Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
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: | \( x^{14} - 2 x^{13} - 49 x^{12} + 79 x^{11} + 956 x^{10} - 1179 x^{9} - 9396 x^{8} + 8315 x^{7} + 48570 x^{6} - 28124 x^{5} - 125592 x^{4} + 40576 x^{3} + 138096 x^{2} + \cdots - 43744 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(1.26062\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.26062 | 0.563767 | 0.281883 | − | 0.959449i | \(-0.409041\pi\) | ||||
0.281883 | + | 0.959449i | \(0.409041\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.87711 | 1.46541 | 0.732706 | − | 0.680546i | \(-0.238257\pi\) | ||||
0.732706 | + | 0.680546i | \(0.238257\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.26062 | 0.398643 | ||||||||
\(11\) | −3.70558 | −1.11727 | −0.558637 | − | 0.829412i | \(-0.688675\pi\) | ||||
−0.558637 | + | 0.829412i | \(0.688675\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 6.90495 | 1.91509 | 0.957544 | − | 0.288288i | \(-0.0930862\pi\) | ||||
0.957544 | + | 0.288288i | \(0.0930862\pi\) | |||||||
\(14\) | 3.87711 | 1.03620 | ||||||||
\(15\) | −1.26062 | −0.325491 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 2.11950 | 0.486247 | 0.243123 | − | 0.969995i | \(-0.421828\pi\) | ||||
0.243123 | + | 0.969995i | \(0.421828\pi\) | |||||||
\(20\) | 1.26062 | 0.281883 | ||||||||
\(21\) | −3.87711 | −0.846056 | ||||||||
\(22\) | −3.70558 | −0.790032 | ||||||||
\(23\) | 2.51141 | 0.523665 | 0.261832 | − | 0.965113i | \(-0.415673\pi\) | ||||
0.261832 | + | 0.965113i | \(0.415673\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −3.41084 | −0.682167 | ||||||||
\(26\) | 6.90495 | 1.35417 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.87711 | 0.732706 | ||||||||
\(29\) | 6.32123 | 1.17382 | 0.586911 | − | 0.809651i | \(-0.300344\pi\) | ||||
0.586911 | + | 0.809651i | \(0.300344\pi\) | |||||||
\(30\) | −1.26062 | −0.230157 | ||||||||
\(31\) | −2.19074 | −0.393468 | −0.196734 | − | 0.980457i | \(-0.563034\pi\) | ||||
−0.196734 | + | 0.980457i | \(0.563034\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.70558 | 0.645058 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 4.88757 | 0.826150 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.33158 | 0.876507 | 0.438253 | − | 0.898851i | \(-0.355597\pi\) | ||||
0.438253 | + | 0.898851i | \(0.355597\pi\) | |||||||
\(38\) | 2.11950 | 0.343828 | ||||||||
\(39\) | −6.90495 | −1.10568 | ||||||||
\(40\) | 1.26062 | 0.199322 | ||||||||
\(41\) | 8.42788 | 1.31621 | 0.658107 | − | 0.752925i | \(-0.271357\pi\) | ||||
0.658107 | + | 0.752925i | \(0.271357\pi\) | |||||||
\(42\) | −3.87711 | −0.598252 | ||||||||
\(43\) | −9.26765 | −1.41330 | −0.706652 | − | 0.707561i | \(-0.749795\pi\) | ||||
−0.706652 | + | 0.707561i | \(0.749795\pi\) | |||||||
\(44\) | −3.70558 | −0.558637 | ||||||||
\(45\) | 1.26062 | 0.187922 | ||||||||
\(46\) | 2.51141 | 0.370287 | ||||||||
\(47\) | −0.566613 | −0.0826490 | −0.0413245 | − | 0.999146i | \(-0.513158\pi\) | ||||
−0.0413245 | + | 0.999146i | \(0.513158\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 8.03201 | 1.14743 | ||||||||
\(50\) | −3.41084 | −0.482365 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 6.90495 | 0.957544 | ||||||||
\(53\) | −10.4207 | −1.43139 | −0.715696 | − | 0.698412i | \(-0.753891\pi\) | ||||
−0.715696 | + | 0.698412i | \(0.753891\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −4.67133 | −0.629882 | ||||||||
\(56\) | 3.87711 | 0.518101 | ||||||||
\(57\) | −2.11950 | −0.280735 | ||||||||
\(58\) | 6.32123 | 0.830018 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | −1.26062 | −0.162745 | ||||||||
\(61\) | −2.78209 | −0.356210 | −0.178105 | − | 0.984011i | \(-0.556997\pi\) | ||||
−0.178105 | + | 0.984011i | \(0.556997\pi\) | |||||||
\(62\) | −2.19074 | −0.278224 | ||||||||
\(63\) | 3.87711 | 0.488470 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 8.70451 | 1.07966 | ||||||||
\(66\) | 3.70558 | 0.456125 | ||||||||
\(67\) | −0.453039 | −0.0553475 | −0.0276738 | − | 0.999617i | \(-0.508810\pi\) | ||||
−0.0276738 | + | 0.999617i | \(0.508810\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | −2.51141 | −0.302338 | ||||||||
\(70\) | 4.88757 | 0.584176 | ||||||||
\(71\) | −12.4635 | −1.47915 | −0.739574 | − | 0.673075i | \(-0.764973\pi\) | ||||
−0.739574 | + | 0.673075i | \(0.764973\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 11.3440 | 1.32771 | 0.663854 | − | 0.747862i | \(-0.268919\pi\) | ||||
0.663854 | + | 0.747862i | \(0.268919\pi\) | |||||||
\(74\) | 5.33158 | 0.619784 | ||||||||
\(75\) | 3.41084 | 0.393849 | ||||||||
\(76\) | 2.11950 | 0.243123 | ||||||||
\(77\) | −14.3669 | −1.63727 | ||||||||
\(78\) | −6.90495 | −0.781831 | ||||||||
\(79\) | −12.9413 | −1.45601 | −0.728007 | − | 0.685570i | \(-0.759553\pi\) | ||||
−0.728007 | + | 0.685570i | \(0.759553\pi\) | |||||||
\(80\) | 1.26062 | 0.140942 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.42788 | 0.930704 | ||||||||
\(83\) | 14.6778 | 1.61110 | 0.805550 | − | 0.592528i | \(-0.201870\pi\) | ||||
0.805550 | + | 0.592528i | \(0.201870\pi\) | |||||||
\(84\) | −3.87711 | −0.423028 | ||||||||
\(85\) | 1.26062 | 0.136733 | ||||||||
\(86\) | −9.26765 | −0.999357 | ||||||||
\(87\) | −6.32123 | −0.677706 | ||||||||
\(88\) | −3.70558 | −0.395016 | ||||||||
\(89\) | −1.22006 | −0.129326 | −0.0646630 | − | 0.997907i | \(-0.520597\pi\) | ||||
−0.0646630 | + | 0.997907i | \(0.520597\pi\) | |||||||
\(90\) | 1.26062 | 0.132881 | ||||||||
\(91\) | 26.7713 | 2.80639 | ||||||||
\(92\) | 2.51141 | 0.261832 | ||||||||
\(93\) | 2.19074 | 0.227169 | ||||||||
\(94\) | −0.566613 | −0.0584417 | ||||||||
\(95\) | 2.67189 | 0.274130 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 8.86837 | 0.900446 | 0.450223 | − | 0.892916i | \(-0.351344\pi\) | ||||
0.450223 | + | 0.892916i | \(0.351344\pi\) | |||||||
\(98\) | 8.03201 | 0.811355 | ||||||||
\(99\) | −3.70558 | −0.372425 | ||||||||
\(100\) | −3.41084 | −0.341084 | ||||||||
\(101\) | −4.60470 | −0.458185 | −0.229093 | − | 0.973405i | \(-0.573576\pi\) | ||||
−0.229093 | + | 0.973405i | \(0.573576\pi\) | |||||||
\(102\) | −1.00000 | −0.0990148 | ||||||||
\(103\) | 8.13422 | 0.801489 | 0.400744 | − | 0.916190i | \(-0.368752\pi\) | ||||
0.400744 | + | 0.916190i | \(0.368752\pi\) | |||||||
\(104\) | 6.90495 | 0.677086 | ||||||||
\(105\) | −4.88757 | −0.476978 | ||||||||
\(106\) | −10.4207 | −1.01215 | ||||||||
\(107\) | 3.07336 | 0.297113 | 0.148556 | − | 0.988904i | \(-0.452537\pi\) | ||||
0.148556 | + | 0.988904i | \(0.452537\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 4.24379 | 0.406481 | 0.203241 | − | 0.979129i | \(-0.434853\pi\) | ||||
0.203241 | + | 0.979129i | \(0.434853\pi\) | |||||||
\(110\) | −4.67133 | −0.445394 | ||||||||
\(111\) | −5.33158 | −0.506052 | ||||||||
\(112\) | 3.87711 | 0.366353 | ||||||||
\(113\) | −4.70750 | −0.442844 | −0.221422 | − | 0.975178i | \(-0.571070\pi\) | ||||
−0.221422 | + | 0.975178i | \(0.571070\pi\) | |||||||
\(114\) | −2.11950 | −0.198509 | ||||||||
\(115\) | 3.16593 | 0.295225 | ||||||||
\(116\) | 6.32123 | 0.586911 | ||||||||
\(117\) | 6.90495 | 0.638362 | ||||||||
\(118\) | 1.00000 | 0.0920575 | ||||||||
\(119\) | 3.87711 | 0.355414 | ||||||||
\(120\) | −1.26062 | −0.115078 | ||||||||
\(121\) | 2.73131 | 0.248301 | ||||||||
\(122\) | −2.78209 | −0.251879 | ||||||||
\(123\) | −8.42788 | −0.759916 | ||||||||
\(124\) | −2.19074 | −0.196734 | ||||||||
\(125\) | −10.6029 | −0.948350 | ||||||||
\(126\) | 3.87711 | 0.345401 | ||||||||
\(127\) | 6.08214 | 0.539703 | 0.269852 | − | 0.962902i | \(-0.413025\pi\) | ||||
0.269852 | + | 0.962902i | \(0.413025\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 9.26765 | 0.815971 | ||||||||
\(130\) | 8.70451 | 0.763436 | ||||||||
\(131\) | −18.8906 | −1.65048 | −0.825241 | − | 0.564780i | \(-0.808961\pi\) | ||||
−0.825241 | + | 0.564780i | \(0.808961\pi\) | |||||||
\(132\) | 3.70558 | 0.322529 | ||||||||
\(133\) | 8.21754 | 0.712551 | ||||||||
\(134\) | −0.453039 | −0.0391366 | ||||||||
\(135\) | −1.26062 | −0.108497 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −7.31949 | −0.625347 | −0.312673 | − | 0.949861i | \(-0.601224\pi\) | ||||
−0.312673 | + | 0.949861i | \(0.601224\pi\) | |||||||
\(138\) | −2.51141 | −0.213785 | ||||||||
\(139\) | 11.0123 | 0.934048 | 0.467024 | − | 0.884245i | \(-0.345326\pi\) | ||||
0.467024 | + | 0.884245i | \(0.345326\pi\) | |||||||
\(140\) | 4.88757 | 0.413075 | ||||||||
\(141\) | 0.566613 | 0.0477174 | ||||||||
\(142\) | −12.4635 | −1.04592 | ||||||||
\(143\) | −25.5868 | −2.13968 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 7.96866 | 0.661762 | ||||||||
\(146\) | 11.3440 | 0.938832 | ||||||||
\(147\) | −8.03201 | −0.662469 | ||||||||
\(148\) | 5.33158 | 0.438253 | ||||||||
\(149\) | −4.08706 | −0.334825 | −0.167412 | − | 0.985887i | \(-0.553541\pi\) | ||||
−0.167412 | + | 0.985887i | \(0.553541\pi\) | |||||||
\(150\) | 3.41084 | 0.278494 | ||||||||
\(151\) | −3.48477 | −0.283587 | −0.141793 | − | 0.989896i | \(-0.545287\pi\) | ||||
−0.141793 | + | 0.989896i | \(0.545287\pi\) | |||||||
\(152\) | 2.11950 | 0.171914 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −14.3669 | −1.15772 | ||||||||
\(155\) | −2.76169 | −0.221824 | ||||||||
\(156\) | −6.90495 | −0.552838 | ||||||||
\(157\) | 6.18739 | 0.493808 | 0.246904 | − | 0.969040i | \(-0.420587\pi\) | ||||
0.246904 | + | 0.969040i | \(0.420587\pi\) | |||||||
\(158\) | −12.9413 | −1.02956 | ||||||||
\(159\) | 10.4207 | 0.826415 | ||||||||
\(160\) | 1.26062 | 0.0996608 | ||||||||
\(161\) | 9.73702 | 0.767384 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −10.2176 | −0.800306 | −0.400153 | − | 0.916448i | \(-0.631043\pi\) | ||||
−0.400153 | + | 0.916448i | \(0.631043\pi\) | |||||||
\(164\) | 8.42788 | 0.658107 | ||||||||
\(165\) | 4.67133 | 0.363662 | ||||||||
\(166\) | 14.6778 | 1.13922 | ||||||||
\(167\) | −20.7844 | −1.60834 | −0.804171 | − | 0.594398i | \(-0.797390\pi\) | ||||
−0.804171 | + | 0.594398i | \(0.797390\pi\) | |||||||
\(168\) | −3.87711 | −0.299126 | ||||||||
\(169\) | 34.6783 | 2.66756 | ||||||||
\(170\) | 1.26062 | 0.0966852 | ||||||||
\(171\) | 2.11950 | 0.162082 | ||||||||
\(172\) | −9.26765 | −0.706652 | ||||||||
\(173\) | 13.8913 | 1.05613 | 0.528067 | − | 0.849203i | \(-0.322917\pi\) | ||||
0.528067 | + | 0.849203i | \(0.322917\pi\) | |||||||
\(174\) | −6.32123 | −0.479211 | ||||||||
\(175\) | −13.2242 | −0.999656 | ||||||||
\(176\) | −3.70558 | −0.279318 | ||||||||
\(177\) | −1.00000 | −0.0751646 | ||||||||
\(178\) | −1.22006 | −0.0914473 | ||||||||
\(179\) | −9.01354 | −0.673704 | −0.336852 | − | 0.941558i | \(-0.609362\pi\) | ||||
−0.336852 | + | 0.941558i | \(0.609362\pi\) | |||||||
\(180\) | 1.26062 | 0.0939611 | ||||||||
\(181\) | −3.59465 | −0.267189 | −0.133594 | − | 0.991036i | \(-0.542652\pi\) | ||||
−0.133594 | + | 0.991036i | \(0.542652\pi\) | |||||||
\(182\) | 26.7713 | 1.98442 | ||||||||
\(183\) | 2.78209 | 0.205658 | ||||||||
\(184\) | 2.51141 | 0.185144 | ||||||||
\(185\) | 6.72110 | 0.494145 | ||||||||
\(186\) | 2.19074 | 0.160633 | ||||||||
\(187\) | −3.70558 | −0.270979 | ||||||||
\(188\) | −0.566613 | −0.0413245 | ||||||||
\(189\) | −3.87711 | −0.282019 | ||||||||
\(190\) | 2.67189 | 0.193839 | ||||||||
\(191\) | −6.31625 | −0.457028 | −0.228514 | − | 0.973541i | \(-0.573387\pi\) | ||||
−0.228514 | + | 0.973541i | \(0.573387\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −13.5834 | −0.977753 | −0.488877 | − | 0.872353i | \(-0.662593\pi\) | ||||
−0.488877 | + | 0.872353i | \(0.662593\pi\) | |||||||
\(194\) | 8.86837 | 0.636712 | ||||||||
\(195\) | −8.70451 | −0.623343 | ||||||||
\(196\) | 8.03201 | 0.573715 | ||||||||
\(197\) | −27.2147 | −1.93897 | −0.969484 | − | 0.245156i | \(-0.921161\pi\) | ||||
−0.969484 | + | 0.245156i | \(0.921161\pi\) | |||||||
\(198\) | −3.70558 | −0.263344 | ||||||||
\(199\) | −11.0485 | −0.783207 | −0.391604 | − | 0.920134i | \(-0.628080\pi\) | ||||
−0.391604 | + | 0.920134i | \(0.628080\pi\) | |||||||
\(200\) | −3.41084 | −0.241183 | ||||||||
\(201\) | 0.453039 | 0.0319549 | ||||||||
\(202\) | −4.60470 | −0.323986 | ||||||||
\(203\) | 24.5081 | 1.72013 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | 10.6244 | 0.742037 | ||||||||
\(206\) | 8.13422 | 0.566738 | ||||||||
\(207\) | 2.51141 | 0.174555 | ||||||||
\(208\) | 6.90495 | 0.478772 | ||||||||
\(209\) | −7.85397 | −0.543271 | ||||||||
\(210\) | −4.88757 | −0.337274 | ||||||||
\(211\) | 23.7933 | 1.63800 | 0.819001 | − | 0.573793i | \(-0.194528\pi\) | ||||
0.819001 | + | 0.573793i | \(0.194528\pi\) | |||||||
\(212\) | −10.4207 | −0.715696 | ||||||||
\(213\) | 12.4635 | 0.853986 | ||||||||
\(214\) | 3.07336 | 0.210091 | ||||||||
\(215\) | −11.6830 | −0.796773 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −8.49375 | −0.576593 | ||||||||
\(218\) | 4.24379 | 0.287426 | ||||||||
\(219\) | −11.3440 | −0.766553 | ||||||||
\(220\) | −4.67133 | −0.314941 | ||||||||
\(221\) | 6.90495 | 0.464477 | ||||||||
\(222\) | −5.33158 | −0.357832 | ||||||||
\(223\) | 14.5096 | 0.971637 | 0.485818 | − | 0.874060i | \(-0.338522\pi\) | ||||
0.485818 | + | 0.874060i | \(0.338522\pi\) | |||||||
\(224\) | 3.87711 | 0.259051 | ||||||||
\(225\) | −3.41084 | −0.227389 | ||||||||
\(226\) | −4.70750 | −0.313138 | ||||||||
\(227\) | −11.2613 | −0.747440 | −0.373720 | − | 0.927542i | \(-0.621918\pi\) | ||||
−0.373720 | + | 0.927542i | \(0.621918\pi\) | |||||||
\(228\) | −2.11950 | −0.140367 | ||||||||
\(229\) | −14.7592 | −0.975312 | −0.487656 | − | 0.873036i | \(-0.662148\pi\) | ||||
−0.487656 | + | 0.873036i | \(0.662148\pi\) | |||||||
\(230\) | 3.16593 | 0.208755 | ||||||||
\(231\) | 14.3669 | 0.945276 | ||||||||
\(232\) | 6.32123 | 0.415009 | ||||||||
\(233\) | −14.1530 | −0.927192 | −0.463596 | − | 0.886047i | \(-0.653441\pi\) | ||||
−0.463596 | + | 0.886047i | \(0.653441\pi\) | |||||||
\(234\) | 6.90495 | 0.451390 | ||||||||
\(235\) | −0.714284 | −0.0465948 | ||||||||
\(236\) | 1.00000 | 0.0650945 | ||||||||
\(237\) | 12.9413 | 0.840630 | ||||||||
\(238\) | 3.87711 | 0.251316 | ||||||||
\(239\) | 19.0349 | 1.23127 | 0.615634 | − | 0.788032i | \(-0.288900\pi\) | ||||
0.615634 | + | 0.788032i | \(0.288900\pi\) | |||||||
\(240\) | −1.26062 | −0.0813727 | ||||||||
\(241\) | 13.6413 | 0.878711 | 0.439355 | − | 0.898313i | \(-0.355207\pi\) | ||||
0.439355 | + | 0.898313i | \(0.355207\pi\) | |||||||
\(242\) | 2.73131 | 0.175575 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −2.78209 | −0.178105 | ||||||||
\(245\) | 10.1253 | 0.646882 | ||||||||
\(246\) | −8.42788 | −0.537342 | ||||||||
\(247\) | 14.6350 | 0.931205 | ||||||||
\(248\) | −2.19074 | −0.139112 | ||||||||
\(249\) | −14.6778 | −0.930169 | ||||||||
\(250\) | −10.6029 | −0.670584 | ||||||||
\(251\) | 23.9674 | 1.51281 | 0.756404 | − | 0.654105i | \(-0.226954\pi\) | ||||
0.756404 | + | 0.654105i | \(0.226954\pi\) | |||||||
\(252\) | 3.87711 | 0.244235 | ||||||||
\(253\) | −9.30622 | −0.585077 | ||||||||
\(254\) | 6.08214 | 0.381628 | ||||||||
\(255\) | −1.26062 | −0.0789431 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −23.0284 | −1.43647 | −0.718235 | − | 0.695800i | \(-0.755050\pi\) | ||||
−0.718235 | + | 0.695800i | \(0.755050\pi\) | |||||||
\(258\) | 9.26765 | 0.576979 | ||||||||
\(259\) | 20.6712 | 1.28444 | ||||||||
\(260\) | 8.70451 | 0.539831 | ||||||||
\(261\) | 6.32123 | 0.391274 | ||||||||
\(262\) | −18.8906 | −1.16707 | ||||||||
\(263\) | 2.30569 | 0.142175 | 0.0710874 | − | 0.997470i | \(-0.477353\pi\) | ||||
0.0710874 | + | 0.997470i | \(0.477353\pi\) | |||||||
\(264\) | 3.70558 | 0.228063 | ||||||||
\(265\) | −13.1365 | −0.806971 | ||||||||
\(266\) | 8.21754 | 0.503850 | ||||||||
\(267\) | 1.22006 | 0.0746664 | ||||||||
\(268\) | −0.453039 | −0.0276738 | ||||||||
\(269\) | 19.7737 | 1.20562 | 0.602811 | − | 0.797884i | \(-0.294047\pi\) | ||||
0.602811 | + | 0.797884i | \(0.294047\pi\) | |||||||
\(270\) | −1.26062 | −0.0767189 | ||||||||
\(271\) | 27.5096 | 1.67109 | 0.835544 | − | 0.549423i | \(-0.185153\pi\) | ||||
0.835544 | + | 0.549423i | \(0.185153\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | −26.7713 | −1.62027 | ||||||||
\(274\) | −7.31949 | −0.442187 | ||||||||
\(275\) | 12.6391 | 0.762168 | ||||||||
\(276\) | −2.51141 | −0.151169 | ||||||||
\(277\) | 13.5731 | 0.815527 | 0.407763 | − | 0.913088i | \(-0.366309\pi\) | ||||
0.407763 | + | 0.913088i | \(0.366309\pi\) | |||||||
\(278\) | 11.0123 | 0.660472 | ||||||||
\(279\) | −2.19074 | −0.131156 | ||||||||
\(280\) | 4.88757 | 0.292088 | ||||||||
\(281\) | 10.0237 | 0.597964 | 0.298982 | − | 0.954259i | \(-0.403353\pi\) | ||||
0.298982 | + | 0.954259i | \(0.403353\pi\) | |||||||
\(282\) | 0.566613 | 0.0337413 | ||||||||
\(283\) | 4.03872 | 0.240077 | 0.120039 | − | 0.992769i | \(-0.461698\pi\) | ||||
0.120039 | + | 0.992769i | \(0.461698\pi\) | |||||||
\(284\) | −12.4635 | −0.739574 | ||||||||
\(285\) | −2.67189 | −0.158269 | ||||||||
\(286\) | −25.5868 | −1.51298 | ||||||||
\(287\) | 32.6758 | 1.92879 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 7.96866 | 0.467936 | ||||||||
\(291\) | −8.86837 | −0.519873 | ||||||||
\(292\) | 11.3440 | 0.663854 | ||||||||
\(293\) | 30.3238 | 1.77154 | 0.885769 | − | 0.464127i | \(-0.153632\pi\) | ||||
0.885769 | + | 0.464127i | \(0.153632\pi\) | |||||||
\(294\) | −8.03201 | −0.468436 | ||||||||
\(295\) | 1.26062 | 0.0733961 | ||||||||
\(296\) | 5.33158 | 0.309892 | ||||||||
\(297\) | 3.70558 | 0.215019 | ||||||||
\(298\) | −4.08706 | −0.236757 | ||||||||
\(299\) | 17.3411 | 1.00286 | ||||||||
\(300\) | 3.41084 | 0.196925 | ||||||||
\(301\) | −35.9317 | −2.07107 | ||||||||
\(302\) | −3.48477 | −0.200526 | ||||||||
\(303\) | 4.60470 | 0.264533 | ||||||||
\(304\) | 2.11950 | 0.121562 | ||||||||
\(305\) | −3.50716 | −0.200819 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | 5.03826 | 0.287549 | 0.143774 | − | 0.989611i | \(-0.454076\pi\) | ||||
0.143774 | + | 0.989611i | \(0.454076\pi\) | |||||||
\(308\) | −14.3669 | −0.818633 | ||||||||
\(309\) | −8.13422 | −0.462740 | ||||||||
\(310\) | −2.76169 | −0.156853 | ||||||||
\(311\) | 14.5697 | 0.826170 | 0.413085 | − | 0.910692i | \(-0.364451\pi\) | ||||
0.413085 | + | 0.910692i | \(0.364451\pi\) | |||||||
\(312\) | −6.90495 | −0.390916 | ||||||||
\(313\) | 15.0211 | 0.849044 | 0.424522 | − | 0.905418i | \(-0.360442\pi\) | ||||
0.424522 | + | 0.905418i | \(0.360442\pi\) | |||||||
\(314\) | 6.18739 | 0.349175 | ||||||||
\(315\) | 4.88757 | 0.275383 | ||||||||
\(316\) | −12.9413 | −0.728007 | ||||||||
\(317\) | 25.7537 | 1.44647 | 0.723237 | − | 0.690600i | \(-0.242653\pi\) | ||||
0.723237 | + | 0.690600i | \(0.242653\pi\) | |||||||
\(318\) | 10.4207 | 0.584364 | ||||||||
\(319\) | −23.4238 | −1.31148 | ||||||||
\(320\) | 1.26062 | 0.0704708 | ||||||||
\(321\) | −3.07336 | −0.171538 | ||||||||
\(322\) | 9.73702 | 0.542623 | ||||||||
\(323\) | 2.11950 | 0.117932 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −23.5516 | −1.30641 | ||||||||
\(326\) | −10.2176 | −0.565902 | ||||||||
\(327\) | −4.24379 | −0.234682 | ||||||||
\(328\) | 8.42788 | 0.465352 | ||||||||
\(329\) | −2.19682 | −0.121115 | ||||||||
\(330\) | 4.67133 | 0.257148 | ||||||||
\(331\) | 9.58716 | 0.526958 | 0.263479 | − | 0.964665i | \(-0.415130\pi\) | ||||
0.263479 | + | 0.964665i | \(0.415130\pi\) | |||||||
\(332\) | 14.6778 | 0.805550 | ||||||||
\(333\) | 5.33158 | 0.292169 | ||||||||
\(334\) | −20.7844 | −1.13727 | ||||||||
\(335\) | −0.571110 | −0.0312031 | ||||||||
\(336\) | −3.87711 | −0.211514 | ||||||||
\(337\) | −12.3053 | −0.670313 | −0.335156 | − | 0.942163i | \(-0.608789\pi\) | ||||
−0.335156 | + | 0.942163i | \(0.608789\pi\) | |||||||
\(338\) | 34.6783 | 1.88625 | ||||||||
\(339\) | 4.70750 | 0.255676 | ||||||||
\(340\) | 1.26062 | 0.0683667 | ||||||||
\(341\) | 8.11796 | 0.439612 | ||||||||
\(342\) | 2.11950 | 0.114609 | ||||||||
\(343\) | 4.00121 | 0.216045 | ||||||||
\(344\) | −9.26765 | −0.499678 | ||||||||
\(345\) | −3.16593 | −0.170448 | ||||||||
\(346\) | 13.8913 | 0.746800 | ||||||||
\(347\) | −33.7675 | −1.81273 | −0.906367 | − | 0.422491i | \(-0.861156\pi\) | ||||
−0.906367 | + | 0.422491i | \(0.861156\pi\) | |||||||
\(348\) | −6.32123 | −0.338853 | ||||||||
\(349\) | 26.2330 | 1.40422 | 0.702110 | − | 0.712069i | \(-0.252241\pi\) | ||||
0.702110 | + | 0.712069i | \(0.252241\pi\) | |||||||
\(350\) | −13.2242 | −0.706863 | ||||||||
\(351\) | −6.90495 | −0.368559 | ||||||||
\(352\) | −3.70558 | −0.197508 | ||||||||
\(353\) | −22.4187 | −1.19323 | −0.596614 | − | 0.802528i | \(-0.703488\pi\) | ||||
−0.596614 | + | 0.802528i | \(0.703488\pi\) | |||||||
\(354\) | −1.00000 | −0.0531494 | ||||||||
\(355\) | −15.7118 | −0.833894 | ||||||||
\(356\) | −1.22006 | −0.0646630 | ||||||||
\(357\) | −3.87711 | −0.205199 | ||||||||
\(358\) | −9.01354 | −0.476381 | ||||||||
\(359\) | 17.3542 | 0.915918 | 0.457959 | − | 0.888973i | \(-0.348581\pi\) | ||||
0.457959 | + | 0.888973i | \(0.348581\pi\) | |||||||
\(360\) | 1.26062 | 0.0664405 | ||||||||
\(361\) | −14.5077 | −0.763564 | ||||||||
\(362\) | −3.59465 | −0.188931 | ||||||||
\(363\) | −2.73131 | −0.143357 | ||||||||
\(364\) | 26.7713 | 1.40320 | ||||||||
\(365\) | 14.3004 | 0.748518 | ||||||||
\(366\) | 2.78209 | 0.145422 | ||||||||
\(367\) | −2.01352 | −0.105105 | −0.0525524 | − | 0.998618i | \(-0.516736\pi\) | ||||
−0.0525524 | + | 0.998618i | \(0.516736\pi\) | |||||||
\(368\) | 2.51141 | 0.130916 | ||||||||
\(369\) | 8.42788 | 0.438738 | ||||||||
\(370\) | 6.72110 | 0.349413 | ||||||||
\(371\) | −40.4022 | −2.09758 | ||||||||
\(372\) | 2.19074 | 0.113585 | ||||||||
\(373\) | 36.9804 | 1.91477 | 0.957386 | − | 0.288813i | \(-0.0932605\pi\) | ||||
0.957386 | + | 0.288813i | \(0.0932605\pi\) | |||||||
\(374\) | −3.70558 | −0.191611 | ||||||||
\(375\) | 10.6029 | 0.547530 | ||||||||
\(376\) | −0.566613 | −0.0292208 | ||||||||
\(377\) | 43.6477 | 2.24797 | ||||||||
\(378\) | −3.87711 | −0.199417 | ||||||||
\(379\) | −19.1842 | −0.985427 | −0.492713 | − | 0.870192i | \(-0.663995\pi\) | ||||
−0.492713 | + | 0.870192i | \(0.663995\pi\) | |||||||
\(380\) | 2.67189 | 0.137065 | ||||||||
\(381\) | −6.08214 | −0.311598 | ||||||||
\(382\) | −6.31625 | −0.323167 | ||||||||
\(383\) | −14.5579 | −0.743875 | −0.371938 | − | 0.928258i | \(-0.621306\pi\) | ||||
−0.371938 | + | 0.928258i | \(0.621306\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −18.1113 | −0.923035 | ||||||||
\(386\) | −13.5834 | −0.691376 | ||||||||
\(387\) | −9.26765 | −0.471101 | ||||||||
\(388\) | 8.86837 | 0.450223 | ||||||||
\(389\) | 0.644984 | 0.0327020 | 0.0163510 | − | 0.999866i | \(-0.494795\pi\) | ||||
0.0163510 | + | 0.999866i | \(0.494795\pi\) | |||||||
\(390\) | −8.70451 | −0.440770 | ||||||||
\(391\) | 2.51141 | 0.127007 | ||||||||
\(392\) | 8.03201 | 0.405678 | ||||||||
\(393\) | 18.8906 | 0.952907 | ||||||||
\(394\) | −27.2147 | −1.37106 | ||||||||
\(395\) | −16.3141 | −0.820852 | ||||||||
\(396\) | −3.70558 | −0.186212 | ||||||||
\(397\) | −34.7272 | −1.74291 | −0.871454 | − | 0.490477i | \(-0.836823\pi\) | ||||
−0.871454 | + | 0.490477i | \(0.836823\pi\) | |||||||
\(398\) | −11.0485 | −0.553811 | ||||||||
\(399\) | −8.21754 | −0.411392 | ||||||||
\(400\) | −3.41084 | −0.170542 | ||||||||
\(401\) | −12.8048 | −0.639442 | −0.319721 | − | 0.947512i | \(-0.603589\pi\) | ||||
−0.319721 | + | 0.947512i | \(0.603589\pi\) | |||||||
\(402\) | 0.453039 | 0.0225955 | ||||||||
\(403\) | −15.1269 | −0.753526 | ||||||||
\(404\) | −4.60470 | −0.229093 | ||||||||
\(405\) | 1.26062 | 0.0626407 | ||||||||
\(406\) | 24.5081 | 1.21632 | ||||||||
\(407\) | −19.7566 | −0.979298 | ||||||||
\(408\) | −1.00000 | −0.0495074 | ||||||||
\(409\) | 30.5691 | 1.51154 | 0.755772 | − | 0.654835i | \(-0.227262\pi\) | ||||
0.755772 | + | 0.654835i | \(0.227262\pi\) | |||||||
\(410\) | 10.6244 | 0.524700 | ||||||||
\(411\) | 7.31949 | 0.361044 | ||||||||
\(412\) | 8.13422 | 0.400744 | ||||||||
\(413\) | 3.87711 | 0.190780 | ||||||||
\(414\) | 2.51141 | 0.123429 | ||||||||
\(415\) | 18.5032 | 0.908284 | ||||||||
\(416\) | 6.90495 | 0.338543 | ||||||||
\(417\) | −11.0123 | −0.539273 | ||||||||
\(418\) | −7.85397 | −0.384150 | ||||||||
\(419\) | −9.79506 | −0.478520 | −0.239260 | − | 0.970956i | \(-0.576905\pi\) | ||||
−0.239260 | + | 0.970956i | \(0.576905\pi\) | |||||||
\(420\) | −4.88757 | −0.238489 | ||||||||
\(421\) | −7.50279 | −0.365663 | −0.182832 | − | 0.983144i | \(-0.558526\pi\) | ||||
−0.182832 | + | 0.983144i | \(0.558526\pi\) | |||||||
\(422\) | 23.7933 | 1.15824 | ||||||||
\(423\) | −0.566613 | −0.0275497 | ||||||||
\(424\) | −10.4207 | −0.506074 | ||||||||
\(425\) | −3.41084 | −0.165450 | ||||||||
\(426\) | 12.4635 | 0.603860 | ||||||||
\(427\) | −10.7865 | −0.521994 | ||||||||
\(428\) | 3.07336 | 0.148556 | ||||||||
\(429\) | 25.5868 | 1.23534 | ||||||||
\(430\) | −11.6830 | −0.563404 | ||||||||
\(431\) | −2.08543 | −0.100452 | −0.0502259 | − | 0.998738i | \(-0.515994\pi\) | ||||
−0.0502259 | + | 0.998738i | \(0.515994\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 7.45018 | 0.358033 | 0.179016 | − | 0.983846i | \(-0.442708\pi\) | ||||
0.179016 | + | 0.983846i | \(0.442708\pi\) | |||||||
\(434\) | −8.49375 | −0.407713 | ||||||||
\(435\) | −7.96866 | −0.382068 | ||||||||
\(436\) | 4.24379 | 0.203241 | ||||||||
\(437\) | 5.32293 | 0.254630 | ||||||||
\(438\) | −11.3440 | −0.542035 | ||||||||
\(439\) | −19.2809 | −0.920226 | −0.460113 | − | 0.887860i | \(-0.652191\pi\) | ||||
−0.460113 | + | 0.887860i | \(0.652191\pi\) | |||||||
\(440\) | −4.67133 | −0.222697 | ||||||||
\(441\) | 8.03201 | 0.382477 | ||||||||
\(442\) | 6.90495 | 0.328435 | ||||||||
\(443\) | −23.5618 | −1.11946 | −0.559728 | − | 0.828676i | \(-0.689095\pi\) | ||||
−0.559728 | + | 0.828676i | \(0.689095\pi\) | |||||||
\(444\) | −5.33158 | −0.253026 | ||||||||
\(445\) | −1.53803 | −0.0729096 | ||||||||
\(446\) | 14.5096 | 0.687051 | ||||||||
\(447\) | 4.08706 | 0.193311 | ||||||||
\(448\) | 3.87711 | 0.183176 | ||||||||
\(449\) | −2.41928 | −0.114173 | −0.0570865 | − | 0.998369i | \(-0.518181\pi\) | ||||
−0.0570865 | + | 0.998369i | \(0.518181\pi\) | |||||||
\(450\) | −3.41084 | −0.160788 | ||||||||
\(451\) | −31.2302 | −1.47057 | ||||||||
\(452\) | −4.70750 | −0.221422 | ||||||||
\(453\) | 3.48477 | 0.163729 | ||||||||
\(454\) | −11.2613 | −0.528520 | ||||||||
\(455\) | 33.7484 | 1.58215 | ||||||||
\(456\) | −2.11950 | −0.0992547 | ||||||||
\(457\) | 4.67152 | 0.218524 | 0.109262 | − | 0.994013i | \(-0.465151\pi\) | ||||
0.109262 | + | 0.994013i | \(0.465151\pi\) | |||||||
\(458\) | −14.7592 | −0.689650 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 3.16593 | 0.147612 | ||||||||
\(461\) | 31.4436 | 1.46447 | 0.732237 | − | 0.681050i | \(-0.238476\pi\) | ||||
0.732237 | + | 0.681050i | \(0.238476\pi\) | |||||||
\(462\) | 14.3669 | 0.668411 | ||||||||
\(463\) | 3.38202 | 0.157176 | 0.0785879 | − | 0.996907i | \(-0.474959\pi\) | ||||
0.0785879 | + | 0.996907i | \(0.474959\pi\) | |||||||
\(464\) | 6.32123 | 0.293456 | ||||||||
\(465\) | 2.76169 | 0.128070 | ||||||||
\(466\) | −14.1530 | −0.655623 | ||||||||
\(467\) | 23.5843 | 1.09135 | 0.545675 | − | 0.837997i | \(-0.316273\pi\) | ||||
0.545675 | + | 0.837997i | \(0.316273\pi\) | |||||||
\(468\) | 6.90495 | 0.319181 | ||||||||
\(469\) | −1.75648 | −0.0811069 | ||||||||
\(470\) | −0.714284 | −0.0329475 | ||||||||
\(471\) | −6.18739 | −0.285100 | ||||||||
\(472\) | 1.00000 | 0.0460287 | ||||||||
\(473\) | 34.3420 | 1.57905 | ||||||||
\(474\) | 12.9413 | 0.594415 | ||||||||
\(475\) | −7.22927 | −0.331702 | ||||||||
\(476\) | 3.87711 | 0.177707 | ||||||||
\(477\) | −10.4207 | −0.477131 | ||||||||
\(478\) | 19.0349 | 0.870638 | ||||||||
\(479\) | 11.2885 | 0.515785 | 0.257892 | − | 0.966174i | \(-0.416972\pi\) | ||||
0.257892 | + | 0.966174i | \(0.416972\pi\) | |||||||
\(480\) | −1.26062 | −0.0575392 | ||||||||
\(481\) | 36.8143 | 1.67859 | ||||||||
\(482\) | 13.6413 | 0.621342 | ||||||||
\(483\) | −9.73702 | −0.443050 | ||||||||
\(484\) | 2.73131 | 0.124150 | ||||||||
\(485\) | 11.1796 | 0.507641 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 10.3474 | 0.468885 | 0.234443 | − | 0.972130i | \(-0.424673\pi\) | ||||
0.234443 | + | 0.972130i | \(0.424673\pi\) | |||||||
\(488\) | −2.78209 | −0.125939 | ||||||||
\(489\) | 10.2176 | 0.462057 | ||||||||
\(490\) | 10.1253 | 0.457415 | ||||||||
\(491\) | −7.75497 | −0.349977 | −0.174988 | − | 0.984571i | \(-0.555989\pi\) | ||||
−0.174988 | + | 0.984571i | \(0.555989\pi\) | |||||||
\(492\) | −8.42788 | −0.379958 | ||||||||
\(493\) | 6.32123 | 0.284694 | ||||||||
\(494\) | 14.6350 | 0.658461 | ||||||||
\(495\) | −4.67133 | −0.209961 | ||||||||
\(496\) | −2.19074 | −0.0983671 | ||||||||
\(497\) | −48.3225 | −2.16756 | ||||||||
\(498\) | −14.6778 | −0.657729 | ||||||||
\(499\) | 9.95739 | 0.445754 | 0.222877 | − | 0.974847i | \(-0.428455\pi\) | ||||
0.222877 | + | 0.974847i | \(0.428455\pi\) | |||||||
\(500\) | −10.6029 | −0.474175 | ||||||||
\(501\) | 20.7844 | 0.928577 | ||||||||
\(502\) | 23.9674 | 1.06972 | ||||||||
\(503\) | −4.70643 | −0.209849 | −0.104925 | − | 0.994480i | \(-0.533460\pi\) | ||||
−0.104925 | + | 0.994480i | \(0.533460\pi\) | |||||||
\(504\) | 3.87711 | 0.172700 | ||||||||
\(505\) | −5.80478 | −0.258309 | ||||||||
\(506\) | −9.30622 | −0.413712 | ||||||||
\(507\) | −34.6783 | −1.54012 | ||||||||
\(508\) | 6.08214 | 0.269852 | ||||||||
\(509\) | −20.0388 | −0.888206 | −0.444103 | − | 0.895976i | \(-0.646478\pi\) | ||||
−0.444103 | + | 0.895976i | \(0.646478\pi\) | |||||||
\(510\) | −1.26062 | −0.0558212 | ||||||||
\(511\) | 43.9818 | 1.94564 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.11950 | −0.0935782 | ||||||||
\(514\) | −23.0284 | −1.01574 | ||||||||
\(515\) | 10.2542 | 0.451852 | ||||||||
\(516\) | 9.26765 | 0.407986 | ||||||||
\(517\) | 2.09963 | 0.0923416 | ||||||||
\(518\) | 20.6712 | 0.908238 | ||||||||
\(519\) | −13.8913 | −0.609759 | ||||||||
\(520\) | 8.70451 | 0.381718 | ||||||||
\(521\) | 7.61921 | 0.333804 | 0.166902 | − | 0.985974i | \(-0.446624\pi\) | ||||
0.166902 | + | 0.985974i | \(0.446624\pi\) | |||||||
\(522\) | 6.32123 | 0.276673 | ||||||||
\(523\) | 2.14711 | 0.0938864 | 0.0469432 | − | 0.998898i | \(-0.485052\pi\) | ||||
0.0469432 | + | 0.998898i | \(0.485052\pi\) | |||||||
\(524\) | −18.8906 | −0.825241 | ||||||||
\(525\) | 13.2242 | 0.577151 | ||||||||
\(526\) | 2.30569 | 0.100533 | ||||||||
\(527\) | −2.19074 | −0.0954301 | ||||||||
\(528\) | 3.70558 | 0.161265 | ||||||||
\(529\) | −16.6928 | −0.725775 | ||||||||
\(530\) | −13.1365 | −0.570615 | ||||||||
\(531\) | 1.00000 | 0.0433963 | ||||||||
\(532\) | 8.21754 | 0.356276 | ||||||||
\(533\) | 58.1940 | 2.52066 | ||||||||
\(534\) | 1.22006 | 0.0527971 | ||||||||
\(535\) | 3.87434 | 0.167502 | ||||||||
\(536\) | −0.453039 | −0.0195683 | ||||||||
\(537\) | 9.01354 | 0.388963 | ||||||||
\(538\) | 19.7737 | 0.852503 | ||||||||
\(539\) | −29.7632 | −1.28199 | ||||||||
\(540\) | −1.26062 | −0.0542485 | ||||||||
\(541\) | −0.386441 | −0.0166144 | −0.00830720 | − | 0.999965i | \(-0.502644\pi\) | ||||
−0.00830720 | + | 0.999965i | \(0.502644\pi\) | |||||||
\(542\) | 27.5096 | 1.18164 | ||||||||
\(543\) | 3.59465 | 0.154261 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 5.34981 | 0.229161 | ||||||||
\(546\) | −26.7713 | −1.14570 | ||||||||
\(547\) | 30.4805 | 1.30325 | 0.651627 | − | 0.758540i | \(-0.274087\pi\) | ||||
0.651627 | + | 0.758540i | \(0.274087\pi\) | |||||||
\(548\) | −7.31949 | −0.312673 | ||||||||
\(549\) | −2.78209 | −0.118737 | ||||||||
\(550\) | 12.6391 | 0.538934 | ||||||||
\(551\) | 13.3978 | 0.570767 | ||||||||
\(552\) | −2.51141 | −0.106893 | ||||||||
\(553\) | −50.1750 | −2.13366 | ||||||||
\(554\) | 13.5731 | 0.576664 | ||||||||
\(555\) | −6.72110 | −0.285295 | ||||||||
\(556\) | 11.0123 | 0.467024 | ||||||||
\(557\) | −44.9059 | −1.90272 | −0.951362 | − | 0.308074i | \(-0.900316\pi\) | ||||
−0.951362 | + | 0.308074i | \(0.900316\pi\) | |||||||
\(558\) | −2.19074 | −0.0927414 | ||||||||
\(559\) | −63.9926 | −2.70660 | ||||||||
\(560\) | 4.88757 | 0.206537 | ||||||||
\(561\) | 3.70558 | 0.156450 | ||||||||
\(562\) | 10.0237 | 0.422825 | ||||||||
\(563\) | 1.23125 | 0.0518912 | 0.0259456 | − | 0.999663i | \(-0.491740\pi\) | ||||
0.0259456 | + | 0.999663i | \(0.491740\pi\) | |||||||
\(564\) | 0.566613 | 0.0238587 | ||||||||
\(565\) | −5.93437 | −0.249661 | ||||||||
\(566\) | 4.03872 | 0.169760 | ||||||||
\(567\) | 3.87711 | 0.162823 | ||||||||
\(568\) | −12.4635 | −0.522958 | ||||||||
\(569\) | −10.0696 | −0.422139 | −0.211070 | − | 0.977471i | \(-0.567695\pi\) | ||||
−0.211070 | + | 0.977471i | \(0.567695\pi\) | |||||||
\(570\) | −2.67189 | −0.111913 | ||||||||
\(571\) | −36.4471 | −1.52526 | −0.762631 | − | 0.646833i | \(-0.776093\pi\) | ||||
−0.762631 | + | 0.646833i | \(0.776093\pi\) | |||||||
\(572\) | −25.5868 | −1.06984 | ||||||||
\(573\) | 6.31625 | 0.263865 | ||||||||
\(574\) | 32.6758 | 1.36386 | ||||||||
\(575\) | −8.56600 | −0.357227 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −16.6992 | −0.695198 | −0.347599 | − | 0.937643i | \(-0.613003\pi\) | ||||
−0.347599 | + | 0.937643i | \(0.613003\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | 13.5834 | 0.564506 | ||||||||
\(580\) | 7.96866 | 0.330881 | ||||||||
\(581\) | 56.9076 | 2.36092 | ||||||||
\(582\) | −8.86837 | −0.367606 | ||||||||
\(583\) | 38.6147 | 1.59926 | ||||||||
\(584\) | 11.3440 | 0.469416 | ||||||||
\(585\) | 8.70451 | 0.359887 | ||||||||
\(586\) | 30.3238 | 1.25267 | ||||||||
\(587\) | −21.6517 | −0.893661 | −0.446831 | − | 0.894619i | \(-0.647447\pi\) | ||||
−0.446831 | + | 0.894619i | \(0.647447\pi\) | |||||||
\(588\) | −8.03201 | −0.331234 | ||||||||
\(589\) | −4.64327 | −0.191323 | ||||||||
\(590\) | 1.26062 | 0.0518989 | ||||||||
\(591\) | 27.2147 | 1.11946 | ||||||||
\(592\) | 5.33158 | 0.219127 | ||||||||
\(593\) | 1.02945 | 0.0422744 | 0.0211372 | − | 0.999777i | \(-0.493271\pi\) | ||||
0.0211372 | + | 0.999777i | \(0.493271\pi\) | |||||||
\(594\) | 3.70558 | 0.152042 | ||||||||
\(595\) | 4.88757 | 0.200371 | ||||||||
\(596\) | −4.08706 | −0.167412 | ||||||||
\(597\) | 11.0485 | 0.452185 | ||||||||
\(598\) | 17.3411 | 0.709132 | ||||||||
\(599\) | −31.7146 | −1.29582 | −0.647912 | − | 0.761716i | \(-0.724357\pi\) | ||||
−0.647912 | + | 0.761716i | \(0.724357\pi\) | |||||||
\(600\) | 3.41084 | 0.139247 | ||||||||
\(601\) | −6.06629 | −0.247449 | −0.123725 | − | 0.992317i | \(-0.539484\pi\) | ||||
−0.123725 | + | 0.992317i | \(0.539484\pi\) | |||||||
\(602\) | −35.9317 | −1.46447 | ||||||||
\(603\) | −0.453039 | −0.0184492 | ||||||||
\(604\) | −3.48477 | −0.141793 | ||||||||
\(605\) | 3.44314 | 0.139984 | ||||||||
\(606\) | 4.60470 | 0.187053 | ||||||||
\(607\) | −15.9535 | −0.647533 | −0.323767 | − | 0.946137i | \(-0.604949\pi\) | ||||
−0.323767 | + | 0.946137i | \(0.604949\pi\) | |||||||
\(608\) | 2.11950 | 0.0859571 | ||||||||
\(609\) | −24.5081 | −0.993119 | ||||||||
\(610\) | −3.50716 | −0.142001 | ||||||||
\(611\) | −3.91243 | −0.158280 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | 14.7853 | 0.597171 | 0.298586 | − | 0.954383i | \(-0.403485\pi\) | ||||
0.298586 | + | 0.954383i | \(0.403485\pi\) | |||||||
\(614\) | 5.03826 | 0.203328 | ||||||||
\(615\) | −10.6244 | −0.428415 | ||||||||
\(616\) | −14.3669 | −0.578861 | ||||||||
\(617\) | −28.4699 | −1.14615 | −0.573077 | − | 0.819501i | \(-0.694250\pi\) | ||||
−0.573077 | + | 0.819501i | \(0.694250\pi\) | |||||||
\(618\) | −8.13422 | −0.327206 | ||||||||
\(619\) | 11.4895 | 0.461803 | 0.230901 | − | 0.972977i | \(-0.425833\pi\) | ||||
0.230901 | + | 0.972977i | \(0.425833\pi\) | |||||||
\(620\) | −2.76169 | −0.110912 | ||||||||
\(621\) | −2.51141 | −0.100779 | ||||||||
\(622\) | 14.5697 | 0.584191 | ||||||||
\(623\) | −4.73031 | −0.189516 | ||||||||
\(624\) | −6.90495 | −0.276419 | ||||||||
\(625\) | 3.68799 | 0.147520 | ||||||||
\(626\) | 15.0211 | 0.600365 | ||||||||
\(627\) | 7.85397 | 0.313658 | ||||||||
\(628\) | 6.18739 | 0.246904 | ||||||||
\(629\) | 5.33158 | 0.212584 | ||||||||
\(630\) | 4.88757 | 0.194725 | ||||||||
\(631\) | 43.2240 | 1.72072 | 0.860361 | − | 0.509685i | \(-0.170238\pi\) | ||||
0.860361 | + | 0.509685i | \(0.170238\pi\) | |||||||
\(632\) | −12.9413 | −0.514779 | ||||||||
\(633\) | −23.7933 | −0.945701 | ||||||||
\(634\) | 25.7537 | 1.02281 | ||||||||
\(635\) | 7.66728 | 0.304267 | ||||||||
\(636\) | 10.4207 | 0.413207 | ||||||||
\(637\) | 55.4606 | 2.19743 | ||||||||
\(638\) | −23.4238 | −0.927357 | ||||||||
\(639\) | −12.4635 | −0.493049 | ||||||||
\(640\) | 1.26062 | 0.0498304 | ||||||||
\(641\) | 13.1489 | 0.519349 | 0.259674 | − | 0.965696i | \(-0.416385\pi\) | ||||
0.259674 | + | 0.965696i | \(0.416385\pi\) | |||||||
\(642\) | −3.07336 | −0.121296 | ||||||||
\(643\) | 11.4488 | 0.451495 | 0.225748 | − | 0.974186i | \(-0.427517\pi\) | ||||
0.225748 | + | 0.974186i | \(0.427517\pi\) | |||||||
\(644\) | 9.73702 | 0.383692 | ||||||||
\(645\) | 11.6830 | 0.460017 | ||||||||
\(646\) | 2.11950 | 0.0833906 | ||||||||
\(647\) | −19.1471 | −0.752749 | −0.376374 | − | 0.926468i | \(-0.622829\pi\) | ||||
−0.376374 | + | 0.926468i | \(0.622829\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −3.70558 | −0.145457 | ||||||||
\(650\) | −23.5516 | −0.923771 | ||||||||
\(651\) | 8.49375 | 0.332896 | ||||||||
\(652\) | −10.2176 | −0.400153 | ||||||||
\(653\) | 9.71651 | 0.380236 | 0.190118 | − | 0.981761i | \(-0.439113\pi\) | ||||
0.190118 | + | 0.981761i | \(0.439113\pi\) | |||||||
\(654\) | −4.24379 | −0.165945 | ||||||||
\(655\) | −23.8139 | −0.930487 | ||||||||
\(656\) | 8.42788 | 0.329053 | ||||||||
\(657\) | 11.3440 | 0.442570 | ||||||||
\(658\) | −2.19682 | −0.0856411 | ||||||||
\(659\) | 26.5758 | 1.03524 | 0.517622 | − | 0.855609i | \(-0.326817\pi\) | ||||
0.517622 | + | 0.855609i | \(0.326817\pi\) | |||||||
\(660\) | 4.67133 | 0.181831 | ||||||||
\(661\) | −2.12483 | −0.0826462 | −0.0413231 | − | 0.999146i | \(-0.513157\pi\) | ||||
−0.0413231 | + | 0.999146i | \(0.513157\pi\) | |||||||
\(662\) | 9.58716 | 0.372615 | ||||||||
\(663\) | −6.90495 | −0.268166 | ||||||||
\(664\) | 14.6778 | 0.569610 | ||||||||
\(665\) | 10.3592 | 0.401713 | ||||||||
\(666\) | 5.33158 | 0.206595 | ||||||||
\(667\) | 15.8752 | 0.614689 | ||||||||
\(668\) | −20.7844 | −0.804171 | ||||||||
\(669\) | −14.5096 | −0.560975 | ||||||||
\(670\) | −0.571110 | −0.0220639 | ||||||||
\(671\) | 10.3093 | 0.397984 | ||||||||
\(672\) | −3.87711 | −0.149563 | ||||||||
\(673\) | −41.2886 | −1.59156 | −0.795780 | − | 0.605586i | \(-0.792939\pi\) | ||||
−0.795780 | + | 0.605586i | \(0.792939\pi\) | |||||||
\(674\) | −12.3053 | −0.473983 | ||||||||
\(675\) | 3.41084 | 0.131283 | ||||||||
\(676\) | 34.6783 | 1.33378 | ||||||||
\(677\) | 20.5424 | 0.789510 | 0.394755 | − | 0.918786i | \(-0.370829\pi\) | ||||
0.394755 | + | 0.918786i | \(0.370829\pi\) | |||||||
\(678\) | 4.70750 | 0.180790 | ||||||||
\(679\) | 34.3837 | 1.31952 | ||||||||
\(680\) | 1.26062 | 0.0483426 | ||||||||
\(681\) | 11.2613 | 0.431535 | ||||||||
\(682\) | 8.11796 | 0.310853 | ||||||||
\(683\) | −38.2641 | −1.46413 | −0.732067 | − | 0.681233i | \(-0.761444\pi\) | ||||
−0.732067 | + | 0.681233i | \(0.761444\pi\) | |||||||
\(684\) | 2.11950 | 0.0810411 | ||||||||
\(685\) | −9.22710 | −0.352549 | ||||||||
\(686\) | 4.00121 | 0.152767 | ||||||||
\(687\) | 14.7592 | 0.563097 | ||||||||
\(688\) | −9.26765 | −0.353326 | ||||||||
\(689\) | −71.9543 | −2.74124 | ||||||||
\(690\) | −3.16593 | −0.120525 | ||||||||
\(691\) | 2.85437 | 0.108585 | 0.0542926 | − | 0.998525i | \(-0.482710\pi\) | ||||
0.0542926 | + | 0.998525i | \(0.482710\pi\) | |||||||
\(692\) | 13.8913 | 0.528067 | ||||||||
\(693\) | −14.3669 | −0.545755 | ||||||||
\(694\) | −33.7675 | −1.28180 | ||||||||
\(695\) | 13.8823 | 0.526585 | ||||||||
\(696\) | −6.32123 | −0.239605 | ||||||||
\(697\) | 8.42788 | 0.319229 | ||||||||
\(698\) | 26.2330 | 0.992933 | ||||||||
\(699\) | 14.1530 | 0.535314 | ||||||||
\(700\) | −13.2242 | −0.499828 | ||||||||
\(701\) | 24.2546 | 0.916083 | 0.458042 | − | 0.888931i | \(-0.348551\pi\) | ||||
0.458042 | + | 0.888931i | \(0.348551\pi\) | |||||||
\(702\) | −6.90495 | −0.260610 | ||||||||
\(703\) | 11.3003 | 0.426199 | ||||||||
\(704\) | −3.70558 | −0.139659 | ||||||||
\(705\) | 0.714284 | 0.0269015 | ||||||||
\(706\) | −22.4187 | −0.843740 | ||||||||
\(707\) | −17.8530 | −0.671430 | ||||||||
\(708\) | −1.00000 | −0.0375823 | ||||||||
\(709\) | 24.1237 | 0.905984 | 0.452992 | − | 0.891515i | \(-0.350357\pi\) | ||||
0.452992 | + | 0.891515i | \(0.350357\pi\) | |||||||
\(710\) | −15.7118 | −0.589652 | ||||||||
\(711\) | −12.9413 | −0.485338 | ||||||||
\(712\) | −1.22006 | −0.0457236 | ||||||||
\(713\) | −5.50184 | −0.206046 | ||||||||
\(714\) | −3.87711 | −0.145097 | ||||||||
\(715\) | −32.2553 | −1.20628 | ||||||||
\(716\) | −9.01354 | −0.336852 | ||||||||
\(717\) | −19.0349 | −0.710873 | ||||||||
\(718\) | 17.3542 | 0.647652 | ||||||||
\(719\) | −18.2711 | −0.681397 | −0.340699 | − | 0.940173i | \(-0.610664\pi\) | ||||
−0.340699 | + | 0.940173i | \(0.610664\pi\) | |||||||
\(720\) | 1.26062 | 0.0469805 | ||||||||
\(721\) | 31.5373 | 1.17451 | ||||||||
\(722\) | −14.5077 | −0.539921 | ||||||||
\(723\) | −13.6413 | −0.507324 | ||||||||
\(724\) | −3.59465 | −0.133594 | ||||||||
\(725\) | −21.5607 | −0.800743 | ||||||||
\(726\) | −2.73131 | −0.101368 | ||||||||
\(727\) | −32.7924 | −1.21620 | −0.608102 | − | 0.793859i | \(-0.708069\pi\) | ||||
−0.608102 | + | 0.793859i | \(0.708069\pi\) | |||||||
\(728\) | 26.7713 | 0.992209 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 14.3004 | 0.529282 | ||||||||
\(731\) | −9.26765 | −0.342776 | ||||||||
\(732\) | 2.78209 | 0.102829 | ||||||||
\(733\) | −23.1275 | −0.854233 | −0.427117 | − | 0.904197i | \(-0.640471\pi\) | ||||
−0.427117 | + | 0.904197i | \(0.640471\pi\) | |||||||
\(734\) | −2.01352 | −0.0743204 | ||||||||
\(735\) | −10.1253 | −0.373478 | ||||||||
\(736\) | 2.51141 | 0.0925718 | ||||||||
\(737\) | 1.67877 | 0.0618384 | ||||||||
\(738\) | 8.42788 | 0.310235 | ||||||||
\(739\) | −10.6500 | −0.391768 | −0.195884 | − | 0.980627i | \(-0.562758\pi\) | ||||
−0.195884 | + | 0.980627i | \(0.562758\pi\) | |||||||
\(740\) | 6.72110 | 0.247073 | ||||||||
\(741\) | −14.6350 | −0.537631 | ||||||||
\(742\) | −40.4022 | −1.48321 | ||||||||
\(743\) | −29.5531 | −1.08420 | −0.542099 | − | 0.840315i | \(-0.682370\pi\) | ||||
−0.542099 | + | 0.840315i | \(0.682370\pi\) | |||||||
\(744\) | 2.19074 | 0.0803164 | ||||||||
\(745\) | −5.15223 | −0.188763 | ||||||||
\(746\) | 36.9804 | 1.35395 | ||||||||
\(747\) | 14.6778 | 0.537033 | ||||||||
\(748\) | −3.70558 | −0.135489 | ||||||||
\(749\) | 11.9158 | 0.435393 | ||||||||
\(750\) | 10.6029 | 0.387162 | ||||||||
\(751\) | −18.0328 | −0.658025 | −0.329012 | − | 0.944326i | \(-0.606716\pi\) | ||||
−0.329012 | + | 0.944326i | \(0.606716\pi\) | |||||||
\(752\) | −0.566613 | −0.0206623 | ||||||||
\(753\) | −23.9674 | −0.873420 | ||||||||
\(754\) | 43.6477 | 1.58956 | ||||||||
\(755\) | −4.39297 | −0.159877 | ||||||||
\(756\) | −3.87711 | −0.141009 | ||||||||
\(757\) | −46.8493 | −1.70277 | −0.851383 | − | 0.524544i | \(-0.824236\pi\) | ||||
−0.851383 | + | 0.524544i | \(0.824236\pi\) | |||||||
\(758\) | −19.1842 | −0.696802 | ||||||||
\(759\) | 9.30622 | 0.337794 | ||||||||
\(760\) | 2.67189 | 0.0969195 | ||||||||
\(761\) | −21.8281 | −0.791267 | −0.395634 | − | 0.918408i | \(-0.629475\pi\) | ||||
−0.395634 | + | 0.918408i | \(0.629475\pi\) | |||||||
\(762\) | −6.08214 | −0.220333 | ||||||||
\(763\) | 16.4537 | 0.595662 | ||||||||
\(764\) | −6.31625 | −0.228514 | ||||||||
\(765\) | 1.26062 | 0.0455778 | ||||||||
\(766\) | −14.5579 | −0.525999 | ||||||||
\(767\) | 6.90495 | 0.249323 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 17.0243 | 0.613911 | 0.306955 | − | 0.951724i | \(-0.400690\pi\) | ||||
0.306955 | + | 0.951724i | \(0.400690\pi\) | |||||||
\(770\) | −18.1113 | −0.652685 | ||||||||
\(771\) | 23.0284 | 0.829347 | ||||||||
\(772\) | −13.5834 | −0.488877 | ||||||||
\(773\) | −8.84541 | −0.318147 | −0.159074 | − | 0.987267i | \(-0.550851\pi\) | ||||
−0.159074 | + | 0.987267i | \(0.550851\pi\) | |||||||
\(774\) | −9.26765 | −0.333119 | ||||||||
\(775\) | 7.47225 | 0.268411 | ||||||||
\(776\) | 8.86837 | 0.318356 | ||||||||
\(777\) | −20.6712 | −0.741574 | ||||||||
\(778\) | 0.644984 | 0.0231238 | ||||||||
\(779\) | 17.8629 | 0.640005 | ||||||||
\(780\) | −8.70451 | −0.311672 | ||||||||
\(781\) | 46.1846 | 1.65261 | ||||||||
\(782\) | 2.51141 | 0.0898078 | ||||||||
\(783\) | −6.32123 | −0.225902 | ||||||||
\(784\) | 8.03201 | 0.286857 | ||||||||
\(785\) | 7.79995 | 0.278392 | ||||||||
\(786\) | 18.8906 | 0.673807 | ||||||||
\(787\) | −37.0025 | −1.31900 | −0.659498 | − | 0.751707i | \(-0.729231\pi\) | ||||
−0.659498 | + | 0.751707i | \(0.729231\pi\) | |||||||
\(788\) | −27.2147 | −0.969484 | ||||||||
\(789\) | −2.30569 | −0.0820846 | ||||||||
\(790\) | −16.3141 | −0.580430 | ||||||||
\(791\) | −18.2515 | −0.648949 | ||||||||
\(792\) | −3.70558 | −0.131672 | ||||||||
\(793\) | −19.2102 | −0.682174 | ||||||||
\(794\) | −34.7272 | −1.23242 | ||||||||
\(795\) | 13.1365 | 0.465905 | ||||||||
\(796\) | −11.0485 | −0.391604 | ||||||||
\(797\) | −5.65890 | −0.200449 | −0.100224 | − | 0.994965i | \(-0.531956\pi\) | ||||
−0.100224 | + | 0.994965i | \(0.531956\pi\) | |||||||
\(798\) | −8.21754 | −0.290898 | ||||||||
\(799\) | −0.566613 | −0.0200453 | ||||||||
\(800\) | −3.41084 | −0.120591 | ||||||||
\(801\) | −1.22006 | −0.0431086 | ||||||||
\(802\) | −12.8048 | −0.452154 | ||||||||
\(803\) | −42.0359 | −1.48341 | ||||||||
\(804\) | 0.453039 | 0.0159775 | ||||||||
\(805\) | 12.2747 | 0.432626 | ||||||||
\(806\) | −15.1269 | −0.532824 | ||||||||
\(807\) | −19.7737 | −0.696066 | ||||||||
\(808\) | −4.60470 | −0.161993 | ||||||||
\(809\) | −16.4805 | −0.579422 | −0.289711 | − | 0.957114i | \(-0.593559\pi\) | ||||
−0.289711 | + | 0.957114i | \(0.593559\pi\) | |||||||
\(810\) | 1.26062 | 0.0442937 | ||||||||
\(811\) | −24.5225 | −0.861100 | −0.430550 | − | 0.902567i | \(-0.641680\pi\) | ||||
−0.430550 | + | 0.902567i | \(0.641680\pi\) | |||||||
\(812\) | 24.5081 | 0.860066 | ||||||||
\(813\) | −27.5096 | −0.964803 | ||||||||
\(814\) | −19.7566 | −0.692468 | ||||||||
\(815\) | −12.8805 | −0.451186 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | −19.6428 | −0.687214 | ||||||||
\(818\) | 30.5691 | 1.06882 | ||||||||
\(819\) | 26.7713 | 0.935463 | ||||||||
\(820\) | 10.6244 | 0.371019 | ||||||||
\(821\) | −15.2085 | −0.530782 | −0.265391 | − | 0.964141i | \(-0.585501\pi\) | ||||
−0.265391 | + | 0.964141i | \(0.585501\pi\) | |||||||
\(822\) | 7.31949 | 0.255297 | ||||||||
\(823\) | 54.4027 | 1.89636 | 0.948179 | − | 0.317737i | \(-0.102923\pi\) | ||||
0.948179 | + | 0.317737i | \(0.102923\pi\) | |||||||
\(824\) | 8.13422 | 0.283369 | ||||||||
\(825\) | −12.6391 | −0.440038 | ||||||||
\(826\) | 3.87711 | 0.134902 | ||||||||
\(827\) | −12.2446 | −0.425787 | −0.212893 | − | 0.977075i | \(-0.568289\pi\) | ||||
−0.212893 | + | 0.977075i | \(0.568289\pi\) | |||||||
\(828\) | 2.51141 | 0.0872775 | ||||||||
\(829\) | −11.1674 | −0.387861 | −0.193930 | − | 0.981015i | \(-0.562124\pi\) | ||||
−0.193930 | + | 0.981015i | \(0.562124\pi\) | |||||||
\(830\) | 18.5032 | 0.642254 | ||||||||
\(831\) | −13.5731 | −0.470844 | ||||||||
\(832\) | 6.90495 | 0.239386 | ||||||||
\(833\) | 8.03201 | 0.278293 | ||||||||
\(834\) | −11.0123 | −0.381324 | ||||||||
\(835\) | −26.2012 | −0.906729 | ||||||||
\(836\) | −7.85397 | −0.271635 | ||||||||
\(837\) | 2.19074 | 0.0757230 | ||||||||
\(838\) | −9.79506 | −0.338365 | ||||||||
\(839\) | −21.5815 | −0.745076 | −0.372538 | − | 0.928017i | \(-0.621512\pi\) | ||||
−0.372538 | + | 0.928017i | \(0.621512\pi\) | |||||||
\(840\) | −4.88757 | −0.168637 | ||||||||
\(841\) | 10.9579 | 0.377858 | ||||||||
\(842\) | −7.50279 | −0.258563 | ||||||||
\(843\) | −10.0237 | −0.345235 | ||||||||
\(844\) | 23.7933 | 0.819001 | ||||||||
\(845\) | 43.7161 | 1.50388 | ||||||||
\(846\) | −0.566613 | −0.0194806 | ||||||||
\(847\) | 10.5896 | 0.363863 | ||||||||
\(848\) | −10.4207 | −0.357848 | ||||||||
\(849\) | −4.03872 | −0.138609 | ||||||||
\(850\) | −3.41084 | −0.116991 | ||||||||
\(851\) | 13.3898 | 0.458996 | ||||||||
\(852\) | 12.4635 | 0.426993 | ||||||||
\(853\) | −32.5547 | −1.11465 | −0.557326 | − | 0.830294i | \(-0.688172\pi\) | ||||
−0.557326 | + | 0.830294i | \(0.688172\pi\) | |||||||
\(854\) | −10.7865 | −0.369106 | ||||||||
\(855\) | 2.67189 | 0.0913765 | ||||||||
\(856\) | 3.07336 | 0.105045 | ||||||||
\(857\) | −32.9809 | −1.12661 | −0.563304 | − | 0.826250i | \(-0.690470\pi\) | ||||
−0.563304 | + | 0.826250i | \(0.690470\pi\) | |||||||
\(858\) | 25.5868 | 0.873519 | ||||||||
\(859\) | 9.08126 | 0.309849 | 0.154924 | − | 0.987926i | \(-0.450487\pi\) | ||||
0.154924 | + | 0.987926i | \(0.450487\pi\) | |||||||
\(860\) | −11.6830 | −0.398387 | ||||||||
\(861\) | −32.6758 | −1.11359 | ||||||||
\(862\) | −2.08543 | −0.0710301 | ||||||||
\(863\) | 2.19803 | 0.0748218 | 0.0374109 | − | 0.999300i | \(-0.488089\pi\) | ||||
0.0374109 | + | 0.999300i | \(0.488089\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 17.5116 | 0.595413 | ||||||||
\(866\) | 7.45018 | 0.253167 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −8.49375 | −0.288297 | ||||||||
\(869\) | 47.9551 | 1.62677 | ||||||||
\(870\) | −7.96866 | −0.270163 | ||||||||
\(871\) | −3.12821 | −0.105995 | ||||||||
\(872\) | 4.24379 | 0.143713 | ||||||||
\(873\) | 8.86837 | 0.300149 | ||||||||
\(874\) | 5.32293 | 0.180051 | ||||||||
\(875\) | −41.1085 | −1.38972 | ||||||||
\(876\) | −11.3440 | −0.383277 | ||||||||
\(877\) | −1.01349 | −0.0342233 | −0.0171116 | − | 0.999854i | \(-0.505447\pi\) | ||||
−0.0171116 | + | 0.999854i | \(0.505447\pi\) | |||||||
\(878\) | −19.2809 | −0.650698 | ||||||||
\(879\) | −30.3238 | −1.02280 | ||||||||
\(880\) | −4.67133 | −0.157470 | ||||||||
\(881\) | 34.3745 | 1.15811 | 0.579053 | − | 0.815290i | \(-0.303422\pi\) | ||||
0.579053 | + | 0.815290i | \(0.303422\pi\) | |||||||
\(882\) | 8.03201 | 0.270452 | ||||||||
\(883\) | −3.37694 | −0.113643 | −0.0568215 | − | 0.998384i | \(-0.518097\pi\) | ||||
−0.0568215 | + | 0.998384i | \(0.518097\pi\) | |||||||
\(884\) | 6.90495 | 0.232238 | ||||||||
\(885\) | −1.26062 | −0.0423753 | ||||||||
\(886\) | −23.5618 | −0.791575 | ||||||||
\(887\) | 34.9691 | 1.17415 | 0.587073 | − | 0.809534i | \(-0.300280\pi\) | ||||
0.587073 | + | 0.809534i | \(0.300280\pi\) | |||||||
\(888\) | −5.33158 | −0.178916 | ||||||||
\(889\) | 23.5812 | 0.790887 | ||||||||
\(890\) | −1.53803 | −0.0515549 | ||||||||
\(891\) | −3.70558 | −0.124142 | ||||||||
\(892\) | 14.5096 | 0.485818 | ||||||||
\(893\) | −1.20094 | −0.0401878 | ||||||||
\(894\) | 4.08706 | 0.136692 | ||||||||
\(895\) | −11.3627 | −0.379812 | ||||||||
\(896\) | 3.87711 | 0.129525 | ||||||||
\(897\) | −17.3411 | −0.579004 | ||||||||
\(898\) | −2.41928 | −0.0807325 | ||||||||
\(899\) | −13.8482 | −0.461862 | ||||||||
\(900\) | −3.41084 | −0.113695 | ||||||||
\(901\) | −10.4207 | −0.347164 | ||||||||
\(902\) | −31.2302 | −1.03985 | ||||||||
\(903\) | 35.9317 | 1.19573 | ||||||||
\(904\) | −4.70750 | −0.156569 | ||||||||
\(905\) | −4.53149 | −0.150632 | ||||||||
\(906\) | 3.48477 | 0.115774 | ||||||||
\(907\) | −44.6523 | −1.48266 | −0.741328 | − | 0.671143i | \(-0.765804\pi\) | ||||
−0.741328 | + | 0.671143i | \(0.765804\pi\) | |||||||
\(908\) | −11.2613 | −0.373720 | ||||||||
\(909\) | −4.60470 | −0.152728 | ||||||||
\(910\) | 33.7484 | 1.11875 | ||||||||
\(911\) | 23.7187 | 0.785835 | 0.392918 | − | 0.919574i | \(-0.371466\pi\) | ||||
0.392918 | + | 0.919574i | \(0.371466\pi\) | |||||||
\(912\) | −2.11950 | −0.0701837 | ||||||||
\(913\) | −54.3898 | −1.80004 | ||||||||
\(914\) | 4.67152 | 0.154520 | ||||||||
\(915\) | 3.50716 | 0.115943 | ||||||||
\(916\) | −14.7592 | −0.487656 | ||||||||
\(917\) | −73.2412 | −2.41864 | ||||||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | −34.6832 | −1.14409 | −0.572046 | − | 0.820221i | \(-0.693850\pi\) | ||||
−0.572046 | + | 0.820221i | \(0.693850\pi\) | |||||||
\(920\) | 3.16593 | 0.104378 | ||||||||
\(921\) | −5.03826 | −0.166016 | ||||||||
\(922\) | 31.4436 | 1.03554 | ||||||||
\(923\) | −86.0599 | −2.83270 | ||||||||
\(924\) | 14.3669 | 0.472638 | ||||||||
\(925\) | −18.1852 | −0.597924 | ||||||||
\(926\) | 3.38202 | 0.111140 | ||||||||
\(927\) | 8.13422 | 0.267163 | ||||||||
\(928\) | 6.32123 | 0.207504 | ||||||||
\(929\) | 24.7481 | 0.811959 | 0.405979 | − | 0.913882i | \(-0.366931\pi\) | ||||
0.405979 | + | 0.913882i | \(0.366931\pi\) | |||||||
\(930\) | 2.76169 | 0.0905594 | ||||||||
\(931\) | 17.0238 | 0.557934 | ||||||||
\(932\) | −14.1530 | −0.463596 | ||||||||
\(933\) | −14.5697 | −0.476990 | ||||||||
\(934\) | 23.5843 | 0.771701 | ||||||||
\(935\) | −4.67133 | −0.152769 | ||||||||
\(936\) | 6.90495 | 0.225695 | ||||||||
\(937\) | 5.35962 | 0.175091 | 0.0875455 | − | 0.996161i | \(-0.472098\pi\) | ||||
0.0875455 | + | 0.996161i | \(0.472098\pi\) | |||||||
\(938\) | −1.75648 | −0.0573512 | ||||||||
\(939\) | −15.0211 | −0.490196 | ||||||||
\(940\) | −0.714284 | −0.0232974 | ||||||||
\(941\) | −0.725685 | −0.0236567 | −0.0118283 | − | 0.999930i | \(-0.503765\pi\) | ||||
−0.0118283 | + | 0.999930i | \(0.503765\pi\) | |||||||
\(942\) | −6.18739 | −0.201596 | ||||||||
\(943\) | 21.1659 | 0.689255 | ||||||||
\(944\) | 1.00000 | 0.0325472 | ||||||||
\(945\) | −4.88757 | −0.158993 | ||||||||
\(946\) | 34.3420 | 1.11656 | ||||||||
\(947\) | 23.4403 | 0.761708 | 0.380854 | − | 0.924635i | \(-0.375630\pi\) | ||||
0.380854 | + | 0.924635i | \(0.375630\pi\) | |||||||
\(948\) | 12.9413 | 0.420315 | ||||||||
\(949\) | 78.3294 | 2.54268 | ||||||||
\(950\) | −7.22927 | −0.234548 | ||||||||
\(951\) | −25.7537 | −0.835122 | ||||||||
\(952\) | 3.87711 | 0.125658 | ||||||||
\(953\) | −4.73220 | −0.153291 | −0.0766455 | − | 0.997058i | \(-0.524421\pi\) | ||||
−0.0766455 | + | 0.997058i | \(0.524421\pi\) | |||||||
\(954\) | −10.4207 | −0.337382 | ||||||||
\(955\) | −7.96239 | −0.257657 | ||||||||
\(956\) | 19.0349 | 0.615634 | ||||||||
\(957\) | 23.4238 | 0.757184 | ||||||||
\(958\) | 11.2885 | 0.364715 | ||||||||
\(959\) | −28.3785 | −0.916390 | ||||||||
\(960\) | −1.26062 | −0.0406863 | ||||||||
\(961\) | −26.2007 | −0.845183 | ||||||||
\(962\) | 36.8143 | 1.18694 | ||||||||
\(963\) | 3.07336 | 0.0990377 | ||||||||
\(964\) | 13.6413 | 0.439355 | ||||||||
\(965\) | −17.1235 | −0.551224 | ||||||||
\(966\) | −9.73702 | −0.313283 | ||||||||
\(967\) | 38.8462 | 1.24921 | 0.624605 | − | 0.780941i | \(-0.285260\pi\) | ||||
0.624605 | + | 0.780941i | \(0.285260\pi\) | |||||||
\(968\) | 2.73131 | 0.0877876 | ||||||||
\(969\) | −2.11950 | −0.0680882 | ||||||||
\(970\) | 11.1796 | 0.358957 | ||||||||
\(971\) | 11.2007 | 0.359449 | 0.179725 | − | 0.983717i | \(-0.442479\pi\) | ||||
0.179725 | + | 0.983717i | \(0.442479\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 42.6958 | 1.36876 | ||||||||
\(974\) | 10.3474 | 0.331552 | ||||||||
\(975\) | 23.5516 | 0.754256 | ||||||||
\(976\) | −2.78209 | −0.0890526 | ||||||||
\(977\) | −11.2555 | −0.360095 | −0.180048 | − | 0.983658i | \(-0.557625\pi\) | ||||
−0.180048 | + | 0.983658i | \(0.557625\pi\) | |||||||
\(978\) | 10.2176 | 0.326724 | ||||||||
\(979\) | 4.52102 | 0.144492 | ||||||||
\(980\) | 10.1253 | 0.323441 | ||||||||
\(981\) | 4.24379 | 0.135494 | ||||||||
\(982\) | −7.75497 | −0.247471 | ||||||||
\(983\) | 52.4257 | 1.67212 | 0.836061 | − | 0.548637i | \(-0.184853\pi\) | ||||
0.836061 | + | 0.548637i | \(0.184853\pi\) | |||||||
\(984\) | −8.42788 | −0.268671 | ||||||||
\(985\) | −34.3074 | −1.09312 | ||||||||
\(986\) | 6.32123 | 0.201309 | ||||||||
\(987\) | 2.19682 | 0.0699257 | ||||||||
\(988\) | 14.6350 | 0.465602 | ||||||||
\(989\) | −23.2749 | −0.740098 | ||||||||
\(990\) | −4.67133 | −0.148465 | ||||||||
\(991\) | −28.7659 | −0.913780 | −0.456890 | − | 0.889523i | \(-0.651037\pi\) | ||||
−0.456890 | + | 0.889523i | \(0.651037\pi\) | |||||||
\(992\) | −2.19074 | −0.0695561 | ||||||||
\(993\) | −9.58716 | −0.304239 | ||||||||
\(994\) | −48.3225 | −1.53270 | ||||||||
\(995\) | −13.9280 | −0.441546 | ||||||||
\(996\) | −14.6778 | −0.465085 | ||||||||
\(997\) | 21.2788 | 0.673907 | 0.336954 | − | 0.941521i | \(-0.390603\pi\) | ||||
0.336954 | + | 0.941521i | \(0.390603\pi\) | |||||||
\(998\) | 9.95739 | 0.315196 | ||||||||
\(999\) | −5.33158 | −0.168684 |
(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 | 6018.2.a.bc.1.9 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.bc.1.9 | ✓ | 14 | 1.1 | even | 1 | trivial |