Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.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: | \(32.1477718538\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.30998405.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 9x^{4} + 8x^{3} + 16x^{2} - 13x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.215842\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.40290 | −0.627398 | −0.313699 | − | 0.949522i | \(-0.601568\pi\) | ||||
−0.313699 | + | 0.949522i | \(0.601568\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.64146 | 0.998377 | 0.499188 | − | 0.866494i | \(-0.333632\pi\) | ||||
0.499188 | + | 0.866494i | \(0.333632\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.40290 | 0.443637 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −2.22074 | −0.615924 | −0.307962 | − | 0.951399i | \(-0.599647\pi\) | ||||
−0.307962 | + | 0.951399i | \(0.599647\pi\) | |||||||
\(14\) | −2.64146 | −0.705959 | ||||||||
\(15\) | 1.40290 | 0.362228 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.42561 | −0.588298 | −0.294149 | − | 0.955760i | \(-0.595036\pi\) | ||||
−0.294149 | + | 0.955760i | \(0.595036\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.90697 | 0.437488 | 0.218744 | − | 0.975782i | \(-0.429804\pi\) | ||||
0.218744 | + | 0.975782i | \(0.429804\pi\) | |||||||
\(20\) | −1.40290 | −0.313699 | ||||||||
\(21\) | −2.64146 | −0.576413 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −0.204870 | −0.0427183 | −0.0213592 | − | 0.999772i | \(-0.506799\pi\) | ||||
−0.0213592 | + | 0.999772i | \(0.506799\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −3.03186 | −0.606372 | ||||||||
\(26\) | 2.22074 | 0.435524 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.64146 | 0.499188 | ||||||||
\(29\) | 0.472061 | 0.0876595 | 0.0438297 | − | 0.999039i | \(-0.486044\pi\) | ||||
0.0438297 | + | 0.999039i | \(0.486044\pi\) | |||||||
\(30\) | −1.40290 | −0.256134 | ||||||||
\(31\) | 9.76569 | 1.75397 | 0.876985 | − | 0.480518i | \(-0.159551\pi\) | ||||
0.876985 | + | 0.480518i | \(0.159551\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 2.42561 | 0.415989 | ||||||||
\(35\) | −3.70571 | −0.626379 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.76367 | −1.11194 | −0.555970 | − | 0.831202i | \(-0.687653\pi\) | ||||
−0.555970 | + | 0.831202i | \(0.687653\pi\) | |||||||
\(38\) | −1.90697 | −0.309351 | ||||||||
\(39\) | 2.22074 | 0.355604 | ||||||||
\(40\) | 1.40290 | 0.221819 | ||||||||
\(41\) | −7.76093 | −1.21205 | −0.606027 | − | 0.795444i | \(-0.707238\pi\) | ||||
−0.606027 | + | 0.795444i | \(0.707238\pi\) | |||||||
\(42\) | 2.64146 | 0.407586 | ||||||||
\(43\) | −1.63963 | −0.250042 | −0.125021 | − | 0.992154i | \(-0.539900\pi\) | ||||
−0.125021 | + | 0.992154i | \(0.539900\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −1.40290 | −0.209133 | ||||||||
\(46\) | 0.204870 | 0.0302064 | ||||||||
\(47\) | 10.0230 | 1.46200 | 0.731000 | − | 0.682377i | \(-0.239054\pi\) | ||||
0.731000 | + | 0.682377i | \(0.239054\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −0.0227093 | −0.00324419 | ||||||||
\(50\) | 3.03186 | 0.428770 | ||||||||
\(51\) | 2.42561 | 0.339654 | ||||||||
\(52\) | −2.22074 | −0.307962 | ||||||||
\(53\) | −9.17082 | −1.25971 | −0.629855 | − | 0.776713i | \(-0.716886\pi\) | ||||
−0.629855 | + | 0.776713i | \(0.716886\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −1.40290 | −0.189168 | ||||||||
\(56\) | −2.64146 | −0.352979 | ||||||||
\(57\) | −1.90697 | −0.252584 | ||||||||
\(58\) | −0.472061 | −0.0619846 | ||||||||
\(59\) | −10.6068 | −1.38088 | −0.690441 | − | 0.723389i | \(-0.742584\pi\) | ||||
−0.690441 | + | 0.723389i | \(0.742584\pi\) | |||||||
\(60\) | 1.40290 | 0.181114 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | −9.76569 | −1.24024 | ||||||||
\(63\) | 2.64146 | 0.332792 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.11549 | 0.386429 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | 6.95159 | 0.849272 | 0.424636 | − | 0.905364i | \(-0.360402\pi\) | ||||
0.424636 | + | 0.905364i | \(0.360402\pi\) | |||||||
\(68\) | −2.42561 | −0.294149 | ||||||||
\(69\) | 0.204870 | 0.0246634 | ||||||||
\(70\) | 3.70571 | 0.442917 | ||||||||
\(71\) | −7.05306 | −0.837044 | −0.418522 | − | 0.908207i | \(-0.637452\pi\) | ||||
−0.418522 | + | 0.908207i | \(0.637452\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 13.5829 | 1.58976 | 0.794878 | − | 0.606769i | \(-0.207535\pi\) | ||||
0.794878 | + | 0.606769i | \(0.207535\pi\) | |||||||
\(74\) | 6.76367 | 0.786261 | ||||||||
\(75\) | 3.03186 | 0.350089 | ||||||||
\(76\) | 1.90697 | 0.218744 | ||||||||
\(77\) | 2.64146 | 0.301022 | ||||||||
\(78\) | −2.22074 | −0.251450 | ||||||||
\(79\) | −11.7867 | −1.32611 | −0.663055 | − | 0.748571i | \(-0.730740\pi\) | ||||
−0.663055 | + | 0.748571i | \(0.730740\pi\) | |||||||
\(80\) | −1.40290 | −0.156849 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.76093 | 0.857052 | ||||||||
\(83\) | 11.9485 | 1.31152 | 0.655760 | − | 0.754970i | \(-0.272349\pi\) | ||||
0.655760 | + | 0.754970i | \(0.272349\pi\) | |||||||
\(84\) | −2.64146 | −0.288206 | ||||||||
\(85\) | 3.40290 | 0.369097 | ||||||||
\(86\) | 1.63963 | 0.176806 | ||||||||
\(87\) | −0.472061 | −0.0506102 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −17.0716 | −1.80958 | −0.904792 | − | 0.425854i | \(-0.859974\pi\) | ||||
−0.904792 | + | 0.425854i | \(0.859974\pi\) | |||||||
\(90\) | 1.40290 | 0.147879 | ||||||||
\(91\) | −5.86600 | −0.614924 | ||||||||
\(92\) | −0.204870 | −0.0213592 | ||||||||
\(93\) | −9.76569 | −1.01266 | ||||||||
\(94\) | −10.0230 | −1.03379 | ||||||||
\(95\) | −2.67529 | −0.274479 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 3.02014 | 0.306649 | 0.153325 | − | 0.988176i | \(-0.451002\pi\) | ||||
0.153325 | + | 0.988176i | \(0.451002\pi\) | |||||||
\(98\) | 0.0227093 | 0.00229399 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −3.03186 | −0.303186 | ||||||||
\(101\) | −6.26627 | −0.623518 | −0.311759 | − | 0.950161i | \(-0.600918\pi\) | ||||
−0.311759 | + | 0.950161i | \(0.600918\pi\) | |||||||
\(102\) | −2.42561 | −0.240172 | ||||||||
\(103\) | 8.42353 | 0.829995 | 0.414997 | − | 0.909823i | \(-0.363782\pi\) | ||||
0.414997 | + | 0.909823i | \(0.363782\pi\) | |||||||
\(104\) | 2.22074 | 0.217762 | ||||||||
\(105\) | 3.70571 | 0.361640 | ||||||||
\(106\) | 9.17082 | 0.890749 | ||||||||
\(107\) | 8.61317 | 0.832666 | 0.416333 | − | 0.909212i | \(-0.363315\pi\) | ||||
0.416333 | + | 0.909212i | \(0.363315\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −0.270369 | −0.0258967 | −0.0129483 | − | 0.999916i | \(-0.504122\pi\) | ||||
−0.0129483 | + | 0.999916i | \(0.504122\pi\) | |||||||
\(110\) | 1.40290 | 0.133762 | ||||||||
\(111\) | 6.76367 | 0.641979 | ||||||||
\(112\) | 2.64146 | 0.249594 | ||||||||
\(113\) | −1.33006 | −0.125121 | −0.0625606 | − | 0.998041i | \(-0.519927\pi\) | ||||
−0.0625606 | + | 0.998041i | \(0.519927\pi\) | |||||||
\(114\) | 1.90697 | 0.178604 | ||||||||
\(115\) | 0.287413 | 0.0268014 | ||||||||
\(116\) | 0.472061 | 0.0438297 | ||||||||
\(117\) | −2.22074 | −0.205308 | ||||||||
\(118\) | 10.6068 | 0.976431 | ||||||||
\(119\) | −6.40715 | −0.587343 | ||||||||
\(120\) | −1.40290 | −0.128067 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.00000 | −0.0905357 | ||||||||
\(123\) | 7.76093 | 0.699780 | ||||||||
\(124\) | 9.76569 | 0.876985 | ||||||||
\(125\) | 11.2679 | 1.00783 | ||||||||
\(126\) | −2.64146 | −0.235320 | ||||||||
\(127\) | 16.8165 | 1.49223 | 0.746113 | − | 0.665820i | \(-0.231918\pi\) | ||||
0.746113 | + | 0.665820i | \(0.231918\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.63963 | 0.144362 | ||||||||
\(130\) | −3.11549 | −0.273247 | ||||||||
\(131\) | −8.83870 | −0.772240 | −0.386120 | − | 0.922448i | \(-0.626185\pi\) | ||||
−0.386120 | + | 0.922448i | \(0.626185\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 5.03717 | 0.436778 | ||||||||
\(134\) | −6.95159 | −0.600526 | ||||||||
\(135\) | 1.40290 | 0.120743 | ||||||||
\(136\) | 2.42561 | 0.207995 | ||||||||
\(137\) | 17.6367 | 1.50680 | 0.753401 | − | 0.657561i | \(-0.228412\pi\) | ||||
0.753401 | + | 0.657561i | \(0.228412\pi\) | |||||||
\(138\) | −0.204870 | −0.0174397 | ||||||||
\(139\) | 12.9773 | 1.10072 | 0.550360 | − | 0.834928i | \(-0.314491\pi\) | ||||
0.550360 | + | 0.834928i | \(0.314491\pi\) | |||||||
\(140\) | −3.70571 | −0.313190 | ||||||||
\(141\) | −10.0230 | −0.844086 | ||||||||
\(142\) | 7.05306 | 0.591880 | ||||||||
\(143\) | −2.22074 | −0.185708 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.662256 | −0.0549974 | ||||||||
\(146\) | −13.5829 | −1.12413 | ||||||||
\(147\) | 0.0227093 | 0.00187303 | ||||||||
\(148\) | −6.76367 | −0.555970 | ||||||||
\(149\) | 2.01437 | 0.165023 | 0.0825116 | − | 0.996590i | \(-0.473706\pi\) | ||||
0.0825116 | + | 0.996590i | \(0.473706\pi\) | |||||||
\(150\) | −3.03186 | −0.247550 | ||||||||
\(151\) | −15.4442 | −1.25683 | −0.628414 | − | 0.777879i | \(-0.716296\pi\) | ||||
−0.628414 | + | 0.777879i | \(0.716296\pi\) | |||||||
\(152\) | −1.90697 | −0.154675 | ||||||||
\(153\) | −2.42561 | −0.196099 | ||||||||
\(154\) | −2.64146 | −0.212855 | ||||||||
\(155\) | −13.7003 | −1.10044 | ||||||||
\(156\) | 2.22074 | 0.177802 | ||||||||
\(157\) | −8.93090 | −0.712763 | −0.356382 | − | 0.934340i | \(-0.615990\pi\) | ||||
−0.356382 | + | 0.934340i | \(0.615990\pi\) | |||||||
\(158\) | 11.7867 | 0.937701 | ||||||||
\(159\) | 9.17082 | 0.727294 | ||||||||
\(160\) | 1.40290 | 0.110909 | ||||||||
\(161\) | −0.541155 | −0.0426490 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −10.0502 | −0.787191 | −0.393595 | − | 0.919284i | \(-0.628769\pi\) | ||||
−0.393595 | + | 0.919284i | \(0.628769\pi\) | |||||||
\(164\) | −7.76093 | −0.606027 | ||||||||
\(165\) | 1.40290 | 0.109216 | ||||||||
\(166\) | −11.9485 | −0.927384 | ||||||||
\(167\) | −14.9634 | −1.15790 | −0.578950 | − | 0.815363i | \(-0.696537\pi\) | ||||
−0.578950 | + | 0.815363i | \(0.696537\pi\) | |||||||
\(168\) | 2.64146 | 0.203793 | ||||||||
\(169\) | −8.06830 | −0.620638 | ||||||||
\(170\) | −3.40290 | −0.260991 | ||||||||
\(171\) | 1.90697 | 0.145829 | ||||||||
\(172\) | −1.63963 | −0.125021 | ||||||||
\(173\) | −19.1504 | −1.45598 | −0.727988 | − | 0.685589i | \(-0.759545\pi\) | ||||
−0.727988 | + | 0.685589i | \(0.759545\pi\) | |||||||
\(174\) | 0.472061 | 0.0357868 | ||||||||
\(175\) | −8.00852 | −0.605387 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 10.6068 | 0.797253 | ||||||||
\(178\) | 17.0716 | 1.27957 | ||||||||
\(179\) | −16.7367 | −1.25096 | −0.625480 | − | 0.780240i | \(-0.715097\pi\) | ||||
−0.625480 | + | 0.780240i | \(0.715097\pi\) | |||||||
\(180\) | −1.40290 | −0.104566 | ||||||||
\(181\) | 5.52794 | 0.410888 | 0.205444 | − | 0.978669i | \(-0.434136\pi\) | ||||
0.205444 | + | 0.978669i | \(0.434136\pi\) | |||||||
\(182\) | 5.86600 | 0.434817 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | 0.204870 | 0.0151032 | ||||||||
\(185\) | 9.48879 | 0.697629 | ||||||||
\(186\) | 9.76569 | 0.716055 | ||||||||
\(187\) | −2.42561 | −0.177378 | ||||||||
\(188\) | 10.0230 | 0.731000 | ||||||||
\(189\) | −2.64146 | −0.192138 | ||||||||
\(190\) | 2.67529 | 0.194086 | ||||||||
\(191\) | 24.8007 | 1.79452 | 0.897259 | − | 0.441504i | \(-0.145555\pi\) | ||||
0.897259 | + | 0.441504i | \(0.145555\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −7.11070 | −0.511839 | −0.255920 | − | 0.966698i | \(-0.582378\pi\) | ||||
−0.255920 | + | 0.966698i | \(0.582378\pi\) | |||||||
\(194\) | −3.02014 | −0.216834 | ||||||||
\(195\) | −3.11549 | −0.223105 | ||||||||
\(196\) | −0.0227093 | −0.00162209 | ||||||||
\(197\) | −26.7828 | −1.90819 | −0.954097 | − | 0.299498i | \(-0.903181\pi\) | ||||
−0.954097 | + | 0.299498i | \(0.903181\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | −0.260455 | −0.0184632 | −0.00923160 | − | 0.999957i | \(-0.502939\pi\) | ||||
−0.00923160 | + | 0.999957i | \(0.502939\pi\) | |||||||
\(200\) | 3.03186 | 0.214385 | ||||||||
\(201\) | −6.95159 | −0.490327 | ||||||||
\(202\) | 6.26627 | 0.440893 | ||||||||
\(203\) | 1.24693 | 0.0875172 | ||||||||
\(204\) | 2.42561 | 0.169827 | ||||||||
\(205\) | 10.8878 | 0.760440 | ||||||||
\(206\) | −8.42353 | −0.586895 | ||||||||
\(207\) | −0.204870 | −0.0142394 | ||||||||
\(208\) | −2.22074 | −0.153981 | ||||||||
\(209\) | 1.90697 | 0.131908 | ||||||||
\(210\) | −3.70571 | −0.255718 | ||||||||
\(211\) | −15.3771 | −1.05860 | −0.529302 | − | 0.848433i | \(-0.677546\pi\) | ||||
−0.529302 | + | 0.848433i | \(0.677546\pi\) | |||||||
\(212\) | −9.17082 | −0.629855 | ||||||||
\(213\) | 7.05306 | 0.483268 | ||||||||
\(214\) | −8.61317 | −0.588784 | ||||||||
\(215\) | 2.30025 | 0.156876 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 25.7957 | 1.75112 | ||||||||
\(218\) | 0.270369 | 0.0183117 | ||||||||
\(219\) | −13.5829 | −0.917846 | ||||||||
\(220\) | −1.40290 | −0.0945838 | ||||||||
\(221\) | 5.38667 | 0.362346 | ||||||||
\(222\) | −6.76367 | −0.453948 | ||||||||
\(223\) | −2.25767 | −0.151185 | −0.0755924 | − | 0.997139i | \(-0.524085\pi\) | ||||
−0.0755924 | + | 0.997139i | \(0.524085\pi\) | |||||||
\(224\) | −2.64146 | −0.176490 | ||||||||
\(225\) | −3.03186 | −0.202124 | ||||||||
\(226\) | 1.33006 | 0.0884741 | ||||||||
\(227\) | −18.0576 | −1.19853 | −0.599264 | − | 0.800552i | \(-0.704540\pi\) | ||||
−0.599264 | + | 0.800552i | \(0.704540\pi\) | |||||||
\(228\) | −1.90697 | −0.126292 | ||||||||
\(229\) | 2.29571 | 0.151705 | 0.0758523 | − | 0.997119i | \(-0.475832\pi\) | ||||
0.0758523 | + | 0.997119i | \(0.475832\pi\) | |||||||
\(230\) | −0.287413 | −0.0189514 | ||||||||
\(231\) | −2.64146 | −0.173795 | ||||||||
\(232\) | −0.472061 | −0.0309923 | ||||||||
\(233\) | 4.14358 | 0.271455 | 0.135728 | − | 0.990746i | \(-0.456663\pi\) | ||||
0.135728 | + | 0.990746i | \(0.456663\pi\) | |||||||
\(234\) | 2.22074 | 0.145175 | ||||||||
\(235\) | −14.0613 | −0.917256 | ||||||||
\(236\) | −10.6068 | −0.690441 | ||||||||
\(237\) | 11.7867 | 0.765630 | ||||||||
\(238\) | 6.40715 | 0.415314 | ||||||||
\(239\) | −5.42149 | −0.350687 | −0.175343 | − | 0.984507i | \(-0.556104\pi\) | ||||
−0.175343 | + | 0.984507i | \(0.556104\pi\) | |||||||
\(240\) | 1.40290 | 0.0905571 | ||||||||
\(241\) | −16.3458 | −1.05293 | −0.526463 | − | 0.850198i | \(-0.676482\pi\) | ||||
−0.526463 | + | 0.850198i | \(0.676482\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.00000 | 0.0640184 | ||||||||
\(245\) | 0.0318590 | 0.00203540 | ||||||||
\(246\) | −7.76093 | −0.494819 | ||||||||
\(247\) | −4.23488 | −0.269459 | ||||||||
\(248\) | −9.76569 | −0.620122 | ||||||||
\(249\) | −11.9485 | −0.757206 | ||||||||
\(250\) | −11.2679 | −0.712647 | ||||||||
\(251\) | 11.3950 | 0.719247 | 0.359624 | − | 0.933097i | \(-0.382905\pi\) | ||||
0.359624 | + | 0.933097i | \(0.382905\pi\) | |||||||
\(252\) | 2.64146 | 0.166396 | ||||||||
\(253\) | −0.204870 | −0.0128801 | ||||||||
\(254\) | −16.8165 | −1.05516 | ||||||||
\(255\) | −3.40290 | −0.213098 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.941786 | −0.0587470 | −0.0293735 | − | 0.999569i | \(-0.509351\pi\) | ||||
−0.0293735 | + | 0.999569i | \(0.509351\pi\) | |||||||
\(258\) | −1.63963 | −0.102079 | ||||||||
\(259\) | −17.8659 | −1.11014 | ||||||||
\(260\) | 3.11549 | 0.193215 | ||||||||
\(261\) | 0.472061 | 0.0292198 | ||||||||
\(262\) | 8.83870 | 0.546056 | ||||||||
\(263\) | −15.9527 | −0.983684 | −0.491842 | − | 0.870684i | \(-0.663676\pi\) | ||||
−0.491842 | + | 0.870684i | \(0.663676\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | 12.8658 | 0.790339 | ||||||||
\(266\) | −5.03717 | −0.308848 | ||||||||
\(267\) | 17.0716 | 1.04476 | ||||||||
\(268\) | 6.95159 | 0.424636 | ||||||||
\(269\) | −31.4983 | −1.92048 | −0.960242 | − | 0.279169i | \(-0.909941\pi\) | ||||
−0.960242 | + | 0.279169i | \(0.909941\pi\) | |||||||
\(270\) | −1.40290 | −0.0853780 | ||||||||
\(271\) | −30.1613 | −1.83217 | −0.916084 | − | 0.400987i | \(-0.868667\pi\) | ||||
−0.916084 | + | 0.400987i | \(0.868667\pi\) | |||||||
\(272\) | −2.42561 | −0.147074 | ||||||||
\(273\) | 5.86600 | 0.355026 | ||||||||
\(274\) | −17.6367 | −1.06547 | ||||||||
\(275\) | −3.03186 | −0.182828 | ||||||||
\(276\) | 0.204870 | 0.0123317 | ||||||||
\(277\) | 8.89171 | 0.534251 | 0.267125 | − | 0.963662i | \(-0.413926\pi\) | ||||
0.267125 | + | 0.963662i | \(0.413926\pi\) | |||||||
\(278\) | −12.9773 | −0.778326 | ||||||||
\(279\) | 9.76569 | 0.584657 | ||||||||
\(280\) | 3.70571 | 0.221459 | ||||||||
\(281\) | −2.33522 | −0.139308 | −0.0696538 | − | 0.997571i | \(-0.522189\pi\) | ||||
−0.0696538 | + | 0.997571i | \(0.522189\pi\) | |||||||
\(282\) | 10.0230 | 0.596859 | ||||||||
\(283\) | 20.7019 | 1.23060 | 0.615299 | − | 0.788294i | \(-0.289035\pi\) | ||||
0.615299 | + | 0.788294i | \(0.289035\pi\) | |||||||
\(284\) | −7.05306 | −0.418522 | ||||||||
\(285\) | 2.67529 | 0.158471 | ||||||||
\(286\) | 2.22074 | 0.131315 | ||||||||
\(287\) | −20.5002 | −1.21009 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −11.1164 | −0.653906 | ||||||||
\(290\) | 0.662256 | 0.0388890 | ||||||||
\(291\) | −3.02014 | −0.177044 | ||||||||
\(292\) | 13.5829 | 0.794878 | ||||||||
\(293\) | −9.73347 | −0.568636 | −0.284318 | − | 0.958730i | \(-0.591767\pi\) | ||||
−0.284318 | + | 0.958730i | \(0.591767\pi\) | |||||||
\(294\) | −0.0227093 | −0.00132443 | ||||||||
\(295\) | 14.8803 | 0.866363 | ||||||||
\(296\) | 6.76367 | 0.393130 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −2.01437 | −0.116689 | ||||||||
\(299\) | 0.454963 | 0.0263112 | ||||||||
\(300\) | 3.03186 | 0.175044 | ||||||||
\(301\) | −4.33102 | −0.249636 | ||||||||
\(302\) | 15.4442 | 0.888712 | ||||||||
\(303\) | 6.26627 | 0.359988 | ||||||||
\(304\) | 1.90697 | 0.109372 | ||||||||
\(305\) | −1.40290 | −0.0803301 | ||||||||
\(306\) | 2.42561 | 0.138663 | ||||||||
\(307\) | −28.0902 | −1.60319 | −0.801596 | − | 0.597866i | \(-0.796016\pi\) | ||||
−0.801596 | + | 0.597866i | \(0.796016\pi\) | |||||||
\(308\) | 2.64146 | 0.150511 | ||||||||
\(309\) | −8.42353 | −0.479198 | ||||||||
\(310\) | 13.7003 | 0.778127 | ||||||||
\(311\) | −21.6072 | −1.22523 | −0.612617 | − | 0.790380i | \(-0.709883\pi\) | ||||
−0.612617 | + | 0.790380i | \(0.709883\pi\) | |||||||
\(312\) | −2.22074 | −0.125725 | ||||||||
\(313\) | 17.7487 | 1.00321 | 0.501607 | − | 0.865095i | \(-0.332742\pi\) | ||||
0.501607 | + | 0.865095i | \(0.332742\pi\) | |||||||
\(314\) | 8.93090 | 0.504000 | ||||||||
\(315\) | −3.70571 | −0.208793 | ||||||||
\(316\) | −11.7867 | −0.663055 | ||||||||
\(317\) | −12.4486 | −0.699182 | −0.349591 | − | 0.936902i | \(-0.613679\pi\) | ||||
−0.349591 | + | 0.936902i | \(0.613679\pi\) | |||||||
\(318\) | −9.17082 | −0.514274 | ||||||||
\(319\) | 0.472061 | 0.0264303 | ||||||||
\(320\) | −1.40290 | −0.0784247 | ||||||||
\(321\) | −8.61317 | −0.480740 | ||||||||
\(322\) | 0.541155 | 0.0301574 | ||||||||
\(323\) | −4.62556 | −0.257373 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 6.73298 | 0.373479 | ||||||||
\(326\) | 10.0502 | 0.556628 | ||||||||
\(327\) | 0.270369 | 0.0149515 | ||||||||
\(328\) | 7.76093 | 0.428526 | ||||||||
\(329\) | 26.4752 | 1.45963 | ||||||||
\(330\) | −1.40290 | −0.0772274 | ||||||||
\(331\) | −0.976434 | −0.0536697 | −0.0268348 | − | 0.999640i | \(-0.508543\pi\) | ||||
−0.0268348 | + | 0.999640i | \(0.508543\pi\) | |||||||
\(332\) | 11.9485 | 0.655760 | ||||||||
\(333\) | −6.76367 | −0.370647 | ||||||||
\(334\) | 14.9634 | 0.818759 | ||||||||
\(335\) | −9.75242 | −0.532831 | ||||||||
\(336\) | −2.64146 | −0.144103 | ||||||||
\(337\) | 17.4423 | 0.950145 | 0.475072 | − | 0.879947i | \(-0.342422\pi\) | ||||
0.475072 | + | 0.879947i | \(0.342422\pi\) | |||||||
\(338\) | 8.06830 | 0.438857 | ||||||||
\(339\) | 1.33006 | 0.0722388 | ||||||||
\(340\) | 3.40290 | 0.184548 | ||||||||
\(341\) | 9.76569 | 0.528842 | ||||||||
\(342\) | −1.90697 | −0.103117 | ||||||||
\(343\) | −18.5502 | −1.00162 | ||||||||
\(344\) | 1.63963 | 0.0884031 | ||||||||
\(345\) | −0.287413 | −0.0154738 | ||||||||
\(346\) | 19.1504 | 1.02953 | ||||||||
\(347\) | 21.7867 | 1.16957 | 0.584785 | − | 0.811188i | \(-0.301179\pi\) | ||||
0.584785 | + | 0.811188i | \(0.301179\pi\) | |||||||
\(348\) | −0.472061 | −0.0253051 | ||||||||
\(349\) | −19.7730 | −1.05842 | −0.529211 | − | 0.848490i | \(-0.677512\pi\) | ||||
−0.529211 | + | 0.848490i | \(0.677512\pi\) | |||||||
\(350\) | 8.00852 | 0.428074 | ||||||||
\(351\) | 2.22074 | 0.118535 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 21.3484 | 1.13626 | 0.568131 | − | 0.822938i | \(-0.307667\pi\) | ||||
0.568131 | + | 0.822938i | \(0.307667\pi\) | |||||||
\(354\) | −10.6068 | −0.563743 | ||||||||
\(355\) | 9.89477 | 0.525160 | ||||||||
\(356\) | −17.0716 | −0.904792 | ||||||||
\(357\) | 6.40715 | 0.339102 | ||||||||
\(358\) | 16.7367 | 0.884563 | ||||||||
\(359\) | 29.6515 | 1.56495 | 0.782474 | − | 0.622683i | \(-0.213957\pi\) | ||||
0.782474 | + | 0.622683i | \(0.213957\pi\) | |||||||
\(360\) | 1.40290 | 0.0739396 | ||||||||
\(361\) | −15.3635 | −0.808604 | ||||||||
\(362\) | −5.52794 | −0.290542 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −5.86600 | −0.307462 | ||||||||
\(365\) | −19.0555 | −0.997410 | ||||||||
\(366\) | 1.00000 | 0.0522708 | ||||||||
\(367\) | −14.4904 | −0.756390 | −0.378195 | − | 0.925726i | \(-0.623455\pi\) | ||||
−0.378195 | + | 0.925726i | \(0.623455\pi\) | |||||||
\(368\) | −0.204870 | −0.0106796 | ||||||||
\(369\) | −7.76093 | −0.404018 | ||||||||
\(370\) | −9.48879 | −0.493299 | ||||||||
\(371\) | −24.2243 | −1.25766 | ||||||||
\(372\) | −9.76569 | −0.506328 | ||||||||
\(373\) | 1.73036 | 0.0895946 | 0.0447973 | − | 0.998996i | \(-0.485736\pi\) | ||||
0.0447973 | + | 0.998996i | \(0.485736\pi\) | |||||||
\(374\) | 2.42561 | 0.125426 | ||||||||
\(375\) | −11.2679 | −0.581873 | ||||||||
\(376\) | −10.0230 | −0.516895 | ||||||||
\(377\) | −1.04833 | −0.0539915 | ||||||||
\(378\) | 2.64146 | 0.135862 | ||||||||
\(379\) | −6.62732 | −0.340422 | −0.170211 | − | 0.985408i | \(-0.554445\pi\) | ||||
−0.170211 | + | 0.985408i | \(0.554445\pi\) | |||||||
\(380\) | −2.67529 | −0.137239 | ||||||||
\(381\) | −16.8165 | −0.861537 | ||||||||
\(382\) | −24.8007 | −1.26892 | ||||||||
\(383\) | −4.86064 | −0.248367 | −0.124184 | − | 0.992259i | \(-0.539631\pi\) | ||||
−0.124184 | + | 0.992259i | \(0.539631\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −3.70571 | −0.188861 | ||||||||
\(386\) | 7.11070 | 0.361925 | ||||||||
\(387\) | −1.63963 | −0.0833472 | ||||||||
\(388\) | 3.02014 | 0.153325 | ||||||||
\(389\) | −31.9781 | −1.62136 | −0.810678 | − | 0.585493i | \(-0.800901\pi\) | ||||
−0.810678 | + | 0.585493i | \(0.800901\pi\) | |||||||
\(390\) | 3.11549 | 0.157759 | ||||||||
\(391\) | 0.496935 | 0.0251311 | ||||||||
\(392\) | 0.0227093 | 0.00114699 | ||||||||
\(393\) | 8.83870 | 0.445853 | ||||||||
\(394\) | 26.7828 | 1.34930 | ||||||||
\(395\) | 16.5356 | 0.831999 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | −31.1227 | −1.56200 | −0.781002 | − | 0.624529i | \(-0.785291\pi\) | ||||
−0.781002 | + | 0.624529i | \(0.785291\pi\) | |||||||
\(398\) | 0.260455 | 0.0130554 | ||||||||
\(399\) | −5.03717 | −0.252174 | ||||||||
\(400\) | −3.03186 | −0.151593 | ||||||||
\(401\) | 33.2402 | 1.65994 | 0.829969 | − | 0.557810i | \(-0.188358\pi\) | ||||
0.829969 | + | 0.557810i | \(0.188358\pi\) | |||||||
\(402\) | 6.95159 | 0.346714 | ||||||||
\(403\) | −21.6871 | −1.08031 | ||||||||
\(404\) | −6.26627 | −0.311759 | ||||||||
\(405\) | −1.40290 | −0.0697109 | ||||||||
\(406\) | −1.24693 | −0.0618840 | ||||||||
\(407\) | −6.76367 | −0.335263 | ||||||||
\(408\) | −2.42561 | −0.120086 | ||||||||
\(409\) | −29.5147 | −1.45941 | −0.729705 | − | 0.683762i | \(-0.760343\pi\) | ||||
−0.729705 | + | 0.683762i | \(0.760343\pi\) | |||||||
\(410\) | −10.8878 | −0.537712 | ||||||||
\(411\) | −17.6367 | −0.869953 | ||||||||
\(412\) | 8.42353 | 0.414997 | ||||||||
\(413\) | −28.0173 | −1.37864 | ||||||||
\(414\) | 0.204870 | 0.0100688 | ||||||||
\(415\) | −16.7626 | −0.822844 | ||||||||
\(416\) | 2.22074 | 0.108881 | ||||||||
\(417\) | −12.9773 | −0.635501 | ||||||||
\(418\) | −1.90697 | −0.0932727 | ||||||||
\(419\) | 4.82984 | 0.235953 | 0.117976 | − | 0.993016i | \(-0.462359\pi\) | ||||
0.117976 | + | 0.993016i | \(0.462359\pi\) | |||||||
\(420\) | 3.70571 | 0.180820 | ||||||||
\(421\) | −6.50405 | −0.316988 | −0.158494 | − | 0.987360i | \(-0.550664\pi\) | ||||
−0.158494 | + | 0.987360i | \(0.550664\pi\) | |||||||
\(422\) | 15.3771 | 0.748546 | ||||||||
\(423\) | 10.0230 | 0.487333 | ||||||||
\(424\) | 9.17082 | 0.445375 | ||||||||
\(425\) | 7.35412 | 0.356727 | ||||||||
\(426\) | −7.05306 | −0.341722 | ||||||||
\(427\) | 2.64146 | 0.127829 | ||||||||
\(428\) | 8.61317 | 0.416333 | ||||||||
\(429\) | 2.22074 | 0.107219 | ||||||||
\(430\) | −2.30025 | −0.110928 | ||||||||
\(431\) | 33.0122 | 1.59014 | 0.795070 | − | 0.606517i | \(-0.207434\pi\) | ||||
0.795070 | + | 0.606517i | \(0.207434\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 23.4933 | 1.12902 | 0.564509 | − | 0.825427i | \(-0.309066\pi\) | ||||
0.564509 | + | 0.825427i | \(0.309066\pi\) | |||||||
\(434\) | −25.7957 | −1.23823 | ||||||||
\(435\) | 0.662256 | 0.0317527 | ||||||||
\(436\) | −0.270369 | −0.0129483 | ||||||||
\(437\) | −0.390680 | −0.0186887 | ||||||||
\(438\) | 13.5829 | 0.649015 | ||||||||
\(439\) | 21.8941 | 1.04495 | 0.522473 | − | 0.852656i | \(-0.325009\pi\) | ||||
0.522473 | + | 0.852656i | \(0.325009\pi\) | |||||||
\(440\) | 1.40290 | 0.0668808 | ||||||||
\(441\) | −0.0227093 | −0.00108140 | ||||||||
\(442\) | −5.38667 | −0.256218 | ||||||||
\(443\) | −31.7620 | −1.50906 | −0.754530 | − | 0.656265i | \(-0.772135\pi\) | ||||
−0.754530 | + | 0.656265i | \(0.772135\pi\) | |||||||
\(444\) | 6.76367 | 0.320990 | ||||||||
\(445\) | 23.9498 | 1.13533 | ||||||||
\(446\) | 2.25767 | 0.106904 | ||||||||
\(447\) | −2.01437 | −0.0952762 | ||||||||
\(448\) | 2.64146 | 0.124797 | ||||||||
\(449\) | −33.8087 | −1.59553 | −0.797765 | − | 0.602968i | \(-0.793985\pi\) | ||||
−0.797765 | + | 0.602968i | \(0.793985\pi\) | |||||||
\(450\) | 3.03186 | 0.142923 | ||||||||
\(451\) | −7.76093 | −0.365448 | ||||||||
\(452\) | −1.33006 | −0.0625606 | ||||||||
\(453\) | 15.4442 | 0.725631 | ||||||||
\(454\) | 18.0576 | 0.847487 | ||||||||
\(455\) | 8.22943 | 0.385802 | ||||||||
\(456\) | 1.90697 | 0.0893018 | ||||||||
\(457\) | −14.3858 | −0.672937 | −0.336469 | − | 0.941695i | \(-0.609233\pi\) | ||||
−0.336469 | + | 0.941695i | \(0.609233\pi\) | |||||||
\(458\) | −2.29571 | −0.107271 | ||||||||
\(459\) | 2.42561 | 0.113218 | ||||||||
\(460\) | 0.287413 | 0.0134007 | ||||||||
\(461\) | −1.24112 | −0.0578046 | −0.0289023 | − | 0.999582i | \(-0.509201\pi\) | ||||
−0.0289023 | + | 0.999582i | \(0.509201\pi\) | |||||||
\(462\) | 2.64146 | 0.122892 | ||||||||
\(463\) | −18.1466 | −0.843343 | −0.421672 | − | 0.906749i | \(-0.638557\pi\) | ||||
−0.421672 | + | 0.906749i | \(0.638557\pi\) | |||||||
\(464\) | 0.472061 | 0.0219149 | ||||||||
\(465\) | 13.7003 | 0.635338 | ||||||||
\(466\) | −4.14358 | −0.191948 | ||||||||
\(467\) | −10.7033 | −0.495290 | −0.247645 | − | 0.968851i | \(-0.579657\pi\) | ||||
−0.247645 | + | 0.968851i | \(0.579657\pi\) | |||||||
\(468\) | −2.22074 | −0.102654 | ||||||||
\(469\) | 18.3623 | 0.847893 | ||||||||
\(470\) | 14.0613 | 0.648598 | ||||||||
\(471\) | 8.93090 | 0.411514 | ||||||||
\(472\) | 10.6068 | 0.488216 | ||||||||
\(473\) | −1.63963 | −0.0753904 | ||||||||
\(474\) | −11.7867 | −0.541382 | ||||||||
\(475\) | −5.78165 | −0.265280 | ||||||||
\(476\) | −6.40715 | −0.293671 | ||||||||
\(477\) | −9.17082 | −0.419903 | ||||||||
\(478\) | 5.42149 | 0.247973 | ||||||||
\(479\) | 12.1296 | 0.554214 | 0.277107 | − | 0.960839i | \(-0.410624\pi\) | ||||
0.277107 | + | 0.960839i | \(0.410624\pi\) | |||||||
\(480\) | −1.40290 | −0.0640335 | ||||||||
\(481\) | 15.0204 | 0.684871 | ||||||||
\(482\) | 16.3458 | 0.744531 | ||||||||
\(483\) | 0.541155 | 0.0246234 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −4.23697 | −0.192391 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 8.75526 | 0.396739 | 0.198369 | − | 0.980127i | \(-0.436435\pi\) | ||||
0.198369 | + | 0.980127i | \(0.436435\pi\) | |||||||
\(488\) | −1.00000 | −0.0452679 | ||||||||
\(489\) | 10.0502 | 0.454485 | ||||||||
\(490\) | −0.0318590 | −0.00143924 | ||||||||
\(491\) | 27.0828 | 1.22223 | 0.611114 | − | 0.791542i | \(-0.290722\pi\) | ||||
0.611114 | + | 0.791542i | \(0.290722\pi\) | |||||||
\(492\) | 7.76093 | 0.349890 | ||||||||
\(493\) | −1.14504 | −0.0515699 | ||||||||
\(494\) | 4.23488 | 0.190536 | ||||||||
\(495\) | −1.40290 | −0.0630559 | ||||||||
\(496\) | 9.76569 | 0.438493 | ||||||||
\(497\) | −18.6303 | −0.835685 | ||||||||
\(498\) | 11.9485 | 0.535425 | ||||||||
\(499\) | −15.6902 | −0.702390 | −0.351195 | − | 0.936302i | \(-0.614225\pi\) | ||||
−0.351195 | + | 0.936302i | \(0.614225\pi\) | |||||||
\(500\) | 11.2679 | 0.503917 | ||||||||
\(501\) | 14.9634 | 0.668514 | ||||||||
\(502\) | −11.3950 | −0.508585 | ||||||||
\(503\) | −13.2252 | −0.589684 | −0.294842 | − | 0.955546i | \(-0.595267\pi\) | ||||
−0.294842 | + | 0.955546i | \(0.595267\pi\) | |||||||
\(504\) | −2.64146 | −0.117660 | ||||||||
\(505\) | 8.79098 | 0.391194 | ||||||||
\(506\) | 0.204870 | 0.00910757 | ||||||||
\(507\) | 8.06830 | 0.358326 | ||||||||
\(508\) | 16.8165 | 0.746113 | ||||||||
\(509\) | 4.07223 | 0.180498 | 0.0902492 | − | 0.995919i | \(-0.471234\pi\) | ||||
0.0902492 | + | 0.995919i | \(0.471234\pi\) | |||||||
\(510\) | 3.40290 | 0.150683 | ||||||||
\(511\) | 35.8786 | 1.58717 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.90697 | −0.0841946 | ||||||||
\(514\) | 0.941786 | 0.0415404 | ||||||||
\(515\) | −11.8174 | −0.520737 | ||||||||
\(516\) | 1.63963 | 0.0721808 | ||||||||
\(517\) | 10.0230 | 0.440810 | ||||||||
\(518\) | 17.8659 | 0.784985 | ||||||||
\(519\) | 19.1504 | 0.840609 | ||||||||
\(520\) | −3.11549 | −0.136623 | ||||||||
\(521\) | −20.4104 | −0.894196 | −0.447098 | − | 0.894485i | \(-0.647543\pi\) | ||||
−0.447098 | + | 0.894485i | \(0.647543\pi\) | |||||||
\(522\) | −0.472061 | −0.0206615 | ||||||||
\(523\) | −11.8863 | −0.519750 | −0.259875 | − | 0.965642i | \(-0.583681\pi\) | ||||
−0.259875 | + | 0.965642i | \(0.583681\pi\) | |||||||
\(524\) | −8.83870 | −0.386120 | ||||||||
\(525\) | 8.00852 | 0.349521 | ||||||||
\(526\) | 15.9527 | 0.695570 | ||||||||
\(527\) | −23.6878 | −1.03186 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −22.9580 | −0.998175 | ||||||||
\(530\) | −12.8658 | −0.558854 | ||||||||
\(531\) | −10.6068 | −0.460294 | ||||||||
\(532\) | 5.03717 | 0.218389 | ||||||||
\(533\) | 17.2350 | 0.746533 | ||||||||
\(534\) | −17.0716 | −0.738759 | ||||||||
\(535\) | −12.0835 | −0.522413 | ||||||||
\(536\) | −6.95159 | −0.300263 | ||||||||
\(537\) | 16.7367 | 0.722243 | ||||||||
\(538\) | 31.4983 | 1.35799 | ||||||||
\(539\) | −0.0227093 | −0.000978160 0 | ||||||||
\(540\) | 1.40290 | 0.0603714 | ||||||||
\(541\) | −11.3744 | −0.489022 | −0.244511 | − | 0.969647i | \(-0.578627\pi\) | ||||
−0.244511 | + | 0.969647i | \(0.578627\pi\) | |||||||
\(542\) | 30.1613 | 1.29554 | ||||||||
\(543\) | −5.52794 | −0.237226 | ||||||||
\(544\) | 2.42561 | 0.103997 | ||||||||
\(545\) | 0.379302 | 0.0162475 | ||||||||
\(546\) | −5.86600 | −0.251042 | ||||||||
\(547\) | 45.7026 | 1.95410 | 0.977051 | − | 0.213007i | \(-0.0683257\pi\) | ||||
0.977051 | + | 0.213007i | \(0.0683257\pi\) | |||||||
\(548\) | 17.6367 | 0.753401 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | 3.03186 | 0.129279 | ||||||||
\(551\) | 0.900203 | 0.0383499 | ||||||||
\(552\) | −0.204870 | −0.00871984 | ||||||||
\(553\) | −31.1341 | −1.32396 | ||||||||
\(554\) | −8.89171 | −0.377772 | ||||||||
\(555\) | −9.48879 | −0.402777 | ||||||||
\(556\) | 12.9773 | 0.550360 | ||||||||
\(557\) | 44.5611 | 1.88811 | 0.944056 | − | 0.329784i | \(-0.106976\pi\) | ||||
0.944056 | + | 0.329784i | \(0.106976\pi\) | |||||||
\(558\) | −9.76569 | −0.413415 | ||||||||
\(559\) | 3.64121 | 0.154007 | ||||||||
\(560\) | −3.70571 | −0.156595 | ||||||||
\(561\) | 2.42561 | 0.102409 | ||||||||
\(562\) | 2.33522 | 0.0985054 | ||||||||
\(563\) | −41.5519 | −1.75120 | −0.875601 | − | 0.483034i | \(-0.839535\pi\) | ||||
−0.875601 | + | 0.483034i | \(0.839535\pi\) | |||||||
\(564\) | −10.0230 | −0.422043 | ||||||||
\(565\) | 1.86594 | 0.0785008 | ||||||||
\(566\) | −20.7019 | −0.870165 | ||||||||
\(567\) | 2.64146 | 0.110931 | ||||||||
\(568\) | 7.05306 | 0.295940 | ||||||||
\(569\) | 13.9534 | 0.584955 | 0.292477 | − | 0.956272i | \(-0.405520\pi\) | ||||
0.292477 | + | 0.956272i | \(0.405520\pi\) | |||||||
\(570\) | −2.67529 | −0.112056 | ||||||||
\(571\) | 30.2505 | 1.26594 | 0.632972 | − | 0.774175i | \(-0.281835\pi\) | ||||
0.632972 | + | 0.774175i | \(0.281835\pi\) | |||||||
\(572\) | −2.22074 | −0.0928540 | ||||||||
\(573\) | −24.8007 | −1.03607 | ||||||||
\(574\) | 20.5002 | 0.855660 | ||||||||
\(575\) | 0.621136 | 0.0259032 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −22.6783 | −0.944108 | −0.472054 | − | 0.881570i | \(-0.656487\pi\) | ||||
−0.472054 | + | 0.881570i | \(0.656487\pi\) | |||||||
\(578\) | 11.1164 | 0.462381 | ||||||||
\(579\) | 7.11070 | 0.295511 | ||||||||
\(580\) | −0.662256 | −0.0274987 | ||||||||
\(581\) | 31.5615 | 1.30939 | ||||||||
\(582\) | 3.02014 | 0.125189 | ||||||||
\(583\) | −9.17082 | −0.379817 | ||||||||
\(584\) | −13.5829 | −0.562064 | ||||||||
\(585\) | 3.11549 | 0.128810 | ||||||||
\(586\) | 9.73347 | 0.402086 | ||||||||
\(587\) | −37.4818 | −1.54704 | −0.773519 | − | 0.633773i | \(-0.781505\pi\) | ||||
−0.773519 | + | 0.633773i | \(0.781505\pi\) | |||||||
\(588\) | 0.0227093 | 0.000936516 0 | ||||||||
\(589\) | 18.6228 | 0.767341 | ||||||||
\(590\) | −14.8803 | −0.612611 | ||||||||
\(591\) | 26.7828 | 1.10170 | ||||||||
\(592\) | −6.76367 | −0.277985 | ||||||||
\(593\) | 29.6644 | 1.21817 | 0.609085 | − | 0.793105i | \(-0.291537\pi\) | ||||
0.609085 | + | 0.793105i | \(0.291537\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 8.98862 | 0.368498 | ||||||||
\(596\) | 2.01437 | 0.0825116 | ||||||||
\(597\) | 0.260455 | 0.0106597 | ||||||||
\(598\) | −0.454963 | −0.0186048 | ||||||||
\(599\) | 3.48715 | 0.142481 | 0.0712405 | − | 0.997459i | \(-0.477304\pi\) | ||||
0.0712405 | + | 0.997459i | \(0.477304\pi\) | |||||||
\(600\) | −3.03186 | −0.123775 | ||||||||
\(601\) | 12.6710 | 0.516862 | 0.258431 | − | 0.966030i | \(-0.416795\pi\) | ||||
0.258431 | + | 0.966030i | \(0.416795\pi\) | |||||||
\(602\) | 4.33102 | 0.176519 | ||||||||
\(603\) | 6.95159 | 0.283091 | ||||||||
\(604\) | −15.4442 | −0.628414 | ||||||||
\(605\) | −1.40290 | −0.0570362 | ||||||||
\(606\) | −6.26627 | −0.254550 | ||||||||
\(607\) | −19.2100 | −0.779712 | −0.389856 | − | 0.920876i | \(-0.627475\pi\) | ||||
−0.389856 | + | 0.920876i | \(0.627475\pi\) | |||||||
\(608\) | −1.90697 | −0.0773377 | ||||||||
\(609\) | −1.24693 | −0.0505281 | ||||||||
\(610\) | 1.40290 | 0.0568019 | ||||||||
\(611\) | −22.2584 | −0.900480 | ||||||||
\(612\) | −2.42561 | −0.0980496 | ||||||||
\(613\) | −35.6456 | −1.43971 | −0.719856 | − | 0.694123i | \(-0.755792\pi\) | ||||
−0.719856 | + | 0.694123i | \(0.755792\pi\) | |||||||
\(614\) | 28.0902 | 1.13363 | ||||||||
\(615\) | −10.8878 | −0.439040 | ||||||||
\(616\) | −2.64146 | −0.106427 | ||||||||
\(617\) | −37.3566 | −1.50392 | −0.751961 | − | 0.659208i | \(-0.770892\pi\) | ||||
−0.751961 | + | 0.659208i | \(0.770892\pi\) | |||||||
\(618\) | 8.42353 | 0.338844 | ||||||||
\(619\) | −16.5413 | −0.664853 | −0.332426 | − | 0.943129i | \(-0.607867\pi\) | ||||
−0.332426 | + | 0.943129i | \(0.607867\pi\) | |||||||
\(620\) | −13.7003 | −0.550219 | ||||||||
\(621\) | 0.204870 | 0.00822114 | ||||||||
\(622\) | 21.6072 | 0.866372 | ||||||||
\(623\) | −45.0938 | −1.80665 | ||||||||
\(624\) | 2.22074 | 0.0889009 | ||||||||
\(625\) | −0.648536 | −0.0259414 | ||||||||
\(626\) | −17.7487 | −0.709380 | ||||||||
\(627\) | −1.90697 | −0.0761569 | ||||||||
\(628\) | −8.93090 | −0.356382 | ||||||||
\(629\) | 16.4061 | 0.654152 | ||||||||
\(630\) | 3.70571 | 0.147639 | ||||||||
\(631\) | 32.9320 | 1.31100 | 0.655500 | − | 0.755195i | \(-0.272458\pi\) | ||||
0.655500 | + | 0.755195i | \(0.272458\pi\) | |||||||
\(632\) | 11.7867 | 0.468851 | ||||||||
\(633\) | 15.3771 | 0.611185 | ||||||||
\(634\) | 12.4486 | 0.494396 | ||||||||
\(635\) | −23.5920 | −0.936219 | ||||||||
\(636\) | 9.17082 | 0.363647 | ||||||||
\(637\) | 0.0504316 | 0.00199817 | ||||||||
\(638\) | −0.472061 | −0.0186891 | ||||||||
\(639\) | −7.05306 | −0.279015 | ||||||||
\(640\) | 1.40290 | 0.0554547 | ||||||||
\(641\) | 30.3581 | 1.19907 | 0.599537 | − | 0.800347i | \(-0.295352\pi\) | ||||
0.599537 | + | 0.800347i | \(0.295352\pi\) | |||||||
\(642\) | 8.61317 | 0.339935 | ||||||||
\(643\) | −18.0158 | −0.710473 | −0.355237 | − | 0.934776i | \(-0.615600\pi\) | ||||
−0.355237 | + | 0.934776i | \(0.615600\pi\) | |||||||
\(644\) | −0.541155 | −0.0213245 | ||||||||
\(645\) | −2.30025 | −0.0905722 | ||||||||
\(646\) | 4.62556 | 0.181990 | ||||||||
\(647\) | 11.6729 | 0.458907 | 0.229454 | − | 0.973320i | \(-0.426306\pi\) | ||||
0.229454 | + | 0.973320i | \(0.426306\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −10.6068 | −0.416352 | ||||||||
\(650\) | −6.73298 | −0.264089 | ||||||||
\(651\) | −25.7957 | −1.01101 | ||||||||
\(652\) | −10.0502 | −0.393595 | ||||||||
\(653\) | 36.4917 | 1.42803 | 0.714015 | − | 0.700130i | \(-0.246875\pi\) | ||||
0.714015 | + | 0.700130i | \(0.246875\pi\) | |||||||
\(654\) | −0.270369 | −0.0105723 | ||||||||
\(655\) | 12.3998 | 0.484502 | ||||||||
\(656\) | −7.76093 | −0.303014 | ||||||||
\(657\) | 13.5829 | 0.529919 | ||||||||
\(658\) | −26.4752 | −1.03211 | ||||||||
\(659\) | 5.48686 | 0.213738 | 0.106869 | − | 0.994273i | \(-0.465918\pi\) | ||||
0.106869 | + | 0.994273i | \(0.465918\pi\) | |||||||
\(660\) | 1.40290 | 0.0546080 | ||||||||
\(661\) | 35.2662 | 1.37170 | 0.685849 | − | 0.727744i | \(-0.259431\pi\) | ||||
0.685849 | + | 0.727744i | \(0.259431\pi\) | |||||||
\(662\) | 0.976434 | 0.0379502 | ||||||||
\(663\) | −5.38667 | −0.209201 | ||||||||
\(664\) | −11.9485 | −0.463692 | ||||||||
\(665\) | −7.06666 | −0.274033 | ||||||||
\(666\) | 6.76367 | 0.262087 | ||||||||
\(667\) | −0.0967110 | −0.00374466 | ||||||||
\(668\) | −14.9634 | −0.578950 | ||||||||
\(669\) | 2.25767 | 0.0872866 | ||||||||
\(670\) | 9.75242 | 0.376769 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 2.64146 | 0.101896 | ||||||||
\(673\) | −41.5066 | −1.59996 | −0.799980 | − | 0.600027i | \(-0.795157\pi\) | ||||
−0.799980 | + | 0.600027i | \(0.795157\pi\) | |||||||
\(674\) | −17.4423 | −0.671854 | ||||||||
\(675\) | 3.03186 | 0.116696 | ||||||||
\(676\) | −8.06830 | −0.310319 | ||||||||
\(677\) | 26.8982 | 1.03378 | 0.516890 | − | 0.856052i | \(-0.327089\pi\) | ||||
0.516890 | + | 0.856052i | \(0.327089\pi\) | |||||||
\(678\) | −1.33006 | −0.0510805 | ||||||||
\(679\) | 7.97758 | 0.306151 | ||||||||
\(680\) | −3.40290 | −0.130495 | ||||||||
\(681\) | 18.0576 | 0.691970 | ||||||||
\(682\) | −9.76569 | −0.373948 | ||||||||
\(683\) | −5.04293 | −0.192962 | −0.0964811 | − | 0.995335i | \(-0.530759\pi\) | ||||
−0.0964811 | + | 0.995335i | \(0.530759\pi\) | |||||||
\(684\) | 1.90697 | 0.0729146 | ||||||||
\(685\) | −24.7426 | −0.945365 | ||||||||
\(686\) | 18.5502 | 0.708249 | ||||||||
\(687\) | −2.29571 | −0.0875867 | ||||||||
\(688\) | −1.63963 | −0.0625104 | ||||||||
\(689\) | 20.3661 | 0.775885 | ||||||||
\(690\) | 0.287413 | 0.0109416 | ||||||||
\(691\) | −39.2907 | −1.49469 | −0.747344 | − | 0.664437i | \(-0.768671\pi\) | ||||
−0.747344 | + | 0.664437i | \(0.768671\pi\) | |||||||
\(692\) | −19.1504 | −0.727988 | ||||||||
\(693\) | 2.64146 | 0.100341 | ||||||||
\(694\) | −21.7867 | −0.827011 | ||||||||
\(695\) | −18.2059 | −0.690589 | ||||||||
\(696\) | 0.472061 | 0.0178934 | ||||||||
\(697\) | 18.8250 | 0.713049 | ||||||||
\(698\) | 19.7730 | 0.748418 | ||||||||
\(699\) | −4.14358 | −0.156725 | ||||||||
\(700\) | −8.00852 | −0.302694 | ||||||||
\(701\) | 30.7614 | 1.16184 | 0.580920 | − | 0.813960i | \(-0.302693\pi\) | ||||
0.580920 | + | 0.813960i | \(0.302693\pi\) | |||||||
\(702\) | −2.22074 | −0.0838166 | ||||||||
\(703\) | −12.8981 | −0.486461 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 14.0613 | 0.529578 | ||||||||
\(706\) | −21.3484 | −0.803459 | ||||||||
\(707\) | −16.5521 | −0.622505 | ||||||||
\(708\) | 10.6068 | 0.398626 | ||||||||
\(709\) | −12.5072 | −0.469716 | −0.234858 | − | 0.972030i | \(-0.575463\pi\) | ||||
−0.234858 | + | 0.972030i | \(0.575463\pi\) | |||||||
\(710\) | −9.89477 | −0.371344 | ||||||||
\(711\) | −11.7867 | −0.442037 | ||||||||
\(712\) | 17.0716 | 0.639784 | ||||||||
\(713\) | −2.00070 | −0.0749266 | ||||||||
\(714\) | −6.40715 | −0.239782 | ||||||||
\(715\) | 3.11549 | 0.116513 | ||||||||
\(716\) | −16.7367 | −0.625480 | ||||||||
\(717\) | 5.42149 | 0.202469 | ||||||||
\(718\) | −29.6515 | −1.10659 | ||||||||
\(719\) | −45.6483 | −1.70240 | −0.851198 | − | 0.524845i | \(-0.824123\pi\) | ||||
−0.851198 | + | 0.524845i | \(0.824123\pi\) | |||||||
\(720\) | −1.40290 | −0.0522832 | ||||||||
\(721\) | 22.2504 | 0.828647 | ||||||||
\(722\) | 15.3635 | 0.571770 | ||||||||
\(723\) | 16.3458 | 0.607907 | ||||||||
\(724\) | 5.52794 | 0.205444 | ||||||||
\(725\) | −1.43122 | −0.0531542 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | 16.8878 | 0.626333 | 0.313166 | − | 0.949698i | \(-0.398610\pi\) | ||||
0.313166 | + | 0.949698i | \(0.398610\pi\) | |||||||
\(728\) | 5.86600 | 0.217408 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 19.0555 | 0.705275 | ||||||||
\(731\) | 3.97712 | 0.147099 | ||||||||
\(732\) | −1.00000 | −0.0369611 | ||||||||
\(733\) | 46.9017 | 1.73235 | 0.866176 | − | 0.499738i | \(-0.166570\pi\) | ||||
0.866176 | + | 0.499738i | \(0.166570\pi\) | |||||||
\(734\) | 14.4904 | 0.534849 | ||||||||
\(735\) | −0.0318590 | −0.00117514 | ||||||||
\(736\) | 0.204870 | 0.00755160 | ||||||||
\(737\) | 6.95159 | 0.256065 | ||||||||
\(738\) | 7.76093 | 0.285684 | ||||||||
\(739\) | 8.48511 | 0.312130 | 0.156065 | − | 0.987747i | \(-0.450119\pi\) | ||||
0.156065 | + | 0.987747i | \(0.450119\pi\) | |||||||
\(740\) | 9.48879 | 0.348815 | ||||||||
\(741\) | 4.23488 | 0.155572 | ||||||||
\(742\) | 24.2243 | 0.889303 | ||||||||
\(743\) | −4.60862 | −0.169074 | −0.0845370 | − | 0.996420i | \(-0.526941\pi\) | ||||
−0.0845370 | + | 0.996420i | \(0.526941\pi\) | |||||||
\(744\) | 9.76569 | 0.358028 | ||||||||
\(745\) | −2.82596 | −0.103535 | ||||||||
\(746\) | −1.73036 | −0.0633530 | ||||||||
\(747\) | 11.9485 | 0.437173 | ||||||||
\(748\) | −2.42561 | −0.0886892 | ||||||||
\(749\) | 22.7513 | 0.831315 | ||||||||
\(750\) | 11.2679 | 0.411447 | ||||||||
\(751\) | −1.59252 | −0.0581117 | −0.0290559 | − | 0.999578i | \(-0.509250\pi\) | ||||
−0.0290559 | + | 0.999578i | \(0.509250\pi\) | |||||||
\(752\) | 10.0230 | 0.365500 | ||||||||
\(753\) | −11.3950 | −0.415258 | ||||||||
\(754\) | 1.04833 | 0.0381778 | ||||||||
\(755\) | 21.6667 | 0.788532 | ||||||||
\(756\) | −2.64146 | −0.0960688 | ||||||||
\(757\) | 47.1004 | 1.71189 | 0.855947 | − | 0.517064i | \(-0.172975\pi\) | ||||
0.855947 | + | 0.517064i | \(0.172975\pi\) | |||||||
\(758\) | 6.62732 | 0.240715 | ||||||||
\(759\) | 0.204870 | 0.00743630 | ||||||||
\(760\) | 2.67529 | 0.0970430 | ||||||||
\(761\) | −9.97039 | −0.361426 | −0.180713 | − | 0.983536i | \(-0.557841\pi\) | ||||
−0.180713 | + | 0.983536i | \(0.557841\pi\) | |||||||
\(762\) | 16.8165 | 0.609199 | ||||||||
\(763\) | −0.714169 | −0.0258546 | ||||||||
\(764\) | 24.8007 | 0.897259 | ||||||||
\(765\) | 3.40290 | 0.123032 | ||||||||
\(766\) | 4.86064 | 0.175622 | ||||||||
\(767\) | 23.5549 | 0.850518 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −24.1099 | −0.869427 | −0.434713 | − | 0.900569i | \(-0.643150\pi\) | ||||
−0.434713 | + | 0.900569i | \(0.643150\pi\) | |||||||
\(770\) | 3.70571 | 0.133545 | ||||||||
\(771\) | 0.941786 | 0.0339176 | ||||||||
\(772\) | −7.11070 | −0.255920 | ||||||||
\(773\) | 46.8756 | 1.68600 | 0.843000 | − | 0.537914i | \(-0.180788\pi\) | ||||
0.843000 | + | 0.537914i | \(0.180788\pi\) | |||||||
\(774\) | 1.63963 | 0.0589354 | ||||||||
\(775\) | −29.6082 | −1.06356 | ||||||||
\(776\) | −3.02014 | −0.108417 | ||||||||
\(777\) | 17.8659 | 0.640937 | ||||||||
\(778\) | 31.9781 | 1.14647 | ||||||||
\(779\) | −14.7998 | −0.530259 | ||||||||
\(780\) | −3.11549 | −0.111552 | ||||||||
\(781\) | −7.05306 | −0.252378 | ||||||||
\(782\) | −0.496935 | −0.0177704 | ||||||||
\(783\) | −0.472061 | −0.0168701 | ||||||||
\(784\) | −0.0227093 | −0.000811047 0 | ||||||||
\(785\) | 12.5292 | 0.447186 | ||||||||
\(786\) | −8.83870 | −0.315266 | ||||||||
\(787\) | 32.5751 | 1.16118 | 0.580589 | − | 0.814197i | \(-0.302822\pi\) | ||||
0.580589 | + | 0.814197i | \(0.302822\pi\) | |||||||
\(788\) | −26.7828 | −0.954097 | ||||||||
\(789\) | 15.9527 | 0.567930 | ||||||||
\(790\) | −16.5356 | −0.588312 | ||||||||
\(791\) | −3.51329 | −0.124918 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | −2.22074 | −0.0788609 | ||||||||
\(794\) | 31.1227 | 1.10450 | ||||||||
\(795\) | −12.8658 | −0.456303 | ||||||||
\(796\) | −0.260455 | −0.00923160 | ||||||||
\(797\) | −32.9894 | −1.16855 | −0.584273 | − | 0.811557i | \(-0.698620\pi\) | ||||
−0.584273 | + | 0.811557i | \(0.698620\pi\) | |||||||
\(798\) | 5.03717 | 0.178314 | ||||||||
\(799\) | −24.3119 | −0.860092 | ||||||||
\(800\) | 3.03186 | 0.107192 | ||||||||
\(801\) | −17.0716 | −0.603195 | ||||||||
\(802\) | −33.2402 | −1.17375 | ||||||||
\(803\) | 13.5829 | 0.479329 | ||||||||
\(804\) | −6.95159 | −0.245164 | ||||||||
\(805\) | 0.759188 | 0.0267579 | ||||||||
\(806\) | 21.6871 | 0.763896 | ||||||||
\(807\) | 31.4983 | 1.10879 | ||||||||
\(808\) | 6.26627 | 0.220447 | ||||||||
\(809\) | 20.2167 | 0.710781 | 0.355390 | − | 0.934718i | \(-0.384348\pi\) | ||||
0.355390 | + | 0.934718i | \(0.384348\pi\) | |||||||
\(810\) | 1.40290 | 0.0492930 | ||||||||
\(811\) | 27.5565 | 0.967641 | 0.483821 | − | 0.875167i | \(-0.339249\pi\) | ||||
0.483821 | + | 0.875167i | \(0.339249\pi\) | |||||||
\(812\) | 1.24693 | 0.0437586 | ||||||||
\(813\) | 30.1613 | 1.05780 | ||||||||
\(814\) | 6.76367 | 0.237067 | ||||||||
\(815\) | 14.0994 | 0.493882 | ||||||||
\(816\) | 2.42561 | 0.0849135 | ||||||||
\(817\) | −3.12672 | −0.109390 | ||||||||
\(818\) | 29.5147 | 1.03196 | ||||||||
\(819\) | −5.86600 | −0.204975 | ||||||||
\(820\) | 10.8878 | 0.380220 | ||||||||
\(821\) | −44.7464 | −1.56166 | −0.780830 | − | 0.624744i | \(-0.785203\pi\) | ||||
−0.780830 | + | 0.624744i | \(0.785203\pi\) | |||||||
\(822\) | 17.6367 | 0.615150 | ||||||||
\(823\) | −10.7699 | −0.375416 | −0.187708 | − | 0.982225i | \(-0.560106\pi\) | ||||
−0.187708 | + | 0.982225i | \(0.560106\pi\) | |||||||
\(824\) | −8.42353 | −0.293447 | ||||||||
\(825\) | 3.03186 | 0.105556 | ||||||||
\(826\) | 28.0173 | 0.974846 | ||||||||
\(827\) | −25.6957 | −0.893526 | −0.446763 | − | 0.894652i | \(-0.647423\pi\) | ||||
−0.446763 | + | 0.894652i | \(0.647423\pi\) | |||||||
\(828\) | −0.204870 | −0.00711972 | ||||||||
\(829\) | −49.0904 | −1.70498 | −0.852490 | − | 0.522744i | \(-0.824908\pi\) | ||||
−0.852490 | + | 0.522744i | \(0.824908\pi\) | |||||||
\(830\) | 16.7626 | 0.581839 | ||||||||
\(831\) | −8.89171 | −0.308450 | ||||||||
\(832\) | −2.22074 | −0.0769904 | ||||||||
\(833\) | 0.0550840 | 0.00190855 | ||||||||
\(834\) | 12.9773 | 0.449367 | ||||||||
\(835\) | 20.9922 | 0.726464 | ||||||||
\(836\) | 1.90697 | 0.0659538 | ||||||||
\(837\) | −9.76569 | −0.337552 | ||||||||
\(838\) | −4.82984 | −0.166844 | ||||||||
\(839\) | −19.7433 | −0.681615 | −0.340808 | − | 0.940133i | \(-0.610700\pi\) | ||||
−0.340808 | + | 0.940133i | \(0.610700\pi\) | |||||||
\(840\) | −3.70571 | −0.127859 | ||||||||
\(841\) | −28.7772 | −0.992316 | ||||||||
\(842\) | 6.50405 | 0.224144 | ||||||||
\(843\) | 2.33522 | 0.0804293 | ||||||||
\(844\) | −15.3771 | −0.529302 | ||||||||
\(845\) | 11.3190 | 0.389387 | ||||||||
\(846\) | −10.0230 | −0.344597 | ||||||||
\(847\) | 2.64146 | 0.0907615 | ||||||||
\(848\) | −9.17082 | −0.314927 | ||||||||
\(849\) | −20.7019 | −0.710486 | ||||||||
\(850\) | −7.35412 | −0.252244 | ||||||||
\(851\) | 1.38567 | 0.0475002 | ||||||||
\(852\) | 7.05306 | 0.241634 | ||||||||
\(853\) | 39.3259 | 1.34649 | 0.673246 | − | 0.739418i | \(-0.264899\pi\) | ||||
0.673246 | + | 0.739418i | \(0.264899\pi\) | |||||||
\(854\) | −2.64146 | −0.0903888 | ||||||||
\(855\) | −2.67529 | −0.0914930 | ||||||||
\(856\) | −8.61317 | −0.294392 | ||||||||
\(857\) | 4.11788 | 0.140664 | 0.0703320 | − | 0.997524i | \(-0.477594\pi\) | ||||
0.0703320 | + | 0.997524i | \(0.477594\pi\) | |||||||
\(858\) | −2.22074 | −0.0758149 | ||||||||
\(859\) | −6.03347 | −0.205859 | −0.102930 | − | 0.994689i | \(-0.532822\pi\) | ||||
−0.102930 | + | 0.994689i | \(0.532822\pi\) | |||||||
\(860\) | 2.30025 | 0.0784378 | ||||||||
\(861\) | 20.5002 | 0.698644 | ||||||||
\(862\) | −33.0122 | −1.12440 | ||||||||
\(863\) | 23.0371 | 0.784193 | 0.392097 | − | 0.919924i | \(-0.371750\pi\) | ||||
0.392097 | + | 0.919924i | \(0.371750\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 26.8662 | 0.913477 | ||||||||
\(866\) | −23.4933 | −0.798336 | ||||||||
\(867\) | 11.1164 | 0.377533 | ||||||||
\(868\) | 25.7957 | 0.875561 | ||||||||
\(869\) | −11.7867 | −0.399837 | ||||||||
\(870\) | −0.662256 | −0.0224526 | ||||||||
\(871\) | −15.4377 | −0.523087 | ||||||||
\(872\) | 0.270369 | 0.00915586 | ||||||||
\(873\) | 3.02014 | 0.102216 | ||||||||
\(874\) | 0.390680 | 0.0132149 | ||||||||
\(875\) | 29.7637 | 1.00620 | ||||||||
\(876\) | −13.5829 | −0.458923 | ||||||||
\(877\) | −30.2921 | −1.02289 | −0.511446 | − | 0.859316i | \(-0.670890\pi\) | ||||
−0.511446 | + | 0.859316i | \(0.670890\pi\) | |||||||
\(878\) | −21.8941 | −0.738889 | ||||||||
\(879\) | 9.73347 | 0.328302 | ||||||||
\(880\) | −1.40290 | −0.0472919 | ||||||||
\(881\) | −34.6308 | −1.16674 | −0.583370 | − | 0.812207i | \(-0.698266\pi\) | ||||
−0.583370 | + | 0.812207i | \(0.698266\pi\) | |||||||
\(882\) | 0.0227093 | 0.000764662 0 | ||||||||
\(883\) | −28.4064 | −0.955951 | −0.477975 | − | 0.878373i | \(-0.658629\pi\) | ||||
−0.477975 | + | 0.878373i | \(0.658629\pi\) | |||||||
\(884\) | 5.38667 | 0.181173 | ||||||||
\(885\) | −14.8803 | −0.500195 | ||||||||
\(886\) | 31.7620 | 1.06707 | ||||||||
\(887\) | −17.6978 | −0.594235 | −0.297118 | − | 0.954841i | \(-0.596025\pi\) | ||||
−0.297118 | + | 0.954841i | \(0.596025\pi\) | |||||||
\(888\) | −6.76367 | −0.226974 | ||||||||
\(889\) | 44.4201 | 1.48980 | ||||||||
\(890\) | −23.9498 | −0.802799 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −2.25767 | −0.0755924 | ||||||||
\(893\) | 19.1135 | 0.639607 | ||||||||
\(894\) | 2.01437 | 0.0673705 | ||||||||
\(895\) | 23.4800 | 0.784850 | ||||||||
\(896\) | −2.64146 | −0.0882449 | ||||||||
\(897\) | −0.454963 | −0.0151908 | ||||||||
\(898\) | 33.8087 | 1.12821 | ||||||||
\(899\) | 4.61000 | 0.153752 | ||||||||
\(900\) | −3.03186 | −0.101062 | ||||||||
\(901\) | 22.2449 | 0.741084 | ||||||||
\(902\) | 7.76093 | 0.258411 | ||||||||
\(903\) | 4.33102 | 0.144127 | ||||||||
\(904\) | 1.33006 | 0.0442371 | ||||||||
\(905\) | −7.75517 | −0.257790 | ||||||||
\(906\) | −15.4442 | −0.513098 | ||||||||
\(907\) | 49.8878 | 1.65650 | 0.828249 | − | 0.560360i | \(-0.189337\pi\) | ||||
0.828249 | + | 0.560360i | \(0.189337\pi\) | |||||||
\(908\) | −18.0576 | −0.599264 | ||||||||
\(909\) | −6.26627 | −0.207839 | ||||||||
\(910\) | −8.22943 | −0.272803 | ||||||||
\(911\) | 49.2332 | 1.63117 | 0.815584 | − | 0.578638i | \(-0.196416\pi\) | ||||
0.815584 | + | 0.578638i | \(0.196416\pi\) | |||||||
\(912\) | −1.90697 | −0.0631459 | ||||||||
\(913\) | 11.9485 | 0.395438 | ||||||||
\(914\) | 14.3858 | 0.475839 | ||||||||
\(915\) | 1.40290 | 0.0463786 | ||||||||
\(916\) | 2.29571 | 0.0758523 | ||||||||
\(917\) | −23.3470 | −0.770987 | ||||||||
\(918\) | −2.42561 | −0.0800572 | ||||||||
\(919\) | 44.7060 | 1.47472 | 0.737358 | − | 0.675503i | \(-0.236073\pi\) | ||||
0.737358 | + | 0.675503i | \(0.236073\pi\) | |||||||
\(920\) | −0.287413 | −0.00947572 | ||||||||
\(921\) | 28.0902 | 0.925604 | ||||||||
\(922\) | 1.24112 | 0.0408740 | ||||||||
\(923\) | 15.6630 | 0.515555 | ||||||||
\(924\) | −2.64146 | −0.0868975 | ||||||||
\(925\) | 20.5065 | 0.674250 | ||||||||
\(926\) | 18.1466 | 0.596334 | ||||||||
\(927\) | 8.42353 | 0.276665 | ||||||||
\(928\) | −0.472061 | −0.0154962 | ||||||||
\(929\) | 7.24383 | 0.237662 | 0.118831 | − | 0.992914i | \(-0.462085\pi\) | ||||
0.118831 | + | 0.992914i | \(0.462085\pi\) | |||||||
\(930\) | −13.7003 | −0.449252 | ||||||||
\(931\) | −0.0433059 | −0.00141929 | ||||||||
\(932\) | 4.14358 | 0.135728 | ||||||||
\(933\) | 21.6072 | 0.707390 | ||||||||
\(934\) | 10.7033 | 0.350223 | ||||||||
\(935\) | 3.40290 | 0.111287 | ||||||||
\(936\) | 2.22074 | 0.0725873 | ||||||||
\(937\) | 0.341181 | 0.0111459 | 0.00557294 | − | 0.999984i | \(-0.498226\pi\) | ||||
0.00557294 | + | 0.999984i | \(0.498226\pi\) | |||||||
\(938\) | −18.3623 | −0.599551 | ||||||||
\(939\) | −17.7487 | −0.579206 | ||||||||
\(940\) | −14.0613 | −0.458628 | ||||||||
\(941\) | −16.4129 | −0.535047 | −0.267523 | − | 0.963551i | \(-0.586205\pi\) | ||||
−0.267523 | + | 0.963551i | \(0.586205\pi\) | |||||||
\(942\) | −8.93090 | −0.290984 | ||||||||
\(943\) | 1.58998 | 0.0517769 | ||||||||
\(944\) | −10.6068 | −0.345221 | ||||||||
\(945\) | 3.70571 | 0.120547 | ||||||||
\(946\) | 1.63963 | 0.0533091 | ||||||||
\(947\) | −22.2932 | −0.724431 | −0.362215 | − | 0.932094i | \(-0.617980\pi\) | ||||
−0.362215 | + | 0.932094i | \(0.617980\pi\) | |||||||
\(948\) | 11.7867 | 0.382815 | ||||||||
\(949\) | −30.1641 | −0.979168 | ||||||||
\(950\) | 5.78165 | 0.187581 | ||||||||
\(951\) | 12.4486 | 0.403673 | ||||||||
\(952\) | 6.40715 | 0.207657 | ||||||||
\(953\) | −25.7282 | −0.833417 | −0.416708 | − | 0.909040i | \(-0.636816\pi\) | ||||
−0.416708 | + | 0.909040i | \(0.636816\pi\) | |||||||
\(954\) | 9.17082 | 0.296916 | ||||||||
\(955\) | −34.7931 | −1.12588 | ||||||||
\(956\) | −5.42149 | −0.175343 | ||||||||
\(957\) | −0.472061 | −0.0152596 | ||||||||
\(958\) | −12.1296 | −0.391888 | ||||||||
\(959\) | 46.5865 | 1.50436 | ||||||||
\(960\) | 1.40290 | 0.0452785 | ||||||||
\(961\) | 64.3688 | 2.07641 | ||||||||
\(962\) | −15.0204 | −0.484277 | ||||||||
\(963\) | 8.61317 | 0.277555 | ||||||||
\(964\) | −16.3458 | −0.526463 | ||||||||
\(965\) | 9.97563 | 0.321127 | ||||||||
\(966\) | −0.541155 | −0.0174114 | ||||||||
\(967\) | 54.0660 | 1.73865 | 0.869323 | − | 0.494245i | \(-0.164555\pi\) | ||||
0.869323 | + | 0.494245i | \(0.164555\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 4.62556 | 0.148594 | ||||||||
\(970\) | 4.23697 | 0.136041 | ||||||||
\(971\) | −45.7026 | −1.46667 | −0.733333 | − | 0.679870i | \(-0.762036\pi\) | ||||
−0.733333 | + | 0.679870i | \(0.762036\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 34.2789 | 1.09893 | ||||||||
\(974\) | −8.75526 | −0.280537 | ||||||||
\(975\) | −6.73298 | −0.215628 | ||||||||
\(976\) | 1.00000 | 0.0320092 | ||||||||
\(977\) | 45.6848 | 1.46159 | 0.730793 | − | 0.682599i | \(-0.239150\pi\) | ||||
0.730793 | + | 0.682599i | \(0.239150\pi\) | |||||||
\(978\) | −10.0502 | −0.321369 | ||||||||
\(979\) | −17.0716 | −0.545610 | ||||||||
\(980\) | 0.0318590 | 0.00101770 | ||||||||
\(981\) | −0.270369 | −0.00863223 | ||||||||
\(982\) | −27.0828 | −0.864246 | ||||||||
\(983\) | 10.5994 | 0.338067 | 0.169034 | − | 0.985610i | \(-0.445935\pi\) | ||||
0.169034 | + | 0.985610i | \(0.445935\pi\) | |||||||
\(984\) | −7.76093 | −0.247409 | ||||||||
\(985\) | 37.5737 | 1.19720 | ||||||||
\(986\) | 1.14504 | 0.0364654 | ||||||||
\(987\) | −26.4752 | −0.842716 | ||||||||
\(988\) | −4.23488 | −0.134730 | ||||||||
\(989\) | 0.335911 | 0.0106814 | ||||||||
\(990\) | 1.40290 | 0.0445872 | ||||||||
\(991\) | 57.0151 | 1.81115 | 0.905573 | − | 0.424191i | \(-0.139441\pi\) | ||||
0.905573 | + | 0.424191i | \(0.139441\pi\) | |||||||
\(992\) | −9.76569 | −0.310061 | ||||||||
\(993\) | 0.976434 | 0.0309862 | ||||||||
\(994\) | 18.6303 | 0.590919 | ||||||||
\(995\) | 0.365394 | 0.0115838 | ||||||||
\(996\) | −11.9485 | −0.378603 | ||||||||
\(997\) | −23.7030 | −0.750681 | −0.375340 | − | 0.926887i | \(-0.622474\pi\) | ||||
−0.375340 | + | 0.926887i | \(0.622474\pi\) | |||||||
\(998\) | 15.6902 | 0.496665 | ||||||||
\(999\) | 6.76367 | 0.213993 |
(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 | 4026.2.a.w.1.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.w.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial |