Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2366,2,Mod(1,2366)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2366, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2366.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2366 = 2 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2366.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: | \(18.8926051182\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2366.1 |
$q$-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 | ||||||||
\(3\) | 0.554958 | 0.320405 | 0.160203 | − | 0.987084i | \(-0.448785\pi\) | ||||
0.160203 | + | 0.987084i | \(0.448785\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.35690 | 0.606822 | 0.303411 | − | 0.952860i | \(-0.401874\pi\) | ||||
0.303411 | + | 0.952860i | \(0.401874\pi\) | |||||||
\(6\) | 0.554958 | 0.226561 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.69202 | −0.897340 | ||||||||
\(10\) | 1.35690 | 0.429088 | ||||||||
\(11\) | 1.80194 | 0.543305 | 0.271652 | − | 0.962395i | \(-0.412430\pi\) | ||||
0.271652 | + | 0.962395i | \(0.412430\pi\) | |||||||
\(12\) | 0.554958 | 0.160203 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0.753020 | 0.194429 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.29590 | 1.28444 | 0.642222 | − | 0.766519i | \(-0.278013\pi\) | ||||
0.642222 | + | 0.766519i | \(0.278013\pi\) | |||||||
\(18\) | −2.69202 | −0.634516 | ||||||||
\(19\) | 1.95108 | 0.447609 | 0.223805 | − | 0.974634i | \(-0.428152\pi\) | ||||
0.223805 | + | 0.974634i | \(0.428152\pi\) | |||||||
\(20\) | 1.35690 | 0.303411 | ||||||||
\(21\) | −0.554958 | −0.121102 | ||||||||
\(22\) | 1.80194 | 0.384174 | ||||||||
\(23\) | 4.85086 | 1.01147 | 0.505737 | − | 0.862688i | \(-0.331221\pi\) | ||||
0.505737 | + | 0.862688i | \(0.331221\pi\) | |||||||
\(24\) | 0.554958 | 0.113280 | ||||||||
\(25\) | −3.15883 | −0.631767 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.15883 | −0.607918 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 5.96077 | 1.10689 | 0.553444 | − | 0.832887i | \(-0.313313\pi\) | ||||
0.553444 | + | 0.832887i | \(0.313313\pi\) | |||||||
\(30\) | 0.753020 | 0.137482 | ||||||||
\(31\) | −3.63102 | −0.652151 | −0.326075 | − | 0.945344i | \(-0.605726\pi\) | ||||
−0.326075 | + | 0.945344i | \(0.605726\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 5.29590 | 0.908239 | ||||||||
\(35\) | −1.35690 | −0.229357 | ||||||||
\(36\) | −2.69202 | −0.448670 | ||||||||
\(37\) | 7.75302 | 1.27459 | 0.637294 | − | 0.770620i | \(-0.280054\pi\) | ||||
0.637294 | + | 0.770620i | \(0.280054\pi\) | |||||||
\(38\) | 1.95108 | 0.316507 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.35690 | 0.214544 | ||||||||
\(41\) | 0.0392287 | 0.00612649 | 0.00306324 | − | 0.999995i | \(-0.499025\pi\) | ||||
0.00306324 | + | 0.999995i | \(0.499025\pi\) | |||||||
\(42\) | −0.554958 | −0.0856319 | ||||||||
\(43\) | 2.26875 | 0.345981 | 0.172991 | − | 0.984923i | \(-0.444657\pi\) | ||||
0.172991 | + | 0.984923i | \(0.444657\pi\) | |||||||
\(44\) | 1.80194 | 0.271652 | ||||||||
\(45\) | −3.65279 | −0.544526 | ||||||||
\(46\) | 4.85086 | 0.715220 | ||||||||
\(47\) | 10.5700 | 1.54180 | 0.770898 | − | 0.636958i | \(-0.219808\pi\) | ||||
0.770898 | + | 0.636958i | \(0.219808\pi\) | |||||||
\(48\) | 0.554958 | 0.0801013 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.15883 | −0.446727 | ||||||||
\(51\) | 2.93900 | 0.411542 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.66487 | −0.503409 | −0.251705 | − | 0.967804i | \(-0.580991\pi\) | ||||
−0.251705 | + | 0.967804i | \(0.580991\pi\) | |||||||
\(54\) | −3.15883 | −0.429863 | ||||||||
\(55\) | 2.44504 | 0.329689 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 1.08277 | 0.143416 | ||||||||
\(58\) | 5.96077 | 0.782688 | ||||||||
\(59\) | 4.07606 | 0.530658 | 0.265329 | − | 0.964158i | \(-0.414519\pi\) | ||||
0.265329 | + | 0.964158i | \(0.414519\pi\) | |||||||
\(60\) | 0.753020 | 0.0972145 | ||||||||
\(61\) | −11.5036 | −1.47289 | −0.736446 | − | 0.676497i | \(-0.763497\pi\) | ||||
−0.736446 | + | 0.676497i | \(0.763497\pi\) | |||||||
\(62\) | −3.63102 | −0.461140 | ||||||||
\(63\) | 2.69202 | 0.339163 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | −2.22521 | −0.271853 | −0.135926 | − | 0.990719i | \(-0.543401\pi\) | ||||
−0.135926 | + | 0.990719i | \(0.543401\pi\) | |||||||
\(68\) | 5.29590 | 0.642222 | ||||||||
\(69\) | 2.69202 | 0.324081 | ||||||||
\(70\) | −1.35690 | −0.162180 | ||||||||
\(71\) | 7.78986 | 0.924486 | 0.462243 | − | 0.886753i | \(-0.347045\pi\) | ||||
0.462243 | + | 0.886753i | \(0.347045\pi\) | |||||||
\(72\) | −2.69202 | −0.317258 | ||||||||
\(73\) | 14.1032 | 1.65066 | 0.825328 | − | 0.564654i | \(-0.190990\pi\) | ||||
0.825328 | + | 0.564654i | \(0.190990\pi\) | |||||||
\(74\) | 7.75302 | 0.901270 | ||||||||
\(75\) | −1.75302 | −0.202421 | ||||||||
\(76\) | 1.95108 | 0.223805 | ||||||||
\(77\) | −1.80194 | −0.205350 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0804 | −1.35915 | −0.679574 | − | 0.733607i | \(-0.737835\pi\) | ||||
−0.679574 | + | 0.733607i | \(0.737835\pi\) | |||||||
\(80\) | 1.35690 | 0.151706 | ||||||||
\(81\) | 6.32304 | 0.702560 | ||||||||
\(82\) | 0.0392287 | 0.00433208 | ||||||||
\(83\) | 2.85086 | 0.312922 | 0.156461 | − | 0.987684i | \(-0.449991\pi\) | ||||
0.156461 | + | 0.987684i | \(0.449991\pi\) | |||||||
\(84\) | −0.554958 | −0.0605509 | ||||||||
\(85\) | 7.18598 | 0.779429 | ||||||||
\(86\) | 2.26875 | 0.244646 | ||||||||
\(87\) | 3.30798 | 0.354653 | ||||||||
\(88\) | 1.80194 | 0.192087 | ||||||||
\(89\) | −6.61894 | −0.701606 | −0.350803 | − | 0.936449i | \(-0.614091\pi\) | ||||
−0.350803 | + | 0.936449i | \(0.614091\pi\) | |||||||
\(90\) | −3.65279 | −0.385038 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.85086 | 0.505737 | ||||||||
\(93\) | −2.01507 | −0.208953 | ||||||||
\(94\) | 10.5700 | 1.09021 | ||||||||
\(95\) | 2.64742 | 0.271619 | ||||||||
\(96\) | 0.554958 | 0.0566402 | ||||||||
\(97\) | −3.64310 | −0.369901 | −0.184951 | − | 0.982748i | \(-0.559213\pi\) | ||||
−0.184951 | + | 0.982748i | \(0.559213\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −4.85086 | −0.487529 | ||||||||
\(100\) | −3.15883 | −0.315883 | ||||||||
\(101\) | 7.85086 | 0.781189 | 0.390595 | − | 0.920563i | \(-0.372269\pi\) | ||||
0.390595 | + | 0.920563i | \(0.372269\pi\) | |||||||
\(102\) | 2.93900 | 0.291004 | ||||||||
\(103\) | −17.0804 | −1.68298 | −0.841490 | − | 0.540273i | \(-0.818321\pi\) | ||||
−0.841490 | + | 0.540273i | \(0.818321\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.753020 | −0.0734873 | ||||||||
\(106\) | −3.66487 | −0.355964 | ||||||||
\(107\) | 13.8562 | 1.33953 | 0.669766 | − | 0.742572i | \(-0.266394\pi\) | ||||
0.669766 | + | 0.742572i | \(0.266394\pi\) | |||||||
\(108\) | −3.15883 | −0.303959 | ||||||||
\(109\) | −2.18060 | −0.208864 | −0.104432 | − | 0.994532i | \(-0.533302\pi\) | ||||
−0.104432 | + | 0.994532i | \(0.533302\pi\) | |||||||
\(110\) | 2.44504 | 0.233126 | ||||||||
\(111\) | 4.30260 | 0.408385 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −17.5090 | −1.64711 | −0.823555 | − | 0.567236i | \(-0.808013\pi\) | ||||
−0.823555 | + | 0.567236i | \(0.808013\pi\) | |||||||
\(114\) | 1.08277 | 0.101411 | ||||||||
\(115\) | 6.58211 | 0.613784 | ||||||||
\(116\) | 5.96077 | 0.553444 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.07606 | 0.375232 | ||||||||
\(119\) | −5.29590 | −0.485474 | ||||||||
\(120\) | 0.753020 | 0.0687410 | ||||||||
\(121\) | −7.75302 | −0.704820 | ||||||||
\(122\) | −11.5036 | −1.04149 | ||||||||
\(123\) | 0.0217703 | 0.00196296 | ||||||||
\(124\) | −3.63102 | −0.326075 | ||||||||
\(125\) | −11.0707 | −0.990192 | ||||||||
\(126\) | 2.69202 | 0.239824 | ||||||||
\(127\) | −4.96316 | −0.440410 | −0.220205 | − | 0.975454i | \(-0.570673\pi\) | ||||
−0.220205 | + | 0.975454i | \(0.570673\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.25906 | 0.110854 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.0761 | −0.967720 | −0.483860 | − | 0.875145i | \(-0.660766\pi\) | ||||
−0.483860 | + | 0.875145i | \(0.660766\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | −1.95108 | −0.169180 | ||||||||
\(134\) | −2.22521 | −0.192229 | ||||||||
\(135\) | −4.28621 | −0.368898 | ||||||||
\(136\) | 5.29590 | 0.454119 | ||||||||
\(137\) | 10.3056 | 0.880466 | 0.440233 | − | 0.897884i | \(-0.354896\pi\) | ||||
0.440233 | + | 0.897884i | \(0.354896\pi\) | |||||||
\(138\) | 2.69202 | 0.229160 | ||||||||
\(139\) | 0.987918 | 0.0837941 | 0.0418971 | − | 0.999122i | \(-0.486660\pi\) | ||||
0.0418971 | + | 0.999122i | \(0.486660\pi\) | |||||||
\(140\) | −1.35690 | −0.114679 | ||||||||
\(141\) | 5.86592 | 0.494000 | ||||||||
\(142\) | 7.78986 | 0.653710 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.69202 | −0.224335 | ||||||||
\(145\) | 8.08815 | 0.671684 | ||||||||
\(146\) | 14.1032 | 1.16719 | ||||||||
\(147\) | 0.554958 | 0.0457722 | ||||||||
\(148\) | 7.75302 | 0.637294 | ||||||||
\(149\) | −5.60627 | −0.459283 | −0.229642 | − | 0.973275i | \(-0.573755\pi\) | ||||
−0.229642 | + | 0.973275i | \(0.573755\pi\) | |||||||
\(150\) | −1.75302 | −0.143134 | ||||||||
\(151\) | −15.5894 | −1.26865 | −0.634324 | − | 0.773068i | \(-0.718721\pi\) | ||||
−0.634324 | + | 0.773068i | \(0.718721\pi\) | |||||||
\(152\) | 1.95108 | 0.158254 | ||||||||
\(153\) | −14.2567 | −1.15258 | ||||||||
\(154\) | −1.80194 | −0.145204 | ||||||||
\(155\) | −4.92692 | −0.395740 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.49827 | −0.678236 | −0.339118 | − | 0.940744i | \(-0.610129\pi\) | ||||
−0.339118 | + | 0.940744i | \(0.610129\pi\) | |||||||
\(158\) | −12.0804 | −0.961063 | ||||||||
\(159\) | −2.03385 | −0.161295 | ||||||||
\(160\) | 1.35690 | 0.107272 | ||||||||
\(161\) | −4.85086 | −0.382301 | ||||||||
\(162\) | 6.32304 | 0.496785 | ||||||||
\(163\) | 5.25906 | 0.411921 | 0.205961 | − | 0.978560i | \(-0.433968\pi\) | ||||
0.205961 | + | 0.978560i | \(0.433968\pi\) | |||||||
\(164\) | 0.0392287 | 0.00306324 | ||||||||
\(165\) | 1.35690 | 0.105634 | ||||||||
\(166\) | 2.85086 | 0.221269 | ||||||||
\(167\) | 14.0954 | 1.09074 | 0.545369 | − | 0.838196i | \(-0.316390\pi\) | ||||
0.545369 | + | 0.838196i | \(0.316390\pi\) | |||||||
\(168\) | −0.554958 | −0.0428159 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 7.18598 | 0.551140 | ||||||||
\(171\) | −5.25236 | −0.401658 | ||||||||
\(172\) | 2.26875 | 0.172991 | ||||||||
\(173\) | 17.8877 | 1.35998 | 0.679988 | − | 0.733223i | \(-0.261985\pi\) | ||||
0.679988 | + | 0.733223i | \(0.261985\pi\) | |||||||
\(174\) | 3.30798 | 0.250777 | ||||||||
\(175\) | 3.15883 | 0.238785 | ||||||||
\(176\) | 1.80194 | 0.135826 | ||||||||
\(177\) | 2.26205 | 0.170026 | ||||||||
\(178\) | −6.61894 | −0.496111 | ||||||||
\(179\) | −0.0556221 | −0.00415739 | −0.00207870 | − | 0.999998i | \(-0.500662\pi\) | ||||
−0.00207870 | + | 0.999998i | \(0.500662\pi\) | |||||||
\(180\) | −3.65279 | −0.272263 | ||||||||
\(181\) | −8.45042 | −0.628115 | −0.314057 | − | 0.949404i | \(-0.601688\pi\) | ||||
−0.314057 | + | 0.949404i | \(0.601688\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.38404 | −0.471922 | ||||||||
\(184\) | 4.85086 | 0.357610 | ||||||||
\(185\) | 10.5200 | 0.773449 | ||||||||
\(186\) | −2.01507 | −0.147752 | ||||||||
\(187\) | 9.54288 | 0.697844 | ||||||||
\(188\) | 10.5700 | 0.770898 | ||||||||
\(189\) | 3.15883 | 0.229771 | ||||||||
\(190\) | 2.64742 | 0.192064 | ||||||||
\(191\) | −4.33273 | −0.313506 | −0.156753 | − | 0.987638i | \(-0.550103\pi\) | ||||
−0.156753 | + | 0.987638i | \(0.550103\pi\) | |||||||
\(192\) | 0.554958 | 0.0400507 | ||||||||
\(193\) | −1.70410 | −0.122664 | −0.0613320 | − | 0.998117i | \(-0.519535\pi\) | ||||
−0.0613320 | + | 0.998117i | \(0.519535\pi\) | |||||||
\(194\) | −3.64310 | −0.261560 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −25.7700 | −1.83604 | −0.918018 | − | 0.396538i | \(-0.870212\pi\) | ||||
−0.918018 | + | 0.396538i | \(0.870212\pi\) | |||||||
\(198\) | −4.85086 | −0.344735 | ||||||||
\(199\) | 6.72587 | 0.476785 | 0.238392 | − | 0.971169i | \(-0.423380\pi\) | ||||
0.238392 | + | 0.971169i | \(0.423380\pi\) | |||||||
\(200\) | −3.15883 | −0.223363 | ||||||||
\(201\) | −1.23490 | −0.0871030 | ||||||||
\(202\) | 7.85086 | 0.552384 | ||||||||
\(203\) | −5.96077 | −0.418364 | ||||||||
\(204\) | 2.93900 | 0.205771 | ||||||||
\(205\) | 0.0532292 | 0.00371769 | ||||||||
\(206\) | −17.0804 | −1.19005 | ||||||||
\(207\) | −13.0586 | −0.907636 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.51573 | 0.243188 | ||||||||
\(210\) | −0.753020 | −0.0519633 | ||||||||
\(211\) | −26.7536 | −1.84179 | −0.920897 | − | 0.389805i | \(-0.872542\pi\) | ||||
−0.920897 | + | 0.389805i | \(0.872542\pi\) | |||||||
\(212\) | −3.66487 | −0.251705 | ||||||||
\(213\) | 4.32304 | 0.296210 | ||||||||
\(214\) | 13.8562 | 0.947193 | ||||||||
\(215\) | 3.07846 | 0.209949 | ||||||||
\(216\) | −3.15883 | −0.214931 | ||||||||
\(217\) | 3.63102 | 0.246490 | ||||||||
\(218\) | −2.18060 | −0.147689 | ||||||||
\(219\) | 7.82669 | 0.528879 | ||||||||
\(220\) | 2.44504 | 0.164845 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4.30260 | 0.288772 | ||||||||
\(223\) | 20.5851 | 1.37848 | 0.689240 | − | 0.724533i | \(-0.257945\pi\) | ||||
0.689240 | + | 0.724533i | \(0.257945\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 8.50365 | 0.566910 | ||||||||
\(226\) | −17.5090 | −1.16468 | ||||||||
\(227\) | −22.2543 | −1.47707 | −0.738534 | − | 0.674216i | \(-0.764482\pi\) | ||||
−0.738534 | + | 0.674216i | \(0.764482\pi\) | |||||||
\(228\) | 1.08277 | 0.0717081 | ||||||||
\(229\) | 16.3230 | 1.07866 | 0.539329 | − | 0.842095i | \(-0.318678\pi\) | ||||
0.539329 | + | 0.842095i | \(0.318678\pi\) | |||||||
\(230\) | 6.58211 | 0.434011 | ||||||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | 5.96077 | 0.391344 | ||||||||
\(233\) | 6.88769 | 0.451228 | 0.225614 | − | 0.974217i | \(-0.427561\pi\) | ||||
0.225614 | + | 0.974217i | \(0.427561\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.3424 | 0.935596 | ||||||||
\(236\) | 4.07606 | 0.265329 | ||||||||
\(237\) | −6.70410 | −0.435478 | ||||||||
\(238\) | −5.29590 | −0.343282 | ||||||||
\(239\) | 14.1709 | 0.916640 | 0.458320 | − | 0.888787i | \(-0.348451\pi\) | ||||
0.458320 | + | 0.888787i | \(0.348451\pi\) | |||||||
\(240\) | 0.753020 | 0.0486073 | ||||||||
\(241\) | 3.91484 | 0.252177 | 0.126088 | − | 0.992019i | \(-0.459758\pi\) | ||||
0.126088 | + | 0.992019i | \(0.459758\pi\) | |||||||
\(242\) | −7.75302 | −0.498383 | ||||||||
\(243\) | 12.9855 | 0.833022 | ||||||||
\(244\) | −11.5036 | −0.736446 | ||||||||
\(245\) | 1.35690 | 0.0866889 | ||||||||
\(246\) | 0.0217703 | 0.00138802 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.63102 | −0.230570 | ||||||||
\(249\) | 1.58211 | 0.100262 | ||||||||
\(250\) | −11.0707 | −0.700172 | ||||||||
\(251\) | 10.3327 | 0.652196 | 0.326098 | − | 0.945336i | \(-0.394266\pi\) | ||||
0.326098 | + | 0.945336i | \(0.394266\pi\) | |||||||
\(252\) | 2.69202 | 0.169581 | ||||||||
\(253\) | 8.74094 | 0.549538 | ||||||||
\(254\) | −4.96316 | −0.311417 | ||||||||
\(255\) | 3.98792 | 0.249733 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.3884 | −0.897521 | −0.448760 | − | 0.893652i | \(-0.648134\pi\) | ||||
−0.448760 | + | 0.893652i | \(0.648134\pi\) | |||||||
\(258\) | 1.25906 | 0.0783857 | ||||||||
\(259\) | −7.75302 | −0.481749 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.0465 | −0.993255 | ||||||||
\(262\) | −11.0761 | −0.684282 | ||||||||
\(263\) | −17.6069 | −1.08569 | −0.542843 | − | 0.839834i | \(-0.682652\pi\) | ||||
−0.542843 | + | 0.839834i | \(0.682652\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | −4.97285 | −0.305480 | ||||||||
\(266\) | −1.95108 | −0.119629 | ||||||||
\(267\) | −3.67324 | −0.224798 | ||||||||
\(268\) | −2.22521 | −0.135926 | ||||||||
\(269\) | −4.15213 | −0.253160 | −0.126580 | − | 0.991956i | \(-0.540400\pi\) | ||||
−0.126580 | + | 0.991956i | \(0.540400\pi\) | |||||||
\(270\) | −4.28621 | −0.260850 | ||||||||
\(271\) | 17.5278 | 1.06474 | 0.532369 | − | 0.846512i | \(-0.321302\pi\) | ||||
0.532369 | + | 0.846512i | \(0.321302\pi\) | |||||||
\(272\) | 5.29590 | 0.321111 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.3056 | 0.622583 | ||||||||
\(275\) | −5.69202 | −0.343242 | ||||||||
\(276\) | 2.69202 | 0.162041 | ||||||||
\(277\) | −29.9855 | −1.80166 | −0.900828 | − | 0.434177i | \(-0.857039\pi\) | ||||
−0.900828 | + | 0.434177i | \(0.857039\pi\) | |||||||
\(278\) | 0.987918 | 0.0592514 | ||||||||
\(279\) | 9.77479 | 0.585201 | ||||||||
\(280\) | −1.35690 | −0.0810900 | ||||||||
\(281\) | −9.24027 | −0.551229 | −0.275614 | − | 0.961268i | \(-0.588881\pi\) | ||||
−0.275614 | + | 0.961268i | \(0.588881\pi\) | |||||||
\(282\) | 5.86592 | 0.349310 | ||||||||
\(283\) | 32.0291 | 1.90393 | 0.951965 | − | 0.306206i | \(-0.0990597\pi\) | ||||
0.951965 | + | 0.306206i | \(0.0990597\pi\) | |||||||
\(284\) | 7.78986 | 0.462243 | ||||||||
\(285\) | 1.46921 | 0.0870282 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.0392287 | −0.00231559 | ||||||||
\(288\) | −2.69202 | −0.158629 | ||||||||
\(289\) | 11.0465 | 0.649796 | ||||||||
\(290\) | 8.08815 | 0.474952 | ||||||||
\(291\) | −2.02177 | −0.118518 | ||||||||
\(292\) | 14.1032 | 0.825328 | ||||||||
\(293\) | −22.1933 | −1.29655 | −0.648273 | − | 0.761408i | \(-0.724508\pi\) | ||||
−0.648273 | + | 0.761408i | \(0.724508\pi\) | |||||||
\(294\) | 0.554958 | 0.0323658 | ||||||||
\(295\) | 5.53079 | 0.322015 | ||||||||
\(296\) | 7.75302 | 0.450635 | ||||||||
\(297\) | −5.69202 | −0.330285 | ||||||||
\(298\) | −5.60627 | −0.324762 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.75302 | −0.101211 | ||||||||
\(301\) | −2.26875 | −0.130769 | ||||||||
\(302\) | −15.5894 | −0.897069 | ||||||||
\(303\) | 4.35690 | 0.250297 | ||||||||
\(304\) | 1.95108 | 0.111902 | ||||||||
\(305\) | −15.6093 | −0.893783 | ||||||||
\(306\) | −14.2567 | −0.814999 | ||||||||
\(307\) | −20.8170 | −1.18809 | −0.594045 | − | 0.804432i | \(-0.702470\pi\) | ||||
−0.594045 | + | 0.804432i | \(0.702470\pi\) | |||||||
\(308\) | −1.80194 | −0.102675 | ||||||||
\(309\) | −9.47889 | −0.539235 | ||||||||
\(310\) | −4.92692 | −0.279830 | ||||||||
\(311\) | 28.1836 | 1.59814 | 0.799072 | − | 0.601235i | \(-0.205324\pi\) | ||||
0.799072 | + | 0.601235i | \(0.205324\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.0248 | 0.905773 | 0.452886 | − | 0.891568i | \(-0.350394\pi\) | ||||
0.452886 | + | 0.891568i | \(0.350394\pi\) | |||||||
\(314\) | −8.49827 | −0.479585 | ||||||||
\(315\) | 3.65279 | 0.205812 | ||||||||
\(316\) | −12.0804 | −0.679574 | ||||||||
\(317\) | 29.0834 | 1.63348 | 0.816742 | − | 0.577003i | \(-0.195778\pi\) | ||||
0.816742 | + | 0.577003i | \(0.195778\pi\) | |||||||
\(318\) | −2.03385 | −0.114053 | ||||||||
\(319\) | 10.7409 | 0.601377 | ||||||||
\(320\) | 1.35690 | 0.0758528 | ||||||||
\(321\) | 7.68963 | 0.429193 | ||||||||
\(322\) | −4.85086 | −0.270328 | ||||||||
\(323\) | 10.3327 | 0.574929 | ||||||||
\(324\) | 6.32304 | 0.351280 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.25906 | 0.291272 | ||||||||
\(327\) | −1.21014 | −0.0669211 | ||||||||
\(328\) | 0.0392287 | 0.00216604 | ||||||||
\(329\) | −10.5700 | −0.582744 | ||||||||
\(330\) | 1.35690 | 0.0746947 | ||||||||
\(331\) | −7.32304 | −0.402511 | −0.201255 | − | 0.979539i | \(-0.564502\pi\) | ||||
−0.201255 | + | 0.979539i | \(0.564502\pi\) | |||||||
\(332\) | 2.85086 | 0.156461 | ||||||||
\(333\) | −20.8713 | −1.14374 | ||||||||
\(334\) | 14.0954 | 0.771268 | ||||||||
\(335\) | −3.01938 | −0.164966 | ||||||||
\(336\) | −0.554958 | −0.0302754 | ||||||||
\(337\) | −27.1618 | −1.47960 | −0.739799 | − | 0.672828i | \(-0.765080\pi\) | ||||
−0.739799 | + | 0.672828i | \(0.765080\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.71678 | −0.527743 | ||||||||
\(340\) | 7.18598 | 0.389715 | ||||||||
\(341\) | −6.54288 | −0.354317 | ||||||||
\(342\) | −5.25236 | −0.284015 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 2.26875 | 0.122323 | ||||||||
\(345\) | 3.65279 | 0.196660 | ||||||||
\(346\) | 17.8877 | 0.961648 | ||||||||
\(347\) | −12.8890 | −0.691919 | −0.345959 | − | 0.938249i | \(-0.612447\pi\) | ||||
−0.345959 | + | 0.938249i | \(0.612447\pi\) | |||||||
\(348\) | 3.30798 | 0.177326 | ||||||||
\(349\) | −19.6732 | −1.05308 | −0.526542 | − | 0.850149i | \(-0.676512\pi\) | ||||
−0.526542 | + | 0.850149i | \(0.676512\pi\) | |||||||
\(350\) | 3.15883 | 0.168847 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.80194 | 0.0960436 | ||||||||
\(353\) | 30.3980 | 1.61792 | 0.808962 | − | 0.587861i | \(-0.200030\pi\) | ||||
0.808962 | + | 0.587861i | \(0.200030\pi\) | |||||||
\(354\) | 2.26205 | 0.120226 | ||||||||
\(355\) | 10.5700 | 0.560999 | ||||||||
\(356\) | −6.61894 | −0.350803 | ||||||||
\(357\) | −2.93900 | −0.155548 | ||||||||
\(358\) | −0.0556221 | −0.00293972 | ||||||||
\(359\) | 2.64310 | 0.139498 | 0.0697489 | − | 0.997565i | \(-0.477780\pi\) | ||||
0.0697489 | + | 0.997565i | \(0.477780\pi\) | |||||||
\(360\) | −3.65279 | −0.192519 | ||||||||
\(361\) | −15.1933 | −0.799646 | ||||||||
\(362\) | −8.45042 | −0.444144 | ||||||||
\(363\) | −4.30260 | −0.225828 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.1366 | 1.00165 | ||||||||
\(366\) | −6.38404 | −0.333699 | ||||||||
\(367\) | 2.46921 | 0.128891 | 0.0644457 | − | 0.997921i | \(-0.479472\pi\) | ||||
0.0644457 | + | 0.997921i | \(0.479472\pi\) | |||||||
\(368\) | 4.85086 | 0.252868 | ||||||||
\(369\) | −0.105604 | −0.00549755 | ||||||||
\(370\) | 10.5200 | 0.546911 | ||||||||
\(371\) | 3.66487 | 0.190271 | ||||||||
\(372\) | −2.01507 | −0.104476 | ||||||||
\(373\) | −5.96615 | −0.308915 | −0.154458 | − | 0.987999i | \(-0.549363\pi\) | ||||
−0.154458 | + | 0.987999i | \(0.549363\pi\) | |||||||
\(374\) | 9.54288 | 0.493450 | ||||||||
\(375\) | −6.14377 | −0.317263 | ||||||||
\(376\) | 10.5700 | 0.545107 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 3.15883 | 0.162473 | ||||||||
\(379\) | 22.0519 | 1.13273 | 0.566365 | − | 0.824155i | \(-0.308349\pi\) | ||||
0.566365 | + | 0.824155i | \(0.308349\pi\) | |||||||
\(380\) | 2.64742 | 0.135810 | ||||||||
\(381\) | −2.75435 | −0.141110 | ||||||||
\(382\) | −4.33273 | −0.221682 | ||||||||
\(383\) | 26.1758 | 1.33752 | 0.668761 | − | 0.743478i | \(-0.266825\pi\) | ||||
0.668761 | + | 0.743478i | \(0.266825\pi\) | |||||||
\(384\) | 0.554958 | 0.0283201 | ||||||||
\(385\) | −2.44504 | −0.124611 | ||||||||
\(386\) | −1.70410 | −0.0867366 | ||||||||
\(387\) | −6.10752 | −0.310463 | ||||||||
\(388\) | −3.64310 | −0.184951 | ||||||||
\(389\) | −15.4655 | −0.784131 | −0.392066 | − | 0.919937i | \(-0.628239\pi\) | ||||
−0.392066 | + | 0.919937i | \(0.628239\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.6896 | 1.29918 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −6.14675 | −0.310063 | ||||||||
\(394\) | −25.7700 | −1.29827 | ||||||||
\(395\) | −16.3918 | −0.824762 | ||||||||
\(396\) | −4.85086 | −0.243765 | ||||||||
\(397\) | −34.9778 | −1.75548 | −0.877742 | − | 0.479134i | \(-0.840951\pi\) | ||||
−0.877742 | + | 0.479134i | \(0.840951\pi\) | |||||||
\(398\) | 6.72587 | 0.337138 | ||||||||
\(399\) | −1.08277 | −0.0542063 | ||||||||
\(400\) | −3.15883 | −0.157942 | ||||||||
\(401\) | −27.3739 | −1.36699 | −0.683493 | − | 0.729957i | \(-0.739540\pi\) | ||||
−0.683493 | + | 0.729957i | \(0.739540\pi\) | |||||||
\(402\) | −1.23490 | −0.0615911 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 7.85086 | 0.390595 | ||||||||
\(405\) | 8.57971 | 0.426329 | ||||||||
\(406\) | −5.96077 | −0.295828 | ||||||||
\(407\) | 13.9705 | 0.692490 | ||||||||
\(408\) | 2.93900 | 0.145502 | ||||||||
\(409\) | −29.0810 | −1.43796 | −0.718981 | − | 0.695030i | \(-0.755391\pi\) | ||||
−0.718981 | + | 0.695030i | \(0.755391\pi\) | |||||||
\(410\) | 0.0532292 | 0.00262880 | ||||||||
\(411\) | 5.71917 | 0.282106 | ||||||||
\(412\) | −17.0804 | −0.841490 | ||||||||
\(413\) | −4.07606 | −0.200570 | ||||||||
\(414\) | −13.0586 | −0.641795 | ||||||||
\(415\) | 3.86831 | 0.189888 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.548253 | 0.0268481 | ||||||||
\(418\) | 3.51573 | 0.171960 | ||||||||
\(419\) | −40.3086 | −1.96920 | −0.984601 | − | 0.174815i | \(-0.944067\pi\) | ||||
−0.984601 | + | 0.174815i | \(0.944067\pi\) | |||||||
\(420\) | −0.753020 | −0.0367436 | ||||||||
\(421\) | 4.26981 | 0.208098 | 0.104049 | − | 0.994572i | \(-0.466820\pi\) | ||||
0.104049 | + | 0.994572i | \(0.466820\pi\) | |||||||
\(422\) | −26.7536 | −1.30235 | ||||||||
\(423\) | −28.4547 | −1.38352 | ||||||||
\(424\) | −3.66487 | −0.177982 | ||||||||
\(425\) | −16.7289 | −0.811469 | ||||||||
\(426\) | 4.32304 | 0.209452 | ||||||||
\(427\) | 11.5036 | 0.556701 | ||||||||
\(428\) | 13.8562 | 0.669766 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.07846 | 0.148456 | ||||||||
\(431\) | −6.25475 | −0.301281 | −0.150640 | − | 0.988589i | \(-0.548134\pi\) | ||||
−0.150640 | + | 0.988589i | \(0.548134\pi\) | |||||||
\(432\) | −3.15883 | −0.151979 | ||||||||
\(433\) | −15.9705 | −0.767491 | −0.383746 | − | 0.923439i | \(-0.625366\pi\) | ||||
−0.383746 | + | 0.923439i | \(0.625366\pi\) | |||||||
\(434\) | 3.63102 | 0.174295 | ||||||||
\(435\) | 4.48858 | 0.215211 | ||||||||
\(436\) | −2.18060 | −0.104432 | ||||||||
\(437\) | 9.46442 | 0.452745 | ||||||||
\(438\) | 7.82669 | 0.373974 | ||||||||
\(439\) | 30.4058 | 1.45119 | 0.725595 | − | 0.688122i | \(-0.241565\pi\) | ||||
0.725595 | + | 0.688122i | \(0.241565\pi\) | |||||||
\(440\) | 2.44504 | 0.116563 | ||||||||
\(441\) | −2.69202 | −0.128191 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.0291 | −0.619030 | −0.309515 | − | 0.950895i | \(-0.600167\pi\) | ||||
−0.309515 | + | 0.950895i | \(0.600167\pi\) | |||||||
\(444\) | 4.30260 | 0.204192 | ||||||||
\(445\) | −8.98121 | −0.425750 | ||||||||
\(446\) | 20.5851 | 0.974732 | ||||||||
\(447\) | −3.11124 | −0.147157 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 20.2258 | 0.954515 | 0.477257 | − | 0.878764i | \(-0.341631\pi\) | ||||
0.477257 | + | 0.878764i | \(0.341631\pi\) | |||||||
\(450\) | 8.50365 | 0.400866 | ||||||||
\(451\) | 0.0706876 | 0.00332855 | ||||||||
\(452\) | −17.5090 | −0.823555 | ||||||||
\(453\) | −8.65146 | −0.406481 | ||||||||
\(454\) | −22.2543 | −1.04444 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.08277 | 0.0507053 | ||||||||
\(457\) | 20.5569 | 0.961610 | 0.480805 | − | 0.876828i | \(-0.340344\pi\) | ||||
0.480805 | + | 0.876828i | \(0.340344\pi\) | |||||||
\(458\) | 16.3230 | 0.762726 | ||||||||
\(459\) | −16.7289 | −0.780836 | ||||||||
\(460\) | 6.58211 | 0.306892 | ||||||||
\(461\) | −15.2513 | −0.710323 | −0.355162 | − | 0.934805i | \(-0.615574\pi\) | ||||
−0.355162 | + | 0.934805i | \(0.615574\pi\) | |||||||
\(462\) | −1.00000 | −0.0465242 | ||||||||
\(463\) | −25.3207 | −1.17675 | −0.588375 | − | 0.808588i | \(-0.700232\pi\) | ||||
−0.588375 | + | 0.808588i | \(0.700232\pi\) | |||||||
\(464\) | 5.96077 | 0.276722 | ||||||||
\(465\) | −2.73423 | −0.126797 | ||||||||
\(466\) | 6.88769 | 0.319066 | ||||||||
\(467\) | 16.8019 | 0.777501 | 0.388750 | − | 0.921343i | \(-0.372907\pi\) | ||||
0.388750 | + | 0.921343i | \(0.372907\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.22521 | 0.102751 | ||||||||
\(470\) | 14.3424 | 0.661567 | ||||||||
\(471\) | −4.71618 | −0.217310 | ||||||||
\(472\) | 4.07606 | 0.187616 | ||||||||
\(473\) | 4.08815 | 0.187973 | ||||||||
\(474\) | −6.70410 | −0.307930 | ||||||||
\(475\) | −6.16315 | −0.282785 | ||||||||
\(476\) | −5.29590 | −0.242737 | ||||||||
\(477\) | 9.86592 | 0.451729 | ||||||||
\(478\) | 14.1709 | 0.648163 | ||||||||
\(479\) | −27.5870 | −1.26048 | −0.630241 | − | 0.776399i | \(-0.717044\pi\) | ||||
−0.630241 | + | 0.776399i | \(0.717044\pi\) | |||||||
\(480\) | 0.753020 | 0.0343705 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.91484 | 0.178316 | ||||||||
\(483\) | −2.69202 | −0.122491 | ||||||||
\(484\) | −7.75302 | −0.352410 | ||||||||
\(485\) | −4.94331 | −0.224464 | ||||||||
\(486\) | 12.9855 | 0.589035 | ||||||||
\(487\) | −29.4698 | −1.33540 | −0.667702 | − | 0.744429i | \(-0.732722\pi\) | ||||
−0.667702 | + | 0.744429i | \(0.732722\pi\) | |||||||
\(488\) | −11.5036 | −0.520746 | ||||||||
\(489\) | 2.91856 | 0.131982 | ||||||||
\(490\) | 1.35690 | 0.0612983 | ||||||||
\(491\) | −8.30691 | −0.374886 | −0.187443 | − | 0.982276i | \(-0.560020\pi\) | ||||
−0.187443 | + | 0.982276i | \(0.560020\pi\) | |||||||
\(492\) | 0.0217703 | 0.000981479 0 | ||||||||
\(493\) | 31.5676 | 1.42173 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.58211 | −0.295844 | ||||||||
\(496\) | −3.63102 | −0.163038 | ||||||||
\(497\) | −7.78986 | −0.349423 | ||||||||
\(498\) | 1.58211 | 0.0708958 | ||||||||
\(499\) | −42.2043 | −1.88932 | −0.944662 | − | 0.328046i | \(-0.893610\pi\) | ||||
−0.944662 | + | 0.328046i | \(0.893610\pi\) | |||||||
\(500\) | −11.0707 | −0.495096 | ||||||||
\(501\) | 7.82238 | 0.349478 | ||||||||
\(502\) | 10.3327 | 0.461172 | ||||||||
\(503\) | 17.5133 | 0.780881 | 0.390441 | − | 0.920628i | \(-0.372323\pi\) | ||||
0.390441 | + | 0.920628i | \(0.372323\pi\) | |||||||
\(504\) | 2.69202 | 0.119912 | ||||||||
\(505\) | 10.6528 | 0.474043 | ||||||||
\(506\) | 8.74094 | 0.388582 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.96316 | −0.220205 | ||||||||
\(509\) | 6.94869 | 0.307995 | 0.153998 | − | 0.988071i | \(-0.450785\pi\) | ||||
0.153998 | + | 0.988071i | \(0.450785\pi\) | |||||||
\(510\) | 3.98792 | 0.176588 | ||||||||
\(511\) | −14.1032 | −0.623889 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.16315 | −0.272110 | ||||||||
\(514\) | −14.3884 | −0.634643 | ||||||||
\(515\) | −23.1763 | −1.02127 | ||||||||
\(516\) | 1.25906 | 0.0554271 | ||||||||
\(517\) | 19.0465 | 0.837665 | ||||||||
\(518\) | −7.75302 | −0.340648 | ||||||||
\(519\) | 9.92692 | 0.435743 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.3889 | −1.46280 | −0.731398 | − | 0.681951i | \(-0.761132\pi\) | ||||
−0.731398 | + | 0.681951i | \(0.761132\pi\) | |||||||
\(522\) | −16.0465 | −0.702337 | ||||||||
\(523\) | −0.281422 | −0.0123057 | −0.00615287 | − | 0.999981i | \(-0.501959\pi\) | ||||
−0.00615287 | + | 0.999981i | \(0.501959\pi\) | |||||||
\(524\) | −11.0761 | −0.483860 | ||||||||
\(525\) | 1.75302 | 0.0765081 | ||||||||
\(526\) | −17.6069 | −0.767696 | ||||||||
\(527\) | −19.2295 | −0.837651 | ||||||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | 0.530795 | 0.0230780 | ||||||||
\(530\) | −4.97285 | −0.216007 | ||||||||
\(531\) | −10.9729 | −0.476181 | ||||||||
\(532\) | −1.95108 | −0.0845902 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.67324 | −0.158956 | ||||||||
\(535\) | 18.8015 | 0.812858 | ||||||||
\(536\) | −2.22521 | −0.0961144 | ||||||||
\(537\) | −0.0308679 | −0.00133205 | ||||||||
\(538\) | −4.15213 | −0.179011 | ||||||||
\(539\) | 1.80194 | 0.0776150 | ||||||||
\(540\) | −4.28621 | −0.184449 | ||||||||
\(541\) | 33.4655 | 1.43879 | 0.719397 | − | 0.694599i | \(-0.244418\pi\) | ||||
0.719397 | + | 0.694599i | \(0.244418\pi\) | |||||||
\(542\) | 17.5278 | 0.752884 | ||||||||
\(543\) | −4.68963 | −0.201251 | ||||||||
\(544\) | 5.29590 | 0.227060 | ||||||||
\(545\) | −2.95885 | −0.126743 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.9148 | 1.10804 | 0.554019 | − | 0.832504i | \(-0.313093\pi\) | ||||
0.554019 | + | 0.832504i | \(0.313093\pi\) | |||||||
\(548\) | 10.3056 | 0.440233 | ||||||||
\(549\) | 30.9681 | 1.32168 | ||||||||
\(550\) | −5.69202 | −0.242709 | ||||||||
\(551\) | 11.6300 | 0.495453 | ||||||||
\(552\) | 2.69202 | 0.114580 | ||||||||
\(553\) | 12.0804 | 0.513710 | ||||||||
\(554\) | −29.9855 | −1.27396 | ||||||||
\(555\) | 5.83818 | 0.247817 | ||||||||
\(556\) | 0.987918 | 0.0418971 | ||||||||
\(557\) | −24.1588 | −1.02364 | −0.511821 | − | 0.859092i | \(-0.671029\pi\) | ||||
−0.511821 | + | 0.859092i | \(0.671029\pi\) | |||||||
\(558\) | 9.77479 | 0.413800 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.35690 | −0.0573393 | ||||||||
\(561\) | 5.29590 | 0.223593 | ||||||||
\(562\) | −9.24027 | −0.389777 | ||||||||
\(563\) | 5.58987 | 0.235585 | 0.117793 | − | 0.993038i | \(-0.462418\pi\) | ||||
0.117793 | + | 0.993038i | \(0.462418\pi\) | |||||||
\(564\) | 5.86592 | 0.247000 | ||||||||
\(565\) | −23.7579 | −0.999503 | ||||||||
\(566\) | 32.0291 | 1.34628 | ||||||||
\(567\) | −6.32304 | −0.265543 | ||||||||
\(568\) | 7.78986 | 0.326855 | ||||||||
\(569\) | 40.5217 | 1.69876 | 0.849379 | − | 0.527783i | \(-0.176977\pi\) | ||||
0.849379 | + | 0.527783i | \(0.176977\pi\) | |||||||
\(570\) | 1.46921 | 0.0615382 | ||||||||
\(571\) | 33.2180 | 1.39013 | 0.695066 | − | 0.718946i | \(-0.255375\pi\) | ||||
0.695066 | + | 0.718946i | \(0.255375\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.40449 | −0.100449 | ||||||||
\(574\) | −0.0392287 | −0.00163737 | ||||||||
\(575\) | −15.3230 | −0.639015 | ||||||||
\(576\) | −2.69202 | −0.112168 | ||||||||
\(577\) | −17.4896 | −0.728104 | −0.364052 | − | 0.931379i | \(-0.618607\pi\) | ||||
−0.364052 | + | 0.931379i | \(0.618607\pi\) | |||||||
\(578\) | 11.0465 | 0.459475 | ||||||||
\(579\) | −0.945706 | −0.0393022 | ||||||||
\(580\) | 8.08815 | 0.335842 | ||||||||
\(581\) | −2.85086 | −0.118273 | ||||||||
\(582\) | −2.02177 | −0.0838051 | ||||||||
\(583\) | −6.60388 | −0.273505 | ||||||||
\(584\) | 14.1032 | 0.583595 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.1933 | −0.916796 | ||||||||
\(587\) | −35.8224 | −1.47855 | −0.739274 | − | 0.673405i | \(-0.764831\pi\) | ||||
−0.739274 | + | 0.673405i | \(0.764831\pi\) | |||||||
\(588\) | 0.554958 | 0.0228861 | ||||||||
\(589\) | −7.08443 | −0.291909 | ||||||||
\(590\) | 5.53079 | 0.227699 | ||||||||
\(591\) | −14.3013 | −0.588276 | ||||||||
\(592\) | 7.75302 | 0.318647 | ||||||||
\(593\) | 12.0750 | 0.495861 | 0.247930 | − | 0.968778i | \(-0.420250\pi\) | ||||
0.247930 | + | 0.968778i | \(0.420250\pi\) | |||||||
\(594\) | −5.69202 | −0.233546 | ||||||||
\(595\) | −7.18598 | −0.294596 | ||||||||
\(596\) | −5.60627 | −0.229642 | ||||||||
\(597\) | 3.73258 | 0.152764 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.6256 | 0.842741 | 0.421371 | − | 0.906889i | \(-0.361549\pi\) | ||||
0.421371 | + | 0.906889i | \(0.361549\pi\) | |||||||
\(600\) | −1.75302 | −0.0715668 | ||||||||
\(601\) | −38.8025 | −1.58279 | −0.791394 | − | 0.611306i | \(-0.790644\pi\) | ||||
−0.791394 | + | 0.611306i | \(0.790644\pi\) | |||||||
\(602\) | −2.26875 | −0.0924673 | ||||||||
\(603\) | 5.99031 | 0.243944 | ||||||||
\(604\) | −15.5894 | −0.634324 | ||||||||
\(605\) | −10.5200 | −0.427701 | ||||||||
\(606\) | 4.35690 | 0.176987 | ||||||||
\(607\) | 2.24459 | 0.0911050 | 0.0455525 | − | 0.998962i | \(-0.485495\pi\) | ||||
0.0455525 | + | 0.998962i | \(0.485495\pi\) | |||||||
\(608\) | 1.95108 | 0.0791269 | ||||||||
\(609\) | −3.30798 | −0.134046 | ||||||||
\(610\) | −15.6093 | −0.632000 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −14.2567 | −0.576292 | ||||||||
\(613\) | 4.24267 | 0.171360 | 0.0856799 | − | 0.996323i | \(-0.472694\pi\) | ||||
0.0856799 | + | 0.996323i | \(0.472694\pi\) | |||||||
\(614\) | −20.8170 | −0.840106 | ||||||||
\(615\) | 0.0295400 | 0.00119117 | ||||||||
\(616\) | −1.80194 | −0.0726021 | ||||||||
\(617\) | 0.147817 | 0.00595089 | 0.00297544 | − | 0.999996i | \(-0.499053\pi\) | ||||
0.00297544 | + | 0.999996i | \(0.499053\pi\) | |||||||
\(618\) | −9.47889 | −0.381297 | ||||||||
\(619\) | 35.3575 | 1.42114 | 0.710569 | − | 0.703628i | \(-0.248438\pi\) | ||||
0.710569 | + | 0.703628i | \(0.248438\pi\) | |||||||
\(620\) | −4.92692 | −0.197870 | ||||||||
\(621\) | −15.3230 | −0.614893 | ||||||||
\(622\) | 28.1836 | 1.13006 | ||||||||
\(623\) | 6.61894 | 0.265182 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.772398 | 0.0308959 | ||||||||
\(626\) | 16.0248 | 0.640478 | ||||||||
\(627\) | 1.95108 | 0.0779187 | ||||||||
\(628\) | −8.49827 | −0.339118 | ||||||||
\(629\) | 41.0592 | 1.63714 | ||||||||
\(630\) | 3.65279 | 0.145531 | ||||||||
\(631\) | 2.33214 | 0.0928411 | 0.0464205 | − | 0.998922i | \(-0.485219\pi\) | ||||
0.0464205 | + | 0.998922i | \(0.485219\pi\) | |||||||
\(632\) | −12.0804 | −0.480532 | ||||||||
\(633\) | −14.8471 | −0.590121 | ||||||||
\(634\) | 29.0834 | 1.15505 | ||||||||
\(635\) | −6.73450 | −0.267250 | ||||||||
\(636\) | −2.03385 | −0.0806475 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 10.7409 | 0.425238 | ||||||||
\(639\) | −20.9705 | −0.829579 | ||||||||
\(640\) | 1.35690 | 0.0536360 | ||||||||
\(641\) | −17.5767 | −0.694239 | −0.347120 | − | 0.937821i | \(-0.612840\pi\) | ||||
−0.347120 | + | 0.937821i | \(0.612840\pi\) | |||||||
\(642\) | 7.68963 | 0.303485 | ||||||||
\(643\) | −3.70410 | −0.146076 | −0.0730378 | − | 0.997329i | \(-0.523269\pi\) | ||||
−0.0730378 | + | 0.997329i | \(0.523269\pi\) | |||||||
\(644\) | −4.85086 | −0.191150 | ||||||||
\(645\) | 1.70841 | 0.0672688 | ||||||||
\(646\) | 10.3327 | 0.406536 | ||||||||
\(647\) | 50.4935 | 1.98510 | 0.992552 | − | 0.121823i | \(-0.0388739\pi\) | ||||
0.992552 | + | 0.121823i | \(0.0388739\pi\) | |||||||
\(648\) | 6.32304 | 0.248393 | ||||||||
\(649\) | 7.34481 | 0.288309 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.01507 | 0.0789766 | ||||||||
\(652\) | 5.25906 | 0.205961 | ||||||||
\(653\) | 33.5109 | 1.31138 | 0.655692 | − | 0.755028i | \(-0.272377\pi\) | ||||
0.655692 | + | 0.755028i | \(0.272377\pi\) | |||||||
\(654\) | −1.21014 | −0.0473204 | ||||||||
\(655\) | −15.0291 | −0.587234 | ||||||||
\(656\) | 0.0392287 | 0.00153162 | ||||||||
\(657\) | −37.9661 | −1.48120 | ||||||||
\(658\) | −10.5700 | −0.412062 | ||||||||
\(659\) | 12.8194 | 0.499373 | 0.249686 | − | 0.968327i | \(-0.419672\pi\) | ||||
0.249686 | + | 0.968327i | \(0.419672\pi\) | |||||||
\(660\) | 1.35690 | 0.0528171 | ||||||||
\(661\) | −24.3163 | −0.945796 | −0.472898 | − | 0.881117i | \(-0.656792\pi\) | ||||
−0.472898 | + | 0.881117i | \(0.656792\pi\) | |||||||
\(662\) | −7.32304 | −0.284618 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.85086 | 0.110635 | ||||||||
\(665\) | −2.64742 | −0.102662 | ||||||||
\(666\) | −20.8713 | −0.808746 | ||||||||
\(667\) | 28.9148 | 1.11959 | ||||||||
\(668\) | 14.0954 | 0.545369 | ||||||||
\(669\) | 11.4239 | 0.441672 | ||||||||
\(670\) | −3.01938 | −0.116649 | ||||||||
\(671\) | −20.7289 | −0.800229 | ||||||||
\(672\) | −0.554958 | −0.0214080 | ||||||||
\(673\) | −17.9812 | −0.693125 | −0.346562 | − | 0.938027i | \(-0.612651\pi\) | ||||
−0.346562 | + | 0.938027i | \(0.612651\pi\) | |||||||
\(674\) | −27.1618 | −1.04623 | ||||||||
\(675\) | 9.97823 | 0.384062 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.81461 | −0.0697411 | −0.0348706 | − | 0.999392i | \(-0.511102\pi\) | ||||
−0.0348706 | + | 0.999392i | \(0.511102\pi\) | |||||||
\(678\) | −9.71678 | −0.373171 | ||||||||
\(679\) | 3.64310 | 0.139810 | ||||||||
\(680\) | 7.18598 | 0.275570 | ||||||||
\(681\) | −12.3502 | −0.473260 | ||||||||
\(682\) | −6.54288 | −0.250540 | ||||||||
\(683\) | −37.9081 | −1.45051 | −0.725257 | − | 0.688478i | \(-0.758279\pi\) | ||||
−0.725257 | + | 0.688478i | \(0.758279\pi\) | |||||||
\(684\) | −5.25236 | −0.200829 | ||||||||
\(685\) | 13.9836 | 0.534286 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 9.05861 | 0.345607 | ||||||||
\(688\) | 2.26875 | 0.0864953 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3.65279 | 0.139059 | ||||||||
\(691\) | 30.0881 | 1.14461 | 0.572304 | − | 0.820042i | \(-0.306050\pi\) | ||||
0.572304 | + | 0.820042i | \(0.306050\pi\) | |||||||
\(692\) | 17.8877 | 0.679988 | ||||||||
\(693\) | 4.85086 | 0.184269 | ||||||||
\(694\) | −12.8890 | −0.489260 | ||||||||
\(695\) | 1.34050 | 0.0508482 | ||||||||
\(696\) | 3.30798 | 0.125389 | ||||||||
\(697\) | 0.207751 | 0.00786913 | ||||||||
\(698\) | −19.6732 | −0.744643 | ||||||||
\(699\) | 3.82238 | 0.144576 | ||||||||
\(700\) | 3.15883 | 0.119393 | ||||||||
\(701\) | −18.4625 | −0.697319 | −0.348660 | − | 0.937249i | \(-0.613363\pi\) | ||||
−0.348660 | + | 0.937249i | \(0.613363\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.1268 | 0.570517 | ||||||||
\(704\) | 1.80194 | 0.0679131 | ||||||||
\(705\) | 7.95944 | 0.299770 | ||||||||
\(706\) | 30.3980 | 1.14405 | ||||||||
\(707\) | −7.85086 | −0.295262 | ||||||||
\(708\) | 2.26205 | 0.0850129 | ||||||||
\(709\) | −3.07308 | −0.115412 | −0.0577060 | − | 0.998334i | \(-0.518379\pi\) | ||||
−0.0577060 | + | 0.998334i | \(0.518379\pi\) | |||||||
\(710\) | 10.5700 | 0.396686 | ||||||||
\(711\) | 32.5206 | 1.21962 | ||||||||
\(712\) | −6.61894 | −0.248055 | ||||||||
\(713\) | −17.6136 | −0.659633 | ||||||||
\(714\) | −2.93900 | −0.109989 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.0556221 | −0.00207870 | ||||||||
\(717\) | 7.86426 | 0.293696 | ||||||||
\(718\) | 2.64310 | 0.0986398 | ||||||||
\(719\) | 28.6213 | 1.06740 | 0.533698 | − | 0.845675i | \(-0.320802\pi\) | ||||
0.533698 | + | 0.845675i | \(0.320802\pi\) | |||||||
\(720\) | −3.65279 | −0.136132 | ||||||||
\(721\) | 17.0804 | 0.636106 | ||||||||
\(722\) | −15.1933 | −0.565435 | ||||||||
\(723\) | 2.17257 | 0.0807988 | ||||||||
\(724\) | −8.45042 | −0.314057 | ||||||||
\(725\) | −18.8291 | −0.699295 | ||||||||
\(726\) | −4.30260 | −0.159685 | ||||||||
\(727\) | 35.8799 | 1.33071 | 0.665356 | − | 0.746526i | \(-0.268280\pi\) | ||||
0.665356 | + | 0.746526i | \(0.268280\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.7627 | −0.435656 | ||||||||
\(730\) | 19.1366 | 0.708277 | ||||||||
\(731\) | 12.0151 | 0.444393 | ||||||||
\(732\) | −6.38404 | −0.235961 | ||||||||
\(733\) | 13.8291 | 0.510789 | 0.255394 | − | 0.966837i | \(-0.417795\pi\) | ||||
0.255394 | + | 0.966837i | \(0.417795\pi\) | |||||||
\(734\) | 2.46921 | 0.0911400 | ||||||||
\(735\) | 0.753020 | 0.0277756 | ||||||||
\(736\) | 4.85086 | 0.178805 | ||||||||
\(737\) | −4.00969 | −0.147699 | ||||||||
\(738\) | −0.105604 | −0.00388735 | ||||||||
\(739\) | 50.6262 | 1.86232 | 0.931158 | − | 0.364616i | \(-0.118800\pi\) | ||||
0.931158 | + | 0.364616i | \(0.118800\pi\) | |||||||
\(740\) | 10.5200 | 0.386724 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.66487 | 0.134542 | ||||||||
\(743\) | −36.8866 | −1.35324 | −0.676620 | − | 0.736333i | \(-0.736556\pi\) | ||||
−0.676620 | + | 0.736333i | \(0.736556\pi\) | |||||||
\(744\) | −2.01507 | −0.0738759 | ||||||||
\(745\) | −7.60712 | −0.278703 | ||||||||
\(746\) | −5.96615 | −0.218436 | ||||||||
\(747\) | −7.67456 | −0.280798 | ||||||||
\(748\) | 9.54288 | 0.348922 | ||||||||
\(749\) | −13.8562 | −0.506296 | ||||||||
\(750\) | −6.14377 | −0.224339 | ||||||||
\(751\) | −10.3556 | −0.377880 | −0.188940 | − | 0.981989i | \(-0.560505\pi\) | ||||
−0.188940 | + | 0.981989i | \(0.560505\pi\) | |||||||
\(752\) | 10.5700 | 0.385449 | ||||||||
\(753\) | 5.73423 | 0.208967 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.1532 | −0.769844 | ||||||||
\(756\) | 3.15883 | 0.114886 | ||||||||
\(757\) | 20.0234 | 0.727764 | 0.363882 | − | 0.931445i | \(-0.381451\pi\) | ||||
0.363882 | + | 0.931445i | \(0.381451\pi\) | |||||||
\(758\) | 22.0519 | 0.800961 | ||||||||
\(759\) | 4.85086 | 0.176075 | ||||||||
\(760\) | 2.64742 | 0.0960319 | ||||||||
\(761\) | 14.9694 | 0.542640 | 0.271320 | − | 0.962489i | \(-0.412540\pi\) | ||||
0.271320 | + | 0.962489i | \(0.412540\pi\) | |||||||
\(762\) | −2.75435 | −0.0997795 | ||||||||
\(763\) | 2.18060 | 0.0789432 | ||||||||
\(764\) | −4.33273 | −0.156753 | ||||||||
\(765\) | −19.3448 | −0.699413 | ||||||||
\(766\) | 26.1758 | 0.945771 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.554958 | 0.0200253 | ||||||||
\(769\) | 6.11290 | 0.220437 | 0.110218 | − | 0.993907i | \(-0.464845\pi\) | ||||
0.110218 | + | 0.993907i | \(0.464845\pi\) | |||||||
\(770\) | −2.44504 | −0.0881132 | ||||||||
\(771\) | −7.98493 | −0.287570 | ||||||||
\(772\) | −1.70410 | −0.0613320 | ||||||||
\(773\) | 21.3870 | 0.769238 | 0.384619 | − | 0.923075i | \(-0.374333\pi\) | ||||
0.384619 | + | 0.923075i | \(0.374333\pi\) | |||||||
\(774\) | −6.10752 | −0.219530 | ||||||||
\(775\) | 11.4698 | 0.412007 | ||||||||
\(776\) | −3.64310 | −0.130780 | ||||||||
\(777\) | −4.30260 | −0.154355 | ||||||||
\(778\) | −15.4655 | −0.554464 | ||||||||
\(779\) | 0.0765384 | 0.00274227 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.0368 | 0.502277 | ||||||||
\(782\) | 25.6896 | 0.918659 | ||||||||
\(783\) | −18.8291 | −0.672897 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −11.5313 | −0.411569 | ||||||||
\(786\) | −6.14675 | −0.219247 | ||||||||
\(787\) | −40.5623 | −1.44589 | −0.722944 | − | 0.690907i | \(-0.757212\pi\) | ||||
−0.722944 | + | 0.690907i | \(0.757212\pi\) | |||||||
\(788\) | −25.7700 | −0.918018 | ||||||||
\(789\) | −9.77107 | −0.347859 | ||||||||
\(790\) | −16.3918 | −0.583195 | ||||||||
\(791\) | 17.5090 | 0.622549 | ||||||||
\(792\) | −4.85086 | −0.172368 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −34.9778 | −1.24131 | ||||||||
\(795\) | −2.75973 | −0.0978774 | ||||||||
\(796\) | 6.72587 | 0.238392 | ||||||||
\(797\) | −40.6698 | −1.44060 | −0.720299 | − | 0.693664i | \(-0.755995\pi\) | ||||
−0.720299 | + | 0.693664i | \(0.755995\pi\) | |||||||
\(798\) | −1.08277 | −0.0383296 | ||||||||
\(799\) | 55.9778 | 1.98035 | ||||||||
\(800\) | −3.15883 | −0.111682 | ||||||||
\(801\) | 17.8183 | 0.629580 | ||||||||
\(802\) | −27.3739 | −0.966605 | ||||||||
\(803\) | 25.4131 | 0.896809 | ||||||||
\(804\) | −1.23490 | −0.0435515 | ||||||||
\(805\) | −6.58211 | −0.231989 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.30426 | −0.0811137 | ||||||||
\(808\) | 7.85086 | 0.276192 | ||||||||
\(809\) | −56.3666 | −1.98174 | −0.990872 | − | 0.134808i | \(-0.956958\pi\) | ||||
−0.990872 | + | 0.134808i | \(0.956958\pi\) | |||||||
\(810\) | 8.57971 | 0.301460 | ||||||||
\(811\) | 10.2397 | 0.359564 | 0.179782 | − | 0.983706i | \(-0.442461\pi\) | ||||
0.179782 | + | 0.983706i | \(0.442461\pi\) | |||||||
\(812\) | −5.96077 | −0.209182 | ||||||||
\(813\) | 9.72720 | 0.341148 | ||||||||
\(814\) | 13.9705 | 0.489664 | ||||||||
\(815\) | 7.13600 | 0.249963 | ||||||||
\(816\) | 2.93900 | 0.102886 | ||||||||
\(817\) | 4.42652 | 0.154864 | ||||||||
\(818\) | −29.0810 | −1.01679 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0532292 | 0.00185884 | ||||||||
\(821\) | −29.6219 | −1.03381 | −0.516906 | − | 0.856042i | \(-0.672916\pi\) | ||||
−0.516906 | + | 0.856042i | \(0.672916\pi\) | |||||||
\(822\) | 5.71917 | 0.199479 | ||||||||
\(823\) | −17.0804 | −0.595384 | −0.297692 | − | 0.954662i | \(-0.596217\pi\) | ||||
−0.297692 | + | 0.954662i | \(0.596217\pi\) | |||||||
\(824\) | −17.0804 | −0.595023 | ||||||||
\(825\) | −3.15883 | −0.109976 | ||||||||
\(826\) | −4.07606 | −0.141824 | ||||||||
\(827\) | −5.46575 | −0.190063 | −0.0950313 | − | 0.995474i | \(-0.530295\pi\) | ||||
−0.0950313 | + | 0.995474i | \(0.530295\pi\) | |||||||
\(828\) | −13.0586 | −0.453818 | ||||||||
\(829\) | 41.7942 | 1.45157 | 0.725786 | − | 0.687921i | \(-0.241476\pi\) | ||||
0.725786 | + | 0.687921i | \(0.241476\pi\) | |||||||
\(830\) | 3.86831 | 0.134271 | ||||||||
\(831\) | −16.6407 | −0.577260 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.29590 | 0.183492 | ||||||||
\(834\) | 0.548253 | 0.0189845 | ||||||||
\(835\) | 19.1260 | 0.661884 | ||||||||
\(836\) | 3.51573 | 0.121594 | ||||||||
\(837\) | 11.4698 | 0.396454 | ||||||||
\(838\) | −40.3086 | −1.39244 | ||||||||
\(839\) | 9.38511 | 0.324010 | 0.162005 | − | 0.986790i | \(-0.448204\pi\) | ||||
0.162005 | + | 0.986790i | \(0.448204\pi\) | |||||||
\(840\) | −0.753020 | −0.0259817 | ||||||||
\(841\) | 6.53079 | 0.225200 | ||||||||
\(842\) | 4.26981 | 0.147148 | ||||||||
\(843\) | −5.12797 | −0.176617 | ||||||||
\(844\) | −26.7536 | −0.920897 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −28.4547 | −0.978294 | ||||||||
\(847\) | 7.75302 | 0.266397 | ||||||||
\(848\) | −3.66487 | −0.125852 | ||||||||
\(849\) | 17.7748 | 0.610029 | ||||||||
\(850\) | −16.7289 | −0.573795 | ||||||||
\(851\) | 37.6088 | 1.28921 | ||||||||
\(852\) | 4.32304 | 0.148105 | ||||||||
\(853\) | 6.23623 | 0.213524 | 0.106762 | − | 0.994285i | \(-0.465952\pi\) | ||||
0.106762 | + | 0.994285i | \(0.465952\pi\) | |||||||
\(854\) | 11.5036 | 0.393647 | ||||||||
\(855\) | −7.12690 | −0.243735 | ||||||||
\(856\) | 13.8562 | 0.473596 | ||||||||
\(857\) | 50.7426 | 1.73333 | 0.866667 | − | 0.498887i | \(-0.166258\pi\) | ||||
0.866667 | + | 0.498887i | \(0.166258\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.7681 | 0.981554 | 0.490777 | − | 0.871285i | \(-0.336713\pi\) | ||||
0.490777 | + | 0.871285i | \(0.336713\pi\) | |||||||
\(860\) | 3.07846 | 0.104975 | ||||||||
\(861\) | −0.0217703 | −0.000741929 0 | ||||||||
\(862\) | −6.25475 | −0.213038 | ||||||||
\(863\) | −32.1473 | −1.09431 | −0.547154 | − | 0.837032i | \(-0.684289\pi\) | ||||
−0.547154 | + | 0.837032i | \(0.684289\pi\) | |||||||
\(864\) | −3.15883 | −0.107466 | ||||||||
\(865\) | 24.2717 | 0.825264 | ||||||||
\(866\) | −15.9705 | −0.542698 | ||||||||
\(867\) | 6.13036 | 0.208198 | ||||||||
\(868\) | 3.63102 | 0.123245 | ||||||||
\(869\) | −21.7681 | −0.738432 | ||||||||
\(870\) | 4.48858 | 0.152177 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −2.18060 | −0.0738446 | ||||||||
\(873\) | 9.80731 | 0.331927 | ||||||||
\(874\) | 9.46442 | 0.320139 | ||||||||
\(875\) | 11.0707 | 0.374258 | ||||||||
\(876\) | 7.82669 | 0.264439 | ||||||||
\(877\) | −24.5123 | −0.827721 | −0.413860 | − | 0.910340i | \(-0.635820\pi\) | ||||
−0.413860 | + | 0.910340i | \(0.635820\pi\) | |||||||
\(878\) | 30.4058 | 1.02615 | ||||||||
\(879\) | −12.3163 | −0.415420 | ||||||||
\(880\) | 2.44504 | 0.0824223 | ||||||||
\(881\) | −48.2653 | −1.62610 | −0.813050 | − | 0.582195i | \(-0.802194\pi\) | ||||
−0.813050 | + | 0.582195i | \(0.802194\pi\) | |||||||
\(882\) | −2.69202 | −0.0906451 | ||||||||
\(883\) | −44.9342 | −1.51216 | −0.756078 | − | 0.654481i | \(-0.772887\pi\) | ||||
−0.756078 | + | 0.654481i | \(0.772887\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.06936 | 0.103175 | ||||||||
\(886\) | −13.0291 | −0.437720 | ||||||||
\(887\) | 41.2610 | 1.38541 | 0.692704 | − | 0.721222i | \(-0.256419\pi\) | ||||
0.692704 | + | 0.721222i | \(0.256419\pi\) | |||||||
\(888\) | 4.30260 | 0.144386 | ||||||||
\(889\) | 4.96316 | 0.166459 | ||||||||
\(890\) | −8.98121 | −0.301051 | ||||||||
\(891\) | 11.3937 | 0.381704 | ||||||||
\(892\) | 20.5851 | 0.689240 | ||||||||
\(893\) | 20.6230 | 0.690122 | ||||||||
\(894\) | −3.11124 | −0.104056 | ||||||||
\(895\) | −0.0754734 | −0.00252280 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.2258 | 0.674944 | ||||||||
\(899\) | −21.6437 | −0.721858 | ||||||||
\(900\) | 8.50365 | 0.283455 | ||||||||
\(901\) | −19.4088 | −0.646601 | ||||||||
\(902\) | 0.0706876 | 0.00235364 | ||||||||
\(903\) | −1.25906 | −0.0418989 | ||||||||
\(904\) | −17.5090 | −0.582341 | ||||||||
\(905\) | −11.4663 | −0.381154 | ||||||||
\(906\) | −8.65146 | −0.287426 | ||||||||
\(907\) | −30.0344 | −0.997277 | −0.498639 | − | 0.866810i | \(-0.666167\pi\) | ||||
−0.498639 | + | 0.866810i | \(0.666167\pi\) | |||||||
\(908\) | −22.2543 | −0.738534 | ||||||||
\(909\) | −21.1347 | −0.700993 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.4069 | −0.510453 | −0.255226 | − | 0.966881i | \(-0.582150\pi\) | ||||
−0.255226 | + | 0.966881i | \(0.582150\pi\) | |||||||
\(912\) | 1.08277 | 0.0358541 | ||||||||
\(913\) | 5.13706 | 0.170012 | ||||||||
\(914\) | 20.5569 | 0.679961 | ||||||||
\(915\) | −8.66248 | −0.286373 | ||||||||
\(916\) | 16.3230 | 0.539329 | ||||||||
\(917\) | 11.0761 | 0.365764 | ||||||||
\(918\) | −16.7289 | −0.552135 | ||||||||
\(919\) | 21.8073 | 0.719357 | 0.359678 | − | 0.933076i | \(-0.382886\pi\) | ||||
0.359678 | + | 0.933076i | \(0.382886\pi\) | |||||||
\(920\) | 6.58211 | 0.217006 | ||||||||
\(921\) | −11.5526 | −0.380670 | ||||||||
\(922\) | −15.2513 | −0.502275 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.00000 | −0.0328976 | ||||||||
\(925\) | −24.4905 | −0.805243 | ||||||||
\(926\) | −25.3207 | −0.832088 | ||||||||
\(927\) | 45.9807 | 1.51021 | ||||||||
\(928\) | 5.96077 | 0.195672 | ||||||||
\(929\) | 38.4523 | 1.26158 | 0.630790 | − | 0.775953i | \(-0.282731\pi\) | ||||
0.630790 | + | 0.775953i | \(0.282731\pi\) | |||||||
\(930\) | −2.73423 | −0.0896591 | ||||||||
\(931\) | 1.95108 | 0.0639442 | ||||||||
\(932\) | 6.88769 | 0.225614 | ||||||||
\(933\) | 15.6407 | 0.512054 | ||||||||
\(934\) | 16.8019 | 0.549776 | ||||||||
\(935\) | 12.9487 | 0.423467 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.4669 | 1.87736 | 0.938681 | − | 0.344786i | \(-0.112048\pi\) | ||||
0.938681 | + | 0.344786i | \(0.112048\pi\) | |||||||
\(938\) | 2.22521 | 0.0726557 | ||||||||
\(939\) | 8.89307 | 0.290214 | ||||||||
\(940\) | 14.3424 | 0.467798 | ||||||||
\(941\) | 14.1347 | 0.460777 | 0.230389 | − | 0.973099i | \(-0.426000\pi\) | ||||
0.230389 | + | 0.973099i | \(0.426000\pi\) | |||||||
\(942\) | −4.71618 | −0.153662 | ||||||||
\(943\) | 0.190293 | 0.00619678 | ||||||||
\(944\) | 4.07606 | 0.132665 | ||||||||
\(945\) | 4.28621 | 0.139430 | ||||||||
\(946\) | 4.08815 | 0.132917 | ||||||||
\(947\) | 19.0858 | 0.620204 | 0.310102 | − | 0.950703i | \(-0.399637\pi\) | ||||
0.310102 | + | 0.950703i | \(0.399637\pi\) | |||||||
\(948\) | −6.70410 | −0.217739 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −6.16315 | −0.199959 | ||||||||
\(951\) | 16.1400 | 0.523377 | ||||||||
\(952\) | −5.29590 | −0.171641 | ||||||||
\(953\) | −31.9571 | −1.03519 | −0.517595 | − | 0.855626i | \(-0.673173\pi\) | ||||
−0.517595 | + | 0.855626i | \(0.673173\pi\) | |||||||
\(954\) | 9.86592 | 0.319421 | ||||||||
\(955\) | −5.87907 | −0.190242 | ||||||||
\(956\) | 14.1709 | 0.458320 | ||||||||
\(957\) | 5.96077 | 0.192684 | ||||||||
\(958\) | −27.5870 | −0.891296 | ||||||||
\(959\) | −10.3056 | −0.332785 | ||||||||
\(960\) | 0.753020 | 0.0243036 | ||||||||
\(961\) | −17.8157 | −0.574699 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −37.3013 | −1.20202 | ||||||||
\(964\) | 3.91484 | 0.126088 | ||||||||
\(965\) | −2.31229 | −0.0744353 | ||||||||
\(966\) | −2.69202 | −0.0866144 | ||||||||
\(967\) | 1.42268 | 0.0457503 | 0.0228752 | − | 0.999738i | \(-0.492718\pi\) | ||||
0.0228752 | + | 0.999738i | \(0.492718\pi\) | |||||||
\(968\) | −7.75302 | −0.249192 | ||||||||
\(969\) | 5.73423 | 0.184210 | ||||||||
\(970\) | −4.94331 | −0.158720 | ||||||||
\(971\) | −4.26742 | −0.136948 | −0.0684740 | − | 0.997653i | \(-0.521813\pi\) | ||||
−0.0684740 | + | 0.997653i | \(0.521813\pi\) | |||||||
\(972\) | 12.9855 | 0.416511 | ||||||||
\(973\) | −0.987918 | −0.0316712 | ||||||||
\(974\) | −29.4698 | −0.944273 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.5036 | −0.368223 | ||||||||
\(977\) | −23.5375 | −0.753031 | −0.376516 | − | 0.926410i | \(-0.622878\pi\) | ||||
−0.376516 | + | 0.926410i | \(0.622878\pi\) | |||||||
\(978\) | 2.91856 | 0.0933252 | ||||||||
\(979\) | −11.9269 | −0.381186 | ||||||||
\(980\) | 1.35690 | 0.0433444 | ||||||||
\(981\) | 5.87023 | 0.187422 | ||||||||
\(982\) | −8.30691 | −0.265084 | ||||||||
\(983\) | 51.9734 | 1.65770 | 0.828848 | − | 0.559474i | \(-0.188997\pi\) | ||||
0.828848 | + | 0.559474i | \(0.188997\pi\) | |||||||
\(984\) | 0.0217703 | 0.000694011 0 | ||||||||
\(985\) | −34.9672 | −1.11415 | ||||||||
\(986\) | 31.5676 | 1.00532 | ||||||||
\(987\) | −5.86592 | −0.186714 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.0054 | 0.349951 | ||||||||
\(990\) | −6.58211 | −0.209193 | ||||||||
\(991\) | −39.9332 | −1.26852 | −0.634259 | − | 0.773121i | \(-0.718695\pi\) | ||||
−0.634259 | + | 0.773121i | \(0.718695\pi\) | |||||||
\(992\) | −3.63102 | −0.115285 | ||||||||
\(993\) | −4.06398 | −0.128967 | ||||||||
\(994\) | −7.78986 | −0.247079 | ||||||||
\(995\) | 9.12631 | 0.289323 | ||||||||
\(996\) | 1.58211 | 0.0501309 | ||||||||
\(997\) | −41.4827 | −1.31377 | −0.656886 | − | 0.753990i | \(-0.728127\pi\) | ||||
−0.656886 | + | 0.753990i | \(0.728127\pi\) | |||||||
\(998\) | −42.2043 | −1.33595 | ||||||||
\(999\) | −24.4905 | −0.774845 |
(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 | 2366.2.a.bd.1.2 | yes | 3 | |
13.5 | odd | 4 | 2366.2.d.p.337.2 | 6 | |||
13.8 | odd | 4 | 2366.2.d.p.337.5 | 6 | |||
13.12 | even | 2 | 2366.2.a.y.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2366.2.a.y.1.2 | ✓ | 3 | 13.12 | even | 2 | ||
2366.2.a.bd.1.2 | yes | 3 | 1.1 | even | 1 | trivial | |
2366.2.d.p.337.2 | 6 | 13.5 | odd | 4 | |||
2366.2.d.p.337.5 | 6 | 13.8 | odd | 4 |