Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1477718538\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 21x^{5} + 39x^{4} + 89x^{3} - 100x^{2} - 96x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.777182\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.777182 | 0.347566 | 0.173783 | − | 0.984784i | \(-0.444401\pi\) | ||||
0.173783 | + | 0.984784i | \(0.444401\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −3.79435 | −1.43413 | −0.717065 | − | 0.697006i | \(-0.754515\pi\) | ||||
−0.717065 | + | 0.697006i | \(0.754515\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.777182 | −0.245767 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −0.829389 | −0.230031 | −0.115016 | − | 0.993364i | \(-0.536692\pi\) | ||||
−0.115016 | + | 0.993364i | \(0.536692\pi\) | |||||||
\(14\) | 3.79435 | 1.01408 | ||||||||
\(15\) | −0.777182 | −0.200668 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.42418 | 1.55809 | 0.779046 | − | 0.626967i | \(-0.215704\pi\) | ||||
0.779046 | + | 0.626967i | \(0.215704\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 3.39222 | 0.778228 | 0.389114 | − | 0.921190i | \(-0.372781\pi\) | ||||
0.389114 | + | 0.921190i | \(0.372781\pi\) | |||||||
\(20\) | 0.777182 | 0.173783 | ||||||||
\(21\) | 3.79435 | 0.827995 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −5.59479 | −1.16659 | −0.583297 | − | 0.812259i | \(-0.698238\pi\) | ||||
−0.583297 | + | 0.812259i | \(0.698238\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.39599 | −0.879198 | ||||||||
\(26\) | 0.829389 | 0.162656 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.79435 | −0.717065 | ||||||||
\(29\) | −0.688882 | −0.127922 | −0.0639611 | − | 0.997952i | \(-0.520373\pi\) | ||||
−0.0639611 | + | 0.997952i | \(0.520373\pi\) | |||||||
\(30\) | 0.777182 | 0.141893 | ||||||||
\(31\) | −2.26002 | −0.405911 | −0.202956 | − | 0.979188i | \(-0.565055\pi\) | ||||
−0.202956 | + | 0.979188i | \(0.565055\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −6.42418 | −1.10174 | ||||||||
\(35\) | −2.94890 | −0.498455 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.5891 | 1.74084 | 0.870418 | − | 0.492313i | \(-0.163848\pi\) | ||||
0.870418 | + | 0.492313i | \(0.163848\pi\) | |||||||
\(38\) | −3.39222 | −0.550290 | ||||||||
\(39\) | 0.829389 | 0.132808 | ||||||||
\(40\) | −0.777182 | −0.122883 | ||||||||
\(41\) | −1.80120 | −0.281300 | −0.140650 | − | 0.990059i | \(-0.544919\pi\) | ||||
−0.140650 | + | 0.990059i | \(0.544919\pi\) | |||||||
\(42\) | −3.79435 | −0.585481 | ||||||||
\(43\) | 1.23959 | 0.189036 | 0.0945179 | − | 0.995523i | \(-0.469869\pi\) | ||||
0.0945179 | + | 0.995523i | \(0.469869\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0.777182 | 0.115855 | ||||||||
\(46\) | 5.59479 | 0.824907 | ||||||||
\(47\) | 9.85707 | 1.43780 | 0.718901 | − | 0.695113i | \(-0.244646\pi\) | ||||
0.718901 | + | 0.695113i | \(0.244646\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 7.39710 | 1.05673 | ||||||||
\(50\) | 4.39599 | 0.621687 | ||||||||
\(51\) | −6.42418 | −0.899565 | ||||||||
\(52\) | −0.829389 | −0.115016 | ||||||||
\(53\) | 7.46497 | 1.02539 | 0.512696 | − | 0.858570i | \(-0.328647\pi\) | ||||
0.512696 | + | 0.858570i | \(0.328647\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −0.777182 | −0.104795 | ||||||||
\(56\) | 3.79435 | 0.507041 | ||||||||
\(57\) | −3.39222 | −0.449310 | ||||||||
\(58\) | 0.688882 | 0.0904547 | ||||||||
\(59\) | −3.77758 | −0.491799 | −0.245899 | − | 0.969295i | \(-0.579083\pi\) | ||||
−0.245899 | + | 0.969295i | \(0.579083\pi\) | |||||||
\(60\) | −0.777182 | −0.100334 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 2.26002 | 0.287023 | ||||||||
\(63\) | −3.79435 | −0.478043 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.644586 | −0.0799510 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | −8.84367 | −1.08043 | −0.540213 | − | 0.841528i | \(-0.681656\pi\) | ||||
−0.540213 | + | 0.841528i | \(0.681656\pi\) | |||||||
\(68\) | 6.42418 | 0.779046 | ||||||||
\(69\) | 5.59479 | 0.673533 | ||||||||
\(70\) | 2.94890 | 0.352461 | ||||||||
\(71\) | −5.68617 | −0.674824 | −0.337412 | − | 0.941357i | \(-0.609552\pi\) | ||||
−0.337412 | + | 0.941357i | \(0.609552\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 0.226192 | 0.0264737 | 0.0132369 | − | 0.999912i | \(-0.495786\pi\) | ||||
0.0132369 | + | 0.999912i | \(0.495786\pi\) | |||||||
\(74\) | −10.5891 | −1.23096 | ||||||||
\(75\) | 4.39599 | 0.507605 | ||||||||
\(76\) | 3.39222 | 0.389114 | ||||||||
\(77\) | 3.79435 | 0.432406 | ||||||||
\(78\) | −0.829389 | −0.0939098 | ||||||||
\(79\) | −10.5300 | −1.18472 | −0.592361 | − | 0.805673i | \(-0.701804\pi\) | ||||
−0.592361 | + | 0.805673i | \(0.701804\pi\) | |||||||
\(80\) | 0.777182 | 0.0868916 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.80120 | 0.198909 | ||||||||
\(83\) | 10.7814 | 1.18341 | 0.591704 | − | 0.806155i | \(-0.298455\pi\) | ||||
0.591704 | + | 0.806155i | \(0.298455\pi\) | |||||||
\(84\) | 3.79435 | 0.413998 | ||||||||
\(85\) | 4.99276 | 0.541540 | ||||||||
\(86\) | −1.23959 | −0.133668 | ||||||||
\(87\) | 0.688882 | 0.0738559 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −4.99276 | −0.529231 | −0.264616 | − | 0.964354i | \(-0.585245\pi\) | ||||
−0.264616 | + | 0.964354i | \(0.585245\pi\) | |||||||
\(90\) | −0.777182 | −0.0819222 | ||||||||
\(91\) | 3.14699 | 0.329894 | ||||||||
\(92\) | −5.59479 | −0.583297 | ||||||||
\(93\) | 2.26002 | 0.234353 | ||||||||
\(94\) | −9.85707 | −1.01668 | ||||||||
\(95\) | 2.63637 | 0.270486 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 2.45363 | 0.249128 | 0.124564 | − | 0.992212i | \(-0.460247\pi\) | ||||
0.124564 | + | 0.992212i | \(0.460247\pi\) | |||||||
\(98\) | −7.39710 | −0.747219 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −4.39599 | −0.439599 | ||||||||
\(101\) | 1.13546 | 0.112982 | 0.0564912 | − | 0.998403i | \(-0.482009\pi\) | ||||
0.0564912 | + | 0.998403i | \(0.482009\pi\) | |||||||
\(102\) | 6.42418 | 0.636088 | ||||||||
\(103\) | 10.7380 | 1.05804 | 0.529021 | − | 0.848609i | \(-0.322559\pi\) | ||||
0.529021 | + | 0.848609i | \(0.322559\pi\) | |||||||
\(104\) | 0.829389 | 0.0813282 | ||||||||
\(105\) | 2.94890 | 0.287783 | ||||||||
\(106\) | −7.46497 | −0.725062 | ||||||||
\(107\) | −11.3332 | −1.09562 | −0.547809 | − | 0.836603i | \(-0.684538\pi\) | ||||
−0.547809 | + | 0.836603i | \(0.684538\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −6.58859 | −0.631072 | −0.315536 | − | 0.948914i | \(-0.602184\pi\) | ||||
−0.315536 | + | 0.948914i | \(0.602184\pi\) | |||||||
\(110\) | 0.777182 | 0.0741014 | ||||||||
\(111\) | −10.5891 | −1.00507 | ||||||||
\(112\) | −3.79435 | −0.358532 | ||||||||
\(113\) | −8.50905 | −0.800464 | −0.400232 | − | 0.916414i | \(-0.631070\pi\) | ||||
−0.400232 | + | 0.916414i | \(0.631070\pi\) | |||||||
\(114\) | 3.39222 | 0.317710 | ||||||||
\(115\) | −4.34817 | −0.405469 | ||||||||
\(116\) | −0.688882 | −0.0639611 | ||||||||
\(117\) | −0.829389 | −0.0766770 | ||||||||
\(118\) | 3.77758 | 0.347754 | ||||||||
\(119\) | −24.3756 | −2.23451 | ||||||||
\(120\) | 0.777182 | 0.0709467 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.00000 | 0.0905357 | ||||||||
\(123\) | 1.80120 | 0.162409 | ||||||||
\(124\) | −2.26002 | −0.202956 | ||||||||
\(125\) | −7.30239 | −0.653146 | ||||||||
\(126\) | 3.79435 | 0.338028 | ||||||||
\(127\) | −16.2682 | −1.44357 | −0.721785 | − | 0.692117i | \(-0.756678\pi\) | ||||
−0.721785 | + | 0.692117i | \(0.756678\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.23959 | −0.109140 | ||||||||
\(130\) | 0.644586 | 0.0565339 | ||||||||
\(131\) | −7.36785 | −0.643732 | −0.321866 | − | 0.946785i | \(-0.604310\pi\) | ||||
−0.321866 | + | 0.946785i | \(0.604310\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | −12.8713 | −1.11608 | ||||||||
\(134\) | 8.84367 | 0.763977 | ||||||||
\(135\) | −0.777182 | −0.0668892 | ||||||||
\(136\) | −6.42418 | −0.550869 | ||||||||
\(137\) | −16.1360 | −1.37859 | −0.689296 | − | 0.724480i | \(-0.742080\pi\) | ||||
−0.689296 | + | 0.724480i | \(0.742080\pi\) | |||||||
\(138\) | −5.59479 | −0.476260 | ||||||||
\(139\) | 3.58929 | 0.304440 | 0.152220 | − | 0.988347i | \(-0.451358\pi\) | ||||
0.152220 | + | 0.988347i | \(0.451358\pi\) | |||||||
\(140\) | −2.94890 | −0.249228 | ||||||||
\(141\) | −9.85707 | −0.830115 | ||||||||
\(142\) | 5.68617 | 0.477173 | ||||||||
\(143\) | 0.829389 | 0.0693570 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.535387 | −0.0444615 | ||||||||
\(146\) | −0.226192 | −0.0187197 | ||||||||
\(147\) | −7.39710 | −0.610102 | ||||||||
\(148\) | 10.5891 | 0.870418 | ||||||||
\(149\) | −8.50326 | −0.696615 | −0.348307 | − | 0.937380i | \(-0.613243\pi\) | ||||
−0.348307 | + | 0.937380i | \(0.613243\pi\) | |||||||
\(150\) | −4.39599 | −0.358931 | ||||||||
\(151\) | 6.45800 | 0.525545 | 0.262772 | − | 0.964858i | \(-0.415363\pi\) | ||||
0.262772 | + | 0.964858i | \(0.415363\pi\) | |||||||
\(152\) | −3.39222 | −0.275145 | ||||||||
\(153\) | 6.42418 | 0.519364 | ||||||||
\(154\) | −3.79435 | −0.305757 | ||||||||
\(155\) | −1.75645 | −0.141081 | ||||||||
\(156\) | 0.829389 | 0.0664042 | ||||||||
\(157\) | 21.4950 | 1.71549 | 0.857744 | − | 0.514077i | \(-0.171865\pi\) | ||||
0.857744 | + | 0.514077i | \(0.171865\pi\) | |||||||
\(158\) | 10.5300 | 0.837725 | ||||||||
\(159\) | −7.46497 | −0.592010 | ||||||||
\(160\) | −0.777182 | −0.0614416 | ||||||||
\(161\) | 21.2286 | 1.67305 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 24.3641 | 1.90834 | 0.954170 | − | 0.299265i | \(-0.0967416\pi\) | ||||
0.954170 | + | 0.299265i | \(0.0967416\pi\) | |||||||
\(164\) | −1.80120 | −0.140650 | ||||||||
\(165\) | 0.777182 | 0.0605035 | ||||||||
\(166\) | −10.7814 | −0.836796 | ||||||||
\(167\) | −15.8209 | −1.22426 | −0.612128 | − | 0.790759i | \(-0.709686\pi\) | ||||
−0.612128 | + | 0.790759i | \(0.709686\pi\) | |||||||
\(168\) | −3.79435 | −0.292740 | ||||||||
\(169\) | −12.3121 | −0.947086 | ||||||||
\(170\) | −4.99276 | −0.382927 | ||||||||
\(171\) | 3.39222 | 0.259409 | ||||||||
\(172\) | 1.23959 | 0.0945179 | ||||||||
\(173\) | −0.495579 | −0.0376782 | −0.0188391 | − | 0.999823i | \(-0.505997\pi\) | ||||
−0.0188391 | + | 0.999823i | \(0.505997\pi\) | |||||||
\(174\) | −0.688882 | −0.0522240 | ||||||||
\(175\) | 16.6799 | 1.26088 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 3.77758 | 0.283940 | ||||||||
\(178\) | 4.99276 | 0.374223 | ||||||||
\(179\) | −11.8556 | −0.886129 | −0.443065 | − | 0.896490i | \(-0.646109\pi\) | ||||
−0.443065 | + | 0.896490i | \(0.646109\pi\) | |||||||
\(180\) | 0.777182 | 0.0579277 | ||||||||
\(181\) | 18.2368 | 1.35553 | 0.677765 | − | 0.735279i | \(-0.262949\pi\) | ||||
0.677765 | + | 0.735279i | \(0.262949\pi\) | |||||||
\(182\) | −3.14699 | −0.233270 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | 5.59479 | 0.412453 | ||||||||
\(185\) | 8.22966 | 0.605056 | ||||||||
\(186\) | −2.26002 | −0.165713 | ||||||||
\(187\) | −6.42418 | −0.469782 | ||||||||
\(188\) | 9.85707 | 0.718901 | ||||||||
\(189\) | 3.79435 | 0.275998 | ||||||||
\(190\) | −2.63637 | −0.191262 | ||||||||
\(191\) | 5.85173 | 0.423416 | 0.211708 | − | 0.977333i | \(-0.432097\pi\) | ||||
0.211708 | + | 0.977333i | \(0.432097\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 23.2053 | 1.67035 | 0.835176 | − | 0.549982i | \(-0.185366\pi\) | ||||
0.835176 | + | 0.549982i | \(0.185366\pi\) | |||||||
\(194\) | −2.45363 | −0.176160 | ||||||||
\(195\) | 0.644586 | 0.0461598 | ||||||||
\(196\) | 7.39710 | 0.528364 | ||||||||
\(197\) | −11.6762 | −0.831898 | −0.415949 | − | 0.909388i | \(-0.636550\pi\) | ||||
−0.415949 | + | 0.909388i | \(0.636550\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | −6.10189 | −0.432552 | −0.216276 | − | 0.976332i | \(-0.569391\pi\) | ||||
−0.216276 | + | 0.976332i | \(0.569391\pi\) | |||||||
\(200\) | 4.39599 | 0.310843 | ||||||||
\(201\) | 8.84367 | 0.623785 | ||||||||
\(202\) | −1.13546 | −0.0798907 | ||||||||
\(203\) | 2.61386 | 0.183457 | ||||||||
\(204\) | −6.42418 | −0.449782 | ||||||||
\(205\) | −1.39986 | −0.0977704 | ||||||||
\(206\) | −10.7380 | −0.748149 | ||||||||
\(207\) | −5.59479 | −0.388865 | ||||||||
\(208\) | −0.829389 | −0.0575078 | ||||||||
\(209\) | −3.39222 | −0.234645 | ||||||||
\(210\) | −2.94890 | −0.203493 | ||||||||
\(211\) | −3.15597 | −0.217266 | −0.108633 | − | 0.994082i | \(-0.534647\pi\) | ||||
−0.108633 | + | 0.994082i | \(0.534647\pi\) | |||||||
\(212\) | 7.46497 | 0.512696 | ||||||||
\(213\) | 5.68617 | 0.389610 | ||||||||
\(214\) | 11.3332 | 0.774719 | ||||||||
\(215\) | 0.963387 | 0.0657025 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 8.57530 | 0.582129 | ||||||||
\(218\) | 6.58859 | 0.446235 | ||||||||
\(219\) | −0.226192 | −0.0152846 | ||||||||
\(220\) | −0.777182 | −0.0523976 | ||||||||
\(221\) | −5.32814 | −0.358409 | ||||||||
\(222\) | 10.5891 | 0.710694 | ||||||||
\(223\) | 12.5155 | 0.838100 | 0.419050 | − | 0.907963i | \(-0.362363\pi\) | ||||
0.419050 | + | 0.907963i | \(0.362363\pi\) | |||||||
\(224\) | 3.79435 | 0.253521 | ||||||||
\(225\) | −4.39599 | −0.293066 | ||||||||
\(226\) | 8.50905 | 0.566013 | ||||||||
\(227\) | −4.01934 | −0.266773 | −0.133387 | − | 0.991064i | \(-0.542585\pi\) | ||||
−0.133387 | + | 0.991064i | \(0.542585\pi\) | |||||||
\(228\) | −3.39222 | −0.224655 | ||||||||
\(229\) | −15.5815 | −1.02966 | −0.514828 | − | 0.857293i | \(-0.672144\pi\) | ||||
−0.514828 | + | 0.857293i | \(0.672144\pi\) | |||||||
\(230\) | 4.34817 | 0.286710 | ||||||||
\(231\) | −3.79435 | −0.249650 | ||||||||
\(232\) | 0.688882 | 0.0452273 | ||||||||
\(233\) | −20.1974 | −1.32317 | −0.661587 | − | 0.749868i | \(-0.730117\pi\) | ||||
−0.661587 | + | 0.749868i | \(0.730117\pi\) | |||||||
\(234\) | 0.829389 | 0.0542188 | ||||||||
\(235\) | 7.66074 | 0.499731 | ||||||||
\(236\) | −3.77758 | −0.245899 | ||||||||
\(237\) | 10.5300 | 0.684000 | ||||||||
\(238\) | 24.3756 | 1.58003 | ||||||||
\(239\) | −16.3488 | −1.05752 | −0.528759 | − | 0.848772i | \(-0.677342\pi\) | ||||
−0.528759 | + | 0.848772i | \(0.677342\pi\) | |||||||
\(240\) | −0.777182 | −0.0501669 | ||||||||
\(241\) | −15.8848 | −1.02323 | −0.511614 | − | 0.859216i | \(-0.670952\pi\) | ||||
−0.511614 | + | 0.859216i | \(0.670952\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | 5.74889 | 0.367283 | ||||||||
\(246\) | −1.80120 | −0.114840 | ||||||||
\(247\) | −2.81347 | −0.179017 | ||||||||
\(248\) | 2.26002 | 0.143511 | ||||||||
\(249\) | −10.7814 | −0.683241 | ||||||||
\(250\) | 7.30239 | 0.461844 | ||||||||
\(251\) | 0.930521 | 0.0587340 | 0.0293670 | − | 0.999569i | \(-0.490651\pi\) | ||||
0.0293670 | + | 0.999569i | \(0.490651\pi\) | |||||||
\(252\) | −3.79435 | −0.239022 | ||||||||
\(253\) | 5.59479 | 0.351741 | ||||||||
\(254\) | 16.2682 | 1.02076 | ||||||||
\(255\) | −4.99276 | −0.312658 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.1287 | 0.756568 | 0.378284 | − | 0.925690i | \(-0.376514\pi\) | ||||
0.378284 | + | 0.925690i | \(0.376514\pi\) | |||||||
\(258\) | 1.23959 | 0.0771735 | ||||||||
\(259\) | −40.1787 | −2.49659 | ||||||||
\(260\) | −0.644586 | −0.0399755 | ||||||||
\(261\) | −0.688882 | −0.0426407 | ||||||||
\(262\) | 7.36785 | 0.455188 | ||||||||
\(263\) | −30.6916 | −1.89252 | −0.946262 | − | 0.323401i | \(-0.895174\pi\) | ||||
−0.946262 | + | 0.323401i | \(0.895174\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | 5.80164 | 0.356392 | ||||||||
\(266\) | 12.8713 | 0.789188 | ||||||||
\(267\) | 4.99276 | 0.305552 | ||||||||
\(268\) | −8.84367 | −0.540213 | ||||||||
\(269\) | −12.9720 | −0.790915 | −0.395457 | − | 0.918484i | \(-0.629414\pi\) | ||||
−0.395457 | + | 0.918484i | \(0.629414\pi\) | |||||||
\(270\) | 0.777182 | 0.0472978 | ||||||||
\(271\) | −12.6657 | −0.769385 | −0.384692 | − | 0.923045i | \(-0.625692\pi\) | ||||
−0.384692 | + | 0.923045i | \(0.625692\pi\) | |||||||
\(272\) | 6.42418 | 0.389523 | ||||||||
\(273\) | −3.14699 | −0.190465 | ||||||||
\(274\) | 16.1360 | 0.974812 | ||||||||
\(275\) | 4.39599 | 0.265088 | ||||||||
\(276\) | 5.59479 | 0.336767 | ||||||||
\(277\) | 14.3557 | 0.862548 | 0.431274 | − | 0.902221i | \(-0.358064\pi\) | ||||
0.431274 | + | 0.902221i | \(0.358064\pi\) | |||||||
\(278\) | −3.58929 | −0.215271 | ||||||||
\(279\) | −2.26002 | −0.135304 | ||||||||
\(280\) | 2.94890 | 0.176231 | ||||||||
\(281\) | −27.3160 | −1.62953 | −0.814767 | − | 0.579788i | \(-0.803135\pi\) | ||||
−0.814767 | + | 0.579788i | \(0.803135\pi\) | |||||||
\(282\) | 9.85707 | 0.586980 | ||||||||
\(283\) | −32.9040 | −1.95594 | −0.977969 | − | 0.208750i | \(-0.933061\pi\) | ||||
−0.977969 | + | 0.208750i | \(0.933061\pi\) | |||||||
\(284\) | −5.68617 | −0.337412 | ||||||||
\(285\) | −2.63637 | −0.156165 | ||||||||
\(286\) | −0.829389 | −0.0490428 | ||||||||
\(287\) | 6.83438 | 0.403421 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 24.2701 | 1.42765 | ||||||||
\(290\) | 0.535387 | 0.0314390 | ||||||||
\(291\) | −2.45363 | −0.143834 | ||||||||
\(292\) | 0.226192 | 0.0132369 | ||||||||
\(293\) | −9.74062 | −0.569053 | −0.284526 | − | 0.958668i | \(-0.591836\pi\) | ||||
−0.284526 | + | 0.958668i | \(0.591836\pi\) | |||||||
\(294\) | 7.39710 | 0.431407 | ||||||||
\(295\) | −2.93587 | −0.170933 | ||||||||
\(296\) | −10.5891 | −0.615479 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 8.50326 | 0.492581 | ||||||||
\(299\) | 4.64025 | 0.268353 | ||||||||
\(300\) | 4.39599 | 0.253802 | ||||||||
\(301\) | −4.70344 | −0.271102 | ||||||||
\(302\) | −6.45800 | −0.371616 | ||||||||
\(303\) | −1.13546 | −0.0652305 | ||||||||
\(304\) | 3.39222 | 0.194557 | ||||||||
\(305\) | −0.777182 | −0.0445013 | ||||||||
\(306\) | −6.42418 | −0.367246 | ||||||||
\(307\) | −8.60709 | −0.491232 | −0.245616 | − | 0.969367i | \(-0.578990\pi\) | ||||
−0.245616 | + | 0.969367i | \(0.578990\pi\) | |||||||
\(308\) | 3.79435 | 0.216203 | ||||||||
\(309\) | −10.7380 | −0.610861 | ||||||||
\(310\) | 1.75645 | 0.0997594 | ||||||||
\(311\) | 5.85160 | 0.331814 | 0.165907 | − | 0.986141i | \(-0.446945\pi\) | ||||
0.165907 | + | 0.986141i | \(0.446945\pi\) | |||||||
\(312\) | −0.829389 | −0.0469549 | ||||||||
\(313\) | 6.45719 | 0.364982 | 0.182491 | − | 0.983208i | \(-0.441584\pi\) | ||||
0.182491 | + | 0.983208i | \(0.441584\pi\) | |||||||
\(314\) | −21.4950 | −1.21303 | ||||||||
\(315\) | −2.94890 | −0.166152 | ||||||||
\(316\) | −10.5300 | −0.592361 | ||||||||
\(317\) | 11.2731 | 0.633160 | 0.316580 | − | 0.948566i | \(-0.397465\pi\) | ||||
0.316580 | + | 0.948566i | \(0.397465\pi\) | |||||||
\(318\) | 7.46497 | 0.418615 | ||||||||
\(319\) | 0.688882 | 0.0385700 | ||||||||
\(320\) | 0.777182 | 0.0434458 | ||||||||
\(321\) | 11.3332 | 0.632555 | ||||||||
\(322\) | −21.2286 | −1.18302 | ||||||||
\(323\) | 21.7922 | 1.21255 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 3.64598 | 0.202243 | ||||||||
\(326\) | −24.3641 | −1.34940 | ||||||||
\(327\) | 6.58859 | 0.364350 | ||||||||
\(328\) | 1.80120 | 0.0994546 | ||||||||
\(329\) | −37.4012 | −2.06199 | ||||||||
\(330\) | −0.777182 | −0.0427825 | ||||||||
\(331\) | −32.4487 | −1.78354 | −0.891770 | − | 0.452489i | \(-0.850536\pi\) | ||||
−0.891770 | + | 0.452489i | \(0.850536\pi\) | |||||||
\(332\) | 10.7814 | 0.591704 | ||||||||
\(333\) | 10.5891 | 0.580279 | ||||||||
\(334\) | 15.8209 | 0.865680 | ||||||||
\(335\) | −6.87314 | −0.375520 | ||||||||
\(336\) | 3.79435 | 0.206999 | ||||||||
\(337\) | −8.74285 | −0.476253 | −0.238127 | − | 0.971234i | \(-0.576533\pi\) | ||||
−0.238127 | + | 0.971234i | \(0.576533\pi\) | |||||||
\(338\) | 12.3121 | 0.669691 | ||||||||
\(339\) | 8.50905 | 0.462148 | ||||||||
\(340\) | 4.99276 | 0.270770 | ||||||||
\(341\) | 2.26002 | 0.122387 | ||||||||
\(342\) | −3.39222 | −0.183430 | ||||||||
\(343\) | −1.50672 | −0.0813552 | ||||||||
\(344\) | −1.23959 | −0.0668342 | ||||||||
\(345\) | 4.34817 | 0.234098 | ||||||||
\(346\) | 0.495579 | 0.0266425 | ||||||||
\(347\) | −25.9734 | −1.39432 | −0.697161 | − | 0.716914i | \(-0.745554\pi\) | ||||
−0.697161 | + | 0.716914i | \(0.745554\pi\) | |||||||
\(348\) | 0.688882 | 0.0369280 | ||||||||
\(349\) | −16.2802 | −0.871457 | −0.435729 | − | 0.900078i | \(-0.643509\pi\) | ||||
−0.435729 | + | 0.900078i | \(0.643509\pi\) | |||||||
\(350\) | −16.6799 | −0.891579 | ||||||||
\(351\) | 0.829389 | 0.0442695 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −27.7773 | −1.47843 | −0.739217 | − | 0.673467i | \(-0.764804\pi\) | ||||
−0.739217 | + | 0.673467i | \(0.764804\pi\) | |||||||
\(354\) | −3.77758 | −0.200776 | ||||||||
\(355\) | −4.41919 | −0.234546 | ||||||||
\(356\) | −4.99276 | −0.264616 | ||||||||
\(357\) | 24.3756 | 1.29009 | ||||||||
\(358\) | 11.8556 | 0.626588 | ||||||||
\(359\) | 11.6724 | 0.616048 | 0.308024 | − | 0.951379i | \(-0.400332\pi\) | ||||
0.308024 | + | 0.951379i | \(0.400332\pi\) | |||||||
\(360\) | −0.777182 | −0.0409611 | ||||||||
\(361\) | −7.49285 | −0.394361 | ||||||||
\(362\) | −18.2368 | −0.958504 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 3.14699 | 0.164947 | ||||||||
\(365\) | 0.175792 | 0.00920137 | ||||||||
\(366\) | −1.00000 | −0.0522708 | ||||||||
\(367\) | 26.9833 | 1.40852 | 0.704259 | − | 0.709943i | \(-0.251279\pi\) | ||||
0.704259 | + | 0.709943i | \(0.251279\pi\) | |||||||
\(368\) | −5.59479 | −0.291649 | ||||||||
\(369\) | −1.80120 | −0.0937667 | ||||||||
\(370\) | −8.22966 | −0.427839 | ||||||||
\(371\) | −28.3247 | −1.47055 | ||||||||
\(372\) | 2.26002 | 0.117177 | ||||||||
\(373\) | −3.69371 | −0.191253 | −0.0956265 | − | 0.995417i | \(-0.530485\pi\) | ||||
−0.0956265 | + | 0.995417i | \(0.530485\pi\) | |||||||
\(374\) | 6.42418 | 0.332186 | ||||||||
\(375\) | 7.30239 | 0.377094 | ||||||||
\(376\) | −9.85707 | −0.508340 | ||||||||
\(377\) | 0.571351 | 0.0294261 | ||||||||
\(378\) | −3.79435 | −0.195160 | ||||||||
\(379\) | −38.5449 | −1.97992 | −0.989960 | − | 0.141347i | \(-0.954857\pi\) | ||||
−0.989960 | + | 0.141347i | \(0.954857\pi\) | |||||||
\(380\) | 2.63637 | 0.135243 | ||||||||
\(381\) | 16.2682 | 0.833446 | ||||||||
\(382\) | −5.85173 | −0.299401 | ||||||||
\(383\) | −13.6304 | −0.696483 | −0.348242 | − | 0.937405i | \(-0.613221\pi\) | ||||
−0.348242 | + | 0.937405i | \(0.613221\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 2.94890 | 0.150290 | ||||||||
\(386\) | −23.2053 | −1.18112 | ||||||||
\(387\) | 1.23959 | 0.0630119 | ||||||||
\(388\) | 2.45363 | 0.124564 | ||||||||
\(389\) | −29.5694 | −1.49923 | −0.749614 | − | 0.661875i | \(-0.769761\pi\) | ||||
−0.749614 | + | 0.661875i | \(0.769761\pi\) | |||||||
\(390\) | −0.644586 | −0.0326399 | ||||||||
\(391\) | −35.9419 | −1.81766 | ||||||||
\(392\) | −7.39710 | −0.373610 | ||||||||
\(393\) | 7.36785 | 0.371659 | ||||||||
\(394\) | 11.6762 | 0.588241 | ||||||||
\(395\) | −8.18376 | −0.411770 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | 32.3149 | 1.62184 | 0.810920 | − | 0.585157i | \(-0.198967\pi\) | ||||
0.810920 | + | 0.585157i | \(0.198967\pi\) | |||||||
\(398\) | 6.10189 | 0.305860 | ||||||||
\(399\) | 12.8713 | 0.644369 | ||||||||
\(400\) | −4.39599 | −0.219799 | ||||||||
\(401\) | 9.61472 | 0.480136 | 0.240068 | − | 0.970756i | \(-0.422830\pi\) | ||||
0.240068 | + | 0.970756i | \(0.422830\pi\) | |||||||
\(402\) | −8.84367 | −0.441082 | ||||||||
\(403\) | 1.87443 | 0.0933722 | ||||||||
\(404\) | 1.13546 | 0.0564912 | ||||||||
\(405\) | 0.777182 | 0.0386185 | ||||||||
\(406\) | −2.61386 | −0.129724 | ||||||||
\(407\) | −10.5891 | −0.524882 | ||||||||
\(408\) | 6.42418 | 0.318044 | ||||||||
\(409\) | −19.8458 | −0.981313 | −0.490656 | − | 0.871353i | \(-0.663243\pi\) | ||||
−0.490656 | + | 0.871353i | \(0.663243\pi\) | |||||||
\(410\) | 1.39986 | 0.0691341 | ||||||||
\(411\) | 16.1360 | 0.795931 | ||||||||
\(412\) | 10.7380 | 0.529021 | ||||||||
\(413\) | 14.3335 | 0.705303 | ||||||||
\(414\) | 5.59479 | 0.274969 | ||||||||
\(415\) | 8.37908 | 0.411313 | ||||||||
\(416\) | 0.829389 | 0.0406641 | ||||||||
\(417\) | −3.58929 | −0.175768 | ||||||||
\(418\) | 3.39222 | 0.165919 | ||||||||
\(419\) | 21.0434 | 1.02804 | 0.514018 | − | 0.857779i | \(-0.328156\pi\) | ||||
0.514018 | + | 0.857779i | \(0.328156\pi\) | |||||||
\(420\) | 2.94890 | 0.143892 | ||||||||
\(421\) | −12.1741 | −0.593331 | −0.296666 | − | 0.954981i | \(-0.595875\pi\) | ||||
−0.296666 | + | 0.954981i | \(0.595875\pi\) | |||||||
\(422\) | 3.15597 | 0.153630 | ||||||||
\(423\) | 9.85707 | 0.479267 | ||||||||
\(424\) | −7.46497 | −0.362531 | ||||||||
\(425\) | −28.2406 | −1.36987 | ||||||||
\(426\) | −5.68617 | −0.275496 | ||||||||
\(427\) | 3.79435 | 0.183621 | ||||||||
\(428\) | −11.3332 | −0.547809 | ||||||||
\(429\) | −0.829389 | −0.0400433 | ||||||||
\(430\) | −0.963387 | −0.0464587 | ||||||||
\(431\) | −7.06839 | −0.340473 | −0.170236 | − | 0.985403i | \(-0.554453\pi\) | ||||
−0.170236 | + | 0.985403i | \(0.554453\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −7.60525 | −0.365485 | −0.182742 | − | 0.983161i | \(-0.558497\pi\) | ||||
−0.182742 | + | 0.983161i | \(0.558497\pi\) | |||||||
\(434\) | −8.57530 | −0.411628 | ||||||||
\(435\) | 0.535387 | 0.0256698 | ||||||||
\(436\) | −6.58859 | −0.315536 | ||||||||
\(437\) | −18.9787 | −0.907877 | ||||||||
\(438\) | 0.226192 | 0.0108078 | ||||||||
\(439\) | 18.6709 | 0.891111 | 0.445556 | − | 0.895254i | \(-0.353006\pi\) | ||||
0.445556 | + | 0.895254i | \(0.353006\pi\) | |||||||
\(440\) | 0.777182 | 0.0370507 | ||||||||
\(441\) | 7.39710 | 0.352243 | ||||||||
\(442\) | 5.32814 | 0.253434 | ||||||||
\(443\) | −10.7433 | −0.510432 | −0.255216 | − | 0.966884i | \(-0.582147\pi\) | ||||
−0.255216 | + | 0.966884i | \(0.582147\pi\) | |||||||
\(444\) | −10.5891 | −0.502536 | ||||||||
\(445\) | −3.88028 | −0.183943 | ||||||||
\(446\) | −12.5155 | −0.592626 | ||||||||
\(447\) | 8.50326 | 0.402191 | ||||||||
\(448\) | −3.79435 | −0.179266 | ||||||||
\(449\) | 36.3330 | 1.71466 | 0.857330 | − | 0.514767i | \(-0.172122\pi\) | ||||
0.857330 | + | 0.514767i | \(0.172122\pi\) | |||||||
\(450\) | 4.39599 | 0.207229 | ||||||||
\(451\) | 1.80120 | 0.0848151 | ||||||||
\(452\) | −8.50905 | −0.400232 | ||||||||
\(453\) | −6.45800 | −0.303424 | ||||||||
\(454\) | 4.01934 | 0.188637 | ||||||||
\(455\) | 2.44578 | 0.114660 | ||||||||
\(456\) | 3.39222 | 0.158855 | ||||||||
\(457\) | −21.9436 | −1.02648 | −0.513238 | − | 0.858246i | \(-0.671554\pi\) | ||||
−0.513238 | + | 0.858246i | \(0.671554\pi\) | |||||||
\(458\) | 15.5815 | 0.728077 | ||||||||
\(459\) | −6.42418 | −0.299855 | ||||||||
\(460\) | −4.34817 | −0.202734 | ||||||||
\(461\) | 19.7455 | 0.919639 | 0.459820 | − | 0.888012i | \(-0.347914\pi\) | ||||
0.459820 | + | 0.888012i | \(0.347914\pi\) | |||||||
\(462\) | 3.79435 | 0.176529 | ||||||||
\(463\) | 36.6840 | 1.70485 | 0.852426 | − | 0.522848i | \(-0.175130\pi\) | ||||
0.852426 | + | 0.522848i | \(0.175130\pi\) | |||||||
\(464\) | −0.688882 | −0.0319806 | ||||||||
\(465\) | 1.75645 | 0.0814532 | ||||||||
\(466\) | 20.1974 | 0.935625 | ||||||||
\(467\) | −36.7614 | −1.70111 | −0.850557 | − | 0.525883i | \(-0.823735\pi\) | ||||
−0.850557 | + | 0.525883i | \(0.823735\pi\) | |||||||
\(468\) | −0.829389 | −0.0383385 | ||||||||
\(469\) | 33.5560 | 1.54947 | ||||||||
\(470\) | −7.66074 | −0.353364 | ||||||||
\(471\) | −21.4950 | −0.990438 | ||||||||
\(472\) | 3.77758 | 0.173877 | ||||||||
\(473\) | −1.23959 | −0.0569964 | ||||||||
\(474\) | −10.5300 | −0.483661 | ||||||||
\(475\) | −14.9122 | −0.684216 | ||||||||
\(476\) | −24.3756 | −1.11725 | ||||||||
\(477\) | 7.46497 | 0.341797 | ||||||||
\(478\) | 16.3488 | 0.747778 | ||||||||
\(479\) | −16.0940 | −0.735356 | −0.367678 | − | 0.929953i | \(-0.619847\pi\) | ||||
−0.367678 | + | 0.929953i | \(0.619847\pi\) | |||||||
\(480\) | 0.777182 | 0.0354733 | ||||||||
\(481\) | −8.78248 | −0.400446 | ||||||||
\(482\) | 15.8848 | 0.723531 | ||||||||
\(483\) | −21.2286 | −0.965934 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 1.90692 | 0.0865886 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 19.4585 | 0.881747 | 0.440873 | − | 0.897569i | \(-0.354669\pi\) | ||||
0.440873 | + | 0.897569i | \(0.354669\pi\) | |||||||
\(488\) | 1.00000 | 0.0452679 | ||||||||
\(489\) | −24.3641 | −1.10178 | ||||||||
\(490\) | −5.74889 | −0.259708 | ||||||||
\(491\) | 18.8815 | 0.852108 | 0.426054 | − | 0.904698i | \(-0.359903\pi\) | ||||
0.426054 | + | 0.904698i | \(0.359903\pi\) | |||||||
\(492\) | 1.80120 | 0.0812043 | ||||||||
\(493\) | −4.42550 | −0.199315 | ||||||||
\(494\) | 2.81347 | 0.126584 | ||||||||
\(495\) | −0.777182 | −0.0349317 | ||||||||
\(496\) | −2.26002 | −0.101478 | ||||||||
\(497\) | 21.5753 | 0.967785 | ||||||||
\(498\) | 10.7814 | 0.483124 | ||||||||
\(499\) | 8.27868 | 0.370605 | 0.185302 | − | 0.982682i | \(-0.440674\pi\) | ||||
0.185302 | + | 0.982682i | \(0.440674\pi\) | |||||||
\(500\) | −7.30239 | −0.326573 | ||||||||
\(501\) | 15.8209 | 0.706824 | ||||||||
\(502\) | −0.930521 | −0.0415312 | ||||||||
\(503\) | 7.73269 | 0.344784 | 0.172392 | − | 0.985028i | \(-0.444850\pi\) | ||||
0.172392 | + | 0.985028i | \(0.444850\pi\) | |||||||
\(504\) | 3.79435 | 0.169014 | ||||||||
\(505\) | 0.882459 | 0.0392689 | ||||||||
\(506\) | −5.59479 | −0.248719 | ||||||||
\(507\) | 12.3121 | 0.546800 | ||||||||
\(508\) | −16.2682 | −0.721785 | ||||||||
\(509\) | 7.99538 | 0.354389 | 0.177195 | − | 0.984176i | \(-0.443298\pi\) | ||||
0.177195 | + | 0.984176i | \(0.443298\pi\) | |||||||
\(510\) | 4.99276 | 0.221083 | ||||||||
\(511\) | −0.858250 | −0.0379667 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.39222 | −0.149770 | ||||||||
\(514\) | −12.1287 | −0.534974 | ||||||||
\(515\) | 8.34535 | 0.367740 | ||||||||
\(516\) | −1.23959 | −0.0545699 | ||||||||
\(517\) | −9.85707 | −0.433514 | ||||||||
\(518\) | 40.1787 | 1.76535 | ||||||||
\(519\) | 0.495579 | 0.0217535 | ||||||||
\(520\) | 0.644586 | 0.0282670 | ||||||||
\(521\) | −12.1788 | −0.533562 | −0.266781 | − | 0.963757i | \(-0.585960\pi\) | ||||
−0.266781 | + | 0.963757i | \(0.585960\pi\) | |||||||
\(522\) | 0.688882 | 0.0301516 | ||||||||
\(523\) | 27.3315 | 1.19512 | 0.597561 | − | 0.801824i | \(-0.296137\pi\) | ||||
0.597561 | + | 0.801824i | \(0.296137\pi\) | |||||||
\(524\) | −7.36785 | −0.321866 | ||||||||
\(525\) | −16.6799 | −0.727971 | ||||||||
\(526\) | 30.6916 | 1.33822 | ||||||||
\(527\) | −14.5188 | −0.632447 | ||||||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | 8.30167 | 0.360942 | ||||||||
\(530\) | −5.80164 | −0.252007 | ||||||||
\(531\) | −3.77758 | −0.163933 | ||||||||
\(532\) | −12.8713 | −0.558040 | ||||||||
\(533\) | 1.49389 | 0.0647077 | ||||||||
\(534\) | −4.99276 | −0.216058 | ||||||||
\(535\) | −8.80793 | −0.380800 | ||||||||
\(536\) | 8.84367 | 0.381988 | ||||||||
\(537\) | 11.8556 | 0.511607 | ||||||||
\(538\) | 12.9720 | 0.559261 | ||||||||
\(539\) | −7.39710 | −0.318615 | ||||||||
\(540\) | −0.777182 | −0.0334446 | ||||||||
\(541\) | −22.7153 | −0.976608 | −0.488304 | − | 0.872674i | \(-0.662384\pi\) | ||||
−0.488304 | + | 0.872674i | \(0.662384\pi\) | |||||||
\(542\) | 12.6657 | 0.544037 | ||||||||
\(543\) | −18.2368 | −0.782615 | ||||||||
\(544\) | −6.42418 | −0.275434 | ||||||||
\(545\) | −5.12053 | −0.219339 | ||||||||
\(546\) | 3.14699 | 0.134679 | ||||||||
\(547\) | 13.3654 | 0.571463 | 0.285732 | − | 0.958310i | \(-0.407763\pi\) | ||||
0.285732 | + | 0.958310i | \(0.407763\pi\) | |||||||
\(548\) | −16.1360 | −0.689296 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | −4.39599 | −0.187446 | ||||||||
\(551\) | −2.33684 | −0.0995527 | ||||||||
\(552\) | −5.59479 | −0.238130 | ||||||||
\(553\) | 39.9547 | 1.69905 | ||||||||
\(554\) | −14.3557 | −0.609913 | ||||||||
\(555\) | −8.22966 | −0.349329 | ||||||||
\(556\) | 3.58929 | 0.152220 | ||||||||
\(557\) | 42.2260 | 1.78917 | 0.894586 | − | 0.446897i | \(-0.147471\pi\) | ||||
0.894586 | + | 0.446897i | \(0.147471\pi\) | |||||||
\(558\) | 2.26002 | 0.0956742 | ||||||||
\(559\) | −1.02810 | −0.0434841 | ||||||||
\(560\) | −2.94890 | −0.124614 | ||||||||
\(561\) | 6.42418 | 0.271229 | ||||||||
\(562\) | 27.3160 | 1.15226 | ||||||||
\(563\) | −27.9142 | −1.17644 | −0.588221 | − | 0.808700i | \(-0.700171\pi\) | ||||
−0.588221 | + | 0.808700i | \(0.700171\pi\) | |||||||
\(564\) | −9.85707 | −0.415058 | ||||||||
\(565\) | −6.61308 | −0.278214 | ||||||||
\(566\) | 32.9040 | 1.38306 | ||||||||
\(567\) | −3.79435 | −0.159348 | ||||||||
\(568\) | 5.68617 | 0.238586 | ||||||||
\(569\) | −17.7914 | −0.745854 | −0.372927 | − | 0.927861i | \(-0.621646\pi\) | ||||
−0.372927 | + | 0.927861i | \(0.621646\pi\) | |||||||
\(570\) | 2.63637 | 0.110425 | ||||||||
\(571\) | 3.42938 | 0.143515 | 0.0717575 | − | 0.997422i | \(-0.477139\pi\) | ||||
0.0717575 | + | 0.997422i | \(0.477139\pi\) | |||||||
\(572\) | 0.829389 | 0.0346785 | ||||||||
\(573\) | −5.85173 | −0.244460 | ||||||||
\(574\) | −6.83438 | −0.285261 | ||||||||
\(575\) | 24.5946 | 1.02567 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −5.76799 | −0.240124 | −0.120062 | − | 0.992766i | \(-0.538309\pi\) | ||||
−0.120062 | + | 0.992766i | \(0.538309\pi\) | |||||||
\(578\) | −24.2701 | −1.00950 | ||||||||
\(579\) | −23.2053 | −0.964378 | ||||||||
\(580\) | −0.535387 | −0.0222307 | ||||||||
\(581\) | −40.9083 | −1.69716 | ||||||||
\(582\) | 2.45363 | 0.101706 | ||||||||
\(583\) | −7.46497 | −0.309167 | ||||||||
\(584\) | −0.226192 | −0.00935987 | ||||||||
\(585\) | −0.644586 | −0.0266503 | ||||||||
\(586\) | 9.74062 | 0.402381 | ||||||||
\(587\) | −5.56488 | −0.229687 | −0.114844 | − | 0.993384i | \(-0.536637\pi\) | ||||
−0.114844 | + | 0.993384i | \(0.536637\pi\) | |||||||
\(588\) | −7.39710 | −0.305051 | ||||||||
\(589\) | −7.66648 | −0.315892 | ||||||||
\(590\) | 2.93587 | 0.120868 | ||||||||
\(591\) | 11.6762 | 0.480296 | ||||||||
\(592\) | 10.5891 | 0.435209 | ||||||||
\(593\) | 7.02105 | 0.288320 | 0.144160 | − | 0.989554i | \(-0.453952\pi\) | ||||
0.144160 | + | 0.989554i | \(0.453952\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | −18.9443 | −0.776639 | ||||||||
\(596\) | −8.50326 | −0.348307 | ||||||||
\(597\) | 6.10189 | 0.249734 | ||||||||
\(598\) | −4.64025 | −0.189754 | ||||||||
\(599\) | 1.00712 | 0.0411498 | 0.0205749 | − | 0.999788i | \(-0.493450\pi\) | ||||
0.0205749 | + | 0.999788i | \(0.493450\pi\) | |||||||
\(600\) | −4.39599 | −0.179465 | ||||||||
\(601\) | −37.9811 | −1.54928 | −0.774640 | − | 0.632402i | \(-0.782069\pi\) | ||||
−0.774640 | + | 0.632402i | \(0.782069\pi\) | |||||||
\(602\) | 4.70344 | 0.191698 | ||||||||
\(603\) | −8.84367 | −0.360142 | ||||||||
\(604\) | 6.45800 | 0.262772 | ||||||||
\(605\) | 0.777182 | 0.0315969 | ||||||||
\(606\) | 1.13546 | 0.0461249 | ||||||||
\(607\) | −44.4593 | −1.80455 | −0.902274 | − | 0.431164i | \(-0.858103\pi\) | ||||
−0.902274 | + | 0.431164i | \(0.858103\pi\) | |||||||
\(608\) | −3.39222 | −0.137573 | ||||||||
\(609\) | −2.61386 | −0.105919 | ||||||||
\(610\) | 0.777182 | 0.0314672 | ||||||||
\(611\) | −8.17534 | −0.330739 | ||||||||
\(612\) | 6.42418 | 0.259682 | ||||||||
\(613\) | 40.8749 | 1.65092 | 0.825461 | − | 0.564459i | \(-0.190915\pi\) | ||||
0.825461 | + | 0.564459i | \(0.190915\pi\) | |||||||
\(614\) | 8.60709 | 0.347354 | ||||||||
\(615\) | 1.39986 | 0.0564478 | ||||||||
\(616\) | −3.79435 | −0.152879 | ||||||||
\(617\) | −33.2297 | −1.33778 | −0.668888 | − | 0.743363i | \(-0.733230\pi\) | ||||
−0.668888 | + | 0.743363i | \(0.733230\pi\) | |||||||
\(618\) | 10.7380 | 0.431944 | ||||||||
\(619\) | 34.7437 | 1.39647 | 0.698233 | − | 0.715871i | \(-0.253970\pi\) | ||||
0.698233 | + | 0.715871i | \(0.253970\pi\) | |||||||
\(620\) | −1.75645 | −0.0705406 | ||||||||
\(621\) | 5.59479 | 0.224511 | ||||||||
\(622\) | −5.85160 | −0.234628 | ||||||||
\(623\) | 18.9443 | 0.758986 | ||||||||
\(624\) | 0.829389 | 0.0332021 | ||||||||
\(625\) | 16.3047 | 0.652186 | ||||||||
\(626\) | −6.45719 | −0.258081 | ||||||||
\(627\) | 3.39222 | 0.135472 | ||||||||
\(628\) | 21.4950 | 0.857744 | ||||||||
\(629\) | 68.0262 | 2.71238 | ||||||||
\(630\) | 2.94890 | 0.117487 | ||||||||
\(631\) | −7.89540 | −0.314311 | −0.157155 | − | 0.987574i | \(-0.550232\pi\) | ||||
−0.157155 | + | 0.987574i | \(0.550232\pi\) | |||||||
\(632\) | 10.5300 | 0.418863 | ||||||||
\(633\) | 3.15597 | 0.125439 | ||||||||
\(634\) | −11.2731 | −0.447712 | ||||||||
\(635\) | −12.6434 | −0.501737 | ||||||||
\(636\) | −7.46497 | −0.296005 | ||||||||
\(637\) | −6.13507 | −0.243080 | ||||||||
\(638\) | −0.688882 | −0.0272731 | ||||||||
\(639\) | −5.68617 | −0.224941 | ||||||||
\(640\) | −0.777182 | −0.0307208 | ||||||||
\(641\) | 30.1269 | 1.18994 | 0.594971 | − | 0.803747i | \(-0.297164\pi\) | ||||
0.594971 | + | 0.803747i | \(0.297164\pi\) | |||||||
\(642\) | −11.3332 | −0.447284 | ||||||||
\(643\) | −33.6686 | −1.32776 | −0.663879 | − | 0.747840i | \(-0.731091\pi\) | ||||
−0.663879 | + | 0.747840i | \(0.731091\pi\) | |||||||
\(644\) | 21.2286 | 0.836524 | ||||||||
\(645\) | −0.963387 | −0.0379333 | ||||||||
\(646\) | −21.7922 | −0.857403 | ||||||||
\(647\) | 46.0336 | 1.80977 | 0.904884 | − | 0.425657i | \(-0.139957\pi\) | ||||
0.904884 | + | 0.425657i | \(0.139957\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 3.77758 | 0.148283 | ||||||||
\(650\) | −3.64598 | −0.143007 | ||||||||
\(651\) | −8.57530 | −0.336093 | ||||||||
\(652\) | 24.3641 | 0.954170 | ||||||||
\(653\) | −27.5881 | −1.07961 | −0.539803 | − | 0.841791i | \(-0.681501\pi\) | ||||
−0.539803 | + | 0.841791i | \(0.681501\pi\) | |||||||
\(654\) | −6.58859 | −0.257634 | ||||||||
\(655\) | −5.72616 | −0.223740 | ||||||||
\(656\) | −1.80120 | −0.0703250 | ||||||||
\(657\) | 0.226192 | 0.00882457 | ||||||||
\(658\) | 37.4012 | 1.45805 | ||||||||
\(659\) | 34.4549 | 1.34217 | 0.671087 | − | 0.741379i | \(-0.265828\pi\) | ||||
0.671087 | + | 0.741379i | \(0.265828\pi\) | |||||||
\(660\) | 0.777182 | 0.0302518 | ||||||||
\(661\) | 5.39462 | 0.209826 | 0.104913 | − | 0.994481i | \(-0.466544\pi\) | ||||
0.104913 | + | 0.994481i | \(0.466544\pi\) | |||||||
\(662\) | 32.4487 | 1.26115 | ||||||||
\(663\) | 5.32814 | 0.206928 | ||||||||
\(664\) | −10.7814 | −0.418398 | ||||||||
\(665\) | −10.0033 | −0.387912 | ||||||||
\(666\) | −10.5891 | −0.410319 | ||||||||
\(667\) | 3.85415 | 0.149233 | ||||||||
\(668\) | −15.8209 | −0.612128 | ||||||||
\(669\) | −12.5155 | −0.483877 | ||||||||
\(670\) | 6.87314 | 0.265533 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | −3.79435 | −0.146370 | ||||||||
\(673\) | −33.7794 | −1.30210 | −0.651051 | − | 0.759034i | \(-0.725672\pi\) | ||||
−0.651051 | + | 0.759034i | \(0.725672\pi\) | |||||||
\(674\) | 8.74285 | 0.336762 | ||||||||
\(675\) | 4.39599 | 0.169202 | ||||||||
\(676\) | −12.3121 | −0.473543 | ||||||||
\(677\) | 3.09741 | 0.119043 | 0.0595215 | − | 0.998227i | \(-0.481043\pi\) | ||||
0.0595215 | + | 0.998227i | \(0.481043\pi\) | |||||||
\(678\) | −8.50905 | −0.326788 | ||||||||
\(679\) | −9.30992 | −0.357282 | ||||||||
\(680\) | −4.99276 | −0.191463 | ||||||||
\(681\) | 4.01934 | 0.154021 | ||||||||
\(682\) | −2.26002 | −0.0865406 | ||||||||
\(683\) | −34.7936 | −1.33134 | −0.665670 | − | 0.746246i | \(-0.731854\pi\) | ||||
−0.665670 | + | 0.746246i | \(0.731854\pi\) | |||||||
\(684\) | 3.39222 | 0.129705 | ||||||||
\(685\) | −12.5406 | −0.479152 | ||||||||
\(686\) | 1.50672 | 0.0575268 | ||||||||
\(687\) | 15.5815 | 0.594473 | ||||||||
\(688\) | 1.23959 | 0.0472589 | ||||||||
\(689\) | −6.19136 | −0.235872 | ||||||||
\(690\) | −4.34817 | −0.165532 | ||||||||
\(691\) | −15.8352 | −0.602401 | −0.301200 | − | 0.953561i | \(-0.597387\pi\) | ||||
−0.301200 | + | 0.953561i | \(0.597387\pi\) | |||||||
\(692\) | −0.495579 | −0.0188391 | ||||||||
\(693\) | 3.79435 | 0.144135 | ||||||||
\(694\) | 25.9734 | 0.985935 | ||||||||
\(695\) | 2.78953 | 0.105813 | ||||||||
\(696\) | −0.688882 | −0.0261120 | ||||||||
\(697\) | −11.5712 | −0.438291 | ||||||||
\(698\) | 16.2802 | 0.616213 | ||||||||
\(699\) | 20.1974 | 0.763935 | ||||||||
\(700\) | 16.6799 | 0.630442 | ||||||||
\(701\) | 23.9830 | 0.905825 | 0.452913 | − | 0.891555i | \(-0.350385\pi\) | ||||
0.452913 | + | 0.891555i | \(0.350385\pi\) | |||||||
\(702\) | −0.829389 | −0.0313033 | ||||||||
\(703\) | 35.9205 | 1.35477 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −7.66074 | −0.288520 | ||||||||
\(706\) | 27.7773 | 1.04541 | ||||||||
\(707\) | −4.30833 | −0.162031 | ||||||||
\(708\) | 3.77758 | 0.141970 | ||||||||
\(709\) | 21.1200 | 0.793178 | 0.396589 | − | 0.917996i | \(-0.370194\pi\) | ||||
0.396589 | + | 0.917996i | \(0.370194\pi\) | |||||||
\(710\) | 4.41919 | 0.165849 | ||||||||
\(711\) | −10.5300 | −0.394907 | ||||||||
\(712\) | 4.99276 | 0.187111 | ||||||||
\(713\) | 12.6443 | 0.473534 | ||||||||
\(714\) | −24.3756 | −0.912233 | ||||||||
\(715\) | 0.644586 | 0.0241061 | ||||||||
\(716\) | −11.8556 | −0.443065 | ||||||||
\(717\) | 16.3488 | 0.610558 | ||||||||
\(718\) | −11.6724 | −0.435612 | ||||||||
\(719\) | −26.3527 | −0.982789 | −0.491394 | − | 0.870937i | \(-0.663513\pi\) | ||||
−0.491394 | + | 0.870937i | \(0.663513\pi\) | |||||||
\(720\) | 0.777182 | 0.0289639 | ||||||||
\(721\) | −40.7436 | −1.51737 | ||||||||
\(722\) | 7.49285 | 0.278855 | ||||||||
\(723\) | 15.8848 | 0.590761 | ||||||||
\(724\) | 18.2368 | 0.677765 | ||||||||
\(725\) | 3.02832 | 0.112469 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | 34.8656 | 1.29310 | 0.646548 | − | 0.762874i | \(-0.276212\pi\) | ||||
0.646548 | + | 0.762874i | \(0.276212\pi\) | |||||||
\(728\) | −3.14699 | −0.116635 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.175792 | −0.00650635 | ||||||||
\(731\) | 7.96335 | 0.294535 | ||||||||
\(732\) | 1.00000 | 0.0369611 | ||||||||
\(733\) | −15.0496 | −0.555871 | −0.277936 | − | 0.960600i | \(-0.589650\pi\) | ||||
−0.277936 | + | 0.960600i | \(0.589650\pi\) | |||||||
\(734\) | −26.9833 | −0.995972 | ||||||||
\(735\) | −5.74889 | −0.212051 | ||||||||
\(736\) | 5.59479 | 0.206227 | ||||||||
\(737\) | 8.84367 | 0.325761 | ||||||||
\(738\) | 1.80120 | 0.0663030 | ||||||||
\(739\) | 2.72565 | 0.100265 | 0.0501324 | − | 0.998743i | \(-0.484036\pi\) | ||||
0.0501324 | + | 0.998743i | \(0.484036\pi\) | |||||||
\(740\) | 8.22966 | 0.302528 | ||||||||
\(741\) | 2.81347 | 0.103355 | ||||||||
\(742\) | 28.3247 | 1.03983 | ||||||||
\(743\) | −35.2118 | −1.29179 | −0.645897 | − | 0.763425i | \(-0.723516\pi\) | ||||
−0.645897 | + | 0.763425i | \(0.723516\pi\) | |||||||
\(744\) | −2.26002 | −0.0828563 | ||||||||
\(745\) | −6.60858 | −0.242120 | ||||||||
\(746\) | 3.69371 | 0.135236 | ||||||||
\(747\) | 10.7814 | 0.394469 | ||||||||
\(748\) | −6.42418 | −0.234891 | ||||||||
\(749\) | 43.0020 | 1.57126 | ||||||||
\(750\) | −7.30239 | −0.266646 | ||||||||
\(751\) | 17.3514 | 0.633161 | 0.316580 | − | 0.948566i | \(-0.397465\pi\) | ||||
0.316580 | + | 0.948566i | \(0.397465\pi\) | |||||||
\(752\) | 9.85707 | 0.359450 | ||||||||
\(753\) | −0.930521 | −0.0339101 | ||||||||
\(754\) | −0.571351 | −0.0208074 | ||||||||
\(755\) | 5.01905 | 0.182662 | ||||||||
\(756\) | 3.79435 | 0.137999 | ||||||||
\(757\) | −16.4900 | −0.599341 | −0.299670 | − | 0.954043i | \(-0.596877\pi\) | ||||
−0.299670 | + | 0.954043i | \(0.596877\pi\) | |||||||
\(758\) | 38.5449 | 1.40002 | ||||||||
\(759\) | −5.59479 | −0.203078 | ||||||||
\(760\) | −2.63637 | −0.0956312 | ||||||||
\(761\) | −1.73716 | −0.0629721 | −0.0314860 | − | 0.999504i | \(-0.510024\pi\) | ||||
−0.0314860 | + | 0.999504i | \(0.510024\pi\) | |||||||
\(762\) | −16.2682 | −0.589335 | ||||||||
\(763\) | 24.9994 | 0.905039 | ||||||||
\(764\) | 5.85173 | 0.211708 | ||||||||
\(765\) | 4.99276 | 0.180513 | ||||||||
\(766\) | 13.6304 | 0.492488 | ||||||||
\(767\) | 3.13308 | 0.113129 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 48.7609 | 1.75836 | 0.879182 | − | 0.476485i | \(-0.158089\pi\) | ||||
0.879182 | + | 0.476485i | \(0.158089\pi\) | |||||||
\(770\) | −2.94890 | −0.106271 | ||||||||
\(771\) | −12.1287 | −0.436805 | ||||||||
\(772\) | 23.2053 | 0.835176 | ||||||||
\(773\) | 16.0776 | 0.578271 | 0.289135 | − | 0.957288i | \(-0.406632\pi\) | ||||
0.289135 | + | 0.957288i | \(0.406632\pi\) | |||||||
\(774\) | −1.23959 | −0.0445561 | ||||||||
\(775\) | 9.93501 | 0.356876 | ||||||||
\(776\) | −2.45363 | −0.0880801 | ||||||||
\(777\) | 40.1787 | 1.44140 | ||||||||
\(778\) | 29.5694 | 1.06011 | ||||||||
\(779\) | −6.11006 | −0.218916 | ||||||||
\(780\) | 0.644586 | 0.0230799 | ||||||||
\(781\) | 5.68617 | 0.203467 | ||||||||
\(782\) | 35.9419 | 1.28528 | ||||||||
\(783\) | 0.688882 | 0.0246186 | ||||||||
\(784\) | 7.39710 | 0.264182 | ||||||||
\(785\) | 16.7055 | 0.596246 | ||||||||
\(786\) | −7.36785 | −0.262803 | ||||||||
\(787\) | −24.7989 | −0.883985 | −0.441992 | − | 0.897019i | \(-0.645728\pi\) | ||||
−0.441992 | + | 0.897019i | \(0.645728\pi\) | |||||||
\(788\) | −11.6762 | −0.415949 | ||||||||
\(789\) | 30.6916 | 1.09265 | ||||||||
\(790\) | 8.18376 | 0.291165 | ||||||||
\(791\) | 32.2863 | 1.14797 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 0.829389 | 0.0294525 | ||||||||
\(794\) | −32.3149 | −1.14681 | ||||||||
\(795\) | −5.80164 | −0.205763 | ||||||||
\(796\) | −6.10189 | −0.216276 | ||||||||
\(797\) | 22.2114 | 0.786767 | 0.393384 | − | 0.919374i | \(-0.371304\pi\) | ||||
0.393384 | + | 0.919374i | \(0.371304\pi\) | |||||||
\(798\) | −12.8713 | −0.455638 | ||||||||
\(799\) | 63.3236 | 2.24023 | ||||||||
\(800\) | 4.39599 | 0.155422 | ||||||||
\(801\) | −4.99276 | −0.176410 | ||||||||
\(802\) | −9.61472 | −0.339507 | ||||||||
\(803\) | −0.226192 | −0.00798213 | ||||||||
\(804\) | 8.84367 | 0.311892 | ||||||||
\(805\) | 16.4985 | 0.581495 | ||||||||
\(806\) | −1.87443 | −0.0660241 | ||||||||
\(807\) | 12.9720 | 0.456635 | ||||||||
\(808\) | −1.13546 | −0.0399453 | ||||||||
\(809\) | −38.3358 | −1.34781 | −0.673907 | − | 0.738816i | \(-0.735385\pi\) | ||||
−0.673907 | + | 0.738816i | \(0.735385\pi\) | |||||||
\(810\) | −0.777182 | −0.0273074 | ||||||||
\(811\) | −12.6512 | −0.444242 | −0.222121 | − | 0.975019i | \(-0.571298\pi\) | ||||
−0.222121 | + | 0.975019i | \(0.571298\pi\) | |||||||
\(812\) | 2.61386 | 0.0917285 | ||||||||
\(813\) | 12.6657 | 0.444204 | ||||||||
\(814\) | 10.5891 | 0.371148 | ||||||||
\(815\) | 18.9353 | 0.663275 | ||||||||
\(816\) | −6.42418 | −0.224891 | ||||||||
\(817\) | 4.20496 | 0.147113 | ||||||||
\(818\) | 19.8458 | 0.693893 | ||||||||
\(819\) | 3.14699 | 0.109965 | ||||||||
\(820\) | −1.39986 | −0.0488852 | ||||||||
\(821\) | −27.8160 | −0.970784 | −0.485392 | − | 0.874297i | \(-0.661323\pi\) | ||||
−0.485392 | + | 0.874297i | \(0.661323\pi\) | |||||||
\(822\) | −16.1360 | −0.562808 | ||||||||
\(823\) | −22.1749 | −0.772969 | −0.386485 | − | 0.922296i | \(-0.626311\pi\) | ||||
−0.386485 | + | 0.922296i | \(0.626311\pi\) | |||||||
\(824\) | −10.7380 | −0.374074 | ||||||||
\(825\) | −4.39599 | −0.153049 | ||||||||
\(826\) | −14.3335 | −0.498725 | ||||||||
\(827\) | 25.2864 | 0.879296 | 0.439648 | − | 0.898170i | \(-0.355103\pi\) | ||||
0.439648 | + | 0.898170i | \(0.355103\pi\) | |||||||
\(828\) | −5.59479 | −0.194432 | ||||||||
\(829\) | 0.481347 | 0.0167179 | 0.00835893 | − | 0.999965i | \(-0.497339\pi\) | ||||
0.00835893 | + | 0.999965i | \(0.497339\pi\) | |||||||
\(830\) | −8.37908 | −0.290842 | ||||||||
\(831\) | −14.3557 | −0.497992 | ||||||||
\(832\) | −0.829389 | −0.0287539 | ||||||||
\(833\) | 47.5203 | 1.64648 | ||||||||
\(834\) | 3.58929 | 0.124287 | ||||||||
\(835\) | −12.2957 | −0.425510 | ||||||||
\(836\) | −3.39222 | −0.117322 | ||||||||
\(837\) | 2.26002 | 0.0781177 | ||||||||
\(838\) | −21.0434 | −0.726931 | ||||||||
\(839\) | −37.0881 | −1.28042 | −0.640212 | − | 0.768198i | \(-0.721153\pi\) | ||||
−0.640212 | + | 0.768198i | \(0.721153\pi\) | |||||||
\(840\) | −2.94890 | −0.101747 | ||||||||
\(841\) | −28.5254 | −0.983636 | ||||||||
\(842\) | 12.1741 | 0.419549 | ||||||||
\(843\) | 27.3160 | 0.940812 | ||||||||
\(844\) | −3.15597 | −0.108633 | ||||||||
\(845\) | −9.56875 | −0.329175 | ||||||||
\(846\) | −9.85707 | −0.338893 | ||||||||
\(847\) | −3.79435 | −0.130375 | ||||||||
\(848\) | 7.46497 | 0.256348 | ||||||||
\(849\) | 32.9040 | 1.12926 | ||||||||
\(850\) | 28.2406 | 0.968645 | ||||||||
\(851\) | −59.2438 | −2.03085 | ||||||||
\(852\) | 5.68617 | 0.194805 | ||||||||
\(853\) | −50.6840 | −1.73539 | −0.867693 | − | 0.497100i | \(-0.834398\pi\) | ||||
−0.867693 | + | 0.497100i | \(0.834398\pi\) | |||||||
\(854\) | −3.79435 | −0.129840 | ||||||||
\(855\) | 2.63637 | 0.0901620 | ||||||||
\(856\) | 11.3332 | 0.387360 | ||||||||
\(857\) | −9.07769 | −0.310088 | −0.155044 | − | 0.987908i | \(-0.549552\pi\) | ||||
−0.155044 | + | 0.987908i | \(0.549552\pi\) | |||||||
\(858\) | 0.829389 | 0.0283149 | ||||||||
\(859\) | 26.3285 | 0.898316 | 0.449158 | − | 0.893452i | \(-0.351724\pi\) | ||||
0.449158 | + | 0.893452i | \(0.351724\pi\) | |||||||
\(860\) | 0.963387 | 0.0328512 | ||||||||
\(861\) | −6.83438 | −0.232915 | ||||||||
\(862\) | 7.06839 | 0.240750 | ||||||||
\(863\) | −24.4367 | −0.831836 | −0.415918 | − | 0.909402i | \(-0.636540\pi\) | ||||
−0.415918 | + | 0.909402i | \(0.636540\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −0.385155 | −0.0130957 | ||||||||
\(866\) | 7.60525 | 0.258437 | ||||||||
\(867\) | −24.2701 | −0.824255 | ||||||||
\(868\) | 8.57530 | 0.291065 | ||||||||
\(869\) | 10.5300 | 0.357207 | ||||||||
\(870\) | −0.535387 | −0.0181513 | ||||||||
\(871\) | 7.33484 | 0.248532 | ||||||||
\(872\) | 6.58859 | 0.223118 | ||||||||
\(873\) | 2.45363 | 0.0830427 | ||||||||
\(874\) | 18.9787 | 0.641966 | ||||||||
\(875\) | 27.7078 | 0.936696 | ||||||||
\(876\) | −0.226192 | −0.00764230 | ||||||||
\(877\) | 30.1107 | 1.01677 | 0.508384 | − | 0.861131i | \(-0.330243\pi\) | ||||
0.508384 | + | 0.861131i | \(0.330243\pi\) | |||||||
\(878\) | −18.6709 | −0.630111 | ||||||||
\(879\) | 9.74062 | 0.328543 | ||||||||
\(880\) | −0.777182 | −0.0261988 | ||||||||
\(881\) | 30.5699 | 1.02992 | 0.514962 | − | 0.857213i | \(-0.327806\pi\) | ||||
0.514962 | + | 0.857213i | \(0.327806\pi\) | |||||||
\(882\) | −7.39710 | −0.249073 | ||||||||
\(883\) | 25.9570 | 0.873523 | 0.436761 | − | 0.899577i | \(-0.356125\pi\) | ||||
0.436761 | + | 0.899577i | \(0.356125\pi\) | |||||||
\(884\) | −5.32814 | −0.179205 | ||||||||
\(885\) | 2.93587 | 0.0986880 | ||||||||
\(886\) | 10.7433 | 0.360930 | ||||||||
\(887\) | 6.81823 | 0.228934 | 0.114467 | − | 0.993427i | \(-0.463484\pi\) | ||||
0.114467 | + | 0.993427i | \(0.463484\pi\) | |||||||
\(888\) | 10.5891 | 0.355347 | ||||||||
\(889\) | 61.7273 | 2.07027 | ||||||||
\(890\) | 3.88028 | 0.130067 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 12.5155 | 0.419050 | ||||||||
\(893\) | 33.4373 | 1.11894 | ||||||||
\(894\) | −8.50326 | −0.284392 | ||||||||
\(895\) | −9.21396 | −0.307989 | ||||||||
\(896\) | 3.79435 | 0.126760 | ||||||||
\(897\) | −4.64025 | −0.154934 | ||||||||
\(898\) | −36.3330 | −1.21245 | ||||||||
\(899\) | 1.55689 | 0.0519251 | ||||||||
\(900\) | −4.39599 | −0.146533 | ||||||||
\(901\) | 47.9563 | 1.59766 | ||||||||
\(902\) | −1.80120 | −0.0599734 | ||||||||
\(903\) | 4.70344 | 0.156521 | ||||||||
\(904\) | 8.50905 | 0.283007 | ||||||||
\(905\) | 14.1733 | 0.471136 | ||||||||
\(906\) | 6.45800 | 0.214553 | ||||||||
\(907\) | 2.04272 | 0.0678274 | 0.0339137 | − | 0.999425i | \(-0.489203\pi\) | ||||
0.0339137 | + | 0.999425i | \(0.489203\pi\) | |||||||
\(908\) | −4.01934 | −0.133387 | ||||||||
\(909\) | 1.13546 | 0.0376608 | ||||||||
\(910\) | −2.44578 | −0.0810770 | ||||||||
\(911\) | −46.0830 | −1.52680 | −0.763398 | − | 0.645928i | \(-0.776471\pi\) | ||||
−0.763398 | + | 0.645928i | \(0.776471\pi\) | |||||||
\(912\) | −3.39222 | −0.112328 | ||||||||
\(913\) | −10.7814 | −0.356811 | ||||||||
\(914\) | 21.9436 | 0.725829 | ||||||||
\(915\) | 0.777182 | 0.0256928 | ||||||||
\(916\) | −15.5815 | −0.514828 | ||||||||
\(917\) | 27.9562 | 0.923196 | ||||||||
\(918\) | 6.42418 | 0.212029 | ||||||||
\(919\) | 4.13868 | 0.136522 | 0.0682612 | − | 0.997667i | \(-0.478255\pi\) | ||||
0.0682612 | + | 0.997667i | \(0.478255\pi\) | |||||||
\(920\) | 4.34817 | 0.143355 | ||||||||
\(921\) | 8.60709 | 0.283613 | ||||||||
\(922\) | −19.7455 | −0.650283 | ||||||||
\(923\) | 4.71604 | 0.155230 | ||||||||
\(924\) | −3.79435 | −0.124825 | ||||||||
\(925\) | −46.5495 | −1.53054 | ||||||||
\(926\) | −36.6840 | −1.20551 | ||||||||
\(927\) | 10.7380 | 0.352681 | ||||||||
\(928\) | 0.688882 | 0.0226137 | ||||||||
\(929\) | 31.4418 | 1.03157 | 0.515785 | − | 0.856718i | \(-0.327500\pi\) | ||||
0.515785 | + | 0.856718i | \(0.327500\pi\) | |||||||
\(930\) | −1.75645 | −0.0575961 | ||||||||
\(931\) | 25.0926 | 0.822376 | ||||||||
\(932\) | −20.1974 | −0.661587 | ||||||||
\(933\) | −5.85160 | −0.191573 | ||||||||
\(934\) | 36.7614 | 1.20287 | ||||||||
\(935\) | −4.99276 | −0.163281 | ||||||||
\(936\) | 0.829389 | 0.0271094 | ||||||||
\(937\) | 49.1285 | 1.60496 | 0.802479 | − | 0.596680i | \(-0.203514\pi\) | ||||
0.802479 | + | 0.596680i | \(0.203514\pi\) | |||||||
\(938\) | −33.5560 | −1.09564 | ||||||||
\(939\) | −6.45719 | −0.210723 | ||||||||
\(940\) | 7.66074 | 0.249866 | ||||||||
\(941\) | 42.3067 | 1.37916 | 0.689580 | − | 0.724210i | \(-0.257795\pi\) | ||||
0.689580 | + | 0.724210i | \(0.257795\pi\) | |||||||
\(942\) | 21.4950 | 0.700345 | ||||||||
\(943\) | 10.0773 | 0.328163 | ||||||||
\(944\) | −3.77758 | −0.122950 | ||||||||
\(945\) | 2.94890 | 0.0959278 | ||||||||
\(946\) | 1.23959 | 0.0403026 | ||||||||
\(947\) | 0.991701 | 0.0322260 | 0.0161130 | − | 0.999870i | \(-0.494871\pi\) | ||||
0.0161130 | + | 0.999870i | \(0.494871\pi\) | |||||||
\(948\) | 10.5300 | 0.342000 | ||||||||
\(949\) | −0.187601 | −0.00608978 | ||||||||
\(950\) | 14.9122 | 0.483814 | ||||||||
\(951\) | −11.2731 | −0.365555 | ||||||||
\(952\) | 24.3756 | 0.790017 | ||||||||
\(953\) | 0.570606 | 0.0184837 | 0.00924187 | − | 0.999957i | \(-0.497058\pi\) | ||||
0.00924187 | + | 0.999957i | \(0.497058\pi\) | |||||||
\(954\) | −7.46497 | −0.241687 | ||||||||
\(955\) | 4.54786 | 0.147165 | ||||||||
\(956\) | −16.3488 | −0.528759 | ||||||||
\(957\) | −0.688882 | −0.0222684 | ||||||||
\(958\) | 16.0940 | 0.519975 | ||||||||
\(959\) | 61.2257 | 1.97708 | ||||||||
\(960\) | −0.777182 | −0.0250834 | ||||||||
\(961\) | −25.8923 | −0.835236 | ||||||||
\(962\) | 8.78248 | 0.283158 | ||||||||
\(963\) | −11.3332 | −0.365206 | ||||||||
\(964\) | −15.8848 | −0.511614 | ||||||||
\(965\) | 18.0347 | 0.580558 | ||||||||
\(966\) | 21.2286 | 0.683019 | ||||||||
\(967\) | 42.4682 | 1.36569 | 0.682843 | − | 0.730565i | \(-0.260743\pi\) | ||||
0.682843 | + | 0.730565i | \(0.260743\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −21.7922 | −0.700067 | ||||||||
\(970\) | −1.90692 | −0.0612274 | ||||||||
\(971\) | 6.39066 | 0.205086 | 0.102543 | − | 0.994729i | \(-0.467302\pi\) | ||||
0.102543 | + | 0.994729i | \(0.467302\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −13.6190 | −0.436606 | ||||||||
\(974\) | −19.4585 | −0.623489 | ||||||||
\(975\) | −3.64598 | −0.116765 | ||||||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | 9.10943 | 0.291436 | 0.145718 | − | 0.989326i | \(-0.453451\pi\) | ||||
0.145718 | + | 0.989326i | \(0.453451\pi\) | |||||||
\(978\) | 24.3641 | 0.779076 | ||||||||
\(979\) | 4.99276 | 0.159569 | ||||||||
\(980\) | 5.74889 | 0.183642 | ||||||||
\(981\) | −6.58859 | −0.210357 | ||||||||
\(982\) | −18.8815 | −0.602532 | ||||||||
\(983\) | −15.7771 | −0.503210 | −0.251605 | − | 0.967830i | \(-0.580958\pi\) | ||||
−0.251605 | + | 0.967830i | \(0.580958\pi\) | |||||||
\(984\) | −1.80120 | −0.0574201 | ||||||||
\(985\) | −9.07456 | −0.289140 | ||||||||
\(986\) | 4.42550 | 0.140937 | ||||||||
\(987\) | 37.4012 | 1.19049 | ||||||||
\(988\) | −2.81347 | −0.0895083 | ||||||||
\(989\) | −6.93525 | −0.220528 | ||||||||
\(990\) | 0.777182 | 0.0247005 | ||||||||
\(991\) | 55.1508 | 1.75192 | 0.875962 | − | 0.482380i | \(-0.160228\pi\) | ||||
0.875962 | + | 0.482380i | \(0.160228\pi\) | |||||||
\(992\) | 2.26002 | 0.0717557 | ||||||||
\(993\) | 32.4487 | 1.02973 | ||||||||
\(994\) | −21.5753 | −0.684327 | ||||||||
\(995\) | −4.74228 | −0.150340 | ||||||||
\(996\) | −10.7814 | −0.341620 | ||||||||
\(997\) | −14.8620 | −0.470686 | −0.235343 | − | 0.971912i | \(-0.575621\pi\) | ||||
−0.235343 | + | 0.971912i | \(0.575621\pi\) | |||||||
\(998\) | −8.27868 | −0.262057 | ||||||||
\(999\) | −10.5891 | −0.335024 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4026.2.a.y.1.5 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.y.1.5 | ✓ | 7 | 1.1 | even | 1 | trivial |