Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,4,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, 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("1859.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(109.684550701\) |
Analytic rank: | \(1\) |
Dimension: | \(39\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.78473 | −1.69166 | −0.845829 | − | 0.533455i | \(-0.820893\pi\) | ||||
−0.845829 | + | 0.533455i | \(0.820893\pi\) | |||||||
\(3\) | 6.91979 | 1.33171 | 0.665857 | − | 0.746079i | \(-0.268066\pi\) | ||||
0.665857 | + | 0.746079i | \(0.268066\pi\) | |||||||
\(4\) | 14.8936 | 1.86170 | ||||||||
\(5\) | 9.47124 | 0.847133 | 0.423567 | − | 0.905865i | \(-0.360778\pi\) | ||||
0.423567 | + | 0.905865i | \(0.360778\pi\) | |||||||
\(6\) | −33.1093 | −2.25280 | ||||||||
\(7\) | 13.6025 | 0.734464 | 0.367232 | − | 0.930129i | \(-0.380305\pi\) | ||||
0.367232 | + | 0.930129i | \(0.380305\pi\) | |||||||
\(8\) | −32.9841 | −1.45771 | ||||||||
\(9\) | 20.8835 | 0.773463 | ||||||||
\(10\) | −45.3173 | −1.43306 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 103.061 | 2.47926 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −65.0841 | −1.24246 | ||||||||
\(15\) | 65.5390 | 1.12814 | ||||||||
\(16\) | 38.6711 | 0.604237 | ||||||||
\(17\) | −124.539 | −1.77677 | −0.888384 | − | 0.459101i | \(-0.848171\pi\) | ||||
−0.888384 | + | 0.459101i | \(0.848171\pi\) | |||||||
\(18\) | −99.9219 | −1.30843 | ||||||||
\(19\) | 65.7203 | 0.793541 | 0.396770 | − | 0.917918i | \(-0.370131\pi\) | ||||
0.396770 | + | 0.917918i | \(0.370131\pi\) | |||||||
\(20\) | 141.061 | 1.57711 | ||||||||
\(21\) | 94.1263 | 0.978097 | ||||||||
\(22\) | −52.6320 | −0.510054 | ||||||||
\(23\) | −58.7387 | −0.532516 | −0.266258 | − | 0.963902i | \(-0.585787\pi\) | ||||
−0.266258 | + | 0.963902i | \(0.585787\pi\) | |||||||
\(24\) | −228.243 | −1.94125 | ||||||||
\(25\) | −35.2956 | −0.282365 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −42.3249 | −0.301683 | ||||||||
\(28\) | 202.590 | 1.36736 | ||||||||
\(29\) | 4.97794 | 0.0318752 | 0.0159376 | − | 0.999873i | \(-0.494927\pi\) | ||||
0.0159376 | + | 0.999873i | \(0.494927\pi\) | |||||||
\(30\) | −313.586 | −1.90843 | ||||||||
\(31\) | −197.904 | −1.14660 | −0.573300 | − | 0.819346i | \(-0.694337\pi\) | ||||
−0.573300 | + | 0.819346i | \(0.694337\pi\) | |||||||
\(32\) | 78.8422 | 0.435546 | ||||||||
\(33\) | 76.1177 | 0.401527 | ||||||||
\(34\) | 595.883 | 3.00568 | ||||||||
\(35\) | 128.832 | 0.622189 | ||||||||
\(36\) | 311.031 | 1.43996 | ||||||||
\(37\) | −376.446 | −1.67263 | −0.836315 | − | 0.548249i | \(-0.815294\pi\) | ||||
−0.836315 | + | 0.548249i | \(0.815294\pi\) | |||||||
\(38\) | −314.454 | −1.34240 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −312.401 | −1.23487 | ||||||||
\(41\) | −4.21141 | −0.0160418 | −0.00802088 | − | 0.999968i | \(-0.502553\pi\) | ||||
−0.00802088 | + | 0.999968i | \(0.502553\pi\) | |||||||
\(42\) | −450.369 | −1.65460 | ||||||||
\(43\) | −179.398 | −0.636231 | −0.318115 | − | 0.948052i | \(-0.603050\pi\) | ||||
−0.318115 | + | 0.948052i | \(0.603050\pi\) | |||||||
\(44\) | 163.830 | 0.561325 | ||||||||
\(45\) | 197.793 | 0.655226 | ||||||||
\(46\) | 281.049 | 0.900834 | ||||||||
\(47\) | 110.741 | 0.343685 | 0.171843 | − | 0.985124i | \(-0.445028\pi\) | ||||
0.171843 | + | 0.985124i | \(0.445028\pi\) | |||||||
\(48\) | 267.596 | 0.804670 | ||||||||
\(49\) | −157.973 | −0.460562 | ||||||||
\(50\) | 168.880 | 0.477665 | ||||||||
\(51\) | −861.781 | −2.36615 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −194.292 | −0.503550 | −0.251775 | − | 0.967786i | \(-0.581014\pi\) | ||||
−0.251775 | + | 0.967786i | \(0.581014\pi\) | |||||||
\(54\) | 202.513 | 0.510344 | ||||||||
\(55\) | 104.184 | 0.255420 | ||||||||
\(56\) | −448.666 | −1.07063 | ||||||||
\(57\) | 454.771 | 1.05677 | ||||||||
\(58\) | −23.8181 | −0.0539218 | ||||||||
\(59\) | 336.203 | 0.741863 | 0.370931 | − | 0.928660i | \(-0.379039\pi\) | ||||
0.370931 | + | 0.928660i | \(0.379039\pi\) | |||||||
\(60\) | 976.113 | 2.10026 | ||||||||
\(61\) | 192.023 | 0.403050 | 0.201525 | − | 0.979483i | \(-0.435410\pi\) | ||||
0.201525 | + | 0.979483i | \(0.435410\pi\) | |||||||
\(62\) | 946.916 | 1.93965 | ||||||||
\(63\) | 284.067 | 0.568081 | ||||||||
\(64\) | −686.608 | −1.34103 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −364.203 | −0.679246 | ||||||||
\(67\) | −438.374 | −0.799341 | −0.399671 | − | 0.916659i | \(-0.630875\pi\) | ||||
−0.399671 | + | 0.916659i | \(0.630875\pi\) | |||||||
\(68\) | −1854.83 | −3.30781 | ||||||||
\(69\) | −406.459 | −0.709159 | ||||||||
\(70\) | −616.427 | −1.05253 | ||||||||
\(71\) | −1116.26 | −1.86585 | −0.932924 | − | 0.360072i | \(-0.882752\pi\) | ||||
−0.932924 | + | 0.360072i | \(0.882752\pi\) | |||||||
\(72\) | −688.824 | −1.12748 | ||||||||
\(73\) | 284.727 | 0.456503 | 0.228252 | − | 0.973602i | \(-0.426699\pi\) | ||||
0.228252 | + | 0.973602i | \(0.426699\pi\) | |||||||
\(74\) | 1801.19 | 2.82952 | ||||||||
\(75\) | −244.238 | −0.376030 | ||||||||
\(76\) | 978.814 | 1.47734 | ||||||||
\(77\) | 149.627 | 0.221449 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 164.629 | 0.234459 | 0.117229 | − | 0.993105i | \(-0.462599\pi\) | ||||
0.117229 | + | 0.993105i | \(0.462599\pi\) | |||||||
\(80\) | 366.264 | 0.511869 | ||||||||
\(81\) | −856.734 | −1.17522 | ||||||||
\(82\) | 20.1505 | 0.0271372 | ||||||||
\(83\) | 69.9203 | 0.0924669 | 0.0462334 | − | 0.998931i | \(-0.485278\pi\) | ||||
0.0462334 | + | 0.998931i | \(0.485278\pi\) | |||||||
\(84\) | 1401.88 | 1.82093 | ||||||||
\(85\) | −1179.53 | −1.50516 | ||||||||
\(86\) | 858.370 | 1.07628 | ||||||||
\(87\) | 34.4463 | 0.0424486 | ||||||||
\(88\) | −362.826 | −0.439515 | ||||||||
\(89\) | −1121.09 | −1.33523 | −0.667617 | − | 0.744505i | \(-0.732686\pi\) | ||||
−0.667617 | + | 0.744505i | \(0.732686\pi\) | |||||||
\(90\) | −946.384 | −1.10842 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −874.832 | −0.991386 | ||||||||
\(93\) | −1369.45 | −1.52694 | ||||||||
\(94\) | −529.865 | −0.581398 | ||||||||
\(95\) | 622.453 | 0.672235 | ||||||||
\(96\) | 545.572 | 0.580023 | ||||||||
\(97\) | −22.4353 | −0.0234841 | −0.0117421 | − | 0.999931i | \(-0.503738\pi\) | ||||
−0.0117421 | + | 0.999931i | \(0.503738\pi\) | |||||||
\(98\) | 755.857 | 0.779113 | ||||||||
\(99\) | 229.718 | 0.233208 | ||||||||
\(100\) | −525.680 | −0.525680 | ||||||||
\(101\) | −1417.33 | −1.39633 | −0.698165 | − | 0.715937i | \(-0.746000\pi\) | ||||
−0.698165 | + | 0.715937i | \(0.746000\pi\) | |||||||
\(102\) | 4123.39 | 4.00271 | ||||||||
\(103\) | −1365.22 | −1.30601 | −0.653007 | − | 0.757352i | \(-0.726493\pi\) | ||||
−0.653007 | + | 0.757352i | \(0.726493\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 891.492 | 0.828578 | ||||||||
\(106\) | 929.637 | 0.851833 | ||||||||
\(107\) | 2146.95 | 1.93975 | 0.969876 | − | 0.243601i | \(-0.0783287\pi\) | ||||
0.969876 | + | 0.243601i | \(0.0783287\pi\) | |||||||
\(108\) | −630.372 | −0.561644 | ||||||||
\(109\) | −1365.59 | −1.20000 | −0.599999 | − | 0.800001i | \(-0.704832\pi\) | ||||
−0.599999 | + | 0.800001i | \(0.704832\pi\) | |||||||
\(110\) | −498.490 | −0.432084 | ||||||||
\(111\) | −2604.93 | −2.22747 | ||||||||
\(112\) | 526.023 | 0.443790 | ||||||||
\(113\) | 986.088 | 0.820915 | 0.410457 | − | 0.911880i | \(-0.365369\pi\) | ||||
0.410457 | + | 0.911880i | \(0.365369\pi\) | |||||||
\(114\) | −2175.95 | −1.78769 | ||||||||
\(115\) | −556.328 | −0.451112 | ||||||||
\(116\) | 74.1395 | 0.0593421 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1608.64 | −1.25498 | ||||||||
\(119\) | −1694.03 | −1.30497 | ||||||||
\(120\) | −2161.75 | −1.64450 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −918.778 | −0.681822 | ||||||||
\(123\) | −29.1421 | −0.0213630 | ||||||||
\(124\) | −2947.51 | −2.13463 | ||||||||
\(125\) | −1518.20 | −1.08633 | ||||||||
\(126\) | −1359.18 | −0.960998 | ||||||||
\(127\) | −1528.53 | −1.06799 | −0.533996 | − | 0.845487i | \(-0.679310\pi\) | ||||
−0.533996 | + | 0.845487i | \(0.679310\pi\) | |||||||
\(128\) | 2654.49 | 1.83302 | ||||||||
\(129\) | −1241.40 | −0.847278 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2838.18 | −1.89292 | −0.946462 | − | 0.322814i | \(-0.895371\pi\) | ||||
−0.946462 | + | 0.322814i | \(0.895371\pi\) | |||||||
\(132\) | 1133.67 | 0.747524 | ||||||||
\(133\) | 893.959 | 0.582827 | ||||||||
\(134\) | 2097.50 | 1.35221 | ||||||||
\(135\) | −400.869 | −0.255565 | ||||||||
\(136\) | 4107.80 | 2.59001 | ||||||||
\(137\) | 1625.31 | 1.01357 | 0.506785 | − | 0.862072i | \(-0.330834\pi\) | ||||
0.506785 | + | 0.862072i | \(0.330834\pi\) | |||||||
\(138\) | 1944.80 | 1.19965 | ||||||||
\(139\) | −525.607 | −0.320730 | −0.160365 | − | 0.987058i | \(-0.551267\pi\) | ||||
−0.160365 | + | 0.987058i | \(0.551267\pi\) | |||||||
\(140\) | 1918.78 | 1.15833 | ||||||||
\(141\) | 766.303 | 0.457691 | ||||||||
\(142\) | 5340.98 | 3.15638 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 807.589 | 0.467354 | ||||||||
\(145\) | 47.1472 | 0.0270025 | ||||||||
\(146\) | −1362.34 | −0.772247 | ||||||||
\(147\) | −1093.14 | −0.613337 | ||||||||
\(148\) | −5606.64 | −3.11394 | ||||||||
\(149\) | 2508.85 | 1.37942 | 0.689708 | − | 0.724088i | \(-0.257739\pi\) | ||||
0.689708 | + | 0.724088i | \(0.257739\pi\) | |||||||
\(150\) | 1168.61 | 0.636113 | ||||||||
\(151\) | 478.191 | 0.257713 | 0.128856 | − | 0.991663i | \(-0.458869\pi\) | ||||
0.128856 | + | 0.991663i | \(0.458869\pi\) | |||||||
\(152\) | −2167.73 | −1.15675 | ||||||||
\(153\) | −2600.80 | −1.37426 | ||||||||
\(154\) | −715.925 | −0.374616 | ||||||||
\(155\) | −1874.39 | −0.971323 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1677.59 | −0.852778 | −0.426389 | − | 0.904540i | \(-0.640215\pi\) | ||||
−0.426389 | + | 0.904540i | \(0.640215\pi\) | |||||||
\(158\) | −787.707 | −0.396624 | ||||||||
\(159\) | −1344.46 | −0.670584 | ||||||||
\(160\) | 746.734 | 0.368965 | ||||||||
\(161\) | −798.991 | −0.391114 | ||||||||
\(162\) | 4099.24 | 1.98807 | ||||||||
\(163\) | 3603.13 | 1.73141 | 0.865703 | − | 0.500558i | \(-0.166872\pi\) | ||||
0.865703 | + | 0.500558i | \(0.166872\pi\) | |||||||
\(164\) | −62.7232 | −0.0298650 | ||||||||
\(165\) | 720.929 | 0.340147 | ||||||||
\(166\) | −334.550 | −0.156422 | ||||||||
\(167\) | −177.653 | −0.0823185 | −0.0411593 | − | 0.999153i | \(-0.513105\pi\) | ||||
−0.0411593 | + | 0.999153i | \(0.513105\pi\) | |||||||
\(168\) | −3104.67 | −1.42578 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 5643.75 | 2.54621 | ||||||||
\(171\) | 1372.47 | 0.613774 | ||||||||
\(172\) | −2671.89 | −1.18447 | ||||||||
\(173\) | 3704.09 | 1.62784 | 0.813921 | − | 0.580975i | \(-0.197329\pi\) | ||||
0.813921 | + | 0.580975i | \(0.197329\pi\) | |||||||
\(174\) | −164.816 | −0.0718085 | ||||||||
\(175\) | −480.108 | −0.207387 | ||||||||
\(176\) | 425.383 | 0.182184 | ||||||||
\(177\) | 2326.45 | 0.987949 | ||||||||
\(178\) | 5364.13 | 2.25876 | ||||||||
\(179\) | 2466.95 | 1.03011 | 0.515053 | − | 0.857159i | \(-0.327772\pi\) | ||||
0.515053 | + | 0.857159i | \(0.327772\pi\) | |||||||
\(180\) | 2945.85 | 1.21984 | ||||||||
\(181\) | −830.340 | −0.340987 | −0.170494 | − | 0.985359i | \(-0.554536\pi\) | ||||
−0.170494 | + | 0.985359i | \(0.554536\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1328.76 | 0.536747 | ||||||||
\(184\) | 1937.44 | 0.776252 | ||||||||
\(185\) | −3565.41 | −1.41694 | ||||||||
\(186\) | 6552.46 | 2.58306 | ||||||||
\(187\) | −1369.92 | −0.535716 | ||||||||
\(188\) | 1649.33 | 0.639840 | ||||||||
\(189\) | −575.723 | −0.221575 | ||||||||
\(190\) | −2978.27 | −1.13719 | ||||||||
\(191\) | 4579.18 | 1.73475 | 0.867376 | − | 0.497654i | \(-0.165805\pi\) | ||||
0.867376 | + | 0.497654i | \(0.165805\pi\) | |||||||
\(192\) | −4751.18 | −1.78587 | ||||||||
\(193\) | 4144.05 | 1.54557 | 0.772785 | − | 0.634668i | \(-0.218863\pi\) | ||||
0.772785 | + | 0.634668i | \(0.218863\pi\) | |||||||
\(194\) | 107.347 | 0.0397270 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2352.79 | −0.857430 | ||||||||
\(197\) | −2329.13 | −0.842353 | −0.421177 | − | 0.906979i | \(-0.638383\pi\) | ||||
−0.421177 | + | 0.906979i | \(0.638383\pi\) | |||||||
\(198\) | −1099.14 | −0.394508 | ||||||||
\(199\) | 1558.02 | 0.555001 | 0.277500 | − | 0.960726i | \(-0.410494\pi\) | ||||
0.277500 | + | 0.960726i | \(0.410494\pi\) | |||||||
\(200\) | 1164.20 | 0.411606 | ||||||||
\(201\) | −3033.45 | −1.06449 | ||||||||
\(202\) | 6781.53 | 2.36211 | ||||||||
\(203\) | 67.7122 | 0.0234112 | ||||||||
\(204\) | −12835.0 | −4.40506 | ||||||||
\(205\) | −39.8873 | −0.0135895 | ||||||||
\(206\) | 6532.22 | 2.20933 | ||||||||
\(207\) | −1226.67 | −0.411881 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 722.923 | 0.239262 | ||||||||
\(210\) | −4265.55 | −1.40167 | ||||||||
\(211\) | −2209.07 | −0.720750 | −0.360375 | − | 0.932807i | \(-0.617351\pi\) | ||||
−0.360375 | + | 0.932807i | \(0.617351\pi\) | |||||||
\(212\) | −2893.72 | −0.937460 | ||||||||
\(213\) | −7724.26 | −2.48478 | ||||||||
\(214\) | −10272.6 | −3.28139 | ||||||||
\(215\) | −1699.12 | −0.538972 | ||||||||
\(216\) | 1396.05 | 0.439765 | ||||||||
\(217\) | −2691.98 | −0.842136 | ||||||||
\(218\) | 6533.97 | 2.02998 | ||||||||
\(219\) | 1970.25 | 0.607932 | ||||||||
\(220\) | 1551.67 | 0.475517 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 12463.9 | 3.76811 | ||||||||
\(223\) | 1157.16 | 0.347485 | 0.173742 | − | 0.984791i | \(-0.444414\pi\) | ||||
0.173742 | + | 0.984791i | \(0.444414\pi\) | |||||||
\(224\) | 1072.45 | 0.319893 | ||||||||
\(225\) | −737.097 | −0.218399 | ||||||||
\(226\) | −4718.16 | −1.38871 | ||||||||
\(227\) | −597.182 | −0.174610 | −0.0873048 | − | 0.996182i | \(-0.527825\pi\) | ||||
−0.0873048 | + | 0.996182i | \(0.527825\pi\) | |||||||
\(228\) | 6773.19 | 1.96739 | ||||||||
\(229\) | 5158.10 | 1.48846 | 0.744229 | − | 0.667924i | \(-0.232817\pi\) | ||||
0.744229 | + | 0.667924i | \(0.232817\pi\) | |||||||
\(230\) | 2661.88 | 0.763126 | ||||||||
\(231\) | 1035.39 | 0.294907 | ||||||||
\(232\) | −164.193 | −0.0464646 | ||||||||
\(233\) | 1911.49 | 0.537449 | 0.268725 | − | 0.963217i | \(-0.413398\pi\) | ||||
0.268725 | + | 0.963217i | \(0.413398\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1048.85 | 0.291147 | ||||||||
\(236\) | 5007.28 | 1.38113 | ||||||||
\(237\) | 1139.20 | 0.312232 | ||||||||
\(238\) | 8105.49 | 2.20757 | ||||||||
\(239\) | 5178.67 | 1.40159 | 0.700796 | − | 0.713362i | \(-0.252829\pi\) | ||||
0.700796 | + | 0.713362i | \(0.252829\pi\) | |||||||
\(240\) | 2534.47 | 0.681663 | ||||||||
\(241\) | 4607.16 | 1.23142 | 0.615712 | − | 0.787971i | \(-0.288869\pi\) | ||||
0.615712 | + | 0.787971i | \(0.288869\pi\) | |||||||
\(242\) | −578.952 | −0.153787 | ||||||||
\(243\) | −4785.65 | −1.26337 | ||||||||
\(244\) | 2859.92 | 0.750359 | ||||||||
\(245\) | −1496.20 | −0.390157 | ||||||||
\(246\) | 139.437 | 0.0361389 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6527.69 | 1.67141 | ||||||||
\(249\) | 483.834 | 0.123139 | ||||||||
\(250\) | 7264.17 | 1.83770 | ||||||||
\(251\) | −49.9181 | −0.0125530 | −0.00627650 | − | 0.999980i | \(-0.501998\pi\) | ||||
−0.00627650 | + | 0.999980i | \(0.501998\pi\) | |||||||
\(252\) | 4230.79 | 1.05760 | ||||||||
\(253\) | −646.125 | −0.160559 | ||||||||
\(254\) | 7313.59 | 1.80668 | ||||||||
\(255\) | −8162.13 | −2.00444 | ||||||||
\(256\) | −7208.17 | −1.75981 | ||||||||
\(257\) | 3151.59 | 0.764945 | 0.382473 | − | 0.923967i | \(-0.375073\pi\) | ||||
0.382473 | + | 0.923967i | \(0.375073\pi\) | |||||||
\(258\) | 5939.74 | 1.43330 | ||||||||
\(259\) | −5120.59 | −1.22849 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 103.957 | 0.0246543 | ||||||||
\(262\) | 13579.9 | 3.20218 | ||||||||
\(263\) | −1309.16 | −0.306943 | −0.153471 | − | 0.988153i | \(-0.549045\pi\) | ||||
−0.153471 | + | 0.988153i | \(0.549045\pi\) | |||||||
\(264\) | −2510.68 | −0.585309 | ||||||||
\(265\) | −1840.19 | −0.426574 | ||||||||
\(266\) | −4277.35 | −0.985944 | ||||||||
\(267\) | −7757.74 | −1.77815 | ||||||||
\(268\) | −6528.97 | −1.48814 | ||||||||
\(269\) | 5664.18 | 1.28383 | 0.641917 | − | 0.766774i | \(-0.278139\pi\) | ||||
0.641917 | + | 0.766774i | \(0.278139\pi\) | |||||||
\(270\) | 1918.05 | 0.432329 | ||||||||
\(271\) | −2358.45 | −0.528655 | −0.264328 | − | 0.964433i | \(-0.585150\pi\) | ||||
−0.264328 | + | 0.964433i | \(0.585150\pi\) | |||||||
\(272\) | −4816.05 | −1.07359 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7776.64 | −1.71461 | ||||||||
\(275\) | −388.252 | −0.0851363 | ||||||||
\(276\) | −6053.65 | −1.32024 | ||||||||
\(277\) | −6248.51 | −1.35537 | −0.677683 | − | 0.735354i | \(-0.737016\pi\) | ||||
−0.677683 | + | 0.735354i | \(0.737016\pi\) | |||||||
\(278\) | 2514.89 | 0.542564 | ||||||||
\(279\) | −4132.92 | −0.886852 | ||||||||
\(280\) | −4249.42 | −0.906970 | ||||||||
\(281\) | −3155.15 | −0.669823 | −0.334912 | − | 0.942250i | \(-0.608706\pi\) | ||||
−0.334912 | + | 0.942250i | \(0.608706\pi\) | |||||||
\(282\) | −3666.55 | −0.774256 | ||||||||
\(283\) | 7581.70 | 1.59253 | 0.796264 | − | 0.604949i | \(-0.206807\pi\) | ||||
0.796264 | + | 0.604949i | \(0.206807\pi\) | |||||||
\(284\) | −16625.1 | −3.47366 | ||||||||
\(285\) | 4307.24 | 0.895225 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −57.2856 | −0.0117821 | ||||||||
\(288\) | 1646.50 | 0.336879 | ||||||||
\(289\) | 10596.9 | 2.15690 | ||||||||
\(290\) | −225.587 | −0.0456790 | ||||||||
\(291\) | −155.247 | −0.0312741 | ||||||||
\(292\) | 4240.62 | 0.849874 | ||||||||
\(293\) | 5090.44 | 1.01497 | 0.507486 | − | 0.861660i | \(-0.330575\pi\) | ||||
0.507486 | + | 0.861660i | \(0.330575\pi\) | |||||||
\(294\) | 5230.37 | 1.03756 | ||||||||
\(295\) | 3184.26 | 0.628457 | ||||||||
\(296\) | 12416.7 | 2.43820 | ||||||||
\(297\) | −465.574 | −0.0909608 | ||||||||
\(298\) | −12004.2 | −2.33350 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3637.60 | −0.700056 | ||||||||
\(301\) | −2440.25 | −0.467289 | ||||||||
\(302\) | −2288.02 | −0.435962 | ||||||||
\(303\) | −9807.61 | −1.85951 | ||||||||
\(304\) | 2541.48 | 0.479486 | ||||||||
\(305\) | 1818.70 | 0.341437 | ||||||||
\(306\) | 12444.1 | 2.32478 | ||||||||
\(307\) | −7020.67 | −1.30518 | −0.652591 | − | 0.757711i | \(-0.726318\pi\) | ||||
−0.652591 | + | 0.757711i | \(0.726318\pi\) | |||||||
\(308\) | 2228.49 | 0.412273 | ||||||||
\(309\) | −9447.05 | −1.73924 | ||||||||
\(310\) | 8968.47 | 1.64314 | ||||||||
\(311\) | −10340.8 | −1.88544 | −0.942721 | − | 0.333584i | \(-0.891742\pi\) | ||||
−0.942721 | + | 0.333584i | \(0.891742\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1080.16 | −0.195061 | −0.0975306 | − | 0.995233i | \(-0.531094\pi\) | ||||
−0.0975306 | + | 0.995233i | \(0.531094\pi\) | |||||||
\(314\) | 8026.81 | 1.44261 | ||||||||
\(315\) | 2690.47 | 0.481240 | ||||||||
\(316\) | 2451.93 | 0.436493 | ||||||||
\(317\) | 9304.71 | 1.64860 | 0.824298 | − | 0.566157i | \(-0.191570\pi\) | ||||
0.824298 | + | 0.566157i | \(0.191570\pi\) | |||||||
\(318\) | 6432.89 | 1.13440 | ||||||||
\(319\) | 54.7573 | 0.00961072 | ||||||||
\(320\) | −6503.03 | −1.13603 | ||||||||
\(321\) | 14856.4 | 2.58319 | ||||||||
\(322\) | 3822.95 | 0.661630 | ||||||||
\(323\) | −8184.72 | −1.40994 | ||||||||
\(324\) | −12759.9 | −2.18791 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −17240.0 | −2.92894 | ||||||||
\(327\) | −9449.59 | −1.59805 | ||||||||
\(328\) | 138.910 | 0.0233842 | ||||||||
\(329\) | 1506.35 | 0.252425 | ||||||||
\(330\) | −3449.45 | −0.575412 | ||||||||
\(331\) | −141.932 | −0.0235689 | −0.0117845 | − | 0.999931i | \(-0.503751\pi\) | ||||
−0.0117845 | + | 0.999931i | \(0.503751\pi\) | |||||||
\(332\) | 1041.37 | 0.172146 | ||||||||
\(333\) | −7861.50 | −1.29372 | ||||||||
\(334\) | 850.021 | 0.139255 | ||||||||
\(335\) | −4151.94 | −0.677149 | ||||||||
\(336\) | 3639.97 | 0.591002 | ||||||||
\(337\) | 2278.75 | 0.368343 | 0.184171 | − | 0.982894i | \(-0.441040\pi\) | ||||
0.184171 | + | 0.982894i | \(0.441040\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6823.52 | 1.09322 | ||||||||
\(340\) | −17567.6 | −2.80216 | ||||||||
\(341\) | −2176.94 | −0.345713 | ||||||||
\(342\) | −6566.90 | −1.03830 | ||||||||
\(343\) | −6814.47 | −1.07273 | ||||||||
\(344\) | 5917.29 | 0.927438 | ||||||||
\(345\) | −3849.67 | −0.600752 | ||||||||
\(346\) | −17723.1 | −2.75375 | ||||||||
\(347\) | −8293.00 | −1.28297 | −0.641487 | − | 0.767134i | \(-0.721682\pi\) | ||||
−0.641487 | + | 0.767134i | \(0.721682\pi\) | |||||||
\(348\) | 513.030 | 0.0790267 | ||||||||
\(349\) | −249.059 | −0.0382000 | −0.0191000 | − | 0.999818i | \(-0.506080\pi\) | ||||
−0.0191000 | + | 0.999818i | \(0.506080\pi\) | |||||||
\(350\) | 2297.19 | 0.350828 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 867.265 | 0.131322 | ||||||||
\(353\) | −6399.58 | −0.964916 | −0.482458 | − | 0.875919i | \(-0.660256\pi\) | ||||
−0.482458 | + | 0.875919i | \(0.660256\pi\) | |||||||
\(354\) | −11131.5 | −1.67127 | ||||||||
\(355\) | −10572.3 | −1.58062 | ||||||||
\(356\) | −16697.2 | −2.48581 | ||||||||
\(357\) | −11722.4 | −1.73785 | ||||||||
\(358\) | −11803.7 | −1.74258 | ||||||||
\(359\) | 7763.63 | 1.14136 | 0.570680 | − | 0.821172i | \(-0.306680\pi\) | ||||
0.570680 | + | 0.821172i | \(0.306680\pi\) | |||||||
\(360\) | −6524.02 | −0.955128 | ||||||||
\(361\) | −2539.84 | −0.370293 | ||||||||
\(362\) | 3972.95 | 0.576833 | ||||||||
\(363\) | 837.295 | 0.121065 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2696.72 | 0.386719 | ||||||||
\(366\) | −6357.75 | −0.907992 | ||||||||
\(367\) | 7599.42 | 1.08089 | 0.540445 | − | 0.841379i | \(-0.318256\pi\) | ||||
0.540445 | + | 0.841379i | \(0.318256\pi\) | |||||||
\(368\) | −2271.49 | −0.321765 | ||||||||
\(369\) | −87.9490 | −0.0124077 | ||||||||
\(370\) | 17059.5 | 2.39698 | ||||||||
\(371\) | −2642.86 | −0.369839 | ||||||||
\(372\) | −20396.1 | −2.84271 | ||||||||
\(373\) | 1585.63 | 0.220109 | 0.110055 | − | 0.993926i | \(-0.464897\pi\) | ||||
0.110055 | + | 0.993926i | \(0.464897\pi\) | |||||||
\(374\) | 6554.72 | 0.906247 | ||||||||
\(375\) | −10505.6 | −1.44669 | ||||||||
\(376\) | −3652.69 | −0.500993 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2754.68 | 0.374829 | ||||||||
\(379\) | −2849.50 | −0.386198 | −0.193099 | − | 0.981179i | \(-0.561854\pi\) | ||||
−0.193099 | + | 0.981179i | \(0.561854\pi\) | |||||||
\(380\) | 9270.58 | 1.25150 | ||||||||
\(381\) | −10577.1 | −1.42226 | ||||||||
\(382\) | −21910.1 | −2.93460 | ||||||||
\(383\) | −4613.59 | −0.615518 | −0.307759 | − | 0.951464i | \(-0.599579\pi\) | ||||
−0.307759 | + | 0.951464i | \(0.599579\pi\) | |||||||
\(384\) | 18368.5 | 2.44106 | ||||||||
\(385\) | 1417.15 | 0.187597 | ||||||||
\(386\) | −19828.1 | −2.61457 | ||||||||
\(387\) | −3746.46 | −0.492101 | ||||||||
\(388\) | −334.143 | −0.0437204 | ||||||||
\(389\) | 11704.3 | 1.52553 | 0.762763 | − | 0.646679i | \(-0.223843\pi\) | ||||
0.762763 | + | 0.646679i | \(0.223843\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7315.23 | 0.946156 | ||||||||
\(392\) | 5210.60 | 0.671364 | ||||||||
\(393\) | −19639.6 | −2.52084 | ||||||||
\(394\) | 11144.3 | 1.42497 | ||||||||
\(395\) | 1559.24 | 0.198618 | ||||||||
\(396\) | 3421.34 | 0.434164 | ||||||||
\(397\) | −7918.29 | −1.00103 | −0.500513 | − | 0.865729i | \(-0.666855\pi\) | ||||
−0.500513 | + | 0.865729i | \(0.666855\pi\) | |||||||
\(398\) | −7454.71 | −0.938871 | ||||||||
\(399\) | 6186.01 | 0.776160 | ||||||||
\(400\) | −1364.92 | −0.170615 | ||||||||
\(401\) | −11600.6 | −1.44466 | −0.722328 | − | 0.691550i | \(-0.756928\pi\) | ||||
−0.722328 | + | 0.691550i | \(0.756928\pi\) | |||||||
\(402\) | 14514.3 | 1.80076 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −21109.2 | −2.59955 | ||||||||
\(405\) | −8114.33 | −0.995566 | ||||||||
\(406\) | −323.985 | −0.0396037 | ||||||||
\(407\) | −4140.90 | −0.504317 | ||||||||
\(408\) | 28425.1 | 3.44915 | ||||||||
\(409\) | 1603.65 | 0.193876 | 0.0969378 | − | 0.995290i | \(-0.469095\pi\) | ||||
0.0969378 | + | 0.995290i | \(0.469095\pi\) | |||||||
\(410\) | 190.850 | 0.0229888 | ||||||||
\(411\) | 11246.8 | 1.34979 | ||||||||
\(412\) | −20333.1 | −2.43141 | ||||||||
\(413\) | 4573.19 | 0.544872 | ||||||||
\(414\) | 5869.28 | 0.696761 | ||||||||
\(415\) | 662.232 | 0.0783318 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3637.09 | −0.427120 | ||||||||
\(418\) | −3458.99 | −0.404748 | ||||||||
\(419\) | −13735.6 | −1.60150 | −0.800748 | − | 0.599001i | \(-0.795565\pi\) | ||||
−0.800748 | + | 0.599001i | \(0.795565\pi\) | |||||||
\(420\) | 13277.6 | 1.54257 | ||||||||
\(421\) | 14940.0 | 1.72953 | 0.864763 | − | 0.502180i | \(-0.167469\pi\) | ||||
0.864763 | + | 0.502180i | \(0.167469\pi\) | |||||||
\(422\) | 10569.8 | 1.21926 | ||||||||
\(423\) | 2312.66 | 0.265828 | ||||||||
\(424\) | 6408.57 | 0.734028 | ||||||||
\(425\) | 4395.67 | 0.501697 | ||||||||
\(426\) | 36958.5 | 4.20339 | ||||||||
\(427\) | 2611.99 | 0.296026 | ||||||||
\(428\) | 31975.9 | 3.61124 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8129.83 | 0.911756 | ||||||||
\(431\) | 9734.67 | 1.08794 | 0.543971 | − | 0.839104i | \(-0.316920\pi\) | ||||
0.543971 | + | 0.839104i | \(0.316920\pi\) | |||||||
\(432\) | −1636.75 | −0.182288 | ||||||||
\(433\) | −12297.0 | −1.36480 | −0.682398 | − | 0.730981i | \(-0.739063\pi\) | ||||
−0.682398 | + | 0.730981i | \(0.739063\pi\) | |||||||
\(434\) | 12880.4 | 1.42461 | ||||||||
\(435\) | 326.249 | 0.0359596 | ||||||||
\(436\) | −20338.6 | −2.23404 | ||||||||
\(437\) | −3860.32 | −0.422573 | ||||||||
\(438\) | −9427.11 | −1.02841 | ||||||||
\(439\) | −3741.54 | −0.406775 | −0.203387 | − | 0.979098i | \(-0.565195\pi\) | ||||
−0.203387 | + | 0.979098i | \(0.565195\pi\) | |||||||
\(440\) | −3436.41 | −0.372328 | ||||||||
\(441\) | −3299.02 | −0.356228 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16586.0 | 1.77884 | 0.889421 | − | 0.457090i | \(-0.151108\pi\) | ||||
0.889421 | + | 0.457090i | \(0.151108\pi\) | |||||||
\(444\) | −38796.8 | −4.14688 | ||||||||
\(445\) | −10618.2 | −1.13112 | ||||||||
\(446\) | −5536.69 | −0.587825 | ||||||||
\(447\) | 17360.7 | 1.83699 | ||||||||
\(448\) | −9339.56 | −0.984939 | ||||||||
\(449\) | −4518.98 | −0.474975 | −0.237487 | − | 0.971391i | \(-0.576324\pi\) | ||||
−0.237487 | + | 0.971391i | \(0.576324\pi\) | |||||||
\(450\) | 3526.81 | 0.369456 | ||||||||
\(451\) | −46.3255 | −0.00483677 | ||||||||
\(452\) | 14686.4 | 1.52830 | ||||||||
\(453\) | 3308.98 | 0.343200 | ||||||||
\(454\) | 2857.36 | 0.295380 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15000.2 | −1.54046 | ||||||||
\(457\) | 11676.9 | 1.19523 | 0.597615 | − | 0.801783i | \(-0.296115\pi\) | ||||
0.597615 | + | 0.801783i | \(0.296115\pi\) | |||||||
\(458\) | −24680.1 | −2.51796 | ||||||||
\(459\) | 5271.09 | 0.536020 | ||||||||
\(460\) | −8285.74 | −0.839836 | ||||||||
\(461\) | 1426.40 | 0.144108 | 0.0720541 | − | 0.997401i | \(-0.477045\pi\) | ||||
0.0720541 | + | 0.997401i | \(0.477045\pi\) | |||||||
\(462\) | −4954.05 | −0.498882 | ||||||||
\(463\) | −3128.59 | −0.314035 | −0.157017 | − | 0.987596i | \(-0.550188\pi\) | ||||
−0.157017 | + | 0.987596i | \(0.550188\pi\) | |||||||
\(464\) | 192.502 | 0.0192601 | ||||||||
\(465\) | −12970.4 | −1.29352 | ||||||||
\(466\) | −9145.94 | −0.909180 | ||||||||
\(467\) | −15810.7 | −1.56666 | −0.783330 | − | 0.621606i | \(-0.786481\pi\) | ||||
−0.783330 | + | 0.621606i | \(0.786481\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5962.96 | −0.587088 | ||||||||
\(470\) | −5018.48 | −0.492521 | ||||||||
\(471\) | −11608.6 | −1.13566 | ||||||||
\(472\) | −11089.4 | −1.08142 | ||||||||
\(473\) | −1973.38 | −0.191831 | ||||||||
\(474\) | −5450.77 | −0.528190 | ||||||||
\(475\) | −2319.64 | −0.224068 | ||||||||
\(476\) | −25230.3 | −2.42947 | ||||||||
\(477\) | −4057.51 | −0.389477 | ||||||||
\(478\) | −24778.5 | −2.37101 | ||||||||
\(479\) | −9792.42 | −0.934086 | −0.467043 | − | 0.884235i | \(-0.654681\pi\) | ||||
−0.467043 | + | 0.884235i | \(0.654681\pi\) | |||||||
\(480\) | 5167.24 | 0.491357 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −22044.0 | −2.08315 | ||||||||
\(483\) | −5528.85 | −0.520852 | ||||||||
\(484\) | 1802.13 | 0.169246 | ||||||||
\(485\) | −212.490 | −0.0198942 | ||||||||
\(486\) | 22898.0 | 2.13719 | ||||||||
\(487\) | 135.188 | 0.0125790 | 0.00628949 | − | 0.999980i | \(-0.497998\pi\) | ||||
0.00628949 | + | 0.999980i | \(0.497998\pi\) | |||||||
\(488\) | −6333.71 | −0.587528 | ||||||||
\(489\) | 24932.9 | 2.30574 | ||||||||
\(490\) | 7158.90 | 0.660013 | ||||||||
\(491\) | 650.322 | 0.0597732 | 0.0298866 | − | 0.999553i | \(-0.490485\pi\) | ||||
0.0298866 | + | 0.999553i | \(0.490485\pi\) | |||||||
\(492\) | −434.032 | −0.0397716 | ||||||||
\(493\) | −619.945 | −0.0566348 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2175.72 | 0.197558 | ||||||||
\(496\) | −7653.17 | −0.692817 | ||||||||
\(497\) | −15183.8 | −1.37040 | ||||||||
\(498\) | −2315.01 | −0.208310 | ||||||||
\(499\) | −17313.7 | −1.55324 | −0.776620 | − | 0.629970i | \(-0.783067\pi\) | ||||
−0.776620 | + | 0.629970i | \(0.783067\pi\) | |||||||
\(500\) | −22611.5 | −2.02243 | ||||||||
\(501\) | −1229.32 | −0.109625 | ||||||||
\(502\) | 238.845 | 0.0212354 | ||||||||
\(503\) | 14852.8 | 1.31661 | 0.658304 | − | 0.752752i | \(-0.271274\pi\) | ||||
0.658304 | + | 0.752752i | \(0.271274\pi\) | |||||||
\(504\) | −9369.71 | −0.828096 | ||||||||
\(505\) | −13423.9 | −1.18288 | ||||||||
\(506\) | 3091.53 | 0.271612 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −22765.3 | −1.98828 | ||||||||
\(509\) | 13500.5 | 1.17564 | 0.587818 | − | 0.808993i | \(-0.299987\pi\) | ||||
0.587818 | + | 0.808993i | \(0.299987\pi\) | |||||||
\(510\) | 39053.6 | 3.39083 | ||||||||
\(511\) | 3872.99 | 0.335286 | ||||||||
\(512\) | 13253.2 | 1.14397 | ||||||||
\(513\) | −2781.61 | −0.239398 | ||||||||
\(514\) | −15079.5 | −1.29403 | ||||||||
\(515\) | −12930.3 | −1.10637 | ||||||||
\(516\) | −18488.9 | −1.57738 | ||||||||
\(517\) | 1218.15 | 0.103625 | ||||||||
\(518\) | 24500.6 | 2.07818 | ||||||||
\(519\) | 25631.5 | 2.16782 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1162.37 | 0.0977433 | 0.0488717 | − | 0.998805i | \(-0.484437\pi\) | ||||
0.0488717 | + | 0.998805i | \(0.484437\pi\) | |||||||
\(522\) | −497.405 | −0.0417065 | ||||||||
\(523\) | −20125.6 | −1.68266 | −0.841329 | − | 0.540523i | \(-0.818226\pi\) | ||||
−0.841329 | + | 0.540523i | \(0.818226\pi\) | |||||||
\(524\) | −42270.8 | −3.52406 | ||||||||
\(525\) | −3322.25 | −0.276180 | ||||||||
\(526\) | 6263.96 | 0.519242 | ||||||||
\(527\) | 24646.7 | 2.03724 | ||||||||
\(528\) | 2943.56 | 0.242617 | ||||||||
\(529\) | −8716.77 | −0.716427 | ||||||||
\(530\) | 8804.81 | 0.721616 | ||||||||
\(531\) | 7021.09 | 0.573803 | ||||||||
\(532\) | 13314.3 | 1.08505 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 37118.7 | 3.00802 | ||||||||
\(535\) | 20334.3 | 1.64323 | ||||||||
\(536\) | 14459.4 | 1.16521 | ||||||||
\(537\) | 17070.8 | 1.37181 | ||||||||
\(538\) | −27101.6 | −2.17181 | ||||||||
\(539\) | −1737.70 | −0.138865 | ||||||||
\(540\) | −5970.40 | −0.475787 | ||||||||
\(541\) | −20346.9 | −1.61698 | −0.808488 | − | 0.588513i | \(-0.799714\pi\) | ||||
−0.808488 | + | 0.588513i | \(0.799714\pi\) | |||||||
\(542\) | 11284.5 | 0.894304 | ||||||||
\(543\) | −5745.78 | −0.454097 | ||||||||
\(544\) | −9818.90 | −0.773864 | ||||||||
\(545\) | −12933.8 | −1.01656 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17583.2 | 1.37441 | 0.687205 | − | 0.726464i | \(-0.258837\pi\) | ||||
0.687205 | + | 0.726464i | \(0.258837\pi\) | |||||||
\(548\) | 24206.7 | 1.88697 | ||||||||
\(549\) | 4010.11 | 0.311744 | ||||||||
\(550\) | 1857.68 | 0.144021 | ||||||||
\(551\) | 327.152 | 0.0252942 | ||||||||
\(552\) | 13406.7 | 1.03375 | ||||||||
\(553\) | 2239.37 | 0.172202 | ||||||||
\(554\) | 29897.4 | 2.29282 | ||||||||
\(555\) | −24671.9 | −1.88696 | ||||||||
\(556\) | −7828.20 | −0.597103 | ||||||||
\(557\) | −5140.53 | −0.391044 | −0.195522 | − | 0.980699i | \(-0.562640\pi\) | ||||
−0.195522 | + | 0.980699i | \(0.562640\pi\) | |||||||
\(558\) | 19774.9 | 1.50025 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 4982.09 | 0.375949 | ||||||||
\(561\) | −9479.59 | −0.713420 | ||||||||
\(562\) | 15096.5 | 1.13311 | ||||||||
\(563\) | −6559.64 | −0.491040 | −0.245520 | − | 0.969391i | \(-0.578959\pi\) | ||||
−0.245520 | + | 0.969391i | \(0.578959\pi\) | |||||||
\(564\) | 11413.0 | 0.852084 | ||||||||
\(565\) | 9339.47 | 0.695424 | ||||||||
\(566\) | −36276.4 | −2.69401 | ||||||||
\(567\) | −11653.7 | −0.863156 | ||||||||
\(568\) | 36818.8 | 2.71986 | ||||||||
\(569\) | −18111.7 | −1.33441 | −0.667206 | − | 0.744874i | \(-0.732510\pi\) | ||||
−0.667206 | + | 0.744874i | \(0.732510\pi\) | |||||||
\(570\) | −20609.0 | −1.51441 | ||||||||
\(571\) | −1142.62 | −0.0837428 | −0.0418714 | − | 0.999123i | \(-0.513332\pi\) | ||||
−0.0418714 | + | 0.999123i | \(0.513332\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 31686.9 | 2.31019 | ||||||||
\(574\) | 274.096 | 0.0199313 | ||||||||
\(575\) | 2073.22 | 0.150364 | ||||||||
\(576\) | −14338.8 | −1.03724 | ||||||||
\(577\) | 15361.9 | 1.10836 | 0.554181 | − | 0.832396i | \(-0.313032\pi\) | ||||
0.554181 | + | 0.832396i | \(0.313032\pi\) | |||||||
\(578\) | −50703.1 | −3.64874 | ||||||||
\(579\) | 28675.9 | 2.05826 | ||||||||
\(580\) | 702.193 | 0.0502707 | ||||||||
\(581\) | 951.089 | 0.0679136 | ||||||||
\(582\) | 742.817 | 0.0529051 | ||||||||
\(583\) | −2137.22 | −0.151826 | ||||||||
\(584\) | −9391.47 | −0.665448 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24356.4 | −1.71698 | ||||||||
\(587\) | 13019.8 | 0.915476 | 0.457738 | − | 0.889087i | \(-0.348660\pi\) | ||||
0.457738 | + | 0.889087i | \(0.348660\pi\) | |||||||
\(588\) | −16280.8 | −1.14185 | ||||||||
\(589\) | −13006.3 | −0.909873 | ||||||||
\(590\) | −15235.8 | −1.06313 | ||||||||
\(591\) | −16117.1 | −1.12177 | ||||||||
\(592\) | −14557.6 | −1.01066 | ||||||||
\(593\) | 14132.0 | 0.978634 | 0.489317 | − | 0.872106i | \(-0.337246\pi\) | ||||
0.489317 | + | 0.872106i | \(0.337246\pi\) | |||||||
\(594\) | 2227.65 | 0.153874 | ||||||||
\(595\) | −16044.6 | −1.10549 | ||||||||
\(596\) | 37365.9 | 2.56806 | ||||||||
\(597\) | 10781.2 | 0.739102 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3010.01 | −0.205318 | −0.102659 | − | 0.994717i | \(-0.532735\pi\) | ||||
−0.102659 | + | 0.994717i | \(0.532735\pi\) | |||||||
\(600\) | 8056.00 | 0.548141 | ||||||||
\(601\) | −14701.2 | −0.997795 | −0.498898 | − | 0.866661i | \(-0.666262\pi\) | ||||
−0.498898 | + | 0.866661i | \(0.666262\pi\) | |||||||
\(602\) | 11676.0 | 0.790493 | ||||||||
\(603\) | −9154.77 | −0.618261 | ||||||||
\(604\) | 7122.00 | 0.479785 | ||||||||
\(605\) | 1146.02 | 0.0770121 | ||||||||
\(606\) | 46926.8 | 3.14566 | ||||||||
\(607\) | −10025.8 | −0.670403 | −0.335201 | − | 0.942147i | \(-0.608804\pi\) | ||||
−0.335201 | + | 0.942147i | \(0.608804\pi\) | |||||||
\(608\) | 5181.54 | 0.345623 | ||||||||
\(609\) | 468.555 | 0.0311770 | ||||||||
\(610\) | −8701.96 | −0.577594 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −38735.4 | −2.55847 | ||||||||
\(613\) | 5228.64 | 0.344507 | 0.172254 | − | 0.985053i | \(-0.444895\pi\) | ||||
0.172254 | + | 0.985053i | \(0.444895\pi\) | |||||||
\(614\) | 33592.0 | 2.20792 | ||||||||
\(615\) | −276.012 | −0.0180973 | ||||||||
\(616\) | −4935.32 | −0.322808 | ||||||||
\(617\) | −18312.7 | −1.19488 | −0.597440 | − | 0.801914i | \(-0.703815\pi\) | ||||
−0.597440 | + | 0.801914i | \(0.703815\pi\) | |||||||
\(618\) | 45201.6 | 2.94219 | ||||||||
\(619\) | −16796.5 | −1.09064 | −0.545322 | − | 0.838227i | \(-0.683593\pi\) | ||||
−0.545322 | + | 0.838227i | \(0.683593\pi\) | |||||||
\(620\) | −27916.5 | −1.80831 | ||||||||
\(621\) | 2486.11 | 0.160651 | ||||||||
\(622\) | 49477.9 | 3.18952 | ||||||||
\(623\) | −15249.7 | −0.980682 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9967.26 | −0.637905 | ||||||||
\(626\) | 5168.27 | 0.329977 | ||||||||
\(627\) | 5002.48 | 0.318628 | ||||||||
\(628\) | −24985.4 | −1.58762 | ||||||||
\(629\) | 46882.0 | 2.97187 | ||||||||
\(630\) | −12873.2 | −0.814094 | ||||||||
\(631\) | −3215.37 | −0.202856 | −0.101428 | − | 0.994843i | \(-0.532341\pi\) | ||||
−0.101428 | + | 0.994843i | \(0.532341\pi\) | |||||||
\(632\) | −5430.16 | −0.341772 | ||||||||
\(633\) | −15286.3 | −0.959833 | ||||||||
\(634\) | −44520.5 | −2.78886 | ||||||||
\(635\) | −14477.1 | −0.904731 | ||||||||
\(636\) | −20023.9 | −1.24843 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −261.999 | −0.0162580 | ||||||||
\(639\) | −23311.3 | −1.44316 | ||||||||
\(640\) | 25141.3 | 1.55281 | ||||||||
\(641\) | 8865.27 | 0.546267 | 0.273134 | − | 0.961976i | \(-0.411940\pi\) | ||||
0.273134 | + | 0.961976i | \(0.411940\pi\) | |||||||
\(642\) | −71084.0 | −4.36988 | ||||||||
\(643\) | −4311.38 | −0.264424 | −0.132212 | − | 0.991221i | \(-0.542208\pi\) | ||||
−0.132212 | + | 0.991221i | \(0.542208\pi\) | |||||||
\(644\) | −11899.9 | −0.728138 | ||||||||
\(645\) | −11757.6 | −0.717757 | ||||||||
\(646\) | 39161.6 | 2.38513 | ||||||||
\(647\) | 14425.5 | 0.876544 | 0.438272 | − | 0.898842i | \(-0.355591\pi\) | ||||
0.438272 | + | 0.898842i | \(0.355591\pi\) | |||||||
\(648\) | 28258.6 | 1.71312 | ||||||||
\(649\) | 3698.23 | 0.223680 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18627.9 | −1.12149 | ||||||||
\(652\) | 53663.7 | 3.22336 | ||||||||
\(653\) | 1884.04 | 0.112907 | 0.0564535 | − | 0.998405i | \(-0.482021\pi\) | ||||
0.0564535 | + | 0.998405i | \(0.482021\pi\) | |||||||
\(654\) | 45213.7 | 2.70336 | ||||||||
\(655\) | −26881.1 | −1.60356 | ||||||||
\(656\) | −162.860 | −0.00969302 | ||||||||
\(657\) | 5946.09 | 0.353088 | ||||||||
\(658\) | −7207.47 | −0.427016 | ||||||||
\(659\) | 23210.1 | 1.37198 | 0.685991 | − | 0.727610i | \(-0.259369\pi\) | ||||
0.685991 | + | 0.727610i | \(0.259369\pi\) | |||||||
\(660\) | 10737.2 | 0.633253 | ||||||||
\(661\) | −115.397 | −0.00679037 | −0.00339518 | − | 0.999994i | \(-0.501081\pi\) | ||||
−0.00339518 | + | 0.999994i | \(0.501081\pi\) | |||||||
\(662\) | 679.108 | 0.0398705 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2306.26 | −0.134790 | ||||||||
\(665\) | 8466.90 | 0.493733 | ||||||||
\(666\) | 37615.2 | 2.18853 | ||||||||
\(667\) | −292.397 | −0.0169740 | ||||||||
\(668\) | −2645.90 | −0.153253 | ||||||||
\(669\) | 8007.30 | 0.462750 | ||||||||
\(670\) | 19865.9 | 1.14550 | ||||||||
\(671\) | 2112.25 | 0.121524 | ||||||||
\(672\) | 7421.12 | 0.426006 | ||||||||
\(673\) | −8293.86 | −0.475044 | −0.237522 | − | 0.971382i | \(-0.576335\pi\) | ||||
−0.237522 | + | 0.971382i | \(0.576335\pi\) | |||||||
\(674\) | −10903.2 | −0.623110 | ||||||||
\(675\) | 1493.89 | 0.0851847 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7252.49 | 0.411722 | 0.205861 | − | 0.978581i | \(-0.434001\pi\) | ||||
0.205861 | + | 0.978581i | \(0.434001\pi\) | |||||||
\(678\) | −32648.7 | −1.84936 | ||||||||
\(679\) | −305.175 | −0.0172482 | ||||||||
\(680\) | 38905.9 | 2.19408 | ||||||||
\(681\) | −4132.38 | −0.232530 | ||||||||
\(682\) | 10416.1 | 0.584827 | ||||||||
\(683\) | 22073.0 | 1.23661 | 0.618303 | − | 0.785940i | \(-0.287821\pi\) | ||||
0.618303 | + | 0.785940i | \(0.287821\pi\) | |||||||
\(684\) | 20441.1 | 1.14267 | ||||||||
\(685\) | 15393.7 | 0.858630 | ||||||||
\(686\) | 32605.4 | 1.81469 | ||||||||
\(687\) | 35693.0 | 1.98220 | ||||||||
\(688\) | −6937.52 | −0.384434 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 18419.6 | 1.01627 | ||||||||
\(691\) | 28633.0 | 1.57634 | 0.788170 | − | 0.615458i | \(-0.211029\pi\) | ||||
0.788170 | + | 0.615458i | \(0.211029\pi\) | |||||||
\(692\) | 55167.3 | 3.03056 | ||||||||
\(693\) | 3124.74 | 0.171283 | ||||||||
\(694\) | 39679.8 | 2.17035 | ||||||||
\(695\) | −4978.15 | −0.271701 | ||||||||
\(696\) | −1136.18 | −0.0618776 | ||||||||
\(697\) | 524.484 | 0.0285025 | ||||||||
\(698\) | 1191.68 | 0.0646213 | ||||||||
\(699\) | 13227.1 | 0.715729 | ||||||||
\(700\) | −7150.55 | −0.386093 | ||||||||
\(701\) | 15832.0 | 0.853018 | 0.426509 | − | 0.904483i | \(-0.359743\pi\) | ||||
0.426509 | + | 0.904483i | \(0.359743\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24740.1 | −1.32730 | ||||||||
\(704\) | −7552.69 | −0.404336 | ||||||||
\(705\) | 7257.84 | 0.387725 | ||||||||
\(706\) | 30620.3 | 1.63231 | ||||||||
\(707\) | −19279.2 | −1.02556 | ||||||||
\(708\) | 34649.3 | 1.83927 | ||||||||
\(709\) | −12423.3 | −0.658064 | −0.329032 | − | 0.944319i | \(-0.606722\pi\) | ||||
−0.329032 | + | 0.944319i | \(0.606722\pi\) | |||||||
\(710\) | 50585.7 | 2.67387 | ||||||||
\(711\) | 3438.04 | 0.181345 | ||||||||
\(712\) | 36978.3 | 1.94638 | ||||||||
\(713\) | 11624.6 | 0.610582 | ||||||||
\(714\) | 56088.3 | 2.93985 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 36741.9 | 1.91775 | ||||||||
\(717\) | 35835.3 | 1.86652 | ||||||||
\(718\) | −37146.8 | −1.93079 | ||||||||
\(719\) | −19323.3 | −1.00227 | −0.501137 | − | 0.865368i | \(-0.667085\pi\) | ||||
−0.501137 | + | 0.865368i | \(0.667085\pi\) | |||||||
\(720\) | 7648.86 | 0.395912 | ||||||||
\(721\) | −18570.4 | −0.959220 | ||||||||
\(722\) | 12152.4 | 0.626409 | ||||||||
\(723\) | 31880.6 | 1.63990 | ||||||||
\(724\) | −12366.8 | −0.634817 | ||||||||
\(725\) | −175.700 | −0.00900044 | ||||||||
\(726\) | −4006.23 | −0.204800 | ||||||||
\(727\) | −9754.61 | −0.497632 | −0.248816 | − | 0.968551i | \(-0.580041\pi\) | ||||
−0.248816 | + | 0.968551i | \(0.580041\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9983.85 | −0.507232 | ||||||||
\(730\) | −12903.1 | −0.654196 | ||||||||
\(731\) | 22342.0 | 1.13043 | ||||||||
\(732\) | 19790.0 | 0.999264 | ||||||||
\(733\) | 1179.05 | 0.0594123 | 0.0297061 | − | 0.999559i | \(-0.490543\pi\) | ||||
0.0297061 | + | 0.999559i | \(0.490543\pi\) | |||||||
\(734\) | −36361.2 | −1.82849 | ||||||||
\(735\) | −10353.4 | −0.519578 | ||||||||
\(736\) | −4631.09 | −0.231935 | ||||||||
\(737\) | −4822.11 | −0.241010 | ||||||||
\(738\) | 420.812 | 0.0209896 | ||||||||
\(739\) | −3361.06 | −0.167305 | −0.0836527 | − | 0.996495i | \(-0.526659\pi\) | ||||
−0.0836527 | + | 0.996495i | \(0.526659\pi\) | |||||||
\(740\) | −53101.9 | −2.63792 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12645.4 | 0.625641 | ||||||||
\(743\) | −27407.8 | −1.35329 | −0.676645 | − | 0.736309i | \(-0.736567\pi\) | ||||
−0.676645 | + | 0.736309i | \(0.736567\pi\) | |||||||
\(744\) | 45170.2 | 2.22583 | ||||||||
\(745\) | 23761.9 | 1.16855 | ||||||||
\(746\) | −7586.81 | −0.372350 | ||||||||
\(747\) | 1460.18 | 0.0715197 | ||||||||
\(748\) | −20403.1 | −0.997344 | ||||||||
\(749\) | 29203.8 | 1.42468 | ||||||||
\(750\) | 50266.5 | 2.44730 | ||||||||
\(751\) | −24340.3 | −1.18268 | −0.591338 | − | 0.806424i | \(-0.701400\pi\) | ||||
−0.591338 | + | 0.806424i | \(0.701400\pi\) | |||||||
\(752\) | 4282.47 | 0.207667 | ||||||||
\(753\) | −345.423 | −0.0167170 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4529.06 | 0.218317 | ||||||||
\(756\) | −8574.61 | −0.412507 | ||||||||
\(757\) | −29842.3 | −1.43281 | −0.716405 | − | 0.697684i | \(-0.754214\pi\) | ||||
−0.716405 | + | 0.697684i | \(0.754214\pi\) | |||||||
\(758\) | 13634.1 | 0.653314 | ||||||||
\(759\) | −4471.05 | −0.213819 | ||||||||
\(760\) | −20531.1 | −0.979921 | ||||||||
\(761\) | −21399.3 | −1.01935 | −0.509674 | − | 0.860368i | \(-0.670234\pi\) | ||||
−0.509674 | + | 0.860368i | \(0.670234\pi\) | |||||||
\(762\) | 50608.5 | 2.40598 | ||||||||
\(763\) | −18575.4 | −0.881355 | ||||||||
\(764\) | 68200.5 | 3.22959 | ||||||||
\(765\) | −24632.8 | −1.16418 | ||||||||
\(766\) | 22074.8 | 1.04125 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −49879.0 | −2.34356 | ||||||||
\(769\) | 414.640 | 0.0194438 | 0.00972190 | − | 0.999953i | \(-0.496905\pi\) | ||||
0.00972190 | + | 0.999953i | \(0.496905\pi\) | |||||||
\(770\) | −6780.70 | −0.317350 | ||||||||
\(771\) | 21808.4 | 1.01869 | ||||||||
\(772\) | 61719.9 | 2.87739 | ||||||||
\(773\) | −28186.7 | −1.31152 | −0.655760 | − | 0.754970i | \(-0.727652\pi\) | ||||
−0.655760 | + | 0.754970i | \(0.727652\pi\) | |||||||
\(774\) | 17925.8 | 0.832466 | ||||||||
\(775\) | 6985.14 | 0.323760 | ||||||||
\(776\) | 740.009 | 0.0342329 | ||||||||
\(777\) | −35433.4 | −1.63599 | ||||||||
\(778\) | −56001.7 | −2.58067 | ||||||||
\(779\) | −276.775 | −0.0127298 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12278.8 | −0.562575 | ||||||||
\(782\) | −35001.4 | −1.60057 | ||||||||
\(783\) | −210.691 | −0.00961619 | ||||||||
\(784\) | −6108.99 | −0.278288 | ||||||||
\(785\) | −15888.8 | −0.722417 | ||||||||
\(786\) | 93970.3 | 4.26439 | ||||||||
\(787\) | −1613.93 | −0.0731007 | −0.0365504 | − | 0.999332i | \(-0.511637\pi\) | ||||
−0.0365504 | + | 0.999332i | \(0.511637\pi\) | |||||||
\(788\) | −34689.2 | −1.56821 | ||||||||
\(789\) | −9059.08 | −0.408760 | ||||||||
\(790\) | −7460.56 | −0.335993 | ||||||||
\(791\) | 13413.2 | 0.602933 | ||||||||
\(792\) | −7577.07 | −0.339949 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 37886.9 | 1.69339 | ||||||||
\(795\) | −12733.7 | −0.568074 | ||||||||
\(796\) | 23204.6 | 1.03325 | ||||||||
\(797\) | 2819.19 | 0.125296 | 0.0626479 | − | 0.998036i | \(-0.480045\pi\) | ||||
0.0626479 | + | 0.998036i | \(0.480045\pi\) | |||||||
\(798\) | −29598.4 | −1.31300 | ||||||||
\(799\) | −13791.5 | −0.610649 | ||||||||
\(800\) | −2782.79 | −0.122983 | ||||||||
\(801\) | −23412.4 | −1.03275 | ||||||||
\(802\) | 55505.8 | 2.44386 | ||||||||
\(803\) | 3131.99 | 0.137641 | ||||||||
\(804\) | −45179.1 | −1.98177 | ||||||||
\(805\) | −7567.43 | −0.331325 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 39195.0 | 1.70970 | ||||||||
\(808\) | 46749.3 | 2.03544 | ||||||||
\(809\) | 29670.9 | 1.28946 | 0.644730 | − | 0.764410i | \(-0.276970\pi\) | ||||
0.644730 | + | 0.764410i | \(0.276970\pi\) | |||||||
\(810\) | 38824.9 | 1.68416 | ||||||||
\(811\) | −10375.4 | −0.449234 | −0.224617 | − | 0.974447i | \(-0.572113\pi\) | ||||
−0.224617 | + | 0.974447i | \(0.572113\pi\) | |||||||
\(812\) | 1008.48 | 0.0435847 | ||||||||
\(813\) | −16320.0 | −0.704018 | ||||||||
\(814\) | 19813.1 | 0.853131 | ||||||||
\(815\) | 34126.1 | 1.46673 | ||||||||
\(816\) | −33326.1 | −1.42971 | ||||||||
\(817\) | −11790.1 | −0.504875 | ||||||||
\(818\) | −7673.01 | −0.327971 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −594.067 | −0.0252996 | ||||||||
\(821\) | 19432.4 | 0.826058 | 0.413029 | − | 0.910718i | \(-0.364471\pi\) | ||||
0.413029 | + | 0.910718i | \(0.364471\pi\) | |||||||
\(822\) | −53812.7 | −2.28338 | ||||||||
\(823\) | −4256.77 | −0.180294 | −0.0901469 | − | 0.995928i | \(-0.528734\pi\) | ||||
−0.0901469 | + | 0.995928i | \(0.528734\pi\) | |||||||
\(824\) | 45030.7 | 1.90378 | ||||||||
\(825\) | −2686.62 | −0.113377 | ||||||||
\(826\) | −21881.5 | −0.921736 | ||||||||
\(827\) | 4083.89 | 0.171718 | 0.0858590 | − | 0.996307i | \(-0.472637\pi\) | ||||
0.0858590 | + | 0.996307i | \(0.472637\pi\) | |||||||
\(828\) | −18269.5 | −0.766800 | ||||||||
\(829\) | −18779.9 | −0.786795 | −0.393398 | − | 0.919368i | \(-0.628700\pi\) | ||||
−0.393398 | + | 0.919368i | \(0.628700\pi\) | |||||||
\(830\) | −3168.60 | −0.132510 | ||||||||
\(831\) | −43238.4 | −1.80496 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19673.7 | 0.818312 | ||||||||
\(834\) | 17402.5 | 0.722541 | ||||||||
\(835\) | −1682.59 | −0.0697348 | ||||||||
\(836\) | 10767.0 | 0.445434 | ||||||||
\(837\) | 8376.26 | 0.345909 | ||||||||
\(838\) | 65721.0 | 2.70918 | ||||||||
\(839\) | 26837.5 | 1.10433 | 0.552165 | − | 0.833735i | \(-0.313802\pi\) | ||||
0.552165 | + | 0.833735i | \(0.313802\pi\) | |||||||
\(840\) | −29405.1 | −1.20782 | ||||||||
\(841\) | −24364.2 | −0.998984 | ||||||||
\(842\) | −71483.8 | −2.92576 | ||||||||
\(843\) | −21833.0 | −0.892013 | ||||||||
\(844\) | −32901.0 | −1.34182 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11065.4 | −0.449690 | ||||||||
\(847\) | 1645.90 | 0.0667695 | ||||||||
\(848\) | −7513.51 | −0.304263 | ||||||||
\(849\) | 52463.8 | 2.12079 | ||||||||
\(850\) | −21032.1 | −0.848700 | ||||||||
\(851\) | 22111.9 | 0.890701 | ||||||||
\(852\) | −115042. | −4.62592 | ||||||||
\(853\) | −18694.5 | −0.750396 | −0.375198 | − | 0.926945i | \(-0.622425\pi\) | ||||
−0.375198 | + | 0.926945i | \(0.622425\pi\) | |||||||
\(854\) | −12497.7 | −0.500774 | ||||||||
\(855\) | 12999.0 | 0.519949 | ||||||||
\(856\) | −70815.3 | −2.82759 | ||||||||
\(857\) | −10730.7 | −0.427718 | −0.213859 | − | 0.976864i | \(-0.568603\pi\) | ||||
−0.213859 | + | 0.976864i | \(0.568603\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20797.6 | 0.826083 | 0.413042 | − | 0.910712i | \(-0.364466\pi\) | ||||
0.413042 | + | 0.910712i | \(0.364466\pi\) | |||||||
\(860\) | −25306.1 | −1.00341 | ||||||||
\(861\) | −396.405 | −0.0156904 | ||||||||
\(862\) | −46577.8 | −1.84042 | ||||||||
\(863\) | 9812.01 | 0.387027 | 0.193514 | − | 0.981098i | \(-0.438012\pi\) | ||||
0.193514 | + | 0.981098i | \(0.438012\pi\) | |||||||
\(864\) | −3336.99 | −0.131397 | ||||||||
\(865\) | 35082.3 | 1.37900 | ||||||||
\(866\) | 58837.9 | 2.30877 | ||||||||
\(867\) | 73328.1 | 2.87238 | ||||||||
\(868\) | −40093.4 | −1.56781 | ||||||||
\(869\) | 1810.92 | 0.0706920 | ||||||||
\(870\) | −1561.01 | −0.0608314 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 45042.8 | 1.74924 | ||||||||
\(873\) | −468.527 | −0.0181641 | ||||||||
\(874\) | 18470.6 | 0.714848 | ||||||||
\(875\) | −20651.2 | −0.797874 | ||||||||
\(876\) | 29344.2 | 1.13179 | ||||||||
\(877\) | 22194.0 | 0.854548 | 0.427274 | − | 0.904122i | \(-0.359474\pi\) | ||||
0.427274 | + | 0.904122i | \(0.359474\pi\) | |||||||
\(878\) | 17902.3 | 0.688123 | ||||||||
\(879\) | 35224.8 | 1.35165 | ||||||||
\(880\) | 4028.90 | 0.154334 | ||||||||
\(881\) | 30618.1 | 1.17089 | 0.585443 | − | 0.810713i | \(-0.300921\pi\) | ||||
0.585443 | + | 0.810713i | \(0.300921\pi\) | |||||||
\(882\) | 15784.9 | 0.602615 | ||||||||
\(883\) | 4940.15 | 0.188278 | 0.0941389 | − | 0.995559i | \(-0.469990\pi\) | ||||
0.0941389 | + | 0.995559i | \(0.469990\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22034.4 | 0.836925 | ||||||||
\(886\) | −79359.7 | −3.00919 | ||||||||
\(887\) | −31193.7 | −1.18081 | −0.590407 | − | 0.807105i | \(-0.701033\pi\) | ||||
−0.590407 | + | 0.807105i | \(0.701033\pi\) | |||||||
\(888\) | 85921.2 | 3.24699 | ||||||||
\(889\) | −20791.8 | −0.784402 | ||||||||
\(890\) | 50805.0 | 1.91347 | ||||||||
\(891\) | −9424.07 | −0.354342 | ||||||||
\(892\) | 17234.3 | 0.646914 | ||||||||
\(893\) | 7277.92 | 0.272728 | ||||||||
\(894\) | −83066.3 | −3.10755 | ||||||||
\(895\) | 23365.1 | 0.872636 | ||||||||
\(896\) | 36107.7 | 1.34629 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21622.1 | 0.803495 | ||||||||
\(899\) | −985.153 | −0.0365480 | ||||||||
\(900\) | −10978.0 | −0.406594 | ||||||||
\(901\) | 24196.9 | 0.894691 | ||||||||
\(902\) | 221.655 | 0.00818216 | ||||||||
\(903\) | −16886.1 | −0.622295 | ||||||||
\(904\) | −32525.3 | −1.19665 | ||||||||
\(905\) | −7864.34 | −0.288861 | ||||||||
\(906\) | −15832.6 | −0.580577 | ||||||||
\(907\) | −26746.4 | −0.979160 | −0.489580 | − | 0.871958i | \(-0.662850\pi\) | ||||
−0.489580 | + | 0.871958i | \(0.662850\pi\) | |||||||
\(908\) | −8894.21 | −0.325071 | ||||||||
\(909\) | −29598.8 | −1.08001 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25483.0 | −0.926773 | −0.463386 | − | 0.886156i | \(-0.653366\pi\) | ||||
−0.463386 | + | 0.886156i | \(0.653366\pi\) | |||||||
\(912\) | 17586.5 | 0.638539 | ||||||||
\(913\) | 769.123 | 0.0278798 | ||||||||
\(914\) | −55870.6 | −2.02192 | ||||||||
\(915\) | 12585.0 | 0.454696 | ||||||||
\(916\) | 76822.8 | 2.77107 | ||||||||
\(917\) | −38606.3 | −1.39029 | ||||||||
\(918\) | −25220.7 | −0.906762 | ||||||||
\(919\) | −41862.9 | −1.50264 | −0.751322 | − | 0.659936i | \(-0.770583\pi\) | ||||
−0.751322 | + | 0.659936i | \(0.770583\pi\) | |||||||
\(920\) | 18350.0 | 0.657589 | ||||||||
\(921\) | −48581.5 | −1.73813 | ||||||||
\(922\) | −6824.92 | −0.243782 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 15420.7 | 0.549030 | ||||||||
\(925\) | 13286.9 | 0.472292 | ||||||||
\(926\) | 14969.5 | 0.531239 | ||||||||
\(927\) | −28510.6 | −1.01015 | ||||||||
\(928\) | 392.472 | 0.0138831 | ||||||||
\(929\) | 8178.69 | 0.288842 | 0.144421 | − | 0.989516i | \(-0.453868\pi\) | ||||
0.144421 | + | 0.989516i | \(0.453868\pi\) | |||||||
\(930\) | 62059.9 | 2.18820 | ||||||||
\(931\) | −10382.0 | −0.365475 | ||||||||
\(932\) | 28469.0 | 1.00057 | ||||||||
\(933\) | −71556.1 | −2.51087 | ||||||||
\(934\) | 75649.8 | 2.65025 | ||||||||
\(935\) | −12974.9 | −0.453823 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25429.5 | −0.886600 | −0.443300 | − | 0.896373i | \(-0.646192\pi\) | ||||
−0.443300 | + | 0.896373i | \(0.646192\pi\) | |||||||
\(938\) | 28531.2 | 0.993151 | ||||||||
\(939\) | −7474.47 | −0.259766 | ||||||||
\(940\) | 15621.2 | 0.542030 | ||||||||
\(941\) | −18030.3 | −0.624625 | −0.312312 | − | 0.949979i | \(-0.601104\pi\) | ||||
−0.312312 | + | 0.949979i | \(0.601104\pi\) | |||||||
\(942\) | 55543.8 | 1.92114 | ||||||||
\(943\) | 247.373 | 0.00854249 | ||||||||
\(944\) | 13001.3 | 0.448260 | ||||||||
\(945\) | −5452.81 | −0.187704 | ||||||||
\(946\) | 9442.07 | 0.324512 | ||||||||
\(947\) | 51078.4 | 1.75272 | 0.876360 | − | 0.481657i | \(-0.159965\pi\) | ||||
0.876360 | + | 0.481657i | \(0.159965\pi\) | |||||||
\(948\) | 16966.8 | 0.581284 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 11098.9 | 0.379047 | ||||||||
\(951\) | 64386.7 | 2.19546 | ||||||||
\(952\) | 55876.2 | 1.90227 | ||||||||
\(953\) | 37024.2 | 1.25848 | 0.629239 | − | 0.777212i | \(-0.283367\pi\) | ||||
0.629239 | + | 0.777212i | \(0.283367\pi\) | |||||||
\(954\) | 19414.1 | 0.658861 | ||||||||
\(955\) | 43370.5 | 1.46957 | ||||||||
\(956\) | 77129.2 | 2.60935 | ||||||||
\(957\) | 378.909 | 0.0127987 | ||||||||
\(958\) | 46854.1 | 1.58015 | ||||||||
\(959\) | 22108.2 | 0.744432 | ||||||||
\(960\) | −44999.6 | −1.51287 | ||||||||
\(961\) | 9374.93 | 0.314690 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 44835.8 | 1.50033 | ||||||||
\(964\) | 68617.3 | 2.29255 | ||||||||
\(965\) | 39249.2 | 1.30930 | ||||||||
\(966\) | 26454.0 | 0.881102 | ||||||||
\(967\) | 45358.6 | 1.50841 | 0.754207 | − | 0.656637i | \(-0.228022\pi\) | ||||
0.754207 | + | 0.656637i | \(0.228022\pi\) | |||||||
\(968\) | −3991.08 | −0.132519 | ||||||||
\(969\) | −56636.5 | −1.87763 | ||||||||
\(970\) | 1016.71 | 0.0336541 | ||||||||
\(971\) | −20674.7 | −0.683299 | −0.341650 | − | 0.939827i | \(-0.610986\pi\) | ||||
−0.341650 | + | 0.939827i | \(0.610986\pi\) | |||||||
\(972\) | −71275.6 | −2.35202 | ||||||||
\(973\) | −7149.56 | −0.235564 | ||||||||
\(974\) | −646.839 | −0.0212793 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7425.75 | 0.243537 | ||||||||
\(977\) | −7864.58 | −0.257533 | −0.128767 | − | 0.991675i | \(-0.541102\pi\) | ||||
−0.128767 | + | 0.991675i | \(0.541102\pi\) | |||||||
\(978\) | −119297. | −3.90052 | ||||||||
\(979\) | −12332.0 | −0.402588 | ||||||||
\(980\) | −22283.8 | −0.726357 | ||||||||
\(981\) | −28518.3 | −0.928153 | ||||||||
\(982\) | −3111.62 | −0.101116 | ||||||||
\(983\) | −40089.5 | −1.30077 | −0.650384 | − | 0.759606i | \(-0.725392\pi\) | ||||
−0.650384 | + | 0.759606i | \(0.725392\pi\) | |||||||
\(984\) | 961.227 | 0.0311411 | ||||||||
\(985\) | −22059.7 | −0.713586 | ||||||||
\(986\) | 2966.27 | 0.0958066 | ||||||||
\(987\) | 10423.6 | 0.336158 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10537.6 | 0.338803 | ||||||||
\(990\) | −10410.2 | −0.334201 | ||||||||
\(991\) | −53389.6 | −1.71138 | −0.855690 | − | 0.517489i | \(-0.826867\pi\) | ||||
−0.855690 | + | 0.517489i | \(0.826867\pi\) | |||||||
\(992\) | −15603.2 | −0.499397 | ||||||||
\(993\) | −982.142 | −0.0313870 | ||||||||
\(994\) | 72650.6 | 2.31825 | ||||||||
\(995\) | 14756.4 | 0.470160 | ||||||||
\(996\) | 7206.04 | 0.229249 | ||||||||
\(997\) | 27207.0 | 0.864246 | 0.432123 | − | 0.901815i | \(-0.357765\pi\) | ||||
0.432123 | + | 0.901815i | \(0.357765\pi\) | |||||||
\(998\) | 82841.2 | 2.62755 | ||||||||
\(999\) | 15933.0 | 0.504604 |
(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 | 1859.4.a.n.1.3 | ✓ | 39 | |
13.12 | even | 2 | 1859.4.a.o.1.37 | yes | 39 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1859.4.a.n.1.3 | ✓ | 39 | 1.1 | even | 1 | trivial | |
1859.4.a.o.1.37 | yes | 39 | 13.12 | even | 2 |