Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1617,2,Mod(1,1617)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1617, 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("1617.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1617 = 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1617.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: | \(12.9118100068\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.11491\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1617.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.47283 | 1.74856 | 0.874279 | − | 0.485424i | \(-0.161335\pi\) | ||||
0.874279 | + | 0.485424i | \(0.161335\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.11491 | 2.05745 | ||||||||
\(5\) | 2.58774 | 1.15727 | 0.578637 | − | 0.815586i | \(-0.303585\pi\) | ||||
0.578637 | + | 0.815586i | \(0.303585\pi\) | |||||||
\(6\) | −2.47283 | −1.00953 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 5.22982 | 1.84902 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 6.39905 | 2.02356 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −4.11491 | −1.18787 | ||||||||
\(13\) | 5.87189 | 1.62857 | 0.814284 | − | 0.580466i | \(-0.197130\pi\) | ||||
0.814284 | + | 0.580466i | \(0.197130\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.58774 | −0.668152 | ||||||||
\(16\) | 4.70265 | 1.17566 | ||||||||
\(17\) | −7.51396 | −1.82240 | −0.911202 | − | 0.411960i | \(-0.864844\pi\) | ||||
−0.911202 | + | 0.411960i | \(0.864844\pi\) | |||||||
\(18\) | 2.47283 | 0.582853 | ||||||||
\(19\) | 2.35793 | 0.540945 | 0.270473 | − | 0.962728i | \(-0.412820\pi\) | ||||
0.270473 | + | 0.962728i | \(0.412820\pi\) | |||||||
\(20\) | 10.6483 | 2.38104 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.47283 | −0.527210 | ||||||||
\(23\) | 6.94567 | 1.44827 | 0.724136 | − | 0.689657i | \(-0.242239\pi\) | ||||
0.724136 | + | 0.689657i | \(0.242239\pi\) | |||||||
\(24\) | −5.22982 | −1.06753 | ||||||||
\(25\) | 1.69641 | 0.339281 | ||||||||
\(26\) | 14.5202 | 2.84765 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.87189 | −1.09038 | −0.545191 | − | 0.838312i | \(-0.683543\pi\) | ||||
−0.545191 | + | 0.838312i | \(0.683543\pi\) | |||||||
\(30\) | −6.39905 | −1.16830 | ||||||||
\(31\) | 3.66152 | 0.657629 | 0.328814 | − | 0.944395i | \(-0.393351\pi\) | ||||
0.328814 | + | 0.944395i | \(0.393351\pi\) | |||||||
\(32\) | 1.16924 | 0.206694 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −18.5808 | −3.18658 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.11491 | 0.685818 | ||||||||
\(37\) | 3.30359 | 0.543108 | 0.271554 | − | 0.962423i | \(-0.412463\pi\) | ||||
0.271554 | + | 0.962423i | \(0.412463\pi\) | |||||||
\(38\) | 5.83076 | 0.945874 | ||||||||
\(39\) | −5.87189 | −0.940255 | ||||||||
\(40\) | 13.5334 | 2.13982 | ||||||||
\(41\) | −5.28415 | −0.825245 | −0.412623 | − | 0.910902i | \(-0.635387\pi\) | ||||
−0.412623 | + | 0.910902i | \(0.635387\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.40530 | 1.12930 | 0.564649 | − | 0.825331i | \(-0.309012\pi\) | ||||
0.564649 | + | 0.825331i | \(0.309012\pi\) | |||||||
\(44\) | −4.11491 | −0.620346 | ||||||||
\(45\) | 2.58774 | 0.385758 | ||||||||
\(46\) | 17.1755 | 2.53239 | ||||||||
\(47\) | −7.53341 | −1.09886 | −0.549430 | − | 0.835540i | \(-0.685155\pi\) | ||||
−0.549430 | + | 0.835540i | \(0.685155\pi\) | |||||||
\(48\) | −4.70265 | −0.678769 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.19493 | 0.593253 | ||||||||
\(51\) | 7.51396 | 1.05217 | ||||||||
\(52\) | 24.1623 | 3.35071 | ||||||||
\(53\) | −4.22982 | −0.581010 | −0.290505 | − | 0.956874i | \(-0.593823\pi\) | ||||
−0.290505 | + | 0.956874i | \(0.593823\pi\) | |||||||
\(54\) | −2.47283 | −0.336510 | ||||||||
\(55\) | −2.58774 | −0.348931 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.35793 | −0.312315 | ||||||||
\(58\) | −14.5202 | −1.90660 | ||||||||
\(59\) | 0.926221 | 0.120584 | 0.0602918 | − | 0.998181i | \(-0.480797\pi\) | ||||
0.0602918 | + | 0.998181i | \(0.480797\pi\) | |||||||
\(60\) | −10.6483 | −1.37469 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 9.05433 | 1.14990 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.51396 | −0.814245 | ||||||||
\(65\) | 15.1949 | 1.88470 | ||||||||
\(66\) | 2.47283 | 0.304385 | ||||||||
\(67\) | −10.1017 | −1.23412 | −0.617060 | − | 0.786916i | \(-0.711676\pi\) | ||||
−0.617060 | + | 0.786916i | \(0.711676\pi\) | |||||||
\(68\) | −30.9193 | −3.74951 | ||||||||
\(69\) | −6.94567 | −0.836160 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.45963 | 0.529261 | 0.264630 | − | 0.964350i | \(-0.414750\pi\) | ||||
0.264630 | + | 0.964350i | \(0.414750\pi\) | |||||||
\(72\) | 5.22982 | 0.616340 | ||||||||
\(73\) | 2.12811 | 0.249077 | 0.124538 | − | 0.992215i | \(-0.460255\pi\) | ||||
0.124538 | + | 0.992215i | \(0.460255\pi\) | |||||||
\(74\) | 8.16924 | 0.949655 | ||||||||
\(75\) | −1.69641 | −0.195884 | ||||||||
\(76\) | 9.70265 | 1.11297 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −14.5202 | −1.64409 | ||||||||
\(79\) | −4.45963 | −0.501748 | −0.250874 | − | 0.968020i | \(-0.580718\pi\) | ||||
−0.250874 | + | 0.968020i | \(0.580718\pi\) | |||||||
\(80\) | 12.1692 | 1.36056 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −13.0668 | −1.44299 | ||||||||
\(83\) | 10.6894 | 1.17332 | 0.586660 | − | 0.809834i | \(-0.300443\pi\) | ||||
0.586660 | + | 0.809834i | \(0.300443\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −19.4442 | −2.10902 | ||||||||
\(86\) | 18.3121 | 1.97464 | ||||||||
\(87\) | 5.87189 | 0.629533 | ||||||||
\(88\) | −5.22982 | −0.557500 | ||||||||
\(89\) | −15.8913 | −1.68448 | −0.842239 | − | 0.539104i | \(-0.818763\pi\) | ||||
−0.842239 | + | 0.539104i | \(0.818763\pi\) | |||||||
\(90\) | 6.39905 | 0.674520 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 28.5808 | 2.97975 | ||||||||
\(93\) | −3.66152 | −0.379682 | ||||||||
\(94\) | −18.6289 | −1.92142 | ||||||||
\(95\) | 6.10170 | 0.626022 | ||||||||
\(96\) | −1.16924 | −0.119335 | ||||||||
\(97\) | −10.1212 | −1.02765 | −0.513824 | − | 0.857896i | \(-0.671771\pi\) | ||||
−0.513824 | + | 0.857896i | \(0.671771\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 6.98055 | 0.698055 | ||||||||
\(101\) | 13.4053 | 1.33388 | 0.666939 | − | 0.745113i | \(-0.267604\pi\) | ||||
0.666939 | + | 0.745113i | \(0.267604\pi\) | |||||||
\(102\) | 18.5808 | 1.83977 | ||||||||
\(103\) | 4.71585 | 0.464667 | 0.232333 | − | 0.972636i | \(-0.425364\pi\) | ||||
0.232333 | + | 0.972636i | \(0.425364\pi\) | |||||||
\(104\) | 30.7089 | 3.01125 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.4596 | −1.01593 | ||||||||
\(107\) | 7.07378 | 0.683848 | 0.341924 | − | 0.939728i | \(-0.388921\pi\) | ||||
0.341924 | + | 0.939728i | \(0.388921\pi\) | |||||||
\(108\) | −4.11491 | −0.395957 | ||||||||
\(109\) | 18.8370 | 1.80426 | 0.902129 | − | 0.431467i | \(-0.142004\pi\) | ||||
0.902129 | + | 0.431467i | \(0.142004\pi\) | |||||||
\(110\) | −6.39905 | −0.610126 | ||||||||
\(111\) | −3.30359 | −0.313563 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.02792 | −0.849276 | −0.424638 | − | 0.905363i | \(-0.639599\pi\) | ||||
−0.424638 | + | 0.905363i | \(0.639599\pi\) | |||||||
\(114\) | −5.83076 | −0.546101 | ||||||||
\(115\) | 17.9736 | 1.67605 | ||||||||
\(116\) | −24.1623 | −2.24341 | ||||||||
\(117\) | 5.87189 | 0.542856 | ||||||||
\(118\) | 2.29039 | 0.210848 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −13.5334 | −1.23543 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 4.94567 | 0.447760 | ||||||||
\(123\) | 5.28415 | 0.476456 | ||||||||
\(124\) | 15.0668 | 1.35304 | ||||||||
\(125\) | −8.54885 | −0.764632 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.2298 | −0.907749 | −0.453875 | − | 0.891066i | \(-0.649959\pi\) | ||||
−0.453875 | + | 0.891066i | \(0.649959\pi\) | |||||||
\(128\) | −18.4464 | −1.63045 | ||||||||
\(129\) | −7.40530 | −0.652000 | ||||||||
\(130\) | 37.5745 | 3.29550 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 4.11491 | 0.358157 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −24.9798 | −2.15793 | ||||||||
\(135\) | −2.58774 | −0.222717 | ||||||||
\(136\) | −39.2966 | −3.36966 | ||||||||
\(137\) | −10.8370 | −0.925868 | −0.462934 | − | 0.886393i | \(-0.653203\pi\) | ||||
−0.462934 | + | 0.886393i | \(0.653203\pi\) | |||||||
\(138\) | −17.1755 | −1.46207 | ||||||||
\(139\) | −0.459630 | −0.0389853 | −0.0194927 | − | 0.999810i | \(-0.506205\pi\) | ||||
−0.0194927 | + | 0.999810i | \(0.506205\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.53341 | 0.634428 | ||||||||
\(142\) | 11.0279 | 0.925443 | ||||||||
\(143\) | −5.87189 | −0.491032 | ||||||||
\(144\) | 4.70265 | 0.391887 | ||||||||
\(145\) | −15.1949 | −1.26187 | ||||||||
\(146\) | 5.26247 | 0.435525 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 13.5940 | 1.11742 | ||||||||
\(149\) | 11.0474 | 0.905036 | 0.452518 | − | 0.891755i | \(-0.350526\pi\) | ||||
0.452518 | + | 0.891755i | \(0.350526\pi\) | |||||||
\(150\) | −4.19493 | −0.342515 | ||||||||
\(151\) | −16.1212 | −1.31192 | −0.655960 | − | 0.754795i | \(-0.727736\pi\) | ||||
−0.655960 | + | 0.754795i | \(0.727736\pi\) | |||||||
\(152\) | 12.3315 | 1.00022 | ||||||||
\(153\) | −7.51396 | −0.607468 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.47507 | 0.761056 | ||||||||
\(156\) | −24.1623 | −1.93453 | ||||||||
\(157\) | −13.0668 | −1.04285 | −0.521423 | − | 0.853298i | \(-0.674599\pi\) | ||||
−0.521423 | + | 0.853298i | \(0.674599\pi\) | |||||||
\(158\) | −11.0279 | −0.877335 | ||||||||
\(159\) | 4.22982 | 0.335446 | ||||||||
\(160\) | 3.02569 | 0.239202 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.47283 | 0.194284 | ||||||||
\(163\) | −10.1017 | −0.791227 | −0.395613 | − | 0.918417i | \(-0.629468\pi\) | ||||
−0.395613 | + | 0.918417i | \(0.629468\pi\) | |||||||
\(164\) | −21.7438 | −1.69790 | ||||||||
\(165\) | 2.58774 | 0.201455 | ||||||||
\(166\) | 26.4332 | 2.05162 | ||||||||
\(167\) | 10.4860 | 0.811434 | 0.405717 | − | 0.913999i | \(-0.367022\pi\) | ||||
0.405717 | + | 0.913999i | \(0.367022\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.4791 | 1.65224 | ||||||||
\(170\) | −48.0823 | −3.68774 | ||||||||
\(171\) | 2.35793 | 0.180315 | ||||||||
\(172\) | 30.4721 | 2.32348 | ||||||||
\(173\) | −14.4985 | −1.10230 | −0.551151 | − | 0.834405i | \(-0.685811\pi\) | ||||
−0.551151 | + | 0.834405i | \(0.685811\pi\) | |||||||
\(174\) | 14.5202 | 1.10077 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.70265 | −0.354476 | ||||||||
\(177\) | −0.926221 | −0.0696190 | ||||||||
\(178\) | −39.2966 | −2.94541 | ||||||||
\(179\) | 14.3510 | 1.07264 | 0.536321 | − | 0.844014i | \(-0.319814\pi\) | ||||
0.536321 | + | 0.844014i | \(0.319814\pi\) | |||||||
\(180\) | 10.6483 | 0.793679 | ||||||||
\(181\) | −9.66152 | −0.718135 | −0.359068 | − | 0.933312i | \(-0.616905\pi\) | ||||
−0.359068 | + | 0.933312i | \(0.616905\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | 36.3246 | 2.67788 | ||||||||
\(185\) | 8.54885 | 0.628524 | ||||||||
\(186\) | −9.05433 | −0.663896 | ||||||||
\(187\) | 7.51396 | 0.549475 | ||||||||
\(188\) | −30.9993 | −2.26086 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 15.0885 | 1.09463 | ||||||||
\(191\) | −9.55286 | −0.691220 | −0.345610 | − | 0.938378i | \(-0.612328\pi\) | ||||
−0.345610 | + | 0.938378i | \(0.612328\pi\) | |||||||
\(192\) | 6.51396 | 0.470105 | ||||||||
\(193\) | −22.1212 | −1.59232 | −0.796158 | − | 0.605089i | \(-0.793137\pi\) | ||||
−0.796158 | + | 0.605089i | \(0.793137\pi\) | |||||||
\(194\) | −25.0279 | −1.79690 | ||||||||
\(195\) | −15.1949 | −1.08813 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.2423 | −1.86969 | −0.934843 | − | 0.355061i | \(-0.884460\pi\) | ||||
−0.934843 | + | 0.355061i | \(0.884460\pi\) | |||||||
\(198\) | −2.47283 | −0.175737 | ||||||||
\(199\) | −1.05433 | −0.0747396 | −0.0373698 | − | 0.999302i | \(-0.511898\pi\) | ||||
−0.0373698 | + | 0.999302i | \(0.511898\pi\) | |||||||
\(200\) | 8.87189 | 0.627337 | ||||||||
\(201\) | 10.1017 | 0.712519 | ||||||||
\(202\) | 33.1491 | 2.33236 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 30.9193 | 2.16478 | ||||||||
\(205\) | −13.6740 | −0.955034 | ||||||||
\(206\) | 11.6615 | 0.812497 | ||||||||
\(207\) | 6.94567 | 0.482757 | ||||||||
\(208\) | 27.6134 | 1.91465 | ||||||||
\(209\) | −2.35793 | −0.163101 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.71585 | −0.600024 | −0.300012 | − | 0.953935i | \(-0.596991\pi\) | ||||
−0.300012 | + | 0.953935i | \(0.596991\pi\) | |||||||
\(212\) | −17.4053 | −1.19540 | ||||||||
\(213\) | −4.45963 | −0.305569 | ||||||||
\(214\) | 17.4923 | 1.19575 | ||||||||
\(215\) | 19.1630 | 1.30691 | ||||||||
\(216\) | −5.22982 | −0.355844 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 46.5808 | 3.15485 | ||||||||
\(219\) | −2.12811 | −0.143804 | ||||||||
\(220\) | −10.6483 | −0.717909 | ||||||||
\(221\) | −44.1212 | −2.96791 | ||||||||
\(222\) | −8.16924 | −0.548283 | ||||||||
\(223\) | 23.7438 | 1.59000 | 0.795000 | − | 0.606609i | \(-0.207471\pi\) | ||||
0.795000 | + | 0.606609i | \(0.207471\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.69641 | 0.113094 | ||||||||
\(226\) | −22.3246 | −1.48501 | ||||||||
\(227\) | 13.1755 | 0.874488 | 0.437244 | − | 0.899343i | \(-0.355955\pi\) | ||||
0.437244 | + | 0.899343i | \(0.355955\pi\) | |||||||
\(228\) | −9.70265 | −0.642574 | ||||||||
\(229\) | −13.3664 | −0.883277 | −0.441638 | − | 0.897193i | \(-0.645603\pi\) | ||||
−0.441638 | + | 0.897193i | \(0.645603\pi\) | |||||||
\(230\) | 44.4457 | 2.93066 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −30.7089 | −2.01614 | ||||||||
\(233\) | 7.13659 | 0.467533 | 0.233767 | − | 0.972293i | \(-0.424895\pi\) | ||||
0.233767 | + | 0.972293i | \(0.424895\pi\) | |||||||
\(234\) | 14.5202 | 0.949216 | ||||||||
\(235\) | −19.4945 | −1.27168 | ||||||||
\(236\) | 3.81131 | 0.248095 | ||||||||
\(237\) | 4.45963 | 0.289684 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.9930 | −1.29324 | −0.646621 | − | 0.762811i | \(-0.723818\pi\) | ||||
−0.646621 | + | 0.762811i | \(0.723818\pi\) | |||||||
\(240\) | −12.1692 | −0.785521 | ||||||||
\(241\) | 9.19493 | 0.592297 | 0.296149 | − | 0.955142i | \(-0.404298\pi\) | ||||
0.296149 | + | 0.955142i | \(0.404298\pi\) | |||||||
\(242\) | 2.47283 | 0.158960 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 8.22982 | 0.526860 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13.0668 | 0.833110 | ||||||||
\(247\) | 13.8455 | 0.880967 | ||||||||
\(248\) | 19.1491 | 1.21597 | ||||||||
\(249\) | −10.6894 | −0.677416 | ||||||||
\(250\) | −21.1399 | −1.33700 | ||||||||
\(251\) | 9.42474 | 0.594885 | 0.297442 | − | 0.954740i | \(-0.403866\pi\) | ||||
0.297442 | + | 0.954740i | \(0.403866\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.94567 | −0.436670 | ||||||||
\(254\) | −25.2966 | −1.58725 | ||||||||
\(255\) | 19.4442 | 1.21764 | ||||||||
\(256\) | −32.5870 | −2.03669 | ||||||||
\(257\) | 0.0194469 | 0.00121307 | 0.000606533 | − | 1.00000i | \(-0.499807\pi\) | ||||
0.000606533 | 1.00000i | \(0.499807\pi\) | ||||||||
\(258\) | −18.3121 | −1.14006 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 62.5257 | 3.87768 | ||||||||
\(261\) | −5.87189 | −0.363461 | ||||||||
\(262\) | −9.89134 | −0.611089 | ||||||||
\(263\) | 27.9930 | 1.72612 | 0.863062 | − | 0.505097i | \(-0.168543\pi\) | ||||
0.863062 | + | 0.505097i | \(0.168543\pi\) | |||||||
\(264\) | 5.22982 | 0.321873 | ||||||||
\(265\) | −10.9457 | −0.672387 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.8913 | 0.972534 | ||||||||
\(268\) | −41.5676 | −2.53914 | ||||||||
\(269\) | −30.9193 | −1.88518 | −0.942590 | − | 0.333951i | \(-0.891618\pi\) | ||||
−0.942590 | + | 0.333951i | \(0.891618\pi\) | |||||||
\(270\) | −6.39905 | −0.389434 | ||||||||
\(271\) | 22.3579 | 1.35815 | 0.679074 | − | 0.734070i | \(-0.262382\pi\) | ||||
0.679074 | + | 0.734070i | \(0.262382\pi\) | |||||||
\(272\) | −35.3355 | −2.14253 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −26.7981 | −1.61893 | ||||||||
\(275\) | −1.69641 | −0.102297 | ||||||||
\(276\) | −28.5808 | −1.72036 | ||||||||
\(277\) | 24.7717 | 1.48839 | 0.744194 | − | 0.667964i | \(-0.232834\pi\) | ||||
0.744194 | + | 0.667964i | \(0.232834\pi\) | |||||||
\(278\) | −1.13659 | −0.0681681 | ||||||||
\(279\) | 3.66152 | 0.219210 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.19493 | −0.0712835 | −0.0356418 | − | 0.999365i | \(-0.511348\pi\) | ||||
−0.0356418 | + | 0.999365i | \(0.511348\pi\) | |||||||
\(282\) | 18.6289 | 1.10933 | ||||||||
\(283\) | 15.5723 | 0.925677 | 0.462839 | − | 0.886443i | \(-0.346831\pi\) | ||||
0.462839 | + | 0.886443i | \(0.346831\pi\) | |||||||
\(284\) | 18.3510 | 1.08893 | ||||||||
\(285\) | −6.10170 | −0.361434 | ||||||||
\(286\) | −14.5202 | −0.858598 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.16924 | 0.0688981 | ||||||||
\(289\) | 39.4596 | 2.32115 | ||||||||
\(290\) | −37.5745 | −2.20645 | ||||||||
\(291\) | 10.1212 | 0.593312 | ||||||||
\(292\) | 8.75698 | 0.512464 | ||||||||
\(293\) | 9.74378 | 0.569238 | 0.284619 | − | 0.958641i | \(-0.408133\pi\) | ||||
0.284619 | + | 0.958641i | \(0.408133\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.39682 | 0.139548 | ||||||||
\(296\) | 17.2772 | 1.00422 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 27.3183 | 1.58251 | ||||||||
\(299\) | 40.7842 | 2.35861 | ||||||||
\(300\) | −6.98055 | −0.403022 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −39.8649 | −2.29397 | ||||||||
\(303\) | −13.4053 | −0.770114 | ||||||||
\(304\) | 11.0885 | 0.635969 | ||||||||
\(305\) | 5.17548 | 0.296347 | ||||||||
\(306\) | −18.5808 | −1.06219 | ||||||||
\(307\) | −6.35097 | −0.362469 | −0.181234 | − | 0.983440i | \(-0.558009\pi\) | ||||
−0.181234 | + | 0.983440i | \(0.558009\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.71585 | −0.268275 | ||||||||
\(310\) | 23.4303 | 1.33075 | ||||||||
\(311\) | −8.00000 | −0.453638 | −0.226819 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | −30.7089 | −1.73855 | ||||||||
\(313\) | −16.9457 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(314\) | −32.3121 | −1.82348 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −18.3510 | −1.03232 | ||||||||
\(317\) | 20.0125 | 1.12401 | 0.562007 | − | 0.827133i | \(-0.310030\pi\) | ||||
0.562007 | + | 0.827133i | \(0.310030\pi\) | |||||||
\(318\) | 10.4596 | 0.586547 | ||||||||
\(319\) | 5.87189 | 0.328763 | ||||||||
\(320\) | −16.8565 | −0.942304 | ||||||||
\(321\) | −7.07378 | −0.394820 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.7174 | −0.985821 | ||||||||
\(324\) | 4.11491 | 0.228606 | ||||||||
\(325\) | 9.96111 | 0.552543 | ||||||||
\(326\) | −24.9798 | −1.38351 | ||||||||
\(327\) | −18.8370 | −1.04169 | ||||||||
\(328\) | −27.6351 | −1.52589 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.39905 | 0.352256 | ||||||||
\(331\) | 7.54037 | 0.414456 | 0.207228 | − | 0.978293i | \(-0.433556\pi\) | ||||
0.207228 | + | 0.978293i | \(0.433556\pi\) | |||||||
\(332\) | 43.9861 | 2.41405 | ||||||||
\(333\) | 3.30359 | 0.181036 | ||||||||
\(334\) | 25.9302 | 1.41884 | ||||||||
\(335\) | −26.1406 | −1.42821 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.6894 | −0.691238 | −0.345619 | − | 0.938375i | \(-0.612331\pi\) | ||||
−0.345619 | + | 0.938375i | \(0.612331\pi\) | |||||||
\(338\) | 53.1142 | 2.88903 | ||||||||
\(339\) | 9.02792 | 0.490330 | ||||||||
\(340\) | −80.0111 | −4.33921 | ||||||||
\(341\) | −3.66152 | −0.198282 | ||||||||
\(342\) | 5.83076 | 0.315291 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 38.7283 | 2.08809 | ||||||||
\(345\) | −17.9736 | −0.967666 | ||||||||
\(346\) | −35.8524 | −1.92744 | ||||||||
\(347\) | 1.13659 | 0.0610153 | 0.0305076 | − | 0.999535i | \(-0.490288\pi\) | ||||
0.0305076 | + | 0.999535i | \(0.490288\pi\) | |||||||
\(348\) | 24.1623 | 1.29523 | ||||||||
\(349\) | 14.7911 | 0.791752 | 0.395876 | − | 0.918304i | \(-0.370441\pi\) | ||||
0.395876 | + | 0.918304i | \(0.370441\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.87189 | −0.313418 | ||||||||
\(352\) | −1.16924 | −0.0623207 | ||||||||
\(353\) | 7.52092 | 0.400298 | 0.200149 | − | 0.979765i | \(-0.435857\pi\) | ||||
0.200149 | + | 0.979765i | \(0.435857\pi\) | |||||||
\(354\) | −2.29039 | −0.121733 | ||||||||
\(355\) | 11.5404 | 0.612499 | ||||||||
\(356\) | −65.3914 | −3.46574 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 35.4876 | 1.87558 | ||||||||
\(359\) | −17.5962 | −0.928693 | −0.464346 | − | 0.885654i | \(-0.653711\pi\) | ||||
−0.464346 | + | 0.885654i | \(0.653711\pi\) | |||||||
\(360\) | 13.5334 | 0.713273 | ||||||||
\(361\) | −13.4402 | −0.707378 | ||||||||
\(362\) | −23.8913 | −1.25570 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.50700 | 0.288250 | ||||||||
\(366\) | −4.94567 | −0.258514 | ||||||||
\(367\) | −14.3121 | −0.747084 | −0.373542 | − | 0.927613i | \(-0.621857\pi\) | ||||
−0.373542 | + | 0.927613i | \(0.621857\pi\) | |||||||
\(368\) | 32.6630 | 1.70268 | ||||||||
\(369\) | −5.28415 | −0.275082 | ||||||||
\(370\) | 21.1399 | 1.09901 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −15.0668 | −0.781178 | ||||||||
\(373\) | −16.4332 | −0.850880 | −0.425440 | − | 0.904987i | \(-0.639881\pi\) | ||||
−0.425440 | + | 0.904987i | \(0.639881\pi\) | |||||||
\(374\) | 18.5808 | 0.960789 | ||||||||
\(375\) | 8.54885 | 0.441461 | ||||||||
\(376\) | −39.3983 | −2.03181 | ||||||||
\(377\) | −34.4791 | −1.77576 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.5334 | 1.00336 | 0.501682 | − | 0.865052i | \(-0.332715\pi\) | ||||
0.501682 | + | 0.865052i | \(0.332715\pi\) | |||||||
\(380\) | 25.1079 | 1.28801 | ||||||||
\(381\) | 10.2298 | 0.524089 | ||||||||
\(382\) | −23.6226 | −1.20864 | ||||||||
\(383\) | −2.35097 | −0.120129 | −0.0600644 | − | 0.998195i | \(-0.519131\pi\) | ||||
−0.0600644 | + | 0.998195i | \(0.519131\pi\) | |||||||
\(384\) | 18.4464 | 0.941340 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −54.7019 | −2.78426 | ||||||||
\(387\) | 7.40530 | 0.376432 | ||||||||
\(388\) | −41.6476 | −2.11434 | ||||||||
\(389\) | −1.74378 | −0.0884130 | −0.0442065 | − | 0.999022i | \(-0.514076\pi\) | ||||
−0.0442065 | + | 0.999022i | \(0.514076\pi\) | |||||||
\(390\) | −37.5745 | −1.90266 | ||||||||
\(391\) | −52.1895 | −2.63934 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.00000 | 0.201773 | ||||||||
\(394\) | −64.8929 | −3.26925 | ||||||||
\(395\) | −11.5404 | −0.580659 | ||||||||
\(396\) | −4.11491 | −0.206782 | ||||||||
\(397\) | −6.54189 | −0.328328 | −0.164164 | − | 0.986433i | \(-0.552493\pi\) | ||||
−0.164164 | + | 0.986433i | \(0.552493\pi\) | |||||||
\(398\) | −2.60719 | −0.130687 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.97760 | 0.398880 | ||||||||
\(401\) | 5.66152 | 0.282723 | 0.141361 | − | 0.989958i | \(-0.454852\pi\) | ||||
0.141361 | + | 0.989958i | \(0.454852\pi\) | |||||||
\(402\) | 24.9798 | 1.24588 | ||||||||
\(403\) | 21.5000 | 1.07099 | ||||||||
\(404\) | 55.1616 | 2.74439 | ||||||||
\(405\) | 2.58774 | 0.128586 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.30359 | −0.163753 | ||||||||
\(408\) | 39.2966 | 1.94547 | ||||||||
\(409\) | 5.48755 | 0.271342 | 0.135671 | − | 0.990754i | \(-0.456681\pi\) | ||||
0.135671 | + | 0.990754i | \(0.456681\pi\) | |||||||
\(410\) | −33.8135 | −1.66993 | ||||||||
\(411\) | 10.8370 | 0.534550 | ||||||||
\(412\) | 19.4053 | 0.956030 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 17.1755 | 0.844129 | ||||||||
\(415\) | 27.6615 | 1.35785 | ||||||||
\(416\) | 6.86565 | 0.336616 | ||||||||
\(417\) | 0.459630 | 0.0225082 | ||||||||
\(418\) | −5.83076 | −0.285192 | ||||||||
\(419\) | −8.24926 | −0.403003 | −0.201501 | − | 0.979488i | \(-0.564582\pi\) | ||||
−0.201501 | + | 0.979488i | \(0.564582\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.2617 | 1.57234 | 0.786171 | − | 0.618009i | \(-0.212061\pi\) | ||||
0.786171 | + | 0.618009i | \(0.212061\pi\) | |||||||
\(422\) | −21.5529 | −1.04918 | ||||||||
\(423\) | −7.53341 | −0.366287 | ||||||||
\(424\) | −22.1212 | −1.07430 | ||||||||
\(425\) | −12.7467 | −0.618307 | ||||||||
\(426\) | −11.0279 | −0.534305 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 29.1079 | 1.40699 | ||||||||
\(429\) | 5.87189 | 0.283497 | ||||||||
\(430\) | 47.3869 | 2.28520 | ||||||||
\(431\) | −23.2772 | −1.12122 | −0.560611 | − | 0.828079i | \(-0.689434\pi\) | ||||
−0.560611 | + | 0.828079i | \(0.689434\pi\) | |||||||
\(432\) | −4.70265 | −0.226256 | ||||||||
\(433\) | 15.9302 | 0.765558 | 0.382779 | − | 0.923840i | \(-0.374967\pi\) | ||||
0.382779 | + | 0.923840i | \(0.374967\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.1949 | 0.728541 | ||||||||
\(436\) | 77.5125 | 3.71218 | ||||||||
\(437\) | 16.3774 | 0.783436 | ||||||||
\(438\) | −5.26247 | −0.251450 | ||||||||
\(439\) | −22.8565 | −1.09088 | −0.545439 | − | 0.838150i | \(-0.683637\pi\) | ||||
−0.545439 | + | 0.838150i | \(0.683637\pi\) | |||||||
\(440\) | −13.5334 | −0.645180 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −109.104 | −5.18956 | ||||||||
\(443\) | 21.5962 | 1.02607 | 0.513034 | − | 0.858368i | \(-0.328522\pi\) | ||||
0.513034 | + | 0.858368i | \(0.328522\pi\) | |||||||
\(444\) | −13.5940 | −0.645142 | ||||||||
\(445\) | −41.1227 | −1.94940 | ||||||||
\(446\) | 58.7144 | 2.78021 | ||||||||
\(447\) | −11.0474 | −0.522523 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.6630 | 0.880763 | 0.440382 | − | 0.897811i | \(-0.354843\pi\) | ||||
0.440382 | + | 0.897811i | \(0.354843\pi\) | |||||||
\(450\) | 4.19493 | 0.197751 | ||||||||
\(451\) | 5.28415 | 0.248821 | ||||||||
\(452\) | −37.1491 | −1.74735 | ||||||||
\(453\) | 16.1212 | 0.757438 | ||||||||
\(454\) | 32.5808 | 1.52909 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.3315 | −0.577476 | ||||||||
\(457\) | 36.4721 | 1.70609 | 0.853047 | − | 0.521834i | \(-0.174752\pi\) | ||||
0.853047 | + | 0.521834i | \(0.174752\pi\) | |||||||
\(458\) | −33.0529 | −1.54446 | ||||||||
\(459\) | 7.51396 | 0.350722 | ||||||||
\(460\) | 73.9597 | 3.44839 | ||||||||
\(461\) | −7.17548 | −0.334196 | −0.167098 | − | 0.985940i | \(-0.553440\pi\) | ||||
−0.167098 | + | 0.985940i | \(0.553440\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.452670 | −0.0210373 | −0.0105187 | − | 0.999945i | \(-0.503348\pi\) | ||||
−0.0105187 | + | 0.999945i | \(0.503348\pi\) | |||||||
\(464\) | −27.6134 | −1.28192 | ||||||||
\(465\) | −9.47507 | −0.439396 | ||||||||
\(466\) | 17.6476 | 0.817509 | ||||||||
\(467\) | 9.68097 | 0.447982 | 0.223991 | − | 0.974591i | \(-0.428091\pi\) | ||||
0.223991 | + | 0.974591i | \(0.428091\pi\) | |||||||
\(468\) | 24.1623 | 1.11690 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −48.2067 | −2.22361 | ||||||||
\(471\) | 13.0668 | 0.602087 | ||||||||
\(472\) | 4.84396 | 0.222962 | ||||||||
\(473\) | −7.40530 | −0.340496 | ||||||||
\(474\) | 11.0279 | 0.506529 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.22982 | −0.193670 | ||||||||
\(478\) | −49.4395 | −2.26131 | ||||||||
\(479\) | −24.3635 | −1.11319 | −0.556597 | − | 0.830782i | \(-0.687893\pi\) | ||||
−0.556597 | + | 0.830782i | \(0.687893\pi\) | |||||||
\(480\) | −3.02569 | −0.138103 | ||||||||
\(481\) | 19.3983 | 0.884488 | ||||||||
\(482\) | 22.7375 | 1.03567 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.11491 | 0.187041 | ||||||||
\(485\) | −26.1909 | −1.18927 | ||||||||
\(486\) | −2.47283 | −0.112170 | ||||||||
\(487\) | −19.2702 | −0.873217 | −0.436609 | − | 0.899652i | \(-0.643821\pi\) | ||||
−0.436609 | + | 0.899652i | \(0.643821\pi\) | |||||||
\(488\) | 10.4596 | 0.473485 | ||||||||
\(489\) | 10.1017 | 0.456815 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.6421 | 1.33773 | 0.668864 | − | 0.743385i | \(-0.266781\pi\) | ||||
0.668864 | + | 0.743385i | \(0.266781\pi\) | |||||||
\(492\) | 21.7438 | 0.980285 | ||||||||
\(493\) | 44.1212 | 1.98712 | ||||||||
\(494\) | 34.2376 | 1.54042 | ||||||||
\(495\) | −2.58774 | −0.116310 | ||||||||
\(496\) | 17.2188 | 0.773149 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −26.4332 | −1.18450 | ||||||||
\(499\) | 29.3719 | 1.31487 | 0.657434 | − | 0.753512i | \(-0.271642\pi\) | ||||
0.657434 | + | 0.753512i | \(0.271642\pi\) | |||||||
\(500\) | −35.1777 | −1.57320 | ||||||||
\(501\) | −10.4860 | −0.468482 | ||||||||
\(502\) | 23.3058 | 1.04019 | ||||||||
\(503\) | −12.5947 | −0.561570 | −0.280785 | − | 0.959771i | \(-0.590595\pi\) | ||||
−0.280785 | + | 0.959771i | \(0.590595\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 34.6894 | 1.54366 | ||||||||
\(506\) | −17.1755 | −0.763543 | ||||||||
\(507\) | −21.4791 | −0.953919 | ||||||||
\(508\) | −42.0947 | −1.86765 | ||||||||
\(509\) | 15.2144 | 0.674365 | 0.337183 | − | 0.941439i | \(-0.390526\pi\) | ||||
0.337183 | + | 0.941439i | \(0.390526\pi\) | |||||||
\(510\) | 48.0823 | 2.12912 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −43.6894 | −1.93082 | ||||||||
\(513\) | −2.35793 | −0.104105 | ||||||||
\(514\) | 0.0480890 | 0.00212112 | ||||||||
\(515\) | 12.2034 | 0.537746 | ||||||||
\(516\) | −30.4721 | −1.34146 | ||||||||
\(517\) | 7.53341 | 0.331319 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.4985 | 0.636415 | ||||||||
\(520\) | 79.4667 | 3.48484 | ||||||||
\(521\) | −20.5180 | −0.898909 | −0.449454 | − | 0.893303i | \(-0.648382\pi\) | ||||
−0.449454 | + | 0.893303i | \(0.648382\pi\) | |||||||
\(522\) | −14.5202 | −0.635532 | ||||||||
\(523\) | 29.8844 | 1.30675 | 0.653376 | − | 0.757033i | \(-0.273352\pi\) | ||||
0.653376 | + | 0.757033i | \(0.273352\pi\) | |||||||
\(524\) | −16.4596 | −0.719042 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 69.2221 | 3.01823 | ||||||||
\(527\) | −27.5125 | −1.19846 | ||||||||
\(528\) | 4.70265 | 0.204657 | ||||||||
\(529\) | 25.2423 | 1.09749 | ||||||||
\(530\) | −27.0668 | −1.17571 | ||||||||
\(531\) | 0.926221 | 0.0401946 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −31.0279 | −1.34397 | ||||||||
\(534\) | 39.2966 | 1.70053 | ||||||||
\(535\) | 18.3051 | 0.791399 | ||||||||
\(536\) | −52.8300 | −2.28191 | ||||||||
\(537\) | −14.3510 | −0.619290 | ||||||||
\(538\) | −76.4582 | −3.29635 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −10.6483 | −0.458231 | ||||||||
\(541\) | 26.9582 | 1.15902 | 0.579511 | − | 0.814965i | \(-0.303244\pi\) | ||||
0.579511 | + | 0.814965i | \(0.303244\pi\) | |||||||
\(542\) | 55.2874 | 2.37480 | ||||||||
\(543\) | 9.66152 | 0.414616 | ||||||||
\(544\) | −8.78562 | −0.376680 | ||||||||
\(545\) | 48.7453 | 2.08802 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.0558 | 1.11407 | 0.557034 | − | 0.830490i | \(-0.311939\pi\) | ||||
0.557034 | + | 0.830490i | \(0.311939\pi\) | |||||||
\(548\) | −44.5933 | −1.90493 | ||||||||
\(549\) | 2.00000 | 0.0853579 | ||||||||
\(550\) | −4.19493 | −0.178872 | ||||||||
\(551\) | −13.8455 | −0.589837 | ||||||||
\(552\) | −36.3246 | −1.54608 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 61.2563 | 2.60253 | ||||||||
\(555\) | −8.54885 | −0.362878 | ||||||||
\(556\) | −1.89134 | −0.0802105 | ||||||||
\(557\) | 8.01945 | 0.339795 | 0.169897 | − | 0.985462i | \(-0.445656\pi\) | ||||
0.169897 | + | 0.985462i | \(0.445656\pi\) | |||||||
\(558\) | 9.05433 | 0.383300 | ||||||||
\(559\) | 43.4831 | 1.83914 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.51396 | −0.317240 | ||||||||
\(562\) | −2.95486 | −0.124643 | ||||||||
\(563\) | −21.9736 | −0.926077 | −0.463038 | − | 0.886338i | \(-0.653241\pi\) | ||||
−0.463038 | + | 0.886338i | \(0.653241\pi\) | |||||||
\(564\) | 30.9993 | 1.30531 | ||||||||
\(565\) | −23.3619 | −0.982844 | ||||||||
\(566\) | 38.5077 | 1.61860 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 23.3230 | 0.978613 | ||||||||
\(569\) | 10.0000 | 0.419222 | 0.209611 | − | 0.977785i | \(-0.432780\pi\) | ||||
0.209611 | + | 0.977785i | \(0.432780\pi\) | |||||||
\(570\) | −15.0885 | −0.631988 | ||||||||
\(571\) | 37.6740 | 1.57661 | 0.788304 | − | 0.615286i | \(-0.210959\pi\) | ||||
0.788304 | + | 0.615286i | \(0.210959\pi\) | |||||||
\(572\) | −24.1623 | −1.01028 | ||||||||
\(573\) | 9.55286 | 0.399076 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.7827 | 0.491371 | ||||||||
\(576\) | −6.51396 | −0.271415 | ||||||||
\(577\) | 7.80908 | 0.325096 | 0.162548 | − | 0.986701i | \(-0.448029\pi\) | ||||
0.162548 | + | 0.986701i | \(0.448029\pi\) | |||||||
\(578\) | 97.5771 | 4.05867 | ||||||||
\(579\) | 22.1212 | 0.919324 | ||||||||
\(580\) | −62.5257 | −2.59624 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 25.0279 | 1.03744 | ||||||||
\(583\) | 4.22982 | 0.175181 | ||||||||
\(584\) | 11.1296 | 0.460547 | ||||||||
\(585\) | 15.1949 | 0.628233 | ||||||||
\(586\) | 24.0947 | 0.995345 | ||||||||
\(587\) | 43.2633 | 1.78567 | 0.892833 | − | 0.450388i | \(-0.148714\pi\) | ||||
0.892833 | + | 0.450388i | \(0.148714\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.63360 | 0.355741 | ||||||||
\(590\) | 5.92694 | 0.244008 | ||||||||
\(591\) | 26.2423 | 1.07946 | ||||||||
\(592\) | 15.5356 | 0.638511 | ||||||||
\(593\) | 29.7438 | 1.22143 | 0.610715 | − | 0.791850i | \(-0.290882\pi\) | ||||
0.610715 | + | 0.791850i | \(0.290882\pi\) | |||||||
\(594\) | 2.47283 | 0.101462 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 45.4589 | 1.86207 | ||||||||
\(597\) | 1.05433 | 0.0431509 | ||||||||
\(598\) | 100.853 | 4.12417 | ||||||||
\(599\) | 11.5404 | 0.471527 | 0.235763 | − | 0.971810i | \(-0.424241\pi\) | ||||
0.235763 | + | 0.971810i | \(0.424241\pi\) | |||||||
\(600\) | −8.87189 | −0.362193 | ||||||||
\(601\) | −7.06129 | −0.288036 | −0.144018 | − | 0.989575i | \(-0.546002\pi\) | ||||
−0.144018 | + | 0.989575i | \(0.546002\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.1017 | −0.411373 | ||||||||
\(604\) | −66.3370 | −2.69922 | ||||||||
\(605\) | 2.58774 | 0.105207 | ||||||||
\(606\) | −33.1491 | −1.34659 | ||||||||
\(607\) | 17.3859 | 0.705670 | 0.352835 | − | 0.935686i | \(-0.385218\pi\) | ||||
0.352835 | + | 0.935686i | \(0.385218\pi\) | |||||||
\(608\) | 2.75698 | 0.111810 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.7981 | 0.518180 | ||||||||
\(611\) | −44.2353 | −1.78957 | ||||||||
\(612\) | −30.9193 | −1.24984 | ||||||||
\(613\) | 39.4611 | 1.59382 | 0.796910 | − | 0.604098i | \(-0.206466\pi\) | ||||
0.796910 | + | 0.604098i | \(0.206466\pi\) | |||||||
\(614\) | −15.7049 | −0.633798 | ||||||||
\(615\) | 13.6740 | 0.551389 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.40378 | −0.177290 | −0.0886448 | − | 0.996063i | \(-0.528254\pi\) | ||||
−0.0886448 | + | 0.996063i | \(0.528254\pi\) | |||||||
\(618\) | −11.6615 | −0.469095 | ||||||||
\(619\) | −16.4163 | −0.659825 | −0.329913 | − | 0.944011i | \(-0.607019\pi\) | ||||
−0.329913 | + | 0.944011i | \(0.607019\pi\) | |||||||
\(620\) | 38.9890 | 1.56584 | ||||||||
\(621\) | −6.94567 | −0.278720 | ||||||||
\(622\) | −19.7827 | −0.793213 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −27.6134 | −1.10542 | ||||||||
\(625\) | −30.6042 | −1.22417 | ||||||||
\(626\) | −41.9038 | −1.67481 | ||||||||
\(627\) | 2.35793 | 0.0941665 | ||||||||
\(628\) | −53.7688 | −2.14561 | ||||||||
\(629\) | −24.8231 | −0.989761 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.4596 | 1.76991 | 0.884955 | − | 0.465677i | \(-0.154189\pi\) | ||||
0.884955 | + | 0.465677i | \(0.154189\pi\) | |||||||
\(632\) | −23.3230 | −0.927741 | ||||||||
\(633\) | 8.71585 | 0.346424 | ||||||||
\(634\) | 49.4876 | 1.96540 | ||||||||
\(635\) | −26.4721 | −1.05051 | ||||||||
\(636\) | 17.4053 | 0.690165 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 14.5202 | 0.574860 | ||||||||
\(639\) | 4.45963 | 0.176420 | ||||||||
\(640\) | −47.7346 | −1.88688 | ||||||||
\(641\) | 10.5419 | 0.416380 | 0.208190 | − | 0.978088i | \(-0.433243\pi\) | ||||
0.208190 | + | 0.978088i | \(0.433243\pi\) | |||||||
\(642\) | −17.4923 | −0.690365 | ||||||||
\(643\) | 23.4053 | 0.923015 | 0.461507 | − | 0.887136i | \(-0.347309\pi\) | ||||
0.461507 | + | 0.887136i | \(0.347309\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.1630 | −0.754542 | ||||||||
\(646\) | −43.8121 | −1.72376 | ||||||||
\(647\) | −11.4945 | −0.451896 | −0.225948 | − | 0.974139i | \(-0.572548\pi\) | ||||
−0.225948 | + | 0.974139i | \(0.572548\pi\) | |||||||
\(648\) | 5.22982 | 0.205447 | ||||||||
\(649\) | −0.926221 | −0.0363574 | ||||||||
\(650\) | 24.6322 | 0.966153 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −41.5676 | −1.62791 | ||||||||
\(653\) | 19.8774 | 0.777863 | 0.388932 | − | 0.921267i | \(-0.372844\pi\) | ||||
0.388932 | + | 0.921267i | \(0.372844\pi\) | |||||||
\(654\) | −46.5808 | −1.82145 | ||||||||
\(655\) | −10.3510 | −0.404446 | ||||||||
\(656\) | −24.8495 | −0.970210 | ||||||||
\(657\) | 2.12811 | 0.0830255 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.0738 | 0.587191 | 0.293596 | − | 0.955930i | \(-0.405148\pi\) | ||||
0.293596 | + | 0.955930i | \(0.405148\pi\) | |||||||
\(660\) | 10.6483 | 0.414485 | ||||||||
\(661\) | 4.74226 | 0.184453 | 0.0922263 | − | 0.995738i | \(-0.470602\pi\) | ||||
0.0922263 | + | 0.995738i | \(0.470602\pi\) | |||||||
\(662\) | 18.6461 | 0.724701 | ||||||||
\(663\) | 44.1212 | 1.71352 | ||||||||
\(664\) | 55.9038 | 2.16949 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.16924 | 0.316552 | ||||||||
\(667\) | −40.7842 | −1.57917 | ||||||||
\(668\) | 43.1491 | 1.66949 | ||||||||
\(669\) | −23.7438 | −0.917987 | ||||||||
\(670\) | −64.6414 | −2.49731 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.87885 | 0.380802 | 0.190401 | − | 0.981706i | \(-0.439021\pi\) | ||||
0.190401 | + | 0.981706i | \(0.439021\pi\) | |||||||
\(674\) | −31.3789 | −1.20867 | ||||||||
\(675\) | −1.69641 | −0.0652947 | ||||||||
\(676\) | 88.3844 | 3.39940 | ||||||||
\(677\) | 29.0279 | 1.11563 | 0.557817 | − | 0.829964i | \(-0.311639\pi\) | ||||
0.557817 | + | 0.829964i | \(0.311639\pi\) | |||||||
\(678\) | 22.3246 | 0.857369 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −101.690 | −3.89962 | ||||||||
\(681\) | −13.1755 | −0.504886 | ||||||||
\(682\) | −9.05433 | −0.346708 | ||||||||
\(683\) | −37.9597 | −1.45249 | −0.726243 | − | 0.687438i | \(-0.758735\pi\) | ||||
−0.726243 | + | 0.687438i | \(0.758735\pi\) | |||||||
\(684\) | 9.70265 | 0.370990 | ||||||||
\(685\) | −28.0434 | −1.07148 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.3664 | 0.509960 | ||||||||
\(688\) | 34.8245 | 1.32767 | ||||||||
\(689\) | −24.8370 | −0.946214 | ||||||||
\(690\) | −44.4457 | −1.69202 | ||||||||
\(691\) | 15.5264 | 0.590654 | 0.295327 | − | 0.955396i | \(-0.404571\pi\) | ||||
0.295327 | + | 0.955396i | \(0.404571\pi\) | |||||||
\(692\) | −59.6601 | −2.26794 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.81060 | 0.106689 | ||||||||
\(695\) | −1.18940 | −0.0451167 | ||||||||
\(696\) | 30.7089 | 1.16402 | ||||||||
\(697\) | 39.7049 | 1.50393 | ||||||||
\(698\) | 36.5761 | 1.38442 | ||||||||
\(699\) | −7.13659 | −0.269931 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.4317 | −1.03608 | −0.518041 | − | 0.855356i | \(-0.673338\pi\) | ||||
−0.518041 | + | 0.855356i | \(0.673338\pi\) | |||||||
\(702\) | −14.5202 | −0.548030 | ||||||||
\(703\) | 7.78963 | 0.293792 | ||||||||
\(704\) | 6.51396 | 0.245504 | ||||||||
\(705\) | 19.4945 | 0.734206 | ||||||||
\(706\) | 18.5980 | 0.699945 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.81131 | −0.143238 | ||||||||
\(709\) | −44.5180 | −1.67191 | −0.835954 | − | 0.548800i | \(-0.815085\pi\) | ||||
−0.835954 | + | 0.548800i | \(0.815085\pi\) | |||||||
\(710\) | 28.5374 | 1.07099 | ||||||||
\(711\) | −4.45963 | −0.167249 | ||||||||
\(712\) | −83.1087 | −3.11463 | ||||||||
\(713\) | 25.4317 | 0.952425 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.1949 | −0.568258 | ||||||||
\(716\) | 59.0529 | 2.20691 | ||||||||
\(717\) | 19.9930 | 0.746654 | ||||||||
\(718\) | −43.5125 | −1.62387 | ||||||||
\(719\) | −17.3859 | −0.648383 | −0.324191 | − | 0.945992i | \(-0.605092\pi\) | ||||
−0.324191 | + | 0.945992i | \(0.605092\pi\) | |||||||
\(720\) | 12.1692 | 0.453521 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −33.2353 | −1.23689 | ||||||||
\(723\) | −9.19493 | −0.341963 | ||||||||
\(724\) | −39.7563 | −1.47753 | ||||||||
\(725\) | −9.96111 | −0.369946 | ||||||||
\(726\) | −2.47283 | −0.0917755 | ||||||||
\(727\) | 18.6506 | 0.691711 | 0.345855 | − | 0.938288i | \(-0.387589\pi\) | ||||
0.345855 | + | 0.938288i | \(0.387589\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 13.6179 | 0.504021 | ||||||||
\(731\) | −55.6431 | −2.05804 | ||||||||
\(732\) | −8.22982 | −0.304183 | ||||||||
\(733\) | −16.3510 | −0.603937 | −0.301968 | − | 0.953318i | \(-0.597644\pi\) | ||||
−0.301968 | + | 0.953318i | \(0.597644\pi\) | |||||||
\(734\) | −35.3914 | −1.30632 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.12115 | 0.299350 | ||||||||
\(737\) | 10.1017 | 0.372101 | ||||||||
\(738\) | −13.0668 | −0.480996 | ||||||||
\(739\) | −32.8370 | −1.20793 | −0.603964 | − | 0.797011i | \(-0.706413\pi\) | ||||
−0.603964 | + | 0.797011i | \(0.706413\pi\) | |||||||
\(740\) | 35.1777 | 1.29316 | ||||||||
\(741\) | −13.8455 | −0.508626 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.9123 | 0.767198 | 0.383599 | − | 0.923500i | \(-0.374685\pi\) | ||||
0.383599 | + | 0.923500i | \(0.374685\pi\) | |||||||
\(744\) | −19.1491 | −0.702039 | ||||||||
\(745\) | 28.5877 | 1.04737 | ||||||||
\(746\) | −40.6366 | −1.48781 | ||||||||
\(747\) | 10.6894 | 0.391106 | ||||||||
\(748\) | 30.9193 | 1.13052 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 21.1399 | 0.771919 | ||||||||
\(751\) | −39.2633 | −1.43274 | −0.716368 | − | 0.697722i | \(-0.754197\pi\) | ||||
−0.716368 | + | 0.697722i | \(0.754197\pi\) | |||||||
\(752\) | −35.4270 | −1.29189 | ||||||||
\(753\) | −9.42474 | −0.343457 | ||||||||
\(754\) | −85.2610 | −3.10502 | ||||||||
\(755\) | −41.7174 | −1.51825 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.3454 | −0.376011 | −0.188006 | − | 0.982168i | \(-0.560202\pi\) | ||||
−0.188006 | + | 0.982168i | \(0.560202\pi\) | |||||||
\(758\) | 48.3029 | 1.75444 | ||||||||
\(759\) | 6.94567 | 0.252112 | ||||||||
\(760\) | 31.9108 | 1.15753 | ||||||||
\(761\) | −30.9582 | −1.12223 | −0.561116 | − | 0.827737i | \(-0.689628\pi\) | ||||
−0.561116 | + | 0.827737i | \(0.689628\pi\) | |||||||
\(762\) | 25.2966 | 0.916400 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −39.3091 | −1.42215 | ||||||||
\(765\) | −19.4442 | −0.703006 | ||||||||
\(766\) | −5.81355 | −0.210052 | ||||||||
\(767\) | 5.43867 | 0.196379 | ||||||||
\(768\) | 32.5870 | 1.17588 | ||||||||
\(769\) | 28.8998 | 1.04215 | 0.521077 | − | 0.853510i | \(-0.325530\pi\) | ||||
0.521077 | + | 0.853510i | \(0.325530\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.0194469 | −0.000700364 0 | ||||||||
\(772\) | −91.0265 | −3.27612 | ||||||||
\(773\) | 26.7523 | 0.962212 | 0.481106 | − | 0.876663i | \(-0.340235\pi\) | ||||
0.481106 | + | 0.876663i | \(0.340235\pi\) | |||||||
\(774\) | 18.3121 | 0.658214 | ||||||||
\(775\) | 6.21142 | 0.223121 | ||||||||
\(776\) | −52.9317 | −1.90014 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.31207 | −0.154595 | ||||||||
\(779\) | −12.4596 | −0.446413 | ||||||||
\(780\) | −62.5257 | −2.23878 | ||||||||
\(781\) | −4.45963 | −0.159578 | ||||||||
\(782\) | −129.056 | −4.61503 | ||||||||
\(783\) | 5.87189 | 0.209844 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −33.8135 | −1.20686 | ||||||||
\(786\) | 9.89134 | 0.352812 | ||||||||
\(787\) | −22.1406 | −0.789227 | −0.394614 | − | 0.918847i | \(-0.629122\pi\) | ||||
−0.394614 | + | 0.918847i | \(0.629122\pi\) | |||||||
\(788\) | −107.985 | −3.84679 | ||||||||
\(789\) | −27.9930 | −0.996579 | ||||||||
\(790\) | −28.5374 | −1.01532 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.22982 | −0.185833 | ||||||||
\(793\) | 11.7438 | 0.417034 | ||||||||
\(794\) | −16.1770 | −0.574100 | ||||||||
\(795\) | 10.9457 | 0.388203 | ||||||||
\(796\) | −4.33848 | −0.153773 | ||||||||
\(797\) | −8.18396 | −0.289891 | −0.144945 | − | 0.989440i | \(-0.546301\pi\) | ||||
−0.144945 | + | 0.989440i | \(0.546301\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 56.6058 | 2.00257 | ||||||||
\(800\) | 1.98351 | 0.0701275 | ||||||||
\(801\) | −15.8913 | −0.561493 | ||||||||
\(802\) | 14.0000 | 0.494357 | ||||||||
\(803\) | −2.12811 | −0.0750994 | ||||||||
\(804\) | 41.5676 | 1.46598 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 53.1660 | 1.87269 | ||||||||
\(807\) | 30.9193 | 1.08841 | ||||||||
\(808\) | 70.1072 | 2.46636 | ||||||||
\(809\) | 17.6685 | 0.621191 | 0.310595 | − | 0.950542i | \(-0.399472\pi\) | ||||
0.310595 | + | 0.950542i | \(0.399472\pi\) | |||||||
\(810\) | 6.39905 | 0.224840 | ||||||||
\(811\) | 43.0210 | 1.51067 | 0.755335 | − | 0.655339i | \(-0.227474\pi\) | ||||
0.755335 | + | 0.655339i | \(0.227474\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.3579 | −0.784127 | ||||||||
\(814\) | −8.16924 | −0.286332 | ||||||||
\(815\) | −26.1406 | −0.915665 | ||||||||
\(816\) | 35.3355 | 1.23699 | ||||||||
\(817\) | 17.4611 | 0.610888 | ||||||||
\(818\) | 13.5698 | 0.474457 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −56.2673 | −1.96494 | ||||||||
\(821\) | 18.0364 | 0.629475 | 0.314737 | − | 0.949179i | \(-0.398084\pi\) | ||||
0.314737 | + | 0.949179i | \(0.398084\pi\) | |||||||
\(822\) | 26.7981 | 0.934691 | ||||||||
\(823\) | −8.21037 | −0.286195 | −0.143098 | − | 0.989709i | \(-0.545706\pi\) | ||||
−0.143098 | + | 0.989709i | \(0.545706\pi\) | |||||||
\(824\) | 24.6630 | 0.859178 | ||||||||
\(825\) | 1.69641 | 0.0590613 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.83148 | 0.237554 | 0.118777 | − | 0.992921i | \(-0.462103\pi\) | ||||
0.118777 | + | 0.992921i | \(0.462103\pi\) | |||||||
\(828\) | 28.5808 | 0.993251 | ||||||||
\(829\) | 25.7438 | 0.894118 | 0.447059 | − | 0.894504i | \(-0.352471\pi\) | ||||
0.447059 | + | 0.894504i | \(0.352471\pi\) | |||||||
\(830\) | 68.4023 | 2.37428 | ||||||||
\(831\) | −24.7717 | −0.859321 | ||||||||
\(832\) | −38.2493 | −1.32605 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.13659 | 0.0393569 | ||||||||
\(835\) | 27.1352 | 0.939051 | ||||||||
\(836\) | −9.70265 | −0.335573 | ||||||||
\(837\) | −3.66152 | −0.126561 | ||||||||
\(838\) | −20.3991 | −0.704674 | ||||||||
\(839\) | 30.6002 | 1.05644 | 0.528219 | − | 0.849108i | \(-0.322860\pi\) | ||||
0.528219 | + | 0.849108i | \(0.322860\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.47908 | 0.188934 | ||||||||
\(842\) | 79.7779 | 2.74933 | ||||||||
\(843\) | 1.19493 | 0.0411556 | ||||||||
\(844\) | −35.8649 | −1.23452 | ||||||||
\(845\) | 55.5823 | 1.91209 | ||||||||
\(846\) | −18.6289 | −0.640474 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −19.8913 | −0.683071 | ||||||||
\(849\) | −15.5723 | −0.534440 | ||||||||
\(850\) | −31.5205 | −1.08115 | ||||||||
\(851\) | 22.9457 | 0.786567 | ||||||||
\(852\) | −18.3510 | −0.628694 | ||||||||
\(853\) | 30.4596 | 1.04292 | 0.521459 | − | 0.853276i | \(-0.325388\pi\) | ||||
0.521459 | + | 0.853276i | \(0.325388\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.10170 | 0.208674 | ||||||||
\(856\) | 36.9946 | 1.26445 | ||||||||
\(857\) | 41.2702 | 1.40976 | 0.704882 | − | 0.709325i | \(-0.251000\pi\) | ||||
0.704882 | + | 0.709325i | \(0.251000\pi\) | |||||||
\(858\) | 14.5202 | 0.495712 | ||||||||
\(859\) | 28.9193 | 0.986712 | 0.493356 | − | 0.869827i | \(-0.335770\pi\) | ||||
0.493356 | + | 0.869827i | \(0.335770\pi\) | |||||||
\(860\) | 78.8540 | 2.68890 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −57.5606 | −1.96052 | ||||||||
\(863\) | 37.0015 | 1.25955 | 0.629773 | − | 0.776779i | \(-0.283148\pi\) | ||||
0.629773 | + | 0.776779i | \(0.283148\pi\) | |||||||
\(864\) | −1.16924 | −0.0397783 | ||||||||
\(865\) | −37.5184 | −1.27566 | ||||||||
\(866\) | 39.3928 | 1.33862 | ||||||||
\(867\) | −39.4596 | −1.34012 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.45963 | 0.151283 | ||||||||
\(870\) | 37.5745 | 1.27390 | ||||||||
\(871\) | −59.3161 | −2.00985 | ||||||||
\(872\) | 98.5140 | 3.33611 | ||||||||
\(873\) | −10.1212 | −0.342549 | ||||||||
\(874\) | 40.4985 | 1.36988 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.75698 | −0.295871 | ||||||||
\(877\) | −6.12562 | −0.206847 | −0.103424 | − | 0.994637i | \(-0.532980\pi\) | ||||
−0.103424 | + | 0.994637i | \(0.532980\pi\) | |||||||
\(878\) | −56.5202 | −1.90746 | ||||||||
\(879\) | −9.74378 | −0.328649 | ||||||||
\(880\) | −12.1692 | −0.410225 | ||||||||
\(881\) | −25.4123 | −0.856161 | −0.428080 | − | 0.903741i | \(-0.640810\pi\) | ||||
−0.428080 | + | 0.903741i | \(0.640810\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.0040 | −0.572230 | −0.286115 | − | 0.958195i | \(-0.592364\pi\) | ||||
−0.286115 | + | 0.958195i | \(0.592364\pi\) | |||||||
\(884\) | −181.554 | −6.10634 | ||||||||
\(885\) | −2.39682 | −0.0805682 | ||||||||
\(886\) | 53.4039 | 1.79414 | ||||||||
\(887\) | −35.2269 | −1.18280 | −0.591401 | − | 0.806378i | \(-0.701425\pi\) | ||||
−0.591401 | + | 0.806378i | \(0.701425\pi\) | |||||||
\(888\) | −17.2772 | −0.579784 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −101.690 | −3.40864 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 97.7034 | 3.27135 | ||||||||
\(893\) | −17.7632 | −0.594424 | ||||||||
\(894\) | −27.3183 | −0.913661 | ||||||||
\(895\) | 37.1366 | 1.24134 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −40.7842 | −1.36174 | ||||||||
\(898\) | 46.1506 | 1.54007 | ||||||||
\(899\) | −21.5000 | −0.717067 | ||||||||
\(900\) | 6.98055 | 0.232685 | ||||||||
\(901\) | 31.7827 | 1.05883 | ||||||||
\(902\) | 13.0668 | 0.435077 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −47.2144 | −1.57033 | ||||||||
\(905\) | −25.0015 | −0.831079 | ||||||||
\(906\) | 39.8649 | 1.32442 | ||||||||
\(907\) | −9.72682 | −0.322974 | −0.161487 | − | 0.986875i | \(-0.551629\pi\) | ||||
−0.161487 | + | 0.986875i | \(0.551629\pi\) | |||||||
\(908\) | 54.2159 | 1.79922 | ||||||||
\(909\) | 13.4053 | 0.444626 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.7717 | −1.41709 | −0.708545 | − | 0.705666i | \(-0.750648\pi\) | ||||
−0.708545 | + | 0.705666i | \(0.750648\pi\) | |||||||
\(912\) | −11.0885 | −0.367177 | ||||||||
\(913\) | −10.6894 | −0.353769 | ||||||||
\(914\) | 90.1895 | 2.98320 | ||||||||
\(915\) | −5.17548 | −0.171096 | ||||||||
\(916\) | −55.0015 | −1.81730 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 18.5808 | 0.613257 | ||||||||
\(919\) | 6.26871 | 0.206786 | 0.103393 | − | 0.994641i | \(-0.467030\pi\) | ||||
0.103393 | + | 0.994641i | \(0.467030\pi\) | |||||||
\(920\) | 93.9986 | 3.09904 | ||||||||
\(921\) | 6.35097 | 0.209271 | ||||||||
\(922\) | −17.7438 | −0.584360 | ||||||||
\(923\) | 26.1865 | 0.861938 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.60424 | 0.184266 | ||||||||
\(926\) | −1.11938 | −0.0367850 | ||||||||
\(927\) | 4.71585 | 0.154889 | ||||||||
\(928\) | −6.86565 | −0.225376 | ||||||||
\(929\) | −20.0194 | −0.656817 | −0.328408 | − | 0.944536i | \(-0.606512\pi\) | ||||
−0.328408 | + | 0.944536i | \(0.606512\pi\) | |||||||
\(930\) | −23.4303 | −0.768309 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 29.3664 | 0.961929 | ||||||||
\(933\) | 8.00000 | 0.261908 | ||||||||
\(934\) | 23.9394 | 0.783322 | ||||||||
\(935\) | 19.4442 | 0.635893 | ||||||||
\(936\) | 30.7089 | 1.00375 | ||||||||
\(937\) | 11.2144 | 0.366358 | 0.183179 | − | 0.983080i | \(-0.441361\pi\) | ||||
0.183179 | + | 0.983080i | \(0.441361\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.9457 | 0.553001 | ||||||||
\(940\) | −80.2181 | −2.61643 | ||||||||
\(941\) | −31.3400 | −1.02165 | −0.510827 | − | 0.859683i | \(-0.670661\pi\) | ||||
−0.510827 | + | 0.859683i | \(0.670661\pi\) | |||||||
\(942\) | 32.3121 | 1.05278 | ||||||||
\(943\) | −36.7019 | −1.19518 | ||||||||
\(944\) | 4.35569 | 0.141766 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18.3121 | −0.595377 | ||||||||
\(947\) | −23.2841 | −0.756633 | −0.378317 | − | 0.925676i | \(-0.623497\pi\) | ||||
−0.378317 | + | 0.925676i | \(0.623497\pi\) | |||||||
\(948\) | 18.3510 | 0.596012 | ||||||||
\(949\) | 12.4960 | 0.405638 | ||||||||
\(950\) | 9.89134 | 0.320917 | ||||||||
\(951\) | −20.0125 | −0.648949 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.8300 | 0.869110 | 0.434555 | − | 0.900645i | \(-0.356906\pi\) | ||||
0.434555 | + | 0.900645i | \(0.356906\pi\) | |||||||
\(954\) | −10.4596 | −0.338643 | ||||||||
\(955\) | −24.7203 | −0.799931 | ||||||||
\(956\) | −82.2695 | −2.66079 | ||||||||
\(957\) | −5.87189 | −0.189811 | ||||||||
\(958\) | −60.2468 | −1.94648 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 16.8565 | 0.544040 | ||||||||
\(961\) | −17.5933 | −0.567525 | ||||||||
\(962\) | 47.9689 | 1.54658 | ||||||||
\(963\) | 7.07378 | 0.227949 | ||||||||
\(964\) | 37.8363 | 1.21862 | ||||||||
\(965\) | −57.2438 | −1.84274 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.2034 | 1.16422 | 0.582112 | − | 0.813109i | \(-0.302227\pi\) | ||||
0.582112 | + | 0.813109i | \(0.302227\pi\) | |||||||
\(968\) | 5.22982 | 0.168093 | ||||||||
\(969\) | 17.7174 | 0.569164 | ||||||||
\(970\) | −64.7658 | −2.07950 | ||||||||
\(971\) | −6.06281 | −0.194565 | −0.0972824 | − | 0.995257i | \(-0.531015\pi\) | ||||
−0.0972824 | + | 0.995257i | \(0.531015\pi\) | |||||||
\(972\) | −4.11491 | −0.131986 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −47.6521 | −1.52687 | ||||||||
\(975\) | −9.96111 | −0.319011 | ||||||||
\(976\) | 9.40530 | 0.301056 | ||||||||
\(977\) | −4.28263 | −0.137013 | −0.0685067 | − | 0.997651i | \(-0.521823\pi\) | ||||
−0.0685067 | + | 0.997651i | \(0.521823\pi\) | |||||||
\(978\) | 24.9798 | 0.798767 | ||||||||
\(979\) | 15.8913 | 0.507889 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.8370 | 0.601419 | ||||||||
\(982\) | 73.2999 | 2.33909 | ||||||||
\(983\) | 17.1894 | 0.548257 | 0.274128 | − | 0.961693i | \(-0.411611\pi\) | ||||
0.274128 | + | 0.961693i | \(0.411611\pi\) | |||||||
\(984\) | 27.6351 | 0.880975 | ||||||||
\(985\) | −67.9083 | −2.16374 | ||||||||
\(986\) | 109.104 | 3.47459 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 56.9729 | 1.81255 | ||||||||
\(989\) | 51.4347 | 1.63553 | ||||||||
\(990\) | −6.39905 | −0.203375 | ||||||||
\(991\) | 35.4945 | 1.12752 | 0.563760 | − | 0.825939i | \(-0.309354\pi\) | ||||
0.563760 | + | 0.825939i | \(0.309354\pi\) | |||||||
\(992\) | 4.28120 | 0.135928 | ||||||||
\(993\) | −7.54037 | −0.239286 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.72834 | −0.0864942 | ||||||||
\(996\) | −43.9861 | −1.39375 | ||||||||
\(997\) | −30.4068 | −0.962993 | −0.481497 | − | 0.876448i | \(-0.659907\pi\) | ||||
−0.481497 | + | 0.876448i | \(0.659907\pi\) | |||||||
\(998\) | 72.6319 | 2.29912 | ||||||||
\(999\) | −3.30359 | −0.104521 |
(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 | 1617.2.a.t.1.3 | 3 | ||
3.2 | odd | 2 | 4851.2.a.bi.1.1 | 3 | |||
7.6 | odd | 2 | 231.2.a.e.1.3 | ✓ | 3 | ||
21.20 | even | 2 | 693.2.a.l.1.1 | 3 | |||
28.27 | even | 2 | 3696.2.a.bo.1.1 | 3 | |||
35.34 | odd | 2 | 5775.2.a.bp.1.1 | 3 | |||
77.76 | even | 2 | 2541.2.a.bg.1.1 | 3 | |||
231.230 | odd | 2 | 7623.2.a.cd.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.a.e.1.3 | ✓ | 3 | 7.6 | odd | 2 | ||
693.2.a.l.1.1 | 3 | 21.20 | even | 2 | |||
1617.2.a.t.1.3 | 3 | 1.1 | even | 1 | trivial | ||
2541.2.a.bg.1.1 | 3 | 77.76 | even | 2 | |||
3696.2.a.bo.1.1 | 3 | 28.27 | even | 2 | |||
4851.2.a.bi.1.1 | 3 | 3.2 | odd | 2 | |||
5775.2.a.bp.1.1 | 3 | 35.34 | odd | 2 | |||
7623.2.a.cd.1.3 | 3 | 231.230 | odd | 2 |