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: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 33x^{8} + 53x^{7} + 356x^{6} - 433x^{5} - 1296x^{4} + 1135x^{3} + 930x^{2} - 186x - 104 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.556815\) 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 | ||||||||
\(5\) | 0.556815 | 0.249015 | 0.124508 | − | 0.992219i | \(-0.460265\pi\) | ||||
0.124508 | + | 0.992219i | \(0.460265\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0.727556 | 0.274990 | 0.137495 | − | 0.990502i | \(-0.456095\pi\) | ||||
0.137495 | + | 0.990502i | \(0.456095\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.556815 | −0.176080 | ||||||||
\(11\) | 4.53073 | 1.36607 | 0.683033 | − | 0.730388i | \(-0.260661\pi\) | ||||
0.683033 | + | 0.730388i | \(0.260661\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.52269 | −0.699669 | −0.349835 | − | 0.936812i | \(-0.613762\pi\) | ||||
−0.349835 | + | 0.936812i | \(0.613762\pi\) | |||||||
\(14\) | −0.727556 | −0.194448 | ||||||||
\(15\) | 0.556815 | 0.143769 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −7.07185 | −1.62239 | −0.811196 | − | 0.584774i | \(-0.801183\pi\) | ||||
−0.811196 | + | 0.584774i | \(0.801183\pi\) | |||||||
\(20\) | 0.556815 | 0.124508 | ||||||||
\(21\) | 0.727556 | 0.158766 | ||||||||
\(22\) | −4.53073 | −0.965954 | ||||||||
\(23\) | −0.184722 | −0.0385172 | −0.0192586 | − | 0.999815i | \(-0.506131\pi\) | ||||
−0.0192586 | + | 0.999815i | \(0.506131\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.68996 | −0.937991 | ||||||||
\(26\) | 2.52269 | 0.494741 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.727556 | 0.137495 | ||||||||
\(29\) | −8.45781 | −1.57058 | −0.785288 | − | 0.619130i | \(-0.787485\pi\) | ||||
−0.785288 | + | 0.619130i | \(0.787485\pi\) | |||||||
\(30\) | −0.556815 | −0.101660 | ||||||||
\(31\) | 3.98591 | 0.715891 | 0.357946 | − | 0.933742i | \(-0.383477\pi\) | ||||
0.357946 | + | 0.933742i | \(0.383477\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.53073 | 0.788698 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 0.405114 | 0.0684768 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.09215 | 0.179548 | 0.0897741 | − | 0.995962i | \(-0.471385\pi\) | ||||
0.0897741 | + | 0.995962i | \(0.471385\pi\) | |||||||
\(38\) | 7.07185 | 1.14720 | ||||||||
\(39\) | −2.52269 | −0.403954 | ||||||||
\(40\) | −0.556815 | −0.0880401 | ||||||||
\(41\) | −4.34727 | −0.678929 | −0.339465 | − | 0.940619i | \(-0.610246\pi\) | ||||
−0.339465 | + | 0.940619i | \(0.610246\pi\) | |||||||
\(42\) | −0.727556 | −0.112264 | ||||||||
\(43\) | 2.87701 | 0.438740 | 0.219370 | − | 0.975642i | \(-0.429600\pi\) | ||||
0.219370 | + | 0.975642i | \(0.429600\pi\) | |||||||
\(44\) | 4.53073 | 0.683033 | ||||||||
\(45\) | 0.556815 | 0.0830050 | ||||||||
\(46\) | 0.184722 | 0.0272358 | ||||||||
\(47\) | 3.17173 | 0.462644 | 0.231322 | − | 0.972877i | \(-0.425695\pi\) | ||||
0.231322 | + | 0.972877i | \(0.425695\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.47066 | −0.924380 | ||||||||
\(50\) | 4.68996 | 0.663260 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −2.52269 | −0.349835 | ||||||||
\(53\) | −11.9287 | −1.63854 | −0.819269 | − | 0.573409i | \(-0.805621\pi\) | ||||
−0.819269 | + | 0.573409i | \(0.805621\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 2.52277 | 0.340171 | ||||||||
\(56\) | −0.727556 | −0.0972238 | ||||||||
\(57\) | −7.07185 | −0.936689 | ||||||||
\(58\) | 8.45781 | 1.11057 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0.556815 | 0.0718845 | ||||||||
\(61\) | −15.1576 | −1.94073 | −0.970363 | − | 0.241653i | \(-0.922311\pi\) | ||||
−0.970363 | + | 0.241653i | \(0.922311\pi\) | |||||||
\(62\) | −3.98591 | −0.506212 | ||||||||
\(63\) | 0.727556 | 0.0916635 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.40467 | −0.174228 | ||||||||
\(66\) | −4.53073 | −0.557694 | ||||||||
\(67\) | 3.20865 | 0.391998 | 0.195999 | − | 0.980604i | \(-0.437205\pi\) | ||||
0.195999 | + | 0.980604i | \(0.437205\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | −0.184722 | −0.0222379 | ||||||||
\(70\) | −0.405114 | −0.0484204 | ||||||||
\(71\) | 3.53239 | 0.419217 | 0.209609 | − | 0.977785i | \(-0.432781\pi\) | ||||
0.209609 | + | 0.977785i | \(0.432781\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −12.2252 | −1.43085 | −0.715423 | − | 0.698691i | \(-0.753766\pi\) | ||||
−0.715423 | + | 0.698691i | \(0.753766\pi\) | |||||||
\(74\) | −1.09215 | −0.126960 | ||||||||
\(75\) | −4.68996 | −0.541550 | ||||||||
\(76\) | −7.07185 | −0.811196 | ||||||||
\(77\) | 3.29636 | 0.375655 | ||||||||
\(78\) | 2.52269 | 0.285639 | ||||||||
\(79\) | −6.38902 | −0.718821 | −0.359410 | − | 0.933180i | \(-0.617022\pi\) | ||||
−0.359410 | + | 0.933180i | \(0.617022\pi\) | |||||||
\(80\) | 0.556815 | 0.0622538 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.34727 | 0.480075 | ||||||||
\(83\) | −12.2390 | −1.34341 | −0.671704 | − | 0.740820i | \(-0.734437\pi\) | ||||
−0.671704 | + | 0.740820i | \(0.734437\pi\) | |||||||
\(84\) | 0.727556 | 0.0793829 | ||||||||
\(85\) | −0.556815 | −0.0603950 | ||||||||
\(86\) | −2.87701 | −0.310236 | ||||||||
\(87\) | −8.45781 | −0.906773 | ||||||||
\(88\) | −4.53073 | −0.482977 | ||||||||
\(89\) | −14.3230 | −1.51823 | −0.759117 | − | 0.650954i | \(-0.774369\pi\) | ||||
−0.759117 | + | 0.650954i | \(0.774369\pi\) | |||||||
\(90\) | −0.556815 | −0.0586934 | ||||||||
\(91\) | −1.83540 | −0.192402 | ||||||||
\(92\) | −0.184722 | −0.0192586 | ||||||||
\(93\) | 3.98591 | 0.413320 | ||||||||
\(94\) | −3.17173 | −0.327139 | ||||||||
\(95\) | −3.93771 | −0.404000 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 8.31606 | 0.844368 | 0.422184 | − | 0.906510i | \(-0.361264\pi\) | ||||
0.422184 | + | 0.906510i | \(0.361264\pi\) | |||||||
\(98\) | 6.47066 | 0.653636 | ||||||||
\(99\) | 4.53073 | 0.455355 | ||||||||
\(100\) | −4.68996 | −0.468996 | ||||||||
\(101\) | 6.06297 | 0.603288 | 0.301644 | − | 0.953421i | \(-0.402465\pi\) | ||||
0.301644 | + | 0.953421i | \(0.402465\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | 17.2773 | 1.70238 | 0.851192 | − | 0.524855i | \(-0.175880\pi\) | ||||
0.851192 | + | 0.524855i | \(0.175880\pi\) | |||||||
\(104\) | 2.52269 | 0.247370 | ||||||||
\(105\) | 0.405114 | 0.0395351 | ||||||||
\(106\) | 11.9287 | 1.15862 | ||||||||
\(107\) | −11.7625 | −1.13712 | −0.568560 | − | 0.822642i | \(-0.692499\pi\) | ||||
−0.568560 | + | 0.822642i | \(0.692499\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 5.36322 | 0.513703 | 0.256852 | − | 0.966451i | \(-0.417315\pi\) | ||||
0.256852 | + | 0.966451i | \(0.417315\pi\) | |||||||
\(110\) | −2.52277 | −0.240537 | ||||||||
\(111\) | 1.09215 | 0.103662 | ||||||||
\(112\) | 0.727556 | 0.0687476 | ||||||||
\(113\) | −4.36168 | −0.410313 | −0.205156 | − | 0.978729i | \(-0.565770\pi\) | ||||
−0.205156 | + | 0.978729i | \(0.565770\pi\) | |||||||
\(114\) | 7.07185 | 0.662339 | ||||||||
\(115\) | −0.102856 | −0.00959136 | ||||||||
\(116\) | −8.45781 | −0.785288 | ||||||||
\(117\) | −2.52269 | −0.233223 | ||||||||
\(118\) | −1.00000 | −0.0920575 | ||||||||
\(119\) | −0.727556 | −0.0666950 | ||||||||
\(120\) | −0.556815 | −0.0508300 | ||||||||
\(121\) | 9.52748 | 0.866135 | ||||||||
\(122\) | 15.1576 | 1.37230 | ||||||||
\(123\) | −4.34727 | −0.391980 | ||||||||
\(124\) | 3.98591 | 0.357946 | ||||||||
\(125\) | −5.39551 | −0.482589 | ||||||||
\(126\) | −0.727556 | −0.0648159 | ||||||||
\(127\) | 9.35619 | 0.830228 | 0.415114 | − | 0.909769i | \(-0.363742\pi\) | ||||
0.415114 | + | 0.909769i | \(0.363742\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.87701 | 0.253307 | ||||||||
\(130\) | 1.40467 | 0.123198 | ||||||||
\(131\) | 20.2038 | 1.76521 | 0.882605 | − | 0.470115i | \(-0.155787\pi\) | ||||
0.882605 | + | 0.470115i | \(0.155787\pi\) | |||||||
\(132\) | 4.53073 | 0.394349 | ||||||||
\(133\) | −5.14517 | −0.446142 | ||||||||
\(134\) | −3.20865 | −0.277185 | ||||||||
\(135\) | 0.556815 | 0.0479230 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | 6.34305 | 0.541923 | 0.270962 | − | 0.962590i | \(-0.412658\pi\) | ||||
0.270962 | + | 0.962590i | \(0.412658\pi\) | |||||||
\(138\) | 0.184722 | 0.0157246 | ||||||||
\(139\) | 7.39186 | 0.626970 | 0.313485 | − | 0.949593i | \(-0.398504\pi\) | ||||
0.313485 | + | 0.949593i | \(0.398504\pi\) | |||||||
\(140\) | 0.405114 | 0.0342384 | ||||||||
\(141\) | 3.17173 | 0.267108 | ||||||||
\(142\) | −3.53239 | −0.296431 | ||||||||
\(143\) | −11.4296 | −0.955794 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −4.70943 | −0.391097 | ||||||||
\(146\) | 12.2252 | 1.01176 | ||||||||
\(147\) | −6.47066 | −0.533691 | ||||||||
\(148\) | 1.09215 | 0.0897741 | ||||||||
\(149\) | −8.91020 | −0.729952 | −0.364976 | − | 0.931017i | \(-0.618923\pi\) | ||||
−0.364976 | + | 0.931017i | \(0.618923\pi\) | |||||||
\(150\) | 4.68996 | 0.382933 | ||||||||
\(151\) | −16.1476 | −1.31408 | −0.657038 | − | 0.753858i | \(-0.728191\pi\) | ||||
−0.657038 | + | 0.753858i | \(0.728191\pi\) | |||||||
\(152\) | 7.07185 | 0.573602 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −3.29636 | −0.265628 | ||||||||
\(155\) | 2.21942 | 0.178268 | ||||||||
\(156\) | −2.52269 | −0.201977 | ||||||||
\(157\) | 3.17083 | 0.253060 | 0.126530 | − | 0.991963i | \(-0.459616\pi\) | ||||
0.126530 | + | 0.991963i | \(0.459616\pi\) | |||||||
\(158\) | 6.38902 | 0.508283 | ||||||||
\(159\) | −11.9287 | −0.946011 | ||||||||
\(160\) | −0.556815 | −0.0440201 | ||||||||
\(161\) | −0.134396 | −0.0105919 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 2.80623 | 0.219801 | 0.109901 | − | 0.993943i | \(-0.464947\pi\) | ||||
0.109901 | + | 0.993943i | \(0.464947\pi\) | |||||||
\(164\) | −4.34727 | −0.339465 | ||||||||
\(165\) | 2.52277 | 0.196398 | ||||||||
\(166\) | 12.2390 | 0.949933 | ||||||||
\(167\) | −23.2163 | −1.79653 | −0.898267 | − | 0.439450i | \(-0.855174\pi\) | ||||
−0.898267 | + | 0.439450i | \(0.855174\pi\) | |||||||
\(168\) | −0.727556 | −0.0561322 | ||||||||
\(169\) | −6.63602 | −0.510463 | ||||||||
\(170\) | 0.556815 | 0.0427057 | ||||||||
\(171\) | −7.07185 | −0.540798 | ||||||||
\(172\) | 2.87701 | 0.219370 | ||||||||
\(173\) | 6.57794 | 0.500112 | 0.250056 | − | 0.968231i | \(-0.419551\pi\) | ||||
0.250056 | + | 0.968231i | \(0.419551\pi\) | |||||||
\(174\) | 8.45781 | 0.641185 | ||||||||
\(175\) | −3.41221 | −0.257939 | ||||||||
\(176\) | 4.53073 | 0.341516 | ||||||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | 14.3230 | 1.07355 | ||||||||
\(179\) | 19.0412 | 1.42321 | 0.711603 | − | 0.702582i | \(-0.247969\pi\) | ||||
0.711603 | + | 0.702582i | \(0.247969\pi\) | |||||||
\(180\) | 0.556815 | 0.0415025 | ||||||||
\(181\) | 9.19753 | 0.683647 | 0.341824 | − | 0.939764i | \(-0.388955\pi\) | ||||
0.341824 | + | 0.939764i | \(0.388955\pi\) | |||||||
\(182\) | 1.83540 | 0.136049 | ||||||||
\(183\) | −15.1576 | −1.12048 | ||||||||
\(184\) | 0.184722 | 0.0136179 | ||||||||
\(185\) | 0.608125 | 0.0447102 | ||||||||
\(186\) | −3.98591 | −0.292261 | ||||||||
\(187\) | −4.53073 | −0.331320 | ||||||||
\(188\) | 3.17173 | 0.231322 | ||||||||
\(189\) | 0.727556 | 0.0529219 | ||||||||
\(190\) | 3.93771 | 0.285671 | ||||||||
\(191\) | −9.74626 | −0.705215 | −0.352607 | − | 0.935771i | \(-0.614705\pi\) | ||||
−0.352607 | + | 0.935771i | \(0.614705\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 10.5626 | 0.760312 | 0.380156 | − | 0.924922i | \(-0.375870\pi\) | ||||
0.380156 | + | 0.924922i | \(0.375870\pi\) | |||||||
\(194\) | −8.31606 | −0.597059 | ||||||||
\(195\) | −1.40467 | −0.100591 | ||||||||
\(196\) | −6.47066 | −0.462190 | ||||||||
\(197\) | 14.7874 | 1.05356 | 0.526780 | − | 0.850002i | \(-0.323399\pi\) | ||||
0.526780 | + | 0.850002i | \(0.323399\pi\) | |||||||
\(198\) | −4.53073 | −0.321985 | ||||||||
\(199\) | 14.8207 | 1.05061 | 0.525305 | − | 0.850914i | \(-0.323951\pi\) | ||||
0.525305 | + | 0.850914i | \(0.323951\pi\) | |||||||
\(200\) | 4.68996 | 0.331630 | ||||||||
\(201\) | 3.20865 | 0.226320 | ||||||||
\(202\) | −6.06297 | −0.426589 | ||||||||
\(203\) | −6.15354 | −0.431894 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | −2.42062 | −0.169064 | ||||||||
\(206\) | −17.2773 | −1.20377 | ||||||||
\(207\) | −0.184722 | −0.0128391 | ||||||||
\(208\) | −2.52269 | −0.174917 | ||||||||
\(209\) | −32.0406 | −2.21629 | ||||||||
\(210\) | −0.405114 | −0.0279555 | ||||||||
\(211\) | −10.2870 | −0.708185 | −0.354092 | − | 0.935210i | \(-0.615210\pi\) | ||||
−0.354092 | + | 0.935210i | \(0.615210\pi\) | |||||||
\(212\) | −11.9287 | −0.819269 | ||||||||
\(213\) | 3.53239 | 0.242035 | ||||||||
\(214\) | 11.7625 | 0.804066 | ||||||||
\(215\) | 1.60196 | 0.109253 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 2.89998 | 0.196863 | ||||||||
\(218\) | −5.36322 | −0.363243 | ||||||||
\(219\) | −12.2252 | −0.826100 | ||||||||
\(220\) | 2.52277 | 0.170085 | ||||||||
\(221\) | 2.52269 | 0.169695 | ||||||||
\(222\) | −1.09215 | −0.0733002 | ||||||||
\(223\) | 18.1422 | 1.21489 | 0.607447 | − | 0.794360i | \(-0.292194\pi\) | ||||
0.607447 | + | 0.794360i | \(0.292194\pi\) | |||||||
\(224\) | −0.727556 | −0.0486119 | ||||||||
\(225\) | −4.68996 | −0.312664 | ||||||||
\(226\) | 4.36168 | 0.290135 | ||||||||
\(227\) | 1.83958 | 0.122097 | 0.0610485 | − | 0.998135i | \(-0.480556\pi\) | ||||
0.0610485 | + | 0.998135i | \(0.480556\pi\) | |||||||
\(228\) | −7.07185 | −0.468344 | ||||||||
\(229\) | −2.39025 | −0.157952 | −0.0789760 | − | 0.996877i | \(-0.525165\pi\) | ||||
−0.0789760 | + | 0.996877i | \(0.525165\pi\) | |||||||
\(230\) | 0.102856 | 0.00678211 | ||||||||
\(231\) | 3.29636 | 0.216884 | ||||||||
\(232\) | 8.45781 | 0.555283 | ||||||||
\(233\) | 13.5052 | 0.884756 | 0.442378 | − | 0.896829i | \(-0.354135\pi\) | ||||
0.442378 | + | 0.896829i | \(0.354135\pi\) | |||||||
\(234\) | 2.52269 | 0.164914 | ||||||||
\(235\) | 1.76606 | 0.115205 | ||||||||
\(236\) | 1.00000 | 0.0650945 | ||||||||
\(237\) | −6.38902 | −0.415011 | ||||||||
\(238\) | 0.727556 | 0.0471605 | ||||||||
\(239\) | −28.3102 | −1.83124 | −0.915618 | − | 0.402049i | \(-0.868298\pi\) | ||||
−0.915618 | + | 0.402049i | \(0.868298\pi\) | |||||||
\(240\) | 0.556815 | 0.0359422 | ||||||||
\(241\) | 18.4711 | 1.18983 | 0.594915 | − | 0.803789i | \(-0.297186\pi\) | ||||
0.594915 | + | 0.803789i | \(0.297186\pi\) | |||||||
\(242\) | −9.52748 | −0.612450 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −15.1576 | −0.970363 | ||||||||
\(245\) | −3.60296 | −0.230185 | ||||||||
\(246\) | 4.34727 | 0.277172 | ||||||||
\(247\) | 17.8401 | 1.13514 | ||||||||
\(248\) | −3.98591 | −0.253106 | ||||||||
\(249\) | −12.2390 | −0.775617 | ||||||||
\(250\) | 5.39551 | 0.341242 | ||||||||
\(251\) | −4.08294 | −0.257713 | −0.128857 | − | 0.991663i | \(-0.541131\pi\) | ||||
−0.128857 | + | 0.991663i | \(0.541131\pi\) | |||||||
\(252\) | 0.727556 | 0.0458317 | ||||||||
\(253\) | −0.836924 | −0.0526170 | ||||||||
\(254\) | −9.35619 | −0.587060 | ||||||||
\(255\) | −0.556815 | −0.0348691 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −24.7228 | −1.54217 | −0.771084 | − | 0.636734i | \(-0.780285\pi\) | ||||
−0.771084 | + | 0.636734i | \(0.780285\pi\) | |||||||
\(258\) | −2.87701 | −0.179115 | ||||||||
\(259\) | 0.794600 | 0.0493740 | ||||||||
\(260\) | −1.40467 | −0.0871141 | ||||||||
\(261\) | −8.45781 | −0.523526 | ||||||||
\(262\) | −20.2038 | −1.24819 | ||||||||
\(263\) | −28.5865 | −1.76272 | −0.881361 | − | 0.472444i | \(-0.843372\pi\) | ||||
−0.881361 | + | 0.472444i | \(0.843372\pi\) | |||||||
\(264\) | −4.53073 | −0.278847 | ||||||||
\(265\) | −6.64210 | −0.408021 | ||||||||
\(266\) | 5.14517 | 0.315470 | ||||||||
\(267\) | −14.3230 | −0.876553 | ||||||||
\(268\) | 3.20865 | 0.195999 | ||||||||
\(269\) | −2.43595 | −0.148523 | −0.0742614 | − | 0.997239i | \(-0.523660\pi\) | ||||
−0.0742614 | + | 0.997239i | \(0.523660\pi\) | |||||||
\(270\) | −0.556815 | −0.0338867 | ||||||||
\(271\) | 20.1234 | 1.22241 | 0.611206 | − | 0.791472i | \(-0.290685\pi\) | ||||
0.611206 | + | 0.791472i | \(0.290685\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | −1.83540 | −0.111084 | ||||||||
\(274\) | −6.34305 | −0.383198 | ||||||||
\(275\) | −21.2489 | −1.28136 | ||||||||
\(276\) | −0.184722 | −0.0111190 | ||||||||
\(277\) | 5.30586 | 0.318798 | 0.159399 | − | 0.987214i | \(-0.449044\pi\) | ||||
0.159399 | + | 0.987214i | \(0.449044\pi\) | |||||||
\(278\) | −7.39186 | −0.443335 | ||||||||
\(279\) | 3.98591 | 0.238630 | ||||||||
\(280\) | −0.405114 | −0.0242102 | ||||||||
\(281\) | 3.68578 | 0.219875 | 0.109938 | − | 0.993938i | \(-0.464935\pi\) | ||||
0.109938 | + | 0.993938i | \(0.464935\pi\) | |||||||
\(282\) | −3.17173 | −0.188874 | ||||||||
\(283\) | 12.2697 | 0.729359 | 0.364680 | − | 0.931133i | \(-0.381178\pi\) | ||||
0.364680 | + | 0.931133i | \(0.381178\pi\) | |||||||
\(284\) | 3.53239 | 0.209609 | ||||||||
\(285\) | −3.93771 | −0.233250 | ||||||||
\(286\) | 11.4296 | 0.675848 | ||||||||
\(287\) | −3.16288 | −0.186699 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 4.70943 | 0.276548 | ||||||||
\(291\) | 8.31606 | 0.487496 | ||||||||
\(292\) | −12.2252 | −0.715423 | ||||||||
\(293\) | −2.57594 | −0.150488 | −0.0752439 | − | 0.997165i | \(-0.523974\pi\) | ||||
−0.0752439 | + | 0.997165i | \(0.523974\pi\) | |||||||
\(294\) | 6.47066 | 0.377377 | ||||||||
\(295\) | 0.556815 | 0.0324190 | ||||||||
\(296\) | −1.09215 | −0.0634799 | ||||||||
\(297\) | 4.53073 | 0.262899 | ||||||||
\(298\) | 8.91020 | 0.516154 | ||||||||
\(299\) | 0.465997 | 0.0269493 | ||||||||
\(300\) | −4.68996 | −0.270775 | ||||||||
\(301\) | 2.09319 | 0.120649 | ||||||||
\(302\) | 16.1476 | 0.929192 | ||||||||
\(303\) | 6.06297 | 0.348309 | ||||||||
\(304\) | −7.07185 | −0.405598 | ||||||||
\(305\) | −8.43995 | −0.483270 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | 8.68684 | 0.495784 | 0.247892 | − | 0.968788i | \(-0.420262\pi\) | ||||
0.247892 | + | 0.968788i | \(0.420262\pi\) | |||||||
\(308\) | 3.29636 | 0.187827 | ||||||||
\(309\) | 17.2773 | 0.982872 | ||||||||
\(310\) | −2.21942 | −0.126054 | ||||||||
\(311\) | 8.99505 | 0.510063 | 0.255031 | − | 0.966933i | \(-0.417914\pi\) | ||||
0.255031 | + | 0.966933i | \(0.417914\pi\) | |||||||
\(312\) | 2.52269 | 0.142819 | ||||||||
\(313\) | −10.0722 | −0.569315 | −0.284657 | − | 0.958629i | \(-0.591880\pi\) | ||||
−0.284657 | + | 0.958629i | \(0.591880\pi\) | |||||||
\(314\) | −3.17083 | −0.178940 | ||||||||
\(315\) | 0.405114 | 0.0228256 | ||||||||
\(316\) | −6.38902 | −0.359410 | ||||||||
\(317\) | −16.3971 | −0.920954 | −0.460477 | − | 0.887672i | \(-0.652322\pi\) | ||||
−0.460477 | + | 0.887672i | \(0.652322\pi\) | |||||||
\(318\) | 11.9287 | 0.668931 | ||||||||
\(319\) | −38.3200 | −2.14551 | ||||||||
\(320\) | 0.556815 | 0.0311269 | ||||||||
\(321\) | −11.7625 | −0.656517 | ||||||||
\(322\) | 0.134396 | 0.00748957 | ||||||||
\(323\) | 7.07185 | 0.393488 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 11.8313 | 0.656284 | ||||||||
\(326\) | −2.80623 | −0.155423 | ||||||||
\(327\) | 5.36322 | 0.296587 | ||||||||
\(328\) | 4.34727 | 0.240038 | ||||||||
\(329\) | 2.30761 | 0.127223 | ||||||||
\(330\) | −2.52277 | −0.138874 | ||||||||
\(331\) | 7.11007 | 0.390805 | 0.195402 | − | 0.980723i | \(-0.437399\pi\) | ||||
0.195402 | + | 0.980723i | \(0.437399\pi\) | |||||||
\(332\) | −12.2390 | −0.671704 | ||||||||
\(333\) | 1.09215 | 0.0598494 | ||||||||
\(334\) | 23.2163 | 1.27034 | ||||||||
\(335\) | 1.78662 | 0.0976135 | ||||||||
\(336\) | 0.727556 | 0.0396915 | ||||||||
\(337\) | 3.44704 | 0.187772 | 0.0938862 | − | 0.995583i | \(-0.470071\pi\) | ||||
0.0938862 | + | 0.995583i | \(0.470071\pi\) | |||||||
\(338\) | 6.63602 | 0.360952 | ||||||||
\(339\) | −4.36168 | −0.236894 | ||||||||
\(340\) | −0.556815 | −0.0301975 | ||||||||
\(341\) | 18.0591 | 0.977955 | ||||||||
\(342\) | 7.07185 | 0.382402 | ||||||||
\(343\) | −9.80067 | −0.529186 | ||||||||
\(344\) | −2.87701 | −0.155118 | ||||||||
\(345\) | −0.102856 | −0.00553757 | ||||||||
\(346\) | −6.57794 | −0.353632 | ||||||||
\(347\) | −0.159048 | −0.00853813 | −0.00426906 | − | 0.999991i | \(-0.501359\pi\) | ||||
−0.00426906 | + | 0.999991i | \(0.501359\pi\) | |||||||
\(348\) | −8.45781 | −0.453386 | ||||||||
\(349\) | −5.25727 | −0.281415 | −0.140708 | − | 0.990051i | \(-0.544938\pi\) | ||||
−0.140708 | + | 0.990051i | \(0.544938\pi\) | |||||||
\(350\) | 3.41221 | 0.182390 | ||||||||
\(351\) | −2.52269 | −0.134651 | ||||||||
\(352\) | −4.53073 | −0.241489 | ||||||||
\(353\) | −20.1464 | −1.07229 | −0.536143 | − | 0.844127i | \(-0.680119\pi\) | ||||
−0.536143 | + | 0.844127i | \(0.680119\pi\) | |||||||
\(354\) | −1.00000 | −0.0531494 | ||||||||
\(355\) | 1.96688 | 0.104391 | ||||||||
\(356\) | −14.3230 | −0.759117 | ||||||||
\(357\) | −0.727556 | −0.0385064 | ||||||||
\(358\) | −19.0412 | −1.00636 | ||||||||
\(359\) | 3.01999 | 0.159389 | 0.0796944 | − | 0.996819i | \(-0.474606\pi\) | ||||
0.0796944 | + | 0.996819i | \(0.474606\pi\) | |||||||
\(360\) | −0.556815 | −0.0293467 | ||||||||
\(361\) | 31.0110 | 1.63216 | ||||||||
\(362\) | −9.19753 | −0.483412 | ||||||||
\(363\) | 9.52748 | 0.500063 | ||||||||
\(364\) | −1.83540 | −0.0962012 | ||||||||
\(365\) | −6.80715 | −0.356302 | ||||||||
\(366\) | 15.1576 | 0.792298 | ||||||||
\(367\) | 29.5906 | 1.54462 | 0.772310 | − | 0.635246i | \(-0.219101\pi\) | ||||
0.772310 | + | 0.635246i | \(0.219101\pi\) | |||||||
\(368\) | −0.184722 | −0.00962930 | ||||||||
\(369\) | −4.34727 | −0.226310 | ||||||||
\(370\) | −0.608125 | −0.0316149 | ||||||||
\(371\) | −8.67883 | −0.450583 | ||||||||
\(372\) | 3.98591 | 0.206660 | ||||||||
\(373\) | −18.9667 | −0.982058 | −0.491029 | − | 0.871143i | \(-0.663379\pi\) | ||||
−0.491029 | + | 0.871143i | \(0.663379\pi\) | |||||||
\(374\) | 4.53073 | 0.234278 | ||||||||
\(375\) | −5.39551 | −0.278623 | ||||||||
\(376\) | −3.17173 | −0.163569 | ||||||||
\(377\) | 21.3365 | 1.09888 | ||||||||
\(378\) | −0.727556 | −0.0374215 | ||||||||
\(379\) | 15.0100 | 0.771010 | 0.385505 | − | 0.922706i | \(-0.374027\pi\) | ||||
0.385505 | + | 0.922706i | \(0.374027\pi\) | |||||||
\(380\) | −3.93771 | −0.202000 | ||||||||
\(381\) | 9.35619 | 0.479332 | ||||||||
\(382\) | 9.74626 | 0.498662 | ||||||||
\(383\) | −23.9175 | −1.22213 | −0.611064 | − | 0.791581i | \(-0.709258\pi\) | ||||
−0.611064 | + | 0.791581i | \(0.709258\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 1.83546 | 0.0935437 | ||||||||
\(386\) | −10.5626 | −0.537622 | ||||||||
\(387\) | 2.87701 | 0.146247 | ||||||||
\(388\) | 8.31606 | 0.422184 | ||||||||
\(389\) | 14.3949 | 0.729850 | 0.364925 | − | 0.931037i | \(-0.381095\pi\) | ||||
0.364925 | + | 0.931037i | \(0.381095\pi\) | |||||||
\(390\) | 1.40467 | 0.0711283 | ||||||||
\(391\) | 0.184722 | 0.00934179 | ||||||||
\(392\) | 6.47066 | 0.326818 | ||||||||
\(393\) | 20.2038 | 1.01914 | ||||||||
\(394\) | −14.7874 | −0.744979 | ||||||||
\(395\) | −3.55750 | −0.178997 | ||||||||
\(396\) | 4.53073 | 0.227678 | ||||||||
\(397\) | −6.29385 | −0.315879 | −0.157940 | − | 0.987449i | \(-0.550485\pi\) | ||||
−0.157940 | + | 0.987449i | \(0.550485\pi\) | |||||||
\(398\) | −14.8207 | −0.742893 | ||||||||
\(399\) | −5.14517 | −0.257580 | ||||||||
\(400\) | −4.68996 | −0.234498 | ||||||||
\(401\) | 30.8031 | 1.53823 | 0.769116 | − | 0.639109i | \(-0.220697\pi\) | ||||
0.769116 | + | 0.639109i | \(0.220697\pi\) | |||||||
\(402\) | −3.20865 | −0.160033 | ||||||||
\(403\) | −10.0552 | −0.500887 | ||||||||
\(404\) | 6.06297 | 0.301644 | ||||||||
\(405\) | 0.556815 | 0.0276683 | ||||||||
\(406\) | 6.15354 | 0.305395 | ||||||||
\(407\) | 4.94823 | 0.245275 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | −31.8845 | −1.57659 | −0.788293 | − | 0.615300i | \(-0.789035\pi\) | ||||
−0.788293 | + | 0.615300i | \(0.789035\pi\) | |||||||
\(410\) | 2.42062 | 0.119546 | ||||||||
\(411\) | 6.34305 | 0.312880 | ||||||||
\(412\) | 17.2773 | 0.851192 | ||||||||
\(413\) | 0.727556 | 0.0358007 | ||||||||
\(414\) | 0.184722 | 0.00907859 | ||||||||
\(415\) | −6.81487 | −0.334529 | ||||||||
\(416\) | 2.52269 | 0.123685 | ||||||||
\(417\) | 7.39186 | 0.361981 | ||||||||
\(418\) | 32.0406 | 1.56716 | ||||||||
\(419\) | 6.97628 | 0.340814 | 0.170407 | − | 0.985374i | \(-0.445492\pi\) | ||||
0.170407 | + | 0.985374i | \(0.445492\pi\) | |||||||
\(420\) | 0.405114 | 0.0197675 | ||||||||
\(421\) | 10.4242 | 0.508043 | 0.254021 | − | 0.967199i | \(-0.418247\pi\) | ||||
0.254021 | + | 0.967199i | \(0.418247\pi\) | |||||||
\(422\) | 10.2870 | 0.500762 | ||||||||
\(423\) | 3.17173 | 0.154215 | ||||||||
\(424\) | 11.9287 | 0.579311 | ||||||||
\(425\) | 4.68996 | 0.227496 | ||||||||
\(426\) | −3.53239 | −0.171145 | ||||||||
\(427\) | −11.0280 | −0.533681 | ||||||||
\(428\) | −11.7625 | −0.568560 | ||||||||
\(429\) | −11.4296 | −0.551828 | ||||||||
\(430\) | −1.60196 | −0.0772535 | ||||||||
\(431\) | 24.4816 | 1.17924 | 0.589618 | − | 0.807682i | \(-0.299278\pi\) | ||||
0.589618 | + | 0.807682i | \(0.299278\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −22.7883 | −1.09514 | −0.547568 | − | 0.836761i | \(-0.684446\pi\) | ||||
−0.547568 | + | 0.836761i | \(0.684446\pi\) | |||||||
\(434\) | −2.89998 | −0.139203 | ||||||||
\(435\) | −4.70943 | −0.225800 | ||||||||
\(436\) | 5.36322 | 0.256852 | ||||||||
\(437\) | 1.30632 | 0.0624900 | ||||||||
\(438\) | 12.2252 | 0.584141 | ||||||||
\(439\) | 3.64730 | 0.174076 | 0.0870381 | − | 0.996205i | \(-0.472260\pi\) | ||||
0.0870381 | + | 0.996205i | \(0.472260\pi\) | |||||||
\(440\) | −2.52277 | −0.120269 | ||||||||
\(441\) | −6.47066 | −0.308127 | ||||||||
\(442\) | −2.52269 | −0.119992 | ||||||||
\(443\) | −15.0337 | −0.714274 | −0.357137 | − | 0.934052i | \(-0.616247\pi\) | ||||
−0.357137 | + | 0.934052i | \(0.616247\pi\) | |||||||
\(444\) | 1.09215 | 0.0518311 | ||||||||
\(445\) | −7.97525 | −0.378063 | ||||||||
\(446\) | −18.1422 | −0.859060 | ||||||||
\(447\) | −8.91020 | −0.421438 | ||||||||
\(448\) | 0.727556 | 0.0343738 | ||||||||
\(449\) | −23.6239 | −1.11488 | −0.557441 | − | 0.830217i | \(-0.688217\pi\) | ||||
−0.557441 | + | 0.830217i | \(0.688217\pi\) | |||||||
\(450\) | 4.68996 | 0.221087 | ||||||||
\(451\) | −19.6963 | −0.927462 | ||||||||
\(452\) | −4.36168 | −0.205156 | ||||||||
\(453\) | −16.1476 | −0.758682 | ||||||||
\(454\) | −1.83958 | −0.0863356 | ||||||||
\(455\) | −1.02198 | −0.0479111 | ||||||||
\(456\) | 7.07185 | 0.331170 | ||||||||
\(457\) | −36.6981 | −1.71667 | −0.858333 | − | 0.513093i | \(-0.828500\pi\) | ||||
−0.858333 | + | 0.513093i | \(0.828500\pi\) | |||||||
\(458\) | 2.39025 | 0.111689 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −0.102856 | −0.00479568 | ||||||||
\(461\) | −28.3825 | −1.32190 | −0.660951 | − | 0.750429i | \(-0.729847\pi\) | ||||
−0.660951 | + | 0.750429i | \(0.729847\pi\) | |||||||
\(462\) | −3.29636 | −0.153360 | ||||||||
\(463\) | −0.789581 | −0.0366949 | −0.0183475 | − | 0.999832i | \(-0.505841\pi\) | ||||
−0.0183475 | + | 0.999832i | \(0.505841\pi\) | |||||||
\(464\) | −8.45781 | −0.392644 | ||||||||
\(465\) | 2.21942 | 0.102923 | ||||||||
\(466\) | −13.5052 | −0.625617 | ||||||||
\(467\) | 2.20236 | 0.101913 | 0.0509566 | − | 0.998701i | \(-0.483773\pi\) | ||||
0.0509566 | + | 0.998701i | \(0.483773\pi\) | |||||||
\(468\) | −2.52269 | −0.116612 | ||||||||
\(469\) | 2.33447 | 0.107796 | ||||||||
\(470\) | −1.76606 | −0.0814625 | ||||||||
\(471\) | 3.17083 | 0.146104 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | 13.0350 | 0.599348 | ||||||||
\(474\) | 6.38902 | 0.293457 | ||||||||
\(475\) | 33.1667 | 1.52179 | ||||||||
\(476\) | −0.727556 | −0.0333475 | ||||||||
\(477\) | −11.9287 | −0.546180 | ||||||||
\(478\) | 28.3102 | 1.29488 | ||||||||
\(479\) | −10.5683 | −0.482880 | −0.241440 | − | 0.970416i | \(-0.577620\pi\) | ||||
−0.241440 | + | 0.970416i | \(0.577620\pi\) | |||||||
\(480\) | −0.556815 | −0.0254150 | ||||||||
\(481\) | −2.75516 | −0.125624 | ||||||||
\(482\) | −18.4711 | −0.841336 | ||||||||
\(483\) | −0.134396 | −0.00611521 | ||||||||
\(484\) | 9.52748 | 0.433067 | ||||||||
\(485\) | 4.63051 | 0.210260 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −12.1501 | −0.550575 | −0.275288 | − | 0.961362i | \(-0.588773\pi\) | ||||
−0.275288 | + | 0.961362i | \(0.588773\pi\) | |||||||
\(488\) | 15.1576 | 0.686150 | ||||||||
\(489\) | 2.80623 | 0.126902 | ||||||||
\(490\) | 3.60296 | 0.162765 | ||||||||
\(491\) | 34.2121 | 1.54397 | 0.771985 | − | 0.635641i | \(-0.219264\pi\) | ||||
0.771985 | + | 0.635641i | \(0.219264\pi\) | |||||||
\(492\) | −4.34727 | −0.195990 | ||||||||
\(493\) | 8.45781 | 0.380921 | ||||||||
\(494\) | −17.8401 | −0.802664 | ||||||||
\(495\) | 2.52277 | 0.113390 | ||||||||
\(496\) | 3.98591 | 0.178973 | ||||||||
\(497\) | 2.57001 | 0.115281 | ||||||||
\(498\) | 12.2390 | 0.548444 | ||||||||
\(499\) | 16.3962 | 0.733996 | 0.366998 | − | 0.930222i | \(-0.380385\pi\) | ||||
0.366998 | + | 0.930222i | \(0.380385\pi\) | |||||||
\(500\) | −5.39551 | −0.241295 | ||||||||
\(501\) | −23.2163 | −1.03723 | ||||||||
\(502\) | 4.08294 | 0.182231 | ||||||||
\(503\) | −27.6603 | −1.23331 | −0.616657 | − | 0.787232i | \(-0.711513\pi\) | ||||
−0.616657 | + | 0.787232i | \(0.711513\pi\) | |||||||
\(504\) | −0.727556 | −0.0324079 | ||||||||
\(505\) | 3.37595 | 0.150228 | ||||||||
\(506\) | 0.836924 | 0.0372058 | ||||||||
\(507\) | −6.63602 | −0.294716 | ||||||||
\(508\) | 9.35619 | 0.415114 | ||||||||
\(509\) | 3.05246 | 0.135298 | 0.0676490 | − | 0.997709i | \(-0.478450\pi\) | ||||
0.0676490 | + | 0.997709i | \(0.478450\pi\) | |||||||
\(510\) | 0.556815 | 0.0246562 | ||||||||
\(511\) | −8.89449 | −0.393469 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −7.07185 | −0.312230 | ||||||||
\(514\) | 24.7228 | 1.09048 | ||||||||
\(515\) | 9.62026 | 0.423919 | ||||||||
\(516\) | 2.87701 | 0.126653 | ||||||||
\(517\) | 14.3702 | 0.632002 | ||||||||
\(518\) | −0.794600 | −0.0349127 | ||||||||
\(519\) | 6.57794 | 0.288740 | ||||||||
\(520\) | 1.40467 | 0.0615989 | ||||||||
\(521\) | 20.0225 | 0.877202 | 0.438601 | − | 0.898682i | \(-0.355474\pi\) | ||||
0.438601 | + | 0.898682i | \(0.355474\pi\) | |||||||
\(522\) | 8.45781 | 0.370188 | ||||||||
\(523\) | 43.3271 | 1.89456 | 0.947281 | − | 0.320405i | \(-0.103819\pi\) | ||||
0.947281 | + | 0.320405i | \(0.103819\pi\) | |||||||
\(524\) | 20.2038 | 0.882605 | ||||||||
\(525\) | −3.41221 | −0.148921 | ||||||||
\(526\) | 28.5865 | 1.24643 | ||||||||
\(527\) | −3.98591 | −0.173629 | ||||||||
\(528\) | 4.53073 | 0.197175 | ||||||||
\(529\) | −22.9659 | −0.998516 | ||||||||
\(530\) | 6.64210 | 0.288514 | ||||||||
\(531\) | 1.00000 | 0.0433963 | ||||||||
\(532\) | −5.14517 | −0.223071 | ||||||||
\(533\) | 10.9668 | 0.475026 | ||||||||
\(534\) | 14.3230 | 0.619816 | ||||||||
\(535\) | −6.54951 | −0.283160 | ||||||||
\(536\) | −3.20865 | −0.138592 | ||||||||
\(537\) | 19.0412 | 0.821688 | ||||||||
\(538\) | 2.43595 | 0.105021 | ||||||||
\(539\) | −29.3168 | −1.26276 | ||||||||
\(540\) | 0.556815 | 0.0239615 | ||||||||
\(541\) | 5.86864 | 0.252313 | 0.126156 | − | 0.992010i | \(-0.459736\pi\) | ||||
0.126156 | + | 0.992010i | \(0.459736\pi\) | |||||||
\(542\) | −20.1234 | −0.864376 | ||||||||
\(543\) | 9.19753 | 0.394704 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 2.98632 | 0.127920 | ||||||||
\(546\) | 1.83540 | 0.0785479 | ||||||||
\(547\) | −20.0022 | −0.855230 | −0.427615 | − | 0.903961i | \(-0.640646\pi\) | ||||
−0.427615 | + | 0.903961i | \(0.640646\pi\) | |||||||
\(548\) | 6.34305 | 0.270962 | ||||||||
\(549\) | −15.1576 | −0.646909 | ||||||||
\(550\) | 21.2489 | 0.906057 | ||||||||
\(551\) | 59.8124 | 2.54809 | ||||||||
\(552\) | 0.184722 | 0.00786229 | ||||||||
\(553\) | −4.64837 | −0.197669 | ||||||||
\(554\) | −5.30586 | −0.225425 | ||||||||
\(555\) | 0.608125 | 0.0258134 | ||||||||
\(556\) | 7.39186 | 0.313485 | ||||||||
\(557\) | −39.0434 | −1.65432 | −0.827162 | − | 0.561964i | \(-0.810046\pi\) | ||||
−0.827162 | + | 0.561964i | \(0.810046\pi\) | |||||||
\(558\) | −3.98591 | −0.168737 | ||||||||
\(559\) | −7.25782 | −0.306973 | ||||||||
\(560\) | 0.405114 | 0.0171192 | ||||||||
\(561\) | −4.53073 | −0.191287 | ||||||||
\(562\) | −3.68578 | −0.155475 | ||||||||
\(563\) | −8.51830 | −0.359003 | −0.179502 | − | 0.983758i | \(-0.557449\pi\) | ||||
−0.179502 | + | 0.983758i | \(0.557449\pi\) | |||||||
\(564\) | 3.17173 | 0.133554 | ||||||||
\(565\) | −2.42865 | −0.102174 | ||||||||
\(566\) | −12.2697 | −0.515735 | ||||||||
\(567\) | 0.727556 | 0.0305545 | ||||||||
\(568\) | −3.53239 | −0.148216 | ||||||||
\(569\) | 10.4497 | 0.438074 | 0.219037 | − | 0.975717i | \(-0.429708\pi\) | ||||
0.219037 | + | 0.975717i | \(0.429708\pi\) | |||||||
\(570\) | 3.93771 | 0.164932 | ||||||||
\(571\) | −1.02766 | −0.0430061 | −0.0215031 | − | 0.999769i | \(-0.506845\pi\) | ||||
−0.0215031 | + | 0.999769i | \(0.506845\pi\) | |||||||
\(572\) | −11.4296 | −0.477897 | ||||||||
\(573\) | −9.74626 | −0.407156 | ||||||||
\(574\) | 3.16288 | 0.132016 | ||||||||
\(575\) | 0.866338 | 0.0361288 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −39.5656 | −1.64714 | −0.823569 | − | 0.567215i | \(-0.808021\pi\) | ||||
−0.823569 | + | 0.567215i | \(0.808021\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 10.5626 | 0.438966 | ||||||||
\(580\) | −4.70943 | −0.195549 | ||||||||
\(581\) | −8.90458 | −0.369424 | ||||||||
\(582\) | −8.31606 | −0.344712 | ||||||||
\(583\) | −54.0459 | −2.23835 | ||||||||
\(584\) | 12.2252 | 0.505881 | ||||||||
\(585\) | −1.40467 | −0.0580760 | ||||||||
\(586\) | 2.57594 | 0.106411 | ||||||||
\(587\) | −43.1650 | −1.78161 | −0.890805 | − | 0.454387i | \(-0.849858\pi\) | ||||
−0.890805 | + | 0.454387i | \(0.849858\pi\) | |||||||
\(588\) | −6.47066 | −0.266846 | ||||||||
\(589\) | −28.1878 | −1.16146 | ||||||||
\(590\) | −0.556815 | −0.0229237 | ||||||||
\(591\) | 14.7874 | 0.608273 | ||||||||
\(592\) | 1.09215 | 0.0448870 | ||||||||
\(593\) | 15.5747 | 0.639578 | 0.319789 | − | 0.947489i | \(-0.396388\pi\) | ||||
0.319789 | + | 0.947489i | \(0.396388\pi\) | |||||||
\(594\) | −4.53073 | −0.185898 | ||||||||
\(595\) | −0.405114 | −0.0166081 | ||||||||
\(596\) | −8.91020 | −0.364976 | ||||||||
\(597\) | 14.8207 | 0.606570 | ||||||||
\(598\) | −0.465997 | −0.0190560 | ||||||||
\(599\) | 31.9373 | 1.30492 | 0.652462 | − | 0.757822i | \(-0.273736\pi\) | ||||
0.652462 | + | 0.757822i | \(0.273736\pi\) | |||||||
\(600\) | 4.68996 | 0.191467 | ||||||||
\(601\) | 11.2085 | 0.457203 | 0.228602 | − | 0.973520i | \(-0.426585\pi\) | ||||
0.228602 | + | 0.973520i | \(0.426585\pi\) | |||||||
\(602\) | −2.09319 | −0.0853120 | ||||||||
\(603\) | 3.20865 | 0.130666 | ||||||||
\(604\) | −16.1476 | −0.657038 | ||||||||
\(605\) | 5.30504 | 0.215681 | ||||||||
\(606\) | −6.06297 | −0.246291 | ||||||||
\(607\) | 21.5682 | 0.875425 | 0.437712 | − | 0.899115i | \(-0.355789\pi\) | ||||
0.437712 | + | 0.899115i | \(0.355789\pi\) | |||||||
\(608\) | 7.07185 | 0.286801 | ||||||||
\(609\) | −6.15354 | −0.249354 | ||||||||
\(610\) | 8.43995 | 0.341723 | ||||||||
\(611\) | −8.00129 | −0.323698 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | −13.7089 | −0.553698 | −0.276849 | − | 0.960913i | \(-0.589290\pi\) | ||||
−0.276849 | + | 0.960913i | \(0.589290\pi\) | |||||||
\(614\) | −8.68684 | −0.350572 | ||||||||
\(615\) | −2.42062 | −0.0976089 | ||||||||
\(616\) | −3.29636 | −0.132814 | ||||||||
\(617\) | −2.28828 | −0.0921228 | −0.0460614 | − | 0.998939i | \(-0.514667\pi\) | ||||
−0.0460614 | + | 0.998939i | \(0.514667\pi\) | |||||||
\(618\) | −17.2773 | −0.694995 | ||||||||
\(619\) | 6.13229 | 0.246477 | 0.123239 | − | 0.992377i | \(-0.460672\pi\) | ||||
0.123239 | + | 0.992377i | \(0.460672\pi\) | |||||||
\(620\) | 2.21942 | 0.0891339 | ||||||||
\(621\) | −0.184722 | −0.00741264 | ||||||||
\(622\) | −8.99505 | −0.360669 | ||||||||
\(623\) | −10.4208 | −0.417500 | ||||||||
\(624\) | −2.52269 | −0.100989 | ||||||||
\(625\) | 20.4455 | 0.817820 | ||||||||
\(626\) | 10.0722 | 0.402566 | ||||||||
\(627\) | −32.0406 | −1.27958 | ||||||||
\(628\) | 3.17083 | 0.126530 | ||||||||
\(629\) | −1.09215 | −0.0435468 | ||||||||
\(630\) | −0.405114 | −0.0161401 | ||||||||
\(631\) | −41.7045 | −1.66023 | −0.830114 | − | 0.557593i | \(-0.811725\pi\) | ||||
−0.830114 | + | 0.557593i | \(0.811725\pi\) | |||||||
\(632\) | 6.38902 | 0.254141 | ||||||||
\(633\) | −10.2870 | −0.408871 | ||||||||
\(634\) | 16.3971 | 0.651213 | ||||||||
\(635\) | 5.20966 | 0.206739 | ||||||||
\(636\) | −11.9287 | −0.473005 | ||||||||
\(637\) | 16.3235 | 0.646760 | ||||||||
\(638\) | 38.3200 | 1.51710 | ||||||||
\(639\) | 3.53239 | 0.139739 | ||||||||
\(640\) | −0.556815 | −0.0220100 | ||||||||
\(641\) | 26.3236 | 1.03972 | 0.519859 | − | 0.854252i | \(-0.325984\pi\) | ||||
0.519859 | + | 0.854252i | \(0.325984\pi\) | |||||||
\(642\) | 11.7625 | 0.464228 | ||||||||
\(643\) | −19.2145 | −0.757747 | −0.378874 | − | 0.925448i | \(-0.623688\pi\) | ||||
−0.378874 | + | 0.925448i | \(0.623688\pi\) | |||||||
\(644\) | −0.134396 | −0.00529593 | ||||||||
\(645\) | 1.60196 | 0.0630772 | ||||||||
\(646\) | −7.07185 | −0.278238 | ||||||||
\(647\) | −15.1523 | −0.595698 | −0.297849 | − | 0.954613i | \(-0.596269\pi\) | ||||
−0.297849 | + | 0.954613i | \(0.596269\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 4.53073 | 0.177847 | ||||||||
\(650\) | −11.8313 | −0.464063 | ||||||||
\(651\) | 2.89998 | 0.113659 | ||||||||
\(652\) | 2.80623 | 0.109901 | ||||||||
\(653\) | −15.2969 | −0.598615 | −0.299308 | − | 0.954157i | \(-0.596756\pi\) | ||||
−0.299308 | + | 0.954157i | \(0.596756\pi\) | |||||||
\(654\) | −5.36322 | −0.209718 | ||||||||
\(655\) | 11.2497 | 0.439564 | ||||||||
\(656\) | −4.34727 | −0.169732 | ||||||||
\(657\) | −12.2252 | −0.476949 | ||||||||
\(658\) | −2.30761 | −0.0899600 | ||||||||
\(659\) | 9.62638 | 0.374990 | 0.187495 | − | 0.982266i | \(-0.439963\pi\) | ||||
0.187495 | + | 0.982266i | \(0.439963\pi\) | |||||||
\(660\) | 2.52277 | 0.0981989 | ||||||||
\(661\) | −29.3777 | −1.14266 | −0.571330 | − | 0.820720i | \(-0.693572\pi\) | ||||
−0.571330 | + | 0.820720i | \(0.693572\pi\) | |||||||
\(662\) | −7.11007 | −0.276341 | ||||||||
\(663\) | 2.52269 | 0.0979733 | ||||||||
\(664\) | 12.2390 | 0.474966 | ||||||||
\(665\) | −2.86490 | −0.111096 | ||||||||
\(666\) | −1.09215 | −0.0423199 | ||||||||
\(667\) | 1.56234 | 0.0604942 | ||||||||
\(668\) | −23.2163 | −0.898267 | ||||||||
\(669\) | 18.1422 | 0.701420 | ||||||||
\(670\) | −1.78662 | −0.0690232 | ||||||||
\(671\) | −68.6747 | −2.65116 | ||||||||
\(672\) | −0.727556 | −0.0280661 | ||||||||
\(673\) | −5.27171 | −0.203210 | −0.101605 | − | 0.994825i | \(-0.532398\pi\) | ||||
−0.101605 | + | 0.994825i | \(0.532398\pi\) | |||||||
\(674\) | −3.44704 | −0.132775 | ||||||||
\(675\) | −4.68996 | −0.180517 | ||||||||
\(676\) | −6.63602 | −0.255232 | ||||||||
\(677\) | −7.47823 | −0.287412 | −0.143706 | − | 0.989620i | \(-0.545902\pi\) | ||||
−0.143706 | + | 0.989620i | \(0.545902\pi\) | |||||||
\(678\) | 4.36168 | 0.167509 | ||||||||
\(679\) | 6.05040 | 0.232193 | ||||||||
\(680\) | 0.556815 | 0.0213529 | ||||||||
\(681\) | 1.83958 | 0.0704927 | ||||||||
\(682\) | −18.0591 | −0.691518 | ||||||||
\(683\) | 34.8078 | 1.33188 | 0.665941 | − | 0.746004i | \(-0.268030\pi\) | ||||
0.665941 | + | 0.746004i | \(0.268030\pi\) | |||||||
\(684\) | −7.07185 | −0.270399 | ||||||||
\(685\) | 3.53190 | 0.134947 | ||||||||
\(686\) | 9.80067 | 0.374191 | ||||||||
\(687\) | −2.39025 | −0.0911936 | ||||||||
\(688\) | 2.87701 | 0.109685 | ||||||||
\(689\) | 30.0925 | 1.14643 | ||||||||
\(690\) | 0.102856 | 0.00391566 | ||||||||
\(691\) | 3.79401 | 0.144331 | 0.0721655 | − | 0.997393i | \(-0.477009\pi\) | ||||
0.0721655 | + | 0.997393i | \(0.477009\pi\) | |||||||
\(692\) | 6.57794 | 0.250056 | ||||||||
\(693\) | 3.29636 | 0.125218 | ||||||||
\(694\) | 0.159048 | 0.00603737 | ||||||||
\(695\) | 4.11590 | 0.156125 | ||||||||
\(696\) | 8.45781 | 0.320593 | ||||||||
\(697\) | 4.34727 | 0.164665 | ||||||||
\(698\) | 5.25727 | 0.198991 | ||||||||
\(699\) | 13.5052 | 0.510814 | ||||||||
\(700\) | −3.41221 | −0.128969 | ||||||||
\(701\) | −28.7902 | −1.08739 | −0.543696 | − | 0.839282i | \(-0.682975\pi\) | ||||
−0.543696 | + | 0.839282i | \(0.682975\pi\) | |||||||
\(702\) | 2.52269 | 0.0952129 | ||||||||
\(703\) | −7.72351 | −0.291298 | ||||||||
\(704\) | 4.53073 | 0.170758 | ||||||||
\(705\) | 1.76606 | 0.0665138 | ||||||||
\(706\) | 20.1464 | 0.758221 | ||||||||
\(707\) | 4.41115 | 0.165899 | ||||||||
\(708\) | 1.00000 | 0.0375823 | ||||||||
\(709\) | 31.2676 | 1.17428 | 0.587140 | − | 0.809486i | \(-0.300254\pi\) | ||||
0.587140 | + | 0.809486i | \(0.300254\pi\) | |||||||
\(710\) | −1.96688 | −0.0738158 | ||||||||
\(711\) | −6.38902 | −0.239607 | ||||||||
\(712\) | 14.3230 | 0.536777 | ||||||||
\(713\) | −0.736286 | −0.0275741 | ||||||||
\(714\) | 0.727556 | 0.0272281 | ||||||||
\(715\) | −6.36418 | −0.238007 | ||||||||
\(716\) | 19.0412 | 0.711603 | ||||||||
\(717\) | −28.3102 | −1.05726 | ||||||||
\(718\) | −3.01999 | −0.112705 | ||||||||
\(719\) | −8.55997 | −0.319233 | −0.159616 | − | 0.987179i | \(-0.551026\pi\) | ||||
−0.159616 | + | 0.987179i | \(0.551026\pi\) | |||||||
\(720\) | 0.556815 | 0.0207513 | ||||||||
\(721\) | 12.5702 | 0.468139 | ||||||||
\(722\) | −31.0110 | −1.15411 | ||||||||
\(723\) | 18.4711 | 0.686948 | ||||||||
\(724\) | 9.19753 | 0.341824 | ||||||||
\(725\) | 39.6668 | 1.47319 | ||||||||
\(726\) | −9.52748 | −0.353598 | ||||||||
\(727\) | −24.9322 | −0.924683 | −0.462342 | − | 0.886702i | \(-0.652991\pi\) | ||||
−0.462342 | + | 0.886702i | \(0.652991\pi\) | |||||||
\(728\) | 1.83540 | 0.0680245 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.80715 | 0.251944 | ||||||||
\(731\) | −2.87701 | −0.106410 | ||||||||
\(732\) | −15.1576 | −0.560239 | ||||||||
\(733\) | −27.5030 | −1.01585 | −0.507924 | − | 0.861402i | \(-0.669587\pi\) | ||||
−0.507924 | + | 0.861402i | \(0.669587\pi\) | |||||||
\(734\) | −29.5906 | −1.09221 | ||||||||
\(735\) | −3.60296 | −0.132897 | ||||||||
\(736\) | 0.184722 | 0.00680894 | ||||||||
\(737\) | 14.5375 | 0.535496 | ||||||||
\(738\) | 4.34727 | 0.160025 | ||||||||
\(739\) | −31.2257 | −1.14866 | −0.574329 | − | 0.818625i | \(-0.694737\pi\) | ||||
−0.574329 | + | 0.818625i | \(0.694737\pi\) | |||||||
\(740\) | 0.608125 | 0.0223551 | ||||||||
\(741\) | 17.8401 | 0.655372 | ||||||||
\(742\) | 8.67883 | 0.318610 | ||||||||
\(743\) | −42.0672 | −1.54330 | −0.771648 | − | 0.636050i | \(-0.780567\pi\) | ||||
−0.771648 | + | 0.636050i | \(0.780567\pi\) | |||||||
\(744\) | −3.98591 | −0.146131 | ||||||||
\(745\) | −4.96133 | −0.181769 | ||||||||
\(746\) | 18.9667 | 0.694420 | ||||||||
\(747\) | −12.2390 | −0.447803 | ||||||||
\(748\) | −4.53073 | −0.165660 | ||||||||
\(749\) | −8.55786 | −0.312697 | ||||||||
\(750\) | 5.39551 | 0.197016 | ||||||||
\(751\) | 50.4787 | 1.84199 | 0.920996 | − | 0.389571i | \(-0.127377\pi\) | ||||
0.920996 | + | 0.389571i | \(0.127377\pi\) | |||||||
\(752\) | 3.17173 | 0.115661 | ||||||||
\(753\) | −4.08294 | −0.148791 | ||||||||
\(754\) | −21.3365 | −0.777028 | ||||||||
\(755\) | −8.99124 | −0.327225 | ||||||||
\(756\) | 0.727556 | 0.0264610 | ||||||||
\(757\) | −13.3679 | −0.485866 | −0.242933 | − | 0.970043i | \(-0.578110\pi\) | ||||
−0.242933 | + | 0.970043i | \(0.578110\pi\) | |||||||
\(758\) | −15.0100 | −0.545186 | ||||||||
\(759\) | −0.836924 | −0.0303784 | ||||||||
\(760\) | 3.93771 | 0.142836 | ||||||||
\(761\) | 16.4010 | 0.594535 | 0.297267 | − | 0.954794i | \(-0.403925\pi\) | ||||
0.297267 | + | 0.954794i | \(0.403925\pi\) | |||||||
\(762\) | −9.35619 | −0.338939 | ||||||||
\(763\) | 3.90204 | 0.141263 | ||||||||
\(764\) | −9.74626 | −0.352607 | ||||||||
\(765\) | −0.556815 | −0.0201317 | ||||||||
\(766\) | 23.9175 | 0.864175 | ||||||||
\(767\) | −2.52269 | −0.0910891 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 53.8744 | 1.94276 | 0.971380 | − | 0.237529i | \(-0.0763375\pi\) | ||||
0.971380 | + | 0.237529i | \(0.0763375\pi\) | |||||||
\(770\) | −1.83546 | −0.0661454 | ||||||||
\(771\) | −24.7228 | −0.890371 | ||||||||
\(772\) | 10.5626 | 0.380156 | ||||||||
\(773\) | 41.6383 | 1.49762 | 0.748812 | − | 0.662782i | \(-0.230624\pi\) | ||||
0.748812 | + | 0.662782i | \(0.230624\pi\) | |||||||
\(774\) | −2.87701 | −0.103412 | ||||||||
\(775\) | −18.6938 | −0.671500 | ||||||||
\(776\) | −8.31606 | −0.298529 | ||||||||
\(777\) | 0.794600 | 0.0285061 | ||||||||
\(778\) | −14.3949 | −0.516082 | ||||||||
\(779\) | 30.7432 | 1.10149 | ||||||||
\(780\) | −1.40467 | −0.0502953 | ||||||||
\(781\) | 16.0043 | 0.572678 | ||||||||
\(782\) | −0.184722 | −0.00660564 | ||||||||
\(783\) | −8.45781 | −0.302258 | ||||||||
\(784\) | −6.47066 | −0.231095 | ||||||||
\(785\) | 1.76556 | 0.0630157 | ||||||||
\(786\) | −20.2038 | −0.720644 | ||||||||
\(787\) | 37.7304 | 1.34494 | 0.672472 | − | 0.740123i | \(-0.265233\pi\) | ||||
0.672472 | + | 0.740123i | \(0.265233\pi\) | |||||||
\(788\) | 14.7874 | 0.526780 | ||||||||
\(789\) | −28.5865 | −1.01771 | ||||||||
\(790\) | 3.55750 | 0.126570 | ||||||||
\(791\) | −3.17337 | −0.112832 | ||||||||
\(792\) | −4.53073 | −0.160992 | ||||||||
\(793\) | 38.2378 | 1.35787 | ||||||||
\(794\) | 6.29385 | 0.223360 | ||||||||
\(795\) | −6.64210 | −0.235571 | ||||||||
\(796\) | 14.8207 | 0.525305 | ||||||||
\(797\) | −27.7615 | −0.983365 | −0.491682 | − | 0.870775i | \(-0.663618\pi\) | ||||
−0.491682 | + | 0.870775i | \(0.663618\pi\) | |||||||
\(798\) | 5.14517 | 0.182137 | ||||||||
\(799\) | −3.17173 | −0.112208 | ||||||||
\(800\) | 4.68996 | 0.165815 | ||||||||
\(801\) | −14.3230 | −0.506078 | ||||||||
\(802\) | −30.8031 | −1.08769 | ||||||||
\(803\) | −55.3889 | −1.95463 | ||||||||
\(804\) | 3.20865 | 0.113160 | ||||||||
\(805\) | −0.0748334 | −0.00263753 | ||||||||
\(806\) | 10.0552 | 0.354181 | ||||||||
\(807\) | −2.43595 | −0.0857497 | ||||||||
\(808\) | −6.06297 | −0.213295 | ||||||||
\(809\) | −22.0325 | −0.774621 | −0.387310 | − | 0.921949i | \(-0.626596\pi\) | ||||
−0.387310 | + | 0.921949i | \(0.626596\pi\) | |||||||
\(810\) | −0.556815 | −0.0195645 | ||||||||
\(811\) | −8.42903 | −0.295983 | −0.147992 | − | 0.988989i | \(-0.547281\pi\) | ||||
−0.147992 | + | 0.988989i | \(0.547281\pi\) | |||||||
\(812\) | −6.15354 | −0.215947 | ||||||||
\(813\) | 20.1234 | 0.705760 | ||||||||
\(814\) | −4.94823 | −0.173435 | ||||||||
\(815\) | 1.56255 | 0.0547338 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | −20.3458 | −0.711809 | ||||||||
\(818\) | 31.8845 | 1.11481 | ||||||||
\(819\) | −1.83540 | −0.0641341 | ||||||||
\(820\) | −2.42062 | −0.0845318 | ||||||||
\(821\) | −14.8318 | −0.517635 | −0.258817 | − | 0.965926i | \(-0.583333\pi\) | ||||
−0.258817 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(822\) | −6.34305 | −0.221239 | ||||||||
\(823\) | −45.7402 | −1.59440 | −0.797202 | − | 0.603713i | \(-0.793687\pi\) | ||||
−0.797202 | + | 0.603713i | \(0.793687\pi\) | |||||||
\(824\) | −17.2773 | −0.601884 | ||||||||
\(825\) | −21.2489 | −0.739792 | ||||||||
\(826\) | −0.727556 | −0.0253149 | ||||||||
\(827\) | −31.7970 | −1.10569 | −0.552844 | − | 0.833285i | \(-0.686458\pi\) | ||||
−0.552844 | + | 0.833285i | \(0.686458\pi\) | |||||||
\(828\) | −0.184722 | −0.00641953 | ||||||||
\(829\) | 0.596329 | 0.0207114 | 0.0103557 | − | 0.999946i | \(-0.496704\pi\) | ||||
0.0103557 | + | 0.999946i | \(0.496704\pi\) | |||||||
\(830\) | 6.81487 | 0.236548 | ||||||||
\(831\) | 5.30586 | 0.184058 | ||||||||
\(832\) | −2.52269 | −0.0874586 | ||||||||
\(833\) | 6.47066 | 0.224195 | ||||||||
\(834\) | −7.39186 | −0.255959 | ||||||||
\(835\) | −12.9272 | −0.447364 | ||||||||
\(836\) | −32.0406 | −1.10815 | ||||||||
\(837\) | 3.98591 | 0.137773 | ||||||||
\(838\) | −6.97628 | −0.240992 | ||||||||
\(839\) | 18.0766 | 0.624072 | 0.312036 | − | 0.950070i | \(-0.398989\pi\) | ||||
0.312036 | + | 0.950070i | \(0.398989\pi\) | |||||||
\(840\) | −0.405114 | −0.0139778 | ||||||||
\(841\) | 42.5346 | 1.46671 | ||||||||
\(842\) | −10.4242 | −0.359240 | ||||||||
\(843\) | 3.68578 | 0.126945 | ||||||||
\(844\) | −10.2870 | −0.354092 | ||||||||
\(845\) | −3.69503 | −0.127113 | ||||||||
\(846\) | −3.17173 | −0.109046 | ||||||||
\(847\) | 6.93178 | 0.238179 | ||||||||
\(848\) | −11.9287 | −0.409635 | ||||||||
\(849\) | 12.2697 | 0.421096 | ||||||||
\(850\) | −4.68996 | −0.160864 | ||||||||
\(851\) | −0.201744 | −0.00691569 | ||||||||
\(852\) | 3.53239 | 0.121018 | ||||||||
\(853\) | 15.8635 | 0.543155 | 0.271578 | − | 0.962417i | \(-0.412455\pi\) | ||||
0.271578 | + | 0.962417i | \(0.412455\pi\) | |||||||
\(854\) | 11.0280 | 0.377369 | ||||||||
\(855\) | −3.93771 | −0.134667 | ||||||||
\(856\) | 11.7625 | 0.402033 | ||||||||
\(857\) | −17.3927 | −0.594125 | −0.297062 | − | 0.954858i | \(-0.596007\pi\) | ||||
−0.297062 | + | 0.954858i | \(0.596007\pi\) | |||||||
\(858\) | 11.4296 | 0.390201 | ||||||||
\(859\) | −19.8118 | −0.675971 | −0.337986 | − | 0.941151i | \(-0.609746\pi\) | ||||
−0.337986 | + | 0.941151i | \(0.609746\pi\) | |||||||
\(860\) | 1.60196 | 0.0546265 | ||||||||
\(861\) | −3.16288 | −0.107791 | ||||||||
\(862\) | −24.4816 | −0.833846 | ||||||||
\(863\) | −39.4009 | −1.34122 | −0.670612 | − | 0.741809i | \(-0.733968\pi\) | ||||
−0.670612 | + | 0.741809i | \(0.733968\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 3.66270 | 0.124535 | ||||||||
\(866\) | 22.7883 | 0.774378 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 2.89998 | 0.0984317 | ||||||||
\(869\) | −28.9469 | −0.981956 | ||||||||
\(870\) | 4.70943 | 0.159665 | ||||||||
\(871\) | −8.09443 | −0.274269 | ||||||||
\(872\) | −5.36322 | −0.181622 | ||||||||
\(873\) | 8.31606 | 0.281456 | ||||||||
\(874\) | −1.30632 | −0.0441871 | ||||||||
\(875\) | −3.92554 | −0.132707 | ||||||||
\(876\) | −12.2252 | −0.413050 | ||||||||
\(877\) | 57.8470 | 1.95335 | 0.976677 | − | 0.214713i | \(-0.0688817\pi\) | ||||
0.976677 | + | 0.214713i | \(0.0688817\pi\) | |||||||
\(878\) | −3.64730 | −0.123090 | ||||||||
\(879\) | −2.57594 | −0.0868842 | ||||||||
\(880\) | 2.52277 | 0.0850427 | ||||||||
\(881\) | 6.65276 | 0.224137 | 0.112069 | − | 0.993700i | \(-0.464252\pi\) | ||||
0.112069 | + | 0.993700i | \(0.464252\pi\) | |||||||
\(882\) | 6.47066 | 0.217879 | ||||||||
\(883\) | 4.61515 | 0.155312 | 0.0776561 | − | 0.996980i | \(-0.475256\pi\) | ||||
0.0776561 | + | 0.996980i | \(0.475256\pi\) | |||||||
\(884\) | 2.52269 | 0.0848473 | ||||||||
\(885\) | 0.556815 | 0.0187171 | ||||||||
\(886\) | 15.0337 | 0.505068 | ||||||||
\(887\) | −36.5812 | −1.22828 | −0.614138 | − | 0.789198i | \(-0.710496\pi\) | ||||
−0.614138 | + | 0.789198i | \(0.710496\pi\) | |||||||
\(888\) | −1.09215 | −0.0366501 | ||||||||
\(889\) | 6.80716 | 0.228305 | ||||||||
\(890\) | 7.97525 | 0.267331 | ||||||||
\(891\) | 4.53073 | 0.151785 | ||||||||
\(892\) | 18.1422 | 0.607447 | ||||||||
\(893\) | −22.4300 | −0.750590 | ||||||||
\(894\) | 8.91020 | 0.298002 | ||||||||
\(895\) | 10.6024 | 0.354400 | ||||||||
\(896\) | −0.727556 | −0.0243060 | ||||||||
\(897\) | 0.465997 | 0.0155592 | ||||||||
\(898\) | 23.6239 | 0.788340 | ||||||||
\(899\) | −33.7121 | −1.12436 | ||||||||
\(900\) | −4.68996 | −0.156332 | ||||||||
\(901\) | 11.9287 | 0.397404 | ||||||||
\(902\) | 19.6963 | 0.655814 | ||||||||
\(903\) | 2.09319 | 0.0696570 | ||||||||
\(904\) | 4.36168 | 0.145067 | ||||||||
\(905\) | 5.12132 | 0.170238 | ||||||||
\(906\) | 16.1476 | 0.536469 | ||||||||
\(907\) | −11.4676 | −0.380775 | −0.190388 | − | 0.981709i | \(-0.560974\pi\) | ||||
−0.190388 | + | 0.981709i | \(0.560974\pi\) | |||||||
\(908\) | 1.83958 | 0.0610485 | ||||||||
\(909\) | 6.06297 | 0.201096 | ||||||||
\(910\) | 1.02198 | 0.0338782 | ||||||||
\(911\) | −8.87475 | −0.294034 | −0.147017 | − | 0.989134i | \(-0.546967\pi\) | ||||
−0.147017 | + | 0.989134i | \(0.546967\pi\) | |||||||
\(912\) | −7.07185 | −0.234172 | ||||||||
\(913\) | −55.4517 | −1.83518 | ||||||||
\(914\) | 36.6981 | 1.21387 | ||||||||
\(915\) | −8.43995 | −0.279016 | ||||||||
\(916\) | −2.39025 | −0.0789760 | ||||||||
\(917\) | 14.6994 | 0.485416 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −1.22425 | −0.0403841 | −0.0201921 | − | 0.999796i | \(-0.506428\pi\) | ||||
−0.0201921 | + | 0.999796i | \(0.506428\pi\) | |||||||
\(920\) | 0.102856 | 0.00339106 | ||||||||
\(921\) | 8.68684 | 0.286241 | ||||||||
\(922\) | 28.3825 | 0.934726 | ||||||||
\(923\) | −8.91112 | −0.293313 | ||||||||
\(924\) | 3.29636 | 0.108442 | ||||||||
\(925\) | −5.12213 | −0.168415 | ||||||||
\(926\) | 0.789581 | 0.0259472 | ||||||||
\(927\) | 17.2773 | 0.567461 | ||||||||
\(928\) | 8.45781 | 0.277641 | ||||||||
\(929\) | 18.1845 | 0.596615 | 0.298307 | − | 0.954470i | \(-0.403578\pi\) | ||||
0.298307 | + | 0.954470i | \(0.403578\pi\) | |||||||
\(930\) | −2.21942 | −0.0727775 | ||||||||
\(931\) | 45.7595 | 1.49971 | ||||||||
\(932\) | 13.5052 | 0.442378 | ||||||||
\(933\) | 8.99505 | 0.294485 | ||||||||
\(934\) | −2.20236 | −0.0720635 | ||||||||
\(935\) | −2.52277 | −0.0825036 | ||||||||
\(936\) | 2.52269 | 0.0824568 | ||||||||
\(937\) | 28.1864 | 0.920808 | 0.460404 | − | 0.887709i | \(-0.347705\pi\) | ||||
0.460404 | + | 0.887709i | \(0.347705\pi\) | |||||||
\(938\) | −2.33447 | −0.0762232 | ||||||||
\(939\) | −10.0722 | −0.328694 | ||||||||
\(940\) | 1.76606 | 0.0576027 | ||||||||
\(941\) | 6.98702 | 0.227770 | 0.113885 | − | 0.993494i | \(-0.463670\pi\) | ||||
0.113885 | + | 0.993494i | \(0.463670\pi\) | |||||||
\(942\) | −3.17083 | −0.103311 | ||||||||
\(943\) | 0.803036 | 0.0261504 | ||||||||
\(944\) | 1.00000 | 0.0325472 | ||||||||
\(945\) | 0.405114 | 0.0131784 | ||||||||
\(946\) | −13.0350 | −0.423803 | ||||||||
\(947\) | 38.0176 | 1.23541 | 0.617703 | − | 0.786412i | \(-0.288064\pi\) | ||||
0.617703 | + | 0.786412i | \(0.288064\pi\) | |||||||
\(948\) | −6.38902 | −0.207506 | ||||||||
\(949\) | 30.8403 | 1.00112 | ||||||||
\(950\) | −33.1667 | −1.07607 | ||||||||
\(951\) | −16.3971 | −0.531713 | ||||||||
\(952\) | 0.727556 | 0.0235802 | ||||||||
\(953\) | −35.3336 | −1.14457 | −0.572284 | − | 0.820055i | \(-0.693943\pi\) | ||||
−0.572284 | + | 0.820055i | \(0.693943\pi\) | |||||||
\(954\) | 11.9287 | 0.386207 | ||||||||
\(955\) | −5.42686 | −0.175609 | ||||||||
\(956\) | −28.3102 | −0.915618 | ||||||||
\(957\) | −38.3200 | −1.23871 | ||||||||
\(958\) | 10.5683 | 0.341448 | ||||||||
\(959\) | 4.61493 | 0.149024 | ||||||||
\(960\) | 0.556815 | 0.0179711 | ||||||||
\(961\) | −15.1125 | −0.487499 | ||||||||
\(962\) | 2.75516 | 0.0888298 | ||||||||
\(963\) | −11.7625 | −0.379040 | ||||||||
\(964\) | 18.4711 | 0.594915 | ||||||||
\(965\) | 5.88141 | 0.189329 | ||||||||
\(966\) | 0.134396 | 0.00432411 | ||||||||
\(967\) | −9.19886 | −0.295815 | −0.147908 | − | 0.989001i | \(-0.547254\pi\) | ||||
−0.147908 | + | 0.989001i | \(0.547254\pi\) | |||||||
\(968\) | −9.52748 | −0.306225 | ||||||||
\(969\) | 7.07185 | 0.227180 | ||||||||
\(970\) | −4.63051 | −0.148677 | ||||||||
\(971\) | 37.0612 | 1.18935 | 0.594676 | − | 0.803966i | \(-0.297280\pi\) | ||||
0.594676 | + | 0.803966i | \(0.297280\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 5.37800 | 0.172411 | ||||||||
\(974\) | 12.1501 | 0.389315 | ||||||||
\(975\) | 11.8313 | 0.378906 | ||||||||
\(976\) | −15.1576 | −0.485181 | ||||||||
\(977\) | −2.53254 | −0.0810231 | −0.0405116 | − | 0.999179i | \(-0.512899\pi\) | ||||
−0.0405116 | + | 0.999179i | \(0.512899\pi\) | |||||||
\(978\) | −2.80623 | −0.0897334 | ||||||||
\(979\) | −64.8936 | −2.07401 | ||||||||
\(980\) | −3.60296 | −0.115092 | ||||||||
\(981\) | 5.36322 | 0.171234 | ||||||||
\(982\) | −34.2121 | −1.09175 | ||||||||
\(983\) | −37.9931 | −1.21179 | −0.605895 | − | 0.795544i | \(-0.707185\pi\) | ||||
−0.605895 | + | 0.795544i | \(0.707185\pi\) | |||||||
\(984\) | 4.34727 | 0.138586 | ||||||||
\(985\) | 8.23385 | 0.262352 | ||||||||
\(986\) | −8.45781 | −0.269352 | ||||||||
\(987\) | 2.30761 | 0.0734521 | ||||||||
\(988\) | 17.8401 | 0.567569 | ||||||||
\(989\) | −0.531447 | −0.0168990 | ||||||||
\(990\) | −2.52277 | −0.0801790 | ||||||||
\(991\) | −22.4659 | −0.713654 | −0.356827 | − | 0.934171i | \(-0.616141\pi\) | ||||
−0.356827 | + | 0.934171i | \(0.616141\pi\) | |||||||
\(992\) | −3.98591 | −0.126553 | ||||||||
\(993\) | 7.11007 | 0.225631 | ||||||||
\(994\) | −2.57001 | −0.0815158 | ||||||||
\(995\) | 8.25237 | 0.261618 | ||||||||
\(996\) | −12.2390 | −0.387808 | ||||||||
\(997\) | 45.4875 | 1.44060 | 0.720301 | − | 0.693662i | \(-0.244004\pi\) | ||||
0.720301 | + | 0.693662i | \(0.244004\pi\) | |||||||
\(998\) | −16.3962 | −0.519014 | ||||||||
\(999\) | 1.09215 | 0.0345541 |
(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.y.1.7 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.y.1.7 | ✓ | 10 | 1.1 | even | 1 | trivial |