||||
\(389\) | 3628.59 | 0.472948 | 0.236474 | − | 0.971638i | \(-0.424008\pi\) | ||||
0.236474 | + | 0.971638i | \(0.424008\pi\) | |||||||
\(390\) | −2413.30 | −0.313339 | ||||||||
\(391\) | 8917.51 | 1.15340 | ||||||||
\(392\) | −6532.84 | −0.841730 | ||||||||
\(393\) | −16607.4 | −2.13163 | ||||||||
\(394\) | 7005.82 | 0.895807 | ||||||||
\(395\) | 6293.46 | 0.801666 | ||||||||
\(396\) | 1007.50 | 0.127851 | ||||||||
\(397\) | 8027.83 | 1.01487 | 0.507437 | − | 0.861689i | \(-0.330593\pi\) | ||||
0.507437 | + | 0.861689i | \(0.330593\pi\) | |||||||
\(398\) | −2018.36 | −0.254199 | ||||||||
\(399\) | −1141.54 | −0.143229 | ||||||||
\(400\) | −431.827 | −0.0539783 | ||||||||
\(401\) | 1041.43 | 0.129692 | 0.0648462 | − | 0.997895i | \(-0.479344\pi\) | ||||
0.0648462 | + | 0.997895i | \(0.479344\pi\) | |||||||
\(402\) | −9292.77 | −1.15294 | ||||||||
\(403\) | −1290.53 | −0.159519 | ||||||||
\(404\) | −4732.01 | −0.582739 | ||||||||
\(405\) | 4069.67 | 0.499318 | ||||||||
\(406\) | −2431.66 | −0.297245 | ||||||||
\(407\) | 730.506 | 0.0889676 | ||||||||
\(408\) | 16770.4 | 2.03495 | ||||||||
\(409\) | −14008.7 | −1.69361 | −0.846805 | − | 0.531903i | \(-0.821477\pi\) | ||||
−0.846805 | + | 0.531903i | \(0.821477\pi\) | |||||||
\(410\) | 5067.55 | 0.610411 | ||||||||
\(411\) | −2493.26 | −0.299229 | ||||||||
\(412\) | 2729.27 | 0.326363 | ||||||||
\(413\) | 5664.08 | 0.674845 | ||||||||
\(414\) | −4288.06 | −0.509050 | ||||||||
\(415\) | 6452.65 | 0.763249 | ||||||||
\(416\) | 5310.76 | 0.625917 | ||||||||
\(417\) | 3866.58 | 0.454070 | ||||||||
\(418\) | 422.158 | 0.0493981 | ||||||||
\(419\) | −10197.5 | −1.18897 | −0.594487 | − | 0.804105i | \(-0.702645\pi\) | ||||
−0.594487 | + | 0.804105i | \(0.702645\pi\) | |||||||
\(420\) | −1177.59 | −0.136811 | ||||||||
\(421\) | −2664.97 | −0.308510 | −0.154255 | − | 0.988031i | \(-0.549298\pi\) | ||||
−0.154255 | + | 0.988031i | \(0.549298\pi\) | |||||||
\(422\) | 11773.6 | 1.35813 | ||||||||
\(423\) | 6307.22 | 0.724983 | ||||||||
\(424\) | −6085.90 | −0.697070 | ||||||||
\(425\) | 2453.66 | 0.280047 | ||||||||
\(426\) | −11081.5 | −1.26033 | ||||||||
\(427\) | 4624.00 | 0.524054 | ||||||||
\(428\) | −2395.97 | −0.270592 | ||||||||
\(429\) | 2628.48 | 0.295814 | ||||||||
\(430\) | −2515.93 | −0.282161 | ||||||||
\(431\) | 5565.87 | 0.622038 | 0.311019 | − | 0.950404i | \(-0.399330\pi\) | ||||
0.311019 | + | 0.950404i | \(0.399330\pi\) | |||||||
\(432\) | 445.610 | 0.0496283 | ||||||||
\(433\) | 10951.1 | 1.21542 | 0.607710 | − | 0.794159i | \(-0.292088\pi\) | ||||
0.607710 | + | 0.794159i | \(0.292088\pi\) | |||||||
\(434\) | 655.422 | 0.0724914 | ||||||||
\(435\) | 5045.88 | 0.556164 | ||||||||
\(436\) | −4349.48 | −0.477757 | ||||||||
\(437\) | 1726.33 | 0.188973 | ||||||||
\(438\) | 9826.23 | 1.07195 | ||||||||
\(439\) | −3597.17 | −0.391079 | −0.195540 | − | 0.980696i | \(-0.562646\pi\) | ||||
−0.195540 | + | 0.980696i | \(0.562646\pi\) | |||||||
\(440\) | 1324.25 | 0.143479 | ||||||||
\(441\) | −6339.56 | −0.684544 | ||||||||
\(442\) | 6675.00 | 0.718320 | ||||||||
\(443\) | 7027.57 | 0.753702 | 0.376851 | − | 0.926274i | \(-0.377007\pi\) | ||||
0.376851 | + | 0.926274i | \(0.377007\pi\) | |||||||
\(444\) | 1847.50 | 0.197474 | ||||||||
\(445\) | 3674.96 | 0.391482 | ||||||||
\(446\) | 8895.36 | 0.944411 | ||||||||
\(447\) | 17864.6 | 1.89031 | ||||||||
\(448\) | −3867.02 | −0.407812 | ||||||||
\(449\) | −12874.1 | −1.35316 | −0.676578 | − | 0.736371i | \(-0.736538\pi\) | ||||
−0.676578 | + | 0.736371i | \(0.736538\pi\) | |||||||
\(450\) | −1179.86 | −0.123598 | ||||||||
\(451\) | −5519.41 | −0.576272 | ||||||||
\(452\) | 3140.03 | 0.326758 | ||||||||
\(453\) | 19130.9 | 1.98421 | ||||||||
\(454\) | 11288.3 | 1.16693 | ||||||||
\(455\) | −1425.25 | −0.146850 | ||||||||
\(456\) | 3246.56 | 0.333408 | ||||||||
\(457\) | 12730.1 | 1.30304 | 0.651522 | − | 0.758630i | \(-0.274131\pi\) | ||||
0.651522 | + | 0.758630i | \(0.274131\pi\) | |||||||
\(458\) | 10325.9 | 1.05349 | ||||||||
\(459\) | −2531.97 | −0.257478 | ||||||||
\(460\) | 1780.86 | 0.180506 | ||||||||
\(461\) | −5008.81 | −0.506038 | −0.253019 | − | 0.967461i | \(-0.581424\pi\) | ||||
−0.253019 | + | 0.967461i | \(0.581424\pi\) | |||||||
\(462\) | −1334.92 | −0.134429 | ||||||||
\(463\) | −8923.88 | −0.895741 | −0.447870 | − | 0.894098i | \(-0.647817\pi\) | ||||
−0.447870 | + | 0.894098i | \(0.647817\pi\) | |||||||
\(464\) | 2456.25 | 0.245751 | ||||||||
\(465\) | −1360.05 | −0.135636 | ||||||||
\(466\) | 7934.29 | 0.788732 | ||||||||
\(467\) | 10392.4 | 1.02977 | 0.514886 | − | 0.857259i | \(-0.327834\pi\) | ||||
0.514886 | + | 0.857259i | \(0.327834\pi\) | |||||||
\(468\) | 3083.91 | 0.304602 | ||||||||
\(469\) | −5488.14 | −0.540339 | ||||||||
\(470\) | 2726.30 | 0.267563 | ||||||||
\(471\) | −16310.9 | −1.59568 | ||||||||
\(472\) | −16108.8 | −1.57091 | ||||||||
\(473\) | 2740.27 | 0.266380 | ||||||||
\(474\) | 18043.1 | 1.74841 | ||||||||
\(475\) | 475.000 | 0.0458831 | ||||||||
\(476\) | 3257.14 | 0.313636 | ||||||||
\(477\) | −5905.85 | −0.566898 | ||||||||
\(478\) | −9376.71 | −0.897240 | ||||||||
\(479\) | 8337.70 | 0.795322 | 0.397661 | − | 0.917532i | \(-0.369822\pi\) | ||||
0.397661 | + | 0.917532i | \(0.369822\pi\) | |||||||
\(480\) | 5596.83 | 0.532206 | ||||||||
\(481\) | 2236.04 | 0.211964 | ||||||||
\(482\) | 7342.61 | 0.693873 | ||||||||
\(483\) | −5458.90 | −0.514262 | ||||||||
\(484\) | −474.324 | −0.0445458 | ||||||||
\(485\) | 5031.29 | 0.471050 | ||||||||
\(486\) | 10260.7 | 0.957681 | ||||||||
\(487\) | 2788.06 | 0.259423 | 0.129712 | − | 0.991552i | \(-0.458595\pi\) | ||||
0.129712 | + | 0.991552i | \(0.458595\pi\) | |||||||
\(488\) | −13150.8 | −1.21989 | ||||||||
\(489\) | −25804.0 | −2.38629 | ||||||||
\(490\) | −2740.28 | −0.252639 | ||||||||
\(491\) | −9107.39 | −0.837089 | −0.418545 | − | 0.908196i | \(-0.637460\pi\) | ||||
−0.418545 | + | 0.908196i | \(0.637460\pi\) | |||||||
\(492\) | −13959.0 | −1.27910 | ||||||||
\(493\) | −13956.5 | −1.27499 | ||||||||
\(494\) | 1292.20 | 0.117690 | ||||||||
\(495\) | 1285.07 | 0.116686 | ||||||||
\(496\) | −662.050 | −0.0599333 | ||||||||
\(497\) | −6544.52 | −0.590668 | ||||||||
\(498\) | 18499.5 | 1.66462 | ||||||||
\(499\) | 4366.94 | 0.391765 | 0.195883 | − | 0.980627i | \(-0.437243\pi\) | ||||
0.195883 | + | 0.980627i | \(0.437243\pi\) | |||||||
\(500\) | 490.004 | 0.0438273 | ||||||||
\(501\) | 28628.4 | 2.55294 | ||||||||
\(502\) | 2250.76 | 0.200112 | ||||||||
\(503\) | 11008.0 | 0.975793 | 0.487896 | − | 0.872902i | \(-0.337764\pi\) | ||||
0.487896 | + | 0.872902i | \(0.337764\pi\) | |||||||
\(504\) | −4762.57 | −0.420916 | ||||||||
\(505\) | −6035.68 | −0.531850 | ||||||||
\(506\) | 2018.79 | 0.177364 | ||||||||
\(507\) | −7546.07 | −0.661011 | ||||||||
\(508\) | 7550.55 | 0.659452 | ||||||||
\(509\) | −8378.75 | −0.729629 | −0.364815 | − | 0.931080i | \(-0.618868\pi\) | ||||
−0.364815 | + | 0.931080i | \(0.618868\pi\) | |||||||
\(510\) | 7034.55 | 0.610775 | ||||||||
\(511\) | 5803.19 | 0.502384 | ||||||||
\(512\) | 6051.54 | 0.522349 | ||||||||
\(513\) | −490.161 | −0.0421854 | ||||||||
\(514\) | 3765.81 | 0.323157 | ||||||||
\(515\) | 3481.18 | 0.297862 | ||||||||
\(516\) | 6930.34 | 0.591262 | ||||||||
\(517\) | −2969.39 | −0.252599 | ||||||||
\(518\) | −1135.62 | −0.0963245 | ||||||||
\(519\) | −6996.30 | −0.591722 | ||||||||
\(520\) | 4053.45 | 0.341837 | ||||||||
\(521\) | 14913.0 | 1.25403 | 0.627016 | − | 0.779006i | \(-0.284276\pi\) | ||||
0.627016 | + | 0.779006i | \(0.284276\pi\) | |||||||
\(522\) | 6711.11 | 0.562715 | ||||||||
\(523\) | 12149.1 | 1.01576 | 0.507882 | − | 0.861426i | \(-0.330428\pi\) | ||||
0.507882 | + | 0.861426i | \(0.330428\pi\) | |||||||
\(524\) | 9173.33 | 0.764769 | ||||||||
\(525\) | −1502.02 | −0.124864 | ||||||||
\(526\) | 6030.81 | 0.499916 | ||||||||
\(527\) | 3761.80 | 0.310942 | ||||||||
\(528\) | 1348.42 | 0.111141 | ||||||||
\(529\) | −3911.60 | −0.321492 | ||||||||
\(530\) | −2552.80 | −0.209220 | ||||||||
\(531\) | −15632.2 | −1.27755 | ||||||||
\(532\) | 630.544 | 0.0513864 | ||||||||
\(533\) | −16894.6 | −1.37296 | ||||||||
\(534\) | 10536.0 | 0.853812 | ||||||||
\(535\) | −3056.06 | −0.246962 | ||||||||
\(536\) | 15608.4 | 1.25780 | ||||||||
\(537\) | −11660.2 | −0.937014 | ||||||||
\(538\) | −4958.60 | −0.397361 | ||||||||
\(539\) | 2984.62 | 0.238509 | ||||||||
\(540\) | −505.644 | −0.0402953 | ||||||||
\(541\) | −2442.51 | −0.194107 | −0.0970535 | − | 0.995279i | \(-0.530942\pi\) | ||||
−0.0970535 | + | 0.995279i | \(0.530942\pi\) | |||||||
\(542\) | −9973.19 | −0.790378 | ||||||||
\(543\) | 6360.38 | 0.502671 | ||||||||
\(544\) | −15480.4 | −1.22007 | ||||||||
\(545\) | −5547.75 | −0.436036 | ||||||||
\(546\) | −4086.13 | −0.320275 | ||||||||
\(547\) | 20864.1 | 1.63087 | 0.815433 | − | 0.578851i | \(-0.196499\pi\) | ||||
0.815433 | + | 0.578851i | \(0.196499\pi\) | |||||||
\(548\) | 1377.19 | 0.107355 | ||||||||
\(549\) | −12761.7 | −0.992089 | ||||||||
\(550\) | 555.471 | 0.0430643 | ||||||||
\(551\) | −2701.82 | −0.208895 | ||||||||
\(552\) | 15525.3 | 1.19710 | ||||||||
\(553\) | 10655.9 | 0.819415 | ||||||||
\(554\) | −17002.4 | −1.30391 | ||||||||
\(555\) | 2356.49 | 0.180229 | ||||||||
\(556\) | −2135.76 | −0.162907 | ||||||||
\(557\) | 172.091 | 0.0130911 | 0.00654553 | − | 0.999979i | \(-0.497916\pi\) | ||||
0.00654553 | + | 0.999979i | \(0.497916\pi\) | |||||||
\(558\) | −1808.89 | −0.137234 | ||||||||
\(559\) | 8387.82 | 0.634646 | ||||||||
\(560\) | −731.159 | −0.0551734 | ||||||||
\(561\) | −7661.80 | −0.576616 | ||||||||
\(562\) | 6925.65 | 0.519824 | ||||||||
\(563\) | 18482.5 | 1.38356 | 0.691779 | − | 0.722109i | \(-0.256827\pi\) | ||||
0.691779 | + | 0.722109i | \(0.256827\pi\) | |||||||
\(564\) | −7509.80 | −0.560673 | ||||||||
\(565\) | 4005.11 | 0.298224 | ||||||||
\(566\) | −6704.03 | −0.497865 | ||||||||
\(567\) | 6890.67 | 0.510372 | ||||||||
\(568\) | 18612.8 | 1.37496 | ||||||||
\(569\) | 14030.7 | 1.03374 | 0.516868 | − | 0.856065i | \(-0.327098\pi\) | ||||
0.516868 | + | 0.856065i | \(0.327098\pi\) | |||||||
\(570\) | 1361.81 | 0.100070 | ||||||||
\(571\) | 185.650 | 0.0136063 | 0.00680317 | − | 0.999977i | \(-0.497834\pi\) | ||||
0.00680317 | + | 0.999977i | \(0.497834\pi\) | |||||||
\(572\) | −1451.88 | −0.106130 | ||||||||
\(573\) | 15905.3 | 1.15961 | ||||||||
\(574\) | 8580.25 | 0.623925 | ||||||||
\(575\) | 2271.48 | 0.164743 | ||||||||
\(576\) | 10672.5 | 0.772030 | ||||||||
\(577\) | −16102.5 | −1.16180 | −0.580898 | − | 0.813976i | \(-0.697299\pi\) | ||||
−0.580898 | + | 0.813976i | \(0.697299\pi\) | |||||||
\(578\) | −9533.31 | −0.686044 | ||||||||
\(579\) | 26051.8 | 1.86990 | ||||||||
\(580\) | −2787.16 | −0.199536 | ||||||||
\(581\) | 10925.5 | 0.780146 | ||||||||
\(582\) | 14424.5 | 1.02735 | ||||||||
\(583\) | 2780.43 | 0.197519 | ||||||||
\(584\) | −16504.4 | −1.16945 | ||||||||
\(585\) | 3933.52 | 0.278002 | ||||||||
\(586\) | 6842.86 | 0.482382 | ||||||||
\(587\) | −10494.4 | −0.737902 | −0.368951 | − | 0.929449i | \(-0.620283\pi\) | ||||
−0.368951 | + | 0.929449i | \(0.620283\pi\) | |||||||
\(588\) | 7548.31 | 0.529400 | ||||||||
\(589\) | 728.240 | 0.0509450 | ||||||||
\(590\) | −6757.02 | −0.471495 | ||||||||
\(591\) | −24614.7 | −1.71322 | ||||||||
\(592\) | 1147.10 | 0.0796376 | ||||||||
\(593\) | −22833.3 | −1.58120 | −0.790600 | − | 0.612333i | \(-0.790231\pi\) | ||||
−0.790600 | + | 0.612333i | \(0.790231\pi\) | |||||||
\(594\) | −573.200 | −0.0395937 | ||||||||
\(595\) | 4154.48 | 0.286247 | ||||||||
\(596\) | −9867.80 | −0.678189 | ||||||||
\(597\) | 7091.44 | 0.486153 | ||||||||
\(598\) | 6179.40 | 0.422566 | ||||||||
\(599\) | 23137.1 | 1.57822 | 0.789112 | − | 0.614250i | \(-0.210541\pi\) | ||||
0.789112 | + | 0.614250i | \(0.210541\pi\) | |||||||
\(600\) | 4271.79 | 0.290658 | ||||||||
\(601\) | 24923.2 | 1.69158 | 0.845790 | − | 0.533516i | \(-0.179130\pi\) | ||||
0.845790 | + | 0.533516i | \(0.179130\pi\) | |||||||
\(602\) | −4259.92 | −0.288407 | ||||||||
\(603\) | 15146.6 | 1.02292 | ||||||||
\(604\) | −10567.2 | −0.711878 | ||||||||
\(605\) | −605.000 | −0.0406558 | ||||||||
\(606\) | −17304.1 | −1.15995 | ||||||||
\(607\) | 25216.6 | 1.68618 | 0.843088 | − | 0.537776i | \(-0.180735\pi\) | ||||
0.843088 | + | 0.537776i | \(0.180735\pi\) | |||||||
\(608\) | −2996.83 | −0.199897 | ||||||||
\(609\) | 8543.55 | 0.568477 | ||||||||
\(610\) | −5516.26 | −0.366142 | ||||||||
\(611\) | −9089.15 | −0.601813 | ||||||||
\(612\) | −8989.33 | −0.593745 | ||||||||
\(613\) | −12880.9 | −0.848701 | −0.424351 | − | 0.905498i | \(-0.639498\pi\) | ||||
−0.424351 | + | 0.905498i | \(0.639498\pi\) | |||||||
\(614\) | 571.616 | 0.0375709 | ||||||||
\(615\) | −17804.7 | −1.16740 | ||||||||
\(616\) | 2242.18 | 0.146656 | ||||||||
\(617\) | −3004.83 | −0.196062 | −0.0980308 | − | 0.995183i | \(-0.531254\pi\) | ||||
−0.0980308 | + | 0.995183i | \(0.531254\pi\) | |||||||
\(618\) | 9980.42 | 0.649630 | ||||||||
\(619\) | 18673.8 | 1.21254 | 0.606271 | − | 0.795258i | \(-0.292665\pi\) | ||||
0.606271 | + | 0.795258i | \(0.292665\pi\) | |||||||
\(620\) | 751.244 | 0.0486624 | ||||||||
\(621\) | −2343.98 | −0.151467 | ||||||||
\(622\) | 2298.55 | 0.148173 | ||||||||
\(623\) | 6222.34 | 0.400149 | ||||||||
\(624\) | 4127.45 | 0.264792 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −13864.9 | −0.885226 | ||||||||
\(627\) | −1483.24 | −0.0944732 | ||||||||
\(628\) | 9009.55 | 0.572484 | ||||||||
\(629\) | −6517.86 | −0.413170 | ||||||||
\(630\) | −1997.71 | −0.126335 | ||||||||
\(631\) | 7662.68 | 0.483433 | 0.241717 | − | 0.970347i | \(-0.422290\pi\) | ||||
0.241717 | + | 0.970347i | \(0.422290\pi\) | |||||||
\(632\) | −30305.8 | −1.90743 | ||||||||
\(633\) | −41366.1 | −2.59740 | ||||||||
\(634\) | 14885.6 | 0.932468 | ||||||||
\(635\) | 9630.72 | 0.601864 | ||||||||
\(636\) | 7031.90 | 0.438417 | ||||||||
\(637\) | 9135.76 | 0.568245 | ||||||||
\(638\) | −3159.54 | −0.196062 | ||||||||
\(639\) | 18062.1 | 1.11820 | ||||||||
\(640\) | −1695.90 | −0.104744 | ||||||||
\(641\) | −23554.0 | −1.45137 | −0.725685 | − | 0.688027i | \(-0.758477\pi\) | ||||
−0.725685 | + | 0.688027i | \(0.758477\pi\) | |||||||
\(642\) | −8761.60 | −0.538618 | ||||||||
\(643\) | 31637.7 | 1.94039 | 0.970194 | − | 0.242331i | \(-0.0779120\pi\) | ||||
0.970194 | + | 0.242331i | \(0.0779120\pi\) | |||||||
\(644\) | 3015.30 | 0.184502 | ||||||||
\(645\) | 8839.64 | 0.539629 | ||||||||
\(646\) | −3766.66 | −0.229407 | ||||||||
\(647\) | 4828.07 | 0.293371 | 0.146686 | − | 0.989183i | \(-0.453139\pi\) | ||||
0.146686 | + | 0.989183i | \(0.453139\pi\) | |||||||
\(648\) | −19597.3 | −1.18804 | ||||||||
\(649\) | 7359.53 | 0.445126 | ||||||||
\(650\) | 1700.27 | 0.102600 | ||||||||
\(651\) | −2302.80 | −0.138639 | ||||||||
\(652\) | 14253.2 | 0.856133 | ||||||||
\(653\) | 22266.6 | 1.33439 | 0.667197 | − | 0.744881i | \(-0.267494\pi\) | ||||
0.667197 | + | 0.744881i | \(0.267494\pi\) | |||||||
\(654\) | −15905.2 | −0.950983 | ||||||||
\(655\) | 11700.6 | 0.697984 | ||||||||
\(656\) | −8667.01 | −0.515838 | ||||||||
\(657\) | −16016.1 | −0.951065 | ||||||||
\(658\) | 4616.10 | 0.273487 | ||||||||
\(659\) | 23347.4 | 1.38010 | 0.690050 | − | 0.723761i | \(-0.257588\pi\) | ||||
0.690050 | + | 0.723761i | \(0.257588\pi\) | |||||||
\(660\) | −1530.09 | −0.0902403 | ||||||||
\(661\) | −690.780 | −0.0406478 | −0.0203239 | − | 0.999793i | \(-0.506470\pi\) | ||||
−0.0203239 | + | 0.999793i | \(0.506470\pi\) | |||||||
\(662\) | 7042.83 | 0.413485 | ||||||||
\(663\) | −23452.4 | −1.37378 | ||||||||
\(664\) | −31072.3 | −1.81603 | ||||||||
\(665\) | 804.258 | 0.0468990 | ||||||||
\(666\) | 3134.17 | 0.182352 | ||||||||
\(667\) | −12920.3 | −0.750038 | ||||||||
\(668\) | −15813.3 | −0.915920 | ||||||||
\(669\) | −31253.5 | −1.80617 | ||||||||
\(670\) | 6547.14 | 0.377519 | ||||||||
\(671\) | 6008.12 | 0.345665 | ||||||||
\(672\) | 9476.41 | 0.543989 | ||||||||
\(673\) | 20393.0 | 1.16804 | 0.584021 | − | 0.811739i | \(-0.301479\pi\) | ||||
0.584021 | + | 0.811739i | \(0.301479\pi\) | |||||||
\(674\) | −17658.8 | −1.00919 | ||||||||
\(675\) | −644.949 | −0.0367764 | ||||||||
\(676\) | 4168.18 | 0.237152 | ||||||||
\(677\) | −17385.9 | −0.986995 | −0.493497 | − | 0.869747i | \(-0.664282\pi\) | ||||
−0.493497 | + | 0.869747i | \(0.664282\pi\) | |||||||
\(678\) | 11482.5 | 0.650418 | ||||||||
\(679\) | 8518.86 | 0.481478 | ||||||||
\(680\) | −11815.4 | −0.666326 | ||||||||
\(681\) | −39661.0 | −2.23174 | ||||||||
\(682\) | 851.612 | 0.0478151 | ||||||||
\(683\) | −24654.3 | −1.38122 | −0.690609 | − | 0.723228i | \(-0.742657\pi\) | ||||
−0.690609 | + | 0.723228i | \(0.742657\pi\) | |||||||
\(684\) | −1740.23 | −0.0972797 | ||||||||
\(685\) | 1756.60 | 0.0979799 | ||||||||
\(686\) | −10505.1 | −0.584676 | ||||||||
\(687\) | −36279.8 | −2.01479 | ||||||||
\(688\) | 4302.99 | 0.238445 | ||||||||
\(689\) | 8510.75 | 0.470586 | ||||||||
\(690\) | 6512.25 | 0.359300 | ||||||||
\(691\) | −24883.5 | −1.36992 | −0.684959 | − | 0.728581i | \(-0.740180\pi\) | ||||
−0.684959 | + | 0.728581i | \(0.740180\pi\) | |||||||
\(692\) | 3864.51 | 0.212293 | ||||||||
\(693\) | 2175.84 | 0.119269 | ||||||||
\(694\) | 5831.44 | 0.318960 | ||||||||
\(695\) | −2724.17 | −0.148681 | ||||||||
\(696\) | −24298.1 | −1.32330 | ||||||||
\(697\) | 49246.3 | 2.67624 | ||||||||
\(698\) | 7545.56 | 0.409174 | ||||||||
\(699\) | −27876.9 | −1.50844 | ||||||||
\(700\) | 829.663 | 0.0447976 | ||||||||
\(701\) | 26129.9 | 1.40786 | 0.703932 | − | 0.710267i | \(-0.251426\pi\) | ||||
0.703932 | + | 0.710267i | \(0.251426\pi\) | |||||||
\(702\) | −1754.53 | −0.0943314 | ||||||||
\(703\) | −1261.78 | −0.0676942 | ||||||||
\(704\) | −5024.55 | −0.268992 | ||||||||
\(705\) | −9578.75 | −0.511711 | ||||||||
\(706\) | −2648.35 | −0.141179 | ||||||||
\(707\) | −10219.5 | −0.543625 | ||||||||
\(708\) | 18612.8 | 0.988009 | ||||||||
\(709\) | −32752.9 | −1.73492 | −0.867462 | − | 0.497503i | \(-0.834250\pi\) | ||||
−0.867462 | + | 0.497503i | \(0.834250\pi\) | |||||||
\(710\) | 7807.36 | 0.412683 | ||||||||
\(711\) | −29409.2 | −1.55124 | ||||||||
\(712\) | −17696.5 | −0.931468 | ||||||||
\(713\) | 3482.49 | 0.182918 | ||||||||
\(714\) | 11910.7 | 0.624297 | ||||||||
\(715\) | −1851.87 | −0.0968617 | ||||||||
\(716\) | 6440.70 | 0.336174 | ||||||||
\(717\) | 32944.7 | 1.71596 | ||||||||
\(718\) | −1145.32 | −0.0595306 | ||||||||
\(719\) | 1736.28 | 0.0900587 | 0.0450294 | − | 0.998986i | \(-0.485662\pi\) | ||||
0.0450294 | + | 0.998986i | \(0.485662\pi\) | |||||||
\(720\) | 2017.91 | 0.104449 | ||||||||
\(721\) | 5894.25 | 0.304457 | ||||||||
\(722\) | −729.181 | −0.0375863 | ||||||||
\(723\) | −25798.0 | −1.32702 | ||||||||
\(724\) | −3513.25 | −0.180344 | ||||||||
\(725\) | −3555.03 | −0.182111 | ||||||||
\(726\) | −1734.51 | −0.0886692 | ||||||||
\(727\) | 10714.3 | 0.546589 | 0.273294 | − | 0.961930i | \(-0.411887\pi\) | ||||
0.273294 | + | 0.961930i | \(0.411887\pi\) | |||||||
\(728\) | 6863.19 | 0.349405 | ||||||||
\(729\) | −14074.2 | −0.715044 | ||||||||
\(730\) | −6922.98 | −0.351001 | ||||||||
\(731\) | −24449.8 | −1.23708 | ||||||||
\(732\) | 15195.0 | 0.767243 | ||||||||
\(733\) | −17240.1 | −0.868729 | −0.434365 | − | 0.900737i | \(-0.643027\pi\) | ||||
−0.434365 | + | 0.900737i | \(0.643027\pi\) | |||||||
\(734\) | 16894.8 | 0.849590 | ||||||||
\(735\) | 9627.86 | 0.483169 | ||||||||
\(736\) | −14331.0 | −0.717729 | ||||||||
\(737\) | −7130.93 | −0.356406 | ||||||||
\(738\) | −23680.5 | −1.18115 | ||||||||
\(739\) | 25523.9 | 1.27052 | 0.635260 | − | 0.772299i | \(-0.280893\pi\) | ||||
0.635260 | + | 0.772299i | \(0.280893\pi\) | |||||||
\(740\) | −1301.64 | −0.0646611 | ||||||||
\(741\) | −4540.11 | −0.225081 | ||||||||
\(742\) | −4322.35 | −0.213852 | ||||||||
\(743\) | −5396.65 | −0.266466 | −0.133233 | − | 0.991085i | \(-0.542536\pi\) | ||||
−0.133233 | + | 0.991085i | \(0.542536\pi\) | |||||||
\(744\) | 6549.23 | 0.322724 | ||||||||
\(745\) | −12586.4 | −0.618965 | ||||||||
\(746\) | −23977.0 | −1.17676 | ||||||||
\(747\) | −30153.1 | −1.47690 | ||||||||
\(748\) | 4232.11 | 0.206873 | ||||||||
\(749\) | −5174.44 | −0.252430 | ||||||||
\(750\) | 1791.85 | 0.0872389 | ||||||||
\(751\) | 16662.9 | 0.809635 | 0.404818 | − | 0.914397i | \(-0.367335\pi\) | ||||
0.404818 | + | 0.914397i | \(0.367335\pi\) | |||||||
\(752\) | −4662.78 | −0.226109 | ||||||||
\(753\) | −7907.96 | −0.382712 | ||||||||
\(754\) | −9671.18 | −0.467114 | ||||||||
\(755\) | −13478.5 | −0.649712 | ||||||||
\(756\) | −856.144 | −0.0411874 | ||||||||
\(757\) | −35292.9 | −1.69451 | −0.847253 | − | 0.531189i | \(-0.821745\pi\) | ||||
−0.847253 | + | 0.531189i | \(0.821745\pi\) | |||||||
\(758\) | 20003.7 | 0.958530 | ||||||||
\(759\) | −7092.93 | −0.339206 | ||||||||
\(760\) | −2287.33 | −0.109171 | ||||||||
\(761\) | −23776.0 | −1.13256 | −0.566281 | − | 0.824212i | \(-0.691618\pi\) | ||||
−0.566281 | + | 0.824212i | \(0.691618\pi\) | |||||||
\(762\) | 27610.9 | 1.31265 | ||||||||
\(763\) | −9393.32 | −0.445689 | ||||||||
\(764\) | −8785.54 | −0.416034 | ||||||||
\(765\) | −11465.9 | −0.541895 | ||||||||
\(766\) | −17928.5 | −0.845671 | ||||||||
\(767\) | 22527.1 | 1.06050 | ||||||||
\(768\) | −30795.4 | −1.44692 | ||||||||
\(769\) | 6885.24 | 0.322872 | 0.161436 | − | 0.986883i | \(-0.448388\pi\) | ||||
0.161436 | + | 0.986883i | \(0.448388\pi\) | |||||||
\(770\) | 940.509 | 0.0440177 | ||||||||
\(771\) | −13231.0 | −0.618034 | ||||||||
\(772\) | −14390.1 | −0.670868 | ||||||||
\(773\) | 6932.66 | 0.322575 | 0.161288 | − | 0.986907i | \(-0.448435\pi\) | ||||
0.161288 | + | 0.986907i | \(0.448435\pi\) | |||||||
\(774\) | 11756.9 | 0.545985 | ||||||||
\(775\) | 958.211 | 0.0444128 | ||||||||
\(776\) | −24227.9 | −1.12079 | ||||||||
\(777\) | 3989.94 | 0.184219 | ||||||||
\(778\) | −7329.36 | −0.337751 | ||||||||
\(779\) | 9533.52 | 0.438477 | ||||||||
\(780\) | −4683.52 | −0.214996 | ||||||||
\(781\) | −8503.52 | −0.389603 | ||||||||
\(782\) | −18012.4 | −0.823686 | ||||||||
\(783\) | 3668.49 | 0.167435 | ||||||||
\(784\) | 4686.68 | 0.213497 | ||||||||
\(785\) | 11491.7 | 0.522491 | ||||||||
\(786\) | 33545.1 | 1.52228 | ||||||||
\(787\) | 35502.7 | 1.60805 | 0.804023 | − | 0.594598i | \(-0.202689\pi\) | ||||
0.804023 | + | 0.594598i | \(0.202689\pi\) | |||||||
\(788\) | 13596.3 | 0.614655 | ||||||||
\(789\) | −21189.0 | −0.956083 | ||||||||
\(790\) | −12712.1 | −0.572502 | ||||||||
\(791\) | 6781.36 | 0.304826 | ||||||||
\(792\) | −6188.16 | −0.277635 | ||||||||
\(793\) | 18390.5 | 0.823540 | ||||||||
\(794\) | −16215.4 | −0.724763 | ||||||||
\(795\) | 8969.19 | 0.400131 | ||||||||
\(796\) | −3917.06 | −0.174418 | ||||||||
\(797\) | −25023.3 | −1.11213 | −0.556067 | − | 0.831137i | \(-0.687690\pi\) | ||||
−0.556067 | + | 0.831137i | \(0.687690\pi\) | |||||||
\(798\) | 2305.78 | 0.102285 | ||||||||
\(799\) | 26494.1 | 1.17308 | ||||||||
\(800\) | −3943.19 | −0.174266 | ||||||||
\(801\) | −17173.0 | −0.757524 | ||||||||
\(802\) | −2103.58 | −0.0926185 | ||||||||
\(803\) | 7540.28 | 0.331371 | ||||||||
\(804\) | −18034.6 | −0.791084 | ||||||||
\(805\) | 3846.02 | 0.168390 | ||||||||
\(806\) | 2606.74 | 0.113919 | ||||||||
\(807\) | 17421.8 | 0.759948 | ||||||||
\(808\) | 29064.4 | 1.26545 | ||||||||
\(809\) | 5913.07 | 0.256975 | 0.128487 | − | 0.991711i | \(-0.458988\pi\) | ||||
0.128487 | + | 0.991711i | \(0.458988\pi\) | |||||||
\(810\) | −8220.30 | −0.356583 | ||||||||
\(811\) | −17566.5 | −0.760594 | −0.380297 | − | 0.924864i | \(-0.624178\pi\) | ||||
−0.380297 | + | 0.924864i | \(0.624178\pi\) | |||||||
\(812\) | −4719.16 | −0.203953 | ||||||||
\(813\) | 35040.4 | 1.51159 | ||||||||
\(814\) | −1475.54 | −0.0635353 | ||||||||
\(815\) | 18180.0 | 0.781369 | ||||||||
\(816\) | −12031.2 | −0.516146 | ||||||||
\(817\) | −4733.19 | −0.202685 | ||||||||
\(818\) | 28296.1 | 1.20947 | ||||||||
\(819\) | 6660.15 | 0.284157 | ||||||||
\(820\) | 9834.66 | 0.418831 | ||||||||
\(821\) | 8776.96 | 0.373103 | 0.186552 | − | 0.982445i | \(-0.440269\pi\) | ||||
0.186552 | + | 0.982445i | \(0.440269\pi\) | |||||||
\(822\) | 5036.11 | 0.213692 | ||||||||
\(823\) | −23197.1 | −0.982505 | −0.491253 | − | 0.871017i | \(-0.663461\pi\) | ||||
−0.491253 | + | 0.871017i | \(0.663461\pi\) | |||||||
\(824\) | −16763.4 | −0.708715 | ||||||||
\(825\) | −1951.63 | −0.0823599 | ||||||||
\(826\) | −11440.8 | −0.481934 | ||||||||
\(827\) | −29552.0 | −1.24259 | −0.621296 | − | 0.783576i | \(-0.713393\pi\) | ||||
−0.621296 | + | 0.783576i | \(0.713393\pi\) | |||||||
\(828\) | −8321.89 | −0.349282 | ||||||||
\(829\) | −19467.4 | −0.815597 | −0.407799 | − | 0.913072i | \(-0.633703\pi\) | ||||
−0.407799 | + | 0.913072i | \(0.633703\pi\) | |||||||
\(830\) | −13033.7 | −0.545066 | ||||||||
\(831\) | 59737.5 | 2.49371 | ||||||||
\(832\) | −15379.9 | −0.640868 | ||||||||
\(833\) | −26629.9 | −1.10765 | ||||||||
\(834\) | −7810.08 | −0.324270 | ||||||||
\(835\) | −20169.8 | −0.835936 | ||||||||
\(836\) | 819.287 | 0.0338943 | ||||||||
\(837\) | −988.794 | −0.0408336 | ||||||||
\(838\) | 20597.8 | 0.849094 | ||||||||
\(839\) | −38868.5 | −1.59939 | −0.799696 | − | 0.600405i | \(-0.795006\pi\) | ||||
−0.799696 | + | 0.600405i | \(0.795006\pi\) | |||||||
\(840\) | 7232.89 | 0.297093 | ||||||||
\(841\) | −4167.87 | −0.170891 | ||||||||
\(842\) | 5382.96 | 0.220319 | ||||||||
\(843\) | −24333.0 | −0.994156 | ||||||||
\(844\) | 22849.2 | 0.931872 | ||||||||
\(845\) | 5316.51 | 0.216442 | ||||||||
\(846\) | −12739.9 | −0.517739 | ||||||||
\(847\) | −1024.37 | −0.0415559 | ||||||||
\(848\) | 4366.05 | 0.176805 | ||||||||
\(849\) | 23554.4 | 0.952160 | ||||||||
\(850\) | −4956.13 | −0.199993 | ||||||||
\(851\) | −6033.93 | −0.243056 | ||||||||
\(852\) | −21506.0 | −0.864769 | ||||||||
\(853\) | −5235.53 | −0.210154 | −0.105077 | − | 0.994464i | \(-0.533509\pi\) | ||||
−0.105077 | + | 0.994464i | \(0.533509\pi\) | |||||||
\(854\) | −9339.99 | −0.374248 | ||||||||
\(855\) | −2219.66 | −0.0887846 | ||||||||
\(856\) | 14716.2 | 0.587606 | ||||||||
\(857\) | −42559.1 | −1.69637 | −0.848186 | − | 0.529698i | \(-0.822305\pi\) | ||||
−0.848186 | + | 0.529698i | \(0.822305\pi\) | |||||||
\(858\) | −5309.25 | −0.211253 | ||||||||
\(859\) | 9352.08 | 0.371465 | 0.185733 | − | 0.982600i | \(-0.440534\pi\) | ||||
0.185733 | + | 0.982600i | \(0.440534\pi\) | |||||||
\(860\) | −4882.71 | −0.193603 | ||||||||
\(861\) | −30146.4 | −1.19325 | ||||||||
\(862\) | −11242.5 | −0.444222 | ||||||||
\(863\) | −21160.7 | −0.834666 | −0.417333 | − | 0.908754i | \(-0.637035\pi\) | ||||
−0.417333 | + | 0.908754i | \(0.637035\pi\) | |||||||
\(864\) | 4069.05 | 0.160222 | ||||||||
\(865\) | 4929.18 | 0.193754 | ||||||||
\(866\) | −22120.1 | −0.867980 | ||||||||
\(867\) | 33494.9 | 1.31205 | ||||||||
\(868\) | 1271.99 | 0.0497397 | ||||||||
\(869\) | 13845.6 | 0.540483 | ||||||||
\(870\) | −10192.1 | −0.397179 | ||||||||
\(871\) | −21827.4 | −0.849131 | ||||||||
\(872\) | 26714.9 | 1.03748 | ||||||||
\(873\) | −23511.1 | −0.911489 | ||||||||
\(874\) | −3486.99 | −0.134953 | ||||||||
\(875\) | 1058.23 | 0.0408856 | ||||||||
\(876\) | 19069.9 | 0.735516 | ||||||||
\(877\) | −10461.9 | −0.402820 | −0.201410 | − | 0.979507i | \(-0.564552\pi\) | ||||
−0.201410 | + | 0.979507i | \(0.564552\pi\) | |||||||
\(878\) | 7265.91 | 0.279285 | ||||||||
\(879\) | −24042.1 | −0.922550 | ||||||||
\(880\) | −950.019 | −0.0363922 | ||||||||
\(881\) | 3846.51 | 0.147097 | 0.0735484 | − | 0.997292i | \(-0.476568\pi\) | ||||
0.0735484 | + | 0.997292i | \(0.476568\pi\) | |||||||
\(882\) | 12805.2 | 0.488860 | ||||||||
\(883\) | −14907.1 | −0.568135 | −0.284068 | − | 0.958804i | \(-0.591684\pi\) | ||||
−0.284068 | + | 0.958804i | \(0.591684\pi\) | |||||||
\(884\) | 12954.3 | 0.492872 | ||||||||
\(885\) | 23740.6 | 0.901729 | ||||||||
\(886\) | −14194.9 | −0.538249 | ||||||||
\(887\) | 33284.1 | 1.25995 | 0.629973 | − | 0.776617i | \(-0.283066\pi\) | ||||
0.629973 | + | 0.776617i | \(0.283066\pi\) | |||||||
\(888\) | −11347.5 | −0.428826 | ||||||||
\(889\) | 16306.5 | 0.615189 | ||||||||
\(890\) | −7423.02 | −0.279573 | ||||||||
\(891\) | 8953.28 | 0.336640 | ||||||||
\(892\) | 17263.3 | 0.648004 | ||||||||
\(893\) | 5128.95 | 0.192199 | ||||||||
\(894\) | −36084.7 | −1.34995 | ||||||||
\(895\) | 8215.11 | 0.306817 | ||||||||
\(896\) | −2871.46 | −0.107063 | ||||||||
\(897\) | −21711.1 | −0.808152 | ||||||||
\(898\) | 26004.3 | 0.966343 | ||||||||
\(899\) | −5450.34 | −0.202201 | ||||||||
\(900\) | −2289.78 | −0.0848065 | ||||||||
\(901\) | −24808.1 | −0.917289 | ||||||||
\(902\) | 11148.6 | 0.411539 | ||||||||
\(903\) | 14967.1 | 0.551575 | ||||||||
\(904\) | −19286.4 | −0.709574 | ||||||||
\(905\) | −4481.15 | −0.164595 | ||||||||
\(906\) | −38642.3 | −1.41700 | ||||||||
\(907\) | −22644.1 | −0.828979 | −0.414489 | − | 0.910054i | \(-0.636040\pi\) | ||||
−0.414489 | + | 0.910054i | \(0.636040\pi\) | |||||||
\(908\) | 21907.3 | 0.800683 | ||||||||
\(909\) | 28204.6 | 1.02914 | ||||||||
\(910\) | 2878.85 | 0.104871 | ||||||||
\(911\) | −53413.8 | −1.94256 | −0.971282 | − | 0.237929i | \(-0.923531\pi\) | ||||
−0.971282 | + | 0.237929i | \(0.923531\pi\) | |||||||
\(912\) | −2329.09 | −0.0845658 | ||||||||
\(913\) | 14195.8 | 0.514582 | ||||||||
\(914\) | −25713.5 | −0.930555 | ||||||||
\(915\) | 19381.2 | 0.700242 | ||||||||
\(916\) | 20039.7 | 0.722849 | ||||||||
\(917\) | 19811.1 | 0.713437 | ||||||||
\(918\) | 5114.32 | 0.183875 | ||||||||
\(919\) | −45492.3 | −1.63292 | −0.816459 | − | 0.577403i | \(-0.804066\pi\) | ||||
−0.816459 | + | 0.577403i | \(0.804066\pi\) | |||||||
\(920\) | −10938.2 | −0.391979 | ||||||||
\(921\) | −2008.35 | −0.0718539 | ||||||||
\(922\) | 10117.3 | 0.361382 | ||||||||
\(923\) | −26028.8 | −0.928222 | ||||||||
\(924\) | −2590.71 | −0.0922381 | ||||||||
\(925\) | −1660.24 | −0.0590145 | ||||||||
\(926\) | 18025.3 | 0.639684 | ||||||||
\(927\) | −16267.5 | −0.576368 | ||||||||
\(928\) | 22429.0 | 0.793394 | ||||||||
\(929\) | 46757.6 | 1.65131 | 0.825655 | − | 0.564175i | \(-0.190806\pi\) | ||||
0.825655 | + | 0.564175i | \(0.190806\pi\) | |||||||
\(930\) | 2747.15 | 0.0968632 | ||||||||
\(931\) | −5155.25 | −0.181478 | ||||||||
\(932\) | 15398.2 | 0.541185 | ||||||||
\(933\) | −8075.87 | −0.283378 | ||||||||
\(934\) | −20991.5 | −0.735401 | ||||||||
\(935\) | 5398.05 | 0.188808 | ||||||||
\(936\) | −18941.6 | −0.661460 | ||||||||
\(937\) | 32214.0 | 1.12314 | 0.561571 | − | 0.827428i | \(-0.310197\pi\) | ||||
0.561571 | + | 0.827428i | \(0.310197\pi\) | |||||||
\(938\) | 11085.5 | 0.385877 | ||||||||
\(939\) | 48713.7 | 1.69298 | ||||||||
\(940\) | 5290.96 | 0.183587 | ||||||||
\(941\) | −5294.98 | −0.183434 | −0.0917170 | − | 0.995785i | \(-0.529236\pi\) | ||||
−0.0917170 | + | 0.995785i | \(0.529236\pi\) | |||||||
\(942\) | 32946.2 | 1.13954 | ||||||||
\(943\) | 45589.9 | 1.57435 | ||||||||
\(944\) | 11556.5 | 0.398445 | ||||||||
\(945\) | −1092.01 | −0.0375906 | ||||||||
\(946\) | −5535.05 | −0.190233 | ||||||||
\(947\) | 24960.7 | 0.856508 | 0.428254 | − | 0.903658i | \(-0.359129\pi\) | ||||
0.428254 | + | 0.903658i | \(0.359129\pi\) | |||||||
\(948\) | 35016.5 | 1.19967 | ||||||||
\(949\) | 23080.4 | 0.789486 | ||||||||
\(950\) | −959.449 | −0.0327670 | ||||||||
\(951\) | −52300.2 | −1.78333 | ||||||||
\(952\) | −20005.6 | −0.681078 | ||||||||
\(953\) | −11933.9 | −0.405642 | −0.202821 | − | 0.979216i | \(-0.565011\pi\) | ||||
−0.202821 | + | 0.979216i | \(0.565011\pi\) | |||||||
\(954\) | 11929.2 | 0.404844 | ||||||||
\(955\) | −11206.0 | −0.379703 | ||||||||
\(956\) | −18197.5 | −0.615637 | ||||||||
\(957\) | 11100.9 | 0.374966 | ||||||||
\(958\) | −16841.3 | −0.567971 | ||||||||
\(959\) | 2974.23 | 0.100149 | ||||||||
\(960\) | −16208.3 | −0.544919 | ||||||||
\(961\) | −28321.9 | −0.950688 | ||||||||
\(962\) | −4516.56 | −0.151372 | ||||||||
\(963\) | 14280.9 | 0.477876 | ||||||||
\(964\) | 14249.9 | 0.476098 | ||||||||
\(965\) | −18354.5 | −0.612283 | ||||||||
\(966\) | 11026.4 | 0.367255 | ||||||||
\(967\) | 1573.62 | 0.0523312 | 0.0261656 | − | 0.999658i | \(-0.491670\pi\) | ||||
0.0261656 | + | 0.999658i | \(0.491670\pi\) | |||||||
\(968\) | 2913.34 | 0.0967338 | ||||||||
\(969\) | 13234.0 | 0.438739 | ||||||||
\(970\) | −10162.7 | −0.336396 | ||||||||
\(971\) | −42094.8 | −1.39123 | −0.695616 | − | 0.718414i | \(-0.744868\pi\) | ||||
−0.695616 | + | 0.718414i | \(0.744868\pi\) | |||||||
\(972\) | 19913.0 | 0.657109 | ||||||||
\(973\) | −4612.49 | −0.151973 | ||||||||
\(974\) | −5631.59 | −0.185265 | ||||||||
\(975\) | −5973.82 | −0.196221 | ||||||||
\(976\) | 9434.43 | 0.309415 | ||||||||
\(977\) | 23184.2 | 0.759188 | 0.379594 | − | 0.925153i | \(-0.376064\pi\) | ||||
0.379594 | + | 0.925153i | \(0.376064\pi\) | |||||||
\(978\) | 52121.3 | 1.70415 | ||||||||
\(979\) | 8084.90 | 0.263937 | ||||||||
\(980\) | −5318.09 | −0.173347 | ||||||||
\(981\) | 25924.5 | 0.843736 | ||||||||
\(982\) | 18395.9 | 0.597799 | ||||||||
\(983\) | −56868.7 | −1.84520 | −0.922599 | − | 0.385760i | \(-0.873939\pi\) | ||||
−0.922599 | + | 0.385760i | \(0.873939\pi\) | |||||||
\(984\) | 85737.2 | 2.77764 | ||||||||
\(985\) | 17342.1 | 0.560979 | ||||||||
\(986\) | 28190.7 | 0.910521 | ||||||||
\(987\) | −16218.5 | −0.523040 | ||||||||
\(988\) | 2507.79 | 0.0807526 | ||||||||
\(989\) | −22634.4 | −0.727739 | ||||||||
\(990\) | −2595.70 | −0.0833300 | ||||||||
\(991\) | 32533.9 | 1.04286 | 0.521430 | − | 0.853294i | \(-0.325399\pi\) | ||||
0.521430 | + | 0.853294i | \(0.325399\pi\) | |||||||
\(992\) | −6045.46 | −0.193491 | ||||||||
\(993\) | −24744.7 | −0.790786 | ||||||||
\(994\) | 13219.2 | 0.421820 | ||||||||
\(995\) | −4996.21 | −0.159186 | ||||||||
\(996\) | 35902.3 | 1.14218 | ||||||||
\(997\) | 60795.3 | 1.93120 | 0.965600 | − | 0.260033i | \(-0.0837335\pi\) | ||||
0.965600 | + | 0.260033i | \(0.0837335\pi\) | |||||||
\(998\) | −8820.74 | −0.279775 | ||||||||
\(999\) | 1713.23 | 0.0542585 |
(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 | 1045.4.a.c.1.8 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.4.a.c.1.8 | ✓ | 20 | 1.1 | even | 1 | trivial |