Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, 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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} - 42 x^{12} + 70 x^{11} + 680 x^{10} - 882 x^{9} - 5559 x^{8} + 5066 x^{7} + 24455 x^{6} - 12990 x^{5} - 55580 x^{4} + 9808 x^{3} + 53551 x^{2} + \cdots - 7083 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.53522\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-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 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.53522 | −0.686571 | −0.343285 | − | 0.939231i | \(-0.611540\pi\) | ||||
−0.343285 | + | 0.939231i | \(0.611540\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.84041 | 1.82950 | 0.914752 | − | 0.404017i | \(-0.132386\pi\) | ||||
0.914752 | + | 0.404017i | \(0.132386\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.53522 | −0.485479 | ||||||||
\(11\) | −3.93574 | −1.18667 | −0.593335 | − | 0.804956i | \(-0.702189\pi\) | ||||
−0.593335 | + | 0.804956i | \(0.702189\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.57898 | 0.992630 | 0.496315 | − | 0.868142i | \(-0.334686\pi\) | ||||
0.496315 | + | 0.868142i | \(0.334686\pi\) | |||||||
\(14\) | 4.84041 | 1.29365 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.48855 | 0.361027 | 0.180514 | − | 0.983572i | \(-0.442224\pi\) | ||||
0.180514 | + | 0.983572i | \(0.442224\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.62957 | −1.75034 | −0.875172 | − | 0.483812i | \(-0.839252\pi\) | ||||
−0.875172 | + | 0.483812i | \(0.839252\pi\) | |||||||
\(20\) | −1.53522 | −0.343285 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.93574 | −0.839102 | ||||||||
\(23\) | −5.95631 | −1.24198 | −0.620989 | − | 0.783820i | \(-0.713269\pi\) | ||||
−0.620989 | + | 0.783820i | \(0.713269\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.64310 | −0.528621 | ||||||||
\(26\) | 3.57898 | 0.701896 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.84041 | 0.914752 | ||||||||
\(29\) | 9.31666 | 1.73006 | 0.865030 | − | 0.501720i | \(-0.167299\pi\) | ||||
0.865030 | + | 0.501720i | \(0.167299\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.91650 | 0.883029 | 0.441514 | − | 0.897254i | \(-0.354441\pi\) | ||||
0.441514 | + | 0.897254i | \(0.354441\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.48855 | 0.255285 | ||||||||
\(35\) | −7.43109 | −1.25608 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.32731 | −0.218209 | −0.109105 | − | 0.994030i | \(-0.534798\pi\) | ||||
−0.109105 | + | 0.994030i | \(0.534798\pi\) | |||||||
\(38\) | −7.62957 | −1.23768 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.53522 | −0.242739 | ||||||||
\(41\) | 3.69856 | 0.577619 | 0.288809 | − | 0.957387i | \(-0.406741\pi\) | ||||
0.288809 | + | 0.957387i | \(0.406741\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.73841 | 1.33260 | 0.666298 | − | 0.745686i | \(-0.267878\pi\) | ||||
0.666298 | + | 0.745686i | \(0.267878\pi\) | |||||||
\(44\) | −3.93574 | −0.593335 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.95631 | −0.878210 | ||||||||
\(47\) | 6.61250 | 0.964532 | 0.482266 | − | 0.876025i | \(-0.339814\pi\) | ||||
0.482266 | + | 0.876025i | \(0.339814\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.4296 | 2.34708 | ||||||||
\(50\) | −2.64310 | −0.373791 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.57898 | 0.496315 | ||||||||
\(53\) | 4.60201 | 0.632134 | 0.316067 | − | 0.948737i | \(-0.397638\pi\) | ||||
0.316067 | + | 0.948737i | \(0.397638\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.04222 | 0.814733 | ||||||||
\(56\) | 4.84041 | 0.646827 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.31666 | 1.22334 | ||||||||
\(59\) | 1.97402 | 0.256996 | 0.128498 | − | 0.991710i | \(-0.458984\pi\) | ||||
0.128498 | + | 0.991710i | \(0.458984\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.88075 | −0.752953 | −0.376476 | − | 0.926426i | \(-0.622864\pi\) | ||||
−0.376476 | + | 0.926426i | \(0.622864\pi\) | |||||||
\(62\) | 4.91650 | 0.624396 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.49452 | −0.681511 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 16.0194 | 1.95708 | 0.978539 | − | 0.206060i | \(-0.0660643\pi\) | ||||
0.978539 | + | 0.206060i | \(0.0660643\pi\) | |||||||
\(68\) | 1.48855 | 0.180514 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.43109 | −0.888185 | ||||||||
\(71\) | −5.26569 | −0.624922 | −0.312461 | − | 0.949931i | \(-0.601153\pi\) | ||||
−0.312461 | + | 0.949931i | \(0.601153\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.32646 | −0.389333 | −0.194667 | − | 0.980869i | \(-0.562362\pi\) | ||||
−0.194667 | + | 0.980869i | \(0.562362\pi\) | |||||||
\(74\) | −1.32731 | −0.154297 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.62957 | −0.875172 | ||||||||
\(77\) | −19.0506 | −2.17102 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.87300 | 0.435747 | 0.217873 | − | 0.975977i | \(-0.430088\pi\) | ||||
0.217873 | + | 0.975977i | \(0.430088\pi\) | |||||||
\(80\) | −1.53522 | −0.171643 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.69856 | 0.408438 | ||||||||
\(83\) | −11.0519 | −1.21311 | −0.606554 | − | 0.795042i | \(-0.707449\pi\) | ||||
−0.606554 | + | 0.795042i | \(0.707449\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.28526 | −0.247871 | ||||||||
\(86\) | 8.73841 | 0.942287 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.93574 | −0.419551 | ||||||||
\(89\) | −12.0548 | −1.27780 | −0.638901 | − | 0.769289i | \(-0.720611\pi\) | ||||
−0.638901 | + | 0.769289i | \(0.720611\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.3237 | 1.81602 | ||||||||
\(92\) | −5.95631 | −0.620989 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.61250 | 0.682027 | ||||||||
\(95\) | 11.7131 | 1.20174 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.1315 | 1.73944 | 0.869721 | − | 0.493543i | \(-0.164299\pi\) | ||||
0.869721 | + | 0.493543i | \(0.164299\pi\) | |||||||
\(98\) | 16.4296 | 1.65964 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.64310 | −0.264310 | ||||||||
\(101\) | 17.0976 | 1.70128 | 0.850640 | − | 0.525749i | \(-0.176215\pi\) | ||||
0.850640 | + | 0.525749i | \(0.176215\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.0020 | 1.08406 | 0.542029 | − | 0.840360i | \(-0.317656\pi\) | ||||
0.542029 | + | 0.840360i | \(0.317656\pi\) | |||||||
\(104\) | 3.57898 | 0.350948 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.60201 | 0.446986 | ||||||||
\(107\) | 16.6560 | 1.61020 | 0.805098 | − | 0.593142i | \(-0.202113\pi\) | ||||
0.805098 | + | 0.593142i | \(0.202113\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.7121 | 1.12182 | 0.560908 | − | 0.827878i | \(-0.310452\pi\) | ||||
0.560908 | + | 0.827878i | \(0.310452\pi\) | |||||||
\(110\) | 6.04222 | 0.576103 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.84041 | 0.457376 | ||||||||
\(113\) | −18.4572 | −1.73631 | −0.868154 | − | 0.496296i | \(-0.834693\pi\) | ||||
−0.868154 | + | 0.496296i | \(0.834693\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.14424 | 0.852705 | ||||||||
\(116\) | 9.31666 | 0.865030 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.97402 | 0.181724 | ||||||||
\(119\) | 7.20521 | 0.660501 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.49004 | 0.408185 | ||||||||
\(122\) | −5.88075 | −0.532418 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.91650 | 0.441514 | ||||||||
\(125\) | 11.7338 | 1.04951 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.99360 | 0.886788 | 0.443394 | − | 0.896327i | \(-0.353774\pi\) | ||||
0.443394 | + | 0.896327i | \(0.353774\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.49452 | −0.481901 | ||||||||
\(131\) | −5.53861 | −0.483911 | −0.241955 | − | 0.970287i | \(-0.577789\pi\) | ||||
−0.241955 | + | 0.970287i | \(0.577789\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −36.9303 | −3.20226 | ||||||||
\(134\) | 16.0194 | 1.38386 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.48855 | 0.127642 | ||||||||
\(137\) | −15.2920 | −1.30648 | −0.653240 | − | 0.757151i | \(-0.726591\pi\) | ||||
−0.653240 | + | 0.757151i | \(0.726591\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.9007 | 1.00940 | 0.504701 | − | 0.863294i | \(-0.331603\pi\) | ||||
0.504701 | + | 0.863294i | \(0.331603\pi\) | |||||||
\(140\) | −7.43109 | −0.628042 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.26569 | −0.441887 | ||||||||
\(143\) | −14.0859 | −1.17792 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.3031 | −1.18781 | ||||||||
\(146\) | −3.32646 | −0.275300 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.32731 | −0.109105 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5282 | 0.938153 | 0.469077 | − | 0.883157i | \(-0.344587\pi\) | ||||
0.469077 | + | 0.883157i | \(0.344587\pi\) | |||||||
\(152\) | −7.62957 | −0.618840 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −19.0506 | −1.53514 | ||||||||
\(155\) | −7.54790 | −0.606262 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.4495 | −0.833959 | −0.416979 | − | 0.908916i | \(-0.636911\pi\) | ||||
−0.416979 | + | 0.908916i | \(0.636911\pi\) | |||||||
\(158\) | 3.87300 | 0.308120 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.53522 | −0.121370 | ||||||||
\(161\) | −28.8310 | −2.27220 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.36679 | −0.342033 | −0.171017 | − | 0.985268i | \(-0.554705\pi\) | ||||
−0.171017 | + | 0.985268i | \(0.554705\pi\) | |||||||
\(164\) | 3.69856 | 0.288809 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.0519 | −0.857797 | ||||||||
\(167\) | −10.7819 | −0.834332 | −0.417166 | − | 0.908830i | \(-0.636977\pi\) | ||||
−0.417166 | + | 0.908830i | \(0.636977\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.190909 | −0.0146853 | ||||||||
\(170\) | −2.28526 | −0.175271 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.73841 | 0.666298 | ||||||||
\(173\) | −7.68331 | −0.584151 | −0.292075 | − | 0.956395i | \(-0.594346\pi\) | ||||
−0.292075 | + | 0.956395i | \(0.594346\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.7937 | −0.967113 | ||||||||
\(176\) | −3.93574 | −0.296667 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.0548 | −0.903542 | ||||||||
\(179\) | 4.84781 | 0.362342 | 0.181171 | − | 0.983452i | \(-0.442011\pi\) | ||||
0.181171 | + | 0.983452i | \(0.442011\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.77213 | −0.577698 | −0.288849 | − | 0.957375i | \(-0.593273\pi\) | ||||
−0.288849 | + | 0.957375i | \(0.593273\pi\) | |||||||
\(182\) | 17.3237 | 1.28412 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.95631 | −0.439105 | ||||||||
\(185\) | 2.03772 | 0.149816 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.85856 | −0.428420 | ||||||||
\(188\) | 6.61250 | 0.482266 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 11.7131 | 0.849755 | ||||||||
\(191\) | 10.0668 | 0.728411 | 0.364206 | − | 0.931319i | \(-0.381340\pi\) | ||||
0.364206 | + | 0.931319i | \(0.381340\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.13138 | 0.0814387 | 0.0407194 | − | 0.999171i | \(-0.487035\pi\) | ||||
0.0407194 | + | 0.999171i | \(0.487035\pi\) | |||||||
\(194\) | 17.1315 | 1.22997 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 16.4296 | 1.17354 | ||||||||
\(197\) | 15.2482 | 1.08639 | 0.543195 | − | 0.839607i | \(-0.317215\pi\) | ||||
0.543195 | + | 0.839607i | \(0.317215\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.4763 | −1.30975 | −0.654875 | − | 0.755737i | \(-0.727279\pi\) | ||||
−0.654875 | + | 0.755737i | \(0.727279\pi\) | |||||||
\(200\) | −2.64310 | −0.186896 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 17.0976 | 1.20299 | ||||||||
\(203\) | 45.0965 | 3.16515 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.67810 | −0.396576 | ||||||||
\(206\) | 11.0020 | 0.766545 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.57898 | 0.248158 | ||||||||
\(209\) | 30.0280 | 2.07708 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.2464 | 1.25614 | 0.628068 | − | 0.778158i | \(-0.283846\pi\) | ||||
0.628068 | + | 0.778158i | \(0.283846\pi\) | |||||||
\(212\) | 4.60201 | 0.316067 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.6560 | 1.13858 | ||||||||
\(215\) | −13.4154 | −0.914921 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.7979 | 1.61550 | ||||||||
\(218\) | 11.7121 | 0.793244 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.04222 | 0.407366 | ||||||||
\(221\) | 5.32750 | 0.358367 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.90348 | 0.194432 | 0.0972158 | − | 0.995263i | \(-0.469006\pi\) | ||||
0.0972158 | + | 0.995263i | \(0.469006\pi\) | |||||||
\(224\) | 4.84041 | 0.323414 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.4572 | −1.22775 | ||||||||
\(227\) | −7.73421 | −0.513338 | −0.256669 | − | 0.966499i | \(-0.582625\pi\) | ||||
−0.256669 | + | 0.966499i | \(0.582625\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.4182 | −1.01886 | −0.509430 | − | 0.860512i | \(-0.670144\pi\) | ||||
−0.509430 | + | 0.860512i | \(0.670144\pi\) | |||||||
\(230\) | 9.14424 | 0.602954 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.31666 | 0.611669 | ||||||||
\(233\) | −13.8473 | −0.907167 | −0.453584 | − | 0.891214i | \(-0.649855\pi\) | ||||
−0.453584 | + | 0.891214i | \(0.649855\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.1516 | −0.662220 | ||||||||
\(236\) | 1.97402 | 0.128498 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.20521 | 0.467044 | ||||||||
\(239\) | −16.1000 | −1.04142 | −0.520710 | − | 0.853733i | \(-0.674333\pi\) | ||||
−0.520710 | + | 0.853733i | \(0.674333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.1158 | −0.909282 | −0.454641 | − | 0.890675i | \(-0.650232\pi\) | ||||
−0.454641 | + | 0.890675i | \(0.650232\pi\) | |||||||
\(242\) | 4.49004 | 0.288630 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.88075 | −0.376476 | ||||||||
\(245\) | −25.2230 | −1.61144 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −27.3061 | −1.73744 | ||||||||
\(248\) | 4.91650 | 0.312198 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.7338 | 0.742113 | ||||||||
\(251\) | 12.6088 | 0.795860 | 0.397930 | − | 0.917416i | \(-0.369729\pi\) | ||||
0.397930 | + | 0.917416i | \(0.369729\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.4425 | 1.47382 | ||||||||
\(254\) | 9.99360 | 0.627054 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.8020 | 1.23522 | 0.617609 | − | 0.786486i | \(-0.288102\pi\) | ||||
0.617609 | + | 0.786486i | \(0.288102\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.42475 | −0.399214 | ||||||||
\(260\) | −5.49452 | −0.340755 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.53861 | −0.342177 | ||||||||
\(263\) | −29.6860 | −1.83052 | −0.915259 | − | 0.402866i | \(-0.868014\pi\) | ||||
−0.915259 | + | 0.402866i | \(0.868014\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.06509 | −0.434005 | ||||||||
\(266\) | −36.9303 | −2.26434 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 16.0194 | 0.978539 | ||||||||
\(269\) | 11.7390 | 0.715739 | 0.357870 | − | 0.933772i | \(-0.383503\pi\) | ||||
0.357870 | + | 0.933772i | \(0.383503\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.34546 | 0.385459 | 0.192730 | − | 0.981252i | \(-0.438266\pi\) | ||||
0.192730 | + | 0.981252i | \(0.438266\pi\) | |||||||
\(272\) | 1.48855 | 0.0902568 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.2920 | −0.923820 | ||||||||
\(275\) | 10.4026 | 0.627298 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.59674 | 0.0959391 | 0.0479695 | − | 0.998849i | \(-0.484725\pi\) | ||||
0.0479695 | + | 0.998849i | \(0.484725\pi\) | |||||||
\(278\) | 11.9007 | 0.713755 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.43109 | −0.444093 | ||||||||
\(281\) | 9.05403 | 0.540118 | 0.270059 | − | 0.962844i | \(-0.412957\pi\) | ||||
0.270059 | + | 0.962844i | \(0.412957\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.8974 | 1.65833 | 0.829163 | − | 0.559006i | \(-0.188817\pi\) | ||||
0.829163 | + | 0.559006i | \(0.188817\pi\) | |||||||
\(284\) | −5.26569 | −0.312461 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.0859 | −0.832918 | ||||||||
\(287\) | 17.9026 | 1.05676 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.7842 | −0.869659 | ||||||||
\(290\) | −14.3031 | −0.839908 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.32646 | −0.194667 | ||||||||
\(293\) | −18.1337 | −1.05938 | −0.529690 | − | 0.848191i | \(-0.677692\pi\) | ||||
−0.529690 | + | 0.848191i | \(0.677692\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.03056 | −0.176446 | ||||||||
\(296\) | −1.32731 | −0.0771486 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | −21.3175 | −1.23282 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 42.2975 | 2.43799 | ||||||||
\(302\) | 11.5282 | 0.663375 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.62957 | −0.437586 | ||||||||
\(305\) | 9.02824 | 0.516955 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.6884 | 1.46611 | 0.733057 | − | 0.680167i | \(-0.238093\pi\) | ||||
0.733057 | + | 0.680167i | \(0.238093\pi\) | |||||||
\(308\) | −19.0506 | −1.08551 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.54790 | −0.428692 | ||||||||
\(311\) | 27.3395 | 1.55028 | 0.775141 | − | 0.631789i | \(-0.217679\pi\) | ||||
0.775141 | + | 0.631789i | \(0.217679\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.7702 | 1.28705 | 0.643524 | − | 0.765426i | \(-0.277472\pi\) | ||||
0.643524 | + | 0.765426i | \(0.277472\pi\) | |||||||
\(314\) | −10.4495 | −0.589698 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.87300 | 0.217873 | ||||||||
\(317\) | −3.03195 | −0.170291 | −0.0851457 | − | 0.996369i | \(-0.527136\pi\) | ||||
−0.0851457 | + | 0.996369i | \(0.527136\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −36.6679 | −2.05301 | ||||||||
\(320\) | −1.53522 | −0.0858213 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −28.8310 | −1.60669 | ||||||||
\(323\) | −11.3570 | −0.631922 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.45961 | −0.524725 | ||||||||
\(326\) | −4.36679 | −0.241854 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.69856 | 0.204219 | ||||||||
\(329\) | 32.0072 | 1.76462 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.5828 | −0.911472 | −0.455736 | − | 0.890115i | \(-0.650624\pi\) | ||||
−0.455736 | + | 0.890115i | \(0.650624\pi\) | |||||||
\(332\) | −11.0519 | −0.606554 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.7819 | −0.589962 | ||||||||
\(335\) | −24.5933 | −1.34367 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.3641 | −1.43614 | −0.718072 | − | 0.695969i | \(-0.754975\pi\) | ||||
−0.718072 | + | 0.695969i | \(0.754975\pi\) | |||||||
\(338\) | −0.190909 | −0.0103841 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.28526 | −0.123935 | ||||||||
\(341\) | −19.3500 | −1.04786 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 45.6430 | 2.46449 | ||||||||
\(344\) | 8.73841 | 0.471144 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.68331 | −0.413057 | ||||||||
\(347\) | 31.0644 | 1.66763 | 0.833813 | − | 0.552047i | \(-0.186153\pi\) | ||||
0.833813 | + | 0.552047i | \(0.186153\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.508899 | −0.0272407 | −0.0136204 | − | 0.999907i | \(-0.504336\pi\) | ||||
−0.0136204 | + | 0.999907i | \(0.504336\pi\) | |||||||
\(350\) | −12.7937 | −0.683852 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.93574 | −0.209776 | ||||||||
\(353\) | 2.14478 | 0.114155 | 0.0570775 | − | 0.998370i | \(-0.481822\pi\) | ||||
0.0570775 | + | 0.998370i | \(0.481822\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.08398 | 0.429053 | ||||||||
\(356\) | −12.0548 | −0.638901 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.84781 | 0.256215 | ||||||||
\(359\) | −16.8255 | −0.888013 | −0.444007 | − | 0.896023i | \(-0.646443\pi\) | ||||
−0.444007 | + | 0.896023i | \(0.646443\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.2104 | 2.06370 | ||||||||
\(362\) | −7.77213 | −0.408494 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 17.3237 | 0.908010 | ||||||||
\(365\) | 5.10685 | 0.267305 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.1270 | −1.05062 | −0.525311 | − | 0.850910i | \(-0.676051\pi\) | ||||
−0.525311 | + | 0.850910i | \(0.676051\pi\) | |||||||
\(368\) | −5.95631 | −0.310494 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.03772 | 0.105936 | ||||||||
\(371\) | 22.2756 | 1.15649 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.5674 | 1.58272 | 0.791359 | − | 0.611352i | \(-0.209374\pi\) | ||||
0.791359 | + | 0.611352i | \(0.209374\pi\) | |||||||
\(374\) | −5.85856 | −0.302939 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.61250 | 0.341014 | ||||||||
\(377\) | 33.3441 | 1.71731 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.5965 | −0.544308 | −0.272154 | − | 0.962254i | \(-0.587736\pi\) | ||||
−0.272154 | + | 0.962254i | \(0.587736\pi\) | |||||||
\(380\) | 11.7131 | 0.600868 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.0668 | 0.515065 | ||||||||
\(383\) | 32.0554 | 1.63795 | 0.818976 | − | 0.573827i | \(-0.194542\pi\) | ||||
0.818976 | + | 0.573827i | \(0.194542\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 29.2468 | 1.49056 | ||||||||
\(386\) | 1.13138 | 0.0575859 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.1315 | 0.869721 | ||||||||
\(389\) | 12.0666 | 0.611801 | 0.305900 | − | 0.952064i | \(-0.401043\pi\) | ||||
0.305900 | + | 0.952064i | \(0.401043\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.86629 | −0.448388 | ||||||||
\(392\) | 16.4296 | 0.829819 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.2482 | 0.768193 | ||||||||
\(395\) | −5.94591 | −0.299171 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.4939 | 1.58063 | 0.790316 | − | 0.612700i | \(-0.209917\pi\) | ||||
0.790316 | + | 0.612700i | \(0.209917\pi\) | |||||||
\(398\) | −18.4763 | −0.926133 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.64310 | −0.132155 | ||||||||
\(401\) | −23.3772 | −1.16740 | −0.583701 | − | 0.811969i | \(-0.698396\pi\) | ||||
−0.583701 | + | 0.811969i | \(0.698396\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.5960 | 0.876521 | ||||||||
\(404\) | 17.0976 | 0.850640 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 45.0965 | 2.23810 | ||||||||
\(407\) | 5.22396 | 0.258942 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.6283 | −1.46502 | −0.732512 | − | 0.680754i | \(-0.761652\pi\) | ||||
−0.732512 | + | 0.680754i | \(0.761652\pi\) | |||||||
\(410\) | −5.67810 | −0.280422 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.0020 | 0.542029 | ||||||||
\(413\) | 9.55509 | 0.470175 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.9672 | 0.832885 | ||||||||
\(416\) | 3.57898 | 0.175474 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 30.0280 | 1.46872 | ||||||||
\(419\) | 34.2472 | 1.67309 | 0.836543 | − | 0.547901i | \(-0.184573\pi\) | ||||
0.836543 | + | 0.547901i | \(0.184573\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.5967 | −1.34498 | −0.672490 | − | 0.740106i | \(-0.734775\pi\) | ||||
−0.672490 | + | 0.740106i | \(0.734775\pi\) | |||||||
\(422\) | 18.2464 | 0.888223 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.60201 | 0.223493 | ||||||||
\(425\) | −3.93440 | −0.190846 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.4652 | −1.37753 | ||||||||
\(428\) | 16.6560 | 0.805098 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.4154 | −0.646947 | ||||||||
\(431\) | 7.48689 | 0.360631 | 0.180315 | − | 0.983609i | \(-0.442288\pi\) | ||||
0.180315 | + | 0.983609i | \(0.442288\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.5640 | −0.747959 | −0.373979 | − | 0.927437i | \(-0.622007\pi\) | ||||
−0.373979 | + | 0.927437i | \(0.622007\pi\) | |||||||
\(434\) | 23.7979 | 1.14233 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.7121 | 0.560908 | ||||||||
\(437\) | 45.4441 | 2.17389 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.9930 | −1.09739 | −0.548697 | − | 0.836021i | \(-0.684876\pi\) | ||||
−0.548697 | + | 0.836021i | \(0.684876\pi\) | |||||||
\(440\) | 6.04222 | 0.288052 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.32750 | 0.253403 | ||||||||
\(443\) | −12.5727 | −0.597346 | −0.298673 | − | 0.954356i | \(-0.596544\pi\) | ||||
−0.298673 | + | 0.954356i | \(0.596544\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.5067 | 0.877301 | ||||||||
\(446\) | 2.90348 | 0.137484 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.84041 | 0.228688 | ||||||||
\(449\) | 0.0886056 | 0.00418156 | 0.00209078 | − | 0.999998i | \(-0.499334\pi\) | ||||
0.00209078 | + | 0.999998i | \(0.499334\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.5566 | −0.685442 | ||||||||
\(452\) | −18.4572 | −0.868154 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.73421 | −0.362985 | ||||||||
\(455\) | −26.5957 | −1.24683 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.92142 | 0.183436 | 0.0917181 | − | 0.995785i | \(-0.470764\pi\) | ||||
0.0917181 | + | 0.995785i | \(0.470764\pi\) | |||||||
\(458\) | −15.4182 | −0.720443 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.14424 | 0.426353 | ||||||||
\(461\) | −34.4851 | −1.60613 | −0.803065 | − | 0.595892i | \(-0.796799\pi\) | ||||
−0.803065 | + | 0.595892i | \(0.796799\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.1591 | −0.750978 | −0.375489 | − | 0.926827i | \(-0.622525\pi\) | ||||
−0.375489 | + | 0.926827i | \(0.622525\pi\) | |||||||
\(464\) | 9.31666 | 0.432515 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.8473 | −0.641464 | ||||||||
\(467\) | 4.05816 | 0.187789 | 0.0938946 | − | 0.995582i | \(-0.470068\pi\) | ||||
0.0938946 | + | 0.995582i | \(0.470068\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 77.5404 | 3.58048 | ||||||||
\(470\) | −10.1516 | −0.468260 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.97402 | 0.0908618 | ||||||||
\(473\) | −34.3921 | −1.58135 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 20.1657 | 0.925268 | ||||||||
\(476\) | 7.20521 | 0.330250 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −16.1000 | −0.736396 | ||||||||
\(479\) | −7.88158 | −0.360119 | −0.180059 | − | 0.983656i | \(-0.557629\pi\) | ||||
−0.180059 | + | 0.983656i | \(0.557629\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.75043 | −0.216601 | ||||||||
\(482\) | −14.1158 | −0.642959 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.49004 | 0.204093 | ||||||||
\(485\) | −26.3006 | −1.19425 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.0202 | 0.816572 | 0.408286 | − | 0.912854i | \(-0.366127\pi\) | ||||
0.408286 | + | 0.912854i | \(0.366127\pi\) | |||||||
\(488\) | −5.88075 | −0.266209 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −25.2230 | −1.13946 | ||||||||
\(491\) | 25.3709 | 1.14497 | 0.572487 | − | 0.819914i | \(-0.305979\pi\) | ||||
0.572487 | + | 0.819914i | \(0.305979\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.8683 | 0.624599 | ||||||||
\(494\) | −27.3061 | −1.22856 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.91650 | 0.220757 | ||||||||
\(497\) | −25.4881 | −1.14330 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.8660 | −1.15792 | −0.578961 | − | 0.815355i | \(-0.696542\pi\) | ||||
−0.578961 | + | 0.815355i | \(0.696542\pi\) | |||||||
\(500\) | 11.7338 | 0.524753 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.6088 | 0.562758 | ||||||||
\(503\) | −10.0085 | −0.446256 | −0.223128 | − | 0.974789i | \(-0.571627\pi\) | ||||
−0.223128 | + | 0.974789i | \(0.571627\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.2486 | −1.16805 | ||||||||
\(506\) | 23.4425 | 1.04215 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.99360 | 0.443394 | ||||||||
\(509\) | −15.4778 | −0.686041 | −0.343020 | − | 0.939328i | \(-0.611450\pi\) | ||||
−0.343020 | + | 0.939328i | \(0.611450\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.1014 | −0.712286 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 19.8020 | 0.873431 | ||||||||
\(515\) | −16.8905 | −0.744282 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.0251 | −1.14458 | ||||||||
\(518\) | −6.42475 | −0.282287 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.49452 | −0.240950 | ||||||||
\(521\) | 40.3112 | 1.76607 | 0.883033 | − | 0.469310i | \(-0.155497\pi\) | ||||
0.883033 | + | 0.469310i | \(0.155497\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.02216 | −0.307058 | −0.153529 | − | 0.988144i | \(-0.549064\pi\) | ||||
−0.153529 | + | 0.988144i | \(0.549064\pi\) | |||||||
\(524\) | −5.53861 | −0.241955 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −29.6860 | −1.29437 | ||||||||
\(527\) | 7.31847 | 0.318798 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.4777 | 0.542507 | ||||||||
\(530\) | −7.06509 | −0.306888 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −36.9303 | −1.60113 | ||||||||
\(533\) | 13.2371 | 0.573362 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.5706 | −1.10551 | ||||||||
\(536\) | 16.0194 | 0.691932 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11.7390 | 0.506104 | ||||||||
\(539\) | −64.6625 | −2.78521 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.2296 | 1.12770 | 0.563849 | − | 0.825878i | \(-0.309320\pi\) | ||||
0.563849 | + | 0.825878i | \(0.309320\pi\) | |||||||
\(542\) | 6.34546 | 0.272561 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.48855 | 0.0638212 | ||||||||
\(545\) | −17.9806 | −0.770206 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.4898 | 1.04711 | 0.523554 | − | 0.851993i | \(-0.324606\pi\) | ||||
0.523554 | + | 0.851993i | \(0.324606\pi\) | |||||||
\(548\) | −15.2920 | −0.653240 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10.4026 | 0.443567 | ||||||||
\(551\) | −71.0821 | −3.02820 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.7469 | 0.797200 | ||||||||
\(554\) | 1.59674 | 0.0678392 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.9007 | 0.504701 | ||||||||
\(557\) | 23.6287 | 1.00118 | 0.500590 | − | 0.865684i | \(-0.333116\pi\) | ||||
0.500590 | + | 0.865684i | \(0.333116\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.2746 | 1.32277 | ||||||||
\(560\) | −7.43109 | −0.314021 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.05403 | 0.381921 | ||||||||
\(563\) | 35.6583 | 1.50282 | 0.751409 | − | 0.659837i | \(-0.229375\pi\) | ||||
0.751409 | + | 0.659837i | \(0.229375\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.3358 | 1.19210 | ||||||||
\(566\) | 27.8974 | 1.17261 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.26569 | −0.220943 | ||||||||
\(569\) | 4.39468 | 0.184234 | 0.0921172 | − | 0.995748i | \(-0.470637\pi\) | ||||
0.0921172 | + | 0.995748i | \(0.470637\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.2049 | −1.30588 | −0.652942 | − | 0.757408i | \(-0.726465\pi\) | ||||
−0.652942 | + | 0.757408i | \(0.726465\pi\) | |||||||
\(572\) | −14.0859 | −0.588962 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 17.9026 | 0.747239 | ||||||||
\(575\) | 15.7431 | 0.656535 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.0890 | −0.877948 | −0.438974 | − | 0.898500i | \(-0.644658\pi\) | ||||
−0.438974 | + | 0.898500i | \(0.644658\pi\) | |||||||
\(578\) | −14.7842 | −0.614942 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −14.3031 | −0.593904 | ||||||||
\(581\) | −53.4960 | −2.21939 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.1123 | −0.750135 | ||||||||
\(584\) | −3.32646 | −0.137650 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.1337 | −0.749095 | ||||||||
\(587\) | −5.57862 | −0.230254 | −0.115127 | − | 0.993351i | \(-0.536728\pi\) | ||||
−0.115127 | + | 0.993351i | \(0.536728\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −37.5108 | −1.54560 | ||||||||
\(590\) | −3.03056 | −0.124766 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.32731 | −0.0545523 | ||||||||
\(593\) | 30.1775 | 1.23924 | 0.619621 | − | 0.784901i | \(-0.287286\pi\) | ||||
0.619621 | + | 0.784901i | \(0.287286\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.0616 | −0.453480 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −21.3175 | −0.871738 | ||||||||
\(599\) | −20.3036 | −0.829582 | −0.414791 | − | 0.909917i | \(-0.636145\pi\) | ||||
−0.414791 | + | 0.909917i | \(0.636145\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.3118 | −0.787747 | −0.393873 | − | 0.919165i | \(-0.628865\pi\) | ||||
−0.393873 | + | 0.919165i | \(0.628865\pi\) | |||||||
\(602\) | 42.2975 | 1.72392 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.5282 | 0.469077 | ||||||||
\(605\) | −6.89319 | −0.280248 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.3632 | 0.461220 | 0.230610 | − | 0.973046i | \(-0.425928\pi\) | ||||
0.230610 | + | 0.973046i | \(0.425928\pi\) | |||||||
\(608\) | −7.62957 | −0.309420 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.02824 | 0.365543 | ||||||||
\(611\) | 23.6660 | 0.957424 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.8732 | −1.48930 | −0.744648 | − | 0.667458i | \(-0.767383\pi\) | ||||
−0.744648 | + | 0.667458i | \(0.767383\pi\) | |||||||
\(614\) | 25.6884 | 1.03670 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −19.0506 | −0.767570 | ||||||||
\(617\) | 29.6642 | 1.19424 | 0.597119 | − | 0.802153i | \(-0.296312\pi\) | ||||
0.597119 | + | 0.802153i | \(0.296312\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.6706 | 0.509273 | 0.254636 | − | 0.967037i | \(-0.418044\pi\) | ||||
0.254636 | + | 0.967037i | \(0.418044\pi\) | |||||||
\(620\) | −7.54790 | −0.303131 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 27.3395 | 1.09621 | ||||||||
\(623\) | −58.3500 | −2.33774 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.79849 | −0.191940 | ||||||||
\(626\) | 22.7702 | 0.910080 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.4495 | −0.416979 | ||||||||
\(629\) | −1.97578 | −0.0787795 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.79223 | 0.310204 | 0.155102 | − | 0.987898i | \(-0.450429\pi\) | ||||
0.155102 | + | 0.987898i | \(0.450429\pi\) | |||||||
\(632\) | 3.87300 | 0.154060 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.03195 | −0.120414 | ||||||||
\(635\) | −15.3424 | −0.608843 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 58.8011 | 2.32978 | ||||||||
\(638\) | −36.6679 | −1.45170 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.53522 | −0.0606849 | ||||||||
\(641\) | −11.8471 | −0.467933 | −0.233966 | − | 0.972245i | \(-0.575171\pi\) | ||||
−0.233966 | + | 0.972245i | \(0.575171\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.4248 | −0.687168 | −0.343584 | − | 0.939122i | \(-0.611641\pi\) | ||||
−0.343584 | + | 0.939122i | \(0.611641\pi\) | |||||||
\(644\) | −28.8310 | −1.13610 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.3570 | −0.446836 | ||||||||
\(647\) | −21.0722 | −0.828433 | −0.414216 | − | 0.910178i | \(-0.635944\pi\) | ||||
−0.414216 | + | 0.910178i | \(0.635944\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.76924 | −0.304969 | ||||||||
\(650\) | −9.45961 | −0.371036 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.36679 | −0.171017 | ||||||||
\(653\) | −5.61278 | −0.219645 | −0.109823 | − | 0.993951i | \(-0.535028\pi\) | ||||
−0.109823 | + | 0.993951i | \(0.535028\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.50298 | 0.332239 | ||||||||
\(656\) | 3.69856 | 0.144405 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 32.0072 | 1.24777 | ||||||||
\(659\) | −34.1742 | −1.33124 | −0.665618 | − | 0.746293i | \(-0.731832\pi\) | ||||
−0.665618 | + | 0.746293i | \(0.731832\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.1521 | 0.744930 | 0.372465 | − | 0.928046i | \(-0.378513\pi\) | ||||
0.372465 | + | 0.928046i | \(0.378513\pi\) | |||||||
\(662\) | −16.5828 | −0.644508 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.0519 | −0.428899 | ||||||||
\(665\) | 56.6960 | 2.19858 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −55.4929 | −2.14870 | ||||||||
\(668\) | −10.7819 | −0.417166 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −24.5933 | −0.950120 | ||||||||
\(671\) | 23.1451 | 0.893507 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.2834 | 1.55281 | 0.776405 | − | 0.630235i | \(-0.217041\pi\) | ||||
0.776405 | + | 0.630235i | \(0.217041\pi\) | |||||||
\(674\) | −26.3641 | −1.01551 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.190909 | −0.00734266 | ||||||||
\(677\) | −18.5612 | −0.713365 | −0.356682 | − | 0.934226i | \(-0.616092\pi\) | ||||
−0.356682 | + | 0.934226i | \(0.616092\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 82.9236 | 3.18232 | ||||||||
\(680\) | −2.28526 | −0.0876356 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −19.3500 | −0.740951 | ||||||||
\(683\) | 3.26406 | 0.124896 | 0.0624478 | − | 0.998048i | \(-0.480109\pi\) | ||||
0.0624478 | + | 0.998048i | \(0.480109\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.4765 | 0.896991 | ||||||||
\(686\) | 45.6430 | 1.74266 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.73841 | 0.333149 | ||||||||
\(689\) | 16.4705 | 0.627476 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.6155 | −0.670124 | −0.335062 | − | 0.942196i | \(-0.608757\pi\) | ||||
−0.335062 | + | 0.942196i | \(0.608757\pi\) | |||||||
\(692\) | −7.68331 | −0.292075 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31.0644 | 1.17919 | ||||||||
\(695\) | −18.2701 | −0.693025 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.50551 | 0.208536 | ||||||||
\(698\) | −0.508899 | −0.0192621 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12.7937 | −0.483557 | ||||||||
\(701\) | −8.52564 | −0.322009 | −0.161005 | − | 0.986954i | \(-0.551473\pi\) | ||||
−0.161005 | + | 0.986954i | \(0.551473\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.1268 | 0.381941 | ||||||||
\(704\) | −3.93574 | −0.148334 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.14478 | 0.0807198 | ||||||||
\(707\) | 82.7596 | 3.11250 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.4327 | −0.579589 | −0.289794 | − | 0.957089i | \(-0.593587\pi\) | ||||
−0.289794 | + | 0.957089i | \(0.593587\pi\) | |||||||
\(710\) | 8.08398 | 0.303386 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.0548 | −0.451771 | ||||||||
\(713\) | −29.2842 | −1.09670 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.6250 | 0.808728 | ||||||||
\(716\) | 4.84781 | 0.181171 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −16.8255 | −0.627920 | ||||||||
\(719\) | −22.2668 | −0.830412 | −0.415206 | − | 0.909727i | \(-0.636290\pi\) | ||||
−0.415206 | + | 0.909727i | \(0.636290\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 53.2541 | 1.98329 | ||||||||
\(722\) | 39.2104 | 1.45926 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.77213 | −0.288849 | ||||||||
\(725\) | −24.6249 | −0.914546 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.5429 | −0.576453 | −0.288226 | − | 0.957562i | \(-0.593066\pi\) | ||||
−0.288226 | + | 0.957562i | \(0.593066\pi\) | |||||||
\(728\) | 17.3237 | 0.642060 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.10685 | 0.189013 | ||||||||
\(731\) | 13.0076 | 0.481103 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.75452 | 0.212548 | 0.106274 | − | 0.994337i | \(-0.466108\pi\) | ||||
0.106274 | + | 0.994337i | \(0.466108\pi\) | |||||||
\(734\) | −20.1270 | −0.742902 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.95631 | −0.219553 | ||||||||
\(737\) | −63.0481 | −2.32241 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.1581 | 1.10938 | 0.554691 | − | 0.832056i | \(-0.312836\pi\) | ||||
0.554691 | + | 0.832056i | \(0.312836\pi\) | |||||||
\(740\) | 2.03772 | 0.0749080 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 22.2756 | 0.817763 | ||||||||
\(743\) | −48.8293 | −1.79137 | −0.895687 | − | 0.444686i | \(-0.853315\pi\) | ||||
−0.895687 | + | 0.444686i | \(0.853315\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.53522 | −0.0562461 | ||||||||
\(746\) | 30.5674 | 1.11915 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.85856 | −0.214210 | ||||||||
\(749\) | 80.6219 | 2.94586 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −50.0249 | −1.82543 | −0.912717 | − | 0.408593i | \(-0.866020\pi\) | ||||
−0.912717 | + | 0.408593i | \(0.866020\pi\) | |||||||
\(752\) | 6.61250 | 0.241133 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 33.3441 | 1.21432 | ||||||||
\(755\) | −17.6983 | −0.644109 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.2400 | −0.626600 | −0.313300 | − | 0.949654i | \(-0.601434\pi\) | ||||
−0.313300 | + | 0.949654i | \(0.601434\pi\) | |||||||
\(758\) | −10.5965 | −0.384884 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 11.7131 | 0.424878 | ||||||||
\(761\) | −29.2370 | −1.05984 | −0.529920 | − | 0.848048i | \(-0.677778\pi\) | ||||
−0.529920 | + | 0.848048i | \(0.677778\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 56.6914 | 2.05237 | ||||||||
\(764\) | 10.0668 | 0.364206 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.0554 | 1.15821 | ||||||||
\(767\) | 7.06499 | 0.255102 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.5756 | 0.489549 | 0.244775 | − | 0.969580i | \(-0.421286\pi\) | ||||
0.244775 | + | 0.969580i | \(0.421286\pi\) | |||||||
\(770\) | 29.2468 | 1.05398 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.13138 | 0.0407194 | ||||||||
\(773\) | −38.1780 | −1.37317 | −0.686583 | − | 0.727051i | \(-0.740890\pi\) | ||||
−0.686583 | + | 0.727051i | \(0.740890\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.9948 | −0.466787 | ||||||||
\(776\) | 17.1315 | 0.614986 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.0666 | 0.432608 | ||||||||
\(779\) | −28.2185 | −1.01103 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.7244 | 0.741576 | ||||||||
\(782\) | −8.86629 | −0.317058 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 16.4296 | 0.586771 | ||||||||
\(785\) | 16.0422 | 0.572572 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.6175 | −0.556705 | −0.278352 | − | 0.960479i | \(-0.589788\pi\) | ||||
−0.278352 | + | 0.960479i | \(0.589788\pi\) | |||||||
\(788\) | 15.2482 | 0.543195 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.94591 | −0.211546 | ||||||||
\(791\) | −89.3404 | −3.17658 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.0471 | −0.747404 | ||||||||
\(794\) | 31.4939 | 1.11768 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.4763 | −0.654875 | ||||||||
\(797\) | 40.5208 | 1.43532 | 0.717660 | − | 0.696393i | \(-0.245213\pi\) | ||||
0.717660 | + | 0.696393i | \(0.245213\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.84306 | 0.348223 | ||||||||
\(800\) | −2.64310 | −0.0934478 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −23.3772 | −0.825478 | ||||||||
\(803\) | 13.0921 | 0.462010 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 44.2619 | 1.56003 | ||||||||
\(806\) | 17.5960 | 0.619794 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 17.0976 | 0.601493 | ||||||||
\(809\) | 2.58457 | 0.0908687 | 0.0454343 | − | 0.998967i | \(-0.485533\pi\) | ||||
0.0454343 | + | 0.998967i | \(0.485533\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.29140 | −0.326265 | −0.163133 | − | 0.986604i | \(-0.552160\pi\) | ||||
−0.163133 | + | 0.986604i | \(0.552160\pi\) | |||||||
\(812\) | 45.0965 | 1.58258 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.22396 | 0.183100 | ||||||||
\(815\) | 6.70398 | 0.234830 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −66.6704 | −2.33250 | ||||||||
\(818\) | −29.6283 | −1.03593 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.67810 | −0.198288 | ||||||||
\(821\) | 38.5886 | 1.34675 | 0.673376 | − | 0.739300i | \(-0.264843\pi\) | ||||
0.673376 | + | 0.739300i | \(0.264843\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.03255 | −0.279997 | −0.139999 | − | 0.990152i | \(-0.544710\pi\) | ||||
−0.139999 | + | 0.990152i | \(0.544710\pi\) | |||||||
\(824\) | 11.0020 | 0.383272 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.55509 | 0.332464 | ||||||||
\(827\) | 6.72217 | 0.233753 | 0.116876 | − | 0.993146i | \(-0.462712\pi\) | ||||
0.116876 | + | 0.993146i | \(0.462712\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −54.1155 | −1.87951 | −0.939754 | − | 0.341852i | \(-0.888946\pi\) | ||||
−0.939754 | + | 0.341852i | \(0.888946\pi\) | |||||||
\(830\) | 16.9672 | 0.588939 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.57898 | 0.124079 | ||||||||
\(833\) | 24.4563 | 0.847361 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.5526 | 0.572828 | ||||||||
\(836\) | 30.0280 | 1.03854 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 34.2472 | 1.18305 | ||||||||
\(839\) | 32.5525 | 1.12384 | 0.561918 | − | 0.827193i | \(-0.310064\pi\) | ||||
0.561918 | + | 0.827193i | \(0.310064\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57.8002 | 1.99311 | ||||||||
\(842\) | −27.5967 | −0.951044 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.2464 | 0.628068 | ||||||||
\(845\) | 0.293087 | 0.0100825 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.7336 | 0.746776 | ||||||||
\(848\) | 4.60201 | 0.158034 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.93440 | −0.134949 | ||||||||
\(851\) | 7.90590 | 0.271011 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −53.9351 | −1.84670 | −0.923351 | − | 0.383957i | \(-0.874561\pi\) | ||||
−0.923351 | + | 0.383957i | \(0.874561\pi\) | |||||||
\(854\) | −28.4652 | −0.974061 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.6560 | 0.569290 | ||||||||
\(857\) | 11.2590 | 0.384601 | 0.192301 | − | 0.981336i | \(-0.438405\pi\) | ||||
0.192301 | + | 0.981336i | \(0.438405\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.1537 | 1.19943 | 0.599714 | − | 0.800214i | \(-0.295281\pi\) | ||||
0.599714 | + | 0.800214i | \(0.295281\pi\) | |||||||
\(860\) | −13.4154 | −0.457461 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.48689 | 0.255004 | ||||||||
\(863\) | 19.4504 | 0.662100 | 0.331050 | − | 0.943613i | \(-0.392597\pi\) | ||||
0.331050 | + | 0.943613i | \(0.392597\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.7956 | 0.401061 | ||||||||
\(866\) | −15.5640 | −0.528887 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 23.7979 | 0.807752 | ||||||||
\(869\) | −15.2431 | −0.517088 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 57.3330 | 1.94266 | ||||||||
\(872\) | 11.7121 | 0.396622 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 45.4441 | 1.53717 | ||||||||
\(875\) | 56.7966 | 1.92008 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.0014 | −1.38452 | −0.692260 | − | 0.721648i | \(-0.743385\pi\) | ||||
−0.692260 | + | 0.721648i | \(0.743385\pi\) | |||||||
\(878\) | −22.9930 | −0.775975 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.04222 | 0.203683 | ||||||||
\(881\) | −18.5960 | −0.626516 | −0.313258 | − | 0.949668i | \(-0.601420\pi\) | ||||
−0.313258 | + | 0.949668i | \(0.601420\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.4135 | 0.956191 | 0.478096 | − | 0.878308i | \(-0.341327\pi\) | ||||
0.478096 | + | 0.878308i | \(0.341327\pi\) | |||||||
\(884\) | 5.32750 | 0.179183 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.5727 | −0.422387 | ||||||||
\(887\) | 7.21603 | 0.242290 | 0.121145 | − | 0.992635i | \(-0.461343\pi\) | ||||
0.121145 | + | 0.992635i | \(0.461343\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 48.3731 | 1.62238 | ||||||||
\(890\) | 18.5067 | 0.620346 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.90348 | 0.0972158 | ||||||||
\(893\) | −50.4506 | −1.68826 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.44245 | −0.248774 | ||||||||
\(896\) | 4.84041 | 0.161707 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.0886056 | 0.00295681 | ||||||||
\(899\) | 45.8053 | 1.52769 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.85034 | 0.228218 | ||||||||
\(902\) | −14.5566 | −0.484681 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.4572 | −0.613877 | ||||||||
\(905\) | 11.9319 | 0.396631 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.2991 | 0.441590 | 0.220795 | − | 0.975320i | \(-0.429135\pi\) | ||||
0.220795 | + | 0.975320i | \(0.429135\pi\) | |||||||
\(908\) | −7.73421 | −0.256669 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −26.5957 | −0.881639 | ||||||||
\(911\) | −21.0959 | −0.698939 | −0.349470 | − | 0.936948i | \(-0.613638\pi\) | ||||
−0.349470 | + | 0.936948i | \(0.613638\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43.4976 | 1.43956 | ||||||||
\(914\) | 3.92142 | 0.129709 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.4182 | −0.509430 | ||||||||
\(917\) | −26.8092 | −0.885316 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.9407 | −1.35051 | −0.675255 | − | 0.737585i | \(-0.735966\pi\) | ||||
−0.675255 | + | 0.737585i | \(0.735966\pi\) | |||||||
\(920\) | 9.14424 | 0.301477 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −34.4851 | −1.13571 | ||||||||
\(923\) | −18.8458 | −0.620316 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.50823 | 0.115350 | ||||||||
\(926\) | −16.1591 | −0.531021 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.31666 | 0.305834 | ||||||||
\(929\) | −22.9216 | −0.752032 | −0.376016 | − | 0.926613i | \(-0.622706\pi\) | ||||
−0.376016 | + | 0.926613i | \(0.622706\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −125.351 | −4.10820 | ||||||||
\(932\) | −13.8473 | −0.453584 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.05816 | 0.132787 | ||||||||
\(935\) | 8.99417 | 0.294141 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.5872 | 0.803228 | 0.401614 | − | 0.915809i | \(-0.368449\pi\) | ||||
0.401614 | + | 0.915809i | \(0.368449\pi\) | |||||||
\(938\) | 77.5404 | 2.53178 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.1516 | −0.331110 | ||||||||
\(941\) | −38.8014 | −1.26489 | −0.632445 | − | 0.774605i | \(-0.717949\pi\) | ||||
−0.632445 | + | 0.774605i | \(0.717949\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.0298 | −0.717389 | ||||||||
\(944\) | 1.97402 | 0.0642490 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34.3921 | −1.11818 | ||||||||
\(947\) | −19.0565 | −0.619254 | −0.309627 | − | 0.950858i | \(-0.600204\pi\) | ||||
−0.309627 | + | 0.950858i | \(0.600204\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.9053 | −0.386464 | ||||||||
\(950\) | 20.1657 | 0.654263 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.20521 | 0.233522 | ||||||||
\(953\) | −5.14649 | −0.166711 | −0.0833557 | − | 0.996520i | \(-0.526564\pi\) | ||||
−0.0833557 | + | 0.996520i | \(0.526564\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.4548 | −0.500106 | ||||||||
\(956\) | −16.1000 | −0.520710 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.88158 | −0.254642 | ||||||||
\(959\) | −74.0193 | −2.39021 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.82806 | −0.220260 | ||||||||
\(962\) | −4.75043 | −0.153160 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.1158 | −0.454641 | ||||||||
\(965\) | −1.73692 | −0.0559134 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.2541 | 1.03722 | 0.518610 | − | 0.855011i | \(-0.326450\pi\) | ||||
0.518610 | + | 0.855011i | \(0.326450\pi\) | |||||||
\(968\) | 4.49004 | 0.144315 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −26.3006 | −0.844463 | ||||||||
\(971\) | −10.7708 | −0.345650 | −0.172825 | − | 0.984953i | \(-0.555290\pi\) | ||||
−0.172825 | + | 0.984953i | \(0.555290\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 57.6041 | 1.84670 | ||||||||
\(974\) | 18.0202 | 0.577404 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.88075 | −0.188238 | ||||||||
\(977\) | −28.3306 | −0.906378 | −0.453189 | − | 0.891415i | \(-0.649714\pi\) | ||||
−0.453189 | + | 0.891415i | \(0.649714\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 47.4444 | 1.51633 | ||||||||
\(980\) | −25.2230 | −0.805719 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 25.3709 | 0.809618 | ||||||||
\(983\) | 52.4704 | 1.67354 | 0.836772 | − | 0.547551i | \(-0.184440\pi\) | ||||
0.836772 | + | 0.547551i | \(0.184440\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.4093 | −0.745883 | ||||||||
\(986\) | 13.8683 | 0.441658 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −27.3061 | −0.868722 | ||||||||
\(989\) | −52.0487 | −1.65505 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.99379 | 0.158633 | 0.0793165 | − | 0.996849i | \(-0.474726\pi\) | ||||
0.0793165 | + | 0.996849i | \(0.474726\pi\) | |||||||
\(992\) | 4.91650 | 0.156099 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −25.4881 | −0.808433 | ||||||||
\(995\) | 28.3652 | 0.899236 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.97773 | −0.315998 | −0.157999 | − | 0.987439i | \(-0.550504\pi\) | ||||
−0.157999 | + | 0.987439i | \(0.550504\pi\) | |||||||
\(998\) | −25.8660 | −0.818775 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8046.2.a.r.1.5 | yes | 14 | |
3.2 | odd | 2 | 8046.2.a.q.1.10 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.q.1.10 | ✓ | 14 | 3.2 | odd | 2 | ||
8046.2.a.r.1.5 | yes | 14 | 1.1 | even | 1 | trivial |