Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,4,Mod(1,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, 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("1323.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.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: | \(78.0595269376\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 40x^{4} + 453x^{2} - 1278 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 189) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.70753\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.70753 | −1.66436 | −0.832182 | − | 0.554503i | \(-0.812908\pi\) | ||||
−0.832182 | + | 0.554503i | \(0.812908\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 14.1608 | 1.77011 | ||||||||
\(5\) | −0.830453 | −0.0742780 | −0.0371390 | − | 0.999310i | \(-0.511824\pi\) | ||||
−0.0371390 | + | 0.999310i | \(0.511824\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −29.0024 | −1.28174 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.90938 | 0.123626 | ||||||||
\(11\) | 68.2503 | 1.87075 | 0.935374 | − | 0.353659i | \(-0.115063\pi\) | ||||
0.935374 | + | 0.353659i | \(0.115063\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −35.7721 | −0.763184 | −0.381592 | − | 0.924331i | \(-0.624624\pi\) | ||||
−0.381592 | + | 0.924331i | \(0.624624\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 23.2429 | 0.363170 | ||||||||
\(17\) | −14.6779 | −0.209406 | −0.104703 | − | 0.994504i | \(-0.533389\pi\) | ||||
−0.104703 | + | 0.994504i | \(0.533389\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 86.7693 | 1.04770 | 0.523849 | − | 0.851811i | \(-0.324496\pi\) | ||||
0.523849 | + | 0.851811i | \(0.324496\pi\) | |||||||
\(20\) | −11.7599 | −0.131480 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −321.290 | −3.11361 | ||||||||
\(23\) | −58.4087 | −0.529524 | −0.264762 | − | 0.964314i | \(-0.585293\pi\) | ||||
−0.264762 | + | 0.964314i | \(0.585293\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.310 | −0.994483 | ||||||||
\(26\) | 168.398 | 1.27022 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 67.1398 | 0.429915 | 0.214958 | − | 0.976623i | \(-0.431039\pi\) | ||||
0.214958 | + | 0.976623i | \(0.431039\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −69.5002 | −0.402665 | −0.201332 | − | 0.979523i | \(-0.564527\pi\) | ||||
−0.201332 | + | 0.979523i | \(0.564527\pi\) | |||||||
\(32\) | 122.603 | 0.677290 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 69.0965 | 0.348528 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −289.240 | −1.28516 | −0.642578 | − | 0.766220i | \(-0.722135\pi\) | ||||
−0.642578 | + | 0.766220i | \(0.722135\pi\) | |||||||
\(38\) | −408.469 | −1.74375 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 24.0851 | 0.0952048 | ||||||||
\(41\) | 357.750 | 1.36271 | 0.681355 | − | 0.731953i | \(-0.261391\pi\) | ||||
0.681355 | + | 0.731953i | \(0.261391\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −235.801 | −0.836263 | −0.418132 | − | 0.908386i | \(-0.637315\pi\) | ||||
−0.418132 | + | 0.908386i | \(0.637315\pi\) | |||||||
\(44\) | 966.482 | 3.31142 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 274.961 | 0.881320 | ||||||||
\(47\) | −450.067 | −1.39679 | −0.698394 | − | 0.715714i | \(-0.746102\pi\) | ||||
−0.698394 | + | 0.715714i | \(0.746102\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 585.195 | 1.65518 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −506.563 | −1.35092 | ||||||||
\(53\) | −172.464 | −0.446977 | −0.223489 | − | 0.974707i | \(-0.571745\pi\) | ||||
−0.223489 | + | 0.974707i | \(0.571745\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −56.6787 | −0.138955 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −316.063 | −0.715535 | ||||||||
\(59\) | 445.856 | 0.983823 | 0.491912 | − | 0.870645i | \(-0.336298\pi\) | ||||
0.491912 | + | 0.870645i | \(0.336298\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 476.314 | 0.999767 | 0.499883 | − | 0.866093i | \(-0.333376\pi\) | ||||
0.499883 | + | 0.866093i | \(0.333376\pi\) | |||||||
\(62\) | 327.174 | 0.670180 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −763.099 | −1.49043 | ||||||||
\(65\) | 29.7070 | 0.0566878 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −804.320 | −1.46662 | −0.733309 | − | 0.679896i | \(-0.762025\pi\) | ||||
−0.733309 | + | 0.679896i | \(0.762025\pi\) | |||||||
\(68\) | −207.851 | −0.370671 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −353.412 | −0.590737 | −0.295368 | − | 0.955383i | \(-0.595442\pi\) | ||||
−0.295368 | + | 0.955383i | \(0.595442\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −778.045 | −1.24744 | −0.623721 | − | 0.781647i | \(-0.714380\pi\) | ||||
−0.623721 | + | 0.781647i | \(0.714380\pi\) | |||||||
\(74\) | 1361.61 | 2.13897 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1228.73 | 1.85454 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −74.1996 | −0.105672 | −0.0528361 | − | 0.998603i | \(-0.516826\pi\) | ||||
−0.0528361 | + | 0.998603i | \(0.516826\pi\) | |||||||
\(80\) | −19.3021 | −0.0269755 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1684.12 | −2.26804 | ||||||||
\(83\) | 1168.49 | 1.54529 | 0.772643 | − | 0.634840i | \(-0.218934\pi\) | ||||
0.772643 | + | 0.634840i | \(0.218934\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.1893 | 0.0155543 | ||||||||
\(86\) | 1110.04 | 1.39185 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1979.42 | −2.39781 | ||||||||
\(89\) | −1514.72 | −1.80405 | −0.902023 | − | 0.431687i | \(-0.857918\pi\) | ||||
−0.902023 | + | 0.431687i | \(0.857918\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −827.116 | −0.937313 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2118.70 | 2.32476 | ||||||||
\(95\) | −72.0579 | −0.0778209 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1631.46 | 1.70772 | 0.853862 | − | 0.520499i | \(-0.174254\pi\) | ||||
0.853862 | + | 0.520499i | \(0.174254\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1760.34 | −1.76034 | ||||||||
\(101\) | −1205.73 | −1.18787 | −0.593934 | − | 0.804514i | \(-0.702426\pi\) | ||||
−0.593934 | + | 0.804514i | \(0.702426\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −485.363 | −0.464313 | −0.232156 | − | 0.972679i | \(-0.574578\pi\) | ||||
−0.232156 | + | 0.972679i | \(0.574578\pi\) | |||||||
\(104\) | 1037.48 | 0.978201 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 811.881 | 0.743933 | ||||||||
\(107\) | 258.101 | 0.233192 | 0.116596 | − | 0.993179i | \(-0.462802\pi\) | ||||
0.116596 | + | 0.993179i | \(0.462802\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 581.246 | 0.510764 | 0.255382 | − | 0.966840i | \(-0.417799\pi\) | ||||
0.255382 | + | 0.966840i | \(0.417799\pi\) | |||||||
\(110\) | 266.817 | 0.231272 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −708.244 | −0.589610 | −0.294805 | − | 0.955557i | \(-0.595255\pi\) | ||||
−0.294805 | + | 0.955557i | \(0.595255\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 48.5057 | 0.0393320 | ||||||||
\(116\) | 950.756 | 0.760996 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2098.88 | −1.63744 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3327.10 | 2.49970 | ||||||||
\(122\) | −2242.26 | −1.66398 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −984.182 | −0.712759 | ||||||||
\(125\) | 207.041 | 0.148146 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2348.04 | 1.64059 | 0.820296 | − | 0.571939i | \(-0.193809\pi\) | ||||
0.820296 | + | 0.571939i | \(0.193809\pi\) | |||||||
\(128\) | 2611.49 | 1.80332 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −139.847 | −0.0943491 | ||||||||
\(131\) | 2405.82 | 1.60456 | 0.802279 | − | 0.596949i | \(-0.203621\pi\) | ||||
0.802279 | + | 0.596949i | \(0.203621\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3786.36 | 2.44098 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 425.693 | 0.268403 | ||||||||
\(137\) | 1187.55 | 0.740579 | 0.370289 | − | 0.928916i | \(-0.379258\pi\) | ||||
0.370289 | + | 0.928916i | \(0.379258\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −712.439 | −0.434736 | −0.217368 | − | 0.976090i | \(-0.569747\pi\) | ||||
−0.217368 | + | 0.976090i | \(0.569747\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1663.70 | 0.983201 | ||||||||
\(143\) | −2441.46 | −1.42773 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −55.7564 | −0.0319332 | ||||||||
\(146\) | 3662.67 | 2.07620 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4095.89 | −2.27486 | ||||||||
\(149\) | 2209.24 | 1.21468 | 0.607342 | − | 0.794441i | \(-0.292236\pi\) | ||||
0.607342 | + | 0.794441i | \(0.292236\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −546.983 | −0.294787 | −0.147394 | − | 0.989078i | \(-0.547088\pi\) | ||||
−0.147394 | + | 0.989078i | \(0.547088\pi\) | |||||||
\(152\) | −2516.52 | −1.34287 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 57.7166 | 0.0299091 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1870.19 | 0.950686 | 0.475343 | − | 0.879801i | \(-0.342324\pi\) | ||||
0.475343 | + | 0.879801i | \(0.342324\pi\) | |||||||
\(158\) | 349.297 | 0.175877 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −101.816 | −0.0503078 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3037.40 | −1.45955 | −0.729777 | − | 0.683685i | \(-0.760376\pi\) | ||||
−0.729777 | + | 0.683685i | \(0.760376\pi\) | |||||||
\(164\) | 5066.04 | 2.41214 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5500.72 | −2.57192 | ||||||||
\(167\) | −2967.09 | −1.37485 | −0.687426 | − | 0.726255i | \(-0.741259\pi\) | ||||
−0.687426 | + | 0.726255i | \(0.741259\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −917.358 | −0.417550 | ||||||||
\(170\) | −57.3814 | −0.0258879 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3339.14 | −1.48028 | ||||||||
\(173\) | 3866.81 | 1.69935 | 0.849677 | − | 0.527303i | \(-0.176797\pi\) | ||||
0.849677 | + | 0.527303i | \(0.176797\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1586.33 | 0.679399 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7130.60 | 3.00259 | ||||||||
\(179\) | −334.726 | −0.139769 | −0.0698844 | − | 0.997555i | \(-0.522263\pi\) | ||||
−0.0698844 | + | 0.997555i | \(0.522263\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1564.56 | −0.642502 | −0.321251 | − | 0.946994i | \(-0.604103\pi\) | ||||
−0.321251 | + | 0.946994i | \(0.604103\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1693.99 | 0.678710 | ||||||||
\(185\) | 240.200 | 0.0954588 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1001.77 | −0.391746 | ||||||||
\(188\) | −6373.33 | −2.47246 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 339.215 | 0.129522 | ||||||||
\(191\) | −3067.14 | −1.16194 | −0.580971 | − | 0.813925i | \(-0.697327\pi\) | ||||
−0.580971 | + | 0.813925i | \(0.697327\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2223.60 | −0.829316 | −0.414658 | − | 0.909977i | \(-0.636099\pi\) | ||||
−0.414658 | + | 0.909977i | \(0.636099\pi\) | |||||||
\(194\) | −7680.13 | −2.84227 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1856.18 | −0.671306 | −0.335653 | − | 0.941986i | \(-0.608957\pi\) | ||||
−0.335653 | + | 0.941986i | \(0.608957\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −993.602 | −0.353943 | −0.176971 | − | 0.984216i | \(-0.556630\pi\) | ||||
−0.176971 | + | 0.984216i | \(0.556630\pi\) | |||||||
\(200\) | 3605.30 | 1.27467 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5676.02 | 1.97704 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −297.094 | −0.101219 | ||||||||
\(206\) | 2284.86 | 0.772785 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −831.446 | −0.277165 | ||||||||
\(209\) | 5922.03 | 1.95998 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −545.079 | −0.177843 | −0.0889213 | − | 0.996039i | \(-0.528342\pi\) | ||||
−0.0889213 | + | 0.996039i | \(0.528342\pi\) | |||||||
\(212\) | −2442.24 | −0.791197 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1215.02 | −0.388116 | ||||||||
\(215\) | 195.822 | 0.0621160 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2736.23 | −0.850097 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −802.618 | −0.245966 | ||||||||
\(221\) | 525.058 | 0.159815 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3446.72 | −1.03502 | −0.517510 | − | 0.855677i | \(-0.673141\pi\) | ||||
−0.517510 | + | 0.855677i | \(0.673141\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3334.08 | 0.981326 | ||||||||
\(227\) | 486.297 | 0.142188 | 0.0710940 | − | 0.997470i | \(-0.477351\pi\) | ||||
0.0710940 | + | 0.997470i | \(0.477351\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4214.68 | 1.21622 | 0.608109 | − | 0.793853i | \(-0.291928\pi\) | ||||
0.608109 | + | 0.793853i | \(0.291928\pi\) | |||||||
\(230\) | −228.342 | −0.0654627 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1947.21 | −0.551038 | ||||||||
\(233\) | 1099.34 | 0.309100 | 0.154550 | − | 0.987985i | \(-0.450607\pi\) | ||||
0.154550 | + | 0.987985i | \(0.450607\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 373.760 | 0.103751 | ||||||||
\(236\) | 6313.71 | 1.74147 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4558.99 | −1.23388 | −0.616939 | − | 0.787011i | \(-0.711627\pi\) | ||||
−0.616939 | + | 0.787011i | \(0.711627\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1089.40 | −0.291181 | −0.145591 | − | 0.989345i | \(-0.546508\pi\) | ||||
−0.145591 | + | 0.989345i | \(0.546508\pi\) | |||||||
\(242\) | −15662.4 | −4.16041 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6745.01 | 1.76969 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3103.92 | −0.799586 | ||||||||
\(248\) | 2015.67 | 0.516110 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −974.650 | −0.246569 | ||||||||
\(251\) | −6356.75 | −1.59855 | −0.799273 | − | 0.600969i | \(-0.794782\pi\) | ||||
−0.799273 | + | 0.600969i | \(0.794782\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3986.41 | −0.990606 | ||||||||
\(254\) | −11053.5 | −2.73054 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6188.88 | −1.51096 | ||||||||
\(257\) | 1063.43 | 0.258113 | 0.129056 | − | 0.991637i | \(-0.458805\pi\) | ||||
0.129056 | + | 0.991637i | \(0.458805\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 420.677 | 0.100343 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11325.5 | −2.67057 | ||||||||
\(263\) | −3674.59 | −0.861539 | −0.430770 | − | 0.902462i | \(-0.641758\pi\) | ||||
−0.430770 | + | 0.902462i | \(0.641758\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 143.224 | 0.0332006 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11389.9 | −2.59607 | ||||||||
\(269\) | −6959.94 | −1.57753 | −0.788764 | − | 0.614696i | \(-0.789279\pi\) | ||||
−0.788764 | + | 0.614696i | \(0.789279\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6595.78 | −1.47847 | −0.739235 | − | 0.673448i | \(-0.764813\pi\) | ||||
−0.739235 | + | 0.673448i | \(0.764813\pi\) | |||||||
\(272\) | −341.155 | −0.0760499 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5590.43 | −1.23259 | ||||||||
\(275\) | −8484.22 | −1.86043 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3121.06 | −0.676990 | −0.338495 | − | 0.940968i | \(-0.609918\pi\) | ||||
−0.338495 | + | 0.940968i | \(0.609918\pi\) | |||||||
\(278\) | 3353.83 | 0.723559 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1662.38 | −0.352915 | −0.176457 | − | 0.984308i | \(-0.556464\pi\) | ||||
−0.176457 | + | 0.984308i | \(0.556464\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 453.279 | 0.0952107 | 0.0476053 | − | 0.998866i | \(-0.484841\pi\) | ||||
0.0476053 | + | 0.998866i | \(0.484841\pi\) | |||||||
\(284\) | −5004.62 | −1.04567 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11493.2 | 2.37625 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4697.56 | −0.956149 | ||||||||
\(290\) | 262.475 | 0.0531485 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11017.8 | −2.20811 | ||||||||
\(293\) | 772.774 | 0.154082 | 0.0770408 | − | 0.997028i | \(-0.475453\pi\) | ||||
0.0770408 | + | 0.997028i | \(0.475453\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −370.263 | −0.0730764 | ||||||||
\(296\) | 8388.65 | 1.64723 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10400.1 | −2.02168 | ||||||||
\(299\) | 2089.40 | 0.404124 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2574.94 | 0.490633 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2016.77 | 0.380492 | ||||||||
\(305\) | −395.557 | −0.0742607 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4193.64 | 0.779621 | 0.389810 | − | 0.920895i | \(-0.372541\pi\) | ||||
0.389810 | + | 0.920895i | \(0.372541\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −271.703 | −0.0497796 | ||||||||
\(311\) | 399.740 | 0.0728848 | 0.0364424 | − | 0.999336i | \(-0.488397\pi\) | ||||
0.0364424 | + | 0.999336i | \(0.488397\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3730.48 | 0.673672 | 0.336836 | − | 0.941563i | \(-0.390643\pi\) | ||||
0.336836 | + | 0.941563i | \(0.390643\pi\) | |||||||
\(314\) | −8803.99 | −1.58229 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1050.73 | −0.187051 | ||||||||
\(317\) | −8373.47 | −1.48360 | −0.741800 | − | 0.670622i | \(-0.766027\pi\) | ||||
−0.741800 | + | 0.670622i | \(0.766027\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4582.31 | 0.804263 | ||||||||
\(320\) | 633.718 | 0.110706 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1273.59 | −0.219394 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4446.84 | 0.758973 | ||||||||
\(326\) | 14298.6 | 2.42923 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10375.6 | −1.74664 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1349.72 | −0.224130 | −0.112065 | − | 0.993701i | \(-0.535747\pi\) | ||||
−0.112065 | + | 0.993701i | \(0.535747\pi\) | |||||||
\(332\) | 16546.9 | 2.73532 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13967.7 | 2.28825 | ||||||||
\(335\) | 667.950 | 0.108937 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6629.72 | −1.07164 | −0.535822 | − | 0.844331i | \(-0.679998\pi\) | ||||
−0.535822 | + | 0.844331i | \(0.679998\pi\) | |||||||
\(338\) | 4318.49 | 0.694955 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 172.610 | 0.0275327 | ||||||||
\(341\) | −4743.41 | −0.753284 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6838.79 | 1.07187 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18203.1 | −2.82834 | ||||||||
\(347\) | −4952.94 | −0.766246 | −0.383123 | − | 0.923697i | \(-0.625152\pi\) | ||||
−0.383123 | + | 0.923697i | \(0.625152\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4498.12 | −0.689911 | −0.344955 | − | 0.938619i | \(-0.612106\pi\) | ||||
−0.344955 | + | 0.938619i | \(0.612106\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8367.67 | 1.26704 | ||||||||
\(353\) | 1613.35 | 0.243258 | 0.121629 | − | 0.992576i | \(-0.461188\pi\) | ||||
0.121629 | + | 0.992576i | \(0.461188\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 293.492 | 0.0438787 | ||||||||
\(356\) | −21449.7 | −3.19335 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1575.73 | 0.232626 | ||||||||
\(359\) | −13186.9 | −1.93866 | −0.969328 | − | 0.245770i | \(-0.920959\pi\) | ||||
−0.969328 | + | 0.245770i | \(0.920959\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 669.919 | 0.0976700 | ||||||||
\(362\) | 7365.22 | 1.06936 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 646.130 | 0.0926575 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5103.39 | 0.725871 | 0.362936 | − | 0.931814i | \(-0.381774\pi\) | ||||
0.362936 | + | 0.931814i | \(0.381774\pi\) | |||||||
\(368\) | −1357.58 | −0.192307 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1130.75 | −0.158878 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1459.19 | −0.202557 | −0.101279 | − | 0.994858i | \(-0.532293\pi\) | ||||
−0.101279 | + | 0.994858i | \(0.532293\pi\) | |||||||
\(374\) | 4715.85 | 0.652008 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13053.0 | 1.79031 | ||||||||
\(377\) | −2401.73 | −0.328104 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2332.75 | 0.316162 | 0.158081 | − | 0.987426i | \(-0.449469\pi\) | ||||
0.158081 | + | 0.987426i | \(0.449469\pi\) | |||||||
\(380\) | −1020.40 | −0.137751 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14438.7 | 1.93389 | ||||||||
\(383\) | 5651.11 | 0.753938 | 0.376969 | − | 0.926226i | \(-0.376966\pi\) | ||||
0.376969 | + | 0.926226i | \(0.376966\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10467.7 | 1.38028 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 23102.8 | 3.02285 | ||||||||
\(389\) | 9040.82 | 1.17838 | 0.589188 | − | 0.807996i | \(-0.299448\pi\) | ||||
0.589188 | + | 0.807996i | \(0.299448\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 857.314 | 0.110886 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8738.02 | 1.11730 | ||||||||
\(395\) | 61.6193 | 0.00784912 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3524.35 | 0.445547 | 0.222774 | − | 0.974870i | \(-0.428489\pi\) | ||||
0.222774 | + | 0.974870i | \(0.428489\pi\) | |||||||
\(398\) | 4677.41 | 0.589089 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2889.33 | −0.361166 | ||||||||
\(401\) | 4469.81 | 0.556638 | 0.278319 | − | 0.960489i | \(-0.410223\pi\) | ||||
0.278319 | + | 0.960489i | \(0.410223\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2486.17 | 0.307307 | ||||||||
\(404\) | −17074.2 | −2.10265 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19740.7 | −2.40420 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7532.36 | −0.910639 | −0.455320 | − | 0.890328i | \(-0.650475\pi\) | ||||
−0.455320 | + | 0.890328i | \(0.650475\pi\) | |||||||
\(410\) | 1398.58 | 0.168466 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6873.15 | −0.821882 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −970.379 | −0.114781 | ||||||||
\(416\) | −4385.75 | −0.516897 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −27878.2 | −3.26212 | ||||||||
\(419\) | 15486.4 | 1.80563 | 0.902814 | − | 0.430031i | \(-0.141498\pi\) | ||||
0.902814 | + | 0.430031i | \(0.141498\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4408.87 | 0.510393 | 0.255196 | − | 0.966889i | \(-0.417860\pi\) | ||||
0.255196 | + | 0.966889i | \(0.417860\pi\) | |||||||
\(422\) | 2565.98 | 0.295995 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5001.88 | 0.572907 | ||||||||
\(425\) | 1824.61 | 0.208251 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3654.93 | 0.412774 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −921.837 | −0.103384 | ||||||||
\(431\) | −10356.6 | −1.15745 | −0.578726 | − | 0.815522i | \(-0.696450\pi\) | ||||
−0.578726 | + | 0.815522i | \(0.696450\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1398.15 | −0.155175 | −0.0775875 | − | 0.996986i | \(-0.524722\pi\) | ||||
−0.0775875 | + | 0.996986i | \(0.524722\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8230.94 | 0.904107 | ||||||||
\(437\) | −5068.08 | −0.554781 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3449.32 | −0.375005 | −0.187502 | − | 0.982264i | \(-0.560039\pi\) | ||||
−0.187502 | + | 0.982264i | \(0.560039\pi\) | |||||||
\(440\) | 1643.82 | 0.178104 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2471.73 | −0.265991 | ||||||||
\(443\) | 2244.65 | 0.240737 | 0.120369 | − | 0.992729i | \(-0.461592\pi\) | ||||
0.120369 | + | 0.992729i | \(0.461592\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1257.91 | 0.134001 | ||||||||
\(446\) | 16225.6 | 1.72265 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7639.18 | −0.802929 | −0.401465 | − | 0.915875i | \(-0.631499\pi\) | ||||
−0.401465 | + | 0.915875i | \(0.631499\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24416.5 | 2.54929 | ||||||||
\(452\) | −10029.3 | −1.04367 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2289.26 | −0.236652 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 540.823 | 0.0553581 | 0.0276790 | − | 0.999617i | \(-0.491188\pi\) | ||||
0.0276790 | + | 0.999617i | \(0.491188\pi\) | |||||||
\(458\) | −19840.8 | −2.02423 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 686.881 | 0.0696217 | ||||||||
\(461\) | 8627.25 | 0.871608 | 0.435804 | − | 0.900042i | \(-0.356464\pi\) | ||||
0.435804 | + | 0.900042i | \(0.356464\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4497.71 | 0.451461 | 0.225730 | − | 0.974190i | \(-0.427523\pi\) | ||||
0.225730 | + | 0.974190i | \(0.427523\pi\) | |||||||
\(464\) | 1560.52 | 0.156132 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5175.19 | −0.514455 | ||||||||
\(467\) | −2493.07 | −0.247035 | −0.123518 | − | 0.992342i | \(-0.539418\pi\) | ||||
−0.123518 | + | 0.992342i | \(0.539418\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1759.48 | −0.172679 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12930.9 | −1.26100 | ||||||||
\(473\) | −16093.5 | −1.56444 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10786.3 | −1.04192 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 21461.6 | 2.05362 | ||||||||
\(479\) | −8339.27 | −0.795472 | −0.397736 | − | 0.917500i | \(-0.630204\pi\) | ||||
−0.397736 | + | 0.917500i | \(0.630204\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10346.7 | 0.980811 | ||||||||
\(482\) | 5128.41 | 0.484632 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 47114.6 | 4.42474 | ||||||||
\(485\) | −1354.85 | −0.126846 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3104.85 | −0.288899 | −0.144450 | − | 0.989512i | \(-0.546141\pi\) | ||||
−0.144450 | + | 0.989512i | \(0.546141\pi\) | |||||||
\(488\) | −13814.2 | −1.28144 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −496.579 | −0.0456421 | −0.0228211 | − | 0.999740i | \(-0.507265\pi\) | ||||
−0.0228211 | + | 0.999740i | \(0.507265\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −985.468 | −0.0900269 | ||||||||
\(494\) | 14611.8 | 1.33080 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1615.38 | −0.146236 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13253.6 | −1.18900 | −0.594501 | − | 0.804095i | \(-0.702650\pi\) | ||||
−0.594501 | + | 0.804095i | \(0.702650\pi\) | |||||||
\(500\) | 2931.87 | 0.262234 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 29924.6 | 2.66056 | ||||||||
\(503\) | −1625.59 | −0.144099 | −0.0720493 | − | 0.997401i | \(-0.522954\pi\) | ||||
−0.0720493 | + | 0.997401i | \(0.522954\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1001.30 | 0.0882325 | ||||||||
\(506\) | 18766.1 | 1.64873 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 33250.3 | 2.90402 | ||||||||
\(509\) | −7083.05 | −0.616799 | −0.308399 | − | 0.951257i | \(-0.599793\pi\) | ||||
−0.308399 | + | 0.951257i | \(0.599793\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 8242.42 | 0.711459 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5006.14 | −0.429594 | ||||||||
\(515\) | 403.071 | 0.0344882 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30717.2 | −2.61304 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −861.575 | −0.0726588 | ||||||||
\(521\) | −16565.3 | −1.39298 | −0.696489 | − | 0.717568i | \(-0.745255\pi\) | ||||
−0.696489 | + | 0.717568i | \(0.745255\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6472.69 | −0.541168 | −0.270584 | − | 0.962696i | \(-0.587217\pi\) | ||||
−0.270584 | + | 0.962696i | \(0.587217\pi\) | |||||||
\(524\) | 34068.4 | 2.84024 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17298.2 | 1.43391 | ||||||||
\(527\) | 1020.11 | 0.0843204 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8755.43 | −0.719605 | ||||||||
\(530\) | −674.229 | −0.0552578 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12797.5 | −1.04000 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −214.341 | −0.0173210 | ||||||||
\(536\) | 23327.2 | 1.87982 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 32764.1 | 2.62558 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3388.92 | −0.269318 | −0.134659 | − | 0.990892i | \(-0.542994\pi\) | ||||
−0.134659 | + | 0.990892i | \(0.542994\pi\) | |||||||
\(542\) | 31049.8 | 2.46071 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1799.54 | −0.141829 | ||||||||
\(545\) | −482.698 | −0.0379385 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10055.2 | 0.785980 | 0.392990 | − | 0.919543i | \(-0.371441\pi\) | ||||
0.392990 | + | 0.919543i | \(0.371441\pi\) | |||||||
\(548\) | 16816.7 | 1.31090 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 39939.7 | 3.09643 | ||||||||
\(551\) | 5825.67 | 0.450421 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 14692.5 | 1.12676 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10088.7 | −0.769529 | ||||||||
\(557\) | 5632.51 | 0.428469 | 0.214234 | − | 0.976782i | \(-0.431274\pi\) | ||||
0.214234 | + | 0.976782i | \(0.431274\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8435.10 | 0.638223 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7825.68 | 0.587378 | ||||||||
\(563\) | −1450.41 | −0.108575 | −0.0542874 | − | 0.998525i | \(-0.517289\pi\) | ||||
−0.0542874 | + | 0.998525i | \(0.517289\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 588.163 | 0.0437951 | ||||||||
\(566\) | −2133.82 | −0.158465 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10249.8 | 0.757169 | ||||||||
\(569\) | 16030.4 | 1.18107 | 0.590536 | − | 0.807012i | \(-0.298916\pi\) | ||||
0.590536 | + | 0.807012i | \(0.298916\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16540.8 | −1.21228 | −0.606139 | − | 0.795359i | \(-0.707282\pi\) | ||||
−0.606139 | + | 0.795359i | \(0.707282\pi\) | |||||||
\(572\) | −34573.1 | −2.52723 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7260.80 | 0.526602 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2039.27 | −0.147133 | −0.0735666 | − | 0.997290i | \(-0.523438\pi\) | ||||
−0.0735666 | + | 0.997290i | \(0.523438\pi\) | |||||||
\(578\) | 22113.9 | 1.59138 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −789.558 | −0.0565252 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11770.7 | −0.836182 | ||||||||
\(584\) | 22565.2 | 1.59889 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3637.86 | −0.256448 | ||||||||
\(587\) | −20392.1 | −1.43385 | −0.716927 | − | 0.697148i | \(-0.754452\pi\) | ||||
−0.716927 | + | 0.697148i | \(0.754452\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6030.49 | −0.421871 | ||||||||
\(590\) | 1743.02 | 0.121626 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6722.77 | −0.466730 | ||||||||
\(593\) | 20269.0 | 1.40362 | 0.701810 | − | 0.712364i | \(-0.252375\pi\) | ||||
0.701810 | + | 0.712364i | \(0.252375\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 31284.7 | 2.15012 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9835.91 | −0.672609 | ||||||||
\(599\) | 22317.8 | 1.52234 | 0.761169 | − | 0.648554i | \(-0.224626\pi\) | ||||
0.761169 | + | 0.648554i | \(0.224626\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1880.78 | 0.127652 | 0.0638259 | − | 0.997961i | \(-0.479670\pi\) | ||||
0.0638259 | + | 0.997961i | \(0.479670\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7745.74 | −0.521804 | ||||||||
\(605\) | −2763.00 | −0.185673 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16361.6 | −1.09407 | −0.547033 | − | 0.837111i | \(-0.684243\pi\) | ||||
−0.547033 | + | 0.837111i | \(0.684243\pi\) | |||||||
\(608\) | 10638.2 | 0.709595 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1862.09 | 0.123597 | ||||||||
\(611\) | 16099.8 | 1.06601 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15921.4 | −1.04904 | −0.524518 | − | 0.851399i | \(-0.675755\pi\) | ||||
−0.524518 | + | 0.851399i | \(0.675755\pi\) | |||||||
\(614\) | −19741.7 | −1.29757 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7690.80 | −0.501815 | −0.250908 | − | 0.968011i | \(-0.580729\pi\) | ||||
−0.250908 | + | 0.968011i | \(0.580729\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −604.012 | −0.0392202 | −0.0196101 | − | 0.999808i | \(-0.506242\pi\) | ||||
−0.0196101 | + | 0.999808i | \(0.506242\pi\) | |||||||
\(620\) | 817.317 | 0.0529423 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1881.79 | −0.121307 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15366.9 | 0.983479 | ||||||||
\(626\) | −17561.3 | −1.12123 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 26483.5 | 1.68281 | ||||||||
\(629\) | 4245.43 | 0.269120 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10806.1 | −0.681752 | −0.340876 | − | 0.940108i | \(-0.610724\pi\) | ||||
−0.340876 | + | 0.940108i | \(0.610724\pi\) | |||||||
\(632\) | 2151.97 | 0.135444 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 39418.4 | 2.46925 | ||||||||
\(635\) | −1949.94 | −0.121860 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −21571.4 | −1.33859 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2168.72 | −0.133947 | ||||||||
\(641\) | 4447.62 | 0.274057 | 0.137029 | − | 0.990567i | \(-0.456245\pi\) | ||||
0.137029 | + | 0.990567i | \(0.456245\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13531.3 | 0.829897 | 0.414949 | − | 0.909845i | \(-0.363800\pi\) | ||||
0.414949 | + | 0.909845i | \(0.363800\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5995.46 | 0.365152 | ||||||||
\(647\) | −18976.9 | −1.15311 | −0.576553 | − | 0.817059i | \(-0.695603\pi\) | ||||
−0.576553 | + | 0.817059i | \(0.695603\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30429.8 | 1.84049 | ||||||||
\(650\) | −20933.6 | −1.26321 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −43012.1 | −2.58357 | ||||||||
\(653\) | 8796.72 | 0.527171 | 0.263585 | − | 0.964636i | \(-0.415095\pi\) | ||||
0.263585 | + | 0.964636i | \(0.415095\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1997.92 | −0.119183 | ||||||||
\(656\) | 8315.13 | 0.494895 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24279.6 | 1.43520 | 0.717601 | − | 0.696455i | \(-0.245240\pi\) | ||||
0.717601 | + | 0.696455i | \(0.245240\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25635.3 | −1.50847 | −0.754234 | − | 0.656605i | \(-0.771992\pi\) | ||||
−0.754234 | + | 0.656605i | \(0.771992\pi\) | |||||||
\(662\) | 6353.83 | 0.373034 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −33889.1 | −1.98065 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3921.54 | −0.227650 | ||||||||
\(668\) | −42016.5 | −2.43363 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3144.40 | −0.181311 | ||||||||
\(671\) | 32508.6 | 1.87031 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23355.1 | −1.33770 | −0.668852 | − | 0.743396i | \(-0.733214\pi\) | ||||
−0.668852 | + | 0.743396i | \(0.733214\pi\) | |||||||
\(674\) | 31209.6 | 1.78361 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12990.6 | −0.739108 | ||||||||
\(677\) | 17993.7 | 1.02150 | 0.510750 | − | 0.859730i | \(-0.329368\pi\) | ||||
0.510750 | + | 0.859730i | \(0.329368\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −353.518 | −0.0199365 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 22329.7 | 1.25374 | ||||||||
\(683\) | 17930.9 | 1.00455 | 0.502275 | − | 0.864708i | \(-0.332496\pi\) | ||||
0.502275 | + | 0.864708i | \(0.332496\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −986.205 | −0.0550087 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5480.69 | −0.303706 | ||||||||
\(689\) | 6169.41 | 0.341126 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25818.0 | 1.42137 | 0.710683 | − | 0.703512i | \(-0.248386\pi\) | ||||
0.710683 | + | 0.703512i | \(0.248386\pi\) | |||||||
\(692\) | 54757.4 | 3.00804 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23316.1 | 1.27531 | ||||||||
\(695\) | 591.647 | 0.0322913 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5251.00 | −0.285360 | ||||||||
\(698\) | 21175.0 | 1.14826 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16727.2 | 0.901250 | 0.450625 | − | 0.892713i | \(-0.351201\pi\) | ||||
0.450625 | + | 0.892713i | \(0.351201\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25097.2 | −1.34646 | ||||||||
\(704\) | −52081.7 | −2.78821 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7594.92 | −0.404870 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6891.41 | −0.365039 | −0.182519 | − | 0.983202i | \(-0.558425\pi\) | ||||
−0.182519 | + | 0.983202i | \(0.558425\pi\) | |||||||
\(710\) | −1381.62 | −0.0730302 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 43930.5 | 2.31231 | ||||||||
\(713\) | 4059.41 | 0.213220 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2027.51 | 0.106049 | ||||||||
\(716\) | −4740.01 | −0.247406 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 62077.7 | 3.22663 | ||||||||
\(719\) | 10406.4 | 0.539767 | 0.269884 | − | 0.962893i | \(-0.413015\pi\) | ||||
0.269884 | + | 0.962893i | \(0.413015\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3153.66 | −0.162558 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −22155.5 | −1.13730 | ||||||||
\(725\) | −8346.17 | −0.427543 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2203.46 | 0.112410 | 0.0562049 | − | 0.998419i | \(-0.482100\pi\) | ||||
0.0562049 | + | 0.998419i | \(0.482100\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3041.68 | −0.154216 | ||||||||
\(731\) | 3461.05 | 0.175119 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8773.70 | −0.442106 | −0.221053 | − | 0.975262i | \(-0.570949\pi\) | ||||
−0.221053 | + | 0.975262i | \(0.570949\pi\) | |||||||
\(734\) | −24024.4 | −1.20811 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7161.06 | −0.358641 | ||||||||
\(737\) | −54895.1 | −2.74367 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27385.9 | 1.36320 | 0.681601 | − | 0.731724i | \(-0.261284\pi\) | ||||
0.681601 | + | 0.731724i | \(0.261284\pi\) | |||||||
\(740\) | 3401.44 | 0.168972 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28890.0 | −1.42648 | −0.713239 | − | 0.700921i | \(-0.752772\pi\) | ||||
−0.713239 | + | 0.700921i | \(0.752772\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1834.67 | −0.0902243 | ||||||||
\(746\) | 6869.17 | 0.337129 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14185.9 | −0.693432 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20807.7 | −1.01103 | −0.505515 | − | 0.862818i | \(-0.668697\pi\) | ||||
−0.505515 | + | 0.862818i | \(0.668697\pi\) | |||||||
\(752\) | −10460.8 | −0.507271 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11306.2 | 0.546085 | ||||||||
\(755\) | 454.244 | 0.0218962 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14372.8 | 0.690078 | 0.345039 | − | 0.938588i | \(-0.387866\pi\) | ||||
0.345039 | + | 0.938588i | \(0.387866\pi\) | |||||||
\(758\) | −10981.5 | −0.526208 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2089.85 | 0.0997459 | ||||||||
\(761\) | −26973.6 | −1.28488 | −0.642439 | − | 0.766337i | \(-0.722077\pi\) | ||||
−0.642439 | + | 0.766337i | \(0.722077\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −43433.4 | −2.05676 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26602.8 | −1.25483 | ||||||||
\(767\) | −15949.2 | −0.750838 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3264.38 | −0.153077 | −0.0765387 | − | 0.997067i | \(-0.524387\pi\) | ||||
−0.0765387 | + | 0.997067i | \(0.524387\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −31488.0 | −1.46798 | ||||||||
\(773\) | 22135.4 | 1.02995 | 0.514977 | − | 0.857204i | \(-0.327800\pi\) | ||||
0.514977 | + | 0.857204i | \(0.327800\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8639.59 | 0.400443 | ||||||||
\(776\) | −47316.1 | −2.18885 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −42560.0 | −1.96124 | ||||||||
\(779\) | 31041.7 | 1.42771 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24120.5 | −1.10512 | ||||||||
\(782\) | −4035.83 | −0.184554 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1553.11 | −0.0706150 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29347.2 | 1.32924 | 0.664622 | − | 0.747180i | \(-0.268593\pi\) | ||||
0.664622 | + | 0.747180i | \(0.268593\pi\) | |||||||
\(788\) | −26285.1 | −1.18828 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −290.075 | −0.0130638 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17038.7 | −0.763006 | ||||||||
\(794\) | −16591.0 | −0.741553 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14070.3 | −0.626516 | ||||||||
\(797\) | −26622.6 | −1.18321 | −0.591606 | − | 0.806227i | \(-0.701506\pi\) | ||||
−0.591606 | + | 0.806227i | \(0.701506\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6606.02 | 0.292496 | ||||||||
\(800\) | −15240.8 | −0.673554 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21041.8 | −0.926448 | ||||||||
\(803\) | −53101.8 | −2.33365 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11703.7 | −0.511471 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 34969.1 | 1.52253 | ||||||||
\(809\) | 21385.7 | 0.929395 | 0.464697 | − | 0.885470i | \(-0.346163\pi\) | ||||
0.464697 | + | 0.885470i | \(0.346163\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26846.2 | −1.16239 | −0.581195 | − | 0.813764i | \(-0.697415\pi\) | ||||
−0.581195 | + | 0.813764i | \(0.697415\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 92930.1 | 4.00147 | ||||||||
\(815\) | 2522.42 | 0.108413 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20460.3 | −0.876151 | ||||||||
\(818\) | 35458.8 | 1.51563 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4207.11 | −0.179169 | ||||||||
\(821\) | −23679.3 | −1.00659 | −0.503296 | − | 0.864114i | \(-0.667880\pi\) | ||||
−0.503296 | + | 0.864114i | \(0.667880\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20546.6 | −0.870242 | −0.435121 | − | 0.900372i | \(-0.643294\pi\) | ||||
−0.435121 | + | 0.900372i | \(0.643294\pi\) | |||||||
\(824\) | 14076.7 | 0.595126 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24006.6 | 1.00942 | 0.504712 | − | 0.863288i | \(-0.331599\pi\) | ||||
0.504712 | + | 0.863288i | \(0.331599\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20544.1 | −0.860706 | −0.430353 | − | 0.902661i | \(-0.641611\pi\) | ||||
−0.430353 | + | 0.902661i | \(0.641611\pi\) | |||||||
\(830\) | 4568.09 | 0.191037 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 27297.6 | 1.13747 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2464.03 | 0.102121 | ||||||||
\(836\) | 83861.0 | 3.46937 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −72902.5 | −3.00522 | ||||||||
\(839\) | −8213.78 | −0.337987 | −0.168993 | − | 0.985617i | \(-0.554052\pi\) | ||||
−0.168993 | + | 0.985617i | \(0.554052\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19881.3 | −0.815173 | ||||||||
\(842\) | −20754.9 | −0.849479 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7718.79 | −0.314800 | ||||||||
\(845\) | 761.823 | 0.0310148 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4008.56 | −0.162329 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8589.41 | −0.346605 | ||||||||
\(851\) | 16894.1 | 0.680521 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9158.34 | 0.367615 | 0.183808 | − | 0.982962i | \(-0.441158\pi\) | ||||
0.183808 | + | 0.982962i | \(0.441158\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7485.54 | −0.298891 | ||||||||
\(857\) | 25763.8 | 1.02692 | 0.513462 | − | 0.858112i | \(-0.328363\pi\) | ||||
0.513462 | + | 0.858112i | \(0.328363\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41844.0 | 1.66205 | 0.831024 | − | 0.556236i | \(-0.187755\pi\) | ||||
0.831024 | + | 0.556236i | \(0.187755\pi\) | |||||||
\(860\) | 2773.00 | 0.109952 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 48754.2 | 1.92642 | ||||||||
\(863\) | −43821.4 | −1.72850 | −0.864250 | − | 0.503062i | \(-0.832207\pi\) | ||||
−0.864250 | + | 0.503062i | \(0.832207\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3211.21 | −0.126225 | ||||||||
\(866\) | 6581.83 | 0.258268 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5064.15 | −0.197686 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28772.2 | 1.11930 | ||||||||
\(872\) | −16857.5 | −0.654665 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 23858.1 | 0.923357 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6690.44 | −0.257606 | −0.128803 | − | 0.991670i | \(-0.541113\pi\) | ||||
−0.128803 | + | 0.991670i | \(0.541113\pi\) | |||||||
\(878\) | 16237.8 | 0.624144 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1317.37 | −0.0504644 | ||||||||
\(881\) | −11946.0 | −0.456835 | −0.228417 | − | 0.973563i | \(-0.573355\pi\) | ||||
−0.228417 | + | 0.973563i | \(0.573355\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4878.25 | −0.185919 | −0.0929593 | − | 0.995670i | \(-0.529633\pi\) | ||||
−0.0929593 | + | 0.995670i | \(0.529633\pi\) | |||||||
\(884\) | 7435.26 | 0.282890 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10566.8 | −0.400674 | ||||||||
\(887\) | 30111.7 | 1.13986 | 0.569928 | − | 0.821695i | \(-0.306971\pi\) | ||||
0.569928 | + | 0.821695i | \(0.306971\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −5921.63 | −0.223026 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −48808.5 | −1.83210 | ||||||||
\(893\) | −39052.0 | −1.46341 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 277.974 | 0.0103817 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 35961.7 | 1.33637 | ||||||||
\(899\) | −4666.23 | −0.173112 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2531.41 | 0.0935998 | ||||||||
\(902\) | −114942. | −4.24294 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 20540.8 | 0.755725 | ||||||||
\(905\) | 1299.30 | 0.0477238 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1986.84 | −0.0727364 | −0.0363682 | − | 0.999338i | \(-0.511579\pi\) | ||||
−0.0363682 | + | 0.999338i | \(0.511579\pi\) | |||||||
\(908\) | 6886.38 | 0.251688 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31604.7 | 1.14941 | 0.574703 | − | 0.818362i | \(-0.305118\pi\) | ||||
0.574703 | + | 0.818362i | \(0.305118\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 79750.0 | 2.89084 | ||||||||
\(914\) | −2545.94 | −0.0921360 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 59683.5 | 2.15284 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26999.8 | −0.969140 | −0.484570 | − | 0.874752i | \(-0.661024\pi\) | ||||
−0.484570 | + | 0.874752i | \(0.661024\pi\) | |||||||
\(920\) | −1406.78 | −0.0504132 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −40613.1 | −1.45067 | ||||||||
\(923\) | 12642.3 | 0.450841 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35955.5 | 1.27807 | ||||||||
\(926\) | −21173.1 | −0.751395 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8231.51 | 0.291177 | ||||||||
\(929\) | −17312.9 | −0.611431 | −0.305715 | − | 0.952123i | \(-0.598896\pi\) | ||||
−0.305715 | + | 0.952123i | \(0.598896\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 15567.6 | 0.547140 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11736.2 | 0.411156 | ||||||||
\(935\) | 831.922 | 0.0290981 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31294.1 | −1.09107 | −0.545535 | − | 0.838088i | \(-0.683673\pi\) | ||||
−0.545535 | + | 0.838088i | \(0.683673\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5292.75 | 0.183650 | ||||||||
\(941\) | 44549.5 | 1.54333 | 0.771665 | − | 0.636029i | \(-0.219424\pi\) | ||||
0.771665 | + | 0.636029i | \(0.219424\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20895.7 | −0.721587 | ||||||||
\(944\) | 10363.0 | 0.357295 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 75760.6 | 2.60380 | ||||||||
\(947\) | 54541.4 | 1.87155 | 0.935775 | − | 0.352596i | \(-0.114701\pi\) | ||||
0.935775 | + | 0.352596i | \(0.114701\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27832.3 | 0.952028 | ||||||||
\(950\) | 50777.0 | 1.73413 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19349.7 | 0.657710 | 0.328855 | − | 0.944380i | \(-0.393337\pi\) | ||||
0.328855 | + | 0.944380i | \(0.393337\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2547.12 | 0.0863066 | ||||||||
\(956\) | −64559.2 | −2.18409 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 39257.4 | 1.32395 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24960.7 | −0.837861 | ||||||||
\(962\) | −48707.5 | −1.63243 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15426.9 | −0.515422 | ||||||||
\(965\) | 1846.59 | 0.0615999 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52450.4 | 1.74425 | 0.872125 | − | 0.489283i | \(-0.162742\pi\) | ||||
0.872125 | + | 0.489283i | \(0.162742\pi\) | |||||||
\(968\) | −96493.9 | −3.20396 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6377.99 | 0.211118 | ||||||||
\(971\) | −13635.8 | −0.450662 | −0.225331 | − | 0.974282i | \(-0.572346\pi\) | ||||
−0.225331 | + | 0.974282i | \(0.572346\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 14616.2 | 0.480834 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11070.9 | 0.363085 | ||||||||
\(977\) | −30018.6 | −0.982989 | −0.491495 | − | 0.870881i | \(-0.663549\pi\) | ||||
−0.491495 | + | 0.870881i | \(0.663549\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −103380. | −3.37492 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2337.66 | 0.0759651 | ||||||||
\(983\) | −6470.42 | −0.209943 | −0.104972 | − | 0.994475i | \(-0.533475\pi\) | ||||
−0.104972 | + | 0.994475i | \(0.533475\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1541.47 | 0.0498633 | ||||||||
\(986\) | 4639.12 | 0.149837 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −43954.2 | −1.41535 | ||||||||
\(989\) | 13772.8 | 0.442821 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23884.4 | −0.765605 | −0.382802 | − | 0.923830i | \(-0.625041\pi\) | ||||
−0.382802 | + | 0.923830i | \(0.625041\pi\) | |||||||
\(992\) | −8520.91 | −0.272721 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 825.140 | 0.0262902 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7790.90 | 0.247483 | 0.123741 | − | 0.992315i | \(-0.460511\pi\) | ||||
0.123741 | + | 0.992315i | \(0.460511\pi\) | |||||||
\(998\) | 62391.6 | 1.97893 | ||||||||
\(999\) | 0 | 0 |
(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 | 1323.4.a.bd.1.1 | 6 | ||
3.2 | odd | 2 | inner | 1323.4.a.bd.1.6 | 6 | ||
7.2 | even | 3 | 189.4.e.e.109.6 | yes | 12 | ||
7.4 | even | 3 | 189.4.e.e.163.6 | yes | 12 | ||
7.6 | odd | 2 | 1323.4.a.be.1.1 | 6 | |||
21.2 | odd | 6 | 189.4.e.e.109.1 | ✓ | 12 | ||
21.11 | odd | 6 | 189.4.e.e.163.1 | yes | 12 | ||
21.20 | even | 2 | 1323.4.a.be.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.4.e.e.109.1 | ✓ | 12 | 21.2 | odd | 6 | ||
189.4.e.e.109.6 | yes | 12 | 7.2 | even | 3 | ||
189.4.e.e.163.1 | yes | 12 | 21.11 | odd | 6 | ||
189.4.e.e.163.6 | yes | 12 | 7.4 | even | 3 | ||
1323.4.a.bd.1.1 | 6 | 1.1 | even | 1 | trivial | ||
1323.4.a.bd.1.6 | 6 | 3.2 | odd | 2 | inner | ||
1323.4.a.be.1.1 | 6 | 7.6 | odd | 2 | |||
1323.4.a.be.1.6 | 6 | 21.20 | even | 2 |