Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [65,4,Mod(1,65)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(65, 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("65.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 65 = 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 65.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: | \(3.83512415037\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 65.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.267949 | 0.0947343 | 0.0473672 | − | 0.998878i | \(-0.484917\pi\) | ||||
0.0473672 | + | 0.998878i | \(0.484917\pi\) | |||||||
\(3\) | 0.196152 | 0.0377496 | 0.0188748 | − | 0.999822i | \(-0.493992\pi\) | ||||
0.0188748 | + | 0.999822i | \(0.493992\pi\) | |||||||
\(4\) | −7.92820 | −0.991025 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0.0525589 | 0.00357618 | ||||||||
\(7\) | −11.0718 | −0.597821 | −0.298910 | − | 0.954281i | \(-0.596623\pi\) | ||||
−0.298910 | + | 0.954281i | \(0.596623\pi\) | |||||||
\(8\) | −4.26795 | −0.188618 | ||||||||
\(9\) | −26.9615 | −0.998575 | ||||||||
\(10\) | −1.33975 | −0.0423665 | ||||||||
\(11\) | −10.1962 | −0.279478 | −0.139739 | − | 0.990188i | \(-0.544626\pi\) | ||||
−0.139739 | + | 0.990188i | \(0.544626\pi\) | |||||||
\(12\) | −1.55514 | −0.0374108 | ||||||||
\(13\) | 13.0000 | 0.277350 | ||||||||
\(14\) | −2.96668 | −0.0566342 | ||||||||
\(15\) | −0.980762 | −0.0168821 | ||||||||
\(16\) | 62.2820 | 0.973157 | ||||||||
\(17\) | −48.5359 | −0.692452 | −0.346226 | − | 0.938151i | \(-0.612537\pi\) | ||||
−0.346226 | + | 0.938151i | \(0.612537\pi\) | |||||||
\(18\) | −7.22432 | −0.0945993 | ||||||||
\(19\) | −36.4449 | −0.440054 | −0.220027 | − | 0.975494i | \(-0.570615\pi\) | ||||
−0.220027 | + | 0.975494i | \(0.570615\pi\) | |||||||
\(20\) | 39.6410 | 0.443200 | ||||||||
\(21\) | −2.17176 | −0.0225675 | ||||||||
\(22\) | −2.73205 | −0.0264761 | ||||||||
\(23\) | 11.8038 | 0.107012 | 0.0535059 | − | 0.998568i | \(-0.482960\pi\) | ||||
0.0535059 | + | 0.998568i | \(0.482960\pi\) | |||||||
\(24\) | −0.837169 | −0.00712026 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 3.48334 | 0.0262746 | ||||||||
\(27\) | −10.5847 | −0.0754453 | ||||||||
\(28\) | 87.7795 | 0.592456 | ||||||||
\(29\) | 103.033 | 0.659752 | 0.329876 | − | 0.944024i | \(-0.392993\pi\) | ||||
0.329876 | + | 0.944024i | \(0.392993\pi\) | |||||||
\(30\) | −0.262794 | −0.00159932 | ||||||||
\(31\) | 156.578 | 0.907170 | 0.453585 | − | 0.891213i | \(-0.350145\pi\) | ||||
0.453585 | + | 0.891213i | \(0.350145\pi\) | |||||||
\(32\) | 50.8320 | 0.280810 | ||||||||
\(33\) | −2.00000 | −0.0105502 | ||||||||
\(34\) | −13.0052 | −0.0655990 | ||||||||
\(35\) | 55.3590 | 0.267354 | ||||||||
\(36\) | 213.756 | 0.989613 | ||||||||
\(37\) | −263.769 | −1.17198 | −0.585992 | − | 0.810317i | \(-0.699295\pi\) | ||||
−0.585992 | + | 0.810317i | \(0.699295\pi\) | |||||||
\(38\) | −9.76537 | −0.0416882 | ||||||||
\(39\) | 2.54998 | 0.0104698 | ||||||||
\(40\) | 21.3397 | 0.0843528 | ||||||||
\(41\) | 185.951 | 0.708310 | 0.354155 | − | 0.935187i | \(-0.384769\pi\) | ||||
0.354155 | + | 0.935187i | \(0.384769\pi\) | |||||||
\(42\) | −0.581921 | −0.00213791 | ||||||||
\(43\) | −418.158 | −1.48299 | −0.741494 | − | 0.670960i | \(-0.765882\pi\) | ||||
−0.741494 | + | 0.670960i | \(0.765882\pi\) | |||||||
\(44\) | 80.8372 | 0.276970 | ||||||||
\(45\) | 134.808 | 0.446576 | ||||||||
\(46\) | 3.16283 | 0.0101377 | ||||||||
\(47\) | −375.492 | −1.16534 | −0.582672 | − | 0.812707i | \(-0.697993\pi\) | ||||
−0.582672 | + | 0.812707i | \(0.697993\pi\) | |||||||
\(48\) | 12.2168 | 0.0367362 | ||||||||
\(49\) | −220.415 | −0.642610 | ||||||||
\(50\) | 6.69873 | 0.0189469 | ||||||||
\(51\) | −9.52043 | −0.0261398 | ||||||||
\(52\) | −103.067 | −0.274861 | ||||||||
\(53\) | −189.397 | −0.490863 | −0.245432 | − | 0.969414i | \(-0.578930\pi\) | ||||
−0.245432 | + | 0.969414i | \(0.578930\pi\) | |||||||
\(54\) | −2.83616 | −0.00714726 | ||||||||
\(55\) | 50.9808 | 0.124986 | ||||||||
\(56\) | 47.2539 | 0.112760 | ||||||||
\(57\) | −7.14875 | −0.0166118 | ||||||||
\(58\) | 27.6077 | 0.0625012 | ||||||||
\(59\) | −194.463 | −0.429100 | −0.214550 | − | 0.976713i | \(-0.568828\pi\) | ||||
−0.214550 | + | 0.976713i | \(0.568828\pi\) | |||||||
\(60\) | 7.77568 | 0.0167306 | ||||||||
\(61\) | 21.8846 | 0.0459350 | 0.0229675 | − | 0.999736i | \(-0.492689\pi\) | ||||
0.0229675 | + | 0.999736i | \(0.492689\pi\) | |||||||
\(62\) | 41.9550 | 0.0859401 | ||||||||
\(63\) | 298.513 | 0.596969 | ||||||||
\(64\) | −484.636 | −0.946554 | ||||||||
\(65\) | −65.0000 | −0.124035 | ||||||||
\(66\) | −0.535898 | −0.000999463 0 | ||||||||
\(67\) | −658.715 | −1.20112 | −0.600559 | − | 0.799581i | \(-0.705055\pi\) | ||||
−0.600559 | + | 0.799581i | \(0.705055\pi\) | |||||||
\(68\) | 384.802 | 0.686238 | ||||||||
\(69\) | 2.31535 | 0.00403965 | ||||||||
\(70\) | 14.8334 | 0.0253276 | ||||||||
\(71\) | 357.755 | 0.597996 | 0.298998 | − | 0.954254i | \(-0.403348\pi\) | ||||
0.298998 | + | 0.954254i | \(0.403348\pi\) | |||||||
\(72\) | 115.070 | 0.188350 | ||||||||
\(73\) | −341.205 | −0.547055 | −0.273528 | − | 0.961864i | \(-0.588190\pi\) | ||||
−0.273528 | + | 0.961864i | \(0.588190\pi\) | |||||||
\(74\) | −70.6767 | −0.111027 | ||||||||
\(75\) | 4.90381 | 0.00754991 | ||||||||
\(76\) | 288.942 | 0.436105 | ||||||||
\(77\) | 112.890 | 0.167078 | ||||||||
\(78\) | 0.683265 | 0.000991854 0 | ||||||||
\(79\) | −1005.58 | −1.43210 | −0.716052 | − | 0.698047i | \(-0.754053\pi\) | ||||
−0.716052 | + | 0.698047i | \(0.754053\pi\) | |||||||
\(80\) | −311.410 | −0.435209 | ||||||||
\(81\) | 725.885 | 0.995727 | ||||||||
\(82\) | 49.8255 | 0.0671013 | ||||||||
\(83\) | 725.349 | 0.959245 | 0.479623 | − | 0.877475i | \(-0.340774\pi\) | ||||
0.479623 | + | 0.877475i | \(0.340774\pi\) | |||||||
\(84\) | 17.2182 | 0.0223649 | ||||||||
\(85\) | 242.679 | 0.309674 | ||||||||
\(86\) | −112.045 | −0.140490 | ||||||||
\(87\) | 20.2102 | 0.0249053 | ||||||||
\(88\) | 43.5167 | 0.0527147 | ||||||||
\(89\) | 1595.76 | 1.90056 | 0.950281 | − | 0.311392i | \(-0.100795\pi\) | ||||
0.950281 | + | 0.311392i | \(0.100795\pi\) | |||||||
\(90\) | 36.1216 | 0.0423061 | ||||||||
\(91\) | −143.933 | −0.165806 | ||||||||
\(92\) | −93.5833 | −0.106051 | ||||||||
\(93\) | 30.7132 | 0.0342453 | ||||||||
\(94\) | −100.613 | −0.110398 | ||||||||
\(95\) | 182.224 | 0.196798 | ||||||||
\(96\) | 9.97082 | 0.0106004 | ||||||||
\(97\) | 1037.94 | 1.08646 | 0.543230 | − | 0.839584i | \(-0.317201\pi\) | ||||
0.543230 | + | 0.839584i | \(0.317201\pi\) | |||||||
\(98\) | −59.0601 | −0.0608773 | ||||||||
\(99\) | 274.904 | 0.279080 | ||||||||
\(100\) | −198.205 | −0.198205 | ||||||||
\(101\) | −484.446 | −0.477269 | −0.238634 | − | 0.971109i | \(-0.576700\pi\) | ||||
−0.238634 | + | 0.971109i | \(0.576700\pi\) | |||||||
\(102\) | −2.55099 | −0.00247633 | ||||||||
\(103\) | −947.040 | −0.905967 | −0.452984 | − | 0.891519i | \(-0.649640\pi\) | ||||
−0.452984 | + | 0.891519i | \(0.649640\pi\) | |||||||
\(104\) | −55.4833 | −0.0523134 | ||||||||
\(105\) | 10.8588 | 0.0100925 | ||||||||
\(106\) | −50.7489 | −0.0465016 | ||||||||
\(107\) | 1676.37 | 1.51458 | 0.757291 | − | 0.653077i | \(-0.226522\pi\) | ||||
0.757291 | + | 0.653077i | \(0.226522\pi\) | |||||||
\(108\) | 83.9175 | 0.0747682 | ||||||||
\(109\) | 1789.78 | 1.57275 | 0.786377 | − | 0.617747i | \(-0.211954\pi\) | ||||
0.786377 | + | 0.617747i | \(0.211954\pi\) | |||||||
\(110\) | 13.6603 | 0.0118405 | ||||||||
\(111\) | −51.7390 | −0.0442418 | ||||||||
\(112\) | −689.574 | −0.581773 | ||||||||
\(113\) | −565.069 | −0.470418 | −0.235209 | − | 0.971945i | \(-0.575577\pi\) | ||||
−0.235209 | + | 0.971945i | \(0.575577\pi\) | |||||||
\(114\) | −1.91550 | −0.00157371 | ||||||||
\(115\) | −59.0192 | −0.0478572 | ||||||||
\(116\) | −816.869 | −0.653831 | ||||||||
\(117\) | −350.500 | −0.276955 | ||||||||
\(118\) | −52.1061 | −0.0406505 | ||||||||
\(119\) | 537.380 | 0.413962 | ||||||||
\(120\) | 4.18584 | 0.00318428 | ||||||||
\(121\) | −1227.04 | −0.921892 | ||||||||
\(122\) | 5.86395 | 0.00435162 | ||||||||
\(123\) | 36.4748 | 0.0267384 | ||||||||
\(124\) | −1241.38 | −0.899028 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 79.9862 | 0.0565535 | ||||||||
\(127\) | −1396.08 | −0.975448 | −0.487724 | − | 0.872998i | \(-0.662173\pi\) | ||||
−0.487724 | + | 0.872998i | \(0.662173\pi\) | |||||||
\(128\) | −536.514 | −0.370481 | ||||||||
\(129\) | −82.0226 | −0.0559821 | ||||||||
\(130\) | −17.4167 | −0.0117503 | ||||||||
\(131\) | −2673.75 | −1.78326 | −0.891629 | − | 0.452766i | \(-0.850437\pi\) | ||||
−0.891629 | + | 0.452766i | \(0.850437\pi\) | |||||||
\(132\) | 15.8564 | 0.0104555 | ||||||||
\(133\) | 403.510 | 0.263073 | ||||||||
\(134\) | −176.502 | −0.113787 | ||||||||
\(135\) | 52.9234 | 0.0337402 | ||||||||
\(136\) | 207.149 | 0.130609 | ||||||||
\(137\) | 2502.70 | 1.56073 | 0.780366 | − | 0.625323i | \(-0.215033\pi\) | ||||
0.780366 | + | 0.625323i | \(0.215033\pi\) | |||||||
\(138\) | 0.620397 | 0.000382694 0 | ||||||||
\(139\) | 272.695 | 0.166400 | 0.0832002 | − | 0.996533i | \(-0.473486\pi\) | ||||
0.0832002 | + | 0.996533i | \(0.473486\pi\) | |||||||
\(140\) | −438.897 | −0.264954 | ||||||||
\(141\) | −73.6537 | −0.0439912 | ||||||||
\(142\) | 95.8602 | 0.0566508 | ||||||||
\(143\) | −132.550 | −0.0775132 | ||||||||
\(144\) | −1679.22 | −0.971770 | ||||||||
\(145\) | −515.167 | −0.295050 | ||||||||
\(146\) | −91.4256 | −0.0518249 | ||||||||
\(147\) | −43.2350 | −0.0242582 | ||||||||
\(148\) | 2091.22 | 1.16147 | ||||||||
\(149\) | 1598.07 | 0.878652 | 0.439326 | − | 0.898328i | \(-0.355217\pi\) | ||||
0.439326 | + | 0.898328i | \(0.355217\pi\) | |||||||
\(150\) | 1.31397 | 0.000715236 0 | ||||||||
\(151\) | −2431.27 | −1.31029 | −0.655145 | − | 0.755503i | \(-0.727392\pi\) | ||||
−0.655145 | + | 0.755503i | \(0.727392\pi\) | |||||||
\(152\) | 155.545 | 0.0830023 | ||||||||
\(153\) | 1308.60 | 0.691465 | ||||||||
\(154\) | 30.2487 | 0.0158280 | ||||||||
\(155\) | −782.891 | −0.405699 | ||||||||
\(156\) | −20.2168 | −0.0103759 | ||||||||
\(157\) | 693.005 | 0.352279 | 0.176140 | − | 0.984365i | \(-0.443639\pi\) | ||||
0.176140 | + | 0.984365i | \(0.443639\pi\) | |||||||
\(158\) | −269.443 | −0.135669 | ||||||||
\(159\) | −37.1508 | −0.0185299 | ||||||||
\(160\) | −254.160 | −0.125582 | ||||||||
\(161\) | −130.690 | −0.0639739 | ||||||||
\(162\) | 194.500 | 0.0943295 | ||||||||
\(163\) | −431.962 | −0.207570 | −0.103785 | − | 0.994600i | \(-0.533095\pi\) | ||||
−0.103785 | + | 0.994600i | \(0.533095\pi\) | |||||||
\(164\) | −1474.26 | −0.701953 | ||||||||
\(165\) | 10.0000 | 0.00471818 | ||||||||
\(166\) | 194.357 | 0.0908735 | ||||||||
\(167\) | −1054.76 | −0.488740 | −0.244370 | − | 0.969682i | \(-0.578581\pi\) | ||||
−0.244370 | + | 0.969682i | \(0.578581\pi\) | |||||||
\(168\) | 9.26896 | 0.00425664 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 65.0258 | 0.0293368 | ||||||||
\(171\) | 982.609 | 0.439427 | ||||||||
\(172\) | 3315.24 | 1.46968 | ||||||||
\(173\) | −2929.16 | −1.28728 | −0.643642 | − | 0.765327i | \(-0.722577\pi\) | ||||
−0.643642 | + | 0.765327i | \(0.722577\pi\) | |||||||
\(174\) | 5.41532 | 0.00235939 | ||||||||
\(175\) | −276.795 | −0.119564 | ||||||||
\(176\) | −635.037 | −0.271976 | ||||||||
\(177\) | −38.1443 | −0.0161983 | ||||||||
\(178\) | 427.582 | 0.180049 | ||||||||
\(179\) | 3717.33 | 1.55221 | 0.776106 | − | 0.630602i | \(-0.217192\pi\) | ||||
0.776106 | + | 0.630602i | \(0.217192\pi\) | |||||||
\(180\) | −1068.78 | −0.442568 | ||||||||
\(181\) | 1923.10 | 0.789739 | 0.394870 | − | 0.918737i | \(-0.370790\pi\) | ||||
0.394870 | + | 0.918737i | \(0.370790\pi\) | |||||||
\(182\) | −38.5668 | −0.0157075 | ||||||||
\(183\) | 4.29271 | 0.00173402 | ||||||||
\(184\) | −50.3782 | −0.0201844 | ||||||||
\(185\) | 1318.85 | 0.524127 | ||||||||
\(186\) | 8.22957 | 0.00324420 | ||||||||
\(187\) | 494.879 | 0.193525 | ||||||||
\(188\) | 2976.98 | 1.15489 | ||||||||
\(189\) | 117.191 | 0.0451028 | ||||||||
\(190\) | 48.8269 | 0.0186435 | ||||||||
\(191\) | −1941.49 | −0.735505 | −0.367752 | − | 0.929924i | \(-0.619873\pi\) | ||||
−0.367752 | + | 0.929924i | \(0.619873\pi\) | |||||||
\(192\) | −95.0625 | −0.0357320 | ||||||||
\(193\) | 2334.49 | 0.870676 | 0.435338 | − | 0.900267i | \(-0.356629\pi\) | ||||
0.435338 | + | 0.900267i | \(0.356629\pi\) | |||||||
\(194\) | 278.115 | 0.102925 | ||||||||
\(195\) | −12.7499 | −0.00468226 | ||||||||
\(196\) | 1747.50 | 0.636843 | ||||||||
\(197\) | 2160.54 | 0.781380 | 0.390690 | − | 0.920522i | \(-0.372236\pi\) | ||||
0.390690 | + | 0.920522i | \(0.372236\pi\) | |||||||
\(198\) | 73.6603 | 0.0264384 | ||||||||
\(199\) | −1985.74 | −0.707365 | −0.353683 | − | 0.935366i | \(-0.615071\pi\) | ||||
−0.353683 | + | 0.935366i | \(0.615071\pi\) | |||||||
\(200\) | −106.699 | −0.0377237 | ||||||||
\(201\) | −129.209 | −0.0453416 | ||||||||
\(202\) | −129.807 | −0.0452138 | ||||||||
\(203\) | −1140.76 | −0.394413 | ||||||||
\(204\) | 75.4799 | 0.0259052 | ||||||||
\(205\) | −929.756 | −0.316766 | ||||||||
\(206\) | −253.759 | −0.0858262 | ||||||||
\(207\) | −318.250 | −0.106859 | ||||||||
\(208\) | 809.666 | 0.269905 | ||||||||
\(209\) | 371.597 | 0.122985 | ||||||||
\(210\) | 2.90961 | 0.000956104 0 | ||||||||
\(211\) | 1052.47 | 0.343389 | 0.171695 | − | 0.985150i | \(-0.445076\pi\) | ||||
0.171695 | + | 0.985150i | \(0.445076\pi\) | |||||||
\(212\) | 1501.58 | 0.486458 | ||||||||
\(213\) | 70.1745 | 0.0225741 | ||||||||
\(214\) | 449.181 | 0.143483 | ||||||||
\(215\) | 2090.79 | 0.663212 | ||||||||
\(216\) | 45.1749 | 0.0142304 | ||||||||
\(217\) | −1733.60 | −0.542325 | ||||||||
\(218\) | 479.571 | 0.148994 | ||||||||
\(219\) | −66.9282 | −0.0206511 | ||||||||
\(220\) | −404.186 | −0.123865 | ||||||||
\(221\) | −630.967 | −0.192052 | ||||||||
\(222\) | −13.8634 | −0.00419122 | ||||||||
\(223\) | −3119.81 | −0.936852 | −0.468426 | − | 0.883503i | \(-0.655179\pi\) | ||||
−0.468426 | + | 0.883503i | \(0.655179\pi\) | |||||||
\(224\) | −562.802 | −0.167874 | ||||||||
\(225\) | −674.038 | −0.199715 | ||||||||
\(226\) | −151.410 | −0.0445647 | ||||||||
\(227\) | −5135.43 | −1.50154 | −0.750772 | − | 0.660561i | \(-0.770318\pi\) | ||||
−0.750772 | + | 0.660561i | \(0.770318\pi\) | |||||||
\(228\) | 56.6767 | 0.0164628 | ||||||||
\(229\) | −1297.62 | −0.374451 | −0.187226 | − | 0.982317i | \(-0.559950\pi\) | ||||
−0.187226 | + | 0.982317i | \(0.559950\pi\) | |||||||
\(230\) | −15.8142 | −0.00453372 | ||||||||
\(231\) | 22.1436 | 0.00630711 | ||||||||
\(232\) | −439.741 | −0.124441 | ||||||||
\(233\) | −4251.77 | −1.19546 | −0.597732 | − | 0.801696i | \(-0.703931\pi\) | ||||
−0.597732 | + | 0.801696i | \(0.703931\pi\) | |||||||
\(234\) | −93.9161 | −0.0262371 | ||||||||
\(235\) | 1877.46 | 0.521158 | ||||||||
\(236\) | 1541.74 | 0.425249 | ||||||||
\(237\) | −197.246 | −0.0540613 | ||||||||
\(238\) | 143.990 | 0.0392164 | ||||||||
\(239\) | −229.286 | −0.0620555 | −0.0310278 | − | 0.999519i | \(-0.509878\pi\) | ||||
−0.0310278 | + | 0.999519i | \(0.509878\pi\) | |||||||
\(240\) | −61.0839 | −0.0164289 | ||||||||
\(241\) | −2829.08 | −0.756171 | −0.378086 | − | 0.925771i | \(-0.623418\pi\) | ||||
−0.378086 | + | 0.925771i | \(0.623418\pi\) | |||||||
\(242\) | −328.784 | −0.0873349 | ||||||||
\(243\) | 428.171 | 0.113034 | ||||||||
\(244\) | −173.505 | −0.0455227 | ||||||||
\(245\) | 1102.08 | 0.287384 | ||||||||
\(246\) | 9.77339 | 0.00253304 | ||||||||
\(247\) | −473.783 | −0.122049 | ||||||||
\(248\) | −668.268 | −0.171109 | ||||||||
\(249\) | 142.279 | 0.0362111 | ||||||||
\(250\) | −33.4936 | −0.00847330 | ||||||||
\(251\) | 3496.34 | 0.879230 | 0.439615 | − | 0.898186i | \(-0.355115\pi\) | ||||
0.439615 | + | 0.898186i | \(0.355115\pi\) | |||||||
\(252\) | −2366.67 | −0.591611 | ||||||||
\(253\) | −120.354 | −0.0299074 | ||||||||
\(254\) | −374.078 | −0.0924084 | ||||||||
\(255\) | 47.6022 | 0.0116901 | ||||||||
\(256\) | 3733.33 | 0.911457 | ||||||||
\(257\) | −3688.28 | −0.895208 | −0.447604 | − | 0.894232i | \(-0.647723\pi\) | ||||
−0.447604 | + | 0.894232i | \(0.647723\pi\) | |||||||
\(258\) | −21.9779 | −0.00530343 | ||||||||
\(259\) | 2920.40 | 0.700636 | ||||||||
\(260\) | 515.333 | 0.122922 | ||||||||
\(261\) | −2777.94 | −0.658812 | ||||||||
\(262\) | −716.430 | −0.168936 | ||||||||
\(263\) | −7176.39 | −1.68257 | −0.841284 | − | 0.540594i | \(-0.818199\pi\) | ||||
−0.841284 | + | 0.540594i | \(0.818199\pi\) | |||||||
\(264\) | 8.53590 | 0.00198996 | ||||||||
\(265\) | 946.987 | 0.219521 | ||||||||
\(266\) | 108.120 | 0.0249221 | ||||||||
\(267\) | 313.012 | 0.0717454 | ||||||||
\(268\) | 5222.43 | 1.19034 | ||||||||
\(269\) | 804.924 | 0.182443 | 0.0912214 | − | 0.995831i | \(-0.470923\pi\) | ||||
0.0912214 | + | 0.995831i | \(0.470923\pi\) | |||||||
\(270\) | 14.1808 | 0.00319635 | ||||||||
\(271\) | 2636.16 | 0.590906 | 0.295453 | − | 0.955357i | \(-0.404529\pi\) | ||||
0.295453 | + | 0.955357i | \(0.404529\pi\) | |||||||
\(272\) | −3022.91 | −0.673864 | ||||||||
\(273\) | −28.2329 | −0.00625909 | ||||||||
\(274\) | 670.597 | 0.147855 | ||||||||
\(275\) | −254.904 | −0.0558956 | ||||||||
\(276\) | −18.3566 | −0.00400339 | ||||||||
\(277\) | 1683.28 | 0.365122 | 0.182561 | − | 0.983195i | \(-0.441561\pi\) | ||||
0.182561 | + | 0.983195i | \(0.441561\pi\) | |||||||
\(278\) | 73.0683 | 0.0157638 | ||||||||
\(279\) | −4221.59 | −0.905877 | ||||||||
\(280\) | −236.269 | −0.0504278 | ||||||||
\(281\) | 2382.17 | 0.505724 | 0.252862 | − | 0.967502i | \(-0.418628\pi\) | ||||
0.252862 | + | 0.967502i | \(0.418628\pi\) | |||||||
\(282\) | −19.7355 | −0.00416748 | ||||||||
\(283\) | −3634.50 | −0.763423 | −0.381711 | − | 0.924282i | \(-0.624665\pi\) | ||||
−0.381711 | + | 0.924282i | \(0.624665\pi\) | |||||||
\(284\) | −2836.35 | −0.592629 | ||||||||
\(285\) | 35.7437 | 0.00742904 | ||||||||
\(286\) | −35.5167 | −0.00734316 | ||||||||
\(287\) | −2058.81 | −0.423442 | ||||||||
\(288\) | −1370.51 | −0.280410 | ||||||||
\(289\) | −2557.27 | −0.520510 | ||||||||
\(290\) | −138.038 | −0.0279514 | ||||||||
\(291\) | 203.594 | 0.0410134 | ||||||||
\(292\) | 2705.14 | 0.542146 | ||||||||
\(293\) | 3491.94 | 0.696250 | 0.348125 | − | 0.937448i | \(-0.386819\pi\) | ||||
0.348125 | + | 0.937448i | \(0.386819\pi\) | |||||||
\(294\) | −11.5848 | −0.00229809 | ||||||||
\(295\) | 972.314 | 0.191899 | ||||||||
\(296\) | 1125.75 | 0.221058 | ||||||||
\(297\) | 107.923 | 0.0210853 | ||||||||
\(298\) | 428.202 | 0.0832385 | ||||||||
\(299\) | 153.450 | 0.0296797 | ||||||||
\(300\) | −38.8784 | −0.00748215 | ||||||||
\(301\) | 4629.76 | 0.886561 | ||||||||
\(302\) | −651.456 | −0.124129 | ||||||||
\(303\) | −95.0252 | −0.0180167 | ||||||||
\(304\) | −2269.86 | −0.428241 | ||||||||
\(305\) | −109.423 | −0.0205427 | ||||||||
\(306\) | 350.639 | 0.0655055 | ||||||||
\(307\) | 1710.16 | 0.317929 | 0.158965 | − | 0.987284i | \(-0.449184\pi\) | ||||
0.158965 | + | 0.987284i | \(0.449184\pi\) | |||||||
\(308\) | −895.013 | −0.165578 | ||||||||
\(309\) | −185.764 | −0.0341999 | ||||||||
\(310\) | −209.775 | −0.0384336 | ||||||||
\(311\) | 8158.33 | 1.48751 | 0.743756 | − | 0.668451i | \(-0.233042\pi\) | ||||
0.743756 | + | 0.668451i | \(0.233042\pi\) | |||||||
\(312\) | −10.8832 | −0.00197481 | ||||||||
\(313\) | 11014.7 | 1.98910 | 0.994552 | − | 0.104246i | \(-0.0332428\pi\) | ||||
0.994552 | + | 0.104246i | \(0.0332428\pi\) | |||||||
\(314\) | 185.690 | 0.0333729 | ||||||||
\(315\) | −1492.56 | −0.266973 | ||||||||
\(316\) | 7972.42 | 1.41925 | ||||||||
\(317\) | −5890.38 | −1.04365 | −0.521825 | − | 0.853053i | \(-0.674749\pi\) | ||||
−0.521825 | + | 0.853053i | \(0.674749\pi\) | |||||||
\(318\) | −9.95452 | −0.00175541 | ||||||||
\(319\) | −1050.54 | −0.184386 | ||||||||
\(320\) | 2423.18 | 0.423312 | ||||||||
\(321\) | 328.823 | 0.0571748 | ||||||||
\(322\) | −35.0182 | −0.00606053 | ||||||||
\(323\) | 1768.88 | 0.304716 | ||||||||
\(324\) | −5754.96 | −0.986791 | ||||||||
\(325\) | 325.000 | 0.0554700 | ||||||||
\(326\) | −115.744 | −0.0196640 | ||||||||
\(327\) | 351.071 | 0.0593708 | ||||||||
\(328\) | −793.630 | −0.133600 | ||||||||
\(329\) | 4157.37 | 0.696667 | ||||||||
\(330\) | 2.67949 | 0.000446973 0 | ||||||||
\(331\) | 15.2227 | 0.00252784 | 0.00126392 | − | 0.999999i | \(-0.499598\pi\) | ||||
0.00126392 | + | 0.999999i | \(0.499598\pi\) | |||||||
\(332\) | −5750.71 | −0.950636 | ||||||||
\(333\) | 7111.62 | 1.17031 | ||||||||
\(334\) | −282.622 | −0.0463005 | ||||||||
\(335\) | 3293.58 | 0.537156 | ||||||||
\(336\) | −135.262 | −0.0219617 | ||||||||
\(337\) | 10544.3 | 1.70441 | 0.852203 | − | 0.523212i | \(-0.175266\pi\) | ||||
0.852203 | + | 0.523212i | \(0.175266\pi\) | |||||||
\(338\) | 45.2834 | 0.00728726 | ||||||||
\(339\) | −110.840 | −0.0177581 | ||||||||
\(340\) | −1924.01 | −0.306895 | ||||||||
\(341\) | −1596.49 | −0.253534 | ||||||||
\(342\) | 263.289 | 0.0416288 | ||||||||
\(343\) | 6238.02 | 0.981987 | ||||||||
\(344\) | 1784.68 | 0.279719 | ||||||||
\(345\) | −11.5768 | −0.00180659 | ||||||||
\(346\) | −784.866 | −0.121950 | ||||||||
\(347\) | −695.585 | −0.107611 | −0.0538054 | − | 0.998551i | \(-0.517135\pi\) | ||||
−0.0538054 | + | 0.998551i | \(0.517135\pi\) | |||||||
\(348\) | −160.231 | −0.0246818 | ||||||||
\(349\) | −1430.88 | −0.219465 | −0.109732 | − | 0.993961i | \(-0.534999\pi\) | ||||
−0.109732 | + | 0.993961i | \(0.534999\pi\) | |||||||
\(350\) | −74.1670 | −0.0113268 | ||||||||
\(351\) | −137.601 | −0.0209248 | ||||||||
\(352\) | −518.291 | −0.0784801 | ||||||||
\(353\) | −12657.8 | −1.90851 | −0.954256 | − | 0.298989i | \(-0.903350\pi\) | ||||
−0.954256 | + | 0.298989i | \(0.903350\pi\) | |||||||
\(354\) | −10.2207 | −0.00153454 | ||||||||
\(355\) | −1788.78 | −0.267432 | ||||||||
\(356\) | −12651.5 | −1.88351 | ||||||||
\(357\) | 105.408 | 0.0156269 | ||||||||
\(358\) | 996.055 | 0.147048 | ||||||||
\(359\) | 5601.01 | 0.823426 | 0.411713 | − | 0.911313i | \(-0.364931\pi\) | ||||
0.411713 | + | 0.911313i | \(0.364931\pi\) | |||||||
\(360\) | −575.352 | −0.0842325 | ||||||||
\(361\) | −5530.77 | −0.806353 | ||||||||
\(362\) | 515.293 | 0.0748154 | ||||||||
\(363\) | −240.687 | −0.0348010 | ||||||||
\(364\) | 1141.13 | 0.164318 | ||||||||
\(365\) | 1706.03 | 0.244651 | ||||||||
\(366\) | 1.15023 | 0.000164272 0 | ||||||||
\(367\) | −12630.3 | −1.79644 | −0.898221 | − | 0.439544i | \(-0.855140\pi\) | ||||
−0.898221 | + | 0.439544i | \(0.855140\pi\) | |||||||
\(368\) | 735.168 | 0.104139 | ||||||||
\(369\) | −5013.53 | −0.707300 | ||||||||
\(370\) | 353.384 | 0.0496528 | ||||||||
\(371\) | 2096.97 | 0.293448 | ||||||||
\(372\) | −243.500 | −0.0339379 | ||||||||
\(373\) | −4193.44 | −0.582112 | −0.291056 | − | 0.956706i | \(-0.594007\pi\) | ||||
−0.291056 | + | 0.956706i | \(0.594007\pi\) | |||||||
\(374\) | 132.603 | 0.0183335 | ||||||||
\(375\) | −24.5191 | −0.00337642 | ||||||||
\(376\) | 1602.58 | 0.219805 | ||||||||
\(377\) | 1339.43 | 0.182982 | ||||||||
\(378\) | 31.4014 | 0.00427278 | ||||||||
\(379\) | 4003.82 | 0.542645 | 0.271323 | − | 0.962488i | \(-0.412539\pi\) | ||||
0.271323 | + | 0.962488i | \(0.412539\pi\) | |||||||
\(380\) | −1444.71 | −0.195032 | ||||||||
\(381\) | −273.844 | −0.0368227 | ||||||||
\(382\) | −520.221 | −0.0696776 | ||||||||
\(383\) | −9524.94 | −1.27076 | −0.635381 | − | 0.772199i | \(-0.719157\pi\) | ||||
−0.635381 | + | 0.772199i | \(0.719157\pi\) | |||||||
\(384\) | −105.239 | −0.0139855 | ||||||||
\(385\) | −564.449 | −0.0747194 | ||||||||
\(386\) | 625.525 | 0.0824829 | ||||||||
\(387\) | 11274.2 | 1.48087 | ||||||||
\(388\) | −8228.98 | −1.07671 | ||||||||
\(389\) | 9924.11 | 1.29350 | 0.646751 | − | 0.762701i | \(-0.276127\pi\) | ||||
0.646751 | + | 0.762701i | \(0.276127\pi\) | |||||||
\(390\) | −3.41633 | −0.000443570 0 | ||||||||
\(391\) | −572.910 | −0.0741006 | ||||||||
\(392\) | 940.721 | 0.121208 | ||||||||
\(393\) | −524.463 | −0.0673172 | ||||||||
\(394\) | 578.914 | 0.0740236 | ||||||||
\(395\) | 5027.88 | 0.640456 | ||||||||
\(396\) | −2179.49 | −0.276575 | ||||||||
\(397\) | −6473.93 | −0.818431 | −0.409216 | − | 0.912438i | \(-0.634198\pi\) | ||||
−0.409216 | + | 0.912438i | \(0.634198\pi\) | |||||||
\(398\) | −532.078 | −0.0670118 | ||||||||
\(399\) | 79.1495 | 0.00993090 | ||||||||
\(400\) | 1557.05 | 0.194631 | ||||||||
\(401\) | −8383.05 | −1.04396 | −0.521982 | − | 0.852957i | \(-0.674807\pi\) | ||||
−0.521982 | + | 0.852957i | \(0.674807\pi\) | |||||||
\(402\) | −34.6213 | −0.00429541 | ||||||||
\(403\) | 2035.52 | 0.251604 | ||||||||
\(404\) | 3840.79 | 0.472986 | ||||||||
\(405\) | −3629.42 | −0.445303 | ||||||||
\(406\) | −305.667 | −0.0373645 | ||||||||
\(407\) | 2689.43 | 0.327543 | ||||||||
\(408\) | 40.6327 | 0.00493044 | ||||||||
\(409\) | −11654.6 | −1.40900 | −0.704502 | − | 0.709702i | \(-0.748830\pi\) | ||||
−0.704502 | + | 0.709702i | \(0.748830\pi\) | |||||||
\(410\) | −249.127 | −0.0300086 | ||||||||
\(411\) | 490.911 | 0.0589169 | ||||||||
\(412\) | 7508.32 | 0.897836 | ||||||||
\(413\) | 2153.05 | 0.256525 | ||||||||
\(414\) | −85.2748 | −0.0101233 | ||||||||
\(415\) | −3626.74 | −0.428988 | ||||||||
\(416\) | 660.816 | 0.0778826 | ||||||||
\(417\) | 53.4897 | 0.00628154 | ||||||||
\(418\) | 99.5692 | 0.0116509 | ||||||||
\(419\) | 2641.37 | 0.307970 | 0.153985 | − | 0.988073i | \(-0.450789\pi\) | ||||
0.153985 | + | 0.988073i | \(0.450789\pi\) | |||||||
\(420\) | −86.0908 | −0.0100019 | ||||||||
\(421\) | −12311.3 | −1.42521 | −0.712607 | − | 0.701563i | \(-0.752486\pi\) | ||||
−0.712607 | + | 0.701563i | \(0.752486\pi\) | |||||||
\(422\) | 282.009 | 0.0325307 | ||||||||
\(423\) | 10123.8 | 1.16368 | ||||||||
\(424\) | 808.339 | 0.0925858 | ||||||||
\(425\) | −1213.40 | −0.138490 | ||||||||
\(426\) | 18.8032 | 0.00213854 | ||||||||
\(427\) | −242.302 | −0.0274609 | ||||||||
\(428\) | −13290.6 | −1.50099 | ||||||||
\(429\) | −26.0000 | −0.00292609 | ||||||||
\(430\) | 560.225 | 0.0628290 | ||||||||
\(431\) | 12155.0 | 1.35844 | 0.679219 | − | 0.733935i | \(-0.262318\pi\) | ||||
0.679219 | + | 0.733935i | \(0.262318\pi\) | |||||||
\(432\) | −659.236 | −0.0734201 | ||||||||
\(433\) | −9899.29 | −1.09868 | −0.549341 | − | 0.835598i | \(-0.685121\pi\) | ||||
−0.549341 | + | 0.835598i | \(0.685121\pi\) | |||||||
\(434\) | −464.517 | −0.0513768 | ||||||||
\(435\) | −101.051 | −0.0111380 | ||||||||
\(436\) | −14189.8 | −1.55864 | ||||||||
\(437\) | −430.190 | −0.0470910 | ||||||||
\(438\) | −17.9334 | −0.00195637 | ||||||||
\(439\) | −11922.9 | −1.29624 | −0.648121 | − | 0.761538i | \(-0.724445\pi\) | ||||
−0.648121 | + | 0.761538i | \(0.724445\pi\) | |||||||
\(440\) | −217.583 | −0.0235747 | ||||||||
\(441\) | 5942.73 | 0.641695 | ||||||||
\(442\) | −169.067 | −0.0181939 | ||||||||
\(443\) | 18171.1 | 1.94884 | 0.974420 | − | 0.224734i | \(-0.0721514\pi\) | ||||
0.974420 | + | 0.224734i | \(0.0721514\pi\) | |||||||
\(444\) | 410.197 | 0.0438448 | ||||||||
\(445\) | −7978.79 | −0.849958 | ||||||||
\(446\) | −835.950 | −0.0887520 | ||||||||
\(447\) | 313.466 | 0.0331687 | ||||||||
\(448\) | 5365.79 | 0.565870 | ||||||||
\(449\) | 13386.5 | 1.40701 | 0.703507 | − | 0.710689i | \(-0.251617\pi\) | ||||
0.703507 | + | 0.710689i | \(0.251617\pi\) | |||||||
\(450\) | −180.608 | −0.0189199 | ||||||||
\(451\) | −1895.99 | −0.197957 | ||||||||
\(452\) | 4479.98 | 0.466196 | ||||||||
\(453\) | −476.899 | −0.0494629 | ||||||||
\(454\) | −1376.03 | −0.142248 | ||||||||
\(455\) | 719.667 | 0.0741505 | ||||||||
\(456\) | 30.5105 | 0.00313330 | ||||||||
\(457\) | 15155.4 | 1.55129 | 0.775645 | − | 0.631170i | \(-0.217425\pi\) | ||||
0.775645 | + | 0.631170i | \(0.217425\pi\) | |||||||
\(458\) | −347.697 | −0.0354734 | ||||||||
\(459\) | 513.737 | 0.0522423 | ||||||||
\(460\) | 467.917 | 0.0474277 | ||||||||
\(461\) | −10147.2 | −1.02517 | −0.512584 | − | 0.858637i | \(-0.671312\pi\) | ||||
−0.512584 | + | 0.858637i | \(0.671312\pi\) | |||||||
\(462\) | 5.93336 | 0.000597500 0 | ||||||||
\(463\) | 8417.13 | 0.844876 | 0.422438 | − | 0.906392i | \(-0.361175\pi\) | ||||
0.422438 | + | 0.906392i | \(0.361175\pi\) | |||||||
\(464\) | 6417.12 | 0.642042 | ||||||||
\(465\) | −153.566 | −0.0153149 | ||||||||
\(466\) | −1139.26 | −0.113251 | ||||||||
\(467\) | 12107.8 | 1.19974 | 0.599872 | − | 0.800096i | \(-0.295218\pi\) | ||||
0.599872 | + | 0.800096i | \(0.295218\pi\) | |||||||
\(468\) | 2778.83 | 0.274469 | ||||||||
\(469\) | 7293.16 | 0.718053 | ||||||||
\(470\) | 503.064 | 0.0493715 | ||||||||
\(471\) | 135.935 | 0.0132984 | ||||||||
\(472\) | 829.957 | 0.0809362 | ||||||||
\(473\) | 4263.60 | 0.414462 | ||||||||
\(474\) | −52.8520 | −0.00512146 | ||||||||
\(475\) | −911.122 | −0.0880108 | ||||||||
\(476\) | −4260.45 | −0.410247 | ||||||||
\(477\) | 5106.44 | 0.490164 | ||||||||
\(478\) | −61.4369 | −0.00587879 | ||||||||
\(479\) | −2068.14 | −0.197277 | −0.0986385 | − | 0.995123i | \(-0.531449\pi\) | ||||
−0.0986385 | + | 0.995123i | \(0.531449\pi\) | |||||||
\(480\) | −49.8541 | −0.00474066 | ||||||||
\(481\) | −3429.00 | −0.325050 | ||||||||
\(482\) | −758.051 | −0.0716354 | ||||||||
\(483\) | −25.6351 | −0.00241499 | ||||||||
\(484\) | 9728.21 | 0.913619 | ||||||||
\(485\) | −5189.69 | −0.485880 | ||||||||
\(486\) | 114.728 | 0.0107082 | ||||||||
\(487\) | −90.2686 | −0.00839930 | −0.00419965 | − | 0.999991i | \(-0.501337\pi\) | ||||
−0.00419965 | + | 0.999991i | \(0.501337\pi\) | |||||||
\(488\) | −93.4022 | −0.00866418 | ||||||||
\(489\) | −84.7303 | −0.00783566 | ||||||||
\(490\) | 295.301 | 0.0272251 | ||||||||
\(491\) | 5422.85 | 0.498432 | 0.249216 | − | 0.968448i | \(-0.419827\pi\) | ||||
0.249216 | + | 0.968448i | \(0.419827\pi\) | |||||||
\(492\) | −289.179 | −0.0264984 | ||||||||
\(493\) | −5000.81 | −0.456847 | ||||||||
\(494\) | −126.950 | −0.0115622 | ||||||||
\(495\) | −1374.52 | −0.124808 | ||||||||
\(496\) | 9752.01 | 0.882818 | ||||||||
\(497\) | −3960.99 | −0.357494 | ||||||||
\(498\) | 38.1235 | 0.00343043 | ||||||||
\(499\) | −10624.1 | −0.953102 | −0.476551 | − | 0.879147i | \(-0.658113\pi\) | ||||
−0.476551 | + | 0.879147i | \(0.658113\pi\) | |||||||
\(500\) | 991.025 | 0.0886400 | ||||||||
\(501\) | −206.893 | −0.0184497 | ||||||||
\(502\) | 936.840 | 0.0832933 | ||||||||
\(503\) | 4451.06 | 0.394559 | 0.197279 | − | 0.980347i | \(-0.436789\pi\) | ||||
0.197279 | + | 0.980347i | \(0.436789\pi\) | |||||||
\(504\) | −1274.04 | −0.112599 | ||||||||
\(505\) | 2422.23 | 0.213441 | ||||||||
\(506\) | −32.2487 | −0.00283326 | ||||||||
\(507\) | 33.1498 | 0.00290381 | ||||||||
\(508\) | 11068.4 | 0.966694 | ||||||||
\(509\) | −8855.36 | −0.771134 | −0.385567 | − | 0.922680i | \(-0.625994\pi\) | ||||
−0.385567 | + | 0.922680i | \(0.625994\pi\) | |||||||
\(510\) | 12.7550 | 0.00110745 | ||||||||
\(511\) | 3777.75 | 0.327041 | ||||||||
\(512\) | 5292.45 | 0.456827 | ||||||||
\(513\) | 385.757 | 0.0332000 | ||||||||
\(514\) | −988.271 | −0.0848069 | ||||||||
\(515\) | 4735.20 | 0.405161 | ||||||||
\(516\) | 650.292 | 0.0554797 | ||||||||
\(517\) | 3828.58 | 0.325688 | ||||||||
\(518\) | 782.518 | 0.0663743 | ||||||||
\(519\) | −574.562 | −0.0485944 | ||||||||
\(520\) | 277.417 | 0.0233952 | ||||||||
\(521\) | −19004.5 | −1.59808 | −0.799042 | − | 0.601276i | \(-0.794659\pi\) | ||||
−0.799042 | + | 0.601276i | \(0.794659\pi\) | |||||||
\(522\) | −744.346 | −0.0624121 | ||||||||
\(523\) | −7819.17 | −0.653745 | −0.326872 | − | 0.945068i | \(-0.605995\pi\) | ||||
−0.326872 | + | 0.945068i | \(0.605995\pi\) | |||||||
\(524\) | 21198.1 | 1.76725 | ||||||||
\(525\) | −54.2940 | −0.00451349 | ||||||||
\(526\) | −1922.91 | −0.159397 | ||||||||
\(527\) | −7599.66 | −0.628172 | ||||||||
\(528\) | −124.564 | −0.0102670 | ||||||||
\(529\) | −12027.7 | −0.988548 | ||||||||
\(530\) | 253.744 | 0.0207961 | ||||||||
\(531\) | 5243.01 | 0.428488 | ||||||||
\(532\) | −3199.11 | −0.260712 | ||||||||
\(533\) | 2417.37 | 0.196450 | ||||||||
\(534\) | 83.8713 | 0.00679675 | ||||||||
\(535\) | −8381.83 | −0.677342 | ||||||||
\(536\) | 2811.36 | 0.226553 | ||||||||
\(537\) | 729.163 | 0.0585953 | ||||||||
\(538\) | 215.679 | 0.0172836 | ||||||||
\(539\) | 2247.39 | 0.179595 | ||||||||
\(540\) | −419.588 | −0.0334374 | ||||||||
\(541\) | −15252.8 | −1.21215 | −0.606073 | − | 0.795409i | \(-0.707256\pi\) | ||||
−0.606073 | + | 0.795409i | \(0.707256\pi\) | |||||||
\(542\) | 706.358 | 0.0559791 | ||||||||
\(543\) | 377.221 | 0.0298123 | ||||||||
\(544\) | −2467.18 | −0.194447 | ||||||||
\(545\) | −8948.92 | −0.703357 | ||||||||
\(546\) | −7.56498 | −0.000592951 0 | ||||||||
\(547\) | −9483.30 | −0.741273 | −0.370637 | − | 0.928778i | \(-0.620860\pi\) | ||||
−0.370637 | + | 0.928778i | \(0.620860\pi\) | |||||||
\(548\) | −19841.9 | −1.54672 | ||||||||
\(549\) | −590.041 | −0.0458695 | ||||||||
\(550\) | −68.3013 | −0.00529523 | ||||||||
\(551\) | −3755.04 | −0.290326 | ||||||||
\(552\) | −9.88181 | −0.000761952 0 | ||||||||
\(553\) | 11133.5 | 0.856142 | ||||||||
\(554\) | 451.035 | 0.0345896 | ||||||||
\(555\) | 258.695 | 0.0197856 | ||||||||
\(556\) | −2161.98 | −0.164907 | ||||||||
\(557\) | 16614.1 | 1.26384 | 0.631921 | − | 0.775033i | \(-0.282267\pi\) | ||||
0.631921 | + | 0.775033i | \(0.282267\pi\) | |||||||
\(558\) | −1131.17 | −0.0858177 | ||||||||
\(559\) | −5436.05 | −0.411307 | ||||||||
\(560\) | 3447.87 | 0.260177 | ||||||||
\(561\) | 97.0718 | 0.00730548 | ||||||||
\(562\) | 638.301 | 0.0479094 | ||||||||
\(563\) | −22459.9 | −1.68130 | −0.840652 | − | 0.541576i | \(-0.817828\pi\) | ||||
−0.840652 | + | 0.541576i | \(0.817828\pi\) | |||||||
\(564\) | 583.942 | 0.0435964 | ||||||||
\(565\) | 2825.35 | 0.210377 | ||||||||
\(566\) | −973.861 | −0.0723223 | ||||||||
\(567\) | −8036.85 | −0.595266 | ||||||||
\(568\) | −1526.88 | −0.112793 | ||||||||
\(569\) | −2376.89 | −0.175122 | −0.0875609 | − | 0.996159i | \(-0.527907\pi\) | ||||
−0.0875609 | + | 0.996159i | \(0.527907\pi\) | |||||||
\(570\) | 9.57751 | 0.000703785 0 | ||||||||
\(571\) | 17585.3 | 1.28883 | 0.644414 | − | 0.764677i | \(-0.277101\pi\) | ||||
0.644414 | + | 0.764677i | \(0.277101\pi\) | |||||||
\(572\) | 1050.88 | 0.0768175 | ||||||||
\(573\) | −380.828 | −0.0277650 | ||||||||
\(574\) | −551.658 | −0.0401145 | ||||||||
\(575\) | 295.096 | 0.0214024 | ||||||||
\(576\) | 13066.5 | 0.945206 | ||||||||
\(577\) | −5989.96 | −0.432176 | −0.216088 | − | 0.976374i | \(-0.569330\pi\) | ||||
−0.216088 | + | 0.976374i | \(0.569330\pi\) | |||||||
\(578\) | −685.218 | −0.0493102 | ||||||||
\(579\) | 457.916 | 0.0328676 | ||||||||
\(580\) | 4084.35 | 0.292402 | ||||||||
\(581\) | −8030.91 | −0.573457 | ||||||||
\(582\) | 54.5529 | 0.00388538 | ||||||||
\(583\) | 1931.13 | 0.137185 | ||||||||
\(584\) | 1456.25 | 0.103185 | ||||||||
\(585\) | 1752.50 | 0.123858 | ||||||||
\(586\) | 935.662 | 0.0659588 | ||||||||
\(587\) | 11523.1 | 0.810240 | 0.405120 | − | 0.914264i | \(-0.367230\pi\) | ||||
0.405120 | + | 0.914264i | \(0.367230\pi\) | |||||||
\(588\) | 342.776 | 0.0240405 | ||||||||
\(589\) | −5706.47 | −0.399204 | ||||||||
\(590\) | 260.531 | 0.0181795 | ||||||||
\(591\) | 423.795 | 0.0294968 | ||||||||
\(592\) | −16428.1 | −1.14052 | ||||||||
\(593\) | 4672.21 | 0.323549 | 0.161775 | − | 0.986828i | \(-0.448278\pi\) | ||||
0.161775 | + | 0.986828i | \(0.448278\pi\) | |||||||
\(594\) | 28.9179 | 0.00199750 | ||||||||
\(595\) | −2686.90 | −0.185130 | ||||||||
\(596\) | −12669.8 | −0.870766 | ||||||||
\(597\) | −389.508 | −0.0267027 | ||||||||
\(598\) | 41.1168 | 0.00281169 | ||||||||
\(599\) | −10245.3 | −0.698850 | −0.349425 | − | 0.936964i | \(-0.613623\pi\) | ||||
−0.349425 | + | 0.936964i | \(0.613623\pi\) | |||||||
\(600\) | −20.9292 | −0.00142405 | ||||||||
\(601\) | 11755.8 | 0.797883 | 0.398942 | − | 0.916976i | \(-0.369378\pi\) | ||||
0.398942 | + | 0.916976i | \(0.369378\pi\) | |||||||
\(602\) | 1240.54 | 0.0839877 | ||||||||
\(603\) | 17760.0 | 1.19941 | ||||||||
\(604\) | 19275.6 | 1.29853 | ||||||||
\(605\) | 6135.19 | 0.412283 | ||||||||
\(606\) | −25.4619 | −0.00170680 | ||||||||
\(607\) | −19364.3 | −1.29484 | −0.647422 | − | 0.762131i | \(-0.724153\pi\) | ||||
−0.647422 | + | 0.762131i | \(0.724153\pi\) | |||||||
\(608\) | −1852.57 | −0.123571 | ||||||||
\(609\) | −223.764 | −0.0148889 | ||||||||
\(610\) | −29.3198 | −0.00194610 | ||||||||
\(611\) | −4881.40 | −0.323208 | ||||||||
\(612\) | −10374.9 | −0.685260 | ||||||||
\(613\) | −21110.0 | −1.39091 | −0.695454 | − | 0.718571i | \(-0.744797\pi\) | ||||
−0.695454 | + | 0.718571i | \(0.744797\pi\) | |||||||
\(614\) | 458.237 | 0.0301188 | ||||||||
\(615\) | −182.374 | −0.0119578 | ||||||||
\(616\) | −481.808 | −0.0315139 | ||||||||
\(617\) | −2427.03 | −0.158361 | −0.0791803 | − | 0.996860i | \(-0.525230\pi\) | ||||
−0.0791803 | + | 0.996860i | \(0.525230\pi\) | |||||||
\(618\) | −49.7754 | −0.00323990 | ||||||||
\(619\) | −4293.14 | −0.278765 | −0.139383 | − | 0.990239i | \(-0.544512\pi\) | ||||
−0.139383 | + | 0.990239i | \(0.544512\pi\) | |||||||
\(620\) | 6206.92 | 0.402058 | ||||||||
\(621\) | −124.940 | −0.00807354 | ||||||||
\(622\) | 2186.02 | 0.140919 | ||||||||
\(623\) | −17667.9 | −1.13620 | ||||||||
\(624\) | 158.818 | 0.0101888 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 2951.39 | 0.188436 | ||||||||
\(627\) | 72.8897 | 0.00464264 | ||||||||
\(628\) | −5494.29 | −0.349118 | ||||||||
\(629\) | 12802.3 | 0.811542 | ||||||||
\(630\) | −399.931 | −0.0252915 | ||||||||
\(631\) | −3099.63 | −0.195554 | −0.0977769 | − | 0.995208i | \(-0.531173\pi\) | ||||
−0.0977769 | + | 0.995208i | \(0.531173\pi\) | |||||||
\(632\) | 4291.75 | 0.270121 | ||||||||
\(633\) | 206.445 | 0.0129628 | ||||||||
\(634\) | −1578.32 | −0.0988695 | ||||||||
\(635\) | 6980.39 | 0.436234 | ||||||||
\(636\) | 294.539 | 0.0183636 | ||||||||
\(637\) | −2865.40 | −0.178228 | ||||||||
\(638\) | −281.492 | −0.0174677 | ||||||||
\(639\) | −9645.62 | −0.597144 | ||||||||
\(640\) | 2682.57 | 0.165684 | ||||||||
\(641\) | 12932.1 | 0.796857 | 0.398429 | − | 0.917199i | \(-0.369556\pi\) | ||||
0.398429 | + | 0.917199i | \(0.369556\pi\) | |||||||
\(642\) | 88.1079 | 0.00541642 | ||||||||
\(643\) | 27965.0 | 1.71514 | 0.857568 | − | 0.514371i | \(-0.171974\pi\) | ||||
0.857568 | + | 0.514371i | \(0.171974\pi\) | |||||||
\(644\) | 1036.14 | 0.0633998 | ||||||||
\(645\) | 410.113 | 0.0250360 | ||||||||
\(646\) | 473.971 | 0.0288671 | ||||||||
\(647\) | −18467.6 | −1.12216 | −0.561080 | − | 0.827762i | \(-0.689614\pi\) | ||||
−0.561080 | + | 0.827762i | \(0.689614\pi\) | |||||||
\(648\) | −3098.04 | −0.187813 | ||||||||
\(649\) | 1982.77 | 0.119924 | ||||||||
\(650\) | 87.0835 | 0.00525492 | ||||||||
\(651\) | −340.050 | −0.0204725 | ||||||||
\(652\) | 3424.68 | 0.205707 | ||||||||
\(653\) | 4411.89 | 0.264396 | 0.132198 | − | 0.991223i | \(-0.457797\pi\) | ||||
0.132198 | + | 0.991223i | \(0.457797\pi\) | |||||||
\(654\) | 94.0691 | 0.00562445 | ||||||||
\(655\) | 13368.8 | 0.797498 | ||||||||
\(656\) | 11581.4 | 0.689296 | ||||||||
\(657\) | 9199.41 | 0.546276 | ||||||||
\(658\) | 1113.97 | 0.0659983 | ||||||||
\(659\) | 18059.6 | 1.06753 | 0.533765 | − | 0.845633i | \(-0.320777\pi\) | ||||
0.533765 | + | 0.845633i | \(0.320777\pi\) | |||||||
\(660\) | −79.2820 | −0.00467583 | ||||||||
\(661\) | 18324.0 | 1.07825 | 0.539125 | − | 0.842226i | \(-0.318755\pi\) | ||||
0.539125 | + | 0.842226i | \(0.318755\pi\) | |||||||
\(662\) | 4.07890 | 0.000239473 0 | ||||||||
\(663\) | −123.766 | −0.00724986 | ||||||||
\(664\) | −3095.75 | −0.180931 | ||||||||
\(665\) | −2017.55 | −0.117650 | ||||||||
\(666\) | 1905.55 | 0.110869 | ||||||||
\(667\) | 1216.19 | 0.0706013 | ||||||||
\(668\) | 8362.34 | 0.484354 | ||||||||
\(669\) | −611.958 | −0.0353657 | ||||||||
\(670\) | 882.511 | 0.0508871 | ||||||||
\(671\) | −223.138 | −0.0128378 | ||||||||
\(672\) | −110.395 | −0.00633717 | ||||||||
\(673\) | 5321.92 | 0.304822 | 0.152411 | − | 0.988317i | \(-0.451296\pi\) | ||||
0.152411 | + | 0.988317i | \(0.451296\pi\) | |||||||
\(674\) | 2825.34 | 0.161466 | ||||||||
\(675\) | −264.617 | −0.0150891 | ||||||||
\(676\) | −1339.87 | −0.0762327 | ||||||||
\(677\) | −17817.6 | −1.01150 | −0.505751 | − | 0.862679i | \(-0.668785\pi\) | ||||
−0.505751 | + | 0.862679i | \(0.668785\pi\) | |||||||
\(678\) | −29.6994 | −0.00168230 | ||||||||
\(679\) | −11491.8 | −0.649509 | ||||||||
\(680\) | −1035.74 | −0.0584102 | ||||||||
\(681\) | −1007.33 | −0.0566826 | ||||||||
\(682\) | −427.779 | −0.0240184 | ||||||||
\(683\) | 24498.3 | 1.37248 | 0.686238 | − | 0.727377i | \(-0.259261\pi\) | ||||
0.686238 | + | 0.727377i | \(0.259261\pi\) | |||||||
\(684\) | −7790.32 | −0.435483 | ||||||||
\(685\) | −12513.5 | −0.697981 | ||||||||
\(686\) | 1671.47 | 0.0930279 | ||||||||
\(687\) | −254.532 | −0.0141354 | ||||||||
\(688\) | −26043.7 | −1.44318 | ||||||||
\(689\) | −2462.17 | −0.136141 | ||||||||
\(690\) | −3.10199 | −0.000171146 0 | ||||||||
\(691\) | 36011.4 | 1.98254 | 0.991271 | − | 0.131839i | \(-0.0420881\pi\) | ||||
0.991271 | + | 0.131839i | \(0.0420881\pi\) | |||||||
\(692\) | 23223.0 | 1.27573 | ||||||||
\(693\) | −3043.68 | −0.166840 | ||||||||
\(694\) | −186.381 | −0.0101944 | ||||||||
\(695\) | −1363.47 | −0.0744165 | ||||||||
\(696\) | −86.2563 | −0.00469761 | ||||||||
\(697\) | −9025.31 | −0.490471 | ||||||||
\(698\) | −383.403 | −0.0207909 | ||||||||
\(699\) | −833.996 | −0.0451282 | ||||||||
\(700\) | 2194.49 | 0.118491 | ||||||||
\(701\) | 19527.5 | 1.05213 | 0.526064 | − | 0.850445i | \(-0.323667\pi\) | ||||
0.526064 | + | 0.850445i | \(0.323667\pi\) | |||||||
\(702\) | −36.8700 | −0.00198229 | ||||||||
\(703\) | 9613.03 | 0.515736 | ||||||||
\(704\) | 4941.42 | 0.264541 | ||||||||
\(705\) | 368.269 | 0.0196735 | ||||||||
\(706\) | −3391.64 | −0.180802 | ||||||||
\(707\) | 5363.69 | 0.285321 | ||||||||
\(708\) | 302.416 | 0.0160530 | ||||||||
\(709\) | −10114.7 | −0.535779 | −0.267889 | − | 0.963450i | \(-0.586326\pi\) | ||||
−0.267889 | + | 0.963450i | \(0.586326\pi\) | |||||||
\(710\) | −479.301 | −0.0253350 | ||||||||
\(711\) | 27111.9 | 1.43006 | ||||||||
\(712\) | −6810.62 | −0.358481 | ||||||||
\(713\) | 1848.22 | 0.0970779 | ||||||||
\(714\) | 28.2441 | 0.00148040 | ||||||||
\(715\) | 662.750 | 0.0346650 | ||||||||
\(716\) | −29471.7 | −1.53828 | ||||||||
\(717\) | −44.9750 | −0.00234257 | ||||||||
\(718\) | 1500.79 | 0.0780068 | ||||||||
\(719\) | −22538.4 | −1.16904 | −0.584522 | − | 0.811378i | \(-0.698718\pi\) | ||||
−0.584522 | + | 0.811378i | \(0.698718\pi\) | |||||||
\(720\) | 8396.09 | 0.434589 | ||||||||
\(721\) | 10485.4 | 0.541606 | ||||||||
\(722\) | −1481.97 | −0.0763893 | ||||||||
\(723\) | −554.932 | −0.0285451 | ||||||||
\(724\) | −15246.7 | −0.782652 | ||||||||
\(725\) | 2575.83 | 0.131950 | ||||||||
\(726\) | −64.4918 | −0.00329685 | ||||||||
\(727\) | −16847.2 | −0.859463 | −0.429731 | − | 0.902957i | \(-0.641392\pi\) | ||||
−0.429731 | + | 0.902957i | \(0.641392\pi\) | |||||||
\(728\) | 614.300 | 0.0312740 | ||||||||
\(729\) | −19514.9 | −0.991460 | ||||||||
\(730\) | 457.128 | 0.0231768 | ||||||||
\(731\) | 20295.7 | 1.02690 | ||||||||
\(732\) | −34.0335 | −0.00171846 | ||||||||
\(733\) | 36464.0 | 1.83742 | 0.918709 | − | 0.394936i | \(-0.129233\pi\) | ||||
0.918709 | + | 0.394936i | \(0.129233\pi\) | |||||||
\(734\) | −3384.27 | −0.170185 | ||||||||
\(735\) | 216.175 | 0.0108486 | ||||||||
\(736\) | 600.013 | 0.0300500 | ||||||||
\(737\) | 6716.36 | 0.335686 | ||||||||
\(738\) | −1343.37 | −0.0670056 | ||||||||
\(739\) | 3230.48 | 0.160805 | 0.0804026 | − | 0.996762i | \(-0.474379\pi\) | ||||
0.0804026 | + | 0.996762i | \(0.474379\pi\) | |||||||
\(740\) | −10456.1 | −0.519423 | ||||||||
\(741\) | −92.9337 | −0.00460730 | ||||||||
\(742\) | 561.881 | 0.0277996 | ||||||||
\(743\) | −28359.4 | −1.40028 | −0.700138 | − | 0.714008i | \(-0.746878\pi\) | ||||
−0.700138 | + | 0.714008i | \(0.746878\pi\) | |||||||
\(744\) | −131.082 | −0.00645929 | ||||||||
\(745\) | −7990.36 | −0.392945 | ||||||||
\(746\) | −1123.63 | −0.0551460 | ||||||||
\(747\) | −19556.5 | −0.957878 | ||||||||
\(748\) | −3923.50 | −0.191788 | ||||||||
\(749\) | −18560.4 | −0.905449 | ||||||||
\(750\) | −6.56986 | −0.000319863 0 | ||||||||
\(751\) | −5885.99 | −0.285996 | −0.142998 | − | 0.989723i | \(-0.545674\pi\) | ||||
−0.142998 | + | 0.989723i | \(0.545674\pi\) | |||||||
\(752\) | −23386.4 | −1.13406 | ||||||||
\(753\) | 685.815 | 0.0331905 | ||||||||
\(754\) | 358.900 | 0.0173347 | ||||||||
\(755\) | 12156.3 | 0.585979 | ||||||||
\(756\) | −929.118 | −0.0446980 | ||||||||
\(757\) | 29892.2 | 1.43521 | 0.717603 | − | 0.696452i | \(-0.245239\pi\) | ||||
0.717603 | + | 0.696452i | \(0.245239\pi\) | |||||||
\(758\) | 1072.82 | 0.0514072 | ||||||||
\(759\) | −23.6077 | −0.00112899 | ||||||||
\(760\) | −777.724 | −0.0371198 | ||||||||
\(761\) | −14562.1 | −0.693661 | −0.346830 | − | 0.937928i | \(-0.612742\pi\) | ||||
−0.346830 | + | 0.937928i | \(0.612742\pi\) | |||||||
\(762\) | −73.3763 | −0.00348838 | ||||||||
\(763\) | −19816.1 | −0.940225 | ||||||||
\(764\) | 15392.5 | 0.728904 | ||||||||
\(765\) | −6543.01 | −0.309233 | ||||||||
\(766\) | −2552.20 | −0.120385 | ||||||||
\(767\) | −2528.02 | −0.119011 | ||||||||
\(768\) | 732.301 | 0.0344071 | ||||||||
\(769\) | 20090.7 | 0.942117 | 0.471058 | − | 0.882102i | \(-0.343872\pi\) | ||||
0.471058 | + | 0.882102i | \(0.343872\pi\) | |||||||
\(770\) | −151.244 | −0.00707849 | ||||||||
\(771\) | −723.464 | −0.0337937 | ||||||||
\(772\) | −18508.3 | −0.862862 | ||||||||
\(773\) | −14955.4 | −0.695871 | −0.347936 | − | 0.937518i | \(-0.613117\pi\) | ||||
−0.347936 | + | 0.937518i | \(0.613117\pi\) | |||||||
\(774\) | 3020.90 | 0.140290 | ||||||||
\(775\) | 3914.45 | 0.181434 | ||||||||
\(776\) | −4429.87 | −0.204927 | ||||||||
\(777\) | 572.843 | 0.0264487 | ||||||||
\(778\) | 2659.16 | 0.122539 | ||||||||
\(779\) | −6776.97 | −0.311695 | ||||||||
\(780\) | 101.084 | 0.00464023 | ||||||||
\(781\) | −3647.73 | −0.167127 | ||||||||
\(782\) | −153.511 | −0.00701987 | ||||||||
\(783\) | −1090.58 | −0.0497752 | ||||||||
\(784\) | −13727.9 | −0.625361 | ||||||||
\(785\) | −3465.03 | −0.157544 | ||||||||
\(786\) | −140.529 | −0.00637725 | ||||||||
\(787\) | 14918.1 | 0.675695 | 0.337848 | − | 0.941201i | \(-0.390301\pi\) | ||||
0.337848 | + | 0.941201i | \(0.390301\pi\) | |||||||
\(788\) | −17129.2 | −0.774368 | ||||||||
\(789\) | −1407.67 | −0.0635162 | ||||||||
\(790\) | 1347.22 | 0.0606732 | ||||||||
\(791\) | 6256.33 | 0.281226 | ||||||||
\(792\) | −1173.28 | −0.0526396 | ||||||||
\(793\) | 284.499 | 0.0127401 | ||||||||
\(794\) | −1734.68 | −0.0775335 | ||||||||
\(795\) | 185.754 | 0.00828681 | ||||||||
\(796\) | 15743.4 | 0.701017 | ||||||||
\(797\) | −9626.31 | −0.427831 | −0.213916 | − | 0.976852i | \(-0.568622\pi\) | ||||
−0.213916 | + | 0.976852i | \(0.568622\pi\) | |||||||
\(798\) | 21.2080 | 0.000940798 0 | ||||||||
\(799\) | 18224.9 | 0.806945 | ||||||||
\(800\) | 1270.80 | 0.0561620 | ||||||||
\(801\) | −43024.1 | −1.89785 | ||||||||
\(802\) | −2246.23 | −0.0988992 | ||||||||
\(803\) | 3478.98 | 0.152890 | ||||||||
\(804\) | 1024.39 | 0.0449347 | ||||||||
\(805\) | 653.449 | 0.0286100 | ||||||||
\(806\) | 545.415 | 0.0238355 | ||||||||
\(807\) | 157.888 | 0.00688713 | ||||||||
\(808\) | 2067.59 | 0.0900218 | ||||||||
\(809\) | 28544.0 | 1.24048 | 0.620242 | − | 0.784410i | \(-0.287034\pi\) | ||||
0.620242 | + | 0.784410i | \(0.287034\pi\) | |||||||
\(810\) | −972.501 | −0.0421855 | ||||||||
\(811\) | −11228.4 | −0.486168 | −0.243084 | − | 0.970005i | \(-0.578159\pi\) | ||||
−0.243084 | + | 0.970005i | \(0.578159\pi\) | |||||||
\(812\) | 9044.21 | 0.390874 | ||||||||
\(813\) | 517.090 | 0.0223064 | ||||||||
\(814\) | 720.631 | 0.0310296 | ||||||||
\(815\) | 2159.81 | 0.0928279 | ||||||||
\(816\) | −592.952 | −0.0254381 | ||||||||
\(817\) | 15239.7 | 0.652594 | ||||||||
\(818\) | −3122.84 | −0.133481 | ||||||||
\(819\) | 3880.66 | 0.165569 | ||||||||
\(820\) | 7371.30 | 0.313923 | ||||||||
\(821\) | 1636.05 | 0.0695474 | 0.0347737 | − | 0.999395i | \(-0.488929\pi\) | ||||
0.0347737 | + | 0.999395i | \(0.488929\pi\) | |||||||
\(822\) | 131.539 | 0.00558146 | ||||||||
\(823\) | −34916.5 | −1.47887 | −0.739437 | − | 0.673225i | \(-0.764908\pi\) | ||||
−0.739437 | + | 0.673225i | \(0.764908\pi\) | |||||||
\(824\) | 4041.92 | 0.170882 | ||||||||
\(825\) | −50.0000 | −0.00211003 | ||||||||
\(826\) | 576.908 | 0.0243017 | ||||||||
\(827\) | −40106.8 | −1.68640 | −0.843198 | − | 0.537603i | \(-0.819330\pi\) | ||||
−0.843198 | + | 0.537603i | \(0.819330\pi\) | |||||||
\(828\) | 2523.15 | 0.105900 | ||||||||
\(829\) | 35438.8 | 1.48473 | 0.742364 | − | 0.669996i | \(-0.233704\pi\) | ||||
0.742364 | + | 0.669996i | \(0.233704\pi\) | |||||||
\(830\) | −971.783 | −0.0406399 | ||||||||
\(831\) | 330.180 | 0.0137832 | ||||||||
\(832\) | −6300.27 | −0.262527 | ||||||||
\(833\) | 10698.1 | 0.444977 | ||||||||
\(834\) | 14.3325 | 0.000595078 0 | ||||||||
\(835\) | 5273.79 | 0.218571 | ||||||||
\(836\) | −2946.10 | −0.121882 | ||||||||
\(837\) | −1657.33 | −0.0684417 | ||||||||
\(838\) | 707.752 | 0.0291753 | ||||||||
\(839\) | −32415.0 | −1.33384 | −0.666919 | − | 0.745130i | \(-0.732387\pi\) | ||||
−0.666919 | + | 0.745130i | \(0.732387\pi\) | |||||||
\(840\) | −46.3448 | −0.00190363 | ||||||||
\(841\) | −13773.1 | −0.564727 | ||||||||
\(842\) | −3298.80 | −0.135017 | ||||||||
\(843\) | 467.269 | 0.0190908 | ||||||||
\(844\) | −8344.21 | −0.340307 | ||||||||
\(845\) | −845.000 | −0.0344010 | ||||||||
\(846\) | 2712.68 | 0.110241 | ||||||||
\(847\) | 13585.5 | 0.551126 | ||||||||
\(848\) | −11796.1 | −0.477687 | ||||||||
\(849\) | −712.916 | −0.0288189 | ||||||||
\(850\) | −325.129 | −0.0131198 | ||||||||
\(851\) | −3113.49 | −0.125416 | ||||||||
\(852\) | −556.358 | −0.0223715 | ||||||||
\(853\) | 36881.7 | 1.48043 | 0.740214 | − | 0.672371i | \(-0.234724\pi\) | ||||
0.740214 | + | 0.672371i | \(0.234724\pi\) | |||||||
\(854\) | −64.9245 | −0.00260149 | ||||||||
\(855\) | −4913.05 | −0.196518 | ||||||||
\(856\) | −7154.64 | −0.285678 | ||||||||
\(857\) | 30112.3 | 1.20025 | 0.600126 | − | 0.799906i | \(-0.295117\pi\) | ||||
0.600126 | + | 0.799906i | \(0.295117\pi\) | |||||||
\(858\) | −6.96668 | −0.000277201 0 | ||||||||
\(859\) | 9640.14 | 0.382907 | 0.191454 | − | 0.981502i | \(-0.438680\pi\) | ||||
0.191454 | + | 0.981502i | \(0.438680\pi\) | |||||||
\(860\) | −16576.2 | −0.657260 | ||||||||
\(861\) | −403.841 | −0.0159848 | ||||||||
\(862\) | 3256.93 | 0.128691 | ||||||||
\(863\) | 22960.7 | 0.905668 | 0.452834 | − | 0.891595i | \(-0.350413\pi\) | ||||
0.452834 | + | 0.891595i | \(0.350413\pi\) | |||||||
\(864\) | −538.041 | −0.0211858 | ||||||||
\(865\) | 14645.8 | 0.575691 | ||||||||
\(866\) | −2652.51 | −0.104083 | ||||||||
\(867\) | −501.614 | −0.0196490 | ||||||||
\(868\) | 13744.3 | 0.537458 | ||||||||
\(869\) | 10253.0 | 0.400241 | ||||||||
\(870\) | −27.0766 | −0.00105515 | ||||||||
\(871\) | −8563.30 | −0.333130 | ||||||||
\(872\) | −7638.71 | −0.296651 | ||||||||
\(873\) | −27984.4 | −1.08491 | ||||||||
\(874\) | −115.269 | −0.00446113 | ||||||||
\(875\) | 1383.97 | 0.0534707 | ||||||||
\(876\) | 530.620 | 0.0204658 | ||||||||
\(877\) | 40801.9 | 1.57102 | 0.785508 | − | 0.618851i | \(-0.212402\pi\) | ||||
0.785508 | + | 0.618851i | \(0.212402\pi\) | |||||||
\(878\) | −3194.74 | −0.122799 | ||||||||
\(879\) | 684.952 | 0.0262831 | ||||||||
\(880\) | 3175.19 | 0.121631 | ||||||||
\(881\) | −3875.57 | −0.148208 | −0.0741040 | − | 0.997251i | \(-0.523610\pi\) | ||||
−0.0741040 | + | 0.997251i | \(0.523610\pi\) | |||||||
\(882\) | 1592.35 | 0.0607905 | ||||||||
\(883\) | −18239.8 | −0.695149 | −0.347574 | − | 0.937652i | \(-0.612995\pi\) | ||||
−0.347574 | + | 0.937652i | \(0.612995\pi\) | |||||||
\(884\) | 5002.43 | 0.190328 | ||||||||
\(885\) | 190.722 | 0.00724411 | ||||||||
\(886\) | 4868.94 | 0.184622 | ||||||||
\(887\) | 2380.14 | 0.0900985 | 0.0450493 | − | 0.998985i | \(-0.485656\pi\) | ||||
0.0450493 | + | 0.998985i | \(0.485656\pi\) | |||||||
\(888\) | 220.819 | 0.00834483 | ||||||||
\(889\) | 15457.1 | 0.583143 | ||||||||
\(890\) | −2137.91 | −0.0805202 | ||||||||
\(891\) | −7401.23 | −0.278284 | ||||||||
\(892\) | 24734.5 | 0.928444 | ||||||||
\(893\) | 13684.8 | 0.512814 | ||||||||
\(894\) | 83.9928 | 0.00314222 | ||||||||
\(895\) | −18586.6 | −0.694171 | ||||||||
\(896\) | 5940.17 | 0.221481 | ||||||||
\(897\) | 30.0996 | 0.00112040 | ||||||||
\(898\) | 3586.91 | 0.133292 | ||||||||
\(899\) | 16132.8 | 0.598507 | ||||||||
\(900\) | 5343.91 | 0.197923 | ||||||||
\(901\) | 9192.58 | 0.339899 | ||||||||
\(902\) | −508.028 | −0.0187533 | ||||||||
\(903\) | 908.138 | 0.0334673 | ||||||||
\(904\) | 2411.69 | 0.0887295 | ||||||||
\(905\) | −9615.50 | −0.353182 | ||||||||
\(906\) | −127.785 | −0.00468583 | ||||||||
\(907\) | 2739.49 | 0.100290 | 0.0501452 | − | 0.998742i | \(-0.484032\pi\) | ||||
0.0501452 | + | 0.998742i | \(0.484032\pi\) | |||||||
\(908\) | 40714.8 | 1.48807 | ||||||||
\(909\) | 13061.4 | 0.476589 | ||||||||
\(910\) | 192.834 | 0.00702460 | ||||||||
\(911\) | −42446.3 | −1.54370 | −0.771850 | − | 0.635805i | \(-0.780668\pi\) | ||||
−0.771850 | + | 0.635805i | \(0.780668\pi\) | |||||||
\(912\) | −445.239 | −0.0161659 | ||||||||
\(913\) | −7395.77 | −0.268088 | ||||||||
\(914\) | 4060.87 | 0.146960 | ||||||||
\(915\) | −21.4636 | −0.000775479 0 | ||||||||
\(916\) | 10287.8 | 0.371091 | ||||||||
\(917\) | 29603.3 | 1.06607 | ||||||||
\(918\) | 137.655 | 0.00494914 | ||||||||
\(919\) | 7246.81 | 0.260120 | 0.130060 | − | 0.991506i | \(-0.458483\pi\) | ||||
0.130060 | + | 0.991506i | \(0.458483\pi\) | |||||||
\(920\) | 251.891 | 0.00902674 | ||||||||
\(921\) | 335.453 | 0.0120017 | ||||||||
\(922\) | −2718.94 | −0.0971187 | ||||||||
\(923\) | 4650.82 | 0.165854 | ||||||||
\(924\) | −175.559 | −0.00625050 | ||||||||
\(925\) | −6594.23 | −0.234397 | ||||||||
\(926\) | 2255.36 | 0.0800387 | ||||||||
\(927\) | 25533.6 | 0.904676 | ||||||||
\(928\) | 5237.39 | 0.185265 | ||||||||
\(929\) | −26804.8 | −0.946648 | −0.473324 | − | 0.880888i | \(-0.656946\pi\) | ||||
−0.473324 | + | 0.880888i | \(0.656946\pi\) | |||||||
\(930\) | −41.1479 | −0.00145085 | ||||||||
\(931\) | 8033.01 | 0.282783 | ||||||||
\(932\) | 33708.9 | 1.18473 | ||||||||
\(933\) | 1600.28 | 0.0561529 | ||||||||
\(934\) | 3244.26 | 0.113657 | ||||||||
\(935\) | −2474.40 | −0.0865470 | ||||||||
\(936\) | 1495.92 | 0.0522388 | ||||||||
\(937\) | 43808.7 | 1.52739 | 0.763696 | − | 0.645576i | \(-0.223383\pi\) | ||||
0.763696 | + | 0.645576i | \(0.223383\pi\) | |||||||
\(938\) | 1954.20 | 0.0680243 | ||||||||
\(939\) | 2160.57 | 0.0750878 | ||||||||
\(940\) | −14884.9 | −0.516481 | ||||||||
\(941\) | −13038.6 | −0.451697 | −0.225848 | − | 0.974162i | \(-0.572515\pi\) | ||||
−0.225848 | + | 0.974162i | \(0.572515\pi\) | |||||||
\(942\) | 36.4236 | 0.00125981 | ||||||||
\(943\) | 2194.94 | 0.0757975 | ||||||||
\(944\) | −12111.5 | −0.417581 | ||||||||
\(945\) | −585.957 | −0.0201706 | ||||||||
\(946\) | 1142.43 | 0.0392638 | ||||||||
\(947\) | −45110.1 | −1.54792 | −0.773961 | − | 0.633233i | \(-0.781727\pi\) | ||||
−0.773961 | + | 0.633233i | \(0.781727\pi\) | |||||||
\(948\) | 1563.81 | 0.0535761 | ||||||||
\(949\) | −4435.67 | −0.151726 | ||||||||
\(950\) | −244.134 | −0.00833764 | ||||||||
\(951\) | −1155.41 | −0.0393973 | ||||||||
\(952\) | −2293.51 | −0.0780809 | ||||||||
\(953\) | 9455.70 | 0.321406 | 0.160703 | − | 0.987003i | \(-0.448624\pi\) | ||||
0.160703 | + | 0.987003i | \(0.448624\pi\) | |||||||
\(954\) | 1368.27 | 0.0464353 | ||||||||
\(955\) | 9707.46 | 0.328928 | ||||||||
\(956\) | 1817.82 | 0.0614986 | ||||||||
\(957\) | −206.067 | −0.00696049 | ||||||||
\(958\) | −554.156 | −0.0186889 | ||||||||
\(959\) | −27709.4 | −0.933038 | ||||||||
\(960\) | 475.312 | 0.0159798 | ||||||||
\(961\) | −5274.28 | −0.177043 | ||||||||
\(962\) | −918.797 | −0.0307934 | ||||||||
\(963\) | −45197.4 | −1.51242 | ||||||||
\(964\) | 22429.6 | 0.749385 | ||||||||
\(965\) | −11672.5 | −0.389378 | ||||||||
\(966\) | −6.86891 | −0.000228782 0 | ||||||||
\(967\) | −5616.97 | −0.186794 | −0.0933969 | − | 0.995629i | \(-0.529773\pi\) | ||||
−0.0933969 | + | 0.995629i | \(0.529773\pi\) | |||||||
\(968\) | 5236.94 | 0.173886 | ||||||||
\(969\) | 346.971 | 0.0115029 | ||||||||
\(970\) | −1390.57 | −0.0460295 | ||||||||
\(971\) | 12009.7 | 0.396919 | 0.198459 | − | 0.980109i | \(-0.436406\pi\) | ||||
0.198459 | + | 0.980109i | \(0.436406\pi\) | |||||||
\(972\) | −3394.62 | −0.112019 | ||||||||
\(973\) | −3019.22 | −0.0994776 | ||||||||
\(974\) | −24.1874 | −0.000795702 0 | ||||||||
\(975\) | 63.7495 | 0.00209397 | ||||||||
\(976\) | 1363.02 | 0.0447019 | ||||||||
\(977\) | −36835.7 | −1.20622 | −0.603111 | − | 0.797657i | \(-0.706073\pi\) | ||||
−0.603111 | + | 0.797657i | \(0.706073\pi\) | |||||||
\(978\) | −22.7034 | −0.000742306 0 | ||||||||
\(979\) | −16270.6 | −0.531165 | ||||||||
\(980\) | −8737.49 | −0.284805 | ||||||||
\(981\) | −48255.3 | −1.57051 | ||||||||
\(982\) | 1453.05 | 0.0472186 | ||||||||
\(983\) | 11311.1 | 0.367006 | 0.183503 | − | 0.983019i | \(-0.441256\pi\) | ||||
0.183503 | + | 0.983019i | \(0.441256\pi\) | |||||||
\(984\) | −155.673 | −0.00504335 | ||||||||
\(985\) | −10802.7 | −0.349444 | ||||||||
\(986\) | −1339.96 | −0.0432791 | ||||||||
\(987\) | 815.479 | 0.0262989 | ||||||||
\(988\) | 3756.25 | 0.120954 | ||||||||
\(989\) | −4935.87 | −0.158697 | ||||||||
\(990\) | −368.301 | −0.0118236 | ||||||||
\(991\) | −45711.2 | −1.46525 | −0.732625 | − | 0.680632i | \(-0.761705\pi\) | ||||
−0.732625 | + | 0.680632i | \(0.761705\pi\) | |||||||
\(992\) | 7959.18 | 0.254742 | ||||||||
\(993\) | 2.98596 | 9.54246e−5 0 | ||||||||
\(994\) | −1061.34 | −0.0338670 | ||||||||
\(995\) | 9928.72 | 0.316343 | ||||||||
\(996\) | −1128.02 | −0.0358861 | ||||||||
\(997\) | −24127.3 | −0.766418 | −0.383209 | − | 0.923662i | \(-0.625181\pi\) | ||||
−0.383209 | + | 0.923662i | \(0.625181\pi\) | |||||||
\(998\) | −2846.71 | −0.0902915 | ||||||||
\(999\) | 2791.91 | 0.0884206 |
(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 | 65.4.a.d.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 585.4.a.f.1.2 | 2 | |||
4.3 | odd | 2 | 1040.4.a.o.1.1 | 2 | |||
5.2 | odd | 4 | 325.4.b.c.274.3 | 4 | |||
5.3 | odd | 4 | 325.4.b.c.274.2 | 4 | |||
5.4 | even | 2 | 325.4.a.e.1.2 | 2 | |||
13.12 | even | 2 | 845.4.a.c.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.4.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
325.4.a.e.1.2 | 2 | 5.4 | even | 2 | |||
325.4.b.c.274.2 | 4 | 5.3 | odd | 4 | |||
325.4.b.c.274.3 | 4 | 5.2 | odd | 4 | |||
585.4.a.f.1.2 | 2 | 3.2 | odd | 2 | |||
845.4.a.c.1.2 | 2 | 13.12 | even | 2 | |||
1040.4.a.o.1.1 | 2 | 4.3 | odd | 2 |